LMFDB - Embedded newform 483.2.q.b.400.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			400.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	483.400
Dual form			483.2.q.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.30075 - 0.675560i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(3.15455 - 2.02730i) q^{4} +(-0.195368 - 1.35881i) q^{5} +(-2.01722 - 1.29639i) q^{6} +(0.415415 - 0.909632i) q^{7} +(2.74769 - 3.17101i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-1.36745 - 2.99430i) q^{10} +(0.857685 + 0.251839i) q^{11} +(-3.59792 - 1.05645i) q^{12} +(-0.561616 - 1.22977i) q^{13} +(0.341254 - 2.37347i) q^{14} +(-0.898983 + 1.03748i) q^{15} +(1.06408 - 2.33001i) q^{16} +(-0.841254 - 0.540641i) q^{17} +(0.341254 + 2.37347i) q^{18} +(-1.12721 + 0.724417i) q^{19} +(-3.37102 - 3.89037i) q^{20} +(-0.959493 + 0.281733i) q^{21} +2.14345 q^{22} +(2.01691 + 4.35110i) q^{23} -4.19584 q^{24} +(2.98926 - 0.877726i) q^{25} +(-2.12292 - 2.44998i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.533654 - 3.71165i) q^{28} +(0.315317 + 0.202642i) q^{29} +(-1.36745 + 2.99430i) q^{30} +(1.30972 - 1.51150i) q^{31} +(-0.320145 + 2.22666i) q^{32} +(-0.371337 - 0.813115i) q^{33} +(-2.30075 - 0.675560i) q^{34} +(-1.31718 - 0.386758i) q^{35} +(1.55773 + 3.41095i) q^{36} +(0.0448692 - 0.312072i) q^{37} +(-2.10405 + 2.42820i) q^{38} +(-0.561616 + 1.22977i) q^{39} +(-4.84562 - 3.11409i) q^{40} +(0.446605 + 3.10620i) q^{41} +(-2.01722 + 1.29639i) q^{42} +(1.23689 + 1.42745i) q^{43} +(3.21616 - 0.944350i) q^{44} +1.37279 q^{45} +(7.57982 + 8.64824i) q^{46} +0.861031 q^{47} +(-2.45773 + 0.721655i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(6.28458 - 4.03885i) q^{50} +(0.142315 + 0.989821i) q^{51} +(-4.26475 - 2.74079i) q^{52} +(-2.90714 + 6.36575i) q^{53} +(1.57028 - 1.81219i) q^{54} +(0.174638 - 1.21463i) q^{55} +(-1.74302 - 3.81667i) q^{56} +(1.28565 + 0.377500i) q^{57} +(0.862362 + 0.253212i) q^{58} +(3.58896 + 7.85873i) q^{59} +(-0.732593 + 5.09530i) q^{60} +(-7.04159 + 8.12643i) q^{61} +(1.99223 - 4.36237i) q^{62} +(0.841254 + 0.540641i) q^{63} +(1.49674 + 10.4101i) q^{64} +(-1.56130 + 1.00339i) q^{65} +(-1.40366 - 1.61991i) q^{66} +(2.50241 - 0.734774i) q^{67} -3.74982 q^{68} +(1.96755 - 4.37364i) q^{69} -3.29177 q^{70} +(7.44808 - 2.18695i) q^{71} +(2.74769 + 3.17101i) q^{72} +(3.63648 - 2.33702i) q^{73} +(-0.107591 - 0.748310i) q^{74} +(-2.62089 - 1.68434i) q^{75} +(-2.08724 + 4.57041i) q^{76} +(0.585376 - 0.675560i) q^{77} +(-0.461354 + 3.20879i) q^{78} +(-4.98057 - 10.9059i) q^{79} +(-3.37394 - 0.990677i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(3.12595 + 6.84488i) q^{82} +(0.115802 - 0.805422i) q^{83} +(-2.45561 + 2.83392i) q^{84} +(-0.570276 + 1.24873i) q^{85} +(3.81010 + 2.44860i) q^{86} +(-0.0533422 - 0.371003i) q^{87} +(3.15524 - 2.02775i) q^{88} +(-7.93804 - 9.16098i) q^{89} +(3.15843 - 0.927399i) q^{90} -1.35194 q^{91} +(15.1834 + 9.63686i) q^{92} -2.00000 q^{93} +(1.98101 - 0.581678i) q^{94} +(1.20457 + 1.39015i) q^{95} +(1.89245 - 1.21620i) q^{96} +(-0.986733 - 6.86288i) q^{97} +(-2.01722 - 1.29639i) q^{98} +(-0.371337 + 0.813115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) $ 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	2.30075	−	0.675560i	1.62687	−	0.477693i	0.664019	−	0.747715i	$-0.268849\pi$
$2$	2.30075	−	0.675560i	1.62687	−	0.477693i	0.962854	+	0.270022i	$0.0870311\pi$
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	3.15455	−	2.02730i	1.57727	−	1.01365i
$5$	−0.195368	−	1.35881i	−0.0873711	−	0.607679i	−0.985719	−	0.168396i	$-0.946141\pi$
$5$	−0.195368	−	1.35881i	−0.0873711	−	0.607679i	0.898348	−	0.439284i	$-0.144768\pi$
$6$	−2.01722	−	1.29639i	−0.823528	−	0.529249i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$8$	2.74769	−	3.17101i	0.971456	−	1.12112i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−1.36745	−	2.99430i	−0.432426	−	0.946881i
$11$	0.857685	+	0.251839i	0.258602	+	0.0759323i	0.408464	−	0.912775i	$-0.366065\pi$
$11$	0.857685	+	0.251839i	0.258602	+	0.0759323i	−0.149862	+	0.988707i	$0.547883\pi$
$12$	−3.59792	−	1.05645i	−1.03863	−	0.304969i
$13$	−0.561616	−	1.22977i	−0.155764	−	0.341076i	0.815621	−	0.578587i	$-0.196396\pi$
$13$	−0.561616	−	1.22977i	−0.155764	−	0.341076i	−0.971385	+	0.237511i	$0.923668\pi$
$14$	0.341254	−	2.37347i	0.0912038	−	0.634337i
$15$	−0.898983	+	1.03748i	−0.232117	+	0.267877i
$16$	1.06408	−	2.33001i	0.266020	−	0.582503i
$17$	−0.841254	−	0.540641i	−0.204034	−	0.131125i	0.434634	−	0.900607i	$-0.356878\pi$
$17$	−0.841254	−	0.540641i	−0.204034	−	0.131125i	−0.638668	+	0.769483i	$0.720514\pi$
$18$	0.341254	+	2.37347i	0.0804342	+	0.559432i
$19$	−1.12721	+	0.724417i	−0.258601	+	0.166193i	−0.663517	−	0.748161i	$-0.730937\pi$
$19$	−1.12721	+	0.724417i	−0.258601	+	0.166193i	0.404916	+	0.914354i	$0.367301\pi$
$20$	−3.37102	−	3.89037i	−0.753783	−	0.869913i
$21$	−0.959493	+	0.281733i	−0.209379	+	0.0614791i
$22$	2.14345			0.456985
$23$	2.01691	+	4.35110i	0.420554	+	0.907267i
$23$	2.01691	+	4.35110i	0.420554	+	0.907267i
$24$	−4.19584			−0.856473
$25$	2.98926	−	0.877726i	0.597852	−	0.175545i
$26$	−2.12292	−	2.44998i	−0.416338	−	0.480480i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.533654	−	3.71165i	−0.100851	−	0.701436i
$29$	0.315317	+	0.202642i	0.0585530	+	0.0376297i	0.569590	−	0.821929i	$-0.307102\pi$
$29$	0.315317	+	0.202642i	0.0585530	+	0.0376297i	−0.511037	+	0.859559i	$0.670738\pi$
$30$	−1.36745	+	2.99430i	−0.249661	+	0.546682i
$31$	1.30972	−	1.51150i	0.235233	−	0.271473i	−0.625844	−	0.779949i	$-0.715245\pi$
$31$	1.30972	−	1.51150i	0.235233	−	0.271473i	0.861077	+	0.508475i	$0.169791\pi$
$32$	−0.320145	+	2.22666i	−0.0565942	+	0.393621i
$33$	−0.371337	−	0.813115i	−0.0646415	−	0.141545i
$34$	−2.30075	−	0.675560i	−0.394575	−	0.115858i
$35$	−1.31718	−	0.386758i	−0.222644	−	0.0653741i
$36$	1.55773	+	3.41095i	0.259622	+	0.568492i
$37$	0.0448692	−	0.312072i	0.00737644	−	0.0513043i	−0.985801	−	0.167919i	$-0.946295\pi$
$37$	0.0448692	−	0.312072i	0.00737644	−	0.0513043i	0.993177	+	0.116615i	$0.0372043\pi$
$38$	−2.10405	+	2.42820i	−0.341322	+	0.393906i
$39$	−0.561616	+	1.22977i	−0.0899305	+	0.196920i
$40$	−4.84562	−	3.11409i	−0.766159	−	0.492381i
$41$	0.446605	+	3.10620i	0.0697479	+	0.485107i	0.994517	+	0.104578i	$0.0333492\pi$
$41$	0.446605	+	3.10620i	0.0697479	+	0.485107i	−0.924769	+	0.380529i	$0.875742\pi$
$42$	−2.01722	+	1.29639i	−0.311264	+	0.200037i
$43$	1.23689	+	1.42745i	0.188624	+	0.217684i	0.842183	−	0.539192i	$-0.181270\pi$
$43$	1.23689	+	1.42745i	0.188624	+	0.217684i	−0.653559	+	0.756876i	$0.726725\pi$
$44$	3.21616	−	0.944350i	0.484855	−	0.142366i
$45$	1.37279			0.204643
$46$	7.57982	+	8.64824i	1.11758	+	1.27511i
$47$	0.861031			0.125594			0.0627971	−	0.998026i	$-0.479998\pi$
$47$	0.861031			0.125594			0.0627971	+	0.998026i	$0.479998\pi$
$48$	−2.45773	+	0.721655i	−0.354743	+	0.104162i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	6.28458	−	4.03885i	0.888773	−	0.571180i
$51$	0.142315	+	0.989821i	0.0199281	+	0.138603i
$52$	−4.26475	−	2.74079i	−0.591415	−	0.380079i
$53$	−2.90714	+	6.36575i	−0.399327	+	0.874403i	0.598011	+	0.801488i	$0.295958\pi$
$53$	−2.90714	+	6.36575i	−0.399327	+	0.874403i	−0.997338	+	0.0729158i	$0.976770\pi$
$54$	1.57028	−	1.81219i	0.213687	−	0.246608i
$55$	0.174638	−	1.21463i	0.0235482	−	0.163781i
$56$	−1.74302	−	3.81667i	−0.232920	−	0.510025i
$57$	1.28565	+	0.377500i	0.170288	+	0.0500011i
$58$	0.862362	+	0.253212i	0.113234	+	0.0332484i
$59$	3.58896	+	7.85873i	0.467243	+	1.02312i	0.985776	+	0.168062i	$0.0537510\pi$
$59$	3.58896	+	7.85873i	0.467243	+	1.02312i	−0.518533	+	0.855058i	$0.673522\pi$
$60$	−0.732593	+	5.09530i	−0.0945774	+	0.657800i
$61$	−7.04159	+	8.12643i	−0.901583	+	1.04048i	0.0973934	+	0.995246i	$0.468949\pi$
$61$	−7.04159	+	8.12643i	−0.901583	+	1.04048i	−0.998976	+	0.0452362i	$0.985596\pi$
$62$	1.99223	−	4.36237i	0.253013	−	0.554022i
$63$	0.841254	+	0.540641i	0.105988	+	0.0681143i
$64$	1.49674	+	10.4101i	0.187093	+	1.30126i
$65$	−1.56130	+	1.00339i	−0.193656	+	0.124455i
$66$	−1.40366	−	1.61991i	−0.172779	−	0.199397i
$67$	2.50241	−	0.734774i	0.305718	−	0.0897670i	−0.125275	−	0.992122i	$-0.539981\pi$
$67$	2.50241	−	0.734774i	0.305718	−	0.0897670i	0.430993	+	0.902355i	$0.358163\pi$
$68$	−3.74982			−0.454732
$69$	1.96755	−	4.37364i	0.236865	−	0.526525i
$70$	−3.29177			−0.393442
$71$	7.44808	−	2.18695i	0.883925	−	0.259544i	0.191897	−	0.981415i	$-0.438536\pi$
$71$	7.44808	−	2.18695i	0.883925	−	0.259544i	0.692027	+	0.721871i	$0.256718\pi$
$72$	2.74769	+	3.17101i	0.323819	+	0.373707i
$73$	3.63648	−	2.33702i	0.425618	−	0.273528i	−0.310248	−	0.950656i	$-0.600412\pi$
$73$	3.63648	−	2.33702i	0.425618	−	0.273528i	0.735865	+	0.677128i	$0.236776\pi$
$74$	−0.107591	−	0.748310i	−0.0125072	−	0.0869893i
$75$	−2.62089	−	1.68434i	−0.302634	−	0.194491i
$76$	−2.08724	+	4.57041i	−0.239423	+	0.524262i
$77$	0.585376	−	0.675560i	0.0667098	−	0.0769872i
$78$	−0.461354	+	3.20879i	−0.0522380	+	0.363324i
$79$	−4.98057	−	10.9059i	−0.560358	−	1.22701i	−0.951774	−	0.306799i	$-0.900742\pi$
$79$	−4.98057	−	10.9059i	−0.560358	−	1.22701i	0.391416	−	0.920214i	$-0.371985\pi$
$80$	−3.37394	−	0.990677i	−0.377217	−	0.110761i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	3.12595	+	6.84488i	0.345203	+	0.755890i
$83$	0.115802	−	0.805422i	0.0127109	−	0.0884066i	−0.982478	−	0.186376i	$-0.940326\pi$
$83$	0.115802	−	0.805422i	0.0127109	−	0.0884066i	0.995189	+	0.0979696i	$0.0312348\pi$
$84$	−2.45561	+	2.83392i	−0.267929	+	0.309206i
$85$	−0.570276	+	1.24873i	−0.0618551	+	0.135444i
$86$	3.81010	+	2.44860i	0.410854	+	0.264040i
$87$	−0.0533422	−	0.371003i	−0.00571889	−	0.0397757i
$88$	3.15524	−	2.02775i	0.336350	−	0.216159i
$89$	−7.93804	−	9.16098i	−0.841430	−	0.971062i	0.158437	−	0.987369i	$-0.449355\pi$
$89$	−7.93804	−	9.16098i	−0.841430	−	0.971062i	−0.999867	+	0.0163069i	$0.994809\pi$
$90$	3.15843	−	0.927399i	0.332928	−	0.0977565i
$91$	−1.35194			−0.141722
$92$	15.1834	+	9.63686i	1.58298	+	1.00471i
$93$	−2.00000			−0.207390
$94$	1.98101	−	0.581678i	0.204326	−	0.0599955i
$95$	1.20457	+	1.39015i	0.123586	+	0.142626i
$96$	1.89245	−	1.21620i	0.193147	−	0.124128i
$97$	−0.986733	−	6.86288i	−0.100188	−	0.696820i	−0.976569	−	0.215203i	$-0.930959\pi$
$97$	−0.986733	−	6.86288i	−0.100188	−	0.696820i	0.876382	−	0.481617i	$-0.159950\pi$
$98$	−2.01722	−	1.29639i	−0.203770	−	0.130955i
$99$	−0.371337	+	0.813115i	−0.0373208	+	0.0817211i
$100$	7.65035	−	8.82897i	0.765035	−	0.882897i
$101$	−2.58987	+	18.0129i	−0.257701	+	1.79235i	0.291405	+	0.956600i	$0.405877\pi$
$101$	−2.58987	+	18.0129i	−0.257701	+	1.79235i	−0.549107	+	0.835752i	$0.685032\pi$
$102$	0.996114	+	2.18119i	0.0986300	+	0.215970i
$103$	−5.29927	−	1.55601i	−0.522153	−	0.153318i	0.0100262	−	0.999950i	$-0.496809\pi$
$103$	−5.29927	−	1.55601i	−0.522153	−	0.153318i	−0.532179	+	0.846632i	$0.678627\pi$
$104$	−5.44275	−	1.59813i	−0.533705	−	0.156710i
$105$	0.570276	+	1.24873i	0.0556532	+	0.121864i
$106$	−2.38815	+	16.6099i	−0.231957	+	1.61330i
$107$	−3.76975	+	4.35053i	−0.364436	+	0.420581i	−0.908121	−	0.418708i	$-0.862483\pi$
$107$	−3.76975	+	4.35053i	−0.364436	+	0.420581i	0.543685	+	0.839289i	$0.317029\pi$
$108$	1.55773	−	3.41095i	0.149893	−	0.328219i
$109$	−10.0013	−	6.42746i	−0.957954	−	0.615639i	−0.0345226	−	0.999404i	$-0.510991\pi$
$109$	−10.0013	−	6.42746i	−0.957954	−	0.615639i	−0.923431	+	0.383765i	$0.874627\pi$
$110$	−0.418761	−	2.91254i	−0.0399273	−	0.277700i
$111$	−0.265231	+	0.170454i	−0.0251746	+	0.0161788i
$112$	−1.67742	−	1.93584i	−0.158501	−	0.182920i
$113$	−1.85837	+	0.545668i	−0.174821	+	0.0513321i	−0.367972	−	0.929837i	$-0.619948\pi$
$113$	−1.85837	+	0.545668i	−0.174821	+	0.0513321i	0.193150	+	0.981169i	$0.438129\pi$
$114$	3.21297			0.300922
$115$	5.51829	−	3.59066i	0.514583	−	0.334831i
$116$	1.40550			0.130497
$117$	1.29718	−	0.380885i	0.119924	−	0.0352128i
$118$	13.5663	+	15.6564i	1.24888	+	1.44129i
$119$	−0.841254	+	0.540641i	−0.0771176	+	0.0495605i
$120$	0.819733	+	5.70137i	0.0748310	+	0.520461i
$121$	−8.58159	−	5.51505i	−0.780144	−	0.501368i
$122$	−10.7110	+	23.4539i	−0.969730	+	2.12341i
$123$	2.05505	−	2.37165i	0.185297	−	0.213845i
$124$	1.06731	−	7.42330i	0.0958472	−	0.666632i
$125$	−4.62805	−	10.1340i	−0.413945	−	0.906414i
$126$	2.30075	+	0.675560i	0.204967	+	0.0601837i
$127$	14.7572	+	4.33310i	1.30949	+	0.384501i	0.860689	−	0.509132i	$-0.170033\pi$
$127$	14.7572	+	4.33310i	1.30949	+	0.384501i	0.448800	+	0.893632i	$0.351852\pi$
$128$	8.60727	+	18.8473i	0.760782	+	1.66588i
$129$	0.268802	−	1.86956i	0.0236667	−	0.164606i
$130$	−2.91431	+	3.36329i	−0.255602	+	0.294980i
$131$	−2.30387	+	5.04477i	−0.201290	+	0.440764i	−0.983177	−	0.182657i	$-0.941530\pi$
$131$	−2.30387	+	5.04477i	−0.201290	+	0.440764i	0.781887	+	0.623420i	$0.214257\pi$
$132$	−2.81983	−	1.81219i	−0.245435	−	0.157731i
$133$	0.190691	+	1.32628i	0.0165350	+	0.115003i
$134$	5.26103	−	3.38106i	0.454484	−	0.292079i
$135$	−0.898983	−	1.03748i	−0.0773722	−	0.0892922i
$136$	−4.02588	+	1.18211i	−0.345217	+	0.101365i
$137$	−17.7619			−1.51750			−0.758751	−	0.651381i	$-0.774190\pi$
$137$	−17.7619			−1.51750			−0.758751	+	0.651381i	$0.774190\pi$
$138$	1.57217	−	11.3918i	0.133832	−	0.969738i
$139$	1.72920			0.146669			0.0733346	−	0.997307i	$-0.476636\pi$
$139$	1.72920			0.146669			0.0733346	+	0.997307i	$0.476636\pi$
$140$	−4.93918	+	1.45027i	−0.417437	+	0.122570i
$141$	−0.563855	−	0.650724i	−0.0474852	−	0.0548008i
$142$	15.6587	−	10.0633i	1.31405	−	0.844489i
$143$	−0.171986	−	1.19619i	−0.0143822	−	0.100030i
$144$	2.15486	+	1.38484i	0.179572	+	0.115404i
$145$	0.213750	−	0.468047i	0.0177510	−	0.0388692i
$146$	6.78782	−	7.83356i	0.561764	−	0.648310i
$147$	−0.142315	+	0.989821i	−0.0117379	+	0.0816391i
$148$	−0.491123	−	1.07541i	−0.0403700	−	0.0883980i
$149$	−14.1871	−	4.16571i	−1.16225	−	0.341268i	−0.356945	−	0.934125i	$-0.616182\pi$
$149$	−14.1871	−	4.16571i	−1.16225	−	0.341268i	−0.805308	+	0.592857i	$0.798000\pi$
$150$	−7.16788	−	2.10468i	−0.585255	−	0.171846i
$151$	−6.99498	−	15.3169i	−0.569244	−	1.24647i	−0.947199	−	0.320646i	$-0.896100\pi$
$151$	−6.99498	−	15.3169i	−0.569244	−	1.24647i	0.377956	−	0.925824i	$-0.376627\pi$
$152$	−0.800109	+	5.56488i	−0.0648974	+	0.451371i
$153$	0.654861	−	0.755750i	0.0529424	−	0.0610987i
$154$	0.890421	−	1.94975i	0.0717521	−	0.157115i
$155$	−2.30972	−	1.48437i	−0.185521	−	0.119227i
$156$	0.721468	+	5.01792i	0.0577637	+	0.401755i
$157$	18.4932	−	11.8848i	1.47591	−	0.948513i	0.478393	−	0.878146i	$-0.341219\pi$
$157$	18.4932	−	11.8848i	1.47591	−	0.948513i	0.997521	−	0.0703670i	$-0.0224170\pi$
$158$	−18.8266	−	21.7271i	−1.49777	−	1.72852i
$159$	6.71469	−	1.97161i	0.532509	−	0.156359i
$160$	3.08816			0.244140
$161$	4.79575	−	0.0271313i	0.377958	−	0.00213825i
$162$	−2.39788			−0.188395
$163$	8.11174	−	2.38182i	0.635361	−	0.186559i	0.0518380	−	0.998656i	$-0.483492\pi$
$163$	8.11174	−	2.38182i	0.635361	−	0.186559i	0.583523	+	0.812097i	$0.301674\pi$
$164$	7.70605	+	8.89326i	0.601741	+	0.694447i
$165$	−1.03232	+	0.663434i	−0.0803663	+	0.0516483i
$166$	−0.277680	−	1.93130i	−0.0215521	−	0.149898i
$167$	4.08067	+	2.62249i	0.315772	+	0.202934i	0.688920	−	0.724838i	$-0.258085\pi$
$167$	4.08067	+	2.62249i	0.315772	+	0.202934i	−0.373148	+	0.927772i	$0.621722\pi$
$168$	−1.74302	+	3.81667i	−0.134477	+	0.294463i
$169$	7.31628	−	8.44343i	0.562790	−	0.649495i
$170$	−0.468468	+	3.25827i	−0.0359299	+	0.249898i
$171$	−0.556624	−	1.21884i	−0.0425661	−	0.0932067i
$172$	6.79570	+	1.99540i	0.518167	+	0.152148i
$173$	−15.0412	−	4.41649i	−1.14356	−	0.335780i	−0.345536	−	0.938405i	$-0.612303\pi$
$173$	−15.0412	−	4.41649i	−1.14356	−	0.335780i	−0.798024	+	0.602626i	$0.794121\pi$
$174$	−0.373362	−	0.817549i	−0.0283045	−	0.0619782i
$175$	0.443376	−	3.08375i	0.0335161	−	0.233109i
$176$	1.49943	−	1.73044i	0.113024	−	0.130437i
$177$	3.58896	−	7.85873i	0.269763	−	0.590699i
$178$	−24.4522	−	15.7145i	−1.83277	−	1.17785i
$179$	−2.44496	−	17.0050i	−0.182745	−	1.27102i	−0.850237	−	0.526400i	$-0.823541\pi$
$179$	−2.44496	−	17.0050i	−0.182745	−	1.27102i	0.667493	−	0.744616i	$-0.267368\pi$
$180$	4.33052	−	2.78305i	0.322778	−	0.207437i
$181$	9.44472	+	10.8998i	0.702021	+	0.810175i	0.989024	−	0.147755i	$-0.0472046\pi$
$181$	9.44472	+	10.8998i	0.702021	+	0.810175i	−0.287003	+	0.957930i	$0.592659\pi$
$182$	−3.11047	+	0.913316i	−0.230563	+	0.0676995i
$183$	10.7528			0.794870
$184$	19.3392	+	5.55986i	1.42571	+	0.409879i
$185$	−0.432813			−0.0318211
$186$	−4.60149	+	1.35112i	−0.337398	+	0.0990689i
$187$	−0.585376	−	0.675560i	−0.0428069	−	0.0494018i
$188$	2.71616	−	1.74557i	0.198096	−	0.127309i
$189$	−0.142315	−	0.989821i	−0.0103519	−	0.0719989i
$190$	3.71053	+	2.38461i	0.269190	+	0.172998i
$191$	−9.77547	+	21.4053i	−0.707328	+	1.54883i	0.123526	+	0.992341i	$0.460580\pi$
$191$	−9.77547	+	21.4053i	−0.707328	+	1.54883i	−0.830854	+	0.556491i	$0.812148\pi$
$192$	6.88726	−	7.94832i	0.497045	−	0.573620i
$193$	2.20353	−	15.3259i	0.158614	−	1.10318i	−0.742577	−	0.669761i	$-0.766397\pi$
$193$	2.20353	−	15.3259i	0.158614	−	1.10318i	0.901191	−	0.433423i	$-0.142694\pi$
$194$	−6.90651	−	15.1231i	−0.495858	−	1.08578i
$195$	1.78074	+	0.522874i	0.127522	+	0.0374438i
$196$	−3.59792	−	1.05645i	−0.256994	−	0.0754604i
$197$	−3.43831	−	7.52885i	−0.244969	−	0.536408i	0.746709	−	0.665151i	$-0.231633\pi$
$197$	−3.43831	−	7.52885i	−0.244969	−	0.536408i	−0.991678	+	0.128743i	$0.958906\pi$
$198$	−0.305045	+	2.12163i	−0.0216786	+	0.150778i
$199$	1.84581	−	2.13018i	0.130846	−	0.151005i	−0.686546	−	0.727087i	$-0.740874\pi$
$199$	1.84581	−	2.13018i	0.130846	−	0.151005i	0.817392	+	0.576082i	$0.195419\pi$
$200$	5.43030	−	11.8907i	0.383980	−	0.840799i
$201$	−2.19404	−	1.41002i	−0.154755	−	0.0994553i
$202$	6.21018	+	43.1928i	0.436947	+	3.03903i
$203$	0.315317	−	0.202642i	0.0221309	−	0.0142227i
$204$	2.45561	+	2.83392i	0.171927	+	0.198414i
$205$	4.13350	−	1.21370i	0.288696	−	0.0847687i
$206$	−13.2435			−0.922715
$207$	−4.59385	+	1.37715i	−0.319295	+	0.0957187i
$208$	−3.46297			−0.240114
$209$	−1.14923	+	0.337445i	−0.0794940	+	0.0233415i
$210$	2.15565	+	2.48775i	0.148754	+	0.171671i
$211$	0.213496	−	0.137206i	0.0146977	−	0.00944563i	−0.533271	−	0.845944i	$-0.679038\pi$
$211$	0.213496	−	0.137206i	0.0146977	−	0.00944563i	0.547969	+	0.836499i	$0.315401\pi$
$212$	3.73460	+	25.9747i	0.256493	+	1.78395i
$213$	−6.53025	−	4.19673i	−0.447445	−	0.287555i
$214$	−5.73421	+	12.5562i	−0.391982	+	0.858321i
$215$	1.69799	−	1.95958i	0.115802	−	0.133642i
$216$	0.597131	−	4.15314i	0.0406296	−	0.282585i
$217$	−0.830830	−	1.81926i	−0.0564004	−	0.123500i
$218$	−27.3527	−	8.03147i	−1.85256	−	0.543959i
$219$	−4.14759	−	1.21784i	−0.280268	−	0.0822942i
$220$	−1.91153	−	4.18567i	−0.128875	−	0.282197i
$221$	−0.192401	+	1.33818i	−0.0129423	+	0.0900156i
$222$	−0.495078	+	0.571350i	−0.0332275	+	0.0383465i
$223$	3.13237	−	6.85893i	0.209759	−	0.459308i	−0.775285	−	0.631611i	$-0.782394\pi$
$223$	3.13237	−	6.85893i	0.209759	−	0.459308i	0.985044	+	0.172304i	$0.0551211\pi$
$224$	1.89245	+	1.21620i	0.126444	+	0.0812608i
$225$	0.443376	+	3.08375i	0.0295584	+	0.205583i
$226$	−3.90702	+	2.51089i	−0.259891	+	0.167022i
$227$	12.0978	+	13.9617i	0.802962	+	0.926667i	0.998540	−	0.0540209i	$-0.0172038\pi$
$227$	12.0978	+	13.9617i	0.802962	+	0.926667i	−0.195578	+	0.980688i	$0.562658\pi$
$228$	4.82094	−	1.41555i	0.319274	−	0.0937474i
$229$	−26.3191			−1.73922			−0.869608	−	0.493743i	$-0.835628\pi$
$229$	−26.3191			−1.73922			−0.869608	+	0.493743i	$0.835628\pi$
$230$	10.2705	−	11.9891i	0.677216	−	0.790541i
$231$	−0.893894			−0.0588139
$232$	1.50897	−	0.443075i	0.0990691	−	0.0290893i
$233$	6.34223	+	7.31933i	0.415494	+	0.479505i	0.924459	−	0.381282i	$-0.124517\pi$
$233$	6.34223	+	7.31933i	0.415494	+	0.479505i	−0.508965	+	0.860787i	$0.669972\pi$
$234$	2.72716	−	1.75264i	0.178280	−	0.114574i
$235$	−0.168218	−	1.16998i	−0.0109733	−	0.0763211i
$236$	27.2536	+	17.5148i	1.77406	+	1.14012i
$237$	−4.98057	+	10.9059i	−0.323523	+	0.708416i
$238$	−1.57028	+	1.81219i	−0.101786	+	0.117467i
$239$	−1.88342	+	13.0995i	−0.121828	+	0.847335i	0.833654	+	0.552287i	$0.186245\pi$
$239$	−1.88342	+	13.0995i	−0.121828	+	0.847335i	−0.955482	+	0.295048i	$0.904664\pi$
$240$	1.46075	+	3.19861i	0.0942913	+	0.206469i
$241$	−2.07226	−	0.608472i	−0.133486	−	0.0391951i	0.214307	−	0.976766i	$-0.431251\pi$
$241$	−2.07226	−	0.608472i	−0.133486	−	0.0391951i	−0.347793	+	0.937571i	$0.613069\pi$
$242$	−23.4698	−	6.89136i	−1.50870	−	0.442993i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	−5.73828	+	39.9106i	−0.367356	+	2.55502i
$245$	−0.898983	+	1.03748i	−0.0574339	+	0.0662823i
$246$	3.12595	−	6.84488i	0.199303	−	0.436413i
$247$	1.52392	+	0.979367i	0.0969650	+	0.0623156i
$248$	−1.19426	−	8.30627i	−0.0758357	−	0.527449i
$249$	−0.684532	+	0.439922i	−0.0433804	+	0.0278789i
$250$	−17.4941	−	20.1893i	−1.10642	−	1.27688i
$251$	4.07533	−	1.19663i	0.257233	−	0.0755304i	−0.150574	−	0.988599i	$-0.548112\pi$
$251$	4.07533	−	1.19663i	0.257233	−	0.0755304i	0.407806	+	0.913068i	$0.366294\pi$
$252$	3.74982			0.236216
$253$	0.634095	+	4.23981i	0.0398652	+	0.266555i
$254$	36.8798			2.31405
$255$	1.31718	−	0.386758i	0.0824849	−	0.0242198i
$256$	18.7611	+	21.6515i	1.17257	+	1.35322i
$257$	−20.3178	+	13.0574i	−1.26739	+	0.814501i	−0.989277	−	0.146048i	$-0.953345\pi$
$257$	−20.3178	+	13.0574i	−1.26739	+	0.814501i	−0.278111	+	0.960549i	$0.589708\pi$
$258$	−0.644555	−	4.48298i	−0.0401282	−	0.279098i
$259$	−0.265231	−	0.170454i	−0.0164807	−	0.0105915i
$260$	−2.89102	+	6.33046i	−0.179294	+	0.392599i
$261$	−0.245454	+	0.283269i	−0.0151932	+	0.0175339i
$262$	−1.89257	+	13.1631i	−0.116924	+	0.813221i
$263$	−4.79901	−	10.5084i	−0.295919	−	0.647973i	0.702019	−	0.712159i	$-0.252282\pi$
$263$	−4.79901	−	10.5084i	−0.295919	−	0.647973i	−0.997938	+	0.0641855i	$0.979555\pi$
$264$	−3.59871	−	1.05668i	−0.221485	−	0.0650340i
$265$	9.21783	+	2.70660i	0.566247	+	0.166265i
$266$	1.33472	+	2.92262i	0.0818367	+	0.179197i
$267$	−1.72510	+	11.9983i	−0.105574	+	0.734286i
$268$	6.40436	−	7.39103i	0.391209	−	0.451479i
$269$	5.30085	−	11.6072i	0.323198	−	0.707705i	−0.676386	−	0.736548i	$-0.736455\pi$
$269$	5.30085	−	11.6072i	0.323198	−	0.707705i	0.999584	+	0.0288421i	$0.00918201\pi$
$270$	−2.76921	−	1.77967i	−0.168529	−	0.108307i
$271$	3.91112	+	27.2024i	0.237583	+	1.65243i	0.663876	+	0.747843i	$0.268910\pi$
$271$	3.91112	+	27.2024i	0.237583	+	1.65243i	−0.426292	+	0.904586i	$0.640180\pi$
$272$	−2.15486	+	1.38484i	−0.130658	+	0.0839686i
$273$	0.885331	+	1.02173i	0.0535827	+	0.0618377i
$274$	−40.8656	+	11.9992i	−2.46878	+	0.724900i
$275$	2.78489			0.167935
$276$	−2.65998	−	17.7857i	−0.160112	−	1.07057i
$277$	−16.5325			−0.993340			−0.496670	−	0.867939i	$-0.665444\pi$
$277$	−16.5325			−0.993340			−0.496670	+	0.867939i	$0.665444\pi$
$278$	3.97846	−	1.16818i	0.238612	−	0.0700628i
$279$	1.30972	+	1.51150i	0.0784110	+	0.0904911i
$280$	−4.84562	+	3.11409i	−0.289581	+	0.186102i
$281$	−1.90938	−	13.2801i	−0.113904	−	0.792222i	−0.964059	−	0.265689i	$-0.914401\pi$
$281$	−1.90938	−	13.2801i	−0.113904	−	0.792222i	0.850155	−	0.526533i	$-0.176508\pi$
$282$	−1.73689	−	1.11623i	−0.103430	−	0.0664707i
$283$	2.36314	−	5.17457i	0.140474	−	0.307596i	−0.826299	−	0.563232i	$-0.809558\pi$
$283$	2.36314	−	5.17457i	0.140474	−	0.307596i	0.966773	+	0.255636i	$0.0822849\pi$
$284$	19.0617	−	21.9984i	1.13110	−	1.30536i
$285$	0.261778	−	1.82070i	0.0155064	−	0.107849i
$286$	−1.20379	−	2.63594i	−0.0711818	−	0.155866i
$287$	3.01103	+	0.884117i	0.177735	+	0.0521878i
$288$	−2.15843	−	0.633773i	−0.127187	−	0.0373454i
$289$	−6.64664	−	14.5541i	−0.390979	−	0.856124i
$290$	0.175590	−	1.22126i	0.0103110	−	0.0717147i
$291$	−4.54044	+	5.23995i	−0.266166	+	0.307171i
$292$	6.73358	−	14.7445i	0.394053	−	0.862856i
$293$	11.0480	+	7.10011i	0.645430	+	0.414793i	0.821994	−	0.569496i	$-0.192862\pi$
$293$	11.0480	+	7.10011i	0.645430	+	0.414793i	−0.176563	+	0.984289i	$0.556498\pi$
$294$	0.341254	+	2.37347i	0.0199023	+	0.138424i
$295$	9.97738	−	6.41207i	0.580905	−	0.373325i
$296$	−0.866295	−	0.999758i	−0.0503524	−	0.0581098i
$297$	0.857685	−	0.251839i	0.0497679	−	0.0146132i
$298$	−35.4551			−2.05386
$299$	4.21811	−	4.92397i	0.243940	−	0.284761i
$300$	−11.6824			−0.674484
$301$	1.81228	−	0.532132i	0.104458	−	0.0306716i
$302$	−26.4412	−	30.5147i	−1.52152	−	1.75592i
$303$	15.3093	−	9.83866i	0.879494	−	0.565216i
$304$	0.488452	+	3.39726i	0.0280147	+	0.194846i
$305$	12.4180	+	7.98056i	0.711052	+	0.456965i
$306$	0.996114	−	2.18119i	0.0569441	−	0.124690i
$307$	−5.48608	+	6.33128i	−0.313107	+	0.361345i	−0.890389	−	0.455200i	$-0.849568\pi$
$307$	−5.48608	+	6.33128i	−0.313107	+	0.361345i	0.577282	+	0.816545i	$0.304113\pi$
$308$	0.477031	−	3.31782i	0.0271813	−	0.189050i
$309$	2.29433	+	5.02389i	0.130520	+	0.285799i
$310$	−6.31686	−	1.85480i	−0.358774	−	0.105345i
$311$	14.8324	+	4.35518i	0.841066	+	0.246959i	0.673764	−	0.738946i	$-0.264676\pi$
$311$	14.8324	+	4.35518i	0.841066	+	0.246959i	0.167302	+	0.985906i	$0.446494\pi$
$312$	2.35645	+	5.15991i	0.133408	+	0.292122i
$313$	2.36295	−	16.4347i	0.133562	−	0.928943i	−0.807297	−	0.590145i	$-0.799071\pi$
$313$	2.36295	−	16.4347i	0.133562	−	0.928943i	0.940859	−	0.338798i	$-0.110020\pi$
$314$	34.5191	−	39.8372i	1.94803	−	2.24814i
$315$	0.570276	−	1.24873i	0.0321314	−	0.0703579i
$316$	−37.8211	−	24.3061i	−2.12760	−	1.36733i
$317$	2.19722	+	15.2820i	0.123408	+	0.858321i	0.953650	+	0.300918i	$0.0972930\pi$
$317$	2.19722	+	15.2820i	0.123408	+	0.858321i	−0.830242	+	0.557403i	$0.811798\pi$
$318$	14.1169	−	9.07235i	0.791634	−	0.508752i
$319$	0.219410	+	0.253212i	0.0122846	+	0.0141772i
$320$	13.8529	−	4.06759i	0.774403	−	0.227385i
$321$	5.75657			0.321301
$322$	11.0155	−	3.30224i	0.613869	−	0.184027i
$323$	1.33992			0.0745553
$324$	−3.59792	+	1.05645i	−0.199885	+	0.0586914i
$325$	−2.75821	−	3.18315i	−0.152998	−	0.176569i
$326$	17.0540	−	10.9599i	0.944534	−	0.607015i
$327$	1.69192	+	11.7676i	0.0935636	+	0.650749i
$328$	11.0769	+	7.11871i	0.611621	+	0.393065i
$329$	0.357685	−	0.783221i	0.0197198	−	0.0431804i
$330$	−1.92692	+	2.22379i	−0.106074	+	0.122416i
$331$	2.78663	−	19.3815i	0.153167	−	1.06530i	−0.757700	−	0.652603i	$-0.773677\pi$
$331$	2.78663	−	19.3815i	0.153167	−	1.06530i	0.910868	−	0.412699i	$-0.135414\pi$
$332$	−1.26753	−	2.77551i	−0.0695649	−	0.152326i
$333$	0.302510	+	0.0888249i	0.0165774	+	0.00486757i
$334$	11.1602	+	3.27694i	0.610661	+	0.179306i
$335$	−1.48731	−	3.25676i	−0.0812605	−	0.177936i
$336$	−0.364538	+	2.53542i	−0.0198872	+	0.138318i
$337$	1.23862	−	1.42944i	0.0674720	−	0.0778668i	−0.721010	−	0.692925i	$-0.756322\pi$
$337$	1.23862	−	1.42944i	0.0674720	−	0.0778668i	0.788482	+	0.615058i	$0.210867\pi$
$338$	11.1288	−	24.3688i	0.605330	−	1.32549i
$339$	1.62936	+	1.04713i	0.0884949	+	0.0568722i
$340$	0.732593	+	5.09530i	0.0397304	+	0.276331i
$341$	1.50398	−	0.966551i	0.0814453	−	0.0523417i
$342$	−2.10405	−	2.42820i	−0.113774	−	0.131302i
$343$	−0.959493	+	0.281733i	−0.0518078	+	0.0152121i
$344$	7.92505			0.427290
$345$	−6.32736	−	1.81906i	−0.340653	−	0.0979350i
$346$	−37.5896			−2.02083
$347$	17.4975	−	5.13773i	0.939315	−	0.275808i	0.223984	−	0.974593i	$-0.428094\pi$
$347$	17.4975	−	5.13773i	0.939315	−	0.275808i	0.715332	+	0.698785i	$0.246276\pi$
$348$	−0.920407	−	1.06221i	−0.0493390	−	0.0569402i
$349$	−16.0928	+	10.3422i	−0.861426	+	0.553605i	−0.895119	−	0.445827i	$-0.852910\pi$
$349$	−16.0928	+	10.3422i	−0.861426	+	0.553605i	0.0336929	+	0.999432i	$0.489273\pi$
$350$	−1.06316	−	7.39445i	−0.0568284	−	0.395250i
$351$	−1.13732	−	0.730913i	−0.0607058	−	0.0390133i
$352$	−0.835343	+	1.82915i	−0.0445239	+	0.0974938i
$353$	12.4691	−	14.3902i	0.663665	−	0.765911i	−0.319706	−	0.947517i	$-0.603584\pi$
$353$	12.4691	−	14.3902i	0.663665	−	0.765911i	0.983371	+	0.181606i	$0.0581296\pi$
$354$	2.94825	−	20.5055i	0.156698	−	1.08986i
$355$	−4.42678	−	9.69329i	−0.234949	−	0.514466i
$356$	−43.6130	−	12.8059i	−2.31148	−	0.678713i
$357$	0.959493	+	0.281733i	0.0507818	+	0.0149109i
$358$	−17.1131	−	37.4726i	−0.904458	−	1.98049i
$359$	1.54413	−	10.7396i	0.0814958	−	0.566816i	−0.907633	−	0.419764i	$-0.862113\pi$
$359$	1.54413	−	10.7396i	0.0814958	−	0.566816i	0.989129	−	0.147051i	$-0.0469782\pi$
$360$	3.77199	−	4.35311i	0.198802	−	0.229429i
$361$	−7.14705	+	15.6499i	−0.376161	+	0.823677i
$362$	29.0934	+	18.6972i	1.52911	+	0.982702i
$363$	1.45175	+	10.0971i	0.0761970	+	0.529961i
$364$	−4.26475	+	2.74079i	−0.223534	+	0.143656i
$365$	−3.88603	−	4.48471i	−0.203404	−	0.234741i
$366$	24.7395	−	7.26416i	1.29315	−	0.379704i
$367$	3.64875			0.190463			0.0952315	−	0.995455i	$-0.469641\pi$
$367$	3.64875			0.190463			0.0952315	+	0.995455i	$0.469641\pi$
$368$	12.2843	−	0.0694965i	0.640362	−	0.00362275i
$369$	−3.13814			−0.163365
$370$	−0.995793	+	0.292391i	−0.0517688	+	0.0152007i
$371$	4.58282	+	5.28886i	0.237928	+	0.274584i
$372$	−6.30909	+	4.05461i	−0.327111	+	0.210222i
$373$	2.99224	+	20.8115i	0.154932	+	1.07758i	0.907799	+	0.419405i	$0.137761\pi$
$373$	2.99224	+	20.8115i	0.154932	+	1.07758i	−0.752867	+	0.658172i	$0.771330\pi$
$374$	−1.80318	−	1.15884i	−0.0932404	−	0.0599220i
$375$	−4.62805	+	10.1340i	−0.238991	+	0.523318i
$376$	2.36585	−	2.73034i	0.122009	−	0.140806i
$377$	0.0721154	−	0.501574i	0.00371413	−	0.0258324i
$378$	−0.996114	−	2.18119i	−0.0512346	−	0.112188i
$379$	7.61397	+	2.23566i	0.391103	+	0.114838i	0.471371	−	0.881935i	$-0.343759\pi$
$379$	7.61397	+	2.23566i	0.391103	+	0.114838i	−0.0802677	+	0.996773i	$0.525578\pi$
$380$	6.61811	+	1.94325i	0.339502	+	0.0996868i
$381$	−6.38916	−	13.9903i	−0.327327	−	0.716746i
$382$	−8.03031	+	55.8520i	−0.410866	+	2.85764i
$383$	−0.355649	+	0.410441i	−0.0181728	+	0.0209725i	−0.764763	−	0.644311i	$-0.777144\pi$
$383$	−0.355649	+	0.410441i	−0.0181728	+	0.0209725i	0.746590	+	0.665284i	$0.231690\pi$
$384$	8.60727	−	18.8473i	0.439238	−	0.961797i
$385$	−1.03232	−	0.663434i	−0.0526121	−	0.0338117i
$386$	−5.28381	−	36.7497i	−0.268939	−	1.87051i
$387$	−1.58895	+	1.02115i	−0.0807707	+	0.0519082i
$388$	−17.0258	−	19.6489i	−0.864355	−	0.997519i
$389$	−9.93810	+	2.91809i	−0.503882	+	0.147953i	−0.523788	−	0.851849i	$-0.675481\pi$
$389$	−9.93810	+	2.91809i	−0.503882	+	0.147953i	0.0199060	+	0.999802i	$0.493663\pi$
$390$	4.45027			0.225348
$391$	0.655652	−	4.75080i	0.0331577	−	0.240258i
$392$	−4.19584			−0.211922
$393$	5.32130	−	1.56247i	0.268424	−	0.0788163i
$394$	−12.9969	−	14.9992i	−0.654773	−	0.755648i
$395$	−13.8461	+	8.89833i	−0.696671	+	0.447724i
$396$	0.477031	+	3.31782i	0.0239717	+	0.166727i
$397$	29.8380	+	19.1757i	1.49753	+	0.962403i	0.995214	+	0.0977180i	$0.0311543\pi$
$397$	29.8380	+	19.1757i	1.49753	+	0.962403i	0.502314	+	0.864685i	$0.332482\pi$
$398$	2.80768	−	6.14797i	0.140736	−	0.308170i
$399$	0.877463	−	1.01265i	0.0439281	−	0.0506957i
$400$	1.13570	−	7.89899i	0.0567851	−	0.394949i
$401$	−3.87512	−	8.48533i	−0.193514	−	0.423737i	0.787857	−	0.615858i	$-0.211191\pi$
$401$	−3.87512	−	8.48533i	−0.193514	−	0.423737i	−0.981371	+	0.192121i	$0.938463\pi$
$402$	−6.00048	−	1.76190i	−0.299277	−	0.0878755i
$403$	−2.59435	−	0.761770i	−0.129234	−	0.0379465i
$404$	28.3478	+	62.0730i	1.41036	+	3.08825i
$405$	−0.195368	+	1.35881i	−0.00970790	+	0.0675199i
$406$	0.588568	−	0.679244i	0.0292102	−	0.0337103i
$407$	0.117075	−	0.256360i	0.00580322	−	0.0127073i
$408$	3.52977	+	2.26844i	0.174750	+	0.112305i
$409$	3.50445	+	24.3740i	0.173284	+	1.20522i	0.871887	+	0.489707i	$0.162896\pi$
$409$	3.50445	+	24.3740i	0.173284	+	1.20522i	−0.698603	+	0.715509i	$0.746195\pi$
$410$	8.69020	−	5.58485i	0.429178	−	0.275816i
$411$	11.6316	+	13.4235i	0.573743	+	0.662135i
$412$	−19.8713	+	5.83474i	−0.978989	+	0.287457i
$413$	8.63947			0.425120
$414$	−9.63893	+	6.27190i	−0.473728	+	0.308247i
$415$	−1.11704			−0.0548334
$416$	2.91807	−	0.856822i	0.143070	−	0.0420091i
$417$	−1.13239	−	1.30684i	−0.0554533	−	0.0639965i
$418$	−2.41613	+	1.55275i	−0.118177	+	0.0759475i
$419$	−1.76211	−	12.2558i	−0.0860848	−	0.598733i	−0.986507	−	0.163717i	$-0.947652\pi$
$419$	−1.76211	−	12.2558i	−0.0860848	−	0.598733i	0.900423	−	0.435016i	$-0.143257\pi$
$420$	4.33052	+	2.78305i	0.211308	+	0.135799i
$421$	6.07300	−	13.2980i	0.295980	−	0.648105i	−0.701963	−	0.712213i	$-0.747693\pi$
$421$	6.07300	−	13.2980i	0.295980	−	0.648105i	0.997943	+	0.0641078i	$0.0204202\pi$
$422$	0.398510	−	0.459905i	0.0193992	−	0.0223878i
$423$	−0.122537	+	0.852267i	−0.00595798	+	0.0414386i
$424$	12.1979	+	26.7097i	0.592383	+	1.29714i
$425$	−2.98926	−	0.877726i	−0.145000	−	0.0425760i
$426$	−17.8596	−	5.24405i	−0.865300	−	0.254075i
$427$	4.46688	+	9.78109i	0.216167	+	0.473340i
$428$	−3.07202	+	21.3664i	−0.148492	+	1.03278i
$429$	−0.791393	+	0.913316i	−0.0382088	+	0.0440953i
$430$	2.58282	−	5.65559i	0.124555	−	0.272737i
$431$	26.1105	+	16.7802i	1.25770	+	0.808274i	0.987967	−	0.154662i	$-0.0494288\pi$
$431$	26.1105	+	16.7802i	1.25770	+	0.808274i	0.269731	+	0.962936i	$0.413065\pi$
$432$	−0.364538	−	2.53542i	−0.0175388	−	0.121985i
$433$	−4.55802	+	2.92926i	−0.219045	+	0.140771i	−0.645562	−	0.763708i	$-0.723377\pi$
$433$	−4.55802	+	2.92926i	−0.219045	+	0.140771i	0.426517	+	0.904479i	$0.359740\pi$
$434$	−3.14055	−	3.62439i	−0.150751	−	0.173976i
$435$	−0.493703	+	0.144964i	−0.0236712	+	0.00695050i
$436$	−44.5801			−2.13500
$437$	−5.42550	−	3.44354i	−0.259537	−	0.164727i
$438$	−10.3653			−0.495272
$439$	−3.17654	+	0.932718i	−0.151608	+	0.0445162i	−0.356656	−	0.934236i	$-0.616083\pi$
$439$	−3.17654	+	0.932718i	−0.151608	+	0.0445162i	0.205048	+	0.978752i	$0.434265\pi$
$440$	−3.37176	−	3.89122i	−0.160743	−	0.185507i
$441$	0.841254	−	0.540641i	0.0400597	−	0.0257448i
$442$	0.461354	+	3.20879i	0.0219444	+	0.152626i
$443$	16.3060	+	10.4792i	0.774720	+	0.497882i	0.867278	−	0.497825i	$-0.165868\pi$
$443$	16.3060	+	10.4792i	0.774720	+	0.497882i	−0.0925574	+	0.995707i	$0.529504\pi$
$444$	−0.491123	+	1.07541i	−0.0233076	+	0.0510366i
$445$	−10.8972	+	12.5761i	−0.516578	+	0.596163i
$446$	2.57316	−	17.8968i	0.121843	−	0.847436i
$447$	6.14234	+	13.4499i	0.290523	+	0.636156i
$448$	10.0911	+	2.96302i	0.476760	+	0.139989i
$449$	28.2456	+	8.29365i	1.33299	+	0.391402i	0.869164	−	0.494524i	$-0.164658\pi$
$449$	28.2456	+	8.29365i	1.33299	+	0.391402i	0.463827	+	0.885926i	$0.346476\pi$
$450$	3.10335	+	6.79540i	0.146294	+	0.320338i
$451$	−0.399217	+	2.77662i	−0.0187984	+	0.130746i
$452$	−4.75609	+	5.48882i	−0.223708	+	0.258173i
$453$	−6.99498	+	15.3169i	−0.328653	+	0.719650i
$454$	37.2660	+	23.9494i	1.74898	+	1.12400i
$455$	0.264125	+	1.83703i	0.0123824	+	0.0861214i
$456$	4.72962	−	3.03954i	0.221485	−	0.142339i
$457$	17.6732	+	20.3959i	0.826716	+	0.954081i	0.999523	−	0.0308748i	$-0.00982931\pi$
$457$	17.6732	+	20.3959i	0.826716	+	0.954081i	−0.172808	+	0.984956i	$0.555284\pi$
$458$	−60.5536	+	17.7801i	−2.82948	+	0.830812i
$459$	−1.00000			−0.0466760
$460$	10.1283	−	22.5142i	0.472236	−	1.04973i
$461$	−19.3210			−0.899870			−0.449935	−	0.893061i	$-0.648553\pi$
$461$	−19.3210			−0.899870			−0.449935	+	0.893061i	$0.648553\pi$
$462$	−2.05662	+	0.603879i	−0.0956828	+	0.0280950i
$463$	−26.2110	−	30.2491i	−1.21813	−	1.40579i	−0.886720	−	0.462306i	$-0.847022\pi$
$463$	−26.2110	−	30.2491i	−1.21813	−	1.40579i	−0.331407	−	0.943488i	$-0.607523\pi$
$464$	0.807681	−	0.519065i	0.0374957	−	0.0240970i
$465$	0.390736	+	2.71763i	0.0181199	+	0.126027i
$466$	19.5365	+	12.5554i	0.905012	+	0.581616i
$467$	−12.9346	+	28.3228i	−0.598541	+	1.31062i	0.331600	+	0.943420i	$0.392412\pi$
$467$	−12.9346	+	28.3228i	−0.598541	+	1.31062i	−0.930141	+	0.367202i	$0.880316\pi$
$468$	3.31983	−	3.83129i	0.153459	−	0.177101i
$469$	0.371165	−	2.58151i	0.0171388	−	0.119203i
$470$	−1.17742	−	2.57819i	−0.0543102	−	0.118923i
$471$	−21.0924	−	6.19329i	−0.971886	−	0.285372i
$472$	34.7815	+	10.2128i	1.60095	+	0.470081i
$473$	0.701376	+	1.53580i	0.0322493	+	0.0706161i
$474$	−4.09142	+	28.4565i	−0.187925	+	1.30705i
$475$	−2.73370	+	3.15486i	−0.125431	+	0.144755i
$476$	−1.55773	+	3.41095i	−0.0713984	+	0.156341i
$477$	−5.88723	−	3.78349i	−0.269558	−	0.173234i
$478$	4.51621	+	31.4110i	0.206567	+	1.43670i
$479$	32.7935	−	21.0751i	1.49838	−	0.962947i	0.503270	−	0.864129i	$-0.332130\pi$
$479$	32.7935	−	21.0751i	1.49838	−	0.962947i	0.995106	−	0.0988179i	$-0.0315061\pi$
$480$	−2.02231	−	2.33387i	−0.0923055	−	0.106526i
$481$	−0.408975	+	0.120086i	−0.0186476	+	0.00547544i
$482$	−5.17881			−0.235889
$483$	−3.16106	−	3.60662i	−0.143833	−	0.164107i
$484$	−38.2517			−1.73871
$485$	−9.13259	+	2.68157i	−0.414689	+	0.121764i
$486$	1.57028	+	1.81219i	0.0712292	+	0.0822028i
$487$	−5.59224	+	3.59391i	−0.253408	+	0.162856i	−0.661178	−	0.750229i	$-0.729943\pi$
$487$	−5.59224	+	3.59391i	−0.253408	+	0.162856i	0.407769	+	0.913085i	$0.366307\pi$
$488$	6.42083	+	44.6579i	0.290657	+	2.02157i
$489$	−7.11212	−	4.57069i	−0.321621	−	0.206694i
$490$	−1.36745	+	2.99430i	−0.0617752	+	0.135269i
$491$	2.53869	−	2.92980i	0.114569	−	0.132220i	−0.695568	−	0.718460i	$-0.744847\pi$
$491$	2.53869	−	2.92980i	0.114569	−	0.132220i	0.810137	+	0.586240i	$0.199393\pi$
$492$	1.67468	−	11.6477i	0.0755006	−	0.525118i
$493$	−0.155705	−	0.340947i	−0.00701261	−	0.0153555i
$494$	4.16779	+	1.22377i	0.187518	+	0.0550601i
$495$	1.17742	+	0.345721i	0.0529210	+	0.0155390i
$496$	−2.12816	−	4.66002i	−0.0955573	−	0.209241i
$497$	1.10472	−	7.68351i	0.0495535	−	0.344652i
$498$	−1.27774	+	1.47459i	−0.0572569	+	0.0660780i
$499$	−8.77134	+	19.2066i	−0.392659	+	0.859803i	0.605303	+	0.795995i	$0.293052\pi$
$499$	−8.77134	+	19.2066i	−0.392659	+	0.859803i	−0.997962	+	0.0638083i	$0.979675\pi$
$500$	−35.1441	−	22.5858i	−1.57169	−	1.01007i
$501$	−0.690327	−	4.80133i	−0.0308416	−	0.214508i
$502$	8.56792	−	5.50627i	0.382405	−	0.245757i
$503$	24.7381	+	28.5493i	1.10302	+	1.27295i	0.959010	+	0.283374i	$0.0914537\pi$
$503$	24.7381	+	28.5493i	1.10302	+	1.27295i	0.144008	+	0.989577i	$0.454001\pi$
$504$	4.02588	−	1.18211i	0.179327	−	0.0526552i
$505$	24.9822			1.11169
$506$	4.32314	+	9.32636i	0.192187	+	0.414607i
$507$	−11.1723			−0.496178
$508$	55.3367	−	16.2483i	2.45517	−	0.720903i
$509$	−11.8731	−	13.7022i	−0.526264	−	0.607341i	0.428924	−	0.903341i	$-0.358893\pi$
$509$	−11.8731	−	13.7022i	−0.526264	−	0.607341i	−0.955188	+	0.296000i	$0.904347\pi$
$510$	2.76921	−	1.77967i	0.122623	−	0.0788049i
$511$	−0.615183	−	4.27869i	−0.0272141	−	0.189278i
$512$	22.9304	+	14.7365i	1.01339	+	0.651266i
$513$	−0.556624	+	1.21884i	−0.0245755	+	0.0538129i
$514$	−37.9250	+	43.7677i	−1.67280	+	1.93051i
$515$	−1.07901	+	7.50471i	−0.0475471	+	0.330697i
$516$	−2.94222	−	6.44256i	−0.129524	−	0.283618i
$517$	0.738493	+	0.216841i	0.0324789	+	0.00953667i
$518$	−0.725382	−	0.212991i	−0.0318714	−	0.00935830i
$519$	6.51212	+	14.2596i	0.285850	+	0.625925i
$520$	−1.10823	+	7.70790i	−0.0485990	+	0.338014i
$521$	−10.6721	+	12.3163i	−0.467554	+	0.539586i	−0.939730	−	0.341919i	$-0.888923\pi$
$521$	−10.6721	+	12.3163i	−0.467554	+	0.539586i	0.472176	+	0.881504i	$0.343469\pi$
$522$	−0.373362	+	0.817549i	−0.0163416	+	0.0357831i
$523$	26.4324	+	16.9870i	1.15581	+	0.742791i	0.970787	−	0.239944i	$-0.0771289\pi$
$523$	26.4324	+	16.9870i	1.15581	+	0.742791i	0.185019	+	0.982735i	$0.440765\pi$
$524$	2.95962	+	20.5846i	0.129292	+	0.899242i
$525$	−2.62089	+	1.68434i	−0.114385	+	0.0735108i
$526$	−18.1403	−	20.9351i	−0.790956	−	0.912812i
$527$	−1.91899	+	0.563465i	−0.0835923	+	0.0245449i
$528$	−2.28970			−0.0996464
$529$	−14.8642	+	17.5515i	−0.646268	+	0.763111i
$530$	23.0364			1.00064
$531$	−8.28951	+	2.43402i	−0.359734	+	0.105627i
$532$	3.29032	+	3.79724i	0.142654	+	0.164631i
$533$	3.56908	−	2.29371i	0.154594	−	0.0993517i
$534$	4.13658	+	28.7705i	0.179007	+	1.24502i
$535$	6.64804	+	4.27244i	0.287420	+	0.184714i
$536$	4.54589	−	9.95410i	0.196352	−	0.429952i
$537$	−11.2504	+	12.9837i	−0.485493	+	0.560288i
$538$	4.35452	−	30.2863i	0.187737	−	1.30574i
$539$	−0.371337	−	0.813115i	−0.0159946	−	0.0350233i
$540$	−4.93918	−	1.45027i	−0.212548	−	0.0624098i
$541$	−8.94745	−	2.62721i	−0.384681	−	0.112953i	0.0836734	−	0.996493i	$-0.473335\pi$
$541$	−8.94745	−	2.62721i	−0.384681	−	0.112953i	−0.468354	+	0.883541i	$0.655153\pi$
$542$	27.3753	+	59.9436i	1.17587	+	2.57480i
$543$	2.05253	−	14.2757i	0.0880827	−	0.612628i
$544$	1.47314	−	1.70010i	0.0631606	−	0.0728912i
$545$	−6.77978	+	14.8457i	−0.290414	+	0.635918i
$546$	2.72716	+	1.75264i	0.116712	+	0.0750061i
$547$	1.10987	+	7.71932i	0.0474547	+	0.330054i	0.999695	+	0.0247043i	$0.00786442\pi$
$547$	1.10987	+	7.71932i	0.0474547	+	0.330054i	−0.952240	+	0.305350i	$0.901226\pi$
$548$	−56.0307	+	36.0088i	−2.39351	+	1.53822i
$549$	−7.04159	−	8.12643i	−0.300528	−	0.346827i
$550$	6.40733	−	1.88136i	0.273209	−	0.0802215i
$551$	−0.502228			−0.0213956
$552$	−8.46263	−	18.2565i	−0.360194	−	0.777050i
$553$	−11.9894			−0.509841
$554$	−38.0370	+	11.1687i	−1.61604	+	0.474512i
$555$	0.283432	+	0.327098i	0.0120310	+	0.0138846i
$556$	5.45485	−	3.50562i	0.231337	−	0.148671i
$557$	3.10774	+	21.6148i	0.131679	+	0.915850i	0.943365	+	0.331756i	$0.107641\pi$
$557$	3.10774	+	21.6148i	0.131679	+	0.915850i	−0.811686	+	0.584094i	$0.801450\pi$
$558$	4.03445	+	2.59278i	0.170792	+	0.109761i
$559$	1.06077	−	2.32276i	0.0448658	−	0.0982425i
$560$	−2.30274	+	2.65750i	−0.0973083	+	0.112300i
$561$	−0.127214	+	0.884796i	−0.00537100	+	0.0373561i
$562$	−13.3645	−	29.2641i	−0.563747	−	1.23443i
$563$	−2.33298	−	0.685024i	−0.0983232	−	0.0288703i	0.232201	−	0.972668i	$-0.425407\pi$
$563$	−2.33298	−	0.685024i	−0.0983232	−	0.0288703i	−0.330524	+	0.943798i	$0.607226\pi$
$564$	−3.09792	−	0.909632i	−0.130446	−	0.0383024i
$565$	1.10453	+	2.41858i	0.0464678	+	0.101750i
$566$	1.94127	−	13.5018i	0.0815975	−	0.567523i
$567$	−0.654861	+	0.755750i	−0.0275016	+	0.0317385i
$568$	13.5302	−	29.6270i	0.567714	−	1.24312i
$569$	4.25236	+	2.73283i	0.178268	+	0.114566i	0.626732	−	0.779235i	$-0.284392\pi$
$569$	4.25236	+	2.73283i	0.178268	+	0.114566i	−0.448463	+	0.893801i	$0.648029\pi$
$570$	−0.627711	−	4.36582i	−0.0262919	−	0.182864i
$571$	10.2350	−	6.57764i	0.428322	−	0.275266i	−0.308668	−	0.951170i	$-0.599883\pi$
$571$	10.2350	−	6.57764i	0.428322	−	0.275266i	0.736989	+	0.675904i	$0.236247\pi$
$572$	−2.96758	−	3.42477i	−0.124081	−	0.143197i
$573$	22.5786	−	6.62968i	0.943235	−	0.276959i
$574$	7.52489			0.314083
$575$	9.84814	+	11.2363i	0.410696	+	0.468586i
$576$	−10.5171			−0.438214
$577$	37.3323	−	10.9617i	1.55416	−	0.456343i	0.611821	−	0.790996i	$-0.290437\pi$
$577$	37.3323	−	10.9617i	1.55416	−	0.456343i	0.942341	+	0.334653i	$0.108619\pi$
$578$	−25.1244	−	28.9951i	−1.04504	−	1.20604i
$579$	−13.0256	+	8.37102i	−0.541324	+	0.347888i
$580$	−0.274589	−	1.90981i	−0.0114017	−	0.0793006i
$581$	−0.684532	−	0.439922i	−0.0283992	−	0.0182510i
$582$	−6.90651	+	15.1231i	−0.286284	+	0.626874i
$583$	−4.09656	+	4.72768i	−0.169662	+	0.195800i
$584$	2.58121	−	17.9527i	0.106811	−	0.742889i
$585$	−0.770978	−	1.68821i	−0.0318760	−	0.0697987i
$586$	30.2152	+	8.87198i	1.24818	+	0.366498i
$587$	−24.3131	−	7.13898i	−1.00351	−	0.294657i	−0.261614	−	0.965172i	$-0.584255\pi$
$587$	−24.3131	−	7.13898i	−1.00351	−	0.294657i	−0.741896	+	0.670515i	$0.766073\pi$
$588$	1.55773	+	3.41095i	0.0642397	+	0.140665i
$589$	−0.381382	+	2.65257i	−0.0157146	+	0.109297i
$590$	18.6237	−	21.4929i	0.766725	−	0.884848i
$591$	−3.43831	+	7.52885i	−0.141433	+	0.309695i
$592$	−0.679387	−	0.436615i	−0.0279226	−	0.0179448i
$593$	−4.28662	−	29.8141i	−0.176030	−	1.22432i	−0.865838	−	0.500325i	$-0.833214\pi$
$593$	−4.28662	−	29.8141i	−0.176030	−	1.22432i	0.689807	−	0.723993i	$-0.257695\pi$
$594$	1.80318	−	1.15884i	0.0739855	−	0.0475476i
$595$	0.898983	+	1.03748i	0.0368547	+	0.0425326i
$596$	−53.1990	+	15.6206i	−2.17912	+	0.639846i
$597$	−2.81863			−0.115359
$598$	6.37837	−	14.1784i	0.260831	−	0.579798i
$599$	−9.78580			−0.399837			−0.199919	−	0.979813i	$-0.564068\pi$
$599$	−9.78580			−0.399837			−0.199919	+	0.979813i	$0.564068\pi$
$600$	−12.5425	+	3.68280i	−0.512044	+	0.150350i
$601$	−9.84951	−	11.3669i	−0.401770	−	0.463667i	0.518428	−	0.855122i	$-0.326518\pi$
$601$	−9.84951	−	11.3669i	−0.401770	−	0.463667i	−0.920198	+	0.391454i	$0.871972\pi$
$602$	3.81010	−	2.44860i	0.155288	−	0.0997976i
$603$	0.371165	+	2.58151i	0.0151150	+	0.105127i
$604$	−53.1180	−	34.1368i	−2.16134	−	1.38901i
$605$	−5.81736	+	12.7382i	−0.236509	+	0.517883i
$606$	28.5761	−	32.9786i	1.16082	−	1.33966i
$607$	6.30595	−	43.8589i	0.255951	−	1.78018i	−0.305025	−	0.952344i	$-0.598665\pi$
$607$	6.30595	−	43.8589i	0.255951	−	1.78018i	0.560976	−	0.827832i	$-0.310426\pi$
$608$	−1.25216	−	2.74184i	−0.0507816	−	0.111196i
$609$	−0.359636	−	0.105599i	−0.0145732	−	0.00427907i
$610$	33.9620	+	9.97214i	1.37508	+	0.403760i
$611$	−0.483568	−	1.05887i	−0.0195631	−	0.0428372i
$612$	0.533654	−	3.71165i	0.0215717	−	0.150034i
$613$	−6.83911	+	7.89276i	−0.276229	+	0.318785i	−0.876864	−	0.480738i	$-0.840369\pi$
$613$	−6.83911	+	7.89276i	−0.276229	+	0.318785i	0.600635	+	0.799523i	$0.294914\pi$
$614$	−8.34493	+	18.2728i	−0.336774	+	0.737432i
$615$	−3.62412	−	2.32908i	−0.146139	−	0.0939176i
$616$	−0.533772	−	3.71246i	−0.0215063	−	0.149579i
$617$	38.0248	−	24.4371i	1.53082	−	0.983799i	0.541074	−	0.840975i	$-0.318018\pi$
$617$	38.0248	−	24.4371i	1.53082	−	0.983799i	0.989748	−	0.142824i	$-0.0456183\pi$
$618$	8.67262	+	10.0087i	0.348864	+	0.402610i
$619$	−20.4532	+	6.00560i	−0.822083	+	0.241385i	−0.665613	−	0.746297i	$-0.731830\pi$
$619$	−20.4532	+	6.00560i	−0.822083	+	0.241385i	−0.156470	+	0.987683i	$0.550012\pi$
$620$	−10.2954			−0.413473
$621$	4.04911	+	2.56996i	0.162485	+	0.103129i
$622$	37.0677			1.48628
$623$	−11.6307	+	3.41508i	−0.465974	+	0.136822i
$624$	2.26777	+	2.61714i	0.0907833	+	0.104770i
$625$	0.238401	−	0.153211i	0.00953604	−	0.00612844i
$626$	−5.66607	−	39.4084i	−0.226462	−	1.57507i
$627$	1.00761	+	0.647552i	0.0402401	+	0.0258607i
$628$	34.2434	−	74.9825i	1.36646	−	2.99213i
$629$	−0.206465	+	0.238273i	−0.00823230	+	0.00950058i
$630$	0.468468	−	3.25827i	0.0186642	−	0.129812i
$631$	8.83904	+	19.3548i	0.351877	+	0.770502i	0.999960	+	0.00893294i	$0.00284348\pi$
$631$	8.83904	+	19.3548i	0.351877	+	0.770502i	−0.648084	+	0.761569i	$0.724429\pi$
$632$	−48.2679	−	14.1727i	−1.91999	−	0.563761i
$633$	−0.243503	−	0.0714990i	−0.00967839	−	0.00284183i
$634$	15.3791	+	33.6756i	0.610783	+	1.33743i
$635$	3.00479	−	20.8988i	0.119242	−	0.829344i
$636$	17.1847	−	19.8322i	0.681419	−	0.786400i
$637$	−0.561616	+	1.22977i	−0.0222520	+	0.0487251i
$638$	0.675866	+	0.434353i	0.0267578	+	0.0171962i
$639$	1.10472	+	7.68351i	0.0437021	+	0.303955i
$640$	23.9283	−	15.3778i	0.945851	−	0.607862i
$641$	−4.66297	−	5.38136i	−0.184176	−	0.212551i	0.656152	−	0.754629i	$-0.272183\pi$
$641$	−4.66297	−	5.38136i	−0.184176	−	0.212551i	−0.840328	+	0.542078i	$0.817638\pi$
$642$	13.2444	−	3.88891i	0.522715	−	0.153483i
$643$	20.8741			0.823194			0.411597	−	0.911366i	$-0.364971\pi$
$643$	20.8741			0.823194			0.411597	+	0.911366i	$0.364971\pi$
$644$	15.0734	−	9.80804i	0.593976	−	0.386491i
$645$	−2.59290			−0.102095
$646$	3.08282	−	0.905198i	0.121292	−	0.0356145i
$647$	−3.31901	−	3.83035i	−0.130484	−	0.150586i	0.686748	−	0.726896i	$-0.259038\pi$
$647$	−3.31901	−	3.83035i	−0.130484	−	0.150586i	−0.817232	+	0.576309i	$0.804492\pi$
$648$	−3.52977	+	2.26844i	−0.138662	+	0.0891129i
$649$	1.09906	+	7.64416i	0.0431421	+	0.300060i
$650$	−8.49636	−	5.46028i	−0.333255	−	0.214170i
$651$	−0.830830	+	1.81926i	−0.0325628	+	0.0713026i
$652$	20.7602	−	23.9585i	0.813032	−	0.938289i
$653$	2.64810	−	18.4180i	0.103628	−	0.720750i	−0.870073	−	0.492922i	$-0.835929\pi$
$653$	2.64810	−	18.4180i	0.103628	−	0.720750i	0.973701	−	0.227828i	$-0.0731623\pi$
$654$	11.8424	+	25.9313i	0.463075	+	1.01399i
$655$	7.30500	+	2.14494i	0.285430	+	0.0838098i
$656$	7.71271	+	2.26466i	0.301131	+	0.0884200i
$657$	1.79571	+	3.93206i	0.0700573	+	0.153404i
$658$	0.293830	−	2.04363i	0.0114547	−	0.0796690i
$659$	4.86228	−	5.61137i	0.189407	−	0.218588i	−0.653101	−	0.757271i	$-0.726532\pi$
$659$	4.86228	−	5.61137i	0.189407	−	0.218588i	0.842509	+	0.538683i	$0.181078\pi$
$660$	−1.91153	+	4.18567i	−0.0744062	+	0.162927i
$661$	11.2944	+	7.25845i	0.439300	+	0.282321i	0.741537	−	0.670912i	$-0.234097\pi$
$661$	11.2944	+	7.25845i	0.439300	+	0.282321i	−0.302237	+	0.953233i	$0.597733\pi$
$662$	−6.68201	−	46.4744i	−0.259704	−	1.80628i
$663$	1.13732	−	0.730913i	0.0441700	−	0.0283863i
$664$	−2.23581	−	2.58026i	−0.0867663	−	0.100134i
$665$	1.76492	−	0.518226i	0.0684405	−	0.0200960i
$666$	0.756005			0.0292946
$667$	−0.245750	+	1.78069i	−0.00951549	+	0.0689485i
$668$	18.1893			0.703763
$669$	−7.23489	+	2.12436i	−0.279717	+	0.0821324i
$670$	−5.62206	−	6.48820i	−0.217199	−	0.250661i
$671$	−8.08602	+	5.19657i	−0.312157	+	0.200611i
$672$	−0.320145	−	2.22666i	−0.0123499	−	0.0858952i
$673$	22.7588	+	14.6262i	0.877286	+	0.563798i	0.899973	−	0.435945i	$-0.143586\pi$
$673$	22.7588	+	14.6262i	0.877286	+	0.563798i	−0.0226870	+	0.999743i	$0.507222\pi$
$674$	1.88408	−	4.12555i	0.0725719	−	0.158910i
$675$	2.04019	−	2.35451i	0.0785270	−	0.0906250i
$676$	5.96213	−	41.4675i	0.229313	−	1.59490i
$677$	−14.5954	−	31.9596i	−0.560948	−	1.22831i	−0.951478	−	0.307716i	$-0.900435\pi$
$677$	−14.5954	−	31.9596i	−0.560948	−	1.22831i	0.390530	−	0.920590i	$-0.372292\pi$
$678$	4.45615	+	1.30844i	0.171138	+	0.0502505i
$679$	−6.65260	−	1.95338i	−0.255303	−	0.0749638i
$680$	2.39279	+	5.23948i	0.0917592	+	0.200925i
$681$	2.62911	−	18.2859i	0.100748	−	0.700716i
$682$	2.80732	−	3.23982i	0.107498	−	0.124059i
$683$	−10.9676	+	24.0156i	−0.419662	+	0.918932i	0.575230	+	0.817992i	$0.304913\pi$
$683$	−10.9676	+	24.0156i	−0.419662	+	0.918932i	−0.994892	+	0.100941i	$0.967815\pi$
$684$	−4.22685	−	2.71643i	−0.161618	−	0.103865i
$685$	3.47010	+	24.1351i	0.132586	+	0.922155i
$686$	−2.01722	+	1.29639i	−0.0770179	+	0.0494964i
$687$	17.2354	+	19.8907i	0.657570	+	0.758876i
$688$	4.64212	−	1.36305i	0.176979	−	0.0519658i
$689$	9.46109			0.360439
$690$	−15.7865	+	0.0893100i	−0.600983	+	0.00339997i
$691$	−6.78963			−0.258290			−0.129145	−	0.991626i	$-0.541223\pi$
$691$	−6.78963			−0.258290			−0.129145	+	0.991626i	$0.541223\pi$
$692$	−56.4017	+	16.5610i	−2.14407	+	0.629556i
$693$	0.585376	+	0.675560i	0.0222366	+	0.0256624i
$694$	36.7865	−	23.6412i	1.39640	−	0.897409i
$695$	−0.337831	−	2.34966i	−0.0128146	−	0.0891278i
$696$	−1.32302	−	0.850255i	−0.0501490	−	0.0322288i
$697$	1.30363	−	2.85456i	0.0493786	−	0.108124i
$698$	−30.0386	+	34.6664i	−1.13698	+	1.31214i
$699$	1.37830	−	9.58628i	0.0521321	−	0.362586i
$700$	−4.85304	−	10.6267i	−0.183428	−	0.401651i
$701$	−21.7549	−	6.38781i	−0.821671	−	0.241264i	−0.156236	−	0.987720i	$-0.549936\pi$
$701$	−21.7549	−	6.38781i	−0.821671	−	0.241264i	−0.665435	+	0.746455i	$0.731754\pi$
$702$	−3.11047	−	0.913316i	−0.117397	−	0.0344709i
$703$	0.175493	+	0.384276i	0.00661884	+	0.0144932i
$704$	−1.33793	+	9.30551i	−0.0504252	+	0.350715i
$705$	−0.774052	+	0.893304i	−0.0291525	+	0.0336438i
$706$	18.9669	−	41.5317i	0.713829	−	1.56307i
$707$	15.3093	+	9.83866i	0.575764	+	0.370021i
$708$	−4.61049	−	32.0667i	−0.173273	−	1.20514i
$709$	−35.1017	+	22.5585i	−1.31827	+	0.847202i	−0.995074	−	0.0991302i	$-0.968394\pi$
$709$	−35.1017	+	22.5585i	−1.31827	+	0.847202i	−0.323197	+	0.946332i	$0.604758\pi$
$710$	−16.7333	−	19.3112i	−0.627989	−	0.724738i
$711$	11.5037	−	3.37780i	0.431424	−	0.126677i
$712$	−50.8608			−1.90609
$713$	9.21827	+	2.65018i	0.345227	+	0.0992499i
$714$	2.39788			0.0897383
$715$	−1.59180	+	0.467394i	−0.0595298	+	0.0174795i
$716$	−42.1871	−	48.6865i	−1.57661	−	1.81950i
$717$	11.1333	−	7.15494i	0.415781	−	0.267206i
$718$	−3.70262	−	25.7523i	−0.138181	−	0.961068i
$719$	−19.9122	−	12.7968i	−0.742601	−	0.477241i	0.113831	−	0.993500i	$-0.463688\pi$
$719$	−19.9122	−	12.7968i	−0.742601	−	0.477241i	−0.856432	+	0.516260i	$0.827324\pi$
$720$	1.46075	−	3.19861i	0.0544391	−	0.119205i
$721$	−3.61679	+	4.17400i	−0.134696	+	0.155448i
$722$	−5.87113	+	40.8346i	−0.218501	+	1.51971i
$723$	0.897192	+	1.96458i	0.0333669	+	0.0730634i
$724$	51.8910	+	15.2366i	1.92851	+	0.566263i
$725$	1.12043	+	0.328988i	0.0416117	+	0.0122183i
$726$	10.1613	+	22.2502i	0.377122	+	0.825781i
$727$	1.34873	−	9.38060i	0.0500215	−	0.347907i	−0.949405	−	0.314054i	$-0.898313\pi$
$727$	1.34873	−	9.38060i	0.0500215	−	0.347907i	0.999427	−	0.0338538i	$-0.0107781\pi$
$728$	−3.71471	+	4.28701i	−0.137676	+	0.158887i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−11.9705	−	7.69295i	−0.443046	−	0.284729i
$731$	−0.268802	−	1.86956i	−0.00994201	−	0.0691482i
$732$	33.9202	−	21.7992i	1.25373	−	0.805721i
$733$	−25.3264	−	29.2282i	−0.935453	−	1.07957i	−0.996678	−	0.0814459i	$-0.974046\pi$
$733$	−25.3264	−	29.2282i	−0.935453	−	1.07957i	0.0612251	−	0.998124i	$-0.480499\pi$
$734$	8.39484	−	2.46495i	0.309859	−	0.0909829i
$735$	1.37279			0.0506360
$736$	−10.3341	+	3.09798i	−0.380920	+	0.114193i
$737$	2.33133			0.0858755
$738$	−7.22008	+	2.12001i	−0.265775	+	0.0780385i
$739$	−15.6167	−	18.0226i	−0.574469	−	0.662972i	0.391938	−	0.919992i	$-0.371805\pi$
$739$	−15.6167	−	18.0226i	−0.574469	−	0.662972i	−0.966406	+	0.257020i	$0.917259\pi$
$740$	−1.36533	+	0.877444i	−0.0501905	+	0.0322555i
$741$	−0.257802	−	1.79305i	−0.00947060	−	0.0658695i
$742$	14.1169	+	9.07235i	0.518246	+	0.333056i
$743$	2.62088	−	5.73893i	0.0961508	−	0.210541i	−0.855445	−	0.517894i	$-0.826716\pi$
$743$	2.62088	−	5.73893i	0.0961508	−	0.210541i	0.951595	+	0.307353i	$0.0994433\pi$
$744$	−5.49539	+	6.34201i	−0.201471	+	0.232510i
$745$	−2.88872	+	20.0915i	−0.105834	+	0.736094i
$746$	20.9438	+	45.8605i	0.766806	+	1.67907i
$747$	0.780744	+	0.229247i	0.0285659	+	0.00838771i
$748$	−3.21616	−	0.944350i	−0.117595	−	0.0345289i
$749$	2.39137	+	5.23636i	0.0873787	+	0.191333i
$750$	−3.80183	+	26.4423i	−0.138823	+	0.965537i
$751$	21.9084	−	25.2836i	0.799449	−	0.922613i	−0.198902	−	0.980019i	$-0.563738\pi$
$751$	21.9084	−	25.2836i	0.799449	−	0.922613i	0.998351	+	0.0574063i	$0.0182830\pi$
$752$	0.916206	−	2.00621i	0.0334106	−	0.0731590i
$753$	−3.57313	−	2.29631i	−0.130212	−	0.0836821i
$754$	−0.172924	−	1.20271i	−0.00629752	−	0.0438002i
$755$	−19.4462	+	12.4973i	−0.707719	+	0.454823i
$756$	−2.45561	−	2.83392i	−0.0893096	−	0.103069i
$757$	−24.3150	+	7.13953i	−0.883744	+	0.259491i	−0.691951	−	0.721945i	$-0.743248\pi$
$757$	−24.3150	+	7.13953i	−0.883744	+	0.259491i	−0.191793	+	0.981435i	$0.561430\pi$
$758$	19.0281			0.691133
$759$	2.78899	−	3.25570i	0.101234	−	0.118175i
$760$	7.71795			0.279959
$761$	11.4692	−	3.36766i	0.415759	−	0.122078i	−0.0671616	−	0.997742i	$-0.521394\pi$
$761$	11.4692	−	3.36766i	0.415759	−	0.122078i	0.482920	+	0.875664i	$0.339576\pi$
$762$	−24.1511	−	27.8719i	−0.874904	−	1.00969i
$763$	−10.0013	+	6.42746i	−0.362072	+	0.232690i
$764$	12.5579	+	87.3418i	0.454327	+	3.15991i
$765$	−1.15486	−	0.742184i	−0.0417541	−	0.0268337i
$766$	−0.540981	+	1.18458i	−0.0195464	+	0.0428007i
$767$	7.64879	−	8.82718i	0.276182	−	0.318731i
$768$	4.07718	−	28.3574i	0.147122	−	1.02326i
$769$	−0.448794	−	0.982722i	−0.0161839	−	0.0354378i	0.901367	−	0.433055i	$-0.142564\pi$
$769$	−0.448794	−	0.982722i	−0.0161839	−	0.0354378i	−0.917551	+	0.397617i	$0.869837\pi$
$770$	−2.82330	−	0.828997i	−0.101745	−	0.0298750i
$771$	23.1735	+	6.80435i	0.834572	+	0.245053i
$772$	−24.1191	−	52.8136i	−0.868067	−	1.90080i
$773$	4.79631	−	33.3591i	0.172511	−	1.19984i	−0.701044	−	0.713118i	$-0.747282\pi$
$773$	4.79631	−	33.3591i	0.172511	−	1.19984i	0.873555	−	0.486725i	$-0.161809\pi$
$774$	−2.96591	+	3.42285i	−0.106608	+	0.123032i
$775$	2.58842	−	5.66784i	0.0929787	−	0.203595i
$776$	−24.4735	−	15.7281i	−0.878546	−	0.564607i
$777$	0.0448692	+	0.312072i	0.00160967	+	0.0111955i
$778$	−20.8937	+	13.4276i	−0.749076	+	0.481402i
$779$	−2.75360	−	3.17783i	−0.0986581	−	0.113858i
$780$	6.67746	−	1.96068i	0.239091	−	0.0702036i
$781$	6.93887			0.248292
$782$	−1.70096	−	11.3733i	−0.0608263	−	0.406709i
$783$	0.374818			0.0133949
$784$	−2.45773	+	0.721655i	−0.0877761	+	0.0257734i
$785$	−19.7622	−	22.8068i	−0.705344	−	0.814010i
$786$	11.1874	−	7.18971i	0.399042	−	0.256448i
$787$	2.74454	+	19.0887i	0.0978324	+	0.680439i	0.978431	+	0.206576i	$0.0662319\pi$
$787$	2.74454	+	19.0887i	0.0978324	+	0.680439i	−0.880598	+	0.473864i	$0.842859\pi$
$788$	−26.1096	−	16.7796i	−0.930115	−	0.597749i
$789$	−4.79901	+	10.5084i	−0.170849	+	0.374107i
$790$	−25.8449	+	29.8267i	−0.919522	+	1.06118i
$791$	−0.275640	+	1.91712i	−0.00980061	+	0.0681648i
$792$	1.55807	+	3.41170i	0.0553637	+	0.121230i
$793$	13.9483	+	4.09558i	0.495318	+	0.145438i
$794$	81.6041	+	23.9611i	2.89602	+	0.850349i
$795$	−3.99088	−	8.73881i	−0.141542	−	0.309934i
$796$	1.50418	−	10.4618i	0.0533141	−	0.370808i
$797$	9.30316	−	10.7364i	0.329535	−	0.380304i	−0.566669	−	0.823945i	$-0.691768\pi$
$797$	9.30316	−	10.7364i	0.329535	−	0.380304i	0.896204	+	0.443642i	$0.146314\pi$
$798$	1.33472	−	2.92262i	0.0472484	−	0.103460i
$799$	−0.724345	−	0.465508i	−0.0256255	−	0.0164685i
$800$	0.997399	+	6.93706i	0.0352634	+	0.245262i
$801$	10.1974	−	6.55349i	0.360309	−	0.231556i
$802$	−14.6480	−	16.9047i	−0.517239	−	0.596926i
$803$	3.70751	−	1.08862i	0.130835	−	0.0384167i
$804$	−9.77973			−0.344905
$805$	−0.973802	−	6.51123i	−0.0343220	−	0.229491i
$806$	−6.48357			−0.228374
$807$	−12.2435	+	3.59501i	−0.430991	+	0.126550i
$808$	50.0029	+	57.7065i	1.75910	+	2.03011i
$809$	16.5660	−	10.6463i	0.582430	−	0.374305i	−0.215999	−	0.976394i	$-0.569301\pi$
$809$	16.5660	−	10.6463i	0.582430	−	0.374305i	0.798429	+	0.602088i	$0.205665\pi$
$810$	0.468468	+	3.25827i	0.0164603	+	0.114484i
$811$	−32.3175	−	20.7692i	−1.13482	−	0.729306i	−0.168261	−	0.985743i	$-0.553815\pi$
$811$	−32.3175	−	20.7692i	−1.13482	−	0.729306i	−0.966561	+	0.256437i	$0.917451\pi$
$812$	0.583866	−	1.27849i	0.0204897	−	0.0448661i
$813$	17.9970	−	20.7696i	0.631181	−	0.728422i
$814$	0.0961747	−	0.668910i	0.00337092	−	0.0234453i
$815$	−4.82122	−	10.5570i	−0.168880	−	0.369796i
$816$	2.45773	+	0.721655i	0.0860377	+	0.0252630i
$817$	−2.42831	−	0.713016i	−0.0849558	−	0.0249453i
$818$	24.5290	+	53.7109i	0.857635	+	1.87796i
$819$	0.192401	−	1.33818i	0.00672303	−	0.0467597i
$820$	10.5788	−	12.2085i	0.369426	−	0.426341i
$821$	7.49698	−	16.4161i	0.261646	−	0.572926i	−0.732525	−	0.680741i	$-0.761658\pi$
$821$	7.49698	−	16.4161i	0.261646	−	0.572926i	0.994171	+	0.107815i	$0.0343854\pi$
$822$	35.8297	+	23.0264i	1.24970	+	0.803136i
$823$	−6.27619	−	43.6518i	−0.218774	−	1.52161i	−0.742573	−	0.669765i	$-0.766395\pi$
$823$	−6.27619	−	43.6518i	−0.218774	−	1.52161i	0.523799	−	0.851842i	$-0.324514\pi$
$824$	−19.4949	+	12.5286i	−0.679137	+	0.436455i
$825$	−1.82372	−	2.10468i	−0.0634936	−	0.0732756i
$826$	19.8772	−	5.83648i	0.691617	−	0.203077i
$827$	54.9858			1.91204			0.956022	−	0.293295i	$-0.0947518\pi$
$827$	54.9858			1.91204			0.956022	+	0.293295i	$0.0947518\pi$
$828$	−11.6996	+	13.6574i	−0.406589	+	0.474628i
$829$	−2.62343			−0.0911155			−0.0455577	−	0.998962i	$-0.514506\pi$
$829$	−2.62343			−0.0911155			−0.0455577	+	0.998962i	$0.514506\pi$
$830$	−2.57003	+	0.754629i	−0.0892071	+	0.0261936i
$831$	10.8265	+	12.4944i	0.375566	+	0.433426i
$832$	11.9614	−	7.68711i	0.414686	−	0.266503i
$833$	0.142315	+	0.989821i	0.00493092	+	0.0342953i
$834$	−3.48819	−	2.24172i	−0.120786	−	0.0776245i
$835$	2.76624	−	6.05722i	0.0957297	−	0.209619i
$836$	−2.94120	+	3.39433i	−0.101724	+	0.117395i
$837$	0.284630	−	1.97964i	0.00983824	−	0.0684265i
$838$	−12.3337	−	27.0070i	−0.426060	−	0.932941i
$839$	−24.8005	−	7.28209i	−0.856209	−	0.251406i	−0.175970	−	0.984396i	$-0.556306\pi$
$839$	−24.8005	−	7.28209i	−0.856209	−	0.251406i	−0.680240	+	0.732990i	$0.738124\pi$
$840$	5.52667	+	1.62278i	0.190688	+	0.0559912i
$841$	−11.9887	−	26.2515i	−0.413403	−	0.905225i
$842$	4.98882	−	34.6980i	0.171926	−	1.19577i
$843$	−8.78602	+	10.1396i	−0.302606	+	0.349226i
$844$	0.395326	−	0.865643i	0.0136077	−	0.0297967i
$845$	−12.9024	−	8.29187i	−0.443856	−	0.285249i
$846$	0.293830	+	2.04363i	0.0101021	+	0.0702615i
$847$	−8.58159	+	5.51505i	−0.294867	+	0.189499i
$848$	11.7388	+	13.5473i	0.403113	+	0.465218i
$849$	−5.45821	+	1.60267i	−0.187325	+	0.0550036i
$850$	−7.47049			−0.256236
$851$	1.44835	−	0.434190i	0.0496489	−	0.0148838i
$852$	−29.1080			−0.997224
$853$	−0.682465	+	0.200390i	−0.0233671	+	0.00686121i	−0.293395	−	0.955991i	$-0.594785\pi$
$853$	−0.682465	+	0.200390i	−0.0233671	+	0.00686121i	0.270028	+	0.962852i	$0.412967\pi$
$854$	16.8849	+	19.4862i	0.577788	+	0.666803i
$855$	−1.54742	+	0.994469i	−0.0529208	+	0.0340101i
$856$	3.43743	+	23.9078i	0.117489	+	0.817153i
$857$	47.8486	+	30.7504i	1.63448	+	1.05041i	0.945496	+	0.325633i	$0.105577\pi$
$857$	47.8486	+	30.7504i	1.63448	+	1.05041i	0.688980	+	0.724781i	$0.258059\pi$
$858$	−1.20379	+	2.63594i	−0.0410969	+	0.0899896i
$859$	−13.8759	+	16.0136i	−0.473439	+	0.546378i	−0.941365	−	0.337390i	$-0.890456\pi$
$859$	−13.8759	+	16.0136i	−0.473439	+	0.546378i	0.467926	+	0.883768i	$0.345001\pi$
$860$	1.38371	−	9.62392i	0.0471842	−	0.328173i
$861$	−1.30363	−	2.85456i	−0.0444277	−	0.0972830i
$862$	71.4097	+	20.9678i	2.43222	+	0.714165i
$863$	1.15028	+	0.337753i	0.0391561	+	0.0114973i	0.301252	−	0.953545i	$-0.402595\pi$
$863$	1.15028	+	0.337753i	0.0391561	+	0.0114973i	−0.262096	+	0.965042i	$0.584414\pi$
$864$	0.934499	+	2.04627i	0.0317923	+	0.0696154i
$865$	−3.06262	+	21.3010i	−0.104132	+	0.724255i
$866$	−8.50797	+	9.81872i	−0.289112	+	0.333654i
$867$	−6.64664	+	14.5541i	−0.225732	+	0.494284i
$868$	−6.30909	−	4.05461i	−0.214145	−	0.137622i
$869$	−1.52522	−	10.6082i	−0.0517396	−	0.359857i
$870$	−1.03795	+	0.667052i	−0.0351899	+	0.0226152i
$871$	−2.30899	−	2.66472i	−0.0782373	−	0.0902906i
$872$	−47.8621	+	14.0536i	−1.62082	+	0.475915i
$873$	6.93345			0.234662
$874$	−14.8090	−	4.25747i	−0.500922	−	0.144011i
$875$	−11.1408			−0.376627
$876$	−15.5527	+	4.56669i	−0.525477	+	0.154294i
$877$	−37.5393	−	43.3226i	−1.26761	−	1.46290i	−0.823903	−	0.566731i	$-0.808208\pi$
$877$	−37.5393	−	43.3226i	−1.26761	−	1.46290i	−0.443709	−	0.896171i	$-0.646337\pi$
$878$	−6.67832	+	4.29189i	−0.225382	+	0.144844i
$879$	−1.86899	−	12.9991i	−0.0630394	−	0.438449i
$880$	−2.64428	−	1.69938i	−0.0891388	−	0.0572860i
$881$	9.52052	−	20.8470i	0.320754	−	0.702354i	−0.678732	−	0.734386i	$-0.737470\pi$
$881$	9.52052	−	20.8470i	0.320754	−	0.702354i	0.999487	+	0.0320313i	$0.0101976\pi$
$882$	1.57028	−	1.81219i	0.0528739	−	0.0610198i
$883$	−2.80384	+	19.5011i	−0.0943566	+	0.656264i	0.886672	+	0.462400i	$0.153011\pi$
$883$	−2.80384	+	19.5011i	−0.0943566	+	0.656264i	−0.981028	+	0.193865i	$0.937898\pi$
$884$	2.10596	+	4.61140i	0.0708309	+	0.155098i
$885$	−11.3797	−	3.34139i	−0.382525	−	0.112319i
$886$	44.5952	+	13.0943i	1.49821	+	0.439913i
$887$	−0.581691	−	1.27372i	−0.0195313	−	0.0427675i	0.899615	−	0.436684i	$-0.143847\pi$
$887$	−0.581691	−	1.27372i	−0.0195313	−	0.0427675i	−0.919146	+	0.393916i	$0.871120\pi$
$888$	−0.188264	+	1.30940i	−0.00631773	+	0.0439407i
$889$	10.0719	−	11.6236i	0.337800	−	0.389842i
$890$	−16.5759	+	36.2961i	−0.555624	+	1.21665i
$891$	−0.751992	−	0.483276i	−0.0251927	−	0.0161903i
$892$	−4.02393	−	27.9871i	−0.134731	−	0.937076i
$893$	−0.970566	+	0.623745i	−0.0324788	+	0.0208728i
$894$	23.2182	+	26.7952i	0.776531	+	0.896165i
$895$	−22.6290	+	6.64447i	−0.756404	+	0.222100i
$896$	20.7197			0.692196
$897$	−6.48357	+	0.0366798i	−0.216480	+	0.00122470i
$898$	70.5888			2.35558
$899$	0.719271	−	0.211197i	0.0239890	−	0.00704382i
$900$	7.65035	+	8.82897i	0.255012	+	0.294299i
$901$	5.88723	−	3.78349i	0.196132	−	0.126046i
$902$	0.957274	+	6.65799i	0.0318737	+	0.221687i
$903$	−1.58895	−	1.02115i	−0.0528768	−	0.0339819i
$904$	−3.37593	+	7.39225i	−0.112282	+	0.245862i
$905$	12.9656	−	14.9631i	0.430990	−	0.497389i
$906$	−5.74621	+	39.9658i	−0.190905	+	1.32777i
$907$	−6.78486	−	14.8568i	−0.225288	−	0.493311i	0.762908	−	0.646507i	$-0.223771\pi$
$907$	−6.78486	−	14.8568i	−0.225288	−	0.493311i	−0.988196	+	0.153196i	$0.951044\pi$
$908$	66.4677	+	19.5167i	2.20581	+	0.647684i
$909$	−17.4610	−	5.12701i	−0.579145	−	0.170052i
$910$	1.84871	+	4.04811i	0.0612841	+	0.134194i
$911$	−3.55345	+	24.7148i	−0.117731	+	0.818838i	0.842313	+	0.538989i	$0.181194\pi$
$911$	−3.55345	+	24.7148i	−0.117731	+	0.818838i	−0.960044	+	0.279849i	$0.909716\pi$
$912$	2.24761	−	2.59388i	0.0744258	−	0.0858919i
$913$	0.302159	−	0.661635i	0.00999999	−	0.0218969i
$914$	54.4401	+	34.9866i	1.80072	+	1.15725i
$915$	−2.10075	−	14.6110i	−0.0694487	−	0.483026i
$916$	−83.0249	+	53.3568i	−2.74322	+	1.76296i
$917$	3.63182	+	4.19135i	0.119933	+	0.138410i
$918$	−2.30075	+	0.675560i	−0.0759360	+	0.0222968i
$919$	−30.4586			−1.00474			−0.502368	−	0.864654i	$-0.667538\pi$
$919$	−30.4586			−1.00474			−0.502368	+	0.864654i	$0.667538\pi$
$920$	3.77655	−	27.3646i	0.124509	−	0.902184i
$921$	8.37748			0.276047
$922$	−44.4528	+	13.0525i	−1.46397	+	0.429862i
$923$	−6.87240	−	7.93117i	−0.226208	−	0.261058i
$924$	−2.81983	+	1.81219i	−0.0927656	+	0.0596168i
$925$	−0.139788	−	0.972247i	−0.00459620	−	0.0319673i
$926$	−80.7399	−	51.8884i	−2.65328	−	1.70516i
$927$	2.29433	−	5.02389i	0.0753558	−	0.165006i
$928$	−0.552162	+	0.637229i	−0.0181256	+	0.0209181i
$929$	6.75333	−	46.9705i	0.221570	−	1.54105i	−0.510534	−	0.859858i	$-0.670552\pi$
$929$	6.75333	−	46.9705i	0.221570	−	1.54105i	0.732104	−	0.681193i	$-0.238539\pi$
$930$	2.73490	+	5.98860i	0.0896810	+	0.196374i
$931$	1.28565	+	0.377500i	0.0421353	+	0.0123721i
$932$	34.8454	+	10.2315i	1.14140	+	0.335145i
$933$	−6.42171	−	14.0616i	−0.210237	−	0.460356i
$934$	−10.6255	+	73.9016i	−0.347675	+	2.41814i
$935$	−0.803596	+	0.927399i	−0.0262804	+	0.0303292i
$936$	2.35645	−	5.15991i	0.0770230	−	0.168657i
$937$	21.7431	+	13.9735i	0.710317	+	0.456493i	0.845256	−	0.534361i	$-0.179448\pi$
$937$	21.7431	+	13.9735i	0.710317	+	0.456493i	−0.134940	+	0.990854i	$0.543084\pi$
$938$	−0.890008	−	6.19014i	−0.0290598	−	0.202115i
$939$	−13.9679	+	8.97663i	−0.455826	+	0.292941i
$940$	−2.90255	−	3.34973i	−0.0946709	−	0.109256i
$941$	−3.94896	+	1.15952i	−0.128732	+	0.0377992i	−0.345464	−	0.938432i	$-0.612278\pi$
$941$	−3.94896	+	1.15952i	−0.128732	+	0.0377992i	0.216732	+	0.976231i	$0.430460\pi$
$942$	−52.7122			−1.71746
$943$	−12.6146	+	8.20815i	−0.410789	+	0.267294i
$944$	22.1299			0.720266
$945$	−1.31718	+	0.386758i	−0.0428478	+	0.0125813i
$946$	2.65121	+	3.05966i	0.0861984	+	0.0994782i
$947$	3.08307	−	1.98137i	0.100186	−	0.0643858i	−0.489588	−	0.871954i	$-0.662853\pi$
$947$	3.08307	−	1.98137i	0.100186	−	0.0643858i	0.589775	+	0.807568i	$0.299217\pi$
$948$	6.39819	+	44.5004i	0.207804	+	1.44531i
$949$	−4.91630	−	3.15951i	−0.159590	−	0.102562i
$950$	−4.15825	+	9.10530i	−0.134912	+	0.295415i
$951$	10.1105	−	11.6681i	0.327854	−	0.378364i
$952$	−0.597131	+	4.15314i	−0.0193531	+	0.134604i
$953$	20.0379	+	43.8768i	0.649090	+	1.42131i	0.892349	+	0.451347i	$0.149056\pi$
$953$	20.0379	+	43.8768i	0.649090	+	1.42131i	−0.243259	+	0.969961i	$0.578216\pi$
$954$	−16.1010	−	4.72768i	−0.521289	−	0.153064i
$955$	30.9956	+	9.10112i	1.00299	+	0.294505i
$956$	20.6153	+	45.1412i	0.666746	+	1.45997i
$957$	0.0476823	−	0.331638i	0.00154135	−	0.0107203i
$958$	61.2121	−	70.6425i	1.97767	−	2.28236i
$959$	−7.37856	+	16.1568i	−0.238266	+	0.521730i
$960$	−12.1458	−	7.80565i	−0.392005	−	0.251926i
$961$	3.84250	+	26.7252i	0.123952	+	0.862103i
$962$	−0.859822	+	0.552574i	−0.0277218	+	0.0178157i
$963$	−3.76975	−	4.35053i	−0.121479	−	0.140194i
$964$	−7.77061	+	2.28166i	−0.250274	+	0.0734872i
$965$	−21.2556			−0.684240
$966$	−9.70928	−	6.16244i	−0.312391	−	0.198273i
$967$	−20.3592			−0.654708			−0.327354	−	0.944902i	$-0.606157\pi$
$967$	−20.3592			−0.654708			−0.327354	+	0.944902i	$0.606157\pi$
$968$	−41.0678	+	12.0586i	−1.31997	+	0.387578i
$969$	−0.877463	−	1.01265i	−0.0281882	−	0.0325309i
$970$	−19.2002	+	12.3392i	−0.616481	+	0.396189i
$971$	−5.39568	−	37.5278i	−0.173156	−	1.20432i	−0.872165	−	0.489211i	$-0.837285\pi$
$971$	−5.39568	−	37.5278i	−0.173156	−	1.20432i	0.699010	−	0.715112i	$-0.253624\pi$
$972$	3.15455	+	2.02730i	0.101182	+	0.0650258i
$973$	0.718337	−	1.57294i	0.0230288	−	0.0504261i
$974$	−10.4384	+	12.0466i	−0.334468	+	0.385997i
$975$	−0.599417	+	4.16904i	−0.0191967	+	0.133516i
$976$	11.4418	+	25.0541i	0.366245	+	0.801964i
$977$	−16.1623	−	4.74568i	−0.517078	−	0.151828i	0.0127731	−	0.999918i	$-0.495934\pi$
$977$	−16.1623	−	4.74568i	−0.517078	−	0.151828i	−0.529851	+	0.848091i	$0.677752\pi$
$978$	−19.4510	−	5.71132i	−0.621973	−	0.182628i
$979$	−4.50124	−	9.85635i	−0.143860	−	0.315010i
$980$	−0.732593	+	5.09530i	−0.0234018	+	0.162763i
$981$	7.78538	−	8.98481i	0.248568	−	0.286863i
$982$	3.86162	−	8.45576i	0.123229	−	0.269834i
$983$	−39.3382	−	25.2811i	−1.25469	−	0.806342i	−0.267144	−	0.963657i	$-0.586080\pi$
$983$	−39.3382	−	25.2811i	−1.25469	−	0.806342i	−0.987549	+	0.157314i	$0.949716\pi$
$984$	−1.87388	−	13.0331i	−0.0597372	−	0.415481i
$985$	−9.55856	+	6.14291i	−0.304561	+	0.195729i
$986$	−0.588568	−	0.679244i	−0.0187438	−	0.0216315i
$987$	−0.826153	+	0.242580i	−0.0262967	+	0.00772142i
$988$	6.79276			0.216107
$989$	−3.71628	+	8.26087i	−0.118171	+	0.262680i
$990$	2.94250			0.0935186
$991$	52.7542	−	15.4900i	1.67579	−	0.492057i	0.700626	−	0.713529i	$-0.252904\pi$
$991$	52.7542	−	15.4900i	1.67579	−	0.492057i	0.975167	+	0.221472i	$0.0710861\pi$
$992$	2.94629	+	3.40020i	0.0935448	+	0.107956i
$993$	−16.4724	+	10.5862i	−0.522735	+	0.335942i
$994$	−2.64899	−	18.4241i	−0.0840207	−	0.584377i
$995$	−3.25513	−	2.09195i	−0.103195	−	0.0663191i
$996$	−1.26753	+	2.77551i	−0.0401633	+	0.0879453i
$997$	−37.9715	+	43.8214i	−1.20257	+	1.38784i	−0.301895	+	0.953341i	$0.597619\pi$
$997$	−37.9715	+	43.8214i	−1.20257	+	1.38784i	−0.900673	+	0.434497i	$0.856926\pi$
$998$	−7.20545	+	50.1150i	−0.228084	+	1.58636i
$999$	−0.130972	−	0.286790i	−0.00414378	−	0.00907362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.b.400.1	yes	10
23.18	even	11	inner	483.2.q.b.64.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.b.64.1	✓	10	23.18	even	11	inner
483.2.q.b.400.1	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30075 - 0.675560i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(3.15455 - 2.02730i) q^{4} +(-0.195368 - 1.35881i) q^{5} +(-2.01722 - 1.29639i) q^{6} +(0.415415 - 0.909632i) q^{7} +(2.74769 - 3.17101i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-1.36745 - 2.99430i) q^{10} +(0.857685 + 0.251839i) q^{11} +(-3.59792 - 1.05645i) q^{12} +(-0.561616 - 1.22977i) q^{13} +(0.341254 - 2.37347i) q^{14} +(-0.898983 + 1.03748i) q^{15} +(1.06408 - 2.33001i) q^{16} +(-0.841254 - 0.540641i) q^{17} +(0.341254 + 2.37347i) q^{18} +(-1.12721 + 0.724417i) q^{19} +(-3.37102 - 3.89037i) q^{20} +(-0.959493 + 0.281733i) q^{21} +2.14345 q^{22} +(2.01691 + 4.35110i) q^{23} -4.19584 q^{24} +(2.98926 - 0.877726i) q^{25} +(-2.12292 - 2.44998i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.533654 - 3.71165i) q^{28} +(0.315317 + 0.202642i) q^{29} +(-1.36745 + 2.99430i) q^{30} +(1.30972 - 1.51150i) q^{31} +(-0.320145 + 2.22666i) q^{32} +(-0.371337 - 0.813115i) q^{33} +(-2.30075 - 0.675560i) q^{34} +(-1.31718 - 0.386758i) q^{35} +(1.55773 + 3.41095i) q^{36} +(0.0448692 - 0.312072i) q^{37} +(-2.10405 + 2.42820i) q^{38} +(-0.561616 + 1.22977i) q^{39} +(-4.84562 - 3.11409i) q^{40} +(0.446605 + 3.10620i) q^{41} +(-2.01722 + 1.29639i) q^{42} +(1.23689 + 1.42745i) q^{43} +(3.21616 - 0.944350i) q^{44} +1.37279 q^{45} +(7.57982 + 8.64824i) q^{46} +0.861031 q^{47} +(-2.45773 + 0.721655i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(6.28458 - 4.03885i) q^{50} +(0.142315 + 0.989821i) q^{51} +(-4.26475 - 2.74079i) q^{52} +(-2.90714 + 6.36575i) q^{53} +(1.57028 - 1.81219i) q^{54} +(0.174638 - 1.21463i) q^{55} +(-1.74302 - 3.81667i) q^{56} +(1.28565 + 0.377500i) q^{57} +(0.862362 + 0.253212i) q^{58} +(3.58896 + 7.85873i) q^{59} +(-0.732593 + 5.09530i) q^{60} +(-7.04159 + 8.12643i) q^{61} +(1.99223 - 4.36237i) q^{62} +(0.841254 + 0.540641i) q^{63} +(1.49674 + 10.4101i) q^{64} +(-1.56130 + 1.00339i) q^{65} +(-1.40366 - 1.61991i) q^{66} +(2.50241 - 0.734774i) q^{67} -3.74982 q^{68} +(1.96755 - 4.37364i) q^{69} -3.29177 q^{70} +(7.44808 - 2.18695i) q^{71} +(2.74769 + 3.17101i) q^{72} +(3.63648 - 2.33702i) q^{73} +(-0.107591 - 0.748310i) q^{74} +(-2.62089 - 1.68434i) q^{75} +(-2.08724 + 4.57041i) q^{76} +(0.585376 - 0.675560i) q^{77} +(-0.461354 + 3.20879i) q^{78} +(-4.98057 - 10.9059i) q^{79} +(-3.37394 - 0.990677i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(3.12595 + 6.84488i) q^{82} +(0.115802 - 0.805422i) q^{83} +(-2.45561 + 2.83392i) q^{84} +(-0.570276 + 1.24873i) q^{85} +(3.81010 + 2.44860i) q^{86} +(-0.0533422 - 0.371003i) q^{87} +(3.15524 - 2.02775i) q^{88} +(-7.93804 - 9.16098i) q^{89} +(3.15843 - 0.927399i) q^{90} -1.35194 q^{91} +(15.1834 + 9.63686i) q^{92} -2.00000 q^{93} +(1.98101 - 0.581678i) q^{94} +(1.20457 + 1.39015i) q^{95} +(1.89245 - 1.21620i) q^{96} +(-0.986733 - 6.86288i) q^{97} +(-2.01722 - 1.29639i) q^{98} +(-0.371337 + 0.813115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more