LMFDB - Embedded newform 637.2.x.b.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not 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:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	637.19
Dual form			637.2.x.b.570.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26733 + 0.607529i) q^{2} +2.76026i q^{3} +(3.03963 + 1.75493i) q^{4} +(-1.53921 + 0.412430i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} -4.61904 q^{9} +O(q^{10})$	\(q+(2.26733 + 0.607529i) q^{2} +2.76026i q^{3} +(3.03963 + 1.75493i) q^{4} +(-1.53921 + 0.412430i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} -4.61904 q^{9} -3.74046 q^{10} +(2.22138 + 2.22138i) q^{11} +(-4.84407 + 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} +(0.649718 + 1.12534i) q^{16} +(0.320795 - 0.555633i) q^{17} +(-10.4729 - 2.80620i) q^{18} +(5.57436 + 5.57436i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +(0.126569 - 0.0730744i) q^{23} +(-6.91743 + 6.91743i) q^{24} +(-2.13106 + 1.23037i) q^{25} +(-0.281008 - 8.45868i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} -10.3246i q^{30} +(1.73252 - 6.46586i) q^{31} +(-1.04513 - 3.90048i) q^{32} +(-6.13158 + 6.13158i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-1.00675 + 3.75725i) q^{37} +(9.25232 + 16.0255i) q^{38} +(9.52232 - 2.89360i) q^{39} +(-4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(2.85380 + 10.6505i) q^{44} +(7.10966 - 1.90503i) q^{45} +(0.331367 - 0.0887896i) q^{46} +(-0.816005 - 3.04537i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(1.53369 + 0.885477i) q^{51} +(2.86768 - 12.3258i) q^{52} +(3.66059 + 6.34033i) q^{53} +(2.71502 - 10.1326i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(4.95989 - 4.95989i) q^{58} +(1.07349 + 4.00631i) q^{59} +(3.99568 - 14.9121i) q^{60} -4.50671i q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(3.03636 + 4.87760i) q^{65} +(-17.6274 + 10.1772i) q^{66} +(-1.00126 + 1.00126i) q^{67} +(1.95020 - 1.12595i) q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(-11.5757 - 11.5757i) q^{72} +(-6.81760 - 1.82677i) q^{73} +(-4.56527 + 7.90729i) q^{74} +(-3.39614 - 5.88228i) q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 - 0.548121i) q^{79} +(-1.46418 - 1.46418i) q^{80} -1.52162 q^{81} +13.6173 q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(6.35443 - 1.70266i) q^{86} +(7.14327 + 4.12417i) q^{87} +11.1339i q^{88} +(-13.1203 - 3.51557i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(17.8475 + 4.78221i) q^{93} -7.40060i q^{94} +(-10.8791 - 6.28107i) q^{95} +(10.7663 - 2.88483i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.26733	+	0.607529i	1.60324	+	0.429588i	0.946020	−	0.324108i	$-0.105064\pi$
$2$	2.26733	+	0.607529i	1.60324	+	0.429588i	0.657223	+	0.753696i	$0.271731\pi$
$3$			2.76026i			1.59364i	0.604219	+	0.796818i	$0.293485\pi$
$3$			2.76026i			1.59364i	−0.604219	+	0.796818i	$0.706515\pi$
$4$	3.03963	+	1.75493i	1.51982	+	0.877467i
$5$	−1.53921	+	0.412430i	−0.688355	+	0.184444i	−0.586009	−	0.810305i	$-0.699302\pi$
$5$	−1.53921	+	0.412430i	−0.688355	+	0.184444i	−0.102346	+	0.994749i	$0.532635\pi$
$6$	−1.67694	+	6.25841i	−0.684607	+	2.55499i
$7$		0			0
$7$		0			0
$8$	2.50608	+	2.50608i	0.886032	+	0.886032i
$9$	−4.61904			−1.53968
$10$	−3.74046			−1.18284
$11$	2.22138	+	2.22138i	0.669770	+	0.669770i	0.957663	−	0.287892i	$-0.0929546\pi$
$11$	2.22138	+	2.22138i	0.669770	+	0.669770i	−0.287892	+	0.957663i	$0.592955\pi$
$12$	−4.84407	+	8.39018i	−1.39836	+	2.42204i
$13$	−1.04831	−	3.44979i	−0.290748	−	0.956800i
$13$	−1.04831	−	3.44979i	−0.290748	−	0.956800i
$14$		0			0
$15$	−1.13841	−	4.24862i	−0.293937	−	1.09699i
$16$	0.649718	+	1.12534i	0.162430	+	0.281336i
$17$	0.320795	−	0.555633i	0.0778042	−	0.134761i	−0.824498	−	0.565865i	$-0.808542\pi$
$17$	0.320795	−	0.555633i	0.0778042	−	0.134761i	0.902302	+	0.431104i	$0.141876\pi$
$18$	−10.4729	−	2.80620i	−2.46848	−	0.661427i
$19$	5.57436	+	5.57436i	1.27885	+	1.27885i	0.941314	+	0.337532i	$0.109592\pi$
$19$	5.57436	+	5.57436i	1.27885	+	1.27885i	0.337532	+	0.941314i	$0.390408\pi$
$20$	−5.40242	−	1.44757i	−1.20802	−	0.323687i
$21$		0			0
$22$	3.68704	+	6.38614i	0.786080	+	1.36153i
$23$	0.126569	−	0.0730744i	0.0263914	−	0.0152371i	−0.486746	−	0.873543i	$-0.661816\pi$
$23$	0.126569	−	0.0730744i	0.0263914	−	0.0152371i	0.513138	+	0.858306i	$0.328483\pi$
$24$	−6.91743	+	6.91743i	−1.41201	+	1.41201i
$25$	−2.13106	+	1.23037i	−0.426212	+	0.246074i
$26$	−0.281008	−	8.45868i	−0.0551103	−	1.65888i
$27$		−	4.46896i		−	0.860051i
$28$		0			0
$29$	1.49412	−	2.58790i	0.277452	−	0.480561i	−0.693299	−	0.720650i	$-0.743843\pi$
$29$	1.49412	−	2.58790i	0.277452	−	0.480561i	0.970751	+	0.240089i	$0.0771768\pi$
$30$		−	10.3246i		−	1.88501i
$31$	1.73252	−	6.46586i	0.311170	−	1.16130i	−0.616333	−	0.787486i	$-0.711382\pi$
$31$	1.73252	−	6.46586i	0.311170	−	1.16130i	0.927503	−	0.373817i	$-0.121951\pi$
$32$	−1.04513	−	3.90048i	−0.184755	−	0.689514i
$33$	−6.13158	+	6.13158i	−1.06737	+	1.06737i
$34$	1.06491	−	1.06491i	0.182631	−	0.182631i
$35$		0			0
$36$	−14.0402	−	8.10610i	−2.34003	−	1.35102i
$37$	−1.00675	+	3.75725i	−0.165509	+	0.617688i	0.832466	+	0.554077i	$0.186929\pi$
$37$	−1.00675	+	3.75725i	−0.165509	+	0.617688i	−0.997975	+	0.0636115i	$0.979738\pi$
$38$	9.25232	+	16.0255i	1.50092	+	2.59968i
$39$	9.52232	−	2.89360i	1.52479	−	0.463347i
$40$	−4.89096	−	2.82380i	−0.773328	−	0.446481i
$41$	5.60356	−	1.50147i	0.875129	−	0.234490i	0.206825	−	0.978378i	$-0.433687\pi$
$41$	5.60356	−	1.50147i	0.875129	−	0.234490i	0.668305	+	0.743888i	$0.267020\pi$
$42$		0			0
$43$	2.42713	−	1.40130i	0.370133	−	0.213697i	−0.303383	−	0.952869i	$-0.598116\pi$
$43$	2.42713	−	1.40130i	0.370133	−	0.213697i	0.673517	+	0.739172i	$0.264783\pi$
$44$	2.85380	+	10.6505i	0.430227	+	1.60563i
$45$	7.10966	−	1.90503i	1.05985	−	0.283985i
$46$	0.331367	−	0.0887896i	0.0488574	−	0.0130913i
$47$	−0.816005	−	3.04537i	−0.119027	−	0.444213i	0.880530	−	0.473990i	$-0.157187\pi$
$47$	−0.816005	−	3.04537i	−0.119027	−	0.444213i	−0.999557	+	0.0297773i	$0.990520\pi$
$48$	−3.10624	+	1.79339i	−0.448348	+	0.258854i
$49$		0			0
$50$	−5.57930	+	1.49497i	−0.789032	+	0.211420i
$51$	1.53369	+	0.885477i	0.214760	+	0.123992i
$52$	2.86768	−	12.3258i	0.397676	−	1.70928i
$53$	3.66059	+	6.34033i	0.502821	+	0.870912i	0.999995	+	0.00326078i	$0.00103794\pi$
$53$	3.66059	+	6.34033i	0.502821	+	0.870912i	−0.497173	+	0.867651i	$0.665629\pi$
$54$	2.71502	−	10.1326i	0.369467	−	1.37887i
$55$	−4.33533	−	2.50300i	−0.584575	−	0.337505i
$56$		0			0
$57$	−15.3867	+	15.3867i	−2.03802	+	2.03802i
$58$	4.95989	−	4.95989i	0.651266	−	0.651266i
$59$	1.07349	+	4.00631i	0.139756	+	0.521578i	0.999933	+	0.0115814i	$0.00368656\pi$
$59$	1.07349	+	4.00631i	0.139756	+	0.521578i	−0.860177	+	0.509996i	$0.829647\pi$
$60$	3.99568	−	14.9121i	0.515840	−	1.92514i
$61$		−	4.50671i		−	0.577025i	−0.957476	−	0.288512i	$-0.906839\pi$
$61$		−	4.50671i		−	0.577025i	0.957476	−	0.288512i	$-0.0931607\pi$
$62$	7.85639	−	13.6077i	0.997763	−	1.72818i
$63$		0			0
$64$		−	12.0775i		−	1.50969i
$65$	3.03636	+	4.87760i	0.376614	+	0.604991i
$66$	−17.6274	+	10.1772i	−2.16978	+	1.25273i
$67$	−1.00126	+	1.00126i	−0.122323	+	0.122323i	−0.765618	−	0.643295i	$-0.777567\pi$
$67$	−1.00126	+	1.00126i	−0.122323	+	0.122323i	0.643295	+	0.765618i	$0.277567\pi$
$68$	1.95020	−	1.12595i	0.236496	−	0.136541i
$69$	0.201704	+	0.349362i	0.0242823	+	0.0420582i
$70$		0			0
$71$	13.8300	+	3.70574i	1.64132	+	0.439791i	0.957165	−	0.289544i	$-0.0935038\pi$
$71$	13.8300	+	3.70574i	1.64132	+	0.439791i	0.684157	+	0.729335i	$0.260170\pi$
$72$	−11.5757	−	11.5757i	−1.36420	−	1.36420i
$73$	−6.81760	−	1.82677i	−0.797940	−	0.213807i	−0.163261	−	0.986583i	$-0.552201\pi$
$73$	−6.81760	−	1.82677i	−0.797940	−	0.213807i	−0.634679	+	0.772776i	$0.718868\pi$
$74$	−4.56527	+	7.90729i	−0.530702	+	0.919203i
$75$	−3.39614	−	5.88228i	−0.392152	−	0.679227i
$76$	7.16138	+	26.7267i	0.821467	+	3.06576i
$77$		0			0
$78$	23.3482	−	0.775656i	2.64366	−	0.0878258i
$79$	0.316458	−	0.548121i	0.0356043	−	0.0616685i	−0.847674	−	0.530517i	$-0.821998\pi$
$79$	0.316458	−	0.548121i	0.0356043	−	0.0616685i	0.883278	+	0.468849i	$0.155331\pi$
$80$	−1.46418	−	1.46418i	−0.163700	−	0.163700i
$81$	−1.52162			−0.169069
$82$	13.6173			1.50378
$83$	1.07813	+	1.07813i	0.118340	+	0.118340i	0.763797	−	0.645457i	$-0.223333\pi$
$83$	1.07813	+	1.07813i	0.118340	+	0.118340i	−0.645457	+	0.763797i	$0.723333\pi$
$84$		0			0
$85$	−0.264611	+	0.987541i	−0.0287011	+	0.107114i
$86$	6.35443	−	1.70266i	0.685215	−	0.183603i
$87$	7.14327	+	4.12417i	0.765839	+	0.442158i
$88$			11.1339i			1.18688i
$89$	−13.1203	−	3.51557i	−1.39075	−	0.372649i	−0.515734	−	0.856749i	$-0.672481\pi$
$89$	−13.1203	−	3.51557i	−1.39075	−	0.372649i	−0.875013	+	0.484099i	$0.839147\pi$
$90$	17.2773			1.82119
$91$		0			0
$92$	0.512963			0.0534801
$93$	17.8475	+	4.78221i	1.85069	+	0.495892i
$94$		−	7.40060i		−	0.763314i
$95$	−10.8791	−	6.28107i	−1.11618	−	0.644425i
$96$	10.7663	−	2.88483i	1.09884	−	0.294432i
$97$	0.0487160	−	0.181811i	0.00494637	−	0.0184601i	−0.963409	−	0.268037i	$-0.913625\pi$
$97$	0.0487160	−	0.181811i	0.00494637	−	0.0184601i	0.968355	+	0.249577i	$0.0802916\pi$
$98$		0			0
$99$	−10.2606	−	10.2606i	−1.03123	−	1.03123i
$100$	−8.63686			−0.863686
$101$	1.19381			0.118788			0.0593942	−	0.998235i	$-0.481083\pi$
$101$	1.19381			0.118788			0.0593942	+	0.998235i	$0.481083\pi$
$102$	2.93943	+	2.93943i	0.291047	+	0.291047i
$103$	−2.39792	+	4.15331i	−0.236274	+	0.409238i	−0.959642	−	0.281224i	$-0.909260\pi$
$103$	−2.39792	+	4.15331i	−0.236274	+	0.409238i	0.723368	+	0.690462i	$0.242593\pi$
$104$	6.01830	−	11.2726i	0.590143	−	1.10537i
$105$		0			0
$106$	4.44783	+	16.5995i	0.432012	+	1.61229i
$107$	−7.64819	−	13.2471i	−0.739378	−	1.28064i	−0.952776	−	0.303675i	$-0.901786\pi$
$107$	−7.64819	−	13.2471i	−0.739378	−	1.28064i	0.213397	−	0.976966i	$-0.431547\pi$
$108$	7.84273	−	13.5840i	0.754667	−	1.30712i
$109$	−12.4638	−	3.33967i	−1.19382	−	0.319883i	−0.393424	−	0.919357i	$-0.628710\pi$
$109$	−12.4638	−	3.33967i	−1.19382	−	0.319883i	−0.800394	+	0.599475i	$0.795376\pi$
$110$	−8.30896	−	8.30896i	−0.792228	−	0.792228i
$111$	−10.3710	−	2.77890i	−0.984370	−	0.263761i
$112$		0			0
$113$	−0.770731	−	1.33494i	−0.0725042	−	0.125581i	0.827494	−	0.561475i	$-0.189766\pi$
$113$	−0.770731	−	1.33494i	−0.0725042	−	0.125581i	−0.899998	+	0.435894i	$0.856432\pi$
$114$	−44.2345	+	25.5388i	−4.14294	+	2.39193i
$115$	−0.164677	+	0.164677i	−0.0153562	+	0.0153562i
$116$	9.08318	−	5.24418i	0.843352	−	0.486910i
$117$	4.84217	+	15.9347i	0.447658	+	1.47316i
$118$			9.73580i			0.896253i
$119$		0			0
$120$	7.79441	−	13.5003i	0.711529	−	1.23240i
$121$		−	1.13097i		−	0.102815i
$122$	2.73796	−	10.2182i	0.247883	−	0.925111i
$123$	4.14445	+	15.4673i	0.373692	+	1.39464i
$124$	16.6134	−	16.6134i	1.49193	−	1.49193i
$125$	8.40660	−	8.40660i	0.751910	−	0.751910i
$126$		0			0
$127$	2.81842	+	1.62722i	0.250095	+	0.144392i	0.619808	−	0.784754i	$-0.287211\pi$
$127$	2.81842	+	1.62722i	0.250095	+	0.144392i	−0.369713	+	0.929146i	$0.620544\pi$
$128$	5.24716	−	19.5827i	0.463788	−	1.73088i
$129$	3.86796	+	6.69950i	0.340555	+	0.589858i
$130$	3.92114	+	12.9038i	0.343907	+	1.13174i
$131$	14.2615	+	8.23390i	1.24604	+	0.719400i	0.970317	−	0.241838i	$-0.0777504\pi$
$131$	14.2615	+	8.23390i	1.24604	+	0.719400i	0.275720	+	0.961238i	$0.411084\pi$
$132$	−29.3983	+	7.87724i	−2.55879	+	0.685626i
$133$		0			0
$134$	−2.87848	+	1.66189i	−0.248663	+	0.143565i
$135$	1.84313	+	6.87866i	0.158632	+	0.592021i
$136$	2.19640	−	0.588523i	0.188339	−	0.0504654i
$137$	0.365056	−	0.0978163i	0.0311888	−	0.00835701i	−0.243191	−	0.969978i	$-0.578194\pi$
$137$	0.365056	−	0.0978163i	0.0311888	−	0.00835701i	0.274380	+	0.961621i	$0.411527\pi$
$138$	0.245082	+	0.914659i	0.0208628	+	0.0778610i
$139$	−8.52132	+	4.91978i	−0.722769	+	0.417291i	−0.815771	−	0.578375i	$-0.803687\pi$
$139$	−8.52132	+	4.91978i	−0.722769	+	0.417291i	0.0930022	+	0.995666i	$0.470354\pi$
$140$		0			0
$141$	8.40602	−	2.25239i	0.707914	−	0.189685i
$142$	29.1058	+	16.8043i	2.44251	+	1.41018i
$143$	5.33460	−	9.99197i	0.446102	−	0.835570i
$144$	−3.00107	−	5.19801i	−0.250089	−	0.433167i
$145$	−1.23244	+	4.59954i	−0.102349	+	0.381971i
$146$	−14.3479	−	8.28378i	−1.18744	−	0.685570i
$147$		0			0
$148$	−9.65388	+	9.65388i	−0.793544	+	0.793544i
$149$	3.92698	−	3.92698i	0.321711	−	0.321711i	−0.527712	−	0.849423i	$-0.676950\pi$
$149$	3.92698	−	3.92698i	0.321711	−	0.321711i	0.849423	+	0.527712i	$0.176950\pi$
$150$	−4.12650	−	15.4003i	−0.336927	−	1.25743i
$151$	1.22809	−	4.58330i	0.0999406	−	0.372983i	−0.897782	−	0.440441i	$-0.854822\pi$
$151$	1.22809	−	4.58330i	0.0999406	−	0.372983i	0.997722	+	0.0674576i	$0.0214887\pi$
$152$			27.9396i			2.26620i
$153$	−1.48176	+	2.56649i	−0.119793	+	0.207488i
$154$		0			0
$155$			10.6669i			0.856782i
$156$	34.0224	+	7.91556i	2.72398	+	0.633752i
$157$	10.9293	−	6.31006i	0.872257	−	0.503598i	0.00415919	−	0.999991i	$-0.498676\pi$
$157$	10.9293	−	6.31006i	0.872257	−	0.503598i	0.868098	+	0.496394i	$0.165343\pi$
$158$	1.05051	−	1.05051i	0.0835744	−	0.0835744i
$159$	−17.5010	+	10.1042i	−1.38792	+	0.801314i
$160$	3.21735	+	5.57262i	0.254354	+	0.440554i
$161$		0			0
$162$	−3.45001	−	0.924428i	−0.271058	−	0.0726299i
$163$	−9.23004	−	9.23004i	−0.722952	−	0.722952i	0.246253	−	0.969206i	$-0.420801\pi$
$163$	−9.23004	−	9.23004i	−0.722952	−	0.722952i	−0.969206	+	0.246253i	$0.920801\pi$
$164$	19.6678	+	5.26996i	1.53579	+	0.411515i
$165$	6.90893	−	11.9666i	0.537860	−	0.931601i
$166$	1.78948	+	3.09948i	0.138891	+	0.240566i
$167$	−4.79697	−	17.9025i	−0.371201	−	1.38534i	−0.858817	−	0.512282i	$-0.828800\pi$
$167$	−4.79697	−	17.9025i	−0.371201	−	1.38534i	0.487616	−	0.873058i	$-0.337867\pi$
$168$		0			0
$169$	−10.8021	+	7.23288i	−0.830931	+	0.556375i
$170$	−1.19992	+	2.07832i	−0.0920296	+	0.159400i
$171$	−25.7482	−	25.7482i	−1.96901	−	1.96901i
$172$	9.83677			0.750047
$173$	5.59369			0.425280			0.212640	−	0.977131i	$-0.431794\pi$
$173$	5.59369			0.425280			0.212640	+	0.977131i	$0.431794\pi$
$174$	13.6906	+	13.6906i	1.03788	+	1.03788i
$175$		0			0
$176$	−1.05655	+	3.94308i	−0.0796402	+	0.297221i
$177$	−11.0585	+	2.96311i	−0.831205	+	0.222721i
$178$	−27.6122	−	15.9419i	−2.06962	−	1.19490i
$179$		−	9.49080i		−	0.709376i	−0.934985	−	0.354688i	$-0.884587\pi$
$179$		−	9.49080i		−	0.709376i	0.934985	−	0.354688i	$-0.115413\pi$
$180$	24.9540	+	6.68640i	1.85996	+	0.498375i
$181$	6.91516			0.514000			0.257000	−	0.966411i	$-0.417266\pi$
$181$	6.91516			0.514000			0.257000	+	0.966411i	$0.417266\pi$
$182$		0			0
$183$	12.4397			0.919568
$184$	0.500321	+	0.134060i	0.0368841	+	0.00988307i
$185$		−	6.19841i		−	0.455716i
$186$	37.5607	+	21.6857i	2.75408	+	1.59007i
$187$	1.94688	−	0.521664i	0.142370	−	0.0381479i
$188$	2.86407	−	10.6889i	0.208884	−	0.779565i
$189$		0			0
$190$	−20.8506	−	20.8506i	−1.51266	−	1.51266i
$191$	−2.50503			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$191$	−2.50503			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$192$	33.3370			2.40589
$193$	−15.9501	−	15.9501i	−1.14811	−	1.14811i	−0.986924	−	0.161187i	$-0.948468\pi$
$193$	−15.9501	−	15.9501i	−1.14811	−	1.14811i	−0.161187	−	0.986924i	$-0.551532\pi$
$194$	0.220911	−	0.382628i	0.0158605	−	0.0274711i
$195$	−13.4634	+	8.38114i	−0.964136	+	0.600186i
$196$		0			0
$197$	−4.63560	−	17.3003i	−0.330273	−	1.23259i	−0.908904	−	0.417005i	$-0.863080\pi$
$197$	−4.63560	−	17.3003i	−0.330273	−	1.23259i	0.578631	−	0.815589i	$-0.303587\pi$
$198$	−17.0306	−	29.4978i	−1.21031	−	2.09632i
$199$	−8.20617	+	14.2135i	−0.581720	+	1.00757i	0.413556	+	0.910479i	$0.364287\pi$
$199$	−8.20617	+	14.2135i	−0.581720	+	1.00757i	−0.995276	+	0.0970896i	$0.969047\pi$
$200$	−8.42400	−	2.25720i	−0.595667	−	0.159608i
$201$	−2.76374	−	2.76374i	−0.194939	−	0.194939i
$202$	2.70675	+	0.725273i	0.190447	+	0.0510300i
$203$		0			0
$204$	3.10791	+	5.38306i	0.217597	+	0.376889i
$205$	−8.00580	+	4.62215i	−0.559150	+	0.322825i
$206$	−7.96012	+	7.96012i	−0.554608	+	0.554608i
$207$	−0.584624	+	0.337533i	−0.0406342	+	0.0234602i
$208$	3.20110	−	3.42110i	0.221956	−	0.237210i
$209$			24.7655i			1.71307i
$210$		0			0
$211$	4.93176	−	8.54207i	0.339517	−	0.588060i	−0.644825	−	0.764330i	$-0.723070\pi$
$211$	4.93176	−	8.54207i	0.339517	−	0.588060i	0.984342	+	0.176270i	$0.0564032\pi$
$212$			25.6964i			1.76484i
$213$	−10.2288	+	38.1744i	−0.700867	+	2.61567i
$214$	−9.29299	−	34.6819i	−0.635256	−	2.37081i
$215$	−3.15792	+	3.15792i	−0.215368	+	0.215368i
$216$	11.1996	−	11.1996i	0.762033	−	0.762033i
$217$		0			0
$218$	−26.2306	−	15.1443i	−1.77656	−	1.02570i
$219$	5.04236	−	18.8184i	0.340731	−	1.27163i
$220$	−8.78520	−	15.2164i	−0.592298	−	1.02589i
$221$	−2.25311	−	0.524201i	−0.151561	−	0.0352616i
$222$	−21.8262	−	12.6013i	−1.46488	−	0.845747i
$223$	−8.41926	+	2.25594i	−0.563796	+	0.151069i	−0.529450	−	0.848341i	$-0.677602\pi$
$223$	−8.41926	+	2.25594i	−0.563796	+	0.151069i	−0.0343461	+	0.999410i	$0.510935\pi$
$224$		0			0
$225$	9.84344	−	5.68312i	0.656230	−	0.378874i
$226$	−0.936482	−	3.49500i	−0.0622939	−	0.232484i
$227$	−16.3175	+	4.37226i	−1.08303	+	0.290197i	−0.755837	−	0.654760i	$-0.772770\pi$
$227$	−16.3175	+	4.37226i	−1.08303	+	0.290197i	−0.327194	+	0.944957i	$0.606103\pi$
$228$	−73.7725	+	19.7673i	−4.88570	+	1.30912i
$229$	0.632892	+	2.36198i	0.0418227	+	0.156084i	0.983679	−	0.179931i	$-0.0575874\pi$
$229$	0.632892	+	2.36198i	0.0418227	+	0.156084i	−0.941857	+	0.336015i	$0.890921\pi$
$230$	−0.473424	+	0.273331i	−0.0312166	+	0.0180229i
$231$		0			0
$232$	10.2299	−	2.74108i	0.671624	−	0.179961i
$233$	−4.65474	−	2.68741i	−0.304942	−	0.176058i	0.339719	−	0.940527i	$-0.389668\pi$
$233$	−4.65474	−	2.68741i	−0.304942	−	0.176058i	−0.644661	+	0.764469i	$0.723001\pi$
$234$	1.29799	+	39.0710i	0.0848521	+	2.55415i
$235$	2.51200	+	4.35092i	0.163865	+	0.283823i
$236$	−3.76780	+	14.0616i	−0.245263	+	0.915334i
$237$	1.51296	+	0.873507i	0.0982772	+	0.0567404i
$238$		0			0
$239$	−11.9572	+	11.9572i	−0.773448	+	0.773448i	−0.978708	−	0.205260i	$-0.934196\pi$
$239$	−11.9572	+	11.9572i	−0.773448	+	0.773448i	0.205260	+	0.978708i	$0.434196\pi$
$240$	4.04151	−	4.04151i	0.260878	−	0.260878i
$241$	−3.48047	−	12.9893i	−0.224197	−	0.836713i	−0.982725	−	0.185073i	$-0.940748\pi$
$241$	−3.48047	−	12.9893i	−0.224197	−	0.836713i	0.758528	−	0.651640i	$-0.225919\pi$
$242$	0.687097	−	2.56428i	0.0441682	−	0.164838i
$243$		−	17.6069i		−	1.12949i
$244$	7.90898	−	13.6987i	0.506320	−	0.876972i
$245$		0			0
$246$			37.5873i			2.39648i
$247$	13.3867	−	25.0740i	0.851778	−	1.59542i
$248$	20.5458	−	11.8621i	1.30466	−	0.753245i
$249$	−2.97593	+	2.97593i	−0.188592	+	0.188592i
$250$	24.1678	−	13.9533i	1.52850	−	0.882483i
$251$	6.40248	+	11.0894i	0.404121	+	0.699958i	0.994219	−	0.107374i	$-0.0342441\pi$
$251$	6.40248	+	11.0894i	0.404121	+	0.699958i	−0.590098	+	0.807332i	$0.700911\pi$
$252$		0			0
$253$	0.443482	+	0.118831i	0.0278815	+	0.00747082i
$254$	5.40171	+	5.40171i	0.338933	+	0.338933i
$255$	−2.72587	−	0.730395i	−0.170701	−	0.0457391i
$256$	11.7166	−	20.2937i	0.732286	−	1.26836i
$257$	5.19036	+	8.98997i	0.323766	+	0.560779i	0.981262	−	0.192679i	$-0.0617176\pi$
$257$	5.19036	+	8.98997i	0.323766	+	0.560779i	−0.657496	+	0.753458i	$0.728384\pi$
$258$	4.69979	+	17.5399i	0.292596	+	1.09198i
$259$		0			0
$260$	0.669566	+	20.1547i	0.0415247	+	1.24994i
$261$	−6.90141	+	11.9536i	−0.427187	+	0.739909i
$262$	27.3333	+	27.3333i	1.68865	+	1.68865i
$263$	−4.37954			−0.270054			−0.135027	−	0.990842i	$-0.543112\pi$
$263$	−4.37954			−0.270054			−0.135027	+	0.990842i	$0.543112\pi$
$264$	−30.7324			−1.89145
$265$	−8.24936	−	8.24936i	−0.506754	−	0.506754i
$266$		0			0
$267$	9.70388	−	36.2154i	0.593868	−	2.21635i
$268$	−4.80061	+	1.28632i	−0.293244	+	0.0785744i
$269$	10.1192	+	5.84233i	0.616980	+	0.356213i	0.775692	−	0.631112i	$-0.217401\pi$
$269$	10.1192	+	5.84233i	0.616980	+	0.356213i	−0.158713	+	0.987325i	$0.550734\pi$
$270$			16.7159i			1.01730i
$271$	−29.6470	−	7.94389i	−1.80093	−	0.482557i	−0.806804	−	0.590819i	$-0.798805\pi$
$271$	−29.6470	−	7.94389i	−1.80093	−	0.482557i	−0.994122	+	0.108262i	$0.965471\pi$
$272$	0.833705			0.0505508
$273$		0			0
$274$	0.887127			0.0535933
$275$	−7.46700	−	2.00078i	−0.450277	−	0.120651i
$276$			1.41591i			0.0852278i
$277$	16.5109	+	9.53260i	0.992047	+	0.572758i	0.905885	−	0.423523i	$-0.139207\pi$
$277$	16.5109	+	9.53260i	0.992047	+	0.572758i	0.0861613	+	0.996281i	$0.472540\pi$
$278$	−22.3095	+	5.97782i	−1.33804	+	0.358526i
$279$	−8.00258	+	29.8660i	−0.479102	+	1.78803i
$280$		0			0
$281$	11.8671	+	11.8671i	0.707931	+	0.707931i	0.966100	−	0.258169i	$-0.0831190\pi$
$281$	11.8671	+	11.8671i	0.707931	+	0.707931i	−0.258169	+	0.966100i	$0.583119\pi$
$282$	20.4276			1.21645
$283$	−8.43728			−0.501544			−0.250772	−	0.968046i	$-0.580685\pi$
$283$	−8.43728			−0.501544			−0.250772	+	0.968046i	$0.580685\pi$
$284$	35.5349	+	35.5349i	2.10861	+	2.10861i
$285$	17.3374	−	30.0292i	1.02698	−	1.77878i
$286$	18.1657	−	19.4141i	1.07416	−	1.14798i
$287$		0			0
$288$	4.82750	+	18.0165i	0.284463	+	1.06163i
$289$	8.29418	+	14.3659i	0.487893	+	0.845055i
$290$	−5.58870	+	9.67992i	−0.328180	+	0.568424i
$291$	0.501845	+	0.134469i	0.0294187	+	0.00788271i
$292$	−17.5172	−	17.5172i	−1.02511	−	1.02511i
$293$	−8.00676	−	2.14541i	−0.467760	−	0.125336i	0.0172376	−	0.999851i	$-0.494513\pi$
$293$	−8.00676	−	2.14541i	−0.467760	−	0.125336i	−0.484998	+	0.874516i	$0.661180\pi$
$294$		0			0
$295$	−3.30465	−	5.72382i	−0.192404	−	0.333253i
$296$	−11.9390	+	6.89296i	−0.693938	+	0.400645i
$297$	9.92724	−	9.92724i	0.576037	−	0.576037i
$298$	11.2895	−	6.51800i	0.653984	−	0.377578i
$299$	−0.384774	−	0.360031i	−0.0222520	−	0.0208211i
$300$		−	23.8400i		−	1.37640i
$301$		0			0
$302$	5.56897	−	9.64574i	0.320458	−	0.555050i
$303$			3.29522i			0.189306i
$304$	−2.65131	+	9.89484i	−0.152063	+	0.567508i
$305$	1.85870	+	6.93677i	0.106429	+	0.397198i
$306$	−4.91886	+	4.91886i	−0.281192	+	0.281192i
$307$	−17.3438	+	17.3438i	−0.989863	+	0.989863i	−0.999949	−	0.0100865i	$-0.996789\pi$
$307$	−17.3438	+	17.3438i	−0.989863	+	0.989863i	0.0100865	+	0.999949i	$0.496789\pi$
$308$		0			0
$309$	−11.4642	−	6.61887i	−0.652177	−	0.376535i
$310$	−6.48042	+	24.1853i	−0.368063	+	1.37363i
$311$	−11.8560	−	20.5353i	−0.672294	−	1.16445i	−0.977252	−	0.212082i	$-0.931976\pi$
$311$	−11.8560	−	20.5353i	−0.672294	−	1.16445i	0.304958	−	0.952366i	$-0.401358\pi$
$312$	31.1153	+	16.6121i	1.76155	+	0.940474i
$313$	12.1862	+	7.03573i	0.688808	+	0.397683i	0.803165	−	0.595756i	$-0.203148\pi$
$313$	12.1862	+	7.03573i	0.688808	+	0.397683i	−0.114358	+	0.993440i	$0.536481\pi$
$314$	28.6140	−	7.66709i	1.61478	−	0.432679i
$315$		0			0
$316$	1.92383	−	1.11073i	0.108224	−	0.0624832i
$317$	4.33262	+	16.1695i	0.243344	+	0.908172i	0.974209	+	0.225649i	$0.0724504\pi$
$317$	4.33262	+	16.1695i	0.243344	+	0.908172i	−0.730865	+	0.682522i	$0.760883\pi$
$318$	−45.8190	+	12.2772i	−2.56940	+	0.688470i
$319$	9.06771	−	2.42969i	0.507694	−	0.136036i
$320$	4.98112	+	18.5898i	0.278453	+	1.03920i
$321$	36.5653	−	21.1110i	2.04088	−	1.17830i
$322$		0			0
$323$	4.88553	−	1.30907i	0.271838	−	0.0728388i
$324$	−4.62517	−	2.67034i	−0.256954	−	0.148352i
$325$	6.47852	+	6.06191i	0.359364	+	0.336254i
$326$	−15.3200	−	26.5350i	−0.848497	−	1.46964i
$327$	9.21836	−	34.4034i	0.509777	−	1.90251i
$328$	17.8058	+	10.2802i	0.983159	+	0.567627i
$329$		0			0
$330$	22.9349	−	22.9349i	1.26252	−	1.26252i
$331$	−6.84348	+	6.84348i	−0.376152	+	0.376152i	−0.869712	−	0.493560i	$-0.835695\pi$
$331$	−6.84348	+	6.84348i	−0.376152	+	0.376152i	0.493560	+	0.869712i	$0.335695\pi$
$332$	1.38508	+	5.16918i	0.0760160	+	0.283696i
$333$	4.65022	−	17.3549i	0.254831	−	0.951041i
$334$		−	43.5052i		−	2.38050i
$335$	1.12820	−	1.95410i	0.0616401	−	0.106764i
$336$		0			0
$337$			20.0838i			1.09403i	0.837122	+	0.547016i	$0.184236\pi$
$337$			20.0838i			1.09403i	−0.837122	+	0.547016i	$0.815764\pi$
$338$	−28.8861	+	9.83671i	−1.57120	+	0.535047i
$339$	3.68479	−	2.12742i	0.200131	−	0.115545i
$340$	−2.53739	+	2.53739i	−0.137609	+	0.137609i
$341$	18.2117	−	10.5145i	0.986218	−	0.569393i
$342$	−42.7368	−	74.0223i	−2.31094	−	4.00267i
$343$		0			0
$344$	9.59434	+	2.57080i	0.517292	+	0.138608i
$345$	−0.454552	−	0.454552i	−0.0244723	−	0.0244723i
$346$	12.6827	+	3.39833i	0.681827	+	0.182695i
$347$	11.1008	−	19.2271i	0.595920	−	1.03216i	−0.397496	−	0.917604i	$-0.630121\pi$
$347$	11.1008	−	19.2271i	0.595920	−	1.03216i	0.993416	−	0.114560i	$-0.0365458\pi$
$348$	14.4753	+	25.0719i	0.775957	+	1.34400i
$349$	−1.38593	−	5.17235i	−0.0741869	−	0.276869i	0.918861	−	0.394582i	$-0.129111\pi$
$349$	−1.38593	−	5.17235i	−0.0741869	−	0.276869i	−0.993048	+	0.117713i	$0.962444\pi$
$350$		0			0
$351$	−15.4170	+	4.68484i	−0.822897	+	0.250058i
$352$	6.34281	−	10.9861i	0.338073	−	0.585560i
$353$	18.4554	+	18.4554i	0.982281	+	0.982281i	0.999846	−	0.0175643i	$-0.00559119\pi$
$353$	18.4554	+	18.4554i	0.982281	+	0.982281i	−0.0175643	+	0.999846i	$0.505591\pi$
$354$	−26.8733			−1.42830
$355$	−22.8157			−1.21093
$356$	−33.7113	−	33.7113i	−1.78669	−	1.78669i
$357$		0			0
$358$	5.76594	−	21.5188i	0.304739	−	1.13730i
$359$	21.8723	−	5.86066i	1.15437	−	0.309314i	0.369658	−	0.929168i	$-0.379475\pi$
$359$	21.8723	−	5.86066i	1.15437	−	0.309314i	0.784717	+	0.619854i	$0.212808\pi$
$360$	22.5915	+	13.0432i	1.19068	+	0.687438i
$361$			43.1470i			2.27089i
$362$	15.6789	+	4.20116i	0.824066	+	0.220808i
$363$	3.12177			0.163850
$364$		0			0
$365$	11.2471			0.588702
$366$	28.2049	+	7.55747i	1.47429	+	0.395035i
$367$		−	14.1961i		−	0.741032i	−0.928826	−	0.370516i	$-0.879181\pi$
$367$		−	14.1961i		−	0.741032i	0.928826	−	0.370516i	$-0.120819\pi$
$368$	0.164468	+	0.0949555i	0.00857347	+	0.00494990i
$369$	−25.8831	+	6.93534i	−1.34742	+	0.361040i
$370$	3.76571	−	14.0538i	0.195770	−	0.730624i
$371$		0			0
$372$	45.8573	+	45.8573i	2.37759	+	2.37759i
$373$	3.50642			0.181556			0.0907778	−	0.995871i	$-0.471065\pi$
$373$	3.50642			0.181556			0.0907778	+	0.995871i	$0.471065\pi$
$374$	4.73114			0.244641
$375$	23.2044	+	23.2044i	1.19827	+	1.19827i
$376$	5.58697	−	9.67691i	0.288126	−	0.499048i
$377$	−10.4940	−	2.44150i	−0.540469	−	0.125744i
$378$		0			0
$379$	6.94797	+	25.9302i	0.356893	+	1.33194i	0.878085	+	0.478504i	$0.158821\pi$
$379$	6.94797	+	25.9302i	0.356893	+	1.33194i	−0.521192	+	0.853439i	$0.674513\pi$
$380$	−22.0457	−	38.1843i	−1.13092	−	1.95882i
$381$	−4.49154	+	7.77958i	−0.230109	+	0.398560i
$382$	−5.67972	−	1.52188i	−0.290600	−	0.0778660i
$383$	24.1497	+	24.1497i	1.23399	+	1.23399i	0.962417	+	0.271576i	$0.0875448\pi$
$383$	24.1497	+	24.1497i	1.23399	+	1.23399i	0.271576	+	0.962417i	$0.412455\pi$
$384$	54.0533	+	14.4835i	2.75839	+	0.739110i
$385$		0			0
$386$	−26.4739	−	45.8542i	−1.34749	−	2.33392i
$387$	−11.2110	+	6.47267i	−0.569887	+	0.329024i
$388$	0.467145	−	0.467145i	0.0237157	−	0.0237157i
$389$	−23.7849	+	13.7322i	−1.20594	+	0.696251i	−0.961870	−	0.273506i	$-0.911817\pi$
$389$	−23.7849	+	13.7322i	−1.20594	+	0.696251i	−0.244072	+	0.969757i	$0.578483\pi$
$390$	−35.6178	+	10.8234i	−1.80358	+	0.548063i
$391$		−	0.0937676i		−	0.00474203i
$392$		0			0
$393$	−22.7277	+	39.3656i	−1.14646	+	1.98573i
$394$		−	42.0417i		−	2.11803i
$395$	−0.261034	+	0.974190i	−0.0131340	+	0.0490168i
$396$	−13.1818	−	49.1952i	−0.662412	−	2.47215i
$397$	−26.2097	+	26.2097i	−1.31543	+	1.31543i	−0.398076	+	0.917352i	$0.630322\pi$
$397$	−26.2097	+	26.2097i	−1.31543	+	1.31543i	−0.917352	+	0.398076i	$0.869678\pi$
$398$	−27.2412	+	27.2412i	−1.36548	+	1.36548i
$399$		0			0
$400$	−2.76918	−	1.59879i	−0.138459	−	0.0799393i
$401$	4.49729	−	16.7841i	0.224584	−	0.838158i	−0.757987	−	0.652269i	$-0.773817\pi$
$401$	4.49729	−	16.7841i	0.224584	−	0.838158i	0.982571	−	0.185888i	$-0.0595163\pi$
$402$	−4.58725	−	7.94535i	−0.228791	−	0.396278i
$403$	−24.1221	+	0.801366i	−1.20161	+	0.0399189i
$404$	3.62874	+	2.09505i	0.180537	+	0.104233i
$405$	2.34209	−	0.627561i	0.116379	−	0.0311838i
$406$		0			0
$407$	−10.5826	+	6.10989i	−0.524562	+	0.302856i
$408$	1.62448	+	6.06263i	0.0804235	+	0.300145i
$409$	−10.8988	+	2.92033i	−0.538913	+	0.144401i	−0.518001	−	0.855380i	$-0.673324\pi$
$409$	−10.8988	+	2.92033i	−0.538913	+	0.144401i	−0.0209119	+	0.999781i	$0.506657\pi$
$410$	−20.9599	+	5.61618i	−1.03513	+	0.277363i
$411$	0.269999	+	1.00765i	0.0133180	+	0.0497036i
$412$	−14.5776	+	8.41637i	−0.718186	+	0.414645i
$413$		0			0
$414$	−1.53060	+	0.410122i	−0.0752247	+	0.0201564i
$415$	−2.10413	−	1.21482i	−0.103287	−	0.0596330i
$416$	−12.3602	+	7.69439i	−0.606010	+	0.377248i
$417$	−13.5799	−	23.5211i	−0.665010	−	1.15183i
$418$	−15.0458	+	56.1515i	−0.735912	+	2.74646i
$419$	16.1248	+	9.30964i	0.787747	+	0.454806i	0.839169	−	0.543871i	$-0.183042\pi$
$419$	16.1248	+	9.30964i	0.787747	+	0.454806i	−0.0514220	+	0.998677i	$0.516375\pi$
$420$		0			0
$421$	18.9024	−	18.9024i	0.921247	−	0.921247i	−0.0758709	−	0.997118i	$-0.524174\pi$
$421$	18.9024	−	18.9024i	0.921247	−	0.921247i	0.997118	+	0.0758709i	$0.0241737\pi$
$422$	16.3715	−	16.3715i	0.796951	−	0.796951i
$423$	3.76916	+	14.0667i	0.183263	+	0.683945i
$424$	−6.71564	+	25.0631i	−0.326140	+	1.21717i
$425$			1.57878i			0.0765823i
$426$	−46.3841	+	80.3397i	−2.24732	+	3.89247i
$427$		0			0
$428$		−	53.6883i		−	2.59512i
$429$	27.5804	+	14.7249i	1.33160	+	0.710924i
$430$	−9.07856	+	5.24151i	−0.437807	+	0.252768i
$431$	−20.8750	+	20.8750i	−1.00552	+	1.00552i	−0.00553055	+	0.999985i	$0.501760\pi$
$431$	−20.8750	+	20.8750i	−1.00552	+	1.00552i	−0.999985	+	0.00553055i	$0.998240\pi$
$432$	5.02912	−	2.90356i	0.241964	−	0.139698i
$433$	17.9660	+	31.1180i	0.863390	+	1.49543i	0.868637	+	0.495449i	$0.164996\pi$
$433$	17.9660	+	31.1180i	0.863390	+	1.49543i	−0.00524758	+	0.999986i	$0.501670\pi$
$434$		0			0
$435$	−12.6959	−	3.40186i	−0.608723	−	0.163107i
$436$	−32.0246	−	32.0246i	−1.53370	−	1.53370i
$437$	1.11288	+	0.298196i	0.0532363	+	0.0142646i
$438$	22.8654	−	39.6040i	1.09255	−	1.89235i
$439$	−4.87991	−	8.45226i	−0.232906	−	0.403404i	0.725756	−	0.687952i	$-0.241490\pi$
$439$	−4.87991	−	8.45226i	−0.232906	−	0.403404i	−0.958662	+	0.284548i	$0.908157\pi$
$440$	−4.59195	−	17.1374i	−0.218912	−	0.816992i
$441$		0			0
$442$	−4.79007	−	2.55737i	−0.227840	−	0.121641i
$443$	−19.3899	+	33.5843i	−0.921241	+	1.59564i	−0.123744	+	0.992314i	$0.539490\pi$
$443$	−19.3899	+	33.5843i	−0.921241	+	1.59564i	−0.797497	+	0.603323i	$0.793843\pi$
$444$	−26.6472	−	26.6472i	−1.26462	−	1.26462i
$445$	21.6448			1.02606
$446$	−20.4598			−0.968799
$447$	10.8395	+	10.8395i	0.512690	+	0.512690i
$448$		0			0
$449$	−2.42216	+	9.03963i	−0.114309	+	0.426606i	−0.999234	−	0.0391263i	$-0.987543\pi$
$449$	−2.42216	+	9.03963i	−0.114309	+	0.426606i	0.884925	+	0.465733i	$0.154209\pi$
$450$	25.7710	−	6.90531i	1.21486	−	0.325520i
$451$	15.7830	+	9.11229i	0.743190	+	0.429081i
$452$		−	5.41033i		−	0.254480i
$453$	12.6511	+	3.38985i	0.594400	+	0.159269i
$454$	−39.6534			−1.86103
$455$		0			0
$456$	−77.1204			−3.61150
$457$	−18.5661	−	4.97477i	−0.868485	−	0.232710i	−0.203053	−	0.979168i	$-0.565086\pi$
$457$	−18.5661	−	4.97477i	−0.868485	−	0.232710i	−0.665433	+	0.746458i	$0.731753\pi$
$458$			5.73989i			0.268208i
$459$	−2.48310	−	1.43362i	−0.115901	−	0.0669156i
$460$	−0.789557	+	0.211561i	−0.0368133	+	0.00986409i
$461$	3.50466	−	13.0796i	0.163228	−	0.609175i	−0.835031	−	0.550202i	$-0.814551\pi$
$461$	3.50466	−	13.0796i	0.163228	−	0.609175i	0.998260	−	0.0589733i	$-0.0187827\pi$
$462$		0			0
$463$	−14.6336	−	14.6336i	−0.680081	−	0.680081i	0.279937	−	0.960018i	$-0.409686\pi$
$463$	−14.6336	−	14.6336i	−0.680081	−	0.680081i	−0.960018	+	0.279937i	$0.909686\pi$
$464$	3.88304			0.180266
$465$	−29.4433			−1.36540
$466$	−8.92114	−	8.92114i	−0.413264	−	0.413264i
$467$	15.4866	−	26.8236i	0.716634	−	1.24125i	−0.245692	−	0.969348i	$-0.579015\pi$
$467$	15.4866	−	26.8236i	0.716634	−	1.24125i	0.962326	−	0.271899i	$-0.0876515\pi$
$468$	−13.2459	+	56.9334i	−0.612294	+	2.63175i
$469$		0			0
$470$	3.05223	+	11.3911i	0.140789	+	0.525431i
$471$	17.4174	+	30.1678i	0.802552	+	1.39006i
$472$	−7.34989	+	12.7304i	−0.338306	+	0.585963i
$473$	8.50439	+	2.27874i	0.391032	+	0.104777i
$474$	2.89969	+	2.89969i	0.133187	+	0.133187i
$475$	−18.7378	−	5.02078i	−0.859750	−	0.230369i
$476$		0			0
$477$	−16.9084	−	29.2862i	−0.774183	−	1.34092i
$478$	−34.3753	+	19.8466i	−1.57229	+	0.907761i
$479$	−5.19377	+	5.19377i	−0.237310	+	0.237310i	−0.815735	−	0.578426i	$-0.803667\pi$
$479$	−5.19377	+	5.19377i	−0.237310	+	0.237310i	0.578426	+	0.815735i	$0.303667\pi$
$480$	−15.3819	+	8.88072i	−0.702083	+	0.405348i
$481$	14.0171	−	0.465666i	0.639125	−	0.0212326i
$482$		−	31.5654i		−	1.43777i
$483$		0			0
$484$	1.98478	−	3.43773i	0.0902171	−	0.156261i
$485$			0.299937i			0.0136194i
$486$	10.6967	−	39.9207i	0.485213	−	1.81084i
$487$	−2.55251	−	9.52611i	−0.115665	−	0.431669i	0.883670	−	0.468110i	$-0.155065\pi$
$487$	−2.55251	−	9.52611i	−0.115665	−	0.431669i	−0.999336	+	0.0364405i	$0.988398\pi$
$488$	11.2942	−	11.2942i	0.511263	−	0.511263i
$489$	25.4773	−	25.4773i	1.15212	−	1.15212i
$490$		0			0
$491$	33.1372	+	19.1318i	1.49546	+	0.863404i	0.999986	−	0.00521946i	$-0.00166141\pi$
$491$	33.1372	+	19.1318i	1.49546	+	0.863404i	0.495473	+	0.868623i	$0.334995\pi$
$492$	−14.5465	+	54.2881i	−0.655805	+	2.44750i
$493$	−0.958615	−	1.66037i	−0.0431738	−	0.0747793i
$494$	45.5853	−	48.7182i	2.05098	−	2.19193i
$495$	20.0250	+	11.5615i	0.900058	+	0.519649i
$496$	8.40197	−	2.25130i	0.377260	−	0.101086i
$497$		0			0
$498$	−8.55536	+	4.93944i	−0.383375	+	0.221342i
$499$	0.000375951		0.00140307i	1.68299e−5		6.28100e-5i	0.965934	−	0.258788i	$-0.0833230\pi$
$499$	0.000375951		0.00140307i	1.68299e−5		6.28100e-5i	−0.965917	+	0.258850i	$0.916656\pi$
$500$	40.3060	−	10.8000i	1.80254	−	0.482989i
$501$	49.4157	−	13.2409i	2.20773	−	0.591559i
$502$	7.77938	+	29.0331i	0.347211	+	1.29581i
$503$	−21.6205	+	12.4826i	−0.964012	+	0.556573i	−0.897406	−	0.441206i	$-0.854551\pi$
$503$	−21.6205	+	12.4826i	−0.964012	+	0.556573i	−0.0666068	+	0.997779i	$0.521217\pi$
$504$		0			0
$505$	−1.83752	+	0.492362i	−0.0817686	+	0.0219098i
$506$	0.933326	+	0.538856i	0.0414914	+	0.0239551i
$507$	−19.9646	−	29.8166i	−0.886660	−	1.32420i
$508$	5.71132	+	9.89229i	0.253399	+	0.438900i
$509$	−0.678383	+	2.53176i	−0.0300688	+	0.112218i	−0.979329	−	0.202273i	$-0.935167\pi$
$509$	−0.678383	+	2.53176i	−0.0300688	+	0.112218i	0.949260	+	0.314491i	$0.101834\pi$
$510$	−5.73671	−	3.31209i	−0.254026	−	0.146662i
$511$		0			0
$512$	10.2233	−	10.2233i	0.451811	−	0.451811i
$513$	24.9116	−	24.9116i	1.09987	−	1.09987i
$514$	6.30659	+	23.5365i	0.278172	+	1.03815i
$515$	1.97795	−	7.38179i	0.0871587	−	0.325281i
$516$			27.1521i			1.19530i
$517$	4.95226	−	8.57757i	0.217800	−	0.377241i
$518$		0			0
$519$			15.4400i			0.677742i
$520$	−4.61428	+	19.8330i	−0.202350	+	0.869734i
$521$	25.8598	−	14.9302i	1.13294	−	0.654102i	0.188266	−	0.982118i	$-0.439713\pi$
$521$	25.8598	−	14.9302i	1.13294	−	0.654102i	0.944672	+	0.328016i	$0.106380\pi$
$522$	−22.9099	+	22.9099i	−1.00274	+	1.00274i
$523$	−13.9268	+	8.04062i	−0.608975	+	0.351592i	−0.772564	−	0.634937i	$-0.781026\pi$
$523$	−13.9268	+	8.04062i	−0.608975	+	0.351592i	0.163589	+	0.986529i	$0.447693\pi$
$524$	28.8999	+	50.0561i	1.26250	+	2.18671i
$525$		0			0
$526$	−9.92985	−	2.66069i	−0.432962	−	0.116012i
$527$	−3.03686	−	3.03686i	−0.132288	−	0.132288i
$528$	−10.8839	−	2.91634i	−0.473663	−	0.126918i
$529$	−11.4893	+	19.9001i	−0.499536	+	0.865221i
$530$	−13.6923	−	23.7157i	−0.594755	−	1.03015i
$531$	−4.95848	−	18.5053i	−0.215180	−	0.803062i
$532$		0			0
$533$	−11.0540	−	17.7571i	−0.478802	−	0.769146i
$534$	44.0038	−	76.2168i	1.90423	−	3.29822i
$535$	17.2356	+	17.2356i	0.745162	+	0.745162i
$536$	−5.01847			−0.216765
$537$	26.1971			1.13049
$538$	19.3942	+	19.3942i	0.836143	+	0.836143i
$539$		0			0
$540$	−6.46915	+	24.1432i	−0.278388	+	1.03896i
$541$	−17.0022	+	4.55572i	−0.730980	+	0.195866i	−0.605066	−	0.796176i	$-0.706853\pi$
$541$	−17.0022	+	4.55572i	−0.730980	+	0.195866i	−0.125915	+	0.992041i	$0.540187\pi$
$542$	−62.3933	−	36.0228i	−2.68002	−	1.54731i
$543$			19.0876i			0.819129i
$544$	−2.50251	−	0.670546i	−0.107294	−	0.0287494i
$545$	20.5618			0.880771
$546$		0			0
$547$	−15.8734			−0.678698			−0.339349	−	0.940661i	$-0.610207\pi$
$547$	−15.8734			−0.678698			−0.339349	+	0.940661i	$0.610207\pi$
$548$	1.28130	+	0.343322i	0.0547343	+	0.0146660i
$549$			20.8166i			0.888433i
$550$	−15.7146	−	9.07284i	−0.670073	−	0.386867i
$551$	22.7547	−	6.09709i	0.969381	−	0.259745i
$552$	−0.370042	+	1.38101i	−0.0157500	+	0.0587799i
$553$		0			0
$554$	31.6444	+	31.6444i	1.34444	+	1.34444i
$555$	17.1092			0.726246
$556$	−34.5356			−1.46464
$557$	1.79108	+	1.79108i	0.0758906	+	0.0758906i	0.744033	−	0.668143i	$-0.232910\pi$
$557$	1.79108	+	1.79108i	0.0758906	+	0.0758906i	−0.668143	+	0.744033i	$0.732910\pi$
$558$	−36.2889	+	62.8543i	−1.53623	+	2.66083i
$559$	−7.37857	−	6.90409i	−0.312080	−	0.292012i
$560$		0			0
$561$	1.43993	+	5.37389i	0.0607938	+	0.226886i
$562$	19.6970	+	34.1162i	0.830867	+	1.43910i
$563$	10.1159	−	17.5213i	0.426336	−	0.738436i	−0.570208	−	0.821500i	$-0.693137\pi$
$563$	10.1159	−	17.5213i	0.426336	−	0.738436i	0.996544	+	0.0830642i	$0.0264707\pi$
$564$	29.5040	+	7.90558i	1.24234	+	0.332885i
$565$	1.73689	+	1.73689i	0.0730714	+	0.0730714i
$566$	−19.1301	−	5.12589i	−0.804098	−	0.215457i
$567$		0			0
$568$	25.3722	+	43.9460i	1.06459	+	1.84393i
$569$	12.8801	−	7.43632i	0.539961	−	0.311747i	−0.205102	−	0.978741i	$-0.565753\pi$
$569$	12.8801	−	7.43632i	0.539961	−	0.311747i	0.745063	+	0.666994i	$0.232419\pi$
$570$	57.5532	−	57.5532i	2.41064	−	2.41064i
$571$	31.9767	−	18.4617i	1.33818	−	0.772600i	0.351645	−	0.936133i	$-0.385622\pi$
$571$	31.9767	−	18.4617i	1.33818	−	0.772600i	0.986538	+	0.163533i	$0.0522891\pi$
$572$	33.7505	−	21.0101i	1.41118	−	0.878475i
$573$		−	6.91453i		−	0.288859i
$574$		0			0
$575$	−0.179817	+	0.311452i	−0.00749888	+	0.0129884i
$576$			55.7864i			2.32443i
$577$	−5.31122	+	19.8217i	−0.221109	+	0.825189i	0.762817	+	0.646614i	$0.223816\pi$
$577$	−5.31122	+	19.8217i	−0.221109	+	0.825189i	−0.983926	+	0.178575i	$0.942851\pi$
$578$	10.0779	+	37.6113i	0.419186	+	1.56442i
$579$	44.0263	−	44.0263i	1.82967	−	1.82967i
$580$	−11.8181	+	11.8181i	−0.490718	+	0.490718i
$581$		0			0
$582$	1.05615	+	0.609771i	0.0437790	+	0.0252758i
$583$	−5.95271	+	22.2158i	−0.246536	+	0.920086i
$584$	−12.5074	−	21.6635i	−0.517560	−	0.896441i
$585$	−14.0251	−	22.5298i	−0.579865	−	0.931492i
$586$	−16.8506	−	9.72867i	−0.696090	−	0.401888i
$587$	19.8321	−	5.31399i	0.818557	−	0.219332i	0.174842	−	0.984597i	$-0.444059\pi$
$587$	19.8321	−	5.31399i	0.818557	−	0.219332i	0.643715	+	0.765265i	$0.277392\pi$
$588$		0			0
$589$	45.7007	−	26.3853i	1.88307	−	1.08719i
$590$	−4.01534	−	14.9854i	−0.165309	−	0.616941i
$591$	47.7533	−	12.7955i	1.96431	−	0.526335i
$592$	−4.88231	+	1.30821i	−0.200662	+	0.0537671i
$593$	−10.7660	−	40.1793i	−0.442107	−	1.64997i	−0.723464	−	0.690362i	$-0.757451\pi$
$593$	−10.7660	−	40.1793i	−0.442107	−	1.64997i	0.281357	−	0.959603i	$-0.409216\pi$
$594$	28.5394	−	16.4772i	1.17099	−	0.676069i
$595$		0			0
$596$	18.8282	−	5.04500i	0.771233	−	0.206651i
$597$	−39.2330	−	22.6512i	−1.60570	−	0.927050i
$598$	−0.653680	−	1.05007i	−0.0267310	−	0.0429405i
$599$	2.16999	+	3.75853i	0.0886634	+	0.153569i	0.906946	−	0.421246i	$-0.138407\pi$
$599$	2.16999	+	3.75853i	0.0886634	+	0.153569i	−0.818283	+	0.574816i	$0.805074\pi$
$600$	6.23047	−	23.2524i	0.254358	−	0.949277i
$601$	−5.72067	−	3.30283i	−0.233351	−	0.134725i	0.378766	−	0.925492i	$-0.376348\pi$
$601$	−5.72067	−	3.30283i	−0.233351	−	0.134725i	−0.612117	+	0.790767i	$0.709682\pi$
$602$		0			0
$603$	4.62485	−	4.62485i	0.188339	−	0.188339i
$604$	11.7763	−	11.7763i	0.479172	−	0.479172i
$605$	0.466446	+	1.74080i	0.0189637	+	0.0707735i
$606$	−2.00194	+	7.47135i	−0.0813233	+	0.303503i
$607$			46.0468i			1.86898i	0.355985	+	0.934492i	$0.384146\pi$
$607$			46.0468i			1.86898i	−0.355985	+	0.934492i	$0.615854\pi$
$608$	15.9168	−	27.5686i	0.645510	−	1.11806i
$609$		0			0
$610$			16.8571i			0.682526i
$611$	−9.65047	+	6.00753i	−0.390416	+	0.243039i
$612$	−9.00804	+	5.20079i	−0.364128	+	0.210230i
$613$	20.2929	−	20.2929i	0.819624	−	0.819624i	−0.166429	−	0.986053i	$-0.553224\pi$
$613$	20.2929	−	20.2929i	0.819624	−	0.819624i	0.986053	+	0.166429i	$0.0532237\pi$
$614$	−49.8609	+	28.7872i	−2.01222	+	1.16176i
$615$	−12.7583	−	22.0981i	−0.514466	−	0.891081i
$616$		0			0
$617$	0.0947548	+	0.0253895i	0.00381469	+	0.00102214i	0.260726	−	0.965413i	$-0.416038\pi$
$617$	0.0947548	+	0.0253895i	0.00381469	+	0.00102214i	−0.256911	+	0.966435i	$0.582705\pi$
$618$	−21.9720	−	21.9720i	−0.883844	−	0.883844i
$619$	−40.8542	−	10.9468i	−1.64207	−	0.439991i	−0.684691	−	0.728834i	$-0.740063\pi$
$619$	−40.8542	−	10.9468i	−1.64207	−	0.439991i	−0.957376	+	0.288843i	$0.906729\pi$
$620$	−18.7196	+	32.4233i	−0.751798	+	1.30215i
$621$	−0.326566	−	0.565629i	−0.0131047	−	0.0226979i
$622$	−14.4058	−	53.7630i	−0.577619	−	2.15570i
$623$		0			0
$624$	9.44312	+	8.83587i	0.378027	+	0.353718i
$625$	−3.32054	+	5.75135i	−0.132822	+	0.230054i
$626$	23.3558	+	23.3558i	0.933486	+	0.933486i
$627$	−68.3592			−2.73001
$628$	44.2950			1.76756
$629$	1.76469	+	1.76469i	0.0703629	+	0.0703629i
$630$		0			0
$631$	2.02584	−	7.56053i	0.0806473	−	0.300980i	−0.913807	−	0.406148i	$-0.866872\pi$
$631$	2.02584	−	7.56053i	0.0806473	−	0.300980i	0.994454	+	0.105169i	$0.0335383\pi$
$632$	2.16670	−	0.580566i	0.0861868	−	0.0230937i
$633$	23.5783	+	13.6130i	0.937154	+	0.541066i
$634$			39.2938i			1.56056i
$635$	−5.00926	−	1.34223i	−0.198786	−	0.0532646i
$636$	−70.9288			−2.81251
$637$		0			0
$638$	22.0356			0.872397
$639$	−63.8813	−	17.1170i	−2.52711	−	0.677136i
$640$			32.3059i			1.27700i
$641$	28.9275	+	16.7013i	1.14257	+	0.659661i	0.947065	−	0.321042i	$-0.104033\pi$
$641$	28.9275	+	16.7013i	1.14257	+	0.659661i	0.195502	+	0.980703i	$0.437366\pi$
$642$	95.7311	−	25.6511i	3.77820	−	1.01237i
$643$	4.94009	−	18.4367i	0.194818	−	0.727071i	−0.797496	−	0.603324i	$-0.793842\pi$
$643$	4.94009	−	18.4367i	0.194818	−	0.727071i	0.992314	−	0.123746i	$-0.0394909\pi$
$644$		0			0
$645$	−8.71667	−	8.71667i	−0.343219	−	0.343219i
$646$	11.8724			0.467113
$647$	32.9045			1.29361			0.646804	−	0.762656i	$-0.276105\pi$
$647$	32.9045			1.29361			0.646804	+	0.762656i	$0.276105\pi$
$648$	−3.81330	−	3.81330i	−0.149800	−	0.149800i
$649$	−6.51491	+	11.2842i	−0.255733	+	0.442942i
$650$	11.0061	+	17.6802i	0.431696	+	0.693475i
$651$		0			0
$652$	−11.8578	−	44.2541i	−0.464389	−	1.73312i
$653$	−13.9982	−	24.2457i	−0.547793	−	0.948806i	−0.998425	−	0.0560961i	$-0.982135\pi$
$653$	−13.9982	−	24.2457i	−0.547793	−	0.948806i	0.450632	−	0.892710i	$-0.351199\pi$
$654$	41.8021	−	72.4034i	1.63459	−	2.83120i
$655$	−25.3474	−	6.79182i	−0.990405	−	0.265378i
$656$	5.33041	+	5.33041i	0.208117	+	0.208117i
$657$	31.4907	+	8.43792i	1.22857	+	0.329195i
$658$		0			0
$659$	−5.35203	−	9.27000i	−0.208486	−	0.361108i	0.742752	−	0.669567i	$-0.233520\pi$
$659$	−5.35203	−	9.27000i	−0.208486	−	0.361108i	−0.951238	+	0.308459i	$0.900187\pi$
$660$	42.0013	−	24.2494i	1.63490	−	0.943908i
$661$	−16.9884	+	16.9884i	−0.660772	+	0.660772i	−0.955562	−	0.294790i	$-0.904750\pi$
$661$	−16.9884	+	16.9884i	−0.660772	+	0.660772i	0.294790	+	0.955562i	$0.404750\pi$
$662$	−19.6740	+	11.3588i	−0.764653	+	0.441473i
$663$	1.44693	−	6.21917i	0.0561942	−	0.241532i
$664$			5.40377i			0.209707i
$665$		0			0
$666$	21.0872	−	36.5240i	0.817111	−	1.41528i
$667$		−	0.436729i		−	0.0169102i
$668$	16.8367	−	62.8356i	0.651433	−	2.43118i
$669$	−6.22697	−	23.2394i	−0.240748	−	0.898486i
$670$	3.74517	−	3.74517i	0.144688	−	0.144688i
$671$	10.0111	−	10.0111i	0.386474	−	0.386474i
$672$		0			0
$673$	4.79792	+	2.77008i	0.184946	+	0.106779i	0.589615	−	0.807685i	$-0.299280\pi$
$673$	4.79792	+	2.77008i	0.184946	+	0.106779i	−0.404668	+	0.914464i	$0.632613\pi$
$674$	−12.2015	+	45.5365i	−0.469983	+	1.75400i
$675$	5.49846	+	9.52362i	0.211636	+	0.366564i
$676$	−45.5277	+	3.02832i	−1.75106	+	0.116474i
$677$	−38.1640	−	22.0340i	−1.46676	−	0.846835i	−0.467454	−	0.884018i	$-0.654828\pi$
$677$	−38.1640	−	22.0340i	−1.46676	−	0.846835i	−0.999309	+	0.0371822i	$0.988162\pi$
$678$	9.64710	−	2.58493i	0.370495	−	0.0992738i
$679$		0			0
$680$	−3.13799	+	1.81172i	−0.120336	+	0.0694763i
$681$	−12.0686	−	45.0406i	−0.462469	−	1.72596i
$682$	47.6798	−	12.7758i	1.82575	−	0.489209i
$683$	−4.97587	+	1.33328i	−0.190396	+	0.0510166i	−0.352757	−	0.935715i	$-0.614756\pi$
$683$	−4.97587	+	1.33328i	−0.190396	+	0.0510166i	0.162361	+	0.986731i	$0.448089\pi$
$684$	−33.0787	−	123.451i	−1.26480	−	4.72028i
$685$	−0.521554	+	0.301120i	−0.0199276	+	0.0115052i
$686$		0			0
$687$	−6.51969	+	1.74695i	−0.248742	+	0.0666501i
$688$	3.15390	+	1.82090i	0.120241	+	0.0694213i
$689$	18.0354	−	19.2749i	0.687094	−	0.734315i
$690$	−0.754466	−	1.30677i	−0.0287220	−	0.0497480i
$691$	0.790947	−	2.95186i	0.0300891	−	0.112294i	−0.949248	−	0.314528i	$-0.898154\pi$
$691$	0.790947	−	2.95186i	0.0300891	−	0.112294i	0.979337	+	0.202234i	$0.0648203\pi$
$692$	17.0028	+	9.81655i	0.646348	+	0.373169i
$693$		0			0
$694$	36.8501	−	36.8501i	1.39881	−	1.39881i
$695$	11.0870	−	11.0870i	0.420555	−	0.420555i
$696$	7.56611	+	28.2371i	0.286793	+	1.07032i
$697$	0.963328	−	3.59519i	0.0364886	−	0.136177i
$698$		−	12.5694i		−	0.475759i
$699$	7.41796	−	12.8483i	0.280573	−	0.485967i
$700$		0			0
$701$		−	11.0158i		−	0.416061i	−0.978122	−	0.208031i	$-0.933295\pi$
$701$		−	11.0158i		−	0.416061i	0.978122	−	0.208031i	$-0.0667054\pi$
$702$	−37.8015	+	1.25581i	−1.42673	+	0.0473977i
$703$	−26.5563	+	15.3323i	−1.00159	+	0.578267i
$704$	26.8287	−	26.8287i	1.01114	−	1.01114i
$705$	−12.0097	+	6.93378i	−0.452310	+	0.261141i
$706$	30.6322	+	53.0566i	1.15286	+	1.99681i
$707$		0			0
$708$	−38.8138	−	10.4001i	−1.45871	−	0.390860i
$709$	19.9197	+	19.9197i	0.748101	+	0.748101i	0.974122	−	0.226021i	$-0.0725719\pi$
$709$	19.9197	+	19.9197i	0.748101	+	0.748101i	−0.226021	+	0.974122i	$0.572572\pi$
$710$	−51.7306	−	13.8612i	−1.94141	−	0.520200i
$711$	−1.46173	+	2.53179i	−0.0548192	+	0.0949496i
$712$	−24.0702	−	41.6907i	−0.902067	−	1.56243i
$713$	−0.253206	−	0.944977i	−0.00948263	−	0.0353897i
$714$		0			0
$715$	−4.09008	+	17.5799i	−0.152960	+	0.657450i
$716$	16.6557	−	28.8486i	0.622454	−	1.07812i
$717$	−33.0050	−	33.0050i	−1.23260	−	1.23260i
$718$	53.1522			1.98362
$719$	42.1118			1.57050			0.785252	−	0.619176i	$-0.212533\pi$
$719$	42.1118			1.57050			0.785252	+	0.619176i	$0.212533\pi$
$720$	6.76309	+	6.76309i	0.252045	+	0.252045i
$721$		0			0
$722$	−26.2130	+	97.8284i	−0.975548	+	3.64079i
$723$	35.8538	−	9.60699i	1.33342	−	0.357288i
$724$	21.0195	+	12.1356i	0.781185	+	0.451018i
$725$			7.35329i			0.273094i
$726$	7.07808	+	1.89657i	0.262692	+	0.0703881i
$727$	−10.0901			−0.374223			−0.187111	−	0.982339i	$-0.559913\pi$
$727$	−10.0901			−0.374223			−0.187111	+	0.982339i	$0.559913\pi$
$728$		0			0
$729$	44.0349			1.63092
$730$	25.5009	+	6.83295i	0.943832	+	0.252899i
$731$		−	1.79812i		−	0.0665060i
$732$	37.8121	+	21.8308i	1.39758	+	0.806891i
$733$	−25.6687	+	6.87790i	−0.948093	+	0.254041i	−0.699553	−	0.714581i	$-0.746618\pi$
$733$	−25.6687	+	6.87790i	−0.948093	+	0.254041i	−0.248540	+	0.968622i	$0.579951\pi$
$734$	8.62455	−	32.1873i	0.318338	−	1.18805i
$735$		0			0
$736$	−0.417306	−	0.417306i	−0.0153821	−	0.0153821i
$737$	−4.44835			−0.163857
$738$	−62.8988			−2.31534
$739$	17.7896	+	17.7896i	0.654402	+	0.654402i	0.954050	−	0.299648i	$-0.0968692\pi$
$739$	17.7896	+	17.7896i	0.654402	+	0.654402i	−0.299648	+	0.954050i	$0.596869\pi$
$740$	10.8778	−	18.8409i	0.399876	−	0.692605i
$741$	69.2108	+	36.9509i	2.54252	+	1.35742i
$742$		0			0
$743$	−2.81817	−	10.5175i	−0.103388	−	0.385851i	0.894769	−	0.446530i	$-0.147340\pi$
$743$	−2.81817	−	10.5175i	−0.103388	−	0.385851i	−0.998157	+	0.0606785i	$0.980674\pi$
$744$	32.7425	+	56.7117i	1.20040	+	2.07915i
$745$	−4.42484	+	7.66405i	−0.162114	+	0.280789i
$746$	7.95021	+	2.13025i	0.291078	+	0.0779941i
$747$	−4.97993	−	4.97993i	−0.182206	−	0.182206i
$748$	6.83328	+	1.83097i	0.249850	+	0.0669470i
$749$		0			0
$750$	38.5147	+	66.7094i	1.40636	+	2.43588i
$751$	27.9154	−	16.1170i	1.01865	−	0.588117i	0.104936	−	0.994479i	$-0.466536\pi$
$751$	27.9154	−	16.1170i	1.01865	−	0.588117i	0.913712	+	0.406362i	$0.133203\pi$
$752$	2.89692	−	2.89692i	0.105640	−	0.105640i
$753$	−30.6097	+	17.6725i	−1.11548	+	0.644022i
$754$	−22.3101	−	11.9111i	−0.812485	−	0.433777i
$755$			7.56115i			0.275179i
$756$		0			0
$757$	−16.9609	+	29.3771i	−0.616453	+	1.06773i	0.373675	+	0.927560i	$0.378098\pi$
$757$	−16.9609	+	29.3771i	−0.616453	+	1.06773i	−0.990128	+	0.140168i	$0.955236\pi$
$758$			63.0133i			2.28875i
$759$	−0.328004	+	1.22413i	−0.0119058	+	0.0444330i
$760$	−11.5231	−	43.0048i	−0.417987	−	1.55995i
$761$	6.85232	−	6.85232i	0.248397	−	0.248397i	−0.571916	−	0.820312i	$-0.693800\pi$
$761$	6.85232	−	6.85232i	0.248397	−	0.248397i	0.820312	+	0.571916i	$0.193800\pi$
$762$	−14.9101	+	14.9101i	−0.540137	+	0.540137i
$763$		0			0
$764$	−7.61437	−	4.39616i	−0.275478	−	0.159047i
$765$	1.22225	−	4.56149i	0.0441904	−	0.164921i
$766$	40.0837	+	69.4270i	1.44828	+	2.50850i
$767$	12.6956	−	7.90316i	0.458411	−	0.285366i
$768$	56.0159	+	32.3408i	2.02130	+	1.16700i
$769$	14.6001	−	3.91210i	0.526495	−	0.141074i	0.0142256	−	0.999899i	$-0.495472\pi$
$769$	14.6001	−	3.91210i	0.526495	−	0.141074i	0.512269	+	0.858825i	$0.328805\pi$
$770$		0			0
$771$	−24.8147	+	14.3268i	−0.893678	+	0.515965i
$772$	−20.4911	−	76.4737i	−0.737490	−	2.75235i
$773$	37.7776	−	10.1225i	1.35877	−	0.364081i	0.495404	−	0.868663i	$-0.335020\pi$
$773$	37.7776	−	10.1225i	1.35877	−	0.364081i	0.863364	+	0.504582i	$0.168353\pi$
$774$	−29.3513	+	7.86466i	−1.05501	+	0.282689i
$775$	4.26328	+	15.9108i	0.153142	+	0.571532i
$776$	0.577718	−	0.333546i	0.0207389	−	0.0119736i
$777$		0			0
$778$	−62.2709	+	16.6854i	−2.23252	+	0.598202i
$779$	39.6060	+	22.8665i	1.41903	+	0.819279i
$780$	−55.6323	+	1.84818i	−1.99195	+	0.0661753i
$781$	22.4898	+	38.9535i	0.804750	+	1.39387i
$782$	0.0569665	−	0.212602i	0.00203712	−	0.00760263i
$783$	−11.5652	−	6.67718i	−0.413307	−	0.238623i
$784$		0			0
$785$	−14.2201	+	14.2201i	−0.507537	+	0.507537i
$786$	−75.4469	+	75.4469i	−2.69110	+	2.69110i
$787$	0.451508	+	1.68505i	0.0160945	+	0.0600656i	0.973506	−	0.228661i	$-0.0734348\pi$
$787$	0.451508	+	1.68505i	0.0160945	+	0.0600656i	−0.957412	+	0.288727i	$0.906768\pi$
$788$	16.2703	−	60.7217i	0.579607	−	2.16312i
$789$		−	12.0887i		−	0.430368i
$790$	−1.18370	+	2.05022i	−0.0421141	+	0.0729437i
$791$		0			0
$792$		−	51.4278i		−	1.82741i
$793$	−15.5472	+	4.72441i	−0.552097	+	0.167769i
$794$	−75.3492	+	43.5029i	−2.67404	+	1.54386i
$795$	22.7704	−	22.7704i	0.807582	−	0.807582i
$796$	−49.8875	+	28.8026i	−1.76822	+	1.02088i
$797$	−12.2921	−	21.2905i	−0.435407	−	0.754148i	0.561921	−	0.827191i	$-0.310062\pi$
$797$	−12.2921	−	21.2905i	−0.435407	−	0.754148i	−0.997329	+	0.0730430i	$0.976729\pi$
$798$		0			0
$799$	−1.95388	−	0.523540i	−0.0691233	−	0.0185215i
$800$	7.02627	+	7.02627i	0.248416	+	0.248416i
$801$	60.6030	+	16.2385i	2.14130	+	0.573760i
$802$	20.3936	−	35.3228i	0.720125	−	1.24729i
$803$	−11.0865	−	19.2024i	−0.391235	−	0.677638i
$804$	−3.55057	−	13.2509i	−0.125219	−	0.467324i
$805$		0			0
$806$	−55.1795	−	12.8379i	−1.94362	−	0.452195i
$807$	−16.1264	+	27.9317i	−0.567675	+	0.983241i
$808$	2.99178	+	2.99178i	0.105250	+	0.105250i
$809$	−2.82935			−0.0994746			−0.0497373	−	0.998762i	$-0.515838\pi$
$809$	−2.82935			−0.0994746			−0.0497373	+	0.998762i	$0.515838\pi$
$810$	5.69155			0.199981
$811$	−6.39483	−	6.39483i	−0.224553	−	0.224553i	0.585860	−	0.810412i	$-0.300757\pi$
$811$	−6.39483	−	6.39483i	−0.224553	−	0.224553i	−0.810412	+	0.585860i	$0.800757\pi$
$812$		0			0
$813$	21.9272	−	81.8334i	0.769020	−	2.87002i
$814$	−27.7063	+	7.42387i	−0.971104	+	0.260207i
$815$	18.0137	+	10.4002i	0.630993	+	0.364304i
$816$			2.30124i			0.0805596i
$817$	21.3410	+	5.71832i	0.746629	+	0.200059i
$818$	−26.4854			−0.926041
$819$		0			0
$820$	−32.4463			−1.13307
$821$	−36.0437	−	9.65789i	−1.25793	−	0.337063i	−0.432538	−	0.901616i	$-0.642382\pi$
$821$	−36.0437	−	9.65789i	−1.25793	−	0.337063i	−0.825397	+	0.564553i	$0.809049\pi$
$822$			2.44870i			0.0854082i
$823$	−34.1966	−	19.7434i	−1.19202	−	0.688212i	−0.233254	−	0.972416i	$-0.574937\pi$
$823$	−34.1966	−	19.7434i	−1.19202	−	0.688212i	−0.958764	+	0.284204i	$0.908271\pi$
$824$	−16.4179	+	4.39916i	−0.571944	+	0.153252i
$825$	5.52266	−	20.6109i	0.192274	−	0.717578i
$826$		0			0
$827$	−24.4804	−	24.4804i	−0.851267	−	0.851267i	0.139022	−	0.990289i	$-0.455604\pi$
$827$	−24.4804	−	24.4804i	−0.851267	−	0.851267i	−0.990289	+	0.139022i	$0.955604\pi$
$828$	−2.36939			−0.0823421
$829$	13.4781			0.468112			0.234056	−	0.972223i	$-0.424800\pi$
$829$	13.4781			0.468112			0.234056	+	0.972223i	$0.424800\pi$
$830$	−4.03271	−	4.03271i	−0.139977	−	0.139977i
$831$	−26.3125	+	45.5745i	−0.912769	+	1.58096i
$832$	−41.6648	+	12.6609i	−1.44447	+	0.438938i
$833$		0			0
$834$	−16.5003	−	61.5801i	−0.571360	−	2.13234i
$835$	14.7671	+	25.5773i	0.511036	+	0.885141i
$836$	−43.4618	+	75.2781i	−1.50316	+	2.60355i
$837$	−28.8957	−	7.74257i	−0.998780	−	0.267622i
$838$	30.9043	+	30.9043i	1.06757	+	1.06757i
$839$	48.1190	+	12.8935i	1.66125	+	0.445132i	0.962732	−	0.270457i	$-0.0871749\pi$
$839$	48.1190	+	12.8935i	1.66125	+	0.445132i	0.698522	+	0.715589i	$0.253842\pi$
$840$		0			0
$841$	10.0352	+	17.3815i	0.346041	+	0.599360i
$842$	54.3417	−	31.3742i	1.87274	−	1.08123i
$843$	−32.7562	+	32.7562i	−1.12819	+	1.12819i
$844$	29.9815	−	17.3098i	1.03201	−	0.595829i
$845$	13.6436	−	15.5880i	0.469356	−	0.536244i
$846$			34.1836i			1.17526i
$847$		0			0
$848$	−4.75671	+	8.23886i	−0.163346	+	0.282924i
$849$		−	23.2891i		−	0.799280i
$850$	−0.959157	+	3.57962i	−0.0328988	+	0.122780i
$851$	0.147136	+	0.549117i	0.00504374	+	0.0188235i
$852$	−98.0855	+	98.0855i	−3.36035	+	3.36035i
$853$	−15.4604	+	15.4604i	−0.529355	+	0.529355i	−0.920380	−	0.391025i	$-0.872121\pi$
$853$	−15.4604	+	15.4604i	−0.529355	+	0.529355i	0.391025	+	0.920380i	$0.372121\pi$
$854$		0			0
$855$	50.2511	+	29.0125i	1.71855	+	0.992207i
$856$	14.0312	−	52.3651i	0.479576	−	1.78980i
$857$	−12.5050	−	21.6594i	−0.427164	−	0.739869i	0.569456	−	0.822022i	$-0.307154\pi$
$857$	−12.5050	−	21.6594i	−0.427164	−	0.739869i	−0.996620	+	0.0821525i	$0.973821\pi$
$858$	53.5881	+	50.1420i	1.82947	+	1.71182i
$859$	−30.9754	−	17.8837i	−1.05687	−	0.610183i	−0.132304	−	0.991209i	$-0.542238\pi$
$859$	−30.9754	−	17.8837i	−1.05687	−	0.610183i	−0.924564	+	0.381026i	$0.875571\pi$
$860$	−15.1409	+	4.05698i	−0.516299	+	0.138342i
$861$		0			0
$862$	−60.0127	+	34.6484i	−2.04404	+	1.18013i
$863$	10.7130	+	39.9815i	0.364675	+	1.36099i	0.867861	+	0.496807i	$0.165494\pi$
$863$	10.7130	+	39.9815i	0.364675	+	1.36099i	−0.503186	+	0.864178i	$0.667839\pi$
$864$	−17.4311	+	4.67065i	−0.593018	+	0.158899i
$865$	−8.60985	+	2.30700i	−0.292744	+	0.0784405i
$866$	21.8297	+	81.4695i	0.741803	+	2.76845i
$867$	−39.6537	+	22.8941i	−1.34671	+	0.777524i
$868$		0			0
$869$	1.92056	−	0.514612i	0.0651504	−	0.0174570i
$870$	−26.7191	−	15.4263i	−0.905862	−	0.523000i
$871$	4.50376	+	2.40451i	0.152604	+	0.0814736i
$872$	−22.8658	−	39.6048i	−0.774335	−	1.34119i
$873$	−0.225021	+	0.839790i	−0.00761581	+	0.0284226i
$874$	2.34210	+	1.35221i	0.0792229	+	0.0457393i
$875$		0			0
$876$	48.3519	−	48.3519i	1.63366	−	1.63366i
$877$	17.7428	−	17.7428i	0.599133	−	0.599133i	−0.340949	−	0.940082i	$-0.610748\pi$
$877$	17.7428	−	17.7428i	0.599133	−	0.599133i	0.940082	+	0.340949i	$0.110748\pi$
$878$	−5.92937	−	22.1287i	−0.200107	−	0.746808i
$879$	5.92188	−	22.1007i	0.199740	−	0.745440i
$880$		−	6.50498i		−	0.219283i
$881$	−18.7477	+	32.4719i	−0.631624	+	1.09401i	0.355595	+	0.934640i	$0.384278\pi$
$881$	−18.7477	+	32.4719i	−0.631624	+	1.09401i	−0.987220	+	0.159365i	$0.949055\pi$
$882$		0			0
$883$			19.9652i			0.671881i	0.941883	+	0.335941i	$0.109054\pi$
$883$			19.9652i			0.671881i	−0.941883	+	0.335941i	$0.890946\pi$
$884$	−5.92869	−	5.54744i	−0.199403	−	0.186581i
$885$	15.7992	−	9.12168i	0.531085	−	0.306622i
$886$	−64.3666	+	64.3666i	−2.16244	+	2.16244i
$887$	44.5877	−	25.7427i	1.49711	−	0.864355i	0.497113	−	0.867686i	$-0.334394\pi$
$887$	44.5877	−	25.7427i	1.49711	−	0.864355i	0.999994	+	0.00333069i	$0.00106019\pi$
$888$	−19.0264	−	32.9546i	−0.638483	−	1.10588i
$889$		0			0
$890$	49.0758	+	13.1498i	1.64502	+	0.440783i
$891$	−3.38009	−	3.38009i	−0.113237	−	0.113237i
$892$	−29.5505	−	7.91803i	−0.989424	−	0.265115i
$893$	12.4273	−	21.5247i	0.415863	−	0.720297i
$894$	17.9914	+	31.1620i	0.601722	+	1.04221i
$895$	3.91429	+	14.6083i	0.130840	+	0.488303i
$896$		0			0
$897$	0.993778	−	1.06208i	0.0331813	−	0.0354617i
$898$	−10.9837	+	19.0243i	−0.366530	+	0.634848i
$899$	−14.1444	−	14.1444i	−0.471742	−	0.471742i
$900$	39.8940			1.32980
$901$	4.69720			0.156486
$902$	30.2492	+	30.2492i	1.00719	+	1.00719i
$903$		0			0
$904$	1.41396	−	5.27699i	0.0470277	−	0.175510i
$905$	−10.6439	+	2.85202i	−0.353814	+	0.0948042i
$906$	26.6247	+	15.3718i	0.884548	+	0.510694i
$907$		−	28.9564i		−	0.961483i	−0.876862	−	0.480742i	$-0.840368\pi$
$907$		−	28.9564i		−	0.961483i	0.876862	−	0.480742i	$-0.159632\pi$
$908$	−57.2723	−	15.3461i	−1.90065	−	0.509277i
$909$	−5.51424			−0.182896
$910$		0			0
$911$	3.65299			0.121029			0.0605144	−	0.998167i	$-0.480726\pi$
$911$	3.65299			0.121029			0.0605144	+	0.998167i	$0.480726\pi$
$912$	−27.3123	−	7.31832i	−0.904402	−	0.242334i
$913$			4.78988i			0.158522i
$914$	−39.0731	−	22.5589i	−1.29242	−	0.746181i
$915$	−19.1473	+	5.13050i	−0.632990	+	0.169609i
$916$	−2.22137	+	8.29025i	−0.0733960	+	0.273918i
$917$		0			0
$918$	−4.75904	−	4.75904i	−0.157072	−	0.157072i
$919$	42.7339			1.40966			0.704831	−	0.709375i	$-0.251023\pi$
$919$	42.7339			1.40966			0.704831	+	0.709375i	$0.251023\pi$
$920$	−0.825389			−0.0272123
$921$	−47.8734	−	47.8734i	−1.57748	−	1.57748i
$922$	15.8924	−	27.5265i	0.523389	−	0.906536i
$923$	−1.71407	−	51.5954i	−0.0564192	−	1.69828i
$924$		0			0
$925$	−2.47735	−	9.24560i	−0.0814548	−	0.303994i
$926$	−24.2888	−	42.0695i	−0.798181	−	1.38249i
$927$	11.0761	−	19.1843i	0.363786	−	0.630095i
$928$	−11.6556	−	3.12311i	−0.382614	−	0.102521i
$929$	−11.9693	−	11.9693i	−0.392700	−	0.392700i	0.482949	−	0.875649i	$-0.339566\pi$
$929$	−11.9693	−	11.9693i	−0.392700	−	0.392700i	−0.875649	+	0.482949i	$0.839566\pi$
$930$	−66.7576	−	17.8876i	−2.18907	−	0.586559i
$931$		0			0
$932$	−9.43247	−	16.3375i	−0.308971	−	0.535153i
$933$	56.6826	−	32.7257i	1.85571	−	1.07139i
$934$	51.4093	−	51.4093i	1.68216	−	1.68216i
$935$	−2.78150	+	1.60590i	−0.0909648	+	0.0525186i
$936$	−27.7988	+	52.0684i	−0.908631	+	1.70191i
$937$		−	46.5686i		−	1.52133i	−0.649145	−	0.760665i	$-0.724873\pi$
$937$		−	46.5686i		−	1.52133i	0.649145	−	0.760665i	$-0.275127\pi$
$938$		0			0
$939$	−19.4205	+	33.6372i	−0.633763	+	1.09771i
$940$			17.6336i			0.575145i
$941$	3.08022	−	11.4955i	0.100412	−	0.374744i	−0.897372	−	0.441275i	$-0.854526\pi$
$941$	3.08022	−	11.4955i	0.100412	−	0.374744i	0.997784	+	0.0665310i	$0.0211931\pi$
$942$	21.1632	+	78.9820i	0.689533	+	2.57337i
$943$	0.599516	−	0.599516i	0.0195229	−	0.0195229i
$944$	−3.81102	+	3.81102i	−0.124038	+	0.124038i
$945$		0			0
$946$	17.8978	+	10.3333i	0.581909	+	0.335965i
$947$	11.1818	−	41.7309i	0.363358	−	1.35607i	−0.506274	−	0.862373i	$-0.668978\pi$
$947$	11.1818	−	41.7309i	0.363358	−	1.35607i	0.869633	−	0.493699i	$-0.164356\pi$
$948$	3.06589	+	5.31028i	0.0995756	+	0.172470i
$949$	0.844961	+	25.4343i	0.0274286	+	0.825633i
$950$	−39.4345	−	22.7675i	−1.27942	−	0.738676i
$951$	−44.6321	+	11.9591i	−1.44730	+	0.387802i
$952$		0			0
$953$	−50.8066	+	29.3332i	−1.64579	+	0.950195i	−0.667066	+	0.744999i	$0.732450\pi$
$953$	−50.8066	+	29.3332i	−1.64579	+	0.950195i	−0.978721	+	0.205196i	$0.934217\pi$
$954$	−20.5447	−	76.6738i	−0.665159	−	2.48241i
$955$	3.85576	−	1.03315i	0.124770	−	0.0334319i
$956$	−57.3297	+	15.3614i	−1.85417	+	0.496825i
$957$	6.70657	+	25.0292i	0.216792	+	0.809080i
$958$	−14.9314	+	8.62062i	−0.482410	+	0.278520i
$959$		0			0
$960$	−51.3127	+	13.7492i	−1.65611	+	0.443753i
$961$	−11.9589	−	6.90448i	−0.385771	−	0.222725i
$962$	32.0643	+	7.45998i	1.03379	+	0.240519i
$963$	35.3273	+	61.1886i	1.13840	+	1.97178i
$964$	12.2160	−	45.5907i	0.393450	−	1.46838i
$965$	31.1288	+	17.9722i	1.00207	+	0.578546i
$966$		0			0
$967$	−7.53769	+	7.53769i	−0.242396	+	0.242396i	−0.817841	−	0.575445i	$-0.804829\pi$
$967$	−7.53769	+	7.53769i	−0.242396	+	0.242396i	0.575445	+	0.817841i	$0.304829\pi$
$968$	2.83430	−	2.83430i	0.0910978	−	0.0910978i
$969$	3.61338	+	13.4853i	0.116079	+	0.433211i
$970$	−0.182220	+	0.680055i	−0.00585074	+	0.0218353i
$971$			31.5596i			1.01280i	0.862300	+	0.506398i	$0.169023\pi$
$971$			31.5596i			1.01280i	−0.862300	+	0.506398i	$0.830977\pi$
$972$	30.8990	−	53.5187i	0.991086	−	1.71661i
$973$		0			0
$974$		−	23.1495i		−	0.741759i
$975$	−16.7324	+	17.8824i	−0.535867	+	0.572695i
$976$	5.07160	−	2.92809i	0.162338	−	0.0937259i
$977$	−0.807539	+	0.807539i	−0.0258355	+	0.0258355i	−0.719907	−	0.694071i	$-0.755815\pi$
$977$	−0.807539	+	0.807539i	−0.0258355	+	0.0258355i	0.694071	+	0.719907i	$0.255815\pi$
$978$	73.2436	−	42.2872i	2.34207	−	1.35220i
$979$	−21.3357	−	36.9545i	−0.681891	−	1.18107i
$980$		0			0
$981$	57.5708	+	15.4261i	1.83810	+	0.492516i
$982$	63.5097	+	63.5097i	2.02668	+	2.02668i
$983$	−28.4968	−	7.63569i	−0.908907	−	0.243541i	−0.226069	−	0.974111i	$-0.572588\pi$
$983$	−28.4968	−	7.63569i	−0.908907	−	0.243541i	−0.682837	+	0.730570i	$0.739254\pi$
$984$	−28.3759	+	49.1485i	−0.904591	+	1.56680i
$985$	14.2703	+	24.7169i	0.454690	+	0.787546i
$986$	−1.16477	−	4.34699i	−0.0370939	−	0.138436i
$987$		0			0
$988$	84.6940	−	52.7230i	2.69448	−	1.67734i
$989$	0.204799	−	0.354722i	0.00651222	−	0.0112795i
$990$	38.3794	+	38.3794i	1.21978	+	1.21978i
$991$	−45.6092			−1.44882			−0.724412	−	0.689367i	$-0.757889\pi$
$991$	−45.6092			−1.44882			−0.724412	+	0.689367i	$0.757889\pi$
$992$	−27.0307			−0.858225
$993$	−18.8898	−	18.8898i	−0.599450	−	0.599450i
$994$		0			0
$995$	6.76894	−	25.2620i	0.214590	−	0.800860i
$996$	−14.2683	+	3.82317i	−0.452108	+	0.121142i
$997$	−22.5784	−	13.0357i	−0.715065	−	0.412843i	0.0978683	−	0.995199i	$-0.468798\pi$
$997$	−22.5784	−	13.0357i	−0.715065	−	0.412843i	−0.812934	+	0.582356i	$0.802131\pi$
$998$			0.00340962i			0.000107930i
$999$	16.7910	+	4.49913i	0.531243	+	0.142346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.19.8		32
7.2	even	3		91.2.bc.a.6.1	✓	32
7.3	odd	6		637.2.bb.b.227.1		32
7.4	even	3		637.2.bb.b.227.2		32
7.5	odd	6		91.2.bc.a.6.2	yes	32
7.6	odd	2	inner	637.2.x.b.19.7		32
13.11	odd	12		637.2.bb.b.362.1		32
21.2	odd	6		819.2.fm.g.370.7		32
21.5	even	6		819.2.fm.g.370.8		32
91.11	odd	12	inner	637.2.x.b.570.8		32
91.24	even	12	inner	637.2.x.b.570.7		32
91.37	odd	12		91.2.bc.a.76.2	yes	32
91.76	even	12		637.2.bb.b.362.2		32
91.89	even	12		91.2.bc.a.76.1	yes	32
273.89	odd	12		819.2.fm.g.622.7		32
273.128	even	12		819.2.fm.g.622.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.1	✓	32	7.2	even	3
91.2.bc.a.6.2	yes	32	7.5	odd	6
91.2.bc.a.76.1	yes	32	91.89	even	12
91.2.bc.a.76.2	yes	32	91.37	odd	12
637.2.x.b.19.7		32	7.6	odd	2	inner
637.2.x.b.19.8		32	1.1	even	1	trivial
637.2.x.b.570.7		32	91.24	even	12	inner
637.2.x.b.570.8		32	91.11	odd	12	inner
637.2.bb.b.227.1		32	7.3	odd	6
637.2.bb.b.227.2		32	7.4	even	3
637.2.bb.b.362.1		32	13.11	odd	12
637.2.bb.b.362.2		32	91.76	even	12
819.2.fm.g.370.7		32	21.2	odd	6
819.2.fm.g.370.8		32	21.5	even	6
819.2.fm.g.622.7		32	273.89	odd	12
819.2.fm.g.622.8		32	273.128	even	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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.26733 + 0.607529i) q^{2} +2.76026i q^{3} +(3.03963 + 1.75493i) q^{4} +(-1.53921 + 0.412430i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} -4.61904 q^{9} +O(q^{10})\)	\(q+(2.26733 + 0.607529i) q^{2} +2.76026i q^{3} +(3.03963 + 1.75493i) q^{4} +(-1.53921 + 0.412430i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} -4.61904 q^{9} -3.74046 q^{10} +(2.22138 + 2.22138i) q^{11} +(-4.84407 + 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} +(0.649718 + 1.12534i) q^{16} +(0.320795 - 0.555633i) q^{17} +(-10.4729 - 2.80620i) q^{18} +(5.57436 + 5.57436i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +(0.126569 - 0.0730744i) q^{23} +(-6.91743 + 6.91743i) q^{24} +(-2.13106 + 1.23037i) q^{25} +(-0.281008 - 8.45868i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} -10.3246i q^{30} +(1.73252 - 6.46586i) q^{31} +(-1.04513 - 3.90048i) q^{32} +(-6.13158 + 6.13158i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-1.00675 + 3.75725i) q^{37} +(9.25232 + 16.0255i) q^{38} +(9.52232 - 2.89360i) q^{39} +(-4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(2.85380 + 10.6505i) q^{44} +(7.10966 - 1.90503i) q^{45} +(0.331367 - 0.0887896i) q^{46} +(-0.816005 - 3.04537i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(1.53369 + 0.885477i) q^{51} +(2.86768 - 12.3258i) q^{52} +(3.66059 + 6.34033i) q^{53} +(2.71502 - 10.1326i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(4.95989 - 4.95989i) q^{58} +(1.07349 + 4.00631i) q^{59} +(3.99568 - 14.9121i) q^{60} -4.50671i q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(3.03636 + 4.87760i) q^{65} +(-17.6274 + 10.1772i) q^{66} +(-1.00126 + 1.00126i) q^{67} +(1.95020 - 1.12595i) q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(-11.5757 - 11.5757i) q^{72} +(-6.81760 - 1.82677i) q^{73} +(-4.56527 + 7.90729i) q^{74} +(-3.39614 - 5.88228i) q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 - 0.548121i) q^{79} +(-1.46418 - 1.46418i) q^{80} -1.52162 q^{81} +13.6173 q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(6.35443 - 1.70266i) q^{86} +(7.14327 + 4.12417i) q^{87} +11.1339i q^{88} +(-13.1203 - 3.51557i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(17.8475 + 4.78221i) q^{93} -7.40060i q^{94} +(-10.8791 - 6.28107i) q^{95} +(10.7663 - 2.88483i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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