LMFDB - Embedded newform 125.2.h.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	125.9
Dual form			125.2.h.a.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48947 - 1.17145i) q^{2} +(0.834394 - 0.0524956i) q^{3} +(3.55029 + 4.29156i) q^{4} +(-2.14236 + 0.640526i) q^{5} +(-2.13869 - 0.846768i) q^{6} +(-3.54615 + 1.15221i) q^{7} +(-2.44251 - 9.51294i) q^{8} +(-2.28289 + 0.288396i) q^{9} +O(q^{10})$	\(q+(-2.48947 - 1.17145i) q^{2} +(0.834394 - 0.0524956i) q^{3} +(3.55029 + 4.29156i) q^{4} +(-2.14236 + 0.640526i) q^{5} +(-2.13869 - 0.846768i) q^{6} +(-3.54615 + 1.15221i) q^{7} +(-2.44251 - 9.51294i) q^{8} +(-2.28289 + 0.288396i) q^{9} +(6.08369 + 0.915114i) q^{10} +(-0.844939 + 1.79559i) q^{11} +(3.18763 + 3.39448i) q^{12} +(0.376351 + 2.97913i) q^{13} +(10.1778 + 1.28575i) q^{14} +(-1.75395 + 0.646916i) q^{15} +(-2.97610 + 15.6012i) q^{16} +(-0.733873 - 0.607112i) q^{17} +(6.02101 + 1.95634i) q^{18} +(0.187107 - 2.97398i) q^{19} +(-10.3549 - 6.92004i) q^{20} +(-2.89840 + 1.14756i) q^{21} +(4.20689 - 3.48024i) q^{22} +(1.60955 + 2.92776i) q^{23} +(-2.53740 - 7.80932i) q^{24} +(4.17945 - 2.74448i) q^{25} +(2.55299 - 7.85731i) q^{26} +(-4.35339 + 0.830454i) q^{27} +(-17.5347 - 11.1278i) q^{28} +(-0.988467 + 1.55757i) q^{29} +(5.12424 + 0.444199i) q^{30} +(-0.895184 + 1.08209i) q^{31} +(14.1392 - 19.4609i) q^{32} +(-0.610752 + 1.54258i) q^{33} +(1.11575 + 2.37108i) q^{34} +(6.85913 - 4.73986i) q^{35} +(-9.34257 - 8.77326i) q^{36} +(1.54420 + 0.294572i) q^{37} +(-3.94967 + 7.18443i) q^{38} +(0.470416 + 2.46601i) q^{39} +(11.3260 + 18.8157i) q^{40} +(-5.14368 - 2.82776i) q^{41} +(8.55979 + 0.538536i) q^{42} +(-3.49232 - 4.80676i) q^{43} +(-10.7056 + 2.74874i) q^{44} +(4.70605 - 2.08010i) q^{45} +(-0.577184 - 9.17407i) q^{46} +(-0.557210 + 2.17019i) q^{47} +(-1.66424 + 13.1738i) q^{48} +(5.58447 - 4.05735i) q^{49} +(-13.6196 + 1.93625i) q^{50} +(-0.644210 - 0.468046i) q^{51} +(-11.4489 + 12.1919i) q^{52} +(4.50755 + 11.3848i) q^{53} +(11.8105 + 3.03241i) q^{54} +(0.660048 - 4.38801i) q^{55} +(19.6224 + 30.9200i) q^{56} -2.49129i q^{57} +(4.28538 - 2.71958i) q^{58} +(-0.524881 + 0.492896i) q^{59} +(-9.00332 - 5.23046i) q^{60} +(8.57968 - 4.71672i) q^{61} +(3.49615 - 1.64516i) q^{62} +(7.76316 - 3.65307i) q^{63} +(-30.1605 + 16.5809i) q^{64} +(-2.71449 - 6.14131i) q^{65} +(3.32751 - 3.12474i) q^{66} +(-5.95228 + 3.77743i) q^{67} -5.30489i q^{68} +(1.49669 + 2.35841i) q^{69} +(-22.6281 + 3.76458i) q^{70} +(-10.4725 - 2.68889i) q^{71} +(8.31946 + 21.0125i) q^{72} +(-1.75437 + 1.86822i) q^{73} +(-3.49916 - 2.54229i) q^{74} +(3.34324 - 2.50938i) q^{75} +(13.4273 - 9.75550i) q^{76} +(0.927380 - 7.34097i) q^{77} +(1.71773 - 6.69012i) q^{78} +(-0.262574 - 4.17350i) q^{79} +(-3.61711 - 35.3298i) q^{80} +(3.09737 - 0.795268i) q^{81} +(9.49242 + 13.0652i) q^{82} +(6.25479 + 0.393518i) q^{83} +(-15.2150 - 8.36451i) q^{84} +(1.96109 + 0.830592i) q^{85} +(3.06311 + 16.0574i) q^{86} +(-0.743005 + 1.35152i) q^{87} +(19.1451 + 3.65212i) q^{88} +(5.99145 + 5.62634i) q^{89} +(-14.1523 - 0.334592i) q^{90} +(-4.76719 - 10.1308i) q^{91} +(-6.85030 + 17.3019i) q^{92} +(-0.690131 + 0.949884i) q^{93} +(3.92943 - 4.74987i) q^{94} +(1.50406 + 6.49119i) q^{95} +(10.7760 - 16.9803i) q^{96} +(-0.114066 - 0.0723885i) q^{97} +(-18.6554 + 3.55870i) q^{98} +(1.41106 - 4.34280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{50}\right)$

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 $

$2$	−2.48947	−	1.17145i	−1.76032	−	0.828343i	−0.978901	−	0.204334i	$-0.934497\pi$
$2$	−2.48947	−	1.17145i	−1.76032	−	0.828343i	−0.781417	−	0.624009i	$-0.785503\pi$
$3$	0.834394	−	0.0524956i	0.481738	−	0.0303084i	0.179935	−	0.983679i	$-0.442411\pi$
$3$	0.834394	−	0.0524956i	0.481738	−	0.0303084i	0.301803	+	0.953370i	$0.402411\pi$
$4$	3.55029	+	4.29156i	1.77514	+	2.14578i
$5$	−2.14236	+	0.640526i	−0.958095	+	0.286452i
$5$	−2.14236	+	0.640526i	−0.958095	+	0.286452i
$6$	−2.13869	−	0.846768i	−0.873118	−	0.345692i
$7$	−3.54615	+	1.15221i	−1.34032	+	0.435496i	−0.889425	−	0.457081i	$-0.848895\pi$
$7$	−3.54615	+	1.15221i	−1.34032	+	0.435496i	−0.450894	+	0.892577i	$0.648895\pi$
$8$	−2.44251	−	9.51294i	−0.863557	−	3.36333i
$9$	−2.28289	+	0.288396i	−0.760962	+	0.0961319i
$10$	6.08369	+	0.915114i	1.92383	+	0.289385i
$11$	−0.844939	+	1.79559i	−0.254759	+	0.541390i	−0.990766	−	0.135584i	$-0.956709\pi$
$11$	−0.844939	+	1.79559i	−0.254759	+	0.541390i	0.736007	+	0.676974i	$0.236709\pi$
$12$	3.18763	+	3.39448i	0.920189	+	0.979902i
$13$	0.376351	+	2.97913i	0.104381	+	0.826261i	0.954197	+	0.299181i	$0.0967133\pi$
$13$	0.376351	+	2.97913i	0.104381	+	0.826261i	−0.849816	+	0.527080i	$0.823287\pi$
$14$	10.1778	+	1.28575i	2.72013	+	0.343632i
$15$	−1.75395	+	0.646916i	−0.452869	+	0.167033i
$16$	−2.97610	+	15.6012i	−0.744024	+	3.90031i
$17$	−0.733873	−	0.607112i	−0.177990	−	0.147246i	0.544163	−	0.838980i	$-0.316847\pi$
$17$	−0.733873	−	0.607112i	−0.177990	−	0.147246i	−0.722153	+	0.691733i	$0.756847\pi$
$18$	6.02101	+	1.95634i	1.41917	+	0.461115i
$19$	0.187107	−	2.97398i	0.0429252	−	0.682277i	−0.916451	−	0.400147i	$-0.868959\pi$
$19$	0.187107	−	2.97398i	0.0429252	−	0.682277i	0.959376	−	0.282130i	$-0.0910410\pi$
$20$	−10.3549	−	6.92004i	−2.31542	−	1.54737i
$21$	−2.89840	+	1.14756i	−0.632483	+	0.250418i
$22$	4.20689	−	3.48024i	0.896913	−	0.741991i
$23$	1.60955	+	2.92776i	0.335614	+	0.610480i	0.989234	−	0.146343i	$-0.0467503\pi$
$23$	1.60955	+	2.92776i	0.335614	+	0.610480i	−0.653620	+	0.756823i	$0.726750\pi$
$24$	−2.53740	−	7.80932i	−0.517945	−	1.59407i
$25$	4.17945	−	2.74448i	0.835891	−	0.548896i
$26$	2.55299	−	7.85731i	0.500683	−	1.54095i
$27$	−4.35339	+	0.830454i	−0.837811	+	0.159821i
$28$	−17.5347	−	11.1278i	−3.31374	−	2.10296i
$29$	−0.988467	+	1.55757i	−0.183554	+	0.289234i	−0.923627	−	0.383291i	$-0.874791\pi$
$29$	−0.988467	+	1.55757i	−0.183554	+	0.289234i	0.740074	+	0.672526i	$0.234791\pi$
$30$	5.12424	+	0.444199i	0.935553	+	0.0810993i
$31$	−0.895184	+	1.08209i	−0.160780	+	0.194349i	−0.844751	−	0.535160i	$-0.820251\pi$
$31$	−0.895184	+	1.08209i	−0.160780	+	0.194349i	0.683971	+	0.729509i	$0.260251\pi$
$32$	14.1392	−	19.4609i	2.49947	−	3.44023i
$33$	−0.610752	+	1.54258i	−0.106318	+	0.268529i
$34$	1.11575	+	2.37108i	0.191349	+	0.406638i
$35$	6.85913	−	4.73986i	1.15940	−	0.801183i
$36$	−9.34257	−	8.77326i	−1.55710	−	1.46221i
$37$	1.54420	+	0.294572i	0.253865	+	0.0484273i	0.312743	−	0.949838i	$-0.398752\pi$
$37$	1.54420	+	0.294572i	0.253865	+	0.0484273i	−0.0588778	+	0.998265i	$0.518752\pi$
$38$	−3.94967	+	7.18443i	−0.640722	+	1.16547i
$39$	0.470416	+	2.46601i	0.0753269	+	0.394877i
$40$	11.3260	+	18.8157i	1.79080	+	2.97502i
$41$	−5.14368	−	2.82776i	−0.803307	−	0.441622i	0.0265157	−	0.999648i	$-0.491559\pi$
$41$	−5.14368	−	2.82776i	−0.803307	−	0.441622i	−0.829823	+	0.558026i	$0.811559\pi$
$42$	8.55979	+	0.538536i	1.32080	+	0.0830979i
$43$	−3.49232	−	4.80676i	−0.532574	−	0.733025i	0.454946	−	0.890519i	$-0.349658\pi$
$43$	−3.49232	−	4.80676i	−0.532574	−	0.733025i	−0.987520	+	0.157494i	$0.949658\pi$
$44$	−10.7056	+	2.74874i	−1.61394	+	0.414389i
$45$	4.70605	−	2.08010i	0.701536	−	0.310082i
$46$	−0.577184	−	9.17407i	−0.0851011	−	1.35264i
$47$	−0.557210	+	2.17019i	−0.0812775	+	0.316555i	−0.996202	−	0.0870696i	$-0.972250\pi$
$47$	−0.557210	+	2.17019i	−0.0812775	+	0.316555i	0.914925	+	0.403624i	$0.132250\pi$
$48$	−1.66424	+	13.1738i	−0.240212	+	1.90148i
$49$	5.58447	−	4.05735i	0.797781	−	0.579622i
$50$	−13.6196	+	1.93625i	−1.92611	+	0.273827i
$51$	−0.644210	−	0.468046i	−0.0902075	−	0.0655396i
$52$	−11.4489	+	12.1919i	−1.58768	+	1.69071i
$53$	4.50755	+	11.3848i	0.619159	+	1.56382i	0.812673	+	0.582720i	$0.198012\pi$
$53$	4.50755	+	11.3848i	0.619159	+	1.56382i	−0.193514	+	0.981098i	$0.561988\pi$
$54$	11.8105	+	3.03241i	1.60720	+	0.412659i
$55$	0.660048	−	4.38801i	0.0890008	−	0.591679i
$56$	19.6224	+	30.9200i	2.62216	+	4.13186i
$57$		−	2.49129i		−	0.329980i
$58$	4.28538	−	2.71958i	0.562698	−	0.357099i
$59$	−0.524881	+	0.492896i	−0.0683337	+	0.0641696i	−0.717962	−	0.696083i	$-0.754925\pi$
$59$	−0.524881	+	0.492896i	−0.0683337	+	0.0641696i	0.649628	+	0.760252i	$0.274925\pi$
$60$	−9.00332	−	5.23046i	−1.16232	−	0.675249i
$61$	8.57968	−	4.71672i	1.09852	−	0.603914i	0.173880	−	0.984767i	$-0.444369\pi$
$61$	8.57968	−	4.71672i	1.09852	−	0.603914i	0.924636	+	0.380853i	$0.124369\pi$
$62$	3.49615	−	1.64516i	0.444011	−	0.208936i
$63$	7.76316	−	3.65307i	0.978067	−	0.460243i
$64$	−30.1605	+	16.5809i	−3.77006	+	2.07261i
$65$	−2.71449	−	6.14131i	−0.336691	−	0.761736i
$66$	3.32751	−	3.12474i	0.409588	−	0.384629i
$67$	−5.95228	+	3.77743i	−0.727186	+	0.461486i	−0.847192	−	0.531287i	$-0.821709\pi$
$67$	−5.95228	+	3.77743i	−0.727186	+	0.461486i	0.120006	+	0.992773i	$0.461709\pi$
$68$		−	5.30489i		−	0.643312i
$69$	1.49669	+	2.35841i	0.180181	+	0.283919i
$70$	−22.6281	+	3.76458i	−2.70457	+	0.449954i
$71$	−10.4725	−	2.68889i	−1.24286	−	0.319112i	−0.430673	−	0.902508i	$-0.641724\pi$
$71$	−10.4725	−	2.68889i	−1.24286	−	0.319112i	−0.812188	+	0.583396i	$0.801724\pi$
$72$	8.31946	+	21.0125i	0.980457	+	2.47635i
$73$	−1.75437	+	1.86822i	−0.205334	+	0.218658i	−0.823390	−	0.567475i	$-0.807920\pi$
$73$	−1.75437	+	1.86822i	−0.205334	+	0.218658i	0.618057	+	0.786134i	$0.287920\pi$
$74$	−3.49916	−	2.54229i	−0.406769	−	0.295535i
$75$	3.34324	−	2.50938i	0.386044	−	0.289758i
$76$	13.4273	−	9.75550i	1.54022	−	1.11903i
$77$	0.927380	−	7.34097i	0.105685	−	0.836581i
$78$	1.71773	−	6.69012i	0.194495	−	0.757506i
$79$	−0.262574	−	4.17350i	−0.0295419	−	0.469556i	−0.984790	−	0.173749i	$-0.944412\pi$
$79$	−0.262574	−	4.17350i	−0.0295419	−	0.469556i	0.955248	−	0.295806i	$-0.0955883\pi$
$80$	−3.61711	−	35.3298i	−0.404406	−	3.94999i
$81$	3.09737	−	0.795268i	0.344152	−	0.0883631i
$82$	9.49242	+	13.0652i	1.04826	+	1.44281i
$83$	6.25479	+	0.393518i	0.686552	+	0.0431942i	0.402235	−	0.915536i	$-0.368233\pi$
$83$	6.25479	+	0.393518i	0.686552	+	0.0431942i	0.284317	+	0.958730i	$0.408233\pi$
$84$	−15.2150	−	8.36451i	−1.66009	−	0.912643i
$85$	1.96109	+	0.830592i	0.212711	+	0.0900903i
$86$	3.06311	+	16.0574i	0.330303	+	1.73151i
$87$	−0.743005	+	1.35152i	−0.0796585	+	0.144898i
$88$	19.1451	+	3.65212i	2.04087	+	0.389317i
$89$	5.99145	+	5.62634i	0.635092	+	0.596391i	0.933731	−	0.357975i	$-0.116533\pi$
$89$	5.99145	+	5.62634i	0.635092	+	0.596391i	−0.298639	+	0.954366i	$0.596533\pi$
$90$	−14.1523	−	0.334592i	−1.49178	−	0.0352691i
$91$	−4.76719	−	10.1308i	−0.499737	−	1.06200i
$92$	−6.85030	+	17.3019i	−0.714193	+	1.80385i
$93$	−0.690131	+	0.949884i	−0.0715633	+	0.0984984i
$94$	3.92943	−	4.74987i	0.405290	−	0.489912i
$95$	1.50406	+	6.49119i	0.154313	+	0.665982i
$96$	10.7760	−	16.9803i	1.09982	−	1.73304i
$97$	−0.114066	−	0.0723885i	−0.0115816	−	0.00734994i	0.530023	−	0.847983i	$-0.322183\pi$
$97$	−0.114066	−	0.0723885i	−0.0115816	−	0.00734994i	−0.541605	+	0.840633i	$0.682183\pi$
$98$	−18.6554	+	3.55870i	−1.88448	+	0.359483i
$99$	1.41106	−	4.34280i	0.141817	−	0.436467i
$100$	26.6164	+	8.19269i	2.66164	+	0.819269i
$101$	4.21153	+	12.9617i	0.419063	+	1.28974i	0.908566	+	0.417741i	$0.137178\pi$
$101$	4.21153	+	12.9617i	0.419063	+	1.28974i	−0.489504	+	0.872001i	$0.662822\pi$
$102$	1.05544	+	1.91985i	0.104505	+	0.190093i
$103$	−11.5605	+	9.56366i	−1.13909	+	0.942335i	−0.998858	−	0.0477837i	$-0.984784\pi$
$103$	−11.5605	+	9.56366i	−1.13909	+	0.942335i	−0.140230	+	0.990119i	$0.544784\pi$
$104$	27.4210	−	10.8567i	2.68885	−	1.06459i
$105$	5.47439	−	4.31499i	0.534246	−	0.421100i
$106$	2.11534	−	33.6224i	0.205460	−	3.26569i
$107$	−11.8571	−	3.85259i	−1.14627	−	0.372444i	−0.326530	−	0.945187i	$-0.605879\pi$
$107$	−11.8571	−	3.85259i	−1.14627	−	0.372444i	−0.819735	+	0.572743i	$0.805879\pi$
$108$	−19.0198	−	15.7345i	−1.83018	−	1.51405i
$109$	−1.84250	+	9.65874i	−0.176480	+	0.925140i	0.778315	+	0.627874i	$0.216075\pi$
$109$	−1.84250	+	9.65874i	−0.176480	+	0.925140i	−0.954795	+	0.297266i	$0.903925\pi$
$110$	−6.78351	+	10.1506i	−0.646783	+	0.967819i
$111$	1.30394	+	0.164725i	0.123764	+	0.0156350i
$112$	−7.42229	−	58.7535i	−0.701341	−	5.55168i
$113$	6.12012	+	6.51726i	0.575732	+	0.613092i	0.949247	−	0.314532i	$-0.101848\pi$
$113$	6.12012	+	6.51726i	0.575732	+	0.613092i	−0.373515	+	0.927624i	$0.621848\pi$
$114$	−2.91843	+	6.20199i	−0.273336	+	0.580869i
$115$	−5.32355	−	5.24137i	−0.496423	−	0.488760i
$116$	−10.1938	+	1.28777i	−0.946468	+	0.119567i
$117$	−1.71833	−	6.69247i	−0.158860	−	0.618719i
$118$	1.88408	−	0.612174i	0.173443	−	0.0563552i
$119$	3.30195	+	1.30733i	0.302689	+	0.119843i
$120$	10.4381	+	15.1051i	0.952865	+	1.37890i
$121$	4.50146	+	5.44132i	0.409223	+	0.494666i
$122$	−26.8843	+	1.69141i	−2.43399	+	0.153133i
$123$	−4.44030	−	2.08945i	−0.400368	−	0.188399i
$124$	−7.82202			−0.702438
$125$	−7.19600	+	8.55672i	−0.643630	+	0.765337i
$126$	−23.6055			−2.10295
$127$	3.44609	+	1.62161i	0.305791	+	0.143894i	0.572552	−	0.819868i	$-0.305953\pi$
$127$	3.44609	+	1.62161i	0.305791	+	0.143894i	−0.266761	+	0.963763i	$0.585953\pi$
$128$	46.4922	−	2.92504i	4.10937	−	0.258540i
$129$	−3.16630	−	3.82741i	−0.278778	−	0.336984i
$130$	−0.436637	+	18.4685i	−0.0382956	+	1.61979i
$131$	0.414269	+	0.164021i	0.0361948	+	0.0143306i	0.386152	−	0.922435i	$-0.373804\pi$
$131$	0.414269	+	0.164021i	0.0361948	+	0.0143306i	−0.349957	+	0.936766i	$0.613804\pi$
$132$	−8.78843	+	2.85554i	−0.764935	+	0.248542i
$133$	2.76315	+	10.7618i	0.239595	+	0.933163i
$134$	19.2431	−	2.43097i	1.66235	−	0.210003i
$135$	8.79463	−	4.56760i	0.756921	−	0.393116i
$136$	−3.98293	+	8.46416i	−0.341534	+	0.725796i
$137$	7.04298	+	7.50002i	0.601723	+	0.640770i	0.955651	−	0.294503i	$-0.0951541\pi$
$137$	7.04298	+	7.50002i	0.601723	+	0.640770i	−0.353928	+	0.935273i	$0.615154\pi$
$138$	−0.963198	−	7.62449i	−0.0819928	−	0.649040i
$139$	−17.5980	−	2.22315i	−1.49265	−	0.188565i	−0.663745	−	0.747959i	$-0.731034\pi$
$139$	−17.5980	−	2.22315i	−1.49265	−	0.188565i	−0.828902	+	0.559394i	$0.811034\pi$
$140$	44.6933	+	12.6085i	3.77727	+	1.06561i
$141$	−0.351008	+	1.84005i	−0.0295602	+	0.154960i
$142$	22.9211	+	18.9620i	1.92350	+	1.59125i
$143$	−5.66727	−	1.84141i	−0.473921	−	0.153986i
$144$	2.29476	−	36.4742i	0.191230	−	3.03951i
$145$	1.11999	−	3.97003i	0.0930101	−	0.329693i
$146$	6.55598	−	2.59570i	0.542577	−	0.214821i
$147$	4.44666	−	3.67859i	0.366754	−	0.303405i
$148$	4.21818	+	7.67285i	0.346732	+	0.630704i
$149$	0.572091	+	1.76071i	0.0468675	+	0.144243i	0.971752	−	0.236006i	$-0.0758384\pi$
$149$	0.572091	+	1.76071i	0.0468675	+	0.144243i	−0.924884	+	0.380249i	$0.875838\pi$
$150$	−11.2625	+	2.33057i	−0.919580	+	0.190290i
$151$	−4.76878	+	14.6768i	−0.388078	+	1.19438i	0.546145	+	0.837691i	$0.316095\pi$
$151$	−4.76878	+	14.6768i	−0.388078	+	1.19438i	−0.934223	+	0.356690i	$0.883905\pi$
$152$	−28.7483	+	5.48403i	−2.33179	+	0.444813i
$153$	1.85044	+	1.17432i	0.149599	+	0.0949384i
$154$	−10.9083	+	17.1887i	−0.879015	+	1.38511i
$155$	1.22470	−	2.89162i	0.0983705	−	0.232261i
$156$	−8.91292	+	10.7739i	−0.713604	+	0.862600i
$157$	1.02364	−	1.40891i	0.0816950	−	0.112443i	−0.766214	−	0.642586i	$-0.777862\pi$
$157$	1.02364	−	1.40891i	0.0816950	−	0.112443i	0.847909	+	0.530142i	$0.177862\pi$
$158$	−4.23539	+	10.6974i	−0.336950	+	0.851038i
$159$	4.35872	+	9.26276i	0.345669	+	0.734584i
$160$	−17.8260	+	50.7488i	−1.40927	+	4.01205i
$161$	−9.08111	−	8.52773i	−0.715692	−	0.672080i
$162$	−8.64241	−	1.64863i	−0.679012	−	0.129528i
$163$	12.1578	−	22.1150i	0.952272	−	1.73218i	0.342704	−	0.939443i	$-0.388657\pi$
$163$	12.1578	−	22.1150i	0.952272	−	1.73218i	0.609568	−	0.792734i	$-0.291343\pi$
$164$	−6.12603	−	32.1138i	−0.478363	−	2.50767i
$165$	0.320389	−	3.69598i	0.0249423	−	0.287731i
$166$	−15.1101	−	8.30684i	−1.17277	−	0.644736i
$167$	22.8467	+	1.43740i	1.76793	+	0.111229i	0.913116	−	0.407699i	$-0.133669\pi$
$167$	22.8467	+	1.43740i	1.76793	+	0.111229i	0.854818	+	0.518928i	$0.173669\pi$
$168$	17.9960	+	24.7694i	1.38842	+	1.91100i
$169$	3.85803	−	0.990574i	0.296772	−	0.0761980i
$170$	−3.90908	−	4.36506i	−0.299813	−	0.334785i
$171$	0.430538	+	6.84321i	0.0329241	+	0.523313i
$172$	8.22979	−	32.0529i	0.627515	−	2.44401i
$173$	3.16455	−	25.0500i	0.240596	−	1.90451i	−0.158086	−	0.987425i	$-0.550532\pi$
$173$	3.16455	−	25.0500i	0.240596	−	1.90451i	0.398682	−	0.917089i	$-0.369468\pi$
$174$	3.43293	−	2.49417i	0.260250	−	0.189083i
$175$	−11.6587	+	14.5480i	−0.881318	+	1.09972i
$176$	−25.4988	−	18.5259i	−1.92204	−	1.39645i
$177$	−0.412083	+	0.438824i	−0.0309740	+	0.0329840i
$178$	−8.32450	−	21.0253i	−0.623948	−	1.57591i
$179$	−13.7746	−	3.53672i	−1.02956	−	0.264347i	−0.304123	−	0.952633i	$-0.598364\pi$
$179$	−13.7746	−	3.53672i	−1.02956	−	0.264347i	−0.725440	+	0.688286i	$0.758364\pi$
$180$	25.6347	+	12.8114i	1.91070	+	0.954903i
$181$	6.68093	+	10.5275i	0.496590	+	0.782500i	0.996501	−	0.0835761i	$-0.0266342\pi$
$181$	6.68093	+	10.5275i	0.496590	+	0.782500i	−0.499912	+	0.866076i	$0.666634\pi$
$182$			30.8048i			2.28340i
$183$	6.91123	−	4.38600i	0.510893	−	0.324223i
$184$	23.9203	−	22.4626i	1.76343	−	1.65597i
$185$	−3.49692	+	0.358019i	−0.257099	+	0.0263221i
$186$	2.83080	−	1.55625i	0.207565	−	0.114110i
$187$	1.71020	−	0.804759i	0.125062	−	0.0588498i
$188$	−11.2918	+	5.31350i	−0.823537	+	0.387527i
$189$	14.4809	−	7.96096i	1.05333	−	0.579075i
$190$	3.85983	−	17.9215i	0.280021	−	1.30016i
$191$	−12.8024	+	12.0223i	−0.926350	+	0.869901i	−0.991780	−	0.127957i	$-0.959158\pi$
$191$	−12.8024	+	12.0223i	−0.926350	+	0.869901i	0.0654298	+	0.997857i	$0.479158\pi$
$192$	−24.2953	+	15.4183i	−1.75336	+	1.11272i
$193$			17.8885i			1.28764i	0.765176	+	0.643821i	$0.222652\pi$
$193$			17.8885i			1.28764i	−0.765176	+	0.643821i	$0.777348\pi$
$194$	0.199164	+	0.313832i	0.0142991	+	0.0225318i
$195$	−2.58735	−	4.98178i	−0.185284	−	0.356752i
$196$	37.2389	+	9.56132i	2.65992	+	0.682951i
$197$	−8.86547	−	22.3916i	−0.631639	−	1.59534i	−0.793532	−	0.608529i	$-0.791760\pi$
$197$	−8.86547	−	22.3916i	−0.631639	−	1.59534i	0.161893	−	0.986808i	$-0.448240\pi$
$198$	−8.60017	+	9.15825i	−0.611187	+	0.650849i
$199$	−15.2456	−	11.0766i	−1.08073	−	0.785199i	−0.102923	−	0.994689i	$-0.532819\pi$
$199$	−15.2456	−	11.0766i	−1.08073	−	0.785199i	−0.977811	+	0.209491i	$0.932819\pi$
$200$	−36.3164	−	33.0555i	−2.56796	−	2.33738i
$201$	−4.76825	+	3.46433i	−0.336326	+	0.244355i
$202$	4.69963	−	37.2014i	0.330665	−	2.61748i
$203$	1.71059	−	6.66232i	0.120060	−	0.467603i
$204$	−0.278483	−	4.42637i	−0.0194977	−	0.309908i
$205$	12.8309	+	2.76344i	0.896148	+	0.193007i
$206$	39.9828	−	10.2658i	2.78573	−	0.715255i
$207$	−4.51877	−	6.21956i	−0.314076	−	0.432289i
$208$	−47.5981	−	2.99462i	−3.30034	−	0.207640i
$209$	5.18194	+	2.84879i	0.358442	+	0.197055i
$210$	−18.6831	+	4.32902i	−1.28926	+	0.298731i
$211$	−0.858861	−	4.50231i	−0.0591264	−	0.309952i	0.940422	−	0.340010i	$-0.110431\pi$
$211$	−0.858861	−	4.50231i	−0.0591264	−	0.309952i	−0.999548	+	0.0300588i	$0.990431\pi$
$212$	−32.8553	+	59.7636i	−2.25651	+	4.10458i
$213$	−8.87938	−	1.69383i	−0.608405	−	0.116059i
$214$	25.0046	+	23.4809i	1.70928	+	1.60512i
$215$	10.5607	+	8.06092i	0.720232	+	0.549750i
$216$	18.5333	+	39.3852i	1.26103	+	2.67982i
$217$	1.92766	−	4.86870i	0.130858	−	0.330509i
$218$	15.9016	−	21.8867i	1.07699	−	1.48235i
$219$	−1.36576	+	1.65093i	−0.0922898	+	0.111559i
$220$	21.1748	−	12.7461i	1.42760	−	0.859339i
$221$	1.53247	−	2.41479i	0.103085	−	0.162436i
$222$	−3.05313	−	1.93758i	−0.204913	−	0.130042i
$223$	2.51035	−	0.478874i	0.168105	−	0.0320678i	−0.102641	−	0.994718i	$-0.532729\pi$
$223$	2.51035	−	0.478874i	0.168105	−	0.0320678i	0.270747	+	0.962651i	$0.412729\pi$
$224$	−27.7165	+	85.3026i	−1.85189	+	5.69952i
$225$	−8.74972	+	7.47067i	−0.583315	+	0.498045i
$226$	−7.60115	−	23.3939i	−0.505621	−	1.55614i
$227$	−0.176563	−	0.321167i	−0.0117189	−	0.0213166i	0.870382	−	0.492376i	$-0.163872\pi$
$227$	−0.176563	−	0.321167i	−0.0117189	−	0.0213166i	−0.882101	+	0.471060i	$0.843872\pi$
$228$	10.6915	−	8.84481i	0.708064	−	0.585762i
$229$	−24.7872	+	9.81396i	−1.63799	+	0.648525i	−0.993262	−	0.115891i	$-0.963028\pi$
$229$	−24.7872	+	9.81396i	−1.63799	+	0.648525i	−0.644724	+	0.764415i	$0.723028\pi$
$230$	7.11277	+	19.2845i	0.469002	+	1.27158i
$231$	0.388432	−	6.17395i	0.0255569	−	0.406216i
$232$	17.2314	+	5.59884i	1.13130	+	0.367582i
$233$	0.969070	+	0.801685i	0.0634859	+	0.0525201i	0.668626	−	0.743599i	$-0.266883\pi$
$233$	0.969070	+	0.801685i	0.0634859	+	0.0525201i	−0.605140	+	0.796119i	$0.706883\pi$
$234$	−3.56218	+	18.6736i	−0.232867	+	1.22073i
$235$	−0.196315	−	5.00625i	−0.0128062	−	0.326572i
$236$	−3.97877	−	0.502636i	−0.258996	−	0.0327188i
$237$	−0.438181	−	3.46856i	−0.0284629	−	0.225307i
$238$	−6.68861	−	7.12264i	−0.433558	−	0.461692i
$239$	−10.7160	+	22.7728i	−0.693163	+	1.47305i	0.179008	+	0.983848i	$0.442711\pi$
$239$	−10.7160	+	22.7728i	−0.693163	+	1.47305i	−0.872172	+	0.489200i	$0.837289\pi$
$240$	−4.87276	−	29.2891i	−0.314535	−	1.89060i
$241$	25.2367	−	3.18814i	1.62564	−	0.205366i	0.740956	−	0.671554i	$-0.234373\pi$
$241$	25.2367	−	3.18814i	1.62564	−	0.205366i	0.884686	+	0.466188i	$0.154373\pi$
$242$	−4.83196	−	18.8192i	−0.310610	−	1.20975i
$243$	15.1876	−	4.93476i	0.974287	−	0.316565i
$244$	50.7025	+	20.0745i	3.24589	+	1.28514i
$245$	−9.36513	+	12.2693i	−0.598316	+	0.783859i
$246$	8.60629	+	10.4032i	0.548717	+	0.663285i
$247$	8.93027	−	0.561845i	0.568219	−	0.0357493i
$248$	12.4804	+	5.87281i	0.792504	+	0.372924i
$249$	5.23962			0.332047
$250$	27.9380	−	12.8719i	1.76696	−	0.814089i
$251$	19.7336			1.24557			0.622786	−	0.782393i	$-0.286001\pi$
$251$	19.7336			1.24557			0.622786	+	0.782393i	$0.286001\pi$
$252$	43.2389	+	20.3467i	2.72379	+	1.28172i
$253$	−6.61702	+	0.416307i	−0.416008	+	0.0261730i
$254$	−6.67928	−	8.07386i	−0.419095	−	0.506599i
$255$	1.67993	+	0.590092i	0.105201	+	0.0369530i
$256$	−55.1658	−	21.8417i	−3.44786	−	1.36510i
$257$	−10.9942	+	3.57224i	−0.685800	+	0.222830i	−0.631133	−	0.775675i	$-0.717410\pi$
$257$	−10.9942	+	3.57224i	−0.685800	+	0.222830i	−0.0546671	+	0.998505i	$0.517410\pi$
$258$	3.39878	+	13.2374i	0.211599	+	0.824123i
$259$	−5.81538	+	0.734653i	−0.361350	+	0.0456491i
$260$	16.7186	−	33.4528i	1.03684	−	2.07466i
$261$	1.80736	−	3.84083i	0.111873	−	0.237742i
$262$	−0.839166	−	0.893621i	−0.0518438	−	0.0552081i
$263$	0.643186	+	5.09134i	0.0396606	+	0.313946i	0.999448	+	0.0332183i	$0.0105757\pi$
$263$	0.643186	+	5.09134i	0.0396606	+	0.313946i	−0.959788	+	0.280727i	$0.909424\pi$
$264$	16.1663	+	2.04227i	0.994965	+	0.125693i
$265$	−16.9490	−	21.5031i	−1.04117	−	1.32093i
$266$	5.72814	−	30.0279i	0.351214	−	1.84113i
$267$	5.29459	+	4.38006i	0.324024	+	0.268056i
$268$	−37.3434	−	12.1336i	−2.28111	−	0.741178i
$269$	1.64452	−	26.1389i	0.100268	−	1.59372i	−0.550758	−	0.834665i	$-0.685661\pi$
$269$	1.64452	−	26.1389i	0.100268	−	1.59372i	0.651027	−	0.759055i	$-0.274339\pi$
$270$	−27.2447	+	1.06837i	−1.65806	+	0.0650191i
$271$	−5.42488	+	2.14786i	−0.329538	+	0.130473i	−0.527067	−	0.849824i	$-0.676708\pi$
$271$	−5.42488	+	2.14786i	−0.329538	+	0.130473i	0.197529	+	0.980297i	$0.436708\pi$
$272$	11.6558	−	9.64251i	0.706736	−	0.584663i
$273$	−4.50954	−	8.20282i	−0.272930	−	0.496457i
$274$	−8.74735	−	26.9216i	−0.528447	−	1.62639i
$275$	1.39657	+	9.82349i	0.0842162	+	0.592379i
$276$	−4.80758	+	14.7962i	−0.289382	+	0.890627i
$277$	−17.2609	+	3.29268i	−1.03710	+	0.197838i	−0.677696	−	0.735342i	$-0.737021\pi$
$277$	−17.2609	+	3.29268i	−1.03710	+	0.197838i	−0.359408	+	0.933180i	$0.617021\pi$
$278$	41.2054	+	26.1498i	2.47134	+	1.56836i
$279$	1.73153	−	2.72846i	0.103664	−	0.163348i
$280$	−61.8435	−	53.6733i	−3.69586	−	3.20759i
$281$	−11.0827	+	13.3967i	−0.661140	+	0.799181i	−0.989370	−	0.145417i	$-0.953548\pi$
$281$	−11.0827	+	13.3967i	−0.661140	+	0.799181i	0.328231	+	0.944598i	$0.393548\pi$
$282$	3.02935	−	4.16954i	0.180395	−	0.248293i
$283$	−4.06682	+	10.2716i	−0.241747	+	0.610584i	−0.999100	−	0.0424223i	$-0.986493\pi$
$283$	−4.06682	+	10.2716i	−0.241747	+	0.610584i	0.757352	+	0.653006i	$0.226493\pi$
$284$	−25.6410	−	54.4899i	−1.52151	−	3.23338i
$285$	1.59574	+	5.33726i	0.0945233	+	0.316152i
$286$	11.9514	+	11.2231i	0.706698	+	0.663634i
$287$	21.4984	+	4.10105i	1.26901	+	0.242077i
$288$	−26.6657	+	48.5047i	−1.57129	+	2.85817i
$289$	−3.01550	−	15.8078i	−0.177382	−	0.929870i
$290$	−7.43888	+	8.57124i	−0.436826	+	0.503320i
$291$	−0.0989761	−	0.0544126i	−0.00580208	−	0.00318972i
$292$	−14.2461	−	0.896288i	−0.833690	−	0.0524513i
$293$	−15.5153	−	21.3550i	−0.906414	−	1.24757i	−0.968377	−	0.249493i	$-0.919736\pi$
$293$	−15.5153	−	21.3550i	−0.906414	−	1.24757i	0.0619629	−	0.998078i	$-0.480264\pi$
$294$	−15.3791	+	3.94868i	−0.896928	+	0.230292i
$295$	0.808774	−	1.39216i	0.0470886	−	0.0810548i
$296$	−0.969476	−	15.4094i	−0.0563496	−	0.895652i
$297$	2.18720	−	8.51858i	0.126914	−	0.494298i
$298$	0.638395	−	5.05341i	0.0369812	−	0.292736i
$299$	−8.11641	+	5.89692i	−0.469384	+	0.341027i
$300$	22.6386	+	5.43869i	1.30704	+	0.314003i
$301$	17.9227	+	13.0216i	1.03305	+	0.750553i
$302$	29.0649	−	30.9510i	1.67250	−	1.78103i
$303$	4.19451	+	10.5941i	0.240968	+	0.608616i
$304$	45.8409	+	11.7699i	2.62916	+	0.675053i
$305$	−15.3596	+	15.6004i	−0.879490	+	0.893279i
$306$	−3.23093	−	5.09114i	−0.184700	−	0.291041i
$307$			3.90217i			0.222709i	0.993781	+	0.111354i	$0.0355189\pi$
$307$			3.90217i			0.222709i	−0.993781	+	0.111354i	$0.964481\pi$
$308$	34.7967	−	22.0827i	1.98273	−	1.25828i
$309$	−9.14395	+	8.58674i	−0.520181	+	0.488482i
$310$	−6.43626	+	5.76391i	−0.365555	+	0.327368i
$311$	14.6523	−	8.05519i	0.830858	−	0.456768i	−0.00874971	−	0.999962i	$-0.502785\pi$
$311$	14.6523	−	8.05519i	0.830858	−	0.456768i	0.839607	+	0.543194i	$0.182785\pi$
$312$	22.3100	−	10.4983i	1.26305	−	0.594348i
$313$	−0.753834	+	0.354727i	−0.0426092	+	0.0200504i	−0.446966	−	0.894551i	$-0.647495\pi$
$313$	−0.753834	+	0.354727i	−0.0426092	+	0.0200504i	0.404357	+	0.914601i	$0.367495\pi$
$314$	−4.19878	+	2.30830i	−0.236951	+	0.130265i
$315$	−14.2916	+	12.7987i	−0.805243	+	0.721126i
$316$	16.9786	−	15.9440i	0.955122	−	0.896920i
$317$	6.84863	−	4.34627i	0.384657	−	0.244111i	−0.329412	−	0.944186i	$-0.606850\pi$
$317$	6.84863	−	4.34627i	0.384657	−	0.244111i	0.714069	+	0.700076i	$0.246850\pi$
$318$		−	28.1654i		−	1.57943i
$319$	−1.96157	−	3.09093i	−0.109827	−	0.173059i
$320$	53.9943	−	54.8409i	3.01837	−	3.06570i
$321$	−10.0957	−	2.59214i	−0.563488	−	0.144679i
$322$	12.6173	+	31.8676i	0.703133	+	1.77591i
$323$	−1.94285	+	2.06893i	−0.108103	+	0.115118i
$324$	14.4095	+	10.4691i	0.800527	+	0.581617i
$325$	9.74909	+	11.4182i	0.540782	+	0.633369i
$326$	−56.1731	+	40.8121i	−3.11114	+	2.26037i
$327$	−1.03033	+	8.15592i	−0.0569775	+	0.451024i
$328$	−14.3368	+	55.8383i	−0.791620	+	3.08316i
$329$	−0.524573	−	8.33785i	−0.0289206	−	0.459680i
$330$	−5.12726	+	8.82569i	−0.282247	+	0.485838i
$331$	4.75066	−	1.21976i	0.261120	−	0.0670442i	−0.115860	−	0.993266i	$-0.536962\pi$
$331$	4.75066	−	1.21976i	0.261120	−	0.0670442i	0.376980	+	0.926221i	$0.376962\pi$
$332$	20.5175	+	28.2399i	1.12604	+	1.54987i
$333$	−3.61019	−	0.227134i	−0.197837	−	0.0124468i
$334$	−55.1924	−	30.3423i	−3.01999	−	1.66025i
$335$	10.3324	−	11.9052i	0.564520	−	0.650452i
$336$	−9.27742	−	48.6339i	−0.506125	−	2.65320i
$337$	−9.92810	+	18.0592i	−0.540818	+	0.983745i	0.454832	+	0.890577i	$0.349699\pi$
$337$	−9.92810	+	18.0592i	−0.540818	+	0.983745i	−0.995650	+	0.0931676i	$0.970301\pi$
$338$	−10.7649	−	2.05351i	−0.585531	−	0.111696i
$339$	5.44872	+	5.11669i	0.295934	+	0.277900i
$340$	3.39792	+	11.3650i	0.184278	+	0.616354i
$341$	−1.18661	−	2.52168i	−0.0642587	−	0.136557i
$342$	6.94470	−	17.5403i	0.375526	−	0.948471i
$343$	0.213062	−	0.293254i	0.0115042	−	0.0158342i
$344$	−37.1964	+	44.9628i	−2.00550	+	2.42423i
$345$	−4.71709	−	4.09391i	−0.253959	−	0.220409i
$346$	−37.2229	+	58.6540i	−2.00112	+	3.15326i
$347$	6.54350	+	4.15263i	0.351274	+	0.222925i	0.699742	−	0.714395i	$-0.253298\pi$
$347$	6.54350	+	4.15263i	0.351274	+	0.222925i	−0.348469	+	0.937320i	$0.613298\pi$
$348$	−8.43802	+	1.60964i	−0.452325	+	0.0862857i
$349$	−0.0325011	+	0.100028i	−0.00173974	+	0.00535438i	−0.951923	−	0.306339i	$-0.900896\pi$
$349$	−0.0325011	+	0.100028i	−0.00173974	+	0.00535438i	0.950183	+	0.311693i	$0.100896\pi$
$350$	46.0663	−	22.5590i	2.46235	−	1.20583i
$351$	−4.11243	−	12.6568i	−0.219505	−	0.675568i
$352$	22.9970	+	41.8314i	1.22574	+	2.22962i
$353$	−3.90538	+	3.23081i	−0.207862	+	0.171959i	−0.735530	−	0.677492i	$-0.763067\pi$
$353$	−3.90538	+	3.23081i	−0.207862	+	0.171959i	0.527667	+	0.849451i	$0.323067\pi$
$354$	1.53993	−	0.609700i	0.0818462	−	0.0324052i
$355$	24.1583	−	0.947344i	1.28219	−	0.0502798i
$356$	−2.87443	+	45.6878i	−0.152345	+	2.42145i
$357$	2.82376	+	0.917494i	0.149449	+	0.0485589i
$358$	30.1483	+	24.9409i	1.59339	+	1.31817i
$359$	−1.27388	+	6.67789i	−0.0672326	+	0.352446i	−0.999967	−	0.00811848i	$-0.997416\pi$
$359$	−1.27388	+	6.67789i	−0.0672326	+	0.352446i	0.932734	+	0.360564i	$0.117416\pi$
$360$	−31.2824	−	39.6877i	−1.64873	−	2.09173i
$361$	10.0406	+	1.26843i	0.528455	+	0.0667594i
$362$	−4.29952	−	34.0342i	−0.225978	−	1.78880i
$363$	4.04163	+	4.30390i	0.212131	+	0.225896i
$364$	26.5520	−	56.4259i	1.39170	−	2.95752i
$365$	2.56186	−	5.12612i	0.134094	−	0.268313i
$366$	−22.3433	+	2.82261i	−1.16790	+	0.147540i
$367$	−1.39392	−	5.42896i	−0.0727620	−	0.283389i	0.921782	−	0.387709i	$-0.126733\pi$
$367$	−1.39392	−	5.42896i	−0.0727620	−	0.283389i	−0.994544	+	0.104320i	$0.966733\pi$
$368$	−50.4669	+	16.3977i	−2.63077	+	0.854788i
$369$	12.5579	+	4.97204i	0.653740	+	0.258834i
$370$	9.12487	+	3.20520i	0.474379	+	0.166631i
$371$	−29.1021	−	35.1784i	−1.51091	−	1.82637i
$372$	−6.52665	+	0.410622i	−0.338391	+	0.0212898i
$373$	−23.3369	−	10.9815i	−1.20834	−	0.568600i	−0.287212	−	0.957867i	$-0.592728\pi$
$373$	−23.3369	−	10.9815i	−1.20834	−	0.568600i	−0.921125	+	0.389267i	$0.872728\pi$
$374$	−5.20022			−0.268897
$375$	−5.55512	+	7.51744i	−0.286865	+	0.388199i
$376$	22.0059			1.13487
$377$	−5.01222	−	2.35857i	−0.258142	−	0.121473i
$378$	−45.3757	+	2.85480i	−2.33387	+	0.146835i
$379$	−3.39367	−	4.10224i	−0.174321	−	0.210718i	0.676115	−	0.736796i	$-0.263662\pi$
$379$	−3.39367	−	4.10224i	−0.174321	−	0.210718i	−0.850436	+	0.526078i	$0.823662\pi$
$380$	−22.5175	+	29.5004i	−1.15512	+	1.51334i
$381$	2.96052	+	1.17215i	0.151672	+	0.0600512i
$382$	45.9547	−	14.9316i	2.35125	−	0.763966i
$383$	−0.932415	−	3.63152i	−0.0476442	−	0.185562i	0.940307	−	0.340327i	$-0.110538\pi$
$383$	−0.932415	−	3.63152i	−0.0476442	−	0.185562i	−0.987951	+	0.154765i	$0.950538\pi$
$384$	38.6393	−	4.88128i	1.97180	−	0.249097i
$385$	2.71529	+	16.3210i	0.138384	+	0.831798i
$386$	20.9555	−	44.5328i	1.06661	−	2.26666i
$387$	9.35881	+	9.96612i	0.475735	+	0.506607i
$388$	−0.0943076	−	0.746521i	−0.00478774	−	0.0378989i
$389$	16.7595	+	2.11722i	0.849740	+	0.107347i	0.538129	−	0.842863i	$-0.319131\pi$
$389$	16.7595	+	2.11722i	0.849740	+	0.107347i	0.311611	+	0.950210i	$0.399131\pi$
$390$	0.605187	+	15.4329i	0.0306448	+	0.781476i
$391$	0.596275	−	3.12578i	0.0301549	−	0.158078i
$392$	−52.2375	−	43.2146i	−2.63839	−	2.18267i
$393$	0.354274	+	0.115111i	0.0178708	+	0.00580656i
$394$	−4.16046	+	66.1287i	−0.209601	+	3.33151i
$395$	3.23576	+	8.77298i	0.162809	+	0.441416i
$396$	23.6470	−	9.36253i	1.18831	−	0.470485i
$397$	17.1154	−	14.1591i	0.858998	−	0.710625i	−0.0997103	−	0.995017i	$-0.531792\pi$
$397$	17.1154	−	14.1591i	0.858998	−	0.710625i	0.958708	+	0.284392i	$0.0917916\pi$
$398$	24.9777	+	45.4343i	1.25202	+	2.27742i
$399$	2.87050	+	8.83450i	0.143705	+	0.442278i
$400$	30.3788	+	73.3725i	1.51894	+	3.66863i
$401$	0.624195	−	1.92108i	0.0311708	−	0.0959339i	−0.934261	−	0.356591i	$-0.883939\pi$
$401$	0.624195	−	1.92108i	0.0311708	−	0.0959339i	0.965432	+	0.260657i	$0.0839391\pi$
$402$	15.9287	−	3.03856i	0.794451	−	0.151550i
$403$	−3.56059	−	2.25962i	−0.177366	−	0.112560i
$404$	−40.6740	+	64.0920i	−2.02361	+	3.18869i
$405$	−6.12630	+	3.68770i	−0.304418	+	0.183243i
$406$	−12.0631	+	14.5817i	−0.598680	+	0.723679i
$407$	−1.83368	+	2.52385i	−0.0908923	+	0.125103i
$408$	−2.87901	+	7.27154i	−0.142532	+	0.359995i
$409$	0.999643	+	2.12435i	0.0494291	+	0.105042i	0.928016	−	0.372540i	$-0.121513\pi$
$409$	0.999643	+	2.12435i	0.0494291	+	0.105042i	−0.878587	+	0.477583i	$0.841513\pi$
$410$	−28.7048	−	21.9103i	−1.41763	−	1.08207i
$411$	6.27034	+	5.88825i	0.309293	+	0.290446i
$412$	−82.0861	−	15.6588i	−4.04409	−	0.771452i
$413$	1.29338	−	2.35266i	0.0636433	−	0.115767i
$414$	3.96341	+	20.7769i	0.194791	+	1.02113i
$415$	−13.6521	+	3.16329i	−0.670155	+	0.155280i
$416$	63.2977	+	34.7982i	3.10343	+	1.70612i
$417$	−14.8004	−	0.931163i	−0.724780	−	0.0455993i
$418$	−9.56303	−	13.1624i	−0.467743	−	0.643793i
$419$	15.1992	−	3.90249i	0.742530	−	0.190649i	0.141570	−	0.989928i	$-0.454785\pi$
$419$	15.1992	−	3.90249i	0.742530	−	0.190649i	0.600960	+	0.799279i	$0.294785\pi$
$420$	37.9537	+	8.17424i	1.85195	+	0.398862i
$421$	2.25081	+	35.7756i	0.109698	+	1.74360i	0.540673	+	0.841233i	$0.318170\pi$
$421$	2.25081	+	35.7756i	0.109698	+	1.74360i	−0.430975	+	0.902364i	$0.641830\pi$
$422$	−3.13614	+	12.2145i	−0.152665	+	0.594590i
$423$	0.646174	−	5.11499i	0.0314181	−	0.248700i
$424$	97.2929	−	70.6874i	4.72496	−	3.43288i
$425$	−4.73339	−	0.523299i	−0.229603	−	0.0253837i
$426$	20.1207	+	14.6185i	0.974849	+	0.708269i
$427$	−24.9902	+	26.6118i	−1.20936	+	1.28784i
$428$	−25.5624	−	64.5631i	−1.23560	−	3.12078i
$429$	−4.82540	−	1.23895i	−0.232973	−	0.0598172i
$430$	−16.8474	−	32.4387i	−0.812456	−	1.56433i
$431$	−5.51583	−	8.69156i	−0.265688	−	0.418658i	0.685123	−	0.728427i	$-0.259748\pi$
$431$	−5.51583	−	8.69156i	−0.265688	−	0.418658i	−0.950812	+	0.309769i	$0.899748\pi$
$432$		−	70.3899i		−	3.38663i
$433$	−19.7610	+	12.5407i	−0.949654	+	0.602669i	−0.917894	−	0.396827i	$-0.870111\pi$
$433$	−19.7610	+	12.5407i	−0.949654	+	0.602669i	−0.0317606	+	0.999496i	$0.510111\pi$
$434$	−10.5023	+	9.86231i	−0.504126	+	0.473406i
$435$	0.726104	−	3.37137i	0.0348140	−	0.161645i
$436$	−47.9925	+	26.3841i	−2.29842	+	1.26357i
$437$	9.00825	−	4.23896i	0.430923	−	0.202777i
$438$	5.33401	−	2.50999i	0.254869	−	0.119932i
$439$	−16.6640	+	9.16112i	−0.795330	+	0.437237i	−0.826958	−	0.562263i	$-0.809931\pi$
$439$	−16.6640	+	9.16112i	−0.795330	+	0.437237i	0.0316280	+	0.999500i	$0.489931\pi$
$440$	−43.3550	+	4.43874i	−2.06687	+	0.211609i
$441$	−11.5786	+	10.8730i	−0.551361	+	0.517763i
$442$	−6.64384	+	4.21631i	−0.316015	+	0.200549i
$443$		−	36.7745i		−	1.74721i	−0.486635	−	0.873605i	$-0.661776\pi$
$443$		−	36.7745i		−	1.74721i	0.486635	−	0.873605i	$-0.338224\pi$
$444$	3.92242	+	6.18074i	0.186150	+	0.293325i
$445$	−16.4397	−	8.21601i	−0.779316	−	0.389476i
$446$	−6.81040	−	1.74861i	−0.322482	−	0.0827993i
$447$	0.569779	+	1.43910i	0.0269496	+	0.0680670i
$448$	87.8490	−	93.5497i	4.15047	−	4.41981i
$449$	6.26642	+	4.55282i	0.295731	+	0.214861i	0.725750	−	0.687959i	$-0.241493\pi$
$449$	6.26642	+	4.55282i	0.295731	+	0.214861i	−0.430019	+	0.902820i	$0.641493\pi$
$450$	30.5337	−	8.34808i	1.43937	−	0.393532i
$451$	9.42358	−	6.84663i	0.443739	−	0.322395i
$452$	−6.24105	+	49.4030i	−0.293554	+	2.32372i
$453$	−3.20858	+	12.4966i	−0.150752	+	0.587141i
$454$	0.0633155	+	1.00637i	0.00297154	+	0.0472313i
$455$	16.7021	+	18.6503i	0.783006	+	0.874342i
$456$	−23.6995	+	6.08500i	−1.10983	+	0.284956i
$457$	2.58484	+	3.55772i	0.120913	+	0.166423i	0.865183	−	0.501456i	$-0.167202\pi$
$457$	2.58484	+	3.55772i	0.120913	+	0.166423i	−0.744270	+	0.667879i	$0.767202\pi$
$458$	73.2036	+	4.60558i	3.42058	+	0.215205i
$459$	3.69902	+	2.03355i	0.172655	+	0.0949181i
$460$	3.59354	−	41.4547i	0.167550	−	1.93284i
$461$	−4.55606	−	23.8837i	−0.212197	−	1.11238i	−0.915755	−	0.401738i	$-0.868406\pi$
$461$	−4.55606	−	23.8837i	−0.212197	−	1.11238i	0.703558	−	0.710638i	$-0.251594\pi$
$462$	−8.19948	+	14.9148i	−0.381474	+	0.693899i
$463$	16.8812	+	3.22025i	0.784534	+	0.149658i	0.564059	−	0.825735i	$-0.309239\pi$
$463$	16.8812	+	3.22025i	0.784534	+	0.149658i	0.220475	+	0.975393i	$0.429239\pi$
$464$	−21.3583	−	20.0568i	−0.991535	−	0.931114i
$465$	0.870087	−	2.47704i	0.0403493	−	0.114870i
$466$	−1.47333	−	3.13099i	−0.0682508	−	0.145040i
$467$	−1.12630	+	2.84471i	−0.0521190	+	0.131638i	−0.953503	−	0.301382i	$-0.902552\pi$
$467$	−1.12630	+	2.84471i	−0.0521190	+	0.131638i	0.901384	+	0.433020i	$0.142552\pi$
$468$	22.6206	−	31.1345i	1.04564	−	1.43919i
$469$	16.7553	−	20.2536i	0.773686	−	0.935226i
$470$	−5.37587	+	12.6929i	−0.247970	+	0.585478i
$471$	0.780154	−	1.22933i	0.0359476	−	0.0566443i
$472$	5.97091	+	3.78926i	0.274834	+	0.174415i
$473$	11.5818	−	2.20934i	0.532530	−	0.101585i
$474$	−2.97242	+	9.14818i	−0.136528	+	0.420190i
$475$	−7.38001	−	12.9431i	−0.338618	−	0.593871i
$476$	6.11236	+	18.8119i	0.280160	+	0.862243i
$477$	−13.5735	−	24.6902i	−0.621489	−	1.13048i
$478$	53.3545	−	44.1387i	2.44038	−	2.01886i
$479$	24.5875	−	9.73488i	1.12343	−	0.444798i	0.268366	−	0.963317i	$-0.413516\pi$
$479$	24.5875	−	9.73488i	1.12343	−	0.444798i	0.855066	+	0.518519i	$0.173516\pi$
$480$	−12.2099	+	43.2803i	−0.557301	+	1.97547i
$481$	−0.296405	+	4.71123i	−0.0135149	+	0.214813i
$482$	−66.5608	−	21.6269i	−3.03176	−	0.985078i
$483$	−8.02490	−	6.63877i	−0.365146	−	0.302075i
$484$	−7.37032	+	38.6366i	−0.335014	+	1.75621i
$485$	0.290738	+	0.0820203i	0.0132017	+	0.00372435i
$486$	−43.5899	−	5.50669i	−1.97728	−	0.249788i
$487$	4.92651	+	38.9973i	0.223241	+	1.76714i	0.562840	+	0.826566i	$0.309709\pi$
$487$	4.92651	+	38.9973i	0.223241	+	1.76714i	−0.339598	+	0.940571i	$0.610291\pi$
$488$	−65.8258	−	70.0974i	−2.97980	−	3.17316i
$489$	8.98346	−	19.0908i	0.406246	−	0.863317i
$490$	37.6871	−	19.5733i	1.70253	−	0.884230i
$491$	13.2538	−	1.67435i	0.598136	−	0.0755621i	0.179565	−	0.983746i	$-0.442531\pi$
$491$	13.2538	−	1.67435i	0.598136	−	0.0755621i	0.418571	+	0.908184i	$0.362531\pi$
$492$	−6.79736	−	26.4740i	−0.306449	−	1.19354i
$493$	1.67103	−	0.542951i	0.0752595	−	0.0244533i
$494$	−22.8898	−	9.06270i	−1.02986	−	0.407750i
$495$	−0.241333	+	10.2077i	−0.0108471	+	0.458801i
$496$	−14.2178	−	17.1864i	−0.638399	−	0.771692i
$497$	40.2354	−	2.53139i	1.80480	−	0.113549i
$498$	−13.0438	−	6.13797i	−0.584509	−	0.275049i
$499$	−4.87807			−0.218372			−0.109186	−	0.994021i	$-0.534824\pi$
$499$	−4.87807			−0.218372			−0.109186	+	0.994021i	$0.534824\pi$
$500$	−62.2696	−	0.503262i	−2.78478	−	0.0225066i
$501$	19.1387			0.855052
$502$	−49.1260	−	23.1170i	−2.19260	−	1.03176i
$503$	1.64497	−	0.103493i	0.0733458	−	0.00461452i	−0.0260752	−	0.999660i	$-0.508301\pi$
$503$	1.64497	−	0.103493i	0.0733458	−	0.00461452i	0.0994210	+	0.995045i	$0.468301\pi$
$504$	−53.7130	−	64.9279i	−2.39257	−	2.89212i
$505$	−17.3250	−	25.0712i	−0.770950	−	1.11565i
$506$	16.9605	+	6.71515i	0.753987	+	0.298525i
$507$	3.16712	−	1.02906i	0.140657	−	0.0457021i
$508$	5.27538	+	20.5463i	0.234057	+	0.911593i
$509$	23.0470	−	2.91152i	1.02154	−	0.129051i	0.403324	−	0.915057i	$-0.367855\pi$
$509$	23.0470	−	2.91152i	1.02154	−	0.129051i	0.618218	+	0.786007i	$0.287855\pi$
$510$	−3.49086	−	3.43697i	−0.154578	−	0.152192i
$511$	4.06868	−	8.64639i	0.179988	−	0.382494i
$512$	47.9687	+	51.0815i	2.11994	+	2.25750i
$513$	1.65520	+	13.1023i	0.0730790	+	0.578480i
$514$	31.5544	+	3.98625i	1.39181	+	0.175826i
$515$	18.6410	−	27.8936i	0.821420	−	1.22914i
$516$	5.18425	−	27.1768i	0.228224	−	1.19639i
$517$	−3.42596	−	2.83420i	−0.150673	−	0.124648i
$518$	15.3378	+	4.98355i	0.673904	+	0.218965i
$519$	1.32547	−	21.0677i	0.0581815	−	0.924769i
$520$	−51.7918	+	40.8230i	−2.27122	+	1.79021i
$521$	17.2478	−	6.82887i	0.755638	−	0.299178i	0.0414579	−	0.999140i	$-0.486800\pi$
$521$	17.2478	−	6.82887i	0.755638	−	0.299178i	0.714180	+	0.699962i	$0.246800\pi$
$522$	−8.99872	+	7.44439i	−0.393863	+	0.325832i
$523$	5.44563	+	9.90557i	0.238121	+	0.433140i	0.968184	−	0.250240i	$-0.0805094\pi$
$523$	5.44563	+	9.90557i	0.238121	+	0.433140i	−0.730063	+	0.683380i	$0.760509\pi$
$524$	0.766870	+	2.36018i	0.0335009	+	0.103105i
$525$	−8.96429	+	12.7508i	−0.391234	+	0.556489i
$526$	4.36308	−	13.4282i	0.190239	−	0.585497i
$527$	1.31390	−	0.250640i	0.0572345	−	0.0109181i
$528$	−22.2486	−	14.1194i	−0.968244	−	0.614466i
$529$	6.34289	−	9.99479i	0.275778	−	0.434556i
$530$	17.0042	+	73.3863i	0.738614	+	3.18770i
$531$	1.05609	−	1.27660i	0.0458306	−	0.0553997i
$532$	−36.3748	+	50.0656i	−1.57705	+	2.17062i
$533$	6.48843	−	16.3879i	0.281045	−	0.709838i
$534$	−8.04966	−	17.1064i	−0.348343	−	0.740266i
$535$	27.8698	+	0.658907i	1.20492	+	0.0284870i
$536$	50.4729	+	47.3973i	2.18010	+	2.04725i
$537$	−11.6791	−	2.22791i	−0.503991	−	0.0961415i
$538$	−34.7146	+	63.1455i	−1.49665	+	2.72240i
$539$	2.56680	+	13.4556i	0.110560	+	0.579574i
$540$	50.8256	+	21.5264i	2.18719	+	0.926349i
$541$	1.29627	+	0.712631i	0.0557311	+	0.0306384i	0.509376	−	0.860544i	$-0.329876\pi$
$541$	1.29627	+	0.712631i	0.0557311	+	0.0306384i	−0.453645	+	0.891183i	$0.649876\pi$
$542$	16.0212	+	1.00797i	0.688168	+	0.0432959i
$543$	6.12718	+	8.43334i	0.262942	+	0.361909i
$544$	−22.1913	+	5.69776i	−0.951444	+	0.244289i
$545$	−2.23936	−	21.8727i	−0.0959235	−	0.936924i
$546$	1.61712	+	25.7034i	0.0692063	+	1.10000i
$547$	−0.666114	+	2.59434i	−0.0284810	+	0.110926i	−0.981234	−	0.192819i	$-0.938237\pi$
$547$	−0.666114	+	2.59434i	−0.0284810	+	0.110926i	0.952753	+	0.303745i	$0.0982370\pi$
$548$	−7.18216	+	56.8526i	−0.306807	+	2.42862i
$549$	−18.2262	+	13.2421i	−0.777873	+	0.565158i
$550$	8.03105	−	26.0913i	0.342445	−	1.11253i
$551$	4.44724	+	3.23111i	0.189459	+	0.137650i
$552$	18.7797	−	19.9984i	0.799319	−	0.851188i
$553$	5.73990	+	14.4973i	0.244085	+	0.616489i
$554$	46.8275	+	12.0233i	1.98951	+	0.510820i
$555$	−2.89902	+	0.482302i	−0.123056	+	0.0204726i
$556$	−52.9374	−	83.4160i	−2.24504	−	3.53762i
$557$			25.2611i			1.07035i	0.844742	+	0.535174i	$0.179754\pi$
$557$			25.2611i			1.07035i	−0.844742	+	0.535174i	$0.820246\pi$
$558$	−7.50685	+	4.76399i	−0.317790	+	0.201676i
$559$	13.0056	−	12.2131i	0.550079	−	0.516558i
$560$	53.5344	+	121.117i	2.26224	+	5.11814i
$561$	1.38474	−	0.761265i	0.0584636	−	0.0321406i
$562$	43.2837	−	20.3678i	1.82581	−	0.859162i
$563$	15.2250	−	7.16433i	0.641657	−	0.301941i	−0.0772873	−	0.997009i	$-0.524626\pi$
$563$	15.2250	−	7.16433i	0.641657	−	0.301941i	0.718944	+	0.695068i	$0.244626\pi$
$564$	−9.14285	+	5.02632i	−0.384983	+	0.211646i
$565$	−17.2860	−	10.0423i	−0.727227	−	0.422481i
$566$	22.1569	−	20.8067i	0.931325	−	0.874573i
$567$	−10.0674	+	6.38897i	−0.422791	+	0.268312i
$568$			106.192i			4.45573i
$569$	−2.33373	−	3.67737i	−0.0978349	−	0.154163i	0.791885	−	0.610671i	$-0.209100\pi$
$569$	−2.33373	−	3.67737i	−0.0978349	−	0.154163i	−0.889720	+	0.456508i	$0.849100\pi$
$570$	2.27982	−	15.1562i	0.0954910	−	0.634825i
$571$	−16.5714	−	4.25480i	−0.693490	−	0.178058i	−0.114537	−	0.993419i	$-0.536539\pi$
$571$	−16.5714	−	4.25480i	−0.693490	−	0.178058i	−0.578953	+	0.815361i	$0.696539\pi$
$572$	−12.2179	−	30.8590i	−0.510857	−	1.29028i
$573$	−10.0511	+	10.7034i	−0.419893	+	0.447140i
$574$	−48.7155	−	35.3939i	−2.03334	−	1.47731i
$575$	14.7622	+	7.81906i	0.615627	+	0.326077i
$576$	64.0711	−	46.5504i	2.66963	−	1.93960i
$577$	3.17714	−	25.1496i	0.132266	−	1.04699i	−0.776626	−	0.629962i	$-0.783071\pi$
$577$	3.17714	−	25.1496i	0.132266	−	1.04699i	0.908892	−	0.417031i	$-0.136929\pi$
$578$	−11.0111	+	42.8855i	−0.458002	+	1.78380i
$579$	0.939068	+	14.9261i	0.0390263	+	0.620306i
$580$	21.0139	−	9.28825i	0.872556	−	0.385674i
$581$	−22.6338	+	5.81138i	−0.939010	+	0.241097i
$582$	0.182656	+	0.251404i	0.00757133	+	0.0104210i
$583$	−24.2509	−	1.52574i	−1.00437	−	0.0631897i
$584$	22.0573	+	12.1261i	0.912737	+	0.501782i
$585$	7.96799	+	13.2371i	0.329436	+	0.547285i
$586$	13.6084	+	71.3380i	0.562160	+	2.94694i
$587$	8.29134	−	15.0819i	0.342220	−	0.622496i	−0.648059	−	0.761590i	$-0.724419\pi$
$587$	8.29134	−	15.0819i	0.342220	−	0.622496i	0.990279	+	0.139094i	$0.0444190\pi$
$588$	31.5738	+	6.02303i	1.30208	+	0.248386i
$589$	3.05062	+	2.86472i	0.125699	+	0.118039i
$590$	−3.64427	+	2.51830i	−0.150032	+	0.103677i
$591$	−8.57276	−	18.2180i	−0.352636	−	0.749390i
$592$	−9.19138	+	23.2148i	−0.377763	+	0.954121i
$593$	−16.4053	+	22.5800i	−0.673685	+	0.927248i	−0.999837	−	0.0180694i	$-0.994248\pi$
$593$	−16.4053	+	22.5800i	−0.673685	+	0.927248i	0.326152	+	0.945317i	$0.394248\pi$
$594$	−15.4241	+	18.6445i	−0.632858	+	0.764993i
$595$	−7.91136	−	0.685803i	−0.324334	−	0.0281152i
$596$	−5.52513	+	8.70621i	−0.226318	+	0.356620i
$597$	−13.3023	−	8.44192i	−0.544428	−	0.345505i
$598$	27.1135	−	5.17217i	1.10875	−	0.211506i
$599$	−1.68847	+	5.19659i	−0.0689892	+	0.212327i	−0.979607	−	0.200922i	$-0.935606\pi$
$599$	−1.68847	+	5.19659i	−0.0689892	+	0.212327i	0.910618	+	0.413249i	$0.135606\pi$
$600$	−32.0375	−	25.6749i	−1.30792	−	1.04817i
$601$	−9.95957	−	30.6524i	−0.406259	−	1.25034i	−0.919839	−	0.392296i	$-0.871681\pi$
$601$	−9.95957	−	30.6524i	−0.406259	−	1.25034i	0.513580	−	0.858042i	$-0.328319\pi$
$602$	−29.3638	−	53.4125i	−1.19678	−	2.17693i
$603$	12.4990	−	10.3401i	0.508998	−	0.421079i
$604$	−79.9170	+	31.6414i	−3.25178	+	1.28747i
$605$	−13.1291	−	8.77400i	−0.533772	−	0.356714i
$606$	1.96843	−	31.2874i	0.0799622	−	1.27096i
$607$	22.0109	+	7.15177i	0.893394	+	0.290281i	0.719508	−	0.694484i	$-0.244367\pi$
$607$	22.0109	+	7.15177i	0.893394	+	0.290281i	0.173886	+	0.984766i	$0.444367\pi$
$608$	−55.2307	−	45.6908i	−2.23990	−	1.85301i
$609$	1.07757	−	5.64880i	0.0436652	−	0.228901i
$610$	56.5125	−	20.8437i	2.28812	−	0.843936i
$611$	−6.67498	−	0.843246i	−0.270041	−	0.0341141i
$612$	1.52991	+	12.1104i	0.0618428	+	0.489536i
$613$	3.49734	+	3.72428i	0.141256	+	0.150422i	0.795706	−	0.605683i	$-0.207100\pi$
$613$	3.49734	+	3.72428i	0.141256	+	0.150422i	−0.654450	+	0.756105i	$0.727100\pi$
$614$	4.57122	−	9.71433i	0.184479	−	0.392038i
$615$	10.8511	+	1.63223i	0.437558	+	0.0658179i
$616$	−72.0993	+	9.10827i	−2.90497	+	0.366982i
$617$	2.81910	+	10.9797i	0.113493	+	0.442025i	0.999777	−	0.0211165i	$-0.00672208\pi$
$617$	2.81910	+	10.9797i	0.113493	+	0.442025i	−0.886284	+	0.463142i	$0.846722\pi$
$618$	32.8225	−	10.6647i	1.32031	−	0.428996i
$619$	2.04050	+	0.807892i	0.0820147	+	0.0324719i	0.408774	−	0.912636i	$-0.365957\pi$
$619$	2.04050	+	0.807892i	0.0820147	+	0.0324719i	−0.326759	+	0.945108i	$0.605957\pi$
$620$	16.7576	−	5.01021i	0.673002	−	0.201215i
$621$	−9.43838	−	11.4090i	−0.378749	−	0.457829i
$622$	−45.9128	+	2.88859i	−1.84093	+	0.115822i
$623$	−27.7293	−	13.0484i	−1.11095	−	0.522774i
$624$	−39.8728			−1.59619
$625$	9.93567	−	22.9408i	0.397427	−	0.917634i
$626$	2.29219			0.0916143
$627$	4.47333	+	2.10499i	0.178648	+	0.0840652i
$628$	9.68064	−	0.609054i	0.386300	−	0.0243039i
$629$	−0.954408	−	1.15368i	−0.0380547	−	0.0460003i
$630$	50.5717	−	15.1200i	2.01482	−	0.602393i
$631$	8.73932	+	3.46014i	0.347907	+	0.137746i	0.535578	−	0.844486i	$-0.320094\pi$
$631$	8.73932	+	3.46014i	0.347907	+	0.137746i	−0.187671	+	0.982232i	$0.560094\pi$
$632$	−39.0609	+	12.6917i	−1.55376	+	0.504847i
$633$	−0.952980	−	3.71161i	−0.0378776	−	0.147523i
$634$	−22.1409	+	2.79704i	−0.879327	+	0.111085i
$635$	−8.42145	−	1.26676i	−0.334195	−	0.0502700i
$636$	−24.2770	+	51.5912i	−0.962645	+	2.04572i
$637$	14.1891	+	15.1098i	0.562192	+	0.598674i
$638$	1.26237	+	9.99265i	0.0499775	+	0.395613i
$639$	24.6831	+	3.11820i	0.976447	+	0.123354i
$640$	−97.7298	+	36.0460i	−3.86311	+	1.42484i
$641$	−5.19177	+	27.2162i	−0.205063	+	1.07498i	0.719658	+	0.694329i	$0.244299\pi$
$641$	−5.19177	+	27.2162i	−0.205063	+	1.07498i	−0.924721	+	0.380647i	$0.875701\pi$
$642$	22.0964	+	18.2797i	0.872074	+	0.721442i
$643$	4.96851	+	1.61437i	0.195939	+	0.0636644i	0.405343	−	0.914165i	$-0.367152\pi$
$643$	4.96851	+	1.61437i	0.195939	+	0.0636644i	−0.209404	+	0.977829i	$0.567152\pi$
$644$	4.35672	−	69.2481i	0.171679	−	2.72876i
$645$	9.23493	+	6.17160i	0.363625	+	0.243006i
$646$	7.26031	−	2.87456i	0.285653	−	0.113098i
$647$	−19.6272	+	16.2371i	−0.771626	+	0.638345i	−0.937572	−	0.347790i	$-0.886932\pi$
$647$	−19.6272	+	16.2371i	−0.771626	+	0.638345i	0.165946	+	0.986135i	$0.446932\pi$
$648$	−15.1307	−	27.5226i	−0.594389	−	1.08119i
$649$	−0.441545	−	1.35894i	−0.0173322	−	0.0533429i
$650$	−10.8941	−	39.8459i	−0.427302	−	1.56288i
$651$	1.35284	−	4.16361i	0.0530219	−	0.163185i
$652$	138.071	−	26.3385i	5.40729	−	1.03150i
$653$	−0.106857	−	0.0678133i	−0.00418163	−	0.00265374i	0.533734	−	0.845652i	$-0.320788\pi$
$653$	−0.106857	−	0.0678133i	−0.00418163	−	0.00265374i	−0.537916	+	0.842998i	$0.680788\pi$
$654$	12.1193	−	19.0969i	0.473901	−	0.746748i
$655$	−0.992575	−	0.0860422i	−0.0387831	−	0.00336195i
$656$	59.4247	−	71.8321i	2.32014	−	2.80457i
$657$	3.46625	−	4.77088i	0.135231	−	0.186130i
$658$	−8.46150	+	21.3713i	−0.329864	+	0.833140i
$659$	13.1037	+	27.8469i	0.510449	+	1.08476i	0.979473	+	0.201575i	$0.0646058\pi$
$659$	13.1037	+	27.8469i	0.510449	+	1.08476i	−0.469024	+	0.883185i	$0.655394\pi$
$660$	16.9990	−	11.7468i	0.661685	−	0.457244i
$661$	−33.6261	−	31.5770i	−1.30790	−	1.22820i	−0.956416	−	0.292009i	$-0.905676\pi$
$661$	−33.6261	−	31.5770i	−1.30790	−	1.22820i	−0.351487	−	0.936193i	$-0.614324\pi$
$662$	−13.2555	−	2.52862i	−0.515190	−	0.0982777i
$663$	1.15192	−	2.09533i	0.0447368	−	0.0813760i
$664$	−11.5339	−	60.4626i	−0.447600	−	2.34640i
$665$	−12.8129	−	21.2857i	−0.496861	−	0.825426i
$666$	8.72136	+	4.79461i	0.337946	+	0.185787i
$667$	−6.15119	−	0.387000i	−0.238175	−	0.0149847i
$668$	74.9439	+	103.151i	2.89967	+	3.99105i
$669$	2.06948	−	0.531352i	0.0800107	−	0.0205433i
$670$	−39.6686	+	17.5337i	−1.53253	+	0.677386i
$671$	1.21997	+	19.3909i	0.0470965	+	0.748577i
$672$	−18.6485	+	72.6310i	−0.719380	+	2.80180i
$673$	0.612633	−	4.84949i	0.0236153	−	0.186934i	−0.975894	−	0.218243i	$-0.929968\pi$
$673$	0.612633	−	4.84949i	0.0236153	−	0.186934i	0.999510	+	0.0313088i	$0.00996752\pi$
$674$	45.8711	−	33.3273i	1.76689	−	1.28372i
$675$	−15.9156	+	15.4186i	−0.612593	+	0.593464i
$676$	17.9482	+	13.0402i	0.690317	+	0.501545i
$677$	−10.1498	+	10.8084i	−0.390087	+	0.415400i	−0.893796	−	0.448473i	$-0.851968\pi$
$677$	−10.1498	+	10.8084i	−0.390087	+	0.415400i	0.503710	+	0.863873i	$0.331968\pi$
$678$	−7.57044	−	19.1207i	−0.290741	−	0.734327i
$679$	0.487902	+	0.125272i	0.0187240	+	0.00480750i
$680$	3.11138	−	20.6845i	0.119316	−	0.793214i
$681$	−0.164183	−	0.258711i	−0.00629151	−	0.00991384i
$682$			7.66770i			0.293611i
$683$	−15.3404	+	9.73529i	−0.586982	+	0.372510i	−0.795905	−	0.605422i	$-0.793004\pi$
$683$	−15.3404	+	9.73529i	−0.586982	+	0.372510i	0.208922	+	0.977932i	$0.433004\pi$
$684$	−27.8395	+	26.1431i	−1.06447	+	0.999605i
$685$	−19.8926	−	11.5566i	−0.760057	−	0.441553i
$686$	−0.873943	+	0.480454i	−0.0333673	+	0.0183438i
$687$	−20.1671	+	9.48993i	−0.769424	+	0.362064i
$688$	85.3850	−	40.1791i	3.25527	−	1.53181i
$689$	−32.2202	+	17.7132i	−1.22749	+	0.674820i
$690$	6.94721	+	15.7175i	0.264476	+	0.598355i
$691$	−7.45531	+	7.00100i	−0.283613	+	0.266331i	−0.813277	−	0.581877i	$-0.802318\pi$
$691$	−7.45531	+	7.00100i	−0.283613	+	0.266331i	0.529663	+	0.848208i	$0.322318\pi$
$692$	118.739	−	75.3538i	4.51376	−	2.86452i
$693$			17.0261i			0.646766i
$694$	−11.4252	−	18.0032i	−0.433695	−	0.683394i
$695$	39.1254	−	6.50920i	1.48411	−	0.246908i
$696$	14.6717	+	3.76706i	0.556131	+	0.142790i
$697$	2.05804	+	5.19801i	0.0779537	+	0.196889i
$698$	0.198089	−	0.210943i	0.00749777	−	0.00798431i
$699$	0.850672	+	0.618049i	0.0321754	+	0.0233768i
$700$	−103.825	+	1.61525i	−3.92423	+	0.0610506i
$701$	−34.6997	+	25.2108i	−1.31059	+	0.952199i	−0.310590	+	0.950544i	$0.600527\pi$
$701$	−34.6997	+	25.2108i	−1.31059	+	0.952199i	−0.999999	+	0.00165460i	$0.999473\pi$
$702$	−4.58905	+	36.3261i	−0.173203	+	1.37104i
$703$	1.16498	−	4.53730i	0.0439381	−	0.171127i
$704$	−4.28862	−	68.1656i	−0.161633	−	2.56909i
$705$	−0.426610	−	4.16688i	−0.0160671	−	0.156934i
$706$	13.5071	−	3.46802i	0.508345	−	0.130521i
$707$	−29.8694	−	41.1117i	−1.12335	−	1.54617i
$708$	−3.34625	−	0.210528i	−0.125760	−	0.00791214i
$709$	33.7487	+	18.5535i	1.26746	+	0.696792i	0.966456	−	0.256831i	$-0.0826784\pi$
$709$	33.7487	+	18.5535i	1.26746	+	0.696792i	0.301004	+	0.953623i	$0.402678\pi$
$710$	−61.2510	−	25.9419i	−2.29871	−	0.973584i
$711$	1.80305	+	9.45190i	0.0676195	+	0.354474i
$712$	38.8889	−	70.7387i	1.45742	−	2.65104i
$713$	−4.60895	−	0.879203i	−0.172606	−	0.0329264i
$714$	−5.95484	−	5.59197i	−0.222854	−	0.209274i
$715$	13.3208	+	0.314935i	0.498171	+	0.0117779i
$716$	−33.7258	−	71.6710i	−1.26039	−	2.67847i
$717$	−7.74594	+	19.5640i	−0.289277	+	0.730631i
$718$	10.9941	−	15.1321i	0.410297	−	0.564725i
$719$	−3.76898	+	4.55592i	−0.140559	+	0.169907i	−0.836095	−	0.548584i	$-0.815167\pi$
$719$	−3.76898	+	4.55592i	−0.140559	+	0.169907i	0.695536	+	0.718491i	$0.255167\pi$
$720$	18.4464	+	79.6108i	0.687458	+	2.96692i
$721$	29.9758	−	47.2343i	1.11636	−	1.75910i
$722$	−23.5099	−	14.9199i	−0.874950	−	0.555260i
$723$	20.8900	−	3.98499i	0.776909	−	0.148203i
$724$	−21.4600	+	66.0472i	−0.797556	+	2.45462i
$725$	0.143480	+	9.22264i	0.00532870	+	0.342520i
$726$	−5.01969	−	15.4490i	−0.186298	−	0.573367i
$727$	22.6318	+	41.1671i	0.839368	+	1.52680i	0.849952	+	0.526860i	$0.176631\pi$
$727$	22.6318	+	41.1671i	0.839368	+	1.52680i	−0.0105839	+	0.999944i	$0.503369\pi$
$728$	−84.7297	+	70.0945i	−3.14029	+	2.59788i
$729$	3.49361	−	1.38322i	0.129393	−	0.0512303i
$730$	−12.3827	+	9.76020i	−0.458304	+	0.361241i
$731$	−0.355328	+	5.64778i	−0.0131423	+	0.208891i
$732$	43.3597	+	14.0884i	1.60262	+	0.520723i
$733$	22.4605	+	18.5810i	0.829599	+	0.686304i	0.951974	−	0.306180i	$-0.0990510\pi$
$733$	22.4605	+	18.5810i	0.829599	+	0.686304i	−0.122375	+	0.992484i	$0.539051\pi$
$734$	−2.88966	+	15.1481i	−0.106659	+	0.559127i
$735$	−7.17013	+	10.7291i	−0.264474	+	0.395748i
$736$	79.7345	+	10.0728i	2.93905	+	0.371289i
$737$	−1.75339	−	13.8795i	−0.0645870	−	0.511259i
$738$	−25.4381	−	27.0888i	−0.936388	−	0.997152i
$739$	−11.5530	+	24.5513i	−0.424983	+	0.903136i	0.571599	+	0.820533i	$0.306323\pi$
$739$	−11.5530	+	24.5513i	−0.424983	+	0.903136i	−0.996583	+	0.0826027i	$0.973677\pi$
$740$	−13.9515	−	13.7362i	−0.512869	−	0.504952i
$741$	7.42187	−	0.937600i	0.272649	−	0.0344436i
$742$	31.2389	+	121.667i	1.14681	+	4.46655i
$743$	−41.4351	+	13.4631i	−1.52011	+	0.493912i	−0.945806	−	0.324733i	$-0.894725\pi$
$743$	−41.4351	+	13.4631i	−1.52011	+	0.493912i	−0.574299	+	0.818645i	$0.694725\pi$
$744$	10.7218	+	4.24508i	0.393082	+	0.155632i
$745$	−2.35341	−	3.40565i	−0.0862222	−	0.124773i
$746$	45.2320	+	54.6761i	1.65606	+	2.00184i
$747$	−14.3925	+	0.905496i	−0.526592	+	0.0331304i
$748$	9.52538	+	4.48230i	0.348282	+	0.163889i
$749$	46.4859			1.69856
$750$	22.6356	−	12.2069i	0.826535	−	0.445731i
$751$	−23.5621			−0.859795			−0.429897	−	0.902878i	$-0.641450\pi$
$751$	−23.5621			−0.859795			−0.429897	+	0.902878i	$0.641450\pi$
$752$	−32.1994	−	15.1519i	−1.17419	−	0.552532i
$753$	16.4656	−	1.03593i	0.600039	−	0.0377512i
$754$	9.71479	+	11.7432i	0.353792	+	0.427661i
$755$	0.815602	−	34.4976i	0.0296828	−	1.25550i
$756$	85.5764	+	33.8821i	3.11239	+	1.23228i
$757$	−11.5483	+	3.75227i	−0.419731	+	0.136379i	−0.511265	−	0.859423i	$-0.670823\pi$
$757$	−11.5483	+	3.75227i	−0.419731	+	0.136379i	0.0915343	+	0.995802i	$0.470823\pi$
$758$	3.64283	+	14.1879i	0.132314	+	0.515328i
$759$	−5.49935	+	0.694729i	−0.199614	+	0.0252171i
$760$	58.0766	−	30.1628i	2.10666	−	1.09412i
$761$	−4.88306	+	10.3770i	−0.177011	+	0.376167i	−0.973568	−	0.228395i	$-0.926652\pi$
$761$	−4.88306	+	10.3770i	−0.177011	+	0.376167i	0.796558	+	0.604563i	$0.206652\pi$
$762$	−5.99700	−	6.38615i	−0.217248	−	0.231346i
$763$	−4.59514	−	36.3743i	−0.166355	−	1.31684i
$764$	−97.0466	−	12.2598i	−3.51102	−	0.443545i
$765$	−4.71649	−	1.33058i	−0.170525	−	0.0481071i
$766$	−1.93294	+	10.1328i	−0.0698399	+	0.366114i
$767$	−1.66594	−	1.37818i	−0.0601535	−	0.0497633i
$768$	−47.1766	−	15.3286i	−1.70234	−	0.553124i
$769$	−1.54393	+	24.5401i	−0.0556755	+	0.884937i	0.866745	+	0.498751i	$0.166208\pi$
$769$	−1.54393	+	24.5401i	−0.0556755	+	0.884937i	−0.922421	+	0.386186i	$0.873792\pi$
$770$	12.3597	−	43.8115i	0.445413	−	1.57886i
$771$	−8.98598	+	3.55780i	−0.323622	+	0.128131i
$772$	−76.7696	+	63.5093i	−2.76300	+	2.28575i
$773$	8.40638	+	15.2911i	0.302356	+	0.549984i	0.983219	−	0.182427i	$-0.0583952\pi$
$773$	8.40638	+	15.2911i	0.302356	+	0.549984i	−0.680863	+	0.732411i	$0.738395\pi$
$774$	−11.6236	−	35.7737i	−0.417802	−	1.28586i
$775$	−0.771602	+	6.97936i	−0.0277168	+	0.250706i
$776$	−0.410020	+	1.26191i	−0.0147189	+	0.0453000i
$777$	−4.81375	+	0.918272i	−0.172692	+	0.0329428i
$778$	−39.2420	−	24.9037i	−1.40689	−	0.892841i
$779$	−9.37211	+	14.7681i	−0.335791	+	0.529122i
$780$	12.1938	−	28.7905i	0.436607	−	1.03087i
$781$	13.6768	−	16.5324i	0.489394	−	0.591575i
$782$	−5.14611	+	7.08302i	−0.184025	+	0.253288i
$783$	3.00969	−	7.60161i	0.107558	−	0.271659i
$784$	46.6799	+	99.1998i	1.66714	+	3.54285i
$785$	−1.29055	+	3.67407i	−0.0460619	+	0.131133i
$786$	−0.747106	−	0.701580i	−0.0266484	−	0.0250245i
$787$	−24.1798	−	4.61254i	−0.861916	−	0.164419i	−0.262574	−	0.964912i	$-0.584571\pi$
$787$	−24.1798	−	4.61254i	−0.861916	−	0.164419i	−0.599343	+	0.800493i	$0.704571\pi$
$788$	64.6201	−	117.543i	2.30199	−	4.18731i
$789$	0.803944	+	4.21442i	0.0286212	+	0.150037i
$790$	2.22181	−	25.6306i	0.0790484	−	0.911895i
$791$	−29.2121	−	16.0595i	−1.03866	−	0.571010i
$792$	−44.7593	−	2.81602i	−1.59045	−	0.100063i
$793$	17.2807	+	23.7848i	0.613655	+	0.844623i
$794$	−59.1950	+	15.1987i	−2.10075	+	0.539381i
$795$	−15.2710	−	17.0523i	−0.541607	−	0.604784i
$796$	−6.59048	−	104.753i	−0.233593	−	3.71286i
$797$	−1.30612	+	5.08700i	−0.0462651	+	0.180191i	−0.987516	−	0.157516i	$-0.949651\pi$
$797$	−1.30612	+	5.08700i	−0.0462651	+	0.180191i	0.941251	+	0.337707i	$0.109651\pi$
$798$	3.20319	−	25.3558i	0.113392	−	0.897587i
$799$	1.72647	−	1.25435i	0.0610782	−	0.0443759i
$800$	5.68397	−	120.141i	0.200959	−	4.24761i
$801$	−15.3004	−	11.1164i	−0.540613	−	0.392779i
$802$	−3.80436	+	4.05124i	−0.134337	+	0.143054i
$803$	−1.87221	−	4.72865i	−0.0660687	−	0.166871i
$804$	−31.7961	−	8.16384i	−1.12136	−	0.287917i
$805$	24.9173	+	12.4528i	0.878219	+	0.438905i
$806$	6.21693	+	9.79631i	0.218982	+	0.345060i
$807$		−	21.8965i		−	0.770794i
$808$	113.018	−	71.7232i	3.97595	−	2.52321i
$809$	1.22216	−	1.14769i	0.0429690	−	0.0403506i	−0.662765	−	0.748827i	$-0.730617\pi$
$809$	1.22216	−	1.14769i	0.0429690	−	0.0403506i	0.705734	+	0.708477i	$0.250617\pi$
$810$	19.5712	−	2.00372i	0.687661	−	0.0704036i
$811$	45.1332	−	24.8122i	1.58484	−	0.871274i	0.586734	−	0.809779i	$-0.300413\pi$
$811$	45.1332	−	24.8122i	1.58484	−	0.871274i	0.998107	−	0.0614948i	$-0.0195868\pi$
$812$	34.6649	−	16.3120i	1.21650	−	0.572440i
$813$	−4.41373	+	2.07694i	−0.154796	+	0.0728416i
$814$	7.52147	−	4.13496i	0.263627	−	0.144930i
$815$	−11.8812	+	55.1657i	−0.416182	+	1.93237i
$816$	9.21933	−	8.65753i	0.322741	−	0.303074i
$817$	−14.9486	+	9.48670i	−0.522987	+	0.331898i
$818$		−	6.45953i		−	0.225852i
$819$	13.8046	+	21.7526i	0.482373	+	0.760098i
$820$	33.6939	+	64.8756i	1.17664	+	2.26555i
$821$	−1.49524	−	0.383913i	−0.0521843	−	0.0133987i	0.222507	−	0.974931i	$-0.428576\pi$
$821$	−1.49524	−	0.383913i	−0.0521843	−	0.0133987i	−0.274692	+	0.961532i	$0.588576\pi$
$822$	−8.71200	−	22.0040i	−0.303866	−	0.767478i
$823$	−38.2311	+	40.7120i	−1.33265	+	1.41913i	−0.499258	+	0.866453i	$0.666394\pi$
$823$	−38.2311	+	40.7120i	−1.33265	+	1.41913i	−0.833395	+	0.552678i	$0.813606\pi$
$824$	119.215	+	86.6148i	4.15305	+	3.01737i
$825$	1.68098	+	8.12335i	0.0585241	+	0.282819i
$826$	−5.97587	+	4.34172i	−0.207927	+	0.151068i
$827$	−3.33950	+	26.4348i	−0.116126	+	0.919230i	0.821167	+	0.570687i	$0.193323\pi$
$827$	−3.33950	+	26.4348i	−0.116126	+	0.919230i	−0.937293	+	0.348542i	$0.886677\pi$
$828$	10.6487	−	41.4738i	0.370067	−	1.44131i
$829$	−2.19516	−	34.8910i	−0.0762410	−	1.21182i	−0.831173	−	0.556013i	$-0.812330\pi$
$829$	−2.19516	−	34.8910i	−0.0762410	−	1.21182i	0.754932	−	0.655803i	$-0.227670\pi$
$830$	37.6921	+	8.11789i	1.30831	+	0.281776i
$831$	−14.2295	+	3.65352i	−0.493616	+	0.126739i
$832$	−60.7475	−	83.6117i	−2.10604	−	2.89871i
$833$	−6.56156	−	0.412818i	−0.227345	−	0.0143033i
$834$	35.7543	+	19.6561i	1.23807	+	0.680635i
$835$	−49.8668	+	11.5545i	−1.72571	+	0.399860i
$836$	6.17160	+	32.3527i	0.213449	+	1.11894i
$837$	2.99846	−	5.45418i	0.103642	−	0.188524i
$838$	−42.4095	−	8.09005i	−1.46501	−	0.279466i
$839$	−33.3401	−	31.3084i	−1.15103	−	1.08089i	−0.995663	−	0.0930292i	$-0.970345\pi$
$839$	−33.3401	−	31.3084i	−1.15103	−	1.08089i	−0.155364	−	0.987857i	$-0.549655\pi$
$840$	−54.4195	−	41.5382i	−1.87765	−	1.43320i
$841$	10.8986	+	23.1608i	0.375815	+	0.798647i
$842$	36.3062	−	91.6989i	1.25119	−	3.16015i
$843$	−8.54409	+	11.7599i	−0.294274	+	0.405034i
$844$	16.2727	−	19.6703i	0.560130	−	0.677081i
$845$	−7.63083	+	4.59334i	−0.262508	+	0.158016i
$846$	−7.60061	+	11.9766i	−0.261314	+	0.411765i
$847$	−22.2324	−	14.1091i	−0.763915	−	0.484795i
$848$	−191.031	+	36.4412i	−6.56005	+	1.25140i
$849$	−2.85412	+	8.78407i	−0.0979530	+	0.301468i
$850$	11.1706	+	6.84769i	0.383149	+	0.234874i
$851$	1.62303	+	4.99518i	0.0556368	+	0.171232i
$852$	−24.2552	−	44.1200i	−0.830969	−	1.51153i
$853$	−34.6624	+	28.6752i	−1.18682	+	0.981820i	−1.00000		0.000574365i	$-0.999817\pi$
$853$	−34.6624	+	28.6752i	−1.18682	+	0.981820i	−0.186817	+	0.982395i	$0.559817\pi$
$854$	93.3867	−	36.9744i	3.19563	−	1.26524i
$855$	−5.30562	−	14.3849i	−0.181448	−	0.491953i
$856$	−7.68852	+	122.206i	−0.262788	+	4.17690i
$857$	11.2542	+	3.65671i	0.384436	+	0.124911i	0.494858	−	0.868974i	$-0.335220\pi$
$857$	11.2542	+	3.65671i	0.384436	+	0.124911i	−0.110422	+	0.993885i	$0.535220\pi$
$858$	10.5613	+	8.73707i	0.360557	+	0.298279i
$859$	10.6265	−	55.7059i	0.362570	−	1.90066i	−0.0672343	−	0.997737i	$-0.521418\pi$
$859$	10.6265	−	55.7059i	0.362570	−	1.90066i	0.429804	−	0.902922i	$-0.358582\pi$
$860$	2.89950	+	73.9404i	0.0988722	+	2.52135i
$861$	18.1535	+	2.29332i	0.618668	+	0.0781560i
$862$	3.54972	+	28.0989i	0.120904	+	0.957052i
$863$	26.7904	+	28.5289i	0.911955	+	0.971134i	0.999687	−	0.0250104i	$-0.00796189\pi$
$863$	26.7904	+	28.5289i	0.911955	+	0.971134i	−0.0877319	+	0.996144i	$0.527962\pi$
$864$	−45.3920	+	96.4629i	−1.54427	+	3.28173i
$865$	9.26554	+	55.6932i	0.315038	+	1.89362i
$866$	63.8853	−	8.07059i	2.17091	−	0.274250i
$867$	−3.34596	−	13.0316i	−0.113635	−	0.442578i
$868$	27.7381	−	9.01265i	0.941491	−	0.305909i
$869$	7.71574	+	3.05488i	0.261739	+	0.103630i
$870$	−5.75701	+	7.54230i	−0.195181	+	0.255708i
$871$	−13.4936	−	16.3109i	−0.457213	−	0.552675i
$872$	96.3833	−	6.06393i	3.26395	−	0.205350i
$873$	0.281276	+	0.132359i	0.00951976	+	0.00447966i
$874$	−27.3915			−0.926531
$875$	15.6589	−	38.6348i	0.529369	−	1.30609i
$876$	−11.9339			−0.403210
$877$	18.6826	+	8.79138i	0.630868	+	0.296864i	0.714503	−	0.699633i	$-0.246653\pi$
$877$	18.6826	+	8.79138i	0.630868	+	0.296864i	−0.0836351	+	0.996496i	$0.526653\pi$
$878$	52.2164	−	3.28517i	1.76222	−	0.110869i
$879$	−14.0669	−	17.0040i	−0.474466	−	0.573530i
$880$	66.4940	+	23.3567i	2.24151	+	0.787354i
$881$	43.8729	+	17.3705i	1.47812	+	0.585228i	0.962425	−	0.271546i	$-0.0875350\pi$
$881$	43.8729	+	17.3705i	1.47812	+	0.585228i	0.515692	+	0.856774i	$0.327535\pi$
$882$	41.5617	−	13.5042i	1.39946	−	0.454711i
$883$	−8.18959	−	31.8964i	−0.275602	−	1.07340i	−0.944093	−	0.329678i	$-0.893060\pi$
$883$	−8.18959	−	31.8964i	−0.275602	−	1.07340i	0.668492	−	0.743720i	$-0.266940\pi$
$884$	15.8039	−	1.99650i	0.531543	−	0.0671495i
$885$	0.601754	−	1.20407i	0.0202277	−	0.0404744i
$886$	−43.0797	+	91.5489i	−1.44729	+	3.07565i
$887$	−14.5050	−	15.4463i	−0.487030	−	0.518635i	0.437770	−	0.899087i	$-0.355768\pi$
$887$	−14.5050	−	15.4463i	−0.487030	−	0.518635i	−0.924801	+	0.380452i	$0.875768\pi$
$888$	−1.61785	−	12.8066i	−0.0542915	−	0.429761i
$889$	−14.0888	−	1.77983i	−0.472522	−	0.0596935i
$890$	31.3014	+	39.7118i	1.04922	+	1.33114i
$891$	−1.18911	+	6.23354i	−0.0398367	+	0.208831i
$892$	10.9676	+	9.07317i	0.367222	+	0.303792i
$893$	6.34984	+	2.06319i	0.212489	+	0.0690419i
$894$	0.267391	−	4.25005i	0.00894288	−	0.142143i
$895$	31.7756	−	1.24605i	1.06214	−	0.0416509i
$896$	−161.498	+	63.9417i	−5.39528	+	2.13614i
$897$	−6.46272	+	5.34643i	−0.215784	+	0.178512i
$898$	−10.2666	−	18.6749i	−0.342602	−	0.623190i
$899$	−0.800578	−	2.46393i	−0.0267008	−	0.0821765i
$900$	−63.1249	−	11.0269i	−2.10416	−	0.367565i
$901$	3.60387	−	11.0916i	0.120062	−	0.369513i
$902$	−31.4802	+	6.00517i	−1.04818	+	0.199950i
$903$	15.6382	+	9.92429i	0.520406	+	0.330260i
$904$	47.0499	−	74.1388i	1.56486	−	2.46582i
$905$	−21.0561	−	18.2744i	−0.699929	−	0.607460i
$906$	22.6268	−	27.3511i	0.751725	−	0.908680i
$907$	−2.94568	+	4.05438i	−0.0978096	+	0.134623i	−0.855117	−	0.518436i	$-0.826515\pi$
$907$	−2.94568	+	4.05438i	−0.0978096	+	0.134623i	0.757307	+	0.653059i	$0.226515\pi$
$908$	0.751459	−	1.89797i	0.0249380	−	0.0629863i
$909$	−13.3525	−	28.3756i	−0.442876	−	0.941159i
$910$	−19.7313	−	65.9951i	−0.654085	−	2.18772i
$911$	−22.7461	−	21.3600i	−0.753610	−	0.707687i	0.209198	−	0.977873i	$-0.432915\pi$
$911$	−22.7461	−	21.3600i	−0.753610	−	0.707687i	−0.962808	+	0.270186i	$0.912915\pi$
$912$	38.8673	+	7.41433i	1.28702	+	0.245513i
$913$	−5.99151	+	10.8985i	−0.198290	+	0.360688i
$914$	−2.26715	−	11.8848i	−0.0749908	−	0.393116i
$915$	−11.9970	+	13.8232i	−0.396610	+	0.456982i
$916$	−130.119	−	71.5336i	−4.29925	−	2.36354i
$917$	−1.65805	−	0.104315i	−0.0547535	−	0.00344480i
$918$	−6.82636	−	9.39568i	−0.225304	−	0.310104i
$919$	36.2741	−	9.31360i	1.19657	−	0.307227i	0.402711	−	0.915327i	$-0.368068\pi$
$919$	36.2741	−	9.31360i	1.19657	−	0.307227i	0.793860	+	0.608100i	$0.208068\pi$
$920$	−36.8581	+	63.4447i	−1.21517	+	2.09171i
$921$	0.204847	+	3.25595i	0.00674994	+	0.107287i
$922$	−16.6365	+	64.7949i	−0.547894	+	2.13391i
$923$	4.06919	−	32.2110i	0.133939	−	1.06024i
$924$	27.8749	−	20.2523i	0.917018	−	0.666252i
$925$	7.26236	−	3.00688i	0.238785	−	0.0988654i
$926$	−38.2527	−	27.7922i	−1.25706	−	0.913309i
$927$	23.6331	−	25.1667i	0.776214	−	0.826584i
$928$	16.3357	+	41.2592i	0.536245	+	1.35440i
$929$	19.6262	+	5.03915i	0.643915	+	0.165329i	0.556506	−	0.830843i	$-0.312141\pi$
$929$	19.6262	+	5.03915i	0.643915	+	0.165329i	0.0874085	+	0.996173i	$0.472141\pi$
$930$	−5.06780	+	5.14725i	−0.166180	+	0.168785i
$931$	−11.0216	−	17.3672i	−0.361218	−	0.569188i
$932$			7.00504i			0.229458i
$933$	11.8030	−	7.49039i	0.386412	−	0.245224i
$934$	6.13634	−	5.76241i	0.200787	−	0.188552i
$935$	−3.14840	+	2.81951i	−0.102964	+	0.0922080i
$936$	−59.4680	+	32.6928i	−1.94377	+	1.06860i
$937$	36.5256	−	17.1876i	1.19324	−	0.561495i	0.276511	−	0.961011i	$-0.410822\pi$
$937$	36.5256	−	17.1876i	1.19324	−	0.561495i	0.916726	+	0.399516i	$0.130822\pi$
$938$	−65.4379	+	30.7927i	−2.13662	+	1.00542i
$939$	−0.610373	+	0.335555i	−0.0199188	+	0.0109504i
$940$	20.7876	−	18.6161i	0.678018	−	0.607191i
$941$	−16.6438	+	15.6295i	−0.542571	+	0.509508i	−0.906663	−	0.421855i	$-0.861379\pi$
$941$	−16.6438	+	15.6295i	−0.542571	+	0.509508i	0.364093	+	0.931363i	$0.381379\pi$
$942$	−3.38226	+	2.14645i	−0.110200	+	0.0699351i
$943$		−	19.6109i		−	0.638618i
$944$	−6.12769	−	9.65570i	−0.199439	−	0.314266i
$945$	−25.9242	+	26.3307i	−0.843316	+	0.856537i
$946$	−31.4205	−	8.06742i	−1.02157	−	0.262294i
$947$	−0.651624	−	1.64581i	−0.0211749	−	0.0534818i	0.918804	−	0.394713i	$-0.129156\pi$
$947$	−0.651624	−	1.64581i	−0.0211749	−	0.0534818i	−0.939979	+	0.341231i	$0.889156\pi$
$948$	13.3299	−	14.1949i	0.432934	−	0.461028i
$949$	−6.22591	−	4.52339i	−0.202102	−	0.146835i
$950$	3.21004	+	40.8668i	0.104147	+	1.32589i
$951$	5.48630	−	3.98603i	0.177905	−	0.129256i
$952$	4.37155	−	34.6044i	0.141683	−	1.12154i
$953$	7.12649	−	27.7559i	0.230850	−	0.899100i	−0.742513	−	0.669831i	$-0.766366\pi$
$953$	7.12649	−	27.7559i	0.230850	−	0.899100i	0.973363	−	0.229269i	$-0.0736336\pi$
$954$	4.86746	+	77.3661i	0.157590	+	2.50482i
$955$	19.7269	−	33.9563i	0.638346	−	1.09880i
$956$	−135.776	+	34.8613i	−4.39130	+	1.12749i
$957$	−1.79898	−	2.47608i	−0.0581527	−	0.0800404i
$958$	−72.6137	−	4.56847i	−2.34604	−	0.147601i
$959$	−33.6171	−	18.4812i	−1.08555	−	0.596788i
$960$	42.1737	−	48.5934i	1.36115	−	1.56834i
$961$	5.43925	+	28.5136i	0.175460	+	0.919792i
$962$	6.25688	−	11.3812i	0.201730	−	0.366945i
$963$	28.1794	+	5.37551i	0.908068	+	0.173223i
$964$	103.280	+	96.9862i	3.32642	+	3.12372i
$965$	−11.4580	−	38.3237i	−0.368847	−	1.23368i
$966$	12.2007	+	25.9278i	0.392551	+	0.834213i
$967$	−1.26284	+	3.18958i	−0.0406103	+	0.102570i	−0.948666	−	0.316279i	$-0.897566\pi$
$967$	−1.26284	+	3.18958i	−0.0406103	+	0.102570i	0.908056	+	0.418849i	$0.137566\pi$
$968$	40.7682	−	56.1126i	1.31034	−	1.80353i
$969$	−1.51249	+	1.82829i	−0.0485883	+	0.0587332i
$970$	−0.627698	−	0.544773i	−0.0201542	−	0.0174916i
$971$	2.30319	−	3.62924i	0.0739128	−	0.116468i	−0.805361	−	0.592785i	$-0.798028\pi$
$971$	2.30319	−	3.62924i	0.0739128	−	0.116468i	0.879274	+	0.476317i	$0.158028\pi$
$972$	75.0983	+	47.6588i	2.40878	+	1.52866i
$973$	64.9669	−	12.3931i	2.08274	−	0.397304i
$974$	33.4192	−	102.854i	1.07082	−	3.29564i
$975$	8.73399	+	9.01552i	0.279712	+	0.288728i
$976$	48.0528	+	147.891i	1.53813	+	4.73388i
$977$	11.5241	+	20.9623i	0.368689	+	0.670643i	0.993957	−	0.109767i	$-0.0350104\pi$
$977$	11.5241	+	20.9623i	0.368689	+	0.670643i	−0.625268	+	0.780410i	$0.715010\pi$
$978$	−44.7280	+	37.0023i	−1.43024	+	1.18320i
$979$	−15.1650	+	6.00425i	−0.484675	+	0.191897i
$980$	−85.9035	+	3.36862i	−2.74409	+	0.107607i
$981$	1.42069	−	22.5812i	0.0453590	−	0.720961i
$982$	−34.9563	−	11.3580i	−1.11550	−	0.362448i
$983$	−2.88668	−	2.38807i	−0.0920708	−	0.0761676i	0.590250	−	0.807221i	$-0.299029\pi$
$983$	−2.88668	−	2.38807i	−0.0920708	−	0.0761676i	−0.682321	+	0.731053i	$0.739029\pi$
$984$	−9.03131	+	47.3438i	−0.287908	+	1.50927i
$985$	33.3355	+	42.2925i	1.06216	+	1.34755i
$986$	−4.79602	−	0.605878i	−0.152736	−	0.0192951i
$987$	−0.875401	−	6.92952i	−0.0278643	−	0.220569i
$988$	34.1162	+	36.3301i	1.08538	+	1.15581i
$989$	8.45199	−	17.9614i	0.268758	−	0.571139i
$990$	12.5586	−	25.1289i	0.399139	−	0.798650i
$991$	45.9680	−	5.80711i	1.46022	−	0.184469i	0.645251	−	0.763970i	$-0.276753\pi$
$991$	45.9680	−	5.80711i	1.46022	−	0.184469i	0.814971	+	0.579501i	$0.196753\pi$
$992$	8.40131	+	32.7209i	0.266742	+	1.03889i
$993$	3.89989	−	1.26715i	0.123759	−	0.0402118i
$994$	−103.130	−	40.8320i	−3.27108	−	1.29511i
$995$	39.7565	+	13.9649i	1.26037	+	0.442717i
$996$	18.6022	+	22.4861i	0.589432	+	0.712501i
$997$	44.7981	−	2.81846i	1.41877	−	0.0892614i	0.665217	−	0.746650i	$-0.268339\pi$
$997$	44.7981	−	2.81846i	1.41877	−	0.0892614i	0.753552	+	0.657388i	$0.228339\pi$
$998$	12.1438	+	5.71443i	0.384405	+	0.180887i
$999$	−6.96714			−0.220431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.9.1	✓	240
5.2	odd	4		625.2.g.b.326.24		480
5.3	odd	4		625.2.g.b.326.1		480
5.4	even	2		625.2.h.a.299.12		240
125.14	even	50	inner	125.2.h.a.14.1	yes	240
125.48	odd	100		625.2.g.b.301.1		480
125.77	odd	100		625.2.g.b.301.24		480
125.111	even	25		625.2.h.a.324.12		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.9.1	✓	240	1.1	even	1	trivial
125.2.h.a.14.1	yes	240	125.14	even	50	inner
625.2.g.b.301.1		480	125.48	odd	100
625.2.g.b.301.24		480	125.77	odd	100
625.2.g.b.326.1		480	5.3	odd	4
625.2.g.b.326.24		480	5.2	odd	4
625.2.h.a.299.12		240	5.4	even	2
625.2.h.a.324.12		240	125.111	even	25

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.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48947 - 1.17145i) q^{2} +(0.834394 - 0.0524956i) q^{3} +(3.55029 + 4.29156i) q^{4} +(-2.14236 + 0.640526i) q^{5} +(-2.13869 - 0.846768i) q^{6} +(-3.54615 + 1.15221i) q^{7} +(-2.44251 - 9.51294i) q^{8} +(-2.28289 + 0.288396i) q^{9} +O(q^{10})\)	\(q+(-2.48947 - 1.17145i) q^{2} +(0.834394 - 0.0524956i) q^{3} +(3.55029 + 4.29156i) q^{4} +(-2.14236 + 0.640526i) q^{5} +(-2.13869 - 0.846768i) q^{6} +(-3.54615 + 1.15221i) q^{7} +(-2.44251 - 9.51294i) q^{8} +(-2.28289 + 0.288396i) q^{9} +(6.08369 + 0.915114i) q^{10} +(-0.844939 + 1.79559i) q^{11} +(3.18763 + 3.39448i) q^{12} +(0.376351 + 2.97913i) q^{13} +(10.1778 + 1.28575i) q^{14} +(-1.75395 + 0.646916i) q^{15} +(-2.97610 + 15.6012i) q^{16} +(-0.733873 - 0.607112i) q^{17} +(6.02101 + 1.95634i) q^{18} +(0.187107 - 2.97398i) q^{19} +(-10.3549 - 6.92004i) q^{20} +(-2.89840 + 1.14756i) q^{21} +(4.20689 - 3.48024i) q^{22} +(1.60955 + 2.92776i) q^{23} +(-2.53740 - 7.80932i) q^{24} +(4.17945 - 2.74448i) q^{25} +(2.55299 - 7.85731i) q^{26} +(-4.35339 + 0.830454i) q^{27} +(-17.5347 - 11.1278i) q^{28} +(-0.988467 + 1.55757i) q^{29} +(5.12424 + 0.444199i) q^{30} +(-0.895184 + 1.08209i) q^{31} +(14.1392 - 19.4609i) q^{32} +(-0.610752 + 1.54258i) q^{33} +(1.11575 + 2.37108i) q^{34} +(6.85913 - 4.73986i) q^{35} +(-9.34257 - 8.77326i) q^{36} +(1.54420 + 0.294572i) q^{37} +(-3.94967 + 7.18443i) q^{38} +(0.470416 + 2.46601i) q^{39} +(11.3260 + 18.8157i) q^{40} +(-5.14368 - 2.82776i) q^{41} +(8.55979 + 0.538536i) q^{42} +(-3.49232 - 4.80676i) q^{43} +(-10.7056 + 2.74874i) q^{44} +(4.70605 - 2.08010i) q^{45} +(-0.577184 - 9.17407i) q^{46} +(-0.557210 + 2.17019i) q^{47} +(-1.66424 + 13.1738i) q^{48} +(5.58447 - 4.05735i) q^{49} +(-13.6196 + 1.93625i) q^{50} +(-0.644210 - 0.468046i) q^{51} +(-11.4489 + 12.1919i) q^{52} +(4.50755 + 11.3848i) q^{53} +(11.8105 + 3.03241i) q^{54} +(0.660048 - 4.38801i) q^{55} +(19.6224 + 30.9200i) q^{56} -2.49129i q^{57} +(4.28538 - 2.71958i) q^{58} +(-0.524881 + 0.492896i) q^{59} +(-9.00332 - 5.23046i) q^{60} +(8.57968 - 4.71672i) q^{61} +(3.49615 - 1.64516i) q^{62} +(7.76316 - 3.65307i) q^{63} +(-30.1605 + 16.5809i) q^{64} +(-2.71449 - 6.14131i) q^{65} +(3.32751 - 3.12474i) q^{66} +(-5.95228 + 3.77743i) q^{67} -5.30489i q^{68} +(1.49669 + 2.35841i) q^{69} +(-22.6281 + 3.76458i) q^{70} +(-10.4725 - 2.68889i) q^{71} +(8.31946 + 21.0125i) q^{72} +(-1.75437 + 1.86822i) q^{73} +(-3.49916 - 2.54229i) q^{74} +(3.34324 - 2.50938i) q^{75} +(13.4273 - 9.75550i) q^{76} +(0.927380 - 7.34097i) q^{77} +(1.71773 - 6.69012i) q^{78} +(-0.262574 - 4.17350i) q^{79} +(-3.61711 - 35.3298i) q^{80} +(3.09737 - 0.795268i) q^{81} +(9.49242 + 13.0652i) q^{82} +(6.25479 + 0.393518i) q^{83} +(-15.2150 - 8.36451i) q^{84} +(1.96109 + 0.830592i) q^{85} +(3.06311 + 16.0574i) q^{86} +(-0.743005 + 1.35152i) q^{87} +(19.1451 + 3.65212i) q^{88} +(5.99145 + 5.62634i) q^{89} +(-14.1523 - 0.334592i) q^{90} +(-4.76719 - 10.1308i) q^{91} +(-6.85030 + 17.3019i) q^{92} +(-0.690131 + 0.949884i) q^{93} +(3.92943 - 4.74987i) q^{94} +(1.50406 + 6.49119i) q^{95} +(10.7760 - 16.9803i) q^{96} +(-0.114066 - 0.0723885i) q^{97} +(-18.6554 + 3.55870i) q^{98} +(1.41106 - 4.34280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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