LMFDB - Embedded newform 403.2.bk.a.9.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(9,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 2]))

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

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

chi := DirichletCharacter("403.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bk (of order $15$, degree $8$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.20
Character	$\chi$	$=$	403.9
Dual form			403.2.bk.a.224.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.169063 + 0.187763i) q^{2} +(-1.38560 + 1.53887i) q^{3} +(0.202384 - 1.92556i) q^{4} +(0.388050 + 0.672122i) q^{5} -0.523196 q^{6} +(-2.21450 - 1.60893i) q^{7} +(0.804576 - 0.584559i) q^{8} +(-0.134633 - 1.28095i) q^{9} +O(q^{10})$	\(q+(0.169063 + 0.187763i) q^{2} +(-1.38560 + 1.53887i) q^{3} +(0.202384 - 1.92556i) q^{4} +(0.388050 + 0.672122i) q^{5} -0.523196 q^{6} +(-2.21450 - 1.60893i) q^{7} +(0.804576 - 0.584559i) q^{8} +(-0.134633 - 1.28095i) q^{9} +(-0.0605950 + 0.186492i) q^{10} +(-4.32041 - 3.13896i) q^{11} +(2.68275 + 2.97950i) q^{12} +(-1.62752 + 3.21732i) q^{13} +(-0.0722919 - 0.687812i) q^{14} +(-1.57199 - 0.334137i) q^{15} +(-3.54192 - 0.752859i) q^{16} +(-3.03741 + 2.20681i) q^{17} +(0.217753 - 0.241840i) q^{18} +(0.634389 - 1.95245i) q^{19} +(1.37274 - 0.611185i) q^{20} +(5.54435 - 1.17849i) q^{21} +(-0.141039 - 1.34189i) q^{22} +(-0.728560 - 6.93179i) q^{23} +(-0.215264 + 2.04810i) q^{24} +(2.19883 - 3.80849i) q^{25} +(-0.879247 + 0.238341i) q^{26} +(-2.86806 - 2.08377i) q^{27} +(-3.54627 + 3.93853i) q^{28} +(-3.93225 - 4.36721i) q^{29} +(-0.203026 - 0.351652i) q^{30} +(5.18019 + 2.04099i) q^{31} +(-1.45196 - 2.51487i) q^{32} +(10.8168 - 2.29919i) q^{33} +(-0.927868 - 0.197224i) q^{34} +(0.222060 - 2.11276i) q^{35} -2.49379 q^{36} +(0.426214 + 0.738225i) q^{37} +(0.473849 - 0.210971i) q^{38} +(-2.69594 - 6.96247i) q^{39} +(0.705111 + 0.313936i) q^{40} +(-2.24785 + 6.91817i) q^{41} +(1.15862 + 0.841786i) q^{42} +(-2.61494 + 8.04795i) q^{43} +(-6.91863 + 7.68392i) q^{44} +(0.808710 - 0.587562i) q^{45} +(1.17836 - 1.30870i) q^{46} +(1.92241 + 5.91656i) q^{47} +(6.06625 - 4.40739i) q^{48} +(0.152247 + 0.468568i) q^{49} +(1.08683 - 0.231014i) q^{50} +(0.812657 - 7.73192i) q^{51} +(5.86575 + 3.78502i) q^{52} +(-1.80544 - 0.803833i) q^{53} +(-0.0936270 - 0.890802i) q^{54} +(0.433231 - 4.12192i) q^{55} -2.72225 q^{56} +(2.12555 + 3.68156i) q^{57} +(0.155204 - 1.47666i) q^{58} +(-4.48443 - 13.8017i) q^{59} +(-0.961545 + 2.95933i) q^{60} +(-2.29696 - 3.97846i) q^{61} +(0.492554 + 1.31770i) q^{62} +(-1.76281 + 3.05328i) q^{63} +(-2.01121 + 6.18986i) q^{64} +(-2.79400 + 0.154589i) q^{65} +(2.26042 + 1.64229i) q^{66} +10.0243 q^{67} +(3.63460 + 6.29532i) q^{68} +(11.6766 + 8.48355i) q^{69} +(0.434241 - 0.315494i) q^{70} +(0.545709 + 5.19208i) q^{71} +(-0.857113 - 0.951921i) q^{72} +(-1.13080 + 10.7588i) q^{73} +(-0.0665544 + 0.204833i) q^{74} +(2.81405 + 8.66077i) q^{75} +(-3.63116 - 1.61670i) q^{76} +(4.51719 + 13.9025i) q^{77} +(0.851512 - 1.68329i) q^{78} +(-0.0542565 - 0.516216i) q^{79} +(-0.868430 - 2.67275i) q^{80} +(10.9602 - 2.32966i) q^{81} +(-1.67900 + 0.747541i) q^{82} +(-1.26488 + 0.268860i) q^{83} +(-1.14716 - 10.9145i) q^{84} +(-2.66191 - 1.18516i) q^{85} +(-1.95319 + 0.869618i) q^{86} +12.1691 q^{87} -5.31101 q^{88} +(-8.56861 + 3.81499i) q^{89} +(0.247045 + 0.0525111i) q^{90} +(8.78060 - 4.50621i) q^{91} -13.4950 q^{92} +(-10.3185 + 5.14362i) q^{93} +(-0.785905 + 1.36123i) q^{94} +(1.55846 - 0.331261i) q^{95} +(5.88188 + 1.25023i) q^{96} +(-1.32017 + 12.5606i) q^{97} +(-0.0622405 + 0.107804i) q^{98} +(-3.43918 + 5.95684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.169063	+	0.187763i	0.119545	+	0.132768i	0.799947	−	0.600071i	$-0.204861\pi$
$2$	0.169063	+	0.187763i	0.119545	+	0.132768i	−0.680401	+	0.732840i	$0.738194\pi$
$3$	−1.38560	+	1.53887i	−0.799978	+	0.888465i	−0.995742	−	0.0921857i	$-0.970615\pi$
$3$	−1.38560	+	1.53887i	−0.799978	+	0.888465i	0.195764	+	0.980651i	$0.437281\pi$
$4$	0.202384	−	1.92556i	0.101192	−	0.962778i
$5$	0.388050	+	0.672122i	0.173541	+	0.300582i	0.939655	−	0.342122i	$-0.111146\pi$
$5$	0.388050	+	0.672122i	0.173541	+	0.300582i	−0.766114	+	0.642704i	$0.777812\pi$
$6$	−0.523196			−0.213594
$7$	−2.21450	−	1.60893i	−0.837004	−	0.608119i	0.0845285	−	0.996421i	$-0.473062\pi$
$7$	−2.21450	−	1.60893i	−0.837004	−	0.608119i	−0.921532	+	0.388302i	$0.873062\pi$
$8$	0.804576	−	0.584559i	0.284461	−	0.206673i
$9$	−0.134633	−	1.28095i	−0.0448777	−	0.426983i
$10$	−0.0605950	+	0.186492i	−0.0191618	+	0.0589740i
$11$	−4.32041	−	3.13896i	−1.30265	−	0.946433i	−0.302675	−	0.953094i	$-0.597880\pi$
$11$	−4.32041	−	3.13896i	−1.30265	−	0.946433i	−0.999978	+	0.00666107i	$0.997880\pi$
$12$	2.68275	+	2.97950i	0.774444	+	0.860107i
$13$	−1.62752	+	3.21732i	−0.451393	+	0.892325i
$13$	−1.62752	+	3.21732i	−0.451393	+	0.892325i
$14$	−0.0722919	−	0.687812i	−0.0193208	−	0.183825i
$15$	−1.57199	−	0.334137i	−0.405886	−	0.0862737i
$16$	−3.54192	−	0.752859i	−0.885481	−	0.188215i
$17$	−3.03741	+	2.20681i	−0.736679	+	0.535229i	−0.891669	−	0.452687i	$-0.850465\pi$
$17$	−3.03741	+	2.20681i	−0.736679	+	0.535229i	0.154990	+	0.987916i	$0.450465\pi$
$18$	0.217753	−	0.241840i	0.0513250	−	0.0570022i
$19$	0.634389	−	1.95245i	0.145539	−	0.447923i	−0.851541	−	0.524288i	$-0.824332\pi$
$19$	0.634389	−	1.95245i	0.145539	−	0.447923i	0.997080	+	0.0763654i	$0.0243315\pi$
$20$	1.37274	−	0.611185i	0.306955	−	0.136665i
$21$	5.54435	−	1.17849i	1.20988	−	0.257167i
$22$	−0.141039	−	1.34189i	−0.0300696	−	0.286093i
$23$	−0.728560	−	6.93179i	−0.151915	−	1.44538i	−0.759181	−	0.650879i	$-0.774400\pi$
$23$	−0.728560	−	6.93179i	−0.151915	−	1.44538i	0.607266	−	0.794499i	$-0.292266\pi$
$24$	−0.215264	+	2.04810i	−0.0439406	+	0.418067i
$25$	2.19883	−	3.80849i	0.439767	−	0.761699i
$26$	−0.879247	+	0.238341i	−0.172435	+	0.0467425i
$27$	−2.86806	−	2.08377i	−0.551958	−	0.401021i
$28$	−3.54627	+	3.93853i	−0.670181	+	0.744312i
$29$	−3.93225	−	4.36721i	−0.730201	−	0.810971i	0.257672	−	0.966232i	$-0.417045\pi$
$29$	−3.93225	−	4.36721i	−0.730201	−	0.810971i	−0.987873	+	0.155262i	$0.950378\pi$
$30$	−0.203026	−	0.351652i	−0.0370673	−	0.0642025i
$31$	5.18019	+	2.04099i	0.930389	+	0.366573i
$31$	5.18019	+	2.04099i	0.930389	+	0.366573i
$32$	−1.45196	−	2.51487i	−0.256672	−	0.444570i
$33$	10.8168	−	2.29919i	1.88297	−	0.400237i
$34$	−0.927868	−	0.197224i	−0.159128	−	0.0338237i
$35$	0.222060	−	2.11276i	0.0375350	−	0.357122i
$36$	−2.49379			−0.415631
$37$	0.426214	+	0.738225i	0.0700692	+	0.121363i	0.898931	−	0.438089i	$-0.144345\pi$
$37$	0.426214	+	0.738225i	0.0700692	+	0.121363i	−0.828862	+	0.559453i	$0.811011\pi$
$38$	0.473849	−	0.210971i	0.0768685	−	0.0342241i
$39$	−2.69594	−	6.96247i	−0.431696	−	1.11489i
$40$	0.705111	+	0.313936i	0.111488	+	0.0496376i
$41$	−2.24785	+	6.91817i	−0.351055	+	1.08044i	0.607206	+	0.794544i	$0.292290\pi$
$41$	−2.24785	+	6.91817i	−0.351055	+	1.08044i	−0.958262	+	0.285893i	$0.907710\pi$
$42$	1.15862	+	0.841786i	0.178779	+	0.129890i
$43$	−2.61494	+	8.04795i	−0.398774	+	1.22730i	0.527209	+	0.849736i	$0.323238\pi$
$43$	−2.61494	+	8.04795i	−0.398774	+	1.22730i	−0.925983	+	0.377565i	$0.876762\pi$
$44$	−6.91863	+	7.68392i	−1.04302	+	1.15839i
$45$	0.808710	−	0.587562i	0.120555	−	0.0875886i
$46$	1.17836	−	1.30870i	0.173740	−	0.192958i
$47$	1.92241	+	5.91656i	0.280412	+	0.863020i	0.987736	+	0.156130i	$0.0499020\pi$
$47$	1.92241	+	5.91656i	0.280412	+	0.863020i	−0.707324	+	0.706889i	$0.750098\pi$
$48$	6.06625	−	4.40739i	0.875587	−	0.636151i
$49$	0.152247	+	0.468568i	0.0217496	+	0.0669384i
$50$	1.08683	−	0.231014i	0.153702	−	0.0326703i
$51$	0.812657	−	7.73192i	0.113795	−	1.08269i
$52$	5.86575	+	3.78502i	0.813434	+	0.524888i
$53$	−1.80544	−	0.803833i	−0.247996	−	0.110415i	0.278974	−	0.960299i	$-0.410006\pi$
$53$	−1.80544	−	0.803833i	−0.247996	−	0.110415i	−0.526971	+	0.849884i	$0.676672\pi$
$54$	−0.0936270	−	0.890802i	−0.0127410	−	0.121223i
$55$	0.433231	−	4.12192i	0.0584169	−	0.555799i
$56$	−2.72225			−0.363776
$57$	2.12555	+	3.68156i	0.281536	+	0.487634i
$58$	0.155204	−	1.47666i	0.0203792	−	0.193895i
$59$	−4.48443	−	13.8017i	−0.583823	−	1.79682i	−0.603944	−	0.797026i	$-0.706405\pi$
$59$	−4.48443	−	13.8017i	−0.583823	−	1.79682i	0.0201210	−	0.999798i	$-0.493595\pi$
$60$	−0.961545	+	2.95933i	−0.124135	+	0.382048i
$61$	−2.29696	−	3.97846i	−0.294096	−	0.509389i	0.680678	−	0.732583i	$-0.261685\pi$
$61$	−2.29696	−	3.97846i	−0.294096	−	0.509389i	−0.974774	+	0.223193i	$0.928352\pi$
$62$	0.492554	+	1.31770i	0.0625544	+	0.167348i
$63$	−1.76281	+	3.05328i	−0.222094	+	0.384677i
$64$	−2.01121	+	6.18986i	−0.251401	+	0.773732i
$65$	−2.79400	+	0.154589i	−0.346552	+	0.0191745i
$66$	2.26042	+	1.64229i	0.278239	+	0.202152i
$67$	10.0243			1.22466			0.612332	−	0.790601i	$-0.290232\pi$
$67$	10.0243			1.22466			0.612332	+	0.790601i	$0.290232\pi$
$68$	3.63460	+	6.29532i	0.440761	+	0.763420i
$69$	11.6766	+	8.48355i	1.40570	+	1.02130i
$70$	0.434241	−	0.315494i	0.0519017	−	0.0377088i
$71$	0.545709	+	5.19208i	0.0647638	+	0.616186i	0.977978	+	0.208707i	$0.0669255\pi$
$71$	0.545709	+	5.19208i	0.0647638	+	0.616186i	−0.913214	+	0.407479i	$0.866408\pi$
$72$	−0.857113	−	0.951921i	−0.101012	−	0.112185i
$73$	−1.13080	+	10.7588i	−0.132350	+	1.25922i	0.703672	+	0.710525i	$0.251543\pi$
$73$	−1.13080	+	10.7588i	−0.132350	+	1.25922i	−0.836021	+	0.548697i	$0.815124\pi$
$74$	−0.0665544	+	0.204833i	−0.00773679	+	0.0238114i
$75$	2.81405	+	8.66077i	0.324939	+	1.00006i
$76$	−3.63116	−	1.61670i	−0.416523	−	0.185448i
$77$	4.51719	+	13.9025i	0.514782	+	1.58434i
$78$	0.851512	−	1.68329i	0.0964148	−	0.190595i
$79$	−0.0542565	−	0.516216i	−0.00610434	−	0.0580789i	0.991046	−	0.133523i	$-0.0426291\pi$
$79$	−0.0542565	−	0.516216i	−0.00610434	−	0.0580789i	−0.997150	+	0.0754445i	$0.975962\pi$
$80$	−0.868430	−	2.67275i	−0.0970934	−	0.298823i
$81$	10.9602	−	2.32966i	1.21780	−	0.258851i
$82$	−1.67900	+	0.747541i	−0.185415	+	0.0825521i
$83$	−1.26488	+	0.268860i	−0.138839	+	0.0295112i	−0.276807	−	0.960926i	$-0.589276\pi$
$83$	−1.26488	+	0.268860i	−0.138839	+	0.0295112i	0.137968	+	0.990437i	$0.455943\pi$
$84$	−1.14716	−	10.9145i	−0.125165	−	1.19087i
$85$	−2.66191	−	1.18516i	−0.288725	−	0.128548i
$86$	−1.95319	+	0.869618i	−0.210618	+	0.0937733i
$87$	12.1691			1.30466
$88$	−5.31101			−0.566155
$89$	−8.56861	+	3.81499i	−0.908271	+	0.404388i	−0.807055	−	0.590476i	$-0.798940\pi$
$89$	−8.56861	+	3.81499i	−0.908271	+	0.404388i	−0.101216	+	0.994865i	$0.532273\pi$
$90$	0.247045	+	0.0525111i	0.0260408	+	0.00553515i
$91$	8.78060	−	4.50621i	0.920457	−	0.472379i
$92$	−13.4950			−1.40695
$93$	−10.3185	+	5.14362i	−1.06998	+	0.533369i
$94$	−0.785905	+	1.36123i	−0.0810599	+	0.140400i
$95$	1.55846	−	0.331261i	0.159895	−	0.0339866i
$96$	5.88188	+	1.25023i	0.600317	+	0.127601i
$97$	−1.32017	+	12.5606i	−0.134043	+	1.27533i	0.696166	+	0.717881i	$0.254888\pi$
$97$	−1.32017	+	12.5606i	−0.134043	+	1.27533i	−0.830209	+	0.557452i	$0.811779\pi$
$98$	−0.0622405	+	0.107804i	−0.00628724	+	0.0108898i
$99$	−3.43918	+	5.95684i	−0.345651	+	0.598685i
$100$	−6.88846	−	5.00476i	−0.688846	−	0.500476i
$101$	0.595780	+	5.66847i	0.0592824	+	0.564034i	0.983339	+	0.181779i	$0.0581857\pi$
$101$	0.595780	+	5.66847i	0.0592824	+	0.564034i	−0.924057	+	0.382255i	$0.875148\pi$
$102$	1.58916	−	1.15459i	0.157350	−	0.114322i
$103$	11.4619	−	2.43631i	1.12938	−	0.240057i	0.394924	−	0.918714i	$-0.370771\pi$
$103$	11.4619	−	2.43631i	1.12938	−	0.240057i	0.734455	+	0.678657i	$0.237438\pi$
$104$	0.571251	+	3.53996i	0.0560157	+	0.347122i
$105$	2.94357	+	3.26917i	0.287263	+	0.319038i
$106$	−0.154302	−	0.474893i	−0.0149871	−	0.0461257i
$107$	−6.22359	−	2.77092i	−0.601657	−	0.267875i	0.0832229	−	0.996531i	$-0.473479\pi$
$107$	−6.22359	−	2.77092i	−0.601657	−	0.267875i	−0.684880	+	0.728656i	$0.740145\pi$
$108$	−4.59286	+	5.10088i	−0.441948	+	0.490833i
$109$	−4.18542	−	12.8814i	−0.400891	−	1.23381i	−0.924278	−	0.381720i	$-0.875332\pi$
$109$	−4.18542	−	12.8814i	−0.400891	−	1.23381i	0.523387	−	0.852095i	$-0.324668\pi$
$110$	0.847187	−	0.615517i	0.0807761	−	0.0586873i
$111$	−1.72659	−	0.366999i	−0.163881	−	0.0348340i
$112$	6.63230	+	7.36592i	0.626694	+	0.696014i
$113$	9.35000	−	4.16289i	0.879574	−	0.391611i	0.0832833	−	0.996526i	$-0.473459\pi$
$113$	9.35000	−	4.16289i	0.879574	−	0.391611i	0.796290	+	0.604914i	$0.206793\pi$
$114$	−0.331910	+	1.02151i	−0.0310862	+	0.0956735i
$115$	4.37629	−	3.17956i	0.408091	−	0.296496i
$116$	−9.20514	+	6.68792i	−0.854676	+	0.620958i
$117$	4.34035	+	1.65161i	0.401265	+	0.152692i
$118$	1.83329	−	3.17536i	0.168768	−	0.292315i
$119$	10.2769			0.942086
$120$	−1.46011	+	0.650082i	−0.133289	+	0.0593441i
$121$	5.41368	+	16.6616i	0.492153	+	1.51469i
$122$	0.358676	−	1.10389i	0.0324730	−	0.0999417i
$123$	−7.53152	−	13.0450i	−0.679094	−	1.17623i
$124$	4.97843	−	9.56168i	0.447076	−	0.858664i
$125$	7.29353			0.652353
$126$	−0.871319	+	0.185205i	−0.0776233	+	0.0164993i
$127$	2.94276	−	3.26826i	0.261128	−	0.290012i	−0.598297	−	0.801275i	$-0.704156\pi$
$127$	2.94276	−	3.26826i	0.261128	−	0.290012i	0.859424	+	0.511263i	$0.170822\pi$
$128$	−6.80797	+	3.03110i	−0.601745	+	0.267914i
$129$	−8.76146	−	15.1753i	−0.771403	−	1.33611i
$130$	−0.501386	−	0.498474i	−0.0439745	−	0.0437190i
$131$	−7.07275	+	3.14899i	−0.617949	+	0.275129i	−0.691742	−	0.722145i	$-0.743156\pi$
$131$	−7.07275	+	3.14899i	−0.617949	+	0.275129i	0.0737925	+	0.997274i	$0.476490\pi$
$132$	−2.23806	−	21.2937i	−0.194798	−	1.85338i
$133$	−4.54621	+	3.30302i	−0.394207	+	0.286408i
$134$	1.69473	+	1.88219i	0.146403	+	0.162597i
$135$	0.287596	−	2.73629i	0.0247523	−	0.235502i
$136$	−1.15382	+	3.55109i	−0.0989391	+	0.304503i
$137$	0.0580371	+	0.0123362i	0.00495844	+	0.00105395i	0.210390	−	0.977617i	$-0.432527\pi$
$137$	0.0580371	+	0.0123362i	0.00495844	+	0.00105395i	−0.205432	+	0.978671i	$0.565860\pi$
$138$	0.381180	+	3.62668i	0.0324482	+	0.308724i
$139$	11.9987	−	13.3259i	1.01772	−	1.13029i	0.0262848	−	0.999654i	$-0.491632\pi$
$139$	11.9987	−	13.3259i	1.01772	−	1.13029i	0.991431	−	0.130633i	$-0.0417010\pi$
$140$	−4.02330	−	0.855179i	−0.340031	−	0.0722758i
$141$	−11.7685	−	5.23967i	−0.991086	−	0.441260i
$142$	−0.882621	+	0.980250i	−0.0740679	+	0.0822608i
$143$	17.1306	−	8.79144i	1.43253	−	0.735177i
$144$	−0.487514	+	4.63839i	−0.0406262	+	0.386532i
$145$	1.40939	−	4.33765i	0.117043	−	0.360222i
$146$	−2.21128	+	1.60659i	−0.183007	+	0.132962i
$147$	−0.932019	−	0.414961i	−0.0768716	−	0.0342254i
$148$	1.50775	−	0.671295i	0.123936	−	0.0551801i
$149$	11.7563			0.963111			0.481556	−	0.876416i	$-0.340072\pi$
$149$	11.7563			0.963111			0.481556	+	0.876416i	$0.340072\pi$
$150$	−1.15042	+	1.99259i	−0.0939315	+	0.162694i
$151$	−16.2236	−	11.7871i	−1.32026	−	0.959224i	−0.999929	−	0.0119181i	$-0.996206\pi$
$151$	−16.2236	−	11.7871i	−1.32026	−	0.959224i	−0.320330	−	0.947306i	$-0.603794\pi$
$152$	−0.630907	−	1.94173i	−0.0511733	−	0.157495i
$153$	3.23574	+	3.59365i	0.261594	+	0.290530i
$154$	−1.84668	+	3.19855i	−0.148810	+	0.257747i
$155$	0.638377	+	4.27373i	0.0512757	+	0.343274i
$156$	−13.9522	+	3.78209i	−1.11707	+	0.302809i
$157$	7.17426	−	22.0801i	0.572568	−	1.76218i	−0.0717467	−	0.997423i	$-0.522857\pi$
$157$	7.17426	−	22.0801i	0.572568	−	1.76218i	0.644315	−	0.764760i	$-0.277143\pi$
$158$	0.0877536	−	0.0974602i	0.00698130	−	0.00775352i
$159$	3.73861	−	1.66454i	0.296491	−	0.132006i
$160$	1.12687	−	1.95179i	0.0890865	−	0.154302i
$161$	−9.53937	+	16.5227i	−0.751808	+	1.30217i
$162$	2.29038	+	1.66406i	0.179950	+	0.130741i
$163$	−12.7827	−	5.69124i	−1.00122	−	0.445773i	−0.160381	−	0.987055i	$-0.551272\pi$
$163$	−12.7827	−	5.69124i	−1.00122	−	0.445773i	−0.840841	+	0.541283i	$0.817939\pi$
$164$	12.8664	+	5.72849i	1.00470	+	0.447320i
$165$	5.74280	+	6.37803i	0.447076	+	0.496529i
$166$	−0.264327	−	0.192044i	−0.0205157	−	0.0149055i
$167$	−10.3487	+	2.19968i	−0.800806	+	0.170217i	−0.590097	−	0.807332i	$-0.700911\pi$
$167$	−10.3487	+	2.19968i	−0.800806	+	0.170217i	−0.210709	+	0.977549i	$0.567577\pi$
$168$	3.77196	−	4.18918i	0.291013	−	0.323203i
$169$	−7.70235	−	10.4725i	−0.592488	−	0.805579i
$170$	−0.227500	−	0.700174i	−0.0174485	−	0.0537009i
$171$	−2.58640	−	0.549756i	−0.197787	−	0.0420409i
$172$	14.9676	+	6.66398i	1.14127	+	0.508124i
$173$	−19.6180	−	4.16994i	−1.49153	−	0.317035i	−0.611232	−	0.791451i	$-0.709326\pi$
$173$	−19.6180	−	4.16994i	−1.49153	−	0.317035i	−0.880301	+	0.474416i	$0.842659\pi$
$174$	2.05734	+	2.28491i	0.155966	+	0.173218i
$175$	−10.9969	+	4.89615i	−0.831290	+	0.370114i
$176$	12.9394	+	14.3706i	0.975342	+	1.08323i
$177$	27.4526	+	12.2227i	2.06346	+	0.918712i
$178$	−2.16494	−	0.963896i	−0.162269	−	0.0722470i
$179$	0.411009	−	3.91049i	0.0307203	−	0.292284i	−0.968366	−	0.249536i	$-0.919722\pi$
$179$	0.411009	−	3.91049i	0.0307203	−	0.292284i	0.999086	−	0.0427482i	$-0.0136113\pi$
$180$	−0.967714	−	1.67613i	−0.0721292	−	0.124931i
$181$	−9.59091	−	16.6119i	−0.712887	−	1.23476i	−0.963769	−	0.266738i	$-0.914054\pi$
$181$	−9.59091	−	16.6119i	−0.712887	−	1.23476i	0.250882	−	0.968018i	$-0.419279\pi$
$182$	2.33057	+	0.886841i	0.172753	+	0.0657371i
$183$	9.30499	+	1.97784i	0.687845	+	0.146206i
$184$	−4.63822	−	5.15127i	−0.341934	−	0.379757i
$185$	−0.330785	+	0.572936i	−0.0243198	+	0.0421231i
$186$	−2.71025	−	1.06784i	−0.198725	−	0.0782976i
$187$	20.0499			1.46620
$188$	11.7817	−	2.50429i	0.859272	−	0.182644i
$189$	2.99869	+	9.22901i	0.218122	+	0.671312i
$190$	0.325676	+	0.236617i	0.0236270	+	0.0171660i
$191$	−7.15716	+	12.3966i	−0.517874	+	0.896984i	0.481911	+	0.876220i	$0.339943\pi$
$191$	−7.15716	+	12.3966i	−0.517874	+	0.896984i	−0.999784	+	0.0207632i	$0.993390\pi$
$192$	−6.73864	−	11.6717i	−0.486319	−	0.842329i
$193$	0.647567	−	6.16119i	0.0466129	−	0.443492i	−0.946179	−	0.323643i	$-0.895092\pi$
$193$	0.647567	−	6.16119i	0.0466129	−	0.443492i	0.992792	−	0.119849i	$-0.0382410\pi$
$194$	−2.58160	+	1.87564i	−0.185348	+	0.134663i
$195$	3.63347	−	4.51379i	0.260198	−	0.323239i
$196$	0.933067	−	0.198330i	0.0666477	−	0.0141664i
$197$	17.4981	+	12.7131i	1.24669	+	0.905770i	0.998025	−	0.0628210i	$-0.0200097\pi$
$197$	17.4981	+	12.7131i	1.24669	+	0.905770i	0.248660	+	0.968591i	$0.420010\pi$
$198$	−1.69991	+	0.361327i	−0.120807	+	0.0256784i
$199$	−11.6441	−	2.47504i	−0.825430	−	0.175451i	−0.224217	−	0.974539i	$-0.571982\pi$
$199$	−11.6441	−	2.47504i	−0.825430	−	0.175451i	−0.601213	+	0.799089i	$0.705316\pi$
$200$	−0.457158	−	4.34957i	−0.0323260	−	0.307561i
$201$	−13.8897	+	15.4261i	−0.979703	+	1.08807i
$202$	−0.963605	+	1.07019i	−0.0677990	+	0.0752984i
$203$	1.68145	+	15.9979i	0.118015	+	1.12283i
$204$	−14.7238	−	3.12964i	−1.03087	−	0.219118i
$205$	−5.52214	+	1.17377i	−0.385683	+	0.0819794i
$206$	2.39524	+	1.74024i	0.166884	+	0.121248i
$207$	−8.78118	+	1.86650i	−0.610334	+	0.129731i
$208$	8.18675	−	10.1702i	0.567649	−	0.705178i
$209$	−8.86949	+	6.44406i	−0.613515	+	0.445745i
$210$	−0.116181	+	1.10539i	−0.00801725	+	0.0762790i
$211$	7.32721	+	12.6911i	0.504426	+	0.873692i	0.999987	+	0.00511858i	$0.00162930\pi$
$211$	7.32721	+	12.6911i	0.504426	+	0.873692i	−0.495561	+	0.868573i	$0.665037\pi$
$212$	−1.91322	+	3.31379i	−0.131400	+	0.227592i
$213$	−8.74605	−	6.35438i	−0.599270	−	0.435395i
$214$	−0.531900	−	1.63702i	−0.0363599	−	0.111904i
$215$	−6.42393	+	1.36545i	−0.438108	+	0.0931228i
$216$	−3.52565			−0.239890
$217$	−8.18773	−	12.8543i	−0.555819	−	0.872610i
$218$	1.71105	−	2.96363i	0.115887	−	0.200722i
$219$	−14.9895	−	16.6476i	−1.01290	−	1.12494i
$220$	−7.84931	−	1.66842i	−0.529200	−	0.112485i
$221$	−2.15656	−	13.3639i	−0.145066	−	0.898956i
$222$	−0.222993	−	0.386236i	−0.0149663	−	0.0259225i
$223$	2.23120	+	3.86455i	0.149412	+	0.258790i	0.931010	−	0.364993i	$-0.118929\pi$
$223$	2.23120	+	3.86455i	0.149412	+	0.258790i	−0.781598	+	0.623782i	$0.785595\pi$
$224$	−0.830878	+	7.90528i	−0.0555154	+	0.528194i
$225$	−5.17452	−	2.30385i	−0.344968	−	0.153590i
$226$	2.36237	+	1.05180i	0.157143	+	0.0699644i
$227$	−8.86746	−	9.84831i	−0.588554	−	0.653656i	0.373142	−	0.927774i	$-0.378281\pi$
$227$	−8.86746	−	9.84831i	−0.588554	−	0.653656i	−0.961696	+	0.274119i	$0.911614\pi$
$228$	7.51923	−	3.34778i	0.497973	−	0.221712i
$229$	7.78664	+	8.64794i	0.514556	+	0.571472i	0.943295	−	0.331956i	$-0.107709\pi$
$229$	7.78664	+	8.64794i	0.514556	+	0.571472i	−0.428739	+	0.903428i	$0.641042\pi$
$230$	1.33687	+	0.284161i	0.0881507	+	0.0187370i
$231$	−27.6531	−	12.3120i	−1.81944	−	0.810067i
$232$	−5.71669	−	1.21512i	−0.375319	−	0.0797765i
$233$	−8.23318	−	25.3391i	−0.539374	−	1.66002i	−0.734004	−	0.679145i	$-0.762351\pi$
$233$	−8.23318	−	25.3391i	−0.539374	−	1.66002i	0.194631	−	0.980877i	$-0.437649\pi$
$234$	0.423678	+	1.09418i	0.0276967	+	0.0715290i
$235$	−3.23066	+	3.58802i	−0.210745	+	0.234056i
$236$	−27.4835	+	5.84179i	−1.78902	+	0.380268i
$237$	0.869566	+	0.631777i	0.0564844	+	0.0410383i
$238$	1.73745	+	1.92963i	0.112622	+	0.125079i
$239$	13.9695	+	6.21962i	0.903611	+	0.402314i	0.805317	−	0.592844i	$-0.201995\pi$
$239$	13.9695	+	6.21962i	0.903611	+	0.402314i	0.0982936	+	0.995157i	$0.468662\pi$
$240$	5.31631	+	2.36697i	0.343166	+	0.152788i
$241$	10.8064	+	7.85131i	0.696101	+	0.505747i	0.878660	−	0.477448i	$-0.158438\pi$
$241$	10.8064	+	7.85131i	0.696101	+	0.505747i	−0.182559	+	0.983195i	$0.558438\pi$
$242$	−2.21318	+	3.83334i	−0.142269	+	0.246416i
$243$	−6.28377	+	10.8838i	−0.403104	+	0.698196i
$244$	−8.12561	+	3.61775i	−0.520189	+	0.231603i
$245$	−0.255856	+	0.284157i	−0.0163460	+	0.0181541i
$246$	1.17607	−	3.61956i	0.0749832	−	0.230775i
$247$	5.24918	+	5.21869i	0.333997	+	0.332057i
$248$	5.36094	−	1.38599i	0.340420	−	0.0880107i
$249$	1.33889	−	2.31902i	0.0848486	−	0.146962i
$250$	1.23306	+	1.36946i	0.0779858	+	0.0866120i
$251$	−3.62420	−	11.1541i	−0.228758	−	0.704044i	−0.997888	−	0.0649521i	$-0.979311\pi$
$251$	−3.62420	−	11.1541i	−0.228758	−	0.704044i	0.769131	−	0.639091i	$-0.220689\pi$
$252$	5.52250	+	4.01233i	0.347885	+	0.252753i
$253$	−18.6109	+	32.2351i	−1.17006	+	2.02660i
$254$	1.11117			0.0697210
$255$	5.51215	−	2.45417i	0.345184	−	0.153686i
$256$	10.1713	+	4.52857i	0.635709	+	0.283036i
$257$	20.2307	−	14.6985i	1.26196	−	0.916865i	0.263105	−	0.964767i	$-0.415254\pi$
$257$	20.2307	−	14.6985i	1.26196	−	0.916865i	0.998852	+	0.0479022i	$0.0152536\pi$
$258$	1.36812	−	4.21065i	0.0851757	−	0.262144i
$259$	0.243900	−	2.32055i	0.0151552	−	0.144192i
$260$	−0.267790	+	5.41128i	−0.0166076	+	0.335593i
$261$	−5.06476	+	5.62499i	−0.313501	+	0.348178i
$262$	−1.78700	−	0.795625i	−0.110401	−	0.0491539i
$263$	−3.26886	−	0.694818i	−0.201567	−	0.0428443i	0.106022	−	0.994364i	$-0.466189\pi$
$263$	−3.26886	−	0.694818i	−0.201567	−	0.0428443i	−0.307588	+	0.951520i	$0.599522\pi$
$264$	7.35895	−	8.17294i	0.452912	−	0.503009i
$265$	−0.160326	−	1.52540i	−0.00984877	−	0.0937048i
$266$	−1.38878	−	0.295194i	−0.0851515	−	0.0180995i
$267$	6.00192	−	18.4720i	0.367312	−	1.13047i
$268$	2.02876	−	19.3024i	0.123926	−	1.17908i
$269$	−15.6800	−	17.4144i	−0.956027	−	1.06178i	−0.998035	−	0.0626584i	$-0.980042\pi$
$269$	−15.6800	−	17.4144i	−0.956027	−	1.06178i	0.0420079	−	0.999117i	$-0.486625\pi$
$270$	0.562396	−	0.408604i	0.0342263	−	0.0248669i
$271$	−0.764550	−	7.27421i	−0.0464431	−	0.441877i	−0.992892	−	0.119022i	$-0.962024\pi$
$271$	−0.764550	−	7.27421i	−0.0464431	−	0.441877i	0.946449	−	0.322855i	$-0.104643\pi$
$272$	12.4197	−	5.52960i	0.753053	−	0.335281i
$273$	−5.23197	+	19.7560i	−0.316653	+	1.19569i
$274$	0.00749563	+	0.0129828i	0.000452827	+	0.000784320i
$275$	−21.4546	+	9.55220i	−1.29376	+	0.576019i
$276$	18.6987	−	20.7670i	1.12553	−	1.25003i
$277$	26.7800	−	5.69227i	1.60906	−	0.342016i	0.686276	−	0.727341i	$-0.259244\pi$
$277$	26.7800	−	5.69227i	1.60906	−	0.342016i	0.922781	+	0.385326i	$0.125911\pi$
$278$	4.53064			0.271730
$279$	1.91698	−	6.91034i	0.114767	−	0.413712i
$280$	−1.05637	−	1.82969i	−0.0631302	−	0.109345i
$281$	1.93612	−	5.95878i	0.115499	−	0.355471i	−0.876551	−	0.481308i	$-0.840162\pi$
$281$	1.93612	−	5.95878i	0.115499	−	0.355471i	0.992051	+	0.125837i	$0.0401618\pi$
$282$	−1.00580	−	3.09552i	−0.0598943	−	0.184336i
$283$	−8.59101	+	3.82497i	−0.510683	+	0.227371i	−0.645867	−	0.763450i	$-0.723504\pi$
$283$	−8.59101	+	3.82497i	−0.510683	+	0.227371i	0.135184	+	0.990820i	$0.456837\pi$
$284$	10.1081			0.599804
$285$	−1.64964	+	2.85726i	−0.0977162	+	0.169249i
$286$	4.54685	+	1.73019i	0.268861	+	0.102309i
$287$	16.1087	−	11.7037i	0.950868	−	0.690846i
$288$	−3.02593	+	2.19847i	−0.178305	+	0.129546i
$289$	−0.897439	+	2.76203i	−0.0527905	+	0.162473i
$290$	1.05273	−	0.468704i	0.0618182	−	0.0275232i
$291$	−17.4998	−	19.4355i	−1.02586	−	1.13933i
$292$	20.4878	+	4.35482i	1.19896	+	0.254847i
$293$	−11.6644	+	8.47465i	−0.681439	+	0.495094i	−0.873835	−	0.486223i	$-0.838374\pi$
$293$	−11.6644	+	8.47465i	−0.681439	+	0.495094i	0.192396	+	0.981317i	$0.438374\pi$
$294$	−0.0796551	−	0.245153i	−0.00464558	−	0.0142976i
$295$	7.53622	−	8.36982i	0.438776	−	0.487310i
$296$	0.774458	+	0.344811i	0.0450144	+	0.0200417i
$297$	5.85032	+	18.0054i	0.339470	+	1.04478i
$298$	1.98755	+	2.20739i	0.115135	+	0.127871i
$299$	23.4876	+	8.93762i	1.35832	+	0.516876i
$300$	17.2463	−	3.66582i	0.995717	−	0.211646i
$301$	18.7394	−	13.6150i	1.08012	−	0.784753i
$302$	−0.529616	−	5.03896i	−0.0304760	−	0.289959i
$303$	−9.54854	−	6.93742i	−0.548549	−	0.398544i
$304$	−3.71688	+	6.43782i	−0.213178	+	0.369234i
$305$	1.78267	−	3.08768i	0.102076	−	0.176800i
$306$	−0.127713	+	1.21510i	−0.00730085	+	0.0694629i
$307$	−18.8558	−	4.00792i	−1.07616	−	0.228744i	−0.364451	−	0.931223i	$-0.618743\pi$
$307$	−18.8558	−	4.00792i	−1.07616	−	0.228744i	−0.711705	+	0.702479i	$0.752077\pi$
$308$	27.6842	−	5.88446i	1.57746	−	0.335298i
$309$	−12.1325	+	21.0142i	−0.690196	+	1.19545i
$310$	−0.694522	+	0.842391i	−0.0394462	+	0.0478446i
$311$	−20.3771			−1.15548			−0.577740	−	0.816221i	$-0.696065\pi$
$311$	−20.3771			−1.15548			−0.577740	+	0.816221i	$0.696065\pi$
$312$	−6.23906	−	4.02590i	−0.353217	−	0.227922i
$313$	11.7994	+	2.50805i	0.666944	+	0.141763i	0.528928	−	0.848667i	$-0.322594\pi$
$313$	11.7994	+	2.50805i	0.666944	+	0.141763i	0.138016	+	0.990430i	$0.455927\pi$
$314$	5.35872	−	2.38586i	0.302410	−	0.134642i
$315$	−2.73624			−0.154170
$316$	−1.00498			−0.0565348
$317$	−21.7159	+	9.66853i	−1.21969	+	0.543039i	−0.912682	−	0.408670i	$-0.865993\pi$
$317$	−21.7159	+	9.66853i	−1.21969	+	0.543039i	−0.307003	+	0.951709i	$0.599326\pi$
$318$	0.944598	+	0.420562i	0.0529704	+	0.0235839i
$319$	3.28044	+	31.2113i	0.183670	+	1.74750i
$320$	−4.94079	+	1.05020i	−0.276199	+	0.0587078i
$321$	12.8875	−	5.73788i	0.719310	−	0.320257i
$322$	−4.71510	+	1.00222i	−0.262762	+	0.0558518i
$323$	2.38178	+	7.33036i	0.132526	+	0.407872i
$324$	−2.26773	−	21.5760i	−0.125985	−	1.19867i
$325$	8.67451	+	13.2728i	0.481175	+	0.736241i
$326$	−1.09248	−	3.36230i	−0.0605068	−	0.186221i
$327$	25.6221	+	11.4077i	1.41691	+	0.630847i
$328$	2.23551	+	6.88020i	0.123435	+	0.379895i
$329$	5.26216	−	16.1953i	0.290112	−	0.892874i
$330$	−0.226665	+	2.15657i	−0.0124775	+	0.118715i
$331$	−9.72794	−	10.8040i	−0.534696	−	0.593840i	0.413903	−	0.910321i	$-0.364165\pi$
$331$	−9.72794	−	10.8040i	−0.534696	−	0.593840i	−0.948599	+	0.316481i	$0.897499\pi$
$332$	0.261712	+	2.49002i	0.0143633	+	0.136658i
$333$	0.888246	−	0.645348i	0.0486756	−	0.0353649i
$334$	−2.16260	−	1.57122i	−0.118332	−	0.0859732i
$335$	3.88993	+	6.73756i	0.212530	+	0.368112i
$336$	−20.5249			−1.11973
$337$	−15.2764	−	11.0989i	−0.832156	−	0.604597i	0.0880124	−	0.996119i	$-0.471948\pi$
$337$	−15.2764	−	11.0989i	−0.832156	−	0.604597i	−0.920169	+	0.391523i	$0.871948\pi$
$338$	0.664174	−	3.21673i	0.0361263	−	0.174967i
$339$	−6.54925	+	20.1565i	−0.355706	+	1.09475i
$340$	−2.82082	+	4.88580i	−0.152980	+	0.264970i
$341$	−15.9740	−	25.0783i	−0.865038	−	1.35807i
$342$	−0.334039	−	0.578573i	−0.0180628	−	0.0312856i
$343$	−5.50431	+	16.9405i	−0.297205	+	0.914703i
$344$	2.60058	+	8.00377i	0.140214	+	0.431534i
$345$	−1.17088	+	11.1401i	−0.0630379	+	0.599765i
$346$	−2.53372	−	4.38853i	−0.136213	−	0.235929i
$347$	10.4738			0.562261			0.281130	−	0.959670i	$-0.409291\pi$
$347$	10.4738			0.562261			0.281130	+	0.959670i	$0.409291\pi$
$348$	2.46283	−	23.4323i	0.132022	−	1.25610i
$349$	−0.473067	−	4.50093i	−0.0253227	−	0.240929i	−0.999860	−	0.0167058i	$-0.994682\pi$
$349$	−0.473067	−	4.50093i	−0.0253227	−	0.240929i	0.974538	−	0.224223i	$-0.0719845\pi$
$350$	−2.77848	−	1.23706i	−0.148516	−	0.0661237i
$351$	11.3720	−	5.83610i	0.606991	−	0.311508i
$352$	−1.62101	+	15.4229i	−0.0864002	+	0.822043i
$353$	−0.119217	+	0.0253403i	−0.00634527	+	0.00134873i	−0.211083	−	0.977468i	$-0.567699\pi$
$353$	−0.119217	+	0.0253403i	−0.00634527	+	0.00134873i	0.204738	+	0.978817i	$0.434366\pi$
$354$	2.34624	+	7.22097i	0.124701	+	0.383790i
$355$	−3.27795	+	2.38157i	−0.173975	+	0.126401i
$356$	5.61183	+	17.2714i	0.297426	+	0.915384i
$357$	−14.2398	+	15.8148i	−0.753648	+	0.837011i
$358$	0.803732	−	0.583946i	0.0424786	−	0.0308625i
$359$	2.71420	−	3.01443i	0.143250	−	0.159095i	−0.667250	−	0.744834i	$-0.732529\pi$
$359$	2.71420	−	3.01443i	0.143250	−	0.159095i	0.810500	+	0.585738i	$0.199195\pi$
$360$	0.307204	−	0.945478i	0.0161911	−	0.0498310i
$361$	11.9617	+	8.69069i	0.629564	+	0.457405i
$362$	1.49764	−	4.60928i	0.0787144	−	0.242258i
$363$	−33.1412	−	14.7554i	−1.73946	−	0.774458i
$364$	−6.89990	−	17.8195i	−0.361653	−	0.933997i
$365$	−7.67004	+	3.41492i	−0.401468	+	0.178745i
$366$	1.20176	+	2.08151i	0.0628171	+	0.108802i
$367$	18.7469			0.978583			0.489291	−	0.872120i	$-0.337255\pi$
$367$	18.7469			0.978583			0.489291	+	0.872120i	$0.337255\pi$
$368$	−2.63816	+	25.1004i	−0.137523	+	1.30845i
$369$	9.16446	+	1.94797i	0.477083	+	0.101407i
$370$	−0.163500	+	0.0347529i	−0.00849994	+	0.00180672i
$371$	2.70484	+	4.68492i	0.140428	+	0.243229i
$372$	7.81603	+	20.9098i	0.405242	+	1.08412i
$373$	11.0904	+	19.2092i	0.574240	+	0.994613i	0.996124	+	0.0879632i	$0.0280358\pi$
$373$	11.0904	+	19.2092i	0.574240	+	0.994613i	−0.421883	+	0.906650i	$0.638631\pi$
$374$	3.38969	+	3.76463i	0.175277	+	0.194665i
$375$	−10.1059	+	11.2238i	−0.521868	+	0.579593i
$376$	5.00530	+	3.63657i	0.258129	+	0.187542i
$377$	20.4506	−	5.54361i	1.05326	−	0.285510i
$378$	−1.22590	+	2.12332i	−0.0630535	+	0.109212i
$379$	2.16925	−	20.6391i	0.111427	−	1.06016i	−0.785768	−	0.618522i	$-0.787732\pi$
$379$	2.16925	−	20.6391i	0.111427	−	1.06016i	0.897195	−	0.441635i	$-0.145601\pi$
$380$	−0.322454	−	3.06794i	−0.0165415	−	0.157382i
$381$	0.951932	+	9.05703i	0.0487690	+	0.464006i
$382$	−3.53762	+	0.751945i	−0.181001	+	0.0384728i
$383$	−17.5008	+	7.79188i	−0.894251	+	0.398146i	−0.801815	−	0.597572i	$-0.796132\pi$
$383$	−17.5008	+	7.79188i	−0.894251	+	0.398146i	−0.0924363	+	0.995719i	$0.529465\pi$
$384$	4.76867	−	14.6765i	0.243350	−	0.748955i
$385$	−7.59127	+	8.43096i	−0.386887	+	0.429682i
$386$	1.26632	−	0.920037i	0.0644541	−	0.0468287i
$387$	10.6611	+	2.26608i	0.541933	+	0.115191i
$388$	23.9189	+	5.08412i	1.21430	+	0.258107i
$389$	1.70995	+	16.2691i	0.0866981	+	0.824877i	0.948318	+	0.317323i	$0.102784\pi$
$389$	1.70995	+	16.2691i	0.0866981	+	0.824877i	−0.861620	+	0.507555i	$0.830550\pi$
$390$	1.46181	−	0.0808805i	0.0740214	−	0.00409554i
$391$	17.5100	+	19.4469i	0.885521	+	0.983471i
$392$	0.396400	+	0.288002i	0.0200212	+	0.0145463i
$393$	4.95414	−	15.2473i	0.249903	−	0.769124i
$394$	0.571220	+	5.43479i	0.0287776	+	0.273801i
$395$	0.325906	−	0.236785i	0.0163981	−	0.0119139i
$396$	10.7742	+	7.82791i	0.541423	+	0.393367i
$397$	−9.88413			−0.496070			−0.248035	−	0.968751i	$-0.579785\pi$
$397$	−9.88413			−0.496070			−0.248035	+	0.968751i	$0.579785\pi$
$398$	−1.50387	−	2.60477i	−0.0753820	−	0.130565i
$399$	1.21634	−	11.5727i	0.0608931	−	0.579359i
$400$	−10.6554	+	11.8340i	−0.532768	+	0.591699i
$401$	−2.16987	−	2.40989i	−0.108358	−	0.120344i	0.686526	−	0.727106i	$-0.259135\pi$
$401$	−2.16987	−	2.40989i	−0.108358	−	0.120344i	−0.794884	+	0.606761i	$0.792468\pi$
$402$	−5.24467			−0.261580
$403$	−14.9974	+	13.3446i	−0.747073	+	0.664741i
$404$	11.0355			0.549039
$405$	5.81892	+	6.46257i	0.289145	+	0.321128i
$406$	−2.71955	+	3.02036i	−0.134969	+	0.149898i
$407$	0.475839	−	4.52730i	0.0235865	−	0.224410i
$408$	−3.86592	−	6.69597i	−0.191391	−	0.331500i
$409$	23.5514			1.16454			0.582270	−	0.812996i	$-0.302165\pi$
$409$	23.5514			1.16454			0.582270	+	0.812996i	$0.302165\pi$
$410$	−1.15398	−	0.838413i	−0.0569908	−	0.0414063i
$411$	−0.0994000	+	0.0722184i	−0.00490304	+	0.00356227i
$412$	−2.37154	−	22.5637i	−0.116837	−	1.11163i
$413$	−12.2751	+	37.7790i	−0.604020	+	1.85898i
$414$	−1.83503	−	1.33323i	−0.0901867	−	0.0655245i
$415$	−0.671545	−	0.745826i	−0.0329649	−	0.0366112i
$416$	10.4542	−	0.578424i	0.512561	−	0.0283596i
$417$	3.88137	+	36.9288i	0.190072	+	1.80841i
$418$	−2.70945	−	0.575912i	−0.132524	−	0.0281688i
$419$	−13.7018	−	2.91240i	−0.669376	−	0.142280i	−0.139326	−	0.990247i	$-0.544494\pi$
$419$	−13.7018	−	2.91240i	−0.669376	−	0.142280i	−0.530050	+	0.847966i	$0.677827\pi$
$420$	6.89070	−	5.00639i	0.336232	−	0.244287i
$421$	9.09619	−	10.1023i	0.443321	−	0.492358i	−0.479524	−	0.877529i	$-0.659191\pi$
$421$	9.09619	−	10.1023i	0.443321	−	0.492358i	0.922845	+	0.385171i	$0.125857\pi$
$422$	−1.14416	+	3.52137i	−0.0556970	+	0.171418i
$423$	7.32000	−	3.25907i	0.355911	−	0.158462i
$424$	−1.92250	+	0.408640i	−0.0933649	+	0.0198453i
$425$	1.72585	+	16.4203i	0.0837159	+	0.796503i
$426$	−0.285513	−	2.71647i	−0.0138331	−	0.131614i
$427$	−1.31443	+	12.5060i	−0.0636097	+	0.605206i
$428$	−6.59512	+	11.4231i	−0.318787	+	0.552155i
$429$	−10.2074	+	38.5432i	−0.492817	+	1.86088i
$430$	−1.34243	−	0.975330i	−0.0647376	−	0.0470346i
$431$	4.65093	−	5.16538i	0.224027	−	0.248808i	−0.620644	−	0.784092i	$-0.713129\pi$
$431$	4.65093	−	5.16538i	0.224027	−	0.248808i	0.844672	+	0.535285i	$0.179796\pi$
$432$	8.58966	+	9.53978i	0.413270	+	0.458983i
$433$	−3.64661	−	6.31611i	−0.175245	−	0.303533i	0.765001	−	0.644029i	$-0.222738\pi$
$433$	−3.64661	−	6.31611i	−0.175245	−	0.303533i	−0.940246	+	0.340496i	$0.889405\pi$
$434$	1.02933	−	3.71054i	0.0494095	−	0.178112i
$435$	4.72222	+	8.17912i	0.226413	+	0.392159i
$436$	−25.6509	+	5.45227i	−1.22846	+	0.261117i
$437$	−13.9962	−	2.97498i	−0.669527	−	0.142312i
$438$	0.591628	−	5.62896i	0.0282691	−	0.268962i
$439$	−29.7344			−1.41914			−0.709572	−	0.704633i	$-0.751112\pi$
$439$	−29.7344			−1.41914			−0.709572	+	0.704633i	$0.751112\pi$
$440$	−2.06094	−	3.56965i	−0.0982513	−	0.170176i
$441$	0.579715	−	0.258106i	0.0276055	−	0.0122907i
$442$	2.14466	−	2.66427i	0.102011	−	0.126726i
$443$	−20.7369	−	9.23266i	−0.985240	−	0.438657i	−0.150086	−	0.988673i	$-0.547955\pi$
$443$	−20.7369	−	9.23266i	−0.985240	−	0.438657i	−0.835154	+	0.550016i	$0.814622\pi$
$444$	−1.05611	+	3.25038i	−0.0501208	+	0.154256i
$445$	−5.88919	−	4.27875i	−0.279174	−	0.202832i
$446$	−0.348408	+	1.07229i	−0.0164976	+	0.0507743i
$447$	−16.2895	+	18.0913i	−0.770468	+	0.855691i
$448$	14.4129	−	10.4716i	0.680944	−	0.494735i
$449$	5.68226	−	6.31079i	0.268162	−	0.297825i	−0.593991	−	0.804472i	$-0.702449\pi$
$449$	5.68226	−	6.31079i	0.268162	−	0.297825i	0.862154	+	0.506647i	$0.169115\pi$
$450$	−0.442241	−	1.36108i	−0.0208474	−	0.0641618i
$451$	31.4275	−	22.8334i	1.47986	−	1.07518i
$452$	−6.12358	−	18.8464i	−0.288029	−	0.886462i
$453$	40.6183	−	8.63369i	1.90842	−	0.405646i
$454$	0.349993	−	3.32996i	0.0164260	−	0.156283i
$455$	6.43603	+	4.15301i	0.301726	+	0.194696i
$456$	3.86225	+	1.71959i	0.180867	+	0.0805270i
$457$	0.0141334	+	0.134470i	0.000661132	+	0.00629025i	0.994847	−	0.101383i	$-0.0323267\pi$
$457$	0.0141334	+	0.134470i	0.000661132	+	0.00629025i	−0.994186	+	0.107673i	$0.965660\pi$
$458$	−0.307334	+	2.92409i	−0.0143608	+	0.136634i
$459$	13.3099			0.621254
$460$	−5.23674	−	9.07029i	−0.244164	−	0.422905i
$461$	−0.885599	+	8.42591i	−0.0412464	+	0.392434i	0.954350	+	0.298691i	$0.0965499\pi$
$461$	−0.885599	+	8.42591i	−0.0412464	+	0.392434i	−0.995596	+	0.0937430i	$0.970117\pi$
$462$	−2.36337	−	7.27372i	−0.109954	−	0.338404i
$463$	−6.90524	+	21.2522i	−0.320914	+	0.987671i	0.652338	+	0.757929i	$0.273788\pi$
$463$	−6.90524	+	21.2522i	−0.320914	+	0.987671i	−0.973251	+	0.229743i	$0.926212\pi$
$464$	10.6399	+	18.4288i	0.493943	+	0.855534i
$465$	−7.46123	−	4.93931i	−0.346006	−	0.229055i
$466$	3.36583	−	5.82978i	0.155919	−	0.270060i
$467$	5.55788	−	17.1054i	0.257188	−	0.791544i	−0.736202	−	0.676761i	$-0.763383\pi$
$467$	5.55788	−	17.1054i	0.257188	−	0.791544i	0.993391	−	0.114783i	$-0.0366171\pi$
$468$	4.05869	−	8.02332i	0.187613	−	0.370878i
$469$	−22.1988	−	16.1284i	−1.02505	−	0.744741i
$470$	−1.21988			−0.0562689
$471$	24.0377	+	41.6345i	1.10760	+	1.91841i
$472$	−11.6760	−	8.48308i	−0.537429	−	0.390465i
$473$	36.5598	−	26.5622i	1.68102	−	1.22133i
$474$	0.0283868	+	0.270082i	0.00130385	+	0.0124053i
$475$	−6.04097	−	6.70918i	−0.277179	−	0.307838i
$476$	2.07989	−	19.7888i	0.0953316	−	0.907020i
$477$	−0.786597	+	2.42090i	−0.0360158	+	0.110845i
$478$	1.19390	+	3.67446i	0.0546079	+	0.168066i
$479$	19.5693	+	8.71280i	0.894143	+	0.398098i	0.801774	−	0.597627i	$-0.203890\pi$
$479$	19.5693	+	8.71280i	0.894143	+	0.398098i	0.0923684	+	0.995725i	$0.470556\pi$
$480$	1.44216	+	4.43850i	0.0658251	+	0.202589i
$481$	−3.06878	+	0.169793i	−0.139924	+	0.00774190i
$482$	0.352772	+	3.35640i	0.0160683	+	0.152880i
$483$	−12.2084	−	37.5737i	−0.555503	−	1.70966i
$484$	33.1785	−	7.05230i	1.50811	−	0.320559i
$485$	−8.95453	+	3.98681i	−0.406604	+	0.181032i
$486$	−3.10593	+	0.660185i	−0.140888	+	0.0299466i
$487$	−0.405058	−	3.85387i	−0.0183549	−	0.174636i	0.981504	−	0.191443i	$-0.0613166\pi$
$487$	−0.405058	−	3.85387i	−0.0183549	−	0.174636i	−0.999859	+	0.0168070i	$0.994650\pi$
$488$	−4.17372	−	1.85826i	−0.188936	−	0.0841196i
$489$	26.4699	−	11.7851i	1.19701	−	0.532943i
$490$	−0.0966098			−0.00436438
$491$	−43.0216			−1.94154			−0.970768	−	0.240018i	$-0.922847\pi$
$491$	−43.0216			−1.94154			−0.970768	+	0.240018i	$0.922847\pi$
$492$	−26.6431	+	11.8623i	−1.20116	+	0.534792i
$493$	21.5814	+	4.58728i	0.971979	+	0.206601i
$494$	−0.0924366	+	1.86789i	−0.00415892	+	0.0840402i
$495$	−5.33830			−0.239939
$496$	−16.8113	−	11.1290i	−0.754848	−	0.499706i
$497$	7.14522	−	12.3759i	0.320507	−	0.555134i
$498$	0.661782	−	0.140666i	0.0296552	−	0.00630340i
$499$	−5.19317	−	1.10384i	−0.232478	−	0.0494148i	0.0901993	−	0.995924i	$-0.471250\pi$
$499$	−5.19317	−	1.10384i	−0.232478	−	0.0494148i	−0.322678	+	0.946509i	$0.604583\pi$
$500$	1.47609	−	14.0441i	0.0660130	−	0.628071i
$501$	10.9542	−	18.9731i	0.489395	−	0.847658i
$502$	1.48162	−	2.56624i	0.0661279	−	0.114537i
$503$	−7.99336	−	5.80751i	−0.356406	−	0.258944i	0.395145	−	0.918619i	$-0.370694\pi$
$503$	−7.99336	−	5.80751i	−0.356406	−	0.258944i	−0.751552	+	0.659674i	$0.770694\pi$
$504$	0.366505	+	3.48707i	0.0163255	+	0.155326i
$505$	−3.57871	+	2.60009i	−0.159251	+	0.115702i
$506$	−9.19897	+	1.95530i	−0.408944	+	0.0869238i
$507$	26.7882	+	2.65786i	1.18971	+	0.118040i
$508$	−5.69766	−	6.32789i	−0.252793	−	0.280755i
$509$	−2.65205	−	8.16218i	−0.117550	−	0.361782i	0.874920	−	0.484267i	$-0.160914\pi$
$509$	−2.65205	−	8.16218i	−0.117550	−	0.361782i	−0.992470	+	0.122485i	$0.960914\pi$
$510$	1.39270	+	0.620070i	0.0616698	+	0.0274571i
$511$	19.8143	−	22.0060i	0.876534	−	0.973489i
$512$	5.47504	+	16.8504i	0.241965	+	0.744691i
$513$	−5.88791	+	4.27782i	−0.259958	+	0.188870i
$514$	6.18008	+	1.31362i	0.272592	+	0.0579412i
$515$	6.08531	+	6.75842i	0.268151	+	0.297812i
$516$	−30.9941	+	13.7994i	−1.36444	+	0.607487i
$517$	10.2663	−	31.5964i	0.451510	−	1.38961i
$518$	0.476948	−	0.346523i	0.0209559	−	0.0152253i
$519$	33.5998	−	24.4117i	1.47487	−	1.07155i
$520$	−2.15762	+	1.75763i	−0.0946177	+	0.0770773i
$521$	21.4926	−	37.2262i	0.941607	−	1.63091i	0.179200	−	0.983813i	$-0.442649\pi$
$521$	21.4926	−	37.2262i	0.941607	−	1.63091i	0.762407	−	0.647098i	$-0.224017\pi$
$522$	−1.91243			−0.0837047
$523$	−8.30962	+	3.69968i	−0.363354	+	0.161776i	−0.580290	−	0.814410i	$-0.697061\pi$
$523$	−8.30962	+	3.69968i	−0.363354	+	0.161776i	0.216935	+	0.976186i	$0.430394\pi$
$524$	4.63215	+	14.2563i	0.202356	+	0.622789i
$525$	7.70285	−	23.7069i	0.336180	−	1.03465i
$526$	−0.422181	−	0.731239i	−0.0184080	−	0.0318835i
$527$	−20.2384	+	5.23235i	−0.881599	+	0.227925i
$528$	−40.0433			−1.74266
$529$	−25.0215	+	5.31849i	−1.08789	+	0.231239i
$530$	0.259309	−	0.287992i	0.0112637	−	0.0125096i
$531$	−17.0755	+	7.60249i	−0.741013	+	0.329920i
$532$	5.44006	+	9.42247i	0.235857	+	0.408516i
$533$	−18.5996	−	18.4915i	−0.805637	−	0.800957i
$534$	4.48306	−	1.99599i	0.194001	−	0.0863748i
$535$	−0.552666	−	5.25827i	−0.0238938	−	0.227335i
$536$	8.06532	−	5.85979i	0.348369	−	0.253105i
$537$	5.44823	+	6.05088i	0.235109	+	0.261115i
$538$	0.618880	−	5.88825i	0.0266818	−	0.253861i
$539$	0.813049	−	2.50231i	0.0350205	−	0.107782i
$540$	−5.21068	−	1.10756i	−0.224232	−	0.0476619i
$541$	0.413562	+	3.93478i	0.0177804	+	0.169170i	0.999809	−	0.0195650i	$-0.00622812\pi$
$541$	0.413562	+	3.93478i	0.0177804	+	0.169170i	−0.982028	+	0.188734i	$0.939561\pi$
$542$	1.23657	−	1.37335i	0.0531152	−	0.0589905i
$543$	38.8528	+	8.25841i	1.66733	+	0.354402i
$544$	9.96001	+	4.43448i	0.427032	+	0.190127i
$545$	7.03373	−	7.81175i	0.301292	−	0.334618i
$546$	−4.59397	+	2.35763i	−0.196604	+	0.100897i
$547$	−0.569738	+	5.42069i	−0.0243602	+	0.231772i	0.975567	+	0.219702i	$0.0705087\pi$
$547$	−0.569738	+	5.42069i	−0.0243602	+	0.231772i	−0.999927	+	0.0120697i	$0.996158\pi$
$548$	0.0354998	−	0.109257i	0.00151648	−	0.00466723i
$549$	−4.78695	+	3.47793i	−0.204302	+	0.148434i
$550$	−5.42072	−	2.41346i	−0.231140	−	0.102910i
$551$	−11.0213	+	4.90702i	−0.469525	+	0.209046i
$552$	14.3538			0.610940
$553$	−0.710405	+	1.23046i	−0.0302095	+	0.0523244i
$554$	5.59630	+	4.06595i	0.237764	+	0.172746i
$555$	−0.423336	−	1.30290i	−0.0179696	−	0.0553048i
$556$	−23.2314	−	25.8011i	−0.985232	−	1.09421i
$557$	1.18972	−	2.06066i	0.0504101	−	0.0873128i	−0.839719	−	0.543021i	$-0.817281\pi$
$557$	1.18972	−	2.06066i	0.0504101	−	0.0873128i	0.890129	+	0.455708i	$0.150614\pi$
$558$	1.62160	−	0.808343i	0.0686477	−	0.0342199i
$559$	−21.6370	−	21.5113i	−0.915147	−	0.909831i
$560$	−2.37713	+	7.31606i	−0.100452	+	0.309160i
$561$	−27.7812	+	30.8542i	−1.17292	+	1.30266i
$562$	1.44616	−	0.643873i	0.0610027	−	0.0271602i
$563$	−10.0205	+	17.3560i	−0.422314	+	0.731469i	−0.996165	−	0.0874903i	$-0.972115\pi$
$563$	−10.0205	+	17.3560i	−0.422314	+	0.731469i	0.573851	+	0.818959i	$0.305449\pi$
$564$	−12.4710	+	21.6005i	−0.525126	+	0.909544i
$565$	6.42624	+	4.66893i	0.270354	+	0.196424i
$566$	−2.17061	−	0.966416i	−0.0912374	−	0.0406215i
$567$	−28.0197	−	12.4752i	−1.17672	−	0.523907i
$568$	3.47414	+	3.85842i	0.145772	+	0.161896i
$569$	20.3093	+	14.7556i	0.851411	+	0.618586i	0.925535	−	0.378663i	$-0.123616\pi$
$569$	20.3093	+	14.7556i	0.851411	+	0.618586i	−0.0741235	+	0.997249i	$0.523616\pi$
$570$	−0.815379	+	0.173314i	−0.0341525	+	0.00725933i
$571$	4.99308	−	5.54538i	0.208954	−	0.232067i	−0.629553	−	0.776957i	$-0.716762\pi$
$571$	4.99308	−	5.54538i	0.208954	−	0.232067i	0.838507	+	0.544890i	$0.183429\pi$
$572$	−13.4614	−	34.7652i	−0.562851	−	1.45361i
$573$	−9.15968	−	28.1906i	−0.382651	−	1.17768i
$574$	4.92090	+	1.04597i	0.205394	+	0.0436579i
$575$	−28.0017	−	12.4671i	−1.16775	−	0.519916i
$576$	8.19967	+	1.74289i	0.341653	+	0.0726206i
$577$	−1.40912	−	1.56498i	−0.0586624	−	0.0651512i	0.713099	−	0.701063i	$-0.247291\pi$
$577$	−1.40912	−	1.56498i	−0.0586624	−	0.0651512i	−0.771762	+	0.635912i	$0.780624\pi$
$578$	−0.670331	+	0.298451i	−0.0278821	+	0.0124139i
$579$	8.58398	+	9.53348i	0.356738	+	0.396198i
$580$	−8.06716	−	3.59173i	−0.334970	−	0.149138i
$581$	3.23367	+	1.43972i	0.134155	+	0.0597297i
$582$	0.690707	−	6.57164i	0.0286307	−	0.272403i
$583$	5.27704	+	9.14009i	0.218552	+	0.378544i
$584$	5.37934	+	9.31730i	0.222599	+	0.385552i
$585$	0.574186	+	3.55815i	0.0237397	+	0.147112i
$586$	−3.56323	−	0.757388i	−0.147196	−	0.0312874i
$587$	−3.05484	−	3.39275i	−0.126087	−	0.140034i	0.676796	−	0.736171i	$-0.263368\pi$
$587$	−3.05484	−	3.39275i	−0.126087	−	0.140034i	−0.802882	+	0.596137i	$0.796701\pi$
$588$	−0.987657	+	1.71067i	−0.0407303	+	0.0705470i
$589$	7.27119	−	8.81927i	0.299604	−	0.363392i
$590$	2.84564			0.117153
$591$	−43.8091	+	9.31191i	−1.80207	+	0.383041i
$592$	−0.953839	−	2.93562i	−0.0392026	−	0.120653i
$593$	1.25869	+	0.914488i	0.0516880	+	0.0375535i	0.613329	−	0.789827i	$-0.289830\pi$
$593$	1.25869	+	0.914488i	0.0516880	+	0.0375535i	−0.561641	+	0.827381i	$0.689830\pi$
$594$	−2.39169	+	4.14252i	−0.0981320	+	0.169970i
$595$	3.98797	+	6.90736i	0.163491	+	0.283174i
$596$	2.37928	−	22.6374i	0.0974592	−	0.927263i
$597$	19.9429	−	14.4893i	0.816208	−	0.593010i
$598$	2.29271	+	5.92111i	0.0937560	+	0.242132i
$599$	−21.9776	+	4.67149i	−0.897982	+	0.190872i	−0.633705	−	0.773575i	$-0.718467\pi$
$599$	−21.9776	+	4.67149i	−0.897982	+	0.190872i	−0.264277	+	0.964447i	$0.585133\pi$
$600$	7.32685	+	5.32327i	0.299117	+	0.217322i
$601$	0.842850	−	0.179153i	0.0343806	−	0.00730781i	−0.190689	−	0.981650i	$-0.561072\pi$
$601$	0.842850	−	0.179153i	0.0343806	−	0.00730781i	0.225070	+	0.974343i	$0.427739\pi$
$602$	5.72451	+	1.21678i	0.233314	+	0.0495923i
$603$	−1.34960	−	12.8406i	−0.0549601	−	0.522911i
$604$	−25.9802	+	28.8539i	−1.05712	+	1.17405i
$605$	−9.09785	+	10.1042i	−0.369880	+	0.410794i
$606$	−0.311710	−	2.96572i	−0.0126623	−	0.120474i
$607$	27.5720	+	5.86060i	1.11911	+	0.237874i	0.730088	−	0.683353i	$-0.239479\pi$
$607$	27.5720	+	5.86060i	1.11911	+	0.237874i	0.389023	+	0.921228i	$0.372813\pi$
$608$	−5.83126	+	1.23947i	−0.236489	+	0.0502672i
$609$	−26.9485	−	19.5792i	−1.09201	−	0.793391i
$610$	0.881135	−	0.187291i	0.0356761	−	0.00758319i
$611$	−22.1643	−	3.44432i	−0.896670	−	0.139342i
$612$	7.57465	−	5.50330i	0.306187	−	0.222458i
$613$	−2.07069	+	19.7013i	−0.0836346	+	0.795730i	0.869653	+	0.493664i	$0.164343\pi$
$613$	−2.07069	+	19.7013i	−0.0836346	+	0.795730i	−0.953287	+	0.302066i	$0.902324\pi$
$614$	−2.43527	−	4.21800i	−0.0982793	−	0.170225i
$615$	5.84521	−	10.1242i	0.235702	−	0.408247i
$616$	11.7612	+	8.54505i	0.473874	+	0.344290i
$617$	−10.7275	−	33.0157i	−0.431871	−	1.32916i	−0.896259	−	0.443531i	$-0.853726\pi$
$617$	−10.7275	−	33.0157i	−0.431871	−	1.32916i	0.464388	−	0.885632i	$-0.346274\pi$
$618$	−5.99684	+	1.27467i	−0.241228	+	0.0512747i
$619$	41.2443			1.65775			0.828874	−	0.559435i	$-0.188982\pi$
$619$	41.2443			1.65775			0.828874	+	0.559435i	$0.188982\pi$
$620$	8.35850	−	0.364297i	0.335685	−	0.0146305i
$621$	−12.3547	+	21.3989i	−0.495776	+	0.858709i
$622$	−3.44500	−	3.82607i	−0.138132	−	0.153411i
$623$	25.1133	+	5.33799i	1.00614	+	0.213862i
$624$	4.30705	+	26.6902i	0.172420	+	1.06846i
$625$	−8.16392	−	14.1403i	−0.326557	−	0.565613i
$626$	1.52393	+	2.63952i	0.0609083	+	0.105496i
$627$	2.37303	−	22.5779i	0.0947697	−	0.901673i
$628$	−41.0645	−	18.2831i	−1.63865	−	0.729575i
$629$	−2.92370	−	1.30172i	−0.116576	−	0.0519029i
$630$	−0.462596	−	0.513764i	−0.0184302	−	0.0204689i
$631$	−27.6515	+	12.3113i	−1.10079	+	0.490104i	−0.875025	−	0.484078i	$-0.839155\pi$
$631$	−27.6515	+	12.3113i	−1.10079	+	0.490104i	−0.225766	+	0.974182i	$0.572488\pi$
$632$	−0.345412	−	0.383619i	−0.0137398	−	0.0152596i
$633$	−29.6825	−	6.30922i	−1.17977	−	0.250769i
$634$	−5.48673	−	2.44285i	−0.217906	−	0.0970180i
$635$	3.33861	+	0.709644i	0.132489	+	0.0281614i
$636$	−2.44852	−	7.53578i	−0.0970903	−	0.298813i
$637$	−1.75532	−	0.272777i	−0.0695484	−	0.0108078i
$638$	−5.30574	+	5.89262i	−0.210056	+	0.233291i
$639$	6.57732	−	1.39805i	0.260195	−	0.0553061i
$640$	−4.67910	−	3.39957i	−0.184958	−	0.134380i
$641$	−16.0901	−	17.8698i	−0.635519	−	0.705815i	0.336244	−	0.941775i	$-0.390843\pi$
$641$	−16.0901	−	17.8698i	−0.635519	−	0.705815i	−0.971763	+	0.235960i	$0.924177\pi$
$642$	3.25615	+	1.44973i	0.128510	+	0.0572164i
$643$	10.6386	+	4.73659i	0.419544	+	0.186793i	0.605640	−	0.795739i	$-0.292917\pi$
$643$	10.6386	+	4.73659i	0.419544	+	0.186793i	−0.186097	+	0.982531i	$0.559584\pi$
$644$	29.8847	+	21.7125i	1.17762	+	0.855593i
$645$	6.79977	−	11.7775i	0.267741	−	0.463740i
$646$	−0.973700	+	1.68650i	−0.0383097	+	0.0663544i
$647$	15.4080	−	6.86007i	0.605750	−	0.269697i	−0.0808575	−	0.996726i	$-0.525766\pi$
$647$	15.4080	−	6.86007i	0.605750	−	0.269697i	0.686607	+	0.727028i	$0.259099\pi$
$648$	7.45649	−	8.28127i	0.292919	−	0.325319i
$649$	−23.9483	+	73.7053i	−0.940054	+	2.89319i
$650$	−1.02560	+	3.87268i	−0.0402273	+	0.151899i
$651$	31.1261	+	5.21118i	1.21993	+	0.204242i
$652$	−13.5458	+	23.4621i	−0.530496	+	0.918846i
$653$	−3.04658	−	3.38357i	−0.119222	−	0.132409i	0.680579	−	0.732675i	$-0.261728\pi$
$653$	−3.04658	−	3.38357i	−0.119222	−	0.132409i	−0.799801	+	0.600265i	$0.795062\pi$
$654$	2.18980	+	6.73950i	0.0856278	+	0.263535i
$655$	−4.86109	−	3.53179i	−0.189939	−	0.137998i
$656$	13.1701	−	22.8113i	0.514207	−	0.890632i
$657$	13.9337			0.543606
$658$	3.93051	−	1.74997i	0.153227	−	0.0682211i
$659$	−9.40590	−	4.18778i	−0.366402	−	0.163133i	0.215273	−	0.976554i	$-0.430936\pi$
$659$	−9.40590	−	4.18778i	−0.366402	−	0.163133i	−0.581675	+	0.813421i	$0.697602\pi$
$660$	13.4435	−	9.76727i	0.523287	−	0.380191i
$661$	−8.71698	+	26.8281i	−0.339051	+	1.04349i	0.625641	+	0.780111i	$0.284838\pi$
$661$	−8.71698	+	26.8281i	−0.339051	+	1.04349i	−0.964692	+	0.263381i	$0.915162\pi$
$662$	0.383956	−	3.65310i	0.0149229	−	0.141982i
$663$	23.5535	+	15.1984i	0.914741	+	0.590259i
$664$	−0.860532	+	0.955718i	−0.0333951	+	0.0370890i
$665$	−3.98419	−	1.77388i	−0.154500	−	0.0687879i
$666$	0.271342	+	0.0576755i	0.0105143	+	0.00223488i
$667$	−27.4077	+	30.4393i	−1.06123	+	1.17862i
$668$	2.14120	+	20.3722i	0.0828456	+	0.788223i
$669$	−9.03859	−	1.92121i	−0.349452	−	0.0742783i
$670$	−0.607422	+	1.86945i	−0.0234668	+	0.0722233i
$671$	−2.56440	+	24.3986i	−0.0989976	+	0.941899i
$672$	−11.0139	−	12.2322i	−0.424871	−	0.471867i
$673$	24.0450	−	17.4697i	0.926868	−	0.673409i	−0.0183563	−	0.999832i	$-0.505843\pi$
$673$	24.0450	−	17.4697i	0.926868	−	0.673409i	0.945224	+	0.326423i	$0.105843\pi$
$674$	−0.498693	−	4.74475i	−0.0192089	−	0.182761i
$675$	−14.2424	+	6.34112i	−0.548190	+	0.244070i
$676$	−21.7243	+	12.7118i	−0.835549	+	0.488917i
$677$	−14.4433	−	25.0165i	−0.555100	−	0.961461i	−0.997896	−	0.0648387i	$-0.979347\pi$
$677$	−14.4433	−	25.0165i	−0.555100	−	0.961461i	0.442796	−	0.896622i	$-0.353987\pi$
$678$	−4.89188	+	2.17800i	−0.187871	+	0.0836458i
$679$	23.1326	−	25.6914i	0.887748	−	0.985944i
$680$	−2.83450	+	0.602492i	−0.108698	+	0.0231045i
$681$	27.4420			1.05158
$682$	2.00819	−	7.23912i	0.0768974	−	0.277200i
$683$	−0.620188	−	1.07420i	−0.0237308	−	0.0411030i	0.853916	−	0.520411i	$-0.174221\pi$
$683$	−0.620188	−	1.07420i	−0.0237308	−	0.0411030i	−0.877647	+	0.479308i	$0.840888\pi$
$684$	−1.58203	+	4.86899i	−0.0604905	+	0.186171i
$685$	0.0142299	+	0.0437951i	0.000543696	+	0.00167332i
$686$	−4.11138	+	1.83050i	−0.156973	+	0.0698889i
$687$	−24.0972			−0.919366
$688$	15.3209	−	26.5365i	0.584103	−	1.01170i
$689$	5.52458	−	4.50043i	0.210470	−	0.171453i
$690$	−2.28966	+	1.66353i	−0.0871658	+	0.0633297i
$691$	−42.2612	+	30.7046i	−1.60769	+	1.16806i	−0.737494	+	0.675354i	$0.763991\pi$
$691$	−42.2612	+	30.7046i	−1.60769	+	1.16806i	−0.870198	+	0.492703i	$0.836009\pi$
$692$	−11.9998	+	36.9317i	−0.456166	+	1.40393i
$693$	17.2002	−	7.65803i	0.653382	−	0.290904i
$694$	1.77072	+	1.96658i	0.0672156	+	0.0746505i
$695$	13.6127	+	2.89347i	0.516360	+	0.109756i
$696$	9.79097	−	7.11355i	0.371126	−	0.269639i
$697$	−8.43942	−	25.9739i	−0.319666	−	0.983830i
$698$	0.765130	−	0.849763i	0.0289606	−	0.0321640i
$699$	50.4015	+	22.4402i	1.90636	+	0.848765i
$700$	7.20220	+	22.1661i	0.272218	+	0.837800i
$701$	28.1986	+	31.3177i	1.06505	+	1.18285i	0.982499	+	0.186268i	$0.0596392\pi$
$701$	28.1986	+	31.3177i	1.06505	+	1.18285i	0.0825482	+	0.996587i	$0.473694\pi$
$702$	3.01838	+	1.14857i	0.113921	+	0.0433500i
$703$	1.71173	−	0.363840i	0.0645592	−	0.0137225i
$704$	28.1190	−	20.4296i	1.05977	−	0.769971i
$705$	−1.04506	−	9.94313i	−0.0393594	−	0.374480i
$706$	−0.0249131	−	0.0181004i	−0.000937616	−	0.000681218i
$707$	7.80082	−	13.5114i	0.293380	−	0.508149i
$708$	29.0914	−	50.3878i	1.09332	−	1.89369i
$709$	−1.94514	+	18.5068i	−0.0730512	+	0.695036i	0.895303	+	0.445457i	$0.146959\pi$
$709$	−1.94514	+	18.5068i	−0.0730512	+	0.695036i	−0.968354	+	0.249579i	$0.919708\pi$
$710$	−1.00135	−	0.212843i	−0.0375800	−	0.00798787i
$711$	−0.653942	+	0.139000i	−0.0245248	+	0.00521290i
$712$	−4.66401	+	8.07831i	−0.174791	+	0.302747i
$713$	10.3736	−	37.3950i	0.388496	−	1.40045i
$714$	−5.37685			−0.201224
$715$	12.5565	+	8.10236i	0.469585	+	0.303011i
$716$	−7.44669	−	1.58284i	−0.278296	−	0.0591536i
$717$	−28.9273	+	12.8793i	−1.08031	+	0.480985i
$718$	1.02487			0.0382477
$719$	−7.43734			−0.277366			−0.138683	−	0.990337i	$-0.544287\pi$
$719$	−7.43734			−0.277366			−0.138683	+	0.990337i	$0.544287\pi$
$720$	−3.30674	+	1.47226i	−0.123235	+	0.0548678i
$721$	−29.3024	−	13.0463i	−1.09128	−	0.485868i
$722$	0.390487	+	3.71524i	0.0145324	+	0.138267i
$723$	−27.0555	+	5.75082i	−1.00620	+	0.213875i
$724$	−33.9283	+	15.1058i	−1.26093	+	0.561404i
$725$	−25.2789	+	5.37319i	−0.938834	+	0.199555i
$726$	−2.83241	−	8.71727i	−0.105121	−	0.323528i
$727$	−0.0804595	−	0.765521i	−0.00298408	−	0.0283916i	0.992929	−	0.118714i	$-0.0378770\pi$
$727$	−0.0804595	−	0.765521i	−0.00298408	−	0.0283916i	−0.995913	+	0.0903220i	$0.971210\pi$
$728$	4.43052	−	8.75837i	0.164206	−	0.324607i
$729$	2.34573	+	7.21943i	0.0868790	+	0.267386i
$730$	−1.93791	−	0.862814i	−0.0717253	−	0.0319342i
$731$	−9.81762	−	30.2155i	−0.363118	−	1.11756i
$732$	5.69162	−	17.5170i	0.210368	−	0.647447i
$733$	0.375739	−	3.57492i	0.0138782	−	0.132043i	−0.985389	−	0.170319i	$-0.945520\pi$
$733$	0.375739	−	3.57492i	0.0138782	−	0.132043i	0.999267	+	0.0382766i	$0.0121868\pi$
$734$	3.16941	+	3.51998i	0.116985	+	0.129925i
$735$	−0.0827650	−	0.787456i	−0.00305283	−	0.0290458i
$736$	−16.3747	+	11.8969i	−0.603579	+	0.438526i
$737$	−43.3091	−	31.4659i	−1.59531	−	1.15906i
$738$	1.18361	+	2.05008i	0.0435693	+	0.0754643i
$739$	9.70672			0.357067			0.178534	−	0.983934i	$-0.442865\pi$
$739$	9.70672			0.357067			0.178534	+	0.983934i	$0.442865\pi$
$740$	1.03628	+	0.752898i	0.0380942	+	0.0276771i
$741$	−15.3041	+	0.846766i	−0.562212	+	0.0311067i
$742$	−0.422367	+	1.29991i	−0.0155056	+	0.0477213i
$743$	−8.37120	+	14.4993i	−0.307110	+	0.531929i	−0.977729	−	0.209872i	$-0.932695\pi$
$743$	−8.37120	+	14.4993i	−0.307110	+	0.531929i	0.670619	+	0.741802i	$0.266028\pi$
$744$	−5.29527	+	10.1702i	−0.194134	+	0.372858i
$745$	4.56202	+	7.90165i	0.167140	+	0.289494i
$746$	−1.73180	+	5.32992i	−0.0634056	+	0.195142i
$747$	0.514691	+	1.58406i	0.0188316	+	0.0579576i
$748$	4.05779	−	38.6073i	0.148367	−	1.41162i
$749$	9.32394	+	16.1495i	0.340689	+	0.590091i
$750$	−3.81594			−0.139339
$751$	0.590471	−	5.61796i	0.0215466	−	0.205002i	−0.978452	−	0.206473i	$-0.933801\pi$
$751$	0.590471	−	5.61796i	0.0215466	−	0.205002i	0.999999	+	0.00147067i	$0.000468130\pi$
$752$	−2.35468	−	22.4033i	−0.0858665	−	0.816965i
$753$	22.1865	+	9.87805i	0.808519	+	0.359976i
$754$	4.49831	+	2.90264i	0.163819	+	0.105708i
$755$	1.62683	−	15.4783i	0.0592064	−	0.563311i
$756$	18.3779	−	3.90634i	0.668396	−	0.142072i
$757$	4.38171	+	13.4855i	0.159256	+	0.490140i	0.998567	−	0.0535116i	$-0.0170414\pi$
$757$	4.38171	+	13.4855i	0.159256	+	0.490140i	−0.839311	+	0.543651i	$0.817041\pi$
$758$	4.24199	−	3.08199i	0.154076	−	0.111943i
$759$	−23.8182	−	73.3048i	−0.864545	−	2.66080i
$760$	1.06026	−	1.17754i	0.0384596	−	0.0427137i
$761$	25.2106	−	18.3165i	0.913882	−	0.663974i	−0.0281116	−	0.999605i	$-0.508949\pi$
$761$	25.2106	−	18.3165i	0.913882	−	0.663974i	0.941994	+	0.335631i	$0.108949\pi$
$762$	−1.53964	+	1.70994i	−0.0557752	+	0.0619447i
$763$	−11.4567	+	35.2600i	−0.414759	+	1.27650i
$764$	22.4218	+	16.2904i	0.811191	+	0.589365i
$765$	−1.15975	+	3.56933i	−0.0419307	+	0.129049i
$766$	−4.42176	−	1.96870i	−0.159765	−	0.0711319i
$767$	51.7029	+	8.03463i	1.86689	+	0.290114i
$768$	−21.0623	+	9.37754i	−0.760020	+	0.338383i
$769$	19.3067	+	33.4401i	0.696216	+	1.20588i	0.969769	+	0.244024i	$0.0784676\pi$
$769$	19.3067	+	33.4401i	0.696216	+	1.20588i	−0.273553	+	0.961857i	$0.588199\pi$
$770$	−2.86642			−0.103299
$771$	−5.41272	+	51.4986i	−0.194934	+	1.85468i
$772$	−11.7327	−	2.49385i	−0.422268	−	0.0897558i
$773$	32.9517	−	7.00409i	1.18519	−	0.251920i	0.427182	−	0.904166i	$-0.359506\pi$
$773$	32.9517	−	7.00409i	1.18519	−	0.251920i	0.758007	+	0.652246i	$0.226173\pi$
$774$	1.37690	+	2.38486i	0.0494917	+	0.0857222i
$775$	19.1635	−	15.2409i	0.688372	−	0.547470i
$776$	6.28022	+	10.8777i	0.225447	+	0.390485i
$777$	3.23307	+	3.59069i	0.115986	+	0.128815i
$778$	−2.76565	+	3.07157i	−0.0991533	+	0.110121i
$779$	12.0814	+	8.77763i	0.432860	+	0.314491i
$780$	−7.95619	−	7.90998i	−0.284877	−	0.283223i
$781$	13.9400	−	24.1449i	0.498814	−	0.863971i
$782$	−0.691110	+	6.57548i	−0.0247141	+	0.235139i
$783$	2.17769	+	20.7193i	0.0778242	+	0.740448i
$784$	−0.186482	−	1.77425i	−0.00666006	−	0.0633662i
$785$	17.6245	−	3.74620i	0.629045	−	0.133708i
$786$	3.70043	−	1.64754i	0.131990	−	0.0587658i
$787$	4.90895	−	15.1082i	0.174985	−	0.538549i	−0.824648	−	0.565647i	$-0.808627\pi$
$787$	4.90895	−	15.1082i	0.174985	−	0.538549i	0.999633	+	0.0270978i	$0.00862655\pi$
$788$	28.0211	−	31.1206i	0.998210	−	1.10862i
$789$	5.59857	−	4.06760i	0.199314	−	0.144810i
$790$	0.0995580	+	0.0211617i	0.00354211	+	0.000752900i
$791$	−27.4034	−	5.82477i	−0.974353	−	0.207105i
$792$	0.715038	+	6.80313i	0.0254078	+	0.241739i
$793$	16.5383	−	0.915053i	0.587294	−	0.0324945i
$794$	−1.67104	−	1.85587i	−0.0593029	−	0.0658625i
$795$	2.56954	+	1.86688i	0.0911322	+	0.0662114i
$796$	−7.12241	+	21.9205i	−0.252447	+	0.776952i
$797$	−0.800444	−	7.61572i	−0.0283532	−	0.269763i	−0.999509	−	0.0313186i	$-0.990029\pi$
$797$	−0.800444	−	7.61572i	−0.0283532	−	0.269763i	0.971156	−	0.238444i	$-0.0766373\pi$
$798$	2.37856	−	1.72812i	0.0842001	−	0.0611749i
$799$	−18.8958	−	13.7286i	−0.668487	−	0.485684i
$800$	−12.7705			−0.451504
$801$	6.04043	+	10.4623i	0.213428	+	0.369668i
$802$	0.0856436	−	0.814844i	0.00302418	−	0.0287732i
$803$	38.6570	−	42.9329i	1.36418	−	1.51507i
$804$	26.8927	+	29.8674i	0.948433	+	1.05334i
$805$	−14.8070			−0.521879
$806$	−5.04112	−	0.559885i	−0.177566	−	0.0197211i
$807$	48.5247			1.70815
$808$	3.79291	+	4.21245i	0.133434	+	0.148193i
$809$	0.483575	−	0.537065i	0.0170016	−	0.0188822i	−0.734584	−	0.678518i	$-0.762623\pi$
$809$	0.483575	−	0.537065i	0.0170016	−	0.0188822i	0.751586	+	0.659636i	$0.229289\pi$
$810$	−0.229669	+	2.18516i	−0.00806976	+	0.0767786i
$811$	−9.11257	−	15.7834i	−0.319986	−	0.554232i	0.660499	−	0.750827i	$-0.270345\pi$
$811$	−9.11257	−	15.7834i	−0.319986	−	0.554232i	−0.980485	+	0.196595i	$0.937011\pi$
$812$	31.1452			1.09298
$813$	12.2534	+	8.90262i	0.429746	+	0.312228i
$814$	0.930507	−	0.676053i	0.0326142	−	0.0236956i
$815$	−1.13513	−	10.8001i	−0.0397619	−	0.378309i
$816$	−8.69942	+	26.7741i	−0.304540	+	0.937279i
$817$	14.0543	+	10.2111i	0.491698	+	0.357240i
$818$	3.98165	+	4.42207i	0.139215	+	0.154614i
$819$	−6.95438	−	10.6408i	−0.243006	−	0.371820i
$820$	1.14256	+	10.8707i	0.0398999	+	0.379623i
$821$	41.2629	+	8.77069i	1.44008	+	0.306099i	0.860765	−	0.509002i	$-0.169985\pi$
$821$	41.2629	+	8.77069i	1.44008	+	0.306099i	0.579318	+	0.815101i	$0.303319\pi$
$822$	−0.0303648	−	0.00645423i	−0.00105909	−	0.000225117i
$823$	−15.0319	+	10.9213i	−0.523978	+	0.380692i	−0.818100	−	0.575075i	$-0.804973\pi$
$823$	−15.0319	+	10.9213i	−0.523978	+	0.380692i	0.294122	+	0.955768i	$0.404973\pi$
$824$	7.79784	−	8.66038i	0.271651	−	0.301699i
$825$	15.0280	−	46.2513i	0.523206	−	1.61026i
$826$	−9.16876	+	4.08219i	−0.319022	+	0.142038i
$827$	−6.90036	+	1.46672i	−0.239949	+	0.0510027i	−0.326316	−	0.945261i	$-0.605807\pi$
$827$	−6.90036	+	1.46672i	−0.239949	+	0.0510027i	0.0863673	+	0.996263i	$0.472474\pi$
$828$	1.81688	+	17.2864i	0.0631408	+	0.600744i
$829$	−1.21550	−	11.5647i	−0.0422160	−	0.401658i	−0.995142	−	0.0984541i	$-0.968610\pi$
$829$	−1.21550	−	11.5647i	−0.0422160	−	0.401658i	0.952926	−	0.303204i	$-0.0980564\pi$
$830$	0.0265055	−	0.252183i	0.000920018	−	0.00875339i
$831$	−28.3468	+	49.0981i	−0.983341	+	1.70320i
$832$	−16.6415	−	16.5448i	−0.576940	−	0.573589i
$833$	−1.49648	−	1.08725i	−0.0518498	−	0.0376711i
$834$	−6.27766	+	6.97205i	−0.217378	+	0.241422i
$835$	−5.49427	−	6.10200i	−0.190137	−	0.211168i
$836$	10.6134	+	18.3829i	0.367071	+	0.635785i
$837$	−10.6041	−	16.6480i	−0.366532	−	0.575438i
$838$	−1.76962	−	3.06507i	−0.0611304	−	0.105881i
$839$	30.6556	−	6.51604i	1.05835	−	0.224959i	0.354315	−	0.935126i	$-0.384714\pi$
$839$	30.6556	−	6.51604i	1.05835	−	0.224959i	0.704033	+	0.710168i	$0.251381\pi$
$840$	4.27935	+	0.909604i	0.147652	+	0.0313843i
$841$	−0.578581	+	5.50483i	−0.0199511	+	0.189822i
$842$	3.43467			0.118367
$843$	6.48707	+	11.2359i	0.223426	+	0.386986i
$844$	25.9204	−	11.5405i	0.892215	−	0.397240i
$845$	4.04992	−	9.24079i	0.139322	−	0.317893i
$846$	1.84947	+	0.823438i	0.0635861	+	0.0283104i
$847$	14.8187	−	45.6074i	0.509178	−	1.56709i
$848$	5.78955	+	4.20636i	0.198814	+	0.144447i
$849$	6.01761	−	18.5203i	0.206524	−	0.635615i
$850$	−2.79136	+	3.10011i	−0.0957427	+	0.106333i
$851$	4.80670	−	3.49227i	0.164771	−	0.119713i
$852$	−14.0058	+	15.5550i	−0.479830	+	0.532905i
$853$	4.40071	+	13.5440i	0.150677	+	0.463737i	0.997697	−	0.0678238i	$-0.0216056\pi$
$853$	4.40071	+	13.5440i	0.150677	+	0.463737i	−0.847020	+	0.531561i	$0.821606\pi$
$854$	−2.57038	+	1.86749i	−0.0879565	+	0.0639041i
$855$	−0.634149	−	1.95171i	−0.0216874	−	0.0667470i
$856$	−6.62712	+	1.40864i	−0.226510	+	0.0481462i
$857$	−2.41889	+	23.0142i	−0.0826277	+	0.786150i	0.872232	+	0.489092i	$0.162672\pi$
$857$	−2.41889	+	23.0142i	−0.0826277	+	0.786150i	−0.954860	+	0.297057i	$0.903995\pi$
$858$	−8.96267	+	4.59964i	−0.305980	+	0.157029i
$859$	2.92625	+	1.30285i	0.0998423	+	0.0444526i	0.456050	−	0.889954i	$-0.349264\pi$
$859$	2.92625	+	1.30285i	0.0998423	+	0.0444526i	−0.356208	+	0.934407i	$0.615930\pi$
$860$	1.32915	+	12.6460i	0.0453235	+	0.431225i
$861$	−4.30989	+	41.0058i	−0.146881	+	1.39747i
$862$	1.75616			0.0598152
$863$	23.9624	+	41.5041i	0.815689	+	1.41281i	0.908832	+	0.417162i	$0.136975\pi$
$863$	23.9624	+	41.5041i	0.815689	+	1.41281i	−0.0931432	+	0.995653i	$0.529691\pi$
$864$	−1.07609	+	10.2383i	−0.0366094	+	0.348315i
$865$	−4.81007	−	14.8039i	−0.163547	−	0.503347i
$866$	0.569427	−	1.75251i	0.0193499	−	0.0595529i
$867$	−3.00691	−	5.20812i	−0.102120	−	0.176877i
$868$	−26.4088	+	13.1644i	−0.896374	+	0.446830i
$869$	−1.38597	+	2.40058i	−0.0470159	+	0.0814340i
$870$	−0.737386	+	2.26944i	−0.0249997	+	0.0769413i
$871$	−16.3148	+	32.2514i	−0.552805	+	1.09280i
$872$	−10.8974	−	7.91745i	−0.369034	−	0.268119i
$873$	16.2672			0.550561
$874$	−1.80764	−	3.13092i	−0.0611442	−	0.105905i
$875$	−16.1515	−	11.7348i	−0.546022	−	0.396708i
$876$	−35.0895	+	25.4940i	−1.18556	+	0.861362i
$877$	−1.09232	−	10.3928i	−0.0368851	−	0.350938i	−0.997363	−	0.0725806i	$-0.976877\pi$
$877$	−1.09232	−	10.3928i	−0.0368851	−	0.350938i	0.960477	−	0.278358i	$-0.0897901\pi$
$878$	−5.02697	−	5.58301i	−0.169652	−	0.188418i
$879$	3.12080	−	29.6924i	0.105262	−	1.00150i
$880$	−4.63770	+	14.2734i	−0.156337	+	0.481155i
$881$	5.87821	+	18.0913i	0.198042	+	0.609510i	0.999928	+	0.0120328i	$0.00383026\pi$
$881$	5.87821	+	18.0913i	0.198042	+	0.609510i	−0.801886	+	0.597477i	$0.796170\pi$
$882$	0.146471	+	0.0652130i	0.00493193	+	0.00219584i
$883$	−10.6069	−	32.6447i	−0.356951	−	1.09858i	−0.954869	−	0.297026i	$-0.904005\pi$
$883$	−10.6069	−	32.6447i	−0.356951	−	1.09858i	0.597918	−	0.801557i	$-0.295995\pi$
$884$	−26.1695	+	1.44794i	−0.880175	+	0.0486993i
$885$	2.43784	+	23.1945i	0.0819471	+	0.779674i
$886$	−1.77228	−	5.45452i	−0.0595410	−	0.183248i
$887$	−44.0299	+	9.35884i	−1.47838	+	0.314239i	−0.875354	−	0.483483i	$-0.839372\pi$
$887$	−44.0299	+	9.35884i	−1.47838	+	0.314239i	−0.603025	+	0.797722i	$0.706038\pi$
$888$	−1.60371	+	0.714017i	−0.0538169	+	0.0239608i
$889$	−11.7752	+	2.50289i	−0.394926	+	0.0839441i
$890$	−0.192251	−	1.82915i	−0.00644427	−	0.0613132i
$891$	−54.6653	−	24.3386i	−1.83136	−	0.815372i
$892$	7.89297	−	3.51418i	0.264276	−	0.117663i
$893$	12.7713			0.427377
$894$	−6.15083			−0.205715
$895$	2.78782	−	1.24122i	0.0931866	−	0.0414893i
$896$	19.9531	+	4.24116i	0.666586	+	0.141687i
$897$	−46.2982	+	23.7603i	−1.54585	+	0.793332i
$898$	2.14559			0.0715993
$899$	−11.4564	−	30.6487i	−0.382092	−	1.02219i
$900$	−5.48343	+	9.49757i	−0.182781	+	0.316586i
$901$	7.25775	−	1.54268i	0.241791	−	0.0513942i
$902$	9.60049	+	2.04065i	0.319661	+	0.0679461i
$903$	−5.01371	+	47.7023i	−0.166846	+	1.58743i
$904$	5.08933	−	8.81499i	0.169269	−	0.293182i
$905$	7.44351	−	12.8925i	0.247431	−	0.428562i
$906$	8.48812	+	6.16698i	0.281999	+	0.204884i
$907$	−0.173792	−	1.65352i	−0.00577067	−	0.0549042i	0.991258	−	0.131941i	$-0.0421209\pi$
$907$	−0.173792	−	1.65352i	−0.00577067	−	0.0549042i	−0.997028	+	0.0770365i	$0.975454\pi$
$908$	−20.7581	+	15.0817i	−0.688882	+	0.500502i
$909$	7.18081	−	1.52633i	0.238173	−	0.0506251i
$910$	0.308312	+	1.91057i	0.0102204	+	0.0633347i
$911$	−30.0274	−	33.3488i	−0.994853	−	1.10490i	−0.994483	−	0.104896i	$-0.966549\pi$
$911$	−30.0274	−	33.3488i	−0.994853	−	1.10490i	−0.000369508	−	1.00000i	$-0.500118\pi$
$912$	−4.75684	−	14.6400i	−0.157515	−	0.484780i
$913$	6.30876	+	2.80884i	0.208790	+	0.0929591i
$914$	−0.0228591	+	0.0253876i	−0.000756112	+	0.000839748i
$915$	2.28145	+	7.02159i	0.0754225	+	0.232127i
$916$	18.2280	−	13.2434i	0.602270	−	0.437575i
$917$	20.7291	+	4.40612i	0.684537	+	0.145503i
$918$	2.25021	+	2.49911i	0.0742680	+	0.0824829i
$919$	40.0633	−	17.8373i	1.32157	−	0.588399i	0.379925	−	0.925017i	$-0.375950\pi$
$919$	40.0633	−	17.8373i	1.32157	−	0.588399i	0.941641	+	0.336618i	$0.109283\pi$
$920$	1.66242	−	5.11640i	0.0548084	−	0.168683i
$921$	32.2942	−	23.4631i	1.06413	−	0.773137i
$922$	−1.73180	+	1.25822i	−0.0570336	+	0.0414374i
$923$	−17.5928	−	6.69449i	−0.579072	−	0.220352i
$924$	−29.3039	+	50.7559i	−0.964028	+	1.66975i
$925$	3.74870			0.123256
$926$	−5.15779	+	2.29639i	−0.169495	+	0.0754642i
$927$	−4.66395	−	14.3542i	−0.153184	−	0.471453i
$928$	−5.27348	+	16.2301i	−0.173110	+	0.532779i
$929$	13.6309	+	23.6095i	0.447217	+	0.774602i	0.998204	−	0.0599117i	$-0.0190819\pi$
$929$	13.6309	+	23.6095i	0.447217	+	0.774602i	−0.550987	+	0.834514i	$0.685749\pi$
$930$	−0.333996	−	2.23600i	−0.0109522	−	0.0733212i
$931$	1.01144			0.0331486
$932$	−50.4582	+	10.7252i	−1.65281	+	0.351316i
$933$	28.2346	−	31.3577i	0.924358	−	1.02660i
$934$	4.15139	−	1.84832i	0.135838	−	0.0604788i
$935$	7.78037	+	13.4760i	0.254445	+	0.440712i
$936$	4.45761	−	1.20834i	0.145701	−	0.0394958i
$937$	−44.5533	+	19.8364i	−1.45549	+	0.648027i	−0.973612	−	0.228211i	$-0.926713\pi$
$937$	−44.5533	+	19.8364i	−1.45549	+	0.648027i	−0.481880	+	0.876237i	$0.660046\pi$
$938$	−0.724676	−	6.89483i	−0.0236615	−	0.225124i
$939$	−20.2089	+	14.6826i	−0.659492	+	0.479149i
$940$	6.25509	+	6.94698i	0.204019	+	0.226586i
$941$	0.0210048	−	0.199847i	0.000684737	−	0.00651483i	−0.994174	−	0.107785i	$-0.965624\pi$
$941$	0.0210048	−	0.199847i	0.000684737	−	0.00651483i	0.994859	+	0.101270i	$0.0322908\pi$
$942$	−3.75354	+	11.5522i	−0.122297	+	0.376391i
$943$	49.5930	+	10.5413i	1.61497	+	0.343273i
$944$	5.49281	+	52.2606i	0.178776	+	1.70094i
$945$	−5.03938	+	5.59680i	−0.163931	+	0.182064i
$946$	11.1683	+	2.37390i	0.363113	+	0.0771820i
$947$	46.3479	+	20.6354i	1.50611	+	0.670561i	0.983317	−	0.181901i	$-0.0582250\pi$
$947$	46.3479	+	20.6354i	1.50611	+	0.670561i	0.522789	+	0.852462i	$0.324892\pi$
$948$	1.39251	−	1.54654i	0.0452266	−	0.0502292i
$949$	−32.7742	−	21.1483i	−1.06389	−	0.686503i
$950$	0.238433	−	2.26854i	0.00773580	−	0.0736012i
$951$	15.2110	−	46.8146i	0.493250	−	1.51807i
$952$	8.26858	−	6.00748i	0.267986	−	0.194703i
$953$	29.4396	+	13.1074i	0.953643	+	0.424589i	0.823759	−	0.566940i	$-0.191873\pi$
$953$	29.4396	+	13.1074i	0.953643	+	0.424589i	0.129884	+	0.991529i	$0.458540\pi$
$954$	−0.587539	+	0.261589i	−0.0190223	+	0.00846927i
$955$	−11.1093			−0.359490
$956$	14.8034	−	25.6403i	0.478777	−	0.829266i
$957$	−52.5755	−	38.1983i	−1.69952	−	1.23478i
$958$	1.67249	+	5.14739i	0.0540357	+	0.166305i
$959$	−0.108675	−	0.120696i	−0.00350931	−	0.00389748i
$960$	5.22986	−	9.05838i	0.168793	−	0.292358i
$961$	22.6687	+	21.1454i	0.731249	+	0.682111i
$962$	−0.550697	−	0.547498i	−0.0177552	−	0.0176520i
$963$	−2.71151	+	8.34516i	−0.0873771	+	0.268919i
$964$	17.3052	−	19.2193i	0.557362	−	0.619014i
$965$	4.39236	−	1.95561i	0.141395	−	0.0629532i
$966$	4.99096	−	8.64459i	0.160581	−	0.278135i
$967$	−25.4745	+	44.1231i	−0.819204	+	1.41890i	0.0870660	+	0.996203i	$0.472251\pi$
$967$	−25.4745	+	44.1231i	−0.819204	+	1.41890i	−0.906270	+	0.422700i	$0.861082\pi$
$968$	14.0954	+	10.2409i	0.453043	+	0.329155i
$969$	−14.5806	−	6.49172i	−0.468398	−	0.208544i
$970$	−2.26245	−	1.00731i	−0.0726430	−	0.0323427i
$971$	37.0723	+	41.1729i	1.18971	+	1.32130i	0.935154	+	0.354243i	$0.115261\pi$
$971$	37.0723	+	41.1729i	1.18971	+	1.32130i	0.254552	+	0.967059i	$0.418072\pi$
$972$	19.6856	+	14.3025i	0.631417	+	0.458752i
$973$	−48.0116	+	10.2052i	−1.53918	+	0.327163i
$974$	0.655135	−	0.727601i	0.0209919	−	0.0233138i
$975$	−32.4444	−	5.04186i	−1.03905	−	0.161469i
$976$	5.14045	+	15.8207i	0.164542	+	0.506408i
$977$	10.5454	+	2.24150i	0.337378	+	0.0717120i	0.373486	−	0.927636i	$-0.378163\pi$
$977$	10.5454	+	2.24150i	0.337378	+	0.0717120i	−0.0361074	+	0.999348i	$0.511496\pi$
$978$	6.68788	+	2.97763i	0.213855	+	0.0952143i
$979$	48.9950	+	10.4142i	1.56589	+	0.332840i
$980$	0.495379	+	0.550174i	0.0158243	+	0.0175747i
$981$	−15.9369	+	7.09558i	−0.508827	+	0.226544i
$982$	−7.27334	−	8.07786i	−0.232102	−	0.257775i
$983$	−9.42247	−	4.19516i	−0.300530	−	0.133805i	0.250932	−	0.968005i	$-0.419263\pi$
$983$	−9.42247	−	4.19516i	−0.300530	−	0.133805i	−0.551462	+	0.834200i	$0.685930\pi$
$984$	−13.6852	−	6.09306i	−0.436269	−	0.194240i
$985$	−1.75463	+	16.6941i	−0.0559070	+	0.531920i
$986$	2.78729	+	4.82773i	0.0887655	+	0.153746i
$987$	17.6311	+	30.5380i	0.561204	+	0.972034i
$988$	11.1112	−	9.05141i	0.353495	−	0.287964i
$989$	57.6918	+	12.2628i	1.83449	+	0.389934i
$990$	−0.902506	−	1.00233i	−0.0286835	−	0.0318563i
$991$	18.1241	−	31.3918i	0.575730	−	0.997193i	−0.420232	−	0.907417i	$-0.638051\pi$
$991$	18.1241	−	31.3918i	0.575730	−	0.997193i	0.995962	−	0.0897768i	$-0.0286154\pi$
$992$	−2.38860	−	15.9909i	−0.0758382	−	0.507712i
$993$	30.1049			0.955352
$994$	3.53172	−	0.750691i	0.112019	−	0.0238105i
$995$	−2.85498	−	8.78671i	−0.0905088	−	0.278558i
$996$	−4.19444	−	3.04744i	−0.132906	−	0.0965618i
$997$	−18.7827	+	32.5326i	−0.594854	+	1.03032i	0.398713	+	0.917076i	$0.369457\pi$
$997$	−18.7827	+	32.5326i	−0.594854	+	1.03032i	−0.993567	+	0.113242i	$0.963876\pi$
$998$	−0.670710	−	1.16170i	−0.0212310	−	0.0367731i
$999$	0.315880	−	3.00540i	0.00999401	−	0.0950867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bk.a.9.20	yes	280
13.3	even	3		403.2.bj.a.133.16	yes	280
31.7	even	15		403.2.bj.a.100.16	✓	280
403.224	even	15	inner	403.2.bk.a.224.20	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bj.a.100.16	✓	280	31.7	even	15
403.2.bj.a.133.16	yes	280	13.3	even	3
403.2.bk.a.9.20	yes	280	1.1	even	1	trivial
403.2.bk.a.224.20	yes	280	403.224	even	15	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bk (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.169063 + 0.187763i) q^{2} +(-1.38560 + 1.53887i) q^{3} +(0.202384 - 1.92556i) q^{4} +(0.388050 + 0.672122i) q^{5} -0.523196 q^{6} +(-2.21450 - 1.60893i) q^{7} +(0.804576 - 0.584559i) q^{8} +(-0.134633 - 1.28095i) q^{9} +O(q^{10})\)	\(q+(0.169063 + 0.187763i) q^{2} +(-1.38560 + 1.53887i) q^{3} +(0.202384 - 1.92556i) q^{4} +(0.388050 + 0.672122i) q^{5} -0.523196 q^{6} +(-2.21450 - 1.60893i) q^{7} +(0.804576 - 0.584559i) q^{8} +(-0.134633 - 1.28095i) q^{9} +(-0.0605950 + 0.186492i) q^{10} +(-4.32041 - 3.13896i) q^{11} +(2.68275 + 2.97950i) q^{12} +(-1.62752 + 3.21732i) q^{13} +(-0.0722919 - 0.687812i) q^{14} +(-1.57199 - 0.334137i) q^{15} +(-3.54192 - 0.752859i) q^{16} +(-3.03741 + 2.20681i) q^{17} +(0.217753 - 0.241840i) q^{18} +(0.634389 - 1.95245i) q^{19} +(1.37274 - 0.611185i) q^{20} +(5.54435 - 1.17849i) q^{21} +(-0.141039 - 1.34189i) q^{22} +(-0.728560 - 6.93179i) q^{23} +(-0.215264 + 2.04810i) q^{24} +(2.19883 - 3.80849i) q^{25} +(-0.879247 + 0.238341i) q^{26} +(-2.86806 - 2.08377i) q^{27} +(-3.54627 + 3.93853i) q^{28} +(-3.93225 - 4.36721i) q^{29} +(-0.203026 - 0.351652i) q^{30} +(5.18019 + 2.04099i) q^{31} +(-1.45196 - 2.51487i) q^{32} +(10.8168 - 2.29919i) q^{33} +(-0.927868 - 0.197224i) q^{34} +(0.222060 - 2.11276i) q^{35} -2.49379 q^{36} +(0.426214 + 0.738225i) q^{37} +(0.473849 - 0.210971i) q^{38} +(-2.69594 - 6.96247i) q^{39} +(0.705111 + 0.313936i) q^{40} +(-2.24785 + 6.91817i) q^{41} +(1.15862 + 0.841786i) q^{42} +(-2.61494 + 8.04795i) q^{43} +(-6.91863 + 7.68392i) q^{44} +(0.808710 - 0.587562i) q^{45} +(1.17836 - 1.30870i) q^{46} +(1.92241 + 5.91656i) q^{47} +(6.06625 - 4.40739i) q^{48} +(0.152247 + 0.468568i) q^{49} +(1.08683 - 0.231014i) q^{50} +(0.812657 - 7.73192i) q^{51} +(5.86575 + 3.78502i) q^{52} +(-1.80544 - 0.803833i) q^{53} +(-0.0936270 - 0.890802i) q^{54} +(0.433231 - 4.12192i) q^{55} -2.72225 q^{56} +(2.12555 + 3.68156i) q^{57} +(0.155204 - 1.47666i) q^{58} +(-4.48443 - 13.8017i) q^{59} +(-0.961545 + 2.95933i) q^{60} +(-2.29696 - 3.97846i) q^{61} +(0.492554 + 1.31770i) q^{62} +(-1.76281 + 3.05328i) q^{63} +(-2.01121 + 6.18986i) q^{64} +(-2.79400 + 0.154589i) q^{65} +(2.26042 + 1.64229i) q^{66} +10.0243 q^{67} +(3.63460 + 6.29532i) q^{68} +(11.6766 + 8.48355i) q^{69} +(0.434241 - 0.315494i) q^{70} +(0.545709 + 5.19208i) q^{71} +(-0.857113 - 0.951921i) q^{72} +(-1.13080 + 10.7588i) q^{73} +(-0.0665544 + 0.204833i) q^{74} +(2.81405 + 8.66077i) q^{75} +(-3.63116 - 1.61670i) q^{76} +(4.51719 + 13.9025i) q^{77} +(0.851512 - 1.68329i) q^{78} +(-0.0542565 - 0.516216i) q^{79} +(-0.868430 - 2.67275i) q^{80} +(10.9602 - 2.32966i) q^{81} +(-1.67900 + 0.747541i) q^{82} +(-1.26488 + 0.268860i) q^{83} +(-1.14716 - 10.9145i) q^{84} +(-2.66191 - 1.18516i) q^{85} +(-1.95319 + 0.869618i) q^{86} +12.1691 q^{87} -5.31101 q^{88} +(-8.56861 + 3.81499i) q^{89} +(0.247045 + 0.0525111i) q^{90} +(8.78060 - 4.50621i) q^{91} -13.4950 q^{92} +(-10.3185 + 5.14362i) q^{93} +(-0.785905 + 1.36123i) q^{94} +(1.55846 - 0.331261i) q^{95} +(5.88188 + 1.25023i) q^{96} +(-1.32017 + 12.5606i) q^{97} +(-0.0622405 + 0.107804i) q^{98} +(-3.43918 + 5.95684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9	\( 280 q - 3 q^{2} - 9 q^{3} + 29 q^{4} - 8 q^{5} - 10 q^{6} - 13 q^{7} - 29 q^{8} + 24 q^{9} - 9 q^{10} - 6 q^{11} - 50 q^{12} - 6 q^{13} - 21 q^{15} + 23 q^{16} + 3 q^{17} - 15 q^{18} - 9 q^{19} + 60 q^{20} - 34 q^{21} + 41 q^{22} - 12 q^{23} - 89 q^{24} - 112 q^{25} + 39 q^{26} + 48 q^{27} + 66 q^{28} - 11 q^{29} + 24 q^{30} - 22 q^{31} + q^{32} - 37 q^{33} - 49 q^{34} + 41 q^{35} + 134 q^{36} + 17 q^{37} - 23 q^{38} + 10 q^{39} + 31 q^{40} + q^{41} - 71 q^{42} - 7 q^{43} - 42 q^{44} - 13 q^{45} + 21 q^{46} - 20 q^{47} - 3 q^{48} - 69 q^{49} - 42 q^{50} - 71 q^{51} - 140 q^{52} - 8 q^{53} - 149 q^{54} + 5 q^{55} - 126 q^{56} + 21 q^{57} + 79 q^{58} + 77 q^{59} + 2 q^{60} + 53 q^{61} + 72 q^{62} + 17 q^{63} - 91 q^{64} - 25 q^{65} - 62 q^{66} - 14 q^{67} + 83 q^{68} - 31 q^{69} + 134 q^{70} + 32 q^{71} - 70 q^{72} - 31 q^{73} + 51 q^{74} + 79 q^{75} + 98 q^{76} - 80 q^{77} - 141 q^{78} - 142 q^{79} + 6 q^{80} + 66 q^{81} - 48 q^{82} + 94 q^{83} + 130 q^{84} + 90 q^{85} - 34 q^{86} + 22 q^{87} - 122 q^{88} - 15 q^{89} + 43 q^{90} + 56 q^{91} - 294 q^{92} - 52 q^{93} - 57 q^{94} + 94 q^{95} + 24 q^{96} + 46 q^{97} + 73 q^{98} + 12 q^{99}+O(q^{100}) \) 280 * q - 3 * q^2 - 9 * q^3 + 29 * q^4 - 8 * q^5 - 10 * q^6 - 13 * q^7 - 29 * q^8 + 24 * q^9 - 9 * q^10 - 6 * q^11 - 50 * q^12 - 6 * q^13 - 21 * q^15 + 23 * q^16 + 3 * q^17 - 15 * q^18 - 9 * q^19 + 60 * q^20 - 34 * q^21 + 41 * q^22 - 12 * q^23 - 89 * q^24 - 112 * q^25 + 39 * q^26 + 48 * q^27 + 66 * q^28 - 11 * q^29 + 24 * q^30 - 22 * q^31 + q^32 - 37 * q^33 - 49 * q^34 + 41 * q^35 + 134 * q^36 + 17 * q^37 - 23 * q^38 + 10 * q^39 + 31 * q^40 + q^41 - 71 * q^42 - 7 * q^43 - 42 * q^44 - 13 * q^45 + 21 * q^46 - 20 * q^47 - 3 * q^48 - 69 * q^49 - 42 * q^50 - 71 * q^51 - 140 * q^52 - 8 * q^53 - 149 * q^54 + 5 * q^55 - 126 * q^56 + 21 * q^57 + 79 * q^58 + 77 * q^59 + 2 * q^60 + 53 * q^61 + 72 * q^62 + 17 * q^63 - 91 * q^64 - 25 * q^65 - 62 * q^66 - 14 * q^67 + 83 * q^68 - 31 * q^69 + 134 * q^70 + 32 * q^71 - 70 * q^72 - 31 * q^73 + 51 * q^74 + 79 * q^75 + 98 * q^76 - 80 * q^77 - 141 * q^78 - 142 * q^79 + 6 * q^80 + 66 * q^81 - 48 * q^82 + 94 * q^83 + 130 * q^84 + 90 * q^85 - 34 * q^86 + 22 * q^87 - 122 * q^88 - 15 * q^89 + 43 * q^90 + 56 * q^91 - 294 * q^92 - 52 * q^93 - 57 * q^94 + 94 * q^95 + 24 * q^96 + 46 * q^97 + 73 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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