LMFDB - Embedded newform 360.2.bi.b.49.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.15
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56081 - 0.750911i) q^{3} +(1.52089 + 1.63917i) q^{5} +(-2.51643 + 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +O(q^{10})$	\(q+(1.56081 - 0.750911i) q^{3} +(1.52089 + 1.63917i) q^{5} +(-2.51643 + 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +(2.96823 + 5.14112i) q^{11} +(1.91871 + 1.10777i) q^{13} +(3.60470 + 1.41638i) q^{15} -7.22957i q^{17} +1.89473 q^{19} +(-2.83671 + 4.15726i) q^{21} +(-7.15829 - 4.13284i) q^{23} +(-0.373764 + 4.98601i) q^{25} +(1.16207 - 5.06454i) q^{27} +(-2.08584 - 3.61278i) q^{29} +(-0.617611 + 1.06973i) q^{31} +(8.49336 + 5.79544i) q^{33} +(-6.20872 - 1.91521i) q^{35} -0.466992i q^{37} +(3.82658 + 0.288236i) q^{39} +(4.84562 - 8.39286i) q^{41} +(-4.29214 + 2.47807i) q^{43} +(6.68983 - 0.496105i) q^{45} +(-0.183041 + 0.105679i) q^{47} +(0.721618 - 1.24988i) q^{49} +(-5.42877 - 11.2840i) q^{51} +3.33797i q^{53} +(-3.91282 + 12.6845i) q^{55} +(2.95732 - 1.42278i) q^{57} +(-2.02942 + 3.51505i) q^{59} +(4.85418 + 8.40768i) q^{61} +(-1.30583 + 8.61881i) q^{63} +(1.10233 + 4.82989i) q^{65} +(-7.62905 - 4.40463i) q^{67} +(-14.2761 - 1.07535i) q^{69} -5.70101 q^{71} +1.17167i q^{73} +(3.16068 + 8.06289i) q^{75} +(-14.9387 - 8.62485i) q^{77} +(-4.36030 - 7.55225i) q^{79} +(-1.98924 - 8.77741i) q^{81} +(10.4401 - 6.02757i) q^{83} +(11.8505 - 10.9954i) q^{85} +(-5.96847 - 4.07258i) q^{87} -12.6768 q^{89} -6.43774 q^{91} +(-0.160700 + 2.13342i) q^{93} +(2.88169 + 3.10579i) q^{95} +(-4.91562 + 2.83803i) q^{97} +(17.6084 + 2.66783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 4 * q^9	$ 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) $ 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.56081	−	0.750911i	0.901135	−	0.433539i
$3$	1.56081	−	0.750911i	0.901135	−	0.433539i
$4$		0			0
$5$	1.52089	+	1.63917i	0.680164	+	0.733060i
$5$	1.52089	+	1.63917i	0.680164	+	0.733060i
$6$		0			0
$7$	−2.51643	+	1.45286i	−0.951122	+	0.549130i	−0.893429	−	0.449204i	$-0.851708\pi$
$7$	−2.51643	+	1.45286i	−0.951122	+	0.549130i	−0.0576925	+	0.998334i	$0.518374\pi$
$8$		0			0
$9$	1.87227	−	2.34406i	0.624088	−	0.781354i
$10$		0			0
$11$	2.96823	+	5.14112i	0.894954	+	1.55011i	0.833862	+	0.551973i	$0.186125\pi$
$11$	2.96823	+	5.14112i	0.894954	+	1.55011i	0.0610922	+	0.998132i	$0.480542\pi$
$12$		0			0
$13$	1.91871	+	1.10777i	0.532155	+	0.307240i	0.741893	−	0.670518i	$-0.233928\pi$
$13$	1.91871	+	1.10777i	0.532155	+	0.307240i	−0.209739	+	0.977757i	$0.567261\pi$
$14$		0			0
$15$	3.60470	+	1.41638i	0.930730	+	0.365708i
$16$		0			0
$17$		−	7.22957i		−	1.75343i	−0.481011	−	0.876715i	$-0.659730\pi$
$17$		−	7.22957i		−	1.75343i	0.481011	−	0.876715i	$-0.340270\pi$
$18$		0			0
$19$	1.89473			0.434682			0.217341	−	0.976096i	$-0.430262\pi$
$19$	1.89473			0.434682			0.217341	+	0.976096i	$0.430262\pi$
$20$		0			0
$21$	−2.83671	+	4.15726i	−0.619020	+	0.907189i
$22$		0			0
$23$	−7.15829	−	4.13284i	−1.49261	−	0.861756i	−0.492642	−	0.870232i	$-0.663969\pi$
$23$	−7.15829	−	4.13284i	−1.49261	−	0.861756i	−0.999964	+	0.00847582i	$0.997302\pi$
$24$		0			0
$25$	−0.373764	+	4.98601i	−0.0747528	+	0.997202i
$26$		0			0
$27$	1.16207	−	5.06454i	0.223641	−	0.974672i
$28$		0			0
$29$	−2.08584	−	3.61278i	−0.387330	−	0.670876i	0.604759	−	0.796408i	$-0.293269\pi$
$29$	−2.08584	−	3.61278i	−0.387330	−	0.670876i	−0.992089	+	0.125533i	$0.959936\pi$
$30$		0			0
$31$	−0.617611	+	1.06973i	−0.110926	+	0.192130i	−0.916144	−	0.400849i	$-0.868715\pi$
$31$	−0.617611	+	1.06973i	−0.110926	+	0.192130i	0.805218	+	0.592979i	$0.202048\pi$
$32$		0			0
$33$	8.49336	+	5.79544i	1.47850	+	1.00886i
$34$		0			0
$35$	−6.20872	−	1.91521i	−1.04946	−	0.323730i
$36$		0			0
$37$		−	0.466992i		−	0.0767730i	−0.999263	−	0.0383865i	$-0.987778\pi$
$37$		−	0.466992i		−	0.0767730i	0.999263	−	0.0383865i	$-0.0122218\pi$
$38$		0			0
$39$	3.82658	+	0.288236i	0.612743	+	0.0461548i
$40$		0			0
$41$	4.84562	−	8.39286i	0.756758	−	1.31074i	−0.187737	−	0.982219i	$-0.560115\pi$
$41$	4.84562	−	8.39286i	0.756758	−	1.31074i	0.944495	−	0.328525i	$-0.106551\pi$
$42$		0			0
$43$	−4.29214	+	2.47807i	−0.654545	+	0.377902i	−0.790196	−	0.612855i	$-0.790021\pi$
$43$	−4.29214	+	2.47807i	−0.654545	+	0.377902i	0.135650	+	0.990757i	$0.456688\pi$
$44$		0			0
$45$	6.68983	−	0.496105i	0.997262	−	0.0739549i
$46$		0			0
$47$	−0.183041	+	0.105679i	−0.0266992	+	0.0154148i	−0.513290	−	0.858215i	$-0.671574\pi$
$47$	−0.183041	+	0.105679i	−0.0266992	+	0.0154148i	0.486591	+	0.873630i	$0.338240\pi$
$48$		0			0
$49$	0.721618	−	1.24988i	0.103088	−	0.178554i
$50$		0			0
$51$	−5.42877	−	11.2840i	−0.760179	−	1.58008i
$52$		0			0
$53$			3.33797i			0.458506i	0.973367	+	0.229253i	$0.0736282\pi$
$53$			3.33797i			0.458506i	−0.973367	+	0.229253i	$0.926372\pi$
$54$		0			0
$55$	−3.91282	+	12.6845i	−0.527604	+	1.71038i
$56$		0			0
$57$	2.95732	−	1.42278i	0.391707	−	0.188451i
$58$		0			0
$59$	−2.02942	+	3.51505i	−0.264208	+	0.457621i	−0.967356	−	0.253422i	$-0.918444\pi$
$59$	−2.02942	+	3.51505i	−0.264208	+	0.457621i	0.703148	+	0.711043i	$0.251777\pi$
$60$		0			0
$61$	4.85418	+	8.40768i	0.621514	+	1.07649i	0.989204	+	0.146545i	$0.0468153\pi$
$61$	4.85418	+	8.40768i	0.621514	+	1.07649i	−0.367690	+	0.929948i	$0.619851\pi$
$62$		0			0
$63$	−1.30583	+	8.61881i	−0.164519	+	1.08587i
$64$		0			0
$65$	1.10233	+	4.82989i	0.136728	+	0.599075i
$66$		0			0
$67$	−7.62905	−	4.40463i	−0.932037	−	0.538112i	−0.0445816	−	0.999006i	$-0.514195\pi$
$67$	−7.62905	−	4.40463i	−0.932037	−	0.538112i	−0.887455	+	0.460894i	$0.847529\pi$
$68$		0			0
$69$	−14.2761	−	1.07535i	−1.71864	−	0.129456i
$70$		0			0
$71$	−5.70101			−0.676585			−0.338292	−	0.941041i	$-0.609849\pi$
$71$	−5.70101			−0.676585			−0.338292	+	0.941041i	$0.609849\pi$
$72$		0			0
$73$			1.17167i			0.137134i	0.997647	+	0.0685670i	$0.0218427\pi$
$73$			1.17167i			0.137134i	−0.997647	+	0.0685670i	$0.978157\pi$
$74$		0			0
$75$	3.16068	+	8.06289i	0.364963	+	0.931022i
$76$		0			0
$77$	−14.9387	−	8.62485i	−1.70242	−	0.982893i
$78$		0			0
$79$	−4.36030	−	7.55225i	−0.490572	−	0.849695i	0.509369	−	0.860548i	$-0.329879\pi$
$79$	−4.36030	−	7.55225i	−0.490572	−	0.849695i	−0.999941	+	0.0108530i	$0.996545\pi$
$80$		0			0
$81$	−1.98924	−	8.77741i	−0.221027	−	0.975268i
$82$		0			0
$83$	10.4401	−	6.02757i	1.14595	−	0.661612i	0.198050	−	0.980192i	$-0.436539\pi$
$83$	10.4401	−	6.02757i	1.14595	−	0.661612i	0.947896	+	0.318580i	$0.103206\pi$
$84$		0			0
$85$	11.8505	−	10.9954i	1.28537	−	1.19262i
$86$		0			0
$87$	−5.96847	−	4.07258i	−0.639887	−	0.436627i
$88$		0			0
$89$	−12.6768			−1.34374			−0.671871	−	0.740669i	$-0.734509\pi$
$89$	−12.6768			−1.34374			−0.671871	+	0.740669i	$0.734509\pi$
$90$		0			0
$91$	−6.43774			−0.674858
$92$		0			0
$93$	−0.160700	+	2.13342i	−0.0166638	+	0.221226i
$94$		0			0
$95$	2.88169	+	3.10579i	0.295655	+	0.318648i
$96$		0			0
$97$	−4.91562	+	2.83803i	−0.499105	+	0.288159i	−0.728344	−	0.685212i	$-0.759710\pi$
$97$	−4.91562	+	2.83803i	−0.499105	+	0.288159i	0.229239	+	0.973370i	$0.426376\pi$
$98$		0			0
$99$	17.6084	+	2.66783i	1.76971	+	0.268128i
$100$		0			0
$101$	−2.10382	−	3.64392i	−0.209338	−	0.362584i	0.742168	−	0.670214i	$-0.233798\pi$
$101$	−2.10382	−	3.64392i	−0.209338	−	0.362584i	−0.951506	+	0.307630i	$0.900464\pi$
$102$		0			0
$103$	3.27744	+	1.89223i	0.322936	+	0.186447i	0.652700	−	0.757616i	$-0.273636\pi$
$103$	3.27744	+	1.89223i	0.322936	+	0.186447i	−0.329765	+	0.944063i	$0.606969\pi$
$104$		0			0
$105$	−11.1288	+	1.67291i	−1.08606	+	0.163259i
$106$		0			0
$107$		−	3.14006i		−	0.303561i	−0.988414	−	0.151781i	$-0.951499\pi$
$107$		−	3.14006i		−	0.303561i	0.988414	−	0.151781i	$-0.0485007\pi$
$108$		0			0
$109$	4.92451			0.471683			0.235841	−	0.971792i	$-0.424215\pi$
$109$	4.92451			0.471683			0.235841	+	0.971792i	$0.424215\pi$
$110$		0			0
$111$	−0.350669	−	0.728886i	−0.0332841	−	0.0691828i
$112$		0			0
$113$	0.810137	+	0.467733i	0.0762113	+	0.0440006i	0.537621	−	0.843186i	$-0.319323\pi$
$113$	0.810137	+	0.467733i	0.0762113	+	0.0440006i	−0.461410	+	0.887187i	$0.652656\pi$
$114$		0			0
$115$	−4.11256	−	18.0193i	−0.383499	−	1.68031i
$116$		0			0
$117$	6.18901	−	2.42354i	0.572174	−	0.224056i
$118$		0			0
$119$	10.5036	+	18.1927i	0.962861	+	1.66772i
$120$		0			0
$121$	−12.1207	+	20.9937i	−1.10188	+	1.90852i
$122$		0			0
$123$	1.26081	−	16.7383i	0.113683	−	1.50924i
$124$		0			0
$125$	−8.74138	+	6.97053i	−0.781853	+	0.623463i
$126$		0			0
$127$		−	4.12343i		−	0.365895i	−0.983123	−	0.182948i	$-0.941436\pi$
$127$		−	4.12343i		−	0.365895i	0.983123	−	0.182948i	$-0.0585639\pi$
$128$		0			0
$129$	−4.83841	+	7.09081i	−0.425999	+	0.624311i
$130$		0			0
$131$	6.75366	−	11.6977i	0.590070	−	1.02203i	−0.404152	−	0.914692i	$-0.632433\pi$
$131$	6.75366	−	11.6977i	0.590070	−	1.02203i	0.994222	−	0.107340i	$-0.0342333\pi$
$132$		0			0
$133$	−4.76797	+	2.75279i	−0.413435	+	0.238697i
$134$		0			0
$135$	10.0690	−	5.79780i	0.866605	−	0.498995i
$136$		0			0
$137$	4.04198	−	2.33364i	0.345330	−	0.199376i	−0.317296	−	0.948326i	$-0.602775\pi$
$137$	4.04198	−	2.33364i	0.345330	−	0.199376i	0.662627	+	0.748950i	$0.269442\pi$
$138$		0			0
$139$	−4.54350	+	7.86958i	−0.385375	+	0.667489i	−0.991821	−	0.127636i	$-0.959261\pi$
$139$	−4.54350	+	7.86958i	−0.385375	+	0.667489i	0.606446	+	0.795124i	$0.292595\pi$
$140$		0			0
$141$	−0.206337	+	0.302391i	−0.0173767	+	0.0254660i
$142$		0			0
$143$			13.1524i			1.09986i
$144$		0			0
$145$	2.74962	−	8.91369i	0.228344	−	0.740242i
$146$		0			0
$147$	0.187762	−	2.49270i	0.0154863	−	0.205594i
$148$		0			0
$149$	5.75153	−	9.96194i	0.471184	−	0.816114i	−0.528273	−	0.849075i	$-0.677160\pi$
$149$	5.75153	−	9.96194i	0.471184	−	0.816114i	0.999457	+	0.0329604i	$0.0104935\pi$
$150$		0			0
$151$	6.12021	+	10.6005i	0.498056	+	0.862658i	0.999997	−	0.00224339i	$-0.000714095\pi$
$151$	6.12021	+	10.6005i	0.498056	+	0.862658i	−0.501942	+	0.864902i	$0.667381\pi$
$152$		0			0
$153$	−16.9466	−	13.5357i	−1.37005	−	1.09430i
$154$		0			0
$155$	−2.69280	+	0.614581i	−0.216291	+	0.0493643i
$156$		0			0
$157$	−6.90624	−	3.98732i	−0.551178	−	0.318223i	0.198419	−	0.980117i	$-0.436419\pi$
$157$	−6.90624	−	3.98732i	−0.551178	−	0.318223i	−0.749597	+	0.661895i	$0.769753\pi$
$158$		0			0
$159$	2.50652	+	5.20994i	0.198780	+	0.413175i
$160$		0			0
$161$	24.0178			1.89287
$162$		0			0
$163$			7.24124i			0.567178i	0.958946	+	0.283589i	$0.0915251\pi$
$163$			7.24124i			0.567178i	−0.958946	+	0.283589i	$0.908475\pi$
$164$		0			0
$165$	3.41778	+	22.7363i	0.266074	+	1.77002i
$166$		0			0
$167$	9.54791	+	5.51249i	0.738839	+	0.426569i	0.821647	−	0.569996i	$-0.193055\pi$
$167$	9.54791	+	5.51249i	0.738839	+	0.426569i	−0.0828078	+	0.996566i	$0.526389\pi$
$168$		0			0
$169$	−4.04570	−	7.00736i	−0.311208	−	0.539027i
$170$		0			0
$171$	3.54745	−	4.44137i	0.271280	−	0.339640i
$172$		0			0
$173$	−3.31133	+	1.91180i	−0.251755	+	0.145351i	−0.620568	−	0.784153i	$-0.713098\pi$
$173$	−3.31133	+	1.91180i	−0.251755	+	0.145351i	0.368812	+	0.929504i	$0.379765\pi$
$174$		0			0
$175$	−6.30344	−	13.0900i	−0.476495	−	0.989510i
$176$		0			0
$177$	−0.528045	+	7.01025i	−0.0396903	+	0.526923i
$178$		0			0
$179$	−8.32162			−0.621987			−0.310994	−	0.950412i	$-0.600662\pi$
$179$	−8.32162			−0.621987			−0.310994	+	0.950412i	$0.600662\pi$
$180$		0			0
$181$	11.8926			0.883967			0.441984	−	0.897023i	$-0.354275\pi$
$181$	11.8926			0.883967			0.441984	+	0.897023i	$0.354275\pi$
$182$		0			0
$183$	13.8899	+	9.47775i	1.02677	+	0.700616i
$184$		0			0
$185$	0.765480	−	0.710245i	0.0562792	−	0.0522183i
$186$		0			0
$187$	37.1681	−	21.4590i	2.71800	−	1.56924i
$188$		0			0
$189$	4.43381	+	14.4329i	0.322512	+	1.04984i
$190$		0			0
$191$	4.75443	+	8.23491i	0.344018	+	0.595857i	0.985175	−	0.171553i	$-0.0548784\pi$
$191$	4.75443	+	8.23491i	0.344018	+	0.595857i	−0.641156	+	0.767410i	$0.721545\pi$
$192$		0			0
$193$	11.8749	+	6.85599i	0.854776	+	0.493505i	0.862259	−	0.506467i	$-0.169049\pi$
$193$	11.8749	+	6.85599i	0.854776	+	0.493505i	−0.00748341	+	0.999972i	$0.502382\pi$
$194$		0			0
$195$	5.34736	+	6.71080i	0.382932	+	0.480570i
$196$		0			0
$197$			10.4085i			0.741578i	0.928717	+	0.370789i	$0.120913\pi$
$197$			10.4085i			0.741578i	−0.928717	+	0.370789i	$0.879087\pi$
$198$		0			0
$199$	16.0444			1.13735			0.568677	−	0.822561i	$-0.307455\pi$
$199$	16.0444			1.13735			0.568677	+	0.822561i	$0.307455\pi$
$200$		0			0
$201$	−15.2150	−	1.14607i	−1.07318	−	0.0808373i
$202$		0			0
$203$	10.4977	+	6.06087i	0.736796	+	0.425390i
$204$		0			0
$205$	21.1270	−	4.82185i	1.47557	−	0.336772i
$206$		0			0
$207$	−23.0898	+	9.04169i	−1.60485	+	0.628441i
$208$		0			0
$209$	5.62400	+	9.74105i	0.389020	+	0.673803i
$210$		0			0
$211$	1.08869	−	1.88566i	0.0749484	−	0.129814i	−0.826115	−	0.563501i	$-0.809454\pi$
$211$	1.08869	−	1.88566i	0.0749484	−	0.129814i	0.901064	+	0.433686i	$0.142787\pi$
$212$		0			0
$213$	−8.89820	+	4.28095i	−0.609694	+	0.293326i
$214$		0			0
$215$	−10.5899	−	3.26667i	−0.722223	−	0.222785i
$216$		0			0
$217$		−	3.58921i		−	0.243652i
$218$		0			0
$219$	0.879823	+	1.82876i	0.0594529	+	0.123576i
$220$		0			0
$221$	8.00869	−	13.8715i	0.538723	−	0.933096i
$222$		0			0
$223$	−2.00302	+	1.15645i	−0.134132	+	0.0774413i	−0.565565	−	0.824704i	$-0.691342\pi$
$223$	−2.00302	+	1.15645i	−0.134132	+	0.0774413i	0.431432	+	0.902145i	$0.358008\pi$
$224$		0			0
$225$	10.9877	+	10.2113i	0.732515	+	0.680751i
$226$		0			0
$227$	−3.98516	+	2.30083i	−0.264504	+	0.152712i	−0.626388	−	0.779512i	$-0.715467\pi$
$227$	−3.98516	+	2.30083i	−0.264504	+	0.152712i	0.361883	+	0.932223i	$0.382134\pi$
$228$		0			0
$229$	4.10373	−	7.10787i	0.271182	−	0.469701i	−0.697983	−	0.716115i	$-0.745919\pi$
$229$	4.10373	−	7.10787i	0.271182	−	0.469701i	0.969165	+	0.246413i	$0.0792521\pi$
$230$		0			0
$231$	−29.7930	−	2.24415i	−1.96023	−	0.147654i
$232$		0			0
$233$		−	4.20542i		−	0.275506i	−0.990467	−	0.137753i	$-0.956012\pi$
$233$		−	4.20542i		−	0.275506i	0.990467	−	0.137753i	$-0.0439881\pi$
$234$		0			0
$235$	−0.451610	−	0.139309i	−0.0294598	−	0.00908752i
$236$		0			0
$237$	−12.4767	−	8.51345i	−0.810447	−	0.553008i
$238$		0			0
$239$	4.49209	−	7.78053i	0.290569	−	0.503281i	−0.683375	−	0.730067i	$-0.739489\pi$
$239$	4.49209	−	7.78053i	0.290569	−	0.503281i	0.973945	+	0.226786i	$0.0728220\pi$
$240$		0			0
$241$	2.65090	+	4.59149i	0.170759	+	0.295764i	0.938686	−	0.344774i	$-0.112045\pi$
$241$	2.65090	+	4.59149i	0.170759	+	0.295764i	−0.767926	+	0.640538i	$0.778711\pi$
$242$		0			0
$243$	−9.69589	−	12.2061i	−0.621992	−	0.783024i
$244$		0			0
$245$	3.14627	−	0.718078i	0.201008	−	0.0458763i
$246$		0			0
$247$	3.63545	+	2.09893i	0.231318	+	0.133551i
$248$		0			0
$249$	11.7688	−	17.2475i	0.745817	−	1.09301i
$250$		0			0
$251$	23.3337			1.47281			0.736405	−	0.676541i	$-0.236522\pi$
$251$	23.3337			1.47281			0.736405	+	0.676541i	$0.236522\pi$
$252$		0			0
$253$		−	49.0688i		−	3.08493i
$254$		0			0
$255$	10.2398	−	26.0604i	0.641243	−	1.63197i
$256$		0			0
$257$	8.16345	+	4.71317i	0.509222	+	0.293999i	0.732514	−	0.680752i	$-0.238347\pi$
$257$	8.16345	+	4.71317i	0.509222	+	0.293999i	−0.223292	+	0.974752i	$0.571680\pi$
$258$		0			0
$259$	0.678475	+	1.17515i	0.0421584	+	0.0730205i
$260$		0			0
$261$	−12.3738	−	1.87475i	−0.765919	−	0.116044i
$262$		0			0
$263$	−3.37773	+	1.95013i	−0.208280	+	0.120250i	−0.600512	−	0.799616i	$-0.705036\pi$
$263$	−3.37773	+	1.95013i	−0.208280	+	0.120250i	0.392232	+	0.919866i	$0.371703\pi$
$264$		0			0
$265$	−5.47151	+	5.07670i	−0.336112	+	0.311859i
$266$		0			0
$267$	−19.7861	+	9.51917i	−1.21089	+	0.582564i
$268$		0			0
$269$	−27.4176			−1.67168			−0.835840	−	0.548974i	$-0.815019\pi$
$269$	−27.4176			−1.67168			−0.835840	+	0.548974i	$0.815019\pi$
$270$		0			0
$271$	−27.0279			−1.64183			−0.820913	−	0.571054i	$-0.806535\pi$
$271$	−27.0279			−1.64183			−0.820913	+	0.571054i	$0.806535\pi$
$272$		0			0
$273$	−10.0481	+	4.83417i	−0.608139	+	0.292577i
$274$		0			0
$275$	−26.7431	+	12.8780i	−1.61267	+	0.776575i
$276$		0			0
$277$	−21.4000	+	12.3553i	−1.28580	+	0.742357i	−0.977902	−	0.209062i	$-0.932959\pi$
$277$	−21.4000	+	12.3553i	−1.28580	+	0.742357i	−0.307898	+	0.951419i	$0.599626\pi$
$278$		0			0
$279$	1.35119	+	3.45054i	0.0808936	+	0.206579i
$280$		0			0
$281$	10.8230	+	18.7459i	0.645644	+	1.11829i	0.984152	+	0.177324i	$0.0567442\pi$
$281$	10.8230	+	18.7459i	0.645644	+	1.11829i	−0.338509	+	0.940963i	$0.609922\pi$
$282$		0			0
$283$	−1.31431	−	0.758817i	−0.0781276	−	0.0451070i	0.460427	−	0.887697i	$-0.347696\pi$
$283$	−1.31431	−	0.758817i	−0.0781276	−	0.0451070i	−0.538555	+	0.842590i	$0.681030\pi$
$284$		0			0
$285$	6.82995	+	2.68367i	0.404571	+	0.158967i
$286$		0			0
$287$			28.1601i			1.66224i
$288$		0			0
$289$	−35.2667			−2.07451
$290$		0			0
$291$	−5.54124	+	8.12083i	−0.324833	+	0.476051i
$292$		0			0
$293$	24.4639	+	14.1243i	1.42920	+	0.825148i	0.997057	−	0.0766581i	$-0.0244250\pi$
$293$	24.4639	+	14.1243i	1.42920	+	0.825148i	0.432141	+	0.901806i	$0.357758\pi$
$294$		0			0
$295$	−8.84830	+	2.01946i	−0.515168	+	0.117578i
$296$		0			0
$297$	29.4867	−	9.05836i	1.71099	−	0.525619i
$298$		0			0
$299$	−9.15645	−	15.8594i	−0.529531	−	0.917175i
$300$		0			0
$301$	7.20059	−	12.4718i	0.415035	−	0.718862i
$302$		0			0
$303$	−6.01993	−	4.10769i	−0.345836	−	0.235981i
$304$		0			0
$305$	−6.39894	+	20.7440i	−0.366402	+	1.18780i
$306$		0			0
$307$			13.5210i			0.771685i	0.922565	+	0.385843i	$0.126089\pi$
$307$			13.5210i			0.771685i	−0.922565	+	0.385843i	$0.873911\pi$
$308$		0			0
$309$	6.53637	+	0.492350i	0.371841	+	0.0280088i
$310$		0			0
$311$	12.7984	−	22.1675i	0.725731	−	1.25700i	−0.232942	−	0.972491i	$-0.574835\pi$
$311$	12.7984	−	22.1675i	0.725731	−	1.25700i	0.958673	−	0.284512i	$-0.0918315\pi$
$312$		0			0
$313$	−6.20370	+	3.58171i	−0.350654	+	0.202450i	−0.664973	−	0.746867i	$-0.731557\pi$
$313$	−6.20370	+	3.58171i	−0.350654	+	0.202450i	0.314319	+	0.949317i	$0.398224\pi$
$314$		0			0
$315$	−16.1137	+	10.9678i	−0.907906	+	0.617967i
$316$		0			0
$317$	2.84343	−	1.64165i	0.159703	−	0.0922045i	−0.418019	−	0.908438i	$-0.637275\pi$
$317$	2.84343	−	1.64165i	0.159703	−	0.0922045i	0.577721	+	0.816234i	$0.303942\pi$
$318$		0			0
$319$	12.3825	−	21.4471i	0.693285	−	1.20081i
$320$		0			0
$321$	−2.35791	−	4.90105i	−0.131606	−	0.273550i
$322$		0			0
$323$		−	13.6981i		−	0.762184i
$324$		0			0
$325$	−6.24049	+	9.15267i	−0.346160	+	0.507699i
$326$		0			0
$327$	7.68624	−	3.69787i	0.425050	−	0.204493i
$328$		0			0
$329$	0.307073	−	0.531866i	0.0169295	−	0.0293227i
$330$		0			0
$331$	5.15985	+	8.93712i	0.283611	+	0.491228i	0.972271	−	0.233855i	$-0.0751343\pi$
$331$	5.15985	+	8.93712i	0.283611	+	0.491228i	−0.688660	+	0.725084i	$0.741801\pi$
$332$		0			0
$333$	−1.09466	−	0.874333i	−0.0599869	−	0.0479131i
$334$		0			0
$335$	−4.38303	−	19.2043i	−0.239470	−	1.04924i
$336$		0			0
$337$	28.0846	+	16.2147i	1.52987	+	0.883269i	0.999367	+	0.0355834i	$0.0113289\pi$
$337$	28.0846	+	16.2147i	1.52987	+	0.883269i	0.530499	+	0.847685i	$0.322004\pi$
$338$		0			0
$339$	1.61570	+	0.121702i	0.0877526	+	0.00660994i
$340$		0			0
$341$	−7.33284			−0.397095
$342$		0			0
$343$		−	16.1464i		−	0.871825i
$344$		0			0
$345$	−19.9498	−	25.0365i	−1.07406	−	1.34792i
$346$		0			0
$347$	14.9112	+	8.60899i	0.800475	+	0.462155i	0.843637	−	0.536913i	$-0.180410\pi$
$347$	14.9112	+	8.60899i	0.800475	+	0.462155i	−0.0431620	+	0.999068i	$0.513743\pi$
$348$		0			0
$349$	−9.12756	−	15.8094i	−0.488587	−	0.846257i	0.511327	−	0.859386i	$-0.329154\pi$
$349$	−9.12756	−	15.8094i	−0.488587	−	0.846257i	−0.999914	+	0.0131290i	$0.995821\pi$
$350$		0			0
$351$	7.84002	−	8.43009i	0.418469	−	0.449965i
$352$		0			0
$353$	−15.5771	+	8.99344i	−0.829085	+	0.478672i	−0.853539	−	0.521028i	$-0.825549\pi$
$353$	−15.5771	+	8.99344i	−0.829085	+	0.478672i	0.0244542	+	0.999701i	$0.492215\pi$
$354$		0			0
$355$	−8.67062	−	9.34492i	−0.460189	−	0.495977i
$356$		0			0
$357$	30.0552	+	20.5082i	1.59069	+	1.08541i
$358$		0			0
$359$	12.1450			0.640989			0.320495	−	0.947250i	$-0.396151\pi$
$359$	12.1450			0.640989			0.320495	+	0.947250i	$0.396151\pi$
$360$		0			0
$361$	−15.4100			−0.811052
$362$		0			0
$363$	−3.15376	+	41.8688i	−0.165530	+	2.19754i
$364$		0			0
$365$	−1.92057	+	1.78199i	−0.100527	+	0.0932737i
$366$		0			0
$367$	5.53122	−	3.19345i	0.288728	−	0.166697i	−0.348640	−	0.937257i	$-0.613357\pi$
$367$	5.53122	−	3.19345i	0.288728	−	0.166697i	0.637368	+	0.770560i	$0.280023\pi$
$368$		0			0
$369$	−10.6011	−	27.0721i	−0.551871	−	1.40932i
$370$		0			0
$371$	−4.84961	−	8.39978i	−0.251779	−	0.436095i
$372$		0			0
$373$	17.7425	+	10.2436i	0.918672	+	0.530396i	0.883211	−	0.468976i	$-0.155377\pi$
$373$	17.7425	+	10.2436i	0.918672	+	0.530396i	0.0354609	+	0.999371i	$0.488710\pi$
$374$		0			0
$375$	−8.40940	+	17.4437i	−0.434259	+	0.900788i
$376$		0			0
$377$		−	9.24250i		−	0.476013i
$378$		0			0
$379$	−2.35672			−0.121057			−0.0605284	−	0.998166i	$-0.519279\pi$
$379$	−2.35672			−0.121057			−0.0605284	+	0.998166i	$0.519279\pi$
$380$		0			0
$381$	−3.09633	−	6.43590i	−0.158630	−	0.329721i
$382$		0			0
$383$	−21.1818	−	12.2293i	−1.08234	−	0.624888i	−0.150812	−	0.988563i	$-0.548189\pi$
$383$	−21.1818	−	12.2293i	−1.08234	−	0.624888i	−0.931526	+	0.363674i	$0.881522\pi$
$384$		0			0
$385$	−8.58254	−	37.6045i	−0.437407	−	1.91650i
$386$		0			0
$387$	−2.22728	+	14.7006i	−0.113219	+	0.747276i
$388$		0			0
$389$	−8.36713	−	14.4923i	−0.424230	−	0.734788i	0.572118	−	0.820171i	$-0.306122\pi$
$389$	−8.36713	−	14.4923i	−0.424230	−	0.734788i	−0.996348	+	0.0853829i	$0.972789\pi$
$390$		0			0
$391$	−29.8787	+	51.7514i	−1.51103	+	2.61718i
$392$		0			0
$393$	1.75727	−	23.3293i	0.0886427	−	1.17681i
$394$		0			0
$395$	5.74789	−	18.6334i	0.289208	−	0.937550i
$396$		0			0
$397$			33.7502i			1.69387i	0.531695	+	0.846936i	$0.321555\pi$
$397$			33.7502i			1.69387i	−0.531695	+	0.846936i	$0.678445\pi$
$398$		0			0
$399$	−5.37480	+	7.87690i	−0.269077	+	0.394338i
$400$		0			0
$401$	−12.4146	+	21.5028i	−0.619958	+	1.07380i	0.369535	+	0.929217i	$0.379517\pi$
$401$	−12.4146	+	21.5028i	−0.619958	+	1.07380i	−0.989493	+	0.144581i	$0.953816\pi$
$402$		0			0
$403$	−2.37003	+	1.36834i	−0.118060	+	0.0681618i
$404$		0			0
$405$	11.3622	−	16.6102i	0.564595	−	0.825368i
$406$		0			0
$407$	2.40086	−	1.38614i	0.119006	−	0.0687083i
$408$		0			0
$409$	5.49793	−	9.52269i	0.271855	−	0.470867i	−0.697482	−	0.716602i	$-0.745696\pi$
$409$	5.49793	−	9.52269i	0.271855	−	0.470867i	0.969337	+	0.245736i	$0.0790296\pi$
$410$		0			0
$411$	4.55642	−	6.67754i	0.224752	−	0.329379i
$412$		0			0
$413$		−	11.7939i		−	0.580338i
$414$		0			0
$415$	25.7584	+	7.94575i	1.26443	+	0.390042i
$416$		0			0
$417$	−1.18220	+	15.6947i	−0.0578925	+	0.768572i
$418$		0			0
$419$	−13.1475	+	22.7722i	−0.642299	+	1.11249i	0.342620	+	0.939474i	$0.388686\pi$
$419$	−13.1475	+	22.7722i	−0.642299	+	1.11249i	−0.984918	+	0.173020i	$0.944648\pi$
$420$		0			0
$421$	10.5242	+	18.2285i	0.512919	+	0.888402i	0.999888	+	0.0149827i	$0.00476932\pi$
$421$	10.5242	+	18.2285i	0.512919	+	0.888402i	−0.486968	+	0.873420i	$0.661897\pi$
$422$		0			0
$423$	−0.0949836	+	0.626917i	−0.00461826	+	0.0304817i
$424$		0			0
$425$	36.0467	+	2.70215i	1.74852	+	0.131074i
$426$		0			0
$427$	−24.4304	−	14.1049i	−1.18227	−	0.682584i
$428$		0			0
$429$	9.87630	+	20.5285i	0.476832	+	0.991123i
$430$		0			0
$431$	−21.0532			−1.01410			−0.507049	−	0.861917i	$-0.669264\pi$
$431$	−21.0532			−1.01410			−0.507049	+	0.861917i	$0.669264\pi$
$432$		0			0
$433$		−	3.68113i		−	0.176904i	−0.996080	−	0.0884519i	$-0.971808\pi$
$433$		−	3.68113i		−	0.176904i	0.996080	−	0.0884519i	$-0.0281920\pi$
$434$		0			0
$435$	−2.40175	−	15.9773i	−0.115155	−	0.766054i
$436$		0			0
$437$	−13.5631	−	7.83063i	−0.648809	−	0.374590i
$438$		0			0
$439$	4.07568	+	7.05929i	0.194522	+	0.336921i	0.946744	−	0.321988i	$-0.104351\pi$
$439$	4.07568	+	7.05929i	0.194522	+	0.336921i	−0.752222	+	0.658910i	$0.771018\pi$
$440$		0			0
$441$	−1.57873	−	4.03162i	−0.0751778	−	0.191982i
$442$		0			0
$443$	−24.0755	+	13.9000i	−1.14386	+	0.660407i	−0.947383	−	0.320101i	$-0.896283\pi$
$443$	−24.0755	+	13.9000i	−1.14386	+	0.660407i	−0.196476	+	0.980509i	$0.562950\pi$
$444$		0			0
$445$	−19.2801	−	20.7795i	−0.913965	−	0.985042i
$446$		0			0
$447$	1.49652	−	19.8676i	0.0707831	−	0.939706i
$448$		0			0
$449$	37.8560			1.78653			0.893267	−	0.449527i	$-0.148408\pi$
$449$	37.8560			1.78653			0.893267	+	0.449527i	$0.148408\pi$
$450$		0			0
$451$	57.5316			2.70906
$452$		0			0
$453$	17.5125	+	11.9497i	0.822811	+	0.561445i
$454$		0			0
$455$	−9.79112	−	10.5526i	−0.459015	−	0.494711i
$456$		0			0
$457$	−8.71532	+	5.03179i	−0.407686	+	0.235377i	−0.689795	−	0.724005i	$-0.742299\pi$
$457$	−8.71532	+	5.03179i	−0.407686	+	0.235377i	0.282109	+	0.959382i	$0.408966\pi$
$458$		0			0
$459$	−36.6145	−	8.40129i	−1.70902	−	0.392139i
$460$		0			0
$461$	−7.84246	−	13.5835i	−0.365260	−	0.632649i	0.623558	−	0.781777i	$-0.285687\pi$
$461$	−7.84246	−	13.5835i	−0.365260	−	0.632649i	−0.988818	+	0.149128i	$0.952353\pi$
$462$		0			0
$463$	2.75034	+	1.58791i	0.127819	+	0.0737965i	0.562546	−	0.826766i	$-0.309822\pi$
$463$	2.75034	+	1.58791i	0.127819	+	0.0737965i	−0.434727	+	0.900562i	$0.643155\pi$
$464$		0			0
$465$	−3.74145	+	2.98130i	−0.173506	+	0.138254i
$466$		0			0
$467$			35.2304i			1.63027i	0.579272	+	0.815134i	$0.303337\pi$
$467$			35.2304i			1.63027i	−0.579272	+	0.815134i	$0.696663\pi$
$468$		0			0
$469$	25.5973			1.18197
$470$		0			0
$471$	−13.7735	−	1.03748i	−0.634648	−	0.0478047i
$472$		0			0
$473$	−25.4801	−	14.7109i	−1.17158	−	0.676410i
$474$		0			0
$475$	−0.708183	+	9.44717i	−0.0324937	+	0.433466i
$476$		0			0
$477$	7.82441	+	6.24957i	0.358255	+	0.286148i
$478$		0			0
$479$	−5.28887	−	9.16059i	−0.241655	−	0.418558i	0.719531	−	0.694460i	$-0.244357\pi$
$479$	−5.28887	−	9.16059i	−0.241655	−	0.418558i	−0.961186	+	0.275902i	$0.911023\pi$
$480$		0			0
$481$	0.517319	−	0.896022i	0.0235877	−	0.0408551i
$482$		0			0
$483$	37.4872	−	18.0352i	1.70573	−	0.820631i
$484$		0			0
$485$	−12.1282	−	3.74119i	−0.550711	−	0.169879i
$486$		0			0
$487$		−	20.8299i		−	0.943892i	−0.881627	−	0.471946i	$-0.843552\pi$
$487$		−	20.8299i		−	0.943892i	0.881627	−	0.471946i	$-0.156448\pi$
$488$		0			0
$489$	5.43753	+	11.3022i	0.245893	+	0.511104i
$490$		0			0
$491$	18.7325	−	32.4456i	0.845385	−	1.46425i	−0.0399023	−	0.999204i	$-0.512705\pi$
$491$	18.7325	−	32.4456i	0.845385	−	1.46425i	0.885287	−	0.465045i	$-0.153962\pi$
$492$		0			0
$493$	−26.1188	+	15.0797i	−1.17633	+	0.679156i
$494$		0			0
$495$	22.4075	+	32.9207i	1.00714	+	1.47967i
$496$		0			0
$497$	14.3462	−	8.28278i	0.643515	−	0.371533i
$498$		0			0
$499$	−5.51059	+	9.54463i	−0.246688	+	0.427276i	−0.962605	−	0.270909i	$-0.912676\pi$
$499$	−5.51059	+	9.54463i	−0.246688	+	0.427276i	0.715917	+	0.698186i	$0.246009\pi$
$500$		0			0
$501$	19.0419	+	1.43433i	0.850728	+	0.0640809i
$502$		0			0
$503$		−	33.2171i		−	1.48108i	−0.672013	−	0.740539i	$-0.734570\pi$
$503$		−	33.2171i		−	1.48108i	0.672013	−	0.740539i	$-0.265430\pi$
$504$		0			0
$505$	2.77333	−	8.99054i	0.123411	−	0.400074i
$506$		0			0
$507$	−11.5765	−	7.89920i	−0.514129	−	0.350816i
$508$		0			0
$509$	−22.0788	+	38.2416i	−0.978626	+	1.69503i	−0.311216	+	0.950339i	$0.600736\pi$
$509$	−22.0788	+	38.2416i	−0.978626	+	1.69503i	−0.667410	+	0.744691i	$0.732597\pi$
$510$		0			0
$511$	−1.70228	−	2.94844i	−0.0753045	−	0.130431i
$512$		0			0
$513$	2.20182	−	9.59596i	0.0972126	−	0.423672i
$514$		0			0
$515$	1.88295	+	8.25017i	0.0829726	+	0.363546i
$516$		0			0
$517$	−1.08661	−	0.627356i	−0.0477891	−	0.0275911i
$518$		0			0
$519$	−3.73277	+	5.47046i	−0.163850	+	0.240127i
$520$		0			0
$521$	28.8358			1.26332			0.631659	−	0.775246i	$-0.282374\pi$
$521$	28.8358			1.26332			0.631659	+	0.775246i	$0.282374\pi$
$522$		0			0
$523$			11.6619i			0.509938i	0.966949	+	0.254969i	$0.0820653\pi$
$523$			11.6619i			0.509938i	−0.966949	+	0.254969i	$0.917935\pi$
$524$		0			0
$525$	−19.6679	−	15.6977i	−0.858377	−	0.685103i
$526$		0			0
$527$	7.73372	+	4.46506i	0.336886	+	0.194501i
$528$		0			0
$529$	22.6607	+	39.2495i	0.985248	+	1.70650i
$530$		0			0
$531$	4.43989	+	11.3382i	0.192675	+	0.492036i
$532$		0			0
$533$	18.5947	−	10.7356i	0.805425	−	0.465012i
$534$		0			0
$535$	5.14710	−	4.77570i	0.222529	−	0.206472i
$536$		0			0
$537$	−12.9885	+	6.24880i	−0.560494	+	0.269655i
$538$		0			0
$539$	8.56771			0.369037
$540$		0			0
$541$	−23.0866			−0.992570			−0.496285	−	0.868160i	$-0.665303\pi$
$541$	−23.0866			−0.992570			−0.496285	+	0.868160i	$0.665303\pi$
$542$		0			0
$543$	18.5621	−	8.93026i	0.796574	−	0.383234i
$544$		0			0
$545$	7.48966	+	8.07212i	0.320822	+	0.345772i
$546$		0			0
$547$	0.736873	−	0.425434i	0.0315064	−	0.0181902i	−0.484164	−	0.874977i	$-0.660876\pi$
$547$	0.736873	−	0.425434i	0.0315064	−	0.0181902i	0.515670	+	0.856787i	$0.327543\pi$
$548$		0			0
$549$	28.7964	+	4.36292i	1.22900	+	0.186205i
$550$		0			0
$551$	−3.95211	−	6.84525i	−0.168365	−	0.291617i
$552$		0			0
$553$	21.9448	+	12.6698i	0.933187	+	0.538776i
$554$		0			0
$555$	0.661439	−	1.68337i	0.0280765	−	0.0714549i
$556$		0			0
$557$		−	40.4513i		−	1.71398i	−0.515337	−	0.856988i	$-0.672333\pi$
$557$		−	40.4513i		−	1.71398i	0.515337	−	0.856988i	$-0.327667\pi$
$558$		0			0
$559$	−10.9805			−0.464426
$560$		0			0
$561$	41.8986	−	61.4034i	1.76896	−	2.59245i
$562$		0			0
$563$	−20.5438	−	11.8610i	−0.865817	−	0.499880i	0.000138724	−	1.00000i	$-0.499956\pi$
$563$	−20.5438	−	11.8610i	−0.865817	−	0.499880i	−0.865956	+	0.500120i	$0.833289\pi$
$564$		0			0
$565$	0.465438	+	2.03932i	0.0195811	+	0.0857950i
$566$		0			0
$567$	17.7582	+	19.1976i	0.745773	+	0.806225i
$568$		0			0
$569$	12.4116	+	21.4975i	0.520320	+	0.901220i	0.999721	+	0.0236242i	$0.00752053\pi$
$569$	12.4116	+	21.4975i	0.520320	+	0.901220i	−0.479401	+	0.877596i	$0.659146\pi$
$570$		0			0
$571$	5.89810	−	10.2158i	0.246828	−	0.427519i	−0.715816	−	0.698289i	$-0.753945\pi$
$571$	5.89810	−	10.2158i	0.246828	−	0.427519i	0.962644	+	0.270770i	$0.0872784\pi$
$572$		0			0
$573$	13.6045	+	9.28300i	0.568334	+	0.387803i
$574$		0			0
$575$	23.2819	−	34.1466i	0.970922	−	1.42401i
$576$		0			0
$577$			44.8446i			1.86691i	0.358699	+	0.933453i	$0.383220\pi$
$577$			44.8446i			1.86691i	−0.358699	+	0.933453i	$0.616780\pi$
$578$		0			0
$579$	23.6828	+	1.78390i	0.984222	+	0.0741363i
$580$		0			0
$581$	−17.5145	+	30.3359i	−0.726623	+	1.25855i
$582$		0			0
$583$	−17.1609	+	9.90785i	−0.710732	+	0.410341i
$584$		0			0
$585$	13.3854	+	6.45890i	0.553419	+	0.267043i
$586$		0			0
$587$	−3.94274	+	2.27634i	−0.162734	+	0.0939547i	−0.579155	−	0.815217i	$-0.696618\pi$
$587$	−3.94274	+	2.27634i	−0.162734	+	0.0939547i	0.416421	+	0.909172i	$0.363284\pi$
$588$		0			0
$589$	−1.17021	+	2.02686i	−0.0482176	+	0.0835153i
$590$		0			0
$591$	7.81589	+	16.2458i	0.321503	+	0.668262i
$592$		0			0
$593$			21.4818i			0.882151i	0.897470	+	0.441076i	$0.145403\pi$
$593$			21.4818i			0.882151i	−0.897470	+	0.441076i	$0.854597\pi$
$594$		0			0
$595$	−13.8462	+	44.8864i	−0.567638	+	1.84016i
$596$		0			0
$597$	25.0422	−	12.0479i	1.02491	−	0.493087i
$598$		0			0
$599$	1.36135	−	2.35792i	0.0556231	−	0.0963421i	−0.836873	−	0.547397i	$-0.815619\pi$
$599$	1.36135	−	2.35792i	0.0556231	−	0.0963421i	0.892496	+	0.451055i	$0.148952\pi$
$600$		0			0
$601$	−10.9773	−	19.0133i	−0.447775	−	0.775568i	0.550466	−	0.834857i	$-0.314450\pi$
$601$	−10.9773	−	19.0133i	−0.447775	−	0.775568i	−0.998241	+	0.0592891i	$0.981117\pi$
$602$		0			0
$603$	−24.6083	+	9.63631i	−1.00213	+	0.392421i
$604$		0			0
$605$	−52.8467	+	12.0613i	−2.14852	+	0.490360i
$606$		0			0
$607$	29.3213	+	16.9287i	1.19012	+	0.687114i	0.958333	−	0.285653i	$-0.0922105\pi$
$607$	29.3213	+	16.9287i	1.19012	+	0.687114i	0.231784	+	0.972767i	$0.425544\pi$
$608$		0			0
$609$	20.9362	+	1.57701i	0.848376	+	0.0639037i
$610$		0			0
$611$	−0.468269			−0.0189441
$612$		0			0
$613$		−	19.0655i		−	0.770049i	−0.922906	−	0.385025i	$-0.874193\pi$
$613$		−	19.0655i		−	0.770049i	0.922906	−	0.385025i	$-0.125807\pi$
$614$		0			0
$615$	29.3545	−	23.3905i	1.18369	−	0.943196i
$616$		0			0
$617$	−14.6262	−	8.44444i	−0.588828	−	0.339960i	0.175806	−	0.984425i	$-0.443747\pi$
$617$	−14.6262	−	8.44444i	−0.588828	−	0.339960i	−0.764634	+	0.644465i	$0.777080\pi$
$618$		0			0
$619$	9.80617	+	16.9848i	0.394143	+	0.682676i	0.992991	−	0.118186i	$-0.0377080\pi$
$619$	9.80617	+	16.9848i	0.394143	+	0.682676i	−0.598848	+	0.800863i	$0.704375\pi$
$620$		0			0
$621$	−29.2494	+	31.4508i	−1.17374	+	1.26208i
$622$		0			0
$623$	31.9004	−	18.4177i	1.27806	−	0.737889i
$624$		0			0
$625$	−24.7206	−	3.72718i	−0.988824	−	0.149087i
$626$		0			0
$627$	16.0927	+	10.9808i	0.642679	+	0.438532i
$628$		0			0
$629$	−3.37615			−0.134616
$630$		0			0
$631$	28.7912			1.14616			0.573079	−	0.819500i	$-0.305749\pi$
$631$	28.7912			1.14616			0.573079	+	0.819500i	$0.305749\pi$
$632$		0			0
$633$	0.283272	−	3.76067i	0.0112590	−	0.149473i
$634$		0			0
$635$	6.75901	−	6.27130i	0.268223	−	0.248869i
$636$		0			0
$637$	2.76915	−	1.59877i	0.109718	−	0.0633456i
$638$		0			0
$639$	−10.6738	+	13.3635i	−0.422249	+	0.528652i
$640$		0			0
$641$	−18.1567	−	31.4484i	−0.717148	−	1.24214i	−0.962125	−	0.272608i	$-0.912114\pi$
$641$	−18.1567	−	31.4484i	−0.717148	−	1.24214i	0.244977	−	0.969529i	$-0.421220\pi$
$642$		0			0
$643$	−6.03311	−	3.48322i	−0.237923	−	0.137365i	0.376299	−	0.926498i	$-0.377197\pi$
$643$	−6.03311	−	3.48322i	−0.237923	−	0.137365i	−0.614222	+	0.789134i	$0.710530\pi$
$644$		0			0
$645$	−18.9818	+	2.85339i	−0.747407	+	0.112352i
$646$		0			0
$647$		−	31.4157i		−	1.23508i	−0.786539	−	0.617540i	$-0.788129\pi$
$647$		−	31.4157i		−	1.23508i	0.786539	−	0.617540i	$-0.211871\pi$
$648$		0			0
$649$	−24.0951			−0.945815
$650$		0			0
$651$	−2.69518	−	5.60209i	−0.105632	−	0.219563i
$652$		0			0
$653$	26.7036	+	15.4173i	1.04499	+	0.603326i	0.921243	−	0.388987i	$-0.127175\pi$
$653$	26.7036	+	15.4173i	1.04499	+	0.603326i	0.123749	+	0.992314i	$0.460508\pi$
$654$		0			0
$655$	29.4461	−	6.72053i	1.15055	−	0.262593i
$656$		0			0
$657$	2.74648	+	2.19369i	0.107150	+	0.0855838i
$658$		0			0
$659$	−15.1953	−	26.3190i	−0.591924	−	1.02524i	−0.993973	−	0.109624i	$-0.965035\pi$
$659$	−15.1953	−	26.3190i	−0.591924	−	1.02524i	0.402049	−	0.915618i	$-0.368298\pi$
$660$		0			0
$661$	−1.52078	+	2.63408i	−0.0591516	+	0.102454i	−0.894085	−	0.447898i	$-0.852173\pi$
$661$	−1.52078	+	2.63408i	−0.0591516	+	0.102454i	0.834933	+	0.550351i	$0.185506\pi$
$662$		0			0
$663$	2.08383	−	27.6646i	0.0809291	−	1.07440i
$664$		0			0
$665$	−11.7639	−	3.62882i	−0.456183	−	0.140720i
$666$		0			0
$667$			34.4817i			1.33514i
$668$		0			0
$669$	−2.25795	+	3.30908i	−0.0872975	+	0.127937i
$670$		0			0
$671$	−28.8166	+	49.9118i	−1.11245	+	1.92682i
$672$		0			0
$673$	−32.3494	+	18.6769i	−1.24698	+	0.719942i	−0.970505	−	0.241080i	$-0.922498\pi$
$673$	−32.3494	+	18.6769i	−1.24698	+	0.719942i	−0.276471	+	0.961022i	$0.589165\pi$
$674$		0			0
$675$	24.8175	+	7.68705i	0.955227	+	0.295875i
$676$		0			0
$677$	−29.6583	+	17.1232i	−1.13986	+	0.658098i	−0.946396	−	0.323009i	$-0.895306\pi$
$677$	−29.6583	+	17.1232i	−1.13986	+	0.658098i	−0.193464	+	0.981107i	$0.561972\pi$
$678$		0			0
$679$	8.24654	−	14.2834i	0.316473	−	0.548148i
$680$		0			0
$681$	−4.49236	+	6.58367i	−0.172148	+	0.252287i
$682$		0			0
$683$		−	3.74858i		−	0.143435i	−0.997425	−	0.0717177i	$-0.977152\pi$
$683$		−	3.74858i		−	0.143435i	0.997425	−	0.0717177i	$-0.0228481\pi$
$684$		0			0
$685$	9.97267	+	3.07628i	0.381036	+	0.117539i
$686$		0			0
$687$	1.06777	−	14.1756i	0.0407381	−	0.540832i
$688$		0			0
$689$	−3.69770	+	6.40460i	−0.140871	+	0.243996i
$690$		0			0
$691$	−11.2610	−	19.5046i	−0.428388	−	0.741990i	0.568342	−	0.822792i	$-0.307585\pi$
$691$	−11.2610	−	19.5046i	−0.428388	−	0.741990i	−0.996730	+	0.0808024i	$0.974252\pi$
$692$		0			0
$693$	−48.1863	+	18.8692i	−1.83045	+	0.716780i
$694$		0			0
$695$	−19.8098	+	4.52121i	−0.751427	+	0.171499i
$696$		0			0
$697$	−60.6768	−	35.0318i	−2.29830	−	1.32692i
$698$		0			0
$699$	−3.15790	−	6.56387i	−0.119443	−	0.248268i
$700$		0			0
$701$	33.9912			1.28383			0.641914	−	0.766776i	$-0.278141\pi$
$701$	33.9912			1.28383			0.641914	+	0.766776i	$0.278141\pi$
$702$		0			0
$703$		−	0.884825i		−	0.0333718i
$704$		0			0
$705$	−0.809487	+	0.121684i	−0.0304871	+	0.00458289i
$706$		0			0
$707$	10.5882	+	6.11312i	0.398212	+	0.229908i
$708$		0			0
$709$	−12.9408	−	22.4142i	−0.486004	−	0.841783i	0.513867	−	0.857870i	$-0.328213\pi$
$709$	−12.9408	−	22.4142i	−0.486004	−	0.841783i	−0.999871	+	0.0160868i	$0.994879\pi$
$710$		0			0
$711$	−25.8666	−	3.91902i	−0.970072	−	0.146975i
$712$		0			0
$713$	8.84207	−	5.10497i	0.331138	−	0.191183i
$714$		0			0
$715$	−21.5591	+	20.0034i	−0.806264	+	0.748086i
$716$		0			0
$717$	1.16882	−	15.5171i	0.0436505	−	0.579497i
$718$		0			0
$719$	−14.7176			−0.548875			−0.274438	−	0.961605i	$-0.588492\pi$
$719$	−14.7176			−0.548875			−0.274438	+	0.961605i	$0.588492\pi$
$720$		0			0
$721$	−10.9966			−0.409535
$722$		0			0
$723$	7.58536	+	5.17586i	0.282102	+	0.192492i
$724$		0			0
$725$	18.7929	−	9.04968i	0.697953	−	0.336097i
$726$		0			0
$727$	16.7583	−	9.67541i	0.621531	−	0.358841i	−0.155934	−	0.987767i	$-0.549839\pi$
$727$	16.7583	−	9.67541i	0.621531	−	0.358841i	0.777465	+	0.628927i	$0.216505\pi$
$728$		0			0
$729$	−24.2992	−	11.7707i	−0.899969	−	0.435953i
$730$		0			0
$731$	17.9154	+	31.0304i	0.662624	+	1.14770i
$732$		0			0
$733$	−19.2598	−	11.1196i	−0.711376	−	0.410713i	0.100194	−	0.994968i	$-0.468054\pi$
$733$	−19.2598	−	11.1196i	−0.711376	−	0.410713i	−0.811570	+	0.584255i	$0.801387\pi$
$734$		0			0
$735$	4.37152	−	3.48335i	0.161246	−	0.128485i
$736$		0			0
$737$		−	52.2958i		−	1.92634i
$738$		0			0
$739$	−13.1529			−0.483837			−0.241919	−	0.970297i	$-0.577777\pi$
$739$	−13.1529			−0.483837			−0.241919	+	0.970297i	$0.577777\pi$
$740$		0			0
$741$	7.25035	+	0.546131i	0.266348	+	0.0200626i
$742$		0			0
$743$	30.4393	+	17.5741i	1.11671	+	0.644732i	0.940559	−	0.339631i	$-0.110302\pi$
$743$	30.4393	+	17.5741i	1.11671	+	0.644732i	0.176150	+	0.984363i	$0.443636\pi$
$744$		0			0
$745$	25.0768	−	5.72332i	0.918743	−	0.209686i
$746$		0			0
$747$	5.41757	−	35.7574i	0.198218	−	1.30829i
$748$		0			0
$749$	4.56208	+	7.90175i	0.166695	+	0.288724i
$750$		0			0
$751$	23.0868	−	39.9875i	0.842450	−	1.45917i	−0.0453681	−	0.998970i	$-0.514446\pi$
$751$	23.0868	−	39.9875i	0.842450	−	1.45917i	0.887818	−	0.460195i	$-0.152221\pi$
$752$		0			0
$753$	36.4195	−	17.5215i	1.32720	−	0.638520i
$754$		0			0
$755$	−8.06787	+	26.1543i	−0.293620	+	0.951854i
$756$		0			0
$757$		−	14.7959i		−	0.537767i	−0.963173	−	0.268884i	$-0.913345\pi$
$757$		−	14.7959i		−	0.537767i	0.963173	−	0.268884i	$-0.0866547\pi$
$758$		0			0
$759$	−36.8463	−	76.5871i	−1.33744	−	2.77994i
$760$		0			0
$761$	−12.6003	+	21.8244i	−0.456760	+	0.791132i	−0.998788	−	0.0492287i	$-0.984324\pi$
$761$	−12.6003	+	21.8244i	−0.456760	+	0.791132i	0.542027	+	0.840361i	$0.317657\pi$
$762$		0			0
$763$	−12.3922	+	7.15464i	−0.448628	+	0.259015i
$764$		0			0
$765$	−3.58663	−	48.3647i	−0.129675	−	1.74863i
$766$		0			0
$767$	−7.78773	+	4.49625i	−0.281199	+	0.162350i
$768$		0			0
$769$	−9.19739	+	15.9304i	−0.331667	+	0.574463i	−0.982839	−	0.184467i	$-0.940944\pi$
$769$	−9.19739	+	15.9304i	−0.331667	+	0.574463i	0.651172	+	0.758930i	$0.274278\pi$
$770$		0			0
$771$	16.2808	+	1.22635i	0.586338	+	0.0441658i
$772$		0			0
$773$			32.2865i			1.16126i	0.814166	+	0.580632i	$0.197194\pi$
$773$			32.2865i			1.16126i	−0.814166	+	0.580632i	$0.802806\pi$
$774$		0			0
$775$	−5.10286	−	3.47924i	−0.183300	−	0.124978i
$776$		0			0
$777$	1.94141	+	1.32472i	0.0696476	+	0.0475240i
$778$		0			0
$779$	9.18116	−	15.9022i	0.328949	−	0.569757i
$780$		0			0
$781$	−16.9219	−	29.3095i	−0.605512	−	1.04878i
$782$		0			0
$783$	−20.7209	+	6.36550i	−0.740506	+	0.227485i
$784$		0			0
$785$	−3.96776	−	17.3848i	−0.141615	−	0.620490i
$786$		0			0
$787$	−16.5653	−	9.56399i	−0.590490	−	0.340919i	0.174801	−	0.984604i	$-0.444072\pi$
$787$	−16.5653	−	9.56399i	−0.590490	−	0.340919i	−0.765291	+	0.643684i	$0.777405\pi$
$788$		0			0
$789$	−3.80762	+	5.58016i	−0.135555	+	0.198659i
$790$		0			0
$791$	−2.71821			−0.0966483
$792$		0			0
$793$			21.5092i			0.763814i
$794$		0			0
$795$	−4.72784	+	12.0324i	−0.167679	+	0.426745i
$796$		0			0
$797$	−13.0257	−	7.52039i	−0.461394	−	0.266386i	0.251236	−	0.967926i	$-0.419163\pi$
$797$	−13.0257	−	7.52039i	−0.461394	−	0.266386i	−0.712630	+	0.701540i	$0.752496\pi$
$798$		0			0
$799$	0.764011	+	1.32331i	0.0270288	+	0.0468152i
$800$		0			0
$801$	−23.7344	+	29.7153i	−0.838613	+	1.04994i
$802$		0			0
$803$	−6.02372	+	3.47779i	−0.212572	+	0.122729i
$804$		0			0
$805$	36.5285	+	39.3693i	1.28746	+	1.38758i
$806$		0			0
$807$	−42.7937	+	20.5882i	−1.50641	+	0.724738i
$808$		0			0
$809$	11.8600			0.416975			0.208488	−	0.978025i	$-0.433146\pi$
$809$	11.8600			0.416975			0.208488	+	0.978025i	$0.433146\pi$
$810$		0			0
$811$	−11.0629			−0.388469			−0.194235	−	0.980955i	$-0.562222\pi$
$811$	−11.0629			−0.388469			−0.194235	+	0.980955i	$0.562222\pi$
$812$		0			0
$813$	−42.1854	+	20.2955i	−1.47951	+	0.711795i
$814$		0			0
$815$	−11.8696	+	11.0132i	−0.415775	+	0.385774i
$816$		0			0
$817$	−8.13247	+	4.69528i	−0.284519	+	0.164267i
$818$		0			0
$819$	−12.0532	+	15.0905i	−0.421171	+	0.527303i
$820$		0			0
$821$	−19.0482	−	32.9925i	−0.664787	−	1.15144i	−0.979343	−	0.202206i	$-0.935189\pi$
$821$	−19.0482	−	32.9925i	−0.664787	−	1.15144i	0.314556	−	0.949239i	$-0.398144\pi$
$822$		0			0
$823$	45.1770	+	26.0829i	1.57477	+	0.909194i	0.995571	+	0.0940077i	$0.0299678\pi$
$823$	45.1770	+	26.0829i	1.57477	+	0.909194i	0.579199	+	0.815186i	$0.303365\pi$
$824$		0			0
$825$	−32.0707	+	40.1819i	−1.11656	+	1.39895i
$826$		0			0
$827$			16.0643i			0.558611i	0.960202	+	0.279305i	$0.0901041\pi$
$827$			16.0643i			0.558611i	−0.960202	+	0.279305i	$0.909896\pi$
$828$		0			0
$829$	54.7655			1.90208			0.951041	−	0.309063i	$-0.100016\pi$
$829$	54.7655			1.90208			0.951041	+	0.309063i	$0.100016\pi$
$830$		0			0
$831$	−24.1236	+	35.3538i	−0.836839	+	1.22641i
$832$		0			0
$833$	−9.03610	−	5.21699i	−0.313082	−	0.180758i
$834$		0			0
$835$	5.48545	+	24.0346i	0.189832	+	0.831751i
$836$		0			0
$837$	4.70000	+	4.37102i	0.162456	+	0.151085i
$838$		0			0
$839$	−22.1462	−	38.3584i	−0.764573	−	1.32428i	−0.940472	−	0.339870i	$-0.889617\pi$
$839$	−22.1462	−	38.3584i	−0.764573	−	1.32428i	0.175900	−	0.984408i	$-0.443717\pi$
$840$		0			0
$841$	5.79857	−	10.0434i	0.199951	−	0.346325i
$842$		0			0
$843$	30.9691	+	21.1318i	1.06663	+	0.727817i
$844$		0			0
$845$	5.33318	−	17.2890i	0.183467	−	0.594761i
$846$		0			0
$847$		−	70.4390i		−	2.42031i
$848$		0			0
$849$	−2.62119	−	0.197441i	−0.0899591	−	0.00677615i
$850$		0			0
$851$	−1.93000	+	3.34286i	−0.0661596	+	0.114592i
$852$		0			0
$853$	25.2942	−	14.6036i	0.866055	−	0.500017i	1.98828e−5	−	1.00000i	$-0.499994\pi$
$853$	25.2942	−	14.6036i	0.866055	−	0.500017i	0.866035	+	0.499983i	$0.166660\pi$
$854$		0			0
$855$	12.6755	−	0.939987i	0.433492	−	0.0321469i
$856$		0			0
$857$	−33.6618	+	19.4346i	−1.14986	+	0.663874i	−0.948854	−	0.315715i	$-0.897756\pi$
$857$	−33.6618	+	19.4346i	−1.14986	+	0.663874i	−0.201010	+	0.979589i	$0.564422\pi$
$858$		0			0
$859$	−7.49861	+	12.9880i	−0.255849	+	0.443144i	−0.965126	−	0.261786i	$-0.915688\pi$
$859$	−7.49861	+	12.9880i	−0.255849	+	0.443144i	0.709276	+	0.704930i	$0.249022\pi$
$860$		0			0
$861$	21.1457	+	43.9526i	0.720644	+	1.49790i
$862$		0			0
$863$			23.8510i			0.811898i	0.913896	+	0.405949i	$0.133059\pi$
$863$			23.8510i			0.811898i	−0.913896	+	0.405949i	$0.866941\pi$
$864$		0			0
$865$	−8.16993	−	2.52019i	−0.277786	−	0.0856891i
$866$		0			0
$867$	−55.0447	+	26.4822i	−1.86942	+	0.899382i
$868$		0			0
$869$	25.8847	−	44.8336i	0.878078	−	1.52088i
$870$		0			0
$871$	−9.75863	−	16.9024i	−0.330658	−	0.572717i
$872$		0			0
$873$	−2.55082	+	16.8361i	−0.0863321	+	0.569814i
$874$		0			0
$875$	11.8699	−	30.2409i	0.401275	−	1.02233i
$876$		0			0
$877$	14.6631	+	8.46576i	0.495139	+	0.285868i	0.726704	−	0.686951i	$-0.241051\pi$
$877$	14.6631	+	8.46576i	0.495139	+	0.285868i	−0.231565	+	0.972819i	$0.574385\pi$
$878$		0			0
$879$	48.7897	+	3.67507i	1.64563	+	0.123957i
$880$		0			0
$881$	−39.7212			−1.33824			−0.669121	−	0.743153i	$-0.733329\pi$
$881$	−39.7212			−1.33824			−0.669121	+	0.743153i	$0.733329\pi$
$882$		0			0
$883$		−	39.8297i		−	1.34038i	−0.742192	−	0.670188i	$-0.766214\pi$
$883$		−	39.8297i		−	1.34038i	0.742192	−	0.670188i	$-0.233786\pi$
$884$		0			0
$885$	−12.2941	+	9.79629i	−0.413262	+	0.329299i
$886$		0			0
$887$	−9.43187	−	5.44549i	−0.316691	−	0.182842i	0.333226	−	0.942847i	$-0.391863\pi$
$887$	−9.43187	−	5.44549i	−0.316691	−	0.182842i	−0.649917	+	0.760005i	$0.725196\pi$
$888$		0			0
$889$	5.99078	+	10.3763i	0.200924	+	0.348011i
$890$		0			0
$891$	39.2212	−	36.2803i	1.31396	−	1.21544i
$892$		0			0
$893$	−0.346813	+	0.200233i	−0.0116057	+	0.00670053i
$894$		0			0
$895$	−12.6563	−	13.6406i	−0.423053	−	0.455954i
$896$		0			0
$897$	−26.2005	−	17.8779i	−0.874810	−	0.596926i
$898$		0			0
$899$	5.15294			0.171860
$900$		0			0
$901$	24.1321			0.803957
$902$		0			0
$903$	1.87356	−	24.8731i	0.0623482	−	0.827725i
$904$		0			0
$905$	18.0873	+	19.4940i	0.601243	+	0.648001i
$906$		0			0
$907$	39.0165	−	22.5262i	1.29552	−	0.747971i	0.315896	−	0.948794i	$-0.397695\pi$
$907$	39.0165	−	22.5262i	1.29552	−	0.747971i	0.979627	+	0.200823i	$0.0643617\pi$
$908$		0			0
$909$	−12.4805	−	1.89091i	−0.413952	−	0.0627175i
$910$		0			0
$911$	3.05101	+	5.28451i	0.101085	+	0.175084i	0.912132	−	0.409897i	$-0.134435\pi$
$911$	3.05101	+	5.28451i	0.101085	+	0.175084i	−0.811047	+	0.584981i	$0.801102\pi$
$912$		0			0
$913$	61.9769	+	35.7824i	2.05114	+	1.18422i
$914$		0			0
$915$	5.58937	+	37.1825i	0.184779	+	1.22922i
$916$		0			0
$917$			39.2486i			1.29610i
$918$		0			0
$919$	−55.7269			−1.83826			−0.919130	−	0.393953i	$-0.871107\pi$
$919$	−55.7269			−1.83826			−0.919130	+	0.393953i	$0.871107\pi$
$920$		0			0
$921$	10.1531	+	21.1038i	0.334555	+	0.695392i
$922$		0			0
$923$	−10.9386	−	6.31539i	−0.360048	−	0.207874i
$924$		0			0
$925$	2.32843	+	0.174545i	0.0765582	+	0.00573899i
$926$		0			0
$927$	10.5717	−	4.13976i	0.347222	−	0.135968i
$928$		0			0
$929$	−1.29990	−	2.25148i	−0.0426482	−	0.0738688i	0.843913	−	0.536479i	$-0.180246\pi$
$929$	−1.29990	−	2.25148i	−0.0426482	−	0.0738688i	−0.886562	+	0.462611i	$0.846913\pi$
$930$		0			0
$931$	1.36728	−	2.36819i	0.0448106	−	0.0776143i
$932$		0			0
$933$	3.33009	−	44.2097i	0.109022	−	1.44736i
$934$		0			0
$935$	91.7037	+	28.2880i	2.99903	+	0.925116i
$936$		0			0
$937$		−	38.8687i		−	1.26979i	−0.772600	−	0.634893i	$-0.781044\pi$
$937$		−	38.8687i		−	1.26979i	0.772600	−	0.634893i	$-0.218956\pi$
$938$		0			0
$939$	−6.99326	+	10.2488i	−0.228216	+	0.334457i
$940$		0			0
$941$	−4.70353	+	8.14675i	−0.153331	+	0.265576i	−0.932450	−	0.361299i	$-0.882333\pi$
$941$	−4.70353	+	8.14675i	−0.153331	+	0.265576i	0.779119	+	0.626876i	$0.215667\pi$
$942$		0			0
$943$	−69.3726	+	40.0523i	−2.25908	+	1.30428i
$944$		0			0
$945$	−16.9146	+	29.2187i	−0.550234	+	0.950484i
$946$		0			0
$947$	17.0814	−	9.86196i	0.555071	−	0.320471i	−0.196094	−	0.980585i	$-0.562826\pi$
$947$	17.0814	−	9.86196i	0.555071	−	0.320471i	0.751165	+	0.660115i	$0.229492\pi$
$948$		0			0
$949$	−1.29794	+	2.24810i	−0.0421330	+	0.0729765i
$950$		0			0
$951$	3.20532	−	4.69747i	0.103940	−	0.152326i
$952$		0			0
$953$		−	9.07522i		−	0.293975i	−0.989138	−	0.146988i	$-0.953042\pi$
$953$		−	9.07522i		−	0.293975i	0.989138	−	0.146988i	$-0.0469578\pi$
$954$		0			0
$955$	−6.26745	+	20.3178i	−0.202810	+	0.657467i
$956$		0			0
$957$	3.22186	−	42.7730i	0.104148	−	1.38265i
$958$		0			0
$959$	−6.78092	+	11.7449i	−0.218967	+	0.379262i
$960$		0			0
$961$	14.7371	+	25.5254i	0.475391	+	0.823401i
$962$		0			0
$963$	−7.36050	−	5.87903i	−0.237189	−	0.189449i
$964$		0			0
$965$	6.82236	+	29.8923i	0.219620	+	0.962266i
$966$		0			0
$967$	−11.7991	−	6.81223i	−0.379435	−	0.219067i	0.298138	−	0.954523i	$-0.403635\pi$
$967$	−11.7991	−	6.81223i	−0.379435	−	0.219067i	−0.677572	+	0.735456i	$0.736968\pi$
$968$		0			0
$969$	−10.2861	−	21.3802i	−0.330436	−	0.686831i
$970$		0			0
$971$	−20.7113			−0.664659			−0.332329	−	0.943163i	$-0.607835\pi$
$971$	−20.7113			−0.664659			−0.332329	+	0.943163i	$0.607835\pi$
$972$		0			0
$973$		−	26.4043i		−	0.846484i
$974$		0			0
$975$	−2.86739	+	18.9716i	−0.0918299	+	0.607579i
$976$		0			0
$977$	51.0750	+	29.4882i	1.63403	+	0.943410i	0.982831	+	0.184506i	$0.0590684\pi$
$977$	51.0750	+	29.4882i	1.63403	+	0.943410i	0.651202	+	0.758904i	$0.274265\pi$
$978$		0			0
$979$	−37.6277	−	65.1731i	−1.20259	−	2.08294i
$980$		0			0
$981$	9.22000	−	11.5434i	0.294372	−	0.368551i
$982$		0			0
$983$	−5.98908	+	3.45780i	−0.191022	+	0.110287i	−0.592461	−	0.805599i	$-0.701844\pi$
$983$	−5.98908	+	3.45780i	−0.191022	+	0.110287i	0.401439	+	0.915886i	$0.368510\pi$
$984$		0			0
$985$	−17.0614	+	15.8303i	−0.543621	+	0.504395i
$986$		0			0
$987$	0.0798990	−	1.06073i	0.00254321	−	0.0337633i
$988$		0			0
$989$	40.9658			1.30264
$990$		0			0
$991$	−49.1582			−1.56156			−0.780780	−	0.624806i	$-0.785178\pi$
$991$	−49.1582			−1.56156			−0.780780	+	0.624806i	$0.785178\pi$
$992$		0			0
$993$	14.7645	+	10.0746i	0.468538	+	0.319707i
$994$		0			0
$995$	24.4018	+	26.2994i	0.773588	+	0.833748i
$996$		0			0
$997$	20.9913	−	12.1193i	0.664802	−	0.383823i	−0.129302	−	0.991605i	$-0.541274\pi$
$997$	20.9913	−	12.1193i	0.664802	−	0.383823i	0.794104	+	0.607782i	$0.207940\pi$
$998$		0			0
$999$	−2.36510	−	0.542678i	−0.0748285	−	0.0171696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.49.15	yes	32
3.2	odd	2		1080.2.bi.b.1009.4		32
4.3	odd	2		720.2.by.f.49.2		32
5.4	even	2	inner	360.2.bi.b.49.2	✓	32
9.2	odd	6		1080.2.bi.b.289.15		32
9.4	even	3		3240.2.f.k.649.9		16
9.5	odd	6		3240.2.f.i.649.8		16
9.7	even	3	inner	360.2.bi.b.169.2	yes	32
12.11	even	2		2160.2.by.f.1009.4		32
15.14	odd	2		1080.2.bi.b.1009.15		32
20.19	odd	2		720.2.by.f.49.15		32
36.7	odd	6		720.2.by.f.529.15		32
36.11	even	6		2160.2.by.f.289.15		32
45.4	even	6		3240.2.f.k.649.10		16
45.14	odd	6		3240.2.f.i.649.7		16
45.29	odd	6		1080.2.bi.b.289.4		32
45.34	even	6	inner	360.2.bi.b.169.15	yes	32
60.59	even	2		2160.2.by.f.1009.15		32
180.79	odd	6		720.2.by.f.529.2		32
180.119	even	6		2160.2.by.f.289.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.2	✓	32	5.4	even	2	inner
360.2.bi.b.49.15	yes	32	1.1	even	1	trivial
360.2.bi.b.169.2	yes	32	9.7	even	3	inner
360.2.bi.b.169.15	yes	32	45.34	even	6	inner
720.2.by.f.49.2		32	4.3	odd	2
720.2.by.f.49.15		32	20.19	odd	2
720.2.by.f.529.2		32	180.79	odd	6
720.2.by.f.529.15		32	36.7	odd	6
1080.2.bi.b.289.4		32	45.29	odd	6
1080.2.bi.b.289.15		32	9.2	odd	6
1080.2.bi.b.1009.4		32	3.2	odd	2
1080.2.bi.b.1009.15		32	15.14	odd	2
2160.2.by.f.289.4		32	180.119	even	6
2160.2.by.f.289.15		32	36.11	even	6
2160.2.by.f.1009.4		32	12.11	even	2
2160.2.by.f.1009.15		32	60.59	even	2
3240.2.f.i.649.7		16	45.14	odd	6
3240.2.f.i.649.8		16	9.5	odd	6
3240.2.f.k.649.9		16	9.4	even	3
3240.2.f.k.649.10		16	45.4	even	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56081 - 0.750911i) q^{3} +(1.52089 + 1.63917i) q^{5} +(-2.51643 + 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +O(q^{10})\)	\(q+(1.56081 - 0.750911i) q^{3} +(1.52089 + 1.63917i) q^{5} +(-2.51643 + 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +(2.96823 + 5.14112i) q^{11} +(1.91871 + 1.10777i) q^{13} +(3.60470 + 1.41638i) q^{15} -7.22957i q^{17} +1.89473 q^{19} +(-2.83671 + 4.15726i) q^{21} +(-7.15829 - 4.13284i) q^{23} +(-0.373764 + 4.98601i) q^{25} +(1.16207 - 5.06454i) q^{27} +(-2.08584 - 3.61278i) q^{29} +(-0.617611 + 1.06973i) q^{31} +(8.49336 + 5.79544i) q^{33} +(-6.20872 - 1.91521i) q^{35} -0.466992i q^{37} +(3.82658 + 0.288236i) q^{39} +(4.84562 - 8.39286i) q^{41} +(-4.29214 + 2.47807i) q^{43} +(6.68983 - 0.496105i) q^{45} +(-0.183041 + 0.105679i) q^{47} +(0.721618 - 1.24988i) q^{49} +(-5.42877 - 11.2840i) q^{51} +3.33797i q^{53} +(-3.91282 + 12.6845i) q^{55} +(2.95732 - 1.42278i) q^{57} +(-2.02942 + 3.51505i) q^{59} +(4.85418 + 8.40768i) q^{61} +(-1.30583 + 8.61881i) q^{63} +(1.10233 + 4.82989i) q^{65} +(-7.62905 - 4.40463i) q^{67} +(-14.2761 - 1.07535i) q^{69} -5.70101 q^{71} +1.17167i q^{73} +(3.16068 + 8.06289i) q^{75} +(-14.9387 - 8.62485i) q^{77} +(-4.36030 - 7.55225i) q^{79} +(-1.98924 - 8.77741i) q^{81} +(10.4401 - 6.02757i) q^{83} +(11.8505 - 10.9954i) q^{85} +(-5.96847 - 4.07258i) q^{87} -12.6768 q^{89} -6.43774 q^{91} +(-0.160700 + 2.13342i) q^{93} +(2.88169 + 3.10579i) q^{95} +(-4.91562 + 2.83803i) q^{97} +(17.6084 + 2.66783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 4 * q^9	\( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

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Database

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