LMFDB - Embedded newform 532.2.cj.a.409.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(33,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 15, 7]))

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

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

chi := DirichletCharacter("532.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$532 = 2^{2} \cdot 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	532.cj (of order $18$ , degree $6$ , 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:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			409.9
Character	$\chi$	$=$	532.409
Dual form			532.2.cj.a.173.9

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194048 + 1.10050i) q^{3} +(-1.74253 + 0.307255i) q^{5} +(2.62371 + 0.340814i) q^{7} +(1.64563 - 0.598960i) q^{9} -0.865134 q^{11} +(2.59449 + 2.17703i) q^{13} +(-0.676269 - 1.85803i) q^{15} +(-0.129993 + 0.357153i) q^{17} +(-0.996646 + 4.24343i) q^{19} +(0.134059 + 2.95353i) q^{21} +(0.845741 + 0.709661i) q^{23} +(-1.75646 + 0.639298i) q^{25} +(2.65470 + 4.59808i) q^{27} +(-0.146747 - 0.0258754i) q^{29} +(4.27871 + 7.41094i) q^{31} +(-0.167877 - 0.952080i) q^{33} +(-4.67661 + 0.212269i) q^{35} +(-2.38619 + 1.37767i) q^{37} +(-1.89237 + 3.27768i) q^{39} +(4.37905 - 3.67446i) q^{41} +(2.34755 + 0.854438i) q^{43} +(-2.68353 + 1.54933i) q^{45} +(-2.75359 - 7.56541i) q^{47} +(6.76769 + 1.78839i) q^{49} +(-0.418272 - 0.0737526i) q^{51} +(-9.81784 - 1.73115i) q^{53} +(1.50752 - 0.265817i) q^{55} +(-4.86330 - 0.273381i) q^{57} +(4.39079 + 1.59812i) q^{59} +(0.263460 - 0.313979i) q^{61} +(4.52179 - 1.01064i) q^{63} +(-5.18987 - 2.99637i) q^{65} +(3.95783 - 4.71676i) q^{67} +(-0.616868 + 1.06845i) q^{69} +(5.13337 - 14.1038i) q^{71} +(-11.7056 + 2.06401i) q^{73} +(-1.04439 - 1.80893i) q^{75} +(-2.26986 - 0.294850i) q^{77} +(4.04409 - 11.1110i) q^{79} +(-0.520464 + 0.436721i) q^{81} +(9.30187 + 5.37044i) q^{83} +(0.116780 - 0.662291i) q^{85} -0.166516i q^{87} +(-0.280994 + 1.59360i) q^{89} +(6.06521 + 6.59614i) q^{91} +(-7.32547 + 6.14680i) q^{93} +(0.432870 - 7.70053i) q^{95} +(-0.297381 - 1.68653i) q^{97} +(-1.42369 + 0.518181i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$78 q + 6 q^{7} - 6 q^{11} + 6 q^{13} - 3 q^{15} + 27 q^{17} + 21 q^{19} - 3 q^{21} - 24 q^{23} + 12 q^{27} - 18 q^{29} + 33 q^{35} + 36 q^{37} - 18 q^{39} - 18 q^{41} - 48 q^{43} - 18 q^{45} - 18 q^{49}+ \cdots + 27 q^{99}+O(q^{100})$ 78 * q + 6 * q^7 - 6 * q^11 + 6 * q^13 - 3 * q^15 + 27 * q^17 + 21 * q^19 - 3 * q^21 - 24 * q^23 + 12 * q^27 - 18 * q^29 + 33 * q^35 + 36 * q^37 - 18 * q^39 - 18 * q^41 - 48 * q^43 - 18 * q^45 - 18 * q^49 + 6 * q^53 - 18 * q^57 + 45 * q^59 + 39 * q^61 - 27 * q^63 - 18 * q^65 + 21 * q^67 + 6 * q^71 - 3 * q^73 - 21 * q^75 - 21 * q^77 + 36 * q^79 + 36 * q^81 - 18 * q^83 + 60 * q^85 - 21 * q^91 - 102 * q^93 + 60 * q^95 - 27 * q^97 + 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$ .

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$

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

)

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

$2$		0			0
$2$		0			0
$3$	0.194048	+	1.10050i	0.112034	+	0.635374i	0.988176	+	0.153322i	$0.0489973\pi$
$3$	0.194048	+	1.10050i	0.112034	+	0.635374i	−0.876143	+	0.482052i	$0.839892\pi$
$4$		0			0
$5$	−1.74253	+	0.307255i	−0.779283	+	0.137409i	−0.549120	−	0.835743i	$-0.685037\pi$
$5$	−1.74253	+	0.307255i	−0.779283	+	0.137409i	−0.230163	+	0.973152i	$0.573926\pi$
$6$		0			0
$7$	2.62371	+	0.340814i	0.991669	+	0.128816i
$7$	2.62371	+	0.340814i	0.991669	+	0.128816i
$8$		0			0
$9$	1.64563	−	0.598960i	0.548543	−	0.199653i
$10$		0			0
$11$	−0.865134			−0.260848			−0.130424	−	0.991458i	$-0.541634\pi$
$11$	−0.865134			−0.260848			−0.130424	+	0.991458i	$0.541634\pi$
$12$		0			0
$13$	2.59449	+	2.17703i	0.719581	+	0.603800i	0.927269	−	0.374395i	$-0.122150\pi$
$13$	2.59449	+	2.17703i	0.719581	+	0.603800i	−0.207688	+	0.978195i	$0.566594\pi$
$14$		0			0
$15$	−0.676269	−	1.85803i	−0.174612	−	0.479742i
$16$		0			0
$17$	−0.129993	+	0.357153i	−0.0315279	+	0.0866223i	−0.954458	−	0.298346i	$-0.903565\pi$
$17$	−0.129993	+	0.357153i	−0.0315279	+	0.0866223i	0.922930	+	0.384968i	$0.125787\pi$
$18$		0			0
$19$	−0.996646	+	4.24343i	−0.228646	+	0.973510i
$19$	−0.996646	+	4.24343i	−0.228646	+	0.973510i
$20$		0			0
$21$	0.134059	+	2.95353i	0.0292541	+	0.644513i
$22$		0			0
$23$	0.845741	+	0.709661i	0.176349	+	0.147975i	0.726690	−	0.686966i	$-0.241058\pi$
$23$	0.845741	+	0.709661i	0.176349	+	0.147975i	−0.550341	+	0.834940i	$0.685502\pi$
$24$		0			0
$25$	−1.75646	+	0.639298i	−0.351292	+	0.127860i
$26$		0			0
$27$	2.65470	+	4.59808i	0.510898	+	0.884902i
$28$		0			0
$29$	−0.146747	−	0.0258754i	−0.0272502	−	0.00480494i	0.160006	−	0.987116i	$-0.448848\pi$
$29$	−0.146747	−	0.0258754i	−0.0272502	−	0.00480494i	−0.187257	+	0.982311i	$0.559960\pi$
$30$		0			0
$31$	4.27871	+	7.41094i	0.768479	+	1.33104i	0.938388	+	0.345584i	$0.112319\pi$
$31$	4.27871	+	7.41094i	0.768479	+	1.33104i	−0.169909	+	0.985460i	$0.554347\pi$
$32$		0			0
$33$	−0.167877	−	0.952080i	−0.0292237	−	0.165736i
$34$		0			0
$35$	−4.67661	+	0.212269i	−0.790491	+	0.0358799i
$36$		0			0
$37$	−2.38619	+	1.37767i	−0.392288	+	0.226488i	−0.683151	−	0.730277i	$-0.739391\pi$
$37$	−2.38619	+	1.37767i	−0.392288	+	0.226488i	0.290863	+	0.956765i	$0.406058\pi$
$38$		0			0
$39$	−1.89237	+	3.27768i	−0.303022	+	0.524849i
$40$		0			0
$41$	4.37905	−	3.67446i	0.683893	−	0.573854i	−0.233248	−	0.972417i	$-0.574935\pi$
$41$	4.37905	−	3.67446i	0.683893	−	0.573854i	0.917141	+	0.398563i	$0.130491\pi$
$42$		0			0
$43$	2.34755	+	0.854438i	0.357998	+	0.130301i	0.514757	−	0.857336i	$-0.327882\pi$
$43$	2.34755	+	0.854438i	0.357998	+	0.130301i	−0.156759	+	0.987637i	$0.550105\pi$
$44$		0			0
$45$	−2.68353	+	1.54933i	−0.400036	+	0.230961i
$46$		0			0
$47$	−2.75359	−	7.56541i	−0.401652	−	1.10353i	−0.961469	−	0.274913i	$-0.911351\pi$
$47$	−2.75359	−	7.56541i	−0.401652	−	1.10353i	0.559817	−	0.828616i	$-0.310871\pi$
$48$		0			0
$49$	6.76769	+	1.78839i	0.966813	+	0.255485i
$50$		0			0
$51$	−0.418272	−	0.0737526i	−0.0585698	−	0.0103274i
$52$		0			0
$53$	−9.81784	−	1.73115i	−1.34858	−	0.237792i	−0.547732	−	0.836654i	$-0.684509\pi$
$53$	−9.81784	−	1.73115i	−1.34858	−	0.237792i	−0.800852	+	0.598862i	$0.795620\pi$
$54$		0			0
$55$	1.50752	−	0.265817i	0.203274	−	0.0358427i
$56$		0			0
$57$	−4.86330	−	0.273381i	−0.644159	−	0.0362102i
$58$		0			0
$59$	4.39079	+	1.59812i	0.571632	+	0.208057i	0.611632	−	0.791142i	$-0.290513\pi$
$59$	4.39079	+	1.59812i	0.571632	+	0.208057i	−0.0399994	+	0.999200i	$0.512736\pi$
$60$		0			0
$61$	0.263460	−	0.313979i	0.0337326	−	0.0402009i	−0.748914	−	0.662667i	$-0.769425\pi$
$61$	0.263460	−	0.313979i	0.0337326	−	0.0402009i	0.782647	+	0.622466i	$0.213869\pi$
$62$		0			0
$63$	4.52179	−	1.01064i	0.569692	−	0.127329i
$64$		0			0
$65$	−5.18987	−	2.99637i	−0.643725	−	0.371655i
$66$		0			0
$67$	3.95783	−	4.71676i	0.483526	−	0.576244i	−0.468033	−	0.883711i	$-0.655037\pi$
$67$	3.95783	−	4.71676i	0.483526	−	0.576244i	0.951559	+	0.307467i	$0.0994815\pi$
$68$		0			0
$69$	−0.616868	+	1.06845i	−0.0742622	+	0.128626i
$70$		0			0
$71$	5.13337	−	14.1038i	0.609219	−	1.67382i	−0.122717	−	0.992442i	$-0.539161\pi$
$71$	5.13337	−	14.1038i	0.609219	−	1.67382i	0.731936	−	0.681374i	$-0.238617\pi$
$72$		0			0
$73$	−11.7056	+	2.06401i	−1.37003	+	0.241574i	−0.809773	−	0.586744i	$-0.800410\pi$
$73$	−11.7056	+	2.06401i	−1.37003	+	0.241574i	−0.560259	+	0.828317i	$0.689298\pi$
$74$		0			0
$75$	−1.04439	−	1.80893i	−0.120595	−	0.208877i
$76$		0			0
$77$	−2.26986	−	0.294850i	−0.258674	−	0.0336013i
$78$		0			0
$79$	4.04409	−	11.1110i	0.454995	−	1.25009i	−0.474173	−	0.880432i	$-0.657253\pi$
$79$	4.04409	−	11.1110i	0.454995	−	1.25009i	0.929168	−	0.369657i	$-0.120525\pi$
$80$		0			0
$81$	−0.520464	+	0.436721i	−0.0578294	+	0.0485246i
$82$		0			0
$83$	9.30187	+	5.37044i	1.02101	+	0.589482i	0.914397	−	0.404818i	$-0.132665\pi$
$83$	9.30187	+	5.37044i	1.02101	+	0.589482i	0.106616	+	0.994300i	$0.465999\pi$
$84$		0			0
$85$	0.116780	−	0.662291i	0.0126665	−	0.0718355i
$86$		0			0
$87$		−	0.166516i		−	0.0178524i
$88$		0			0
$89$	−0.280994	+	1.59360i	−0.0297853	+	0.168921i	−0.996072	−	0.0885479i	$-0.971777\pi$
$89$	−0.280994	+	1.59360i	−0.0297853	+	0.168921i	0.966287	+	0.257469i	$0.0828885\pi$
$90$		0			0
$91$	6.06521	+	6.59614i	0.635807	+	0.691463i
$92$		0			0
$93$	−7.32547	+	6.14680i	−0.759616	+	0.637393i
$94$		0			0
$95$	0.432870	−	7.70053i	0.0444116	−	0.790058i
$96$		0			0
$97$	−0.297381	−	1.68653i	−0.0301944	−	0.171241i	0.965981	−	0.258611i	$-0.0832648\pi$
$97$	−0.297381	−	1.68653i	−0.0301944	−	0.171241i	−0.996176	+	0.0873701i	$0.972154\pi$
$98$		0			0
$99$	−1.42369	+	0.518181i	−0.143086	+	0.0520791i
$100$		0			0
$101$	−2.10765	−	5.79071i	−0.209719	−	0.576197i	0.789580	−	0.613648i	$-0.210299\pi$
$101$	−2.10765	−	5.79071i	−0.209719	−	0.576197i	−0.999298	+	0.0374507i	$0.988076\pi$
$102$		0			0
$103$	1.20476	−	2.08670i	0.118708	−	0.205609i	−0.800548	−	0.599269i	$-0.795458\pi$
$103$	1.20476	−	2.08670i	0.118708	−	0.205609i	0.919256	+	0.393660i	$0.128791\pi$
$104$		0			0
$105$	−1.14109	−	5.10542i	−0.111359	−	0.498238i
$106$		0			0
$107$			10.9072i			1.05444i	0.849728	+	0.527221i	$0.176766\pi$
$107$			10.9072i			1.05444i	−0.849728	+	0.527221i	$0.823234\pi$
$108$		0			0
$109$	−2.22794	−	2.65516i	−0.213398	−	0.254318i	0.648718	−	0.761029i	$-0.275306\pi$
$109$	−2.22794	−	2.65516i	−0.213398	−	0.254318i	−0.862116	+	0.506711i	$0.830861\pi$
$110$		0			0
$111$	−1.97916	−	2.35868i	−0.187854	−	0.223876i
$112$		0			0
$113$			2.37339i			0.223270i	0.993749	+	0.111635i	$0.0356087\pi$
$113$			2.37339i			0.223270i	−0.993749	+	0.111635i	$0.964391\pi$
$114$		0			0
$115$	−1.69178	−	0.976748i	−0.157759	−	0.0910822i
$116$		0			0
$117$	5.57352	+	2.02860i	0.515272	+	0.187544i
$118$		0			0
$119$	−0.462787	+	0.892762i	−0.0424236	+	0.0818393i
$120$		0			0
$121$	−10.2515			−0.931959
$122$		0			0
$123$	4.89349	+	4.10613i	0.441231	+	0.370237i
$124$		0			0
$125$	10.5260	−	6.07721i	0.941477	−	0.543562i
$126$		0			0
$127$	10.4642	−	12.4708i	0.928552	−	1.10661i	−0.0655168	−	0.997851i	$-0.520870\pi$
$127$	10.4642	−	12.4708i	0.928552	−	1.10661i	0.994069	−	0.108754i	$-0.0346860\pi$
$128$		0			0
$129$	−0.484773	+	2.74928i	−0.0426818	+	0.242061i
$130$		0			0
$131$	−5.77569	−	6.88320i	−0.504625	−	0.601388i	0.452249	−	0.891892i	$-0.350622\pi$
$131$	−5.77569	−	6.88320i	−0.504625	−	0.601388i	−0.956874	+	0.290503i	$0.906177\pi$
$132$		0			0
$133$	−4.06113	+	10.7939i	−0.352145	+	0.935946i
$134$		0			0
$135$	−6.03869	−	7.19663i	−0.519727	−	0.619387i
$136$		0			0
$137$	1.68518	−	9.55715i	0.143975	−	0.816522i	−0.824210	−	0.566285i	$-0.808380\pi$
$137$	1.68518	−	9.55715i	0.143975	−	0.816522i	0.968184	−	0.250237i	$-0.0805087\pi$
$138$		0			0
$139$	4.44188	−	5.29362i	0.376755	−	0.448999i	−0.544032	−	0.839064i	$-0.683103\pi$
$139$	4.44188	−	5.29362i	0.376755	−	0.448999i	0.920787	+	0.390065i	$0.127548\pi$
$140$		0			0
$141$	7.79142	−	4.49838i	0.656156	−	0.378832i
$142$		0			0
$143$	−2.24458	−	1.88342i	−0.187701	−	0.157500i
$144$		0			0
$145$	0.263661			0.0218959
$146$		0			0
$147$	−0.654873	+	7.79488i	−0.0540130	+	0.642911i
$148$		0			0
$149$	−21.7982	−	7.93389i	−1.78578	−	0.649969i	−0.999484	−	0.0321146i	$-0.989776\pi$
$149$	−21.7982	−	7.93389i	−1.78578	−	0.649969i	−0.786292	−	0.617855i	$-0.788002\pi$
$150$		0			0
$151$	−4.39509	−	2.53750i	−0.357667	−	0.206499i	0.310390	−	0.950609i	$-0.399540\pi$
$151$	−4.39509	−	2.53750i	−0.357667	−	0.206499i	−0.668057	+	0.744110i	$0.732874\pi$
$152$		0			0
$153$			0.665602i			0.0538108i
$154$		0			0
$155$	−9.73283	−	11.5991i	−0.781759	−	0.931664i
$156$		0			0
$157$	−8.45556	−	10.0769i	−0.674827	−	0.804228i	0.314605	−	0.949223i	$-0.398128\pi$
$157$	−8.45556	−	10.0769i	−0.674827	−	0.804228i	−0.989432	+	0.144995i	$0.953684\pi$
$158$		0			0
$159$		−	11.1405i		−	0.883496i
$160$		0			0
$161$	1.97712	+	2.15018i	0.155819	+	0.169458i
$162$		0			0
$163$	0.0161036	−	0.0278923i	0.00126133	−	0.00218469i	−0.865394	−	0.501092i	$-0.832932\pi$
$163$	0.0161036	−	0.0278923i	0.00126133	−	0.00218469i	0.866655	+	0.498907i	$0.166265\pi$
$164$		0			0
$165$	0.585063	+	1.60745i	0.0455471	+	0.125140i
$166$		0			0
$167$	−16.4005	+	5.96928i	−1.26910	+	0.461916i	−0.886814	−	0.462126i	$-0.847087\pi$
$167$	−16.4005	+	5.96928i	−1.26910	+	0.461916i	−0.382291	+	0.924042i	$0.624865\pi$
$168$		0			0
$169$	−0.265538	−	1.50594i	−0.0204260	−	0.115842i
$170$		0			0
$171$	0.901536	+	7.58007i	0.0689422	+	0.579662i
$172$		0			0
$173$	−4.18857	+	3.51463i	−0.318451	+	0.267212i	−0.787975	−	0.615708i	$-0.788870\pi$
$173$	−4.18857	+	3.51463i	−0.318451	+	0.267212i	0.469523	+	0.882920i	$0.344426\pi$
$174$		0			0
$175$	−4.82632	+	1.07871i	−0.364835	+	0.0815426i
$176$		0			0
$177$	−0.906706	+	5.14218i	−0.0681522	+	0.386510i
$178$		0			0
$179$			0.978463i			0.0731337i	0.999331	+	0.0365669i	$0.0116422\pi$
$179$			0.978463i			0.0731337i	−0.999331	+	0.0365669i	$0.988358\pi$
$180$		0			0
$181$	0.958806	−	5.43766i	0.0712675	−	0.404178i	−0.928216	−	0.372042i	$-0.878658\pi$
$181$	0.958806	−	5.43766i	0.0712675	−	0.404178i	0.999483	−	0.0321363i	$-0.0102311\pi$
$182$		0			0
$183$	0.396659	+	0.229011i	0.0293218	+	0.0169290i
$184$		0			0
$185$	3.73472	−	3.13380i	0.274582	−	0.230402i
$186$		0			0
$187$	0.112461	−	0.308985i	0.00822399	−	0.0225952i
$188$		0			0
$189$	5.39808	+	12.9688i	0.392652	+	0.943341i
$190$		0			0
$191$	11.3881	+	19.7247i	0.824011	+	1.42723i	0.902673	+	0.430328i	$0.141602\pi$
$191$	11.3881	+	19.7247i	0.824011	+	1.42723i	−0.0786614	+	0.996901i	$0.525065\pi$
$192$		0			0
$193$	7.38621	−	1.30239i	0.531671	−	0.0937479i	0.0986333	−	0.995124i	$-0.468553\pi$
$193$	7.38621	−	1.30239i	0.531671	−	0.0937479i	0.433037	+	0.901376i	$0.357442\pi$
$194$		0			0
$195$	2.29043	−	6.29290i	0.164021	−	0.450644i
$196$		0			0
$197$	4.59338	−	7.95597i	0.327265	−	0.566839i	−0.654703	−	0.755886i	$-0.727206\pi$
$197$	4.59338	−	7.95597i	0.327265	−	0.566839i	0.981968	+	0.189047i	$0.0605398\pi$
$198$		0			0
$199$	−4.58703	+	5.46661i	−0.325166	+	0.387518i	−0.903718	−	0.428128i	$-0.859173\pi$
$199$	−4.58703	+	5.46661i	−0.325166	+	0.387518i	0.578552	+	0.815645i	$0.303618\pi$
$200$		0			0
$201$	5.95881	+	3.44032i	0.420302	+	0.242661i
$202$		0			0
$203$	−0.376202	−	0.117903i	−0.0264042	−	0.00827516i
$204$		0			0
$205$	−6.50163	+	7.74834i	−0.454094	+	0.541168i
$206$		0			0
$207$	1.81684	+	0.661274i	0.126279	+	0.0459617i
$208$		0			0
$209$	0.862232	−	3.67113i	0.0596418	−	0.253938i
$210$		0			0
$211$	−2.40840	+	0.424665i	−0.165801	+	0.0292351i	−0.255932	−	0.966695i	$-0.582382\pi$
$211$	−2.40840	+	0.424665i	−0.165801	+	0.0292351i	0.0901315	+	0.995930i	$0.471271\pi$
$212$		0			0
$213$	16.5174	+	2.91246i	1.13175	+	0.199559i
$214$		0			0
$215$	−4.35320	−	0.767587i	−0.296886	−	0.0523490i
$216$		0			0
$217$	8.70033	+	20.9024i	0.590617	+	1.41895i
$218$		0			0
$219$	−4.54288	−	12.4815i	−0.306979	−	0.843419i
$220$		0			0
$221$	−1.11480	+	0.643629i	−0.0749895	+	0.0432952i
$222$		0			0
$223$	19.0027	+	6.91640i	1.27251	+	0.463156i	0.887949	−	0.459942i	$-0.152130\pi$
$223$	19.0027	+	6.91640i	1.27251	+	0.463156i	0.384563	+	0.923099i	$0.374352\pi$
$224$		0			0
$225$	−2.50757	+	2.10410i	−0.167171	+	0.140273i
$226$		0			0
$227$	−3.19958	+	5.54184i	−0.212364	+	0.367825i	−0.952454	−	0.304683i	$-0.901449\pi$
$227$	−3.19958	+	5.54184i	−0.212364	+	0.367825i	0.740090	+	0.672508i	$0.234783\pi$
$228$		0			0
$229$	−11.1646	+	6.44586i	−0.737775	+	0.425955i	−0.821260	−	0.570554i	$-0.806728\pi$
$229$	−11.1646	+	6.44586i	−0.737775	+	0.425955i	0.0834847	+	0.996509i	$0.473395\pi$
$230$		0			0
$231$	−0.115979	−	2.55520i	−0.00763085	−	0.168120i
$232$		0			0
$233$	3.92342	+	22.2508i	0.257032	+	1.45770i	0.790804	+	0.612070i	$0.209663\pi$
$233$	3.92342	+	22.2508i	0.257032	+	1.45770i	−0.533772	+	0.845628i	$0.679226\pi$
$234$		0			0
$235$	7.12272	+	12.3369i	0.464635	+	0.804771i
$236$		0			0
$237$	13.0125	+	2.29445i	0.845249	+	0.149040i
$238$		0			0
$239$	−13.4314	−	23.2639i	−0.868805	−	1.50481i	−0.863219	−	0.504830i	$-0.831555\pi$
$239$	−13.4314	−	23.2639i	−0.868805	−	1.50481i	−0.00558567	−	0.999984i	$-0.501778\pi$
$240$		0			0
$241$	23.4473	−	8.53411i	1.51037	−	0.549730i	0.551650	−	0.834076i	$-0.313999\pi$
$241$	23.4473	−	8.53411i	1.51037	−	0.549730i	0.958722	+	0.284346i	$0.0917763\pi$
$242$		0			0
$243$	11.6201	+	9.75044i	0.745431	+	0.625491i
$244$		0			0
$245$	−12.3424	−	1.03692i	−0.788527	−	0.0662466i
$246$		0			0
$247$	−11.8239	+	8.83979i	−0.752335	+	0.562462i
$248$		0			0
$249$	−4.10516	+	11.2788i	−0.260154	+	0.714767i
$250$		0			0
$251$	8.83095	+	24.2628i	0.557405	+	1.53146i	0.823388	+	0.567479i	$0.192081\pi$
$251$	8.83095	+	24.2628i	0.557405	+	1.53146i	−0.265984	+	0.963978i	$0.585697\pi$
$252$		0			0
$253$	−0.731679	−	0.613952i	−0.0460003	−	0.0385988i
$254$		0			0
$255$	0.751512			0.0470615
$256$		0			0
$257$	−2.86673	+	1.04340i	−0.178822	+	0.0650858i	−0.429879	−	0.902886i	$-0.641444\pi$
$257$	−2.86673	+	1.04340i	−0.178822	+	0.0650858i	0.251058	+	0.967972i	$0.419222\pi$
$258$		0			0
$259$	−6.73021	+	2.80136i	−0.418195	+	0.174068i
$260$		0			0
$261$	−0.256989	+	0.0453141i	−0.0159072	+	0.00280488i
$262$		0			0
$263$	−2.89405	−	16.4130i	−0.178455	−	1.01207i	−0.934080	−	0.357064i	$-0.883778\pi$
$263$	−2.89405	−	16.4130i	−0.178455	−	1.01207i	0.755625	−	0.655004i	$-0.227333\pi$
$264$		0			0
$265$	17.6398			1.08360
$266$		0			0
$267$	−1.80828			−0.110665
$268$		0			0
$269$	−5.29998	−	30.0577i	−0.323145	−	1.83265i	−0.522399	−	0.852701i	$-0.674963\pi$
$269$	−5.29998	−	30.0577i	−0.323145	−	1.83265i	0.199254	−	0.979948i	$-0.436148\pi$
$270$		0			0
$271$	14.7843	−	2.60688i	0.898084	−	0.158356i	0.294496	−	0.955653i	$-0.404848\pi$
$271$	14.7843	−	2.60688i	0.898084	−	0.158356i	0.603588	+	0.797296i	$0.293737\pi$
$272$		0			0
$273$	−6.08211	+	7.95474i	−0.368106	+	0.481443i
$274$		0			0
$275$	1.51957	−	0.553079i	0.0916336	−	0.0333519i
$276$		0			0
$277$	−20.5918			−1.23724			−0.618622	−	0.785689i	$-0.712309\pi$
$277$	−20.5918			−1.23724			−0.618622	+	0.785689i	$0.712309\pi$
$278$		0			0
$279$	11.4800	+	9.63289i	0.687291	+	0.576706i
$280$		0			0
$281$	2.93459	+	8.06273i	0.175063	+	0.480982i	0.995929	−	0.0901385i	$-0.0287310\pi$
$281$	2.93459	+	8.06273i	0.175063	+	0.480982i	−0.820866	+	0.571121i	$0.806509\pi$
$282$		0			0
$283$	−6.53417	+	17.9525i	−0.388416	+	1.06716i	0.579299	+	0.815115i	$0.303326\pi$
$283$	−6.53417	+	17.9525i	−0.388416	+	1.06716i	−0.967715	+	0.252048i	$0.918896\pi$
$284$		0			0
$285$	8.55844	−	1.01790i	0.506958	−	0.0602951i
$286$		0			0
$287$	12.7417	−	8.14827i	0.752117	−	0.480977i
$288$		0			0
$289$	12.9121	+	10.8345i	0.759535	+	0.637326i
$290$		0			0
$291$	1.79832	−	0.654535i	0.105419	−	0.0383695i
$292$		0			0
$293$	7.01055	+	12.1426i	0.409561	+	0.709380i	0.994841	−	0.101451i	$-0.0323486\pi$
$293$	7.01055	+	12.1426i	0.409561	+	0.709380i	−0.585280	+	0.810831i	$0.699015\pi$
$294$		0			0
$295$	−8.14212	−	1.43567i	−0.474052	−	0.0835882i
$296$		0			0
$297$	−2.29667	−	3.97796i	−0.133267	−	0.230824i
$298$		0			0
$299$	0.649309	+	3.68241i	0.0375505	+	0.212959i
$300$		0			0
$301$	5.86808	+	3.04187i	0.338230	+	0.175331i
$302$		0			0
$303$	5.96370	−	3.44314i	0.342605	−	0.197803i
$304$		0			0
$305$	−0.362615	+	0.628068i	−0.0207633	+	0.0359631i
$306$		0			0
$307$	10.6114	−	8.90398i	0.605622	−	0.508177i	−0.287625	−	0.957743i	$-0.592866\pi$
$307$	10.6114	−	8.90398i	0.605622	−	0.508177i	0.893247	+	0.449566i	$0.148421\pi$
$308$		0			0
$309$	2.53020	+	0.920917i	0.143938	+	0.0523891i
$310$		0			0
$311$	−9.63561	+	5.56312i	−0.546386	+	0.315456i	−0.747663	−	0.664078i	$-0.768824\pi$
$311$	−9.63561	+	5.56312i	−0.546386	+	0.315456i	0.201277	+	0.979534i	$0.435491\pi$
$312$		0			0
$313$	−4.63531	−	12.7354i	−0.262003	−	0.719848i	−0.999032	−	0.0439865i	$-0.985994\pi$
$313$	−4.63531	−	12.7354i	−0.262003	−	0.719848i	0.737029	−	0.675861i	$-0.236228\pi$
$314$		0			0
$315$	−7.56883	+	3.15042i	−0.426455	+	0.177506i
$316$		0			0
$317$	14.6387	+	2.58120i	0.822191	+	0.144974i	0.568891	−	0.822413i	$-0.307373\pi$
$317$	14.6387	+	2.58120i	0.822191	+	0.144974i	0.253300	+	0.967388i	$0.418484\pi$
$318$		0			0
$319$	0.126956	+	0.0223857i	0.00710815	+	0.00125336i
$320$		0			0
$321$	−12.0034	+	2.11653i	−0.669965	+	0.118133i
$322$		0			0
$323$	−1.38600	−	0.907571i	−0.0771189	−	0.0504986i
$324$		0			0
$325$	−5.94888	−	2.16522i	−0.329984	−	0.120105i
$326$		0			0
$327$	2.48968	−	2.96708i	0.137679	−	0.164080i
$328$		0			0
$329$	−4.64620	−	20.7879i	−0.256154	−	1.14607i
$330$		0			0
$331$	−2.59275	−	1.49693i	−0.142511	−	0.0822785i	0.427049	−	0.904228i	$-0.359553\pi$
$331$	−2.59275	−	1.49693i	−0.142511	−	0.0822785i	−0.569560	+	0.821950i	$0.692886\pi$
$332$		0			0
$333$	−3.10162	+	3.69637i	−0.169968	+	0.202560i
$334$		0			0
$335$	−5.44739	+	9.43516i	−0.297623	+	0.515498i
$336$		0			0
$337$	0.773904	−	2.12628i	0.0421572	−	0.115826i	−0.916828	−	0.399283i	$-0.869259\pi$
$337$	0.773904	−	2.12628i	0.0421572	−	0.115826i	0.958985	+	0.283457i	$0.0914813\pi$
$338$		0			0
$339$	−2.61192	+	0.460552i	−0.141860	+	0.0250138i
$340$		0			0
$341$	−3.70165	−	6.41145i	−0.200456	−	0.347200i
$342$		0			0
$343$	17.1469	+	6.99875i	0.925848	+	0.377897i
$344$		0			0
$345$	0.746626	−	2.05134i	0.0401970	−	0.110440i
$346$		0			0
$347$	5.10198	−	4.28107i	0.273889	−	0.229820i	−0.495489	−	0.868614i	$-0.665011\pi$
$347$	5.10198	−	4.28107i	0.273889	−	0.229820i	0.769377	+	0.638794i	$0.220567\pi$
$348$		0			0
$349$	−8.51870	−	4.91828i	−0.455996	−	0.263269i	0.254363	−	0.967109i	$-0.418134\pi$
$349$	−8.51870	−	4.91828i	−0.455996	−	0.263269i	−0.710359	+	0.703839i	$0.751467\pi$
$350$		0			0
$351$	−3.12258	+	17.7090i	−0.166671	+	0.945239i
$352$		0			0
$353$			14.4828i			0.770840i	0.922741	+	0.385420i	$0.125943\pi$
$353$			14.4828i			0.770840i	−0.922741	+	0.385420i	$0.874057\pi$
$354$		0			0
$355$	−4.61158	+	26.1536i	−0.244757	+	1.38809i
$356$		0			0
$357$	−1.07229	−	0.336058i	−0.0567515	−	0.0177861i
$358$		0			0
$359$	−15.1212	+	12.6882i	−0.798066	+	0.669657i	−0.947728	−	0.319080i	$-0.896626\pi$
$359$	−15.1212	+	12.6882i	−0.798066	+	0.669657i	0.149662	+	0.988737i	$0.452182\pi$
$360$		0			0
$361$	−17.0134	−	8.45839i	−0.895442	−	0.445179i
$362$		0			0
$363$	−1.98929	−	11.2818i	−0.104411	−	0.592143i
$364$		0			0
$365$	19.7631	−	7.19318i	1.03445	−	0.376508i
$366$		0			0
$367$	1.09506	+	3.00864i	0.0571615	+	0.157050i	0.964987	−	0.262299i	$-0.0844807\pi$
$367$	1.09506	+	3.00864i	0.0571615	+	0.157050i	−0.907825	+	0.419349i	$0.862258\pi$
$368$		0			0
$369$	5.00544	−	8.66968i	0.260573	−	0.451326i
$370$		0			0
$371$	−25.1691	−	7.88809i	−1.30672	−	0.409529i
$372$		0			0
$373$		−	21.3570i		−	1.10582i	−0.833241	−	0.552911i	$-0.813517\pi$
$373$		−	21.3570i		−	1.10582i	0.833241	−	0.552911i	$-0.186483\pi$
$374$		0			0
$375$	8.73053	+	10.4046i	0.450842	+	0.537293i
$376$		0			0
$377$	−0.324401	−	0.386606i	−0.0167075	−	0.0199112i
$378$		0			0
$379$		−	13.7741i		−	0.707530i	−0.935334	−	0.353765i	$-0.884901\pi$
$379$		−	13.7741i		−	0.707530i	0.935334	−	0.353765i	$-0.115099\pi$
$380$		0			0
$381$	15.7547	+	9.09598i	0.807138	+	0.466001i
$382$		0			0
$383$	−10.5763	−	3.84944i	−0.540422	−	0.196697i	0.0573640	−	0.998353i	$-0.481730\pi$
$383$	−10.5763	−	3.84944i	−0.540422	−	0.196697i	−0.597786	+	0.801656i	$0.703953\pi$
$384$		0			0
$385$	4.04589	−	0.183641i	0.206198	−	0.00935919i
$386$		0			0
$387$	4.37497			0.222392
$388$		0			0
$389$	−16.2275	−	13.6165i	−0.822766	−	0.690383i	0.130852	−	0.991402i	$-0.458229\pi$
$389$	−16.2275	−	13.6165i	−0.822766	−	0.690383i	−0.953618	+	0.301019i	$0.902673\pi$
$390$		0			0
$391$	−0.363398	+	0.209808i	−0.0183778	+	0.0106104i
$392$		0			0
$393$	6.45421	−	7.69183i	0.325572	−	0.388001i
$394$		0			0
$395$	−3.63302	+	20.6039i	−0.182797	+	1.03669i
$396$		0			0
$397$	21.9657	+	26.1777i	1.10243	+	1.31382i	0.945285	+	0.326245i	$0.105783\pi$
$397$	21.9657	+	26.1777i	1.10243	+	1.31382i	0.157141	+	0.987576i	$0.449772\pi$
$398$		0			0
$399$	−12.6667	−	2.37475i	−0.634128	−	0.118886i
$400$		0			0
$401$	−6.46569	−	7.70550i	−0.322881	−	0.384795i	0.580049	−	0.814581i	$-0.303033\pi$
$401$	−6.46569	−	7.70550i	−0.322881	−	0.384795i	−0.902930	+	0.429787i	$0.858589\pi$
$402$		0			0
$403$	−5.03281	+	28.5425i	−0.250702	+	1.42180i
$404$		0			0
$405$	0.772740	−	0.920916i	0.0383978	−	0.0457607i
$406$		0			0
$407$	2.06438	−	1.19187i	0.102327	−	0.0590788i
$408$		0			0
$409$	−18.7789	−	15.7573i	−0.928554	−	0.779150i	0.0470028	−	0.998895i	$-0.485033\pi$
$409$	−18.7789	−	15.7573i	−0.928554	−	0.779150i	−0.975557	+	0.219745i	$0.929477\pi$
$410$		0			0
$411$	10.8447			0.534928
$412$		0			0
$413$	10.9755	+	5.68944i	0.540069	+	0.279959i
$414$		0			0
$415$	−17.8589	−	6.50010i	−0.876658	−	0.319077i
$416$		0			0
$417$	6.68757	+	3.86107i	0.327492	+	0.189077i
$418$		0			0
$419$		−	14.1798i		−	0.692727i	−0.938100	−	0.346363i	$-0.887416\pi$
$419$		−	14.1798i		−	0.692727i	0.938100	−	0.346363i	$-0.112584\pi$
$420$		0			0
$421$	25.1679	+	29.9939i	1.22661	+	1.46181i	0.842648	+	0.538466i	$0.180996\pi$
$421$	25.1679	+	29.9939i	1.22661	+	1.46181i	0.383961	+	0.923349i	$0.374560\pi$
$422$		0			0
$423$	−9.06277	−	10.8006i	−0.440647	−	0.525142i
$424$		0			0
$425$		−	0.710428i		−	0.0344608i
$426$		0			0
$427$	0.798251	−	0.734000i	0.0386301	−	0.0355207i
$428$		0			0
$429$	1.63715	−	2.83563i	0.0790425	−	0.136906i
$430$		0			0
$431$	0.132315	+	0.363532i	0.00637337	+	0.0175107i	0.942839	−	0.333250i	$-0.108145\pi$
$431$	0.132315	+	0.363532i	0.00637337	+	0.0175107i	−0.936465	+	0.350761i	$0.885923\pi$
$432$		0			0
$433$	−28.5547	+	10.3931i	−1.37225	+	0.499459i	−0.919821	−	0.392339i	$-0.871666\pi$
$433$	−28.5547	+	10.3931i	−1.37225	+	0.499459i	−0.452433	+	0.891798i	$0.649444\pi$
$434$		0			0
$435$	0.0511629	+	0.290159i	0.00245307	+	0.0139121i
$436$		0			0
$437$	−3.85430	+	2.88156i	−0.184376	+	0.137844i
$438$		0			0
$439$	−2.16028	+	1.81269i	−0.103105	+	0.0865150i	−0.692883	−	0.721050i	$-0.743660\pi$
$439$	−2.16028	+	1.81269i	−0.103105	+	0.0865150i	0.589778	+	0.807565i	$0.299215\pi$
$440$		0			0
$441$	12.2083	−	1.11054i	0.581347	−	0.0528830i
$442$		0			0
$443$	−1.24944	+	7.08592i	−0.0593627	+	0.336662i	−0.999996	−	0.00276150i	$-0.999121\pi$
$443$	−1.24944	+	7.08592i	−0.0593627	+	0.336662i	0.940634	+	0.339424i	$0.110232\pi$
$444$		0			0
$445$		−	2.86323i		−	0.135730i
$446$		0			0
$447$	4.50136	−	25.5285i	0.212907	−	1.20746i
$448$		0			0
$449$	−11.0263	−	6.36606i	−0.520365	−	0.300433i	0.216719	−	0.976234i	$-0.430465\pi$
$449$	−11.0263	−	6.36606i	−0.520365	−	0.300433i	−0.737084	+	0.675801i	$0.763798\pi$
$450$		0			0
$451$	−3.78846	+	3.17890i	−0.178392	+	0.149689i
$452$		0			0
$453$	1.93967	−	5.32919i	0.0911335	−	0.250387i
$454$		0			0
$455$	−12.5955	−	9.63040i	−0.590486	−	0.451480i
$456$		0			0
$457$	9.57961	+	16.5924i	0.448115	+	0.776158i	0.998263	−	0.0589088i	$-0.0187621\pi$
$457$	9.57961	+	16.5924i	0.448115	+	0.776158i	−0.550148	+	0.835067i	$0.685429\pi$
$458$		0			0
$459$	−1.98731	+	0.350417i	−0.0927598	+	0.0163561i
$460$		0			0
$461$	10.8948	−	29.9332i	0.507421	−	1.39413i	−0.376467	−	0.926430i	$-0.622861\pi$
$461$	10.8948	−	29.9332i	0.507421	−	1.39413i	0.883888	−	0.467699i	$-0.154917\pi$
$462$		0			0
$463$	5.78780	−	10.0248i	0.268982	−	0.465890i	−0.699617	−	0.714518i	$-0.746646\pi$
$463$	5.78780	−	10.0248i	0.268982	−	0.465890i	0.968599	+	0.248628i	$0.0799795\pi$
$464$		0			0
$465$	10.8762	−	12.9618i	0.504372	−	0.601088i
$466$		0			0
$467$	−18.4632	−	10.6597i	−0.854375	−	0.493274i	0.00774933	−	0.999970i	$-0.497533\pi$
$467$	−18.4632	−	10.6597i	−0.854375	−	0.493274i	−0.862125	+	0.506696i	$0.830867\pi$
$468$		0			0
$469$	11.9917	−	11.0265i	0.553727	−	0.509157i
$470$		0			0
$471$	9.44891	−	11.2608i	0.435383	−	0.518869i
$472$		0			0
$473$	−2.03094	−	0.739203i	−0.0933829	−	0.0339886i
$474$		0			0
$475$	−0.962251	−	8.09056i	−0.0441511	−	0.371220i
$476$		0			0
$477$	−17.1934	+	3.03166i	−0.787233	+	0.138810i
$478$		0			0
$479$	−21.6472	−	3.81698i	−0.989084	−	0.174402i	−0.344377	−	0.938832i	$-0.611910\pi$
$479$	−21.6472	−	3.81698i	−0.989084	−	0.174402i	−0.644708	+	0.764429i	$0.723021\pi$
$480$		0			0
$481$	−9.19018	−	1.62048i	−0.419036	−	0.0738874i
$482$		0			0
$483$	−1.98262	+	2.59306i	−0.0902126	+	0.117988i
$484$		0			0
$485$	1.03639	+	2.84746i	0.0470600	+	0.129296i
$486$		0			0
$487$	34.9209	−	20.1616i	1.58242	−	0.913609i	0.587911	−	0.808926i	$-0.299951\pi$
$487$	34.9209	−	20.1616i	1.58242	−	0.913609i	0.994506	−	0.104683i	$-0.0333827\pi$
$488$		0			0
$489$	0.0338203	+	0.0123096i	0.00152941	+	0.000556659i
$490$		0			0
$491$	−20.6413	+	17.3201i	−0.931527	+	0.781644i	−0.976091	−	0.217363i	$-0.930255\pi$
$491$	−20.6413	+	17.3201i	−0.931527	+	0.781644i	0.0445639	+	0.999007i	$0.485810\pi$
$492$		0			0
$493$	0.0283175	−	0.0490474i	0.00127536	−	0.00220898i
$494$		0			0
$495$	2.32161	−	1.34038i	0.104349	−	0.0602457i
$496$		0			0
$497$	18.2752	−	35.2548i	0.819757	−	1.58139i
$498$		0			0
$499$	−5.84935	−	33.1733i	−0.261853	−	1.48504i	−0.777850	−	0.628450i	$-0.783690\pi$
$499$	−5.84935	−	33.1733i	−0.261853	−	1.48504i	0.515997	−	0.856590i	$-0.327422\pi$
$500$		0			0
$501$	−9.75167	−	16.8904i	−0.435672	−	0.754607i
$502$		0			0
$503$	−33.2085	−	5.85556i	−1.48069	−	0.261086i	−0.625839	−	0.779952i	$-0.715243\pi$
$503$	−33.2085	−	5.85556i	−1.48069	−	0.261086i	−0.854856	+	0.518866i	$0.826354\pi$
$504$		0			0
$505$	5.45186	+	9.44290i	0.242605	+	0.420204i
$506$		0			0
$507$	1.60576	−	0.584450i	0.0713144	−	0.0259563i
$508$		0			0
$509$	−10.5921	−	8.88779i	−0.469485	−	0.393945i	0.377122	−	0.926164i	$-0.376914\pi$
$509$	−10.5921	−	8.88779i	−0.469485	−	0.393945i	−0.846607	+	0.532219i	$0.821358\pi$
$510$		0			0
$511$	−31.4154	+	1.42593i	−1.38974	+	0.0630793i
$512$		0			0
$513$	−22.1574	+	6.68239i	−0.978275	+	0.295035i
$514$		0			0
$515$	−1.45818	+	4.00631i	−0.0642550	+	0.176539i
$516$		0			0
$517$	2.38222	+	6.54509i	0.104770	+	0.287853i
$518$		0			0
$519$	−4.68064	−	3.92752i	−0.205457	−	0.172399i
$520$		0			0
$521$	32.1850			1.41005			0.705024	−	0.709183i	$-0.250936\pi$
$521$	32.1850			1.41005			0.705024	+	0.709183i	$0.250936\pi$
$522$		0			0
$523$	19.2201	−	6.99556i	0.840438	−	0.305895i	0.114303	−	0.993446i	$-0.463537\pi$
$523$	19.2201	−	6.99556i	0.840438	−	0.305895i	0.726136	+	0.687551i	$0.241314\pi$
$524$		0			0
$525$	−2.12365	−	5.10204i	−0.0926839	−	0.222671i
$526$		0			0
$527$	−3.20304	+	0.564782i	−0.139527	+	0.0246023i
$528$		0			0
$529$	−3.78225	−	21.4502i	−0.164446	−	0.932617i
$530$		0			0
$531$	8.18283			0.355105
$532$		0			0
$533$	19.3608			0.838610
$534$		0			0
$535$	−3.35130	−	19.0062i	−0.144889	−	0.821708i
$536$		0			0
$537$	−1.07680	+	0.189869i	−0.0464673	+	0.00819344i
$538$		0			0
$539$	−5.85496	−	1.54720i	−0.252191	−	0.0666426i
$540$		0			0
$541$	22.2699	−	8.10559i	0.957459	−	0.348486i	0.184421	−	0.982847i	$-0.440959\pi$
$541$	22.2699	−	8.10559i	0.957459	−	0.348486i	0.773037	+	0.634361i	$0.218737\pi$
$542$		0			0
$543$	6.17020			0.264789
$544$		0			0
$545$	4.69806	+	3.94214i	0.201243	+	0.168863i
$546$		0			0
$547$	7.49092	+	20.5811i	0.320288	+	0.879985i	0.990463	+	0.137781i	$0.0439972\pi$
$547$	7.49092	+	20.5811i	0.320288	+	0.879985i	−0.670174	+	0.742204i	$0.733781\pi$
$548$		0			0
$549$	0.245497	−	0.674496i	0.0104775	−	0.0287868i
$550$		0			0
$551$	0.256055	−	0.596921i	0.0109083	−	0.0254297i
$552$		0			0
$553$	14.3973	−	27.7738i	0.612236	−	1.18106i
$554$		0			0
$555$	4.17347	+	3.50195i	0.177154	+	0.148650i
$556$		0			0
$557$	18.1889	−	6.62022i	0.770688	−	0.280508i	0.0734040	−	0.997302i	$-0.476614\pi$
$557$	18.1889	−	6.62022i	0.770688	−	0.280508i	0.697284	+	0.716795i	$0.254392\pi$
$558$		0			0
$559$	4.23054	+	7.32752i	0.178933	+	0.309921i
$560$		0			0
$561$	0.361861	+	0.0638059i	0.0152778	+	0.00269389i
$562$		0			0
$563$	15.8506	+	27.4540i	0.668023	+	1.15705i	0.978456	+	0.206455i	$0.0661926\pi$
$563$	15.8506	+	27.4540i	0.668023	+	1.15705i	−0.310433	+	0.950595i	$0.600474\pi$
$564$		0			0
$565$	−0.729237	−	4.13571i	−0.0306792	−	0.173991i
$566$		0			0
$567$	−1.51439	+	0.968448i	−0.0635983	+	0.0406710i
$568$		0			0
$569$	31.7623	−	18.3380i	1.33154	−	0.768768i	0.346008	−	0.938231i	$-0.387537\pi$
$569$	31.7623	−	18.3380i	1.33154	−	0.768768i	0.985536	+	0.169464i	$0.0542035\pi$
$570$		0			0
$571$	−9.32073	+	16.1440i	−0.390060	+	0.675604i	−0.992457	−	0.122593i	$-0.960879\pi$
$571$	−9.32073	+	16.1440i	−0.390060	+	0.675604i	0.602397	+	0.798197i	$0.294212\pi$
$572$		0			0
$573$	−19.4972	+	16.3601i	−0.814508	+	0.683453i
$574$		0			0
$575$	−1.93919	−	0.705809i	−0.0808700	−	0.0294343i
$576$		0			0
$577$	−28.8750	+	16.6710i	−1.20208	+	0.694023i	−0.961018	−	0.276486i	$-0.910830\pi$
$577$	−28.8750	+	16.6710i	−1.20208	+	0.694023i	−0.241065	+	0.970509i	$0.577497\pi$
$578$		0			0
$579$	2.86656	+	7.87580i	0.119130	+	0.327307i
$580$		0			0
$581$	22.5751	+	17.2607i	0.936572	+	0.716093i
$582$		0			0
$583$	8.49374	+	1.49768i	0.351775	+	0.0620274i
$584$		0			0
$585$	−10.3353	−	1.82240i	−0.427313	−	0.0753468i
$586$		0			0
$587$	−33.1655	+	5.84798i	−1.36889	+	0.241372i	−0.809298	−	0.587398i	$-0.800152\pi$
$587$	−33.1655	+	5.84798i	−1.36889	+	0.241372i	−0.559589	+	0.828770i	$0.689041\pi$
$588$		0			0
$589$	−35.7122	+	10.7703i	−1.47149	+	0.443783i
$590$		0			0
$591$	9.64689	+	3.51118i	0.396820	+	0.144431i
$592$		0			0
$593$	4.35242	−	5.18701i	0.178732	−	0.213005i	−0.669239	−	0.743047i	$-0.733380\pi$
$593$	4.35242	−	5.18701i	0.178732	−	0.213005i	0.847971	+	0.530043i	$0.177824\pi$
$594$		0			0
$595$	0.532114	−	1.69786i	0.0218145	−	0.0696054i
$596$		0			0
$597$	−6.90611	−	3.98725i	−0.282648	−	0.163187i
$598$		0			0
$599$	16.6129	−	19.7984i	0.678783	−	0.808942i	−0.311167	−	0.950355i	$-0.600720\pi$
$599$	16.6129	−	19.7984i	0.678783	−	0.808942i	0.989951	+	0.141413i	$0.0451644\pi$
$600$		0			0
$601$	1.57019	−	2.71966i	0.0640495	−	0.110937i	−0.832222	−	0.554442i	$-0.812932\pi$
$601$	1.57019	−	2.71966i	0.0640495	−	0.110937i	0.896272	+	0.443505i	$0.146265\pi$
$602$		0			0
$603$	3.68797	−	10.1326i	0.150186	−	0.412632i
$604$		0			0
$605$	17.8636	−	3.14984i	0.726260	−	0.128059i
$606$		0			0
$607$	−12.2682	−	21.2491i	−0.497951	−	0.862476i	0.502046	−	0.864841i	$-0.332581\pi$
$607$	−12.2682	−	21.2491i	−0.497951	−	0.862476i	−0.999997	+	0.00236445i	$0.999247\pi$
$608$		0			0
$609$	0.0567510	−	0.436889i	0.00229967	−	0.0177037i
$610$		0			0
$611$	9.32601	−	25.6230i	0.377290	−	1.03660i
$612$		0			0
$613$	−9.96250	+	8.35953i	−0.402382	+	0.337638i	−0.821413	−	0.570333i	$-0.806814\pi$
$613$	−9.96250	+	8.35953i	−0.402382	+	0.337638i	0.419032	+	0.907972i	$0.362370\pi$
$614$		0			0
$615$	−9.78869	−	5.65150i	−0.394718	−	0.227891i
$616$		0			0
$617$	−7.22491	+	40.9745i	−0.290864	+	1.64957i	0.392691	+	0.919671i	$0.371544\pi$
$617$	−7.22491	+	40.9745i	−0.290864	+	1.64957i	−0.683554	+	0.729900i	$0.739567\pi$
$618$		0			0
$619$			3.67021i			0.147518i	0.997276	+	0.0737592i	$0.0234996\pi$
$619$			3.67021i			0.147518i	−0.997276	+	0.0737592i	$0.976500\pi$
$620$		0			0
$621$	−1.01789	+	5.77273i	−0.0408464	+	0.231652i
$622$		0			0
$623$	−1.28037	+	4.08537i	−0.0512968	+	0.163677i
$624$		0			0
$625$	−9.31528	+	7.81645i	−0.372611	+	0.312658i
$626$		0			0
$627$	4.20740	+	0.236511i	0.168027	+	0.00944534i
$628$		0			0
$629$	−0.181850	−	1.03132i	−0.00725084	−	0.0411216i
$630$		0			0
$631$	−15.0312	+	5.47093i	−0.598384	+	0.217794i	−0.623413	−	0.781893i	$-0.714255\pi$
$631$	−15.0312	+	5.47093i	−0.598384	+	0.217794i	0.0250287	+	0.999687i	$0.492032\pi$
$632$		0			0
$633$	−0.934688	−	2.56804i	−0.0371505	−	0.102070i
$634$		0			0
$635$	−14.4025	+	24.9459i	−0.571548	+	0.989950i
$636$		0			0
$637$	13.6653	+	19.3734i	0.541438	+	0.767604i
$638$		0			0
$639$		−	26.2844i		−	1.03979i
$640$		0			0
$641$	5.65164	+	6.73537i	0.223227	+	0.266031i	0.866021	−	0.500008i	$-0.166670\pi$
$641$	5.65164	+	6.73537i	0.223227	+	0.266031i	−0.642794	+	0.766039i	$0.722225\pi$
$642$		0			0
$643$	−12.4523	−	14.8401i	−0.491070	−	0.585235i	0.462419	−	0.886662i	$-0.346982\pi$
$643$	−12.4523	−	14.8401i	−0.491070	−	0.585235i	−0.953489	+	0.301427i	$0.902537\pi$
$644$		0			0
$645$		−	4.93965i		−	0.194499i
$646$		0			0
$647$	21.9038	+	12.6461i	0.861126	+	0.497171i	0.864389	−	0.502823i	$-0.167705\pi$
$647$	21.9038	+	12.6461i	0.861126	+	0.497171i	−0.00326323	+	0.999995i	$0.501039\pi$
$648$		0			0
$649$	−3.79862	−	1.38259i	−0.149109	−	0.0542712i
$650$		0			0
$651$	−21.3148	+	13.6308i	−0.835394	+	0.534233i
$652$		0			0
$653$	37.4666			1.46618			0.733090	−	0.680131i	$-0.238077\pi$
$653$	37.4666			1.46618			0.733090	+	0.680131i	$0.238077\pi$
$654$		0			0
$655$	12.1792	+	10.2196i	0.475881	+	0.399312i
$656$		0			0
$657$	−18.0268	+	10.4078i	−0.703291	+	0.406045i
$658$		0			0
$659$	−15.2125	+	18.1296i	−0.592596	+	0.706228i	−0.976103	−	0.217310i	$-0.930272\pi$
$659$	−15.2125	+	18.1296i	−0.592596	+	0.706228i	0.383507	+	0.923538i	$0.374716\pi$
$660$		0			0
$661$	1.27502	−	7.23102i	0.0495927	−	0.281254i	−0.949919	−	0.312496i	$-0.898835\pi$
$661$	1.27502	−	7.23102i	0.0495927	−	0.281254i	0.999512	+	0.0312417i	$0.00994615\pi$
$662$		0			0
$663$	−0.924639	−	1.10194i	−0.0359100	−	0.0427959i
$664$		0			0
$665$	3.76018	−	20.0564i	0.145813	−	0.777754i
$666$		0			0
$667$	−0.105747	−	0.126024i	−0.00409454	−	0.00487968i
$668$		0			0
$669$	−3.92408	+	22.2546i	−0.151714	+	0.860411i
$670$		0			0
$671$	−0.227928	+	0.271634i	−0.00879907	+	0.0104863i
$672$		0			0
$673$	17.8613	−	10.3122i	0.688503	−	0.397507i	−0.114548	−	0.993418i	$-0.536542\pi$
$673$	17.8613	−	10.3122i	0.688503	−	0.397507i	0.803051	+	0.595910i	$0.203209\pi$
$674$		0			0
$675$	−7.60243	−	6.37919i	−0.292617	−	0.245535i
$676$		0			0
$677$	−32.9182			−1.26515			−0.632574	−	0.774500i	$-0.718002\pi$
$677$	−32.9182			−1.26515			−0.632574	+	0.774500i	$0.718002\pi$
$678$		0			0
$679$	−0.205447	−	4.52631i	−0.00788432	−	0.173704i
$680$		0			0
$681$	−6.71967	−	2.44576i	−0.257498	−	0.0937217i
$682$		0			0
$683$	33.1695	+	19.1504i	1.26920	+	0.732771i	0.974836	−	0.222923i	$-0.0715600\pi$
$683$	33.1695	+	19.1504i	1.26920	+	0.732771i	0.294361	+	0.955694i	$0.404893\pi$
$684$		0			0
$685$			17.1714i			0.656085i
$686$		0			0
$687$	−9.26014	−	11.0358i	−0.353296	−	0.421042i
$688$		0			0
$689$	−21.7035	−	25.8652i	−0.826836	−	0.985385i
$690$		0			0
$691$		−	36.0983i		−	1.37324i	−0.727014	−	0.686622i	$-0.759093\pi$
$691$		−	36.0983i		−	1.37324i	0.727014	−	0.686622i	$-0.240907\pi$
$692$		0			0
$693$	−3.91195	+	0.874341i	−0.148603	+	0.0332135i
$694$		0			0
$695$	−6.11361	+	10.5891i	−0.231902	+	0.401667i
$696$		0			0
$697$	0.743098	+	2.04165i	0.0281468	+	0.0773328i
$698$		0			0
$699$	−23.7257	+	8.63545i	−0.897388	+	0.326623i
$700$		0			0
$701$	6.76708	+	38.3780i	0.255589	+	1.44952i	0.794556	+	0.607190i	$0.207703\pi$
$701$	6.76708	+	38.3780i	0.255589	+	1.44952i	−0.538967	+	0.842327i	$0.681185\pi$
$702$		0			0
$703$	−3.46786	−	11.4987i	−0.130793	−	0.433682i
$704$		0			0
$705$	−12.1946	+	10.2325i	−0.459276	+	0.385379i
$706$		0			0
$707$	−3.55629	−	15.9114i	−0.133748	−	0.598412i
$708$		0			0
$709$	2.38137	−	13.5054i	0.0894343	−	0.507207i	−0.906877	−	0.421395i	$-0.861541\pi$
$709$	2.38137	−	13.5054i	0.0894343	−	0.507207i	0.996311	−	0.0858118i	$-0.0273484\pi$
$710$		0			0
$711$		−	20.7069i		−	0.776570i
$712$		0			0
$713$	−1.64058	+	9.30417i	−0.0614401	+	0.348444i
$714$		0			0
$715$	4.48993	+	2.59226i	0.167914	+	0.0969452i
$716$		0			0
$717$	22.9956	−	19.2956i	0.858785	−	0.720606i
$718$		0			0
$719$	−11.4831	+	31.5495i	−0.428246	+	1.17660i	0.518631	+	0.854998i	$0.326442\pi$
$719$	−11.4831	+	31.5495i	−0.428246	+	1.17660i	−0.946876	+	0.321598i	$0.895780\pi$
$720$		0			0
$721$	3.87211	−	5.06430i	0.144205	−	0.188604i
$722$		0			0
$723$	13.9417	+	24.1477i	0.518497	+	0.898063i
$724$		0			0
$725$	0.274297	−	0.0483659i	0.0101871	−	0.00179626i
$726$		0			0
$727$	−8.06016	+	22.1451i	−0.298935	+	0.821317i	0.695744	+	0.718290i	$0.255075\pi$
$727$	−8.06016	+	22.1451i	−0.298935	+	0.821317i	−0.994679	+	0.103027i	$0.967147\pi$
$728$		0			0
$729$	−9.49463	+	16.4452i	−0.351653	+	0.609081i
$730$		0			0
$731$	−0.610330	+	0.727363i	−0.0225739	+	0.0269025i
$732$		0			0
$733$	30.8166	+	17.7920i	1.13824	+	0.657162i	0.945993	−	0.324186i	$-0.105090\pi$
$733$	30.8166	+	17.7920i	1.13824	+	0.657162i	0.192244	+	0.981347i	$0.438424\pi$
$734$		0			0
$735$	−1.25388	−	13.7840i	−0.0462501	−	0.508432i
$736$		0			0
$737$	−3.42405	+	4.08063i	−0.126127	+	0.150312i
$738$		0			0
$739$	29.2721	+	10.6542i	1.07679	+	0.391919i	0.818712	−	0.574205i	$-0.194689\pi$
$739$	29.2721	+	10.6542i	1.07679	+	0.391919i	0.258078	+	0.966124i	$0.416911\pi$
$740$		0			0
$741$	−12.0226	−	11.2968i	−0.441661	−	0.415000i
$742$		0			0
$743$	41.6348	−	7.34134i	1.52743	−	0.269328i	0.654083	−	0.756423i	$-0.273055\pi$
$743$	41.6348	−	7.34134i	1.52743	−	0.269328i	0.873349	+	0.487095i	$0.161943\pi$
$744$		0			0
$745$	40.4217	+	7.12744i	1.48094	+	0.261129i
$746$		0			0
$747$	18.5241	+	3.26630i	0.677762	+	0.119508i
$748$		0			0
$749$	−3.71734	+	28.6174i	−0.135829	+	1.04566i
$750$		0			0
$751$	−0.457072	−	1.25579i	−0.0166788	−	0.0458246i	0.931074	−	0.364831i	$-0.118873\pi$
$751$	−0.457072	−	1.25579i	−0.0166788	−	0.0458246i	−0.947753	+	0.319006i	$0.896651\pi$
$752$		0			0
$753$	−24.9876	+	14.4266i	−0.910600	+	0.525735i
$754$		0			0
$755$	8.43823	+	3.07126i	0.307099	+	0.111775i
$756$		0			0
$757$	−6.53313	+	5.48195i	−0.237451	+	0.199245i	−0.753746	−	0.657166i	$-0.771755\pi$
$757$	−6.53313	+	5.48195i	−0.237451	+	0.199245i	0.516295	+	0.856411i	$0.327311\pi$
$758$		0			0
$759$	0.533674	−	0.924350i	0.0193711	−	0.0335518i
$760$		0			0
$761$	−4.68599	+	2.70546i	−0.169867	+	0.0980727i	−0.582523	−	0.812814i	$-0.697934\pi$
$761$	−4.68599	+	2.70546i	−0.169867	+	0.0980727i	0.412656	+	0.910887i	$0.364601\pi$
$762$		0			0
$763$	−4.94055	−	7.72567i	−0.178860	−	0.279688i
$764$		0			0
$765$	−0.204510	−	1.15983i	−0.00739406	−	0.0419338i
$766$		0			0
$767$	7.91270	+	13.7052i	0.285711	+	0.494866i
$768$		0			0
$769$	−39.7233	−	7.00429i	−1.43246	−	0.252581i	−0.597047	−	0.802206i	$-0.703659\pi$
$769$	−39.7233	−	7.00429i	−1.43246	−	0.252581i	−0.835411	+	0.549625i	$0.814771\pi$
$770$		0			0
$771$	−1.70455	−	2.95237i	−0.0613879	−	0.106327i
$772$		0			0
$773$	2.05716	−	0.748744i	0.0739908	−	0.0269304i	−0.304760	−	0.952429i	$-0.598576\pi$
$773$	2.05716	−	0.748744i	0.0739908	−	0.0269304i	0.378750	+	0.925499i	$0.376354\pi$
$774$		0			0
$775$	−12.2532	−	10.2816i	−0.440147	−	0.369327i
$776$		0			0
$777$	−4.38888	−	6.86300i	−0.157450	−	0.246209i
$778$		0			0
$779$	11.2280	+	22.2443i	0.402283	+	0.796986i
$780$		0			0
$781$	−4.44105	+	12.2017i	−0.158913	+	0.436611i
$782$		0			0
$783$	−0.270592	−	0.743445i	−0.00967017	−	0.0265686i
$784$		0			0
$785$	17.8303	+	14.9614i	0.636389	+	0.533994i
$786$		0			0
$787$	4.61867			0.164638			0.0823190	−	0.996606i	$-0.473767\pi$
$787$	4.61867			0.164638			0.0823190	+	0.996606i	$0.473767\pi$
$788$		0			0
$789$	17.5009	−	6.36981i	0.623049	−	0.226771i
$790$		0			0
$791$	−0.808886	+	6.22709i	−0.0287607	+	0.221410i
$792$		0			0
$793$	1.36709	−	0.241054i	0.0485467	−	0.00856009i
$794$		0			0
$795$	3.42296	+	19.4126i	0.121400	+	0.688494i
$796$		0			0
$797$	−24.3832			−0.863697			−0.431849	−	0.901946i	$-0.642139\pi$
$797$	−24.3832			−0.863697			−0.431849	+	0.901946i	$0.642139\pi$
$798$		0			0
$799$	3.05996			0.108253
$800$		0			0
$801$	0.492089	+	2.79078i	0.0173871	+	0.0986072i
$802$		0			0
$803$	10.1269	−	1.78564i	0.357370	−	0.0630139i
$804$		0			0
$805$	−4.10584	−	3.13928i	−0.144712	−	0.110645i
$806$		0			0
$807$	32.0500	−	11.6653i	1.12822	−	0.410637i
$808$		0			0
$809$	37.4635			1.31714			0.658572	−	0.752517i	$-0.271161\pi$
$809$	37.4635			1.31714			0.658572	+	0.752517i	$0.271161\pi$
$810$		0			0
$811$	−3.06379	−	2.57083i	−0.107584	−	0.0902739i	0.587409	−	0.809290i	$-0.300148\pi$
$811$	−3.06379	−	2.57083i	−0.107584	−	0.0902739i	−0.694993	+	0.719016i	$0.744593\pi$
$812$		0			0
$813$	5.73774	+	15.7643i	0.201231	+	0.552878i
$814$		0			0
$815$	−0.0194910	+	0.0535510i	−0.000682739	+	0.00187581i
$816$		0			0
$817$	−5.96542	+	9.11009i	−0.208704	+	0.318722i
$818$		0			0
$819$	13.9319	+	7.22198i	0.486821	+	0.252356i
$820$		0			0
$821$	1.16746	+	0.979615i	0.0407446	+	0.0341888i	0.662933	−	0.748679i	$-0.269312\pi$
$821$	1.16746	+	0.979615i	0.0407446	+	0.0341888i	−0.622188	+	0.782868i	$0.713756\pi$
$822$		0			0
$823$	−30.4448	+	11.0810i	−1.06124	+	0.386259i	−0.812894	−	0.582412i	$-0.802109\pi$
$823$	−30.4448	+	11.0810i	−1.06124	+	0.386259i	−0.248345	+	0.968672i	$0.579887\pi$
$824$		0			0
$825$	0.903533	+	1.56497i	0.0314570	+	0.0544851i
$826$		0			0
$827$	−0.288957	−	0.0509509i	−0.0100480	−	0.00177174i	0.168622	−	0.985681i	$-0.446068\pi$
$827$	−0.288957	−	0.0509509i	−0.0100480	−	0.00177174i	−0.178670	+	0.983909i	$0.557179\pi$
$828$		0			0
$829$	−3.37999	−	5.85432i	−0.117392	−	0.203329i	0.801341	−	0.598207i	$-0.204120\pi$
$829$	−3.37999	−	5.85432i	−0.117392	−	0.203329i	−0.918733	+	0.394878i	$0.870787\pi$
$830$		0			0
$831$	−3.99581	−	22.6613i	−0.138613	−	0.786113i
$832$		0			0
$833$	−1.51848	+	2.18462i	−0.0526123	+	0.0756927i
$834$		0			0
$835$	26.7442	−	15.4408i	0.925521	−	0.534350i
$836$		0			0
$837$	−22.7174	+	39.3477i	−0.785229	+	1.36006i
$838$		0			0
$839$	3.06761	−	2.57403i	0.105906	−	0.0888655i	−0.588297	−	0.808645i	$-0.700201\pi$
$839$	3.06761	−	2.57403i	0.105906	−	0.0888655i	0.694203	+	0.719779i	$0.255757\pi$
$840$		0			0
$841$	−27.2302	−	9.91099i	−0.938973	−	0.341758i
$842$		0			0
$843$	−8.30359	+	4.79408i	−0.285991	+	0.165117i
$844$		0			0
$845$	0.925416	+	2.54256i	0.0318353	+	0.0874668i
$846$		0			0
$847$	−26.8971	−	3.49387i	−0.924194	−	0.120051i
$848$		0			0
$849$	−21.0247	−	3.70721i	−0.721564	−	0.127231i
$850$		0			0
$851$	−2.99578	−	0.528237i	−0.102694	−	0.0181077i
$852$		0			0
$853$	−13.1781	+	2.32366i	−0.451210	+	0.0795605i	−0.394635	−	0.918838i	$-0.629129\pi$
$853$	−13.1781	+	2.32366i	−0.451210	+	0.0795605i	−0.0565748	+	0.998398i	$0.518018\pi$
$854$		0			0
$855$	−3.89997	−	12.9315i	−0.133376	−	0.442248i
$856$		0			0
$857$	26.6434	+	9.69739i	0.910120	+	0.331257i	0.754301	−	0.656529i	$-0.227976\pi$
$857$	26.6434	+	9.69739i	0.910120	+	0.331257i	0.155819	+	0.987786i	$0.450198\pi$
$858$		0			0
$859$	−14.4153	+	17.1795i	−0.491843	+	0.586156i	−0.953685	−	0.300806i	$-0.902744\pi$
$859$	−14.4153	+	17.1795i	−0.491843	+	0.586156i	0.461842	+	0.886962i	$0.347189\pi$
$860$		0			0
$861$	11.4397	+	12.4411i	0.389863	+	0.423990i
$862$		0			0
$863$	43.3219	+	25.0119i	1.47470	+	0.851416i	0.999593	−	0.0285149i	$-0.00907780\pi$
$863$	43.3219	+	25.0119i	1.47470	+	0.851416i	0.475102	+	0.879931i	$0.342411\pi$
$864$		0			0
$865$	6.21883	−	7.41131i	0.211446	−	0.251992i
$866$		0			0
$867$	−9.41785	+	16.3122i	−0.319847	+	0.553991i
$868$		0			0
$869$	−3.49868	+	9.61253i	−0.118684	+	0.326083i
$870$		0			0
$871$	20.5371	−	3.62124i	0.695872	−	0.122701i
$872$		0			0
$873$	−1.49954	−	2.59728i	−0.0507518	−	0.0879048i
$874$		0			0
$875$	29.6884	−	12.3574i	1.00365	−	0.417756i
$876$		0			0
$877$	16.9218	−	46.4923i	0.571409	−	1.56993i	−0.230869	−	0.972985i	$-0.574157\pi$
$877$	16.9218	−	46.4923i	0.571409	−	1.56993i	0.802279	−	0.596950i	$-0.203621\pi$
$878$		0			0
$879$	−12.0026	+	10.0714i	−0.404837	+	0.339699i
$880$		0			0
$881$	18.5459	+	10.7075i	0.624829	+	0.360745i	0.778747	−	0.627339i	$-0.215856\pi$
$881$	18.5459	+	10.7075i	0.624829	+	0.360745i	−0.153918	+	0.988084i	$0.549189\pi$
$882$		0			0
$883$	−0.894478	+	5.07284i	−0.0301016	+	0.170715i	−0.996152	−	0.0876374i	$-0.972068\pi$
$883$	−0.894478	+	5.07284i	−0.0301016	+	0.170715i	0.966051	+	0.258352i	$0.0831794\pi$
$884$		0			0
$885$		−	9.23900i		−	0.310565i
$886$		0			0
$887$	−5.46759	+	31.0082i	−0.183584	+	1.04115i	0.744178	+	0.667981i	$0.232841\pi$
$887$	−5.46759	+	31.0082i	−0.183584	+	1.04115i	−0.927762	+	0.373173i	$0.878270\pi$
$888$		0			0
$889$	31.7054	−	29.1534i	1.06336	−	0.977773i
$890$		0			0
$891$	0.450271	−	0.377822i	0.0150847	−	0.0126575i
$892$		0			0
$893$	34.8477	−	4.14461i	1.16613	−	0.138694i
$894$		0			0
$895$	−0.300638	−	1.70500i	−0.0100492	−	0.0569919i
$896$		0			0
$897$	−3.92650	+	1.42913i	−0.131102	+	0.0477172i
$898$		0			0
$899$	−0.436125	−	1.19824i	−0.0145456	−	0.0399637i
$900$		0			0
$901$	1.89454	−	3.28143i	0.0631161	−	0.109320i
$902$		0			0
$903$	−2.20890	+	7.04810i	−0.0735075	+	0.234546i
$904$		0			0
$905$			9.76988i			0.324762i
$906$		0			0
$907$	−8.43843	−	10.0565i	−0.280193	−	0.333922i	0.607532	−	0.794295i	$-0.292160\pi$
$907$	−8.43843	−	10.0565i	−0.280193	−	0.333922i	−0.887725	+	0.460374i	$0.847715\pi$
$908$		0			0
$909$	−6.93681	−	8.26697i	−0.230080	−	0.274198i
$910$		0			0
$911$			43.1832i			1.43072i	0.698755	+	0.715361i	$0.253738\pi$
$911$			43.1832i			1.43072i	−0.698755	+	0.715361i	$0.746262\pi$
$912$		0			0
$913$	−8.04736	−	4.64615i	−0.266329	−	0.153765i
$914$		0			0
$915$	−0.761554	−	0.277183i	−0.0251762	−	0.00916339i
$916$		0			0
$917$	−12.8078	−	20.0280i	−0.422952	−	0.661381i
$918$		0			0
$919$	55.8357			1.84185			0.920925	−	0.389739i	$-0.127435\pi$
$919$	55.8357			1.84185			0.920925	+	0.389739i	$0.127435\pi$
$920$		0			0
$921$	11.8580	+	9.95000i	0.390733	+	0.327864i
$922$		0			0
$923$	44.0229	−	25.4166i	1.44903	−	0.836599i
$924$		0			0
$925$	3.31051	−	3.94531i	0.108849	−	0.129721i
$926$		0			0
$927$	0.732734	−	4.15554i	0.0240662	−	0.136486i
$928$		0			0
$929$	−4.54221	−	5.41319i	−0.149025	−	0.177601i	0.686368	−	0.727255i	$-0.259204\pi$
$929$	−4.54221	−	5.41319i	−0.149025	−	0.177601i	−0.835393	+	0.549654i	$0.814760\pi$
$930$		0			0
$931$	−14.3339	+	26.9358i	−0.469775	+	0.882786i
$932$		0			0
$933$	−7.99200	−	9.52449i	−0.261646	−	0.311818i
$934$		0			0
$935$	−0.101030	+	0.572970i	−0.00330404	+	0.0187381i
$936$		0			0
$937$	−14.6448	+	17.4529i	−0.478423	+	0.570163i	−0.950234	−	0.311537i	$-0.899156\pi$
$937$	−14.6448	+	17.4529i	−0.478423	+	0.570163i	0.471811	+	0.881700i	$0.343601\pi$
$938$		0			0
$939$	13.1158	−	7.57244i	0.428020	−	0.247117i
$940$		0			0
$941$	−25.1121	−	21.0716i	−0.818632	−	0.686914i	0.134019	−	0.990979i	$-0.457212\pi$
$941$	−25.1121	−	21.0716i	−0.818632	−	0.686914i	−0.952651	+	0.304065i	$0.901656\pi$
$942$		0			0
$943$	6.31117			0.205520
$944$		0			0
$945$	−13.3910	−	20.9399i	−0.435611	−	0.681176i
$946$		0			0
$947$	−21.1120	−	7.68414i	−0.686048	−	0.249701i	−0.0246059	−	0.999697i	$-0.507833\pi$
$947$	−21.1120	−	7.68414i	−0.686048	−	0.249701i	−0.661442	+	0.749996i	$0.730055\pi$
$948$		0			0
$949$	−34.8633	−	20.1283i	−1.13171	−	0.653394i
$950$		0			0
$951$			16.6108i			0.538641i
$952$		0			0
$953$	25.4835	+	30.3700i	0.825490	+	0.983781i	1.00000		0.000874876i	$-0.000278482\pi$
$953$	25.4835	+	30.3700i	0.825490	+	0.983781i	−0.174510	+	0.984655i	$0.555834\pi$
$954$		0			0
$955$	−25.9046	−	30.8718i	−0.838252	−	0.998989i
$956$		0			0
$957$			0.144059i			0.00465675i
$958$		0			0
$959$	7.67864	−	24.5008i	0.247956	−	0.791173i
$960$		0			0
$961$	−21.1147	+	36.5717i	−0.681119	+	1.17973i
$962$		0			0
$963$	6.53300	+	17.9493i	0.210523	+	0.578407i
$964$		0			0
$965$	−12.4705	+	4.53890i	−0.401440	+	0.146112i
$966$		0			0
$967$	−2.27212	−	12.8858i	−0.0730664	−	0.414380i	−0.999299	−	0.0374285i	$-0.988083\pi$
$967$	−2.27212	−	12.8858i	−0.0730664	−	0.414380i	0.926233	−	0.376952i	$-0.123028\pi$
$968$		0			0
$969$	0.729833	−	1.70140i	0.0234456	−	0.0546569i
$970$		0			0
$971$	−32.1504	+	26.9774i	−1.03175	+	0.865745i	−0.991059	−	0.133427i	$-0.957402\pi$
$971$	−32.1504	+	26.9774i	−1.03175	+	0.865745i	−0.0406959	+	0.999172i	$0.512957\pi$
$972$		0			0
$973$	13.4583	−	12.3751i	0.431454	−	0.396726i
$974$		0			0
$975$	1.22845	−	6.96690i	0.0393420	−	0.223119i
$976$		0			0
$977$		−	23.0409i		−	0.737143i	−0.929599	−	0.368571i	$-0.879847\pi$
$977$		−	23.0409i		−	0.737143i	0.929599	−	0.368571i	$-0.120153\pi$
$978$		0			0
$979$	0.243098	−	1.37867i	0.00776943	−	0.0440626i
$980$		0			0
$981$	−5.25670	−	3.03496i	−0.167834	−	0.0968987i
$982$		0			0
$983$	−39.1544	+	32.8545i	−1.24883	+	1.04789i	−0.252051	+	0.967714i	$0.581105\pi$
$983$	−39.1544	+	32.8545i	−1.24883	+	1.04789i	−0.996780	+	0.0801805i	$0.974450\pi$
$984$		0			0
$985$	−5.55959	+	15.2749i	−0.177143	+	0.486697i
$986$		0			0
$987$	21.9755	−	9.14700i	0.699488	−	0.291152i
$988$		0			0
$989$	1.37906	+	2.38860i	0.0438515	+	0.0759530i
$990$		0			0
$991$	5.63241	−	0.993146i	0.178919	−	0.0315483i	−0.0834706	−	0.996510i	$-0.526600\pi$
$991$	5.63241	−	0.993146i	0.178919	−	0.0315483i	0.262390	+	0.964962i	$0.415489\pi$
$992$		0			0
$993$	1.14425	−	3.14380i	0.0363117	−	0.0997656i
$994$		0			0
$995$	6.31339	−	10.9351i	0.200148	−	0.346667i
$996$		0			0
$997$	−10.8448	+	12.9243i	−0.343457	+	0.409316i	−0.909928	−	0.414765i	$-0.863864\pi$
$997$	−10.8448	+	12.9243i	−0.343457	+	0.409316i	0.566472	+	0.824081i	$0.308308\pi$
$998$		0			0
$999$	−12.6693	−	7.31462i	−0.400838	−	0.231424i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.cj.a.409.9	yes	78
7.5	odd	6		532.2.bw.a.257.9	✓	78
19.2	odd	18		532.2.bw.a.325.9	yes	78
133.40	even	18	inner	532.2.cj.a.173.9	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.bw.a.257.9	✓	78	7.5	odd	6
532.2.bw.a.325.9	yes	78	19.2	odd	18
532.2.cj.a.173.9	yes	78	133.40	even	18	inner
532.2.cj.a.409.9	yes	78	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	532.2.cj.a.409.9

Level	$532$
Weight	$2$
Character	532.409
Analytic conductor	$4.248$
Analytic rank	$0$
Dimension	$78$
Inner twists	$2$