LMFDB - Embedded newform 336.4.bj.e.95.14

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			95.14
Character	$\chi$	$=$	336.95
Dual form			336.4.bj.e.191.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.18844 - 0.283083i) q^{3} +(-8.90809 + 5.14309i) q^{5} +(-9.06303 - 16.1512i) q^{7} +(26.8397 - 2.93751i) q^{9} +(-23.0995 + 40.0094i) q^{11} +26.5424 q^{13} +(-44.7631 + 29.2063i) q^{15} +(102.989 + 59.4610i) q^{17} +(142.904 - 82.5056i) q^{19} +(-51.5951 - 81.2339i) q^{21} +(65.7775 + 113.930i) q^{23} +(-9.59729 + 16.6230i) q^{25} +(138.425 - 22.8390i) q^{27} -15.1194i q^{29} +(101.152 + 58.4004i) q^{31} +(-108.524 + 214.126i) q^{33} +(163.801 + 97.2644i) q^{35} +(113.596 + 196.753i) q^{37} +(137.714 - 7.51370i) q^{39} +220.200i q^{41} -338.962i q^{43} +(-223.983 + 164.207i) q^{45} +(-169.340 - 293.305i) q^{47} +(-178.723 + 292.758i) q^{49} +(551.187 + 279.355i) q^{51} +(-660.198 - 381.166i) q^{53} -475.210i q^{55} +(718.092 - 468.529i) q^{57} +(-238.395 + 412.913i) q^{59} +(-148.601 - 257.384i) q^{61} +(-290.694 - 406.871i) q^{63} +(-236.442 + 136.510i) q^{65} +(596.062 + 344.137i) q^{67} +(373.534 + 572.498i) q^{69} +700.236 q^{71} +(-155.048 + 268.552i) q^{73} +(-45.0893 + 88.9642i) q^{75} +(855.552 + 10.4773i) q^{77} +(248.663 - 143.566i) q^{79} +(711.742 - 157.684i) q^{81} +906.485 q^{83} -1223.25 q^{85} +(-4.28003 - 78.4459i) q^{87} +(-616.098 + 355.704i) q^{89} +(-240.555 - 428.692i) q^{91} +(541.355 + 274.372i) q^{93} +(-848.667 + 1469.93i) q^{95} +354.982 q^{97} +(-502.455 + 1141.70i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	5.18844	−	0.283083i	0.998515	−	0.0544793i
$3$	5.18844	−	0.283083i	0.998515	−	0.0544793i
$4$		0			0
$5$	−8.90809	+	5.14309i	−0.796764	+	0.460012i	−0.842338	−	0.538949i	$-0.818821\pi$
$5$	−8.90809	+	5.14309i	−0.796764	+	0.460012i	0.0455745	+	0.998961i	$0.485488\pi$
$6$		0			0
$7$	−9.06303	−	16.1512i	−0.489358	−	0.872083i
$7$	−9.06303	−	16.1512i	−0.489358	−	0.872083i
$8$		0			0
$9$	26.8397	−	2.93751i	0.994064	−	0.108797i
$10$		0			0
$11$	−23.0995	+	40.0094i	−0.633159	+	1.09666i	0.353743	+	0.935343i	$0.384909\pi$
$11$	−23.0995	+	40.0094i	−0.633159	+	1.09666i	−0.986902	+	0.161321i	$0.948425\pi$
$12$		0			0
$13$	26.5424			0.566272			0.283136	−	0.959080i	$-0.408625\pi$
$13$	26.5424			0.566272			0.283136	+	0.959080i	$0.408625\pi$
$14$		0			0
$15$	−44.7631	+	29.2063i	−0.770519	+	0.502736i
$16$		0			0
$17$	102.989	+	59.4610i	1.46933	+	0.848318i	0.999409	−	0.0343895i	$-0.0109487\pi$
$17$	102.989	+	59.4610i	1.46933	+	0.848318i	0.469922	+	0.882708i	$0.344282\pi$
$18$		0			0
$19$	142.904	−	82.5056i	1.72550	−	0.996215i	0.819286	−	0.573385i	$-0.194370\pi$
$19$	142.904	−	82.5056i	1.72550	−	0.996215i	0.906209	−	0.422830i	$-0.138963\pi$
$20$		0			0
$21$	−51.5951	−	81.2339i	−0.536141	−	0.844128i
$22$		0			0
$23$	65.7775	+	113.930i	0.596328	+	1.03287i	0.993358	+	0.115065i	$0.0367077\pi$
$23$	65.7775	+	113.930i	0.596328	+	1.03287i	−0.397030	+	0.917806i	$0.629959\pi$
$24$		0			0
$25$	−9.59729	+	16.6230i	−0.0767784	+	0.132984i
$26$		0			0
$27$	138.425	−	22.8390i	0.986661	−	0.162791i
$28$		0			0
$29$		−	15.1194i		−	0.0968137i	−0.998828	−	0.0484068i	$-0.984586\pi$
$29$		−	15.1194i		−	0.0968137i	0.998828	−	0.0484068i	$-0.0154144\pi$
$30$		0			0
$31$	101.152	+	58.4004i	0.586049	+	0.338355i	0.763534	−	0.645768i	$-0.223463\pi$
$31$	101.152	+	58.4004i	0.586049	+	0.338355i	−0.177485	+	0.984124i	$0.556796\pi$
$32$		0			0
$33$	−108.524	+	214.126i	−0.572473	+	1.12953i
$34$		0			0
$35$	163.801	+	97.2644i	0.791071	+	0.469734i
$36$		0			0
$37$	113.596	+	196.753i	0.504730	+	0.874218i	0.999985	+	0.00547025i	$0.00174124\pi$
$37$	113.596	+	196.753i	0.504730	+	0.874218i	−0.495255	+	0.868748i	$0.664925\pi$
$38$		0			0
$39$	137.714	−	7.51370i	0.565431	−	0.0308501i
$40$		0			0
$41$			220.200i			0.838768i	0.907809	+	0.419384i	$0.137754\pi$
$41$			220.200i			0.838768i	−0.907809	+	0.419384i	$0.862246\pi$
$42$		0			0
$43$		−	338.962i		−	1.20212i	−0.799203	−	0.601061i	$-0.794745\pi$
$43$		−	338.962i		−	1.20212i	0.799203	−	0.601061i	$-0.205255\pi$
$44$		0			0
$45$	−223.983	+	164.207i	−0.741986	+	0.543966i
$46$		0			0
$47$	−169.340	−	293.305i	−0.525547	−	0.910274i	−0.999557	−	0.0297547i	$-0.990527\pi$
$47$	−169.340	−	293.305i	−0.525547	−	0.910274i	0.474010	−	0.880519i	$-0.342806\pi$
$48$		0			0
$49$	−178.723	+	292.758i	−0.521058	+	0.853521i
$50$		0			0
$51$	551.187	+	279.355i	1.51336	+	0.767010i
$52$		0			0
$53$	−660.198	−	381.166i	−1.71104	−	0.987870i	−0.933162	−	0.359456i	$-0.882962\pi$
$53$	−660.198	−	381.166i	−1.71104	−	0.987870i	−0.777879	−	0.628414i	$-0.783704\pi$
$54$		0			0
$55$		−	475.210i		−	1.16504i
$56$		0			0
$57$	718.092	−	468.529i	1.66866	−	1.08874i
$58$		0			0
$59$	−238.395	+	412.913i	−0.526041	+	0.911130i	0.473498	+	0.880795i	$0.342991\pi$
$59$	−238.395	+	412.913i	−0.526041	+	0.911130i	−0.999540	+	0.0303356i	$0.990342\pi$
$60$		0			0
$61$	−148.601	−	257.384i	−0.311908	−	0.540240i	0.666867	−	0.745176i	$-0.267635\pi$
$61$	−148.601	−	257.384i	−0.311908	−	0.540240i	−0.978775	+	0.204936i	$0.934301\pi$
$62$		0			0
$63$	−290.694	−	406.871i	−0.581333	−	0.813666i
$64$		0			0
$65$	−236.442	+	136.510i	−0.451185	+	0.260492i
$66$		0			0
$67$	596.062	+	344.137i	1.08687	+	0.627507i	0.932743	−	0.360543i	$-0.117409\pi$
$67$	596.062	+	344.137i	1.08687	+	0.627507i	0.154132	+	0.988050i	$0.450742\pi$
$68$		0			0
$69$	373.534	+	572.498i	0.651713	+	0.998850i
$70$		0			0
$71$	700.236			1.17046			0.585230	−	0.810867i	$-0.301004\pi$
$71$	700.236			1.17046			0.585230	+	0.810867i	$0.301004\pi$
$72$		0			0
$73$	−155.048	+	268.552i	−0.248590	+	0.430570i	−0.963135	−	0.269020i	$-0.913300\pi$
$73$	−155.048	+	268.552i	−0.248590	+	0.430570i	0.714545	+	0.699589i	$0.246634\pi$
$74$		0			0
$75$	−45.0893	+	88.9642i	−0.0694195	+	0.136969i
$76$		0			0
$77$	855.552	+	10.4773i	1.26622	+	0.0155065i
$78$		0			0
$79$	248.663	−	143.566i	0.354136	−	0.204461i	−0.312369	−	0.949961i	$-0.601123\pi$
$79$	248.663	−	143.566i	0.354136	−	0.204461i	0.666506	+	0.745500i	$0.267789\pi$
$80$		0			0
$81$	711.742	−	157.684i	0.976327	−	0.216302i
$82$		0			0
$83$	906.485			1.19879			0.599395	−	0.800453i	$-0.295408\pi$
$83$	906.485			1.19879			0.599395	+	0.800453i	$0.295408\pi$
$84$		0			0
$85$	−1223.25			−1.56095
$86$		0			0
$87$	−4.28003	−	78.4459i	−0.00527434	−	0.0966699i
$88$		0			0
$89$	−616.098	+	355.704i	−0.733778	+	0.423647i	−0.819803	−	0.572646i	$-0.805917\pi$
$89$	−616.098	+	355.704i	−0.733778	+	0.423647i	0.0860247	+	0.996293i	$0.472584\pi$
$90$		0			0
$91$	−240.555	−	428.692i	−0.277110	−	0.493837i
$92$		0			0
$93$	541.355	+	274.372i	0.603612	+	0.305925i
$94$		0			0
$95$	−848.667	+	1469.93i	−0.916541	+	1.58750i
$96$		0			0
$97$	354.982			0.371576			0.185788	−	0.982590i	$-0.440516\pi$
$97$	354.982			0.371576			0.185788	+	0.982590i	$0.440516\pi$
$98$		0			0
$99$	−502.455	+	1141.70i	−0.510087	+	1.15904i
$100$		0			0
$101$	244.408	+	141.109i	0.240787	+	0.139018i	0.615538	−	0.788107i	$-0.288939\pi$
$101$	244.408	+	141.109i	0.240787	+	0.139018i	−0.374751	+	0.927125i	$0.622272\pi$
$102$		0			0
$103$	−332.881	+	192.189i	−0.318444	+	0.183854i	−0.650699	−	0.759336i	$-0.725524\pi$
$103$	−332.881	+	192.189i	−0.318444	+	0.183854i	0.332255	+	0.943190i	$0.392191\pi$
$104$		0			0
$105$	877.407	+	458.281i	0.815487	+	0.425939i
$106$		0			0
$107$	−453.666	−	785.772i	−0.409883	−	0.709939i	0.584993	−	0.811038i	$-0.301097\pi$
$107$	−453.666	−	785.772i	−0.409883	−	0.709939i	−0.994876	+	0.101100i	$0.967764\pi$
$108$		0			0
$109$	−13.2311	+	22.9170i	−0.0116267	+	0.0201381i	−0.871780	−	0.489897i	$-0.837034\pi$
$109$	−13.2311	+	22.9170i	−0.0116267	+	0.0201381i	0.860154	+	0.510035i	$0.170368\pi$
$110$		0			0
$111$	645.081	+	988.685i	0.551607	+	0.845422i
$112$		0			0
$113$		−	141.133i		−	0.117493i	−0.998273	−	0.0587465i	$-0.981290\pi$
$113$		−	141.133i		−	0.117493i	0.998273	−	0.0587465i	$-0.0187104\pi$
$114$		0			0
$115$	−1171.90	−	676.599i	−0.950266	−	0.548636i
$116$		0			0
$117$	712.391	−	77.9687i	0.562911	−	0.0616086i
$118$		0			0
$119$	26.9699	−	2202.30i	0.0207759	−	1.69651i
$120$		0			0
$121$	−401.671	−	695.714i	−0.301781	−	0.522700i
$122$		0			0
$123$	62.3348	+	1142.49i	0.0456955	+	0.837522i
$124$		0			0
$125$		−	1483.21i		−	1.06130i
$126$		0			0
$127$			83.0109i			0.0580002i	0.999579	+	0.0290001i	$0.00923232\pi$
$127$			83.0109i			0.0580002i	−0.999579	+	0.0290001i	$0.990768\pi$
$128$		0			0
$129$	−95.9544	−	1758.68i	−0.0654908	−	1.20034i
$130$		0			0
$131$	−891.896	−	1544.81i	−0.594850	−	1.03031i	−0.993568	−	0.113236i	$-0.963878\pi$
$131$	−891.896	−	1544.81i	−0.594850	−	1.03031i	0.398719	−	0.917073i	$-0.369455\pi$
$132$		0			0
$133$	−2627.71	−	1560.32i	−1.71317	−	1.01727i
$134$		0			0
$135$	−1115.64	+	915.382i	−0.711250	+	0.583582i
$136$		0			0
$137$	1480.51	+	854.774i	0.923275	+	0.533053i	0.884678	−	0.466202i	$-0.154378\pi$
$137$	1480.51	+	854.774i	0.923275	+	0.533053i	0.0385966	+	0.999255i	$0.487711\pi$
$138$		0			0
$139$		−	1054.62i		−	0.643537i	−0.946818	−	0.321769i	$-0.895723\pi$
$139$		−	1054.62i		−	0.643537i	0.946818	−	0.321769i	$-0.104277\pi$
$140$		0			0
$141$	−961.637	−	1473.86i	−0.574358	−	0.880291i
$142$		0			0
$143$	−613.116	+	1061.95i	−0.358541	+	0.621010i
$144$		0			0
$145$	77.7602	+	134.685i	0.0445354	+	0.0771376i
$146$		0			0
$147$	−844.418	+	1569.55i	−0.473785	+	0.880641i
$148$		0			0
$149$	−1108.12	+	639.771i	−0.609265	+	0.351759i	−0.772678	−	0.634799i	$-0.781083\pi$
$149$	−1108.12	+	639.771i	−0.609265	+	0.351759i	0.163413	+	0.986558i	$0.447750\pi$
$150$		0			0
$151$	−895.560	−	517.052i	−0.482647	−	0.278656i	0.238872	−	0.971051i	$-0.423222\pi$
$151$	−895.560	−	517.052i	−0.482647	−	0.278656i	−0.721519	+	0.692395i	$0.756556\pi$
$152$		0			0
$153$	2938.88	+	1293.38i	1.55290	+	0.683424i
$154$		0			0
$155$	−1201.43			−0.622590
$156$		0			0
$157$	−1357.37	+	2351.04i	−0.690000	+	1.19512i	0.281837	+	0.959462i	$0.409056\pi$
$157$	−1357.37	+	2351.04i	−0.690000	+	1.19512i	−0.971837	+	0.235653i	$0.924277\pi$
$158$		0			0
$159$	−3533.30	−	1790.76i	−1.76232	−	0.893187i
$160$		0			0
$161$	1243.96	−	2094.94i	0.608932	−	1.02549i
$162$		0			0
$163$	−852.102	+	491.962i	−0.409459	+	0.236401i	−0.690557	−	0.723278i	$-0.742635\pi$
$163$	−852.102	+	491.962i	−0.409459	+	0.236401i	0.281098	+	0.959679i	$0.409301\pi$
$164$		0			0
$165$	−134.524	−	2465.60i	−0.0634707	−	1.16331i
$166$		0			0
$167$	1061.36			0.491799			0.245900	−	0.969295i	$-0.420917\pi$
$167$	1061.36			0.491799			0.245900	+	0.969295i	$0.420917\pi$
$168$		0			0
$169$	−1492.50			−0.679336
$170$		0			0
$171$	3593.14	−	2634.21i	1.60687	−	1.17803i
$172$		0			0
$173$	905.923	−	523.035i	0.398127	−	0.229859i	−0.287548	−	0.957766i	$-0.592840\pi$
$173$	905.923	−	523.035i	0.398127	−	0.229859i	0.685676	+	0.727907i	$0.259507\pi$
$174$		0			0
$175$	355.462	+	4.35307i	0.153545	+	0.00188035i
$176$		0			0
$177$	−1120.01	+	2209.86i	−0.475622	+	0.938435i
$178$		0			0
$179$	425.015	−	736.148i	0.177470	−	0.307387i	−0.763543	−	0.645757i	$-0.776542\pi$
$179$	425.015	−	736.148i	0.177470	−	0.307387i	0.941013	+	0.338370i	$0.109875\pi$
$180$		0			0
$181$	−4169.39			−1.71220			−0.856101	−	0.516808i	$-0.827120\pi$
$181$	−4169.39			−1.71220			−0.856101	+	0.516808i	$0.827120\pi$
$182$		0			0
$183$	−843.867	−	1293.35i	−0.340877	−	0.522446i
$184$		0			0
$185$	−2023.84	−	1168.46i	−0.804301	−	0.464363i
$186$		0			0
$187$	−4758.00	+	2747.04i	−1.86064	+	1.07424i
$188$		0			0
$189$	−1623.42	−	2028.73i	−0.624797	−	0.780787i
$190$		0			0
$191$	5.25965	+	9.10997i	0.00199254	+	0.00345118i	0.867020	−	0.498273i	$-0.166032\pi$
$191$	5.25965	+	9.10997i	0.00199254	+	0.00345118i	−0.865027	+	0.501725i	$0.832699\pi$
$192$		0			0
$193$	1099.62	−	1904.59i	0.410115	−	0.710339i	−0.584787	−	0.811187i	$-0.698822\pi$
$193$	1099.62	−	1904.59i	0.410115	−	0.710339i	0.994902	+	0.100847i	$0.0321554\pi$
$194$		0			0
$195$	−1188.12	+	775.206i	−0.436324	+	0.284685i
$196$		0			0
$197$		−	273.840i		−	0.0990371i	−0.998773	−	0.0495185i	$-0.984231\pi$
$197$		−	273.840i		−	0.0990371i	0.998773	−	0.0495185i	$-0.0157687\pi$
$198$		0			0
$199$	553.900	+	319.794i	0.197311	+	0.113918i	0.595401	−	0.803429i	$-0.296993\pi$
$199$	553.900	+	319.794i	0.197311	+	0.113918i	−0.398089	+	0.917347i	$0.630327\pi$
$200$		0			0
$201$	3190.05	+	1616.80i	1.11945	+	0.567363i
$202$		0			0
$203$	−244.196	+	137.027i	−0.0844296	+	0.0473765i
$204$		0			0
$205$	−1132.51	−	1961.56i	−0.385843	−	0.668300i
$206$		0			0
$207$	2100.12	+	2864.63i	0.705162	+	0.961861i
$208$		0			0
$209$			7623.34i			2.52305i
$210$		0			0
$211$		−	4168.54i		−	1.36007i	−0.733181	−	0.680034i	$-0.761965\pi$
$211$		−	4168.54i		−	1.36007i	0.733181	−	0.680034i	$-0.238035\pi$
$212$		0			0
$213$	3633.13	−	198.225i	1.16872	−	0.0637659i
$214$		0			0
$215$	1743.31	+	3019.51i	0.552990	+	0.957807i
$216$		0			0
$217$	26.4888	−	2163.02i	0.00828654	−	0.676660i
$218$		0			0
$219$	−728.436	+	1437.25i	−0.224763	+	0.443473i
$220$		0			0
$221$	2733.59	+	1578.24i	0.832041	+	0.480379i
$222$		0			0
$223$			2173.86i			0.652790i	0.945234	+	0.326395i	$0.105834\pi$
$223$			2173.86i			0.652790i	−0.945234	+	0.326395i	$0.894166\pi$
$224$		0			0
$225$	−208.758	+	474.349i	−0.0618544	+	0.140548i
$226$		0			0
$227$	323.916	−	561.038i	0.0947094	−	0.164041i	−0.814778	−	0.579773i	$-0.803141\pi$
$227$	323.916	−	561.038i	0.0947094	−	0.164041i	0.909487	+	0.415732i	$0.136474\pi$
$228$		0			0
$229$	2312.58	+	4005.51i	0.667335	+	1.15586i	0.978646	+	0.205551i	$0.0658985\pi$
$229$	2312.58	+	4005.51i	0.667335	+	1.15586i	−0.311311	+	0.950308i	$0.600768\pi$
$230$		0			0
$231$	4441.94	−	187.831i	1.26519	−	0.0534995i
$232$		0			0
$233$	4316.55	−	2492.16i	1.21368	−	0.700717i	0.250119	−	0.968215i	$-0.419530\pi$
$233$	4316.55	−	2492.16i	1.21368	−	0.700717i	0.963558	+	0.267498i	$0.0861968\pi$
$234$		0			0
$235$	3016.98	+	1741.86i	0.837474	+	0.483516i
$236$		0			0
$237$	1249.53	−	815.273i	0.342472	−	0.223450i
$238$		0			0
$239$	1928.51			0.521944			0.260972	−	0.965346i	$-0.415957\pi$
$239$	1928.51			0.521944			0.260972	+	0.965346i	$0.415957\pi$
$240$		0			0
$241$	−637.435	+	1104.07i	−0.170377	+	0.295101i	−0.938552	−	0.345139i	$-0.887832\pi$
$241$	−637.435	+	1104.07i	−0.170377	+	0.295101i	0.768175	+	0.640240i	$0.221165\pi$
$242$		0			0
$243$	3648.19	−	1019.62i	0.963093	−	0.269170i
$244$		0			0
$245$	86.4004	−	3527.10i	0.0225303	−	0.919748i
$246$		0			0
$247$	3793.01	−	2189.90i	0.977100	−	0.564129i
$248$		0			0
$249$	4703.24	−	256.610i	1.19701	−	0.0653093i
$250$		0			0
$251$	−6391.89			−1.60738			−0.803690	−	0.595048i	$-0.797133\pi$
$251$	−6391.89			−1.60738			−0.803690	+	0.595048i	$0.797133\pi$
$252$		0			0
$253$	−6077.70			−1.51028
$254$		0			0
$255$	−6346.77	+	346.282i	−1.55863	+	0.0850392i
$256$		0			0
$257$	−4908.79	+	2834.09i	−1.19145	+	0.687882i	−0.958635	−	0.284640i	$-0.908126\pi$
$257$	−4908.79	+	2834.09i	−1.19145	+	0.687882i	−0.232812	+	0.972522i	$0.574793\pi$
$258$		0			0
$259$	2148.28	−	3617.89i	0.515397	−	0.867972i
$260$		0			0
$261$	−44.4133	−	405.800i	−0.0105330	−	0.0962390i
$262$		0			0
$263$	−1633.34	+	2829.03i	−0.382951	+	0.663290i	−0.991483	−	0.130239i	$-0.958426\pi$
$263$	−1633.34	+	2829.03i	−0.382951	+	0.663290i	0.608532	+	0.793530i	$0.291759\pi$
$264$		0			0
$265$	7841.47			1.81773
$266$		0			0
$267$	−3095.89	+	2019.96i	−0.709608	+	0.462993i
$268$		0			0
$269$	−5303.41	−	3061.92i	−1.20206	−	0.694011i	−0.241048	−	0.970513i	$-0.577491\pi$
$269$	−5303.41	−	3061.92i	−1.20206	−	0.694011i	−0.961013	+	0.276503i	$0.910825\pi$
$270$		0			0
$271$	3323.07	−	1918.58i	0.744879	−	0.430056i	−0.0789619	−	0.996878i	$-0.525161\pi$
$271$	3323.07	−	1918.58i	0.744879	−	0.430056i	0.823840	+	0.566822i	$0.191827\pi$
$272$		0			0
$273$	−1369.46	−	2156.14i	−0.303602	−	0.478006i
$274$		0			0
$275$	−443.385	−	767.965i	−0.0972258	−	0.168400i
$276$		0			0
$277$	2231.60	−	3865.25i	0.484058	−	0.838413i	−0.515774	−	0.856724i	$-0.672496\pi$
$277$	2231.60	−	3865.25i	0.484058	−	0.838413i	0.999832	+	0.0183116i	$0.00582907\pi$
$278$		0			0
$279$	2886.46	+	1270.31i	0.619382	+	0.272587i
$280$		0			0
$281$		−	120.474i		−	0.0255761i	−0.999918	−	0.0127881i	$-0.995929\pi$
$281$		−	120.474i		−	0.0255761i	0.999918	−	0.0127881i	$-0.00407068\pi$
$282$		0			0
$283$	−25.9998	−	15.0110i	−0.00546124	−	0.00315305i	0.497267	−	0.867598i	$-0.334337\pi$
$283$	−25.9998	−	15.0110i	−0.00546124	−	0.00315305i	−0.502728	+	0.864445i	$0.667670\pi$
$284$		0			0
$285$	−3987.14	+	7866.91i	−0.828694	+	1.63507i
$286$		0			0
$287$	3556.50	−	1995.68i	0.731475	−	0.410457i
$288$		0			0
$289$	4614.72	+	7992.93i	0.939288	+	1.62689i
$290$		0			0
$291$	1841.80	−	100.489i	0.371025	−	0.0202432i
$292$		0			0
$293$		−	5144.02i		−	1.02565i	−0.858492	−	0.512827i	$-0.828598\pi$
$293$		−	5144.02i		−	1.02565i	0.858492	−	0.512827i	$-0.171402\pi$
$294$		0			0
$295$		−	4904.35i		−	0.967941i
$296$		0			0
$297$	−2283.76	+	6065.86i	−0.446186	+	1.18511i
$298$		0			0
$299$	1745.89	+	3023.98i	0.337684	+	0.584886i
$300$		0			0
$301$	−5474.65	+	3072.03i	−1.04835	+	0.588268i
$302$		0			0
$303$	1308.04	+	662.946i	0.248003	+	0.125694i
$304$		0			0
$305$	2647.50	+	1528.53i	0.497034	+	0.286963i
$306$		0			0
$307$		−	1899.14i		−	0.353060i	−0.984295	−	0.176530i	$-0.943513\pi$
$307$		−	1899.14i		−	0.353060i	0.984295	−	0.176530i	$-0.0564873\pi$
$308$		0			0
$309$	−1672.73	+	1091.39i	−0.307955	+	0.200930i
$310$		0			0
$311$	1249.59	−	2164.35i	0.227838	−	0.394627i	−0.729329	−	0.684163i	$-0.760168\pi$
$311$	1249.59	−	2164.35i	0.227838	−	0.394627i	0.957167	+	0.289536i	$0.0935011\pi$
$312$		0			0
$313$	2677.63	+	4637.79i	0.483542	+	0.837519i	0.999821	−	0.0189010i	$-0.00601672\pi$
$313$	2677.63	+	4637.79i	0.483542	+	0.837519i	−0.516279	+	0.856420i	$0.672683\pi$
$314$		0			0
$315$	4682.10	+	2129.38i	0.837481	+	0.380880i
$316$		0			0
$317$	−4683.20	+	2703.85i	−0.829763	+	0.479064i	−0.853771	−	0.520648i	$-0.825690\pi$
$317$	−4683.20	+	2703.85i	−0.829763	+	0.479064i	0.0240088	+	0.999712i	$0.492357\pi$
$318$		0			0
$319$	604.918	+	349.249i	0.106172	+	0.0612985i
$320$		0			0
$321$	−2576.25	−	3948.50i	−0.447951	−	0.686554i
$322$		0			0
$323$	19623.5			3.38043
$324$		0			0
$325$	−254.735	+	441.215i	−0.0434775	+	0.0753052i
$326$		0			0
$327$	−62.1615	+	122.649i	−0.0105124	+	0.0207416i
$328$		0			0
$329$	−3202.49	+	5393.27i	−0.536654	+	0.903770i
$330$		0			0
$331$	−384.614	+	222.057i	−0.0638680	+	0.0368742i	−0.531594	−	0.846999i	$-0.678407\pi$
$331$	−384.614	+	222.057i	−0.0638680	+	0.0368742i	0.467726	+	0.883874i	$0.345073\pi$
$332$		0			0
$333$	3626.84	+	4947.12i	0.596846	+	0.814115i
$334$		0			0
$335$	−7079.70			−1.15464
$336$		0			0
$337$	−2057.65			−0.332603			−0.166302	−	0.986075i	$-0.553183\pi$
$337$	−2057.65			−0.332603			−0.166302	+	0.986075i	$0.553183\pi$
$338$		0			0
$339$	−39.9524	−	732.262i	−0.00640094	−	0.117319i
$340$		0			0
$341$	−4673.14	+	2698.04i	−0.742124	+	0.428466i
$342$		0			0
$343$	6348.16	+	233.317i	0.999325	+	0.0367286i
$344$		0			0
$345$	−6271.88	−	3178.74i	−0.978744	−	0.496052i
$346$		0			0
$347$	−786.088	+	1361.54i	−0.121612	+	0.210638i	−0.920404	−	0.390970i	$-0.872140\pi$
$347$	−786.088	+	1361.54i	−0.121612	+	0.210638i	0.798791	+	0.601608i	$0.205473\pi$
$348$		0			0
$349$	6576.76			1.00873			0.504364	−	0.863491i	$-0.331727\pi$
$349$	6576.76			1.00873			0.504364	+	0.863491i	$0.331727\pi$
$350$		0			0
$351$	3674.12	−	606.201i	0.558719	−	0.0921841i
$352$		0			0
$353$	−4637.28	−	2677.33i	−0.699199	−	0.403683i	0.107850	−	0.994167i	$-0.465603\pi$
$353$	−4637.28	−	2677.33i	−0.699199	−	0.403683i	−0.807049	+	0.590484i	$0.798937\pi$
$354$		0			0
$355$	−6237.76	+	3601.37i	−0.932581	+	0.538426i
$356$		0			0
$357$	−483.502	−	11434.1i	−0.0716796	−	1.69512i
$358$		0			0
$359$	−2238.44	−	3877.08i	−0.329081	−	0.569985i	0.653249	−	0.757143i	$-0.273406\pi$
$359$	−2238.44	−	3877.08i	−0.329081	−	0.569985i	−0.982330	+	0.187158i	$0.940072\pi$
$360$		0			0
$361$	10184.9	−	17640.7i	1.48489	−	2.57190i
$362$		0			0
$363$	−2280.99	−	3495.96i	−0.329809	−	0.505483i
$364$		0			0
$365$		−	3189.71i		−	0.457417i
$366$		0			0
$367$	6293.20	+	3633.38i	0.895101	+	0.516787i	0.875608	−	0.483023i	$-0.160461\pi$
$367$	6293.20	+	3633.38i	0.895101	+	0.516787i	0.0194937	+	0.999810i	$0.493795\pi$
$368$		0			0
$369$	646.841	+	5910.11i	0.0912552	+	0.833789i
$370$		0			0
$371$	−172.886	+	14117.5i	−0.0241936	+	1.97559i
$372$		0			0
$373$	3548.78	+	6146.66i	0.492624	+	0.853250i	0.999964	−	0.00849638i	$-0.00270451\pi$
$373$	3548.78	+	6146.66i	0.492624	+	0.853250i	−0.507340	+	0.861746i	$0.669371\pi$
$374$		0			0
$375$	−419.871	−	7695.54i	−0.0578188	−	1.05972i
$376$		0			0
$377$		−	401.305i		−	0.0548229i
$378$		0			0
$379$		−	6866.01i		−	0.930562i	−0.885163	−	0.465281i	$-0.845953\pi$
$379$		−	6866.01i		−	0.930562i	0.885163	−	0.465281i	$-0.154047\pi$
$380$		0			0
$381$	23.4990	+	430.697i	0.00315981	+	0.0579141i
$382$		0			0
$383$	−4522.00	−	7832.33i	−0.603299	−	1.04494i	−0.992318	−	0.123714i	$-0.960519\pi$
$383$	−4522.00	−	7832.33i	−0.603299	−	1.04494i	0.389019	−	0.921230i	$-0.372814\pi$
$384$		0			0
$385$	−7675.22	+	4306.85i	−1.01601	+	0.570123i
$386$		0			0
$387$	−995.706	−	9097.65i	−0.130787	−	1.19499i
$388$		0			0
$389$	5996.28	+	3461.95i	0.781551	+	0.451229i	0.836980	−	0.547234i	$-0.184319\pi$
$389$	5996.28	+	3461.95i	0.781551	+	0.451229i	−0.0554287	+	0.998463i	$0.517653\pi$
$390$		0			0
$391$			15644.8i			2.02351i
$392$		0			0
$393$	−5064.85	−	7762.66i	−0.650097	−	0.996372i
$394$		0			0
$395$	−1476.74	+	2557.79i	−0.188109	+	0.325814i
$396$		0			0
$397$	−43.4716	−	75.2951i	−0.00549567	−	0.00951877i	0.863264	−	0.504752i	$-0.168416\pi$
$397$	−43.4716	−	75.2951i	−0.00549567	−	0.00951877i	−0.868760	+	0.495233i	$0.835083\pi$
$398$		0			0
$399$	−14075.4	−	7351.76i	−1.76604	−	0.922427i
$400$		0			0
$401$	6816.88	−	3935.73i	0.848925	−	0.490127i	−0.0113630	−	0.999935i	$-0.503617\pi$
$401$	6816.88	−	3935.73i	0.848925	−	0.490127i	0.860288	+	0.509808i	$0.170284\pi$
$402$		0			0
$403$	2684.83	+	1550.09i	0.331863	+	0.191601i
$404$		0			0
$405$	−5529.28	+	5065.22i	−0.678400	+	0.621463i
$406$		0			0
$407$	−10496.0			−1.27830
$408$		0			0
$409$	−1204.58	+	2086.40i	−0.145630	+	0.252239i	−0.929608	−	0.368550i	$-0.879854\pi$
$409$	−1204.58	+	2086.40i	−0.145630	+	0.252239i	0.783978	+	0.620789i	$0.213188\pi$
$410$		0			0
$411$	7923.51	+	4015.83i	0.950944	+	0.481962i
$412$		0			0
$413$	8829.63	+	108.130i	1.05200	+	0.0128831i
$414$		0			0
$415$	−8075.05	+	4662.13i	−0.955153	+	0.551458i
$416$		0			0
$417$	−298.545	−	5471.83i	−0.0350595	−	0.642582i
$418$		0			0
$419$	−1198.61			−0.139752			−0.0698759	−	0.997556i	$-0.522260\pi$
$419$	−1198.61			−0.139752			−0.0698759	+	0.997556i	$0.522260\pi$
$420$		0			0
$421$	14676.6			1.69903			0.849517	−	0.527560i	$-0.176893\pi$
$421$	14676.6			1.69903			0.849517	+	0.527560i	$0.176893\pi$
$422$		0			0
$423$	−5406.61	−	7374.78i	−0.621462	−	0.847693i
$424$		0			0
$425$	−1976.84	+	1141.33i	−0.225626	+	0.130265i
$426$		0			0
$427$	−2810.29	+	4732.76i	−0.318500	+	0.536381i
$428$		0			0
$429$	−2880.49	+	5683.41i	−0.324176	+	0.639621i
$430$		0			0
$431$	−517.940	+	897.099i	−0.0578847	+	0.100259i	−0.893516	−	0.449032i	$-0.851769\pi$
$431$	−517.940	+	897.099i	−0.0578847	+	0.100259i	0.835631	+	0.549291i	$0.185102\pi$
$432$		0			0
$433$	265.669			0.0294856			0.0147428	−	0.999891i	$-0.495307\pi$
$433$	265.669			0.0294856			0.0147428	+	0.999891i	$0.495307\pi$
$434$		0			0
$435$	441.581	+	676.790i	0.0486717	+	0.0745968i
$436$		0			0
$437$	18799.7	+	10854.0i	2.05792	+	1.18814i
$438$		0			0
$439$	−10568.1	+	6101.48i	−1.14895	+	0.663344i	−0.948630	−	0.316388i	$-0.897530\pi$
$439$	−10568.1	+	6101.48i	−1.14895	+	0.663344i	−0.200315	+	0.979731i	$0.564197\pi$
$440$		0			0
$441$	−3936.89	+	8382.54i	−0.425105	+	0.905144i
$442$		0			0
$443$	−1990.83	−	3448.21i	−0.213515	−	0.369818i	0.739297	−	0.673379i	$-0.235158\pi$
$443$	−1990.83	−	3448.21i	−0.213515	−	0.369818i	−0.952812	+	0.303561i	$0.901824\pi$
$444$		0			0
$445$	3658.84	−	6337.29i	0.389765	−	0.675093i
$446$		0			0
$447$	−5568.28	+	3633.10i	−0.589196	+	0.384429i
$448$		0			0
$449$		−	11976.2i		−	1.25878i	−0.777090	−	0.629390i	$-0.783305\pi$
$449$		−	11976.2i		−	1.25878i	0.777090	−	0.629390i	$-0.216695\pi$
$450$		0			0
$451$	−8810.08	−	5086.50i	−0.919846	−	0.531073i
$452$		0			0
$453$	−4792.92	−	2429.17i	−0.497111	−	0.251948i
$454$		0			0
$455$	4347.68	+	2581.63i	0.447962	+	0.265997i
$456$		0			0
$457$	−7780.24	−	13475.8i	−0.796377	−	1.37937i	−0.921961	−	0.387283i	$-0.873414\pi$
$457$	−7780.24	−	13475.8i	−0.796377	−	1.37937i	0.125584	−	0.992083i	$-0.459920\pi$
$458$		0			0
$459$	15614.3	+	5878.70i	1.58783	+	0.597808i
$460$		0			0
$461$		−	3643.51i		−	0.368102i	−0.982917	−	0.184051i	$-0.941079\pi$
$461$		−	3643.51i		−	0.368102i	0.982917	−	0.184051i	$-0.0589212\pi$
$462$		0			0
$463$			6689.74i			0.671487i	0.941953	+	0.335744i	$0.108988\pi$
$463$			6689.74i			0.671487i	−0.941953	+	0.335744i	$0.891012\pi$
$464$		0			0
$465$	−6233.56	+	340.105i	−0.621665	+	0.0339183i
$466$		0			0
$467$	−3809.87	−	6598.88i	−0.377515	−	0.653876i	0.613185	−	0.789940i	$-0.289888\pi$
$467$	−3809.87	−	6598.88i	−0.377515	−	0.653876i	−0.990700	+	0.136064i	$0.956555\pi$
$468$		0			0
$469$	156.091	−	12746.0i	0.0153681	−	1.25492i
$470$		0			0
$471$	−6377.10	+	12582.4i	−0.623866	+	1.23093i
$472$		0			0
$473$	13561.7	+	7829.85i	1.31832	+	0.761135i
$474$		0			0
$475$			3167.32i			0.305951i
$476$		0			0
$477$	−18839.2	−	8291.04i	−1.80836	−	0.795850i
$478$		0			0
$479$	7645.37	−	13242.2i	0.729281	−	1.26315i	−0.227906	−	0.973683i	$-0.573188\pi$
$479$	7645.37	−	13242.2i	0.729281	−	1.26315i	0.957187	−	0.289469i	$-0.0934788\pi$
$480$		0			0
$481$	3015.10	+	5222.31i	0.285815	+	0.495045i
$482$		0			0
$483$	5861.18	−	11221.6i	0.552159	−	1.05714i
$484$		0			0
$485$	−3162.21	+	1825.70i	−0.296059	+	0.170930i
$486$		0			0
$487$	8234.35	+	4754.10i	0.766189	+	0.442359i	0.831513	−	0.555505i	$-0.187475\pi$
$487$	8234.35	+	4754.10i	0.766189	+	0.442359i	−0.0653246	+	0.997864i	$0.520808\pi$
$488$		0			0
$489$	−4281.81	+	2793.73i	−0.395972	+	0.258357i
$490$		0			0
$491$	−8714.87			−0.801011			−0.400505	−	0.916294i	$-0.631165\pi$
$491$	−8714.87			−0.801011			−0.400505	+	0.916294i	$0.631165\pi$
$492$		0			0
$493$	899.013	−	1557.14i	0.0821288	−	0.142251i
$494$		0			0
$495$	−1395.94	−	12754.5i	−0.126753	−	1.15813i
$496$		0			0
$497$	−6346.26	−	11309.7i	−0.572774	−	1.02074i
$498$		0			0
$499$	−13070.1	+	7546.00i	−1.17254	+	0.676965i	−0.954277	−	0.298925i	$-0.903372\pi$
$499$	−13070.1	+	7546.00i	−1.17254	+	0.676965i	−0.218261	+	0.975890i	$0.570039\pi$
$500$		0			0
$501$	5506.80	−	300.453i	0.491069	−	0.0267929i
$502$		0			0
$503$	−331.156			−0.0293549			−0.0146775	−	0.999892i	$-0.504672\pi$
$503$	−331.156			−0.0293549			−0.0146775	+	0.999892i	$0.504672\pi$
$504$		0			0
$505$	−2902.94			−0.255800
$506$		0			0
$507$	−7743.74	+	422.501i	−0.678327	+	0.0370097i
$508$		0			0
$509$	−12688.4	+	7325.67i	−1.10492	+	0.637926i	−0.937509	−	0.347961i	$-0.886874\pi$
$509$	−12688.4	+	7325.67i	−1.10492	+	0.637926i	−0.167412	+	0.985887i	$0.553541\pi$
$510$		0			0
$511$	5742.64	+	70.3258i	0.497142	+	0.00608812i
$512$		0			0
$513$	17897.1	−	14684.6i	1.54030	−	1.26382i
$514$		0			0
$515$	1976.89	−	3424.08i	0.169150	−	0.292976i
$516$		0			0
$517$	15646.6			1.33102
$518$		0			0
$519$	4552.26	−	2970.18i	0.385014	−	0.251207i
$520$		0			0
$521$	−7534.02	−	4349.77i	−0.633534	−	0.365771i	0.148585	−	0.988900i	$-0.452528\pi$
$521$	−7534.02	−	4349.77i	−0.633534	−	0.365771i	−0.782120	+	0.623128i	$0.785861\pi$
$522$		0			0
$523$	−11948.8	+	6898.65i	−0.999015	+	0.576782i	−0.907957	−	0.419064i	$-0.862358\pi$
$523$	−11948.8	+	6898.65i	−0.999015	+	0.576782i	−0.0910584	+	0.995846i	$0.529025\pi$
$524$		0			0
$525$	1845.52	−	78.0396i	0.153420	−	0.00648748i
$526$		0			0
$527$	6945.09	+	12029.3i	0.574066	+	0.994312i
$528$		0			0
$529$	−2569.86	+	4451.12i	−0.211215	+	0.365835i
$530$		0			0
$531$	−5185.53	+	11782.8i	−0.423791	+	0.962953i
$532$		0			0
$533$			5844.64i			0.474971i
$534$		0			0
$535$	8082.59	+	4666.48i	0.653160	+	0.377102i
$536$		0			0
$537$	1996.77	−	3939.77i	0.160460	−	0.316599i
$538$		0			0
$539$	−7584.67	−	13913.2i	−0.606113	−	1.11184i
$540$		0			0
$541$	4621.58	+	8004.81i	0.367278	+	0.636144i	0.989139	−	0.146984i	$-0.0469565\pi$
$541$	4621.58	+	8004.81i	0.367278	+	0.636144i	−0.621861	+	0.783128i	$0.713623\pi$
$542$		0			0
$543$	−21632.6	+	1180.28i	−1.70966	+	0.0932796i
$544$		0			0
$545$		−	272.196i		−	0.0213937i
$546$		0			0
$547$		−	3127.25i		−	0.244445i	−0.992503	−	0.122223i	$-0.960998\pi$
$547$		−	3127.25i		−	0.244445i	0.992503	−	0.122223i	$-0.0390022\pi$
$548$		0			0
$549$	−4744.48	−	6471.60i	−0.368833	−	0.503099i
$550$		0			0
$551$	−1247.43	−	2160.62i	−0.0964472	−	0.167052i
$552$		0			0
$553$	−4572.40	−	2715.07i	−0.351606	−	0.208782i
$554$		0			0
$555$	−10831.3	−	5489.59i	−0.828405	−	0.419856i
$556$		0			0
$557$	−17984.4	−	10383.3i	−1.36809	−	0.789866i	−0.377405	−	0.926048i	$-0.623183\pi$
$557$	−17984.4	−	10383.3i	−1.36809	−	0.789866i	−0.990684	+	0.136182i	$0.956517\pi$
$558$		0			0
$559$		−	8996.88i		−	0.680729i
$560$		0			0
$561$	−23909.0	+	15599.7i	−1.79935	+	1.17401i
$562$		0			0
$563$	−3127.18	+	5416.43i	−0.234094	+	0.405462i	−0.959009	−	0.283376i	$-0.908546\pi$
$563$	−3127.18	+	5416.43i	−0.234094	+	0.405462i	0.724915	+	0.688838i	$0.241879\pi$
$564$		0			0
$565$	725.861	+	1257.23i	0.0540482	+	0.0936142i
$566$		0			0
$567$	−8997.33	−	10066.4i	−0.666406	−	0.745589i
$568$		0			0
$569$	−6412.61	+	3702.32i	−0.472462	+	0.272776i	−0.717270	−	0.696796i	$-0.754608\pi$
$569$	−6412.61	+	3702.32i	−0.472462	+	0.272776i	0.244808	+	0.969572i	$0.421275\pi$
$570$		0			0
$571$	−17462.8	−	10082.1i	−1.27985	−	0.738922i	−0.303029	−	0.952981i	$-0.597998\pi$
$571$	−17462.8	−	10082.1i	−1.27985	−	0.738922i	−0.976821	+	0.214060i	$0.931331\pi$
$572$		0			0
$573$	29.8682	+	45.7776i	0.00217760	+	0.00333750i
$574$		0			0
$575$	−2525.14			−0.183140
$576$		0			0
$577$	−11609.9	+	20109.0i	−0.837655	+	1.45086i	0.0541958	+	0.998530i	$0.482740\pi$
$577$	−11609.9	+	20109.0i	−0.837655	+	1.45086i	−0.891851	+	0.452330i	$0.850593\pi$
$578$		0			0
$579$	5166.13	−	10193.1i	0.370807	−	0.731627i
$580$		0			0
$581$	−8215.50	−	14640.8i	−0.586638	−	1.04545i
$582$		0			0
$583$	30500.4	−	17609.4i	2.16672	−	1.25096i
$584$		0			0
$585$	−5945.04	+	4358.44i	−0.420166	+	0.308033i
$586$		0			0
$587$	18902.3			1.32910			0.664548	−	0.747245i	$-0.268624\pi$
$587$	18902.3			1.32910			0.664548	+	0.747245i	$0.268624\pi$
$588$		0			0
$589$	19273.4			1.34830
$590$		0			0
$591$	−77.5194	−	1420.80i	−0.00539547	−	0.0988900i
$592$		0			0
$593$	7207.29	−	4161.13i	0.499103	−	0.288157i	−0.229240	−	0.973370i	$-0.573624\pi$
$593$	7207.29	−	4161.13i	0.499103	−	0.288157i	0.728343	+	0.685213i	$0.240291\pi$
$594$		0			0
$595$	11086.4	+	19757.0i	0.763861	+	1.36127i
$596$		0			0
$597$	2964.40	+	1502.43i	0.203224	+	0.102999i
$598$		0			0
$599$	5083.16	−	8804.29i	0.346732	−	0.600557i	−0.638935	−	0.769261i	$-0.720625\pi$
$599$	5083.16	−	8804.29i	0.346732	−	0.600557i	0.985667	+	0.168704i	$0.0539581\pi$
$600$		0			0
$601$	7382.80			0.501082			0.250541	−	0.968106i	$-0.419391\pi$
$601$	7382.80			0.501082			0.250541	+	0.968106i	$0.419391\pi$
$602$		0			0
$603$	17009.1	+	7485.59i	1.14869	+	0.505534i
$604$		0			0
$605$	7156.24	+	4131.66i	0.480896	+	0.277646i
$606$		0			0
$607$	−22555.6	+	13022.5i	−1.50825	+	0.870786i	−0.508292	+	0.861185i	$0.669723\pi$
$607$	−22555.6	+	13022.5i	−1.50825	+	0.870786i	−0.999954	+	0.00960128i	$0.996944\pi$
$608$		0			0
$609$	−1228.21	+	780.085i	−0.0817231	+	0.0519058i
$610$		0			0
$611$	−4494.68	−	7785.01i	−0.297603	−	0.515463i
$612$		0			0
$613$	13474.9	−	23339.3i	0.887843	−	1.53779i	0.0454229	−	0.998968i	$-0.485536\pi$
$613$	13474.9	−	23339.3i	0.887843	−	1.53779i	0.842420	−	0.538821i	$-0.181130\pi$
$614$		0			0
$615$	−6431.23	−	9856.84i	−0.421678	−	0.646287i
$616$		0			0
$617$		−	14682.5i		−	0.958015i	−0.877811	−	0.479008i	$-0.840997\pi$
$617$		−	14682.5i		−	0.958015i	0.877811	−	0.479008i	$-0.159003\pi$
$618$		0			0
$619$	1044.45	+	603.014i	0.0678191	+	0.0391554i	0.533526	−	0.845784i	$-0.320867\pi$
$619$	1044.45	+	603.014i	0.0678191	+	0.0391554i	−0.465707	+	0.884939i	$0.654200\pi$
$620$		0			0
$621$	11707.3	+	14268.4i	0.756516	+	0.922016i
$622$		0			0
$623$	11328.8	+	6726.96i	0.728535	+	0.432600i
$624$		0			0
$625$	6428.62	+	11134.7i	0.411432	+	0.712621i
$626$		0			0
$627$	2158.04	+	39553.2i	0.137454	+	2.51930i
$628$		0			0
$629$			27018.0i			1.71269i
$630$		0			0
$631$		−	13176.2i		−	0.831278i	−0.909530	−	0.415639i	$-0.863558\pi$
$631$		−	13176.2i		−	0.831278i	0.909530	−	0.415639i	$-0.136442\pi$
$632$		0			0
$633$	−1180.04	−	21628.2i	−0.0740956	−	1.35805i
$634$		0			0
$635$	−426.932	−	739.469i	−0.0266808	−	0.0462125i
$636$		0			0
$637$	−4743.74	+	7770.50i	−0.295061	+	0.483326i
$638$		0			0
$639$	18794.1	−	2056.95i	1.16351	−	0.127342i
$640$		0			0
$641$	−1227.53	−	708.712i	−0.0756386	−	0.0436700i	0.461704	−	0.887034i	$-0.347238\pi$
$641$	−1227.53	−	708.712i	−0.0756386	−	0.0436700i	−0.537342	+	0.843364i	$0.680572\pi$
$642$		0			0
$643$		−	25482.4i		−	1.56287i	−0.623986	−	0.781435i	$-0.714488\pi$
$643$		−	25482.4i		−	1.56287i	0.623986	−	0.781435i	$-0.285512\pi$
$644$		0			0
$645$	9899.83	+	15173.0i	0.604350	+	0.926258i
$646$		0			0
$647$	−14423.4	+	24982.1i	−0.876419	+	1.51800i	−0.0211764	+	0.999776i	$0.506741\pi$
$647$	−14423.4	+	24982.1i	−0.876419	+	1.51800i	−0.855243	+	0.518227i	$0.826592\pi$
$648$		0			0
$649$	−11013.6	−	19076.1i	−0.666136	−	1.15378i
$650$		0			0
$651$	−474.878	−	11230.2i	−0.0285897	−	0.676107i
$652$		0			0
$653$	−12400.6	+	7159.50i	−0.743145	+	0.429055i	−0.823212	−	0.567734i	$-0.807820\pi$
$653$	−12400.6	+	7159.50i	−0.743145	+	0.429055i	0.0800665	+	0.996790i	$0.474487\pi$
$654$		0			0
$655$	15890.2	+	9174.20i	0.947909	+	0.547276i
$656$		0			0
$657$	−3372.58	+	7663.31i	−0.200269	+	0.455060i
$658$		0			0
$659$	−14347.2			−0.848087			−0.424044	−	0.905642i	$-0.639390\pi$
$659$	−14347.2			−0.848087			−0.424044	+	0.905642i	$0.639390\pi$
$660$		0			0
$661$	4791.01	−	8298.28i	0.281920	−	0.488299i	−0.689938	−	0.723868i	$-0.742362\pi$
$661$	4791.01	−	8298.28i	0.281920	−	0.488299i	0.971857	+	0.235570i	$0.0756955\pi$
$662$		0			0
$663$	14629.8	+	7414.76i	0.856976	+	0.434337i
$664$		0			0
$665$	31432.7	+	384.933i	1.83295	+	0.0224467i
$666$		0			0
$667$	1722.55	−	994.514i	0.0999960	−	0.0577327i
$668$		0			0
$669$	615.381	+	11278.9i	0.0355635	+	0.651820i
$670$		0			0
$671$	13730.4			0.789950
$672$		0			0
$673$	−14186.2			−0.812536			−0.406268	−	0.913754i	$-0.633170\pi$
$673$	−14186.2			−0.812536			−0.406268	+	0.913754i	$0.633170\pi$
$674$		0			0
$675$	−948.850	+	2520.23i	−0.0541056	+	0.143709i
$676$		0			0
$677$	29942.4	−	17287.3i	1.69982	−	0.981394i	0.753911	−	0.656977i	$-0.228165\pi$
$677$	29942.4	−	17287.3i	1.69982	−	0.981394i	0.945914	−	0.324417i	$-0.105168\pi$
$678$		0			0
$679$	−3217.21	−	5733.38i	−0.181834	−	0.324046i
$680$		0			0
$681$	1521.79	−	3002.61i	0.0856319	−	0.168958i
$682$		0			0
$683$	−9232.44	+	15991.1i	−0.517232	+	0.895873i	0.482567	+	0.875859i	$0.339704\pi$
$683$	−9232.44	+	15991.1i	−0.517232	+	0.895873i	−0.999800	+	0.0200138i	$0.993629\pi$
$684$		0			0
$685$	−17584.7			−0.980843
$686$		0			0
$687$	13132.6	+	20127.7i	0.729315	+	1.11779i
$688$		0			0
$689$	−17523.3	−	10117.1i	−0.968915	−	0.559404i
$690$		0			0
$691$	9805.41	−	5661.16i	0.539820	−	0.311665i	−0.205186	−	0.978723i	$-0.565780\pi$
$691$	9805.41	−	5661.16i	0.539820	−	0.311665i	0.745006	+	0.667058i	$0.232447\pi$
$692$		0			0
$693$	22993.6	−	2231.99i	1.26039	−	0.122347i
$694$		0			0
$695$	5424.00	+	9394.65i	0.296035	+	0.512747i
$696$		0			0
$697$	−13093.3	+	22678.3i	−0.711542	+	1.23243i
$698$		0			0
$699$	21690.7	−	14152.4i	1.17370	−	0.765797i
$700$		0			0
$701$			30474.6i			1.64196i	0.570960	+	0.820978i	$0.306571\pi$
$701$			30474.6i			1.64196i	−0.570960	+	0.820978i	$0.693429\pi$
$702$		0			0
$703$	32466.5	+	18744.6i	1.74182	+	1.00564i
$704$		0			0
$705$	16146.5	+	8183.45i	0.862571	+	0.437173i
$706$		0			0
$707$	64.0032	−	5226.35i	0.00340465	−	0.278016i
$708$		0			0
$709$	1460.53	+	2529.71i	0.0773642	+	0.133999i	0.902112	−	0.431502i	$-0.142016\pi$
$709$	1460.53	+	2529.71i	0.0773642	+	0.133999i	−0.824748	+	0.565501i	$0.808683\pi$
$710$		0			0
$711$	6252.32	−	4583.71i	0.329790	−	0.241776i
$712$		0			0
$713$			15365.7i			0.807084i
$714$		0			0
$715$		−	12613.2i		−	0.659732i
$716$		0			0
$717$	10005.9	−	545.927i	0.521169	−	0.0284352i
$718$		0			0
$719$	12648.1	+	21907.2i	0.656043	+	1.13630i	0.981631	+	0.190788i	$0.0611044\pi$
$719$	12648.1	+	21907.2i	0.656043	+	1.13630i	−0.325588	+	0.945512i	$0.605562\pi$
$720$		0			0
$721$	6121.00	+	3634.62i	0.316169	+	0.187740i
$722$		0			0
$723$	−2994.75	+	5908.85i	−0.154047	+	0.303945i
$724$		0			0
$725$	251.329	+	145.105i	0.0128747	+	0.00743319i
$726$		0			0
$727$			16158.5i			0.824326i	0.911110	+	0.412163i	$0.135227\pi$
$727$			16158.5i			0.824326i	−0.911110	+	0.412163i	$0.864773\pi$
$728$		0			0
$729$	18639.8	−	6322.95i	0.946998	−	0.321239i
$730$		0			0
$731$	20155.0	−	34909.5i	1.01978	−	1.76631i
$732$		0			0
$733$	12158.6	+	21059.2i	0.612669	+	1.06117i	0.990789	+	0.135418i	$0.0432376\pi$
$733$	12158.6	+	21059.2i	0.612669	+	1.06117i	−0.378119	+	0.925757i	$0.623429\pi$
$734$		0			0
$735$	−550.178	−	18324.6i	−0.0276104	−	0.919609i
$736$		0			0
$737$	−27537.4	+	15898.7i	−1.37633	+	0.794624i
$738$		0			0
$739$	−11107.7	−	6413.05i	−0.552915	−	0.319226i	0.197382	−	0.980327i	$-0.436756\pi$
$739$	−11107.7	−	6413.05i	−0.552915	−	0.319226i	−0.750297	+	0.661101i	$0.770089\pi$
$740$		0			0
$741$	19059.9	−	12435.9i	0.944916	−	0.616523i
$742$		0			0
$743$	−20204.7			−0.997630			−0.498815	−	0.866708i	$-0.666231\pi$
$743$	−20204.7			−0.997630			−0.498815	+	0.866708i	$0.666231\pi$
$744$		0			0
$745$	6580.80	−	11398.3i	0.323627	−	0.560538i
$746$		0			0
$747$	24329.8	−	2662.81i	1.19167	−	0.130425i
$748$		0			0
$749$	−8579.58	+	14448.7i	−0.418546	+	0.704866i
$750$		0			0
$751$	18460.2	−	10658.0i	0.896966	−	0.517863i	0.0207513	−	0.999785i	$-0.493394\pi$
$751$	18460.2	−	10658.0i	0.896966	−	0.517863i	0.876215	+	0.481921i	$0.160061\pi$
$752$		0			0
$753$	−33163.9	+	1809.43i	−1.60499	+	0.0875689i
$754$		0			0
$755$	10637.0			0.512740
$756$		0			0
$757$	−13791.8			−0.662183			−0.331091	−	0.943599i	$-0.607417\pi$
$757$	−13791.8			−0.662183			−0.331091	+	0.943599i	$0.607417\pi$
$758$		0			0
$759$	−31533.8	+	1720.49i	−1.50804	+	0.0822792i
$760$		0			0
$761$	−4722.71	+	2726.66i	−0.224965	+	0.129883i	−0.608247	−	0.793748i	$-0.708127\pi$
$761$	−4722.71	+	2726.66i	−0.224965	+	0.129883i	0.383282	+	0.923631i	$0.374794\pi$
$762$		0			0
$763$	490.052	+	6.00129i	0.0232517	+	0.000284746i
$764$		0			0
$765$	−32831.8	+	3593.32i	−1.55168	+	0.169826i
$766$		0			0
$767$	−6327.59	+	10959.7i	−0.297883	+	0.515948i
$768$		0			0
$769$	−55.4518			−0.00260032			−0.00130016	−	0.999999i	$-0.500414\pi$
$769$	−55.4518			−0.00260032			−0.00130016	+	0.999999i	$0.500414\pi$
$770$		0			0
$771$	−24666.6	+	16094.1i	−1.15220	+	0.751770i
$772$		0			0
$773$	8936.18	+	5159.30i	0.415798	+	0.240061i	0.693278	−	0.720670i	$-0.256166\pi$
$773$	8936.18	+	5159.30i	0.415798	+	0.240061i	−0.277480	+	0.960731i	$0.589499\pi$
$774$		0			0
$775$	−1941.58	+	1120.97i	−0.0899917	+	0.0519568i
$776$		0			0
$777$	10122.1	−	19379.3i	0.467345	−	0.894761i
$778$		0			0
$779$	18167.7	+	31467.5i	0.835593	+	1.44729i
$780$		0			0
$781$	−16175.1	+	28016.0i	−0.741088	+	1.28360i
$782$		0			0
$783$	−345.311	−	2092.89i	−0.0157604	−	0.0955222i
$784$		0			0
$785$		−	27924.3i		−	1.26963i
$786$		0			0
$787$	3830.02	+	2211.27i	0.173476	+	0.100156i	0.584224	−	0.811593i	$-0.301399\pi$
$787$	3830.02	+	2211.27i	0.173476	+	0.100156i	−0.410748	+	0.911749i	$0.634732\pi$
$788$		0			0
$789$	−7673.63	+	15140.6i	−0.346247	+	0.683168i
$790$		0			0
$791$	−2279.47	+	1279.10i	−0.102464	+	0.0574961i
$792$		0			0
$793$	−3944.22	−	6831.60i	−0.176625	−	0.305923i
$794$		0			0
$795$	40685.0	−	2219.79i	1.81503	−	0.0990285i
$796$		0			0
$797$		−	41181.2i		−	1.83025i	−0.403166	−	0.915127i	$-0.632090\pi$
$797$		−	41181.2i		−	1.83025i	0.403166	−	0.915127i	$-0.367910\pi$
$798$		0			0
$799$		−	40276.4i		−	1.78332i
$800$		0			0
$801$	−15491.0	+	11356.8i	−0.683331	+	0.500965i
$802$		0			0
$803$	−7163.07	−	12406.8i	−0.314794	−	0.545238i
$804$		0			0
$805$	−306.887	+	25059.7i	−0.0134365	+	1.09719i
$806$		0			0
$807$	−28383.2	−	14385.3i	−1.23809	−	0.627492i
$808$		0			0
$809$	9981.59	+	5762.88i	0.433788	+	0.250447i	0.700959	−	0.713202i	$-0.252756\pi$
$809$	9981.59	+	5762.88i	0.433788	+	0.250447i	−0.267171	+	0.963649i	$0.586089\pi$
$810$		0			0
$811$		−	32671.1i		−	1.41460i	−0.706916	−	0.707298i	$-0.749914\pi$
$811$		−	32671.1i		−	1.41460i	0.706916	−	0.707298i	$-0.250086\pi$
$812$		0			0
$813$	16698.4	−	10895.1i	0.720343	−	0.469998i
$814$		0			0
$815$	5060.40	−	8764.88i	0.217495	−	0.376712i
$816$		0			0
$817$	−27966.3	−	48439.0i	−1.19757	−	2.07426i
$818$		0			0
$819$	−7715.71	−	10799.3i	−0.329193	−	0.460757i
$820$		0			0
$821$	21050.2	−	12153.4i	0.894834	−	0.516633i	0.0193135	−	0.999813i	$-0.493852\pi$
$821$	21050.2	−	12153.4i	0.894834	−	0.516633i	0.875521	+	0.483181i	$0.160519\pi$
$822$		0			0
$823$	−27531.1	−	15895.1i	−1.16607	−	0.673229i	−0.213316	−	0.976983i	$-0.568427\pi$
$823$	−27531.1	−	15895.1i	−1.16607	−	0.673229i	−0.952750	+	0.303754i	$0.901760\pi$
$824$		0			0
$825$	−2517.87	−	3859.02i	−0.106256	−	0.162853i
$826$		0			0
$827$	−6134.87			−0.257957			−0.128978	−	0.991647i	$-0.541170\pi$
$827$	−6134.87			−0.257957			−0.128978	+	0.991647i	$0.541170\pi$
$828$		0			0
$829$	−3983.44	+	6899.52i	−0.166889	+	0.289060i	−0.937324	−	0.348458i	$-0.886705\pi$
$829$	−3983.44	+	6899.52i	−0.166889	+	0.289060i	0.770436	+	0.637518i	$0.220039\pi$
$830$		0			0
$831$	10484.3	−	20686.3i	0.437663	−	0.863539i
$832$		0			0
$833$	−35814.3	+	19523.9i	−1.48966	+	0.812082i
$834$		0			0
$835$	−9454.68	+	5458.66i	−0.391848	+	0.226233i
$836$		0			0
$837$	15335.8	+	5773.84i	0.633313	+	0.238438i
$838$		0			0
$839$	7513.33			0.309164			0.154582	−	0.987980i	$-0.450597\pi$
$839$	7513.33			0.309164			0.154582	+	0.987980i	$0.450597\pi$
$840$		0			0
$841$	24160.4			0.990627
$842$		0			0
$843$	−34.1042	−	625.073i	−0.00139337	−	0.0255382i
$844$		0			0
$845$	13295.3	−	7676.06i	0.541270	−	0.312502i
$846$		0			0
$847$	−7596.27	+	12792.7i	−0.308159	+	0.518966i
$848$		0			0
$849$	−139.148	−	70.5236i	−0.00562490	−	0.00285084i
$850$		0			0
$851$	−14944.1	+	25883.9i	−0.601970	+	1.04264i
$852$		0			0
$853$	−9449.12			−0.379287			−0.189643	−	0.981853i	$-0.560733\pi$
$853$	−9449.12			−0.379287			−0.189643	+	0.981853i	$0.560733\pi$
$854$		0			0
$855$	−18460.0	+	41945.6i	−0.738386	+	1.67779i
$856$		0			0
$857$	12638.9	+	7297.05i	0.503775	+	0.290855i	0.730271	−	0.683158i	$-0.239394\pi$
$857$	12638.9	+	7297.05i	0.503775	+	0.290855i	−0.226496	+	0.974012i	$0.572727\pi$
$858$		0			0
$859$	−11743.5	+	6780.09i	−0.466451	+	0.269306i	−0.714753	−	0.699377i	$-0.753461\pi$
$859$	−11743.5	+	6780.09i	−0.466451	+	0.269306i	0.248302	+	0.968683i	$0.420128\pi$
$860$		0			0
$861$	17887.7	−	11361.2i	0.708027	−	0.449698i
$862$		0			0
$863$	−1866.70	−	3233.22i	−0.0736307	−	0.127532i	0.826859	−	0.562409i	$-0.190125\pi$
$863$	−1866.70	−	3233.22i	−0.0736307	−	0.127532i	−0.900490	+	0.434877i	$0.856792\pi$
$864$		0			0
$865$	−5380.03	+	9318.48i	−0.211476	+	0.366287i
$866$		0			0
$867$	26205.9	+	40164.5i	1.02653	+	1.57331i
$868$		0			0
$869$			13265.2i			0.517825i
$870$		0			0
$871$	15820.9	+	9134.22i	0.615467	+	0.355340i
$872$		0			0
$873$	9527.61	−	1042.76i	0.369371	−	0.0404263i
$874$		0			0
$875$	−23955.6	+	13442.4i	−0.925541	+	0.519355i
$876$		0			0
$877$	8209.54	+	14219.3i	0.316096	+	0.547495i	0.979670	−	0.200616i	$-0.0642944\pi$
$877$	8209.54	+	14219.3i	0.316096	+	0.547495i	−0.663574	+	0.748111i	$0.730961\pi$
$878$		0			0
$879$	−1456.18	−	26689.4i	−0.0558770	−	1.02413i
$880$		0			0
$881$		−	962.335i		−	0.0368012i	−0.999831	−	0.0184006i	$-0.994143\pi$
$881$		−	962.335i		−	0.0368012i	0.999831	−	0.0184006i	$-0.00585743\pi$
$882$		0			0
$883$		−	33314.0i		−	1.26966i	−0.772653	−	0.634828i	$-0.781071\pi$
$883$		−	33314.0i		−	1.26966i	0.772653	−	0.634828i	$-0.218929\pi$
$884$		0			0
$885$	−1388.34	−	25445.9i	−0.0527327	−	0.966503i
$886$		0			0
$887$	−23752.6	−	41140.8i	−0.899138	−	1.55735i	−0.828598	−	0.559844i	$-0.810861\pi$
$887$	−23752.6	−	41140.8i	−0.899138	−	1.55735i	−0.0705404	−	0.997509i	$-0.522472\pi$
$888$		0			0
$889$	1340.73	−	752.331i	0.0505810	−	0.0283829i
$890$		0			0
$891$	−10132.0	+	32118.8i	−0.380960	+	1.20766i
$892$		0			0
$893$	−48398.6	−	27942.9i	−1.81366	−	1.04712i
$894$		0			0
$895$			8743.57i			0.326553i
$896$		0			0
$897$	9914.49	+	15195.5i	0.369047	+	0.565621i
$898$		0			0
$899$	882.977	−	1529.36i	0.0327574	−	0.0567375i
$900$		0			0
$901$	−45329.0	−	78512.1i	−1.67606	−	2.90302i
$902$		0			0
$903$	−27535.2	+	17488.8i	−1.01475	+	0.644508i
$904$		0			0
$905$	37141.3	−	21443.6i	1.36422	−	0.787633i
$906$		0			0
$907$	−26136.2	−	15089.8i	−0.956824	−	0.552423i	−0.0616301	−	0.998099i	$-0.519630\pi$
$907$	−26136.2	−	15089.8i	−0.956824	−	0.552423i	−0.895194	+	0.445676i	$0.852963\pi$
$908$		0			0
$909$	6974.34	+	3069.37i	0.254482	+	0.111996i
$910$		0			0
$911$	41036.3			1.49242			0.746209	−	0.665711i	$-0.231872\pi$
$911$	41036.3			1.49242			0.746209	+	0.665711i	$0.231872\pi$
$912$		0			0
$913$	−20939.3	+	36268.0i	−0.759025	+	1.31467i
$914$		0			0
$915$	14169.1	+	7181.24i	0.511929	+	0.259458i
$916$		0			0
$917$	−16867.2	+	28405.8i	−0.607421	+	1.02295i
$918$		0			0
$919$	45414.4	−	26220.0i	1.63012	−	0.941151i	0.646068	−	0.763280i	$-0.276412\pi$
$919$	45414.4	−	26220.0i	1.63012	−	0.941151i	0.984054	−	0.177871i	$-0.0569209\pi$
$920$		0			0
$921$	−537.613	−	9853.55i	−0.0192345	−	0.352536i
$922$		0			0
$923$	18585.9			0.662799
$924$		0			0
$925$	−4360.84			−0.155009
$926$		0			0
$927$	−8369.89	+	6136.15i	−0.296551	+	0.217408i
$928$		0			0
$929$	2104.90	−	1215.26i	0.0743373	−	0.0429187i	−0.462371	−	0.886687i	$-0.653001\pi$
$929$	2104.90	−	1215.26i	0.0743373	−	0.0429187i	0.536708	+	0.843768i	$0.319668\pi$
$930$		0			0
$931$	−1386.04	+	56581.9i	−0.0487922	+	1.99183i
$932$		0			0
$933$	5870.71	−	11583.3i	0.206000	−	0.406453i
$934$		0			0
$935$	28256.5	−	48941.7i	0.988327	−	1.71183i
$936$		0			0
$937$	−37791.5			−1.31760			−0.658802	−	0.752316i	$-0.728937\pi$
$937$	−37791.5			−1.31760			−0.658802	+	0.752316i	$0.728937\pi$
$938$		0			0
$939$	15205.6	+	23304.9i	0.528451	+	0.809932i
$940$		0			0
$941$	−2206.46	−	1273.90i	−0.0764385	−	0.0441318i	0.461294	−	0.887248i	$-0.347385\pi$
$941$	−2206.46	−	1273.90i	−0.0764385	−	0.0441318i	−0.537732	+	0.843116i	$0.680719\pi$
$942$		0			0
$943$	−25087.4	+	14484.2i	−0.866339	+	0.500181i
$944$		0			0
$945$	24895.6	+	9722.74i	0.856987	+	0.334689i
$946$		0			0
$947$	−22338.2	−	38690.9i	−0.766520	−	1.32765i	−0.939439	−	0.342716i	$-0.888653\pi$
$947$	−22338.2	−	38690.9i	−0.766520	−	1.32765i	0.172919	−	0.984936i	$-0.444680\pi$
$948$		0			0
$949$	−4115.36	+	7128.01i	−0.140769	+	0.243820i
$950$		0			0
$951$	−23533.1	+	15354.5i	−0.802431	+	0.523557i
$952$		0			0
$953$			19279.1i			0.655312i	0.944797	+	0.327656i	$0.106259\pi$
$953$			19279.1i			0.655312i	−0.944797	+	0.327656i	$0.893741\pi$
$954$		0			0
$955$	−93.7068	−	54.1016i	−0.00317516	−	0.00183318i
$956$		0			0
$957$	3237.44	+	1640.82i	0.109354	+	0.0554232i
$958$		0			0
$959$	387.702	−	31658.9i	0.0130548	−	1.06603i
$960$		0			0
$961$	−8074.29	−	13985.1i	−0.271031	−	0.469440i
$962$		0			0
$963$	−14484.5	−	19757.3i	−0.484689	−	0.661130i
$964$		0			0
$965$			22621.7i			0.754630i
$966$		0			0
$967$			57463.4i			1.91096i	0.295056	+	0.955480i	$0.404662\pi$
$967$			57463.4i			1.91096i	−0.295056	+	0.955480i	$0.595338\pi$
$968$		0			0
$969$	101815.	−	5555.07i	3.37541	−	0.184163i
$970$		0			0
$971$	4687.33	+	8118.69i	0.154916	+	0.268323i	0.933028	−	0.359802i	$-0.117156\pi$
$971$	4687.33	+	8118.69i	0.154916	+	0.268323i	−0.778112	+	0.628125i	$0.783823\pi$
$972$		0			0
$973$	−17033.4	+	9558.05i	−0.561218	+	0.314920i
$974$		0			0
$975$	−1196.78	+	2361.32i	−0.0393103	+	0.0775620i
$976$		0			0
$977$	12444.4	+	7184.77i	0.407504	+	0.235272i	0.689717	−	0.724079i	$-0.257735\pi$
$977$	12444.4	+	7184.77i	0.407504	+	0.235272i	−0.282213	+	0.959352i	$0.591068\pi$
$978$		0			0
$979$		−	32866.3i		−	1.07294i
$980$		0			0
$981$	−287.801	+	653.953i	−0.00936675	+	0.0212835i
$982$		0			0
$983$	−15117.9	+	26185.0i	−0.490525	+	0.849614i	−0.999941	−	0.0109064i	$-0.996528\pi$
$983$	−15117.9	+	26185.0i	−0.490525	+	0.849614i	0.509415	+	0.860521i	$0.329862\pi$
$984$		0			0
$985$	1408.38	+	2439.39i	0.0455582	+	0.0789091i
$986$		0			0
$987$	−15089.2	+	28889.2i	−0.486620	+	0.931665i
$988$		0			0
$989$	38617.9	−	22296.1i	1.24164	−	0.716860i
$990$		0			0
$991$	−44663.4	−	25786.4i	−1.43167	−	0.826573i	−0.434418	−	0.900712i	$-0.643046\pi$
$991$	−44663.4	−	25786.4i	−1.43167	−	0.826573i	−0.997248	+	0.0741390i	$0.976379\pi$
$992$		0			0
$993$	−1932.69	+	1261.01i	−0.0617643	+	0.0402989i
$994$		0			0
$995$	−6578.92			−0.209614
$996$		0			0
$997$	−3761.60	+	6515.28i	−0.119489	+	0.206962i	−0.919565	−	0.392937i	$-0.871459\pi$
$997$	−3761.60	+	6515.28i	−0.119489	+	0.206962i	0.800076	+	0.599899i	$0.204792\pi$
$998$		0			0
$999$	20218.1	+	24641.1i	0.640312	+	0.780391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.e.95.14	yes	28
3.2	odd	2	inner	336.4.bj.e.95.10	✓	28
4.3	odd	2		336.4.bj.f.95.1	yes	28
7.2	even	3		336.4.bj.f.191.5	yes	28
12.11	even	2		336.4.bj.f.95.5	yes	28
21.2	odd	6		336.4.bj.f.191.1	yes	28
28.23	odd	6	inner	336.4.bj.e.191.10	yes	28
84.23	even	6	inner	336.4.bj.e.191.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.e.95.10	✓	28	3.2	odd	2	inner
336.4.bj.e.95.14	yes	28	1.1	even	1	trivial
336.4.bj.e.191.10	yes	28	28.23	odd	6	inner
336.4.bj.e.191.14	yes	28	84.23	even	6	inner
336.4.bj.f.95.1	yes	28	4.3	odd	2
336.4.bj.f.95.5	yes	28	12.11	even	2
336.4.bj.f.191.1	yes	28	21.2	odd	6
336.4.bj.f.191.5	yes	28	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(5.18844 - 0.283083i) q^{3} +(-8.90809 + 5.14309i) q^{5} +(-9.06303 - 16.1512i) q^{7} +(26.8397 - 2.93751i) q^{9} +(-23.0995 + 40.0094i) q^{11} +26.5424 q^{13} +(-44.7631 + 29.2063i) q^{15} +(102.989 + 59.4610i) q^{17} +(142.904 - 82.5056i) q^{19} +(-51.5951 - 81.2339i) q^{21} +(65.7775 + 113.930i) q^{23} +(-9.59729 + 16.6230i) q^{25} +(138.425 - 22.8390i) q^{27} -15.1194i q^{29} +(101.152 + 58.4004i) q^{31} +(-108.524 + 214.126i) q^{33} +(163.801 + 97.2644i) q^{35} +(113.596 + 196.753i) q^{37} +(137.714 - 7.51370i) q^{39} +220.200i q^{41} -338.962i q^{43} +(-223.983 + 164.207i) q^{45} +(-169.340 - 293.305i) q^{47} +(-178.723 + 292.758i) q^{49} +(551.187 + 279.355i) q^{51} +(-660.198 - 381.166i) q^{53} -475.210i q^{55} +(718.092 - 468.529i) q^{57} +(-238.395 + 412.913i) q^{59} +(-148.601 - 257.384i) q^{61} +(-290.694 - 406.871i) q^{63} +(-236.442 + 136.510i) q^{65} +(596.062 + 344.137i) q^{67} +(373.534 + 572.498i) q^{69} +700.236 q^{71} +(-155.048 + 268.552i) q^{73} +(-45.0893 + 88.9642i) q^{75} +(855.552 + 10.4773i) q^{77} +(248.663 - 143.566i) q^{79} +(711.742 - 157.684i) q^{81} +906.485 q^{83} -1223.25 q^{85} +(-4.28003 - 78.4459i) q^{87} +(-616.098 + 355.704i) q^{89} +(-240.555 - 428.692i) q^{91} +(541.355 + 274.372i) q^{93} +(-848.667 + 1469.93i) q^{95} +354.982 q^{97} +(-502.455 + 1141.70i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) \) 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

Fields

Representations

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Database

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