LMFDB - Embedded newform 608.2.t.a.49.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(49,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("608.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	608.49
Dual form			608.2.t.a.273.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0638311 + 0.0368529i) q^{3} +(1.95840 + 1.13068i) q^{5} +4.70260 q^{7} +(-1.49728 - 2.59337i) q^{9} -1.98019i q^{11} +(-0.432449 + 0.249675i) q^{13} +(0.0833377 + 0.144345i) q^{15} +(0.371220 - 0.642972i) q^{17} +(1.13983 + 4.20723i) q^{19} +(0.300172 + 0.173304i) q^{21} +(-1.59672 - 2.76560i) q^{23} +(0.0568756 + 0.0985114i) q^{25} -0.441834i q^{27} +(-5.22471 + 3.01649i) q^{29} +5.44101 q^{31} +(0.0729758 - 0.126398i) q^{33} +(9.20955 + 5.31714i) q^{35} +10.3168i q^{37} -0.0368049 q^{39} +(2.77027 - 4.79824i) q^{41} +(-6.56065 - 3.78779i) q^{43} -6.77180i q^{45} +(0.782377 + 1.35512i) q^{47} +15.1145 q^{49} +(0.0473908 - 0.0273611i) q^{51} +(10.0885 - 5.82458i) q^{53} +(2.23896 - 3.87800i) q^{55} +(-0.0822924 + 0.310558i) q^{57} +(4.10945 + 2.37259i) q^{59} +(1.51215 - 0.873042i) q^{61} +(-7.04113 - 12.1956i) q^{63} -1.12921 q^{65} +(-9.42749 + 5.44296i) q^{67} -0.235375i q^{69} +(-5.42083 + 9.38916i) q^{71} +(-6.23576 + 10.8007i) q^{73} +0.00838412i q^{75} -9.31205i q^{77} +(-0.834855 + 1.44601i) q^{79} +(-4.47557 + 7.75191i) q^{81} -15.5733i q^{83} +(1.45399 - 0.839462i) q^{85} -0.444666 q^{87} +(-2.90236 - 5.02703i) q^{89} +(-2.03364 + 1.17412i) q^{91} +(0.347306 + 0.200517i) q^{93} +(-2.52480 + 9.52820i) q^{95} +(-0.605380 + 1.04855i) q^{97} +(-5.13537 + 2.96491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 8 q^{7} + 12 q^{9} + 6 q^{15} - 2 q^{17} + 2 q^{23} + 8 q^{25} + 48 q^{31} + 12 q^{33} + 20 q^{39} + 2 q^{41} - 10 q^{47} - 12 q^{49} - 8 q^{55} - 6 q^{57} + 28 q^{63} - 28 q^{65} + 30 q^{71} - 10 q^{73}+ \cdots - 18 q^{97}+O(q^{100}) $ 36 * q + 8 * q^7 + 12 * q^9 + 6 * q^15 - 2 * q^17 + 2 * q^23 + 8 * q^25 + 48 * q^31 + 12 * q^33 + 20 * q^39 + 2 * q^41 - 10 * q^47 - 12 * q^49 - 8 * q^55 - 6 * q^57 + 28 * q^63 - 28 * q^65 + 30 * q^71 - 10 * q^73 - 34 * q^79 - 2 * q^81 - 36 * q^87 - 2 * q^89 - 38 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$	0.0638311	+	0.0368529i	0.0368529	+	0.0212770i	0.518313	−	0.855191i	$-0.326560\pi$
$3$	0.0638311	+	0.0368529i	0.0368529	+	0.0212770i	−0.481460	+	0.876468i	$0.659893\pi$
$4$		0			0
$5$	1.95840	+	1.13068i	0.875821	+	0.505656i	0.869278	−	0.494323i	$-0.164584\pi$
$5$	1.95840	+	1.13068i	0.875821	+	0.505656i	0.00654285	+	0.999979i	$0.497917\pi$
$6$		0			0
$7$	4.70260			1.77742			0.888708	−	0.458474i	$-0.151604\pi$
$7$	4.70260			1.77742			0.888708	+	0.458474i	$0.151604\pi$
$8$		0			0
$9$	−1.49728	−	2.59337i	−0.499095	−	0.864457i
$10$		0			0
$11$		−	1.98019i		−	0.597050i	−0.954402	−	0.298525i	$-0.903505\pi$
$11$		−	1.98019i		−	0.597050i	0.954402	−	0.298525i	$-0.0964947\pi$
$12$		0			0
$13$	−0.432449	+	0.249675i	−0.119940	+	0.0692473i	−0.558770	−	0.829323i	$-0.688726\pi$
$13$	−0.432449	+	0.249675i	−0.119940	+	0.0692473i	0.438830	+	0.898570i	$0.355393\pi$
$14$		0			0
$15$	0.0833377	+	0.144345i	0.0215177	+	0.0372698i
$16$		0			0
$17$	0.371220	−	0.642972i	0.0900341	−	0.155944i	−0.817491	−	0.575941i	$-0.804636\pi$
$17$	0.371220	−	0.642972i	0.0900341	−	0.155944i	0.907525	+	0.419998i	$0.137969\pi$
$18$		0			0
$19$	1.13983	+	4.20723i	0.261494	+	0.965205i
$19$	1.13983	+	4.20723i	0.261494	+	0.965205i
$20$		0			0
$21$	0.300172	+	0.173304i	0.0655029	+	0.0378181i
$22$		0			0
$23$	−1.59672	−	2.76560i	−0.332939	−	0.576668i	0.650147	−	0.759808i	$-0.274707\pi$
$23$	−1.59672	−	2.76560i	−0.332939	−	0.576668i	−0.983087	+	0.183140i	$0.941374\pi$
$24$		0			0
$25$	0.0568756	+	0.0985114i	0.0113751	+	0.0197023i
$26$		0			0
$27$		−	0.441834i		−	0.0850311i
$28$		0			0
$29$	−5.22471	+	3.01649i	−0.970205	+	0.560148i	−0.899299	−	0.437335i	$-0.855922\pi$
$29$	−5.22471	+	3.01649i	−0.970205	+	0.560148i	−0.0709062	+	0.997483i	$0.522589\pi$
$30$		0			0
$31$	5.44101			0.977234			0.488617	−	0.872498i	$-0.337502\pi$
$31$	5.44101			0.977234			0.488617	+	0.872498i	$0.337502\pi$
$32$		0			0
$33$	0.0729758	−	0.126398i	0.0127035	−	0.0220030i
$34$		0			0
$35$	9.20955	+	5.31714i	1.55670	+	0.898760i
$36$		0			0
$37$			10.3168i			1.69608i	0.529932	+	0.848040i	$0.322217\pi$
$37$			10.3168i			1.69608i	−0.529932	+	0.848040i	$0.677783\pi$
$38$		0			0
$39$	−0.0368049			−0.00589351
$40$		0			0
$41$	2.77027	−	4.79824i	0.432643	−	0.749359i	−0.564457	−	0.825462i	$-0.690914\pi$
$41$	2.77027	−	4.79824i	0.432643	−	0.749359i	0.997100	+	0.0761031i	$0.0242478\pi$
$42$		0			0
$43$	−6.56065	−	3.78779i	−1.00049	−	0.577633i	−0.0920962	−	0.995750i	$-0.529357\pi$
$43$	−6.56065	−	3.78779i	−1.00049	−	0.577633i	−0.908393	+	0.418117i	$0.862690\pi$
$44$		0			0
$45$		−	6.77180i		−	1.00948i
$46$		0			0
$47$	0.782377	+	1.35512i	0.114121	+	0.197664i	0.917428	−	0.397901i	$-0.130261\pi$
$47$	0.782377	+	1.35512i	0.114121	+	0.197664i	−0.803307	+	0.595565i	$0.796928\pi$
$48$		0			0
$49$	15.1145			2.15921
$50$		0			0
$51$	0.0473908	−	0.0273611i	0.00663604	−	0.00383132i
$52$		0			0
$53$	10.0885	−	5.82458i	1.38576	−	0.800068i	0.392925	−	0.919571i	$-0.371463\pi$
$53$	10.0885	−	5.82458i	1.38576	−	0.800068i	0.992834	+	0.119503i	$0.0381300\pi$
$54$		0			0
$55$	2.23896	−	3.87800i	0.301902	−	0.522909i
$56$		0			0
$57$	−0.0822924	+	0.310558i	−0.0108999	+	0.0411344i
$58$		0			0
$59$	4.10945	+	2.37259i	0.535005	+	0.308885i	0.743052	−	0.669233i	$-0.233377\pi$
$59$	4.10945	+	2.37259i	0.535005	+	0.308885i	−0.208047	+	0.978119i	$0.566711\pi$
$60$		0			0
$61$	1.51215	−	0.873042i	0.193611	−	0.111782i	−0.400061	−	0.916489i	$-0.631011\pi$
$61$	1.51215	−	0.873042i	0.193611	−	0.111782i	0.593672	+	0.804707i	$0.297678\pi$
$62$		0			0
$63$	−7.04113	−	12.1956i	−0.887099	−	1.53650i
$64$		0			0
$65$	−1.12921			−0.140061
$66$		0			0
$67$	−9.42749	+	5.44296i	−1.15175	+	0.664964i	−0.949313	−	0.314332i	$-0.898220\pi$
$67$	−9.42749	+	5.44296i	−1.15175	+	0.664964i	−0.202438	+	0.979295i	$0.564886\pi$
$68$		0			0
$69$		−	0.235375i		−	0.0283359i
$70$		0			0
$71$	−5.42083	+	9.38916i	−0.643335	+	1.11429i	0.341349	+	0.939937i	$0.389116\pi$
$71$	−5.42083	+	9.38916i	−0.643335	+	1.11429i	−0.984683	+	0.174352i	$0.944217\pi$
$72$		0			0
$73$	−6.23576	+	10.8007i	−0.729841	+	1.26412i	0.227109	+	0.973869i	$0.427073\pi$
$73$	−6.23576	+	10.8007i	−0.729841	+	1.26412i	−0.956950	+	0.290252i	$0.906261\pi$
$74$		0			0
$75$			0.00838412i			0.000968115i
$76$		0			0
$77$		−	9.31205i		−	1.06121i
$78$		0			0
$79$	−0.834855	+	1.44601i	−0.0939285	+	0.162689i	−0.909161	−	0.416445i	$-0.863276\pi$
$79$	−0.834855	+	1.44601i	−0.0939285	+	0.162689i	0.815232	+	0.579134i	$0.196609\pi$
$80$		0			0
$81$	−4.47557	+	7.75191i	−0.497285	+	0.861324i
$82$		0			0
$83$		−	15.5733i		−	1.70939i	−0.519130	−	0.854695i	$-0.673744\pi$
$83$		−	15.5733i		−	1.70939i	0.519130	−	0.854695i	$-0.326256\pi$
$84$		0			0
$85$	1.45399	−	0.839462i	0.157708	−	0.0910525i
$86$		0			0
$87$	−0.444666			−0.0476732
$88$		0			0
$89$	−2.90236	−	5.02703i	−0.307649	−	0.532864i	0.670198	−	0.742182i	$-0.266209\pi$
$89$	−2.90236	−	5.02703i	−0.307649	−	0.532864i	−0.977848	+	0.209318i	$0.932876\pi$
$90$		0			0
$91$	−2.03364	+	1.17412i	−0.213183	+	0.123081i
$92$		0			0
$93$	0.347306	+	0.200517i	0.0360139	+	0.0207926i
$94$		0			0
$95$	−2.52480	+	9.52820i	−0.259040	+	0.977573i
$96$		0			0
$97$	−0.605380	+	1.04855i	−0.0614670	+	0.106464i	−0.895121	−	0.445823i	$-0.852911\pi$
$97$	−0.605380	+	1.04855i	−0.0614670	+	0.106464i	0.833654	+	0.552287i	$0.186245\pi$
$98$		0			0
$99$	−5.13537	+	2.96491i	−0.516124	+	0.297985i
$100$		0			0
$101$	−12.9353	+	7.46822i	−1.28711	+	0.743115i	−0.978138	−	0.207955i	$-0.933319\pi$
$101$	−12.9353	+	7.46822i	−1.28711	+	0.743115i	−0.308975	+	0.951070i	$0.599986\pi$
$102$		0			0
$103$	−11.6211			−1.14506			−0.572530	−	0.819884i	$-0.694038\pi$
$103$	−11.6211			−1.14506			−0.572530	+	0.819884i	$0.694038\pi$
$104$		0			0
$105$	0.391904	+	0.678798i	0.0382459	+	0.0662439i
$106$		0			0
$107$			7.66606i			0.741106i	0.928811	+	0.370553i	$0.120832\pi$
$107$			7.66606i			0.741106i	−0.928811	+	0.370553i	$0.879168\pi$
$108$		0			0
$109$	−2.28507	−	1.31929i	−0.218870	−	0.126365i	0.386557	−	0.922266i	$-0.373664\pi$
$109$	−2.28507	−	1.31929i	−0.218870	−	0.126365i	−0.605427	+	0.795901i	$0.706998\pi$
$110$		0			0
$111$	−0.380206	+	0.658536i	−0.0360875	+	0.0625055i
$112$		0			0
$113$	−8.94264			−0.841253			−0.420627	−	0.907234i	$-0.638190\pi$
$113$	−8.94264			−0.841253			−0.420627	+	0.907234i	$0.638190\pi$
$114$		0			0
$115$		−	7.22153i		−	0.673411i
$116$		0			0
$117$	1.29500	+	0.747668i	0.119723	+	0.0691219i
$118$		0			0
$119$	1.74570	−	3.02364i	0.160028	−	0.277177i
$120$		0			0
$121$	7.07884			0.643531
$122$		0			0
$123$	0.353658	−	0.204185i	0.0318883	−	0.0184107i
$124$		0			0
$125$		−	11.0496i		−	0.988304i
$126$		0			0
$127$	2.38102	+	4.12405i	0.211281	+	0.365950i	0.952116	−	0.305738i	$-0.0989030\pi$
$127$	2.38102	+	4.12405i	0.211281	+	0.365950i	−0.740834	+	0.671688i	$0.765570\pi$
$128$		0			0
$129$	−0.279182	−	0.483558i	−0.0245806	−	0.0425749i
$130$		0			0
$131$	−4.31780	−	2.49288i	−0.377248	−	0.217804i	0.299372	−	0.954136i	$-0.403223\pi$
$131$	−4.31780	−	2.49288i	−0.377248	−	0.217804i	−0.676620	+	0.736332i	$0.736556\pi$
$132$		0			0
$133$	5.36014	+	19.7849i	0.464783	+	1.71557i
$134$		0			0
$135$	0.499573	−	0.865287i	0.0429964	−	0.0744720i
$136$		0			0
$137$	−4.00007	−	6.92833i	−0.341749	−	0.591927i	0.643008	−	0.765859i	$-0.277686\pi$
$137$	−4.00007	−	6.92833i	−0.341749	−	0.591927i	−0.984758	+	0.173932i	$0.944353\pi$
$138$		0			0
$139$	6.90837	−	3.98855i	0.585960	−	0.338304i	−0.177538	−	0.984114i	$-0.556813\pi$
$139$	6.90837	−	3.98855i	0.585960	−	0.338304i	0.763498	+	0.645810i	$0.223480\pi$
$140$		0			0
$141$			0.115331i			0.00971266i
$142$		0			0
$143$	0.494404	+	0.856333i	0.0413441	+	0.0716101i
$144$		0			0
$145$	−13.6427			−1.13297
$146$		0			0
$147$	0.964772	+	0.557012i	0.0795731	+	0.0459415i
$148$		0			0
$149$	−4.57651	−	2.64225i	−0.374922	−	0.216462i	0.300684	−	0.953724i	$-0.402785\pi$
$149$	−4.57651	−	2.64225i	−0.374922	−	0.216462i	−0.675607	+	0.737262i	$0.736118\pi$
$150$		0			0
$151$	3.63598			0.295892			0.147946	−	0.988995i	$-0.452734\pi$
$151$	3.63598			0.295892			0.147946	+	0.988995i	$0.452734\pi$
$152$		0			0
$153$	−2.22329			−0.179742
$154$		0			0
$155$	10.6556	+	6.15204i	0.855882	+	0.494144i
$156$		0			0
$157$	−16.5481	−	9.55404i	−1.32068	−	0.762496i	−0.336844	−	0.941561i	$-0.609359\pi$
$157$	−16.5481	−	9.55404i	−1.32068	−	0.762496i	−0.983837	+	0.179065i	$0.942693\pi$
$158$		0			0
$159$	0.858611			0.0680923
$160$		0			0
$161$	−7.50874	−	13.0055i	−0.591772	−	1.02498i
$162$		0			0
$163$		−	9.73237i		−	0.762298i	−0.924514	−	0.381149i	$-0.875528\pi$
$163$		−	9.73237i		−	0.762298i	0.924514	−	0.381149i	$-0.124472\pi$
$164$		0			0
$165$	0.285831	−	0.165025i	0.0222519	−	0.0128472i
$166$		0			0
$167$	9.40182	+	16.2844i	0.727535	+	1.26013i	0.957922	+	0.287029i	$0.0926675\pi$
$167$	9.40182	+	16.2844i	0.727535	+	1.26013i	−0.230387	+	0.973099i	$0.573999\pi$
$168$		0			0
$169$	−6.37533	+	11.0424i	−0.490410	+	0.849414i
$170$		0			0
$171$	9.20427	−	9.25541i	0.703868	−	0.707779i
$172$		0			0
$173$	−10.1721	−	5.87286i	−0.773370	−	0.446505i	0.0607055	−	0.998156i	$-0.480665\pi$
$173$	−10.1721	−	5.87286i	−0.773370	−	0.446505i	−0.834075	+	0.551650i	$0.813998\pi$
$174$		0			0
$175$	0.267463	+	0.463260i	0.0202183	+	0.0350192i
$176$		0			0
$177$	0.174874	+	0.302890i	0.0131443	+	0.0227666i
$178$		0			0
$179$		−	11.1964i		−	0.836860i	−0.908249	−	0.418430i	$-0.862580\pi$
$179$		−	11.1964i		−	0.836860i	0.908249	−	0.418430i	$-0.137420\pi$
$180$		0			0
$181$	10.2345	−	5.90892i	0.760728	−	0.439206i	−0.0688293	−	0.997628i	$-0.521926\pi$
$181$	10.2345	−	5.90892i	0.760728	−	0.439206i	0.829557	+	0.558422i	$0.188593\pi$
$182$		0			0
$183$	0.128697			0.00951352
$184$		0			0
$185$	−11.6651	+	20.2045i	−0.857632	+	1.48546i
$186$		0			0
$187$	−1.27321	−	0.735087i	−0.0931062	−	0.0537549i
$188$		0			0
$189$		−	2.07777i		−	0.151136i
$190$		0			0
$191$	−12.6474			−0.915135			−0.457568	−	0.889175i	$-0.651279\pi$
$191$	−12.6474			−0.915135			−0.457568	+	0.889175i	$0.651279\pi$
$192$		0			0
$193$	−3.67277	+	6.36143i	−0.264372	+	0.457906i	−0.967399	−	0.253258i	$-0.918498\pi$
$193$	−3.67277	+	6.36143i	−0.264372	+	0.457906i	0.703027	+	0.711163i	$0.251831\pi$
$194$		0			0
$195$	−0.0720786	−	0.0416146i	−0.00516166	−	0.00298009i
$196$		0			0
$197$			12.1000i			0.862092i	0.902330	+	0.431046i	$0.141855\pi$
$197$			12.1000i			0.862092i	−0.902330	+	0.431046i	$0.858145\pi$
$198$		0			0
$199$	3.73560	+	6.47025i	0.264810	+	0.458664i	0.967514	−	0.252819i	$-0.0813576\pi$
$199$	3.73560	+	6.47025i	0.264810	+	0.458664i	−0.702704	+	0.711482i	$0.748024\pi$
$200$		0			0
$201$	−0.802356			−0.0565938
$202$		0			0
$203$	−24.5697	+	14.1853i	−1.72446	+	0.995616i
$204$		0			0
$205$	10.8505	−	6.26457i	0.757835	−	0.437536i
$206$		0			0
$207$	−4.78149	+	8.28178i	−0.332337	+	0.575624i
$208$		0			0
$209$	8.33113	−	2.25707i	0.576276	−	0.156125i
$210$		0			0
$211$	−5.04276	−	2.91144i	−0.347158	−	0.200432i	0.316275	−	0.948668i	$-0.397568\pi$
$211$	−5.04276	−	2.91144i	−0.347158	−	0.200432i	−0.663433	+	0.748236i	$0.730901\pi$
$212$		0			0
$213$	−0.692036	+	0.399547i	−0.0474175	+	0.0273765i
$214$		0			0
$215$	−8.56556	−	14.8360i	−0.584166	−	1.01181i
$216$		0			0
$217$	25.5869			1.73695
$218$		0			0
$219$	−0.796071	+	0.459612i	−0.0537935	+	0.0310577i
$220$		0			0
$221$			0.370737i			0.0249385i
$222$		0			0
$223$	3.54133	−	6.13377i	0.237145	−	0.410748i	−0.722749	−	0.691111i	$-0.757122\pi$
$223$	3.54133	−	6.13377i	0.237145	−	0.410748i	0.959894	+	0.280363i	$0.0904549\pi$
$224$		0			0
$225$	0.170318	−	0.294999i	0.0113545	−	0.0196666i
$226$		0			0
$227$		−	10.8506i		−	0.720179i	−0.932918	−	0.360090i	$-0.882746\pi$
$227$		−	10.8506i		−	0.720179i	0.932918	−	0.360090i	$-0.117254\pi$
$228$		0			0
$229$		−	5.71559i		−	0.377697i	−0.982006	−	0.188848i	$-0.939525\pi$
$229$		−	5.71559i		−	0.377697i	0.982006	−	0.188848i	$-0.0604755\pi$
$230$		0			0
$231$	0.343176	−	0.594399i	0.0225793	−	0.0391086i
$232$		0			0
$233$	11.6711	−	20.2149i	0.764598	−	1.32432i	−0.175860	−	0.984415i	$-0.556271\pi$
$233$	11.6711	−	20.2149i	0.764598	−	1.32432i	0.940459	−	0.339908i	$-0.110396\pi$
$234$		0			0
$235$			3.53847i			0.230825i
$236$		0			0
$237$	−0.106579	+	0.0615336i	−0.00692307	+	0.00399704i
$238$		0			0
$239$	10.4517			0.676063			0.338032	−	0.941135i	$-0.390239\pi$
$239$	10.4517			0.676063			0.338032	+	0.941135i	$0.390239\pi$
$240$		0			0
$241$	−10.3416	−	17.9122i	−0.666160	−	1.15382i	−0.978969	−	0.204007i	$-0.934603\pi$
$241$	−10.3416	−	17.9122i	−0.666160	−	1.15382i	0.312809	−	0.949816i	$-0.398730\pi$
$242$		0			0
$243$	−1.71928	+	0.992627i	−0.110292	+	0.0636770i
$244$		0			0
$245$	29.6001	+	17.0896i	1.89108	+	1.09182i
$246$		0			0
$247$	−1.54336	−	1.53483i	−0.0982014	−	0.0976588i
$248$		0			0
$249$	0.573921	−	0.994060i	0.0363708	−	0.0629960i
$250$		0			0
$251$	0.147363	−	0.0850803i	0.00930149	−	0.00537022i	−0.495342	−	0.868698i	$-0.664957\pi$
$251$	0.147363	−	0.0850803i	0.00930149	−	0.00537022i	0.504644	+	0.863328i	$0.331624\pi$
$252$		0			0
$253$	−5.47643	+	3.16182i	−0.344300	+	0.198782i
$254$		0			0
$255$	0.123747			0.00774931
$256$		0			0
$257$	7.27034	+	12.5926i	0.453511	+	0.785504i	0.998601	−	0.0528730i	$-0.0168379\pi$
$257$	7.27034	+	12.5926i	0.453511	+	0.785504i	−0.545090	+	0.838378i	$0.683505\pi$
$258$		0			0
$259$			48.5160i			3.01464i
$260$		0			0
$261$	15.6458	+	9.03308i	0.968448	+	0.559134i
$262$		0			0
$263$	7.54036	−	13.0603i	0.464959	−	0.805332i	−0.534241	−	0.845332i	$-0.679402\pi$
$263$	7.54036	−	13.0603i	0.464959	−	0.805332i	0.999200	+	0.0400000i	$0.0127358\pi$
$264$		0			0
$265$	26.3430			1.61824
$266$		0			0
$267$		−	0.427841i		−	0.0261835i
$268$		0			0
$269$	−6.34397	−	3.66269i	−0.386799	−	0.223318i	0.293973	−	0.955814i	$-0.405022\pi$
$269$	−6.34397	−	3.66269i	−0.386799	−	0.223318i	−0.680772	+	0.732495i	$0.738356\pi$
$270$		0			0
$271$	4.12352	−	7.14215i	0.250486	−	0.433855i	−0.713174	−	0.700987i	$-0.752743\pi$
$271$	4.12352	−	7.14215i	0.250486	−	0.433855i	0.963660	+	0.267133i	$0.0860762\pi$
$272$		0			0
$273$	−0.173079			−0.0104752
$274$		0			0
$275$	0.195072	−	0.112625i	0.0117633	−	0.00679152i
$276$		0			0
$277$			17.2973i			1.03929i	0.854382	+	0.519646i	$0.173936\pi$
$277$			17.2973i			1.03929i	−0.854382	+	0.519646i	$0.826064\pi$
$278$		0			0
$279$	−8.14673	−	14.1106i	−0.487732	−	0.844777i
$280$		0			0
$281$	−12.5105	−	21.6688i	−0.746312	−	1.29265i	−0.949579	−	0.313527i	$-0.898489\pi$
$281$	−12.5105	−	21.6688i	−0.746312	−	1.29265i	0.203267	−	0.979123i	$-0.434844\pi$
$282$		0			0
$283$	16.0653	+	9.27531i	0.954984	+	0.551360i	0.894626	−	0.446817i	$-0.147442\pi$
$283$	16.0653	+	9.27531i	0.954984	+	0.551360i	0.0603582	+	0.998177i	$0.480776\pi$
$284$		0			0
$285$	−0.512303	+	0.515149i	−0.0303462	+	0.0305148i
$286$		0			0
$287$	13.0275	−	22.5642i	0.768986	−	1.33192i
$288$		0			0
$289$	8.22439	+	14.2451i	0.483788	+	0.837945i
$290$		0			0
$291$	−0.0772841	+	0.0446200i	−0.00453048	+	0.00261567i
$292$		0			0
$293$		−	1.02282i		−	0.0597535i	−0.999554	−	0.0298768i	$-0.990489\pi$
$293$		−	1.02282i		−	0.0597535i	0.999554	−	0.0298768i	$-0.00951149\pi$
$294$		0			0
$295$	5.36529	+	9.29295i	0.312379	+	0.541057i
$296$		0			0
$297$	−0.874917			−0.0507678
$298$		0			0
$299$	1.38100	+	0.797322i	0.0798654	+	0.0461103i
$300$		0			0
$301$	−30.8521	−	17.8125i	−1.77829	−	1.02669i
$302$		0			0
$303$	−1.10090			−0.0632451
$304$		0			0
$305$	3.94853			0.226092
$306$		0			0
$307$	22.7524	+	13.1361i	1.29855	+	0.749717i	0.980153	−	0.198241i	$-0.0635227\pi$
$307$	22.7524	+	13.1361i	1.29855	+	0.749717i	0.318395	+	0.947958i	$0.396856\pi$
$308$		0			0
$309$	−0.741787	−	0.428271i	−0.0421988	−	0.0243635i
$310$		0			0
$311$	−24.2028			−1.37241			−0.686207	−	0.727407i	$-0.740725\pi$
$311$	−24.2028			−1.37241			−0.686207	+	0.727407i	$0.740725\pi$
$312$		0			0
$313$	14.3528	+	24.8598i	0.811270	+	1.40516i	0.911976	+	0.410244i	$0.134557\pi$
$313$	14.3528	+	24.8598i	0.811270	+	1.40516i	−0.100706	+	0.994916i	$0.532110\pi$
$314$		0			0
$315$		−	31.8451i		−	1.79427i
$316$		0			0
$317$	−8.87555	+	5.12430i	−0.498501	+	0.287809i	−0.728094	−	0.685477i	$-0.759594\pi$
$317$	−8.87555	+	5.12430i	−0.498501	+	0.287809i	0.229594	+	0.973287i	$0.426260\pi$
$318$		0			0
$319$	5.97323	+	10.3459i	0.334437	+	0.579261i
$320$		0			0
$321$	−0.282517	+	0.489333i	−0.0157685	+	0.0273119i
$322$		0			0
$323$	3.12826	+	0.828933i	0.174061	+	0.0461231i
$324$		0			0
$325$	−0.0491916	−	0.0284008i	−0.00272866	−	0.00157539i
$326$		0			0
$327$	−0.0972391	−	0.168423i	−0.00537733	−	0.00931381i
$328$		0			0
$329$	3.67921	+	6.37257i	0.202841	+	0.351331i
$330$		0			0
$331$			16.6930i			0.917528i	0.888558	+	0.458764i	$0.151708\pi$
$331$			16.6930i			0.917528i	−0.888558	+	0.458764i	$0.848292\pi$
$332$		0			0
$333$	26.7554	−	15.4473i	1.46619	−	0.846504i
$334$		0			0
$335$	−24.6170			−1.34497
$336$		0			0
$337$	14.1278	−	24.4701i	0.769591	−	1.33297i	−0.168194	−	0.985754i	$-0.553794\pi$
$337$	14.1278	−	24.4701i	0.769591	−	1.33297i	0.937785	−	0.347216i	$-0.112873\pi$
$338$		0			0
$339$	−0.570819	−	0.329562i	−0.0310026	−	0.0178994i
$340$		0			0
$341$		−	10.7742i		−	0.583458i
$342$		0			0
$343$	38.1591			2.06040
$344$		0			0
$345$	0.266134	−	0.460958i	0.0143282	−	0.0248171i
$346$		0			0
$347$	−22.6793	−	13.0939i	−1.21749	−	0.702918i	−0.253110	−	0.967438i	$-0.581453\pi$
$347$	−22.6793	−	13.0939i	−1.21749	−	0.702918i	−0.964380	+	0.264519i	$0.914787\pi$
$348$		0			0
$349$		−	7.01947i		−	0.375743i	−0.982194	−	0.187872i	$-0.939841\pi$
$349$		−	7.01947i		−	0.375743i	0.982194	−	0.187872i	$-0.0601589\pi$
$350$		0			0
$351$	0.110315	+	0.191071i	0.00588817	+	0.0101986i
$352$		0			0
$353$	13.7525			0.731969			0.365985	−	0.930621i	$-0.380732\pi$
$353$	13.7525			0.731969			0.365985	+	0.930621i	$0.380732\pi$
$354$		0			0
$355$	−21.2323	+	12.2585i	−1.12689	+	0.650612i
$356$		0			0
$357$	0.222860	−	0.128668i	0.0117950	−	0.00680984i
$358$		0			0
$359$	−1.49285	+	2.58569i	−0.0787895	+	0.136467i	−0.902728	−	0.430212i	$-0.858439\pi$
$359$	−1.49285	+	2.58569i	−0.0787895	+	0.136467i	0.823938	+	0.566679i	$0.191772\pi$
$360$		0			0
$361$	−16.4016	+	9.59102i	−0.863242	+	0.504790i
$362$		0			0
$363$	0.451850	+	0.260876i	0.0237160	+	0.0136924i
$364$		0			0
$365$	−24.4242	+	14.1013i	−1.27842	+	0.738096i
$366$		0			0
$367$	9.97261	+	17.2731i	0.520566	+	0.901647i	0.999714	+	0.0239129i	$0.00761244\pi$
$367$	9.97261	+	17.2731i	0.520566	+	0.901647i	−0.479148	+	0.877734i	$0.659054\pi$
$368$		0			0
$369$	−16.5915			−0.863719
$370$		0			0
$371$	47.4421	−	27.3907i	2.46307	−	1.42205i
$372$		0			0
$373$			16.8878i			0.874416i	0.899360	+	0.437208i	$0.144033\pi$
$373$			16.8878i			0.874416i	−0.899360	+	0.437208i	$0.855967\pi$
$374$		0			0
$375$	0.407209	−	0.705306i	0.0210282	−	0.0364219i
$376$		0			0
$377$	1.50628	−	2.60896i	0.0775775	−	0.134368i
$378$		0			0
$379$		−	26.5474i		−	1.36365i	−0.731517	−	0.681824i	$-0.761187\pi$
$379$		−	26.5474i		−	1.36365i	0.731517	−	0.681824i	$-0.238813\pi$
$380$		0			0
$381$			0.350990i			0.0179818i
$382$		0			0
$383$	−2.38085	+	4.12375i	−0.121656	+	0.210714i	−0.920421	−	0.390929i	$-0.872154\pi$
$383$	−2.38085	+	4.12375i	−0.121656	+	0.210714i	0.798765	+	0.601643i	$0.205487\pi$
$384$		0			0
$385$	10.5290	−	18.2367i	0.536605	−	0.929428i
$386$		0			0
$387$			22.6856i			1.15317i
$388$		0			0
$389$	17.0129	−	9.82241i	0.862589	−	0.498016i	−0.00228917	−	0.999997i	$-0.500729\pi$
$389$	17.0129	−	9.82241i	0.862589	−	0.498016i	0.864879	+	0.501981i	$0.167395\pi$
$390$		0			0
$391$	−2.37094			−0.119904
$392$		0			0
$393$	−0.183740	−	0.318247i	−0.00926845	−	0.0160534i
$394$		0			0
$395$	−3.26995	+	1.88791i	−0.164529	+	0.0949909i
$396$		0			0
$397$	22.1285	+	12.7759i	1.11060	+	0.641203i	0.938984	−	0.343962i	$-0.111769\pi$
$397$	22.1285	+	12.7759i	1.11060	+	0.641203i	0.171612	+	0.985165i	$0.445102\pi$
$398$		0			0
$399$	−0.386988	+	1.46043i	−0.0193736	+	0.0731130i
$400$		0			0
$401$	4.14055	−	7.17165i	0.206769	−	0.358135i	−0.743926	−	0.668262i	$-0.767038\pi$
$401$	4.14055	−	7.17165i	0.206769	−	0.358135i	0.950695	+	0.310127i	$0.100372\pi$
$402$		0			0
$403$	−2.35296	+	1.35848i	−0.117209	+	0.0676708i
$404$		0			0
$405$	−17.5299	+	10.1209i	−0.871066	+	0.502910i
$406$		0			0
$407$	20.4293			1.01265
$408$		0			0
$409$	−8.00331	−	13.8621i	−0.395738	−	0.685439i	0.597457	−	0.801901i	$-0.296178\pi$
$409$	−8.00331	−	13.8621i	−0.395738	−	0.685439i	−0.993195	+	0.116462i	$0.962845\pi$
$410$		0			0
$411$		−	0.589657i		−	0.0290856i
$412$		0			0
$413$	19.3251	+	11.1574i	0.950927	+	0.549018i
$414$		0			0
$415$	17.6084	−	30.4987i	0.864363	−	1.49712i
$416$		0			0
$417$	0.587958			0.0287924
$418$		0			0
$419$			24.4736i			1.19562i	0.801640	+	0.597808i	$0.203961\pi$
$419$			24.4736i			1.19562i	−0.801640	+	0.597808i	$0.796039\pi$
$420$		0			0
$421$	10.0033	+	5.77541i	0.487532	+	0.281476i	0.723550	−	0.690272i	$-0.242509\pi$
$421$	10.0033	+	5.77541i	0.487532	+	0.281476i	−0.236018	+	0.971749i	$0.575843\pi$
$422$		0			0
$423$	2.34288	−	4.05799i	0.113915	−	0.197306i
$424$		0			0
$425$	0.0844535			0.00409659
$426$		0			0
$427$	7.11106	−	4.10557i	0.344128	−	0.198682i
$428$		0			0
$429$			0.0728809i			0.00351872i
$430$		0			0
$431$	−6.07769	−	10.5269i	−0.292752	−	0.507061i	0.681707	−	0.731625i	$-0.261238\pi$
$431$	−6.07769	−	10.5269i	−0.292752	−	0.507061i	−0.974459	+	0.224564i	$0.927904\pi$
$432$		0			0
$433$	19.2219	+	33.2932i	0.923744	+	1.59997i	0.793570	+	0.608480i	$0.208220\pi$
$433$	19.2219	+	33.2932i	0.923744	+	1.59997i	0.130174	+	0.991491i	$0.458446\pi$
$434$		0			0
$435$	−0.870831	−	0.502775i	−0.0417532	−	0.0241062i
$436$		0			0
$437$	9.81555	−	9.87008i	0.469541	−	0.472150i
$438$		0			0
$439$	−9.70327	+	16.8066i	−0.463112	+	0.802133i	−0.999114	−	0.0420834i	$-0.986600\pi$
$439$	−9.70327	+	16.8066i	−0.463112	+	0.802133i	0.536002	+	0.844217i	$0.319934\pi$
$440$		0			0
$441$	−22.6306	−	39.1974i	−1.07765	−	1.86654i
$442$		0			0
$443$	−16.3666	+	9.44924i	−0.777599	+	0.448947i	−0.835579	−	0.549371i	$-0.814867\pi$
$443$	−16.3666	+	9.44924i	−0.777599	+	0.448947i	0.0579798	+	0.998318i	$0.481534\pi$
$444$		0			0
$445$		−	13.1266i		−	0.622259i
$446$		0			0
$447$	−0.194749	−	0.337315i	−0.00921132	−	0.0159545i
$448$		0			0
$449$	−25.1997			−1.18925			−0.594624	−	0.804004i	$-0.702699\pi$
$449$	−25.1997			−1.18925			−0.594624	+	0.804004i	$0.702699\pi$
$450$		0			0
$451$	−9.50144	−	5.48566i	−0.447405	−	0.258310i
$452$		0			0
$453$	0.232088	+	0.133996i	0.0109045	+	0.00629570i
$454$		0			0
$455$	−5.31022			−0.248947
$456$		0			0
$457$	6.45543			0.301972			0.150986	−	0.988536i	$-0.451755\pi$
$457$	6.45543			0.301972			0.150986	+	0.988536i	$0.451755\pi$
$458$		0			0
$459$	−0.284087	−	0.164018i	−0.0132601	−	0.00765570i
$460$		0			0
$461$	2.49112	+	1.43825i	0.116023	+	0.0669858i	0.556888	−	0.830587i	$-0.311995\pi$
$461$	2.49112	+	1.43825i	0.116023	+	0.0669858i	−0.440866	+	0.897573i	$0.645328\pi$
$462$		0			0
$463$	29.6723			1.37899			0.689494	−	0.724292i	$-0.257833\pi$
$463$	29.6723			1.37899			0.689494	+	0.724292i	$0.257833\pi$
$464$		0			0
$465$	0.453441	+	0.785383i	0.0210278	+	0.0364213i
$466$		0			0
$467$		−	12.3400i		−	0.571026i	−0.958375	−	0.285513i	$-0.907836\pi$
$467$		−	12.3400i		−	0.571026i	0.958375	−	0.285513i	$-0.0921639\pi$
$468$		0			0
$469$	−44.3337	+	25.5961i	−2.04714	+	1.18192i
$470$		0			0
$471$	−0.704188	−	1.21969i	−0.0324473	−	0.0562003i
$472$		0			0
$473$	−7.50055	+	12.9913i	−0.344876	+	0.597342i
$474$		0			0
$475$	−0.349632	+	0.351575i	−0.0160422	+	0.0161314i
$476$		0			0
$477$	−30.2106	−	17.4421i	−1.38325	−	0.798619i
$478$		0			0
$479$	3.99982	+	6.92789i	0.182756	+	0.316543i	0.942818	−	0.333307i	$-0.108165\pi$
$479$	3.99982	+	6.92789i	0.182756	+	0.316543i	−0.760062	+	0.649851i	$0.774831\pi$
$480$		0			0
$481$	−2.57586	−	4.46151i	−0.117449	−	0.203428i
$482$		0			0
$483$		−	1.10688i		−	0.0503646i
$484$		0			0
$485$	−2.37115	+	1.36898i	−0.107668	+	0.0621623i
$486$		0			0
$487$	−11.3433			−0.514013			−0.257007	−	0.966410i	$-0.582736\pi$
$487$	−11.3433			−0.514013			−0.257007	+	0.966410i	$0.582736\pi$
$488$		0			0
$489$	0.358666	−	0.621228i	0.0162194	−	0.0280929i
$490$		0			0
$491$	20.0056	+	11.5502i	0.902840	+	0.521255i	0.878121	−	0.478439i	$-0.158797\pi$
$491$	20.0056	+	11.5502i	0.902840	+	0.521255i	0.0247197	+	0.999694i	$0.492131\pi$
$492$		0			0
$493$			4.47913i			0.201730i
$494$		0			0
$495$	−13.4095			−0.602710
$496$		0			0
$497$	−25.4920	+	44.1535i	−1.14347	+	1.98055i
$498$		0			0
$499$	−17.4946	−	10.1005i	−0.783166	−	0.452161i	0.0543850	−	0.998520i	$-0.482680\pi$
$499$	−17.4946	−	10.1005i	−0.783166	−	0.452161i	−0.837551	+	0.546359i	$0.816014\pi$
$500$		0			0
$501$			1.38594i			0.0619191i
$502$		0			0
$503$	2.59755	+	4.49909i	0.115819	+	0.200604i	0.918107	−	0.396333i	$-0.129717\pi$
$503$	2.59755	+	4.49909i	0.115819	+	0.200604i	−0.802288	+	0.596937i	$0.796384\pi$
$504$		0			0
$505$	−33.7767			−1.50304
$506$		0			0
$507$	−0.813888	+	0.469898i	−0.0361460	+	0.0208689i
$508$		0			0
$509$	26.5099	−	15.3055i	1.17503	−	0.678404i	0.220171	−	0.975461i	$-0.429338\pi$
$509$	26.5099	−	15.3055i	1.17503	−	0.678404i	0.954860	+	0.297057i	$0.0960051\pi$
$510$		0			0
$511$	−29.3243	+	50.7912i	−1.29723	+	2.24687i
$512$		0			0
$513$	1.85890	−	0.503614i	0.0820724	−	0.0222351i
$514$		0			0
$515$	−22.7587	−	13.1397i	−1.00287	−	0.579006i
$516$		0			0
$517$	2.68339	−	1.54926i	0.118015	−	0.0681363i
$518$		0			0
$519$	−0.432864	−	0.749742i	−0.0190006	−	0.0329100i
$520$		0			0
$521$	−24.6215			−1.07869			−0.539343	−	0.842086i	$-0.681327\pi$
$521$	−24.6215			−1.07869			−0.539343	+	0.842086i	$0.681327\pi$
$522$		0			0
$523$	−28.6708	+	16.5531i	−1.25369	+	0.723816i	−0.971840	−	0.235643i	$-0.924280\pi$
$523$	−28.6708	+	16.5531i	−1.25369	+	0.723816i	−0.281847	+	0.959459i	$0.590947\pi$
$524$		0			0
$525$			0.0394272i			0.00172074i
$526$		0			0
$527$	2.01981	−	3.49842i	0.0879844	−	0.152393i
$528$		0			0
$529$	6.40096	−	11.0868i	0.278303	−	0.482034i
$530$		0			0
$531$		−	14.2098i		−	0.616652i
$532$		0			0
$533$			2.76666i			0.119837i
$534$		0			0
$535$	−8.66787	+	15.0132i	−0.374745	+	0.649077i
$536$		0			0
$537$	0.412621	−	0.714680i	0.0178059	−	0.0308407i
$538$		0			0
$539$		−	29.9295i		−	1.28916i
$540$		0			0
$541$	15.7964	−	9.12004i	0.679139	−	0.392101i	−0.120391	−	0.992727i	$-0.538415\pi$
$541$	15.7964	−	9.12004i	0.679139	−	0.392101i	0.799531	+	0.600625i	$0.205082\pi$
$542$		0			0
$543$	0.871043			0.0373800
$544$		0			0
$545$	−2.98338	−	5.16737i	−0.127794	−	0.221346i
$546$		0			0
$547$	18.9714	−	10.9532i	0.811160	−	0.468323i	−0.0361988	−	0.999345i	$-0.511525\pi$
$547$	18.9714	−	10.9532i	0.811160	−	0.468323i	0.847358	+	0.531021i	$0.178192\pi$
$548$		0			0
$549$	−4.52825	−	2.61438i	−0.193261	−	0.111579i
$550$		0			0
$551$	−18.6463	−	18.5433i	−0.794360	−	0.789971i
$552$		0			0
$553$	−3.92599	+	6.80001i	−0.166950	+	0.289166i
$554$		0			0
$555$	−1.48919	+	0.859782i	−0.0632125	+	0.0364957i
$556$		0			0
$557$	−24.5414	+	14.1690i	−1.03985	+	0.600359i	−0.919791	−	0.392408i	$-0.871642\pi$
$557$	−24.5414	+	14.1690i	−1.03985	+	0.600359i	−0.120061	+	0.992767i	$0.538309\pi$
$558$		0			0
$559$	3.78286			0.159998
$560$		0			0
$561$	−0.0541802	−	0.0938428i	−0.00228749	−	0.00396205i
$562$		0			0
$563$		−	5.98383i		−	0.252188i	−0.992018	−	0.126094i	$-0.959756\pi$
$563$		−	5.98383i		−	0.252188i	0.992018	−	0.126094i	$-0.0402442\pi$
$564$		0			0
$565$	−17.5132	−	10.1113i	−0.736787	−	0.425384i
$566$		0			0
$567$	−21.0468	+	36.4541i	−0.883883	+	1.53093i
$568$		0			0
$569$	26.0900			1.09375			0.546875	−	0.837214i	$-0.315817\pi$
$569$	26.0900			1.09375			0.546875	+	0.837214i	$0.315817\pi$
$570$		0			0
$571$		−	17.5053i		−	0.732573i	−0.930502	−	0.366287i	$-0.880629\pi$
$571$		−	17.5053i		−	0.732573i	0.930502	−	0.366287i	$-0.119371\pi$
$572$		0			0
$573$	−0.807299	−	0.466094i	−0.0337254	−	0.0194714i
$574$		0			0
$575$	0.181629	−	0.314591i	0.00757445	−	0.0131193i
$576$		0			0
$577$	−4.31463			−0.179621			−0.0898103	−	0.995959i	$-0.528626\pi$
$577$	−4.31463			−0.179621			−0.0898103	+	0.995959i	$0.528626\pi$
$578$		0			0
$579$	−0.468874	+	0.270705i	−0.0194858	+	0.0112501i
$580$		0			0
$581$		−	73.2350i		−	3.03830i
$582$		0			0
$583$	−11.5338	−	19.9771i	−0.477681	−	0.827368i
$584$		0			0
$585$	1.69075	+	2.92846i	0.0699037	+	0.121077i
$586$		0			0
$587$	22.3055	+	12.8781i	0.920645	+	0.531535i	0.883841	−	0.467788i	$-0.154949\pi$
$587$	22.3055	+	12.8781i	0.920645	+	0.531535i	0.0368044	+	0.999322i	$0.488282\pi$
$588$		0			0
$589$	6.20180	+	22.8916i	0.255541	+	0.943231i
$590$		0			0
$591$	−0.445922	+	0.772359i	−0.0183428	+	0.0317706i
$592$		0			0
$593$	18.0229	+	31.2166i	0.740112	+	1.28191i	0.952444	+	0.304714i	$0.0985610\pi$
$593$	18.0229	+	31.2166i	0.740112	+	1.28191i	−0.212331	+	0.977198i	$0.568106\pi$
$594$		0			0
$595$	6.83754	−	3.94766i	0.280312	−	0.161838i
$596$		0			0
$597$			0.550671i			0.0225374i
$598$		0			0
$599$	6.14336	+	10.6406i	0.251011	+	0.434763i	0.963804	−	0.266610i	$-0.0859037\pi$
$599$	6.14336	+	10.6406i	0.251011	+	0.434763i	−0.712794	+	0.701374i	$0.752570\pi$
$600$		0			0
$601$	−9.74846			−0.397648			−0.198824	−	0.980035i	$-0.563712\pi$
$601$	−9.74846			−0.397648			−0.198824	+	0.980035i	$0.563712\pi$
$602$		0			0
$603$	28.2312	+	16.2993i	1.14967	+	0.663760i
$604$		0			0
$605$	13.8632	+	8.00390i	0.563618	+	0.325405i
$606$		0			0
$607$	−28.3299			−1.14988			−0.574938	−	0.818197i	$-0.694974\pi$
$607$	−28.3299			−1.14988			−0.574938	+	0.818197i	$0.694974\pi$
$608$		0			0
$609$	−2.09108			−0.0847350
$610$		0			0
$611$	−0.676677	−	0.390680i	−0.0273754	−	0.0158052i
$612$		0			0
$613$	−17.4855	−	10.0952i	−0.706232	−	0.407743i	0.103433	−	0.994636i	$-0.467017\pi$
$613$	−17.4855	−	10.0952i	−0.706232	−	0.407743i	−0.809664	+	0.586893i	$0.800351\pi$
$614$		0			0
$615$	0.923470			0.0372379
$616$		0			0
$617$	6.87561	+	11.9089i	0.276801	+	0.479434i	0.970588	−	0.240746i	$-0.0773922\pi$
$617$	6.87561	+	11.9089i	0.276801	+	0.479434i	−0.693787	+	0.720181i	$0.744059\pi$
$618$		0			0
$619$		−	4.39271i		−	0.176558i	−0.996096	−	0.0882791i	$-0.971863\pi$
$619$		−	4.39271i		−	0.176558i	0.996096	−	0.0882791i	$-0.0281367\pi$
$620$		0			0
$621$	−1.22194	+	0.705487i	−0.0490347	+	0.0283102i
$622$		0			0
$623$	−13.6486	−	23.6401i	−0.546821	−	0.947122i
$624$		0			0
$625$	12.7779	−	22.1320i	0.511116	−	0.885279i
$626$		0			0
$627$	0.614965	+	0.162955i	0.0245593	+	0.00650779i
$628$		0			0
$629$	6.63345	+	3.82982i	0.264493	+	0.152705i
$630$		0			0
$631$	−13.8673	−	24.0188i	−0.552047	−	0.956173i	−0.998127	−	0.0611800i	$-0.980514\pi$
$631$	−13.8673	−	24.0188i	−0.552047	−	0.956173i	0.446080	−	0.894993i	$-0.352820\pi$
$632$		0			0
$633$	−0.214590	−	0.371681i	−0.00852919	−	0.0147730i
$634$		0			0
$635$			10.7687i			0.427343i
$636$		0			0
$637$	−6.53623	+	3.77370i	−0.258975	+	0.149519i
$638$		0			0
$639$	32.4661			1.28434
$640$		0			0
$641$	2.60078	−	4.50468i	0.102725	−	0.177924i	−0.810082	−	0.586317i	$-0.800577\pi$
$641$	2.60078	−	4.50468i	0.102725	−	0.177924i	0.912806	+	0.408393i	$0.133911\pi$
$642$		0			0
$643$	−9.12347	−	5.26744i	−0.359794	−	0.207727i	0.309196	−	0.950998i	$-0.399940\pi$
$643$	−9.12347	−	5.26744i	−0.359794	−	0.207727i	−0.668991	+	0.743271i	$0.733273\pi$
$644$		0			0
$645$		−	1.26266i		−	0.0497173i
$646$		0			0
$647$	29.5690			1.16248			0.581239	−	0.813733i	$-0.302568\pi$
$647$	29.5690			1.16248			0.581239	+	0.813733i	$0.302568\pi$
$648$		0			0
$649$	4.69819	−	8.13750i	0.184420	−	0.319425i
$650$		0			0
$651$	1.63324	+	0.942951i	0.0640117	+	0.0369572i
$652$		0			0
$653$		−	5.92429i		−	0.231835i	−0.993259	−	0.115918i	$-0.963019\pi$
$653$		−	5.92429i		−	0.231835i	0.993259	−	0.115918i	$-0.0369809\pi$
$654$		0			0
$655$	−5.63730	−	9.76410i	−0.220268	−	0.381515i
$656$		0			0
$657$	37.3468			1.45704
$658$		0			0
$659$	−13.1894	+	7.61488i	−0.513785	+	0.296634i	−0.734388	−	0.678730i	$-0.762531\pi$
$659$	−13.1894	+	7.61488i	−0.513785	+	0.296634i	0.220603	+	0.975364i	$0.429197\pi$
$660$		0			0
$661$	7.12782	−	4.11525i	0.277240	−	0.160065i	−0.354933	−	0.934892i	$-0.615496\pi$
$661$	7.12782	−	4.11525i	0.277240	−	0.160065i	0.632173	+	0.774827i	$0.282163\pi$
$662$		0			0
$663$	−0.0136627	+	0.0236645i	−0.000530617	+	0.000919055i
$664$		0			0
$665$	−11.8731	+	44.8073i	−0.460421	+	1.73755i
$666$		0			0
$667$	16.6848	+	9.63299i	0.646039	+	0.372991i
$668$		0			0
$669$	0.452094	−	0.261017i	0.0174790	−	0.0100915i
$670$		0			0
$671$	−1.72879	−	2.99435i	−0.0667393	−	0.115596i
$672$		0			0
$673$	−5.85922			−0.225856			−0.112928	−	0.993603i	$-0.536023\pi$
$673$	−5.85922			−0.225856			−0.112928	+	0.993603i	$0.536023\pi$
$674$		0			0
$675$	0.0435257	−	0.0251296i	0.00167531	−	0.000967239i
$676$		0			0
$677$		−	2.54790i		−	0.0979236i	−0.998801	−	0.0489618i	$-0.984409\pi$
$677$		−	2.54790i		−	0.0979236i	0.998801	−	0.0489618i	$-0.0155913\pi$
$678$		0			0
$679$	−2.84686	+	4.93091i	−0.109252	+	0.189231i
$680$		0			0
$681$	0.399876	−	0.692605i	0.0153233	−	0.0265407i
$682$		0			0
$683$			24.9303i			0.953930i	0.878922	+	0.476965i	$0.158263\pi$
$683$			24.9303i			0.953930i	−0.878922	+	0.476965i	$0.841737\pi$
$684$		0			0
$685$		−	18.0912i		−	0.691230i
$686$		0			0
$687$	0.210636	−	0.364832i	0.00803627	−	0.0139192i
$688$		0			0
$689$	−2.90850	+	5.03767i	−0.110805	+	0.191920i
$690$		0			0
$691$		−	51.3756i		−	1.95442i	−0.212277	−	0.977209i	$-0.568088\pi$
$691$		−	51.3756i		−	1.95442i	0.212277	−	0.977209i	$-0.431912\pi$
$692$		0			0
$693$	−24.1496	+	13.9428i	−0.917368	+	0.529643i
$694$		0			0
$695$	18.0391			0.684262
$696$		0			0
$697$	−2.05676	−	3.56241i	−0.0779052	−	0.134936i
$698$		0			0
$699$	1.48996	−	0.860227i	0.0563553	−	0.0325368i
$700$		0			0
$701$	10.9994	+	6.35049i	0.415441	+	0.239855i	0.693125	−	0.720818i	$-0.256234\pi$
$701$	10.9994	+	6.35049i	0.415441	+	0.239855i	−0.277684	+	0.960672i	$0.589567\pi$
$702$		0			0
$703$	−43.4054	+	11.7594i	−1.63706	+	0.443514i
$704$		0			0
$705$	−0.130403	+	0.225865i	−0.00491126	+	0.00850656i
$706$		0			0
$707$	−60.8297	+	35.1200i	−2.28774	+	1.32082i
$708$		0			0
$709$	10.6515	−	6.14967i	0.400027	−	0.230956i	−0.286469	−	0.958090i	$-0.592481\pi$
$709$	10.6515	−	6.14967i	0.400027	−	0.230956i	0.686496	+	0.727134i	$0.259148\pi$
$710$		0			0
$711$	5.00006			0.187517
$712$		0			0
$713$	−8.68778	−	15.0477i	−0.325360	−	0.563540i
$714$		0			0
$715$			2.23605i			0.0836235i
$716$		0			0
$717$	0.667142	+	0.385175i	0.0249149	+	0.0143846i
$718$		0			0
$719$	−17.5424	+	30.3843i	−0.654222	+	1.13314i	0.327867	+	0.944724i	$0.393670\pi$
$719$	−17.5424	+	30.3843i	−0.654222	+	1.13314i	−0.982088	+	0.188421i	$0.939663\pi$
$720$		0			0
$721$	−54.6494			−2.03525
$722$		0			0
$723$		−	1.52447i		−	0.0566957i
$724$		0			0
$725$	−0.594317	−	0.343129i	−0.0220724	−	0.0127435i
$726$		0			0
$727$	12.3695	−	21.4246i	0.458759	−	0.794593i	−0.540137	−	0.841577i	$-0.681628\pi$
$727$	12.3695	−	21.4246i	0.458759	−	0.794593i	0.998896	+	0.0469839i	$0.0149609\pi$
$728$		0			0
$729$	26.7071			0.989151
$730$		0			0
$731$	−4.87089	+	2.81221i	−0.180156	+	0.104013i
$732$		0			0
$733$		−	20.0808i		−	0.741701i	−0.928693	−	0.370851i	$-0.879066\pi$
$733$		−	20.0808i		−	0.741701i	0.928693	−	0.370851i	$-0.120934\pi$
$734$		0			0
$735$	1.25960	+	2.18170i	0.0464612	+	0.0804731i
$736$		0			0
$737$	10.7781	+	18.6682i	0.397017	+	0.687653i
$738$		0			0
$739$	−1.16064	−	0.670093i	−0.0426947	−	0.0246498i	0.478501	−	0.878087i	$-0.341180\pi$
$739$	−1.16064	−	0.670093i	−0.0426947	−	0.0246498i	−0.521195	+	0.853437i	$0.674514\pi$
$740$		0			0
$741$	−0.0419512	−	0.154847i	−0.00154112	−	0.00568844i
$742$		0			0
$743$	−5.99092	+	10.3766i	−0.219786	+	0.380680i	−0.954742	−	0.297434i	$-0.903869\pi$
$743$	−5.99092	+	10.3766i	−0.219786	+	0.380680i	0.734957	+	0.678114i	$0.237202\pi$
$744$		0			0
$745$	−5.97508	−	10.3491i	−0.218910	−	0.379163i
$746$		0			0
$747$	−40.3873	+	23.3176i	−1.47770	+	0.853148i
$748$		0			0
$749$			36.0504i			1.31725i
$750$		0			0
$751$	−9.58183	−	16.5962i	−0.349646	−	0.605605i	0.636541	−	0.771243i	$-0.280365\pi$
$751$	−9.58183	−	16.5962i	−0.349646	−	0.605605i	−0.986187	+	0.165639i	$0.947031\pi$
$752$		0			0
$753$	0.0125418			0.000457049
$754$		0			0
$755$	7.12068	+	4.11113i	0.259148	+	0.149619i
$756$		0			0
$757$	35.7919	+	20.6645i	1.30088	+	0.751062i	0.980555	−	0.196246i	$-0.0628750\pi$
$757$	35.7919	+	20.6645i	1.30088	+	0.751062i	0.320324	+	0.947308i	$0.396208\pi$
$758$		0			0
$759$	−0.466088			−0.0169179
$760$		0			0
$761$	30.3361			1.09968			0.549841	−	0.835269i	$-0.314688\pi$
$761$	30.3361			1.09968			0.549841	+	0.835269i	$0.314688\pi$
$762$		0			0
$763$	−10.7458	−	6.20408i	−0.389023	−	0.224603i
$764$		0			0
$765$	−4.35408	−	2.51383i	−0.157422	−	0.0908876i
$766$		0			0
$767$	−2.36951			−0.0855579
$768$		0			0
$769$	7.68635	+	13.3131i	0.277177	+	0.480084i	0.970682	−	0.240367i	$-0.0772679\pi$
$769$	7.68635	+	13.3131i	0.277177	+	0.480084i	−0.693505	+	0.720452i	$0.743935\pi$
$770$		0			0
$771$			1.07173i			0.0385975i
$772$		0			0
$773$	14.3035	−	8.25814i	0.514462	−	0.297025i	−0.220204	−	0.975454i	$-0.570672\pi$
$773$	14.3035	−	8.25814i	0.514462	−	0.297025i	0.734666	+	0.678429i	$0.237339\pi$
$774$		0			0
$775$	0.309461	+	0.536001i	0.0111162	+	0.0192537i
$776$		0			0
$777$	−1.78796	+	3.09683i	−0.0641426	+	0.111098i
$778$		0			0
$779$	23.3449	+	6.18599i	0.836419	+	0.221636i
$780$		0			0
$781$	18.5923	+	10.7343i	0.665286	+	0.384103i
$782$		0			0
$783$	1.33279	+	2.30846i	0.0476300	+	0.0824976i
$784$		0			0
$785$	−21.6051	−	37.4212i	−0.771120	−	1.33562i
$786$		0			0
$787$		−	45.6546i		−	1.62741i	−0.581277	−	0.813705i	$-0.697447\pi$
$787$		−	45.6546i		−	1.62741i	0.581277	−	0.813705i	$-0.302553\pi$
$788$		0			0
$789$	0.962620	−	0.555769i	0.0342702	−	0.0197859i
$790$		0			0
$791$	−42.0537			−1.49526
$792$		0			0
$793$	−0.435953	+	0.755093i	−0.0154811	+	0.0268141i
$794$		0			0
$795$	1.68150	+	0.970815i	0.0596367	+	0.0344312i
$796$		0			0
$797$			21.7112i			0.769052i	0.923114	+	0.384526i	$0.125635\pi$
$797$			21.7112i			0.769052i	−0.923114	+	0.384526i	$0.874365\pi$
$798$		0			0
$799$	1.16174			0.0410993
$800$		0			0
$801$	−8.69131	+	15.0538i	−0.307092	+	0.531900i
$802$		0			0
$803$	21.3874	+	12.3480i	0.754744	+	0.435752i
$804$		0			0
$805$		−	33.9600i		−	1.19693i
$806$		0			0
$807$	−0.269962	−	0.467588i	−0.00950310	−	0.0164599i
$808$		0			0
$809$	4.74208			0.166723			0.0833613	−	0.996519i	$-0.473434\pi$
$809$	4.74208			0.166723			0.0833613	+	0.996519i	$0.473434\pi$
$810$		0			0
$811$	−17.1243	+	9.88671i	−0.601315	+	0.347169i	−0.769559	−	0.638576i	$-0.779524\pi$
$811$	−17.1243	+	9.88671i	−0.601315	+	0.347169i	0.168244	+	0.985745i	$0.446190\pi$
$812$		0			0
$813$	0.526418	−	0.303928i	0.0184623	−	0.0106592i
$814$		0			0
$815$	11.0042	−	19.0598i	0.385460	−	0.667637i
$816$		0			0
$817$	8.45812	−	31.9196i	0.295912	−	1.11672i
$818$		0			0
$819$	6.08986	+	3.51598i	0.212797	+	0.122858i
$820$		0			0
$821$	−4.45174	+	2.57021i	−0.155367	+	0.0897011i	−0.575668	−	0.817684i	$-0.695258\pi$
$821$	−4.45174	+	2.57021i	−0.155367	+	0.0897011i	0.420301	+	0.907385i	$0.361925\pi$
$822$		0			0
$823$	11.4962	+	19.9120i	0.400731	+	0.694087i	0.993814	−	0.111054i	$-0.0354228\pi$
$823$	11.4962	+	19.9120i	0.400731	+	0.694087i	−0.593083	+	0.805141i	$0.702089\pi$
$824$		0			0
$825$	0.0166022			0.000578014
$826$		0			0
$827$	−12.7107	+	7.33853i	−0.441994	+	0.255186i	−0.704443	−	0.709760i	$-0.748803\pi$
$827$	−12.7107	+	7.33853i	−0.441994	+	0.255186i	0.262449	+	0.964946i	$0.415470\pi$
$828$		0			0
$829$			41.7030i			1.44840i	0.689588	+	0.724202i	$0.257792\pi$
$829$			41.7030i			1.44840i	−0.689588	+	0.724202i	$0.742208\pi$
$830$		0			0
$831$	−0.637454	+	1.10410i	−0.0221130	+	0.0383009i
$832$		0			0
$833$	5.61079	−	9.71817i	0.194402	−	0.336715i
$834$		0			0
$835$			42.5218i			1.47153i
$836$		0			0
$837$		−	2.40402i		−	0.0830952i
$838$		0			0
$839$	21.9878	−	38.0839i	0.759102	−	1.31480i	−0.184208	−	0.982887i	$-0.558972\pi$
$839$	21.9878	−	38.0839i	0.759102	−	1.31480i	0.943309	−	0.331915i	$-0.107695\pi$
$840$		0			0
$841$	3.69842	−	6.40585i	0.127532	−	0.220891i
$842$		0			0
$843$		−	1.84419i		−	0.0635172i
$844$		0			0
$845$	−24.9708	+	14.4169i	−0.859022	+	0.495957i
$846$		0			0
$847$	33.2890			1.14382
$848$		0			0
$849$	0.683644	+	1.18411i	0.0234626	+	0.0406384i
$850$		0			0
$851$	28.5323	−	16.4731i	0.978075	−	0.564692i
$852$		0			0
$853$	−35.8544	−	20.7005i	−1.22763	−	0.708773i	−0.261097	−	0.965313i	$-0.584084\pi$
$853$	−35.8544	−	20.7005i	−1.22763	−	0.708773i	−0.966534	+	0.256540i	$0.917417\pi$
$854$		0			0
$855$	28.4905	−	7.71867i	0.974355	−	0.263973i
$856$		0			0
$857$	11.4143	−	19.7701i	0.389903	−	0.675333i	−0.602533	−	0.798094i	$-0.705842\pi$
$857$	11.4143	−	19.7701i	0.389903	−	0.675333i	0.992436	+	0.122762i	$0.0391750\pi$
$858$		0			0
$859$	41.9571	−	24.2239i	1.43156	−	0.826509i	0.434317	−	0.900760i	$-0.356990\pi$
$859$	41.9571	−	24.2239i	1.43156	−	0.826509i	0.997240	+	0.0742508i	$0.0236565\pi$
$860$		0			0
$861$	1.66311	−	0.960199i	0.0566787	−	0.0327235i
$862$		0			0
$863$	54.0511			1.83992			0.919960	−	0.392013i	$-0.128221\pi$
$863$	54.0511			1.83992			0.919960	+	0.392013i	$0.128221\pi$
$864$		0			0
$865$	−13.2807	−	23.0028i	−0.451556	−	0.782118i
$866$		0			0
$867$			1.21237i			0.0411743i
$868$		0			0
$869$	2.86338	+	1.65317i	0.0971335	+	0.0560800i
$870$		0			0
$871$	2.71794	−	4.70761i	0.0920939	−	0.159511i
$872$		0			0
$873$	3.62570			0.122711
$874$		0			0
$875$		−	51.9617i		−	1.75663i
$876$		0			0
$877$	21.3846	+	12.3464i	0.722106	+	0.416908i	0.815527	−	0.578718i	$-0.196447\pi$
$877$	21.3846	+	12.3464i	0.722106	+	0.416908i	−0.0934212	+	0.995627i	$0.529780\pi$
$878$		0			0
$879$	0.0376937	−	0.0652875i	0.00127138	−	0.00220209i
$880$		0			0
$881$	22.1718			0.746988			0.373494	−	0.927633i	$-0.378160\pi$
$881$	22.1718			0.746988			0.373494	+	0.927633i	$0.378160\pi$
$882$		0			0
$883$	37.4154	−	21.6018i	1.25913	−	0.726959i	0.286224	−	0.958163i	$-0.407600\pi$
$883$	37.4154	−	21.6018i	1.25913	−	0.726959i	0.972905	+	0.231204i	$0.0742664\pi$
$884$		0			0
$885$			0.790906i			0.0265860i
$886$		0			0
$887$	15.8289	+	27.4165i	0.531483	+	0.920556i	0.999325	+	0.0367436i	$0.0116985\pi$
$887$	15.8289	+	27.4165i	0.531483	+	0.920556i	−0.467841	+	0.883812i	$0.654968\pi$
$888$		0			0
$889$	11.1970	+	19.3938i	0.375535	+	0.650446i
$890$		0			0
$891$	15.3503	+	8.86249i	0.514254	+	0.296904i
$892$		0			0
$893$	−4.80952	+	4.83624i	−0.160944	+	0.161839i
$894$		0			0
$895$	12.6596	−	21.9270i	0.423163	−	0.732940i
$896$		0			0
$897$	0.0587673	+	0.101788i	0.00196218	+	0.00339860i
$898$		0			0
$899$	−28.4277	+	16.4127i	−0.948117	+	0.547396i
$900$		0			0
$901$		−	8.64881i		−	0.288134i
$902$		0			0
$903$	−1.31288	−	2.27398i	−0.0436900	−	0.0756733i
$904$		0			0
$905$	26.7244			0.888348
$906$		0			0
$907$	24.1186	+	13.9249i	0.800847	+	0.462369i	0.843767	−	0.536709i	$-0.180333\pi$
$907$	24.1186	+	13.9249i	0.800847	+	0.462369i	−0.0429205	+	0.999078i	$0.513666\pi$
$908$		0			0
$909$	38.7357	+	22.3641i	1.28478	+	0.741770i
$910$		0			0
$911$	45.6102			1.51113			0.755567	−	0.655071i	$-0.227361\pi$
$911$	45.6102			1.51113			0.755567	+	0.655071i	$0.227361\pi$
$912$		0			0
$913$	−30.8381			−1.02059
$914$		0			0
$915$	0.252039	+	0.145515i	0.00833215	+	0.00481057i
$916$		0			0
$917$	−20.3049	−	11.7230i	−0.670526	−	0.387128i
$918$		0			0
$919$	41.3141			1.36283			0.681413	−	0.731899i	$-0.261366\pi$
$919$	41.3141			1.36283			0.681413	+	0.731899i	$0.261366\pi$
$920$		0			0
$921$	0.968208	+	1.67698i	0.0319035	+	0.0552585i
$922$		0			0
$923$		−	5.41378i		−	0.178197i
$924$		0			0
$925$	−1.01633	+	0.586777i	−0.0334166	+	0.0192931i
$926$		0			0
$927$	17.4001	+	30.1378i	0.571494	+	0.989856i
$928$		0			0
$929$	3.58663	−	6.21223i	0.117674	−	0.203817i	−0.801172	−	0.598435i	$-0.795790\pi$
$929$	3.58663	−	6.21223i	0.117674	−	0.203817i	0.918845	+	0.394618i	$0.129123\pi$
$930$		0			0
$931$	17.2278	+	63.5900i	0.564620	+	2.08408i
$932$		0			0
$933$	−1.54489	−	0.891942i	−0.0505774	−	0.0292009i
$934$		0			0
$935$	−1.66230	−	2.87918i	−0.0543629	−	0.0941593i
$936$		0			0
$937$	−10.0009	−	17.3221i	−0.326716	−	0.565889i	0.655142	−	0.755506i	$-0.272609\pi$
$937$	−10.0009	−	17.3221i	−0.326716	−	0.565889i	−0.981858	+	0.189616i	$0.939276\pi$
$938$		0			0
$939$			2.11577i			0.0690457i
$940$		0			0
$941$	−31.3632	+	18.1076i	−1.02241	+	0.590289i	−0.914801	−	0.403904i	$-0.867653\pi$
$941$	−31.3632	+	18.1076i	−1.02241	+	0.590289i	−0.107610	+	0.994193i	$0.534320\pi$
$942$		0			0
$943$	−17.6934			−0.576175
$944$		0			0
$945$	2.34929	−	4.06910i	0.0764226	−	0.132368i
$946$		0			0
$947$	29.1318	+	16.8192i	0.946656	+	0.546552i	0.892041	−	0.451955i	$-0.149273\pi$
$947$	29.1318	+	16.8192i	0.946656	+	0.546552i	0.0546155	+	0.998507i	$0.482607\pi$
$948$		0			0
$949$		−	6.22765i		−	0.202158i
$950$		0			0
$951$	−0.755381			−0.0244949
$952$		0			0
$953$	19.7258	−	34.1662i	0.638983	−	1.10675i	−0.346674	−	0.937986i	$-0.612689\pi$
$953$	19.7258	−	34.1662i	0.638983	−	1.10675i	0.985656	−	0.168765i	$-0.0539777\pi$
$954$		0			0
$955$	−24.7687	−	14.3002i	−0.801495	−	0.462743i
$956$		0			0
$957$			0.880523i			0.0284633i
$958$		0			0
$959$	−18.8107	−	32.5812i	−0.607431	−	1.05210i
$960$		0			0
$961$	−1.39543			−0.0450140
$962$		0			0
$963$	19.8810	−	11.4783i	0.640655	−	0.369882i
$964$		0			0
$965$	−14.3855	+	8.30546i	−0.463085	+	0.267362i
$966$		0			0
$967$	6.05042	−	10.4796i	0.194568	−	0.337002i	−0.752191	−	0.658946i	$-0.771003\pi$
$967$	6.05042	−	10.4796i	0.194568	−	0.337002i	0.946759	+	0.321943i	$0.104336\pi$
$968$		0			0
$969$	0.169132	+	0.168197i	0.00543329	+	0.00540327i
$970$		0			0
$971$	−24.1496	−	13.9428i	−0.774997	−	0.447445i	0.0596571	−	0.998219i	$-0.480999\pi$
$971$	−24.1496	−	13.9428i	−0.774997	−	0.447445i	−0.834654	+	0.550774i	$0.814333\pi$
$972$		0			0
$973$	32.4873	−	18.7565i	1.04149	−	0.601307i
$974$		0			0
$975$	−0.00209330	−	0.00362571i	−6.70394e−5	−	0.000116116i
$976$		0			0
$977$	6.91747			0.221310			0.110655	−	0.993859i	$-0.464705\pi$
$977$	6.91747			0.221310			0.110655	+	0.993859i	$0.464705\pi$
$978$		0			0
$979$	−9.95449	+	5.74723i	−0.318147	+	0.183682i
$980$		0			0
$981$			7.90138i			0.252272i
$982$		0			0
$983$	−20.4691	+	35.4536i	−0.652864	+	1.13079i	0.329560	+	0.944135i	$0.393099\pi$
$983$	−20.4691	+	35.4536i	−0.652864	+	1.13079i	−0.982425	+	0.186660i	$0.940234\pi$
$984$		0			0
$985$	−13.6813	+	23.6967i	−0.435922	+	0.755039i
$986$		0			0
$987$			0.542358i			0.0172634i
$988$		0			0
$989$			24.1922i			0.769267i
$990$		0			0
$991$	0.898204	−	1.55573i	0.0285324	−	0.0494195i	−0.851407	−	0.524506i	$-0.824250\pi$
$991$	0.898204	−	1.55573i	0.0285324	−	0.0494195i	0.879939	+	0.475087i	$0.157583\pi$
$992$		0			0
$993$	−0.615184	+	1.06553i	−0.0195223	+	0.0338136i
$994$		0			0
$995$			16.8951i			0.535610i
$996$		0			0
$997$	−1.49295	+	0.861952i	−0.0472821	+	0.0272983i	−0.523455	−	0.852054i	$-0.675357\pi$
$997$	−1.49295	+	0.861952i	−0.0472821	+	0.0272983i	0.476173	+	0.879352i	$0.342024\pi$
$998$		0			0
$999$	4.55834			0.144219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.t.a.49.10		36
4.3	odd	2		152.2.p.a.125.18	yes	36
8.3	odd	2		152.2.p.a.125.7	yes	36
8.5	even	2	inner	608.2.t.a.49.9		36
19.7	even	3	inner	608.2.t.a.273.9		36
76.7	odd	6		152.2.p.a.45.7	✓	36
152.45	even	6	inner	608.2.t.a.273.10		36
152.83	odd	6		152.2.p.a.45.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.p.a.45.7	✓	36	76.7	odd	6
152.2.p.a.45.18	yes	36	152.83	odd	6
152.2.p.a.125.7	yes	36	8.3	odd	2
152.2.p.a.125.18	yes	36	4.3	odd	2
608.2.t.a.49.9		36	8.5	even	2	inner
608.2.t.a.49.10		36	1.1	even	1	trivial
608.2.t.a.273.9		36	19.7	even	3	inner
608.2.t.a.273.10		36	152.45	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0638311 + 0.0368529i) q^{3} +(1.95840 + 1.13068i) q^{5} +4.70260 q^{7} +(-1.49728 - 2.59337i) q^{9} -1.98019i q^{11} +(-0.432449 + 0.249675i) q^{13} +(0.0833377 + 0.144345i) q^{15} +(0.371220 - 0.642972i) q^{17} +(1.13983 + 4.20723i) q^{19} +(0.300172 + 0.173304i) q^{21} +(-1.59672 - 2.76560i) q^{23} +(0.0568756 + 0.0985114i) q^{25} -0.441834i q^{27} +(-5.22471 + 3.01649i) q^{29} +5.44101 q^{31} +(0.0729758 - 0.126398i) q^{33} +(9.20955 + 5.31714i) q^{35} +10.3168i q^{37} -0.0368049 q^{39} +(2.77027 - 4.79824i) q^{41} +(-6.56065 - 3.78779i) q^{43} -6.77180i q^{45} +(0.782377 + 1.35512i) q^{47} +15.1145 q^{49} +(0.0473908 - 0.0273611i) q^{51} +(10.0885 - 5.82458i) q^{53} +(2.23896 - 3.87800i) q^{55} +(-0.0822924 + 0.310558i) q^{57} +(4.10945 + 2.37259i) q^{59} +(1.51215 - 0.873042i) q^{61} +(-7.04113 - 12.1956i) q^{63} -1.12921 q^{65} +(-9.42749 + 5.44296i) q^{67} -0.235375i q^{69} +(-5.42083 + 9.38916i) q^{71} +(-6.23576 + 10.8007i) q^{73} +0.00838412i q^{75} -9.31205i q^{77} +(-0.834855 + 1.44601i) q^{79} +(-4.47557 + 7.75191i) q^{81} -15.5733i q^{83} +(1.45399 - 0.839462i) q^{85} -0.444666 q^{87} +(-2.90236 - 5.02703i) q^{89} +(-2.03364 + 1.17412i) q^{91} +(0.347306 + 0.200517i) q^{93} +(-2.52480 + 9.52820i) q^{95} +(-0.605380 + 1.04855i) q^{97} +(-5.13537 + 2.96491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 8 q^{7} + 12 q^{9} + 6 q^{15} - 2 q^{17} + 2 q^{23} + 8 q^{25} + 48 q^{31} + 12 q^{33} + 20 q^{39} + 2 q^{41} - 10 q^{47} - 12 q^{49} - 8 q^{55} - 6 q^{57} + 28 q^{63} - 28 q^{65} + 30 q^{71} - 10 q^{73}+ \cdots - 18 q^{97}+O(q^{100}) \) 36 * q + 8 * q^7 + 12 * q^9 + 6 * q^15 - 2 * q^17 + 2 * q^23 + 8 * q^25 + 48 * q^31 + 12 * q^33 + 20 * q^39 + 2 * q^41 - 10 * q^47 - 12 * q^49 - 8 * q^55 - 6 * q^57 + 28 * q^63 - 28 * q^65 + 30 * q^71 - 10 * q^73 - 34 * q^79 - 2 * q^81 - 36 * q^87 - 2 * q^89 - 38 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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