LMFDB - Embedded newform 690.2.r.b.169.6

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			169.6
Character	$\chi$	$=$	690.169
Dual form			690.2.r.b.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 - 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(2.01587 + 0.967617i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(-0.0999940 + 0.155594i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.989821 - 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(2.01587 + 0.967617i) 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} +(-1.85764 - 1.24466i) 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} +(2.23566 + 0.0427543i) 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} +(1.66160 + 1.49636i) q^{20} +(-0.0263218 + 0.183072i) q^{21} +4.15868i q^{22} +(4.79536 + 0.0673348i) q^{23} -1.00000 q^{24} +(3.12743 + 3.90117i) 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} +(-2.20682 - 0.360487i) 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} +(-0.352130 + 0.216900i) 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} +(-1.43173 - 1.71760i) 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} +(-2.54041 - 4.30655i) 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} +(2.78997 - 8.87068i) 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} +(2.13305 + 0.670880i) 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} +(-1.57447 - 12.6654i) 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} +(4.46542 + 2.24945i) 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} +(1.17272 + 1.90387i) 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} +(2.28782 - 14.0055i) 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} +(-2.15714 + 0.588836i) q^{90} +1.05567 q^{91} +(4.58214 + 1.41562i) q^{92} +4.90467i q^{93} +(-0.347502 + 2.41693i) q^{94} +(3.56817 + 3.21332i) 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
$5$	2.01587	+	0.967617i	0.901523	+	0.432732i
$5$	2.01587	+	0.967617i	0.901523	+	0.432732i
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	−0.0999940	+	0.155594i	−0.0377942	+	0.0588089i	−0.859637	−	0.510906i	$-0.829310\pi$
$7$	−0.0999940	+	0.155594i	−0.0377942	+	0.0588089i	0.821842	+	0.569715i	$0.192946\pi$
$8$	−0.909632	−	0.415415i	−0.321603	−	0.146871i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	−1.85764	−	1.24466i	−0.587438	−	0.393595i
$11$	−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	$-0.891109\pi$
$13$	−3.08583	−	4.80164i	−0.855855	−	1.33174i	0.0862003	−	0.996278i	$-0.472527\pi$
$14$	0.121120	−	0.139779i	0.0323706	−	0.0373576i
$15$	2.23566	+	0.0427543i	0.577245	+	0.0110391i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.78801	−	6.08939i	−0.433656	−	1.47690i	−0.829463	−	0.558562i	$-0.811353\pi$
$17$	−1.78801	−	6.08939i	−0.433656	−	1.47690i	0.395808	−	0.918333i	$-0.370465\pi$
$18$	−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	$0.511685\pi$
$20$	1.66160	+	1.49636i	0.371545	+	0.334596i
$21$	−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
$25$	3.12743	+	3.90117i	0.625487	+	0.780235i
$26$	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	$0.258525\pi$
$30$	−2.20682	−	0.360487i	−0.402908	−	0.0658155i
$31$	−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
$35$	−0.352130	+	0.216900i	−0.0595208	+	0.0366628i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	4.72024	+	4.09011i	0.776003	+	0.672410i	0.949970	−	0.312341i	$-0.101113\pi$
$37$	4.72024	+	4.09011i	0.776003	+	0.672410i	−0.173967	+	0.984751i	$0.555659\pi$
$38$	−1.95337	−	0.892074i	−0.316878	−	0.144713i
$39$	−4.80164	−	3.08583i	−0.768878	−	0.494128i
$40$	−1.43173	−	1.71760i	−0.226377	−	0.271576i
$41$	−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	−0.0142653	−	0.999898i	$-0.504541\pi$
$43$	4.80047	−	2.19230i	0.732066	−	0.334323i	0.746331	+	0.665575i	$0.231814\pi$
$44$	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	$-0.943010\pi$
$47$		−	2.44178i		−	0.356171i	0.984015	−	0.178085i	$-0.0569903\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	2.89369	+	6.33631i	0.413385	+	0.905187i
$50$	−2.54041	−	4.30655i	−0.359268	−	0.609037i
$51$	−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	$0.502930\pi$
$53$	−6.66112	+	10.3649i	−0.914975	+	1.42373i	−0.905769	+	0.423771i	$0.860706\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	2.78997	−	8.87068i	0.376200	−	1.19612i
$56$	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	$0.0681502\pi$
$60$	2.13305	+	0.670880i	0.275376	+	0.0866103i
$61$	−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
$65$	−1.57447	−	12.6654i	−0.195288	−	1.57095i
$66$	1.72758	+	3.78287i	0.212650	+	0.465639i
$67$	−8.92008	−	1.28251i	−1.08976	−	0.156684i	−0.426070	−	0.904690i	$-0.640102\pi$
$67$	−8.92008	−	1.28251i	−1.08976	−	0.156684i	−0.663692	+	0.748006i	$0.731011\pi$
$68$		−	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	$0.416589\pi$
$73$	−4.11019	+	13.9980i	−0.481061	+	1.63834i	−0.740115	+	0.672481i	$0.765229\pi$
$74$	−4.09011	−	4.72024i	−0.475466	−	0.548717i
$75$	4.46542	+	2.24945i	0.515622	+	0.259744i
$76$	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	$-0.0570238\pi$
$80$	1.17272	+	1.90387i	0.131114	+	0.212859i
$81$	−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	0.677939	−	0.735118i	$-0.262873\pi$
$83$	0.426230	+	0.369330i	0.0467848	+	0.0405393i	−0.631155	+	0.775657i	$0.717419\pi$
$84$	−0.0768329	+	0.168241i	−0.00838316	+	0.0183566i
$85$	2.28782	−	14.0055i	0.248149	−	1.51911i
$86$	−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	$-0.517715\pi$
$90$	−2.15714	+	0.588836i	−0.227383	+	0.0620687i
$91$	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
$95$	3.56817	+	3.21332i	0.366086	+	0.329680i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	−1.35952	+	1.17803i	−0.138038	+	0.119611i	−0.721143	−	0.692786i	$-0.756383\pi$
$97$	−1.35952	+	1.17803i	−0.138038	+	0.119611i	0.583105	+	0.812397i	$0.301838\pi$
$98$	−1.96249	−	6.68363i	−0.198241	−	0.675148i
$99$	−3.49850	−	2.24835i	−0.351613	−	0.225968i
$100$	1.90166	+	4.62425i	0.190166	+	0.462425i
$101$	−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	−0.841091	−	0.540894i	$-0.818086\pi$
$103$	−15.1799	+	2.18255i	−1.49572	+	0.215053i	−0.654633	+	0.755946i	$0.727177\pi$
$104$	0.812294	+	5.64963i	0.0796520	+	0.553992i
$105$	−0.230205	+	0.343579i	−0.0224657	+	0.0335299i
$106$	8.06840	−	9.31143i	0.783672	−	0.904406i
$107$	11.0425	+	5.04296i	1.06752	+	0.487521i	0.870139	−	0.492806i	$-0.164029\pi$
$107$	11.0425	+	5.04296i	1.06752	+	0.487521i	0.197383	+	0.980327i	$0.436756\pi$
$108$	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	$0.377944\pi$
$110$	−4.02401	+	8.38334i	−0.383674	+	0.799320i
$111$	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	0.342281	−	0.939597i	$-0.388800\pi$
$113$	4.31566	+	0.620498i	0.405983	+	0.0583715i	0.0637014	+	0.997969i	$0.479709\pi$
$114$	−2.14743			−0.201125
$115$	9.60165	+	4.77581i	0.895358	+	0.445346i
$116$	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
$120$	−2.01587	−	0.967617i	−0.184023	−	0.0883309i
$121$	−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
$125$	2.52965	+	10.8904i	0.226259	+	0.974067i
$126$	−0.0263218	−	0.183072i	−0.00234493	−	0.0163094i
$127$	3.81477	−	0.548481i	0.338506	−	0.0486699i	0.0290343	−	0.999578i	$-0.490757\pi$
$127$	3.81477	−	0.548481i	0.338506	−	0.0486699i	0.309472	+	0.950909i	$0.399848\pi$
$128$	−0.540641	−	0.841254i	−0.0477863	−	0.0743570i
$129$	3.45595	−	3.98838i	0.304279	−	0.351157i
$130$	−0.244030	+	12.7605i	−0.0214028	+	1.11917i
$131$	−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
$135$	1.49636	−	1.66160i	0.128786	−	0.143008i
$136$	−0.903197	+	6.28187i	−0.0774485	+	0.538666i
$137$			15.3728i			1.31338i	0.754159	+	0.656692i	$0.228045\pi$
$137$			15.3728i			1.31338i	−0.754159	+	0.656692i	$0.771955\pi$
$138$	−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	$0.830972\pi$
$140$	−0.398974	+	0.108908i	−0.0337194	+	0.00920439i
$141$	−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
$145$	10.8281	+	1.76879i	0.899229	+	0.146890i
$146$	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	$-0.0995069\pi$
$150$	−4.09984	−	2.86205i	−0.334750	−	0.233685i
$151$	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
$155$	−8.42425	+	7.02218i	−0.676652	+	0.564035i
$156$	−3.73776	−	4.31361i	−0.299261	−	0.345365i
$157$	−0.368706	+	1.25570i	−0.0294260	+	0.100216i	−0.972897	−	0.231240i	$-0.925722\pi$
$157$	−0.368706	+	1.25570i	−0.0294260	+	0.100216i	0.943471	+	0.331456i	$0.107540\pi$
$158$	−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	0.553549	−	0.832817i	$-0.313273\pi$
$163$	10.8526	+	1.56037i	0.850043	+	0.122218i	0.296495	+	0.955035i	$0.404182\pi$
$164$	−1.04951	−	2.29810i	−0.0819526	−	0.179451i
$165$	−1.14716	−	9.22805i	−0.0893066	−	0.718403i
$166$	−0.369330	−	0.426230i	−0.0286656	−	0.0330819i
$167$	1.16885	+	3.98074i	0.0904485	+	0.308039i	0.992275	−	0.124060i	$-0.0395914\pi$
$167$	1.16885	+	3.98074i	0.0904485	+	0.308039i	−0.901826	+	0.432099i	$0.857773\pi$
$168$	0.0999940	−	0.155594i	0.00771471	−	0.0120043i
$169$	−8.13304	+	17.8089i	−0.625618	+	1.36991i
$170$	−4.25772	+	13.5374i	−0.326552	+	1.03827i
$171$	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	−0.268477	−	0.963286i	$-0.586520\pi$
$173$	−3.34992	+	0.481646i	−0.254690	+	0.0366189i	0.0137871	+	0.999905i	$0.495611\pi$
$174$	−4.12776	+	2.65275i	−0.312925	+	0.201104i
$175$	−0.919723	+	0.0965152i	−0.0695245	+	0.00729586i
$176$	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	$0.602007\pi$
$180$	2.21899	−	0.275848i	0.165394	−	0.0205605i
$181$	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
$190$	−3.07455	−	3.68841i	−0.223051	−	0.267586i
$191$	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	$-0.993018\pi$
$193$	−16.1673	−	14.0091i	−1.16375	−	1.00840i	−0.163992	−	0.986462i	$-0.552437\pi$
$194$	1.51333	−	0.972558i	0.108651	−	0.0698256i
$195$	−6.69357	−	10.8668i	−0.479336	−	0.778185i
$196$	0.991336	+	6.89489i	0.0708097	+	0.492492i
$197$	−1.88225	−	2.92883i	−0.134104	−	0.208671i	0.767706	−	0.640802i	$-0.221398\pi$
$197$	−1.88225	−	2.92883i	−0.134104	−	0.208671i	−0.901811	+	0.432131i	$0.857762\pi$
$198$	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	$0.0948309\pi$
$200$	−1.22421	−	4.84782i	−0.0865646	−	0.342792i
$201$	−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
$205$	−1.48764	−	5.44982i	−0.103901	−	0.380632i
$206$	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
$210$	0.276758	−	0.307321i	0.0190981	−	0.0212071i
$211$	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
$215$	11.7984	+	0.225631i	0.804646	+	0.0153879i
$216$	−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
$220$	5.17612	−	7.72533i	0.348974	−	0.520842i
$221$	−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	−0.851635	−	0.524135i	$-0.824389\pi$
$223$	−0.314846	+	0.489911i	−0.0210837	+	0.0328068i	0.830552	+	0.556941i	$0.188025\pi$
$224$	0.177463	−	0.0521077i	0.0118572	−	0.00348159i
$225$	4.99634	+	0.191168i	0.333090	+	0.0127445i
$226$	−4.18342	−	1.22836i	−0.278277	−	0.0817096i
$227$	12.8057	−	5.84818i	0.849946	−	0.388158i	0.0576817	−	0.998335i	$-0.481629\pi$
$227$	12.8057	−	5.84818i	0.849946	−	0.388158i	0.792265	+	0.610177i	$0.208902\pi$
$228$	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	$0.299110\pi$
$230$	−8.82425	−	6.09366i	−0.581854	−	0.401804i
$231$	0.769166			0.0506074
$232$	−4.85673	−	0.698293i	−0.318860	−	0.0458452i
$233$	−22.0576	+	10.0734i	−1.44504	+	0.659927i	−0.974896	−	0.222662i	$-0.928525\pi$
$233$	−22.0576	+	10.0734i	−1.44504	+	0.659927i	−0.470144	+	0.882590i	$0.655798\pi$
$234$	5.47652	+	1.60805i	0.358011	+	0.105122i
$235$	2.36271	−	4.92231i	0.154126	−	0.321096i
$236$	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	$0.287913\pi$
$240$	1.85764	+	1.24466i	0.119910	+	0.0803422i
$241$	−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
$245$	−0.297817	+	15.5731i	−0.0190269	+	0.994931i
$246$	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
$250$	−0.954034	−	11.1396i	−0.0603384	−	0.704528i
$251$	−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
$255$	−3.73703	−	13.6903i	−0.234022	−	0.857317i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	2.48459	−	8.46173i	0.154984	−	0.527828i	−0.844991	−	0.534780i	$-0.820395\pi$
$257$	2.48459	−	8.46173i	0.154984	−	0.527828i	0.999976	+	0.00695146i	$0.00221274\pi$
$258$	−3.98838	+	3.45595i	−0.248306	+	0.215158i
$259$	−1.10839	+	0.325453i	−0.0688721	+	0.0202227i
$260$	2.05756	−	12.5959i	0.127604	−	0.781165i
$261$	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	0.999831	−	0.0183814i	$-0.00585131\pi$
$263$	9.20762	+	14.3273i	0.567766	+	0.883461i	−0.432065	+	0.901842i	$0.642215\pi$
$264$	0.591841	+	4.11635i	0.0364253	+	0.253344i
$265$	−23.4572	+	14.4488i	−1.44096	+	0.887586i
$266$	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	$0.517735\pi$
$270$	−1.71760	+	1.43173i	−0.104530	+	0.0871325i
$271$	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	$-0.912309\pi$
$277$		−	9.05454i		−	0.544035i	0.962292	−	0.272017i	$-0.0876908\pi$
$278$	20.1256	+	2.89362i	1.20705	+	0.173548i
$279$	2.03747	+	4.46145i	0.121980	+	0.267100i
$280$	0.410412	−	0.0510194i	0.0245268	−	0.00304899i
$281$	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	−0.473813	−	0.880626i	$-0.657123\pi$
$283$	8.81608	−	13.7181i	0.524062	−	0.815456i	0.997874	+	0.0651699i	$0.0207589\pi$
$284$	2.83208	−	6.20138i	0.168053	−	0.367984i
$285$	4.58058	+	1.44067i	0.271330	+	0.0853378i
$286$	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
$290$	−10.4662	−	3.29179i	−0.614597	−	0.193301i
$291$	−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	$0.102438\pi$
$293$	5.50485	+	18.7478i	0.321597	+	1.09526i	−0.627065	+	0.778967i	$0.715744\pi$
$294$	−4.56162	−	5.26439i	−0.266039	−	0.307026i
$295$	24.1068	−	2.99678i	1.40355	−	0.174479i
$296$	−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
$305$	−20.7850	+	17.3257i	−1.19015	+	0.992069i
$306$	5.33899	+	3.43116i	0.305210	+	0.196146i
$307$	22.1282	+	10.1056i	1.26292	+	0.576757i	0.930472	−	0.366364i	$-0.119398\pi$
$307$	22.1282	+	10.1056i	1.26292	+	0.576757i	0.332450	+	0.943121i	$0.392125\pi$
$308$	0.581297	+	0.503697i	0.0331225	+	0.0287008i
$309$	−12.9015	+	8.29129i	−0.733941	+	0.471675i
$310$	9.33786	−	5.75181i	0.530355	−	0.326681i
$311$	−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	0.881886	−	0.471463i	$-0.156274\pi$
$313$	9.56643	+	8.28936i	0.540727	+	0.468542i	−0.341159	+	0.940006i	$0.610819\pi$
$314$	0.543658	−	1.19044i	0.0306804	−	0.0671807i
$315$	−0.0666737	+	0.408161i	−0.00375664	+	0.0229973i
$316$	15.7622	−	4.62820i	0.886693	−	0.260357i
$317$	4.65999	−	4.03790i	0.261731	−	0.226791i	−0.514103	−	0.857729i	$-0.671875\pi$
$317$	4.65999	−	4.03790i	0.261731	−	0.226791i	0.775834	+	0.630937i	$0.217330\pi$
$318$	3.47117	−	11.8217i	0.194653	−	0.662928i
$319$	−8.47666	−	18.5613i	−0.474602	−	1.03923i
$320$	0.588836	+	2.15714i	0.0329169	+	0.120588i
$321$	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
$325$	9.08131	−	27.0552i	0.503741	−	1.50075i
$326$	−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
$330$	−0.177801	+	9.29738i	−0.00978764	+	0.511804i
$331$	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
$335$	−16.7407	−	11.2166i	−0.914642	−	0.612828i
$336$	−0.121120	+	0.139779i	−0.00660761	+	0.00762559i
$337$	11.5701	+	5.28387i	0.630262	+	0.287831i	0.704820	−	0.709386i	$-0.251028\pi$
$337$	11.5701	+	5.28387i	0.630262	+	0.287831i	−0.0745587	+	0.997217i	$0.523755\pi$
$338$	10.5847	−	16.4702i	0.575733	−	0.895858i
$339$	4.18342	−	1.22836i	0.227212	−	0.0667156i
$340$	6.14095	−	12.7936i	0.333040	−	0.693832i
$341$	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
$345$	10.7179	+	0.355560i	0.577033	+	0.0191427i
$346$	3.38437			0.181945
$347$	−6.77192	−	0.973654i	−0.363535	−	0.0522685i	−0.0418731	−	0.999123i	$-0.513333\pi$
$347$	−6.77192	−	0.973654i	−0.363535	−	0.0522685i	−0.321662	+	0.946854i	$0.604242\pi$
$348$	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	$0.666948\pi$
$350$	0.924097	+	0.0353574i	0.0493951	+	0.00188993i
$351$	−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	0.528067	−	0.849202i	$-0.322917\pi$
$353$	4.36065	+	1.99144i	0.232094	+	0.105994i	−0.295974	+	0.955196i	$0.595644\pi$
$354$	−7.11431	+	8.21036i	−0.378122	+	0.436376i
$355$	8.48539	−	12.6644i	0.450358	−	0.672156i
$356$	−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	$0.0254966\pi$
$360$	−2.23566	−	0.0427543i	−0.117830	−	0.00225335i
$361$	−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
$365$	−21.8303	+	24.2410i	−1.14265	+	1.26883i
$366$	1.72218	−	11.9781i	0.0900200	−	0.626103i
$367$			11.7148i			0.611507i	0.952111	+	0.305753i	$0.0989083\pi$
$367$			11.7148i			0.611507i	−0.952111	+	0.305753i	$0.901092\pi$
$368$	3.99771	+	2.64921i	0.208395	+	0.138100i
$369$	−2.52640			−0.131519
$370$	−3.67773	−	13.4730i	−0.191196	−	0.700430i
$371$	−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	−0.464375	−	0.885639i	$-0.653721\pi$
$373$	6.68549	−	5.79301i	0.346162	−	0.299951i	0.810537	+	0.585688i	$0.199176\pi$
$374$	25.3238	−	7.43574i	1.30946	−	0.384493i
$375$	6.82509	+	8.85541i	0.352446	+	0.457291i
$376$	−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	$0.793798\pi$
$380$	2.51833	+	4.08843i	0.129188	+	0.209732i
$381$	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	0.111452	−	0.993770i	$-0.464450\pi$
$383$	−11.0887	−	5.06402i	−0.566604	−	0.258760i	−0.678056	+	0.735010i	$0.737177\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	1.10124	+	1.32112i	0.0561245	+	0.0673304i
$386$	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
$395$	36.4527	−	4.53154i	1.83414	−	0.228006i
$396$	−2.72335	−	3.14292i	−0.136854	−	0.157938i
$397$	1.35070	+	4.60006i	0.0677897	+	0.230870i	0.986419	−	0.164251i	$-0.0525207\pi$
$397$	1.35070	+	4.60006i	0.0677897	+	0.230870i	−0.918629	+	0.395121i	$0.870703\pi$
$398$	−1.98460	+	3.08810i	−0.0994789	+	0.154792i
$399$	−0.164993	+	0.361285i	−0.00825999	+	0.0180869i
$400$	0.521832	+	4.97269i	0.0260916	+	0.248635i
$401$	−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
$405$	0.670880	−	2.13305i	0.0333363	−	0.105992i
$406$	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	$0.453526\pi$
$410$	0.696904	+	5.60606i	0.0344176	+	0.276863i
$411$	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	$0.851505\pi$
$420$	−0.317677	+	0.264806i	−0.0155011	+	0.0129212i
$421$	−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
$425$	18.1639	−	26.0195i	0.881079	−	1.26213i
$426$	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
$430$	−11.6462	−	1.90243i	−0.561631	−	0.0917431i
$431$	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	$-0.794341\pi$
$433$	4.13586	−	14.0854i	0.198757	−	0.676903i	0.997196	−	0.0748281i	$-0.0238408\pi$
$434$	0.376840	+	0.825165i	0.0180889	+	0.0396092i
$435$	10.5844	−	2.88923i	0.507484	−	0.138528i
$436$	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	$0.801835\pi$
$440$	−6.22286	+	6.91006i	−0.296663	+	0.329424i
$441$	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	$-0.890744\pi$
$443$	−6.97586	−	23.7576i	−0.331433	−	1.12876i	0.610237	−	0.792219i	$-0.291074\pi$
$444$	5.25428	+	3.37672i	0.249357	+	0.160252i
$445$	0.751292	−	39.2857i	0.0356146	−	1.86232i
$446$	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	$0.727604\pi$
$450$	−4.91828	−	0.900276i	−0.231850	−	0.0424394i
$451$	−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
$455$	2.12809	+	1.02148i	0.0997664	+	0.0478879i
$456$	−2.06044	−	0.605000i	−0.0964890	−	0.0283317i
$457$	1.56167	−	0.713192i	0.0730520	−	0.0333617i	−0.378554	−	0.925579i	$-0.623579\pi$
$457$	1.56167	−	0.713192i	0.0730520	−	0.0333617i	0.451606	+	0.892217i	$0.350851\pi$
$458$	−17.6762	−	2.54146i	−0.825956	−	0.118755i
$459$	−6.34647			−0.296228
$460$	7.86721	+	7.28745i	0.366811	+	0.339779i
$461$	−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	−0.276525	−	0.961007i	$-0.589183\pi$
$463$	5.78109	−	2.64014i	0.268670	−	0.122698i	0.545195	+	0.838309i	$0.316456\pi$
$464$	4.70792	+	1.38237i	0.218560	+	0.0641750i
$465$	−4.74584	+	9.88716i	−0.220083	+	0.458506i
$466$	23.2666	−	6.83170i	1.07781	−	0.316473i
$467$	−11.6970	+	18.2009i	−0.541274	+	0.842239i	−0.998899	−	0.0469063i	$-0.985064\pi$
$467$	−11.6970	+	18.2009i	−0.541274	+	0.842239i	0.457625	+	0.889145i	$0.348700\pi$
$468$	−5.19193	−	2.37107i	−0.239997	−	0.109603i
$469$	1.09151	−	1.25966i	0.0504011	−	0.0581659i
$470$	−3.03918	+	4.53596i	−0.140187	+	0.209228i
$471$	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
$475$	4.08369	+	9.93024i	0.187372	+	0.455631i
$476$	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	$0.583479\pi$
$480$	−1.66160	−	1.49636i	−0.0758413	−	0.0682990i
$481$	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
$485$	−3.88048	+	1.05926i	−0.176204	+	0.0480983i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	−7.17898	+	24.4493i	−0.325310	+	1.10791i	0.620775	+	0.783989i	$0.286818\pi$
$487$	−7.17898	+	24.4493i	−0.325310	+	1.10791i	−0.946086	+	0.323917i	$0.895000\pi$
$488$	9.14550	−	7.92462i	0.413997	−	0.358731i
$489$	10.5201	−	3.08898i	0.475735	−	0.139689i
$490$	2.51107	−	15.3722i	0.113439	−	0.694447i
$491$	−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
$495$	−4.87697	−	7.91758i	−0.219203	−	0.355869i
$496$	−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	$0.880489\pi$
$500$	−0.641002	+	11.1619i	−0.0286665	+	0.499178i
$501$	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	0.0991757	−	0.995070i	$-0.468379\pi$
$503$	20.5470	−	9.38350i	0.916146	−	0.418390i	0.816970	+	0.576680i	$0.195652\pi$
$504$	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	$0.998259\pi$
$510$	1.75066	+	14.0827i	0.0775207	+	0.623594i
$511$	−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
$515$	−32.7126	−	10.2887i	−1.44149	−	0.453372i
$516$	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
$520$	−3.82920	+	12.1749i	−0.167922	+	0.533904i
$521$	−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	0.986612	−	0.163082i	$-0.0521437\pi$
$523$	1.56545	+	5.33142i	0.0684522	+	0.233127i	−0.918160	+	0.396209i	$0.870325\pi$
$524$	−11.6094	−	13.3980i	−0.507160	−	0.585294i
$525$	−0.796516	+	0.469860i	−0.0347628	+	0.0205064i
$526$	−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
$535$	17.3806	+	20.8509i	0.751430	+	0.901462i
$536$	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
$540$	1.90387	−	1.17272i	0.0819296	−	0.0504659i
$541$	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
$545$	4.50171	+	0.735360i	0.192832	+	0.0314994i
$546$	−1.01291	+	0.297417i	−0.0433485	+	0.0127283i
$547$	−17.3837	+	15.0630i	−0.743272	+	0.644049i	−0.941849	−	0.336037i	$-0.890913\pi$
$547$	−17.3837	+	15.0630i	−0.743272	+	0.644049i	0.198577	+	0.980085i	$0.436368\pi$
$548$	−4.33101	+	14.7501i	−0.185012	+	0.630091i
$549$	5.02703	+	11.0077i	0.214549	+	0.469796i
$550$	−16.2237	+	13.0060i	−0.691782	+	0.554577i
$551$	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
$555$	10.3780	+	9.34590i	0.440521	+	0.396712i
$556$	−19.5089	−	5.72834i	−0.827363	−	0.242936i
$557$	−32.8176	+	28.4366i	−1.39053	+	1.20490i	−0.438560	+	0.898702i	$0.644511\pi$
$557$	−32.8176	+	28.4366i	−1.39053	+	1.20490i	−0.951968	+	0.306197i	$0.900943\pi$
$558$	−1.38181	−	4.70600i	−0.0584965	−	0.199221i
$559$	−25.3401	−	16.2851i	−1.07177	−	0.688786i
$560$	−0.413496	−	0.00790760i	−0.0174734	−	0.000334157i
$561$	−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	−0.321734	−	0.946830i	$-0.604266\pi$
$563$	−8.62933	+	1.24071i	−0.363683	+	0.0522897i	−0.0419488	+	0.999120i	$0.513357\pi$
$564$	−0.347502	−	2.41693i	−0.0146325	−	0.101771i
$565$	8.09938	+	5.42674i	0.340744	+	0.228305i
$566$	−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	$0.333213\pi$
$570$	−4.32893	−	2.07789i	−0.181319	−	0.0870331i
$571$	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
$575$	14.7345	+	18.9181i	0.614471	+	0.788940i
$576$	1.00000			0.0416667
$577$	−18.7407	−	2.69451i	−0.780187	−	0.112174i	−0.259297	−	0.965798i	$-0.583491\pi$
$577$	−18.7407	−	2.69451i	−0.780187	−	0.112174i	−0.520890	+	0.853624i	$0.674400\pi$
$578$	21.1741	−	9.66990i	0.880728	−	0.402215i
$579$	−20.5259	−	6.02695i	−0.853028	−	0.250472i
$580$	9.89121	+	4.74779i	0.410710	+	0.197141i
$581$	−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
$585$	−10.6029	−	7.10415i	−0.438376	−	0.293721i
$586$	−2.78073	−	19.3404i	−0.114871	−	0.798944i
$587$	−39.3061	+	5.65137i	−1.62234	+	0.233257i	−0.892725	−	0.450603i	$-0.851209\pi$
$587$	−39.3061	+	5.65137i	−1.62234	+	0.233257i	−0.729614	+	0.683860i	$0.760300\pi$
$588$	3.76599	+	5.86000i	0.155307	+	0.241662i
$589$	−6.89727	+	7.95988i	−0.284197	+	0.327981i
$590$	−24.2879	−	0.464477i	−0.999916	−	0.0191222i
$591$	−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	−0.640309	−	0.768117i	$-0.721194\pi$
$593$	0.702890	−	0.609058i	0.0288643	−	0.0250110i	0.669173	+	0.743106i	$0.266648\pi$
$594$	3.99022	+	1.17163i	0.163721	+	0.0480727i
$595$	1.95040	+	1.75644i	0.0799587	+	0.0720069i
$596$	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	$0.518196\pi$
$600$	−3.12743	−	3.90117i	−0.127677	−	0.159265i
$601$	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
$605$	−13.8910	−	2.26912i	−0.564750	−	0.0922527i
$606$	5.13302	−	11.2398i	0.208515	−	0.456584i
$607$	−0.220457	−	0.191027i	−0.00894807	−	0.00775354i	0.650375	−	0.759613i	$-0.274612\pi$
$607$	−0.220457	−	0.191027i	−0.00894807	−	0.00775354i	−0.659323	+	0.751860i	$0.729157\pi$
$608$	−1.16099	−	1.80653i	−0.0470842	−	0.0732645i
$609$	0.129153	+	0.898276i	0.00523352	+	0.0364000i
$610$	23.0392	−	14.1914i	0.932829	−	0.574592i
$611$	−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	0.762836	−	0.646591i	$-0.223806\pi$
$613$	19.1566	+	8.74852i	0.773727	+	0.353349i	0.0108905	+	0.999941i	$0.496533\pi$
$614$	−20.4648	−	13.1519i	−0.825890	−	0.530768i
$615$	−3.61714	−	4.33934i	−0.145857	−	0.174979i
$616$	−0.503697	−	0.581297i	−0.0202945	−	0.0234211i
$617$	0.289794	−	0.986949i	0.0116667	−	0.0397331i	−0.953454	−	0.301539i	$-0.902500\pi$
$617$	0.289794	−	0.986949i	0.0116667	−	0.0397331i	0.965121	+	0.261806i	$0.0843179\pi$
$618$	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
$625$	−5.43831	+	24.4013i	−0.217532	+	0.976053i
$626$	−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
$630$	0.124082	−	0.394518i	0.00494356	−	0.0157180i
$631$	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
$635$	8.22079	+	2.58557i	0.326232	+	0.102605i
$636$	−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
$640$	−0.275848	−	2.21899i	−0.0109039	−	0.0877132i
$641$	−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	$0.0446042\pi$
$643$			7.08335i			0.279340i	−0.990198	+	0.139670i	$0.955396\pi$
$644$	−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	$-0.215721\pi$
$647$	44.8445	−	20.4798i	1.76302	−	0.805144i	0.984006	−	0.178135i	$-0.0570064\pi$
$648$	−0.281733	+	0.959493i	−0.0110675	+	0.0376924i
$649$	−29.5861	−	34.1442i	−1.16136	−	1.34028i
$650$	−12.8392	+	25.4874i	−0.503596	+	0.999697i
$651$	−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	0.288981	−	0.957335i	$-0.406684\pi$
$653$	−15.7791	−	13.6727i	−0.617484	−	0.535053i	−0.906464	+	0.422282i	$0.861229\pi$
$654$	−1.71608	+	1.10286i	−0.0671041	+	0.0431252i
$655$	−20.7901	−	33.7520i	−0.812336	−	1.31880i
$656$	−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	$0.907092\pi$
$660$	1.49915	−	9.17745i	0.0583542	−	0.357232i
$661$	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
$665$	−0.856768	+	0.233872i	−0.0332240	+	0.00906916i
$666$	−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
$670$	14.9740	+	13.4849i	0.578497	+	0.520966i
$671$	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	0.934204	−	0.356740i	$-0.116112\pi$
$673$	−1.15615	−	3.93749i	−0.0445664	−	0.151779i	−0.978770	+	0.204960i	$0.934293\pi$
$674$	−10.7003	−	6.87668i	−0.412161	−	0.264880i
$675$	4.62425	−	1.90166i	0.177987	−	0.0731951i
$676$	−12.8209	+	14.7961i	−0.493113	+	0.569083i
$677$	17.4042	+	27.0814i	0.668896	+	1.04082i	0.995417	+	0.0956330i	$0.0304875\pi$
$677$	17.4042	+	27.0814i	0.668896	+	1.04082i	−0.326520	+	0.945190i	$0.605876\pi$
$678$	−4.31566	+	0.620498i	−0.165742	+	0.0238301i
$679$	−0.0473502	−	0.329328i	−0.00181713	−	0.0126384i
$680$	−7.89917	+	11.7895i	−0.302919	+	0.452105i
$681$	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	−0.740759	−	0.671770i	$-0.765534\pi$
$683$	4.65261	−	7.23960i	0.178027	−	0.277016i	0.918786	+	0.394755i	$0.129171\pi$
$684$	2.06044	−	0.605000i	0.0787830	−	0.0231328i
$685$	−14.8749	+	30.9894i	−0.568343	+	1.18405i
$686$	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
$690$	−10.5582	−	1.87726i	−0.401944	−	0.0714660i
$691$	−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
$695$	−40.9877	−	19.6741i	−1.55475	−	0.746282i
$696$	−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
$700$	−0.909659	−	0.166510i	−0.0343819	−	0.00629350i
$701$	−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
$705$	0.104397	−	5.45900i	0.00393181	−	0.205598i
$706$	−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	$0.380441\pi$
$710$	−10.2014	+	11.3279i	−0.382850	+	0.425128i
$711$	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
$715$	−51.2032	+	13.9769i	−1.91489	+	0.522708i
$716$	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	$0.271138\pi$
$720$	2.20682	+	0.360487i	0.0822433	+	0.0134345i
$721$	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
$725$	20.1166	+	14.0431i	0.747111	+	0.521549i
$726$	5.29535	−	3.40311i	0.196529	−	0.126301i
$727$	−13.3300	−	11.5505i	−0.494384	−	0.428386i	0.371649	−	0.928373i	$-0.378792\pi$
$727$	−13.3300	−	11.5505i	−0.494384	−	0.428386i	−0.866033	+	0.499988i	$0.833338\pi$
$728$	−0.960271	−	0.438541i	−0.0355900	−	0.0162534i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	25.0580	−	20.8875i	0.927437	−	0.773082i
$731$	−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	0.188021	−	0.982165i	$-0.439793\pi$
$733$	28.5202	−	13.0248i	1.05342	−	0.481080i	0.865398	+	0.501085i	$0.167065\pi$
$734$	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	$0.871336\pi$
$740$	1.72289	+	13.8593i	0.0633345	+	0.509478i
$741$	−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	$-0.551972\pi$
$743$	21.8748	−	34.0379i	0.802510	−	1.24873i	0.965060	−	0.262029i	$-0.0843917\pi$
$744$	2.03747	−	4.46145i	0.0746974	−	0.163565i
$745$	2.76786	−	8.80036i	0.101407	−	0.322420i
$746$	−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
$750$	−5.49536	−	9.73658i	−0.200662	−	0.355530i
$751$	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
$755$	12.8159	−	1.59318i	0.466419	−	0.0579818i
$756$	0.0768329	+	0.168241i	0.00279439	+	0.00611885i
$757$	16.6307	+	2.39113i	0.604453	+	0.0869072i	0.437745	−	0.899099i	$-0.355777\pi$
$757$	16.6307	+	2.39113i	0.604453	+	0.0869072i	0.166708	+	0.986006i	$0.446686\pi$
$758$		−	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
$765$	−9.08646	−	10.9007i	−0.328522	−	0.394115i
$766$	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	$0.293421\pi$
$770$	−0.902018	−	1.46439i	−0.0325065	−	0.0527731i
$771$	−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	0.767280	−	0.641312i	$-0.221610\pi$
$773$	6.71972	+	5.82267i	0.241691	+	0.209427i	−0.525589	+	0.850739i	$0.676155\pi$
$774$	−2.19230	+	4.80047i	−0.0788007	+	0.172549i
$775$	−23.7769	+	6.00434i	−0.854093	+	0.215682i
$776$	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
$780$	−3.36091	−	12.3124i	−0.120340	−	0.440854i
$781$	−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
$785$	−1.95830	+	2.17455i	−0.0698946	+	0.0776131i
$786$	17.0100	+	4.99458i	0.606725	+	0.178151i
$787$	−4.13462	+	3.58267i	−0.147383	+	0.127708i	−0.725432	−	0.688294i	$-0.758360\pi$
$787$	−4.13462	+	3.58267i	−0.147383	+	0.127708i	0.578048	+	0.816002i	$0.303814\pi$
$788$	−0.980854	−	3.34048i	−0.0349415	−	0.119000i
$789$	14.3273	+	9.20762i	0.510066	+	0.327800i
$790$	−36.7266	−	0.702352i	−1.30667	−	0.0249886i
$791$	−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
$795$	−15.3351	+	22.8876i	−0.543881	+	0.811740i
$796$	2.40388	−	2.77423i	0.0852033	−	0.0983298i
$797$	14.2875	+	6.52488i	0.506089	+	0.231123i	0.652062	−	0.758165i	$-0.273904\pi$
$797$	14.2875	+	6.52488i	0.506089	+	0.231123i	−0.145973	+	0.989289i	$0.546631\pi$
$798$	0.214730	−	0.334126i	0.00760136	−	0.0118279i
$799$	−14.8690	+	4.36593i	−0.526027	+	0.154455i
$800$	0.191168	−	4.99634i	0.00675881	−	0.176647i
$801$	−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
$805$	−1.70319	+	1.01640i	−0.0600297	+	0.0358235i
$806$	−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	$0.470194\pi$
$810$	−0.967617	+	2.01587i	−0.0339986	+	0.0708303i
$811$	−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
$815$	20.3676	+	13.6467i	0.713446	+	0.478023i
$816$	−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
$820$	0.108015	−	5.64818i	0.00377203	−	0.197243i
$821$	−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	−0.739757	−	0.672874i	$-0.765060\pi$
$823$	−5.13546	+	4.44990i	−0.179011	+	0.155114i	0.560746	+	0.827988i	$0.310514\pi$
$824$	14.7148	+	4.32066i	0.512615	+	0.150517i
$825$	6.61669	−	19.7125i	0.230364	−	0.686302i
$826$	0.285956	−	1.98887i	0.00994969	−	0.0692016i
$827$		−	52.5877i		−	1.82865i	−0.404976	−	0.914327i	$-0.632720\pi$
$827$		−	52.5877i		−	1.82865i	0.404976	−	0.914327i	$-0.367280\pi$
$828$	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	$0.429264\pi$
$830$	−0.332093	−	1.21659i	−0.0115271	−	0.0422286i
$831$	−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
$835$	−1.49559	+	9.15565i	−0.0517569	+	0.316844i
$836$	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	$-0.270690\pi$
$840$	0.352130	−	0.216900i	0.0121496	−	0.00748377i
$841$	−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
$845$	−33.6273	+	28.0306i	−1.15681	+	0.964283i
$846$	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	−0.716212	−	0.697883i	$-0.754126\pi$
$853$	−46.7307	−	6.71886i	−1.60003	−	0.230049i	−0.883817	+	0.467833i	$0.845035\pi$
$854$	0.929773	+	2.03592i	0.0318162	+	0.0696677i
$855$	4.76512	−	0.592364i	0.162964	−	0.0202584i
$856$	−7.94972	−	9.17447i	−0.271716	−	0.313577i
$857$	−10.8893	−	37.0856i	−0.371972	−	1.26682i	−0.906693	−	0.421791i	$-0.861402\pi$
$857$	−10.8893	−	37.0856i	−0.371972	−	1.26682i	0.534721	−	0.845029i	$-0.320417\pi$
$858$	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	$0.878248\pi$
$860$	11.2569	+	3.54049i	0.383858	+	0.120730i
$861$	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	−0.0532120	−	0.998583i	$-0.516946\pi$
$863$	5.20161	−	0.747879i	0.177065	−	0.0254581i	0.230277	+	0.973125i	$0.426037\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	−7.21905	−	2.27051i	−0.245455	−	0.0771996i
$866$	−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
$870$	−10.8879	+	1.35350i	−0.369133	+	0.0458879i
$871$	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	−0.624708	−	0.780858i	$-0.714782\pi$
$877$	−13.1390	+	6.00037i	−0.443672	+	0.202618i	0.181036	+	0.983476i	$0.442055\pi$
$878$	8.17904	−	27.8553i	0.276029	−	0.940069i
$879$	12.7955	+	14.7668i	0.431582	+	0.498072i
$880$	7.14293	−	5.95412i	0.240788	−	0.200713i
$881$	−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	0.331756	−	0.943365i	$-0.392359\pi$
$883$	−16.4859	−	14.2851i	−0.554793	−	0.480731i	−0.886549	+	0.462634i	$0.846904\pi$
$884$	−30.4735	+	19.5841i	−1.02493	+	0.658685i
$885$	20.6834	−	12.7403i	0.695264	−	0.428260i
$886$	3.52380	+	24.5085i	0.118384	+	0.823381i
$887$	4.47969	+	6.97053i	0.150413	+	0.234047i	0.908281	−	0.418361i	$-0.137395\pi$
$887$	4.47969	+	6.97053i	0.150413	+	0.234047i	−0.757868	+	0.652408i	$0.773759\pi$
$888$	−4.72024	−	4.09011i	−0.158401	−	0.137255i
$889$	−0.296114	+	0.648400i	−0.00993135	+	0.0217466i
$890$	−6.33458	+	38.7789i	−0.212336	+	1.29987i
$891$	−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
$895$	8.05122	+	29.4949i	0.269122	+	0.985905i
$896$	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
$900$	4.74010	+	1.59106i	0.158003	+	0.0530352i
$901$	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
$905$	−0.552511	+	28.8913i	−0.0183661	+	0.960378i
$906$	−3.78219	+	4.36488i	−0.125655	+	0.145014i
$907$	23.0359	+	35.8446i	0.764895	+	1.19020i	0.977060	+	0.212966i	$0.0683123\pi$
$907$	23.0359	+	35.8446i	0.764895	+	1.19020i	−0.212165	+	0.977234i	$0.568051\pi$
$908$	13.9346	−	2.00350i	0.462437	−	0.0664884i
$909$	1.75850	+	12.2306i	0.0583256	+	0.405664i
$910$	−1.96106	−	1.31395i	−0.0650084	−	0.0435569i
$911$	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
$915$	−11.7094	+	24.3945i	−0.387099	+	0.806456i
$916$	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	$0.320923\pi$
$920$	−6.75002	−	8.33290i	−0.222542	−	0.274727i
$921$	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
$925$	−1.19399	+	31.2060i	−0.0392582	+	1.02605i
$926$	−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	$0.331470\pi$
$930$	6.10463	−	9.11112i	0.200179	−	0.298765i
$931$	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
$935$	−59.0056	−	1.12841i	−1.92969	−	0.0369030i
$936$	4.80164	+	3.08583i	0.156947	+	0.100863i
$937$	−0.0467759	−	0.159304i	−0.00152810	−	0.00520423i	0.958725	−	0.284334i	$-0.0917723\pi$
$937$	−0.0467759	−	0.159304i	−0.00152810	−	0.00520423i	−0.960253	+	0.279129i	$0.909954\pi$
$938$	−1.25966	+	1.09151i	−0.0411295	+	0.0356389i
$939$	12.1455	+	3.56623i	0.396352	+	0.116379i
$940$	3.65378	−	4.05727i	0.119173	−	0.132334i
$941$	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
$945$	0.108908	+	0.398974i	0.00354277	+	0.0129786i
$946$	9.11708	+	19.9636i	0.296422	+	0.649073i
$947$	9.27106	−	31.5743i	0.301269	−	1.02603i	−0.660194	−	0.751095i	$-0.729526\pi$
$947$	9.27106	−	31.5743i	0.301269	−	1.02603i	0.961463	−	0.274933i	$-0.0886557\pi$
$948$	12.4152	−	10.7578i	0.403226	−	0.349397i
$949$	79.8968	−	23.4598i	2.59356	−	0.761538i
$950$	−2.62890	−	10.4103i	−0.0852927	−	0.337756i
$951$	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	0.885606	−	0.464438i	$-0.153743\pi$
$953$	2.94027	+	4.57515i	0.0952447	+	0.148204i	−0.790361	+	0.612641i	$0.790107\pi$
$954$	−1.75343	−	12.1954i	−0.0567694	−	0.394840i
$955$	8.42068	+	13.6707i	0.272487	+	0.442373i
$956$	−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
$960$	1.43173	+	1.71760i	0.0462090	+	0.0554352i
$961$	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	$-0.930979\pi$
$967$		−	13.3804i		−	0.430284i	0.976583	−	0.215142i	$-0.0690214\pi$
$968$	6.23052	+	0.895814i	0.200256	+	0.0287925i
$969$	−5.66152	−	12.3970i	−0.181874	−	0.398249i
$970$	3.99173	−	0.496223i	0.128167	−	0.0159328i
$971$	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
$975$	−2.97847	−	28.3828i	−0.0953874	−	0.908976i
$976$	−10.1802	+	6.54242i	−0.325860	+	0.209418i
$977$	−27.8093	+	3.99838i	−0.889699	+	0.127919i	−0.571982	−	0.820266i	$-0.693825\pi$
$977$	−27.8093	+	3.99838i	−0.889699	+	0.127919i	−0.317717	+	0.948185i	$0.602916\pi$
$978$	−10.8526	+	1.56037i	−0.347029	+	0.0498952i
$979$	−61.4767	+	39.5087i	−1.96481	+	1.26270i
$980$	−4.67321	+	14.8584i	−0.149280	+	0.474635i
$981$	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	$-0.932888\pi$
$983$	−8.41437	−	28.6567i	−0.268377	−	0.914007i	0.709479	−	0.704727i	$-0.248930\pi$
$984$	1.65444	+	1.90933i	0.0527417	+	0.0608671i
$985$	−0.960369	−	7.72543i	−0.0305999	−	0.246153i
$986$	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
$995$	6.30500	−	5.25565i	0.199882	−	0.166615i
$996$	0.474453	+	0.304912i	0.0150336	+	0.00966152i
$997$	9.49509	+	4.33626i	0.300712	+	0.137331i	0.560057	−	0.828454i	$-0.310779\pi$
$997$	9.49509	+	4.33626i	0.300712	+	0.137331i	−0.259344	+	0.965785i	$0.583507\pi$
$998$	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.169.6	yes	120
5.4	even	2	inner	690.2.r.b.169.10	yes	120
23.3	even	11	inner	690.2.r.b.49.10	yes	120
115.49	even	22	inner	690.2.r.b.49.6	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.b.49.6	✓	120	115.49	even	22	inner
690.2.r.b.49.10	yes	120	23.3	even	11	inner
690.2.r.b.169.6	yes	120	1.1	even	1	trivial
690.2.r.b.169.10	yes	120	5.4	even	2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989821 - 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(2.01587 + 0.967617i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(-0.0999940 + 0.155594i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.989821 - 0.142315i) q^{2} +(0.909632 - 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(2.01587 + 0.967617i) 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} +(-1.85764 - 1.24466i) 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} +(2.23566 + 0.0427543i) 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} +(1.66160 + 1.49636i) q^{20} +(-0.0263218 + 0.183072i) q^{21} +4.15868i q^{22} +(4.79536 + 0.0673348i) q^{23} -1.00000 q^{24} +(3.12743 + 3.90117i) 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} +(-2.20682 - 0.360487i) 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} +(-0.352130 + 0.216900i) 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} +(-1.43173 - 1.71760i) 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} +(-2.54041 - 4.30655i) 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} +(2.78997 - 8.87068i) 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} +(2.13305 + 0.670880i) 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} +(-1.57447 - 12.6654i) 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} +(4.46542 + 2.24945i) 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} +(1.17272 + 1.90387i) 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} +(2.28782 - 14.0055i) 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} +(-2.15714 + 0.588836i) q^{90} +1.05567 q^{91} +(4.58214 + 1.41562i) q^{92} +4.90467i q^{93} +(-0.347502 + 2.41693i) q^{94} +(3.56817 + 3.21332i) 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

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