LMFDB - Embedded newform 637.2.q.j.491.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.13
Character	$\chi$	$=$	637.491
Dual form			637.2.q.j.589.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81104 - 1.04560i) q^{2} +(-0.663994 - 1.15007i) q^{3} +(1.18657 - 2.05519i) q^{4} -3.48900i q^{5} +(-2.40503 - 1.38855i) q^{6} -0.780297i q^{8} +(0.618224 - 1.07080i) q^{9} +O(q^{10})$	\(q+(1.81104 - 1.04560i) q^{2} +(-0.663994 - 1.15007i) q^{3} +(1.18657 - 2.05519i) q^{4} -3.48900i q^{5} +(-2.40503 - 1.38855i) q^{6} -0.780297i q^{8} +(0.618224 - 1.07080i) q^{9} +(-3.64811 - 6.31871i) q^{10} +(-0.817625 + 0.472056i) q^{11} -3.15149 q^{12} +(3.60500 + 0.0632937i) q^{13} +(-4.01260 + 2.31668i) q^{15} +(1.55725 + 2.69724i) q^{16} +(-2.12944 + 3.68829i) q^{17} -2.58566i q^{18} +(-2.95654 - 1.70696i) q^{19} +(-7.17058 - 4.13993i) q^{20} +(-0.987165 + 1.70982i) q^{22} +(2.72995 + 4.72840i) q^{23} +(-0.897397 + 0.518112i) q^{24} -7.17315 q^{25} +(6.59496 - 3.65476i) q^{26} -5.62595 q^{27} +(-4.54098 - 7.86521i) q^{29} +(-4.84464 + 8.39117i) q^{30} +1.15555i q^{31} +(6.99200 + 4.03683i) q^{32} +(1.08580 + 0.626885i) q^{33} +8.90617i q^{34} +(-1.46713 - 2.54114i) q^{36} +(3.81050 - 2.19999i) q^{37} -7.13919 q^{38} +(-2.32090 - 4.18803i) q^{39} -2.72246 q^{40} +(8.09942 - 4.67620i) q^{41} +(3.84817 - 6.66522i) q^{43} +2.24050i q^{44} +(-3.73601 - 2.15699i) q^{45} +(9.88805 + 5.70887i) q^{46} +7.96288i q^{47} +(2.06801 - 3.58190i) q^{48} +(-12.9908 + 7.50025i) q^{50} +5.65573 q^{51} +(4.40765 - 7.33386i) q^{52} +7.50701 q^{53} +(-10.1888 + 5.88251i) q^{54} +(1.64701 + 2.85270i) q^{55} +4.53364i q^{57} +(-16.4478 - 9.49612i) q^{58} +(9.25339 + 5.34245i) q^{59} +10.9956i q^{60} +(-3.44103 + 5.96004i) q^{61} +(1.20824 + 2.09274i) q^{62} +10.6547 q^{64} +(0.220832 - 12.5778i) q^{65} +2.62189 q^{66} +(-6.42303 + 3.70834i) q^{67} +(5.05343 + 8.75280i) q^{68} +(3.62533 - 6.27926i) q^{69} +(-11.3759 - 6.56790i) q^{71} +(-0.835538 - 0.482398i) q^{72} +1.73195i q^{73} +(4.60063 - 7.96853i) q^{74} +(4.76293 + 8.24963i) q^{75} +(-7.01625 + 4.05083i) q^{76} +(-8.58225 - 5.15793i) q^{78} +12.2866 q^{79} +(9.41069 - 5.43326i) q^{80} +(1.88093 + 3.25786i) q^{81} +(9.77889 - 16.9375i) q^{82} +1.54011i q^{83} +(12.8685 + 7.42961i) q^{85} -16.0946i q^{86} +(-6.03037 + 10.4449i) q^{87} +(0.368344 + 0.637990i) q^{88} +(3.52562 - 2.03552i) q^{89} -9.02139 q^{90} +12.9570 q^{92} +(1.32896 - 0.767276i) q^{93} +(8.32600 + 14.4211i) q^{94} +(-5.95558 + 10.3154i) q^{95} -10.7217i q^{96} +(1.32503 + 0.765009i) q^{97} +1.16735i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 28 * q^9	$ 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.81104	−	1.04560i	1.28060	−	0.739352i	0.303638	−	0.952787i	$-0.401799\pi$
$2$	1.81104	−	1.04560i	1.28060	−	0.739352i	0.976957	+	0.213435i	$0.0684652\pi$
$3$	−0.663994	−	1.15007i	−0.383357	−	0.663994i	0.608183	−	0.793797i	$-0.291899\pi$
$3$	−0.663994	−	1.15007i	−0.383357	−	0.663994i	−0.991540	+	0.129803i	$0.958565\pi$
$4$	1.18657	−	2.05519i	0.593283	−	1.02760i
$5$		−	3.48900i		−	1.56033i	−0.625574	−	0.780165i	$-0.715135\pi$
$5$		−	3.48900i		−	1.56033i	0.625574	−	0.780165i	$-0.284865\pi$
$6$	−2.40503	−	1.38855i	−0.981851	−	0.566872i
$7$		0			0
$7$		0			0
$8$		−	0.780297i		−	0.275876i
$9$	0.618224	−	1.07080i	0.206075	−	0.356932i
$10$	−3.64811	−	6.31871i	−1.15363	−	1.99815i
$11$	−0.817625	+	0.472056i	−0.246523	+	0.142330i	−0.618171	−	0.786043i	$-0.712126\pi$
$11$	−0.817625	+	0.472056i	−0.246523	+	0.142330i	0.371648	+	0.928374i	$0.378793\pi$
$12$	−3.15149			−0.909757
$13$	3.60500	+	0.0632937i	0.999846	+	0.0175545i
$13$	3.60500	+	0.0632937i	0.999846	+	0.0175545i
$14$		0			0
$15$	−4.01260	+	2.31668i	−1.03605	+	0.598164i
$16$	1.55725	+	2.69724i	0.389313	+	0.674310i
$17$	−2.12944	+	3.68829i	−0.516464	+	0.894542i	0.483353	+	0.875425i	$0.339419\pi$
$17$	−2.12944	+	3.68829i	−0.516464	+	0.894542i	−0.999817	+	0.0191164i	$0.993915\pi$
$18$		−	2.58566i		−	0.609447i
$19$	−2.95654	−	1.70696i	−0.678276	−	0.391603i	0.120929	−	0.992661i	$-0.461413\pi$
$19$	−2.95654	−	1.70696i	−0.678276	−	0.391603i	−0.799205	+	0.601058i	$0.794746\pi$
$20$	−7.17058	−	4.13993i	−1.60339	−	0.925717i
$21$		0			0
$22$	−0.987165	+	1.70982i	−0.210464	+	0.364535i
$23$	2.72995	+	4.72840i	0.569233	+	0.985940i	0.996642	+	0.0818820i	$0.0260931\pi$
$23$	2.72995	+	4.72840i	0.569233	+	0.985940i	−0.427409	+	0.904058i	$0.640574\pi$
$24$	−0.897397	+	0.518112i	−0.183180	+	0.105759i
$25$	−7.17315			−1.43463
$26$	6.59496	−	3.65476i	1.29338	−	0.716758i
$27$	−5.62595			−1.08271
$28$		0			0
$29$	−4.54098	−	7.86521i	−0.843239	−	1.46053i	−0.887142	−	0.461497i	$-0.847313\pi$
$29$	−4.54098	−	7.86521i	−0.843239	−	1.46053i	0.0439029	−	0.999036i	$-0.486021\pi$
$30$	−4.84464	+	8.39117i	−0.884507	+	1.53201i
$31$			1.15555i			0.207542i	0.994601	+	0.103771i	$0.0330909\pi$
$31$			1.15555i			0.207542i	−0.994601	+	0.103771i	$0.966909\pi$
$32$	6.99200	+	4.03683i	1.23602	+	0.713618i
$33$	1.08580	+	0.626885i	0.189013	+	0.109127i
$34$			8.90617i			1.52739i
$35$		0			0
$36$	−1.46713	−	2.54114i	−0.244521	−	0.423523i
$37$	3.81050	−	2.19999i	0.626442	−	0.361677i	−0.152931	−	0.988237i	$-0.548871\pi$
$37$	3.81050	−	2.19999i	0.626442	−	0.361677i	0.779373	+	0.626560i	$0.215538\pi$
$38$	−7.13919			−1.15813
$39$	−2.32090	−	4.18803i	−0.371642	−	0.670621i
$40$	−2.72246			−0.430458
$41$	8.09942	−	4.67620i	1.26492	−	0.730300i	0.290895	−	0.956755i	$-0.406047\pi$
$41$	8.09942	−	4.67620i	1.26492	−	0.730300i	0.974022	+	0.226455i	$0.0727135\pi$
$42$		0			0
$43$	3.84817	−	6.66522i	0.586840	−	1.01644i	−0.407803	−	0.913070i	$-0.633705\pi$
$43$	3.84817	−	6.66522i	0.586840	−	1.01644i	0.994643	−	0.103367i	$-0.0329617\pi$
$44$			2.24050i			0.337769i
$45$	−3.73601	−	2.15699i	−0.556931	−	0.321544i
$46$	9.88805	+	5.70887i	1.45791	+	0.841727i
$47$			7.96288i			1.16150i	0.814080	+	0.580752i	$0.197242\pi$
$47$			7.96288i			1.16150i	−0.814080	+	0.580752i	$0.802758\pi$
$48$	2.06801	−	3.58190i	0.298492	−	0.517003i
$49$		0			0
$50$	−12.9908	+	7.50025i	−1.83718	+	1.06070i
$51$	5.65573			0.791961
$52$	4.40765	−	7.33386i	0.611231	−	1.01702i
$53$	7.50701			1.03117			0.515583	−	0.856839i	$-0.327575\pi$
$53$	7.50701			1.03117			0.515583	+	0.856839i	$0.327575\pi$
$54$	−10.1888	+	5.88251i	−1.38652	+	0.800508i
$55$	1.64701	+	2.85270i	0.222082	+	0.384658i
$56$		0			0
$57$			4.53364i			0.600495i
$58$	−16.4478	−	9.49612i	−2.15970	−	1.24690i
$59$	9.25339	+	5.34245i	1.20469	+	0.695527i	0.961594	−	0.274475i	$-0.0885041\pi$
$59$	9.25339	+	5.34245i	1.20469	+	0.695527i	0.243095	+	0.970003i	$0.421837\pi$
$60$			10.9956i			1.41952i
$61$	−3.44103	+	5.96004i	−0.440579	+	0.763105i	−0.997732	−	0.0673047i	$-0.978560\pi$
$61$	−3.44103	+	5.96004i	−0.440579	+	0.763105i	0.557154	+	0.830409i	$0.311893\pi$
$62$	1.20824	+	2.09274i	0.153447	+	0.265778i
$63$		0			0
$64$	10.6547			1.33183
$65$	0.220832	−	12.5778i	0.0273908	−	1.56009i
$66$	2.62189			0.322732
$67$	−6.42303	+	3.70834i	−0.784698	+	0.453046i	−0.838093	−	0.545528i	$-0.816329\pi$
$67$	−6.42303	+	3.70834i	−0.784698	+	0.453046i	0.0533944	+	0.998574i	$0.482996\pi$
$68$	5.05343	+	8.75280i	0.612819	+	1.06143i
$69$	3.62533	−	6.27926i	0.436439	−	0.755934i
$70$		0			0
$71$	−11.3759	−	6.56790i	−1.35008	−	0.779466i	−0.361816	−	0.932250i	$-0.617843\pi$
$71$	−11.3759	−	6.56790i	−1.35008	−	0.779466i	−0.988260	+	0.152783i	$0.951176\pi$
$72$	−0.835538	−	0.482398i	−0.0984691	−	0.0568511i
$73$			1.73195i			0.202710i	0.994850	+	0.101355i	$0.0323177\pi$
$73$			1.73195i			0.202710i	−0.994850	+	0.101355i	$0.967682\pi$
$74$	4.60063	−	7.96853i	0.534813	−	0.926323i
$75$	4.76293	+	8.24963i	0.549975	+	0.952585i
$76$	−7.01625	+	4.05083i	−0.804819	+	0.464663i
$77$		0			0
$78$	−8.58225	−	5.15793i	−0.971748	−	0.584020i
$79$	12.2866			1.38235			0.691177	−	0.722685i	$-0.257092\pi$
$79$	12.2866			1.38235			0.691177	+	0.722685i	$0.257092\pi$
$80$	9.41069	−	5.43326i	1.05215	−	0.607457i
$81$	1.88093	+	3.25786i	0.208992	+	0.361984i
$82$	9.77889	−	16.9375i	1.07990	−	1.87044i
$83$			1.54011i			0.169049i	0.996421	+	0.0845244i	$0.0269371\pi$
$83$			1.54011i			0.169049i	−0.996421	+	0.0845244i	$0.973063\pi$
$84$		0			0
$85$	12.8685	+	7.42961i	1.39578	+	0.805854i
$86$		−	16.0946i		−	1.73553i
$87$	−6.03037	+	10.4449i	−0.646523	+	1.11981i
$88$	0.368344	+	0.637990i	0.0392656	+	0.0680100i
$89$	3.52562	−	2.03552i	0.373715	−	0.215765i	−0.301365	−	0.953509i	$-0.597442\pi$
$89$	3.52562	−	2.03552i	0.373715	−	0.215765i	0.675080	+	0.737744i	$0.264109\pi$
$90$	−9.02139			−0.950938
$91$		0			0
$92$	12.9570			1.35087
$93$	1.32896	−	0.767276i	0.137807	−	0.0795628i
$94$	8.32600	+	14.4211i	0.858761	+	1.48742i
$95$	−5.95558	+	10.3154i	−0.611029	+	1.05833i
$96$		−	10.7217i		−	1.09428i
$97$	1.32503	+	0.765009i	0.134537	+	0.0776749i	0.565758	−	0.824571i	$-0.308584\pi$
$97$	1.32503	+	0.765009i	0.134537	+	0.0776749i	−0.431221	+	0.902246i	$0.641917\pi$
$98$		0			0
$99$			1.16735i			0.117323i
$100$	−8.51141	+	14.7422i	−0.851141	+	1.47422i
$101$	−8.12919	−	14.0802i	−0.808884	−	1.40103i	−0.913637	−	0.406531i	$-0.866738\pi$
$101$	−8.12919	−	14.0802i	−0.808884	−	1.40103i	0.104753	−	0.994498i	$-0.466595\pi$
$102$	10.2427	−	5.91364i	1.01418	−	0.585538i
$103$	7.99651			0.787919			0.393960	−	0.919128i	$-0.371105\pi$
$103$	7.99651			0.787919			0.393960	+	0.919128i	$0.371105\pi$
$104$	0.0493879	−	2.81297i	0.00484288	−	0.275834i
$105$		0			0
$106$	13.5955	−	7.84934i	1.32051	−	0.762395i
$107$	−8.03215	−	13.9121i	−0.776498	−	1.34493i	−0.933949	−	0.357406i	$-0.883661\pi$
$107$	−8.03215	−	13.9121i	−0.776498	−	1.34493i	0.157451	−	0.987527i	$-0.449672\pi$
$108$	−6.67557	+	11.5624i	−0.642357	+	1.11259i
$109$			6.18902i			0.592800i	0.955064	+	0.296400i	$0.0957862\pi$
$109$			6.18902i			0.592800i	−0.955064	+	0.296400i	$0.904214\pi$
$110$	5.96557	+	3.44422i	0.568795	+	0.328394i
$111$	−5.06030	−	2.92156i	−0.480302	−	0.277303i
$112$		0			0
$113$	−2.79511	+	4.84127i	−0.262942	+	0.455428i	−0.967022	−	0.254692i	$-0.918026\pi$
$113$	−2.79511	+	4.84127i	−0.262942	+	0.455428i	0.704081	+	0.710120i	$0.251359\pi$
$114$	4.74038	+	8.21057i	0.443977	+	0.768991i
$115$	16.4974	−	9.52479i	1.53839	−	0.888191i
$116$	−21.5527			−2.00112
$117$	2.29647	−	3.82108i	0.212309	−	0.353259i
$118$	22.3443			2.05696
$119$		0			0
$120$	1.80770	+	3.13102i	0.165019	+	0.285822i
$121$	−5.05433	+	8.75435i	−0.459484	+	0.795850i
$122$			14.3918i			1.30297i
$123$	−10.7559	−	6.20994i	−0.969830	−	0.559932i
$124$	2.37487	+	1.37113i	0.213270	+	0.123131i
$125$			7.58211i			0.678165i
$126$		0			0
$127$	7.63108	+	13.2174i	0.677149	+	1.17286i	0.975836	+	0.218505i	$0.0701179\pi$
$127$	7.63108	+	13.2174i	0.677149	+	1.17286i	−0.298687	+	0.954351i	$0.596549\pi$
$128$	5.31197	−	3.06687i	0.469516	−	0.271075i
$129$	−10.2206			−0.899878
$130$	−12.7515	−	23.0098i	−1.11838	−	2.01809i
$131$	−5.74043			−0.501543			−0.250772	−	0.968046i	$-0.580684\pi$
$131$	−5.74043			−0.501543			−0.250772	+	0.968046i	$0.580684\pi$
$132$	2.57674	−	1.48768i	0.224276	−	0.129486i
$133$		0			0
$134$	−7.75489	+	13.4319i	−0.669921	+	1.16034i
$135$			19.6290i			1.68939i
$136$	2.87796	+	1.66159i	0.246783	+	0.142480i
$137$	−4.47879	−	2.58583i	−0.382649	−	0.220923i	0.296321	−	0.955088i	$-0.404240\pi$
$137$	−4.47879	−	2.58583i	−0.382649	−	0.220923i	−0.678970	+	0.734166i	$0.737573\pi$
$138$		−	15.1626i		−	1.29073i
$139$	−6.55319	+	11.3505i	−0.555835	+	0.962734i	0.442003	+	0.897013i	$0.354268\pi$
$139$	−6.55319	+	11.3505i	−0.555835	+	0.962734i	−0.997838	+	0.0657206i	$0.979065\pi$
$140$		0			0
$141$	9.15788	−	5.28730i	0.771232	−	0.445271i
$142$	−27.4696			−2.30520
$143$	−2.97741	+	1.65001i	−0.248984	+	0.137981i
$144$	3.85092			0.320910
$145$	−27.4417	+	15.8435i	−2.27891	+	1.31573i
$146$	1.81093	+	3.13662i	0.149874	+	0.259589i
$147$		0			0
$148$		−	10.4417i		−	0.858306i
$149$	15.8588	+	9.15606i	1.29920	+	0.750094i	0.980266	−	0.197683i	$-0.0633417\pi$
$149$	15.8588	+	9.15606i	1.29920	+	0.750094i	0.318934	+	0.947777i	$0.396675\pi$
$150$	17.2517	+	9.96025i	1.40859	+	0.813251i
$151$			8.42351i			0.685495i	0.939427	+	0.342748i	$0.111358\pi$
$151$			8.42351i			0.685495i	−0.939427	+	0.342748i	$0.888642\pi$
$152$	−1.33193	+	2.30697i	−0.108034	+	0.187120i
$153$	2.63294	+	4.56038i	0.212860	+	0.368685i
$154$		0			0
$155$	4.03170			0.323834
$156$	−11.3611	−	0.199470i	−0.909617	−	0.0159703i
$157$	4.37902			0.349484			0.174742	−	0.984614i	$-0.444091\pi$
$157$	4.37902			0.349484			0.174742	+	0.984614i	$0.444091\pi$
$158$	22.2515	−	12.8469i	1.77024	−	1.02205i
$159$	−4.98461	−	8.63359i	−0.395305	−	0.684688i
$160$	14.0845	−	24.3951i	1.11348	−	1.92860i
$161$		0			0
$162$	6.81285	+	3.93340i	0.535268	+	0.309037i
$163$	8.19730	+	4.73271i	0.642062	+	0.370695i	0.785408	−	0.618978i	$-0.212453\pi$
$163$	8.19730	+	4.73271i	0.642062	+	0.370695i	−0.143346	+	0.989673i	$0.545786\pi$
$164$		−	22.1945i		−	1.73310i
$165$	2.18720	−	3.78835i	0.170274	−	0.294922i
$166$	1.61034	+	2.78919i	0.124987	+	0.216483i
$167$	4.17440	−	2.41009i	0.323024	−	0.186498i	−0.329715	−	0.944080i	$-0.606953\pi$
$167$	4.17440	−	2.41009i	0.323024	−	0.186498i	0.652740	+	0.757582i	$0.273619\pi$
$168$		0			0
$169$	12.9920	+	0.456347i	0.999384	+	0.0351036i
$170$	31.0736			2.38324
$171$	−3.65560	+	2.11056i	−0.279551	+	0.161399i
$172$	−9.13222	−	15.8175i	−0.696325	−	1.20607i
$173$	6.01034	−	10.4102i	0.456957	−	0.791473i	−0.541841	−	0.840481i	$-0.682273\pi$
$173$	6.01034	−	10.4102i	0.456957	−	0.791473i	0.998798	+	0.0490076i	$0.0156059\pi$
$174$			25.2215i			1.91203i
$175$		0			0
$176$	−2.54650	−	1.47022i	−0.191950	−	0.110822i
$177$		−	14.1894i		−	1.06654i
$178$	4.25668	−	7.37279i	0.319052	−	0.552614i
$179$	−9.25268	−	16.0261i	−0.691578	−	1.19785i	−0.971321	−	0.237773i	$-0.923583\pi$
$179$	−9.25268	−	16.0261i	−0.691578	−	1.19785i	0.279743	−	0.960075i	$-0.409751\pi$
$180$	−8.86604	+	5.11881i	−0.660836	+	0.381534i
$181$	−0.554493			−0.0412152			−0.0206076	−	0.999788i	$-0.506560\pi$
$181$	−0.554493			−0.0412152			−0.0206076	+	0.999788i	$0.506560\pi$
$182$		0			0
$183$	9.13929			0.675596
$184$	3.68956	−	2.13017i	0.271998	−	0.157038i
$185$	−7.67578	−	13.2948i	−0.564335	−	0.977456i
$186$	1.60453	−	2.77913i	0.117650	−	0.203775i
$187$		−	4.02085i		−	0.294034i
$188$	16.3652	+	9.44848i	1.19356	+	0.689101i
$189$		0			0
$190$			24.9086i			1.80706i
$191$	−10.0135	+	17.3439i	−0.724553	+	1.25496i	0.234605	+	0.972091i	$0.424620\pi$
$191$	−10.0135	+	17.3439i	−0.724553	+	1.25496i	−0.959158	+	0.282872i	$0.908713\pi$
$192$	−7.07463	−	12.2536i	−0.510567	−	0.884328i
$193$	−9.08389	+	5.24459i	−0.653873	+	0.377514i	−0.789938	−	0.613186i	$-0.789888\pi$
$193$	−9.08389	+	5.24459i	−0.653873	+	0.377514i	0.136066	+	0.990700i	$0.456554\pi$
$194$	3.19958			0.229716
$195$	−14.6120	+	8.09764i	−1.04639	+	0.579884i
$196$		0			0
$197$	−11.9380	+	6.89242i	−0.850548	+	0.491064i	−0.860836	−	0.508883i	$-0.830059\pi$
$197$	−11.9380	+	6.89242i	−0.850548	+	0.491064i	0.0102874	+	0.999947i	$0.496725\pi$
$198$	1.22058	+	2.11410i	0.0867427	+	0.150243i
$199$	−4.35480	+	7.54274i	−0.308704	+	0.534691i	−0.978079	−	0.208234i	$-0.933229\pi$
$199$	−4.35480	+	7.54274i	−0.308704	+	0.534691i	0.669375	+	0.742924i	$0.266562\pi$
$200$			5.59718i			0.395780i
$201$	8.52971	+	4.92463i	0.601639	+	0.347357i
$202$	−29.4445	−	16.9998i	−2.07171	−	1.19610i
$203$		0			0
$204$	6.71090	−	11.6236i	0.469857	−	0.813816i
$205$	−16.3153	−	28.2589i	−1.13951	−	1.97369i
$206$	14.4820	−	8.36116i	1.00901	−	0.582550i
$207$	6.75087			0.469218
$208$	5.44317	+	9.82211i	0.377416	+	0.681041i
$209$	3.22312			0.222948
$210$		0			0
$211$	−9.41712	−	16.3109i	−0.648302	−	1.12289i	−0.983528	−	0.180754i	$-0.942146\pi$
$211$	−9.41712	−	16.3109i	−0.648302	−	1.12289i	0.335227	−	0.942137i	$-0.391187\pi$
$212$	8.90756	−	15.4283i	0.611774	−	1.05962i
$213$			17.4442i			1.19526i
$214$	−29.0930	−	16.7969i	−1.98876	−	1.14821i
$215$	−23.2550	−	13.4263i	−1.58598	−	0.915664i
$216$			4.38991i			0.298696i
$217$		0			0
$218$	6.47125	+	11.2085i	0.438288	+	0.759137i
$219$	1.99187	−	1.15000i	0.134598	−	0.0777101i
$220$	7.81712			0.527030
$221$	−7.91005	+	13.1615i	−0.532088	+	0.885338i
$222$	−12.2192			−0.820097
$223$	−2.56339	+	1.47998i	−0.171658	+	0.0991065i	−0.583367	−	0.812209i	$-0.698265\pi$
$223$	−2.56339	+	1.47998i	−0.171658	+	0.0991065i	0.411710	+	0.911315i	$0.364932\pi$
$224$		0			0
$225$	−4.43461	+	7.68097i	−0.295641	+	0.512065i
$226$			11.6903i			0.777626i
$227$	−0.00371813	−	0.00214666i	−0.000246781	−	0.000142479i	0.499877	−	0.866097i	$-0.333379\pi$
$227$	−0.00371813	−	0.00214666i	−0.000246781	−	0.000142479i	−0.500123	+	0.865954i	$0.666712\pi$
$228$	9.31750	+	5.37946i	0.617066	+	0.356263i
$229$			2.40397i			0.158859i	0.996840	+	0.0794294i	$0.0253098\pi$
$229$			2.40397i			0.158859i	−0.996840	+	0.0794294i	$0.974690\pi$
$230$	19.9183	−	34.4995i	1.31337	−	2.27483i
$231$		0			0
$232$	−6.13720	+	3.54331i	−0.402927	+	0.232630i
$233$	−14.6605			−0.960442			−0.480221	−	0.877147i	$-0.659444\pi$
$233$	−14.6605			−0.960442			−0.480221	+	0.877147i	$0.659444\pi$
$234$	0.163656	−	9.32131i	0.0106985	−	0.609353i
$235$	27.7825			1.81233
$236$	21.9595	−	12.6783i	1.42944	−	0.825290i
$237$	−8.15825	−	14.1305i	−0.529935	−	0.917875i
$238$		0			0
$239$			1.83515i			0.118706i	0.998237	+	0.0593530i	$0.0189037\pi$
$239$			1.83515i			0.118706i	−0.998237	+	0.0593530i	$0.981096\pi$
$240$	−12.4973	−	7.21531i	−0.806696	−	0.465746i
$241$	10.3944	+	6.00120i	0.669561	+	0.386571i	0.795910	−	0.605415i	$-0.206993\pi$
$241$	10.3944	+	6.00120i	0.669561	+	0.386571i	−0.126349	+	0.991986i	$0.540326\pi$
$242$			21.1393i			1.35888i
$243$	−5.94108	+	10.2903i	−0.381120	+	0.660120i
$244$	8.16602	+	14.1440i	0.522776	+	0.905474i
$245$		0			0
$246$	−25.9725			−1.65595
$247$	−10.5503	−	6.34070i	−0.671297	−	0.403449i
$248$	0.901669			0.0572560
$249$	1.77123	−	1.02262i	0.112247	−	0.0648060i
$250$	7.92787	+	13.7315i	0.501403	+	0.868455i
$251$	5.17757	−	8.96781i	0.326805	−	0.566043i	−0.655071	−	0.755567i	$-0.727361\pi$
$251$	5.17757	−	8.96781i	0.326805	−	0.566043i	0.981876	+	0.189524i	$0.0606946\pi$
$252$		0			0
$253$	−4.46414	−	2.57737i	−0.280658	−	0.162038i
$254$	27.6403	+	15.9581i	1.73431	+	1.00130i
$255$		−	19.7329i		−	1.23572i
$256$	−4.24121	+	7.34600i	−0.265076	+	0.459125i
$257$	−11.0695	−	19.1729i	−0.690496	−	1.19597i	−0.971676	−	0.236318i	$-0.924059\pi$
$257$	−11.0695	−	19.1729i	−0.690496	−	1.19597i	0.281180	−	0.959655i	$-0.409274\pi$
$258$	−18.5099	+	10.6867i	−1.15238	+	0.665326i
$259$		0			0
$260$	−25.5879	−	15.3783i	−1.58689	−	0.953722i
$261$	−11.2294			−0.695081
$262$	−10.3961	+	6.00220i	−0.642274	+	0.370817i
$263$	2.06241	+	3.57220i	0.127174	+	0.220271i	0.922581	−	0.385805i	$-0.126076\pi$
$263$	2.06241	+	3.57220i	0.127174	+	0.220271i	−0.795407	+	0.606076i	$0.792743\pi$
$264$	0.489156	−	0.847243i	0.0301055	−	0.0521442i
$265$		−	26.1920i		−	1.60896i
$266$		0			0
$267$	−4.68198	−	2.70314i	−0.286533	−	0.165430i
$268$			17.6008i			1.07514i
$269$	−8.35362	+	14.4689i	−0.509329	+	0.882184i	0.490613	+	0.871378i	$0.336773\pi$
$269$	−8.35362	+	14.4689i	−0.509329	+	0.882184i	−0.999942	+	0.0108060i	$0.996560\pi$
$270$	20.5241	+	35.5488i	1.24906	+	2.16343i
$271$	6.35832	−	3.67098i	0.386240	−	0.222996i	−0.294290	−	0.955716i	$-0.595083\pi$
$271$	6.35832	−	3.67098i	0.386240	−	0.222996i	0.680530	+	0.732720i	$0.261750\pi$
$272$	−13.2643			−0.804265
$273$		0			0
$274$	−10.8150			−0.653358
$275$	5.86494	−	3.38613i	0.353669	−	0.204191i
$276$	−8.60340	−	14.9015i	−0.517864	−	0.896966i
$277$	−1.66245	+	2.87945i	−0.0998870	+	0.173009i	−0.911638	−	0.410995i	$-0.865181\pi$
$277$	−1.66245	+	2.87945i	−0.0998870	+	0.173009i	0.811751	+	0.584004i	$0.198515\pi$
$278$			27.4081i			1.64383i
$279$	1.23735	+	0.714386i	0.0740784	+	0.0427692i
$280$		0			0
$281$			5.67497i			0.338540i	0.985570	+	0.169270i	$0.0541410\pi$
$281$			5.67497i			0.338540i	−0.985570	+	0.169270i	$0.945859\pi$
$282$	11.0568	−	19.1510i	0.658424	−	1.14042i
$283$	13.2173	+	22.8929i	0.785684	+	1.36084i	0.928590	+	0.371108i	$0.121022\pi$
$283$	13.2173	+	22.8929i	0.785684	+	1.36084i	−0.142906	+	0.989736i	$0.545645\pi$
$284$	−26.9966	+	15.5865i	−1.60195	+	0.924889i
$285$	15.8179			0.936970
$286$	−3.66695	+	6.10141i	−0.216831	+	0.360784i
$287$		0			0
$288$	8.64524	−	4.99133i	0.509425	−	0.294117i
$289$	−0.568990	−	0.985520i	−0.0334700	−	0.0579718i
$290$	−33.1320	+	57.3863i	−1.94558	+	3.36984i
$291$		−	2.03185i		−	0.119109i
$292$	3.55949	+	2.05507i	0.208304	+	0.120264i
$293$	−10.5899	−	6.11409i	−0.618669	−	0.357189i	0.157681	−	0.987490i	$-0.449598\pi$
$293$	−10.5899	−	6.11409i	−0.618669	−	0.357189i	−0.776351	+	0.630301i	$0.782931\pi$
$294$		0			0
$295$	18.6398	−	32.2851i	1.08525	−	1.87971i
$296$	−1.71665	−	2.97332i	−0.0997780	−	0.172821i
$297$	4.59992	−	2.65576i	0.266914	−	0.154103i
$298$	38.2944			2.21833
$299$	9.54216	+	17.2187i	0.551837	+	0.995781i
$300$	22.6061			1.30516
$301$		0			0
$302$	8.80764	+	15.2553i	0.506823	+	0.877842i
$303$	−10.7955	+	18.6983i	−0.620183	+	1.07419i
$304$		−	10.6327i		−	0.609825i
$305$	20.7946	+	12.0058i	1.19069	+	0.687448i
$306$	9.53668	+	5.50601i	0.545176	+	0.314757i
$307$			32.1068i			1.83243i	0.400684	+	0.916216i	$0.368773\pi$
$307$			32.1068i			1.83243i	−0.400684	+	0.916216i	$0.631227\pi$
$308$		0			0
$309$	−5.30963	−	9.19655i	−0.302054	−	0.523174i
$310$	7.30156	−	4.21556i	0.414701	−	0.239428i
$311$	−20.0037			−1.13431			−0.567154	−	0.823612i	$-0.691956\pi$
$311$	−20.0037			−1.13431			−0.567154	+	0.823612i	$0.691956\pi$
$312$	−3.26790	+	1.81099i	−0.185009	+	0.102527i
$313$	4.55679			0.257565			0.128782	−	0.991673i	$-0.458893\pi$
$313$	4.55679			0.257565			0.128782	+	0.991673i	$0.458893\pi$
$314$	7.93056	−	4.57871i	0.447547	−	0.258392i
$315$		0			0
$316$	14.5789	−	25.2514i	0.820128	−	1.42050i
$317$		−	7.19866i		−	0.404317i	−0.979353	−	0.202158i	$-0.935204\pi$
$317$		−	7.19866i		−	0.404317i	0.979353	−	0.202158i	$-0.0647956\pi$
$318$	−18.0546	−	10.4238i	−1.01245	−	0.584539i
$319$	7.42564	+	4.28719i	0.415756	+	0.240037i
$320$		−	37.1741i		−	2.07810i
$321$	−10.6666	+	18.4751i	−0.595352	+	1.03118i
$322$		0			0
$323$	12.5915	−	7.26971i	0.700610	−	0.404497i
$324$	8.92738			0.495965
$325$	−25.8592	−	0.454015i	−1.43441	−	0.0251842i
$326$	19.7941			1.09630
$327$	7.11781	−	4.10947i	0.393616	−	0.227254i
$328$	−3.64883	−	6.31995i	−0.201473	−	0.348961i
$329$		0			0
$330$		−	9.14777i		−	0.503568i
$331$	8.83061	+	5.09836i	0.485374	+	0.280231i	0.722653	−	0.691211i	$-0.242922\pi$
$331$	8.83061	+	5.09836i	0.485374	+	0.280231i	−0.237279	+	0.971441i	$0.576256\pi$
$332$	3.16522	+	1.82744i	0.173714	+	0.100294i
$333$		−	5.44035i		−	0.298129i
$334$	5.03999	−	8.72951i	0.275776	−	0.477658i
$335$	12.9384	+	22.4100i	0.706901	+	1.22439i
$336$		0			0
$337$	−13.6882			−0.745643			−0.372822	−	0.927903i	$-0.621610\pi$
$337$	−13.6882			−0.745643			−0.372822	+	0.927903i	$0.621610\pi$
$338$	24.0061	−	12.7580i	1.30576	−	0.693943i
$339$	7.42374			0.403202
$340$	30.5386	−	17.6314i	1.65619	−	0.956199i
$341$	−0.545483	−	0.944803i	−0.0295395	−	0.0511640i
$342$	−4.41362	+	7.64461i	−0.238661	+	0.413373i
$343$		0			0
$344$	−5.20085	−	3.00271i	−0.280411	−	0.161895i
$345$	−21.9084	−	12.6488i	−1.17951	−	0.680989i
$346$		−	25.1377i		−	1.35141i
$347$	3.76114	−	6.51448i	0.201908	−	0.349716i	−0.747235	−	0.664560i	$-0.768619\pi$
$347$	3.76114	−	6.51448i	0.201908	−	0.349716i	0.949143	+	0.314844i	$0.101952\pi$
$348$	14.3109	+	24.7871i	0.767143	+	1.32873i
$349$	−15.2409	+	8.79931i	−0.815824	+	0.471016i	−0.848974	−	0.528434i	$-0.822779\pi$
$349$	−15.2409	+	8.79931i	−0.815824	+	0.471016i	0.0331501	+	0.999450i	$0.489446\pi$
$350$		0			0
$351$	−20.2815	−	0.356087i	−1.08255	−	0.0190065i
$352$	−7.62244			−0.406277
$353$	19.0738	−	11.0123i	1.01520	−	0.586124i	0.102488	−	0.994734i	$-0.467320\pi$
$353$	19.0738	−	11.0123i	1.01520	−	0.586124i	0.912709	+	0.408610i	$0.133986\pi$
$354$	−14.8365	−	25.6975i	−0.788550	−	1.36581i
$355$	−22.9154	+	39.6907i	−1.21622	+	2.10656i
$356$		−	9.66111i		−	0.512038i
$357$		0			0
$358$	−33.5139	−	19.3492i	−1.77126	−	1.02264i
$359$			33.8796i			1.78809i	0.447973	+	0.894047i	$0.352146\pi$
$359$			33.8796i			1.78809i	−0.447973	+	0.894047i	$0.647854\pi$
$360$	−1.68309	+	2.91519i	−0.0887065	+	0.153644i
$361$	−3.67260	−	6.36113i	−0.193295	−	0.334796i
$362$	−1.00421	+	0.579779i	−0.0527800	+	0.0304725i
$363$	13.4242			0.704586
$364$		0			0
$365$	6.04278			0.316294
$366$	16.5516	−	9.55606i	0.865165	−	0.499503i
$367$	8.34228	+	14.4493i	0.435464	+	0.754245i	0.997333	−	0.0729805i	$-0.0232511\pi$
$367$	8.34228	+	14.4493i	0.435464	+	0.754245i	−0.561870	+	0.827226i	$0.689918\pi$
$368$	−8.50243	+	14.7266i	−0.443220	+	0.767679i
$369$		−	11.5638i		−	0.601985i
$370$	−27.8022	−	16.0516i	−1.44537	−	0.834484i
$371$		0			0
$372$		−	3.64169i		−	0.188813i
$373$	8.18026	−	14.1686i	0.423558	−	0.733624i	−0.572727	−	0.819746i	$-0.694114\pi$
$373$	8.18026	−	14.1686i	0.423558	−	0.733624i	0.996285	+	0.0861226i	$0.0274477\pi$
$374$	−4.20421	−	7.28190i	−0.217394	−	0.376538i
$375$	8.71997	−	5.03448i	0.450297	−	0.259979i
$376$	6.21340			0.320432
$377$	−15.8724	−	28.6415i	−0.817470	−	1.47511i
$378$		0			0
$379$	−5.97150	+	3.44765i	−0.306735	+	0.177094i	−0.645465	−	0.763790i	$-0.723336\pi$
$379$	−5.97150	+	3.44765i	−0.306735	+	0.177094i	0.338729	+	0.940884i	$0.390003\pi$
$380$	14.1334	+	24.4797i	0.725027	+	1.25578i
$381$	10.1340	−	17.5526i	0.519180	−	0.899245i
$382$			41.8806i			2.14280i
$383$	−1.84283	−	1.06396i	−0.0941644	−	0.0543658i	0.452178	−	0.891928i	$-0.350647\pi$
$383$	−1.84283	−	1.06396i	−0.0941644	−	0.0543658i	−0.546343	+	0.837562i	$0.683980\pi$
$384$	−7.05423	−	4.07276i	−0.359985	−	0.207837i
$385$		0			0
$386$	−10.9675	+	18.9963i	−0.558231	+	0.966884i
$387$	−4.75806	−	8.24120i	−0.241866	−	0.418924i
$388$	3.14448	−	1.81547i	0.159637	−	0.0921664i
$389$	−22.9584			−1.16404			−0.582018	−	0.813176i	$-0.697737\pi$
$389$	−22.9584			−1.16404			−0.582018	+	0.813176i	$0.697737\pi$
$390$	−17.9960	+	29.9435i	−0.911264	+	1.51625i
$391$	−23.2530			−1.17595
$392$		0			0
$393$	3.81161	+	6.60190i	0.192270	+	0.333022i
$394$	−14.4134	+	24.9648i	−0.726139	+	1.25771i
$395$		−	42.8681i		−	2.15693i
$396$	2.39912	+	1.38513i	0.120560	+	0.0696055i
$397$	−20.9224	−	12.0795i	−1.05006	−	0.606255i	−0.127397	−	0.991852i	$-0.540662\pi$
$397$	−20.9224	−	12.0795i	−1.05006	−	0.606255i	−0.922667	+	0.385597i	$0.873996\pi$
$398$			18.2136i			0.912963i
$399$		0			0
$400$	−11.1704	−	19.3477i	−0.558520	−	0.967385i
$401$	7.28451	−	4.20571i	0.363771	−	0.210023i	−0.306963	−	0.951722i	$-0.599313\pi$
$401$	7.28451	−	4.20571i	0.363771	−	0.210023i	0.670734	+	0.741698i	$0.265979\pi$
$402$	20.5968			1.02728
$403$	−0.0731388	+	4.16574i	−0.00364330	+	0.207510i
$404$	−38.5833			−1.91959
$405$	11.3667	−	6.56256i	0.564815	−	0.326096i
$406$		0			0
$407$	−2.07704	+	3.59754i	−0.102955	+	0.178323i
$408$		−	4.41315i		−	0.218483i
$409$	−5.77809	−	3.33598i	−0.285708	−	0.164954i	0.350297	−	0.936639i	$-0.386081\pi$
$409$	−5.77809	−	3.33598i	−0.285708	−	0.164954i	−0.636005	+	0.771685i	$0.719414\pi$
$410$	−59.0951	−	34.1186i	−2.91850	−	1.68500i
$411$			6.86791i			0.338769i
$412$	9.48839	−	16.4344i	0.467459	−	0.809663i
$413$		0			0
$414$	12.2261	−	7.05872i	0.600878	−	0.346917i
$415$	5.37344			0.263772
$416$	24.9506	+	14.9953i	1.22330	+	0.735205i
$417$	17.4051			0.852333
$418$	5.83718	−	3.37010i	0.285506	−	0.164837i
$419$	7.74625	+	13.4169i	0.378429	+	0.655458i	0.990834	−	0.135086i	$-0.0431311\pi$
$419$	7.74625	+	13.4169i	0.378429	+	0.655458i	−0.612405	+	0.790544i	$0.709798\pi$
$420$		0			0
$421$			26.7232i			1.30241i	0.758903	+	0.651203i	$0.225736\pi$
$421$			26.7232i			1.30241i	−0.758903	+	0.651203i	$0.774264\pi$
$422$	−34.1095	−	19.6931i	−1.66042	−	0.958646i
$423$	8.52661	+	4.92284i	0.414578	+	0.239357i
$424$		−	5.85769i		−	0.284475i
$425$	15.2748	−	26.4566i	0.740934	−	1.28334i
$426$	18.2397	+	31.5920i	0.883715	+	1.53064i
$427$		0			0
$428$	−38.1227			−1.84273
$429$	3.87461	+	2.32864i	0.187068	+	0.112428i
$430$	−56.1542			−2.70799
$431$	25.2387	−	14.5716i	1.21570	−	0.701887i	0.251708	−	0.967803i	$-0.419008\pi$
$431$	25.2387	−	14.5716i	1.21570	−	0.701887i	0.963996	+	0.265916i	$0.0856745\pi$
$432$	−8.76103	−	15.1746i	−0.421515	−	0.730086i
$433$	2.68761	−	4.65508i	0.129158	−	0.223709i	−0.794192	−	0.607666i	$-0.792106\pi$
$433$	2.68761	−	4.65508i	0.129158	−	0.223709i	0.923351	+	0.383958i	$0.125439\pi$
$434$		0			0
$435$	36.4423	+	21.0400i	1.74727	+	1.00879i
$436$	12.7196	+	7.34368i	0.609160	+	0.351698i
$437$		−	18.6396i		−	0.891652i
$438$	2.40489	−	4.16540i	0.114910	−	0.199030i
$439$	2.55668	+	4.42830i	0.122024	+	0.211351i	0.920566	−	0.390588i	$-0.127728\pi$
$439$	2.55668	+	4.42830i	0.122024	+	0.211351i	−0.798542	+	0.601939i	$0.794395\pi$
$440$	2.22595	−	1.28515i	0.106118	−	0.0612672i
$441$		0			0
$442$	−0.563704	+	32.1067i	−0.0268127	+	1.52716i
$443$	−1.62414			−0.0771651			−0.0385826	−	0.999255i	$-0.512284\pi$
$443$	−1.62414			−0.0771651			−0.0385826	+	0.999255i	$0.512284\pi$
$444$	−12.0088	+	6.93326i	−0.569910	+	0.329038i
$445$	−7.10193	−	12.3009i	−0.336664	−	0.583119i
$446$	−3.09493	+	5.36058i	−0.146549	+	0.253831i
$447$		−	24.3183i		−	1.15021i
$448$		0			0
$449$	−7.21311	−	4.16449i	−0.340408	−	0.196534i	0.320045	−	0.947402i	$-0.396302\pi$
$449$	−7.21311	−	4.16449i	−0.340408	−	0.196534i	−0.660452	+	0.750868i	$0.729635\pi$
$450$			18.5473i			0.874330i
$451$	−4.41486	+	7.64676i	−0.207888	+	0.360072i
$452$	6.63316	+	11.4890i	0.311998	+	0.540396i
$453$	9.68764	−	5.59316i	0.455165	−	0.262790i
$454$	−0.00897822			−0.000421369
$455$		0			0
$456$	3.53758			0.165662
$457$	4.95805	−	2.86253i	0.231928	−	0.133904i	−0.379533	−	0.925178i	$-0.623915\pi$
$457$	4.95805	−	2.86253i	0.231928	−	0.133904i	0.611461	+	0.791274i	$0.290582\pi$
$458$	2.51360	+	4.35368i	0.117453	+	0.203434i
$459$	11.9801	−	20.7501i	0.559183	−	0.968534i
$460$		−	45.2072i		−	2.10780i
$461$	−29.2623	−	16.8946i	−1.36288	−	0.786861i	−0.372876	−	0.927881i	$-0.621628\pi$
$461$	−29.2623	−	16.8946i	−1.36288	−	0.786861i	−0.990007	+	0.141020i	$0.954962\pi$
$462$		0			0
$463$		−	0.103015i		−	0.00478753i	−0.999997	−	0.00239376i	$-0.999238\pi$
$463$		−	0.103015i		−	0.00478753i	0.999997	−	0.00239376i	$-0.000761960\pi$
$464$	14.1429	−	24.4962i	0.656568	−	1.13721i
$465$	−2.67703	−	4.63675i	−0.124144	−	0.215024i
$466$	−26.5507	+	15.3291i	−1.22994	+	0.710105i
$467$	11.6717			0.540101			0.270051	−	0.962846i	$-0.412960\pi$
$467$	11.6717			0.540101			0.270051	+	0.962846i	$0.412960\pi$
$468$	−5.12815	−	9.25366i	−0.237049	−	0.427750i
$469$		0			0
$470$	50.3151	−	29.0494i	2.32086	−	1.33995i
$471$	−2.90764	−	5.03619i	−0.133977	−	0.232055i
$472$	4.16869	−	7.22039i	0.191880	−	0.332345i
$473$			7.26621i			0.334100i
$474$	−29.5498	−	17.0606i	−1.35727	−	0.783618i
$475$	21.2077	+	12.2442i	0.973074	+	0.561805i
$476$		0			0
$477$	4.64101	−	8.03847i	0.212497	−	0.368056i
$478$	1.91884	+	3.32352i	0.0877655	+	0.152014i
$479$	−22.5678	+	13.0295i	−1.03115	+	0.595334i	−0.917313	−	0.398166i	$-0.869647\pi$
$479$	−22.5678	+	13.0295i	−1.03115	+	0.595334i	−0.113835	+	0.993500i	$0.536313\pi$
$480$	−37.4081			−1.70744
$481$	13.8761	−	7.68978i	0.632695	−	0.350624i
$482$	25.0995			1.14325
$483$		0			0
$484$	11.9946	+	20.7752i	0.545208	+	0.944329i
$485$	2.66912	−	4.62305i	0.121198	−	0.209922i
$486$			24.8480i			1.12713i
$487$	−11.2802	−	6.51265i	−0.511157	−	0.295117i	0.222152	−	0.975012i	$-0.428692\pi$
$487$	−11.2802	−	6.51265i	−0.511157	−	0.295117i	−0.733309	+	0.679895i	$0.762025\pi$
$488$	4.65060	+	2.68502i	0.210523	+	0.121545i
$489$		−	12.5700i		−	0.568434i
$490$		0			0
$491$	8.42767	+	14.5971i	0.380335	+	0.658760i	0.991110	−	0.133044i	$-0.0424753\pi$
$491$	8.42767	+	14.5971i	0.380335	+	0.658760i	−0.610775	+	0.791804i	$0.709142\pi$
$492$	−25.5253	+	14.7370i	−1.15077	+	0.664396i
$493$	38.6789			1.74201
$494$	−25.7367	−	0.451866i	−1.15795	−	0.0203304i
$495$	4.07287			0.183062
$496$	−3.11679	+	1.79948i	−0.139948	+	0.0807990i
$497$		0			0
$498$	2.13851	−	3.70401i	0.0958290	−	0.165981i
$499$			16.6519i			0.745441i	0.927944	+	0.372720i	$0.121575\pi$
$499$			16.6519i			0.745441i	−0.927944	+	0.372720i	$0.878425\pi$
$500$	15.5827	+	8.99668i	0.696880	+	0.402344i
$501$	−5.54355	−	3.20057i	−0.247667	−	0.142991i
$502$		−	21.6547i		−	0.966497i
$503$	12.3133	−	21.3273i	0.549023	−	0.950935i	−0.449319	−	0.893371i	$-0.648333\pi$
$503$	12.3133	−	21.3273i	0.549023	−	0.950935i	0.998342	−	0.0575638i	$-0.0183333\pi$
$504$		0			0
$505$	−49.1258	+	28.3628i	−2.18607	+	1.26213i
$506$	−10.7796			−0.479213
$507$	−8.10177	−	15.2447i	−0.359812	−	0.677042i
$508$	36.2191			1.60696
$509$	25.8161	−	14.9049i	1.14428	−	0.660650i	0.196792	−	0.980445i	$-0.436948\pi$
$509$	25.8161	−	14.9049i	1.14428	−	0.660650i	0.947487	+	0.319796i	$0.103614\pi$
$510$	−20.6327	−	35.7369i	−0.913632	−	1.58246i
$511$		0			0
$512$			30.0059i			1.32609i
$513$	16.6333	+	9.60326i	0.734379	+	0.423994i
$514$	−40.0945	−	23.1486i	−1.76849	−	1.02104i
$515$		−	27.8998i		−	1.22941i
$516$	−12.1275	+	21.0054i	−0.533882	+	0.924711i
$517$	−3.75892	−	6.51065i	−0.165317	−	0.286338i
$518$		0			0
$519$	−15.9633			−0.700711
$520$	−9.81445	−	0.172314i	−0.430392	−	0.00755649i
$521$	31.1105			1.36297			0.681487	−	0.731830i	$-0.261334\pi$
$521$	31.1105			1.36297			0.681487	+	0.731830i	$0.261334\pi$
$522$	−20.3368	+	11.7415i	−0.890117	+	0.513909i
$523$	−6.96121	−	12.0572i	−0.304393	−	0.527223i	0.672733	−	0.739885i	$-0.265120\pi$
$523$	−6.96121	−	12.0572i	−0.304393	−	0.527223i	−0.977126	+	0.212662i	$0.931787\pi$
$524$	−6.81140	+	11.7977i	−0.297557	+	0.515384i
$525$		0			0
$526$	7.47020	+	4.31292i	0.325716	+	0.188052i
$527$	−4.26199	−	2.46066i	−0.185655	−	0.107188i
$528$			3.90487i			0.169938i
$529$	−3.40520	+	5.89798i	−0.148052	+	0.256434i
$530$	−27.3864	−	47.4346i	−1.18959	−	2.06043i
$531$	11.4413	−	6.60566i	0.496512	−	0.286661i
$532$		0			0
$533$	29.4944	−	16.3450i	1.27754	−	0.707983i
$534$	−11.3056			−0.489243
$535$	−48.5394	+	28.0242i	−2.09854	+	1.21159i
$536$	2.89360	+	5.01187i	0.124985	+	0.216480i
$537$	−12.2874	+	21.2825i	−0.530243	+	0.918407i
$538$			34.9382i			1.50629i
$539$		0			0
$540$	40.3413	+	23.2911i	1.73601	+	1.00229i
$541$		−	1.80171i		−	0.0774617i	−0.999250	−	0.0387308i	$-0.987669\pi$
$541$		−	1.80171i		−	0.0774617i	0.999250	−	0.0387308i	$-0.0123315\pi$
$542$	7.67676	−	13.2965i	0.329745	−	0.571135i
$543$	0.368180	+	0.637707i	0.0158001	+	0.0273666i
$544$	−29.7780	+	17.1923i	−1.27672	+	0.737115i
$545$	21.5935			0.924964
$546$		0			0
$547$	18.9823			0.811625			0.405813	−	0.913956i	$-0.366989\pi$
$547$	18.9823			0.811625			0.405813	+	0.913956i	$0.366989\pi$
$548$	−10.6288	+	6.13653i	−0.454039	+	0.262139i
$549$	4.25465	+	7.36928i	0.181584	+	0.314513i
$550$	7.08108	−	12.2648i	0.301938	−	0.522972i
$551$			31.0050i			1.32086i
$552$	−4.89969	−	2.82884i	−0.208545	−	0.120403i
$553$		0			0
$554$			6.95305i			0.295407i
$555$	−10.1933	+	17.6554i	−0.432683	+	0.749430i
$556$	15.5516	+	26.9362i	0.659535	+	1.14235i
$557$	14.0222	−	8.09572i	0.594140	−	0.343027i	−0.172593	−	0.984993i	$-0.555215\pi$
$557$	14.0222	−	8.09572i	0.594140	−	0.343027i	0.766733	+	0.641967i	$0.221881\pi$
$558$	2.98785			0.126486
$559$	14.2945	−	23.7845i	0.604593	−	1.00598i
$560$		0			0
$561$	−4.62427	+	2.66982i	−0.195237	+	0.112720i
$562$	5.93376	+	10.2776i	0.250300	+	0.433533i
$563$	11.9228	−	20.6509i	0.502486	−	0.870332i	−0.497510	−	0.867458i	$-0.665752\pi$
$563$	11.9228	−	20.6509i	0.502486	−	0.870332i	0.999996	−	0.00287326i	$-0.000914588\pi$
$564$		−	25.0949i		−	1.05669i
$565$	16.8912	+	9.75214i	0.710618	+	0.410276i
$566$	47.8738	+	27.6400i	2.01229	+	1.16179i
$567$		0			0
$568$	−5.12491	+	8.87660i	−0.215036	+	0.372454i
$569$	11.5877	+	20.0705i	0.485782	+	0.841399i	0.999866	−	0.0163404i	$-0.00520154\pi$
$569$	11.5877	+	20.0705i	0.485782	+	0.841399i	−0.514084	+	0.857740i	$0.671868\pi$
$570$	28.6467	−	16.5392i	1.19988	−	0.692751i
$571$	15.2222			0.637030			0.318515	−	0.947918i	$-0.396816\pi$
$571$	15.2222			0.637030			0.318515	+	0.947918i	$0.396816\pi$
$572$	−0.141810	+	8.07700i	−0.00592936	+	0.337717i
$573$	26.5957			1.11105
$574$		0			0
$575$	−19.5823	−	33.9175i	−0.816638	−	1.41446i
$576$	6.58696	−	11.4090i	0.274457	−	0.475373i
$577$			1.39559i			0.0580992i	0.999578	+	0.0290496i	$0.00924807\pi$
$577$			1.39559i			0.0580992i	−0.999578	+	0.0290496i	$0.990752\pi$
$578$	−2.06092	−	1.18987i	−0.0857231	−	0.0494923i
$579$	12.0633	+	6.96475i	0.501333	+	0.289445i
$580$			75.1974i			3.12240i
$581$		0			0
$582$	−2.12450	−	3.67974i	−0.0880634	−	0.152530i
$583$	−6.13792	+	3.54373i	−0.254206	+	0.146766i
$584$	1.35144			0.0559228
$585$	−13.3318	−	8.01239i	−0.551201	−	0.331272i
$586$	−25.5716			−1.05635
$587$	2.54847	−	1.47136i	0.105187	−	0.0607295i	−0.446484	−	0.894792i	$-0.647324\pi$
$587$	2.54847	−	1.47136i	0.105187	−	0.0607295i	0.551670	+	0.834062i	$0.313991\pi$
$588$		0			0
$589$	1.97247	−	3.41641i	0.0812741	−	0.140771i
$590$		−	77.9593i		−	3.20953i
$591$	15.8535	+	9.15305i	0.652128	+	0.376506i
$592$	11.8678	+	6.85189i	0.487764	+	0.281611i
$593$			37.9606i			1.55885i	0.626494	+	0.779427i	$0.284489\pi$
$593$			37.9606i			1.55885i	−0.626494	+	0.779427i	$0.715511\pi$
$594$	5.55374	−	9.61937i	0.227873	−	0.394687i
$595$		0			0
$596$	37.6349	−	21.7285i	1.54159	−	0.890036i
$597$	11.5663			0.473375
$598$	35.2851	+	21.2063i	1.44291	+	0.867190i
$599$	−38.3754			−1.56798			−0.783988	−	0.620776i	$-0.786818\pi$
$599$	−38.3754			−1.56798			−0.783988	+	0.620776i	$0.786818\pi$
$600$	6.43716	−	3.71649i	0.262796	−	0.151725i
$601$	−4.26063	−	7.37962i	−0.173795	−	0.301021i	0.765949	−	0.642902i	$-0.222270\pi$
$601$	−4.26063	−	7.37962i	−0.173795	−	0.301021i	−0.939743	+	0.341880i	$0.888936\pi$
$602$		0			0
$603$			9.17034i			0.373445i
$604$	17.3119	+	9.99505i	0.704413	+	0.406693i
$605$	30.5440	+	17.6346i	1.24179	+	0.716947i
$606$			45.1510i			1.83414i
$607$	17.9868	−	31.1541i	0.730064	−	1.26451i	−0.226792	−	0.973943i	$-0.572824\pi$
$607$	17.9868	−	31.1541i	0.730064	−	1.26451i	0.956856	−	0.290564i	$-0.0938429\pi$
$608$	−13.7814	−	23.8701i	−0.558909	−	0.968059i
$609$		0			0
$610$	50.2130			2.03306
$611$	−0.504000	+	28.7061i	−0.0203897	+	1.16133i
$612$	12.4966			0.505146
$613$	1.00606	−	0.580851i	0.0406345	−	0.0234604i	−0.479545	−	0.877517i	$-0.659198\pi$
$613$	1.00606	−	0.580851i	0.0406345	−	0.0234604i	0.520180	+	0.854057i	$0.325865\pi$
$614$	33.5709	+	58.1466i	1.35481	+	2.34660i
$615$	−21.6665	+	37.5275i	−0.873678	+	1.51325i
$616$		0			0
$617$	−3.17973	−	1.83582i	−0.128011	−	0.0739072i	0.434627	−	0.900611i	$-0.356880\pi$
$617$	−3.17973	−	1.83582i	−0.128011	−	0.0739072i	−0.562638	+	0.826703i	$0.690214\pi$
$618$	−19.2319	−	11.1035i	−0.773619	−	0.446649i
$619$		−	1.56312i		−	0.0628272i	−0.999506	−	0.0314136i	$-0.989999\pi$
$619$		−	1.56312i		−	0.0628272i	0.999506	−	0.0314136i	$-0.0100009\pi$
$620$	4.78389	−	8.28593i	0.192125	−	0.332771i
$621$	−15.3585	−	26.6018i	−0.616317	−	1.06749i
$622$	−36.2275	+	20.9159i	−1.45259	+	0.838653i
$623$		0			0
$624$	7.68189	−	12.7819i	0.307522	−	0.511684i
$625$	−9.41171			−0.376468
$626$	8.25251	−	4.76459i	0.329837	−	0.190431i
$627$	−2.14013	−	3.70681i	−0.0854686	−	0.148036i
$628$	5.19600	−	8.99973i	0.207343	−	0.359128i
$629$			18.7390i			0.747172i
$630$		0			0
$631$	−42.5630	−	24.5738i	−1.69441	−	0.978266i	−0.950880	−	0.309560i	$-0.899818\pi$
$631$	−42.5630	−	24.5738i	−1.69441	−	0.978266i	−0.743527	−	0.668706i	$-0.766848\pi$
$632$		−	9.58722i		−	0.381359i
$633$	−12.5058	+	21.6607i	−0.497062	+	0.860937i
$634$	−7.52693	−	13.0370i	−0.298933	−	0.517766i
$635$	46.1156	−	26.6249i	1.83004	−	1.05658i
$636$	−23.6583			−0.938111
$637$		0			0
$638$	17.9308			0.709887
$639$	−14.0658	+	8.12087i	−0.556433	+	0.321257i
$640$	−10.7003	−	18.5335i	−0.422967	−	0.732600i
$641$	8.48176	−	14.6908i	0.335009	−	0.580253i	−0.648477	−	0.761234i	$-0.724594\pi$
$641$	8.48176	−	14.6908i	0.335009	−	0.580253i	0.983487	+	0.180981i	$0.0579272\pi$
$642$			44.6121i			1.76070i
$643$	29.2077	+	16.8631i	1.15184	+	0.665015i	0.949335	−	0.314266i	$-0.101758\pi$
$643$	29.2077	+	16.8631i	1.15184	+	0.665015i	0.202505	+	0.979281i	$0.435092\pi$
$644$		0			0
$645$			35.6599i			1.40411i
$646$	15.2024	−	26.3314i	0.598132	−	1.03599i
$647$	−7.75233	−	13.4274i	−0.304775	−	0.527887i	0.672436	−	0.740155i	$-0.265248\pi$
$647$	−7.75233	−	13.4274i	−0.304775	−	0.527887i	−0.977211	+	0.212269i	$0.931915\pi$
$648$	2.54210	−	1.46768i	0.0998630	−	0.0576559i
$649$	−10.0877			−0.395978
$650$	−47.3066	+	26.2161i	−1.85552	+	1.02828i
$651$		0			0
$652$	19.4533	−	11.2314i	0.761849	−	0.439854i
$653$	−21.5054	−	37.2484i	−0.841570	−	1.45764i	−0.888567	−	0.458746i	$-0.848299\pi$
$653$	−21.5054	−	37.2484i	−0.841570	−	1.45764i	0.0469976	−	0.998895i	$-0.485035\pi$
$654$	8.59374	−	14.8848i	0.336042	−	0.582041i
$655$			20.0284i			0.782573i
$656$	25.2257	+	14.5641i	0.984898	+	0.568631i
$657$	1.85456	+	1.07073i	0.0723535	+	0.0417733i
$658$		0			0
$659$	1.36016	−	2.35586i	0.0529842	−	0.0917713i	−0.838317	−	0.545183i	$-0.816460\pi$
$659$	1.36016	−	2.35586i	0.0529842	−	0.0917713i	0.891301	+	0.453412i	$0.149793\pi$
$660$	−5.19052	−	8.99025i	−0.202041	−	0.349945i
$661$	−41.1078	+	23.7336i	−1.59891	+	0.923131i	−0.607212	+	0.794540i	$0.707712\pi$
$661$	−41.1078	+	23.7336i	−1.59891	+	0.923131i	−0.991698	+	0.128591i	$0.958954\pi$
$662$	21.3234			0.828757
$663$	20.3889	+	0.357972i	0.791838	+	0.0139025i
$664$	1.20174			0.0466366
$665$		0			0
$666$	−5.68844	−	9.85267i	−0.220423	−	0.381783i
$667$	24.7933	−	42.9432i	0.959999	−	1.66277i
$668$		−	11.4389i		−	0.442585i
$669$	3.40416	+	1.96539i	0.131612	+	0.0759864i
$670$	46.8638	+	27.0569i	1.81051	+	1.04530i
$671$		−	6.49743i		−	0.250831i
$672$		0			0
$673$	−13.9418	−	24.1479i	−0.537417	−	0.930833i	−0.999042	−	0.0437582i	$-0.986067\pi$
$673$	−13.9418	−	24.1479i	−0.537417	−	0.930833i	0.461625	−	0.887075i	$-0.347266\pi$
$674$	−24.7898	+	14.3124i	−0.954867	+	0.551293i
$675$	40.3558			1.55329
$676$	16.3537	−	26.1596i	0.628990	−	1.00614i
$677$	43.7495			1.68143			0.840715	−	0.541479i	$-0.182135\pi$
$677$	43.7495			1.68143			0.840715	+	0.541479i	$0.182135\pi$
$678$	13.4447	−	7.76227i	0.516339	−	0.298108i
$679$		0			0
$680$	5.79730	−	10.0412i	0.222316	−	0.385063i
$681$			0.00570149i			0.000218482i
$682$	−1.97578	−	1.14072i	−0.0756564	−	0.0436802i
$683$	−7.06356	−	4.07815i	−0.270279	−	0.156046i	0.358735	−	0.933439i	$-0.383208\pi$
$683$	−7.06356	−	4.07815i	−0.270279	−	0.156046i	−0.629015	+	0.777393i	$0.716541\pi$
$684$			10.0173i			0.383021i
$685$	−9.02198	+	15.6265i	−0.344712	+	0.597059i
$686$		0			0
$687$	2.76474	−	1.59622i	0.105481	−	0.0608997i
$688$	23.9703			0.913859
$689$	27.0627	+	0.475146i	1.03101	+	0.0181016i
$690$	−52.9025			−2.01396
$691$	−25.4247	+	14.6790i	−0.967201	+	0.558414i	−0.898382	−	0.439215i	$-0.855257\pi$
$691$	−25.4247	+	14.6790i	−0.967201	+	0.558414i	−0.0688194	+	0.997629i	$0.521923\pi$
$692$	−14.2633	−	24.7048i	−0.542210	−	0.939136i
$693$		0			0
$694$		−	15.7306i		−	0.597126i
$695$	39.6018	+	22.8641i	1.50218	+	0.867286i
$696$	8.15012	+	4.70547i	0.308930	+	0.178361i
$697$			39.8307i			1.50869i
$698$	−18.4012	+	31.8717i	−0.696494	+	1.20636i
$699$	9.73449	+	16.8606i	0.368192	+	0.637728i
$700$		0			0
$701$	18.7737			0.709073			0.354536	−	0.935042i	$-0.384639\pi$
$701$	18.7737			0.709073			0.354536	+	0.935042i	$0.384639\pi$
$702$	−37.1029	+	20.5615i	−1.40036	+	0.776045i
$703$	−15.0212			−0.566534
$704$	−8.71151	+	5.02959i	−0.328327	+	0.189560i
$705$	−18.4474	−	31.9519i	−0.694770	−	1.20338i
$706$	23.0289	−	39.8872i	0.866704	−	1.50118i
$707$		0			0
$708$	−29.1620	−	16.8367i	−1.09597	−	0.632761i
$709$	9.82475	+	5.67232i	0.368976	+	0.213028i	0.673011	−	0.739632i	$-0.265001\pi$
$709$	9.82475	+	5.67232i	0.368976	+	0.213028i	−0.304035	+	0.952661i	$0.598334\pi$
$710$			95.8417i			3.59687i
$711$	7.59589	−	13.1565i	0.284868	−	0.493406i
$712$	−1.58831	−	2.75103i	−0.0595244	−	0.103099i
$713$	−5.46389	+	3.15458i	−0.204624	+	0.118140i
$714$		0			0
$715$	5.75689	+	10.3882i	0.215295	+	0.388497i
$716$	−43.9157			−1.64121
$717$	2.11055	−	1.21853i	0.0788200	−	0.0455068i
$718$	35.4245	+	61.3571i	1.32203	+	2.28983i
$719$	2.14570	−	3.71646i	0.0800210	−	0.138600i	−0.823238	−	0.567697i	$-0.807835\pi$
$719$	2.14570	−	3.71646i	0.0800210	−	0.138600i	0.903259	+	0.429096i	$0.141168\pi$
$720$		−	13.4359i		−	0.500726i
$721$		0			0
$722$	−13.3024	−	7.68015i	−0.495065	−	0.285826i
$723$		−	15.9390i		−	0.592779i
$724$	−0.657943	+	1.13959i	−0.0244523	+	0.0423526i
$725$	32.5731	+	56.4183i	1.20974	+	2.09532i
$726$	24.3116	−	14.0363i	0.902290	−	0.520937i
$727$	−3.97703			−0.147500			−0.0737500	−	0.997277i	$-0.523497\pi$
$727$	−3.97703			−0.147500			−0.0737500	+	0.997277i	$0.523497\pi$
$728$		0			0
$729$	27.0649			1.00240
$730$	10.9437	−	6.31834i	0.405044	−	0.233852i
$731$	16.3889	+	28.3863i	0.606164	+	1.04991i
$732$	10.8444	−	18.7830i	0.400820	−	0.694240i
$733$			5.08853i			0.187949i	0.995575	+	0.0939746i	$0.0299573\pi$
$733$			5.08853i			0.187949i	−0.995575	+	0.0939746i	$0.970043\pi$
$734$	30.2163	+	17.4454i	1.11531	+	0.643922i
$735$		0			0
$736$			44.0813i			1.62486i
$737$	3.50109	−	6.06406i	0.128964	−	0.223373i
$738$	−12.0911	−	20.9424i	−0.445079	−	0.770900i
$739$	−7.00033	+	4.04164i	−0.257511	+	0.148674i	−0.623199	−	0.782064i	$-0.714167\pi$
$739$	−7.00033	+	4.04164i	−0.257511	+	0.148674i	0.365688	+	0.930738i	$0.380834\pi$
$740$	−36.4313			−1.33924
$741$	−0.286951	+	16.3437i	−0.0105414	+	0.600402i
$742$		0			0
$743$	−31.5287	+	18.2031i	−1.15667	+	0.667807i	−0.950505	−	0.310710i	$-0.899433\pi$
$743$	−31.5287	+	18.2031i	−1.15667	+	0.667807i	−0.206170	+	0.978516i	$0.566100\pi$
$744$	−0.598703	−	1.03698i	−0.0219495	−	0.0380177i
$745$	31.9455	−	55.3313i	1.17039	−	2.02718i
$746$		−	34.2132i		−	1.25263i
$747$	1.64914	+	0.952131i	0.0603389	+	0.0348367i
$748$	−8.26363	−	4.77101i	−0.302148	−	0.174445i
$749$		0			0
$750$	10.5281	−	18.2352i	0.384432	−	0.665857i
$751$	−11.3659	−	19.6864i	−0.414749	−	0.718366i	0.580653	−	0.814151i	$-0.302797\pi$
$751$	−11.3659	−	19.6864i	−0.414749	−	0.718366i	−0.995402	+	0.0957847i	$0.969464\pi$
$752$	−21.4778	+	12.4002i	−0.783215	+	0.452189i
$753$	−13.7515			−0.501132
$754$	−58.6930	−	35.2745i	−2.13747	−	1.28462i
$755$	29.3897			1.06960
$756$		0			0
$757$	9.38394	+	16.2535i	0.341065	+	0.590742i	0.984631	−	0.174649i	$-0.0558790\pi$
$757$	9.38394	+	16.2535i	0.341065	+	0.590742i	−0.643566	+	0.765391i	$0.722546\pi$
$758$	−7.20973	+	12.4876i	−0.261869	+	0.453571i
$759$			6.84544i			0.248474i
$760$	8.04904	+	4.64712i	0.291969	+	0.168569i
$761$	−3.27132	−	1.88870i	−0.118585	−	0.0684652i	0.439534	−	0.898226i	$-0.355144\pi$
$761$	−3.27132	−	1.88870i	−0.118585	−	0.0684652i	−0.558119	+	0.829761i	$0.688477\pi$
$762$		−	42.3844i		−	1.53543i
$763$		0			0
$764$	23.7634	+	41.1594i	0.859730	+	1.48910i
$765$	15.9112	−	9.18632i	0.575270	−	0.332132i
$766$	−4.44992			−0.160782
$767$	33.0203	+	19.8452i	1.19229	+	0.716568i
$768$	11.2646			0.406475
$769$	30.9588	−	17.8741i	1.11640	−	0.644556i	0.175923	−	0.984404i	$-0.443709\pi$
$769$	30.9588	−	17.8741i	1.11640	−	0.644556i	0.940480	+	0.339848i	$0.110376\pi$
$770$		0			0
$771$	−14.7001	+	25.4614i	−0.529413	+	0.916970i
$772$			24.8922i			0.895890i
$773$	23.4218	+	13.5226i	0.842425	+	0.486374i	0.858088	−	0.513503i	$-0.171653\pi$
$773$	23.4218	+	13.5226i	0.842425	+	0.486374i	−0.0156629	+	0.999877i	$0.504986\pi$
$774$	−17.2340	−	9.95007i	−0.619464	−	0.357648i
$775$		−	8.28890i		−	0.297746i
$776$	0.596934	−	1.03392i	0.0214287	−	0.0371156i
$777$		0			0
$778$	−41.5785	+	24.0053i	−1.49066	+	0.860633i
$779$	−31.9283			−1.14395
$780$	−0.695950	+	39.6390i	−0.0249190	+	1.41930i
$781$	12.4017			0.443767
$782$	−42.1119	+	24.3133i	−1.50592	+	0.869443i
$783$	25.5473	+	44.2493i	0.912987	+	1.58134i
$784$		0			0
$785$		−	15.2784i		−	0.545310i
$786$	13.8059	+	7.97085i	0.492441	+	0.284311i
$787$	−42.7559	−	24.6852i	−1.52408	−	0.879931i	−0.999593	−	0.0285152i	$-0.990922\pi$
$787$	−42.7559	−	24.6852i	−1.52408	−	0.879931i	−0.524492	−	0.851416i	$-0.675745\pi$
$788$			32.7132i			1.16536i
$789$	2.73886	−	4.74384i	0.0975059	−	0.168885i
$790$	−44.8230	−	77.6357i	−1.59473	−	2.76215i
$791$		0			0
$792$	0.910876			0.0323666
$793$	−12.7821	+	21.2681i	−0.453907	+	0.755253i
$794$	−50.5216			−1.79294
$795$	−30.1226	+	17.3913i	−1.06834	+	0.616806i
$796$	10.3345	+	17.8999i	0.366298	+	0.634446i
$797$	18.6768	−	32.3492i	0.661566	−	1.14587i	−0.318638	−	0.947876i	$-0.603226\pi$
$797$	18.6768	−	32.3492i	0.661566	−	1.14587i	0.980204	−	0.197989i	$-0.0634411\pi$
$798$		0			0
$799$	−29.3694	−	16.9564i	−1.03901	−	0.599875i
$800$	−50.1546	−	28.9568i	−1.77323	−	1.02378i
$801$		−	5.03362i		−	0.177854i
$802$	8.79500	−	15.2334i	0.310562	−	0.537910i
$803$	−0.817578	−	1.41609i	−0.0288517	−	0.0499726i
$804$	20.2421	−	11.6868i	0.713885	−	0.412162i
$805$		0			0
$806$	4.22325	+	7.62078i	0.148758	+	0.268430i
$807$	22.1870			0.781020
$808$	−10.9867	+	6.34318i	−0.386511	+	0.223152i
$809$	2.30300	+	3.98891i	0.0809692	+	0.140243i	0.903666	−	0.428237i	$-0.140865\pi$
$809$	2.30300	+	3.98891i	0.0809692	+	0.140243i	−0.822697	+	0.568480i	$0.807532\pi$
$810$	13.7236	−	23.7701i	0.482200	−	0.835195i
$811$			26.4209i			0.927765i	0.885897	+	0.463882i	$0.153544\pi$
$811$			26.4209i			0.927765i	−0.885897	+	0.463882i	$0.846456\pi$
$812$		0			0
$813$	−8.44377	−	4.87501i	−0.296136	−	0.170974i
$814$			8.68702i			0.304480i
$815$	16.5125	−	28.6004i	0.578406	−	1.00183i
$816$	8.80740	+	15.2549i	0.308321	+	0.534027i
$817$	−22.7545	+	13.1373i	−0.796079	+	0.459616i
$818$	−13.9524			−0.487835
$819$		0			0
$820$	−77.4367			−2.70421
$821$	−29.6700	+	17.1300i	−1.03549	+	0.597840i	−0.918552	−	0.395300i	$-0.870641\pi$
$821$	−29.6700	+	17.1300i	−1.03549	+	0.597840i	−0.116936	+	0.993139i	$0.537307\pi$
$822$	7.18110	+	12.4380i	0.250470	+	0.433826i
$823$	7.52897	−	13.0406i	0.262443	−	0.454565i	−0.704447	−	0.709756i	$-0.748805\pi$
$823$	7.52897	−	13.0406i	0.262443	−	0.454565i	0.966891	+	0.255191i	$0.0821383\pi$
$824$		−	6.23965i		−	0.217368i
$825$	−7.78857	−	4.49674i	−0.271163	−	0.156556i
$826$		0			0
$827$		−	53.2912i		−	1.85312i	−0.376152	−	0.926558i	$-0.622753\pi$
$827$		−	53.2912i		−	1.85312i	0.376152	−	0.926558i	$-0.377247\pi$
$828$	8.01035	−	13.8743i	0.278379	−	0.482167i
$829$	−5.47461	−	9.48230i	−0.190141	−	0.329334i	0.755156	−	0.655545i	$-0.227561\pi$
$829$	−5.47461	−	9.48230i	−0.190141	−	0.329334i	−0.945297	+	0.326211i	$0.894228\pi$
$830$	9.73149	−	5.61848i	0.337785	−	0.195020i
$831$	4.41543			0.153170
$832$	38.4100	+	0.674373i	1.33163	+	0.0233797i
$833$		0			0
$834$	31.5213	−	18.1988i	1.09149	−	0.630174i
$835$	−8.40881	−	14.5645i	−0.290999	−	0.504025i
$836$	3.82444	−	6.62413i	0.132271	−	0.229100i
$837$		−	6.50105i		−	0.224709i
$838$	28.0575	+	16.1990i	0.969229	+	0.559584i
$839$	−1.70671	−	0.985369i	−0.0589222	−	0.0340187i	0.470250	−	0.882534i	$-0.344164\pi$
$839$	−1.70671	−	0.985369i	−0.0589222	−	0.0340187i	−0.529172	+	0.848515i	$0.677497\pi$
$840$		0			0
$841$	−26.7410	+	46.3168i	−0.922104	+	1.59713i
$842$	27.9418	+	48.3966i	0.962937	+	1.66786i
$843$	6.52662	−	3.76814i	0.224789	−	0.129782i
$844$	−44.6962			−1.53851
$845$	1.59220	−	45.3291i	0.0547732	−	1.55937i
$846$	20.5893			0.707876
$847$		0			0
$848$	11.6903	+	20.2482i	0.401447	+	0.695326i
$849$	17.5524	−	30.4016i	0.602395	−	1.04338i
$850$		−	63.8852i		−	2.19125i
$851$	20.8049	+	12.0117i	0.713183	+	0.411756i
$852$	35.8512	+	20.6987i	1.22824	+	0.709125i
$853$		−	29.4473i		−	1.00826i	−0.863629	−	0.504128i	$-0.831814\pi$
$853$		−	29.4473i		−	1.00826i	0.863629	−	0.504128i	$-0.168186\pi$
$854$		0			0
$855$	7.36376	+	12.7544i	0.251835	+	0.436192i
$856$	−10.8556	+	6.26746i	−0.371035	+	0.214217i
$857$	−14.4517			−0.493660			−0.246830	−	0.969059i	$-0.579389\pi$
$857$	−14.4517			−0.493660			−0.246830	+	0.969059i	$0.579389\pi$
$858$	9.45189	+	0.165949i	0.322682	+	0.00566540i
$859$	−20.5302			−0.700482			−0.350241	−	0.936660i	$-0.613900\pi$
$859$	−20.5302			−0.700482			−0.350241	+	0.936660i	$0.613900\pi$
$860$	−55.1872	+	31.8623i	−1.88187	+	1.08650i
$861$		0			0
$862$	30.4721	−	52.7792i	1.03788	−	1.79767i
$863$			9.79734i			0.333505i	0.985999	+	0.166753i	$0.0533281\pi$
$863$			9.79734i			0.333505i	−0.985999	+	0.166753i	$0.946672\pi$
$864$	−39.3366	−	22.7110i	−1.33826	−	0.772644i
$865$	−36.3212	−	20.9701i	−1.23496	−	0.713004i
$866$		−	11.2407i		−	0.381974i
$867$	−0.755612	+	1.30876i	−0.0256619	+	0.0444478i
$868$		0			0
$869$	−10.0459	+	5.79998i	−0.340782	+	0.196751i
$870$	87.9977			2.98340
$871$	−23.3897	+	12.9620i	−0.792531	+	0.439201i
$872$	4.82927			0.163540
$873$	1.63834	−	0.945894i	0.0554493	−	0.0320137i
$874$	−19.4896	−	33.7570i	−0.659245	−	1.14185i
$875$		0			0
$876$		−	5.45823i		−	0.184416i
$877$	9.94810	+	5.74354i	0.335924	+	0.193946i	0.658468	−	0.752609i	$-0.271205\pi$
$877$	9.94810	+	5.74354i	0.335924	+	0.193946i	−0.322544	+	0.946554i	$0.604538\pi$
$878$	9.26047	+	5.34654i	0.312526	+	0.180437i
$879$			16.2389i			0.547724i
$880$	−5.12961	+	8.88474i	−0.172919	+	0.299505i
$881$	−8.59366	−	14.8847i	−0.289528	−	0.501477i	0.684169	−	0.729323i	$-0.260165\pi$
$881$	−8.59366	−	14.8847i	−0.289528	−	0.501477i	−0.973697	+	0.227846i	$0.926832\pi$
$882$		0			0
$883$	34.5738			1.16350			0.581750	−	0.813368i	$-0.302368\pi$
$883$	34.5738			1.16350			0.581750	+	0.813368i	$0.302368\pi$
$884$	17.6636	+	31.8737i	0.594091	+	1.07203i
$885$	−49.5069			−1.66416
$886$	−2.94137	+	1.69820i	−0.0988173	+	0.0570522i
$887$	−9.43739	−	16.3460i	−0.316877	−	0.548846i	0.662958	−	0.748657i	$-0.269301\pi$
$887$	−9.43739	−	16.3460i	−0.316877	−	0.548846i	−0.979835	+	0.199810i	$0.935967\pi$
$888$	−2.27969	+	3.94853i	−0.0765012	+	0.132504i
$889$		0			0
$890$	−25.7237	−	14.8516i	−0.862260	−	0.497826i
$891$	−3.07579	−	1.77581i	−0.103043	−	0.0594917i
$892$			7.02436i			0.235193i
$893$	13.5923	−	23.5425i	0.454848	−	0.787821i
$894$	−25.4272	−	44.0413i	−0.850414	−	1.47296i
$895$	−55.9152	+	32.2826i	−1.86904	+	1.07909i
$896$		0			0
$897$	13.4668	−	22.4073i	0.449642	−	0.748156i
$898$	−17.4176			−0.581233
$899$	9.08861	−	5.24731i	0.303122	−	0.175008i
$900$	10.5239	+	18.2280i	0.350797	+	0.607599i
$901$	−15.9857	+	27.6880i	−0.532560	+	0.922422i
$902$			18.4647i			0.614809i
$903$		0			0
$904$	3.77762	+	2.18101i	0.125642	+	0.0725394i
$905$			1.93463i			0.0643092i
$906$	11.6964	−	20.2588i	0.388588	−	0.673054i
$907$	−29.6575	−	51.3683i	−0.984762	−	1.70566i	−0.642990	−	0.765875i	$-0.722306\pi$
$907$	−29.6575	−	51.3683i	−0.984762	−	1.70566i	−0.341772	−	0.939783i	$-0.611027\pi$
$908$	−0.00882362	+	0.00509432i	−0.000292822	+	0.000169061i
$909$	−20.1026			−0.666762
$910$		0			0
$911$	−2.24809			−0.0744824			−0.0372412	−	0.999306i	$-0.511857\pi$
$911$	−2.24809			−0.0744824			−0.0372412	+	0.999306i	$0.511857\pi$
$912$	−12.2283	+	7.06002i	−0.404920	+	0.233781i
$913$	−0.727017	−	1.25923i	−0.0240608	−	0.0416744i
$914$	5.98614	−	10.3683i	0.198004	−	0.342953i
$915$		−	31.8870i		−	1.05415i
$916$	4.94062	+	2.85247i	0.163243	+	0.0942483i
$917$		0			0
$918$		−	50.1057i		−	1.65373i
$919$	9.32919	−	16.1586i	0.307742	−	0.533024i	−0.670126	−	0.742247i	$-0.733760\pi$
$919$	9.32919	−	16.1586i	0.307742	−	0.533024i	0.977868	+	0.209223i	$0.0670935\pi$
$920$	−7.43216	−	12.8729i	−0.245031	−	0.424406i
$921$	36.9251	−	21.3187i	1.21672	−	0.702476i
$922$	−70.6602			−2.32707
$923$	−40.5945	−	24.3973i	−1.33618	−	0.803046i
$924$		0			0
$925$	−27.3333	+	15.7809i	−0.898712	+	0.518872i
$926$	−0.107713	−	0.186564i	−0.00353967	−	0.00613089i
$927$	4.94363	−	8.56262i	0.162370	−	0.281233i
$928$		−	73.3247i		−	2.40700i
$929$	−39.2544	−	22.6635i	−1.28789	−	0.743566i	−0.309616	−	0.950862i	$-0.600201\pi$
$929$	−39.2544	−	22.6635i	−1.28789	−	0.743566i	−0.978278	+	0.207295i	$0.933534\pi$
$930$	−9.69638	−	5.59821i	−0.317957	−	0.183573i
$931$		0			0
$932$	−17.3957	+	30.1302i	−0.569814	+	0.986947i
$933$	13.2824	+	23.0057i	0.434845	+	0.753174i
$934$	21.1378	−	12.2039i	0.691651	−	0.399325i
$935$	−14.0288			−0.458790
$936$	−2.98158	−	1.79193i	−0.0974559	−	0.0585710i
$937$	−31.1994			−1.01924			−0.509620	−	0.860400i	$-0.670214\pi$
$937$	−31.1994			−1.01924			−0.509620	+	0.860400i	$0.670214\pi$
$938$		0			0
$939$	−3.02568	−	5.24063i	−0.0987394	−	0.171022i
$940$	32.9658	−	57.0984i	1.07523	−	1.86234i
$941$		−	11.0928i		−	0.361614i	−0.983519	−	0.180807i	$-0.942129\pi$
$941$		−	11.0928i		−	0.361614i	0.983519	−	0.180807i	$-0.0578709\pi$
$942$	−10.5317	−	6.08047i	−0.343141	−	0.198113i
$943$	44.2220	+	25.5316i	1.44006	+	0.831422i
$944$			33.2782i			1.08311i
$945$		0			0
$946$	7.59756	+	13.1594i	0.247018	+	0.427848i
$947$	−22.4733	+	12.9750i	−0.730284	+	0.421630i	−0.818526	−	0.574469i	$-0.805208\pi$
$947$	−22.4733	+	12.9750i	−0.730284	+	0.421630i	0.0882421	+	0.996099i	$0.471875\pi$
$948$	−38.7212			−1.25761
$949$	−0.109622	+	6.24368i	−0.00355847	+	0.202678i
$950$	51.2104			1.66149
$951$	−8.27897	+	4.77986i	−0.268464	+	0.154998i
$952$		0			0
$953$	−2.52008	+	4.36490i	−0.0816333	+	0.141393i	−0.903952	−	0.427635i	$-0.859347\pi$
$953$	−2.52008	+	4.36490i	−0.0816333	+	0.141393i	0.822318	+	0.569028i	$0.192680\pi$
$954$		−	19.4106i		−	0.628441i
$955$	60.5130	+	34.9372i	1.95816	+	1.13054i
$956$	3.77159	+	2.17753i	0.121982	+	0.0704262i
$957$		−	11.3867i		−	0.368079i
$958$	−27.2474	+	47.1938i	−0.880322	+	1.52476i
$959$		0			0
$960$	−42.7529	+	24.6834i	−1.37984	+	0.796653i
$961$	29.6647			0.956926
$962$	17.0896	−	28.4353i	0.550991	−	0.916791i
$963$	−19.8627			−0.640066
$964$	24.6672	−	14.2416i	0.794479	−	0.458692i
$965$	18.2984	+	31.6937i	0.589046	+	1.02026i
$966$		0			0
$967$		−	32.8852i		−	1.05752i	−0.848772	−	0.528759i	$-0.822658\pi$
$967$		−	32.8852i		−	1.05752i	0.848772	−	0.528759i	$-0.177342\pi$
$968$	6.83099	+	3.94387i	0.219556	+	0.126761i
$969$	−16.7214	−	9.65408i	−0.537168	−	0.310134i
$970$		−	11.1633i		−	0.358433i
$971$	−23.4370	+	40.5941i	−0.752130	+	1.30273i	0.194659	+	0.980871i	$0.437640\pi$
$971$	−23.4370	+	40.5941i	−0.752130	+	1.30273i	−0.946789	+	0.321856i	$0.895693\pi$
$972$	14.0990	+	24.4201i	0.452225	+	0.783276i
$973$		0			0
$974$	−27.2386			−0.872780
$975$	16.6482	+	30.0413i	0.533168	+	0.962093i
$976$	−21.4342			−0.686093
$977$	−32.2643	+	18.6278i	−1.03223	+	0.595957i	−0.917622	−	0.397454i	$-0.869894\pi$
$977$	−32.2643	+	18.6278i	−1.03223	+	0.595957i	−0.114605	+	0.993411i	$0.536560\pi$
$978$	−13.1432	−	22.7647i	−0.420273	−	0.727934i
$979$	−1.92176	+	3.32858i	−0.0614196	+	0.106382i
$980$		0			0
$981$	6.62717	+	3.82620i	0.211589	+	0.122161i
$982$	30.5256	+	17.6240i	0.974111	+	0.562403i
$983$		−	58.0698i		−	1.85214i	−0.377353	−	0.926069i	$-0.623166\pi$
$983$		−	58.0698i		−	1.85214i	0.377353	−	0.926069i	$-0.376834\pi$
$984$	−4.84560	+	8.39282i	−0.154472	+	0.267553i
$985$	24.0477	+	41.6518i	0.766222	+	1.32714i
$986$	70.0489	−	40.4427i	2.23081	−	1.28796i
$987$		0			0
$988$	−25.5499	+	14.1592i	−0.812852	+	0.450463i
$989$	42.0212			1.33620
$990$	7.37612	−	4.25860i	0.234428	−	0.135347i
$991$	−26.0420	−	45.1060i	−0.827251	−	1.43284i	−0.900187	−	0.435504i	$-0.856570\pi$
$991$	−26.0420	−	45.1060i	−0.827251	−	1.43284i	0.0729363	−	0.997337i	$-0.476763\pi$
$992$	−4.66474	+	8.07957i	−0.148106	+	0.256527i
$993$		−	13.5411i		−	0.429714i
$994$		0			0
$995$	26.3166	+	15.1939i	0.834294	+	0.481680i
$996$		−	4.85364i		−	0.153793i
$997$	4.44178	−	7.69340i	0.140673	−	0.243652i	−0.787077	−	0.616854i	$-0.788407\pi$
$997$	4.44178	−	7.69340i	0.140673	−	0.243652i	0.927750	+	0.373202i	$0.121740\pi$
$998$	17.4112	+	30.1572i	0.551143	+	0.954608i
$999$	−21.4377	+	12.3771i	−0.678258	+	0.391593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.j.491.13	✓	32
7.2	even	3		637.2.u.j.361.4		32
7.3	odd	6		637.2.k.j.569.14		32
7.4	even	3		637.2.k.j.569.13		32
7.5	odd	6		637.2.u.j.361.3		32
7.6	odd	2	inner	637.2.q.j.491.14	yes	32
13.2	odd	12		8281.2.a.cx.1.26		32
13.4	even	6	inner	637.2.q.j.589.13	yes	32
13.11	odd	12		8281.2.a.cx.1.8		32
91.4	even	6		637.2.u.j.30.4		32
91.17	odd	6		637.2.u.j.30.3		32
91.30	even	6		637.2.k.j.459.3		32
91.41	even	12		8281.2.a.cx.1.25		32
91.69	odd	6	inner	637.2.q.j.589.14	yes	32
91.76	even	12		8281.2.a.cx.1.7		32
91.82	odd	6		637.2.k.j.459.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.3		32	91.30	even	6
637.2.k.j.459.4		32	91.82	odd	6
637.2.k.j.569.13		32	7.4	even	3
637.2.k.j.569.14		32	7.3	odd	6
637.2.q.j.491.13	✓	32	1.1	even	1	trivial
637.2.q.j.491.14	yes	32	7.6	odd	2	inner
637.2.q.j.589.13	yes	32	13.4	even	6	inner
637.2.q.j.589.14	yes	32	91.69	odd	6	inner
637.2.u.j.30.3		32	91.17	odd	6
637.2.u.j.30.4		32	91.4	even	6
637.2.u.j.361.3		32	7.5	odd	6
637.2.u.j.361.4		32	7.2	even	3
8281.2.a.cx.1.7		32	91.76	even	12
8281.2.a.cx.1.8		32	13.11	odd	12
8281.2.a.cx.1.25		32	91.41	even	12
8281.2.a.cx.1.26		32	13.2	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81104 - 1.04560i) q^{2} +(-0.663994 - 1.15007i) q^{3} +(1.18657 - 2.05519i) q^{4} -3.48900i q^{5} +(-2.40503 - 1.38855i) q^{6} -0.780297i q^{8} +(0.618224 - 1.07080i) q^{9} +O(q^{10})\)	\(q+(1.81104 - 1.04560i) q^{2} +(-0.663994 - 1.15007i) q^{3} +(1.18657 - 2.05519i) q^{4} -3.48900i q^{5} +(-2.40503 - 1.38855i) q^{6} -0.780297i q^{8} +(0.618224 - 1.07080i) q^{9} +(-3.64811 - 6.31871i) q^{10} +(-0.817625 + 0.472056i) q^{11} -3.15149 q^{12} +(3.60500 + 0.0632937i) q^{13} +(-4.01260 + 2.31668i) q^{15} +(1.55725 + 2.69724i) q^{16} +(-2.12944 + 3.68829i) q^{17} -2.58566i q^{18} +(-2.95654 - 1.70696i) q^{19} +(-7.17058 - 4.13993i) q^{20} +(-0.987165 + 1.70982i) q^{22} +(2.72995 + 4.72840i) q^{23} +(-0.897397 + 0.518112i) q^{24} -7.17315 q^{25} +(6.59496 - 3.65476i) q^{26} -5.62595 q^{27} +(-4.54098 - 7.86521i) q^{29} +(-4.84464 + 8.39117i) q^{30} +1.15555i q^{31} +(6.99200 + 4.03683i) q^{32} +(1.08580 + 0.626885i) q^{33} +8.90617i q^{34} +(-1.46713 - 2.54114i) q^{36} +(3.81050 - 2.19999i) q^{37} -7.13919 q^{38} +(-2.32090 - 4.18803i) q^{39} -2.72246 q^{40} +(8.09942 - 4.67620i) q^{41} +(3.84817 - 6.66522i) q^{43} +2.24050i q^{44} +(-3.73601 - 2.15699i) q^{45} +(9.88805 + 5.70887i) q^{46} +7.96288i q^{47} +(2.06801 - 3.58190i) q^{48} +(-12.9908 + 7.50025i) q^{50} +5.65573 q^{51} +(4.40765 - 7.33386i) q^{52} +7.50701 q^{53} +(-10.1888 + 5.88251i) q^{54} +(1.64701 + 2.85270i) q^{55} +4.53364i q^{57} +(-16.4478 - 9.49612i) q^{58} +(9.25339 + 5.34245i) q^{59} +10.9956i q^{60} +(-3.44103 + 5.96004i) q^{61} +(1.20824 + 2.09274i) q^{62} +10.6547 q^{64} +(0.220832 - 12.5778i) q^{65} +2.62189 q^{66} +(-6.42303 + 3.70834i) q^{67} +(5.05343 + 8.75280i) q^{68} +(3.62533 - 6.27926i) q^{69} +(-11.3759 - 6.56790i) q^{71} +(-0.835538 - 0.482398i) q^{72} +1.73195i q^{73} +(4.60063 - 7.96853i) q^{74} +(4.76293 + 8.24963i) q^{75} +(-7.01625 + 4.05083i) q^{76} +(-8.58225 - 5.15793i) q^{78} +12.2866 q^{79} +(9.41069 - 5.43326i) q^{80} +(1.88093 + 3.25786i) q^{81} +(9.77889 - 16.9375i) q^{82} +1.54011i q^{83} +(12.8685 + 7.42961i) q^{85} -16.0946i q^{86} +(-6.03037 + 10.4449i) q^{87} +(0.368344 + 0.637990i) q^{88} +(3.52562 - 2.03552i) q^{89} -9.02139 q^{90} +12.9570 q^{92} +(1.32896 - 0.767276i) q^{93} +(8.32600 + 14.4211i) q^{94} +(-5.95558 + 10.3154i) q^{95} -10.7217i q^{96} +(1.32503 + 0.765009i) q^{97} +1.16735i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 28 * q^9	\( 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Introduction

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