LMFDB - Embedded newform 592.2.bc.g.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	592.81
Dual form			592.2.bc.g.497.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.77384 - 1.00960i) q^{3} +(-0.559739 - 3.17444i) q^{5} +(-0.344404 - 1.95321i) q^{7} +(4.37680 + 3.67257i) q^{9} +(2.07341 - 3.59126i) q^{11} +(3.83038 - 3.21407i) q^{13} +(-1.65227 + 9.37051i) q^{15} +(-4.21619 - 3.53781i) q^{17} +(-3.27814 - 1.19315i) q^{19} +(-1.01663 + 5.76562i) q^{21} +(1.93561 + 3.35258i) q^{23} +(-5.06529 + 1.84361i) q^{25} +(-4.00494 - 6.93676i) q^{27} +(-4.98749 + 8.63859i) q^{29} +2.40270 q^{31} +(-9.37705 + 7.86828i) q^{33} +(-6.00758 + 2.18658i) q^{35} +(-0.0640620 - 6.08243i) q^{37} +(-13.8698 + 5.04819i) q^{39} +(-5.90914 + 4.95836i) q^{41} +7.73423 q^{43} +(9.20847 - 15.9495i) q^{45} +(0.226280 + 0.391929i) q^{47} +(2.88142 - 1.04875i) q^{49} +(8.12331 + 14.0700i) q^{51} +(0.390820 - 2.21645i) q^{53} +(-12.5608 - 4.57176i) q^{55} +(7.88846 + 6.61920i) q^{57} +(0.968242 - 5.49118i) q^{59} +(-4.96752 + 4.16824i) q^{61} +(5.66592 - 9.81367i) q^{63} +(-12.3469 - 10.3603i) q^{65} +(-0.136928 - 0.776559i) q^{67} +(-1.98433 - 11.2537i) q^{69} +(-1.52963 - 0.556739i) q^{71} +7.19429 q^{73} +15.9116 q^{75} +(-7.72859 - 2.81298i) q^{77} +(2.11586 + 11.9997i) q^{79} +(1.12934 + 6.40478i) q^{81} +(-0.306457 - 0.257148i) q^{83} +(-8.87058 + 15.3643i) q^{85} +(22.5560 - 18.9268i) q^{87} +(1.44886 - 8.21691i) q^{89} +(-7.59697 - 6.37461i) q^{91} +(-6.66472 - 2.42576i) q^{93} +(-1.95266 + 11.0741i) q^{95} +(6.06712 + 10.5086i) q^{97} +(22.2640 - 8.10345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{5} + 3 q^{7} + 3 q^{11} + 9 q^{13} - 3 q^{15} - 27 q^{17} - 9 q^{19} + 15 q^{21} + 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{29} + 6 q^{31} - 6 q^{33} - 9 q^{35} + 9 q^{37} + 12 q^{39} + 48 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) $ 30 * q - 6 * q^5 + 3 * q^7 + 3 * q^11 + 9 * q^13 - 3 * q^15 - 27 * q^17 - 9 * q^19 + 15 * q^21 + 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^29 + 6 * q^31 - 6 * q^33 - 9 * q^35 + 9 * q^37 + 12 * q^39 + 48 * q^43 + 51 * q^45 - 6 * q^47 - 21 * q^49 - 12 * q^51 - 15 * q^53 - 21 * q^55 + 51 * q^57 + 36 * q^61 + 36 * q^63 - 6 * q^65 + 27 * q^67 - 15 * q^69 - 27 * q^71 - 114 * q^73 - 84 * q^75 - 105 * q^77 + 18 * q^79 - 12 * q^81 + 30 * q^83 + 21 * q^85 + 99 * q^87 + 39 * q^89 + 72 * q^91 - 3 * q^93 - 66 * q^95 - 12 * q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	−2.77384	−	1.00960i	−1.60148	−	0.582891i	−0.621750	−	0.783215i	$-0.713578\pi$
$3$	−2.77384	−	1.00960i	−1.60148	−	0.582891i	−0.979730	+	0.200324i	$0.935800\pi$
$4$		0			0
$5$	−0.559739	−	3.17444i	−0.250323	−	1.41965i	−0.807799	−	0.589459i	$-0.799341\pi$
$5$	−0.559739	−	3.17444i	−0.250323	−	1.41965i	0.557476	−	0.830193i	$-0.311770\pi$
$6$		0			0
$7$	−0.344404	−	1.95321i	−0.130173	−	0.738246i	−0.978100	−	0.208134i	$-0.933261\pi$
$7$	−0.344404	−	1.95321i	−0.130173	−	0.738246i	0.847928	−	0.530112i	$-0.177850\pi$
$8$		0			0
$9$	4.37680	+	3.67257i	1.45893	+	1.22419i
$10$		0			0
$11$	2.07341	−	3.59126i	0.625158	−	1.08280i	−0.363353	−	0.931652i	$-0.618368\pi$
$11$	2.07341	−	3.59126i	0.625158	−	1.08280i	0.988510	−	0.151153i	$-0.0482987\pi$
$12$		0			0
$13$	3.83038	−	3.21407i	1.06236	−	0.891423i	0.0680183	−	0.997684i	$-0.478332\pi$
$13$	3.83038	−	3.21407i	1.06236	−	0.891423i	0.994338	+	0.106261i	$0.0338879\pi$
$14$		0			0
$15$	−1.65227	+	9.37051i	−0.426615	+	2.41946i
$16$		0			0
$17$	−4.21619	−	3.53781i	−1.02258	−	0.858044i	−0.0326280	−	0.999468i	$-0.510388\pi$
$17$	−4.21619	−	3.53781i	−1.02258	−	0.858044i	−0.989949	+	0.141423i	$0.954832\pi$
$18$		0			0
$19$	−3.27814	−	1.19315i	−0.752057	−	0.273726i	−0.0625861	−	0.998040i	$-0.519935\pi$
$19$	−3.27814	−	1.19315i	−0.752057	−	0.273726i	−0.689471	+	0.724313i	$0.742157\pi$
$20$		0			0
$21$	−1.01663	+	5.76562i	−0.221848	+	1.25816i
$22$		0			0
$23$	1.93561	+	3.35258i	0.403603	+	0.699060i	0.994158	−	0.107937i	$-0.0344245\pi$
$23$	1.93561	+	3.35258i	0.403603	+	0.699060i	−0.590555	+	0.806997i	$0.701091\pi$
$24$		0			0
$25$	−5.06529	+	1.84361i	−1.01306	+	0.368723i
$26$		0			0
$27$	−4.00494	−	6.93676i	−0.770751	−	1.33498i
$28$		0			0
$29$	−4.98749	+	8.63859i	−0.926154	+	1.60415i	−0.136461	+	0.990645i	$0.543573\pi$
$29$	−4.98749	+	8.63859i	−0.926154	+	1.60415i	−0.789694	+	0.613501i	$0.789761\pi$
$30$		0			0
$31$	2.40270			0.431538			0.215769	−	0.976444i	$-0.430774\pi$
$31$	2.40270			0.431538			0.215769	+	0.976444i	$0.430774\pi$
$32$		0			0
$33$	−9.37705	+	7.86828i	−1.63233	+	1.36969i
$34$		0			0
$35$	−6.00758	+	2.18658i	−1.01547	+	0.369600i
$36$		0			0
$37$	−0.0640620	−	6.08243i	−0.0105317	−	0.999945i
$37$	−0.0640620	−	6.08243i	−0.0105317	−	0.999945i
$38$		0			0
$39$	−13.8698	+	5.04819i	−2.22095	+	0.808358i
$40$		0			0
$41$	−5.90914	+	4.95836i	−0.922853	+	0.774365i	−0.974520	−	0.224299i	$-0.927991\pi$
$41$	−5.90914	+	4.95836i	−0.922853	+	0.774365i	0.0516678	+	0.998664i	$0.483546\pi$
$42$		0			0
$43$	7.73423			1.17946			0.589729	−	0.807601i	$-0.299235\pi$
$43$	7.73423			1.17946			0.589729	+	0.807601i	$0.299235\pi$
$44$		0			0
$45$	9.20847	−	15.9495i	1.37272	−	2.37762i
$46$		0			0
$47$	0.226280	+	0.391929i	0.0330064	+	0.0571687i	0.882057	−	0.471143i	$-0.156159\pi$
$47$	0.226280	+	0.391929i	0.0330064	+	0.0571687i	−0.849050	+	0.528312i	$0.822825\pi$
$48$		0			0
$49$	2.88142	−	1.04875i	0.411631	−	0.149821i
$50$		0			0
$51$	8.12331	+	14.0700i	1.13749	+	1.97019i
$52$		0			0
$53$	0.390820	−	2.21645i	0.0536832	−	0.304453i	−0.946130	−	0.323787i	$-0.895044\pi$
$53$	0.390820	−	2.21645i	0.0536832	−	0.304453i	0.999813	+	0.0193348i	$0.00615484\pi$
$54$		0			0
$55$	−12.5608	−	4.57176i	−1.69370	−	0.616455i
$56$		0			0
$57$	7.88846	+	6.61920i	1.04485	+	0.876735i
$58$		0			0
$59$	0.968242	−	5.49118i	0.126054	−	0.714890i	−0.854622	−	0.519251i	$-0.826211\pi$
$59$	0.968242	−	5.49118i	0.126054	−	0.714890i	0.980676	−	0.195639i	$-0.0626780\pi$
$60$		0			0
$61$	−4.96752	+	4.16824i	−0.636025	+	0.533688i	−0.902795	−	0.430072i	$-0.858488\pi$
$61$	−4.96752	+	4.16824i	−0.636025	+	0.533688i	0.266770	+	0.963760i	$0.414044\pi$
$62$		0			0
$63$	5.66592	−	9.81367i	0.713839	−	1.23641i
$64$		0			0
$65$	−12.3469	−	10.3603i	−1.53144	−	1.28503i
$66$		0			0
$67$	−0.136928	−	0.776559i	−0.0167284	−	0.0948717i	0.975300	−	0.220882i	$-0.0708937\pi$
$67$	−0.136928	−	0.776559i	−0.0167284	−	0.0948717i	−0.992029	+	0.126011i	$0.959783\pi$
$68$		0			0
$69$	−1.98433	−	11.2537i	−0.238886	−	1.35479i
$70$		0			0
$71$	−1.52963	−	0.556739i	−0.181533	−	0.0660727i	0.249654	−	0.968335i	$-0.419683\pi$
$71$	−1.52963	−	0.556739i	−0.181533	−	0.0660727i	−0.431188	+	0.902262i	$0.641905\pi$
$72$		0			0
$73$	7.19429			0.842028			0.421014	−	0.907054i	$-0.361674\pi$
$73$	7.19429			0.842028			0.421014	+	0.907054i	$0.361674\pi$
$74$		0			0
$75$	15.9116			1.83732
$76$		0			0
$77$	−7.72859	−	2.81298i	−0.880754	−	0.320568i
$78$		0			0
$79$	2.11586	+	11.9997i	0.238053	+	1.35007i	0.836087	+	0.548597i	$0.184838\pi$
$79$	2.11586	+	11.9997i	0.238053	+	1.35007i	−0.598034	+	0.801471i	$0.704051\pi$
$80$		0			0
$81$	1.12934	+	6.40478i	0.125482	+	0.711642i
$82$		0			0
$83$	−0.306457	−	0.257148i	−0.0336380	−	0.0282257i	0.625814	−	0.779973i	$-0.284767\pi$
$83$	−0.306457	−	0.257148i	−0.0336380	−	0.0282257i	−0.659452	+	0.751747i	$0.729211\pi$
$84$		0			0
$85$	−8.87058	+	15.3643i	−0.962150	+	1.66649i
$86$		0			0
$87$	22.5560	−	18.9268i	2.41826	−	2.02916i
$88$		0			0
$89$	1.44886	−	8.21691i	0.153579	−	0.870991i	−0.806494	−	0.591242i	$-0.798638\pi$
$89$	1.44886	−	8.21691i	0.153579	−	0.870991i	0.960073	−	0.279749i	$-0.0902511\pi$
$90$		0			0
$91$	−7.59697	−	6.37461i	−0.796379	−	0.668241i
$92$		0			0
$93$	−6.66472	−	2.42576i	−0.691100	−	0.251540i
$94$		0			0
$95$	−1.95266	+	11.0741i	−0.200339	+	1.13618i
$96$		0			0
$97$	6.06712	+	10.5086i	0.616023	+	1.06698i	0.990204	+	0.139627i	$0.0445904\pi$
$97$	6.06712	+	10.5086i	0.616023	+	1.06698i	−0.374181	+	0.927355i	$0.622076\pi$
$98$		0			0
$99$	22.2640	−	8.10345i	2.23762	−	0.814427i
$100$		0			0
$101$	2.91435	+	5.04780i	0.289989	+	0.502275i	0.973807	−	0.227377i	$-0.0730151\pi$
$101$	2.91435	+	5.04780i	0.289989	+	0.502275i	−0.683818	+	0.729653i	$0.739682\pi$
$102$		0			0
$103$	6.62187	−	11.4694i	0.652472	−	1.13012i	−0.330049	−	0.943964i	$-0.607065\pi$
$103$	6.62187	−	11.4694i	0.652472	−	1.13012i	0.982521	−	0.186152i	$-0.0596015\pi$
$104$		0			0
$105$	18.8717			1.84169
$106$		0			0
$107$	−13.4607	+	11.2949i	−1.30130	+	1.09192i	−0.311379	+	0.950286i	$0.600791\pi$
$107$	−13.4607	+	11.2949i	−1.30130	+	1.09192i	−0.989919	+	0.141633i	$0.954765\pi$
$108$		0			0
$109$	2.26506	−	0.824416i	0.216954	−	0.0789647i	−0.231257	−	0.972893i	$-0.574284\pi$
$109$	2.26506	−	0.824416i	0.216954	−	0.0789647i	0.448210	+	0.893928i	$0.352062\pi$
$110$		0			0
$111$	−5.96310	+	16.9364i	−0.565992	+	1.60753i
$112$		0			0
$113$	10.5843	−	3.85237i	0.995688	−	0.362401i	0.207768	−	0.978178i	$-0.433380\pi$
$113$	10.5843	−	3.85237i	0.995688	−	0.362401i	0.787920	+	0.615777i	$0.211158\pi$
$114$		0			0
$115$	9.55911	−	8.02104i	0.891391	−	0.747966i
$116$		0			0
$117$	28.5687			2.64118
$118$		0			0
$119$	−5.45802	+	9.45357i	−0.500336	+	0.866607i
$120$		0			0
$121$	−3.09809	−	5.36604i	−0.281644	−	0.487822i
$122$		0			0
$123$	21.3970	−	7.78786i	1.92930	−	0.702208i
$124$		0			0
$125$	0.629153	+	1.08972i	0.0562731	+	0.0974679i
$126$		0			0
$127$	−1.51567	+	8.59579i	−0.134494	+	0.762753i	0.840717	+	0.541475i	$0.182134\pi$
$127$	−1.51567	+	8.59579i	−0.134494	+	0.762753i	−0.975211	+	0.221278i	$0.928977\pi$
$128$		0			0
$129$	−21.4535	−	7.80845i	−1.88888	−	0.687496i
$130$		0			0
$131$	5.85026	+	4.90895i	0.511139	+	0.428897i	0.861530	−	0.507707i	$-0.169507\pi$
$131$	5.85026	+	4.90895i	0.511139	+	0.428897i	−0.350390	+	0.936604i	$0.613951\pi$
$132$		0			0
$133$	−1.20146	+	6.81384i	−0.104180	+	0.590835i
$134$		0			0
$135$	−19.7786	+	16.5962i	−1.70227	+	1.42838i
$136$		0			0
$137$	7.79340	−	13.4986i	0.665835	−	1.15326i	−0.313224	−	0.949679i	$-0.601409\pi$
$137$	7.79340	−	13.4986i	0.665835	−	1.15326i	0.979058	−	0.203580i	$-0.0652578\pi$
$138$		0			0
$139$	−14.6137	−	12.2624i	−1.23952	−	1.04008i	−0.997562	−	0.0697926i	$-0.977766\pi$
$139$	−14.6137	−	12.2624i	−1.23952	−	1.04008i	−0.241957	−	0.970287i	$-0.577789\pi$
$140$		0			0
$141$	−0.231976	−	1.31560i	−0.0195359	−	0.110794i
$142$		0			0
$143$	−3.60059	−	20.4200i	−0.301097	−	1.70760i
$144$		0			0
$145$	30.2144	+	10.9971i	2.50917	+	0.913262i
$146$		0			0
$147$	−9.05142			−0.746548
$148$		0			0
$149$	12.5414			1.02743			0.513716	−	0.857960i	$-0.328268\pi$
$149$	12.5414			1.02743			0.513716	+	0.857960i	$0.328268\pi$
$150$		0			0
$151$	−3.03053	−	1.10302i	−0.246621	−	0.0897626i	0.215752	−	0.976448i	$-0.430780\pi$
$151$	−3.03053	−	1.10302i	−0.246621	−	0.0897626i	−0.462373	+	0.886686i	$0.653002\pi$
$152$		0			0
$153$	−5.46058	−	30.9685i	−0.441462	−	2.50366i
$154$		0			0
$155$	−1.34489	−	7.62723i	−0.108024	−	0.612634i
$156$		0			0
$157$	−5.22035	−	4.38039i	−0.416629	−	0.349593i	0.410250	−	0.911973i	$-0.365441\pi$
$157$	−5.22035	−	4.38039i	−0.416629	−	0.349593i	−0.826879	+	0.562380i	$0.809886\pi$
$158$		0			0
$159$	−3.32179	+	5.75351i	−0.263435	+	0.456283i
$160$		0			0
$161$	5.88167	−	4.93530i	0.463540	−	0.388956i
$162$		0			0
$163$	2.79912	−	15.8746i	0.219244	−	1.24340i	−0.654144	−	0.756370i	$-0.726971\pi$
$163$	2.79912	−	15.8746i	0.219244	−	1.24340i	0.873388	−	0.487025i	$-0.161918\pi$
$164$		0			0
$165$	30.2261	+	25.3627i	2.35310	+	1.97448i
$166$		0			0
$167$	−18.3985	−	6.69650i	−1.42372	−	0.518191i	−0.488593	−	0.872512i	$-0.662490\pi$
$167$	−18.3985	−	6.69650i	−1.42372	−	0.518191i	−0.935124	+	0.354321i	$0.884712\pi$
$168$		0			0
$169$	2.08414	−	11.8197i	0.160318	−	0.909210i
$170$		0			0
$171$	−9.96585	−	17.2614i	−0.762107	−	1.32001i
$172$		0			0
$173$	−13.1192	+	4.77500i	−0.997434	+	0.363036i	−0.788594	−	0.614914i	$-0.789191\pi$
$173$	−13.1192	+	4.77500i	−0.997434	+	0.363036i	−0.208839	+	0.977950i	$0.566969\pi$
$174$		0			0
$175$	5.34548	+	9.25864i	0.404080	+	0.699887i
$176$		0			0
$177$	−8.22963	+	14.2541i	−0.618577	+	1.07141i
$178$		0			0
$179$	4.36255			0.326072			0.163036	−	0.986620i	$-0.447871\pi$
$179$	4.36255			0.326072			0.163036	+	0.986620i	$0.447871\pi$
$180$		0			0
$181$	−0.320019	+	0.268528i	−0.0237868	+	0.0199595i	−0.654604	−	0.755972i	$-0.727164\pi$
$181$	−0.320019	+	0.268528i	−0.0237868	+	0.0199595i	0.630817	+	0.775932i	$0.282720\pi$
$182$		0			0
$183$	17.9874	−	6.54686i	1.32966	−	0.483958i
$184$		0			0
$185$	−19.2724	+	3.60793i	−1.41694	+	0.265260i
$186$		0			0
$187$	−21.4471	+	7.80610i	−1.56837	+	0.570839i
$188$		0			0
$189$	−12.1697	+	10.2116i	−0.885213	+	0.742782i
$190$		0			0
$191$	−14.9184			−1.07946			−0.539728	−	0.841839i	$-0.681473\pi$
$191$	−14.9184			−1.07946			−0.539728	+	0.841839i	$0.681473\pi$
$192$		0			0
$193$	−4.16789	+	7.21900i	−0.300012	+	0.519635i	−0.976138	−	0.217150i	$-0.930324\pi$
$193$	−4.16789	+	7.21900i	−0.300012	+	0.519635i	0.676127	+	0.736785i	$0.263657\pi$
$194$		0			0
$195$	23.7886	+	41.2031i	1.70354	+	2.95062i
$196$		0			0
$197$	−21.0015	+	7.64393i	−1.49630	+	0.544607i	−0.955099	−	0.296288i	$-0.904251\pi$
$197$	−21.0015	+	7.64393i	−1.49630	+	0.544607i	−0.541198	+	0.840895i	$0.682029\pi$
$198$		0			0
$199$	7.87668	+	13.6428i	0.558363	+	0.967114i	0.997633	+	0.0687586i	$0.0219038\pi$
$199$	7.87668	+	13.6428i	0.558363	+	0.967114i	−0.439270	+	0.898355i	$0.644763\pi$
$200$		0			0
$201$	−0.404194	+	2.29230i	−0.0285096	+	0.161686i
$202$		0			0
$203$	18.5907	+	6.76648i	1.30481	+	0.474913i
$204$		0			0
$205$	19.0476	+	15.9828i	1.33034	+	1.11629i
$206$		0			0
$207$	−3.84079	+	21.7822i	−0.266953	+	1.51397i
$208$		0			0
$209$	−11.0818	+	9.29877i	−0.766547	+	0.643209i
$210$		0			0
$211$	−1.35270	+	2.34294i	−0.0931235	+	0.161295i	−0.908824	−	0.417180i	$-0.863018\pi$
$211$	−1.35270	+	2.34294i	−0.0931235	+	0.161295i	0.815700	+	0.578475i	$0.196352\pi$
$212$		0			0
$213$	3.68087	+	3.08861i	0.252209	+	0.211628i
$214$		0			0
$215$	−4.32915	−	24.5518i	−0.295245	−	1.67442i
$216$		0			0
$217$	−0.827501	−	4.69299i	−0.0561744	−	0.318581i
$218$		0			0
$219$	−19.9558	−	7.26333i	−1.34849	−	0.490811i
$220$		0			0
$221$	−27.5204			−1.85122
$222$		0			0
$223$	5.04066			0.337547			0.168774	−	0.985655i	$-0.446019\pi$
$223$	5.04066			0.337547			0.168774	+	0.985655i	$0.446019\pi$
$224$		0			0
$225$	−28.9405	−	10.5335i	−1.92937	−	0.702232i
$226$		0			0
$227$	−4.18743	−	23.7481i	−0.277930	−	1.57622i	−0.729499	−	0.683982i	$-0.760247\pi$
$227$	−4.18743	−	23.7481i	−0.277930	−	1.57622i	0.451570	−	0.892236i	$-0.350864\pi$
$228$		0			0
$229$	−0.374896	−	2.12614i	−0.0247738	−	0.140499i	0.969912	−	0.243455i	$-0.0782810\pi$
$229$	−0.374896	−	2.12614i	−0.0247738	−	0.140499i	−0.994686	+	0.102956i	$0.967170\pi$
$230$		0			0
$231$	18.5979	+	15.6055i	1.22365	+	1.02677i
$232$		0			0
$233$	13.4442	−	23.2861i	0.880761	−	1.52552i	0.0302643	−	0.999542i	$-0.490365\pi$
$233$	13.4442	−	23.2861i	0.880761	−	1.52552i	0.850497	−	0.525981i	$-0.176302\pi$
$234$		0			0
$235$	1.11750	−	0.937691i	0.0728974	−	0.0611682i
$236$		0			0
$237$	6.24574	−	35.4214i	0.405705	−	2.30086i
$238$		0			0
$239$	−8.60609	−	7.22137i	−0.556682	−	0.467111i	0.320514	−	0.947244i	$-0.396144\pi$
$239$	−8.60609	−	7.22137i	−0.556682	−	0.467111i	−0.877196	+	0.480132i	$0.840589\pi$
$240$		0			0
$241$	13.9330	+	5.07120i	0.897504	+	0.326665i	0.749252	−	0.662285i	$-0.230413\pi$
$241$	13.9330	+	5.07120i	0.897504	+	0.326665i	0.148252	+	0.988950i	$0.452635\pi$
$242$		0			0
$243$	−0.839059	+	4.75854i	−0.0538257	+	0.305261i
$244$		0			0
$245$	−4.94203	−	8.55985i	−0.315735	−	0.546869i
$246$		0			0
$247$	−16.3914	+	5.96598i	−1.04296	+	0.379606i
$248$		0			0
$249$	0.590449	+	1.02269i	0.0374182	+	0.0648102i
$250$		0			0
$251$	0.541269	−	0.937505i	0.0341646	−	0.0591748i	−0.848438	−	0.529296i	$-0.822456\pi$
$251$	0.541269	−	0.937505i	0.0341646	−	0.0591748i	0.882602	+	0.470121i	$0.155790\pi$
$252$		0			0
$253$	16.0533			1.00926
$254$		0			0
$255$	40.1174	−	33.6625i	2.51225	−	2.10802i
$256$		0			0
$257$	19.5965	−	7.13255i	1.22240	−	0.444916i	0.351410	−	0.936222i	$-0.385702\pi$
$257$	19.5965	−	7.13255i	1.22240	−	0.444916i	0.870987	+	0.491305i	$0.163480\pi$
$258$		0			0
$259$	−11.8582	+	2.21994i	−0.736834	+	0.137940i
$260$		0			0
$261$	−53.5551	+	19.4924i	−3.31498	+	1.20655i
$262$		0			0
$263$	8.87559	−	7.44751i	0.547293	−	0.459233i	−0.326730	−	0.945118i	$-0.605947\pi$
$263$	8.87559	−	7.44751i	0.547293	−	0.459233i	0.874023	+	0.485885i	$0.161502\pi$
$264$		0			0
$265$	−7.25474			−0.445655
$266$		0			0
$267$	−12.3147	+	21.3297i	−0.753647	+	1.30535i
$268$		0			0
$269$	0.362310	+	0.627539i	0.0220904	+	0.0382617i	0.876859	−	0.480747i	$-0.159634\pi$
$269$	0.362310	+	0.627539i	0.0220904	+	0.0382617i	−0.854769	+	0.519009i	$0.826301\pi$
$270$		0			0
$271$	5.86671	−	2.13531i	0.356377	−	0.129711i	−0.157626	−	0.987499i	$-0.550384\pi$
$271$	5.86671	−	2.13531i	0.356377	−	0.129711i	0.514003	+	0.857788i	$0.328162\pi$
$272$		0			0
$273$	14.6370	+	25.3521i	0.885873	+	1.53438i
$274$		0			0
$275$	−3.88154	+	22.0133i	−0.234066	+	1.32745i
$276$		0			0
$277$	−2.84973	−	1.03722i	−0.171223	−	0.0623203i	0.254986	−	0.966945i	$-0.417929\pi$
$277$	−2.84973	−	1.03722i	−0.171223	−	0.0623203i	−0.426209	+	0.904624i	$0.640151\pi$
$278$		0			0
$279$	10.5161	+	8.82409i	0.629585	+	0.528284i
$280$		0			0
$281$	−2.09296	+	11.8697i	−0.124855	+	0.708089i	0.856539	+	0.516083i	$0.172610\pi$
$281$	−2.09296	+	11.8697i	−0.124855	+	0.708089i	−0.981394	+	0.192006i	$0.938501\pi$
$282$		0			0
$283$	12.3858	−	10.3929i	0.736261	−	0.617796i	−0.195570	−	0.980690i	$-0.562656\pi$
$283$	12.3858	−	10.3929i	0.736261	−	0.617796i	0.931831	+	0.362893i	$0.118211\pi$
$284$		0			0
$285$	16.5968	−	28.7465i	0.983108	−	1.70279i
$286$		0			0
$287$	11.7199	+	9.83413i	0.691802	+	0.580491i
$288$		0			0
$289$	2.30820	+	13.0904i	0.135776	+	0.770025i
$290$		0			0
$291$	−6.21984	−	35.2745i	−0.364613	−	2.06783i
$292$		0			0
$293$	14.1521	+	5.15095i	0.826775	+	0.300921i	0.720535	−	0.693419i	$-0.243896\pi$
$293$	14.1521	+	5.15095i	0.826775	+	0.300921i	0.106240	+	0.994340i	$0.466119\pi$
$294$		0			0
$295$	−17.9734			−1.04645
$296$		0			0
$297$	−33.2156			−1.92736
$298$		0			0
$299$	18.1895	+	6.62045i	1.05193	+	0.382871i
$300$		0			0
$301$	−2.66370	−	15.1066i	−0.153533	−	0.870730i
$302$		0			0
$303$	−2.98771	−	16.9441i	−0.171639	−	0.973416i
$304$		0			0
$305$	16.0123	+	13.4359i	0.916863	+	0.769340i
$306$		0			0
$307$	−9.49960	+	16.4538i	−0.542171	+	0.939067i	0.456608	+	0.889668i	$0.349064\pi$
$307$	−9.49960	+	16.4538i	−0.542171	+	0.939067i	−0.998779	+	0.0493994i	$0.984269\pi$
$308$		0			0
$309$	−29.9475	+	25.1290i	−1.70366	+	1.42954i
$310$		0			0
$311$	−2.36240	+	13.3978i	−0.133959	+	0.759721i	0.841619	+	0.540071i	$0.181603\pi$
$311$	−2.36240	+	13.3978i	−0.133959	+	0.759721i	−0.975579	+	0.219650i	$0.929508\pi$
$312$		0			0
$313$	−15.0943	−	12.6657i	−0.853183	−	0.715905i	0.107305	−	0.994226i	$-0.465778\pi$
$313$	−15.0943	−	12.6657i	−0.853183	−	0.715905i	−0.960488	+	0.278321i	$0.910222\pi$
$314$		0			0
$315$	−34.3243	−	12.4930i	−1.93396	−	0.703902i
$316$		0			0
$317$	−0.833503	+	4.72703i	−0.0468142	+	0.265497i	−0.999227	−	0.0393151i	$-0.987482\pi$
$317$	−0.833503	+	4.72703i	−0.0468142	+	0.265497i	0.952413	+	0.304812i	$0.0985935\pi$
$318$		0			0
$319$	20.6823	+	35.8228i	1.15799	+	2.00569i
$320$		0			0
$321$	48.7413	−	17.7404i	2.72047	−	0.990171i
$322$		0			0
$323$	9.60016	+	16.6280i	0.534167	+	0.925205i
$324$		0			0
$325$	−13.4765	+	23.3419i	−0.747540	+	1.29478i
$326$		0			0
$327$	−7.11526			−0.393475
$328$		0			0
$329$	0.687589	−	0.576956i	0.0379080	−	0.0318086i
$330$		0			0
$331$	30.9736	−	11.2735i	1.70246	−	0.619645i	0.706359	−	0.707853i	$-0.250336\pi$
$331$	30.9736	−	11.2735i	1.70246	−	0.619645i	0.996102	+	0.0882081i	$0.0281140\pi$
$332$		0			0
$333$	22.0577	−	26.8568i	1.20876	−	1.47174i
$334$		0			0
$335$	−2.38849	+	0.869340i	−0.130497	+	0.0474971i
$336$		0			0
$337$	−1.97404	+	1.65642i	−0.107533	+	0.0902307i	−0.694969	−	0.719040i	$-0.744582\pi$
$337$	−1.97404	+	1.65642i	−0.107533	+	0.0902307i	0.587436	+	0.809271i	$0.300137\pi$
$338$		0			0
$339$	−33.2486			−1.80582
$340$		0			0
$341$	4.98180	−	8.62872i	0.269779	−	0.467272i
$342$		0			0
$343$	−9.98252	−	17.2902i	−0.539005	−	0.933584i
$344$		0			0
$345$	−34.6135	+	12.5983i	−1.86353	+	0.678269i
$346$		0			0
$347$	−13.9203	−	24.1107i	−0.747282	−	1.29433i	−0.949121	−	0.314912i	$-0.898025\pi$
$347$	−13.9203	−	24.1107i	−0.747282	−	1.29433i	0.201839	−	0.979419i	$-0.435308\pi$
$348$		0			0
$349$	0.0446079	−	0.252984i	0.00238781	−	0.0135419i	−0.983591	−	0.180415i	$-0.942256\pi$
$349$	0.0446079	−	0.252984i	0.00238781	−	0.0135419i	0.985978	+	0.166873i	$0.0533670\pi$
$350$		0			0
$351$	−37.6357	−	13.6983i	−2.00885	−	0.731160i
$352$		0			0
$353$	−25.7778	−	21.6301i	−1.37201	−	1.15126i	−0.972063	−	0.234718i	$-0.924583\pi$
$353$	−25.7778	−	21.6301i	−1.37201	−	1.15126i	−0.399949	−	0.916537i	$-0.630972\pi$
$354$		0			0
$355$	−0.911140	+	5.16733i	−0.0483583	+	0.274254i
$356$		0			0
$357$	24.6840	−	20.7123i	1.30642	−	1.09621i
$358$		0			0
$359$	11.6309	−	20.1453i	0.613855	−	1.06323i	−0.376730	−	0.926323i	$-0.622951\pi$
$359$	11.6309	−	20.1453i	0.613855	−	1.06323i	0.990584	−	0.136904i	$-0.0437153\pi$
$360$		0			0
$361$	−5.23223	−	4.39036i	−0.275380	−	0.231072i
$362$		0			0
$363$	3.17607	+	18.0124i	0.166700	+	0.945405i
$364$		0			0
$365$	−4.02693	−	22.8378i	−0.210779	−	1.19539i
$366$		0			0
$367$	23.9674	+	8.72343i	1.25109	+	0.455359i	0.880770	−	0.473545i	$-0.157026\pi$
$367$	23.9674	+	8.72343i	1.25109	+	0.455359i	0.370320	+	0.928904i	$0.379248\pi$
$368$		0			0
$369$	−44.0730			−2.29435
$370$		0			0
$371$	−4.46380			−0.231749
$372$		0			0
$373$	−14.3915	−	5.23808i	−0.745164	−	0.271218i	−0.0585949	−	0.998282i	$-0.518662\pi$
$373$	−14.3915	−	5.23808i	−0.745164	−	0.271218i	−0.686570	+	0.727064i	$0.740884\pi$
$374$		0			0
$375$	−0.644990	−	3.65792i	−0.0333071	−	0.188894i
$376$		0			0
$377$	8.66105	+	49.1193i	0.446067	+	2.52977i
$378$		0			0
$379$	2.34419	+	1.96701i	0.120413	+	0.101038i	0.701006	−	0.713156i	$-0.252735\pi$
$379$	2.34419	+	1.96701i	0.120413	+	0.101038i	−0.580593	+	0.814194i	$0.697179\pi$
$380$		0			0
$381$	12.8825	−	22.3132i	0.659991	−	1.14314i
$382$		0			0
$383$	−27.0787	+	22.7217i	−1.38366	+	1.16103i	−0.415821	+	0.909446i	$0.636506\pi$
$383$	−27.0787	+	22.7217i	−1.38366	+	1.16103i	−0.967837	+	0.251580i	$0.919050\pi$
$384$		0			0
$385$	−4.60363	+	26.1085i	−0.234622	+	1.33061i
$386$		0			0
$387$	33.8511	+	28.4045i	1.72075	+	1.44388i
$388$		0			0
$389$	−3.43601	−	1.25061i	−0.174213	−	0.0634083i	0.253441	−	0.967351i	$-0.418438\pi$
$389$	−3.43601	−	1.25061i	−0.174213	−	0.0634083i	−0.427654	+	0.903943i	$0.640660\pi$
$390$		0			0
$391$	3.69986	−	20.9829i	0.187110	−	1.06115i
$392$		0			0
$393$	−11.2716	−	19.5231i	−0.568579	−	0.984809i
$394$		0			0
$395$	36.9078	−	13.4334i	1.85704	−	0.675906i
$396$		0			0
$397$	11.1654	+	19.3390i	0.560376	+	0.970599i	0.997463	+	0.0711801i	$0.0226765\pi$
$397$	11.1654	+	19.3390i	0.560376	+	0.970599i	−0.437088	+	0.899419i	$0.643990\pi$
$398$		0			0
$399$	10.2119	−	17.6875i	0.511235	−	0.885484i
$400$		0			0
$401$	−12.8094			−0.639673			−0.319836	−	0.947473i	$-0.603628\pi$
$401$	−12.8094			−0.639673			−0.319836	+	0.947473i	$0.603628\pi$
$402$		0			0
$403$	9.20326	−	7.72246i	0.458447	−	0.384683i
$404$		0			0
$405$	19.6995	−	7.17001i	0.978874	−	0.356281i
$406$		0			0
$407$	−21.9764	−	12.3813i	−1.08933	−	0.613719i
$408$		0			0
$409$	8.34233	−	3.03636i	0.412502	−	0.150138i	−0.127429	−	0.991848i	$-0.540673\pi$
$409$	8.34233	−	3.03636i	0.412502	−	0.150138i	0.539931	+	0.841709i	$0.318450\pi$
$410$		0			0
$411$	−35.2458	+	29.5747i	−1.73855	+	1.45881i
$412$		0			0
$413$	−11.0589			−0.544173
$414$		0			0
$415$	−0.644765	+	1.11677i	−0.0316503	+	0.0548198i
$416$		0			0
$417$	28.1561	+	48.7678i	1.37881	+	2.38817i
$418$		0			0
$419$	17.3058	−	6.29878i	0.845442	−	0.307716i	0.117261	−	0.993101i	$-0.462588\pi$
$419$	17.3058	−	6.29878i	0.845442	−	0.307716i	0.728181	+	0.685385i	$0.240366\pi$
$420$		0			0
$421$	−12.9174	−	22.3736i	−0.629555	−	1.09042i	−0.987641	−	0.156733i	$-0.949904\pi$
$421$	−12.9174	−	22.3736i	−0.629555	−	1.09042i	0.358086	−	0.933689i	$-0.383429\pi$
$422$		0			0
$423$	−0.449003	+	2.54642i	−0.0218313	+	0.123811i
$424$		0			0
$425$	27.8786	+	10.1470i	1.35231	+	0.492200i
$426$		0			0
$427$	9.85230	+	8.26706i	0.476786	+	0.400071i
$428$		0			0
$429$	−10.6285	+	60.2770i	−0.513147	+	2.91020i
$430$		0			0
$431$	5.11647	−	4.29322i	0.246451	−	0.206797i	−0.511191	−	0.859467i	$-0.670796\pi$
$431$	5.11647	−	4.29322i	0.246451	−	0.206797i	0.757643	+	0.652670i	$0.226351\pi$
$432$		0			0
$433$	15.1072	−	26.1664i	0.726004	−	1.25748i	−0.232556	−	0.972583i	$-0.574709\pi$
$433$	15.1072	−	26.1664i	0.726004	−	1.25748i	0.958560	−	0.284892i	$-0.0919578\pi$
$434$		0			0
$435$	−72.7073	−	61.0087i	−3.48605	−	2.92514i
$436$		0			0
$437$	−2.34509	−	13.2997i	−0.112181	−	0.636210i
$438$		0			0
$439$	0.483373	+	2.74134i	0.0230701	+	0.130837i	0.994168	−	0.107846i	$-0.0343954\pi$
$439$	0.483373	+	2.74134i	0.0230701	+	0.130837i	−0.971097	+	0.238683i	$0.923284\pi$
$440$		0			0
$441$	16.4630	+	5.99203i	0.783951	+	0.285335i
$442$		0			0
$443$	−23.4084			−1.11217			−0.556083	−	0.831127i	$-0.687696\pi$
$443$	−23.4084			−1.11217			−0.556083	+	0.831127i	$0.687696\pi$
$444$		0			0
$445$	−26.8951			−1.27495
$446$		0			0
$447$	−34.7879	−	12.6618i	−1.64541	−	0.598881i
$448$		0			0
$449$	1.68858	+	9.57640i	0.0796889	+	0.451938i	0.998377	+	0.0569539i	$0.0181388\pi$
$449$	1.68858	+	9.57640i	0.0796889	+	0.451938i	−0.918688	+	0.394984i	$0.870750\pi$
$450$		0			0
$451$	5.55465	+	31.5020i	0.261558	+	1.48337i
$452$		0			0
$453$	7.29260	+	6.11922i	0.342636	+	0.287506i
$454$		0			0
$455$	−15.9835	+	27.6842i	−0.749318	+	1.29786i
$456$		0			0
$457$	3.74396	−	3.14156i	0.175135	−	0.146956i	−0.551007	−	0.834501i	$-0.685756\pi$
$457$	3.74396	−	3.14156i	0.175135	−	0.146956i	0.726142	+	0.687545i	$0.241312\pi$
$458$		0			0
$459$	−7.65532	+	43.4155i	−0.357320	+	2.02646i
$460$		0			0
$461$	0.0983711	+	0.0825432i	0.00458160	+	0.00384442i	0.645076	−	0.764119i	$-0.276826\pi$
$461$	0.0983711	+	0.0825432i	0.00458160	+	0.00384442i	−0.640494	+	0.767963i	$0.721270\pi$
$462$		0			0
$463$	0.233551	+	0.0850057i	0.0108540	+	0.00395055i	0.347441	−	0.937702i	$-0.387051\pi$
$463$	0.233551	+	0.0850057i	0.0108540	+	0.00395055i	−0.336587	+	0.941652i	$0.609273\pi$
$464$		0			0
$465$	−3.96992	+	22.5145i	−0.184101	+	1.04409i
$466$		0			0
$467$	12.3962	+	21.4709i	0.573628	+	0.993553i	0.996189	+	0.0872187i	$0.0277979\pi$
$467$	12.3962	+	21.4709i	0.573628	+	0.993553i	−0.422561	+	0.906335i	$0.638869\pi$
$468$		0			0
$469$	−1.46963	+	0.534900i	−0.0678610	+	0.0246994i
$470$		0			0
$471$	10.0580	+	17.4210i	0.463448	+	0.802716i
$472$		0			0
$473$	16.0362	−	27.7756i	0.737347	−	1.27712i
$474$		0			0
$475$	18.8044			0.862806
$476$		0			0
$477$	9.85060	−	8.26563i	0.451028	−	0.378457i
$478$		0			0
$479$	6.09084	−	2.21689i	0.278298	−	0.101292i	−0.199101	−	0.979979i	$-0.563802\pi$
$479$	6.09084	−	2.21689i	0.278298	−	0.101292i	0.477398	+	0.878687i	$0.341580\pi$
$480$		0			0
$481$	−19.7947	−	23.0921i	−0.902562	−	1.05291i
$482$		0			0
$483$	−21.2975	+	7.75165i	−0.969069	+	0.352712i
$484$		0			0
$485$	29.9628	−	25.1417i	1.36054	−	1.14163i
$486$		0			0
$487$	36.4698			1.65261			0.826303	−	0.563226i	$-0.190440\pi$
$487$	36.4698			1.65261			0.826303	+	0.563226i	$0.190440\pi$
$488$		0			0
$489$	−23.7913	+	41.2077i	−1.07588	+	1.86348i
$490$		0			0
$491$	10.6636	+	18.4698i	0.481240	+	0.833532i	0.999768	−	0.0215284i	$-0.00685323\pi$
$491$	10.6636	+	18.4698i	0.481240	+	0.833532i	−0.518528	+	0.855060i	$0.673520\pi$
$492$		0			0
$493$	51.5899	−	18.7772i	2.32349	−	0.845682i
$494$		0			0
$495$	−38.1859	−	66.1400i	−1.71633	−	2.97277i
$496$		0			0
$497$	−0.560620	+	3.17943i	−0.0251472	+	0.142617i
$498$		0			0
$499$	−20.2959	−	7.38712i	−0.908571	−	0.330693i	−0.154889	−	0.987932i	$-0.549502\pi$
$499$	−20.2959	−	7.38712i	−0.908571	−	0.330693i	−0.753682	+	0.657239i	$0.771724\pi$
$500$		0			0
$501$	44.2738	+	37.1501i	1.97801	+	1.65974i
$502$		0			0
$503$	1.11663	−	6.33272i	0.0497880	−	0.282362i	−0.949741	−	0.313035i	$-0.898654\pi$
$503$	1.11663	−	6.33272i	0.0497880	−	0.282362i	0.999529	+	0.0306736i	$0.00976525\pi$
$504$		0			0
$505$	14.3927	−	12.0769i	0.640465	−	0.537414i
$506$		0			0
$507$	−17.7142	+	30.6820i	−0.786717	+	1.36263i
$508$		0			0
$509$	−7.28715	−	6.11465i	−0.322997	−	0.271027i	0.466842	−	0.884341i	$-0.345392\pi$
$509$	−7.28715	−	6.11465i	−0.322997	−	0.271027i	−0.789839	+	0.613314i	$0.789836\pi$
$510$		0			0
$511$	−2.47775	−	14.0520i	−0.109609	−	0.621623i
$512$		0			0
$513$	4.85220	+	27.5182i	0.214230	+	1.21496i
$514$		0			0
$515$	−40.1155	−	14.6008i	−1.76770	−	0.643390i
$516$		0			0
$517$	1.87669			0.0825367
$518$		0			0
$519$	41.2114			1.80898
$520$		0			0
$521$	−14.3083	−	5.20781i	−0.626859	−	0.228158i	0.00900446	−	0.999959i	$-0.497134\pi$
$521$	−14.3083	−	5.20781i	−0.626859	−	0.228158i	−0.635864	+	0.771801i	$0.719356\pi$
$522$		0			0
$523$	5.78150	+	32.7885i	0.252807	+	1.43374i	0.801639	+	0.597808i	$0.203962\pi$
$523$	5.78150	+	32.7885i	0.252807	+	1.43374i	−0.548832	+	0.835933i	$0.684927\pi$
$524$		0			0
$525$	−5.48003	−	31.0788i	−0.239168	−	1.35639i
$526$		0			0
$527$	−10.1303	−	8.50030i	−0.441281	−	0.370279i
$528$		0			0
$529$	4.00683	−	6.94003i	0.174210	−	0.301740i
$530$		0			0
$531$	24.4045	−	20.4778i	1.05907	−	0.888662i
$532$		0			0
$533$	−6.69774	+	37.9848i	−0.290111	+	1.64530i
$534$		0			0
$535$	43.3894	+	36.4081i	1.87589	+	1.57406i
$536$		0			0
$537$	−12.1010	−	4.40442i	−0.522198	−	0.190065i
$538$		0			0
$539$	2.20804	−	12.5224i	0.0951069	−	0.539378i
$540$		0			0
$541$	4.75496	+	8.23584i	0.204432	+	0.354086i	0.949952	−	0.312397i	$-0.101132\pi$
$541$	4.75496	+	8.23584i	0.204432	+	0.354086i	−0.745520	+	0.666484i	$0.767799\pi$
$542$		0			0
$543$	1.15879	−	0.421764i	0.0497283	−	0.0180996i
$544$		0			0
$545$	−3.88490	−	6.72885i	−0.166411	−	0.288232i
$546$		0			0
$547$	−15.0058	+	25.9908i	−0.641601	+	1.11129i	0.343474	+	0.939162i	$0.388396\pi$
$547$	−15.0058	+	25.9908i	−0.641601	+	1.11129i	−0.985075	+	0.172124i	$0.944937\pi$
$548$		0			0
$549$	−37.0499			−1.58125
$550$		0			0
$551$	26.6568	−	22.3677i	1.13562	−	0.952897i
$552$		0			0
$553$	22.7092	−	8.26547i	0.965693	−	0.351484i
$554$		0			0
$555$	57.1013	+	9.44954i	2.42381	+	0.401110i
$556$		0			0
$557$	26.3098	−	9.57600i	1.11478	−	0.405748i	0.282038	−	0.959403i	$-0.408990\pi$
$557$	26.3098	−	9.57600i	1.11478	−	0.405748i	0.832746	+	0.553655i	$0.186767\pi$
$558$		0			0
$559$	29.6250	−	24.8584i	1.25301	−	1.05140i
$560$		0			0
$561$	67.3719			2.84444
$562$		0			0
$563$	1.75906	−	3.04678i	0.0741355	−	0.128407i	−0.826574	−	0.562827i	$-0.809714\pi$
$563$	1.75906	−	3.04678i	0.0741355	−	0.128407i	0.900710	+	0.434421i	$0.143047\pi$
$564$		0			0
$565$	−18.1536	−	31.4429i	−0.763727	−	1.32281i
$566$		0			0
$567$	12.1210	−	4.41167i	0.509033	−	0.185273i
$568$		0			0
$569$	0.968401	+	1.67732i	0.0405975	+	0.0703169i	0.885610	−	0.464429i	$-0.153741\pi$
$569$	0.968401	+	1.67732i	0.0405975	+	0.0703169i	−0.845013	+	0.534746i	$0.820407\pi$
$570$		0			0
$571$	2.73229	−	15.4956i	0.114343	−	0.648470i	−0.872731	−	0.488202i	$-0.837653\pi$
$571$	2.73229	−	15.4956i	0.114343	−	0.648470i	0.987073	−	0.160268i	$-0.0512360\pi$
$572$		0			0
$573$	41.3813	+	15.0616i	1.72873	+	0.629206i
$574$		0			0
$575$	−15.9853	−	13.4132i	−0.666632	−	0.559371i
$576$		0			0
$577$	−1.39975	+	7.93837i	−0.0582723	+	0.330479i	−0.999982	−	0.00594697i	$-0.998107\pi$
$577$	−1.39975	+	7.93837i	−0.0582723	+	0.330479i	0.941710	+	0.336426i	$0.109218\pi$
$578$		0			0
$579$	18.8494	−	15.8165i	0.783353	−	0.657311i
$580$		0			0
$581$	−0.396720	+	0.687139i	−0.0164587	+	0.0285073i
$582$		0			0
$583$	−7.14951	−	5.99915i	−0.296102	−	0.248459i
$584$		0			0
$585$	−15.9910	−	90.6895i	−0.661147	−	3.74955i
$586$		0			0
$587$	−3.28276	−	18.6174i	−0.135494	−	0.768424i	−0.974515	−	0.224324i	$-0.927982\pi$
$587$	−3.28276	−	18.6174i	−0.135494	−	0.768424i	0.839021	−	0.544100i	$-0.183129\pi$
$588$		0			0
$589$	−7.87640	−	2.86677i	−0.324541	−	0.118123i
$590$		0			0
$591$	65.9722			2.71374
$592$		0			0
$593$	−0.0459905			−0.00188860			−0.000944302	−	1.00000i	$-0.500301\pi$
$593$	−0.0459905			−0.00188860			−0.000944302		1.00000i	$0.500301\pi$
$594$		0			0
$595$	33.0648	+	12.0346i	1.35553	+	0.493371i
$596$		0			0
$597$	−8.07495	−	45.7953i	−0.330486	−	1.87428i
$598$		0			0
$599$	2.73704	+	15.5225i	0.111832	+	0.634232i	0.988270	+	0.152717i	$0.0488023\pi$
$599$	2.73704	+	15.5225i	0.111832	+	0.634232i	−0.876438	+	0.481515i	$0.840087\pi$
$600$		0			0
$601$	−19.3900	−	16.2701i	−0.790934	−	0.663673i	0.155042	−	0.987908i	$-0.450449\pi$
$601$	−19.3900	−	16.2701i	−0.790934	−	0.663673i	−0.945976	+	0.324235i	$0.894893\pi$
$602$		0			0
$603$	2.25266	−	3.90172i	0.0917353	−	0.158890i
$604$		0			0
$605$	−15.3001	+	12.8383i	−0.622036	+	0.521950i
$606$		0			0
$607$	3.83181	−	21.7313i	0.155528	−	0.882046i	−0.802773	−	0.596285i	$-0.796643\pi$
$607$	3.83181	−	21.7313i	0.155528	−	0.882046i	0.958301	−	0.285760i	$-0.0922462\pi$
$608$		0			0
$609$	−44.7364	−	37.5383i	−1.81281	−	1.52113i
$610$		0			0
$611$	2.12643	+	0.773956i	0.0860260	+	0.0313109i
$612$		0			0
$613$	−3.72973	+	21.1523i	−0.150642	+	0.854335i	0.812020	+	0.583630i	$0.198368\pi$
$613$	−3.72973	+	21.1523i	−0.150642	+	0.854335i	−0.962662	+	0.270705i	$0.912743\pi$
$614$		0			0
$615$	−36.6988	−	63.5642i	−1.47984	−	2.56316i
$616$		0			0
$617$	9.86174	−	3.58938i	0.397019	−	0.144503i	−0.135792	−	0.990737i	$-0.543358\pi$
$617$	9.86174	−	3.58938i	0.397019	−	0.144503i	0.532811	+	0.846234i	$0.321136\pi$
$618$		0			0
$619$	−3.03524	−	5.25718i	−0.121996	−	0.211304i	0.798558	−	0.601917i	$-0.205596\pi$
$619$	−3.03524	−	5.25718i	−0.121996	−	0.211304i	−0.920555	+	0.390613i	$0.872263\pi$
$620$		0			0
$621$	15.5040	−	26.8537i	0.622155	−	1.07760i
$622$		0			0
$623$	−16.5484			−0.662997
$624$		0			0
$625$	−17.5392	+	14.7171i	−0.701568	+	0.588685i
$626$		0			0
$627$	40.1273	−	14.6051i	1.60253	−	0.583273i
$628$		0			0
$629$	−21.2483	+	25.8713i	−0.847227	+	1.03156i
$630$		0			0
$631$	12.5478	−	4.56701i	0.499519	−	0.181810i	−0.0799588	−	0.996798i	$-0.525479\pi$
$631$	12.5478	−	4.56701i	0.499519	−	0.181810i	0.579478	+	0.814988i	$0.303257\pi$
$632$		0			0
$633$	6.11760	−	5.13327i	0.243153	−	0.204029i
$634$		0			0
$635$	28.1352			1.11651
$636$		0			0
$637$	7.66617	−	13.2782i	0.303745	−	0.526101i
$638$		0			0
$639$	−4.65020	−	8.05439i	−0.183959	−	0.318627i
$640$		0			0
$641$	0.500557	−	0.182188i	0.0197708	−	0.00719598i	−0.332116	−	0.943239i	$-0.607762\pi$
$641$	0.500557	−	0.182188i	0.0197708	−	0.00719598i	0.351887	+	0.936043i	$0.385540\pi$
$642$		0			0
$643$	−17.1027	−	29.6228i	−0.674466	−	1.16821i	−0.976625	−	0.214952i	$-0.931040\pi$
$643$	−17.1027	−	29.6228i	−0.674466	−	1.16821i	0.302158	−	0.953258i	$-0.402293\pi$
$644$		0			0
$645$	−12.7791	+	72.4736i	−0.503175	+	2.85365i
$646$		0			0
$647$	−1.57022	−	0.571513i	−0.0617317	−	0.0224685i	0.310970	−	0.950420i	$-0.399346\pi$
$647$	−1.57022	−	0.571513i	−0.0617317	−	0.0224685i	−0.372701	+	0.927951i	$0.621568\pi$
$648$		0			0
$649$	−17.7127	−	14.8627i	−0.695283	−	0.583411i
$650$		0			0
$651$	−2.44267	+	13.8531i	−0.0957358	+	0.542945i
$652$		0			0
$653$	−6.36187	+	5.33824i	−0.248959	+	0.208901i	−0.758724	−	0.651412i	$-0.774177\pi$
$653$	−6.36187	+	5.33824i	−0.248959	+	0.208901i	0.509765	+	0.860314i	$0.329732\pi$
$654$		0			0
$655$	12.3085	−	21.3190i	0.480934	−	0.833003i
$656$		0			0
$657$	31.4879	+	26.4215i	1.22846	+	1.03080i
$658$		0			0
$659$	−0.288229	−	1.63463i	−0.0112278	−	0.0636760i	0.978679	−	0.205395i	$-0.0658480\pi$
$659$	−0.288229	−	1.63463i	−0.0112278	−	0.0636760i	−0.989907	+	0.141719i	$0.954737\pi$
$660$		0			0
$661$	4.98168	+	28.2525i	0.193765	+	1.09889i	0.914167	+	0.405338i	$0.132846\pi$
$661$	4.98168	+	28.2525i	0.193765	+	1.09889i	−0.720402	+	0.693557i	$0.756043\pi$
$662$		0			0
$663$	76.3373	+	27.7845i	2.96469	+	1.07906i
$664$		0			0
$665$	22.3026			0.864858
$666$		0			0
$667$	−38.6154			−1.49519
$668$		0			0
$669$	−13.9820	−	5.08903i	−0.540575	−	0.196753i
$670$		0			0
$671$	4.66951	+	26.4821i	0.180264	+	1.02233i
$672$		0			0
$673$	0.144573	+	0.819914i	0.00557288	+	0.0316054i	0.987467	−	0.157823i	$-0.0504476\pi$
$673$	0.144573	+	0.819914i	0.00557288	+	0.0316054i	−0.981895	+	0.189429i	$0.939336\pi$
$674$		0			0
$675$	33.0749	+	27.7531i	1.27305	+	1.06822i
$676$		0			0
$677$	−17.9783	+	31.1393i	−0.690962	+	1.19678i	0.280561	+	0.959836i	$0.409480\pi$
$677$	−17.9783	+	31.1393i	−0.690962	+	1.19678i	−0.971523	+	0.236946i	$0.923854\pi$
$678$		0			0
$679$	18.4359	−	15.4696i	0.707506	−	0.593668i
$680$		0			0
$681$	−12.3607	+	70.1012i	−0.473664	+	2.68628i
$682$		0			0
$683$	19.1706	+	16.0860i	0.733542	+	0.615514i	0.931095	−	0.364778i	$-0.118855\pi$
$683$	19.1706	+	16.0860i	0.733542	+	0.615514i	−0.197553	+	0.980292i	$0.563299\pi$
$684$		0			0
$685$	−47.2126	−	17.1840i	−1.80390	−	0.656566i
$686$		0			0
$687$	−1.10664	+	6.27607i	−0.0422210	+	0.239447i
$688$		0			0
$689$	−5.62684	−	9.74597i	−0.214365	−	0.371292i
$690$		0			0
$691$	3.91150	−	1.42367i	0.148801	−	0.0541590i	−0.266546	−	0.963822i	$-0.585882\pi$
$691$	3.91150	−	1.42367i	0.148801	−	0.0541590i	0.415347	+	0.909663i	$0.363660\pi$
$692$		0			0
$693$	−23.4956	−	40.6956i	−0.892524	−	1.54590i
$694$		0			0
$695$	−30.7462	+	53.2540i	−1.16627	+	2.02004i
$696$		0			0
$697$	42.4558			1.60813
$698$		0			0
$699$	−60.8018	+	51.0187i	−2.29973	+	1.92971i
$700$		0			0
$701$	18.8486	−	6.86034i	0.711903	−	0.259111i	0.0394183	−	0.999223i	$-0.487450\pi$
$701$	18.8486	−	6.86034i	0.711903	−	0.259111i	0.672484	+	0.740111i	$0.265227\pi$
$702$		0			0
$703$	−7.04722	+	20.0155i	−0.265791	+	0.754898i
$704$		0			0
$705$	−4.04645	+	1.47279i	−0.152398	+	0.0554684i
$706$		0			0
$707$	8.85573	−	7.43084i	0.333054	−	0.279465i
$708$		0			0
$709$	−2.99804			−0.112594			−0.0562969	−	0.998414i	$-0.517929\pi$
$709$	−2.99804			−0.112594			−0.0562969	+	0.998414i	$0.517929\pi$
$710$		0			0
$711$	−34.8089	+	60.2907i	−1.30543	+	2.26108i
$712$		0			0
$713$	4.65070	+	8.05524i	0.174170	+	0.301671i
$714$		0			0
$715$	−62.8066	+	22.8597i	−2.34883	+	0.854905i
$716$		0			0
$717$	16.5813	+	28.7196i	0.619240	+	1.07255i
$718$		0			0
$719$	−2.89135	+	16.3977i	−0.107829	+	0.611530i	0.882223	+	0.470831i	$0.156046\pi$
$719$	−2.89135	+	16.3977i	−0.107829	+	0.611530i	−0.990052	+	0.140698i	$0.955065\pi$
$720$		0			0
$721$	−24.6828	−	8.98382i	−0.919237	−	0.334575i
$722$		0			0
$723$	−33.5281	−	28.1334i	−1.24692	−	1.04629i
$724$		0			0
$725$	9.33686	−	52.9520i	0.346762	−	1.96659i
$726$		0			0
$727$	−1.55136	+	1.30174i	−0.0575367	+	0.0482790i	−0.671103	−	0.741365i	$-0.734179\pi$
$727$	−1.55136	+	1.30174i	−0.0575367	+	0.0482790i	0.613566	+	0.789644i	$0.289735\pi$
$728$		0			0
$729$	16.8870	−	29.2492i	0.625445	−	1.08330i
$730$		0			0
$731$	−32.6090	−	27.3622i	−1.20609	−	1.01203i
$732$		0			0
$733$	4.93029	+	27.9611i	0.182105	+	1.03277i	0.929619	+	0.368521i	$0.120136\pi$
$733$	4.93029	+	27.9611i	0.182105	+	1.03277i	−0.747515	+	0.664245i	$0.768753\pi$
$734$		0			0
$735$	5.06643	+	28.7332i	0.186878	+	1.05984i
$736$		0			0
$737$	−3.07273	−	1.11838i	−0.113185	−	0.0411962i
$738$		0			0
$739$	−9.48954			−0.349078			−0.174539	−	0.984650i	$-0.555844\pi$
$739$	−9.48954			−0.349078			−0.174539	+	0.984650i	$0.555844\pi$
$740$		0			0
$741$	51.4904			1.89155
$742$		0			0
$743$	33.1885	+	12.0796i	1.21757	+	0.443158i	0.869322	−	0.494245i	$-0.164556\pi$
$743$	33.1885	+	12.0796i	1.21757	+	0.443158i	0.348245	+	0.937404i	$0.386778\pi$
$744$		0			0
$745$	−7.01992	−	39.8119i	−0.257190	−	1.45860i
$746$		0			0
$747$	−0.396907	−	2.25097i	−0.0145221	−	0.0823587i
$748$		0			0
$749$	26.6973	+	22.4017i	0.975498	+	0.818540i
$750$		0			0
$751$	−14.3820	+	24.9103i	−0.524806	+	0.908991i	0.474777	+	0.880106i	$0.342529\pi$
$751$	−14.3820	+	24.9103i	−0.524806	+	0.908991i	−0.999583	+	0.0288846i	$0.990804\pi$
$752$		0			0
$753$	−2.44790	+	2.05403i	−0.0892064	+	0.0748530i
$754$		0			0
$755$	−1.80517	+	10.2376i	−0.0656968	+	0.372585i
$756$		0			0
$757$	−1.63620	−	1.37294i	−0.0594688	−	0.0499002i	0.612569	−	0.790417i	$-0.290136\pi$
$757$	−1.63620	−	1.37294i	−0.0594688	−	0.0499002i	−0.672038	+	0.740517i	$0.734581\pi$
$758$		0			0
$759$	−44.5293	−	16.2073i	−1.61631	−	0.588289i
$760$		0			0
$761$	−5.54491	+	31.4468i	−0.201003	+	1.13994i	0.702604	+	0.711581i	$0.252021\pi$
$761$	−5.54491	+	31.4468i	−0.201003	+	1.13994i	−0.903607	+	0.428363i	$0.859090\pi$
$762$		0			0
$763$	−2.39036	−	4.14022i	−0.0865368	−	0.149886i
$764$		0			0
$765$	−95.2511	+	34.6686i	−3.44381	+	1.25344i
$766$		0			0
$767$	−13.9403	−	24.1453i	−0.503355	−	0.871836i
$768$		0			0
$769$	18.8985	−	32.7331i	0.681497	−	1.18039i	−0.293027	−	0.956104i	$-0.594663\pi$
$769$	18.8985	−	32.7331i	0.681497	−	1.18039i	0.974524	−	0.224283i	$-0.0720040\pi$
$770$		0			0
$771$	−61.5587			−2.21698
$772$		0			0
$773$	−10.2212	+	8.57661i	−0.367631	+	0.308479i	−0.807824	−	0.589424i	$-0.799355\pi$
$773$	−10.2212	+	8.57661i	−0.367631	+	0.308479i	0.440192	+	0.897903i	$0.354910\pi$
$774$		0			0
$775$	−12.1704	+	4.42965i	−0.437173	+	0.159118i
$776$		0			0
$777$	35.1341	+	5.81425i	1.26043	+	0.208585i
$778$		0			0
$779$	25.2870	−	9.20373i	0.906002	−	0.329758i
$780$		0			0
$781$	−5.17094	+	4.33893i	−0.185031	+	0.155259i
$782$		0			0
$783$	79.8985			2.85534
$784$		0			0
$785$	−10.9832	+	19.0235i	−0.392009	+	0.678979i
$786$		0			0
$787$	−19.4063	−	33.6127i	−0.691759	−	1.19816i	−0.971261	−	0.238017i	$-0.923503\pi$
$787$	−19.4063	−	33.6127i	−0.691759	−	1.19816i	0.279502	−	0.960145i	$-0.409831\pi$
$788$		0			0
$789$	−32.1385	+	11.6975i	−1.14416	+	0.416440i
$790$		0			0
$791$	−11.1698	−	19.3467i	−0.397152	−	0.687888i
$792$		0			0
$793$	−5.63045	+	31.9319i	−0.199943	+	1.13393i
$794$		0			0
$795$	20.1235	+	7.32436i	0.713707	+	0.259768i
$796$		0			0
$797$	2.00613	+	1.68334i	0.0710609	+	0.0596271i	0.677626	−	0.735406i	$-0.263009\pi$
$797$	2.00613	+	1.68334i	0.0710609	+	0.0596271i	−0.606565	+	0.795034i	$0.707453\pi$
$798$		0			0
$799$	0.432527	−	2.45298i	0.0153017	−	0.0867803i
$800$		0			0
$801$	36.5185	−	30.6427i	1.29032	−	1.08271i
$802$		0			0
$803$	14.9167	−	25.8366i	0.526400	−	0.911752i
$804$		0			0
$805$	−18.9590	−	15.9085i	−0.668217	−	0.560701i
$806$		0			0
$807$	−0.371430	−	2.10648i	−0.0130749	−	0.0741517i
$808$		0			0
$809$	4.12160	+	23.3748i	0.144908	+	0.821813i	0.967441	+	0.253096i	$0.0814488\pi$
$809$	4.12160	+	23.3748i	0.144908	+	0.821813i	−0.822533	+	0.568717i	$0.807440\pi$
$810$		0			0
$811$	25.8143	+	9.39563i	0.906462	+	0.329925i	0.752839	−	0.658204i	$-0.228684\pi$
$811$	25.8143	+	9.39563i	0.906462	+	0.329925i	0.153623	+	0.988130i	$0.450906\pi$
$812$		0			0
$813$	−18.4291			−0.646338
$814$		0			0
$815$	−51.9597			−1.82007
$816$		0			0
$817$	−25.3539	−	9.22806i	−0.887020	−	0.322849i
$818$		0			0
$819$	−9.83918	−	55.8008i	−0.343809	−	1.94984i
$820$		0			0
$821$	7.13296	+	40.4530i	0.248942	+	1.41182i	0.811157	+	0.584829i	$0.198838\pi$
$821$	7.13296	+	40.4530i	0.248942	+	1.41182i	−0.562214	+	0.826991i	$0.690050\pi$
$822$		0			0
$823$	−34.4218	−	28.8833i	−1.19987	−	1.00681i	−0.999634	−	0.0270603i	$-0.991385\pi$
$823$	−34.4218	−	28.8833i	−1.19987	−	1.00681i	−0.200234	−	0.979748i	$-0.564170\pi$
$824$		0			0
$825$	32.9914	−	57.1427i	1.14861	−	1.98945i
$826$		0			0
$827$	9.81220	−	8.23341i	0.341204	−	0.286304i	−0.456043	−	0.889958i	$-0.650734\pi$
$827$	9.81220	−	8.23341i	0.341204	−	0.286304i	0.797246	+	0.603654i	$0.206289\pi$
$828$		0			0
$829$	−7.16742	+	40.6484i	−0.248935	+	1.41178i	0.562240	+	0.826974i	$0.309940\pi$
$829$	−7.16742	+	40.6484i	−0.248935	+	1.41178i	−0.811174	+	0.584805i	$0.801171\pi$
$830$		0			0
$831$	6.85753	+	5.75415i	0.237885	+	0.199609i
$832$		0			0
$833$	−15.8589	−	5.77216i	−0.549478	−	0.199994i
$834$		0			0
$835$	−10.9593	+	62.1531i	−0.379261	+	2.15090i
$836$		0			0
$837$	−9.62268	−	16.6670i	−0.332609	−	0.576095i
$838$		0			0
$839$	−27.4460	+	9.98953i	−0.947541	+	0.344877i	−0.769139	−	0.639081i	$-0.779315\pi$
$839$	−27.4460	+	9.98953i	−0.947541	+	0.344877i	−0.178402	+	0.983958i	$0.557093\pi$
$840$		0			0
$841$	−35.2502	−	61.0551i	−1.21552	−	2.10535i
$842$		0			0
$843$	17.7892	−	30.8118i	0.612692	−	1.06121i
$844$		0			0
$845$	−38.6876			−1.33089
$846$		0			0
$847$	−9.41404	+	7.89932i	−0.323470	+	0.271424i
$848$		0			0
$849$	−44.8491	+	16.3237i	−1.53922	+	0.560229i
$850$		0			0
$851$	20.2678	−	11.9880i	0.694771	−	0.410943i
$852$		0			0
$853$	45.7675	−	16.6580i	1.56705	−	0.570360i	0.594713	−	0.803938i	$-0.297266\pi$
$853$	45.7675	−	16.6580i	1.56705	−	0.570360i	0.972338	+	0.233578i	$0.0750435\pi$
$854$		0			0
$855$	−49.2168	+	41.2978i	−1.68318	+	1.41236i
$856$		0			0
$857$	−34.9333			−1.19330			−0.596649	−	0.802502i	$-0.703502\pi$
$857$	−34.9333			−1.19330			−0.596649	+	0.802502i	$0.703502\pi$
$858$		0			0
$859$	15.7999	−	27.3663i	0.539086	−	0.933725i	−0.459867	−	0.887988i	$-0.652103\pi$
$859$	15.7999	−	27.3663i	0.539086	−	0.933725i	0.998954	−	0.0457372i	$-0.0145637\pi$
$860$		0			0
$861$	−22.5806	−	39.1107i	−0.769544	−	1.33289i
$862$		0			0
$863$	14.2520	−	5.18730i	0.485144	−	0.176578i	−0.0878564	−	0.996133i	$-0.528002\pi$
$863$	14.2520	−	5.18730i	0.485144	−	0.176578i	0.573000	+	0.819555i	$0.305779\pi$
$864$		0			0
$865$	22.5013	+	38.9733i	0.765066	+	1.32513i
$866$		0			0
$867$	6.81348	−	38.6412i	0.231398	−	1.31232i
$868$		0			0
$869$	47.4809	+	17.2816i	1.61068	+	0.586240i
$870$		0			0
$871$	−3.02040	−	2.53442i	−0.102342	−	0.0858755i
$872$		0			0
$873$	−12.0389	+	68.2757i	−0.407453	+	2.31078i
$874$		0			0
$875$	1.91178	−	1.60418i	0.0646301	−	0.0542311i
$876$		0			0
$877$	6.26878	−	10.8579i	0.211682	−	0.366644i	−0.740559	−	0.671991i	$-0.765439\pi$
$877$	6.26878	−	10.8579i	0.211682	−	0.366644i	0.952241	+	0.305348i	$0.0987726\pi$
$878$		0			0
$879$	−34.0554	−	28.5758i	−1.14866	−	0.963839i
$880$		0			0
$881$	5.08647	+	28.8468i	0.171368	+	0.971874i	0.942253	+	0.334901i	$0.108703\pi$
$881$	5.08647	+	28.8468i	0.171368	+	0.971874i	−0.770886	+	0.636973i	$0.780186\pi$
$882$		0			0
$883$	6.85987	+	38.9043i	0.230853	+	1.30923i	0.851174	+	0.524884i	$0.175891\pi$
$883$	6.85987	+	38.9043i	0.230853	+	1.30923i	−0.620320	+	0.784348i	$0.712997\pi$
$884$		0			0
$885$	49.8553	+	18.1458i	1.67587	+	0.609966i
$886$		0			0
$887$	−6.04928			−0.203115			−0.101557	−	0.994830i	$-0.532383\pi$
$887$	−6.04928			−0.203115			−0.101557	+	0.994830i	$0.532383\pi$
$888$		0			0
$889$	17.3114			0.580607
$890$		0			0
$891$	25.3428	+	9.22403i	0.849016	+	0.309017i
$892$		0			0
$893$	−0.274150	−	1.55478i	−0.00917409	−	0.0520289i
$894$		0			0
$895$	−2.44189	−	13.8486i	−0.0816234	−	0.462909i
$896$		0			0
$897$	−43.7710	−	36.7282i	−1.46147	−	1.22632i
$898$		0			0
$899$	−11.9835	+	20.7560i	−0.399671	+	0.692250i
$900$		0			0
$901$	−9.48914	+	7.96233i	−0.316129	+	0.265264i
$902$		0			0
$903$	−7.86288	+	44.5926i	−0.261660	+	1.48395i
$904$		0			0
$905$	1.03155	+	0.865574i	0.0342899	+	0.0287727i
$906$		0			0
$907$	−8.25040	−	3.00290i	−0.273950	−	0.0997096i	0.201392	−	0.979511i	$-0.435453\pi$
$907$	−8.25040	−	3.00290i	−0.273950	−	0.0997096i	−0.475342	+	0.879801i	$0.657676\pi$
$908$		0			0
$909$	−5.78288	+	32.7964i	−0.191806	+	1.08779i
$910$		0			0
$911$	9.45213	+	16.3716i	0.313163	+	0.542414i	0.979045	−	0.203643i	$-0.0652780\pi$
$911$	9.45213	+	16.3716i	0.313163	+	0.542414i	−0.665882	+	0.746057i	$0.731945\pi$
$912$		0			0
$913$	−1.55890	+	0.567392i	−0.0515920	+	0.0187779i
$914$		0			0
$915$	−30.8508	−	53.4352i	−1.01990	−	1.76651i
$916$		0			0
$917$	7.57338	−	13.1175i	0.250095	−	0.433177i
$918$		0			0
$919$	−20.4702			−0.675248			−0.337624	−	0.941281i	$-0.609623\pi$
$919$	−20.4702			−0.675248			−0.337624	+	0.941281i	$0.609623\pi$
$920$		0			0
$921$	42.9621	−	36.0495i	1.41565	−	1.18787i
$922$		0			0
$923$	−7.64845	+	2.78381i	−0.251752	+	0.0916302i
$924$		0			0
$925$	11.5381	+	30.6911i	0.379371	+	1.00912i
$926$		0			0
$927$	71.1048	−	25.8800i	2.33539	−	0.850012i
$928$		0			0
$929$	31.3579	−	26.3124i	1.02882	−	0.863282i	0.0381094	−	0.999274i	$-0.487866\pi$
$929$	31.3579	−	26.3124i	1.02882	−	0.863282i	0.990710	+	0.135992i	$0.0434220\pi$
$930$		0			0
$931$	−10.6970			−0.350580
$932$		0			0
$933$	20.0793	−	34.7784i	0.657368	−	1.13859i
$934$		0			0
$935$	36.7848	+	63.7131i	1.20299	+	2.08364i
$936$		0			0
$937$	−42.5162	+	15.4746i	−1.38894	+	0.505534i	−0.924877	−	0.380266i	$-0.875832\pi$
$937$	−42.5162	+	15.4746i	−1.38894	+	0.505534i	−0.464066	+	0.885800i	$0.653610\pi$
$938$		0			0
$939$	29.0822	+	50.3718i	0.949060	+	1.64382i
$940$		0			0
$941$	2.90384	−	16.4685i	0.0946626	−	0.536858i	−0.900188	−	0.435502i	$-0.856571\pi$
$941$	2.90384	−	16.4685i	0.0946626	−	0.536858i	0.994850	−	0.101356i	$-0.0323181\pi$
$942$		0			0
$943$	−28.0611	−	10.2134i	−0.913794	−	0.332594i
$944$		0			0
$945$	39.2278	+	32.9160i	1.27608	+	1.07076i
$946$		0			0
$947$	−6.44292	+	36.5396i	−0.209367	+	1.18738i	0.681052	+	0.732235i	$0.261523\pi$
$947$	−6.44292	+	36.5396i	−0.209367	+	1.18738i	−0.890419	+	0.455142i	$0.849588\pi$
$948$		0			0
$949$	27.5569	−	23.1230i	0.894534	−	0.750603i
$950$		0			0
$951$	7.08441	−	12.2706i	0.229728	−	0.397900i
$952$		0			0
$953$	−13.3130	−	11.1709i	−0.431250	−	0.361862i	0.401173	−	0.916002i	$-0.368603\pi$
$953$	−13.3130	−	11.1709i	−0.431250	−	0.361862i	−0.832423	+	0.554141i	$0.813047\pi$
$954$		0			0
$955$	8.35041	+	47.3575i	0.270213	+	1.53245i
$956$		0			0
$957$	−21.2029	−	120.248i	−0.685392	−	3.88705i
$958$		0			0
$959$	−29.0497	−	10.5732i	−0.938062	−	0.341427i
$960$		0			0
$961$	−25.2270			−0.813775
$962$		0			0
$963$	−100.396			−3.23522
$964$		0			0
$965$	25.2492	+	9.18996i	0.812801	+	0.295835i
$966$		0			0
$967$	−2.86578	−	16.2526i	−0.0921572	−	0.522650i	−0.995581	−	0.0939019i	$-0.970066\pi$
$967$	−2.86578	−	16.2526i	−0.0921572	−	0.522650i	0.903424	−	0.428748i	$-0.141045\pi$
$968$		0			0
$969$	−9.84181	−	55.8157i	−0.316165	−	1.79306i
$970$		0			0
$971$	−36.9213	−	30.9806i	−1.18486	−	0.994216i	−0.999934	−	0.0114637i	$-0.996351\pi$
$971$	−36.9213	−	30.9806i	−1.18486	−	0.994216i	−0.184926	−	0.982752i	$-0.559205\pi$
$972$		0			0
$973$	−18.9180	+	32.7669i	−0.606483	+	1.05046i
$974$		0			0
$975$	60.9476	−	51.1411i	1.95188	−	1.63783i
$976$		0			0
$977$	10.4892	−	59.4873i	0.335580	−	1.90317i	−0.0858534	−	0.996308i	$-0.527362\pi$
$977$	10.4892	−	59.4873i	0.335580	−	1.90317i	0.421433	−	0.906859i	$-0.361527\pi$
$978$		0			0
$979$	−26.5050	−	22.2403i	−0.847102	−	0.710803i
$980$		0			0
$981$	12.9414	+	4.71030i	0.413188	+	0.150388i
$982$		0			0
$983$	7.35928	−	41.7365i	0.234724	−	1.33119i	−0.608469	−	0.793578i	$-0.708216\pi$
$983$	7.35928	−	41.7365i	0.234724	−	1.33119i	0.843193	−	0.537611i	$-0.180673\pi$
$984$		0			0
$985$	36.0205	+	62.3894i	1.14771	+	1.98789i
$986$		0			0
$987$	−2.48976	+	0.906198i	−0.0792499	+	0.0288446i
$988$		0			0
$989$	14.9704	+	25.9296i	0.476032	+	0.824512i
$990$		0			0
$991$	19.3921	−	33.5881i	0.616010	−	1.06696i	−0.374196	−	0.927350i	$-0.622081\pi$
$991$	19.3921	−	33.5881i	0.616010	−	1.06696i	0.990206	−	0.139612i	$-0.0445854\pi$
$992$		0			0
$993$	−97.2975			−3.08764
$994$		0			0
$995$	38.8994	−	32.6405i	1.23319	−	1.03477i
$996$		0			0
$997$	−28.2992	+	10.3001i	−0.896243	+	0.326206i	−0.748746	−	0.662857i	$-0.769344\pi$
$997$	−28.2992	+	10.3001i	−0.896243	+	0.326206i	−0.147497	+	0.989063i	$0.547122\pi$
$998$		0			0
$999$	−41.9358	+	24.8041i	−1.32679	+	0.784768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.g.81.1		30
4.3	odd	2		296.2.u.b.81.5	✓	30
37.16	even	9	inner	592.2.bc.g.497.1		30
148.127	odd	18		296.2.u.b.201.5	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.u.b.81.5	✓	30	4.3	odd	2
296.2.u.b.201.5	yes	30	148.127	odd	18
592.2.bc.g.81.1		30	1.1	even	1	trivial
592.2.bc.g.497.1		30	37.16	even	9	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.77384 - 1.00960i) q^{3} +(-0.559739 - 3.17444i) q^{5} +(-0.344404 - 1.95321i) q^{7} +(4.37680 + 3.67257i) q^{9} +(2.07341 - 3.59126i) q^{11} +(3.83038 - 3.21407i) q^{13} +(-1.65227 + 9.37051i) q^{15} +(-4.21619 - 3.53781i) q^{17} +(-3.27814 - 1.19315i) q^{19} +(-1.01663 + 5.76562i) q^{21} +(1.93561 + 3.35258i) q^{23} +(-5.06529 + 1.84361i) q^{25} +(-4.00494 - 6.93676i) q^{27} +(-4.98749 + 8.63859i) q^{29} +2.40270 q^{31} +(-9.37705 + 7.86828i) q^{33} +(-6.00758 + 2.18658i) q^{35} +(-0.0640620 - 6.08243i) q^{37} +(-13.8698 + 5.04819i) q^{39} +(-5.90914 + 4.95836i) q^{41} +7.73423 q^{43} +(9.20847 - 15.9495i) q^{45} +(0.226280 + 0.391929i) q^{47} +(2.88142 - 1.04875i) q^{49} +(8.12331 + 14.0700i) q^{51} +(0.390820 - 2.21645i) q^{53} +(-12.5608 - 4.57176i) q^{55} +(7.88846 + 6.61920i) q^{57} +(0.968242 - 5.49118i) q^{59} +(-4.96752 + 4.16824i) q^{61} +(5.66592 - 9.81367i) q^{63} +(-12.3469 - 10.3603i) q^{65} +(-0.136928 - 0.776559i) q^{67} +(-1.98433 - 11.2537i) q^{69} +(-1.52963 - 0.556739i) q^{71} +7.19429 q^{73} +15.9116 q^{75} +(-7.72859 - 2.81298i) q^{77} +(2.11586 + 11.9997i) q^{79} +(1.12934 + 6.40478i) q^{81} +(-0.306457 - 0.257148i) q^{83} +(-8.87058 + 15.3643i) q^{85} +(22.5560 - 18.9268i) q^{87} +(1.44886 - 8.21691i) q^{89} +(-7.59697 - 6.37461i) q^{91} +(-6.66472 - 2.42576i) q^{93} +(-1.95266 + 11.0741i) q^{95} +(6.06712 + 10.5086i) q^{97} +(22.2640 - 8.10345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{5} + 3 q^{7} + 3 q^{11} + 9 q^{13} - 3 q^{15} - 27 q^{17} - 9 q^{19} + 15 q^{21} + 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{29} + 6 q^{31} - 6 q^{33} - 9 q^{35} + 9 q^{37} + 12 q^{39} + 48 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) \) 30 * q - 6 * q^5 + 3 * q^7 + 3 * q^11 + 9 * q^13 - 3 * q^15 - 27 * q^17 - 9 * q^19 + 15 * q^21 + 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^29 + 6 * q^31 - 6 * q^33 - 9 * q^35 + 9 * q^37 + 12 * q^39 + 48 * q^43 + 51 * q^45 - 6 * q^47 - 21 * q^49 - 12 * q^51 - 15 * q^53 - 21 * q^55 + 51 * q^57 + 36 * q^61 + 36 * q^63 - 6 * q^65 + 27 * q^67 - 15 * q^69 - 27 * q^71 - 114 * q^73 - 84 * q^75 - 105 * q^77 + 18 * q^79 - 12 * q^81 + 30 * q^83 + 21 * q^85 + 99 * q^87 + 39 * q^89 + 72 * q^91 - 3 * q^93 - 66 * q^95 - 12 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more