LMFDB - Embedded newform 672.2.bb.a.271.5

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			271.5
Character	$\chi$	$=$	672.271
Dual form			672.2.bb.a.367.5

$q$-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 $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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	$-0.811211\pi$
$5$	0.155280	−	0.268953i	0.0694432	−	0.120279i	0.898656	+	0.438653i	$0.144544\pi$
$6$		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	0.944486	−	0.328552i	$-0.106560\pi$
$11$	0.622560	+	1.07831i	0.187709	+	0.325121i	−0.756777	+	0.653673i	$0.773227\pi$
$12$		0			0
$13$	2.68845			0.745642			0.372821	−	0.927903i	$-0.378391\pi$
$13$	2.68845			0.745642			0.372821	+	0.927903i	$0.378391\pi$
$14$		0			0
$15$			0.310560i			0.0801862i
$16$		0			0
$17$	1.93094	−	1.11483i	0.468321	−	0.270386i	−0.247215	−	0.968961i	$-0.579516\pi$
$17$	1.93094	−	1.11483i	0.468321	−	0.270386i	0.715537	+	0.698575i	$0.246182\pi$
$18$		0			0
$19$	5.14286	+	2.96923i	1.17985	+	0.681188i	0.955980	−	0.293431i	$-0.0947970\pi$
$19$	5.14286	+	2.96923i	1.17985	+	0.681188i	0.223872	+	0.974619i	$0.428130\pi$
$20$		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	$-0.221388\pi$
$23$	2.86149	+	1.65208i	0.596662	+	0.344483i	−0.171066	+	0.985260i	$0.554721\pi$
$24$		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	$-0.280982\pi$
$31$	−1.95686	−	3.38939i	−0.351463	−	0.608752i	−0.986506	+	0.163725i	$0.947649\pi$
$32$		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	$-0.313876\pi$
$37$	0.643623	+	0.371596i	0.105811	+	0.0610900i	−0.446161	+	0.894953i	$0.647209\pi$
$38$		0			0
$39$	−2.32827	+	1.34423i	−0.372821	+	0.215248i
$40$		0			0
$41$			9.28628i			1.45027i	0.688605	+	0.725137i	$0.258224\pi$
$41$			9.28628i			1.45027i	−0.688605	+	0.725137i	$0.741776\pi$
$42$		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	−0.130450	−	0.991455i	$-0.541642\pi$
$47$	5.43928	−	9.42111i	0.793400	−	1.37421i	0.923850	−	0.382755i	$-0.125025\pi$
$48$		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	$-0.995034\pi$
$53$	−10.8205	+	6.24721i	−1.48631	+	0.858120i	−0.486429	+	0.873720i	$0.661701\pi$
$54$		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	−0.797019	−	0.603954i	$-0.793591\pi$
$59$	−5.16549	+	2.98230i	−0.672490	+	0.388262i	0.124530	+	0.992216i	$0.460258\pi$
$60$		0			0
$61$	4.58974	−	7.94967i	0.587656	−	1.01785i	−0.406882	−	0.913481i	$-0.633384\pi$
$61$	4.58974	−	7.94967i	0.587656	−	1.01785i	0.994539	−	0.104370i	$-0.0332826\pi$
$62$		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	0.970361	−	0.241661i	$-0.0776923\pi$
$67$	2.25830	+	3.91150i	0.275896	+	0.477865i	−0.694465	+	0.719526i	$0.744359\pi$
$68$		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	−0.0326645	−	0.999466i	$-0.510399\pi$
$73$	6.97675	−	4.02803i	0.816567	−	0.471445i	0.849231	+	0.528021i	$0.177066\pi$
$74$		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	$-0.00199173\pi$
$79$	13.2839	+	7.66944i	1.49455	+	0.862880i	0.494571	+	0.869137i	$0.335325\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	14.2247i		−	1.56137i	−0.624926	−	0.780684i	$-0.714871\pi$
$83$		−	14.2247i		−	1.56137i	0.624926	−	0.780684i	$-0.285129\pi$
$84$		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	0.177184	−	0.984178i	$-0.443301\pi$
$89$	−5.53347	−	3.19475i	−0.586547	−	0.338643i	−0.763731	+	0.645535i	$0.776635\pi$
$90$		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	$-0.973638\pi$
$97$		−	1.62950i		−	0.165450i	0.996572	−	0.0827252i	$-0.0263624\pi$
$98$		0			0
$99$	1.24512			0.125139
$100$		0			0
$101$	−1.08936	−	1.88683i	−0.108396	−	0.187747i	0.806725	−	0.590927i	$-0.201238\pi$
$101$	−1.08936	−	1.88683i	−0.108396	−	0.187747i	−0.915121	+	0.403180i	$0.867905\pi$
$102$		0			0
$103$	−1.59794	+	2.76772i	−0.157450	+	0.272711i	−0.933948	−	0.357408i	$-0.883661\pi$
$103$	−1.59794	+	2.76772i	−0.157450	+	0.272711i	0.776499	+	0.630119i	$0.216994\pi$
$104$		0			0
$105$	0.173914	−	0.803047i	0.0169722	−	0.0783694i
$106$		0			0
$107$	−1.10533	+	1.91448i	−0.106856	+	0.185080i	−0.914495	−	0.404597i	$-0.867412\pi$
$107$	−1.10533	+	1.91448i	−0.106856	+	0.185080i	0.807639	+	0.589677i	$0.200745\pi$
$108$		0			0
$109$	−10.6676	+	6.15892i	−1.02177	+	0.589918i	−0.914615	−	0.404325i	$-0.867507\pi$
$109$	−10.6676	+	6.15892i	−1.02177	+	0.589918i	−0.107152	+	0.994243i	$0.534173\pi$
$110$		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	−0.194975	−	0.980808i	$-0.562462\pi$
$131$	−13.0693	−	7.54554i	−1.14187	−	0.659257i	−0.946892	+	0.321551i	$0.895796\pi$
$132$		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	−0.986879	−	0.161463i	$-0.948379\pi$
$137$	−7.41224	−	12.8384i	−0.633270	−	1.09686i	0.353608	−	0.935394i	$-0.384955\pi$
$138$		0			0
$139$		−	0.758344i		−	0.0643219i	−0.999483	−	0.0321610i	$-0.989761\pi$
$139$		−	0.758344i		−	0.0643219i	0.999483	−	0.0321610i	$-0.0102389\pi$
$140$		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	$-0.0822124\pi$
$149$	15.0025	+	8.66168i	1.22905	+	0.709593i	0.262219	+	0.965008i	$0.415546\pi$
$150$		0			0
$151$	−18.9094	+	10.9173i	−1.53882	+	0.888441i	−0.539917	+	0.841718i	$0.681544\pi$
$151$	−18.9094	+	10.9173i	−1.53882	+	0.888441i	−0.998908	+	0.0467227i	$0.985122\pi$
$152$		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	0.995882	+	0.0906554i	$0.0288962\pi$
$157$	7.22291	+	12.5104i	0.576451	+	0.998443i	−0.419431	+	0.907787i	$0.637770\pi$
$158$		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	−0.719150	−	0.694855i	$-0.755468\pi$
$163$	3.09204	−	5.35558i	0.242188	−	0.419481i	0.961337	+	0.275374i	$0.0888017\pi$
$164$		0			0
$165$	−0.334878	+	0.193342i	−0.0260702	+	0.0150517i
$166$		0			0
$167$	−23.2344			−1.79793			−0.898965	−	0.438021i	$-0.855680\pi$
$167$	−23.2344			−1.79793			−0.898965	+	0.438021i	$0.855680\pi$
$168$		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	−0.295232	−	0.955426i	$-0.595397\pi$
$173$	8.94146	−	15.4871i	0.679807	−	1.17746i	0.975039	−	0.222034i	$-0.0712697\pi$
$174$		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	0.986960	+	0.160964i	$0.0514604\pi$
$179$	8.46735	+	14.6659i	0.632879	+	1.09618i	−0.354081	+	0.935215i	$0.615206\pi$
$180$		0			0
$181$	6.35921			0.472676			0.236338	−	0.971671i	$-0.424053\pi$
$181$	6.35921			0.472676			0.236338	+	0.971671i	$0.424053\pi$
$182$		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	$-0.303912\pi$
$191$	2.20942	+	1.27561i	0.159868	+	0.0922997i	−0.417932	+	0.908478i	$0.637245\pi$
$192$		0			0
$193$	−1.47346	−	2.55211i	−0.106062	−	0.183705i	0.808110	−	0.589032i	$-0.200491\pi$
$193$	−1.47346	−	2.55211i	−0.106062	−	0.183705i	−0.914172	+	0.405327i	$0.867158\pi$
$194$		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	$-0.0870891\pi$
$199$	3.49007	+	6.04497i	0.247404	+	0.428517i	−0.715401	+	0.698715i	$0.753756\pi$
$200$		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	$-0.391029\pi$
$223$	10.0260			0.671389			0.335695	+	0.941971i	$0.391029\pi$
$224$		0			0
$225$	4.90355			0.326904
$226$		0			0
$227$	−5.79831	+	3.34766i	−0.384847	+	0.222192i	−0.679925	−	0.733281i	$-0.737988\pi$
$227$	−5.79831	+	3.34766i	−0.384847	+	0.222192i	0.295078	+	0.955473i	$0.404654\pi$
$228$		0			0
$229$	1.61186	−	2.79182i	0.106515	−	0.184489i	−0.807841	−	0.589400i	$-0.799364\pi$
$229$	1.61186	−	2.79182i	0.106515	−	0.184489i	0.914356	+	0.404911i	$0.132698\pi$
$230$		0			0
$231$	2.43966	+	2.21367i	0.160518	+	0.145649i
$232$		0			0
$233$	7.24196	−	12.5435i	0.474437	−	0.821749i	−0.525135	−	0.851019i	$-0.675985\pi$
$233$	7.24196	−	12.5435i	0.474437	−	0.821749i	0.999572	+	0.0292704i	$0.00931839\pi$
$234$		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	−0.675665	−	0.737209i	$-0.736143\pi$
$241$	−5.82242	+	3.36158i	−0.375055	+	0.216538i	0.300610	+	0.953747i	$0.402810\pi$
$242$		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	$-0.995804\pi$
$251$		−	0.417637i		−	0.0263610i	0.999913	−	0.0131805i	$-0.00419561\pi$
$252$		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	0.840196	−	0.542282i	$-0.182440\pi$
$257$	12.6753	+	7.31810i	0.790665	+	0.456490i	−0.0495318	+	0.998773i	$0.515773\pi$
$258$		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	$-0.812458\pi$
$263$	−12.4202	+	7.17081i	−0.765863	+	0.442171i	0.0655336	+	0.997850i	$0.479125\pi$
$264$		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	−0.962901	−	0.269856i	$-0.913024\pi$
$269$	−11.7294	−	20.3159i	−0.715152	−	1.23868i	0.247748	−	0.968824i	$-0.420309\pi$
$270$		0			0
$271$	6.85210	−	11.8682i	0.416235	−	0.720941i	−0.579322	−	0.815099i	$-0.696683\pi$
$271$	6.85210	−	11.8682i	0.416235	−	0.720941i	0.995557	+	0.0941581i	$0.0300159\pi$
$272$		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	$-0.603673\pi$
$277$	5.66771	−	3.27225i	0.340540	−	0.196611i	0.660511	+	0.750817i	$0.270340\pi$
$278$		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	−0.0995073	−	0.995037i	$-0.531727\pi$
$283$	11.9855	−	6.91985i	0.712466	−	0.411343i	0.811974	+	0.583694i	$0.198393\pi$
$284$		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	$-0.613349\pi$
$293$	−11.9348			−0.697238			−0.348619	+	0.937265i	$0.613349\pi$
$294$		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	$0.0177930\pi$
$307$			1.95782i			0.111739i	−0.998438	+	0.0558693i	$0.982207\pi$
$308$		0			0
$309$		−	3.19588i		−	0.181807i
$310$		0			0
$311$	10.9125	+	18.9010i	0.618790	+	1.07178i	0.989707	+	0.143110i	$0.0457103\pi$
$311$	10.9125	+	18.9010i	0.618790	+	1.07178i	−0.370916	+	0.928666i	$0.620956\pi$
$312$		0			0
$313$	−14.9776	−	8.64730i	−0.846582	−	0.488774i	0.0129144	−	0.999917i	$-0.495889\pi$
$313$	−14.9776	−	8.64730i	−0.846582	−	0.488774i	−0.859496	+	0.511142i	$0.829222\pi$
$314$		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	$-0.270212\pi$
$317$	6.07528	+	3.50757i	0.341222	+	0.197005i	−0.319590	+	0.947556i	$0.603545\pi$
$318$		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	−0.837531	−	0.546389i	$-0.816002\pi$
$331$	0.990108	−	1.71492i	0.0544212	−	0.0942604i	0.891953	+	0.452129i	$0.149335\pi$
$332$		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	0.974628	−	0.223830i	$-0.0718560\pi$
$347$	5.46677	+	9.46873i	0.293472	+	0.508308i	−0.681157	+	0.732138i	$0.738523\pi$
$348$		0			0
$349$	12.1290			0.649250			0.324625	−	0.945843i	$-0.394762\pi$
$349$	12.1290			0.649250			0.324625	+	0.945843i	$0.394762\pi$
$350$		0			0
$351$			2.68845i			0.143499i
$352$		0			0
$353$	25.3752	−	14.6503i	1.35058	−	0.779759i	0.362252	−	0.932080i	$-0.382008\pi$
$353$	25.3752	−	14.6503i	1.35058	−	0.779759i	0.988331	+	0.152321i	$0.0486747\pi$
$354$		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	$-0.304409\pi$
$359$	2.97798	+	1.71934i	0.157172	+	0.0907431i	−0.419351	+	0.907824i	$0.637742\pi$
$360$		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	$-0.0699974\pi$
$367$	5.72895	+	9.92283i	0.299049	+	0.517968i	−0.676870	+	0.736103i	$0.736664\pi$
$368$		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	$-0.271318\pi$
$373$	6.47611	+	3.73898i	0.335320	+	0.193597i	−0.322880	+	0.946440i	$0.604651\pi$
$374$		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	$-0.685812\pi$
$383$	8.74870	−	15.1532i	0.447038	−	0.774292i	0.998192	+	0.0601114i	$0.0191456\pi$
$384$		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	$-0.725700\pi$
$389$	−6.29925	+	3.63687i	−0.319384	+	0.184397i	0.331734	+	0.943373i	$0.392366\pi$
$390$		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	0.0560911	+	0.998426i	$0.482136\pi$
$397$	−16.6695	+	28.8724i	−0.836616	+	1.44906i	−0.892708	+	0.450637i	$0.851197\pi$
$398$		0			0
$399$	15.3557	+	3.32554i	0.768747	+	0.166485i
$400$		0			0
$401$	−16.5661	+	28.6934i	−0.827272	+	1.43288i	0.0728978	+	0.997339i	$0.476775\pi$
$401$	−16.5661	+	28.6934i	−0.827272	+	1.43288i	−0.900170	+	0.435538i	$0.856558\pi$
$402$		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	−0.883287	−	0.468832i	$-0.844675\pi$
$409$	−18.5838	+	10.7294i	−0.918911	+	0.530533i	−0.0356233	+	0.999365i	$0.511342\pi$
$410$		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	$0.243808\pi$
$419$			28.3797i			1.38644i	−0.720727	+	0.693219i	$0.756192\pi$
$420$		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	$-0.537453\pi$
$431$	14.1992	−	8.19790i	0.683950	−	0.394879i	0.801342	+	0.598207i	$0.204120\pi$
$432$		0			0
$433$		−	33.3810i		−	1.60419i	−0.597198	−	0.802094i	$-0.703719\pi$
$433$		−	33.3810i		−	1.60419i	0.597198	−	0.802094i	$-0.296281\pi$
$434$		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	0.122018	+	0.992528i	$0.461063\pi$
$439$	−16.7314	+	28.9796i	−0.798545	+	1.38312i	−0.920564	+	0.390593i	$0.872270\pi$
$440$		0			0
$441$	5.69450	−	4.07095i	0.271167	−	0.193855i
$442$		0			0
$443$	16.2807	−	28.1990i	0.773519	−	1.33977i	−0.162104	−	0.986774i	$-0.551828\pi$
$443$	16.2807	−	28.1990i	0.773519	−	1.33977i	0.935623	−	0.353001i	$-0.114839\pi$
$444$		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	−0.786094	−	0.618107i	$-0.787900\pi$
$457$	3.04095	−	5.26709i	0.142250	−	0.246384i	0.928344	+	0.371723i	$0.121233\pi$
$458$		0			0
$459$	1.11483	+	1.93094i	0.0520357	+	0.0901285i
$460$		0			0
$461$	−35.1038			−1.63495			−0.817474	−	0.575966i	$-0.804626\pi$
$461$	−35.1038			−1.63495			−0.817474	+	0.575966i	$0.804626\pi$
$462$		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	0.154232	−	0.988035i	$-0.450710\pi$
$467$	−13.4916	−	7.78937i	−0.624316	−	0.360449i	−0.778547	+	0.627586i	$0.784043\pi$
$468$		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	$-0.279005\pi$
$479$	−7.56471	−	13.1025i	−0.345641	−	0.598667i	−0.985470	+	0.169850i	$0.945672\pi$
$480$		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	$-0.702649\pi$
$487$	−4.31159	+	2.48930i	−0.195377	+	0.112801i	0.399120	+	0.916899i	$0.369316\pi$
$488$		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	−0.941778	−	0.336236i	$-0.890846\pi$
$499$	−4.01418	+	6.95277i	−0.179700	+	0.311249i	0.762078	+	0.647485i	$0.224179\pi$
$500$		0			0
$501$	20.1216	−	11.6172i	0.898965	−	0.519018i
$502$		0			0
$503$	−3.41092			−0.152085			−0.0760427	−	0.997105i	$-0.524229\pi$
$503$	−3.41092			−0.152085			−0.0760427	+	0.997105i	$0.524229\pi$
$504$		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	−0.155842	−	0.987782i	$-0.549809\pi$
$509$	17.5417	−	30.3832i	0.777523	−	1.34671i	0.933365	−	0.358928i	$-0.116858\pi$
$510$		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	−0.372513	−	0.928027i	$-0.621504\pi$
$521$	5.59051	−	3.22768i	0.244925	−	0.141407i	0.617438	+	0.786620i	$0.288171\pi$
$522$		0			0
$523$	−11.2493	−	6.49478i	−0.491897	−	0.283997i	0.233464	−	0.972365i	$-0.424994\pi$
$523$	−11.2493	−	6.49478i	−0.491897	−	0.283997i	−0.725361	+	0.688368i	$0.758327\pi$
$524$		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	$-0.0771692\pi$
$541$	29.0331	+	16.7623i	1.24823	+	0.720667i	0.277475	+	0.960733i	$0.410503\pi$
$542$		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	$-0.718304\pi$
$557$	−6.60225	+	3.81181i	−0.279746	+	0.161512i	0.353562	+	0.935411i	$0.384970\pi$
$558$		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	−0.990859	−	0.134899i	$-0.956929\pi$
$563$	−32.4941	+	18.7605i	−1.36946	+	0.790660i	−0.378603	+	0.925559i	$0.623596\pi$
$564$		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	−0.831900	−	0.554926i	$-0.812747\pi$
$569$	1.54166	−	2.67024i	0.0646299	−	0.111942i	0.896530	+	0.442984i	$0.146080\pi$
$570$		0			0
$571$	−14.4810	−	25.0818i	−0.606011	−	1.04964i	−0.991891	−	0.127093i	$-0.959435\pi$
$571$	−14.4810	−	25.0818i	−0.606011	−	1.04964i	0.385880	−	0.922549i	$-0.373898\pi$
$572$		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	−0.637519	−	0.770435i	$-0.720039\pi$
$577$	−6.94353	+	4.00885i	−0.289063	+	0.166890i	0.348456	+	0.937325i	$0.386706\pi$
$578$		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	$-0.804052\pi$
$587$		−	27.9804i		−	1.15488i	0.816434	−	0.577438i	$-0.195948\pi$
$588$		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	0.634701	−	0.772757i	$-0.281123\pi$
$593$	6.88723	+	3.97634i	0.282825	+	0.163289i	−0.351877	+	0.936046i	$0.614456\pi$
$594$		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	$-0.422076\pi$
$599$	29.4613	−	17.0095i	1.20376	−	0.694989i	0.961388	+	0.275195i	$0.0887425\pi$
$600$		0			0
$601$		−	21.9849i		−	0.896782i	−0.893837	−	0.448391i	$-0.851997\pi$
$601$		−	21.9849i		−	0.896782i	0.893837	−	0.448391i	$-0.148003\pi$
$602$		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	0.495627	+	0.868536i	$0.334938\pi$
$607$	−12.4261	+	21.5227i	−0.504361	+	0.873578i	−0.999987	+	0.00504253i	$0.998395\pi$
$608$		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	$-0.788486\pi$
$613$	−16.0142	+	9.24578i	−0.646806	+	0.373434i	0.140425	+	0.990091i	$0.455153\pi$
$614$		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	−0.335480	−	0.942047i	$-0.608898\pi$
$619$	7.77783	−	4.49053i	0.312617	−	0.180490i	0.648097	+	0.761558i	$0.275565\pi$
$620$		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	−0.984850	−	0.173408i	$-0.944522\pi$
$641$	−16.2694	−	28.1793i	−0.642601	−	1.11302i	0.342249	−	0.939609i	$-0.388811\pi$
$642$		0			0
$643$		−	41.5394i		−	1.63815i	−0.573684	−	0.819077i	$-0.694486\pi$
$643$		−	41.5394i		−	1.63815i	0.573684	−	0.819077i	$-0.305514\pi$
$644$		0			0
$645$			3.37811i			0.133013i
$646$		0			0
$647$	−13.6161	−	23.5838i	−0.535304	−	0.927174i	−0.999149	−	0.0412571i	$-0.986864\pi$
$647$	−13.6161	−	23.5838i	−0.535304	−	0.927174i	0.463845	−	0.885917i	$-0.346470\pi$
$648$		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	$-0.604430\pi$
$653$	−33.3010	−	19.2263i	−1.30317	−	0.752385i	−0.980946	+	0.194279i	$0.937763\pi$
$654$		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	$-0.0941408\pi$
$661$	5.80736	+	10.0586i	0.225880	+	0.391236i	−0.730703	+	0.682696i	$0.760808\pi$
$662$		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	0.454141	+	0.890930i	$0.349946\pi$
$677$	−14.1674	+	24.5387i	−0.544498	+	0.943098i	−0.998638	+	0.0521678i	$0.983387\pi$
$678$		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	−0.988165	−	0.153394i	$-0.950980\pi$
$683$	−16.3842	−	28.3783i	−0.626926	−	1.08587i	0.361239	−	0.932473i	$-0.382354\pi$
$684$		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	0.192728	−	0.981252i	$-0.438266\pi$
$691$	−14.7390	−	8.50955i	−0.560697	−	0.323719i	−0.753425	+	0.657534i	$0.771600\pi$
$692$		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	$-0.418167\pi$
$709$	−12.1464	−	7.01270i	−0.456166	−	0.263367i	−0.710431	+	0.703767i	$0.751500\pi$
$710$		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	0.266288	+	0.963894i	$0.414203\pi$
$719$	−18.8132	+	32.5854i	−0.701613	+	1.21523i	−0.967900	+	0.251335i	$0.919130\pi$
$720$		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	$-0.239732\pi$
$727$	39.3414			1.45909			0.729545	+	0.683933i	$0.239732\pi$
$728$		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	0.201824	+	0.979422i	$0.435313\pi$
$733$	−20.2322	+	35.0431i	−0.747292	+	1.29435i	−0.949116	+	0.314926i	$0.898020\pi$
$734$		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	0.932731	−	0.360574i	$-0.117419\pi$
$739$	4.18911	+	7.25575i	0.154099	+	0.266907i	−0.778632	+	0.627481i	$0.784086\pi$
$740$		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	$-0.407942\pi$
$751$	−11.0239	−	6.36463i	−0.402266	−	0.232249i	−0.687461	+	0.726221i	$0.741275\pi$
$752$		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	−0.998411	−	0.0563444i	$-0.982056\pi$
$761$	−42.6597	−	24.6296i	−1.54641	−	0.892822i	−0.548001	−	0.836477i	$-0.684611\pi$
$762$		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	$0.116534\pi$
$769$			19.8541i			0.715957i	−0.933730	+	0.357979i	$0.883466\pi$
$770$		0			0
$771$	−14.6362			−0.527110
$772$		0			0
$773$	−6.55810	−	11.3590i	−0.235879	−	0.408554i	0.723649	−	0.690168i	$-0.242463\pi$
$773$	−6.55810	−	11.3590i	−0.235879	−	0.408554i	−0.959528	+	0.281614i	$0.909130\pi$
$774$		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	−0.251175	−	0.967942i	$-0.580817\pi$
$787$	12.9467	−	7.47476i	0.461499	−	0.266447i	0.712674	+	0.701495i	$0.247484\pi$
$788$		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	$-0.175312\pi$
$797$	48.1132			1.70426			0.852128	+	0.523333i	$0.175312\pi$
$798$		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	0.997109	+	0.0759908i	$0.0242120\pi$
$809$	16.0522	+	27.8032i	0.564364	+	0.977508i	−0.432744	+	0.901517i	$0.642455\pi$
$810$		0			0
$811$			0.924758i			0.0324726i	0.999868	+	0.0162363i	$0.00516841\pi$
$811$			0.924758i			0.0324726i	−0.999868	+	0.0162363i	$0.994832\pi$
$812$		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	$-0.515588\pi$
$821$	−26.8884	−	15.5240i	−0.938413	−	0.541793i	−0.889462	+	0.457008i	$0.848921\pi$
$822$		0			0
$823$	4.91080	−	2.83525i	0.171180	−	0.0988307i	−0.411962	−	0.911201i	$-0.635156\pi$
$823$	4.91080	−	2.83525i	0.171180	−	0.0988307i	0.583142	+	0.812370i	$0.301823\pi$
$824$		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	$-0.145642\pi$
$829$	1.90039	+	3.29157i	0.0660032	+	0.114321i	−0.831135	+	0.556070i	$0.812309\pi$
$830$		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	$-0.560481\pi$
$839$	−10.9412			−0.377732			−0.188866	+	0.982003i	$0.560481\pi$
$840$		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	$-0.337071\pi$
$853$	28.6102			0.979594			0.489797	+	0.871837i	$0.337071\pi$
$854$		0			0
$855$		−	1.84425i		−	0.0630719i
$856$		0			0
$857$	24.9796	−	14.4220i	0.853287	−	0.492645i	−0.00847183	−	0.999964i	$-0.502697\pi$
$857$	24.9796	−	14.4220i	0.853287	−	0.492645i	0.861758	+	0.507319i	$0.169363\pi$
$858$		0			0
$859$	13.6240	+	7.86585i	0.464846	+	0.268379i	0.714080	−	0.700064i	$-0.246845\pi$
$859$	13.6240	+	7.86585i	0.464846	+	0.268379i	−0.249233	+	0.968443i	$0.580179\pi$
$860$		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	$-0.410039\pi$
$863$	−12.1432	−	7.01089i	−0.413360	−	0.238654i	−0.692232	+	0.721675i	$0.743373\pi$
$864$		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	$-0.507569\pi$
$877$	−26.6956	−	15.4127i	−0.901446	−	0.520450i	−0.877669	+	0.479267i	$0.840903\pi$
$878$		0			0
$879$	10.3358	−	5.96739i	0.348619	−	0.201275i
$880$		0			0
$881$		−	9.33799i		−	0.314605i	−0.987550	−	0.157302i	$-0.949720\pi$
$881$		−	9.33799i		−	0.314605i	0.987550	−	0.157302i	$-0.0502797\pi$
$882$		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	$-0.725564\pi$
$887$	9.89190	−	17.1333i	0.332138	−	0.575279i	0.982931	+	0.183976i	$0.0588969\pi$
$888$		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	0.997261	−	0.0739661i	$-0.0235657\pi$
$907$	13.0878	+	22.6688i	0.434574	+	0.752704i	−0.562687	+	0.826670i	$0.690232\pi$
$908$		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	$-0.489879\pi$
$919$	−24.7946	−	14.3152i	−0.817899	−	0.472214i	−0.849692	+	0.527280i	$0.823212\pi$
$920$		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	0.827767	−	0.561072i	$-0.189611\pi$
$929$	23.0348	+	13.2992i	0.755747	+	0.436331i	−0.0720194	+	0.997403i	$0.522944\pi$
$930$		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	$0.194601\pi$
$937$			35.1395i			1.14796i	−0.818870	+	0.573979i	$0.805399\pi$
$938$		0			0
$939$	17.2946			0.564388
$940$		0			0
$941$	−10.5715	−	18.3104i	−0.344621	−	0.596902i	0.640663	−	0.767822i	$-0.278659\pi$
$941$	−10.5715	−	18.3104i	−0.344621	−	0.596902i	−0.985285	+	0.170920i	$0.945326\pi$
$942$		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	−0.903992	−	0.427549i	$-0.859377\pi$
$947$	−2.51505	+	4.35619i	−0.0817280	+	0.141557i	0.822264	+	0.569106i	$0.192711\pi$
$948$		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	0.980233	−	0.197849i	$-0.0633955\pi$
$971$	40.4782	+	23.3701i	1.29901	+	0.749982i	0.318774	+	0.947831i	$0.396729\pi$
$972$		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	0.604402	−	0.796679i	$-0.293412\pi$
$977$	−12.1197	−	20.9919i	−0.387743	−	0.671591i	−0.992146	+	0.125088i	$0.960079\pi$
$978$		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	−0.999958	−	0.00918542i	$-0.997076\pi$
$983$	−15.9252	−	27.5832i	−0.507934	−	0.879767i	0.492024	−	0.870582i	$-0.336257\pi$
$984$		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	$-0.647219\pi$
$991$	3.32918	−	1.92210i	0.105755	−	0.0610575i	0.551945	+	0.833881i	$0.313886\pi$
$992$		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	−0.818479	−	0.574537i	$-0.805182\pi$
$997$	−28.6326	−	49.5931i	−0.906803	−	1.57063i	−0.0883239	−	0.996092i	$-0.528151\pi$
$998$		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.271.5		32
3.2	odd	2		2016.2.bs.c.271.7		32
4.3	odd	2		168.2.t.a.19.3	✓	32
7.2	even	3		4704.2.p.a.3919.13		32
7.3	odd	6	inner	672.2.bb.a.367.4		32
7.5	odd	6		4704.2.p.a.3919.22		32
8.3	odd	2	inner	672.2.bb.a.271.4		32
8.5	even	2		168.2.t.a.19.15	yes	32
12.11	even	2		504.2.bk.c.19.14		32
21.17	even	6		2016.2.bs.c.1711.10		32
24.5	odd	2		504.2.bk.c.19.2		32
24.11	even	2		2016.2.bs.c.271.10		32
28.3	even	6		168.2.t.a.115.15	yes	32
28.19	even	6		1176.2.p.a.979.15		32
28.23	odd	6		1176.2.p.a.979.16		32
56.3	even	6	inner	672.2.bb.a.367.5		32
56.5	odd	6		1176.2.p.a.979.14		32
56.19	even	6		4704.2.p.a.3919.14		32
56.37	even	6		1176.2.p.a.979.13		32
56.45	odd	6		168.2.t.a.115.3	yes	32
56.51	odd	6		4704.2.p.a.3919.21		32
84.59	odd	6		504.2.bk.c.451.2		32
168.59	odd	6		2016.2.bs.c.1711.7		32
168.101	even	6		504.2.bk.c.451.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.3	✓	32	4.3	odd	2
168.2.t.a.19.15	yes	32	8.5	even	2
168.2.t.a.115.3	yes	32	56.45	odd	6
168.2.t.a.115.15	yes	32	28.3	even	6
504.2.bk.c.19.2		32	24.5	odd	2
504.2.bk.c.19.14		32	12.11	even	2
504.2.bk.c.451.2		32	84.59	odd	6
504.2.bk.c.451.14		32	168.101	even	6
672.2.bb.a.271.4		32	8.3	odd	2	inner
672.2.bb.a.271.5		32	1.1	even	1	trivial
672.2.bb.a.367.4		32	7.3	odd	6	inner
672.2.bb.a.367.5		32	56.3	even	6	inner
1176.2.p.a.979.13		32	56.37	even	6
1176.2.p.a.979.14		32	56.5	odd	6
1176.2.p.a.979.15		32	28.19	even	6
1176.2.p.a.979.16		32	28.23	odd	6
2016.2.bs.c.271.7		32	3.2	odd	2
2016.2.bs.c.271.10		32	24.11	even	2
2016.2.bs.c.1711.7		32	168.59	odd	6
2016.2.bs.c.1711.10		32	21.17	even	6
4704.2.p.a.3919.13		32	7.2	even	3
4704.2.p.a.3919.14		32	56.19	even	6
4704.2.p.a.3919.21		32	56.51	odd	6
4704.2.p.a.3919.22		32	7.5	odd	6

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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Representations

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Database

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