LMFDB - Embedded newform 336.2.bj.f.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(95,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("336.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.1
Root			$-1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	336.191
Dual form			336.2.bj.f.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26217 - 1.18614i) q^{3} +(2.87228 + 1.65831i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+(-1.26217 - 1.18614i) q^{3} +(2.87228 + 1.65831i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.186141 + 2.99422i) q^{9} +(1.65831 + 2.87228i) q^{11} -4.00000 q^{13} +(-1.65831 - 5.50000i) q^{15} +(2.87228 - 1.65831i) q^{17} +(6.06218 + 3.50000i) q^{19} +(4.55842 - 0.469882i) q^{21} +(1.65831 - 2.87228i) q^{23} +(3.00000 + 5.19615i) q^{25} +(3.31662 - 4.00000i) q^{27} +6.63325i q^{29} +(-2.59808 + 1.50000i) q^{31} +(1.31386 - 5.59230i) q^{33} +(-8.29156 + 2.87228i) q^{35} +(0.500000 - 0.866025i) q^{37} +(5.04868 + 4.74456i) q^{39} -6.63325i q^{41} +2.00000i q^{43} +(-4.43070 + 8.90892i) q^{45} +(4.97494 - 8.61684i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-5.59230 - 1.31386i) q^{51} +(-2.87228 + 1.65831i) q^{53} +11.0000i q^{55} +(-3.50000 - 11.6082i) q^{57} +(-1.65831 - 2.87228i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-6.31084 - 4.81386i) q^{63} +(-11.4891 - 6.63325i) q^{65} +(-7.79423 + 4.50000i) q^{67} +(-5.50000 + 1.65831i) q^{69} -13.2665 q^{71} +(-3.50000 - 6.06218i) q^{73} +(2.37686 - 10.1168i) q^{75} +(-8.61684 - 1.65831i) q^{77} +(7.79423 + 4.50000i) q^{79} +(-8.93070 + 1.11469i) q^{81} +13.2665 q^{83} +11.0000 q^{85} +(7.86797 - 8.37228i) q^{87} +(-2.87228 - 1.65831i) q^{89} +(6.92820 - 8.00000i) q^{91} +(5.05842 + 1.18843i) q^{93} +(11.6082 + 20.1060i) q^{95} +8.00000 q^{97} +(-8.29156 + 5.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{9}+O(q^{10}) $ 8 * q - 10 * q^9	$ 8 q - 10 q^{9} - 32 q^{13} + 2 q^{21} + 24 q^{25} + 22 q^{33} + 4 q^{37} + 22 q^{45} - 8 q^{49} - 28 q^{57} - 12 q^{61} - 44 q^{69} - 28 q^{73} - 14 q^{81} + 88 q^{85} + 6 q^{93} + 64 q^{97}+O(q^{100}) $ 8 * q - 10 * q^9 - 32 * q^13 + 2 * q^21 + 24 * q^25 + 22 * q^33 + 4 * q^37 + 22 * q^45 - 8 * q^49 - 28 * q^57 - 12 * q^61 - 44 * q^69 - 28 * q^73 - 14 * q^81 + 88 * q^85 + 6 * q^93 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.26217	−	1.18614i	−0.728714	−	0.684819i
$3$	−1.26217	−	1.18614i	−0.728714	−	0.684819i
$4$		0			0
$5$	2.87228	+	1.65831i	1.28452	+	0.741620i	0.977672	−	0.210138i	$-0.0673912\pi$
$5$	2.87228	+	1.65831i	1.28452	+	0.741620i	0.306851	+	0.951757i	$0.400725\pi$
$6$		0			0
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		0			0
$9$	0.186141	+	2.99422i	0.0620469	+	0.998073i
$10$		0			0
$11$	1.65831	+	2.87228i	0.500000	+	0.866025i	1.00000			$0$
$11$	1.65831	+	2.87228i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	−1.65831	−	5.50000i	−0.428174	−	1.42009i
$16$		0			0
$17$	2.87228	−	1.65831i	0.696631	−	0.402200i	−0.109461	−	0.993991i	$-0.534912\pi$
$17$	2.87228	−	1.65831i	0.696631	−	0.402200i	0.806091	+	0.591791i	$0.201579\pi$
$18$		0			0
$19$	6.06218	+	3.50000i	1.39076	+	0.802955i	0.993399	−	0.114708i	$-0.0365932\pi$
$19$	6.06218	+	3.50000i	1.39076	+	0.802955i	0.397360	+	0.917663i	$0.369927\pi$
$20$		0			0
$21$	4.55842	−	0.469882i	0.994729	−	0.102537i
$22$		0			0
$23$	1.65831	−	2.87228i	0.345782	−	0.598912i	−0.639713	−	0.768613i	$-0.720947\pi$
$23$	1.65831	−	2.87228i	0.345782	−	0.598912i	0.985496	+	0.169701i	$0.0542803\pi$
$24$		0			0
$25$	3.00000	+	5.19615i	0.600000	+	1.03923i
$26$		0			0
$27$	3.31662	−	4.00000i	0.638285	−	0.769800i
$28$		0			0
$29$			6.63325i			1.23176i	0.787839	+	0.615882i	$0.211200\pi$
$29$			6.63325i			1.23176i	−0.787839	+	0.615882i	$0.788800\pi$
$30$		0			0
$31$	−2.59808	+	1.50000i	−0.466628	+	0.269408i	−0.714827	−	0.699301i	$-0.753495\pi$
$31$	−2.59808	+	1.50000i	−0.466628	+	0.269408i	0.248199	+	0.968709i	$0.420161\pi$
$32$		0			0
$33$	1.31386	−	5.59230i	0.228714	−	0.973494i
$34$		0			0
$35$	−8.29156	+	2.87228i	−1.40153	+	0.485504i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$	5.04868	+	4.74456i	0.808435	+	0.759738i
$40$		0			0
$41$		−	6.63325i		−	1.03594i	−0.855399	−	0.517970i	$-0.826688\pi$
$41$		−	6.63325i		−	1.03594i	0.855399	−	0.517970i	$-0.173312\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$		0			0
$45$	−4.43070	+	8.90892i	−0.660490	+	1.32806i
$46$		0			0
$47$	4.97494	−	8.61684i	0.725669	−	1.25690i	−0.233029	−	0.972470i	$-0.574864\pi$
$47$	4.97494	−	8.61684i	0.725669	−	1.25690i	0.958698	−	0.284426i	$-0.0918030\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−5.59230	−	1.31386i	−0.783078	−	0.183977i
$52$		0			0
$53$	−2.87228	+	1.65831i	−0.394538	+	0.227787i	−0.684125	−	0.729365i	$-0.739816\pi$
$53$	−2.87228	+	1.65831i	−0.394538	+	0.227787i	0.289586	+	0.957152i	$0.406482\pi$
$54$		0			0
$55$			11.0000i			1.48324i
$56$		0			0
$57$	−3.50000	−	11.6082i	−0.463586	−	1.53754i
$58$		0			0
$59$	−1.65831	−	2.87228i	−0.215894	−	0.373939i	0.737655	−	0.675178i	$-0.235933\pi$
$59$	−1.65831	−	2.87228i	−0.215894	−	0.373939i	−0.953549	+	0.301239i	$0.902600\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$		0			0
$63$	−6.31084	−	4.81386i	−0.795092	−	0.606489i
$64$		0			0
$65$	−11.4891	−	6.63325i	−1.42505	−	0.822753i
$66$		0			0
$67$	−7.79423	+	4.50000i	−0.952217	+	0.549762i	−0.893769	−	0.448528i	$-0.851948\pi$
$67$	−7.79423	+	4.50000i	−0.952217	+	0.549762i	−0.0584478	+	0.998290i	$0.518615\pi$
$68$		0			0
$69$	−5.50000	+	1.65831i	−0.662122	+	0.199637i
$70$		0			0
$71$	−13.2665			−1.57444			−0.787222	−	0.616670i	$-0.788481\pi$
$71$	−13.2665			−1.57444			−0.787222	+	0.616670i	$0.788481\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$	2.37686	−	10.1168i	0.274456	−	1.16819i
$76$		0			0
$77$	−8.61684	−	1.65831i	−0.981981	−	0.188982i
$78$		0			0
$79$	7.79423	+	4.50000i	0.876919	+	0.506290i	0.869641	−	0.493684i	$-0.164350\pi$
$79$	7.79423	+	4.50000i	0.876919	+	0.506290i	0.00727784	+	0.999974i	$0.497683\pi$
$80$		0			0
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$		0			0
$83$	13.2665			1.45619			0.728094	−	0.685478i	$-0.240407\pi$
$83$	13.2665			1.45619			0.728094	+	0.685478i	$0.240407\pi$
$84$		0			0
$85$	11.0000			1.19312
$86$		0			0
$87$	7.86797	−	8.37228i	0.843535	−	0.897603i
$88$		0			0
$89$	−2.87228	−	1.65831i	−0.304461	−	0.175781i	0.339984	−	0.940431i	$-0.389578\pi$
$89$	−2.87228	−	1.65831i	−0.304461	−	0.175781i	−0.644445	+	0.764650i	$0.722912\pi$
$90$		0			0
$91$	6.92820	−	8.00000i	0.726273	−	0.838628i
$92$		0			0
$93$	5.05842	+	1.18843i	0.524534	+	0.123235i
$94$		0			0
$95$	11.6082	+	20.1060i	1.19097	+	2.06283i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−8.29156	+	5.50000i	−0.833333	+	0.552771i
$100$		0			0
$101$	2.87228	−	1.65831i	0.285803	−	0.165008i	−0.350245	−	0.936658i	$-0.613902\pi$
$101$	2.87228	−	1.65831i	0.285803	−	0.165008i	0.636047	+	0.771650i	$0.280568\pi$
$102$		0			0
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.0491146	−	0.998793i	$-0.515640\pi$
$103$	−9.52628	−	5.50000i	−0.938652	−	0.541931i	−0.889538	+	0.456862i	$0.848973\pi$
$104$		0			0
$105$	13.8723	+	6.20965i	1.35380	+	0.606000i
$106$		0			0
$107$	−1.65831	+	2.87228i	−0.160315	+	0.277674i	−0.934982	−	0.354696i	$-0.884584\pi$
$107$	−1.65831	+	2.87228i	−0.160315	+	0.277674i	0.774667	+	0.632370i	$0.217918\pi$
$108$		0			0
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$		0			0
$111$	−1.65831	+	0.500000i	−0.157400	+	0.0474579i
$112$		0			0
$113$			6.63325i			0.624004i	0.950082	+	0.312002i	$0.101000\pi$
$113$			6.63325i			0.624004i	−0.950082	+	0.312002i	$0.899000\pi$
$114$		0			0
$115$	9.52628	−	5.50000i	0.888330	−	0.512878i
$116$		0			0
$117$	−0.744563	−	11.9769i	−0.0688348	−	1.10726i
$118$		0			0
$119$	−1.65831	+	8.61684i	−0.152017	+	0.789905i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−7.86797	+	8.37228i	−0.709431	+	0.754903i
$124$		0			0
$125$			3.31662i			0.296648i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$		0			0
$129$	2.37228	−	2.52434i	0.208868	−	0.222256i
$130$		0			0
$131$	8.29156	−	14.3614i	0.724437	−	1.25476i	−0.234768	−	0.972051i	$-0.575433\pi$
$131$	8.29156	−	14.3614i	0.724437	−	1.25476i	0.959205	−	0.282711i	$-0.0912336\pi$
$132$		0			0
$133$	−17.5000	+	6.06218i	−1.51744	+	0.525657i
$134$		0			0
$135$	16.1595	−	5.98913i	1.39079	−	0.515462i
$136$		0			0
$137$	14.3614	−	8.29156i	1.22698	−	0.708396i	0.260581	−	0.965452i	$-0.416086\pi$
$137$	14.3614	−	8.29156i	1.22698	−	0.708396i	0.966397	+	0.257056i	$0.0827525\pi$
$138$		0			0
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$		0			0
$141$	−16.5000	+	4.97494i	−1.38955	+	0.418965i
$142$		0			0
$143$	−6.63325	−	11.4891i	−0.554700	−	0.960769i
$144$		0			0
$145$	−11.0000	+	19.0526i	−0.913500	+	1.58223i
$146$		0			0
$147$	−6.95565	+	9.93070i	−0.573693	+	0.819071i
$148$		0			0
$149$	14.3614	+	8.29156i	1.17653	+	0.679271i	0.955210	−	0.295929i	$-0.0956293\pi$
$149$	14.3614	+	8.29156i	1.17653	+	0.679271i	0.221322	+	0.975201i	$0.428963\pi$
$150$		0			0
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	−0.725956	−	0.687741i	$-0.758602\pi$
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	0.232623	+	0.972567i	$0.425269\pi$
$152$		0			0
$153$	5.50000	+	8.29156i	0.444649	+	0.670333i
$154$		0			0
$155$	−9.94987			−0.799193
$156$		0			0
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	0.799941	−	0.600079i	$-0.204864\pi$
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	−0.919654	+	0.392730i	$0.871531\pi$
$158$		0			0
$159$	5.59230	+	1.31386i	0.443498	+	0.104196i
$160$		0			0
$161$	2.87228	+	8.29156i	0.226367	+	0.653467i
$162$		0			0
$163$	−6.06218	−	3.50000i	−0.474826	−	0.274141i	0.243432	−	0.969918i	$-0.421727\pi$
$163$	−6.06218	−	3.50000i	−0.474826	−	0.274141i	−0.718258	+	0.695777i	$0.755060\pi$
$164$		0			0
$165$	13.0475	−	13.8839i	1.01575	−	1.08086i
$166$		0			0
$167$	−6.63325			−0.513296			−0.256648	−	0.966505i	$-0.582618\pi$
$167$	−6.63325			−0.513296			−0.256648	+	0.966505i	$0.582618\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−9.35135	+	18.8030i	−0.715116	+	1.43790i
$172$		0			0
$173$	8.61684	+	4.97494i	0.655127	+	0.378237i	0.790418	−	0.612568i	$-0.209864\pi$
$173$	8.61684	+	4.97494i	0.655127	+	0.378237i	−0.135291	+	0.990806i	$0.543197\pi$
$174$		0			0
$175$	−15.5885	−	3.00000i	−1.17838	−	0.226779i
$176$		0			0
$177$	−1.31386	+	5.59230i	−0.0987557	+	0.420343i
$178$		0			0
$179$	1.65831	+	2.87228i	0.123948	+	0.214684i	0.921321	−	0.388802i	$-0.127111\pi$
$179$	1.65831	+	2.87228i	0.123948	+	0.214684i	−0.797373	+	0.603487i	$0.793778\pi$
$180$		0			0
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$	4.97494	−	1.50000i	0.367758	−	0.110883i
$184$		0			0
$185$	2.87228	−	1.65831i	0.211174	−	0.121922i
$186$		0			0
$187$	9.52628	+	5.50000i	0.696631	+	0.402200i
$188$		0			0
$189$	2.25544	+	13.5615i	0.164059	+	0.986451i
$190$		0			0
$191$	4.97494	−	8.61684i	0.359974	−	0.623493i	−0.627982	−	0.778228i	$-0.716119\pi$
$191$	4.97494	−	8.61684i	0.359974	−	0.623493i	0.987956	+	0.154735i	$0.0494523\pi$
$192$		0			0
$193$	1.50000	+	2.59808i	0.107972	+	0.187014i	0.914949	−	0.403570i	$-0.132231\pi$
$193$	1.50000	+	2.59808i	0.107972	+	0.187014i	−0.806976	+	0.590584i	$0.798898\pi$
$194$		0			0
$195$	6.63325	+	22.0000i	0.475017	+	1.57545i
$196$		0			0
$197$		−	19.8997i		−	1.41780i	−0.705310	−	0.708899i	$-0.749192\pi$
$197$		−	19.8997i		−	1.41780i	0.705310	−	0.708899i	$-0.250808\pi$
$198$		0			0
$199$	0.866025	−	0.500000i	0.0613909	−	0.0354441i	−0.468990	−	0.883203i	$-0.655382\pi$
$199$	0.866025	−	0.500000i	0.0613909	−	0.0354441i	0.530381	+	0.847759i	$0.322049\pi$
$200$		0			0
$201$	15.1753	+	3.56529i	1.07038	+	0.251476i
$202$		0			0
$203$	−13.2665	−	11.4891i	−0.931126	−	0.806379i
$204$		0			0
$205$	11.0000	−	19.0526i	0.768273	−	1.33069i
$206$		0			0
$207$	8.90892	+	4.43070i	0.619213	+	0.307955i
$208$		0			0
$209$			23.2164i			1.60591i
$210$		0			0
$211$		−	26.0000i		−	1.78991i	−0.446153	−	0.894957i	$-0.647206\pi$
$211$		−	26.0000i		−	1.78991i	0.446153	−	0.894957i	$-0.352794\pi$
$212$		0			0
$213$	16.7446	+	15.7359i	1.14732	+	1.07821i
$214$		0			0
$215$	−3.31662	+	5.74456i	−0.226192	+	0.391776i
$216$		0			0
$217$	1.50000	−	7.79423i	0.101827	−	0.529107i
$218$		0			0
$219$	−2.77300	+	11.8030i	−0.187382	+	0.797572i
$220$		0			0
$221$	−11.4891	+	6.63325i	−0.772842	+	0.446201i
$222$		0			0
$223$		−	14.0000i		−	0.937509i	−0.883328	−	0.468755i	$-0.844703\pi$
$223$		−	14.0000i		−	0.937509i	0.883328	−	0.468755i	$-0.155297\pi$
$224$		0			0
$225$	−15.0000	+	9.94987i	−1.00000	+	0.663325i
$226$		0			0
$227$	1.65831	+	2.87228i	0.110066	+	0.190640i	0.915797	−	0.401642i	$-0.131560\pi$
$227$	1.65831	+	2.87228i	0.110066	+	0.190640i	−0.805731	+	0.592282i	$0.798227\pi$
$228$		0			0
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.231287	+	0.972886i	$0.574293\pi$
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	8.90892	+	12.3139i	0.586164	+	0.810192i
$232$		0			0
$233$	14.3614	+	8.29156i	0.940847	+	0.543198i	0.890226	−	0.455520i	$-0.150547\pi$
$233$	14.3614	+	8.29156i	0.940847	+	0.543198i	0.0506213	+	0.998718i	$0.483880\pi$
$234$		0			0
$235$	28.5788	−	16.5000i	1.86428	−	1.07634i
$236$		0			0
$237$	−4.50000	−	14.9248i	−0.292306	−	0.969471i
$238$		0			0
$239$	6.63325			0.429069			0.214535	−	0.976716i	$-0.431177\pi$
$239$	6.63325			0.429069			0.214535	+	0.976716i	$0.431177\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$		0			0
$243$	12.5942	+	9.18614i	0.807921	+	0.589291i
$244$		0			0
$245$	8.61684	−	21.5581i	0.550510	−	1.37729i
$246$		0			0
$247$	−24.2487	−	14.0000i	−1.54291	−	0.890799i
$248$		0			0
$249$	−16.7446	−	15.7359i	−1.06114	−	0.997224i
$250$		0			0
$251$	19.8997			1.25606			0.628031	−	0.778189i	$-0.283861\pi$
$251$	19.8997			1.25606			0.628031	+	0.778189i	$0.283861\pi$
$252$		0			0
$253$	11.0000			0.691564
$254$		0			0
$255$	−13.8839	−	13.0475i	−0.869441	−	0.817069i
$256$		0			0
$257$	−20.1060	−	11.6082i	−1.25418	−	0.724099i	−0.282240	−	0.959344i	$-0.591077\pi$
$257$	−20.1060	−	11.6082i	−1.25418	−	0.724099i	−0.971936	+	0.235245i	$0.924411\pi$
$258$		0			0
$259$	0.866025	+	2.50000i	0.0538122	+	0.155342i
$260$		0			0
$261$	−19.8614	+	1.23472i	−1.22939	+	0.0764271i
$262$		0			0
$263$	−1.65831	−	2.87228i	−0.102256	−	0.177112i	0.810358	−	0.585935i	$-0.199273\pi$
$263$	−1.65831	−	2.87228i	−0.102256	−	0.177112i	−0.912614	+	0.408823i	$0.865939\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$		0			0
$267$	1.65831	+	5.50000i	0.101487	+	0.336595i
$268$		0			0
$269$	−14.3614	+	8.29156i	−0.875630	+	0.505545i	−0.869215	−	0.494434i	$-0.835375\pi$
$269$	−14.3614	+	8.29156i	−0.875630	+	0.505545i	−0.00641522	+	0.999979i	$0.502042\pi$
$270$		0			0
$271$	14.7224	+	8.50000i	0.894324	+	0.516338i	0.875354	−	0.483482i	$-0.160628\pi$
$271$	14.7224	+	8.50000i	0.894324	+	0.516338i	0.0189696	+	0.999820i	$0.493961\pi$
$272$		0			0
$273$	−18.2337	+	1.87953i	−1.10355	+	0.113754i
$274$		0			0
$275$	−9.94987	+	17.2337i	−0.600000	+	1.03923i
$276$		0			0
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	0.992522	−	0.122068i	$-0.0389525\pi$
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	−0.601975	+	0.798515i	$0.705619\pi$
$278$		0			0
$279$	−4.97494	−	7.50000i	−0.297842	−	0.449013i
$280$		0			0
$281$		−	6.63325i		−	0.395706i	−0.980232	−	0.197853i	$-0.936603\pi$
$281$		−	6.63325i		−	0.395706i	0.980232	−	0.197853i	$-0.0633969\pi$
$282$		0			0
$283$	−12.9904	+	7.50000i	−0.772198	+	0.445829i	−0.833658	−	0.552281i	$-0.813758\pi$
$283$	−12.9904	+	7.50000i	−0.772198	+	0.445829i	0.0614601	+	0.998110i	$0.480424\pi$
$284$		0			0
$285$	9.19702	−	39.1461i	0.544784	−	2.31881i
$286$		0			0
$287$	13.2665	+	11.4891i	0.783097	+	0.678182i
$288$		0			0
$289$	−3.00000	+	5.19615i	−0.176471	+	0.305656i
$290$		0			0
$291$	−10.0974	−	9.48913i	−0.591917	−	0.556262i
$292$		0			0
$293$		−	13.2665i		−	0.775037i	−0.921862	−	0.387519i	$-0.873332\pi$
$293$		−	13.2665i		−	0.775037i	0.921862	−	0.387519i	$-0.126668\pi$
$294$		0			0
$295$		−	11.0000i		−	0.640445i
$296$		0			0
$297$	16.9891	+	2.89303i	0.985809	+	0.167871i
$298$		0			0
$299$	−6.63325	+	11.4891i	−0.383611	+	0.664433i
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$		0			0
$303$	−5.59230	−	1.31386i	−0.321269	−	0.0754792i
$304$		0			0
$305$	−8.61684	+	4.97494i	−0.493399	+	0.284864i
$306$		0			0
$307$			6.00000i			0.342438i	0.985233	+	0.171219i	$0.0547706\pi$
$307$			6.00000i			0.342438i	−0.985233	+	0.171219i	$0.945229\pi$
$308$		0			0
$309$	5.50000	+	18.2414i	0.312884	+	1.03772i
$310$		0			0
$311$	4.97494	+	8.61684i	0.282103	+	0.488616i	0.971902	−	0.235384i	$-0.0756347\pi$
$311$	4.97494	+	8.61684i	0.282103	+	0.488616i	−0.689800	+	0.724000i	$0.742301\pi$
$312$		0			0
$313$	4.50000	−	7.79423i	0.254355	−	0.440556i	−0.710365	−	0.703833i	$-0.751470\pi$
$313$	4.50000	−	7.79423i	0.254355	−	0.440556i	0.964720	+	0.263278i	$0.0848035\pi$
$314$		0			0
$315$	−10.1436	−	24.2921i	−0.571529	−	1.36871i
$316$		0			0
$317$	−25.8505	−	14.9248i	−1.45191	−	0.838261i	−0.453321	−	0.891348i	$-0.649761\pi$
$317$	−25.8505	−	14.9248i	−1.45191	−	0.838261i	−0.998590	+	0.0530866i	$0.983094\pi$
$318$		0			0
$319$	−19.0526	+	11.0000i	−1.06674	+	0.615882i
$320$		0			0
$321$	5.50000	−	1.65831i	0.306980	−	0.0925580i
$322$		0			0
$323$	23.2164			1.29179
$324$		0			0
$325$	−12.0000	−	20.7846i	−0.665640	−	1.15292i
$326$		0			0
$327$	−1.98072	+	8.43070i	−0.109534	+	0.466219i
$328$		0			0
$329$	8.61684	+	24.8747i	0.475062	+	1.37139i
$330$		0			0
$331$	14.7224	+	8.50000i	0.809218	+	0.467202i	0.846684	−	0.532096i	$-0.178595\pi$
$331$	14.7224	+	8.50000i	0.809218	+	0.467202i	−0.0374662	+	0.999298i	$0.511929\pi$
$332$		0			0
$333$	2.68614	+	1.33591i	0.147200	+	0.0732073i
$334$		0			0
$335$	−29.8496			−1.63086
$336$		0			0
$337$	28.0000			1.52526			0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000			1.52526			0.762629	+	0.646837i	$0.223908\pi$
$338$		0			0
$339$	7.86797	−	8.37228i	0.427329	−	0.454720i
$340$		0			0
$341$	−8.61684	−	4.97494i	−0.466628	−	0.269408i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$	−18.5475	−	4.35758i	−0.998566	−	0.234604i
$346$		0			0
$347$	−14.9248	−	25.8505i	−0.801206	−	1.38773i	−0.918823	−	0.394670i	$-0.870859\pi$
$347$	−14.9248	−	25.8505i	−0.801206	−	1.38773i	0.117617	−	0.993059i	$-0.462474\pi$
$348$		0			0
$349$	−8.00000			−0.428230			−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000			−0.428230			−0.214115	+	0.976808i	$0.568687\pi$
$350$		0			0
$351$	−13.2665	+	16.0000i	−0.708113	+	0.854017i
$352$		0			0
$353$	−31.5951	+	18.2414i	−1.68164	+	0.970894i	−0.721063	+	0.692869i	$0.756346\pi$
$353$	−31.5951	+	18.2414i	−1.68164	+	0.970894i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		0			0
$355$	−38.1051	−	22.0000i	−2.02241	−	1.16764i
$356$		0			0
$357$	12.3139	−	8.90892i	0.651719	−	0.471510i
$358$		0			0
$359$	18.2414	−	31.5951i	0.962746	−	1.66753i	0.247194	−	0.968966i	$-0.420491\pi$
$359$	18.2414	−	31.5951i	0.962746	−	1.66753i	0.715552	−	0.698559i	$-0.246175\pi$
$360$		0			0
$361$	15.0000	+	25.9808i	0.789474	+	1.36741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	23.2164i		−	1.21520i
$366$		0			0
$367$	−0.866025	+	0.500000i	−0.0452062	+	0.0260998i	−0.522433	−	0.852680i	$-0.674975\pi$
$367$	−0.866025	+	0.500000i	−0.0452062	+	0.0260998i	0.477227	+	0.878780i	$0.341642\pi$
$368$		0			0
$369$	19.8614	−	1.23472i	1.03394	−	0.0642768i
$370$		0			0
$371$	1.65831	−	8.61684i	0.0860953	−	0.447364i
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$		0			0
$375$	3.93398	−	4.18614i	0.203150	−	0.216171i
$376$		0			0
$377$		−	26.5330i		−	1.36652i
$378$		0			0
$379$			24.0000i			1.23280i	0.787434	+	0.616399i	$0.211409\pi$
$379$			24.0000i			1.23280i	−0.787434	+	0.616399i	$0.788591\pi$
$380$		0			0
$381$	2.37228	−	2.52434i	0.121536	−	0.129326i
$382$		0			0
$383$	−8.29156	+	14.3614i	−0.423679	+	0.733834i	−0.996296	−	0.0859894i	$-0.972595\pi$
$383$	−8.29156	+	14.3614i	−0.423679	+	0.733834i	0.572617	+	0.819823i	$0.305928\pi$
$384$		0			0
$385$	−22.0000	−	19.0526i	−1.12122	−	0.971008i
$386$		0			0
$387$	−5.98844	+	0.372281i	−0.304409	+	0.0189241i
$388$		0			0
$389$	2.87228	−	1.65831i	0.145630	−	0.0840798i	−0.425414	−	0.904999i	$-0.639872\pi$
$389$	2.87228	−	1.65831i	0.145630	−	0.0840798i	0.571045	+	0.820919i	$0.306538\pi$
$390$		0			0
$391$		−	11.0000i		−	0.556294i
$392$		0			0
$393$	−27.5000	+	8.29156i	−1.38719	+	0.418254i
$394$		0			0
$395$	14.9248	+	25.8505i	0.750949	+	1.30068i
$396$		0			0
$397$	−6.50000	+	11.2583i	−0.326226	+	0.565039i	−0.981760	−	0.190126i	$-0.939110\pi$
$397$	−6.50000	+	11.2583i	−0.326226	+	0.565039i	0.655534	+	0.755166i	$0.272444\pi$
$398$		0			0
$399$	29.2786	+	13.1060i	1.46576	+	0.656119i
$400$		0			0
$401$	14.3614	+	8.29156i	0.717174	+	0.414061i	0.813712	−	0.581269i	$-0.197443\pi$
$401$	14.3614	+	8.29156i	0.717174	+	0.414061i	−0.0965374	+	0.995329i	$0.530777\pi$
$402$		0			0
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$		0			0
$405$	−27.5000	−	11.6082i	−1.36649	−	0.576815i
$406$		0			0
$407$	3.31662			0.164399
$408$		0			0
$409$	7.50000	+	12.9904i	0.370851	+	0.642333i	0.989697	−	0.143180i	$-0.0457327\pi$
$409$	7.50000	+	12.9904i	0.370851	+	0.642333i	−0.618846	+	0.785513i	$0.712399\pi$
$410$		0			0
$411$	−27.9615	−	6.56930i	−1.37924	−	0.324040i
$412$		0			0
$413$	8.61684	+	1.65831i	0.424007	+	0.0816002i
$414$		0			0
$415$	38.1051	+	22.0000i	1.87051	+	1.07994i
$416$		0			0
$417$	−11.8614	+	12.6217i	−0.580856	+	0.618087i
$418$		0			0
$419$	−26.5330			−1.29622			−0.648111	−	0.761546i	$-0.724441\pi$
$419$	−26.5330			−1.29622			−0.648111	+	0.761546i	$0.724441\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$	26.7268	+	13.2921i	1.29950	+	0.646285i
$424$		0			0
$425$	17.2337	+	9.94987i	0.835957	+	0.482640i
$426$		0			0
$427$	−2.59808	−	7.50000i	−0.125730	−	0.362950i
$428$		0			0
$429$	−5.25544	+	22.3692i	−0.253735	+	1.07999i
$430$		0			0
$431$	−11.6082	−	20.1060i	−0.559147	−	0.968470i	−0.997568	−	0.0697009i	$-0.977796\pi$
$431$	−11.6082	−	20.1060i	−0.559147	−	0.968470i	0.438421	−	0.898770i	$-0.355538\pi$
$432$		0			0
$433$	−20.0000			−0.961139			−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000			−0.961139			−0.480569	+	0.876957i	$0.659570\pi$
$434$		0			0
$435$	36.4829	−	11.0000i	1.74922	−	0.527410i
$436$		0			0
$437$	20.1060	−	11.6082i	0.961799	−	0.555295i
$438$		0			0
$439$	−7.79423	−	4.50000i	−0.371998	−	0.214773i	0.302333	−	0.953202i	$-0.402235\pi$
$439$	−7.79423	−	4.50000i	−0.371998	−	0.214773i	−0.674331	+	0.738429i	$0.735568\pi$
$440$		0			0
$441$	20.5584	−	4.28384i	0.978972	−	0.203992i
$442$		0			0
$443$	−14.9248	+	25.8505i	−0.709099	+	1.22820i	0.256092	+	0.966652i	$0.417565\pi$
$443$	−14.9248	+	25.8505i	−0.709099	+	1.22820i	−0.965192	+	0.261544i	$0.915768\pi$
$444$		0			0
$445$	−5.50000	−	9.52628i	−0.260725	−	0.451589i
$446$		0			0
$447$	−8.29156	−	27.5000i	−0.392177	−	1.30071i
$448$		0			0
$449$			19.8997i			0.939127i	0.882899	+	0.469564i	$0.155589\pi$
$449$			19.8997i			0.939127i	−0.882899	+	0.469564i	$0.844411\pi$
$450$		0			0
$451$	19.0526	−	11.0000i	0.897150	−	0.517970i
$452$		0			0
$453$	11.8030	+	2.77300i	0.554553	+	0.130287i
$454$		0			0
$455$	33.1662	−	11.4891i	1.55486	−	0.538619i
$456$		0			0
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	−0.898974	−	0.438001i	$-0.855687\pi$
$457$	−1.50000	+	2.59808i	−0.0701670	+	0.121533i	0.828807	+	0.559534i	$0.189020\pi$
$458$		0			0
$459$	2.89303	−	16.9891i	0.135035	−	0.792984i
$460$		0			0
$461$			33.1662i			1.54471i	0.635193	+	0.772353i	$0.280920\pi$
$461$			33.1662i			1.54471i	−0.635193	+	0.772353i	$0.719080\pi$
$462$		0			0
$463$			38.0000i			1.76601i	0.469364	+	0.883005i	$0.344483\pi$
$463$			38.0000i			1.76601i	−0.469364	+	0.883005i	$0.655517\pi$
$464$		0			0
$465$	12.5584	+	11.8020i	0.582383	+	0.547302i
$466$		0			0
$467$	1.65831	−	2.87228i	0.0767375	−	0.132913i	−0.825103	−	0.564982i	$-0.808883\pi$
$467$	1.65831	−	2.87228i	0.0767375	−	0.132913i	0.901841	+	0.432069i	$0.142216\pi$
$468$		0			0
$469$	4.50000	−	23.3827i	0.207791	−	1.07971i
$470$		0			0
$471$	−1.18843	+	5.05842i	−0.0547600	+	0.233080i
$472$		0			0
$473$	−5.74456	+	3.31662i	−0.264135	+	0.152499i
$474$		0			0
$475$			42.0000i			1.92709i
$476$		0			0
$477$	−5.50000	−	8.29156i	−0.251828	−	0.379645i
$478$		0			0
$479$	−8.29156	−	14.3614i	−0.378851	−	0.656189i	0.612044	−	0.790824i	$-0.290347\pi$
$479$	−8.29156	−	14.3614i	−0.378851	−	0.656189i	−0.990895	+	0.134634i	$0.957014\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$	6.20965	−	13.8723i	0.282549	−	0.631211i
$484$		0			0
$485$	22.9783	+	13.2665i	1.04339	+	0.602401i
$486$		0			0
$487$	−14.7224	+	8.50000i	−0.667137	+	0.385172i	−0.794991	−	0.606621i	$-0.792524\pi$
$487$	−14.7224	+	8.50000i	−0.667137	+	0.385172i	0.127854	+	0.991793i	$0.459191\pi$
$488$		0			0
$489$	3.50000	+	11.6082i	0.158275	+	0.524940i
$490$		0			0
$491$	6.63325			0.299354			0.149677	−	0.988735i	$-0.452177\pi$
$491$	6.63325			0.299354			0.149677	+	0.988735i	$0.452177\pi$
$492$		0			0
$493$	11.0000	+	19.0526i	0.495415	+	0.858084i
$494$		0			0
$495$	−32.9364	+	2.04755i	−1.48038	+	0.0920304i
$496$		0			0
$497$	22.9783	−	26.5330i	1.03072	−	1.19017i
$498$		0			0
$499$	−30.3109	−	17.5000i	−1.35690	−	0.783408i	−0.367697	−	0.929946i	$-0.619854\pi$
$499$	−30.3109	−	17.5000i	−1.35690	−	0.783408i	−0.989205	+	0.146538i	$0.953187\pi$
$500$		0			0
$501$	8.37228	+	7.86797i	0.374046	+	0.351515i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	11.0000			0.489494
$506$		0			0
$507$	−3.78651	−	3.55842i	−0.168165	−	0.158035i
$508$		0			0
$509$	14.3614	+	8.29156i	0.636558	+	0.367517i	0.783287	−	0.621660i	$-0.213541\pi$
$509$	14.3614	+	8.29156i	0.636558	+	0.367517i	−0.146729	+	0.989177i	$0.546875\pi$
$510$		0			0
$511$	18.1865	+	3.50000i	0.804525	+	0.154831i
$512$		0			0
$513$	34.1060	−	12.6405i	1.50582	−	0.558093i
$514$		0			0
$515$	−18.2414	−	31.5951i	−0.803814	−	1.39225i
$516$		0			0
$517$	33.0000			1.45134
$518$		0			0
$519$	−4.97494	−	16.5000i	−0.218376	−	0.724270i
$520$		0			0
$521$	20.1060	−	11.6082i	0.880859	−	0.508564i	0.00991713	−	0.999951i	$-0.496843\pi$
$521$	20.1060	−	11.6082i	0.880859	−	0.508564i	0.870941	+	0.491387i	$0.163510\pi$
$522$		0			0
$523$	16.4545	+	9.50000i	0.719504	+	0.415406i	0.814570	−	0.580065i	$-0.196973\pi$
$523$	16.4545	+	9.50000i	0.719504	+	0.415406i	−0.0950659	+	0.995471i	$0.530306\pi$
$524$		0			0
$525$	16.1168	+	22.2766i	0.703397	+	0.972231i
$526$		0			0
$527$	−4.97494	+	8.61684i	−0.216712	+	0.375356i
$528$		0			0
$529$	6.00000	+	10.3923i	0.260870	+	0.451839i
$530$		0			0
$531$	8.29156	−	5.50000i	0.359823	−	0.238680i
$532$		0			0
$533$			26.5330i			1.14927i
$534$		0			0
$535$	−9.52628	+	5.50000i	−0.411857	+	0.237786i
$536$		0			0
$537$	1.31386	−	5.59230i	0.0566972	−	0.241325i
$538$		0			0
$539$	18.2414	−	14.3614i	0.785714	−	0.618590i
$540$		0			0
$541$	−18.5000	+	32.0429i	−0.795377	+	1.37763i	0.127222	+	0.991874i	$0.459394\pi$
$541$	−18.5000	+	32.0429i	−0.795377	+	1.37763i	−0.922599	+	0.385759i	$0.873939\pi$
$542$		0			0
$543$	−22.7190	−	21.3505i	−0.974967	−	0.916239i
$544$		0			0
$545$		−	16.5831i		−	0.710343i
$546$		0			0
$547$			40.0000i			1.71028i	0.518400	+	0.855138i	$0.326528\pi$
$547$			40.0000i			1.71028i	−0.518400	+	0.855138i	$0.673472\pi$
$548$		0			0
$549$	−8.05842	−	4.00772i	−0.343925	−	0.171045i
$550$		0			0
$551$	−23.2164	+	40.2119i	−0.989051	+	1.71309i
$552$		0			0
$553$	−22.5000	+	7.79423i	−0.956797	+	0.331444i
$554$		0			0
$555$	−5.59230	−	1.31386i	−0.237380	−	0.0557702i
$556$		0			0
$557$	2.87228	−	1.65831i	0.121702	−	0.0702650i	−0.437913	−	0.899017i	$-0.644282\pi$
$557$	2.87228	−	1.65831i	0.121702	−	0.0702650i	0.559615	+	0.828752i	$0.310949\pi$
$558$		0			0
$559$		−	8.00000i		−	0.338364i
$560$		0			0
$561$	−5.50000	−	18.2414i	−0.232210	−	0.770154i
$562$		0			0
$563$	4.97494	+	8.61684i	0.209669	+	0.363157i	0.951610	−	0.307308i	$-0.0994282\pi$
$563$	4.97494	+	8.61684i	0.209669	+	0.363157i	−0.741942	+	0.670465i	$0.766095\pi$
$564$		0			0
$565$	−11.0000	+	19.0526i	−0.462773	+	0.801547i
$566$		0			0
$567$	13.2390	−	19.7921i	0.555988	−	0.831190i
$568$		0			0
$569$	−25.8505	−	14.9248i	−1.08371	−	0.625681i	−0.151816	−	0.988409i	$-0.548512\pi$
$569$	−25.8505	−	14.9248i	−1.08371	−	0.625681i	−0.931895	+	0.362728i	$0.881845\pi$
$570$		0			0
$571$	4.33013	−	2.50000i	0.181210	−	0.104622i	−0.406651	−	0.913584i	$-0.633303\pi$
$571$	4.33013	−	2.50000i	0.181210	−	0.104622i	0.587861	+	0.808962i	$0.299970\pi$
$572$		0			0
$573$	−16.5000	+	4.97494i	−0.689297	+	0.207831i
$574$		0			0
$575$	19.8997			0.829877
$576$		0			0
$577$	−17.5000	−	30.3109i	−0.728535	−	1.26186i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−17.5000	−	30.3109i	−0.728535	−	1.26186i	0.228968	−	0.973434i	$-0.426465\pi$
$578$		0			0
$579$	1.18843	−	5.05842i	0.0493895	−	0.210221i
$580$		0			0
$581$	−22.9783	+	26.5330i	−0.953298	+	1.10077i
$582$		0			0
$583$	−9.52628	−	5.50000i	−0.394538	−	0.227787i
$584$		0			0
$585$	17.7228	−	35.6357i	0.732748	−	1.47335i
$586$		0			0
$587$	26.5330			1.09513			0.547567	−	0.836762i	$-0.315554\pi$
$587$	26.5330			1.09513			0.547567	+	0.836762i	$0.315554\pi$
$588$		0			0
$589$	−21.0000			−0.865290
$590$		0			0
$591$	−23.6039	+	25.1168i	−0.970935	+	1.03317i
$592$		0			0
$593$	2.87228	+	1.65831i	0.117950	+	0.0680987i	0.557815	−	0.829966i	$-0.311640\pi$
$593$	2.87228	+	1.65831i	0.117950	+	0.0680987i	−0.439864	+	0.898064i	$0.644973\pi$
$594$		0			0
$595$	−19.0526	+	22.0000i	−0.781079	+	0.901912i
$596$		0			0
$597$	−1.68614	−	0.396143i	−0.0690091	−	0.0162131i
$598$		0			0
$599$	4.97494	+	8.61684i	0.203270	+	0.352075i	0.949580	−	0.313524i	$-0.101510\pi$
$599$	4.97494	+	8.61684i	0.203270	+	0.352075i	−0.746310	+	0.665599i	$0.768176\pi$
$600$		0			0
$601$	−16.0000			−0.652654			−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000			−0.652654			−0.326327	+	0.945257i	$0.605811\pi$
$602$		0			0
$603$	−14.9248	−	22.5000i	−0.607785	−	0.916271i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.06218	+	3.50000i	0.246056	+	0.142061i	0.617957	−	0.786212i	$-0.287961\pi$
$607$	6.06218	+	3.50000i	0.246056	+	0.142061i	−0.371901	+	0.928272i	$0.621294\pi$
$608$		0			0
$609$	3.11684	+	30.2372i	0.126301	+	1.22527i
$610$		0			0
$611$	−19.8997	+	34.4674i	−0.805058	+	1.39440i
$612$		0			0
$613$	−0.500000	−	0.866025i	−0.0201948	−	0.0349784i	0.855751	−	0.517387i	$-0.173095\pi$
$613$	−0.500000	−	0.866025i	−0.0201948	−	0.0349784i	−0.875946	+	0.482409i	$0.839762\pi$
$614$		0			0
$615$	−36.4829	+	11.0000i	−1.47113	+	0.443563i
$616$		0			0
$617$		−	6.63325i		−	0.267045i	−0.991046	−	0.133522i	$-0.957371\pi$
$617$		−	6.63325i		−	0.267045i	0.991046	−	0.133522i	$-0.0426288\pi$
$618$		0			0
$619$	−21.6506	+	12.5000i	−0.870212	+	0.502417i	−0.867419	−	0.497579i	$-0.834223\pi$
$619$	−21.6506	+	12.5000i	−0.870212	+	0.502417i	−0.00279365	+	0.999996i	$0.500889\pi$
$620$		0			0
$621$	−5.98913	−	16.1595i	−0.240335	−	0.648460i
$622$		0			0
$623$	8.29156	−	2.87228i	0.332194	−	0.115076i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$	27.5379	−	29.3030i	1.09976	−	1.17025i
$628$		0			0
$629$		−	3.31662i		−	0.132242i
$630$		0			0
$631$		−	18.0000i		−	0.716569i	−0.933613	−	0.358284i	$-0.883362\pi$
$631$		−	18.0000i		−	0.716569i	0.933613	−	0.358284i	$-0.116638\pi$
$632$		0			0
$633$	−30.8397	+	32.8164i	−1.22577	+	1.30433i
$634$		0			0
$635$	−3.31662	+	5.74456i	−0.131616	+	0.227966i
$636$		0			0
$637$	4.00000	+	27.7128i	0.158486	+	1.09802i
$638$		0			0
$639$	−2.46943	−	39.7228i	−0.0976893	−	1.57141i
$640$		0			0
$641$	31.5951	−	18.2414i	1.24793	−	0.720493i	0.277235	−	0.960802i	$-0.410582\pi$
$641$	31.5951	−	18.2414i	1.24793	−	0.720493i	0.970696	+	0.240309i	$0.0772487\pi$
$642$		0			0
$643$		−	2.00000i		−	0.0788723i	−0.999222	−	0.0394362i	$-0.987444\pi$
$643$		−	2.00000i		−	0.0788723i	0.999222	−	0.0394362i	$-0.0125562\pi$
$644$		0			0
$645$	11.0000	−	3.31662i	0.433125	−	0.130592i
$646$		0			0
$647$	−1.65831	−	2.87228i	−0.0651950	−	0.112921i	0.831585	−	0.555397i	$-0.187434\pi$
$647$	−1.65831	−	2.87228i	−0.0651950	−	0.112921i	−0.896780	+	0.442476i	$0.854100\pi$
$648$		0			0
$649$	5.50000	−	9.52628i	0.215894	−	0.373939i
$650$		0			0
$651$	−11.1383	+	8.05842i	−0.436545	+	0.315834i
$652$		0			0
$653$	−2.87228	−	1.65831i	−0.112401	−	0.0648948i	0.442746	−	0.896647i	$-0.354005\pi$
$653$	−2.87228	−	1.65831i	−0.112401	−	0.0648948i	−0.555147	+	0.831753i	$0.687338\pi$
$654$		0			0
$655$	47.6314	−	27.5000i	1.86111	−	1.07451i
$656$		0			0
$657$	17.5000	−	11.6082i	0.682740	−	0.452878i
$658$		0			0
$659$	26.5330			1.03358			0.516789	−	0.856113i	$-0.327127\pi$
$659$	26.5330			1.03358			0.516789	+	0.856113i	$0.327127\pi$
$660$		0			0
$661$	−19.5000	−	33.7750i	−0.758462	−	1.31369i	−0.943635	−	0.330989i	$-0.892618\pi$
$661$	−19.5000	−	33.7750i	−0.758462	−	1.31369i	0.185173	−	0.982706i	$-0.440716\pi$
$662$		0			0
$663$	22.3692	+	5.25544i	0.868747	+	0.204104i
$664$		0			0
$665$	−60.3179	−	11.6082i	−2.33903	−	0.450146i
$666$		0			0
$667$	19.0526	+	11.0000i	0.737718	+	0.425922i
$668$		0			0
$669$	−16.6060	+	17.6704i	−0.642024	+	0.683176i
$670$		0			0
$671$	−9.94987			−0.384111
$672$		0			0
$673$	40.0000			1.54189			0.770943	−	0.636904i	$-0.219785\pi$
$673$	40.0000			1.54189			0.770943	+	0.636904i	$0.219785\pi$
$674$		0			0
$675$	30.7345	+	5.23369i	1.18297	+	0.201445i
$676$		0			0
$677$	−8.61684	−	4.97494i	−0.331172	−	0.191202i	0.325189	−	0.945649i	$-0.394572\pi$
$677$	−8.61684	−	4.97494i	−0.331172	−	0.191202i	−0.656361	+	0.754447i	$0.727905\pi$
$678$		0			0
$679$	−13.8564	+	16.0000i	−0.531760	+	0.614024i
$680$		0			0
$681$	1.31386	−	5.59230i	0.0503472	−	0.214297i
$682$		0			0
$683$	−11.6082	−	20.1060i	−0.444175	−	0.769334i	0.553819	−	0.832637i	$-0.313170\pi$
$683$	−11.6082	−	20.1060i	−0.444175	−	0.769334i	−0.997994	+	0.0633033i	$0.979836\pi$
$684$		0			0
$685$	55.0000			2.10144
$686$		0			0
$687$	48.0911	−	14.5000i	1.83479	−	0.553210i
$688$		0			0
$689$	11.4891	−	6.63325i	0.437701	−	0.252707i
$690$		0			0
$691$	28.5788	+	16.5000i	1.08719	+	0.627690i	0.932827	−	0.360325i	$-0.117334\pi$
$691$	28.5788	+	16.5000i	1.08719	+	0.627690i	0.154363	+	0.988014i	$0.450667\pi$
$692$		0			0
$693$	3.36141	−	26.1094i	0.127689	−	0.991814i
$694$		0			0
$695$	16.5831	−	28.7228i	0.629034	−	1.08952i
$696$		0			0
$697$	−11.0000	−	19.0526i	−0.416655	−	0.721667i
$698$		0			0
$699$	−8.29156	−	27.5000i	−0.313616	−	1.04015i
$700$		0			0
$701$			13.2665i			0.501069i	0.968108	+	0.250534i	$0.0806063\pi$
$701$			13.2665i			0.501069i	−0.968108	+	0.250534i	$0.919394\pi$
$702$		0			0
$703$	6.06218	−	3.50000i	0.228639	−	0.132005i
$704$		0			0
$705$	−55.6426	−	13.0727i	−2.09562	−	0.492348i
$706$		0			0
$707$	−1.65831	+	8.61684i	−0.0623673	+	0.324070i
$708$		0			0
$709$	16.5000	−	28.5788i	0.619671	−	1.07330i	−0.369875	−	0.929081i	$-0.620600\pi$
$709$	16.5000	−	28.5788i	0.619671	−	1.07330i	0.989546	−	0.144219i	$-0.0460671\pi$
$710$		0			0
$711$	−12.0232	+	24.1753i	−0.450904	+	0.906643i
$712$		0			0
$713$			9.94987i			0.372626i
$714$		0			0
$715$		−	44.0000i		−	1.64551i
$716$		0			0
$717$	−8.37228	−	7.86797i	−0.312669	−	0.293835i
$718$		0			0
$719$	−11.6082	+	20.1060i	−0.432912	+	0.749826i	−0.997123	−	0.0758050i	$-0.975847\pi$
$719$	−11.6082	+	20.1060i	−0.432912	+	0.749826i	0.564210	+	0.825631i	$0.309181\pi$
$720$		0			0
$721$	27.5000	−	9.52628i	1.02415	−	0.354777i
$722$		0			0
$723$	−7.52673	+	32.0367i	−0.279922	+	1.19146i
$724$		0			0
$725$	−34.4674	+	19.8997i	−1.28009	+	0.739058i
$726$		0			0
$727$		−	10.0000i		−	0.370879i	−0.982656	−	0.185440i	$-0.940629\pi$
$727$		−	10.0000i		−	0.370879i	0.982656	−	0.185440i	$-0.0593710\pi$
$728$		0			0
$729$	−5.00000	−	26.5330i	−0.185185	−	0.982704i
$730$		0			0
$731$	3.31662	+	5.74456i	0.122670	+	0.212470i
$732$		0			0
$733$	−3.50000	+	6.06218i	−0.129275	+	0.223912i	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−3.50000	+	6.06218i	−0.129275	+	0.223912i	0.794121	+	0.607760i	$0.207932\pi$
$734$		0			0
$735$	−36.4468	+	16.9891i	−1.34436	+	0.626653i
$736$		0			0
$737$	−25.8505	−	14.9248i	−0.952217	−	0.549762i
$738$		0			0
$739$	−26.8468	+	15.5000i	−0.987575	+	0.570177i	−0.904549	−	0.426371i	$-0.859792\pi$
$739$	−26.8468	+	15.5000i	−0.987575	+	0.570177i	−0.0830265	+	0.996547i	$0.526459\pi$
$740$		0			0
$741$	14.0000	+	46.4327i	0.514303	+	1.70575i
$742$		0			0
$743$	−13.2665			−0.486701			−0.243350	−	0.969938i	$-0.578246\pi$
$743$	−13.2665			−0.486701			−0.243350	+	0.969938i	$0.578246\pi$
$744$		0			0
$745$	27.5000	+	47.6314i	1.00752	+	1.74508i
$746$		0			0
$747$	2.46943	+	39.7228i	0.0903519	+	1.45338i
$748$		0			0
$749$	−2.87228	−	8.29156i	−0.104951	−	0.302967i
$750$		0			0
$751$	−4.33013	−	2.50000i	−0.158009	−	0.0912263i	0.418911	−	0.908027i	$-0.362412\pi$
$751$	−4.33013	−	2.50000i	−0.158009	−	0.0912263i	−0.576919	+	0.816801i	$0.695745\pi$
$752$		0			0
$753$	−25.1168	−	23.6039i	−0.915309	−	0.860174i
$754$		0			0
$755$	−23.2164			−0.844930
$756$		0			0
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$		0			0
$759$	−13.8839	−	13.0475i	−0.503952	−	0.473596i
$760$		0			0
$761$	−20.1060	−	11.6082i	−0.728841	−	0.420796i	0.0891571	−	0.996018i	$-0.471583\pi$
$761$	−20.1060	−	11.6082i	−0.728841	−	0.420796i	−0.817998	+	0.575221i	$0.804916\pi$
$762$		0			0
$763$	12.9904	+	2.50000i	0.470283	+	0.0905061i
$764$		0			0
$765$	2.04755	+	32.9364i	0.0740292	+	1.19082i
$766$		0			0
$767$	6.63325	+	11.4891i	0.239513	+	0.414848i
$768$		0			0
$769$	−16.0000			−0.576975			−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000			−0.576975			−0.288487	+	0.957484i	$0.593152\pi$
$770$		0			0
$771$	11.6082	+	38.5000i	0.418059	+	1.38654i
$772$		0			0
$773$	14.3614	−	8.29156i	0.516544	−	0.298227i	−0.218976	−	0.975730i	$-0.570272\pi$
$773$	14.3614	−	8.29156i	0.516544	−	0.298227i	0.735519	+	0.677504i	$0.236938\pi$
$774$		0			0
$775$	−15.5885	−	9.00000i	−0.559954	−	0.323290i
$776$		0			0
$777$	1.87228	−	4.18265i	0.0671677	−	0.150052i
$778$		0			0
$779$	23.2164	−	40.2119i	0.831813	−	1.44074i
$780$		0			0
$781$	−22.0000	−	38.1051i	−0.787222	−	1.36351i
$782$		0			0
$783$	26.5330	+	22.0000i	0.948212	+	0.786216i
$784$		0			0
$785$		−	9.94987i		−	0.355126i
$786$		0			0
$787$	−38.9711	+	22.5000i	−1.38917	+	0.802038i	−0.993222	−	0.116234i	$-0.962918\pi$
$787$	−38.9711	+	22.5000i	−1.38917	+	0.802038i	−0.395949	+	0.918272i	$0.629584\pi$
$788$		0			0
$789$	−1.31386	+	5.59230i	−0.0467746	+	0.199091i
$790$		0			0
$791$	−13.2665	−	11.4891i	−0.471702	−	0.408506i
$792$		0			0
$793$	6.00000	−	10.3923i	0.213066	−	0.369042i
$794$		0			0
$795$	13.8839	+	13.0475i	0.492410	+	0.462749i
$796$		0			0
$797$		−	6.63325i		−	0.234962i	−0.993075	−	0.117481i	$-0.962518\pi$
$797$		−	6.63325i		−	0.234962i	0.993075	−	0.117481i	$-0.0374819\pi$
$798$		0			0
$799$		−	33.0000i		−	1.16746i
$800$		0			0
$801$	4.43070	−	8.90892i	0.156551	−	0.314781i
$802$		0			0
$803$	11.6082	−	20.1060i	0.409644	−	0.709524i
$804$		0			0
$805$	−5.50000	+	28.5788i	−0.193850	+	1.00727i
$806$		0			0
$807$	27.9615	+	6.56930i	0.984291	+	0.231250i
$808$		0			0
$809$	−2.87228	+	1.65831i	−0.100984	+	0.0583032i	−0.549641	−	0.835401i	$-0.685236\pi$
$809$	−2.87228	+	1.65831i	−0.100984	+	0.0583032i	0.448657	+	0.893704i	$0.351902\pi$
$810$		0			0
$811$		−	30.0000i		−	1.05344i	−0.850038	−	0.526721i	$-0.823421\pi$
$811$		−	30.0000i		−	1.05344i	0.850038	−	0.526721i	$-0.176579\pi$
$812$		0			0
$813$	−8.50000	−	28.1913i	−0.298108	−	0.988712i
$814$		0			0
$815$	−11.6082	−	20.1060i	−0.406617	−	0.704281i
$816$		0			0
$817$	−7.00000	+	12.1244i	−0.244899	+	0.424178i
$818$		0			0
$819$	25.2434	+	19.2554i	0.882075	+	0.672839i
$820$		0			0
$821$	−31.5951	−	18.2414i	−1.10268	−	0.636631i	−0.165754	−	0.986167i	$-0.553006\pi$
$821$	−31.5951	−	18.2414i	−1.10268	−	0.636631i	−0.936923	+	0.349537i	$0.886339\pi$
$822$		0			0
$823$	12.9904	−	7.50000i	0.452816	−	0.261434i	−0.256203	−	0.966623i	$-0.582471\pi$
$823$	12.9904	−	7.50000i	0.452816	−	0.261434i	0.709019	+	0.705190i	$0.249138\pi$
$824$		0			0
$825$	33.0000	−	9.94987i	1.14891	−	0.346410i
$826$		0			0
$827$	−39.7995			−1.38396			−0.691982	−	0.721915i	$-0.743262\pi$
$827$	−39.7995			−1.38396			−0.691982	+	0.721915i	$0.743262\pi$
$828$		0			0
$829$	−14.5000	−	25.1147i	−0.503606	−	0.872271i	−0.999991	−	0.00416865i	$-0.998673\pi$
$829$	−14.5000	−	25.1147i	−0.503606	−	0.872271i	0.496385	−	0.868102i	$-0.334660\pi$
$830$		0			0
$831$	5.14987	−	21.9198i	0.178647	−	0.760390i
$832$		0			0
$833$	−14.3614	−	18.2414i	−0.497593	−	0.632028i
$834$		0			0
$835$	−19.0526	−	11.0000i	−0.659341	−	0.380671i
$836$		0			0
$837$	−2.61684	+	15.3672i	−0.0904514	+	0.531170i
$838$		0			0
$839$	−13.2665			−0.458010			−0.229005	−	0.973425i	$-0.573547\pi$
$839$	−13.2665			−0.458010			−0.229005	+	0.973425i	$0.573547\pi$
$840$		0			0
$841$	−15.0000			−0.517241
$842$		0			0
$843$	−7.86797	+	8.37228i	−0.270987	+	0.288357i
$844$		0			0
$845$	8.61684	+	4.97494i	0.296428	+	0.171143i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	25.2921	+	5.94215i	0.868023	+	0.203934i
$850$		0			0
$851$	−1.65831	−	2.87228i	−0.0568462	−	0.0984605i
$852$		0			0
$853$	−20.0000			−0.684787			−0.342393	−	0.939557i	$-0.611238\pi$
$853$	−20.0000			−0.684787			−0.342393	+	0.939557i	$0.611238\pi$
$854$		0			0
$855$	−58.0409	+	38.5000i	−1.98496	+	1.31667i
$856$		0			0
$857$	−14.3614	+	8.29156i	−0.490576	+	0.283234i	−0.724814	−	0.688945i	$-0.758074\pi$
$857$	−14.3614	+	8.29156i	−0.490576	+	0.283234i	0.234237	+	0.972179i	$0.424741\pi$
$858$		0			0
$859$	−14.7224	−	8.50000i	−0.502323	−	0.290016i	0.227349	−	0.973813i	$-0.426994\pi$
$859$	−14.7224	−	8.50000i	−0.502323	−	0.290016i	−0.729672	+	0.683797i	$0.760327\pi$
$860$		0			0
$861$	−3.11684	−	30.2372i	−0.106222	−	1.03048i
$862$		0			0
$863$	−18.2414	+	31.5951i	−0.620946	+	1.07551i	0.368364	+	0.929682i	$0.379918\pi$
$863$	−18.2414	+	31.5951i	−0.620946	+	1.07551i	−0.989310	+	0.145828i	$0.953415\pi$
$864$		0			0
$865$	16.5000	+	28.5788i	0.561017	+	0.971710i
$866$		0			0
$867$	9.94987	−	3.00000i	0.337915	−	0.101885i
$868$		0			0
$869$			29.8496i			1.01258i
$870$		0			0
$871$	31.1769	−	18.0000i	1.05639	−	0.609907i
$872$		0			0
$873$	1.48913	+	23.9538i	0.0503993	+	0.810712i
$874$		0			0
$875$	−6.63325	−	5.74456i	−0.224245	−	0.194202i
$876$		0			0
$877$	11.5000	−	19.9186i	0.388327	−	0.672603i	−0.603897	−	0.797062i	$-0.706386\pi$
$877$	11.5000	−	19.9186i	0.388327	−	0.672603i	0.992225	+	0.124459i	$0.0397196\pi$
$878$		0			0
$879$	−15.7359	+	16.7446i	−0.530760	+	0.564780i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$		−	6.00000i		−	0.201916i	−0.994891	−	0.100958i	$-0.967809\pi$
$883$		−	6.00000i		−	0.201916i	0.994891	−	0.100958i	$-0.0321908\pi$
$884$		0			0
$885$	−13.0475	+	13.8839i	−0.438589	+	0.466701i
$886$		0			0
$887$	11.6082	−	20.1060i	0.389765	−	0.675092i	−0.602653	−	0.798003i	$-0.705890\pi$
$887$	11.6082	−	20.1060i	0.389765	−	0.675092i	0.992418	+	0.122911i	$0.0392230\pi$
$888$		0			0
$889$	−4.00000	−	3.46410i	−0.134156	−	0.116182i
$890$		0			0
$891$	−18.0116	−	23.8030i	−0.603411	−	0.797430i
$892$		0			0
$893$	60.3179	−	34.8246i	2.01846	−	1.16536i
$894$		0			0
$895$			11.0000i			0.367689i
$896$		0			0
$897$	22.0000	−	6.63325i	0.734559	−	0.221478i
$898$		0			0
$899$	−9.94987	−	17.2337i	−0.331847	−	0.574776i
$900$		0			0
$901$	−5.50000	+	9.52628i	−0.183232	+	0.317366i
$902$		0			0
$903$	0.939764	+	9.11684i	0.0312734	+	0.303390i
$904$		0			0
$905$	51.7011	+	29.8496i	1.71860	+	0.992235i
$906$		0			0
$907$	−45.8993	+	26.5000i	−1.52406	+	0.879918i	−0.524469	+	0.851430i	$0.675736\pi$
$907$	−45.8993	+	26.5000i	−1.52406	+	0.879918i	−0.999594	+	0.0284883i	$0.990931\pi$
$908$		0			0
$909$	5.50000	+	8.29156i	0.182423	+	0.275014i
$910$		0			0
$911$	26.5330			0.879077			0.439539	−	0.898224i	$-0.355142\pi$
$911$	26.5330			0.879077			0.439539	+	0.898224i	$0.355142\pi$
$912$		0			0
$913$	22.0000	+	38.1051i	0.728094	+	1.26110i
$914$		0			0
$915$	16.7769	+	3.94158i	0.554627	+	0.130305i
$916$		0			0
$917$	14.3614	+	41.4578i	0.474255	+	1.36906i
$918$		0			0
$919$	19.9186	+	11.5000i	0.657053	+	0.379350i	0.791153	−	0.611618i	$-0.209481\pi$
$919$	19.9186	+	11.5000i	0.657053	+	0.379350i	−0.134100	+	0.990968i	$0.542814\pi$
$920$		0			0
$921$	7.11684	−	7.57301i	0.234508	−	0.249539i
$922$		0			0
$923$	53.0660			1.74669
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	14.6950	−	29.5475i	0.482646	−	0.970469i
$928$		0			0
$929$	20.1060	+	11.6082i	0.659655	+	0.380852i	0.792146	−	0.610332i	$-0.208964\pi$
$929$	20.1060	+	11.6082i	0.659655	+	0.380852i	−0.132490	+	0.991184i	$0.542297\pi$
$930$		0			0
$931$	18.1865	−	45.5000i	0.596040	−	1.49120i
$932$		0			0
$933$	3.94158	−	16.7769i	0.129041	−	0.549251i
$934$		0			0
$935$	18.2414	+	31.5951i	0.596559	+	1.03327i
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	−14.9248	+	4.50000i	−0.487053	+	0.146852i
$940$		0			0
$941$	8.61684	−	4.97494i	0.280901	−	0.162178i	−0.352930	−	0.935650i	$-0.614815\pi$
$941$	8.61684	−	4.97494i	0.280901	−	0.162178i	0.633831	+	0.773471i	$0.281481\pi$
$942$		0			0
$943$	−19.0526	−	11.0000i	−0.620437	−	0.358209i
$944$		0			0
$945$	−16.0109	+	42.6925i	−0.520834	+	1.38879i
$946$		0			0
$947$	−4.97494	+	8.61684i	−0.161664	+	0.280010i	−0.935465	−	0.353418i	$-0.885019\pi$
$947$	−4.97494	+	8.61684i	−0.161664	+	0.280010i	0.773802	+	0.633428i	$0.218353\pi$
$948$		0			0
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$	14.9248	+	49.5000i	0.483970	+	1.60515i
$952$		0			0
$953$			19.8997i			0.644616i	0.946635	+	0.322308i	$0.104459\pi$
$953$			19.8997i			0.644616i	−0.946635	+	0.322308i	$0.895541\pi$
$954$		0			0
$955$	28.5788	−	16.5000i	0.924789	−	0.533927i
$956$		0			0
$957$	37.0951	+	8.71516i	1.19911	+	0.281721i
$958$		0			0
$959$	−8.29156	+	43.0842i	−0.267749	+	1.39126i
$960$		0			0
$961$	−11.0000	+	19.0526i	−0.354839	+	0.614599i
$962$		0			0
$963$	−8.90892	−	4.43070i	−0.287086	−	0.142777i
$964$		0			0
$965$			9.94987i			0.320298i
$966$		0			0
$967$			2.00000i			0.0643157i	0.999483	+	0.0321578i	$0.0102379\pi$
$967$			2.00000i			0.0643157i	−0.999483	+	0.0321578i	$0.989762\pi$
$968$		0			0
$969$	−29.3030	−	27.5379i	−0.941347	−	0.884644i
$970$		0			0
$971$	8.29156	−	14.3614i	0.266089	−	0.460879i	−0.701759	−	0.712414i	$-0.747602\pi$
$971$	8.29156	−	14.3614i	0.266089	−	0.460879i	0.967848	+	0.251535i	$0.0809352\pi$
$972$		0			0
$973$	20.0000	+	17.3205i	0.641171	+	0.555270i
$974$		0			0
$975$	−9.50744	+	40.4674i	−0.304482	+	1.29599i
$976$		0			0
$977$	2.87228	−	1.65831i	0.0918924	−	0.0530541i	−0.453350	−	0.891333i	$-0.649771\pi$
$977$	2.87228	−	1.65831i	0.0918924	−	0.0530541i	0.545242	+	0.838279i	$0.316438\pi$
$978$		0			0
$979$		−	11.0000i		−	0.351562i
$980$		0			0
$981$	12.5000	−	8.29156i	0.399094	−	0.264729i
$982$		0			0
$983$	28.1913	+	48.8288i	0.899163	+	1.55740i	0.828566	+	0.559891i	$0.189157\pi$
$983$	28.1913	+	48.8288i	0.899163	+	1.55740i	0.0705972	+	0.997505i	$0.477510\pi$
$984$		0			0
$985$	33.0000	−	57.1577i	1.05147	−	1.82120i
$986$		0			0
$987$	18.6290	−	41.6168i	0.592966	−	1.32468i
$988$		0			0
$989$	5.74456	+	3.31662i	0.182666	+	0.105463i
$990$		0			0
$991$	37.2391	−	21.5000i	1.18294	−	0.682970i	0.226246	−	0.974070i	$-0.427355\pi$
$991$	37.2391	−	21.5000i	1.18294	−	0.682970i	0.956693	+	0.291100i	$0.0940213\pi$
$992$		0			0
$993$	−8.50000	−	28.1913i	−0.269739	−	0.894624i
$994$		0			0
$995$	3.31662			0.105144
$996$		0			0
$997$	2.50000	+	4.33013i	0.0791758	+	0.137136i	0.902895	−	0.429862i	$-0.141438\pi$
$997$	2.50000	+	4.33013i	0.0791758	+	0.137136i	−0.823719	+	0.566999i	$0.808104\pi$
$998$		0			0
$999$	−1.80579	−	4.87228i	−0.0571326	−	0.154152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bj.f.191.1	yes	8
3.2	odd	2	inner	336.2.bj.f.191.3	yes	8
4.3	odd	2	inner	336.2.bj.f.191.4	yes	8
7.2	even	3		2352.2.h.i.2255.3		4
7.4	even	3	inner	336.2.bj.f.95.2	yes	8
7.5	odd	6		2352.2.h.j.2255.2		4
12.11	even	2	inner	336.2.bj.f.191.2	yes	8
21.2	odd	6		2352.2.h.i.2255.1		4
21.5	even	6		2352.2.h.j.2255.4		4
21.11	odd	6	inner	336.2.bj.f.95.4	yes	8
28.11	odd	6	inner	336.2.bj.f.95.3	yes	8
28.19	even	6		2352.2.h.j.2255.3		4
28.23	odd	6		2352.2.h.i.2255.2		4
84.11	even	6	inner	336.2.bj.f.95.1	✓	8
84.23	even	6		2352.2.h.i.2255.4		4
84.47	odd	6		2352.2.h.j.2255.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bj.f.95.1	✓	8	84.11	even	6	inner
336.2.bj.f.95.2	yes	8	7.4	even	3	inner
336.2.bj.f.95.3	yes	8	28.11	odd	6	inner
336.2.bj.f.95.4	yes	8	21.11	odd	6	inner
336.2.bj.f.191.1	yes	8	1.1	even	1	trivial
336.2.bj.f.191.2	yes	8	12.11	even	2	inner
336.2.bj.f.191.3	yes	8	3.2	odd	2	inner
336.2.bj.f.191.4	yes	8	4.3	odd	2	inner
2352.2.h.i.2255.1		4	21.2	odd	6
2352.2.h.i.2255.2		4	28.23	odd	6
2352.2.h.i.2255.3		4	7.2	even	3
2352.2.h.i.2255.4		4	84.23	even	6
2352.2.h.j.2255.1		4	84.47	odd	6
2352.2.h.j.2255.2		4	7.5	odd	6
2352.2.h.j.2255.3		4	28.19	even	6
2352.2.h.j.2255.4		4	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26217 - 1.18614i) q^{3} +(2.87228 + 1.65831i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+(-1.26217 - 1.18614i) q^{3} +(2.87228 + 1.65831i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.186141 + 2.99422i) q^{9} +(1.65831 + 2.87228i) q^{11} -4.00000 q^{13} +(-1.65831 - 5.50000i) q^{15} +(2.87228 - 1.65831i) q^{17} +(6.06218 + 3.50000i) q^{19} +(4.55842 - 0.469882i) q^{21} +(1.65831 - 2.87228i) q^{23} +(3.00000 + 5.19615i) q^{25} +(3.31662 - 4.00000i) q^{27} +6.63325i q^{29} +(-2.59808 + 1.50000i) q^{31} +(1.31386 - 5.59230i) q^{33} +(-8.29156 + 2.87228i) q^{35} +(0.500000 - 0.866025i) q^{37} +(5.04868 + 4.74456i) q^{39} -6.63325i q^{41} +2.00000i q^{43} +(-4.43070 + 8.90892i) q^{45} +(4.97494 - 8.61684i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-5.59230 - 1.31386i) q^{51} +(-2.87228 + 1.65831i) q^{53} +11.0000i q^{55} +(-3.50000 - 11.6082i) q^{57} +(-1.65831 - 2.87228i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-6.31084 - 4.81386i) q^{63} +(-11.4891 - 6.63325i) q^{65} +(-7.79423 + 4.50000i) q^{67} +(-5.50000 + 1.65831i) q^{69} -13.2665 q^{71} +(-3.50000 - 6.06218i) q^{73} +(2.37686 - 10.1168i) q^{75} +(-8.61684 - 1.65831i) q^{77} +(7.79423 + 4.50000i) q^{79} +(-8.93070 + 1.11469i) q^{81} +13.2665 q^{83} +11.0000 q^{85} +(7.86797 - 8.37228i) q^{87} +(-2.87228 - 1.65831i) q^{89} +(6.92820 - 8.00000i) q^{91} +(5.05842 + 1.18843i) q^{93} +(11.6082 + 20.1060i) q^{95} +8.00000 q^{97} +(-8.29156 + 5.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{9}+O(q^{10}) \) 8 * q - 10 * q^9	\( 8 q - 10 q^{9} - 32 q^{13} + 2 q^{21} + 24 q^{25} + 22 q^{33} + 4 q^{37} + 22 q^{45} - 8 q^{49} - 28 q^{57} - 12 q^{61} - 44 q^{69} - 28 q^{73} - 14 q^{81} + 88 q^{85} + 6 q^{93} + 64 q^{97}+O(q^{100}) \) 8 * q - 10 * q^9 - 32 * q^13 + 2 * q^21 + 24 * q^25 + 22 * q^33 + 4 * q^37 + 22 * q^45 - 8 * q^49 - 28 * q^57 - 12 * q^61 - 44 * q^69 - 28 * q^73 - 14 * q^81 + 88 * q^85 + 6 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

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Database

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