LMFDB - Embedded newform 538.2.d.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(5,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([104]))

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

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

chi := DirichletCharacter("538.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.d (of order $67$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$726$
Relative dimension:	$11$ over $\Q(\zeta_{67})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{67}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	538.5
Dual form			538.2.d.a.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.762685 - 0.646770i) q^{2} +(-0.591238 + 1.87944i) q^{3} +(0.163377 - 0.986564i) q^{4} +(-0.0746505 - 0.348523i) q^{5} +(0.764634 + 1.81581i) q^{6} +(2.45258 - 2.51077i) q^{7} +(-0.513474 - 0.858105i) q^{8} +(-0.723021 - 0.504862i) q^{9} +(-0.282349 - 0.217532i) q^{10} +(0.0872830 - 3.72225i) q^{11} +(1.75759 + 0.890352i) q^{12} +(-1.20750 - 0.930304i) q^{13} +(0.246659 - 3.50118i) q^{14} +(0.699164 + 0.0657597i) q^{15} +(-0.946616 - 0.322364i) q^{16} +(0.0214150 + 0.913257i) q^{17} +(-0.877967 + 0.0825770i) q^{18} +(6.81272 + 1.62714i) q^{19} +(-0.356037 + 0.0167066i) q^{20} +(3.26876 + 6.09393i) q^{21} +(-2.34087 - 2.89535i) q^{22} +(-0.536750 + 1.70623i) q^{23} +(1.91634 - 0.457697i) q^{24} +(4.44545 - 1.99592i) q^{25} +(-1.52264 + 0.0714480i) q^{26} +(-3.30591 + 2.54699i) q^{27} +(-2.07633 - 2.82983i) q^{28} +(7.10871 + 3.19167i) q^{29} +(0.575773 - 0.402044i) q^{30} +(-3.46208 - 0.162454i) q^{31} +(-0.930465 + 0.366380i) q^{32} +(6.94412 + 2.36478i) q^{33} +(0.607000 + 0.682677i) q^{34} +(-1.05815 - 0.667352i) q^{35} +(-0.616204 + 0.630823i) q^{36} +(-0.401372 - 3.40829i) q^{37} +(6.24835 - 3.16526i) q^{38} +(2.46237 - 1.71939i) q^{39} +(-0.260739 + 0.243016i) q^{40} +(-9.09451 - 7.71229i) q^{41} +(6.43441 + 2.53361i) q^{42} +(7.67640 + 3.44655i) q^{43} +(-3.65797 - 0.694241i) q^{44} +(-0.121983 + 0.289678i) q^{45} +(0.694165 + 1.64847i) q^{46} +(-4.35072 + 2.46676i) q^{47} +(1.16554 - 1.58851i) q^{48} +(-0.124693 - 5.31764i) q^{49} +(2.09958 - 4.39744i) q^{50} +(-1.72907 - 0.499705i) q^{51} +(-1.11508 + 1.03929i) q^{52} +(0.833288 + 0.328115i) q^{53} +(-0.874052 + 4.08072i) q^{54} +(-1.30381 + 0.247447i) q^{55} +(-3.41384 - 0.815359i) q^{56} +(-7.08606 + 11.8420i) q^{57} +(7.48598 - 2.16346i) q^{58} +(-0.182782 + 1.10374i) q^{59} +(0.179104 - 0.679026i) q^{60} +(-4.31332 - 6.49647i) q^{61} +(-2.74555 + 2.11527i) q^{62} +(-3.04086 + 0.577120i) q^{63} +(-0.472689 + 0.881230i) q^{64} +(-0.234092 + 0.490291i) q^{65} +(6.82564 - 2.68766i) q^{66} +(0.893511 + 5.39552i) q^{67} +(0.904485 + 0.128078i) q^{68} +(-2.88940 - 2.01757i) q^{69} +(-1.23866 + 0.175398i) q^{70} +(0.735467 + 10.4395i) q^{71} +(-0.0619725 + 0.879662i) q^{72} +(-14.4607 - 2.04768i) q^{73} +(-2.51050 - 2.33986i) q^{74} +(1.12288 + 9.53500i) q^{75} +(2.71833 - 6.45534i) q^{76} +(-9.13162 - 9.34826i) q^{77} +(0.765960 - 2.90394i) q^{78} +(5.67401 + 7.01802i) q^{79} +(-0.0416862 + 0.353982i) q^{80} +(-3.74362 - 10.2027i) q^{81} -11.9243 q^{82} +(-1.21155 - 3.30193i) q^{83} +(6.54609 - 2.22923i) q^{84} +(0.316693 - 0.0756387i) q^{85} +(8.08380 - 2.33623i) q^{86} +(-10.2015 + 11.4733i) q^{87} +(-3.23889 + 1.83638i) q^{88} +(-3.13439 - 1.97679i) q^{89} +(0.0943207 + 0.299828i) q^{90} +(-5.29727 + 0.750113i) q^{91} +(1.59561 + 0.808297i) q^{92} +(2.35224 - 6.41071i) q^{93} +(-1.72280 + 4.69527i) q^{94} +(0.0585254 - 2.49586i) q^{95} +(-0.138461 - 1.96537i) q^{96} +(-6.96520 + 10.4906i) q^{97} +(-3.53439 - 3.97504i) q^{98} +(-1.94233 + 2.64719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 726 q + 11 q^{2} + q^{3} - 11 q^{4} + q^{5} - q^{6} + 4 q^{7} + 11 q^{8} - 10 q^{9} - q^{10} + 5 q^{11} + q^{12} - 7 q^{13} - 4 q^{14} - 2 q^{15} - 11 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} + q^{20}+ \cdots + 25 q^{99}+O(q^{100}) $ 726 * q + 11 * q^2 + q^3 - 11 * q^4 + q^5 - q^6 + 4 * q^7 + 11 * q^8 - 10 * q^9 - q^10 + 5 * q^11 + q^12 - 7 * q^13 - 4 * q^14 - 2 * q^15 - 11 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 + q^20 - 191 * q^21 - 5 * q^22 + 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 185 * q^27 + 4 * q^28 + 7 * q^29 - 65 * q^30 + 4 * q^31 + 11 * q^32 + 18 * q^33 - 4 * q^34 + 22 * q^35 - 10 * q^36 + 216 * q^37 - 5 * q^38 - 4 * q^39 - q^40 - 122 * q^41 - 10 * q^42 + 5 * q^43 - 62 * q^44 + 9 * q^45 - 6 * q^46 + 211 * q^47 + q^48 + 9 * q^49 + 8 * q^50 + 18 * q^51 - 7 * q^52 - 141 * q^53 - 16 * q^54 - 28 * q^55 - 4 * q^56 + 4 * q^57 - 7 * q^58 + q^59 + 132 * q^60 - 60 * q^61 - 4 * q^62 - 11 * q^64 + 24 * q^65 - 18 * q^66 + 15 * q^67 + 4 * q^68 - 8 * q^69 - 22 * q^70 + 8 * q^71 + 10 * q^72 + 65 * q^73 - 15 * q^74 - 15 * q^75 + 5 * q^76 - 2 * q^77 + 4 * q^78 - 61 * q^79 + q^80 - 315 * q^81 - 280 * q^82 + 198 * q^83 - 258 * q^84 - 126 * q^85 - 5 * q^86 + 6 * q^87 - 5 * q^88 - 36 * q^89 - 9 * q^90 + 28 * q^91 + 6 * q^92 + 152 * q^93 - 10 * q^94 + 6 * q^95 - q^96 - 24 * q^97 - 9 * q^98 + 25 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{52}{67}\right)$

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 $

$2$	0.762685	−	0.646770i	0.539300	−	0.457335i
$2$	0.762685	−	0.646770i	0.539300	−	0.457335i
$3$	−0.591238	+	1.87944i	−0.341352	+	1.08509i	0.613921	+	0.789367i	$0.289591\pi$
$3$	−0.591238	+	1.87944i	−0.341352	+	1.08509i	−0.955273	+	0.295726i	$0.904439\pi$
$4$	0.163377	−	0.986564i	0.0816887	−	0.493282i
$5$	−0.0746505	−	0.348523i	−0.0333847	−	0.155864i	0.958019	−	0.286706i	$-0.0925604\pi$
$5$	−0.0746505	−	0.348523i	−0.0333847	−	0.155864i	−0.991403	+	0.130842i	$0.958232\pi$
$6$	0.764634	+	1.81581i	0.312160	+	0.741303i
$7$	2.45258	−	2.51077i	0.926989	−	0.948980i	−0.0718378	−	0.997416i	$-0.522886\pi$
$7$	2.45258	−	2.51077i	0.926989	−	0.948980i	0.998826	+	0.0484360i	$0.0154237\pi$
$8$	−0.513474	−	0.858105i	−0.181541	−	0.303386i
$9$	−0.723021	−	0.504862i	−0.241007	−	0.168287i
$10$	−0.282349	−	0.217532i	−0.0892867	−	0.0687896i
$11$	0.0872830	−	3.72225i	0.0263168	−	1.12230i	−0.814224	−	0.580551i	$-0.802837\pi$
$11$	0.0872830	−	3.72225i	0.0263168	−	1.12230i	0.840541	−	0.541748i	$-0.182237\pi$
$12$	1.75759	+	0.890352i	0.507372	+	0.257022i
$13$	−1.20750	−	0.930304i	−0.334901	−	0.258020i	0.429069	−	0.903272i	$-0.358842\pi$
$13$	−1.20750	−	0.930304i	−0.334901	−	0.258020i	−0.763970	+	0.645252i	$0.776752\pi$
$14$	0.246659	−	3.50118i	0.0659225	−	0.935730i
$15$	0.699164	+	0.0657597i	0.180523	+	0.0169791i
$16$	−0.946616	−	0.322364i	−0.236654	−	0.0805911i
$17$	0.0214150	+	0.913257i	0.00519389	+	0.221497i	0.996169	+	0.0874504i	$0.0278719\pi$
$17$	0.0214150	+	0.913257i	0.00519389	+	0.221497i	−0.990975	+	0.134047i	$0.957203\pi$
$18$	−0.877967	+	0.0825770i	−0.206939	+	0.0194636i
$19$	6.81272	+	1.62714i	1.56294	+	0.373293i	0.919780	−	0.392435i	$-0.128367\pi$
$19$	6.81272	+	1.62714i	1.56294	+	0.373293i	0.643165	+	0.765728i	$0.277621\pi$
$20$	−0.356037	+	0.0167066i	−0.0796122	+	0.00373571i
$21$	3.26876	+	6.09393i	0.713303	+	1.32980i
$22$	−2.34087	−	2.89535i	−0.499074	−	0.617291i
$23$	−0.536750	+	1.70623i	−0.111920	+	0.355773i	−0.993140	−	0.116934i	$-0.962693\pi$
$23$	−0.536750	+	1.70623i	−0.111920	+	0.355773i	0.881220	+	0.472707i	$0.156723\pi$
$24$	1.91634	−	0.457697i	0.391171	−	0.0934270i
$25$	4.44545	−	1.99592i	0.889090	−	0.399183i
$26$	−1.52264	+	0.0714480i	−0.298614	+	0.0140121i
$27$	−3.30591	+	2.54699i	−0.636223	+	0.490169i
$28$	−2.07633	−	2.82983i	−0.392390	−	0.534788i
$29$	7.10871	+	3.19167i	1.32005	+	0.592678i	0.942777	−	0.333423i	$-0.108204\pi$
$29$	7.10871	+	3.19167i	1.32005	+	0.592678i	0.377277	+	0.926100i	$0.376860\pi$
$30$	0.575773	−	0.402044i	0.105121	−	0.0734029i
$31$	−3.46208	−	0.162454i	−0.621808	−	0.0291776i	−0.266360	−	0.963874i	$-0.585821\pi$
$31$	−3.46208	−	0.162454i	−0.621808	−	0.0291776i	−0.355448	+	0.934696i	$0.615672\pi$
$32$	−0.930465	+	0.366380i	−0.164485	+	0.0647675i
$33$	6.94412	+	2.36478i	1.20882	+	0.411655i
$34$	0.607000	+	0.682677i	0.104100	+	0.117078i
$35$	−1.05815	−	0.667352i	−0.178859	−	0.112803i
$36$	−0.616204	+	0.630823i	−0.102701	+	0.105137i
$37$	−0.401372	−	3.40829i	−0.0659851	−	0.560319i	−0.985795	−	0.167954i	$-0.946284\pi$
$37$	−0.401372	−	3.40829i	−0.0659851	−	0.560319i	0.919810	−	0.392365i	$-0.128343\pi$
$38$	6.24835	−	3.16526i	1.01362	−	0.513473i
$39$	2.46237	−	1.71939i	0.394294	−	0.275323i
$40$	−0.260739	+	0.243016i	−0.0412264	+	0.0384242i
$41$	−9.09451	−	7.71229i	−1.42032	−	1.20446i	−0.946025	−	0.324094i	$-0.894941\pi$
$41$	−9.09451	−	7.71229i	−1.42032	−	1.20446i	−0.474298	−	0.880364i	$-0.657298\pi$
$42$	6.43441	+	2.53361i	0.992851	+	0.390945i
$43$	7.67640	+	3.44655i	1.17064	+	0.525593i	0.899489	−	0.436944i	$-0.143939\pi$
$43$	7.67640	+	3.44655i	1.17064	+	0.525593i	0.271151	+	0.962537i	$0.412596\pi$
$44$	−3.65797	−	0.694241i	−0.551460	−	0.104661i
$45$	−0.121983	+	0.289678i	−0.0181841	+	0.0431826i
$46$	0.694165	+	1.64847i	0.102349	+	0.243053i
$47$	−4.35072	+	2.46676i	−0.634617	+	0.359813i	−0.776543	−	0.630064i	$-0.783029\pi$
$47$	−4.35072	+	2.46676i	−0.634617	+	0.359813i	0.141926	+	0.989877i	$0.454670\pi$
$48$	1.16554	−	1.58851i	0.168231	−	0.229282i
$49$	−0.124693	−	5.31764i	−0.0178133	−	0.759663i
$50$	2.09958	−	4.39744i	0.296926	−	0.621892i
$51$	−1.72907	−	0.499705i	−0.242118	−	0.0699726i
$52$	−1.11508	+	1.03929i	−0.154634	+	0.144123i
$53$	0.833288	+	0.328115i	0.114461	+	0.0450701i	0.422917	−	0.906169i	$-0.361006\pi$
$53$	0.833288	+	0.328115i	0.114461	+	0.0450701i	−0.308456	+	0.951239i	$0.599812\pi$
$54$	−0.874052	+	4.08072i	−0.118943	+	0.555316i
$55$	−1.30381	+	0.247447i	−0.175805	+	0.0333658i
$56$	−3.41384	−	0.815359i	−0.456193	−	0.108957i
$57$	−7.08606	+	11.8420i	−0.938571	+	1.56852i
$58$	7.48598	−	2.16346i	0.982958	−	0.284077i
$59$	−0.182782	+	1.10374i	−0.0237962	+	0.143694i	−0.995842	−	0.0910963i	$-0.970963\pi$
$59$	−0.182782	+	1.10374i	−0.0237962	+	0.143694i	0.972046	+	0.234791i	$0.0754405\pi$
$60$	0.179104	−	0.679026i	0.0231222	−	0.0876618i
$61$	−4.31332	−	6.49647i	−0.552264	−	0.831788i	0.445726	−	0.895170i	$-0.352946\pi$
$61$	−4.31332	−	6.49647i	−0.552264	−	0.831788i	−0.997989	+	0.0633820i	$0.979811\pi$
$62$	−2.74555	+	2.11527i	−0.348685	+	0.268639i
$63$	−3.04086	+	0.577120i	−0.383112	+	0.0727103i
$64$	−0.472689	+	0.881230i	−0.0590861	+	0.110154i
$65$	−0.234092	+	0.490291i	−0.0290355	+	0.0608131i
$66$	6.82564	−	2.68766i	0.840178	−	0.330829i
$67$	0.893511	+	5.39552i	0.109160	+	0.659167i	0.984463	+	0.175593i	$0.0561842\pi$
$67$	0.893511	+	5.39552i	0.109160	+	0.659167i	−0.875303	+	0.483575i	$0.839338\pi$
$68$	0.904485	+	0.128078i	0.109685	+	0.0155318i
$69$	−2.88940	−	2.01757i	−0.347842	−	0.242887i
$70$	−1.23866	+	0.175398i	−0.148048	+	0.0209641i
$71$	0.735467	+	10.4395i	0.0872839	+	1.23894i	0.825510	+	0.564388i	$0.190888\pi$
$71$	0.735467	+	10.4395i	0.0872839	+	1.23894i	−0.738226	+	0.674554i	$0.764336\pi$
$72$	−0.0619725	+	0.879662i	−0.00730353	+	0.103669i
$73$	−14.4607	−	2.04768i	−1.69249	−	0.239663i	−0.773460	−	0.633845i	$-0.781476\pi$
$73$	−14.4607	−	2.04768i	−1.69249	−	0.239663i	−0.919033	+	0.394182i	$0.871028\pi$
$74$	−2.51050	−	2.33986i	−0.291840	−	0.272003i
$75$	1.12288	+	9.53500i	0.129659	+	1.10101i
$76$	2.71833	−	6.45534i	0.311813	−	0.740478i
$77$	−9.13162	−	9.34826i	−1.04064	−	1.06533i
$78$	0.765960	−	2.90394i	0.0867279	−	0.328807i
$79$	5.67401	+	7.01802i	0.638376	+	0.789589i	0.989156	−	0.146869i	$-0.0469194\pi$
$79$	5.67401	+	7.01802i	0.638376	+	0.789589i	−0.350780	+	0.936458i	$0.614084\pi$
$80$	−0.0416862	+	0.353982i	−0.00466066	+	0.0395764i
$81$	−3.74362	−	10.2027i	−0.415958	−	1.13364i
$82$	−11.9243			−1.31682
$83$	−1.21155	−	3.30193i	−0.132985	−	0.362434i	0.854650	−	0.519205i	$-0.173772\pi$
$83$	−1.21155	−	3.30193i	−0.132985	−	0.362434i	−0.987635	+	0.156771i	$0.949891\pi$
$84$	6.54609	−	2.22923i	0.714237	−	0.243229i
$85$	0.316693	−	0.0756387i	0.0343502	−	0.00820417i
$86$	8.08380	−	2.33623i	0.871698	−	0.251923i
$87$	−10.2015	+	11.4733i	−1.09371	+	1.23007i
$88$	−3.23889	+	1.83638i	−0.345267	+	0.195759i
$89$	−3.13439	−	1.97679i	−0.332244	−	0.209540i	0.356938	−	0.934128i	$-0.383821\pi$
$89$	−3.13439	−	1.97679i	−0.332244	−	0.209540i	−0.689182	+	0.724589i	$0.742030\pi$
$90$	0.0943207	+	0.299828i	0.00994227	+	0.0316046i
$91$	−5.29727	+	0.750113i	−0.555305	+	0.0786332i
$92$	1.59561	+	0.808297i	0.166354	+	0.0842707i
$93$	2.35224	−	6.41071i	0.243916	−	0.664760i
$94$	−1.72280	+	4.69527i	−0.177694	+	0.484280i
$95$	0.0585254	−	2.49586i	0.00600458	−	0.256070i
$96$	−0.138461	−	1.96537i	−0.0141316	−	0.200590i
$97$	−6.96520	+	10.4906i	−0.707209	+	1.06516i	0.287025	+	0.957923i	$0.407334\pi$
$97$	−6.96520	+	10.4906i	−0.707209	+	1.06516i	−0.994234	+	0.107234i	$0.965801\pi$
$98$	−3.53439	−	3.97504i	−0.357027	−	0.401539i
$99$	−1.94233	+	2.64719i	−0.195211	+	0.266053i
$100$	−1.24281	−	4.71181i	−0.124281	−	0.471181i
$101$	−5.26772	+	8.80328i	−0.524158	+	0.875959i	−0.999994	−	0.00357520i	$-0.998862\pi$
$101$	−5.26772	+	8.80328i	−0.524158	+	0.875959i	0.475836	+	0.879534i	$0.342146\pi$
$102$	−1.64193	+	0.737193i	−0.162575	+	0.0729929i
$103$	6.08556	+	3.45037i	0.599628	+	0.339975i	0.762812	−	0.646620i	$-0.223818\pi$
$103$	6.08556	+	3.45037i	0.599628	+	0.339975i	−0.163184	+	0.986596i	$0.552176\pi$
$104$	−0.178276	+	1.51385i	−0.0174814	+	0.148445i
$105$	1.87986	−	1.59416i	0.183456	−	0.155574i
$106$	0.847751	−	0.288697i	0.0823409	−	0.0280407i
$107$	−4.08478	−	2.31598i	−0.394891	−	0.223894i	0.282899	−	0.959150i	$-0.408704\pi$
$107$	−4.08478	−	2.31598i	−0.394891	−	0.223894i	−0.677790	+	0.735256i	$0.737062\pi$
$108$	1.97266	+	3.67762i	0.189819	+	0.353879i
$109$	−0.170168	−	0.256297i	−0.0162991	−	0.0245488i	0.824854	−	0.565345i	$-0.191257\pi$
$109$	−0.170168	−	0.256297i	−0.0162991	−	0.0245488i	−0.841153	+	0.540797i	$0.818123\pi$
$110$	−0.834352	+	1.03199i	−0.0795523	+	0.0983960i
$111$	6.64296	+	1.26076i	0.630522	+	0.119666i
$112$	−3.13103	+	1.58611i	−0.295855	+	0.149873i
$113$	−3.57941	−	7.49685i	−0.336723	−	0.705244i	0.662310	−	0.749230i	$-0.269576\pi$
$113$	−3.57941	−	7.49685i	−0.336723	−	0.705244i	−0.999032	+	0.0439860i	$0.985994\pi$
$114$	2.25464	+	13.6148i	0.211167	+	1.27514i
$115$	0.634729	+	0.0596992i	0.0591887	+	0.00556698i
$116$	4.31018	−	6.49175i	0.400191	−	0.602744i
$117$	0.403375	+	1.28225i	0.0372920	+	0.118544i
$118$	0.574460	+	0.960022i	0.0528833	+	0.0883772i
$119$	2.34550	+	2.18607i	0.215011	+	0.200397i
$120$	−0.302574	−	0.633722i	−0.0276211	−	0.0578506i
$121$	−2.85958	−	0.134183i	−0.259962	−	0.0121984i
$122$	−7.49142	−	2.16504i	−0.678242	−	0.196013i
$123$	19.8718	−	12.5327i	1.79178	−	1.13004i
$124$	−0.725897	+	3.38902i	−0.0651875	+	0.304343i
$125$	−2.08174	−	2.83720i	−0.186197	−	0.253767i
$126$	−1.94595	+	2.40690i	−0.173359	+	0.214423i
$127$	−7.24271	−	7.41454i	−0.642687	−	0.657934i	0.313875	−	0.949464i	$-0.398373\pi$
$127$	−7.24271	−	7.41454i	−0.642687	−	0.657934i	−0.956562	+	0.291530i	$0.905836\pi$
$128$	0.209440	+	0.977821i	0.0185121	+	0.0864280i
$129$	−11.0161	+	12.3896i	−0.969917	+	1.09084i
$130$	0.138567	+	0.525341i	0.0121531	+	0.0460755i
$131$	−13.7727	+	1.29538i	−1.20332	+	0.113178i	−0.676270	−	0.736654i	$-0.736405\pi$
$131$	−13.7727	+	1.29538i	−1.20332	+	0.113178i	−0.527053	+	0.849832i	$0.676703\pi$
$132$	3.46751	−	6.46446i	0.301808	−	0.562659i
$133$	20.7941	−	13.1144i	1.80308	−	1.13717i
$134$	4.17113	+	3.53719i	0.360330	+	0.305566i
$135$	1.13448	+	0.962054i	0.0976401	+	0.0828004i
$136$	0.772674	−	0.487310i	0.0662563	−	0.0417865i
$137$	4.79250	−	8.93462i	0.409451	−	0.763336i	−0.589564	−	0.807722i	$-0.700700\pi$
$137$	4.79250	−	8.93462i	0.409451	−	0.763336i	0.999014	+	0.0443861i	$0.0141332\pi$
$138$	−3.50861	+	0.330001i	−0.298672	+	0.0280916i
$139$	−2.34102	−	8.87539i	−0.198563	−	0.752801i	−0.989942	−	0.141475i	$-0.954816\pi$
$139$	−2.34102	−	8.87539i	−0.198563	−	0.752801i	0.791379	−	0.611326i	$-0.209364\pi$
$140$	−0.831263	+	0.934899i	−0.0702545	+	0.0790134i
$141$	−2.06380	−	9.63533i	−0.173803	−	0.811441i
$142$	7.31289	+	7.48638i	0.613684	+	0.628243i
$143$	−3.56821	+	4.41342i	−0.298389	+	0.369069i
$144$	0.521673	+	0.710987i	0.0434728	+	0.0592489i
$145$	0.581702	−	2.71581i	0.0483077	−	0.225536i
$146$	−12.3533	+	7.79099i	−1.02237	+	0.644787i
$147$	10.0679	+	2.90964i	0.830385	+	0.239983i
$148$	−3.42807	−	0.160858i	−0.281785	−	0.0132225i
$149$	6.93472	+	14.5243i	0.568115	+	1.18988i	0.962587	+	0.270973i	$0.0873453\pi$
$149$	6.93472	+	14.5243i	0.568115	+	1.18988i	−0.394472	+	0.918908i	$0.629073\pi$
$150$	7.02335	+	6.54596i	0.573454	+	0.534476i
$151$	12.2802	+	20.5224i	0.999350	+	1.67009i	0.697274	+	0.716805i	$0.254396\pi$
$151$	12.2802	+	20.5224i	0.999350	+	1.67009i	0.302076	+	0.953284i	$0.402320\pi$
$152$	−2.10189	−	6.68152i	−0.170486	−	0.541943i
$153$	0.445586	−	0.671115i	0.0360235	−	0.0542565i
$154$	−13.0107	−	1.22372i	−1.04843	−	0.0986102i
$155$	0.201827	+	1.21874i	0.0162111	+	0.0978919i
$156$	−1.29400	−	2.71019i	−0.103603	−	0.216989i
$157$	9.65162	−	4.88927i	0.770283	−	0.390207i	−0.0224719	−	0.999747i	$-0.507154\pi$
$157$	9.65162	−	4.88927i	0.770283	−	0.390207i	0.792755	+	0.609541i	$0.208646\pi$
$158$	8.86653	+	1.68276i	0.705383	+	0.133874i
$159$	−1.10934	+	1.37212i	−0.0879767	+	0.108816i
$160$	0.197152	+	0.296938i	0.0155862	+	0.0234750i
$161$	2.96751	+	5.53231i	0.233873	+	0.436007i
$162$	−9.45404	−	5.36022i	−0.742779	−	0.421139i
$163$	−12.0793	+	4.11354i	−0.946125	+	0.322197i	−0.752287	−	0.658836i	$-0.771049\pi$
$163$	−12.0793	+	4.11354i	−0.946125	+	0.322197i	−0.193839	+	0.981033i	$0.562094\pi$
$164$	−9.09451	+	7.71229i	−0.710162	+	0.602229i
$165$	0.305799	−	2.59672i	0.0238064	−	0.202154i
$166$	−3.05962	−	1.73474i	−0.237473	−	0.134642i
$167$	−10.5708	+	4.74607i	−0.817992	+	0.367262i	−0.775116	−	0.631819i	$-0.782309\pi$
$167$	−10.5708	+	4.74607i	−0.817992	+	0.367262i	−0.0428759	+	0.999080i	$0.513652\pi$
$168$	3.55081	−	5.93402i	0.273951	−	0.457819i
$169$	−2.72296	−	10.3234i	−0.209458	−	0.794108i
$170$	0.192616	−	0.262516i	0.0147730	−	0.0201340i
$171$	−4.10425	−	4.61595i	−0.313860	−	0.352990i
$172$	4.65439	−	7.01017i	0.354894	−	0.534520i
$173$	1.64889	+	23.4050i	0.125363	+	1.77945i	0.513736	+	0.857949i	$0.328261\pi$
$173$	1.64889	+	23.4050i	0.125363	+	1.77945i	−0.388373	+	0.921502i	$0.626963\pi$
$174$	−0.359908	+	15.3485i	−0.0272846	+	1.16357i
$175$	5.89155	−	16.0566i	0.445359	−	1.21377i
$176$	−1.28254	+	3.49540i	−0.0966753	+	0.263476i
$177$	−1.96634	−	0.996099i	−0.147799	−	0.0748714i
$178$	−3.66908	+	0.519555i	−0.275009	+	0.0389423i
$179$	4.12720	+	13.1196i	0.308481	+	0.980603i	0.972503	+	0.232890i	$0.0748183\pi$
$179$	4.12720	+	13.1196i	0.308481	+	0.980603i	−0.664022	+	0.747713i	$0.731152\pi$
$180$	0.265856	+	0.167670i	0.0198158	+	0.0124974i
$181$	12.6318	−	7.16195i	0.938916	−	0.532344i	0.0542287	−	0.998529i	$-0.482730\pi$
$181$	12.6318	−	7.16195i	0.938916	−	0.532344i	0.884687	+	0.466185i	$0.154372\pi$
$182$	−3.55500	+	3.99822i	−0.263514	+	0.296368i
$183$	14.7599	−	4.26564i	1.09108	−	0.315325i
$184$	1.73973	−	0.415516i	0.128255	−	0.0306322i
$185$	−1.15791	+	0.394318i	−0.0851309	+	0.0289908i
$186$	−2.35224	−	6.41071i	−0.172474	−	0.470056i
$187$	3.40124			0.248723
$188$	1.72280	+	4.69527i	0.125648	+	0.342438i
$189$	−1.71312	+	14.5471i	−0.124611	+	1.05814i
$190$	−1.56961	−	1.94141i	−0.113871	−	0.140844i
$191$	−3.25006	+	12.3218i	−0.235166	+	0.891573i	0.740454	+	0.672107i	$0.234610\pi$
$191$	−3.25006	+	12.3218i	−0.235166	+	0.891573i	−0.975620	+	0.219466i	$0.929569\pi$
$192$	−1.37674	−	1.40940i	−0.0993579	−	0.101715i
$193$	−4.93856	+	11.7278i	−0.355485	+	0.844188i	0.641539	+	0.767091i	$0.278296\pi$
$193$	−4.93856	+	11.7278i	−0.355485	+	0.844188i	−0.997024	+	0.0770970i	$0.975435\pi$
$194$	1.47274	+	12.5059i	0.105736	+	0.897870i
$195$	−0.783066	−	0.729839i	−0.0560765	−	0.0522649i
$196$	−5.26656	−	0.745764i	−0.376183	−	0.0532688i
$197$	0.616582	−	8.75201i	0.0439297	−	0.623555i	−0.925588	−	0.378533i	$-0.876429\pi$
$197$	0.616582	−	8.75201i	0.0439297	−	0.623555i	0.969518	−	0.245022i	$-0.0787951\pi$
$198$	0.230740	+	3.27522i	0.0163980	+	0.232759i
$199$	20.9601	−	2.96802i	1.48582	−	0.210397i	0.650224	−	0.759743i	$-0.274675\pi$
$199$	20.9601	−	2.96802i	1.48582	−	0.210397i	0.835595	+	0.549346i	$0.185123\pi$
$200$	−3.99533	−	2.78981i	−0.282513	−	0.197270i
$201$	−10.6688	−	1.51074i	−0.752520	−	0.106559i
$202$	1.67608	+	10.1211i	0.117929	+	0.712120i
$203$	25.4482	−	10.0205i	1.78612	−	0.703301i
$204$	−0.775481	+	1.62420i	−0.0542945	+	0.113716i
$205$	−2.00901	+	3.74537i	−0.140315	+	0.261588i
$206$	6.87296	−	1.30441i	0.478862	−	0.0908825i
$207$	1.24949	−	0.962652i	0.0868456	−	0.0669090i
$208$	0.843145	+	1.26990i	0.0584616	+	0.0880514i
$209$	6.65127	−	25.2166i	0.460078	−	1.74427i
$210$	0.402692	−	2.43168i	0.0277884	−	0.167802i
$211$	−3.45249	+	0.997776i	−0.237679	+	0.0686898i	−0.394347	−	0.918962i	$-0.629029\pi$
$211$	−3.45249	+	0.997776i	−0.237679	+	0.0686898i	0.156668	+	0.987651i	$0.449925\pi$
$212$	0.459847	−	0.768485i	0.0315824	−	0.0527798i
$213$	−20.0552	−	4.78998i	−1.37416	−	0.328204i
$214$	−4.61330	+	0.875552i	−0.315359	+	0.0598515i
$215$	0.628155	−	2.93269i	0.0428398	−	0.200008i
$216$	3.88309	+	1.52901i	0.264211	+	0.104036i
$217$	−8.89892	+	8.29405i	−0.604098	+	0.563037i
$218$	−0.295549	−	0.0854143i	−0.0200171	−	0.00578499i
$219$	12.3982	−	25.9672i	0.837792	−	1.75470i
$220$	0.0311101	+	1.32671i	0.00209745	+	0.0894470i
$221$	0.823747	−	1.12268i	0.0554113	−	0.0755198i
$222$	5.88191	−	3.33491i	0.394768	−	0.223824i
$223$	2.89562	+	6.87637i	0.193905	+	0.460475i	0.989351	−	0.145549i	$-0.0464948\pi$
$223$	2.89562	+	6.87637i	0.193905	+	0.460475i	−0.795446	+	0.606024i	$0.792763\pi$
$224$	−1.36215	+	3.23476i	−0.0910123	+	0.216131i
$225$	−4.22182	−	0.801252i	−0.281455	−	0.0534168i
$226$	−7.57870	−	3.40268i	−0.504128	−	0.226343i
$227$	18.5686	+	7.31157i	1.23244	+	0.485286i	0.890736	−	0.454521i	$-0.150190\pi$
$227$	18.5686	+	7.31157i	1.23244	+	0.485286i	0.341705	+	0.939807i	$0.388996\pi$
$228$	10.5252	+	8.92557i	0.697050	+	0.591110i
$229$	15.8397	−	14.7631i	1.04672	−	0.975571i	0.0469900	−	0.998895i	$-0.485037\pi$
$229$	15.8397	−	14.7631i	1.04672	−	0.975571i	0.999728	+	0.0233248i	$0.00742518\pi$
$230$	0.522710	−	0.364992i	0.0344665	−	0.0240668i
$231$	22.9684	−	11.6352i	1.51121	−	0.765543i
$232$	−0.911355	−	7.73886i	−0.0598334	−	0.508081i
$233$	−17.5810	+	17.9981i	−1.15177	+	1.17910i	−0.170726	+	0.985319i	$0.554611\pi$
$233$	−17.5810	+	17.9981i	−1.15177	+	1.17910i	−0.981046	+	0.193777i	$0.937926\pi$
$234$	1.13697	+	0.717064i	0.0743260	+	0.0468759i
$235$	1.18451	+	1.33218i	0.0772686	+	0.0869020i
$236$	1.05905	+	0.360652i	0.0689380	+	0.0234764i
$237$	−16.5446	+	6.51461i	−1.07469	+	0.423169i
$238$	3.20276	+	0.150286i	0.207604	+	0.00974158i
$239$	−8.65376	+	6.04264i	−0.559765	+	0.390866i	−0.818002	−	0.575216i	$-0.804918\pi$
$239$	−8.65376	+	6.04264i	−0.559765	+	0.390866i	0.258237	+	0.966082i	$0.416858\pi$
$240$	−0.640641	−	0.287635i	−0.0413532	−	0.0185667i
$241$	−11.2830	−	15.3775i	−0.726800	−	0.990553i	−0.999594	−	0.0284810i	$-0.990933\pi$
$241$	−11.2830	−	15.3775i	−0.726800	−	0.990553i	0.272795	−	0.962072i	$-0.412052\pi$
$242$	−2.26775	+	1.74715i	−0.145776	+	0.112311i
$243$	8.88272	−	0.416811i	0.569826	−	0.0267384i
$244$	−7.11388	+	3.19399i	−0.455419	+	0.204474i
$245$	−1.84401	+	0.440423i	−0.117810	+	0.0281376i
$246$	7.05012	−	22.4110i	0.449499	−	1.42887i
$247$	−6.71264	−	8.30268i	−0.427115	−	0.528287i
$248$	1.63829	+	3.05425i	0.104031	+	0.193945i
$249$	6.92208	−	0.324811i	0.438669	−	0.0205840i
$250$	−3.42273	−	0.817483i	−0.216473	−	0.0517022i
$251$	15.1237	−	1.42245i	0.954597	−	0.0897844i	0.395120	−	0.918630i	$-0.370703\pi$
$251$	15.1237	−	1.42245i	0.954597	−	0.0897844i	0.559478	+	0.828845i	$0.311002\pi$
$252$	0.0725580	+	3.09429i	0.00457073	+	0.194922i
$253$	6.30414	+	2.14684i	0.396338	+	0.134971i
$254$	−10.3194	−	0.970590i	−0.647498	−	0.0609002i
$255$	−0.0450829	+	0.639924i	−0.00282320	+	0.0400736i
$256$	0.792162	+	0.610310i	0.0495102	+	0.0381444i
$257$	−17.5707	−	8.90087i	−1.09603	−	0.555221i	−0.191438	−	0.981505i	$-0.561315\pi$
$257$	−17.5707	−	8.90087i	−1.09603	−	0.555221i	−0.904589	+	0.426284i	$0.859822\pi$
$258$	−0.388650	+	16.5742i	−0.0241963	+	1.03187i
$259$	−9.54181	−	7.35135i	−0.592899	−	0.456791i
$260$	0.445458	+	0.311049i	0.0276261	+	0.0192904i
$261$	−3.52839	−	5.89656i	−0.218402	−	0.364988i
$262$	−9.66639	+	9.89571i	−0.597191	+	0.611359i
$263$	−7.63791	−	18.1381i	−0.470974	−	1.11844i	−0.968054	−	0.250740i	$-0.919326\pi$
$263$	−7.63791	−	18.1381i	−0.470974	−	1.11844i	0.497081	−	0.867704i	$-0.334405\pi$
$264$	−1.53640	−	7.17303i	−0.0945587	−	0.441470i
$265$	0.0521506	−	0.314914i	0.00320358	−	0.0193450i
$266$	7.37735	−	23.4512i	0.452334	−	1.43789i
$267$	5.56843	−	4.72212i	0.340782	−	0.288989i
$268$	5.46900			0.334072
$269$	16.3785	−	0.862957i	0.998615	−	0.0526154i
$269$	16.3785	−	0.862957i	0.998615	−	0.0526154i
$270$	1.48748			0.0905248
$271$	−6.09431	+	5.16808i	−0.370203	+	0.313938i	−0.812534	−	0.582913i	$-0.801913\pi$
$271$	−6.09431	+	5.16808i	−0.370203	+	0.313938i	0.442331	+	0.896852i	$0.354152\pi$
$272$	0.274130	−	0.871407i	0.0166216	−	0.0528368i
$273$	1.72216	−	10.3994i	0.104230	−	0.629399i
$274$	−2.12347	−	9.91394i	−0.128284	−	0.598923i
$275$	−7.04128	−	16.7213i	−0.424605	−	1.00833i
$276$	−2.46253	+	2.52095i	−0.148227	+	0.151743i
$277$	0.746654	+	1.24779i	0.0448621	+	0.0749724i	0.879717	−	0.475498i	$-0.157732\pi$
$277$	0.746654	+	1.24779i	0.0448621	+	0.0749724i	−0.834855	+	0.550470i	$0.814448\pi$
$278$	−7.52580	−	5.25503i	−0.451367	−	0.315176i
$279$	2.42114	+	1.86533i	0.144950	+	0.111675i
$280$	−0.0293270	+	1.25067i	−0.00175262	+	0.0747418i
$281$	−26.2532	−	13.2992i	−1.56614	−	0.793367i	−0.566605	−	0.823989i	$-0.691743\pi$
$281$	−26.2532	−	13.2992i	−1.56614	−	0.793367i	−0.999531	+	0.0306228i	$0.990251\pi$
$282$	−7.80587	−	6.01392i	−0.464833	−	0.358124i
$283$	−0.454874	+	6.45666i	−0.0270395	+	0.383809i	0.965375	+	0.260868i	$0.0840087\pi$
$283$	−0.454874	+	6.45666i	−0.0270395	+	0.383809i	−0.992414	+	0.122941i	$0.960767\pi$
$284$	10.4194	+	0.979994i	0.618278	+	0.0581520i
$285$	4.65620	+	1.58564i	0.275810	+	0.0939254i
$286$	0.133047	+	5.67386i	0.00786721	+	0.335503i
$287$	−41.6688	+	3.91915i	−2.45963	+	0.231340i
$288$	0.857717	+	0.204857i	0.0505415	+	0.0120713i
$289$	16.1477	−	0.757714i	0.949867	−	0.0445714i
$290$	−1.31285	−	2.44754i	−0.0770932	−	0.143724i
$291$	−15.5983	−	19.2931i	−0.914387	−	1.13098i
$292$	−4.38271	+	13.9318i	−0.256479	+	0.815298i
$293$	14.8539	−	3.54770i	0.867776	−	0.207259i	0.225978	−	0.974133i	$-0.427442\pi$
$293$	14.8539	−	3.54770i	0.867776	−	0.207259i	0.641798	+	0.766874i	$0.278189\pi$
$294$	9.56049	−	4.29246i	0.557579	−	0.250342i
$295$	0.398323	−	0.0186909i	0.0231913	−	0.00108822i
$296$	−2.71857	+	2.09449i	−0.158014	+	0.121740i
$297$	9.19199	+	12.5277i	0.533373	+	0.726933i
$298$	14.6829	+	6.59233i	0.850558	+	0.381883i
$299$	2.23544	−	1.56093i	0.129279	−	0.0902711i
$300$	9.59034	+	0.450016i	0.553699	+	0.0259817i
$301$	27.4805	−	10.8207i	1.58395	−	0.623695i
$302$	22.6392	+	7.70965i	1.30274	+	0.443640i
$303$	−13.4307	−	15.1052i	−0.771574	−	0.867770i
$304$	−5.92449	−	3.73646i	−0.339793	−	0.214301i
$305$	−1.94218	+	1.98826i	−0.111209	+	0.113847i
$306$	−0.0942156	−	0.800041i	−0.00538595	−	0.0457353i
$307$	−1.72323	+	0.872945i	−0.0983498	+	0.0498216i	−0.500388	−	0.865801i	$-0.666809\pi$
$307$	−1.72323	+	0.872945i	−0.0983498	+	0.0498216i	0.402038	+	0.915623i	$0.368302\pi$
$308$	−10.7145	+	7.48163i	−0.610518	+	0.426305i
$309$	−10.0828	+	9.39742i	−0.573589	+	0.534601i
$310$	0.942177	+	0.798982i	0.0535121	+	0.0453791i
$311$	−13.6704	−	5.38285i	−0.775176	−	0.305233i	−0.0545078	−	0.998513i	$-0.517359\pi$
$311$	−13.6704	−	5.38285i	−0.775176	−	0.305233i	−0.720668	+	0.693280i	$0.756165\pi$
$312$	−2.73978	−	1.23011i	−0.155110	−	0.0696411i
$313$	−11.6944	−	2.21946i	−0.661006	−	0.125451i	−0.154910	−	0.987929i	$-0.549509\pi$
$313$	−11.6944	−	2.21946i	−0.661006	−	0.125451i	−0.506096	+	0.862477i	$0.668912\pi$
$314$	4.19891	−	9.97135i	0.236958	−	0.562716i
$315$	0.428141	+	1.01673i	0.0241230	+	0.0572861i
$316$	7.85073	−	4.45118i	0.441638	−	0.250399i
$317$	−4.53502	+	6.18076i	−0.254712	+	0.347146i	−0.914703	−	0.404128i	$-0.867575\pi$
$317$	−4.53502	+	6.18076i	−0.254712	+	0.347146i	0.659991	+	0.751274i	$0.270560\pi$
$318$	0.0413637	+	1.76398i	0.00231956	+	0.0989193i
$319$	12.5006	−	26.1818i	0.699901	−	1.46590i
$320$	0.342416	+	0.0989588i	0.0191416	+	0.00553197i
$321$	6.76781	−	6.30779i	0.377742	−	0.352066i
$322$	5.84141	+	2.30011i	0.325529	+	0.128180i
$323$	−1.34011	+	6.25661i	−0.0745656	+	0.348127i
$324$	−10.6773	+	2.02643i	−0.593183	+	0.112579i
$325$	−7.22471	−	1.72554i	−0.400755	−	0.0957159i
$326$	−6.55220	+	10.9499i	−0.362893	+	0.606458i
$327$	0.582303	−	0.168287i	0.0322014	−	0.00930627i
$328$	−1.94816	+	11.7641i	−0.107569	+	0.649564i
$329$	−4.47704	+	16.9735i	−0.246827	+	0.935782i
$330$	−1.44625	−	2.17826i	−0.0796135	−	0.119909i
$331$	7.23007	−	5.57031i	0.397401	−	0.306172i	−0.392098	−	0.919923i	$-0.628251\pi$
$331$	7.23007	−	5.57031i	0.397401	−	0.306172i	0.789499	+	0.613751i	$0.210340\pi$
$332$	−3.45551	+	0.655815i	−0.189645	+	0.0359925i
$333$	−1.43052	+	2.66690i	−0.0783918	+	0.146145i
$334$	−4.99257	+	10.4566i	−0.273181	+	0.572161i
$335$	1.81376	−	0.714187i	0.0990965	−	0.0390202i
$336$	−1.12980	−	6.82234i	−0.0616355	−	0.372189i
$337$	27.2981	+	3.86552i	1.48702	+	0.210568i	0.836101	−	0.548575i	$-0.184830\pi$
$337$	27.2981	+	3.86552i	1.48702	+	0.210568i	0.650924	+	0.759143i	$0.274382\pi$
$338$	−8.75362	−	6.11238i	−0.476134	−	0.332469i
$339$	16.2061	−	2.29485i	0.880196	−	0.124639i
$340$	−0.0228819	−	0.324795i	−0.00124095	−	0.0176145i
$341$	−0.906875	+	12.8725i	−0.0491100	+	0.697087i
$342$	−6.11571	−	0.866006i	−0.330700	−	0.0468282i
$343$	4.31583	+	4.02248i	0.233033	+	0.217193i
$344$	−0.984134	−	8.35687i	−0.0530610	−	0.450572i
$345$	−0.487477	+	1.15763i	−0.0262449	+	0.0623250i
$346$	16.3953	+	16.7842i	0.881414	+	0.902325i
$347$	1.67514	−	6.35087i	0.0899263	−	0.340933i	−0.906822	−	0.421514i	$-0.861499\pi$
$347$	1.67514	−	6.35087i	0.0899263	−	0.340933i	0.996748	+	0.0805818i	$0.0256778\pi$
$348$	9.65248	+	11.9389i	0.517427	+	0.639992i
$349$	−0.0696748	+	0.591651i	−0.00372961	+	0.0316703i	−0.994876	−	0.101105i	$-0.967762\pi$
$349$	−0.0696748	+	0.591651i	−0.00372961	+	0.0316703i	0.991146	+	0.132776i	$0.0423890\pi$
$350$	−5.89155	−	16.0566i	−0.314917	−	0.858263i
$351$	6.36138			0.339545
$352$	1.28254	+	3.49540i	0.0683597	+	0.186305i
$353$	−18.0291	+	6.13970i	−0.959591	+	0.326783i	−0.757684	−	0.652622i	$-0.773669\pi$
$353$	−18.0291	+	6.13970i	−0.959591	+	0.326783i	−0.201907	+	0.979405i	$0.564714\pi$
$354$	−2.14394	+	0.512058i	−0.113949	+	0.0272156i
$355$	3.58351	−	1.03564i	0.190193	−	0.0549662i
$356$	−2.46232	+	2.76931i	−0.130503	+	0.146773i
$357$	−5.49532	+	3.11572i	−0.290843	+	0.164901i
$358$	11.6331	+	7.33676i	0.614828	+	0.387760i
$359$	2.09837	+	6.67031i	0.110748	+	0.352046i	0.992905	−	0.118909i	$-0.0379396\pi$
$359$	2.09837	+	6.67031i	0.110748	+	0.352046i	−0.882158	+	0.470954i	$0.843910\pi$
$360$	0.311209	−	0.0440683i	0.0164022	−	0.00232260i
$361$	26.8162	+	13.5845i	1.41138	+	0.714971i
$362$	5.00197	−	13.6322i	0.262898	−	0.716493i
$363$	1.94288	−	5.29507i	0.101975	−	0.277919i
$364$	−0.125421	+	5.34865i	−0.00657382	+	0.280345i
$365$	0.365831	+	5.19274i	0.0191484	+	0.271800i
$366$	8.49827	−	12.7996i	0.444211	−	0.669046i
$367$	19.1092	+	21.4916i	0.997491	+	1.12185i	0.992547	+	0.121864i	$0.0388873\pi$
$367$	19.1092	+	21.4916i	0.997491	+	1.12185i	0.00494438	+	0.999988i	$0.498426\pi$
$368$	1.05812	−	1.44211i	0.0551584	−	0.0751753i
$369$	2.68187	+	10.1676i	0.139613	+	0.529305i
$370$	−0.628084	+	1.04964i	−0.0326526	+	0.0545681i
$371$	2.86753	−	1.28746i	0.148875	−	0.0668416i
$372$	−5.94027	−	3.36800i	−0.307989	−	0.174623i
$373$	−2.77858	+	23.5945i	−0.143869	+	1.22168i	0.711134	+	0.703056i	$0.248182\pi$
$373$	−2.77858	+	23.5945i	−0.143869	+	1.22168i	−0.855003	+	0.518623i	$0.826445\pi$
$374$	2.59407	−	2.19982i	0.134136	−	0.113750i
$375$	6.56315	−	2.23504i	0.338920	−	0.115417i
$376$	4.35072	+	2.46676i	0.224371	+	0.127213i
$377$	−5.61457	−	10.4672i	−0.289165	−	0.539089i
$378$	8.10205	+	12.2028i	0.416724	+	0.627646i
$379$	14.8741	−	18.3974i	0.764032	−	0.945010i	−0.235608	−	0.971848i	$-0.575708\pi$
$379$	14.8741	−	18.3974i	0.764032	−	0.945010i	0.999640	+	0.0268383i	$0.00854394\pi$
$380$	−2.45276	−	0.465506i	−0.125824	−	0.0238799i
$381$	18.2173	−	9.22846i	0.933302	−	0.472788i
$382$	5.49058	+	11.4997i	0.280923	+	0.588375i
$383$	0.344174	+	2.07831i	0.0175865	+	0.106197i	0.993927	−	0.110042i	$-0.0350986\pi$
$383$	0.344174	+	2.07831i	0.0175865	+	0.106197i	−0.976340	+	0.216239i	$0.930621\pi$
$384$	−1.96158	−	0.184496i	−0.100102	−	0.00941503i
$385$	−2.57641	+	3.88043i	−0.131306	+	0.197765i
$386$	3.81864	+	12.1388i	0.194364	+	0.617846i
$387$	−3.81016	−	6.36745i	−0.193682	−	0.323676i
$388$	9.21167	+	8.58553i	0.467651	+	0.435864i
$389$	9.19111	+	19.2502i	0.466008	+	0.976024i	0.992083	+	0.125586i	$0.0400810\pi$
$389$	9.19111	+	19.2502i	0.466008	+	0.976024i	−0.526075	+	0.850438i	$0.676337\pi$
$390$	−1.06927	−	0.0501743i	−0.0541446	−	0.00254067i
$391$	−1.56972	−	0.453652i	−0.0793840	−	0.0229421i
$392$	−4.49906	+	2.83747i	−0.227237	+	0.143314i
$393$	5.70833	−	26.6507i	0.287947	−	1.34435i
$394$	−5.19028	−	7.07381i	−0.261482	−	0.356373i
$395$	2.02238	−	2.50142i	0.101757	−	0.125860i
$396$	2.29429	+	2.34872i	0.115293	+	0.118028i
$397$	5.35459	+	24.9992i	0.268739	+	1.25467i	0.884426	+	0.466681i	$0.154550\pi$
$397$	5.35459	+	24.9992i	0.268739	+	1.25467i	−0.615687	+	0.787991i	$0.711121\pi$
$398$	14.0663	−	15.8200i	0.705080	−	0.792985i
$399$	12.3535	+	46.8350i	0.618446	+	2.34468i
$400$	−4.85155	+	0.456311i	−0.242577	+	0.0228156i
$401$	8.40058	−	15.6611i	0.419505	−	0.782080i	−0.579965	−	0.814642i	$-0.696934\pi$
$401$	8.40058	−	15.6611i	0.419505	−	0.782080i	0.999470	+	0.0325616i	$0.0103665\pi$
$402$	−9.11404	+	5.74804i	−0.454567	+	0.286686i
$403$	4.02934	+	3.41695i	0.200716	+	0.170210i
$404$	7.82437	+	6.63520i	0.389277	+	0.330113i
$405$	−3.27643	+	2.06638i	−0.162807	+	0.102679i
$406$	12.9280	−	24.1016i	0.641607	−	1.19614i
$407$	−12.7215	+	1.19652i	−0.630582	+	0.0593093i
$408$	0.459033	+	1.74031i	0.0227255	+	0.0861581i
$409$	−7.12022	+	8.00792i	−0.352072	+	0.395966i	−0.896647	−	0.442746i	$-0.854004\pi$
$409$	−7.12022	+	8.00792i	−0.352072	+	0.395966i	0.544575	+	0.838712i	$0.316691\pi$
$410$	0.890156	+	4.15591i	0.0439617	+	0.205246i
$411$	13.9585	+	14.2897i	0.688523	+	0.704858i
$412$	4.39825	−	5.44008i	0.216686	−	0.268013i
$413$	2.32294	+	3.16593i	0.114304	+	0.155785i
$414$	0.330354	−	1.54233i	0.0162360	−	0.0758016i
$415$	−1.06036	+	0.668746i	−0.0520509	+	0.0328274i
$416$	1.46438	+	0.423210i	0.0717974	+	0.0207496i
$417$	18.0648	+	0.847671i	0.884639	+	0.0415106i
$418$	−11.2365	−	23.5342i	−0.549595	−	1.15109i
$419$	7.67856	+	7.15663i	0.375122	+	0.349624i	0.846577	−	0.532266i	$-0.178659\pi$
$419$	7.67856	+	7.15663i	0.375122	+	0.349624i	−0.471455	+	0.881890i	$0.656271\pi$
$420$	−1.26561	−	2.11505i	−0.0617554	−	0.103204i
$421$	−6.90127	−	21.9378i	−0.336347	−	1.06918i	−0.958212	−	0.286060i	$-0.907654\pi$
$421$	−6.90127	−	21.9378i	−0.336347	−	1.06918i	0.621864	−	0.783125i	$-0.286375\pi$
$422$	−1.98783	+	2.99395i	−0.0967661	+	0.145743i
$423$	4.39103	+	0.412997i	0.213499	+	0.0200806i
$424$	−0.146314	−	0.883527i	−0.00710565	−	0.0429079i
$425$	1.91798	+	4.01710i	0.0930359	+	0.194858i
$426$	−18.3938	+	9.31787i	−0.891184	+	0.451452i
$427$	−26.8899	−	5.10339i	−1.30129	−	0.246970i
$428$	−2.95222	+	3.65152i	−0.142701	+	0.176503i
$429$	−6.18508	−	9.31561i	−0.298619	−	0.449762i
$430$	−1.41769	−	2.64299i	−0.0683672	−	0.127456i
$431$	1.47458	+	0.836055i	0.0710282	+	0.0402713i	0.528320	−	0.849045i	$-0.322822\pi$
$431$	1.47458	+	0.836055i	0.0710282	+	0.0402713i	−0.457292	+	0.889317i	$0.651180\pi$
$432$	3.95049	−	1.34532i	0.190068	−	0.0647265i
$433$	−24.9217	+	21.1340i	−1.19766	+	1.01563i	−0.198289	+	0.980144i	$0.563538\pi$
$433$	−24.9217	+	21.1340i	−1.19766	+	1.01563i	−0.999370	+	0.0354911i	$0.988700\pi$
$434$	−1.42274	+	12.0813i	−0.0682935	+	0.579921i
$435$	4.76027	+	2.69896i	0.228237	+	0.129405i
$436$	−0.280654	+	0.126008i	−0.0134409	+	0.00603469i
$437$	−6.43300	+	10.7507i	−0.307732	+	0.514274i
$438$	−7.33891	−	27.8236i	−0.350666	−	1.32946i
$439$	−5.80056	+	7.90557i	−0.276846	+	0.377312i	−0.922292	−	0.386493i	$-0.873686\pi$
$439$	−5.80056	+	7.90557i	−0.276846	+	0.377312i	0.645447	+	0.763805i	$0.276671\pi$
$440$	0.881806	+	0.991744i	0.0420385	+	0.0472795i
$441$	−2.59452	+	3.90772i	−0.123549	+	0.186082i
$442$	−0.0978576	−	1.38903i	−0.00465461	−	0.0660694i
$443$	0.274730	−	11.7161i	0.0130528	−	0.556646i	−0.953675	−	0.300839i	$-0.902733\pi$
$443$	0.274730	−	11.7161i	0.0130528	−	0.556646i	0.966728	−	0.255807i	$-0.0823413\pi$
$444$	2.32913	−	6.34773i	0.110536	−	0.301250i
$445$	−0.454976	+	1.23998i	−0.0215679	+	0.0587805i
$446$	6.65587	+	3.37170i	0.315165	+	0.159655i
$447$	−31.3976	+	4.44602i	−1.48506	+	0.210289i
$448$	1.05325	+	3.34810i	0.0497616	+	0.158183i
$449$	−28.6555	−	18.0725i	−1.35234	−	0.852892i	−0.355682	−	0.934607i	$-0.615751\pi$
$449$	−28.6555	−	18.0725i	−1.35234	−	0.852892i	−0.996656	+	0.0817151i	$0.973960\pi$
$450$	−3.73814	+	2.11944i	−0.176218	+	0.0999114i
$451$	−29.5008	+	33.1788i	−1.38914	+	1.56233i
$452$	−7.98091	+	2.30650i	−0.375391	+	0.108489i
$453$	−45.8311	+	10.9463i	−2.15333	+	0.514300i
$454$	18.8909	−	6.43318i	0.886594	−	0.301924i
$455$	0.656876	+	1.79023i	0.0307948	+	0.0839272i
$456$	13.8002			0.646254
$457$	−5.23739	−	14.2738i	−0.244995	−	0.667701i	−0.999929	−	0.0119004i	$-0.996212\pi$
$457$	−5.23739	−	14.2738i	−0.244995	−	0.667701i	0.754934	−	0.655800i	$-0.227669\pi$
$458$	2.53241	−	21.5042i	0.118332	−	1.00483i
$459$	−2.39686	−	2.96461i	−0.111876	−	0.138376i
$460$	0.162597	−	0.616447i	0.00758114	−	0.0287420i
$461$	−21.1637	−	21.6658i	−0.985692	−	1.00908i	−0.999958	−	0.00917871i	$-0.997078\pi$
$461$	−21.1637	−	21.6658i	−0.985692	−	1.00908i	0.0142654	−	0.999898i	$-0.495459\pi$
$462$	9.99234	−	23.7293i	0.464886	−	1.10399i
$463$	−3.64801	−	30.9774i	−0.169537	−	1.43964i	−0.769005	−	0.639243i	$-0.779248\pi$
$463$	−3.64801	−	30.9774i	−0.169537	−	1.43964i	0.599467	−	0.800399i	$-0.295379\pi$
$464$	−5.70034	−	5.31288i	−0.264632	−	0.246644i
$465$	−2.40988	−	0.341247i	−0.111755	−	0.0158250i
$466$	−1.76815	+	25.0978i	−0.0819079	+	1.16263i
$467$	0.672827	+	9.55037i	0.0311347	+	0.441938i	0.988313	+	0.152439i	$0.0487127\pi$
$467$	0.672827	+	9.55037i	0.0311347	+	0.441938i	−0.957178	+	0.289499i	$0.906511\pi$
$468$	1.33093	−	0.188464i	0.0615220	−	0.00871174i
$469$	15.7383	+	10.9895i	0.726727	+	0.507450i
$470$	1.76502	+	0.249933i	0.0814143	+	0.0115286i
$471$	3.48267	+	21.0303i	0.160473	+	0.969026i
$472$	1.04098	−	0.409895i	0.0479148	−	0.0188670i
$473$	13.4989	−	28.2726i	0.620680	−	1.29998i
$474$	−8.40488	+	15.6692i	−0.386049	+	0.719708i
$475$	33.5333	−	6.36423i	1.53861	−	0.292011i
$476$	2.53990	−	1.95683i	0.116416	−	0.0896910i
$477$	−0.436831	−	0.657930i	−0.0200011	−	0.0301245i
$478$	−2.69189	+	10.2056i	−0.123124	+	0.466794i
$479$	0.403221	−	2.43488i	0.0184237	−	0.111252i	−0.975782	−	0.218744i	$-0.929804\pi$
$479$	0.403221	−	2.43488i	0.0184237	−	0.111252i	0.994206	+	0.107491i	$0.0342818\pi$
$480$	−0.674640	+	0.194972i	−0.0307930	+	0.00889924i
$481$	−2.68608	+	4.48892i	−0.122475	+	0.204677i
$482$	−18.5511	−	4.43072i	−0.844978	−	0.201814i
$483$	−12.1521	+	2.30633i	−0.552941	+	0.104942i
$484$	−0.599570	+	2.79924i	−0.0272532	+	0.127238i
$485$	4.17617	+	1.64441i	0.189630	+	0.0746687i
$486$	6.50513	−	6.06297i	0.295079	−	0.275022i
$487$	−28.0288	−	8.10038i	−1.27011	−	0.367063i	−0.426726	−	0.904381i	$-0.640333\pi$
$487$	−28.0288	−	8.10038i	−1.27011	−	0.367063i	−0.843380	+	0.537318i	$0.819438\pi$
$488$	−3.35988	+	7.03705i	−0.152094	+	0.318552i
$489$	−0.589377	−	25.1344i	−0.0266525	−	1.13662i
$490$	−1.12155	+	1.52856i	−0.0506664	+	0.0690531i
$491$	1.36441	−	0.773591i	0.0615751	−	0.0349117i	−0.462120	−	0.886817i	$-0.652911\pi$
$491$	1.36441	−	0.773591i	0.0615751	−	0.0349117i	0.523695	+	0.851906i	$0.324553\pi$
$492$	−9.11774	−	21.6523i	−0.411059	−	0.976163i
$493$	−2.76258	+	6.56043i	−0.124420	+	0.295467i
$494$	−10.4896	−	1.99080i	−0.471947	−	0.0895702i
$495$	1.06761	+	0.479333i	0.0479853	+	0.0215444i
$496$	3.22489	+	1.26983i	0.144802	+	0.0570172i
$497$	28.0150	+	23.7572i	1.25664	+	1.06565i
$498$	5.06929	−	4.72472i	0.227160	−	0.211720i
$499$	−10.4720	+	7.31227i	−0.468792	+	0.327342i	−0.783011	−	0.622008i	$-0.786317\pi$
$499$	−10.4720	+	7.31227i	−0.468792	+	0.327342i	0.314219	+	0.949350i	$0.398257\pi$
$500$	−3.13919	+	1.59024i	−0.140389	+	0.0711176i
$501$	−2.67007	−	22.6732i	−0.119290	−	1.01296i
$502$	10.6146	−	10.8664i	0.473753	−	0.484992i
$503$	19.7169	+	12.4350i	0.879132	+	0.554451i	0.895323	−	0.445418i	$-0.146945\pi$
$503$	19.7169	+	12.4350i	0.879132	+	0.554451i	−0.0161904	+	0.999869i	$0.505154\pi$
$504$	2.05663	+	2.31304i	0.0916097	+	0.103031i
$505$	3.46139	+	1.17875i	0.154030	+	0.0524539i
$506$	6.19659	−	2.43997i	0.275472	−	0.108470i
$507$	21.0121	+	0.985967i	0.933179	+	0.0437884i
$508$	−8.49821	+	5.93403i	−0.377047	+	0.263280i
$509$	−16.8658	−	7.57240i	−0.747564	−	0.335641i	−0.000150216	−	1.00000i	$-0.500048\pi$
$509$	−16.8658	−	7.57240i	−0.747564	−	0.335641i	−0.747413	+	0.664359i	$0.768705\pi$
$510$	0.379500	+	0.517219i	0.0168045	+	0.0229028i
$511$	−40.6072	+	31.2852i	−1.79636	+	1.38398i
$512$	0.998901	−	0.0468723i	0.0441456	−	0.00207148i
$513$	−26.6666	+	11.9728i	−1.17736	+	0.528610i
$514$	−19.1577	+	4.57561i	−0.845010	+	0.201821i
$515$	0.748245	−	2.37853i	0.0329716	−	0.104811i
$516$	10.4233	+	12.8923i	0.458861	+	0.567552i
$517$	8.80213	+	16.4097i	0.387117	+	0.721699i
$518$	−12.0320	+	0.564589i	−0.528657	+	0.0248066i
$519$	−44.9631	−	10.7390i	−1.97366	−	0.471388i
$520$	0.540921	−	0.0508762i	0.0237210	−	0.00223107i
$521$	−0.371184	−	15.8294i	−0.0162619	−	0.693499i	−0.945796	−	0.324762i	$-0.894716\pi$
$521$	−0.371184	−	15.8294i	−0.0162619	−	0.693499i	0.929534	−	0.368737i	$-0.120210\pi$
$522$	−6.50477	−	2.21516i	−0.284706	−	0.0969550i
$523$	0.991745	+	0.0932783i	0.0433660	+	0.00407878i	0.115302	−	0.993330i	$-0.463216\pi$
$523$	0.991745	+	0.0932783i	0.0433660	+	0.00407878i	−0.0719363	+	0.997409i	$0.522918\pi$
$524$	−0.972162	+	13.7992i	−0.0424691	+	0.602823i
$525$	26.6941	+	20.5661i	1.16503	+	0.897578i
$526$	−17.5565	−	8.89370i	−0.765500	−	0.387784i
$527$	0.0742220	−	3.16525i	0.00323316	−	0.137880i
$528$	−5.81109	−	4.47707i	−0.252895	−	0.194839i
$529$	16.2346	+	11.3361i	0.705850	+	0.492873i
$530$	−0.163903	−	0.273910i	−0.00711947	−	0.0118979i
$531$	0.689391	−	0.705746i	0.0299170	−	0.0306268i
$532$	−9.54094	−	22.6573i	−0.413652	−	0.982320i
$533$	3.80687	+	17.7733i	0.164894	+	0.769846i
$534$	1.19283	−	7.20298i	0.0516189	−	0.311703i
$535$	−0.502241	+	1.59653i	−0.0217138	+	0.0690240i
$536$	4.17113	−	3.53719i	0.180165	−	0.152783i
$537$	−27.0976			−1.16935
$538$	11.9335	−	11.2513i	0.514490	−	0.485077i
$539$	−19.8044			−0.853037
$540$	1.13448	−	0.962054i	0.0488200	−	0.0414002i
$541$	2.61331	−	8.30722i	0.112355	−	0.357155i	−0.880871	−	0.473357i	$-0.843042\pi$
$541$	2.61331	−	8.30722i	0.112355	−	0.357155i	0.993226	+	0.116202i	$0.0370719\pi$
$542$	−1.30548	+	7.88323i	−0.0560753	+	0.338614i
$543$	5.99201	+	27.9751i	0.257142	+	1.20053i
$544$	−0.354525	−	0.841908i	−0.0152001	−	0.0360965i
$545$	−0.0766223	+	0.0784400i	−0.00328214	+	0.00336000i
$546$	−5.41254	−	9.04530i	−0.231635	−	0.387103i
$547$	7.77691	+	5.43037i	0.332517	+	0.232186i	0.726873	−	0.686772i	$-0.240973\pi$
$547$	7.77691	+	5.43037i	0.332517	+	0.232186i	−0.394356	+	0.918958i	$0.629032\pi$
$548$	−8.03158	−	6.18782i	−0.343092	−	0.264330i
$549$	−0.161205	+	6.87471i	−0.00688007	+	0.293406i
$550$	−16.1851	−	8.19898i	−0.690135	−	0.349606i
$551$	43.2364	+	33.3108i	1.84193	+	1.41909i
$552$	−0.247660	+	3.51538i	−0.0105411	+	0.149624i
$553$	31.5366	+	2.96617i	1.34107	+	0.126134i
$554$	1.37649	+	0.468757i	0.0584816	+	0.0199156i
$555$	−0.0564968	−	2.40934i	−0.00239815	−	0.102271i
$556$	−9.13861	+	0.859530i	−0.387563	+	0.0364522i
$557$	−21.8340	−	5.21483i	−0.925138	−	0.220959i	−0.258216	−	0.966087i	$-0.583135\pi$
$557$	−21.8340	−	5.21483i	−0.925138	−	0.220959i	−0.666922	+	0.745128i	$0.732388\pi$
$558$	3.05301	−	0.143259i	0.129244	−	0.00606463i
$559$	−6.06294	−	11.3031i	−0.256435	−	0.478070i
$560$	0.786528	+	0.972835i	0.0332369	+	0.0411098i
$561$	−2.01094	+	6.39240i	−0.0849020	+	0.269887i
$562$	−28.6245	+	6.83666i	−1.20745	+	0.288387i
$563$	−18.3979	+	8.26027i	−0.775378	+	0.348129i	−0.758453	−	0.651728i	$-0.774044\pi$
$563$	−18.3979	+	8.26027i	−0.775378	+	0.348129i	−0.0169251	+	0.999857i	$0.505388\pi$
$564$	−9.84305	+	0.461874i	−0.414467	+	0.0194484i
$565$	−2.34562	+	1.80715i	−0.0986811	+	0.0760274i
$566$	3.82905	+	5.21860i	0.160947	+	0.219354i
$567$	−34.7983	−	15.6237i	−1.46139	−	0.656134i
$568$	8.58055	−	5.99153i	0.360032	−	0.251399i
$569$	−13.5075	−	0.633822i	−0.566262	−	0.0265712i	−0.238181	−	0.971221i	$-0.576551\pi$
$569$	−13.5075	−	0.633822i	−0.566262	−	0.0265712i	−0.328081	+	0.944650i	$0.606402\pi$
$570$	4.57676	−	1.80215i	0.191700	−	0.0754836i
$571$	9.47012	+	3.22499i	0.396312	+	0.134962i	0.513378	−	0.858162i	$-0.328394\pi$
$571$	9.47012	+	3.22499i	0.396312	+	0.134962i	−0.117066	+	0.993124i	$0.537349\pi$
$572$	3.77116	+	4.24132i	0.157680	+	0.177339i
$573$	−21.2364	−	13.3934i	−0.887165	−	0.559517i
$574$	−29.2454	+	29.9392i	−1.22068	+	1.24964i
$575$	1.01939	+	8.65626i	0.0425115	+	0.360991i
$576$	0.786663	−	0.398505i	0.0327776	−	0.0166044i
$577$	7.32383	−	5.11400i	0.304895	−	0.212899i	−0.410078	−	0.912050i	$-0.634499\pi$
$577$	7.32383	−	5.11400i	0.304895	−	0.212899i	0.714973	+	0.699152i	$0.246439\pi$
$578$	11.8256	−	11.0218i	0.491879	−	0.458445i
$579$	−19.1218	−	16.2156i	−0.794677	−	0.673899i
$580$	−2.58428	−	1.01759i	−0.107307	−	0.0422530i
$581$	−11.2618	−	5.05632i	−0.467219	−	0.209772i
$582$	−24.3748	−	4.62605i	−1.01037	−	0.191756i
$583$	1.29406	−	3.07306i	0.0535944	−	0.127273i
$584$	5.66805	+	13.4602i	0.234546	+	0.556987i
$585$	0.416783	−	0.236306i	0.0172318	−	0.00977006i
$586$	9.03432	−	12.3129i	0.373204	−	0.508639i
$587$	−0.111341	−	4.74821i	−0.00459553	−	0.195980i	−0.997209	−	0.0746602i	$-0.976213\pi$
$587$	−0.111341	−	4.74821i	−0.00459553	−	0.195980i	0.992614	−	0.121320i	$-0.0387126\pi$
$588$	4.51541	−	9.45724i	0.186212	−	0.390010i
$589$	−23.3219	−	6.74006i	−0.960960	−	0.277720i
$590$	0.291707	−	0.271879i	0.0120094	−	0.0111931i
$591$	16.0843	+	6.33335i	0.661619	+	0.260519i
$592$	−0.718765	+	3.35573i	−0.0295411	+	0.137920i
$593$	23.8633	−	4.52897i	0.979946	−	0.185983i	0.328356	−	0.944554i	$-0.393505\pi$
$593$	23.8633	−	4.52897i	0.979946	−	0.185983i	0.651590	+	0.758571i	$0.274102\pi$
$594$	15.1132	+	3.60961i	0.620100	+	0.148104i
$595$	0.586804	−	0.980651i	0.0240566	−	0.0402028i
$596$	15.4622	−	4.46860i	0.633355	−	0.183041i
$597$	−6.81419	+	41.1479i	−0.278886	+	1.68407i
$598$	0.695369	−	2.63631i	0.0284357	−	0.107807i
$599$	−18.9845	−	28.5933i	−0.775684	−	1.16829i	−0.981829	−	0.189769i	$-0.939226\pi$
$599$	−18.9845	−	28.5933i	−0.775684	−	1.16829i	0.206144	−	0.978522i	$-0.433908\pi$
$600$	7.60547	−	5.85952i	0.310492	−	0.239214i
$601$	42.0890	−	7.98801i	1.71685	−	0.325838i	0.767733	−	0.640770i	$-0.221385\pi$
$601$	42.0890	−	7.98801i	1.71685	−	0.325838i	0.949114	+	0.314932i	$0.101982\pi$
$602$	13.9604	−	26.0263i	0.568985	−	1.06075i
$603$	2.07797	−	4.35217i	0.0846214	−	0.177234i
$604$	22.2530	−	8.76232i	0.905460	−	0.356534i
$605$	0.166703	+	1.00665i	0.00677745	+	0.0409260i
$606$	−20.0130	−	2.83391i	−0.812972	−	0.115120i
$607$	6.95512	+	4.85654i	0.282300	+	0.197121i	0.705111	−	0.709097i	$-0.250897\pi$
$607$	6.95512	+	4.85654i	0.282300	+	0.197121i	−0.422812	+	0.906218i	$0.638957\pi$
$608$	−6.93515	+	0.982042i	−0.281258	+	0.0398271i
$609$	3.78690	+	53.7528i	0.153453	+	2.17817i
$610$	−0.195328	+	2.77256i	−0.00790859	+	0.112258i
$611$	7.54834	+	1.06887i	0.305373	+	0.0432419i
$612$	−0.589299	−	0.549244i	−0.0238210	−	0.0222019i
$613$	−3.97201	−	33.7287i	−0.160428	−	1.36229i	−0.802961	−	0.596032i	$-0.796743\pi$
$613$	−3.97201	−	33.7287i	−0.160428	−	1.36229i	0.642533	−	0.766258i	$-0.277884\pi$
$614$	−0.749685	+	1.78031i	−0.0302548	+	0.0718476i
$615$	−5.85139	−	5.99021i	−0.235951	−	0.241548i
$616$	−3.33293	+	12.6360i	−0.134288	+	0.509118i
$617$	−13.3056	−	16.4573i	−0.535663	−	0.662546i	0.435716	−	0.900084i	$-0.356495\pi$
$617$	−13.3056	−	16.4573i	−0.535663	−	0.662546i	−0.971378	+	0.237538i	$0.923660\pi$
$618$	−1.61201	+	13.6885i	−0.0648444	+	0.550633i
$619$	−13.5649	−	36.9693i	−0.545219	−	1.48592i	−0.846502	−	0.532386i	$-0.821296\pi$
$619$	−13.5649	−	36.9693i	−0.545219	−	1.48592i	0.301283	−	0.953535i	$-0.402585\pi$
$620$	1.23534			0.0496125
$621$	−2.57130	−	7.00774i	−0.103183	−	0.281211i
$622$	−13.9077	+	4.73617i	−0.557646	+	0.189903i
$623$	−12.6506	+	3.02146i	−0.506836	+	0.121052i
$624$	−2.88519	+	0.833825i	−0.115500	+	0.0333797i
$625$	15.3563	−	17.2708i	0.614251	−	0.690832i
$626$	−10.3546	+	5.87083i	−0.413854	+	0.234646i
$627$	43.4605	+	27.4096i	1.73564	+	1.09464i
$628$	−3.24673	−	10.3207i	−0.129558	−	0.411842i
$629$	3.10405	−	0.439544i	0.123766	−	0.0175258i
$630$	0.984126	+	0.498535i	0.0392085	+	0.0198621i
$631$	7.94045	−	21.6406i	0.316104	−	0.861500i	−0.676092	−	0.736817i	$-0.736328\pi$
$631$	7.94045	−	21.6406i	0.316104	−	0.861500i	0.992197	−	0.124683i	$-0.0397914\pi$
$632$	3.10874	−	8.47247i	0.123659	−	0.337017i
$633$	0.165987	−	7.07865i	0.00659741	−	0.281351i
$634$	0.538740	+	7.64709i	0.0213961	+	0.303705i
$635$	−2.04347	+	3.07775i	−0.0810926	+	0.122137i
$636$	1.17244	+	1.31861i	0.0464902	+	0.0522863i
$637$	−4.79645	+	6.53707i	−0.190042	+	0.259008i
$638$	−7.39955	−	28.0535i	−0.292951	−	1.11065i
$639$	4.73876	−	7.91929i	0.187462	−	0.313282i
$640$	0.325159	−	0.145990i	0.0128530	−	0.00577075i
$641$	18.9216	+	10.7281i	0.747360	+	0.423736i	0.819073	−	0.573690i	$-0.194488\pi$
$641$	18.9216	+	10.7281i	0.747360	+	0.423736i	−0.0717132	+	0.997425i	$0.522847\pi$
$642$	1.08202	−	9.18807i	0.0427039	−	0.362624i
$643$	−4.58357	+	3.88695i	−0.180758	+	0.153286i	−0.732592	−	0.680668i	$-0.761690\pi$
$643$	−4.58357	+	3.88695i	−0.180758	+	0.153286i	0.551833	+	0.833954i	$0.313928\pi$
$644$	5.94280	−	2.02379i	0.234179	−	0.0797483i
$645$	5.14041	+	2.91450i	0.202404	+	0.114758i
$646$	3.02451	+	5.63856i	0.118998	+	0.221846i
$647$	13.0040	+	19.5859i	0.511241	+	0.770002i	0.994417	−	0.105522i	$-0.0336512\pi$
$647$	13.0040	+	19.5859i	0.511241	+	0.770002i	−0.483176	+	0.875523i	$0.660517\pi$
$648$	−6.83278	+	8.45127i	−0.268417	+	0.331997i
$649$	4.09243	+	0.776696i	0.160642	+	0.0304880i
$650$	−6.62621	+	3.35668i	−0.259901	+	0.131660i
$651$	−10.3267	−	21.6287i	−0.404737	−	0.847696i
$652$	2.08478	+	12.5891i	0.0816464	+	0.493026i
$653$	−17.6105	−	1.65635i	−0.689151	−	0.0648179i	−0.256721	−	0.966486i	$-0.582642\pi$
$653$	−17.6105	−	1.65635i	−0.689151	−	0.0648179i	−0.432430	+	0.901668i	$0.642344\pi$
$654$	0.335271	−	0.504966i	0.0131101	−	0.0197457i
$655$	1.47961	+	4.70339i	0.0578130	+	0.183777i
$656$	6.12283	+	10.2323i	0.239056	+	0.399505i
$657$	9.42156	+	8.78116i	0.367570	+	0.342586i
$658$	7.56341	+	15.8411i	0.294852	+	0.617550i
$659$	26.8257	+	1.25877i	1.04498	+	0.0490346i	0.562440	−	0.826838i	$-0.309863\pi$
$659$	26.8257	+	1.25877i	1.04498	+	0.0490346i	0.482542	+	0.875873i	$0.339714\pi$
$660$	−2.51187	−	0.725935i	−0.0977743	−	0.0282570i
$661$	8.32012	−	5.24733i	0.323615	−	0.204098i	−0.361790	−	0.932260i	$-0.617834\pi$
$661$	8.32012	−	5.24733i	0.323615	−	0.204098i	0.685405	+	0.728162i	$0.259625\pi$
$662$	1.91156	−	8.92459i	0.0742950	−	0.346864i
$663$	1.62298	+	2.21195i	0.0630313	+	0.0859052i
$664$	−2.21130	+	2.73510i	−0.0858151	+	0.106142i
$665$	−6.12298	−	6.26824i	−0.237439	−	0.243072i
$666$	0.633837	+	2.95922i	0.0245607	+	0.114667i
$667$	−9.26131	+	10.4159i	−0.358599	+	0.403307i
$668$	2.95527	+	11.2042i	0.114343	+	0.433502i
$669$	−14.6357	+	1.37656i	−0.565848	+	0.0532207i
$670$	0.921415	−	1.71779i	0.0355974	−	0.0663639i
$671$	−24.5579	+	15.4882i	−0.948048	+	0.597915i
$672$	−5.27416	−	4.47258i	−0.203455	−	0.172534i
$673$	−11.3421	−	9.61828i	−0.437205	−	0.370758i	0.401031	−	0.916064i	$-0.368652\pi$
$673$	−11.3421	−	9.61828i	−0.437205	−	0.370758i	−0.838236	+	0.545307i	$0.816413\pi$
$674$	23.3200	−	14.7075i	0.898253	−	0.566510i
$675$	−9.61269	+	17.9209i	−0.369993	+	0.689775i
$676$	−10.6296	+	0.999761i	−0.408829	+	0.0384523i
$677$	−3.24526	−	12.3036i	−0.124726	−	0.472865i	0.875215	−	0.483733i	$-0.160720\pi$
$677$	−3.24526	−	12.3036i	−0.124726	−	0.472865i	−0.999941	+	0.0108683i	$0.996540\pi$
$678$	10.8759	−	12.2319i	0.417688	−	0.469763i
$679$	9.25667	+	43.2170i	0.355238	+	1.65852i
$680$	−0.227519	−	0.232917i	−0.00872497	−	0.00893196i
$681$	−24.7201	+	30.5756i	−0.947276	+	1.17166i
$682$	7.63391	+	10.4042i	0.292318	+	0.398399i
$683$	−1.70592	+	7.96450i	−0.0652753	+	0.304753i	−0.998513	−	0.0545050i	$-0.982642\pi$
$683$	−1.70592	+	7.96450i	−0.0652753	+	0.304753i	0.933238	+	0.359258i	$0.116970\pi$
$684$	−5.22447	+	3.29497i	−0.199762	+	0.125986i
$685$	−3.47168	−	1.00332i	−0.132646	−	0.0383350i
$686$	5.89324	+	0.276533i	0.225005	+	0.0105581i
$687$	18.3812	+	38.4982i	0.701286	+	1.46880i
$688$	−6.15556	−	5.73715i	−0.234678	−	0.218727i
$689$	−0.700951	−	1.17141i	−0.0267041	−	0.0446272i
$690$	0.376932	+	1.19820i	0.0143496	+	0.0456146i
$691$	7.73706	−	11.6531i	0.294332	−	0.443306i	−0.655901	−	0.754847i	$-0.727711\pi$
$691$	7.73706	−	11.6531i	0.294332	−	0.443306i	0.950233	+	0.311542i	$0.100845\pi$
$692$	23.3599	+	2.19711i	0.888012	+	0.0835217i
$693$	1.88277	+	11.3692i	0.0715204	+	0.431880i
$694$	−2.82995	−	5.92714i	−0.107423	−	0.224991i
$695$	−2.91852	+	1.47845i	−0.110706	+	0.0560809i
$696$	15.0835	+	2.86268i	0.571739	+	0.108510i
$697$	6.84855	−	8.47078i	0.259407	−	0.320854i
$698$	0.329522	+	0.496307i	0.0124726	+	0.0187855i
$699$	−23.4317	−	43.6836i	−0.886269	−	1.65227i
$700$	−14.8783	−	8.43568i	−0.562349	−	0.318839i
$701$	27.3170	−	9.30263i	1.03175	−	0.351355i	0.245585	−	0.969375i	$-0.421020\pi$
$701$	27.3170	−	9.30263i	1.03175	−	0.351355i	0.786163	+	0.618020i	$0.212065\pi$
$702$	4.85173	−	4.11435i	0.183117	−	0.155286i
$703$	2.81134	−	23.8728i	0.106032	−	0.900379i
$704$	3.23889	+	1.83638i	0.122070	+	0.0692111i
$705$	−3.20408	+	1.43856i	−0.120672	+	0.0541795i
$706$	−9.77954	+	16.3433i	−0.368058	+	0.615089i
$707$	9.18346	+	34.8168i	0.345380	+	1.30942i
$708$	−1.30397	+	1.77718i	−0.0490062	+	0.0667904i
$709$	0.217926	+	0.245095i	0.00818437	+	0.00920475i	0.751392	−	0.659856i	$-0.229383\pi$
$709$	0.217926	+	0.245095i	0.00818437	+	0.00920475i	−0.743207	+	0.669061i	$0.766696\pi$
$710$	2.06327	−	3.10758i	0.0774331	−	0.116625i
$711$	−0.559289	−	7.93877i	−0.0209750	−	0.297727i
$712$	−0.0868707	+	3.70466i	−0.00325562	+	0.138838i
$713$	2.13546	−	5.81990i	0.0799734	−	0.217957i
$714$	−2.17605	+	5.93052i	−0.0814365	+	0.221944i
$715$	1.80455	+	0.914141i	0.0674863	+	0.0341869i
$716$	13.6176	−	1.92830i	0.508913	−	0.0720639i
$717$	−6.24033	−	19.8368i	−0.233049	−	0.740820i
$718$	5.91455	+	3.73019i	0.220729	+	0.139209i
$719$	−24.4080	+	13.8388i	−0.910265	+	0.516100i	−0.875458	−	0.483295i	$-0.839440\pi$
$719$	−24.4080	+	13.8388i	−0.910265	+	0.516100i	−0.0348076	+	0.999394i	$0.511082\pi$
$720$	0.208852	−	0.234891i	0.00778347	−	0.00875386i
$721$	23.5884	−	6.81710i	0.878478	−	0.253882i
$722$	29.2384	−	6.98327i	1.08814	−	0.259890i
$723$	35.5720	−	12.1138i	1.32294	−	0.450518i
$724$	−5.00197	−	13.6322i	−0.185897	−	0.506637i
$725$	37.9717			1.41024
$726$	−1.94288	−	5.29507i	−0.0721071	−	0.196518i
$727$	0.519388	−	4.41043i	0.0192630	−	0.163574i	−0.980132	−	0.198345i	$-0.936443\pi$
$727$	0.519388	−	4.41043i	0.0192630	−	0.163574i	0.999395	+	0.0347712i	$0.0110702\pi$
$728$	3.36369	+	4.16045i	0.124667	+	0.154197i
$729$	3.84689	−	14.5845i	0.142477	−	0.540167i
$730$	3.63752	+	3.72382i	0.134631	+	0.137825i
$731$	−2.98319	+	7.08433i	−0.110337	+	0.262023i
$732$	−1.79689	−	15.2585i	−0.0664151	−	0.563970i
$733$	7.98663	+	7.44377i	0.294993	+	0.274942i	0.815302	−	0.579036i	$-0.196571\pi$
$733$	7.98663	+	7.44377i	0.294993	+	0.274942i	−0.520309	+	0.853978i	$0.674183\pi$
$734$	28.4744	+	4.03208i	1.05101	+	0.148827i
$735$	0.262505	−	3.72610i	0.00968264	−	0.137439i
$736$	−0.125700	−	1.78424i	−0.00463337	−	0.0657679i
$737$	20.1614	−	2.85493i	0.742656	−	0.105163i
$738$	8.62153	+	6.02014i	0.317363	+	0.221605i
$739$	−20.7186	−	2.93383i	−0.762147	−	0.107923i	−0.251669	−	0.967813i	$-0.580979\pi$
$739$	−20.7186	−	2.93383i	−0.762147	−	0.107923i	−0.510478	+	0.859891i	$0.670532\pi$
$740$	0.199844	+	1.20677i	0.00734641	+	0.0443617i
$741$	19.5731	−	7.70711i	0.719037	−	0.283128i
$742$	1.35433	−	2.83656i	0.0497190	−	0.104133i
$743$	−2.46832	+	4.60166i	−0.0905538	+	0.168819i	−0.922455	−	0.386106i	$-0.873820\pi$
$743$	−2.46832	+	4.60166i	−0.0905538	+	0.168819i	0.831901	+	0.554924i	$0.187253\pi$
$744$	−6.70888	+	1.27327i	−0.245959	+	0.0466803i
$745$	4.54439	−	3.50116i	0.166494	−	0.128273i
$746$	13.1411	+	19.7923i	0.481128	+	0.724648i
$747$	−0.791042	+	2.99903i	−0.0289427	+	0.109729i
$748$	0.555685	−	3.35554i	0.0203179	−	0.122691i
$749$	−15.8331	+	4.57581i	−0.578530	+	0.167196i
$750$	3.56006	−	5.94948i	0.129995	−	0.217244i
$751$	21.0733	+	5.03313i	0.768976	+	0.183662i	0.597872	−	0.801591i	$-0.296013\pi$
$751$	21.0733	+	5.03313i	0.768976	+	0.183662i	0.171103	+	0.985253i	$0.445267\pi$
$752$	4.91365	−	0.932554i	0.179182	−	0.0340067i
$753$	−6.26828	+	29.2650i	−0.228429	+	1.06647i
$754$	−11.0520	−	4.35185i	−0.402491	−	0.158485i
$755$	6.23581	−	5.81195i	0.226944	−	0.211519i
$756$	14.0717	+	4.06676i	0.511784	+	0.147907i
$757$	−10.5729	+	22.1442i	−0.384278	+	0.804846i	0.615581	+	0.788073i	$0.288921\pi$
$757$	−10.5729	+	22.1442i	−0.384278	+	0.804846i	−0.999859	+	0.0167729i	$0.994661\pi$
$758$	−0.554605	−	23.6515i	−0.0201442	−	0.859062i
$759$	−7.76210	+	10.5789i	−0.281746	+	0.383991i
$760$	−2.17176	+	1.23134i	−0.0787780	+	0.0446653i
$761$	6.64926	+	15.7903i	0.241036	+	0.572399i	0.996574	−	0.0827052i	$-0.0263560\pi$
$761$	6.64926	+	15.7903i	0.241036	+	0.572399i	−0.755538	+	0.655104i	$0.772625\pi$
$762$	7.92539	−	18.8208i	0.287107	−	0.681806i
$763$	−1.06085	−	0.201337i	−0.0384054	−	0.00728890i
$764$	11.6252	+	5.21949i	0.420586	+	0.188835i
$765$	−0.267163	−	0.105198i	−0.00965928	−	0.00380344i
$766$	1.60669	+	1.36250i	0.0580520	+	0.0492291i
$767$	1.24752	−	1.16272i	0.0450454	−	0.0419836i
$768$	−1.61540	+	1.12798i	−0.0582906	+	0.0407025i
$769$	−20.8417	+	10.5579i	−0.751571	+	0.380728i	−0.785634	−	0.618692i	$-0.787663\pi$
$769$	−20.8417	+	10.5579i	−0.751571	+	0.380728i	0.0340625	+	0.999420i	$0.489155\pi$
$770$	0.544761	+	4.62589i	0.0196318	+	0.166706i
$771$	27.1171	−	27.7604i	0.976597	−	0.999766i
$772$	10.7634	+	6.78826i	0.387383	+	0.244315i
$773$	3.02910	+	3.40675i	0.108949	+	0.122532i	0.799273	−	0.600969i	$-0.205218\pi$
$773$	3.02910	+	3.40675i	0.108949	+	0.122532i	−0.690323	+	0.723501i	$0.742532\pi$
$774$	−7.02423	−	2.39206i	−0.252481	−	0.0859808i
$775$	−15.7148	+	6.18785i	−0.564491	+	0.222274i
$776$	12.5785	+	0.590230i	0.451541	+	0.0211880i
$777$	19.4579	−	13.5868i	0.698047	−	0.487424i
$778$	19.4604	+	8.73731i	0.697688	+	0.313248i
$779$	−49.4093	−	67.3398i	−1.77027	−	2.41270i
$780$	−0.847968	+	0.653305i	−0.0303621	+	0.0233921i
$781$	38.9226	−	1.82640i	1.39276	−	0.0653537i
$782$	−1.49061	+	0.669253i	−0.0533041	+	0.0239324i
$783$	−31.6299	+	7.55448i	−1.13036	+	0.269975i
$784$	−1.59618	+	5.07396i	−0.0570064	+	0.181213i
$785$	−2.42452	−	2.99883i	−0.0865350	−	0.107033i
$786$	−12.8832	−	24.0181i	−0.459529	−	0.856697i
$787$	−43.9273	+	2.06124i	−1.56584	+	0.0734751i	−0.812028	−	0.583618i	$-0.801637\pi$
$787$	−43.9273	+	2.06124i	−1.56584	+	0.0734751i	−0.753809	+	0.657093i	$0.771786\pi$
$788$	−8.53367	−	2.03818i	−0.304000	−	0.0726070i
$789$	38.6053	−	3.63101i	1.37438	−	0.129267i
$790$	−0.0754076	−	3.21581i	−0.00268288	−	0.114413i
$791$	−27.6016	−	9.39957i	−0.981401	−	0.334210i
$792$	3.26891	+	0.307456i	0.116156	+	0.0109250i
$793$	−0.835344	+	11.8572i	−0.0296639	+	0.421062i
$794$	20.2526	+	15.6033i	0.718737	+	0.553741i
$795$	0.561028	+	0.284203i	0.0198976	+	0.0100796i
$796$	0.496259	−	21.1633i	0.0175894	−	0.750114i
$797$	1.96842	+	1.51654i	0.0697252	+	0.0537188i	0.644582	−	0.764536i	$-0.277032\pi$
$797$	1.96842	+	1.51654i	0.0697252	+	0.0537188i	−0.574856	+	0.818254i	$0.694942\pi$
$798$	39.7133	+	27.7305i	1.40583	+	0.981649i
$799$	−2.34595	−	3.92050i	−0.0829938	−	0.138697i
$800$	−3.40507	+	3.48586i	−0.120388	+	0.123244i
$801$	1.26822	+	3.01170i	0.0448102	+	0.106413i
$802$	−3.72215	−	17.3778i	−0.131434	−	0.613630i
$803$	−8.88414	+	53.6474i	−0.313515	+	1.89318i
$804$	−3.23348	+	10.2786i	−0.114036	+	0.362500i
$805$	1.70661	−	1.44724i	0.0601502	−	0.0510084i
$806$	5.28310			0.186089
$807$	−8.06173	+	31.2926i	−0.283786	+	1.10155i
$808$	10.2590			0.360909
$809$	18.7158	−	15.8713i	0.658012	−	0.558005i	−0.254491	−	0.967075i	$-0.581908\pi$
$809$	18.7158	−	15.8713i	0.658012	−	0.558005i	0.912503	+	0.409070i	$0.134147\pi$
$810$	−1.16241	+	3.69510i	−0.0408431	+	0.129832i
$811$	8.07765	−	48.7773i	0.283645	−	1.71280i	−0.347956	−	0.937511i	$-0.613124\pi$
$811$	8.07765	−	48.7773i	0.283645	−	1.71280i	0.631601	−	0.775294i	$-0.282398\pi$
$812$	−5.72819	−	26.7434i	−0.201020	−	0.938510i
$813$	−6.10988	−	14.5094i	−0.214283	−	0.508868i
$814$	−8.92864	+	9.14046i	−0.312949	+	0.320373i
$815$	2.33539	+	3.90285i	0.0818052	+	0.136711i
$816$	1.47568	+	1.03042i	0.0516590	+	0.0360719i
$817$	46.6891	+	35.9710i	1.63345	+	1.25846i
$818$	−0.251202	+	10.7127i	−0.00878306	+	0.374560i
$819$	4.20874	+	2.13205i	0.147065	+	0.0744998i
$820$	3.36682	+	2.59392i	0.117575	+	0.0905837i
$821$	2.12128	−	30.1102i	0.0740330	−	1.05085i	−0.810915	−	0.585164i	$-0.801030\pi$
$821$	2.12128	−	30.1102i	0.0740330	−	1.05085i	0.884948	−	0.465690i	$-0.154194\pi$
$822$	19.8881	+	1.87057i	0.693677	+	0.0652436i
$823$	−23.4670	−	7.99156i	−0.818009	−	0.278568i	−0.118284	−	0.992980i	$-0.537739\pi$
$823$	−23.4670	−	7.99156i	−0.818009	−	0.278568i	−0.699726	+	0.714412i	$0.746694\pi$
$824$	−0.163996	−	6.99373i	−0.00571307	−	0.243638i
$825$	35.5896	−	3.34737i	1.23907	−	0.116541i
$826$	3.81930	+	0.912199i	0.132890	+	0.0317395i
$827$	13.8720	−	0.650929i	0.482378	−	0.0226350i	0.195704	−	0.980663i	$-0.437301\pi$
$827$	13.8720	−	0.650929i	0.482378	−	0.0226350i	0.286674	+	0.958028i	$0.407450\pi$
$828$	−0.745579	−	1.38998i	−0.0259107	−	0.0483051i
$829$	−1.53973	−	1.90445i	−0.0534771	−	0.0661444i	0.750195	−	0.661216i	$-0.229959\pi$
$829$	−1.53973	−	1.90445i	−0.0534771	−	0.0661444i	−0.803673	+	0.595072i	$0.797124\pi$
$830$	−0.376194	+	1.19585i	−0.0130579	+	0.0415085i
$831$	−2.78659	+	0.665547i	−0.0966657	+	0.0230876i
$832$	1.39058	−	0.624344i	0.0482098	−	0.0216452i
$833$	4.85370	−	0.227754i	0.168171	−	0.00789121i
$834$	14.3260	−	11.0373i	0.496070	−	0.382190i
$835$	2.44323	+	3.32987i	0.0845514	+	0.115235i
$836$	−23.7911	−	10.6817i	−0.822832	−	0.369435i
$837$	11.8591	−	8.28084i	0.409911	−	0.286228i
$838$	10.4850	+	0.491997i	0.362199	+	0.0169958i
$839$	27.0248	−	10.6413i	0.933000	−	0.367378i	0.149494	−	0.988763i	$-0.452235\pi$
$839$	27.0248	−	10.6413i	0.933000	−	0.367378i	0.783506	+	0.621384i	$0.213429\pi$
$840$	−2.33321	−	0.794562i	−0.0805035	−	0.0274150i
$841$	21.0774	+	23.7052i	0.726807	+	0.817420i
$842$	−19.4522	−	12.2681i	−0.670368	−	0.422788i
$843$	40.5170	−	41.4782i	1.39548	−	1.42859i
$844$	0.420311	+	3.56911i	0.0144677	+	0.122854i
$845$	−3.39468	+	1.71966i	−0.116780	+	0.0591581i
$846$	3.61609	−	2.52500i	0.124324	−	0.0868113i
$847$	−7.35026	+	6.85065i	−0.252558	+	0.235391i
$848$	−0.683031	−	0.579222i	−0.0234554	−	0.0198905i
$849$	−11.8659	−	4.67233i	−0.407238	−	0.160354i
$850$	4.06096	+	1.82329i	0.139290	+	0.0625382i
$851$	6.03075	+	1.14457i	0.206731	+	0.0392352i
$852$	−8.00219	+	19.0032i	−0.274150	+	0.651038i
$853$	−18.4186	−	43.7395i	−0.630640	−	1.49761i	−0.852605	−	0.522556i	$-0.824979\pi$
$853$	−18.4186	−	43.7395i	−0.630640	−	1.49761i	0.221965	−	0.975055i	$-0.428753\pi$
$854$	−23.8092	+	13.4993i	−0.814735	+	0.461936i
$855$	−1.30238	+	1.77501i	−0.0445405	+	0.0607041i
$856$	0.110078	+	4.69436i	0.00376240	+	0.160450i
$857$	−5.03825	+	10.5523i	−0.172103	+	0.360459i	−0.970288	−	0.241954i	$-0.922212\pi$
$857$	−5.03825	+	10.5523i	−0.172103	+	0.360459i	0.798185	+	0.602413i	$0.205794\pi$
$858$	−10.7423	−	3.10455i	−0.366737	−	0.105988i
$859$	33.3632	−	31.0955i	1.13834	−	1.06096i	0.140857	−	0.990030i	$-0.455014\pi$
$859$	33.3632	−	31.0955i	1.13834	−	1.06096i	0.997481	−	0.0709332i	$-0.0225977\pi$
$860$	−2.79066	−	1.09885i	−0.0951607	−	0.0374705i
$861$	17.2704	−	80.6309i	0.588574	−	2.74790i
$862$	1.66538	−	0.316069i	0.0567230	−	0.0107654i
$863$	55.8997	+	13.3510i	1.90285	+	0.454475i	0.999683	+	0.0251785i	$0.00801541\pi$
$863$	55.8997	+	13.3510i	1.90285	+	0.454475i	0.903164	+	0.429296i	$0.141238\pi$
$864$	2.14287	−	3.58111i	0.0729019	−	0.121832i
$865$	8.03411	−	2.32187i	0.273168	−	0.0789461i
$866$	−5.33855	+	32.2372i	−0.181411	+	1.09546i
$867$	−8.12309	+	30.7966i	−0.275875	+	1.04591i
$868$	6.72872	+	10.1344i	0.228388	+	0.343984i
$869$	26.6180	−	20.5075i	0.902955	−	0.695669i
$870$	5.37620	−	1.02034i	0.182270	−	0.0345928i
$871$	3.94055	−	7.34634i	0.133521	−	0.248921i
$872$	−0.132553	+	0.277623i	−0.00448880	+	0.00940151i
$873$	10.3323	−	4.06844i	0.349695	−	0.137696i
$874$	2.04685	+	12.3601i	0.0692359	+	0.418085i
$875$	−12.2292	−	1.73170i	−0.413422	−	0.0585421i
$876$	−23.5927	−	16.4741i	−0.797125	−	0.556607i
$877$	−26.1321	+	3.70040i	−0.882419	+	0.124954i	−0.566725	−	0.823907i	$-0.691790\pi$
$877$	−26.1321	+	3.70040i	−0.882419	+	0.124954i	−0.315694	+	0.948861i	$0.602237\pi$
$878$	0.689081	+	9.78109i	0.0232554	+	0.330096i
$879$	−2.11454	+	30.0145i	−0.0713215	+	1.01237i
$880$	1.31397	+	0.186063i	0.0442939	+	0.00627218i
$881$	−33.4485	−	31.1750i	−1.12691	−	1.05031i	−0.998280	−	0.0586192i	$-0.981330\pi$
$881$	−33.4485	−	31.1750i	−1.12691	−	1.05031i	−0.128630	−	0.991693i	$-0.541058\pi$
$882$	0.548591	+	4.65841i	0.0184720	+	0.156857i
$883$	−0.0357222	+	0.0848313i	−0.00120215	+	0.00285480i	−0.922221	−	0.386664i	$-0.873627\pi$
$883$	−0.0357222	+	0.0848313i	−0.00120215	+	0.00285480i	0.921019	+	0.389519i	$0.127359\pi$
$884$	−0.973017	−	0.996100i	−0.0327261	−	0.0335025i
$885$	−0.200376	+	0.759674i	−0.00673556	+	0.0255362i
$886$	−7.36806	−	9.11335i	−0.247535	−	0.306169i
$887$	2.83039	−	24.0345i	0.0950352	−	0.807000i	−0.859956	−	0.510368i	$-0.829509\pi$
$887$	2.83039	−	24.0345i	0.0950352	−	0.807000i	0.954992	−	0.296633i	$-0.0958638\pi$
$888$	−2.32913	−	6.34773i	−0.0781604	−	0.213016i
$889$	−36.3795			−1.22013
$890$	0.454976	+	1.23998i	0.0152508	+	0.0415641i
$891$	−38.3039	+	13.0442i	−1.28323	+	0.436996i
$892$	7.25705	−	1.73327i	0.242984	−	0.0580341i
$893$	−33.6540	+	9.72607i	−1.12619	+	0.325470i
$894$	−21.0710	+	23.6980i	−0.704718	+	0.792578i
$895$	4.26438	−	2.41781i	0.142543	−	0.0808184i
$896$	2.96875	+	1.87233i	0.0991790	+	0.0625502i
$897$	1.61200	+	5.12424i	0.0538231	+	0.171093i
$898$	−33.5439	+	4.74993i	−1.11937	+	0.158507i
$899$	−24.0924	−	12.2047i	−0.803528	−	0.407048i
$900$	−1.48024	+	4.03419i	−0.0493412	+	0.134473i
$901$	−0.281809	+	0.768032i	−0.00938841	+	0.0255869i
$902$	−1.04079	+	44.3853i	−0.0346545	+	1.47787i
$903$	4.08932	+	58.0454i	0.136084	+	1.93163i
$904$	−4.59515	+	6.92095i	−0.152832	+	0.230187i
$905$	−3.43908	−	3.86784i	−0.114319	−	0.128571i
$906$	−27.8750	+	37.9907i	−0.926083	+	1.26216i
$907$	0.805300	+	3.05309i	0.0267396	+	0.101376i	0.978970	−	0.204004i	$-0.0653956\pi$
$907$	0.805300	+	3.05309i	0.0267396	+	0.101376i	−0.952231	+	0.305380i	$0.901216\pi$
$908$	10.2470	−	17.1246i	0.340059	−	0.568298i
$909$	8.25311	−	3.70548i	0.273738	−	0.122903i
$910$	1.65885	+	0.940532i	0.0549905	+	0.0311783i
$911$	3.27859	−	27.8404i	0.108624	−	0.922395i	−0.825244	−	0.564777i	$-0.808962\pi$
$911$	3.27859	−	27.8404i	0.108624	−	0.922395i	0.933868	−	0.357618i	$-0.116411\pi$
$912$	10.5252	−	8.92557i	0.348525	−	0.295555i
$913$	−12.3963	+	4.22150i	−0.410259	+	0.139711i
$914$	−13.2264	−	7.49904i	−0.437489	−	0.248046i
$915$	−2.58851	−	4.82574i	−0.0855734	−	0.159534i
$916$	−11.9768	−	18.0388i	−0.395726	−	0.596020i
$917$	−30.5262	+	37.7570i	−1.00806	+	1.24684i
$918$	−3.74546	−	0.710846i	−0.123619	−	0.0234614i
$919$	−35.1116	+	17.7867i	−1.15822	+	0.586728i	−0.922843	−	0.385175i	$-0.874141\pi$
$919$	−35.1116	+	17.7867i	−1.15822	+	0.586728i	−0.235380	+	0.971903i	$0.575634\pi$
$920$	−0.274688	−	0.575318i	−0.00905621	−	0.0189677i
$921$	−0.621806	−	3.75481i	−0.0204892	−	0.123725i
$922$	−30.1540	−	2.83613i	−0.993070	−	0.0934030i
$923$	8.82383	−	13.2899i	0.290440	−	0.437444i
$924$	−7.72639	−	24.5607i	−0.254179	−	0.807989i
$925$	−8.58694	−	14.3503i	−0.282337	−	0.471834i
$926$	−22.8175	−	21.2666i	−0.749831	−	0.698863i
$927$	−2.65802	−	5.56706i	−0.0873009	−	0.182846i
$928$	−7.78377	−	0.365245i	−0.255515	−	0.0119897i
$929$	38.8748	+	11.2349i	1.27544	+	0.368605i	0.845366	−	0.534188i	$-0.179382\pi$
$929$	38.8748	+	11.2349i	1.27544	+	0.368605i	0.430075	+	0.902793i	$0.358487\pi$
$930$	−2.05869	+	1.29837i	−0.0675070	+	0.0425753i
$931$	7.80307	−	36.4305i	0.255735	−	1.19396i
$932$	14.8839	+	20.2853i	0.487540	+	0.664467i
$933$	18.1992	−	22.5101i	0.595814	−	0.736946i
$934$	6.69005	+	6.84876i	0.218905	+	0.224098i
$935$	−0.253904	−	1.18541i	−0.00830354	−	0.0387671i
$936$	0.893184	−	1.00454i	0.0291946	−	0.0328344i
$937$	0.600230	+	2.27562i	0.0196087	+	0.0743413i	0.976019	−	0.217684i	$-0.0698501\pi$
$937$	0.600230	+	2.27562i	0.0196087	+	0.0743413i	−0.956411	+	0.292025i	$0.905671\pi$
$938$	19.1111	−	1.79749i	0.623999	−	0.0586900i
$939$	11.0855	−	20.6666i	0.361762	−	0.674430i
$940$	1.50780	−	0.950941i	0.0491791	−	0.0310163i
$941$	−16.5780	−	14.0584i	−0.540427	−	0.458291i	0.334604	−	0.942359i	$-0.391398\pi$
$941$	−16.5780	−	14.0584i	−0.540427	−	0.458291i	−0.875030	+	0.484068i	$0.839159\pi$
$942$	16.2580	+	13.7870i	0.529713	+	0.449206i
$943$	18.0404	−	11.3777i	0.587476	−	0.370509i
$944$	0.528830	−	0.985894i	0.0172119	−	0.0320881i
$945$	5.19788	−	0.488886i	0.169087	−	0.0159035i
$946$	−7.99046	−	30.2938i	−0.259792	−	0.984936i
$947$	12.3552	−	13.8955i	0.401489	−	0.451545i	−0.511649	−	0.859195i	$-0.670965\pi$
$947$	12.3552	−	13.8955i	0.401489	−	0.451545i	0.913138	+	0.407650i	$0.133652\pi$
$948$	3.72406	+	17.3867i	0.120952	+	0.564692i
$949$	15.5563	+	15.9254i	0.504980	+	0.516960i
$950$	21.4591	−	26.5422i	0.696226	−	0.861143i
$951$	−8.93507	−	12.1776i	−0.289740	−	0.394885i
$952$	0.671525	−	3.13517i	0.0217642	−	0.101612i
$953$	47.5905	−	30.0144i	1.54161	−	0.972261i	0.551156	−	0.834402i	$-0.314187\pi$
$953$	47.5905	−	30.0144i	1.54161	−	0.972261i	0.990452	−	0.137859i	$-0.0440221\pi$
$954$	−0.758694	−	0.219264i	−0.0245636	−	0.00709894i
$955$	4.53705	+	0.212896i	0.146815	+	0.00688914i
$956$	4.54762	+	9.52471i	0.147081	+	0.308051i
$957$	41.8161	+	38.9738i	1.35172	+	1.25984i
$958$	−1.26727	−	2.11783i	−0.0409437	−	0.0684241i
$959$	−10.6787	−	33.9457i	−0.344835	−	1.09616i
$960$	−0.388436	+	0.585040i	−0.0125367	+	0.0188821i
$961$	−18.9042	−	1.77803i	−0.609812	−	0.0573557i
$962$	0.854659	+	5.16091i	0.0275553	+	0.166394i
$963$	1.78413	+	3.73675i	0.0574928	+	0.120415i
$964$	−17.0143	+	8.61903i	−0.547993	+	0.277600i
$965$	4.45609	+	0.845714i	0.143447	+	0.0272245i
$966$	−7.77658	+	9.61864i	−0.250207	+	0.309475i
$967$	−26.3108	−	39.6278i	−0.846099	−	1.27435i	−0.959759	−	0.280826i	$-0.909392\pi$
$967$	−26.3108	−	39.6278i	−0.846099	−	1.27435i	0.113660	−	0.993520i	$-0.463743\pi$
$968$	1.35318	+	2.52272i	0.0434928	+	0.0810833i
$969$	−10.9666	−	6.21779i	−0.352297	−	0.199744i
$970$	4.24865	−	1.44685i	0.136416	−	0.0464557i
$971$	29.9370	−	25.3870i	0.960723	−	0.814709i	−0.0220067	−	0.999758i	$-0.507006\pi$
$971$	29.9370	−	25.3870i	0.960723	−	0.814709i	0.982729	+	0.185049i	$0.0592443\pi$
$972$	1.04002	−	8.83146i	0.0333588	−	0.283269i
$973$	−28.0256	−	15.8899i	−0.898459	−	0.509405i
$974$	−26.6162	+	11.9501i	−0.852839	+	0.382907i
$975$	7.51457	−	12.5582i	0.240659	−	0.402183i
$976$	1.98882	+	7.54012i	0.0636607	+	0.241353i
$977$	−9.45350	+	12.8841i	−0.302444	+	0.412200i	−0.930687	−	0.365817i	$-0.880790\pi$
$977$	−9.45350	+	12.8841i	−0.302444	+	0.412200i	0.628242	+	0.778018i	$0.283775\pi$
$978$	−16.7057	−	18.7884i	−0.534189	−	0.600788i
$979$	−7.63169	+	11.4944i	−0.243910	+	0.367363i
$980$	0.133235	+	1.89119i	0.00425604	+	0.0604119i
$981$	−0.00635982	+	0.271219i	−0.000203053	+	0.00865936i
$982$	0.540283	−	1.47247i	0.0172411	−	0.0469884i
$983$	11.0546	−	30.1277i	0.352586	−	0.960926i	−0.630242	−	0.776399i	$-0.717044\pi$
$983$	11.0546	−	30.1277i	0.352586	−	0.960926i	0.982827	−	0.184527i	$-0.0590752\pi$
$984$	−20.9580	−	10.6168i	−0.668118	−	0.338453i
$985$	−3.09631	+	0.438448i	−0.0986565	+	0.0139701i
$986$	2.13611	+	6.79030i	0.0680276	+	0.216247i
$987$	−29.2537	−	18.4497i	−0.931155	−	0.587261i
$988$	−9.28781	+	5.26598i	−0.295485	+	0.167533i
$989$	−10.0009	+	11.2477i	−0.318010	+	0.357657i
$990$	1.12426	−	0.324915i	0.0357315	−	0.0103265i
$991$	−37.7591	+	9.01835i	−1.19946	+	0.286477i	−0.782617	−	0.622503i	$-0.786116\pi$
$991$	−37.7591	+	9.01835i	−1.19946	+	0.286477i	−0.416839	+	0.908980i	$0.636862\pi$
$992$	3.28087	−	1.11728i	0.104168	−	0.0354737i
$993$	6.19434	+	16.8818i	0.196571	+	0.535729i
$994$	36.7320			1.16507
$995$	−2.59910	−	7.08351i	−0.0823971	−	0.224562i
$996$	0.810465	−	6.88214i	0.0256806	−	0.218069i
$997$	7.68601	+	9.50661i	0.243418	+	0.301077i	0.884637	−	0.466281i	$-0.154407\pi$
$997$	7.68601	+	9.50661i	0.243418	+	0.301077i	−0.641218	+	0.767359i	$0.721571\pi$
$998$	−3.25749	+	12.3499i	−0.103114	+	0.390931i
$999$	10.0078	+	10.2452i	0.316632	+	0.324144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.d.a.5.3	✓	726
269.54	even	67	inner	538.2.d.a.323.3	yes	726

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.d.a.5.3	✓	726	1.1	even	1	trivial
538.2.d.a.323.3	yes	726	269.54	even	67	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.d (of order \(67\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(0.762685 - 0.646770i) q^{2} +(-0.591238 + 1.87944i) q^{3} +(0.163377 - 0.986564i) q^{4} +(-0.0746505 - 0.348523i) q^{5} +(0.764634 + 1.81581i) q^{6} +(2.45258 - 2.51077i) q^{7} +(-0.513474 - 0.858105i) q^{8} +(-0.723021 - 0.504862i) q^{9} +(-0.282349 - 0.217532i) q^{10} +(0.0872830 - 3.72225i) q^{11} +(1.75759 + 0.890352i) q^{12} +(-1.20750 - 0.930304i) q^{13} +(0.246659 - 3.50118i) q^{14} +(0.699164 + 0.0657597i) q^{15} +(-0.946616 - 0.322364i) q^{16} +(0.0214150 + 0.913257i) q^{17} +(-0.877967 + 0.0825770i) q^{18} +(6.81272 + 1.62714i) q^{19} +(-0.356037 + 0.0167066i) q^{20} +(3.26876 + 6.09393i) q^{21} +(-2.34087 - 2.89535i) q^{22} +(-0.536750 + 1.70623i) q^{23} +(1.91634 - 0.457697i) q^{24} +(4.44545 - 1.99592i) q^{25} +(-1.52264 + 0.0714480i) q^{26} +(-3.30591 + 2.54699i) q^{27} +(-2.07633 - 2.82983i) q^{28} +(7.10871 + 3.19167i) q^{29} +(0.575773 - 0.402044i) q^{30} +(-3.46208 - 0.162454i) q^{31} +(-0.930465 + 0.366380i) q^{32} +(6.94412 + 2.36478i) q^{33} +(0.607000 + 0.682677i) q^{34} +(-1.05815 - 0.667352i) q^{35} +(-0.616204 + 0.630823i) q^{36} +(-0.401372 - 3.40829i) q^{37} +(6.24835 - 3.16526i) q^{38} +(2.46237 - 1.71939i) q^{39} +(-0.260739 + 0.243016i) q^{40} +(-9.09451 - 7.71229i) q^{41} +(6.43441 + 2.53361i) q^{42} +(7.67640 + 3.44655i) q^{43} +(-3.65797 - 0.694241i) q^{44} +(-0.121983 + 0.289678i) q^{45} +(0.694165 + 1.64847i) q^{46} +(-4.35072 + 2.46676i) q^{47} +(1.16554 - 1.58851i) q^{48} +(-0.124693 - 5.31764i) q^{49} +(2.09958 - 4.39744i) q^{50} +(-1.72907 - 0.499705i) q^{51} +(-1.11508 + 1.03929i) q^{52} +(0.833288 + 0.328115i) q^{53} +(-0.874052 + 4.08072i) q^{54} +(-1.30381 + 0.247447i) q^{55} +(-3.41384 - 0.815359i) q^{56} +(-7.08606 + 11.8420i) q^{57} +(7.48598 - 2.16346i) q^{58} +(-0.182782 + 1.10374i) q^{59} +(0.179104 - 0.679026i) q^{60} +(-4.31332 - 6.49647i) q^{61} +(-2.74555 + 2.11527i) q^{62} +(-3.04086 + 0.577120i) q^{63} +(-0.472689 + 0.881230i) q^{64} +(-0.234092 + 0.490291i) q^{65} +(6.82564 - 2.68766i) q^{66} +(0.893511 + 5.39552i) q^{67} +(0.904485 + 0.128078i) q^{68} +(-2.88940 - 2.01757i) q^{69} +(-1.23866 + 0.175398i) q^{70} +(0.735467 + 10.4395i) q^{71} +(-0.0619725 + 0.879662i) q^{72} +(-14.4607 - 2.04768i) q^{73} +(-2.51050 - 2.33986i) q^{74} +(1.12288 + 9.53500i) q^{75} +(2.71833 - 6.45534i) q^{76} +(-9.13162 - 9.34826i) q^{77} +(0.765960 - 2.90394i) q^{78} +(5.67401 + 7.01802i) q^{79} +(-0.0416862 + 0.353982i) q^{80} +(-3.74362 - 10.2027i) q^{81} -11.9243 q^{82} +(-1.21155 - 3.30193i) q^{83} +(6.54609 - 2.22923i) q^{84} +(0.316693 - 0.0756387i) q^{85} +(8.08380 - 2.33623i) q^{86} +(-10.2015 + 11.4733i) q^{87} +(-3.23889 + 1.83638i) q^{88} +(-3.13439 - 1.97679i) q^{89} +(0.0943207 + 0.299828i) q^{90} +(-5.29727 + 0.750113i) q^{91} +(1.59561 + 0.808297i) q^{92} +(2.35224 - 6.41071i) q^{93} +(-1.72280 + 4.69527i) q^{94} +(0.0585254 - 2.49586i) q^{95} +(-0.138461 - 1.96537i) q^{96} +(-6.96520 + 10.4906i) q^{97} +(-3.53439 - 3.97504i) q^{98} +(-1.94233 + 2.64719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 726 q + 11 q^{2} + q^{3} - 11 q^{4} + q^{5} - q^{6} + 4 q^{7} + 11 q^{8} - 10 q^{9} - q^{10} + 5 q^{11} + q^{12} - 7 q^{13} - 4 q^{14} - 2 q^{15} - 11 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} + q^{20}+ \cdots + 25 q^{99}+O(q^{100}) \) 726 * q + 11 * q^2 + q^3 - 11 * q^4 + q^5 - q^6 + 4 * q^7 + 11 * q^8 - 10 * q^9 - q^10 + 5 * q^11 + q^12 - 7 * q^13 - 4 * q^14 - 2 * q^15 - 11 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 + q^20 - 191 * q^21 - 5 * q^22 + 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 185 * q^27 + 4 * q^28 + 7 * q^29 - 65 * q^30 + 4 * q^31 + 11 * q^32 + 18 * q^33 - 4 * q^34 + 22 * q^35 - 10 * q^36 + 216 * q^37 - 5 * q^38 - 4 * q^39 - q^40 - 122 * q^41 - 10 * q^42 + 5 * q^43 - 62 * q^44 + 9 * q^45 - 6 * q^46 + 211 * q^47 + q^48 + 9 * q^49 + 8 * q^50 + 18 * q^51 - 7 * q^52 - 141 * q^53 - 16 * q^54 - 28 * q^55 - 4 * q^56 + 4 * q^57 - 7 * q^58 + q^59 + 132 * q^60 - 60 * q^61 - 4 * q^62 - 11 * q^64 + 24 * q^65 - 18 * q^66 + 15 * q^67 + 4 * q^68 - 8 * q^69 - 22 * q^70 + 8 * q^71 + 10 * q^72 + 65 * q^73 - 15 * q^74 - 15 * q^75 + 5 * q^76 - 2 * q^77 + 4 * q^78 - 61 * q^79 + q^80 - 315 * q^81 - 280 * q^82 + 198 * q^83 - 258 * q^84 - 126 * q^85 - 5 * q^86 + 6 * q^87 - 5 * q^88 - 36 * q^89 - 9 * q^90 + 28 * q^91 + 6 * q^92 + 152 * q^93 - 10 * q^94 + 6 * q^95 - q^96 - 24 * q^97 - 9 * q^98 + 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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