LMFDB - Embedded newform 627.2.l.a.197.4

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			197.4
Character	$\chi$	$=$	627.197
Dual form			627.2.l.a.296.4

$q$-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} +(-5.32547 - 6.50662i) 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} +(-0.910449 - 5.67196i) 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} +(-5.19010 + 13.7347i) 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} +(-7.50011 + 6.13861i) 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} +(-11.2987 + 9.18851i) 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} +(-9.82902 + 1.54606i) 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	$-0.812905\pi$
$2$	−1.26757	−	2.19550i	−0.896310	−	1.55245i	−0.0641344	−	0.997941i	$-0.520429\pi$
$3$	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	$0.0566890\pi$
$7$			0.937410i			0.354308i	−0.984183	+	0.177154i	$0.943311\pi$
$8$	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	0.881091	−	0.472947i	$-0.156810\pi$
$13$	3.28845	+	1.89859i	0.912052	+	0.526574i	0.0309612	+	0.999521i	$0.490143\pi$
$14$	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	$-0.959509\pi$
$17$	−2.49789	−	4.32647i	−0.605827	−	1.04932i	0.386093	−	0.922460i	$-0.373824\pi$
$18$	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
$22$	−5.32547	−	6.50662i	−1.13539	−	1.38722i
$23$	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	−0.720384	−	0.693576i	$-0.756034\pi$
$29$	1.29493	−	2.24288i	0.240462	−	0.416493i	0.960846	+	0.277083i	$0.0893676\pi$
$30$	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
$33$	−0.910449	−	5.67196i	−0.158489	−	0.987361i
$34$	−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	0.969825	−	0.243802i	$-0.0783946\pi$
$41$	1.75301	+	3.03630i	0.273774	+	0.474191i	−0.696051	+	0.717992i	$0.745061\pi$
$42$	−2.04687	−	3.57116i	−0.315839	−	0.551042i
$43$	8.71037	−	5.02893i	1.32832	−	0.766905i	0.343279	−	0.939233i	$-0.388462\pi$
$43$	8.71037	−	5.02893i	1.32832	−	0.766905i	0.985040	+	0.172328i	$0.0551290\pi$
$44$	−5.19010	+	13.7347i	−0.782437	+	2.07058i
$45$	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
$55$	−7.50011	+	6.13861i	−1.01132	+	0.827730i
$56$			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	0.456645	−	0.889649i	$-0.349051\pi$
$61$	−0.667708	−	0.385502i	−0.0854913	−	0.0493584i	−0.542136	+	0.840291i	$0.682384\pi$
$62$	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
$66$	−11.2987	+	9.18851i	−1.39078	+	1.13103i
$67$	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	−0.675461	−	0.737396i	$-0.736055\pi$
$73$	−3.20047	+	1.84779i	−0.374587	+	0.216268i	0.300873	+	0.953664i	$0.402722\pi$
$74$	−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	0.384893	−	0.922961i	$-0.374238\pi$
$79$	12.2359	−	7.06441i	1.37665	−	0.794808i	0.991754	+	0.128153i	$0.0409050\pi$
$80$	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	$-0.347673\pi$
$83$	8.39058			0.920986			0.460493	+	0.887663i	$0.347673\pi$
$84$	−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
$99$	−9.82902	+	1.54606i	−0.987854	+	0.155385i
$100$	7.83458	+	13.5699i	0.783458	+	1.35699i
$101$	0.627986	−	1.08770i	0.0624869	−	0.108231i	−0.833090	−	0.553138i	$-0.813430\pi$
$101$	0.627986	−	1.08770i	0.0624869	−	0.108231i	0.895576	+	0.444908i	$0.146763\pi$
$102$	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	$-0.651153\pi$
$107$	−9.45893			−0.914429			−0.457215	+	0.889356i	$0.651153\pi$
$108$	−19.8120	−	11.6889i	−1.90641	−	1.12477i
$109$	1.73003	−	0.998836i	0.165707	−	0.0956711i	−0.414853	−	0.909889i	$-0.636167\pi$
$109$	1.73003	−	0.998836i	0.165707	−	0.0956711i	0.580560	+	0.814217i	$0.302834\pi$
$110$	22.9843	+	8.68537i	2.19146	+	0.828117i
$111$	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	0.863464	−	0.504410i	$-0.168290\pi$
$127$	9.67328	+	5.58487i	0.858365	+	0.495577i	−0.00509958	+	0.999987i	$0.501623\pi$
$128$	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	0.855170	−	0.518347i	$-0.173452\pi$
$131$	−0.243979	−	0.422584i	−0.0213166	−	0.0369214i	−0.876487	+	0.481426i	$0.840119\pi$
$132$	23.7608	+	9.06424i	2.06811	+	0.788941i
$133$	−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	0.898783	−	0.438394i	$-0.144453\pi$
$139$	11.4186	+	6.59253i	0.968513	+	0.559171i	0.0697307	+	0.997566i	$0.477786\pi$
$140$	12.1270			1.02491
$141$	0.556229	−	0.956461i	0.0468429	−	0.0805486i
$142$	−21.5240	−	12.4269i	−1.80626	−	1.04284i
$143$	11.7807	+	4.45174i	0.985155	+	0.372273i
$144$	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	0.988430	−	0.151677i	$-0.0484673\pi$
$149$	4.42926	+	7.67171i	0.362859	+	0.628491i	−0.625571	+	0.780167i	$0.715134\pi$
$150$	−0.0488472	+	15.5418i	−0.00398836	+	1.26898i
$151$		−	6.47237i		−	0.526714i	−0.964698	−	0.263357i	$-0.915170\pi$
$151$		−	6.47237i		−	0.526714i	0.964698	−	0.263357i	$-0.0848298\pi$
$152$	11.0904	+	24.4186i	0.899548	+	1.98061i
$153$	7.41193	+	13.0263i	0.599219	+	1.05311i
$154$	6.09937	−	4.99215i	0.491501	−	0.402279i
$155$	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
$165$	10.5915	+	13.0239i	0.824548	+	1.01391i
$166$	−10.6357	−	18.4215i	−0.825488	−	1.42979i
$167$	−2.46810	+	4.27488i	−0.190987	+	0.330800i	−0.945578	−	0.325396i	$-0.894502\pi$
$167$	−2.46810	+	4.27488i	−0.190987	+	0.330800i	0.754590	+	0.656196i	$0.227836\pi$
$168$	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	0.996574	−	0.0827084i	$-0.0263570\pi$
$173$	5.61183	+	9.71997i	0.426659	+	0.738996i	−0.569914	+	0.821704i	$0.693024\pi$
$174$	−0.0357418	+	11.3720i	−0.00270958	+	0.862111i
$175$	2.87342	+	1.65897i	0.217210	+	0.125406i
$176$	−14.1671	−	17.3092i	−1.06788	−	1.30473i
$177$	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
$187$	−10.4944	−	12.8220i	−0.767426	−	0.937636i
$188$	−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	−0.921076	−	0.389382i	$-0.872689\pi$
$193$	−14.5093	+	8.37693i	−1.04440	+	0.602984i	−0.123323	+	0.992367i	$0.539355\pi$
$194$	−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	$-0.309276\pi$
$197$	15.8312			1.12793			0.563963	+	0.825800i	$0.309276\pi$
$198$	15.8534	+	19.6199i	1.12665	+	1.39432i
$199$	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
$209$	8.02670	+	12.0238i	0.555218	+	0.831705i
$210$	10.3980	+	6.04693i	0.717528	+	0.417278i
$211$	−5.90764	+	3.41078i	−0.406699	+	0.234808i	−0.689370	−	0.724409i	$-0.742113\pi$
$211$	−5.90764	+	3.41078i	−0.406699	+	0.234808i	0.282672	+	0.959217i	$0.408779\pi$
$212$	−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	$-0.251076\pi$
$227$	21.2351			1.40943			0.704713	+	0.709492i	$0.251076\pi$
$228$	−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
$231$	5.31695	−	0.853464i	0.349830	−	0.0561538i
$232$	7.96734	−	13.7998i	0.523082	−	0.906004i
$233$	−4.34272	−	7.52181i	−0.284501	−	0.492770i	0.687987	−	0.725723i	$-0.258495\pi$
$233$	−4.34272	−	7.52181i	−0.284501	−	0.492770i	−0.972488	+	0.232953i	$0.925161\pi$
$234$	−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	$-0.417943\pi$
$239$	7.88269			0.509889			0.254944	+	0.966956i	$0.417943\pi$
$240$	17.1604	−	29.5081i	1.10770	−	1.90474i
$241$	−19.1101	−	11.0332i	−1.23099	−	0.710712i	−0.263753	−	0.964590i	$-0.584960\pi$
$241$	−19.1101	−	11.0332i	−1.23099	−	0.710712i	−0.967236	+	0.253878i	$0.918294\pi$
$242$	−20.9176	−	18.4423i	−1.34463	−	1.18551i
$243$	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
$253$	4.22497	+	1.59655i	0.265622	+	0.100374i
$254$		−	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	0.999267	−	0.0382701i	$-0.0121847\pi$
$263$	7.56521	+	13.1033i	0.466491	+	0.807986i	−0.532777	+	0.846256i	$0.678851\pi$
$264$	−5.60174	−	34.8980i	−0.344763	−	2.14782i
$265$	−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	−0.637913	−	0.770108i	$-0.720202\pi$
$271$	−4.77296	+	2.75567i	−0.289937	+	0.167395i	0.347977	+	0.937503i	$0.386869\pi$
$272$	−16.8460	+	29.1782i	−1.02144	+	1.76919i
$273$	5.32955	+	3.09939i	0.322559	+	0.187584i
$274$			13.7030i			0.827826i
$275$	4.14962	−	10.9812i	0.250232	−	0.662194i
$276$	5.19249	+	9.05930i	0.312551	+	0.545306i
$277$			15.4880i			0.930587i	0.885157	+	0.465293i	$0.154051\pi$
$277$			15.4880i			0.930587i	−0.885157	+	0.465293i	$0.845949\pi$
$278$		−	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	−0.995418	−	0.0956229i	$-0.969516\pi$
$281$	−6.95494	+	12.0463i	−0.414897	+	0.718623i	0.580521	+	0.814246i	$0.302849\pi$
$282$	−2.80497	−	0.00881592i	−0.167034	−	0.000524980i
$283$	1.93719	−	1.11844i	0.115154	−	0.0664843i	−0.441317	−	0.897351i	$-0.645488\pi$
$283$	1.93719	−	1.11844i	0.115154	−	0.0664843i	0.556471	+	0.830867i	$0.312155\pi$
$284$			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	$-0.467104\pi$
$293$	3.53172			0.206325			0.103163	+	0.994665i	$0.467104\pi$
$294$	−23.3196	+	13.3660i	−1.36002	+	0.779522i
$295$	19.0702	−	33.0305i	1.11031	−	1.92311i
$296$	51.4257			2.98906
$297$	2.62433	+	17.0327i	0.152279	+	0.988337i
$298$	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	−0.692013	−	0.721885i	$-0.743276\pi$
$307$	−7.23370	+	4.17638i	−0.412849	+	0.238358i	0.279164	+	0.960243i	$0.409943\pi$
$308$	−12.8750	−	4.86525i	−0.733623	−	0.277224i
$309$	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
$319$	3.03631	−	8.03504i	0.170001	−	0.449876i
$320$	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
$330$	15.1685	−	39.7625i	0.835001	−	2.18885i
$331$	−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	0.0271299	−	0.999632i	$-0.491363\pi$
$337$	16.6393	−	9.60671i	0.906401	−	0.523311i	0.879272	+	0.476321i	$0.158030\pi$
$338$	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	$-0.794017\pi$
$347$	−17.1569	−	29.7165i	−0.921028	−	1.59527i	−0.123201	−	0.992382i	$-0.539316\pi$
$348$	17.2290	−	9.87508i	0.923569	−	0.529360i
$349$			16.6724i			0.892455i	0.894920	+	0.446227i	$0.147233\pi$
$349$			16.6724i			0.892455i	−0.894920	+	0.446227i	$0.852767\pi$
$350$		−	8.41147i		−	0.449612i
$351$	−10.0260	+	16.9935i	−0.535150	+	0.907047i
$352$	−5.61791	+	14.8668i	−0.299436	+	0.792404i
$353$			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	$-0.864995\pi$
$359$	−15.3870	−	26.6510i	−0.812093	−	1.40659i	0.0993033	−	0.995057i	$-0.468339\pi$
$360$	46.8813	−	26.6754i	2.47086	−	1.40592i
$361$	−12.5019	+	14.3074i	−0.657993	+	0.753024i
$362$	−35.5439			−1.86815
$363$	−6.01975	−	18.0766i	−0.315955	−	0.948774i
$364$	−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	$-0.766884\pi$
$373$		−	25.8265i		−	1.33725i	0.743602	−	0.668623i	$-0.233116\pi$
$374$	−14.8483	+	39.2933i	−0.767785	+	2.03181i
$375$	−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
$385$	−5.75440	−	7.03068i	−0.293271	−	0.358317i
$386$	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
$396$	15.8290	−	41.1054i	0.795437	−	2.06562i
$397$	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	0.986729	−	0.162375i	$-0.0519155\pi$
$409$	27.0892	+	15.6399i	1.33947	+	0.773345i	0.352743	+	0.935720i	$0.385249\pi$
$410$			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
$418$	16.2239	−	32.8637i	0.793535	−	1.60742i
$419$		−	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
$429$	7.77474	−	20.3805i	0.375368	−	0.983980i
$430$	74.5117			3.59327
$431$	5.03978	−	8.72915i	0.242757	−	0.420468i	−0.718741	−	0.695278i	$-0.755281\pi$
$431$	5.03978	−	8.72915i	0.242757	−	0.420468i	0.961499	+	0.274809i	$0.0886147\pi$
$432$	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	−0.999144	−	0.0413568i	$-0.986832\pi$
$439$	−30.6512	+	17.6965i	−1.46290	+	0.844606i	−0.463756	+	0.885963i	$0.653499\pi$
$440$	−46.1461	+	37.7692i	−2.19993	+	1.80057i
$441$	−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
$451$	7.36493	+	8.99842i	0.346801	+	0.423719i
$452$	−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	$0.219728\pi$
$457$			27.2250i			1.27353i	−0.771058	+	0.636765i	$0.780272\pi$
$458$	−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	$-0.982223\pi$
$461$	−11.7566	−	20.3631i	−0.547560	−	0.948402i	0.450881	−	0.892584i	$-0.351110\pi$
$462$	−8.61340	−	10.5915i	−0.400732	−	0.492763i
$463$	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
$473$	25.8142	−	21.1281i	1.18694	−	0.971471i
$474$	−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	−0.540416	−	0.841398i	$-0.681733\pi$
$479$	10.0340	−	17.3794i	0.458464	−	0.794083i	0.998880	+	0.0473147i	$0.0150664\pi$
$480$	−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
$484$	−9.62646	+	47.7357i	−0.437566	+	2.16980i
$485$	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	$-0.914617\pi$
$491$	−15.7690	−	27.3127i	−0.711645	−	1.23261i	0.252594	−	0.967572i	$-0.418716\pi$
$492$	−0.0844925	+	26.8831i	−0.00380921	+	1.21198i
$493$	−12.9384			−0.582714
$494$	38.2047	−	17.3517i	1.71891	−	0.780691i
$495$	22.6157	−	18.2740i	1.01650	−	0.821357i
$496$	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	−0.926988	−	0.375092i	$-0.877611\pi$
$503$	−3.10971	+	5.38617i	−0.138655	+	0.240157i	0.788333	+	0.615249i	$0.210945\pi$
$504$	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
$517$	1.98189	+	0.748922i	0.0871633	+	0.0329375i
$518$	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	0.117554	−	0.993066i	$-0.462495\pi$
$523$	−15.6354	−	9.02712i	−0.683690	−	0.394729i	−0.801244	+	0.598338i	$0.795828\pi$
$524$	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
$528$	−30.0574	+	24.4437i	−1.30808	+	1.06378i
$529$	−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	0.0525108	−	0.998620i	$-0.483278\pi$
$541$	−18.2834	−	10.5559i	−0.786064	−	0.453834i	−0.838575	+	0.544786i	$0.816611\pi$
$542$	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	0.284241	−	0.958753i	$-0.408258\pi$
$547$	−9.44743	−	5.45448i	−0.403943	−	0.233217i	−0.688184	+	0.725536i	$0.741592\pi$
$548$	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	−0.841773	−	0.539831i	$-0.818488\pi$
$557$	1.10030	−	1.90577i	0.0466212	−	0.0807503i	0.888394	+	0.459081i	$0.151821\pi$
$558$	−36.5076	−	64.1611i	−1.54549	−	2.71616i
$559$	38.1915			1.61533
$560$	−9.23720	+	15.9993i	−0.390343	+	0.676094i
$561$	−22.2653	+	18.1069i	−0.940043	+	0.764476i
$562$	35.2636			1.48750
$563$	36.6285			1.54371			0.771853	−	0.635801i	$-0.219330\pi$
$563$	36.6285			1.54371			0.771853	+	0.635801i	$0.219330\pi$
$564$	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	$-0.246127\pi$
$569$	34.1422			1.43131			0.715657	+	0.698452i	$0.246127\pi$
$570$	55.6497	+	5.60715i	2.33091	+	0.234858i
$571$		−	20.7207i		−	0.867132i	−0.901122	−	0.433566i	$-0.857255\pi$
$571$		−	20.7207i		−	0.867132i	0.901122	−	0.433566i	$-0.142745\pi$
$572$	−43.1439	+	35.3120i	−1.80394	+	1.47647i
$573$	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
$583$	30.4573	+	11.5093i	1.26141	+	0.476666i
$584$	−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	$-0.654657\pi$
$593$	12.9626	−	22.4520i	0.532312	−	0.921992i	0.999288	−	0.0377219i	$-0.0120101\pi$
$594$	34.0688	−	27.3519i	1.39786	−	1.12226i
$595$	−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	$-0.599584\pi$
$601$		−	46.6506i		−	1.90292i	0.307773	−	0.951460i	$-0.400416\pi$
$602$	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
$605$	−21.2582	+	24.1115i	−0.864270	+	0.980272i
$606$	−0.0173333	+	5.51495i	−0.000704115	+	0.224029i
$607$		−	35.0581i		−	1.42297i	−0.702703	−	0.711483i	$-0.748024\pi$
$607$		−	35.0581i		−	1.42297i	0.702703	−	0.711483i	$-0.251976\pi$
$608$	−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	−0.221666	−	0.975123i	$-0.571150\pi$
$613$	12.6761	−	7.31853i	0.511982	−	0.295593i	0.733648	+	0.679530i	$0.237816\pi$
$614$	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
$627$	20.8694	−	13.8371i	0.833445	−	0.552602i
$628$	−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
$649$	−33.4981	+	27.4172i	−1.31492	+	1.07622i
$650$	−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	$-0.559378\pi$
$659$	19.4655	−	33.7153i	0.758270	−	1.31336i	0.943732	−	0.330710i	$-0.107288\pi$
$660$	−73.3762	+	11.7782i	−2.85616	+	0.458465i
$661$	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
$671$	−2.39204	−	0.903911i	−0.0923436	−	0.0348951i
$672$	−3.91130	+	6.72567i	−0.150882	+	0.259448i
$673$		−	5.05379i		−	0.194809i	−0.995245	−	0.0974047i	$-0.968946\pi$
$673$		−	5.05379i		−	0.194809i	0.995245	−	0.0974047i	$-0.0310541\pi$
$674$	−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	$-0.590873\pi$
$677$	−14.6553			−0.563248			−0.281624	+	0.959525i	$0.590873\pi$
$678$	−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
$682$	51.6904	+	63.1550i	1.97933	+	2.41833i
$683$			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
$693$	−1.44929	−	9.21383i	−0.0550541	−	0.350004i
$694$	−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	$0.0828196\pi$
$701$	18.6914	+	32.3745i	0.705965	+	1.22277i	−0.260378	+	0.965507i	$0.583847\pi$
$702$	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
$726$	−32.0567	+	36.1298i	−1.18973	+	1.34090i
$727$	−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	$0.245063\pi$
$733$			37.6900i			1.39211i	−0.717988	+	0.696055i	$0.754937\pi$
$734$	28.2683			1.04340
$735$	15.4069	+	26.8802i	0.568291	+	0.991493i
$736$	−5.65130	+	3.26278i	−0.208310	+	0.120268i
$737$	2.29827	−	6.08197i	0.0846580	−	0.224032i
$738$	−13.4773	+	23.0081i	−0.496106	+	0.846942i
$739$	33.8877	−	19.5651i	1.24658	−	0.719713i	0.276154	−	0.961113i	$-0.410940\pi$
$739$	33.8877	−	19.5651i	1.24658	−	0.719713i	0.970426	+	0.241401i	$0.0776068\pi$
$740$		−	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	$0.150024\pi$
$743$	22.8616	+	39.5975i	0.838711	+	1.45269i	−0.0522615	+	0.998633i	$0.516643\pi$
$744$	−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
$759$	2.78828	−	7.30914i	0.101208	−	0.265305i
$760$	−63.7453	−	45.5926i	−2.31228	−	1.65382i
$761$	9.02435			0.327132			0.163566	−	0.986532i	$-0.447700\pi$
$761$	9.02435			0.327132			0.163566	+	0.986532i	$0.447700\pi$
$762$	−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	0.331046	−	0.943615i	$-0.392599\pi$
$769$	−8.89122	−	5.13335i	−0.320626	−	0.185113i	−0.651671	+	0.758501i	$0.725932\pi$
$770$	−8.14175	+	21.5457i	−0.293408	+	0.776453i
$771$	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
$781$	25.1618	−	20.5942i	0.900360	−	0.736917i
$782$	−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	$-0.714352\pi$
$787$		−	43.8589i		−	1.56340i	0.623654	−	0.781701i	$-0.285648\pi$
$788$	−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
$792$	−60.4752	+	9.51248i	−2.14889	+	0.338011i
$793$	−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
$803$	−9.48497	+	7.76315i	−0.334717	+	0.273956i
$804$	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	$-0.821436\pi$
$809$	−48.1673			−1.69347			−0.846736	+	0.532013i	$0.821436\pi$
$810$	57.3184	+	34.0606i	2.01396	+	1.19677i
$811$	−18.1961	−	10.5055i	−0.638951	−	0.368899i	0.145259	−	0.989394i	$-0.453598\pi$
$811$	−18.1961	−	10.5055i	−0.638951	−	0.368899i	−0.784210	+	0.620495i	$0.786932\pi$
$812$	−9.30771	+	5.37381i	−0.326637	+	0.188584i
$813$	4.74696	+	8.28197i	0.166483	+	0.290461i
$814$	−44.5113	−	54.3836i	−1.56012	−	1.90614i
$815$	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	−0.893053	−	0.449951i	$-0.851441\pi$
$821$	−1.62913	+	2.82174i	−0.0568572	+	0.0984795i	0.836196	+	0.548431i	$0.184775\pi$
$822$	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
$825$	−18.9974	−	7.24710i	−0.661404	−	0.252312i
$826$	−15.5086	+	26.8616i	−0.539612	+	0.934635i
$827$	10.5957	−	18.3523i	0.368449	−	0.638173i	−0.620874	−	0.783910i	$-0.713222\pi$
$827$	10.5957	−	18.3523i	0.368449	−	0.638173i	0.989323	+	0.145737i	$0.0465555\pi$
$828$	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
$836$	−63.8647	+	4.15878i	−2.20881	+	0.143835i
$837$	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	−0.899922	−	0.436052i	$-0.856376\pi$
$853$	−28.3957	+	16.3943i	−0.972251	+	0.561329i	−0.0723290	+	0.997381i	$0.523043\pi$
$854$	−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	0.841659	−	0.540009i	$-0.181579\pi$
$857$	−1.37098	−	2.37461i	−0.0468319	−	0.0811153i	−0.888491	+	0.458894i	$0.848246\pi$
$858$	−54.6005	+	8.76435i	−1.86403	+	0.299210i
$859$	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
$869$	36.2625	−	29.6797i	1.23012	−	1.00682i
$870$	−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	−0.422034	−	0.906580i	$-0.638684\pi$
$877$	4.50341	−	2.60005i	0.152069	−	0.0877973i	0.574104	+	0.818782i	$0.305351\pi$
$878$	77.7052	+	44.8631i	2.62242	+	1.51406i
$879$	0.0192257	−	6.11708i	0.000648468	−	0.206324i
$880$	61.1438	+	23.1052i	2.06116	+	0.778877i
$881$			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	$-0.485018\pi$
$887$	26.4645	−	45.8378i	0.888591	−	1.53908i	0.841542	−	0.540192i	$-0.181648\pi$
$888$	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
$891$	29.5156	−	4.45274i	0.988811	−	0.149172i
$892$	−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
$902$	10.4205	−	27.5759i	0.346963	−	0.918176i
$903$	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	$-0.801070\pi$
$919$		−	35.4723i		−	1.17012i	0.810988	−	0.585062i	$-0.198930\pi$
$920$	−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
$924$	−8.49691	+	22.2736i	−0.279528	+	0.732748i
$925$	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
$935$	45.2930	+	17.1154i	1.48124	+	0.559735i
$936$	−60.4773	−	35.4253i	−1.97676	−	1.15791i
$937$	18.9731	+	10.9541i	0.619825	+	0.357856i	0.776801	−	0.629746i	$-0.216841\pi$
$937$	18.9731	+	10.9541i	0.619825	+	0.357856i	−0.156976	+	0.987602i	$0.550175\pi$
$938$		−	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	$0.466545\pi$
$941$	−24.8103	+	42.9727i	−0.808793	+	1.40087i	−0.913701	+	0.406388i	$0.866788\pi$
$942$	−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
$946$	−79.1081	−	29.8936i	−2.57203	−	0.971925i
$947$	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	$0.00715286\pi$
$953$	16.0322	+	27.7685i	0.519333	+	0.899511i	−0.480415	+	0.877042i	$0.659514\pi$
$954$	−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
$957$	−13.9005	−	5.30275i	−0.449340	−	0.171414i
$958$	−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	−0.828423	−	0.560103i	$-0.810762\pi$
$967$	−23.5579	+	13.6012i	−0.757571	+	0.437384i	0.0708517	+	0.997487i	$0.477428\pi$
$968$	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
$979$	5.65376	+	2.13646i	0.180695	+	0.0682816i
$980$		−	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
$990$	−68.7877	−	26.4890i	−2.18622	−	0.841876i
$991$	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	0.0878511	−	0.996134i	$-0.472000\pi$
$997$	−23.0784	−	13.3243i	−0.730900	−	0.421986i	−0.818751	+	0.574148i	$0.805333\pi$
$998$	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.197.4	yes	152
3.2	odd	2	inner	627.2.l.a.197.73	yes	152
11.10	odd	2	inner	627.2.l.a.197.74	yes	152
19.11	even	3	inner	627.2.l.a.296.3	yes	152
33.32	even	2	inner	627.2.l.a.197.3	✓	152
57.11	odd	6	inner	627.2.l.a.296.74	yes	152
209.87	odd	6	inner	627.2.l.a.296.73	yes	152
627.296	even	6	inner	627.2.l.a.296.4	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.l.a.197.3	✓	152	33.32	even	2	inner
627.2.l.a.197.4	yes	152	1.1	even	1	trivial
627.2.l.a.197.73	yes	152	3.2	odd	2	inner
627.2.l.a.197.74	yes	152	11.10	odd	2	inner
627.2.l.a.296.3	yes	152	19.11	even	3	inner
627.2.l.a.296.4	yes	152	627.296	even	6	inner
627.2.l.a.296.73	yes	152	209.87	odd	6	inner
627.2.l.a.296.74	yes	152	57.11	odd	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} +(-5.32547 - 6.50662i) 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} +(-0.910449 - 5.67196i) 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} +(-5.19010 + 13.7347i) 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} +(-7.50011 + 6.13861i) 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} +(-11.2987 + 9.18851i) 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} +(-9.82902 + 1.54606i) 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