LMFDB - Embedded newform 256.4.g.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,4,Mod(33,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("256.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	256.g (of order $8$, degree $4$, not 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:	$15.1044889615$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	256.97
Dual form			256.4.g.b.161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.56924 + 1.89264i) q^{3} +(-1.37033 + 3.30826i) q^{5} +(-6.14642 - 6.14642i) q^{7} +(-1.79604 + 1.79604i) q^{9} +O(q^{10})$	\(q+(-4.56924 + 1.89264i) q^{3} +(-1.37033 + 3.30826i) q^{5} +(-6.14642 - 6.14642i) q^{7} +(-1.79604 + 1.79604i) q^{9} +(-17.2398 - 7.14095i) q^{11} +(25.9810 + 62.7238i) q^{13} -17.7098i q^{15} -87.5919i q^{17} +(-48.8193 - 117.860i) q^{19} +(39.7174 + 16.4515i) q^{21} +(-55.7254 + 55.7254i) q^{23} +(79.3216 + 79.3216i) q^{25} +(55.9086 - 134.975i) q^{27} +(114.139 - 47.2779i) q^{29} +229.997 q^{31} +92.2879 q^{33} +(28.7565 - 11.9113i) q^{35} +(123.846 - 298.992i) q^{37} +(-237.427 - 237.427i) q^{39} +(111.562 - 111.562i) q^{41} +(-76.5574 - 31.7111i) q^{43} +(-3.48061 - 8.40293i) q^{45} -367.843i q^{47} -267.443i q^{49} +(165.780 + 400.228i) q^{51} +(244.994 + 101.480i) q^{53} +(47.2482 - 47.2482i) q^{55} +(446.134 + 446.134i) q^{57} +(183.495 - 442.997i) q^{59} +(-524.604 + 217.298i) q^{61} +22.0784 q^{63} -243.109 q^{65} +(-393.028 + 162.797i) q^{67} +(149.155 - 360.091i) q^{69} +(-354.722 - 354.722i) q^{71} +(-22.2443 + 22.2443i) q^{73} +(-512.566 - 212.312i) q^{75} +(62.0716 + 149.854i) q^{77} +396.453i q^{79} +653.969i q^{81} +(410.445 + 990.903i) q^{83} +(289.777 + 120.029i) q^{85} +(-432.048 + 432.048i) q^{87} +(170.977 + 170.977i) q^{89} +(225.836 - 545.217i) q^{91} +(-1050.91 + 435.301i) q^{93} +456.811 q^{95} -1723.11 q^{97} +(43.7888 - 18.1379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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
$3$	−4.56924	+	1.89264i	−0.879350	+	0.364239i	−0.776245	−	0.630432i	$-0.782878\pi$
$3$	−4.56924	+	1.89264i	−0.879350	+	0.364239i	−0.103105	+	0.994670i	$0.532878\pi$
$4$		0			0
$5$	−1.37033	+	3.30826i	−0.122566	+	0.295900i	−0.973239	−	0.229795i	$-0.926194\pi$
$5$	−1.37033	+	3.30826i	−0.122566	+	0.295900i	0.850673	+	0.525695i	$0.176194\pi$
$6$		0			0
$7$	−6.14642	−	6.14642i	−0.331875	−	0.331875i	0.521423	−	0.853298i	$-0.325401\pi$
$7$	−6.14642	−	6.14642i	−0.331875	−	0.331875i	−0.853298	+	0.521423i	$0.825401\pi$
$8$		0			0
$9$	−1.79604	+	1.79604i	−0.0665200	+	0.0665200i
$10$		0			0
$11$	−17.2398	−	7.14095i	−0.472544	−	0.195734i	0.133685	−	0.991024i	$-0.457319\pi$
$11$	−17.2398	−	7.14095i	−0.472544	−	0.195734i	−0.606230	+	0.795290i	$0.707319\pi$
$12$		0			0
$13$	25.9810	+	62.7238i	0.554296	+	1.33819i	0.914224	+	0.405209i	$0.132801\pi$
$13$	25.9810	+	62.7238i	0.554296	+	1.33819i	−0.359928	+	0.932980i	$0.617199\pi$
$14$		0			0
$15$		−	17.7098i		−	0.304843i
$16$		0			0
$17$		−	87.5919i		−	1.24966i	−0.780762	−	0.624828i	$-0.785169\pi$
$17$		−	87.5919i		−	1.24966i	0.780762	−	0.624828i	$-0.214831\pi$
$18$		0			0
$19$	−48.8193	−	117.860i	−0.589470	−	1.42311i	−0.884011	−	0.467467i	$-0.845167\pi$
$19$	−48.8193	−	117.860i	−0.589470	−	1.42311i	0.294541	−	0.955639i	$-0.404833\pi$
$20$		0			0
$21$	39.7174	+	16.4515i	0.412716	+	0.170953i
$22$		0			0
$23$	−55.7254	+	55.7254i	−0.505198	+	0.505198i	−0.913049	−	0.407851i	$-0.866278\pi$
$23$	−55.7254	+	55.7254i	−0.505198	+	0.505198i	0.407851	+	0.913049i	$0.366278\pi$
$24$		0			0
$25$	79.3216	+	79.3216i	0.634572	+	0.634572i
$26$		0			0
$27$	55.9086	−	134.975i	0.398504	−	0.962074i
$28$		0			0
$29$	114.139	−	47.2779i	0.730865	−	0.302734i	0.0139575	−	0.999903i	$-0.495557\pi$
$29$	114.139	−	47.2779i	0.730865	−	0.302734i	0.716907	+	0.697168i	$0.245557\pi$
$30$		0			0
$31$	229.997			1.33254			0.666269	−	0.745711i	$-0.267890\pi$
$31$	229.997			1.33254			0.666269	+	0.745711i	$0.267890\pi$
$32$		0			0
$33$	92.2879			0.486826
$34$		0			0
$35$	28.7565	−	11.9113i	0.138878	−	0.0575253i
$36$		0			0
$37$	123.846	−	298.992i	0.550277	−	1.32849i	−0.366995	−	0.930223i	$-0.619613\pi$
$37$	123.846	−	298.992i	0.550277	−	1.32849i	0.917272	−	0.398262i	$-0.130387\pi$
$38$		0			0
$39$	−237.427	−	237.427i	−0.974840	−	0.974840i
$40$		0			0
$41$	111.562	−	111.562i	0.424952	−	0.424952i	−0.461953	−	0.886904i	$-0.652851\pi$
$41$	111.562	−	111.562i	0.424952	−	0.424952i	0.886904	+	0.461953i	$0.152851\pi$
$42$		0			0
$43$	−76.5574	−	31.7111i	−0.271509	−	0.112463i	0.242775	−	0.970083i	$-0.421942\pi$
$43$	−76.5574	−	31.7111i	−0.271509	−	0.112463i	−0.514284	+	0.857620i	$0.671942\pi$
$44$		0			0
$45$	−3.48061	−	8.40293i	−0.0115302	−	0.0278363i
$46$		0			0
$47$		−	367.843i		−	1.14161i	−0.821087	−	0.570803i	$-0.806632\pi$
$47$		−	367.843i		−	1.14161i	0.821087	−	0.570803i	$-0.193368\pi$
$48$		0			0
$49$		−	267.443i		−	0.779718i
$50$		0			0
$51$	165.780	+	400.228i	0.455173	+	1.09889i
$52$		0			0
$53$	244.994	+	101.480i	0.634952	+	0.263006i	0.676855	−	0.736116i	$-0.263342\pi$
$53$	244.994	+	101.480i	0.634952	+	0.263006i	−0.0419036	+	0.999122i	$0.513342\pi$
$54$		0			0
$55$	47.2482	−	47.2482i	0.115835	−	0.115835i
$56$		0			0
$57$	446.134	+	446.134i	1.03670	+	1.03670i
$58$		0			0
$59$	183.495	−	442.997i	0.404899	−	0.977513i	−0.581560	−	0.813504i	$-0.697557\pi$
$59$	183.495	−	442.997i	0.404899	−	0.977513i	0.986459	−	0.164009i	$-0.0524427\pi$
$60$		0			0
$61$	−524.604	+	217.298i	−1.10113	+	0.456101i	−0.857873	−	0.513862i	$-0.828214\pi$
$61$	−524.604	+	217.298i	−1.10113	+	0.456101i	−0.243252	+	0.969963i	$0.578214\pi$
$62$		0			0
$63$	22.0784			0.0441527
$64$		0			0
$65$	−243.109			−0.463907
$66$		0			0
$67$	−393.028	+	162.797i	−0.716656	+	0.296849i	−0.711056	−	0.703136i	$-0.751783\pi$
$67$	−393.028	+	162.797i	−0.716656	+	0.296849i	−0.00560040	+	0.999984i	$0.501783\pi$
$68$		0			0
$69$	149.155	−	360.091i	0.260233	−	0.628259i
$70$		0			0
$71$	−354.722	−	354.722i	−0.592926	−	0.592926i	0.345495	−	0.938421i	$-0.387711\pi$
$71$	−354.722	−	354.722i	−0.592926	−	0.592926i	−0.938421	+	0.345495i	$0.887711\pi$
$72$		0			0
$73$	−22.2443	+	22.2443i	−0.0356644	+	0.0356644i	−0.724714	−	0.689050i	$-0.758028\pi$
$73$	−22.2443	+	22.2443i	−0.0356644	+	0.0356644i	0.689050	+	0.724714i	$0.258028\pi$
$74$		0			0
$75$	−512.566	−	212.312i	−0.789147	−	0.326876i
$76$		0			0
$77$	62.0716	+	149.854i	0.0918664	+	0.221785i
$78$		0			0
$79$			396.453i			0.564614i	0.959324	+	0.282307i	$0.0910996\pi$
$79$			396.453i			0.564614i	−0.959324	+	0.282307i	$0.908900\pi$
$80$		0			0
$81$			653.969i			0.897077i
$82$		0			0
$83$	410.445	+	990.903i	0.542798	+	1.31043i	0.922741	+	0.385420i	$0.125943\pi$
$83$	410.445	+	990.903i	0.542798	+	1.31043i	−0.379943	+	0.925010i	$0.624057\pi$
$84$		0			0
$85$	289.777	+	120.029i	0.369773	+	0.153165i
$86$		0			0
$87$	−432.048	+	432.048i	−0.532419	+	0.532419i
$88$		0			0
$89$	170.977	+	170.977i	0.203635	+	0.203635i	0.801555	−	0.597920i	$-0.204006\pi$
$89$	170.977	+	170.977i	0.203635	+	0.203635i	−0.597920	+	0.801555i	$0.704006\pi$
$90$		0			0
$91$	225.836	−	545.217i	0.260155	−	0.628069i
$92$		0			0
$93$	−1050.91	+	435.301i	−1.17177	+	0.485362i
$94$		0			0
$95$	456.811			0.493345
$96$		0			0
$97$	−1723.11			−1.80367			−0.901833	−	0.432085i	$-0.857778\pi$
$97$	−1723.11			−1.80367			−0.901833	+	0.432085i	$0.857778\pi$
$98$		0			0
$99$	43.7888	−	18.1379i	0.0444539	−	0.0184134i
$100$		0			0
$101$	134.279	−	324.178i	0.132290	−	0.319376i	−0.843829	−	0.536612i	$-0.819704\pi$
$101$	134.279	−	324.178i	0.132290	−	0.319376i	0.976119	+	0.217236i	$0.0697041\pi$
$102$		0			0
$103$	694.181	+	694.181i	0.664075	+	0.664075i	0.956338	−	0.292263i	$-0.0944084\pi$
$103$	694.181	+	694.181i	0.664075	+	0.664075i	−0.292263	+	0.956338i	$0.594408\pi$
$104$		0			0
$105$	−108.852	+	108.852i	−0.101170	+	0.101170i
$106$		0			0
$107$	264.682	+	109.635i	0.239138	+	0.0990544i	0.499034	−	0.866582i	$-0.333688\pi$
$107$	264.682	+	109.635i	0.239138	+	0.0990544i	−0.259896	+	0.965637i	$0.583688\pi$
$108$		0			0
$109$	−69.2899	−	167.281i	−0.0608878	−	0.146996i	0.890507	−	0.454969i	$-0.150350\pi$
$109$	−69.2899	−	167.281i	−0.0608878	−	0.146996i	−0.951395	+	0.307973i	$0.900350\pi$
$110$		0			0
$111$			1600.56i			1.36864i
$112$		0			0
$113$		−	2198.94i		−	1.83061i	−0.402758	−	0.915306i	$-0.631949\pi$
$113$		−	2198.94i		−	1.83061i	0.402758	−	0.915306i	$-0.368051\pi$
$114$		0			0
$115$	−107.992	−	260.716i	−0.0875680	−	0.211408i
$116$		0			0
$117$	−159.318	−	65.9915i	−0.125888	−	0.0521446i
$118$		0			0
$119$	−538.376	+	538.376i	−0.414730	+	0.414730i
$120$		0			0
$121$	−694.943	−	694.943i	−0.522121	−	0.522121i
$122$		0			0
$123$	−298.606	+	720.898i	−0.218897	+	0.528465i
$124$		0			0
$125$	−784.645	+	325.011i	−0.561446	+	0.232559i
$126$		0			0
$127$	1982.34			1.38507			0.692535	−	0.721384i	$-0.256494\pi$
$127$	1982.34			1.38507			0.692535	+	0.721384i	$0.256494\pi$
$128$		0			0
$129$	409.827			0.279715
$130$		0			0
$131$	−201.609	+	83.5090i	−0.134463	+	0.0556963i	−0.448900	−	0.893582i	$-0.648184\pi$
$131$	−201.609	+	83.5090i	−0.134463	+	0.0556963i	0.314437	+	0.949278i	$0.398184\pi$
$132$		0			0
$133$	−424.354	+	1024.48i	−0.276663	+	0.667924i
$134$		0			0
$135$	369.920	+	369.920i	0.235834	+	0.235834i
$136$		0			0
$137$	−332.511	+	332.511i	−0.207360	+	0.207360i	−0.803144	−	0.595784i	$-0.796841\pi$
$137$	−332.511	+	332.511i	−0.207360	+	0.207360i	0.595784	+	0.803144i	$0.296841\pi$
$138$		0			0
$139$	917.619	+	380.090i	0.559938	+	0.231934i	0.644658	−	0.764471i	$-0.277000\pi$
$139$	917.619	+	380.090i	0.559938	+	0.231934i	−0.0847201	+	0.996405i	$0.527000\pi$
$140$		0			0
$141$	696.195	+	1680.76i	0.415817	+	1.00387i
$142$		0			0
$143$		−	1266.87i		−	0.740848i
$144$		0			0
$145$			442.388i			0.253368i
$146$		0			0
$147$	506.174	+	1222.01i	0.284003	+	0.685645i
$148$		0			0
$149$	−2064.41	−	855.107i	−1.13505	−	0.470155i	−0.265558	−	0.964095i	$-0.585556\pi$
$149$	−2064.41	−	855.107i	−1.13505	−	0.470155i	−0.869496	+	0.493940i	$0.835556\pi$
$150$		0			0
$151$	−609.506	+	609.506i	−0.328482	+	0.328482i	−0.852009	−	0.523527i	$-0.824616\pi$
$151$	−609.506	+	609.506i	−0.328482	+	0.328482i	0.523527	+	0.852009i	$0.324616\pi$
$152$		0			0
$153$	157.319	+	157.319i	0.0831272	+	0.0831272i
$154$		0			0
$155$	−315.171	+	760.890i	−0.163323	+	0.394298i
$156$		0			0
$157$	2898.83	−	1200.73i	1.47358	−	0.610376i	0.505906	−	0.862589i	$-0.331158\pi$
$157$	2898.83	−	1200.73i	1.47358	−	0.610376i	0.967672	+	0.252213i	$0.0811584\pi$
$158$		0			0
$159$	−1311.50			−0.654142
$160$		0			0
$161$	685.023			0.335325
$162$		0			0
$163$	−112.364	+	46.5428i	−0.0539942	+	0.0223651i	−0.409517	−	0.912302i	$-0.634303\pi$
$163$	−112.364	+	46.5428i	−0.0539942	+	0.0223651i	0.355523	+	0.934668i	$0.384303\pi$
$164$		0			0
$165$	−126.464	+	305.312i	−0.0596681	+	0.144052i
$166$		0			0
$167$	−1557.93	−	1557.93i	−0.721895	−	0.721895i	0.247096	−	0.968991i	$-0.420524\pi$
$167$	−1557.93	−	1557.93i	−0.721895	−	0.721895i	−0.968991	+	0.247096i	$0.920524\pi$
$168$		0			0
$169$	−1705.75	+	1705.75i	−0.776398	+	0.776398i
$170$		0			0
$171$	299.363	+	124.000i	0.133877	+	0.0554535i
$172$		0			0
$173$	−1117.57	−	2698.06i	−0.491141	−	1.18572i	−0.954140	−	0.299361i	$-0.903227\pi$
$173$	−1117.57	−	2698.06i	−0.491141	−	1.18572i	0.462999	−	0.886359i	$-0.346773\pi$
$174$		0			0
$175$		−	975.087i		−	0.421198i
$176$		0			0
$177$			2371.45i			1.00706i
$178$		0			0
$179$	−1394.97	−	3367.75i	−0.582485	−	1.40624i	−0.890553	−	0.454879i	$-0.849683\pi$
$179$	−1394.97	−	3367.75i	−0.582485	−	1.40624i	0.308069	−	0.951364i	$-0.400317\pi$
$180$		0			0
$181$	16.5037	+	6.83606i	0.00677741	+	0.00280730i	0.386070	−	0.922470i	$-0.373832\pi$
$181$	16.5037	+	6.83606i	0.00677741	+	0.00280730i	−0.379292	+	0.925277i	$0.623832\pi$
$182$		0			0
$183$	1985.77	−	1985.77i	0.802145	−	0.802145i
$184$		0			0
$185$	819.433	+	819.433i	0.325653	+	0.325653i
$186$		0			0
$187$	−625.489	+	1510.06i	−0.244600	+	0.590518i
$188$		0			0
$189$	−1173.25	+	485.977i	−0.451542	+	0.187035i
$190$		0			0
$191$	−3640.57			−1.37917			−0.689587	−	0.724203i	$-0.742208\pi$
$191$	−3640.57			−1.37917			−0.689587	+	0.724203i	$0.742208\pi$
$192$		0			0
$193$	3234.02			1.20616			0.603082	−	0.797679i	$-0.293939\pi$
$193$	3234.02			1.20616			0.603082	+	0.797679i	$0.293939\pi$
$194$		0			0
$195$	1110.82	−	460.118i	0.407937	−	0.168973i
$196$		0			0
$197$	556.709	−	1344.01i	0.201339	−	0.486076i	−0.790670	−	0.612243i	$-0.790267\pi$
$197$	556.709	−	1344.01i	0.201339	−	0.486076i	0.992009	+	0.126167i	$0.0402674\pi$
$198$		0			0
$199$	1366.73	+	1366.73i	0.486860	+	0.486860i	0.907314	−	0.420454i	$-0.138129\pi$
$199$	1366.73	+	1366.73i	0.486860	+	0.486860i	−0.420454	+	0.907314i	$0.638129\pi$
$200$		0			0
$201$	1487.72	−	1487.72i	0.522068	−	0.522068i
$202$		0			0
$203$	−992.136	−	410.956i	−0.343026	−	0.142086i
$204$		0			0
$205$	216.199	+	521.951i	0.0736586	+	0.177828i
$206$		0			0
$207$		−	200.170i		−	0.0672116i
$208$		0			0
$209$			2380.50i			0.787860i
$210$		0			0
$211$	−1144.59	−	2763.28i	−0.373444	−	0.901574i	−0.993161	−	0.116749i	$-0.962753\pi$
$211$	−1144.59	−	2763.28i	−0.373444	−	0.901574i	0.619717	−	0.784825i	$-0.287247\pi$
$212$		0			0
$213$	2292.17	+	949.447i	0.737356	+	0.305423i
$214$		0			0
$215$	209.817	−	209.817i	0.0665554	−	0.0665554i
$216$		0			0
$217$	−1413.66	−	1413.66i	−0.442236	−	0.442236i
$218$		0			0
$219$	59.5391	−	143.740i	0.0183711	−	0.0443519i
$220$		0			0
$221$	5494.09	−	2275.73i	1.67228	−	0.692679i
$222$		0			0
$223$	−1712.42			−0.514226			−0.257113	−	0.966381i	$-0.582771\pi$
$223$	−1712.42			−0.514226			−0.257113	+	0.966381i	$0.582771\pi$
$224$		0			0
$225$	−284.930			−0.0844236
$226$		0			0
$227$	2071.09	−	857.873i	0.605564	−	0.250833i	−0.0587668	−	0.998272i	$-0.518717\pi$
$227$	2071.09	−	857.873i	0.605564	−	0.250833i	0.664330	+	0.747439i	$0.268717\pi$
$228$		0			0
$229$	−1656.50	+	3999.14i	−0.478010	+	1.15402i	0.482530	+	0.875879i	$0.339718\pi$
$229$	−1656.50	+	3999.14i	−0.478010	+	1.15402i	−0.960541	+	0.278140i	$0.910282\pi$
$230$		0			0
$231$	−567.240	−	567.240i	−0.161565	−	0.161565i
$232$		0			0
$233$	4732.54	−	4732.54i	1.33064	−	1.33064i	0.425844	−	0.904797i	$-0.359977\pi$
$233$	4732.54	−	4732.54i	1.33064	−	1.33064i	0.904797	−	0.425844i	$-0.140023\pi$
$234$		0			0
$235$	1216.92	+	504.065i	0.337801	+	0.139922i
$236$		0			0
$237$	−750.343	−	1811.49i	−0.205654	−	0.496493i
$238$		0			0
$239$		−	3120.14i		−	0.844457i	−0.906489	−	0.422229i	$-0.861248\pi$
$239$		−	3120.14i		−	0.844457i	0.906489	−	0.422229i	$-0.138752\pi$
$240$		0			0
$241$		−	1994.40i		−	0.533073i	−0.963825	−	0.266537i	$-0.914121\pi$
$241$		−	1994.40i		−	0.533073i	0.963825	−	0.266537i	$-0.0858793\pi$
$242$		0			0
$243$	271.803	+	656.192i	0.0717539	+	0.173229i
$244$		0			0
$245$	884.771	+	366.484i	0.230718	+	0.0955666i
$246$		0			0
$247$	6124.27	−	6124.27i	1.57764	−	1.57764i
$248$		0			0
$249$	−3750.84	−	3750.84i	−0.954619	−	0.954619i
$250$		0			0
$251$	759.835	−	1834.40i	0.191077	−	0.461301i	−0.799086	−	0.601216i	$-0.794683\pi$
$251$	759.835	−	1834.40i	0.191077	−	0.461301i	0.990163	+	0.139915i	$0.0446830\pi$
$252$		0			0
$253$	1358.63	−	562.761i	0.337613	−	0.139844i
$254$		0			0
$255$	−1551.23			−0.380948
$256$		0			0
$257$	5357.21			1.30029			0.650143	−	0.759812i	$-0.274709\pi$
$257$	5357.21			1.30029			0.650143	+	0.759812i	$0.274709\pi$
$258$		0			0
$259$	−2598.94	+	1076.52i	−0.623515	+	0.258268i
$260$		0			0
$261$	−120.085	+	289.911i	−0.0284793	+	0.0687551i
$262$		0			0
$263$	3387.07	+	3387.07i	0.794127	+	0.794127i	0.982162	−	0.188035i	$-0.0602118\pi$
$263$	3387.07	+	3387.07i	0.794127	+	0.794127i	−0.188035	+	0.982162i	$0.560212\pi$
$264$		0			0
$265$	−671.442	+	671.442i	−0.155647	+	0.155647i
$266$		0			0
$267$	−1104.83	−	457.636i	−0.253238	−	0.104895i
$268$		0			0
$269$	225.824	+	545.188i	0.0511849	+	0.123571i	0.947404	−	0.320041i	$-0.103697\pi$
$269$	225.824	+	545.188i	0.0511849	+	0.123571i	−0.896219	+	0.443612i	$0.853697\pi$
$270$		0			0
$271$			4177.50i			0.936403i	0.883622	+	0.468201i	$0.155098\pi$
$271$			4177.50i			0.936403i	−0.883622	+	0.468201i	$0.844902\pi$
$272$		0			0
$273$			2918.65i			0.647051i
$274$		0			0
$275$	−801.055	−	1933.92i	−0.175656	−	0.424071i
$276$		0			0
$277$	2459.54	+	1018.78i	0.533500	+	0.220983i	0.633136	−	0.774041i	$-0.281768\pi$
$277$	2459.54	+	1018.78i	0.533500	+	0.220983i	−0.0996351	+	0.995024i	$0.531768\pi$
$278$		0			0
$279$	−413.084	+	413.084i	−0.0886405	+	0.0886405i
$280$		0			0
$281$	−1012.51	−	1012.51i	−0.214952	−	0.214952i	0.591415	−	0.806367i	$-0.298569\pi$
$281$	−1012.51	−	1012.51i	−0.214952	−	0.214952i	−0.806367	+	0.591415i	$0.798569\pi$
$282$		0			0
$283$	−567.782	+	1370.75i	−0.119262	+	0.287924i	−0.972225	−	0.234047i	$-0.924803\pi$
$283$	−567.782	+	1370.75i	−0.119262	+	0.287924i	0.852963	+	0.521971i	$0.174803\pi$
$284$		0			0
$285$	−2087.28	+	864.578i	−0.433823	+	0.179695i
$286$		0			0
$287$	−1371.41			−0.282062
$288$		0			0
$289$	−2759.34			−0.561640
$290$		0			0
$291$	7873.31	−	3261.23i	1.58605	−	0.656965i
$292$		0			0
$293$	421.800	−	1018.32i	0.0841018	−	0.203040i	−0.876234	−	0.481886i	$-0.839952\pi$
$293$	421.800	−	1018.32i	0.0841018	−	0.203040i	0.960336	+	0.278846i	$0.0899520\pi$
$294$		0			0
$295$	1214.10	+	1214.10i	0.239619	+	0.239619i
$296$		0			0
$297$	−1927.70	+	1927.70i	−0.376622	+	0.376622i
$298$		0			0
$299$	−4943.12	−	2047.51i	−0.956079	−	0.396021i
$300$		0			0
$301$	275.644	+	665.464i	0.0527836	+	0.127431i
$302$		0			0
$303$			1735.39i			0.329028i
$304$		0			0
$305$		−	2033.29i		−	0.381725i
$306$		0			0
$307$	−2140.75	−	5168.22i	−0.397977	−	0.960800i	−0.988145	−	0.153521i	$-0.950939\pi$
$307$	−2140.75	−	5168.22i	−0.397977	−	0.960800i	0.590169	−	0.807280i	$-0.299061\pi$
$308$		0			0
$309$	−4485.71	−	1858.04i	−0.825836	−	0.342072i
$310$		0			0
$311$	−5781.99	+	5781.99i	−1.05423	+	1.05423i	−0.0557904	+	0.998443i	$0.517768\pi$
$311$	−5781.99	+	5781.99i	−1.05423	+	1.05423i	−0.998443	+	0.0557904i	$0.982232\pi$
$312$		0			0
$313$	804.942	+	804.942i	0.145361	+	0.145361i	0.776042	−	0.630681i	$-0.217224\pi$
$313$	804.942	+	804.942i	0.145361	+	0.145361i	−0.630681	+	0.776042i	$0.717224\pi$
$314$		0			0
$315$	−30.2546	+	73.0412i	−0.00541161	+	0.0130648i
$316$		0			0
$317$	1951.08	−	808.164i	0.345690	−	0.143189i	−0.203082	−	0.979162i	$-0.565096\pi$
$317$	1951.08	−	808.164i	0.345690	−	0.143189i	0.548771	+	0.835972i	$0.315096\pi$
$318$		0			0
$319$	−2305.34			−0.404621
$320$		0			0
$321$	−1416.90			−0.246366
$322$		0			0
$323$	−10323.6	+	4276.18i	−1.77839	+	0.736634i
$324$		0			0
$325$	−2914.49	+	7036.21i	−0.497437	+	1.20092i
$326$		0			0
$327$	633.204	+	633.204i	0.107083	+	0.107083i
$328$		0			0
$329$	−2260.92	+	2260.92i	−0.378871	+	0.378871i
$330$		0			0
$331$	7533.21	+	3120.36i	1.25095	+	0.518158i	0.907119	−	0.420875i	$-0.138277\pi$
$331$	7533.21	+	3120.36i	1.25095	+	0.518158i	0.343826	+	0.939033i	$0.388277\pi$
$332$		0			0
$333$	314.568	+	759.435i	0.0517665	+	0.124975i
$334$		0			0
$335$		−	1523.32i		−	0.248442i
$336$		0			0
$337$			3018.53i			0.487922i	0.969785	+	0.243961i	$0.0784469\pi$
$337$			3018.53i			0.487922i	−0.969785	+	0.243961i	$0.921553\pi$
$338$		0			0
$339$	4161.81	+	10047.5i	0.666780	+	1.60975i
$340$		0			0
$341$	−3965.10	−	1642.40i	−0.629683	−	0.260823i
$342$		0			0
$343$	−3752.04	+	3752.04i	−0.590644	+	0.590644i
$344$		0			0
$345$	986.884	+	986.884i	0.154006	+	0.154006i
$346$		0			0
$347$	−1631.78	+	3939.46i	−0.252445	+	0.609456i	−0.998400	−	0.0565400i	$-0.981993\pi$
$347$	−1631.78	+	3939.46i	−0.252445	+	0.609456i	0.745955	+	0.665996i	$0.231993\pi$
$348$		0			0
$349$	−2555.50	+	1058.52i	−0.391956	+	0.162354i	−0.569953	−	0.821678i	$-0.693038\pi$
$349$	−2555.50	+	1058.52i	−0.391956	+	0.162354i	0.177996	+	0.984031i	$0.443038\pi$
$350$		0			0
$351$	9918.72			1.50833
$352$		0			0
$353$	−4332.58			−0.653257			−0.326629	−	0.945153i	$-0.605913\pi$
$353$	−4332.58			−0.653257			−0.326629	+	0.945153i	$0.605913\pi$
$354$		0			0
$355$	1659.60	−	687.427i	0.248119	−	0.102774i
$356$		0			0
$357$	1441.02	−	3478.92i	0.213632	−	0.515753i
$358$		0			0
$359$	−9290.59	−	9290.59i	−1.36585	−	1.36585i	−0.866271	−	0.499574i	$-0.833490\pi$
$359$	−9290.59	−	9290.59i	−1.36585	−	1.36585i	−0.499574	−	0.866271i	$-0.666510\pi$
$360$		0			0
$361$	−6657.67	+	6657.67i	−0.970648	+	0.970648i
$362$		0			0
$363$	4490.63	+	1860.08i	0.649303	+	0.268950i
$364$		0			0
$365$	−43.1080	−	104.072i	−0.00618186	−	0.0149243i
$366$		0			0
$367$			2140.92i			0.304511i	0.988341	+	0.152255i	$0.0486536\pi$
$367$			2140.92i			0.304511i	−0.988341	+	0.152255i	$0.951346\pi$
$368$		0			0
$369$			400.739i			0.0565356i
$370$		0			0
$371$	−882.096	−	2129.57i	−0.123440	−	0.298010i
$372$		0			0
$373$	−4123.46	−	1707.99i	−0.572399	−	0.237095i	0.0776592	−	0.996980i	$-0.475255\pi$
$373$	−4123.46	−	1707.99i	−0.572399	−	0.237095i	−0.650058	+	0.759885i	$0.725255\pi$
$374$		0			0
$375$	2970.10	−	2970.10i	0.409001	−	0.409001i
$376$		0			0
$377$	5930.90	+	5930.90i	0.810231	+	0.810231i
$378$		0			0
$379$	−2989.05	+	7216.20i	−0.405111	+	0.978025i	0.581294	+	0.813694i	$0.302547\pi$
$379$	−2989.05	+	7216.20i	−0.405111	+	0.978025i	−0.986405	+	0.164331i	$0.947453\pi$
$380$		0			0
$381$	−9057.77	+	3751.85i	−1.21796	+	0.504496i
$382$		0			0
$383$	6358.57			0.848323			0.424161	−	0.905587i	$-0.360569\pi$
$383$	6358.57			0.848323			0.424161	+	0.905587i	$0.360569\pi$
$384$		0			0
$385$	−580.814			−0.0768858
$386$		0			0
$387$	194.455	−	80.5458i	0.0255418	−	0.0105798i
$388$		0			0
$389$	3947.57	−	9530.27i	0.514523	−	1.24217i	−0.426703	−	0.904392i	$-0.640325\pi$
$389$	3947.57	−	9530.27i	0.514523	−	1.24217i	0.941226	−	0.337777i	$-0.109675\pi$
$390$		0			0
$391$	4881.09	+	4881.09i	0.631324	+	0.631324i
$392$		0			0
$393$	763.145	−	763.145i	0.0979531	−	0.0979531i
$394$		0			0
$395$	−1311.57	−	543.270i	−0.167069	−	0.0692022i
$396$		0			0
$397$	−1253.91	−	3027.20i	−0.158519	−	0.382698i	0.824587	−	0.565735i	$-0.191407\pi$
$397$	−1253.91	−	3027.20i	−0.158519	−	0.382698i	−0.983106	+	0.183037i	$0.941407\pi$
$398$		0			0
$399$		−	5484.25i		−	0.688110i
$400$		0			0
$401$		−	13053.8i		−	1.62562i	−0.582528	−	0.812810i	$-0.697937\pi$
$401$		−	13053.8i		−	1.62562i	0.582528	−	0.812810i	$-0.302063\pi$
$402$		0			0
$403$	5975.56	+	14426.3i	0.738620	+	1.78319i
$404$		0			0
$405$	−2163.50	−	896.150i	−0.265445	−	0.109951i
$406$		0			0
$407$	−4270.17	+	4270.17i	−0.520060	+	0.520060i
$408$		0			0
$409$	652.548	+	652.548i	0.0788910	+	0.0788910i	0.745451	−	0.666560i	$-0.232234\pi$
$409$	652.548	+	652.548i	0.0788910	+	0.0788910i	−0.666560	+	0.745451i	$0.732234\pi$
$410$		0			0
$411$	889.998	−	2148.65i	0.106814	−	0.257871i
$412$		0			0
$413$	−3850.68	+	1595.00i	−0.458789	+	0.190036i
$414$		0			0
$415$	−3840.61			−0.454284
$416$		0			0
$417$	−4912.19			−0.576861
$418$		0			0
$419$	382.177	−	158.303i	0.0445598	−	0.0184573i	−0.360292	−	0.932839i	$-0.617323\pi$
$419$	382.177	−	158.303i	0.0445598	−	0.0184573i	0.404852	+	0.914382i	$0.367323\pi$
$420$		0			0
$421$	171.786	−	414.729i	0.0198868	−	0.0480111i	−0.913624	−	0.406560i	$-0.866728\pi$
$421$	171.786	−	414.729i	0.0198868	−	0.0480111i	0.933511	+	0.358549i	$0.116728\pi$
$422$		0			0
$423$	660.662	+	660.662i	0.0759396	+	0.0759396i
$424$		0			0
$425$	6947.92	−	6947.92i	0.792997	−	0.792997i
$426$		0			0
$427$	4560.04	+	1888.83i	0.516805	+	0.214068i
$428$		0			0
$429$	2397.73	+	5788.64i	0.269846	+	0.651465i
$430$		0			0
$431$			3644.76i			0.407336i	0.979040	+	0.203668i	$0.0652863\pi$
$431$			3644.76i			0.407336i	−0.979040	+	0.203668i	$0.934714\pi$
$432$		0			0
$433$			361.093i			0.0400763i	0.999799	+	0.0200382i	$0.00637877\pi$
$433$			361.093i			0.0400763i	−0.999799	+	0.0200382i	$0.993621\pi$
$434$		0			0
$435$	−837.280	−	2021.37i	−0.0922863	−	0.222799i
$436$		0			0
$437$	9288.29	+	3847.34i	1.01675	+	0.421151i
$438$		0			0
$439$	2187.45	−	2187.45i	0.237817	−	0.237817i	−0.578129	−	0.815945i	$-0.696217\pi$
$439$	2187.45	−	2187.45i	0.237817	−	0.237817i	0.815945	+	0.578129i	$0.196217\pi$
$440$		0			0
$441$	480.339	+	480.339i	0.0518668	+	0.0518668i
$442$		0			0
$443$	6147.99	−	14842.6i	0.659367	−	1.59185i	−0.139415	−	0.990234i	$-0.544522\pi$
$443$	6147.99	−	14842.6i	0.659367	−	1.59185i	0.798783	−	0.601620i	$-0.205478\pi$
$444$		0			0
$445$	−799.930	+	331.342i	−0.0852142	+	0.0352969i
$446$		0			0
$447$	11051.2			1.16936
$448$		0			0
$449$	−13620.0			−1.43156			−0.715779	−	0.698326i	$-0.753928\pi$
$449$	−13620.0			−1.43156			−0.715779	+	0.698326i	$0.753928\pi$
$450$		0			0
$451$	−2719.96	+	1126.64i	−0.283986	+	0.117631i
$452$		0			0
$453$	1631.40	−	3938.55i	0.169205	−	0.408497i
$454$		0			0
$455$	1494.25	+	1494.25i	0.153959	+	0.153959i
$456$		0			0
$457$	−3302.76	+	3302.76i	−0.338067	+	0.338067i	−0.855639	−	0.517573i	$-0.826836\pi$
$457$	−3302.76	+	3302.76i	−0.338067	+	0.338067i	0.517573	+	0.855639i	$0.326836\pi$
$458$		0			0
$459$	−11822.7	−	4897.14i	−1.20226	−	0.497993i
$460$		0			0
$461$	2319.14	+	5598.89i	0.234301	+	0.565654i	0.996675	−	0.0814840i	$-0.0259659\pi$
$461$	2319.14	+	5598.89i	0.234301	+	0.565654i	−0.762373	+	0.647138i	$0.775966\pi$
$462$		0			0
$463$			11103.9i			1.11456i	0.830326	+	0.557279i	$0.188154\pi$
$463$			11103.9i			1.11456i	−0.830326	+	0.557279i	$0.811846\pi$
$464$		0			0
$465$		−	4073.19i		−	0.406214i
$466$		0			0
$467$	3094.31	+	7470.32i	0.306611	+	0.740225i	0.999810	+	0.0194791i	$0.00620077\pi$
$467$	3094.31	+	7470.32i	0.306611	+	0.740225i	−0.693199	+	0.720746i	$0.743799\pi$
$468$		0			0
$469$	3416.33	+	1415.09i	0.336357	+	0.139324i
$470$		0			0
$471$	−10972.9	+	10972.9i	−1.07347	+	1.07347i
$472$		0			0
$473$	1093.39	+	1093.39i	0.106287	+	0.106287i
$474$		0			0
$475$	5476.44	−	13221.3i	0.529002	−	1.27712i
$476$		0			0
$477$	−622.280	+	257.757i	−0.0597322	+	0.0247419i
$478$		0			0
$479$	−2969.80			−0.283285			−0.141643	−	0.989918i	$-0.545238\pi$
$479$	−2969.80			−0.283285			−0.141643	+	0.989918i	$0.545238\pi$
$480$		0			0
$481$	21971.6			2.08278
$482$		0			0
$483$	−3130.03	+	1296.50i	−0.294868	+	0.122139i
$484$		0			0
$485$	2361.23	−	5700.50i	0.221067	−	0.533704i
$486$		0			0
$487$	−14166.3	−	14166.3i	−1.31814	−	1.31814i	−0.915246	−	0.402895i	$-0.868004\pi$
$487$	−14166.3	−	14166.3i	−1.31814	−	1.31814i	−0.402895	−	0.915246i	$-0.631996\pi$
$488$		0			0
$489$	425.331	−	425.331i	0.0393336	−	0.0393336i
$490$		0			0
$491$	−16702.1	−	6918.24i	−1.53514	−	0.635877i	−0.554589	−	0.832124i	$-0.687125\pi$
$491$	−16702.1	−	6918.24i	−1.53514	−	0.635877i	−0.980555	+	0.196247i	$0.937125\pi$
$492$		0			0
$493$	−4141.16	−	9997.65i	−0.378314	−	0.913330i
$494$		0			0
$495$			169.719i			0.0154108i
$496$		0			0
$497$			4360.54i			0.393555i
$498$		0			0
$499$	−4361.00	−	10528.4i	−0.391232	−	0.944519i	−0.989672	−	0.143351i	$-0.954212\pi$
$499$	−4361.00	−	10528.4i	−0.391232	−	0.944519i	0.598439	−	0.801168i	$-0.295788\pi$
$500$		0			0
$501$	10067.2	+	4169.96i	0.897741	+	0.371856i
$502$		0			0
$503$	9988.91	−	9988.91i	0.885454	−	0.885454i	−0.108628	−	0.994082i	$-0.534646\pi$
$503$	9988.91	−	9988.91i	0.885454	−	0.885454i	0.994082	+	0.108628i	$0.0346458\pi$
$504$		0			0
$505$	888.460	+	888.460i	0.0782890	+	0.0782890i
$506$		0			0
$507$	4565.59	−	11022.3i	0.399931	−	0.965520i
$508$		0			0
$509$	1708.35	−	707.622i	0.148765	−	0.0616204i	−0.307059	−	0.951691i	$-0.599345\pi$
$509$	1708.35	−	707.622i	0.148765	−	0.0616204i	0.455824	+	0.890070i	$0.349345\pi$
$510$		0			0
$511$	273.446			0.0236723
$512$		0			0
$513$	−18637.6			−1.60404
$514$		0			0
$515$	−3247.78	+	1345.28i	−0.277892	+	0.115107i
$516$		0			0
$517$	−2626.75	+	6341.53i	−0.223451	+	0.539459i
$518$		0			0
$519$	10212.9	+	10212.9i	0.863770	+	0.863770i
$520$		0			0
$521$	11373.3	−	11373.3i	0.956377	−	0.956377i	−0.0427108	−	0.999087i	$-0.513599\pi$
$521$	11373.3	−	11373.3i	0.956377	−	0.956377i	0.999087	+	0.0427108i	$0.0135994\pi$
$522$		0			0
$523$	3452.22	+	1429.96i	0.288633	+	0.119556i	0.522302	−	0.852760i	$-0.325073\pi$
$523$	3452.22	+	1429.96i	0.288633	+	0.119556i	−0.233669	+	0.972316i	$0.575073\pi$
$524$		0			0
$525$	1845.49	+	4455.40i	0.153417	+	0.370380i
$526$		0			0
$527$		−	20145.9i		−	1.66521i
$528$		0			0
$529$			5956.35i			0.489550i
$530$		0			0
$531$	466.075	+	1125.21i	0.0380903	+	0.0919581i
$532$		0			0
$533$	9896.07	+	4099.08i	0.804214	+	0.333116i
$534$		0			0
$535$	−725.402	+	725.402i	−0.0586203	+	0.0586203i
$536$		0			0
$537$	12747.9	+	12747.9i	1.02442	+	1.02442i
$538$		0			0
$539$	−1909.80	+	4610.66i	−0.152617	+	0.368451i
$540$		0			0
$541$	−13493.1	+	5589.03i	−1.07230	+	0.444161i	−0.847802	−	0.530314i	$-0.822074\pi$
$541$	−13493.1	+	5589.03i	−1.07230	+	0.444161i	−0.224498	+	0.974475i	$0.572074\pi$
$542$		0			0
$543$	−88.3476			−0.00698224
$544$		0			0
$545$	648.357			0.0509588
$546$		0			0
$547$	10714.7	−	4438.16i	0.837525	−	0.346914i	0.0776476	−	0.996981i	$-0.475259\pi$
$547$	10714.7	−	4438.16i	0.837525	−	0.346914i	0.759877	+	0.650067i	$0.225259\pi$
$548$		0			0
$549$	551.934	−	1332.49i	0.0429070	−	0.103587i
$550$		0			0
$551$	−11144.4	−	11144.4i	−0.861645	−	0.861645i
$552$		0			0
$553$	2436.77	−	2436.77i	0.187381	−	0.187381i
$554$		0			0
$555$	−5295.07	−	2193.29i	−0.404979	−	0.167748i
$556$		0			0
$557$	8959.38	+	21629.9i	0.681546	+	1.64540i	0.761154	+	0.648571i	$0.224633\pi$
$557$	8959.38	+	21629.9i	0.681546	+	1.64540i	−0.0796083	+	0.996826i	$0.525367\pi$
$558$		0			0
$559$		−	5625.86i		−	0.425668i
$560$		0			0
$561$		−	8083.67i		−	0.608365i
$562$		0			0
$563$	−144.332	−	348.448i	−0.0108044	−	0.0260841i	0.918385	−	0.395687i	$-0.129494\pi$
$563$	−144.332	−	348.448i	−0.0108044	−	0.0260841i	−0.929190	+	0.369603i	$0.879494\pi$
$564$		0			0
$565$	7274.68	+	3013.27i	0.541678	+	0.224370i
$566$		0			0
$567$	4019.56	−	4019.56i	0.297718	−	0.297718i
$568$		0			0
$569$	−8107.90	−	8107.90i	−0.597365	−	0.597365i	0.342246	−	0.939611i	$-0.388813\pi$
$569$	−8107.90	−	8107.90i	−0.597365	−	0.597365i	−0.939611	+	0.342246i	$0.888813\pi$
$570$		0			0
$571$	−3680.55	+	8885.63i	−0.269748	+	0.651229i	−0.999471	−	0.0325132i	$-0.989649\pi$
$571$	−3680.55	+	8885.63i	−0.269748	+	0.651229i	0.729723	+	0.683743i	$0.239649\pi$
$572$		0			0
$573$	16634.6	−	6890.28i	1.21278	−	0.502349i
$574$		0			0
$575$	−8840.46			−0.641170
$576$		0			0
$577$	20668.9			1.49126			0.745629	−	0.666361i	$-0.232149\pi$
$577$	20668.9			1.49126			0.745629	+	0.666361i	$0.232149\pi$
$578$		0			0
$579$	−14777.0	+	6120.83i	−1.06064	+	0.439331i
$580$		0			0
$581$	3567.73	−	8613.27i	0.254758	−	0.615040i
$582$		0			0
$583$	−3498.97	−	3498.97i	−0.248564	−	0.248564i
$584$		0			0
$585$	436.634	−	436.634i	0.0308591	−	0.0308591i
$586$		0			0
$587$	834.858	+	345.810i	0.0587024	+	0.0243153i	0.411841	−	0.911256i	$-0.364886\pi$
$587$	834.858	+	345.810i	0.0587024	+	0.0243153i	−0.353139	+	0.935571i	$0.614886\pi$
$588$		0			0
$589$	−11228.3	−	27107.5i	−0.785491	−	1.89634i
$590$		0			0
$591$			7194.77i			0.500767i
$592$		0			0
$593$		−	8473.46i		−	0.586785i	−0.955992	−	0.293392i	$-0.905216\pi$
$593$		−	8473.46i		−	0.586785i	0.955992	−	0.293392i	$-0.0947842\pi$
$594$		0			0
$595$	−1043.34	−	2518.84i	−0.0718868	−	0.173550i
$596$		0			0
$597$	−8831.67	−	3658.20i	−0.605454	−	0.250787i
$598$		0			0
$599$	−4342.08	+	4342.08i	−0.296181	+	0.296181i	−0.839516	−	0.543335i	$-0.817161\pi$
$599$	−4342.08	+	4342.08i	−0.296181	+	0.296181i	0.543335	+	0.839516i	$0.317161\pi$
$600$		0			0
$601$	−6136.50	−	6136.50i	−0.416494	−	0.416494i	0.467499	−	0.883993i	$-0.345155\pi$
$601$	−6136.50	−	6136.50i	−0.416494	−	0.416494i	−0.883993	+	0.467499i	$0.845155\pi$
$602$		0			0
$603$	413.503	−	998.284i	0.0279256	−	0.0674184i
$604$		0			0
$605$	3251.35	−	1346.75i	0.218489	−	0.0905013i
$606$		0			0
$607$	3622.97			0.242260			0.121130	−	0.992637i	$-0.461348\pi$
$607$	3622.97			0.242260			0.121130	+	0.992637i	$0.461348\pi$
$608$		0			0
$609$	5311.10			0.353393
$610$		0			0
$611$	23072.5	−	9556.95i	1.52768	−	0.632787i
$612$		0			0
$613$	−1515.46	+	3658.63i	−0.0998510	+	0.241062i	−0.965909	−	0.258882i	$-0.916646\pi$
$613$	−1515.46	+	3658.63i	−0.0998510	+	0.241062i	0.866058	+	0.499944i	$0.166646\pi$
$614$		0			0
$615$	−1975.73	−	1975.73i	−0.129543	−	0.129543i
$616$		0			0
$617$	−5257.77	+	5257.77i	−0.343063	+	0.343063i	−0.857518	−	0.514454i	$-0.827994\pi$
$617$	−5257.77	+	5257.77i	−0.343063	+	0.343063i	0.514454	+	0.857518i	$0.327994\pi$
$618$		0			0
$619$	23417.3	+	9699.75i	1.52055	+	0.629831i	0.977701	−	0.210000i	$-0.0673466\pi$
$619$	23417.3	+	9699.75i	1.52055	+	0.629831i	0.542846	+	0.839832i	$0.317347\pi$
$620$		0			0
$621$	4406.02	+	10637.1i	0.284714	+	0.687361i
$622$		0			0
$623$		−	2101.79i		−	0.135163i
$624$		0			0
$625$			10981.0i			0.702786i
$626$		0			0
$627$	−4505.43	−	10877.1i	−0.286969	−	0.692804i
$628$		0			0
$629$	−26189.3	−	10847.9i	−1.66015	−	0.687656i
$630$		0			0
$631$	19776.5	−	19776.5i	1.24768	−	1.24768i	0.290944	−	0.956740i	$-0.406031\pi$
$631$	19776.5	−	19776.5i	1.24768	−	1.24768i	0.956740	−	0.290944i	$-0.0939693\pi$
$632$		0			0
$633$	10459.8	+	10459.8i	0.656776	+	0.656776i
$634$		0			0
$635$	−2716.45	+	6558.08i	−0.169762	+	0.409842i
$636$		0			0
$637$	16775.0	−	6948.45i	1.04341	−	0.432194i
$638$		0			0
$639$	1274.19			0.0788829
$640$		0			0
$641$	304.324			0.0187521			0.00937603	−	0.999956i	$-0.497015\pi$
$641$	304.324			0.0187521			0.00937603	+	0.999956i	$0.497015\pi$
$642$		0			0
$643$	−16207.7	+	6713.43i	−0.994040	+	0.411745i	−0.819608	−	0.572924i	$-0.805809\pi$
$643$	−16207.7	+	6713.43i	−0.994040	+	0.411745i	−0.174432	+	0.984669i	$0.555809\pi$
$644$		0			0
$645$	−561.596	+	1355.81i	−0.0342835	+	0.0827676i
$646$		0			0
$647$	13156.7	+	13156.7i	0.799450	+	0.799450i	0.983009	−	0.183559i	$-0.0587619\pi$
$647$	13156.7	+	13156.7i	0.799450	+	0.799450i	−0.183559	+	0.983009i	$0.558762\pi$
$648$		0			0
$649$	−6326.83	+	6326.83i	−0.382666	+	0.382666i
$650$		0			0
$651$	9134.88	+	3783.79i	0.549960	+	0.227801i
$652$		0			0
$653$	−7533.14	−	18186.6i	−0.451447	−	1.08989i	−0.971772	−	0.235921i	$-0.924189\pi$
$653$	−7533.14	−	18186.6i	−0.451447	−	1.08989i	0.520326	−	0.853968i	$-0.325811\pi$
$654$		0			0
$655$		−	781.408i		−	0.0466139i
$656$		0			0
$657$		−	79.9035i		−	0.00474480i
$658$		0			0
$659$	4387.91	+	10593.4i	0.259376	+	0.626189i	0.998898	−	0.0469438i	$-0.0149482\pi$
$659$	4387.91	+	10593.4i	0.259376	+	0.626189i	−0.739521	+	0.673133i	$0.764948\pi$
$660$		0			0
$661$	−17601.5	−	7290.76i	−1.03573	−	0.429013i	−0.200953	−	0.979601i	$-0.564404\pi$
$661$	−17601.5	−	7290.76i	−1.03573	−	0.429013i	−0.834777	+	0.550588i	$0.814404\pi$
$662$		0			0
$663$	−20796.7	+	20796.7i	−1.21821	+	1.21821i
$664$		0			0
$665$	−2807.75	−	2807.75i	−0.163729	−	0.163729i
$666$		0			0
$667$	−3725.86	+	8995.03i	−0.216291	+	0.522172i
$668$		0			0
$669$	7824.47	−	3241.00i	0.452185	−	0.187301i
$670$		0			0
$671$	10595.8			0.609605
$672$		0			0
$673$	1023.41			0.0586174			0.0293087	−	0.999570i	$-0.490669\pi$
$673$	1023.41			0.0586174			0.0293087	+	0.999570i	$0.490669\pi$
$674$		0			0
$675$	15141.2	−	6271.69i	0.863385	−	0.357626i
$676$		0			0
$677$	3769.24	−	9099.74i	0.213979	−	0.516590i	−0.780049	−	0.625718i	$-0.784806\pi$
$677$	3769.24	−	9099.74i	0.213979	−	0.516590i	0.994028	+	0.109128i	$0.0348059\pi$
$678$		0			0
$679$	10591.0	+	10591.0i	0.598592	+	0.598592i
$680$		0			0
$681$	−7839.65	+	7839.65i	−0.441139	+	0.441139i
$682$		0			0
$683$	2058.49	+	852.656i	0.115324	+	0.0477686i	0.439599	−	0.898194i	$-0.355120\pi$
$683$	2058.49	+	852.656i	0.115324	+	0.0477686i	−0.324276	+	0.945963i	$0.605120\pi$
$684$		0			0
$685$	−644.384	−	1555.68i	−0.0359426	−	0.0867731i
$686$		0			0
$687$		−	21408.2i		−	1.18890i
$688$		0			0
$689$			18003.5i			0.995468i
$690$		0			0
$691$	−11541.0	−	27862.4i	−0.635370	−	1.53392i	−0.832784	−	0.553598i	$-0.813255\pi$
$691$	−11541.0	−	27862.4i	−0.635370	−	1.53392i	0.197415	−	0.980320i	$-0.436745\pi$
$692$		0			0
$693$	−380.627	−	157.661i	−0.0208641	−	0.00864220i
$694$		0			0
$695$	−2514.87	+	2514.87i	−0.137258	+	0.137258i
$696$		0			0
$697$	−9771.90	−	9771.90i	−0.531043	−	0.531043i
$698$		0			0
$699$	−12667.1	+	30581.1i	−0.685428	+	1.65477i
$700$		0			0
$701$	−3783.29	+	1567.09i	−0.203841	+	0.0844339i	−0.482268	−	0.876024i	$-0.660187\pi$
$701$	−3783.29	+	1567.09i	−0.203841	+	0.0844339i	0.278427	+	0.960457i	$0.410187\pi$
$702$		0			0
$703$	−41285.4			−2.21495
$704$		0			0
$705$	−6514.41			−0.348010
$706$		0			0
$707$	−2817.87	+	1167.20i	−0.149897	+	0.0620892i
$708$		0			0
$709$	−7928.02	+	19139.9i	−0.419948	+	1.01384i	0.562414	+	0.826856i	$0.309873\pi$
$709$	−7928.02	+	19139.9i	−0.419948	+	1.01384i	−0.982362	+	0.186988i	$0.940127\pi$
$710$		0			0
$711$	−712.046	−	712.046i	−0.0375581	−	0.0375581i
$712$		0			0
$713$	−12816.7	+	12816.7i	−0.673196	+	0.673196i
$714$		0			0
$715$	4191.15	+	1736.03i	0.219217	+	0.0908025i
$716$		0			0
$717$	5905.31	+	14256.7i	0.307584	+	0.742573i
$718$		0			0
$719$			35836.7i			1.85881i	0.369064	+	0.929404i	$0.379678\pi$
$719$			35836.7i			1.85881i	−0.369064	+	0.929404i	$0.620322\pi$
$720$		0			0
$721$		−	8533.45i		−	0.440780i
$722$		0			0
$723$	3774.68	+	9112.89i	0.194166	+	0.468758i
$724$		0			0
$725$	12803.8	+	5303.53i	0.655894	+	0.271680i
$726$		0			0
$727$	17934.8	−	17934.8i	0.914946	−	0.914946i	−0.0817100	−	0.996656i	$-0.526038\pi$
$727$	17934.8	−	17934.8i	0.914946	−	0.914946i	0.996656	+	0.0817100i	$0.0260381\pi$
$728$		0			0
$729$	−14969.4	−	14969.4i	−0.760523	−	0.760523i
$730$		0			0
$731$	−2777.64	+	6705.81i	−0.140540	+	0.339293i
$732$		0			0
$733$	−12620.5	+	5227.58i	−0.635946	+	0.263418i	−0.677277	−	0.735728i	$-0.736840\pi$
$733$	−12620.5	+	5227.58i	−0.635946	+	0.263418i	0.0413310	+	0.999146i	$0.486840\pi$
$734$		0			0
$735$	−4736.35			−0.237691
$736$		0			0
$737$	7938.23			0.396755
$738$		0			0
$739$	12203.1	−	5054.70i	0.607441	−	0.251610i	−0.0576928	−	0.998334i	$-0.518374\pi$
$739$	12203.1	−	5054.70i	0.607441	−	0.251610i	0.665134	+	0.746724i	$0.268374\pi$
$740$		0			0
$741$	−16392.2	+	39574.3i	−0.812662	+	1.96194i
$742$		0			0
$743$	3084.12	+	3084.12i	0.152282	+	0.152282i	0.779136	−	0.626854i	$-0.215658\pi$
$743$	3084.12	+	3084.12i	0.152282	+	0.152282i	−0.626854	+	0.779136i	$0.715658\pi$
$744$		0			0
$745$	5657.83	−	5657.83i	0.278237	−	0.278237i
$746$		0			0
$747$	−2516.88	−	1042.53i	−0.123277	−	0.0510629i
$748$		0			0
$749$	−952.985	−	2300.71i	−0.0464904	−	0.112238i
$750$		0			0
$751$			30535.2i			1.48368i	0.670575	+	0.741842i	$0.266048\pi$
$751$			30535.2i			1.48368i	−0.670575	+	0.741842i	$0.733952\pi$
$752$		0			0
$753$			9819.92i			0.475243i
$754$		0			0
$755$	−1181.18	−	2851.62i	−0.0569372	−	0.137459i
$756$		0			0
$757$	8109.52	+	3359.07i	0.389360	+	0.161278i	0.568771	−	0.822496i	$-0.307419\pi$
$757$	8109.52	+	3359.07i	0.389360	+	0.161278i	−0.179411	+	0.983774i	$0.557419\pi$
$758$		0			0
$759$	−5142.78	+	5142.78i	−0.245943	+	0.245943i
$760$		0			0
$761$	−13700.0	−	13700.0i	−0.652595	−	0.652595i	0.301022	−	0.953617i	$-0.402672\pi$
$761$	−13700.0	−	13700.0i	−0.652595	−	0.652595i	−0.953617	+	0.301022i	$0.902672\pi$
$762$		0			0
$763$	−602.292	+	1454.06i	−0.0285772	+	0.0689915i
$764$		0			0
$765$	−736.028	+	304.873i	−0.0347858	+	0.0144088i
$766$		0			0
$767$	32553.8			1.53253
$768$		0			0
$769$	−5576.68			−0.261509			−0.130754	−	0.991415i	$-0.541740\pi$
$769$	−5576.68			−0.261509			−0.130754	+	0.991415i	$0.541740\pi$
$770$		0			0
$771$	−24478.4	+	10139.3i	−1.14341	+	0.473614i
$772$		0			0
$773$	−12414.0	+	29969.9i	−0.577618	+	1.39449i	0.317327	+	0.948316i	$0.397215\pi$
$773$	−12414.0	+	29969.9i	−0.577618	+	1.39449i	−0.894945	+	0.446177i	$0.852785\pi$
$774$		0			0
$775$	18243.7	+	18243.7i	0.845592	+	0.845592i
$776$		0			0
$777$	9837.72	−	9837.72i	0.454216	−	0.454216i
$778$		0			0
$779$	−18595.1	−	7702.33i	−0.855247	−	0.354255i
$780$		0			0
$781$	3582.27	+	8648.37i	0.164128	+	0.396240i
$782$		0			0
$783$		−	18049.2i		−	0.823787i
$784$		0			0
$785$			11235.5i			0.510842i
$786$		0			0
$787$	−1888.35	−	4558.87i	−0.0855302	−	0.206488i	0.875328	−	0.483530i	$-0.160646\pi$
$787$	−1888.35	−	4558.87i	−0.0855302	−	0.206488i	−0.960858	+	0.277042i	$0.910646\pi$
$788$		0			0
$789$	−21886.8	−	9065.82i	−0.987568	−	0.409064i
$790$		0			0
$791$	−13515.6	+	13515.6i	−0.607535	+	0.607535i
$792$		0			0
$793$	−27259.5	−	27259.5i	−1.22070	−	1.22070i
$794$		0			0
$795$	1797.18	−	4338.78i	0.0801753	−	0.193560i
$796$		0			0
$797$	−8355.80	+	3461.09i	−0.371365	+	0.153824i	−0.560557	−	0.828116i	$-0.689413\pi$
$797$	−8355.80	+	3461.09i	−0.371365	+	0.153824i	0.189192	+	0.981940i	$0.439413\pi$
$798$		0			0
$799$	−32220.1			−1.42661
$800$		0			0
$801$	−614.163			−0.0270916
$802$		0			0
$803$	542.333	−	224.642i	0.0238338	−	0.00987227i
$804$		0			0
$805$	−938.705	+	2266.23i	−0.0410994	+	0.0992227i
$806$		0			0
$807$	−2063.69	−	2063.69i	−0.0900189	−	0.0900189i
$808$		0			0
$809$	9416.77	−	9416.77i	0.409241	−	0.409241i	−0.472233	−	0.881474i	$-0.656552\pi$
$809$	9416.77	−	9416.77i	0.409241	−	0.409241i	0.881474	+	0.472233i	$0.156552\pi$
$810$		0			0
$811$	4597.28	+	1904.26i	0.199053	+	0.0824506i	0.479983	−	0.877278i	$-0.340643\pi$
$811$	4597.28	+	1904.26i	0.199053	+	0.0824506i	−0.280930	+	0.959728i	$0.590643\pi$
$812$		0			0
$813$	−7906.51	−	19088.0i	−0.341074	−	0.823426i
$814$		0			0
$815$		−	435.509i		−	0.0187181i
$816$		0			0
$817$			10571.2i			0.452680i
$818$		0			0
$819$	573.621	+	1384.84i	0.0244737	+	0.0590847i
$820$		0			0
$821$	−12716.7	−	5267.45i	−0.540581	−	0.223916i	0.0956491	−	0.995415i	$-0.469507\pi$
$821$	−12716.7	−	5267.45i	−0.540581	−	0.223916i	−0.636231	+	0.771499i	$0.719507\pi$
$822$		0			0
$823$	18764.2	−	18764.2i	0.794751	−	0.794751i	−0.187511	−	0.982262i	$-0.560042\pi$
$823$	18764.2	−	18764.2i	0.794751	−	0.794751i	0.982262	+	0.187511i	$0.0600422\pi$
$824$		0			0
$825$	7320.42	+	7320.42i	0.308926	+	0.308926i
$826$		0			0
$827$	6248.37	−	15084.9i	0.262729	−	0.634284i	−0.736376	−	0.676572i	$-0.763465\pi$
$827$	6248.37	−	15084.9i	0.262729	−	0.634284i	0.999105	+	0.0422880i	$0.0134647\pi$
$828$		0			0
$829$	23591.6	−	9771.95i	0.988383	−	0.409401i	0.170858	−	0.985296i	$-0.445346\pi$
$829$	23591.6	−	9771.95i	0.988383	−	0.409401i	0.817524	+	0.575894i	$0.195346\pi$
$830$		0			0
$831$	−13166.4			−0.549624
$832$		0			0
$833$	−23425.8			−0.974379
$834$		0			0
$835$	7288.92	−	3019.17i	0.302088	−	0.125129i
$836$		0			0
$837$	12858.8	−	31043.9i	0.531022	−	1.28200i
$838$		0			0
$839$	26103.1	+	26103.1i	1.07411	+	1.07411i	0.997024	+	0.0770872i	$0.0245620\pi$
$839$	26103.1	+	26103.1i	1.07411	+	1.07411i	0.0770872	+	0.997024i	$0.475438\pi$
$840$		0			0
$841$	−6453.12	+	6453.12i	−0.264591	+	0.264591i
$842$		0			0
$843$	6542.73	+	2710.09i	0.267312	+	0.110724i
$844$		0			0
$845$	−3305.62	−	7980.48i	−0.134576	−	0.324896i
$846$		0			0
$847$			8542.81i			0.346558i
$848$		0			0
$849$		−	7337.88i		−	0.296626i
$850$		0			0
$851$	9760.05	+	23562.8i	0.393150	+	0.949147i
$852$		0			0
$853$	44742.9	+	18533.1i	1.79598	+	0.743918i	0.987950	+	0.154770i	$0.0494638\pi$
$853$	44742.9	+	18533.1i	1.79598	+	0.743918i	0.808026	+	0.589147i	$0.200536\pi$
$854$		0			0
$855$	−820.451	+	820.451i	−0.0328173	+	0.0328173i
$856$		0			0
$857$	21556.5	+	21556.5i	0.859225	+	0.859225i	0.991247	−	0.132022i	$-0.0421469\pi$
$857$	21556.5	+	21556.5i	0.859225	+	0.859225i	−0.132022	+	0.991247i	$0.542147\pi$
$858$		0			0
$859$	−10150.3	+	24505.0i	−0.403171	+	0.973342i	0.583720	+	0.811955i	$0.301597\pi$
$859$	−10150.3	+	24505.0i	−0.403171	+	0.973342i	−0.986891	+	0.161387i	$0.948403\pi$
$860$		0			0
$861$	6266.30	−	2595.58i	0.248031	−	0.102738i
$862$		0			0
$863$	−9799.79			−0.386545			−0.193273	−	0.981145i	$-0.561910\pi$
$863$	−9799.79			−0.386545			−0.193273	+	0.981145i	$0.561910\pi$
$864$		0			0
$865$	10457.3			0.411051
$866$		0			0
$867$	12608.1	−	5222.43i	0.493878	−	0.204571i
$868$		0			0
$869$	2831.05	−	6834.76i	0.110514	−	0.266805i
$870$		0			0
$871$	−20422.5	−	20422.5i	−0.794479	−	0.794479i
$872$		0			0
$873$	3094.78	−	3094.78i	0.119980	−	0.119980i
$874$		0			0
$875$	6820.41	+	2825.10i	0.263511	+	0.109150i
$876$		0			0
$877$	−5253.32	−	12682.6i	−0.202271	−	0.488326i	0.789896	−	0.613241i	$-0.210134\pi$
$877$	−5253.32	−	12682.6i	−0.202271	−	0.488326i	−0.992168	+	0.124914i	$0.960134\pi$
$878$		0			0
$879$			5451.24i			0.209176i
$880$		0			0
$881$			9710.12i			0.371331i	0.982613	+	0.185665i	$0.0594440\pi$
$881$			9710.12i			0.371331i	−0.982613	+	0.185665i	$0.940556\pi$
$882$		0			0
$883$	−6324.17	−	15267.9i	−0.241025	−	0.581887i	0.756360	−	0.654156i	$-0.226976\pi$
$883$	−6324.17	−	15267.9i	−0.241025	−	0.581887i	−0.997385	+	0.0722692i	$0.976976\pi$
$884$		0			0
$885$	−7845.37	−	3249.66i	−0.297988	−	0.123431i
$886$		0			0
$887$	33197.6	−	33197.6i	1.25667	−	1.25667i	0.303999	−	0.952672i	$-0.401678\pi$
$887$	33197.6	−	33197.6i	1.25667	−	1.25667i	0.952672	−	0.303999i	$-0.0983219\pi$
$888$		0			0
$889$	−12184.3	−	12184.3i	−0.459671	−	0.459671i
$890$		0			0
$891$	4669.96	−	11274.3i	0.175589	−	0.423908i
$892$		0			0
$893$	−43354.1	+	17957.9i	−1.62462	+	0.672942i
$894$		0			0
$895$	13053.0			0.487499
$896$		0			0
$897$	26461.5			0.984975
$898$		0			0
$899$	26251.6	−	10873.8i	0.973905	−	0.403405i
$900$		0			0
$901$	8888.79	−	21459.4i	0.328667	−	0.793471i
$902$		0			0
$903$	−2518.97	−	2518.97i	−0.0928305	−	0.0928305i
$904$		0			0
$905$	−45.2309	+	45.2309i	−0.00166136	+	0.00166136i
$906$		0			0
$907$	−4347.03	−	1800.60i	−0.159141	−	0.0659183i	0.301691	−	0.953406i	$-0.402449\pi$
$907$	−4347.03	−	1800.60i	−0.159141	−	0.0659183i	−0.460832	+	0.887487i	$0.652449\pi$
$908$		0			0
$909$	341.067	+	823.408i	0.0124450	+	0.0300448i
$910$		0			0
$911$		−	27597.7i		−	1.00368i	−0.864961	−	0.501840i	$-0.832657\pi$
$911$		−	27597.7i		−	1.00368i	0.864961	−	0.501840i	$-0.167343\pi$
$912$		0			0
$913$		−	20013.9i		−	0.725480i
$914$		0			0
$915$	3848.29	+	9290.60i	0.139039	+	0.335670i
$916$		0			0
$917$	1752.45	+	725.889i	0.0631091	+	0.0261406i
$918$		0			0
$919$	−10437.8	+	10437.8i	−0.374658	+	0.374658i	−0.869171	−	0.494512i	$-0.835347\pi$
$919$	−10437.8	+	10437.8i	−0.374658	+	0.374658i	0.494512	+	0.869171i	$0.335347\pi$
$920$		0			0
$921$	19563.2	+	19563.2i	0.699922	+	0.699922i
$922$		0			0
$923$	13033.5	−	31465.5i	0.464790	−	1.12210i
$924$		0			0
$925$	33540.2	−	13892.8i	1.19221	−	0.493830i
$926$		0			0
$927$	−2493.56			−0.0883485
$928$		0			0
$929$	−692.011			−0.0244393			−0.0122197	−	0.999925i	$-0.503890\pi$
$929$	−692.011			−0.0244393			−0.0122197	+	0.999925i	$0.503890\pi$
$930$		0			0
$931$	−31520.9	+	13056.4i	−1.10962	+	0.459620i
$932$		0			0
$933$	15476.1	−	37362.5i	0.543047	−	1.31103i
$934$		0			0
$935$	−4138.56	−	4138.56i	−0.144754	−	0.144754i
$936$		0			0
$937$	−7694.36	+	7694.36i	−0.268264	+	0.268264i	−0.828401	−	0.560136i	$-0.810749\pi$
$937$	−7694.36	+	7694.36i	−0.268264	+	0.268264i	0.560136	+	0.828401i	$0.310749\pi$
$938$		0			0
$939$	−5201.44	−	2154.51i	−0.180769	−	0.0748772i
$940$		0			0
$941$	7735.22	+	18674.5i	0.267971	+	0.646940i	0.999388	−	0.0349914i	$-0.0111404\pi$
$941$	7735.22	+	18674.5i	0.267971	+	0.646940i	−0.731416	+	0.681931i	$0.761140\pi$
$942$		0			0
$943$			12433.6i			0.429369i
$944$		0			0
$945$		−	4547.36i		−	0.156535i
$946$		0			0
$947$	−258.346	−	623.702i	−0.00886496	−	0.0214019i	0.919385	−	0.393359i	$-0.128687\pi$
$947$	−258.346	−	623.702i	−0.00886496	−	0.0214019i	−0.928250	+	0.371957i	$0.878687\pi$
$948$		0			0
$949$	−1973.18	−	817.318i	−0.0674943	−	0.0279571i
$950$		0			0
$951$	−7385.39	+	7385.39i	−0.251827	+	0.251827i
$952$		0			0
$953$	29841.2	+	29841.2i	1.01433	+	1.01433i	0.999896	+	0.0144302i	$0.00459343\pi$
$953$	29841.2	+	29841.2i	1.01433	+	1.01433i	0.0144302	+	0.999896i	$0.495407\pi$
$954$		0			0
$955$	4988.76	−	12043.9i	0.169039	−	0.408097i
$956$		0			0
$957$	10533.6	−	4363.18i	0.355804	−	0.147379i
$958$		0			0
$959$	4087.50			0.137635
$960$		0			0
$961$	23107.6			0.775657
$962$		0			0
$963$	−672.289	+	278.471i	−0.0224966	+	0.00931840i
$964$		0			0
$965$	−4431.66	+	10699.0i	−0.147834	+	0.356903i
$966$		0			0
$967$	−28561.9	−	28561.9i	−0.949834	−	0.949834i	0.0489665	−	0.998800i	$-0.484407\pi$
$967$	−28561.9	−	28561.9i	−0.949834	−	0.949834i	−0.998800	+	0.0489665i	$0.984407\pi$
$968$		0			0
$969$	39077.7	−	39077.7i	1.29552	−	1.29552i
$970$		0			0
$971$	9671.99	+	4006.27i	0.319659	+	0.132407i	0.536743	−	0.843746i	$-0.319655\pi$
$971$	9671.99	+	4006.27i	0.319659	+	0.132407i	−0.217084	+	0.976153i	$0.569655\pi$
$972$		0			0
$973$	−3303.88	−	7976.26i	−0.108857	−	0.262803i
$974$		0			0
$975$		−	37666.2i		−	1.23721i
$976$		0			0
$977$			35356.3i			1.15778i	0.815407	+	0.578889i	$0.196513\pi$
$977$			35356.3i			1.15778i	−0.815407	+	0.578889i	$0.803487\pi$
$978$		0			0
$979$	−1726.67	−	4168.54i	−0.0563682	−	0.136085i
$980$		0			0
$981$	424.890	+	175.995i	0.0138284	+	0.00572793i
$982$		0			0
$983$	−26544.3	+	26544.3i	−0.861274	+	0.861274i	−0.991486	−	0.130213i	$-0.958434\pi$
$983$	−26544.3	+	26544.3i	−0.861274	+	0.861274i	0.130213	+	0.991486i	$0.458434\pi$
$984$		0			0
$985$	3683.47	+	3683.47i	0.119153	+	0.119153i
$986$		0			0
$987$	6051.57	−	14609.8i	0.195161	−	0.471159i
$988$		0			0
$989$	6033.31	−	2499.08i	0.193982	−	0.0803500i
$990$		0			0
$991$	40304.4			1.29194			0.645969	−	0.763364i	$-0.276453\pi$
$991$	40304.4			1.29194			0.645969	+	0.763364i	$0.276453\pi$
$992$		0			0
$993$	−40326.8			−1.28875
$994$		0			0
$995$	−6394.38	+	2648.64i	−0.203734	+	0.0843895i
$996$		0			0
$997$	−11444.4	+	27629.1i	−0.363537	+	0.877656i	0.631240	+	0.775587i	$0.282546\pi$
$997$	−11444.4	+	27629.1i	−0.363537	+	0.877656i	−0.994777	+	0.102069i	$0.967454\pi$
$998$		0			0
$999$	−33432.4	−	33432.4i	−1.05881	−	1.05881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.g.b.97.4		44
4.3	odd	2		256.4.g.a.97.8		44
8.3	odd	2		128.4.g.a.49.4		44
8.5	even	2		32.4.g.a.21.9	✓	44
32.3	odd	8		256.4.g.a.161.8		44
32.13	even	8		32.4.g.a.29.9	yes	44
32.19	odd	8		128.4.g.a.81.4		44
32.29	even	8	inner	256.4.g.b.161.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.9	✓	44	8.5	even	2
32.4.g.a.29.9	yes	44	32.13	even	8
128.4.g.a.49.4		44	8.3	odd	2
128.4.g.a.81.4		44	32.19	odd	8
256.4.g.a.97.8		44	4.3	odd	2
256.4.g.a.161.8		44	32.3	odd	8
256.4.g.b.97.4		44	1.1	even	1	trivial
256.4.g.b.161.4		44	32.29	even	8	inner

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	256.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.56924 + 1.89264i) q^{3} +(-1.37033 + 3.30826i) q^{5} +(-6.14642 - 6.14642i) q^{7} +(-1.79604 + 1.79604i) q^{9} +O(q^{10})\)	\(q+(-4.56924 + 1.89264i) q^{3} +(-1.37033 + 3.30826i) q^{5} +(-6.14642 - 6.14642i) q^{7} +(-1.79604 + 1.79604i) q^{9} +(-17.2398 - 7.14095i) q^{11} +(25.9810 + 62.7238i) q^{13} -17.7098i q^{15} -87.5919i q^{17} +(-48.8193 - 117.860i) q^{19} +(39.7174 + 16.4515i) q^{21} +(-55.7254 + 55.7254i) q^{23} +(79.3216 + 79.3216i) q^{25} +(55.9086 - 134.975i) q^{27} +(114.139 - 47.2779i) q^{29} +229.997 q^{31} +92.2879 q^{33} +(28.7565 - 11.9113i) q^{35} +(123.846 - 298.992i) q^{37} +(-237.427 - 237.427i) q^{39} +(111.562 - 111.562i) q^{41} +(-76.5574 - 31.7111i) q^{43} +(-3.48061 - 8.40293i) q^{45} -367.843i q^{47} -267.443i q^{49} +(165.780 + 400.228i) q^{51} +(244.994 + 101.480i) q^{53} +(47.2482 - 47.2482i) q^{55} +(446.134 + 446.134i) q^{57} +(183.495 - 442.997i) q^{59} +(-524.604 + 217.298i) q^{61} +22.0784 q^{63} -243.109 q^{65} +(-393.028 + 162.797i) q^{67} +(149.155 - 360.091i) q^{69} +(-354.722 - 354.722i) q^{71} +(-22.2443 + 22.2443i) q^{73} +(-512.566 - 212.312i) q^{75} +(62.0716 + 149.854i) q^{77} +396.453i q^{79} +653.969i q^{81} +(410.445 + 990.903i) q^{83} +(289.777 + 120.029i) q^{85} +(-432.048 + 432.048i) q^{87} +(170.977 + 170.977i) q^{89} +(225.836 - 545.217i) q^{91} +(-1050.91 + 435.301i) q^{93} +456.811 q^{95} -1723.11 q^{97} +(43.7888 - 18.1379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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