LMFDB - Embedded newform 936.2.q.d.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(313,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("936.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.q (of order $3$, degree $2$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 29 x^{10} - 90 x^{9} + 217 x^{8} - 394 x^{7} + 555 x^{6} - 598 x^{5} + 483 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 29x^10 - 90x^9 + 217x^8 - 394x^7 + 555x^6 - 598x^5 + 483x^4 - 282x^3 + 112x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.2
Root			$0.500000 + 1.30710i$ of defining polynomial
Character	$\chi$	$=$	936.625
Dual form			936.2.q.d.313.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69504 - 0.356160i) q^{3} +(0.348249 - 0.603184i) q^{5} +(-0.902727 - 1.56357i) q^{7} +(2.74630 + 1.20741i) q^{9} +(1.77560 + 3.07543i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-0.805124 + 0.898387i) q^{15} +4.15178 q^{17} -3.92509 q^{19} +(0.973275 + 2.97182i) q^{21} +(1.22602 - 2.12353i) q^{23} +(2.25745 + 3.91001i) q^{25} +(-4.22505 - 3.02472i) q^{27} +(-4.05379 - 7.02137i) q^{29} +(2.87972 - 4.98782i) q^{31} +(-1.91436 - 5.84537i) q^{33} -1.25749 q^{35} +11.3044 q^{37} +(1.15596 - 1.28987i) q^{39} +(2.04834 - 3.54783i) q^{41} +(4.75114 + 8.22921i) q^{43} +(1.68468 - 1.23605i) q^{45} +(-6.09061 - 10.5492i) q^{47} +(1.87017 - 3.23923i) q^{49} +(-7.03742 - 1.47870i) q^{51} +5.68715 q^{53} +2.47340 q^{55} +(6.65318 + 1.39796i) q^{57} +(-0.315470 + 0.546410i) q^{59} +(0.556113 + 0.963216i) q^{61} +(-0.591293 - 5.38399i) q^{63} +(0.348249 + 0.603184i) q^{65} +(7.05120 - 12.2130i) q^{67} +(-2.83446 + 3.16280i) q^{69} +4.85378 q^{71} -0.187674 q^{73} +(-2.43386 - 7.43162i) q^{75} +(3.20577 - 5.55255i) q^{77} +(1.82959 + 3.16894i) q^{79} +(6.08433 + 6.63181i) q^{81} +(1.34871 + 2.33604i) q^{83} +(1.44585 - 2.50429i) q^{85} +(4.37060 + 13.3453i) q^{87} -7.04438 q^{89} +1.80545 q^{91} +(-6.65770 + 7.42890i) q^{93} +(-1.36691 + 2.36755i) q^{95} +(6.95836 + 12.0522i) q^{97} +(1.16303 + 10.5899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - q^{5} + 2 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 12 q^{17} - 14 q^{19} - 24 q^{21} + 19 q^{23} + 5 q^{25} - 7 q^{27} - 2 q^{29} + 8 q^{31} - 9 q^{33} + 2 q^{35} - 34 q^{37}+ \cdots - 39 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 - q^5 + 2 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - 2 * q^15 + 12 * q^17 - 14 * q^19 - 24 * q^21 + 19 * q^23 + 5 * q^25 - 7 * q^27 - 2 * q^29 + 8 * q^31 - 9 * q^33 + 2 * q^35 - 34 * q^37 - q^39 - 2 * q^41 + 15 * q^43 + 10 * q^45 - 9 * q^47 + 12 * q^49 + 4 * q^51 + 32 * q^53 - 10 * q^55 - 14 * q^57 + 5 * q^59 + 6 * q^61 + 18 * q^63 - q^65 + 8 * q^67 + 15 * q^69 - 42 * q^71 - 2 * q^73 + 10 * q^75 + 3 * q^77 + 34 * q^79 + 62 * q^81 + 44 * q^83 + 7 * q^85 - 21 * q^87 + 22 * q^89 - 4 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 - 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.69504	−	0.356160i	−0.978630	−	0.205629i
$3$	−1.69504	−	0.356160i	−0.978630	−	0.205629i
$4$		0			0
$5$	0.348249	−	0.603184i	0.155741	−	0.269752i	−0.777587	−	0.628775i	$-0.783557\pi$
$5$	0.348249	−	0.603184i	0.155741	−	0.269752i	0.933329	+	0.359023i	$0.116890\pi$
$6$		0			0
$7$	−0.902727	−	1.56357i	−0.341199	−	0.590973i	0.643457	−	0.765482i	$-0.277500\pi$
$7$	−0.902727	−	1.56357i	−0.341199	−	0.590973i	−0.984656	+	0.174509i	$0.944166\pi$
$8$		0			0
$9$	2.74630	+	1.20741i	0.915433	+	0.402469i
$10$		0			0
$11$	1.77560	+	3.07543i	0.535364	+	0.927278i	0.999146	+	0.0413280i	$0.0131589\pi$
$11$	1.77560	+	3.07543i	0.535364	+	0.927278i	−0.463782	+	0.885950i	$0.653508\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$		0			0
$15$	−0.805124	+	0.898387i	−0.207882	+	0.231963i
$16$		0			0
$17$	4.15178			1.00695			0.503477	−	0.864009i	$-0.332054\pi$
$17$	4.15178			1.00695			0.503477	+	0.864009i	$0.332054\pi$
$18$		0			0
$19$	−3.92509			−0.900478			−0.450239	−	0.892908i	$-0.648661\pi$
$19$	−3.92509			−0.900478			−0.450239	+	0.892908i	$0.648661\pi$
$20$		0			0
$21$	0.973275	+	2.97182i	0.212386	+	0.648505i
$22$		0			0
$23$	1.22602	−	2.12353i	0.255643	−	0.442786i	−0.709427	−	0.704779i	$-0.751046\pi$
$23$	1.22602	−	2.12353i	0.255643	−	0.442786i	0.965070	+	0.261992i	$0.0843796\pi$
$24$		0			0
$25$	2.25745	+	3.91001i	0.451489	+	0.782002i
$26$		0			0
$27$	−4.22505	−	3.02472i	−0.813111	−	0.582108i
$28$		0			0
$29$	−4.05379	−	7.02137i	−0.752770	−	1.30384i	−0.946475	−	0.322777i	$-0.895384\pi$
$29$	−4.05379	−	7.02137i	−0.752770	−	1.30384i	0.193705	−	0.981060i	$-0.437950\pi$
$30$		0			0
$31$	2.87972	−	4.98782i	0.517213	−	0.895840i	−0.482587	−	0.875848i	$-0.660303\pi$
$31$	2.87972	−	4.98782i	0.517213	−	0.895840i	0.999800	−	0.0199915i	$-0.00636393\pi$
$32$		0			0
$33$	−1.91436	−	5.84537i	−0.333248	−	1.01755i
$34$		0			0
$35$	−1.25749			−0.212555
$36$		0			0
$37$	11.3044			1.85844			0.929220	−	0.369528i	$-0.120481\pi$
$37$	11.3044			1.85844			0.929220	+	0.369528i	$0.120481\pi$
$38$		0			0
$39$	1.15596	−	1.28987i	0.185102	−	0.206544i
$40$		0			0
$41$	2.04834	−	3.54783i	0.319897	−	0.554079i	−0.660569	−	0.750765i	$-0.729685\pi$
$41$	2.04834	−	3.54783i	0.319897	−	0.554079i	0.980466	+	0.196687i	$0.0630182\pi$
$42$		0			0
$43$	4.75114	+	8.22921i	0.724541	+	1.25494i	0.959162	+	0.282856i	$0.0912818\pi$
$43$	4.75114	+	8.22921i	0.724541	+	1.25494i	−0.234621	+	0.972087i	$0.575385\pi$
$44$		0			0
$45$	1.68468	−	1.23605i	0.251138	−	0.184259i
$46$		0			0
$47$	−6.09061	−	10.5492i	−0.888406	−	1.53876i	−0.841759	−	0.539853i	$-0.818480\pi$
$47$	−6.09061	−	10.5492i	−0.888406	−	1.53876i	−0.0466473	−	0.998911i	$-0.514854\pi$
$48$		0			0
$49$	1.87017	−	3.23923i	0.267167	−	0.462747i
$50$		0			0
$51$	−7.03742	−	1.47870i	−0.985436	−	0.207059i
$52$		0			0
$53$	5.68715			0.781190			0.390595	−	0.920563i	$-0.372269\pi$
$53$	5.68715			0.781190			0.390595	+	0.920563i	$0.372269\pi$
$54$		0			0
$55$	2.47340			0.333513
$56$		0			0
$57$	6.65318	+	1.39796i	0.881235	+	0.185164i
$58$		0			0
$59$	−0.315470	+	0.546410i	−0.0410707	+	0.0711365i	−0.885830	−	0.464010i	$-0.846410\pi$
$59$	−0.315470	+	0.546410i	−0.0410707	+	0.0711365i	0.844759	+	0.535146i	$0.179744\pi$
$60$		0			0
$61$	0.556113	+	0.963216i	0.0712030	+	0.123327i	0.899429	−	0.437067i	$-0.143983\pi$
$61$	0.556113	+	0.963216i	0.0712030	+	0.123327i	−0.828226	+	0.560394i	$0.810650\pi$
$62$		0			0
$63$	−0.591293	−	5.38399i	−0.0744959	−	0.678319i
$64$		0			0
$65$	0.348249	+	0.603184i	0.0431949	+	0.0748158i
$66$		0			0
$67$	7.05120	−	12.2130i	0.861441	−	1.49206i	−0.00909658	−	0.999959i	$-0.502896\pi$
$67$	7.05120	−	12.2130i	0.861441	−	1.49206i	0.870538	−	0.492101i	$-0.163771\pi$
$68$		0			0
$69$	−2.83446	+	3.16280i	−0.341229	+	0.380756i
$70$		0			0
$71$	4.85378			0.576037			0.288019	−	0.957625i	$-0.407003\pi$
$71$	4.85378			0.576037			0.288019	+	0.957625i	$0.407003\pi$
$72$		0			0
$73$	−0.187674			−0.0219656			−0.0109828	−	0.999940i	$-0.503496\pi$
$73$	−0.187674			−0.0219656			−0.0109828	+	0.999940i	$0.503496\pi$
$74$		0			0
$75$	−2.43386	−	7.43162i	−0.281039	−	0.858130i
$76$		0			0
$77$	3.20577	−	5.55255i	0.365331	−	0.632772i
$78$		0			0
$79$	1.82959	+	3.16894i	0.205845	+	0.356534i	0.950402	−	0.311025i	$-0.100672\pi$
$79$	1.82959	+	3.16894i	0.205845	+	0.356534i	−0.744557	+	0.667559i	$0.767339\pi$
$80$		0			0
$81$	6.08433	+	6.63181i	0.676037	+	0.736868i
$82$		0			0
$83$	1.34871	+	2.33604i	0.148040	+	0.256414i	0.930503	−	0.366284i	$-0.119370\pi$
$83$	1.34871	+	2.33604i	0.148040	+	0.256414i	−0.782463	+	0.622697i	$0.786037\pi$
$84$		0			0
$85$	1.44585	−	2.50429i	0.156825	−	0.271628i
$86$		0			0
$87$	4.37060	+	13.3453i	0.468577	+	1.43076i
$88$		0			0
$89$	−7.04438			−0.746703			−0.373351	−	0.927690i	$-0.621791\pi$
$89$	−7.04438			−0.746703			−0.373351	+	0.927690i	$0.621791\pi$
$90$		0			0
$91$	1.80545			0.189263
$92$		0			0
$93$	−6.65770	+	7.42890i	−0.690371	+	0.770342i
$94$		0			0
$95$	−1.36691	+	2.36755i	−0.140242	+	0.242906i
$96$		0			0
$97$	6.95836	+	12.0522i	0.706515	+	1.22372i	0.966142	+	0.258010i	$0.0830669\pi$
$97$	6.95836	+	12.0522i	0.706515	+	1.22372i	−0.259628	+	0.965709i	$0.583600\pi$
$98$		0			0
$99$	1.16303	+	10.5899i	0.116889	+	1.06433i
$100$		0			0
$101$	−3.69245	−	6.39550i	−0.367412	−	0.636376i	0.621748	−	0.783217i	$-0.286423\pi$
$101$	−3.69245	−	6.39550i	−0.367412	−	0.636376i	−0.989160	+	0.146841i	$0.953089\pi$
$102$		0			0
$103$	4.06357	−	7.03830i	0.400395	−	0.693505i	−0.593378	−	0.804924i	$-0.702206\pi$
$103$	4.06357	−	7.03830i	0.400395	−	0.693505i	0.993774	+	0.111419i	$0.0355396\pi$
$104$		0			0
$105$	2.13150	+	0.447869i	0.208013	+	0.0437075i
$106$		0			0
$107$	−2.42349			−0.234288			−0.117144	−	0.993115i	$-0.537374\pi$
$107$	−2.42349			−0.234288			−0.117144	+	0.993115i	$0.537374\pi$
$108$		0			0
$109$	−9.67961			−0.927139			−0.463569	−	0.886061i	$-0.653432\pi$
$109$	−9.67961			−0.927139			−0.463569	+	0.886061i	$0.653432\pi$
$110$		0			0
$111$	−19.1615	−	4.02619i	−1.81872	−	0.382149i
$112$		0			0
$113$	10.1084	−	17.5083i	0.950919	−	1.64704i	0.207478	−	0.978240i	$-0.433474\pi$
$113$	10.1084	−	17.5083i	0.950919	−	1.64704i	0.743441	−	0.668801i	$-0.233192\pi$
$114$		0			0
$115$	−0.853919	−	1.47903i	−0.0796284	−	0.137920i
$116$		0			0
$117$	−2.41880	+	1.77466i	−0.223618	+	0.164068i
$118$		0			0
$119$	−3.74792	−	6.49159i	−0.343571	−	0.595083i
$120$		0			0
$121$	−0.805520	+	1.39520i	−0.0732291	+	0.126837i
$122$		0			0
$123$	−4.73561	+	5.28417i	−0.426996	+	0.476458i
$124$		0			0
$125$	6.62709			0.592745
$126$		0			0
$127$	2.93094			0.260079			0.130040	−	0.991509i	$-0.458490\pi$
$127$	2.93094			0.260079			0.130040	+	0.991509i	$0.458490\pi$
$128$		0			0
$129$	−5.12244	−	15.6410i	−0.451005	−	1.37711i
$130$		0			0
$131$	3.27910	−	5.67956i	0.286496	−	0.496226i	−0.686475	−	0.727154i	$-0.740843\pi$
$131$	3.27910	−	5.67956i	0.286496	−	0.496226i	0.972971	+	0.230928i	$0.0741761\pi$
$132$		0			0
$133$	3.54329	+	6.13715i	0.307242	+	0.532158i
$134$		0			0
$135$	−3.29583	+	1.49513i	−0.283660	+	0.128680i
$136$		0			0
$137$	−8.17862	−	14.1658i	−0.698746	−	1.21026i	−0.968901	−	0.247447i	$-0.920408\pi$
$137$	−8.17862	−	14.1658i	−0.698746	−	1.21026i	0.270155	−	0.962817i	$-0.412925\pi$
$138$		0			0
$139$	−10.6367	+	18.4233i	−0.902195	+	1.56265i	−0.0775552	+	0.996988i	$0.524711\pi$
$139$	−10.6367	+	18.4233i	−0.902195	+	1.56265i	−0.824639	+	0.565659i	$0.808622\pi$
$140$		0			0
$141$	6.56659	+	20.0506i	0.553006	+	1.68856i
$142$		0			0
$143$	−3.55120			−0.296966
$144$		0			0
$145$	−5.64691			−0.468950
$146$		0			0
$147$	−4.32369	+	4.82453i	−0.356612	+	0.397921i
$148$		0			0
$149$	−8.20028	+	14.2033i	−0.671793	+	1.16358i	0.305602	+	0.952159i	$0.401142\pi$
$149$	−8.20028	+	14.2033i	−0.671793	+	1.16358i	−0.977395	+	0.211420i	$0.932191\pi$
$150$		0			0
$151$	5.23882	+	9.07390i	0.426329	+	0.738424i	0.996544	−	0.0830721i	$-0.0264732\pi$
$151$	5.23882	+	9.07390i	0.426329	+	0.738424i	−0.570214	+	0.821496i	$0.693140\pi$
$152$		0			0
$153$	11.4020	+	5.01289i	0.921800	+	0.405268i
$154$		0			0
$155$	−2.00572	−	3.47400i	−0.161103	−	0.279039i
$156$		0			0
$157$	−2.07795	+	3.59912i	−0.165839	+	0.287241i	−0.936953	−	0.349456i	$-0.886366\pi$
$157$	−2.07795	+	3.59912i	−0.165839	+	0.287241i	0.771114	+	0.636697i	$0.219700\pi$
$158$		0			0
$159$	−9.63992	−	2.02553i	−0.764496	−	0.160635i
$160$		0			0
$161$	−4.42704			−0.348900
$162$		0			0
$163$	10.7460			0.841690			0.420845	−	0.907133i	$-0.361734\pi$
$163$	10.7460			0.841690			0.420845	+	0.907133i	$0.361734\pi$
$164$		0			0
$165$	−4.19251	−	0.880927i	−0.326386	−	0.0685801i
$166$		0			0
$167$	0.104236	−	0.180542i	0.00806604	−	0.0139708i	−0.861964	−	0.506969i	$-0.830766\pi$
$167$	0.104236	−	0.180542i	0.00806604	−	0.0139708i	0.870030	+	0.492998i	$0.164099\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	−10.7795	−	4.73919i	−0.824328	−	0.362415i
$172$		0			0
$173$	9.83238	+	17.0302i	0.747542	+	1.29478i	0.948998	+	0.315283i	$0.102099\pi$
$173$	9.83238	+	17.0302i	0.747542	+	1.29478i	−0.201456	+	0.979498i	$0.564567\pi$
$174$		0			0
$175$	4.07571	−	7.05934i	0.308095	−	0.533636i
$176$		0			0
$177$	0.729342	−	0.813827i	0.0548207	−	0.0611710i
$178$		0			0
$179$	−21.4050			−1.59989			−0.799944	−	0.600075i	$-0.795137\pi$
$179$	−21.4050			−1.59989			−0.799944	+	0.600075i	$0.795137\pi$
$180$		0			0
$181$	−20.4190			−1.51773			−0.758866	−	0.651247i	$-0.774246\pi$
$181$	−20.4190			−1.51773			−0.758866	+	0.651247i	$0.774246\pi$
$182$		0			0
$183$	−0.599573	−	1.83075i	−0.0443217	−	0.135333i
$184$		0			0
$185$	3.93676	−	6.81866i	0.289436	−	0.501318i
$186$		0			0
$187$	7.37190	+	12.7685i	0.539087	+	0.933726i
$188$		0			0
$189$	−0.915298	+	9.33665i	−0.0665781	+	0.679142i
$190$		0			0
$191$	7.83237	+	13.5661i	0.566730	+	0.981606i	0.996886	+	0.0788510i	$0.0251251\pi$
$191$	7.83237	+	13.5661i	0.566730	+	0.981606i	−0.430156	+	0.902754i	$0.641542\pi$
$192$		0			0
$193$	−2.59025	+	4.48644i	−0.186450	+	0.322941i	−0.944064	−	0.329762i	$-0.893032\pi$
$193$	−2.59025	+	4.48644i	−0.186450	+	0.322941i	0.757614	+	0.652703i	$0.226365\pi$
$194$		0			0
$195$	−0.375464	−	1.14645i	−0.0268875	−	0.0820991i
$196$		0			0
$197$	−4.94429			−0.352266			−0.176133	−	0.984366i	$-0.556359\pi$
$197$	−4.94429			−0.352266			−0.176133	+	0.984366i	$0.556359\pi$
$198$		0			0
$199$	18.2528			1.29391			0.646954	−	0.762529i	$-0.276043\pi$
$199$	18.2528			1.29391			0.646954	+	0.762529i	$0.276043\pi$
$200$		0			0
$201$	−16.3018	+	18.1902i	−1.14984	+	1.28304i
$202$		0			0
$203$	−7.31893	+	12.6768i	−0.513688	+	0.889734i
$204$		0			0
$205$	−1.42666	−	2.47106i	−0.0996426	−	0.172586i
$206$		0			0
$207$	5.93098	−	4.35154i	0.412232	−	0.302453i
$208$		0			0
$209$	−6.96940	−	12.0714i	−0.482083	−	0.834993i
$210$		0			0
$211$	−8.04187	+	13.9289i	−0.553625	+	0.958907i	0.444384	+	0.895837i	$0.353423\pi$
$211$	−8.04187	+	13.9289i	−0.553625	+	0.958907i	−0.998009	+	0.0630706i	$0.979911\pi$
$212$		0			0
$213$	−8.22733	−	1.72872i	−0.563727	−	0.118450i
$214$		0			0
$215$	6.61830			0.451365
$216$		0			0
$217$	−10.3984			−0.705890
$218$		0			0
$219$	0.318115	+	0.0668420i	0.0214962	+	0.00451676i
$220$		0			0
$221$	−2.07589	+	3.59555i	−0.139639	+	0.241863i
$222$		0			0
$223$	−3.16846	−	5.48793i	−0.212176	−	0.367499i	0.740219	−	0.672365i	$-0.234722\pi$
$223$	−3.16846	−	5.48793i	−0.212176	−	0.367499i	−0.952395	+	0.304866i	$0.901388\pi$
$224$		0			0
$225$	1.47864	+	13.4637i	0.0985763	+	0.897582i
$226$		0			0
$227$	6.20062	+	10.7398i	0.411550	+	0.712825i	0.995059	−	0.0992813i	$-0.0316544\pi$
$227$	6.20062	+	10.7398i	0.411550	+	0.712825i	−0.583510	+	0.812106i	$0.698321\pi$
$228$		0			0
$229$	−5.21552	+	9.03354i	−0.344651	+	0.596953i	−0.985290	−	0.170889i	$-0.945336\pi$
$229$	−5.21552	+	9.03354i	−0.344651	+	0.596953i	0.640639	+	0.767842i	$0.278669\pi$
$230$		0			0
$231$	−7.41149	+	8.27001i	−0.487640	+	0.544127i
$232$		0			0
$233$	1.96225			0.128551			0.0642757	−	0.997932i	$-0.479526\pi$
$233$	1.96225			0.128551			0.0642757	+	0.997932i	$0.479526\pi$
$234$		0			0
$235$	−8.48418			−0.553447
$236$		0			0
$237$	−1.97257	−	6.02310i	−0.128132	−	0.391242i
$238$		0			0
$239$	8.77271	−	15.1948i	0.567460	−	0.982869i	−0.429357	−	0.903135i	$-0.641260\pi$
$239$	8.77271	−	15.1948i	0.567460	−	0.982869i	0.996816	−	0.0797339i	$-0.0254071\pi$
$240$		0			0
$241$	8.02013	+	13.8913i	0.516622	+	0.894816i	0.999814	+	0.0193011i	$0.00614411\pi$
$241$	8.02013	+	13.8913i	0.516622	+	0.894816i	−0.483192	+	0.875515i	$0.660523\pi$
$242$		0			0
$243$	−7.95118	−	13.4082i	−0.510068	−	0.860134i
$244$		0			0
$245$	−1.30257	−	2.25611i	−0.0832180	−	0.144138i
$246$		0			0
$247$	1.96255	−	3.39923i	0.124874	−	0.216288i
$248$		0			0
$249$	−1.45411	−	4.44003i	−0.0921508	−	0.281375i
$250$		0			0
$251$	2.71819			0.171571			0.0857854	−	0.996314i	$-0.472660\pi$
$251$	2.71819			0.171571			0.0857854	+	0.996314i	$0.472660\pi$
$252$		0			0
$253$	8.70769			0.547448
$254$		0			0
$255$	−3.34270	+	3.72991i	−0.209328	+	0.233576i
$256$		0			0
$257$	−0.334101	+	0.578680i	−0.0208407	+	0.0360971i	−0.876258	−	0.481843i	$-0.839968\pi$
$257$	−0.334101	+	0.578680i	−0.0208407	+	0.0360971i	0.855417	+	0.517940i	$0.173301\pi$
$258$		0			0
$259$	−10.2048	−	17.6753i	−0.634097	−	1.09829i
$260$		0			0
$261$	−2.65526	−	24.1774i	−0.164357	−	1.49654i
$262$		0			0
$263$	11.8478	+	20.5210i	0.730566	+	1.26538i	0.956641	+	0.291268i	$0.0940772\pi$
$263$	11.8478	+	20.5210i	0.730566	+	1.26538i	−0.226075	+	0.974110i	$0.572589\pi$
$264$		0			0
$265$	1.98054	−	3.43040i	0.121664	−	0.210728i
$266$		0			0
$267$	11.9405	+	2.50893i	0.730746	+	0.153544i
$268$		0			0
$269$	−0.337101			−0.0205534			−0.0102767	−	0.999947i	$-0.503271\pi$
$269$	−0.337101			−0.0205534			−0.0102767	+	0.999947i	$0.503271\pi$
$270$		0			0
$271$	−7.27424			−0.441879			−0.220939	−	0.975288i	$-0.570912\pi$
$271$	−7.27424			−0.441879			−0.220939	+	0.975288i	$0.570912\pi$
$272$		0			0
$273$	−3.06031	−	0.643030i	−0.185218	−	0.0389179i
$274$		0			0
$275$	−8.01665	+	13.8852i	−0.483422	+	0.837312i
$276$		0			0
$277$	10.0808	+	17.4604i	0.605696	+	1.04910i	0.991941	+	0.126700i	$0.0404385\pi$
$277$	10.0808	+	17.4604i	0.605696	+	1.04910i	−0.386245	+	0.922396i	$0.626228\pi$
$278$		0			0
$279$	13.9309	−	10.2211i	0.834022	−	0.611919i
$280$		0			0
$281$	−7.44369	−	12.8929i	−0.444053	−	0.769123i	0.553932	−	0.832562i	$-0.313127\pi$
$281$	−7.44369	−	12.8929i	−0.444053	−	0.769123i	−0.997986	+	0.0634386i	$0.979793\pi$
$282$		0			0
$283$	12.5905	−	21.8075i	0.748430	−	1.29632i	−0.200145	−	0.979766i	$-0.564141\pi$
$283$	12.5905	−	21.8075i	0.748430	−	1.29632i	0.948575	−	0.316553i	$-0.102525\pi$
$284$		0			0
$285$	3.16019	−	3.52625i	0.187193	−	0.208877i
$286$		0			0
$287$	−7.39637			−0.436594
$288$		0			0
$289$	0.237270			0.0139571
$290$		0			0
$291$	−7.50216	−	22.9073i	−0.439784	−	1.34285i
$292$		0			0
$293$	10.1289	−	17.5438i	0.591738	−	1.02492i	−0.402260	−	0.915526i	$-0.631775\pi$
$293$	10.1289	−	17.5438i	0.591738	−	1.02492i	0.993998	−	0.109395i	$-0.0348915\pi$
$294$		0			0
$295$	0.219724	+	0.380573i	0.0127928	+	0.0221578i
$296$		0			0
$297$	1.80033	−	18.3646i	0.104466	−	1.06562i
$298$		0			0
$299$	1.22602	+	2.12353i	0.0709026	+	0.122807i
$300$		0			0
$301$	8.57795	−	14.8575i	0.494425	−	0.856369i
$302$		0			0
$303$	3.98101	+	12.1557i	0.228703	+	0.698328i
$304$		0			0
$305$	0.774662			0.0443570
$306$		0			0
$307$	11.7802			0.672332			0.336166	−	0.941803i	$-0.390870\pi$
$307$	11.7802			0.672332			0.336166	+	0.941803i	$0.390870\pi$
$308$		0			0
$309$	−9.39466	+	10.4829i	−0.534443	+	0.596352i
$310$		0			0
$311$	8.41319	−	14.5721i	0.477068	−	0.826306i	−0.522587	−	0.852586i	$-0.675033\pi$
$311$	8.41319	−	14.5721i	0.477068	−	0.826306i	0.999655	+	0.0262802i	$0.00836620\pi$
$312$		0			0
$313$	8.22111	+	14.2394i	0.464684	+	0.804857i	0.999187	−	0.0403097i	$-0.0128345\pi$
$313$	8.22111	+	14.2394i	0.464684	+	0.804857i	−0.534503	+	0.845167i	$0.679501\pi$
$314$		0			0
$315$	−3.45345	−	1.51831i	−0.194580	−	0.0855469i
$316$		0			0
$317$	−6.95342	−	12.0437i	−0.390543	−	0.676440i	0.601978	−	0.798512i	$-0.294379\pi$
$317$	−6.95342	−	12.0437i	−0.390543	−	0.676440i	−0.992521	+	0.122072i	$0.961046\pi$
$318$		0			0
$319$	14.3958	−	24.9343i	0.806012	−	1.39605i
$320$		0			0
$321$	4.10791	+	0.863151i	0.229281	+	0.0481764i
$322$		0			0
$323$	−16.2961			−0.906740
$324$		0			0
$325$	−4.51489			−0.250441
$326$		0			0
$327$	16.4073	+	3.44749i	0.907326	+	0.190647i
$328$		0			0
$329$	−10.9963	+	19.0462i	−0.606246	+	1.05005i
$330$		0			0
$331$	10.2230	+	17.7067i	0.561906	+	0.973251i	0.997330	+	0.0730249i	$0.0232652\pi$
$331$	10.2230	+	17.7067i	0.561906	+	0.973251i	−0.435424	+	0.900226i	$0.643401\pi$
$332$		0			0
$333$	31.0454	+	13.6491i	1.70128	+	0.747965i
$334$		0			0
$335$	−4.91114	−	8.50635i	−0.268324	−	0.464751i
$336$		0			0
$337$	−3.89422	+	6.74498i	−0.212131	+	0.367422i	−0.952381	−	0.304909i	$-0.901374\pi$
$337$	−3.89422	+	6.74498i	−0.212131	+	0.367422i	0.740250	+	0.672332i	$0.234707\pi$
$338$		0			0
$339$	−23.3699	+	26.0770i	−1.26928	+	1.41631i
$340$		0			0
$341$	20.4530			1.10759
$342$		0			0
$343$	−19.3912			−1.04703
$344$		0			0
$345$	0.920653	+	2.81114i	0.0495663	+	0.151347i
$346$		0			0
$347$	−13.3992	+	23.2081i	−0.719306	+	1.24588i	0.241969	+	0.970284i	$0.422207\pi$
$347$	−13.3992	+	23.2081i	−0.719306	+	1.24588i	−0.961275	+	0.275591i	$0.911126\pi$
$348$		0			0
$349$	−17.1874	−	29.7695i	−0.920022	−	1.59352i	−0.799378	−	0.600829i	$-0.794837\pi$
$349$	−17.1874	−	29.7695i	−0.920022	−	1.59352i	−0.120644	−	0.992696i	$-0.538496\pi$
$350$		0			0
$351$	4.73201	−	2.14664i	0.252576	−	0.114579i
$352$		0			0
$353$	−3.07875	−	5.33255i	−0.163865	−	0.283823i	0.772387	−	0.635153i	$-0.219063\pi$
$353$	−3.07875	−	5.33255i	−0.163865	−	0.283823i	−0.936252	+	0.351330i	$0.885730\pi$
$354$		0			0
$355$	1.69032	−	2.92772i	0.0897129	−	0.155387i
$356$		0			0
$357$	4.04082	+	12.3383i	0.213863	+	0.653014i
$358$		0			0
$359$	7.04536			0.371840			0.185920	−	0.982565i	$-0.440474\pi$
$359$	7.04536			0.371840			0.185920	+	0.982565i	$0.440474\pi$
$360$		0			0
$361$	−3.59365			−0.189139
$362$		0			0
$363$	1.86230	−	2.07803i	0.0977455	−	0.109068i
$364$		0			0
$365$	−0.0653572	+	0.113202i	−0.00342095	+	0.00592527i
$366$		0			0
$367$	1.64224	+	2.84445i	0.0857244	+	0.148479i	0.905700	−	0.423920i	$-0.139346\pi$
$367$	1.64224	+	2.84445i	0.0857244	+	0.148479i	−0.819975	+	0.572399i	$0.806013\pi$
$368$		0			0
$369$	9.90905	−	7.27023i	0.515845	−	0.378473i
$370$		0			0
$371$	−5.13394	−	8.89224i	−0.266541	−	0.461662i
$372$		0			0
$373$	9.45547	−	16.3774i	0.489586	−	0.847987i	−0.510342	−	0.859971i	$-0.670481\pi$
$373$	9.45547	−	16.3774i	0.489586	−	0.847987i	0.999928	+	0.0119839i	$0.00381469\pi$
$374$		0			0
$375$	−11.2332	−	2.36031i	−0.580078	−	0.121886i
$376$		0			0
$377$	8.10758			0.417562
$378$		0			0
$379$	−1.51134			−0.0776324			−0.0388162	−	0.999246i	$-0.512359\pi$
$379$	−1.51134			−0.0776324			−0.0388162	+	0.999246i	$0.512359\pi$
$380$		0			0
$381$	−4.96806	−	1.04388i	−0.254521	−	0.0534798i
$382$		0			0
$383$	1.33954	−	2.32015i	0.0684471	−	0.118554i	−0.829771	−	0.558104i	$-0.811529\pi$
$383$	1.33954	−	2.32015i	0.0684471	−	0.118554i	0.898218	+	0.439550i	$0.144862\pi$
$384$		0			0
$385$	−2.23281	−	3.86733i	−0.113794	−	0.197098i
$386$		0			0
$387$	3.11203	+	28.3364i	0.158193	+	1.44042i
$388$		0			0
$389$	−8.85533	−	15.3379i	−0.448983	−	0.777662i	0.549337	−	0.835601i	$-0.314880\pi$
$389$	−8.85533	−	15.3379i	−0.448983	−	0.777662i	−0.998320	+	0.0579394i	$0.981547\pi$
$390$		0			0
$391$	5.09016	−	8.81642i	0.257421	−	0.445866i
$392$		0			0
$393$	−7.58103	+	8.45919i	−0.382412	+	0.426710i
$394$		0			0
$395$	2.54861			0.128234
$396$		0			0
$397$	−24.2097			−1.21505			−0.607526	−	0.794300i	$-0.707838\pi$
$397$	−24.2097			−1.21505			−0.607526	+	0.794300i	$0.707838\pi$
$398$		0			0
$399$	−3.82019	−	11.6647i	−0.191249	−	0.583964i
$400$		0			0
$401$	12.5256	−	21.6949i	0.625497	−	1.08339i	−0.362948	−	0.931809i	$-0.618230\pi$
$401$	12.5256	−	21.6949i	0.625497	−	1.08339i	0.988445	−	0.151582i	$-0.0484369\pi$
$402$		0			0
$403$	2.87972	+	4.98782i	0.143449	+	0.248461i
$404$		0			0
$405$	6.11906	−	1.36045i	0.304059	−	0.0676014i
$406$		0			0
$407$	20.0722	+	34.7660i	0.994941	+	1.72329i
$408$		0			0
$409$	−8.11655	+	14.0583i	−0.401338	+	0.695137i	−0.993888	−	0.110397i	$-0.964788\pi$
$409$	−8.11655	+	14.0583i	−0.401338	+	0.695137i	0.592550	+	0.805534i	$0.298121\pi$
$410$		0			0
$411$	8.81777	+	26.9244i	0.434949	+	1.32808i
$412$		0			0
$413$	1.13913			0.0560530
$414$		0			0
$415$	1.87875			0.0922242
$416$		0			0
$417$	24.5913	−	27.4399i	1.20424	−	1.34374i
$418$		0			0
$419$	4.60405	−	7.97445i	0.224923	−	0.389577i	−0.731374	−	0.681977i	$-0.761120\pi$
$419$	4.60405	−	7.97445i	0.224923	−	0.389577i	0.956296	+	0.292400i	$0.0944537\pi$
$420$		0			0
$421$	−4.75579	−	8.23726i	−0.231783	−	0.401460i	0.726550	−	0.687114i	$-0.241123\pi$
$421$	−4.75579	−	8.23726i	−0.231783	−	0.401460i	−0.958333	+	0.285654i	$0.907789\pi$
$422$		0			0
$423$	−3.98939	−	36.3252i	−0.193971	−	1.76619i
$424$		0			0
$425$	9.37242	+	16.2335i	0.454629	+	0.787441i
$426$		0			0
$427$	1.00404	−	1.73904i	0.0485887	−	0.0841581i
$428$		0			0
$429$	6.01942	+	1.26480i	0.290620	+	0.0610649i
$430$		0			0
$431$	18.3694			0.884825			0.442413	−	0.896812i	$-0.354123\pi$
$431$	18.3694			0.884825			0.442413	+	0.896812i	$0.354123\pi$
$432$		0			0
$433$	−38.8940			−1.86913			−0.934563	−	0.355796i	$-0.884210\pi$
$433$	−38.8940			−1.86913			−0.934563	+	0.355796i	$0.884210\pi$
$434$		0			0
$435$	9.57172	+	2.01120i	0.458929	+	0.0964298i
$436$		0			0
$437$	−4.81224	+	8.33505i	−0.230201	+	0.398719i
$438$		0			0
$439$	9.34985	+	16.1944i	0.446244	+	0.772917i	0.998138	−	0.0609970i	$-0.0194280\pi$
$439$	9.34985	+	16.1944i	0.446244	+	0.772917i	−0.551894	+	0.833914i	$0.686095\pi$
$440$		0			0
$441$	9.04712	−	6.63784i	0.430815	−	0.316087i
$442$		0			0
$443$	12.8261	+	22.2155i	0.609386	+	1.05549i	0.991342	+	0.131307i	$0.0419175\pi$
$443$	12.8261	+	22.2155i	0.609386	+	1.05549i	−0.381955	+	0.924181i	$0.624749\pi$
$444$		0			0
$445$	−2.45319	+	4.24906i	−0.116293	+	0.201425i
$446$		0			0
$447$	18.9584	−	21.1545i	0.896702	−	1.00057i
$448$		0			0
$449$	−36.1563			−1.70632			−0.853160	−	0.521649i	$-0.825317\pi$
$449$	−36.1563			−1.70632			−0.853160	+	0.521649i	$0.825317\pi$
$450$		0			0
$451$	14.5482			0.685046
$452$		0			0
$453$	−5.64823	−	17.2465i	−0.265377	−	0.810309i
$454$		0			0
$455$	0.628746	−	1.08902i	0.0294761	−	0.0510541i
$456$		0			0
$457$	6.18955	+	10.7206i	0.289535	+	0.501489i	0.973699	−	0.227839i	$-0.0731661\pi$
$457$	6.18955	+	10.7206i	0.289535	+	0.501489i	−0.684164	+	0.729328i	$0.739833\pi$
$458$		0			0
$459$	−17.5415	−	12.5580i	−0.818766	−	0.586157i
$460$		0			0
$461$	−7.39618	−	12.8106i	−0.344474	−	0.596647i	0.640784	−	0.767721i	$-0.278610\pi$
$461$	−7.39618	−	12.8106i	−0.344474	−	0.596647i	−0.985258	+	0.171074i	$0.945276\pi$
$462$		0			0
$463$	11.5625	−	20.0269i	0.537356	−	0.930728i	−0.461689	−	0.887042i	$-0.652756\pi$
$463$	11.5625	−	20.0269i	0.537356	−	0.930728i	0.999045	−	0.0436862i	$-0.0139102\pi$
$464$		0			0
$465$	2.16246	+	6.60292i	0.100282	+	0.306203i
$466$		0			0
$467$	25.1537			1.16398			0.581988	−	0.813197i	$-0.302275\pi$
$467$	25.1537			1.16398			0.581988	+	0.813197i	$0.302275\pi$
$468$		0			0
$469$	−25.4612			−1.17569
$470$		0			0
$471$	4.80407	−	5.36056i	0.221360	−	0.247002i
$472$		0			0
$473$	−16.8722	+	29.2236i	−0.775787	+	1.34370i
$474$		0			0
$475$	−8.86068	−	15.3472i	−0.406556	−	0.704176i
$476$		0			0
$477$	15.6186	+	6.86671i	0.715127	+	0.314405i
$478$		0			0
$479$	2.48945	+	4.31186i	0.113746	+	0.197014i	0.917278	−	0.398248i	$-0.130382\pi$
$479$	2.48945	+	4.31186i	0.113746	+	0.197014i	−0.803532	+	0.595262i	$0.797048\pi$
$480$		0			0
$481$	−5.65222	+	9.78994i	−0.257719	+	0.446383i
$482$		0			0
$483$	7.50400	+	1.57674i	0.341444	+	0.0717439i
$484$		0			0
$485$	9.69296			0.440134
$486$		0			0
$487$	11.6666			0.528666			0.264333	−	0.964431i	$-0.414848\pi$
$487$	11.6666			0.528666			0.264333	+	0.964431i	$0.414848\pi$
$488$		0			0
$489$	−18.2148	−	3.82729i	−0.823703	−	0.173076i
$490$		0			0
$491$	−6.24985	+	10.8251i	−0.282052	+	0.488528i	−0.971890	−	0.235436i	$-0.924348\pi$
$491$	−6.24985	+	10.8251i	−0.282052	+	0.488528i	0.689838	+	0.723964i	$0.257682\pi$
$492$		0			0
$493$	−16.8304	−	29.1512i	−0.758005	−	1.31290i
$494$		0			0
$495$	6.79271	+	2.98641i	0.305309	+	0.134229i
$496$		0			0
$497$	−4.38163	−	7.58921i	−0.196543	−	0.340423i
$498$		0			0
$499$	−3.67802	+	6.37051i	−0.164651	+	0.285183i	−0.936531	−	0.350584i	$-0.885983\pi$
$499$	−3.67802	+	6.37051i	−0.164651	+	0.285183i	0.771881	+	0.635768i	$0.219316\pi$
$500$		0			0
$501$	−0.240986	+	0.268901i	−0.0107665	+	0.0120136i
$502$		0			0
$503$	−25.8567			−1.15289			−0.576447	−	0.817134i	$-0.695561\pi$
$503$	−25.8567			−1.15289			−0.576447	+	0.817134i	$0.695561\pi$
$504$		0			0
$505$	−5.14356			−0.228885
$506$		0			0
$507$	0.539075	+	1.64602i	0.0239412	+	0.0731025i
$508$		0			0
$509$	−10.6033	+	18.3655i	−0.469983	+	0.814035i	−0.999411	−	0.0343202i	$-0.989073\pi$
$509$	−10.6033	+	18.3655i	−0.469983	+	0.814035i	0.529428	+	0.848355i	$0.322407\pi$
$510$		0			0
$511$	0.169418	+	0.293441i	0.00749463	+	0.0129811i
$512$		0			0
$513$	16.5837	+	11.8723i	0.732189	+	0.524176i
$514$		0			0
$515$	−2.83026	−	4.90216i	−0.124716	−	0.216015i
$516$		0			0
$517$	21.6290	−	37.4625i	0.951241	−	1.64760i
$518$		0			0
$519$	−10.6008	−	32.3687i	−0.465323	−	1.42083i
$520$		0			0
$521$	3.52661			0.154504			0.0772519	−	0.997012i	$-0.475385\pi$
$521$	3.52661			0.154504			0.0772519	+	0.997012i	$0.475385\pi$
$522$		0			0
$523$	−16.7172			−0.730991			−0.365495	−	0.930813i	$-0.619100\pi$
$523$	−16.7172			−0.730991			−0.365495	+	0.930813i	$0.619100\pi$
$524$		0			0
$525$	−9.42274	+	10.5142i	−0.411242	+	0.458879i
$526$		0			0
$527$	11.9560	−	20.7083i	0.520810	−	0.902070i
$528$		0			0
$529$	8.49375	+	14.7116i	0.369294	+	0.639635i
$530$		0			0
$531$	−1.52611	+	1.11970i	−0.0662277	+	0.0485910i
$532$		0			0
$533$	2.04834	+	3.54783i	0.0887236	+	0.153674i
$534$		0			0
$535$	−0.843977	+	1.46181i	−0.0364883	+	0.0631996i
$536$		0			0
$537$	36.2823	+	7.62361i	1.56570	+	0.328983i
$538$		0			0
$539$	13.2827			0.572126
$540$		0			0
$541$	35.5683			1.52920			0.764600	−	0.644505i	$-0.222936\pi$
$541$	35.5683			1.52920			0.764600	+	0.644505i	$0.222936\pi$
$542$		0			0
$543$	34.6110	+	7.27243i	1.48530	+	0.312090i
$544$		0			0
$545$	−3.37091	+	5.83859i	−0.144394	+	0.250098i
$546$		0			0
$547$	−2.95765	−	5.12281i	−0.126460	−	0.219035i	0.795843	−	0.605504i	$-0.207028\pi$
$547$	−2.95765	−	5.12281i	−0.126460	−	0.219035i	−0.922303	+	0.386468i	$0.873695\pi$
$548$		0			0
$549$	0.364258	+	3.31674i	0.0155462	+	0.141555i
$550$		0			0
$551$	15.9115	+	27.5595i	0.677853	+	1.17408i
$552$		0			0
$553$	3.30324	−	5.72138i	0.140468	−	0.243298i
$554$		0			0
$555$	−9.10148	+	10.1558i	−0.386336	+	0.431088i
$556$		0			0
$557$	31.9707			1.35464			0.677320	−	0.735689i	$-0.263141\pi$
$557$	31.9707			1.35464			0.677320	+	0.735689i	$0.263141\pi$
$558$		0			0
$559$	−9.50227			−0.401903
$560$		0			0
$561$	−7.94802	−	24.2687i	−0.335566	−	1.02462i
$562$		0			0
$563$	15.0985	−	26.1514i	0.636326	−	1.10215i	−0.349906	−	0.936785i	$-0.613787\pi$
$563$	15.0985	−	26.1514i	0.636326	−	1.10215i	0.986232	−	0.165365i	$-0.0528801\pi$
$564$		0			0
$565$	−7.04048	−	12.1945i	−0.296195	−	0.513025i
$566$		0			0
$567$	4.87680	−	15.5000i	0.204807	−	0.650938i
$568$		0			0
$569$	2.85197	+	4.93976i	0.119561	+	0.207086i	0.919594	−	0.392871i	$-0.128518\pi$
$569$	2.85197	+	4.93976i	0.119561	+	0.207086i	−0.800033	+	0.599956i	$0.795185\pi$
$570$		0			0
$571$	8.84404	−	15.3183i	0.370112	−	0.641052i	−0.619471	−	0.785020i	$-0.712653\pi$
$571$	8.84404	−	15.3183i	0.370112	−	0.641052i	0.989582	+	0.143968i	$0.0459861\pi$
$572$		0			0
$573$	−8.44447	−	25.7845i	−0.352773	−	1.07716i
$574$		0			0
$575$	11.0707			0.461680
$576$		0			0
$577$	−10.1515			−0.422612			−0.211306	−	0.977420i	$-0.567772\pi$
$577$	−10.1515			−0.422612			−0.211306	+	0.977420i	$0.567772\pi$
$578$		0			0
$579$	5.98846	−	6.68215i	0.248872	−	0.277701i
$580$		0			0
$581$	2.43504	−	4.21761i	0.101022	−	0.174976i
$582$		0			0
$583$	10.0981	+	17.4904i	0.418221	+	0.724380i
$584$		0			0
$585$	0.228105	+	2.07700i	0.00943100	+	0.0858735i
$586$		0			0
$587$	−9.67084	−	16.7504i	−0.399158	−	0.691362i	0.594464	−	0.804122i	$-0.297364\pi$
$587$	−9.67084	−	16.7504i	−0.399158	−	0.691362i	−0.993622	+	0.112760i	$0.964031\pi$
$588$		0			0
$589$	−11.3032	+	19.5777i	−0.465739	+	0.806684i
$590$		0			0
$591$	8.38075	+	1.76096i	0.344738	+	0.0724361i
$592$		0			0
$593$	−42.4280			−1.74231			−0.871155	−	0.491008i	$-0.836629\pi$
$593$	−42.4280			−1.74231			−0.871155	+	0.491008i	$0.836629\pi$
$594$		0			0
$595$	−5.22083			−0.214033
$596$		0			0
$597$	−30.9392	−	6.50092i	−1.26626	−	0.266065i
$598$		0			0
$599$	−0.259848	+	0.450070i	−0.0106171	+	0.0183894i	−0.871285	−	0.490777i	$-0.836713\pi$
$599$	−0.259848	+	0.450070i	−0.0106171	+	0.0183894i	0.860668	+	0.509166i	$0.170046\pi$
$600$		0			0
$601$	3.78973	+	6.56400i	0.154586	+	0.267751i	0.932908	−	0.360114i	$-0.117262\pi$
$601$	3.78973	+	6.56400i	0.154586	+	0.267751i	−0.778322	+	0.627865i	$0.783929\pi$
$602$		0			0
$603$	34.1108	−	25.0270i	1.38910	−	1.01918i
$604$		0			0
$605$	0.561043	+	0.971754i	0.0228096	+	0.0395074i
$606$		0			0
$607$	−6.44836	+	11.1689i	−0.261731	+	0.453331i	−0.966702	−	0.255905i	$-0.917627\pi$
$607$	−6.44836	+	11.1689i	−0.261731	+	0.453331i	0.704971	+	0.709236i	$0.250960\pi$
$608$		0			0
$609$	16.9208	−	18.8809i	0.685666	−	0.765091i
$610$		0			0
$611$	12.1812			0.492799
$612$		0			0
$613$	−11.2150			−0.452970			−0.226485	−	0.974015i	$-0.572723\pi$
$613$	−11.2150			−0.452970			−0.226485	+	0.974015i	$0.572723\pi$
$614$		0			0
$615$	1.53816	+	4.69665i	0.0620245	+	0.189387i
$616$		0			0
$617$	−13.8094	+	23.9186i	−0.555946	+	0.962927i	0.441883	+	0.897073i	$0.354311\pi$
$617$	−13.8094	+	23.9186i	−0.555946	+	0.962927i	−0.997829	+	0.0658541i	$0.979023\pi$
$618$		0			0
$619$	−13.1002	−	22.6903i	−0.526543	−	0.911999i	−0.999522	−	0.0309249i	$-0.990155\pi$
$619$	−13.1002	−	22.6903i	−0.526543	−	0.911999i	0.472979	−	0.881074i	$-0.343179\pi$
$620$		0			0
$621$	−11.6031	+	5.26364i	−0.465616	+	0.211223i
$622$		0			0
$623$	6.35915	+	11.0144i	0.254774	+	0.441281i
$624$		0			0
$625$	−8.97935	+	15.5527i	−0.359174	+	0.622108i
$626$		0			0
$627$	7.51406	+	22.9436i	0.300083	+	0.916280i
$628$		0			0
$629$	46.9336			1.87136
$630$		0			0
$631$	−5.06798			−0.201753			−0.100876	−	0.994899i	$-0.532165\pi$
$631$	−5.06798			−0.201753			−0.100876	+	0.994899i	$0.532165\pi$
$632$		0			0
$633$	18.5922	−	20.7459i	0.738973	−	0.824574i
$634$		0			0
$635$	1.02070	−	1.76790i	0.0405051	−	0.0701569i
$636$		0			0
$637$	1.87017	+	3.23923i	0.0740988	+	0.128343i
$638$		0			0
$639$	13.3299	+	5.86049i	0.527324	+	0.231837i
$640$		0			0
$641$	−17.9428	−	31.0778i	−0.708698	−	1.22750i	−0.965340	−	0.260994i	$-0.915950\pi$
$641$	−17.9428	−	31.0778i	−0.708698	−	1.22750i	0.256643	−	0.966506i	$-0.417384\pi$
$642$		0			0
$643$	−13.8261	+	23.9475i	−0.545248	+	0.944398i	0.453343	+	0.891336i	$0.350231\pi$
$643$	−13.8261	+	23.9475i	−0.545248	+	0.944398i	−0.998591	+	0.0530617i	$0.983102\pi$
$644$		0			0
$645$	−11.2183	−	2.35717i	−0.441719	−	0.0928137i
$646$		0			0
$647$	−47.7112			−1.87572			−0.937860	−	0.347014i	$-0.887195\pi$
$647$	−47.7112			−1.87572			−0.937860	+	0.347014i	$0.887195\pi$
$648$		0			0
$649$	−2.24059			−0.0879510
$650$		0			0
$651$	17.6257	+	3.70350i	0.690805	+	0.145151i
$652$		0			0
$653$	−23.3713	+	40.4804i	−0.914591	+	1.58412i	−0.107093	+	0.994249i	$0.534154\pi$
$653$	−23.3713	+	40.4804i	−0.914591	+	1.58412i	−0.807498	+	0.589870i	$0.799179\pi$
$654$		0			0
$655$	−2.28388	−	3.95580i	−0.0892387	−	0.154566i
$656$		0			0
$657$	−0.515409	−	0.226599i	−0.0201080	−	0.00884048i
$658$		0			0
$659$	14.4402	+	25.0112i	0.562511	+	0.974298i	0.997276	+	0.0737540i	$0.0234980\pi$
$659$	14.4402	+	25.0112i	0.562511	+	0.974298i	−0.434765	+	0.900544i	$0.643169\pi$
$660$		0			0
$661$	23.7801	−	41.1884i	0.924939	−	1.60204i	0.133281	−	0.991078i	$-0.457449\pi$
$661$	23.7801	−	41.1884i	0.924939	−	1.60204i	0.791659	−	0.610964i	$-0.209218\pi$
$662$		0			0
$663$	4.79930	−	5.35523i	0.186389	−	0.207980i
$664$		0			0
$665$	4.93578			0.191401
$666$		0			0
$667$	−19.8801			−0.769761
$668$		0			0
$669$	3.41607	+	10.4307i	0.132073	+	0.403275i
$670$		0			0
$671$	−1.97487	+	3.42057i	−0.0762390	+	0.132050i
$672$		0			0
$673$	−0.252044	−	0.436553i	−0.00971558	−	0.0168279i	0.861127	−	0.508390i	$-0.169759\pi$
$673$	−0.252044	−	0.436553i	−0.00971558	−	0.0168279i	−0.870842	+	0.491562i	$0.836426\pi$
$674$		0			0
$675$	2.28888	−	23.3481i	0.0880991	−	0.898670i
$676$		0			0
$677$	15.6821	+	27.1623i	0.602714	+	1.04393i	0.992408	+	0.122987i	$0.0392473\pi$
$677$	15.6821	+	27.1623i	0.602714	+	1.04393i	−0.389694	+	0.920944i	$0.627419\pi$
$678$		0			0
$679$	12.5630	−	21.7597i	0.482124	−	0.835062i
$680$		0			0
$681$	−6.68520	−	20.4127i	−0.256177	−	0.782218i
$682$		0			0
$683$	−30.0446			−1.14962			−0.574812	−	0.818286i	$-0.694925\pi$
$683$	−30.0446			−1.14962			−0.574812	+	0.818286i	$0.694925\pi$
$684$		0			0
$685$	−11.3928			−0.435295
$686$		0			0
$687$	12.0579	−	13.4546i	0.460037	−	0.513326i
$688$		0			0
$689$	−2.84357	+	4.92521i	−0.108332	+	0.187636i
$690$		0			0
$691$	2.61256	+	4.52508i	0.0993864	+	0.172142i	0.911431	−	0.411453i	$-0.134979\pi$
$691$	2.61256	+	4.52508i	0.0993864	+	0.172142i	−0.812044	+	0.583596i	$0.801645\pi$
$692$		0			0
$693$	15.5082	−	11.3783i	0.589107	−	0.432226i
$694$		0			0
$695$	7.40844	+	12.8318i	0.281018	+	0.486738i
$696$		0			0
$697$	8.50427	−	14.7298i	0.322122	−	0.557932i
$698$		0			0
$699$	−3.32609	−	0.698875i	−0.125804	−	0.0264339i
$700$		0			0
$701$	27.5913			1.04211			0.521054	−	0.853524i	$-0.325539\pi$
$701$	27.5913			1.04211			0.521054	+	0.853524i	$0.325539\pi$
$702$		0			0
$703$	−44.3710			−1.67348
$704$		0			0
$705$	14.3810	+	3.02172i	0.541620	+	0.113805i
$706$		0			0
$707$	−6.66654	+	11.5468i	−0.250721	+	0.434261i
$708$		0			0
$709$	−6.58122	−	11.3990i	−0.247163	−	0.428099i	0.715575	−	0.698536i	$-0.246165\pi$
$709$	−6.58122	−	11.3990i	−0.247163	−	0.428099i	−0.962738	+	0.270438i	$0.912832\pi$
$710$		0			0
$711$	1.19839	+	10.9119i	0.0449433	+	0.409229i
$712$		0			0
$713$	−7.06119	−	12.2303i	−0.264444	−	0.458030i
$714$		0			0
$715$	−1.23670	+	2.14203i	−0.0462500	+	0.0801074i
$716$		0			0
$717$	−20.2818	+	22.6312i	−0.757439	+	0.845179i
$718$		0			0
$719$	−16.5971			−0.618969			−0.309484	−	0.950905i	$-0.600156\pi$
$719$	−16.5971			−0.618969			−0.309484	+	0.950905i	$0.600156\pi$
$720$		0			0
$721$	−14.6732			−0.546457
$722$		0			0
$723$	−8.64690	−	26.4027i	−0.321582	−	0.981926i
$724$		0			0
$725$	18.3024	−	31.7007i	0.679735	−	1.17734i
$726$		0			0
$727$	4.63973	+	8.03625i	0.172078	+	0.298048i	0.939146	−	0.343518i	$-0.111619\pi$
$727$	4.63973	+	8.03625i	0.172078	+	0.298048i	−0.767068	+	0.641566i	$0.778285\pi$
$728$		0			0
$729$	8.70209	+	25.5592i	0.322300	+	0.946638i
$730$		0			0
$731$	19.7257	+	34.1659i	0.729580	+	1.26367i
$732$		0			0
$733$	−11.5406	+	19.9888i	−0.426260	+	0.738304i	−0.996537	−	0.0831483i	$-0.973502\pi$
$733$	−11.5406	+	19.9888i	−0.426260	+	0.738304i	0.570277	+	0.821452i	$0.306836\pi$
$734$		0			0
$735$	1.40436	+	4.28812i	0.0518007	+	0.158170i
$736$		0			0
$737$	50.0805			1.84474
$738$		0			0
$739$	−53.0459			−1.95132			−0.975662	−	0.219279i	$-0.929629\pi$
$739$	−53.0459			−1.95132			−0.975662	+	0.219279i	$0.929629\pi$
$740$		0			0
$741$	−4.53726	+	5.06284i	−0.166680	+	0.185988i
$742$		0			0
$743$	15.3325	−	26.5567i	0.562495	−	0.974270i	−0.434783	−	0.900535i	$-0.643175\pi$
$743$	15.3325	−	26.5567i	0.562495	−	0.974270i	0.997278	−	0.0737346i	$-0.0234918\pi$
$744$		0			0
$745$	5.71147	+	9.89255i	0.209252	+	0.362435i
$746$		0			0
$747$	0.883417	+	8.04391i	0.0323225	+	0.294311i
$748$		0			0
$749$	2.18775	+	3.78929i	0.0799387	+	0.138458i
$750$		0			0
$751$	−5.26530	+	9.11977i	−0.192134	+	0.332785i	−0.945957	−	0.324292i	$-0.894874\pi$
$751$	−5.26530	+	9.11977i	−0.192134	+	0.332785i	0.753823	+	0.657077i	$0.228207\pi$
$752$		0			0
$753$	−4.60744	−	0.968111i	−0.167904	−	0.0352799i
$754$		0			0
$755$	7.29765			0.265589
$756$		0			0
$757$	3.52510			0.128122			0.0640610	−	0.997946i	$-0.479595\pi$
$757$	3.52510			0.128122			0.0640610	+	0.997946i	$0.479595\pi$
$758$		0			0
$759$	−14.7599	−	3.10133i	−0.535749	−	0.112571i
$760$		0			0
$761$	−9.56064	+	16.5595i	−0.346573	+	0.600282i	−0.985638	−	0.168871i	$-0.945988\pi$
$761$	−9.56064	+	16.5595i	−0.346573	+	0.600282i	0.639065	+	0.769152i	$0.279321\pi$
$762$		0			0
$763$	8.73804	+	15.1347i	0.316338	+	0.547914i
$764$		0			0
$765$	6.99444	−	5.13179i	0.252884	−	0.185540i
$766$		0			0
$767$	−0.315470	−	0.546410i	−0.0113910	−	0.0197297i
$768$		0			0
$769$	12.0960	−	20.9509i	0.436194	−	0.755510i	−0.561199	−	0.827681i	$-0.689660\pi$
$769$	12.0960	−	20.9509i	0.436194	−	0.755510i	0.997392	+	0.0721716i	$0.0229929\pi$
$770$		0			0
$771$	0.772417	−	0.861891i	0.0278179	−	0.0310402i
$772$		0			0
$773$	−13.1466			−0.472851			−0.236425	−	0.971650i	$-0.575976\pi$
$773$	−13.1466			−0.472851			−0.236425	+	0.971650i	$0.575976\pi$
$774$		0			0
$775$	26.0033			0.934065
$776$		0			0
$777$	11.0023	+	33.5948i	0.394706	+	1.20521i
$778$		0			0
$779$	−8.03994	+	13.9256i	−0.288061	+	0.498936i
$780$		0			0
$781$	8.61837	+	14.9275i	0.308390	+	0.534147i
$782$		0			0
$783$	−4.11024	+	41.9273i	−0.146888	+	1.49836i
$784$		0			0
$785$	1.44729	+	2.50678i	0.0516560	+	0.0894707i
$786$		0			0
$787$	26.4594	−	45.8289i	0.943174	−	1.63363i	0.183807	−	0.982962i	$-0.441158\pi$
$787$	26.4594	−	45.8289i	0.943174	−	1.63363i	0.759367	−	0.650663i	$-0.225509\pi$
$788$		0			0
$789$	−12.7737	−	39.0035i	−0.454756	−	1.38856i
$790$		0			0
$791$	−36.5005			−1.29781
$792$		0			0
$793$	−1.11223			−0.0394963
$794$		0			0
$795$	−4.57886	+	5.10926i	−0.162395	+	0.181207i
$796$		0			0
$797$	−1.94357	+	3.36637i	−0.0688449	+	0.119243i	−0.898393	−	0.439192i	$-0.855265\pi$
$797$	−1.94357	+	3.36637i	−0.0688449	+	0.119243i	0.829548	+	0.558435i	$0.188598\pi$
$798$		0			0
$799$	−25.2869	−	43.7981i	−0.894585	−	1.54947i
$800$		0			0
$801$	−19.3460	−	8.50544i	−0.683557	−	0.300525i
$802$		0			0
$803$	−0.333234	−	0.577179i	−0.0117596	−	0.0203682i
$804$		0			0
$805$	−1.54171	+	2.67032i	−0.0543382	+	0.0941165i
$806$		0			0
$807$	0.571399	+	0.120062i	0.0201142	+	0.00422638i
$808$		0			0
$809$	−42.6227			−1.49854			−0.749268	−	0.662267i	$-0.769594\pi$
$809$	−42.6227			−1.49854			−0.749268	+	0.662267i	$0.769594\pi$
$810$		0			0
$811$	−6.30097			−0.221257			−0.110629	−	0.993862i	$-0.535286\pi$
$811$	−6.30097			−0.221257			−0.110629	+	0.993862i	$0.535286\pi$
$812$		0			0
$813$	12.3301	+	2.59079i	0.432436	+	0.0908631i
$814$		0			0
$815$	3.74227	−	6.48180i	0.131086	−	0.227048i
$816$		0			0
$817$	−18.6486	−	32.3004i	−0.652434	−	1.13005i
$818$		0			0
$819$	4.95832	+	2.17992i	0.173258	+	0.0761725i
$820$		0			0
$821$	8.21531	+	14.2293i	0.286716	+	0.496607i	0.973024	−	0.230704i	$-0.0741030\pi$
$821$	8.21531	+	14.2293i	0.286716	+	0.496607i	−0.686308	+	0.727311i	$0.740770\pi$
$822$		0			0
$823$	−11.0820	+	19.1946i	−0.386295	+	0.669083i	−0.991948	−	0.126646i	$-0.959579\pi$
$823$	−11.0820	+	19.1946i	−0.386295	+	0.669083i	0.605653	+	0.795729i	$0.292912\pi$
$824$		0			0
$825$	18.5339	−	20.6808i	0.645267	−	0.720013i
$826$		0			0
$827$	−7.17190			−0.249392			−0.124696	−	0.992195i	$-0.539795\pi$
$827$	−7.17190			−0.249392			−0.124696	+	0.992195i	$0.539795\pi$
$828$		0			0
$829$	34.2513			1.18960			0.594799	−	0.803875i	$-0.297232\pi$
$829$	34.2513			1.18960			0.594799	+	0.803875i	$0.297232\pi$
$830$		0			0
$831$	−10.8686	−	33.1865i	−0.377027	−	1.15123i
$832$		0			0
$833$	7.76453	−	13.4486i	0.269025	−	0.465965i
$834$		0			0
$835$	−0.0726002	−	0.125747i	−0.00251243	−	0.00435166i
$836$		0			0
$837$	−27.2538	+	12.3634i	−0.942028	+	0.427343i
$838$		0			0
$839$	−18.2783	−	31.6590i	−0.631038	−	1.09299i	−0.987340	−	0.158619i	$-0.949296\pi$
$839$	−18.2783	−	31.6590i	−0.631038	−	1.09299i	0.356302	−	0.934371i	$-0.384037\pi$
$840$		0			0
$841$	−18.3665	+	31.8116i	−0.633326	+	1.09695i
$842$		0			0
$843$	8.02542	+	24.5050i	0.276410	+	0.843997i
$844$		0			0
$845$	−0.696497			−0.0239602
$846$		0			0
$847$	2.90866			0.0999427
$848$		0			0
$849$	−29.1084	+	32.4802i	−0.998997	+	1.11472i
$850$		0			0
$851$	13.8595	−	24.0053i	0.475097	−	0.822891i
$852$		0			0
$853$	−22.6160	−	39.1721i	−0.774358	−	1.34123i	−0.935155	−	0.354240i	$-0.884740\pi$
$853$	−22.6160	−	39.1721i	−0.774358	−	1.34123i	0.160796	−	0.986988i	$-0.448594\pi$
$854$		0			0
$855$	−6.61254	+	4.85160i	−0.226144	+	0.165921i
$856$		0			0
$857$	14.4563	+	25.0390i	0.493817	+	0.855317i	0.999975	−	0.00712441i	$-0.00226779\pi$
$857$	14.4563	+	25.0390i	0.493817	+	0.855317i	−0.506157	+	0.862441i	$0.668934\pi$
$858$		0			0
$859$	−10.3717	+	17.9643i	−0.353878	+	0.612934i	−0.986925	−	0.161179i	$-0.948470\pi$
$859$	−10.3717	+	17.9643i	−0.353878	+	0.612934i	0.633048	+	0.774113i	$0.281804\pi$
$860$		0			0
$861$	12.5371	+	2.63429i	0.427264	+	0.0897764i
$862$		0			0
$863$	−7.76234			−0.264233			−0.132116	−	0.991234i	$-0.542177\pi$
$863$	−7.76234			−0.264233			−0.132116	+	0.991234i	$0.542177\pi$
$864$		0			0
$865$	13.6964			0.465693
$866$		0			0
$867$	−0.402181	−	0.0845060i	−0.0136588	−	0.00286998i
$868$		0			0
$869$	−6.49724	+	11.2536i	−0.220404	+	0.381751i
$870$		0			0
$871$	7.05120	+	12.2130i	0.238921	+	0.413823i
$872$		0			0
$873$	4.55778	+	41.5006i	0.154257	+	1.40458i
$874$		0			0
$875$	−5.98245	−	10.3619i	−0.202244	−	0.350297i
$876$		0			0
$877$	−0.956091	+	1.65600i	−0.0322849	+	0.0559191i	−0.881716	−	0.471780i	$-0.843612\pi$
$877$	−0.956091	+	1.65600i	−0.0322849	+	0.0559191i	0.849432	+	0.527699i	$0.176945\pi$
$878$		0			0
$879$	−23.4173	+	26.1299i	−0.789846	+	0.881340i
$880$		0			0
$881$	−15.5972			−0.525484			−0.262742	−	0.964866i	$-0.584627\pi$
$881$	−15.5972			−0.525484			−0.262742	+	0.964866i	$0.584627\pi$
$882$		0			0
$883$	−42.2610			−1.42220			−0.711098	−	0.703093i	$-0.751802\pi$
$883$	−42.2610			−1.42220			−0.711098	+	0.703093i	$0.751802\pi$
$884$		0			0
$885$	−0.236895	−	0.723342i	−0.00796314	−	0.0243149i
$886$		0			0
$887$	−20.0105	+	34.6592i	−0.671886	+	1.16374i	0.305483	+	0.952198i	$0.401182\pi$
$887$	−20.0105	+	34.6592i	−0.671886	+	1.16374i	−0.977369	+	0.211543i	$0.932151\pi$
$888$		0			0
$889$	−2.64584	−	4.58273i	−0.0887386	−	0.153700i
$890$		0			0
$891$	−9.59234	+	30.4874i	−0.321356	+	1.02137i
$892$		0			0
$893$	23.9062	+	41.4067i	0.799990	+	1.38562i
$894$		0			0
$895$	−7.45427	+	12.9112i	−0.249169	+	0.431573i
$896$		0			0
$897$	−1.32183	−	4.03612i	−0.0441347	−	0.134762i
$898$		0			0
$899$	−46.6952			−1.55737
$900$		0			0
$901$	23.6118			0.786622
$902$		0			0
$903$	−19.8316	+	22.1288i	−0.659954	+	0.736401i
$904$		0			0
$905$	−7.11089	+	12.3164i	−0.236374	+	0.409412i
$906$		0			0
$907$	20.7794	+	35.9909i	0.689968	+	1.19506i	0.971848	+	0.235609i	$0.0757086\pi$
$907$	20.7794	+	35.9909i	0.689968	+	1.19506i	−0.281880	+	0.959450i	$0.590958\pi$
$908$		0			0
$909$	−2.41858	−	22.0223i	−0.0802192	−	0.730432i
$910$		0			0
$911$	10.8960	+	18.8723i	0.360999	+	0.625269i	0.988126	−	0.153649i	$-0.0491025\pi$
$911$	10.8960	+	18.8723i	0.360999	+	0.625269i	−0.627127	+	0.778917i	$0.715769\pi$
$912$		0			0
$913$	−4.78955	+	8.29575i	−0.158511	+	0.274549i
$914$		0			0
$915$	−1.31308	−	0.275904i	−0.0434091	−	0.00912109i
$916$		0			0
$917$	−11.8405			−0.391008
$918$		0			0
$919$	−35.2425			−1.16254			−0.581271	−	0.813710i	$-0.697445\pi$
$919$	−35.2425			−1.16254			−0.581271	+	0.813710i	$0.697445\pi$
$920$		0			0
$921$	−19.9679	−	4.19564i	−0.657964	−	0.138251i
$922$		0			0
$923$	−2.42689	+	4.20349i	−0.0798820	+	0.138360i
$924$		0			0
$925$	25.5192	+	44.2005i	0.839065	+	1.45330i
$926$		0			0
$927$	19.6579	−	14.4229i	0.645649	−	0.473710i
$928$		0			0
$929$	15.0106	+	25.9991i	0.492481	+	0.853002i	0.999962	−	0.00866066i	$-0.00275681\pi$
$929$	15.0106	+	25.9991i	0.492481	+	0.853002i	−0.507482	+	0.861663i	$0.669423\pi$
$930$		0			0
$931$	−7.34059	+	12.7143i	−0.240578	+	0.416693i
$932$		0			0
$933$	−19.4506	+	21.7037i	−0.636786	+	0.710549i
$934$		0			0
$935$	10.2690			0.335833
$936$		0			0
$937$	51.2435			1.67405			0.837026	−	0.547163i	$-0.184292\pi$
$937$	51.2435			1.67405			0.837026	+	0.547163i	$0.184292\pi$
$938$		0			0
$939$	−8.86358	−	27.0643i	−0.289252	−	0.883210i
$940$		0			0
$941$	2.04301	−	3.53860i	0.0666002	−	0.115355i	−0.830802	−	0.556567i	$-0.812118\pi$
$941$	2.04301	−	3.53860i	0.0666002	−	0.115355i	0.897403	+	0.441212i	$0.145451\pi$
$942$		0			0
$943$	−5.02262	−	8.69943i	−0.163559	−	0.283292i
$944$		0			0
$945$	5.31297	+	3.80357i	0.172831	+	0.123730i
$946$		0			0
$947$	−17.3466	−	30.0453i	−0.563690	−	0.976340i	−0.997170	−	0.0751770i	$-0.976048\pi$
$947$	−17.3466	−	30.0453i	−0.563690	−	0.976340i	0.433480	−	0.901163i	$-0.357286\pi$
$948$		0			0
$949$	0.0938370	−	0.162531i	0.00304608	−	0.00527596i
$950$		0			0
$951$	7.49683	+	22.8910i	0.243101	+	0.742291i
$952$		0			0
$953$	0.656353			0.0212614			0.0106307	−	0.999943i	$-0.496616\pi$
$953$	0.656353			0.0212614			0.0106307	+	0.999943i	$0.496616\pi$
$954$		0			0
$955$	10.9104			0.353054
$956$		0			0
$957$	−33.2821	+	37.1374i	−1.07586	+	1.20048i
$958$		0			0
$959$	−14.7661	+	25.5757i	−0.476823	+	0.825881i
$960$		0			0
$961$	−1.08559	−	1.88030i	−0.0350191	−	0.0606549i
$962$		0			0
$963$	−6.65564	−	2.92614i	−0.214475	−	0.0942937i
$964$		0			0
$965$	1.80410	+	3.12480i	0.0580761	+	0.100591i
$966$		0			0
$967$	−18.4643	+	31.9812i	−0.593773	+	1.02845i	0.399946	+	0.916539i	$0.369029\pi$
$967$	−18.4643	+	31.9812i	−0.593773	+	1.02845i	−0.993719	+	0.111906i	$0.964304\pi$
$968$		0			0
$969$	27.6225	+	5.80402i	0.887363	+	0.186452i
$970$		0			0
$971$	29.2096			0.937379			0.468690	−	0.883363i	$-0.344726\pi$
$971$	29.2096			0.937379			0.468690	+	0.883363i	$0.344726\pi$
$972$		0			0
$973$	38.4082			1.23131
$974$		0			0
$975$	7.65291	+	1.60802i	0.245089	+	0.0514980i
$976$		0			0
$977$	−3.90425	+	6.76235i	−0.124908	+	0.216347i	−0.921697	−	0.387911i	$-0.873197\pi$
$977$	−3.90425	+	6.76235i	−0.124908	+	0.216347i	0.796789	+	0.604258i	$0.206530\pi$
$978$		0			0
$979$	−12.5080	−	21.6645i	−0.399758	−	0.692401i
$980$		0			0
$981$	−26.5831	−	11.6872i	−0.848734	−	0.373145i
$982$		0			0
$983$	−21.8145	−	37.7839i	−0.695775	−	1.20512i	−0.969919	−	0.243429i	$-0.921728\pi$
$983$	−21.8145	−	37.7839i	−0.695775	−	1.20512i	0.274143	−	0.961689i	$-0.411606\pi$
$984$		0			0
$985$	−1.72184	+	2.98232i	−0.0548624	+	0.0950245i
$986$		0			0
$987$	25.4226	−	28.3675i	0.809211	−	0.902947i
$988$		0			0
$989$	23.2999			0.740895
$990$		0			0
$991$	−1.46775			−0.0466247			−0.0233123	−	0.999728i	$-0.507421\pi$
$991$	−1.46775			−0.0466247			−0.0233123	+	0.999728i	$0.507421\pi$
$992$		0			0
$993$	−11.0219	−	33.6546i	−0.349770	−	1.06800i
$994$		0			0
$995$	6.35652	−	11.0098i	0.201515	−	0.349034i
$996$		0			0
$997$	−12.9705	−	22.4655i	−0.410779	−	0.711489i	0.584197	−	0.811612i	$-0.301410\pi$
$997$	−12.9705	−	22.4655i	−0.410779	−	0.711489i	−0.994975	+	0.100123i	$0.968076\pi$
$998$		0			0
$999$	−47.7618	−	34.1928i	−1.51112	−	1.08181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.d.625.2	yes	12
3.2	odd	2		2808.2.q.d.1873.3		12
9.2	odd	6		2808.2.q.d.937.3		12
9.4	even	3		8424.2.a.v.1.3		6
9.5	odd	6		8424.2.a.u.1.4		6
9.7	even	3	inner	936.2.q.d.313.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.d.313.2	✓	12	9.7	even	3	inner
936.2.q.d.625.2	yes	12	1.1	even	1	trivial
2808.2.q.d.937.3		12	9.2	odd	6
2808.2.q.d.1873.3		12	3.2	odd	2
8424.2.a.u.1.4		6	9.5	odd	6
8424.2.a.v.1.3		6	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69504 - 0.356160i) q^{3} +(0.348249 - 0.603184i) q^{5} +(-0.902727 - 1.56357i) q^{7} +(2.74630 + 1.20741i) q^{9} +(1.77560 + 3.07543i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-0.805124 + 0.898387i) q^{15} +4.15178 q^{17} -3.92509 q^{19} +(0.973275 + 2.97182i) q^{21} +(1.22602 - 2.12353i) q^{23} +(2.25745 + 3.91001i) q^{25} +(-4.22505 - 3.02472i) q^{27} +(-4.05379 - 7.02137i) q^{29} +(2.87972 - 4.98782i) q^{31} +(-1.91436 - 5.84537i) q^{33} -1.25749 q^{35} +11.3044 q^{37} +(1.15596 - 1.28987i) q^{39} +(2.04834 - 3.54783i) q^{41} +(4.75114 + 8.22921i) q^{43} +(1.68468 - 1.23605i) q^{45} +(-6.09061 - 10.5492i) q^{47} +(1.87017 - 3.23923i) q^{49} +(-7.03742 - 1.47870i) q^{51} +5.68715 q^{53} +2.47340 q^{55} +(6.65318 + 1.39796i) q^{57} +(-0.315470 + 0.546410i) q^{59} +(0.556113 + 0.963216i) q^{61} +(-0.591293 - 5.38399i) q^{63} +(0.348249 + 0.603184i) q^{65} +(7.05120 - 12.2130i) q^{67} +(-2.83446 + 3.16280i) q^{69} +4.85378 q^{71} -0.187674 q^{73} +(-2.43386 - 7.43162i) q^{75} +(3.20577 - 5.55255i) q^{77} +(1.82959 + 3.16894i) q^{79} +(6.08433 + 6.63181i) q^{81} +(1.34871 + 2.33604i) q^{83} +(1.44585 - 2.50429i) q^{85} +(4.37060 + 13.3453i) q^{87} -7.04438 q^{89} +1.80545 q^{91} +(-6.65770 + 7.42890i) q^{93} +(-1.36691 + 2.36755i) q^{95} +(6.95836 + 12.0522i) q^{97} +(1.16303 + 10.5899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - q^{5} + 2 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 12 q^{17} - 14 q^{19} - 24 q^{21} + 19 q^{23} + 5 q^{25} - 7 q^{27} - 2 q^{29} + 8 q^{31} - 9 q^{33} + 2 q^{35} - 34 q^{37}+ \cdots - 39 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 - q^5 + 2 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - 2 * q^15 + 12 * q^17 - 14 * q^19 - 24 * q^21 + 19 * q^23 + 5 * q^25 - 7 * q^27 - 2 * q^29 + 8 * q^31 - 9 * q^33 + 2 * q^35 - 34 * q^37 - q^39 - 2 * q^41 + 15 * q^43 + 10 * q^45 - 9 * q^47 + 12 * q^49 + 4 * q^51 + 32 * q^53 - 10 * q^55 - 14 * q^57 + 5 * q^59 + 6 * q^61 + 18 * q^63 - q^65 + 8 * q^67 + 15 * q^69 - 42 * q^71 - 2 * q^73 + 10 * q^75 + 3 * q^77 + 34 * q^79 + 62 * q^81 + 44 * q^83 + 7 * q^85 - 21 * q^87 + 22 * q^89 - 4 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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