LMFDB - Embedded newform 690.2.r.b.169.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			169.10
Character	$\chi$	$=$	690.169
Dual form			690.2.r.b.49.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(0.670880 + 2.13305i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.0999940 - 0.155594i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(0.670880 + 2.13305i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.0999940 - 0.155594i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(0.360487 + 2.20682i) q^{10} +(-0.591841 - 4.11635i) q^{11} +(-0.989821 + 0.142315i) q^{12} +(3.08583 + 4.80164i) q^{13} +(0.121120 - 0.139779i) q^{14} +(-1.49636 - 1.66160i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.78801 + 6.08939i) q^{17} +(0.755750 - 0.654861i) q^{18} +(2.06044 + 0.605000i) q^{19} +(0.0427543 + 2.23566i) q^{20} +(-0.0263218 + 0.183072i) q^{21} -4.15868i q^{22} +(-4.79536 - 0.0673348i) q^{23} -1.00000 q^{24} +(-4.09984 + 2.86205i) q^{25} +(2.37107 + 5.19193i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(0.139779 - 0.121120i) q^{28} +(4.70792 - 1.38237i) q^{29} +(-1.24466 - 1.85764i) q^{30} +(-2.03747 + 4.46145i) q^{31} +(0.755750 + 0.654861i) q^{32} +(2.24835 + 3.49850i) q^{33} +(0.903197 + 6.28187i) q^{34} +(0.398974 + 0.108908i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-4.72024 - 4.09011i) q^{37} +(1.95337 + 0.892074i) q^{38} +(-4.80164 - 3.08583i) q^{39} +(-0.275848 + 2.21899i) q^{40} +(-1.65444 - 1.90933i) q^{41} +(-0.0521077 + 0.177463i) q^{42} +(-4.80047 + 2.19230i) q^{43} +(0.591841 - 4.11635i) q^{44} +(2.05139 + 0.889836i) q^{45} +(-4.73697 - 0.749100i) q^{46} +2.44178i q^{47} +(-0.989821 - 0.142315i) q^{48} +(2.89369 + 6.33631i) q^{49} +(-4.46542 + 2.24945i) q^{50} +(-4.15605 - 4.79634i) q^{51} +(1.60805 + 5.47652i) q^{52} +(6.66112 - 10.3649i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(8.38334 - 4.02401i) q^{55} +(0.155594 - 0.0999940i) q^{56} +(-2.12557 + 0.305611i) q^{57} +(4.85673 - 0.698293i) q^{58} +(9.13926 - 5.87345i) q^{59} +(-0.967617 - 2.01587i) q^{60} +(-5.02703 + 11.0077i) q^{61} +(-2.65167 + 4.12607i) q^{62} +(-0.0521077 - 0.177463i) q^{63} +(0.654861 + 0.755750i) q^{64} +(-8.17194 + 9.80357i) q^{65} +(1.72758 + 3.78287i) q^{66} +(8.92008 + 1.28251i) q^{67} +6.34647i q^{68} +(4.38998 - 1.93081i) q^{69} +(0.379414 + 0.164579i) q^{70} +(0.970226 - 6.74807i) q^{71} +(0.909632 - 0.415415i) q^{72} +(4.11019 - 13.9980i) q^{73} +(-4.09011 - 4.72024i) q^{74} +(2.54041 - 4.30655i) q^{75} +(1.80653 + 1.16099i) q^{76} +(-0.699658 - 0.319523i) q^{77} +(-4.31361 - 3.73776i) q^{78} +(13.8198 - 8.88145i) q^{79} +(-0.588836 + 2.15714i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-1.36588 - 2.12535i) q^{82} +(-0.426230 - 0.369330i) q^{83} +(-0.0768329 + 0.168241i) q^{84} +(-11.7895 + 7.89917i) q^{85} +(-5.06361 + 1.48681i) q^{86} +(-3.70822 + 3.21319i) q^{87} +(1.17163 - 3.99022i) q^{88} +(-7.29980 - 15.9843i) q^{89} +(1.90387 + 1.17272i) q^{90} +1.05567 q^{91} +(-4.58214 - 1.41562i) q^{92} -4.90467i q^{93} +(-0.347502 + 2.41693i) q^{94} +(0.0918117 + 4.80092i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(1.35952 - 1.17803i) q^{97} +(1.96249 + 6.68363i) q^{98} +(-3.49850 - 2.24835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.989821	+	0.142315i	0.699909	+	0.100632i
$2$	0.989821	+	0.142315i	0.699909	+	0.100632i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	0.959493	+	0.281733i	0.479746	+	0.140866i
$5$	0.670880	+	2.13305i	0.300027	+	0.953931i
$5$	0.670880	+	2.13305i	0.300027	+	0.953931i
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	0.0999940	−	0.155594i	0.0377942	−	0.0588089i	−0.821842	−	0.569715i	$-0.807054\pi$
$7$	0.0999940	−	0.155594i	0.0377942	−	0.0588089i	0.859637	+	0.510906i	$0.170690\pi$
$8$	0.909632	+	0.415415i	0.321603	+	0.146871i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	0.360487	+	2.20682i	0.113996	+	0.697857i
$11$	−0.591841	−	4.11635i	−0.178447	−	1.24113i	−0.860358	−	0.509690i	$-0.829760\pi$
$11$	−0.591841	−	4.11635i	−0.178447	−	1.24113i	0.681911	−	0.731435i	$-0.261149\pi$
$12$	−0.989821	+	0.142315i	−0.285737	+	0.0410828i
$13$	3.08583	+	4.80164i	0.855855	+	1.33174i	0.942055	+	0.335458i	$0.108891\pi$
$13$	3.08583	+	4.80164i	0.855855	+	1.33174i	−0.0862003	+	0.996278i	$0.527473\pi$
$14$	0.121120	−	0.139779i	0.0323706	−	0.0373576i
$15$	−1.49636	−	1.66160i	−0.386358	−	0.429023i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	1.78801	+	6.08939i	0.433656	+	1.47690i	0.829463	+	0.558562i	$0.188647\pi$
$17$	1.78801	+	6.08939i	0.433656	+	1.47690i	−0.395808	+	0.918333i	$0.629535\pi$
$18$	0.755750	−	0.654861i	0.178132	−	0.154352i
$19$	2.06044	+	0.605000i	0.472698	+	0.138797i	0.509400	−	0.860530i	$-0.329867\pi$
$19$	2.06044	+	0.605000i	0.472698	+	0.138797i	−0.0367026	+	0.999326i	$0.511685\pi$
$20$	0.0427543	+	2.23566i	0.00956015	+	0.499909i
$21$	−0.0263218	+	0.183072i	−0.00574389	+	0.0399496i
$22$		−	4.15868i		−	0.886633i
$23$	−4.79536	−	0.0673348i	−0.999901	−	0.0140403i
$23$	−4.79536	−	0.0673348i	−0.999901	−	0.0140403i
$24$	−1.00000			−0.204124
$25$	−4.09984	+	2.86205i	−0.819968	+	0.572410i
$26$	2.37107	+	5.19193i	0.465006	+	1.01822i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	0.139779	−	0.121120i	0.0264158	−	0.0228894i
$29$	4.70792	−	1.38237i	0.874239	−	0.256700i	0.186322	−	0.982489i	$-0.440343\pi$
$29$	4.70792	−	1.38237i	0.874239	−	0.256700i	0.687917	+	0.725789i	$0.258525\pi$
$30$	−1.24466	−	1.85764i	−0.227242	−	0.339157i
$31$	−2.03747	+	4.46145i	−0.365941	+	0.801299i	0.633675	+	0.773599i	$0.281546\pi$
$31$	−2.03747	+	4.46145i	−0.365941	+	0.801299i	−0.999616	+	0.0277001i	$0.991182\pi$
$32$	0.755750	+	0.654861i	0.133599	+	0.115764i
$33$	2.24835	+	3.49850i	0.391388	+	0.609011i
$34$	0.903197	+	6.28187i	0.154897	+	1.07733i
$35$	0.398974	+	0.108908i	0.0674389	+	0.0184088i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−4.72024	−	4.09011i	−0.776003	−	0.672410i	0.173967	−	0.984751i	$-0.444341\pi$
$37$	−4.72024	−	4.09011i	−0.776003	−	0.672410i	−0.949970	+	0.312341i	$0.898887\pi$
$38$	1.95337	+	0.892074i	0.316878	+	0.144713i
$39$	−4.80164	−	3.08583i	−0.768878	−	0.494128i
$40$	−0.275848	+	2.21899i	−0.0436155	+	0.350853i
$41$	−1.65444	−	1.90933i	−0.258380	−	0.298187i	0.611707	−	0.791084i	$-0.290483\pi$
$41$	−1.65444	−	1.90933i	−0.258380	−	0.298187i	−0.870087	+	0.492898i	$0.835938\pi$
$42$	−0.0521077	+	0.177463i	−0.00804040	+	0.0273831i
$43$	−4.80047	+	2.19230i	−0.732066	+	0.334323i	−0.746331	−	0.665575i	$-0.768186\pi$
$43$	−4.80047	+	2.19230i	−0.732066	+	0.334323i	0.0142653	+	0.999898i	$0.495459\pi$
$44$	0.591841	−	4.11635i	0.0892234	−	0.620563i
$45$	2.05139	+	0.889836i	0.305803	+	0.132649i
$46$	−4.73697	−	0.749100i	−0.698428	−	0.110449i
$47$			2.44178i			0.356171i	0.984015	+	0.178085i	$0.0569903\pi$
$47$			2.44178i			0.356171i	−0.984015	+	0.178085i	$0.943010\pi$
$48$	−0.989821	−	0.142315i	−0.142868	−	0.0205414i
$49$	2.89369	+	6.33631i	0.413385	+	0.905187i
$50$	−4.46542	+	2.24945i	−0.631506	+	0.318120i
$51$	−4.15605	−	4.79634i	−0.581964	−	0.671622i
$52$	1.60805	+	5.47652i	0.222997	+	0.759457i
$53$	6.66112	−	10.3649i	0.914975	−	1.42373i	0.00920600	−	0.999958i	$-0.497070\pi$
$53$	6.66112	−	10.3649i	0.914975	−	1.42373i	0.905769	−	0.423771i	$-0.139294\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	8.38334	−	4.02401i	1.13041	−	0.542597i
$56$	0.155594	−	0.0999940i	0.0207921	−	0.0133623i
$57$	−2.12557	+	0.305611i	−0.281539	+	0.0404791i
$58$	4.85673	−	0.698293i	0.637721	−	0.0916904i
$59$	9.13926	−	5.87345i	1.18983	−	0.764657i	0.212662	−	0.977126i	$-0.431787\pi$
$59$	9.13926	−	5.87345i	1.18983	−	0.764657i	0.977168	+	0.212468i	$0.0681502\pi$
$60$	−0.967617	−	2.01587i	−0.124919	−	0.260247i
$61$	−5.02703	+	11.0077i	−0.643646	+	1.40939i	0.253362	+	0.967372i	$0.418464\pi$
$61$	−5.02703	+	11.0077i	−0.643646	+	1.40939i	−0.897007	+	0.442016i	$0.854263\pi$
$62$	−2.65167	+	4.12607i	−0.336762	+	0.524012i
$63$	−0.0521077	−	0.177463i	−0.00656496	−	0.0223582i
$64$	0.654861	+	0.755750i	0.0818576	+	0.0944687i
$65$	−8.17194	+	9.80357i	−1.01360	+	1.21598i
$66$	1.72758	+	3.78287i	0.212650	+	0.465639i
$67$	8.92008	+	1.28251i	1.08976	+	0.156684i	0.663692	−	0.748006i	$-0.268989\pi$
$67$	8.92008	+	1.28251i	1.08976	+	0.156684i	0.426070	+	0.904690i	$0.359898\pi$
$68$			6.34647i			0.769623i
$69$	4.38998	−	1.93081i	0.528492	−	0.232443i
$70$	0.379414	+	0.164579i	0.0453486	+	0.0196710i
$71$	0.970226	−	6.74807i	0.115145	−	0.800848i	−0.847639	−	0.530574i	$-0.821976\pi$
$71$	0.970226	−	6.74807i	0.115145	−	0.800848i	0.962783	−	0.270274i	$-0.0871145\pi$
$72$	0.909632	−	0.415415i	0.107201	−	0.0489571i
$73$	4.11019	−	13.9980i	0.481061	−	1.63834i	−0.259054	−	0.965863i	$-0.583411\pi$
$73$	4.11019	−	13.9980i	0.481061	−	1.63834i	0.740115	−	0.672481i	$-0.234771\pi$
$74$	−4.09011	−	4.72024i	−0.475466	−	0.548717i
$75$	2.54041	−	4.30655i	0.293341	−	0.497277i
$76$	1.80653	+	1.16099i	0.207223	+	0.133174i
$77$	−0.699658	−	0.319523i	−0.0797335	−	0.0364131i
$78$	−4.31361	−	3.73776i	−0.488420	−	0.423218i
$79$	13.8198	−	8.88145i	1.55485	−	0.999241i	0.570853	−	0.821052i	$-0.306613\pi$
$79$	13.8198	−	8.88145i	1.55485	−	0.999241i	0.983996	−	0.178189i	$-0.0570238\pi$
$80$	−0.588836	+	2.15714i	−0.0658338	+	0.241176i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−1.36588	−	2.12535i	−0.150836	−	0.234705i
$83$	−0.426230	−	0.369330i	−0.0467848	−	0.0405393i	0.631155	−	0.775657i	$-0.282581\pi$
$83$	−0.426230	−	0.369330i	−0.0467848	−	0.0405393i	−0.677939	+	0.735118i	$0.737127\pi$
$84$	−0.0768329	+	0.168241i	−0.00838316	+	0.0183566i
$85$	−11.7895	+	7.89917i	−1.27875	+	0.856785i
$86$	−5.06361	+	1.48681i	−0.546023	+	0.160327i
$87$	−3.70822	+	3.21319i	−0.397563	+	0.344490i
$88$	1.17163	−	3.99022i	0.124897	−	0.425359i
$89$	−7.29980	−	15.9843i	−0.773777	−	1.69434i	−0.718154	−	0.695884i	$-0.755013\pi$
$89$	−7.29980	−	15.9843i	−0.773777	−	1.69434i	−0.0556235	−	0.998452i	$-0.517715\pi$
$90$	1.90387	+	1.17272i	0.200686	+	0.123616i
$91$	1.05567			0.110664
$92$	−4.58214	−	1.41562i	−0.477721	−	0.147588i
$93$		−	4.90467i		−	0.508591i
$94$	−0.347502	+	2.41693i	−0.0358421	+	0.249287i
$95$	0.0918117	+	4.80092i	0.00941969	+	0.492564i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	1.35952	−	1.17803i	0.138038	−	0.119611i	−0.583105	−	0.812397i	$-0.698162\pi$
$97$	1.35952	−	1.17803i	0.138038	−	0.119611i	0.721143	+	0.692786i	$0.243617\pi$
$98$	1.96249	+	6.68363i	0.198241	+	0.675148i
$99$	−3.49850	−	2.24835i	−0.351613	−	0.225968i
$100$	−4.74010	+	1.59106i	−0.474010	+	0.159106i
$101$	−8.09171	+	9.33833i	−0.805155	+	0.929198i	−0.998652	−	0.0519026i	$-0.983471\pi$
$101$	−8.09171	+	9.33833i	−0.805155	+	0.929198i	0.193497	+	0.981101i	$0.438017\pi$
$102$	−3.43116	−	5.33899i	−0.339736	−	0.528639i
$103$	15.1799	−	2.18255i	1.49572	−	0.215053i	0.654633	−	0.755946i	$-0.272823\pi$
$103$	15.1799	−	2.18255i	1.49572	−	0.215053i	0.841091	+	0.540894i	$0.181914\pi$
$104$	0.812294	+	5.64963i	0.0796520	+	0.553992i
$105$	−0.408161	+	0.0666737i	−0.0398325	+	0.00650668i
$106$	8.06840	−	9.31143i	0.783672	−	0.904406i
$107$	−11.0425	−	5.04296i	−1.06752	−	0.487521i	−0.197383	−	0.980327i	$-0.563244\pi$
$107$	−11.0425	−	5.04296i	−1.06752	−	0.487521i	−0.870139	+	0.492806i	$0.835971\pi$
$108$	−0.540641	+	0.841254i	−0.0520232	+	0.0809497i
$109$	1.95728	−	0.574709i	0.187473	−	0.0550472i	−0.186648	−	0.982427i	$-0.559762\pi$
$109$	1.95728	−	0.574709i	0.187473	−	0.0550472i	0.374122	+	0.927380i	$0.377944\pi$
$110$	8.87068	−	2.78997i	0.845786	−	0.266014i
$111$	5.99277	+	1.75964i	0.568809	+	0.167017i
$112$	0.168241	−	0.0768329i	0.0158972	−	0.00726003i
$113$	−4.31566	−	0.620498i	−0.405983	−	0.0583715i	−0.0637014	−	0.997969i	$-0.520291\pi$
$113$	−4.31566	−	0.620498i	−0.405983	−	0.0583715i	−0.342281	+	0.939597i	$0.611200\pi$
$114$	−2.14743			−0.201125
$115$	−3.07348	−	10.2739i	−0.286604	−	0.958049i
$116$	4.90668			0.455574
$117$	5.64963	+	0.812294i	0.522308	+	0.0750966i
$118$	9.88211	−	4.51301i	0.909722	−	0.415456i
$119$	1.12626	+	0.330700i	0.103244	+	0.0303152i
$120$	−0.670880	−	2.13305i	−0.0612427	−	0.194720i
$121$	−6.03961	+	1.77339i	−0.549056	+	0.161217i
$122$	−6.54242	+	10.1802i	−0.592323	+	0.921672i
$123$	2.29810	+	1.04951i	0.207212	+	0.0946307i
$124$	−3.21188	+	3.70670i	−0.288435	+	0.332872i
$125$	−8.85541	−	6.82509i	−0.792052	−	0.610454i
$126$	−0.0263218	−	0.183072i	−0.00234493	−	0.0163094i
$127$	−3.81477	+	0.548481i	−0.338506	+	0.0486699i	−0.309472	−	0.950909i	$-0.600152\pi$
$127$	−3.81477	+	0.548481i	−0.338506	+	0.0486699i	−0.0290343	+	0.999578i	$0.509243\pi$
$128$	0.540641	+	0.841254i	0.0477863	+	0.0743570i
$129$	3.45595	−	3.98838i	0.304279	−	0.351157i
$130$	−9.48396	+	8.54079i	−0.831798	+	0.749077i
$131$	−14.9138	−	9.58452i	−1.30303	−	0.837404i	−0.309488	−	0.950903i	$-0.600158\pi$
$131$	−14.9138	−	9.58452i	−1.30303	−	0.837404i	−0.993538	+	0.113500i	$0.963794\pi$
$132$	1.17163	+	3.99022i	0.101978	+	0.347304i
$133$	0.300166	−	0.260095i	0.0260277	−	0.0225531i
$134$	8.64676	+	2.53892i	0.746967	+	0.219329i
$135$	−2.23566	+	0.0427543i	−0.192415	+	0.00367970i
$136$	−0.903197	+	6.28187i	−0.0774485	+	0.538666i
$137$		−	15.3728i		−	1.31338i	−0.754159	−	0.656692i	$-0.771955\pi$
$137$		−	15.3728i		−	1.31338i	0.754159	−	0.656692i	$-0.228045\pi$
$138$	4.62008	−	1.28640i	0.393288	−	0.109506i
$139$	−20.3326			−1.72458			−0.862292	−	0.506411i	$-0.830972\pi$
$139$	−20.3326			−1.72458			−0.862292	+	0.506411i	$0.830972\pi$
$140$	0.352130	+	0.216900i	0.0297604	+	0.0183314i
$141$	−1.01435	−	2.22112i	−0.0854240	−	0.187052i
$142$	1.92070	−	6.54131i	0.161182	−	0.548934i
$143$	17.9389	−	15.5442i	1.50013	−	1.29987i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	6.10712	+	9.11485i	0.507169	+	0.756947i
$146$	6.06048	−	13.2706i	0.501569	−	1.09828i
$147$	−5.26439	−	4.56162i	−0.434200	−	0.376236i
$148$	−3.37672	−	5.25428i	−0.277565	−	0.431899i
$149$	−0.587150	−	4.08372i	−0.0481012	−	0.334551i	−0.999635	−	0.0270077i	$-0.991402\pi$
$149$	−0.587150	−	4.08372i	−0.0481012	−	0.334551i	0.951534	−	0.307543i	$-0.0995069\pi$
$150$	3.12743	−	3.90117i	0.255354	−	0.318529i
$151$	4.85872	−	3.12251i	0.395397	−	0.254106i	−0.327801	−	0.944747i	$-0.606308\pi$
$151$	4.85872	−	3.12251i	0.395397	−	0.254106i	0.723198	+	0.690641i	$0.242671\pi$
$152$	1.62292	+	1.40627i	0.131636	+	0.114063i
$153$	5.77295	+	2.63642i	0.466716	+	0.213142i
$154$	−0.647064	−	0.415843i	−0.0521419	−	0.0335096i
$155$	−10.8834	−	1.35295i	−0.874176	−	0.108671i
$156$	−3.73776	−	4.31361i	−0.299261	−	0.345365i
$157$	0.368706	−	1.25570i	0.0294260	−	0.100216i	−0.943471	−	0.331456i	$-0.892460\pi$
$157$	0.368706	−	1.25570i	0.0294260	−	0.100216i	0.972897	+	0.231240i	$0.0742784\pi$
$158$	14.9431	−	6.82429i	1.18881	−	0.542911i
$159$	−1.75343	+	12.1954i	−0.139056	+	0.967156i
$160$	−0.889836	+	2.05139i	−0.0703477	+	0.162176i
$161$	−0.489984	+	0.739395i	−0.0386162	+	0.0582725i
$162$		−	1.00000i		−	0.0785674i
$163$	−10.8526	−	1.56037i	−0.850043	−	0.122218i	−0.296495	−	0.955035i	$-0.595818\pi$
$163$	−10.8526	−	1.56037i	−0.850043	−	0.122218i	−0.553549	+	0.832817i	$0.686727\pi$
$164$	−1.04951	−	2.29810i	−0.0819526	−	0.179451i
$165$	−5.95412	+	7.14293i	−0.463527	+	0.556076i
$166$	−0.369330	−	0.426230i	−0.0286656	−	0.0330819i
$167$	−1.16885	−	3.98074i	−0.0904485	−	0.308039i	0.901826	−	0.432099i	$-0.142227\pi$
$167$	−1.16885	−	3.98074i	−0.0904485	−	0.308039i	−0.992275	+	0.124060i	$0.960409\pi$
$168$	−0.0999940	+	0.155594i	−0.00771471	+	0.0120043i
$169$	−8.13304	+	17.8089i	−0.625618	+	1.36991i
$170$	−12.7936	+	6.14095i	−0.981227	+	0.470990i
$171$	1.80653	−	1.16099i	0.138149	−	0.0887829i
$172$	−5.22366	+	0.751050i	−0.398301	+	0.0572670i
$173$	3.34992	−	0.481646i	0.254690	−	0.0366189i	−0.0137871	−	0.999905i	$-0.504389\pi$
$173$	3.34992	−	0.481646i	0.254690	−	0.0366189i	0.268477	+	0.963286i	$0.413480\pi$
$174$	−4.12776	+	2.65275i	−0.312925	+	0.201104i
$175$	0.0353574	+	0.924097i	0.00267277	+	0.0698552i
$176$	1.72758	−	3.78287i	0.130221	−	0.285144i
$177$	−5.87345	+	9.13926i	−0.441475	+	0.686949i
$178$	−4.95069	−	16.8605i	−0.371070	−	1.26375i
$179$	8.95399	+	10.3335i	0.669252	+	0.772358i	0.984259	−	0.176731i	$-0.0565523\pi$
$179$	8.95399	+	10.3335i	0.669252	+	0.772358i	−0.315007	+	0.949089i	$0.602007\pi$
$180$	1.71760	+	1.43173i	0.128022	+	0.106715i
$181$	5.36838	+	11.7551i	0.399028	+	0.873750i	0.997368	+	0.0725077i	$0.0231002\pi$
$181$	5.36838	+	11.7551i	0.399028	+	0.873750i	−0.598339	+	0.801243i	$0.704173\pi$
$182$	1.04492	+	0.150237i	0.0774550	+	0.0111363i
$183$		−	12.1012i		−	0.894549i
$184$	−4.33404	−	2.05331i	−0.319510	−	0.151372i
$185$	5.55771	−	12.8125i	0.408611	−	0.941994i
$186$	0.698008	−	4.85475i	0.0511804	−	0.355967i
$187$	24.0078	−	10.9640i	1.75563	−	0.801768i
$188$	−0.687930	+	2.34287i	−0.0501725	+	0.170872i
$189$	0.121120	+	0.139779i	0.00881015	+	0.0101675i
$190$	−0.592364	+	4.76512i	−0.0429746	+	0.345698i
$191$	6.04059	+	3.88205i	0.437082	+	0.280895i	0.740620	−	0.671924i	$-0.234532\pi$
$191$	6.04059	+	3.88205i	0.437082	+	0.280895i	−0.303539	+	0.952819i	$0.598168\pi$
$192$	−0.909632	−	0.415415i	−0.0656470	−	0.0299800i
$193$	16.1673	+	14.0091i	1.16375	+	1.00840i	0.999759	+	0.0219343i	$0.00698247\pi$
$193$	16.1673	+	14.0091i	1.16375	+	1.00840i	0.163992	+	0.986462i	$0.447563\pi$
$194$	1.51333	−	0.972558i	0.108651	−	0.0698256i
$195$	3.36091	−	12.3124i	0.240680	−	0.881708i
$196$	0.991336	+	6.89489i	0.0708097	+	0.492492i
$197$	1.88225	+	2.92883i	0.134104	+	0.208671i	0.901811	−	0.432131i	$-0.142238\pi$
$197$	1.88225	+	2.92883i	0.134104	+	0.208671i	−0.767706	+	0.640802i	$0.778602\pi$
$198$	−3.14292	−	2.72335i	−0.223357	−	0.193540i
$199$	1.52492	−	3.33910i	0.108098	−	0.236703i	−0.847851	−	0.530235i	$-0.822104\pi$
$199$	1.52492	−	3.33910i	0.108098	−	0.236703i	0.955949	+	0.293533i	$0.0948309\pi$
$200$	−4.91828	+	0.900276i	−0.347775	+	0.0636591i
$201$	−8.64676	+	2.53892i	−0.609896	+	0.179082i
$202$	−9.33833	+	8.09171i	−0.657042	+	0.569330i
$203$	0.255676	−	0.870752i	0.0179449	−	0.0611148i
$204$	−2.63642	−	5.77295i	−0.184586	−	0.404188i
$205$	2.96277	−	4.80994i	0.206929	−	0.335941i
$206$	15.3360			1.06851
$207$	−3.19118	+	3.58000i	−0.221802	+	0.248827i
$208$			5.70772i			0.395759i
$209$	1.27094	−	8.83956i	0.0879125	−	0.611445i
$210$	−0.413496	+	0.00790760i	−0.0285339	+	0.000545677i
$211$	3.81638	+	1.12059i	0.262731	+	0.0771447i	0.410445	−	0.911885i	$-0.365373\pi$
$211$	3.81638	+	1.12059i	0.262731	+	0.0771447i	−0.147714	+	0.989030i	$0.547192\pi$
$212$	9.31143	−	8.06840i	0.639512	−	0.554140i
$213$	1.92070	+	6.54131i	0.131604	+	0.448203i
$214$	−10.2124	−	6.56314i	−0.698109	−	0.448647i
$215$	−7.89685	−	8.76890i	−0.538560	−	0.598034i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	0.490438	+	0.763136i	0.0332931	+	0.0518051i
$218$	2.01915	−	0.290310i	0.136754	−	0.0196622i
$219$	2.07623	+	14.4405i	0.140298	+	0.975797i
$220$	9.17745	−	1.49915i	0.618743	−	0.101072i
$221$	−23.7216	+	27.3762i	−1.59569	+	1.84152i
$222$	5.68135	+	2.59459i	0.381307	+	0.174137i
$223$	0.314846	−	0.489911i	0.0210837	−	0.0328068i	−0.830552	−	0.556941i	$-0.811975\pi$
$223$	0.314846	−	0.489911i	0.0210837	−	0.0328068i	0.851635	+	0.524135i	$0.175611\pi$
$224$	0.177463	−	0.0521077i	0.0118572	−	0.00348159i
$225$	−0.521832	+	4.97269i	−0.0347888	+	0.331513i
$226$	−4.18342	−	1.22836i	−0.278277	−	0.0817096i
$227$	−12.8057	+	5.84818i	−0.849946	+	0.388158i	−0.792265	−	0.610177i	$-0.791098\pi$
$227$	−12.8057	+	5.84818i	−0.849946	+	0.388158i	−0.0576817	+	0.998335i	$0.518371\pi$
$228$	−2.12557	−	0.305611i	−0.140769	−	0.0202396i
$229$	17.8580			1.18009			0.590045	−	0.807370i	$-0.299110\pi$
$229$	17.8580			1.18009			0.590045	+	0.807370i	$0.299110\pi$
$230$	−1.58007	−	10.6068i	−0.104187	−	0.699389i
$231$	0.769166			0.0506074
$232$	4.85673	+	0.698293i	0.318860	+	0.0458452i
$233$	22.0576	−	10.0734i	1.44504	−	0.659927i	0.470144	−	0.882590i	$-0.344202\pi$
$233$	22.0576	−	10.0734i	1.44504	−	0.659927i	0.974896	+	0.222662i	$0.0714748\pi$
$234$	5.47652	+	1.60805i	0.358011	+	0.105122i
$235$	−5.20846	+	1.63815i	−0.339762	+	0.106861i
$236$	10.4238	−	3.06070i	0.678531	−	0.199235i
$237$	−8.88145	+	13.8198i	−0.576912	+	0.897693i
$238$	1.06773	+	0.487618i	0.0692109	+	0.0316076i
$239$	−3.83403	+	4.42470i	−0.248003	+	0.286210i	−0.866078	−	0.499908i	$-0.833367\pi$
$239$	−3.83403	+	4.42470i	−0.248003	+	0.286210i	0.618076	+	0.786119i	$0.287913\pi$
$240$	−0.360487	−	2.20682i	−0.0232693	−	0.142450i
$241$	−2.80219	−	19.4896i	−0.180505	−	1.25544i	−0.855573	−	0.517682i	$-0.826795\pi$
$241$	−2.80219	−	19.4896i	−0.180505	−	1.25544i	0.675068	−	0.737755i	$-0.264114\pi$
$242$	−6.23052	+	0.895814i	−0.400513	+	0.0575851i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	−7.92462	+	9.14550i	−0.507322	+	0.585481i
$245$	−11.5744	+	10.4233i	−0.739459	+	0.665921i
$246$	2.12535	+	1.36588i	0.135507	+	0.0870851i
$247$	3.45317	+	11.7604i	0.219720	+	0.748298i
$248$	−3.70670	+	3.21188i	−0.235376	+	0.203954i
$249$	0.541138	+	0.158892i	0.0342932	+	0.0100694i
$250$	−7.79396	−	8.01587i	−0.492933	−	0.506968i
$251$	−1.40565	+	9.77652i	−0.0887239	+	0.617089i	0.896142	+	0.443768i	$0.146359\pi$
$251$	−1.40565	+	9.77652i	−0.0887239	+	0.617089i	−0.984866	+	0.173320i	$0.944550\pi$
$252$		−	0.184955i		−	0.0116510i
$253$	2.56092	+	19.7792i	0.161004	+	1.24351i
$254$	−3.85400			−0.241821
$255$	7.44264	−	12.0829i	0.466076	−	0.756658i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−2.48459	+	8.46173i	−0.154984	+	0.527828i	−0.999976	−	0.00695146i	$-0.997787\pi$
$257$	−2.48459	+	8.46173i	−0.154984	+	0.527828i	0.844991	+	0.534780i	$0.179605\pi$
$258$	3.98838	−	3.45595i	0.248306	−	0.215158i
$259$	−1.10839	+	0.325453i	−0.0688721	+	0.0202227i
$260$	−10.6029	+	7.10415i	−0.657564	+	0.440581i
$261$	2.03831	−	4.46327i	0.126168	−	0.276270i
$262$	−13.3980	−	11.6094i	−0.827731	−	0.717233i
$263$	−9.20762	−	14.3273i	−0.567766	−	0.883461i	0.432065	−	0.901842i	$-0.357785\pi$
$263$	−9.20762	−	14.3273i	−0.567766	−	0.883461i	−0.999831	+	0.0183814i	$0.994149\pi$
$264$	0.591841	+	4.11635i	0.0364253	+	0.253344i
$265$	26.5777	+	7.25492i	1.63266	+	0.445666i
$266$	0.334126	−	0.214730i	0.0204866	−	0.0131659i
$267$	13.2803	+	11.5074i	0.812739	+	0.704242i
$268$	8.19743	+	3.74364i	0.500738	+	0.228679i
$269$	13.6032	+	8.74224i	0.829401	+	0.533024i	0.885087	−	0.465425i	$-0.154098\pi$
$269$	13.6032	+	8.74224i	0.829401	+	0.533024i	−0.0556866	+	0.998448i	$0.517735\pi$
$270$	−2.21899	−	0.275848i	−0.135043	−	0.0167876i
$271$	7.00171	+	8.08040i	0.425324	+	0.490850i	0.927451	−	0.373944i	$-0.121995\pi$
$271$	7.00171	+	8.08040i	0.425324	+	0.490850i	−0.502128	+	0.864793i	$0.667449\pi$
$272$	−1.78801	+	6.08939i	−0.108414	+	0.369224i
$273$	−0.960271	+	0.438541i	−0.0581183	+	0.0265417i
$274$	2.18777	−	15.2163i	0.132168	−	0.919250i
$275$	14.2076	+	15.1825i	0.856753	+	0.915538i
$276$	4.75613	−	0.615801i	0.286285	−	0.0370669i
$277$			9.05454i			0.544035i	0.962292	+	0.272017i	$0.0876908\pi$
$277$			9.05454i			0.544035i	−0.962292	+	0.272017i	$0.912309\pi$
$278$	−20.1256	−	2.89362i	−1.20705	−	0.173548i
$279$	2.03747	+	4.46145i	0.121980	+	0.267100i
$280$	0.317677	+	0.264806i	0.0189849	+	0.0158252i
$281$	3.11410	+	3.59386i	0.185772	+	0.214392i	0.840994	−	0.541044i	$-0.181971\pi$
$281$	3.11410	+	3.59386i	0.185772	+	0.214392i	−0.655223	+	0.755436i	$0.727425\pi$
$282$	−0.687930	−	2.34287i	−0.0409656	−	0.139516i
$283$	−8.81608	+	13.7181i	−0.524062	+	0.815456i	−0.997874	−	0.0651699i	$-0.979241\pi$
$283$	−8.81608	+	13.7181i	−0.524062	+	0.815456i	0.473813	+	0.880626i	$0.342877\pi$
$284$	2.83208	−	6.20138i	0.168053	−	0.367984i
$285$	−2.07789	−	4.32893i	−0.123083	−	0.256424i
$286$	19.9685	−	12.8330i	1.18076	−	0.758829i
$287$	−0.462514	+	0.0664994i	−0.0273013	+	0.00392534i
$288$	0.989821	−	0.142315i	0.0583258	−	0.00838598i
$289$	−19.5824	+	12.5849i	−1.15191	+	0.740287i
$290$	4.74779	+	9.89121i	0.278800	+	0.580832i
$291$	−0.747289	+	1.63634i	−0.0438069	+	0.0959237i
$292$	7.88739	−	12.2730i	0.461575	−	0.718224i
$293$	−5.50485	−	18.7478i	−0.321597	−	1.09526i	−0.948662	−	0.316291i	$-0.897562\pi$
$293$	−5.50485	−	18.7478i	−0.321597	−	1.09526i	0.627065	−	0.778967i	$-0.284256\pi$
$294$	−4.56162	−	5.26439i	−0.266039	−	0.307026i
$295$	18.6597	+	15.5542i	1.08641	+	0.905598i
$296$	−2.59459	−	5.68135i	−0.150807	−	0.330222i
$297$	4.11635	+	0.591841i	0.238855	+	0.0343421i
$298$		−	4.12571i		−	0.238996i
$299$	−14.4743	−	23.2334i	−0.837072	−	1.34362i
$300$	3.65080	−	3.41638i	0.210779	−	0.197245i
$301$	−0.138910	+	0.966141i	−0.00800665	+	0.0556874i
$302$	5.25364	−	2.39926i	0.302313	−	0.138062i
$303$	3.48119	−	11.8559i	0.199989	−	0.681101i
$304$	1.40627	+	1.62292i	0.0806549	+	0.0930807i
$305$	−26.8525	−	3.33811i	−1.53757	−	0.191139i
$306$	5.33899	+	3.43116i	0.305210	+	0.196146i
$307$	−22.1282	−	10.1056i	−1.26292	−	0.576757i	−0.332450	−	0.943121i	$-0.607875\pi$
$307$	−22.1282	−	10.1056i	−1.26292	−	0.576757i	−0.930472	+	0.366364i	$0.880602\pi$
$308$	−0.581297	−	0.503697i	−0.0331225	−	0.0287008i
$309$	−12.9015	+	8.29129i	−0.733941	+	0.471675i
$310$	−10.5801	−	2.88804i	−0.600908	−	0.164030i
$311$	−0.824021	−	5.73119i	−0.0467259	−	0.324986i	−0.999756	−	0.0221089i	$-0.992962\pi$
$311$	−0.824021	−	5.73119i	−0.0467259	−	0.324986i	0.953030	−	0.302877i	$-0.0979471\pi$
$312$	−3.08583	−	4.80164i	−0.174701	−	0.271839i
$313$	−9.56643	−	8.28936i	−0.540727	−	0.468542i	0.341159	−	0.940006i	$-0.389181\pi$
$313$	−9.56643	−	8.28936i	−0.540727	−	0.468542i	−0.881886	+	0.471463i	$0.843726\pi$
$314$	0.543658	−	1.19044i	0.0306804	−	0.0671807i
$315$	0.343579	−	0.230205i	0.0193585	−	0.0129706i
$316$	15.7622	−	4.62820i	0.886693	−	0.260357i
$317$	−4.65999	+	4.03790i	−0.261731	+	0.226791i	−0.775834	−	0.630937i	$-0.782670\pi$
$317$	−4.65999	+	4.03790i	−0.261731	+	0.226791i	0.514103	+	0.857729i	$0.328125\pi$
$318$	−3.47117	+	11.8217i	−0.194653	+	0.662928i
$319$	−8.47666	−	18.5613i	−0.474602	−	1.03923i
$320$	−1.17272	+	1.90387i	−0.0655571	+	0.106430i
$321$	12.1396			0.677564
$322$	−0.590224	+	0.662137i	−0.0328919	+	0.0368994i
$323$			13.6286i			0.758315i
$324$	0.142315	−	0.989821i	0.00790638	−	0.0549901i
$325$	−26.3939	−	10.8542i	−1.46407	−	0.602081i
$326$	−10.5201	−	3.08898i	−0.582654	−	0.171083i
$327$	−1.54166	+	1.33586i	−0.0852541	+	0.0738731i
$328$	−0.711770	−	2.42407i	−0.0393009	−	0.133847i
$329$	0.379926	+	0.244164i	0.0209460	+	0.0134612i
$330$	−6.91006	+	6.22286i	−0.380386	+	0.342557i
$331$	1.18166	−	1.36370i	0.0649497	−	0.0749560i	−0.722345	−	0.691533i	$-0.756936\pi$
$331$	1.18166	−	1.36370i	0.0649497	−	0.0749560i	0.787295	+	0.616577i	$0.211481\pi$
$332$	−0.304912	−	0.474453i	−0.0167342	−	0.0260390i
$333$	−6.18220	+	0.888866i	−0.338782	+	0.0487096i
$334$	−0.590436	−	4.10657i	−0.0323072	−	0.224702i
$335$	3.24864	+	19.8874i	0.177492	+	1.08657i
$336$	−0.121120	+	0.139779i	−0.00660761	+	0.00762559i
$337$	−11.5701	−	5.28387i	−0.630262	−	0.287831i	0.0745587	−	0.997217i	$-0.476245\pi$
$337$	−11.5701	−	5.28387i	−0.630262	−	0.287831i	−0.704820	+	0.709386i	$0.748972\pi$
$338$	−10.5847	+	16.4702i	−0.575733	+	0.895858i
$339$	4.18342	−	1.22836i	0.227212	−	0.0667156i
$340$	−13.5374	+	4.25772i	−0.734167	+	0.230907i
$341$	19.5707	+	5.74648i	1.05981	+	0.311189i
$342$	1.95337	−	0.892074i	0.105626	−	0.0482378i
$343$	2.55675	+	0.367605i	0.138051	+	0.0198488i
$344$	−5.27738			−0.284537
$345$	7.06368	+	8.06873i	0.380296	+	0.434406i
$346$	3.38437			0.181945
$347$	6.77192	+	0.973654i	0.363535	+	0.0522685i	0.321662	−	0.946854i	$-0.395758\pi$
$347$	6.77192	+	0.973654i	0.363535	+	0.0522685i	0.0418731	+	0.999123i	$0.486667\pi$
$348$	−4.46327	+	2.03831i	−0.239256	+	0.109265i
$349$	−8.48265	−	2.49073i	−0.454066	−	0.133326i	0.0466992	−	0.998909i	$-0.485130\pi$
$349$	−8.48265	−	2.49073i	−0.454066	−	0.133326i	−0.500765	+	0.865583i	$0.666948\pi$
$350$	−0.0965152	+	0.919723i	−0.00515895	+	0.0491613i
$351$	−5.47652	+	1.60805i	−0.292315	+	0.0858314i
$352$	2.24835	−	3.49850i	0.119837	−	0.186471i
$353$	−4.36065	−	1.99144i	−0.232094	−	0.105994i	0.295974	−	0.955196i	$-0.404356\pi$
$353$	−4.36065	−	1.99144i	−0.232094	−	0.105994i	−0.528067	+	0.849202i	$0.677083\pi$
$354$	−7.11431	+	8.21036i	−0.378122	+	0.436376i
$355$	15.0449	−	2.45760i	0.798500	−	0.130436i
$356$	−2.50080	−	17.3934i	−0.132542	−	0.921851i
$357$	−1.16186	+	0.167050i	−0.0614922	+	0.00884125i
$358$	7.39224	+	11.5026i	0.390692	+	0.607929i
$359$	14.6981	−	16.9625i	0.775735	−	0.895246i	−0.221058	−	0.975261i	$-0.570951\pi$
$359$	14.6981	−	16.9625i	0.775735	−	0.895246i	0.996794	+	0.0800143i	$0.0254966\pi$
$360$	1.49636	+	1.66160i	0.0788649	+	0.0875740i
$361$	−12.1044	−	7.77904i	−0.637075	−	0.409423i
$362$	3.64081	+	12.3995i	0.191357	+	0.651701i
$363$	4.75713	−	4.12208i	0.249685	−	0.216353i
$364$	1.01291	+	0.297417i	0.0530908	+	0.0155889i
$365$	32.6160	−	0.623741i	1.70720	−	0.0326481i
$366$	1.72218	−	11.9781i	0.0900200	−	0.626103i
$367$		−	11.7148i		−	0.611507i	−0.952111	−	0.305753i	$-0.901092\pi$
$367$		−	11.7148i		−	0.611507i	0.952111	−	0.305753i	$-0.0989083\pi$
$368$	−3.99771	−	2.64921i	−0.208395	−	0.138100i
$369$	−2.52640			−0.131519
$370$	7.32455	−	11.8911i	0.380785	−	0.618191i
$371$	−0.946642	−	2.07286i	−0.0491472	−	0.107617i
$372$	1.38181	−	4.70600i	0.0716433	−	0.243995i
$373$	−6.68549	+	5.79301i	−0.346162	+	0.299951i	−0.810537	−	0.585688i	$-0.800824\pi$
$373$	−6.68549	+	5.79301i	−0.346162	+	0.299951i	0.464375	+	0.885639i	$0.346279\pi$
$374$	25.3238	−	7.43574i	1.30946	−	0.384493i
$375$	10.8904	+	2.52965i	0.562378	+	0.130630i
$376$	−1.01435	+	2.22112i	−0.0523113	+	0.114546i
$377$	21.1655	+	18.3400i	1.09008	+	0.944558i
$378$	0.0999940	+	0.155594i	0.00514314	+	0.00800288i
$379$	2.68086	+	18.6458i	0.137707	+	0.957770i	0.935119	+	0.354335i	$0.115293\pi$
$379$	2.68086	+	18.6458i	0.137707	+	0.957770i	−0.797412	+	0.603435i	$0.793798\pi$
$380$	−1.26448	+	4.63231i	−0.0648665	+	0.237633i
$381$	3.24219	−	2.08363i	0.166103	−	0.106748i
$382$	5.42663	+	4.70220i	0.277651	+	0.240586i
$383$	11.0887	+	5.06402i	0.566604	+	0.258760i	0.678056	−	0.735010i	$-0.262823\pi$
$383$	11.0887	+	5.06402i	0.566604	+	0.258760i	−0.111452	+	0.993770i	$0.535550\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	0.212173	−	1.70677i	0.0108134	−	0.0869851i
$386$	14.0091	+	16.1673i	0.713044	+	0.822896i
$387$	−1.48681	+	5.06361i	−0.0755788	+	0.257398i
$388$	1.63634	−	0.747289i	0.0830723	−	0.0379379i
$389$	1.27432	−	8.86309i	0.0646106	−	0.449377i	−0.931677	−	0.363288i	$-0.881654\pi$
$389$	1.27432	−	8.86309i	0.0646106	−	0.449377i	0.996287	−	0.0860886i	$-0.0274368\pi$
$390$	5.07894	−	11.7088i	0.257182	−	0.592896i
$391$	−8.16411	−	29.3212i	−0.412877	−	1.48284i
$392$			6.96579i			0.351826i
$393$	17.5476	+	2.52297i	0.885161	+	0.127267i
$394$	1.44627	+	3.16689i	0.0728621	+	0.159546i
$395$	28.2160	+	23.5200i	1.41970	+	1.18342i
$396$	−2.72335	−	3.14292i	−0.136854	−	0.157938i
$397$	−1.35070	−	4.60006i	−0.0677897	−	0.230870i	0.918629	−	0.395121i	$-0.129297\pi$
$397$	−1.35070	−	4.60006i	−0.0677897	−	0.230870i	−0.986419	+	0.164251i	$0.947479\pi$
$398$	1.98460	−	3.08810i	0.0994789	−	0.154792i
$399$	−0.164993	+	0.361285i	−0.00825999	+	0.0180869i
$400$	−4.99634	+	0.191168i	−0.249817	+	0.00955840i
$401$	−4.96815	+	3.19283i	−0.248097	+	0.159442i	−0.658779	−	0.752336i	$-0.728927\pi$
$401$	−4.96815	+	3.19283i	−0.248097	+	0.159442i	0.410682	+	0.911779i	$0.365291\pi$
$402$	−8.92008	+	1.28251i	−0.444893	+	0.0639660i
$403$	−27.7096	+	3.98403i	−1.38031	+	0.198459i
$404$	−10.3948	+	6.68036i	−0.517163	+	0.332360i
$405$	2.01587	−	0.967617i	0.100169	−	0.0480813i
$406$	0.376994	−	0.825503i	0.0187099	−	0.0409690i
$407$	−14.0427	+	21.8508i	−0.696070	+	1.08311i
$408$	−1.78801	−	6.08939i	−0.0885196	−	0.301470i
$409$	22.3285	+	25.7684i	1.10407	+	1.27417i	0.958585	+	0.284805i	$0.0919289\pi$
$409$	22.3285	+	25.7684i	1.10407	+	1.27417i	0.145485	+	0.989360i	$0.453526\pi$
$410$	3.61714	−	4.33934i	0.178638	−	0.214305i
$411$	6.38608	+	13.9836i	0.315002	+	0.689758i
$412$	15.1799	+	2.18255i	0.747862	+	0.107526i
$413$		−	2.00932i		−	0.0988722i
$414$	−3.66819	+	3.08940i	−0.180281	+	0.151836i
$415$	0.501852	−	1.15695i	0.0246350	−	0.0567924i
$416$	−0.812294	+	5.64963i	−0.0398260	+	0.276996i
$417$	18.4951	−	8.44645i	0.905711	−	0.413624i
$418$	2.51600	−	8.56871i	0.123062	−	0.419109i
$419$	−6.56746	−	7.57925i	−0.320841	−	0.370271i	0.572302	−	0.820043i	$-0.306051\pi$
$419$	−6.56746	−	7.57925i	−0.320841	−	0.370271i	−0.893143	+	0.449772i	$0.851505\pi$
$420$	−0.410412	−	0.0510194i	−0.0200261	−	0.00248949i
$421$	−31.0905	−	19.9807i	−1.51526	−	0.973798i	−0.992623	−	0.121243i	$-0.961312\pi$
$421$	−31.0905	−	19.9807i	−1.51526	−	0.973798i	−0.522637	−	0.852556i	$-0.675052\pi$
$422$	3.61806	+	1.65231i	0.176124	+	0.0804334i
$423$	1.84538	+	1.59903i	0.0897253	+	0.0777474i
$424$	10.3649	−	6.66112i	0.503364	−	0.323493i
$425$	−24.7587	−	19.8482i	−1.20097	−	0.962778i
$426$	0.970226	+	6.74807i	0.0470076	+	0.326945i
$427$	1.21005	+	1.88288i	0.0585585	+	0.0911188i
$428$	−9.17447	−	7.94972i	−0.443465	−	0.384264i
$429$	−9.86053	+	21.5915i	−0.476071	+	1.04245i
$430$	−6.56852	−	9.80348i	−0.316762	−	0.472766i
$431$	16.5380	−	4.85600i	0.796609	−	0.233905i	0.141993	−	0.989868i	$-0.454649\pi$
$431$	16.5380	−	4.85600i	0.796609	−	0.233905i	0.654615	+	0.755962i	$0.272831\pi$
$432$	−0.755750	+	0.654861i	−0.0363610	+	0.0315070i
$433$	−4.13586	+	14.0854i	−0.198757	+	0.676903i	0.798440	+	0.602074i	$0.205659\pi$
$433$	−4.13586	+	14.0854i	−0.198757	+	0.676903i	−0.997196	+	0.0748281i	$0.976159\pi$
$434$	0.376840	+	0.825165i	0.0180889	+	0.0396092i
$435$	−9.34168	−	5.75417i	−0.447899	−	0.275891i
$436$	2.03991			0.0976940
$437$	−9.83982	−	3.03993i	−0.470702	−	0.145420i
$438$			14.5890i			0.697088i
$439$	−4.13157	+	28.7357i	−0.197189	+	1.37148i	0.615202	+	0.788369i	$0.289074\pi$
$439$	−4.13157	+	28.7357i	−0.197189	+	1.37148i	−0.812392	+	0.583112i	$0.801835\pi$
$440$	9.29738	−	0.177801i	0.443235	−	0.00847634i
$441$	6.68363	+	1.96249i	0.318268	+	0.0934519i
$442$	−27.3762	+	23.7216i	−1.30215	+	1.12832i
$443$	6.97586	+	23.7576i	0.331433	+	1.12876i	0.941670	+	0.336538i	$0.109256\pi$
$443$	6.97586	+	23.7576i	0.331433	+	1.12876i	−0.610237	+	0.792219i	$0.708926\pi$
$444$	5.25428	+	3.37672i	0.249357	+	0.160252i
$445$	29.1982	−	26.2944i	1.38413	−	1.24648i
$446$	0.381363	−	0.440117i	0.0180581	−	0.0208401i
$447$	2.23053	+	3.47077i	0.105500	+	0.164162i
$448$	0.183072	−	0.0263218i	0.00864934	−	0.00124359i
$449$	3.94484	+	27.4370i	0.186169	+	1.29483i	0.841816	+	0.539764i	$0.181487\pi$
$449$	3.94484	+	27.4370i	0.186169	+	1.29483i	−0.655647	+	0.755067i	$0.727604\pi$
$450$	−1.22421	+	4.84782i	−0.0577097	+	0.228528i
$451$	−6.88029	+	7.94028i	−0.323980	+	0.373893i
$452$	−3.96603	−	1.81122i	−0.186546	−	0.0851928i
$453$	−3.12251	+	4.85872i	−0.146708	+	0.228282i
$454$	−13.5077	+	3.96621i	−0.633947	+	0.186143i
$455$	0.708228	+	2.25180i	0.0332023	+	0.105566i
$456$	−2.06044	−	0.605000i	−0.0964890	−	0.0283317i
$457$	−1.56167	+	0.713192i	−0.0730520	+	0.0333617i	−0.451606	−	0.892217i	$-0.649149\pi$
$457$	−1.56167	+	0.713192i	−0.0730520	+	0.0333617i	0.378554	+	0.925579i	$0.376421\pi$
$458$	17.6762	+	2.54146i	0.825956	+	0.118755i
$459$	−6.34647			−0.296228
$460$	−0.0544845	−	10.7237i	−0.00254035	−	0.499994i
$461$	−26.5370			−1.23595			−0.617976	−	0.786197i	$-0.712047\pi$
$461$	−26.5370			−1.23595			−0.617976	+	0.786197i	$0.712047\pi$
$462$	0.761337	+	0.109464i	0.0354206	+	0.00509272i
$463$	−5.78109	+	2.64014i	−0.268670	+	0.122698i	−0.545195	−	0.838309i	$-0.683544\pi$
$463$	−5.78109	+	2.64014i	−0.268670	+	0.122698i	0.276525	+	0.961007i	$0.410817\pi$
$464$	4.70792	+	1.38237i	0.218560	+	0.0641750i
$465$	10.4619	−	3.29045i	0.485160	−	0.152591i
$466$	23.2666	−	6.83170i	1.07781	−	0.316473i
$467$	11.6970	−	18.2009i	0.541274	−	0.842239i	−0.457625	−	0.889145i	$-0.651300\pi$
$467$	11.6970	−	18.2009i	0.541274	−	0.842239i	0.998899	+	0.0469063i	$0.0149362\pi$
$468$	5.19193	+	2.37107i	0.239997	+	0.109603i
$469$	1.09151	−	1.25966i	0.0504011	−	0.0581659i
$470$	−5.38858	+	0.880230i	−0.248556	+	0.0406020i
$471$	0.186249	+	1.29539i	0.00858189	+	0.0596884i
$472$	10.7533	−	1.54609i	0.494960	−	0.0711645i
$473$	11.8654	+	18.4629i	0.545572	+	0.848926i
$474$	−10.7578	+	12.4152i	−0.494123	+	0.570248i
$475$	−10.1790	+	3.41668i	−0.467045	+	0.156768i
$476$	0.987471	+	0.634609i	0.0452607	+	0.0290873i
$477$	−3.47117	−	11.8217i	−0.158934	−	0.541279i
$478$	−4.42470	+	3.83403i	−0.202381	+	0.175364i
$479$	0.980297	+	0.287841i	0.0447909	+	0.0131518i	0.304051	−	0.952656i	$-0.401661\pi$
$479$	0.980297	+	0.287841i	0.0447909	+	0.0131518i	−0.259260	+	0.965807i	$0.583479\pi$
$480$	−0.0427543	−	2.23566i	−0.00195146	−	0.102043i
$481$	5.07340	−	35.2863i	0.231327	−	1.60892i
$482$		−	19.6900i		−	0.896857i
$483$	0.138550	−	0.876124i	0.00630422	−	0.0398650i
$484$	−6.29459			−0.286118
$485$	3.42487	+	2.10961i	0.155515	+	0.0957923i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	7.17898	−	24.4493i	0.325310	−	1.10791i	−0.620775	−	0.783989i	$-0.713182\pi$
$487$	7.17898	−	24.4493i	0.325310	−	1.10791i	0.946086	−	0.323917i	$-0.105000\pi$
$488$	−9.14550	+	7.92462i	−0.413997	+	0.358731i
$489$	10.5201	−	3.08898i	0.475735	−	0.139689i
$490$	−12.9399	+	8.67001i	−0.584567	+	0.391671i
$491$	−18.2594	+	39.9826i	−0.824037	+	1.80439i	−0.295935	+	0.955208i	$0.595631\pi$
$491$	−18.2594	+	39.9826i	−0.824037	+	1.80439i	−0.528102	+	0.849181i	$0.677096\pi$
$492$	1.90933	+	1.65444i	0.0860791	+	0.0745880i
$493$	16.8356	+	26.1967i	0.758237	+	1.17984i
$494$	1.74434	+	12.1322i	0.0784817	+	0.545852i
$495$	2.44878	−	8.97087i	0.110064	−	0.403210i
$496$	−4.12607	+	2.65167i	−0.185266	+	0.119063i
$497$	−0.952940	−	0.825728i	−0.0427452	−	0.0370389i
$498$	0.513017	+	0.234287i	0.0229888	+	0.0104987i
$499$	−21.9644	−	14.1157i	−0.983262	−	0.631904i	−0.0529206	−	0.998599i	$-0.516853\pi$
$499$	−21.9644	−	14.1157i	−0.983262	−	0.631904i	−0.930341	+	0.366695i	$0.880489\pi$
$500$	−6.57385	−	9.04348i	−0.293992	−	0.404437i
$501$	2.71689	+	3.13545i	0.121382	+	0.140082i
$502$	−2.78269	+	9.47697i	−0.124197	+	0.422978i
$503$	−20.5470	+	9.38350i	−0.916146	+	0.418390i	−0.816970	−	0.576680i	$-0.804348\pi$
$503$	−20.5470	+	9.38350i	−0.916146	+	0.418390i	−0.0991757	+	0.995070i	$0.531621\pi$
$504$	0.0263218	−	0.183072i	0.00117247	−	0.00815468i
$505$	−25.3477	−	10.9951i	−1.12796	−	0.489278i
$506$	−0.280024	+	19.9423i	−0.0124486	+	0.886545i
$507$		−	19.5781i		−	0.869494i
$508$	−3.81477	−	0.548481i	−0.169253	−	0.0243349i
$509$	−7.69332	−	16.8460i	−0.341000	−	0.746686i	0.658985	−	0.752156i	$-0.270986\pi$
$509$	−7.69332	−	16.8460i	−0.341000	−	0.746686i	−0.999985	+	0.00546993i	$0.998259\pi$
$510$	9.08646	−	10.9007i	0.402355	−	0.482690i
$511$	−1.76701	−	2.03924i	−0.0781679	−	0.0902105i
$512$	0.281733	+	0.959493i	0.0124509	+	0.0424040i
$513$	−1.16099	+	1.80653i	−0.0512588	+	0.0797603i
$514$	−3.66353	+	8.02201i	−0.161591	+	0.353836i
$515$	14.8394	+	30.9154i	0.653903	+	1.36230i
$516$	4.43962	−	2.85317i	0.195443	−	0.125604i
$517$	10.0512	−	1.44515i	0.442053	−	0.0635576i
$518$	−1.14343	+	0.164400i	−0.0502393	+	0.00722332i
$519$	−2.84712	+	1.82973i	−0.124975	+	0.0803162i
$520$	−11.5060	+	5.52289i	−0.504572	+	0.242195i
$521$	−16.8644	+	36.9279i	−0.738843	+	1.61784i	0.0466049	+	0.998913i	$0.485160\pi$
$521$	−16.8644	+	36.9279i	−0.738843	+	1.61784i	−0.785448	+	0.618928i	$0.787567\pi$
$522$	2.65275	−	4.12776i	0.116108	−	0.180667i
$523$	−1.56545	−	5.33142i	−0.0684522	−	0.233127i	0.918160	−	0.396209i	$-0.129675\pi$
$523$	−1.56545	−	5.33142i	−0.0684522	−	0.233127i	−0.986612	+	0.163082i	$0.947856\pi$
$524$	−11.6094	−	13.3980i	−0.507160	−	0.585294i
$525$	−0.416046	−	0.825900i	−0.0181577	−	0.0360452i
$526$	−7.07490	−	15.4919i	−0.308480	−	0.675478i
$527$	−30.8105	−	4.42988i	−1.34213	−	0.192969i
$528$			4.15868i			0.180983i
$529$	22.9909	+	0.645789i	0.999606	+	0.0280778i
$530$	25.2747	+	10.9635i	1.09786	+	0.476223i
$531$	1.54609	−	10.7533i	0.0670945	−	0.466653i
$532$	0.361285	−	0.164993i	0.0156637	−	0.00715336i
$533$	4.06259	−	13.8359i	0.175970	−	0.599299i
$534$	11.5074	+	13.2803i	0.497975	+	0.574693i
$535$	3.34868	−	26.9375i	0.144776	−	1.16461i
$536$	7.58121	+	4.87215i	0.327459	+	0.210445i
$537$	−12.4375	−	5.68002i	−0.536718	−	0.245111i
$538$	12.2206	+	10.5892i	0.526866	+	0.456532i
$539$	24.3698	−	15.6615i	1.04968	−	0.674590i
$540$	−2.15714	−	0.588836i	−0.0928287	−	0.0253394i
$541$	5.33096	+	37.0777i	0.229196	+	1.59409i	0.701508	+	0.712661i	$0.252510\pi$
$541$	5.33096	+	37.0777i	0.229196	+	1.59409i	−0.472312	+	0.881431i	$0.656581\pi$
$542$	5.78048	+	8.99461i	0.248293	+	0.386351i
$543$	−9.76650	−	8.46272i	−0.419121	−	0.363170i
$544$	−2.63642	+	5.77295i	−0.113036	+	0.247513i
$545$	2.53899	+	3.78942i	0.108758	+	0.162321i
$546$	−1.01291	+	0.297417i	−0.0433485	+	0.0127283i
$547$	17.3837	−	15.0630i	0.743272	−	0.644049i	−0.198577	−	0.980085i	$-0.563632\pi$
$547$	17.3837	−	15.0630i	0.743272	−	0.644049i	0.941849	+	0.336037i	$0.109087\pi$
$548$	4.33101	−	14.7501i	0.185012	−	0.630091i
$549$	5.02703	+	11.0077i	0.214549	+	0.469796i
$550$	11.9023	+	17.0499i	0.507517	+	0.727010i
$551$	10.5367			0.448880
$552$	4.79536	+	0.0673348i	0.204104	+	0.00286596i
$553$		−	3.03837i		−	0.129204i
$554$	−1.28860	+	8.96238i	−0.0547472	+	0.380775i
$555$	0.267034	+	13.9634i	0.0113349	+	0.592714i
$556$	−19.5089	−	5.72834i	−0.827363	−	0.242936i
$557$	32.8176	−	28.4366i	1.39053	−	1.20490i	0.438560	−	0.898702i	$-0.355489\pi$
$557$	32.8176	−	28.4366i	1.39053	−	1.20490i	0.951968	−	0.306197i	$-0.0990567\pi$
$558$	1.38181	+	4.70600i	0.0584965	+	0.199221i
$559$	−25.3401	−	16.2851i	−1.07177	−	0.688786i
$560$	0.276758	+	0.307321i	0.0116952	+	0.0129867i
$561$	−17.2837	+	19.9464i	−0.729718	+	0.842139i
$562$	2.57094	+	4.00046i	0.108449	+	0.168749i
$563$	8.62933	−	1.24071i	0.363683	−	0.0522897i	0.0419488	−	0.999120i	$-0.486643\pi$
$563$	8.62933	−	1.24071i	0.363683	−	0.0522897i	0.321734	+	0.946830i	$0.395734\pi$
$564$	−0.347502	−	2.41693i	−0.0146325	−	0.101771i
$565$	−1.57173	−	9.62181i	−0.0661234	−	0.404793i
$566$	−10.6786	+	12.3238i	−0.448856	+	0.518008i
$567$	−0.168241	−	0.0768329i	−0.00706544	−	0.00322668i
$568$	3.68580	−	5.73521i	0.154653	−	0.240644i
$569$	10.8087	−	3.17371i	0.453123	−	0.133049i	−0.0472042	−	0.998885i	$-0.515031\pi$
$569$	10.8087	−	3.17371i	0.453123	−	0.133049i	0.500327	+	0.865836i	$0.333213\pi$
$570$	−1.44067	−	4.58058i	−0.0603429	−	0.191859i
$571$	2.70273	+	0.793593i	0.113106	+	0.0332108i	0.337796	−	0.941219i	$-0.390319\pi$
$571$	2.70273	+	0.793593i	0.113106	+	0.0332108i	−0.224690	+	0.974430i	$0.572137\pi$
$572$	21.5915	−	9.86053i	0.902788	−	0.412289i
$573$	−7.10738	−	1.02189i	−0.296915	−	0.0426899i
$574$	−0.467270			−0.0195035
$575$	19.8529	−	13.4485i	0.827924	−	0.560841i
$576$	1.00000			0.0416667
$577$	18.7407	+	2.69451i	0.780187	+	0.112174i	0.520890	−	0.853624i	$-0.325600\pi$
$577$	18.7407	+	2.69451i	0.780187	+	0.112174i	0.259297	+	0.965798i	$0.416509\pi$
$578$	−21.1741	+	9.66990i	−0.880728	+	0.402215i
$579$	−20.5259	−	6.02695i	−0.853028	−	0.250472i
$580$	3.29179	+	10.4662i	0.136684	+	0.434586i
$581$	−0.100086	+	0.0293879i	−0.00415227	+	0.00121922i
$582$	−0.972558	+	1.51333i	−0.0403138	+	0.0627295i
$583$	−46.6079	−	21.2851i	−1.93030	−	0.881539i
$584$	9.55374	−	11.0256i	0.395337	−	0.456243i
$585$	2.05756	+	12.5959i	0.0850695	+	0.520777i
$586$	−2.78073	−	19.3404i	−0.114871	−	0.798944i
$587$	39.3061	−	5.65137i	1.62234	−	0.233257i	0.729614	−	0.683860i	$-0.239700\pi$
$587$	39.3061	−	5.65137i	1.62234	−	0.233257i	0.892725	+	0.450603i	$0.148791\pi$
$588$	−3.76599	−	5.86000i	−0.155307	−	0.241662i
$589$	−6.89727	+	7.95988i	−0.284197	+	0.327981i
$590$	16.2562	+	18.0514i	0.669258	+	0.743164i
$591$	−2.92883	−	1.88225i	−0.120476	−	0.0774253i
$592$	−1.75964	−	5.99277i	−0.0723206	−	0.246301i
$593$	−0.702890	+	0.609058i	−0.0288643	+	0.0250110i	−0.669173	−	0.743106i	$-0.733352\pi$
$593$	−0.702890	+	0.609058i	−0.0288643	+	0.0250110i	0.640309	+	0.768117i	$0.278806\pi$
$594$	3.99022	+	1.17163i	0.163721	+	0.0480727i
$595$	0.0501854	+	2.62424i	0.00205740	+	0.107583i
$596$	0.587150	−	4.08372i	0.0240506	−	0.167276i
$597$			3.67083i			0.150237i
$598$	−11.0206	−	25.0568i	−0.450664	−	1.02465i
$599$	−2.79655			−0.114264			−0.0571320	−	0.998367i	$-0.518196\pi$
$599$	−2.79655			−0.114264			−0.0571320	+	0.998367i	$0.518196\pi$
$600$	4.09984	−	2.86205i	0.167375	−	0.116843i
$601$	5.59738	+	12.2565i	0.228322	+	0.499955i	0.988770	−	0.149443i	$-0.0477482\pi$
$601$	5.59738	+	12.2565i	0.228322	+	0.499955i	−0.760449	+	0.649398i	$0.775021\pi$
$602$	−0.274992	+	0.936538i	−0.0112079	+	0.0381704i
$603$	6.81067	−	5.90148i	0.277352	−	0.240327i
$604$	5.54162	−	1.62717i	0.225485	−	0.0662084i
$605$	−7.83460	−	11.6931i	−0.318522	−	0.475392i
$606$	5.13302	−	11.2398i	0.208515	−	0.456584i
$607$	0.220457	+	0.191027i	0.00894807	+	0.00775354i	0.659323	−	0.751860i	$-0.270843\pi$
$607$	0.220457	+	0.191027i	0.00894807	+	0.00775354i	−0.650375	+	0.759613i	$0.725388\pi$
$608$	1.16099	+	1.80653i	0.0470842	+	0.0732645i
$609$	0.129153	+	0.898276i	0.00523352	+	0.0364000i
$610$	−26.1041	−	7.12564i	−1.05692	−	0.288509i
$611$	−11.7246	+	7.53493i	−0.474326	+	0.304830i
$612$	4.79634	+	4.15605i	0.193881	+	0.167999i
$613$	−19.1566	−	8.74852i	−0.773727	−	0.353349i	−0.0108905	−	0.999941i	$-0.503467\pi$
$613$	−19.1566	−	8.74852i	−0.773727	−	0.353349i	−0.762836	+	0.646591i	$0.776194\pi$
$614$	−20.4648	−	13.1519i	−0.825890	−	0.530768i
$615$	−0.696904	+	5.60606i	−0.0281019	+	0.226058i
$616$	−0.503697	−	0.581297i	−0.0202945	−	0.0234211i
$617$	−0.289794	+	0.986949i	−0.0116667	+	0.0397331i	−0.965121	−	0.261806i	$-0.915682\pi$
$617$	−0.289794	+	0.986949i	−0.0116667	+	0.0397331i	0.953454	+	0.301539i	$0.0975002\pi$
$618$	−13.9502	+	6.37082i	−0.561158	+	0.256272i
$619$	5.53263	−	38.4803i	0.222375	−	1.54665i	−0.506642	−	0.862157i	$-0.669113\pi$
$619$	5.53263	−	38.4803i	0.222375	−	1.54665i	0.729017	−	0.684496i	$-0.239978\pi$
$620$	−10.0614	−	4.36435i	−0.404075	−	0.175277i
$621$	1.41562	−	4.58214i	0.0568067	−	0.183875i
$622$		−	5.79012i		−	0.232163i
$623$	−3.21700	−	0.462535i	−0.128886	−	0.0185311i
$624$	−2.37107	−	5.19193i	−0.0949189	−	0.207843i
$625$	8.61736	−	23.4679i	0.344694	−	0.938715i
$626$	−8.28936	−	9.56643i	−0.331309	−	0.382352i
$627$	2.51600	+	8.56871i	0.100479	+	0.342201i
$628$	0.707542	−	1.10096i	0.0282340	−	0.0439330i
$629$	16.4665	−	36.0565i	0.656561	−	1.43767i
$630$	0.372844	−	0.178965i	0.0148545	−	0.00713015i
$631$	5.06079	−	3.25237i	0.201467	−	0.129475i	−0.436017	−	0.899938i	$-0.643611\pi$
$631$	5.06079	−	3.25237i	0.201467	−	0.129475i	0.637484	+	0.770463i	$0.279975\pi$
$632$	16.2604	−	2.33790i	0.646805	−	0.0929965i
$633$	−3.93702	+	0.566057i	−0.156482	+	0.0224988i
$634$	−5.18721	+	3.33362i	−0.206010	+	0.132395i
$635$	−3.72920	−	7.76915i	−0.147989	−	0.308309i
$636$	−5.11824	+	11.2074i	−0.202951	+	0.444402i
$637$	−21.4952	+	33.4472i	−0.851672	+	1.32523i
$638$	−5.74883	−	19.5787i	−0.227598	−	0.775129i
$639$	−4.46449	−	5.15229i	−0.176612	−	0.203822i
$640$	−1.43173	+	1.71760i	−0.0565943	+	0.0678940i
$641$	−7.44370	−	16.2994i	−0.294008	−	0.643789i	0.703769	−	0.710429i	$-0.251499\pi$
$641$	−7.44370	−	16.2994i	−0.294008	−	0.643789i	−0.997777	+	0.0666405i	$0.978772\pi$
$642$	12.0160	+	1.72764i	0.474234	+	0.0681845i
$643$		−	7.08335i		−	0.279340i	−0.990198	−	0.139670i	$-0.955396\pi$
$643$		−	7.08335i		−	0.279340i	0.990198	−	0.139670i	$-0.0446042\pi$
$644$	−0.678448	+	0.571400i	−0.0267346	+	0.0225163i
$645$	10.8260	+	4.69600i	0.426272	+	0.184905i
$646$	−1.93955	+	13.4899i	−0.0763106	+	0.530752i
$647$	−44.8445	+	20.4798i	−1.76302	+	0.805144i	−0.779013	+	0.627008i	$0.784279\pi$
$647$	−44.8445	+	20.4798i	−1.76302	+	0.805144i	−0.984006	+	0.178135i	$0.942994\pi$
$648$	0.281733	−	0.959493i	0.0110675	−	0.0376924i
$649$	−29.5861	−	34.1442i	−1.16136	−	1.34028i
$650$	−24.5806	−	14.4999i	−0.964129	−	0.568734i
$651$	−0.763136	−	0.490438i	−0.0299097	−	0.0192218i
$652$	−9.97341	−	4.55471i	−0.390589	−	0.178376i
$653$	15.7791	+	13.6727i	0.617484	+	0.535053i	0.906464	−	0.422282i	$-0.138771\pi$
$653$	15.7791	+	13.6727i	0.617484	+	0.535053i	−0.288981	+	0.957335i	$0.593316\pi$
$654$	−1.71608	+	1.10286i	−0.0671041	+	0.0431252i
$655$	10.4389	−	38.2420i	0.407883	−	1.49424i
$656$	−0.359545	−	2.50069i	−0.0140379	−	0.0976354i
$657$	−7.88739	−	12.2730i	−0.307716	−	0.478816i
$658$	0.341311	+	0.295748i	0.0133057	+	0.0115294i
$659$	−14.0680	+	30.8046i	−0.548010	+	1.19998i	0.409695	+	0.912223i	$0.365635\pi$
$659$	−14.0680	+	30.8046i	−0.548010	+	1.19998i	−0.957705	+	0.287752i	$0.907092\pi$
$660$	−7.72533	+	5.17612i	−0.300708	+	0.201480i
$661$	19.3339	−	5.67694i	0.752001	−	0.220808i	0.116802	−	0.993155i	$-0.462736\pi$
$661$	19.3339	−	5.67694i	0.752001	−	0.220808i	0.635200	+	0.772348i	$0.280918\pi$
$662$	1.36370	−	1.18166i	0.0530019	−	0.0459264i
$663$	10.2055	−	34.7566i	0.396347	−	1.34983i
$664$	−0.234287	−	0.513017i	−0.00909210	−	0.0199089i
$665$	0.756173	+	0.465778i	0.0293231	+	0.0180621i
$666$	−6.24577			−0.242019
$667$	−22.6693	+	6.31196i	−0.877757	+	0.244400i
$668$		−	4.14880i		−	0.160522i
$669$	−0.0828782	+	0.576430i	−0.00320426	+	0.0222861i
$670$	0.385293	+	20.1473i	0.0148852	+	0.778359i
$671$	48.2866	+	14.1782i	1.86408	+	0.547344i
$672$	−0.139779	+	0.121120i	−0.00539211	+	0.00467229i
$673$	1.15615	+	3.93749i	0.0445664	+	0.151779i	0.978770	−	0.204960i	$-0.0657066\pi$
$673$	1.15615	+	3.93749i	0.0445664	+	0.151779i	−0.934204	+	0.356740i	$0.883888\pi$
$674$	−10.7003	−	6.87668i	−0.412161	−	0.264880i
$675$	−1.59106	−	4.74010i	−0.0612398	−	0.182446i
$676$	−12.8209	+	14.7961i	−0.493113	+	0.569083i
$677$	−17.4042	−	27.0814i	−0.668896	−	1.04082i	−0.995417	−	0.0956330i	$-0.969512\pi$
$677$	−17.4042	−	27.0814i	−0.668896	−	1.04082i	0.326520	−	0.945190i	$-0.394124\pi$
$678$	4.31566	−	0.620498i	0.165742	−	0.0238301i
$679$	−0.0473502	−	0.329328i	−0.00181713	−	0.0126384i
$680$	−14.0055	+	2.28782i	−0.537087	+	0.0877338i
$681$	9.21908	−	10.6394i	0.353276	−	0.407702i
$682$	18.5537	+	8.47320i	0.710458	+	0.324455i
$683$	−4.65261	+	7.23960i	−0.178027	+	0.277016i	−0.918786	−	0.394755i	$-0.870829\pi$
$683$	−4.65261	+	7.23960i	−0.178027	+	0.277016i	0.740759	+	0.671770i	$0.234466\pi$
$684$	2.06044	−	0.605000i	0.0787830	−	0.0231328i
$685$	32.7909	−	10.3133i	1.25288	−	0.394050i
$686$	2.47841	+	0.727726i	0.0946260	+	0.0277847i
$687$	−16.2442	+	7.41848i	−0.619755	+	0.283033i
$688$	−5.22366	−	0.751050i	−0.199150	−	0.0286335i
$689$	70.3236			2.67912
$690$	5.84349	+	8.99187i	0.222458	+	0.342314i
$691$	−46.7648			−1.77902			−0.889509	−	0.456918i	$-0.848953\pi$
$691$	−46.7648			−1.77902			−0.889509	+	0.456918i	$0.848953\pi$
$692$	3.34992	+	0.481646i	0.127345	+	0.0183095i
$693$	−0.699658	+	0.319523i	−0.0265778	+	0.0121377i
$694$	6.56442	+	1.92749i	0.249182	+	0.0731664i
$695$	−13.6407	−	43.3704i	−0.517422	−	1.64513i
$696$	−4.70792	+	1.38237i	−0.178453	+	0.0523986i
$697$	8.66849	−	13.4884i	0.328343	−	0.510911i
$698$	−8.04184	−	3.67259i	−0.304388	−	0.139009i
$699$	−15.8796	+	18.3261i	−0.600623	+	0.693156i
$700$	−0.226423	+	0.896626i	−0.00855799	+	0.0338893i
$701$	−3.69931	−	25.7292i	−0.139721	−	0.971780i	−0.932216	−	0.361902i	$-0.882127\pi$
$701$	−3.69931	−	25.7292i	−0.139721	−	0.971780i	0.792495	−	0.609878i	$-0.208782\pi$
$702$	−5.64963	+	0.812294i	−0.213231	+	0.0306581i
$703$	−7.25126	−	11.2832i	−0.273486	−	0.425553i
$704$	2.72335	−	3.14292i	0.102640	−	0.118453i
$705$	4.05727	−	3.65378i	0.152806	−	0.137609i
$706$	−4.03285	−	2.59176i	−0.151778	−	0.0975420i
$707$	0.643863	+	2.19280i	0.0242150	+	0.0824686i
$708$	−8.21036	+	7.11431i	−0.308564	+	0.267372i
$709$	31.3771	+	9.21313i	1.17839	+	0.346007i	0.811553	−	0.584279i	$-0.198623\pi$
$709$	31.3771	+	9.21313i	1.17839	+	0.346007i	0.366837	+	0.930285i	$0.380441\pi$
$710$	15.2415	−	0.291476i	0.572004	−	0.0109389i
$711$	2.33790	−	16.2604i	0.0876779	−	0.609813i
$712$		−	17.5723i		−	0.658550i
$713$	10.0708	−	21.2570i	0.377156	−	0.796082i
$714$	−1.17381			−0.0439287
$715$	45.1914	+	27.8364i	1.69006	+	1.04102i
$716$	5.68002	+	12.4375i	0.212272	+	0.464811i
$717$	1.64947	−	5.61757i	0.0616004	−	0.209792i
$718$	16.9625	−	14.6981i	0.633035	−	0.548528i
$719$	21.6091	−	6.34500i	0.805883	−	0.236629i	0.147256	−	0.989098i	$-0.452956\pi$
$719$	21.6091	−	6.34500i	0.805883	−	0.236629i	0.658627	+	0.752470i	$0.271138\pi$
$720$	1.24466	+	1.85764i	0.0463856	+	0.0692302i
$721$	1.17831	−	2.58015i	0.0438827	−	0.0960897i
$722$	−10.8741	−	9.42250i	−0.404694	−	0.350669i
$723$	10.6452	+	16.5643i	0.395901	+	0.616034i
$724$	1.83912	+	12.7914i	0.0683505	+	0.475388i
$725$	−15.3453	+	19.1418i	−0.569911	+	0.710909i
$726$	5.29535	−	3.40311i	0.196529	−	0.126301i
$727$	13.3300	+	11.5505i	0.494384	+	0.428386i	0.866033	−	0.499988i	$-0.166662\pi$
$727$	13.3300	+	11.5505i	0.494384	+	0.428386i	−0.371649	+	0.928373i	$0.621208\pi$
$728$	0.960271	+	0.438541i	0.0355900	+	0.0162534i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	32.3727	+	4.02434i	1.19817	+	0.148948i
$731$	−21.9331	−	25.3121i	−0.811224	−	0.936203i
$732$	3.40931	−	11.6110i	0.126012	−	0.429157i
$733$	−28.5202	+	13.0248i	−1.05342	+	0.481080i	−0.865398	−	0.501085i	$-0.832935\pi$
$733$	−28.5202	+	13.0248i	−1.05342	+	0.481080i	−0.188021	+	0.982165i	$0.560207\pi$
$734$	1.66719	−	11.5955i	0.0615370	−	0.428000i
$735$	6.19841	−	14.2895i	0.228632	−	0.527078i
$736$	−3.58000	−	3.19118i	−0.131960	−	0.117628i
$737$		−	37.4772i		−	1.38049i
$738$	−2.50069	−	0.359545i	−0.0920516	−	0.0132350i
$739$	−0.546267	−	1.19616i	−0.0200947	−	0.0440013i	0.899319	−	0.437294i	$-0.144063\pi$
$739$	−0.546267	−	1.19616i	−0.0200947	−	0.0440013i	−0.919413	+	0.393293i	$0.871336\pi$
$740$	8.94228	−	10.7277i	0.328725	−	0.394359i
$741$	−8.02658	−	9.26316i	−0.294864	−	0.340291i
$742$	−0.642008	−	2.18648i	−0.0235689	−	0.0802682i
$743$	−21.8748	+	34.0379i	−0.802510	+	1.24873i	0.162550	+	0.986700i	$0.448028\pi$
$743$	−21.8748	+	34.0379i	−0.802510	+	1.24873i	−0.965060	+	0.262029i	$0.915608\pi$
$744$	2.03747	−	4.46145i	0.0746974	−	0.163565i
$745$	8.31688	−	3.99211i	0.304707	−	0.146260i
$746$	−7.44188	+	4.78260i	−0.272466	+	0.175104i
$747$	−0.558243	+	0.0802632i	−0.0204250	+	0.00293668i
$748$	26.1243	−	3.75610i	0.955198	−	0.137337i
$749$	−1.88884	+	1.21388i	−0.0690167	+	0.0443543i
$750$	10.4195	+	4.05377i	0.380468	+	0.148023i
$751$	19.8169	−	43.3930i	0.723130	−	1.58343i	−0.0863344	−	0.996266i	$-0.527515\pi$
$751$	19.8169	−	43.3930i	0.723130	−	1.58343i	0.809465	−	0.587168i	$-0.199757\pi$
$752$	−1.32013	+	2.05416i	−0.0481401	+	0.0749075i
$753$	−2.78269	−	9.47697i	−0.101407	−	0.345360i
$754$	18.3400	+	21.1655i	0.667904	+	0.770802i
$755$	9.92010	+	8.26908i	0.361029	+	0.300942i
$756$	0.0768329	+	0.168241i	0.00279439	+	0.00611885i
$757$	−16.6307	−	2.39113i	−0.604453	−	0.0869072i	−0.166708	−	0.986006i	$-0.553314\pi$
$757$	−16.6307	−	2.39113i	−0.604453	−	0.0869072i	−0.437745	+	0.899099i	$0.644223\pi$
$758$			18.8375i			0.684210i
$759$	−10.5461	−	16.9280i	−0.382798	−	0.614446i
$760$	−1.91086	+	4.40521i	−0.0693141	+	0.159794i
$761$	1.37004	−	9.52885i	0.0496640	−	0.345421i	−0.949805	−	0.312842i	$-0.898719\pi$
$761$	1.37004	−	9.52885i	0.0496640	−	0.345421i	0.999469	−	0.0325786i	$-0.0103719\pi$
$762$	3.50572	−	1.60101i	0.126999	−	0.0579985i
$763$	0.106295	−	0.362008i	0.00384814	−	0.0131056i
$764$	4.70220	+	5.42663i	0.170120	+	0.196329i
$765$	−1.75066	+	14.0827i	−0.0632954	+	0.509163i
$766$	10.2551	+	6.59056i	0.370532	+	0.238127i
$767$	56.4044	+	25.7590i	2.03664	+	0.930104i
$768$	−0.755750	−	0.654861i	−0.0272708	−	0.0236303i
$769$	3.62571	−	2.33011i	0.130747	−	0.0840257i	−0.473633	−	0.880723i	$-0.657058\pi$
$769$	3.62571	−	2.33011i	0.130747	−	0.0840257i	0.604379	+	0.796697i	$0.293421\pi$
$770$	0.452913	−	1.65920i	0.0163218	−	0.0597935i
$771$	−1.25507	−	8.72920i	−0.0452002	−	0.314374i
$772$	11.5656	+	17.9965i	0.416256	+	0.647708i
$773$	−6.71972	−	5.82267i	−0.241691	−	0.209427i	0.525589	−	0.850739i	$-0.323845\pi$
$773$	−6.71972	−	5.82267i	−0.241691	−	0.209427i	−0.767280	+	0.641312i	$0.778390\pi$
$774$	−2.19230	+	4.80047i	−0.0788007	+	0.172549i
$775$	−4.41556	−	24.1226i	−0.158612	−	0.866508i
$776$	1.72603	−	0.506808i	0.0619609	−	0.0181934i
$777$	0.873030	−	0.756485i	0.0313198	−	0.0271387i
$778$	2.52270	−	8.59153i	0.0904432	−	0.308021i
$779$	−2.25374	−	4.93500i	−0.0807485	−	0.176815i
$780$	6.69357	−	10.8668i	0.239668	−	0.389093i
$781$	−28.3516			−1.01450
$782$	−3.90816	−	30.1847i	−0.139756	−	1.07940i
$783$			4.90668i			0.175350i
$784$	−0.991336	+	6.89489i	−0.0354048	+	0.246246i
$785$	2.92583	−	0.0559530i	0.104427	−	0.00199705i
$786$	17.0100	+	4.99458i	0.606725	+	0.178151i
$787$	4.13462	−	3.58267i	0.147383	−	0.127708i	−0.578048	−	0.816002i	$-0.696186\pi$
$787$	4.13462	−	3.58267i	0.147383	−	0.127708i	0.725432	+	0.688294i	$0.241640\pi$
$788$	0.980854	+	3.34048i	0.0349415	+	0.119000i
$789$	14.3273	+	9.20762i	0.510066	+	0.327800i
$790$	24.5816	+	27.2962i	0.874574	+	0.971154i
$791$	−0.528086	+	0.609443i	−0.0187766	+	0.0216693i
$792$	−2.24835	−	3.49850i	−0.0798916	−	0.124314i
$793$	−68.3675	+	9.82976i	−2.42780	+	0.349065i
$794$	−0.682295	−	4.74546i	−0.0242137	−	0.168410i
$795$	−27.1897	+	4.44148i	−0.964321	+	0.157523i
$796$	2.40388	−	2.77423i	0.0852033	−	0.0983298i
$797$	−14.2875	−	6.52488i	−0.506089	−	0.231123i	0.145973	−	0.989289i	$-0.453369\pi$
$797$	−14.2875	−	6.52488i	−0.506089	−	0.231123i	−0.652062	+	0.758165i	$0.726096\pi$
$798$	−0.214730	+	0.334126i	−0.00760136	+	0.0118279i
$799$	−14.8690	+	4.36593i	−0.526027	+	0.154455i
$800$	−4.97269	−	0.521832i	−0.175811	−	0.0184495i
$801$	−16.8605	−	4.95069i	−0.595737	−	0.174924i
$802$	−5.37197	+	2.45329i	−0.189691	+	0.0866288i
$803$	−60.0533	−	8.63435i	−2.11923	−	0.304700i
$804$	−9.01181			−0.317822
$805$	−1.90589	−	0.549117i	−0.0671738	−	0.0193538i
$806$	−27.9945			−0.986064
$807$	−16.0055	−	2.30125i	−0.563422	−	0.0810079i
$808$	−11.2398	+	5.13302i	−0.395413	+	0.180579i
$809$	20.2067	+	5.93322i	0.710430	+	0.208601i	0.616930	−	0.787018i	$-0.288376\pi$
$809$	20.2067	+	5.93322i	0.710430	+	0.208601i	0.0935001	+	0.995619i	$0.470194\pi$
$810$	2.13305	−	0.670880i	0.0749479	−	0.0235723i
$811$	−2.73598	+	0.803357i	−0.0960734	+	0.0282097i	−0.329416	−	0.944185i	$-0.606852\pi$
$811$	−2.73598	+	0.803357i	−0.0960734	+	0.0282097i	0.233343	+	0.972395i	$0.425034\pi$
$812$	0.490638	−	0.763448i	0.0172180	−	0.0267918i
$813$	−9.72570	−	4.44158i	−0.341095	−	0.155773i
$814$	−17.0094	+	19.6299i	−0.596181	+	0.688029i
$815$	−3.95246	−	24.1961i	−0.138449	−	0.847551i
$816$	−0.903197	−	6.28187i	−0.0316182	−	0.219910i
$817$	−11.2174	+	1.61282i	−0.392449	+	0.0564256i
$818$	18.4340	+	28.6838i	0.644528	+	1.00291i
$819$	0.691317	−	0.797822i	0.0241566	−	0.0278782i
$820$	4.19787	−	3.78040i	0.146596	−	0.132017i
$821$	−40.4507	−	25.9961i	−1.41174	−	0.907271i	−0.411749	−	0.911297i	$-0.635082\pi$
$821$	−40.4507	−	25.9961i	−1.41174	−	0.907271i	−0.999992	+	0.00402691i	$0.998718\pi$
$822$	4.33101	+	14.7501i	0.151061	+	0.514467i
$823$	5.13546	−	4.44990i	0.179011	−	0.155114i	−0.560746	−	0.827988i	$-0.689486\pi$
$823$	5.13546	−	4.44990i	0.179011	−	0.155114i	0.739757	+	0.672874i	$0.234940\pi$
$824$	14.7148	+	4.32066i	0.512615	+	0.150517i
$825$	−19.2308	−	7.90840i	−0.669529	−	0.275335i
$826$	0.285956	−	1.98887i	0.00994969	−	0.0692016i
$827$			52.5877i			1.82865i	0.404976	+	0.914327i	$0.367280\pi$
$827$			52.5877i			1.82865i	−0.404976	+	0.914327i	$0.632720\pi$
$828$	−4.07052	+	2.53592i	−0.141460	+	0.0881293i
$829$	12.6916			0.440798			0.220399	−	0.975410i	$-0.429264\pi$
$829$	12.6916			0.440798			0.220399	+	0.975410i	$0.429264\pi$
$830$	0.661395	−	1.07375i	0.0229574	−	0.0372705i
$831$	−3.76139	−	8.23630i	−0.130481	−	0.285714i
$832$	−1.60805	+	5.47652i	−0.0557492	+	0.189864i
$833$	−33.4103	+	28.9502i	−1.15760	+	1.00307i
$834$	19.5089	−	5.72834i	0.675539	−	0.198356i
$835$	7.70698	−	5.16383i	0.266711	−	0.178702i
$836$	3.70985	−	8.12343i	0.128308	−	0.280955i
$837$	−3.70670	−	3.21188i	−0.128122	−	0.111019i
$838$	−5.42197	−	8.43675i	−0.187299	−	0.291443i
$839$	−5.35897	−	37.2724i	−0.185012	−	1.28679i	−0.844697	−	0.535245i	$-0.820219\pi$
$839$	−5.35897	−	37.2724i	−0.185012	−	1.28679i	0.659685	−	0.751542i	$-0.270690\pi$
$840$	−0.398974	−	0.108908i	−0.0137659	−	0.00375768i
$841$	−4.14276	+	2.66239i	−0.142854	+	0.0918067i
$842$	−27.9305	−	24.2019i	−0.962549	−	0.834054i
$843$	−4.32563	−	1.97545i	−0.148982	−	0.0680380i
$844$	3.34609	+	2.15040i	0.115177	+	0.0740198i
$845$	−43.4436	−	5.40059i	−1.49450	−	0.185786i
$846$	1.59903	+	1.84538i	0.0549757	+	0.0634454i
$847$	−0.327997	+	1.11705i	−0.0112701	+	0.0383825i
$848$	11.2074	−	5.11824i	0.384863	−	0.175761i
$849$	2.32069	−	16.1407i	0.0796458	−	0.553949i
$850$	−21.6820	−	23.1697i	−0.743686	−	0.794713i
$851$	22.3598	+	19.9314i	0.766485	+	0.683239i
$852$			6.81746i			0.233562i
$853$	46.7307	+	6.71886i	1.60003	+	0.230049i	0.883817	−	0.467833i	$-0.154965\pi$
$853$	46.7307	+	6.71886i	1.60003	+	0.230049i	0.716212	+	0.697883i	$0.245874\pi$
$854$	0.929773	+	2.03592i	0.0318162	+	0.0696677i
$855$	3.68841	+	3.07455i	0.126141	+	0.105147i
$856$	−7.94972	−	9.17447i	−0.271716	−	0.313577i
$857$	10.8893	+	37.0856i	0.371972	+	1.26682i	0.906693	+	0.421791i	$0.138598\pi$
$857$	10.8893	+	37.0856i	0.371972	+	1.26682i	−0.534721	+	0.845029i	$0.679583\pi$
$858$	−12.8330	+	19.9685i	−0.438110	+	0.681713i
$859$	−17.6518	+	38.6520i	−0.602271	+	1.31879i	0.325465	+	0.945554i	$0.394479\pi$
$859$	−17.6518	+	38.6520i	−0.602271	+	1.31879i	−0.927736	+	0.373236i	$0.878248\pi$
$860$	−5.10648	−	10.6385i	−0.174130	−	0.362770i
$861$	0.393092	−	0.252625i	0.0133966	−	0.00860944i
$862$	17.0608	−	2.45297i	0.581092	−	0.0835484i
$863$	−5.20161	+	0.747879i	−0.177065	+	0.0254581i	−0.230277	−	0.973125i	$-0.573963\pi$
$863$	−5.20161	+	0.747879i	−0.177065	+	0.0254581i	0.0532120	+	0.998583i	$0.483054\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	3.27478	+	6.82244i	0.111346	+	0.231970i
$866$	−6.09832	+	13.3535i	−0.207229	+	0.453769i
$867$	12.5849	−	19.5824i	0.427405	−	0.665055i
$868$	0.255571	+	0.870396i	0.00867466	+	0.0295432i
$869$	−44.7383	−	51.6307i	−1.51764	−	1.75145i
$870$	−8.42769	−	7.02506i	−0.285726	−	0.238172i
$871$	21.3677	+	46.7886i	0.724016	+	1.58537i
$872$	2.01915	+	0.290310i	0.0683770	+	0.00983112i
$873$		−	1.79890i		−	0.0608835i
$874$	−9.30704	−	4.40934i	−0.314815	−	0.149148i
$875$	−1.94743	+	0.695378i	−0.0658351	+	0.0235081i
$876$	−2.07623	+	14.4405i	−0.0701492	+	0.487898i
$877$	13.1390	−	6.00037i	0.443672	−	0.202618i	−0.181036	−	0.983476i	$-0.557945\pi$
$877$	13.1390	−	6.00037i	0.443672	−	0.202618i	0.624708	+	0.780858i	$0.285218\pi$
$878$	−8.17904	+	27.8553i	−0.276029	+	0.940069i
$879$	12.7955	+	14.7668i	0.431582	+	0.498072i
$880$	9.22805	+	1.14716i	0.311078	+	0.0386709i
$881$	−18.8624	−	12.1221i	−0.635490	−	0.408405i	0.182848	−	0.983141i	$-0.441468\pi$
$881$	−18.8624	−	12.1221i	−0.635490	−	0.408405i	−0.818339	+	0.574736i	$0.805105\pi$
$882$	6.33631	+	2.89369i	0.213355	+	0.0974358i
$883$	16.4859	+	14.2851i	0.554793	+	0.480731i	0.886549	−	0.462634i	$-0.153096\pi$
$883$	16.4859	+	14.2851i	0.554793	+	0.480731i	−0.331756	+	0.943365i	$0.607641\pi$
$884$	−30.4735	+	19.5841i	−1.02493	+	0.658685i
$885$	−23.4349	−	6.39703i	−0.787756	−	0.215034i
$886$	3.52380	+	24.5085i	0.118384	+	0.823381i
$887$	−4.47969	−	6.97053i	−0.150413	−	0.234047i	0.757868	−	0.652408i	$-0.226241\pi$
$887$	−4.47969	−	6.97053i	−0.150413	−	0.234047i	−0.908281	+	0.418361i	$0.862605\pi$
$888$	4.72024	+	4.09011i	0.158401	+	0.137255i
$889$	−0.296114	+	0.648400i	−0.00993135	+	0.0217466i
$890$	32.6431	−	21.8715i	1.09420	−	0.733134i
$891$	−3.99022	+	1.17163i	−0.133677	+	0.0392512i
$892$	0.440117	−	0.381363i	0.0147362	−	0.0127690i
$893$	−1.47728	+	5.03115i	−0.0494353	+	0.168361i
$894$	1.71388	+	3.75288i	0.0573208	+	0.125515i
$895$	−16.0348	+	26.0318i	−0.535983	+	0.870149i
$896$	0.184955			0.00617890
$897$	22.8178	+	15.1210i	0.761865	+	0.504875i
$898$			27.7191i			0.924999i
$899$	−3.42490	+	23.8207i	−0.114227	+	0.794464i
$900$	−1.90166	+	4.62425i	−0.0633888	+	0.154142i
$901$	75.0261	+	22.0297i	2.49948	+	0.733914i
$902$	−7.94028	+	6.88029i	−0.264382	+	0.229089i
$903$	−0.274992	−	0.936538i	−0.00915117	−	0.0311660i
$904$	−3.66790	−	2.35721i	−0.121992	−	0.0783998i
$905$	−21.4727	+	19.3373i	−0.713778	+	0.642794i
$906$	−3.78219	+	4.36488i	−0.125655	+	0.145014i
$907$	−23.0359	−	35.8446i	−0.764895	−	1.19020i	−0.977060	−	0.212966i	$-0.931688\pi$
$907$	−23.0359	−	35.8446i	−0.764895	−	1.19020i	0.212165	−	0.977234i	$-0.431949\pi$
$908$	−13.9346	+	2.00350i	−0.462437	+	0.0664884i
$909$	1.75850	+	12.2306i	0.0583256	+	0.405664i
$910$	0.380555	+	2.32967i	0.0126153	+	0.0772279i
$911$	9.45456	−	10.9111i	0.313244	−	0.361502i	−0.577195	−	0.816607i	$-0.695853\pi$
$911$	9.45456	−	10.9111i	0.313244	−	0.361502i	0.890438	+	0.455104i	$0.150398\pi$
$912$	−1.95337	−	0.892074i	−0.0646825	−	0.0295395i
$913$	−1.26803	+	1.97310i	−0.0419657	+	0.0652999i
$914$	−1.64727	+	0.483684i	−0.0544870	+	0.0159988i
$915$	25.8126	−	8.11848i	0.853338	−	0.268389i
$916$	17.1346	+	5.03118i	0.566144	+	0.166235i
$917$	−2.98258	+	1.36210i	−0.0984936	+	0.0449805i
$918$	−6.28187	−	0.903197i	−0.207333	−	0.0298099i
$919$	32.3386			1.06675			0.533376	−	0.845878i	$-0.320923\pi$
$919$	32.3386			1.06675			0.533376	+	0.845878i	$0.320923\pi$
$920$	1.47221	−	10.6223i	0.0485372	−	0.350206i
$921$	24.3265			0.801586
$922$	−26.2669	−	3.77661i	−0.865055	−	0.124376i
$923$	35.3958	−	16.1647i	1.16507	−	0.532068i
$924$	0.738010	+	0.216699i	0.0242787	+	0.00712888i
$925$	31.0583	+	3.25924i	1.02119	+	0.107163i
$926$	−6.09798	+	1.79053i	−0.200392	+	0.0588404i
$927$	8.29129	−	12.9015i	0.272322	−	0.423741i
$928$	4.46327	+	2.03831i	0.146514	+	0.0669107i
$929$	−12.8353	+	14.8128i	−0.421114	+	0.485991i	−0.926176	−	0.377092i	$-0.876924\pi$
$929$	−12.8353	+	14.8128i	−0.421114	+	0.485991i	0.505062	+	0.863083i	$0.331470\pi$
$930$	10.8237	−	1.76807i	0.354924	−	0.0579772i
$931$	2.12882	+	14.8063i	0.0697693	+	0.485256i
$932$	24.0021	−	3.45098i	0.786214	−	0.113041i
$933$	3.13038	+	4.87096i	0.102484	+	0.159468i
$934$	14.1682	−	16.3510i	0.463599	−	0.535022i
$935$	39.4932	+	43.8545i	1.29157	+	1.43419i
$936$	4.80164	+	3.08583i	0.156947	+	0.100863i
$937$	0.0467759	+	0.159304i	0.00152810	+	0.00520423i	0.960253	−	0.279129i	$-0.0900458\pi$
$937$	0.0467759	+	0.159304i	0.00152810	+	0.00520423i	−0.958725	+	0.284334i	$0.908228\pi$
$938$	1.25966	−	1.09151i	0.0411295	−	0.0356389i
$939$	12.1455	+	3.56623i	0.396352	+	0.116379i
$940$	−5.45900	+	0.104397i	−0.178053	+	0.00340505i
$941$	1.97886	−	13.7633i	0.0645089	−	0.448670i	−0.931810	−	0.362946i	$-0.881771\pi$
$941$	1.97886	−	13.7633i	0.0645089	−	0.448670i	0.996319	−	0.0857232i	$-0.0273201\pi$
$942$			1.30871i			0.0426401i
$943$	7.80508	+	9.26731i	0.254168	+	0.301785i
$944$	10.8639			0.353588
$945$	−0.216900	+	0.352130i	−0.00705577	+	0.0114548i
$946$	9.11708	+	19.9636i	0.296422	+	0.649073i
$947$	−9.27106	+	31.5743i	−0.301269	+	1.02603i	0.660194	+	0.751095i	$0.270474\pi$
$947$	−9.27106	+	31.5743i	−0.301269	+	1.02603i	−0.961463	+	0.274933i	$0.911344\pi$
$948$	−12.4152	+	10.7578i	−0.403226	+	0.349397i
$949$	79.8968	−	23.4598i	2.59356	−	0.761538i
$950$	−10.5617	+	1.93328i	−0.342665	+	0.0627238i
$951$	2.56147	−	5.60883i	0.0830613	−	0.181879i
$952$	0.887106	+	0.768682i	0.0287513	+	0.0249131i
$953$	−2.94027	−	4.57515i	−0.0952447	−	0.148204i	0.790361	−	0.612641i	$-0.209893\pi$
$953$	−2.94027	−	4.57515i	−0.0952447	−	0.148204i	−0.885606	+	0.464438i	$0.846257\pi$
$954$	−1.75343	−	12.1954i	−0.0567694	−	0.394840i
$955$	−4.22811	+	15.4893i	−0.136818	+	0.501222i
$956$	−4.92531	+	3.16530i	−0.159296	+	0.102373i
$957$	15.4213	+	13.3626i	0.498499	+	0.431952i
$958$	0.929355	+	0.424422i	0.0300261	+	0.0137125i
$959$	−2.39191	−	1.53718i	−0.0772387	−	0.0496383i
$960$	0.275848	−	2.21899i	0.00890297	−	0.0716175i
$961$	4.54748	+	5.24808i	0.146693	+	0.169293i
$962$	10.0435	−	34.2051i	0.323816	−	1.10282i
$963$	−11.0425	+	5.04296i	−0.355841	+	0.162507i
$964$	2.80219	−	19.4896i	0.0902523	−	0.627719i
$965$	−19.0358	+	43.8842i	−0.612783	+	1.41268i
$966$	0.261825	−	0.847489i	0.00842407	−	0.0272675i
$967$			13.3804i			0.430284i	0.976583	+	0.215142i	$0.0690214\pi$
$967$			13.3804i			0.430284i	−0.976583	+	0.215142i	$0.930979\pi$
$968$	−6.23052	−	0.895814i	−0.200256	−	0.0287925i
$969$	−5.66152	−	12.3970i	−0.181874	−	0.398249i
$970$	3.08978	+	2.57554i	0.0992069	+	0.0826957i
$971$	17.3474	+	20.0200i	0.556706	+	0.642472i	0.962432	−	0.271522i	$-0.0875270\pi$
$971$	17.3474	+	20.0200i	0.556706	+	0.642472i	−0.405727	+	0.913994i	$0.632982\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	−2.03313	+	3.16362i	−0.0651793	+	0.101421i
$974$	10.5854	−	23.1788i	0.339178	−	0.742697i
$975$	28.5178	−	1.09113i	0.913299	−	0.0349443i
$976$	−10.1802	+	6.54242i	−0.325860	+	0.209418i
$977$	27.8093	−	3.99838i	0.889699	−	0.127919i	0.317717	−	0.948185i	$-0.397084\pi$
$977$	27.8093	−	3.99838i	0.889699	−	0.127919i	0.571982	+	0.820266i	$0.306175\pi$
$978$	10.8526	−	1.56037i	0.347029	−	0.0498952i
$979$	−61.4767	+	39.5087i	−1.96481	+	1.26270i
$980$	−14.0421	+	6.74022i	−0.448559	+	0.215308i
$981$	0.847410	−	1.85557i	0.0270557	−	0.0592437i
$982$	−23.7637	+	36.9770i	−0.758330	+	1.17998i
$983$	8.41437	+	28.6567i	0.268377	+	0.914007i	0.977856	+	0.209281i	$0.0671122\pi$
$983$	8.41437	+	28.6567i	0.268377	+	0.914007i	−0.709479	+	0.704727i	$0.751070\pi$
$984$	1.65444	+	1.90933i	0.0527417	+	0.0608671i
$985$	−4.98459	+	5.97983i	−0.158822	+	0.190533i
$986$	12.9361	+	28.3260i	0.411968	+	0.902084i
$987$	−0.447022	−	0.0642721i	−0.0142289	−	0.00204580i
$988$			12.2569i			0.389945i
$989$	23.1676	−	10.1896i	0.736687	−	0.324012i
$990$	3.70054	−	8.53106i	0.117611	−	0.271135i
$991$	−2.03199	+	14.1328i	−0.0645484	+	0.448944i	0.931758	+	0.363079i	$0.118275\pi$
$991$	−2.03199	+	14.1328i	−0.0645484	+	0.448944i	−0.996307	+	0.0858651i	$0.972635\pi$
$992$	−4.46145	+	2.03747i	−0.141651	+	0.0646899i
$993$	−0.508369	+	1.73135i	−0.0161326	+	0.0549426i
$994$	−0.825728	−	0.952940i	−0.0261905	−	0.0302254i
$995$	8.14552	+	1.01259i	0.258230	+	0.0321013i
$996$	0.474453	+	0.304912i	0.0150336	+	0.00966152i
$997$	−9.49509	−	4.33626i	−0.300712	−	0.137331i	0.259344	−	0.965785i	$-0.416493\pi$
$997$	−9.49509	−	4.33626i	−0.300712	−	0.137331i	−0.560057	+	0.828454i	$0.689221\pi$
$998$	−19.7320	−	17.0979i	−0.624605	−	0.541223i
$999$	5.25428	−	3.37672i	0.166238	−	0.106835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.b.169.10	yes	120
5.4	even	2	inner	690.2.r.b.169.6	yes	120
23.3	even	11	inner	690.2.r.b.49.6	✓	120
115.49	even	22	inner	690.2.r.b.49.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.b.49.6	✓	120	23.3	even	11	inner
690.2.r.b.49.10	yes	120	115.49	even	22	inner
690.2.r.b.169.6	yes	120	5.4	even	2	inner
690.2.r.b.169.10	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(0.670880 + 2.13305i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.0999940 - 0.155594i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.989821 + 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(0.670880 + 2.13305i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.0999940 - 0.155594i) q^{7} +(0.909632 + 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(0.360487 + 2.20682i) q^{10} +(-0.591841 - 4.11635i) q^{11} +(-0.989821 + 0.142315i) q^{12} +(3.08583 + 4.80164i) q^{13} +(0.121120 - 0.139779i) q^{14} +(-1.49636 - 1.66160i) q^{15} +(0.841254 + 0.540641i) q^{16} +(1.78801 + 6.08939i) q^{17} +(0.755750 - 0.654861i) q^{18} +(2.06044 + 0.605000i) q^{19} +(0.0427543 + 2.23566i) q^{20} +(-0.0263218 + 0.183072i) q^{21} -4.15868i q^{22} +(-4.79536 - 0.0673348i) q^{23} -1.00000 q^{24} +(-4.09984 + 2.86205i) q^{25} +(2.37107 + 5.19193i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(0.139779 - 0.121120i) q^{28} +(4.70792 - 1.38237i) q^{29} +(-1.24466 - 1.85764i) q^{30} +(-2.03747 + 4.46145i) q^{31} +(0.755750 + 0.654861i) q^{32} +(2.24835 + 3.49850i) q^{33} +(0.903197 + 6.28187i) q^{34} +(0.398974 + 0.108908i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-4.72024 - 4.09011i) q^{37} +(1.95337 + 0.892074i) q^{38} +(-4.80164 - 3.08583i) q^{39} +(-0.275848 + 2.21899i) q^{40} +(-1.65444 - 1.90933i) q^{41} +(-0.0521077 + 0.177463i) q^{42} +(-4.80047 + 2.19230i) q^{43} +(0.591841 - 4.11635i) q^{44} +(2.05139 + 0.889836i) q^{45} +(-4.73697 - 0.749100i) q^{46} +2.44178i q^{47} +(-0.989821 - 0.142315i) q^{48} +(2.89369 + 6.33631i) q^{49} +(-4.46542 + 2.24945i) q^{50} +(-4.15605 - 4.79634i) q^{51} +(1.60805 + 5.47652i) q^{52} +(6.66112 - 10.3649i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(8.38334 - 4.02401i) q^{55} +(0.155594 - 0.0999940i) q^{56} +(-2.12557 + 0.305611i) q^{57} +(4.85673 - 0.698293i) q^{58} +(9.13926 - 5.87345i) q^{59} +(-0.967617 - 2.01587i) q^{60} +(-5.02703 + 11.0077i) q^{61} +(-2.65167 + 4.12607i) q^{62} +(-0.0521077 - 0.177463i) q^{63} +(0.654861 + 0.755750i) q^{64} +(-8.17194 + 9.80357i) q^{65} +(1.72758 + 3.78287i) q^{66} +(8.92008 + 1.28251i) q^{67} +6.34647i q^{68} +(4.38998 - 1.93081i) q^{69} +(0.379414 + 0.164579i) q^{70} +(0.970226 - 6.74807i) q^{71} +(0.909632 - 0.415415i) q^{72} +(4.11019 - 13.9980i) q^{73} +(-4.09011 - 4.72024i) q^{74} +(2.54041 - 4.30655i) q^{75} +(1.80653 + 1.16099i) q^{76} +(-0.699658 - 0.319523i) q^{77} +(-4.31361 - 3.73776i) q^{78} +(13.8198 - 8.88145i) q^{79} +(-0.588836 + 2.15714i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-1.36588 - 2.12535i) q^{82} +(-0.426230 - 0.369330i) q^{83} +(-0.0768329 + 0.168241i) q^{84} +(-11.7895 + 7.89917i) q^{85} +(-5.06361 + 1.48681i) q^{86} +(-3.70822 + 3.21319i) q^{87} +(1.17163 - 3.99022i) q^{88} +(-7.29980 - 15.9843i) q^{89} +(1.90387 + 1.17272i) q^{90} +1.05567 q^{91} +(-4.58214 - 1.41562i) q^{92} -4.90467i q^{93} +(-0.347502 + 2.41693i) q^{94} +(0.0918117 + 4.80092i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(1.35952 - 1.17803i) q^{97} +(1.96249 + 6.68363i) q^{98} +(-3.49850 - 2.24835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more