LMFDB - Embedded newform 483.2.u.a.113.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.20
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.437059 + 0.680077i) q^{2} +(1.47311 - 0.911006i) q^{3} +(0.559346 + 1.22480i) q^{4} +(2.18862 + 0.642637i) q^{5} +(-0.0242835 + 1.39999i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-2.67778 - 0.385007i) q^{8} +(1.34013 - 2.68403i) q^{9} +O(q^{10})$	\(q+(-0.437059 + 0.680077i) q^{2} +(1.47311 - 0.911006i) q^{3} +(0.559346 + 1.22480i) q^{4} +(2.18862 + 0.642637i) q^{5} +(-0.0242835 + 1.39999i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-2.67778 - 0.385007i) q^{8} +(1.34013 - 2.68403i) q^{9} +(-1.39360 + 1.20756i) q^{10} +(0.217683 - 0.139896i) q^{11} +(1.93978 + 1.29470i) q^{12} +(3.44772 + 3.97888i) q^{13} +(0.775662 - 0.227755i) q^{14} +(3.80954 - 1.04717i) q^{15} +(-0.331325 + 0.382369i) q^{16} +(-0.548570 + 1.20120i) q^{17} +(1.23963 + 2.08447i) q^{18} +(5.58784 - 2.55188i) q^{19} +(0.437097 + 3.04007i) q^{20} +(-1.70989 - 0.276192i) q^{21} +0.209184i q^{22} +(-4.72589 - 0.816081i) q^{23} +(-4.29543 + 1.87232i) q^{24} +(0.170813 + 0.109775i) q^{25} +(-4.21280 + 0.605709i) q^{26} +(-0.471001 - 5.17476i) q^{27} +(0.379346 - 1.29193i) q^{28} +(-5.82973 - 2.66235i) q^{29} +(-0.952836 + 3.04845i) q^{30} +(-0.227086 + 1.57942i) q^{31} +(-1.63959 - 5.58391i) q^{32} +(0.193225 - 0.404394i) q^{33} +(-0.577152 - 0.898065i) q^{34} +(-1.23321 - 1.91891i) q^{35} +(4.03700 + 0.140089i) q^{36} +(2.19293 + 7.46844i) q^{37} +(-0.706739 + 4.91548i) q^{38} +(8.70368 + 2.72045i) q^{39} +(-5.61323 - 2.56348i) q^{40} +(0.0861414 - 0.293371i) q^{41} +(0.935153 - 1.04214i) q^{42} +(3.89568 - 0.560115i) q^{43} +(0.293105 + 0.188367i) q^{44} +(4.65791 - 5.01311i) q^{45} +(2.62049 - 2.85729i) q^{46} +3.75289i q^{47} +(-0.139739 + 0.865113i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-0.149310 + 0.0681878i) q^{50} +(0.286195 + 2.26926i) q^{51} +(-2.94485 + 6.44833i) q^{52} +(-2.10654 + 2.43108i) q^{53} +(3.72509 + 1.94136i) q^{54} +(0.566328 - 0.166289i) q^{55} +(1.77161 + 2.04454i) q^{56} +(5.90675 - 8.84977i) q^{57} +(4.35854 - 2.80106i) q^{58} +(6.46005 - 5.59766i) q^{59} +(3.41342 + 4.08018i) q^{60} +(-12.9640 - 1.86394i) q^{61} +(-0.974877 - 0.844736i) q^{62} +(-2.77047 + 1.15086i) q^{63} +(3.54318 + 1.04037i) q^{64} +(4.98878 + 10.9239i) q^{65} +(0.190568 + 0.308152i) q^{66} +(6.17187 - 9.60362i) q^{67} -1.77807 q^{68} +(-7.70523 + 3.10313i) q^{69} +1.84400 q^{70} +(4.25892 - 6.62702i) q^{71} +(-4.62196 + 6.67130i) q^{72} +(-2.05888 - 4.50833i) q^{73} +(-6.03755 - 1.77278i) q^{74} +(0.351632 + 0.00609920i) q^{75} +(6.25107 + 5.41658i) q^{76} +(-0.256126 - 0.0368254i) q^{77} +(-5.65414 + 4.73017i) q^{78} +(-7.31938 + 6.34228i) q^{79} +(-0.970870 + 0.623940i) q^{80} +(-5.40808 - 7.19393i) q^{81} +(0.161866 + 0.186803i) q^{82} +(-13.2563 + 3.89239i) q^{83} +(-0.618140 - 2.24875i) q^{84} +(-1.97255 + 2.27644i) q^{85} +(-1.32172 + 2.89417i) q^{86} +(-11.0133 + 1.38898i) q^{87} +(-0.636769 + 0.290803i) q^{88} +(-0.594332 - 4.13367i) q^{89} +(1.37352 + 5.35876i) q^{90} -5.26482i q^{91} +(-1.64387 - 6.24473i) q^{92} +(1.10434 + 2.53355i) q^{93} +(-2.55225 - 1.64023i) q^{94} +(13.8696 - 1.99415i) q^{95} +(-7.50228 - 6.73207i) q^{96} +(-1.27154 + 4.33046i) q^{97} +(-0.735354 - 0.335825i) q^{98} +(-0.0837621 - 0.771748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36} - 44 q^{37} - 308 q^{40} - 44 q^{43} - 184 q^{46} + 98 q^{48} + 48 q^{49} - 28 q^{52} + 28 q^{54} - 44 q^{55} + 66 q^{57} + 4 q^{58} + 220 q^{60} + 84 q^{64} + 176 q^{66} + 44 q^{67} + 102 q^{69} - 8 q^{70} - 60 q^{72} + 4 q^{73} - 8 q^{75} + 176 q^{76} + 18 q^{78} - 16 q^{81} + 20 q^{82} - 154 q^{84} + 84 q^{85} + 28 q^{87} - 418 q^{90} - 188 q^{93} + 12 q^{94} - 412 q^{96} - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.437059	+	0.680077i	−0.309047	+	0.480887i	−0.960684	−	0.277644i	$-0.910446\pi$
$2$	−0.437059	+	0.680077i	−0.309047	+	0.480887i	0.651637	+	0.758531i	$0.274083\pi$
$3$	1.47311	−	0.911006i	0.850503	−	0.525970i
$3$	1.47311	−	0.911006i	0.850503	−	0.525970i
$4$	0.559346	+	1.22480i	0.279673	+	0.612399i
$5$	2.18862	+	0.642637i	0.978781	+	0.287396i	0.731721	−	0.681604i	$-0.238717\pi$
$5$	2.18862	+	0.642637i	0.978781	+	0.287396i	0.247060	+	0.969000i	$0.420536\pi$
$6$	−0.0242835	+	1.39999i	−0.00991368	+	0.571545i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	−2.67778	−	0.385007i	−0.946739	−	0.136121i
$9$	1.34013	−	2.68403i	0.446711	−	0.894678i
$10$	−1.39360	+	1.20756i	−0.440695	+	0.381864i
$11$	0.217683	−	0.139896i	0.0656339	−	0.0421803i	−0.507412	−	0.861703i	$-0.669398\pi$
$11$	0.217683	−	0.139896i	0.0656339	−	0.0421803i	0.573046	+	0.819523i	$0.305762\pi$
$12$	1.93978	+	1.29470i	0.559966	+	0.373747i
$13$	3.44772	+	3.97888i	0.956226	+	1.10354i	0.994548	+	0.104278i	$0.0332532\pi$
$13$	3.44772	+	3.97888i	0.956226	+	1.10354i	−0.0383222	+	0.999265i	$0.512201\pi$
$14$	0.775662	−	0.227755i	0.207304	−	0.0608701i
$15$	3.80954	−	1.04717i	0.983618	−	0.270378i
$16$	−0.331325	+	0.382369i	−0.0828312	+	0.0955923i
$17$	−0.548570	+	1.20120i	−0.133048	+	0.291334i	−0.964417	−	0.264387i	$-0.914830\pi$
$17$	−0.548570	+	1.20120i	−0.133048	+	0.291334i	0.831369	+	0.555721i	$0.187558\pi$
$18$	1.23963	+	2.08447i	0.292184	+	0.491315i
$19$	5.58784	−	2.55188i	1.28194	−	0.585441i	0.346208	−	0.938158i	$-0.387469\pi$
$19$	5.58784	−	2.55188i	1.28194	−	0.585441i	0.935730	+	0.352716i	$0.114742\pi$
$20$	0.437097	+	3.04007i	0.0977378	+	0.679781i
$21$	−1.70989	−	0.276192i	−0.373128	−	0.0602701i
$22$			0.209184i			0.0445982i
$23$	−4.72589	−	0.816081i	−0.985416	−	0.170165i
$23$	−4.72589	−	0.816081i	−0.985416	−	0.170165i
$24$	−4.29543	+	1.87232i	−0.876800	+	0.382185i
$25$	0.170813	+	0.109775i	0.0341625	+	0.0219549i
$26$	−4.21280	+	0.605709i	−0.826198	+	0.118789i
$27$	−0.471001	−	5.17476i	−0.0906441	−	0.995883i
$28$	0.379346	−	1.29193i	0.0716897	−	0.244153i
$29$	−5.82973	−	2.66235i	−1.08255	−	0.494386i	−0.207413	−	0.978253i	$-0.566504\pi$
$29$	−5.82973	−	2.66235i	−1.08255	−	0.494386i	−0.875141	+	0.483867i	$0.839232\pi$
$30$	−0.952836	+	3.04845i	−0.173963	+	0.556569i
$31$	−0.227086	+	1.57942i	−0.0407859	+	0.283672i	0.959214	+	0.282682i	$0.0912242\pi$
$31$	−0.227086	+	1.57942i	−0.0407859	+	0.283672i	−1.00000		0.000990031i	$0.999685\pi$
$32$	−1.63959	−	5.58391i	−0.289840	−	0.987106i
$33$	0.193225	−	0.404394i	0.0336362	−	0.0703959i
$34$	−0.577152	−	0.898065i	−0.0989807	−	0.154017i
$35$	−1.23321	−	1.91891i	−0.208451	−	0.324356i
$36$	4.03700	+	0.140089i	0.672833	+	0.0233481i
$37$	2.19293	+	7.46844i	0.360516	+	1.22780i	0.917653	+	0.397383i	$0.130082\pi$
$37$	2.19293	+	7.46844i	0.360516	+	1.22780i	−0.557137	+	0.830421i	$0.688100\pi$
$38$	−0.706739	+	4.91548i	−0.114648	+	0.797396i
$39$	8.70368	+	2.72045i	1.39370	+	0.435621i
$40$	−5.61323	−	2.56348i	−0.887530	−	0.405321i
$41$	0.0861414	−	0.293371i	0.0134530	−	0.0458168i	−0.952493	−	0.304561i	$-0.901490\pi$
$41$	0.0861414	−	0.293371i	0.0134530	−	0.0458168i	0.965946	+	0.258744i	$0.0833085\pi$
$42$	0.935153	−	1.04214i	0.144297	−	0.160806i
$43$	3.89568	−	0.560115i	0.594086	−	0.0854167i	0.161288	−	0.986907i	$-0.448435\pi$
$43$	3.89568	−	0.560115i	0.594086	−	0.0854167i	0.432798	+	0.901491i	$0.357526\pi$
$44$	0.293105	+	0.188367i	0.0441872	+	0.0283974i
$45$	4.65791	−	5.01311i	0.694360	−	0.747311i
$46$	2.62049	−	2.85729i	0.386370	−	0.421284i
$47$			3.75289i			0.547416i	0.961813	+	0.273708i	$0.0882501\pi$
$47$			3.75289i			0.547416i	−0.961813	+	0.273708i	$0.911750\pi$
$48$	−0.139739	+	0.865113i	−0.0201695	+	0.124868i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−0.149310	+	0.0681878i	−0.0211157	+	0.00964321i
$51$	0.286195	+	2.26926i	0.0400754	+	0.317760i
$52$	−2.94485	+	6.44833i	−0.408378	+	0.894223i
$53$	−2.10654	+	2.43108i	−0.289355	+	0.333934i	−0.881753	−	0.471712i	$-0.843636\pi$
$53$	−2.10654	+	2.43108i	−0.289355	+	0.333934i	0.592397	+	0.805646i	$0.298182\pi$
$54$	3.72509	+	1.94136i	0.506920	+	0.264185i
$55$	0.566328	−	0.166289i	0.0763637	−	0.0224224i
$56$	1.77161	+	2.04454i	0.236741	+	0.273214i
$57$	5.90675	−	8.84977i	0.782368	−	1.17218i
$58$	4.35854	−	2.80106i	0.572304	−	0.367797i
$59$	6.46005	−	5.59766i	0.841026	−	0.728753i	−0.123612	−	0.992331i	$-0.539448\pi$
$59$	6.46005	−	5.59766i	0.841026	−	0.728753i	0.964638	+	0.263577i	$0.0849024\pi$
$60$	3.41342	+	4.08018i	0.440671	+	0.526749i
$61$	−12.9640	−	1.86394i	−1.65987	−	0.238653i	−0.752381	−	0.658729i	$-0.771094\pi$
$61$	−12.9640	−	1.86394i	−1.65987	−	0.238653i	−0.907489	+	0.420076i	$0.862004\pi$
$62$	−0.974877	−	0.844736i	−0.123810	−	0.107282i
$63$	−2.77047	+	1.15086i	−0.349047	+	0.144994i
$64$	3.54318	+	1.04037i	0.442897	+	0.130046i
$65$	4.98878	+	10.9239i	0.618782	+	1.35494i
$66$	0.190568	+	0.308152i	0.0234573	+	0.0379309i
$67$	6.17187	−	9.60362i	0.754014	−	1.17327i	−0.225959	−	0.974137i	$-0.572551\pi$
$67$	6.17187	−	9.60362i	0.754014	−	1.17327i	0.979973	−	0.199132i	$-0.0638122\pi$
$68$	−1.77807			−0.215623
$69$	−7.70523	+	3.10313i	−0.927601	+	0.373573i
$70$	1.84400			0.220400
$71$	4.25892	−	6.62702i	0.505441	−	0.786482i	−0.490965	−	0.871179i	$-0.663356\pi$
$71$	4.25892	−	6.62702i	0.505441	−	0.786482i	0.996407	+	0.0846969i	$0.0269922\pi$
$72$	−4.62196	+	6.67130i	−0.544703	+	0.786220i
$73$	−2.05888	−	4.50833i	−0.240974	−	0.527660i	0.750044	−	0.661388i	$-0.230032\pi$
$73$	−2.05888	−	4.50833i	−0.240974	−	0.527660i	−0.991018	+	0.133728i	$0.957305\pi$
$74$	−6.03755	−	1.77278i	−0.701851	−	0.206082i
$75$	0.351632	+	0.00609920i	0.0406030	+	0.000704275i
$76$	6.25107	+	5.41658i	0.717047	+	0.621325i
$77$	−0.256126	−	0.0368254i	−0.0291883	−	0.00419665i
$78$	−5.65414	+	4.73017i	−0.640205	+	0.535586i
$79$	−7.31938	+	6.34228i	−0.823495	+	0.713563i	−0.960883	−	0.276955i	$-0.910675\pi$
$79$	−7.31938	+	6.34228i	−0.823495	+	0.713563i	0.137388	+	0.990517i	$0.456129\pi$
$80$	−0.970870	+	0.623940i	−0.108547	+	0.0697586i
$81$	−5.40808	−	7.19393i	−0.600898	−	0.799326i
$82$	0.161866	+	0.186803i	0.0178751	+	0.0206289i
$83$	−13.2563	+	3.89239i	−1.45506	+	0.427245i	−0.911212	−	0.411937i	$-0.864852\pi$
$83$	−13.2563	+	3.89239i	−1.45506	+	0.427245i	−0.543850	+	0.839182i	$0.683034\pi$
$84$	−0.618140	−	2.24875i	−0.0674446	−	0.245359i
$85$	−1.97255	+	2.27644i	−0.213953	+	0.246915i
$86$	−1.32172	+	2.89417i	−0.142525	+	0.312086i
$87$	−11.0133	+	1.38898i	−1.18075	+	0.148914i
$88$	−0.636769	+	0.290803i	−0.0678798	+	0.0309997i
$89$	−0.594332	−	4.13367i	−0.0629991	−	0.438168i	−0.996771	−	0.0802990i	$-0.974412\pi$
$89$	−0.594332	−	4.13367i	−0.0629991	−	0.438168i	0.933772	−	0.357869i	$-0.116497\pi$
$90$	1.37352	+	5.35876i	0.144782	+	0.564863i
$91$		−	5.26482i		−	0.551903i
$92$	−1.64387	−	6.24473i	−0.171386	−	0.651058i
$93$	1.10434	+	2.53355i	0.114515	+	0.262716i
$94$	−2.55225	−	1.64023i	−0.263245	−	0.169177i
$95$	13.8696	−	1.99415i	1.42299	−	0.204595i
$96$	−7.50228	−	6.73207i	−0.765698	−	0.687089i
$97$	−1.27154	+	4.33046i	−0.129105	+	0.439691i	−0.998520	−	0.0543919i	$-0.982678\pi$
$97$	−1.27154	+	4.33046i	−0.129105	+	0.439691i	0.869415	+	0.494083i	$0.164496\pi$
$98$	−0.735354	−	0.335825i	−0.0742820	−	0.0339235i
$99$	−0.0837621	−	0.771748i	−0.00841841	−	0.0775636i
$100$	−0.0389083	+	0.270613i	−0.00389083	+	0.0270613i
$101$	−4.51859	−	15.3889i	−0.449617	−	1.53125i	−0.803118	−	0.595820i	$-0.796827\pi$
$101$	−4.51859	−	15.3889i	−0.449617	−	1.53125i	0.353502	−	0.935434i	$-0.384991\pi$
$102$	−1.66835	−	0.797165i	−0.165192	−	0.0789311i
$103$	−0.451626	−	0.702743i	−0.0445000	−	0.0692434i	0.818291	−	0.574804i	$-0.194922\pi$
$103$	−0.451626	−	0.702743i	−0.0445000	−	0.0692434i	−0.862791	+	0.505561i	$0.831286\pi$
$104$	−7.70035	−	11.9820i	−0.755082	−	1.17493i
$105$	−3.56481	−	1.70332i	−0.347889	−	0.166227i
$106$	−0.732637	−	2.49513i	−0.0711600	−	0.242349i
$107$	−1.19248	+	8.29387i	−0.115281	+	0.801799i	0.847360	+	0.531019i	$0.178191\pi$
$107$	−1.19248	+	8.29387i	−0.115281	+	0.801799i	−0.962641	+	0.270780i	$0.912718\pi$
$108$	6.07458	−	3.47136i	0.584527	−	0.334032i
$109$	−13.9670	−	6.37850i	−1.33779	−	0.610950i	−0.387375	−	0.921922i	$-0.626618\pi$
$109$	−13.9670	−	6.37850i	−1.33779	−	0.610950i	−0.950419	+	0.310973i	$0.899345\pi$
$110$	−0.134429	+	0.457824i	−0.0128173	+	0.0436518i
$111$	10.0342	+	9.00409i	0.952408	+	0.854631i
$112$	0.500797	−	0.0720038i	0.0473209	−	0.00680372i
$113$	9.07294	+	5.83083i	0.853511	+	0.548518i	0.892668	−	0.450715i	$-0.148831\pi$
$113$	9.07294	+	5.83083i	0.853511	+	0.548518i	−0.0391573	+	0.999233i	$0.512467\pi$
$114$	3.43693	+	7.88491i	0.321898	+	0.738489i
$115$	−9.81873	−	4.82312i	−0.915602	−	0.449758i
$116$		−	8.62942i		−	0.801221i
$117$	15.2999	−	3.92156i	1.41447	−	0.362549i
$118$	0.983420	+	6.83983i	0.0905311	+	0.629658i
$119$	1.20120	−	0.548570i	0.110114	−	0.0502874i
$120$	−10.6043	+	1.33739i	−0.968034	+	0.122087i
$121$	−4.54175	+	9.94505i	−0.412886	+	0.904095i
$122$	6.93365	−	8.00186i	0.627743	−	0.724454i
$123$	−0.140366	−	0.510644i	−0.0126564	−	0.0460432i
$124$	−2.06149	+	0.605308i	−0.185127	+	0.0543583i
$125$	−7.16545	−	8.26937i	−0.640897	−	0.739635i
$126$	0.428190	−	2.38713i	0.0381462	−	0.212662i
$127$	16.6503	−	10.7005i	1.47747	−	0.949515i	0.480091	−	0.877219i	$-0.340604\pi$
$127$	16.6503	−	10.7005i	1.47747	−	0.949515i	0.997383	−	0.0722960i	$-0.0230326\pi$
$128$	6.54029	−	5.66719i	0.578085	−	0.500914i
$129$	5.22852	−	4.37411i	0.460346	−	0.385119i
$130$	−9.60948	−	1.38163i	−0.842807	−	0.121177i
$131$	−2.49968	−	2.16598i	−0.218398	−	0.189243i	0.538790	−	0.842440i	$-0.318882\pi$
$131$	−2.49968	−	2.16598i	−0.218398	−	0.189243i	−0.757188	+	0.653197i	$0.773427\pi$
$132$	0.603380	+	0.0104659i	0.0525175	+	0.000910937i
$133$	−5.89413	−	1.73067i	−0.511086	−	0.150068i
$134$	3.83373	+	8.39469i	0.331184	+	0.725191i
$135$	2.29465	−	11.6283i	0.197492	−	1.00080i
$136$	1.93142	−	3.00535i	0.165618	−	0.257707i
$137$	4.36079			0.372568			0.186284	−	0.982496i	$-0.440356\pi$
$137$	4.36079			0.372568			0.186284	+	0.982496i	$0.440356\pi$
$138$	1.25727	−	6.59640i	0.107026	−	0.561523i
$139$	4.36859			0.370539			0.185270	−	0.982688i	$-0.440684\pi$
$139$	4.36859			0.370539			0.185270	+	0.982688i	$0.440684\pi$
$140$	1.66049	−	2.58377i	0.140337	−	0.218369i
$141$	3.41891	+	5.52844i	0.287924	+	0.465579i
$142$	2.64548	+	5.79279i	0.222004	+	0.486120i
$143$	1.30714	+	0.383811i	0.109309	+	0.0320959i
$144$	0.582272	+	1.40171i	0.0485227	+	0.116809i
$145$	−11.0482	−	9.57328i	−0.917499	−	0.795018i
$146$	3.96586	+	0.570205i	0.328217	+	0.0471905i
$147$	1.11138	+	1.32847i	0.0916651	+	0.109570i
$148$	−7.92072	+	6.86334i	−0.651079	+	0.564163i
$149$	−15.5194	+	9.97372i	−1.27140	+	0.817079i	−0.989802	−	0.142453i	$-0.954501\pi$
$149$	−15.5194	+	9.97372i	−1.27140	+	0.817079i	−0.281599	+	0.959532i	$0.590865\pi$
$150$	−0.157832	+	0.236471i	−0.0128869	+	0.0193078i
$151$	−11.0391	−	12.7398i	−0.898347	−	1.03675i	−0.999124	−	0.0418382i	$-0.986679\pi$
$151$	−11.0391	−	12.7398i	−0.898347	−	1.03675i	0.100778	−	0.994909i	$-0.467867\pi$
$152$	−15.9455	+	4.68202i	−1.29335	+	0.379762i
$153$	2.48891	+	3.08215i	0.201216	+	0.249177i
$154$	0.136986	−	0.158091i	0.0110387	−	0.0127393i
$155$	−1.51200	+	3.31082i	−0.121447	+	0.265931i
$156$	1.53636	+	12.1819i	0.123008	+	0.975334i
$157$	13.1785	−	6.01842i	1.05176	−	0.480322i	0.186921	−	0.982375i	$-0.440149\pi$
$157$	13.1785	−	6.01842i	1.05176	−	0.480322i	0.864837	+	0.502053i	$0.167422\pi$
$158$	−1.11424	−	7.74969i	−0.0886440	−	0.616532i
$159$	−0.888448	+	5.50033i	−0.0704585	+	0.436204i
$160$		−	13.2747i		−	1.04946i
$161$	3.03717	+	3.71155i	0.239362	+	0.292511i
$162$	7.25607	−	0.533737i	0.570091	−	0.0419343i
$163$	−2.51863	−	1.61862i	−0.197274	−	0.126780i	0.438275	−	0.898841i	$-0.355590\pi$
$163$	−2.51863	−	1.61862i	−0.197274	−	0.126780i	−0.635549	+	0.772061i	$0.719226\pi$
$164$	0.407503	−	0.0585900i	0.0318206	−	0.00457511i
$165$	0.682776	−	0.760891i	0.0531540	−	0.0592353i
$166$	3.14664	−	10.7165i	0.244227	−	0.831759i
$167$	−12.3323	−	5.63195i	−0.954298	−	0.435814i	−0.123474	−	0.992348i	$-0.539404\pi$
$167$	−12.3323	−	5.63195i	−0.954298	−	0.435814i	−0.830825	+	0.556534i	$0.812131\pi$
$168$	4.47237	+	1.39790i	0.345051	+	0.107851i
$169$	−2.09463	+	14.5685i	−0.161126	+	1.12065i
$170$	−0.686036	−	2.33642i	−0.0526166	−	0.179196i
$171$	0.639121	−	18.4178i	0.0488748	−	1.40845i
$172$	2.86506	+	4.45812i	0.218459	+	0.339929i
$173$	9.49501	+	14.7745i	0.721892	+	1.12329i	0.987256	+	0.159138i	$0.0508713\pi$
$173$	9.49501	+	14.7745i	0.721892	+	1.12329i	−0.265365	+	0.964148i	$0.585492\pi$
$174$	3.86884	−	8.09694i	0.293296	−	0.613828i
$175$	−0.0572045	−	0.194821i	−0.00432426	−	0.0147271i
$176$	−0.0186317	+	0.129586i	−0.00140442	+	0.00976794i
$177$	4.41688	−	14.1311i	0.331993	−	1.06216i
$178$	3.07097	+	1.40247i	0.230179	+	0.105119i
$179$	−3.13683	+	10.6831i	−0.234458	+	0.798490i	0.755256	+	0.655430i	$0.227513\pi$
$179$	−3.13683	+	10.6831i	−0.234458	+	0.798490i	−0.989714	+	0.143061i	$0.954306\pi$
$180$	8.74543	+	2.90093i	0.651846	+	0.216222i
$181$	3.92202	−	0.563902i	0.291522	−	0.0419145i	0.00499759	−	0.999988i	$-0.498409\pi$
$181$	3.92202	−	0.563902i	0.291522	−	0.0419145i	0.286524	+	0.958073i	$0.407500\pi$
$182$	3.58048	+	2.30103i	0.265403	+	0.170564i
$183$	−20.7955	+	9.06449i	−1.53725	+	0.670066i
$184$	12.3407	+	4.00479i	0.909769	+	0.295237i
$185$			17.7548i			1.30536i
$186$	−2.20567	−	0.356274i	−0.161727	−	0.0261232i
$187$	0.0486293	+	0.338224i	0.00355612	+	0.0247334i
$188$	−4.59653	+	2.09917i	−0.335237	+	0.153097i
$189$	−3.03279	+	4.21926i	−0.220603	+	0.306906i
$190$	−4.70565	+	10.3039i	−0.341384	+	0.747527i
$191$	8.85253	−	10.2164i	0.640546	−	0.739230i	−0.338925	−	0.940813i	$-0.610063\pi$
$191$	8.85253	−	10.2164i	0.640546	−	0.739230i	0.979471	+	0.201584i	$0.0646087\pi$
$192$	6.16729	−	1.69527i	0.445086	−	0.122346i
$193$	4.63198	−	1.36007i	0.333418	−	0.0979002i	−0.110739	−	0.993850i	$-0.535322\pi$
$193$	4.63198	−	1.36007i	0.333418	−	0.0979002i	0.444156	+	0.895949i	$0.353503\pi$
$194$	−2.38931	−	2.75741i	−0.171542	−	0.197970i
$195$	17.3008	+	11.5474i	1.23894	+	0.826923i
$196$	−1.13273	+	0.727960i	−0.0809091	+	0.0519971i
$197$	−9.86771	+	8.55042i	−0.703045	+	0.609192i	−0.931233	−	0.364425i	$-0.881266\pi$
$197$	−9.86771	+	8.55042i	−0.703045	+	0.609192i	0.228188	+	0.973617i	$0.426720\pi$
$198$	0.561457	+	0.280335i	0.0399010	+	0.0199225i
$199$	−3.56458	−	0.512509i	−0.252686	−	0.0363308i	0.0148075	−	0.999890i	$-0.495286\pi$
$199$	−3.56458	−	0.512509i	−0.252686	−	0.0363308i	−0.267494	+	0.963560i	$0.586196\pi$
$200$	−0.415135	−	0.359717i	−0.0293545	−	0.0254358i
$201$	0.342916	−	19.7698i	0.0241874	−	1.39446i
$202$	12.4405	+	3.65287i	0.875312	+	0.257015i
$203$	2.66235	+	5.82973i	0.186860	+	0.409167i
$204$	−2.61930	+	1.61983i	−0.183388	+	0.113411i
$205$	0.377062	−	0.586720i	0.0263352	−	0.0409783i
$206$	0.675306			0.0470508
$207$	−8.52371	+	11.5908i	−0.592439	+	0.805615i
$208$	−2.66372			−0.184696
$209$	0.859378	−	1.33722i	0.0594444	−	0.0924973i
$210$	2.71642	−	1.67989i	0.187451	−	0.115924i
$211$	−10.7110	−	23.4538i	−0.737374	−	1.61462i	−0.787827	−	0.615897i	$-0.788794\pi$
$211$	−10.7110	−	23.4538i	−0.737374	−	1.61462i	0.0504531	−	0.998726i	$-0.483933\pi$
$212$	−4.15586	−	1.22027i	−0.285426	−	0.0838085i
$213$	0.236630	−	13.6423i	0.0162137	−	0.934753i
$214$	−5.11928	−	4.43588i	−0.349947	−	0.303231i
$215$	8.88613	+	1.27763i	0.606029	+	0.0871338i
$216$	−0.731082	+	14.0382i	−0.0497439	+	0.955181i
$217$	1.20592	−	1.04494i	0.0818633	−	0.0709349i
$218$	10.4423	−	6.71083i	0.707239	−	0.454515i
$219$	−7.14009	−	4.76563i	−0.482482	−	0.322031i
$220$	0.520444	+	0.600624i	0.0350883	+	0.0404941i
$221$	−6.67076	+	1.95871i	−0.448724	+	0.131757i
$222$	−10.5090	+	2.88873i	−0.705320	+	0.193879i
$223$	−4.00960	+	4.62733i	−0.268503	+	0.309869i	−0.873949	−	0.486017i	$-0.838449\pi$
$223$	−4.00960	+	4.62733i	−0.268503	+	0.309869i	0.605446	+	0.795886i	$0.292995\pi$
$224$	−2.41757	+	5.29374i	−0.161531	+	0.353703i
$225$	0.523551	−	0.311354i	0.0349034	−	0.0207570i
$226$	−7.93082	+	3.62188i	−0.527550	+	0.240924i
$227$	−0.306437	−	2.13132i	−0.0203390	−	0.141461i	0.977122	−	0.212681i	$-0.0682196\pi$
$227$	−0.306437	−	2.13132i	−0.0203390	−	0.141461i	−0.997461	+	0.0712208i	$0.977311\pi$
$228$	14.1431	+	2.28448i	0.936649	+	0.151294i
$229$			17.9244i			1.18448i	0.805762	+	0.592239i	$0.201756\pi$
$229$			17.9244i			1.18448i	−0.805762	+	0.592239i	$0.798244\pi$
$230$	7.57146	−	4.56950i	0.499247	−	0.301304i
$231$	−0.410852	+	0.179085i	−0.0270321	+	0.0117829i
$232$	14.5857	+	9.37369i	0.957601	+	0.615413i
$233$	15.2467	−	2.19214i	0.998842	−	0.143612i	0.376549	−	0.926397i	$-0.377110\pi$
$233$	15.2467	−	2.19214i	0.998842	−	0.143612i	0.622293	+	0.782785i	$0.286201\pi$
$234$	−4.01998	+	12.1190i	−0.262794	+	0.792246i
$235$	−2.41175	+	8.21366i	−0.157325	+	0.535800i
$236$	10.4694	+	4.78122i	0.681500	+	0.311231i
$237$	−5.00443	+	16.0109i	−0.325073	+	1.04002i
$238$	−0.151926	+	1.05667i	−0.00984788	+	0.0684935i
$239$	7.16750	+	24.4102i	0.463627	+	1.57897i	0.777104	+	0.629372i	$0.216688\pi$
$239$	7.16750	+	24.4102i	0.463627	+	1.57897i	−0.313477	+	0.949596i	$0.601494\pi$
$240$	−0.861789	+	1.80360i	−0.0556282	+	0.116422i
$241$	0.629268	+	0.979161i	0.0405347	+	0.0630733i	0.860930	−	0.508724i	$-0.169883\pi$
$241$	0.629268	+	0.979161i	0.0405347	+	0.0630733i	−0.820395	+	0.571797i	$0.806246\pi$
$242$	−4.77838	−	7.43531i	−0.307166	−	0.477960i
$243$	−14.5204	−	5.67069i	−0.931487	−	0.363775i
$244$	−4.96841	−	16.9209i	−0.318070	−	1.08325i
$245$	−0.324623	+	2.25780i	−0.0207394	+	0.144246i
$246$	0.408626	+	0.127722i	0.0260530	+	0.00814323i
$247$	29.4189	+	13.4352i	1.87188	+	0.854860i
$248$	1.21618	−	4.14192i	0.0772273	−	0.263012i
$249$	−15.9820	+	17.8105i	−1.01282	+	1.12869i
$250$	8.75553	−	1.25885i	0.553748	−	0.0796169i
$251$	−1.62053	−	1.04145i	−0.102287	−	0.0657359i	0.488497	−	0.872565i	$-0.337545\pi$
$251$	−1.62053	−	1.04145i	−0.102287	−	0.0657359i	−0.590784	+	0.806830i	$0.701182\pi$
$252$	−2.95922	−	2.74954i	−0.186413	−	0.173205i
$253$	−1.14291	+	0.483487i	−0.0718542	+	0.0303966i
$254$			16.0002i			1.00394i
$255$	−0.831937	+	5.15047i	−0.0520979	+	0.322535i
$256$	2.04670	+	14.2351i	0.127919	+	0.889696i
$257$	26.5657	−	12.1322i	1.65713	−	0.756784i	0.657130	−	0.753778i	$-0.271770\pi$
$257$	26.5657	−	12.1322i	1.65713	−	0.756784i	0.999995	−	0.00300596i	$-0.000956827\pi$
$258$	0.689557	+	5.46754i	0.0429299	+	0.340394i
$259$	3.23348	−	7.08034i	0.200919	−	0.439951i
$260$	−10.5891	+	12.2205i	−0.656709	+	0.757882i
$261$	−14.9585	+	12.0793i	−0.925906	+	0.747690i
$262$	2.56554	−	0.753311i	0.158500	−	0.0465397i
$263$	15.1046	+	17.4317i	0.931390	+	1.07488i	0.997028	+	0.0770381i	$0.0245463\pi$
$263$	15.1046	+	17.4317i	0.931390	+	1.07488i	−0.0656379	+	0.997844i	$0.520908\pi$
$264$	−0.673110	+	1.00849i	−0.0414271	+	0.0620680i
$265$	−6.17272	+	3.96696i	−0.379187	+	0.243689i
$266$	3.75307	−	3.25206i	0.230116	−	0.199396i
$267$	−4.64132	−	5.54793i	−0.284044	−	0.339528i
$268$	15.2147	+	2.18754i	0.929385	+	0.133625i
$269$	−7.48733	−	6.48781i	−0.456511	−	0.395569i	0.396023	−	0.918240i	$-0.370390\pi$
$269$	−7.48733	−	6.48781i	−0.456511	−	0.395569i	−0.852534	+	0.522672i	$0.824935\pi$
$270$	6.90522	+	6.64278i	0.420238	+	0.404267i
$271$	2.75470	+	0.808854i	0.167336	+	0.0491344i	0.364328	−	0.931271i	$-0.381299\pi$
$271$	2.75470	+	0.808854i	0.167336	+	0.0491344i	−0.196991	+	0.980405i	$0.563117\pi$
$272$	−0.277548	−	0.607745i	−0.0168288	−	0.0368499i
$273$	−4.79628	−	7.75568i	−0.290284	−	0.469395i
$274$	−1.90592	+	2.96567i	−0.115141	+	0.179163i
$275$	0.0525401			0.00316829
$276$	−8.11060	−	7.70162i	−0.488201	−	0.463583i
$277$	7.03530			0.422710			0.211355	−	0.977409i	$-0.432212\pi$
$277$	7.03530			0.422710			0.211355	+	0.977409i	$0.432212\pi$
$278$	−1.90933	+	2.97098i	−0.114514	+	0.178187i
$279$	3.93489	+	2.72614i	0.235576	+	0.163210i
$280$	2.56348	+	5.61323i	0.153197	+	0.335455i
$281$	16.7330	+	4.91326i	0.998210	+	0.293101i	0.739721	−	0.672914i	$-0.234957\pi$
$281$	16.7330	+	4.91326i	0.998210	+	0.293101i	0.258488	+	0.966014i	$0.416776\pi$
$282$	−5.25403	−	0.0911332i	−0.312873	−	0.00542690i
$283$	13.6638	+	11.8398i	0.812232	+	0.703803i	0.958391	−	0.285458i	$-0.0921458\pi$
$283$	13.6638	+	11.8398i	0.812232	+	0.703803i	−0.146160	+	0.989261i	$0.546691\pi$
$284$	10.4990	+	1.50952i	0.622999	+	0.0895737i
$285$	18.6148	−	15.5729i	1.10265	−	0.922459i
$286$	−0.832318	+	0.721208i	−0.0492160	+	0.0426459i
$287$	−0.257218	+	0.165304i	−0.0151831	+	0.00975760i
$288$	−17.1847	−	3.08249i	−1.01262	−	0.181638i
$289$	9.99068	+	11.5299i	0.587687	+	0.678227i
$290$	11.3393	−	3.32951i	0.665864	−	0.195515i
$291$	2.07195	+	7.53764i	0.121460	+	0.441864i
$292$	4.37016	−	5.04343i	0.255744	−	0.295145i
$293$	−7.02370	+	15.3798i	−0.410329	+	0.898495i	0.585789	+	0.810464i	$0.300785\pi$
$293$	−7.02370	+	15.3798i	−0.410329	+	0.898495i	−0.996118	+	0.0880314i	$0.971942\pi$
$294$	−1.38920	+	0.175204i	−0.0810198	+	0.0102181i
$295$	17.7359	−	8.09970i	1.03262	−	0.471583i
$296$	−2.99679	−	20.8432i	−0.174185	−	1.21148i
$297$	−0.826459	−	1.06057i	−0.0479560	−	0.0615403i
$298$		−	14.9135i		−	0.863916i
$299$	−13.0465	−	21.6174i	−0.754496	−	1.25016i
$300$	0.189214	+	0.434090i	0.0109243	+	0.0250622i
$301$	−3.31096	−	2.12782i	−0.190840	−	0.122646i
$302$	13.4887	−	1.93939i	0.776189	−	0.111599i
$303$	−20.6758	−	18.5532i	−1.18779	−	1.06585i
$304$	−0.875629	+	2.98212i	−0.0502208	+	0.171036i
$305$	−27.1754	−	12.4106i	−1.55606	−	0.710629i
$306$	−3.18390	+	0.345566i	−0.182011	+	0.0197547i
$307$	−1.90118	+	13.2230i	−0.108506	+	0.754678i	0.860822	+	0.508907i	$0.169950\pi$
$307$	−1.90118	+	13.2230i	−0.108506	+	0.754678i	−0.969328	+	0.245771i	$0.920959\pi$
$308$	−0.0981596	−	0.334301i	−0.00559316	−	0.0190486i
$309$	−1.30550	−	0.623788i	−0.0742673	−	0.0354860i
$310$	−1.59078	−	2.47530i	−0.0903501	−	0.140588i
$311$	9.00841	+	14.0174i	0.510820	+	0.794852i	0.996868	−	0.0790802i	$-0.0251983\pi$
$311$	9.00841	+	14.0174i	0.510820	+	0.794852i	−0.486048	+	0.873932i	$0.661562\pi$
$312$	−22.2592	−	10.6358i	−1.26018	−	0.602132i
$313$	2.89648	+	9.86450i	0.163719	+	0.557575i	0.999958	+	0.00920941i	$0.00293149\pi$
$313$	2.89648	+	9.86450i	0.163719	+	0.557575i	−0.836239	+	0.548365i	$0.815250\pi$
$314$	−1.66679	+	11.5928i	−0.0940625	+	0.654219i
$315$	−6.80310	+	0.738379i	−0.383311	+	0.0416029i
$316$	−11.8621	−	5.41723i	−0.667294	−	0.304743i
$317$	−0.992355	+	3.37965i	−0.0557362	+	0.189820i	−0.982655	−	0.185441i	$-0.940629\pi$
$317$	−0.992355	+	3.37965i	−0.0557362	+	0.189820i	0.926919	+	0.375261i	$0.122447\pi$
$318$	−3.35234	−	3.00818i	−0.187990	−	0.168690i
$319$	−1.64149	+	0.236010i	−0.0919056	+	0.0132140i
$320$	7.08610	+	4.55396i	0.396125	+	0.254574i
$321$	5.79911	+	13.3042i	0.323675	+	0.742567i
$322$	−3.85156	+	0.443342i	−0.214639	+	0.0247065i
$323$			8.11201i			0.451364i
$324$	5.78612	−	10.6477i	0.321451	−	0.591539i
$325$	0.152134	+	1.05812i	0.00843889	+	0.0586937i
$326$	2.20157	−	1.00543i	0.121934	−	0.0556854i
$327$	−26.3858	+	3.32774i	−1.45914	+	0.184024i
$328$	−0.343618	+	0.752418i	−0.0189731	+	0.0415454i
$329$	2.45762	−	2.83625i	0.135493	−	0.156367i
$330$	0.219051	+	0.796894i	0.0120584	+	0.0438676i
$331$	9.82537	−	2.88499i	0.540051	−	0.158573i	−0.000320104	−	1.00000i	$-0.500102\pi$
$331$	9.82537	−	2.88499i	0.540051	−	0.158573i	0.540372	+	0.841427i	$0.318284\pi$
$332$	−12.1822	−	14.0590i	−0.668586	−	0.771589i
$333$	22.9844	+	4.12281i	1.25954	+	0.225929i
$334$	9.22008	−	5.92538i	0.504500	−	0.324223i
$335$	19.6795	−	17.0524i	1.07521	−	0.931673i
$336$	0.672136	−	0.562299i	0.0366680	−	0.0306760i
$337$	−15.4348	−	2.21919i	−0.840787	−	0.120887i	−0.291552	−	0.956555i	$-0.594172\pi$
$337$	−15.4348	−	2.21919i	−0.840787	−	0.120887i	−0.549235	+	0.835668i	$0.685081\pi$
$338$	−8.99221	−	7.79179i	−0.489112	−	0.423818i
$339$	18.6774	+	0.323967i	1.01442	+	0.0175955i
$340$	−3.89152	−	1.14265i	−0.211047	−	0.0619691i
$341$	0.171522	+	0.375582i	0.00928845	+	0.0203389i
$342$	12.2462	+	8.48432i	0.662198	+	0.458779i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−10.6474			−0.574072
$345$	−18.8580	+	1.83992i	−1.01528	+	0.0990578i
$346$	−14.1977			−0.763272
$347$	11.2615	−	17.5233i	0.604551	−	0.940700i	−0.395205	−	0.918593i	$-0.629326\pi$
$347$	11.2615	−	17.5233i	0.604551	−	0.940700i	0.999756	−	0.0221067i	$-0.00703735\pi$
$348$	−7.86145	−	12.7121i	−0.421418	−	0.681441i
$349$	−4.05597	−	8.88134i	−0.217111	−	0.475407i	0.769469	−	0.638684i	$-0.220521\pi$
$349$	−4.05597	−	8.88134i	−0.217111	−	0.475407i	−0.986580	+	0.163277i	$0.947794\pi$
$350$	0.157495	+	0.0462446i	0.00841845	+	0.00247188i
$351$	18.9659	−	19.7152i	1.01232	−	1.05232i
$352$	−1.13808	−	0.986151i	−0.0606598	−	0.0525620i
$353$	1.77171	+	0.254734i	0.0942986	+	0.0135581i	0.189303	−	0.981919i	$-0.439377\pi$
$353$	1.77171	+	0.254734i	0.0942986	+	0.0135581i	−0.0950040	+	0.995477i	$0.530286\pi$
$354$	7.67982	+	9.17996i	0.408178	+	0.487909i
$355$	13.5799	−	11.7671i	0.720748	−	0.624532i
$356$	4.73047	−	3.04009i	0.250714	−	0.161124i
$357$	1.26976	−	1.90241i	0.0672026	−	0.100686i
$358$	−5.89433	−	6.80242i	−0.311525	−	0.359519i
$359$	−11.0421	+	3.24224i	−0.582778	+	0.171119i	−0.559816	−	0.828617i	$-0.689128\pi$
$359$	−11.0421	+	3.24224i	−0.582778	+	0.171119i	−0.0229626	+	0.999736i	$0.507310\pi$
$360$	−14.4030	+	11.6307i	−0.759102	+	0.612992i
$361$	12.2695	−	14.1597i	0.645762	−	0.745250i
$362$	−1.33066	+	2.91374i	−0.0699378	+	0.153143i
$363$	2.36948	+	18.7878i	0.124366	+	0.986102i
$364$	6.44833	−	2.94485i	0.337984	−	0.154352i
$365$	−1.60890	−	11.1901i	−0.0842136	−	0.585719i
$366$	2.92432	−	18.1043i	0.152857	−	0.946325i
$367$		−	20.9318i		−	1.09263i	−0.837579	−	0.546316i	$-0.816030\pi$
$367$		−	20.9318i		−	1.09263i	0.837579	−	0.546316i	$-0.183970\pi$
$368$	1.87785	−	1.53665i	0.0978896	−	0.0801032i
$369$	−0.671976	−	0.624363i	−0.0349817	−	0.0325030i
$370$	−12.0747	−	7.75991i	−0.627731	−	0.403418i
$371$	3.18403	−	0.457795i	0.165307	−	0.0237675i
$372$	−2.48537	+	2.76972i	−0.128861	+	0.143603i
$373$	−8.85270	+	30.1495i	−0.458375	+	1.56108i	0.328829	+	0.944390i	$0.393346\pi$
$373$	−8.85270	+	30.1495i	−0.458375	+	1.56108i	−0.787204	+	0.616693i	$0.788472\pi$
$374$	−0.251272	−	0.114752i	−0.0129930	−	0.00593369i
$375$	−18.0890	−	5.65396i	−0.934111	−	0.291969i
$376$	1.44489	−	10.0494i	0.0745145	−	0.518260i
$377$	−9.50612	−	32.3749i	−0.489590	−	1.66739i
$378$	−1.54392	−	3.90660i	−0.0794104	−	0.200934i
$379$	8.64303	+	13.4488i	0.443963	+	0.690819i	0.989053	−	0.147558i	$-0.0471412\pi$
$379$	8.64303	+	13.4488i	0.443963	+	0.690819i	−0.545091	+	0.838377i	$0.683505\pi$
$380$	10.2003	+	15.8720i	0.523266	+	0.814217i
$381$	14.7796	−	30.9316i	0.757180	−	1.58467i
$382$	3.07883	+	10.4855i	0.157527	+	0.536487i
$383$	−2.97505	+	20.6919i	−0.152018	+	1.05731i	0.760813	+	0.648971i	$0.224800\pi$
$383$	−2.97505	+	20.6919i	−0.152018	+	1.05731i	−0.912831	+	0.408337i	$0.866109\pi$
$384$	4.47175	−	14.3067i	0.228198	−	0.730084i
$385$	−0.536898	−	0.245193i	−0.0273629	−	0.0124962i
$386$	−1.09950	+	3.74454i	−0.0559628	+	0.190592i
$387$	3.71737	−	11.2068i	0.188965	−	0.569672i
$388$	−6.01516	+	0.864849i	−0.305373	+	0.0439061i
$389$	0.490620	+	0.315302i	0.0248754	+	0.0159865i	0.553019	−	0.833168i	$-0.313476\pi$
$389$	0.490620	+	0.315302i	0.0248754	+	0.0159865i	−0.528144	+	0.849155i	$0.677112\pi$
$390$	−15.4145	+	6.71899i	−0.780546	+	0.340229i
$391$	3.57276	−	5.22907i	0.180682	−	0.264445i
$392$		−	2.70532i		−	0.136639i
$393$	−5.65554	−	0.913519i	−0.285284	−	0.0460810i
$394$	−1.50217	−	10.4478i	−0.0756783	−	0.526354i
$395$	−20.0951	+	9.17715i	−1.01110	+	0.461752i
$396$	0.898383	−	0.534266i	0.0451454	−	0.0268479i
$397$	−7.65639	+	16.7652i	−0.384263	+	0.841419i	0.614363	+	0.789023i	$0.289413\pi$
$397$	−7.65639	+	16.7652i	−0.384263	+	0.841419i	−0.998626	+	0.0523958i	$0.983314\pi$
$398$	1.90648	−	2.20019i	0.0955631	−	0.110286i
$399$	−10.2594	+	2.82011i	−0.513612	+	0.141182i
$400$	−0.0985690	+	0.0289425i	−0.00492845	+	0.00144712i
$401$	4.47372	+	5.16295i	0.223407	+	0.257825i	0.856377	−	0.516351i	$-0.172710\pi$
$401$	4.47372	+	5.16295i	0.223407	+	0.257825i	−0.632970	+	0.774176i	$0.718164\pi$
$402$	13.2951	+	8.87379i	0.663101	+	0.442585i
$403$	−7.06726	+	4.54185i	−0.352045	+	0.226246i
$404$	16.3208	−	14.1421i	0.811992	−	0.703595i
$405$	−7.21315	−	19.2202i	−0.358424	−	0.955061i
$406$	−5.12827	−	0.737334i	−0.254512	−	0.0365933i
$407$	1.52217	+	1.31897i	0.0754512	+	0.0653788i
$408$	0.107312	−	6.18677i	0.00531273	−	0.306291i
$409$	−30.0478	−	8.82283i	−1.48577	−	0.436261i	−0.564579	−	0.825379i	$-0.690962\pi$
$409$	−30.0478	−	8.82283i	−1.48577	−	0.436261i	−0.921188	+	0.389118i	$0.872780\pi$
$410$	0.234216	+	0.512862i	0.0115671	+	0.0253285i
$411$	6.42395	−	3.97271i	0.316870	−	0.195959i
$412$	0.608103	−	0.946227i	0.0299591	−	0.0466172i
$413$	−8.54787			−0.420613
$414$	−4.15726	−	10.8626i	−0.204318	−	0.533869i
$415$	−31.5143			−1.54698
$416$	16.5649	−	25.7755i	0.812161	−	1.26375i
$417$	6.43544	−	3.97982i	0.315145	−	0.194893i
$418$	0.533812	+	1.16889i	0.0261096	+	0.0571721i
$419$	26.5344	+	7.79119i	1.29629	+	0.380625i	0.855881	−	0.517173i	$-0.173016\pi$
$419$	26.5344	+	7.79119i	1.29629	+	0.380625i	0.440408	+	0.897798i	$0.354834\pi$
$420$	0.0922586	−	5.31891i	0.00450176	−	0.259536i
$421$	9.74869	+	8.44729i	0.475122	+	0.411696i	0.859228	−	0.511593i	$-0.170945\pi$
$421$	9.74869	+	8.44729i	0.475122	+	0.411696i	−0.384105	+	0.923289i	$0.625490\pi$
$422$	20.6317	+	2.96639i	1.00433	+	0.144401i
$423$	10.0729	+	5.02938i	0.489761	+	0.244537i
$424$	6.57684	−	5.69886i	0.319399	−	0.276761i
$425$	−0.225564	+	0.144961i	−0.0109415	+	0.00703166i
$426$	9.17436	+	6.12340i	0.444499	+	0.296680i
$427$	8.57691	+	9.89829i	0.415066	+	0.479012i
$428$	−10.8253	+	3.17860i	−0.523261	+	0.153643i
$429$	2.27522	−	0.625416i	0.109849	−	0.0301954i
$430$	−4.75265	+	5.48485i	−0.229193	+	0.264503i
$431$	1.24634	−	2.72910i	0.0600339	−	0.131456i	−0.877237	−	0.480057i	$-0.840616\pi$
$431$	1.24634	−	2.72910i	0.0600339	−	0.131456i	0.937271	+	0.348601i	$0.113343\pi$
$432$	2.13472	+	1.53443i	0.102707	+	0.0738254i
$433$	−36.9460	+	16.8727i	−1.77551	+	0.810848i	−0.797195	+	0.603722i	$0.793684\pi$
$433$	−36.9460	+	16.8727i	−1.77551	+	0.810848i	−0.978314	+	0.207125i	$0.933589\pi$
$434$	0.183579	+	1.27682i	0.00881206	+	0.0612892i
$435$	−24.9965	−	4.03760i	−1.19849	−	0.193588i
$436$		−	20.6745i		−	0.990129i
$437$	−28.4900	+	7.49977i	−1.36286	+	0.358763i
$438$	6.36163	−	2.77295i	0.303970	−	0.132497i
$439$	30.2803	+	19.4599i	1.44520	+	0.928772i	0.999435	+	0.0336216i	$0.0107041\pi$
$439$	30.2803	+	19.4599i	1.44520	+	0.928772i	0.445763	+	0.895151i	$0.352932\pi$
$440$	−1.58053	+	0.227245i	−0.0753486	+	0.0108335i
$441$	2.84744	+	0.944516i	0.135592	+	0.0449769i
$442$	1.58344	−	5.39270i	0.0753165	−	0.256505i
$443$	36.4956	+	16.6670i	1.73396	+	0.791871i	0.992694	+	0.120655i	$0.0384996\pi$
$443$	36.4956	+	16.6670i	1.73396	+	0.791871i	0.741262	+	0.671216i	$0.234228\pi$
$444$	−5.41558	+	17.3263i	−0.257012	+	0.822270i
$445$	1.35568	−	9.42898i	0.0642655	−	0.446976i
$446$	−1.39451	−	4.74925i	−0.0660317	−	0.224883i
$447$	−13.7758	+	28.8307i	−0.651571	+	1.36365i
$448$	−1.99646	−	3.10655i	−0.0943238	−	0.146771i
$449$	−0.312907	−	0.486893i	−0.0147670	−	0.0229779i	0.833792	−	0.552079i	$-0.186165\pi$
$449$	−0.312907	−	0.486893i	−0.0147670	−	0.0229779i	−0.848559	+	0.529101i	$0.822529\pi$
$450$	−0.0170777	+	0.492135i	−0.000805050	+	0.0231995i
$451$	−0.0222900	−	0.0759127i	−0.00104959	−	0.00357459i
$452$	−2.06666	+	14.3740i	−0.0972077	+	0.676094i
$453$	−27.8678	−	8.71047i	−1.30934	−	0.409254i
$454$	1.58339	+	0.723110i	0.0743122	+	0.0339372i
$455$	3.38337	−	11.5227i	0.158615	−	0.540192i
$456$	−19.2242	+	21.4236i	−0.900256	+	1.00325i
$457$	−28.3784	+	4.08019i	−1.32748	+	0.190863i	−0.769318	−	0.638866i	$-0.779404\pi$
$457$	−28.3784	+	4.08019i	−1.32748	+	0.190863i	−0.558166	+	0.829729i	$0.688495\pi$
$458$	−12.1900	−	7.83402i	−0.569600	−	0.366059i
$459$	6.47431	+	2.27295i	0.302195	+	0.106092i
$460$	0.415276	−	14.7238i	0.0193623	−	0.686498i
$461$		−	33.7110i		−	1.57008i	−0.619448	−	0.785038i	$-0.712643\pi$
$461$		−	33.7110i		−	1.57008i	0.619448	−	0.785038i	$-0.287357\pi$
$462$	0.0577750	−	0.357681i	0.00268794	−	0.0166408i
$463$	−1.72398	−	11.9906i	−0.0801204	−	0.557249i	−0.989857	−	0.142064i	$-0.954626\pi$
$463$	−1.72398	−	11.9906i	−0.0801204	−	0.557249i	0.909737	−	0.415185i	$-0.136283\pi$
$464$	2.94954	−	1.34701i	0.136929	−	0.0625333i
$465$	0.788828	+	6.25466i	0.0365810	+	0.290053i
$466$	−5.17286	+	11.3270i	−0.239628	+	0.524713i
$467$	−1.20126	+	1.38633i	−0.0555879	+	0.0641518i	−0.782863	−	0.622195i	$-0.786241\pi$
$467$	−1.20126	+	1.38633i	−0.0555879	+	0.0641518i	0.727275	+	0.686347i	$0.240787\pi$
$468$	13.3610	+	16.5457i	0.617614	+	0.764826i
$469$	−10.9534	+	3.21621i	−0.505782	+	0.148511i
$470$	−4.53184	−	5.23003i	−0.209038	−	0.241243i
$471$	13.9306	−	20.8715i	0.641889	−	0.961708i
$472$	−19.4537	+	12.5022i	−0.895431	+	0.575459i
$473$	0.769666	−	0.666919i	0.0353893	−	0.0306650i
$474$	−8.70142	−	10.4011i	−0.399669	−	0.477739i
$475$	1.23461	+	0.177510i	0.0566476	+	0.00814469i
$476$	1.34377	+	1.16439i	0.0615918	+	0.0533696i
$477$	3.70205	+	8.91199i	0.169505	+	0.408052i
$478$	−19.7335	−	5.79427i	−0.902587	−	0.265024i
$479$	11.4076	+	24.9791i	0.521225	+	1.14132i	0.968974	+	0.247164i	$0.0794988\pi$
$479$	11.4076	+	24.9791i	0.521225	+	1.14132i	−0.447748	+	0.894160i	$0.647774\pi$
$480$	−12.0934	−	19.5552i	−0.551984	−	0.892569i
$481$	−22.1554	+	34.4745i	−1.01020	+	1.57190i
$482$	−0.940932			−0.0428583
$483$	7.85534	+	2.70066i	0.357431	+	0.122884i
$484$	−14.7211			−0.669140
$485$	−5.56582	+	8.66059i	−0.252731	+	0.393257i
$486$	10.2028	−	7.39659i	0.462808	−	0.335516i
$487$	14.0891	+	30.8509i	0.638440	+	1.39799i	0.901318	+	0.433159i	$0.142601\pi$
$487$	14.0891	+	30.8509i	0.638440	+	1.39799i	−0.262878	+	0.964829i	$0.584672\pi$
$488$	33.9971	+	9.98246i	1.53898	+	0.451885i
$489$	−5.18480	−	0.0899324i	−0.234465	−	0.00406688i
$490$	−1.39360	−	1.20756i	−0.0629564	−	0.0545520i
$491$	11.4459	+	1.64567i	0.516546	+	0.0742681i	0.395658	−	0.918398i	$-0.370517\pi$
$491$	11.4459	+	1.64567i	0.516546	+	0.0742681i	0.120888	+	0.992666i	$0.461426\pi$
$492$	0.546922	−	0.457547i	0.0246572	−	0.0206278i
$493$	6.39604	−	5.54220i	0.288063	−	0.249608i
$494$	−21.9948	+	14.1352i	−0.989591	+	0.635971i
$495$	0.312631	−	1.74289i	0.0140517	−	0.0783372i
$496$	−0.528683	−	0.610132i	−0.0237386	−	0.0273958i
$497$	−7.55845	+	2.21936i	−0.339043	+	0.0995520i
$498$	−5.12741	−	18.6532i	−0.229765	−	0.835870i
$499$	9.15150	−	10.5614i	0.409678	−	0.472793i	−0.512987	−	0.858396i	$-0.671461\pi$
$499$	9.15150	−	10.5614i	0.409678	−	0.472793i	0.922665	+	0.385603i	$0.126007\pi$
$500$	6.12033	−	13.4017i	0.273710	−	0.599340i
$501$	−23.2976	+	2.93825i	−1.04086	+	0.131271i
$502$	1.41653	−	0.646910i	0.0632230	−	0.0288730i
$503$	2.22373	+	15.4664i	0.0991513	+	0.689613i	0.977398	+	0.211406i	$0.0678041\pi$
$503$	2.22373	+	15.4664i	0.0991513	+	0.689613i	−0.878247	+	0.478207i	$0.841287\pi$
$504$	7.86182	−	2.01509i	0.350193	−	0.0897593i
$505$		−	36.5843i		−	1.62798i
$506$	0.170711	−	0.988580i	0.00758903	−	0.0439477i
$507$	10.1863	+	23.3693i	0.452392	+	1.03787i
$508$	22.4192	+	14.4079i	0.994691	+	0.639249i
$509$	23.3659	−	3.35951i	1.03568	−	0.148908i	0.396552	−	0.918012i	$-0.370206\pi$
$509$	23.3659	−	3.35951i	1.03568	−	0.148908i	0.639123	+	0.769104i	$0.279297\pi$
$510$	−3.13911	−	2.81684i	−0.139002	−	0.124732i
$511$	−1.39633	+	4.75545i	−0.0617698	+	0.210369i
$512$	5.16847	+	2.36036i	0.228416	+	0.104314i
$513$	−15.8372	−	27.7138i	−0.699231	−	1.22359i
$514$	−3.35998	+	23.3692i	−0.148203	+	1.03077i
$515$	−0.536829	−	1.82827i	−0.0236555	−	0.0805632i
$516$	8.28195	+	3.95724i	0.364592	+	0.174208i
$517$	0.525016	+	0.816941i	0.0230902	+	0.0359290i
$518$	3.40195	+	5.29354i	0.149473	+	0.232585i
$519$	27.4469	+	13.1145i	1.20479	+	0.575665i
$520$	−9.15309	−	31.1726i	−0.401390	−	1.36701i
$521$	−1.01580	+	7.06501i	−0.0445028	+	0.309524i	0.955396	+	0.295326i	$0.0954284\pi$
$521$	−1.01580	+	7.06501i	−0.0445028	+	0.309524i	−0.999899	+	0.0141973i	$0.995481\pi$
$522$	−1.67712	−	15.4523i	−0.0734055	−	0.676327i
$523$	−40.6481	−	18.5634i	−1.77742	−	0.811719i	−0.977296	−	0.211879i	$-0.932042\pi$
$523$	−40.6481	−	18.5634i	−1.77742	−	0.811719i	−0.800120	−	0.599840i	$-0.795231\pi$
$524$	1.25471	−	4.27313i	0.0548120	−	0.186673i
$525$	−0.261752	−	0.234880i	−0.0114238	−	0.0102510i
$526$	−18.4565	+	2.65364i	−0.804740	+	0.115704i
$527$	−1.77263	−	1.13920i	−0.0772170	−	0.0496243i
$528$	0.0906074	+	0.207869i	0.00394318	+	0.00904635i
$529$	21.6680	+	7.71341i	0.942088	+	0.335366i
$530$		−	5.93172i		−	0.257657i
$531$	−6.36699	−	24.8406i	−0.276304	−	1.07799i
$532$	−1.17714	−	8.18716i	−0.0510353	−	0.354958i
$533$	1.46428	−	0.668714i	0.0634250	−	0.0289652i
$534$	5.80155	−	0.731682i	0.251057	−	0.0316630i
$535$	−7.93983	+	17.3858i	−0.343269	+	0.751654i
$536$	−20.2244	+	23.3402i	−0.873561	+	1.00814i
$537$	5.11143	+	18.5951i	0.220575	+	0.802437i
$538$	7.68461	−	2.25641i	0.331307	−	0.0972805i
$539$	0.169452	+	0.195558i	0.00729881	+	0.00842327i
$540$	15.5258	−	3.69375i	0.668123	−	0.158954i
$541$	34.4349	−	22.1299i	1.48047	−	0.951440i	0.483364	−	0.875419i	$-0.339415\pi$
$541$	34.4349	−	22.1299i	1.48047	−	0.951440i	0.997106	−	0.0760210i	$-0.0242216\pi$
$542$	−1.75405	+	1.51989i	−0.0753429	+	0.0652850i
$543$	5.26387	−	4.40368i	0.225894	−	0.188980i
$544$	7.60683	+	1.09370i	0.326140	+	0.0468919i
$545$	−26.4694	−	22.9358i	−1.13382	−	0.982463i
$546$	7.37071	+	0.127848i	0.315437	+	0.00547139i
$547$	−9.57209	−	2.81062i	−0.409273	−	0.120173i	0.0706139	−	0.997504i	$-0.477504\pi$
$547$	−9.57209	−	2.81062i	−0.409273	−	0.120173i	−0.479887	+	0.877330i	$0.659322\pi$
$548$	2.43919	+	5.34108i	0.104197	+	0.228160i
$549$	−22.3764	+	32.2979i	−0.955001	+	1.37844i
$550$	−0.0229631	+	0.0357313i	−0.000979150	+	0.00152359i
$551$	−39.3696			−1.67720
$552$	21.8277	−	5.34295i	0.929047	−	0.227411i
$553$	9.68493			0.411845
$554$	−3.07484	+	4.78455i	−0.130637	+	0.203276i
$555$	16.1748	+	26.1549i	0.686581	+	1.11021i
$556$	2.44356	+	5.35064i	0.103630	+	0.226918i
$557$	−7.89490	−	2.31815i	−0.334518	−	0.0982232i	0.110160	−	0.993914i	$-0.464864\pi$
$557$	−7.89490	−	2.31815i	−0.334518	−	0.0982232i	−0.444678	+	0.895691i	$0.646682\pi$
$558$	−3.57377	+	1.48454i	−0.151290	+	0.0628458i
$559$	15.6599	+	13.5693i	0.662342	+	0.573922i
$560$	1.14233	+	0.164242i	0.0482722	+	0.00694049i
$561$	0.379761	+	0.453941i	0.0160335	+	0.0191654i
$562$	−10.6547	+	9.23237i	−0.449442	+	0.389444i
$563$	−5.75101	+	3.69595i	−0.242376	+	0.155766i	−0.656190	−	0.754596i	$-0.727833\pi$
$563$	−5.75101	+	3.69595i	−0.242376	+	0.155766i	0.413813	+	0.910362i	$0.364197\pi$
$564$	−4.85887	+	7.27978i	−0.204595	+	0.306534i
$565$	16.1101	+	18.5921i	0.677758	+	0.782175i
$566$	−14.0239	+	4.11778i	−0.589467	+	0.173083i
$567$	−0.623871	+	8.97835i	−0.0262001	+	0.377055i
$568$	−13.9559	+	16.1060i	−0.585578	+	0.675793i
$569$	−0.884775	+	1.93739i	−0.0370917	+	0.0812195i	−0.927271	−	0.374391i	$-0.877852\pi$
$569$	−0.884775	+	1.93739i	−0.0370917	+	0.0812195i	0.890179	+	0.455611i	$0.150579\pi$
$570$	2.45499	+	19.4658i	0.102828	+	0.815332i
$571$	20.2995	−	9.27046i	0.849507	−	0.387957i	0.0574090	−	0.998351i	$-0.481716\pi$
$571$	20.2995	−	9.27046i	0.849507	−	0.387957i	0.792098	+	0.610394i	$0.208989\pi$
$572$	0.261053	+	1.81567i	0.0109152	+	0.0759168i
$573$	3.73362	−	23.1146i	0.155974	−	0.965625i
$574$		−	0.247176i		−	0.0103169i
$575$	−0.717657	−	0.658180i	−0.0299284	−	0.0274480i
$576$	7.54073	−	8.11578i	0.314197	−	0.338157i
$577$	5.18407	+	3.33160i	0.215816	+	0.138696i	0.644083	−	0.764956i	$-0.277239\pi$
$577$	5.18407	+	3.33160i	0.215816	+	0.138696i	−0.428267	+	0.903652i	$0.640876\pi$
$578$	−12.2077	+	1.75520i	−0.507773	+	0.0730068i
$579$	5.58441	−	6.22331i	0.232080	−	0.258632i
$580$	5.54558	−	18.8865i	0.230268	−	0.784220i
$581$	12.5674	+	5.73933i	0.521383	+	0.238107i
$582$	−6.03174	−	1.88530i	−0.250023	−	0.0781483i
$583$	−0.118459	+	0.823901i	−0.00490607	+	0.0341225i
$584$	3.77751	+	12.8650i	0.156314	+	0.532358i
$585$	36.0058	+	1.24944i	1.48865	+	0.0516582i
$586$	−7.38965	−	11.4985i	−0.305263	−	0.474999i
$587$	−19.3530	−	30.1138i	−0.798783	−	1.24293i	−0.966391	−	0.257077i	$-0.917241\pi$
$587$	−19.3530	−	30.1138i	−0.798783	−	1.24293i	0.167608	−	0.985854i	$-0.446396\pi$
$588$	−1.00546	+	2.10429i	−0.0414645	+	0.0867795i
$589$	2.76157	+	9.40505i	0.113789	+	0.387528i
$590$	−2.24320	+	15.6018i	−0.0923510	+	0.642315i
$591$	−6.74678	+	21.5853i	−0.277526	+	0.887900i
$592$	−3.58228	−	1.63597i	−0.147231	−	0.0672380i
$593$	−10.9083	+	37.1503i	−0.447951	+	1.52558i	0.358070	+	0.933695i	$0.383435\pi$
$593$	−10.9083	+	37.1503i	−0.447951	+	1.52558i	−0.806021	+	0.591887i	$0.798383\pi$
$594$	1.08248	−	0.0985258i	0.0444146	−	0.00404256i
$595$	2.98151	−	0.428676i	0.122230	−	0.0175740i
$596$	−20.8965	−	13.4294i	−0.855955	−	0.550089i
$597$	−5.71794	+	2.49237i	−0.234020	+	0.102006i
$598$	20.4035	+	0.575472i	0.834363	+	0.0235328i
$599$		−	40.6236i		−	1.65983i	−0.557887	−	0.829917i	$-0.688388\pi$
$599$		−	40.6236i		−	1.65983i	0.557887	−	0.829917i	$-0.311612\pi$
$600$	−0.939247	−	0.151713i	−0.0383446	−	0.00619367i
$601$	−5.81259	−	40.4274i	−0.237100	−	1.64907i	−0.666172	−	0.745798i	$-0.732068\pi$
$601$	−5.81259	−	40.4274i	−0.237100	−	1.64907i	0.429072	−	0.903270i	$-0.358841\pi$
$602$	2.89417	−	1.32172i	0.117957	−	0.0538693i
$603$	−17.5053	−	29.4357i	−0.712871	−	1.19871i
$604$	9.42897	−	20.6466i	0.383659	−	0.840096i
$605$	−16.3312	+	18.8472i	−0.663959	+	0.766249i
$606$	21.6541	−	5.95231i	0.879638	−	0.241796i
$607$	−8.68054	+	2.54884i	−0.352332	+	0.103454i	−0.453109	−	0.891455i	$-0.649685\pi$
$607$	−8.68054	+	2.54884i	−0.352332	+	0.103454i	0.100777	+	0.994909i	$0.467867\pi$
$608$	−23.4112	−	27.0180i	−0.949450	−	1.09572i
$609$	9.23287	+	6.16245i	0.374135	+	0.249715i
$610$	20.3174	−	13.0572i	0.822629	−	0.528671i
$611$	−14.9323	+	12.9389i	−0.604097	+	0.523453i
$612$	−2.38285	+	4.77240i	−0.0963211	+	0.192913i
$613$	29.7147	+	4.27233i	1.20016	+	0.172558i	0.713261	−	0.700898i	$-0.247217\pi$
$613$	29.7147	+	4.27233i	1.20016	+	0.172558i	0.486903	+	0.873456i	$0.338126\pi$
$614$	−8.16174	−	7.07219i	−0.329381	−	0.285410i
$615$	0.0209500	−	1.20781i	0.000844784	−	0.0487037i
$616$	0.671673	+	0.197221i	0.0270625	+	0.00794626i
$617$	8.47162	+	18.5503i	0.341055	+	0.746806i	0.999985	−	0.00539792i	$-0.00171822\pi$
$617$	8.47162	+	18.5503i	0.341055	+	0.746806i	−0.658931	+	0.752204i	$0.728991\pi$
$618$	0.994804	−	0.615208i	0.0400169	−	0.0247473i
$619$	11.4049	−	17.7464i	0.458402	−	0.713287i	−0.532713	−	0.846296i	$-0.678828\pi$
$619$	11.4049	−	17.7464i	0.458402	−	0.713287i	0.991115	+	0.133009i	$0.0424639\pi$
$620$	−4.90081			−0.196821
$621$	−1.99713	+	24.8397i	−0.0801420	+	0.996783i
$622$	−13.4701			−0.540101
$623$	−2.25781	+	3.51322i	−0.0904573	+	0.140754i
$624$	−3.92396	+	2.42667i	−0.157084	+	0.0971444i
$625$	−10.7900	−	23.6268i	−0.431600	−	0.945071i
$626$	−7.97455	−	2.34154i	−0.318727	−	0.0935867i
$627$	0.0477480	−	2.75278i	0.00190687	−	0.109935i
$628$	14.7427	+	12.7746i	0.588297	+	0.509762i
$629$	−10.1741	−	1.46281i	−0.405667	−	0.0583261i
$630$	2.47120	−	4.94935i	0.0984550	−	0.197187i
$631$	−0.421188	+	0.364961i	−0.0167672	+	0.0145289i	−0.663204	−	0.748439i	$-0.730804\pi$
$631$	−0.421188	+	0.364961i	−0.0167672	+	0.0145289i	0.646437	+	0.762968i	$0.276258\pi$
$632$	22.0416	−	14.1652i	0.876766	−	0.563463i
$633$	−37.1450	−	24.7923i	−1.47638	−	0.985406i
$634$	−1.86470	−	2.15198i	−0.0740569	−	0.0854662i
$635$	43.3177	−	12.7192i	1.71901	−	0.504747i
$636$	−7.23373	+	1.98842i	−0.286836	+	0.0788458i
$637$	−3.44772	+	3.97888i	−0.136604	+	0.157649i
$638$	0.556921	−	1.21949i	0.0220487	−	0.0482799i
$639$	−12.0796	−	20.3122i	−0.477862	−	0.803538i
$640$	17.9562	−	8.20030i	0.709780	−	0.324146i
$641$	−3.36961	−	23.4361i	−0.133091	−	0.925671i	−0.941491	−	0.337037i	$-0.890575\pi$
$641$	−3.36961	−	23.4361i	−0.133091	−	0.925671i	0.808400	−	0.588634i	$-0.200334\pi$
$642$	−11.5824	−	1.87087i	−0.457121	−	0.0738372i
$643$		−	37.2226i		−	1.46791i	−0.679196	−	0.733957i	$-0.737671\pi$
$643$		−	37.2226i		−	1.46791i	0.679196	−	0.733957i	$-0.262329\pi$
$644$	−2.84707	+	5.79596i	−0.112190	+	0.228393i
$645$	14.2542	−	6.21322i	0.561259	−	0.244645i
$646$	−5.51679	−	3.54542i	−0.217055	−	0.139493i
$647$	35.4627	−	5.09877i	1.39418	−	0.200453i	0.596056	−	0.802943i	$-0.296734\pi$
$647$	35.4627	−	5.09877i	1.39418	−	0.200453i	0.798127	+	0.602489i	$0.205824\pi$
$648$	11.7119	+	21.3459i	0.460089	+	0.838548i
$649$	0.623149	−	2.12225i	0.0244608	−	0.0833057i
$650$	−0.786092	−	0.358996i	−0.0308331	−	0.0140810i
$651$	0.824516	−	2.63791i	0.0323153	−	0.103388i
$652$	0.573701	−	3.99018i	0.0224679	−	0.156267i
$653$	2.44364	+	8.32229i	0.0956272	+	0.325676i	0.993388	−	0.114807i	$-0.0366251\pi$
$653$	2.44364	+	8.32229i	0.0956272	+	0.325676i	−0.897761	+	0.440484i	$0.854807\pi$
$654$	9.26903	−	19.3988i	0.362448	−	0.758553i
$655$	−4.07891	−	6.34690i	−0.159376	−	0.247994i
$656$	0.0836352	+	0.130139i	0.00326541	+	0.00508107i
$657$	−14.8597	−	0.515649i	−0.579732	−	0.0201174i
$658$	0.854740	+	2.91098i	0.0333212	+	0.113482i
$659$	−1.66962	+	11.6125i	−0.0650392	+	0.452358i	0.931114	+	0.364729i	$0.118838\pi$
$659$	−1.66962	+	11.6125i	−0.0650392	+	0.452358i	−0.996153	+	0.0876294i	$0.972071\pi$
$660$	1.31385	+	0.410660i	0.0511414	+	0.0159849i
$661$	−5.63370	−	2.57283i	−0.219126	−	0.100071i	0.302828	−	0.953045i	$-0.402069\pi$
$661$	−5.63370	−	2.57283i	−0.219126	−	0.100071i	−0.521953	+	0.852974i	$0.674797\pi$
$662$	−2.33225	+	7.94292i	−0.0906455	+	0.308710i
$663$	−8.04239	+	8.96251i	−0.312341	+	0.348075i
$664$	36.9960	−	5.31922i	1.43572	−	0.206426i
$665$	−11.7878	−	7.57558i	−0.457112	−	0.293768i
$666$	−12.8493	+	13.8292i	−0.497902	+	0.535872i
$667$	25.3780	+	17.3395i	0.982639	+	0.671388i
$668$		−	18.2547i		−	0.706296i
$669$	−1.69108	+	10.4694i	−0.0653809	+	0.404769i
$670$	2.99584	+	20.8365i	0.115739	+	0.804984i
$671$	−3.08280	+	1.40787i	−0.119010	+	0.0543501i
$672$	1.26127	+	10.0007i	0.0486547	+	0.385786i
$673$	11.8101	−	25.8605i	0.455245	−	0.996848i	−0.533301	−	0.845926i	$-0.679049\pi$
$673$	11.8101	−	25.8605i	0.455245	−	0.996848i	0.988546	−	0.150922i	$-0.0482242\pi$
$674$	8.25513	−	9.52693i	0.317976	−	0.366963i
$675$	0.487605	−	0.935619i	0.0187679	−	0.0360120i
$676$	−19.0151	+	5.58333i	−0.731349	+	0.214743i
$677$	3.63405	+	4.19391i	0.139668	+	0.161185i	0.821274	−	0.570534i	$-0.193264\pi$
$677$	3.63405	+	4.19391i	0.139668	+	0.161185i	−0.681606	+	0.731719i	$0.738718\pi$
$678$	−8.38344	+	12.5605i	−0.321964	+	0.482382i
$679$	3.79681	−	2.44006i	0.145708	−	0.0936409i
$680$	6.15851	−	5.33638i	0.236168	−	0.204641i
$681$	−2.39306	−	2.86051i	−0.0917023	−	0.109615i
$682$	−0.330390	−	0.0475028i	−0.0126513	−	0.00181898i
$683$	−16.2372	−	14.0696i	−0.621299	−	0.538358i	0.286331	−	0.958131i	$-0.407564\pi$
$683$	−16.2372	−	14.0696i	−0.621299	−	0.538358i	−0.907629	+	0.419773i	$0.862110\pi$
$684$	22.9156	−	9.51914i	0.876199	−	0.363973i
$685$	9.54412	+	2.80241i	0.364662	+	0.107074i
$686$	0.335825	+	0.735354i	0.0128219	+	0.0280760i
$687$	16.3292	+	26.4047i	0.623000	+	1.00740i
$688$	−1.07657	+	1.67517i	−0.0410437	+	0.0638653i
$689$	−16.9357			−0.645200
$690$	6.99078	−	13.6290i	0.266134	−	0.518849i
$691$	−28.4624			−1.08276			−0.541380	−	0.840778i	$-0.682098\pi$
$691$	−28.4624			−1.08276			−0.541380	+	0.840778i	$0.682098\pi$
$692$	−12.7848	+	19.8935i	−0.486005	+	0.756238i
$693$	−0.442084	+	0.638101i	−0.0167934	+	0.0242395i
$694$	6.99523	+	15.3174i	0.265535	+	0.581441i
$695$	9.56120	+	2.80742i	0.362677	+	0.106492i
$696$	30.0260	+	0.520812i	1.13813	+	0.0197413i
$697$	0.305143	+	0.264408i	0.0115581	+	0.0100152i
$698$	7.81269	+	1.12329i	0.295715	+	0.0425173i
$699$	20.4630	−	17.1191i	0.773983	−	0.647503i
$700$	0.206619	−	0.179036i	0.00780945	−	0.00676693i
$701$	18.5452	−	11.9183i	0.700442	−	0.450147i	−0.141342	−	0.989961i	$-0.545142\pi$
$701$	18.5452	−	11.9183i	0.700442	−	0.450147i	0.841784	+	0.539814i	$0.181505\pi$
$702$	5.11863	+	21.5150i	0.193190	+	0.812030i
$703$	31.3123	+	36.1363i	1.18097	+	1.36291i
$704$	0.916834	−	0.269207i	0.0345545	−	0.0101461i
$705$	3.92992	+	14.2968i	0.148009	+	0.538448i
$706$	−0.947580	+	1.09357i	−0.0356626	+	0.0411569i
$707$	−6.66267	+	14.5892i	−0.250575	+	0.548684i
$708$	19.7783	−	2.49441i	0.743316	−	0.0937458i
$709$	−44.3360	+	20.2476i	−1.66507	+	0.760413i	−0.665166	+	0.746695i	$0.731639\pi$
$709$	−44.3360	+	20.2476i	−1.66507	+	0.760413i	−0.999906	+	0.0137177i	$0.995633\pi$
$710$	2.06729	+	14.3783i	0.0775840	+	0.539608i
$711$	7.21394	+	28.1450i	0.270544	+	1.05552i
$712$			11.2979i			0.423407i
$713$	2.36212	−	7.27884i	0.0884621	−	0.272595i
$714$	0.738826	+	1.69500i	0.0276499	+	0.0634336i
$715$	2.61419	+	1.68004i	0.0977650	+	0.0628297i
$716$	−14.8392	+	2.13355i	−0.554566	+	0.0797346i
$717$	32.7964	+	29.4295i	1.22481	+	1.09906i
$718$	2.62106	−	8.92651i	0.0978170	−	0.333134i
$719$	−30.2253	−	13.8034i	−1.12721	−	0.514782i	−0.237541	−	0.971378i	$-0.576341\pi$
$719$	−30.2253	−	13.8034i	−1.12721	−	0.514782i	−0.889674	+	0.456596i	$0.849069\pi$
$720$	0.373581	+	3.44201i	0.0139225	+	0.128276i
$721$	−0.118883	+	0.826850i	−0.00442744	+	0.0307935i
$722$	4.26722	+	14.5328i	0.158810	+	0.540856i
$723$	1.81901	+	0.869149i	0.0676496	+	0.0323240i
$724$	2.88443	+	4.48827i	0.107199	+	0.166805i
$725$	−0.703534	−	1.09472i	−0.0261286	−	0.0406569i
$726$	−13.8127	−	6.59992i	−0.512638	−	0.244946i
$727$	9.36751	+	31.9028i	0.347422	+	1.18321i	0.929112	+	0.369799i	$0.120574\pi$
$727$	9.36751	+	31.9028i	0.347422	+	1.18321i	−0.581690	+	0.813411i	$0.697608\pi$
$728$	−2.02699	+	14.0980i	−0.0751253	+	0.522508i
$729$	−26.5563	+	4.87463i	−0.983567	+	0.180542i
$730$	8.31333	+	3.79657i	0.307690	+	0.140517i
$731$	−1.46425	+	4.98676i	−0.0541571	+	0.184442i
$732$	−22.7340	−	20.4001i	−0.840275	−	0.754010i
$733$	26.2622	−	3.77593i	0.970016	−	0.139467i	0.360949	−	0.932586i	$-0.382453\pi$
$733$	26.2622	−	3.77593i	0.970016	−	0.139467i	0.609067	+	0.793119i	$0.291544\pi$
$734$	14.2352	+	9.14843i	0.525432	+	0.337675i
$735$	1.57866	+	3.62173i	0.0582299	+	0.133590i
$736$	3.19157	+	27.7270i	0.117643	+	1.02203i
$737$		−	2.95397i		−	0.108811i
$738$	0.718308	−	0.184112i	0.0264413	−	0.00677726i
$739$	1.70425	+	11.8533i	0.0626919	+	0.436032i	0.996859	+	0.0791960i	$0.0252353\pi$
$739$	1.70425	+	11.8533i	0.0626919	+	0.436032i	−0.934167	+	0.356836i	$0.883856\pi$
$740$	−21.7461	+	9.93110i	−0.799402	+	0.365075i
$741$	55.5770	−	7.00928i	2.04167	−	0.257492i
$742$	−1.08027	+	2.36547i	−0.0396581	+	0.0868391i
$743$	27.1932	−	31.3826i	0.997622	−	1.15132i	0.00914307	−	0.999958i	$-0.497090\pi$
$743$	27.1932	−	31.3826i	0.997622	−	1.15132i	0.988479	−	0.151359i	$-0.0483649\pi$
$744$	−1.98175	−	7.20946i	−0.0726543	−	0.264312i
$745$	−40.3756	+	11.8554i	−1.47925	+	0.434346i
$746$	−16.6348	−	19.1976i	−0.609044	−	0.702875i
$747$	−7.31786	+	40.7966i	−0.267747	+	1.49267i
$748$	−0.387055	+	0.248745i	−0.0141521	+	0.00909503i
$749$	6.33254	−	5.48718i	0.231386	−	0.200497i
$750$	11.7511	−	9.83078i	0.429088	−	0.358969i
$751$	−13.1931	−	1.89687i	−0.481421	−	0.0692179i	−0.102668	−	0.994716i	$-0.532738\pi$
$751$	−13.1931	−	1.89687i	−0.481421	−	0.0692179i	−0.378753	+	0.925498i	$0.623647\pi$
$752$	−1.43499	−	1.24343i	−0.0523287	−	0.0453431i
$753$	−3.33600	−	0.0578642i	−0.121571	−	0.00210869i
$754$	26.1721	+	7.68483i	0.953132	+	0.279865i
$755$	−15.9733	−	34.9766i	−0.581328	−	1.27293i
$756$	−6.86412	−	1.35452i	−0.249646	−	0.0492635i
$757$	11.7886	−	18.3434i	0.428462	−	0.666701i	−0.558158	−	0.829735i	$-0.688492\pi$
$757$	11.7886	−	18.3434i	0.428462	−	0.666701i	0.986620	+	0.163034i	$0.0521281\pi$
$758$	−12.9237			−0.469411
$759$	−1.24318	+	1.75343i	−0.0451246	+	0.0636456i
$760$	−37.9075			−1.37505
$761$	−23.1558	+	36.0311i	−0.839397	+	1.30613i	0.110599	+	0.993865i	$0.464723\pi$
$761$	−23.1558	+	36.0311i	−0.839397	+	1.30613i	−0.949996	+	0.312262i	$0.898913\pi$
$762$	14.5763	+	23.5701i	0.528044	+	0.853856i
$763$	6.37850	+	13.9670i	0.230917	+	0.505638i
$764$	17.4646	+	5.12807i	0.631847	+	0.185527i
$765$	3.46657	+	8.34513i	0.125334	+	0.301719i
$766$	−12.7718	−	11.0668i	−0.461465	−	0.399861i
$767$	44.5449	+	6.40459i	1.60842	+	0.231256i
$768$	15.9833	+	19.1054i	0.576749	+	0.689408i
$769$	−3.71795	+	3.22162i	−0.134073	+	0.116175i	−0.719316	−	0.694683i	$-0.755545\pi$
$769$	−3.71795	+	3.22162i	−0.134073	+	0.116175i	0.585243	+	0.810858i	$0.300999\pi$
$770$	0.401406	−	0.257968i	0.0144657	−	0.00929653i
$771$	28.0819	−	42.0736i	1.01134	−	1.51524i
$772$	4.25670	+	4.91249i	0.153202	+	0.176804i
$773$	−24.0670	+	7.06672i	−0.865631	+	0.254172i	−0.684256	−	0.729242i	$-0.739873\pi$
$773$	−24.0670	+	7.06672i	−0.865631	+	0.254172i	−0.181375	+	0.983414i	$0.558055\pi$
$774$	5.99676	+	7.42612i	0.215549	+	0.266926i
$775$	−0.212170	+	0.244857i	−0.00762136	+	0.00879552i
$776$	5.07216	−	11.1065i	0.182080	−	0.398699i
$777$	−1.68694	−	13.3759i	−0.0605187	−	0.479857i
$778$	−0.428860	+	0.195854i	−0.0153754	+	0.00702169i
$779$	−0.267303	−	1.85913i	−0.00957711	−	0.0666103i
$780$	−4.46603	+	27.6489i	−0.159910	+	0.989990i
$781$		−	2.03840i		−	0.0729395i
$782$	1.99466	+	4.71516i	0.0713289	+	0.168614i
$783$	−11.0312	+	31.4214i	−0.394224	+	1.12291i
$784$	−0.425630	−	0.273536i	−0.0152011	−	0.00976913i
$785$	32.7104	−	4.70304i	1.16748	−	0.167859i
$786$	3.09307	−	3.44694i	0.110326	−	0.122948i
$787$	2.12007	−	7.22029i	0.0755723	−	0.257375i	−0.913038	−	0.407875i	$-0.866270\pi$
$787$	2.12007	−	7.22029i	0.0755723	−	0.257375i	0.988610	+	0.150499i	$0.0480881\pi$
$788$	−15.9920	−	7.30330i	−0.569691	−	0.260169i
$789$	38.1312	+	11.9184i	1.35751	+	0.424307i
$790$	2.54160	−	17.6772i	0.0904259	−	0.628926i
$791$	−3.03849	−	10.3482i	−0.108036	−	0.367938i
$792$	−0.0728318	+	2.09882i	−0.00258796	+	0.0745785i
$793$	−37.2798	−	58.0086i	−1.32385	−	2.05994i
$794$	−8.05530	−	12.5343i	−0.285872	−	0.444825i
$795$	−5.47919	+	11.4672i	−0.194327	+	0.406699i
$796$	−1.36611	−	4.65256i	−0.0484207	−	0.164906i
$797$	−5.66518	+	39.4022i	−0.200671	+	1.39570i	0.601629	+	0.798776i	$0.294519\pi$
$797$	−5.66518	+	39.4022i	−0.200671	+	1.39570i	−0.802300	+	0.596921i	$0.796391\pi$
$798$	2.56606	−	8.20972i	0.0908376	−	0.290621i
$799$	−4.50798	−	2.05873i	−0.159481	−	0.0728325i
$800$	0.332910	−	1.13379i	0.0117702	−	0.0400855i
$801$	−11.8914	−	3.94447i	−0.420162	−	0.139371i
$802$	−5.46648	+	0.785961i	−0.193028	+	0.0277533i
$803$	−1.07888	−	0.693356i	−0.0380729	−	0.0244680i
$804$	24.4059	−	10.6382i	0.860728	−	0.375180i
$805$	4.26203	+	10.0750i	0.150217	+	0.355096i
$806$		−	6.79134i		−	0.239215i
$807$	−16.9401	−	2.73628i	−0.596321	−	0.0963216i
$808$	6.17497	+	42.9479i	0.217235	+	1.51090i
$809$	−43.7986	+	20.0022i	−1.53988	+	0.703239i	−0.991148	−	0.132761i	$-0.957616\pi$
$809$	−43.7986	+	20.0022i	−1.53988	+	0.703239i	−0.548730	+	0.836000i	$0.684888\pi$
$810$	16.2238	+	3.49487i	0.570046	+	0.122797i
$811$	−9.83278	+	21.5308i	−0.345276	+	0.756048i	0.654724	+	0.755868i	$0.272785\pi$
$811$	−9.83278	+	21.5308i	−0.345276	+	0.756048i	−1.00000		0.000180641i	$0.999943\pi$
$812$	−5.65107	+	6.52168i	−0.198314	+	0.228866i
$813$	4.79487	−	1.31802i	0.168163	−	0.0462249i
$814$	−1.56228	+	0.458726i	−0.0547578	+	0.0160783i
$815$	−4.47213	−	5.16111i	−0.156652	−	0.180786i
$816$	−0.962519	−	0.642430i	−0.0336949	−	0.0224895i
$817$	20.3391	−	13.0711i	0.711575	−	0.457302i
$818$	19.1328	−	16.5787i	0.668964	−	0.579661i
$819$	−14.1309	−	7.05556i	−0.493775	−	0.246541i
$820$	0.929521	+	0.133645i	0.0324603	+	0.00466708i
$821$	−6.12398	−	5.30646i	−0.213728	−	0.185197i	0.541417	−	0.840754i	$-0.317888\pi$
$821$	−6.12398	−	5.30646i	−0.213728	−	0.185197i	−0.755145	+	0.655558i	$0.772434\pi$
$822$	−0.105895	+	6.10508i	−0.00369351	+	0.212939i
$823$	−24.0830	−	7.07142i	−0.839482	−	0.246494i	−0.166397	−	0.986059i	$-0.553213\pi$
$823$	−24.0830	−	7.07142i	−0.839482	−	0.246494i	−0.673085	+	0.739565i	$0.735031\pi$
$824$	0.938795	+	2.05567i	0.0327045	+	0.0716128i
$825$	0.0773976	−	0.0478644i	0.00269464	−	0.00166642i
$826$	3.73592	−	5.81320i	0.129989	−	0.202267i
$827$	−13.7968			−0.479762			−0.239881	−	0.970802i	$-0.577108\pi$
$827$	−13.7968			−0.479762			−0.239881	+	0.970802i	$0.577108\pi$
$828$	−18.9641	−	3.95656i	−0.659047	−	0.137500i
$829$	35.3863			1.22902			0.614508	−	0.788910i	$-0.289354\pi$
$829$	35.3863			1.22902			0.614508	+	0.788910i	$0.289354\pi$
$830$	13.7736	−	21.4321i	0.478089	−	0.743921i
$831$	10.3638	−	6.40921i	0.359517	−	0.222333i
$832$	8.07638	+	17.6848i	0.279998	+	0.613110i
$833$	−1.26704	−	0.372038i	−0.0439005	−	0.0128903i
$834$	−0.106085	+	6.11601i	−0.00367341	+	0.211780i
$835$	−23.3713	−	20.2514i	−0.808798	−	0.700828i
$836$	2.11851	+	0.304596i	0.0732702	+	0.0105347i
$837$	8.28008	+	0.431210i	0.286202	+	0.0149048i
$838$	−16.8957	+	14.6402i	−0.583652	+	0.505737i
$839$	−26.9659	+	17.3299i	−0.930967	+	0.598296i	−0.915820	−	0.401589i	$-0.868458\pi$
$839$	−26.9659	+	17.3299i	−0.930967	+	0.598296i	−0.0151467	+	0.999885i	$0.504822\pi$
$840$	8.88999	+	5.93359i	0.306734	+	0.204728i
$841$	7.90672	+	9.12484i	0.272646	+	0.314650i
$842$	−10.0056	+	2.93790i	−0.344814	+	0.101247i
$843$	29.1257	−	8.00611i	1.00314	−	0.275745i
$844$	22.7350	−	26.2375i	0.782569	−	0.903133i
$845$	−13.9466	+	30.5388i	−0.479778	+	1.05057i
$846$	−7.82281	+	4.65220i	−0.268954	+	0.159946i
$847$	9.94505	−	4.54175i	0.341716	−	0.156056i
$848$	−0.231620	−	1.61095i	−0.00795386	−	0.0553203i
$849$	30.9145	+	4.99352i	1.06098	+	0.171377i
$850$		−	0.216758i		−	0.00743473i
$851$	−4.26870	−	37.0846i	−0.146329	−	1.27124i
$852$	16.8414	−	7.34092i	0.576976	−	0.251496i
$853$	−0.814331	−	0.523339i	−0.0278822	−	0.0179188i	0.526625	−	0.850097i	$-0.323457\pi$
$853$	−0.814331	−	0.523339i	−0.0278822	−	0.0179188i	−0.554508	+	0.832179i	$0.687093\pi$
$854$	−10.4802	+	1.50683i	−0.358625	+	0.0515625i
$855$	13.2348	−	39.8989i	0.452619	−	1.36451i
$856$	6.38640	−	21.7501i	0.218283	−	0.743402i
$857$	0.919409	+	0.419880i	0.0314064	+	0.0143428i	0.431056	−	0.902325i	$-0.358141\pi$
$857$	0.919409	+	0.419880i	0.0314064	+	0.0143428i	−0.399650	+	0.916668i	$0.630868\pi$
$858$	−0.569075	+	1.82067i	−0.0194279	+	0.0621566i
$859$	7.07480	−	49.2063i	0.241389	−	1.67890i	−0.403779	−	0.914857i	$-0.632303\pi$
$859$	7.07480	−	49.2063i	0.241389	−	1.67890i	0.645168	−	0.764041i	$-0.276788\pi$
$860$	3.40558	+	11.5983i	0.116129	+	0.395500i
$861$	−0.228319	+	0.477840i	−0.00778109	+	0.0162847i
$862$	1.31127	+	2.04038i	0.0446621	+	0.0694956i
$863$	−15.8021	−	24.5886i	−0.537910	−	0.837004i	0.460814	−	0.887496i	$-0.347557\pi$
$863$	−15.8021	−	24.5886i	−0.537910	−	0.837004i	−0.998724	+	0.0504922i	$0.983921\pi$
$864$	−28.1232	+	11.1145i	−0.956770	+	0.378123i
$865$	11.2863	+	38.4377i	0.383746	+	1.30692i
$866$	4.67285	−	32.5004i	0.158790	−	1.10441i
$867$	25.2212	+	7.88323i	0.856556	+	0.267729i
$868$	1.95436	+	0.892528i	0.0663354	+	0.0302944i
$869$	−0.706043	+	2.40456i	−0.0239509	+	0.0815692i
$870$	13.6708	−	15.2349i	0.463484	−	0.516511i
$871$	59.4906	−	8.55345i	2.01576	−	0.289823i
$872$	34.9448	+	22.4576i	1.18338	+	0.760511i
$873$	9.91906	+	9.21624i	0.335709	+	0.311922i
$874$	7.35140	−	22.6532i	0.248665	−	0.766257i
$875$			10.9419i			0.369905i
$876$	1.84315	−	11.4108i	0.0622741	−	0.385535i
$877$	−0.0827008	−	0.575197i	−0.00279261	−	0.0194230i	0.988377	−	0.152019i	$-0.0485777\pi$
$877$	−0.0827008	−	0.575197i	−0.00279261	−	0.0194230i	−0.991170	+	0.132596i	$0.957669\pi$
$878$	−26.4685	+	12.0878i	−0.893269	+	0.407942i
$879$	3.66434	+	29.0548i	0.123595	+	0.979994i
$880$	−0.124055	+	0.271642i	−0.00418189	+	0.00915705i
$881$	−25.3479	+	29.2530i	−0.853992	+	0.985559i	−0.999993	−	0.00372522i	$-0.998814\pi$
$881$	−25.3479	+	29.2530i	−0.853992	+	0.985559i	0.146001	+	0.989284i	$0.453360\pi$
$882$	−1.88684	+	1.52367i	−0.0635332	+	0.0513045i
$883$	5.16116	−	1.51545i	0.173687	−	0.0509991i	−0.193733	−	0.981054i	$-0.562059\pi$
$883$	5.16116	−	1.51545i	0.173687	−	0.0509991i	0.367420	+	0.930055i	$0.380241\pi$
$884$	−6.13029	−	7.07473i	−0.206184	−	0.237949i
$885$	18.7481	−	28.0893i	0.630210	−	0.944210i
$886$	−27.2855	+	17.5353i	−0.916675	+	0.589111i
$887$	−32.0565	+	27.7771i	−1.07635	+	0.932665i	−0.997933	−	0.0642560i	$-0.979533\pi$
$887$	−32.0565	+	27.7771i	−1.07635	+	0.932665i	−0.0784188	+	0.996921i	$0.524987\pi$
$888$	−23.4029	−	27.9743i	−0.785349	−	0.938755i
$889$	−19.5908	−	2.81673i	−0.657054	−	0.0944700i
$890$	5.81992	+	5.04299i	0.195084	+	0.169041i
$891$	−2.18365	−	0.809426i	−0.0731551	−	0.0271168i
$892$	−7.91029	−	2.32267i	−0.264856	−	0.0777688i
$893$	9.57693	+	20.9706i	0.320480	+	0.701753i
$894$	−13.5863	−	21.9693i	−0.454394	−	0.734763i
$895$	−13.7307	+	21.3654i	−0.458966	+	0.714165i
$896$	−8.65404			−0.289111
$897$	−38.9125	−	19.9595i	−1.29925	−	0.666427i
$898$	0.467883			0.0156135
$899$	5.52882	−	8.60302i	0.184397	−	0.286927i
$900$	0.674192	+	0.467089i	0.0224731	+	0.0155696i
$901$	−1.76463	−	3.86399i	−0.0587883	−	0.128728i
$902$	0.0613685	+	0.0180194i	0.00204335	+	0.000599981i
$903$	−6.81588	−	0.118224i	−0.226818	−	0.00393425i
$904$	−22.0505	−	19.1068i	−0.733387	−	0.635484i
$905$	8.94621	+	1.28627i	0.297382	+	0.0427571i
$906$	18.1037	−	15.1453i	0.601454	−	0.503168i
$907$	−31.4228	+	27.2280i	−1.04338	+	0.904090i	−0.995500	−	0.0947632i	$-0.969791\pi$
$907$	−31.4228	+	27.2280i	−1.04338	+	0.904090i	−0.0478757	+	0.998853i	$0.515245\pi$
$908$	2.43903	−	1.56747i	0.0809420	−	0.0520183i
$909$	−47.3599	−	8.49515i	−1.57083	−	0.281766i
$910$	6.35758	+	7.33704i	0.210752	+	0.243221i
$911$	37.1457	−	10.9070i	1.23069	−	0.361364i	0.399181	−	0.916872i	$-0.369295\pi$
$911$	37.1457	−	10.9070i	1.23069	−	0.361364i	0.831511	+	0.555509i	$0.187476\pi$
$912$	1.42683	+	5.19071i	0.0472470	+	0.171882i
$913$	−2.34113	+	2.70181i	−0.0774801	+	0.0894168i
$914$	9.62817	−	21.0828i	0.318472	−	0.697356i
$915$	−51.3387	+	6.47475i	−1.69720	+	0.214049i
$916$	−21.9538	+	10.0259i	−0.725372	+	0.331267i
$917$	0.470713	+	3.27388i	0.0155443	+	0.108113i
$918$	−4.37544	+	3.40961i	−0.144411	+	0.112534i
$919$		−	52.9536i		−	1.74678i	−0.487025	−	0.873388i	$-0.661918\pi$
$919$		−	52.9536i		−	1.74678i	0.487025	−	0.873388i	$-0.338082\pi$
$920$	24.4355	+	16.6956i	0.805615	+	0.550436i
$921$	9.24560	+	21.2110i	0.304653	+	0.698927i
$922$	22.9260	+	14.7337i	0.755029	+	0.485228i
$923$	41.0517	−	5.90234i	1.35123	−	0.194278i
$924$	−0.449151	−	0.403040i	−0.0147760	−	0.0132590i
$925$	−0.445265	+	1.51643i	−0.0146402	+	0.0498600i
$926$	8.90799	+	4.06814i	0.292735	+	0.133688i
$927$	−2.49143	+	0.270408i	−0.0818292	+	0.00888137i
$928$	−5.30799	+	36.9179i	−0.174243	+	1.21189i
$929$	−13.0719	−	44.5188i	−0.428875	−	1.46061i	−0.836754	−	0.547579i	$-0.815550\pi$
$929$	−13.0719	−	44.5188i	−0.428875	−	1.46061i	0.407879	−	0.913036i	$-0.366269\pi$
$930$	−4.59841	−	2.19719i	−0.150788	−	0.0720487i
$931$	3.32114	+	5.16779i	0.108846	+	0.169368i
$932$	11.2131	+	17.4479i	0.367297	+	0.571525i
$933$	26.0403	+	12.4425i	0.852522	+	0.407348i
$934$	−0.417790	−	1.42286i	−0.0136705	−	0.0465574i
$935$	−0.110924	+	0.771495i	−0.00362761	+	0.0252306i
$936$	−42.4796	+	4.61054i	−1.38849	+	0.150700i
$937$	−10.0448	−	4.58732i	−0.328150	−	0.149861i	0.244526	−	0.969643i	$-0.421368\pi$
$937$	−10.0448	−	4.58732i	−0.328150	−	0.149861i	−0.572677	+	0.819781i	$0.694095\pi$
$938$	2.60002	−	8.85484i	0.0848935	−	0.289121i
$939$	13.2535	+	11.8928i	0.432511	+	0.388108i
$940$	−11.4091	+	1.64038i	−0.372123	+	0.0535032i
$941$	−7.96412	−	5.11823i	−0.259623	−	0.166849i	0.404354	−	0.914603i	$-0.367496\pi$
$941$	−7.96412	−	5.11823i	−0.259623	−	0.166849i	−0.663977	+	0.747753i	$0.731133\pi$
$942$	8.10573	+	18.5960i	0.264099	+	0.605889i
$943$	−0.646509	+	1.31614i	−0.0210532	+	0.0428594i
$944$			4.32477i			0.140759i
$945$	−9.34908	+	7.28539i	−0.304126	+	0.236994i
$946$	0.117167	+	0.814914i	0.00380943	+	0.0264952i
$947$	15.6565	−	7.15008i	0.508768	−	0.232346i	−0.144456	−	0.989511i	$-0.546143\pi$
$947$	15.6565	−	7.15008i	0.508768	−	0.232346i	0.653224	+	0.757165i	$0.273416\pi$
$948$	−22.4093	+	2.82623i	−0.727821	+	0.0917917i
$949$	10.8396	−	23.7355i	0.351870	−	0.770488i
$950$	−0.660315	+	0.762044i	−0.0214235	+	0.0247240i
$951$	1.61703	+	5.88266i	0.0524358	+	0.190758i
$952$	−3.42776	+	1.00648i	−0.111094	+	0.0326203i
$953$	−3.37015	−	3.88936i	−0.109170	−	0.125989i	0.698535	−	0.715576i	$-0.253836\pi$
$953$	−3.37015	−	3.88936i	−0.109170	−	0.125989i	−0.807705	+	0.589587i	$0.799290\pi$
$954$	−7.67885	−	1.37739i	−0.248612	−	0.0445946i
$955$	25.9402	−	16.6708i	0.839406	−	0.539454i
$956$	−25.8885	+	22.4325i	−0.837294	+	0.725519i
$957$	−2.20309	+	1.84307i	−0.0712158	+	0.0595781i
$958$	−21.9735	−	3.15931i	−0.709931	−	0.102073i
$959$	−3.29567	−	2.85571i	−0.106423	−	0.0922157i
$960$	14.5873	+	0.253023i	0.470804	+	0.00816627i
$961$	27.3013	+	8.01638i	0.880686	+	0.258593i
$962$	−13.7621	−	30.1348i	−0.443708	−	0.971584i
$963$	20.6629	+	14.3156i	0.665854	+	0.461312i
$964$	−0.847295	+	1.31842i	−0.0272895	+	0.0424633i
$965$	11.0117			0.354479
$966$	−5.26990	+	4.16189i	−0.169556	+	0.133907i
$967$	−30.0365			−0.965910			−0.482955	−	0.875645i	$-0.660436\pi$
$967$	−30.0365			−0.965910			−0.482955	+	0.875645i	$0.660436\pi$
$968$	15.9907	−	24.8821i	0.513962	−	0.799740i
$969$	7.39009	+	11.9499i	0.237404	+	0.383887i
$970$	−3.45727	−	7.57037i	−0.111006	−	0.243070i
$971$	12.4931	+	3.66831i	0.400923	+	0.117722i	0.475977	−	0.879458i	$-0.342095\pi$
$971$	12.4931	+	3.66831i	0.400923	+	0.117722i	−0.0750536	+	0.997179i	$0.523913\pi$
$972$	−1.17650	−	20.9565i	−0.0377363	−	0.672179i
$973$	−3.30156	−	2.86082i	−0.105843	−	0.0917137i
$974$	−27.1388	−	3.90196i	−0.869582	−	0.125027i
$975$	1.18806	+	1.42013i	0.0380484	+	0.0454806i
$976$	5.00801	−	4.33946i	0.160302	−	0.138903i
$977$	−21.3992	+	13.7524i	−0.684621	+	0.439979i	−0.836170	−	0.548470i	$-0.815210\pi$
$977$	−21.3992	+	13.7524i	−0.684621	+	0.439979i	0.151549	+	0.988450i	$0.451574\pi$
$978$	2.32722	−	3.48676i	0.0744164	−	0.111494i
$979$	−0.707661	−	0.816685i	−0.0226169	−	0.0261014i
$980$	−2.94692	+	0.865295i	−0.0941361	+	0.0276408i
$981$	−35.8377	+	28.9398i	−1.14421	+	0.923976i
$982$	−6.12171	+	7.06483i	−0.195352	+	0.225448i
$983$	9.00136	−	19.7102i	0.287099	−	0.628659i	−0.710047	−	0.704154i	$-0.751326\pi$
$983$	9.00136	−	19.7102i	0.287099	−	0.628659i	0.997146	+	0.0754951i	$0.0240537\pi$
$984$	0.179269	+	1.42144i	0.00571490	+	0.0453138i
$985$	−27.0915	+	12.3723i	−0.863207	+	0.394213i
$986$	0.973675	+	6.77206i	0.0310081	+	0.215666i
$987$	1.03652	−	6.41703i	0.0329928	−	0.204256i
$988$			43.5472i			1.38542i
$989$	−18.8677	−	0.532153i	−0.599957	−	0.0169215i
$990$	1.04866	+	0.974359i	0.0333287	+	0.0309672i
$991$	−17.3440	−	11.1463i	−0.550951	−	0.354074i	0.235358	−	0.971909i	$-0.424374\pi$
$991$	−17.3440	−	11.1463i	−0.550951	−	0.354074i	−0.786308	+	0.617834i	$0.788010\pi$
$992$	9.19168	−	1.32156i	0.291836	−	0.0419597i
$993$	11.8457	−	13.2009i	0.375911	−	0.418918i
$994$	1.79415	−	6.11032i	0.0569070	−	0.193808i
$995$	−7.47216	−	3.41242i	−0.236883	−	0.108181i
$996$	−30.7537	−	9.61248i	−0.974467	−	0.304583i
$997$	5.97938	−	41.5875i	0.189369	−	1.31709i	−0.644278	−	0.764791i	$-0.722842\pi$
$997$	5.97938	−	41.5875i	0.189369	−	1.31709i	0.833647	−	0.552298i	$-0.186249\pi$
$998$	3.18282	+	10.8397i	0.100750	+	0.343124i
$999$	37.6145	−	14.8655i	1.19007	−	0.470325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.20	✓	480
3.2	odd	2	inner	483.2.u.a.113.29	yes	480
23.11	odd	22	inner	483.2.u.a.218.29	yes	480
69.11	even	22	inner	483.2.u.a.218.20	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.20	✓	480	1.1	even	1	trivial
483.2.u.a.113.29	yes	480	3.2	odd	2	inner
483.2.u.a.218.20	yes	480	69.11	even	22	inner
483.2.u.a.218.29	yes	480	23.11	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.437059 + 0.680077i) q^{2} +(1.47311 - 0.911006i) q^{3} +(0.559346 + 1.22480i) q^{4} +(2.18862 + 0.642637i) q^{5} +(-0.0242835 + 1.39999i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-2.67778 - 0.385007i) q^{8} +(1.34013 - 2.68403i) q^{9} +O(q^{10})\)	\(q+(-0.437059 + 0.680077i) q^{2} +(1.47311 - 0.911006i) q^{3} +(0.559346 + 1.22480i) q^{4} +(2.18862 + 0.642637i) q^{5} +(-0.0242835 + 1.39999i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-2.67778 - 0.385007i) q^{8} +(1.34013 - 2.68403i) q^{9} +(-1.39360 + 1.20756i) q^{10} +(0.217683 - 0.139896i) q^{11} +(1.93978 + 1.29470i) q^{12} +(3.44772 + 3.97888i) q^{13} +(0.775662 - 0.227755i) q^{14} +(3.80954 - 1.04717i) q^{15} +(-0.331325 + 0.382369i) q^{16} +(-0.548570 + 1.20120i) q^{17} +(1.23963 + 2.08447i) q^{18} +(5.58784 - 2.55188i) q^{19} +(0.437097 + 3.04007i) q^{20} +(-1.70989 - 0.276192i) q^{21} +0.209184i q^{22} +(-4.72589 - 0.816081i) q^{23} +(-4.29543 + 1.87232i) q^{24} +(0.170813 + 0.109775i) q^{25} +(-4.21280 + 0.605709i) q^{26} +(-0.471001 - 5.17476i) q^{27} +(0.379346 - 1.29193i) q^{28} +(-5.82973 - 2.66235i) q^{29} +(-0.952836 + 3.04845i) q^{30} +(-0.227086 + 1.57942i) q^{31} +(-1.63959 - 5.58391i) q^{32} +(0.193225 - 0.404394i) q^{33} +(-0.577152 - 0.898065i) q^{34} +(-1.23321 - 1.91891i) q^{35} +(4.03700 + 0.140089i) q^{36} +(2.19293 + 7.46844i) q^{37} +(-0.706739 + 4.91548i) q^{38} +(8.70368 + 2.72045i) q^{39} +(-5.61323 - 2.56348i) q^{40} +(0.0861414 - 0.293371i) q^{41} +(0.935153 - 1.04214i) q^{42} +(3.89568 - 0.560115i) q^{43} +(0.293105 + 0.188367i) q^{44} +(4.65791 - 5.01311i) q^{45} +(2.62049 - 2.85729i) q^{46} +3.75289i q^{47} +(-0.139739 + 0.865113i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-0.149310 + 0.0681878i) q^{50} +(0.286195 + 2.26926i) q^{51} +(-2.94485 + 6.44833i) q^{52} +(-2.10654 + 2.43108i) q^{53} +(3.72509 + 1.94136i) q^{54} +(0.566328 - 0.166289i) q^{55} +(1.77161 + 2.04454i) q^{56} +(5.90675 - 8.84977i) q^{57} +(4.35854 - 2.80106i) q^{58} +(6.46005 - 5.59766i) q^{59} +(3.41342 + 4.08018i) q^{60} +(-12.9640 - 1.86394i) q^{61} +(-0.974877 - 0.844736i) q^{62} +(-2.77047 + 1.15086i) q^{63} +(3.54318 + 1.04037i) q^{64} +(4.98878 + 10.9239i) q^{65} +(0.190568 + 0.308152i) q^{66} +(6.17187 - 9.60362i) q^{67} -1.77807 q^{68} +(-7.70523 + 3.10313i) q^{69} +1.84400 q^{70} +(4.25892 - 6.62702i) q^{71} +(-4.62196 + 6.67130i) q^{72} +(-2.05888 - 4.50833i) q^{73} +(-6.03755 - 1.77278i) q^{74} +(0.351632 + 0.00609920i) q^{75} +(6.25107 + 5.41658i) q^{76} +(-0.256126 - 0.0368254i) q^{77} +(-5.65414 + 4.73017i) q^{78} +(-7.31938 + 6.34228i) q^{79} +(-0.970870 + 0.623940i) q^{80} +(-5.40808 - 7.19393i) q^{81} +(0.161866 + 0.186803i) q^{82} +(-13.2563 + 3.89239i) q^{83} +(-0.618140 - 2.24875i) q^{84} +(-1.97255 + 2.27644i) q^{85} +(-1.32172 + 2.89417i) q^{86} +(-11.0133 + 1.38898i) q^{87} +(-0.636769 + 0.290803i) q^{88} +(-0.594332 - 4.13367i) q^{89} +(1.37352 + 5.35876i) q^{90} -5.26482i q^{91} +(-1.64387 - 6.24473i) q^{92} +(1.10434 + 2.53355i) q^{93} +(-2.55225 - 1.64023i) q^{94} +(13.8696 - 1.99415i) q^{95} +(-7.50228 - 6.73207i) q^{96} +(-1.27154 + 4.33046i) q^{97} +(-0.735354 - 0.335825i) q^{98} +(-0.0837621 - 0.771748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36} - 44 q^{37} - 308 q^{40} - 44 q^{43} - 184 q^{46} + 98 q^{48} + 48 q^{49} - 28 q^{52} + 28 q^{54} - 44 q^{55} + 66 q^{57} + 4 q^{58} + 220 q^{60} + 84 q^{64} + 176 q^{66} + 44 q^{67} + 102 q^{69} - 8 q^{70} - 60 q^{72} + 4 q^{73} - 8 q^{75} + 176 q^{76} + 18 q^{78} - 16 q^{81} + 20 q^{82} - 154 q^{84} + 84 q^{85} + 28 q^{87} - 418 q^{90} - 188 q^{93} + 12 q^{94} - 412 q^{96} - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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