LMFDB - Embedded newform 125.2.g.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	125.11
Dual form			125.2.g.a.91.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97173 + 1.85157i) q^{2} +(3.22832e-5 + 5.08701e-5i) q^{3} +(0.333796 - 5.30554i) q^{4} +(2.21278 - 0.321903i) q^{5} +(-0.000157843 - 4.05273e-5i) q^{6} +(0.678693 - 2.08880i) q^{7} +(5.71721 + 6.91092i) q^{8} +(1.27734 - 2.71448i) q^{9} +O(q^{10})$	\(q+(-1.97173 + 1.85157i) q^{2} +(3.22832e-5 + 5.08701e-5i) q^{3} +(0.333796 - 5.30554i) q^{4} +(2.21278 - 0.321903i) q^{5} +(-0.000157843 - 4.05273e-5i) q^{6} +(0.678693 - 2.08880i) q^{7} +(5.71721 + 6.91092i) q^{8} +(1.27734 - 2.71448i) q^{9} +(-3.76696 + 4.73182i) q^{10} +(-0.314780 + 0.295598i) q^{11} +(0.000280669 - 0.000154299i) q^{12} +(-0.700216 + 1.48803i) q^{13} +(2.52937 + 5.37519i) q^{14} +(8.78107e-5 + 0.000102172i) q^{15} +(-13.5206 - 1.70805i) q^{16} +(0.391418 + 6.22142i) q^{17} +(2.50750 + 7.71730i) q^{18} +(0.817669 - 1.28844i) q^{19} +(-0.969253 - 11.8474i) q^{20} +(0.000128168 - 3.29079e-5i) q^{21} +(0.0733381 - 1.16568i) q^{22} +(1.52291 - 7.98337i) q^{23} +(-0.000166990 + 0.000513942i) q^{24} +(4.79276 - 1.42460i) q^{25} +(-1.37457 - 4.23050i) q^{26} +(0.000358645 - 4.53074e-5i) q^{27} +(-10.8557 - 4.29806i) q^{28} +(2.66016 + 1.05323i) q^{29} +(-0.000362318 - 3.88675e-5i) q^{30} +(0.396798 + 6.30693i) q^{31} +(15.3090 - 11.1226i) q^{32} +(-2.51992e-5 - 6.47005e-6i) q^{33} +(-12.2912 - 11.5422i) q^{34} +(0.829403 - 4.84052i) q^{35} +(-13.9754 - 7.68305i) q^{36} +(-4.09227 - 0.516973i) q^{37} +(0.773423 + 4.05443i) q^{38} +(-9.83017e-5 + 1.24184e-5i) q^{39} +(14.8755 + 13.4519i) q^{40} +(0.991411 + 5.19716i) q^{41} +(-0.000191781 + 0.000302198i) q^{42} +(-8.79304 - 6.38852i) q^{43} +(1.46323 + 1.76875i) q^{44} +(1.95266 - 6.41772i) q^{45} +(11.7790 + 18.5608i) q^{46} +(-4.96020 + 5.99585i) q^{47} +(-0.000349600 - 0.000742937i) q^{48} +(1.76065 + 1.27919i) q^{49} +(-6.81225 + 11.6831i) q^{50} +(-0.000303848 + 0.000220759i) q^{51} +(7.66109 + 4.21172i) q^{52} +(-6.71104 + 1.72310i) q^{53} +(-0.000623260 + 0.000753392i) q^{54} +(-0.601383 + 0.755421i) q^{55} +(18.3158 - 7.25172i) q^{56} +9.19401e-5 q^{57} +(-7.19525 + 2.84880i) q^{58} +(-7.99250 + 4.39391i) q^{59} +(0.000571389 - 0.000431778i) q^{60} +(1.00389 - 5.26259i) q^{61} +(-12.4601 - 11.7008i) q^{62} +(-4.80309 - 4.51040i) q^{63} +(-4.48347 + 23.5032i) q^{64} +(-1.07042 + 3.51809i) q^{65} +(6.16657e-5 - 3.39010e-5i) q^{66} +(6.20136 - 2.45529i) q^{67} +33.1386 q^{68} +(0.000455280 - 0.000180258i) q^{69} +(7.32723 + 11.0799i) q^{70} +(0.931146 - 1.12556i) q^{71} +(26.0624 - 6.69168i) q^{72} +(4.80805 + 2.64325i) q^{73} +(9.02604 - 6.55780i) q^{74} +(0.000227195 + 0.000197818i) q^{75} +(-6.56293 - 4.76825i) q^{76} +(0.403806 + 0.858132i) q^{77} +(0.000170830 - 0.000206498i) q^{78} +(-1.18238 - 1.86314i) q^{79} +(-30.4679 + 0.572794i) q^{80} +(-5.73682 - 6.93462i) q^{81} +(-11.5777 - 8.41170i) q^{82} +(-3.90119 + 6.14729i) q^{83} +(-0.000131812 - 0.000690984i) q^{84} +(2.86882 + 13.6406i) q^{85} +(29.1663 - 3.68456i) q^{86} +(3.23004e-5 + 0.000169325i) q^{87} +(-3.84251 - 0.485422i) q^{88} +(-8.79991 - 4.83779i) q^{89} +(8.03276 + 16.2695i) q^{90} +(2.63298 + 2.47253i) q^{91} +(-41.8477 - 10.7447i) q^{92} +(-0.000308024 + 0.000223793i) q^{93} +(-1.32161 - 21.0064i) q^{94} +(1.39457 - 3.11424i) q^{95} +(0.00106003 + 0.000419697i) q^{96} +(3.97492 + 1.57378i) q^{97} +(-5.84004 + 0.737769i) q^{98} +(0.400315 + 1.23204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.97173	+	1.85157i	−1.39422	+	1.30926i	−0.496950	+	0.867779i	$0.665547\pi$
$2$	−1.97173	+	1.85157i	−1.39422	+	1.30926i	−0.897271	+	0.441481i	$0.854453\pi$
$3$	3.22832e−5	0	5.08701e-5i	1.86387e−5	0	2.93699e-5i	0.844337	−	0.535812i	$-0.179994\pi$
$3$	3.22832e−5	0	5.08701e-5i	1.86387e−5	0	2.93699e-5i	−0.844319	+	0.535841i	$0.819994\pi$
$4$	0.333796	−	5.30554i	0.166898	−	2.65277i
$5$	2.21278	−	0.321903i	0.989584	−	0.143959i
$5$	2.21278	−	0.321903i	0.989584	−	0.143959i
$6$	−0.000157843	0	4.05273e-5i	−6.44393e−5	0	1.65452e-5i
$7$	0.678693	−	2.08880i	0.256522	−	0.789493i	−0.737004	−	0.675888i	$-0.763760\pi$
$7$	0.678693	−	2.08880i	0.256522	−	0.789493i	0.993526	−	0.113605i	$-0.0362397\pi$
$8$	5.71721	+	6.91092i	2.02134	+	2.44338i
$9$	1.27734	−	2.71448i	0.425779	−	0.904827i
$10$	−3.76696	+	4.73182i	−1.19122	+	1.49633i
$11$	−0.314780	+	0.295598i	−0.0949097	+	0.0891261i	−0.730550	−	0.682859i	$-0.760736\pi$
$11$	−0.314780	+	0.295598i	−0.0949097	+	0.0891261i	0.635640	+	0.771985i	$0.280736\pi$
$12$	0.000280669	0	0.000154299i	8.10223e−5	0	4.45424e-5i
$13$	−0.700216	+	1.48803i	−0.194205	+	0.412706i	−0.978085	−	0.208206i	$-0.933238\pi$
$13$	−0.700216	+	1.48803i	−0.194205	+	0.412706i	0.783880	+	0.620912i	$0.213238\pi$
$14$	2.52937	+	5.37519i	0.676003	+	1.43658i
$15$	8.78107e−5	0	0.000102172i	2.26726e−5	0	2.63807e-5i
$16$	−13.5206	−	1.70805i	−3.38016	−	0.427013i
$17$	0.391418	+	6.22142i	0.0949329	+	1.50892i	0.700805	+	0.713353i	$0.252824\pi$
$17$	0.391418	+	6.22142i	0.0949329	+	1.50892i	−0.605872	+	0.795562i	$0.707176\pi$
$18$	2.50750	+	7.71730i	0.591024	+	1.81898i
$19$	0.817669	−	1.28844i	0.187586	−	0.295588i	−0.737499	−	0.675348i	$-0.763993\pi$
$19$	0.817669	−	1.28844i	0.187586	−	0.295588i	0.925085	+	0.379760i	$0.123993\pi$
$20$	−0.969253	−	11.8474i	−0.216731	−	2.64916i
$21$	0.000128168	0	3.29079e-5i	2.79685e−5	0	7.18110e-6i
$22$	0.0733381	−	1.16568i	0.0156357	−	0.248523i
$23$	1.52291	−	7.98337i	0.317549	−	1.66465i	−0.362882	−	0.931835i	$-0.618207\pi$
$23$	1.52291	−	7.98337i	0.317549	−	1.66465i	0.680430	−	0.732813i	$-0.261793\pi$
$24$	−0.000166990	0	0.000513942i	−3.40866e−5	0	0.000104908i
$25$	4.79276	−	1.42460i	0.958551	−	0.284920i
$26$	−1.37457	−	4.23050i	−0.269576	−	0.829668i
$27$	0.000358645	0	4.53074e-5i	6.90213e−5	0	8.71942e-6i
$28$	−10.8557	−	4.29806i	−2.05153	−	0.812257i
$29$	2.66016	+	1.05323i	0.493980	+	0.195581i	0.601888	−	0.798580i	$-0.294415\pi$
$29$	2.66016	+	1.05323i	0.493980	+	0.195581i	−0.107908	+	0.994161i	$0.534415\pi$
$30$	−0.000362318	0	3.88675e-5i	−6.61499e−5	0	7.09621e-6i
$31$	0.396798	+	6.30693i	0.0712671	+	1.13276i	0.857383	+	0.514679i	$0.172089\pi$
$31$	0.396798	+	6.30693i	0.0712671	+	1.13276i	−0.786116	+	0.618079i	$0.787911\pi$
$32$	15.3090	−	11.1226i	2.70628	−	1.96622i
$33$	−2.51992e−5	0	6.47005e-6i	−4.38662e−6	0	1.12629e-6i
$34$	−12.2912	−	11.5422i	−2.10792	−	1.97947i
$35$	0.829403	−	4.84052i	0.140195	−	0.818198i
$36$	−13.9754	−	7.68305i	−2.32923	−	1.28051i
$37$	−4.09227	−	0.516973i	−0.672764	−	0.0849899i	−0.218473	−	0.975843i	$-0.570108\pi$
$37$	−4.09227	−	0.516973i	−0.672764	−	0.0849899i	−0.454291	+	0.890853i	$0.650108\pi$
$38$	0.773423	+	4.05443i	0.125466	+	0.657715i
$39$	−9.83017e−5	0	1.24184e-5i	−1.57409e−5	0	1.98853e-6i
$40$	14.8755	+	13.4519i	2.35203	+	2.12694i
$41$	0.991411	+	5.19716i	0.154832	+	0.811659i	0.971950	+	0.235188i	$0.0755707\pi$
$41$	0.991411	+	5.19716i	0.154832	+	0.811659i	−0.817118	+	0.576471i	$0.804429\pi$
$42$	−0.000191781	0	0.000302198i	−2.95924e−5	0	4.66301e-5i
$43$	−8.79304	−	6.38852i	−1.34093	−	0.974240i	−0.999409	−	0.0343647i	$-0.989059\pi$
$43$	−8.79304	−	6.38852i	−1.34093	−	0.974240i	−0.341517	−	0.939875i	$-0.610941\pi$
$44$	1.46323	+	1.76875i	0.220591	+	0.266648i
$45$	1.95266	−	6.41772i	0.291086	−	0.956697i
$46$	11.7790	+	18.5608i	1.73672	+	2.73664i
$47$	−4.96020	+	5.99585i	−0.723520	+	0.874585i	−0.996162	−	0.0875304i	$-0.972103\pi$
$47$	−4.96020	+	5.99585i	−0.723520	+	0.874585i	0.272642	+	0.962116i	$0.412103\pi$
$48$	−0.000349600	0	0.000742937i	−5.04604e−5	0	0.000107234i
$49$	1.76065	+	1.27919i	0.251522	+	0.182741i
$50$	−6.81225	+	11.6831i	−0.963398	+	1.65223i
$51$	−0.000303848	0	0.000220759i	−4.25473e−5	0	3.09124e-5i
$52$	7.66109	+	4.21172i	1.06240	+	0.584060i
$53$	−6.71104	+	1.72310i	−0.921832	+	0.236686i	−0.679643	−	0.733543i	$-0.737865\pi$
$53$	−6.71104	+	1.72310i	−0.921832	+	0.236686i	−0.242189	+	0.970229i	$0.577865\pi$
$54$	−0.000623260	0	0.000753392i	−8.48149e−5	0	0.000102524i
$55$	−0.601383	+	0.755421i	−0.0810905	+	0.101861i
$56$	18.3158	−	7.25172i	2.44755	−	0.969052i
$57$	9.19401e−5	0		1.21778e−5	0
$58$	−7.19525	+	2.84880i	−0.944783	+	0.374066i
$59$	−7.99250	+	4.39391i	−1.04053	+	0.572039i	−0.907926	−	0.419130i	$-0.862335\pi$
$59$	−7.99250	+	4.39391i	−1.04053	+	0.572039i	−0.132608	+	0.991169i	$0.542335\pi$
$60$	0.000571389	0	0.000431778i	7.37660e−5	0	5.57423e-5i
$61$	1.00389	−	5.26259i	0.128535	−	0.673806i	−0.858437	−	0.512918i	$-0.828564\pi$
$61$	1.00389	−	5.26259i	0.128535	−	0.673806i	0.986973	−	0.160888i	$-0.0514357\pi$
$62$	−12.4601	−	11.7008i	−1.58244	−	1.48601i
$63$	−4.80309	−	4.51040i	−0.605133	−	0.568257i
$64$	−4.48347	+	23.5032i	−0.560434	+	2.93790i
$65$	−1.07042	+	3.51809i	−0.132769	+	0.436365i
$66$	6.16657e−5	0	3.39010e-5i	7.59052e−6	0	4.17292e-6i
$67$	6.20136	−	2.45529i	0.757617	−	0.299962i	0.0426220	−	0.999091i	$-0.486429\pi$
$67$	6.20136	−	2.45529i	0.757617	−	0.299962i	0.714995	+	0.699129i	$0.246429\pi$
$68$	33.1386			4.01865
$69$	0.000455280	0	0.000180258i	5.48092e−5	0	2.17005e-5i
$70$	7.32723	+	11.0799i	0.875771	+	1.32430i
$71$	0.931146	−	1.12556i	0.110507	−	0.133580i	−0.712360	−	0.701815i	$-0.752374\pi$
$71$	0.931146	−	1.12556i	0.110507	−	0.133580i	0.822866	+	0.568235i	$0.192374\pi$
$72$	26.0624	−	6.69168i	3.07148	−	0.788622i
$73$	4.80805	+	2.64325i	0.562740	+	0.309369i	0.737615	−	0.675222i	$-0.235952\pi$
$73$	4.80805	+	2.64325i	0.562740	+	0.309369i	−0.174875	+	0.984591i	$0.555952\pi$
$74$	9.02604	−	6.55780i	1.04926	−	0.762329i
$75$	0.000227195	0	0.000197818i	2.62342e−5	0	2.28420e-5i
$76$	−6.56293	−	4.76825i	−0.752820	−	0.546956i
$77$	0.403806	+	0.858132i	0.0460180	+	0.0977933i
$78$	0.000170830	0	0.000206498i	1.93427e−5	0	2.33813e-5i
$79$	−1.18238	−	1.86314i	−0.133028	−	0.209619i	0.771283	−	0.636492i	$-0.219615\pi$
$79$	−1.18238	−	1.86314i	−0.133028	−	0.209619i	−0.904312	+	0.426873i	$0.859615\pi$
$80$	−30.4679	+	0.572794i	−3.40642	+	0.0640403i
$81$	−5.73682	−	6.93462i	−0.637424	−	0.770513i
$82$	−11.5777	−	8.41170i	−1.27854	−	0.928916i
$83$	−3.90119	+	6.14729i	−0.428211	+	0.674752i	−0.988100	−	0.153815i	$-0.950844\pi$
$83$	−3.90119	+	6.14729i	−0.428211	+	0.674752i	0.559889	+	0.828568i	$0.310844\pi$
$84$	−0.000131812	0	0.000690984i	−1.43819e−5	0	7.53926e-5i
$85$	2.86882	+	13.6406i	0.311167	+	1.47953i
$86$	29.1663	−	3.68456i	3.14508	−	0.397316i
$87$	3.23004e−5	0	0.000169325i	3.46297e−6	0	1.81535e-5i
$88$	−3.84251	−	0.485422i	−0.409613	−	0.0517462i
$89$	−8.79991	−	4.83779i	−0.932789	−	0.512805i	−0.0585410	−	0.998285i	$-0.518645\pi$
$89$	−8.79991	−	4.83779i	−0.932789	−	0.512805i	−0.874248	+	0.485480i	$0.838645\pi$
$90$	8.03276	+	16.2695i	0.846727	+	1.71495i
$91$	2.63298	+	2.47253i	0.276011	+	0.259191i
$92$	−41.8477	−	10.7447i	−4.36293	−	1.12021i
$93$	−0.000308024	0	0.000223793i	−3.19406e−5	0	2.32062e-5i
$94$	−1.32161	−	21.0064i	−0.136313	−	2.16664i
$95$	1.39457	−	3.11424i	0.143079	−	0.319514i
$96$	0.00106003		0.000419697i	0.000108189		4.28352e-5i
$97$	3.97492	+	1.57378i	0.403592	+	0.159793i	0.561146	−	0.827717i	$-0.310361\pi$
$97$	3.97492	+	1.57378i	0.403592	+	0.159793i	−0.157554	+	0.987510i	$0.550361\pi$
$98$	−5.84004	+	0.737769i	−0.589933	+	0.0745259i
$99$	0.400315	+	1.23204i	0.0402331	+	0.123825i
$100$	−5.95846	−	25.9037i	−0.595846	−	2.59037i
$101$	−5.40168	+	16.6247i	−0.537487	+	1.65422i	0.200726	+	0.979647i	$0.435670\pi$
$101$	−5.40168	+	16.6247i	−0.537487	+	1.65422i	−0.738213	+	0.674568i	$0.764330\pi$
$102$	0.000190354	0	0.000997873i	1.88479e−5	0	9.88041e-5i
$103$	0.375166	−	5.96309i	0.0369662	−	0.587560i	−0.935325	−	0.353789i	$-0.884893\pi$
$103$	0.375166	−	5.96309i	0.0369662	−	0.587560i	0.972292	−	0.233772i	$-0.0751068\pi$
$104$	−14.2870	+	3.66827i	−1.40095	+	0.359703i
$105$	0.000273014	0	0.000114076i	2.66434e−5	0	1.11326e-5i
$106$	10.0419	−	15.8235i	0.975353	−	1.53691i
$107$	1.56224	+	4.80809i	0.151028	+	0.464816i	0.997737	−	0.0672404i	$-0.0214194\pi$
$107$	1.56224	+	4.80809i	0.151028	+	0.464816i	−0.846709	+	0.532056i	$0.821419\pi$
$108$	−0.000120666	−	0.00191793i	−1.16111e−5	−	0.000184553i
$109$	4.67234	+	0.590254i	0.447529	+	0.0565361i	0.345868	−	0.938283i	$-0.387584\pi$
$109$	4.67234	+	0.590254i	0.447529	+	0.0565361i	0.101661	+	0.994819i	$0.467584\pi$
$110$	−0.212954	−	2.60299i	−0.0203044	−	0.248185i
$111$	−0.000105813	0	0.000224864i	−1.00433e−5	0	2.13431e-5i
$112$	−12.7441	+	27.0826i	−1.20421	+	2.55907i
$113$	−3.85780	+	2.12084i	−0.362912	+	0.199512i	−0.652768	−	0.757558i	$-0.726392\pi$
$113$	−3.85780	+	2.12084i	−0.362912	+	0.199512i	0.289857	+	0.957070i	$0.406392\pi$
$114$	−0.000181281	0	0.000170234i	−1.69785e−5	0	1.59439e-5i
$115$	0.799986	−	18.1556i	0.0745991	−	1.69302i
$116$	6.47592	−	13.7620i	0.601274	−	1.27777i
$117$	3.14483	+	3.80144i	0.290739	+	0.351444i
$118$	7.62336	−	23.4623i	0.701787	−	2.15988i
$119$	13.2610	+	3.40483i	1.21563	+	0.312121i
$120$	−0.000204072		0.00119099i	−1.86291e−5		0.000108722i
$121$	−0.678988	+	10.7922i	−0.0617261	+	0.981109i
$122$	7.76468	+	12.2352i	0.702981	+	1.10772i
$123$	−0.000232374	0	0.000218214i	−2.09525e−5	0	1.96757e-5i
$124$	33.5941			3.01684
$125$	10.1467	−	4.69512i	0.907550	−	0.419944i
$126$	17.8217			1.58768
$127$	−8.49167	+	7.97421i	−0.753514	+	0.707597i	−0.962787	−	0.270261i	$-0.912890\pi$
$127$	−8.49167	+	7.97421i	−0.753514	+	0.707597i	0.209273	+	0.977857i	$0.432890\pi$
$128$	−14.3988	−	22.6889i	−1.27269	−	2.00543i
$129$	4.11176e−5	0	0.000653545i	3.62020e−6	0	5.75414e-5i
$130$	−4.40343	−	8.91866i	−0.386206	−	0.782218i
$131$	−9.61001	−	2.46743i	−0.839631	−	0.215580i	−0.195699	−	0.980664i	$-0.562698\pi$
$131$	−9.61001	−	2.46743i	−0.839631	−	0.215580i	−0.643931	+	0.765083i	$0.722698\pi$
$132$	−4.27385e−5	0	0.000131536i	−3.71991e−6	0	1.14487e-5i
$133$	−2.13635	−	2.58240i	−0.185245	−	0.223923i
$134$	−7.68123	+	16.3234i	−0.663557	+	1.41013i
$135$	0.000779017	0	0.000215704i	6.70471e−5	0	1.85649e-5i
$136$	−40.7579	+	38.2742i	−3.49496	+	3.28199i
$137$	13.4887	−	7.41549i	1.15242	−	0.633548i	0.213248	−	0.976998i	$-0.431596\pi$
$137$	13.4887	−	7.41549i	1.15242	−	0.633548i	0.939171	+	0.343450i	$0.111596\pi$
$138$	−0.000563926		0.00119840i	−4.80045e−5		0.000102015i
$139$	−0.832840	−	1.76988i	−0.0706406	−	0.150119i	0.866388	−	0.499371i	$-0.166436\pi$
$139$	−0.832840	−	1.76988i	−0.0706406	−	0.150119i	−0.937029	+	0.349252i	$0.886436\pi$
$140$	−25.4047	−	6.01618i	−2.14709	−	0.508460i
$141$	−0.000465141	0	5.87610e-5i	−3.91719e−5	0	4.94857e-6i
$142$	0.248097	+	3.94339i	0.0208198	+	0.330922i
$143$	−0.219446	−	0.675385i	−0.0183510	−	0.0564786i
$144$	−21.9069	+	34.5197i	−1.82557	+	2.87664i
$145$	6.22539	+	1.47425i	0.516990	+	0.122430i
$146$	−14.3743	+	3.69070i	−1.18963	+	0.305445i
$147$	−8.23308e−6	0	0.000130861i	−6.79053e−7	0	1.07932e-5i
$148$	−4.10880	+	21.5391i	−0.337742	+	1.77050i
$149$	0.941892	−	2.89885i	0.0771628	−	0.237483i	−0.905033	−	0.425340i	$-0.860154\pi$
$149$	0.941892	−	2.89885i	0.0771628	−	0.237483i	0.982196	+	0.187858i	$0.0601544\pi$
$150$	−0.000814240	0	3.06261e-5i	−6.64824e−5	0	2.50061e-6i
$151$	0.337284	+	1.03805i	0.0274478	+	0.0844756i	0.963842	−	0.266474i	$-0.0858587\pi$
$151$	0.337284	+	1.03805i	0.0274478	+	0.0844756i	−0.936394	+	0.350950i	$0.885859\pi$
$152$	13.5791	−	1.71544i	1.10141	−	0.139140i
$153$	17.3879	+	6.88435i	1.40573	+	0.556567i
$154$	−2.38509	−	0.944324i	−0.192196	−	0.0760958i
$155$	2.90825	+	13.8281i	0.233596	+	1.11070i
$156$	3.30735e−5	0	0.000525688i	2.64800e−6	0	4.20888e-5i
$157$	5.25569	−	3.81848i	0.419449	−	0.304748i	−0.357967	−	0.933734i	$-0.616530\pi$
$157$	5.25569	−	3.81848i	0.419449	−	0.304748i	0.777416	+	0.628986i	$0.216530\pi$
$158$	5.78107	+	1.48433i	0.459917	+	0.118087i
$159$	−0.000304308	0	0.000285764i	−2.41332e−5	0	2.26626e-5i
$160$	30.2950	−	29.5399i	2.39503	−	2.33534i
$161$	−15.6421	−	8.59931i	−1.23277	−	0.677720i
$162$	24.1514	+	3.05103i	1.89751	+	0.239712i
$163$	0.811295	+	4.25296i	0.0635455	+	0.333117i	0.999836	−	0.0181093i	$-0.00576467\pi$
$163$	0.811295	+	4.25296i	0.0635455	+	0.333117i	−0.936290	+	0.351227i	$0.885765\pi$
$164$	27.9046	−	3.52517i	2.17899	−	0.275270i
$165$	−5.78429e−5	0	6.20508e-6i	−4.50306e−6	0	4.83065e-7i
$166$	−3.69008	−	19.3441i	−0.286406	−	1.50139i
$167$	4.68264	−	7.37865i	0.362353	−	0.570977i	−0.613421	−	0.789756i	$-0.710207\pi$
$167$	4.68264	−	7.37865i	0.362353	−	0.570977i	0.975775	+	0.218779i	$0.0702072\pi$
$168$	0.000960187	0	0.000697617i	7.40800e−5	0	5.38223e-5i
$169$	6.56257	+	7.93278i	0.504813	+	0.610214i
$170$	−30.9131	−	21.5837i	−2.37093	−	1.65539i
$171$	−2.45301	−	3.86532i	−0.187586	−	0.295588i
$172$	−36.8296	+	44.5194i	−2.80823	+	3.39457i
$173$	−5.79784	−	12.3210i	−0.440802	−	0.936751i	−0.994569	−	0.104080i	$-0.966810\pi$
$173$	−5.79784	−	12.3210i	−0.440802	−	0.936751i	0.553767	−	0.832672i	$-0.313190\pi$
$174$	−0.000377205	0	0.000274055i	−2.85958e−5	0	2.07761e-5i
$175$	0.277105	−	10.9780i	0.0209471	−	0.829857i
$176$	4.76092	−	3.45901i	0.358868	−	0.260733i
$177$	−0.000481542	0	0.000264730i	−3.61949e−5	0	1.98983e-5i
$178$	26.3085	−	6.75488i	1.97191	−	0.506300i
$179$	−14.3724	+	17.3733i	−1.07425	+	1.29854i	−0.122228	+	0.992502i	$0.539004\pi$
$179$	−14.3724	+	17.3733i	−1.07425	+	1.29854i	−0.952019	+	0.306039i	$0.900996\pi$
$180$	−33.3976	−	12.5021i	−2.48931	−	0.931854i
$181$	3.94386	−	1.56148i	0.293145	−	0.116064i	−0.216949	−	0.976183i	$-0.569611\pi$
$181$	3.94386	−	1.56148i	0.293145	−	0.116064i	0.510094	+	0.860119i	$0.329611\pi$
$182$	−9.76957			−0.724169
$183$	0.000300118	0	0.000118825i	2.21853e−5	0	8.78380e-6i
$184$	63.8792	−	35.1179i	4.70924	−	2.58893i
$185$	−9.22168	+	0.173367i	−0.677992	+	0.0127462i
$186$	0.000192971	−	0.00101159i	1.41493e−5	−	7.41732e-5i
$187$	−1.96225	−	1.84267i	−0.143494	−	0.134750i
$188$	30.1555	+	28.3179i	2.19932	+	2.06530i
$189$	0.000148772	0	0.000779888i	1.08215e−5	0	5.67285e-5i
$190$	3.01654	+	8.72257i	0.218843	+	0.632802i
$191$	11.0827	−	6.09274i	0.801913	−	0.440855i	−0.0274106	−	0.999624i	$-0.508726\pi$
$191$	11.0827	−	6.09274i	0.801913	−	0.440855i	0.829323	+	0.558769i	$0.188726\pi$
$192$	−0.00134035		0.000530682i	−9.67315e−5		3.82987e-5i
$193$	−15.5144			−1.11675			−0.558376	−	0.829588i	$-0.688575\pi$
$193$	−15.5144			−1.11675			−0.558376	+	0.829588i	$0.688575\pi$
$194$	−10.7514	+	4.25679i	−0.771907	+	0.305620i
$195$	−0.000213522	0	5.91227e-5i	−1.52906e−5	0	4.23387e-6i
$196$	7.37449	−	8.91422i	0.526749	−	0.636730i
$197$	2.16862	−	0.556807i	0.154508	−	0.0396709i	−0.170644	−	0.985333i	$-0.554585\pi$
$197$	2.16862	−	0.556807i	0.154508	−	0.0396709i	0.325152	+	0.945662i	$0.394585\pi$
$198$	−3.07053	−	1.68804i	−0.218213	−	0.119964i
$199$	−4.51235	+	3.27841i	−0.319872	+	0.232401i	−0.736121	−	0.676850i	$-0.763345\pi$
$199$	−4.51235	+	3.27841i	−0.319872	+	0.232401i	0.416249	+	0.909251i	$0.363345\pi$
$200$	37.2465	+	24.9776i	2.63372	+	1.76618i
$201$	0.000325101	0	0.000236200i	2.29308e−5	0	1.66602e-5i
$202$	−20.1311	−	42.7809i	−1.41642	−	3.01005i
$203$	4.00543	−	4.84173i	0.281126	−	0.339823i
$204$	0.00106982	+	0.00168577i	7.49024e−5	+	0.000118027i
$205$	3.86675	+	11.1810i	0.270066	+	0.780915i
$206$	10.3014	+	12.4522i	0.717730	+	0.867587i
$207$	−19.7254	−	14.3314i	−1.37101	−	0.996099i
$208$	12.0090	−	18.9231i	0.832674	−	1.31208i
$209$	0.123475	+	0.647276i	0.00854091	+	0.0447730i
$210$	−0.000327089	0	0.000730431i	−2.25713e−5	0	5.04045e-5i
$211$	1.21500	−	0.153491i	0.0836443	−	0.0105667i	−0.0833997	−	0.996516i	$-0.526578\pi$
$211$	1.21500	−	0.153491i	0.0836443	−	0.0105667i	0.167044	+	0.985949i	$0.446578\pi$
$212$	6.90186	+	36.1808i	0.474022	+	2.48491i
$213$	8.73179e−5	0	1.10308e-5i	5.98292e−6	0	7.55819e-7i
$214$	−11.9829	−	6.58763i	−0.819131	−	0.450321i
$215$	−21.5135	−	11.3059i	−1.46721	−	0.771053i
$216$	0.00236356	+	0.00221954i	0.000160820	+	0.000151020i
$217$	13.4432	+	3.45163i	0.912585	+	0.234312i
$218$	−10.3055	+	7.48737i	−0.697975	+	0.507109i
$219$	2.07567e−5	0	0.000329919i	1.40261e−6	0	2.22939e-5i
$220$	3.80717	+	3.44282i	0.256679	+	0.232115i
$221$	−9.53176	−	3.77389i	−0.641175	−	0.253859i
$222$	0.000624985	0	0.000247449i	4.19463e−5	0	1.66077e-5i
$223$	14.7946	−	1.86899i	0.990718	−	0.125157i	0.386766	−	0.922178i	$-0.373592\pi$
$223$	14.7946	−	1.86899i	0.990718	−	0.125157i	0.603952	+	0.797021i	$0.293592\pi$
$224$	−12.8429	−	39.5263i	−0.858101	−	2.64096i
$225$	2.25492	−	14.8295i	0.150328	−	0.988636i
$226$	3.67963	−	11.3247i	0.244765	−	0.753310i
$227$	−1.71861	+	9.00924i	−0.114068	+	0.597965i	0.878646	+	0.477473i	$0.158447\pi$
$227$	−1.71861	+	9.00924i	−0.114068	+	0.597965i	−0.992714	+	0.120492i	$0.961553\pi$
$228$	3.06892e−5	0	0.000487792i	2.03244e−6	0	3.23048e-5i
$229$	−13.3320	+	3.42308i	−0.881005	+	0.226204i	−0.661986	−	0.749517i	$-0.730286\pi$
$229$	−13.3320	+	3.42308i	−0.881005	+	0.226204i	−0.219020	+	0.975720i	$0.570286\pi$
$230$	32.0392	+	37.2792i	2.11260	+	2.45812i
$231$	−3.06172e−5	0	4.82449e-5i	−2.01446e−6	0	3.17428e-6i
$232$	7.92990	+	24.4057i	0.520624	+	1.60231i
$233$	1.24972	+	19.8637i	0.0818719	+	1.30132i	0.797706	+	0.603046i	$0.206047\pi$
$233$	1.24972	+	19.8637i	0.0818719	+	1.30132i	−0.715834	+	0.698270i	$0.753953\pi$
$234$	−13.2394	−	1.67252i	−0.865486	−	0.109336i
$235$	−9.04573	+	14.8642i	−0.590078	+	0.969633i
$236$	20.6442	+	43.8712i	1.34382	+	2.85577i
$237$	5.66070e−5	0	0.000120296i	3.67702e−6	0	7.81406e-6i
$238$	−32.4513	+	17.8402i	−2.10350	+	1.15641i
$239$	11.6946	−	10.9820i	0.756463	−	0.710366i	−0.206961	−	0.978349i	$-0.566357\pi$
$239$	11.6946	−	10.9820i	0.756463	−	0.710366i	0.963424	+	0.267983i	$0.0863573\pi$
$240$	−0.00101274	−	0.00153142i	−6.53721e−5	−	9.88525e-5i
$241$	−0.864756	+	1.83770i	−0.0557038	+	0.118377i	−0.930741	−	0.365679i	$-0.880837\pi$
$241$	−0.864756	+	1.83770i	−0.0557038	+	0.118377i	0.875037	+	0.484056i	$0.160837\pi$
$242$	−18.6438	−	22.5364i	−1.19847	−	1.44870i
$243$	0.000502687	−	0.00154711i	3.22474e−5	−	9.92473e-5i
$244$	−27.5858	−	7.08283i	−1.76600	−	0.453432i
$245$	4.30771	+	2.26380i	0.275209	+	0.144629i
$246$	5.41391e−5	0	0.000860516i	3.45178e−6	0	5.48645e-5i
$247$	1.34470	+	2.11891i	0.0855611	+	0.134823i
$248$	−41.3181	+	38.8003i	−2.62370	+	2.46382i
$249$	−0.000438656	0		−2.77987e−5	0
$250$	−11.3132	+	28.0449i	−0.715508	+	1.77371i
$251$	−13.2705			−0.837625			−0.418812	−	0.908073i	$-0.637554\pi$
$251$	−13.2705			−0.837625			−0.418812	+	0.908073i	$0.637554\pi$
$252$	−25.5334	+	23.9774i	−1.60845	+	1.51044i
$253$	1.88049	+	2.96317i	0.118225	+	0.186293i
$254$	1.97841	−	31.4459i	0.124136	−	1.97309i
$255$	−0.000601285	0	0.000586299i	−3.76539e−5	0	3.67155e-5i
$256$	24.0501	+	6.17501i	1.50313	+	0.385938i
$257$	4.11620	−	12.6684i	0.256761	−	0.790230i	−0.736716	−	0.676202i	$-0.763625\pi$
$257$	4.11620	−	12.6684i	0.256761	−	0.790230i	0.993478	−	0.114028i	$-0.0363754\pi$
$258$	0.00112901	+	0.00136474i	7.02894e−5	+	8.49652e-5i
$259$	−3.85724	+	8.19706i	−0.239678	+	0.509341i
$260$	18.3080	+	6.85346i	1.13542	+	0.425034i
$261$	6.25691	−	5.87563i	0.387293	−	0.363692i
$262$	23.5169	−	12.9285i	1.45288	−	0.798728i
$263$	7.16407	−	15.2244i	0.441756	−	0.938779i	−0.552676	−	0.833396i	$-0.686393\pi$
$263$	7.16407	−	15.2244i	0.441756	−	0.938779i	0.994432	−	0.105382i	$-0.0336067\pi$
$264$	−9.93551e−5	0	0.000211140i	−6.11488e−6	0	1.29948e-5i
$265$	−14.2954	+	5.97314i	−0.878156	+	0.366927i
$266$	8.99380	+	1.13618i	0.551445	+	0.0696638i
$267$	−3.79899e−5	0	0.000603832i	−2.32494e−6	0	3.69539e-5i
$268$	−10.9567	−	33.7211i	−0.669284	−	2.05985i
$269$	5.99660	−	9.44913i	0.365619	−	0.576124i	−0.610859	−	0.791739i	$-0.709176\pi$
$269$	5.99660	−	9.44913i	0.365619	−	0.576124i	0.976478	+	0.215616i	$0.0691758\pi$
$270$	−0.00113662	+	0.00186772i	−6.91722e−5	+	0.000113666i
$271$	21.7033	−	5.57245i	1.31838	−	0.338502i	0.476979	−	0.878915i	$-0.341732\pi$
$271$	21.7033	−	5.57245i	1.31838	−	0.338502i	0.841400	+	0.540412i	$0.181732\pi$
$272$	5.33428	−	84.7860i	0.323438	−	5.14091i
$273$	−4.07771e−5	0	0.000213761i	−2.46794e−6	0	1.29374e-5i
$274$	−12.8657	+	39.5967i	−0.777248	+	2.39212i
$275$	−1.08755	+	1.86516i	−0.0655820	+	0.112474i
$276$	−0.000804395	−	0.00247567i	−4.84189e−5	−	0.000149018i
$277$	5.05679	−	0.638822i	0.303833	−	0.0383831i	0.0280615	−	0.999606i	$-0.491067\pi$
$277$	5.05679	−	0.638822i	0.303833	−	0.0383831i	0.275772	+	0.961223i	$0.411067\pi$
$278$	4.91919	+	1.94764i	0.295033	+	0.116812i
$279$	17.6269	+	6.97898i	1.05529	+	0.417820i
$280$	38.1943	−	21.9423i	2.28255	−	1.31131i
$281$	−1.53102	−	24.3349i	−0.0913330	−	1.45170i	−0.730649	−	0.682753i	$-0.760783\pi$
$281$	−1.53102	−	24.3349i	−0.0913330	−	1.45170i	0.639316	−	0.768944i	$-0.279217\pi$
$282$	0.00102593		0.000745382i	6.10933e−5		4.43869e-5i
$283$	11.9511	+	3.06852i	0.710418	+	0.182404i	0.586572	−	0.809897i	$-0.300477\pi$
$283$	11.9511	+	3.06852i	0.710418	+	0.182404i	0.123846	+	0.992301i	$0.460477\pi$
$284$	−5.66090	−	5.31594i	−0.335913	−	0.315443i
$285$	0.000203443	0	2.95958e-5i	1.20509e−5	0	1.75310e-6i
$286$	1.68321	+	0.925354i	0.0995305	+	0.0547173i
$287$	11.5287	+	1.45641i	0.680517	+	0.0859693i
$288$	−10.6374	−	55.7634i	−0.626817	−	3.28589i
$289$	−21.6869	+	2.73969i	−1.27570	+	0.161158i
$290$	−15.0044	+	8.61994i	−0.881091	+	0.506180i
$291$	4.82645e−5	0	0.000253011i	2.82931e−6	0	1.48318e-5i
$292$	15.6288	−	24.6270i	0.914604	−	1.44119i
$293$	9.62087	+	6.98997i	0.562057	+	0.408358i	0.832211	−	0.554459i	$-0.187075\pi$
$293$	9.62087	+	6.98997i	0.562057	+	0.408358i	−0.270154	+	0.962817i	$0.587075\pi$
$294$	−0.000226065	0	0.000273266i	−1.31844e−5	0	1.59372e-5i
$295$	−16.2712	+	12.2956i	−0.947346	+	0.715875i
$296$	−19.8236	−	31.2370i	−1.15222	−	1.81561i
$297$	−9.95015e−5	0	0.000120277i	−5.77366e−6	0	6.97916e-6i
$298$	3.51027	+	7.45971i	0.203345	+	0.432129i
$299$	10.8132	+	7.85622i	0.625341	+	0.454337i
$300$	0.00112537	−	0.00113936i	6.49730e−5	−	6.57810e-5i
$301$	−19.3121	+	14.0311i	−1.11313	+	0.808738i
$302$	−2.58706	−	1.42225i	−0.148869	−	0.0818413i
$303$	−0.00102008		0.000261913i	−5.86022e−5		1.50465e-5i
$304$	−13.2561	+	16.0239i	−0.760291	+	0.919033i
$305$	0.527346	−	11.9681i	0.0301958	−	0.685291i
$306$	−47.0310	+	18.6209i	−2.68859	+	1.06449i
$307$	1.45526			0.0830561			0.0415281	−	0.999137i	$-0.486777\pi$
$307$	1.45526			0.0830561			0.0415281	+	0.999137i	$0.486777\pi$
$308$	4.68764	−	1.85597i	0.267103	−	0.105754i
$309$	0.000315455	0	0.000173423i	1.79456e−5	0	9.86567e-6i
$310$	−31.3380	−	21.8804i	−1.77988	−	1.24272i
$311$	4.97537	−	26.0818i	0.282127	−	1.47896i	−0.505509	−	0.862822i	$-0.668695\pi$
$311$	4.97537	−	26.0818i	0.282127	−	1.47896i	0.787636	−	0.616141i	$-0.211305\pi$
$312$	−0.000647834	0	0.000608356i	−3.66764e−5	0	3.44414e-5i
$313$	−18.0338	−	16.9349i	−1.01933	−	0.957216i	−0.0202380	−	0.999795i	$-0.506442\pi$
$313$	−18.0338	−	16.9349i	−1.01933	−	0.957216i	−0.999093	+	0.0425796i	$0.986442\pi$
$314$	−3.29257	+	17.2603i	−0.185811	+	0.974054i
$315$	−12.0801	−	8.43438i	−0.680635	−	0.475224i
$316$	−10.2796	+	5.65126i	−0.578273	+	0.317908i
$317$	11.8112	−	4.67637i	0.663381	−	0.262651i	−0.0122124	−	0.999925i	$-0.503887\pi$
$317$	11.8112	−	4.67637i	0.663381	−	0.262651i	0.675594	+	0.737274i	$0.263887\pi$
$318$	0.00112913			6.33182e−5
$319$	−1.14870	+	0.454802i	−0.0643148	+	0.0254640i
$320$	−2.35517	+	53.4505i	−0.131658	+	2.98797i
$321$	−0.000194154	0	0.000234692i	−1.08366e−5	0	1.30992e-5i
$322$	46.7642	−	12.0070i	2.60606	−	0.669124i
$323$	8.33598	+	4.58274i	0.463826	+	0.254991i
$324$	−38.7068	+	28.1221i	−2.15038	+	1.56234i
$325$	−1.23611	+	8.12931i	−0.0685671	+	0.450933i
$326$	−9.47432	−	6.88349i	−0.524734	−	0.381241i
$327$	0.000120812	0	0.000256738i	6.68090e−6	0	1.41976e-5i
$328$	−30.2490	+	36.5648i	−1.67022	+	2.01895i
$329$	9.15769	+	14.4302i	0.504880	+	0.795563i
$330$	0.000125540	0	9.48657e-5i	6.91072e−6	0	5.22218e-6i
$331$	1.21032	+	1.46302i	0.0665251	+	0.0804150i	0.802726	−	0.596348i	$-0.203382\pi$
$331$	1.21032	+	1.46302i	0.0665251	+	0.0804150i	−0.736201	+	0.676763i	$0.763382\pi$
$332$	31.3125	+	22.7498i	1.71849	+	1.24856i
$333$	−6.63052	+	10.4480i	−0.363350	+	0.572548i
$334$	4.42925	+	23.2189i	0.242358	+	1.27048i
$335$	12.9319	−	7.42925i	0.706543	−	0.405903i
$336$	−0.00178912		0.000226018i	−9.76044e−5		1.23303e-5i
$337$	−6.39888	−	33.5441i	−0.348569	−	1.82726i	−0.535069	−	0.844809i	$-0.679714\pi$
$337$	−6.39888	−	33.5441i	−0.348569	−	1.82726i	0.186500	−	0.982455i	$-0.440286\pi$
$338$	−27.6277	−	3.49019i	−1.50275	−	0.189841i
$339$	−0.000232430	0	0.000127779i	−1.26239e−5	0	6.94002e-6i
$340$	73.3283	−	10.6674i	3.97679	−	0.578522i
$341$	−1.98922	−	1.86800i	−0.107722	−	0.101158i
$342$	11.9936	+	3.07943i	0.648539	+	0.166516i
$343$	16.3048	−	11.8461i	0.880376	−	0.639631i
$344$	−6.12113	−	97.2925i	−0.330029	−	5.24566i
$345$	0.000949406	0	0.000545426i	5.11143e−5	0	2.93648e-5i
$346$	34.2451	+	13.5586i	1.84103	+	0.728914i
$347$	−6.16481	−	2.44082i	−0.330944	−	0.131030i	0.196776	−	0.980449i	$-0.436953\pi$
$347$	−6.16481	−	2.44082i	−0.330944	−	0.131030i	−0.527720	+	0.849418i	$0.676953\pi$
$348$	0.000909140	0	0.000114851i	4.87350e−5	0	6.15666e-6i
$349$	1.79107	+	5.51234i	0.0958737	+	0.295069i	0.987480	−	0.157742i	$-0.0504214\pi$
$349$	1.79107	+	5.51234i	0.0958737	+	0.295069i	−0.891607	+	0.452811i	$0.850421\pi$
$350$	19.7802	+	22.1586i	1.05729	+	1.18443i
$351$	−0.000183710	0	0.000565401i	−9.80571e−6	0	3.01789e-5i
$352$	−1.53114	+	8.02649i	−0.0816098	+	0.427814i
$353$	−0.669684	+	10.6443i	−0.0356437	+	0.566540i	0.939161	+	0.343478i	$0.111605\pi$
$353$	−0.669684	+	10.6443i	−0.0356437	+	0.566540i	−0.974804	+	0.223062i	$0.928395\pi$
$354$	0.00143964		0.000369636i	7.65158e−5		1.96459e-5i
$355$	1.69810	−	2.79036i	0.0901256	−	0.148097i
$356$	−28.6045	+	45.0734i	−1.51603	+	2.38889i
$357$	0.000254901	0	0.000784506i	1.34908e−5	0	4.15204e-5i
$358$	−3.82943	−	60.8670i	−0.202392	−	3.21692i
$359$	−4.37216	−	0.552332i	−0.230754	−	0.0291510i	0.00910593	−	0.999959i	$-0.497101\pi$
$359$	−4.37216	−	0.552332i	−0.230754	−	0.0291510i	−0.239860	+	0.970808i	$0.577101\pi$
$360$	55.5161	−	23.1967i	2.92596	−	1.22258i
$361$	7.09831	+	15.0847i	0.373595	+	0.793930i
$362$	−4.88501	+	10.3812i	−0.256750	+	0.545622i
$363$	−0.000570920	0	0.000313866i	−2.99656e−5	0	1.64737e-5i
$364$	13.9970	−	13.1440i	0.733640	−	0.688934i
$365$	11.4900	+	4.30119i	0.601415	+	0.225135i
$366$	−0.000371737	0	0.000789980i	−1.94310e−5	0	4.12929e-5i
$367$	19.3431	+	23.3818i	1.00970	+	1.22052i	0.975248	+	0.221112i	$0.0709686\pi$
$367$	19.3431	+	23.3818i	1.00970	+	1.22052i	0.0344520	+	0.999406i	$0.489031\pi$
$368$	−34.2267	+	105.339i	−1.78419	+	5.49117i
$369$	15.3739	+	3.94736i	0.800336	+	0.205491i
$370$	17.8616	−	17.4165i	0.928582	−	0.905438i
$371$	−0.955515	+	15.1875i	−0.0496079	+	0.788494i
$372$	0.00108452	+	0.00170894i	5.62299e−5	+	8.86042e-5i
$373$	21.2336	−	19.9397i	1.09943	−	1.03244i	0.100136	−	0.994974i	$-0.468072\pi$
$373$	21.2336	−	19.9397i	1.09943	−	1.03244i	0.999298	−	0.0374630i	$-0.0119276\pi$
$374$	7.28086			0.376484
$375$	0.000566410	0	0.000364591i	2.92493e−5	0	1.88274e-5i
$376$	−69.7954			−3.59942
$377$	−3.42994	+	3.22092i	−0.176651	+	0.165886i
$378$	0.00115068	+	0.00181319i	5.91848e−5	+	9.32603e-5i
$379$	−2.14008	+	34.0156i	−0.109929	+	1.74726i	0.427554	+	0.903990i	$0.359375\pi$
$379$	−2.14008	+	34.0156i	−0.109929	+	1.74726i	−0.537483	+	0.843275i	$0.680625\pi$
$380$	−16.0572	−	8.43844i	−0.823718	−	0.432883i
$381$	−0.000679787	0	0.000174540i	−3.48266e−5	0	8.94194e-6i
$382$	−10.5708	+	32.5336i	−0.540849	+	1.66456i
$383$	13.9127	+	16.8176i	0.710905	+	0.859337i	0.995043	−	0.0994466i	$-0.0317072\pi$
$383$	13.9127	+	16.8176i	0.710905	+	0.859337i	−0.284138	+	0.958784i	$0.591707\pi$
$384$	0.000689348	−	0.00146494i	3.51781e−5	−	7.47573e-5i
$385$	1.16977	+	1.76887i	0.0596169	+	0.0901499i
$386$	30.5902	−	28.7261i	1.55700	−	1.46212i
$387$	−28.5732	+	15.7083i	−1.45246	+	0.798495i
$388$	9.67657	−	20.5638i	0.491253	−	1.04397i
$389$	−13.8921	−	29.5222i	−0.704357	−	1.49683i	−0.860690	−	0.509130i	$-0.829967\pi$
$389$	−13.8921	−	29.5222i	−0.704357	−	1.49683i	0.156333	−	0.987704i	$-0.450033\pi$
$390$	0.000311537	0	0.000511926i	1.57753e−5	0	2.59224e-5i
$391$	50.2640	+	6.34982i	2.54196	+	0.321124i
$392$	1.22565	+	19.4811i	0.0619046	+	0.983945i
$393$	−0.000184723	0	0.000568519i	−9.31805e−6	0	2.86780e-5i
$394$	−3.24496	+	5.11323i	−0.163479	+	0.257601i
$395$	−3.21610	−	3.74209i	−0.161819	−	0.188285i
$396$	6.67027	−	1.71263i	0.335194	−	0.0860631i
$397$	0.758978	−	12.0636i	0.0380920	−	0.605455i	−0.931961	−	0.362560i	$-0.881903\pi$
$397$	0.758978	−	12.0636i	0.0380920	−	0.605455i	0.970053	−	0.242895i	$-0.0780971\pi$
$398$	2.82689	−	14.8191i	0.141699	−	0.742813i
$399$	6.23991e−5	0	0.000192045i	3.12386e−6	0	9.61425e-6i
$400$	−67.2343	+	11.0752i	−3.36172	+	0.553759i
$401$	−6.57281	−	20.2290i	−0.328230	−	1.01019i	−0.969961	−	0.243259i	$-0.921783\pi$
$401$	−6.57281	−	20.2290i	−0.328230	−	1.01019i	0.641731	−	0.766930i	$-0.278217\pi$
$402$	−0.00107835		0.000136227i	−5.37832e−5		6.79440e-6i
$403$	−9.66277	−	3.82576i	−0.481337	−	0.190575i
$404$	86.3997	+	34.2080i	4.29854	+	1.70191i
$405$	−14.9266	−	13.4981i	−0.741707	−	0.670724i
$406$	1.06722	+	16.9629i	0.0529650	+	0.841855i
$407$	1.44098	−	1.04693i	0.0714267	−	0.0518945i
$408$	−0.00326281		0.000837747i	−0.000161533		4.14746e-5i
$409$	−26.6271	−	25.0046i	−1.31663	−	1.23640i	−0.952314	−	0.305119i	$-0.901304\pi$
$409$	−26.6271	−	25.0046i	−1.31663	−	1.23640i	−0.364313	−	0.931276i	$-0.618696\pi$
$410$	−28.3266	−	14.8863i	−1.39895	−	0.735182i
$411$	0.000812686	0	0.000446778i	4.00868e−5	0	2.20379e-5i
$412$	−31.5121	−	3.98091i	−1.55249	−	0.196125i
$413$	3.75356	+	19.6769i	0.184701	+	0.968235i
$414$	65.4287	−	8.26557i	3.21565	−	0.406231i
$415$	−6.65362	+	14.8584i	−0.326613	+	0.729369i
$416$	5.83127	+	30.5686i	0.285901	+	1.49875i
$417$	6.31471e−5	0	9.95039e-5i	3.09233e−6	0	4.87273e-6i
$418$	−1.44194	−	1.04763i	−0.0705275	−	0.0512412i
$419$	−5.00501	−	6.05002i	−0.244511	−	0.295563i	0.633953	−	0.773372i	$-0.281431\pi$
$419$	−5.00501	−	6.05002i	−0.244511	−	0.295563i	−0.878464	+	0.477809i	$0.841431\pi$
$420$	−0.000514101	−	0.00148656i	−2.50856e−5	−	7.25368e-5i
$421$	−5.36959	−	8.46112i	−0.261698	−	0.412370i	0.687917	−	0.725789i	$-0.258525\pi$
$421$	−5.36959	−	8.46112i	−0.261698	−	0.412370i	−0.949615	+	0.313420i	$0.898525\pi$
$422$	−2.11146	+	2.55231i	−0.102784	+	0.124245i
$423$	9.93978	+	21.1231i	0.483289	+	1.02704i
$424$	−50.2766	−	36.5281i	−2.44165	−	1.77396i
$425$	10.7390	+	29.2601i	0.520918	+	1.41932i
$426$	−0.000192591	0	0.000139926i	−9.33107e−6	0	6.77942e-6i
$427$	−10.3112	−	5.66862i	−0.498993	−	0.274324i
$428$	26.0310	−	6.68362i	1.25826	−	0.323065i
$429$	2.72725e−5	0	3.29668e-5i	1.31673e−6	0	1.59165e-6i
$430$	63.3524	−	17.5418i	3.05512	−	0.845942i
$431$	4.65307	−	1.84228i	0.224131	−	0.0887396i	−0.253376	−	0.967368i	$-0.581541\pi$
$431$	4.65307	−	1.84228i	0.224131	−	0.0887396i	0.477506	+	0.878628i	$0.341541\pi$
$432$	−0.00492649			−0.000237026
$433$	−8.77505	+	3.47429i	−0.421702	+	0.166964i	−0.569385	−	0.822071i	$-0.692819\pi$
$433$	−8.77505	+	3.47429i	−0.421702	+	0.166964i	0.147683	+	0.989035i	$0.452819\pi$
$434$	−32.8973	+	18.0854i	−1.57912	+	0.868129i
$435$	0.000125980	0	0.000364280i	6.04026e−6	0	1.74659e-5i
$436$	4.69123	−	24.5923i	0.224669	−	1.17776i
$437$	−9.04086	−	8.48993i	−0.432483	−	0.406129i
$438$	−0.000651796	0	0.000612077i	−3.11440e−5	0	2.92462e-5i
$439$	−2.15522	+	11.2981i	−0.102863	+	0.539227i	0.893130	+	0.449798i	$0.148504\pi$
$439$	−2.15522	+	11.2981i	−0.102863	+	0.539227i	−0.995993	+	0.0894289i	$0.971496\pi$
$440$	−8.65888	+	0.162786i	−0.412796	+	0.00776052i
$441$	5.72129	−	3.14530i	0.272442	−	0.149776i
$442$	25.7816	−	10.2077i	1.22631	−	0.485530i
$443$	−32.2155			−1.53060			−0.765302	−	0.643671i	$-0.777410\pi$
$443$	−32.2155			−1.53060			−0.765302	+	0.643671i	$0.777410\pi$
$444$	−0.00122834		0.000486335i	−5.82945e−5		2.30804e-5i
$445$	−21.0295	−	7.87223i	−0.996896	−	0.373180i
$446$	−25.7103	+	31.0784i	−1.21742	+	1.47160i
$447$	0.000177872	0	4.56698e-5i	8.41306e−6	0	2.16011e-6i
$448$	46.0505	+	25.3165i	2.17568	+	1.19609i
$449$	16.6923	−	12.1276i	0.787756	−	0.572339i	−0.119540	−	0.992829i	$-0.538142\pi$
$449$	16.6923	−	12.1276i	0.787756	−	0.572339i	0.907297	+	0.420491i	$0.138142\pi$
$450$	23.0119	+	33.4149i	1.08479	+	1.57520i
$451$	−1.84834	−	1.34290i	−0.0870351	−	0.0632347i
$452$	9.96450	+	21.1756i	0.468691	+	0.996018i
$453$	−4.19173e−5	0	5.06693e-5i	−1.96945e−6	0	2.38065e-6i
$454$	−13.2927	−	20.9459i	−0.623856	−	0.983039i
$455$	6.62210	+	4.62359i	0.310449	+	0.216757i
$456$	0.000525641	0	0.000635390i	2.46154e−5	0	2.97549e-5i
$457$	0.653020	+	0.474447i	0.0305470	+	0.0221937i	0.602954	−	0.797776i	$-0.293990\pi$
$457$	0.653020	+	0.474447i	0.0305470	+	0.0221937i	−0.572407	+	0.819970i	$0.693990\pi$
$458$	19.9490	−	31.4346i	0.932156	−	1.46884i
$459$	0.000422257		0.00221355i	1.97093e−5		0.000103320i
$460$	−96.0584	−	10.3046i	−4.47875	−	0.480456i
$461$	−30.3011	+	3.82792i	−1.41126	+	0.178284i	−0.793735	−	0.608264i	$-0.791866\pi$
$461$	−30.3011	+	3.82792i	−1.41126	+	0.178284i	−0.617529	+	0.786548i	$0.711866\pi$
$462$	−2.89604e−5	0	0.000151816i	−1.34736e−6	0	7.06310e-6i
$463$	6.50315	+	0.821539i	0.302227	+	0.0381801i	0.274984	−	0.961449i	$-0.411327\pi$
$463$	6.50315	+	0.821539i	0.302227	+	0.0381801i	0.0272426	+	0.999629i	$0.491327\pi$
$464$	−34.1681	−	18.7841i	−1.58621	−	0.872029i
$465$	−0.000609550	0	0.000594358i	−2.82672e−5	0	2.75627e-5i
$466$	−39.2433	−	36.8519i	−1.81791	−	1.70713i
$467$	2.18616	+	0.561310i	0.101163	+	0.0259743i	0.298932	−	0.954274i	$-0.403370\pi$
$467$	2.18616	+	0.561310i	0.101163	+	0.0259743i	−0.197769	+	0.980249i	$0.563370\pi$
$468$	21.2184	−	15.4161i	0.980822	−	0.712609i
$469$	−0.919800	−	14.6198i	−0.0424724	−	0.675080i
$470$	−9.68643	−	46.0569i	−0.446802	−	2.12445i
$471$	0.000363917	0	0.000144085i	1.67684e−5	0	6.63908e-6i
$472$	−76.0607	−	30.1146i	−3.50098	−	1.38614i
$473$	4.65631	−	0.588228i	0.214097	−	0.0270468i
$474$	0.000111123	0	0.000342002i	5.10406e−6	0	1.57087e-5i
$475$	2.08338	−	7.34003i	0.0955919	−	0.336784i
$476$	22.4909	−	69.2200i	1.03087	−	3.17269i
$477$	−3.89494	+	20.4180i	−0.178337	+	0.934874i
$478$	−2.72464	+	43.3069i	−0.124622	+	1.98081i
$479$	9.78410	−	2.51213i	0.447047	−	0.114782i	−0.0184536	−	0.999830i	$-0.505874\pi$
$479$	9.78410	−	2.51213i	0.447047	−	0.114782i	0.465501	+	0.885048i	$0.345874\pi$
$480$	0.00248072		0.000587468i	0.000113229		2.68141e-5i
$481$	3.63474	−	5.72744i	0.165730	−	0.261149i
$482$	−1.69757	−	5.22460i	−0.0773224	−	0.237974i
$483$	−6.75281e−5	−	0.00107333i	−3.07263e−6	−	4.88381e-5i
$484$	57.0318	+	7.20479i	2.59235	+	0.327490i
$485$	9.30221	+	2.20289i	0.422392	+	0.100028i
$486$	0.00187343	+	0.00398124i	8.49806e−5	+	0.000180593i
$487$	3.64939	−	7.75536i	0.165370	−	0.351429i	−0.804917	−	0.593388i	$-0.797790\pi$
$487$	3.64939	−	7.75536i	0.165370	−	0.351429i	0.970286	+	0.241959i	$0.0777900\pi$
$488$	42.1088	−	23.1495i	1.90618	−	1.04793i
$489$	−0.000190157	0	0.000178570i	−8.59921e−6	0	8.07520e-6i
$490$	−12.6852	+	3.51244i	−0.573059	+	0.158676i
$491$	−17.9482	+	38.1418i	−0.809990	+	1.72132i	−0.125748	+	0.992062i	$0.540133\pi$
$491$	−17.9482	+	38.1418i	−0.809990	+	1.72132i	−0.684243	+	0.729254i	$0.739867\pi$
$492$	0.00108018	+	0.00130571i	4.86981e−5	+	5.88659e-5i
$493$	−5.51137	+	16.9622i	−0.248220	+	0.763941i
$494$	−6.57468	−	1.68809i	−0.295809	−	0.0759509i
$495$	1.28241	+	2.59737i	0.0576398	+	0.116743i
$496$	5.40760	−	85.9514i	0.242808	−	3.85933i
$497$	−1.71911	−	2.70889i	−0.0771128	−	0.121510i
$498$	0.000864909	0	0.000812204i	3.87575e−5	0	3.63957e-5i
$499$	14.1706			0.634364			0.317182	−	0.948365i	$-0.397263\pi$
$499$	14.1706			0.634364			0.317182	+	0.948365i	$0.397263\pi$
$500$	−21.5232	−	55.4010i	−0.962547	−	2.47761i
$501$	0.000526523	0		2.35233e−5	0
$502$	26.1657	−	24.5713i	1.16783	−	1.09667i
$503$	6.40546	+	10.0934i	0.285605	+	0.450042i	0.956593	−	0.291426i	$-0.0941298\pi$
$503$	6.40546	+	10.0934i	0.285605	+	0.450042i	−0.670988	+	0.741468i	$0.734130\pi$
$504$	3.71075	−	58.9807i	0.165290	−	2.62721i
$505$	−6.60118	+	38.5255i	−0.293748	+	1.71436i
$506$	−9.19434	−	2.36070i	−0.408738	−	0.104946i
$507$	−0.000191681	0	0.000589934i	−8.51286e−6	0	2.61999e-5i
$508$	39.4730	+	47.7146i	1.75133	+	2.11699i
$509$	11.4191	−	24.2669i	0.506144	−	1.07561i	−0.474580	−	0.880213i	$-0.657400\pi$
$509$	11.4191	−	24.2669i	0.506144	−	1.07561i	0.980724	−	0.195399i	$-0.0626001\pi$
$510$	9.99933e−5	−	0.00226934i	4.42778e−6	−	0.000100488i
$511$	8.78441	−	8.24911i	0.388600	−	0.364919i
$512$	−11.7572	+	6.46359i	−0.519601	+	0.285653i
$513$	0.000234877	0	0.000499139i	1.03701e−5	0	2.20375e-5i
$514$	15.3404	+	32.6000i	0.676635	+	1.43792i
$515$	−1.08938	−	13.3157i	−0.0480037	−	0.586762i
$516$	−0.00345368		0.000436302i	−0.000152040		1.92071e-5i
$517$	−0.210991	−	3.35360i	−0.00927935	−	0.147491i
$518$	−7.57204	−	23.3043i	−0.332696	−	1.02393i
$519$	0.000439600	0	0.000692699i	1.92963e−5	0	3.04061e-5i
$520$	−30.4330	+	12.7161i	−1.33458	+	0.557637i
$521$	19.8422	−	5.09460i	0.869301	−	0.223198i	0.212407	−	0.977181i	$-0.431870\pi$
$521$	19.8422	−	5.09460i	0.869301	−	0.223198i	0.656894	+	0.753983i	$0.271870\pi$
$522$	−1.45775	+	23.1703i	−0.0638039	+	1.01413i
$523$	1.56299	−	8.19348i	0.0683447	−	0.358276i	−0.931642	−	0.363377i	$-0.881624\pi$
$523$	1.56299	−	8.19348i	0.0683447	−	0.358276i	0.999987	+	0.00510116i	$0.00162376\pi$
$524$	−16.2988	+	50.1626i	−0.712018	+	2.19137i
$525$	0.000567397	0	0.000340308i	2.47632e−5	0	1.48522e-5i
$526$	14.0636	+	43.2832i	0.613201	+	1.88724i
$527$	−39.0827	+	4.93730i	−1.70247	+	0.215072i
$528$	0.000329658	0	0.000130521i	1.43465e−5	0	5.68018e-6i
$529$	−40.0301	−	15.8490i	−1.74044	−	0.689089i
$530$	17.1268	−	38.2463i	0.743941	−	1.66131i
$531$	1.71807	+	27.3080i	0.0745580	+	1.18507i
$532$	−14.4141	+	10.4725i	−0.624932	+	0.454040i
$533$	−8.42775	−	2.16388i	−0.365046	−	0.0937279i
$534$	0.00119295	+	0.00112025i	5.16238e−5	+	4.84780e-5i
$535$	5.00464	+	10.1363i	0.216369	+	0.438232i
$536$	52.4228	+	28.8197i	2.26432	+	1.24482i
$537$	−0.00134777		0.000170263i	−5.81606e−5		7.34739e-6i
$538$	5.67211	+	29.7342i	0.244542	+	1.28193i
$539$	−0.932344	+	0.117782i	−0.0401589	+	0.00507325i
$540$	−0.000884394	−	0.00420510i	−3.80582e−5	−	0.000180959i
$541$	−2.93672	−	15.3948i	−0.126260	−	0.661876i	−0.987991	−	0.154511i	$-0.950620\pi$
$541$	−2.93672	−	15.3948i	−0.126260	−	0.661876i	0.861732	−	0.507365i	$-0.169380\pi$
$542$	−32.4751	+	51.1725i	−1.39492	+	2.19805i
$543$	0.000206753	0	0.000150215i	8.87263e−6	0	6.44634e-6i
$544$	75.1909	+	90.8901i	3.22378	+	3.89688i
$545$	10.5289	−	0.197941i	0.451007	−	0.00847888i
$546$	−0.000315393	0	0.000496980i	−1.34976e−5	0	2.12688e-5i
$547$	−14.2805	+	17.2621i	−0.610589	+	0.738076i	−0.981683	−	0.190520i	$-0.938983\pi$
$547$	−14.2805	+	17.2621i	−0.610589	+	0.738076i	0.371094	+	0.928595i	$0.378983\pi$
$548$	−34.8407	−	74.0402i	−1.48832	−	3.16284i
$549$	−13.0029	−	9.44716i	−0.554950	−	0.403195i
$550$	−1.30913	−	5.69128i	−0.0558214	−	0.242677i
$551$	3.53216	−	2.56627i	0.150475	−	0.109327i
$552$	0.00384868	+	0.00211583i	0.000163811	+	9.00556e-5i
$553$	−4.69419	+	1.20526i	−0.199617	+	0.0512531i
$554$	−8.78778	+	10.6226i	−0.373357	+	0.451311i
$555$	−0.000306524	0	0.000463512i	−1.30112e−5	0	1.96750e-5i
$556$	−9.66814	+	3.82789i	−0.410020	+	0.162339i
$557$	−23.5117			−0.996223			−0.498111	−	0.867113i	$-0.665973\pi$
$557$	−23.5117			−0.996223			−0.498111	+	0.867113i	$0.665973\pi$
$558$	−47.6775	+	18.8768i	−2.01835	+	0.799121i
$559$	15.6634	−	8.61101i	0.662490	−	0.364207i
$560$	−19.4819	+	64.0302i	−0.823261	+	2.70577i
$561$	3.03895e−5	0	0.000159307i	1.28304e−6	0	6.72596e-6i
$562$	48.0766	+	45.1469i	2.02799	+	1.90441i
$563$	−25.7254	−	24.1577i	−1.08419	−	1.01813i	−0.999765	−	0.0216971i	$-0.993093\pi$
$563$	−25.7254	−	24.1577i	−1.08419	−	1.01813i	−0.0844300	−	0.996429i	$-0.526907\pi$
$564$	−0.000467021		0.00244821i	−1.96651e−5		0.000103088i
$565$	−7.85375	+	5.93479i	−0.330410	+	0.249679i
$566$	−29.2459	+	16.0780i	−1.22929	+	0.675811i
$567$	−18.3786	+	7.27659i	−0.771827	+	0.305588i
$568$	13.1022			0.549757
$569$	5.83744	−	2.31121i	0.244718	−	0.0968909i	−0.242564	−	0.970135i	$-0.577988\pi$
$569$	5.83744	−	2.31121i	0.244718	−	0.0968909i	0.487282	+	0.873245i	$0.337988\pi$
$570$	−0.000346335	0	0.000435044i	−1.45064e−5	0	1.82220e-5i
$571$	−5.57440	+	6.73829i	−0.233281	+	0.281989i	−0.874144	−	0.485667i	$-0.838577\pi$
$571$	−5.57440	+	6.73829i	−0.233281	+	0.281989i	0.640863	+	0.767656i	$0.278577\pi$
$572$	−3.65653	+	0.938838i	−0.152887	+	0.0392548i
$573$	0.000667722	0	0.000367083i	2.78945e−5	0	1.53351e-5i
$574$	−25.4281	+	18.4746i	−1.06135	+	0.771114i
$575$	−4.07417	−	40.4319i	−0.169905	−	1.68613i
$576$	58.0720	+	42.1918i	2.41967	+	1.75799i
$577$	11.9426	+	25.3793i	0.497177	+	1.05656i	0.983187	+	0.182602i	$0.0584520\pi$
$577$	11.9426	+	25.3793i	0.497177	+	1.05656i	−0.486010	+	0.873953i	$0.661548\pi$
$578$	37.6878	−	45.5568i	1.56761	−	1.89491i
$579$	−0.000500855	0	0.000789221i	−2.08148e−5	0	3.27989e-5i
$580$	9.89972	−	32.5369i	0.411064	−	1.35102i
$581$	10.1928	+	12.3209i	0.422867	+	0.511158i
$582$	−0.000563633	0	0.000409504i	−2.33634e−5	0	1.69745e-5i
$583$	1.60315	−	2.52617i	0.0663958	−	0.104623i
$584$	9.22136	+	48.3401i	0.381583	+	2.00033i
$585$	8.18250	+	7.39942i	0.338305	+	0.305928i
$586$	−31.9122	+	4.03144i	−1.31828	+	0.166537i
$587$	6.25469	+	32.7882i	0.258159	+	1.35331i	0.841135	+	0.540825i	$0.181888\pi$
$587$	6.25469	+	32.7882i	0.258159	+	1.35331i	−0.582976	+	0.812489i	$0.698112\pi$
$588$	0.000691540	0	8.73618e-5i	2.85186e−5	0	3.60274e-6i
$589$	8.45055	+	4.64573i	0.348199	+	0.191424i
$590$	9.31620	−	54.3708i	0.383542	−	2.23841i
$591$	9.83348e−5	0	9.23426e-5i	4.04495e−6	0	3.79847e-6i
$592$	54.4470	+	13.9796i	2.23776	+	0.574558i
$593$	−11.0837	+	8.05277i	−0.455153	+	0.330688i	−0.791627	−	0.611005i	$-0.790766\pi$
$593$	−11.0837	+	8.05277i	−0.455153	+	0.330688i	0.336474	+	0.941693i	$0.390766\pi$
$594$	−2.65114e−5	0	0.000421387i	−1.08778e−6	0	1.72897e-5i
$595$	30.4396	+	3.26539i	1.24790	+	0.133868i
$596$	−15.0655	−	5.96487i	−0.617108	−	0.244330i
$597$	−0.000312446	0	0.000123706i	−1.27876e−5	0	5.06296e-6i
$598$	−35.8670	+	4.53105i	−1.46671	+	0.185288i
$599$	−9.24261	−	28.4458i	−0.377643	−	1.16226i	−0.941678	−	0.336514i	$-0.890752\pi$
$599$	−9.24261	−	28.4458i	−0.377643	−	1.16226i	0.564036	−	0.825750i	$-0.309248\pi$
$600$	−6.81805e−5		0.00270109i	−2.78346e−6		0.000110272i
$601$	−11.8290	+	36.4060i	−0.482516	+	1.48503i	0.353029	+	0.935612i	$0.385152\pi$
$601$	−11.8290	+	36.4060i	−0.482516	+	1.48503i	−0.835546	+	0.549421i	$0.814848\pi$
$602$	12.0986	−	63.4232i	0.493103	−	2.58494i
$603$	1.25639	−	19.9697i	0.0511641	−	0.813230i
$604$	5.62001	−	1.44297i	0.228675	−	0.0587138i
$605$	1.97159	+	24.0993i	0.0801567	+	0.979775i
$606$	0.00152637	−	0.00240518i	6.20046e−5	−	9.77036e-5i
$607$	−7.94424	−	24.4499i	−0.322447	−	0.992389i	−0.972580	−	0.232569i	$-0.925287\pi$
$607$	−7.94424	−	24.4499i	−0.322447	−	0.992389i	0.650133	−	0.759820i	$-0.274713\pi$
$608$	−1.81316	−	28.8194i	−0.0735334	−	1.16878i
$609$	0.000375607	0	4.74503e-5i	1.52204e−5	0	1.92278e-6i
$610$	21.1200	+	24.5742i	0.855125	+	0.994981i
$611$	−5.44882	−	11.5793i	−0.220436	−	0.468450i
$612$	42.3292	−	89.9541i	1.71106	−	3.63618i
$613$	−15.0893	+	8.29539i	−0.609449	+	0.335048i	−0.756413	−	0.654094i	$-0.773050\pi$
$613$	−15.0893	+	8.29539i	−0.609449	+	0.335048i	0.146964	+	0.989142i	$0.453050\pi$
$614$	−2.86938	+	2.69452i	−0.115799	+	0.108742i
$615$	−0.000443948	0	0.000557660i	−1.79017e−5	0	2.24870e-5i
$616$	−3.62184	+	7.69680i	−0.145928	+	0.310113i
$617$	−5.84953	−	7.07086i	−0.235493	−	0.284662i	0.639507	−	0.768785i	$-0.279139\pi$
$617$	−5.84953	−	7.07086i	−0.235493	−	0.284662i	−0.875000	+	0.484123i	$0.839139\pi$
$618$	−0.000300885	0	0.000926029i	−1.21034e−5	0	3.72504e-5i
$619$	−0.599399	−	0.153900i	−0.0240919	−	0.00618575i	0.236625	−	0.971601i	$-0.423959\pi$
$619$	−0.599399	−	0.153900i	−0.0240919	−	0.00618575i	−0.260717	+	0.965415i	$0.583959\pi$
$620$	74.3362	−	10.8140i	2.98541	−	0.434302i
$621$	0.000184478	−	0.00293220i	7.40285e−6	−	0.000117665i
$622$	38.4823	+	60.6384i	1.54300	+	2.43138i
$623$	−16.0776	+	15.0979i	−0.644136	+	0.604884i
$624$	0.00135031			5.40557e−5
$625$	20.9410	−	13.6555i	0.837641	−	0.546221i
$626$	66.9139			2.67442
$627$	−2.89409e−5	0	2.71773e-5i	−1.15579e−6	0	1.08536e-6i
$628$	−18.5048	−	29.1588i	−0.738420	−	1.16356i
$629$	1.61452	−	25.6620i	0.0643751	−	1.02321i
$630$	39.4355	−	5.73687i	1.57115	−	0.228562i
$631$	9.13861	+	2.34640i	0.363802	+	0.0934085i	0.426166	−	0.904645i	$-0.359864\pi$
$631$	9.13861	+	2.34640i	0.363802	+	0.0934085i	−0.0623639	+	0.998053i	$0.519864\pi$
$632$	6.11606	−	18.8233i	0.243284	−	0.748750i
$633$	4.70323e−5	0	5.68523e-5i	1.86937e−6	0	2.25967e-6i
$634$	−14.6297	+	31.0898i	−0.581021	+	1.23473i
$635$	−16.2232	+	20.3786i	−0.643800	+	0.808701i
$636$	−0.00161771	+	0.00151913i	−6.41463e−5	+	6.02374e-5i
$637$	−3.13631	+	1.72420i	−0.124265	+	0.0683154i
$638$	1.42282	−	3.02365i	0.0563300	−	0.119707i
$639$	−1.86593	−	3.96530i	−0.0738150	−	0.156865i
$640$	−39.1650	−	45.5704i	−1.54813	−	1.80133i
$641$	4.93365	+	0.623265i	0.194868	+	0.0246175i	0.222161	−	0.975010i	$-0.428689\pi$
$641$	4.93365	+	0.623265i	0.194868	+	0.0246175i	−0.0272936	+	0.999627i	$0.508689\pi$
$642$	−5.17309e−5	0	0.000822239i	−2.04166e−6	0	3.24512e-5i
$643$	−4.83486	−	14.8802i	−0.190668	−	0.586817i	0.809332	−	0.587352i	$-0.199830\pi$
$643$	−4.83486	−	14.8802i	−0.190668	−	0.586817i	−1.00000		0.000535419i	$0.999830\pi$
$644$	−50.8452	+	80.1192i	−2.00358	+	3.15714i
$645$	−0.000119394	−	0.00145938i	−4.70114e−6	−	5.74632e-5i
$646$	−24.9215	+	6.39876i	−0.980525	+	0.251756i
$647$	1.17172	−	18.6240i	0.0460651	−	0.732183i	−0.905425	−	0.424505i	$-0.860448\pi$
$647$	1.17172	−	18.6240i	0.0460651	−	0.732183i	0.951491	−	0.307678i	$-0.0995520\pi$
$648$	15.1260	−	79.2933i	0.594206	−	3.11494i
$649$	1.21705	−	3.74568i	0.0477732	−	0.147031i
$650$	−12.6147	−	18.3175i	−0.494791	−	0.718472i
$651$	0.000258405	0	0.000795288i	1.01277e−5	0	3.11698e-5i
$652$	22.8350	−	2.88474i	0.894289	−	0.112975i
$653$	−26.1173	−	10.3406i	−1.02205	−	0.404658i	−0.203488	−	0.979077i	$-0.565228\pi$
$653$	−26.1173	−	10.3406i	−1.02205	−	0.404658i	−0.818561	+	0.574420i	$0.805228\pi$
$654$	−0.000713577	0	0.000282525i	−2.79031e−5	0	1.10476e-5i
$655$	−22.0591	−	2.36638i	−0.861919	−	0.0924622i
$656$	−4.52748	−	71.9622i	−0.176768	−	2.80965i
$657$	13.3166	−	9.67505i	0.519529	−	0.377460i
$658$	−44.7751	−	11.4963i	−1.74551	−	0.448172i
$659$	10.8198	+	10.1605i	0.421481	+	0.395797i	0.866058	−	0.499944i	$-0.166646\pi$
$659$	10.8198	+	10.1605i	0.421481	+	0.395797i	−0.444577	+	0.895741i	$0.646646\pi$
$660$	−5.22290e−5	0	0.000304816i	−2.03301e−6	0	1.18650e-5i
$661$	13.3011	+	7.31237i	0.517355	+	0.284418i	0.718963	−	0.695048i	$-0.244617\pi$
$661$	13.3011	+	7.31237i	0.517355	+	0.284418i	−0.201609	+	0.979466i	$0.564617\pi$
$662$	−5.09531	−	0.643687i	−0.198035	−	0.0250176i
$663$	−0.000115737	0	0.000606715i	−4.49486e−6	0	2.35629e-5i
$664$	−64.7873	+	8.18454i	−2.51423	+	0.317622i
$665$	−5.55855	−	5.02658i	−0.215551	−	0.194922i
$666$	−6.27173	−	32.8775i	−0.243024	−	1.27398i
$667$	12.4595	−	19.6331i	0.482435	−	0.760197i
$668$	−37.5847	−	27.3069i	−1.45419	−	1.05653i
$669$	0.000572692	0	0.000692265i	2.21415e−5	0	2.67645e-5i
$670$	−11.7423	+	38.5927i	−0.453644	+	1.49097i
$671$	1.23961	+	1.95331i	0.0478545	+	0.0754066i
$672$	0.00159610	−	0.00192935i	6.15709e−5	−	7.44265e-5i
$673$	0.643562	+	1.36764i	0.0248075	+	0.0527186i	0.916847	−	0.399239i	$-0.130726\pi$
$673$	0.643562	+	1.36764i	0.0248075	+	0.0527186i	−0.892039	+	0.451958i	$0.850726\pi$
$674$	74.7262	+	54.2918i	2.87835	+	2.09124i
$675$	0.00165435		0.000728073i	6.36761e−5		2.80235e-5i
$676$	44.2782	−	32.1700i	1.70301	−	1.23731i
$677$	−0.939932	−	0.516732i	−0.0361245	−	0.0198596i	0.463589	−	0.886050i	$-0.346561\pi$
$677$	−0.939932	−	0.516732i	−0.0361245	−	0.0198596i	−0.499714	+	0.866191i	$0.666561\pi$
$678$	0.000694881	0	0.000178415i	2.66867e−5	0	6.85199e-6i
$679$	5.98506	−	7.23470i	0.229686	−	0.277642i
$680$	−77.8675	+	97.8123i	−2.98608	+	3.75093i
$681$	−0.000513784	0	0.000203421i	−1.96882e−5	0	7.79512e-6i
$682$	7.38093			0.282631
$683$	37.3312	−	14.7805i	1.42844	−	0.565559i	0.478525	−	0.878074i	$-0.341172\pi$
$683$	37.3312	−	14.7805i	1.42844	−	0.565559i	0.949913	+	0.312515i	$0.101172\pi$
$684$	−21.3264	+	11.7243i	−0.815435	+	0.448289i
$685$	27.4605	−	20.7509i	1.04921	−	0.792850i
$686$	−10.2146	+	53.5468i	−0.389995	+	2.04443i
$687$	−0.000604533	0	0.000567694i	−2.30644e−5	0	2.16589e-5i
$688$	107.976	+	101.396i	4.11653	+	3.86568i
$689$	2.13514	−	11.1928i	0.0813423	−	0.426411i
$690$	−0.000862071		0.00283333i	−3.28185e−5		0.000107863i
$691$	24.6154	−	13.5324i	0.936413	−	0.514797i	0.0609811	−	0.998139i	$-0.480577\pi$
$691$	24.6154	−	13.5324i	0.936413	−	0.514797i	0.875432	+	0.483342i	$0.160577\pi$
$692$	−67.3050	+	26.6479i	−2.55855	+	1.01300i
$693$	2.84518			0.108080
$694$	16.6747	−	6.60197i	0.632962	−	0.250607i
$695$	−2.41262	−	3.64824i	−0.0915158	−	0.138386i
$696$	−0.000985520		0.00119129i	−3.73561e−5		4.51557e-5i
$697$	−31.9456	+	8.20224i	−1.21003	+	0.310682i
$698$	−13.7380	−	7.55253i	−0.519991	−	0.285867i
$699$	−0.000970126	0	0.000704838i	−3.66935e−5	0	2.66594e-5i
$700$	−58.1516	−	5.13459i	−2.19792	−	0.194069i
$701$	26.1147	+	18.9734i	0.986337	+	0.716616i	0.959116	−	0.283014i	$-0.0913342\pi$
$701$	26.1147	+	18.9734i	0.986337	+	0.716616i	0.0272209	+	0.999629i	$0.491334\pi$
$702$	−0.000684656	−	0.00145497i	−2.58407e−5	−	5.49142e-5i
$703$	−4.01221	+	4.84993i	−0.151323	+	0.182918i
$704$	−5.53618	−	8.72363i	−0.208653	−	0.328784i
$705$	−0.00104817		1.97054e-5i	−3.94763e−5		7.42150e-7i
$706$	−18.3883	−	22.2277i	−0.692053	−	0.836549i
$707$	31.0595	+	22.5661i	1.16811	+	0.848684i
$708$	−0.00156527	+	0.00246647i	−5.88265e−5	+	9.26958e-5i
$709$	1.48027	+	7.75987i	0.0555928	+	0.291428i	0.999216	−	0.0395942i	$-0.0126065\pi$
$709$	1.48027	+	7.75987i	0.0555928	+	0.291428i	−0.943623	+	0.331022i	$0.892607\pi$
$710$	1.81837	+	8.64597i	0.0682422	+	0.324477i
$711$	−6.56775	+	0.829700i	−0.246310	+	0.0311162i
$712$	−16.8773	−	88.4741i	−0.632505	−	3.31571i
$713$	50.9548	+	6.43709i	1.90827	+	0.241071i
$714$	−0.00195517	−	0.00107486i	−7.31702e−5	−	4.02257e-5i
$715$	−0.702993	−	1.42384i	−0.0262905	−	0.0532485i
$716$	87.3772	+	82.0527i	3.26544	+	3.06645i
$717$	0.000936195	0	0.000240374i	3.49628e−5	0	8.97693e-6i
$718$	9.64338	−	7.00633i	0.359888	−	0.261474i
$719$	2.37589	+	37.7637i	0.0886058	+	1.40835i	0.751548	+	0.659678i	$0.229307\pi$
$719$	2.37589	+	37.7637i	0.0886058	+	1.40835i	−0.662942	+	0.748670i	$0.730693\pi$
$720$	−37.3630	+	83.4363i	−1.39244	+	3.10949i
$721$	−12.2011	−	4.83075i	−0.454392	−	0.179906i
$722$	−41.9263	−	16.5998i	−1.56034	−	0.617781i
$723$	−0.000121401	0	1.53365e-5i	−4.51496e−6	0	5.70372e-7i
$724$	−6.96807	−	21.4455i	−0.258966	−	0.797016i
$725$	14.2500	+	1.25822i	0.529230	+	0.0467293i
$726$	0.000544552	−	0.00167596i	2.02102e−5	−	6.22007e-5i
$727$	2.74830	−	14.4071i	0.101929	−	0.534329i	−0.894293	−	0.447482i	$-0.852321\pi$
$727$	2.74830	−	14.4071i	0.101929	−	0.534329i	0.996222	−	0.0868470i	$-0.0276791\pi$
$728$	−2.03417	+	32.3322i	−0.0753914	+	1.19831i
$729$	−26.1517	+	6.71463i	−0.968583	+	0.248690i
$730$	−30.6191	+	12.7938i	−1.13327	+	0.473521i
$731$	36.3039	−	57.2058i	1.34275	−	2.11583i
$732$	−0.000530252	−	0.00163195i	−1.95987e−5	−	6.03186e-5i
$733$	1.25039	+	19.8744i	0.0461842	+	0.734076i	0.951176	+	0.308648i	$0.0998765\pi$
$733$	1.25039	+	19.8744i	0.0461842	+	0.734076i	−0.904992	+	0.425428i	$0.860123\pi$
$734$	−81.4323	−	10.2873i	−3.00572	−	0.379711i
$735$	2.39066e−5	0	0.000292216i	8.81808e−7	0	1.07786e-5i
$736$	−65.4820	−	139.156i	−2.41370	−	5.12937i
$737$	−1.22628	+	2.60599i	−0.0451708	+	0.0959927i
$738$	−37.6220	+	20.6829i	−1.38489	+	0.761348i
$739$	2.59774	−	2.43944i	0.0955595	−	0.0897364i	−0.635295	−	0.772269i	$-0.719122\pi$
$739$	2.59774	−	2.43944i	0.0955595	−	0.0897364i	0.730855	+	0.682533i	$0.239122\pi$
$740$	−2.15836	+	48.9838i	−0.0793428	+	1.80068i
$741$	−6.43779e−5	0	0.000136810i	−2.36498e−6	0	5.02584e-6i
$742$	−26.2367	−	31.7147i	−0.963180	−	1.16428i
$743$	3.53016	−	10.8647i	0.129509	−	0.398588i	−0.865187	−	0.501450i	$-0.832800\pi$
$743$	3.53016	−	10.8647i	0.129509	−	0.398588i	0.994696	+	0.102862i	$0.0328001\pi$
$744$	−0.00330765		0.000849261i	−0.000121264		3.11354e-5i
$745$	1.15105	−	6.71770i	0.0421712	−	0.246117i
$746$	−4.94705	+	78.6311i	−0.181124	+	2.87889i
$747$	11.7036	+	18.4419i	0.428211	+	0.674752i
$748$	−10.4314	+	9.79570i	−0.381409	+	0.358166i
$749$	11.1034			0.405711
$750$	−0.00179187		0.000329875i	−6.54299e−5		1.20453e-5i
$751$	44.0022			1.60566			0.802831	−	0.596206i	$-0.203326\pi$
$751$	44.0022			1.60566			0.802831	+	0.596206i	$0.203326\pi$
$752$	77.3062	−	72.5954i	2.81907	−	2.64728i
$753$	−0.000428413	0	0.000675071i	−1.56122e−5	0	2.46009e-5i
$754$	0.799114	−	12.7016i	0.0291020	−	0.462563i
$755$	1.08049	+	2.18841i	0.0393229	+	0.0796443i
$756$	−0.00408807	−	0.00104964i	−0.000148681	−	3.81749e-5i
$757$	1.40285	−	4.31752i	0.0509874	−	0.156923i	−0.922321	−	0.386425i	$-0.873710\pi$
$757$	1.40285	−	4.31752i	0.0509874	−	0.156923i	0.973308	+	0.229502i	$0.0737098\pi$
$758$	−58.7628	−	71.0320i	−2.13436	−	2.58000i
$759$	−9.00289e−5	0	0.000191321i	−3.26784e−6	0	6.94452e-6i
$760$	29.4953	−	8.16703i	1.06991	−	0.296249i
$761$	12.9457	−	12.1568i	0.469281	−	0.440684i	−0.413475	−	0.910515i	$-0.635685\pi$
$761$	12.9457	−	12.1568i	0.469281	−	0.440684i	0.882756	+	0.469831i	$0.155685\pi$
$762$	0.00166353		0.000914532i	6.02632e−5		3.31300e-5i
$763$	4.40401	−	9.35899i	0.159436	−	0.338818i
$764$	−28.6259	−	60.8332i	−1.03565	−	2.20087i
$765$	40.6916	+	9.63632i	1.47121	+	0.348402i
$766$	−58.5710	−	7.39923i	−2.11625	−	0.267345i
$767$	−0.941820	−	14.9698i	−0.0340071	−	0.540528i
$768$	0.000462289		0.00142278i	1.66814e−5		5.13402e-5i
$769$	17.0979	−	26.9420i	0.616567	−	0.971554i	−0.382304	−	0.924037i	$-0.624869\pi$
$769$	17.0979	−	26.9420i	0.616567	−	0.971554i	0.998870	−	0.0475168i	$-0.0151308\pi$
$770$	−5.58165	−	1.32181i	−0.201149	−	0.0476347i
$771$	0.000777325	0	0.000199583i	2.79947e−5	0	7.18781e-6i
$772$	−5.17865	+	82.3124i	−0.186384	+	2.96249i
$773$	−4.09441	+	21.4637i	−0.147266	+	0.771994i	0.829636	+	0.558305i	$0.188548\pi$
$773$	−4.09441	+	21.4637i	−0.147266	+	0.771994i	−0.976902	+	0.213689i	$0.931452\pi$
$774$	27.2535	−	83.8778i	0.979608	−	3.01492i
$775$	10.8866	+	29.6623i	0.391058	+	1.06550i
$776$	11.8492	+	36.4680i	0.425360	+	1.30912i
$777$	−0.000541510	0	6.84086e-5i	−1.94266e−5	0	2.45414e-6i
$778$	82.0539	+	32.4874i	2.94177	+	1.16473i
$779$	7.50687	+	2.97218i	0.268962	+	0.106489i
$780$	0.000242405		0.00115258i	8.67949e−6		4.12691e-5i
$781$	0.0396079	+	0.629549i	0.00141728	+	0.0225270i
$782$	−110.864	+	80.5474i	−3.96449	+	2.88037i
$783$	0.00100177		0.000257212i	3.58005e−5		9.19200e-6i
$784$	−21.6202	−	20.3027i	−0.772150	−	0.725098i
$785$	10.4005	−	10.1413i	0.371209	−	0.361957i
$786$	0.00141688		0.000778935i	5.05384e−5		2.77837e-5i
$787$	−36.3939	−	4.59761i	−1.29730	−	0.163887i	−0.553816	−	0.832639i	$-0.686829\pi$
$787$	−36.3939	−	4.59761i	−1.29730	−	0.163887i	−0.743485	+	0.668752i	$0.766829\pi$
$788$	−2.23028	−	11.6916i	−0.0794506	−	0.416495i
$789$	0.00100575		0.000127056i	3.58056e−5		4.52330e-6i
$790$	13.2700	+	1.42354i	0.472126	+	0.0506472i
$791$	1.81176	+	9.49758i	0.0644188	+	0.337695i
$792$	−6.22586	+	9.81038i	−0.221226	+	0.348597i
$793$	7.12798	+	5.17878i	0.253122	+	0.183904i
$794$	20.8402	+	25.1914i	0.739590	+	0.894010i
$795$	−0.000765354	0	0.000534375i	−2.71443e−5	0	1.89523e-5i
$796$	15.8875	+	25.0348i	0.563119	+	0.887333i
$797$	14.9072	−	18.0197i	0.528041	−	0.638292i	−0.437290	−	0.899320i	$-0.644062\pi$
$797$	14.9072	−	18.0197i	0.528041	−	0.638292i	0.965331	+	0.261029i	$0.0840618\pi$
$798$	0.000232551	0	0.000494196i	8.23221e−6	0	1.74943e-5i
$799$	−39.2442	−	28.5126i	−1.38836	−	1.00870i
$800$	57.5270	−	75.1173i	2.03389	−	2.65580i
$801$	−24.3726	+	17.7077i	−0.861162	+	0.625671i
$802$	50.4153	+	27.7160i	1.78023	+	0.978687i
$803$	−2.29482	+	0.589209i	−0.0809823	+	0.0207927i
$804$	0.00136168	−	0.00164599i	4.80228e−5	−	5.80497e-5i
$805$	−37.3806	−	13.9931i	−1.31749	−	0.493192i
$806$	26.1360	−	10.3480i	0.920601	−	0.364492i
$807$	0.000674268	0		2.37354e−5	0
$808$	−145.774	+	57.7161i	−5.12832	+	2.03044i
$809$	40.7412	−	22.3976i	1.43238	−	0.787459i	0.438588	−	0.898688i	$-0.355479\pi$
$809$	40.7412	−	22.3976i	1.43238	−	0.787459i	0.993795	+	0.111229i	$0.0354786\pi$
$810$	54.4237	−	1.02316i	1.91226	−	0.0359502i
$811$	−8.54388	+	44.7886i	−0.300016	+	1.57274i	0.438644	+	0.898661i	$0.355459\pi$
$811$	−8.54388	+	44.7886i	−0.300016	+	1.57274i	−0.738660	+	0.674079i	$0.764541\pi$
$812$	−24.3510	−	22.8671i	−0.854552	−	0.802478i
$813$	0.000984122	0	0.000924152i	3.45147e−5	0	3.24114e-5i
$814$	−0.902742	+	4.73234i	−0.0316411	+	0.165868i
$815$	3.16425	+	9.14969i	0.110839	+	0.320500i
$816$	0.00448528	−	0.00246581i	0.000157016	−	8.63205e-5i
$817$	−15.4210	+	6.10562i	−0.539513	+	0.213608i
$818$	98.7992			3.45443
$819$	10.0748	−	3.98891i	0.352043	−	0.139384i
$820$	60.6119	−	16.7830i	2.11666	−	0.586088i
$821$	21.9166	−	26.4926i	0.764894	−	0.924598i	−0.233971	−	0.972244i	$-0.575172\pi$
$821$	21.9166	−	26.4926i	0.764894	−	0.924598i	0.998864	+	0.0476460i	$0.0151719\pi$
$822$	−0.00242963		0.000623824i	−8.47432e−5		2.17584e-5i
$823$	−9.51186	−	5.22919i	−0.331563	−	0.182278i	0.307273	−	0.951621i	$-0.400584\pi$
$823$	−9.51186	−	5.22919i	−0.331563	−	0.182278i	−0.638836	+	0.769343i	$0.720584\pi$
$824$	43.3553	−	31.4995i	1.51035	−	1.09734i
$825$	−0.000129991	0	4.88936e-6i	−4.52570e−6	0	1.70226e-7i
$826$	−43.8341	−	31.8474i	−1.52518	−	1.10811i
$827$	8.37502	+	17.7978i	0.291228	+	0.618891i	0.995882	−	0.0906603i	$-0.0288978\pi$
$827$	8.37502	+	17.7978i	0.291228	+	0.618891i	−0.704654	+	0.709551i	$0.748898\pi$
$828$	−82.6199	+	99.8703i	−2.87124	+	3.47073i
$829$	5.56079	+	8.76240i	0.193134	+	0.304331i	0.927070	−	0.374888i	$-0.122319\pi$
$829$	5.56079	+	8.76240i	0.193134	+	0.304331i	−0.733936	+	0.679219i	$0.762319\pi$
$830$	−14.3923	−	41.6163i	−0.499562	−	1.44452i
$831$	0.000195746	0	0.000236617i	6.79036e−6	0	8.20814e-6i
$832$	−31.8341	−	23.1288i	−1.10365	−	0.801848i
$833$	−7.26922	+	11.4545i	−0.251864	+	0.396874i
$834$	5.97300e−5	0	0.000313116i	2.06828e−6	0	1.08423e-5i
$835$	7.98641	−	17.8347i	0.276381	−	0.617194i
$836$	3.47536	−	0.439040i	0.120198	−	0.0151845i
$837$	0.000428060		0.00224397i	1.47959e−5		7.75630e-5i
$838$	21.0706	+	2.66183i	0.727871	+	0.0919515i
$839$	−34.5727	−	19.0065i	−1.19358	−	0.656177i	−0.244024	−	0.969769i	$-0.578468\pi$
$839$	−34.5727	−	19.0065i	−1.19358	−	0.656177i	−0.949558	+	0.313592i	$0.898468\pi$
$840$	0.00234924	+	0.00123458i	8.10566e−5	+	4.25971e-5i
$841$	−15.1729	−	14.2483i	−0.523204	−	0.491321i
$842$	26.2537	+	6.74081i	0.904764	+	0.232304i
$843$	0.00118849		0.000863490i	4.09338e−5		2.97402e-5i
$844$	−0.408787	−	6.49748i	−0.0140710	−	0.223653i
$845$	17.0751	+	15.4410i	0.587401	+	0.531185i
$846$	−58.7095	−	23.2447i	−2.01847	−	0.799170i
$847$	22.0819	+	8.74285i	0.758744	+	0.300408i
$848$	93.6805	−	11.8346i	3.21700	−	0.406402i
$849$	0.000229723	0	0.000707015i	7.88408e−6	0	2.42647e-5i
$850$	−75.3516	−	37.8089i	−2.58454	−	1.29683i
$851$	−10.3593	+	31.8828i	−0.355114	+	1.09293i
$852$	8.76707e−5	0	0.000459586i	3.00355e−6	0	1.57452e-5i
$853$	1.33577	−	21.2315i	0.0457360	−	0.726953i	−0.906617	−	0.421955i	$-0.861344\pi$
$853$	1.33577	−	21.2315i	0.0457360	−	0.726953i	0.952353	−	0.304999i	$-0.0986560\pi$
$854$	30.8267	−	7.91494i	1.05487	−	0.270844i
$855$	−6.67221	−	7.76346i	−0.228185	−	0.265505i
$856$	−24.2967	+	38.2854i	−0.830443	+	1.30857i
$857$	0.979764	+	3.01540i	0.0334681	+	0.103004i	0.966395	−	0.257061i	$-0.0827543\pi$
$857$	0.979764	+	3.01540i	0.0334681	+	0.103004i	−0.932927	+	0.360066i	$0.882754\pi$
$858$	7.26656e−6	0	0.000115499i	2.48076e−7	0	3.94306e-6i
$859$	−13.6291	−	1.72175i	−0.465018	−	0.0587455i	−0.110666	−	0.993858i	$-0.535299\pi$
$859$	−13.6291	−	1.72175i	−0.465018	−	0.0587455i	−0.354352	+	0.935112i	$0.615299\pi$
$860$	−67.1648	+	110.367i	−2.29030	+	3.76348i
$861$	0.000298095	0	0.000633484i	1.01590e−5	0	2.15891e-5i
$862$	−5.76346	+	12.2480i	−0.196304	+	0.417168i
$863$	−30.1256	+	16.5617i	−1.02549	+	0.563767i	−0.903421	−	0.428755i	$-0.858953\pi$
$863$	−30.1256	+	16.5617i	−1.02549	+	0.563767i	−0.122068	+	0.992522i	$0.538953\pi$
$864$	0.00498656	−	0.00468269i	0.000169646	−	0.000159308i
$865$	−16.7955	−	25.3974i	−0.571064	−	0.863536i
$866$	10.8691	−	23.0980i	0.369347	−	0.784902i
$867$	−0.000839490	−	0.00101477i	−2.85106e−5	−	3.44634e-5i
$868$	22.8001	−	70.1714i	0.773884	−	2.38177i
$869$	0.922929	+	0.236968i	0.0313082	+	0.00803859i
$870$	−0.000922888	0	0.000484999i	−3.12888e−5	0	1.64430e-5i
$871$	−0.688731	+	10.9471i	−0.0233368	+	0.370927i
$872$	22.6336	+	35.6648i	0.766469	+	1.20776i
$873$	9.34931	−	8.77959i	0.316426	−	0.297144i
$874$	33.5458			1.13470
$875$	−2.92068	−	24.3810i	−0.0987368	−	0.824229i
$876$	0.00175733			5.93745e−5
$877$	27.4652	−	25.7915i	0.927433	−	0.870917i	−0.0644696	−	0.997920i	$-0.520536\pi$
$877$	27.4652	−	25.7915i	0.927433	−	0.870917i	0.991902	+	0.127002i	$0.0405355\pi$
$878$	−16.6697	−	26.2672i	−0.562575	−	0.886476i
$879$	−4.49886e−5	0	0.000715073i	−1.51743e−6	0	2.41188e-5i
$880$	9.42138	−	9.18656i	0.317595	−	0.309679i
$881$	−36.7121	−	9.42606i	−1.23686	−	0.317572i	−0.427032	−	0.904237i	$-0.640441\pi$
$881$	−36.7121	−	9.42606i	−1.23686	−	0.317572i	−0.809830	+	0.586664i	$0.800441\pi$
$882$	−5.45704	+	16.7951i	−0.183748	+	0.565519i
$883$	−17.6393	−	21.3222i	−0.593609	−	0.717550i	0.385083	−	0.922882i	$-0.374173\pi$
$883$	−17.6393	−	21.3222i	−0.593609	−	0.717550i	−0.978692	+	0.205332i	$0.934173\pi$
$884$	−23.2042	+	49.3114i	−0.780441	+	1.65852i
$885$	−0.00115076		0.000430778i	−3.86825e−5		1.44805e-5i
$886$	63.5201	−	59.6494i	2.13400	−	2.00396i
$887$	−41.7970	+	22.9781i	−1.40341	+	0.771530i	−0.990273	−	0.139140i	$-0.955566\pi$
$887$	−41.7970	+	22.9781i	−1.40341	+	0.771530i	−0.413135	+	0.910670i	$0.635566\pi$
$888$	0.000949060	−	0.00201686i	3.18484e−5	−	6.76813e-5i
$889$	10.8933	+	23.1494i	0.365350	+	0.776407i
$890$	56.0405	−	23.4158i	1.87848	−	0.784901i
$891$	3.85569	+	0.487087i	0.129171	+	0.0163180i
$892$	−4.97762	−	79.1170i	−0.166663	−	2.64903i
$893$	3.66950	+	11.2935i	0.122795	+	0.377924i
$894$	−0.000266154	0	0.000419391i	−8.90152e−6	0	1.40265e-5i
$895$	−26.2105	+	43.0698i	−0.876120	+	1.43966i
$896$	−57.1649	+	14.6775i	−1.90975	+	0.490340i
$897$	−5.05639e−5	0	0.000803691i	−1.68828e−6	0	2.68345e-5i
$898$	−10.4573	+	54.8193i	−0.348966	+	1.82934i
$899$	−5.58712	+	17.1954i	−0.186341	+	0.573498i
$900$	−77.9260	−	16.9136i	−2.59753	−	0.563787i
$901$	−13.3470	−	41.0777i	−0.444652	−	1.36850i
$902$	6.13091	−	0.774514i	0.204137	−	0.0257885i
$903$	−0.00133722		0.000529443i	−4.44999e−5		1.76187e-5i
$904$	−36.7128	−	14.5356i	−1.22105	−	0.483448i
$905$	8.22423	−	4.72476i	0.273383	−	0.157056i
$906$	−1.11686e−5	0	0.000177519i	−3.71050e−7	0	5.89768e-6i
$907$	23.5493	−	17.1095i	0.781941	−	0.568113i	−0.123620	−	0.992330i	$-0.539450\pi$
$907$	23.5493	−	17.1095i	0.781941	−	0.568113i	0.905561	+	0.424216i	$0.139450\pi$
$908$	47.2252	+	12.1254i	1.56722	+	0.402395i
$909$	38.2275	+	35.8981i	1.26793	+	1.19066i
$910$	−21.6179	+	3.14486i	−0.716626	+	0.104251i
$911$	−28.8585	−	15.8651i	−0.956125	−	0.525634i	−0.0743132	−	0.997235i	$-0.523676\pi$
$911$	−28.8585	−	15.8651i	−0.956125	−	0.525634i	−0.881812	+	0.471601i	$0.843676\pi$
$912$	−0.00124309		0.000157038i	−4.11627e−5		5.20006e-6i
$913$	−0.589110	−	3.08822i	−0.0194967	−	0.102205i
$914$	−2.16605	+	0.273636i	−0.0716466	+	0.00905107i
$915$	0.000625843	0	0.000359542i	2.06897e−5	0	1.18861e-5i
$916$	13.7111	+	71.8762i	0.453028	+	2.37486i
$917$	−11.6762	+	18.3988i	−0.385583	+	0.607581i
$918$	−0.00493112	−	0.00358267i	−0.000162751	−	0.000118246i
$919$	−2.37828	−	2.87485i	−0.0784522	−	0.0948324i	0.729827	−	0.683632i	$-0.239601\pi$
$919$	−2.37828	−	2.87485i	−0.0784522	−	0.0948324i	−0.808279	+	0.588800i	$0.799601\pi$
$920$	130.046	−	98.2710i	4.28748	−	3.23990i
$921$	4.69805e−5	0	7.40293e-5i	1.54806e−6	0	2.43935e-6i
$922$	52.6578	−	63.6524i	1.73419	−	2.09628i
$923$	1.02287	+	2.17371i	0.0336682	+	0.0715486i
$924$	0.000245745	0	0.000178544i	8.08443e−6	0	5.87368e-6i
$925$	−20.3497	+	3.35211i	−0.669094	+	0.110217i
$926$	−14.3436	+	10.4212i	−0.471359	+	0.342462i
$927$	−15.7075	−	8.63526i	−0.515901	−	0.283619i
$928$	52.4392	−	13.4641i	1.72140	−	0.441981i
$929$	18.2798	−	22.0964i	0.599740	−	0.724961i	−0.380056	−	0.924964i	$-0.624095\pi$
$929$	18.2798	−	22.0964i	0.599740	−	0.724961i	0.979795	+	0.200003i	$0.0640952\pi$
$930$	0.000101368	−	0.00230054i	3.32398e−6	−	7.54375e-5i
$931$	3.08779	−	1.22254i	0.101198	−	0.0400672i
$932$	105.805			3.46576
$933$	0.00148741		0.000588905i	4.86955e−5		1.92799e-5i
$934$	−5.34981	+	2.94109i	−0.175051	+	0.0962353i
$935$	−4.93518	−	3.44577i	−0.161398	−	0.112689i
$936$	−8.29183	+	43.4673i	−0.271027	+	1.42077i
$937$	33.8641	+	31.8005i	1.10629	+	1.03888i	0.999003	+	0.0446480i	$0.0142166\pi$
$937$	33.8641	+	31.8005i	1.10629	+	1.03888i	0.107288	+	0.994228i	$0.465783\pi$
$938$	28.8832	+	27.1232i	0.943071	+	0.885603i
$939$	0.000279291	−	0.00146409i	9.11431e−6	−	4.77789e-5i
$940$	75.8431	+	52.9541i	2.47373	+	1.72717i
$941$	−47.4824	+	26.1037i	−1.54788	+	0.850956i	−0.547987	+	0.836487i	$0.684606\pi$
$941$	−47.4824	+	26.1037i	−1.54788	+	0.850956i	−0.999895	+	0.0144690i	$0.995394\pi$
$942$	−0.000984328	0	0.000389723i	−3.20711e−5	0	1.26979e-5i
$943$	43.0007			1.40029
$944$	115.569	−	45.7568i	3.76144	−	1.48926i
$945$	7.81499e−5	−	0.00177361i	2.54222e−6	−	5.76955e-5i
$946$	−8.09181	+	9.78132i	−0.263087	+	0.318018i
$947$	18.9624	−	4.86873i	0.616197	−	0.158212i	0.0723253	−	0.997381i	$-0.476958\pi$
$947$	18.9624	−	4.86873i	0.616197	−	0.158212i	0.543871	+	0.839169i	$0.316958\pi$
$948$	−0.000619339	0	0.000340485i	−2.01152e−5	0	1.10584e-5i
$949$	−7.29992	+	5.30370i	−0.236965	+	0.172165i
$950$	9.48276	+	18.3301i	0.307661	+	0.594706i
$951$	0.000619190	0	0.000449868i	2.00786e−5	0	1.45880e-5i
$952$	52.2851	+	111.112i	1.69457	+	3.60115i
$953$	−8.94542	+	10.8132i	−0.289770	+	0.350272i	−0.895230	−	0.445603i	$-0.852989\pi$
$953$	−8.94542	+	10.8132i	−0.289770	+	0.350272i	0.605460	+	0.795876i	$0.292989\pi$
$954$	−30.1256	−	47.4704i	−0.975353	−	1.53691i
$955$	22.5622	−	17.0494i	0.730094	−	0.551706i
$956$	−54.3617	−	65.7120i	−1.75818	−	2.12528i
$957$	−6.02195e−5	0	4.37520e-5i	−1.94662e−6	0	1.41430e-6i
$958$	−14.6402	+	23.0692i	−0.473002	+	0.745333i
$959$	−6.33478	−	33.2081i	−0.204561	−	1.07235i
$960$	−0.00279507	+	0.00160574i	−9.02104e−5	+	5.18252e-5i
$961$	−8.86434	+	1.11983i	−0.285947	+	0.0361234i
$962$	3.43806	+	18.0229i	0.110847	+	0.581082i
$963$	15.0470	+	1.90088i	0.484883	+	0.0612549i
$964$	9.46133	+	5.20141i	0.304729	+	0.167526i
$965$	−34.3300	+	4.99414i	−1.10512	+	0.160767i
$966$	0.00212049	+	0.00199128i	6.82257e−5	+	6.40682e-5i
$967$	−32.3660	−	8.31018i	−1.04082	−	0.267237i	−0.310666	−	0.950519i	$-0.600552\pi$
$967$	−32.3660	−	8.31018i	−1.04082	−	0.267237i	−0.730155	+	0.683282i	$0.760552\pi$
$968$	−78.4659	+	57.0088i	−2.52199	+	1.83233i
$969$	3.59870e−5	0	0.000571998i	1.15607e−6	0	1.83752e-5i
$970$	−22.4202	+	12.8802i	−0.719870	+	0.413559i
$971$	−34.2104	−	13.5449i	−1.09787	−	0.434676i	−0.251813	−	0.967776i	$-0.581027\pi$
$971$	−34.2104	−	13.5449i	−1.09787	−	0.434676i	−0.846052	+	0.533100i	$0.821027\pi$
$972$	−0.00804047	−	0.00318345i	−0.000257898	−	0.000102109i
$973$	−4.26216	+	0.538436i	−0.136639	+	0.0172615i
$974$	7.16401	+	22.0486i	0.229550	+	0.706481i
$975$	−0.000453445	0	0.000199559i	−1.45219e−5	0	6.39100e-6i
$976$	−22.5620	+	69.4388i	−0.722194	+	2.22268i
$977$	−1.39634	+	7.31986i	−0.0446728	+	0.234183i	−0.997620	−	0.0689538i	$-0.978034\pi$
$977$	−1.39634	+	7.31986i	−0.0446728	+	0.234183i	0.952947	+	0.303137i	$0.0980339\pi$
$978$	4.43033e−5	0	0.000704181i	1.41666e−6	0	2.25172e-5i
$979$	4.20008	−	1.07840i	0.134235	−	0.0344657i
$980$	13.4486	−	22.0991i	0.429599	−	0.705928i
$981$	7.57039	−	11.9290i	0.241704	−	0.380865i
$982$	−35.2335	−	108.438i	−1.12435	−	3.46038i
$983$	2.14171	+	34.0415i	0.0683100	+	1.08576i	0.871616	+	0.490190i	$0.163072\pi$
$983$	2.14171	+	34.0415i	0.0683100	+	1.08576i	−0.803306	+	0.595567i	$0.796928\pi$
$984$	−0.00283659		0.000358345i	−9.04272e−5		1.14236e-5i
$985$	4.61944	−	1.93018i	0.147187	−	0.0615005i
$986$	−20.5399	−	43.6496i	−0.654125	−	1.39009i
$987$	−0.000438428	0	0.000931706i	−1.39553e−5	0	2.96565e-5i
$988$	11.6908	−	6.42706i	0.371933	−	0.204472i
$989$	−64.3929	+	60.4690i	−2.04758	+	1.92280i
$990$	−7.33777	−	2.74684i	−0.233210	−	0.0873002i
$991$	−7.98134	+	16.9612i	−0.253536	+	0.538791i	−0.990561	−	0.137075i	$-0.956230\pi$
$991$	−7.98134	+	16.9612i	−0.253536	+	0.538791i	0.737025	+	0.675865i	$0.236230\pi$
$992$	76.2243	+	92.1394i	2.42012	+	2.92543i
$993$	−3.53513e−5	0	0.000108800i	−1.12184e−6	0	3.45266e-6i
$994$	8.40533	+	2.15812i	0.266601	+	0.0684515i
$995$	−8.92949	+	8.70693i	−0.283084	+	0.276028i
$996$	−0.000146422		0.00232731i	−4.63955e−6		7.37435e-5i
$997$	−18.0683	−	28.4712i	−0.572230	−	0.901691i	0.427767	−	0.903889i	$-0.359300\pi$
$997$	−18.0683	−	28.4712i	−0.572230	−	0.901691i	−0.999998	+	0.00219829i	$0.999300\pi$
$998$	−27.9406	+	26.2379i	−0.884443	+	0.830547i
$999$	−0.00149109			−4.71761e−5

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.11.1	✓	220
5.2	odd	4		625.2.h.b.199.1		440
5.3	odd	4		625.2.h.b.199.22		440
5.4	even	2		625.2.g.a.426.11		220
125.34	even	50		625.2.g.a.201.11		220
125.62	odd	100		625.2.h.b.424.22		440
125.63	odd	100		625.2.h.b.424.1		440
125.91	even	25	inner	125.2.g.a.91.1	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.11.1	✓	220	1.1	even	1	trivial
125.2.g.a.91.1	yes	220	125.91	even	25	inner
625.2.g.a.201.11		220	125.34	even	50
625.2.g.a.426.11		220	5.4	even	2
625.2.h.b.199.1		440	5.2	odd	4
625.2.h.b.199.22		440	5.3	odd	4
625.2.h.b.424.1		440	125.63	odd	100
625.2.h.b.424.22		440	125.62	odd	100

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97173 + 1.85157i) q^{2} +(3.22832e-5 + 5.08701e-5i) q^{3} +(0.333796 - 5.30554i) q^{4} +(2.21278 - 0.321903i) q^{5} +(-0.000157843 - 4.05273e-5i) q^{6} +(0.678693 - 2.08880i) q^{7} +(5.71721 + 6.91092i) q^{8} +(1.27734 - 2.71448i) q^{9} +O(q^{10})\)	\(q+(-1.97173 + 1.85157i) q^{2} +(3.22832e-5 + 5.08701e-5i) q^{3} +(0.333796 - 5.30554i) q^{4} +(2.21278 - 0.321903i) q^{5} +(-0.000157843 - 4.05273e-5i) q^{6} +(0.678693 - 2.08880i) q^{7} +(5.71721 + 6.91092i) q^{8} +(1.27734 - 2.71448i) q^{9} +(-3.76696 + 4.73182i) q^{10} +(-0.314780 + 0.295598i) q^{11} +(0.000280669 - 0.000154299i) q^{12} +(-0.700216 + 1.48803i) q^{13} +(2.52937 + 5.37519i) q^{14} +(8.78107e-5 + 0.000102172i) q^{15} +(-13.5206 - 1.70805i) q^{16} +(0.391418 + 6.22142i) q^{17} +(2.50750 + 7.71730i) q^{18} +(0.817669 - 1.28844i) q^{19} +(-0.969253 - 11.8474i) q^{20} +(0.000128168 - 3.29079e-5i) q^{21} +(0.0733381 - 1.16568i) q^{22} +(1.52291 - 7.98337i) q^{23} +(-0.000166990 + 0.000513942i) q^{24} +(4.79276 - 1.42460i) q^{25} +(-1.37457 - 4.23050i) q^{26} +(0.000358645 - 4.53074e-5i) q^{27} +(-10.8557 - 4.29806i) q^{28} +(2.66016 + 1.05323i) q^{29} +(-0.000362318 - 3.88675e-5i) q^{30} +(0.396798 + 6.30693i) q^{31} +(15.3090 - 11.1226i) q^{32} +(-2.51992e-5 - 6.47005e-6i) q^{33} +(-12.2912 - 11.5422i) q^{34} +(0.829403 - 4.84052i) q^{35} +(-13.9754 - 7.68305i) q^{36} +(-4.09227 - 0.516973i) q^{37} +(0.773423 + 4.05443i) q^{38} +(-9.83017e-5 + 1.24184e-5i) q^{39} +(14.8755 + 13.4519i) q^{40} +(0.991411 + 5.19716i) q^{41} +(-0.000191781 + 0.000302198i) q^{42} +(-8.79304 - 6.38852i) q^{43} +(1.46323 + 1.76875i) q^{44} +(1.95266 - 6.41772i) q^{45} +(11.7790 + 18.5608i) q^{46} +(-4.96020 + 5.99585i) q^{47} +(-0.000349600 - 0.000742937i) q^{48} +(1.76065 + 1.27919i) q^{49} +(-6.81225 + 11.6831i) q^{50} +(-0.000303848 + 0.000220759i) q^{51} +(7.66109 + 4.21172i) q^{52} +(-6.71104 + 1.72310i) q^{53} +(-0.000623260 + 0.000753392i) q^{54} +(-0.601383 + 0.755421i) q^{55} +(18.3158 - 7.25172i) q^{56} +9.19401e-5 q^{57} +(-7.19525 + 2.84880i) q^{58} +(-7.99250 + 4.39391i) q^{59} +(0.000571389 - 0.000431778i) q^{60} +(1.00389 - 5.26259i) q^{61} +(-12.4601 - 11.7008i) q^{62} +(-4.80309 - 4.51040i) q^{63} +(-4.48347 + 23.5032i) q^{64} +(-1.07042 + 3.51809i) q^{65} +(6.16657e-5 - 3.39010e-5i) q^{66} +(6.20136 - 2.45529i) q^{67} +33.1386 q^{68} +(0.000455280 - 0.000180258i) q^{69} +(7.32723 + 11.0799i) q^{70} +(0.931146 - 1.12556i) q^{71} +(26.0624 - 6.69168i) q^{72} +(4.80805 + 2.64325i) q^{73} +(9.02604 - 6.55780i) q^{74} +(0.000227195 + 0.000197818i) q^{75} +(-6.56293 - 4.76825i) q^{76} +(0.403806 + 0.858132i) q^{77} +(0.000170830 - 0.000206498i) q^{78} +(-1.18238 - 1.86314i) q^{79} +(-30.4679 + 0.572794i) q^{80} +(-5.73682 - 6.93462i) q^{81} +(-11.5777 - 8.41170i) q^{82} +(-3.90119 + 6.14729i) q^{83} +(-0.000131812 - 0.000690984i) q^{84} +(2.86882 + 13.6406i) q^{85} +(29.1663 - 3.68456i) q^{86} +(3.23004e-5 + 0.000169325i) q^{87} +(-3.84251 - 0.485422i) q^{88} +(-8.79991 - 4.83779i) q^{89} +(8.03276 + 16.2695i) q^{90} +(2.63298 + 2.47253i) q^{91} +(-41.8477 - 10.7447i) q^{92} +(-0.000308024 + 0.000223793i) q^{93} +(-1.32161 - 21.0064i) q^{94} +(1.39457 - 3.11424i) q^{95} +(0.00106003 + 0.000419697i) q^{96} +(3.97492 + 1.57378i) q^{97} +(-5.84004 + 0.737769i) q^{98} +(0.400315 + 1.23204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more