LMFDB - Embedded newform 867.2.e.f.616.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.5473632256.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 49x^{4} + 256 $ x^8 + 49*x^4 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			616.1
Root			$1.10418 + 1.10418i$ of defining polynomial
Character	$\chi$	$=$	867.616
Dual form			867.2.e.f.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -4.56155 q^{4} +(-2.51840 + 2.51840i) q^{5} +(1.81129 + 1.81129i) q^{6} +6.56155i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-2.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -4.56155 q^{4} +(-2.51840 + 2.51840i) q^{5} +(1.81129 + 1.81129i) q^{6} +6.56155i q^{8} -1.00000i q^{9} +(6.45101 + 6.45101i) q^{10} +(1.10418 + 1.10418i) q^{11} +(3.22550 - 3.22550i) q^{12} -0.438447 q^{13} -3.56155i q^{15} +7.68466 q^{16} -2.56155 q^{18} -4.68466i q^{19} +(11.4878 - 11.4878i) q^{20} +(2.82843 - 2.82843i) q^{22} +(-1.72424 - 1.72424i) q^{23} +(-4.63972 - 4.63972i) q^{24} -7.68466i q^{25} +1.12311i q^{26} +(0.707107 + 0.707107i) q^{27} +(5.83095 - 5.83095i) q^{29} -9.12311 q^{30} +(2.20837 - 2.20837i) q^{31} -6.56155i q^{32} -1.56155 q^{33} +4.56155i q^{36} +(-3.62258 + 3.62258i) q^{37} -12.0000 q^{38} +(0.310029 - 0.310029i) q^{39} +(-16.5246 - 16.5246i) q^{40} +(2.51840 + 2.51840i) q^{41} -4.68466i q^{43} +(-5.03680 - 5.03680i) q^{44} +(2.51840 + 2.51840i) q^{45} +(-4.41674 + 4.41674i) q^{46} +11.1231 q^{47} +(-5.43387 + 5.43387i) q^{48} -7.00000i q^{49} -19.6847 q^{50} +2.00000 q^{52} +12.2462i q^{53} +(1.81129 - 1.81129i) q^{54} -5.56155 q^{55} +(3.31255 + 3.31255i) q^{57} +(-14.9363 - 14.9363i) q^{58} -7.12311i q^{59} +16.2462i q^{60} +(-6.45101 - 6.45101i) q^{61} +(-5.65685 - 5.65685i) q^{62} -1.43845 q^{64} +(1.10418 - 1.10418i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +2.43845 q^{69} +(-4.41674 + 4.41674i) q^{71} +6.56155 q^{72} +(8.65938 - 8.65938i) q^{73} +(9.27944 + 9.27944i) q^{74} +(5.43387 + 5.43387i) q^{75} +21.3693i q^{76} +(-0.794156 - 0.794156i) q^{78} +(-6.62511 - 6.62511i) q^{79} +(-19.3530 + 19.3530i) q^{80} -1.00000 q^{81} +(6.45101 - 6.45101i) q^{82} -0.876894i q^{83} -12.0000 q^{86} +8.24621i q^{87} +(-7.24517 + 7.24517i) q^{88} +1.12311 q^{89} +(6.45101 - 6.45101i) q^{90} +(7.86522 + 7.86522i) q^{92} +3.12311i q^{93} -28.4924i q^{94} +(11.7978 + 11.7978i) q^{95} +(4.63972 + 4.63972i) q^{96} +(2.03427 - 2.03427i) q^{97} -17.9309 q^{98} +(1.10418 - 1.10418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 20 q^{4}+O(q^{10}) $ 8 * q - 20 * q^4	$ 8 q - 20 q^{4} - 20 q^{13} + 12 q^{16} - 4 q^{18} - 40 q^{30} + 4 q^{33} - 96 q^{38} + 56 q^{47} - 108 q^{50} + 16 q^{52} - 28 q^{55} - 28 q^{64} + 32 q^{67} + 36 q^{69} + 36 q^{72} - 8 q^{81} - 96 q^{86} - 24 q^{89} - 28 q^{98}+O(q^{100}) $ 8 * q - 20 * q^4 - 20 * q^13 + 12 * q^16 - 4 * q^18 - 40 * q^30 + 4 * q^33 - 96 * q^38 + 56 * q^47 - 108 * q^50 + 16 * q^52 - 28 * q^55 - 28 * q^64 + 32 * q^67 + 36 * q^69 + 36 * q^72 - 8 * q^81 - 96 * q^86 - 24 * q^89 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	2.56155i		−	1.81129i	−0.424035	−	0.905646i	$-0.639387\pi$
$2$		−	2.56155i		−	1.81129i	0.424035	−	0.905646i	$-0.360613\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−4.56155			−2.28078
$5$	−2.51840	+	2.51840i	−1.12626	+	1.12626i	−0.135482	+	0.990780i	$0.543258\pi$
$5$	−2.51840	+	2.51840i	−1.12626	+	1.12626i	−0.990780	+	0.135482i	$0.956742\pi$
$6$	1.81129	+	1.81129i	0.739457	+	0.739457i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$			6.56155i			2.31986i
$9$		−	1.00000i		−	0.333333i
$10$	6.45101	+	6.45101i	2.03999	+	2.03999i
$11$	1.10418	+	1.10418i	0.332924	+	0.332924i	0.853696	−	0.520772i	$-0.174356\pi$
$11$	1.10418	+	1.10418i	0.332924	+	0.332924i	−0.520772	+	0.853696i	$0.674356\pi$
$12$	3.22550	−	3.22550i	0.931123	−	0.931123i
$13$	−0.438447			−0.121603			−0.0608017	−	0.998150i	$-0.519366\pi$
$13$	−0.438447			−0.121603			−0.0608017	+	0.998150i	$0.519366\pi$
$14$		0			0
$15$		−	3.56155i		−	0.919589i
$16$	7.68466			1.92116
$17$		0			0
$17$		0			0
$18$	−2.56155			−0.603764
$19$		−	4.68466i		−	1.07473i	−0.843348	−	0.537367i	$-0.819419\pi$
$19$		−	4.68466i		−	1.07473i	0.843348	−	0.537367i	$-0.180581\pi$
$20$	11.4878	−	11.4878i	2.56875	−	2.56875i
$21$		0			0
$22$	2.82843	−	2.82843i	0.603023	−	0.603023i
$23$	−1.72424	−	1.72424i	−0.359529	−	0.359529i	0.504110	−	0.863639i	$-0.331821\pi$
$23$	−1.72424	−	1.72424i	−0.359529	−	0.359529i	−0.863639	+	0.504110i	$0.831821\pi$
$24$	−4.63972	−	4.63972i	−0.947079	−	0.947079i
$25$		−	7.68466i		−	1.53693i
$26$			1.12311i			0.220259i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	5.83095	−	5.83095i	1.08278	−	1.08278i	0.0865315	−	0.996249i	$-0.472422\pi$
$29$	5.83095	−	5.83095i	1.08278	−	1.08278i	0.996249	−	0.0865315i	$-0.0275783\pi$
$30$	−9.12311			−1.66564
$31$	2.20837	−	2.20837i	0.396635	−	0.396635i	−0.480409	−	0.877044i	$-0.659512\pi$
$31$	2.20837	−	2.20837i	0.396635	−	0.396635i	0.877044	+	0.480409i	$0.159512\pi$
$32$		−	6.56155i		−	1.15993i
$33$	−1.56155			−0.271831
$34$		0			0
$35$		0			0
$36$			4.56155i			0.760259i
$37$	−3.62258	+	3.62258i	−0.595549	+	0.595549i	−0.939125	−	0.343576i	$-0.888362\pi$
$37$	−3.62258	+	3.62258i	−0.595549	+	0.595549i	0.343576	+	0.939125i	$0.388362\pi$
$38$	−12.0000			−1.94666
$39$	0.310029	−	0.310029i	0.0496444	−	0.0496444i
$40$	−16.5246	−	16.5246i	−2.61277	−	2.61277i
$41$	2.51840	+	2.51840i	0.393308	+	0.393308i	0.875865	−	0.482557i	$-0.160292\pi$
$41$	2.51840	+	2.51840i	0.393308	+	0.393308i	−0.482557	+	0.875865i	$0.660292\pi$
$42$		0			0
$43$		−	4.68466i		−	0.714404i	−0.934027	−	0.357202i	$-0.883731\pi$
$43$		−	4.68466i		−	0.714404i	0.934027	−	0.357202i	$-0.116269\pi$
$44$	−5.03680	−	5.03680i	−0.759326	−	0.759326i
$45$	2.51840	+	2.51840i	0.375421	+	0.375421i
$46$	−4.41674	+	4.41674i	−0.651213	+	0.651213i
$47$	11.1231			1.62247			0.811236	−	0.584719i	$-0.198795\pi$
$47$	11.1231			1.62247			0.811236	+	0.584719i	$0.198795\pi$
$48$	−5.43387	+	5.43387i	−0.784312	+	0.784312i
$49$		−	7.00000i		−	1.00000i
$50$	−19.6847			−2.78383
$51$		0			0
$52$	2.00000			0.277350
$53$			12.2462i			1.68215i	0.540921	+	0.841073i	$0.318076\pi$
$53$			12.2462i			1.68215i	−0.540921	+	0.841073i	$0.681924\pi$
$54$	1.81129	−	1.81129i	0.246486	−	0.246486i
$55$	−5.56155			−0.749920
$56$		0			0
$57$	3.31255	+	3.31255i	0.438758	+	0.438758i
$58$	−14.9363	−	14.9363i	−1.96123	−	1.96123i
$59$		−	7.12311i		−	0.927349i	−0.886006	−	0.463675i	$-0.846531\pi$
$59$		−	7.12311i		−	0.927349i	0.886006	−	0.463675i	$-0.153469\pi$
$60$			16.2462i			2.09738i
$61$	−6.45101	−	6.45101i	−0.825967	−	0.825967i	0.160989	−	0.986956i	$-0.448532\pi$
$61$	−6.45101	−	6.45101i	−0.825967	−	0.825967i	−0.986956	+	0.160989i	$0.948532\pi$
$62$	−5.65685	−	5.65685i	−0.718421	−	0.718421i
$63$		0			0
$64$	−1.43845			−0.179806
$65$	1.10418	−	1.10418i	0.136957	−	0.136957i
$66$			4.00000i			0.492366i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	2.43845			0.293555
$70$		0			0
$71$	−4.41674	+	4.41674i	−0.524170	+	0.524170i	−0.918828	−	0.394658i	$-0.870863\pi$
$71$	−4.41674	+	4.41674i	−0.524170	+	0.524170i	0.394658	+	0.918828i	$0.370863\pi$
$72$	6.56155			0.773286
$73$	8.65938	−	8.65938i	1.01350	−	1.01350i	0.0135961	−	0.999908i	$-0.495672\pi$
$73$	8.65938	−	8.65938i	1.01350	−	1.01350i	0.999908	−	0.0135961i	$-0.00432790\pi$
$74$	9.27944	+	9.27944i	1.07871	+	1.07871i
$75$	5.43387	+	5.43387i	0.627450	+	0.627450i
$76$			21.3693i			2.45123i
$77$		0			0
$78$	−0.794156	−	0.794156i	−0.0899204	−	0.0899204i
$79$	−6.62511	−	6.62511i	−0.745383	−	0.745383i	0.228225	−	0.973608i	$-0.426708\pi$
$79$	−6.62511	−	6.62511i	−0.745383	−	0.745383i	−0.973608	+	0.228225i	$0.926708\pi$
$80$	−19.3530	+	19.3530i	−2.16373	+	2.16373i
$81$	−1.00000			−0.111111
$82$	6.45101	−	6.45101i	0.712395	−	0.712395i
$83$		−	0.876894i		−	0.0962517i	−0.998841	−	0.0481258i	$-0.984675\pi$
$83$		−	0.876894i		−	0.0962517i	0.998841	−	0.0481258i	$-0.0153248\pi$
$84$		0			0
$85$		0			0
$86$	−12.0000			−1.29399
$87$			8.24621i			0.884087i
$88$	−7.24517	+	7.24517i	−0.772337	+	0.772337i
$89$	1.12311			0.119049			0.0595245	−	0.998227i	$-0.481042\pi$
$89$	1.12311			0.119049			0.0595245	+	0.998227i	$0.481042\pi$
$90$	6.45101	−	6.45101i	0.679996	−	0.679996i
$91$		0			0
$92$	7.86522	+	7.86522i	0.820006	+	0.820006i
$93$			3.12311i			0.323851i
$94$		−	28.4924i		−	2.93877i
$95$	11.7978	+	11.7978i	1.21043	+	1.21043i
$96$	4.63972	+	4.63972i	0.473539	+	0.473539i
$97$	2.03427	−	2.03427i	0.206549	−	0.206549i	−0.596250	−	0.802799i	$-0.703343\pi$
$97$	2.03427	−	2.03427i	0.206549	−	0.206549i	0.802799	+	0.596250i	$0.203343\pi$
$98$	−17.9309			−1.81129
$99$	1.10418	−	1.10418i	0.110975	−	0.110975i
$100$			35.0540i			3.50540i
$101$	10.8769			1.08229			0.541146	−	0.840929i	$-0.317991\pi$
$101$	10.8769			1.08229			0.541146	+	0.840929i	$0.317991\pi$
$102$		0			0
$103$	16.6847			1.64399			0.821994	−	0.569496i	$-0.192862\pi$
$103$	16.6847			1.64399			0.821994	+	0.569496i	$0.192862\pi$
$104$		−	2.87689i		−	0.282103i
$105$		0			0
$106$	31.3693			3.04686
$107$	3.31255	−	3.31255i	0.320237	−	0.320237i	−0.528621	−	0.848858i	$-0.677291\pi$
$107$	3.31255	−	3.31255i	0.320237	−	0.320237i	0.848858	+	0.528621i	$0.177291\pi$
$108$	−3.22550	−	3.22550i	−0.310374	−	0.310374i
$109$	4.86270	+	4.86270i	0.465762	+	0.465762i	0.900538	−	0.434776i	$-0.143173\pi$
$109$	4.86270	+	4.86270i	0.465762	+	0.465762i	−0.434776	+	0.900538i	$0.643173\pi$
$110$			14.2462i			1.35832i
$111$		−	5.12311i		−	0.486264i
$112$		0			0
$113$	−0.310029	−	0.310029i	−0.0291651	−	0.0291651i	0.692374	−	0.721539i	$-0.256565\pi$
$113$	−0.310029	−	0.310029i	−0.0291651	−	0.0291651i	−0.721539	+	0.692374i	$0.756565\pi$
$114$	8.48528	−	8.48528i	0.794719	−	0.794719i
$115$	8.68466			0.809849
$116$	−26.5982	+	26.5982i	−2.46958	+	2.46958i
$117$			0.438447i			0.0405345i
$118$	−18.2462			−1.67970
$119$		0			0
$120$	23.3693			2.13332
$121$		−	8.56155i		−	0.778323i
$122$	−16.5246	+	16.5246i	−1.49607	+	1.49607i
$123$	−3.56155			−0.321134
$124$	−10.0736	+	10.0736i	−0.904635	+	0.904635i
$125$	6.76104	+	6.76104i	0.604726	+	0.604726i
$126$		0			0
$127$		−	19.8078i		−	1.75765i	−0.477140	−	0.878827i	$-0.658326\pi$
$127$		−	19.8078i		−	1.75765i	0.477140	−	0.878827i	$-0.341674\pi$
$128$		−	9.43845i		−	0.834249i
$129$	3.31255	+	3.31255i	0.291654	+	0.291654i
$130$	−2.82843	−	2.82843i	−0.248069	−	0.248069i
$131$	−10.2095	+	10.2095i	−0.892010	+	0.892010i	−0.994712	−	0.102702i	$-0.967251\pi$
$131$	−10.2095	+	10.2095i	−0.892010	+	0.892010i	0.102702	+	0.994712i	$0.467251\pi$
$132$	7.12311			0.619987
$133$		0			0
$134$		−	10.2462i		−	0.885138i
$135$	−3.56155			−0.306530
$136$		0			0
$137$	0.246211			0.0210352			0.0105176	−	0.999945i	$-0.496652\pi$
$137$	0.246211			0.0210352			0.0105176	+	0.999945i	$0.496652\pi$
$138$		−	6.24621i		−	0.531713i
$139$	−0.620058	+	0.620058i	−0.0525926	+	0.0525926i	−0.732914	−	0.680321i	$-0.761840\pi$
$139$	−0.620058	+	0.620058i	−0.0525926	+	0.0525926i	0.680321	+	0.732914i	$0.261840\pi$
$140$		0			0
$141$	−7.86522	+	7.86522i	−0.662371	+	0.662371i
$142$	11.3137	+	11.3137i	0.949425	+	0.949425i
$143$	−0.484127	−	0.484127i	−0.0404847	−	0.0404847i
$144$		−	7.68466i		−	0.640388i
$145$			29.3693i			2.43899i
$146$	−22.1815	−	22.1815i	−1.83575	−	1.83575i
$147$	4.94975	+	4.94975i	0.408248	+	0.408248i
$148$	16.5246	−	16.5246i	1.35831	−	1.35831i
$149$	−12.2462			−1.00325			−0.501624	−	0.865086i	$-0.667264\pi$
$149$	−12.2462			−1.00325			−0.501624	+	0.865086i	$0.667264\pi$
$150$	13.9192	−	13.9192i	1.13649	−	1.13649i
$151$			8.00000i			0.651031i	0.945537	+	0.325515i	$0.105538\pi$
$151$			8.00000i			0.651031i	−0.945537	+	0.325515i	$0.894462\pi$
$152$	30.7386			2.49323
$153$		0			0
$154$		0			0
$155$			11.1231i			0.893429i
$156$	−1.41421	+	1.41421i	−0.113228	+	0.113228i
$157$	−6.68466			−0.533494			−0.266747	−	0.963767i	$-0.585949\pi$
$157$	−6.68466			−0.533494			−0.266747	+	0.963767i	$0.585949\pi$
$158$	−16.9706	+	16.9706i	−1.35011	+	1.35011i
$159$	−8.65938	−	8.65938i	−0.686733	−	0.686733i
$160$	16.5246	+	16.5246i	1.30638	+	1.30638i
$161$		0			0
$162$			2.56155i			0.201255i
$163$	10.6937	+	10.6937i	0.837591	+	0.837591i	0.988541	−	0.150950i	$-0.0482333\pi$
$163$	10.6937	+	10.6937i	0.837591	+	0.837591i	−0.150950	+	0.988541i	$0.548233\pi$
$164$	−11.4878	−	11.4878i	−0.897047	−	0.897047i
$165$	3.93261	−	3.93261i	0.306153	−	0.306153i
$166$	−2.24621			−0.174340
$167$	14.0062	−	14.0062i	1.08383	−	1.08383i	0.0876843	−	0.996148i	$-0.472053\pi$
$167$	14.0062	−	14.0062i	1.08383	−	1.08383i	0.996148	−	0.0876843i	$-0.0279467\pi$
$168$		0			0
$169$	−12.8078			−0.985213
$170$		0			0
$171$	−4.68466			−0.358245
$172$			21.3693i			1.62940i
$173$	1.27828	−	1.27828i	0.0971860	−	0.0971860i	−0.656842	−	0.754028i	$-0.728108\pi$
$173$	1.27828	−	1.27828i	0.0971860	−	0.0971860i	0.754028	+	0.656842i	$0.228108\pi$
$174$	21.1231			1.60134
$175$		0			0
$176$	8.48528	+	8.48528i	0.639602	+	0.639602i
$177$	5.03680	+	5.03680i	0.378589	+	0.378589i
$178$		−	2.87689i		−	0.215632i
$179$			0.876894i			0.0655422i	0.999463	+	0.0327711i	$0.0104332\pi$
$179$			0.876894i			0.0655422i	−0.999463	+	0.0327711i	$0.989567\pi$
$180$	−11.4878	−	11.4878i	−0.856251	−	0.856251i
$181$	4.24264	+	4.24264i	0.315353	+	0.315353i	0.846979	−	0.531626i	$-0.178419\pi$
$181$	4.24264	+	4.24264i	0.315353	+	0.315353i	−0.531626	+	0.846979i	$0.678419\pi$
$182$		0			0
$183$	9.12311			0.674399
$184$	11.3137	−	11.3137i	0.834058	−	0.834058i
$185$		−	18.2462i		−	1.34149i
$186$	8.00000			0.586588
$187$		0			0
$188$	−50.7386			−3.70050
$189$		0			0
$190$	30.2208	−	30.2208i	2.19245	−	2.19245i
$191$	4.87689			0.352880			0.176440	−	0.984311i	$-0.443542\pi$
$191$	4.87689			0.352880			0.176440	+	0.984311i	$0.443542\pi$
$192$	1.01714	−	1.01714i	0.0734055	−	0.0734055i
$193$	−5.48276	−	5.48276i	−0.394657	−	0.394657i	0.481686	−	0.876344i	$-0.340024\pi$
$193$	−5.48276	−	5.48276i	−0.394657	−	0.394657i	−0.876344	+	0.481686i	$0.840024\pi$
$194$	−5.21089	−	5.21089i	−0.374120	−	0.374120i
$195$			1.56155i			0.111825i
$196$			31.9309i			2.28078i
$197$	6.31508	+	6.31508i	0.449931	+	0.449931i	0.895331	−	0.445401i	$-0.146939\pi$
$197$	6.31508	+	6.31508i	0.449931	+	0.449931i	−0.445401	+	0.895331i	$0.646939\pi$
$198$	−2.82843	−	2.82843i	−0.201008	−	0.201008i
$199$	−11.3137	+	11.3137i	−0.802008	+	0.802008i	−0.983409	−	0.181402i	$-0.941937\pi$
$199$	−11.3137	+	11.3137i	−0.802008	+	0.802008i	0.181402	+	0.983409i	$0.441937\pi$
$200$	50.4233			3.56547
$201$	−2.82843	+	2.82843i	−0.199502	+	0.199502i
$202$		−	27.8617i		−	1.96035i
$203$		0			0
$204$		0			0
$205$	−12.6847			−0.885935
$206$		−	42.7386i		−	2.97774i
$207$	−1.72424	+	1.72424i	−0.119843	+	0.119843i
$208$	−3.36932			−0.233620
$209$	5.17273	−	5.17273i	0.357805	−	0.357805i
$210$		0			0
$211$	−9.45353	−	9.45353i	−0.650808	−	0.650808i	0.302379	−	0.953188i	$-0.402219\pi$
$211$	−9.45353	−	9.45353i	−0.650808	−	0.650808i	−0.953188	+	0.302379i	$0.902219\pi$
$212$		−	55.8617i		−	3.83660i
$213$		−	6.24621i		−	0.427983i
$214$	−8.48528	−	8.48528i	−0.580042	−	0.580042i
$215$	11.7978	+	11.7978i	0.804606	+	0.804606i
$216$	−4.63972	+	4.63972i	−0.315693	+	0.315693i
$217$		0			0
$218$	12.4561	−	12.4561i	0.843631	−	0.843631i
$219$			12.2462i			0.827522i
$220$	25.3693			1.71040
$221$		0			0
$222$	−13.1231			−0.880765
$223$		−	14.9309i		−	0.999845i	−0.866070	−	0.499922i	$-0.833362\pi$
$223$		−	14.9309i		−	0.999845i	0.866070	−	0.499922i	$-0.166638\pi$
$224$		0			0
$225$	−7.68466			−0.512311
$226$	−0.794156	+	0.794156i	−0.0528264	+	0.0528264i
$227$	−9.93766	−	9.93766i	−0.659586	−	0.659586i	0.295696	−	0.955282i	$-0.404448\pi$
$227$	−9.93766	−	9.93766i	−0.659586	−	0.659586i	−0.955282	+	0.295696i	$0.904448\pi$
$228$	−15.1104	−	15.1104i	−1.00071	−	1.00071i
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		−	22.2462i		−	1.46687i
$231$		0			0
$232$	38.2601	+	38.2601i	2.51190	+	2.51190i
$233$	2.51840	−	2.51840i	0.164986	−	0.164986i	−0.619786	−	0.784771i	$-0.712780\pi$
$233$	2.51840	−	2.51840i	0.164986	−	0.164986i	0.784771	+	0.619786i	$0.212780\pi$
$234$	1.12311			0.0734197
$235$	−28.0124	+	28.0124i	−1.82733	+	1.82733i
$236$			32.4924i			2.11508i
$237$	9.36932			0.608603
$238$		0			0
$239$	−6.24621			−0.404034			−0.202017	−	0.979382i	$-0.564750\pi$
$239$	−6.24621			−0.404034			−0.202017	+	0.979382i	$0.564750\pi$
$240$		−	27.3693i		−	1.76668i
$241$	2.38247	−	2.38247i	0.153468	−	0.153468i	−0.626197	−	0.779665i	$-0.715389\pi$
$241$	2.38247	−	2.38247i	0.153468	−	0.153468i	0.779665	+	0.626197i	$0.215389\pi$
$242$	−21.9309			−1.40977
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	29.4266	+	29.4266i	1.88385	+	1.88385i
$245$	17.6288	+	17.6288i	1.12626	+	1.12626i
$246$			9.12311i			0.581668i
$247$			2.05398i			0.130691i
$248$	14.4903	+	14.4903i	0.920137	+	0.920137i
$249$	0.620058	+	0.620058i	0.0392946	+	0.0392946i
$250$	17.3188	−	17.3188i	1.09533	−	1.09533i
$251$	−8.49242			−0.536037			−0.268018	−	0.963414i	$-0.586369\pi$
$251$	−8.49242			−0.536037			−0.268018	+	0.963414i	$0.586369\pi$
$252$		0			0
$253$		−	3.80776i		−	0.239392i
$254$	−50.7386			−3.18363
$255$		0			0
$256$	−27.0540			−1.69087
$257$		−	15.3693i		−	0.958712i	−0.877621	−	0.479356i	$-0.840870\pi$
$257$		−	15.3693i		−	0.958712i	0.877621	−	0.479356i	$-0.159130\pi$
$258$	8.48528	−	8.48528i	0.528271	−	0.528271i
$259$		0			0
$260$	−5.03680	+	5.03680i	−0.312369	+	0.312369i
$261$	−5.83095	−	5.83095i	−0.360927	−	0.360927i
$262$	26.1522	+	26.1522i	1.61569	+	1.61569i
$263$			20.4924i			1.26362i	0.775125	+	0.631808i	$0.217687\pi$
$263$			20.4924i			1.26362i	−0.775125	+	0.631808i	$0.782313\pi$
$264$		−	10.2462i		−	0.630611i
$265$	−30.8408	−	30.8408i	−1.89454	−	1.89454i
$266$		0			0
$267$	−0.794156	+	0.794156i	−0.0486015	+	0.0486015i
$268$	−18.2462			−1.11456
$269$	11.6237	−	11.6237i	0.708712	−	0.708712i	−0.257553	−	0.966264i	$-0.582916\pi$
$269$	11.6237	−	11.6237i	0.708712	−	0.708712i	0.966264	+	0.257553i	$0.0829160\pi$
$270$			9.12311i			0.555215i
$271$	19.8078			1.20324			0.601618	−	0.798784i	$-0.294523\pi$
$271$	19.8078			1.20324			0.601618	+	0.798784i	$0.294523\pi$
$272$		0			0
$273$		0			0
$274$		−	0.630683i		−	0.0381010i
$275$	8.48528	−	8.48528i	0.511682	−	0.511682i
$276$	−11.1231			−0.669532
$277$	−4.24264	+	4.24264i	−0.254916	+	0.254916i	−0.822982	−	0.568067i	$-0.807691\pi$
$277$	−4.24264	+	4.24264i	−0.254916	+	0.254916i	0.568067	+	0.822982i	$0.307691\pi$
$278$	1.58831	+	1.58831i	0.0952606	+	0.0952606i
$279$	−2.20837	−	2.20837i	−0.132212	−	0.132212i
$280$		0			0
$281$			10.8769i			0.648861i	0.945910	+	0.324431i	$0.105173\pi$
$281$			10.8769i			0.648861i	−0.945910	+	0.324431i	$0.894827\pi$
$282$	20.1472	+	20.1472i	1.19975	+	1.19975i
$283$	15.1104	+	15.1104i	0.898219	+	0.898219i	0.995279	−	0.0970592i	$-0.0309436\pi$
$283$	15.1104	+	15.1104i	0.898219	+	0.898219i	−0.0970592	+	0.995279i	$0.530944\pi$
$284$	20.1472	−	20.1472i	1.19552	−	1.19552i
$285$	−16.6847			−0.988314
$286$	−1.24012	+	1.24012i	−0.0733296	+	0.0733296i
$287$		0			0
$288$	−6.56155			−0.386643
$289$		0			0
$290$	75.2311			4.41772
$291$			2.87689i			0.168647i
$292$	−39.5002	+	39.5002i	−2.31158	+	2.31158i
$293$	−1.12311			−0.0656125			−0.0328063	−	0.999462i	$-0.510444\pi$
$293$	−1.12311			−0.0656125			−0.0328063	+	0.999462i	$0.510444\pi$
$294$	12.6790	−	12.6790i	0.739457	−	0.739457i
$295$	17.9388	+	17.9388i	1.04444	+	1.04444i
$296$	−23.7698	−	23.7698i	−1.38159	−	1.38159i
$297$			1.56155i			0.0906105i
$298$			31.3693i			1.81718i
$299$	0.755989	+	0.755989i	0.0437200	+	0.0437200i
$300$	−24.7869	−	24.7869i	−1.43107	−	1.43107i
$301$		0			0
$302$	20.4924			1.17921
$303$	−7.69113	+	7.69113i	−0.441844	+	0.441844i
$304$		−	36.0000i		−	2.06474i
$305$	32.4924			1.86051
$306$		0			0
$307$	32.4924			1.85444			0.927220	−	0.374516i	$-0.122191\pi$
$307$	32.4924			1.85444			0.927220	+	0.374516i	$0.122191\pi$
$308$		0			0
$309$	−11.7978	+	11.7978i	−0.671155	+	0.671155i
$310$	28.4924			1.61826
$311$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$311$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$312$	2.03427	+	2.03427i	0.115168	+	0.115168i
$313$	−23.7698	−	23.7698i	−1.34355	−	1.34355i	−0.892501	−	0.451046i	$-0.851051\pi$
$313$	−23.7698	−	23.7698i	−1.34355	−	1.34355i	−0.451046	−	0.892501i	$-0.648949\pi$
$314$			17.1231i			0.966313i
$315$		0			0
$316$	30.2208	+	30.2208i	1.70005	+	1.70005i
$317$	−12.7279	−	12.7279i	−0.714871	−	0.714871i	0.252679	−	0.967550i	$-0.418688\pi$
$317$	−12.7279	−	12.7279i	−0.714871	−	0.714871i	−0.967550	+	0.252679i	$0.918688\pi$
$318$	−22.1815	+	22.1815i	−1.24387	+	1.24387i
$319$	12.8769			0.720968
$320$	3.62258	−	3.62258i	0.202509	−	0.202509i
$321$			4.68466i			0.261472i
$322$		0			0
$323$		0			0
$324$	4.56155			0.253420
$325$			3.36932i			0.186896i
$326$	27.3924	−	27.3924i	1.51712	−	1.51712i
$327$	−6.87689			−0.380293
$328$	−16.5246	+	16.5246i	−0.912419	+	0.912419i
$329$		0			0
$330$	−10.0736	−	10.0736i	−0.554533	−	0.554533i
$331$			34.9309i			1.91997i	0.280044	+	0.959987i	$0.409651\pi$
$331$			34.9309i			1.91997i	−0.280044	+	0.959987i	$0.590349\pi$
$332$			4.00000i			0.219529i
$333$	3.62258	+	3.62258i	0.198516	+	0.198516i
$334$	−35.8776	−	35.8776i	−1.96314	−	1.96314i
$335$	−10.0736	+	10.0736i	−0.550379	+	0.550379i
$336$		0			0
$337$	−11.8360	+	11.8360i	−0.644748	+	0.644748i	−0.951719	−	0.306971i	$-0.900685\pi$
$337$	−11.8360	+	11.8360i	−0.644748	+	0.644748i	0.306971	+	0.951719i	$0.400685\pi$
$338$			32.8078i			1.78451i
$339$	0.438447			0.0238132
$340$		0			0
$341$	4.87689			0.264099
$342$			12.0000i			0.648886i
$343$		0			0
$344$	30.7386			1.65732
$345$	−6.14098	+	6.14098i	−0.330619	+	0.330619i
$346$	−3.27439	−	3.27439i	−0.176032	−	0.176032i
$347$	6.00505	+	6.00505i	0.322368	+	0.322368i	0.849675	−	0.527307i	$-0.176798\pi$
$347$	6.00505	+	6.00505i	0.322368	+	0.322368i	−0.527307	+	0.849675i	$0.676798\pi$
$348$		−	37.6155i		−	2.01640i
$349$		−	11.5616i		−	0.618876i	−0.950920	−	0.309438i	$-0.899859\pi$
$349$		−	11.5616i		−	0.618876i	0.950920	−	0.309438i	$-0.100141\pi$
$350$		0			0
$351$	−0.310029	−	0.310029i	−0.0165481	−	0.0165481i
$352$	7.24517	−	7.24517i	0.386169	−	0.386169i
$353$	10.4924			0.558455			0.279228	−	0.960225i	$-0.409922\pi$
$353$	10.4924			0.558455			0.279228	+	0.960225i	$0.409922\pi$
$354$	12.9020	−	12.9020i	0.685735	−	0.685735i
$355$		−	22.2462i		−	1.18071i
$356$	−5.12311			−0.271524
$357$		0			0
$358$	2.24621			0.118716
$359$			14.2462i			0.751886i	0.926643	+	0.375943i	$0.122681\pi$
$359$			14.2462i			0.751886i	−0.926643	+	0.375943i	$0.877319\pi$
$360$	−16.5246	+	16.5246i	−0.870923	+	0.870923i
$361$	−2.94602			−0.155054
$362$	10.8677	−	10.8677i	0.571196	−	0.571196i
$363$	6.05393	+	6.05393i	0.317749	+	0.317749i
$364$		0			0
$365$			43.6155i			2.28294i
$366$		−	23.3693i		−	1.22153i
$367$	1.24012	+	1.24012i	0.0647335	+	0.0647335i	0.738732	−	0.673999i	$-0.235425\pi$
$367$	1.24012	+	1.24012i	0.0647335	+	0.0647335i	−0.673999	+	0.738732i	$0.735425\pi$
$368$	−13.2502	−	13.2502i	−0.690715	−	0.690715i
$369$	2.51840	−	2.51840i	0.131103	−	0.131103i
$370$	−46.7386			−2.42983
$371$		0			0
$372$		−	14.2462i		−	0.738632i
$373$	−0.246211			−0.0127483			−0.00637417	−	0.999980i	$-0.502029\pi$
$373$	−0.246211			−0.0127483			−0.00637417	+	0.999980i	$0.502029\pi$
$374$		0			0
$375$	−9.56155			−0.493756
$376$			72.9848i			3.76391i
$377$	−2.55656	+	2.55656i	−0.131670	+	0.131670i
$378$		0			0
$379$	8.48528	−	8.48528i	0.435860	−	0.435860i	−0.454756	−	0.890616i	$-0.650274\pi$
$379$	8.48528	−	8.48528i	0.435860	−	0.435860i	0.890616	+	0.454756i	$0.150274\pi$
$380$	−53.8164	−	53.8164i	−2.76073	−	2.76073i
$381$	14.0062	+	14.0062i	0.717560	+	0.717560i
$382$		−	12.4924i		−	0.639168i
$383$		−	6.24621i		−	0.319166i	−0.987184	−	0.159583i	$-0.948985\pi$
$383$		−	6.24621i		−	0.319166i	0.987184	−	0.159583i	$-0.0510150\pi$
$384$	6.67399	+	6.67399i	0.340581	+	0.340581i
$385$		0			0
$386$	−14.0444	+	14.0444i	−0.714840	+	0.714840i
$387$	−4.68466			−0.238135
$388$	−9.27944	+	9.27944i	−0.471092	+	0.471092i
$389$			35.8617i			1.81826i	0.416510	+	0.909131i	$0.363253\pi$
$389$			35.8617i			1.81826i	−0.416510	+	0.909131i	$0.636747\pi$
$390$	4.00000			0.202548
$391$		0			0
$392$	45.9309			2.31986
$393$		−	14.4384i		−	0.728323i
$394$	16.1764	−	16.1764i	0.814956	−	0.814956i
$395$	33.3693			1.67899
$396$	−5.03680	+	5.03680i	−0.253109	+	0.253109i
$397$	−13.6962	−	13.6962i	−0.687391	−	0.687391i	0.274263	−	0.961655i	$-0.411566\pi$
$397$	−13.6962	−	13.6962i	−0.687391	−	0.687391i	−0.961655	+	0.274263i	$0.911566\pi$
$398$	28.9807	+	28.9807i	1.45267	+	1.45267i
$399$		0			0
$400$		−	59.0540i		−	2.95270i
$401$	−27.7024	−	27.7024i	−1.38339	−	1.38339i	−0.838520	−	0.544871i	$-0.816579\pi$
$401$	−27.7024	−	27.7024i	−1.38339	−	1.38339i	−0.544871	−	0.838520i	$-0.683421\pi$
$402$	7.24517	+	7.24517i	0.361356	+	0.361356i
$403$	−0.968253	+	0.968253i	−0.0482321	+	0.0482321i
$404$	−49.6155			−2.46846
$405$	2.51840	−	2.51840i	0.125140	−	0.125140i
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−14.6847			−0.726110			−0.363055	−	0.931768i	$-0.618266\pi$
$409$	−14.6847			−0.726110			−0.363055	+	0.931768i	$0.618266\pi$
$410$			32.4924i			1.60469i
$411$	−0.174098	+	0.174098i	−0.00858760	+	0.00858760i
$412$	−76.1080			−3.74957
$413$		0			0
$414$	4.41674	+	4.41674i	0.217071	+	0.217071i
$415$	2.20837	+	2.20837i	0.108405	+	0.108405i
$416$			2.87689i			0.141051i
$417$		−	0.876894i		−	0.0429417i
$418$	−13.2502	−	13.2502i	−0.648089	−	0.648089i
$419$	−0.348195	−	0.348195i	−0.0170105	−	0.0170105i	0.698550	−	0.715561i	$-0.253829\pi$
$419$	−0.348195	−	0.348195i	−0.0170105	−	0.0170105i	−0.715561	+	0.698550i	$0.753829\pi$
$420$		0			0
$421$	−24.4384			−1.19106			−0.595529	−	0.803334i	$-0.703057\pi$
$421$	−24.4384			−1.19106			−0.595529	+	0.803334i	$0.703057\pi$
$422$	−24.2157	+	24.2157i	−1.17880	+	1.17880i
$423$		−	11.1231i		−	0.540824i
$424$	−80.3542			−3.90234
$425$		0			0
$426$	−16.0000			−0.775203
$427$		0			0
$428$	−15.1104	+	15.1104i	−0.730388	+	0.730388i
$429$	0.684658			0.0330556
$430$	30.2208	−	30.2208i	1.45738	−	1.45738i
$431$	−16.9706	−	16.9706i	−0.817443	−	0.817443i	0.168294	−	0.985737i	$-0.446174\pi$
$431$	−16.9706	−	16.9706i	−0.817443	−	0.817443i	−0.985737	+	0.168294i	$0.946174\pi$
$432$	5.43387	+	5.43387i	0.261437	+	0.261437i
$433$		−	26.6847i		−	1.28238i	−0.767381	−	0.641191i	$-0.778440\pi$
$433$		−	26.6847i		−	1.28238i	0.767381	−	0.641191i	$-0.221560\pi$
$434$		0			0
$435$	−20.7672	−	20.7672i	−0.995713	−	0.995713i
$436$	−22.1815	−	22.1815i	−1.06230	−	1.06230i
$437$	−8.07749	+	8.07749i	−0.386399	+	0.386399i
$438$	31.3693			1.49888
$439$	−15.7304	+	15.7304i	−0.750773	+	0.750773i	−0.974624	−	0.223850i	$-0.928137\pi$
$439$	−15.7304	+	15.7304i	−0.750773	+	0.750773i	0.223850	+	0.974624i	$0.428137\pi$
$440$		−	36.4924i		−	1.73971i
$441$	−7.00000			−0.333333
$442$		0			0
$443$	−31.1231			−1.47870			−0.739352	−	0.673319i	$-0.764868\pi$
$443$	−31.1231			−1.47870			−0.739352	+	0.673319i	$0.764868\pi$
$444$			23.3693i			1.10906i
$445$	−2.82843	+	2.82843i	−0.134080	+	0.134080i
$446$	−38.2462			−1.81101
$447$	8.65938	−	8.65938i	0.409575	−	0.409575i
$448$		0			0
$449$	−25.9781	−	25.9781i	−1.22598	−	1.22598i	−0.965470	−	0.260514i	$-0.916108\pi$
$449$	−25.9781	−	25.9781i	−1.22598	−	1.22598i	−0.260514	−	0.965470i	$-0.583892\pi$
$450$			19.6847i			0.927944i
$451$			5.56155i			0.261883i
$452$	1.41421	+	1.41421i	0.0665190	+	0.0665190i
$453$	−5.65685	−	5.65685i	−0.265782	−	0.265782i
$454$	−25.4558	+	25.4558i	−1.19470	+	1.19470i
$455$		0			0
$456$	−21.7355	+	21.7355i	−1.01786	+	1.01786i
$457$			13.8078i			0.645900i	0.946416	+	0.322950i	$0.104675\pi$
$457$			13.8078i			0.645900i	−0.946416	+	0.322950i	$0.895325\pi$
$458$	−15.3693			−0.718161
$459$		0			0
$460$	−39.6155			−1.84708
$461$		−	8.24621i		−	0.384064i	−0.981389	−	0.192032i	$-0.938492\pi$
$461$		−	8.24621i		−	0.384064i	0.981389	−	0.192032i	$-0.0615078\pi$
$462$		0			0
$463$	40.9848			1.90473			0.952364	−	0.304965i	$-0.0986447\pi$
$463$	40.9848			1.90473			0.952364	+	0.304965i	$0.0986447\pi$
$464$	44.8089	−	44.8089i	2.08020	−	2.08020i
$465$	−7.86522	−	7.86522i	−0.364741	−	0.364741i
$466$	−6.45101	−	6.45101i	−0.298837	−	0.298837i
$467$		−	21.3693i		−	0.988854i	−0.869219	−	0.494427i	$-0.835378\pi$
$467$		−	21.3693i		−	0.988854i	0.869219	−	0.494427i	$-0.164622\pi$
$468$		−	2.00000i		−	0.0924500i
$469$		0			0
$470$	71.7553	+	71.7553i	3.30982	+	3.30982i
$471$	4.72677	−	4.72677i	0.217798	−	0.217798i
$472$	46.7386			2.15132
$473$	5.17273	−	5.17273i	0.237842	−	0.237842i
$474$		−	24.0000i		−	1.10236i
$475$	−36.0000			−1.65179
$476$		0			0
$477$	12.2462			0.560715
$478$			16.0000i			0.731823i
$479$	17.1828	−	17.1828i	0.785103	−	0.785103i	−0.195584	−	0.980687i	$-0.562660\pi$
$479$	17.1828	−	17.1828i	0.785103	−	0.785103i	0.980687	+	0.195584i	$0.0626601\pi$
$480$	−23.3693			−1.06666
$481$	1.58831	−	1.58831i	0.0724208	−	0.0724208i
$482$	−6.10281	−	6.10281i	−0.277976	−	0.277976i
$483$		0			0
$484$			39.0540i			1.77518i
$485$			10.2462i			0.465256i
$486$	−1.81129	−	1.81129i	−0.0821618	−	0.0821618i
$487$	12.2820	+	12.2820i	0.556549	+	0.556549i	0.928323	−	0.371774i	$-0.121250\pi$
$487$	12.2820	+	12.2820i	0.556549	+	0.556549i	−0.371774	+	0.928323i	$0.621250\pi$
$488$	42.3286	−	42.3286i	1.91613	−	1.91613i
$489$	−15.1231			−0.683890
$490$	45.1571	−	45.1571i	2.03999	−	2.03999i
$491$		−	21.3693i		−	0.964384i	−0.876066	−	0.482192i	$-0.839841\pi$
$491$		−	21.3693i		−	0.964384i	0.876066	−	0.482192i	$-0.160159\pi$
$492$	16.2462			0.732436
$493$		0			0
$494$	5.26137			0.236720
$495$			5.56155i			0.249973i
$496$	16.9706	−	16.9706i	0.762001	−	0.762001i
$497$		0			0
$498$	1.58831	−	1.58831i	0.0711739	−	0.0711739i
$499$	9.45353	+	9.45353i	0.423198	+	0.423198i	0.886303	−	0.463105i	$-0.153265\pi$
$499$	9.45353	+	9.45353i	0.423198	+	0.423198i	−0.463105	+	0.886303i	$0.653265\pi$
$500$	−30.8408	−	30.8408i	−1.37924	−	1.37924i
$501$			19.8078i			0.884946i
$502$			21.7538i			0.970919i
$503$	20.9032	+	20.9032i	0.932026	+	0.932026i	0.997832	−	0.0658060i	$-0.0209618\pi$
$503$	20.9032	+	20.9032i	0.932026	+	0.932026i	−0.0658060	+	0.997832i	$0.520962\pi$
$504$		0			0
$505$	−27.3924	+	27.3924i	−1.21894	+	1.21894i
$506$	−9.75379			−0.433609
$507$	9.05646	−	9.05646i	0.402211	−	0.402211i
$508$			90.3542i			4.00882i
$509$	25.1231			1.11356			0.556781	−	0.830659i	$-0.312036\pi$
$509$	25.1231			1.11356			0.556781	+	0.830659i	$0.312036\pi$
$510$		0			0
$511$		0			0
$512$			50.4233i			2.22842i
$513$	3.31255	−	3.31255i	0.146253	−	0.146253i
$514$	−39.3693			−1.73651
$515$	−42.0186	+	42.0186i	−1.85156	+	1.85156i
$516$	−15.1104	−	15.1104i	−0.665198	−	0.665198i
$517$	12.2820	+	12.2820i	0.540160	+	0.540160i
$518$		0			0
$519$			1.80776i			0.0793520i
$520$	7.24517	+	7.24517i	0.317722	+	0.317722i
$521$	−25.1458	−	25.1458i	−1.10166	−	1.10166i	−0.994211	−	0.107447i	$-0.965732\pi$
$521$	−25.1458	−	25.1458i	−1.10166	−	1.10166i	−0.107447	−	0.994211i	$-0.534268\pi$
$522$	−14.9363	+	14.9363i	−0.653744	+	0.653744i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	46.5713	−	46.5713i	2.03448	−	2.03448i
$525$		0			0
$526$	52.4924			2.28878
$527$		0			0
$528$	−12.0000			−0.522233
$529$		−	17.0540i		−	0.741477i
$530$	−79.0004	+	79.0004i	−3.43156	+	3.43156i
$531$	−7.12311			−0.309116
$532$		0			0
$533$	−1.10418	−	1.10418i	−0.0478275	−	0.0478275i
$534$	2.03427	+	2.03427i	0.0880315	+	0.0880315i
$535$			16.6847i			0.721341i
$536$			26.2462i			1.13366i
$537$	−0.620058	−	0.620058i	−0.0267575	−	0.0267575i
$538$	−29.7748	−	29.7748i	−1.28368	−	1.28368i
$539$	7.72929	−	7.72929i	0.332924	−	0.332924i
$540$	16.2462			0.699126
$541$	24.1180	−	24.1180i	1.03691	−	1.03691i	0.0376201	−	0.999292i	$-0.488022\pi$
$541$	24.1180	−	24.1180i	1.03691	−	1.03691i	0.999292	−	0.0376201i	$-0.0119777\pi$
$542$		−	50.7386i		−	2.17941i
$543$	−6.00000			−0.257485
$544$		0			0
$545$	−24.4924			−1.04914
$546$		0			0
$547$	19.7990	−	19.7990i	0.846544	−	0.846544i	−0.143156	−	0.989700i	$-0.545725\pi$
$547$	19.7990	−	19.7990i	0.846544	−	0.846544i	0.989700	+	0.143156i	$0.0457252\pi$
$548$	−1.12311			−0.0479767
$549$	−6.45101	+	6.45101i	−0.275322	+	0.275322i
$550$	−21.7355	−	21.7355i	−0.926805	−	0.926805i
$551$	−27.3160	−	27.3160i	−1.16370	−	1.16370i
$552$			16.0000i			0.681005i
$553$		0			0
$554$	10.8677	+	10.8677i	0.461726	+	0.461726i
$555$	12.9020	+	12.9020i	0.547660	+	0.547660i
$556$	2.82843	−	2.82843i	0.119952	−	0.119952i
$557$	−26.4924			−1.12252			−0.561260	−	0.827640i	$-0.689683\pi$
$557$	−26.4924			−1.12252			−0.561260	+	0.827640i	$0.689683\pi$
$558$	−5.65685	+	5.65685i	−0.239474	+	0.239474i
$559$			2.05398i			0.0868739i
$560$		0			0
$561$		0			0
$562$	27.8617			1.17528
$563$			31.1231i			1.31168i	0.754899	+	0.655841i	$0.227686\pi$
$563$			31.1231i			1.31168i	−0.754899	+	0.655841i	$0.772314\pi$
$564$	35.8776	−	35.8776i	1.51072	−	1.51072i
$565$	1.56155			0.0656950
$566$	38.7061	−	38.7061i	1.62694	−	1.62694i
$567$		0			0
$568$	−28.9807	−	28.9807i	−1.21600	−	1.21600i
$569$		−	21.1231i		−	0.885527i	−0.896639	−	0.442763i	$-0.853998\pi$
$569$		−	21.1231i		−	0.885527i	0.896639	−	0.442763i	$-0.146002\pi$
$570$			42.7386i			1.79012i
$571$	21.7355	+	21.7355i	0.909602	+	0.909602i	0.996240	−	0.0866377i	$-0.0276122\pi$
$571$	21.7355	+	21.7355i	0.909602	+	0.909602i	−0.0866377	+	0.996240i	$0.527612\pi$
$572$	2.20837	+	2.20837i	0.0923366	+	0.0923366i
$573$	−3.44849	+	3.44849i	−0.144063	+	0.144063i
$574$		0			0
$575$	−13.2502	+	13.2502i	−0.552572	+	0.552572i
$576$			1.43845i			0.0599353i
$577$	−3.94602			−0.164275			−0.0821376	−	0.996621i	$-0.526175\pi$
$577$	−3.94602			−0.164275			−0.0821376	+	0.996621i	$0.526175\pi$
$578$		0			0
$579$	7.75379			0.322236
$580$		−	133.970i		−	5.56279i
$581$		0			0
$582$	7.36932			0.305468
$583$	−13.5221	+	13.5221i	−0.560027	+	0.560027i
$584$	56.8190	+	56.8190i	2.35119	+	2.35119i
$585$	−1.10418	−	1.10418i	−0.0456524	−	0.0456524i
$586$			2.87689i			0.118843i
$587$			28.9848i			1.19633i	0.801372	+	0.598166i	$0.204104\pi$
$587$			28.9848i			1.19633i	−0.801372	+	0.598166i	$0.795896\pi$
$588$	−22.5785	−	22.5785i	−0.931123	−	0.931123i
$589$	−10.3455	−	10.3455i	−0.426277	−	0.426277i
$590$	45.9512	−	45.9512i	1.89178	−	1.89178i
$591$	−8.93087			−0.367367
$592$	−27.8383	+	27.8383i	−1.14415	+	1.14415i
$593$			27.7538i			1.13971i	0.821745	+	0.569856i	$0.193001\pi$
$593$			27.7538i			1.13971i	−0.821745	+	0.569856i	$0.806999\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	55.8617			2.28819
$597$		−	16.0000i		−	0.654836i
$598$	1.93651	−	1.93651i	0.0791896	−	0.0791896i
$599$	0.384472			0.0157091			0.00785455	−	0.999969i	$-0.497500\pi$
$599$	0.384472			0.0157091			0.00785455	+	0.999969i	$0.497500\pi$
$600$	−35.6547	+	35.6547i	−1.45560	+	1.45560i
$601$	−21.9096	−	21.9096i	−0.893711	−	0.893711i	0.101159	−	0.994870i	$-0.467745\pi$
$601$	−21.9096	−	21.9096i	−0.893711	−	0.893711i	−0.994870	+	0.101159i	$0.967745\pi$
$602$		0			0
$603$		−	4.00000i		−	0.162893i
$604$		−	36.4924i		−	1.48486i
$605$	21.5614	+	21.5614i	0.876596	+	0.876596i
$606$	19.7012	+	19.7012i	0.800308	+	0.800308i
$607$	6.62511	−	6.62511i	0.268905	−	0.268905i	−0.559754	−	0.828659i	$-0.689104\pi$
$607$	6.62511	−	6.62511i	0.268905	−	0.268905i	0.828659	+	0.559754i	$0.189104\pi$
$608$	−30.7386			−1.24662
$609$		0			0
$610$		−	83.2311i		−	3.36993i
$611$	−4.87689			−0.197298
$612$		0			0
$613$	14.6847			0.593108			0.296554	−	0.955016i	$-0.404163\pi$
$613$	14.6847			0.593108			0.296554	+	0.955016i	$0.404163\pi$
$614$		−	83.2311i		−	3.35893i
$615$	8.96941	−	8.96941i	0.361681	−	0.361681i
$616$		0			0
$617$	31.2868	−	31.2868i	1.25956	−	1.25956i	0.308255	−	0.951304i	$-0.400255\pi$
$617$	31.2868	−	31.2868i	1.25956	−	1.25956i	0.951304	−	0.308255i	$-0.0997451\pi$
$618$	30.2208	+	30.2208i	1.21566	+	1.21566i
$619$	−3.79668	−	3.79668i	−0.152601	−	0.152601i	0.626677	−	0.779279i	$-0.284414\pi$
$619$	−3.79668	−	3.79668i	−0.152601	−	0.152601i	−0.779279	+	0.626677i	$0.784414\pi$
$620$		−	50.7386i		−	2.03771i
$621$		−	2.43845i		−	0.0978515i
$622$		0			0
$623$		0			0
$624$	2.38247	−	2.38247i	0.0953750	−	0.0953750i
$625$	4.36932			0.174773
$626$	−60.8875	+	60.8875i	−2.43355	+	2.43355i
$627$			7.31534i			0.292147i
$628$	30.4924			1.21678
$629$		0			0
$630$		0			0
$631$		−	0.684658i		−	0.0272558i	−0.999907	−	0.0136279i	$-0.995662\pi$
$631$		−	0.684658i		−	0.0272558i	0.999907	−	0.0136279i	$-0.00433803\pi$
$632$	43.4710	−	43.4710i	1.72918	−	1.72918i
$633$	13.3693			0.531383
$634$	−32.6032	+	32.6032i	−1.29484	+	1.29484i
$635$	49.8838	+	49.8838i	1.97958	+	1.97958i
$636$	39.5002	+	39.5002i	1.56629	+	1.56629i
$637$			3.06913i			0.121603i
$638$		−	32.9848i		−	1.30588i
$639$	4.41674	+	4.41674i	0.174723	+	0.174723i
$640$	23.7698	+	23.7698i	0.939583	+	0.939583i
$641$	20.4572	−	20.4572i	0.808011	−	0.808011i	−0.176321	−	0.984333i	$-0.556420\pi$
$641$	20.4572	−	20.4572i	0.808011	−	0.808011i	0.984333	+	0.176321i	$0.0564198\pi$
$642$	12.0000			0.473602
$643$	−9.72540	+	9.72540i	−0.383532	+	0.383532i	−0.872373	−	0.488841i	$-0.837420\pi$
$643$	−9.72540	+	9.72540i	−0.383532	+	0.383532i	0.488841	+	0.872373i	$0.337420\pi$
$644$		0			0
$645$	−16.6847			−0.656958
$646$		0			0
$647$	−9.36932			−0.368346			−0.184173	−	0.982894i	$-0.558961\pi$
$647$	−9.36932			−0.368346			−0.184173	+	0.982894i	$0.558961\pi$
$648$		−	6.56155i		−	0.257762i
$649$	7.86522	−	7.86522i	0.308737	−	0.308737i
$650$	8.63068			0.338523
$651$		0			0
$652$	−48.7797	−	48.7797i	−1.91036	−	1.91036i
$653$	23.2856	+	23.2856i	0.911238	+	0.911238i	0.996370	−	0.0851321i	$-0.0271312\pi$
$653$	23.2856	+	23.2856i	0.911238	+	0.911238i	−0.0851321	+	0.996370i	$0.527131\pi$
$654$			17.6155i			0.688822i
$655$		−	51.4233i		−	2.00927i
$656$	19.3530	+	19.3530i	0.755609	+	0.755609i
$657$	−8.65938	−	8.65938i	−0.337835	−	0.337835i
$658$		0			0
$659$	9.86174			0.384159			0.192079	−	0.981379i	$-0.438477\pi$
$659$	9.86174			0.384159			0.192079	+	0.981379i	$0.438477\pi$
$660$	−17.9388	+	17.9388i	−0.698267	+	0.698267i
$661$			13.3153i			0.517907i	0.965890	+	0.258953i	$0.0833776\pi$
$661$			13.3153i			0.517907i	−0.965890	+	0.258953i	$0.916622\pi$
$662$	89.4773			3.47763
$663$		0			0
$664$	5.75379			0.223290
$665$		0			0
$666$	9.27944	−	9.27944i	0.359571	−	0.359571i
$667$	−20.1080			−0.778583
$668$	−63.8900	+	63.8900i	−2.47198	+	2.47198i
$669$	10.5577	+	10.5577i	0.408185	+	0.408185i
$670$	25.8040	+	25.8040i	0.996897	+	0.996897i
$671$		−	14.2462i		−	0.549969i
$672$		0			0
$673$	0.522293	+	0.522293i	0.0201329	+	0.0201329i	0.717102	−	0.696969i	$-0.245468\pi$
$673$	0.522293	+	0.522293i	0.0201329	+	0.0201329i	−0.696969	+	0.717102i	$0.745468\pi$
$674$	30.3185	+	30.3185i	1.16783	+	1.16783i
$675$	5.43387	−	5.43387i	0.209150	−	0.209150i
$676$	58.4233			2.24705
$677$	−0.930087	+	0.930087i	−0.0357461	+	0.0357461i	−0.724754	−	0.689008i	$-0.758047\pi$
$677$	−0.930087	+	0.930087i	−0.0357461	+	0.0357461i	0.689008	+	0.724754i	$0.258047\pi$
$678$		−	1.12311i		−	0.0431326i
$679$		0			0
$680$		0			0
$681$	14.0540			0.538550
$682$		−	12.4924i		−	0.478360i
$683$	−6.76104	+	6.76104i	−0.258704	+	0.258704i	−0.824527	−	0.565823i	$-0.808559\pi$
$683$	−6.76104	+	6.76104i	−0.258704	+	0.258704i	0.565823	+	0.824527i	$0.308559\pi$
$684$	21.3693			0.817076
$685$	−0.620058	+	0.620058i	−0.0236912	+	0.0236912i
$686$		0			0
$687$	4.24264	+	4.24264i	0.161867	+	0.161867i
$688$		−	36.0000i		−	1.37249i
$689$		−	5.36932i		−	0.204555i
$690$	15.7304	+	15.7304i	0.598848	+	0.598848i
$691$	−20.4954	−	20.4954i	−0.779681	−	0.779681i	0.200095	−	0.979776i	$-0.435875\pi$
$691$	−20.4954	−	20.4954i	−0.779681	−	0.779681i	−0.979776	+	0.200095i	$0.935875\pi$
$692$	−5.83095	+	5.83095i	−0.221660	+	0.221660i
$693$		0			0
$694$	15.3823	−	15.3823i	0.583902	−	0.583902i
$695$		−	3.12311i		−	0.118466i
$696$	−54.1080			−2.05096
$697$		0			0
$698$	−29.6155			−1.12096
$699$			3.56155i			0.134710i
$700$		0			0
$701$	−15.3693			−0.580491			−0.290246	−	0.956952i	$-0.593737\pi$
$701$	−15.3693			−0.580491			−0.290246	+	0.956952i	$0.593737\pi$
$702$	−0.794156	+	0.794156i	−0.0299735	+	0.0299735i
$703$	16.9706	+	16.9706i	0.640057	+	0.640057i
$704$	−1.58831	−	1.58831i	−0.0598617	−	0.0598617i
$705$		−	39.6155i		−	1.49201i
$706$		−	26.8769i		−	1.01153i
$707$		0			0
$708$	−22.9756	−	22.9756i	−0.863476	−	0.863476i
$709$	31.6350	−	31.6350i	1.18808	−	1.18808i	0.210479	−	0.977598i	$-0.432498\pi$
$709$	31.6350	−	31.6350i	1.18808	−	1.18808i	0.977598	−	0.210479i	$-0.0675022\pi$
$710$	−56.9848			−2.13860
$711$	−6.62511	+	6.62511i	−0.248461	+	0.248461i
$712$			7.36932i			0.276177i
$713$	−7.61553			−0.285204
$714$		0			0
$715$	2.43845			0.0911928
$716$		−	4.00000i		−	0.149487i
$717$	4.41674	−	4.41674i	0.164946	−	0.164946i
$718$	36.4924			1.36189
$719$	8.34935	−	8.34935i	0.311378	−	0.311378i	−0.534065	−	0.845443i	$-0.679336\pi$
$719$	8.34935	−	8.34935i	0.311378	−	0.311378i	0.845443	+	0.534065i	$0.179336\pi$
$720$	19.3530	+	19.3530i	0.721245	+	0.721245i
$721$		0			0
$722$			7.54640i			0.280848i
$723$			3.36932i			0.125306i
$724$	−19.3530	−	19.3530i	−0.719250	−	0.719250i
$725$	−44.8089	−	44.8089i	−1.66416	−	1.66416i
$726$	15.5075	−	15.5075i	0.575536	−	0.575536i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	111.723			4.13507
$731$		0			0
$732$	−41.6155			−1.53815
$733$		−	11.7538i		−	0.434136i	−0.976156	−	0.217068i	$-0.930351\pi$
$733$		−	11.7538i		−	0.434136i	0.976156	−	0.217068i	$-0.0696494\pi$
$734$	3.17662	−	3.17662i	0.117251	−	0.117251i
$735$	−24.9309			−0.919589
$736$	−11.3137	+	11.3137i	−0.417029	+	0.417029i
$737$	4.41674	+	4.41674i	0.162693	+	0.162693i
$738$	−6.45101	−	6.45101i	−0.237465	−	0.237465i
$739$			20.6847i			0.760897i	0.924802	+	0.380449i	$0.124230\pi$
$739$			20.6847i			0.760897i	−0.924802	+	0.380449i	$0.875770\pi$
$740$			83.2311i			3.05963i
$741$	−1.45238	−	1.45238i	−0.0533545	−	0.0533545i
$742$		0			0
$743$	−20.1472	+	20.1472i	−0.739129	+	0.739129i	−0.972409	−	0.233281i	$-0.925054\pi$
$743$	−20.1472	+	20.1472i	−0.739129	+	0.739129i	0.233281	+	0.972409i	$0.425054\pi$
$744$	−20.4924			−0.751289
$745$	30.8408	−	30.8408i	1.12992	−	1.12992i
$746$			0.630683i			0.0230909i
$747$	−0.876894			−0.0320839
$748$		0			0
$749$		0			0
$750$			24.4924i			0.894337i
$751$	−17.9388	+	17.9388i	−0.654597	+	0.654597i	−0.954096	−	0.299500i	$-0.903180\pi$
$751$	−17.9388	+	17.9388i	−0.654597	+	0.654597i	0.299500	+	0.954096i	$0.403180\pi$
$752$	85.4773			3.11704
$753$	6.00505	−	6.00505i	0.218836	−	0.218836i
$754$	6.54877	+	6.54877i	0.238492	+	0.238492i
$755$	−20.1472	−	20.1472i	−0.733231	−	0.733231i
$756$		0			0
$757$		−	16.0540i		−	0.583492i	−0.956496	−	0.291746i	$-0.905764\pi$
$757$		−	16.0540i		−	0.583492i	0.956496	−	0.291746i	$-0.0942361\pi$
$758$	−21.7355	−	21.7355i	−0.789469	−	0.789469i
$759$	2.69250	+	2.69250i	0.0977314	+	0.0977314i
$760$	−77.4121	+	77.4121i	−2.80803	+	2.80803i
$761$	15.7538			0.571074			0.285537	−	0.958368i	$-0.407828\pi$
$761$	15.7538			0.571074			0.285537	+	0.958368i	$0.407828\pi$
$762$	35.8776	−	35.8776i	1.29971	−	1.29971i
$763$		0			0
$764$	−22.2462			−0.804840
$765$		0			0
$766$	−16.0000			−0.578103
$767$			3.12311i			0.112769i
$768$	19.1300	−	19.1300i	0.690296	−	0.690296i
$769$	−40.5464			−1.46214			−0.731070	−	0.682302i	$-0.760979\pi$
$769$	−40.5464			−1.46214			−0.731070	+	0.682302i	$0.760979\pi$
$770$		0			0
$771$	10.8677	+	10.8677i	0.391392	+	0.391392i
$772$	25.0099	+	25.0099i	0.900125	+	0.900125i
$773$			8.63068i			0.310424i	0.987881	+	0.155212i	$0.0496061\pi$
$773$			8.63068i			0.310424i	−0.987881	+	0.155212i	$0.950394\pi$
$774$			12.0000i			0.431331i
$775$	−16.9706	−	16.9706i	−0.609601	−	0.609601i
$776$	13.3480	+	13.3480i	0.479165	+	0.479165i
$777$		0			0
$778$	91.8617			3.29340
$779$	11.7978	−	11.7978i	0.422701	−	0.422701i
$780$		−	7.12311i		−	0.255048i
$781$	−9.75379			−0.349018
$782$		0			0
$783$	8.24621			0.294696
$784$		−	53.7926i		−	1.92116i
$785$	16.8346	−	16.8346i	0.600854	−	0.600854i
$786$	−36.9848			−1.31921
$787$	7.24517	−	7.24517i	0.258262	−	0.258262i	−0.566085	−	0.824347i	$-0.691543\pi$
$787$	7.24517	−	7.24517i	0.258262	−	0.258262i	0.824347	+	0.566085i	$0.191543\pi$
$788$	−28.8066	−	28.8066i	−1.02619	−	1.02619i
$789$	−14.4903	−	14.4903i	−0.515869	−	0.515869i
$790$		−	85.4773i		−	3.04114i
$791$		0			0
$792$	7.24517	+	7.24517i	0.257446	+	0.257446i
$793$	2.82843	+	2.82843i	0.100440	+	0.100440i
$794$	−35.0835	+	35.0835i	−1.24507	+	1.24507i
$795$	43.6155			1.54688
$796$	51.6081	−	51.6081i	1.82920	−	1.82920i
$797$		−	9.61553i		−	0.340599i	−0.985392	−	0.170300i	$-0.945526\pi$
$797$		−	9.61553i		−	0.340599i	0.985392	−	0.170300i	$-0.0544736\pi$
$798$		0			0
$799$		0			0
$800$	−50.4233			−1.78273
$801$		−	1.12311i		−	0.0396830i
$802$	−70.9611	+	70.9611i	−2.50572	+	2.50572i
$803$	19.1231			0.674840
$804$	12.9020	−	12.9020i	0.455019	−	0.455019i
$805$		0			0
$806$	2.48023	+	2.48023i	0.0873624	+	0.0873624i
$807$			16.4384i			0.578661i
$808$			71.3693i			2.51076i
$809$	−11.2755	−	11.2755i	−0.396427	−	0.396427i	0.480544	−	0.876971i	$-0.340439\pi$
$809$	−11.2755	−	11.2755i	−0.396427	−	0.396427i	−0.876971	+	0.480544i	$0.840439\pi$
$810$	−6.45101	−	6.45101i	−0.226665	−	0.226665i
$811$	32.0810	−	32.0810i	1.12651	−	1.12651i	0.135775	−	0.990740i	$-0.456648\pi$
$811$	32.0810	−	32.0810i	1.12651	−	1.12651i	0.990740	−	0.135775i	$-0.0433524\pi$
$812$		0			0
$813$	−14.0062	+	14.0062i	−0.491219	+	0.491219i
$814$			20.4924i			0.718259i
$815$	−53.8617			−1.88669
$816$		0			0
$817$	−21.9460			−0.767794
$818$			37.6155i			1.31520i
$819$		0			0
$820$	57.8617			2.02062
$821$	8.79531	−	8.79531i	0.306958	−	0.306958i	−0.536770	−	0.843729i	$-0.680356\pi$
$821$	8.79531	−	8.79531i	0.306958	−	0.306958i	0.843729	+	0.536770i	$0.180356\pi$
$822$	0.445960	+	0.445960i	0.0155547	+	0.0155547i
$823$	−2.48023	−	2.48023i	−0.0864554	−	0.0864554i	0.662556	−	0.749012i	$-0.269471\pi$
$823$	−2.48023	−	2.48023i	−0.0864554	−	0.0864554i	−0.749012	+	0.662556i	$0.769471\pi$
$824$			109.477i			3.81382i
$825$			12.0000i			0.417786i
$826$		0			0
$827$	33.5333	+	33.5333i	1.16607	+	1.16607i	0.983123	+	0.182945i	$0.0585630\pi$
$827$	33.5333	+	33.5333i	1.16607	+	1.16607i	0.182945	+	0.983123i	$0.441437\pi$
$828$	7.86522	−	7.86522i	0.273335	−	0.273335i
$829$	−17.5076			−0.608063			−0.304032	−	0.952662i	$-0.598333\pi$
$829$	−17.5076			−0.608063			−0.304032	+	0.952662i	$0.598333\pi$
$830$	5.65685	−	5.65685i	0.196352	−	0.196352i
$831$		−	6.00000i		−	0.208138i
$832$	0.630683			0.0218650
$833$		0			0
$834$	−2.24621			−0.0777799
$835$			70.5464i			2.44136i
$836$	−23.5957	+	23.5957i	−0.816073	+	0.816073i
$837$	3.12311			0.107950
$838$	−0.891921	+	0.891921i	−0.0308109	+	0.0308109i
$839$	−18.4229	−	18.4229i	−0.636031	−	0.636031i	0.313543	−	0.949574i	$-0.398484\pi$
$839$	−18.4229	−	18.4229i	−0.636031	−	0.636031i	−0.949574	+	0.313543i	$0.898484\pi$
$840$		0			0
$841$		−	39.0000i		−	1.34483i
$842$			62.6004i			2.15735i
$843$	−7.69113	−	7.69113i	−0.264896	−	0.264896i
$844$	43.1228	+	43.1228i	1.48435	+	1.48435i
$845$	32.2550	−	32.2550i	1.10961	−	1.10961i
$846$	−28.4924			−0.979590
$847$		0			0
$848$			94.1080i			3.23168i
$849$	−21.3693			−0.733393
$850$		0			0
$851$	12.4924			0.428235
$852$			28.4924i			0.976134i
$853$	−20.3213	+	20.3213i	−0.695787	+	0.695787i	−0.963499	−	0.267712i	$-0.913733\pi$
$853$	−20.3213	+	20.3213i	−0.695787	+	0.695787i	0.267712	+	0.963499i	$0.413733\pi$
$854$		0			0
$855$	11.7978	−	11.7978i	0.403477	−	0.403477i
$856$	21.7355	+	21.7355i	0.742904	+	0.742904i
$857$	4.24264	+	4.24264i	0.144926	+	0.144926i	0.775847	−	0.630921i	$-0.217323\pi$
$857$	4.24264	+	4.24264i	0.144926	+	0.144926i	−0.630921	+	0.775847i	$0.717323\pi$
$858$		−	1.75379i		−	0.0598734i
$859$		−	12.0000i		−	0.409435i	−0.978821	−	0.204717i	$-0.934372\pi$
$859$		−	12.0000i		−	0.409435i	0.978821	−	0.204717i	$-0.0656275\pi$
$860$	−53.8164	−	53.8164i	−1.83513	−	1.83513i
$861$		0			0
$862$	−43.4710	+	43.4710i	−1.48063	+	1.48063i
$863$	9.75379			0.332023			0.166011	−	0.986124i	$-0.446911\pi$
$863$	9.75379			0.332023			0.166011	+	0.986124i	$0.446911\pi$
$864$	4.63972	−	4.63972i	0.157846	−	0.157846i
$865$			6.43845i			0.218914i
$866$	−68.3542			−2.32277
$867$		0			0
$868$		0			0
$869$		−	14.6307i		−	0.496312i
$870$	−53.1964	+	53.1964i	−1.80353	+	1.80353i
$871$	−1.75379			−0.0594249
$872$	−31.9069	+	31.9069i	−1.08050	+	1.08050i
$873$	−2.03427	−	2.03427i	−0.0688497	−	0.0688497i
$874$	20.6909	+	20.6909i	0.699880	+	0.699880i
$875$		0			0
$876$		−	55.8617i		−	1.88739i
$877$	24.0416	+	24.0416i	0.811828	+	0.811828i	0.984908	−	0.173080i	$-0.0553718\pi$
$877$	24.0416	+	24.0416i	0.811828	+	0.811828i	−0.173080	+	0.984908i	$0.555372\pi$
$878$	40.2944	+	40.2944i	1.35987	+	1.35987i
$879$	0.794156	−	0.794156i	0.0267862	−	0.0267862i
$880$	−42.7386			−1.44072
$881$	28.4584	−	28.4584i	0.958787	−	0.958787i	−0.0403969	−	0.999184i	$-0.512862\pi$
$881$	28.4584	−	28.4584i	0.958787	−	0.958787i	0.999184	+	0.0403969i	$0.0128622\pi$
$882$			17.9309i			0.603764i
$883$	−23.4233			−0.788257			−0.394128	−	0.919055i	$-0.628953\pi$
$883$	−23.4233			−0.788257			−0.394128	+	0.919055i	$0.628953\pi$
$884$		0			0
$885$	−25.3693			−0.852780
$886$			79.7235i			2.67836i
$887$	13.0380	−	13.0380i	0.437772	−	0.437772i	−0.453490	−	0.891261i	$-0.649821\pi$
$887$	13.0380	−	13.0380i	0.437772	−	0.437772i	0.891261	+	0.453490i	$0.149821\pi$
$888$	33.6155			1.12806
$889$		0			0
$890$	7.24517	+	7.24517i	0.242858	+	0.242858i
$891$	−1.10418	−	1.10418i	−0.0369916	−	0.0369916i
$892$			68.1080i			2.28042i
$893$		−	52.1080i		−	1.74373i
$894$	−22.1815	−	22.1815i	−0.741859	−	0.741859i
$895$	−2.20837	−	2.20837i	−0.0738176	−	0.0738176i
$896$		0			0
$897$	−1.06913			−0.0356972
$898$	−66.5444	+	66.5444i	−2.22061	+	2.22061i
$899$		−	25.7538i		−	0.858937i
$900$	35.0540			1.16847
$901$		0			0
$902$	14.2462			0.474347
$903$		0			0
$904$	2.03427	−	2.03427i	0.0676589	−	0.0676589i
$905$	−21.3693			−0.710340
$906$	−14.4903	+	14.4903i	−0.481409	+	0.481409i
$907$	−6.97330	−	6.97330i	−0.231545	−	0.231545i	0.581793	−	0.813337i	$-0.302352\pi$
$907$	−6.97330	−	6.97330i	−0.231545	−	0.231545i	−0.813337	+	0.581793i	$0.802352\pi$
$908$	45.3312	+	45.3312i	1.50437	+	1.50437i
$909$		−	10.8769i		−	0.360764i
$910$		0			0
$911$	−17.1828	−	17.1828i	−0.569292	−	0.569292i	0.362638	−	0.931930i	$-0.381876\pi$
$911$	−17.1828	−	17.1828i	−0.569292	−	0.569292i	−0.931930	+	0.362638i	$0.881876\pi$
$912$	25.4558	+	25.4558i	0.842927	+	0.842927i
$913$	0.968253	−	0.968253i	0.0320445	−	0.0320445i
$914$	35.3693			1.16991
$915$	−22.9756	+	22.9756i	−0.759550	+	0.759550i
$916$			27.3693i			0.904308i
$917$		0			0
$918$		0			0
$919$	−16.6847			−0.550376			−0.275188	−	0.961390i	$-0.588740\pi$
$919$	−16.6847			−0.550376			−0.275188	+	0.961390i	$0.588740\pi$
$920$			56.9848i			1.87873i
$921$	−22.9756	+	22.9756i	−0.757072	+	0.757072i
$922$	−21.1231			−0.695652
$923$	1.93651	−	1.93651i	0.0637409	−	0.0637409i
$924$		0			0
$925$	27.8383	+	27.8383i	0.915318	+	0.915318i
$926$		−	104.985i		−	3.45002i
$927$		−	16.6847i		−	0.547996i
$928$	−38.2601	−	38.2601i	−1.25595	−	1.25595i
$929$	2.17020	+	2.17020i	0.0712020	+	0.0712020i	0.741811	−	0.670609i	$-0.233967\pi$
$929$	2.17020	+	2.17020i	0.0712020	+	0.0712020i	−0.670609	+	0.741811i	$0.733967\pi$
$930$	−20.1472	+	20.1472i	−0.660652	+	0.660652i
$931$	−32.7926			−1.07473
$932$	−11.4878	+	11.4878i	−0.376296	+	0.376296i
$933$		0			0
$934$	−54.7386			−1.79110
$935$		0			0
$936$	−2.87689			−0.0940342
$937$		−	22.0000i		−	0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$		−	22.0000i		−	0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$		0			0
$939$	33.6155			1.09700
$940$	127.780	−	127.780i	4.16773	−	4.16773i
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	0.962569	−	0.271038i	$-0.0873669\pi$
$941$	21.2132	+	21.2132i	0.691531	+	0.691531i	−0.271038	+	0.962569i	$0.587367\pi$
$942$	−12.1079	−	12.1079i	−0.394496	−	0.394496i
$943$		−	8.68466i		−	0.282811i
$944$		−	54.7386i		−	1.78159i
$945$		0			0
$946$	−13.2502	−	13.2502i	−0.430802	−	0.430802i
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	−0.831404	−	0.555669i	$-0.812462\pi$
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	0.555669	+	0.831404i	$0.312462\pi$
$948$	−42.7386			−1.38809
$949$	−3.79668	+	3.79668i	−0.123245	+	0.123245i
$950$			92.2159i			2.99188i
$951$	18.0000			0.583690
$952$		0			0
$953$	36.3542			1.17763			0.588813	−	0.808269i	$-0.299595\pi$
$953$	36.3542			1.17763			0.588813	+	0.808269i	$0.299595\pi$
$954$		−	31.3693i		−	1.01562i
$955$	−12.2820	+	12.2820i	−0.397435	+	0.397435i
$956$	28.4924			0.921511
$957$	−9.10534	+	9.10534i	−0.294334	+	0.294334i
$958$	−44.0147	−	44.0147i	−1.42205	−	1.42205i
$959$		0			0
$960$			5.12311i			0.165348i
$961$			21.2462i			0.685362i
$962$	−4.06854	−	4.06854i	−0.131175	−	0.131175i
$963$	−3.31255	−	3.31255i	−0.106746	−	0.106746i
$964$	−10.8677	+	10.8677i	−0.350027	+	0.350027i
$965$	27.6155			0.888975
$966$		0			0
$967$			42.4384i			1.36473i	0.731012	+	0.682364i	$0.239048\pi$
$967$			42.4384i			1.36473i	−0.731012	+	0.682364i	$0.760952\pi$
$968$	56.1771			1.80560
$969$		0			0
$970$	26.2462			0.842715
$971$		−	43.6155i		−	1.39969i	−0.714295	−	0.699844i	$-0.753253\pi$
$971$		−	43.6155i		−	1.39969i	0.714295	−	0.699844i	$-0.246747\pi$
$972$	−3.22550	+	3.22550i	−0.103458	+	0.103458i
$973$		0			0
$974$	31.4609	−	31.4609i	1.00807	−	1.00807i
$975$	−2.38247	−	2.38247i	−0.0763000	−	0.0763000i
$976$	−49.5738	−	49.5738i	−1.58682	−	1.58682i
$977$		−	8.24621i		−	0.263820i	−0.991262	−	0.131910i	$-0.957889\pi$
$977$		−	8.24621i		−	0.263820i	0.991262	−	0.131910i	$-0.0421109\pi$
$978$			38.7386i			1.23872i
$979$	1.24012	+	1.24012i	0.0396343	+	0.0396343i
$980$	−80.4146	−	80.4146i	−2.56875	−	2.56875i
$981$	4.86270	−	4.86270i	0.155254	−	0.155254i
$982$	−54.7386			−1.74678
$983$	21.8714	−	21.8714i	0.697590	−	0.697590i	−0.266300	−	0.963890i	$-0.585801\pi$
$983$	21.8714	−	21.8714i	0.697590	−	0.697590i	0.963890	+	0.266300i	$0.0858012\pi$
$984$		−	23.3693i		−	0.744987i
$985$	−31.8078			−1.01348
$986$		0			0
$987$		0			0
$988$		−	9.36932i		−	0.298078i
$989$	−8.07749	+	8.07749i	−0.256849	+	0.256849i
$990$	14.2462			0.452774
$991$	−30.2208	+	30.2208i	−0.959995	+	0.959995i	−0.999230	−	0.0392354i	$-0.987508\pi$
$991$	−30.2208	+	30.2208i	−0.959995	+	0.959995i	0.0392354	+	0.999230i	$0.487508\pi$
$992$	−14.4903	−	14.4903i	−0.460068	−	0.460068i
$993$	−24.6999	−	24.6999i	−0.783826	−	0.783826i
$994$		0			0
$995$		−	56.9848i		−	1.80654i
$996$	−2.82843	−	2.82843i	−0.0896221	−	0.0896221i
$997$	−7.07107	−	7.07107i	−0.223943	−	0.223943i	0.586214	−	0.810157i	$-0.300618\pi$
$997$	−7.07107	−	7.07107i	−0.223943	−	0.223943i	−0.810157	+	0.586214i	$0.800618\pi$
$998$	24.2157	−	24.2157i	0.766535	−	0.766535i
$999$	−5.12311			−0.162088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.f.616.1		8
17.2	even	8		867.2.d.c.577.4		4
17.3	odd	16		867.2.h.j.733.1		16
17.4	even	4	inner	867.2.e.f.829.4		8
17.5	odd	16		867.2.h.j.712.3		16
17.6	odd	16		867.2.h.j.688.3		16
17.7	odd	16		867.2.h.j.757.2		16
17.8	even	8		867.2.a.f.1.1		2
17.9	even	8		51.2.a.b.1.1	✓	2
17.10	odd	16		867.2.h.j.757.1		16
17.11	odd	16		867.2.h.j.688.4		16
17.12	odd	16		867.2.h.j.712.4		16
17.13	even	4	inner	867.2.e.f.829.3		8
17.14	odd	16		867.2.h.j.733.2		16
17.15	even	8		867.2.d.c.577.3		4
17.16	even	2	inner	867.2.e.f.616.2		8
51.8	odd	8		2601.2.a.t.1.2		2
51.26	odd	8		153.2.a.e.1.2		2
68.43	odd	8		816.2.a.m.1.2		2
85.9	even	8		1275.2.a.n.1.2		2
85.43	odd	8		1275.2.b.d.1174.4		4
85.77	odd	8		1275.2.b.d.1174.1		4
119.111	odd	8		2499.2.a.o.1.1		2
136.43	odd	8		3264.2.a.bg.1.1		2
136.77	even	8		3264.2.a.bl.1.1		2
187.43	odd	8		6171.2.a.p.1.2		2
204.179	even	8		2448.2.a.v.1.1		2
221.77	even	8		8619.2.a.q.1.2		2
255.179	odd	8		3825.2.a.s.1.1		2
357.230	even	8		7497.2.a.v.1.2		2
408.77	odd	8		9792.2.a.cy.1.2		2
408.179	even	8		9792.2.a.cz.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.1	✓	2	17.9	even	8
153.2.a.e.1.2		2	51.26	odd	8
816.2.a.m.1.2		2	68.43	odd	8
867.2.a.f.1.1		2	17.8	even	8
867.2.d.c.577.3		4	17.15	even	8
867.2.d.c.577.4		4	17.2	even	8
867.2.e.f.616.1		8	1.1	even	1	trivial
867.2.e.f.616.2		8	17.16	even	2	inner
867.2.e.f.829.3		8	17.13	even	4	inner
867.2.e.f.829.4		8	17.4	even	4	inner
867.2.h.j.688.3		16	17.6	odd	16
867.2.h.j.688.4		16	17.11	odd	16
867.2.h.j.712.3		16	17.5	odd	16
867.2.h.j.712.4		16	17.12	odd	16
867.2.h.j.733.1		16	17.3	odd	16
867.2.h.j.733.2		16	17.14	odd	16
867.2.h.j.757.1		16	17.10	odd	16
867.2.h.j.757.2		16	17.7	odd	16
1275.2.a.n.1.2		2	85.9	even	8
1275.2.b.d.1174.1		4	85.77	odd	8
1275.2.b.d.1174.4		4	85.43	odd	8
2448.2.a.v.1.1		2	204.179	even	8
2499.2.a.o.1.1		2	119.111	odd	8
2601.2.a.t.1.2		2	51.8	odd	8
3264.2.a.bg.1.1		2	136.43	odd	8
3264.2.a.bl.1.1		2	136.77	even	8
3825.2.a.s.1.1		2	255.179	odd	8
6171.2.a.p.1.2		2	187.43	odd	8
7497.2.a.v.1.2		2	357.230	even	8
8619.2.a.q.1.2		2	221.77	even	8
9792.2.a.cy.1.2		2	408.77	odd	8
9792.2.a.cz.1.2		2	408.179	even	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -4.56155 q^{4} +(-2.51840 + 2.51840i) q^{5} +(1.81129 + 1.81129i) q^{6} +6.56155i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-2.56155i q^{2} +(-0.707107 + 0.707107i) q^{3} -4.56155 q^{4} +(-2.51840 + 2.51840i) q^{5} +(1.81129 + 1.81129i) q^{6} +6.56155i q^{8} -1.00000i q^{9} +(6.45101 + 6.45101i) q^{10} +(1.10418 + 1.10418i) q^{11} +(3.22550 - 3.22550i) q^{12} -0.438447 q^{13} -3.56155i q^{15} +7.68466 q^{16} -2.56155 q^{18} -4.68466i q^{19} +(11.4878 - 11.4878i) q^{20} +(2.82843 - 2.82843i) q^{22} +(-1.72424 - 1.72424i) q^{23} +(-4.63972 - 4.63972i) q^{24} -7.68466i q^{25} +1.12311i q^{26} +(0.707107 + 0.707107i) q^{27} +(5.83095 - 5.83095i) q^{29} -9.12311 q^{30} +(2.20837 - 2.20837i) q^{31} -6.56155i q^{32} -1.56155 q^{33} +4.56155i q^{36} +(-3.62258 + 3.62258i) q^{37} -12.0000 q^{38} +(0.310029 - 0.310029i) q^{39} +(-16.5246 - 16.5246i) q^{40} +(2.51840 + 2.51840i) q^{41} -4.68466i q^{43} +(-5.03680 - 5.03680i) q^{44} +(2.51840 + 2.51840i) q^{45} +(-4.41674 + 4.41674i) q^{46} +11.1231 q^{47} +(-5.43387 + 5.43387i) q^{48} -7.00000i q^{49} -19.6847 q^{50} +2.00000 q^{52} +12.2462i q^{53} +(1.81129 - 1.81129i) q^{54} -5.56155 q^{55} +(3.31255 + 3.31255i) q^{57} +(-14.9363 - 14.9363i) q^{58} -7.12311i q^{59} +16.2462i q^{60} +(-6.45101 - 6.45101i) q^{61} +(-5.65685 - 5.65685i) q^{62} -1.43845 q^{64} +(1.10418 - 1.10418i) q^{65} +4.00000i q^{66} +4.00000 q^{67} +2.43845 q^{69} +(-4.41674 + 4.41674i) q^{71} +6.56155 q^{72} +(8.65938 - 8.65938i) q^{73} +(9.27944 + 9.27944i) q^{74} +(5.43387 + 5.43387i) q^{75} +21.3693i q^{76} +(-0.794156 - 0.794156i) q^{78} +(-6.62511 - 6.62511i) q^{79} +(-19.3530 + 19.3530i) q^{80} -1.00000 q^{81} +(6.45101 - 6.45101i) q^{82} -0.876894i q^{83} -12.0000 q^{86} +8.24621i q^{87} +(-7.24517 + 7.24517i) q^{88} +1.12311 q^{89} +(6.45101 - 6.45101i) q^{90} +(7.86522 + 7.86522i) q^{92} +3.12311i q^{93} -28.4924i q^{94} +(11.7978 + 11.7978i) q^{95} +(4.63972 + 4.63972i) q^{96} +(2.03427 - 2.03427i) q^{97} -17.9309 q^{98} +(1.10418 - 1.10418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 20 q^{4}+O(q^{10}) \) 8 * q - 20 * q^4	\( 8 q - 20 q^{4} - 20 q^{13} + 12 q^{16} - 4 q^{18} - 40 q^{30} + 4 q^{33} - 96 q^{38} + 56 q^{47} - 108 q^{50} + 16 q^{52} - 28 q^{55} - 28 q^{64} + 32 q^{67} + 36 q^{69} + 36 q^{72} - 8 q^{81} - 96 q^{86} - 24 q^{89} - 28 q^{98}+O(q^{100}) \) 8 * q - 20 * q^4 - 20 * q^13 + 12 * q^16 - 4 * q^18 - 40 * q^30 + 4 * q^33 - 96 * q^38 + 56 * q^47 - 108 * q^50 + 16 * q^52 - 28 * q^55 - 28 * q^64 + 32 * q^67 + 36 * q^69 + 36 * q^72 - 8 * q^81 - 96 * q^86 - 24 * q^89 - 28 * q^98

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