LMFDB - Embedded newform 336.4.bj.g.95.7

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 = [32,0,0,0,0,0,0] 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.7
Character	$\chi$	$=$	336.95
Dual form			336.4.bj.g.191.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.29238 + 4.66315i) q^{3} +(6.70049 - 3.86853i) q^{5} +(-13.9129 + 12.2242i) q^{7} +(-16.4900 - 21.3795i) q^{9} +(-2.34284 + 4.05791i) q^{11} +32.7753 q^{13} +(2.67945 + 40.1135i) q^{15} +(-63.6042 - 36.7219i) q^{17} +(-79.1618 + 45.7041i) q^{19} +(-25.1093 - 92.9006i) q^{21} +(-70.5000 - 122.110i) q^{23} +(-32.5690 + 56.4111i) q^{25} +(137.497 - 27.8853i) q^{27} -155.744i q^{29} +(76.0386 + 43.9009i) q^{31} +(-13.5520 - 20.2273i) q^{33} +(-45.9340 + 135.730i) q^{35} +(97.5712 + 168.998i) q^{37} +(-75.1336 + 152.836i) q^{39} -371.669i q^{41} -353.083i q^{43} +(-193.198 - 79.4609i) q^{45} +(20.4859 + 35.4826i) q^{47} +(44.1397 - 340.148i) q^{49} +(317.045 - 212.415i) q^{51} +(-617.427 - 356.471i) q^{53} +36.2533i q^{55} +(-31.6559 - 473.915i) q^{57} +(114.655 - 198.588i) q^{59} +(-208.757 - 361.577i) q^{61} +(490.770 + 95.8751i) q^{63} +(219.611 - 126.792i) q^{65} +(-524.154 - 302.620i) q^{67} +(731.028 - 48.8302i) q^{69} +419.021 q^{71} +(-82.5712 + 143.018i) q^{73} +(-188.393 - 281.190i) q^{75} +(-17.0088 - 85.0967i) q^{77} +(-486.508 + 280.886i) q^{79} +(-185.162 + 705.093i) q^{81} -447.063 q^{83} -568.239 q^{85} +(726.260 + 357.026i) q^{87} +(418.887 - 241.845i) q^{89} +(-456.001 + 400.651i) q^{91} +(-379.026 + 253.942i) q^{93} +(-353.615 + 612.480i) q^{95} +1165.63 q^{97} +(125.389 - 16.8262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{9} - 40 q^{13} - 148 q^{21} + 316 q^{25} - 128 q^{33} - 644 q^{37} + 316 q^{45} + 632 q^{49} + 1136 q^{57} + 328 q^{61} - 1424 q^{69} + 1124 q^{73} + 1564 q^{81} - 912 q^{85} + 24 q^{93} - 3304 q^{97}+O(q^{100}) $ 32 * q + 32 * q^9 - 40 * q^13 - 148 * q^21 + 316 * q^25 - 128 * q^33 - 644 * q^37 + 316 * q^45 + 632 * q^49 + 1136 * q^57 + 328 * q^61 - 1424 * q^69 + 1124 * q^73 + 1564 * q^81 - 912 * q^85 + 24 * q^93 - 3304 * 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
$3$	−2.29238	+	4.66315i	−0.441169	+	0.897424i
$3$	−2.29238	+	4.66315i	−0.441169	+	0.897424i
$4$		0			0
$5$	6.70049	−	3.86853i	0.599310	−	0.346012i	−0.169460	−	0.985537i	$-0.554202\pi$
$5$	6.70049	−	3.86853i	0.599310	−	0.346012i	0.768770	+	0.639525i	$0.220869\pi$
$6$		0			0
$7$	−13.9129	+	12.2242i	−0.751228	+	0.660043i
$7$	−13.9129	+	12.2242i	−0.751228	+	0.660043i
$8$		0			0
$9$	−16.4900	−	21.3795i	−0.610739	−	0.791832i
$10$		0			0
$11$	−2.34284	+	4.05791i	−0.0642174	+	0.111228i	−0.896347	−	0.443354i	$-0.853788\pi$
$11$	−2.34284	+	4.05791i	−0.0642174	+	0.111228i	0.832129	+	0.554582i	$0.187122\pi$
$12$		0			0
$13$	32.7753			0.699250			0.349625	−	0.936890i	$-0.386309\pi$
$13$	32.7753			0.699250			0.349625	+	0.936890i	$0.386309\pi$
$14$		0			0
$15$	2.67945	+	40.1135i	0.0461221	+	0.690485i
$16$		0			0
$17$	−63.6042	−	36.7219i	−0.907428	−	0.523904i	−0.0278253	−	0.999613i	$-0.508858\pi$
$17$	−63.6042	−	36.7219i	−0.907428	−	0.523904i	−0.879603	+	0.475709i	$0.842192\pi$
$18$		0			0
$19$	−79.1618	+	45.7041i	−0.955841	+	0.551855i	−0.894890	−	0.446286i	$-0.852746\pi$
$19$	−79.1618	+	45.7041i	−0.955841	+	0.551855i	−0.0609501	+	0.998141i	$0.519413\pi$
$20$		0			0
$21$	−25.1093	−	92.9006i	−0.260919	−	0.965361i
$22$		0			0
$23$	−70.5000	−	122.110i	−0.639142	−	1.10703i	−0.985621	−	0.168969i	$-0.945956\pi$
$23$	−70.5000	−	122.110i	−0.639142	−	1.10703i	0.346480	−	0.938057i	$-0.387377\pi$
$24$		0			0
$25$	−32.5690	+	56.4111i	−0.260552	+	0.451289i
$26$		0			0
$27$	137.497	−	27.8853i	0.980048	−	0.198760i
$28$		0			0
$29$		−	155.744i		−	0.997277i	−0.866810	−	0.498638i	$-0.833834\pi$
$29$		−	155.744i		−	0.997277i	0.866810	−	0.498638i	$-0.166166\pi$
$30$		0			0
$31$	76.0386	+	43.9009i	0.440546	+	0.254350i	0.703829	−	0.710369i	$-0.251472\pi$
$31$	76.0386	+	43.9009i	0.440546	+	0.254350i	−0.263283	+	0.964719i	$0.584805\pi$
$32$		0			0
$33$	−13.5520	−	20.2273i	−0.0714878	−	0.106701i
$34$		0			0
$35$	−45.9340	+	135.730i	−0.221836	+	0.655504i
$36$		0			0
$37$	97.5712	+	168.998i	0.433530	+	0.750896i	0.997174	−	0.0751215i	$-0.0239345\pi$
$37$	97.5712	+	168.998i	0.433530	+	0.750896i	−0.563644	+	0.826018i	$0.690601\pi$
$38$		0			0
$39$	−75.1336	+	152.836i	−0.308487	+	0.627523i
$40$		0			0
$41$		−	371.669i		−	1.41573i	−0.706347	−	0.707865i	$-0.749658\pi$
$41$		−	371.669i		−	1.41573i	0.706347	−	0.707865i	$-0.250342\pi$
$42$		0			0
$43$		−	353.083i		−	1.25220i	−0.779742	−	0.626100i	$-0.784650\pi$
$43$		−	353.083i		−	1.25220i	0.779742	−	0.626100i	$-0.215350\pi$
$44$		0			0
$45$	−193.198	−	79.4609i	−0.640005	−	0.263230i
$46$		0			0
$47$	20.4859	+	35.4826i	0.0635782	+	0.110121i	0.896062	−	0.443928i	$-0.146415\pi$
$47$	20.4859	+	35.4826i	0.0635782	+	0.110121i	−0.832484	+	0.554049i	$0.813082\pi$
$48$		0			0
$49$	44.1397	−	340.148i	0.128687	−	0.991685i
$50$		0			0
$51$	317.045	−	212.415i	0.870493	−	0.583217i
$52$		0			0
$53$	−617.427	−	356.471i	−1.60019	−	0.923870i	−0.991448	−	0.130502i	$-0.958341\pi$
$53$	−617.427	−	356.471i	−1.60019	−	0.923870i	−0.608742	−	0.793368i	$-0.708325\pi$
$54$		0			0
$55$			36.2533i			0.0888800i
$56$		0			0
$57$	−31.6559	−	473.915i	−0.0735602	−	1.10126i
$58$		0			0
$59$	114.655	−	198.588i	0.252996	−	0.438202i	−0.711353	−	0.702835i	$-0.751917\pi$
$59$	114.655	−	198.588i	0.252996	−	0.438202i	0.964349	+	0.264632i	$0.0852506\pi$
$60$		0			0
$61$	−208.757	−	361.577i	−0.438173	−	0.758938i	0.559376	−	0.828914i	$-0.311041\pi$
$61$	−208.757	−	361.577i	−0.438173	−	0.758938i	−0.997549	+	0.0699762i	$0.977708\pi$
$62$		0			0
$63$	490.770	+	95.8751i	0.981447	+	0.191732i
$64$		0			0
$65$	219.611	−	126.792i	0.419067	−	0.241949i
$66$		0			0
$67$	−524.154	−	302.620i	−0.955755	−	0.551805i	−0.0608909	−	0.998144i	$-0.519394\pi$
$67$	−524.154	−	302.620i	−0.955755	−	0.551805i	−0.894864	+	0.446339i	$0.852727\pi$
$68$		0			0
$69$	731.028	−	48.8302i	1.27544	−	0.0851952i
$70$		0			0
$71$	419.021			0.700403			0.350201	−	0.936674i	$-0.386113\pi$
$71$	419.021			0.700403			0.350201	+	0.936674i	$0.386113\pi$
$72$		0			0
$73$	−82.5712	+	143.018i	−0.132387	+	0.229301i	−0.924596	−	0.380949i	$-0.875597\pi$
$73$	−82.5712	+	143.018i	−0.132387	+	0.229301i	0.792209	+	0.610249i	$0.208931\pi$
$74$		0			0
$75$	−188.393	−	281.190i	−0.290050	−	0.432920i
$76$		0			0
$77$	−17.0088	−	85.0967i	−0.0251732	−	0.125944i
$78$		0			0
$79$	−486.508	+	280.886i	−0.692866	+	0.400026i	−0.804685	−	0.593702i	$-0.797666\pi$
$79$	−486.508	+	280.886i	−0.692866	+	0.400026i	0.111819	+	0.993729i	$0.464332\pi$
$80$		0			0
$81$	−185.162	+	705.093i	−0.253995	+	0.967206i
$82$		0			0
$83$	−447.063			−0.591223			−0.295611	−	0.955308i	$-0.595523\pi$
$83$	−447.063			−0.591223			−0.295611	+	0.955308i	$0.595523\pi$
$84$		0			0
$85$	−568.239			−0.725107
$86$		0			0
$87$	726.260	+	357.026i	0.894980	+	0.439968i
$88$		0			0
$89$	418.887	−	241.845i	0.498898	−	0.288039i	−0.229360	−	0.973342i	$-0.573663\pi$
$89$	418.887	−	241.845i	0.498898	−	0.288039i	0.728258	+	0.685303i	$0.240330\pi$
$90$		0			0
$91$	−456.001	+	400.651i	−0.525296	+	0.461535i
$92$		0			0
$93$	−379.026	+	253.942i	−0.422615	+	0.283146i
$94$		0			0
$95$	−353.615	+	612.480i	−0.381896	+	0.661464i
$96$		0			0
$97$	1165.63			1.22012			0.610058	−	0.792356i	$-0.291146\pi$
$97$	1165.63			1.22012			0.610058	+	0.792356i	$0.291146\pi$
$98$		0			0
$99$	125.389	−	16.8262i	0.127294	−	0.0170818i
$100$		0			0
$101$	−473.348	−	273.288i	−0.466336	−	0.269239i	0.248369	−	0.968666i	$-0.420105\pi$
$101$	−473.348	−	273.288i	−0.466336	−	0.269239i	−0.714704	+	0.699427i	$0.753439\pi$
$102$		0			0
$103$	−1226.20	+	707.949i	−1.17302	+	0.677246i	−0.954390	−	0.298562i	$-0.903493\pi$
$103$	−1226.20	+	707.949i	−1.17302	+	0.677246i	−0.218633	+	0.975807i	$0.570160\pi$
$104$		0			0
$105$	−527.634	−	525.343i	−0.490398	−	0.488269i
$106$		0			0
$107$	463.957	+	803.596i	0.419181	+	0.726043i	0.995857	−	0.0909299i	$-0.0289839\pi$
$107$	463.957	+	803.596i	0.419181	+	0.726043i	−0.576676	+	0.816973i	$0.695651\pi$
$108$		0			0
$109$	−588.950	+	1020.09i	−0.517534	+	0.896395i	0.482259	+	0.876029i	$0.339817\pi$
$109$	−588.950	+	1020.09i	−0.517534	+	0.896395i	−0.999793	+	0.0203661i	$0.993517\pi$
$110$		0			0
$111$	−1011.74	+	67.5805i	−0.865132	+	0.0577879i
$112$		0			0
$113$			1483.38i			1.23491i	0.786606	+	0.617456i	$0.211837\pi$
$113$			1483.38i			1.23491i	−0.786606	+	0.617456i	$0.788163\pi$
$114$		0			0
$115$	−944.769	−	545.462i	−0.766088	−	0.442301i
$116$		0			0
$117$	−540.464	−	700.719i	−0.427059	−	0.553688i
$118$		0			0
$119$	1333.82	−	266.598i	1.02748	−	0.205370i
$120$		0			0
$121$	654.522	+	1133.67i	0.491752	+	0.851740i
$122$		0			0
$123$	1733.15	+	852.008i	1.27051	+	0.624577i
$124$		0			0
$125$			1471.11i			1.05264i
$126$		0			0
$127$			104.505i			0.0730182i	0.999333	+	0.0365091i	$0.0116238\pi$
$127$			104.505i			0.0730182i	−0.999333	+	0.0365091i	$0.988376\pi$
$128$		0			0
$129$	1646.48	+	809.401i	1.12375	+	0.552432i
$130$		0			0
$131$	−1173.78	−	2033.05i	−0.782853	−	1.35594i	−0.930273	−	0.366867i	$-0.880430\pi$
$131$	−1173.78	−	2033.05i	−0.782853	−	1.35594i	0.147421	−	0.989074i	$-0.452903\pi$
$132$		0			0
$133$	542.679	−	1603.57i	0.353806	−	1.04546i
$134$		0			0
$135$	813.422	−	718.756i	0.518579	−	0.458227i
$136$		0			0
$137$	2066.20	+	1192.92i	1.28852	+	0.743927i	0.978390	−	0.206768i	$-0.0662945\pi$
$137$	2066.20	+	1192.92i	1.28852	+	0.743927i	0.310129	+	0.950695i	$0.399628\pi$
$138$		0			0
$139$		−	1294.66i		−	0.790012i	−0.918679	−	0.395006i	$-0.870743\pi$
$139$		−	1294.66i		−	0.790012i	0.918679	−	0.395006i	$-0.129257\pi$
$140$		0			0
$141$	−212.422	+	14.1891i	−0.126874	+	0.00847474i
$142$		0			0
$143$	−76.7873	+	132.999i	−0.0449040	+	0.0777761i
$144$		0			0
$145$	−602.502	−	1043.56i	−0.345069	−	0.597678i
$146$		0			0
$147$	1484.98	+	985.580i	0.833189	+	0.552988i
$148$		0			0
$149$	−415.385	+	239.823i	−0.228387	+	0.131859i	−0.609828	−	0.792534i	$-0.708761\pi$
$149$	−415.385	+	239.823i	−0.228387	+	0.131859i	0.381441	+	0.924393i	$0.375428\pi$
$150$		0			0
$151$	−1765.12	−	1019.09i	−0.951279	−	0.549221i	−0.0578012	−	0.998328i	$-0.518409\pi$
$151$	−1765.12	−	1019.09i	−0.951279	−	0.549221i	−0.893478	+	0.449107i	$0.851742\pi$
$152$		0			0
$153$	263.736	+	1965.36i	0.139358	+	1.03850i
$154$		0			0
$155$	679.328			0.352032
$156$		0			0
$157$	−502.495	+	870.347i	−0.255436	+	0.442428i	−0.965014	−	0.262199i	$-0.915552\pi$
$157$	−502.495	+	870.347i	−0.255436	+	0.442428i	0.709578	+	0.704627i	$0.248886\pi$
$158$		0			0
$159$	3077.66	−	2061.98i	1.53506	−	1.02847i
$160$		0			0
$161$	2473.55	+	837.099i	1.21083	+	0.409768i
$162$		0			0
$163$	−795.545	+	459.308i	−0.382281	+	0.220710i	−0.678810	−	0.734314i	$-0.737504\pi$
$163$	−795.545	+	459.308i	−0.382281	+	0.220710i	0.296529	+	0.955024i	$0.404171\pi$
$164$		0			0
$165$	−169.055	−	83.1065i	−0.0797630	−	0.0392111i
$166$		0			0
$167$	−517.384			−0.239739			−0.119869	−	0.992790i	$-0.538248\pi$
$167$	−517.384			−0.239739			−0.119869	+	0.992790i	$0.538248\pi$
$168$		0			0
$169$	−1122.78			−0.511050
$170$		0			0
$171$	2282.50	+	938.778i	1.02075	+	0.419825i
$172$		0			0
$173$	−2570.64	+	1484.16i	−1.12972	+	0.652247i	−0.943866	−	0.330330i	$-0.892840\pi$
$173$	−2570.64	+	1484.16i	−1.12972	+	0.652247i	−0.185859	+	0.982576i	$0.559507\pi$
$174$		0			0
$175$	−236.449	−	1182.97i	−0.102136	−	0.510996i
$176$		0			0
$177$	663.213	+	989.892i	0.281639	+	0.420366i
$178$		0			0
$179$	−2046.60	+	3544.82i	−0.854582	+	1.48018i	0.0224493	+	0.999748i	$0.492854\pi$
$179$	−2046.60	+	3544.82i	−0.854582	+	1.48018i	−0.877032	+	0.480432i	$0.840480\pi$
$180$		0			0
$181$	2003.11			0.822598			0.411299	−	0.911501i	$-0.365075\pi$
$181$	2003.11			0.822598			0.411299	+	0.911501i	$0.365075\pi$
$182$		0			0
$183$	2164.64	−	144.591i	0.874398	−	0.0584068i
$184$		0			0
$185$	1307.55	+	754.914i	0.519638	+	0.300013i
$186$		0			0
$187$	298.028	−	172.067i	0.116545	−	0.0672875i
$188$		0			0
$189$	−1572.11	+	2068.75i	−0.605049	+	0.796188i
$190$		0			0
$191$	−1742.49	−	3018.09i	−0.660117	−	1.14336i	−0.980585	−	0.196097i	$-0.937173\pi$
$191$	−1742.49	−	3018.09i	−0.660117	−	1.14336i	0.320467	−	0.947260i	$-0.396160\pi$
$192$		0			0
$193$	−1021.77	+	1769.75i	−0.381080	+	0.660050i	−0.991217	−	0.132246i	$-0.957781\pi$
$193$	−1021.77	+	1769.75i	−0.381080	+	0.660050i	0.610137	+	0.792296i	$0.291114\pi$
$194$		0			0
$195$	87.8199	+	1314.74i	0.0322508	+	0.482821i
$196$		0			0
$197$			1279.11i			0.462602i	0.972882	+	0.231301i	$0.0742983\pi$
$197$			1279.11i			0.462602i	−0.972882	+	0.231301i	$0.925702\pi$
$198$		0			0
$199$	−4193.05	−	2420.86i	−1.49366	−	0.862363i	−0.493683	−	0.869642i	$-0.664350\pi$
$199$	−4193.05	−	2420.86i	−1.49366	−	0.862363i	−0.999974	+	0.00727877i	$0.997683\pi$
$200$		0			0
$201$	2612.73	−	1750.49i	0.916853	−	0.614278i
$202$		0			0
$203$	1903.85	+	2166.86i	0.658245	+	0.749182i
$204$		0			0
$205$	−1437.81	−	2490.36i	−0.489859	−	0.848461i
$206$		0			0
$207$	−1448.09	+	3520.83i	−0.486229	+	1.18220i
$208$		0			0
$209$		−	428.309i		−	0.141755i
$210$		0			0
$211$			2992.48i			0.976353i	0.872745	+	0.488177i	$0.162338\pi$
$211$			2992.48i			0.976353i	−0.872745	+	0.488177i	$0.837662\pi$
$212$		0			0
$213$	−960.556	+	1953.96i	−0.308996	+	0.628558i
$214$		0			0
$215$	−1365.91	−	2365.83i	−0.433276	−	0.750456i
$216$		0			0
$217$	−1594.57	+	318.718i	−0.498832	+	0.0997049i
$218$		0			0
$219$	−477.628	−	712.893i	−0.147375	−	0.219967i
$220$		0			0
$221$	−2084.65	−	1203.57i	−0.634519	−	0.366340i
$222$		0			0
$223$			3390.92i			1.01827i	0.860688	+	0.509133i	$0.170034\pi$
$223$			3390.92i			1.01827i	−0.860688	+	0.509133i	$0.829966\pi$
$224$		0			0
$225$	1743.10	−	233.910i	0.516474	−	0.0693067i
$226$		0			0
$227$	2329.02	−	4033.98i	0.680980	−	1.17949i	−0.293702	−	0.955897i	$-0.594887\pi$
$227$	2329.02	−	4033.98i	0.680980	−	1.17949i	0.974682	−	0.223596i	$-0.0717795\pi$
$228$		0			0
$229$	1455.53	+	2521.06i	0.420019	+	0.727494i	0.995941	−	0.0900105i	$-0.0286901\pi$
$229$	1455.53	+	2521.06i	0.420019	+	0.727494i	−0.575922	+	0.817505i	$0.695357\pi$
$230$		0			0
$231$	435.810	+	115.759i	0.124131	+	0.0329715i
$232$		0			0
$233$	2639.30	−	1523.80i	0.742086	−	0.428444i	−0.0807410	−	0.996735i	$-0.525729\pi$
$233$	2639.30	−	1523.80i	0.742086	−	0.428444i	0.822827	+	0.568291i	$0.192395\pi$
$234$		0			0
$235$	274.531	+	158.501i	0.0762061	+	0.0439976i
$236$		0			0
$237$	−194.549	−	2912.56i	−0.0533220	−	0.798274i
$238$		0			0
$239$	5931.88			1.60545			0.802723	−	0.596353i	$-0.203384\pi$
$239$	5931.88			1.60545			0.802723	+	0.596353i	$0.203384\pi$
$240$		0			0
$241$	2596.74	−	4497.68i	0.694068	−	1.20216i	−0.276426	−	0.961035i	$-0.589150\pi$
$241$	2596.74	−	4497.68i	0.694068	−	1.20216i	0.970494	−	0.241126i	$-0.0775167\pi$
$242$		0			0
$243$	−2863.49	−	2479.78i	−0.755939	−	0.654643i
$244$		0			0
$245$	−1020.12	−	2449.91i	−0.266011	−	0.638854i
$246$		0			0
$247$	−2594.56	+	1497.97i	−0.668371	+	0.385884i
$248$		0			0
$249$	1024.84	−	2084.72i	0.260829	−	0.530578i
$250$		0			0
$251$	−4028.98			−1.01318			−0.506588	−	0.862188i	$-0.669093\pi$
$251$	−4028.98			−1.01318			−0.506588	+	0.862188i	$0.669093\pi$
$252$		0			0
$253$	660.680			0.164176
$254$		0			0
$255$	1302.62	−	2649.78i	0.319895	−	0.650729i
$256$		0			0
$257$	1404.49	−	810.884i	0.340894	−	0.196815i	−0.319773	−	0.947494i	$-0.603607\pi$
$257$	1404.49	−	810.884i	0.340894	−	0.196815i	0.660667	+	0.750679i	$0.270273\pi$
$258$		0			0
$259$	−3423.37	−	1158.54i	−0.821303	−	0.277946i
$260$		0			0
$261$	−3329.73	+	2568.22i	−0.789675	+	0.609076i
$262$		0			0
$263$	−3878.71	+	6718.12i	−0.909397	+	1.57512i	−0.0944932	+	0.995526i	$0.530123\pi$
$263$	−3878.71	+	6718.12i	−0.909397	+	1.57512i	−0.814904	+	0.579596i	$0.803210\pi$
$264$		0			0
$265$	−5516.08			−1.27868
$266$		0			0
$267$	167.508	+	2507.73i	0.0383945	+	0.574797i
$268$		0			0
$269$	−7067.44	−	4080.39i	−1.60189	−	0.924854i	−0.991108	−	0.133058i	$-0.957520\pi$
$269$	−7067.44	−	4080.39i	−1.60189	−	0.924854i	−0.610786	−	0.791796i	$-0.709146\pi$
$270$		0			0
$271$	1378.58	−	795.924i	0.309014	−	0.178409i	−0.337471	−	0.941336i	$-0.609572\pi$
$271$	1378.58	−	795.924i	0.309014	−	0.178409i	0.646485	+	0.762927i	$0.276238\pi$
$272$		0			0
$273$	−822.967	−	3044.85i	−0.182448	−	0.675028i
$274$		0			0
$275$	−152.608	−	264.324i	−0.0334639	−	0.0579612i
$276$		0			0
$277$	2066.86	−	3579.90i	0.448323	−	0.776517i	−0.549954	−	0.835195i	$-0.685355\pi$
$277$	2066.86	−	3579.90i	0.448323	−	0.776517i	0.998277	+	0.0586772i	$0.0186883\pi$
$278$		0			0
$279$	−315.296	−	2349.59i	−0.0676569	−	0.504180i
$280$		0			0
$281$		−	2820.59i		−	0.598799i	−0.954128	−	0.299399i	$-0.903214\pi$
$281$		−	2820.59i		−	0.598799i	0.954128	−	0.299399i	$-0.0967863\pi$
$282$		0			0
$283$	4201.91	+	2425.97i	0.882606	+	0.509573i	0.871517	−	0.490366i	$-0.163137\pi$
$283$	4201.91	+	2425.97i	0.882606	+	0.509573i	0.0110894	+	0.999939i	$0.496470\pi$
$284$		0			0
$285$	−2045.46	−	3053.00i	−0.425133	−	0.634541i
$286$		0			0
$287$	4543.34	+	5171.01i	0.934443	+	1.06354i
$288$		0			0
$289$	240.493	+	416.546i	0.0489504	+	0.0847845i
$290$		0			0
$291$	−2672.06	+	5435.49i	−0.538278	+	1.09496i
$292$		0			0
$293$		−	5793.57i		−	1.15517i	−0.816332	−	0.577583i	$-0.803996\pi$
$293$		−	5793.57i		−	1.15517i	0.816332	−	0.577583i	$-0.196004\pi$
$294$		0			0
$295$		−	1774.18i		−	0.350159i
$296$		0			0
$297$	−208.977	+	623.281i	−0.0408285	+	0.121773i
$298$		0			0
$299$	−2310.66	−	4002.18i	−0.446920	−	0.774088i
$300$		0			0
$301$	4316.14	+	4912.42i	0.826506	+	0.940688i
$302$		0			0
$303$	2359.48	−	1580.81i	0.447354	−	0.299721i
$304$		0			0
$305$	−2797.54	−	1615.16i	−0.525203	−	0.303226i
$306$		0			0
$307$		−	7217.02i		−	1.34169i	−0.741600	−	0.670843i	$-0.765933\pi$
$307$		−	7217.02i		−	1.34169i	0.741600	−	0.670843i	$-0.234067\pi$
$308$		0			0
$309$	−490.345	−	7340.86i	−0.0902743	−	1.35148i
$310$		0			0
$311$	922.733	−	1598.22i	0.168242	−	0.291404i	−0.769560	−	0.638575i	$-0.779524\pi$
$311$	922.733	−	1598.22i	0.168242	−	0.291404i	0.937802	+	0.347171i	$0.112858\pi$
$312$		0			0
$313$	4176.03	+	7233.10i	0.754132	+	1.30619i	0.945805	+	0.324736i	$0.105275\pi$
$313$	4176.03	+	7233.10i	0.754132	+	1.30619i	−0.191673	+	0.981459i	$0.561391\pi$
$314$		0			0
$315$	3659.29	−	1256.15i	0.654533	−	0.224685i
$316$		0			0
$317$	1141.27	−	658.913i	0.202209	−	0.116745i	−0.395477	−	0.918476i	$-0.629421\pi$
$317$	1141.27	−	658.913i	0.202209	−	0.116745i	0.597685	+	0.801731i	$0.296087\pi$
$318$		0			0
$319$	631.997	+	364.884i	0.110925	+	0.0640426i
$320$		0			0
$321$	−4810.86	+	321.349i	−0.836498	+	0.0558753i
$322$		0			0
$323$	6713.36			1.15648
$324$		0			0
$325$	−1067.46	+	1848.89i	−0.182191	+	0.315564i
$326$		0			0
$327$	−3406.74	−	5084.80i	−0.576126	−	0.859909i
$328$		0			0
$329$	−718.765	−	243.245i	−0.120446	−	0.0407614i
$330$		0			0
$331$	6350.28	−	3666.33i	1.05451	−	0.608822i	0.130601	−	0.991435i	$-0.458309\pi$
$331$	6350.28	−	3666.33i	1.05451	−	0.608822i	0.923909	+	0.382613i	$0.124976\pi$
$332$		0			0
$333$	2004.15	−	4872.80i	0.329810	−	0.801885i
$334$		0			0
$335$	−4682.78			−0.763724
$336$		0			0
$337$	1339.02			0.216442			0.108221	−	0.994127i	$-0.465485\pi$
$337$	1339.02			0.216442			0.108221	+	0.994127i	$0.465485\pi$
$338$		0			0
$339$	−6917.24	−	3400.48i	−1.10824	−	0.544805i
$340$		0			0
$341$	−356.292	+	205.705i	−0.0565815	+	0.0326674i
$342$		0			0
$343$	3543.91	+	5272.03i	0.557881	+	0.829921i
$344$		0			0
$345$	4709.34	−	3155.19i	0.734906	−	0.492376i
$346$		0			0
$347$	−2398.86	+	4154.95i	−0.371117	+	0.642794i	−0.989738	−	0.142896i	$-0.954358\pi$
$347$	−2398.86	+	4154.95i	−0.371117	+	0.642794i	0.618621	+	0.785690i	$0.287692\pi$
$348$		0			0
$349$	−3512.47			−0.538735			−0.269367	−	0.963038i	$-0.586815\pi$
$349$	−3512.47			−0.538735			−0.269367	+	0.963038i	$0.586815\pi$
$350$		0			0
$351$	4506.51	−	913.950i	0.685298	−	0.138983i
$352$		0			0
$353$	988.134	+	570.499i	0.148989	+	0.0860187i	0.572641	−	0.819806i	$-0.305919\pi$
$353$	988.134	+	570.499i	0.148989	+	0.0860187i	−0.423652	+	0.905825i	$0.639252\pi$
$354$		0			0
$355$	2807.64	−	1620.99i	0.419758	−	0.242348i
$356$		0			0
$357$	−1814.43	+	6830.93i	−0.268991	+	1.01269i
$358$		0			0
$359$	−232.914	−	403.419i	−0.0342416	−	0.0593081i	0.848397	−	0.529361i	$-0.177568\pi$
$359$	−232.914	−	403.419i	−0.0342416	−	0.0593081i	−0.882638	+	0.470053i	$0.844235\pi$
$360$		0			0
$361$	748.230	−	1295.97i	0.109087	−	0.188945i
$362$		0			0
$363$	−6786.87	+	453.340i	−0.981318	+	0.0655487i
$364$		0			0
$365$			1277.72i			0.183229i
$366$		0			0
$367$	7755.37	+	4477.57i	1.10307	+	0.636858i	0.937026	−	0.349260i	$-0.113567\pi$
$367$	7755.37	+	4477.57i	1.10307	+	0.636858i	0.166045	+	0.986118i	$0.446900\pi$
$368$		0			0
$369$	−7946.08	+	6128.81i	−1.12102	+	0.864642i
$370$		0			0
$371$	12947.8	−	2587.96i	1.81190	−	0.362157i
$372$		0			0
$373$	−5666.81	−	9815.21i	−0.786639	−	1.36250i	−0.928015	−	0.372543i	$-0.878486\pi$
$373$	−5666.81	−	9815.21i	−0.786639	−	1.36250i	0.141376	−	0.989956i	$-0.454847\pi$
$374$		0			0
$375$	−6860.00	−	3372.34i	−0.944664	−	0.464392i
$376$		0			0
$377$		−	5104.58i		−	0.697345i
$378$		0			0
$379$		−	8721.01i		−	1.18197i	−0.806681	−	0.590987i	$-0.798739\pi$
$379$		−	8721.01i		−	1.18197i	0.806681	−	0.590987i	$-0.201261\pi$
$380$		0			0
$381$	−487.322	−	239.565i	−0.0655283	−	0.0322134i
$382$		0			0
$383$	−7220.73	−	12506.7i	−0.963348	−	1.66857i	−0.713991	−	0.700155i	$-0.753114\pi$
$383$	−7220.73	−	12506.7i	−0.963348	−	1.66857i	−0.249357	−	0.968412i	$-0.580219\pi$
$384$		0			0
$385$	−443.167	−	504.390i	−0.0586646	−	0.0667691i
$386$		0			0
$387$	−7548.72	+	5822.32i	−0.991532	+	0.764768i
$388$		0			0
$389$	1697.54	+	980.076i	0.221257	+	0.127743i	0.606532	−	0.795059i	$-0.292560\pi$
$389$	1697.54	+	980.076i	0.221257	+	0.127743i	−0.385275	+	0.922802i	$0.625894\pi$
$390$		0			0
$391$			10355.6i			1.33940i
$392$		0			0
$393$	12171.2	−	812.993i	1.56222	−	0.104351i
$394$		0			0
$395$	−2173.23	+	3764.14i	−0.276828	+	0.479480i
$396$		0			0
$397$	1987.93	+	3443.20i	0.251313	+	0.435287i	0.963888	−	0.266309i	$-0.0858042\pi$
$397$	1987.93	+	3443.20i	0.251313	+	0.435287i	−0.712574	+	0.701597i	$0.752471\pi$
$398$		0			0
$399$	6233.64	+	6206.58i	0.782136	+	0.778741i
$400$		0			0
$401$	−5696.07	+	3288.63i	−0.709346	+	0.409541i	−0.810819	−	0.585297i	$-0.800978\pi$
$401$	−5696.07	+	3288.63i	−0.709346	+	0.409541i	0.101473	+	0.994838i	$0.467645\pi$
$402$		0			0
$403$	2492.19	+	1438.87i	0.308052	+	0.177854i
$404$		0			0
$405$	1486.99	+	5440.77i	0.182443	+	0.667541i
$406$		0			0
$407$	−914.374			−0.111361
$408$		0			0
$409$	5615.62	−	9726.54i	0.678911	−	1.17591i	−0.296399	−	0.955064i	$-0.595786\pi$
$409$	5615.62	−	9726.54i	0.678911	−	1.17591i	0.975309	−	0.220843i	$-0.0708810\pi$
$410$		0			0
$411$	−10299.3	+	6900.36i	−1.23607	+	0.828150i
$412$		0			0
$413$	832.386	+	4164.50i	0.0991744	+	0.496178i
$414$		0			0
$415$	−2995.54	+	1729.47i	−0.354326	+	0.204570i
$416$		0			0
$417$	6037.20	+	2967.86i	0.708976	+	0.348529i
$418$		0			0
$419$	−6390.84			−0.745138			−0.372569	−	0.928004i	$-0.621523\pi$
$419$	−6390.84			−0.745138			−0.372569	+	0.928004i	$0.621523\pi$
$420$		0			0
$421$	−8934.00			−1.03424			−0.517122	−	0.855912i	$-0.672996\pi$
$421$	−8934.00			−1.03424			−0.517122	+	0.855912i	$0.672996\pi$
$422$		0			0
$423$	420.788	−	1023.08i	0.0483674	−	0.117598i
$424$		0			0
$425$	4143.04	−	2391.99i	0.472864	−	0.273008i
$426$		0			0
$427$	7324.40	+	2478.73i	0.830100	+	0.280923i
$428$		0			0
$429$	−444.171	−	662.956i	−0.0499878	−	0.0746103i
$430$		0			0
$431$	−7639.35	+	13231.7i	−0.853770	+	1.47877i	0.0240120	+	0.999712i	$0.492356\pi$
$431$	−7639.35	+	13231.7i	−0.853770	+	1.47877i	−0.877782	+	0.479061i	$0.840977\pi$
$432$		0			0
$433$	−10344.9			−1.14813			−0.574067	−	0.818808i	$-0.694635\pi$
$433$	−10344.9			−1.14813			−0.574067	+	0.818808i	$0.694635\pi$
$434$		0			0
$435$	6247.46	−	417.310i	0.688604	−	0.0459965i
$436$		0			0
$437$	11161.8	+	6444.28i	1.22184	+	0.705427i
$438$		0			0
$439$	−2626.01	+	1516.13i	−0.285496	+	0.164831i	−0.635909	−	0.771764i	$-0.719375\pi$
$439$	−2626.01	+	1516.13i	−0.285496	+	0.164831i	0.350413	+	0.936595i	$0.386041\pi$
$440$		0			0
$441$	−8000.04	+	4665.35i	−0.863842	+	0.503763i
$442$		0			0
$443$	32.5423	+	56.3650i	0.00349014	+	0.00604510i	0.867765	−	0.496974i	$-0.165556\pi$
$443$	32.5423	+	56.3650i	0.00349014	+	0.00604510i	−0.864275	+	0.503020i	$0.832222\pi$
$444$		0			0
$445$	1871.17	−	3240.95i	0.199330	−	0.345249i
$446$		0			0
$447$	−166.108	−	2486.77i	−0.0175764	−	0.263132i
$448$		0			0
$449$			13810.5i			1.45157i	0.687921	+	0.725786i	$0.258524\pi$
$449$			13810.5i			1.45157i	−0.687921	+	0.725786i	$0.741476\pi$
$450$		0			0
$451$	1508.20	+	870.760i	0.157469	+	0.0909146i
$452$		0			0
$453$	8798.50	−	5894.86i	0.912560	−	0.611401i
$454$		0			0
$455$	−1505.50	+	4448.61i	−0.155119	+	0.458361i
$456$		0			0
$457$	3947.83	+	6837.84i	0.404095	+	0.699914i	0.994216	−	0.107401i	$-0.0342530\pi$
$457$	3947.83	+	6837.84i	0.404095	+	0.699914i	−0.590120	+	0.807315i	$0.700920\pi$
$458$		0			0
$459$	−9769.38	−	3275.53i	−0.993454	−	0.333090i
$460$		0			0
$461$			17511.7i			1.76920i	0.466351	+	0.884600i	$0.345568\pi$
$461$			17511.7i			1.76920i	−0.466351	+	0.884600i	$0.654432\pi$
$462$		0			0
$463$			12405.7i			1.24523i	0.782530	+	0.622613i	$0.213929\pi$
$463$			12405.7i			1.24523i	−0.782530	+	0.622613i	$0.786071\pi$
$464$		0			0
$465$	−1557.28	+	3167.81i	−0.155306	+	0.315922i
$466$		0			0
$467$	−6418.39	−	11117.0i	−0.635990	−	1.10157i	−0.986304	−	0.164935i	$-0.947258\pi$
$467$	−6418.39	−	11117.0i	−0.635990	−	1.10157i	0.350314	−	0.936632i	$-0.386075\pi$
$468$		0			0
$469$	10991.8	−	2197.00i	1.08220	−	0.216307i
$470$		0			0
$471$	−2906.65	−	4338.38i	−0.284355	−	0.424420i
$472$		0			0
$473$	1432.78	+	827.216i	0.139280	+	0.0804131i
$474$		0			0
$475$		−	5954.14i		−	0.575147i
$476$		0			0
$477$	2560.18	+	19078.4i	0.245749	+	1.83132i
$478$		0			0
$479$	8391.40	−	14534.3i	0.800445	−	1.38641i	−0.118879	−	0.992909i	$-0.537930\pi$
$479$	8391.40	−	14534.3i	0.800445	−	1.38641i	0.919324	−	0.393502i	$-0.128737\pi$
$480$		0			0
$481$	3197.93	+	5538.98i	0.303146	+	0.525064i
$482$		0			0
$483$	−9573.84	+	9615.58i	−0.901915	+	0.905847i
$484$		0			0
$485$	7810.26	−	4509.26i	0.731228	−	0.422175i
$486$		0			0
$487$	4036.18	+	2330.29i	0.375558	+	0.216828i	0.675884	−	0.737008i	$-0.263762\pi$
$487$	4036.18	+	2330.29i	0.375558	+	0.216828i	−0.300326	+	0.953837i	$0.597095\pi$
$488$		0			0
$489$	−318.129	−	4762.65i	−0.0294198	−	0.440439i
$490$		0			0
$491$	11557.6			1.06230			0.531150	−	0.847278i	$-0.321760\pi$
$491$	11557.6			1.06230			0.531150	+	0.847278i	$0.321760\pi$
$492$		0			0
$493$	−5719.23	+	9906.00i	−0.522477	+	0.904957i
$494$		0			0
$495$	775.077	−	597.816i	0.0703780	−	0.0542825i
$496$		0			0
$497$	−5829.81	+	5122.18i	−0.526162	+	0.462296i
$498$		0			0
$499$	17114.6	−	9881.11i	1.53538	−	0.886452i	0.536279	−	0.844041i	$-0.319830\pi$
$499$	17114.6	−	9881.11i	1.53538	−	0.886452i	0.999100	−	0.0424107i	$-0.0135038\pi$
$500$		0			0
$501$	1186.04	−	2412.64i	0.105765	−	0.215147i
$502$		0			0
$503$	6607.52			0.585715			0.292858	−	0.956156i	$-0.405394\pi$
$503$	6607.52			0.585715			0.292858	+	0.956156i	$0.405394\pi$
$504$		0			0
$505$	−4228.88			−0.372639
$506$		0			0
$507$	2573.83	−	5235.68i	0.225460	−	0.458628i
$508$		0			0
$509$	−3471.97	+	2004.54i	−0.302343	+	0.174558i	−0.643495	−	0.765451i	$-0.722516\pi$
$509$	−3471.97	+	2004.54i	−0.302343	+	0.174558i	0.341152	+	0.940008i	$0.389183\pi$
$510$		0			0
$511$	−599.462	−	2999.16i	−0.0518955	−	0.259638i
$512$		0			0
$513$	−9610.04	+	8491.63i	−0.827083	+	0.730827i
$514$		0			0
$515$	−5477.44	+	9487.21i	−0.468670	+	0.811760i
$516$		0			0
$517$	−191.981			−0.0163313
$518$		0			0
$519$	−1027.97	−	15389.6i	−0.0869420	−	1.30159i
$520$		0			0
$521$	−187.285	−	108.129i	−0.0157488	−	0.00909255i	0.492105	−	0.870536i	$-0.336228\pi$
$521$	−187.285	−	108.129i	−0.0157488	−	0.00909255i	−0.507854	+	0.861443i	$0.669561\pi$
$522$		0			0
$523$	9201.01	−	5312.20i	0.769277	−	0.444142i	−0.0633395	−	0.997992i	$-0.520175\pi$
$523$	9201.01	−	5312.20i	0.769277	−	0.444142i	0.832617	+	0.553850i	$0.186842\pi$
$524$		0			0
$525$	6058.41	+	1609.23i	0.503639	+	0.133776i
$526$		0			0
$527$	−3224.25	−	5584.56i	−0.266509	−	0.461608i
$528$		0			0
$529$	−3856.99	+	6680.51i	−0.317004	+	0.549068i
$530$		0			0
$531$	−6136.35	+	823.450i	−0.501497	+	0.0672969i
$532$		0			0
$533$		−	12181.6i		−	0.989949i
$534$		0			0
$535$	6217.47	+	3589.66i	0.502439	+	0.290083i
$536$		0			0
$537$	−11838.4	−	17669.7i	−0.951334	−	1.41993i
$538$		0			0
$539$	1276.88	+	976.026i	0.102039	+	0.0779971i
$540$		0			0
$541$	−1314.29	−	2276.42i	−0.104447	−	0.180908i	0.809065	−	0.587719i	$-0.199974\pi$
$541$	−1314.29	−	2276.42i	−0.104447	−	0.180908i	−0.913512	+	0.406811i	$0.866641\pi$
$542$		0			0
$543$	−4591.90	+	9340.82i	−0.362905	+	0.738219i
$544$		0			0
$545$			9113.48i			0.716291i
$546$		0			0
$547$		−	655.077i		−	0.0512049i	−0.999672	−	0.0256024i	$-0.991850\pi$
$547$		−	655.077i		−	0.0512049i	0.999672	−	0.0256024i	$-0.00815040\pi$
$548$		0			0
$549$	−4287.94	+	10425.5i	−0.333342	+	0.810473i
$550$		0			0
$551$	7118.16	+	12329.0i	0.550352	+	0.953237i
$552$		0			0
$553$	3335.17	−	9855.10i	0.256466	−	0.757832i
$554$		0			0
$555$	−6517.68	+	4366.75i	−0.498487	+	0.333979i
$556$		0			0
$557$	19261.3	+	11120.5i	1.46522	+	0.845943i	0.999245	−	0.0388564i	$-0.0123715\pi$
$557$	19261.3	+	11120.5i	1.46522	+	0.845943i	0.465972	+	0.884800i	$0.345705\pi$
$558$		0			0
$559$		−	11572.4i		−	0.875601i
$560$		0			0
$561$	119.178	+	1784.19i	0.00896918	+	0.134276i
$562$		0			0
$563$	−2355.47	+	4079.80i	−0.176326	+	0.305405i	−0.940619	−	0.339464i	$-0.889754\pi$
$563$	−2355.47	+	4079.80i	−0.176326	+	0.305405i	0.764294	+	0.644868i	$0.223088\pi$
$564$		0			0
$565$	5738.51	+	9939.39i	0.427294	+	0.740095i
$566$		0			0
$567$	−6043.02	−	12073.4i	−0.447589	−	0.894239i
$568$		0			0
$569$	−7762.55	+	4481.71i	−0.571921	+	0.330199i	−0.757916	−	0.652352i	$-0.773782\pi$
$569$	−7762.55	+	4481.71i	−0.571921	+	0.330199i	0.185995	+	0.982551i	$0.440449\pi$
$570$		0			0
$571$	10869.6	+	6275.54i	0.796632	+	0.459936i	0.842292	−	0.539021i	$-0.181206\pi$
$571$	10869.6	+	6275.54i	0.796632	+	0.459936i	−0.0456601	+	0.998957i	$0.514539\pi$
$572$		0			0
$573$	18068.3	−	1206.90i	1.31730	−	0.0879911i
$574$		0			0
$575$	9184.45			0.666118
$576$		0			0
$577$	10267.9	−	17784.5i	0.740827	−	1.28315i	−0.211292	−	0.977423i	$-0.567767\pi$
$577$	10267.9	−	17784.5i	0.740827	−	1.28315i	0.952119	−	0.305728i	$-0.0988997\pi$
$578$		0			0
$579$	−5910.35	−	8821.61i	−0.424224	−	0.633184i
$580$		0			0
$581$	6219.95	−	5464.97i	0.444143	−	0.390232i
$582$		0			0
$583$	2893.06	−	1670.31i	0.205520	−	0.118657i
$584$		0			0
$585$	−6332.13	−	2604.36i	−0.447523	−	0.184063i
$586$		0			0
$587$	−6864.64			−0.482681			−0.241341	−	0.970440i	$-0.577587\pi$
$587$	−6864.64			−0.482681			−0.241341	+	0.970440i	$0.577587\pi$
$588$		0			0
$589$	−8025.81			−0.561456
$590$		0			0
$591$	−5964.67	−	2932.21i	−0.415150	−	0.204086i
$592$		0			0
$593$	−13106.1	+	7566.82i	−0.907595	+	0.524000i	−0.879657	−	0.475609i	$-0.842228\pi$
$593$	−13106.1	+	7566.82i	−0.907595	+	0.524000i	−0.0279385	+	0.999610i	$0.508894\pi$
$594$		0			0
$595$	7905.87	−	6946.24i	0.544721	−	0.478602i
$596$		0			0
$597$	20900.9	−	14003.3i	1.43286	−	0.959995i
$598$		0			0
$599$	−2088.66	+	3617.67i	−0.142472	+	0.246768i	−0.928427	−	0.371515i	$-0.878838\pi$
$599$	−2088.66	+	3617.67i	−0.142472	+	0.246768i	0.785955	+	0.618283i	$0.212172\pi$
$600$		0			0
$601$	11389.3			0.773013			0.386506	−	0.922287i	$-0.373682\pi$
$601$	11389.3			0.773013			0.386506	+	0.922287i	$0.373682\pi$
$602$		0			0
$603$	2173.42	+	16196.3i	0.146780	+	1.09381i
$604$		0			0
$605$	8771.24	+	5064.08i	0.589424	+	0.340304i
$606$		0			0
$607$	−3355.86	+	1937.50i	−0.224399	+	0.129557i	−0.607985	−	0.793948i	$-0.708022\pi$
$607$	−3355.86	+	1937.50i	−0.224399	+	0.129557i	0.383587	+	0.923505i	$0.374689\pi$
$608$		0			0
$609$	−14468.8	+	3910.64i	−0.962732	+	0.260209i
$610$		0			0
$611$	671.433	+	1162.96i	0.0444570	+	0.0770019i
$612$		0			0
$613$	−9363.76	+	16218.5i	−0.616963	+	1.06861i	0.373073	+	0.927802i	$0.378304\pi$
$613$	−9363.76	+	16218.5i	−0.616963	+	1.06861i	−0.990037	+	0.140810i	$0.955029\pi$
$614$		0			0
$615$	14909.0	−	995.869i	0.977541	−	0.0652964i
$616$		0			0
$617$		−	23711.0i		−	1.54712i	−0.633726	−	0.773558i	$-0.718475\pi$
$617$		−	23711.0i		−	1.54712i	0.633726	−	0.773558i	$-0.281525\pi$
$618$		0			0
$619$	−6835.41	−	3946.43i	−0.443842	−	0.256253i	0.261384	−	0.965235i	$-0.415821\pi$
$619$	−6835.41	−	3946.43i	−0.443842	−	0.256253i	−0.705226	+	0.708982i	$0.749155\pi$
$620$		0			0
$621$	−13098.6	−	14823.8i	−0.846422	−	0.957903i
$622$		0			0
$623$	−2871.60	+	8485.31i	−0.184668	+	0.545677i
$624$		0			0
$625$	1619.90	+	2805.76i	0.103674	+	0.179568i
$626$		0			0
$627$	1997.27	+	981.848i	0.127214	+	0.0625379i
$628$		0			0
$629$		−	14332.0i		−	0.908512i
$630$		0			0
$631$			6704.56i			0.422986i	0.977379	+	0.211493i	$0.0678326\pi$
$631$			6704.56i			0.422986i	−0.977379	+	0.211493i	$0.932167\pi$
$632$		0			0
$633$	−13954.4	−	6859.90i	−0.876203	−	0.430737i
$634$		0			0
$635$	404.280	+	700.234i	0.0252652	+	0.0437606i
$636$		0			0
$637$	1446.69	−	11148.5i	0.0899844	−	0.693436i
$638$		0			0
$639$	−6909.63	−	8958.43i	−0.427763	−	0.554601i
$640$		0			0
$641$	−23997.4	−	13854.9i	−1.47869	−	0.853721i	−0.478979	−	0.877827i	$-0.658993\pi$
$641$	−23997.4	−	13854.9i	−1.47869	−	0.853721i	−0.999709	+	0.0241056i	$0.992326\pi$
$642$		0			0
$643$			24577.1i			1.50735i	0.657247	+	0.753676i	$0.271721\pi$
$643$			24577.1i			1.50735i	−0.657247	+	0.753676i	$0.728279\pi$
$644$		0			0
$645$	14163.4	−	946.068i	0.864626	−	0.0577541i
$646$		0			0
$647$	4572.00	−	7918.94i	0.277811	−	0.481184i	−0.693029	−	0.720910i	$-0.743724\pi$
$647$	4572.00	−	7918.94i	0.277811	−	0.481184i	0.970841	+	0.239726i	$0.0770576\pi$
$648$		0			0
$649$	537.235	+	930.518i	0.0324935	+	0.0562805i
$650$		0			0
$651$	2169.14	−	8166.36i	0.130592	−	0.491651i
$652$		0			0
$653$	−14696.3	+	8484.90i	−0.880720	+	0.508484i	−0.870896	−	0.491468i	$-0.836460\pi$
$653$	−14696.3	+	8484.90i	−0.880720	+	0.508484i	−0.00982398	+	0.999952i	$0.503127\pi$
$654$		0			0
$655$	−15729.8	−	9081.61i	−0.938343	−	0.541752i
$656$		0			0
$657$	4419.23	−	593.026i	0.262421	−	0.0352148i
$658$		0			0
$659$	−11800.2			−0.697529			−0.348765	−	0.937210i	$-0.613399\pi$
$659$	−11800.2			−0.697529			−0.348765	+	0.937210i	$0.613399\pi$
$660$		0			0
$661$	4685.00	−	8114.67i	0.275682	−	0.477495i	−0.694625	−	0.719372i	$-0.744430\pi$
$661$	4685.00	−	8114.67i	0.275682	−	0.477495i	0.970307	+	0.241877i	$0.0777631\pi$
$662$		0			0
$663$	10391.3	−	6961.98i	0.608692	−	0.407814i
$664$		0			0
$665$	−2567.22	−	12844.0i	−0.149703	−	0.748978i
$666$		0			0
$667$	−19017.9	+	10980.0i	−1.10401	+	0.637401i
$668$		0			0
$669$	−15812.4	−	7773.30i	−0.913815	−	0.449227i
$670$		0			0
$671$	1956.33			0.112553
$672$		0			0
$673$	−23801.7			−1.36328			−0.681640	−	0.731688i	$-0.738733\pi$
$673$	−23801.7			−1.36328			−0.681640	+	0.731688i	$0.738733\pi$
$674$		0			0
$675$	−2905.09	+	8664.55i	−0.165655	+	0.494072i
$676$		0			0
$677$	22076.9	−	12746.1i	1.25330	−	0.723594i	0.281538	−	0.959550i	$-0.409156\pi$
$677$	22076.9	−	12746.1i	1.25330	−	0.723594i	0.971764	+	0.235956i	$0.0758222\pi$
$678$		0			0
$679$	−16217.3	+	14248.8i	−0.916586	+	0.805329i
$680$		0			0
$681$	13472.1	+	20108.0i	0.758077	+	1.13148i
$682$		0			0
$683$	15739.5	−	27261.5i	0.881777	−	1.52728i	0.0324129	−	0.999475i	$-0.489681\pi$
$683$	15739.5	−	27261.5i	0.881777	−	1.52728i	0.849364	−	0.527808i	$-0.176986\pi$
$684$		0			0
$685$	18459.4			1.02963
$686$		0			0
$687$	−15092.7	+	1008.14i	−0.838170	+	0.0559870i
$688$		0			0
$689$	−20236.4	−	11683.5i	−1.11893	−	0.646016i
$690$		0			0
$691$	13038.4	−	7527.71i	0.717805	−	0.414425i	−0.0961394	−	0.995368i	$-0.530649\pi$
$691$	13038.4	−	7527.71i	0.717805	−	0.414425i	0.813944	+	0.580943i	$0.197316\pi$
$692$		0			0
$693$	−1538.85	+	1766.88i	−0.0843520	+	0.0968518i
$694$		0			0
$695$	−5008.43	−	8674.86i	−0.273353	−	0.473462i
$696$		0			0
$697$	−13648.4	+	23639.7i	−0.741707	+	1.28467i
$698$		0			0
$699$	1055.43	+	15800.6i	0.0571100	+	0.854982i
$700$		0			0
$701$		−	9108.30i		−	0.490750i	−0.969428	−	0.245375i	$-0.921089\pi$
$701$		−	9108.30i		−	0.490750i	0.969428	−	0.245375i	$-0.0789111\pi$
$702$		0			0
$703$	−15447.8	−	8918.81i	−0.828771	−	0.478491i
$704$		0			0
$705$	−1368.44	+	916.836i	−0.0731043	+	0.0489788i
$706$		0			0
$707$	9926.38	−	1984.05i	0.528034	−	0.105542i
$708$		0			0
$709$	−2242.61	−	3884.32i	−0.118791	−	0.205753i	0.800498	−	0.599336i	$-0.204569\pi$
$709$	−2242.61	−	3884.32i	−0.118791	−	0.205753i	−0.919289	+	0.393583i	$0.871235\pi$
$710$		0			0
$711$	14027.7	+	5769.49i	0.739914	+	0.304322i
$712$		0			0
$713$		−	12380.1i		−	0.650262i
$714$		0			0
$715$			1188.22i			0.0621493i
$716$		0			0
$717$	−13598.1	+	27661.3i	−0.708273	+	1.44077i
$718$		0			0
$719$	1481.41	+	2565.87i	0.0768388	+	0.133089i	0.901884	−	0.431977i	$-0.142184\pi$
$719$	1481.41	+	2565.87i	0.0768388	+	0.133089i	−0.825046	+	0.565066i	$0.808851\pi$
$720$		0			0
$721$	8406.01	−	24839.0i	0.434197	−	1.28301i
$722$		0			0
$723$	15020.6	+	22419.4i	0.772647	+	1.15323i
$724$		0			0
$725$	8785.72	+	5072.44i	0.450060	+	0.259842i
$726$		0			0
$727$			1003.13i			0.0511746i	0.999673	+	0.0255873i	$0.00814559\pi$
$727$			1003.13i			0.0511746i	−0.999673	+	0.0255873i	$0.991854\pi$
$728$		0			0
$729$	18127.8	−	7668.28i	0.920989	−	0.389589i
$730$		0			0
$731$	−12965.9	+	22457.5i	−0.656033	+	1.13628i
$732$		0			0
$733$	−2822.38	−	4888.51i	−0.142220	−	0.246332i	0.786113	−	0.618083i	$-0.212091\pi$
$733$	−2822.38	−	4888.51i	−0.142220	−	0.246332i	−0.928332	+	0.371752i	$0.878757\pi$
$734$		0			0
$735$	13762.8	+	859.189i	0.690679	+	0.0431179i
$736$		0			0
$737$	2456.01	−	1417.98i	0.122752	−	0.0708710i
$738$		0			0
$739$	−6173.16	−	3564.08i	−0.307285	−	0.177411i	0.338426	−	0.940993i	$-0.390105\pi$
$739$	−6173.16	−	3564.08i	−0.307285	−	0.177411i	−0.645711	+	0.763582i	$0.723439\pi$
$740$		0			0
$741$	−1037.53	−	15532.7i	−0.0514369	−	0.770052i
$742$		0			0
$743$	−8399.72			−0.414746			−0.207373	−	0.978262i	$-0.566491\pi$
$743$	−8399.72			−0.414746			−0.207373	+	0.978262i	$0.566491\pi$
$744$		0			0
$745$	−1855.52	+	3213.86i	−0.0912498	+	0.158049i
$746$		0			0
$747$	7372.05	+	9557.96i	0.361083	+	0.468149i
$748$		0			0
$749$	−16278.3	−	5508.91i	−0.794120	−	0.268746i
$750$		0			0
$751$	−13791.0	+	7962.22i	−0.670093	+	0.386878i	−0.796112	−	0.605150i	$-0.793113\pi$
$751$	−13791.0	+	7962.22i	−0.670093	+	0.386878i	0.126019	+	0.992028i	$0.459780\pi$
$752$		0			0
$753$	9235.97	−	18787.8i	0.446982	−	0.909248i
$754$		0			0
$755$	−15769.5			−0.760148
$756$		0			0
$757$	−24367.3			−1.16994			−0.584971	−	0.811054i	$-0.698894\pi$
$757$	−24367.3			−1.16994			−0.584971	+	0.811054i	$0.698894\pi$
$758$		0			0
$759$	−1514.53	+	3080.85i	−0.0724295	+	0.147336i
$760$		0			0
$761$	16822.7	−	9712.61i	0.801345	−	0.462657i	−0.0425963	−	0.999092i	$-0.513563\pi$
$761$	16822.7	−	9712.61i	0.801345	−	0.462657i	0.843941	+	0.536436i	$0.180230\pi$
$762$		0			0
$763$	−4275.74	−	21391.9i	−0.202873	−	1.01499i
$764$		0			0
$765$	9370.23	+	12148.6i	0.442852	+	0.574163i
$766$		0			0
$767$	3757.85	−	6508.79i	0.176908	−	0.306413i
$768$		0			0
$769$	11198.2			0.525122			0.262561	−	0.964915i	$-0.415433\pi$
$769$	11198.2			0.525122			0.262561	+	0.964915i	$0.415433\pi$
$770$		0			0
$771$	561.641	+	8408.22i	0.0262348	+	0.392756i
$772$		0			0
$773$	−14571.8	−	8413.06i	−0.678024	−	0.391458i	0.121086	−	0.992642i	$-0.461362\pi$
$773$	−14571.8	−	8413.06i	−0.678024	−	0.391458i	−0.799110	+	0.601184i	$0.794696\pi$
$774$		0			0
$775$	−4953.00	+	2859.61i	−0.229570	+	0.132542i
$776$		0			0
$777$	13250.1	−	13307.9i	0.611769	−	0.614436i
$778$		0			0
$779$	16986.8	+	29422.0i	0.781278	+	1.35321i
$780$		0			0
$781$	−981.697	+	1700.35i	−0.0449781	+	0.0779043i
$782$		0			0
$783$	−4342.98	−	21414.4i	−0.198219	−	0.977379i
$784$		0			0
$785$			7775.66i			0.353535i
$786$		0			0
$787$	8664.27	+	5002.32i	0.392437	+	0.226574i	0.683216	−	0.730217i	$-0.260581\pi$
$787$	8664.27	+	5002.32i	0.392437	+	0.226574i	−0.290779	+	0.956790i	$0.593914\pi$
$788$		0			0
$789$	−22436.1	−	33487.5i	−1.01235	−	1.51101i
$790$		0			0
$791$	−18133.1	−	20638.2i	−0.815094	−	0.927700i
$792$		0			0
$793$	−6842.07	−	11850.8i	−0.306392	−	0.530687i
$794$		0			0
$795$	12645.0	−	25722.3i	0.564114	−	1.14752i
$796$		0			0
$797$			5849.67i			0.259982i	0.991515	+	0.129991i	$0.0414949\pi$
$797$			5849.67i			0.259982i	−0.991515	+	0.129991i	$0.958505\pi$
$798$		0			0
$799$		−	3009.12i		−	0.133235i
$800$		0			0
$801$	−12077.9	−	4967.57i	−0.532775	−	0.219127i
$802$		0			0
$803$	−386.902	−	670.134i	−0.0170031	−	0.0294502i
$804$		0			0
$805$	19812.3	−	3960.02i	0.867444	−	0.173382i
$806$		0			0
$807$	35228.7	−	23602.7i	1.53669	−	1.02956i
$808$		0			0
$809$	−23767.3	−	13722.1i	−1.03290	−	0.596344i	−0.115084	−	0.993356i	$-0.536714\pi$
$809$	−23767.3	−	13722.1i	−1.03290	−	0.596344i	−0.917813	+	0.397012i	$0.870047\pi$
$810$		0			0
$811$		−	38119.2i		−	1.65049i	−0.564776	−	0.825244i	$-0.691037\pi$
$811$		−	38119.2i		−	1.65049i	0.564776	−	0.825244i	$-0.308963\pi$
$812$		0			0
$813$	551.279	+	8253.09i	0.0237813	+	0.356025i
$814$		0			0
$815$	−3553.69	+	6155.17i	−0.152737	+	0.264548i
$816$		0			0
$817$	16137.3	+	27950.7i	0.691033	+	1.19690i
$818$		0			0
$819$	16085.1	+	3142.34i	0.686277	+	0.134069i
$820$		0			0
$821$	13598.4	−	7851.04i	0.578060	−	0.333743i	−0.182302	−	0.983243i	$-0.558355\pi$
$821$	13598.4	−	7851.04i	0.578060	−	0.333743i	0.760362	+	0.649499i	$0.225021\pi$
$822$		0			0
$823$	23489.8	+	13561.9i	0.994902	+	0.574407i	0.906736	−	0.421699i	$-0.138566\pi$
$823$	23489.8	+	13561.9i	0.994902	+	0.574407i	0.0881660	+	0.996106i	$0.471899\pi$
$824$		0			0
$825$	1582.42	−	105.700i	0.0667791	−	0.00446062i
$826$		0			0
$827$	−31071.7			−1.30649			−0.653245	−	0.757146i	$-0.726593\pi$
$827$	−31071.7			−1.30649			−0.653245	+	0.757146i	$0.726593\pi$
$828$		0			0
$829$	11439.1	−	19813.1i	0.479248	−	0.830081i	−0.520469	−	0.853880i	$-0.674243\pi$
$829$	11439.1	−	19813.1i	0.479248	−	0.830081i	0.999717	+	0.0237993i	$0.00757626\pi$
$830$		0			0
$831$	11955.6	+	17844.6i	0.499079	+	0.744911i
$832$		0			0
$833$	−15298.3	+	20013.9i	−0.636322	+	0.832463i
$834$		0			0
$835$	−3466.73	+	2001.52i	−0.143678	+	0.0829524i
$836$		0			0
$837$	11679.3	+	3915.88i	0.482311	+	0.161712i
$838$		0			0
$839$	32438.5			1.33480			0.667402	−	0.744698i	$-0.267406\pi$
$839$	32438.5			1.33480			0.667402	+	0.744698i	$0.267406\pi$
$840$		0			0
$841$	132.662			0.00543941
$842$		0			0
$843$	13152.9	+	6465.88i	0.537376	+	0.264172i
$844$		0			0
$845$	−7523.15	+	4343.49i	−0.306277	+	0.176829i
$846$		0			0
$847$	−22964.4	−	7771.63i	−0.931603	−	0.315273i
$848$		0			0
$849$	−20945.1	+	14032.9i	−0.846682	+	0.567264i
$850$		0			0
$851$	13757.5	−	23828.8i	0.554174	−	0.959858i
$852$		0			0
$853$	4830.11			0.193880			0.0969401	−	0.995290i	$-0.469094\pi$
$853$	4830.11			0.193880			0.0969401	+	0.995290i	$0.469094\pi$
$854$		0			0
$855$	18925.6	−	2539.66i	0.757007	−	0.101584i
$856$		0			0
$857$	43058.1	+	24859.6i	1.71626	+	0.990884i	0.925489	+	0.378774i	$0.123654\pi$
$857$	43058.1	+	24859.6i	1.71626	+	0.990884i	0.790773	+	0.612110i	$0.209679\pi$
$858$		0			0
$859$	−15768.1	+	9103.74i	−0.626312	+	0.361601i	−0.779322	−	0.626623i	$-0.784436\pi$
$859$	−15768.1	+	9103.74i	−0.626312	+	0.361601i	0.153011	+	0.988225i	$0.451103\pi$
$860$		0			0
$861$	−34528.3	+	9332.37i	−1.36669	+	0.369392i
$862$		0			0
$863$	−8185.47	−	14177.7i	−0.322870	−	0.559227i	0.658209	−	0.752835i	$-0.271314\pi$
$863$	−8185.47	−	14177.7i	−0.322870	−	0.559227i	−0.981079	+	0.193608i	$0.937981\pi$
$864$		0			0
$865$	−11483.0	+	19889.2i	−0.451370	+	0.781796i
$866$		0			0
$867$	−2493.72	+	166.572i	−0.0976831	+	0.00652490i
$868$		0			0
$869$		−	2632.28i		−	0.102755i
$870$		0			0
$871$	−17179.3	−	9918.48i	−0.668311	−	0.385850i
$872$		0			0
$873$	−19221.1	−	24920.4i	−0.745173	−	0.966127i
$874$		0			0
$875$	−17983.1	−	20467.4i	−0.694787	−	0.790772i
$876$		0			0
$877$	−4503.10	−	7799.60i	−0.173385	−	0.300312i	0.766216	−	0.642583i	$-0.222137\pi$
$877$	−4503.10	−	7799.60i	−0.173385	−	0.300312i	−0.939601	+	0.342271i	$0.888804\pi$
$878$		0			0
$879$	27016.3	+	13281.1i	1.03667	+	0.509624i
$880$		0			0
$881$			14494.2i			0.554282i	0.960829	+	0.277141i	$0.0893868\pi$
$881$			14494.2i			0.554282i	−0.960829	+	0.277141i	$0.910613\pi$
$882$		0			0
$883$		−	47753.9i		−	1.81999i	−0.414625	−	0.909993i	$-0.636087\pi$
$883$		−	47753.9i		−	1.81999i	0.414625	−	0.909993i	$-0.363913\pi$
$884$		0			0
$885$	8273.27	+	4067.10i	0.314241	+	0.154479i
$886$		0			0
$887$	20676.1	+	35812.0i	0.782677	+	1.35564i	0.930377	+	0.366604i	$0.119480\pi$
$887$	20676.1	+	35812.0i	0.782677	+	1.35564i	−0.147700	+	0.989032i	$0.547187\pi$
$888$		0			0
$889$	−1277.49	−	1453.97i	−0.0481952	−	0.0548533i
$890$		0			0
$891$	−2427.40	−	2403.29i	−0.0912693	−	0.0903628i
$892$		0			0
$893$	−3243.40	−	1872.58i	−0.121541	−	0.0701719i
$894$		0			0
$895$			31669.4i			1.18278i
$896$		0			0
$897$	23959.7	−	1600.43i	0.891852	−	0.0595727i
$898$		0			0
$899$	6837.32	−	11842.6i	0.253657	−	0.439347i
$900$		0			0
$901$	26180.6	+	45346.1i	0.968038	+	1.67669i
$902$		0			0
$903$	−32801.6	+	8865.68i	−1.20883	+	0.326723i
$904$		0			0
$905$	13421.8	−	7749.10i	0.492991	−	0.284629i
$906$		0			0
$907$	−31748.2	−	18329.9i	−1.16227	−	0.671040i	−0.210427	−	0.977610i	$-0.567485\pi$
$907$	−31748.2	−	18329.9i	−1.16227	−	0.671040i	−0.951848	+	0.306570i	$0.900819\pi$
$908$		0			0
$909$	1962.75	+	14626.4i	0.0716175	+	0.533694i
$910$		0			0
$911$	5857.49			0.213027			0.106513	−	0.994311i	$-0.466031\pi$
$911$	5857.49			0.213027			0.106513	+	0.994311i	$0.466031\pi$
$912$		0			0
$913$	1047.39	−	1814.14i	0.0379668	−	0.0657605i
$914$		0			0
$915$	13944.8	−	9342.80i	0.503826	−	0.337556i
$916$		0			0
$917$	41183.1	+	13937.2i	1.48308	+	0.501904i
$918$		0			0
$919$	−1338.60	+	772.843i	−0.0480483	+	0.0277407i	−0.523832	−	0.851822i	$-0.675498\pi$
$919$	−1338.60	+	772.843i	−0.0480483	+	0.0277407i	0.475783	+	0.879562i	$0.342165\pi$
$920$		0			0
$921$	33654.1	+	16544.2i	1.20406	+	0.591910i
$922$		0			0
$923$	13733.5			0.489756
$924$		0			0
$925$	−12711.2			−0.451828
$926$		0			0
$927$	35355.6	+	14541.5i	1.25268	+	0.515217i
$928$		0			0
$929$	−23951.8	+	13828.6i	−0.845892	+	0.488376i	−0.859263	−	0.511535i	$-0.829077\pi$
$929$	−23951.8	+	13828.6i	−0.845892	+	0.488376i	0.0133709	+	0.999911i	$0.495744\pi$
$930$		0			0
$931$	12052.0	+	28944.1i	0.424262	+	1.01891i
$932$		0			0
$933$	5337.49	+	7966.58i	0.187290	+	0.279543i
$934$		0			0
$935$	1331.29	−	2305.86i	0.0465646	−	0.0806522i
$936$		0			0
$937$	−28569.7			−0.996084			−0.498042	−	0.867153i	$-0.665947\pi$
$937$	−28569.7			−0.996084			−0.498042	+	0.867153i	$0.665947\pi$
$938$		0			0
$939$	−43302.1	+	2892.43i	−1.50491	+	0.100523i
$940$		0			0
$941$	3767.92	+	2175.41i	0.130532	+	0.0753628i	0.563844	−	0.825881i	$-0.309322\pi$
$941$	3767.92	+	2175.41i	0.130532	+	0.0753628i	−0.433312	+	0.901244i	$0.642655\pi$
$942$		0			0
$943$	−45384.3	+	26202.7i	−1.56725	+	0.904853i
$944$		0			0
$945$	−2530.90	+	19943.4i	−0.0871218	+	0.686518i
$946$		0			0
$947$	21550.1	+	37325.9i	0.739476	+	1.28081i	0.952731	+	0.303814i	$0.0982602\pi$
$947$	21550.1	+	37325.9i	0.739476	+	1.28081i	−0.213255	+	0.976997i	$0.568406\pi$
$948$		0			0
$949$	−2706.30	+	4687.45i	−0.0925714	+	0.160338i
$950$		0			0
$951$	456.381	+	6832.40i	0.0155617	+	0.232971i
$952$		0			0
$953$			28162.0i			0.957246i	0.878020	+	0.478623i	$0.158864\pi$
$953$			28162.0i			0.957246i	−0.878020	+	0.478623i	$0.841136\pi$
$954$		0			0
$955$	−23351.1	−	13481.8i	−0.791230	−	0.456817i
$956$		0			0
$957$	−3150.29	+	2110.65i	−0.106410	+	0.0712931i
$958$		0			0
$959$	−43329.3	+	8660.51i	−1.45899	+	0.291619i
$960$		0			0
$961$	−11040.9	−	19123.4i	−0.370613	−	0.641920i
$962$		0			0
$963$	9529.83	−	23170.4i	0.318893	−	0.775344i
$964$		0			0
$965$			15811.0i			0.527433i
$966$		0			0
$967$			37267.7i			1.23935i	0.784859	+	0.619674i	$0.212735\pi$
$967$			37267.7i			1.23935i	−0.784859	+	0.619674i	$0.787265\pi$
$968$		0			0
$969$	−15389.6	+	31305.4i	−0.510201	+	1.03785i
$970$		0			0
$971$	13459.9	+	23313.3i	0.444851	+	0.770504i	0.998042	−	0.0625501i	$-0.0199233\pi$
$971$	13459.9	+	23313.3i	0.444851	+	0.770504i	−0.553191	+	0.833055i	$0.686590\pi$
$972$		0			0
$973$	15826.1	+	18012.5i	0.521442	+	0.593479i
$974$		0			0
$975$	−6174.64	−	9216.09i	−0.202817	−	0.302719i
$976$		0			0
$977$	44198.1	+	25517.8i	1.44731	+	0.835605i	0.998321	−	0.0579314i	$-0.0184505\pi$
$977$	44198.1	+	25517.8i	1.44731	+	0.835605i	0.448990	+	0.893537i	$0.351784\pi$
$978$		0			0
$979$			2266.41i			0.0739885i
$980$		0			0
$981$	31520.8	−	4229.84i	1.02587	−	0.137664i
$982$		0			0
$983$	−16279.8	+	28197.5i	−0.528225	+	0.914913i	0.471233	+	0.882009i	$0.343809\pi$
$983$	−16279.8	+	28197.5i	−0.528225	+	0.914913i	−0.999458	+	0.0329045i	$0.989524\pi$
$984$		0			0
$985$	4948.27	+	8570.65i	0.160066	+	0.277242i
$986$		0			0
$987$	2781.97	−	2794.10i	0.0897174	−	0.0901085i
$988$		0			0
$989$	−43114.8	+	24892.3i	−1.38622	+	0.800334i
$990$		0			0
$991$	−49932.4	−	28828.5i	−1.60056	−	0.924084i	−0.991375	−	0.131055i	$-0.958164\pi$
$991$	−49932.4	−	28828.5i	−1.60056	−	0.924084i	−0.609185	−	0.793028i	$-0.708503\pi$
$992$		0			0
$993$	2539.40	+	38016.9i	0.0811536	+	1.21494i
$994$		0			0
$995$	−37460.7			−1.19355
$996$		0			0
$997$	22275.1	−	38581.7i	0.707583	−	1.22557i	−0.258168	−	0.966100i	$-0.583119\pi$
$997$	22275.1	−	38581.7i	0.707583	−	1.22557i	0.965751	−	0.259470i	$-0.0835479\pi$
$998$		0			0
$999$	18128.3	+	20516.0i	0.574129	+	0.649746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.g.95.7	yes	32
3.2	odd	2	inner	336.4.bj.g.95.12	yes	32
4.3	odd	2	inner	336.4.bj.g.95.10	yes	32
7.2	even	3	inner	336.4.bj.g.191.5	yes	32
12.11	even	2	inner	336.4.bj.g.95.5	✓	32
21.2	odd	6	inner	336.4.bj.g.191.10	yes	32
28.23	odd	6	inner	336.4.bj.g.191.12	yes	32
84.23	even	6	inner	336.4.bj.g.191.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.g.95.5	✓	32	12.11	even	2	inner
336.4.bj.g.95.7	yes	32	1.1	even	1	trivial
336.4.bj.g.95.10	yes	32	4.3	odd	2	inner
336.4.bj.g.95.12	yes	32	3.2	odd	2	inner
336.4.bj.g.191.5	yes	32	7.2	even	3	inner
336.4.bj.g.191.7	yes	32	84.23	even	6	inner
336.4.bj.g.191.10	yes	32	21.2	odd	6	inner
336.4.bj.g.191.12	yes	32	28.23	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-2.29238 + 4.66315i) q^{3} +(6.70049 - 3.86853i) q^{5} +(-13.9129 + 12.2242i) q^{7} +(-16.4900 - 21.3795i) q^{9} +(-2.34284 + 4.05791i) q^{11} +32.7753 q^{13} +(2.67945 + 40.1135i) q^{15} +(-63.6042 - 36.7219i) q^{17} +(-79.1618 + 45.7041i) q^{19} +(-25.1093 - 92.9006i) q^{21} +(-70.5000 - 122.110i) q^{23} +(-32.5690 + 56.4111i) q^{25} +(137.497 - 27.8853i) q^{27} -155.744i q^{29} +(76.0386 + 43.9009i) q^{31} +(-13.5520 - 20.2273i) q^{33} +(-45.9340 + 135.730i) q^{35} +(97.5712 + 168.998i) q^{37} +(-75.1336 + 152.836i) q^{39} -371.669i q^{41} -353.083i q^{43} +(-193.198 - 79.4609i) q^{45} +(20.4859 + 35.4826i) q^{47} +(44.1397 - 340.148i) q^{49} +(317.045 - 212.415i) q^{51} +(-617.427 - 356.471i) q^{53} +36.2533i q^{55} +(-31.6559 - 473.915i) q^{57} +(114.655 - 198.588i) q^{59} +(-208.757 - 361.577i) q^{61} +(490.770 + 95.8751i) q^{63} +(219.611 - 126.792i) q^{65} +(-524.154 - 302.620i) q^{67} +(731.028 - 48.8302i) q^{69} +419.021 q^{71} +(-82.5712 + 143.018i) q^{73} +(-188.393 - 281.190i) q^{75} +(-17.0088 - 85.0967i) q^{77} +(-486.508 + 280.886i) q^{79} +(-185.162 + 705.093i) q^{81} -447.063 q^{83} -568.239 q^{85} +(726.260 + 357.026i) q^{87} +(418.887 - 241.845i) q^{89} +(-456.001 + 400.651i) q^{91} +(-379.026 + 253.942i) q^{93} +(-353.615 + 612.480i) q^{95} +1165.63 q^{97} +(125.389 - 16.8262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{9} - 40 q^{13} - 148 q^{21} + 316 q^{25} - 128 q^{33} - 644 q^{37} + 316 q^{45} + 632 q^{49} + 1136 q^{57} + 328 q^{61} - 1424 q^{69} + 1124 q^{73} + 1564 q^{81} - 912 q^{85} + 24 q^{93} - 3304 q^{97}+O(q^{100}) \) 32 * q + 32 * q^9 - 40 * q^13 - 148 * q^21 + 316 * q^25 - 128 * q^33 - 644 * q^37 + 316 * q^45 + 632 * q^49 + 1136 * q^57 + 328 * q^61 - 1424 * q^69 + 1124 * q^73 + 1564 * q^81 - 912 * q^85 + 24 * q^93 - 3304 * q^97

Introduction

L-functions

Modular forms

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Database

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