LMFDB - Embedded newform 304.2.k.b.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.6
Character	$\chi$	$=$	304.229
Dual form			304.2.k.b.77.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26466 + 0.632956i) q^{2} +(1.26193 - 1.26193i) q^{3} +(1.19873 - 1.60095i) q^{4} +(0.588594 + 0.588594i) q^{5} +(-0.797168 + 2.39466i) q^{6} +3.53958i q^{7} +(-0.502658 + 2.78340i) q^{8} -0.184946i q^{9} +O(q^{10})$	\(q+(-1.26466 + 0.632956i) q^{2} +(1.26193 - 1.26193i) q^{3} +(1.19873 - 1.60095i) q^{4} +(0.588594 + 0.588594i) q^{5} +(-0.797168 + 2.39466i) q^{6} +3.53958i q^{7} +(-0.502658 + 2.78340i) q^{8} -0.184946i q^{9} +(-1.11693 - 0.371817i) q^{10} +(1.70629 + 1.70629i) q^{11} +(-0.507572 - 3.53301i) q^{12} +(-2.66076 + 2.66076i) q^{13} +(-2.24040 - 4.47636i) q^{14} +1.48553 q^{15} +(-1.12608 - 3.83822i) q^{16} +7.43076 q^{17} +(0.117063 + 0.233894i) q^{18} +(0.707107 - 0.707107i) q^{19} +(1.64788 - 0.236743i) q^{20} +(4.46671 + 4.46671i) q^{21} +(-3.23789 - 1.07787i) q^{22} -9.22644i q^{23} +(2.87815 + 4.14679i) q^{24} -4.30711i q^{25} +(1.68081 - 5.04910i) q^{26} +(3.55241 + 3.55241i) q^{27} +(5.66669 + 4.24301i) q^{28} +(-0.767522 + 0.767522i) q^{29} +(-1.87869 + 0.940277i) q^{30} -10.2761 q^{31} +(3.85354 + 4.14129i) q^{32} +4.30645 q^{33} +(-9.39739 + 4.70335i) q^{34} +(-2.08338 + 2.08338i) q^{35} +(-0.296089 - 0.221701i) q^{36} +(4.19450 + 4.19450i) q^{37} +(-0.446682 + 1.34182i) q^{38} +6.71539i q^{39} +(-1.93416 + 1.34243i) q^{40} +2.96619i q^{41} +(-8.47610 - 2.82164i) q^{42} +(-6.52927 - 6.52927i) q^{43} +(4.77708 - 0.686301i) q^{44} +(0.108858 - 0.108858i) q^{45} +(5.83994 + 11.6683i) q^{46} +7.69612 q^{47} +(-6.26461 - 3.42254i) q^{48} -5.52861 q^{49} +(2.72622 + 5.44704i) q^{50} +(9.37712 - 9.37712i) q^{51} +(1.07020 + 7.44928i) q^{52} +(0.775893 + 0.775893i) q^{53} +(-6.74111 - 2.24407i) q^{54} +2.00863i q^{55} +(-9.85207 - 1.77920i) q^{56} -1.78464i q^{57} +(0.484847 - 1.45646i) q^{58} +(-6.49885 - 6.49885i) q^{59} +(1.78076 - 2.37826i) q^{60} +(-3.70184 + 3.70184i) q^{61} +(12.9957 - 6.50430i) q^{62} +0.654631 q^{63} +(-7.49467 - 2.79820i) q^{64} -3.13221 q^{65} +(-5.44620 + 2.72580i) q^{66} +(-0.684611 + 0.684611i) q^{67} +(8.90750 - 11.8963i) q^{68} +(-11.6431 - 11.6431i) q^{69} +(1.31608 - 3.95345i) q^{70} -7.87186i q^{71} +(0.514780 + 0.0929646i) q^{72} -5.74127i q^{73} +(-7.95956 - 2.64968i) q^{74} +(-5.43529 - 5.43529i) q^{75} +(-0.284411 - 1.97967i) q^{76} +(-6.03955 + 6.03955i) q^{77} +(-4.25055 - 8.49269i) q^{78} +9.25466 q^{79} +(1.59635 - 2.92196i) q^{80} +9.52063 q^{81} +(-1.87747 - 3.75123i) q^{82} +(-0.337972 + 0.337972i) q^{83} +(12.5054 - 1.79659i) q^{84} +(4.37371 + 4.37371i) q^{85} +(12.3901 + 4.12457i) q^{86} +1.93712i q^{87} +(-5.60698 + 3.89162i) q^{88} +8.02811i q^{89} +(-0.0687662 + 0.206571i) q^{90} +(-9.41796 - 9.41796i) q^{91} +(-14.7711 - 11.0600i) q^{92} +(-12.9677 + 12.9677i) q^{93} +(-9.73298 + 4.87131i) q^{94} +0.832398 q^{95} +(10.0889 + 0.363118i) q^{96} -3.50154 q^{97} +(6.99181 - 3.49937i) q^{98} +(0.315572 - 0.315572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.26466	+	0.632956i	−0.894250	+	0.447568i
$2$	−1.26466	+	0.632956i	−0.894250	+	0.447568i
$3$	1.26193	−	1.26193i	0.728577	−	0.728577i	−0.241759	−	0.970336i	$-0.577724\pi$
$3$	1.26193	−	1.26193i	0.728577	−	0.728577i	0.970336	+	0.241759i	$0.0777244\pi$
$4$	1.19873	−	1.60095i	0.599366	−	0.800475i
$5$	0.588594	+	0.588594i	0.263227	+	0.263227i	0.826364	−	0.563136i	$-0.190405\pi$
$5$	0.588594	+	0.588594i	0.263227	+	0.263227i	−0.563136	+	0.826364i	$0.690405\pi$
$6$	−0.797168	+	2.39466i	−0.325442	+	0.977617i
$7$			3.53958i			1.33783i	0.743337	+	0.668917i	$0.233242\pi$
$7$			3.53958i			1.33783i	−0.743337	+	0.668917i	$0.766758\pi$
$8$	−0.502658	+	2.78340i	−0.177716	+	0.984082i
$9$		−	0.184946i		−	0.0616487i
$10$	−1.11693	−	0.371817i	−0.353203	−	0.117579i
$11$	1.70629	+	1.70629i	0.514466	+	0.514466i	0.915892	−	0.401425i	$-0.131485\pi$
$11$	1.70629	+	1.70629i	0.514466	+	0.514466i	−0.401425	+	0.915892i	$0.631485\pi$
$12$	−0.507572	−	3.53301i	−0.146523	−	1.01989i
$13$	−2.66076	+	2.66076i	−0.737961	+	0.737961i	−0.972183	−	0.234222i	$-0.924746\pi$
$13$	−2.66076	+	2.66076i	−0.737961	+	0.737961i	0.234222	+	0.972183i	$0.424746\pi$
$14$	−2.24040	−	4.47636i	−0.598772	−	1.19636i
$15$	1.48553			0.383563
$16$	−1.12608	−	3.83822i	−0.281520	−	0.959555i
$17$	7.43076			1.80223			0.901113	−	0.433585i	$-0.142752\pi$
$17$	7.43076			1.80223			0.901113	+	0.433585i	$0.142752\pi$
$18$	0.117063	+	0.233894i	0.0275920	+	0.0551293i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$20$	1.64788	−	0.236743i	0.368477	−	0.0529374i
$21$	4.46671	+	4.46671i	0.974715	+	0.974715i
$22$	−3.23789	−	1.07787i	−0.690320	−	0.229803i
$23$		−	9.22644i		−	1.92385i	−0.273320	−	0.961923i	$-0.588122\pi$
$23$		−	9.22644i		−	1.92385i	0.273320	−	0.961923i	$-0.411878\pi$
$24$	2.87815	+	4.14679i	0.587499	+	0.846459i
$25$		−	4.30711i		−	0.861423i
$26$	1.68081	−	5.04910i	0.329634	−	0.990210i
$27$	3.55241	+	3.55241i	0.683661	+	0.683661i
$28$	5.66669	+	4.24301i	1.07090	+	0.801853i
$29$	−0.767522	+	0.767522i	−0.142525	+	0.142525i	−0.774769	−	0.632244i	$-0.782134\pi$
$29$	−0.767522	+	0.767522i	−0.142525	+	0.142525i	0.632244	+	0.774769i	$0.282134\pi$
$30$	−1.87869	+	0.940277i	−0.343001	+	0.171670i
$31$	−10.2761			−1.84563			−0.922817	−	0.385239i	$-0.874119\pi$
$31$	−10.2761			−1.84563			−0.922817	+	0.385239i	$0.874119\pi$
$32$	3.85354	+	4.14129i	0.681216	+	0.732083i
$33$	4.30645			0.749657
$34$	−9.39739	+	4.70335i	−1.61164	+	0.806618i
$35$	−2.08338	+	2.08338i	−0.352155	+	0.352155i
$36$	−0.296089	−	0.221701i	−0.0493482	−	0.0369501i
$37$	4.19450	+	4.19450i	0.689572	+	0.689572i	0.962137	−	0.272565i	$-0.0878721\pi$
$37$	4.19450	+	4.19450i	0.689572	+	0.689572i	−0.272565	+	0.962137i	$0.587872\pi$
$38$	−0.446682	+	1.34182i	−0.0724614	+	0.217672i
$39$			6.71539i			1.07532i
$40$	−1.93416	+	1.34243i	−0.305817	+	0.212257i
$41$			2.96619i			0.463242i	0.972806	+	0.231621i	$0.0744029\pi$
$41$			2.96619i			0.463242i	−0.972806	+	0.231621i	$0.925597\pi$
$42$	−8.47610	−	2.82164i	−1.30789	−	0.435388i
$43$	−6.52927	−	6.52927i	−0.995704	−	0.995704i	0.00428636	−	0.999991i	$-0.498636\pi$
$43$	−6.52927	−	6.52927i	−0.995704	−	0.995704i	−0.999991	+	0.00428636i	$0.998636\pi$
$44$	4.77708	−	0.686301i	0.720171	−	0.103464i
$45$	0.108858	−	0.108858i	0.0162276	−	0.0162276i
$46$	5.83994	+	11.6683i	0.861052	+	1.72040i
$47$	7.69612			1.12260			0.561298	−	0.827614i	$-0.310302\pi$
$47$	7.69612			1.12260			0.561298	+	0.827614i	$0.310302\pi$
$48$	−6.26461	−	3.42254i	−0.904219	−	0.494000i
$49$	−5.52861			−0.789801
$50$	2.72622	+	5.44704i	0.385545	+	0.770327i
$51$	9.37712	−	9.37712i	1.31306	−	1.31306i
$52$	1.07020	+	7.44928i	0.148411	+	1.03303i
$53$	0.775893	+	0.775893i	0.106577	+	0.106577i	0.758385	−	0.651807i	$-0.225989\pi$
$53$	0.775893	+	0.775893i	0.106577	+	0.106577i	−0.651807	+	0.758385i	$0.725989\pi$
$54$	−6.74111	−	2.24407i	−0.917349	−	0.305379i
$55$			2.00863i			0.270843i
$56$	−9.85207	−	1.77920i	−1.31654	−	0.237755i
$57$		−	1.78464i		−	0.236382i
$58$	0.484847	−	1.45646i	0.0636635	−	0.191243i
$59$	−6.49885	−	6.49885i	−0.846079	−	0.846079i	0.143563	−	0.989641i	$-0.454144\pi$
$59$	−6.49885	−	6.49885i	−0.846079	−	0.846079i	−0.989641	+	0.143563i	$0.954144\pi$
$60$	1.78076	−	2.37826i	0.229895	−	0.307032i
$61$	−3.70184	+	3.70184i	−0.473972	+	0.473972i	−0.903198	−	0.429225i	$-0.858787\pi$
$61$	−3.70184	+	3.70184i	−0.473972	+	0.473972i	0.429225	+	0.903198i	$0.358787\pi$
$62$	12.9957	−	6.50430i	1.65046	−	0.826046i
$63$	0.654631			0.0824757
$64$	−7.49467	−	2.79820i	−0.936834	−	0.349775i
$65$	−3.13221			−0.388503
$66$	−5.44620	+	2.72580i	−0.670381	+	0.335522i
$67$	−0.684611	+	0.684611i	−0.0836386	+	0.0836386i	−0.747688	−	0.664050i	$-0.768836\pi$
$67$	−0.684611	+	0.684611i	−0.0836386	+	0.0836386i	0.664050	+	0.747688i	$0.268836\pi$
$68$	8.90750	−	11.8963i	1.08019	−	1.44264i
$69$	−11.6431	−	11.6431i	−1.40167	−	1.40167i
$70$	1.31608	−	3.95345i	0.157301	−	0.472527i
$71$		−	7.87186i		−	0.934218i	−0.884200	−	0.467109i	$-0.845296\pi$
$71$		−	7.87186i		−	0.934218i	0.884200	−	0.467109i	$-0.154704\pi$
$72$	0.514780	+	0.0929646i	0.0606674	+	0.0109560i
$73$		−	5.74127i		−	0.671965i	−0.941868	−	0.335982i	$-0.890932\pi$
$73$		−	5.74127i		−	0.671965i	0.941868	−	0.335982i	$-0.109068\pi$
$74$	−7.95956	−	2.64968i	−0.925280	−	0.308019i
$75$	−5.43529	−	5.43529i	−0.627613	−	0.627613i
$76$	−0.284411	−	1.97967i	−0.0326242	−	0.227084i
$77$	−6.03955	+	6.03955i	−0.688271	+	0.688271i
$78$	−4.25055	−	8.49269i	−0.481280	−	0.961608i
$79$	9.25466			1.04123			0.520615	−	0.853791i	$-0.325703\pi$
$79$	9.25466			1.04123			0.520615	+	0.853791i	$0.325703\pi$
$80$	1.59635	−	2.92196i	0.178477	−	0.326685i
$81$	9.52063			1.05785
$82$	−1.87747	−	3.75123i	−0.207332	−	0.414254i
$83$	−0.337972	+	0.337972i	−0.0370972	+	0.0370972i	−0.725412	−	0.688315i	$-0.758351\pi$
$83$	−0.337972	+	0.337972i	−0.0370972	+	0.0370972i	0.688315	+	0.725412i	$0.258351\pi$
$84$	12.5054	−	1.79659i	1.36445	−	0.196024i
$85$	4.37371	+	4.37371i	0.474395	+	0.474395i
$86$	12.3901	+	4.12457i	1.33605	+	0.444763i
$87$			1.93712i			0.207681i
$88$	−5.60698	+	3.89162i	−0.597706	+	0.414848i
$89$			8.02811i			0.850977i	0.904964	+	0.425489i	$0.139898\pi$
$89$			8.02811i			0.850977i	−0.904964	+	0.425489i	$0.860102\pi$
$90$	−0.0687662	+	0.206571i	−0.00724859	+	0.0217745i
$91$	−9.41796	−	9.41796i	−0.987270	−	0.987270i
$92$	−14.7711	−	11.0600i	−1.53999	−	1.15309i
$93$	−12.9677	+	12.9677i	−1.34469	+	1.34469i
$94$	−9.73298	+	4.87131i	−1.00388	+	0.502437i
$95$	0.832398			0.0854022
$96$	10.0889	+	0.363118i	1.02970	+	0.0370605i
$97$	−3.50154			−0.355528			−0.177764	−	0.984073i	$-0.556886\pi$
$97$	−3.50154			−0.355528			−0.177764	+	0.984073i	$0.556886\pi$
$98$	6.99181	−	3.49937i	0.706280	−	0.353489i
$99$	0.315572	−	0.315572i	0.0317162	−	0.0317162i
$100$	−6.89547	−	5.16308i	−0.689547	−	0.516308i
$101$	6.61998	+	6.61998i	0.658713	+	0.658713i	0.955075	−	0.296363i	$-0.0957737\pi$
$101$	6.61998	+	6.61998i	0.658713	+	0.658713i	−0.296363	+	0.955075i	$0.595774\pi$
$102$	−5.92357	+	17.7942i	−0.586520	+	1.76189i
$103$		−	8.44043i		−	0.831660i	−0.909442	−	0.415830i	$-0.863491\pi$
$103$		−	8.44043i		−	0.831660i	0.909442	−	0.415830i	$-0.136509\pi$
$104$	−6.06851	−	8.74341i	−0.595067	−	0.857362i
$105$			5.25816i			0.513144i
$106$	−1.47235	−	0.490135i	−0.143007	−	0.0476061i
$107$	−12.6971	−	12.6971i	−1.22747	−	1.22747i	−0.964916	−	0.262558i	$-0.915434\pi$
$107$	−12.6971	−	12.6971i	−1.22747	−	1.22747i	−0.262558	−	0.964916i	$-0.584566\pi$
$108$	9.94561	−	1.42884i	0.957017	−	0.137490i
$109$	−7.97397	+	7.97397i	−0.763767	+	0.763767i	−0.977001	−	0.213234i	$-0.931600\pi$
$109$	−7.97397	+	7.97397i	−0.763767	+	0.763767i	0.213234	+	0.977001i	$0.431600\pi$
$110$	−1.27137	−	2.54023i	−0.121221	−	0.242202i
$111$	10.5864			1.00481
$112$	13.5857	−	3.98585i	1.28373	−	0.376628i
$113$	6.15820			0.579314			0.289657	−	0.957130i	$-0.406459\pi$
$113$	6.15820			0.579314			0.289657	+	0.957130i	$0.406459\pi$
$114$	1.12960	+	2.25697i	0.105797	+	0.211384i
$115$	5.43063	−	5.43063i	0.506409	−	0.506409i
$116$	0.308711	+	2.14882i	0.0286631	+	0.199513i
$117$	0.492097	+	0.492097i	0.0454944	+	0.0454944i
$118$	12.3323	+	4.10535i	1.13528	+	0.377928i
$119$			26.3018i			2.41108i
$120$	−0.746714	+	4.13484i	−0.0681654	+	0.377457i
$121$		−	5.17713i		−	0.470649i
$122$	2.33847	−	7.02468i	0.211715	−	0.635985i
$123$	3.74314	+	3.74314i	0.337507	+	0.337507i
$124$	−12.3182	+	16.4515i	−1.10621	+	1.47738i
$125$	5.47811	−	5.47811i	0.489977	−	0.489977i
$126$	−0.827886	+	0.414353i	−0.0737539	+	0.0369135i
$127$	−3.26504			−0.289725			−0.144863	−	0.989452i	$-0.546274\pi$
$127$	−3.26504			−0.289725			−0.144863	+	0.989452i	$0.546274\pi$
$128$	11.2494	−	1.20503i	0.994312	−	0.106511i
$129$	−16.4790			−1.45089
$130$	3.96119	−	1.98256i	0.347419	−	0.173882i
$131$	−2.96211	+	2.96211i	−0.258801	+	0.258801i	−0.824566	−	0.565765i	$-0.808581\pi$
$131$	−2.96211	+	2.96211i	−0.258801	+	0.258801i	0.565765	+	0.824566i	$0.308581\pi$
$132$	5.16228	−	6.89441i	0.449319	−	0.600082i
$133$	2.50286	+	2.50286i	0.217025	+	0.217025i
$134$	0.432472	−	1.29913i	0.0373599	−	0.112228i
$135$			4.18185i			0.359917i
$136$	−3.73513	+	20.6828i	−0.320285	+	1.77354i
$137$		−	1.56391i		−	0.133614i	−0.997766	−	0.0668070i	$-0.978719\pi$
$137$		−	1.56391i		−	0.133614i	0.997766	−	0.0668070i	$-0.0212812\pi$
$138$	22.0942	+	7.35502i	1.88079	+	0.626101i
$139$	7.57000	+	7.57000i	0.642079	+	0.642079i	0.951066	−	0.308987i	$-0.0999900\pi$
$139$	7.57000	+	7.57000i	0.642079	+	0.642079i	−0.308987	+	0.951066i	$0.599990\pi$
$140$	0.837971	+	5.83279i	0.0708214	+	0.492961i
$141$	9.71199	−	9.71199i	0.817897	−	0.817897i
$142$	4.98255	+	9.95523i	0.418126	+	0.835425i
$143$	−9.08006			−0.759313
$144$	−0.709864	+	0.208264i	−0.0591553	+	0.0173554i
$145$	−0.903518			−0.0750331
$146$	3.63397	+	7.26076i	0.300750	+	0.600904i
$147$	−6.97673	+	6.97673i	−0.575431	+	0.575431i
$148$	11.7433	−	1.68710i	0.965291	−	0.138679i
$149$	−13.2868	−	13.2868i	−1.08850	−	1.08850i	−0.995683	−	0.0928145i	$-0.970414\pi$
$149$	−13.2868	−	13.2868i	−1.08850	−	1.08850i	−0.0928145	−	0.995683i	$-0.529586\pi$
$150$	10.3141	+	3.43349i	0.842142	+	0.280343i
$151$		−	0.187298i		−	0.0152421i	−0.999971	−	0.00762103i	$-0.997574\pi$
$151$		−	0.187298i		−	0.0152421i	0.999971	−	0.00762103i	$-0.00242587\pi$
$152$	1.61273	+	2.32360i	0.130810	+	0.188469i
$153$		−	1.37429i		−	0.111105i
$154$	3.81521	−	11.4608i	0.307438	−	0.923534i
$155$	−6.04843	−	6.04843i	−0.485821	−	0.485821i
$156$	10.7510	+	8.04996i	0.860769	+	0.644512i
$157$	0.330478	−	0.330478i	0.0263750	−	0.0263750i	−0.693796	−	0.720171i	$-0.744063\pi$
$157$	0.330478	−	0.330478i	0.0263750	−	0.0263750i	0.720171	+	0.693796i	$0.244063\pi$
$158$	−11.7040	+	5.85780i	−0.931120	+	0.466021i
$159$	1.95825			0.155299
$160$	−0.169366	+	4.70571i	−0.0133896	+	0.372019i
$161$	32.6577			2.57379
$162$	−12.0404	+	6.02615i	−0.945981	+	0.473459i
$163$	−10.9494	+	10.9494i	−0.857623	+	0.857623i	−0.991058	−	0.133434i	$-0.957399\pi$
$163$	−10.9494	+	10.9494i	−0.857623	+	0.857623i	0.133434	+	0.991058i	$0.457399\pi$
$164$	4.74873	+	3.55567i	0.370813	+	0.277651i
$165$	2.53475	+	2.53475i	0.197330	+	0.197330i
$166$	0.213498	−	0.641341i	0.0165707	−	0.0497777i
$167$		−	3.79635i		−	0.293770i	−0.989154	−	0.146885i	$-0.953075\pi$
$167$		−	3.79635i		−	0.293770i	0.989154	−	0.146885i	$-0.0469248\pi$
$168$	−14.6779	+	10.1874i	−1.13242	+	0.785977i
$169$		−	1.15926i		−	0.0891742i
$170$	−8.29962	−	2.76289i	−0.636552	−	0.211904i
$171$	−0.130777	−	0.130777i	−0.0100007	−	0.0100007i
$172$	−18.2799	+	2.62619i	−1.39383	+	0.200245i
$173$	14.4035	−	14.4035i	1.09508	−	1.09508i	0.100104	−	0.994977i	$-0.468082\pi$
$173$	14.4035	−	14.4035i	1.09508	−	1.09508i	0.994977	−	0.100104i	$-0.0319176\pi$
$174$	−1.22611	−	2.44980i	−0.0929514	−	0.185719i
$175$	15.2454			1.15244
$176$	4.62770	−	8.47055i	0.348826	−	0.638492i
$177$	−16.4022			−1.23287
$178$	−5.08144	−	10.1528i	−0.380870	−	0.760987i
$179$	−10.3915	+	10.3915i	−0.776694	+	0.776694i	−0.979267	−	0.202573i	$-0.935070\pi$
$179$	−10.3915	+	10.3915i	−0.776694	+	0.776694i	0.202573	+	0.979267i	$0.435070\pi$
$180$	−0.0437847	−	0.304768i	−0.00326352	−	0.0227161i
$181$	−4.83110	−	4.83110i	−0.359093	−	0.359093i	0.504386	−	0.863478i	$-0.331719\pi$
$181$	−4.83110	−	4.83110i	−0.359093	−	0.359093i	−0.863478	+	0.504386i	$0.831719\pi$
$182$	17.8717	+	5.94936i	1.32474	+	0.440996i
$183$			9.34295i			0.690651i
$184$	25.6809	+	4.63774i	1.89322	+	0.341899i
$185$			4.93772i			0.363028i
$186$	8.19174	−	24.6077i	0.600647	−	1.80432i
$187$	12.6791	+	12.6791i	0.927184	+	0.927184i
$188$	9.22559	−	12.3211i	0.672846	−	0.898609i
$189$	−12.5740	+	12.5740i	−0.914625	+	0.914625i
$190$	−1.05270	+	0.526872i	−0.0763710	+	0.0382233i
$191$	−11.6570			−0.843472			−0.421736	−	0.906719i	$-0.638579\pi$
$191$	−11.6570			−0.843472			−0.421736	+	0.906719i	$0.638579\pi$
$192$	−12.9889	+	5.92663i	−0.937393	+	0.427718i
$193$	17.2338			1.24052			0.620258	−	0.784398i	$-0.287028\pi$
$193$	17.2338			1.24052			0.620258	+	0.784398i	$0.287028\pi$
$194$	4.42826	−	2.21632i	0.317931	−	0.159123i
$195$	−3.95264	+	3.95264i	−0.283055	+	0.283055i
$196$	−6.62732	+	8.85102i	−0.473380	+	0.632216i
$197$	−1.83509	−	1.83509i	−0.130745	−	0.130745i	0.638706	−	0.769451i	$-0.279470\pi$
$197$	−1.83509	−	1.83509i	−0.130745	−	0.130745i	−0.769451	+	0.638706i	$0.779470\pi$
$198$	−0.199348	+	0.598835i	−0.0141671	+	0.0425573i
$199$		−	11.2806i		−	0.799660i	−0.916589	−	0.399830i	$-0.869069\pi$
$199$		−	11.2806i		−	0.799660i	0.916589	−	0.399830i	$-0.130931\pi$
$200$	11.9884	+	2.16500i	0.847710	+	0.153089i
$201$			1.72787i			0.121874i
$202$	−12.5622	−	4.18187i	−0.883873	−	0.294235i
$203$	−2.71670	−	2.71670i	−0.190675	−	0.190675i
$204$	−3.77164	−	26.2530i	−0.264068	−	1.83807i
$205$	−1.74589	+	1.74589i	−0.121938	+	0.121938i
$206$	5.34242	+	10.6743i	0.372224	+	0.743712i
$207$	−1.70639			−0.118603
$208$	13.2088	+	7.21634i	0.915866	+	0.500363i
$209$	2.41306			0.166915
$210$	−3.32818	−	6.64978i	−0.229667	−	0.458879i
$211$	6.78982	−	6.78982i	0.467431	−	0.467431i	−0.433651	−	0.901081i	$-0.642775\pi$
$211$	6.78982	−	6.78982i	0.467431	−	0.467431i	0.901081	+	0.433651i	$0.142775\pi$
$212$	2.17225	−	0.312078i	0.149191	−	0.0214336i
$213$	−9.93376	−	9.93376i	−0.680650	−	0.680650i
$214$	24.0942	+	8.02080i	1.64705	+	0.548291i
$215$		−	7.68618i		−	0.524193i
$216$	−11.6734	+	8.10214i	−0.794276	+	0.551281i
$217$		−	36.3729i		−	2.46915i
$218$	5.03719	−	15.1315i	0.341161	−	1.02484i
$219$	−7.24509	−	7.24509i	−0.489578	−	0.489578i
$220$	3.21571	+	2.40781i	0.216803	+	0.162334i
$221$	−19.7715	+	19.7715i	−1.32997	+	1.32997i
$222$	−13.3881	+	6.70070i	−0.898553	+	0.449722i
$223$	13.7199			0.918752			0.459376	−	0.888242i	$-0.348073\pi$
$223$	13.7199			0.918752			0.459376	+	0.888242i	$0.348073\pi$
$224$	−14.6584	+	13.6399i	−0.979406	+	0.911354i
$225$	−0.796584			−0.0531056
$226$	−7.78803	+	3.89787i	−0.518052	+	0.259282i
$227$	5.80514	−	5.80514i	0.385301	−	0.385301i	−0.487707	−	0.873008i	$-0.662166\pi$
$227$	5.80514	−	5.80514i	0.385301	−	0.385301i	0.873008	+	0.487707i	$0.162166\pi$
$228$	−2.85712	−	2.13931i	−0.189218	−	0.141679i
$229$	−13.2909	−	13.2909i	−0.878288	−	0.878288i	0.115070	−	0.993357i	$-0.463291\pi$
$229$	−13.2909	−	13.2909i	−0.878288	−	0.878288i	−0.993357	+	0.115070i	$0.963291\pi$
$230$	−3.43055	+	10.3053i	−0.226204	+	0.679509i
$231$			15.2430i			1.00292i
$232$	−1.75052	−	2.52212i	−0.114927	−	0.165586i
$233$		−	18.2068i		−	1.19277i	−0.802700	−	0.596383i	$-0.796604\pi$
$233$		−	18.2068i		−	1.19277i	0.802700	−	0.596383i	$-0.203396\pi$
$234$	−0.933811	−	0.310859i	−0.0610451	−	0.0203215i
$235$	4.52990	+	4.52990i	0.295498	+	0.295498i
$236$	−18.1947	+	2.61395i	−1.18438	+	0.170154i
$237$	11.6788	−	11.6788i	0.758616	−	0.758616i
$238$	−16.6479	−	33.2628i	−1.07912	−	2.15611i
$239$	−3.40119			−0.220005			−0.110002	−	0.993931i	$-0.535086\pi$
$239$	−3.40119			−0.220005			−0.110002	+	0.993931i	$0.535086\pi$
$240$	−1.67283	−	5.70180i	−0.107981	−	0.368050i
$241$	−20.9780			−1.35131			−0.675656	−	0.737217i	$-0.736139\pi$
$241$	−20.9780			−1.35131			−0.675656	+	0.737217i	$0.736139\pi$
$242$	3.27690	+	6.54732i	0.210647	+	0.420877i
$243$	1.35717	−	1.35717i	0.0870626	−	0.0870626i
$244$	1.48895	+	10.3640i	0.0953201	+	0.663486i
$245$	−3.25411	−	3.25411i	−0.207897	−	0.207897i
$246$	−7.10304	−	2.36455i	−0.452873	−	0.150758i
$247$			3.76288i			0.239426i
$248$	5.16534	−	28.6024i	0.327999	−	1.81625i
$249$			0.852995i			0.0540564i
$250$	−3.46055	+	10.3954i	−0.218864	+	0.657460i
$251$	0.00362161	+	0.00362161i	0.000228594	+	0.000228594i	0.707221	−	0.706992i	$-0.249949\pi$
$251$	0.00362161	+	0.00362161i	0.000228594	+	0.000228594i	−0.706992	+	0.707221i	$0.749949\pi$
$252$	0.784727	−	1.04803i	0.0494332	−	0.0660198i
$253$	15.7430	−	15.7430i	0.989754	−	0.989754i
$254$	4.12917	−	2.06663i	0.259087	−	0.129672i
$255$	11.0386			0.691267
$256$	−13.4639	+	8.64430i	−0.841492	+	0.540269i
$257$	16.2559			1.01401			0.507006	−	0.861942i	$-0.330752\pi$
$257$	16.2559			1.01401			0.507006	+	0.861942i	$0.330752\pi$
$258$	20.8403	−	10.4305i	1.29746	−	0.649374i
$259$	−14.8468	+	14.8468i	−0.922533	+	0.922533i
$260$	−3.75469	+	5.01452i	−0.232856	+	0.310987i
$261$	0.141950	+	0.141950i	0.00878649	+	0.00878649i
$262$	1.87118	−	5.62096i	0.115602	−	0.347264i
$263$			23.3764i			1.44145i	0.693221	+	0.720725i	$0.256191\pi$
$263$			23.3764i			1.44145i	−0.693221	+	0.720725i	$0.743809\pi$
$264$	−2.16467	+	11.9866i	−0.133226	+	0.737724i
$265$			0.913372i			0.0561080i
$266$	−4.74947	−	1.58107i	−0.291209	−	0.0969414i
$267$	10.1309	+	10.1309i	0.620003	+	0.620003i
$268$	0.275363	+	1.91669i	0.0168205	+	0.117081i
$269$	2.68322	−	2.68322i	0.163599	−	0.163599i	−0.620560	−	0.784159i	$-0.713095\pi$
$269$	2.68322	−	2.68322i	0.163599	−	0.163599i	0.784159	+	0.620560i	$0.213095\pi$
$270$	−2.64693	−	5.28863i	−0.161087	−	0.321855i
$271$	4.93257			0.299632			0.149816	−	0.988714i	$-0.452132\pi$
$271$	4.93257			0.299632			0.149816	+	0.988714i	$0.452132\pi$
$272$	−8.36765	−	28.5209i	−0.507363	−	1.72933i
$273$	−23.7696			−1.43860
$274$	0.989888	+	1.97782i	0.0598013	+	0.119484i
$275$	7.34919	−	7.34919i	0.443173	−	0.443173i
$276$	−32.5971	+	4.68308i	−1.96212	+	0.281888i
$277$	6.65345	+	6.65345i	0.399767	+	0.399767i	0.878151	−	0.478384i	$-0.158777\pi$
$277$	6.65345	+	6.65345i	0.399767	+	0.399767i	−0.478384	+	0.878151i	$0.658777\pi$
$278$	−14.3650	−	4.78200i	−0.861553	−	0.286805i
$279$			1.90052i			0.113781i
$280$	−4.75165	−	6.84610i	−0.283965	−	0.409133i
$281$			7.68828i			0.458644i	0.973351	+	0.229322i	$0.0736509\pi$
$281$			7.68828i			0.458644i	−0.973351	+	0.229322i	$0.926349\pi$
$282$	−6.13510	+	18.4296i	−0.365340	+	1.09747i
$283$	−14.0057	−	14.0057i	−0.832551	−	0.832551i	0.155314	−	0.987865i	$-0.450361\pi$
$283$	−14.0057	−	14.0057i	−0.832551	−	0.832551i	−0.987865	+	0.155314i	$0.950361\pi$
$284$	−12.6025	−	9.43625i	−0.747818	−	0.559939i
$285$	1.05043	−	1.05043i	0.0622221	−	0.0622221i
$286$	11.4832	−	5.74728i	0.679015	−	0.339844i
$287$	−10.4991			−0.619741
$288$	0.765914	−	0.712697i	0.0451319	−	0.0419961i
$289$	38.2163			2.24802
$290$	1.14264	−	0.571888i	0.0670983	−	0.0335824i
$291$	−4.41871	+	4.41871i	−0.259029	+	0.259029i
$292$	−9.19148	−	6.88224i	−0.537891	−	0.402753i
$293$	2.93186	+	2.93186i	0.171281	+	0.171281i	0.787542	−	0.616261i	$-0.211353\pi$
$293$	2.93186	+	2.93186i	0.171281	+	0.171281i	−0.616261	+	0.787542i	$0.711353\pi$
$294$	4.40723	−	13.2392i	0.257035	−	0.772123i
$295$		−	7.65038i		−	0.445422i
$296$	−13.7834	+	9.56659i	−0.801143	+	0.556047i
$297$			12.1229i			0.703441i
$298$	25.2133	+	8.39333i	1.46057	+	0.486213i
$299$	24.5493	+	24.5493i	1.41972	+	1.41972i
$300$	−15.2171	+	2.18617i	−0.878558	+	0.126218i
$301$	23.1109	−	23.1109i	1.33209	−	1.33209i
$302$	0.118551	+	0.236868i	0.00682186	+	0.0136302i
$303$	16.7079			0.959846
$304$	−3.51029	−	1.91777i	−0.201329	−	0.109992i
$305$	−4.35777			−0.249525
$306$	0.869866	+	1.73801i	0.0497269	+	0.0993555i
$307$	9.05048	−	9.05048i	0.516538	−	0.516538i	−0.399984	−	0.916522i	$-0.630984\pi$
$307$	9.05048	−	9.05048i	0.516538	−	0.516538i	0.916522	+	0.399984i	$0.130984\pi$
$308$	2.42922	+	16.9088i	0.138417	+	0.963470i
$309$	−10.6513	−	10.6513i	−0.605928	−	0.605928i
$310$	11.4776	+	3.82082i	0.651884	+	0.217008i
$311$			1.81840i			0.103112i	0.998670	+	0.0515559i	$0.0164180\pi$
$311$			1.81840i			0.103112i	−0.998670	+	0.0515559i	$0.983582\pi$
$312$	−18.6916	−	3.37554i	−1.05821	−	0.191103i
$313$			24.2205i			1.36902i	0.729002	+	0.684511i	$0.239984\pi$
$313$			24.2205i			1.36902i	−0.729002	+	0.684511i	$0.760016\pi$
$314$	−0.208764	+	0.627120i	−0.0117812	+	0.0353904i
$315$	0.385312	+	0.385312i	0.0217099	+	0.0217099i
$316$	11.0939	−	14.8162i	0.624078	−	0.833479i
$317$	4.90971	−	4.90971i	0.275757	−	0.275757i	−0.555656	−	0.831413i	$-0.687533\pi$
$317$	4.90971	−	4.90971i	0.275757	−	0.275757i	0.831413	+	0.555656i	$0.187533\pi$
$318$	−2.47652	+	1.23949i	−0.138876	+	0.0695069i
$319$	−2.61923			−0.146649
$320$	−2.76432	−	6.05832i	−0.154530	−	0.338671i
$321$	−32.0457			−1.78862
$322$	−41.3009	+	20.6709i	−2.30161	+	1.15194i
$323$	5.25434	−	5.25434i	0.292360	−	0.292360i
$324$	11.4127	−	15.2421i	0.634038	−	0.846781i
$325$	11.4602	+	11.4602i	0.635697	+	0.635697i
$326$	6.91678	−	20.7778i	0.383085	−	1.15077i
$327$			20.1252i			1.11293i
$328$	−8.25612	−	1.49098i	−0.455868	−	0.0823256i
$329$			27.2410i			1.50185i
$330$	−4.80999	−	1.60121i	−0.264781	−	0.0881439i
$331$	13.0941	+	13.0941i	0.719714	+	0.719714i	0.968547	−	0.248832i	$-0.0800468\pi$
$331$	13.0941	+	13.0941i	0.719714	+	0.719714i	−0.248832	+	0.968547i	$0.580047\pi$
$332$	0.135938	+	0.946214i	0.00746058	+	0.0519302i
$333$	0.775757	−	0.775757i	0.0425112	−	0.0425112i
$334$	2.40292	+	4.80109i	0.131482	+	0.262704i
$335$	−0.805917			−0.0440319
$336$	12.1143	−	22.1741i	0.660891	−	1.20970i
$337$	−32.5222			−1.77160			−0.885800	−	0.464068i	$-0.846389\pi$
$337$	−32.5222			−1.77160			−0.885800	+	0.464068i	$0.846389\pi$
$338$	0.733764	+	1.46608i	0.0399115	+	0.0797440i
$339$	7.77123	−	7.77123i	0.422075	−	0.422075i
$340$	12.2450	−	1.75918i	0.664078	−	0.0954051i
$341$	−17.5340	−	17.5340i	−0.949517	−	0.949517i
$342$	0.248164	+	0.0826121i	0.0134192	+	0.00446715i
$343$			5.20811i			0.281211i
$344$	21.4556	−	14.8916i	1.15681	−	0.802902i
$345$		−	13.7062i		−	0.737916i
$346$	−9.09878	+	27.3324i	−0.489153	+	1.46940i
$347$	14.2329	+	14.2329i	0.764062	+	0.764062i	0.977054	−	0.212992i	$-0.0683208\pi$
$347$	14.2329	+	14.2329i	0.764062	+	0.764062i	−0.212992	+	0.977054i	$0.568321\pi$
$348$	3.10123	+	2.32209i	0.166244	+	0.124477i
$349$	−5.34292	+	5.34292i	−0.286000	+	0.286000i	−0.835496	−	0.549496i	$-0.814820\pi$
$349$	−5.34292	+	5.34292i	−0.286000	+	0.286000i	0.549496	+	0.835496i	$0.314820\pi$
$350$	−19.2802	+	9.64965i	−1.03057	+	0.515795i
$351$	−18.9042			−1.00903
$352$	−0.490981	+	13.6415i	−0.0261694	+	0.727095i
$353$	6.02819			0.320848			0.160424	−	0.987048i	$-0.448714\pi$
$353$	6.02819			0.320848			0.160424	+	0.987048i	$0.448714\pi$
$354$	20.7432	−	10.3819i	1.10249	−	0.551792i
$355$	4.63333	−	4.63333i	0.245912	−	0.245912i
$356$	12.8526	+	9.62355i	0.681186	+	0.510047i
$357$	33.1910	+	33.1910i	1.75666	+	1.75666i
$358$	6.56433	−	19.7190i	0.346936	−	1.04218i
$359$			13.0947i			0.691110i	0.938399	+	0.345555i	$0.112309\pi$
$359$			13.0947i			0.691110i	−0.938399	+	0.345555i	$0.887691\pi$
$360$	0.248278	+	0.357715i	0.0130854	+	0.0188532i
$361$		−	1.00000i		−	0.0526316i
$362$	9.16757	+	3.05182i	0.481837	+	0.160400i
$363$	−6.53319	−	6.53319i	−0.342904	−	0.342904i
$364$	−26.3673	+	3.78807i	−1.38202	+	0.198549i
$365$	3.37928	−	3.37928i	0.176880	−	0.176880i
$366$	−5.91368	−	11.8157i	−0.309113	−	0.617614i
$367$	−2.91312			−0.152064			−0.0760318	−	0.997105i	$-0.524225\pi$
$367$	−2.91312			−0.152064			−0.0760318	+	0.997105i	$0.524225\pi$
$368$	−35.4131	+	10.3897i	−1.84604	+	0.541602i
$369$	0.548586			0.0285582
$370$	−3.12536	−	6.24454i	−0.162480	−	0.324638i
$371$	−2.74633	+	2.74633i	−0.142582	+	0.142582i
$372$	5.21583	+	36.3054i	0.270428	+	1.88235i
$373$	16.2799	+	16.2799i	0.842941	+	0.842941i	0.989240	−	0.146299i	$-0.0467362\pi$
$373$	16.2799	+	16.2799i	0.842941	+	0.842941i	−0.146299	+	0.989240i	$0.546736\pi$
$374$	−24.0600	−	8.00941i	−1.24411	−	0.414157i
$375$		−	13.8260i		−	0.713973i
$376$	−3.86852	+	21.4214i	−0.199503	+	1.10473i
$377$		−	4.08438i		−	0.210356i
$378$	7.94306	−	23.8607i	0.408547	−	1.22726i
$379$	−5.93552	−	5.93552i	−0.304887	−	0.304887i	0.538035	−	0.842922i	$-0.319167\pi$
$379$	−5.93552	−	5.93552i	−0.304887	−	0.304887i	−0.842922	+	0.538035i	$0.819167\pi$
$380$	0.997823	−	1.33263i	0.0511872	−	0.0683624i
$381$	−4.12026	+	4.12026i	−0.211087	+	0.211087i
$382$	14.7422	−	7.37838i	0.754274	−	0.377511i
$383$	−3.82541			−0.195469			−0.0977346	−	0.995213i	$-0.531160\pi$
$383$	−3.82541			−0.195469			−0.0977346	+	0.995213i	$0.531160\pi$
$384$	12.6753	−	15.7166i	0.646831	−	0.802034i
$385$	−7.10969			−0.362344
$386$	−21.7949	+	10.9082i	−1.10933	+	0.555215i
$387$	−1.20756	+	1.20756i	−0.0613839	+	0.0613839i
$388$	−4.19741	+	5.60580i	−0.213091	+	0.284591i
$389$	18.8932	+	18.8932i	0.957925	+	0.957925i	0.999150	−	0.0412248i	$-0.0131260\pi$
$389$	18.8932	+	18.8932i	0.957925	+	0.957925i	−0.0412248	+	0.999150i	$0.513126\pi$
$390$	2.49690	−	7.50060i	0.126435	−	0.379808i
$391$		−	68.5595i		−	3.46720i
$392$	2.77900	−	15.3883i	0.140361	−	0.777229i
$393$			7.47597i			0.377113i
$394$	3.48230	+	1.15923i	0.175436	+	0.0584014i
$395$	5.44724	+	5.44724i	0.274080	+	0.274080i
$396$	−0.126929	−	0.883501i	−0.00637841	−	0.0443976i
$397$	−6.00741	+	6.00741i	−0.301503	+	0.301503i	−0.841602	−	0.540098i	$-0.818387\pi$
$397$	−6.00741	+	6.00741i	−0.301503	+	0.301503i	0.540098	+	0.841602i	$0.318387\pi$
$398$	7.14013	+	14.2661i	0.357902	+	0.715096i
$399$	6.31688			0.316239
$400$	−16.5317	+	4.85016i	−0.826583	+	0.242508i
$401$	24.6269			1.22981			0.614905	−	0.788601i	$-0.289194\pi$
$401$	24.6269			1.22981			0.614905	+	0.788601i	$0.289194\pi$
$402$	−1.09366	−	2.18516i	−0.0545470	−	0.108986i
$403$	27.3421	−	27.3421i	1.36201	−	1.36201i
$404$	18.5338	−	2.66267i	0.922093	−	0.132473i
$405$	5.60379	+	5.60379i	0.278455	+	0.278455i
$406$	5.15526	+	1.71615i	0.255851	+	0.0851712i
$407$			14.3141i			0.709523i
$408$	21.3868	+	30.8138i	1.05881	+	1.52551i
$409$		−	31.5920i		−	1.56212i	−0.624454	−	0.781062i	$-0.714678\pi$
$409$		−	31.5920i		−	1.56212i	0.624454	−	0.781062i	$-0.285322\pi$
$410$	1.10288	−	3.31302i	0.0544675	−	0.163618i
$411$	−1.97355	−	1.97355i	−0.0973481	−	0.0973481i
$412$	−13.5127	−	10.1178i	−0.665723	−	0.498469i
$413$	23.0032	−	23.0032i	1.13191	−	1.13191i
$414$	2.15801	−	1.08007i	0.106060	−	0.0530827i
$415$	−0.397857			−0.0195300
$416$	−21.2723	−	0.765626i	−1.04296	−	0.0375379i
$417$	19.1057			0.935608
$418$	−3.05170	+	1.52736i	−0.149264	+	0.0747058i
$419$	−23.8353	+	23.8353i	−1.16443	+	1.16443i	−0.180936	+	0.983495i	$0.557913\pi$
$419$	−23.8353	+	23.8353i	−1.16443	+	1.16443i	−0.983495	+	0.180936i	$0.942087\pi$
$420$	8.41805	+	6.30312i	0.410759	+	0.307561i
$421$	−20.0488	−	20.0488i	−0.977119	−	0.977119i	0.0226248	−	0.999744i	$-0.492798\pi$
$421$	−20.0488	−	20.0488i	−0.977119	−	0.977119i	−0.999744	+	0.0226248i	$0.992798\pi$
$422$	−4.28916	+	12.8845i	−0.208793	+	0.627207i
$423$		−	1.42337i		−	0.0692065i
$424$	−2.54963	+	1.76961i	−0.123821	+	0.0859401i
$425$		−	32.0051i		−	1.55248i
$426$	18.8505	+	6.27519i	0.913308	+	0.304034i
$427$	−13.1030	−	13.1030i	−0.634097	−	0.634097i
$428$	−35.5478	+	5.10700i	−1.71827	+	0.246856i
$429$	−11.4584	+	11.4584i	−0.553218	+	0.553218i
$430$	4.86502	+	9.72041i	0.234612	+	0.468760i
$431$	−15.4016			−0.741870			−0.370935	−	0.928659i	$-0.620963\pi$
$431$	−15.4016			−0.741870			−0.370935	+	0.928659i	$0.620963\pi$
$432$	9.63462	−	17.6352i	0.463546	−	0.848475i
$433$	15.0633			0.723897			0.361948	−	0.932198i	$-0.382112\pi$
$433$	15.0633			0.723897			0.361948	+	0.932198i	$0.382112\pi$
$434$	23.0225	+	45.9994i	1.10511	+	2.20804i
$435$	−1.14018	+	1.14018i	−0.0546674	+	0.0546674i
$436$	3.20727	+	22.3246i	0.153600	+	1.06915i
$437$	−6.52408	−	6.52408i	−0.312089	−	0.312089i
$438$	13.7484	+	4.57675i	0.656924	+	0.218686i
$439$		−	22.5275i		−	1.07518i	−0.843207	−	0.537589i	$-0.819335\pi$
$439$		−	22.5275i		−	1.07518i	0.843207	−	0.537589i	$-0.180665\pi$
$440$	−5.59082	−	1.00965i	−0.266532	−	0.0481333i
$441$			1.02249i			0.0486902i
$442$	12.4897	−	37.5187i	0.594075	−	1.78458i
$443$	11.6669	+	11.6669i	0.554312	+	0.554312i	0.927682	−	0.373370i	$-0.121798\pi$
$443$	11.6669	+	11.6669i	0.554312	+	0.554312i	−0.373370	+	0.927682i	$0.621798\pi$
$444$	12.6902	−	16.9482i	0.602250	−	0.804327i
$445$	−4.72530	+	4.72530i	−0.224001	+	0.224001i
$446$	−17.3510	+	8.68410i	−0.821594	+	0.411204i
$447$	−33.5341			−1.58611
$448$	9.90444	−	26.5280i	0.467941	−	1.25333i
$449$	−26.2828			−1.24036			−0.620181	−	0.784458i	$-0.712941\pi$
$449$	−26.2828			−1.24036			−0.620181	+	0.784458i	$0.712941\pi$
$450$	1.00741	−	0.504203i	0.0474897	−	0.0237683i
$451$	−5.06119	+	5.06119i	−0.238322	+	0.238322i
$452$	7.38203	−	9.85896i	0.347221	−	0.463727i
$453$	−0.236357	−	0.236357i	−0.0111050	−	0.0111050i
$454$	−3.66713	+	11.0159i	−0.172107	+	0.517004i
$455$		−	11.0867i		−	0.519753i
$456$	4.96738	+	0.897064i	0.232619	+	0.0420089i
$457$			9.74205i			0.455714i	0.973695	+	0.227857i	$0.0731719\pi$
$457$			9.74205i			0.455714i	−0.973695	+	0.227857i	$0.926828\pi$
$458$	25.2210	+	8.39592i	1.17850	+	0.392315i
$459$	26.3971	+	26.3971i	1.23211	+	1.23211i
$460$	−2.18430	−	15.2040i	−0.101843	−	0.708892i
$461$	−26.5734	+	26.5734i	−1.23765	+	1.23765i	−0.276690	+	0.960959i	$0.589237\pi$
$461$	−26.5734	+	26.5734i	−1.23765	+	1.23765i	−0.960959	+	0.276690i	$0.910763\pi$
$462$	−9.64816	−	19.2772i	−0.448873	−	0.896858i
$463$	−9.76980			−0.454041			−0.227021	−	0.973890i	$-0.572898\pi$
$463$	−9.76980			−0.454041			−0.227021	+	0.973890i	$0.572898\pi$
$464$	3.81021	+	2.08163i	0.176885	+	0.0966370i
$465$	−15.2654			−0.707917
$466$	11.5241	+	23.0254i	0.533844	+	1.06663i
$467$	−15.0644	+	15.0644i	−0.697097	+	0.697097i	−0.963783	−	0.266687i	$-0.914071\pi$
$467$	−15.0644	+	15.0644i	−0.697097	+	0.697097i	0.266687	+	0.963783i	$0.414071\pi$
$468$	1.37771	−	0.197930i	0.0636849	−	0.00914932i
$469$	−2.42323	−	2.42323i	−0.111895	−	0.111895i
$470$	−8.59601	−	2.86155i	−0.396504	−	0.131994i
$471$		−	0.834081i		−	0.0384324i
$472$	21.3556	−	14.8222i	0.982973	−	0.682249i
$473$		−	22.2817i		−	1.02451i
$474$	−7.37751	+	22.1618i	−0.338860	+	1.01793i
$475$	−3.04559	−	3.04559i	−0.139741	−	0.139741i
$476$	42.1078	+	31.5288i	1.93001	+	1.44512i
$477$	0.143498	−	0.143498i	0.00657034	−	0.00657034i
$478$	4.30135	−	2.15281i	0.196739	−	0.0984670i
$479$	34.1433			1.56005			0.780024	−	0.625750i	$-0.215207\pi$
$479$	34.1433			1.56005			0.780024	+	0.625750i	$0.215207\pi$
$480$	5.72456	+	6.15201i	0.261289	+	0.280800i
$481$	−22.3211			−1.01775
$482$	26.5300	−	13.2782i	1.20841	−	0.604803i
$483$	41.2118	−	41.2118i	1.87520	−	1.87520i
$484$	−8.28833	−	6.20600i	−0.376742	−	0.282091i
$485$	−2.06099	−	2.06099i	−0.0935847	−	0.0935847i
$486$	−0.857331	+	2.57539i	−0.0388893	+	0.116822i
$487$			4.43918i			0.201159i	0.994929	+	0.100579i	$0.0320696\pi$
$487$			4.43918i			0.201159i	−0.994929	+	0.100579i	$0.967930\pi$
$488$	−8.44296	−	12.1645i	−0.382195	−	0.550660i
$489$			27.6348i			1.24969i
$490$	6.17505	+	2.05563i	0.278960	+	0.0928640i
$491$	10.2696	+	10.2696i	0.463459	+	0.463459i	0.899787	−	0.436329i	$-0.143722\pi$
$491$	10.2696	+	10.2696i	0.463459	+	0.463459i	−0.436329	+	0.899787i	$0.643722\pi$
$492$	10.4796	−	1.50556i	0.472456	−	0.0678757i
$493$	−5.70327	+	5.70327i	−0.256862	+	0.256862i
$494$	−2.38174	−	4.75877i	−0.107160	−	0.214107i
$495$	0.371488			0.0166971
$496$	11.5717	+	39.4418i	0.519584	+	1.77099i
$497$	27.8631			1.24983
$498$	−0.539909	−	1.07875i	−0.0241939	−	0.0483399i
$499$	−14.2313	+	14.2313i	−0.637081	+	0.637081i	−0.949834	−	0.312754i	$-0.898749\pi$
$499$	−14.2313	+	14.2313i	−0.637081	+	0.637081i	0.312754	+	0.949834i	$0.398749\pi$
$500$	−2.20340	−	15.3370i	−0.0985388	−	0.685891i
$501$	−4.79074	−	4.79074i	−0.214034	−	0.214034i
$502$	−0.00687243	−	0.00228779i	−0.000306731	−	0.000102109i
$503$		−	3.35106i		−	0.149416i	−0.997205	−	0.0747082i	$-0.976197\pi$
$503$		−	3.35106i		−	0.149416i	0.997205	−	0.0747082i	$-0.0238025\pi$
$504$	−0.329055	+	1.82210i	−0.0146573	+	0.0811629i
$505$			7.79297i			0.346783i
$506$	−9.94492	+	29.8742i	−0.442106	+	1.32807i
$507$	−1.46291	−	1.46291i	−0.0649702	−	0.0649702i
$508$	−3.91391	+	5.22716i	−0.173652	+	0.231918i
$509$	9.61837	−	9.61837i	0.426327	−	0.426327i	−0.461048	−	0.887375i	$-0.652527\pi$
$509$	9.61837	−	9.61837i	0.426327	−	0.426327i	0.887375	+	0.461048i	$0.152527\pi$
$510$	−13.9601	+	6.98698i	−0.618165	+	0.309389i
$511$	20.3217			0.898978
$512$	11.5558	−	19.4542i	0.510698	−	0.859760i
$513$	5.02386			0.221809
$514$	−20.5581	+	10.2892i	−0.906781	+	0.453839i
$515$	4.96799	−	4.96799i	0.218916	−	0.218916i
$516$	−19.7539	+	26.3820i	−0.869617	+	1.16140i
$517$	13.1318	+	13.1318i	0.577538	+	0.577538i
$518$	9.37876	−	28.1735i	0.412079	−	1.23787i
$519$		−	36.3526i		−	1.59570i
$520$	1.57443	−	8.71822i	0.0690434	−	0.382319i
$521$			27.7033i			1.21370i	0.794815	+	0.606852i	$0.207568\pi$
$521$			27.7033i			1.21370i	−0.794815	+	0.606852i	$0.792432\pi$
$522$	−0.269367	−	0.0896705i	−0.0117899	−	0.00392477i
$523$	7.27884	+	7.27884i	0.318281	+	0.318281i	0.848107	−	0.529825i	$-0.177743\pi$
$523$	7.27884	+	7.27884i	0.318281	+	0.318281i	−0.529825	+	0.848107i	$0.677743\pi$
$524$	1.19141	+	8.29298i	0.0520472	+	0.362280i
$525$	19.2386	−	19.2386i	0.839642	−	0.839642i
$526$	−14.7962	−	29.5632i	−0.645146	−	1.28902i
$527$	−76.3589			−3.32625
$528$	−4.84942	−	16.5291i	−0.211044	−	0.719337i
$529$	−62.1272			−2.70118
$530$	−0.578125	−	1.15511i	−0.0251121	−	0.0501746i
$531$	−1.20194	+	1.20194i	−0.0521596	+	0.0521596i
$532$	7.00721	−	1.00669i	0.303801	−	0.0436457i
$533$	−7.89232	−	7.89232i	−0.341855	−	0.341855i
$534$	−19.2246	−	6.39975i	−0.831930	−	0.276944i
$535$		−	14.9469i		−	0.646210i
$536$	−1.56142	−	2.24967i	−0.0674433	−	0.0971711i
$537$			26.2266i			1.13176i
$538$	−1.69500	+	5.09172i	−0.0730766	+	0.219520i
$539$	−9.43342	−	9.43342i	−0.406326	−	0.406326i
$540$	6.69494	+	5.01292i	0.288104	+	0.215722i
$541$	−12.6156	+	12.6156i	−0.542387	+	0.542387i	−0.924228	−	0.381841i	$-0.875290\pi$
$541$	−12.6156	+	12.6156i	−0.542387	+	0.542387i	0.381841	+	0.924228i	$0.375290\pi$
$542$	−6.23802	+	3.12210i	−0.267946	+	0.134106i
$543$	−12.1930			−0.523253
$544$	28.6347	+	30.7729i	1.22770	+	1.31938i
$545$	−9.38686			−0.402089
$546$	30.0605	−	15.0452i	1.28647	−	0.643873i
$547$	−30.3878	+	30.3878i	−1.29929	+	1.29929i	−0.370430	+	0.928860i	$0.620790\pi$
$547$	−30.3878	+	30.3878i	−1.29929	+	1.29929i	−0.928860	+	0.370430i	$0.879210\pi$
$548$	−2.50374	−	1.87471i	−0.106955	−	0.0800837i
$549$	0.684641	+	0.684641i	0.0292198	+	0.0292198i
$550$	−4.64252	+	13.9460i	−0.197958	+	0.594657i
$551$			1.08544i			0.0462413i
$552$	38.2601	−	26.5551i	1.62846	−	1.13026i
$553$			32.7576i			1.39299i
$554$	−12.6257	−	4.20301i	−0.536415	−	0.178569i
$555$	6.23107	+	6.23107i	0.264494	+	0.264494i
$556$	21.1936	−	3.04479i	0.898809	−	0.129128i
$557$	1.72135	−	1.72135i	0.0729360	−	0.0729360i	−0.669698	−	0.742634i	$-0.733576\pi$
$557$	1.72135	−	1.72135i	0.0729360	−	0.0729360i	0.742634	+	0.669698i	$0.233576\pi$
$558$	−1.20294	−	2.40351i	−0.0509247	−	0.101749i
$559$	34.7456			1.46958
$560$	10.3425	+	5.65040i	0.437051	+	0.238773i
$561$	32.0002			1.35105
$562$	−4.86635	−	9.72306i	−0.205274	−	0.410143i
$563$	12.4526	−	12.4526i	0.524815	−	0.524815i	−0.394207	−	0.919022i	$-0.628981\pi$
$563$	12.4526	−	12.4526i	0.524815	−	0.524815i	0.919022	+	0.394207i	$0.128981\pi$
$564$	−3.90633	−	27.1905i	−0.164486	−	1.14493i
$565$	3.62468	+	3.62468i	0.152491	+	0.152491i
$566$	26.5774	+	8.84744i	1.11713	+	0.371886i
$567$			33.6990i			1.41523i
$568$	21.9106	+	3.95685i	0.919347	+	0.166026i
$569$		−	3.19682i		−	0.134018i	−0.997752	−	0.0670088i	$-0.978654\pi$
$569$		−	3.19682i		−	0.134018i	0.997752	−	0.0670088i	$-0.0213456\pi$
$570$	−0.663561	+	1.99331i	−0.0277935	+	0.0834907i
$571$	24.2520	+	24.2520i	1.01491	+	1.01491i	0.999887	+	0.0150261i	$0.00478313\pi$
$571$	24.2520	+	24.2520i	1.01491	+	1.01491i	0.0150261	+	0.999887i	$0.495217\pi$
$572$	−10.8846	+	14.5367i	−0.455106	+	0.607811i
$573$	−14.7104	+	14.7104i	−0.614534	+	0.614534i
$574$	13.2778	−	6.64546i	0.554203	−	0.277376i
$575$	−39.7393			−1.65724
$576$	−0.517516	+	1.38611i	−0.0215632	+	0.0577546i
$577$	31.0902			1.29430			0.647152	−	0.762361i	$-0.275960\pi$
$577$	31.0902			1.29430			0.647152	+	0.762361i	$0.275960\pi$
$578$	−48.3306	+	24.1892i	−2.01029	+	1.00614i
$579$	21.7479	−	21.7479i	0.903811	−	0.903811i
$580$	−1.08308	+	1.44649i	−0.0449723	+	0.0600621i
$581$	−1.19628	−	1.19628i	−0.0496300	−	0.0496300i
$582$	2.79132	−	8.38502i	0.115704	−	0.347570i
$583$			2.64780i			0.109661i
$584$	15.9803	+	2.88589i	0.661268	+	0.119419i
$585$			0.579291i			0.0239507i
$586$	−5.56354	−	1.85207i	−0.229828	−	0.0765082i
$587$	−13.5074	−	13.5074i	−0.557509	−	0.557509i	0.371089	−	0.928597i	$-0.378985\pi$
$587$	−13.5074	−	13.5074i	−0.557509	−	0.557509i	−0.928597	+	0.371089i	$0.878985\pi$
$588$	2.80616	+	19.5326i	0.115724	+	0.805512i
$589$	−7.26627	+	7.26627i	−0.299401	+	0.299401i
$590$	4.84236	+	9.67513i	0.199357	+	0.398319i
$591$	−4.63152			−0.190515
$592$	11.3761	−	20.8228i	0.467554	−	0.855811i
$593$	−19.4673			−0.799427			−0.399714	−	0.916640i	$-0.630890\pi$
$593$	−19.4673			−0.799427			−0.399714	+	0.916640i	$0.630890\pi$
$594$	−7.67326	−	15.3313i	−0.314838	−	0.629052i
$595$	−15.4811	+	15.4811i	−0.634662	+	0.634662i
$596$	−37.1988	+	5.34419i	−1.52372	+	0.218907i
$597$	−14.2354	−	14.2354i	−0.582614	−	0.582614i
$598$	−46.5852	−	15.5079i	−1.90501	−	0.634166i
$599$		−	21.9404i		−	0.896462i	−0.893918	−	0.448231i	$-0.852054\pi$
$599$		−	21.9404i		−	0.896462i	0.893918	−	0.448231i	$-0.147946\pi$
$600$	17.8607	−	12.3965i	0.729159	−	0.506085i
$601$			5.24762i			0.214055i	0.994256	+	0.107027i	$0.0341332\pi$
$601$			5.24762i			0.214055i	−0.994256	+	0.107027i	$0.965867\pi$
$602$	−14.5992	+	43.8556i	−0.595020	+	1.78742i
$603$	0.126616	+	0.126616i	0.00515621	+	0.00515621i
$604$	−0.299854	−	0.224520i	−0.0122009	−	0.00913557i
$605$	3.04723	−	3.04723i	0.123888	−	0.123888i
$606$	−21.1299	+	10.5754i	−0.858342	+	0.429596i
$607$	5.94622			0.241349			0.120675	−	0.992692i	$-0.461494\pi$
$607$	5.94622			0.241349			0.120675	+	0.992692i	$0.461494\pi$
$608$	5.65319	+	0.203468i	0.229267	+	0.00825172i
$609$	−6.85659			−0.277843
$610$	5.51110	−	2.75828i	0.223138	−	0.111679i
$611$	−20.4775	+	20.4775i	−0.828432	+	0.828432i
$612$	−2.20017	−	1.64741i	−0.0889366	−	0.0665925i
$613$	16.4459	+	16.4459i	0.664242	+	0.664242i	0.956377	−	0.292135i	$-0.0943657\pi$
$613$	16.4459	+	16.4459i	0.664242	+	0.664242i	−0.292135	+	0.956377i	$0.594366\pi$
$614$	−5.71723	+	17.1743i	−0.230728	+	0.693100i
$615$			4.40638i			0.177682i
$616$	−13.7747	−	19.8463i	−0.554998	−	0.799632i
$617$		−	24.5030i		−	0.986455i	−0.869900	−	0.493228i	$-0.835817\pi$
$617$		−	24.5030i		−	0.986455i	0.869900	−	0.493228i	$-0.164183\pi$
$618$	20.2120	+	6.72844i	0.813046	+	0.270657i
$619$	19.6506	+	19.6506i	0.789825	+	0.789825i	0.981465	−	0.191640i	$-0.0613806\pi$
$619$	19.6506	+	19.6506i	0.789825	+	0.789825i	−0.191640	+	0.981465i	$0.561381\pi$
$620$	−16.9337	+	2.43279i	−0.680073	+	0.0977030i
$621$	32.7761	−	32.7761i	1.31526	−	1.31526i
$622$	−1.15097	−	2.29966i	−0.0461496	−	0.0922078i
$623$	−28.4161			−1.13847
$624$	25.7752	−	7.56208i	1.03183	−	0.302726i
$625$	−15.0868			−0.603472
$626$	−15.3305	−	30.6307i	−0.612730	−	1.22425i
$627$	3.04512	−	3.04512i	0.121610	−	0.121610i
$628$	−0.132924	−	0.925232i	−0.00530424	−	0.0369208i
$629$	31.1684	+	31.1684i	1.24276	+	1.24276i
$630$	−0.731175	−	0.243403i	−0.0291307	−	0.00969742i
$631$		−	30.8707i		−	1.22894i	−0.788939	−	0.614471i	$-0.789369\pi$
$631$		−	30.8707i		−	1.22894i	0.788939	−	0.614471i	$-0.210631\pi$
$632$	−4.65192	+	25.7594i	−0.185044	+	1.02466i
$633$		−	17.1366i		−	0.681118i
$634$	−3.10148	+	9.31675i	−0.123176	+	0.370015i
$635$	−1.92178	−	1.92178i	−0.0762637	−	0.0762637i
$636$	2.34741	−	3.13506i	0.0930811	−	0.124313i
$637$	14.7103	−	14.7103i	0.582843	−	0.582843i
$638$	3.31244	−	1.65786i	0.131141	−	0.0656353i
$639$	−1.45587			−0.0575933
$640$	7.33058	+	5.91203i	0.289767	+	0.233694i
$641$	−11.1810			−0.441623			−0.220812	−	0.975316i	$-0.570871\pi$
$641$	−11.1810			−0.441623			−0.220812	+	0.975316i	$0.570871\pi$
$642$	40.5270	−	20.2836i	1.59947	−	0.800528i
$643$	20.6052	−	20.6052i	0.812590	−	0.812590i	−0.172431	−	0.985022i	$-0.555162\pi$
$643$	20.6052	−	20.6052i	0.812590	−	0.812590i	0.985022	+	0.172431i	$0.0551623\pi$
$644$	39.1478	−	52.2834i	1.54264	−	2.06025i
$645$	−9.69944	−	9.69944i	−0.381915	−	0.381915i
$646$	−3.31919	+	9.97073i	−0.130592	+	0.392293i
$647$		−	40.4401i		−	1.58987i	−0.606698	−	0.794933i	$-0.707506\pi$
$647$		−	40.4401i		−	1.58987i	0.606698	−	0.794933i	$-0.292494\pi$
$648$	−4.78562	+	26.4998i	−0.187997	+	1.04101i
$649$		−	22.1779i		−	0.870558i
$650$	−21.7470	−	7.23945i	−0.852989	−	0.283954i
$651$	−45.9001	−	45.9001i	−1.79897	−	1.79897i
$652$	4.40404	+	30.6548i	0.172476	+	1.20054i
$653$	8.96334	−	8.96334i	0.350763	−	0.350763i	−0.509631	−	0.860393i	$-0.670218\pi$
$653$	8.96334	−	8.96334i	0.350763	−	0.350763i	0.860393	+	0.509631i	$0.170218\pi$
$654$	−12.7384	−	25.4516i	−0.498110	−	0.995235i
$655$	−3.48697			−0.136247
$656$	11.3849	−	3.34018i	0.444506	−	0.130412i
$657$	−1.06183			−0.0414257
$658$	−17.2424	−	34.4507i	−0.672178	−	1.34303i
$659$	−0.449023	+	0.449023i	−0.0174915	+	0.0174915i	−0.715798	−	0.698307i	$-0.753937\pi$
$659$	−0.449023	+	0.449023i	−0.0174915	+	0.0174915i	0.698307	+	0.715798i	$0.253937\pi$
$660$	7.09650	−	1.01952i	0.276231	−	0.0396849i
$661$	−21.4914	−	21.4914i	−0.835919	−	0.835919i	0.152400	−	0.988319i	$-0.451300\pi$
$661$	−21.4914	−	21.4914i	−0.835919	−	0.835919i	−0.988319	+	0.152400i	$0.951300\pi$
$662$	−24.8475	−	8.27157i	−0.965725	−	0.321484i
$663$			49.9005i			1.93797i
$664$	−0.770828	−	1.11060i	−0.0299139	−	0.0430995i
$665$			2.94634i			0.114254i
$666$	−0.490049	+	1.47209i	−0.0189890	+	0.0570423i
$667$	7.08149	+	7.08149i	0.274197	+	0.274197i
$668$	−6.07777	−	4.55081i	−0.235156	−	0.176076i
$669$	17.3136	−	17.3136i	0.669382	−	0.669382i
$670$	1.01921	−	0.510110i	0.0393756	−	0.0197073i
$671$	−12.6329			−0.487686
$672$	−1.28528	+	35.7105i	−0.0495809	+	1.37756i
$673$	−18.0433			−0.695517			−0.347758	−	0.937584i	$-0.613057\pi$
$673$	−18.0433			−0.695517			−0.347758	+	0.937584i	$0.613057\pi$
$674$	41.1296	−	20.5852i	1.58425	−	0.792911i
$675$	15.3006	−	15.3006i	0.588921	−	0.588921i
$676$	−1.85592	−	1.38965i	−0.0713817	−	0.0534480i
$677$	10.4319	+	10.4319i	0.400931	+	0.400931i	0.878561	−	0.477630i	$-0.158504\pi$
$677$	10.4319	+	10.4319i	0.400931	+	0.400931i	−0.477630	+	0.878561i	$0.658504\pi$
$678$	−4.90911	+	14.7468i	−0.188533	+	0.566348i
$679$		−	12.3940i		−	0.475637i
$680$	−14.3723	+	9.97531i	−0.551151	+	0.382536i
$681$		−	14.6514i		−	0.561443i
$682$	33.2727	+	11.0763i	1.27408	+	0.424132i
$683$	−7.46424	−	7.46424i	−0.285611	−	0.285611i	0.549731	−	0.835342i	$-0.314730\pi$
$683$	−7.46424	−	7.46424i	−0.285611	−	0.285611i	−0.835342	+	0.549731i	$0.814730\pi$
$684$	−0.366133	+	0.0526007i	−0.0139994	+	0.00201124i
$685$	0.920510	−	0.920510i	0.0351709	−	0.0351709i
$686$	−3.29651	−	6.58649i	−0.125861	−	0.251473i
$687$	−33.5444			−1.27980
$688$	−17.7083	+	32.4133i	−0.675122	+	1.23574i
$689$	−4.12892			−0.157300
$690$	8.67541	+	17.3337i	0.330267	+	0.659881i
$691$	−11.4475	+	11.4475i	−0.435484	+	0.435484i	−0.890489	−	0.455005i	$-0.849637\pi$
$691$	−11.4475	+	11.4475i	−0.435484	+	0.435484i	0.455005	+	0.890489i	$0.349637\pi$
$692$	−5.79336	−	40.3253i	−0.220231	−	1.53294i
$693$	1.11699	+	1.11699i	0.0424310	+	0.0424310i
$694$	−27.0086	−	8.99098i	−1.02523	−	0.341293i
$695$			8.91132i			0.338026i
$696$	−5.39179	−	0.973709i	−0.204375	−	0.0369083i
$697$			22.0411i			0.834866i
$698$	3.37515	−	10.1388i	0.127751	−	0.383760i
$699$	−22.9757	−	22.9757i	−0.869022	−	0.869022i
$700$	18.2751	−	24.4071i	0.690734	−	0.922500i
$701$	−14.4073	+	14.4073i	−0.544157	+	0.544157i	−0.924745	−	0.380588i	$-0.875722\pi$
$701$	−14.4073	+	14.4073i	−0.544157	+	0.544157i	0.380588	+	0.924745i	$0.375722\pi$
$702$	23.9074	−	11.9655i	0.902326	−	0.451610i
$703$	5.93192			0.223727
$704$	−8.01355	−	17.5626i	−0.302022	−	0.661917i
$705$	11.4328			0.430586
$706$	−7.62361	+	3.81558i	−0.286918	+	0.143601i
$707$	−23.4319	+	23.4319i	−0.881249	+	0.881249i
$708$	−19.6619	+	26.2591i	−0.738939	+	0.986879i
$709$	−30.8642	−	30.8642i	−1.15913	−	1.15913i	−0.984663	−	0.174466i	$-0.944180\pi$
$709$	−30.8642	−	30.8642i	−1.15913	−	1.15913i	−0.174466	−	0.984663i	$-0.555820\pi$
$710$	−2.92690	+	8.79229i	−0.109844	+	0.329969i
$711$		−	1.71161i		−	0.0641905i
$712$	−22.3455	−	4.03539i	−0.837431	−	0.151233i
$713$			94.8114i			3.55072i
$714$	−62.9839	−	20.9669i	−2.35711	−	0.784667i
$715$	−5.34447	−	5.34447i	−0.199872	−	0.199872i
$716$	4.17963	+	29.0928i	0.156200	+	1.08725i
$717$	−4.29207	+	4.29207i	−0.160290	+	0.160290i
$718$	−8.28835	−	16.5603i	−0.309319	−	0.618025i
$719$	51.2709			1.91208			0.956041	−	0.293234i	$-0.0947315\pi$
$719$	51.2709			1.91208			0.956041	+	0.293234i	$0.0947315\pi$
$720$	−0.540405	−	0.295239i	−0.0201397	−	0.0110029i
$721$	29.8756			1.11262
$722$	0.632956	+	1.26466i	0.0235562	+	0.0470658i
$723$	−26.4728	+	26.4728i	−0.984534	+	0.984534i
$724$	−13.5255	+	1.94315i	−0.502673	+	0.0722167i
$725$	3.30580	+	3.30580i	0.122774	+	0.122774i
$726$	12.3975	+	4.12704i	0.460114	+	0.153169i
$727$		−	4.31251i		−	0.159942i	−0.996797	−	0.0799710i	$-0.974517\pi$
$727$		−	4.31251i		−	0.159942i	0.996797	−	0.0799710i	$-0.0254828\pi$
$728$	30.9480	−	21.4800i	1.14701	−	0.796101i
$729$			25.1366i			0.930984i
$730$	−2.13470	+	6.41258i	−0.0790089	+	0.237340i
$731$	−48.5175	−	48.5175i	−1.79448	−	1.79448i
$732$	14.9576	+	11.1997i	0.552849	+	0.413953i
$733$	−1.05147	+	1.05147i	−0.0388368	+	0.0388368i	−0.726258	−	0.687422i	$-0.758742\pi$
$733$	−1.05147	+	1.05147i	−0.0388368	+	0.0388368i	0.687422	+	0.726258i	$0.258742\pi$
$734$	3.68411	−	1.84388i	0.135983	−	0.0680588i
$735$	−8.21292			−0.302938
$736$	38.2093	−	35.5544i	1.40841	−	1.31055i
$737$	−2.33629			−0.0860585
$738$	−0.693775	+	0.347231i	−0.0255382	+	0.0127818i
$739$	−8.28452	+	8.28452i	−0.304751	+	0.304751i	−0.842869	−	0.538118i	$-0.819135\pi$
$739$	−8.28452	+	8.28452i	−0.304751	+	0.304751i	0.538118	+	0.842869i	$0.319135\pi$
$740$	7.90504	+	5.91900i	0.290595	+	0.217587i
$741$	4.74850	+	4.74850i	0.174440	+	0.174440i
$742$	1.73487	−	5.21149i	0.0636890	−	0.191320i
$743$		−	7.16003i		−	0.262676i	−0.991338	−	0.131338i	$-0.958073\pi$
$743$		−	7.16003i		−	0.262676i	0.991338	−	0.131338i	$-0.0419273\pi$
$744$	−29.5760	−	42.6126i	−1.08431	−	1.56225i
$745$		−	15.6411i		−	0.573045i
$746$	−30.8930	−	10.2841i	−1.13107	−	0.376527i
$747$	0.0625066	+	0.0625066i	0.00228700	+	0.00228700i
$748$	35.4973	−	5.09974i	1.29791	−	0.186465i
$749$	44.9423	−	44.9423i	1.64216	−	1.64216i
$750$	8.75127	+	17.4852i	0.319551	+	0.638470i
$751$	7.62147			0.278111			0.139056	−	0.990285i	$-0.455593\pi$
$751$	7.62147			0.278111			0.139056	+	0.990285i	$0.455593\pi$
$752$	−8.66647	−	29.5394i	−0.316034	−	1.07719i
$753$	0.00914045			0.000333097
$754$	2.58523	+	5.16535i	0.0941487	+	0.188111i
$755$	0.110242	−	0.110242i	0.00401213	−	0.00401213i
$756$	5.05749	+	35.2033i	0.183939	+	1.28033i
$757$	−3.25060	−	3.25060i	−0.118145	−	0.118145i	0.645562	−	0.763707i	$-0.276623\pi$
$757$	−3.25060	−	3.25060i	−0.118145	−	0.118145i	−0.763707	+	0.645562i	$0.776623\pi$
$758$	11.2633	+	3.74949i	0.409103	+	0.136188i
$759$		−	39.7332i		−	1.44222i
$760$	−0.418411	+	2.31690i	−0.0151774	+	0.0840428i
$761$			4.35555i			0.157889i	0.996879	+	0.0789443i	$0.0251549\pi$
$761$			4.35555i			0.157889i	−0.996879	+	0.0789443i	$0.974845\pi$
$762$	2.60278	−	7.81867i	0.0942889	−	0.283241i
$763$	−28.2245	−	28.2245i	−1.02179	−	1.02179i
$764$	−13.9736	+	18.6623i	−0.505548	+	0.675178i
$765$	0.808900	−	0.808900i	0.0292458	−	0.0292458i
$766$	4.83784	−	2.42132i	0.174798	−	0.0874857i
$767$	34.5838			1.24875
$768$	−6.08198	+	27.8990i	−0.219464	+	1.00672i
$769$	−24.5135			−0.883979			−0.441990	−	0.897020i	$-0.645727\pi$
$769$	−24.5135			−0.883979			−0.441990	+	0.897020i	$0.645727\pi$
$770$	8.99135	−	4.50013i	0.324026	−	0.162173i
$771$	20.5138	−	20.5138i	0.738786	−	0.738786i
$772$	20.6587	−	27.5904i	0.743523	−	0.993002i
$773$	13.9100	+	13.9100i	0.500307	+	0.500307i	0.911533	−	0.411226i	$-0.134899\pi$
$773$	13.9100	+	13.9100i	0.500307	+	0.500307i	−0.411226	+	0.911533i	$0.634899\pi$
$774$	0.762822	−	2.29149i	0.0274191	−	0.0823660i
$775$			44.2601i			1.58987i
$776$	1.76008	−	9.74621i	0.0631831	−	0.349868i
$777$			37.4712i			1.34427i
$778$	−35.8521	−	11.9349i	−1.28536	−	0.427888i
$779$	2.09742	+	2.09742i	0.0751477	+	0.0751477i
$780$	1.58982	+	11.0661i	0.0569248	+	0.396231i
$781$	13.4317	−	13.4317i	0.480624	−	0.480624i
$782$	43.3952	+	86.7045i	1.55181	+	3.10055i
$783$	−5.45310			−0.194878
$784$	6.22566	+	21.2200i	0.222345	+	0.757858i
$785$	0.389035			0.0138852
$786$	−4.73197	−	9.45457i	−0.168784	−	0.337233i
$787$	−3.45067	+	3.45067i	−0.123003	+	0.123003i	−0.765929	−	0.642926i	$-0.777720\pi$
$787$	−3.45067	+	3.45067i	−0.123003	+	0.123003i	0.642926	+	0.765929i	$0.277720\pi$
$788$	−5.13767	+	0.738106i	−0.183022	+	0.0262939i
$789$	29.4994	+	29.4994i	1.05021	+	1.05021i
$790$	−10.3368	−	3.44104i	−0.367766	−	0.122427i
$791$			21.7974i			0.775027i
$792$	0.719740	+	1.03699i	0.0255748	+	0.0368478i
$793$		−	19.6994i		−	0.699547i
$794$	3.79491	−	11.3998i	0.134676	−	0.404563i
$795$	1.15261	+	1.15261i	0.0408790	+	0.0408790i
$796$	−18.0597	−	13.5224i	−0.640108	−	0.479289i
$797$	−14.6402	+	14.6402i	−0.518582	+	0.518582i	−0.917142	−	0.398560i	$-0.869510\pi$
$797$	−14.6402	+	14.6402i	−0.518582	+	0.518582i	0.398560	+	0.917142i	$0.369510\pi$
$798$	−7.98870	+	3.99831i	−0.282797	+	0.141539i
$799$	57.1881			2.02317
$800$	17.8370	−	16.5976i	0.630633	−	0.586815i
$801$	1.48477			0.0524616
$802$	−31.1447	+	15.5878i	−1.09976	+	0.550423i
$803$	9.79628	−	9.79628i	0.345703	−	0.345703i
$804$	2.76623	+	2.07125i	0.0975573	+	0.0730473i
$805$	19.2221	+	19.2221i	0.677491	+	0.677491i
$806$	−17.2721	+	51.8848i	−0.608384	+	1.82756i
$807$		−	6.77208i		−	0.238388i
$808$	−21.7537	+	15.0985i	−0.765291	+	0.531163i
$809$			14.1372i			0.497038i	0.968627	+	0.248519i	$0.0799439\pi$
$809$			14.1372i			0.497038i	−0.968627	+	0.248519i	$0.920056\pi$
$810$	−10.6338	−	3.53994i	−0.373635	−	0.124381i
$811$	33.9808	+	33.9808i	1.19323	+	1.19323i	0.976156	+	0.217072i	$0.0696507\pi$
$811$	33.9808	+	33.9808i	1.19323	+	1.19323i	0.217072	+	0.976156i	$0.430349\pi$
$812$	−7.60590	+	1.09271i	−0.266915	+	0.0383465i
$813$	6.22456	−	6.22456i	0.218305	−	0.218305i
$814$	−9.06020	−	18.1025i	−0.317560	−	0.634491i
$815$	−12.8895			−0.451500
$816$	−46.5509	−	25.4321i	−1.62961	−	0.890300i
$817$	−9.23378			−0.323049
$818$	19.9964	+	39.9531i	0.699156	+	1.39693i
$819$	−1.74181	+	1.74181i	−0.0608639	+	0.0608639i
$820$	0.702226	+	4.88792i	0.0245228	+	0.170694i
$821$	−29.5655	−	29.5655i	−1.03184	−	1.03184i	−0.999476	−	0.0323686i	$-0.989695\pi$
$821$	−29.5655	−	29.5655i	−1.03184	−	1.03184i	−0.0323686	−	0.999476i	$-0.510305\pi$
$822$	3.74504	+	1.24670i	0.130623	+	0.0434837i
$823$		−	13.3895i		−	0.466728i	−0.972389	−	0.233364i	$-0.925027\pi$
$823$		−	13.3895i		−	0.466728i	0.972389	−	0.233364i	$-0.0749733\pi$
$824$	23.4931	+	4.24265i	0.818422	+	0.147800i
$825$		−	18.5484i		−	0.645771i
$826$	−14.5312	+	43.6513i	−0.505605	+	1.51882i
$827$	12.0100	+	12.0100i	0.417628	+	0.417628i	0.884385	−	0.466758i	$-0.154578\pi$
$827$	12.0100	+	12.0100i	0.417628	+	0.417628i	−0.466758	+	0.884385i	$0.654578\pi$
$828$	−2.04551	+	2.73185i	−0.0710864	+	0.0949384i
$829$	−29.2025	+	29.2025i	−1.01425	+	1.01425i	−0.0143492	+	0.999897i	$0.504568\pi$
$829$	−29.2025	+	29.2025i	−1.01425	+	1.01425i	−0.999897	+	0.0143492i	$0.995432\pi$
$830$	0.503154	−	0.251826i	0.0174647	−	0.00874101i
$831$	16.7924			0.582522
$832$	27.3868	−	12.4962i	0.949468	−	0.433227i
$833$	−41.0818			−1.42340
$834$	−24.1622	+	12.0930i	−0.836667	+	0.418748i
$835$	2.23451	−	2.23451i	0.0773284	−	0.0773284i
$836$	2.89261	−	3.86319i	0.100043	−	0.133611i
$837$	−36.5047	−	36.5047i	−1.26179	−	1.26179i
$838$	15.0569	−	45.2303i	0.520131	−	1.56245i
$839$		−	19.0038i		−	0.656083i	−0.944663	−	0.328042i	$-0.893611\pi$
$839$		−	19.0038i		−	0.656083i	0.944663	−	0.328042i	$-0.106389\pi$
$840$	−14.6356	−	2.64305i	−0.504975	−	0.0911940i
$841$			27.8218i			0.959373i
$842$	38.0450	+	12.6649i	1.31112	+	0.436462i
$843$	9.70209	+	9.70209i	0.334158	+	0.334158i
$844$	−2.73099	−	19.0093i	−0.0940045	−	0.654329i
$845$	0.682336	−	0.682336i	0.0234731	−	0.0234731i
$846$	0.900930	+	1.80008i	0.0309746	+	0.0618879i
$847$	18.3249			0.629650
$848$	2.10433	−	3.85177i	0.0722629	−	0.132270i
$849$	−35.3484			−1.21316
$850$	20.2579	+	40.4756i	0.694839	+	1.38830i
$851$	38.7003	−	38.7003i	1.32663	−	1.32663i
$852$	−27.8114	+	3.99553i	−0.952802	+	0.136885i
$853$	−10.6197	−	10.6197i	−0.363612	−	0.363612i	0.501529	−	0.865141i	$-0.332771\pi$
$853$	−10.6197	−	10.6197i	−0.363612	−	0.363612i	−0.865141	+	0.501529i	$0.832771\pi$
$854$	24.8644	+	8.27719i	0.850842	+	0.283240i
$855$		−	0.153949i		−	0.00526494i
$856$	41.7234	−	28.9588i	1.42608	−	0.989793i
$857$			22.3653i			0.763985i	0.924165	+	0.381992i	$0.124762\pi$
$857$			22.3653i			0.763985i	−0.924165	+	0.381992i	$0.875238\pi$
$858$	7.23833	−	21.7437i	0.247113	−	0.742317i
$859$	11.8735	+	11.8735i	0.405119	+	0.405119i	0.880033	−	0.474913i	$-0.157521\pi$
$859$	11.8735	+	11.8735i	0.405119	+	0.405119i	−0.474913	+	0.880033i	$0.657521\pi$
$860$	−12.3052	−	9.21368i	−0.419604	−	0.314184i
$861$	−13.2491	+	13.2491i	−0.451529	+	0.451529i
$862$	19.4778	−	9.74856i	0.663417	−	0.332037i
$863$	0.216392			0.00736608			0.00368304	−	0.999993i	$-0.498828\pi$
$863$	0.216392			0.00736608			0.00368304	+	0.999993i	$0.498828\pi$
$864$	−1.02220	+	28.4009i	−0.0347758	+	0.966217i
$865$	16.9557			0.576511
$866$	−19.0500	+	9.53442i	−0.647345	+	0.323993i
$867$	48.2263	−	48.2263i	1.63785	−	1.63785i
$868$	−58.2312	−	43.6014i	−1.97650	−	1.47993i
$869$	15.7912	+	15.7912i	0.535678	+	0.535678i
$870$	0.720255	−	2.16362i	0.0244189	−	0.0733537i
$871$		−	3.64317i		−	0.123444i
$872$	−18.1866	−	26.2029i	−0.615876	−	0.887344i
$873$			0.647597i			0.0219178i
$874$	12.3802	+	4.12129i	0.418767	+	0.139405i
$875$	19.3902	+	19.3902i	0.655509	+	0.655509i
$876$	−20.2840	+	2.91411i	−0.685331	+	0.0984585i
$877$	0.586134	−	0.586134i	0.0197923	−	0.0197923i	−0.697141	−	0.716934i	$-0.745545\pi$
$877$	0.586134	−	0.586134i	0.0197923	−	0.0197923i	0.716934	+	0.697141i	$0.245545\pi$
$878$	14.2589	+	28.4896i	0.481215	+	0.961479i
$879$	7.39961			0.249583
$880$	7.70956	−	2.26188i	0.259889	−	0.0762480i
$881$	12.1356			0.408858			0.204429	−	0.978881i	$-0.434466\pi$
$881$	12.1356			0.408858			0.204429	+	0.978881i	$0.434466\pi$
$882$	−0.647194	−	1.29311i	−0.0217922	−	0.0435412i
$883$	−36.1826	+	36.1826i	−1.21764	+	1.21764i	−0.249187	+	0.968455i	$0.580164\pi$
$883$	−36.1826	+	36.1826i	−1.21764	+	1.21764i	−0.968455	+	0.249187i	$0.919836\pi$
$884$	7.95243	+	55.3538i	0.267469	+	1.86175i
$885$	−9.65426	−	9.65426i	−0.324524	−	0.324524i
$886$	−22.1393	−	7.37004i	−0.743786	−	0.247601i
$887$			18.1329i			0.608843i	0.952537	+	0.304422i	$0.0984632\pi$
$887$			18.1329i			0.608843i	−0.952537	+	0.304422i	$0.901537\pi$
$888$	−5.32131	+	29.4661i	−0.178572	+	0.988817i
$889$		−	11.5569i		−	0.387605i
$890$	2.98499	−	8.96680i	0.100057	−	0.300568i
$891$	16.2450	+	16.2450i	0.544227	+	0.544227i
$892$	16.4465	−	21.9649i	0.550669	−	0.735438i
$893$	5.44198	−	5.44198i	0.182109	−	0.182109i
$894$	42.4093	−	21.2256i	1.41838	−	0.709891i
$895$	−12.2327			−0.408894
$896$	4.26529	+	39.8179i	0.142494	+	1.33022i
$897$	61.9592			2.06876
$898$	33.2388	−	16.6359i	1.10919	−	0.555147i
$899$	7.88710	−	7.88710i	0.263049	−	0.263049i
$900$	−0.954891	+	1.27529i	−0.0318297	+	0.0425097i
$901$	5.76548	+	5.76548i	0.192076	+	0.192076i
$902$	3.19718	−	9.60421i	0.106454	−	0.319785i
$903$		−	58.3287i		−	1.94106i
$904$	−3.09546	+	17.1407i	−0.102954	+	0.570093i
$905$		−	5.68711i		−	0.189046i
$906$	0.448515	+	0.149308i	0.0149009	+	0.00496041i
$907$	−12.7479	−	12.7479i	−0.423288	−	0.423288i	0.463046	−	0.886334i	$-0.346757\pi$
$907$	−12.7479	−	12.7479i	−0.423288	−	0.423288i	−0.886334	+	0.463046i	$0.846757\pi$
$908$	−2.33493	−	16.2526i	−0.0774874	−	0.539360i
$909$	1.22434	−	1.22434i	0.0406088	−	0.0406088i
$910$	7.01741	+	14.0209i	0.232625	+	0.464789i
$911$	7.48358			0.247942			0.123971	−	0.992286i	$-0.460437\pi$
$911$	7.48358			0.247942			0.123971	+	0.992286i	$0.460437\pi$
$912$	−6.84985	+	2.00965i	−0.226821	+	0.0665463i
$913$	−1.15336			−0.0381706
$914$	−6.16629	−	12.3204i	−0.203963	−	0.407522i
$915$	−5.49921	+	5.49921i	−0.181798	+	0.181798i
$916$	−37.2103	+	5.34584i	−1.22946	+	0.176631i
$917$	−10.4846	−	10.4846i	−0.346233	−	0.346233i
$918$	−50.0916	−	16.6752i	−1.65327	−	0.550362i
$919$			18.2640i			0.602472i	0.953550	+	0.301236i	$0.0973993\pi$
$919$			18.2640i			0.602472i	−0.953550	+	0.301236i	$0.902601\pi$
$920$	12.3859	+	17.8454i	0.408351	+	0.588345i
$921$		−	22.8422i		−	0.752676i
$922$	16.7866	−	50.4262i	0.552836	−	1.66070i
$923$	20.9451	+	20.9451i	0.689417	+	0.689417i
$924$	24.4033	+	18.2723i	0.802810	+	0.601114i
$925$	18.0662	−	18.0662i	0.594013	−	0.594013i
$926$	12.3555	−	6.18386i	0.406026	−	0.203214i
$927$	−1.56102			−0.0512708
$928$	−6.13620	−	0.220852i	−0.201431	−	0.00724983i
$929$	39.3903			1.29236			0.646178	−	0.763187i	$-0.276367\pi$
$929$	39.3903			1.29236			0.646178	+	0.763187i	$0.276367\pi$
$930$	19.3056	−	9.66234i	0.633054	−	0.316841i
$931$	−3.90932	+	3.90932i	−0.128123	+	0.128123i
$932$	−29.1482	−	21.8251i	−0.954780	−	0.714904i
$933$	2.29469	+	2.29469i	0.0751249	+	0.0751249i
$934$	9.51623	−	28.5864i	0.311381	−	0.935377i
$935$			14.9256i			0.488121i
$936$	−1.61706	+	1.12235i	−0.0528553	+	0.0366851i
$937$			31.2614i			1.02127i	0.859799	+	0.510633i	$0.170589\pi$
$937$			31.2614i			1.02127i	−0.859799	+	0.510633i	$0.829411\pi$
$938$	4.59837	+	1.53077i	0.150142	+	0.0499813i
$939$	30.5646	+	30.5646i	0.997438	+	0.997438i
$940$	12.6823	−	1.82200i	0.413650	−	0.0594272i
$941$	34.6337	−	34.6337i	1.12903	−	1.12903i	0.138692	−	0.990336i	$-0.455710\pi$
$941$	34.6337	−	34.6337i	1.12903	−	1.12903i	0.990336	−	0.138692i	$-0.0442897\pi$
$942$	0.527937	+	1.05483i	0.0172011	+	0.0343682i
$943$	27.3674			0.891206
$944$	−17.6258	+	32.2623i	−0.573671	+	1.05005i
$945$	−14.8020			−0.481509
$946$	14.1033	+	28.1788i	0.458539	+	0.916171i
$947$	13.7013	−	13.7013i	0.445232	−	0.445232i	−0.448534	−	0.893766i	$-0.648054\pi$
$947$	13.7013	−	13.7013i	0.445232	−	0.445232i	0.893766	+	0.448534i	$0.148054\pi$
$948$	−4.69740	−	32.6968i	−0.152565	−	1.06194i
$949$	15.2761	+	15.2761i	0.495884	+	0.495884i
$950$	5.77936	+	1.92391i	0.187507	+	0.0624199i
$951$		−	12.3914i		−	0.401820i
$952$	−73.2084	−	13.2208i	−2.37270	−	0.428488i
$953$		−	21.0946i		−	0.683322i	−0.939823	−	0.341661i	$-0.889011\pi$
$953$		−	21.0946i		−	0.683322i	0.939823	−	0.341661i	$-0.110989\pi$
$954$	−0.0906485	+	0.272305i	−0.00293485	+	0.00881619i
$955$	−6.86125	−	6.86125i	−0.222025	−	0.222025i
$956$	−4.07712	+	5.44514i	−0.131863	+	0.176108i
$957$	−3.30529	+	3.30529i	−0.106845	+	0.106845i
$958$	−43.1797	+	21.6112i	−1.39507	+	0.698227i
$959$	5.53559			0.178753
$960$	−11.1336	−	4.15681i	−0.359335	−	0.134161i
$961$	74.5973			2.40636
$962$	28.2286	−	14.1283i	0.910127	−	0.455514i
$963$	−2.34828	+	2.34828i	−0.0756722	+	0.0756722i
$964$	−25.1470	+	33.5847i	−0.809930	+	1.08169i
$965$	10.1437	+	10.1437i	0.326538	+	0.326538i
$966$	−26.0337	+	78.2042i	−0.837619	+	2.51618i
$967$			47.6784i			1.53323i	0.642104	+	0.766617i	$0.278062\pi$
$967$			47.6784i			1.53323i	−0.642104	+	0.766617i	$0.721938\pi$
$968$	14.4101	+	2.60233i	0.463157	+	0.0836419i
$969$		−	13.2613i		−	0.426013i
$970$	3.91097	+	1.30193i	0.125574	+	0.0418026i
$971$	−32.5828	−	32.5828i	−1.04563	−	1.04563i	−0.998908	−	0.0467229i	$-0.985122\pi$
$971$	−32.5828	−	32.5828i	−1.04563	−	1.04563i	−0.0467229	−	0.998908i	$-0.514878\pi$
$972$	−0.545879	−	3.79965i	−0.0175091	−	0.121874i
$973$	−26.7946	+	26.7946i	−0.858995	+	0.858995i
$974$	−2.80981	−	5.61406i	−0.0900321	−	0.179886i
$975$	28.9240			0.926308
$976$	18.3771	+	10.0399i	0.588236	+	0.321370i
$977$	26.8776			0.859890			0.429945	−	0.902855i	$-0.358533\pi$
$977$	26.8776			0.859890			0.429945	+	0.902855i	$0.358533\pi$
$978$	−17.4916	−	34.9486i	−0.559321	−	1.11753i
$979$	−13.6983	+	13.6983i	−0.437799	+	0.437799i
$980$	−9.11047	+	1.30886i	−0.291023	+	0.0418100i
$981$	1.47475	+	1.47475i	0.0470853	+	0.0470853i
$982$	−19.4877	−	6.48732i	−0.621877	−	0.207019i
$983$			48.9660i			1.56177i	0.624672	+	0.780887i	$0.285233\pi$
$983$			48.9660i			1.56177i	−0.624672	+	0.780887i	$0.714767\pi$
$984$	−12.3002	+	8.53714i	−0.392115	+	0.272154i
$985$		−	2.16025i		−	0.0688312i
$986$	3.60278	−	10.8226i	0.114736	−	0.344663i
$987$	34.3763	+	34.3763i	1.09421	+	1.09421i
$988$	6.02418	+	4.51069i	0.191655	+	0.143504i
$989$	−60.2419	+	60.2419i	−1.91558	+	1.91558i
$990$	−0.469806	+	0.235136i	−0.0149314	+	0.00747310i
$991$	47.0627			1.49500			0.747499	−	0.664263i	$-0.231255\pi$
$991$	47.0627			1.49500			0.747499	+	0.664263i	$0.231255\pi$
$992$	−39.5992	−	42.5561i	−1.25727	−	1.35116i
$993$	33.0476			1.04873
$994$	−35.2373	+	17.6361i	−1.11766	+	0.559383i
$995$	6.63970	−	6.63970i	0.210493	−	0.210493i
$996$	1.36560	+	1.02251i	0.0432708	+	0.0323996i
$997$	39.5905	+	39.5905i	1.25385	+	1.25385i	0.953982	+	0.299863i	$0.0969408\pi$
$997$	39.5905	+	39.5905i	1.25385	+	1.25385i	0.299863	+	0.953982i	$0.403059\pi$
$998$	8.98997	−	27.0056i	0.284573	−	0.854846i
$999$			29.8012i			0.942867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.229.6	yes	68
4.3	odd	2		1216.2.k.b.305.9		68
16.3	odd	4		1216.2.k.b.913.9		68
16.13	even	4	inner	304.2.k.b.77.6	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.6	✓	68	16.13	even	4	inner
304.2.k.b.229.6	yes	68	1.1	even	1	trivial
1216.2.k.b.305.9		68	4.3	odd	2
1216.2.k.b.913.9		68	16.3	odd	4

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26466 + 0.632956i) q^{2} +(1.26193 - 1.26193i) q^{3} +(1.19873 - 1.60095i) q^{4} +(0.588594 + 0.588594i) q^{5} +(-0.797168 + 2.39466i) q^{6} +3.53958i q^{7} +(-0.502658 + 2.78340i) q^{8} -0.184946i q^{9} +O(q^{10})\)	\(q+(-1.26466 + 0.632956i) q^{2} +(1.26193 - 1.26193i) q^{3} +(1.19873 - 1.60095i) q^{4} +(0.588594 + 0.588594i) q^{5} +(-0.797168 + 2.39466i) q^{6} +3.53958i q^{7} +(-0.502658 + 2.78340i) q^{8} -0.184946i q^{9} +(-1.11693 - 0.371817i) q^{10} +(1.70629 + 1.70629i) q^{11} +(-0.507572 - 3.53301i) q^{12} +(-2.66076 + 2.66076i) q^{13} +(-2.24040 - 4.47636i) q^{14} +1.48553 q^{15} +(-1.12608 - 3.83822i) q^{16} +7.43076 q^{17} +(0.117063 + 0.233894i) q^{18} +(0.707107 - 0.707107i) q^{19} +(1.64788 - 0.236743i) q^{20} +(4.46671 + 4.46671i) q^{21} +(-3.23789 - 1.07787i) q^{22} -9.22644i q^{23} +(2.87815 + 4.14679i) q^{24} -4.30711i q^{25} +(1.68081 - 5.04910i) q^{26} +(3.55241 + 3.55241i) q^{27} +(5.66669 + 4.24301i) q^{28} +(-0.767522 + 0.767522i) q^{29} +(-1.87869 + 0.940277i) q^{30} -10.2761 q^{31} +(3.85354 + 4.14129i) q^{32} +4.30645 q^{33} +(-9.39739 + 4.70335i) q^{34} +(-2.08338 + 2.08338i) q^{35} +(-0.296089 - 0.221701i) q^{36} +(4.19450 + 4.19450i) q^{37} +(-0.446682 + 1.34182i) q^{38} +6.71539i q^{39} +(-1.93416 + 1.34243i) q^{40} +2.96619i q^{41} +(-8.47610 - 2.82164i) q^{42} +(-6.52927 - 6.52927i) q^{43} +(4.77708 - 0.686301i) q^{44} +(0.108858 - 0.108858i) q^{45} +(5.83994 + 11.6683i) q^{46} +7.69612 q^{47} +(-6.26461 - 3.42254i) q^{48} -5.52861 q^{49} +(2.72622 + 5.44704i) q^{50} +(9.37712 - 9.37712i) q^{51} +(1.07020 + 7.44928i) q^{52} +(0.775893 + 0.775893i) q^{53} +(-6.74111 - 2.24407i) q^{54} +2.00863i q^{55} +(-9.85207 - 1.77920i) q^{56} -1.78464i q^{57} +(0.484847 - 1.45646i) q^{58} +(-6.49885 - 6.49885i) q^{59} +(1.78076 - 2.37826i) q^{60} +(-3.70184 + 3.70184i) q^{61} +(12.9957 - 6.50430i) q^{62} +0.654631 q^{63} +(-7.49467 - 2.79820i) q^{64} -3.13221 q^{65} +(-5.44620 + 2.72580i) q^{66} +(-0.684611 + 0.684611i) q^{67} +(8.90750 - 11.8963i) q^{68} +(-11.6431 - 11.6431i) q^{69} +(1.31608 - 3.95345i) q^{70} -7.87186i q^{71} +(0.514780 + 0.0929646i) q^{72} -5.74127i q^{73} +(-7.95956 - 2.64968i) q^{74} +(-5.43529 - 5.43529i) q^{75} +(-0.284411 - 1.97967i) q^{76} +(-6.03955 + 6.03955i) q^{77} +(-4.25055 - 8.49269i) q^{78} +9.25466 q^{79} +(1.59635 - 2.92196i) q^{80} +9.52063 q^{81} +(-1.87747 - 3.75123i) q^{82} +(-0.337972 + 0.337972i) q^{83} +(12.5054 - 1.79659i) q^{84} +(4.37371 + 4.37371i) q^{85} +(12.3901 + 4.12457i) q^{86} +1.93712i q^{87} +(-5.60698 + 3.89162i) q^{88} +8.02811i q^{89} +(-0.0687662 + 0.206571i) q^{90} +(-9.41796 - 9.41796i) q^{91} +(-14.7711 - 11.0600i) q^{92} +(-12.9677 + 12.9677i) q^{93} +(-9.73298 + 4.87131i) q^{94} +0.832398 q^{95} +(10.0889 + 0.363118i) q^{96} -3.50154 q^{97} +(6.99181 - 3.49937i) q^{98} +(0.315572 - 0.315572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more