LMFDB - Embedded newform 336.4.bj.e.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(95,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.95"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,0,0,0,-38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.1
Character	$\chi$	$=$	336.191
Dual form			336.4.bj.e.95.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.77395 + 2.05167i) q^{3} +(-13.4200 - 7.74804i) q^{5} +(-15.7299 - 9.77601i) q^{7} +(18.5813 - 19.5892i) q^{9} +(-31.0035 - 53.6997i) q^{11} +39.3264 q^{13} +(79.9629 + 9.45536i) q^{15} +(-25.3292 + 14.6238i) q^{17} +(-7.16713 - 4.13795i) q^{19} +(95.1510 + 14.3977i) q^{21} +(-78.8896 + 136.641i) q^{23} +(57.5644 + 99.7044i) q^{25} +(-48.5157 + 131.641i) q^{27} -296.354i q^{29} +(-196.737 + 113.586i) q^{31} +(258.183 + 192.751i) q^{33} +(135.350 + 253.070i) q^{35} +(11.5861 - 20.0677i) q^{37} +(-187.743 + 80.6849i) q^{39} +175.780i q^{41} +257.358i q^{43} +(-401.139 + 118.918i) q^{45} +(194.065 - 336.131i) q^{47} +(151.859 + 307.551i) q^{49} +(90.9173 - 121.781i) q^{51} +(228.240 - 131.774i) q^{53} +960.866i q^{55} +(42.7053 + 5.04976i) q^{57} +(-95.0928 - 164.706i) q^{59} +(-234.249 + 405.732i) q^{61} +(-483.786 + 126.485i) q^{63} +(-527.761 - 304.703i) q^{65} +(280.189 - 161.767i) q^{67} +(96.2733 - 814.172i) q^{69} -490.223 q^{71} +(461.186 + 798.797i) q^{73} +(-479.370 - 357.881i) q^{75} +(-37.2867 + 1147.78i) q^{77} +(346.282 + 199.926i) q^{79} +(-38.4716 - 727.984i) q^{81} +673.416 q^{83} +453.225 q^{85} +(608.021 + 1414.78i) q^{87} +(1059.20 + 611.531i) q^{89} +(-618.600 - 384.456i) q^{91} +(706.171 - 945.894i) q^{93} +(64.1220 + 111.063i) q^{95} +805.185 q^{97} +(-1628.02 - 390.476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) $ 28 * q - 38 * q^7 - 70 * q^9 + 124 * q^13 + 462 * q^19 + 500 * q^21 + 566 * q^25 - 1266 * q^31 + 64 * q^33 + 338 * q^37 - 1254 * q^39 - 488 * q^45 - 206 * q^49 - 522 * q^51 + 2324 * q^57 - 340 * q^61 + 840 * q^63 - 2934 * q^67 - 776 * q^69 + 2050 * q^73 + 1458 * q^75 - 2070 * q^79 + 910 * q^81 + 2400 * q^85 - 3132 * q^87 + 5170 * q^91 + 714 * q^93 - 3344 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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
$3$	−4.77395	+	2.05167i	−0.918748	+	0.394844i
$3$	−4.77395	+	2.05167i	−0.918748	+	0.394844i
$4$		0			0
$5$	−13.4200	−	7.74804i	−1.20032	−	0.693006i	−0.239695	−	0.970848i	$-0.577047\pi$
$5$	−13.4200	−	7.74804i	−1.20032	−	0.693006i	−0.960627	+	0.277842i	$0.910381\pi$
$6$		0			0
$7$	−15.7299	−	9.77601i	−0.849334	−	0.527855i
$7$	−15.7299	−	9.77601i	−0.849334	−	0.527855i
$8$		0			0
$9$	18.5813	−	19.5892i	0.688196	−	0.725525i
$10$		0			0
$11$	−31.0035	−	53.6997i	−0.849810	−	1.47191i	−0.881377	−	0.472413i	$-0.843383\pi$
$11$	−31.0035	−	53.6997i	−0.849810	−	1.47191i	0.0315673	−	0.999502i	$-0.489950\pi$
$12$		0			0
$13$	39.3264			0.839014			0.419507	−	0.907752i	$-0.362203\pi$
$13$	39.3264			0.839014			0.419507	+	0.907752i	$0.362203\pi$
$14$		0			0
$15$	79.9629	+	9.45536i	1.37642	+	0.162758i
$16$		0			0
$17$	−25.3292	+	14.6238i	−0.361367	+	0.208635i	−0.669680	−	0.742650i	$-0.733569\pi$
$17$	−25.3292	+	14.6238i	−0.361367	+	0.208635i	0.308313	+	0.951285i	$0.400236\pi$
$18$		0			0
$19$	−7.16713	−	4.13795i	−0.0865396	−	0.0499637i	0.456106	−	0.889926i	$-0.349244\pi$
$19$	−7.16713	−	4.13795i	−0.0865396	−	0.0499637i	−0.542645	+	0.839962i	$0.682577\pi$
$20$		0			0
$21$	95.1510	+	14.3977i	0.988745	+	0.149611i
$22$		0			0
$23$	−78.8896	+	136.641i	−0.715200	+	1.23876i	0.247682	+	0.968841i	$0.420331\pi$
$23$	−78.8896	+	136.641i	−0.715200	+	1.23876i	−0.962882	+	0.269922i	$0.913002\pi$
$24$		0			0
$25$	57.5644	+	99.7044i	0.460515	+	0.797635i
$26$		0			0
$27$	−48.5157	+	131.641i	−0.345809	+	0.938305i
$28$		0			0
$29$		−	296.354i		−	1.89764i	−0.315817	−	0.948820i	$-0.602279\pi$
$29$		−	296.354i		−	1.89764i	0.315817	−	0.948820i	$-0.397721\pi$
$30$		0			0
$31$	−196.737	+	113.586i	−1.13984	+	0.658086i	−0.946390	−	0.323025i	$-0.895300\pi$
$31$	−196.737	+	113.586i	−1.13984	+	0.658086i	−0.193447	+	0.981111i	$0.561967\pi$
$32$		0			0
$33$	258.183	+	192.751i	1.36194	+	1.01678i
$34$		0			0
$35$	135.350	+	253.070i	0.653668	+	1.22219i
$36$		0			0
$37$	11.5861	−	20.0677i	0.0514796	−	0.0891653i	−0.839137	−	0.543920i	$-0.816940\pi$
$37$	11.5861	−	20.0677i	0.0514796	−	0.0891653i	0.890617	+	0.454754i	$0.150273\pi$
$38$		0			0
$39$	−187.743	+	80.6849i	−0.770843	+	0.331280i
$40$		0			0
$41$			175.780i			0.669565i	0.942295	+	0.334782i	$0.108663\pi$
$41$			175.780i			0.669565i	−0.942295	+	0.334782i	$0.891337\pi$
$42$		0			0
$43$			257.358i			0.912714i	0.889797	+	0.456357i	$0.150846\pi$
$43$			257.358i			0.912714i	−0.889797	+	0.456357i	$0.849154\pi$
$44$		0			0
$45$	−401.139	+	118.918i	−1.32885	+	0.393940i
$46$		0			0
$47$	194.065	−	336.131i	0.602284	−	1.04319i	−0.390190	−	0.920734i	$-0.627591\pi$
$47$	194.065	−	336.131i	0.602284	−	1.04319i	0.992474	−	0.122452i	$-0.0390759\pi$
$48$		0			0
$49$	151.859	+	307.551i	0.442738	+	0.896651i
$50$		0			0
$51$	90.9173	−	121.781i	0.249627	−	0.334367i
$52$		0			0
$53$	228.240	−	131.774i	0.591531	−	0.341521i	−0.174172	−	0.984715i	$-0.555725\pi$
$53$	228.240	−	131.774i	0.591531	−	0.341521i	0.765703	+	0.643195i	$0.222391\pi$
$54$		0			0
$55$			960.866i			2.35569i
$56$		0			0
$57$	42.7053	+	5.04976i	0.0992360	+	0.0117343i
$58$		0			0
$59$	−95.0928	−	164.706i	−0.209831	−	0.363438i	0.741830	−	0.670588i	$-0.233958\pi$
$59$	−95.0928	−	164.706i	−0.209831	−	0.363438i	−0.951661	+	0.307150i	$0.900625\pi$
$60$		0			0
$61$	−234.249	+	405.732i	−0.491681	+	0.851617i	−0.999954	−	0.00957919i	$-0.996951\pi$
$61$	−234.249	+	405.732i	−0.491681	+	0.851617i	0.508273	+	0.861196i	$0.330284\pi$
$62$		0			0
$63$	−483.786	+	126.485i	−0.967480	+	0.252946i
$64$		0			0
$65$	−527.761	−	304.703i	−1.00709	−	0.581442i
$66$		0			0
$67$	280.189	−	161.767i	0.510904	−	0.294970i	−0.222301	−	0.974978i	$-0.571357\pi$
$67$	280.189	−	161.767i	0.510904	−	0.294970i	0.733205	+	0.680008i	$0.238024\pi$
$68$		0			0
$69$	96.2733	−	814.172i	0.167970	−	1.42050i
$70$		0			0
$71$	−490.223			−0.819419			−0.409710	−	0.912216i	$-0.634370\pi$
$71$	−490.223			−0.819419			−0.409710	+	0.912216i	$0.634370\pi$
$72$		0			0
$73$	461.186	+	798.797i	0.739421	+	1.28071i	0.952756	+	0.303736i	$0.0982339\pi$
$73$	461.186	+	798.797i	0.739421	+	1.28071i	−0.213335	+	0.976979i	$0.568433\pi$
$74$		0			0
$75$	−479.370	−	357.881i	−0.738039	−	0.550994i
$76$		0			0
$77$	−37.2867	+	1147.78i	−0.0551845	+	1.69872i
$78$		0			0
$79$	346.282	+	199.926i	0.493162	+	0.284727i	0.725885	−	0.687816i	$-0.241430\pi$
$79$	346.282	+	199.926i	0.493162	+	0.284727i	−0.232723	+	0.972543i	$0.574764\pi$
$80$		0			0
$81$	−38.4716	−	727.984i	−0.0527731	−	0.998607i
$82$		0			0
$83$	673.416			0.890566			0.445283	−	0.895390i	$-0.353103\pi$
$83$	673.416			0.890566			0.445283	+	0.895390i	$0.353103\pi$
$84$		0			0
$85$	453.225			0.578342
$86$		0			0
$87$	608.021	+	1414.78i	0.749273	+	1.74345i
$88$		0			0
$89$	1059.20	+	611.531i	1.26152	+	0.728339i	0.973369	−	0.229246i	$-0.0736259\pi$
$89$	1059.20	+	611.531i	1.26152	+	0.728339i	0.288152	+	0.957585i	$0.406959\pi$
$90$		0			0
$91$	−618.600	−	384.456i	−0.712604	−	0.442878i
$92$		0			0
$93$	706.171	−	945.894i	0.787382	−	1.05467i
$94$		0			0
$95$	64.1220	+	111.063i	0.0692503	+	0.119945i
$96$		0			0
$97$	805.185			0.842826			0.421413	−	0.906869i	$-0.361534\pi$
$97$	805.185			0.842826			0.421413	+	0.906869i	$0.361534\pi$
$98$		0			0
$99$	−1628.02	−	390.476i	−1.65275	−	0.396407i
$100$		0			0
$101$	148.405	−	85.6817i	0.146206	−	0.0844123i	−0.425112	−	0.905141i	$-0.639765\pi$
$101$	148.405	−	85.6817i	0.146206	−	0.0844123i	0.571319	+	0.820728i	$0.306432\pi$
$102$		0			0
$103$	−96.8756	−	55.9311i	−0.0926741	−	0.0535054i	0.452947	−	0.891538i	$-0.350373\pi$
$103$	−96.8756	−	55.9311i	−0.0926741	−	0.0535054i	−0.545621	+	0.838032i	$0.683706\pi$
$104$		0			0
$105$	−1165.37	−	930.451i	−1.08313	−	0.864788i
$106$		0			0
$107$	−151.076	+	261.672i	−0.136496	+	0.236418i	−0.926168	−	0.377111i	$-0.876917\pi$
$107$	−151.076	+	261.672i	−0.136496	+	0.236418i	0.789672	+	0.613529i	$0.210251\pi$
$108$		0			0
$109$	−939.689	−	1627.59i	−0.825742	−	1.43023i	−0.901351	−	0.433089i	$-0.857424\pi$
$109$	−939.689	−	1627.59i	−0.825742	−	1.43023i	0.0756094	−	0.997138i	$-0.475910\pi$
$110$		0			0
$111$	−14.1392	+	119.573i	−0.0120904	+	0.102247i
$112$		0			0
$113$		−	1412.68i		−	1.17605i	−0.808842	−	0.588026i	$-0.799905\pi$
$113$		−	1412.68i		−	1.17605i	0.808842	−	0.588026i	$-0.200095\pi$
$114$		0			0
$115$	2117.40	−	1222.48i	1.71694	−	0.991277i
$116$		0			0
$117$	730.736	−	770.372i	0.577406	−	0.608726i
$118$		0			0
$119$	541.389	+	17.5875i	0.417051	+	0.0135483i
$120$		0			0
$121$	−1256.94	+	2177.08i	−0.944355	+	1.63567i
$122$		0			0
$123$	−360.642	−	839.164i	−0.264374	−	0.615161i
$124$		0			0
$125$			152.966i			0.109454i
$126$		0			0
$127$		−	2585.08i		−	1.80621i	−0.429422	−	0.903104i	$-0.641283\pi$
$127$		−	2585.08i		−	1.80621i	0.429422	−	0.903104i	$-0.358717\pi$
$128$		0			0
$129$	−528.014	−	1228.61i	−0.360380	−	0.838554i
$130$		0			0
$131$	−408.884	+	708.207i	−0.272705	+	0.472338i	−0.969553	−	0.244880i	$-0.921252\pi$
$131$	−408.884	+	708.207i	−0.272705	+	0.472338i	0.696849	+	0.717218i	$0.254585\pi$
$132$		0			0
$133$	72.2856	+	135.155i	0.0471275	+	0.0881163i
$134$		0			0
$135$	1671.04	−	1390.72i	1.06533	−	0.886620i
$136$		0			0
$137$	−1915.51	+	1105.92i	−1.19455	+	0.689673i	−0.959335	−	0.282271i	$-0.908912\pi$
$137$	−1915.51	+	1105.92i	−1.19455	+	0.689673i	−0.235214	+	0.971944i	$0.575579\pi$
$138$		0			0
$139$			839.342i			0.512173i	0.966654	+	0.256087i	$0.0824332\pi$
$139$			839.342i			0.512173i	−0.966654	+	0.256087i	$0.917567\pi$
$140$		0			0
$141$	−236.829	+	2002.83i	−0.141451	+	1.19623i
$142$		0			0
$143$	−1219.26	−	2111.82i	−0.713003	−	1.23496i
$144$		0			0
$145$	−2296.16	+	3977.07i	−1.31508	+	2.27778i
$146$		0			0
$147$	−1355.96	−	1156.67i	−0.760802	−	0.648984i
$148$		0			0
$149$	280.208	+	161.778i	0.154064	+	0.0889489i	0.575050	−	0.818118i	$-0.304983\pi$
$149$	280.208	+	161.778i	0.154064	+	0.0889489i	−0.420986	+	0.907067i	$0.638316\pi$
$150$		0			0
$151$	2240.23	−	1293.40i	1.20733	−	0.697053i	0.245156	−	0.969484i	$-0.421161\pi$
$151$	2240.23	−	1293.40i	1.20733	−	0.697053i	0.962175	+	0.272431i	$0.0878275\pi$
$152$		0			0
$153$	−184.181	+	767.908i	−0.0973211	+	0.405763i
$154$		0			0
$155$	3520.28			1.82423
$156$		0			0
$157$	−17.3800	−	30.1031i	−0.00883490	−	0.0153025i	0.861574	−	0.507632i	$-0.169479\pi$
$157$	−17.3800	−	30.1031i	−0.00883490	−	0.0153025i	−0.870409	+	0.492329i	$0.836146\pi$
$158$		0			0
$159$	−819.249	+	1097.36i	−0.408620	+	0.547334i
$160$		0			0
$161$	2576.73	−	1378.12i	1.26133	−	0.674602i
$162$		0			0
$163$	2420.34	+	1397.38i	1.16304	+	0.671482i	0.952031	−	0.306002i	$-0.0989915\pi$
$163$	2420.34	+	1397.38i	1.16304	+	0.671482i	0.211010	+	0.977484i	$0.432325\pi$
$164$		0			0
$165$	−1971.38	−	4587.13i	−0.930133	−	2.16429i
$166$		0			0
$167$	−2587.18			−1.19882			−0.599408	−	0.800444i	$-0.704597\pi$
$167$	−2587.18			−1.19882			−0.599408	+	0.800444i	$0.704597\pi$
$168$		0			0
$169$	−650.433			−0.296055
$170$		0			0
$171$	−214.233	+	63.5098i	−0.0958061	+	0.0284019i
$172$		0			0
$173$	−3197.80	−	1846.25i	−1.40534	−	0.811376i	−0.410410	−	0.911901i	$-0.634614\pi$
$173$	−3197.80	−	1846.25i	−1.40534	−	0.811376i	−0.994935	+	0.100525i	$0.967948\pi$
$174$		0			0
$175$	69.2303	−	2131.09i	0.0299047	−	0.920544i
$176$		0			0
$177$	791.891	+	591.198i	0.336283	+	0.251057i
$178$		0			0
$179$	−756.315	−	1309.98i	−0.315808	−	0.546995i	0.663801	−	0.747909i	$-0.268942\pi$
$179$	−756.315	−	1309.98i	−0.315808	−	0.546995i	−0.979609	+	0.200914i	$0.935609\pi$
$180$		0			0
$181$	−2333.92			−0.958447			−0.479223	−	0.877693i	$-0.659082\pi$
$181$	−2333.92			−0.958447			−0.479223	+	0.877693i	$0.659082\pi$
$182$		0			0
$183$	285.867	−	2417.55i	0.115475	−	0.976559i
$184$		0			0
$185$	−310.971	+	179.539i	−0.123584	+	0.0713513i
$186$		0			0
$187$	1570.59	+	906.781i	0.614187	+	0.354601i
$188$		0			0
$189$	2050.07	−	1596.40i	0.788997	−	0.614398i
$190$		0			0
$191$	−2056.72	+	3562.34i	−0.779156	+	1.34954i	0.153273	+	0.988184i	$0.451019\pi$
$191$	−2056.72	+	3562.34i	−0.779156	+	1.34954i	−0.932429	+	0.361354i	$0.882315\pi$
$192$		0			0
$193$	151.707	+	262.764i	0.0565807	+	0.0980007i	0.892928	−	0.450199i	$-0.148647\pi$
$193$	151.707	+	262.764i	0.0565807	+	0.0980007i	−0.836348	+	0.548199i	$0.815314\pi$
$194$		0			0
$195$	3144.66	+	371.846i	1.15484	+	0.136556i
$196$		0			0
$197$			542.248i			0.196109i	0.995181	+	0.0980547i	$0.0312620\pi$
$197$			542.248i			0.196109i	−0.995181	+	0.0980547i	$0.968738\pi$
$198$		0			0
$199$	1552.74	−	896.473i	0.553119	−	0.319343i	−0.197260	−	0.980351i	$-0.563204\pi$
$199$	1552.74	−	896.473i	0.553119	−	0.319343i	0.750379	+	0.661008i	$0.229871\pi$
$200$		0			0
$201$	−1005.72	+	1347.13i	−0.352924	+	0.472731i
$202$		0			0
$203$	−2897.16	+	4661.62i	−1.00168	+	1.61173i
$204$		0			0
$205$	1361.95	−	2358.96i	0.464013	−	0.803693i
$206$		0			0
$207$	1210.81	+	4084.34i	0.406556	+	1.37141i
$208$		0			0
$209$			513.163i			0.169839i
$210$		0			0
$211$			575.851i			0.187882i	0.995578	+	0.0939412i	$0.0299466\pi$
$211$			575.851i			0.187882i	−0.995578	+	0.0939412i	$0.970053\pi$
$212$		0			0
$213$	2340.30	−	1005.78i	0.752840	−	0.323543i
$214$		0			0
$215$	1994.02	−	3453.74i	0.632516	−	1.09555i
$216$		0			0
$217$	4205.07	+	136.605i	1.31548	+	0.0427344i
$218$		0			0
$219$	−3840.55	−	2867.22i	−1.18502	−	0.884698i
$220$		0			0
$221$	−996.108	+	575.103i	−0.303192	+	0.175048i
$222$		0			0
$223$			327.662i			0.0983941i	0.998789	+	0.0491971i	$0.0156662\pi$
$223$			327.662i			0.0983941i	−0.998789	+	0.0491971i	$0.984334\pi$
$224$		0			0
$225$	3022.75	+	724.998i	0.895629	+	0.214814i
$226$		0			0
$227$	−1692.25	−	2931.07i	−0.494797	−	0.857013i	0.505185	−	0.863011i	$-0.331424\pi$
$227$	−1692.25	−	2931.07i	−0.494797	−	0.857013i	−0.999982	+	0.00599789i	$0.998091\pi$
$228$		0			0
$229$	−1641.81	+	2843.70i	−0.473773	+	0.820599i	−0.999549	−	0.0300237i	$-0.990442\pi$
$229$	−1641.81	+	2843.70i	−0.473773	+	0.820599i	0.525776	+	0.850623i	$0.323775\pi$
$230$		0			0
$231$	−2176.86	−	5555.95i	−0.620031	−	1.58249i
$232$		0			0
$233$	4356.88	+	2515.45i	1.22502	+	0.707263i	0.965983	−	0.258605i	$-0.0832629\pi$
$233$	4356.88	+	2515.45i	1.22502	+	0.707263i	0.259033	+	0.965869i	$0.416596\pi$
$234$		0			0
$235$	−5208.72	+	3007.25i	−1.44587	+	0.834773i
$236$		0			0
$237$	−2063.32	−	243.981i	−0.565515	−	0.0668703i
$238$		0			0
$239$	3351.80			0.907154			0.453577	−	0.891217i	$-0.350148\pi$
$239$	3351.80			0.907154			0.453577	+	0.891217i	$0.350148\pi$
$240$		0			0
$241$	2095.73	+	3629.91i	0.560156	+	0.970219i	0.997482	+	0.0709161i	$0.0225923\pi$
$241$	2095.73	+	3629.91i	0.560156	+	0.970219i	−0.437326	+	0.899303i	$0.644074\pi$
$242$		0			0
$243$	1677.25	+	3396.43i	0.442779	+	0.896631i
$244$		0			0
$245$	344.971	−	5303.95i	0.0899567	−	1.38309i
$246$		0			0
$247$	−281.858	−	162.731i	−0.0726080	−	0.0419202i
$248$		0			0
$249$	−3214.86	+	1381.63i	−0.818206	+	0.351635i
$250$		0			0
$251$	2525.42			0.635073			0.317536	−	0.948246i	$-0.397144\pi$
$251$	2525.42			0.635073			0.317536	+	0.948246i	$0.397144\pi$
$252$		0			0
$253$	9783.41			2.43114
$254$		0			0
$255$	−2163.67	+	929.868i	−0.531351	+	0.228355i
$256$		0			0
$257$	−3150.04	−	1818.67i	−0.764567	−	0.441423i	0.0663659	−	0.997795i	$-0.478860\pi$
$257$	−3150.04	−	1818.67i	−0.764567	−	0.441423i	−0.830933	+	0.556372i	$0.812193\pi$
$258$		0			0
$259$	−378.431	+	202.397i	−0.0907897	+	0.0485574i
$260$		0			0
$261$	−5805.33	−	5506.64i	−1.37679	−	1.30595i
$262$		0			0
$263$	1194.13	+	2068.30i	0.279975	+	0.484931i	0.971378	−	0.237538i	$-0.0763404\pi$
$263$	1194.13	+	2068.30i	0.279975	+	0.484931i	−0.691403	+	0.722469i	$0.743007\pi$
$264$		0			0
$265$	−4083.97			−0.946703
$266$		0			0
$267$	−6311.25	−	746.285i	−1.44660	−	0.171056i
$268$		0			0
$269$	−1100.78	+	635.534i	−0.249500	+	0.144049i	−0.619535	−	0.784969i	$-0.712679\pi$
$269$	−1100.78	+	635.534i	−0.249500	+	0.144049i	0.370035	+	0.929018i	$0.379346\pi$
$270$		0			0
$271$	1231.53	+	711.026i	0.276053	+	0.159379i	0.631635	−	0.775266i	$-0.282384\pi$
$271$	1231.53	+	711.026i	0.276053	+	0.159379i	−0.355582	+	0.934645i	$0.615717\pi$
$272$		0			0
$273$	3741.95	+	566.209i	0.829571	+	0.125526i
$274$		0			0
$275$	3569.40	−	6182.37i	0.782700	−	1.35568i
$276$		0			0
$277$	−3050.94	−	5284.39i	−0.661781	−	1.14624i	−0.980147	−	0.198271i	$-0.936467\pi$
$277$	−3050.94	−	5284.39i	−0.661781	−	1.14624i	0.318366	−	0.947968i	$-0.396866\pi$
$278$		0			0
$279$	−1430.57	+	5964.49i	−0.306974	+	1.27987i
$280$		0			0
$281$			4248.25i			0.901883i	0.892553	+	0.450942i	$0.148912\pi$
$281$			4248.25i			0.901883i	−0.892553	+	0.450942i	$0.851088\pi$
$282$		0			0
$283$	−2058.65	+	1188.56i	−0.432418	+	0.249657i	−0.700376	−	0.713774i	$-0.746984\pi$
$283$	−2058.65	+	1188.56i	−0.432418	+	0.249657i	0.267958	+	0.963431i	$0.413651\pi$
$284$		0			0
$285$	−533.979	−	398.650i	−0.110983	−	0.0828561i
$286$		0			0
$287$	1718.42	−	2764.99i	0.353433	−	0.568685i
$288$		0			0
$289$	−2028.79	+	3513.96i	−0.412943	+	0.715237i
$290$		0			0
$291$	−3843.92	+	1651.98i	−0.774345	+	0.332785i
$292$		0			0
$293$			4830.23i			0.963089i	0.876422	+	0.481544i	$0.159924\pi$
$293$			4830.23i			0.963089i	−0.876422	+	0.481544i	$0.840076\pi$
$294$		0			0
$295$			2947.13i			0.581657i
$296$		0			0
$297$	8573.21	−	1476.04i	1.67498	−	0.288380i
$298$		0			0
$299$	−3102.44	+	5373.59i	−0.600063	+	1.03934i
$300$		0			0
$301$	2515.93	−	4048.21i	0.481781	−	0.775199i
$302$		0			0
$303$	−532.688	+	713.519i	−0.100997	+	0.135282i
$304$		0			0
$305$	6287.25	−	3629.95i	1.18035	−	0.681476i
$306$		0			0
$307$			1168.04i			0.217144i	0.994089	+	0.108572i	$0.0346279\pi$
$307$			1168.04i			0.217144i	−0.994089	+	0.108572i	$0.965372\pi$
$308$		0			0
$309$	577.232	+	68.2558i	0.106270	+	0.0125661i
$310$		0			0
$311$	3912.59	+	6776.80i	0.713384	+	1.23562i	0.963580	+	0.267422i	$0.0861717\pi$
$311$	3912.59	+	6776.80i	0.713384	+	1.23562i	−0.250196	+	0.968195i	$0.580495\pi$
$312$		0			0
$313$	−4530.57	+	7847.18i	−0.818157	+	1.41709i	0.0888820	+	0.996042i	$0.471671\pi$
$313$	−4530.57	+	7847.18i	−0.818157	+	1.41709i	−0.907039	+	0.421047i	$0.861663\pi$
$314$		0			0
$315$	7472.42	+	2050.97i	1.33658	+	0.366854i
$316$		0			0
$317$	3912.35	+	2258.80i	0.693185	+	0.400211i	0.804804	−	0.593540i	$-0.202270\pi$
$317$	3912.35	+	2258.80i	0.693185	+	0.400211i	−0.111619	+	0.993751i	$0.535604\pi$
$318$		0			0
$319$	−15914.1	+	9188.02i	−2.79316	+	1.61263i
$320$		0			0
$321$	184.367	−	1559.17i	0.0320571	−	0.271104i
$322$		0			0
$323$	242.051			0.0416968
$324$		0			0
$325$	2263.80	+	3921.02i	0.386379	+	0.669227i
$326$		0			0
$327$	7825.31	+	5842.10i	1.32337	+	0.987978i
$328$		0			0
$329$	−6338.65	+	3390.12i	−1.06219	+	0.568096i
$330$		0			0
$331$	1880.65	+	1085.79i	0.312296	+	0.180304i	0.647953	−	0.761680i	$-0.275625\pi$
$331$	1880.65	+	1085.79i	0.312296	+	0.180304i	−0.335657	+	0.941984i	$0.608958\pi$
$332$		0			0
$333$	−177.826	−	599.847i	−0.0292636	−	0.0987129i
$334$		0			0
$335$	−5013.52			−0.817665
$336$		0			0
$337$	6020.96			0.973242			0.486621	−	0.873613i	$-0.338229\pi$
$337$	6020.96			0.973242			0.486621	+	0.873613i	$0.338229\pi$
$338$		0			0
$339$	2898.36	+	6744.08i	0.464358	+	1.08050i
$340$		0			0
$341$	12199.1	+	7043.13i	1.93729	+	1.11850i
$342$		0			0
$343$	617.898	−	6322.33i	0.0972693	−	0.995258i
$344$		0			0
$345$	−7600.23	+	10180.3i	−1.18604	+	1.58866i
$346$		0			0
$347$	−1320.11	−	2286.51i	−0.204229	−	0.353735i	0.745658	−	0.666329i	$-0.232135\pi$
$347$	−1320.11	−	2286.51i	−0.204229	−	0.353735i	−0.949887	+	0.312594i	$0.898802\pi$
$348$		0			0
$349$	−6443.17			−0.988237			−0.494119	−	0.869395i	$-0.664509\pi$
$349$	−6443.17			−0.988237			−0.494119	+	0.869395i	$0.664509\pi$
$350$		0			0
$351$	−1907.95	+	5176.95i	−0.290139	+	0.787251i
$352$		0			0
$353$	−7227.90	+	4173.03i	−1.08981	+	0.629201i	−0.933525	−	0.358511i	$-0.883285\pi$
$353$	−7227.90	+	4173.03i	−1.08981	+	0.629201i	−0.156283	+	0.987712i	$0.549951\pi$
$354$		0			0
$355$	6578.80	+	3798.27i	0.983567	+	0.567863i
$356$		0			0
$357$	−2620.65	+	1026.79i	−0.388514	+	0.152223i
$358$		0			0
$359$	−2028.99	+	3514.31i	−0.298289	+	0.516652i	−0.975745	−	0.218912i	$-0.929749\pi$
$359$	−2028.99	+	3514.31i	−0.298289	+	0.516652i	0.677455	+	0.735564i	$0.263083\pi$
$360$		0			0
$361$	−3395.25	−	5880.75i	−0.495007	−	0.857378i
$362$		0			0
$363$	1533.91	−	12972.1i	0.221789	−	1.87564i
$364$		0			0
$365$		−	14293.2i		−	2.04969i
$366$		0			0
$367$	1528.67	−	882.577i	0.217427	−	0.125532i	−0.387331	−	0.921941i	$-0.626603\pi$
$367$	1528.67	−	882.577i	0.217427	−	0.125532i	0.604759	+	0.796409i	$0.293270\pi$
$368$		0			0
$369$	3443.38	+	3266.21i	0.485786	+	0.460792i
$370$		0			0
$371$	−4878.41	−	158.480i	−0.682681	−	0.0221775i
$372$		0			0
$373$	−720.649	+	1248.20i	−0.100037	+	0.173269i	−0.911700	−	0.410857i	$-0.865229\pi$
$373$	−720.649	+	1248.20i	−0.100037	+	0.173269i	0.811663	+	0.584126i	$0.198563\pi$
$374$		0			0
$375$	−313.836	−	730.253i	−0.0432172	−	0.100560i
$376$		0			0
$377$		−	11654.5i		−	1.59215i
$378$		0			0
$379$			730.381i			0.0989899i	0.998774	+	0.0494949i	$0.0157612\pi$
$379$			730.381i			0.0989899i	−0.998774	+	0.0494949i	$0.984239\pi$
$380$		0			0
$381$	5303.73	+	12341.0i	0.713171	+	1.65945i
$382$		0			0
$383$	6685.33	−	11579.3i	0.891918	−	1.54485i	0.0543443	−	0.998522i	$-0.482693\pi$
$383$	6685.33	−	11579.3i	0.891918	−	1.54485i	0.837573	−	0.546325i	$-0.183974\pi$
$384$		0			0
$385$	9393.44	−	15114.3i	1.24347	−	2.00077i
$386$		0			0
$387$	5041.43	+	4782.04i	0.662197	+	0.628126i
$388$		0			0
$389$	−9056.03	+	5228.50i	−1.18036	+	0.681480i	−0.956097	−	0.293049i	$-0.905330\pi$
$389$	−9056.03	+	5228.50i	−1.18036	+	0.681480i	−0.224260	+	0.974529i	$0.571997\pi$
$390$		0			0
$391$		−	4614.67i		−	0.596865i
$392$		0			0
$393$	498.983	−	4219.84i	0.0640467	−	0.541636i
$394$		0			0
$395$	−3098.07	−	5366.02i	−0.394635	−	0.683528i
$396$		0			0
$397$	1987.76	−	3442.91i	0.251292	−	0.435251i	−0.712590	−	0.701581i	$-0.752478\pi$
$397$	1987.76	−	3442.91i	0.251292	−	0.435251i	0.963882	+	0.266330i	$0.0858112\pi$
$398$		0			0
$399$	−622.383	−	496.920i	−0.0780905	−	0.0623486i
$400$		0			0
$401$	−5977.63	−	3451.18i	−0.744410	−	0.429785i	0.0792605	−	0.996854i	$-0.474744\pi$
$401$	−5977.63	−	3451.18i	−0.744410	−	0.429785i	−0.823671	+	0.567069i	$0.808077\pi$
$402$		0			0
$403$	−7736.96	+	4466.93i	−0.956340	+	0.552143i
$404$		0			0
$405$	−5124.16	+	10067.6i	−0.628696	+	1.23522i
$406$		0			0
$407$	−1436.84			−0.174992
$408$		0			0
$409$	−7287.10	−	12621.6i	−0.880987	−	1.52591i	−0.850245	−	0.526387i	$-0.823546\pi$
$409$	−7287.10	−	12621.6i	−0.880987	−	1.52591i	−0.0307418	−	0.999527i	$-0.509787\pi$
$410$		0			0
$411$	6875.58	−	9209.61i	0.825176	−	1.10530i
$412$		0			0
$413$	−114.364	+	3520.43i	−0.0136259	+	0.419441i
$414$		0			0
$415$	−9037.24	−	5217.65i	−1.06897	−	0.617168i
$416$		0			0
$417$	−1722.05	−	4006.98i	−0.202229	−	0.470558i
$418$		0			0
$419$	−1316.11			−0.153452			−0.0767258	−	0.997052i	$-0.524447\pi$
$419$	−1316.11			−0.153452			−0.0767258	+	0.997052i	$0.524447\pi$
$420$		0			0
$421$	8931.39			1.03394			0.516971	−	0.856003i	$-0.327060\pi$
$421$	8931.39			1.03394			0.516971	+	0.856003i	$0.327060\pi$
$422$		0			0
$423$	−2978.55	−	10047.3i	−0.342369	−	1.15489i
$424$		0			0
$425$	−2916.12	−	1683.62i	−0.332830	−	0.192159i
$426$		0			0
$427$	7651.16	−	4092.09i	0.867132	−	0.463771i
$428$		0			0
$429$	10153.4	+	7580.20i	1.14269	+	0.853089i
$430$		0			0
$431$	3480.15	+	6027.79i	0.388939	+	0.673662i	0.992307	−	0.123801i	$-0.0395083\pi$
$431$	3480.15	+	6027.79i	0.388939	+	0.673662i	−0.603368	+	0.797463i	$0.706175\pi$
$432$		0			0
$433$	6336.46			0.703258			0.351629	−	0.936139i	$-0.385628\pi$
$433$	6336.46			0.703258			0.351629	+	0.936139i	$0.385628\pi$
$434$		0			0
$435$	2802.14	−	23697.3i	0.308855	−	2.61196i
$436$		0			0
$437$	1130.82	−	652.881i	0.123786	−	0.0714681i
$438$		0			0
$439$	−8769.31	−	5062.96i	−0.953385	−	0.550437i	−0.0592543	−	0.998243i	$-0.518872\pi$
$439$	−8769.31	−	5062.96i	−0.953385	−	0.550437i	−0.894131	+	0.447806i	$0.852206\pi$
$440$		0			0
$441$	8846.41	+	2739.90i	0.955233	+	0.295854i
$442$		0			0
$443$	−4446.49	+	7701.54i	−0.476883	+	0.825985i	−0.999649	−	0.0264911i	$-0.991567\pi$
$443$	−4446.49	+	7701.54i	−0.476883	+	0.825985i	0.522766	+	0.852476i	$0.324900\pi$
$444$		0			0
$445$	−9476.34	−	16413.5i	−1.00949	−	1.74848i
$446$		0			0
$447$	−1669.62	−	197.427i	−0.176667	−	0.0208903i
$448$		0			0
$449$		−	543.759i		−	0.0571527i	−0.999592	−	0.0285764i	$-0.990903\pi$
$449$		−	543.759i		−	0.0571527i	0.999592	−	0.0285764i	$-0.00909737\pi$
$450$		0			0
$451$	9439.31	−	5449.79i	0.985542	−	0.569003i
$452$		0			0
$453$	−8041.12	+	10770.8i	−0.834006	+	1.11712i
$454$		0			0
$455$	5322.84	+	9952.34i	0.548437	+	1.02543i
$456$		0			0
$457$	809.155	−	1401.50i	0.0828242	−	0.143456i	−0.821638	−	0.570010i	$-0.806939\pi$
$457$	809.155	−	1401.50i	0.0828242	−	0.143456i	0.904462	+	0.426554i	$0.140273\pi$
$458$		0			0
$459$	−696.225	−	4043.84i	−0.0707996	−	0.411221i
$460$		0			0
$461$		−	3628.16i		−	0.366551i	−0.983062	−	0.183276i	$-0.941330\pi$
$461$		−	3628.16i		−	0.366551i	0.983062	−	0.183276i	$-0.0586701\pi$
$462$		0			0
$463$		−	5409.74i		−	0.543007i	−0.962438	−	0.271503i	$-0.912479\pi$
$463$		−	5409.74i		−	0.543007i	0.962438	−	0.271503i	$-0.0875208\pi$
$464$		0			0
$465$	−16805.7	+	7222.46i	−1.67601	+	0.720287i
$466$		0			0
$467$	1404.77	−	2433.14i	0.139197	−	0.241097i	−0.787996	−	0.615681i	$-0.788881\pi$
$467$	1404.77	−	2433.14i	0.139197	−	0.241097i	0.927193	+	0.374584i	$0.122214\pi$
$468$		0			0
$469$	−5988.78	−	194.551i	−0.589630	−	0.0191546i
$470$		0			0
$471$	144.733	+	108.053i	0.0141591	+	0.0105707i
$472$		0			0
$473$	13820.0	−	7978.99i	1.34344	−	0.775633i
$474$		0			0
$475$		−	952.793i		−	0.0920361i
$476$		0			0
$477$	1659.64	−	6919.56i	0.159307	−	0.664203i
$478$		0			0
$479$	1430.72	+	2478.08i	0.136474	+	0.236380i	0.926160	−	0.377132i	$-0.123090\pi$
$479$	1430.72	+	2478.08i	0.136474	+	0.236380i	−0.789685	+	0.613512i	$0.789756\pi$
$480$		0			0
$481$	455.640	−	789.192i	0.0431921	−	0.0748109i
$482$		0			0
$483$	−9473.73	+	11865.7i	−0.892483	+	1.11782i
$484$		0			0
$485$	−10805.6	−	6238.61i	−1.01166	−	0.584084i
$486$		0			0
$487$	9266.75	−	5350.16i	0.862251	−	0.497821i	−0.00251428	−	0.999997i	$-0.500800\pi$
$487$	9266.75	−	5350.16i	0.862251	−	0.497821i	0.864766	+	0.502176i	$0.167467\pi$
$488$		0			0
$489$	−14421.6	−	1705.30i	−1.33367	−	0.157702i
$490$		0			0
$491$	−12123.5			−1.11431			−0.557154	−	0.830409i	$-0.688107\pi$
$491$	−12123.5			−1.11431			−0.557154	+	0.830409i	$0.688107\pi$
$492$		0			0
$493$	4333.83	+	7506.42i	0.395915	+	0.685745i
$494$		0			0
$495$	18822.6	+	17854.1i	1.70912	+	1.62118i
$496$		0			0
$497$	7711.16	+	4792.43i	0.695961	+	0.432535i
$498$		0			0
$499$	7073.78	+	4084.05i	0.634601	+	0.366387i	0.782532	−	0.622611i	$-0.213928\pi$
$499$	7073.78	+	4084.05i	0.634601	+	0.366387i	−0.147931	+	0.988998i	$0.547261\pi$
$500$		0			0
$501$	12351.1	−	5308.05i	1.10141	−	0.473346i
$502$		0			0
$503$	−4506.57			−0.399479			−0.199740	−	0.979849i	$-0.564010\pi$
$503$	−4506.57			−0.399479			−0.199740	+	0.979849i	$0.564010\pi$
$504$		0			0
$505$	−2655.46			−0.233993
$506$		0			0
$507$	3105.14	−	1334.47i	0.272000	−	0.116896i
$508$		0			0
$509$	4939.09	+	2851.58i	0.430100	+	0.248319i	0.699389	−	0.714741i	$-0.253455\pi$
$509$	4939.09	+	2851.58i	0.430100	+	0.248319i	−0.269289	+	0.963059i	$0.586789\pi$
$510$		0			0
$511$	554.649	−	17073.6i	0.0480161	−	1.47806i
$512$		0			0
$513$	892.440	−	742.730i	0.0768073	−	0.0639227i
$514$		0			0
$515$	866.714	+	1501.19i	0.0741592	+	0.128447i
$516$		0			0
$517$	−24066.8			−2.04731
$518$		0			0
$519$	19054.1	+	2253.08i	1.61152	+	0.190558i
$520$		0			0
$521$	4714.84	−	2722.12i	0.396470	−	0.228902i	−0.288490	−	0.957483i	$-0.593153\pi$
$521$	4714.84	−	2722.12i	0.396470	−	0.228902i	0.684960	+	0.728581i	$0.259820\pi$
$522$		0			0
$523$	−7075.47	−	4085.02i	−0.591565	−	0.341540i	0.174151	−	0.984719i	$-0.444282\pi$
$523$	−7075.47	−	4085.02i	−0.591565	−	0.341540i	−0.765716	+	0.643179i	$0.777615\pi$
$524$		0			0
$525$	4041.79	+	10315.8i	0.335997	+	0.857556i
$526$		0			0
$527$	3322.13	−	5754.10i	0.274600	−	0.475621i
$528$		0			0
$529$	−6363.62	−	11022.1i	−0.523023	−	0.905903i
$530$		0			0
$531$	−4993.39	−	1197.65i	−0.408088	−	0.0978789i
$532$		0			0
$533$			6912.78i			0.561775i
$534$		0			0
$535$	4054.89	−	2341.09i	0.327679	−	0.189185i
$536$		0			0
$537$	6298.25	+	4702.05i	0.506126	+	0.377856i
$538$		0			0
$539$	11807.2	−	17690.0i	0.943550	−	1.41366i
$540$		0			0
$541$	7110.39	−	12315.5i	0.565063	−	0.978719i	−0.431980	−	0.901883i	$-0.642185\pi$
$541$	7110.39	−	12315.5i	0.565063	−	0.978719i	0.997044	−	0.0768356i	$-0.0244817\pi$
$542$		0			0
$543$	11142.0	−	4788.44i	0.880571	−	0.378437i
$544$		0			0
$545$			29123.0i			2.28898i
$546$		0			0
$547$			5348.61i			0.418080i	0.977907	+	0.209040i	$0.0670340\pi$
$547$			5348.61i			0.418080i	−0.977907	+	0.209040i	$0.932966\pi$
$548$		0			0
$549$	3595.30	+	12127.8i	0.279496	+	0.942806i
$550$		0			0
$551$	−1226.30	+	2124.01i	−0.0948131	+	0.164221i
$552$		0			0
$553$	−3492.50	−	6530.08i	−0.268565	−	0.502147i
$554$		0			0
$555$	1116.21	−	1495.12i	0.0853700	−	0.114350i
$556$		0			0
$557$	−19532.6	+	11277.1i	−1.48586	+	0.857859i	−0.999870	−	0.0161074i	$-0.994873\pi$
$557$	−19532.6	+	11277.1i	−1.48586	+	0.857859i	−0.485986	+	0.873967i	$0.661539\pi$
$558$		0			0
$559$			10121.0i			0.765780i
$560$		0			0
$561$	−9358.34	−	1106.59i	−0.704295	−	0.0832807i
$562$		0			0
$563$	2388.36	+	4136.75i	0.178787	+	0.309668i	0.941465	−	0.337110i	$-0.109449\pi$
$563$	2388.36	+	4136.75i	0.178787	+	0.309668i	−0.762678	+	0.646778i	$0.776116\pi$
$564$		0			0
$565$	−10945.5	+	18958.2i	−0.815011	+	1.41164i
$566$		0			0
$567$	−6511.63	+	11827.2i	−0.482298	+	0.876007i
$568$		0			0
$569$	2195.46	+	1267.55i	0.161755	+	0.0933892i	0.578692	−	0.815546i	$-0.303563\pi$
$569$	2195.46	+	1267.55i	0.161755	+	0.0933892i	−0.416937	+	0.908935i	$0.636897\pi$
$570$		0			0
$571$	−12195.9	+	7041.30i	−0.893838	+	0.516058i	−0.875196	−	0.483768i	$-0.839268\pi$
$571$	−12195.9	+	7041.30i	−0.893838	+	0.516058i	−0.0186424	+	0.999826i	$0.505934\pi$
$572$		0			0
$573$	2509.92	−	21226.1i	0.182991	−	1.54753i
$574$		0			0
$575$	−18164.9			−1.31744
$576$		0			0
$577$	−9575.43	−	16585.1i	−0.690867	−	1.19662i	−0.971554	−	0.236818i	$-0.923896\pi$
$577$	−9575.43	−	16585.1i	−0.690867	−	1.19662i	0.280687	−	0.959799i	$-0.409438\pi$
$578$		0			0
$579$	−1263.35	−	943.169i	−0.0906785	−	0.0676974i
$580$		0			0
$581$	−10592.8	−	6583.32i	−0.756388	−	0.470090i
$582$		0			0
$583$	−14152.5	−	8170.93i	−1.00538	−	0.580455i
$584$		0			0
$585$	−15775.4	+	4676.63i	−1.11492	+	0.330521i
$586$		0			0
$587$	25335.1			1.78141			0.890707	−	0.454578i	$-0.150210\pi$
$587$	25335.1			1.78141			0.890707	+	0.454578i	$0.150210\pi$
$588$		0			0
$589$	1880.05			0.131522
$590$		0			0
$591$	−1112.51	−	2588.67i	−0.0774327	−	0.180175i
$592$		0			0
$593$	−2842.14	−	1640.91i	−0.196818	−	0.113633i	0.398353	−	0.917232i	$-0.369582\pi$
$593$	−2842.14	−	1640.91i	−0.196818	−	0.113633i	−0.595170	+	0.803600i	$0.702915\pi$
$594$		0			0
$595$	−7129.17	−	4430.73i	−0.491206	−	0.305281i
$596$		0			0
$597$	−5573.43	+	7465.43i	−0.382086	+	0.511792i
$598$		0			0
$599$	−10423.7	−	18054.4i	−0.711022	−	1.23153i	−0.964474	−	0.264178i	$-0.914899\pi$
$599$	−10423.7	−	18054.4i	−0.711022	−	1.23153i	0.253452	−	0.967348i	$-0.418434\pi$
$600$		0			0
$601$	12158.9			0.825245			0.412623	−	0.910902i	$-0.364613\pi$
$601$	12158.9			0.825245			0.412623	+	0.910902i	$0.364613\pi$
$602$		0			0
$603$	2037.39	−	8494.52i	0.137593	−	0.573671i
$604$		0			0
$605$	33736.2	−	19477.6i	2.26706	−	1.30889i
$606$		0			0
$607$	−4543.08	−	2622.95i	−0.303786	−	0.175391i	0.340356	−	0.940297i	$-0.389452\pi$
$607$	−4543.08	−	2622.95i	−0.303786	−	0.175391i	−0.644142	+	0.764906i	$0.722786\pi$
$608$		0			0
$609$	4266.81	−	28198.4i	0.283908	−	1.87628i
$610$		0			0
$611$	7631.90	−	13218.8i	0.505325	−	0.875249i
$612$		0			0
$613$	9580.88	+	16594.6i	0.631269	+	1.09339i	0.987293	+	0.158913i	$0.0507990\pi$
$613$	9580.88	+	16594.6i	0.631269	+	1.09339i	−0.356023	+	0.934477i	$0.615868\pi$
$614$		0			0
$615$	−1662.06	+	14055.9i	−0.108977	+	0.921605i
$616$		0			0
$617$			14709.4i			0.959768i	0.877332	+	0.479884i	$0.159321\pi$
$617$			14709.4i			0.959768i	−0.877332	+	0.479884i	$0.840679\pi$
$618$		0			0
$619$	−2283.91	+	1318.62i	−0.148301	+	0.0856215i	−0.572314	−	0.820034i	$-0.693954\pi$
$619$	−2283.91	+	1318.62i	−0.148301	+	0.0856215i	0.424013	+	0.905656i	$0.360621\pi$
$620$		0			0
$621$	−14160.1	−	17014.3i	−0.915015	−	1.09945i
$622$		0			0
$623$	−10682.8	−	19974.1i	−0.686995	−	1.28450i
$624$		0			0
$625$	8380.73	−	14515.9i	0.536367	−	0.929015i
$626$		0			0
$627$	−1052.84	−	2449.82i	−0.0670598	−	0.156039i
$628$		0			0
$629$			677.734i			0.0429619i
$630$		0			0
$631$			2852.17i			0.179941i	0.995944	+	0.0899707i	$0.0286773\pi$
$631$			2852.17i			0.179941i	−0.995944	+	0.0899707i	$0.971323\pi$
$632$		0			0
$633$	−1181.46	−	2749.08i	−0.0741843	−	0.172617i
$634$		0			0
$635$	−20029.3	+	34691.7i	−1.25171	+	2.16803i
$636$		0			0
$637$	5972.08	+	12094.9i	0.371463	+	0.752303i
$638$		0			0
$639$	−9108.98	+	9603.07i	−0.563921	+	0.594509i
$640$		0			0
$641$	−7055.43	+	4073.46i	−0.434747	+	0.251001i	−0.701367	−	0.712800i	$-0.747427\pi$
$641$	−7055.43	+	4073.46i	−0.434747	+	0.251001i	0.266620	+	0.963802i	$0.414093\pi$
$642$		0			0
$643$			28066.9i			1.72139i	0.509123	+	0.860694i	$0.329970\pi$
$643$			28066.9i			1.72139i	−0.509123	+	0.860694i	$0.670030\pi$
$644$		0			0
$645$	−2433.41	+	20579.1i	−0.148551	+	1.25628i
$646$		0			0
$647$	7957.81	+	13783.3i	0.483545	+	0.837525i	0.999821	−	0.0188974i	$-0.00601560\pi$
$647$	7957.81	+	13783.3i	0.483545	+	0.837525i	−0.516276	+	0.856422i	$0.672682\pi$
$648$		0			0
$649$	−5896.42	+	10212.9i	−0.356633	+	0.617707i
$650$		0			0
$651$	−20355.1	+	7975.27i	−1.22547	+	0.480147i
$652$		0			0
$653$	1678.98	+	969.357i	0.100618	+	0.0580917i	0.549465	−	0.835517i	$-0.314832\pi$
$653$	1678.98	+	969.357i	0.100618	+	0.0580917i	−0.448847	+	0.893609i	$0.648165\pi$
$654$		0			0
$655$	10974.4	−	6336.10i	0.654667	−	0.377972i
$656$		0			0
$657$	24217.2	+	5808.43i	1.43806	+	0.344914i
$658$		0			0
$659$	10131.9			0.598909			0.299454	−	0.954111i	$-0.403195\pi$
$659$	10131.9			0.598909			0.299454	+	0.954111i	$0.403195\pi$
$660$		0			0
$661$	2055.02	+	3559.40i	0.120924	+	0.209447i	0.920132	−	0.391607i	$-0.128081\pi$
$661$	2055.02	+	3559.40i	0.120924	+	0.209447i	−0.799208	+	0.601054i	$0.794748\pi$
$662$		0			0
$663$	3575.45	−	4789.20i	0.209440	−	0.280539i
$664$		0			0
$665$	77.1169	−	2373.86i	0.00449694	−	0.138427i
$666$		0			0
$667$	40494.0	+	23379.2i	2.35073	+	1.35719i
$668$		0			0
$669$	−672.255	−	1564.24i	−0.0388504	−	0.0903994i
$670$		0			0
$671$	29050.2			1.67134
$672$		0			0
$673$	28029.2			1.60542			0.802709	−	0.596371i	$-0.203391\pi$
$673$	28029.2			1.60542			0.802709	+	0.596371i	$0.203391\pi$
$674$		0			0
$675$	−15917.9	+	2740.58i	−0.907675	+	0.156274i
$676$		0			0
$677$	−8700.06	−	5022.98i	−0.493900	−	0.285154i	0.232291	−	0.972646i	$-0.425378\pi$
$677$	−8700.06	−	5022.98i	−0.493900	−	0.285154i	−0.726191	+	0.687493i	$0.758711\pi$
$678$		0			0
$679$	−12665.5	−	7871.50i	−0.715842	−	0.444890i
$680$		0			0
$681$	14092.3	+	10520.8i	0.792980	+	0.592011i
$682$		0			0
$683$	17116.8	+	29647.1i	0.958938	+	1.66093i	0.725088	+	0.688656i	$0.241799\pi$
$683$	17116.8	+	29647.1i	0.958938	+	1.66093i	0.233850	+	0.972273i	$0.424868\pi$
$684$		0			0
$685$	34274.9			1.91179
$686$		0			0
$687$	2003.60	−	16944.2i	0.111269	−	0.940991i
$688$		0			0
$689$	8975.85	−	5182.21i	0.496303	−	0.286541i
$690$		0			0
$691$	−27128.7	−	15662.8i	−1.49353	−	0.862287i	−0.493553	−	0.869716i	$-0.664302\pi$
$691$	−27128.7	−	15662.8i	−1.49353	−	0.862287i	−0.999972	+	0.00742839i	$0.997635\pi$
$692$		0			0
$693$	21791.2	+	22057.7i	1.19449	+	1.20909i
$694$		0			0
$695$	6503.26	−	11264.0i	0.354939	−	0.614773i
$696$		0			0
$697$	−2570.57	−	4452.36i	−0.139695	−	0.241959i
$698$		0			0
$699$	−25960.4	−	3069.74i	−1.40474	−	0.166106i
$700$		0			0
$701$			16642.7i			0.896699i	0.893858	+	0.448350i	$0.147988\pi$
$701$			16642.7i			0.896699i	−0.893858	+	0.448350i	$0.852012\pi$
$702$		0			0
$703$	−166.078	+	95.8854i	−0.00891005	+	0.00514422i
$704$		0			0
$705$	18696.3	−	25043.1i	0.998784	−	1.33784i
$706$		0			0
$707$	−3172.02	−	103.046i	−0.168736	−	0.00548152i
$708$		0			0
$709$	−9588.94	+	16608.5i	−0.507927	+	0.879756i	0.492031	+	0.870578i	$0.336255\pi$
$709$	−9588.94	+	16608.5i	−0.507927	+	0.879756i	−0.999958	+	0.00917780i	$0.997079\pi$
$710$		0			0
$711$	10350.8	−	3068.50i	0.545969	−	0.161853i
$712$		0			0
$713$		−	35843.0i		−	1.88265i
$714$		0			0
$715$			37787.4i			1.97646i
$716$		0			0
$717$	−16001.3	+	6876.79i	−0.833446	+	0.358185i
$718$		0			0
$719$	−14270.7	+	24717.6i	−0.740205	+	1.28207i	0.212197	+	0.977227i	$0.431938\pi$
$719$	−14270.7	+	24717.6i	−0.740205	+	1.28207i	−0.952402	+	0.304845i	$0.901395\pi$
$720$		0			0
$721$	977.059	+	1826.85i	0.0504682	+	0.0943625i
$722$		0			0
$723$	−17452.3	−	13029.3i	−0.897728	−	0.670212i
$724$		0			0
$725$	29547.8	−	17059.4i	1.51362	−	0.873892i
$726$		0			0
$727$			11364.8i			0.579777i	0.957060	+	0.289889i	$0.0936183\pi$
$727$			11364.8i			0.579777i	−0.957060	+	0.289889i	$0.906382\pi$
$728$		0			0
$729$	−14975.5	−	12773.3i	−0.760832	−	0.648949i
$730$		0			0
$731$	−3763.56	−	6518.67i	−0.190424	−	0.329825i
$732$		0			0
$733$	−4427.68	+	7668.97i	−0.223111	+	0.386439i	−0.955751	−	0.294177i	$-0.904955\pi$
$733$	−4427.68	+	7668.97i	−0.223111	+	0.386439i	0.732640	+	0.680616i	$0.238288\pi$
$734$		0			0
$735$	9235.09	+	26028.6i	0.463458	+	1.30623i
$736$		0			0
$737$	−17373.7	−	10030.7i	−0.868342	−	0.501338i
$738$		0			0
$739$	−15051.7	+	8690.10i	−0.749236	+	0.432572i	−0.825418	−	0.564522i	$-0.809060\pi$
$739$	−15051.7	+	8690.10i	−0.749236	+	0.432572i	0.0761816	+	0.997094i	$0.475727\pi$
$740$		0			0
$741$	1679.45	+	198.589i	0.0832604	+	0.00984528i
$742$		0			0
$743$	−8996.83			−0.444228			−0.222114	−	0.975021i	$-0.571296\pi$
$743$	−8996.83			−0.444228			−0.222114	+	0.975021i	$0.571296\pi$
$744$		0			0
$745$	−2506.93	−	4342.13i	−0.123284	−	0.213534i
$746$		0			0
$747$	12512.9	−	13191.7i	0.612884	−	0.646128i
$748$		0			0
$749$	4934.52	−	2639.15i	0.240726	−	0.128748i
$750$		0			0
$751$	1271.67	+	734.198i	0.0617894	+	0.0356741i	0.530576	−	0.847637i	$-0.321975\pi$
$751$	1271.67	+	734.198i	0.0617894	+	0.0356741i	−0.468787	+	0.883311i	$0.655309\pi$
$752$		0			0
$753$	−12056.3	+	5181.34i	−0.583472	+	0.250755i
$754$		0			0
$755$	−40085.1			−1.93225
$756$		0			0
$757$	6471.73			0.310725			0.155363	−	0.987858i	$-0.450345\pi$
$757$	6471.73			0.310725			0.155363	+	0.987858i	$0.450345\pi$
$758$		0			0
$759$	−46705.6	+	20072.4i	−2.23360	+	0.959921i
$760$		0			0
$761$	−19589.4	−	11310.0i	−0.933135	−	0.538746i	−0.0453332	−	0.998972i	$-0.514435\pi$
$761$	−19589.4	−	11310.0i	−0.933135	−	0.538746i	−0.887802	+	0.460226i	$0.847768\pi$
$762$		0			0
$763$	−1130.12	+	34788.2i	−0.0536216	+	1.65061i
$764$		0			0
$765$	8421.50	−	8878.30i	0.398013	−	0.419602i
$766$		0			0
$767$	−3739.66	−	6477.28i	−0.176051	−	0.304930i
$768$		0			0
$769$	15161.7			0.710981			0.355491	−	0.934680i	$-0.384314\pi$
$769$	15161.7			0.710981			0.355491	+	0.934680i	$0.384314\pi$
$770$		0			0
$771$	18769.4	+	2219.43i	0.876738	+	0.103672i
$772$		0			0
$773$	−20583.0	+	11883.6i	−0.957722	+	0.552941i	−0.895471	−	0.445120i	$-0.853161\pi$
$773$	−20583.0	+	11883.6i	−0.957722	+	0.552941i	−0.0622506	+	0.998061i	$0.519828\pi$
$774$		0			0
$775$	−22650.1	−	13077.0i	−1.04982	−	0.606117i
$776$		0			0
$777$	1391.36	−	1742.65i	0.0642403	−	0.0804598i
$778$		0			0
$779$	727.366	−	1259.84i	0.0334539	−	0.0579439i
$780$		0			0
$781$	15198.6	+	26324.8i	0.696351	+	1.20612i
$782$		0			0
$783$	39012.2	+	14377.8i	1.78057	+	0.656221i
$784$		0			0
$785$			538.645i			0.0244905i
$786$		0			0
$787$	26847.9	−	15500.6i	1.21604	−	0.702082i	0.251972	−	0.967734i	$-0.418921\pi$
$787$	26847.9	−	15500.6i	1.21604	−	0.702082i	0.964069	+	0.265653i	$0.0855875\pi$
$788$		0			0
$789$	−9944.22	−	7424.01i	−0.448699	−	0.334983i
$790$		0			0
$791$	−13810.4	+	22221.3i	−0.620785	+	0.998862i
$792$		0			0
$793$	−9212.19	+	15956.0i	−0.412528	+	0.714519i
$794$		0			0
$795$	19496.7	−	8378.97i	0.869782	−	0.373800i
$796$		0			0
$797$			24322.0i			1.08097i	0.841355	+	0.540483i	$0.181759\pi$
$797$			24322.0i			1.08097i	−0.841355	+	0.540483i	$0.818241\pi$
$798$		0			0
$799$			11351.9i			0.502631i
$800$		0			0
$801$	31660.8	−	9385.88i	1.39660	−	0.414025i
$802$		0			0
$803$	28596.8	−	49531.1i	1.25673	−	2.17673i
$804$		0			0
$805$	−45257.4	−	1470.23i	−1.98151	−	0.0643710i
$806$		0			0
$807$	3951.15	−	5292.44i	0.172351	−	0.230859i
$808$		0			0
$809$	−21704.1	+	12530.9i	−0.943233	+	0.544576i	−0.890972	−	0.454058i	$-0.849976\pi$
$809$	−21704.1	+	12530.9i	−0.943233	+	0.544576i	−0.0522604	+	0.998633i	$0.516643\pi$
$810$		0			0
$811$		−	19821.0i		−	0.858213i	−0.903254	−	0.429106i	$-0.858829\pi$
$811$		−	19821.0i		−	0.858213i	0.903254	−	0.429106i	$-0.141171\pi$
$812$		0			0
$813$	−7338.08	−	867.705i	−0.316553	−	0.0374314i
$814$		0			0
$815$	−21654.0	−	37505.8i	−0.930682	−	1.61199i
$816$		0			0
$817$	1064.93	−	1844.52i	0.0456025	−	0.0789859i
$818$		0			0
$819$	−19025.6	+	4974.19i	−0.811730	+	0.212225i
$820$		0			0
$821$	17330.1	+	10005.6i	0.736694	+	0.425331i	0.820866	−	0.571121i	$-0.193491\pi$
$821$	17330.1	+	10005.6i	0.736694	+	0.425331i	−0.0841719	+	0.996451i	$0.526824\pi$
$822$		0			0
$823$	4394.33	−	2537.07i	0.186120	−	0.107457i	−0.404045	−	0.914739i	$-0.632396\pi$
$823$	4394.33	−	2537.07i	0.186120	−	0.107457i	0.590165	+	0.807283i	$0.299063\pi$
$824$		0			0
$825$	−4355.93	+	36837.6i	−0.183823	+	1.55457i
$826$		0			0
$827$	9791.10			0.411693			0.205846	−	0.978584i	$-0.434005\pi$
$827$	9791.10			0.411693			0.205846	+	0.978584i	$0.434005\pi$
$828$		0			0
$829$	12903.0	+	22348.6i	0.540578	+	0.936308i	0.998871	+	0.0475068i	$0.0151276\pi$
$829$	12903.0	+	22348.6i	0.540578	+	0.936308i	−0.458293	+	0.888801i	$0.651539\pi$
$830$		0			0
$831$	25406.9	+	18967.9i	1.06060	+	0.791804i
$832$		0			0
$833$	−8344.06	−	5569.28i	−0.347064	−	0.231649i
$834$		0			0
$835$	34720.0	+	20045.6i	1.43896	+	0.830786i
$836$		0			0
$837$	−5407.71	−	31409.2i	−0.223319	−	1.29709i
$838$		0			0
$839$	8846.19			0.364010			0.182005	−	0.983298i	$-0.441741\pi$
$839$	8846.19			0.364010			0.182005	+	0.983298i	$0.441741\pi$
$840$		0			0
$841$	−63436.7			−2.60104
$842$		0			0
$843$	−8716.01	−	20280.9i	−0.356103	−	0.828603i
$844$		0			0
$845$	8728.81	+	5039.58i	0.355361	+	0.205168i
$846$		0			0
$847$	41054.6	−	21957.4i	1.66547	−	0.890749i
$848$		0			0
$849$	7389.38	−	9897.84i	0.298708	−	0.400109i
$850$		0			0
$851$	1828.05	+	3166.27i	0.0736365	+	0.127542i
$852$		0			0
$853$	1298.87			0.0521367			0.0260684	−	0.999660i	$-0.491701\pi$
$853$	1298.87			0.0521367			0.0260684	+	0.999660i	$0.491701\pi$
$854$		0			0
$855$	3367.09	+	807.588i	0.134681	+	0.0323028i
$856$		0			0
$857$	−19606.6	+	11319.9i	−0.781506	+	0.451202i	−0.836964	−	0.547259i	$-0.815671\pi$
$857$	−19606.6	+	11319.9i	−0.781506	+	0.451202i	0.0554580	+	0.998461i	$0.482338\pi$
$858$		0			0
$859$	−25436.0	−	14685.5i	−1.01032	−	0.583310i	−0.0990361	−	0.995084i	$-0.531576\pi$
$859$	−25436.0	−	14685.5i	−1.01032	−	0.583310i	−0.911286	+	0.411774i	$0.864909\pi$
$860$		0			0
$861$	−2530.82	+	16725.6i	−0.100174	+	0.662029i
$862$		0			0
$863$	−2314.52	+	4008.87i	−0.0912946	+	0.158127i	−0.908056	−	0.418849i	$-0.862434\pi$
$863$	−2314.52	+	4008.87i	−0.0912946	+	0.158127i	0.816762	+	0.576975i	$0.195767\pi$
$864$		0			0
$865$	28609.7	+	49553.5i	1.12458	+	1.94782i
$866$		0			0
$867$	2475.84	−	20937.9i	0.0969826	−	0.820171i
$868$		0			0
$869$		−	24793.7i		−	0.967856i
$870$		0			0
$871$	11018.8	−	6361.73i	0.428656	−	0.247484i
$872$		0			0
$873$	14961.4	−	15772.9i	0.580030	−	0.611492i
$874$		0			0
$875$	1495.40	−	2406.14i	0.0577757	−	0.0929628i
$876$		0			0
$877$	9245.62	−	16013.9i	0.355989	−	0.616591i	−0.631298	−	0.775541i	$-0.717477\pi$
$877$	9245.62	−	16013.9i	0.355989	−	0.616591i	0.987287	+	0.158949i	$0.0508106\pi$
$878$		0			0
$879$	−9910.04	−	23059.3i	−0.380270	−	0.884836i
$880$		0			0
$881$		−	45563.2i		−	1.74241i	−0.490920	−	0.871205i	$-0.663339\pi$
$881$		−	45563.2i		−	1.74241i	0.490920	−	0.871205i	$-0.336661\pi$
$882$		0			0
$883$		−	9315.02i		−	0.355012i	−0.984120	−	0.177506i	$-0.943197\pi$
$883$		−	9315.02i		−	0.355012i	0.984120	−	0.177506i	$-0.0568029\pi$
$884$		0			0
$885$	−6046.55	−	14069.5i	−0.229664	−	0.534396i
$886$		0			0
$887$	−7972.79	+	13809.3i	−0.301804	+	0.522740i	−0.976545	−	0.215315i	$-0.930922\pi$
$887$	−7972.79	+	13809.3i	−0.301804	+	0.522740i	0.674741	+	0.738055i	$0.264255\pi$
$888$		0			0
$889$	−25271.7	+	40663.0i	−0.953416	+	1.53407i
$890$		0			0
$891$	−37899.8	+	24636.0i	−1.42502	+	0.926303i
$892$		0			0
$893$	−2781.79	+	1606.06i	−0.104243	+	0.0601847i
$894$		0			0
$895$			23439.8i			0.875427i
$896$		0			0
$897$	3786.08	−	32018.5i	0.140929	−	1.19182i
$898$		0			0
$899$	33661.7	+	58303.8i	1.24881	+	2.16300i
$900$		0			0
$901$	−3854.09	+	6675.48i	−0.142507	+	0.246829i
$902$		0			0
$903$	−3705.35	+	24487.8i	−0.136552	+	0.902441i
$904$		0			0
$905$	31321.2	+	18083.3i	1.15044	+	0.664209i
$906$		0			0
$907$	37061.9	−	21397.7i	1.35680	−	0.783351i	0.367613	−	0.929979i	$-0.380175\pi$
$907$	37061.9	−	21397.7i	1.35680	−	0.783351i	0.989192	+	0.146628i	$0.0468419\pi$
$908$		0			0
$909$	1079.12	−	4499.21i	0.0393754	−	0.164169i
$910$		0			0
$911$	2779.49			0.101085			0.0505425	−	0.998722i	$-0.483905\pi$
$911$	2779.49			0.101085			0.0505425	+	0.998722i	$0.483905\pi$
$912$		0			0
$913$	−20878.3	−	36162.2i	−0.756812	−	1.31084i
$914$		0			0
$915$	−22567.6	+	30228.6i	−0.815368	+	1.09216i
$916$		0			0
$917$	13355.1	−	7142.77i	0.480944	−	0.257225i
$918$		0			0
$919$	−37158.9	−	21453.7i	−1.33380	−	0.770068i	−0.347917	−	0.937525i	$-0.613111\pi$
$919$	−37158.9	−	21453.7i	−1.33380	−	0.770068i	−0.985879	+	0.167457i	$0.946444\pi$
$920$		0			0
$921$	−2396.43	−	5576.15i	−0.0857383	−	0.199501i
$922$		0			0
$923$	−19278.7			−0.687505
$924$		0			0
$925$	2667.79			0.0948285
$926$		0			0
$927$	−2895.72	+	858.440i	−0.102597	+	0.0304152i
$928$		0			0
$929$	42949.8	+	24797.1i	1.51683	+	0.875744i	0.999804	+	0.0197758i	$0.00629526\pi$
$929$	42949.8	+	24797.1i	1.51683	+	0.875744i	0.517029	+	0.855968i	$0.327038\pi$
$930$		0			0
$931$	184.236	−	2832.65i	0.00648561	−	0.0997167i
$932$		0			0
$933$	−32582.3	−	24324.8i	−1.14330	−	0.853545i
$934$		0			0
$935$	−14051.6	−	24338.0i	−0.491481	−	0.851271i
$936$		0			0
$937$	−12548.9			−0.437519			−0.218759	−	0.975779i	$-0.570201\pi$
$937$	−12548.9			−0.437519			−0.218759	+	0.975779i	$0.570201\pi$
$938$		0			0
$939$	5528.91	−	46757.3i	0.192150	−	1.62499i
$940$		0			0
$941$	−27024.9	+	15602.9i	−0.936225	+	0.540530i	−0.888775	−	0.458344i	$-0.848443\pi$
$941$	−27024.9	+	15602.9i	−0.936225	+	0.540530i	−0.0474499	+	0.998874i	$0.515109\pi$
$942$		0			0
$943$	−24018.7	−	13867.2i	−0.829433	−	0.478873i
$944$		0			0
$945$	−39880.9	+	5539.72i	−1.37283	+	0.190695i
$946$		0			0
$947$	−16747.1	+	29006.8i	−0.574664	+	0.995348i	0.421413	+	0.906869i	$0.361534\pi$
$947$	−16747.1	+	29006.8i	−0.574664	+	0.995348i	−0.996078	+	0.0884795i	$0.971799\pi$
$948$		0			0
$949$	18136.8	+	31413.8i	0.620385	+	1.07454i
$950$		0			0
$951$	−23311.7	−	2756.54i	−0.794883	−	0.0939924i
$952$		0			0
$953$			26762.2i			0.909667i	0.890576	+	0.454834i	$0.150301\pi$
$953$			26762.2i			0.909667i	−0.890576	+	0.454834i	$0.849699\pi$
$954$		0			0
$955$	55202.3	−	31871.1i	1.87048	−	1.07992i
$956$		0			0
$957$	57122.5	−	76513.7i	1.92947	−	2.58447i
$958$		0			0
$959$	40942.3	+	1330.05i	1.37862	+	0.0447856i
$960$		0			0
$961$	10908.1	−	18893.4i	0.366154	−	0.634197i
$962$		0			0
$963$	2318.74	+	7821.66i	0.0775913	+	0.261734i
$964$		0			0
$965$		−	4701.72i		−	0.156843i
$966$		0			0
$967$			32470.8i			1.07982i	0.841721	+	0.539912i	$0.181543\pi$
$967$			32470.8i			1.07982i	−0.841721	+	0.539912i	$0.818457\pi$
$968$		0			0
$969$	−1155.54	+	496.608i	−0.0383088	+	0.0164637i
$970$		0			0
$971$	21906.6	−	37943.4i	0.724013	−	1.25403i	−0.235366	−	0.971907i	$-0.575629\pi$
$971$	21906.6	−	37943.4i	0.724013	−	1.25403i	0.959379	−	0.282121i	$-0.0910378\pi$
$972$		0			0
$973$	8205.42	−	13202.8i	0.270353	−	0.435006i
$974$		0			0
$975$	−18851.9	−	14074.2i	−0.619225	−	0.462292i
$976$		0			0
$977$	49257.0	−	28438.6i	1.61297	−	0.931249i	0.624294	−	0.781190i	$-0.285387\pi$
$977$	49257.0	−	28438.6i	1.61297	−	0.931249i	0.988677	−	0.150059i	$-0.0479465\pi$
$978$		0			0
$979$		−	75838.5i		−	2.47580i
$980$		0			0
$981$	−49343.7	−	11835.0i	−1.60594	−	0.385180i
$982$		0			0
$983$	28731.5	+	49764.4i	0.932241	+	1.61469i	0.779482	+	0.626425i	$0.215482\pi$
$983$	28731.5	+	49764.4i	0.932241	+	1.61469i	0.152759	+	0.988264i	$0.451184\pi$
$984$		0			0
$985$	4201.36	−	7276.97i	0.135905	−	0.235394i
$986$		0			0
$987$	23305.0	−	29189.1i	0.751577	−	0.941337i
$988$		0			0
$989$	−35165.5	−	20302.8i	−1.13064	−	0.652773i
$990$		0			0
$991$	26263.7	−	15163.4i	0.841871	−	0.486055i	−0.0160287	−	0.999872i	$-0.505102\pi$
$991$	26263.7	−	15163.4i	0.841871	−	0.486055i	0.857900	+	0.513817i	$0.171769\pi$
$992$		0			0
$993$	−11205.8	−	1325.05i	−0.358113	−	0.0423458i
$994$		0			0
$995$	−27783.7			−0.885227
$996$		0			0
$997$	−26930.2	−	46644.5i	−0.855454	−	1.48169i	−0.876223	−	0.481905i	$-0.839945\pi$
$997$	−26930.2	−	46644.5i	−0.855454	−	1.48169i	0.0207692	−	0.999784i	$-0.493388\pi$
$998$		0			0
$999$	2079.62	+	2498.80i	0.0658621	+	0.0791377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.e.191.1	yes	28
3.2	odd	2	inner	336.4.bj.e.191.3	yes	28
4.3	odd	2		336.4.bj.f.191.14	yes	28
7.4	even	3		336.4.bj.f.95.12	yes	28
12.11	even	2		336.4.bj.f.191.12	yes	28
21.11	odd	6		336.4.bj.f.95.14	yes	28
28.11	odd	6	inner	336.4.bj.e.95.3	yes	28
84.11	even	6	inner	336.4.bj.e.95.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.e.95.1	✓	28	84.11	even	6	inner
336.4.bj.e.95.3	yes	28	28.11	odd	6	inner
336.4.bj.e.191.1	yes	28	1.1	even	1	trivial
336.4.bj.e.191.3	yes	28	3.2	odd	2	inner
336.4.bj.f.95.12	yes	28	7.4	even	3
336.4.bj.f.95.14	yes	28	21.11	odd	6
336.4.bj.f.191.12	yes	28	12.11	even	2
336.4.bj.f.191.14	yes	28	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.77395 + 2.05167i) q^{3} +(-13.4200 - 7.74804i) q^{5} +(-15.7299 - 9.77601i) q^{7} +(18.5813 - 19.5892i) q^{9} +(-31.0035 - 53.6997i) q^{11} +39.3264 q^{13} +(79.9629 + 9.45536i) q^{15} +(-25.3292 + 14.6238i) q^{17} +(-7.16713 - 4.13795i) q^{19} +(95.1510 + 14.3977i) q^{21} +(-78.8896 + 136.641i) q^{23} +(57.5644 + 99.7044i) q^{25} +(-48.5157 + 131.641i) q^{27} -296.354i q^{29} +(-196.737 + 113.586i) q^{31} +(258.183 + 192.751i) q^{33} +(135.350 + 253.070i) q^{35} +(11.5861 - 20.0677i) q^{37} +(-187.743 + 80.6849i) q^{39} +175.780i q^{41} +257.358i q^{43} +(-401.139 + 118.918i) q^{45} +(194.065 - 336.131i) q^{47} +(151.859 + 307.551i) q^{49} +(90.9173 - 121.781i) q^{51} +(228.240 - 131.774i) q^{53} +960.866i q^{55} +(42.7053 + 5.04976i) q^{57} +(-95.0928 - 164.706i) q^{59} +(-234.249 + 405.732i) q^{61} +(-483.786 + 126.485i) q^{63} +(-527.761 - 304.703i) q^{65} +(280.189 - 161.767i) q^{67} +(96.2733 - 814.172i) q^{69} -490.223 q^{71} +(461.186 + 798.797i) q^{73} +(-479.370 - 357.881i) q^{75} +(-37.2867 + 1147.78i) q^{77} +(346.282 + 199.926i) q^{79} +(-38.4716 - 727.984i) q^{81} +673.416 q^{83} +453.225 q^{85} +(608.021 + 1414.78i) q^{87} +(1059.20 + 611.531i) q^{89} +(-618.600 - 384.456i) q^{91} +(706.171 - 945.894i) q^{93} +(64.1220 + 111.063i) q^{95} +805.185 q^{97} +(-1628.02 - 390.476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) \) 28 * q - 38 * q^7 - 70 * q^9 + 124 * q^13 + 462 * q^19 + 500 * q^21 + 566 * q^25 - 1266 * q^31 + 64 * q^33 + 338 * q^37 - 1254 * q^39 - 488 * q^45 - 206 * q^49 - 522 * q^51 + 2324 * q^57 - 340 * q^61 + 840 * q^63 - 2934 * q^67 - 776 * q^69 + 2050 * q^73 + 1458 * q^75 - 2070 * q^79 + 910 * q^81 + 2400 * q^85 - 3132 * q^87 + 5170 * q^91 + 714 * q^93 - 3344 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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