LMFDB - Embedded newform 197.2.g.a.100.4

Error: no document with id 193240579 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(16,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(98)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.g (of order $49$, degree $42$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$630$
Relative dimension:	$15$ over $\Q(\zeta_{49})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{49}]$

Embedding invariants

Embedding label			100.4
Character	$\chi$	$=$	197.100
Dual form			197.2.g.a.132.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.92615 + 0.505096i) q^{2} +(1.00252 + 0.853459i) q^{3} +(1.71230 - 0.964349i) q^{4} +(1.28820 - 1.41845i) q^{5} +(-2.36209 - 1.13752i) q^{6} +(1.12284 + 0.294444i) q^{7} +(0.0498044 - 0.0482328i) q^{8} +(-0.202143 - 1.25032i) q^{9} +(-1.76481 + 3.38282i) q^{10} +(1.12178 - 2.53412i) q^{11} +(2.53965 + 0.494597i) q^{12} +(-0.808829 + 0.104287i) q^{13} -2.31148 q^{14} +(2.50204 - 0.322602i) q^{15} +(-2.10904 + 3.47908i) q^{16} +(3.53391 + 0.226885i) q^{17} +(1.02089 + 2.30621i) q^{18} +(0.523401 + 2.29317i) q^{19} +(0.837902 - 3.67109i) q^{20} +(0.874377 + 1.25349i) q^{21} +(-0.880742 + 5.44770i) q^{22} +(2.83043 + 2.11240i) q^{23} +(0.0910947 - 0.00584847i) q^{24} +(0.127571 + 1.32240i) q^{25} +(1.50525 - 0.609409i) q^{26} +(2.91200 - 4.80365i) q^{27} +(2.20659 - 0.578635i) q^{28} +(-0.183556 - 0.0357476i) q^{29} +(-4.65636 + 1.88515i) q^{30} +(0.136036 + 4.24211i) q^{31} +(2.26561 - 7.63358i) q^{32} +(3.28737 - 1.58312i) q^{33} +(-6.92145 + 1.34795i) q^{34} +(1.86410 - 1.21339i) q^{35} +(-1.55188 - 1.94599i) q^{36} +(-1.79761 - 2.96534i) q^{37} +(-2.16642 - 4.15262i) q^{38} +(-0.899873 - 0.585752i) q^{39} +(-0.00425795 - 0.132778i) q^{40} +(-7.77897 - 0.499427i) q^{41} +(-2.31731 - 1.97276i) q^{42} +(-2.87841 + 6.50237i) q^{43} +(-0.522953 - 5.42096i) q^{44} +(-2.03392 - 1.32394i) q^{45} +(-6.51880 - 2.63917i) q^{46} +(0.807657 - 2.19466i) q^{47} +(-5.08361 + 1.68788i) q^{48} +(-4.92516 - 2.77380i) q^{49} +(-0.913661 - 2.48271i) q^{50} +(3.34919 + 3.24351i) q^{51} +(-1.28439 + 0.958564i) q^{52} +(-5.13876 - 2.08045i) q^{53} +(-3.18265 + 10.7234i) q^{54} +(-2.14945 - 4.85564i) q^{55} +(0.0701242 - 0.0394932i) q^{56} +(-1.43240 + 2.74565i) q^{57} +(0.371613 - 0.0238583i) q^{58} +(-0.597605 - 1.14550i) q^{59} +(3.97314 - 2.96523i) q^{60} +(-2.93475 + 2.49839i) q^{61} +(-2.40470 - 8.10224i) q^{62} +(0.141176 - 1.46343i) q^{63} +(-0.247409 + 7.71511i) q^{64} +(-0.894007 + 1.28163i) q^{65} +(-5.53235 + 4.70976i) q^{66} +(4.73085 - 12.8552i) q^{67} +(6.26992 - 3.01943i) q^{68} +(1.03471 + 4.53338i) q^{69} +(-2.97765 + 3.27873i) q^{70} +(-0.197980 - 1.22457i) q^{71} +(-0.0703742 - 0.0525216i) q^{72} +(7.34958 + 12.1239i) q^{73} +(4.96025 + 4.80374i) q^{74} +(-1.00072 + 1.43461i) q^{75} +(3.10763 + 3.42185i) q^{76} +(2.00573 - 2.51511i) q^{77} +(2.02915 + 0.673725i) q^{78} +(3.98689 + 4.39001i) q^{79} +(2.21804 + 7.47332i) q^{80} +(3.41295 - 1.13318i) q^{81} +(15.2357 - 2.96716i) q^{82} +(0.127822 - 0.560024i) q^{83} +(2.70599 + 1.30314i) q^{84} +(4.87421 - 4.72041i) q^{85} +(2.25992 - 13.9784i) q^{86} +(-0.153510 - 0.192495i) q^{87} +(-0.0663582 - 0.180317i) q^{88} +(-0.113920 + 3.55246i) q^{89} +(4.58636 + 1.52278i) q^{90} +(-0.938893 - 0.121057i) q^{91} +(6.88363 + 0.887546i) q^{92} +(-3.48409 + 4.36891i) q^{93} +(-0.447152 + 4.63520i) q^{94} +(3.92699 + 2.21164i) q^{95} +(8.78626 - 5.71922i) q^{96} +(-10.7233 - 15.3726i) q^{97} +(10.8876 + 2.85507i) q^{98} +(-3.39523 - 0.890333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 630 q - 42 q^{2} - 42 q^{3} - 28 q^{4} - 42 q^{5} - 21 q^{6} - 28 q^{7} - 28 q^{8} - 42 q^{9} - 28 q^{10} - 28 q^{11} - 28 q^{12} - 42 q^{13} - 28 q^{14} - 154 q^{15} - 42 q^{17} - 21 q^{18} - 7 q^{19}+ \cdots - 161 q^{99}+O(q^{100}) $ 630 * q - 42 * q^2 - 42 * q^3 - 28 * q^4 - 42 * q^5 - 21 * q^6 - 28 * q^7 - 28 * q^8 - 42 * q^9 - 28 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 - 28 * q^14 - 154 * q^15 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 35 * q^20 - 42 * q^21 - 42 * q^23 + 28 * q^24 - 42 * q^25 - 7 * q^26 + 42 * q^27 - 49 * q^28 - 182 * q^29 + 77 * q^30 - 14 * q^31 - 28 * q^32 + 35 * q^33 - 14 * q^34 - 42 * q^35 + 84 * q^36 + 14 * q^37 - 28 * q^38 - 21 * q^39 + 28 * q^40 - 28 * q^41 - 112 * q^42 - 56 * q^43 - 210 * q^44 + 49 * q^45 - 7 * q^47 + 42 * q^48 + 42 * q^49 + 98 * q^50 - 14 * q^51 + 49 * q^52 - 42 * q^53 + 63 * q^54 - 161 * q^56 - 175 * q^57 - 42 * q^58 + 42 * q^59 + 126 * q^60 - 14 * q^61 + 42 * q^62 + 49 * q^63 + 98 * q^64 + 56 * q^65 + 175 * q^66 + 28 * q^67 + 273 * q^68 - 7 * q^69 - 252 * q^70 - 77 * q^71 - 364 * q^72 - 28 * q^73 + 35 * q^74 + 7 * q^75 + 133 * q^76 + 21 * q^77 + 210 * q^78 + 42 * q^79 - 14 * q^80 - 14 * q^81 - 42 * q^82 + 161 * q^83 - 245 * q^84 - 266 * q^85 - 147 * q^86 - 35 * q^87 + 77 * q^88 + 28 * q^89 + 315 * q^90 + 154 * q^91 + 84 * q^92 - 7 * q^93 + 182 * q^94 + 126 * q^95 + 245 * q^96 + 42 * q^97 - 308 * q^98 - 161 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{45}{49}\right)$

Coefficient data

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

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

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

$2$	−1.92615	+	0.505096i	−1.36199	+	0.357157i	−0.861137	−	0.508373i	$-0.830247\pi$
$2$	−1.92615	+	0.505096i	−1.36199	+	0.357157i	−0.500858	+	0.865530i	$0.666982\pi$
$3$	1.00252	+	0.853459i	0.578806	+	0.492745i	0.888987	−	0.457933i	$-0.151410\pi$
$3$	1.00252	+	0.853459i	0.578806	+	0.492745i	−0.310181	+	0.950678i	$0.600390\pi$
$4$	1.71230	−	0.964349i	0.856150	−	0.482175i
$5$	1.28820	−	1.41845i	0.576100	−	0.634350i	−0.380838	−	0.924642i	$-0.624364\pi$
$5$	1.28820	−	1.41845i	0.576100	−	0.634350i	0.956938	+	0.290291i	$0.0937523\pi$
$6$	−2.36209	−	1.13752i	−0.964318	−	0.464391i
$7$	1.12284	+	0.294444i	0.424394	+	0.111289i	0.459673	−	0.888088i	$-0.347967\pi$
$7$	1.12284	+	0.294444i	0.424394	+	0.111289i	−0.0352789	+	0.999378i	$0.511232\pi$
$8$	0.0498044	−	0.0482328i	0.0176085	−	0.0170529i
$9$	−0.202143	−	1.25032i	−0.0673809	−	0.416774i
$10$	−1.76481	+	3.38282i	−0.558083	+	1.06974i
$11$	1.12178	−	2.53412i	0.338229	−	0.764066i	−0.661669	−	0.749796i	$-0.730152\pi$
$11$	1.12178	−	2.53412i	0.338229	−	0.764066i	0.999898	−	0.0142695i	$-0.00454227\pi$
$12$	2.53965	+	0.494597i	0.733134	+	0.142778i
$13$	−0.808829	+	0.104287i	−0.224329	+	0.0289240i	−0.239221	−	0.970965i	$-0.576892\pi$
$13$	−0.808829	+	0.104287i	−0.224329	+	0.0289240i	0.0148924	+	0.999889i	$0.495259\pi$
$14$	−2.31148			−0.617770
$15$	2.50204	−	0.322602i	0.646023	−	0.0832954i
$16$	−2.10904	+	3.47908i	−0.527260	+	0.869771i
$17$	3.53391	+	0.226885i	0.857100	+	0.0550277i	0.486412	−	0.873730i	$-0.338305\pi$
$17$	3.53391	+	0.226885i	0.857100	+	0.0550277i	0.370688	+	0.928757i	$0.379122\pi$
$18$	1.02089	+	2.30621i	0.240626	+	0.543579i
$19$	0.523401	+	2.29317i	0.120076	+	0.526089i	0.998810	+	0.0487760i	$0.0155320\pi$
$19$	0.523401	+	2.29317i	0.120076	+	0.526089i	−0.878733	+	0.477313i	$0.841611\pi$
$20$	0.837902	−	3.67109i	0.187360	−	0.820880i
$21$	0.874377	+	1.25349i	0.190805	+	0.273533i
$22$	−0.880742	+	5.44770i	−0.187775	+	1.16145i
$23$	2.83043	+	2.11240i	0.590185	+	0.440466i	0.851180	−	0.524874i	$-0.175887\pi$
$23$	2.83043	+	2.11240i	0.590185	+	0.440466i	−0.260995	+	0.965340i	$0.584051\pi$
$24$	0.0910947	−	0.00584847i	0.0185946	−	0.00119381i
$25$	0.127571	+	1.32240i	0.0255141	+	0.264481i
$26$	1.50525	−	0.609409i	0.295204	−	0.119515i
$27$	2.91200	−	4.80365i	0.560414	−	0.924462i
$28$	2.20659	−	0.578635i	0.417006	−	0.109352i
$29$	−0.183556	−	0.0357476i	−0.0340855	−	0.00663815i	0.174087	−	0.984730i	$-0.444303\pi$
$29$	−0.183556	−	0.0357476i	−0.0340855	−	0.00663815i	−0.208173	+	0.978092i	$0.566752\pi$
$30$	−4.65636	+	1.88515i	−0.850130	+	0.344180i
$31$	0.136036	+	4.24211i	0.0244328	+	0.761906i	0.936255	+	0.351321i	$0.114267\pi$
$31$	0.136036	+	4.24211i	0.0244328	+	0.761906i	−0.911822	+	0.410585i	$0.865324\pi$
$32$	2.26561	−	7.63358i	0.400506	−	1.34944i
$33$	3.28737	−	1.58312i	0.572258	−	0.275585i
$34$	−6.92145	+	1.34795i	−1.18702	+	0.231172i
$35$	1.86410	−	1.21339i	0.315090	−	0.205101i
$36$	−1.55188	−	1.94599i	−0.258646	−	0.324332i
$37$	−1.79761	−	2.96534i	−0.295525	−	0.487500i	0.671905	−	0.740637i	$-0.265476\pi$
$37$	−1.79761	−	2.96534i	−0.295525	−	0.487500i	−0.967430	+	0.253138i	$0.918537\pi$
$38$	−2.16642	−	4.15262i	−0.351440	−	0.673644i
$39$	−0.899873	−	0.585752i	−0.144095	−	0.0937954i
$40$	−0.00425795	−	0.132778i	−0.000673241	−	0.0209941i
$41$	−7.77897	−	0.499427i	−1.21487	−	0.0779974i	−0.556602	−	0.830779i	$-0.687895\pi$
$41$	−7.77897	−	0.499427i	−1.21487	−	0.0779974i	−0.658270	+	0.752782i	$0.728711\pi$
$42$	−2.31731	−	1.97276i	−0.357569	−	0.304403i
$43$	−2.87841	+	6.50237i	−0.438953	+	0.991603i	0.548854	+	0.835918i	$0.315064\pi$
$43$	−2.87841	+	6.50237i	−0.438953	+	0.991603i	−0.987807	+	0.155684i	$0.950242\pi$
$44$	−0.522953	−	5.42096i	−0.0788382	−	0.817240i
$45$	−2.03392	−	1.32394i	−0.303199	−	0.197361i
$46$	−6.51880	−	2.63917i	−0.961144	−	0.389124i
$47$	0.807657	−	2.19466i	0.117809	−	0.320125i	−0.865813	−	0.500367i	$-0.833198\pi$
$47$	0.807657	−	2.19466i	0.117809	−	0.320125i	0.983622	+	0.180242i	$0.0576882\pi$
$48$	−5.08361	+	1.68788i	−0.733756	+	0.243624i
$49$	−4.92516	−	2.77380i	−0.703594	−	0.396257i
$50$	−0.913661	−	2.48271i	−0.129211	−	0.351109i
$51$	3.34919	+	3.24351i	0.468980	+	0.454182i
$52$	−1.28439	+	0.958564i	−0.178113	+	0.132929i
$53$	−5.13876	−	2.08045i	−0.705863	−	0.285772i	−0.00593160	−	0.999982i	$-0.501888\pi$
$53$	−5.13876	−	2.08045i	−0.705863	−	0.285772i	−0.699931	+	0.714210i	$0.746786\pi$
$54$	−3.18265	+	10.7234i	−0.433103	+	1.45927i
$55$	−2.14945	−	4.85564i	−0.289831	−	0.654734i
$56$	0.0701242	−	0.0394932i	0.00937074	−	0.00527750i
$57$	−1.43240	+	2.74565i	−0.189727	+	0.363670i
$58$	0.371613	−	0.0238583i	0.0487952	−	0.00313275i
$59$	−0.597605	−	1.14550i	−0.0778016	−	0.149131i	0.844557	−	0.535465i	$-0.179864\pi$
$59$	−0.597605	−	1.14550i	−0.0778016	−	0.149131i	−0.922359	+	0.386334i	$0.873741\pi$
$60$	3.97314	−	2.96523i	0.512930	−	0.382809i
$61$	−2.93475	+	2.49839i	−0.375757	+	0.319886i	−0.816065	−	0.577960i	$-0.803849\pi$
$61$	−2.93475	+	2.49839i	−0.375757	+	0.319886i	0.440308	+	0.897847i	$0.354869\pi$
$62$	−2.40470	−	8.10224i	−0.305398	−	1.02899i
$63$	0.141176	−	1.46343i	0.0177865	−	0.184375i
$64$	−0.247409	+	7.71511i	−0.0309261	+	0.964389i
$65$	−0.894007	+	1.28163i	−0.110888	+	0.158966i
$66$	−5.53235	+	4.70976i	−0.680986	+	0.579732i
$67$	4.73085	−	12.8552i	0.577965	−	1.57052i	−0.224916	−	0.974378i	$-0.572211\pi$
$67$	4.73085	−	12.8552i	0.577965	−	1.57052i	0.802881	−	0.596140i	$-0.203300\pi$
$68$	6.26992	−	3.01943i	0.760339	−	0.366160i
$69$	1.03471	+	4.53338i	0.124565	+	0.545755i
$70$	−2.97765	+	3.27873i	−0.355898	+	0.391883i
$71$	−0.197980	−	1.22457i	−0.0234959	−	0.145330i	0.972756	−	0.231832i	$-0.0744720\pi$
$71$	−0.197980	−	1.22457i	−0.0234959	−	0.145330i	−0.996252	+	0.0865019i	$0.972431\pi$
$72$	−0.0703742	−	0.0525216i	−0.00829368	−	0.00618973i
$73$	7.34958	+	12.1239i	0.860203	+	1.41899i	0.907472	+	0.420112i	$0.138009\pi$
$73$	7.34958	+	12.1239i	0.860203	+	1.41899i	−0.0472694	+	0.998882i	$0.515052\pi$
$74$	4.96025	+	4.80374i	0.576618	+	0.558423i
$75$	−1.00072	+	1.43461i	−0.115554	+	0.165655i
$76$	3.10763	+	3.42185i	0.356470	+	0.392513i
$77$	2.00573	−	2.51511i	0.228575	−	0.286624i
$78$	2.02915	+	0.673725i	0.229756	+	0.0762844i
$79$	3.98689	+	4.39001i	0.448560	+	0.493914i	0.922151	−	0.386831i	$-0.126430\pi$
$79$	3.98689	+	4.39001i	0.448560	+	0.493914i	−0.473591	+	0.880745i	$0.657042\pi$
$80$	2.21804	+	7.47332i	0.247985	+	0.835543i
$81$	3.41295	−	1.13318i	0.379217	−	0.125909i
$82$	15.2357	−	2.96716i	1.68251	−	0.327668i
$83$	0.127822	−	0.560024i	0.0140303	−	0.0614706i	−0.967428	−	0.253146i	$-0.918535\pi$
$83$	0.127822	−	0.560024i	0.0140303	−	0.0614706i	0.981458	+	0.191675i	$0.0613920\pi$
$84$	2.70599	+	1.30314i	0.295248	+	0.142184i
$85$	4.87421	−	4.72041i	0.528682	−	0.512000i
$86$	2.25992	−	13.9784i	0.243694	−	1.50733i
$87$	−0.153510	−	0.192495i	−0.0164580	−	0.0206377i
$88$	−0.0663582	−	0.180317i	−0.00707381	−	0.0192218i
$89$	−0.113920	+	3.55246i	−0.0120755	+	0.376560i	0.975555	+	0.219758i	$0.0705267\pi$
$89$	−0.113920	+	3.55246i	−0.0120755	+	0.376560i	−0.987630	+	0.156802i	$0.949882\pi$
$90$	4.58636	+	1.52278i	0.483444	+	0.160515i
$91$	−0.938893	−	0.121057i	−0.0984227	−	0.0126902i
$92$	6.88363	+	0.887546i	0.717668	+	0.0925331i
$93$	−3.48409	+	4.36891i	−0.361283	+	0.453035i
$94$	−0.447152	+	4.63520i	−0.0461202	+	0.478085i
$95$	3.92699	+	2.21164i	0.402901	+	0.226909i
$96$	8.78626	−	5.71922i	0.896744	−	0.583716i
$97$	−10.7233	−	15.3726i	−1.08879	−	1.56086i	−0.796612	−	0.604491i	$-0.793377\pi$
$97$	−10.7233	−	15.3726i	−1.08879	−	1.56086i	−0.292173	−	0.956365i	$-0.594378\pi$
$98$	10.8876	+	2.85507i	1.09982	+	0.288406i
$99$	−3.39523	−	0.890333i	−0.341233	−	0.0894819i
$100$	1.49370	+	2.14133i	0.149370	+	0.214133i
$101$	−9.11247	+	5.93156i	−0.906725	+	0.590213i	−0.912188	−	0.409772i	$-0.865608\pi$
$101$	−9.11247	+	5.93156i	−0.906725	+	0.590213i	0.00546269	+	0.999985i	$0.498261\pi$
$102$	−8.08933	−	4.55583i	−0.800963	−	0.451094i
$103$	−1.08365	+	11.2332i	−0.106775	+	1.10684i	0.773962	+	0.633232i	$0.218272\pi$
$103$	−1.08365	+	11.2332i	−0.106775	+	1.10684i	−0.880737	+	0.473606i	$0.842952\pi$
$104$	−0.0352531	+	0.0442060i	−0.00345685	+	0.00433476i
$105$	2.90438	+	0.374478i	0.283438	+	0.0365453i
$106$	10.9489	+	1.41170i	1.06345	+	0.137116i
$107$	−0.524692	−	0.174210i	−0.0507239	−	0.0168415i	0.289634	−	0.957138i	$-0.406467\pi$
$107$	−0.524692	−	0.174210i	−0.0507239	−	0.0168415i	−0.340358	+	0.940296i	$0.610548\pi$
$108$	0.353822	−	11.0335i	0.0340465	−	1.06170i
$109$	5.05776	+	13.7436i	0.484446	+	1.31640i	0.911176	+	0.412017i	$0.135175\pi$
$109$	5.05776	+	13.7436i	0.484446	+	1.31640i	−0.426731	+	0.904379i	$0.640335\pi$
$110$	6.59272	+	8.26702i	0.628592	+	0.788229i
$111$	0.728658	−	4.50701i	0.0691611	−	0.427786i
$112$	−3.39251	+	3.28546i	−0.320562	+	0.310447i
$113$	−12.1592	−	5.85555i	−1.14384	−	0.550844i	−0.236662	−	0.971592i	$-0.576053\pi$
$113$	−12.1592	−	5.85555i	−1.14384	−	0.550844i	−0.907178	+	0.420748i	$0.861768\pi$
$114$	1.37221	−	6.01204i	0.128519	−	0.563079i
$115$	6.64249	−	1.29362i	0.619415	−	0.120631i
$116$	−0.348776	+	0.115802i	−0.0323831	+	0.0107519i
$117$	0.293891	+	0.990217i	0.0271702	+	0.0915456i
$118$	1.72967	+	1.90455i	0.159229	+	0.175328i
$119$	3.90122	+	1.29529i	0.357624	+	0.118739i
$120$	0.109052	−	0.136747i	0.00995507	−	0.0124833i
$121$	2.23194	+	2.45762i	0.202904	+	0.223420i
$122$	4.39085	−	6.29461i	0.397529	−	0.569888i
$123$	−7.37235	−	7.13972i	−0.664742	−	0.643767i
$124$	4.32382	+	7.13259i	0.388290	+	0.640525i
$125$	9.71806	+	7.25278i	0.869210	+	0.648708i
$126$	0.467250	+	2.89010i	0.0416259	+	0.257471i
$127$	10.1111	−	11.1335i	0.897217	−	0.987936i	−0.102760	−	0.994706i	$-0.532767\pi$
$127$	10.1111	−	11.1335i	0.897217	−	0.987936i	0.999977	+	0.00677025i	$0.00215505\pi$
$128$	0.123403	+	0.540665i	0.0109074	+	0.0477885i
$129$	−8.43518	+	4.06217i	−0.742676	+	0.357654i
$130$	1.07465	−	2.92016i	0.0942528	−	0.256115i
$131$	−7.48306	+	6.37042i	−0.653798	+	0.556586i	−0.912350	−	0.409411i	$-0.865734\pi$
$131$	−7.48306	+	6.37042i	−0.653798	+	0.556586i	0.258552	+	0.965997i	$0.416755\pi$
$132$	4.10229	−	5.88095i	0.357059	−	0.511871i
$133$	−0.0875129	+	2.72898i	−0.00758834	+	0.236632i
$134$	−2.61919	+	27.1507i	−0.226264	+	2.34546i
$135$	−3.06250	−	10.3186i	−0.263578	−	0.888082i
$136$	0.186948	−	0.159151i	0.0160306	−	0.0136471i
$137$	−2.90879	+	2.17089i	−0.248515	+	0.185471i	−0.715135	−	0.698986i	$-0.753635\pi$
$137$	−2.90879	+	2.17089i	−0.248515	+	0.185471i	0.466620	+	0.884458i	$0.345472\pi$
$138$	−4.28281	−	8.20935i	−0.364577	−	0.698826i
$139$	−16.9038	+	1.08526i	−1.43376	+	0.0920505i	−0.761452	−	0.648221i	$-0.775513\pi$
$139$	−16.9038	+	1.08526i	−1.43376	+	0.0920505i	−0.672308	+	0.740271i	$0.734697\pi$
$140$	2.02176	−	3.87533i	0.170870	−	0.327525i
$141$	2.68275	−	1.51090i	0.225928	−	0.127240i
$142$	0.999866	+	2.25872i	0.0839069	+	0.189547i
$143$	−0.643052	+	2.16665i	−0.0537747	+	0.181185i
$144$	4.77631	+	1.93371i	0.398025	+	0.161143i
$145$	−0.287163	+	0.214315i	−0.0238476	+	0.0177979i
$146$	−20.2801	−	19.6402i	−1.67840	−	1.62544i
$147$	−2.57025	−	6.98421i	−0.211991	−	0.576048i
$148$	−5.93767	−	3.34404i	−0.488074	−	0.274878i
$149$	−6.32741	+	2.10085i	−0.518362	+	0.172108i	−0.562311	−	0.826926i	$-0.690088\pi$
$149$	−6.32741	+	2.10085i	−0.518362	+	0.172108i	0.0439493	+	0.999034i	$0.486006\pi$
$150$	1.20293	−	3.26875i	0.0982187	−	0.266892i
$151$	−14.7532	−	5.97292i	−1.20060	−	0.486070i	−0.314365	−	0.949302i	$-0.601792\pi$
$151$	−14.7532	−	5.97292i	−1.20060	−	0.486070i	−0.886237	+	0.463232i	$0.846689\pi$
$152$	0.136674	+	0.0889647i	0.0110857	+	0.00721599i
$153$	−0.430675	−	4.46440i	−0.0348180	−	0.360925i
$154$	−2.59298	+	5.85758i	−0.208948	+	0.472017i
$155$	6.19247	+	5.27173i	0.497391	+	0.423435i
$156$	−2.10572	−	0.135192i	−0.168593	−	0.0108240i
$157$	0.0340716	+	1.06248i	0.00271921	+	0.0847949i	0.999946	+	0.0103747i	$0.00330243\pi$
$157$	0.0340716	+	1.06248i	0.00271921	+	0.0847949i	−0.997227	+	0.0744202i	$0.976289\pi$
$158$	−9.89673	−	6.44205i	−0.787341	−	0.512502i
$159$	−3.37614	−	6.47142i	−0.267745	−	0.513217i
$160$	−7.90930	−	13.0472i	−0.625285	−	1.03147i
$161$	2.55614	+	3.20529i	0.201452	+	0.252613i
$162$	−6.00150	+	3.90654i	−0.471522	+	0.306927i
$163$	13.3980	−	2.60926i	1.04941	−	0.204373i	0.363153	−	0.931729i	$-0.381700\pi$
$163$	13.3980	−	2.60926i	1.04941	−	0.204373i	0.686260	+	0.727356i	$0.259251\pi$
$164$	−13.8016	+	6.64648i	−1.07772	+	0.519003i
$165$	1.98922	−	6.70234i	0.154861	−	0.521777i
$166$	0.0366619	+	1.14325i	0.00284551	+	0.0887336i
$167$	−4.60986	+	1.86632i	−0.356721	+	0.144421i	−0.546615	−	0.837384i	$-0.684084\pi$
$167$	−4.60986	+	1.86632i	−0.356721	+	0.144421i	0.189893	+	0.981805i	$0.439186\pi$
$168$	0.104007	+	0.0202553i	0.00802431	+	0.00156273i
$169$	−11.9315	+	3.12881i	−0.917808	+	0.240678i
$170$	−7.00421	+	11.5542i	−0.537198	+	0.886164i
$171$	2.76140	−	1.11797i	0.211170	−	0.0854931i
$172$	1.34186	+	13.9098i	0.102316	+	1.06061i
$173$	8.28598	−	0.531977i	0.629971	−	0.0404455i	0.254191	−	0.967154i	$-0.418191\pi$
$173$	8.28598	−	0.531977i	0.629971	−	0.0404455i	0.375781	+	0.926709i	$0.377375\pi$
$174$	0.392912	+	0.293238i	0.0297866	+	0.0222303i
$175$	−0.246132	+	1.52241i	−0.0186058	+	0.115083i
$176$	6.45053	+	9.24732i	0.486227	+	0.697043i
$177$	0.378523	−	1.65842i	0.0284515	−	0.124654i
$178$	−1.57491	−	6.90011i	−0.118044	−	0.517185i
$179$	−4.99900	−	11.2928i	−0.373643	−	0.844065i	−0.998017	−	0.0629403i	$-0.979952\pi$
$179$	−4.99900	−	11.2928i	−0.373643	−	0.844065i	0.624375	−	0.781125i	$-0.285354\pi$
$180$	−4.75942	−	0.305565i	−0.354746	−	0.0227755i
$181$	−1.30811	+	2.15786i	−0.0972310	+	0.160393i	−0.899989	−	0.435912i	$-0.856426\pi$
$181$	−1.30811	+	2.15786i	−0.0972310	+	0.160393i	0.802759	+	0.596304i	$0.203365\pi$
$182$	1.86960	−	0.241058i	0.138584	−	0.0178684i
$183$	−5.07443			−0.375113
$184$	0.242855	−	0.0313126i	0.0179035	−	0.00230840i
$185$	−6.52187	−	1.27013i	−0.479498	−	0.0933821i
$186$	4.50417	−	10.1750i	0.330261	−	0.746066i
$187$	4.53922	−	8.70084i	0.331941	−	0.636269i
$188$	−0.733473	−	4.53679i	−0.0534940	−	0.330879i
$189$	4.68411	−	4.53631i	0.340719	−	0.329968i
$190$	−8.68107	−	2.27644i	−0.629791	−	0.165151i
$191$	7.84050	+	3.77579i	0.567319	+	0.273206i	0.695478	−	0.718547i	$-0.255193\pi$
$191$	7.84050	+	3.77579i	0.567319	+	0.273206i	−0.128159	+	0.991754i	$0.540907\pi$
$192$	−6.83256	+	7.52341i	−0.493098	+	0.542955i
$193$	4.79171	−	2.69864i	0.344915	−	0.194253i	−0.308552	−	0.951207i	$-0.599844\pi$
$193$	4.79171	−	2.69864i	0.344915	−	0.194253i	0.653467	+	0.756955i	$0.273314\pi$
$194$	28.4194	+	24.1938i	2.04039	+	1.73701i
$195$	−1.99008	+	0.521859i	−0.142512	+	0.0373711i
$196$	−11.1083			−0.793447
$197$	−9.49577	+	10.3359i	−0.676546	+	0.736401i
$197$	−9.49577	+	10.3359i	−0.676546	+	0.736401i
$198$	6.98943			0.496717
$199$	2.33387	−	0.612013i	0.165444	−	0.0433845i	−0.170003	−	0.985443i	$-0.554378\pi$
$199$	2.33387	−	0.612013i	0.165444	−	0.0433845i	0.335447	+	0.942059i	$0.391113\pi$
$200$	0.0701368	+	0.0597083i	0.00495942	+	0.00422202i
$201$	15.7142	−	8.85007i	1.10839	−	0.624236i
$202$	14.5560	−	16.0278i	1.02416	−	1.12771i
$203$	−0.195579	−	0.0941858i	−0.0137269	−	0.00661054i
$204$	8.86269	+	2.32407i	0.620512	+	0.162718i
$205$	−10.7293	+	10.3907i	−0.749365	+	0.725720i
$206$	−3.58656	−	22.1842i	−0.249888	−	1.54564i
$207$	2.06904	−	3.96596i	0.143808	−	0.275653i
$208$	1.34303	−	3.03393i	0.0931224	−	0.210365i
$209$	6.39830	+	1.24607i	0.442580	+	0.0861924i
$210$	−5.78342	+	0.745689i	−0.399094	+	0.0514575i
$211$	10.5814			0.728455			0.364228	−	0.931310i	$-0.381333\pi$
$211$	10.5814			0.728455			0.364228	+	0.931310i	$0.381333\pi$
$212$	−10.8054	+	1.39320i	−0.742117	+	0.0956853i
$213$	0.846645	−	1.39663i	0.0580111	−	0.0956954i
$214$	1.09863	+	0.0705344i	0.0751008	+	0.00482163i
$215$	5.51533	+	12.4592i	0.376143	+	0.849713i
$216$	−0.0866632	−	0.379696i	−0.00589668	−	0.0258351i
$217$	−1.09632	+	4.80328i	−0.0744228	+	0.326068i
$218$	−16.6838	−	23.9175i	−1.12997	−	1.61990i
$219$	−2.97914	+	18.4270i	−0.201312	+	1.24518i
$220$	−8.36303	−	6.24149i	−0.563835	−	0.420801i
$221$	−2.88199	+	0.185030i	−0.193864	+	0.0124465i
$222$	0.872967	+	9.04922i	0.0585897	+	0.607344i
$223$	8.85721	−	3.58589i	0.593123	−	0.240129i	−0.0589801	−	0.998259i	$-0.518785\pi$
$223$	8.85721	−	3.58589i	0.593123	−	0.240129i	0.652103	+	0.758130i	$0.273887\pi$
$224$	4.79157	−	7.90420i	0.320150	−	0.528122i
$225$	1.62764	−	0.426818i	0.108510	−	0.0284546i
$226$	26.3780	+	5.13712i	1.75464	+	0.341716i
$227$	10.3324	−	4.18311i	0.685783	−	0.277643i	−0.00575457	−	0.999983i	$-0.501832\pi$
$227$	10.3324	−	4.18311i	0.685783	−	0.277643i	0.691537	+	0.722341i	$0.256934\pi$
$228$	0.195061	+	6.08272i	0.0129182	+	0.402838i
$229$	−4.68274	+	15.7777i	−0.309444	+	1.04262i	0.649815	+	0.760093i	$0.274846\pi$
$229$	−4.68274	+	15.7777i	−0.309444	+	1.04262i	−0.959259	+	0.282528i	$0.908827\pi$
$230$	−12.1410	+	5.84682i	−0.800556	+	0.385528i
$231$	4.15734	−	0.809641i	0.273533	−	0.0532705i
$232$	−0.0108661	+	0.00707305i	−0.000713394	+	0.000464368i
$233$	15.5696	+	19.5237i	1.02000	+	1.27904i	0.959750	+	0.280856i	$0.0906185\pi$
$233$	15.5696	+	19.5237i	1.02000	+	1.27904i	0.0602504	+	0.998183i	$0.480810\pi$
$234$	−1.06623	−	1.75886i	−0.0697019	−	0.114981i
$235$	−2.07260	−	3.97279i	−0.135202	−	0.259156i
$236$	−2.12794	−	1.38514i	−0.138517	−	0.0901646i
$237$	0.250250	+	7.80372i	0.0162555	+	0.506906i
$238$	−8.16859	−	0.524441i	−0.529491	−	0.0339945i
$239$	16.6372	+	14.1635i	1.07617	+	0.916159i	0.996740	−	0.0806814i	$-0.0257096\pi$
$239$	16.6372	+	14.1635i	1.07617	+	0.916159i	0.0794324	+	0.996840i	$0.474689\pi$
$240$	−4.15454	+	9.38517i	−0.268174	+	0.605810i
$241$	−0.926370	−	9.60279i	−0.0596727	−	0.618570i	−0.975945	−	0.218015i	$-0.930042\pi$
$241$	−0.926370	−	9.60279i	−0.0596727	−	0.618570i	0.916273	−	0.400555i	$-0.131183\pi$
$242$	−5.54039	−	3.60639i	−0.356150	−	0.231828i
$243$	−11.2318	−	4.54725i	−0.720520	−	0.291706i
$244$	−2.61586	+	7.10812i	−0.167463	+	0.455051i
$245$	−10.2791	+	3.41289i	−0.656706	+	0.218041i
$246$	17.8065	+	10.0284i	1.13530	+	0.639390i
$247$	−0.662489	−	1.80020i	−0.0421532	−	0.114544i
$248$	0.211384	+	0.204714i	0.0134229	+	0.0129994i
$249$	0.606101	−	0.452345i	0.0384101	−	0.0286662i
$250$	−22.3818	−	9.06139i	−1.41555	−	0.573093i
$251$	4.31054	−	14.5236i	0.272079	−	0.916724i	−0.705951	−	0.708260i	$-0.749480\pi$
$251$	4.31054	−	14.5236i	0.272079	−	0.916724i	0.978030	−	0.208463i	$-0.0668462\pi$
$252$	−1.16953	−	2.64198i	−0.0736733	−	0.166429i
$253$	8.52819	−	4.80299i	0.536163	−	0.301961i
$254$	−13.8521	+	26.5518i	−0.869157	+	1.66601i
$255$	8.91518	−	0.572373i	0.558290	−	0.0358434i
$256$	−7.65152	−	14.6665i	−0.478220	−	0.916658i
$257$	−11.0260	+	8.22892i	−0.687783	+	0.513306i	−0.884137	−	0.467227i	$-0.845253\pi$
$257$	−11.0260	+	8.22892i	−0.687783	+	0.513306i	0.196354	+	0.980533i	$0.437090\pi$
$258$	14.1956	−	12.0849i	0.883782	−	0.752375i
$259$	−1.14530	−	3.85891i	−0.0711657	−	0.239781i
$260$	−0.294873	+	3.05666i	−0.0182872	+	0.189566i
$261$	−0.00759149	+	0.236731i	−0.000469901	+	0.0146533i
$262$	11.1958	−	16.0501i	0.691681	−	0.991576i
$263$	−20.9488	+	17.8340i	−1.29176	+	1.09969i	−0.302556	+	0.953131i	$0.597840\pi$
$263$	−20.9488	+	17.8340i	−1.29176	+	1.09969i	−0.989202	+	0.146559i	$0.953180\pi$
$264$	0.0873674	−	0.237405i	0.00537709	−	0.0146113i
$265$	−9.57076	+	4.60904i	−0.587927	+	0.283131i
$266$	−1.20983	−	5.30062i	−0.0741796	−	0.325002i
$267$	−3.14608	+	3.46419i	−0.192537	+	0.212005i
$268$	−4.29631	−	26.5742i	−0.262439	−	1.62328i
$269$	−20.0952	−	14.9974i	−1.22523	−	0.914409i	−0.226996	−	0.973896i	$-0.572890\pi$
$269$	−20.0952	−	14.9974i	−1.22523	−	0.914409i	−0.998229	+	0.0594863i	$0.981054\pi$
$270$	11.1107	+	18.3283i	0.676176	+	1.11542i
$271$	19.7071	+	19.0853i	1.19712	+	1.15935i	0.983206	+	0.182498i	$0.0584183\pi$
$271$	19.7071	+	19.0853i	1.19712	+	1.15935i	0.213918	+	0.976852i	$0.431378\pi$
$272$	−8.24252	+	11.8163i	−0.499776	+	0.716467i
$273$	−0.837943	−	0.922669i	−0.0507146	−	0.0558424i
$274$	4.50626	−	5.65068i	0.272233	−	0.341370i
$275$	3.49423	+	1.16016i	0.210710	+	0.0699606i
$276$	6.14351	+	6.76468i	0.369796	+	0.407186i
$277$	2.39954	+	8.08486i	0.144175	+	0.485772i	0.999476	−	0.0323582i	$-0.0103017\pi$
$277$	2.39954	+	8.08486i	0.144175	+	0.485772i	−0.855302	+	0.518130i	$0.826628\pi$
$278$	32.0111	−	10.6284i	1.91990	−	0.637450i
$279$	5.27652	−	1.02760i	0.315897	−	0.0615209i
$280$	0.0343148	−	0.150343i	0.00205070	−	0.00898470i
$281$	−15.1083	−	7.27576i	−0.901284	−	0.434035i	−0.0749313	−	0.997189i	$-0.523874\pi$
$281$	−15.1083	−	7.27576i	−0.901284	−	0.434035i	−0.826352	+	0.563153i	$0.809588\pi$
$282$	−4.40423	+	4.26526i	−0.262268	+	0.253993i
$283$	5.11815	−	31.6576i	0.304242	−	1.88185i	−0.146528	−	0.989206i	$-0.546810\pi$
$283$	5.11815	−	31.6576i	0.304242	−	1.88185i	0.450771	−	0.892640i	$-0.351149\pi$
$284$	−1.51992	−	1.90592i	−0.0901905	−	0.113095i
$285$	2.04935	+	5.56874i	0.121393	+	0.329864i
$286$	0.144246	−	4.49811i	0.00852942	−	0.265979i
$287$	−8.58750	−	2.85125i	−0.506904	−	0.168304i
$288$	−10.0024	−	1.28967i	−0.589398	−	0.0759945i
$289$	−4.42335	−	0.570328i	−0.260197	−	0.0335487i
$290$	0.444870	−	0.557849i	0.0261236	−	0.0327580i
$291$	2.36959	−	24.5633i	0.138908	−	1.43993i
$292$	24.2763	+	13.6722i	1.42067	+	0.800104i
$293$	14.6225	−	9.51819i	0.854255	−	0.556059i	−0.0422422	−	0.999107i	$-0.513450\pi$
$293$	14.6225	−	9.51819i	0.854255	−	0.556059i	0.896497	+	0.443049i	$0.146103\pi$
$294$	8.47840	+	12.1544i	0.494470	+	0.708860i
$295$	−2.39467	−	0.627955i	−0.139423	−	0.0365610i
$296$	−0.232556	−	0.0609833i	−0.0135170	−	0.00354458i
$297$	−8.90639	−	12.7680i	−0.516801	−	0.740873i
$298$	11.1264	−	7.24250i	0.644537	−	0.419547i
$299$	−2.50963	−	1.41340i	−0.145135	−	0.0817388i
$300$	−0.330072	+	3.42154i	−0.0190567	+	0.197543i
$301$	−5.14658	+	6.45360i	−0.296644	+	0.371980i
$302$	31.4339	+	4.05295i	1.80882	+	0.233221i
$303$	−14.1978	−	1.83060i	−0.815642	−	0.105165i
$304$	−9.08200	−	3.01543i	−0.520888	−	0.172947i
$305$	−0.236702	+	7.38123i	−0.0135535	+	0.422648i
$306$	3.08450	+	8.38158i	0.176329	+	0.479143i
$307$	18.3716	+	23.0373i	1.04852	+	1.31481i	0.947441	+	0.319929i	$0.103659\pi$
$307$	18.3716	+	23.0373i	1.04852	+	1.31481i	0.101082	+	0.994878i	$0.467769\pi$
$308$	1.00897	−	6.24086i	0.0574916	−	0.355606i
$309$	−10.6734	+	10.3367i	−0.607191	+	0.588032i
$310$	−14.5904	−	7.02635i	−0.828677	−	0.399070i
$311$	1.78884	−	7.83744i	0.101436	−	0.444420i	−0.898549	−	0.438874i	$-0.855377\pi$
$311$	1.78884	−	7.83744i	0.101436	−	0.444420i	0.999985	−	0.00554628i	$-0.00176545\pi$
$312$	−0.0730701	+	0.0142304i	−0.00413678	+	0.000805637i
$313$	−22.8786	+	7.59623i	−1.29318	+	0.429364i	−0.877250	−	0.480034i	$-0.840624\pi$
$313$	−22.8786	+	7.59623i	−1.29318	+	0.429364i	−0.415927	+	0.909398i	$0.636543\pi$
$314$	−0.602280	−	2.02928i	−0.0339886	−	0.114519i
$315$	−1.89395	−	2.08545i	−0.106712	−	0.117502i
$316$	11.0602	+	3.67226i	0.622188	+	0.206580i
$317$	11.6316	−	14.5856i	0.653297	−	0.819209i	−0.339298	−	0.940679i	$-0.610189\pi$
$317$	11.6316	−	14.5856i	0.653297	−	0.819209i	0.992595	+	0.121470i	$0.0387609\pi$
$318$	9.77164	+	10.7597i	0.547966	+	0.603372i
$319$	−0.296498	+	0.425052i	−0.0166007	+	0.0237984i
$320$	10.6248	+	10.2895i	0.593944	+	0.575202i
$321$	−0.377334	−	0.622453i	−0.0210608	−	0.0347419i
$322$	−6.54249	−	4.88279i	−0.364599	−	0.272107i
$323$	1.32937	+	8.22261i	0.0739680	+	0.457518i
$324$	4.75122	−	5.23162i	0.263956	−	0.290645i
$325$	−0.241092	−	1.05629i	−0.0133734	−	0.0585926i
$326$	−24.4887	+	11.7931i	−1.35630	+	0.653161i
$327$	−6.65906	+	18.0948i	−0.368247	+	1.00065i
$328$	−0.411516	+	0.350328i	−0.0227221	+	0.0193436i
$329$	1.55308	−	2.22645i	0.0856238	−	0.122748i
$330$	−0.446210	+	13.9145i	−0.0245631	+	0.765967i
$331$	−0.874558	+	9.06570i	−0.0480700	+	0.498296i	0.939658	+	0.342114i	$0.111143\pi$
$331$	−0.874558	+	9.06570i	−0.0480700	+	0.498296i	−0.987728	+	0.156182i	$0.950081\pi$
$332$	−0.321189	−	1.08219i	−0.0176276	−	0.0593931i
$333$	−3.34427	+	2.84702i	−0.183265	+	0.156015i
$334$	7.93661	−	5.92325i	0.434272	−	0.324106i
$335$	−12.1402	−	23.2706i	−0.663293	−	1.27141i
$336$	−6.20507	+	0.398379i	−0.338515	+	0.0217334i
$337$	12.0103	−	23.0215i	0.654243	−	1.25406i	−0.299688	−	0.954037i	$-0.596883\pi$
$337$	12.0103	−	23.0215i	0.654243	−	1.25406i	0.953931	−	0.300025i	$-0.0969950\pi$
$338$	21.4015	−	12.0531i	1.16409	−	0.655603i
$339$	−7.19237	−	16.2477i	−0.390636	−	0.882453i
$340$	3.79399	−	12.7832i	0.205758	−	0.693266i
$341$	10.9026	+	4.41398i	0.590410	+	0.239031i
$342$	−4.75419	+	3.54815i	−0.257077	+	0.191862i
$343$	−10.5505	−	10.2176i	−0.569673	−	0.551697i
$344$	0.170271	+	0.462680i	0.00918038	+	0.0249460i
$345$	7.76330	+	4.37221i	0.417962	+	0.235392i
$346$	−15.6914	+	5.20989i	−0.843572	+	0.280085i
$347$	5.58763	−	15.1834i	0.299960	−	0.815087i	−0.695379	−	0.718643i	$-0.744763\pi$
$347$	5.58763	−	15.1834i	0.299960	−	0.815087i	0.995338	−	0.0964439i	$-0.0307468\pi$
$348$	−0.448488	−	0.181573i	−0.0240415	−	0.00973331i
$349$	−26.9600	−	17.5490i	−1.44314	−	0.939378i	−0.999058	−	0.0433907i	$-0.986184\pi$
$349$	−26.9600	−	17.5490i	−1.44314	−	0.939378i	−0.444079	−	0.895988i	$-0.646469\pi$
$350$	−0.294878	−	3.05671i	−0.0157619	−	0.163388i
$351$	−1.85435	+	4.18901i	−0.0989779	+	0.223593i
$352$	−16.8029	−	14.3045i	−0.895597	−	0.762432i
$353$	19.2287	+	1.23453i	1.02344	+	0.0657072i	0.566727	−	0.823906i	$-0.308209\pi$
$353$	19.2287	+	1.23453i	1.02344	+	0.0657072i	0.456716	+	0.889613i	$0.349026\pi$
$354$	0.108568	+	3.38555i	0.00577033	+	0.179940i
$355$	−1.99203	−	1.29667i	−0.105726	−	0.0688201i
$356$	3.23074	+	6.19273i	0.171229	+	0.328214i
$357$	2.80558	+	4.62809i	0.148487	+	0.244945i
$358$	15.3328	+	19.2267i	0.810363	+	1.01616i
$359$	21.3906	−	13.9237i	1.12895	−	0.734866i	0.161238	−	0.986916i	$-0.448451\pi$
$359$	21.3906	−	13.9237i	1.12895	−	0.734866i	0.967714	+	0.252049i	$0.0811045\pi$
$360$	−0.165155	+	0.0321640i	−0.00870445	+	0.00169519i
$361$	12.1337	−	5.84330i	0.638618	−	0.307542i
$362$	1.42969	−	4.81709i	0.0751427	−	0.253181i
$363$	0.140095	+	4.36868i	0.00735309	+	0.229296i
$364$	−1.72441	+	0.698135i	−0.0903835	+	0.0365922i
$365$	26.6649	+	5.19298i	1.39570	+	0.271813i
$366$	9.77412	−	2.56308i	0.510901	−	0.133974i
$367$	−18.7486	+	30.9277i	−0.978667	+	1.61441i	−0.207045	+	0.978331i	$0.566385\pi$
$367$	−18.7486	+	30.9277i	−0.978667	+	1.61441i	−0.771622	+	0.636082i	$0.780554\pi$
$368$	−13.3187	+	5.39215i	−0.694286	+	0.281085i
$369$	0.948017	+	9.82719i	0.0493518	+	0.511583i
$370$	13.2037	−	0.847703i	0.686425	−	0.0440700i
$371$	−5.15743	−	3.84909i	−0.267761	−	0.199835i
$372$	−1.75265	+	10.8408i	−0.0908707	+	0.562068i
$373$	12.5960	+	18.0573i	0.652195	+	0.934970i	0.999997	−	0.00259790i	$-0.000826938\pi$
$373$	12.5960	+	18.0573i	0.652195	+	0.934970i	−0.347802	+	0.937568i	$0.613072\pi$
$374$	−4.34847	+	19.0519i	−0.224854	+	0.985150i
$375$	3.55262	+	15.5650i	0.183456	+	0.803775i
$376$	−0.0656300	−	0.148259i	−0.00338461	−	0.00764590i
$377$	0.152193	+	0.00977115i	0.00783836	+	0.000503240i
$378$	−6.73104	+	11.1036i	−0.346207	+	0.571105i
$379$	25.5936	−	3.29993i	1.31466	−	0.169506i	0.561571	−	0.827429i	$-0.310197\pi$
$379$	25.5936	−	3.29993i	1.31466	−	0.169506i	0.753086	+	0.657923i	$0.228565\pi$
$380$	8.85698			0.454353
$381$	19.6386	−	2.53211i	1.00612	−	0.129724i
$382$	−17.0091	−	3.31253i	−0.870263	−	0.169484i
$383$	−4.51228	+	10.1933i	−0.230567	+	0.520854i	−0.991827	−	0.127593i	$-0.959275\pi$
$383$	−4.51228	+	10.1933i	−0.230567	+	0.520854i	0.761260	+	0.648447i	$0.224581\pi$
$384$	−0.337721	+	0.647348i	−0.0172343	+	0.0330348i
$385$	−0.983776	−	6.08500i	−0.0501379	−	0.310120i
$386$	−7.86649	+	7.61827i	−0.400394	+	0.387760i
$387$	8.71192	+	2.28453i	0.442852	+	0.116129i
$388$	−33.1861	−	15.9816i	−1.68477	−	0.811342i
$389$	2.06244	−	2.27097i	0.104570	−	0.115143i	−0.685751	−	0.727836i	$-0.740526\pi$
$389$	2.06244	−	2.27097i	0.104570	−	0.115143i	0.790321	+	0.612693i	$0.209914\pi$
$390$	3.56960	−	2.01036i	0.180754	−	0.101799i
$391$	9.52321	+	8.10723i	0.481610	+	0.410000i
$392$	−0.379082	+	0.0994071i	−0.0191465	+	0.00502081i
$393$	−12.9388			−0.652677
$394$	13.0697	−	24.7047i	0.658441	−	1.24461i
$395$	11.3629			0.571730
$396$	−6.67224	+	1.74967i	−0.335293	+	0.0879241i
$397$	19.4297	+	16.5408i	0.975150	+	0.830157i	0.985480	−	0.169790i	$-0.0543088\pi$
$397$	19.4297	+	16.5408i	0.975150	+	0.830157i	−0.0103307	+	0.999947i	$0.503288\pi$
$398$	−4.18627	+	2.35766i	−0.209839	+	0.118179i
$399$	−2.41680	+	2.66117i	−0.120991	+	0.133225i
$400$	−4.86980	−	2.34517i	−0.243490	−	0.117259i
$401$	−17.0529	−	4.47179i	−0.851580	−	0.223311i	−0.198032	−	0.980196i	$-0.563455\pi$
$401$	−17.0529	−	4.47179i	−0.851580	−	0.223311i	−0.653548	+	0.756885i	$0.726720\pi$
$402$	−25.7978	+	24.9838i	−1.28668	+	1.24608i
$403$	−0.552427	−	3.41696i	−0.0275184	−	0.170211i
$404$	−9.88319	+	18.9442i	−0.491707	+	0.942510i
$405$	2.78920	−	6.30086i	0.138597	−	0.313092i
$406$	0.424287	+	0.0826299i	0.0210570	+	0.00410085i
$407$	−9.53105	+	1.22889i	−0.472437	+	0.0609140i
$408$	0.323248			0.0160031
$409$	4.14695	−	0.534691i	0.205054	−	0.0264387i	−0.0246652	−	0.999696i	$-0.507852\pi$
$409$	4.14695	−	0.534691i	0.205054	−	0.0264387i	0.229719	+	0.973257i	$0.426219\pi$
$410$	15.4179	−	25.4334i	0.761436	−	1.25607i
$411$	−4.76889	−	0.306173i	−0.235232	−	0.0151024i
$412$	8.97717	+	20.2796i	0.442274	+	0.999104i
$413$	−0.333731	−	1.46217i	−0.0164218	−	0.0719488i
$414$	−1.98209	+	8.68409i	−0.0974143	+	0.426800i
$415$	−0.629706	−	0.902731i	−0.0309110	−	0.0443133i
$416$	−1.03640	+	6.41053i	−0.0508139	+	0.314302i
$417$	−17.8726	−	13.3387i	−0.875227	−	0.653199i
$418$	−12.9535	+	0.831641i	−0.633576	+	0.0406769i
$419$	−2.18559	−	22.6559i	−0.106773	−	1.10681i	−0.880744	−	0.473592i	$-0.842957\pi$
$419$	−2.18559	−	22.6559i	−0.106773	−	1.10681i	0.773971	−	0.633220i	$-0.218267\pi$
$420$	5.33429	−	2.15962i	0.260287	−	0.105378i
$421$	14.7417	−	24.3180i	0.718466	−	1.18519i	−0.257292	−	0.966334i	$-0.582830\pi$
$421$	14.7417	−	24.3180i	0.718466	−	1.18519i	0.975758	−	0.218852i	$-0.0702311\pi$
$422$	−20.3814	+	5.34464i	−0.992152	+	0.260173i
$423$	−2.90730	−	0.566197i	−0.141358	−	0.0275294i
$424$	−0.356279	+	0.144241i	−0.0173024	+	0.00700497i
$425$	0.150790	+	4.70220i	0.00731441	+	0.228090i
$426$	−0.925334	+	3.11776i	−0.0448326	+	0.151056i
$427$	−4.03090	+	1.94118i	−0.195069	+	0.0939402i
$428$	−1.06643	+	0.207687i	−0.0515479	+	0.0100389i
$429$	−2.49382	+	1.62330i	−0.120403	+	0.0783736i
$430$	−16.9165	−	21.2126i	−0.815785	−	1.02296i
$431$	3.66805	+	6.05083i	0.176684	+	0.291458i	0.930976	−	0.365081i	$-0.118959\pi$
$431$	3.66805	+	6.05083i	0.176684	+	0.291458i	−0.754292	+	0.656539i	$0.772020\pi$
$432$	10.5708	+	20.2622i	0.508586	+	0.974864i
$433$	−12.7878	−	8.32394i	−0.614543	−	0.400023i	0.200275	−	0.979740i	$-0.435816\pi$
$433$	−12.7878	−	8.32394i	−0.614543	−	0.400023i	−0.814818	+	0.579717i	$0.803163\pi$
$434$	−0.314446	−	9.80558i	−0.0150939	−	0.470683i
$435$	−0.470796	−	0.0302261i	−0.0225730	−	0.00144923i
$436$	21.9140	+	18.6557i	1.04949	+	0.893444i
$437$	−3.36265	+	7.59628i	−0.160857	+	0.363379i
$438$	−3.56915	−	36.9980i	−0.170541	−	1.76783i
$439$	−14.5935	−	9.49929i	−0.696508	−	0.453376i	0.147953	−	0.988994i	$-0.452732\pi$
$439$	−14.5935	−	9.49929i	−0.696508	−	0.453376i	−0.844460	+	0.535618i	$0.820079\pi$
$440$	−0.341253	−	0.138158i	−0.0162686	−	0.00658642i
$441$	−2.47256	+	6.71874i	−0.117741	+	0.319940i
$442$	5.45770	−	1.81208i	0.259596	−	0.0861919i
$443$	−14.4184	−	8.12027i	−0.685037	−	0.385806i	0.108694	−	0.994075i	$-0.465333\pi$
$443$	−14.4184	−	8.12027i	−0.685037	−	0.385806i	−0.793730	+	0.608270i	$0.791864\pi$
$444$	−3.09865	−	8.42003i	−0.147055	−	0.399597i
$445$	4.89223	+	4.73786i	0.231914	+	0.224596i
$446$	−15.2491	+	11.3807i	−0.722067	+	0.538892i
$447$	−8.13635	−	3.29404i	−0.384836	−	0.155803i
$448$	−2.54947	+	8.59000i	−0.120451	+	0.405839i
$449$	−13.8479	−	31.2827i	−0.653523	−	1.47632i	−0.866456	−	0.499254i	$-0.833608\pi$
$449$	−13.8479	−	31.2827i	−0.653523	−	1.47632i	0.212932	−	0.977067i	$-0.431699\pi$
$450$	−2.91950	+	1.64423i	−0.137627	+	0.0775099i
$451$	−9.99190	+	19.1526i	−0.470500	+	0.901861i
$452$	−26.4670	+	1.69924i	−1.24490	+	0.0799253i
$453$	−9.69279	−	18.5793i	−0.455407	−	0.872930i
$454$	−17.7888	+	13.2761i	−0.834870	+	0.623080i
$455$	−1.38119	+	1.17583i	−0.0647514	+	0.0551236i
$456$	0.0610905	+	0.205834i	0.00286083	+	0.00963907i
$457$	0.308580	−	3.19876i	0.0144348	−	0.149632i	−0.985346	−	0.170567i	$-0.945440\pi$
$457$	0.308580	−	3.19876i	0.0144348	−	0.149632i	0.999781	+	0.0209356i	$0.00666449\pi$
$458$	1.05040	−	32.7555i	0.0490822	−	1.53056i
$459$	11.3806	−	16.3150i	0.531202	−	0.761518i
$460$	10.1264	−	8.62076i	0.472147	−	0.401945i
$461$	4.84024	−	13.1525i	0.225432	−	0.612572i	−0.774364	−	0.632740i	$-0.781930\pi$
$461$	4.84024	−	13.1525i	0.225432	−	0.612572i	0.999797	+	0.0201677i	$0.00642002\pi$
$462$	−7.59872	+	3.65935i	−0.353524	+	0.170248i
$463$	7.80439	+	34.1932i	0.362701	+	1.58909i	0.746309	+	0.665599i	$0.231824\pi$
$463$	7.80439	+	34.1932i	0.362701	+	1.58909i	−0.383609	+	0.923496i	$0.625319\pi$
$464$	0.511496	−	0.563214i	0.0237456	−	0.0261465i
$465$	1.70888	+	10.5700i	0.0792475	+	0.490174i
$466$	−39.8508	−	29.7414i	−1.84605	−	1.37775i
$467$	−8.12854	−	13.4089i	−0.376144	−	0.620489i	0.608808	−	0.793318i	$-0.291648\pi$
$467$	−8.12854	−	13.4089i	−0.376144	−	0.620489i	−0.984952	+	0.172829i	$0.944709\pi$
$468$	1.45814	+	1.41213i	0.0674028	+	0.0652759i
$469$	9.09714	−	13.0414i	0.420067	−	0.602197i
$470$	5.99878	+	6.60533i	0.276703	+	0.304681i
$471$	−0.872623	+	1.09423i	−0.0402083	+	0.0504197i
$472$	−0.0850139	−	0.0282266i	−0.00391308	−	0.00129923i
$473$	13.2488	+	14.5885i	0.609183	+	0.670778i
$474$	−4.42365	−	14.9047i	−0.203185	−	0.684598i
$475$	−2.96572	+	0.984687i	−0.136077	+	0.0451806i
$476$	7.92918	−	1.54421i	0.363433	−	0.0707786i
$477$	−1.56248	+	6.84566i	−0.0715409	+	0.313441i
$478$	−39.1997	−	18.8776i	−1.79295	−	0.863441i
$479$	−8.33024	+	8.06739i	−0.380619	+	0.368608i	−0.861134	−	0.508378i	$-0.830245\pi$
$479$	−8.33024	+	8.06739i	−0.380619	+	0.368608i	0.480516	+	0.876986i	$0.340450\pi$
$480$	3.20602	−	19.8304i	0.146334	−	0.905129i
$481$	1.76320	+	2.21099i	0.0803952	+	0.100812i
$482$	6.63467	+	18.0285i	0.302201	+	0.821177i
$483$	−0.173005	+	5.39493i	−0.00787200	+	0.245478i
$484$	6.19175	+	2.05580i	0.281443	+	0.0934456i
$485$	−35.6191	−	4.59257i	−1.61738	−	0.208538i
$486$	23.9309	+	3.08555i	1.08553	+	0.139964i
$487$	3.29210	−	4.12817i	0.149180	−	0.187065i	−0.701627	−	0.712545i	$-0.747543\pi$
$487$	3.29210	−	4.12817i	0.149180	−	0.187065i	0.850806	+	0.525479i	$0.176114\pi$
$488$	−0.0256590	+	0.265982i	−0.00116153	+	0.0120404i
$489$	15.6587	+	8.81881i	0.708111	+	0.398800i
$490$	18.0752	−	11.7657i	0.816555	−	0.531518i
$491$	−8.77901	−	12.5854i	−0.396191	−	0.567970i	0.571342	−	0.820712i	$-0.306423\pi$
$491$	−8.77901	−	12.5854i	−0.396191	−	0.567970i	−0.967534	+	0.252742i	$0.918668\pi$
$492$	−19.5089	−	5.11583i	−0.879527	−	0.230639i
$493$	−0.640561	−	0.167975i	−0.0288494	−	0.00756521i
$494$	2.18533	+	3.13283i	0.0983225	+	0.140953i
$495$	−5.63662	+	3.66903i	−0.253347	+	0.164911i
$496$	−15.0456	−	8.47351i	−0.675566	−	0.380472i
$497$	0.138268	−	1.43330i	0.00620218	−	0.0642921i
$498$	−0.938965	+	1.17742i	−0.0420760	+	0.0527617i
$499$	28.9242	+	3.72936i	1.29482	+	0.166949i	0.744286	−	0.667861i	$-0.232790\pi$
$499$	28.9242	+	3.72936i	1.29482	+	0.166949i	0.550538	+	0.834810i	$0.314423\pi$
$500$	23.6345	+	3.04733i	1.05696	+	0.136281i
$501$	−6.21431	−	2.06329i	−0.277635	−	0.0921812i
$502$	−0.966915	+	30.1520i	−0.0431555	+	1.34575i
$503$	3.83225	+	10.4135i	0.170871	+	0.464313i	0.994736	−	0.102474i	$-0.0326760\pi$
$503$	3.83225	+	10.4135i	0.170871	+	0.464313i	−0.823864	+	0.566787i	$0.808186\pi$
$504$	−0.0635544	−	0.0796947i	−0.00283094	−	0.00354988i
$505$	−3.32505	+	20.5666i	−0.147963	+	0.915203i
$506$	−14.0006	+	13.5588i	−0.622403	+	0.602764i
$507$	−14.6319	−	7.04635i	−0.649826	−	0.312939i
$508$	6.57672	−	28.8145i	0.291795	−	1.27844i
$509$	37.9779	−	7.39620i	1.68334	−	0.327831i	0.743318	−	0.668938i	$-0.233251\pi$
$509$	37.9779	−	7.39620i	1.68334	−	0.327831i	0.940025	+	0.341107i	$0.110802\pi$
$510$	−16.8829	+	5.60550i	−0.747586	+	0.248216i
$511$	4.68260	+	15.7772i	0.207146	+	0.697944i
$512$	21.4003	+	23.5641i	0.945769	+	1.04140i
$513$	12.5397	+	4.16347i	0.553642	+	0.183822i
$514$	17.0814	−	21.4193i	0.753426	−	0.944767i
$515$	14.5377	+	16.0077i	0.640610	+	0.705383i
$516$	−10.5262	+	15.0901i	−0.463390	+	0.664305i
$517$	−4.65553	−	4.50863i	−0.204750	−	0.198289i
$518$	4.15515	+	6.85435i	0.182567	+	0.301163i
$519$	8.76089	+	6.53842i	0.384560	+	0.287005i
$520$	0.0172910	+	0.106951i	0.000758261	+	0.00469011i
$521$	5.94126	−	6.54199i	0.260292	−	0.286610i	−0.596129	−	0.802889i	$-0.703295\pi$
$521$	5.94126	−	6.54199i	0.260292	−	0.286610i	0.856421	+	0.516279i	$0.172683\pi$
$522$	−0.104949	−	0.459814i	−0.00459351	−	0.0201255i
$523$	21.5927	−	10.3985i	0.944183	−	0.454695i	0.102540	−	0.994729i	$-0.467303\pi$
$523$	21.5927	−	10.3985i	0.944183	−	0.454695i	0.841643	+	0.540034i	$0.181589\pi$
$524$	−6.66993	+	18.1244i	−0.291377	+	0.791766i
$525$	−1.54607	+	1.31619i	−0.0674759	+	0.0574431i
$526$	31.3427	−	44.9321i	1.36661	−	1.95913i
$527$	−0.481731	+	15.0221i	−0.0209845	+	0.654374i
$528$	−1.42541	+	14.7759i	−0.0620332	+	0.643039i
$529$	−2.99506	−	10.0914i	−0.130220	−	0.438755i
$530$	16.1067	−	13.7119i	0.699632	−	0.595605i
$531$	−1.31144	+	0.978754i	−0.0569117	+	0.0424743i
$532$	2.48184	+	4.75722i	0.107601	+	0.206252i
$533$	6.34394	−	0.407295i	0.274787	−	0.0176419i
$534$	4.31009	−	8.26163i	0.186516	−	0.357516i
$535$	−0.923016	+	0.519833i	−0.0399055	+	0.0224743i
$536$	−0.384428	−	0.868429i	−0.0166048	−	0.0375104i
$537$	4.62636	−	15.5877i	0.199642	−	0.672661i
$538$	46.2815	+	18.7373i	1.99534	+	0.807823i
$539$	−12.5541	+	9.36934i	−0.540742	+	0.403566i
$540$	−15.1946	−	14.7152i	−0.653873	−	0.633240i
$541$	−4.25629	−	11.5657i	−0.182992	−	0.497249i	0.813440	−	0.581649i	$-0.197592\pi$
$541$	−4.25629	−	11.5657i	−0.182992	−	0.497249i	−0.996432	+	0.0844002i	$0.973103\pi$
$542$	−47.5989	−	26.8072i	−2.04455	−	1.15147i
$543$	−3.15305	+	1.04689i	−0.135311	+	0.0449262i
$544$	9.73840	−	26.4624i	0.417530	−	1.13457i
$545$	26.0100	+	10.5303i	1.11414	+	0.451067i
$546$	2.08004	+	1.35396i	0.0890176	+	0.0579440i
$547$	0.678024	+	7.02843i	0.0289902	+	0.300514i	0.998468	+	0.0553343i	$0.0176225\pi$
$547$	0.678024	+	7.02843i	0.0289902	+	0.300514i	−0.969478	+	0.245180i	$0.921153\pi$
$548$	−2.88723	+	6.52230i	−0.123336	+	0.278619i
$549$	3.71704	+	3.16436i	0.158639	+	0.135052i
$550$	−7.31641	−	0.469729i	−0.311973	−	0.0200293i
$551$	−0.0140983	−	0.439635i	−0.000600606	−	0.0187291i
$552$	0.270191	+	0.175875i	0.0115001	+	0.00748573i
$553$	3.18403	+	6.10319i	0.135399	+	0.259534i
$554$	−8.70552	−	14.3607i	−0.369862	−	0.610126i
$555$	−5.45431	−	6.83949i	−0.231523	−	0.290320i
$556$	−27.8978	+	18.1595i	−1.18313	+	0.770132i
$557$	−26.2208	+	5.10649i	−1.11101	+	0.216369i	−0.713105	−	0.701058i	$-0.752712\pi$
$557$	−26.2208	+	5.10649i	−1.11101	+	0.216369i	−0.397905	+	0.917427i	$0.630263\pi$
$558$	−9.64433	+	4.64447i	−0.408277	+	0.196616i
$559$	1.65003	−	5.55949i	0.0697887	−	0.235141i
$560$	0.290038	+	9.04444i	0.0122563	+	0.382197i
$561$	11.9765	−	4.84874i	0.505648	−	0.204714i
$562$	32.7758	+	6.38308i	1.38256	+	0.269254i
$563$	−1.55754	+	0.408435i	−0.0656425	+	0.0172135i	−0.286330	−	0.958131i	$-0.592435\pi$
$563$	−1.55754	+	0.408435i	−0.0656425	+	0.0172135i	0.220687	+	0.975345i	$0.429170\pi$
$564$	3.13664	−	5.17422i	0.132076	−	0.217874i
$565$	−23.9693	+	9.70408i	−1.00839	+	0.408254i
$566$	6.13179	+	63.5624i	0.257738	+	2.67173i
$567$	4.16586	−	0.267457i	0.174950	−	0.0112321i
$568$	−0.0689249	−	0.0514400i	−0.00289202	−	0.00215837i
$569$	6.98721	−	43.2184i	0.292919	−	1.81181i	−0.245797	−	0.969321i	$-0.579050\pi$
$569$	6.98721	−	43.2184i	0.292919	−	1.81181i	0.538716	−	0.842487i	$-0.318910\pi$
$570$	−6.76011	−	9.69112i	−0.283150	−	0.405916i
$571$	−5.12376	+	22.4487i	−0.214423	+	0.939448i	0.747098	+	0.664714i	$0.231447\pi$
$571$	−5.12376	+	22.4487i	−0.214423	+	0.939448i	−0.961520	+	0.274733i	$0.911410\pi$
$572$	0.988315	+	4.33009i	0.0413235	+	0.181050i
$573$	4.63779	+	10.4769i	0.193747	+	0.437677i
$574$	17.9810	+	1.15442i	0.750512	+	0.0481844i
$575$	−2.43237	+	4.01244i	−0.101437	+	0.167331i
$576$	9.69639	−	1.25021i	0.404016	−	0.0520922i
$577$	27.2938			1.13625			0.568127	−	0.822941i	$-0.307668\pi$
$577$	27.2938			1.13625			0.568127	+	0.822941i	$0.307668\pi$
$578$	8.80812	−	1.13568i	0.366370	−	0.0472381i
$579$	7.10698	+	1.38408i	0.295356	+	0.0575206i
$580$	−0.285034	+	0.643898i	−0.0118354	+	0.0267364i
$581$	0.308419	−	0.591181i	0.0127954	−	0.0245263i
$582$	7.84264	+	48.5095i	0.325088	+	2.01078i
$583$	−11.0367	+	10.6884i	−0.457092	+	0.442669i
$584$	0.950810	+	0.249332i	0.0393448	+	0.0103174i
$585$	1.78316	+	0.858726i	0.0737247	+	0.0355040i
$586$	−23.3575	+	25.7192i	−0.964891	+	1.06245i
$587$	28.1722	−	15.8663i	1.16279	−	0.654872i	0.215897	−	0.976416i	$-0.430732\pi$
$587$	28.1722	−	15.8663i	1.16279	−	0.654872i	0.946895	+	0.321544i	$0.104202\pi$
$588$	−11.1363	−	9.48044i	−0.459252	−	0.390967i
$589$	−9.65668	+	2.53228i	−0.397897	+	0.104341i
$590$	4.92967			0.202951
$591$	−18.3410	+	2.25769i	−0.754446	+	0.0928688i
$592$	14.1079			0.579831
$593$	27.8885	−	7.31322i	1.14524	−	0.300318i	0.368188	−	0.929751i	$-0.379978\pi$
$593$	27.8885	−	7.31322i	1.14524	−	0.300318i	0.777054	+	0.629433i	$0.216713\pi$
$594$	23.6041	+	20.0945i	0.968488	+	0.824486i
$595$	6.86286	−	3.86509i	0.281350	−	0.158453i
$596$	−8.80848	+	9.69911i	−0.360809	+	0.397291i
$597$	2.86208	+	1.37831i	0.117137	+	0.0564104i
$598$	5.54782	+	1.45481i	0.226867	+	0.0594916i
$599$	−33.3723	+	32.3193i	−1.36356	+	1.32053i	−0.462636	+	0.886548i	$0.653096\pi$
$599$	−33.3723	+	32.3193i	−1.36356	+	1.32053i	−0.900921	+	0.433983i	$0.857108\pi$
$600$	0.0193550	+	0.119718i	0.000790166	+	0.00488746i
$601$	−6.89566	+	13.2177i	−0.281280	+	0.539161i	−0.985261	−	0.171058i	$-0.945281\pi$
$601$	−6.89566	+	13.2177i	−0.281280	+	0.539161i	0.703981	+	0.710219i	$0.251404\pi$
$602$	6.65340	−	15.0301i	0.271172	−	0.612583i
$603$	−17.0295	−	3.31650i	−0.693496	−	0.135058i
$604$	−31.0220	+	3.99984i	−1.26227	+	0.162751i
$605$	6.36119			0.258619
$606$	28.2717	−	3.64524i	1.14846	−	0.148078i
$607$	−12.9545	+	21.3697i	−0.525805	+	0.867371i	−0.999914	−	0.0130952i	$-0.995832\pi$
$607$	−12.9545	+	21.3697i	−0.525805	+	0.867371i	0.474109	+	0.880466i	$0.342770\pi$
$608$	18.6909	+	1.20000i	0.758016	+	0.0486662i
$609$	−0.115688	−	0.261342i	−0.00468792	−	0.0105901i
$610$	−3.27231	−	14.3369i	−0.132492	−	0.580485i
$611$	−0.424381	+	1.85934i	−0.0171686	+	0.0752207i
$612$	−5.04269	−	7.22907i	−0.203839	−	0.292218i
$613$	1.11059	−	6.86941i	0.0448564	−	0.277453i	−0.954958	−	0.296743i	$-0.904100\pi$
$613$	1.11059	−	6.86941i	0.0448564	−	0.277453i	0.999814	+	0.0192897i	$0.00614049\pi$
$614$	−47.0226	−	35.0939i	−1.89768	−	1.41627i
$615$	−19.6244	+	1.25993i	−0.791332	+	0.0508052i
$616$	−0.0214166	−	0.222006i	−0.000862901	−	0.00894487i
$617$	34.7487	−	14.0682i	1.39893	−	0.566364i	0.453226	−	0.891395i	$-0.350273\pi$
$617$	34.7487	−	14.0682i	1.39893	−	0.566364i	0.945703	+	0.325032i	$0.105375\pi$
$618$	15.3377	−	25.3011i	0.616971	−	1.01776i
$619$	30.1335	−	7.90193i	1.21117	−	0.317606i	0.407790	−	0.913076i	$-0.366300\pi$
$619$	30.1335	−	7.90193i	1.21117	−	0.317606i	0.803377	+	0.595470i	$0.203034\pi$
$620$	15.6872	+	3.05507i	0.630011	+	0.122695i
$621$	18.3894	−	7.44505i	0.737942	−	0.298760i
$622$	0.513077	+	15.9996i	0.0205725	+	0.641527i
$623$	−1.17391	+	3.95530i	−0.0470318	+	0.158466i
$624$	3.93575	−	1.89536i	0.157556	−	0.0758750i
$625$	16.2863	−	3.17176i	0.651452	−	0.126870i
$626$	40.2309	−	26.1874i	1.60795	−	1.04666i
$627$	5.35097	+	6.70990i	0.213697	+	0.267968i
$628$	1.08294	+	1.78642i	0.0432140	+	0.0712860i
$629$	−5.67981	−	10.8871i	−0.226469	−	0.434098i
$630$	4.70138	+	3.06026i	0.187307	+	0.121924i
$631$	0.0797850	+	2.48799i	0.00317619	+	0.0990453i	0.999847	+	0.0175104i	$0.00557402\pi$
$631$	0.0797850	+	2.48799i	0.00317619	+	0.0990453i	−0.996670	+	0.0815348i	$0.974018\pi$
$632$	0.410307	+	0.0263426i	0.0163211	+	0.00104785i
$633$	10.6081	+	9.03081i	0.421634	+	0.358942i
$634$	−15.0371	+	33.9692i	−0.597201	+	1.34909i
$635$	−2.76714	−	28.6843i	−0.109810	−	1.13830i
$636$	−12.0217	−	7.82524i	−0.476690	−	0.310291i
$637$	4.27288	+	1.72990i	0.169298	+	0.0685410i
$638$	0.356408	−	0.968475i	0.0141103	−	0.0383423i
$639$	−1.49109	+	0.495077i	−0.0589867	+	0.0195849i
$640$	0.925874	+	0.521443i	0.0365984	+	0.0206118i
$641$	4.42505	+	12.0243i	0.174779	+	0.474931i	0.995317	−	0.0966604i	$-0.0308161\pi$
$641$	4.42505	+	12.0243i	0.174779	+	0.474931i	−0.820538	+	0.571591i	$0.806326\pi$
$642$	1.04120	+	1.00835i	0.0410930	+	0.0397963i
$643$	−6.11933	+	4.56697i	−0.241323	+	0.180104i	−0.711954	−	0.702226i	$-0.752190\pi$
$643$	−6.11933	+	4.56697i	−0.241323	+	0.180104i	0.470631	+	0.882330i	$0.344026\pi$
$644$	7.46790	+	3.02342i	0.294276	+	0.119139i
$645$	−5.10420	+	17.1978i	−0.200978	+	0.677161i
$646$	−6.71378	−	15.1665i	−0.264150	−	0.596720i
$647$	−8.58668	+	4.83593i	−0.337577	+	0.190120i	−0.650211	−	0.759754i	$-0.725319\pi$
$647$	−8.58668	+	4.83593i	−0.337577	+	0.190120i	0.312634	+	0.949874i	$0.398789\pi$
$648$	0.115323	−	0.221053i	0.00453033	−	0.00868380i
$649$	−3.57321	+	0.229408i	−0.140261	+	0.00900503i
$650$	0.997910	+	1.91281i	0.0391413	+	0.0750264i
$651$	−5.19848	+	3.87973i	−0.203744	+	0.152058i
$652$	20.4252	−	17.3882i	0.799912	−	0.680975i
$653$	−7.67181	−	25.8489i	−0.300221	−	1.01154i	−0.964505	−	0.264064i	$-0.914937\pi$
$653$	−7.67181	−	25.8489i	−0.300221	−	1.01154i	0.664284	−	0.747480i	$-0.268736\pi$
$654$	3.68673	−	38.2168i	0.144163	−	1.49440i
$655$	−0.603544	+	18.8207i	−0.0235824	+	0.735386i
$656$	18.1437	−	26.0104i	0.708393	−	1.01553i
$657$	13.6731	−	11.6401i	0.533439	−	0.454124i
$658$	−1.86689	+	5.07293i	−0.0727788	+	0.197764i
$659$	0.0884260	−	0.0425837i	0.00344459	−	0.00165883i	−0.432161	−	0.901797i	$-0.642249\pi$
$659$	0.0884260	−	0.0425837i	0.00344459	−	0.00165883i	0.435605	+	0.900138i	$0.356534\pi$
$660$	−3.05726	−	13.3947i	−0.119004	−	0.521389i
$661$	4.27552	−	4.70783i	0.166299	−	0.183113i	−0.651445	−	0.758696i	$-0.725837\pi$
$661$	4.27552	−	4.70783i	0.166299	−	0.183113i	0.817744	+	0.575583i	$0.195225\pi$
$662$	−2.89452	−	17.9037i	−0.112499	−	0.695845i
$663$	−3.04718	−	2.27417i	−0.118342	−	0.0883213i
$664$	−0.0206454	−	0.0340568i	−0.000801199	−	0.00132166i
$665$	3.75818	+	3.63960i	0.145736	+	0.141138i
$666$	5.00355	−	7.17296i	0.193883	−	0.277947i
$667$	−0.444029	−	0.488925i	−0.0171929	−	0.0189313i
$668$	−6.09367	+	7.64122i	−0.235771	+	0.295648i
$669$	11.9400	+	3.96434i	0.461625	+	0.153270i
$670$	35.1378	+	38.6907i	1.35749	+	1.49475i
$671$	3.03908	+	10.2397i	0.117322	+	0.395298i
$672$	11.5496	−	3.83472i	0.445534	−	0.147928i
$673$	−8.79910	+	1.71362i	−0.339180	+	0.0660553i	−0.357874	−	0.933770i	$-0.616498\pi$
$673$	−8.79910	+	1.71362i	−0.339180	+	0.0660553i	0.0186937	+	0.999825i	$0.494049\pi$
$674$	−11.5056	+	50.4093i	−0.443179	+	1.94169i
$675$	6.72384	+	3.23803i	0.258801	+	0.124632i
$676$	−17.4131	+	16.8636i	−0.669733	+	0.648600i
$677$	5.16872	−	31.9704i	0.198650	−	1.22872i	−0.673391	−	0.739287i	$-0.735163\pi$
$677$	5.16872	−	31.9704i	0.198650	−	1.22872i	0.872041	−	0.489434i	$-0.162796\pi$
$678$	22.0602	+	27.6627i	0.847218	+	1.06238i
$679$	−7.51418	−	20.4185i	−0.288368	−	0.783588i
$680$	0.0150782	−	0.470194i	0.000578223	−	0.0180311i
$681$	13.9285	+	4.62459i	0.533742	+	0.177215i
$682$	−23.2296	−	2.99512i	−0.889507	−	0.114689i
$683$	−6.03474	−	0.778094i	−0.230913	−	0.0297729i	0.0115512	−	0.999933i	$-0.496323\pi$
$683$	−6.03474	−	0.778094i	−0.230913	−	0.0297729i	−0.242464	+	0.970160i	$0.577956\pi$
$684$	3.65024	−	4.57725i	0.139570	−	0.175016i
$685$	−0.667806	+	6.92251i	−0.0255156	+	0.264495i
$686$	25.4827	+	14.3516i	0.972934	+	0.547946i
$687$	−18.1602	+	11.8210i	−0.692854	+	0.450998i
$688$	−16.5516	−	23.7280i	−0.631025	−	0.904621i
$689$	4.37334	+	1.14682i	0.166611	+	0.0436905i
$690$	−17.1617	−	4.50032i	−0.653334	−	0.171324i
$691$	−11.6160	−	16.6524i	−0.441894	−	0.633488i	0.535595	−	0.844475i	$-0.320087\pi$
$691$	−11.6160	−	16.6524i	−0.441894	−	0.633488i	−0.977489	+	0.210987i	$0.932332\pi$
$692$	13.6751	−	8.90148i	0.519848	−	0.338384i
$693$	−3.55015	−	1.99941i	−0.134859	−	0.0759512i
$694$	−3.09354	+	32.0678i	−0.117429	+	1.21728i
$695$	−20.2361	+	25.3752i	−0.767598	+	0.962537i
$696$	−0.0169301	−	0.00218289i	−0.000641732	−	8.27422e-5i
$697$	−27.3769	−	3.52986i	−1.03697	−	0.133703i
$698$	60.7931	+	20.1847i	2.30105	+	0.764002i
$699$	−1.05379	+	32.8610i	−0.0398579	+	1.24292i
$700$	1.04668	+	2.84418i	0.0395610	+	0.107500i
$701$	−25.6184	−	32.1244i	−0.967592	−	1.21332i	−0.976972	−	0.213366i	$-0.931557\pi$
$701$	−25.6184	−	32.1244i	−0.967592	−	1.21332i	0.00938048	−	0.999956i	$-0.497014\pi$
$702$	1.45591	−	9.00529i	0.0549496	−	0.339883i
$703$	5.85916	−	5.67428i	0.220983	−	0.214010i
$704$	19.2735	+	9.28161i	0.726396	+	0.349814i
$705$	1.31278	−	5.75168i	0.0494423	−	0.216621i
$706$	−37.6610	+	7.33449i	−1.41739	+	0.276037i
$707$	−11.9784	+	3.97709i	−0.450493	+	0.149574i
$708$	−0.951149	−	3.20474i	−0.0357464	−	0.120441i
$709$	−19.1290	−	21.0631i	−0.718403	−	0.791042i	0.266558	−	0.963819i	$-0.414114\pi$
$709$	−19.1290	−	21.0631i	−0.718403	−	0.791042i	−0.984961	+	0.172777i	$0.944726\pi$
$710$	4.49190	+	1.49141i	0.168578	+	0.0559718i
$711$	4.68301	−	5.87231i	0.175627	−	0.220229i
$712$	0.165671	+	0.182423i	0.00620880	+	0.00683657i
$713$	−8.57601	+	12.2944i	−0.321174	+	0.460427i
$714$	−7.74160	−	7.49732i	−0.289722	−	0.280580i
$715$	2.24491	+	3.70322i	0.0839550	+	0.138493i
$716$	−19.4500	−	14.5159i	−0.726881	−	0.542486i
$717$	4.59123	+	28.3984i	0.171463	+	1.06056i
$718$	−34.1687	+	37.6235i	−1.27516	+	1.40410i
$719$	2.36477	+	10.3607i	0.0881910	+	0.386390i	0.999690	−	0.0249131i	$-0.00793090\pi$
$719$	2.36477	+	10.3607i	0.0881910	+	0.386390i	−0.911499	+	0.411303i	$0.865074\pi$
$720$	8.89571	−	4.28395i	0.331523	−	0.159653i
$721$	−4.52431	+	12.2940i	−0.168494	+	0.457853i
$722$	−20.4200	+	17.3838i	−0.759953	+	0.646958i
$723$	7.26689	−	10.4176i	0.270258	−	0.387436i
$724$	−0.158942	+	4.95638i	−0.00590702	+	0.184203i
$725$	0.0238563	−	0.247295i	0.000886001	−	0.00918432i
$726$	−2.47645	−	8.34398i	−0.0919097	−	0.309674i
$727$	24.8207	−	21.1302i	0.920549	−	0.783675i	−0.0561202	−	0.998424i	$-0.517873\pi$
$727$	24.8207	−	21.1302i	0.920549	−	0.783675i	0.976669	+	0.214749i	$0.0688934\pi$
$728$	−0.0525999	+	0.0392563i	−0.00194948	+	0.00145494i
$729$	−12.3693	−	23.7096i	−0.458122	−	0.878135i
$730$	−53.9835	+	3.46586i	−1.99802	+	0.128277i
$731$	−11.6473	+	22.3258i	−0.430792	+	0.825748i
$732$	−8.68894	+	4.89352i	−0.321153	+	0.180870i
$733$	−6.90631	−	15.6015i	−0.255090	−	0.576254i	0.740287	−	0.672291i	$-0.234689\pi$
$733$	−6.90631	−	15.6015i	−0.255090	−	0.576254i	−0.995378	+	0.0960369i	$0.969383\pi$
$734$	20.4911	−	69.0413i	0.756340	−	2.54836i
$735$	−13.2178	−	5.35127i	−0.487544	−	0.197385i
$736$	22.5378	−	16.8204i	0.830755	−	0.620009i
$737$	−27.2697	−	26.4093i	−1.00449	−	0.972798i
$738$	−6.78970	−	18.4498i	−0.249932	−	0.679147i
$739$	−23.7985	−	13.4031i	−0.875444	−	0.493041i	−0.0134208	−	0.999910i	$-0.504272\pi$
$739$	−23.7985	−	13.4031i	−0.875444	−	0.493041i	−0.862023	+	0.506869i	$0.830803\pi$
$740$	−12.3923	+	4.11451i	−0.455548	+	0.151252i
$741$	0.872235	−	2.37014i	0.0320423	−	0.0870694i
$742$	11.8782	+	4.80894i	0.436061	+	0.176542i
$743$	−28.4690	−	18.5313i	−1.04443	−	0.679846i	−0.0955277	−	0.995427i	$-0.530454\pi$
$743$	−28.4690	−	18.5313i	−1.04443	−	0.679846i	−0.948899	+	0.315580i	$0.897801\pi$
$744$	0.0372021	+	0.385638i	0.00136389	+	0.0141382i
$745$	−5.17102	+	11.6814i	−0.189452	+	0.427974i
$746$	−33.3824	−	28.4189i	−1.22222	−	1.04049i
$747$	−0.726049	−	0.0466139i	−0.0265647	−	0.00170551i
$748$	−0.618139	−	19.2759i	−0.0226014	−	0.704795i
$749$	−0.537851	−	0.350102i	−0.0196527	−	0.0127925i
$750$	−14.7047	−	28.1862i	−0.536941	−	1.02921i
$751$	8.36818	+	13.8042i	0.305359	+	0.503722i	0.969891	−	0.243538i	$-0.0783079\pi$
$751$	8.36818	+	13.8042i	0.305359	+	0.503722i	−0.664532	+	0.747260i	$0.731369\pi$
$752$	5.93204	+	7.43854i	0.216319	+	0.271256i
$753$	16.7167	−	10.8814i	0.609192	−	0.396540i
$754$	−0.298083	+	0.0580517i	−0.0108555	+	0.00211412i
$755$	−27.4774	+	13.2324i	−1.00001	+	0.481577i
$756$	3.64602	−	12.2846i	0.132604	−	0.446788i
$757$	−0.741675	−	23.1282i	−0.0269566	−	0.840608i	−0.920296	−	0.391224i	$-0.872052\pi$
$757$	−0.741675	−	23.1282i	−0.0269566	−	0.840608i	0.893339	−	0.449384i	$-0.148356\pi$
$758$	−47.6304	+	19.2834i	−1.73001	+	0.700405i
$759$	12.6488	+	2.46336i	0.459124	+	0.0894144i
$760$	0.302255	−	0.0792605i	0.0109639	−	0.00287508i
$761$	−19.2623	+	31.7751i	−0.698257	+	1.15185i	0.282996	+	0.959121i	$0.408672\pi$
$761$	−19.2623	+	31.7751i	−0.698257	+	1.15185i	−0.981253	+	0.192726i	$0.938267\pi$
$762$	−36.5479	+	14.7966i	−1.32399	+	0.536025i
$763$	1.63236	+	16.9211i	0.0590952	+	0.612584i
$764$	17.0665	−	1.09570i	0.617443	−	0.0396412i
$765$	−6.88732	−	5.14014i	−0.249012	−	0.185842i
$766$	3.54273	−	21.9130i	0.128004	−	0.791749i
$767$	0.602821	+	0.864189i	0.0217666	+	0.0312041i
$768$	4.84647	−	21.2338i	0.174882	−	0.766208i
$769$	4.75123	+	20.8165i	0.171334	+	0.750663i	0.985451	+	0.169962i	$0.0543644\pi$
$769$	4.75123	+	20.8165i	0.171334	+	0.750663i	−0.814117	+	0.580701i	$0.802778\pi$
$770$	4.96841	+	11.2237i	0.179049	+	0.404475i
$771$	−18.0769	−	1.16057i	−0.651022	−	0.0417970i
$772$	5.60242	−	9.24177i	0.201635	−	0.332619i
$773$	35.9264	−	4.63219i	1.29218	−	0.166608i	0.549070	−	0.835776i	$-0.314982\pi$
$773$	35.9264	−	4.63219i	1.29218	−	0.166608i	0.743111	+	0.669168i	$0.233349\pi$
$774$	−17.9344			−0.644638
$775$	−5.59243	+	0.721064i	−0.200886	+	0.0259014i
$776$	−1.27553	−	0.248410i	−0.0457890	−	0.00891740i
$777$	2.14523	−	4.84610i	0.0769596	−	0.173853i
$778$	−2.82551	+	5.41597i	−0.101299	+	0.194172i
$779$	−2.92625	−	18.0999i	−0.104844	−	0.648496i
$780$	−2.90435	+	2.81271i	−0.103992	+	0.100711i
$781$	−3.32530	−	0.871997i	−0.118989	−	0.0312025i
$782$	−22.4381	−	10.8056i	−0.802384	−	0.386408i
$783$	−0.706234	+	0.777642i	−0.0252387	+	0.0277906i
$784$	20.0376	−	11.2850i	0.715629	−	0.403035i
$785$	1.55096	+	1.32035i	0.0553562	+	0.0471254i
$786$	24.9221	−	6.53535i	0.888943	−	0.233108i
$787$	1.85309			0.0660555			0.0330278	−	0.999454i	$-0.489485\pi$
$787$	1.85309			0.0660555			0.0330278	+	0.999454i	$0.489485\pi$
$788$	−6.29221	+	26.8554i	−0.224151	+	0.956683i
$789$	−36.2222			−1.28954
$790$	−21.8867	+	5.73936i	−0.778693	+	0.204197i
$791$	−11.9287	−	10.1550i	−0.424136	−	0.361072i
$792$	−0.212040	+	0.119419i	−0.00753453	+	0.00424337i
$793$	2.11316	−	2.32683i	0.0750406	−	0.0826281i
$794$	−45.7793	−	22.0461i	−1.62465	−	0.782388i
$795$	−13.5285	−	3.54760i	−0.479807	−	0.125820i
$796$	3.40609	−	3.29862i	0.120726	−	0.116916i
$797$	2.53535	+	15.6820i	0.0898068	+	0.555487i	0.992208	+	0.124590i	$0.0397617\pi$
$797$	2.53535	+	15.6820i	0.0898068	+	0.555487i	−0.902401	+	0.430896i	$0.858198\pi$
$798$	3.31098	−	6.34653i	0.117207	−	0.224665i
$799$	3.35213	−	7.57251i	0.118590	−	0.267896i
$800$	10.3837	+	2.02222i	0.367119	+	0.0714964i
$801$	4.46475	−	0.575666i	0.157754	−	0.0203401i
$802$	35.1051			1.23960
$803$	38.9680	−	5.02437i	1.37515	−	0.177306i
$804$	18.3729	−	30.3080i	0.647961	−	1.06888i
$805$	7.83936	+	0.503304i	0.276301	+	0.0177391i
$806$	2.78995	+	6.30255i	0.0982718	+	0.221998i
$807$	−7.34617	−	32.1857i	−0.258597	−	1.13299i
$808$	−0.167745	+	0.734938i	−0.00590124	+	0.0258550i
$809$	13.9973	+	20.0662i	0.492119	+	0.705489i	0.986501	−	0.163755i	$-0.0523607\pi$
$809$	13.9973	+	20.0662i	0.492119	+	0.705489i	−0.494382	+	0.869245i	$0.664606\pi$
$810$	−2.18989	+	13.5452i	−0.0769448	+	0.475931i
$811$	0.849254	+	0.633815i	0.0298213	+	0.0222562i	0.612918	−	0.790147i	$-0.289996\pi$
$811$	0.849254	+	0.633815i	0.0298213	+	0.0222562i	−0.583096	+	0.812403i	$0.698159\pi$
$812$	−0.425718	+	0.0273320i	−0.0149398	+	0.000959164i
$813$	3.46831	+	35.9527i	0.121639	+	1.26092i
$814$	17.7375	−	7.18114i	0.621701	−	0.251699i
$815$	13.5582	−	22.3657i	0.474923	−	0.783435i
$816$	−18.3480	+	4.81141i	−0.642309	+	0.168433i
$817$	−16.4176	−	3.19733i	−0.574379	−	0.111860i
$818$	−7.71759	+	3.12451i	−0.269839	+	0.109246i
$819$	0.0384301	+	1.19839i	0.00134285	+	0.0418752i
$820$	−8.35145	+	28.1388i	−0.291645	+	0.982650i
$821$	−30.6845	+	14.7769i	−1.07090	+	0.515717i	−0.884396	−	0.466738i	$-0.845429\pi$
$821$	−30.6845	+	14.7769i	−1.07090	+	0.515717i	−0.186502	+	0.982455i	$0.559715\pi$
$822$	9.34025	−	1.81901i	0.325779	−	0.0634454i
$823$	−43.0277	+	28.0079i	−1.49985	+	0.976296i	−0.506369	+	0.862317i	$0.669013\pi$
$823$	−43.0277	+	28.0079i	−1.49985	+	0.976296i	−0.993483	+	0.113979i	$0.963640\pi$
$824$	0.487837	+	0.611729i	0.0169946	+	0.0213106i
$825$	2.51289	+	4.14527i	0.0874876	+	0.144320i
$826$	1.38136	+	2.64780i	0.0480635	+	0.0921287i
$827$	−35.3358	−	23.0010i	−1.22875	−	0.799825i	−0.243322	−	0.969945i	$-0.578237\pi$
$827$	−35.3358	−	23.0010i	−1.22875	−	0.799825i	−0.985423	+	0.170121i	$0.945584\pi$
$828$	−0.281756	−	8.78618i	−0.00979169	−	0.305341i
$829$	19.1547	+	1.22978i	0.665272	+	0.0427119i	0.393042	−	0.919520i	$-0.371423\pi$
$829$	19.1547	+	1.22978i	0.665272	+	0.0427119i	0.272230	+	0.962232i	$0.412239\pi$
$830$	1.66887	+	1.42073i	0.0579275	+	0.0493144i
$831$	−4.49450	+	10.1532i	−0.155913	+	0.352209i
$832$	−0.604474	−	6.26600i	−0.0209564	−	0.217235i
$833$	−16.7757	−	10.9198i	−0.581245	−	0.378349i
$834$	41.1627	+	16.6649i	1.42535	+	0.577060i
$835$	−3.29113	+	8.94305i	−0.113894	+	0.309487i
$836$	12.1575	−	4.03655i	0.420474	−	0.139607i
$837$	20.7737	+	11.6996i	0.718046	+	0.404396i
$838$	15.6532	+	42.5347i	0.540730	+	1.46934i
$839$	31.4656	+	30.4728i	1.08631	+	1.05204i	0.998436	+	0.0559057i	$0.0178046\pi$
$839$	31.4656	+	30.4728i	1.08631	+	1.05204i	0.0878784	+	0.996131i	$0.471991\pi$
$840$	0.162713	−	0.121436i	0.00561412	−	0.00418993i
$841$	−26.8482	−	10.8696i	−0.925799	−	0.374814i
$842$	−16.1118	+	54.2861i	−0.555250	+	1.87082i
$843$	−8.93680	−	20.1884i	−0.307800	−	0.695325i
$844$	18.1186	−	10.2042i	0.623667	−	0.351243i
$845$	−10.9321	+	20.9548i	−0.376075	+	0.720866i
$846$	5.88589	−	0.377887i	0.202361	−	0.0129920i
$847$	1.78249	+	3.41669i	0.0612470	+	0.117399i
$848$	18.0759	−	13.4904i	0.620730	−	0.463263i
$849$	32.1495	−	27.3692i	1.10337	−	0.939310i
$850$	−2.66551	−	8.98099i	−0.0914263	−	0.308045i
$851$	1.17600	−	12.1905i	0.0403127	−	0.417884i
$852$	0.102871	−	3.20791i	0.00352432	−	0.109901i
$853$	12.0010	−	17.2043i	0.410905	−	0.589063i	−0.560010	−	0.828486i	$-0.689203\pi$
$853$	12.0010	−	17.2043i	0.410905	−	0.589063i	0.970916	+	0.239422i	$0.0769580\pi$
$854$	6.78364	−	5.77499i	0.232131	−	0.197616i
$855$	1.97145	−	5.35707i	0.0674223	−	0.183208i
$856$	−0.0345346	+	0.0166310i	−0.00118037	+	0.000568435i
$857$	10.6534	+	46.6755i	0.363913	+	1.59441i	0.743162	+	0.669111i	$0.233325\pi$
$857$	10.6534	+	46.6755i	0.363913	+	1.59441i	−0.379249	+	0.925294i	$0.623818\pi$
$858$	3.98356	−	4.38634i	0.135997	−	0.149747i
$859$	4.12993	+	25.5451i	0.140911	+	0.871587i	0.956239	+	0.292587i	$0.0945161\pi$
$859$	4.12993	+	25.5451i	0.140911	+	0.871587i	−0.815327	+	0.579000i	$0.803443\pi$
$860$	21.4590	+	16.0152i	0.731744	+	0.546115i
$861$	−6.17573	−	10.1875i	−0.210468	−	0.347190i
$862$	−10.1215	−	9.80209i	−0.344738	−	0.333861i
$863$	−16.6791	+	23.9107i	−0.567762	+	0.813930i	−0.995964	−	0.0897532i	$-0.971392\pi$
$863$	−16.6791	+	23.9107i	−0.567762	+	0.813930i	0.428202	+	0.903683i	$0.359147\pi$
$864$	−30.0716	−	33.1121i	−1.02306	−	1.12650i
$865$	9.91941	−	12.4385i	0.337270	−	0.422923i
$866$	28.8356	+	9.57409i	0.979875	+	0.325341i
$867$	−3.94776	−	4.34692i	−0.134073	−	0.147629i
$868$	2.75481	+	9.28188i	0.0935045	+	0.315048i
$869$	15.5972	−	5.17863i	0.529099	−	0.175673i
$870$	0.922092	−	0.179577i	0.0312619	−	0.00608825i
$871$	−2.48581	+	10.8911i	−0.0842285	+	0.369029i
$872$	0.914790	+	0.440539i	0.0309787	+	0.0149185i
$873$	−17.0531	+	16.5151i	−0.577162	+	0.558950i
$874$	2.64011	−	16.3300i	0.0893032	−	0.552372i
$875$	8.77631	+	11.0051i	0.296693	+	0.372042i
$876$	12.6689	+	34.4255i	0.428043	+	1.16313i
$877$	1.08105	−	33.7111i	0.0365044	−	1.13834i	−0.803342	−	0.595518i	$-0.796947\pi$
$877$	1.08105	−	33.7111i	0.0365044	−	1.13834i	0.839846	−	0.542825i	$-0.182645\pi$
$878$	32.9073	+	10.9260i	1.11057	+	0.368733i
$879$	22.7827	+	2.93751i	0.768443	+	0.0990798i
$880$	21.4264	+	2.76263i	0.722285	+	0.0931283i
$881$	−12.9571	+	16.2477i	−0.436535	+	0.547398i	−0.950626	−	0.310338i	$-0.899558\pi$
$881$	−12.9571	+	16.2477i	−0.436535	+	0.547398i	0.514091	+	0.857736i	$0.328129\pi$
$882$	1.36891	−	14.1902i	0.0460936	−	0.477809i
$883$	33.5774	+	18.9104i	1.12997	+	0.636386i	0.938557	−	0.345124i	$-0.112163\pi$
$883$	33.5774	+	18.9104i	1.12997	+	0.636386i	0.191411	+	0.981510i	$0.438694\pi$
$884$	−4.75640	+	3.09608i	−0.159975	+	0.104132i
$885$	−1.86477	−	2.67329i	−0.0626836	−	0.0898616i
$886$	31.8735	+	8.35821i	1.07081	+	0.280799i
$887$	12.6672	+	3.32174i	0.425324	+	0.111533i	0.460110	−	0.887862i	$-0.347810\pi$
$887$	12.6672	+	3.32174i	0.425324	+	0.111533i	−0.0347864	+	0.999395i	$0.511075\pi$
$888$	−0.181095	−	0.259614i	−0.00607716	−	0.00871207i
$889$	14.6314	−	9.52397i	0.490720	−	0.319424i
$890$	−11.8163	−	6.65479i	−0.396082	−	0.223069i
$891$	0.956970	−	9.92000i	0.0320597	−	0.332332i
$892$	11.7082	−	14.6816i	0.392018	−	0.491575i
$893$	5.45546	+	0.703404i	0.182560	+	0.0235385i
$894$	17.3357	+	2.23519i	0.579791	+	0.0747558i
$895$	−22.4580	−	7.45657i	−0.750689	−	0.249246i
$896$	−0.0206331	+	0.643416i	−0.000689304	+	0.0214950i
$897$	−1.30968	−	3.55882i	−0.0437289	−	0.118826i
$898$	42.4739	+	53.2606i	1.41737	+	1.77733i
$899$	0.126675	−	0.783529i	0.00422484	−	0.0261322i
$900$	2.37541	−	2.30046i	0.0791804	−	0.0766820i
$901$	−17.6879	−	8.51805i	−0.589270	−	0.283777i
$902$	9.57200	−	41.9377i	0.318713	−	1.39637i
$903$	−10.6674	+	2.07748i	−0.354990	+	0.0691343i
$904$	−0.888010	+	0.294840i	−0.0295348	+	0.00980622i
$905$	1.37572	+	4.63524i	0.0457304	+	0.154081i
$906$	28.0541	+	30.8907i	0.932035	+	1.02627i
$907$	36.5963	+	12.1508i	1.21516	+	0.403461i	0.849650	−	0.527347i	$-0.176813\pi$
$907$	36.5963	+	12.1508i	1.21516	+	0.403461i	0.365509	+	0.930808i	$0.380895\pi$
$908$	13.6581	−	17.1267i	0.453261	−	0.568371i
$909$	9.25839	+	10.1945i	0.307081	+	0.338131i
$910$	2.06648	−	2.96246i	0.0685032	−	0.0982045i
$911$	−32.0528	−	31.0414i	−1.06196	−	1.02845i	−0.999538	−	0.0303977i	$-0.990323\pi$
$911$	−32.0528	−	31.0414i	−1.06196	−	1.02845i	−0.0624189	−	0.998050i	$-0.519881\pi$
$912$	−6.53135	−	10.7741i	−0.216275	−	0.356768i
$913$	−1.27578	−	0.952138i	−0.0422221	−	0.0315112i
$914$	1.02131	+	6.31716i	0.0337819	+	0.208953i
$915$	−6.53687	+	7.19782i	−0.216102	+	0.237953i
$916$	7.19697	+	31.5320i	0.237794	+	1.04185i
$917$	−10.2780	+	4.94963i	−0.339410	+	0.163451i
$918$	−13.6802	+	37.1734i	−0.451513	+	1.22691i
$919$	9.94520	−	8.46647i	0.328062	−	0.279283i	−0.468978	−	0.883210i	$-0.655378\pi$
$919$	9.94520	−	8.46647i	0.328062	−	0.279283i	0.797040	+	0.603927i	$0.206398\pi$
$920$	0.268430	−	0.384814i	0.00884987	−	0.0126869i
$921$	−1.24343	+	38.7748i	−0.0409725	+	1.27767i
$922$	−2.67975	+	27.7785i	−0.0882530	+	0.914835i
$923$	0.287839	+	0.969824i	0.00947432	+	0.0319221i
$924$	6.33783	−	5.39548i	0.208499	−	0.177498i
$925$	3.69206	−	2.75545i	0.121394	−	0.0905988i
$926$	−32.3033	−	61.9194i	−1.06155	−	2.03480i
$927$	14.2642	−	0.915790i	0.468497	−	0.0300785i
$928$	−0.688748	+	1.32020i	−0.0226092	+	0.0433377i
$929$	−24.7841	+	13.9582i	−0.813141	+	0.457952i	−0.840591	−	0.541671i	$-0.817792\pi$
$929$	−24.7841	+	13.9582i	−0.813141	+	0.457952i	0.0274498	+	0.999623i	$0.491261\pi$
$930$	−8.63045	−	19.4963i	−0.283004	−	0.639310i
$931$	3.78295	−	12.7460i	0.123981	−	0.417734i
$932$	45.4875	+	18.4159i	1.48999	+	0.603232i
$933$	8.48229	−	6.33050i	0.277698	−	0.207251i
$934$	22.4296	+	21.7218i	0.733919	+	0.710761i
$935$	−6.49429	−	17.6471i	−0.212386	−	0.577121i
$936$	0.0623980	+	0.0351419i	0.00203954	+	0.00114865i
$937$	12.8826	−	4.27731i	0.420856	−	0.139734i	−0.0968372	−	0.995300i	$-0.530873\pi$
$937$	12.8826	−	4.27731i	0.420856	−	0.139734i	0.517693	+	0.855566i	$0.326791\pi$
$938$	−10.9353	+	29.7147i	−0.357050	+	0.970219i
$939$	−29.4194	−	11.9106i	−0.960065	−	0.388687i
$940$	−7.38007	−	4.80389i	−0.240711	−	0.156686i
$941$	1.53117	+	15.8721i	0.0499146	+	0.517417i	0.986128	+	0.165985i	$0.0530805\pi$
$941$	1.53117	+	15.8721i	0.0499146	+	0.517417i	−0.936214	+	0.351431i	$0.885695\pi$
$942$	1.12811	−	2.54842i	0.0367558	−	0.0830320i
$943$	−20.9628	−	17.8459i	−0.682644	−	0.581143i
$944$	5.24565	+	0.336782i	0.170731	+	0.0109613i
$945$	−0.400461	−	12.4879i	−0.0130270	−	0.406230i
$946$	−32.8879	−	21.4076i	−1.06928	−	0.696022i
$947$	−18.4840	−	35.4304i	−0.600650	−	1.15133i	−0.974614	−	0.223891i	$-0.928124\pi$
$947$	−18.4840	−	35.4304i	−0.600650	−	1.15133i	0.373964	−	0.927443i	$-0.377998\pi$
$948$	7.95402	+	13.1210i	0.258334	+	0.426150i
$949$	−7.20891	−	9.03969i	−0.234011	−	0.293441i
$950$	5.21507	−	3.39463i	0.169199	−	0.110136i
$951$	24.1092	−	4.69526i	0.781793	−	0.152254i
$952$	0.256773	−	0.123656i	0.00832207	−	0.00400770i
$953$	−1.32310	+	4.45797i	−0.0428595	+	0.144408i	−0.977375	−	0.211515i	$-0.932160\pi$
$953$	−1.32310	+	4.45797i	−0.0428595	+	0.144408i	0.934515	+	0.355923i	$0.115834\pi$
$954$	−0.448150	−	13.9750i	−0.0145094	−	0.452457i
$955$	15.4559	−	6.25740i	0.500141	−	0.202485i
$956$	42.1465	+	8.20802i	1.36311	+	0.265466i
$957$	−0.660010	+	0.173075i	−0.0213351	+	0.00559472i
$958$	11.9705	−	19.7466i	0.386749	−	0.637983i
$959$	−3.90531	+	1.58109i	−0.126109	+	0.0510559i
$960$	1.86988	+	19.3833i	0.0603502	+	0.625593i
$961$	12.9593	−	0.832014i	0.418041	−	0.0268391i
$962$	−4.51296	−	3.36811i	−0.145504	−	0.108592i
$963$	−0.111756	+	0.691251i	−0.00360129	+	0.0222752i
$964$	−10.8467	−	15.5495i	−0.349348	−	0.500816i
$965$	2.34479	−	10.2732i	0.0754815	−	0.330706i
$966$	−2.39173	−	10.4788i	−0.0769526	−	0.337151i
$967$	3.20204	+	7.23347i	0.102971	+	0.232613i	0.958471	−	0.285189i	$-0.0920565\pi$
$967$	3.20204	+	7.23347i	0.102971	+	0.232613i	−0.855500	+	0.517802i	$0.826750\pi$
$968$	0.229698	+	0.0147471i	0.00738278	+	0.000473990i
$969$	−5.68494	+	9.37791i	−0.182627	+	0.301262i
$970$	70.9274	−	9.14508i	2.27734	−	0.293631i
$971$	11.0415			0.354339			0.177169	−	0.984180i	$-0.443306\pi$
$971$	11.0415			0.354339			0.177169	+	0.984180i	$0.443306\pi$
$972$	−23.6174	+	3.04512i	−0.757527	+	0.0976723i
$973$	−19.2998	−	3.75864i	−0.618724	−	0.120496i
$974$	−4.25597	+	9.61431i	−0.136370	+	0.308062i
$975$	0.659803	−	1.26472i	0.0211306	−	0.0405034i
$976$	−2.50260	−	15.4795i	−0.0801062	−	0.495485i
$977$	−22.3225	+	21.6181i	−0.714160	+	0.691625i	−0.960725	−	0.277501i	$-0.910494\pi$
$977$	−22.3225	+	21.6181i	−0.714160	+	0.691625i	0.246566	+	0.969126i	$0.420698\pi$
$978$	−34.6154	−	9.07722i	−1.10688	−	0.290257i
$979$	8.87456	+	4.27376i	0.283632	+	0.136590i
$980$	−14.3096	+	15.7565i	−0.457105	+	0.503323i
$981$	16.1615	−	9.10200i	0.515998	−	0.290604i
$982$	23.2665	+	19.8071i	0.742465	+	0.632070i
$983$	37.7022	−	9.88669i	1.20251	−	0.315336i	0.402558	−	0.915395i	$-0.368121\pi$
$983$	37.7022	−	9.88669i	1.20251	−	0.315336i	0.799956	+	0.600058i	$0.204856\pi$
$984$	−0.711544			−0.0226832
$985$	2.42848	+	26.7839i	0.0773779	+	0.853407i
$986$	1.31866			0.0419947
$987$	3.45718	−	0.906578i	0.110043	−	0.0288567i
$988$	−2.87040	−	2.44361i	−0.0913195	−	0.0777415i
$989$	−21.8828	+	12.3241i	−0.695831	+	0.391885i
$990$	9.00377	−	9.91415i	0.286159	−	0.315093i
$991$	4.97100	+	2.39391i	0.157909	+	0.0760449i	0.511169	−	0.859480i	$-0.329213\pi$
$991$	4.97100	+	2.39391i	0.157909	+	0.0760449i	−0.353260	+	0.935525i	$0.614927\pi$
$992$	32.6907	+	8.57251i	1.03793	+	0.272178i
$993$	−8.61397	+	8.34216i	−0.273356	+	0.264731i
$994$	0.457627	+	2.83058i	0.0145150	+	0.0897806i
$995$	2.13838	−	4.09888i	0.0677912	−	0.129943i
$996$	0.601608	−	1.35904i	0.0190627	−	0.0430630i
$997$	−36.4224	−	7.09326i	−1.15351	−	0.224646i	−0.422076	−	0.906560i	$-0.638699\pi$
$997$	−36.4224	−	7.09326i	−1.15351	−	0.224646i	−0.731432	+	0.681915i	$0.761148\pi$
$998$	−57.5960	+	7.42619i	−1.82317	+	0.235072i
$999$	−19.4791			−0.616291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.g.a.100.4	✓	630
197.132	even	49	inner	197.2.g.a.132.4	yes	630

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.g.a.100.4	✓	630	1.1	even	1	trivial
197.2.g.a.132.4	yes	630	197.132	even	49	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.g (of order \(49\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92615 + 0.505096i) q^{2} +(1.00252 + 0.853459i) q^{3} +(1.71230 - 0.964349i) q^{4} +(1.28820 - 1.41845i) q^{5} +(-2.36209 - 1.13752i) q^{6} +(1.12284 + 0.294444i) q^{7} +(0.0498044 - 0.0482328i) q^{8} +(-0.202143 - 1.25032i) q^{9} +(-1.76481 + 3.38282i) q^{10} +(1.12178 - 2.53412i) q^{11} +(2.53965 + 0.494597i) q^{12} +(-0.808829 + 0.104287i) q^{13} -2.31148 q^{14} +(2.50204 - 0.322602i) q^{15} +(-2.10904 + 3.47908i) q^{16} +(3.53391 + 0.226885i) q^{17} +(1.02089 + 2.30621i) q^{18} +(0.523401 + 2.29317i) q^{19} +(0.837902 - 3.67109i) q^{20} +(0.874377 + 1.25349i) q^{21} +(-0.880742 + 5.44770i) q^{22} +(2.83043 + 2.11240i) q^{23} +(0.0910947 - 0.00584847i) q^{24} +(0.127571 + 1.32240i) q^{25} +(1.50525 - 0.609409i) q^{26} +(2.91200 - 4.80365i) q^{27} +(2.20659 - 0.578635i) q^{28} +(-0.183556 - 0.0357476i) q^{29} +(-4.65636 + 1.88515i) q^{30} +(0.136036 + 4.24211i) q^{31} +(2.26561 - 7.63358i) q^{32} +(3.28737 - 1.58312i) q^{33} +(-6.92145 + 1.34795i) q^{34} +(1.86410 - 1.21339i) q^{35} +(-1.55188 - 1.94599i) q^{36} +(-1.79761 - 2.96534i) q^{37} +(-2.16642 - 4.15262i) q^{38} +(-0.899873 - 0.585752i) q^{39} +(-0.00425795 - 0.132778i) q^{40} +(-7.77897 - 0.499427i) q^{41} +(-2.31731 - 1.97276i) q^{42} +(-2.87841 + 6.50237i) q^{43} +(-0.522953 - 5.42096i) q^{44} +(-2.03392 - 1.32394i) q^{45} +(-6.51880 - 2.63917i) q^{46} +(0.807657 - 2.19466i) q^{47} +(-5.08361 + 1.68788i) q^{48} +(-4.92516 - 2.77380i) q^{49} +(-0.913661 - 2.48271i) q^{50} +(3.34919 + 3.24351i) q^{51} +(-1.28439 + 0.958564i) q^{52} +(-5.13876 - 2.08045i) q^{53} +(-3.18265 + 10.7234i) q^{54} +(-2.14945 - 4.85564i) q^{55} +(0.0701242 - 0.0394932i) q^{56} +(-1.43240 + 2.74565i) q^{57} +(0.371613 - 0.0238583i) q^{58} +(-0.597605 - 1.14550i) q^{59} +(3.97314 - 2.96523i) q^{60} +(-2.93475 + 2.49839i) q^{61} +(-2.40470 - 8.10224i) q^{62} +(0.141176 - 1.46343i) q^{63} +(-0.247409 + 7.71511i) q^{64} +(-0.894007 + 1.28163i) q^{65} +(-5.53235 + 4.70976i) q^{66} +(4.73085 - 12.8552i) q^{67} +(6.26992 - 3.01943i) q^{68} +(1.03471 + 4.53338i) q^{69} +(-2.97765 + 3.27873i) q^{70} +(-0.197980 - 1.22457i) q^{71} +(-0.0703742 - 0.0525216i) q^{72} +(7.34958 + 12.1239i) q^{73} +(4.96025 + 4.80374i) q^{74} +(-1.00072 + 1.43461i) q^{75} +(3.10763 + 3.42185i) q^{76} +(2.00573 - 2.51511i) q^{77} +(2.02915 + 0.673725i) q^{78} +(3.98689 + 4.39001i) q^{79} +(2.21804 + 7.47332i) q^{80} +(3.41295 - 1.13318i) q^{81} +(15.2357 - 2.96716i) q^{82} +(0.127822 - 0.560024i) q^{83} +(2.70599 + 1.30314i) q^{84} +(4.87421 - 4.72041i) q^{85} +(2.25992 - 13.9784i) q^{86} +(-0.153510 - 0.192495i) q^{87} +(-0.0663582 - 0.180317i) q^{88} +(-0.113920 + 3.55246i) q^{89} +(4.58636 + 1.52278i) q^{90} +(-0.938893 - 0.121057i) q^{91} +(6.88363 + 0.887546i) q^{92} +(-3.48409 + 4.36891i) q^{93} +(-0.447152 + 4.63520i) q^{94} +(3.92699 + 2.21164i) q^{95} +(8.78626 - 5.71922i) q^{96} +(-10.7233 - 15.3726i) q^{97} +(10.8876 + 2.85507i) q^{98} +(-3.39523 - 0.890333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 630 q - 42 q^{2} - 42 q^{3} - 28 q^{4} - 42 q^{5} - 21 q^{6} - 28 q^{7} - 28 q^{8} - 42 q^{9} - 28 q^{10} - 28 q^{11} - 28 q^{12} - 42 q^{13} - 28 q^{14} - 154 q^{15} - 42 q^{17} - 21 q^{18} - 7 q^{19}+ \cdots - 161 q^{99}+O(q^{100}) \) 630 * q - 42 * q^2 - 42 * q^3 - 28 * q^4 - 42 * q^5 - 21 * q^6 - 28 * q^7 - 28 * q^8 - 42 * q^9 - 28 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 - 28 * q^14 - 154 * q^15 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 35 * q^20 - 42 * q^21 - 42 * q^23 + 28 * q^24 - 42 * q^25 - 7 * q^26 + 42 * q^27 - 49 * q^28 - 182 * q^29 + 77 * q^30 - 14 * q^31 - 28 * q^32 + 35 * q^33 - 14 * q^34 - 42 * q^35 + 84 * q^36 + 14 * q^37 - 28 * q^38 - 21 * q^39 + 28 * q^40 - 28 * q^41 - 112 * q^42 - 56 * q^43 - 210 * q^44 + 49 * q^45 - 7 * q^47 + 42 * q^48 + 42 * q^49 + 98 * q^50 - 14 * q^51 + 49 * q^52 - 42 * q^53 + 63 * q^54 - 161 * q^56 - 175 * q^57 - 42 * q^58 + 42 * q^59 + 126 * q^60 - 14 * q^61 + 42 * q^62 + 49 * q^63 + 98 * q^64 + 56 * q^65 + 175 * q^66 + 28 * q^67 + 273 * q^68 - 7 * q^69 - 252 * q^70 - 77 * q^71 - 364 * q^72 - 28 * q^73 + 35 * q^74 + 7 * q^75 + 133 * q^76 + 21 * q^77 + 210 * q^78 + 42 * q^79 - 14 * q^80 - 14 * q^81 - 42 * q^82 + 161 * q^83 - 245 * q^84 - 266 * q^85 - 147 * q^86 - 35 * q^87 + 77 * q^88 + 28 * q^89 + 315 * q^90 + 154 * q^91 + 84 * q^92 - 7 * q^93 + 182 * q^94 + 126 * q^95 + 245 * q^96 + 42 * q^97 - 308 * q^98 - 161 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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