LMFDB - Embedded newform 672.2.bb.a.367.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.4
Character	$\chi$	$=$	672.367
Dual form			672.2.bb.a.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-0.155280 - 0.268953i) q^{5} +(2.58581 - 0.560001i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.155280 - 0.268953i) q^{5} +(2.58581 - 0.560001i) q^{7} +(0.500000 + 0.866025i) q^{9} +(0.622560 - 1.07831i) q^{11} -2.68845 q^{13} +0.310560i q^{15} +(1.93094 + 1.11483i) q^{17} +(5.14286 - 2.96923i) q^{19} +(-2.51938 - 0.807929i) q^{21} +(-2.86149 + 1.65208i) q^{23} +(2.45178 - 4.24660i) q^{25} -1.00000i q^{27} +0.191829i q^{29} +(1.95686 - 3.38939i) q^{31} +(-1.07831 + 0.622560i) q^{33} +(-0.552137 - 0.608503i) q^{35} +(-0.643623 + 0.371596i) q^{37} +(2.32827 + 1.34423i) q^{39} -9.28628i q^{41} +10.8775 q^{43} +(0.155280 - 0.268953i) q^{45} +(-5.43928 - 9.42111i) q^{47} +(6.37280 - 2.89611i) q^{49} +(-1.11483 - 1.93094i) q^{51} +(10.8205 + 6.24721i) q^{53} -0.386684 q^{55} -5.93846 q^{57} +(-5.16549 - 2.98230i) q^{59} +(-4.58974 - 7.94967i) q^{61} +(1.77788 + 1.95937i) q^{63} +(0.417462 + 0.723066i) q^{65} +(2.25830 - 3.91150i) q^{67} +3.30416 q^{69} +7.92636i q^{71} +(6.97675 + 4.02803i) q^{73} +(-4.24660 + 2.45178i) q^{75} +(1.00597 - 3.13693i) q^{77} +(-13.2839 + 7.66944i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.2247i q^{83} -0.692441i q^{85} +(0.0959146 - 0.166129i) q^{87} +(-5.53347 + 3.19475i) q^{89} +(-6.95181 + 1.50553i) q^{91} +(-3.38939 + 1.95686i) q^{93} +(-1.59716 - 0.922123i) q^{95} +1.62950i q^{97} +1.24512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	−0.155280	−	0.268953i	−0.0694432	−	0.120279i	0.829213	−	0.558933i	$-0.188789\pi$
$5$	−0.155280	−	0.268953i	−0.0694432	−	0.120279i	−0.898656	+	0.438653i	$0.855456\pi$
$6$		0			0
$7$	2.58581	−	0.560001i	0.977343	−	0.211660i
$7$	2.58581	−	0.560001i	0.977343	−	0.211660i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	0.622560	−	1.07831i	0.187709	−	0.325121i	−0.756777	−	0.653673i	$-0.773227\pi$
$11$	0.622560	−	1.07831i	0.187709	−	0.325121i	0.944486	+	0.328552i	$0.106560\pi$
$12$		0			0
$13$	−2.68845			−0.745642			−0.372821	−	0.927903i	$-0.621609\pi$
$13$	−2.68845			−0.745642			−0.372821	+	0.927903i	$0.621609\pi$
$14$		0			0
$15$			0.310560i			0.0801862i
$16$		0			0
$17$	1.93094	+	1.11483i	0.468321	+	0.270386i	0.715537	−	0.698575i	$-0.246182\pi$
$17$	1.93094	+	1.11483i	0.468321	+	0.270386i	−0.247215	+	0.968961i	$0.579516\pi$
$18$		0			0
$19$	5.14286	−	2.96923i	1.17985	−	0.681188i	0.223872	−	0.974619i	$-0.428130\pi$
$19$	5.14286	−	2.96923i	1.17985	−	0.681188i	0.955980	+	0.293431i	$0.0947970\pi$
$20$		0			0
$21$	−2.51938	−	0.807929i	−0.549773	−	0.176305i
$22$		0			0
$23$	−2.86149	+	1.65208i	−0.596662	+	0.344483i	−0.767727	−	0.640777i	$-0.778612\pi$
$23$	−2.86149	+	1.65208i	−0.596662	+	0.344483i	0.171066	+	0.985260i	$0.445279\pi$
$24$		0			0
$25$	2.45178	−	4.24660i	0.490355	−	0.849320i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			0.191829i			0.0356218i	0.999841	+	0.0178109i	$0.00566968\pi$
$29$			0.191829i			0.0356218i	−0.999841	+	0.0178109i	$0.994330\pi$
$30$		0			0
$31$	1.95686	−	3.38939i	0.351463	−	0.608752i	−0.635043	−	0.772477i	$-0.719018\pi$
$31$	1.95686	−	3.38939i	0.351463	−	0.608752i	0.986506	+	0.163725i	$0.0523510\pi$
$32$		0			0
$33$	−1.07831	+	0.622560i	−0.187709	+	0.108374i
$34$		0			0
$35$	−0.552137	−	0.608503i	−0.0933282	−	0.102856i
$36$		0			0
$37$	−0.643623	+	0.371596i	−0.105811	+	0.0610900i	−0.551972	−	0.833863i	$-0.686124\pi$
$37$	−0.643623	+	0.371596i	−0.105811	+	0.0610900i	0.446161	+	0.894953i	$0.352791\pi$
$38$		0			0
$39$	2.32827	+	1.34423i	0.372821	+	0.215248i
$40$		0			0
$41$		−	9.28628i		−	1.45027i	−0.688605	−	0.725137i	$-0.741776\pi$
$41$		−	9.28628i		−	1.45027i	0.688605	−	0.725137i	$-0.258224\pi$
$42$		0			0
$43$	10.8775			1.65880			0.829401	−	0.558654i	$-0.188682\pi$
$43$	10.8775			1.65880			0.829401	+	0.558654i	$0.188682\pi$
$44$		0			0
$45$	0.155280	−	0.268953i	0.0231477	−	0.0400931i
$46$		0			0
$47$	−5.43928	−	9.42111i	−0.793400	−	1.37421i	−0.923850	−	0.382755i	$-0.874975\pi$
$47$	−5.43928	−	9.42111i	−0.793400	−	1.37421i	0.130450	−	0.991455i	$-0.458358\pi$
$48$		0			0
$49$	6.37280	−	2.89611i	0.910400	−	0.413730i
$50$		0			0
$51$	−1.11483	−	1.93094i	−0.156107	−	0.270386i
$52$		0			0
$53$	10.8205	+	6.24721i	1.48631	+	0.858120i	0.999878	−	0.0156002i	$-0.00496591\pi$
$53$	10.8205	+	6.24721i	1.48631	+	0.858120i	0.486429	+	0.873720i	$0.338299\pi$
$54$		0			0
$55$	−0.386684			−0.0521405
$56$		0			0
$57$	−5.93846			−0.786568
$58$		0			0
$59$	−5.16549	−	2.98230i	−0.672490	−	0.388262i	0.124530	−	0.992216i	$-0.460258\pi$
$59$	−5.16549	−	2.98230i	−0.672490	−	0.388262i	−0.797019	+	0.603954i	$0.793591\pi$
$60$		0			0
$61$	−4.58974	−	7.94967i	−0.587656	−	1.01785i	−0.994539	−	0.104370i	$-0.966717\pi$
$61$	−4.58974	−	7.94967i	−0.587656	−	1.01785i	0.406882	−	0.913481i	$-0.366616\pi$
$62$		0			0
$63$	1.77788	+	1.95937i	0.223992	+	0.246858i
$64$		0			0
$65$	0.417462	+	0.723066i	0.0517798	+	0.0896852i
$66$		0			0
$67$	2.25830	−	3.91150i	0.275896	−	0.477865i	−0.694465	−	0.719526i	$-0.744359\pi$
$67$	2.25830	−	3.91150i	0.275896	−	0.477865i	0.970361	+	0.241661i	$0.0776923\pi$
$68$		0			0
$69$	3.30416			0.397774
$70$		0			0
$71$			7.92636i			0.940686i	0.882484	+	0.470343i	$0.155870\pi$
$71$			7.92636i			0.940686i	−0.882484	+	0.470343i	$0.844130\pi$
$72$		0			0
$73$	6.97675	+	4.02803i	0.816567	+	0.471445i	0.849231	−	0.528021i	$-0.177066\pi$
$73$	6.97675	+	4.02803i	0.816567	+	0.471445i	−0.0326645	+	0.999466i	$0.510399\pi$
$74$		0			0
$75$	−4.24660	+	2.45178i	−0.490355	+	0.283107i
$76$		0			0
$77$	1.00597	−	3.13693i	0.114641	−	0.357486i
$78$		0			0
$79$	−13.2839	+	7.66944i	−1.49455	+	0.862880i	−0.999980	−	0.00625715i	$-0.998008\pi$
$79$	−13.2839	+	7.66944i	−1.49455	+	0.862880i	−0.494571	+	0.869137i	$0.664675\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			14.2247i			1.56137i	0.624926	+	0.780684i	$0.285129\pi$
$83$			14.2247i			1.56137i	−0.624926	+	0.780684i	$0.714871\pi$
$84$		0			0
$85$		−	0.692441i		−	0.0751058i
$86$		0			0
$87$	0.0959146	−	0.166129i	0.0102831	−	0.0178109i
$88$		0			0
$89$	−5.53347	+	3.19475i	−0.586547	+	0.338643i	−0.763731	−	0.645535i	$-0.776635\pi$
$89$	−5.53347	+	3.19475i	−0.586547	+	0.338643i	0.177184	+	0.984178i	$0.443301\pi$
$90$		0			0
$91$	−6.95181	+	1.50553i	−0.728748	+	0.157823i
$92$		0			0
$93$	−3.38939	+	1.95686i	−0.351463	+	0.202917i
$94$		0			0
$95$	−1.59716	−	0.922123i	−0.163865	−	0.0946078i
$96$		0			0
$97$			1.62950i			0.165450i	0.996572	+	0.0827252i	$0.0263624\pi$
$97$			1.62950i			0.165450i	−0.996572	+	0.0827252i	$0.973638\pi$
$98$		0			0
$99$	1.24512			0.125139
$100$		0			0
$101$	1.08936	−	1.88683i	0.108396	−	0.187747i	−0.806725	−	0.590927i	$-0.798762\pi$
$101$	1.08936	−	1.88683i	0.108396	−	0.187747i	0.915121	+	0.403180i	$0.132095\pi$
$102$		0			0
$103$	1.59794	+	2.76772i	0.157450	+	0.272711i	0.933948	−	0.357408i	$-0.116339\pi$
$103$	1.59794	+	2.76772i	0.157450	+	0.272711i	−0.776499	+	0.630119i	$0.783006\pi$
$104$		0			0
$105$	0.173914	+	0.803047i	0.0169722	+	0.0783694i
$106$		0			0
$107$	−1.10533	−	1.91448i	−0.106856	−	0.185080i	0.807639	−	0.589677i	$-0.200745\pi$
$107$	−1.10533	−	1.91448i	−0.106856	−	0.185080i	−0.914495	+	0.404597i	$0.867412\pi$
$108$		0			0
$109$	10.6676	+	6.15892i	1.02177	+	0.589918i	0.914615	−	0.404325i	$-0.132493\pi$
$109$	10.6676	+	6.15892i	1.02177	+	0.589918i	0.107152	+	0.994243i	$0.465827\pi$
$110$		0			0
$111$	0.743191			0.0705406
$112$		0			0
$113$	−10.3212			−0.970936			−0.485468	−	0.874254i	$-0.661351\pi$
$113$	−10.3212			−0.970936			−0.485468	+	0.874254i	$0.661351\pi$
$114$		0			0
$115$	0.888663	+	0.513070i	0.0828682	+	0.0478440i
$116$		0			0
$117$	−1.34423	−	2.32827i	−0.124274	−	0.215248i
$118$		0			0
$119$	5.61734	+	1.80140i	0.514941	+	0.165134i
$120$		0			0
$121$	4.72484	+	8.18366i	0.429531	+	0.743969i
$122$		0			0
$123$	−4.64314	+	8.04216i	−0.418658	+	0.725137i
$124$		0			0
$125$	−3.07564			−0.275094
$126$		0			0
$127$		−	15.9029i		−	1.41115i	−0.708634	−	0.705576i	$-0.750688\pi$
$127$		−	15.9029i		−	1.41115i	0.708634	−	0.705576i	$-0.249312\pi$
$128$		0			0
$129$	−9.42018	−	5.43874i	−0.829401	−	0.478855i
$130$		0			0
$131$	−13.0693	+	7.54554i	−1.14187	+	0.659257i	−0.946892	−	0.321551i	$-0.895796\pi$
$131$	−13.0693	+	7.54554i	−1.14187	+	0.659257i	−0.194975	+	0.980808i	$0.562462\pi$
$132$		0			0
$133$	11.6357	−	10.5579i	1.00894	−	0.915482i
$134$		0			0
$135$	−0.268953	+	0.155280i	−0.0231477	+	0.0133644i
$136$		0			0
$137$	−7.41224	+	12.8384i	−0.633270	+	1.09686i	0.353608	+	0.935394i	$0.384955\pi$
$137$	−7.41224	+	12.8384i	−0.633270	+	1.09686i	−0.986879	+	0.161463i	$0.948379\pi$
$138$		0			0
$139$			0.758344i			0.0643219i	0.999483	+	0.0321610i	$0.0102389\pi$
$139$			0.758344i			0.0643219i	−0.999483	+	0.0321610i	$0.989761\pi$
$140$		0			0
$141$			10.8786i			0.916140i
$142$		0			0
$143$	−1.67372	+	2.89897i	−0.139964	+	0.242424i
$144$		0			0
$145$	0.0515929	−	0.0297872i	0.00428456	−	0.00247369i
$146$		0			0
$147$	−6.96706	−	0.678296i	−0.574633	−	0.0559449i
$148$		0			0
$149$	−15.0025	+	8.66168i	−1.22905	+	0.709593i	−0.966831	−	0.255416i	$-0.917788\pi$
$149$	−15.0025	+	8.66168i	−1.22905	+	0.709593i	−0.262219	+	0.965008i	$0.584454\pi$
$150$		0			0
$151$	18.9094	+	10.9173i	1.53882	+	0.888441i	0.998908	+	0.0467227i	$0.0148777\pi$
$151$	18.9094	+	10.9173i	1.53882	+	0.888441i	0.539917	+	0.841718i	$0.318456\pi$
$152$		0			0
$153$			2.22966i			0.180257i
$154$		0			0
$155$	−1.21545			−0.0976269
$156$		0			0
$157$	−7.22291	+	12.5104i	−0.576451	+	0.998443i	0.419431	+	0.907787i	$0.362230\pi$
$157$	−7.22291	+	12.5104i	−0.576451	+	0.998443i	−0.995882	+	0.0906554i	$0.971104\pi$
$158$		0			0
$159$	−6.24721	−	10.8205i	−0.495436	−	0.858120i
$160$		0			0
$161$	−6.47409	+	5.87440i	−0.510230	+	0.462967i
$162$		0			0
$163$	3.09204	+	5.35558i	0.242188	+	0.419481i	0.961337	−	0.275374i	$-0.0888017\pi$
$163$	3.09204	+	5.35558i	0.242188	+	0.419481i	−0.719150	+	0.694855i	$0.755468\pi$
$164$		0			0
$165$	0.334878	+	0.193342i	0.0260702	+	0.0150517i
$166$		0			0
$167$	23.2344			1.79793			0.898965	−	0.438021i	$-0.144320\pi$
$167$	23.2344			1.79793			0.898965	+	0.438021i	$0.144320\pi$
$168$		0			0
$169$	−5.77223			−0.444018
$170$		0			0
$171$	5.14286	+	2.96923i	0.393284	+	0.227063i
$172$		0			0
$173$	−8.94146	−	15.4871i	−0.679807	−	1.17746i	−0.975039	−	0.222034i	$-0.928730\pi$
$173$	−8.94146	−	15.4871i	−0.679807	−	1.17746i	0.295232	−	0.955426i	$-0.404603\pi$
$174$		0			0
$175$	3.96172	−	12.3539i	0.299478	−	0.933866i
$176$		0			0
$177$	2.98230	+	5.16549i	0.224163	+	0.388262i
$178$		0			0
$179$	8.46735	−	14.6659i	0.632879	−	1.09618i	−0.354081	−	0.935215i	$-0.615206\pi$
$179$	8.46735	−	14.6659i	0.632879	−	1.09618i	0.986960	−	0.160964i	$-0.0514604\pi$
$180$		0			0
$181$	−6.35921			−0.472676			−0.236338	−	0.971671i	$-0.575947\pi$
$181$	−6.35921			−0.472676			−0.236338	+	0.971671i	$0.575947\pi$
$182$		0			0
$183$			9.17948i			0.678567i
$184$		0			0
$185$	0.199883	+	0.115403i	0.0146957	+	0.00848457i
$186$		0			0
$187$	2.40425	−	1.38810i	0.175816	−	0.101508i
$188$		0			0
$189$	−0.560001	−	2.58581i	−0.0407341	−	0.188090i
$190$		0			0
$191$	−2.20942	+	1.27561i	−0.159868	+	0.0922997i	−0.577800	−	0.816179i	$-0.696088\pi$
$191$	−2.20942	+	1.27561i	−0.159868	+	0.0922997i	0.417932	+	0.908478i	$0.362755\pi$
$192$		0			0
$193$	−1.47346	+	2.55211i	−0.106062	+	0.183705i	−0.914172	−	0.405327i	$-0.867158\pi$
$193$	−1.47346	+	2.55211i	−0.106062	+	0.183705i	0.808110	+	0.589032i	$0.200491\pi$
$194$		0			0
$195$		−	0.834924i		−	0.0597902i
$196$		0			0
$197$			17.6687i			1.25884i	0.777065	+	0.629420i	$0.216708\pi$
$197$			17.6687i			1.25884i	−0.777065	+	0.629420i	$0.783292\pi$
$198$		0			0
$199$	−3.49007	+	6.04497i	−0.247404	+	0.428517i	−0.962805	−	0.270198i	$-0.912911\pi$
$199$	−3.49007	+	6.04497i	−0.247404	+	0.428517i	0.715401	+	0.698715i	$0.246244\pi$
$200$		0			0
$201$	−3.91150	+	2.25830i	−0.275896	+	0.159288i
$202$		0			0
$203$	0.107424	+	0.496033i	0.00753972	+	0.0348147i
$204$		0			0
$205$	−2.49757	+	1.44197i	−0.174438	+	0.100712i
$206$		0			0
$207$	−2.86149	−	1.65208i	−0.198887	−	0.114828i
$208$		0			0
$209$		−	7.39410i		−	0.511460i
$210$		0			0
$211$	−9.18555			−0.632359			−0.316180	−	0.948699i	$-0.602400\pi$
$211$	−9.18555			−0.632359			−0.316180	+	0.948699i	$0.602400\pi$
$212$		0			0
$213$	3.96318	−	6.86443i	0.271553	−	0.470343i
$214$		0			0
$215$	−1.68905	−	2.92553i	−0.115193	−	0.199519i
$216$		0			0
$217$	3.16201	−	9.86014i	0.214651	−	0.669350i
$218$		0			0
$219$	−4.02803	−	6.97675i	−0.272189	−	0.471445i
$220$		0			0
$221$	−5.19123	−	2.99716i	−0.349200	−	0.201611i
$222$		0			0
$223$	−10.0260			−0.671389			−0.335695	−	0.941971i	$-0.608971\pi$
$223$	−10.0260			−0.671389			−0.335695	+	0.941971i	$0.608971\pi$
$224$		0			0
$225$	4.90355			0.326904
$226$		0			0
$227$	−5.79831	−	3.34766i	−0.384847	−	0.222192i	0.295078	−	0.955473i	$-0.404654\pi$
$227$	−5.79831	−	3.34766i	−0.384847	−	0.222192i	−0.679925	+	0.733281i	$0.737988\pi$
$228$		0			0
$229$	−1.61186	−	2.79182i	−0.106515	−	0.184489i	0.807841	−	0.589400i	$-0.200636\pi$
$229$	−1.61186	−	2.79182i	−0.106515	−	0.184489i	−0.914356	+	0.404911i	$0.867302\pi$
$230$		0			0
$231$	−2.43966	+	2.21367i	−0.160518	+	0.145649i
$232$		0			0
$233$	7.24196	+	12.5435i	0.474437	+	0.821749i	0.999572	−	0.0292704i	$-0.00931839\pi$
$233$	7.24196	+	12.5435i	0.474437	+	0.821749i	−0.525135	+	0.851019i	$0.675985\pi$
$234$		0			0
$235$	−1.68922	+	2.92582i	−0.110193	+	0.190859i
$236$		0			0
$237$	15.3389			0.996368
$238$		0			0
$239$			8.19957i			0.530386i	0.964195	+	0.265193i	$0.0854357\pi$
$239$			8.19957i			0.530386i	−0.964195	+	0.265193i	$0.914564\pi$
$240$		0			0
$241$	−5.82242	−	3.36158i	−0.375055	−	0.216538i	0.300610	−	0.953747i	$-0.402810\pi$
$241$	−5.82242	−	3.36158i	−0.375055	−	0.216538i	−0.675665	+	0.737209i	$0.736143\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−1.76848	−	1.26427i	−0.112984	−	0.0807715i
$246$		0			0
$247$	−13.8263	+	7.98262i	−0.879747	+	0.507922i
$248$		0			0
$249$	7.11237	−	12.3190i	0.450728	−	0.780684i
$250$		0			0
$251$			0.417637i			0.0263610i	0.999913	+	0.0131805i	$0.00419561\pi$
$251$			0.417637i			0.0263610i	−0.999913	+	0.0131805i	$0.995804\pi$
$252$		0			0
$253$			4.11408i			0.258650i
$254$		0			0
$255$	−0.346221	+	0.599672i	−0.0216812	+	0.0375529i
$256$		0			0
$257$	12.6753	−	7.31810i	0.790665	−	0.456490i	−0.0495318	−	0.998773i	$-0.515773\pi$
$257$	12.6753	−	7.31810i	0.790665	−	0.456490i	0.840196	+	0.542282i	$0.182440\pi$
$258$		0			0
$259$	−1.45619	+	1.32130i	−0.0904833	+	0.0821018i
$260$		0			0
$261$	−0.166129	+	0.0959146i	−0.0102831	+	0.00593696i
$262$		0			0
$263$	12.4202	+	7.17081i	0.765863	+	0.442171i	0.831397	−	0.555679i	$-0.187542\pi$
$263$	12.4202	+	7.17081i	0.765863	+	0.442171i	−0.0655336	+	0.997850i	$0.520875\pi$
$264$		0			0
$265$		−	3.88026i		−	0.238363i
$266$		0			0
$267$	6.38950			0.391031
$268$		0			0
$269$	11.7294	−	20.3159i	0.715152	−	1.23868i	−0.247748	−	0.968824i	$-0.579691\pi$
$269$	11.7294	−	20.3159i	0.715152	−	1.23868i	0.962901	−	0.269856i	$-0.0869760\pi$
$270$		0			0
$271$	−6.85210	−	11.8682i	−0.416235	−	0.720941i	0.579322	−	0.815099i	$-0.303317\pi$
$271$	−6.85210	−	11.8682i	−0.416235	−	0.720941i	−0.995557	+	0.0941581i	$0.969984\pi$
$272$		0			0
$273$	6.77322	+	2.17208i	0.409934	+	0.131460i
$274$		0			0
$275$	−3.05276	−	5.28753i	−0.184088	−	0.318850i
$276$		0			0
$277$	−5.66771	−	3.27225i	−0.340540	−	0.196611i	0.319971	−	0.947427i	$-0.396327\pi$
$277$	−5.66771	−	3.27225i	−0.340540	−	0.196611i	−0.660511	+	0.750817i	$0.729660\pi$
$278$		0			0
$279$	3.91373			0.234309
$280$		0			0
$281$	22.5178			1.34330			0.671650	−	0.740869i	$-0.265586\pi$
$281$	22.5178			1.34330			0.671650	+	0.740869i	$0.265586\pi$
$282$		0			0
$283$	11.9855	+	6.91985i	0.712466	+	0.411343i	0.811974	−	0.583694i	$-0.198393\pi$
$283$	11.9855	+	6.91985i	0.712466	+	0.411343i	−0.0995073	+	0.995037i	$0.531727\pi$
$284$		0			0
$285$	0.922123	+	1.59716i	0.0546218	+	0.0946078i
$286$		0			0
$287$	−5.20033	−	24.0125i	−0.306966	−	1.41742i
$288$		0			0
$289$	−6.01432	−	10.4171i	−0.353783	−	0.612771i
$290$		0			0
$291$	0.814749	−	1.41119i	0.0477614	−	0.0827252i
$292$		0			0
$293$	11.9348			0.697238			0.348619	−	0.937265i	$-0.386651\pi$
$293$	11.9348			0.697238			0.348619	+	0.937265i	$0.386651\pi$
$294$		0			0
$295$			1.85236i			0.107849i
$296$		0			0
$297$	−1.07831	−	0.622560i	−0.0625697	−	0.0361246i
$298$		0			0
$299$	7.69297	−	4.44154i	0.444896	−	0.256861i
$300$		0			0
$301$	28.1271	−	6.09140i	1.62122	−	0.351103i
$302$		0			0
$303$	−1.88683	+	1.08936i	−0.108396	+	0.0625823i
$304$		0			0
$305$	−1.42539	+	2.46885i	−0.0816175	+	0.141366i
$306$		0			0
$307$		−	1.95782i		−	0.111739i	−0.998438	−	0.0558693i	$-0.982207\pi$
$307$		−	1.95782i		−	0.111739i	0.998438	−	0.0558693i	$-0.0177930\pi$
$308$		0			0
$309$		−	3.19588i		−	0.181807i
$310$		0			0
$311$	−10.9125	+	18.9010i	−0.618790	+	1.07178i	0.370916	+	0.928666i	$0.379044\pi$
$311$	−10.9125	+	18.9010i	−0.618790	+	1.07178i	−0.989707	+	0.143110i	$0.954290\pi$
$312$		0			0
$313$	−14.9776	+	8.64730i	−0.846582	+	0.488774i	−0.859496	−	0.511142i	$-0.829222\pi$
$313$	−14.9776	+	8.64730i	−0.846582	+	0.488774i	0.0129144	+	0.999917i	$0.495889\pi$
$314$		0			0
$315$	0.250910	−	0.782416i	0.0141372	−	0.0440842i
$316$		0			0
$317$	−6.07528	+	3.50757i	−0.341222	+	0.197005i	−0.660812	−	0.750551i	$-0.729788\pi$
$317$	−6.07528	+	3.50757i	−0.341222	+	0.197005i	0.319590	+	0.947556i	$0.396455\pi$
$318$		0			0
$319$	0.206851	+	0.119425i	0.0115814	+	0.00668653i
$320$		0			0
$321$			2.21066i			0.123387i
$322$		0			0
$323$	13.2407			0.736733
$324$		0			0
$325$	−6.59148	+	11.4168i	−0.365629	+	0.633289i
$326$		0			0
$327$	−6.15892	−	10.6676i	−0.340589	−	0.589918i
$328$		0			0
$329$	−19.3408	−	21.3152i	−1.06629	−	1.17514i
$330$		0			0
$331$	0.990108	+	1.71492i	0.0544212	+	0.0942604i	0.891953	−	0.452129i	$-0.149335\pi$
$331$	0.990108	+	1.71492i	0.0544212	+	0.0942604i	−0.837531	+	0.546389i	$0.816002\pi$
$332$		0			0
$333$	−0.643623	−	0.371596i	−0.0352703	−	0.0203633i
$334$		0			0
$335$	−1.40268			−0.0766363
$336$		0			0
$337$	2.53342			0.138004			0.0690021	−	0.997617i	$-0.478018\pi$
$337$	2.53342			0.138004			0.0690021	+	0.997617i	$0.478018\pi$
$338$		0			0
$339$	8.93841	+	5.16059i	0.485468	+	0.280285i
$340$		0			0
$341$	−2.43653	−	4.22019i	−0.131945	−	0.228536i
$342$		0			0
$343$	14.8570	−	11.0575i	0.802203	−	0.597051i
$344$		0			0
$345$	−0.513070	−	0.888663i	−0.0276227	−	0.0478440i
$346$		0			0
$347$	5.46677	−	9.46873i	0.293472	−	0.508308i	−0.681157	−	0.732138i	$-0.738523\pi$
$347$	5.46677	−	9.46873i	0.293472	−	0.508308i	0.974628	+	0.223830i	$0.0718560\pi$
$348$		0			0
$349$	−12.1290			−0.649250			−0.324625	−	0.945843i	$-0.605238\pi$
$349$	−12.1290			−0.649250			−0.324625	+	0.945843i	$0.605238\pi$
$350$		0			0
$351$			2.68845i			0.143499i
$352$		0			0
$353$	25.3752	+	14.6503i	1.35058	+	0.779759i	0.988331	−	0.152321i	$-0.0486747\pi$
$353$	25.3752	+	14.6503i	1.35058	+	0.779759i	0.362252	+	0.932080i	$0.382008\pi$
$354$		0			0
$355$	2.13182	−	1.23080i	0.113145	−	0.0653243i
$356$		0			0
$357$	−3.96406	−	4.36873i	−0.209800	−	0.231218i
$358$		0			0
$359$	−2.97798	+	1.71934i	−0.157172	+	0.0907431i	−0.576523	−	0.817081i	$-0.695591\pi$
$359$	−2.97798	+	1.71934i	−0.157172	+	0.0907431i	0.419351	+	0.907824i	$0.362258\pi$
$360$		0			0
$361$	8.13264	−	14.0861i	0.428034	−	0.741376i
$362$		0			0
$363$		−	9.44967i		−	0.495979i
$364$		0			0
$365$		−	2.50189i		−	0.130955i
$366$		0			0
$367$	−5.72895	+	9.92283i	−0.299049	+	0.517968i	−0.975919	−	0.218135i	$-0.930003\pi$
$367$	−5.72895	+	9.92283i	−0.299049	+	0.517968i	0.676870	+	0.736103i	$0.263336\pi$
$368$		0			0
$369$	8.04216	−	4.64314i	0.418658	−	0.241712i
$370$		0			0
$371$	31.4781	+	10.0946i	1.63426	+	0.524085i
$372$		0			0
$373$	−6.47611	+	3.73898i	−0.335320	+	0.193597i	−0.658201	−	0.752843i	$-0.728682\pi$
$373$	−6.47611	+	3.73898i	−0.335320	+	0.193597i	0.322880	+	0.946440i	$0.395349\pi$
$374$		0			0
$375$	2.66359	+	1.53782i	0.137547	+	0.0794128i
$376$		0			0
$377$		−	0.515723i		−	0.0265611i
$378$		0			0
$379$	−22.1705			−1.13882			−0.569412	−	0.822052i	$-0.692829\pi$
$379$	−22.1705			−1.13882			−0.569412	+	0.822052i	$0.692829\pi$
$380$		0			0
$381$	−7.95144	+	13.7723i	−0.407364	+	0.705576i
$382$		0			0
$383$	−8.74870	−	15.1532i	−0.447038	−	0.774292i	0.551154	−	0.834404i	$-0.314188\pi$
$383$	−8.74870	−	15.1532i	−0.447038	−	0.774292i	−0.998192	+	0.0601114i	$0.980854\pi$
$384$		0			0
$385$	−0.999891	+	0.216543i	−0.0509592	+	0.0110361i
$386$		0			0
$387$	5.43874	+	9.42018i	0.276467	+	0.478855i
$388$		0			0
$389$	6.29925	+	3.63687i	0.319384	+	0.184397i	0.651118	−	0.758976i	$-0.274300\pi$
$389$	6.29925	+	3.63687i	0.319384	+	0.184397i	−0.331734	+	0.943373i	$0.607634\pi$
$390$		0			0
$391$	−7.36715			−0.372573
$392$		0			0
$393$	15.0911			0.761245
$394$		0			0
$395$	4.12543	+	2.38182i	0.207573	+	0.119842i
$396$		0			0
$397$	16.6695	+	28.8724i	0.836616	+	1.44906i	0.892708	+	0.450637i	$0.148803\pi$
$397$	16.6695	+	28.8724i	0.836616	+	1.44906i	−0.0560911	+	0.998426i	$0.517864\pi$
$398$		0			0
$399$	−15.3557	+	3.32554i	−0.768747	+	0.166485i
$400$		0			0
$401$	−16.5661	−	28.6934i	−0.827272	−	1.43288i	−0.900170	−	0.435538i	$-0.856558\pi$
$401$	−16.5661	−	28.6934i	−0.827272	−	1.43288i	0.0728978	−	0.997339i	$-0.476775\pi$
$402$		0			0
$403$	−5.26093	+	9.11219i	−0.262065	+	0.453911i
$404$		0			0
$405$	0.310560			0.0154318
$406$		0			0
$407$			0.925363i			0.0458685i
$408$		0			0
$409$	−18.5838	−	10.7294i	−0.918911	−	0.530533i	−0.0356233	−	0.999365i	$-0.511342\pi$
$409$	−18.5838	−	10.7294i	−0.918911	−	0.530533i	−0.883287	+	0.468832i	$0.844675\pi$
$410$		0			0
$411$	12.8384	−	7.41224i	0.633270	−	0.365619i
$412$		0			0
$413$	−15.0271	−	4.81897i	−0.739433	−	0.237126i
$414$		0			0
$415$	3.82578	−	2.20882i	0.187800	−	0.108426i
$416$		0			0
$417$	0.379172	−	0.656745i	0.0185681	−	0.0321610i
$418$		0			0
$419$		−	28.3797i		−	1.38644i	−0.720727	−	0.693219i	$-0.756192\pi$
$419$		−	28.3797i		−	1.38644i	0.720727	−	0.693219i	$-0.243808\pi$
$420$		0			0
$421$		−	35.8768i		−	1.74853i	−0.485453	−	0.874263i	$-0.661345\pi$
$421$		−	35.8768i		−	1.74853i	0.485453	−	0.874263i	$-0.338655\pi$
$422$		0			0
$423$	5.43928	−	9.42111i	0.264467	−	0.458070i
$424$		0			0
$425$	9.46846	−	5.46662i	0.459288	−	0.265170i
$426$		0			0
$427$	−16.3200	−	17.9860i	−0.789781	−	0.870406i
$428$		0			0
$429$	2.89897	−	1.67372i	0.139964	−	0.0808081i
$430$		0			0
$431$	−14.1992	−	8.19790i	−0.683950	−	0.394879i	0.117392	−	0.993086i	$-0.462547\pi$
$431$	−14.1992	−	8.19790i	−0.683950	−	0.394879i	−0.801342	+	0.598207i	$0.795880\pi$
$432$		0			0
$433$			33.3810i			1.60419i	0.597198	+	0.802094i	$0.296281\pi$
$433$			33.3810i			1.60419i	−0.597198	+	0.802094i	$0.703719\pi$
$434$		0			0
$435$	−0.0595744			−0.00285637
$436$		0			0
$437$	−9.81081	+	16.9928i	−0.469315	+	0.812877i
$438$		0			0
$439$	16.7314	+	28.9796i	0.798545	+	1.38312i	0.920564	+	0.390593i	$0.127730\pi$
$439$	16.7314	+	28.9796i	0.798545	+	1.38312i	−0.122018	+	0.992528i	$0.538937\pi$
$440$		0			0
$441$	5.69450	+	4.07095i	0.271167	+	0.193855i
$442$		0			0
$443$	16.2807	+	28.1990i	0.773519	+	1.33977i	0.935623	+	0.353001i	$0.114839\pi$
$443$	16.2807	+	28.1990i	0.773519	+	1.33977i	−0.162104	+	0.986774i	$0.551828\pi$
$444$		0			0
$445$	1.71847	+	0.992161i	0.0814634	+	0.0470329i
$446$		0			0
$447$	17.3234			0.819367
$448$		0			0
$449$	11.9136			0.562238			0.281119	−	0.959673i	$-0.409294\pi$
$449$	11.9136			0.562238			0.281119	+	0.959673i	$0.409294\pi$
$450$		0			0
$451$	−10.0135	−	5.78127i	−0.471515	−	0.272229i
$452$		0			0
$453$	−10.9173	−	18.9094i	−0.512942	−	0.888441i
$454$		0			0
$455$	1.48439	+	1.63593i	0.0695895	+	0.0766935i
$456$		0			0
$457$	3.04095	+	5.26709i	0.142250	+	0.246384i	0.928344	−	0.371723i	$-0.121233\pi$
$457$	3.04095	+	5.26709i	0.142250	+	0.246384i	−0.786094	+	0.618107i	$0.787900\pi$
$458$		0			0
$459$	1.11483	−	1.93094i	0.0520357	−	0.0901285i
$460$		0			0
$461$	35.1038			1.63495			0.817474	−	0.575966i	$-0.195374\pi$
$461$	35.1038			1.63495			0.817474	+	0.575966i	$0.195374\pi$
$462$		0			0
$463$		−	5.53696i		−	0.257324i	−0.991688	−	0.128662i	$-0.958932\pi$
$463$		−	5.53696i		−	0.257324i	0.991688	−	0.128662i	$-0.0410683\pi$
$464$		0			0
$465$	1.05261	+	0.607723i	0.0488135	+	0.0281825i
$466$		0			0
$467$	−13.4916	+	7.78937i	−0.624316	+	0.360449i	−0.778547	−	0.627586i	$-0.784043\pi$
$467$	−13.4916	+	7.78937i	−0.624316	+	0.360449i	0.154232	+	0.988035i	$0.450710\pi$
$468$		0			0
$469$	3.64910	−	11.3790i	0.168500	−	0.525435i
$470$		0			0
$471$	12.5104	−	7.22291i	0.576451	−	0.332814i
$472$		0			0
$473$	6.77189	−	11.7293i	0.311372	−	0.539312i
$474$		0			0
$475$		−	29.1195i		−	1.33610i
$476$		0			0
$477$			12.4944i			0.572080i
$478$		0			0
$479$	7.56471	−	13.1025i	0.345641	−	0.598667i	−0.639829	−	0.768517i	$-0.720995\pi$
$479$	7.56471	−	13.1025i	0.345641	−	0.598667i	0.985470	+	0.169850i	$0.0543283\pi$
$480$		0			0
$481$	1.73035	−	0.999017i	0.0788970	−	0.0455512i
$482$		0			0
$483$	8.54393	−	1.85033i	0.388762	−	0.0841931i
$484$		0			0
$485$	0.438258	−	0.253028i	0.0199003	−	0.0114894i
$486$		0			0
$487$	4.31159	+	2.48930i	0.195377	+	0.112801i	0.594497	−	0.804098i	$-0.297351\pi$
$487$	4.31159	+	2.48930i	0.195377	+	0.112801i	−0.399120	+	0.916899i	$0.630684\pi$
$488$		0			0
$489$		−	6.18409i		−	0.279654i
$490$		0			0
$491$	−12.9363			−0.583807			−0.291903	−	0.956448i	$-0.594289\pi$
$491$	−12.9363			−0.583807			−0.291903	+	0.956448i	$0.594289\pi$
$492$		0			0
$493$	−0.213857	+	0.370410i	−0.00963161	+	0.0166824i
$494$		0			0
$495$	−0.193342	−	0.334878i	−0.00869008	−	0.0150517i
$496$		0			0
$497$	4.43877	+	20.4960i	0.199106	+	0.919373i
$498$		0			0
$499$	−4.01418	−	6.95277i	−0.179700	−	0.311249i	0.762078	−	0.647485i	$-0.224179\pi$
$499$	−4.01418	−	6.95277i	−0.179700	−	0.311249i	−0.941778	+	0.336236i	$0.890846\pi$
$500$		0			0
$501$	−20.1216	−	11.6172i	−0.898965	−	0.519018i
$502$		0			0
$503$	3.41092			0.152085			0.0760427	−	0.997105i	$-0.475771\pi$
$503$	3.41092			0.152085			0.0760427	+	0.997105i	$0.475771\pi$
$504$		0			0
$505$	−0.676625			−0.0301094
$506$		0			0
$507$	4.99890	+	2.88612i	0.222009	+	0.128177i
$508$		0			0
$509$	−17.5417	−	30.3832i	−0.777523	−	1.34671i	−0.933365	−	0.358928i	$-0.883142\pi$
$509$	−17.5417	−	30.3832i	−0.777523	−	1.34671i	0.155842	−	0.987782i	$-0.450191\pi$
$510$		0			0
$511$	20.2962	+	6.50872i	0.897852	+	0.287929i
$512$		0			0
$513$	−2.96923	−	5.14286i	−0.131095	−	0.227063i
$514$		0			0
$515$	0.496256	−	0.859541i	0.0218677	−	0.0378759i
$516$		0			0
$517$	−13.5451			−0.595713
$518$		0			0
$519$			17.8829i			0.784973i
$520$		0			0
$521$	5.59051	+	3.22768i	0.244925	+	0.141407i	0.617438	−	0.786620i	$-0.288171\pi$
$521$	5.59051	+	3.22768i	0.244925	+	0.141407i	−0.372513	+	0.928027i	$0.621504\pi$
$522$		0			0
$523$	−11.2493	+	6.49478i	−0.491897	+	0.283997i	−0.725361	−	0.688368i	$-0.758327\pi$
$523$	−11.2493	+	6.49478i	−0.491897	+	0.283997i	0.233464	+	0.972365i	$0.424994\pi$
$524$		0			0
$525$	−9.60790	+	8.71792i	−0.419323	+	0.380481i
$526$		0			0
$527$	7.55716	−	4.36313i	0.329195	−	0.190061i
$528$		0			0
$529$	−6.04126	+	10.4638i	−0.262663	+	0.454946i
$530$		0			0
$531$		−	5.96460i		−	0.258841i
$532$		0			0
$533$			24.9657i			1.08139i
$534$		0			0
$535$	−0.343270	+	0.594561i	−0.0148409	+	0.0257051i
$536$		0			0
$537$	−14.6659	+	8.46735i	−0.632879	+	0.365393i
$538$		0			0
$539$	0.844561	−	8.67483i	0.0363778	−	0.373651i
$540$		0			0
$541$	−29.0331	+	16.7623i	−1.24823	+	0.720667i	−0.970756	−	0.240066i	$-0.922831\pi$
$541$	−29.0331	+	16.7623i	−1.24823	+	0.720667i	−0.277475	+	0.960733i	$0.589497\pi$
$542$		0			0
$543$	5.50723	+	3.17960i	0.236338	+	0.136450i
$544$		0			0
$545$		−	3.82543i		−	0.163863i
$546$		0			0
$547$	−12.5739			−0.537623			−0.268811	−	0.963193i	$-0.586631\pi$
$547$	−12.5739			−0.537623			−0.268811	+	0.963193i	$0.586631\pi$
$548$		0			0
$549$	4.58974	−	7.94967i	0.195885	−	0.339284i
$550$		0			0
$551$	0.569585	+	0.986549i	0.0242651	+	0.0420284i
$552$		0			0
$553$	−30.0546	+	27.2707i	−1.27805	+	1.15967i
$554$		0			0
$555$	−0.115403	−	0.199883i	−0.00489857	−	0.00848457i
$556$		0			0
$557$	6.60225	+	3.81181i	0.279746	+	0.161512i	0.633309	−	0.773899i	$-0.281696\pi$
$557$	6.60225	+	3.81181i	0.279746	+	0.161512i	−0.353562	+	0.935411i	$0.615030\pi$
$558$		0			0
$559$	−29.2436			−1.23687
$560$		0			0
$561$	−2.77619			−0.117211
$562$		0			0
$563$	−32.4941	−	18.7605i	−1.36946	−	0.790660i	−0.378603	−	0.925559i	$-0.623596\pi$
$563$	−32.4941	−	18.7605i	−1.36946	−	0.790660i	−0.990859	+	0.134899i	$0.956929\pi$
$564$		0			0
$565$	1.60267	+	2.77591i	0.0674249	+	0.116783i
$566$		0			0
$567$	−0.807929	+	2.51938i	−0.0339298	+	0.105804i
$568$		0			0
$569$	1.54166	+	2.67024i	0.0646299	+	0.111942i	0.896530	−	0.442984i	$-0.146080\pi$
$569$	1.54166	+	2.67024i	0.0646299	+	0.111942i	−0.831900	+	0.554926i	$0.812747\pi$
$570$		0			0
$571$	−14.4810	+	25.0818i	−0.606011	+	1.04964i	0.385880	+	0.922549i	$0.373898\pi$
$571$	−14.4810	+	25.0818i	−0.606011	+	1.04964i	−0.991891	+	0.127093i	$0.959435\pi$
$572$		0			0
$573$	2.55121			0.106578
$574$		0			0
$575$			16.2021i			0.675676i
$576$		0			0
$577$	−6.94353	−	4.00885i	−0.289063	−	0.166890i	0.348456	−	0.937325i	$-0.386706\pi$
$577$	−6.94353	−	4.00885i	−0.289063	−	0.166890i	−0.637519	+	0.770435i	$0.720039\pi$
$578$		0			0
$579$	2.55211	−	1.47346i	0.106062	−	0.0612349i
$580$		0			0
$581$	7.96587	+	36.7824i	0.330480	+	1.52599i
$582$		0			0
$583$	13.4728	−	7.77853i	0.557986	−	0.322154i
$584$		0			0
$585$	−0.417462	+	0.723066i	−0.0172599	+	0.0298951i
$586$		0			0
$587$			27.9804i			1.15488i	0.816434	+	0.577438i	$0.195948\pi$
$587$			27.9804i			1.15488i	−0.816434	+	0.577438i	$0.804052\pi$
$588$		0			0
$589$		−	23.2415i		−	0.957649i
$590$		0			0
$591$	8.83434	−	15.3015i	0.363396	−	0.629420i
$592$		0			0
$593$	6.88723	−	3.97634i	0.282825	−	0.163289i	−0.351877	−	0.936046i	$-0.614456\pi$
$593$	6.88723	−	3.97634i	0.282825	−	0.163289i	0.634701	+	0.772757i	$0.281123\pi$
$594$		0			0
$595$	−0.387768	−	1.79052i	−0.0158969	−	0.0734041i
$596$		0			0
$597$	6.04497	−	3.49007i	0.247404	−	0.142839i
$598$		0			0
$599$	−29.4613	−	17.0095i	−1.20376	−	0.694989i	−0.242368	−	0.970184i	$-0.577924\pi$
$599$	−29.4613	−	17.0095i	−1.20376	−	0.694989i	−0.961388	+	0.275195i	$0.911257\pi$
$600$		0			0
$601$			21.9849i			0.896782i	0.893837	+	0.448391i	$0.148003\pi$
$601$			21.9849i			0.896782i	−0.893837	+	0.448391i	$0.851997\pi$
$602$		0			0
$603$	4.51661			0.183930
$604$		0			0
$605$	1.46734	−	2.54151i	0.0596560	−	0.103327i
$606$		0			0
$607$	12.4261	+	21.5227i	0.504361	+	0.873578i	0.999987	+	0.00504253i	$0.00160509\pi$
$607$	12.4261	+	21.5227i	0.504361	+	0.873578i	−0.495627	+	0.868536i	$0.665062\pi$
$608$		0			0
$609$	0.154984	−	0.483290i	0.00628028	−	0.0195839i
$610$		0			0
$611$	14.6232	+	25.3282i	0.591593	+	1.02467i
$612$		0			0
$613$	16.0142	+	9.24578i	0.646806	+	0.373434i	0.787231	−	0.616658i	$-0.211514\pi$
$613$	16.0142	+	9.24578i	0.646806	+	0.373434i	−0.140425	+	0.990091i	$0.544847\pi$
$614$		0			0
$615$	2.88395			0.116292
$616$		0			0
$617$	−4.59522			−0.184997			−0.0924983	−	0.995713i	$-0.529485\pi$
$617$	−4.59522			−0.184997			−0.0924983	+	0.995713i	$0.529485\pi$
$618$		0			0
$619$	7.77783	+	4.49053i	0.312617	+	0.180490i	0.648097	−	0.761558i	$-0.275565\pi$
$619$	7.77783	+	4.49053i	0.312617	+	0.180490i	−0.335480	+	0.942047i	$0.608898\pi$
$620$		0			0
$621$	1.65208	+	2.86149i	0.0662957	+	0.114828i
$622$		0			0
$623$	−12.5194	+	11.3598i	−0.501580	+	0.455119i
$624$		0			0
$625$	−11.7813	−	20.4058i	−0.471252	−	0.816232i
$626$		0			0
$627$	−3.69705	+	6.40347i	−0.147646	+	0.255730i
$628$		0			0
$629$	−1.65706			−0.0660714
$630$		0			0
$631$		−	19.3801i		−	0.771511i	−0.922601	−	0.385756i	$-0.873941\pi$
$631$		−	19.3801i		−	0.771511i	0.922601	−	0.385756i	$-0.126059\pi$
$632$		0			0
$633$	7.95492	+	4.59277i	0.316180	+	0.182546i
$634$		0			0
$635$	−4.27712	+	2.46940i	−0.169732	+	0.0979950i
$636$		0			0
$637$	−17.1330	+	7.78604i	−0.678832	+	0.308494i
$638$		0			0
$639$	−6.86443	+	3.96318i	−0.271553	+	0.156781i
$640$		0			0
$641$	−16.2694	+	28.1793i	−0.642601	+	1.11302i	0.342249	+	0.939609i	$0.388811\pi$
$641$	−16.2694	+	28.1793i	−0.642601	+	1.11302i	−0.984850	+	0.173408i	$0.944522\pi$
$642$		0			0
$643$			41.5394i			1.63815i	0.573684	+	0.819077i	$0.305514\pi$
$643$			41.5394i			1.63815i	−0.573684	+	0.819077i	$0.694486\pi$
$644$		0			0
$645$			3.37811i			0.133013i
$646$		0			0
$647$	13.6161	−	23.5838i	0.535304	−	0.927174i	−0.463845	−	0.885917i	$-0.653530\pi$
$647$	13.6161	−	23.5838i	0.535304	−	0.927174i	0.999149	−	0.0412571i	$-0.0131363\pi$
$648$		0			0
$649$	−6.43166	+	3.71332i	−0.252465	+	0.145761i
$650$		0			0
$651$	−7.66845	+	6.95813i	−0.300550	+	0.272711i
$652$		0			0
$653$	33.3010	−	19.2263i	1.30317	−	0.752385i	0.322222	−	0.946664i	$-0.395570\pi$
$653$	33.3010	−	19.2263i	1.30317	−	0.752385i	0.980946	+	0.194279i	$0.0622368\pi$
$654$		0			0
$655$	4.05879	+	2.34334i	0.158590	+	0.0915619i
$656$		0			0
$657$			8.05605i			0.314297i
$658$		0			0
$659$	0.588734			0.0229338			0.0114669	−	0.999934i	$-0.496350\pi$
$659$	0.588734			0.0229338			0.0114669	+	0.999934i	$0.496350\pi$
$660$		0			0
$661$	−5.80736	+	10.0586i	−0.225880	+	0.391236i	−0.956583	−	0.291459i	$-0.905859\pi$
$661$	−5.80736	+	10.0586i	−0.225880	+	0.391236i	0.730703	+	0.682696i	$0.239192\pi$
$662$		0			0
$663$	2.99716	+	5.19123i	0.116400	+	0.201611i
$664$		0			0
$665$	−4.64635	−	1.49002i	−0.180178	−	0.0577805i
$666$		0			0
$667$	−0.316917	−	0.548917i	−0.0122711	−	0.0212541i
$668$		0			0
$669$	8.68275	+	5.01299i	0.335695	+	0.193813i
$670$		0			0
$671$	−11.4296			−0.441233
$672$		0			0
$673$	−38.1246			−1.46960			−0.734798	−	0.678286i	$-0.762723\pi$
$673$	−38.1246			−1.46960			−0.734798	+	0.678286i	$0.762723\pi$
$674$		0			0
$675$	−4.24660	−	2.45178i	−0.163452	−	0.0943689i
$676$		0			0
$677$	14.1674	+	24.5387i	0.544498	+	0.943098i	0.998638	+	0.0521678i	$0.0166131\pi$
$677$	14.1674	+	24.5387i	0.544498	+	0.943098i	−0.454141	+	0.890930i	$0.650054\pi$
$678$		0			0
$679$	0.912520	+	4.21357i	0.0350193	+	0.161702i
$680$		0			0
$681$	3.34766	+	5.79831i	0.128282	+	0.222192i
$682$		0			0
$683$	−16.3842	+	28.3783i	−0.626926	+	1.08587i	0.361239	+	0.932473i	$0.382354\pi$
$683$	−16.3842	+	28.3783i	−0.626926	+	1.08587i	−0.988165	+	0.153394i	$0.950980\pi$
$684$		0			0
$685$	4.60389			0.175905
$686$		0			0
$687$			3.22372i			0.122993i
$688$		0			0
$689$	−29.0903	−	16.7953i	−1.10825	−	0.639850i
$690$		0			0
$691$	−14.7390	+	8.50955i	−0.560697	+	0.323719i	−0.753425	−	0.657534i	$-0.771600\pi$
$691$	−14.7390	+	8.50955i	−0.560697	+	0.323719i	0.192728	+	0.981252i	$0.438266\pi$
$692$		0			0
$693$	3.21964	−	0.697268i	0.122304	−	0.0264870i
$694$		0			0
$695$	0.203959	−	0.117756i	0.00773659	−	0.00446672i
$696$		0			0
$697$	10.3526	−	17.9312i	0.392133	−	0.679194i
$698$		0			0
$699$		−	14.4839i		−	0.547832i
$700$		0			0
$701$		−	30.8763i		−	1.16618i	−0.812406	−	0.583092i	$-0.801843\pi$
$701$		−	30.8763i		−	1.16618i	0.812406	−	0.583092i	$-0.198157\pi$
$702$		0			0
$703$	−2.20671	+	3.82213i	−0.0832275	+	0.144154i
$704$		0			0
$705$	2.92582	−	1.68922i	0.110193	−	0.0636197i
$706$		0			0
$707$	1.76026	−	5.48903i	0.0662013	−	0.206436i
$708$		0			0
$709$	12.1464	−	7.01270i	0.456166	−	0.263367i	−0.254265	−	0.967135i	$-0.581833\pi$
$709$	12.1464	−	7.01270i	0.456166	−	0.263367i	0.710431	+	0.703767i	$0.248500\pi$
$710$		0			0
$711$	−13.2839	−	7.66944i	−0.498184	−	0.287627i
$712$		0			0
$713$			12.9316i			0.484292i
$714$		0			0
$715$	1.03958			0.0388781
$716$		0			0
$717$	4.09979	−	7.10104i	0.153109	−	0.265193i
$718$		0			0
$719$	18.8132	+	32.5854i	0.701613	+	1.21523i	0.967900	+	0.251335i	$0.0808696\pi$
$719$	18.8132	+	32.5854i	0.701613	+	1.21523i	−0.266288	+	0.963894i	$0.585797\pi$
$720$		0			0
$721$	5.68189	+	6.26193i	0.211605	+	0.233207i
$722$		0			0
$723$	3.36158	+	5.82242i	0.125018	+	0.216538i
$724$		0			0
$725$	0.814622	+	0.470322i	0.0302543	+	0.0174673i
$726$		0			0
$727$	−39.3414			−1.45909			−0.729545	−	0.683933i	$-0.760268\pi$
$727$	−39.3414			−1.45909			−0.729545	+	0.683933i	$0.760268\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	21.0038	+	12.1265i	0.776852	+	0.448516i
$732$		0			0
$733$	20.2322	+	35.0431i	0.747292	+	1.29435i	0.949116	+	0.314926i	$0.101980\pi$
$733$	20.2322	+	35.0431i	0.747292	+	1.29435i	−0.201824	+	0.979422i	$0.564687\pi$
$734$		0			0
$735$	0.899414	+	1.97913i	0.0331754	+	0.0730015i
$736$		0			0
$737$	−2.81186	−	4.87028i	−0.103576	−	0.179399i
$738$		0			0
$739$	4.18911	−	7.25575i	0.154099	−	0.266907i	−0.778632	−	0.627481i	$-0.784086\pi$
$739$	4.18911	−	7.25575i	0.154099	−	0.266907i	0.932731	+	0.360574i	$0.117419\pi$
$740$		0			0
$741$	15.9652			0.586498
$742$		0			0
$743$			16.9962i			0.623529i	0.950159	+	0.311764i	$0.100920\pi$
$743$			16.9962i			0.623529i	−0.950159	+	0.311764i	$0.899080\pi$
$744$		0			0
$745$	4.65916	+	2.68997i	0.170699	+	0.0985528i
$746$		0			0
$747$	−12.3190	+	7.11237i	−0.450728	+	0.260228i
$748$		0			0
$749$	−3.93028	−	4.33150i	−0.143609	−	0.158270i
$750$		0			0
$751$	11.0239	−	6.36463i	0.402266	−	0.232249i	−0.285195	−	0.958469i	$-0.592058\pi$
$751$	11.0239	−	6.36463i	0.402266	−	0.232249i	0.687461	+	0.726221i	$0.258725\pi$
$752$		0			0
$753$	0.208818	−	0.361684i	0.00760977	−	0.0131805i
$754$		0			0
$755$		−	6.78097i		−	0.246785i
$756$		0			0
$757$		−	36.5299i		−	1.32770i	−0.747864	−	0.663852i	$-0.768921\pi$
$757$		−	36.5299i		−	1.32770i	0.747864	−	0.663852i	$-0.231079\pi$
$758$		0			0
$759$	2.05704	−	3.56290i	0.0746658	−	0.129325i
$760$		0			0
$761$	−42.6597	+	24.6296i	−1.54641	+	0.892822i	−0.548001	+	0.836477i	$0.684611\pi$
$761$	−42.6597	+	24.6296i	−1.54641	+	0.892822i	−0.998411	+	0.0563444i	$0.982056\pi$
$762$		0			0
$763$	31.0333	+	9.95194i	1.12348	+	0.360284i
$764$		0			0
$765$	0.599672	−	0.346221i	0.0216812	−	0.0125176i
$766$		0			0
$767$	13.8872	+	8.01776i	0.501437	+	0.289505i
$768$		0			0
$769$		−	19.8541i		−	0.715957i	−0.933730	−	0.357979i	$-0.883466\pi$
$769$		−	19.8541i		−	0.715957i	0.933730	−	0.357979i	$-0.116534\pi$
$770$		0			0
$771$	−14.6362			−0.527110
$772$		0			0
$773$	6.55810	−	11.3590i	0.235879	−	0.408554i	−0.723649	−	0.690168i	$-0.757537\pi$
$773$	6.55810	−	11.3590i	0.235879	−	0.408554i	0.959528	+	0.281614i	$0.0908699\pi$
$774$		0			0
$775$	−9.59558	−	16.6200i	−0.344683	−	0.597009i
$776$		0			0
$777$	1.92175	−	0.416188i	0.0689424	−	0.0149306i
$778$		0			0
$779$	−27.5731	−	47.7580i	−0.987909	−	1.71111i
$780$		0			0
$781$	8.54704	+	4.93464i	0.305837	+	0.176575i
$782$		0			0
$783$	0.191829			0.00685541
$784$		0			0
$785$	4.48629			0.160123
$786$		0			0
$787$	12.9467	+	7.47476i	0.461499	+	0.266447i	0.712674	−	0.701495i	$-0.247484\pi$
$787$	12.9467	+	7.47476i	0.461499	+	0.266447i	−0.251175	+	0.967942i	$0.580817\pi$
$788$		0			0
$789$	−7.17081	−	12.4202i	−0.255288	−	0.442171i
$790$		0			0
$791$	−26.6886	+	5.77987i	−0.948938	+	0.205509i
$792$		0			0
$793$	12.3393	+	21.3723i	0.438181	+	0.758952i
$794$		0			0
$795$	−1.94013	+	3.36040i	−0.0688093	+	0.119181i
$796$		0			0
$797$	−48.1132			−1.70426			−0.852128	−	0.523333i	$-0.824688\pi$
$797$	−48.1132			−1.70426			−0.852128	+	0.523333i	$0.824688\pi$
$798$		0			0
$799$		−	24.2554i		−	0.858096i
$800$		0			0
$801$	−5.53347	−	3.19475i	−0.195516	−	0.112881i
$802$		0			0
$803$	8.68689	−	5.01538i	0.306554	−	0.176989i
$804$		0			0
$805$	2.58523	+	0.829048i	0.0911174	+	0.0292201i
$806$		0			0
$807$	−20.3159	+	11.7294i	−0.715152	+	0.412893i
$808$		0			0
$809$	16.0522	−	27.8032i	0.564364	−	0.977508i	−0.432744	−	0.901517i	$-0.642455\pi$
$809$	16.0522	−	27.8032i	0.564364	−	0.977508i	0.997109	−	0.0759908i	$-0.0242120\pi$
$810$		0			0
$811$		−	0.924758i		−	0.0324726i	−0.999868	−	0.0162363i	$-0.994832\pi$
$811$		−	0.924758i		−	0.0324726i	0.999868	−	0.0162363i	$-0.00516841\pi$
$812$		0			0
$813$			13.7042i			0.480627i
$814$		0			0
$815$	0.960264	−	1.66323i	0.0336366	−	0.0582603i
$816$		0			0
$817$	55.9414	−	32.2978i	1.95714	−	1.12996i
$818$		0			0
$819$	−4.77974	−	5.26768i	−0.167018	−	0.184068i
$820$		0			0
$821$	26.8884	−	15.5240i	0.938413	−	0.541793i	0.0489502	−	0.998801i	$-0.484412\pi$
$821$	26.8884	−	15.5240i	0.938413	−	0.541793i	0.889462	+	0.457008i	$0.151079\pi$
$822$		0			0
$823$	−4.91080	−	2.83525i	−0.171180	−	0.0988307i	0.411962	−	0.911201i	$-0.364844\pi$
$823$	−4.91080	−	2.83525i	−0.171180	−	0.0988307i	−0.583142	+	0.812370i	$0.698177\pi$
$824$		0			0
$825$			6.10551i			0.212567i
$826$		0			0
$827$	−15.9930			−0.556130			−0.278065	−	0.960562i	$-0.589693\pi$
$827$	−15.9930			−0.556130			−0.278065	+	0.960562i	$0.589693\pi$
$828$		0			0
$829$	−1.90039	+	3.29157i	−0.0660032	+	0.114321i	−0.897139	−	0.441749i	$-0.854358\pi$
$829$	−1.90039	+	3.29157i	−0.0660032	+	0.114321i	0.831135	+	0.556070i	$0.187691\pi$
$830$		0			0
$831$	3.27225	+	5.66771i	0.113513	+	0.196611i
$832$		0			0
$833$	15.5341	+	1.51237i	0.538226	+	0.0524004i
$834$		0			0
$835$	−3.60783	−	6.24894i	−0.124854	−	0.216254i
$836$		0			0
$837$	−3.38939	−	1.95686i	−0.117154	−	0.0676391i
$838$		0			0
$839$	10.9412			0.377732			0.188866	−	0.982003i	$-0.439519\pi$
$839$	10.9412			0.377732			0.188866	+	0.982003i	$0.439519\pi$
$840$		0			0
$841$	28.9632			0.998731
$842$		0			0
$843$	−19.5010	−	11.2589i	−0.671650	−	0.387777i
$844$		0			0
$845$	0.896312	+	1.55246i	0.0308341	+	0.0534061i
$846$		0			0
$847$	16.8004	+	18.5155i	0.577268	+	0.636198i
$848$		0			0
$849$	−6.91985	−	11.9855i	−0.237489	−	0.411343i
$850$		0			0
$851$	1.22781	−	2.12663i	0.0420889	−	0.0729001i
$852$		0			0
$853$	−28.6102			−0.979594			−0.489797	−	0.871837i	$-0.662929\pi$
$853$	−28.6102			−0.979594			−0.489797	+	0.871837i	$0.662929\pi$
$854$		0			0
$855$		−	1.84425i		−	0.0630719i
$856$		0			0
$857$	24.9796	+	14.4220i	0.853287	+	0.492645i	0.861758	−	0.507319i	$-0.169363\pi$
$857$	24.9796	+	14.4220i	0.853287	+	0.492645i	−0.00847183	+	0.999964i	$0.502697\pi$
$858$		0			0
$859$	13.6240	−	7.86585i	0.464846	−	0.268379i	−0.249233	−	0.968443i	$-0.580179\pi$
$859$	13.6240	−	7.86585i	0.464846	−	0.268379i	0.714080	+	0.700064i	$0.246845\pi$
$860$		0			0
$861$	−7.50266	+	23.3956i	−0.255690	+	0.797321i
$862$		0			0
$863$	12.1432	−	7.01089i	0.413360	−	0.238654i	−0.278872	−	0.960328i	$-0.589961\pi$
$863$	12.1432	−	7.01089i	0.413360	−	0.238654i	0.692232	+	0.721675i	$0.256627\pi$
$864$		0			0
$865$	−2.77686	+	4.80966i	−0.0944160	+	0.163533i
$866$		0			0
$867$			12.0286i			0.408514i
$868$		0			0
$869$			19.0988i			0.647881i
$870$		0			0
$871$	−6.07134	+	10.5159i	−0.205719	+	0.356316i
$872$		0			0
$873$	−1.41119	+	0.814749i	−0.0477614	+	0.0275751i
$874$		0			0
$875$	−7.95302	+	1.72236i	−0.268861	+	0.0582265i
$876$		0			0
$877$	26.6956	−	15.4127i	0.901446	−	0.520450i	0.0237773	−	0.999717i	$-0.492431\pi$
$877$	26.6956	−	15.4127i	0.901446	−	0.520450i	0.877669	+	0.479267i	$0.159097\pi$
$878$		0			0
$879$	−10.3358	−	5.96739i	−0.348619	−	0.201275i
$880$		0			0
$881$			9.33799i			0.314605i	0.987550	+	0.157302i	$0.0502797\pi$
$881$			9.33799i			0.314605i	−0.987550	+	0.157302i	$0.949720\pi$
$882$		0			0
$883$	21.7043			0.730408			0.365204	−	0.930927i	$-0.380999\pi$
$883$	21.7043			0.730408			0.365204	+	0.930927i	$0.380999\pi$
$884$		0			0
$885$	0.926182	−	1.60419i	0.0311333	−	0.0539244i
$886$		0			0
$887$	−9.89190	−	17.1333i	−0.332138	−	0.575279i	0.650793	−	0.759255i	$-0.274436\pi$
$887$	−9.89190	−	17.1333i	−0.332138	−	0.575279i	−0.982931	+	0.183976i	$0.941103\pi$
$888$		0			0
$889$	−8.90562	−	41.1218i	−0.298685	−	1.37918i
$890$		0			0
$891$	0.622560	+	1.07831i	0.0208566	+	0.0361246i
$892$		0			0
$893$	−55.9468	−	32.3009i	−1.87219	−	1.08091i
$894$		0			0
$895$	−5.25923			−0.175797
$896$		0			0
$897$	−8.88308			−0.296597
$898$		0			0
$899$	0.650183	+	0.375383i	0.0216848	+	0.0125197i
$900$		0			0
$901$	13.9291	+	24.1259i	0.464046	+	0.803752i
$902$		0			0
$903$	−27.4045	−	8.78824i	−0.911964	−	0.292454i
$904$		0			0
$905$	0.987456	+	1.71032i	0.0328242	+	0.0568531i
$906$		0			0
$907$	13.0878	−	22.6688i	0.434574	−	0.752704i	−0.562687	−	0.826670i	$-0.690232\pi$
$907$	13.0878	−	22.6688i	0.434574	−	0.752704i	0.997261	+	0.0739661i	$0.0235657\pi$
$908$		0			0
$909$	2.17873			0.0722639
$910$		0			0
$911$		−	0.701753i		−	0.0232501i	−0.999932	−	0.0116251i	$-0.996300\pi$
$911$		−	0.701753i		−	0.0232501i	0.999932	−	0.0116251i	$-0.00370045\pi$
$912$		0			0
$913$	15.3386	+	8.85576i	0.507634	+	0.293083i
$914$		0			0
$915$	2.46885	−	1.42539i	0.0816175	−	0.0471219i
$916$		0			0
$917$	−29.5691	+	26.8301i	−0.976457	+	0.886009i
$918$		0			0
$919$	24.7946	−	14.3152i	0.817899	−	0.472214i	−0.0317922	−	0.999494i	$-0.510121\pi$
$919$	24.7946	−	14.3152i	0.817899	−	0.472214i	0.849692	+	0.527280i	$0.176788\pi$
$920$		0			0
$921$	−0.978909	+	1.69552i	−0.0322562	+	0.0558693i
$922$		0			0
$923$		−	21.3096i		−	0.701415i
$924$		0			0
$925$			3.64428i			0.119823i
$926$		0			0
$927$	−1.59794	+	2.76772i	−0.0524833	+	0.0909037i
$928$		0			0
$929$	23.0348	−	13.2992i	0.755747	−	0.436331i	−0.0720194	−	0.997403i	$-0.522944\pi$
$929$	23.0348	−	13.2992i	0.755747	−	0.436331i	0.827767	+	0.561072i	$0.189611\pi$
$930$		0			0
$931$	24.1752	−	33.8166i	0.792309	−	1.10829i
$932$		0			0
$933$	18.9010	−	10.9125i	0.618790	−	0.357259i
$934$		0			0
$935$	−0.746663	−	0.431086i	−0.0244185	−	0.0140980i
$936$		0			0
$937$		−	35.1395i		−	1.14796i	−0.818870	−	0.573979i	$-0.805399\pi$
$937$		−	35.1395i		−	1.14796i	0.818870	−	0.573979i	$-0.194601\pi$
$938$		0			0
$939$	17.2946			0.564388
$940$		0			0
$941$	10.5715	−	18.3104i	0.344621	−	0.596902i	−0.640663	−	0.767822i	$-0.721341\pi$
$941$	10.5715	−	18.3104i	0.344621	−	0.596902i	0.985285	+	0.170920i	$0.0546739\pi$
$942$		0			0
$943$	15.3417	+	26.5726i	0.499594	+	0.865323i
$944$		0			0
$945$	−0.608503	+	0.552137i	−0.0197946	+	0.0179610i
$946$		0			0
$947$	−2.51505	−	4.35619i	−0.0817280	−	0.141557i	0.822264	−	0.569106i	$-0.192711\pi$
$947$	−2.51505	−	4.35619i	−0.0817280	−	0.141557i	−0.903992	+	0.427549i	$0.859377\pi$
$948$		0			0
$949$	−18.7566	−	10.8292i	−0.608866	−	0.351529i
$950$		0			0
$951$	7.01513			0.227481
$952$		0			0
$953$	7.79671			0.252560			0.126280	−	0.991995i	$-0.459696\pi$
$953$	7.79671			0.252560			0.126280	+	0.991995i	$0.459696\pi$
$954$		0			0
$955$	0.686156	+	0.396152i	0.0222035	+	0.0128192i
$956$		0			0
$957$	−0.119425	−	0.206851i	−0.00386047	−	0.00668653i
$958$		0			0
$959$	−11.9771	+	37.3484i	−0.386762	+	1.20604i
$960$		0			0
$961$	7.84138	+	13.5817i	0.252948	+	0.438118i
$962$		0			0
$963$	1.10533	−	1.91448i	0.0356187	−	0.0616934i
$964$		0			0
$965$	0.915195			0.0294612
$966$		0			0
$967$		−	43.5181i		−	1.39945i	−0.714413	−	0.699725i	$-0.753306\pi$
$967$		−	43.5181i		−	1.39945i	0.714413	−	0.699725i	$-0.246694\pi$
$968$		0			0
$969$	−11.4668	−	6.62036i	−0.368367	−	0.212677i
$970$		0			0
$971$	40.4782	−	23.3701i	1.29901	−	0.749982i	0.318774	−	0.947831i	$-0.396729\pi$
$971$	40.4782	−	23.3701i	1.29901	−	0.749982i	0.980233	+	0.197849i	$0.0633955\pi$
$972$		0			0
$973$	0.424673	+	1.96093i	0.0136144	+	0.0628646i
$974$		0			0
$975$	11.4168	−	6.59148i	0.365629	−	0.211096i
$976$		0			0
$977$	−12.1197	+	20.9919i	−0.387743	+	0.671591i	−0.992146	−	0.125088i	$-0.960079\pi$
$977$	−12.1197	+	20.9919i	−0.387743	+	0.671591i	0.604402	+	0.796679i	$0.293412\pi$
$978$		0			0
$979$			7.95570i			0.254265i
$980$		0			0
$981$			12.3178i			0.393278i
$982$		0			0
$983$	15.9252	−	27.5832i	0.507934	−	0.879767i	−0.492024	−	0.870582i	$-0.663743\pi$
$983$	15.9252	−	27.5832i	0.507934	−	0.879767i	0.999958	−	0.00918542i	$-0.00292385\pi$
$984$		0			0
$985$	4.75203	−	2.74359i	0.151412	−	0.0874180i
$986$		0			0
$987$	6.09200	+	28.1299i	0.193910	+	0.895383i
$988$		0			0
$989$	−31.1258	+	17.9705i	−0.989743	+	0.571428i
$990$		0			0
$991$	−3.32918	−	1.92210i	−0.105755	−	0.0610575i	0.446190	−	0.894938i	$-0.352781\pi$
$991$	−3.32918	−	1.92210i	−0.105755	−	0.0610575i	−0.551945	+	0.833881i	$0.686114\pi$
$992$		0			0
$993$		−	1.98022i		−	0.0628402i
$994$		0			0
$995$	2.16775			0.0687222
$996$		0			0
$997$	28.6326	−	49.5931i	0.906803	−	1.57063i	0.0883239	−	0.996092i	$-0.471849\pi$
$997$	28.6326	−	49.5931i	0.906803	−	1.57063i	0.818479	−	0.574537i	$-0.194818\pi$
$998$		0			0
$999$	0.371596	+	0.643623i	0.0117568	+	0.0203633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.367.4		32
3.2	odd	2		2016.2.bs.c.1711.10		32
4.3	odd	2		168.2.t.a.115.15	yes	32
7.3	odd	6		4704.2.p.a.3919.13		32
7.4	even	3		4704.2.p.a.3919.22		32
7.5	odd	6	inner	672.2.bb.a.271.5		32
8.3	odd	2	inner	672.2.bb.a.367.5		32
8.5	even	2		168.2.t.a.115.3	yes	32
12.11	even	2		504.2.bk.c.451.2		32
21.5	even	6		2016.2.bs.c.271.7		32
24.5	odd	2		504.2.bk.c.451.14		32
24.11	even	2		2016.2.bs.c.1711.7		32
28.3	even	6		1176.2.p.a.979.16		32
28.11	odd	6		1176.2.p.a.979.15		32
28.19	even	6		168.2.t.a.19.3	✓	32
56.3	even	6		4704.2.p.a.3919.21		32
56.5	odd	6		168.2.t.a.19.15	yes	32
56.11	odd	6		4704.2.p.a.3919.14		32
56.19	even	6	inner	672.2.bb.a.271.4		32
56.45	odd	6		1176.2.p.a.979.13		32
56.53	even	6		1176.2.p.a.979.14		32
84.47	odd	6		504.2.bk.c.19.14		32
168.5	even	6		504.2.bk.c.19.2		32
168.131	odd	6		2016.2.bs.c.271.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.3	✓	32	28.19	even	6
168.2.t.a.19.15	yes	32	56.5	odd	6
168.2.t.a.115.3	yes	32	8.5	even	2
168.2.t.a.115.15	yes	32	4.3	odd	2
504.2.bk.c.19.2		32	168.5	even	6
504.2.bk.c.19.14		32	84.47	odd	6
504.2.bk.c.451.2		32	12.11	even	2
504.2.bk.c.451.14		32	24.5	odd	2
672.2.bb.a.271.4		32	56.19	even	6	inner
672.2.bb.a.271.5		32	7.5	odd	6	inner
672.2.bb.a.367.4		32	1.1	even	1	trivial
672.2.bb.a.367.5		32	8.3	odd	2	inner
1176.2.p.a.979.13		32	56.45	odd	6
1176.2.p.a.979.14		32	56.53	even	6
1176.2.p.a.979.15		32	28.11	odd	6
1176.2.p.a.979.16		32	28.3	even	6
2016.2.bs.c.271.7		32	21.5	even	6
2016.2.bs.c.271.10		32	168.131	odd	6
2016.2.bs.c.1711.7		32	24.11	even	2
2016.2.bs.c.1711.10		32	3.2	odd	2
4704.2.p.a.3919.13		32	7.3	odd	6
4704.2.p.a.3919.14		32	56.11	odd	6
4704.2.p.a.3919.21		32	56.3	even	6
4704.2.p.a.3919.22		32	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.155280 - 0.268953i) q^{5} +(2.58581 - 0.560001i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-0.155280 - 0.268953i) q^{5} +(2.58581 - 0.560001i) q^{7} +(0.500000 + 0.866025i) q^{9} +(0.622560 - 1.07831i) q^{11} -2.68845 q^{13} +0.310560i q^{15} +(1.93094 + 1.11483i) q^{17} +(5.14286 - 2.96923i) q^{19} +(-2.51938 - 0.807929i) q^{21} +(-2.86149 + 1.65208i) q^{23} +(2.45178 - 4.24660i) q^{25} -1.00000i q^{27} +0.191829i q^{29} +(1.95686 - 3.38939i) q^{31} +(-1.07831 + 0.622560i) q^{33} +(-0.552137 - 0.608503i) q^{35} +(-0.643623 + 0.371596i) q^{37} +(2.32827 + 1.34423i) q^{39} -9.28628i q^{41} +10.8775 q^{43} +(0.155280 - 0.268953i) q^{45} +(-5.43928 - 9.42111i) q^{47} +(6.37280 - 2.89611i) q^{49} +(-1.11483 - 1.93094i) q^{51} +(10.8205 + 6.24721i) q^{53} -0.386684 q^{55} -5.93846 q^{57} +(-5.16549 - 2.98230i) q^{59} +(-4.58974 - 7.94967i) q^{61} +(1.77788 + 1.95937i) q^{63} +(0.417462 + 0.723066i) q^{65} +(2.25830 - 3.91150i) q^{67} +3.30416 q^{69} +7.92636i q^{71} +(6.97675 + 4.02803i) q^{73} +(-4.24660 + 2.45178i) q^{75} +(1.00597 - 3.13693i) q^{77} +(-13.2839 + 7.66944i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.2247i q^{83} -0.692441i q^{85} +(0.0959146 - 0.166129i) q^{87} +(-5.53347 + 3.19475i) q^{89} +(-6.95181 + 1.50553i) q^{91} +(-3.38939 + 1.95686i) q^{93} +(-1.59716 - 0.922123i) q^{95} +1.62950i q^{97} +1.24512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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