LMFDB - Embedded newform 990.2.bg.a.301.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] 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("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			301.5
Character	$\chi$	$=$	990.301
Dual form			990.2.bg.a.421.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.845166 - 1.51185i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(1.59191 - 0.682504i) q^{6} +(3.24799 - 3.60726i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.57139 + 2.55553i) q^{9} +1.00000 q^{10} +(2.72632 + 1.88870i) q^{11} +(0.512365 + 1.65453i) q^{12} +(-0.947048 + 0.421653i) q^{13} +(3.24799 + 3.60726i) q^{14} +(-1.41523 + 0.998567i) q^{15} +(0.913545 + 0.406737i) q^{16} +(5.36196 - 3.89569i) q^{17} +(-2.37728 - 1.82991i) q^{18} +(-1.19530 + 3.67875i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(-8.19873 - 1.86175i) q^{21} +(-2.16333 + 2.51396i) q^{22} +(1.73527 - 3.00558i) q^{23} +(-1.69903 + 0.336613i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(-0.320349 - 0.985934i) q^{26} +(5.19167 + 0.215861i) q^{27} +(-3.92700 + 2.85314i) q^{28} +(4.51647 - 5.01604i) q^{29} +(-0.845166 - 1.51185i) q^{30} +(-6.89732 + 3.07088i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.551242 - 5.71805i) q^{33} +(3.31387 + 5.73980i) q^{34} +(-3.92700 - 2.85314i) q^{35} +(2.06838 - 2.17298i) q^{36} +(1.14144 + 3.51298i) q^{37} +(-3.53365 - 1.57328i) q^{38} +(1.43789 + 1.07543i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(-7.47930 - 8.30660i) q^{41} +(2.70855 - 7.95921i) q^{42} +(-4.30459 - 7.45578i) q^{43} +(-2.27406 - 2.41426i) q^{44} +(2.70579 + 1.29566i) q^{45} +(2.80773 + 2.03993i) q^{46} +(-4.19337 + 0.891329i) q^{47} +(-0.157172 - 1.72490i) q^{48} +(-1.73117 - 16.4710i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-10.4215 - 4.81398i) q^{51} +(1.01402 - 0.215536i) q^{52} +(0.579223 + 0.420830i) q^{53} +(-0.757356 + 5.14066i) q^{54} +(1.59338 - 2.90881i) q^{55} +(-2.42702 - 4.20373i) q^{56} +(6.57195 - 1.30204i) q^{57} +(4.51647 + 5.01604i) q^{58} +(11.9772 + 2.54584i) q^{59} +(1.59191 - 0.682504i) q^{60} +(3.04976 + 1.35784i) q^{61} +(-2.33309 - 7.18053i) q^{62} +(4.11460 + 13.9687i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.518336 + 0.897785i) q^{65} +(5.62911 + 1.14592i) q^{66} +(2.20207 - 3.81410i) q^{67} +(-6.05475 + 2.69575i) q^{68} +(-6.01058 - 0.0832607i) q^{69} +(3.24799 - 3.60726i) q^{70} +(-0.537178 + 0.390282i) q^{71} +(1.94487 + 2.28418i) q^{72} +(2.15909 + 6.64500i) q^{73} +(-3.61305 + 0.767977i) q^{74} +(1.14103 + 1.30309i) q^{75} +(1.93403 - 3.34984i) q^{76} +(15.6681 - 3.70006i) q^{77} +(-1.21984 + 1.31760i) q^{78} +(0.305998 - 2.91137i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-4.06147 - 8.03147i) q^{81} +(9.04290 - 6.57005i) q^{82} +(-6.86527 - 3.05662i) q^{83} +(7.63249 + 3.52567i) q^{84} +(-4.43483 - 4.92538i) q^{85} +(7.86489 - 3.50167i) q^{86} +(-11.4007 - 2.58884i) q^{87} +(2.63874 - 2.00924i) q^{88} +9.51896 q^{89} +(-1.57139 + 2.55553i) q^{90} +(-1.55499 + 4.78577i) q^{91} +(-2.32224 + 2.57911i) q^{92} +(10.4721 + 7.83231i) q^{93} +(-0.448119 - 4.26357i) q^{94} +(3.78354 + 0.804216i) q^{95} +(1.73188 + 0.0239907i) q^{96} +(-0.721757 + 6.86706i) q^{97} +16.5617 q^{98} +(-9.11074 + 3.99931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.845166	−	1.51185i	−0.487957	−	0.872868i
$3$	−0.845166	−	1.51185i	−0.487957	−	0.872868i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$6$	1.59191	−	0.682504i	0.649896	−	0.278631i
$7$	3.24799	−	3.60726i	1.22762	−	1.36342i	0.317942	−	0.948110i	$-0.397008\pi$
$7$	3.24799	−	3.60726i	1.22762	−	1.36342i	0.909682	−	0.415305i	$-0.136325\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.57139	+	2.55553i	−0.523797	+	0.851843i
$10$	1.00000			0.316228
$11$	2.72632	+	1.88870i	0.822016	+	0.569464i
$11$	2.72632	+	1.88870i	0.822016	+	0.569464i
$12$	0.512365	+	1.65453i	0.147907	+	0.477623i
$13$	−0.947048	+	0.421653i	−0.262664	+	0.116945i	−0.533844	−	0.845583i	$-0.679253\pi$
$13$	−0.947048	+	0.421653i	−0.262664	+	0.116945i	0.271180	+	0.962529i	$0.412586\pi$
$14$	3.24799	+	3.60726i	0.868062	+	0.964080i
$15$	−1.41523	+	0.998567i	−0.365410	+	0.257829i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	5.36196	−	3.89569i	1.30047	−	0.944844i	0.300506	−	0.953780i	$-0.402844\pi$
$17$	5.36196	−	3.89569i	1.30047	−	0.944844i	0.999960	+	0.00893564i	$0.00284434\pi$
$18$	−2.37728	−	1.82991i	−0.560329	−	0.431313i
$19$	−1.19530	+	3.67875i	−0.274220	+	0.843963i	0.715204	+	0.698915i	$0.246334\pi$
$19$	−1.19530	+	3.67875i	−0.274220	+	0.843963i	−0.989425	+	0.145048i	$0.953666\pi$
$20$	−0.104528	+	0.994522i	−0.0233733	+	0.222382i
$21$	−8.19873	−	1.86175i	−1.78911	−	0.406266i
$22$	−2.16333	+	2.51396i	−0.461224	+	0.535978i
$23$	1.73527	−	3.00558i	0.361829	−	0.626706i	−0.626433	−	0.779475i	$-0.715486\pi$
$23$	1.73527	−	3.00558i	0.361829	−	0.626706i	0.988262	+	0.152769i	$0.0488191\pi$
$24$	−1.69903	+	0.336613i	−0.346812	+	0.0687108i
$25$	−0.978148	+	0.207912i	−0.195630	+	0.0415823i
$26$	−0.320349	−	0.985934i	−0.0628257	−	0.193358i
$27$	5.19167	+	0.215861i	0.999137	+	0.0415425i
$28$	−3.92700	+	2.85314i	−0.742134	+	0.539192i
$29$	4.51647	−	5.01604i	0.838687	−	0.931456i	−0.159761	−	0.987156i	$-0.551072\pi$
$29$	4.51647	−	5.01604i	0.838687	−	0.931456i	0.998448	+	0.0556998i	$0.0177390\pi$
$30$	−0.845166	−	1.51185i	−0.154305	−	0.276025i
$31$	−6.89732	+	3.07088i	−1.23879	+	0.551547i	−0.918368	−	0.395727i	$-0.870493\pi$
$31$	−6.89732	+	3.07088i	−1.23879	+	0.551547i	−0.320426	+	0.947273i	$0.603826\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.551242	−	5.71805i	0.0959589	−	0.995385i
$34$	3.31387	+	5.73980i	0.568325	+	0.984367i
$35$	−3.92700	−	2.85314i	−0.663785	−	0.482268i
$36$	2.06838	−	2.17298i	0.344729	−	0.362163i
$37$	1.14144	+	3.51298i	0.187651	+	0.577530i	0.999984	−	0.00566374i	$-0.00180283\pi$
$37$	1.14144	+	3.51298i	0.187651	+	0.577530i	−0.812333	+	0.583194i	$0.801803\pi$
$38$	−3.53365	−	1.57328i	−0.573234	−	0.255220i
$39$	1.43789	+	1.07543i	0.230246	+	0.172206i
$40$	−0.978148	−	0.207912i	−0.154659	−	0.0328737i
$41$	−7.47930	−	8.30660i	−1.16807	−	1.29727i	−0.946712	−	0.322081i	$-0.895618\pi$
$41$	−7.47930	−	8.30660i	−1.16807	−	1.29727i	−0.221358	−	0.975193i	$-0.571049\pi$
$42$	2.70855	−	7.95921i	0.417938	−	1.22813i
$43$	−4.30459	−	7.45578i	−0.656445	−	1.13700i	−0.981530	−	0.191310i	$-0.938726\pi$
$43$	−4.30459	−	7.45578i	−0.656445	−	1.13700i	0.325085	−	0.945685i	$-0.394607\pi$
$44$	−2.27406	−	2.41426i	−0.342827	−	0.363963i
$45$	2.70579	+	1.29566i	0.403355	+	0.193145i
$46$	2.80773	+	2.03993i	0.413977	+	0.300772i
$47$	−4.19337	+	0.891329i	−0.611666	+	0.130014i	−0.503321	−	0.864100i	$-0.667889\pi$
$47$	−4.19337	+	0.891329i	−0.611666	+	0.130014i	−0.108346	+	0.994113i	$0.534555\pi$
$48$	−0.157172	−	1.72490i	−0.0226858	−	0.248969i
$49$	−1.73117	−	16.4710i	−0.247310	−	2.35300i
$50$	−0.104528	−	0.994522i	−0.0147826	−	0.140647i
$51$	−10.4215	−	4.81398i	−1.45930	−	0.674092i
$52$	1.01402	−	0.215536i	0.140619	−	0.0298895i
$53$	0.579223	+	0.420830i	0.0795624	+	0.0578055i	0.626855	−	0.779136i	$-0.284342\pi$
$53$	0.579223	+	0.420830i	0.0795624	+	0.0578055i	−0.547293	+	0.836941i	$0.684342\pi$
$54$	−0.757356	+	5.14066i	−0.103063	+	0.699556i
$55$	1.59338	−	2.90881i	0.214851	−	0.392223i
$56$	−2.42702	−	4.20373i	−0.324324	−	0.561746i
$57$	6.57195	−	1.30204i	0.870476	−	0.172459i
$58$	4.51647	+	5.01604i	0.593041	+	0.658639i
$59$	11.9772	+	2.54584i	1.55930	+	0.331440i	0.905206	−	0.424973i	$-0.139717\pi$
$59$	11.9772	+	2.54584i	1.55930	+	0.331440i	0.654095	+	0.756413i	$0.273050\pi$
$60$	1.59191	−	0.682504i	0.205515	−	0.0881109i
$61$	3.04976	+	1.35784i	0.390482	+	0.173854i	0.592580	−	0.805512i	$-0.298109\pi$
$61$	3.04976	+	1.35784i	0.390482	+	0.173854i	−0.202098	+	0.979365i	$0.564776\pi$
$62$	−2.33309	−	7.18053i	−0.296303	−	0.911928i
$63$	4.11460	+	13.9687i	0.518391	+	1.75990i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.518336	+	0.897785i	0.0642917	+	0.111357i
$66$	5.62911	+	1.14592i	0.692895	+	0.141053i
$67$	2.20207	−	3.81410i	0.269026	−	0.465967i	−0.699585	−	0.714550i	$-0.746632\pi$
$67$	2.20207	−	3.81410i	0.269026	−	0.465967i	0.968611	+	0.248583i	$0.0799649\pi$
$68$	−6.05475	+	2.69575i	−0.734246	+	0.326907i
$69$	−6.01058	−	0.0832607i	−0.723588	−	0.0100234i
$70$	3.24799	−	3.60726i	0.388209	−	0.431150i
$71$	−0.537178	+	0.390282i	−0.0637512	+	0.0463180i	−0.619204	−	0.785230i	$-0.712545\pi$
$71$	−0.537178	+	0.390282i	−0.0637512	+	0.0463180i	0.555453	+	0.831548i	$0.312545\pi$
$72$	1.94487	+	2.28418i	0.229205	+	0.269194i
$73$	2.15909	+	6.64500i	0.252703	+	0.777739i	0.994274	+	0.106864i	$0.0340810\pi$
$73$	2.15909	+	6.64500i	0.252703	+	0.777739i	−0.741571	+	0.670874i	$0.765919\pi$
$74$	−3.61305	+	0.767977i	−0.420008	+	0.0892755i
$75$	1.14103	+	1.30309i	0.131755	+	0.150468i
$76$	1.93403	−	3.34984i	0.221849	−	0.384253i
$77$	15.6681	−	3.70006i	1.78554	−	0.421661i
$78$	−1.21984	+	1.31760i	−0.138119	+	0.149189i
$79$	0.305998	−	2.91137i	0.0344274	−	0.327555i	−0.963730	−	0.266879i	$-0.914008\pi$
$79$	0.305998	−	2.91137i	0.0344274	−	0.327555i	0.998158	−	0.0606762i	$-0.0193257\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	−4.06147	−	8.03147i	−0.451274	−	0.892385i
$82$	9.04290	−	6.57005i	0.998621	−	0.725541i
$83$	−6.86527	−	3.05662i	−0.753561	−	0.335507i	−0.00624946	−	0.999980i	$-0.501989\pi$
$83$	−6.86527	−	3.05662i	−0.753561	−	0.335507i	−0.747312	+	0.664473i	$0.768656\pi$
$84$	7.63249	+	3.52567i	0.832772	+	0.384683i
$85$	−4.43483	−	4.92538i	−0.481025	−	0.534232i
$86$	7.86489	−	3.50167i	0.848092	−	0.377595i
$87$	−11.4007	−	2.58884i	−1.22228	−	0.277552i
$88$	2.63874	−	2.00924i	0.281291	−	0.214186i
$89$	9.51896			1.00901			0.504504	−	0.863409i	$-0.331675\pi$
$89$	9.51896			1.00901			0.504504	+	0.863409i	$0.331675\pi$
$90$	−1.57139	+	2.55553i	−0.165639	+	0.269377i
$91$	−1.55499	+	4.78577i	−0.163007	+	0.501685i
$92$	−2.32224	+	2.57911i	−0.242111	+	0.268891i
$93$	10.4721	+	7.83231i	1.08591	+	0.812173i
$94$	−0.448119	−	4.26357i	−0.0462200	−	0.439754i
$95$	3.78354	+	0.804216i	0.388183	+	0.0825108i
$96$	1.73188	+	0.0239907i	0.176760	+	0.00244854i
$97$	−0.721757	+	6.86706i	−0.0732833	+	0.697244i	0.894775	+	0.446518i	$0.147336\pi$
$97$	−0.721757	+	6.86706i	−0.0732833	+	0.697244i	−0.968058	+	0.250726i	$0.919331\pi$
$98$	16.5617			1.67299
$99$	−9.11074	+	3.99931i	−0.915664	+	0.401945i
$100$	1.00000			0.100000
$101$	1.42376	−	13.5462i	0.141669	−	1.34790i	−0.660512	−	0.750815i	$-0.729661\pi$
$101$	1.42376	−	13.5462i	0.141669	−	1.34790i	0.802182	−	0.597080i	$-0.203672\pi$
$102$	5.87695	−	9.86117i	0.581905	−	0.976401i
$103$	−8.28983	−	1.76206i	−0.816821	−	0.173621i	−0.219489	−	0.975615i	$-0.570439\pi$
$103$	−8.28983	−	1.76206i	−0.816821	−	0.173621i	−0.597332	+	0.801994i	$0.703772\pi$
$104$	0.108362	+	1.03099i	0.0106257	+	0.101097i
$105$	−0.994548	+	8.34842i	−0.0970579	+	0.814722i
$106$	−0.479070	+	0.532061i	−0.0465314	+	0.0516784i
$107$	−4.15727	+	12.7948i	−0.401899	+	1.23692i	0.521559	+	0.853215i	$0.325351\pi$
$107$	−4.15727	+	12.7948i	−0.401899	+	1.23692i	−0.923457	+	0.383701i	$0.874649\pi$
$108$	−5.03334	−	1.29055i	−0.484333	−	0.124183i
$109$	0.992504			0.0950647			0.0475323	−	0.998870i	$-0.484864\pi$
$109$	0.992504			0.0950647			0.0475323	+	0.998870i	$0.484864\pi$
$110$	2.72632	+	1.88870i	0.259944	+	0.180080i
$111$	4.34640	−	4.69473i	0.412542	−	0.445604i
$112$	4.43439	−	1.97432i	0.419010	−	0.186555i
$113$	−8.16071	−	9.06338i	−0.767695	−	0.852611i	0.224863	−	0.974390i	$-0.427807\pi$
$113$	−8.16071	−	9.06338i	−0.767695	−	0.852611i	−0.992557	+	0.121779i	$0.961140\pi$
$114$	0.607952	+	6.67205i	0.0569399	+	0.624894i
$115$	−3.17050	−	1.41160i	−0.295650	−	0.131632i
$116$	−5.46066	+	3.96741i	−0.507010	+	0.368364i
$117$	0.410634	−	3.08279i	0.0379632	−	0.285004i
$118$	−3.78385	+	11.6455i	−0.348332	+	1.07205i
$119$	3.36282	−	31.9951i	0.308270	−	2.93299i
$120$	0.512365	+	1.65453i	0.0467723	+	0.151038i
$121$	3.86563	+	10.2984i	0.351421	+	0.936218i
$122$	−1.66919	+	2.89112i	−0.151121	+	0.261750i
$123$	−6.23710	+	18.3280i	−0.562381	+	1.65258i
$124$	7.38507	−	1.56974i	0.663199	−	0.140967i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−14.3223	+	2.63193i	−1.27593	+	0.234471i
$127$	5.30109	−	3.85147i	0.470396	−	0.341763i	−0.327200	−	0.944955i	$-0.606105\pi$
$127$	5.30109	−	3.85147i	0.470396	−	0.341763i	0.797596	+	0.603193i	$0.206105\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−7.63393	+	12.8093i	−0.672130	+	1.12779i
$130$	−0.947048	+	0.421653i	−0.0830616	+	0.0369814i
$131$	−2.57362	+	4.45764i	−0.224858	+	0.389466i	−0.956277	−	0.292463i	$-0.905525\pi$
$131$	−2.57362	+	4.45764i	−0.224858	+	0.389466i	0.731419	+	0.681929i	$0.238859\pi$
$132$	−1.72805	+	5.47849i	−0.150407	+	0.476841i
$133$	9.38788	+	16.2603i	0.814032	+	1.40995i
$134$	3.56303	+	2.58869i	0.307799	+	0.223629i
$135$	−0.327998	−	5.18579i	−0.0282296	−	0.446322i
$136$	−2.04809	−	6.30336i	−0.175622	−	0.540509i
$137$	−7.68354	−	3.42093i	−0.656449	−	0.292270i	0.0513531	−	0.998681i	$-0.483647\pi$
$137$	−7.68354	−	3.42093i	−0.656449	−	0.292270i	−0.707802	+	0.706411i	$0.750313\pi$
$138$	0.711081	−	5.96895i	0.0605312	−	0.508110i
$139$	−21.5482	−	4.58021i	−1.82769	−	0.388488i	−0.839708	−	0.543038i	$-0.817274\pi$
$139$	−21.5482	−	4.58021i	−1.82769	−	0.388488i	−0.987985	+	0.154549i	$0.950607\pi$
$140$	3.24799	+	3.60726i	0.274505	+	0.304869i
$141$	4.89165	+	5.58644i	0.411952	+	0.470463i
$142$	−0.331994	−	0.575030i	−0.0278603	−	0.0482555i
$143$	−3.37833	−	0.639129i	−0.282510	−	0.0534466i
$144$	−2.47496	+	1.69545i	−0.206247	+	0.141288i
$145$	−5.46066	−	3.96741i	−0.453484	−	0.329475i
$146$	−6.83429	+	1.45267i	−0.565610	+	0.120224i
$147$	−23.4386	+	16.5380i	−1.93318	+	1.36403i
$148$	−0.386103	−	3.67353i	−0.0317375	−	0.301962i
$149$	2.09787	+	19.9599i	0.171864	+	1.63518i	0.652168	+	0.758075i	$0.273860\pi$
$149$	2.09787	+	19.9599i	0.171864	+	1.63518i	−0.480304	+	0.877102i	$0.659473\pi$
$150$	−1.41523	+	0.998567i	−0.115553	+	0.0815327i
$151$	−0.0870236	+	0.0184974i	−0.00708188	+	0.00150530i	−0.211451	−	0.977389i	$-0.567819\pi$
$151$	−0.0870236	+	0.0184974i	−0.00708188	+	0.00150530i	0.204369	+	0.978894i	$0.434486\pi$
$152$	3.12933	+	2.27359i	0.253822	+	0.184413i
$153$	1.52983	+	19.8243i	0.123679	+	1.60270i
$154$	2.04203	+	15.9690i	0.164551	+	1.28682i
$155$	3.77503	+	6.53854i	0.303217	+	0.525188i
$156$	−1.18287	−	1.35088i	−0.0947056	−	0.108157i
$157$	5.07749	+	5.63912i	0.405228	+	0.450051i	0.910871	−	0.412692i	$-0.135411\pi$
$157$	5.07749	+	5.63912i	0.405228	+	0.450051i	−0.505643	+	0.862743i	$0.668745\pi$
$158$	2.86344	+	0.608643i	0.227803	+	0.0484210i
$159$	0.146693	−	1.23137i	0.0116335	−	0.0976540i
$160$	0.913545	+	0.406737i	0.0722221	+	0.0321554i
$161$	−5.20575	−	16.0216i	−0.410270	−	1.26268i
$162$	8.41201	−	3.19970i	0.660910	−	0.251392i
$163$	6.23975	+	4.53345i	0.488735	+	0.355087i	0.804698	−	0.593685i	$-0.202327\pi$
$163$	6.23975	+	4.53345i	0.488735	+	0.355087i	−0.315962	+	0.948772i	$0.602327\pi$
$164$	5.58882	+	9.68012i	0.436413	+	0.755890i
$165$	−5.74435	+	0.0494772i	−0.447197	+	0.00385179i
$166$	3.75749	−	6.50816i	0.291638	−	0.505131i
$167$	19.3005	−	8.59316i	1.49352	−	0.664958i	0.512469	−	0.858705i	$-0.328731\pi$
$167$	19.3005	−	8.59316i	1.49352	−	0.664958i	0.981052	+	0.193747i	$0.0620641\pi$
$168$	−4.30417	+	7.22214i	−0.332074	+	0.557200i
$169$	−7.97959	+	8.86223i	−0.613815	+	0.681710i
$170$	5.36196	−	3.89569i	0.411244	−	0.298786i
$171$	−7.52288	−	8.83537i	−0.575289	−	0.675658i
$172$	2.66039	+	8.18783i	0.202853	+	0.624316i
$173$	10.3536	−	2.20073i	0.787170	−	0.167318i	0.203247	−	0.979127i	$-0.434851\pi$
$173$	10.3536	−	2.20073i	0.787170	−	0.167318i	0.583923	+	0.811809i	$0.301517\pi$
$174$	3.76635	−	11.0676i	0.285526	−	0.839034i
$175$	−2.42702	+	4.20373i	−0.183466	+	0.317772i
$176$	1.72241	+	2.83431i	0.129832	+	0.213644i
$177$	−6.27381	−	20.2594i	−0.471568	−	1.52279i
$178$	−0.995002	+	9.46681i	−0.0745786	+	0.709568i
$179$	−2.55860	+	7.87456i	−0.191239	+	0.588572i	0.808761	+	0.588137i	$0.200138\pi$
$179$	−2.55860	+	7.87456i	−0.191239	+	0.588572i	−1.00000		0.000434881i	$0.999862\pi$
$180$	−2.37728	−	1.82991i	−0.177192	−	0.136393i
$181$	4.34697	−	3.15826i	0.323108	−	0.234751i	−0.414393	−	0.910098i	$-0.636006\pi$
$181$	4.34697	−	3.15826i	0.323108	−	0.234751i	0.737500	+	0.675347i	$0.236006\pi$
$182$	−4.59701	−	2.04672i	−0.340753	−	0.151713i
$183$	−0.524699	−	5.75838i	−0.0387869	−	0.425672i
$184$	−2.32224	−	2.57911i	−0.171198	−	0.190135i
$185$	3.37442	−	1.50239i	0.248092	−	0.110458i
$186$	−8.88404	+	9.59603i	−0.651409	+	0.703615i
$187$	21.9762	−	0.493767i	1.60706	−	0.0361078i
$188$	4.28706			0.312666
$189$	17.6411	−	18.0266i	1.28320	−	1.31124i
$190$	−1.19530	+	3.67875i	−0.0867160	+	0.266885i
$191$	−10.8905	+	12.0951i	−0.788006	+	0.875170i	−0.994656	−	0.103245i	$-0.967077\pi$
$191$	−10.8905	+	12.0951i	−0.788006	+	0.875170i	0.206650	+	0.978415i	$0.433744\pi$
$192$	−0.204891	+	1.71989i	−0.0147867	+	0.124122i
$193$	2.32546	+	22.1253i	0.167390	+	1.59261i	0.679488	+	0.733687i	$0.262202\pi$
$193$	2.32546	+	22.1253i	0.167390	+	1.59261i	−0.512097	+	0.858927i	$0.671131\pi$
$194$	−6.75399	−	1.43561i	−0.484909	−	0.103070i
$195$	0.919237	−	1.54242i	0.0658279	−	0.110455i
$196$	−1.73117	+	16.4710i	−0.123655	+	1.17650i
$197$	13.6473			0.972331			0.486166	−	0.873867i	$-0.338395\pi$
$197$	13.6473			0.972331			0.486166	+	0.873867i	$0.338395\pi$
$198$	−3.02507	−	9.47887i	−0.214982	−	0.673634i
$199$	−15.5621			−1.10317			−0.551583	−	0.834120i	$-0.685976\pi$
$199$	−15.5621			−1.10317			−0.551583	+	0.834120i	$0.685976\pi$
$200$	−0.104528	+	0.994522i	−0.00739128	+	0.0703233i
$201$	−7.62747	−	0.105659i	−0.538000	−	0.00745258i
$202$	13.3231	+	2.83192i	0.937413	+	0.199253i
$203$	−3.42473	−	32.5841i	−0.240369	−	2.28696i
$204$	9.19284	+	6.87553i	0.643627	+	0.481383i
$205$	−7.47930	+	8.30660i	−0.522377	+	0.580158i
$206$	2.61893	−	8.06023i	0.182469	−	0.561583i
$207$	4.95406	+	9.15747i	0.344331	+	0.636488i
$208$	−1.03667			−0.0718803
$209$	−10.2068	+	7.77188i	−0.706020	+	0.537592i
$210$	−8.19873	−	1.86175i	−0.565766	−	0.128473i
$211$	6.66017	−	2.96530i	0.458505	−	0.204140i	−0.164469	−	0.986382i	$-0.552591\pi$
$211$	6.66017	−	2.96530i	0.458505	−	0.204140i	0.622974	+	0.782243i	$0.285924\pi$
$212$	−0.479070	−	0.532061i	−0.0329027	−	0.0365421i
$213$	1.04405	+	0.482279i	0.0715373	+	0.0330452i
$214$	−12.2901	−	5.47192i	−0.840136	−	0.374052i
$215$	−6.96498	+	5.06035i	−0.475008	+	0.345113i
$216$	1.80961	−	4.87086i	0.123128	−	0.331420i
$217$	−11.3249	+	34.8546i	−0.768787	+	2.36608i
$218$	−0.103745	+	0.987067i	−0.00702650	+	0.0668526i
$219$	8.22146	−	8.88035i	0.555555	−	0.600079i
$220$	−2.16333	+	2.51396i	−0.145852	+	0.169491i
$221$	−3.43540	+	5.95029i	−0.231090	+	0.400260i
$222$	4.21469	+	4.81332i	0.282871	+	0.323049i
$223$	5.93244	−	1.26098i	0.397265	−	0.0844414i	−0.00494694	−	0.999988i	$-0.501575\pi$
$223$	5.93244	−	1.26098i	0.397265	−	0.0844414i	0.402212	+	0.915546i	$0.368241\pi$
$224$	1.49998	+	4.61647i	0.100222	+	0.308451i
$225$	1.00573	−	2.82640i	0.0670484	−	0.188426i
$226$	9.86676	−	7.16862i	0.656327	−	0.476849i
$227$	12.7394	−	14.1485i	0.845540	−	0.939068i	−0.153252	−	0.988187i	$-0.548975\pi$
$227$	12.7394	−	14.1485i	0.845540	−	0.939068i	0.998793	+	0.0491192i	$0.0156414\pi$
$228$	−6.69904	−	0.0927976i	−0.443655	−	0.00614567i
$229$	10.3469	−	4.60676i	0.683745	−	0.304423i	−0.0353094	−	0.999376i	$-0.511242\pi$
$229$	10.3469	−	4.60676i	0.683745	−	0.304423i	0.719055	+	0.694953i	$0.244575\pi$
$230$	1.73527	−	3.00558i	0.114420	−	0.198182i
$231$	−18.8361	−	20.5606i	−1.23932	−	1.35279i
$232$	−3.37488	−	5.84546i	−0.221571	−	0.383773i
$233$	1.44817	+	1.05216i	0.0948729	+	0.0689292i	0.634210	−	0.773160i	$-0.281325\pi$
$233$	1.44817	+	1.05216i	0.0948729	+	0.0689292i	−0.539338	+	0.842090i	$0.681325\pi$
$234$	3.02298	+	0.730624i	0.197618	+	0.0477624i
$235$	1.32477	+	4.07723i	0.0864187	+	0.265969i
$236$	−11.1862	−	4.98041i	−0.728158	−	0.324197i
$237$	−4.66018	+	1.99797i	−0.302711	+	0.129782i
$238$	31.4684	+	6.68881i	2.03979	+	0.433571i
$239$	−5.22248	−	5.80015i	−0.337814	−	0.375181i	0.550172	−	0.835052i	$-0.314562\pi$
$239$	−5.22248	−	5.80015i	−0.337814	−	0.375181i	−0.887986	+	0.459871i	$0.847896\pi$
$240$	−1.69903	+	0.336613i	−0.109672	+	0.0217283i
$241$	2.18692	+	3.78785i	0.140872	+	0.243997i	0.927825	−	0.373016i	$-0.121676\pi$
$241$	2.18692	+	3.78785i	0.140872	+	0.243997i	−0.786953	+	0.617012i	$0.788343\pi$
$242$	−10.6460	+	2.76798i	−0.684354	+	0.177932i
$243$	−8.70977	+	12.9283i	−0.558732	+	0.829348i
$244$	−2.70080	−	1.96225i	−0.172901	−	0.125620i
$245$	−16.1998	+	3.44338i	−1.03497	+	0.219989i
$246$	−17.5757	−	8.11874i	−1.12059	−	0.517632i
$247$	−0.419151	−	3.98795i	−0.0266699	−	0.253747i
$248$	0.789195	+	7.50869i	0.0501140	+	0.476803i
$249$	1.18114	+	12.9626i	0.0748519	+	0.821473i
$250$	−0.978148	+	0.207912i	−0.0618635	+	0.0131495i
$251$	−12.5557	−	9.12227i	−0.792511	−	0.575793i	0.116197	−	0.993226i	$-0.462930\pi$
$251$	−12.5557	−	9.12227i	−0.792511	−	0.575793i	−0.908707	+	0.417434i	$0.862930\pi$
$252$	−1.12042	−	14.5190i	−0.0705798	−	0.914609i
$253$	10.4075	−	4.91675i	0.654316	−	0.309114i
$254$	3.27626	+	5.67464i	0.205571	+	0.356059i
$255$	−3.69827	+	10.8676i	−0.231595	+	0.680553i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	8.37737	+	1.78067i	0.522566	+	0.111075i	0.461640	−	0.887067i	$-0.347261\pi$
$257$	8.37737	+	1.78067i	0.522566	+	0.111075i	0.0609263	+	0.998142i	$0.480595\pi$
$258$	−11.9411	−	8.93104i	−0.743423	−	0.556023i
$259$	16.3796	+	7.29266i	1.01778	+	0.453144i
$260$	−0.320349	−	0.985934i	−0.0198672	−	0.0611450i
$261$	5.72152	+	19.4241i	0.354153	+	1.20232i
$262$	−4.16420	−	3.02547i	−0.257265	−	0.186914i
$263$	5.79553	+	10.0381i	0.357368	+	0.618979i	0.987520	−	0.157493i	$-0.0503410\pi$
$263$	5.79553	+	10.0381i	0.357368	+	0.618979i	−0.630153	+	0.776471i	$0.717008\pi$
$264$	−5.26785	−	2.29124i	−0.324214	−	0.141016i
$265$	0.357980	−	0.620039i	0.0219905	−	0.0380887i
$266$	−17.1525	+	7.63679i	−1.05169	+	0.468242i
$267$	−8.04510	−	14.3913i	−0.492352	−	0.880730i
$268$	−2.94695	+	3.27292i	−0.180014	+	0.199925i
$269$	3.92130	−	2.84899i	0.239086	−	0.173706i	−0.461790	−	0.886989i	$-0.652793\pi$
$269$	3.92130	−	2.84899i	0.239086	−	0.173706i	0.700876	+	0.713283i	$0.252793\pi$
$270$	5.19167	+	0.215861i	0.315955	+	0.0131369i
$271$	0.787353	+	2.42322i	0.0478283	+	0.147200i	0.972118	−	0.234490i	$-0.0753421\pi$
$271$	0.787353	+	2.42322i	0.0478283	+	0.147200i	−0.924290	+	0.381690i	$0.875342\pi$
$272$	6.48292	−	1.37799i	0.393084	−	0.0835527i
$273$	8.54959	−	1.69385i	0.517445	−	0.102517i
$274$	4.20534	−	7.28386i	0.254054	−	0.440034i
$275$	−3.05942	−	1.28059i	−0.184490	−	0.0772227i
$276$	5.86192	+	1.33111i	0.352846	+	0.0801234i
$277$	−2.48506	+	23.6438i	−0.149313	+	1.42062i	0.621429	+	0.783470i	$0.286552\pi$
$277$	−2.48506	+	23.6438i	−0.149313	+	1.42062i	−0.770742	+	0.637147i	$0.780114\pi$
$278$	6.80752	−	20.9514i	0.408288	−	1.25658i
$279$	2.99064	−	22.4519i	0.179045	−	1.34416i
$280$	−3.92700	+	2.85314i	−0.234683	+	0.170507i
$281$	24.0685	+	10.7160i	1.43581	+	0.639262i	0.969440	−	0.245330i	$-0.0788963\pi$
$281$	24.0685	+	10.7160i	1.43581	+	0.639262i	0.466366	+	0.884592i	$0.345563\pi$
$282$	−6.06715	+	4.28091i	−0.361294	+	0.254925i
$283$	−14.2838	−	15.8637i	−0.849082	−	0.943002i	0.149873	−	0.988705i	$-0.452114\pi$
$283$	−14.2838	−	15.8637i	−0.849082	−	0.943002i	−0.998955	+	0.0457037i	$0.985447\pi$
$284$	0.606583	−	0.270068i	0.0359941	−	0.0160256i
$285$	−1.98186	−	6.39985i	−0.117395	−	0.379094i
$286$	0.988759	−	3.29301i	0.0584665	−	0.194720i
$287$	−54.2567			−3.20267
$288$	−1.42746	−	2.63863i	−0.0841138	−	0.155483i
$289$	8.32091	−	25.6091i	0.489465	−	1.50642i
$290$	4.51647	−	5.01604i	0.265216	−	0.294552i
$291$	10.9920	−	4.71261i	0.644361	−	0.276258i
$292$	−0.730337	−	6.94869i	−0.0427397	−	0.406641i
$293$	32.7588	+	6.96309i	1.91379	+	0.406788i	1.00000		0.000596327i	$0.000189817\pi$
$293$	32.7588	+	6.96309i	1.91379	+	0.406788i	0.913788	+	0.406192i	$0.133144\pi$
$294$	−13.9974	−	25.0389i	−0.816346	−	1.46030i
$295$	1.27993	−	12.1777i	0.0745204	−	0.709014i
$296$	3.69376			0.214696
$297$	13.7464	+	10.3940i	0.797649	+	0.603121i
$298$	−20.0698			−1.16261
$299$	−0.376074	+	3.57811i	−0.0217489	+	0.206927i
$300$	−0.845166	−	1.51185i	−0.0487957	−	0.0872868i
$301$	−40.8762	−	8.68850i	−2.35606	−	0.500797i
$302$	−0.00929966	−	0.0884804i	−0.000535135	−	0.00509147i
$303$	−21.6831	+	9.29625i	−1.24566	+	0.534056i
$304$	−2.58824	+	2.87453i	−0.148446	+	0.164866i
$305$	1.03162	−	3.17499i	0.0590701	−	0.181799i
$306$	−19.8756	−	0.550754i	−1.13621	−	0.0314845i
$307$	7.29580			0.416394			0.208197	−	0.978087i	$-0.433241\pi$
$307$	7.29580			0.416394			0.208197	+	0.978087i	$0.433241\pi$
$308$	−16.0950	+	0.361626i	−0.917097	+	0.0206055i
$309$	4.34231	+	14.0222i	0.247025	+	0.797696i
$310$	−6.89732	+	3.07088i	−0.391741	+	0.174414i
$311$	4.80105	+	5.33211i	0.272243	+	0.302356i	0.863727	−	0.503961i	$-0.168124\pi$
$311$	4.80105	+	5.33211i	0.272243	+	0.302356i	−0.591484	+	0.806317i	$0.701458\pi$
$312$	1.46713	−	1.03519i	0.0830596	−	0.0586059i
$313$	−14.9847	−	6.67162i	−0.846985	−	0.377102i	−0.0630997	−	0.998007i	$-0.520099\pi$
$313$	−14.9847	−	6.67162i	−0.846985	−	0.377102i	−0.783886	+	0.620905i	$0.786765\pi$
$314$	−6.13897	+	4.46022i	−0.346442	+	0.251705i
$315$	13.4621	−	5.55219i	0.758505	−	0.312830i
$316$	−0.904619	+	2.78413i	−0.0508888	+	0.156620i
$317$	−2.55255	+	24.2859i	−0.143366	+	1.36403i	0.652146	+	0.758093i	$0.273869\pi$
$317$	−2.55255	+	24.2859i	−0.143366	+	1.36403i	−0.795511	+	0.605939i	$0.792798\pi$
$318$	1.20929	+	0.274603i	0.0678137	+	0.0153990i
$319$	21.7871	−	5.14509i	1.21984	−	0.288070i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	22.8574	−	4.52852i	1.27577	−	0.252757i
$322$	16.4780	−	3.50251i	0.918285	−	0.195187i
$323$	7.92213	+	24.3818i	0.440799	+	1.35664i
$324$	2.30288	+	8.70039i	0.127938	+	0.483355i
$325$	0.838686	−	0.609341i	0.0465219	−	0.0338002i
$326$	−5.16084	+	5.73170i	−0.285833	+	0.317449i
$327$	−0.838831	−	1.50052i	−0.0463875	−	0.0829789i
$328$	−10.2113	+	4.54636i	−0.563824	+	0.251030i
$329$	−10.4048	+	18.0216i	−0.573634	+	0.993563i
$330$	0.551242	−	5.71805i	0.0303449	−	0.314768i
$331$	9.01615	+	15.6164i	0.495572	+	0.858357i	0.999987	−	0.00510505i	$-0.00162499\pi$
$331$	9.01615	+	15.6164i	0.495572	+	0.858357i	−0.504415	+	0.863462i	$0.668292\pi$
$332$	6.07974	+	4.41719i	0.333669	+	0.242425i
$333$	−10.7712	−	2.60328i	−0.590256	−	0.142659i
$334$	6.52863	+	20.0930i	0.357231	+	1.09944i
$335$	−4.02339	−	1.79133i	−0.219821	−	0.0978707i
$336$	−6.73267	−	5.03551i	−0.367297	−	0.274710i
$337$	1.68472	+	0.358098i	0.0917726	+	0.0195069i	0.253569	−	0.967317i	$-0.418395\pi$
$337$	1.68472	+	0.358098i	0.0917726	+	0.0195069i	−0.161797	+	0.986824i	$0.551729\pi$
$338$	−7.97959	−	8.86223i	−0.434032	−	0.482042i
$339$	−6.80534	+	19.9978i	−0.369615	+	1.08613i
$340$	3.31387	+	5.73980i	0.179720	+	0.311284i
$341$	−24.6043	−	4.65475i	−1.33240	−	0.252069i
$342$	9.57332	−	6.55812i	0.517666	−	0.354622i
$343$	−37.5490	−	27.2809i	−2.02745	−	1.47303i
$344$	−8.42106	+	1.78995i	−0.454033	+	0.0965077i
$345$	0.545472	+	5.98635i	0.0293672	+	0.322294i
$346$	1.10642	+	10.5269i	0.0594817	+	0.565931i
$347$	1.15097	+	10.9508i	0.0617875	+	0.587869i	0.980987	+	0.194076i	$0.0621708\pi$
$347$	1.15097	+	10.9508i	0.0617875	+	0.587869i	−0.919199	+	0.393793i	$0.871163\pi$
$348$	10.6133	+	4.90260i	0.568932	+	0.262807i
$349$	−10.3876	+	2.20796i	−0.556038	+	0.118190i	−0.477356	−	0.878710i	$-0.658405\pi$
$349$	−10.3876	+	2.20796i	−0.556038	+	0.118190i	−0.0786824	+	0.996900i	$0.525071\pi$
$350$	−3.92700	−	2.85314i	−0.209907	−	0.152506i
$351$	−5.00777	+	1.98465i	−0.267295	+	0.105933i
$352$	−2.99882	+	1.41671i	−0.159838	+	0.0755110i
$353$	−9.84523	−	17.0524i	−0.524009	−	0.907610i	−0.999609	−	0.0279487i	$-0.991102\pi$
$353$	−9.84523	−	17.0524i	−0.524009	−	0.907610i	0.475600	−	0.879661i	$-0.342231\pi$
$354$	20.8042	−	4.12175i	1.10573	−	0.219069i
$355$	0.444295	+	0.493439i	0.0235807	+	0.0261890i
$356$	−9.31095	−	1.97910i	−0.493479	−	0.104892i
$357$	−51.2140	+	21.9571i	−2.71053	+	1.16209i
$358$	−7.56397	−	3.36770i	−0.399768	−	0.177988i
$359$	2.03676	+	6.26850i	0.107496	+	0.330839i	0.990308	−	0.138887i	$-0.0443526\pi$
$359$	2.03676	+	6.26850i	0.107496	+	0.330839i	−0.882812	+	0.469726i	$0.844353\pi$
$360$	2.06838	−	2.17298i	0.109013	−	0.114526i
$361$	3.26686	+	2.37352i	0.171940	+	0.124922i
$362$	2.68657	+	4.65328i	0.141203	+	0.244571i
$363$	12.3025	−	14.5481i	0.645716	−	0.763578i
$364$	2.51603	−	4.35789i	0.131876	−	0.228415i
$365$	6.38291	−	2.84186i	0.334097	−	0.148750i
$366$	5.78168	+	0.0800900i	0.302213	+	0.00418637i
$367$	−3.61342	+	4.01311i	−0.188619	+	0.209482i	−0.830036	−	0.557710i	$-0.811680\pi$
$367$	−3.61342	+	4.01311i	−0.188619	+	0.209482i	0.641417	+	0.767192i	$0.278347\pi$
$368$	2.80773	−	2.03993i	0.146363	−	0.106339i
$369$	32.9807	−	6.06067i	1.71691	−	0.315506i
$370$	1.14144	+	3.51298i	0.0593404	+	0.182631i
$371$	3.39935	−	0.722555i	0.176486	−	0.0375132i
$372$	−8.61483	−	9.83843i	−0.446658	−	0.510099i
$373$	19.2637	−	33.3657i	0.997436	−	1.72761i	0.436744	−	0.899586i	$-0.356132\pi$
$373$	19.2637	−	33.3657i	0.997436	−	1.72761i	0.560692	−	0.828024i	$-0.310535\pi$
$374$	−1.80608	+	21.9074i	−0.0933900	+	1.13281i
$375$	1.17669	−	1.27099i	0.0607638	−	0.0656335i
$376$	−0.448119	+	4.26357i	−0.0231100	+	0.219877i
$377$	−2.16228	+	6.65481i	−0.111363	+	0.342740i
$378$	16.0838	+	19.4288i	0.827262	+	0.999309i
$379$	−11.3999	+	8.28251i	−0.585574	+	0.425444i	−0.840729	−	0.541456i	$-0.817873\pi$
$379$	−11.3999	+	8.28251i	−0.585574	+	0.425444i	0.255156	+	0.966900i	$0.417873\pi$
$380$	−3.53365	−	1.57328i	−0.181273	−	0.0807078i
$381$	−10.3032	−	4.75934i	−0.527847	−	0.243828i
$382$	−10.8905	−	12.0951i	−0.557205	−	0.618838i
$383$	7.52054	−	3.34836i	0.384282	−	0.171093i	−0.205498	−	0.978658i	$-0.565881\pi$
$383$	7.52054	−	3.34836i	0.384282	−	0.171093i	0.589779	+	0.807564i	$0.299215\pi$
$384$	−1.68905	−	0.383546i	−0.0861940	−	0.0195727i
$385$	−5.31755	−	15.1955i	−0.271007	−	0.774434i
$386$	−22.2472			−1.13235
$387$	25.8177	+	0.715409i	1.31239	+	0.0363663i
$388$	2.13373	−	6.56693i	0.108324	−	0.333386i
$389$	12.6855	−	14.0887i	0.643181	−	0.714325i	−0.330099	−	0.943946i	$-0.607082\pi$
$389$	12.6855	−	14.0887i	0.643181	−	0.714325i	0.973280	+	0.229622i	$0.0737489\pi$
$390$	1.43789	+	1.07543i	0.0728103	+	0.0544565i
$391$	−2.40435	−	22.8759i	−0.121593	−	1.15688i
$392$	−16.1998	−	3.44338i	−0.818215	−	0.173917i
$393$	8.91442	+	0.123486i	0.449673	+	0.00622903i
$394$	−1.42653	+	13.5726i	−0.0718677	+	0.683776i
$395$	−2.92741			−0.147294
$396$	9.74315	−	2.01768i	0.489612	−	0.101392i
$397$	17.7942			0.893067			0.446533	−	0.894767i	$-0.352658\pi$
$397$	17.7942			0.893067			0.446533	+	0.894767i	$0.352658\pi$
$398$	1.62668	−	15.4768i	0.0815381	−	0.775783i
$399$	16.6488	−	27.9357i	0.833484	−	1.39854i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	1.43048	+	13.6101i	0.0714346	+	0.679655i	0.970378	+	0.241591i	$0.0776691\pi$
$401$	1.43048	+	13.6101i	0.0714346	+	0.679655i	−0.898944	+	0.438064i	$0.855664\pi$
$402$	0.902368	−	7.57464i	0.0450060	−	0.377789i
$403$	5.23724	−	5.81655i	0.260886	−	0.289743i
$404$	−4.20906	+	12.9541i	−0.209408	+	0.644493i
$405$	−7.56293	+	4.87874i	−0.375805	+	0.242426i
$406$	32.7636			1.62603
$407$	−3.52304	+	11.7333i	−0.174631	+	0.581599i
$408$	−7.79878	+	8.42379i	−0.386097	+	0.417040i
$409$	11.4599	−	5.10229i	0.566658	−	0.252292i	−0.103352	−	0.994645i	$-0.532957\pi$
$409$	11.4599	−	5.10229i	0.566658	−	0.252292i	0.670009	+	0.742353i	$0.266290\pi$
$410$	−7.47930	−	8.30660i	−0.369376	−	0.410234i
$411$	1.32192	+	14.5076i	0.0652057	+	0.715609i
$412$	7.74233	+	3.44711i	0.381437	+	0.169827i
$413$	48.0853	−	34.9360i	2.36613	−	1.71909i
$414$	−9.62514	+	3.96970i	−0.473050	+	0.195100i
$415$	−2.32226	+	7.14717i	−0.113995	+	0.350841i
$416$	0.108362	−	1.03099i	0.00531287	−	0.0505486i
$417$	11.2872	+	36.4487i	0.552736	+	1.78490i
$418$	−6.66241	−	10.9633i	−0.325869	−	0.536232i
$419$	2.24278	−	3.88462i	0.109567	−	0.189776i	−0.806028	−	0.591878i	$-0.798387\pi$
$419$	2.24278	−	3.88462i	0.109567	−	0.189776i	0.915595	+	0.402102i	$0.131720\pi$
$420$	2.70855	−	7.95921i	0.132164	−	0.388370i
$421$	31.0157	−	6.59258i	1.51161	−	0.321303i	0.623827	−	0.781563i	$-0.285577\pi$
$421$	31.0157	−	6.59258i	1.51161	−	0.321303i	0.887784	+	0.460260i	$0.152244\pi$
$422$	2.25288	+	6.93364i	0.109668	+	0.337524i
$423$	4.31161	−	12.1169i	0.209637	−	0.589145i
$424$	0.579223	−	0.420830i	0.0281296	−	0.0204373i
$425$	−4.43483	+	4.92538i	−0.215121	+	0.238916i
$426$	−0.588771	+	0.987922i	−0.0285260	+	0.0478650i
$427$	14.8037	−	6.59102i	0.716400	−	0.318962i
$428$	6.72661	−	11.6508i	0.325143	−	0.563164i
$429$	1.88898	+	5.64770i	0.0912008	+	0.272674i
$430$	−4.30459	−	7.45578i	−0.207586	−	0.359549i
$431$	17.7754	+	12.9146i	0.856209	+	0.622073i	0.926851	−	0.375429i	$-0.122505\pi$
$431$	17.7754	+	12.9146i	0.856209	+	0.622073i	−0.0706417	+	0.997502i	$0.522505\pi$
$432$	4.65503	+	2.30884i	0.223965	+	0.111084i
$433$	−6.02320	−	18.5375i	−0.289457	−	0.890856i	−0.985027	−	0.172398i	$-0.944848\pi$
$433$	−6.02320	−	18.5375i	−0.289457	−	0.890856i	0.695571	−	0.718458i	$-0.255152\pi$
$434$	−33.4799	−	14.9062i	−1.60709	−	0.715521i
$435$	−1.38296	+	11.6088i	−0.0663079	+	0.556601i
$436$	−0.970816	−	0.206353i	−0.0464936	−	0.00988253i
$437$	8.98260	+	9.97618i	0.429696	+	0.477226i
$438$	7.97233	+	9.10468i	0.380933	+	0.435038i
$439$	11.5743	+	20.0473i	0.552412	+	0.956805i	0.998100	+	0.0616169i	$0.0196257\pi$
$439$	11.5743	+	20.0473i	0.552412	+	0.956805i	−0.445688	+	0.895188i	$0.647041\pi$
$440$	−2.27406	−	2.41426i	−0.108412	−	0.115095i
$441$	44.8125	+	21.4583i	2.13393	+	1.02182i
$442$	−5.55860	−	4.03856i	−0.264396	−	0.192095i
$443$	28.9171	−	6.14651i	1.37389	−	0.292030i	0.538936	−	0.842347i	$-0.318827\pi$
$443$	28.9171	−	6.14651i	1.37389	−	0.292030i	0.834956	+	0.550317i	$0.185493\pi$
$444$	−5.22751	+	3.68847i	−0.248087	+	0.175047i
$445$	−0.995002	−	9.46681i	−0.0471676	−	0.448770i
$446$	0.633962	+	6.03175i	0.0300190	+	0.285612i
$447$	28.4033	−	20.0411i	1.34343	−	0.947910i
$448$	−4.74797	+	1.00921i	−0.224321	+	0.0476808i
$449$	−24.4537	−	17.7666i	−1.15404	−	0.838459i	−0.165027	−	0.986289i	$-0.552771\pi$
$449$	−24.4537	−	17.7666i	−1.15404	−	0.838459i	−0.989013	+	0.147830i	$0.952771\pi$
$450$	2.70579	+	1.29566i	0.127552	+	0.0610778i
$451$	−4.70228	−	36.7726i	−0.221422	−	1.73155i
$452$	6.09799	+	10.5620i	0.286825	+	0.496796i
$453$	0.101515	+	0.115933i	0.00476958	+	0.00544702i
$454$	12.7394	+	14.1485i	0.597887	+	0.664021i
$455$	4.92209	+	1.04622i	0.230751	+	0.0490477i
$456$	0.792530	−	6.65265i	0.0371136	−	0.311539i
$457$	−9.91974	−	4.41655i	−0.464026	−	0.206598i	0.161388	−	0.986891i	$-0.448403\pi$
$457$	−9.91974	−	4.41655i	−0.464026	−	0.206598i	−0.625414	+	0.780293i	$0.715070\pi$
$458$	3.49997	+	10.7718i	0.163543	+	0.503333i
$459$	28.6784	−	19.0677i	1.33859	−	0.890004i
$460$	2.80773	+	2.03993i	0.130911	+	0.0951123i
$461$	14.5187	+	25.1471i	0.676203	+	1.17122i	0.976116	+	0.217251i	$0.0697090\pi$
$461$	14.5187	+	25.1471i	0.676203	+	1.17122i	−0.299913	+	0.953967i	$0.596958\pi$
$462$	22.4169	−	16.5837i	1.04293	−	0.771544i
$463$	−18.0774	+	31.3110i	−0.840129	+	1.45515i	0.0496553	+	0.998766i	$0.484188\pi$
$463$	−18.0774	+	31.3110i	−0.840129	+	1.45515i	−0.889785	+	0.456380i	$0.849146\pi$
$464$	6.16621	−	2.74537i	0.286259	−	0.127451i
$465$	6.69477	−	11.2334i	0.310463	−	0.520938i
$466$	−1.19777	+	1.33026i	−0.0554856	+	0.0616230i
$467$	−1.36925	+	0.994821i	−0.0633615	+	0.0460348i	−0.619015	−	0.785379i	$-0.712468\pi$
$467$	−1.36925	+	0.994821i	−0.0633615	+	0.0460348i	0.555654	+	0.831414i	$0.312468\pi$
$468$	−1.04261	+	2.93005i	−0.0481946	+	0.135441i
$469$	−6.60614	−	20.3316i	−0.305043	−	0.938826i
$470$	−4.19337	+	0.891329i	−0.193426	+	0.0411140i
$471$	4.23419	−	12.4424i	0.195101	−	0.573315i
$472$	6.12240	−	10.6043i	0.281806	−	0.488103i
$473$	2.34602	−	28.4569i	0.107870	−	1.30845i
$474$	−1.49990	−	4.84350i	−0.0688928	−	0.222469i
$475$	0.404323	−	3.84688i	0.0185516	−	0.176507i
$476$	−9.94150	+	30.5968i	−0.455668	+	1.40240i
$477$	−1.98563	+	0.818934i	−0.0909157	+	0.0374964i
$478$	6.31428	−	4.58759i	0.288808	−	0.209831i
$479$	−17.9096	−	7.97385i	−0.818309	−	0.364334i	−0.0454926	−	0.998965i	$-0.514486\pi$
$479$	−17.9096	−	7.97385i	−0.818309	−	0.364334i	−0.772816	+	0.634630i	$0.781152\pi$
$480$	−0.157172	−	1.72490i	−0.00717389	−	0.0787308i
$481$	−2.56225	−	2.84567i	−0.116829	−	0.129751i
$482$	−3.99569	+	1.77900i	−0.181999	+	0.0810311i
$483$	−19.8226	+	21.4113i	−0.901961	+	0.974246i
$484$	−1.64000	−	10.8771i	−0.0745454	−	0.494412i
$485$	6.90488			0.313535
$486$	−11.9470	−	10.0134i	−0.541928	−	0.454218i
$487$	−11.6123	+	35.7390i	−0.526204	+	1.61949i	0.235718	+	0.971822i	$0.424256\pi$
$487$	−11.6123	+	35.7390i	−0.526204	+	1.61949i	−0.761922	+	0.647669i	$0.775744\pi$
$488$	2.23381	−	2.48090i	0.101120	−	0.112305i
$489$	1.58027	−	13.2651i	0.0714624	−	0.599868i
$490$	−1.73117	−	16.4710i	−0.0782064	−	0.744085i
$491$	−11.9459	−	2.53919i	−0.539113	−	0.114592i	−0.0696954	−	0.997568i	$-0.522203\pi$
$491$	−11.9459	−	2.53919i	−0.539113	−	0.114592i	−0.469418	+	0.882976i	$0.655536\pi$
$492$	9.91142	−	16.6308i	0.446841	−	0.749773i
$493$	4.67615	−	44.4906i	0.210603	−	2.00376i
$494$	4.00992			0.180415
$495$	4.92973	+	8.64279i	0.221575	+	0.388464i
$496$	−7.55005			−0.339007
$497$	−0.336898	+	3.20537i	−0.0151119	+	0.143781i
$498$	−13.0151	−	0.180290i	−0.583219	−	0.00807897i
$499$	23.6159	+	5.01971i	1.05719	+	0.224713i	0.703534	−	0.710661i	$-0.251604\pi$
$499$	23.6159	+	5.01971i	1.05719	+	0.224713i	0.353659	+	0.935375i	$0.384937\pi$
$500$	−0.104528	−	0.994522i	−0.00467465	−	0.0444764i
$501$	−29.3037	−	21.9169i	−1.30919	−	0.979176i
$502$	10.3847	−	11.5334i	0.463493	−	0.514761i
$503$	0.0567672	−	0.174711i	0.00253112	−	0.00779000i	−0.949783	−	0.312909i	$-0.898696\pi$
$503$	0.0567672	−	0.174711i	0.00253112	−	0.00779000i	0.952314	+	0.305119i	$0.0986964\pi$
$504$	14.5565	+	0.403363i	0.648400	+	0.0179672i
$505$	−13.6208			−0.606117
$506$	3.80194	+	10.8645i	0.169017	+	0.482984i
$507$	20.1425	+	4.57390i	0.894558	+	0.203134i
$508$	−5.98602	+	2.66515i	−0.265587	+	0.118247i
$509$	6.62300	+	7.35558i	0.293559	+	0.326030i	0.871825	−	0.489818i	$-0.162937\pi$
$509$	6.62300	+	7.35558i	0.293559	+	0.326030i	−0.578265	+	0.815849i	$0.696270\pi$
$510$	−10.4215	−	4.81398i	−0.461470	−	0.213167i
$511$	30.9829	+	13.7945i	1.37060	+	0.610232i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.99969	+	18.8408i	−0.309044	+	0.831843i
$514$	−2.64659	+	8.14535i	−0.116736	+	0.359276i
$515$	−0.885882	+	8.42860i	−0.0390366	+	0.371409i
$516$	10.1303	−	10.9422i	0.445962	−	0.481703i
$517$	−13.1159	−	5.48998i	−0.576838	−	0.241449i
$518$	−8.96485	+	15.5276i	−0.393893	+	0.682242i
$519$	−12.0777	−	13.7931i	−0.530151	−	0.605451i
$520$	1.01402	−	0.215536i	0.0444677	−	0.00945189i
$521$	−1.10119	−	3.38910i	−0.0482439	−	0.148479i	0.924033	−	0.382314i	$-0.124873\pi$
$521$	−1.10119	−	3.38910i	−0.0482439	−	0.148479i	−0.972276	+	0.233834i	$0.924873\pi$
$522$	−19.9158	+	3.65981i	−0.871690	+	0.160185i
$523$	−10.0319	+	7.28859i	−0.438664	+	0.318708i	−0.785104	−	0.619364i	$-0.787390\pi$
$523$	−10.0319	+	7.28859i	−0.438664	+	0.318708i	0.346440	+	0.938072i	$0.387390\pi$
$524$	3.44417	−	3.82514i	0.150459	−	0.167102i
$525$	8.40664	+	0.116452i	0.366896	+	0.00508238i
$526$	−10.5890	+	4.71451i	−0.461700	+	0.205562i
$527$	−25.0199	+	43.3358i	−1.08989	+	1.88774i
$528$	2.82933	−	4.99949i	0.123131	−	0.217575i
$529$	5.47767	+	9.48761i	0.238160	+	0.412505i
$530$	0.579223	+	0.420830i	0.0251598	+	0.0182797i
$531$	−25.3268	+	26.6076i	−1.09909	+	1.15467i
$532$	−5.80203	−	17.8568i	−0.251550	−	0.774191i
$533$	10.5858	+	4.71308i	0.458520	+	0.204146i
$534$	15.1534	−	6.49673i	0.655750	−	0.281141i
$535$	13.1592	+	2.79708i	0.568923	+	0.120928i
$536$	−2.94695	−	3.27292i	−0.127289	−	0.141369i
$537$	14.0676	−	2.78708i	0.607062	−	0.120272i
$538$	2.42349	+	4.19762i	0.104484	+	0.180972i
$539$	26.3891	−	48.1749i	1.13666	−	2.07504i
$540$	−0.757356	+	5.14066i	−0.0325914	+	0.221219i
$541$	−22.7400	−	16.5216i	−0.977668	−	0.710318i	−0.0204822	−	0.999790i	$-0.506520\pi$
$541$	−22.7400	−	16.5216i	−0.977668	−	0.710318i	−0.957186	+	0.289472i	$0.906520\pi$
$542$	−2.49225	+	0.529744i	−0.107051	+	0.0227544i
$543$	−8.44872	−	3.90272i	−0.362569	−	0.167482i
$544$	0.692788	+	6.59144i	0.0297031	+	0.282606i
$545$	−0.103745	−	0.987067i	−0.00444395	−	0.0422813i
$546$	0.790898	+	8.67982i	0.0338473	+	0.371462i
$547$	35.3738	−	7.51893i	1.51247	−	0.321486i	0.624370	−	0.781129i	$-0.285356\pi$
$547$	35.3738	−	7.51893i	1.51247	−	0.321486i	0.888104	+	0.459643i	$0.152023\pi$
$548$	6.80439	+	4.94368i	0.290669	+	0.211183i
$549$	−8.26236	+	5.66006i	−0.352629	+	0.241565i
$550$	1.59338	−	2.90881i	0.0679417	−	0.124032i
$551$	13.0542	+	22.6106i	0.556129	+	0.963245i
$552$	−1.93656	+	5.69067i	−0.0824253	+	0.242211i
$553$	−9.50820	−	10.5599i	−0.404330	−	0.449054i
$554$	−23.2545	−	4.94290i	−0.987989	−	0.210004i
$555$	−5.12333	−	3.83186i	−0.217473	−	0.162653i
$556$	20.1250	+	8.96024i	0.853491	+	0.379999i
$557$	2.55093	+	7.85094i	0.108086	+	0.332655i	0.990442	−	0.137927i	$-0.0440439\pi$
$557$	2.55093	+	7.85094i	0.108086	+	0.332655i	−0.882356	+	0.470582i	$0.844044\pi$
$558$	22.0163	+	5.32111i	0.932022	+	0.225261i
$559$	7.22040	+	5.24593i	0.305391	+	0.221879i
$560$	−2.42702	−	4.20373i	−0.102560	−	0.177640i
$561$	−19.3200	−	32.8074i	−0.815693	−	1.38513i
$562$	−13.1731	+	22.8165i	−0.555675	+	0.962457i
$563$	−23.5306	+	10.4765i	−0.991696	+	0.441531i	−0.837458	−	0.546502i	$-0.815959\pi$
$563$	−23.5306	+	10.4765i	−0.991696	+	0.441531i	−0.154238	+	0.988034i	$0.549292\pi$
$564$	−3.62327	−	6.48139i	−0.152567	−	0.272916i
$565$	−8.16071	+	9.06338i	−0.343323	+	0.381299i
$566$	17.2699	−	12.5473i	0.725908	−	0.527403i
$567$	−42.1632	−	11.4354i	−1.77069	−	0.480240i
$568$	0.205184	+	0.631490i	0.00860931	+	0.0264967i
$569$	−36.4876	+	7.75569i	−1.52964	+	0.325135i	−0.894432	−	0.447204i	$-0.852420\pi$
$569$	−36.4876	+	7.75569i	−1.52964	+	0.325135i	−0.635210	+	0.772340i	$0.719086\pi$
$570$	6.57195	−	1.30204i	0.275269	−	0.0545364i
$571$	−15.1010	+	26.1557i	−0.631957	+	1.09458i	0.355194	+	0.934792i	$0.384415\pi$
$571$	−15.1010	+	26.1557i	−0.631957	+	1.09458i	−0.987151	+	0.159789i	$0.948919\pi$
$572$	3.17162	+	1.32756i	0.132612	+	0.0555079i
$573$	27.4902	+	6.24241i	1.14842	+	0.260780i
$574$	5.67137	−	53.9595i	0.236719	−	2.25223i
$575$	−1.07246	+	3.30068i	−0.0447245	+	0.137648i
$576$	2.77338	−	1.14383i	0.115558	−	0.0476595i
$577$	0.775600	−	0.563507i	0.0322887	−	0.0234591i	−0.571524	−	0.820585i	$-0.693648\pi$
$577$	0.775600	−	0.563507i	0.0322887	−	0.0234591i	0.603813	+	0.797126i	$0.293648\pi$
$578$	24.5991	+	10.9522i	1.02319	+	0.455552i
$579$	31.4848	−	22.2153i	1.30846	−	0.923237i
$580$	4.51647	+	5.01604i	0.187536	+	0.208280i
$581$	−33.3243	+	14.8369i	−1.38253	+	0.615540i
$582$	3.53782	+	11.4244i	0.146647	+	0.473555i
$583$	0.784325	+	2.24130i	0.0324834	+	0.0928250i
$584$	6.98697			0.289123
$585$	−3.10882	−	0.0861457i	−0.128534	−	0.00356169i
$586$	−10.3492	+	31.8515i	−0.427520	+	1.31577i
$587$	15.3670	−	17.0668i	0.634263	−	0.704421i	−0.337247	−	0.941416i	$-0.609496\pi$
$587$	15.3670	−	17.0668i	0.634263	−	0.704421i	0.971511	+	0.236995i	$0.0761626\pi$
$588$	26.3649	−	11.3035i	1.08727	−	0.466147i
$589$	−3.05266	−	29.0441i	−0.125783	−	1.19674i
$590$	11.9772	+	2.54584i	0.493094	+	0.104810i
$591$	−11.5342	−	20.6327i	−0.474456	−	0.848717i
$592$	−0.386103	+	3.67353i	−0.0158688	+	0.150981i
$593$	16.7648			0.688448			0.344224	−	0.938887i	$-0.388142\pi$
$593$	16.7648			0.688448			0.344224	+	0.938887i	$0.388142\pi$
$594$	−11.7740	+	12.5847i	−0.483091	+	0.516355i
$595$	−32.1714			−1.31890
$596$	2.09787	−	19.9599i	0.0859320	−	0.817589i
$597$	13.1525	+	23.5276i	0.538297	+	0.962919i
$598$	−3.51919	−	0.748028i	−0.143911	−	0.0305891i
$599$	1.42523	+	13.5602i	0.0582335	+	0.554054i	0.984276	+	0.176636i	$0.0565215\pi$
$599$	1.42523	+	13.5602i	0.0582335	+	0.554054i	−0.926043	+	0.377418i	$0.876812\pi$
$600$	1.59191	−	0.682504i	0.0649896	−	0.0278631i
$601$	−2.17337	+	2.41377i	−0.0886534	+	0.0984596i	−0.785839	−	0.618431i	$-0.787769\pi$
$601$	−2.17337	+	2.41377i	−0.0886534	+	0.0984596i	0.697186	+	0.716891i	$0.254435\pi$
$602$	12.9136	−	39.7441i	0.526320	−	1.61985i
$603$	6.28674	+	11.6209i	0.256016	+	0.473240i
$604$	0.0889678			0.00362005
$605$	9.83791	−	4.92093i	0.399968	−	0.200064i
$606$	−6.97882	−	22.5361i	−0.283495	−	0.915465i
$607$	−22.2295	+	9.89721i	−0.902267	+	0.401715i	−0.804816	−	0.593525i	$-0.797736\pi$
$607$	−22.2295	+	9.89721i	−0.902267	+	0.401715i	−0.0974518	+	0.995240i	$0.531069\pi$
$608$	−2.58824	−	2.87453i	−0.104967	−	0.116578i
$609$	−46.3679	+	32.7167i	−1.87892	+	1.32575i
$610$	3.04976	+	1.35784i	0.123481	+	0.0549773i
$611$	3.59549	−	2.61228i	0.145458	−	0.105681i
$612$	2.62530	−	19.7092i	0.106122	−	0.796696i
$613$	−9.76876	+	30.0651i	−0.394556	+	1.21432i	0.534750	+	0.845010i	$0.320406\pi$
$613$	−9.76876	+	30.0651i	−0.394556	+	1.21432i	−0.929306	+	0.369310i	$0.879594\pi$
$614$	−0.762619	+	7.25584i	−0.0307768	+	0.292822i
$615$	18.8796	+	4.28713i	0.761299	+	0.172874i
$616$	1.32274	−	16.0446i	0.0532947	−	0.646456i
$617$	24.1248	−	41.7854i	0.971228	−	1.68222i	0.279369	−	0.960184i	$-0.409875\pi$
$617$	24.1248	−	41.7854i	0.971228	−	1.68222i	0.691859	−	0.722033i	$-0.256792\pi$
$618$	−14.3993	+	2.85280i	−0.579225	+	0.114757i
$619$	−18.7718	+	3.99008i	−0.754504	+	0.160375i	−0.569078	−	0.822284i	$-0.692700\pi$
$619$	−18.7718	+	3.99008i	−0.754504	+	0.160375i	−0.185426	+	0.982658i	$0.559366\pi$
$620$	−2.33309	−	7.18053i	−0.0936993	−	0.288377i
$621$	9.65773	−	15.2294i	0.387551	−	0.611134i
$622$	−5.80475	+	4.21740i	−0.232749	+	0.169102i
$623$	30.9175	−	34.3373i	1.23868	−	1.37570i
$624$	0.876160	+	1.56730i	0.0350745	+	0.0627420i
$625$	0.913545	−	0.406737i	0.0365418	−	0.0162695i
$626$	8.20140	−	14.2052i	0.327794	−	0.567756i
$627$	20.3764	+	8.86266i	0.813754	+	0.353940i
$628$	−3.79409	−	6.57156i	−0.151401	−	0.262234i
$629$	19.8058	+	14.3898i	0.789710	+	0.573758i
$630$	4.11460	+	13.9687i	0.163930	+	0.556528i
$631$	0.503302	+	1.54900i	0.0200361	+	0.0616649i	0.960575	−	0.278022i	$-0.0896789\pi$
$631$	0.503302	+	1.54900i	0.0200361	+	0.0616649i	−0.940539	+	0.339687i	$0.889679\pi$
$632$	−2.67432	−	1.19068i	−0.106379	−	0.0473629i
$633$	−10.1120	−	7.56302i	−0.401917	−	0.300603i
$634$	−23.8860	−	5.07714i	−0.948636	−	0.201639i
$635$	−4.38449	−	4.86947i	−0.173993	−	0.193239i
$636$	−0.399504	+	1.17396i	−0.0158414	+	0.0465507i
$637$	8.58455	+	14.8689i	0.340132	+	0.589126i
$638$	2.83953	+	22.2056i	0.112418	+	0.879127i
$639$	−0.153263	−	1.98606i	−0.00606299	−	0.0785673i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	11.9725	−	2.54483i	0.472884	−	0.100515i	0.0346960	−	0.999398i	$-0.488954\pi$
$641$	11.9725	−	2.54483i	0.472884	−	0.100515i	0.438188	+	0.898883i	$0.355620\pi$
$642$	2.11447	+	23.2055i	0.0834514	+	0.915849i
$643$	2.64234	+	25.1402i	0.104204	+	0.991431i	0.914273	+	0.405098i	$0.132762\pi$
$643$	2.64234	+	25.1402i	0.104204	+	0.991431i	−0.810070	+	0.586333i	$0.800571\pi$
$644$	1.76090	+	16.7539i	0.0693893	+	0.660195i
$645$	13.5371	+	6.25318i	0.533021	+	0.246219i
$646$	−25.0763	+	5.33014i	−0.986616	+	0.209712i
$647$	−24.3901	−	17.7204i	−0.958872	−	0.696661i	−0.00598349	−	0.999982i	$-0.501905\pi$
$647$	−24.3901	−	17.7204i	−0.958872	−	0.696661i	−0.952888	+	0.303321i	$0.901905\pi$
$648$	−8.89344	+	1.38083i	−0.349367	+	0.0542440i
$649$	27.8454	+	29.5621i	1.09303	+	1.16041i
$650$	0.518336	+	0.897785i	0.0203308	+	0.0352140i
$651$	62.2664	−	12.3363i	2.44041	−	0.483497i
$652$	−5.16084	−	5.73170i	−0.202114	−	0.224471i
$653$	22.2862	+	4.73707i	0.872125	+	0.185376i	0.622171	−	0.782882i	$-0.286251\pi$
$653$	22.2862	+	4.73707i	0.872125	+	0.185376i	0.249955	+	0.968258i	$0.419584\pi$
$654$	1.57998	−	0.677389i	0.0617821	−	0.0264880i
$655$	4.70223	+	2.09357i	0.183731	+	0.0818025i
$656$	−3.45408	−	10.6306i	−0.134859	−	0.415054i
$657$	−20.3743	−	4.92426i	−0.794876	−	0.192114i
$658$	−16.8353	−	12.2316i	−0.656308	−	0.476836i
$659$	20.2077	+	35.0007i	0.787179	+	1.36343i	0.927689	+	0.373355i	$0.121793\pi$
$659$	20.2077	+	35.0007i	0.787179	+	1.36343i	−0.140510	+	0.990079i	$0.544874\pi$
$660$	5.62911	+	1.14592i	0.219113	+	0.0446049i
$661$	18.4901	−	32.0257i	0.719180	−	1.24566i	−0.242144	−	0.970240i	$-0.577851\pi$
$661$	18.4901	−	32.0257i	0.719180	−	1.24566i	0.961325	−	0.275417i	$-0.0888159\pi$
$662$	−16.4733	+	7.33440i	−0.640254	+	0.285059i
$663$	11.8994	+	0.164835i	0.462136	+	0.00640168i
$664$	−5.02850	+	5.58472i	−0.195144	+	0.216729i
$665$	15.1899	−	11.0361i	0.589039	−	0.427962i
$666$	3.71492	−	10.4400i	0.143950	−	0.404543i
$667$	−7.23881	−	22.2788i	−0.280288	−	0.862638i
$668$	−20.6654	+	4.39257i	−0.799568	+	0.169953i
$669$	−6.92031	−	7.90323i	−0.267555	−	0.305557i
$670$	2.20207	−	3.81410i	0.0850735	−	0.147352i
$671$	5.75006	+	9.46198i	0.221979	+	0.365276i
$672$	5.71168	−	6.16943i	0.220333	−	0.237991i
$673$	4.90669	−	46.6840i	0.189139	−	1.79954i	−0.329094	−	0.944297i	$-0.606743\pi$
$673$	4.90669	−	46.6840i	0.189139	−	1.79954i	0.518233	−	0.855240i	$-0.326590\pi$
$674$	−0.532238	+	1.63806i	−0.0205010	+	0.0630957i
$675$	−5.12310	+	0.868264i	−0.197188	+	0.0334195i
$676$	9.64778	−	7.00952i	0.371068	−	0.269597i
$677$	21.5057	+	9.57494i	0.826530	+	0.367995i	0.776004	−	0.630728i	$-0.217244\pi$
$677$	21.5057	+	9.57494i	0.826530	+	0.367995i	0.0505260	+	0.998723i	$0.483910\pi$
$678$	−19.1769	−	8.85840i	−0.736486	−	0.340205i
$679$	22.4270	+	24.9077i	0.860669	+	0.955869i
$680$	−6.05475	+	2.69575i	−0.232189	+	0.103377i
$681$	−32.1573	−	7.30219i	−1.23227	−	0.279821i
$682$	7.20110	−	23.9829i	0.275744	−	0.918354i
$683$	−38.6581			−1.47921			−0.739606	−	0.673040i	$-0.764988\pi$
$683$	−38.6581			−1.47921			−0.739606	+	0.673040i	$0.764988\pi$
$684$	5.52151	+	10.2064i	0.211120	+	0.390251i
$685$	−2.59904	+	7.99903i	−0.0993044	+	0.305627i
$686$	31.0564	−	34.4917i	1.18574	−	1.31690i
$687$	−15.7096	−	11.7496i	−0.599359	−	0.448274i
$688$	−0.899905	−	8.56203i	−0.0343086	−	0.326424i
$689$	−0.725996	−	0.154315i	−0.0276582	−	0.00587894i
$690$	−6.01058	−	0.0832607i	−0.228819	−	0.00316968i
$691$	1.85396	−	17.6392i	0.0705279	−	0.671028i	−0.900954	−	0.433915i	$-0.857132\pi$
$691$	1.85396	−	17.6392i	0.0705279	−	0.671028i	0.971482	−	0.237114i	$-0.0762014\pi$
$692$	−10.5849			−0.402378
$693$	−15.1650	+	45.8545i	−0.576073	+	1.74187i
$694$	−11.0111			−0.417976
$695$	−2.30272	+	21.9089i	−0.0873471	+	0.831052i
$696$	−5.98513	+	10.0427i	−0.226866	+	0.380667i
$697$	−72.4637	−	15.4026i	−2.74476	−	0.583416i
$698$	−1.11006	−	10.5615i	−0.0420165	−	0.399760i
$699$	0.366762	−	3.07867i	0.0138722	−	0.116446i
$700$	3.24799	−	3.60726i	0.122762	−	0.136342i
$701$	−12.1048	+	37.2547i	−0.457191	+	1.40709i	0.411352	+	0.911476i	$0.365057\pi$
$701$	−12.1048	+	37.2547i	−0.457191	+	1.40709i	−0.868543	+	0.495613i	$0.834943\pi$
$702$	−1.45032	−	5.18779i	−0.0547389	−	0.195801i
$703$	−14.2877			−0.538872
$704$	−1.09549	−	3.13048i	−0.0412878	−	0.117984i
$705$	5.04452	−	5.44880i	0.189988	−	0.205214i
$706$	17.9881	−	8.00884i	0.676993	−	0.301417i
$707$	−44.2402	−	49.1337i	−1.66382	−	1.84786i
$708$	1.92454	+	21.1211i	0.0723286	+	0.793780i
$709$	−17.4814	−	7.78322i	−0.656527	−	0.292305i	0.0513073	−	0.998683i	$-0.483661\pi$
$709$	−17.4814	−	7.78322i	−0.656527	−	0.292305i	−0.707835	+	0.706378i	$0.750328\pi$
$710$	−0.537178	+	0.390282i	−0.0201599	+	0.0146470i
$711$	6.95926	+	5.35689i	0.260993	+	0.200899i
$712$	2.94152	−	9.05307i	0.110238	−	0.339278i
$713$	−2.73893	+	26.0592i	−0.102574	+	0.975926i
$714$	−16.4835	−	53.2286i	−0.616879	−	1.99203i
$715$	−0.282496	+	3.42663i	−0.0105647	+	0.128149i
$716$	4.13990	−	7.17052i	0.154715	−	0.267975i
$717$	−4.35511	+	12.7977i	−0.162644	+	0.477939i
$718$	−6.44706	+	1.37036i	−0.240602	+	0.0511416i
$719$	−11.9036	−	36.6355i	−0.443929	−	1.36627i	−0.883654	−	0.468141i	$-0.844924\pi$
$719$	−11.9036	−	36.6355i	−0.443929	−	1.36627i	0.439724	−	0.898133i	$-0.355076\pi$
$720$	1.94487	+	2.28418i	0.0724809	+	0.0851265i
$721$	−33.2815	+	24.1804i	−1.23947	+	0.900525i
$722$	−2.70199	+	3.00087i	−0.100558	+	0.111681i
$723$	3.87836	−	6.50765i	0.144238	−	0.242022i
$724$	−4.90861	+	2.18546i	−0.182427	+	0.0812218i
$725$	−3.37488	+	5.84546i	−0.125340	+	0.217095i
$726$	13.1824	+	13.7558i	0.489246	+	0.510527i
$727$	−20.8218	−	36.0644i	−0.772238	−	1.33755i	−0.936334	−	0.351111i	$-0.885804\pi$
$727$	−20.8218	−	36.0644i	−0.772238	−	1.33755i	0.164096	−	0.986444i	$-0.447529\pi$
$728$	4.07102	+	2.95777i	0.150882	+	0.109622i
$729$	26.9068	+	2.24136i	0.996548	+	0.0830132i
$730$	2.15909	+	6.64500i	0.0799116	+	0.245943i
$731$	−52.1265	−	23.2082i	−1.92797	−	0.858386i
$732$	−0.684002	+	5.74164i	−0.0252814	+	0.212217i
$733$	37.8816	+	8.05198i	1.39919	+	0.297407i	0.844903	−	0.534920i	$-0.179658\pi$
$733$	37.8816	+	8.05198i	1.39919	+	0.297407i	0.554286	+	0.832327i	$0.312992\pi$
$734$	−3.61342	−	4.01311i	−0.133374	−	0.148126i
$735$	18.8974	+	21.5815i	0.697042	+	0.796046i
$736$	1.73527	+	3.00558i	0.0639629	+	0.110787i
$737$	13.2072	−	6.23940i	0.486495	−	0.229831i
$738$	2.58005	+	33.4335i	0.0949728	+	1.23070i
$739$	−33.9099	−	24.6370i	−1.24740	−	0.906287i	−0.249329	−	0.968419i	$-0.580210\pi$
$739$	−33.9099	−	24.6370i	−1.24740	−	0.906287i	−0.998068	+	0.0621319i	$0.980210\pi$
$740$	−3.61305	+	0.767977i	−0.132818	+	0.0282314i
$741$	−5.67494	+	4.00417i	−0.208474	+	0.147097i
$742$	0.363267	+	3.45626i	0.0133360	+	0.126883i
$743$	−2.46018	−	23.4071i	−0.0902554	−	0.858723i	−0.942191	−	0.335076i	$-0.891238\pi$
$743$	−2.46018	−	23.4071i	−0.0902554	−	0.858723i	0.851936	−	0.523647i	$-0.175429\pi$
$744$	10.6850	−	7.53924i	0.391732	−	0.276402i
$745$	19.6313	−	4.17275i	0.719233	−	0.152878i
$746$	31.1693	+	22.6458i	1.14119	+	0.829123i
$747$	18.5993	−	12.7413i	0.680512	−	0.466179i
$748$	−21.5986	−	4.08613i	−0.789724	−	0.149404i
$749$	32.6512	+	56.5536i	1.19305	+	2.06642i
$750$	1.14103	+	1.30309i	0.0416645	+	0.0475823i
$751$	0.114271	+	0.126911i	0.00416982	+	0.00463105i	0.745226	−	0.666812i	$-0.232342\pi$
$751$	0.114271	+	0.126911i	0.00416982	+	0.00463105i	−0.741056	+	0.671443i	$0.765675\pi$
$752$	−4.19337	−	0.891329i	−0.152917	−	0.0325034i
$753$	−3.17985	+	26.6922i	−0.115880	+	0.972719i
$754$	−6.39234	−	2.84605i	−0.232795	−	0.103647i
$755$	0.0274925	+	0.0846134i	0.00100056	+	0.00307940i
$756$	−21.0036	+	13.9648i	−0.763893	+	0.507896i
$757$	11.0840	+	8.05300i	0.402855	+	0.292691i	0.770703	−	0.637195i	$-0.219905\pi$
$757$	11.0840	+	8.05300i	0.402855	+	0.292691i	−0.367848	+	0.929886i	$0.619905\pi$
$758$	−7.04553	−	12.2032i	−0.255905	−	0.443241i
$759$	−16.2295	−	11.5792i	−0.589093	−	0.420297i
$760$	1.93403	−	3.34984i	0.0701547	−	0.121512i
$761$	−4.30569	+	1.91702i	−0.156081	+	0.0694919i	−0.483290	−	0.875460i	$-0.660558\pi$
$761$	−4.30569	+	1.91702i	−0.156081	+	0.0694919i	0.327209	+	0.944952i	$0.393892\pi$
$762$	5.81024	−	9.74923i	0.210483	−	0.353177i
$763$	3.22364	−	3.58022i	0.116704	−	0.129613i
$764$	13.1672	−	9.56652i	0.476372	−	0.346105i
$765$	19.5558	−	3.59365i	0.707041	−	0.129929i
$766$	2.54391	+	7.82934i	0.0919151	+	0.282886i
$767$	−12.4164	+	2.63920i	−0.448332	+	0.0952959i
$768$	0.557998	−	1.63971i	0.0201350	−	0.0591678i
$769$	−20.5956	+	35.6726i	−0.742695	+	1.28639i	0.208569	+	0.978008i	$0.433119\pi$
$769$	−20.5956	+	35.6726i	−0.742695	+	1.28639i	−0.951264	+	0.308378i	$0.900214\pi$
$770$	15.6681	−	3.70006i	0.564638	−	0.133341i
$771$	−4.38817	−	14.1703i	−0.158036	−	0.510331i
$772$	2.32546	−	22.1253i	0.0836952	−	0.796307i
$773$	−3.67394	+	11.3072i	−0.132142	+	0.406692i	−0.995135	−	0.0985248i	$-0.968588\pi$
$773$	−3.67394	+	11.3072i	−0.132142	+	0.406692i	0.862992	+	0.505217i	$0.168588\pi$
$774$	−3.41017	+	25.6014i	−0.122576	+	0.920225i
$775$	6.10812	−	4.43781i	0.219410	−	0.159411i
$776$	6.30792	+	2.80847i	0.226441	+	0.100818i
$777$	−2.81804	−	30.9270i	−0.101097	−	1.10950i
$778$	12.6855	+	14.0887i	0.454797	+	0.505104i
$779$	39.4979	−	17.5856i	1.41516	−	0.630070i
$780$	−1.21984	+	1.31760i	−0.0436772	+	0.0471776i
$781$	−2.20164	+	0.0494670i	−0.0787810	+	0.00177007i
$782$	23.0019			0.822545
$783$	24.5308	−	25.0667i	0.876658	−	0.895811i
$784$	5.11786	−	15.7512i	0.182781	−	0.562541i
$785$	5.07749	−	5.63912i	0.181223	−	0.201269i
$786$	−1.05462	+	8.85268i	−0.0376170	+	0.315765i
$787$	−3.26943	−	31.1066i	−0.116543	−	1.10883i	−0.883921	−	0.467635i	$-0.845106\pi$
$787$	−3.26943	−	31.1066i	−0.116543	−	1.10883i	0.767379	−	0.641194i	$-0.221561\pi$
$788$	−13.3491	−	2.83744i	−0.475542	−	0.101080i
$789$	10.2780	−	17.2459i	0.365907	−	0.613969i
$790$	0.305998	−	2.91137i	0.0108869	−	0.103582i
$791$	−59.1998			−2.10490
$792$	0.988194	+	9.90068i	0.0351139	+	0.351805i
$793$	−3.46080			−0.122897
$794$	−1.86000	+	17.6967i	−0.0660090	+	0.628034i
$795$	−1.23996	−	0.0171764i	−0.0439768	−	0.000609183i
$796$	15.2220	+	3.23554i	0.539530	+	0.114681i
$797$	−0.322299	−	3.06647i	−0.0114164	−	0.108620i	0.987330	−	0.158682i	$-0.0507246\pi$
$797$	−0.322299	−	3.06647i	−0.0114164	−	0.108620i	−0.998746	+	0.0500625i	$0.984058\pi$
$798$	26.0424	+	19.4777i	0.921891	+	0.689503i
$799$	−19.0124	+	21.1154i	−0.672609	+	0.747008i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	−14.9580	+	24.3260i	−0.528515	+	0.859516i
$802$	−13.6850			−0.483236
$803$	−6.66404	+	22.1943i	−0.235169	+	0.783219i
$804$	7.43883	+	1.68919i	0.262347	+	0.0595732i
$805$	−15.3897	+	6.85195i	−0.542417	+	0.241499i
$806$	5.23724	+	5.81655i	0.184474	+	0.204879i
$807$	−7.62139	−	3.52055i	−0.268286	−	0.123929i
$808$	−12.4432	−	5.54008i	−0.437751	−	0.194899i
$809$	−34.8810	+	25.3425i	−1.22635	+	0.890996i	−0.996611	−	0.0822557i	$-0.973788\pi$
$809$	−34.8810	+	25.3425i	−1.22635	+	0.890996i	−0.229740	+	0.973252i	$0.573788\pi$
$810$	−4.06147	−	8.03147i	−0.142705	−	0.282197i
$811$	−5.15542	+	15.8667i	−0.181031	+	0.557157i	−0.999857	−	0.0168846i	$-0.994625\pi$
$811$	−5.15542	+	15.8667i	−0.181031	+	0.557157i	0.818826	+	0.574042i	$0.194625\pi$
$812$	−3.42473	+	32.5841i	−0.120184	+	1.14348i
$813$	2.99811	−	3.23838i	0.105148	−	0.113575i
$814$	−11.3008	−	4.73021i	−0.396093	−	0.165794i
$815$	3.85638	−	6.67945i	0.135083	−	0.233971i
$816$	−7.56245	−	8.63658i	−0.264739	−	0.302341i
$817$	32.5732	−	6.92365i	1.13959	−	0.242228i
$818$	3.87645	+	11.9305i	0.135537	+	0.417140i
$819$	−9.78668	−	11.4941i	−0.341974	−	0.401637i
$820$	9.04290	−	6.57005i	0.315792	−	0.229436i
$821$	−23.3592	+	25.9430i	−0.815242	+	0.905418i	−0.996959	−	0.0779332i	$-0.975168\pi$
$821$	−23.3592	+	25.9430i	−0.815242	+	0.905418i	0.181717	+	0.983351i	$0.441835\pi$
$822$	−14.5663	−	0.201778i	−0.508059	−	0.00703782i
$823$	−32.4358	+	14.4414i	−1.13064	+	0.503394i	−0.884826	−	0.465922i	$-0.845723\pi$
$823$	−32.4358	+	14.4414i	−1.13064	+	0.503394i	−0.245817	+	0.969316i	$0.579056\pi$
$824$	−4.23752	+	7.33959i	−0.147621	+	0.255687i
$825$	0.649654	+	5.70771i	0.0226181	+	0.198717i
$826$	29.7184	+	51.4737i	1.03403	+	1.79100i
$827$	22.3248	+	16.2199i	0.776310	+	0.564022i	0.903869	−	0.427809i	$-0.140714\pi$
$827$	22.3248	+	16.2199i	0.776310	+	0.564022i	−0.127560	+	0.991831i	$0.540714\pi$
$828$	−2.94185	−	9.98736i	−0.102236	−	0.347085i
$829$	−7.43679	−	22.8881i	−0.258290	−	0.794936i	−0.993164	−	0.116732i	$-0.962758\pi$
$829$	−7.43679	−	22.8881i	−0.258290	−	0.794936i	0.734873	−	0.678205i	$-0.237242\pi$
$830$	−6.86527	−	3.05662i	−0.238297	−	0.106097i
$831$	37.8462	−	16.2259i	1.31287	−	0.562869i
$832$	1.01402	+	0.215536i	0.0351548	+	0.00747238i
$833$	−73.4485	−	81.5728i	−2.54484	−	2.82633i
$834$	−37.4289	+	7.41544i	−1.29606	+	0.256776i
$835$	−10.5635	−	18.2966i	−0.365566	−	0.633179i
$836$	11.5996	−	5.47993i	0.401182	−	0.189527i
$837$	−36.4715	+	14.4541i	−1.26064	+	0.499608i
$838$	3.62890	+	2.63655i	0.125358	+	0.0910781i
$839$	−30.6555	+	6.51604i	−1.05835	+	0.224959i	−0.704033	−	0.710168i	$-0.748619\pi$
$839$	−30.6555	+	6.51604i	−1.05835	+	0.224959i	−0.354314	+	0.935126i	$0.615286\pi$
$840$	7.63249	+	3.52567i	0.263346	+	0.121647i
$841$	−1.73090	−	16.4684i	−0.0596863	−	0.567878i
$842$	3.31445	+	31.5349i	0.114223	+	1.08676i
$843$	−4.14089	−	45.4448i	−0.142620	−	1.56520i
$844$	−7.13115	+	1.51577i	−0.245464	+	0.0521750i
$845$	9.64778	+	7.00952i	0.331894	+	0.241135i
$846$	11.5999	+	5.55455i	0.398811	+	0.190969i
$847$	49.7045	+	19.5048i	1.70787	+	0.670191i
$848$	0.357980	+	0.620039i	0.0122931	+	0.0212922i
$849$	−11.9115	+	35.0024i	−0.408800	+	1.20128i
$850$	−4.43483	−	4.92538i	−0.152113	−	0.168939i
$851$	12.5392	+	2.66529i	0.429839	+	0.0913651i
$852$	−0.920966	−	0.688811i	−0.0315518	−	0.0235983i
$853$	−28.5869	−	12.7277i	−0.978795	−	0.435788i	−0.145949	−	0.989292i	$-0.546624\pi$
$853$	−28.5869	−	12.7277i	−0.978795	−	0.435788i	−0.832846	+	0.553504i	$0.813290\pi$
$854$	5.00751	+	15.4115i	0.171353	+	0.527371i
$855$	−8.00061	+	8.40521i	−0.273615	+	0.287452i
$856$	10.8839	+	7.90760i	0.372003	+	0.270276i
$857$	−18.2500	−	31.6099i	−0.623407	−	1.07977i	−0.988847	−	0.148937i	$-0.952415\pi$
$857$	−18.2500	−	31.6099i	−0.623407	−	1.07977i	0.365440	−	0.930835i	$-0.380919\pi$
$858$	−5.81421	+	1.28829i	−0.198494	+	0.0439814i
$859$	−18.8016	+	32.5654i	−0.641503	+	1.11112i	0.343594	+	0.939118i	$0.388355\pi$
$859$	−18.8016	+	32.5654i	−0.641503	+	1.11112i	−0.985097	+	0.171998i	$0.944978\pi$
$860$	7.86489	−	3.50167i	0.268190	−	0.119406i
$861$	45.8559	+	82.0281i	1.56277	+	2.79551i
$862$	−14.7018	+	16.3281i	−0.500747	+	0.556136i
$863$	−23.6791	+	17.2039i	−0.806045	+	0.585626i	−0.912681	−	0.408672i	$-0.865992\pi$
$863$	−23.6791	+	17.2039i	−0.806045	+	0.585626i	0.106636	+	0.994298i	$0.465992\pi$
$864$	−2.78277	+	4.38818i	−0.0946719	+	0.149289i
$865$	−3.27092	−	10.0668i	−0.111214	−	0.342283i
$866$	19.0656	−	4.05251i	0.647874	−	0.137710i
$867$	−45.7498	+	9.06398i	−1.55374	+	0.307829i
$868$	18.3241	−	31.7383i	0.621962	−	1.07727i
$869$	6.33296	−	7.35939i	0.214831	−	0.249650i
$870$	−11.4007	−	2.58884i	−0.386519	−	0.0877698i
$871$	−0.477241	+	4.54065i	−0.0161707	+	0.153854i
$872$	0.306701	−	0.943928i	0.0103862	−	0.0319654i
$873$	−16.4148	−	12.6353i	−0.555557	−	0.427640i
$874$	−10.8605	+	7.89059i	−0.367361	+	0.266903i
$875$	4.43439	+	1.97432i	0.149910	+	0.0667441i
$876$	−9.88814	+	6.97696i	−0.334089	+	0.235730i
$877$	10.8172	+	12.0137i	0.365271	+	0.405675i	0.897563	−	0.440886i	$-0.145336\pi$
$877$	10.8172	+	12.0137i	0.365271	+	0.405675i	−0.532292	+	0.846561i	$0.678669\pi$
$878$	−21.1473	+	9.41539i	−0.713687	+	0.317754i
$879$	−17.1594	−	55.4114i	−0.578773	−	1.86898i
$880$	2.63874	−	2.00924i	0.0889519	−	0.0677316i
$881$	13.3765			0.450664			0.225332	−	0.974282i	$-0.427653\pi$
$881$	13.3765			0.450664			0.225332	+	0.974282i	$0.427653\pi$
$882$	−26.0249	+	42.3240i	−0.876306	+	1.42512i
$883$	0.882077	−	2.71475i	0.0296842	−	0.0913587i	−0.935117	−	0.354340i	$-0.884706\pi$
$883$	0.882077	−	2.71475i	0.0296842	−	0.0913587i	0.964801	+	0.262981i	$0.0847057\pi$
$884$	4.59747	−	5.10600i	0.154630	−	0.171733i
$885$	−19.4926	+	8.35712i	−0.655238	+	0.280922i
$886$	3.09019	+	29.4011i	0.103817	+	0.987751i
$887$	3.10156	+	0.659258i	0.104140	+	0.0221357i	0.259687	−	0.965693i	$-0.416381\pi$
$887$	3.10156	+	0.659258i	0.104140	+	0.0221357i	−0.155547	+	0.987829i	$0.549714\pi$
$888$	−3.12184	−	5.58442i	−0.104762	−	0.187401i
$889$	3.32465	−	31.6319i	0.111505	−	1.06090i
$890$	9.51896			0.319076
$891$	4.09617	−	29.5672i	0.137227	−	0.990540i
$892$	−6.06497			−0.203070
$893$	1.73336	−	16.4918i	0.0580045	−	0.551876i
$894$	16.9623	+	30.3426i	0.567305	+	1.01481i
$895$	8.09886	+	1.72147i	0.270715	+	0.0575423i
$896$	−0.507386	−	4.82745i	−0.0169506	−	0.161274i
$897$	5.72741	−	2.45552i	0.191233	−	0.0819876i
$898$	20.2254	−	22.4626i	0.674931	−	0.749586i
$899$	−15.7478	+	48.4668i	−0.525219	+	1.61646i
$900$	−1.57139	+	2.55553i	−0.0523797	+	0.0851843i
$901$	4.74520			0.158085
$902$	37.0627	−	0.832733i	1.23405	−	0.0277270i
$903$	21.4114	+	69.1419i	0.712528	+	2.30090i
$904$	−11.1416	+	4.96055i	−0.370564	+	0.164986i
$905$	−3.59534	−	3.99303i	−0.119513	−	0.132733i
$906$	−0.125909	+	0.0888403i	−0.00418306	+	0.00295152i
$907$	−0.877050	−	0.390488i	−0.0291220	−	0.0129659i	0.392124	−	0.919912i	$-0.371740\pi$
$907$	−0.877050	−	0.390488i	−0.0291220	−	0.0129659i	−0.421246	+	0.906946i	$0.638407\pi$
$908$	−15.4026	+	11.1906i	−0.511153	+	0.371375i
$909$	32.3804	+	24.9248i	1.07399	+	0.826703i
$910$	−1.55499	+	4.78577i	−0.0515474	+	0.158647i
$911$	−1.37447	+	13.0772i	−0.0455383	+	0.433268i	0.947872	+	0.318653i	$0.103230\pi$
$911$	−1.37447	+	13.0772i	−0.0455383	+	0.433268i	−0.993410	+	0.114616i	$0.963436\pi$
$912$	6.53336	+	1.48358i	0.216341	+	0.0491262i
$913$	−12.9439	−	21.2997i	−0.428380	−	0.704919i
$914$	5.42925	−	9.40374i	0.179584	−	0.311048i
$915$	−5.67199	+	1.12374i	−0.187510	+	0.0371497i
$916$	−11.0786	+	2.35484i	−0.366049	+	0.0778060i
$917$	7.72076	+	23.7621i	0.254962	+	0.784692i
$918$	15.9655	+	30.5145i	0.526941	+	1.00713i
$919$	22.6928	−	16.4873i	0.748568	−	0.543866i	−0.146815	−	0.989164i	$-0.546902\pi$
$919$	22.6928	−	16.4873i	0.748568	−	0.543866i	0.895383	+	0.445298i	$0.146902\pi$
$920$	−2.32224	+	2.57911i	−0.0765621	+	0.0850309i
$921$	−6.16616	−	11.0302i	−0.203182	−	0.363457i
$922$	−26.5270	+	11.8106i	−0.873619	+	0.388960i
$923$	0.344169	−	0.596118i	0.0113285	−	0.0196215i
$924$	14.1497	+	24.0276i	0.465489	+	0.790450i
$925$	−1.84688	−	3.19889i	−0.0607251	−	0.105179i
$926$	−29.2499	−	21.2513i	−0.961211	−	0.698361i
$927$	17.5295	−	18.4160i	0.575746	−	0.604862i
$928$	2.08579	+	6.41940i	0.0684694	+	0.210727i
$929$	−20.6274	−	9.18390i	−0.676763	−	0.301314i	0.0394244	−	0.999223i	$-0.487448\pi$
$929$	−20.6274	−	9.18390i	−0.676763	−	0.301314i	−0.716187	+	0.697908i	$0.754114\pi$
$930$	10.4721	+	7.83231i	0.343394	+	0.256832i
$931$	62.6620	+	13.3192i	2.05366	+	0.436520i
$932$	−1.19777	−	1.33026i	−0.0392343	−	0.0435741i
$933$	4.00367	−	11.7650i	0.131074	−	0.385169i
$934$	−0.846245	−	1.46574i	−0.0276900	−	0.0479605i
$935$	−2.78820	−	21.8042i	−0.0911839	−	0.713074i
$936$	−2.80501	−	1.34317i	−0.0916847	−	0.0439029i
$937$	26.9835	+	19.6047i	0.881512	+	0.640456i	0.933651	−	0.358184i	$-0.116604\pi$
$937$	26.9835	+	19.6047i	0.881512	+	0.640456i	−0.0521389	+	0.998640i	$0.516604\pi$
$938$	20.9108	−	4.44472i	0.682760	−	0.145125i
$939$	2.57806	+	28.2933i	0.0841318	+	0.923316i
$940$	−0.448119	−	4.26357i	−0.0146160	−	0.139062i
$941$	2.65633	+	25.2732i	0.0865937	+	0.823884i	0.948492	+	0.316802i	$0.102609\pi$
$941$	2.65633	+	25.2732i	0.0865937	+	0.823884i	−0.861898	+	0.507082i	$0.830724\pi$
$942$	11.9316	+	5.51158i	0.388754	+	0.179577i
$943$	−37.9447	+	8.06540i	−1.23565	+	0.262646i
$944$	9.90624	+	7.19731i	0.322421	+	0.234252i
$945$	−19.7718	−	15.6602i	−0.643177	−	0.509427i
$946$	28.0558	+	5.30773i	0.912173	+	0.172569i
$947$	−1.83164	−	3.17250i	−0.0595204	−	0.103092i	0.834730	−	0.550660i	$-0.185624\pi$
$947$	−1.83164	−	3.17250i	−0.0595204	−	0.103092i	−0.894250	+	0.447567i	$0.852290\pi$
$948$	4.97375	−	0.985403i	0.161540	−	0.0320044i
$949$	−4.84665	−	5.38275i	−0.157329	−	0.174731i
$950$	3.78354	+	0.804216i	0.122754	+	0.0260922i
$951$	38.8740	−	16.6665i	1.26058	−	0.540449i
$952$	−29.3900	−	13.0853i	−0.952536	−	0.424096i
$953$	−6.25713	−	19.2575i	−0.202688	−	0.623810i	−0.999800	−	0.0199791i	$-0.993640\pi$
$953$	−6.25713	−	19.2575i	−0.202688	−	0.623810i	0.797112	−	0.603831i	$-0.206360\pi$
$954$	−0.606893	−	2.06035i	−0.0196489	−	0.0667064i
$955$	13.1672	+	9.56652i	0.426080	+	0.309565i
$956$	3.90244	+	6.75922i	0.126214	+	0.218609i
$957$	−26.1923	−	28.5904i	−0.846678	−	0.924198i
$958$	9.80223	−	16.9780i	0.316696	−	0.548533i
$959$	−37.2962	+	16.6054i	−1.20436	+	0.536215i
$960$	1.73188	+	0.0239907i	0.0558963	+	0.000774296i
$961$	17.3996	−	19.3242i	0.561278	−	0.623362i
$962$	3.09791	−	2.25076i	0.0998805	−	0.0725675i
$963$	−26.1647	−	30.7296i	−0.843146	−	0.990248i
$964$	−1.35159	−	4.15976i	−0.0435317	−	0.133977i
$965$	21.7610	−	4.62545i	0.700512	−	0.148898i
$966$	−19.2219	−	21.9521i	−0.618456	−	0.706298i
$967$	3.49045	−	6.04563i	0.112245	−	0.194414i	−0.804430	−	0.594047i	$-0.797529\pi$
$967$	3.49045	−	6.04563i	0.112245	−	0.194414i	0.916675	+	0.399633i	$0.130862\pi$
$968$	10.9889	−	0.494052i	0.353197	−	0.0158794i
$969$	30.1662	−	32.5838i	0.969077	−	1.04674i
$970$	−0.721757	+	6.86706i	−0.0231742	+	0.220488i
$971$	−14.2275	+	43.7877i	−0.456582	+	1.40521i	0.412686	+	0.910873i	$0.364591\pi$
$971$	−14.2275	+	43.7877i	−0.456582	+	1.40521i	−0.869268	+	0.494341i	$0.835409\pi$
$972$	11.2074	−	10.8349i	0.359477	−	0.347529i
$973$	−86.5103	+	62.8534i	−2.77339	+	2.01499i
$974$	−34.3294	−	15.2844i	−1.09999	−	0.489745i
$975$	−1.63006	−	0.752974i	−0.0522037	−	0.0241145i
$976$	2.23381	+	2.48090i	0.0715025	+	0.0794116i
$977$	−17.4036	+	7.74860i	−0.556792	+	0.247900i	−0.665786	−	0.746143i	$-0.731904\pi$
$977$	−17.4036	+	7.74860i	−0.556792	+	0.247900i	0.108994	+	0.994042i	$0.465237\pi$
$978$	13.0272	+	2.95819i	0.416565	+	0.0945926i
$979$	25.9517	+	17.9785i	0.829420	+	0.574594i
$980$	16.5617			0.529045
$981$	−1.55961	+	2.53638i	−0.0497946	+	0.0809802i
$982$	3.77397	−	11.6151i	0.120432	−	0.370652i
$983$	4.95664	−	5.50490i	0.158092	−	0.175579i	−0.658895	−	0.752235i	$-0.728976\pi$
$983$	4.95664	−	5.50490i	0.158092	−	0.175579i	0.816987	+	0.576656i	$0.195643\pi$
$984$	15.5036	+	11.5955i	0.494238	+	0.369652i
$985$	−1.42653	−	13.5726i	−0.0454531	−	0.432458i
$986$	43.7581	+	9.30107i	1.39354	+	0.296206i
$987$	36.0398	+	0.499236i	1.14716	+	0.0158909i
$988$	−0.419151	+	3.98795i	−0.0133350	+	0.126874i
$989$	−29.8785			−0.950082
$990$	−9.11074	+	3.99931i	−0.289558	+	0.127106i
$991$	48.3897			1.53715			0.768575	−	0.639760i	$-0.220966\pi$
$991$	48.3897			1.53715			0.768575	+	0.639760i	$0.220966\pi$
$992$	0.789195	−	7.50869i	0.0250570	−	0.238401i
$993$	15.9896	−	26.8295i	0.507414	−	0.851410i
$994$	−3.15260	−	0.670105i	−0.0999943	−	0.0212544i
$995$	1.62668	+	15.4768i	0.0515692	+	0.490648i
$996$	1.53975	−	12.9249i	0.0487888	−	0.409542i
$997$	−25.7735	+	28.6244i	−0.816256	+	0.906544i	−0.997033	−	0.0769805i	$-0.975472\pi$
$997$	−25.7735	+	28.6244i	−0.816256	+	0.906544i	0.180777	+	0.983524i	$0.442139\pi$
$998$	−7.46075	+	22.9618i	−0.236166	+	0.726844i
$999$	5.16764	+	18.4846i	0.163497	+	0.584827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.301.5	✓	88
9.7	even	3	inner	990.2.bg.a.961.9	yes	88
11.3	even	5	inner	990.2.bg.a.751.9	yes	88
99.25	even	15	inner	990.2.bg.a.421.5	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.301.5	✓	88	1.1	even	1	trivial
990.2.bg.a.421.5	yes	88	99.25	even	15	inner
990.2.bg.a.751.9	yes	88	11.3	even	5	inner
990.2.bg.a.961.9	yes	88	9.7	even	3	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.845166 - 1.51185i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(1.59191 - 0.682504i) q^{6} +(3.24799 - 3.60726i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.57139 + 2.55553i) q^{9} +1.00000 q^{10} +(2.72632 + 1.88870i) q^{11} +(0.512365 + 1.65453i) q^{12} +(-0.947048 + 0.421653i) q^{13} +(3.24799 + 3.60726i) q^{14} +(-1.41523 + 0.998567i) q^{15} +(0.913545 + 0.406737i) q^{16} +(5.36196 - 3.89569i) q^{17} +(-2.37728 - 1.82991i) q^{18} +(-1.19530 + 3.67875i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(-8.19873 - 1.86175i) q^{21} +(-2.16333 + 2.51396i) q^{22} +(1.73527 - 3.00558i) q^{23} +(-1.69903 + 0.336613i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(-0.320349 - 0.985934i) q^{26} +(5.19167 + 0.215861i) q^{27} +(-3.92700 + 2.85314i) q^{28} +(4.51647 - 5.01604i) q^{29} +(-0.845166 - 1.51185i) q^{30} +(-6.89732 + 3.07088i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.551242 - 5.71805i) q^{33} +(3.31387 + 5.73980i) q^{34} +(-3.92700 - 2.85314i) q^{35} +(2.06838 - 2.17298i) q^{36} +(1.14144 + 3.51298i) q^{37} +(-3.53365 - 1.57328i) q^{38} +(1.43789 + 1.07543i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(-7.47930 - 8.30660i) q^{41} +(2.70855 - 7.95921i) q^{42} +(-4.30459 - 7.45578i) q^{43} +(-2.27406 - 2.41426i) q^{44} +(2.70579 + 1.29566i) q^{45} +(2.80773 + 2.03993i) q^{46} +(-4.19337 + 0.891329i) q^{47} +(-0.157172 - 1.72490i) q^{48} +(-1.73117 - 16.4710i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-10.4215 - 4.81398i) q^{51} +(1.01402 - 0.215536i) q^{52} +(0.579223 + 0.420830i) q^{53} +(-0.757356 + 5.14066i) q^{54} +(1.59338 - 2.90881i) q^{55} +(-2.42702 - 4.20373i) q^{56} +(6.57195 - 1.30204i) q^{57} +(4.51647 + 5.01604i) q^{58} +(11.9772 + 2.54584i) q^{59} +(1.59191 - 0.682504i) q^{60} +(3.04976 + 1.35784i) q^{61} +(-2.33309 - 7.18053i) q^{62} +(4.11460 + 13.9687i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.518336 + 0.897785i) q^{65} +(5.62911 + 1.14592i) q^{66} +(2.20207 - 3.81410i) q^{67} +(-6.05475 + 2.69575i) q^{68} +(-6.01058 - 0.0832607i) q^{69} +(3.24799 - 3.60726i) q^{70} +(-0.537178 + 0.390282i) q^{71} +(1.94487 + 2.28418i) q^{72} +(2.15909 + 6.64500i) q^{73} +(-3.61305 + 0.767977i) q^{74} +(1.14103 + 1.30309i) q^{75} +(1.93403 - 3.34984i) q^{76} +(15.6681 - 3.70006i) q^{77} +(-1.21984 + 1.31760i) q^{78} +(0.305998 - 2.91137i) q^{79} +(0.309017 - 0.951057i) q^{80} +(-4.06147 - 8.03147i) q^{81} +(9.04290 - 6.57005i) q^{82} +(-6.86527 - 3.05662i) q^{83} +(7.63249 + 3.52567i) q^{84} +(-4.43483 - 4.92538i) q^{85} +(7.86489 - 3.50167i) q^{86} +(-11.4007 - 2.58884i) q^{87} +(2.63874 - 2.00924i) q^{88} +9.51896 q^{89} +(-1.57139 + 2.55553i) q^{90} +(-1.55499 + 4.78577i) q^{91} +(-2.32224 + 2.57911i) q^{92} +(10.4721 + 7.83231i) q^{93} +(-0.448119 - 4.26357i) q^{94} +(3.78354 + 0.804216i) q^{95} +(1.73188 + 0.0239907i) q^{96} +(-0.721757 + 6.86706i) q^{97} +16.5617 q^{98} +(-9.11074 + 3.99931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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