LMFDB - Embedded newform 360.2.bi.b.49.2

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			49.2
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56081 + 0.750911i) q^{3} +(-2.18001 - 0.497547i) q^{5} +(2.51643 - 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +O(q^{10})$	\(q+(-1.56081 + 0.750911i) q^{3} +(-2.18001 - 0.497547i) q^{5} +(2.51643 - 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +(2.96823 + 5.14112i) q^{11} +(-1.91871 - 1.10777i) q^{13} +(3.77620 - 0.860417i) q^{15} +7.22957i q^{17} +1.89473 q^{19} +(-2.83671 + 4.15726i) q^{21} +(7.15829 + 4.13284i) q^{23} +(4.50489 + 2.16932i) q^{25} +(-1.16207 + 5.06454i) q^{27} +(-2.08584 - 3.61278i) q^{29} +(-0.617611 + 1.06973i) q^{31} +(-8.49336 - 5.79544i) q^{33} +(-6.20872 + 1.91521i) q^{35} +0.466992i q^{37} +(3.82658 + 0.288236i) q^{39} +(4.84562 - 8.39286i) q^{41} +(4.29214 - 2.47807i) q^{43} +(-5.24784 + 4.17854i) q^{45} +(0.183041 - 0.105679i) q^{47} +(0.721618 - 1.24988i) q^{49} +(-5.42877 - 11.2840i) q^{51} -3.33797i q^{53} +(-3.91282 - 12.6845i) q^{55} +(-2.95732 + 1.42278i) q^{57} +(-2.02942 + 3.51505i) q^{59} +(4.85418 + 8.40768i) q^{61} +(1.30583 - 8.61881i) q^{63} +(3.63164 + 3.36960i) q^{65} +(7.62905 + 4.40463i) q^{67} +(-14.2761 - 1.07535i) q^{69} -5.70101 q^{71} -1.17167i q^{73} +(-8.66025 - 0.00311964i) q^{75} +(14.9387 + 8.62485i) q^{77} +(-4.36030 - 7.55225i) q^{79} +(-1.98924 - 8.77741i) q^{81} +(-10.4401 + 6.02757i) q^{83} +(3.59705 - 15.7605i) q^{85} +(5.96847 + 4.07258i) q^{87} -12.6768 q^{89} -6.43774 q^{91} +(0.160700 - 2.13342i) q^{93} +(-4.13054 - 0.942720i) q^{95} +(4.91562 - 2.83803i) q^{97} +(17.6084 + 2.66783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.18001	−	0.497547i	−0.974930	−	0.222510i
$5$	−2.18001	−	0.497547i	−0.974930	−	0.222510i
$6$		0			0
$7$	2.51643	−	1.45286i	0.951122	−	0.549130i	0.0576925	−	0.998334i	$-0.481626\pi$
$7$	2.51643	−	1.45286i	0.951122	−	0.549130i	0.893429	+	0.449204i	$0.148292\pi$
$8$		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	0.209739	−	0.977757i	$-0.432739\pi$
$13$	−1.91871	−	1.10777i	−0.532155	−	0.307240i	−0.741893	+	0.670518i	$0.766072\pi$
$14$		0			0
$15$	3.77620	−	0.860417i	0.975011	−	0.222159i
$16$		0			0
$17$			7.22957i			1.75343i	0.481011	+	0.876715i	$0.340270\pi$
$17$			7.22957i			1.75343i	−0.481011	+	0.876715i	$0.659730\pi$
$18$		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	0.999964	−	0.00847582i	$-0.00269797\pi$
$23$	7.15829	+	4.13284i	1.49261	+	0.861756i	0.492642	+	0.870232i	$0.336031\pi$
$24$		0			0
$25$	4.50489	+	2.16932i	0.900979	+	0.433863i
$26$		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	$0.0122218\pi$
$37$			0.466992i			0.0767730i	−0.999263	+	0.0383865i	$0.987778\pi$
$38$		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	−0.135650	−	0.990757i	$-0.543312\pi$
$43$	4.29214	−	2.47807i	0.654545	−	0.377902i	0.790196	+	0.612855i	$0.209979\pi$
$44$		0			0
$45$	−5.24784	+	4.17854i	−0.782302	+	0.622900i
$46$		0			0
$47$	0.183041	−	0.105679i	0.0266992	−	0.0154148i	−0.486591	−	0.873630i	$-0.661760\pi$
$47$	0.183041	−	0.105679i	0.0266992	−	0.0154148i	0.513290	+	0.858215i	$0.328426\pi$
$48$		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	$-0.926372\pi$
$53$		−	3.33797i		−	0.458506i	0.973367	−	0.229253i	$-0.0736282\pi$
$54$		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
$65$	3.63164	+	3.36960i	0.450450	+	0.417947i
$66$		0			0
$67$	7.62905	+	4.40463i	0.932037	+	0.538112i	0.887455	−	0.460894i	$-0.152471\pi$
$67$	7.62905	+	4.40463i	0.932037	+	0.538112i	0.0445816	+	0.999006i	$0.485805\pi$
$68$		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	$-0.978157\pi$
$73$		−	1.17167i		−	0.137134i	0.997647	−	0.0685670i	$-0.0218427\pi$
$74$		0			0
$75$	−8.66025	−	0.00311964i	−1.00000	−	0.000360225i
$76$		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	−0.947896	−	0.318580i	$-0.896794\pi$
$83$	−10.4401	+	6.02757i	−1.14595	+	0.661612i	−0.198050	+	0.980192i	$0.563461\pi$
$84$		0			0
$85$	3.59705	−	15.7605i	0.390155	−	1.70947i
$86$		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
$95$	−4.13054	−	0.942720i	−0.423785	−	0.0967210i
$96$		0			0
$97$	4.91562	−	2.83803i	0.499105	−	0.288159i	−0.229239	−	0.973370i	$-0.573624\pi$
$97$	4.91562	−	2.83803i	0.499105	−	0.288159i	0.728344	+	0.685212i	$0.240290\pi$
$98$		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	0.329765	−	0.944063i	$-0.393031\pi$
$103$	−3.27744	−	1.89223i	−0.322936	−	0.186447i	−0.652700	+	0.757616i	$0.726364\pi$
$104$		0			0
$105$	8.25248	−	7.65148i	0.805360	−	0.746708i
$106$		0			0
$107$			3.14006i			0.303561i	0.988414	+	0.151781i	$0.0485007\pi$
$107$			3.14006i			0.303561i	−0.988414	+	0.151781i	$0.951499\pi$
$108$		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	0.461410	−	0.887187i	$-0.347344\pi$
$113$	−0.810137	−	0.467733i	−0.0762113	−	0.0440006i	−0.537621	+	0.843186i	$0.680677\pi$
$114$		0			0
$115$	−13.5489	−	12.5712i	−1.26344	−	1.17227i
$116$		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	$0.0585639\pi$
$127$			4.12343i			0.365895i	−0.983123	+	0.182948i	$0.941436\pi$
$128$		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
$135$	5.05318	−	10.4626i	0.434908	−	0.900475i
$136$		0			0
$137$	−4.04198	+	2.33364i	−0.345330	+	0.199376i	−0.662627	−	0.748950i	$-0.730558\pi$
$137$	−4.04198	+	2.33364i	−0.345330	+	0.199376i	0.317296	+	0.948326i	$0.397225\pi$
$138$		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
$155$	1.87864	−	2.02474i	0.150896	−	0.162631i
$156$		0			0
$157$	6.90624	+	3.98732i	0.551178	+	0.318223i	0.749597	−	0.661895i	$-0.230247\pi$
$157$	6.90624	+	3.98732i	0.551178	+	0.318223i	−0.198419	+	0.980117i	$0.563581\pi$
$158$		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	$-0.908475\pi$
$163$		−	7.24124i		−	0.567178i	0.958946	−	0.283589i	$-0.0915251\pi$
$164$		0			0
$165$	15.6321	+	16.8600i	1.21696	+	1.31255i
$166$		0			0
$167$	−9.54791	−	5.51249i	−0.738839	−	0.426569i	0.0828078	−	0.996566i	$-0.473611\pi$
$167$	−9.54791	−	5.51249i	−0.738839	−	0.426569i	−0.821647	+	0.569996i	$0.806945\pi$
$168$		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	−0.368812	−	0.929504i	$-0.620235\pi$
$173$	3.31133	−	1.91180i	0.251755	−	0.145351i	0.620568	+	0.784153i	$0.286902\pi$
$174$		0			0
$175$	14.4880	−	1.08606i	1.09519	−	0.0820980i
$176$		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
$185$	0.232350	−	1.01805i	0.0170827	−	0.0748483i
$186$		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	0.00748341	−	0.999972i	$-0.497618\pi$
$193$	−11.8749	−	6.85599i	−0.854776	−	0.493505i	−0.862259	+	0.506467i	$0.830951\pi$
$194$		0			0
$195$	−8.19858	−	2.53226i	−0.587112	−	0.181339i
$196$		0			0
$197$		−	10.4085i		−	0.741578i	−0.928717	−	0.370789i	$-0.879087\pi$
$197$		−	10.4085i		−	0.741578i	0.928717	−	0.370789i	$-0.120913\pi$
$198$		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
$205$	−14.7393	+	15.8856i	−1.02944	+	1.10950i
$206$		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	−0.431432	−	0.902145i	$-0.641992\pi$
$223$	2.00302	−	1.15645i	0.134132	−	0.0774413i	0.565565	+	0.824704i	$0.308658\pi$
$224$		0			0
$225$	13.5194	−	6.49821i	0.901291	−	0.433214i
$226$		0			0
$227$	3.98516	−	2.30083i	0.264504	−	0.152712i	−0.361883	−	0.932223i	$-0.617866\pi$
$227$	3.98516	−	2.30083i	0.264504	−	0.152712i	0.626388	+	0.779512i	$0.284533\pi$
$228$		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	$0.0439881\pi$
$233$			4.20542i			0.275506i	−0.990467	+	0.137753i	$0.956012\pi$
$234$		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
$245$	−2.19501	+	2.36571i	−0.140234	+	0.151140i
$246$		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
$255$	6.22045	+	27.3003i	0.389539	+	1.70961i
$256$		0			0
$257$	−8.16345	−	4.71317i	−0.509222	−	0.293999i	0.223292	−	0.974752i	$-0.428320\pi$
$257$	−8.16345	−	4.71317i	−0.509222	−	0.293999i	−0.732514	+	0.680752i	$0.761653\pi$
$258$		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	−0.392232	−	0.919866i	$-0.628297\pi$
$263$	3.37773	−	1.95013i	0.208280	−	0.120250i	0.600512	+	0.799616i	$0.294964\pi$
$264$		0			0
$265$	−1.66080	+	7.27681i	−0.102022	+	0.447011i
$266$		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
$275$	2.21883	+	29.5992i	0.133801	+	1.78490i
$276$		0			0
$277$	21.4000	−	12.3553i	1.28580	−	0.742357i	0.307898	−	0.951419i	$-0.400374\pi$
$277$	21.4000	−	12.3553i	1.28580	−	0.742357i	0.977902	+	0.209062i	$0.0670410\pi$
$278$		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	0.538555	−	0.842590i	$-0.318970\pi$
$283$	1.31431	+	0.758817i	0.0781276	+	0.0451070i	−0.460427	+	0.887697i	$0.652304\pi$
$284$		0			0
$285$	7.15489	−	1.63026i	0.423819	−	0.0965683i
$286$		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	−0.432141	−	0.901806i	$-0.642242\pi$
$293$	−24.4639	−	14.1243i	−1.42920	−	0.825148i	−0.997057	+	0.0766581i	$0.975575\pi$
$294$		0			0
$295$	6.17306	−	6.65313i	0.359409	−	0.387360i
$296$		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	$-0.873911\pi$
$307$		−	13.5210i		−	0.771685i	0.922565	−	0.385843i	$-0.126089\pi$
$308$		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	−0.314319	−	0.949317i	$-0.601776\pi$
$313$	6.20370	−	3.58171i	0.350654	−	0.202450i	0.664973	+	0.746867i	$0.268443\pi$
$314$		0			0
$315$	−7.13499	+	18.1394i	−0.402011	+	1.02204i
$316$		0			0
$317$	−2.84343	+	1.64165i	−0.159703	+	0.0922045i	−0.577721	−	0.816234i	$-0.696058\pi$
$317$	−2.84343	+	1.64165i	−0.159703	+	0.0922045i	0.418019	+	0.908438i	$0.362725\pi$
$318$		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
$335$	−14.4399	−	13.3980i	−0.788936	−	0.732009i
$336$		0			0
$337$	−28.0846	−	16.2147i	−1.52987	−	0.883269i	−0.999367	−	0.0355834i	$-0.988671\pi$
$337$	−28.0846	−	16.2147i	−1.52987	−	0.883269i	−0.530499	−	0.847685i	$-0.677996\pi$
$338$		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
$345$	30.5871	+	9.44731i	1.64675	+	0.508626i
$346$		0			0
$347$	−14.9112	−	8.60899i	−0.800475	−	0.462155i	0.0431620	−	0.999068i	$-0.486257\pi$
$347$	−14.9112	−	8.60899i	−0.800475	−	0.462155i	−0.843637	+	0.536913i	$0.819590\pi$
$348$		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	−0.0244542	−	0.999701i	$-0.507785\pi$
$353$	15.5771	−	8.99344i	0.829085	−	0.478672i	0.853539	+	0.521028i	$0.174451\pi$
$354$		0			0
$355$	12.4283	+	2.83652i	0.659623	+	0.150547i
$356$		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
$365$	−0.582963	+	2.55426i	−0.0305137	+	0.133696i
$366$		0			0
$367$	−5.53122	+	3.19345i	−0.288728	+	0.166697i	−0.637368	−	0.770560i	$-0.719977\pi$
$367$	−5.53122	+	3.19345i	−0.288728	+	0.166697i	0.348640	+	0.937257i	$0.386643\pi$
$368$		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	−0.0354609	−	0.999371i	$-0.511290\pi$
$373$	−17.7425	−	10.2436i	−0.918672	−	0.530396i	−0.883211	+	0.468976i	$0.844623\pi$
$374$		0			0
$375$	18.8779	+	4.31569i	0.974850	+	0.222861i
$376$		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	0.931526	−	0.363674i	$-0.118478\pi$
$383$	21.1818	+	12.2293i	1.08234	+	0.624888i	0.150812	+	0.988563i	$0.451811\pi$
$384$		0			0
$385$	−28.2752	−	26.2350i	−1.44104	−	1.33706i
$386$		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	$-0.678445\pi$
$397$		−	33.7502i		−	1.69387i	0.531695	−	0.846936i	$-0.321555\pi$
$398$		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
$405$	−0.0306000	+	20.1246i	−0.00152053	+	0.999999i
$406$		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
$425$	−15.6832	+	32.5685i	−0.760749	+	1.57980i
$426$		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	$0.0281920\pi$
$433$			3.68113i			0.176904i	−0.996080	+	0.0884519i	$0.971808\pi$
$434$		0			0
$435$	−10.9850	−	11.8479i	−0.526692	−	0.568062i
$436$		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	0.196476	−	0.980509i	$-0.437050\pi$
$443$	24.0755	−	13.9000i	1.14386	−	0.660407i	0.947383	+	0.320101i	$0.103717\pi$
$444$		0			0
$445$	27.6356	+	6.30732i	1.31005	+	0.298996i
$446$		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
$455$	14.0343	+	3.20308i	0.657940	+	0.150163i
$456$		0			0
$457$	8.71532	−	5.03179i	0.407686	−	0.235377i	−0.282109	−	0.959382i	$-0.591034\pi$
$457$	8.71532	−	5.03179i	0.407686	−	0.235377i	0.689795	+	0.724005i	$0.257701\pi$
$458$		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	0.434727	−	0.900562i	$-0.356845\pi$
$463$	−2.75034	−	1.58791i	−0.127819	−	0.0737965i	−0.562546	+	0.826766i	$0.690178\pi$
$464$		0			0
$465$	−1.41181	+	4.57093i	−0.0654709	+	0.211972i
$466$		0			0
$467$		−	35.2304i		−	1.63027i	−0.579272	−	0.815134i	$-0.696663\pi$
$467$		−	35.2304i		−	1.63027i	0.579272	−	0.815134i	$-0.303337\pi$
$468$		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
$475$	8.53558	+	4.11028i	0.391639	+	0.188592i
$476$		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	$0.156448\pi$
$487$			20.8299i			0.943892i	−0.881627	+	0.471946i	$0.843552\pi$
$488$		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
$495$	−37.0591	−	14.5769i	−1.66568	−	0.655184i
$496$		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	$0.265430\pi$
$503$			33.2171i			1.48108i	−0.672013	+	0.740539i	$0.734570\pi$
$504$		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
$515$	6.20338	+	5.75577i	0.273354	+	0.253629i
$516$		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	$-0.917935\pi$
$523$		−	11.6619i		−	0.509938i	0.966949	−	0.254969i	$-0.0820653\pi$
$524$		0			0
$525$	−21.7975	+	12.5743i	−0.951319	+	0.548788i
$526$		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
$535$	1.56233	−	6.84537i	0.0675454	−	0.295951i
$536$		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
$545$	−10.7355	−	2.45018i	−0.459858	−	0.104954i
$546$		0			0
$547$	−0.736873	+	0.425434i	−0.0315064	+	0.0181902i	−0.515670	−	0.856787i	$-0.672457\pi$
$547$	−0.736873	+	0.425434i	−0.0315064	+	0.0181902i	0.484164	+	0.874977i	$0.339124\pi$
$548$		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
$555$	0.401808	+	1.76345i	0.0170558	+	0.0748545i
$556$		0			0
$557$			40.4513i			1.71398i	0.515337	+	0.856988i	$0.327667\pi$
$557$			40.4513i			1.71398i	−0.515337	+	0.856988i	$0.672333\pi$
$558$		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	0.865956	−	0.500120i	$-0.166711\pi$
$563$	20.5438	+	11.8610i	0.865817	+	0.499880i	−0.000138724		1.00000i	$0.500044\pi$
$564$		0			0
$565$	1.53339	+	1.42274i	0.0645101	+	0.0598553i
$566$		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	$-0.616780\pi$
$577$		−	44.8446i		−	1.86691i	0.358699	−	0.933453i	$-0.383220\pi$
$578$		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
$585$	14.6979	−	2.20402i	0.607685	−	0.0911249i
$586$		0			0
$587$	3.94274	−	2.27634i	0.162734	−	0.0939547i	−0.416421	−	0.909172i	$-0.636716\pi$
$587$	3.94274	−	2.27634i	0.162734	−	0.0939547i	0.579155	+	0.815217i	$0.303382\pi$
$588$		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	$-0.854597\pi$
$593$		−	21.4818i		−	0.882151i	0.897470	−	0.441076i	$-0.145403\pi$
$594$		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
$605$	36.8687	−	39.7359i	1.49893	−	1.61549i
$606$		0			0
$607$	−29.3213	−	16.9287i	−1.19012	−	0.687114i	−0.231784	−	0.972767i	$-0.574456\pi$
$607$	−29.3213	−	16.9287i	−1.19012	−	0.687114i	−0.958333	+	0.285653i	$0.907789\pi$
$608$		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	$0.125807\pi$
$613$			19.0655i			0.770049i	−0.922906	+	0.385025i	$0.874193\pi$
$614$		0			0
$615$	11.0767	−	35.8624i	0.446654	−	1.44611i
$616$		0			0
$617$	14.6262	+	8.44444i	0.588828	+	0.339960i	0.764634	−	0.644465i	$-0.222920\pi$
$617$	14.6262	+	8.44444i	0.588828	+	0.339960i	−0.175806	+	0.984425i	$0.556253\pi$
$618$		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
$625$	15.5881	+	19.5451i	0.623525	+	0.781803i
$626$		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
$635$	2.05160	−	8.98912i	0.0814153	−	0.356723i
$636$		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	0.614222	−	0.789134i	$-0.289470\pi$
$643$	6.03311	+	3.48322i	0.237923	+	0.137365i	−0.376299	+	0.926498i	$0.622803\pi$
$644$		0			0
$645$	14.0758	−	13.0507i	0.554234	−	0.513871i
$646$		0			0
$647$			31.4157i			1.23508i	0.786539	+	0.617540i	$0.211871\pi$
$647$			31.4157i			1.23508i	−0.786539	+	0.617540i	$0.788129\pi$
$648$		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	−0.123749	−	0.992314i	$-0.539492\pi$
$653$	−26.7036	−	15.4173i	−1.04499	−	0.603326i	−0.921243	+	0.388987i	$0.872825\pi$
$654$		0			0
$655$	−20.5432	+	22.1408i	−0.802690	+	0.865113i
$656$		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	0.276471	−	0.961022i	$-0.410835\pi$
$673$	32.3494	−	18.6769i	1.24698	−	0.719942i	0.970505	+	0.241080i	$0.0775016\pi$
$674$		0			0
$675$	−16.2216	+	20.2943i	−0.624370	+	0.781129i
$676$		0			0
$677$	29.6583	−	17.1232i	1.13986	−	0.658098i	0.193464	−	0.981107i	$-0.438028\pi$
$677$	29.6583	−	17.1232i	1.13986	−	0.658098i	0.946396	+	0.323009i	$0.104694\pi$
$678$		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	$0.0228481\pi$
$683$			3.74858i			0.143435i	−0.997425	+	0.0717177i	$0.977152\pi$
$684$		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
$695$	13.8204	−	14.8952i	0.524237	−	0.565005i
$696$		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
$705$	0.600270	−	0.556554i	0.0226075	−	0.0209611i
$706$		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
$715$	−6.54395	+	28.6724i	−0.244730	+	1.07229i
$716$		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
$725$	−1.55922	−	20.8000i	−0.0579080	−	0.772493i
$726$		0			0
$727$	−16.7583	+	9.67541i	−0.621531	+	0.358841i	−0.777465	−	0.628927i	$-0.783495\pi$
$727$	−16.7583	+	9.67541i	−0.621531	+	0.358841i	0.155934	+	0.987767i	$0.450161\pi$
$728$		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	0.811570	−	0.584255i	$-0.198613\pi$
$733$	19.2598	+	11.1196i	0.711376	+	0.410713i	−0.100194	+	0.994968i	$0.531946\pi$
$734$		0			0
$735$	1.64956	−	5.34069i	0.0608448	−	0.196994i
$736$		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	−0.176150	−	0.984363i	$-0.556364\pi$
$743$	−30.4393	−	17.5741i	−1.11671	−	0.644732i	−0.940559	+	0.339631i	$0.889698\pi$
$744$		0			0
$745$	−17.4949	+	18.8555i	−0.640965	+	0.690812i
$746$		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	$0.0866547\pi$
$757$			14.7959i			0.537767i	−0.963173	+	0.268884i	$0.913345\pi$
$758$		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
$765$	−30.2091	−	37.9396i	−1.09221	−	1.37171i
$766$		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	$-0.802806\pi$
$773$		−	32.2865i		−	1.16126i	0.814166	−	0.580632i	$-0.197194\pi$
$774$		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
$785$	−13.0718	−	12.1286i	−0.466553	−	0.432888i
$786$		0			0
$787$	16.5653	+	9.56399i	0.590490	+	0.340919i	0.765291	−	0.643684i	$-0.222595\pi$
$787$	16.5653	+	9.56399i	0.590490	+	0.340919i	−0.174801	+	0.984604i	$0.555928\pi$
$788$		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
$795$	−2.87205	−	12.6048i	−0.101861	−	0.447048i
$796$		0			0
$797$	13.0257	+	7.52039i	0.461394	+	0.266386i	0.712630	−	0.701540i	$-0.247504\pi$
$797$	13.0257	+	7.52039i	0.461394	+	0.266386i	−0.251236	+	0.967926i	$0.580837\pi$
$798$		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
$805$	−52.3590	−	11.9500i	−1.84541	−	0.421181i
$806$		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
$815$	−3.60286	+	15.7860i	−0.126203	+	0.552959i
$816$		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	$-0.970032\pi$
$823$	−45.1770	−	26.0829i	−1.57477	−	0.909194i	−0.579199	−	0.815186i	$-0.696635\pi$
$824$		0			0
$825$	−25.6896	−	44.5327i	−0.894395	−	1.55043i
$826$		0			0
$827$		−	16.0643i		−	0.558611i	−0.960202	−	0.279305i	$-0.909896\pi$
$827$		−	16.0643i		−	0.558611i	0.960202	−	0.279305i	$-0.0901041\pi$
$828$		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
$835$	18.0718	+	16.7678i	0.625401	+	0.580274i
$836$		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	−0.866035	−	0.499983i	$-0.833340\pi$
$853$	−25.2942	+	14.6036i	−0.866055	+	0.500017i	−1.98828e−5		1.00000i	$0.500006\pi$
$854$		0			0
$855$	−9.94326	+	7.91722i	−0.340052	+	0.270763i
$856$		0			0
$857$	33.6618	−	19.4346i	1.14986	−	0.663874i	0.201010	−	0.979589i	$-0.435578\pi$
$857$	33.6618	−	19.4346i	1.14986	−	0.663874i	0.948854	+	0.315715i	$0.102244\pi$
$858$		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	$-0.866941\pi$
$863$		−	23.8510i		−	0.811898i	0.913896	−	0.405949i	$-0.133059\pi$
$864$		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
$875$	−32.1243	−	4.84084i	−1.08600	−	0.163650i
$876$		0			0
$877$	−14.6631	−	8.46576i	−0.495139	−	0.285868i	0.231565	−	0.972819i	$-0.425615\pi$
$877$	−14.6631	−	8.46576i	−0.495139	−	0.285868i	−0.726704	+	0.686951i	$0.758949\pi$
$878$		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	$0.233786\pi$
$883$			39.8297i			1.34038i	−0.742192	+	0.670188i	$0.766214\pi$
$884$		0			0
$885$	−4.63907	+	15.0197i	−0.155941	+	0.504881i
$886$		0			0
$887$	9.43187	+	5.44549i	0.316691	+	0.182842i	0.649917	−	0.760005i	$-0.274804\pi$
$887$	9.43187	+	5.44549i	0.316691	+	0.182842i	−0.333226	+	0.942847i	$0.608137\pi$
$888$		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
$895$	18.1412	+	4.14040i	0.606394	+	0.138398i
$896$		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
$905$	−25.9259	−	5.91711i	−0.861807	−	0.196691i
$906$		0			0
$907$	−39.0165	+	22.5262i	−1.29552	+	0.747971i	−0.979627	−	0.200823i	$-0.935638\pi$
$907$	−39.0165	+	22.5262i	−1.29552	+	0.747971i	−0.315896	+	0.948794i	$0.602305\pi$
$908$		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
$915$	25.5645	+	27.5725i	0.845135	+	0.911518i
$916$		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
$925$	−1.01305	+	2.10375i	−0.0333090	+	0.0691708i
$926$		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	$0.218956\pi$
$937$			38.8687i			1.26979i	−0.772600	+	0.634893i	$0.781044\pi$
$938$		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
$945$	−2.48470	−	33.6699i	−0.0808272	−	1.09528i
$946$		0			0
$947$	−17.0814	+	9.86196i	−0.555071	+	0.320471i	−0.751165	−	0.660115i	$-0.770508\pi$
$947$	−17.0814	+	9.86196i	−0.555071	+	0.320471i	0.196094	+	0.980585i	$0.437174\pi$
$948$		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	$0.0469578\pi$
$953$			9.07522i			0.293975i	−0.989138	+	0.146988i	$0.953042\pi$
$954$		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
$965$	22.4763	+	20.8545i	0.723537	+	0.671329i
$966$		0			0
$967$	11.7991	+	6.81223i	0.379435	+	0.219067i	0.677572	−	0.735456i	$-0.263032\pi$
$967$	11.7991	+	6.81223i	0.379435	+	0.219067i	−0.298138	+	0.954523i	$0.596365\pi$
$968$		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
$975$	16.6131	+	9.59954i	0.532044	+	0.307431i
$976$		0			0
$977$	−51.0750	−	29.4882i	−1.63403	−	0.943410i	−0.982831	−	0.184506i	$-0.940932\pi$
$977$	−51.0750	−	29.4882i	−1.63403	−	0.943410i	−0.651202	−	0.758904i	$-0.725735\pi$
$978$		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	−0.401439	−	0.915886i	$-0.631490\pi$
$983$	5.98908	−	3.45780i	0.191022	−	0.110287i	0.592461	+	0.805599i	$0.298156\pi$
$984$		0			0
$985$	−5.17874	+	22.6907i	−0.165008	+	0.722987i
$986$		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
$995$	−34.9769	−	7.98282i	−1.10884	−	0.253072i
$996$		0			0
$997$	−20.9913	+	12.1193i	−0.664802	+	0.383823i	−0.794104	−	0.607782i	$-0.792060\pi$
$997$	−20.9913	+	12.1193i	−0.664802	+	0.383823i	0.129302	+	0.991605i	$0.458726\pi$
$998$		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.49.2	✓	32
3.2	odd	2		1080.2.bi.b.1009.15		32
4.3	odd	2		720.2.by.f.49.15		32
5.4	even	2	inner	360.2.bi.b.49.15	yes	32
9.2	odd	6		1080.2.bi.b.289.4		32
9.4	even	3		3240.2.f.k.649.10		16
9.5	odd	6		3240.2.f.i.649.7		16
9.7	even	3	inner	360.2.bi.b.169.15	yes	32
12.11	even	2		2160.2.by.f.1009.15		32
15.14	odd	2		1080.2.bi.b.1009.4		32
20.19	odd	2		720.2.by.f.49.2		32
36.7	odd	6		720.2.by.f.529.2		32
36.11	even	6		2160.2.by.f.289.4		32
45.4	even	6		3240.2.f.k.649.9		16
45.14	odd	6		3240.2.f.i.649.8		16
45.29	odd	6		1080.2.bi.b.289.15		32
45.34	even	6	inner	360.2.bi.b.169.2	yes	32
60.59	even	2		2160.2.by.f.1009.4		32
180.79	odd	6		720.2.by.f.529.15		32
180.119	even	6		2160.2.by.f.289.15		32

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

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)

\(f(q)\)	\(=\)	\(q+(-1.56081 + 0.750911i) q^{3} +(-2.18001 - 0.497547i) q^{5} +(2.51643 - 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +O(q^{10})\)	\(q+(-1.56081 + 0.750911i) q^{3} +(-2.18001 - 0.497547i) q^{5} +(2.51643 - 1.45286i) q^{7} +(1.87227 - 2.34406i) q^{9} +(2.96823 + 5.14112i) q^{11} +(-1.91871 - 1.10777i) q^{13} +(3.77620 - 0.860417i) q^{15} +7.22957i q^{17} +1.89473 q^{19} +(-2.83671 + 4.15726i) q^{21} +(7.15829 + 4.13284i) q^{23} +(4.50489 + 2.16932i) q^{25} +(-1.16207 + 5.06454i) q^{27} +(-2.08584 - 3.61278i) q^{29} +(-0.617611 + 1.06973i) q^{31} +(-8.49336 - 5.79544i) q^{33} +(-6.20872 + 1.91521i) q^{35} +0.466992i q^{37} +(3.82658 + 0.288236i) q^{39} +(4.84562 - 8.39286i) q^{41} +(4.29214 - 2.47807i) q^{43} +(-5.24784 + 4.17854i) q^{45} +(0.183041 - 0.105679i) q^{47} +(0.721618 - 1.24988i) q^{49} +(-5.42877 - 11.2840i) q^{51} -3.33797i q^{53} +(-3.91282 - 12.6845i) q^{55} +(-2.95732 + 1.42278i) q^{57} +(-2.02942 + 3.51505i) q^{59} +(4.85418 + 8.40768i) q^{61} +(1.30583 - 8.61881i) q^{63} +(3.63164 + 3.36960i) q^{65} +(7.62905 + 4.40463i) q^{67} +(-14.2761 - 1.07535i) q^{69} -5.70101 q^{71} -1.17167i q^{73} +(-8.66025 - 0.00311964i) q^{75} +(14.9387 + 8.62485i) q^{77} +(-4.36030 - 7.55225i) q^{79} +(-1.98924 - 8.77741i) q^{81} +(-10.4401 + 6.02757i) q^{83} +(3.59705 - 15.7605i) q^{85} +(5.96847 + 4.07258i) q^{87} -12.6768 q^{89} -6.43774 q^{91} +(0.160700 - 2.13342i) q^{93} +(-4.13054 - 0.942720i) q^{95} +(4.91562 - 2.83803i) q^{97} +(17.6084 + 2.66783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 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

Varieties

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Representations

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Database

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