LMFDB - Embedded newform 627.2.l.a.197.74

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(197,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("627.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.l (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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			197.74
Character	$\chi$	$=$	627.197
Dual form			627.2.l.a.296.74

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26757 + 2.19550i) q^{2} +(0.00544374 - 1.73204i) q^{3} +(-2.21348 + 3.83387i) q^{4} +(-2.53073 + 1.46112i) q^{5} +(3.80960 - 2.18354i) q^{6} -0.937410i q^{7} -6.15272 q^{8} +(-2.99994 - 0.0188576i) q^{9} +(-6.41578 - 3.70415i) q^{10} +(-3.27304 - 0.535938i) q^{11} +(6.62837 + 3.85472i) q^{12} +(-3.28845 - 1.89859i) q^{13} +(2.05809 - 1.18824i) q^{14} +(2.51694 + 4.39129i) q^{15} +(-3.37206 - 5.84058i) q^{16} +(2.49789 + 4.32647i) q^{17} +(-3.76124 - 6.61028i) q^{18} +(-1.80252 - 3.96875i) q^{19} -12.9367i q^{20} +(-1.62363 - 0.00510302i) q^{21} +(-2.97216 - 7.86530i) q^{22} +(1.17935 + 0.680898i) q^{23} +(-0.0334938 + 10.6568i) q^{24} +(1.76974 - 3.06528i) q^{25} -9.62640i q^{26} +(-0.0489930 + 5.19592i) q^{27} +(3.59391 + 2.07494i) q^{28} +(-1.29493 + 2.24288i) q^{29} +(-6.45067 + 11.0922i) q^{30} -9.70627 q^{31} +(2.39594 - 4.14989i) q^{32} +(-0.946084 + 5.66612i) q^{33} +(-6.33251 + 10.9682i) q^{34} +(1.36967 + 2.37233i) q^{35} +(6.71262 - 11.4596i) q^{36} +8.35820 q^{37} +(6.42856 - 8.98810i) q^{38} +(-3.30634 + 5.68540i) q^{39} +(15.5709 - 8.98986i) q^{40} +(-1.75301 - 3.03630i) q^{41} +(-2.04687 - 3.57116i) q^{42} +(-8.71037 + 5.02893i) q^{43} +(9.29953 - 11.3621i) q^{44} +(7.61960 - 4.33555i) q^{45} +3.45235i q^{46} +(0.553220 + 0.319402i) q^{47} +(-10.1345 + 5.80875i) q^{48} +6.12126 q^{49} +8.97310 q^{50} +(7.50722 - 4.30290i) q^{51} +(14.5579 - 8.40499i) q^{52} +(8.50178 + 4.90851i) q^{53} +(-11.4698 + 6.47865i) q^{54} +(9.06625 - 3.42598i) q^{55} +5.76762i q^{56} +(-6.88385 + 3.10043i) q^{57} -6.56567 q^{58} +(-11.3031 + 6.52587i) q^{59} +(-22.4068 - 0.0704238i) q^{60} +(0.667708 + 0.385502i) q^{61} +(-12.3034 - 21.3101i) q^{62} +(-0.0176773 + 2.81217i) q^{63} -1.34012 q^{64} +11.0963 q^{65} +(-13.6392 + 5.10509i) q^{66} +(0.980172 - 1.69771i) q^{67} -22.1161 q^{68} +(1.18576 - 2.03898i) q^{69} +(-3.47231 + 6.01422i) q^{70} +(8.49025 - 4.90185i) q^{71} +(18.4578 + 0.116025i) q^{72} +(3.20047 - 1.84779i) q^{73} +(10.5946 + 18.3504i) q^{74} +(-5.29956 - 3.08195i) q^{75} +(19.2055 + 1.87415i) q^{76} +(-0.502393 + 3.06818i) q^{77} +(-16.6733 - 0.0524036i) q^{78} +(-12.2359 + 7.06441i) q^{79} +(17.0676 + 9.85396i) q^{80} +(8.99929 + 0.113143i) q^{81} +(4.44414 - 7.69747i) q^{82} -8.39058 q^{83} +(3.61345 - 6.21350i) q^{84} +(-12.6430 - 7.29942i) q^{85} +(-22.0821 - 12.7491i) q^{86} +(3.87772 + 2.25508i) q^{87} +(20.1381 + 3.29748i) q^{88} +(1.57818 + 0.911162i) q^{89} +(19.1771 + 11.2332i) q^{90} +(-1.77976 + 3.08263i) q^{91} +(-5.22094 + 3.01431i) q^{92} +(-0.0528384 + 16.8117i) q^{93} +1.61946i q^{94} +(10.3605 + 7.41014i) q^{95} +(-7.17474 - 4.17246i) q^{96} +(-0.468735 - 0.811873i) q^{97} +(7.75915 + 13.4392i) q^{98} +(9.80881 + 1.66950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 76 q^{4} - 8 q^{9} - 14 q^{15} - 76 q^{16} + 4 q^{22} + 60 q^{25} + 12 q^{27} - 16 q^{31} + 16 q^{33} - 16 q^{34} - 10 q^{36} - 16 q^{37} + 50 q^{42} - 108 q^{45} + 54 q^{48} - 80 q^{49} + 32 q^{55}+ \cdots + 60 q^{99}+O(q^{100}) $ 152 * q - 76 * q^4 - 8 * q^9 - 14 * q^15 - 76 * q^16 + 4 * q^22 + 60 * q^25 + 12 * q^27 - 16 * q^31 + 16 * q^33 - 16 * q^34 - 10 * q^36 - 16 * q^37 + 50 * q^42 - 108 * q^45 + 54 * q^48 - 80 * q^49 + 32 * q^55 - 40 * q^58 + 2 * q^60 + 152 * q^64 - 10 * q^66 - 16 * q^67 - 32 * q^69 - 4 * q^70 - 20 * q^75 - 58 * q^78 + 16 * q^81 - 40 * q^82 - 120 * q^88 - 16 * q^91 - 12 * q^93 + 4 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.26757	+	2.19550i	0.896310	+	1.55245i	0.832175	+	0.554513i	$0.187095\pi$
$2$	1.26757	+	2.19550i	0.896310	+	1.55245i	0.0641344	+	0.997941i	$0.479571\pi$
$3$	0.00544374	−	1.73204i	0.00314294	−	0.999995i
$3$	0.00544374	−	1.73204i	0.00314294	−	0.999995i
$4$	−2.21348	+	3.83387i	−1.10674	+	1.91693i
$5$	−2.53073	+	1.46112i	−1.13178	+	0.653432i	−0.944382	−	0.328852i	$-0.893338\pi$
$5$	−2.53073	+	1.46112i	−1.13178	+	0.653432i	−0.187397	+	0.982284i	$0.560005\pi$
$6$	3.80960	−	2.18354i	1.55526	−	0.891426i
$7$		−	0.937410i		−	0.354308i	−0.984183	−	0.177154i	$-0.943311\pi$
$7$		−	0.937410i		−	0.354308i	0.984183	−	0.177154i	$-0.0566890\pi$
$8$	−6.15272			−2.17532
$9$	−2.99994	−	0.0188576i	−0.999980	−	0.00628586i
$10$	−6.41578	−	3.70415i	−2.02885	−	1.17136i
$11$	−3.27304	−	0.535938i	−0.986858	−	0.161591i
$11$	−3.27304	−	0.535938i	−0.986858	−	0.161591i
$12$	6.62837	+	3.85472i	1.91345	+	1.11276i
$13$	−3.28845	−	1.89859i	−0.912052	−	0.526574i	−0.0309612	−	0.999521i	$-0.509857\pi$
$13$	−3.28845	−	1.89859i	−0.912052	−	0.526574i	−0.881091	+	0.472947i	$0.843190\pi$
$14$	2.05809	−	1.18824i	0.550046	−	0.317569i
$15$	2.51694	+	4.39129i	0.649872	+	1.13383i
$16$	−3.37206	−	5.84058i	−0.843014	−	1.46014i
$17$	2.49789	+	4.32647i	0.605827	+	1.04932i	0.991920	+	0.126863i	$0.0404909\pi$
$17$	2.49789	+	4.32647i	0.605827	+	1.04932i	−0.386093	+	0.922460i	$0.626176\pi$
$18$	−3.76124	−	6.61028i	−0.886533	−	1.55806i
$19$	−1.80252	−	3.96875i	−0.413525	−	0.910493i
$19$	−1.80252	−	3.96875i	−0.413525	−	0.910493i
$20$		−	12.9367i		−	2.89273i
$21$	−1.62363	−	0.00510302i	−0.354306	−	0.00111357i
$22$	−2.97216	−	7.86530i	−0.633667	−	1.67689i
$23$	1.17935	+	0.680898i	0.245911	+	0.141977i	0.617891	−	0.786264i	$-0.287987\pi$
$23$	1.17935	+	0.680898i	0.245911	+	0.141977i	−0.371979	+	0.928241i	$0.621321\pi$
$24$	−0.0334938	+	10.6568i	−0.00683690	+	2.17530i
$25$	1.76974	−	3.06528i	0.353948	−	0.613056i
$26$		−	9.62640i		−	1.88789i
$27$	−0.0489930	+	5.19592i	−0.00942871	+	0.999956i
$28$	3.59391	+	2.07494i	0.679184	+	0.392127i
$29$	−1.29493	+	2.24288i	−0.240462	+	0.416493i	−0.960846	−	0.277083i	$-0.910632\pi$
$29$	−1.29493	+	2.24288i	−0.240462	+	0.416493i	0.720384	+	0.693576i	$0.243966\pi$
$30$	−6.45067	+	11.0922i	−1.17773	+	2.02516i
$31$	−9.70627			−1.74330			−0.871648	−	0.490132i	$-0.836949\pi$
$31$	−9.70627			−1.74330			−0.871648	+	0.490132i	$0.836949\pi$
$32$	2.39594	−	4.14989i	0.423546	−	0.733603i
$33$	−0.946084	+	5.66612i	−0.164692	+	0.986345i
$34$	−6.33251	+	10.9682i	−1.08602	+	1.88104i
$35$	1.36967	+	2.37233i	0.231516	+	0.400998i
$36$	6.71262	−	11.4596i	1.11877	−	1.90994i
$37$	8.35820			1.37408			0.687040	−	0.726620i	$-0.258910\pi$
$37$	8.35820			1.37408			0.687040	+	0.726620i	$0.258910\pi$
$38$	6.42856	−	8.98810i	1.04285	−	1.45806i
$39$	−3.30634	+	5.68540i	−0.529437	+	0.910393i
$40$	15.5709	−	8.98986i	2.46197	−	1.42142i
$41$	−1.75301	−	3.03630i	−0.273774	−	0.474191i	0.696051	−	0.717992i	$-0.254939\pi$
$41$	−1.75301	−	3.03630i	−0.273774	−	0.474191i	−0.969825	+	0.243802i	$0.921605\pi$
$42$	−2.04687	−	3.57116i	−0.315839	−	0.551042i
$43$	−8.71037	+	5.02893i	−1.32832	+	0.766905i	−0.985040	−	0.172328i	$-0.944871\pi$
$43$	−8.71037	+	5.02893i	−1.32832	+	0.766905i	−0.343279	+	0.939233i	$0.611538\pi$
$44$	9.29953	−	11.3621i	1.40196	−	1.71290i
$45$	7.61960	−	4.33555i	1.13586	−	0.646305i
$46$			3.45235i			0.509021i
$47$	0.553220	+	0.319402i	0.0806954	+	0.0465895i	0.539805	−	0.841790i	$-0.318498\pi$
$47$	0.553220	+	0.319402i	0.0806954	+	0.0465895i	−0.459109	+	0.888380i	$0.651831\pi$
$48$	−10.1345	+	5.80875i	−1.46279	+	0.838421i
$49$	6.12126			0.874466
$50$	8.97310			1.26899
$51$	7.50722	−	4.30290i	1.05122	−	0.602526i
$52$	14.5579	−	8.40499i	2.01881	−	1.16556i
$53$	8.50178	+	4.90851i	1.16781	+	0.674235i	0.953163	−	0.302456i	$-0.0978067\pi$
$53$	8.50178	+	4.90851i	1.16781	+	0.674235i	0.214647	+	0.976692i	$0.431140\pi$
$54$	−11.4698	+	6.47865i	−1.56084	+	0.881632i
$55$	9.06625	−	3.42598i	1.22249	−	0.461959i
$56$			5.76762i			0.770731i
$57$	−6.88385	+	3.10043i	−0.911788	+	0.410662i
$58$	−6.56567			−0.862115
$59$	−11.3031	+	6.52587i	−1.47154	+	0.849596i	−0.999489	−	0.0319725i	$-0.989821\pi$
$59$	−11.3031	+	6.52587i	−1.47154	+	0.849596i	−0.472055	+	0.881569i	$0.656488\pi$
$60$	−22.4068	−	0.0704238i	−2.89271	−	0.00909167i
$61$	0.667708	+	0.385502i	0.0854913	+	0.0493584i	0.542136	−	0.840291i	$-0.317616\pi$
$61$	0.667708	+	0.385502i	0.0854913	+	0.0493584i	−0.456645	+	0.889649i	$0.650949\pi$
$62$	−12.3034	−	21.3101i	−1.56253	−	2.70639i
$63$	−0.0176773	+	2.81217i	−0.00222713	+	0.354301i
$64$	−1.34012			−0.167515
$65$	11.0963			1.37632
$66$	−13.6392	+	5.10509i	−1.67887	+	0.628394i
$67$	0.980172	−	1.69771i	0.119747	−	0.207408i	−0.799920	−	0.600106i	$-0.795125\pi$
$67$	0.980172	−	1.69771i	0.119747	−	0.207408i	0.919667	+	0.392698i	$0.128458\pi$
$68$	−22.1161			−2.68198
$69$	1.18576	−	2.03898i	0.142749	−	0.245464i
$70$	−3.47231	+	6.01422i	−0.415020	+	0.718836i
$71$	8.49025	−	4.90185i	1.00761	−	0.581742i	0.0971169	−	0.995273i	$-0.469038\pi$
$71$	8.49025	−	4.90185i	1.00761	−	0.581742i	0.910490	+	0.413531i	$0.135705\pi$
$72$	18.4578	+	0.116025i	2.17527	+	0.0136737i
$73$	3.20047	−	1.84779i	0.374587	−	0.216268i	−0.300873	−	0.953664i	$-0.597278\pi$
$73$	3.20047	−	1.84779i	0.374587	−	0.216268i	0.675461	+	0.737396i	$0.263945\pi$
$74$	10.5946	+	18.3504i	1.23160	+	2.13319i
$75$	−5.29956	−	3.08195i	−0.611940	−	0.355873i
$76$	19.2055	+	1.87415i	2.20302	+	0.214980i
$77$	−0.502393	+	3.06818i	−0.0572530	+	0.349651i
$78$	−16.6733	−	0.0524036i	−1.88788	−	0.00593354i
$79$	−12.2359	+	7.06441i	−1.37665	+	0.794808i	−0.991754	−	0.128153i	$-0.959095\pi$
$79$	−12.2359	+	7.06441i	−1.37665	+	0.794808i	−0.384893	+	0.922961i	$0.625762\pi$
$80$	17.0676	+	9.85396i	1.90821	+	1.10171i
$81$	8.99929	+	0.113143i	0.999921	+	0.0125715i
$82$	4.44414	−	7.69747i	0.490773	−	0.850043i
$83$	−8.39058			−0.920986			−0.460493	−	0.887663i	$-0.652327\pi$
$83$	−8.39058			−0.920986			−0.460493	+	0.887663i	$0.652327\pi$
$84$	3.61345	−	6.21350i	0.394260	−	0.677949i
$85$	−12.6430	−	7.29942i	−1.37132	−	0.791734i
$86$	−22.0821	−	12.7491i	−2.38117	−	1.37477i
$87$	3.87772	+	2.25508i	0.415735	+	0.241770i
$88$	20.1381	+	3.29748i	2.14673	+	0.351512i
$89$	1.57818	+	0.911162i	0.167287	+	0.0965830i	0.581306	−	0.813685i	$-0.302542\pi$
$89$	1.57818	+	0.911162i	0.167287	+	0.0965830i	−0.414019	+	0.910268i	$0.635875\pi$
$90$	19.1771	+	11.2332i	2.02144	+	1.18409i
$91$	−1.77976	+	3.08263i	−0.186569	+	0.323147i
$92$	−5.22094	+	3.01431i	−0.544321	+	0.314264i
$93$	−0.0528384	+	16.8117i	−0.00547909	+	1.74329i
$94$			1.61946i			0.167034i
$95$	10.3605	+	7.41014i	1.06296	+	0.760265i
$96$	−7.17474	−	4.17246i	−0.732269	−	0.425850i
$97$	−0.468735	−	0.811873i	−0.0475929	−	0.0824333i	0.841248	−	0.540650i	$-0.181822\pi$
$97$	−0.468735	−	0.811873i	−0.0475929	−	0.0824333i	−0.888840	+	0.458217i	$0.848488\pi$
$98$	7.75915	+	13.4392i	0.783792	+	1.35757i
$99$	9.80881	+	1.66950i	0.985823	+	0.167791i
$100$	7.83458	+	13.5699i	0.783458	+	1.35699i
$101$	−0.627986	+	1.08770i	−0.0624869	+	0.108231i	−0.895576	−	0.444908i	$-0.853237\pi$
$101$	−0.627986	+	1.08770i	−0.0624869	+	0.108231i	0.833090	+	0.553138i	$0.186570\pi$
$102$	18.9630	+	11.0279i	1.87761	+	1.09192i
$103$	5.51984			0.543886			0.271943	−	0.962313i	$-0.412334\pi$
$103$	5.51984			0.543886			0.271943	+	0.962313i	$0.412334\pi$
$104$	20.2329	+	11.6815i	1.98400	+	1.14546i
$105$	4.11644	−	2.35941i	0.401723	−	0.230255i
$106$			24.8876i			2.41729i
$107$	9.45893			0.914429			0.457215	−	0.889356i	$-0.348847\pi$
$107$	9.45893			0.914429			0.457215	+	0.889356i	$0.348847\pi$
$108$	−19.8120	−	11.6889i	−1.90641	−	1.12477i
$109$	−1.73003	+	0.998836i	−0.165707	+	0.0956711i	−0.580560	−	0.814217i	$-0.697166\pi$
$109$	−1.73003	+	0.998836i	−0.165707	+	0.0956711i	0.414853	+	0.909889i	$0.363833\pi$
$110$	19.0139	+	15.5623i	1.81290	+	1.48381i
$111$	0.0454999	−	14.4768i	0.00431865	−	1.37407i
$112$	−5.47501	+	3.16100i	−0.517340	+	0.298686i
$113$			18.4691i			1.73742i	0.495318	+	0.868712i	$0.335052\pi$
$113$			18.4691i			1.73742i	−0.495318	+	0.868712i	$0.664948\pi$
$114$	−15.5328	−	11.1835i	−1.45478	−	1.04743i
$115$	−3.97949			−0.371089
$116$	−5.73261	−	9.92918i	−0.532260	−	0.921901i
$117$	9.82935	+	5.75766i	0.908724	+	0.532296i
$118$	−28.6551	−	16.5440i	−2.63792	−	1.52300i
$119$	4.05568	−	2.34155i	0.371783	−	0.214649i
$120$	−15.4861	−	27.0184i	−1.41368	−	2.46643i
$121$	10.4255	+	3.50829i	0.947776	+	0.318935i
$122$			1.95461i			0.176962i
$123$	−5.26854	+	3.01976i	−0.475049	+	0.272282i
$124$	21.4847	−	37.2125i	1.92938	−	3.34178i
$125$		−	4.26799i		−	0.381741i
$126$	−6.19654	+	3.52583i	−0.552032	+	0.314106i
$127$	−9.67328	−	5.58487i	−0.858365	−	0.495577i	0.00509958	−	0.999987i	$-0.498377\pi$
$127$	−9.67328	−	5.58487i	−0.858365	−	0.495577i	−0.863464	+	0.504410i	$0.831710\pi$
$128$	−6.49058	−	11.2420i	−0.573691	−	0.993662i
$129$	8.66291	+	15.1141i	0.762726	+	1.33072i
$130$	14.0653	+	24.3618i	1.23361	+	2.13667i
$131$	0.243979	+	0.422584i	0.0213166	+	0.0369214i	0.876487	−	0.481426i	$-0.159881\pi$
$131$	0.243979	+	0.422584i	0.0213166	+	0.0369214i	−0.855170	+	0.518347i	$0.826548\pi$
$132$	−19.6290	−	16.1690i	−1.70849	−	1.40733i
$133$	−3.72034	+	1.68970i	−0.322595	+	0.146515i
$134$	4.96976			0.429322
$135$	−7.46787	−	13.2211i	−0.642732	−	1.13789i
$136$	−15.3688	−	26.6196i	−1.31786	−	2.28261i
$137$	−4.68104	−	2.70260i	−0.399928	−	0.230898i	0.286525	−	0.958073i	$-0.407500\pi$
$137$	−4.68104	−	2.70260i	−0.399928	−	0.230898i	−0.686453	+	0.727174i	$0.740833\pi$
$138$	5.97962	+	0.0187937i	0.509019	+	0.00159983i
$139$	−11.4186	−	6.59253i	−0.968513	−	0.559171i	−0.0697307	−	0.997566i	$-0.522214\pi$
$139$	−11.4186	−	6.59253i	−0.968513	−	0.559171i	−0.898783	+	0.438394i	$0.855547\pi$
$140$	−12.1270			−1.02491
$141$	0.556229	−	0.956461i	0.0468429	−	0.0805486i
$142$	21.5240	+	12.4269i	1.80626	+	1.04284i
$143$	9.74570	+	7.97655i	0.814976	+	0.667033i
$144$	10.0058	+	17.5850i	0.833819	+	1.46541i
$145$		−	7.56819i		−	0.628504i
$146$	8.11367	+	4.68443i	0.671492	+	0.387686i
$147$	0.0333226	−	10.6023i	0.00274840	−	0.874462i
$148$	−18.5007	+	32.0442i	−1.52075	+	2.63402i
$149$	−4.42926	−	7.67171i	−0.362859	−	0.628491i	0.625571	−	0.780167i	$-0.284866\pi$
$149$	−4.42926	−	7.67171i	−0.362859	−	0.628491i	−0.988430	+	0.151677i	$0.951533\pi$
$150$	0.0488472	−	15.5418i	0.00398836	−	1.26898i
$151$			6.47237i			0.526714i	0.964698	+	0.263357i	$0.0848298\pi$
$151$			6.47237i			0.526714i	−0.964698	+	0.263357i	$0.915170\pi$
$152$	11.0904	+	24.4186i	0.899548	+	1.98061i
$153$	−7.41193	−	13.0263i	−0.599219	−	1.05311i
$154$	−7.37301	+	2.78613i	−0.594134	+	0.224513i
$155$	24.5640	−	14.1820i	1.97303	−	1.13913i
$156$	−14.4785	−	25.2606i	−1.15921	−	2.02247i
$157$	1.60111	+	2.77321i	0.127783	+	0.221326i	0.922817	−	0.385238i	$-0.125881\pi$
$157$	1.60111	+	2.77321i	0.127783	+	0.221326i	−0.795035	+	0.606564i	$0.792547\pi$
$158$	−31.0198	−	17.9093i	−2.46781	−	1.42479i
$159$	8.54802	−	14.6987i	0.677902	−	1.16568i
$160$			14.0030i			1.10704i
$161$	0.638280	−	1.10553i	0.0503035	−	0.0871283i
$162$	11.1589	+	19.9014i	0.876722	+	1.56360i
$163$	−18.1401			−1.42085			−0.710423	−	0.703775i	$-0.751496\pi$
$163$	−18.1401			−1.42085			−0.710423	+	0.703775i	$0.751496\pi$
$164$	15.5210			1.21199
$165$	−5.88459	−	15.7218i	−0.458115	−	1.22394i
$166$	−10.6357	−	18.4215i	−0.825488	−	1.42979i
$167$	2.46810	−	4.27488i	0.190987	−	0.330800i	−0.754590	−	0.656196i	$-0.772164\pi$
$167$	2.46810	−	4.27488i	0.190987	−	0.330800i	0.945578	+	0.325396i	$0.105498\pi$
$168$	9.98977	+	0.0313974i	0.770727	+	0.00242237i
$169$	0.709271	+	1.22849i	0.0545593	+	0.0944995i
$170$		−	37.0102i		−	2.83855i
$171$	5.33260	+	11.9400i	0.407794	+	0.913074i
$172$		−	44.5259i		−	3.39506i
$173$	−5.61183	−	9.71997i	−0.426659	−	0.738996i	0.569914	−	0.821704i	$-0.306976\pi$
$173$	−5.61183	−	9.71997i	−0.426659	−	0.738996i	−0.996574	+	0.0827084i	$0.973643\pi$
$174$	−0.0357418	+	11.3720i	−0.00270958	+	0.862111i
$175$	−2.87342	−	1.65897i	−0.217210	−	0.125406i
$176$	7.90668	+	20.9236i	0.595989	+	1.57718i
$177$	11.2416	+	19.6130i	0.844967	+	1.47421i
$178$			4.61986i			0.346273i
$179$			17.0114i			1.27149i	0.771900	+	0.635744i	$0.219307\pi$
$179$			17.0114i			1.27149i	−0.771900	+	0.635744i	$0.780693\pi$
$180$	−0.243954	+	38.8092i	−0.0181833	+	2.89267i
$181$	7.01023	−	12.1421i	0.521066	−	0.902513i	−0.478634	−	0.878015i	$-0.658868\pi$
$181$	7.01023	−	12.1421i	0.521066	−	0.902513i	0.999700	−	0.0244984i	$-0.00779887\pi$
$182$	−9.02388			−0.668895
$183$	0.671340	−	1.15440i	0.0496269	−	0.0853357i
$184$	−7.25621	−	4.18937i	−0.534935	−	0.308845i
$185$	−21.1524	+	12.2123i	−1.55515	+	0.897868i
$186$	−36.9770	+	21.1940i	−2.71129	+	1.55402i
$187$	−5.85696	−	15.4994i	−0.428303	−	1.13343i
$188$	−2.44909	+	1.41398i	−0.178618	+	0.103125i
$189$	4.87071	+	0.0459265i	0.354292	+	0.00334066i
$190$	−3.13629	+	32.1394i	−0.227531	+	2.33164i
$191$			7.63549i			0.552485i	0.961088	+	0.276242i	$0.0890892\pi$
$191$			7.63549i			0.552485i	−0.961088	+	0.276242i	$0.910911\pi$
$192$	−0.00729525	+	2.32114i	−0.000526490	+	0.167514i
$193$	14.5093	−	8.37693i	1.04440	−	0.602984i	0.123323	−	0.992367i	$-0.460645\pi$
$193$	14.5093	−	8.37693i	1.04440	−	0.602984i	0.921076	+	0.389382i	$0.127311\pi$
$194$	1.18831	−	2.05822i	0.0853159	−	0.147771i
$195$	0.0604051	−	19.2192i	0.00432570	−	1.37631i
$196$	−13.5493	+	23.4681i	−0.967808	+	1.67629i
$197$	−15.8312			−1.12793			−0.563963	−	0.825800i	$-0.690724\pi$
$197$	−15.8312			−1.12793			−0.563963	+	0.825800i	$0.690724\pi$
$198$	8.76799	+	23.6515i	0.623114	+	1.68084i
$199$	8.77390	−	15.1968i	0.621965	−	1.07728i	−0.367154	−	0.930160i	$-0.619668\pi$
$199$	8.77390	−	15.1968i	0.621965	−	1.07728i	0.989119	−	0.147115i	$-0.0469988\pi$
$200$	−10.8887	+	18.8598i	−0.769948	+	1.33359i
$201$	−2.93516	−	1.70694i	−0.207031	−	0.120398i
$202$	−3.18407			−0.224031
$203$	2.10250	+	1.21388i	0.147567	+	0.0851977i
$204$	−0.120395	+	38.3061i	−0.00842930	+	2.68196i
$205$	8.87280	+	5.12271i	0.619703	+	0.357786i
$206$	6.99681	+	12.1188i	0.487491	+	0.844359i
$207$	−3.52514	−	2.06489i	−0.245014	−	0.143520i
$208$			25.6086i			1.77564i
$209$	3.77270	+	13.9559i	0.260963	+	0.965349i
$210$	10.3980	+	6.04693i	0.717528	+	0.417278i
$211$	5.90764	−	3.41078i	0.406699	−	0.234808i	−0.282672	−	0.959217i	$-0.591221\pi$
$211$	5.90764	−	3.41078i	0.406699	−	0.234808i	0.689370	+	0.724409i	$0.257887\pi$
$212$	−37.6371	+	21.7298i	−2.58493	+	1.49241i
$213$	−8.44399	−	14.7322i	−0.578572	−	1.00943i
$214$	11.9899	+	20.7671i	0.819612	+	1.41961i
$215$	14.6957	−	25.4538i	1.00224	−	1.73593i
$216$	0.301440	−	31.9691i	0.0205104	−	2.17522i
$217$			9.09875i			0.617664i
$218$	−4.38589	−	2.53220i	−0.297050	−	0.171502i
$219$	−3.18304	−	5.55341i	−0.215090	−	0.375265i
$220$	−6.93324	+	42.3422i	−0.467439	+	2.85471i
$221$		−	18.9698i		−	1.27605i
$222$	31.8414	−	18.2505i	2.13706	−	1.22489i
$223$	8.68403	+	15.0412i	0.581525	+	1.00723i	0.995299	+	0.0968516i	$0.0308772\pi$
$223$	8.68403	+	15.0412i	0.581525	+	1.00723i	−0.413773	+	0.910380i	$0.635789\pi$
$224$	−3.89015	−	2.24598i	−0.259921	−	0.150066i
$225$	−5.36692	+	9.16228i	−0.357795	+	0.610819i
$226$	−40.5489	+	23.4109i	−2.69727	+	1.55727i
$227$	−21.2351			−1.40943			−0.704713	−	0.709492i	$-0.748924\pi$
$227$	−21.2351			−1.40943			−0.704713	+	0.709492i	$0.748924\pi$
$228$	3.35066	−	33.2545i	0.221903	−	2.20233i
$229$	1.46257			0.0966493			0.0483246	−	0.998832i	$-0.484612\pi$
$229$	1.46257			0.0966493			0.0483246	+	0.998832i	$0.484612\pi$
$230$	−5.04430	−	8.73698i	−0.332611	−	0.576099i
$231$	5.31148	+	0.886869i	0.349470	+	0.0583517i
$232$	7.96734	−	13.7998i	0.523082	−	0.906004i
$233$	4.34272	+	7.52181i	0.284501	+	0.492770i	0.972488	−	0.232953i	$-0.0748388\pi$
$233$	4.34272	+	7.52181i	0.284501	+	0.492770i	−0.687987	+	0.725723i	$0.741505\pi$
$234$	−0.181530	+	28.8786i	−0.0118670	+	1.88785i
$235$	−1.86673			−0.121772
$236$		−	57.7797i		−	3.76114i
$237$	12.1692	+	21.2316i	0.790477	+	1.37914i
$238$	10.2817	+	5.93616i	0.666466	+	0.384784i
$239$	−7.88269			−0.509889			−0.254944	−	0.966956i	$-0.582057\pi$
$239$	−7.88269			−0.509889			−0.254944	+	0.966956i	$0.582057\pi$
$240$	17.1604	−	29.5081i	1.10770	−	1.90474i
$241$	19.1101	+	11.0332i	1.23099	+	0.710712i	0.967236	−	0.253878i	$-0.0817062\pi$
$241$	19.1101	+	11.0332i	1.23099	+	0.710712i	0.263753	+	0.964590i	$0.415040\pi$
$242$	5.51269	+	27.3363i	0.354369	+	1.75724i
$243$	0.244959	−	15.5865i	0.0157141	−	0.999877i
$244$	−2.95592	+	1.70660i	−0.189234	+	0.109254i
$245$	−15.4913	+	8.94389i	−0.989702	+	0.571404i
$246$	−13.3081	−	7.73933i	−0.848497	−	0.493442i
$247$	−1.60753	+	16.4733i	−0.102285	+	1.04817i
$248$	59.7200			3.79222
$249$	−0.0456761	+	14.5328i	−0.00289461	+	0.920981i
$250$	9.37038	−	5.40999i	0.592635	−	0.342158i
$251$	−25.0659	−	14.4718i	−1.58215	−	0.913452i	−0.994546	−	0.104301i	$-0.966739\pi$
$251$	−25.0659	−	14.4718i	−1.58215	−	0.913452i	−0.587600	−	0.809151i	$-0.699927\pi$
$252$	−10.7424	−	6.29248i	−0.676706	−	0.396389i
$253$	−3.49513	−	2.86066i	−0.219737	−	0.179848i
$254$		−	28.3169i		−	1.77676i
$255$	−12.7117	+	21.8584i	−0.796040	+	1.36883i
$256$	15.1144	−	26.1790i	0.944653	−	1.63619i
$257$	2.51504	+	1.45206i	0.156884	+	0.0905770i	0.576387	−	0.817177i	$-0.304462\pi$
$257$	2.51504	+	1.45206i	0.156884	+	0.0905770i	−0.419503	+	0.907754i	$0.637796\pi$
$258$	−22.2022	+	38.1777i	−1.38225	+	2.37684i
$259$		−	7.83506i		−	0.486847i
$260$	−24.5614	+	42.5416i	−1.52323	+	2.63832i
$261$	3.92701	−	6.70410i	0.243076	−	0.414973i
$262$	−0.618523	+	1.07131i	−0.0382125	+	0.0661860i
$263$	−7.56521	−	13.1033i	−0.466491	−	0.807986i	0.532777	−	0.846256i	$-0.321149\pi$
$263$	−7.56521	−	13.1033i	−0.466491	−	0.807986i	−0.999267	+	0.0382701i	$0.987815\pi$
$264$	5.82099	−	34.8621i	0.358257	−	2.14561i
$265$	−28.6877			−1.76227
$266$	−8.42554	−	6.02620i	−0.516603	−	0.369490i
$267$	1.58676	−	2.72851i	0.0971083	−	0.166982i
$268$	4.33919	+	7.51570i	0.265058	+	0.459094i
$269$	−3.40392	+	1.96525i	−0.207541	+	0.119824i	−0.600168	−	0.799874i	$-0.704900\pi$
$269$	−3.40392	+	1.96525i	−0.207541	+	0.119824i	0.392627	+	0.919698i	$0.371566\pi$
$270$	19.5608	−	33.1544i	1.19043	−	2.01771i
$271$	4.77296	−	2.75567i	0.289937	−	0.167395i	−0.347977	−	0.937503i	$-0.613131\pi$
$271$	4.77296	−	2.75567i	0.289937	−	0.167395i	0.637913	+	0.770108i	$0.279798\pi$
$272$	16.8460	−	29.1782i	1.02144	−	1.76919i
$273$	5.32955	+	3.09939i	0.322559	+	0.187584i
$274$		−	13.7030i		−	0.827826i
$275$	−7.43522	+	9.08430i	−0.448361	+	0.547804i
$276$	5.19249	+	9.05930i	0.312551	+	0.545306i
$277$		−	15.4880i		−	0.930587i	−0.885157	−	0.465293i	$-0.845949\pi$
$277$		−	15.4880i		−	0.930587i	0.885157	−	0.465293i	$-0.154051\pi$
$278$		−	33.4261i		−	2.00476i
$279$	29.1182	+	0.183037i	1.74326	+	0.0109581i
$280$	−8.42719	−	14.5963i	−0.503621	−	0.872297i
$281$	6.95494	−	12.0463i	0.414897	−	0.718623i	−0.580521	−	0.814246i	$-0.697151\pi$
$281$	6.95494	−	12.0463i	0.414897	−	0.718623i	0.995418	+	0.0956229i	$0.0304843\pi$
$282$	2.80497	+	0.00881592i	0.167034	+	0.000524980i
$283$	−1.93719	+	1.11844i	−0.115154	+	0.0664843i	−0.556471	−	0.830867i	$-0.687845\pi$
$283$	−1.93719	+	1.11844i	−0.115154	+	0.0664843i	0.441317	+	0.897351i	$0.354512\pi$
$284$			43.4006i			2.57535i
$285$	12.8911	−	17.9045i	0.763602	−	1.06057i
$286$	−5.15915	+	31.5076i	−0.305067	+	1.86308i
$287$	−2.84626	+	1.64329i	−0.168009	+	0.0970003i
$288$	−7.26593	+	12.4042i	−0.428149	+	0.730927i
$289$	−3.97889	+	6.89164i	−0.234052	+	0.405390i
$290$	16.6160	−	9.59323i	0.975723	−	0.563334i
$291$	−1.40875	+	0.807450i	−0.0825824	+	0.0473335i
$292$			16.3603i			0.957412i
$293$	−3.53172			−0.206325			−0.103163	−	0.994665i	$-0.532896\pi$
$293$	−3.53172			−0.206325			−0.103163	+	0.994665i	$0.532896\pi$
$294$	23.3196	−	13.3660i	1.36002	−	0.779522i
$295$	19.0702	−	33.0305i	1.11031	−	1.92311i
$296$	−51.4257			−2.98906
$297$	2.94505	−	16.9802i	0.170889	−	0.985290i
$298$	11.2288	−	19.4489i	0.650468	−	1.12664i
$299$	−2.58549	−	4.47820i	−0.149523	−	0.258981i
$300$	23.5463	−	13.4960i	1.35945	−	0.779189i
$301$	4.71417	+	8.16519i	0.271720	+	0.470634i
$302$	−14.2101	+	8.20421i	−0.817700	+	0.472099i
$303$	1.88053	+	1.09362i	0.108034	+	0.0628268i
$304$	−17.1016	+	23.9106i	−0.980842	+	1.37136i
$305$	−2.25305			−0.129010
$306$	19.2040	−	32.7846i	1.09782	−	1.87417i
$307$	7.23370	−	4.17638i	0.412849	−	0.238358i	−0.279164	−	0.960243i	$-0.590057\pi$
$307$	7.23370	−	4.17638i	0.412849	−	0.238358i	0.692013	+	0.721885i	$0.256724\pi$
$308$	−10.6509	−	8.71747i	−0.606894	−	0.496724i
$309$	0.0300486	−	9.56060i	0.00170940	−	0.543884i
$310$	62.2733	+	35.9535i	3.53688	+	2.04202i
$311$			9.52807i			0.540287i	0.962820	+	0.270144i	$0.0870712\pi$
$311$			9.52807i			0.540287i	−0.962820	+	0.270144i	$0.912929\pi$
$312$	20.3430	−	34.9807i	1.15169	−	1.98039i
$313$	9.96106	−	17.2531i	0.563032	−	0.975201i	−0.434197	−	0.900818i	$-0.642968\pi$
$313$	9.96106	−	17.2531i	0.563032	−	0.975201i	0.997230	−	0.0743831i	$-0.0236988\pi$
$314$	−4.05906	+	7.03049i	−0.229066	+	0.396754i
$315$	−4.06419	−	7.14269i	−0.228991	−	0.402445i
$316$		−	62.5478i		−	3.51859i
$317$	−9.78685	−	5.65044i	−0.549684	−	0.317360i	0.199310	−	0.979936i	$-0.436130\pi$
$317$	−9.78685	−	5.65044i	−0.549684	−	0.317360i	−0.748995	+	0.662576i	$0.769463\pi$
$318$	43.1063	+	0.135481i	2.41728	+	0.00759742i
$319$	5.44040	−	6.64704i	0.304604	−	0.372163i
$320$	3.39148	−	1.95807i	0.189590	−	0.109460i
$321$	0.0514920	−	16.3833i	0.00287400	−	0.914425i
$322$	3.23627			0.180350
$323$	12.6682	−	17.7120i	0.704876	−	0.985522i
$324$	−20.3536	+	34.2516i	−1.13075	+	1.90287i
$325$	−11.6394	+	6.72001i	−0.645638	+	0.372759i
$326$	−22.9940	−	39.8267i	−1.27352	−	2.20580i
$327$	1.72061	+	3.00193i	0.0951499	+	0.166007i
$328$	10.7858	+	18.6815i	0.595545	+	1.03151i
$329$	0.299410	−	0.518594i	0.0165070	−	0.0285910i
$330$	27.0580	−	32.8481i	1.48950	−	1.80823i
$331$	−22.2771			−1.22446			−0.612229	−	0.790681i	$-0.709727\pi$
$331$	−22.2771			−1.22446			−0.612229	+	0.790681i	$0.709727\pi$
$332$	18.5724	−	32.1684i	1.01929	−	1.76547i
$333$	−25.0741	−	0.157615i	−1.37405	−	0.00863727i
$334$	12.5140			0.684736
$335$			5.72859i			0.312986i
$336$	5.44518	+	9.50016i	0.297059	+	0.518276i
$337$	−16.6393	+	9.60671i	−0.906401	+	0.523311i	−0.879272	−	0.476321i	$-0.841970\pi$
$337$	−16.6393	+	9.60671i	−0.906401	+	0.523311i	−0.0271299	+	0.999632i	$0.508637\pi$
$338$	−1.79811	+	3.11441i	−0.0978041	+	0.169402i
$339$	31.9892	+	0.100541i	1.73741	+	0.00546063i
$340$	55.9701	−	32.3143i	3.03540	−	1.75249i
$341$	31.7690	+	5.20195i	1.72039	+	0.281702i
$342$	−19.4548	+	26.8425i	−1.05200	+	1.45148i
$343$		−	12.3000i		−	0.664138i
$344$	53.5925	−	30.9416i	2.88951	−	1.66826i
$345$	−0.0216633	+	6.89265i	−0.00116631	+	0.371088i
$346$	14.2268	−	24.6415i	0.764838	−	1.32474i
$347$	17.1569	+	29.7165i	0.921028	+	1.59527i	0.797827	+	0.602886i	$0.205983\pi$
$347$	17.1569	+	29.7165i	0.921028	+	1.59527i	0.123201	+	0.992382i	$0.460684\pi$
$348$	−17.2290	+	9.87508i	−0.923569	+	0.529360i
$349$		−	16.6724i		−	0.892455i	−0.894920	−	0.446227i	$-0.852767\pi$
$349$		−	16.6724i		−	0.892455i	0.894920	−	0.446227i	$-0.147233\pi$
$350$		−	8.41147i		−	0.449612i
$351$	10.0260	−	16.9935i	0.535150	−	0.907047i
$352$	−10.0661	+	12.2987i	−0.536524	+	0.655521i
$353$			26.7012i			1.42116i	0.703617	+	0.710580i	$0.251567\pi$
$353$			26.7012i			1.42116i	−0.703617	+	0.710580i	$0.748433\pi$
$354$	−28.8110	+	49.5418i	−1.53129	+	2.63312i
$355$	−14.3244	+	24.8105i	−0.760258	+	1.31681i
$356$	−6.98655	+	4.03369i	−0.370286	+	0.213785i
$357$	−4.03358	−	7.03735i	−0.213480	−	0.372456i
$358$	−37.3485	+	21.5631i	−1.97393	+	1.13965i
$359$	15.3870	+	26.6510i	0.812093	+	1.40659i	0.911396	+	0.411529i	$0.135005\pi$
$359$	15.3870	+	26.6510i	0.812093	+	1.40659i	−0.0993033	+	0.995057i	$0.531661\pi$
$360$	−46.8813	+	26.6754i	−2.47086	+	1.40592i
$361$	−12.5019	+	14.3074i	−0.657993	+	0.753024i
$362$	35.5439			1.86815
$363$	6.13326	−	18.0384i	0.321913	−	0.946769i
$364$	−7.87892	−	13.6467i	−0.412968	−	0.715281i
$365$	−5.39970	+	9.35255i	−0.282633	+	0.489535i
$366$	3.38546	+	0.0106404i	0.176961	+	0.000556181i
$367$	−5.57528	+	9.65667i	−0.291027	+	0.504074i	−0.974053	−	0.226320i	$-0.927330\pi$
$367$	−5.57528	+	9.65667i	−0.291027	+	0.504074i	0.683026	+	0.730394i	$0.260664\pi$
$368$		−	9.18410i		−	0.478754i
$369$	5.20167	+	9.14178i	0.270788	+	0.475902i
$370$	−53.6244	−	30.9600i	−2.78780	−	1.60954i
$371$	4.60128	−	7.96966i	0.238887	−	0.413764i
$372$	−64.3367	−	37.4149i	−3.33570	−	1.93987i
$373$			25.8265i			1.33725i	0.743602	+	0.668623i	$0.233116\pi$
$373$			25.8265i			1.33725i	−0.743602	+	0.668623i	$0.766884\pi$
$374$	26.6048	−	32.5056i	1.37570	−	1.68082i
$375$	−7.39234	−	0.0232338i	−0.381739	−	0.00119979i
$376$	−3.40381	−	1.96519i	−0.175538	−	0.101347i
$377$	8.51663	−	4.91708i	0.438629	−	0.253242i
$378$	6.07315	+	10.7519i	0.312369	+	0.553016i
$379$	4.20282			0.215884			0.107942	−	0.994157i	$-0.465574\pi$
$379$	4.20282			0.215884			0.107942	+	0.994157i	$0.465574\pi$
$380$	−51.3423	+	23.3185i	−2.63380	+	1.19622i
$381$	−9.72589	+	16.7241i	−0.498272	+	0.856803i
$382$	−16.7637	+	9.67854i	−0.857707	+	0.495197i
$383$	17.4092	−	10.0512i	0.889570	−	0.513594i	0.0157684	−	0.999876i	$-0.494981\pi$
$383$	17.4092	−	10.0512i	0.889570	−	0.513594i	0.873802	+	0.486282i	$0.161647\pi$
$384$	−19.5070	+	11.1808i	−0.995461	+	0.570565i
$385$	−3.21155	−	8.49880i	−0.163676	−	0.433139i
$386$	36.7831	+	21.2367i	1.87221	+	1.08092i
$387$	26.2254	−	14.9222i	1.33311	−	0.758540i
$388$	4.15015			0.210692
$389$	1.67702	+	0.968227i	0.0850282	+	0.0490911i	0.541911	−	0.840436i	$-0.317701\pi$
$389$	1.67702	+	0.968227i	0.0850282	+	0.0490911i	−0.456883	+	0.889527i	$0.651034\pi$
$390$	42.2723	−	24.2291i	2.14054	−	1.22689i
$391$			6.80322i			0.344054i
$392$	−37.6624			−1.90224
$393$	0.733262	−	0.420282i	0.0369882	−	0.0212004i
$394$	−20.0672	−	34.7574i	−1.01097	−	1.75105i
$395$	20.6439	−	35.7563i	1.03871	−	1.79909i
$396$	−28.1123	+	33.9103i	−1.41270	+	1.70405i
$397$	4.21868	+	7.30697i	0.211729	+	0.366726i	0.952256	−	0.305301i	$-0.0987571\pi$
$397$	4.21868	+	7.30697i	0.211729	+	0.366726i	−0.740526	+	0.672027i	$0.765424\pi$
$398$	44.4862			2.22989
$399$	2.90637	+	6.45299i	0.145501	+	0.323053i
$400$	−23.8707			−1.19353
$401$	−31.1703	+	17.9962i	−1.55657	+	0.898686i	−0.558988	+	0.829176i	$0.688810\pi$
$401$	−31.1703	+	17.9962i	−1.55657	+	0.898686i	−0.997581	+	0.0695102i	$0.977856\pi$
$402$	0.0270541	−	8.60783i	0.00134933	−	0.429320i
$403$	31.9186	+	18.4282i	1.58998	+	0.917974i
$404$	−2.78007	−	4.81523i	−0.138314	−	0.239567i
$405$	−22.9401	+	12.8627i	−1.13990	+	0.639153i
$406$			6.15473i			0.305454i
$407$	−27.3567	−	4.47947i	−1.35602	−	0.222039i
$408$	−46.1899	+	26.4745i	−2.28674	+	1.31068i
$409$	−27.0892	−	15.6399i	−1.33947	−	0.773345i	−0.352743	−	0.935720i	$-0.614751\pi$
$409$	−27.0892	−	15.6399i	−1.33947	−	0.773345i	−0.986729	+	0.162375i	$0.948085\pi$
$410$			25.9737i			1.28275i
$411$	−4.70650	+	8.09304i	−0.232154	+	0.399200i
$412$	−12.2181	+	21.1623i	−0.601942	+	1.04259i
$413$	6.11742	+	10.5957i	0.301019	+	0.521379i
$414$	0.0651029	−	10.3568i	0.00319964	−	0.509011i
$415$	21.2343	−	12.2596i	1.04235	−	0.601802i
$416$	−15.7579	+	9.09780i	−0.772592	+	0.446056i
$417$	−11.4807	+	19.7416i	−0.562213	+	0.966751i
$418$	−25.8580	+	25.9731i	−1.26476	+	1.27038i
$419$		−	15.4339i		−	0.753995i	−0.926214	−	0.376998i	$-0.876956\pi$
$419$		−	15.4339i		−	0.753995i	0.926214	−	0.376998i	$-0.123044\pi$
$420$	−0.0660160	+	21.0044i	−0.00322125	+	1.02491i
$421$	14.0816	+	24.3900i	0.686294	+	1.18870i	0.973028	+	0.230686i	$0.0740971\pi$
$421$	14.0816	+	24.3900i	0.686294	+	1.18870i	−0.286734	+	0.958010i	$0.592570\pi$
$422$	14.9767	+	8.64682i	0.729056	+	0.420921i
$423$	−1.65360	−	0.968618i	−0.0804009	−	0.0470958i
$424$	−52.3091	−	30.2007i	−2.54035	−	1.46667i
$425$	17.6824			0.857725
$426$	21.6411	−	37.2129i	1.04851	−	1.80297i
$427$	0.361373	−	0.625916i	0.0174881	−	0.0302902i
$428$	−20.9372	+	36.2643i	−1.01204	+	1.75290i
$429$	13.8688	−	16.8365i	0.669591	−	0.812875i
$430$	74.5117			3.59327
$431$	−5.03978	+	8.72915i	−0.242757	+	0.420468i	−0.961499	−	0.274809i	$-0.911385\pi$
$431$	−5.03978	+	8.72915i	−0.242757	+	0.420468i	0.718741	+	0.695278i	$0.244719\pi$
$432$	30.5124	−	17.2348i	1.46803	−	0.829210i
$433$	−17.6800	+	30.6226i	−0.849646	+	1.47163i	0.0318779	+	0.999492i	$0.489851\pi$
$433$	−17.6800	+	30.6226i	−0.849646	+	1.47163i	−0.881524	+	0.472139i	$0.843482\pi$
$434$	−19.9763	+	11.5333i	−0.958894	+	0.553618i
$435$	−13.1084	−	0.0411992i	−0.628501	−	0.00197535i
$436$		−	8.84363i		−	0.423533i
$437$	0.576514	−	5.90786i	0.0275784	−	0.282611i
$438$	8.15780	−	14.0277i	0.389795	−	0.670270i
$439$	30.6512	−	17.6965i	1.46290	−	0.844606i	0.463756	−	0.885963i	$-0.346501\pi$
$439$	30.6512	−	17.6965i	1.46290	−	0.844606i	0.999144	+	0.0413568i	$0.0131680\pi$
$440$	−55.7821	+	21.0791i	−2.65931	+	1.00491i
$441$	−18.3634	−	0.115432i	−0.874449	−	0.00549677i
$442$	41.6483	−	24.0457i	1.98101	−	1.14374i
$443$	−15.8848	−	9.17108i	−0.754709	−	0.435731i	0.0726842	−	0.997355i	$-0.476843\pi$
$443$	−15.8848	−	9.17108i	−0.754709	−	0.435731i	−0.827393	+	0.561624i	$0.810177\pi$
$444$	55.4012	+	32.2185i	2.62923	+	1.52902i
$445$	−5.32526			−0.252442
$446$	−22.0153	+	38.1316i	−1.04245	+	1.80558i
$447$	−13.3118	+	7.62990i	−0.629628	+	0.360882i
$448$			1.25624i			0.0593518i
$449$			11.7311i			0.553623i	0.960924	+	0.276812i	$0.0892778\pi$
$449$			11.7311i			0.553623i	−0.960924	+	0.276812i	$0.910722\pi$
$450$	−26.9188	−	0.169211i	−1.26896	−	0.00797668i
$451$	4.11040	+	10.8774i	0.193551	+	0.512198i
$452$	−70.8079	−	40.8810i	−3.33053	−	1.92288i
$453$	11.2104	+	0.0352339i	0.526712	+	0.00165543i
$454$	−26.9171	−	46.6218i	−1.26328	−	2.18807i
$455$		−	10.4017i		−	0.487641i
$456$	42.3544	−	19.0761i	1.98343	−	0.893319i
$457$		−	27.2250i		−	1.27353i	−0.771058	−	0.636765i	$-0.780272\pi$
$457$		−	27.2250i		−	1.27353i	0.771058	−	0.636765i	$-0.219728\pi$
$458$	1.85391	+	3.21107i	0.0866277	+	0.150044i
$459$	−22.6024	+	12.7669i	−1.05499	+	0.595906i
$460$	8.80854	−	15.2568i	0.410700	−	0.711354i
$461$	11.7566	+	20.3631i	0.547560	+	0.948402i	0.998441	+	0.0558177i	$0.0177766\pi$
$461$	11.7566	+	20.3631i	0.547560	+	0.948402i	−0.450881	+	0.892584i	$0.648890\pi$
$462$	4.78557	+	12.7855i	0.222645	+	0.594837i
$463$	14.0105			0.651122			0.325561	−	0.945521i	$-0.394447\pi$
$463$	14.0105			0.651122			0.325561	+	0.945521i	$0.394447\pi$
$464$	17.4663			0.810853
$465$	−24.4301	−	42.6230i	−1.13292	−	1.97660i
$466$	−11.0094	+	19.0689i	−0.510002	+	0.883349i
$467$			7.81970i			0.361853i	0.983497	+	0.180926i	$0.0579095\pi$
$467$			7.81970i			0.361853i	−0.983497	+	0.180926i	$0.942090\pi$
$468$	−43.8312	+	24.9399i	−2.02610	+	1.15285i
$469$	−1.59145	−	0.918823i	−0.0734862	−	0.0424273i
$470$	−2.36622	−	4.09842i	−0.109146	−	0.189046i
$471$	4.81203	−	2.75810i	0.221727	−	0.127086i
$472$	69.5451	−	40.1519i	3.20107	−	1.84814i
$473$	31.2046	−	11.7917i	1.43479	−	0.542182i
$474$	−31.1885	+	53.6302i	−1.43254	+	2.46331i
$475$	−15.3553	−	1.49843i	−0.704549	−	0.0687528i
$476$			20.7319i			0.950245i
$477$	−25.4123	−	14.8856i	−1.16355	−	0.681563i
$478$	−9.99189	−	17.3065i	−0.457018	−	0.791579i
$479$	−10.0340	+	17.3794i	−0.458464	+	0.794083i	−0.998880	−	0.0473147i	$-0.984934\pi$
$479$	−10.0340	+	17.3794i	−0.458464	+	0.794083i	0.540416	+	0.841398i	$0.318267\pi$
$480$	24.2538	+	0.0762287i	1.10703	+	0.00347935i
$481$	−27.4855	−	15.8688i	−1.25323	−	0.723554i
$482$			55.9417i			2.54807i
$483$	−1.91136	−	1.11155i	−0.0869697	−	0.0505771i
$484$	−36.5271	+	32.2046i	−1.66032	+	1.46385i
$485$	2.37249	+	1.36976i	0.107729	+	0.0621974i
$486$	34.5308	−	19.2193i	1.56635	−	0.871804i
$487$	3.49219			0.158246			0.0791232	−	0.996865i	$-0.474788\pi$
$487$	3.49219			0.158246			0.0791232	+	0.996865i	$0.474788\pi$
$488$	−4.10822	−	2.37188i	−0.185971	−	0.107370i
$489$	−0.0987502	+	31.4195i	−0.00446564	+	1.42084i
$490$	−39.2727	−	22.6741i	−1.77416	−	1.02431i
$491$	15.7690	+	27.3127i	0.711645	+	1.23261i	0.964239	+	0.265033i	$0.0853829\pi$
$491$	15.7690	+	27.3127i	0.711645	+	1.23261i	−0.252594	+	0.967572i	$0.581284\pi$
$492$	0.0844925	−	26.8831i	0.00380921	−	1.21198i
$493$	−12.9384			−0.582714
$494$	−38.2047	+	17.3517i	−1.71891	+	0.780691i
$495$	−27.2628	+	10.1068i	−1.22537	+	0.454266i
$496$	32.7301	+	56.6902i	1.46962	+	2.54546i
$497$	−4.59504	−	7.95884i	−0.206116	−	0.357003i
$498$	−31.9648	+	18.3212i	−1.43238	+	0.820991i
$499$	21.2436	+	36.7951i	0.950996	+	1.64717i	0.743275	+	0.668986i	$0.233271\pi$
$499$	21.2436	+	36.7951i	0.950996	+	1.64717i	0.207721	+	0.978188i	$0.433395\pi$
$500$	16.3629	+	9.44713i	0.731772	+	0.422489i
$501$	−7.39083	−	4.29813i	−0.330198	−	0.192026i
$502$		−	73.3763i		−	3.27495i
$503$	3.10971	−	5.38617i	0.138655	−	0.240157i	−0.788333	−	0.615249i	$-0.789055\pi$
$503$	3.10971	−	5.38617i	0.138655	−	0.240157i	0.926988	+	0.375092i	$0.122389\pi$
$504$	0.108763	−	17.3025i	0.00484471	−	0.770716i
$505$		−	3.67025i		−	0.163324i
$506$	1.85024	−	11.2997i	0.0822534	−	0.502332i
$507$	2.13166	−	1.22180i	0.0946705	−	0.0542620i
$508$	42.8233	−	24.7240i	1.89998	−	1.09695i
$509$	−7.15984	−	4.13373i	−0.317354	−	0.183225i	0.332858	−	0.942977i	$-0.391987\pi$
$509$	−7.15984	−	4.13373i	−0.317354	−	0.183225i	−0.650213	+	0.759752i	$0.725320\pi$
$510$	−64.1033	−	0.201474i	−2.83854	−	0.00892142i
$511$	−1.73214	−	3.00016i	−0.0766254	−	0.132719i
$512$	50.6724			2.23942
$513$	20.7096	−	9.17129i	0.914351	−	0.404922i
$514$			7.36237i			0.324740i
$515$	−13.9693	+	8.06515i	−0.615559	+	0.355393i
$516$	−77.1207	−	0.242387i	−3.39505	−	0.0106705i
$517$	−1.63953	−	1.34190i	−0.0721064	−	0.0590169i
$518$	17.2019	−	9.93151i	0.755807	−	0.436366i
$519$	−16.8659	+	9.66701i	−0.740333	+	0.424335i
$520$	−68.2722			−2.99393
$521$			31.9325i			1.39899i	0.714637	+	0.699495i	$0.246592\pi$
$521$			31.9325i			1.39899i	−0.714637	+	0.699495i	$0.753408\pi$
$522$	19.6966	+	0.123813i	0.862098	+	0.00541913i
$523$	15.6354	+	9.02712i	0.683690	+	0.394729i	0.801244	−	0.598338i	$-0.204172\pi$
$523$	15.6354	+	9.02712i	0.683690	+	0.394729i	−0.117554	+	0.993066i	$0.537505\pi$
$524$	−2.16018			−0.0943678
$525$	−2.88905	+	4.96786i	−0.126089	+	0.216815i
$526$	19.1789	−	33.2189i	0.836241	−	1.44841i
$527$	−24.2452	−	41.9939i	−1.05614	−	1.82928i
$528$	36.2837	−	13.5808i	1.57904	−	0.591029i
$529$	−10.5728	−	18.3126i	−0.459685	−	0.796198i
$530$	−36.3637	−	62.9838i	−1.57954	−	2.73584i
$531$	34.0318	−	19.3641i	1.47686	−	0.840330i
$532$	1.75685	−	18.0034i	0.0761690	−	0.780547i
$533$			13.3130i			0.576649i
$534$	8.00179	+	0.0251493i	0.346271	+	0.00108832i
$535$	−23.9380	+	13.8206i	−1.03493	+	0.597518i
$536$	−6.03072	+	10.4455i	−0.260488	+	0.451178i
$537$	29.4644	+	0.0926054i	1.27148	+	0.00399622i
$538$	−8.62943	−	4.98220i	−0.372041	−	0.214798i
$539$	−20.0351	−	3.28062i	−0.862974	−	0.141306i
$540$	67.2179	+	0.633806i	2.89260	+	0.0272747i
$541$	18.2834	+	10.5559i	0.786064	+	0.453834i	0.838575	−	0.544786i	$-0.183389\pi$
$541$	18.2834	+	10.5559i	0.786064	+	0.453834i	−0.0525108	+	0.998620i	$0.516722\pi$
$542$	12.1002	+	6.98603i	0.519746	+	0.300076i
$543$	−20.9924	−	12.2081i	−0.900871	−	0.523900i
$544$	23.9391			1.02638
$545$	2.91884	−	5.05557i	0.125029	−	0.216557i
$546$	−0.0491237	+	15.6297i	−0.00210230	+	0.668891i
$547$	9.44743	+	5.45448i	0.403943	+	0.233217i	0.688184	−	0.725536i	$-0.258408\pi$
$547$	9.44743	+	5.45448i	0.403943	+	0.233217i	−0.284241	+	0.958753i	$0.591742\pi$
$548$	20.7228	−	11.9643i	0.885234	−	0.511090i
$549$	−1.99582	−	1.16907i	−0.0851793	−	0.0498948i
$550$	−29.3693	−	4.80902i	−1.25231	−	0.205057i
$551$	11.2356	+	1.09641i	0.478651	+	0.0467087i
$552$	−7.29567	+	12.5453i	−0.310524	+	0.533961i
$553$	6.62225	+	11.4701i	0.281607	+	0.487757i
$554$	34.0040	−	19.6322i	1.44469	−	0.834094i
$555$	21.0371	+	36.7033i	0.892976	+	1.55797i
$556$	50.5498	−	29.1849i	2.14379	−	1.23772i
$557$	−1.10030	+	1.90577i	−0.0466212	+	0.0807503i	−0.888394	−	0.459081i	$-0.848179\pi$
$557$	−1.10030	+	1.90577i	−0.0466212	+	0.0807503i	0.841773	+	0.539831i	$0.181512\pi$
$558$	36.5076	+	64.1611i	1.54549	+	2.71616i
$559$	38.1915			1.61533
$560$	9.23720	−	15.9993i	0.390343	−	0.676094i
$561$	−26.8775	+	10.0601i	−1.13477	+	0.424739i
$562$	35.2636			1.48750
$563$	−36.6285			−1.54371			−0.771853	−	0.635801i	$-0.780670\pi$
$563$	−36.6285			−1.54371			−0.771853	+	0.635801i	$0.780670\pi$
$564$	2.43574	+	4.24962i	0.102563	+	0.178941i
$565$	−26.9855	−	46.7403i	−1.13529	−	1.96638i
$566$	−4.91107	−	2.83541i	−0.206428	−	0.119181i
$567$	0.106062	−	8.43602i	0.00445417	−	0.354280i
$568$	−52.2381	+	30.1597i	−2.19186	+	1.26547i
$569$	−34.1422			−1.43131			−0.715657	−	0.698452i	$-0.753873\pi$
$569$	−34.1422			−1.43131			−0.715657	+	0.698452i	$0.753873\pi$
$570$	55.6497	+	5.60715i	2.33091	+	0.234858i
$571$			20.7207i			0.867132i	0.901122	+	0.433566i	$0.142745\pi$
$571$			20.7207i			0.867132i	−0.901122	+	0.433566i	$0.857255\pi$
$572$	−52.1530	+	19.7077i	−2.18063	+	0.824021i
$573$	13.2250	+	0.0415656i	0.552482	+	0.00173643i
$574$	−7.21568	−	4.16598i	−0.301177	−	0.173885i
$575$	4.17428	−	2.41002i	0.174080	−	0.100505i
$576$	4.02028	+	0.0252714i	0.167511	+	0.00105297i
$577$	−32.2444			−1.34235			−0.671177	−	0.741297i	$-0.734211\pi$
$577$	−32.2444			−1.34235			−0.671177	+	0.741297i	$0.734211\pi$
$578$	−20.1741			−0.839133
$579$	−14.4302	−	25.1763i	−0.599699	−	1.04629i
$580$	29.0154	+	16.7521i	1.20480	+	0.695592i
$581$			7.86541i			0.326312i
$582$	−3.55845	−	2.06941i	−0.147503	−	0.0857799i
$583$	−25.1960	−	20.6222i	−1.04351	−	0.854082i
$584$	−19.6916	+	11.3690i	−0.814845	+	0.470451i
$585$	−33.2881	−	0.209248i	−1.37629	−	0.00865136i
$586$	−4.47671	−	7.75389i	−0.184931	−	0.320310i
$587$	27.3446	−	15.7874i	1.12863	−	0.651617i	0.185043	−	0.982730i	$-0.440757\pi$
$587$	27.3446	−	15.7874i	1.12863	−	0.651617i	0.943591	+	0.331113i	$0.107424\pi$
$588$	40.5740	+	23.5957i	1.67324	+	0.973072i
$589$	17.4957	+	38.5217i	0.720898	+	1.58726i
$590$	96.6913			3.98072
$591$	−0.0861809	+	27.4203i	−0.00354501	+	1.12792i
$592$	−28.1843	−	48.8167i	−1.15837	−	2.00635i
$593$	−12.9626	+	22.4520i	−0.532312	+	0.921992i	0.466976	+	0.884270i	$0.345343\pi$
$593$	−12.9626	+	22.4520i	−0.532312	+	0.921992i	−0.999288	+	0.0377219i	$0.987990\pi$
$594$	41.0131	−	15.0578i	1.68279	−	0.617828i
$595$	−6.84255	+	11.8517i	−0.280517	+	0.485870i
$596$	39.2164			1.60637
$597$	−26.2738	−	15.2795i	−1.07531	−	0.625348i
$598$	6.55459	−	11.3529i	0.268037	−	0.464254i
$599$	−33.5459	−	19.3678i	−1.37065	−	0.791345i	−0.379640	−	0.925134i	$-0.623952\pi$
$599$	−33.5459	−	19.3678i	−1.37065	−	0.791345i	−0.991010	+	0.133789i	$0.957285\pi$
$600$	32.6067	+	18.9624i	1.33116	+	0.774136i
$601$			46.6506i			1.90292i	0.307773	+	0.951460i	$0.400416\pi$
$601$			46.6506i			1.90292i	−0.307773	+	0.951460i	$0.599584\pi$
$602$	−11.9511	+	20.6999i	−0.487091	+	0.843667i
$603$	−2.97247	+	5.07454i	−0.121048	+	0.206651i
$604$	−24.8142	−	14.3265i	−1.00968	−	0.582937i
$605$	−31.5103	+	6.35442i	−1.28108	+	0.258344i
$606$	−0.0173333	+	5.51495i	−0.000704115	+	0.224029i
$607$			35.0581i			1.42297i	0.702703	+	0.711483i	$0.251976\pi$
$607$			35.0581i			1.42297i	−0.702703	+	0.711483i	$0.748024\pi$
$608$	−20.7886	−	2.02863i	−0.843088	−	0.0822719i
$609$	2.11394	−	3.63501i	0.0856611	−	0.147298i
$610$	−2.85591	−	4.94659i	−0.115633	−	0.200281i
$611$	−1.21282	−	2.10067i	−0.0490656	−	0.0849841i
$612$	66.3471	+	0.417057i	2.68192	+	0.0168585i
$613$	−12.6761	+	7.31853i	−0.511982	+	0.295593i	−0.733648	−	0.679530i	$-0.762184\pi$
$613$	−12.6761	+	7.31853i	−0.511982	+	0.295593i	0.221666	+	0.975123i	$0.428850\pi$
$614$	18.3385	+	10.5877i	0.740081	+	0.427286i
$615$	8.92105	−	15.3402i	0.359732	−	0.618575i
$616$	3.09109	−	18.8776i	0.124543	−	0.760602i
$617$	15.9509	+	9.20927i	0.642160	+	0.370751i	0.785446	−	0.618930i	$-0.212434\pi$
$617$	15.9509	+	9.20927i	0.642160	+	0.370751i	−0.143286	+	0.989681i	$0.545767\pi$
$618$	21.0284	−	12.0528i	0.845887	−	0.484834i
$619$	−12.0139			−0.482881			−0.241440	−	0.970416i	$-0.577620\pi$
$619$	−12.0139			−0.482881			−0.241440	+	0.970416i	$0.577620\pi$
$620$			125.567i			5.04288i
$621$	−3.59567	+	6.09445i	−0.144289	+	0.244562i
$622$	−20.9189	+	12.0775i	−0.838771	+	0.484265i
$623$	0.854132	−	1.47940i	0.0342201	−	0.0592709i
$624$	44.3552	+	0.139406i	1.77563	+	0.00558073i
$625$	15.0847	+	26.1275i	0.603390	+	1.04510i
$626$	50.5055			2.01861
$627$	24.1927	−	6.45850i	0.966164	−	0.257928i
$628$	−14.1762			−0.565690
$629$	20.8778	+	36.1615i	0.832454	+	1.44185i
$630$	10.5301	−	17.9768i	0.419531	−	0.716213i
$631$	18.0953	−	31.3420i	0.720364	−	1.24771i	−0.240490	−	0.970652i	$-0.577308\pi$
$631$	18.0953	−	31.3420i	0.720364	−	1.24771i	0.960854	−	0.277055i	$-0.0893585\pi$
$632$	75.2842	−	43.4653i	2.99464	−	1.72896i
$633$	−5.87545	−	10.2508i	−0.233528	−	0.407435i
$634$		−	28.6494i		−	1.13781i
$635$	32.6407			1.29530
$636$	37.4321	+	65.3074i	1.48428	+	2.58961i
$637$	−20.1295	−	11.6218i	−0.797559	−	0.460471i
$638$	21.4897	+	3.51879i	0.850785	+	0.139310i
$639$	−25.5627	+	14.5451i	−1.01124	+	0.575397i
$640$	32.8518	+	18.9670i	1.29858	+	0.749737i
$641$	−16.7886	+	9.69293i	−0.663112	+	0.382848i	−0.793462	−	0.608620i	$-0.791723\pi$
$641$	−16.7886	+	9.69293i	−0.663112	+	0.382848i	0.130350	+	0.991468i	$0.458390\pi$
$642$	36.0348	−	20.6539i	1.42218	−	0.815146i
$643$	−1.17945	−	2.04287i	−0.0465130	−	0.0805628i	0.841832	−	0.539740i	$-0.181478\pi$
$643$	−1.17945	−	2.04287i	−0.0465130	−	0.0805628i	−0.888345	+	0.459177i	$0.848144\pi$
$644$	2.82565	+	4.89416i	0.111346	+	0.192857i
$645$	−44.0070	−	25.5922i	−1.73277	−	1.00769i
$646$	54.9446	+	5.36172i	2.16177	+	0.210954i
$647$		−	6.10126i		−	0.239865i	−0.992782	−	0.119933i	$-0.961732\pi$
$647$		−	6.10126i		−	0.239865i	0.992782	−	0.119933i	$-0.0382679\pi$
$648$	−55.3701	−	0.696139i	−2.17514	−	0.0273469i
$649$	40.4931	−	15.3016i	1.58949	−	0.600642i
$650$	−29.5076	−	17.0362i	−1.15738	−	0.668215i
$651$	15.7594	+	0.0495312i	0.617660	+	0.00194128i
$652$	40.1529	−	69.5469i	1.57251	−	2.72367i
$653$		−	48.8226i		−	1.91058i	−0.295675	−	0.955289i	$-0.595544\pi$
$653$		−	48.8226i		−	1.91058i	0.295675	−	0.955289i	$-0.404456\pi$
$654$	−4.40975	+	7.58277i	−0.172435	+	0.296510i
$655$	−1.23489	−	0.712966i	−0.0482513	−	0.0278579i
$656$	−11.8225	+	20.4772i	−0.461591	+	0.799499i
$657$	−9.63608	+	5.48292i	−0.375939	+	0.213909i
$658$	1.51810			0.0591816
$659$	−19.4655	+	33.7153i	−0.758270	+	1.31336i	0.185463	+	0.982651i	$0.440622\pi$
$659$	−19.4655	+	33.7153i	−0.758270	+	1.31336i	−0.943732	+	0.330710i	$0.892712\pi$
$660$	73.3007	+	12.2392i	2.85322	+	0.476409i
$661$	4.00663	−	6.93969i	0.155840	−	0.269923i	−0.777525	−	0.628852i	$-0.783525\pi$
$661$	4.00663	−	6.93969i	0.155840	−	0.269923i	0.933365	+	0.358930i	$0.116858\pi$
$662$	−28.2378	−	48.9093i	−1.09749	−	1.90091i
$663$	−32.8566	−	0.103267i	−1.27604	−	0.00401055i
$664$	51.6249			2.00343
$665$	6.94634	−	9.71203i	0.269368	−	0.376616i
$666$	−31.4372	−	55.2500i	−1.21817	−	2.14089i
$667$	−3.05435	+	1.76343i	−0.118265	+	0.0682802i
$668$	10.9262	+	18.9248i	0.422748	+	0.732221i
$669$	26.0992	−	14.9592i	1.00905	−	0.578357i
$670$	−12.5771	+	7.26141i	−0.485897	+	0.280533i
$671$	−1.97883	−	1.61961i	−0.0763918	−	0.0625244i
$672$	−3.91130	+	6.72567i	−0.150882	+	0.259448i
$673$			5.05379i			0.194809i	0.995245	+	0.0974047i	$0.0310541\pi$
$673$			5.05379i			0.194809i	−0.995245	+	0.0974047i	$0.968946\pi$
$674$	−42.1831	−	24.3544i	−1.62483	−	0.938098i
$675$	15.8402	+	9.34561i	0.609691	+	0.359713i
$676$	−6.27984			−0.241532
$677$	14.6553			0.563248			0.281624	−	0.959525i	$-0.409127\pi$
$677$	14.6553			0.563248			0.281624	+	0.959525i	$0.409127\pi$
$678$	40.3279	+	70.3598i	1.54878	+	2.70215i
$679$	−0.761058	+	0.439397i	−0.0292067	+	0.0168625i
$680$	77.7887	+	44.9113i	2.98306	+	1.72227i
$681$	−0.115599	+	36.7802i	−0.00442975	+	1.40942i
$682$	28.8486	+	76.3427i	1.10467	+	2.92331i
$683$			10.0045i			0.382811i	0.981511	+	0.191406i	$0.0613046\pi$
$683$			10.0045i			0.382811i	−0.981511	+	0.191406i	$0.938695\pi$
$684$	−57.5800	−	5.98451i	−2.20163	−	0.228823i
$685$	15.7953			0.603506
$686$	27.0047	−	15.5912i	1.03104	−	0.595273i
$687$	0.00796184	−	2.53323i	0.000303763	−	0.0966488i
$688$	58.7437	+	33.9157i	2.23958	+	1.29302i
$689$	−18.6385	−	32.2828i	−0.710069	−	1.22988i
$690$	−15.1603	+	8.68937i	−0.577142	+	0.330799i
$691$	10.5218			0.400270			0.200135	−	0.979768i	$-0.435862\pi$
$691$	10.5218			0.400270			0.200135	+	0.979768i	$0.435862\pi$
$692$	49.6868			1.88881
$693$	1.56501	−	9.19488i	0.0594498	−	0.349285i
$694$	−43.4951	+	75.3358i	−1.65105	+	2.85971i
$695$	38.5299			1.46152
$696$	−23.8585	−	13.8749i	−0.904356	−	0.525927i
$697$	8.75764	−	15.1687i	0.331719	−	0.574555i
$698$	36.6044	−	21.1335i	1.38550	−	0.799916i
$699$	13.0517	−	7.48083i	0.493662	−	0.282951i
$700$	12.7206	−	7.34422i	0.480792	−	0.277585i
$701$	−18.6914	−	32.3745i	−0.705965	−	1.22277i	−0.966342	−	0.257260i	$-0.917180\pi$
$701$	−18.6914	−	32.3745i	−0.705965	−	1.22277i	0.260378	−	0.965507i	$-0.416153\pi$
$702$	50.0180	+	0.471626i	1.88781	+	0.0178004i
$703$	−15.0658	−	33.1716i	−0.568217	−	1.25109i
$704$	4.38626	+	0.718220i	0.165313	+	0.0270689i
$705$	−0.0101620	+	3.23326i	−0.000382724	+	0.121772i
$706$	−58.6225	+	33.8457i	−2.20629	+	1.27380i
$707$	1.01962	+	0.588680i	0.0383469	+	0.0221396i
$708$	−100.077	−	0.314538i	−3.76112	−	0.0118210i
$709$	−0.0770954	+	0.133533i	−0.00289538	+	0.00501494i	−0.867469	−	0.497490i	$-0.834255\pi$
$709$	−0.0770954	+	0.133533i	−0.00289538	+	0.00501494i	0.864574	+	0.502505i	$0.167588\pi$
$710$	−72.6287			−2.72571
$711$	36.8402	−	20.9621i	1.38162	−	0.786139i
$712$	−9.71009	−	5.60613i	−0.363901	−	0.210098i
$713$	−11.4471	−	6.60897i	−0.428696	−	0.247508i
$714$	10.3377	−	17.7761i	0.386877	−	0.665253i
$715$	−36.3184	−	5.94690i	−1.35823	−	0.222402i
$716$	−65.2193	−	37.6544i	−2.43736	−	1.40721i
$717$	−0.0429113	+	13.6532i	−0.00160255	+	0.509886i
$718$	−39.0082	+	67.5642i	−1.45577	+	2.52147i
$719$	−19.2503	+	11.1141i	−0.717914	+	0.414488i	−0.813984	−	0.580887i	$-0.802706\pi$
$719$	−19.2503	+	11.1141i	−0.717914	+	0.414488i	0.0960707	+	0.995375i	$0.469373\pi$
$720$	−51.0158	−	29.8831i	−1.90125	−	1.11368i
$721$		−	5.17436i		−	0.192703i
$722$	−47.2591	−	9.31214i	−1.75880	−	0.346562i
$723$	19.2140	−	33.0394i	0.714578	−	1.22875i
$724$	31.0341	+	53.7526i	1.15337	+	1.99770i
$725$	4.58338	+	7.93864i	0.170222	+	0.294834i
$726$	47.3776	−	9.39939i	1.75835	−	0.348844i
$727$	−7.83337	−	13.5678i	−0.290524	−	0.503202i	0.683410	−	0.730035i	$-0.260496\pi$
$727$	−7.83337	−	13.5678i	−0.290524	−	0.503202i	−0.973934	+	0.226833i	$0.927163\pi$
$728$	10.9503	−	18.9665i	0.405847	−	0.702947i
$729$	−26.9952	−	0.509128i	−0.999822	−	0.0188566i
$730$	−27.3780			−1.01331
$731$	−43.5150	−	25.1234i	−1.60946	−	0.929223i
$732$	2.93982	+	5.12907i	0.108659	+	0.189576i
$733$		−	37.6900i		−	1.39211i	−0.717988	−	0.696055i	$-0.754937\pi$
$733$		−	37.6900i		−	1.39211i	0.717988	−	0.696055i	$-0.245063\pi$
$734$	−28.2683			−1.04340
$735$	15.4069	+	26.8802i	0.568291	+	0.991493i
$736$	5.65130	−	3.26278i	0.208310	−	0.120268i
$737$	−4.11800	+	5.03135i	−0.151689	+	0.185332i
$738$	−13.4773	+	23.0081i	−0.496106	+	0.846942i
$739$	−33.8877	+	19.5651i	−1.24658	+	0.719713i	−0.970426	−	0.241401i	$-0.922393\pi$
$739$	−33.8877	+	19.5651i	−1.24658	+	0.719713i	−0.276154	+	0.961113i	$0.589060\pi$
$740$		−	108.127i		−	3.97483i
$741$	28.5236	+	2.87398i	1.04784	+	0.105578i
$742$	23.3299			0.856466
$743$	−22.8616	−	39.5975i	−0.838711	−	1.45269i	−0.890973	−	0.454057i	$-0.849976\pi$
$743$	−22.8616	−	39.5975i	−0.838711	−	1.45269i	0.0522615	−	0.998633i	$-0.483357\pi$
$744$	0.325100	−	103.437i	0.0119187	−	3.79220i
$745$	22.4186	+	12.9434i	0.821352	+	0.474208i
$746$	−56.7021	+	32.7370i	−2.07601	+	1.19859i
$747$	25.1712	+	0.158226i	0.920968	+	0.00578919i
$748$	72.3870	+	11.8529i	2.64673	+	0.433384i
$749$		−	8.86690i		−	0.323989i
$750$	−9.31932	−	16.2593i	−0.340294	−	0.593707i
$751$	19.2943	−	33.4187i	0.704059	−	1.21947i	−0.262972	−	0.964804i	$-0.584703\pi$
$751$	19.2943	−	33.4187i	0.704059	−	1.21947i	0.967030	−	0.254662i	$-0.0819641\pi$
$752$		−	4.30816i		−	0.157102i
$753$	−25.2022	+	43.3364i	−0.918420	+	1.57927i
$754$	21.5909	+	12.4655i	0.786294	+	0.453967i
$755$	−9.45691	−	16.3798i	−0.344172	−	0.596124i
$756$	−10.9573	+	18.5720i	−0.398514	+	0.675457i
$757$	−13.9906	−	24.2325i	−0.508499	−	0.880746i	−0.999952	−	0.00984142i	$-0.996867\pi$
$757$	−13.9906	−	24.2325i	−0.508499	−	0.880746i	0.491453	−	0.870904i	$-0.336466\pi$
$758$	5.32738	+	9.22730i	0.193499	+	0.335151i
$759$	−4.97381	+	6.03815i	−0.180538	+	0.219171i
$760$	−63.7453	−	45.5926i	−2.31228	−	1.65382i
$761$	−9.02435			−0.327132			−0.163566	−	0.986532i	$-0.552300\pi$
$761$	−9.02435			−0.327132			−0.163566	+	0.986532i	$0.552300\pi$
$762$	−49.0461	−	0.154150i	−1.77675	−	0.00558427i
$763$	0.936319	+	1.62175i	0.0338970	+	0.0587114i
$764$	−29.2735	−	16.9010i	−1.05908	−	0.611458i
$765$	37.7905	+	22.1363i	1.36632	+	0.800338i
$766$	44.1350	+	25.4813i	1.59466	+	0.920678i
$767$	49.5598			1.78950
$768$	−45.2608	−	26.3214i	−1.63321	−	0.949790i
$769$	8.89122	+	5.13335i	0.320626	+	0.185113i	0.651671	−	0.758501i	$-0.274068\pi$
$769$	8.89122	+	5.13335i	0.320626	+	0.185113i	−0.331046	+	0.943615i	$0.607401\pi$
$770$	14.5882	−	17.8238i	0.525724	−	0.642326i
$771$	2.52872	−	4.34825i	0.0910696	−	0.156599i
$772$			74.1688i			2.66939i
$773$	−9.12018	−	5.26554i	−0.328030	−	0.189388i	0.326936	−	0.945046i	$-0.393984\pi$
$773$	−9.12018	−	5.26554i	−0.328030	−	0.189388i	−0.654966	+	0.755658i	$0.727317\pi$
$774$	66.0045	+	38.6629i	2.37248	+	1.38971i
$775$	−17.1776	+	29.7524i	−0.617036	+	1.06874i
$776$	2.88400	+	4.99523i	0.103530	+	0.179318i
$777$	−13.5707	−	0.0426520i	−0.486844	−	0.00153013i
$778$			4.90919i			0.176003i
$779$	−8.89048	+	12.4302i	−0.318534	+	0.445359i
$780$	73.5501	+	42.7729i	2.63352	+	1.53152i
$781$	−30.4160	+	11.4937i	−1.08837	+	0.411276i
$782$	−14.9365	+	8.62358i	−0.534128	+	0.308379i
$783$	−11.5904	−	6.83824i	−0.414207	−	0.244379i
$784$	−20.6412	−	35.7517i	−0.737187	−	1.27685i
$785$	−8.10398	−	4.67883i	−0.289243	−	0.166995i
$786$	1.85219	+	1.07714i	0.0660656	+	0.0384203i
$787$			43.8589i			1.56340i	0.623654	+	0.781701i	$0.285648\pi$
$787$			43.8589i			1.56340i	−0.623654	+	0.781701i	$0.714352\pi$
$788$	35.0421	−	60.6947i	1.24832	−	2.16216i
$789$	−22.7367	+	13.0319i	−0.809448	+	0.463949i
$790$	104.671			3.72401
$791$	17.3131			0.615583
$792$	−60.3509	−	10.2720i	−2.14448	−	0.364999i
$793$	−1.46382	−	2.53541i	−0.0519817	−	0.0900349i
$794$	−10.6950	+	18.5242i	−0.379550	+	0.657401i
$795$	−0.156168	+	49.6882i	−0.00553871	+	1.76226i
$796$	38.8418	+	67.2759i	1.37671	+	2.38453i
$797$		−	20.4897i		−	0.725782i	−0.931832	−	0.362891i	$-0.881790\pi$
$797$		−	20.4897i		−	0.725782i	0.931832	−	0.362891i	$-0.118210\pi$
$798$	−10.4835	+	14.5606i	−0.371112	+	0.515439i
$799$			3.19132i			0.112901i
$800$	−8.48038	−	14.6884i	−0.299827	−	0.519315i
$801$	−4.71726	−	2.76319i	−0.166676	−	0.0976326i
$802$	−79.0212	−	45.6229i	−2.79034	−	1.61100i
$803$	−11.4656	+	4.33264i	−0.404611	+	0.152896i
$804$	13.0411	−	7.47475i	0.459925	−	0.263614i
$805$			3.73041i			0.131480i
$806$			93.4364i			3.29116i
$807$	3.38537	+	5.90643i	0.119171	+	0.207916i
$808$	3.86382	−	6.69234i	0.135929	−	0.235436i
$809$	48.1673			1.69347			0.846736	−	0.532013i	$-0.178564\pi$
$809$	48.1673			1.69347			0.846736	+	0.532013i	$0.178564\pi$
$810$	−57.3184	−	34.0606i	−2.01396	−	1.19677i
$811$	18.1961	+	10.5055i	0.638951	+	0.368899i	0.784210	−	0.620495i	$-0.213068\pi$
$811$	18.1961	+	10.5055i	0.638951	+	0.368899i	−0.145259	+	0.989394i	$0.546402\pi$
$812$	−9.30771	+	5.37381i	−0.326637	+	0.188584i
$813$	−4.74696	−	8.28197i	−0.166483	−	0.290461i
$814$	−24.8419	−	65.7397i	−0.870709	−	2.30418i
$815$	45.9078	−	26.5049i	1.60808	−	0.928426i
$816$	−50.4462	−	29.3369i	−1.76597	−	1.02700i
$817$	35.6591	+	25.5045i	1.24755	+	0.892289i
$818$		−	79.2990i		−	2.77263i
$819$	5.39729	−	9.21414i	0.188597	−	0.321968i
$820$	−39.2796	+	22.6781i	−1.37170	+	0.791953i
$821$	1.62913	−	2.82174i	0.0568572	−	0.0984795i	−0.836196	−	0.548431i	$-0.815225\pi$
$821$	1.62913	−	2.82174i	0.0568572	−	0.0984795i	0.893053	+	0.449951i	$0.148559\pi$
$822$	−23.7341	−	0.0745954i	−0.827822	−	0.00260181i
$823$	10.9492	−	18.9645i	0.381664	−	0.661061i	−0.609637	−	0.792681i	$-0.708685\pi$
$823$	10.9492	−	18.9645i	0.381664	−	0.661061i	0.991300	+	0.131620i	$0.0420179\pi$
$824$	−33.9621			−1.18312
$825$	15.6939	+	12.9276i	0.546392	+	0.450080i
$826$	−15.5086	+	26.8616i	−0.539612	+	0.934635i
$827$	−10.5957	+	18.3523i	−0.368449	+	0.638173i	−0.989323	−	0.145737i	$-0.953445\pi$
$827$	−10.5957	+	18.3523i	−0.368449	+	0.638173i	0.620874	+	0.783910i	$0.286778\pi$
$828$	15.7194	−	8.94430i	0.546285	−	0.310836i
$829$	−41.4697			−1.44030			−0.720151	−	0.693817i	$-0.755928\pi$
$829$	−41.4697			−1.44030			−0.720151	+	0.693817i	$0.755928\pi$
$830$	53.8321	+	31.0800i	1.86854	+	1.07880i
$831$	−26.8260	−	0.0843129i	−0.930582	−	0.00292478i
$832$	4.40691	+	2.54433i	0.152782	+	0.0882088i
$833$	15.2902	+	26.4835i	0.529775	+	0.917597i
$834$	−57.8954	−	0.181963i	−2.00475	−	0.00630086i
$835$			14.4248i			0.499190i
$836$	−61.8558	−	16.4271i	−2.13933	−	0.568143i
$837$	0.475539	−	50.4330i	0.0164370	−	1.74322i
$838$	33.8851	−	19.5636i	1.17054	−	0.675813i
$839$	−12.3969	+	7.15734i	−0.427988	+	0.247099i	−0.698489	−	0.715621i	$-0.746144\pi$
$839$	−12.3969	+	7.15734i	−0.427988	+	0.247099i	0.270501	+	0.962720i	$0.412811\pi$
$840$	−25.3273	+	14.5168i	−0.873875	+	0.500877i
$841$	11.1463	+	19.3060i	0.384356	+	0.665723i
$842$	−35.6989	+	61.8323i	−1.23026	+	2.13088i
$843$	−20.8269	−	12.1118i	−0.717315	−	0.417154i
$844$			30.1988i			1.03949i
$845$	−3.58995	−	2.07266i	−0.123498	−	0.0713017i
$846$	0.0305391	−	4.85828i	0.00104996	−	0.167031i
$847$	3.28870	−	9.77301i	0.113001	−	0.335805i
$848$		−	66.2071i		−	2.27356i
$849$	1.92664	+	3.36139i	0.0661221	+	0.115363i
$850$	22.4138	+	38.8218i	0.768787	+	1.33158i
$851$	9.85723	+	5.69108i	0.337902	+	0.195088i
$852$	75.1718	+	0.236262i	2.57534	+	0.00809420i
$853$	28.3957	−	16.3943i	0.972251	−	0.561329i	0.0723290	−	0.997381i	$-0.476957\pi$
$853$	28.3957	−	16.3943i	0.972251	−	0.561329i	0.899922	+	0.436052i	$0.143624\pi$
$854$	1.83227			0.0626989
$855$	−30.9411	−	22.4254i	−1.05816	−	0.766931i
$856$	−58.1982			−1.98917
$857$	1.37098	+	2.37461i	0.0468319	+	0.0811153i	0.888491	−	0.458894i	$-0.151754\pi$
$857$	1.37098	+	2.37461i	0.0468319	+	0.0811153i	−0.841659	+	0.540009i	$0.818421\pi$
$858$	54.5443	+	9.10738i	1.86211	+	0.310921i
$859$	11.0908	−	19.2099i	0.378414	−	0.655432i	−0.612418	−	0.790534i	$-0.709803\pi$
$859$	11.0908	−	19.2099i	0.378414	−	0.655432i	0.990832	+	0.135102i	$0.0431362\pi$
$860$	65.0576	+	112.683i	2.21845	+	3.84246i
$861$	2.83075	+	4.93879i	0.0964717	+	0.168313i
$862$	−25.5531			−0.870344
$863$		−	15.3460i		−	0.522385i	−0.965287	−	0.261193i	$-0.915884\pi$
$863$		−	15.3460i		−	0.522385i	0.965287	−	0.261193i	$-0.0841158\pi$
$864$	21.4451	+	12.6524i	0.729577	+	0.430444i
$865$	28.4041	+	16.3991i	0.965767	+	0.557586i
$866$	−89.6428			−3.04618
$867$	11.9149	+	6.92912i	0.404653	+	0.235325i
$868$	−34.8834	−	20.1399i	−1.18402	−	0.683594i
$869$	43.8347	−	16.5644i	1.48699	−	0.561908i
$870$	−16.5254	−	28.8318i	−0.560265	−	0.977489i
$871$	−6.44649	+	3.72188i	−0.218431	+	0.126111i
$872$	10.6444	−	6.14556i	0.360466	−	0.208115i
$873$	1.39087	+	2.44441i	0.0470738	+	0.0827308i
$874$	13.7015	−	6.22292i	0.463460	−	0.210493i
$875$	−4.00086			−0.135254
$876$	28.3367	+	0.0890610i	0.957407	+	0.00300909i
$877$	−4.50341	+	2.60005i	−0.152069	+	0.0877973i	−0.574104	−	0.818782i	$-0.694649\pi$
$877$	−4.50341	+	2.60005i	−0.152069	+	0.0877973i	0.422034	+	0.906580i	$0.361316\pi$
$878$	77.7052	+	44.8631i	2.62242	+	1.51406i
$879$	−0.0192257	+	6.11708i	−0.000648468	+	0.206324i
$880$	−50.5816	−	41.3995i	−1.70511	−	1.39558i
$881$			29.6070i			0.997484i	0.866751	+	0.498742i	$0.166204\pi$
$881$			29.6070i			0.997484i	−0.866751	+	0.498742i	$0.833796\pi$
$882$	−23.0236	−	40.4632i	−0.775243	−	1.36247i
$883$	8.72428	−	15.1109i	0.293595	−	0.508522i	−0.681062	−	0.732226i	$-0.738482\pi$
$883$	8.72428	−	15.1109i	0.293595	−	0.508522i	0.974657	+	0.223704i	$0.0718149\pi$
$884$	72.7278	+	41.9894i	2.44610	+	1.41226i
$885$	−57.1064	−	33.2101i	−1.91961	−	1.11635i
$886$		−	46.5001i		−	1.56220i
$887$	−26.4645	+	45.8378i	−0.888591	+	1.53908i	−0.0470488	+	0.998893i	$0.514982\pi$
$887$	−26.4645	+	45.8378i	−0.888591	+	1.53908i	−0.841542	+	0.540192i	$0.818352\pi$
$888$	−0.279948	+	89.0714i	−0.00939444	+	2.98904i
$889$	−5.23531	+	9.06783i	−0.175587	+	0.304125i
$890$	−6.75016	−	11.6916i	−0.226266	−	0.391904i
$891$	−29.3944	−	5.19338i	−0.984748	−	0.173985i
$892$	−76.8878			−2.57439
$893$	0.270436	−	2.77131i	0.00904980	−	0.0927385i
$894$	−33.6252	−	19.5547i	−1.12459	−	0.654006i
$895$	−24.8556	−	43.0512i	−0.830832	−	1.43904i
$896$	−10.5384	+	6.08433i	−0.352062	+	0.203263i
$897$	−7.77050	+	4.45380i	−0.259449	+	0.148708i
$898$	−25.7556	+	14.8700i	−0.859474	+	0.496218i
$899$	12.5689	−	21.7700i	0.419197	−	0.726071i
$900$	−23.2474	−	40.8566i	−0.774913	−	1.36189i
$901$			49.0436i			1.63388i
$902$	−18.6712	+	22.8123i	−0.621682	+	0.759567i
$903$	14.1681	−	8.12070i	0.471485	−	0.270240i
$904$		−	113.635i		−	3.77944i
$905$			40.9711i			1.36193i
$906$	14.1327	+	24.6572i	0.469527	+	0.819179i
$907$	−18.0344	−	31.2364i	−0.598821	−	1.03719i	−0.992995	−	0.118153i	$-0.962303\pi$
$907$	−18.0344	−	31.2364i	−0.598821	−	1.03719i	0.394174	−	0.919036i	$-0.371031\pi$
$908$	47.0037	−	81.4127i	1.55987	−	2.70178i
$909$	1.90443	−	3.25120i	0.0631660	−	0.107836i
$910$	22.8370	−	13.1850i	0.757040	−	0.437077i
$911$			12.1131i			0.401324i	0.979661	+	0.200662i	$0.0643093\pi$
$911$			12.1131i			0.401324i	−0.979661	+	0.200662i	$0.935691\pi$
$912$	41.3210	+	29.7508i	1.36828	+	0.985147i
$913$	27.4627	+	4.49683i	0.908882	+	0.148823i
$914$	59.7724	−	34.5096i	1.97710	−	1.14148i
$915$	−0.0122650	+	3.90239i	−0.000405470	+	0.129009i
$916$	−3.23737	+	5.60730i	−0.106966	+	0.185270i
$917$	0.396135	−	0.228709i	0.0130815	−	0.00755262i
$918$	−56.6798	−	33.4406i	−1.87071	−	1.10370i
$919$			35.4723i			1.17012i	0.810988	+	0.585062i	$0.198930\pi$
$919$			35.4723i			1.17012i	−0.810988	+	0.585062i	$0.801070\pi$
$920$	24.4847			0.807237
$921$	−7.19428	−	12.5518i	−0.237060	−	0.413596i
$922$	−29.8047	+	51.6233i	−0.981567	+	1.70012i
$923$	−37.2263			−1.22532
$924$	−15.1570	+	18.4004i	−0.498629	+	0.605330i
$925$	14.7918	−	25.6202i	0.486353	−	0.842387i
$926$	17.7593	+	30.7600i	0.583607	+	1.01084i
$927$	−16.5592	−	0.104091i	−0.543876	−	0.00341879i
$928$	6.20514	+	10.7476i	0.203694	+	0.352808i
$929$	13.0741	−	7.54834i	0.428947	−	0.247653i	−0.269951	−	0.962874i	$-0.587007\pi$
$929$	13.0741	−	7.54834i	0.428947	−	0.247653i	0.698898	+	0.715221i	$0.253674\pi$
$930$	62.6120	−	107.664i	2.05313	−	3.53045i
$931$	−11.0337	−	24.2937i	−0.361614	−	0.796195i
$932$	−38.4502			−1.25948
$933$	16.5030	+	0.0518683i	0.540284	+	0.00169809i
$934$	−17.1682	+	9.91204i	−0.561759	+	0.324332i
$935$	37.4689	+	30.6671i	1.22536	+	1.00292i
$936$	−60.4773	−	35.4253i	−1.97676	−	1.15791i
$937$	−18.9731	−	10.9541i	−0.619825	−	0.357856i	0.156976	−	0.987602i	$-0.449825\pi$
$937$	−18.9731	−	10.9541i	−0.619825	−	0.357856i	−0.776801	+	0.629746i	$0.783159\pi$
$938$		−	4.65870i		−	0.152112i
$939$	−29.8288	−	17.3469i	−0.973426	−	0.566095i
$940$	4.13199	−	7.15681i	0.134771	−	0.233430i
$941$	24.8103	−	42.9727i	0.808793	−	1.40087i	−0.104908	−	0.994482i	$-0.533455\pi$
$941$	24.8103	−	42.9727i	0.808793	−	1.40087i	0.913701	−	0.406388i	$-0.133212\pi$
$942$	12.1550	+	7.06873i	0.396032	+	0.230312i
$943$		−	4.77448i		−	0.155478i
$944$	76.2297	+	44.0112i	2.48107	+	1.43244i
$945$	−12.3936	+	7.00046i	−0.403163	+	0.227725i
$946$	65.4427	+	53.5628i	2.12773	+	1.74148i
$947$	13.7035	−	7.91171i	0.445303	−	0.257096i	−0.260541	−	0.965463i	$-0.583901\pi$
$947$	13.7035	−	7.91171i	0.445303	−	0.257096i	0.705845	+	0.708367i	$0.250568\pi$
$948$	−108.335	−	0.340494i	−3.51857	−	0.0110587i
$949$	−14.0328			−0.455524
$950$	−16.1742	−	35.6119i	−0.524759	−	1.15540i
$951$	−9.84008	+	16.9205i	−0.319086	+	0.548684i
$952$	−24.9534	+	14.4069i	−0.808746	+	0.466930i
$953$	−16.0322	−	27.7685i	−0.519333	−	0.899511i	−0.999748	−	0.0224695i	$-0.992847\pi$
$953$	−16.0322	−	27.7685i	−0.519333	−	0.899511i	0.480415	−	0.877042i	$-0.340486\pi$
$954$	0.469319	−	74.6612i	0.0151948	−	2.41725i
$955$	−11.1564	−	19.3234i	−0.361011	−	0.625290i
$956$	17.4482	−	30.2212i	0.564316	−	0.977423i
$957$	−11.4833	−	9.45919i	−0.371204	−	0.305772i
$958$	−50.8752			−1.64370
$959$	−2.53344	+	4.38805i	−0.0818091	+	0.141698i
$960$	−3.37300	−	5.88485i	−0.108863	−	0.189933i
$961$	63.2116			2.03908
$962$		−	80.4593i		−	2.59411i
$963$	−28.3762	−	0.178372i	−0.914411	−	0.00574797i
$964$	−84.5998	+	48.8437i	−2.72478	+	1.57315i
$965$	−24.4794	+	42.3995i	−0.788019	+	1.36489i
$966$	0.0176174	−	5.60535i	0.000566831	−	0.180349i
$967$	23.5579	−	13.6012i	0.757571	−	0.437384i	−0.0708517	−	0.997487i	$-0.522572\pi$
$967$	23.5579	−	13.6012i	0.757571	−	0.437384i	0.828423	+	0.560103i	$0.189238\pi$
$968$	−64.1455	−	21.5855i	−2.06171	−	0.693785i
$969$	−30.6090	−	22.0382i	−0.983302	−	0.707970i
$970$			6.94507i			0.222993i
$971$	2.40816	−	1.39035i	0.0772814	−	0.0446185i	−0.460861	−	0.887472i	$-0.652459\pi$
$971$	2.40816	−	1.39035i	0.0772814	−	0.0446185i	0.538143	+	0.842854i	$0.319126\pi$
$972$	59.2145	+	35.4397i	1.89931	+	1.13673i
$973$	−6.17991	+	10.7039i	−0.198119	+	0.343152i
$974$	4.42661	+	7.66712i	0.141838	+	0.245670i
$975$	11.5760	+	20.1965i	0.370728	+	0.646806i
$976$		−	5.19973i		−	0.166439i
$977$		−	4.64506i		−	0.148608i	−0.997236	−	0.0743042i	$-0.976326\pi$
$977$		−	4.64506i		−	0.148608i	0.997236	−	0.0743042i	$-0.0236736\pi$
$978$	−69.1067	+	39.6097i	−2.20979	+	1.26658i
$979$	−4.67711	−	3.82807i	−0.149481	−	0.122346i
$980$		−	79.1887i		−	2.52959i
$981$	5.20884	−	2.96382i	0.166305	−	0.0946276i
$982$	−39.9767	+	69.2417i	−1.27571	+	2.20959i
$983$	−1.82504	+	1.05369i	−0.0582098	+	0.0336075i	−0.528822	−	0.848732i	$-0.677366\pi$
$983$	−1.82504	+	1.05369i	−0.0582098	+	0.0336075i	0.470613	+	0.882340i	$0.344033\pi$
$984$	32.4159	−	18.5797i	1.03338	−	0.592300i
$985$	40.0645	−	23.1313i	1.27656	−	0.737023i
$986$	−16.4003	−	28.4062i	−0.522293	−	0.904637i
$987$	−0.896596	−	0.521414i	−0.0285390	−	0.0165968i
$988$	−59.5980	−	42.6263i	−1.89607	−	1.35612i
$989$	−13.6968			−0.435531
$990$	−56.7471	−	47.0445i	−1.80354	−	1.49517i
$991$	28.1957	+	48.8364i	0.895666	+	1.55134i	0.832978	+	0.553306i	$0.186634\pi$
$991$	28.1957	+	48.8364i	0.895666	+	1.55134i	0.0626876	+	0.998033i	$0.480033\pi$
$992$	−23.2556	+	40.2799i	−0.738367	+	1.27889i
$993$	−0.121270	+	38.5848i	−0.00384840	+	1.22445i
$994$	11.6491	−	20.1768i	0.369487	−	0.639970i
$995$			51.2788i			1.62565i
$996$	−55.6159	−	32.3433i	−1.76226	−	1.02484i
$997$	23.0784	+	13.3243i	0.730900	+	0.421986i	0.818751	−	0.574148i	$-0.194667\pi$
$997$	23.0784	+	13.3243i	0.730900	+	0.421986i	−0.0878511	+	0.996134i	$0.528000\pi$
$998$	−53.8558	+	93.2809i	−1.70477	+	2.95276i
$999$	−0.409493	+	43.4285i	−0.0129558	+	1.37402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.l.a.197.74	yes	152
3.2	odd	2	inner	627.2.l.a.197.3	✓	152
11.10	odd	2	inner	627.2.l.a.197.4	yes	152
19.11	even	3	inner	627.2.l.a.296.73	yes	152
33.32	even	2	inner	627.2.l.a.197.73	yes	152
57.11	odd	6	inner	627.2.l.a.296.4	yes	152
209.87	odd	6	inner	627.2.l.a.296.3	yes	152
627.296	even	6	inner	627.2.l.a.296.74	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.l.a.197.3	✓	152	3.2	odd	2	inner
627.2.l.a.197.4	yes	152	11.10	odd	2	inner
627.2.l.a.197.73	yes	152	33.32	even	2	inner
627.2.l.a.197.74	yes	152	1.1	even	1	trivial
627.2.l.a.296.3	yes	152	209.87	odd	6	inner
627.2.l.a.296.4	yes	152	57.11	odd	6	inner
627.2.l.a.296.73	yes	152	19.11	even	3	inner
627.2.l.a.296.74	yes	152	627.296	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26757 + 2.19550i) q^{2} +(0.00544374 - 1.73204i) q^{3} +(-2.21348 + 3.83387i) q^{4} +(-2.53073 + 1.46112i) q^{5} +(3.80960 - 2.18354i) q^{6} -0.937410i q^{7} -6.15272 q^{8} +(-2.99994 - 0.0188576i) q^{9} +(-6.41578 - 3.70415i) q^{10} +(-3.27304 - 0.535938i) q^{11} +(6.62837 + 3.85472i) q^{12} +(-3.28845 - 1.89859i) q^{13} +(2.05809 - 1.18824i) q^{14} +(2.51694 + 4.39129i) q^{15} +(-3.37206 - 5.84058i) q^{16} +(2.49789 + 4.32647i) q^{17} +(-3.76124 - 6.61028i) q^{18} +(-1.80252 - 3.96875i) q^{19} -12.9367i q^{20} +(-1.62363 - 0.00510302i) q^{21} +(-2.97216 - 7.86530i) q^{22} +(1.17935 + 0.680898i) q^{23} +(-0.0334938 + 10.6568i) q^{24} +(1.76974 - 3.06528i) q^{25} -9.62640i q^{26} +(-0.0489930 + 5.19592i) q^{27} +(3.59391 + 2.07494i) q^{28} +(-1.29493 + 2.24288i) q^{29} +(-6.45067 + 11.0922i) q^{30} -9.70627 q^{31} +(2.39594 - 4.14989i) q^{32} +(-0.946084 + 5.66612i) q^{33} +(-6.33251 + 10.9682i) q^{34} +(1.36967 + 2.37233i) q^{35} +(6.71262 - 11.4596i) q^{36} +8.35820 q^{37} +(6.42856 - 8.98810i) q^{38} +(-3.30634 + 5.68540i) q^{39} +(15.5709 - 8.98986i) q^{40} +(-1.75301 - 3.03630i) q^{41} +(-2.04687 - 3.57116i) q^{42} +(-8.71037 + 5.02893i) q^{43} +(9.29953 - 11.3621i) q^{44} +(7.61960 - 4.33555i) q^{45} +3.45235i q^{46} +(0.553220 + 0.319402i) q^{47} +(-10.1345 + 5.80875i) q^{48} +6.12126 q^{49} +8.97310 q^{50} +(7.50722 - 4.30290i) q^{51} +(14.5579 - 8.40499i) q^{52} +(8.50178 + 4.90851i) q^{53} +(-11.4698 + 6.47865i) q^{54} +(9.06625 - 3.42598i) q^{55} +5.76762i q^{56} +(-6.88385 + 3.10043i) q^{57} -6.56567 q^{58} +(-11.3031 + 6.52587i) q^{59} +(-22.4068 - 0.0704238i) q^{60} +(0.667708 + 0.385502i) q^{61} +(-12.3034 - 21.3101i) q^{62} +(-0.0176773 + 2.81217i) q^{63} -1.34012 q^{64} +11.0963 q^{65} +(-13.6392 + 5.10509i) q^{66} +(0.980172 - 1.69771i) q^{67} -22.1161 q^{68} +(1.18576 - 2.03898i) q^{69} +(-3.47231 + 6.01422i) q^{70} +(8.49025 - 4.90185i) q^{71} +(18.4578 + 0.116025i) q^{72} +(3.20047 - 1.84779i) q^{73} +(10.5946 + 18.3504i) q^{74} +(-5.29956 - 3.08195i) q^{75} +(19.2055 + 1.87415i) q^{76} +(-0.502393 + 3.06818i) q^{77} +(-16.6733 - 0.0524036i) q^{78} +(-12.2359 + 7.06441i) q^{79} +(17.0676 + 9.85396i) q^{80} +(8.99929 + 0.113143i) q^{81} +(4.44414 - 7.69747i) q^{82} -8.39058 q^{83} +(3.61345 - 6.21350i) q^{84} +(-12.6430 - 7.29942i) q^{85} +(-22.0821 - 12.7491i) q^{86} +(3.87772 + 2.25508i) q^{87} +(20.1381 + 3.29748i) q^{88} +(1.57818 + 0.911162i) q^{89} +(19.1771 + 11.2332i) q^{90} +(-1.77976 + 3.08263i) q^{91} +(-5.22094 + 3.01431i) q^{92} +(-0.0528384 + 16.8117i) q^{93} +1.61946i q^{94} +(10.3605 + 7.41014i) q^{95} +(-7.17474 - 4.17246i) q^{96} +(-0.468735 - 0.811873i) q^{97} +(7.75915 + 13.4392i) q^{98} +(9.80881 + 1.66950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 76 q^{4} - 8 q^{9} - 14 q^{15} - 76 q^{16} + 4 q^{22} + 60 q^{25} + 12 q^{27} - 16 q^{31} + 16 q^{33} - 16 q^{34} - 10 q^{36} - 16 q^{37} + 50 q^{42} - 108 q^{45} + 54 q^{48} - 80 q^{49} + 32 q^{55}+ \cdots + 60 q^{99}+O(q^{100}) \) 152 * q - 76 * q^4 - 8 * q^9 - 14 * q^15 - 76 * q^16 + 4 * q^22 + 60 * q^25 + 12 * q^27 - 16 * q^31 + 16 * q^33 - 16 * q^34 - 10 * q^36 - 16 * q^37 + 50 * q^42 - 108 * q^45 + 54 * q^48 - 80 * q^49 + 32 * q^55 - 40 * q^58 + 2 * q^60 + 152 * q^64 - 10 * q^66 - 16 * q^67 - 32 * q^69 - 4 * q^70 - 20 * q^75 - 58 * q^78 + 16 * q^81 - 40 * q^82 - 120 * q^88 - 16 * q^91 - 12 * q^93 + 4 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more