LMFDB - Embedded newform 513.2.t.a.179.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(179,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.11
Character	$\chi$	$=$	513.179
Dual form			513.2.t.a.278.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.691402 q^{2} -1.52196 q^{4} +(0.0926192 - 0.0534737i) q^{5} +(1.77987 + 3.08283i) q^{7} -2.43509 q^{8} +(0.0640371 - 0.0369718i) q^{10} +(-3.79750 + 2.19249i) q^{11} +0.416721i q^{13} +(1.23061 + 2.13148i) q^{14} +1.36030 q^{16} +(3.21900 + 1.85849i) q^{17} +(-4.10727 + 1.45956i) q^{19} +(-0.140963 + 0.0813850i) q^{20} +(-2.62560 + 1.51589i) q^{22} +5.41300i q^{23} +(-2.49428 + 4.32022i) q^{25} +0.288122i q^{26} +(-2.70890 - 4.69195i) q^{28} +(2.75398 - 4.77004i) q^{29} +(3.01840 + 1.74267i) q^{31} +5.81070 q^{32} +(2.22562 + 1.28496i) q^{34} +(0.329701 + 0.190353i) q^{35} -1.84627i q^{37} +(-2.83978 + 1.00914i) q^{38} +(-0.225536 + 0.130213i) q^{40} +(4.98642 + 8.63673i) q^{41} -10.8041 q^{43} +(5.77965 - 3.33688i) q^{44} +3.74256i q^{46} +(-0.217456 - 0.125549i) q^{47} +(-2.83590 + 4.91192i) q^{49} +(-1.72455 + 2.98701i) q^{50} -0.634234i q^{52} +(-1.44192 - 2.49748i) q^{53} +(-0.234481 + 0.406133i) q^{55} +(-4.33416 - 7.50698i) q^{56} +(1.90411 - 3.29802i) q^{58} +(1.18744 + 2.05671i) q^{59} +(6.42834 - 11.1342i) q^{61} +(2.08693 + 1.20489i) q^{62} +1.29694 q^{64} +(0.0222836 + 0.0385964i) q^{65} -10.5987i q^{67} +(-4.89919 - 2.82855i) q^{68} +(0.227956 + 0.131610i) q^{70} +(5.43426 - 9.41241i) q^{71} +(2.47284 - 4.28309i) q^{73} -1.27652i q^{74} +(6.25111 - 2.22140i) q^{76} +(-13.5181 - 7.80470i) q^{77} +1.09434i q^{79} +(0.125990 - 0.0727401i) q^{80} +(3.44762 + 5.97145i) q^{82} +(-7.21082 + 4.16317i) q^{83} +0.397521 q^{85} -7.46996 q^{86} +(9.24726 - 5.33891i) q^{88} +(-2.61637 - 4.53168i) q^{89} +(-1.28468 + 0.741711i) q^{91} -8.23838i q^{92} +(-0.150350 - 0.0868045i) q^{94} +(-0.302364 + 0.354814i) q^{95} +13.1177i q^{97} +(-1.96075 + 3.39611i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.691402			0.488895			0.244448	−	0.969662i	$-0.421393\pi$
$2$	0.691402			0.488895			0.244448	+	0.969662i	$0.421393\pi$
$3$		0			0
$3$		0			0
$4$	−1.52196			−0.760981
$5$	0.0926192	−	0.0534737i	0.0414206	−	0.0239142i	−0.479147	−	0.877735i	$-0.659054\pi$
$5$	0.0926192	−	0.0534737i	0.0414206	−	0.0239142i	0.520567	+	0.853821i	$0.325720\pi$
$6$		0			0
$7$	1.77987	+	3.08283i	0.672729	+	1.16520i	0.977127	+	0.212656i	$0.0682113\pi$
$7$	1.77987	+	3.08283i	0.672729	+	1.16520i	−0.304398	+	0.952545i	$0.598455\pi$
$8$	−2.43509			−0.860936
$9$		0			0
$10$	0.0640371	−	0.0369718i	0.0202503	−	0.0116915i
$11$	−3.79750	+	2.19249i	−1.14499	+	0.661060i	−0.947661	−	0.319278i	$-0.896560\pi$
$11$	−3.79750	+	2.19249i	−1.14499	+	0.661060i	−0.197328	+	0.980338i	$0.563226\pi$
$12$		0			0
$13$			0.416721i			0.115578i	0.998329	+	0.0577888i	$0.0184050\pi$
$13$			0.416721i			0.115578i	−0.998329	+	0.0577888i	$0.981595\pi$
$14$	1.23061	+	2.13148i	0.328894	+	0.569661i
$15$		0			0
$16$	1.36030			0.340074
$17$	3.21900	+	1.85849i	0.780721	+	0.450749i	0.836686	−	0.547683i	$-0.184490\pi$
$17$	3.21900	+	1.85849i	0.780721	+	0.450749i	−0.0559647	+	0.998433i	$0.517823\pi$
$18$		0			0
$19$	−4.10727	+	1.45956i	−0.942273	+	0.334846i
$19$	−4.10727	+	1.45956i	−0.942273	+	0.334846i
$20$	−0.140963	+	0.0813850i	−0.0315203	+	0.0181982i
$21$		0			0
$22$	−2.62560	+	1.51589i	−0.559780	+	0.323189i
$23$			5.41300i			1.12869i	0.825540	+	0.564344i	$0.190871\pi$
$23$			5.41300i			1.12869i	−0.825540	+	0.564344i	$0.809129\pi$
$24$		0			0
$25$	−2.49428	+	4.32022i	−0.498856	+	0.864044i
$26$			0.288122i			0.0565054i
$27$		0			0
$28$	−2.70890	−	4.69195i	−0.511934	−	0.886696i
$29$	2.75398	−	4.77004i	0.511402	−	0.885774i	−0.488511	−	0.872558i	$-0.662460\pi$
$29$	2.75398	−	4.77004i	0.511402	−	0.885774i	0.999913	−	0.0132161i	$-0.00420693\pi$
$30$		0			0
$31$	3.01840	+	1.74267i	0.542120	+	0.312993i	0.745938	−	0.666016i	$-0.232002\pi$
$31$	3.01840	+	1.74267i	0.542120	+	0.312993i	−0.203817	+	0.979009i	$0.565335\pi$
$32$	5.81070			1.02720
$33$		0			0
$34$	2.22562	+	1.28496i	0.381691	+	0.220369i
$35$	0.329701	+	0.190353i	0.0557296	+	0.0321755i
$36$		0			0
$37$		−	1.84627i		−	0.303525i	−0.988417	−	0.151763i	$-0.951505\pi$
$37$		−	1.84627i		−	0.303525i	0.988417	−	0.151763i	$-0.0484949\pi$
$38$	−2.83978	+	1.00914i	−0.460673	+	0.163705i
$39$		0			0
$40$	−0.225536	+	0.130213i	−0.0356604	+	0.0205886i
$41$	4.98642	+	8.63673i	0.778747	+	1.34883i	0.932664	+	0.360746i	$0.117478\pi$
$41$	4.98642	+	8.63673i	0.778747	+	1.34883i	−0.153917	+	0.988084i	$0.549189\pi$
$42$		0			0
$43$	−10.8041			−1.64761			−0.823803	−	0.566877i	$-0.808152\pi$
$43$	−10.8041			−1.64761			−0.823803	+	0.566877i	$0.808152\pi$
$44$	5.77965	−	3.33688i	0.871315	−	0.503054i
$45$		0			0
$46$			3.74256i			0.551810i
$47$	−0.217456	−	0.125549i	−0.0317193	−	0.0183131i	0.484057	−	0.875037i	$-0.339163\pi$
$47$	−0.217456	−	0.125549i	−0.0317193	−	0.0183131i	−0.515776	+	0.856724i	$0.672496\pi$
$48$		0			0
$49$	−2.83590	+	4.91192i	−0.405128	+	0.701703i
$50$	−1.72455	+	2.98701i	−0.243888	+	0.422427i
$51$		0			0
$52$		−	0.634234i		−	0.0879524i
$53$	−1.44192	−	2.49748i	−0.198063	−	0.343055i	0.749837	−	0.661622i	$-0.230132\pi$
$53$	−1.44192	−	2.49748i	−0.198063	−	0.343055i	−0.947900	+	0.318567i	$0.896798\pi$
$54$		0			0
$55$	−0.234481	+	0.406133i	−0.0316174	+	0.0547629i
$56$	−4.33416	−	7.50698i	−0.579176	−	1.00316i
$57$		0			0
$58$	1.90411	−	3.29802i	0.250022	−	0.433051i
$59$	1.18744	+	2.05671i	0.154592	+	0.267761i	0.932910	−	0.360109i	$-0.117260\pi$
$59$	1.18744	+	2.05671i	0.154592	+	0.267761i	−0.778318	+	0.627870i	$0.783927\pi$
$60$		0			0
$61$	6.42834	−	11.1342i	0.823064	−	1.42559i	−0.0803253	−	0.996769i	$-0.525596\pi$
$61$	6.42834	−	11.1342i	0.823064	−	1.42559i	0.903390	−	0.428821i	$-0.141071\pi$
$62$	2.08693	+	1.20489i	0.265040	+	0.153021i
$63$		0			0
$64$	1.29694			0.162117
$65$	0.0222836	+	0.0385964i	0.00276394	+	0.00478729i
$66$		0			0
$67$		−	10.5987i		−	1.29484i	−0.762134	−	0.647419i	$-0.775848\pi$
$67$		−	10.5987i		−	1.29484i	0.762134	−	0.647419i	$-0.224152\pi$
$68$	−4.89919	−	2.82855i	−0.594114	−	0.343012i
$69$		0			0
$70$	0.227956	+	0.131610i	0.0272459	+	0.0157305i
$71$	5.43426	−	9.41241i	0.644928	−	1.11705i	−0.339390	−	0.940646i	$-0.610221\pi$
$71$	5.43426	−	9.41241i	0.644928	−	1.11705i	0.984318	−	0.176402i	$-0.0564459\pi$
$72$		0			0
$73$	2.47284	−	4.28309i	0.289424	−	0.501297i	−0.684248	−	0.729249i	$-0.739870\pi$
$73$	2.47284	−	4.28309i	0.289424	−	0.501297i	0.973672	+	0.227952i	$0.0732029\pi$
$74$		−	1.27652i		−	0.148392i
$75$		0			0
$76$	6.25111	−	2.22140i	0.717052	−	0.254812i
$77$	−13.5181	−	7.80470i	−1.54053	−	0.889428i
$78$		0			0
$79$			1.09434i			0.123123i	0.998103	+	0.0615614i	$0.0196080\pi$
$79$			1.09434i			0.123123i	−0.998103	+	0.0615614i	$0.980392\pi$
$80$	0.125990	−	0.0727401i	0.0140861	−	0.00813259i
$81$		0			0
$82$	3.44762	+	5.97145i	0.380726	+	0.659437i
$83$	−7.21082	+	4.16317i	−0.791490	+	0.456967i	−0.840487	−	0.541832i	$-0.817731\pi$
$83$	−7.21082	+	4.16317i	−0.791490	+	0.456967i	0.0489969	+	0.998799i	$0.484398\pi$
$84$		0			0
$85$	0.397521			0.0431172
$86$	−7.46996			−0.805507
$87$		0			0
$88$	9.24726	−	5.33891i	0.985761	−	0.569130i
$89$	−2.61637	−	4.53168i	−0.277335	−	0.480358i	0.693387	−	0.720565i	$-0.256118\pi$
$89$	−2.61637	−	4.53168i	−0.277335	−	0.480358i	−0.970721	+	0.240208i	$0.922784\pi$
$90$		0			0
$91$	−1.28468	+	0.741711i	−0.134671	+	0.0777524i
$92$		−	8.23838i		−	0.858910i
$93$		0			0
$94$	−0.150350	−	0.0868045i	−0.0155074	−	0.00895320i
$95$	−0.302364	+	0.354814i	−0.0310219	+	0.0364032i
$96$		0			0
$97$			13.1177i			1.33190i	0.745998	+	0.665948i	$0.231973\pi$
$97$			13.1177i			1.33190i	−0.745998	+	0.665948i	$0.768027\pi$
$98$	−1.96075	+	3.39611i	−0.198065	+	0.343059i
$99$		0			0
$100$	3.79620	−	6.57522i	0.379620	−	0.657522i
$101$	1.53229	+	0.884667i	0.152468	+	0.0880276i	0.574293	−	0.818650i	$-0.305277\pi$
$101$	1.53229	+	0.884667i	0.152468	+	0.0880276i	−0.421825	+	0.906677i	$0.638610\pi$
$102$		0			0
$103$	−1.56658	−	0.904463i	−0.154359	−	0.0891194i	0.420831	−	0.907139i	$-0.361739\pi$
$103$	−1.56658	−	0.904463i	−0.154359	−	0.0891194i	−0.575190	+	0.818020i	$0.695072\pi$
$104$		−	1.01475i		−	0.0995049i
$105$		0			0
$106$	−0.996947	−	1.72676i	−0.0968320	−	0.167718i
$107$	13.6046			1.31520			0.657601	−	0.753366i	$-0.271571\pi$
$107$	13.6046			1.31520			0.657601	+	0.753366i	$0.271571\pi$
$108$		0			0
$109$	10.9897	+	6.34490i	1.05262	+	0.607731i	0.923382	−	0.383883i	$-0.125413\pi$
$109$	10.9897	+	6.34490i	1.05262	+	0.607731i	0.129239	+	0.991613i	$0.458747\pi$
$110$	−0.162121	+	0.280801i	−0.0154576	+	0.0267733i
$111$		0			0
$112$	2.42115	+	4.19356i	0.228778	+	0.396255i
$113$	2.83696	−	4.91376i	0.266879	−	0.462247i	−0.701175	−	0.712989i	$-0.747341\pi$
$113$	2.83696	−	4.91376i	0.266879	−	0.462247i	0.968054	+	0.250741i	$0.0806744\pi$
$114$		0			0
$115$	0.289453	+	0.501347i	0.0269916	+	0.0467509i
$116$	−4.19146	+	7.25982i	−0.389167	+	0.674057i
$117$		0			0
$118$	0.821001	+	1.42202i	0.0755793	+	0.130907i
$119$			13.2315i			1.21293i
$120$		0			0
$121$	4.11399	−	7.12565i	0.374000	−	0.647786i
$122$	4.44457	−	7.69822i	0.402392	−	0.696964i
$123$		0			0
$124$	−4.59389	−	2.65228i	−0.412543	−	0.238182i
$125$			1.06825i			0.0955473i
$126$		0			0
$127$	−14.2508	+	8.22768i	−1.26455	+	0.730089i	−0.973951	−	0.226756i	$-0.927188\pi$
$127$	−14.2508	+	8.22768i	−1.26455	+	0.730089i	−0.290599	+	0.956845i	$0.593855\pi$
$128$	−10.7247			−0.947938
$129$		0			0
$130$	0.0154069	+	0.0266856i	0.00135128	+	0.00234048i
$131$	8.36952	−	4.83215i	0.731249	−	0.422187i	−0.0876301	−	0.996153i	$-0.527929\pi$
$131$	8.36952	−	4.83215i	0.731249	−	0.422187i	0.818879	+	0.573966i	$0.194596\pi$
$132$		0			0
$133$	−11.8100	−	10.0642i	−1.02406	−	0.872676i
$134$		−	7.32797i		−	0.633040i
$135$		0			0
$136$	−7.83855	−	4.52559i	−0.672150	−	0.388066i
$137$	10.9082	+	6.29788i	0.931954	+	0.538064i	0.887429	−	0.460944i	$-0.152489\pi$
$137$	10.9082	+	6.29788i	0.931954	+	0.538064i	0.0445252	+	0.999008i	$0.485823\pi$
$138$		0			0
$139$	10.1589			0.861666			0.430833	−	0.902432i	$-0.358220\pi$
$139$	10.1589			0.861666			0.430833	+	0.902432i	$0.358220\pi$
$140$	−0.501792	−	0.289710i	−0.0424092	−	0.0244850i
$141$		0			0
$142$	3.75726	−	6.50776i	0.315302	−	0.546119i
$143$	−0.913655	−	1.58250i	−0.0764037	−	0.132335i
$144$		0			0
$145$		−	0.589063i		−	0.0489190i
$146$	1.70973	−	2.96134i	0.141498	−	0.245082i
$147$		0			0
$148$			2.80996i			0.230977i
$149$	−14.8285	+	8.56125i	−1.21480	+	0.701365i	−0.963801	−	0.266622i	$-0.914092\pi$
$149$	−14.8285	+	8.56125i	−1.21480	+	0.701365i	−0.250999	+	0.967987i	$0.580759\pi$
$150$		0			0
$151$	−0.724901	+	0.418522i	−0.0589916	+	0.0340588i	−0.529206	−	0.848494i	$-0.677510\pi$
$151$	−0.724901	+	0.418522i	−0.0589916	+	0.0340588i	0.470214	+	0.882552i	$0.344177\pi$
$152$	10.0016	−	3.55417i	0.811236	−	0.288281i
$153$		0			0
$154$	−9.34647	−	5.39619i	−0.753160	−	0.434837i
$155$	0.372749			0.0299399
$156$		0			0
$157$	7.46395	+	12.9279i	0.595688	+	1.03176i	0.993449	+	0.114273i	$0.0364539\pi$
$157$	7.46395	+	12.9279i	0.595688	+	1.03176i	−0.397761	+	0.917489i	$0.630213\pi$
$158$			0.756629i			0.0601942i
$159$		0			0
$160$	0.538182	−	0.310720i	0.0425470	−	0.0245645i
$161$	−16.6874	+	9.63445i	−1.31515	+	0.759301i
$162$		0			0
$163$	3.88920			0.304626			0.152313	−	0.988332i	$-0.451328\pi$
$163$	3.88920			0.304626			0.152313	+	0.988332i	$0.451328\pi$
$164$	−7.58914	−	13.1448i	−0.592612	−	1.02643i
$165$		0			0
$166$	−4.98558	+	2.87842i	−0.386956	+	0.223409i
$167$	9.57355			0.740823			0.370412	−	0.928868i	$-0.379217\pi$
$167$	9.57355			0.740823			0.370412	+	0.928868i	$0.379217\pi$
$168$		0			0
$169$	12.8263			0.986642
$170$	0.274847			0.0210798
$171$		0			0
$172$	16.4434			1.25380
$173$	−4.48553			−0.341028			−0.170514	−	0.985355i	$-0.554543\pi$
$173$	−4.48553			−0.341028			−0.170514	+	0.985355i	$0.554543\pi$
$174$		0			0
$175$	−17.7580			−1.34238
$176$	−5.16572	+	2.98243i	−0.389381	+	0.224809i
$177$		0			0
$178$	−1.80896	−	3.13322i	−0.135588	−	0.234845i
$179$	5.02157			0.375330			0.187665	−	0.982233i	$-0.439908\pi$
$179$	5.02157			0.375330			0.187665	+	0.982233i	$0.439908\pi$
$180$		0			0
$181$	10.9563	−	6.32561i	0.814374	−	0.470179i	−0.0340985	−	0.999418i	$-0.510856\pi$
$181$	10.9563	−	6.32561i	0.814374	−	0.470179i	0.848473	+	0.529239i	$0.177523\pi$
$182$	−0.888231	+	0.512821i	−0.0658401	+	0.0380128i
$183$		0			0
$184$		−	13.1812i		−	0.971727i
$185$	−0.0987270	−	0.171000i	−0.00725855	−	0.0125722i
$186$		0			0
$187$	−16.2988			−1.19189
$188$	0.330961	+	0.191080i	0.0241378	+	0.0139360i
$189$		0			0
$190$	−0.209055	+	0.245320i	−0.0151665	+	0.0177973i
$191$	−12.8859	+	7.43970i	−0.932394	+	0.538318i	−0.887568	−	0.460677i	$-0.847607\pi$
$191$	−12.8859	+	7.43970i	−0.932394	+	0.538318i	−0.0448259	+	0.998995i	$0.514273\pi$
$192$		0			0
$193$	−11.5602	+	6.67430i	−0.832123	+	0.480426i	−0.854579	−	0.519321i	$-0.826185\pi$
$193$	−11.5602	+	6.67430i	−0.832123	+	0.480426i	0.0224561	+	0.999748i	$0.492851\pi$
$194$			9.06958i			0.651158i
$195$		0			0
$196$	4.31613	−	7.47576i	0.308295	−	0.533983i
$197$		−	21.4163i		−	1.52585i	−0.646488	−	0.762925i	$-0.723763\pi$
$197$		−	21.4163i		−	1.52585i	0.646488	−	0.762925i	$-0.276237\pi$
$198$		0			0
$199$	2.50917	+	4.34600i	0.177870	+	0.308080i	0.941151	−	0.337987i	$-0.109746\pi$
$199$	2.50917	+	4.34600i	0.177870	+	0.308080i	−0.763281	+	0.646067i	$0.776413\pi$
$200$	6.07381	−	10.5201i	0.429483	−	0.743886i
$201$		0			0
$202$	1.05943	+	0.611661i	0.0745411	+	0.0430363i
$203$	19.6070			1.37614
$204$		0			0
$205$	0.923675	+	0.533284i	0.0645123	+	0.0372462i
$206$	−1.08313	−	0.625348i	−0.0754655	−	0.0435700i
$207$		0			0
$208$			0.566864i			0.0393050i
$209$	12.3973	−	14.5478i	0.857538	−	1.00629i
$210$		0			0
$211$	−13.8645	+	8.00470i	−0.954474	+	0.551066i	−0.894468	−	0.447132i	$-0.852445\pi$
$211$	−13.8645	+	8.00470i	−0.954474	+	0.551066i	−0.0600064	+	0.998198i	$0.519112\pi$
$212$	2.19455	+	3.80107i	0.150722	+	0.261059i
$213$		0			0
$214$	9.40622			0.642996
$215$	−1.00066	+	0.577734i	−0.0682447	+	0.0394011i
$216$		0			0
$217$			12.4069i			0.842239i
$218$	7.59829	+	4.38688i	0.514621	+	0.297117i
$219$		0			0
$220$	0.356871	−	0.618119i	0.0240602	−	0.0416736i
$221$	−0.774471	+	1.34142i	−0.0520966	+	0.0902339i
$222$		0			0
$223$			8.20407i			0.549385i	0.961532	+	0.274693i	$0.0885761\pi$
$223$			8.20407i			0.549385i	−0.961532	+	0.274693i	$0.911424\pi$
$224$	10.3423	+	17.9134i	0.691024	+	1.19689i
$225$		0			0
$226$	1.96148	−	3.39738i	0.130476	−	0.225991i
$227$	14.4019	+	24.9448i	0.955888	+	1.65565i	0.732322	+	0.680958i	$0.238437\pi$
$227$	14.4019	+	24.9448i	0.955888	+	1.65565i	0.223566	+	0.974689i	$0.428230\pi$
$228$		0			0
$229$	9.25025	−	16.0219i	0.611274	−	1.05876i	−0.379753	−	0.925088i	$-0.623991\pi$
$229$	9.25025	−	16.0219i	0.611274	−	1.05876i	0.991026	−	0.133669i	$-0.0426758\pi$
$230$	0.200128	+	0.346633i	0.0131961	+	0.0228563i
$231$		0			0
$232$	−6.70621	+	11.6155i	−0.440284	+	0.762594i
$233$	−17.8445	−	10.3025i	−1.16903	−	0.674941i	−0.215580	−	0.976486i	$-0.569164\pi$
$233$	−17.8445	−	10.3025i	−1.16903	−	0.674941i	−0.953452	+	0.301545i	$0.902498\pi$
$234$		0			0
$235$	−0.0268542			−0.00175177
$236$	−1.80725	−	3.13024i	−0.117642	−	0.203761i
$237$		0			0
$238$			9.14828i			0.592995i
$239$	25.5747	+	14.7655i	1.65429	+	0.955104i	0.975280	+	0.220972i	$0.0709231\pi$
$239$	25.5747	+	14.7655i	1.65429	+	0.955104i	0.679008	+	0.734131i	$0.262410\pi$
$240$		0			0
$241$	−3.73128	−	2.15426i	−0.240353	−	0.138768i	0.374986	−	0.927030i	$-0.377648\pi$
$241$	−3.73128	−	2.15426i	−0.240353	−	0.138768i	−0.615339	+	0.788263i	$0.710981\pi$
$242$	2.84443	−	4.92669i	0.182847	−	0.316700i
$243$		0			0
$244$	−9.78369	+	16.9459i	−0.626337	+	1.08485i
$245$			0.606584i			0.0387532i
$246$		0			0
$247$	−0.608230	−	1.71159i	−0.0387008	−	0.108906i
$248$	−7.35008	−	4.24357i	−0.466731	−	0.269467i
$249$		0			0
$250$			0.738591i			0.0467126i
$251$	−10.3715	+	5.98796i	−0.654640	+	0.377957i	−0.790232	−	0.612808i	$-0.790040\pi$
$251$	−10.3715	+	5.98796i	−0.654640	+	0.377957i	0.135592	+	0.990765i	$0.456707\pi$
$252$		0			0
$253$	−11.8679	−	20.5558i	−0.746130	−	1.29233i
$254$	−9.85301	+	5.68864i	−0.618233	+	0.356937i
$255$		0			0
$256$	−10.0090			−0.625560
$257$	−19.9740			−1.24594			−0.622972	−	0.782245i	$-0.714075\pi$
$257$	−19.9740			−1.24594			−0.622972	+	0.782245i	$0.714075\pi$
$258$		0			0
$259$	5.69174	−	3.28613i	0.353668	−	0.204190i
$260$	−0.0339148	−	0.0587422i	−0.00210331	−	0.00364304i
$261$		0			0
$262$	5.78671	−	3.34096i	0.357504	−	0.206405i
$263$			8.43192i			0.519935i	0.965617	+	0.259967i	$0.0837118\pi$
$263$			8.43192i			0.519935i	−0.965617	+	0.259967i	$0.916288\pi$
$264$		0			0
$265$	−0.267099	−	0.154210i	−0.0164078	−	0.00947302i
$266$	−8.16546	−	6.95840i	−0.500657	−	0.426647i
$267$		0			0
$268$			16.1308i			0.985348i
$269$	−10.9044	+	18.8870i	−0.664856	+	1.15156i	0.314469	+	0.949268i	$0.398174\pi$
$269$	−10.9044	+	18.8870i	−0.664856	+	1.15156i	−0.979324	+	0.202296i	$0.935160\pi$
$270$		0			0
$271$	2.11392	−	3.66142i	0.128412	−	0.222416i	−0.794650	−	0.607068i	$-0.792345\pi$
$271$	2.11392	−	3.66142i	0.128412	−	0.222416i	0.923061	+	0.384653i	$0.125679\pi$
$272$	4.37879	+	2.52809i	0.265503	+	0.153288i
$273$		0			0
$274$	7.54199	+	4.35437i	0.455628	+	0.263057i
$275$		−	21.8747i		−	1.31909i
$276$		0			0
$277$	8.28717	+	14.3538i	0.497928	+	0.862436i	0.999997	−	0.00239145i	$-0.000761224\pi$
$277$	8.28717	+	14.3538i	0.497928	+	0.862436i	−0.502070	+	0.864827i	$0.667428\pi$
$278$	7.02389			0.421265
$279$		0			0
$280$	−0.802852	−	0.463527i	−0.0479796	−	0.0277010i
$281$	8.80430	−	15.2495i	0.525220	−	0.909708i	−0.474348	−	0.880337i	$-0.657316\pi$
$281$	8.80430	−	15.2495i	0.525220	−	0.909708i	0.999569	−	0.0293711i	$-0.00935045\pi$
$282$		0			0
$283$	15.9644	+	27.6511i	0.948983	+	1.64369i	0.747574	+	0.664179i	$0.231219\pi$
$283$	15.9644	+	27.6511i	0.948983	+	1.64369i	0.201409	+	0.979507i	$0.435448\pi$
$284$	−8.27074	+	14.3253i	−0.490778	+	0.850053i
$285$		0			0
$286$	−0.631703	−	1.09414i	−0.0373534	−	0.0646980i
$287$	−17.7504	+	30.7446i	−1.04777	+	1.81479i
$288$		0			0
$289$	−1.59205	−	2.75751i	−0.0936498	−	0.162206i
$290$		−	0.407279i		−	0.0239163i
$291$		0			0
$292$	−3.76357	+	6.51870i	−0.220246	+	0.381478i
$293$	14.0550	−	24.3440i	0.821101	−	1.42219i	−0.0837616	−	0.996486i	$-0.526693\pi$
$293$	14.0550	−	24.3440i	0.821101	−	1.42219i	0.904863	−	0.425703i	$-0.139973\pi$
$294$		0			0
$295$	0.219960	+	0.126994i	0.0128066	+	0.00739388i
$296$			4.49584i			0.261316i
$297$		0			0
$298$	−10.2525	+	5.91927i	−0.593910	+	0.342894i
$299$	−2.25571			−0.130451
$300$		0			0
$301$	−19.2299	−	33.3071i	−1.10839	−	1.91979i
$302$	−0.501198	+	0.289367i	−0.0288407	+	0.0166512i
$303$		0			0
$304$	−5.58711	+	1.98544i	−0.320443	+	0.113873i
$305$		−	1.37499i		−	0.0787316i
$306$		0			0
$307$	−8.38574	−	4.84151i	−0.478599	−	0.276319i	0.241233	−	0.970467i	$-0.422448\pi$
$307$	−8.38574	−	4.84151i	−0.478599	−	0.276319i	−0.719833	+	0.694148i	$0.755781\pi$
$308$	20.5741	+	11.8785i	1.17232	+	0.676838i
$309$		0			0
$310$	0.257719			0.0146375
$311$	−0.0989162	−	0.0571093i	−0.00560902	−	0.00323837i	0.497193	−	0.867640i	$-0.334364\pi$
$311$	−0.0989162	−	0.0571093i	−0.00560902	−	0.00323837i	−0.502802	+	0.864402i	$0.667697\pi$
$312$		0			0
$313$	1.13376	−	1.96374i	0.0640841	−	0.110997i	−0.832203	−	0.554471i	$-0.812921\pi$
$313$	1.13376	−	1.96374i	0.0640841	−	0.110997i	0.896287	+	0.443474i	$0.146254\pi$
$314$	5.16059	+	8.93841i	0.291229	+	0.504424i
$315$		0			0
$316$		−	1.66554i		−	0.0936942i
$317$	−4.93192	+	8.54234i	−0.277004	+	0.479786i	−0.970639	−	0.240541i	$-0.922675\pi$
$317$	−4.93192	+	8.54234i	−0.277004	+	0.479786i	0.693634	+	0.720327i	$0.256008\pi$
$318$		0			0
$319$			24.1523i			1.35227i
$320$	0.120121	−	0.0693521i	0.00671499	−	0.00387690i
$321$		0			0
$322$	−11.5377	+	6.66128i	−0.642969	+	0.371219i
$323$	−15.9339	−	2.93499i	−0.886584	−	0.163307i
$324$		0			0
$325$	−1.80033	−	1.03942i	−0.0998642	−	0.0576566i
$326$	2.68900			0.148930
$327$		0			0
$328$	−12.1424	−	21.0312i	−0.670451	−	1.16126i
$329$		−	0.893842i		−	0.0492791i
$330$		0			0
$331$	6.56652	−	3.79118i	0.360929	−	0.208382i	−0.308559	−	0.951205i	$-0.599847\pi$
$331$	6.56652	−	3.79118i	0.360929	−	0.208382i	0.669488	+	0.742823i	$0.266514\pi$
$332$	10.9746	−	6.33618i	0.602309	−	0.347743i
$333$		0			0
$334$	6.61917			0.362185
$335$	−0.566752	−	0.981643i	−0.0309650	−	0.0536329i
$336$		0			0
$337$	12.2220	−	7.05635i	0.665773	−	0.384384i	−0.128700	−	0.991684i	$-0.541080\pi$
$337$	12.2220	−	7.05635i	0.665773	−	0.384384i	0.794473	+	0.607299i	$0.207747\pi$
$338$	8.86816			0.482365
$339$		0			0
$340$	−0.605012			−0.0328114
$341$	−15.2831			−0.827629
$342$		0			0
$343$	4.72808			0.255292
$344$	26.3089			1.41848
$345$		0			0
$346$	−3.10131			−0.166727
$347$	5.94283	−	3.43109i	0.319028	−	0.184191i	−0.331931	−	0.943304i	$-0.607700\pi$
$347$	5.94283	−	3.43109i	0.319028	−	0.184191i	0.650959	+	0.759113i	$0.274367\pi$
$348$		0			0
$349$	3.10669	+	5.38094i	0.166297	+	0.288035i	0.937115	−	0.349020i	$-0.113486\pi$
$349$	3.10669	+	5.38094i	0.166297	+	0.288035i	−0.770818	+	0.637056i	$0.780152\pi$
$350$	−12.2779			−0.656283
$351$		0			0
$352$	−22.0661	+	12.7399i	−1.17613	+	0.679038i
$353$	11.0335	−	6.37017i	0.587252	−	0.339050i	−0.176758	−	0.984254i	$-0.556561\pi$
$353$	11.0335	−	6.37017i	0.587252	−	0.339050i	0.764010	+	0.645204i	$0.223228\pi$
$354$		0			0
$355$		−	1.16236i		−	0.0616916i
$356$	3.98202	+	6.89705i	0.211046	+	0.365543i
$357$		0			0
$358$	3.47193			0.183497
$359$	13.1829	+	7.61116i	0.695767	+	0.401701i	0.805769	−	0.592230i	$-0.201752\pi$
$359$	13.1829	+	7.61116i	0.695767	+	0.401701i	−0.110002	+	0.993931i	$0.535086\pi$
$360$		0			0
$361$	14.7394	−	11.9896i	0.775756	−	0.631033i
$362$	7.57520	−	4.37354i	0.398144	−	0.229868i
$363$		0			0
$364$	1.95524	−	1.12886i	0.102482	−	0.0591681i
$365$		−	0.528928i		−	0.0276853i
$366$		0			0
$367$	3.83282	−	6.63863i	0.200071	−	0.346534i	−0.748480	−	0.663158i	$-0.769216\pi$
$367$	3.83282	−	6.63863i	0.200071	−	0.346534i	0.948551	+	0.316624i	$0.102549\pi$
$368$			7.36328i			0.383837i
$369$		0			0
$370$	−0.0682601	−	0.118230i	−0.00354867	−	0.00614648i
$371$	5.13287	−	8.89039i	0.266485	−	0.461566i
$372$		0			0
$373$	16.3704	+	9.45148i	0.847629	+	0.489379i	0.859850	−	0.510546i	$-0.170557\pi$
$373$	16.3704	+	9.45148i	0.847629	+	0.489379i	−0.0122211	+	0.999925i	$0.503890\pi$
$374$	−11.2691			−0.582709
$375$		0			0
$376$	0.529527	+	0.305722i	0.0273083	+	0.0157664i
$377$	1.98778	+	1.14764i	0.102376	+	0.0591066i
$378$		0			0
$379$			24.7158i			1.26957i	0.772690	+	0.634784i	$0.218911\pi$
$379$			24.7158i			1.26957i	−0.772690	+	0.634784i	$0.781089\pi$
$380$	0.460187	−	0.540014i	0.0236071	−	0.0277022i
$381$		0			0
$382$	−8.90937	+	5.14383i	−0.455843	+	0.263181i
$383$	−11.4456	−	19.8244i	−0.584845	−	1.01298i	−0.994895	−	0.100918i	$-0.967822\pi$
$383$	−11.4456	−	19.8244i	−0.584845	−	1.01298i	0.410050	−	0.912063i	$-0.365511\pi$
$384$		0			0
$385$	−1.66938			−0.0850797
$386$	−7.99276	+	4.61462i	−0.406821	+	0.234878i
$387$		0			0
$388$		−	19.9646i		−	1.01355i
$389$	−3.28308	−	1.89549i	−0.166459	−	0.0961049i	0.414456	−	0.910069i	$-0.363972\pi$
$389$	−3.28308	−	1.89549i	−0.166459	−	0.0961049i	−0.580915	+	0.813964i	$0.697305\pi$
$390$		0			0
$391$	−10.0600	+	17.4244i	−0.508755	+	0.881190i
$392$	6.90567	−	11.9610i	0.348789	−	0.604121i
$393$		0			0
$394$		−	14.8073i		−	0.745980i
$395$	0.0585184	+	0.101357i	0.00294438	+	0.00509982i
$396$		0			0
$397$	3.53802	−	6.12804i	0.177568	−	0.307557i	−0.763479	−	0.645833i	$-0.776510\pi$
$397$	3.53802	−	6.12804i	0.177568	−	0.307557i	0.941047	+	0.338276i	$0.109844\pi$
$398$	1.73484	+	3.00484i	0.0869598	+	0.150619i
$399$		0			0
$400$	−3.39296	+	5.87678i	−0.169648	+	0.293839i
$401$	6.32826	+	10.9609i	0.316018	+	0.547360i	0.979653	−	0.200697i	$-0.0643206\pi$
$401$	6.32826	+	10.9609i	0.316018	+	0.547360i	−0.663635	+	0.748056i	$0.730987\pi$
$402$		0			0
$403$	−0.726209	+	1.25783i	−0.0361750	+	0.0626570i
$404$	−2.33209	−	1.34643i	−0.116026	−	0.0669874i
$405$		0			0
$406$	13.5563			0.672788
$407$	4.04793	+	7.01121i	0.200648	+	0.347533i
$408$		0			0
$409$		−	24.1720i		−	1.19523i	−0.801783	−	0.597615i	$-0.796115\pi$
$409$		−	24.1720i		−	1.19523i	0.801783	−	0.597615i	$-0.203885\pi$
$410$	0.638631	+	0.368714i	0.0315398	+	0.0182095i
$411$		0			0
$412$	2.38427	+	1.37656i	0.117465	+	0.0678182i
$413$	−4.22700	+	7.32138i	−0.207997	+	0.360261i
$414$		0			0
$415$	−0.445240	+	0.771178i	−0.0218560	+	0.0378556i
$416$			2.42144i			0.118721i
$417$		0			0
$418$	8.57151	−	10.0584i	0.419246	−	0.491972i
$419$	−23.3582	−	13.4859i	−1.14112	−	0.658828i	−0.194415	−	0.980919i	$-0.562281\pi$
$419$	−23.3582	−	13.4859i	−1.14112	−	0.658828i	−0.946709	+	0.322091i	$0.895614\pi$
$420$		0			0
$421$			26.5459i			1.29377i	0.762588	+	0.646885i	$0.223929\pi$
$421$			26.5459i			1.29377i	−0.762588	+	0.646885i	$0.776071\pi$
$422$	−9.58598	+	5.53447i	−0.466638	+	0.269414i
$423$		0			0
$424$	3.51121	+	6.08159i	0.170519	+	0.295348i
$425$	−16.0582	+	9.27118i	−0.778935	+	0.449718i
$426$		0			0
$427$	45.7665			2.21480
$428$	−20.7056			−1.00084
$429$		0			0
$430$	−0.691862	+	0.399446i	−0.0333645	+	0.0192630i
$431$	−8.45285	−	14.6408i	−0.407159	−	0.705221i	0.587411	−	0.809289i	$-0.300147\pi$
$431$	−8.45285	−	14.6408i	−0.407159	−	0.705221i	−0.994570	+	0.104068i	$0.966814\pi$
$432$		0			0
$433$	−13.0398	+	7.52854i	−0.626653	+	0.361799i	−0.779455	−	0.626458i	$-0.784504\pi$
$433$	−13.0398	+	7.52854i	−0.626653	+	0.361799i	0.152801	+	0.988257i	$0.451171\pi$
$434$			8.57819i			0.411766i
$435$		0			0
$436$	−16.7259	−	9.65670i	−0.801025	−	0.462472i
$437$	−7.90060	−	22.2326i	−0.377937	−	1.06353i
$438$		0			0
$439$		−	14.9731i		−	0.714626i	−0.933985	−	0.357313i	$-0.883693\pi$
$439$		−	14.9731i		−	0.714626i	0.933985	−	0.357313i	$-0.116307\pi$
$440$	0.570983	−	0.988971i	0.0272205	−	0.0471473i
$441$		0			0
$442$	−0.535471	+	0.927463i	−0.0254698	+	0.0441149i
$443$	−12.0457	−	6.95458i	−0.572308	−	0.330422i	0.185763	−	0.982595i	$-0.440524\pi$
$443$	−12.0457	−	6.95458i	−0.572308	−	0.330422i	−0.758071	+	0.652172i	$0.773858\pi$
$444$		0			0
$445$	−0.484652	−	0.279814i	−0.0229747	−	0.0132644i
$446$			5.67231i			0.268592i
$447$		0			0
$448$	2.30839	+	3.99824i	0.109061	+	0.188899i
$449$	33.9028			1.59997			0.799986	−	0.600018i	$-0.204840\pi$
$449$	33.9028			1.59997			0.799986	+	0.600018i	$0.204840\pi$
$450$		0			0
$451$	−37.8718	−	21.8653i	−1.78331	−	1.02960i
$452$	−4.31775	+	7.47855i	−0.203090	+	0.351762i
$453$		0			0
$454$	9.95751	+	17.2469i	0.467329	+	0.809438i
$455$	−0.0793240	+	0.137393i	−0.00371877	+	0.00644110i
$456$		0			0
$457$	−17.4349	−	30.1981i	−0.815569	−	1.41261i	−0.908919	−	0.416973i	$-0.863091\pi$
$457$	−17.4349	−	30.1981i	−0.815569	−	1.41261i	0.0933501	−	0.995633i	$-0.470242\pi$
$458$	6.39564	−	11.0776i	0.298849	−	0.517621i
$459$		0			0
$460$	−0.440537	−	0.763032i	−0.0205401	−	0.0355765i
$461$		−	12.2003i		−	0.568223i	−0.958791	−	0.284112i	$-0.908301\pi$
$461$		−	12.2003i		−	0.568223i	0.958791	−	0.284112i	$-0.0916986\pi$
$462$		0			0
$463$	7.89622	−	13.6766i	0.366968	−	0.635608i	−0.622122	−	0.782921i	$-0.713729\pi$
$463$	7.89622	−	13.6766i	0.366968	−	0.635608i	0.989090	+	0.147313i	$0.0470624\pi$
$464$	3.74623	−	6.48867i	0.173914	−	0.301229i
$465$		0			0
$466$	−12.3377	−	7.12319i	−0.571534	−	0.329976i
$467$			1.00890i			0.0466861i	0.999728	+	0.0233430i	$0.00743100\pi$
$467$			1.00890i			0.0466861i	−0.999728	+	0.0233430i	$0.992569\pi$
$468$		0			0
$469$	32.6740	−	18.8644i	1.50875	−	0.871075i
$470$	−0.0185670			−0.000856434
$471$		0			0
$472$	−2.89154	−	5.00829i	−0.133094	−	0.230525i
$473$	41.0284	−	23.6878i	1.88649	−	1.08917i
$474$		0			0
$475$	3.93906	−	21.3849i	0.180737	−	0.981206i
$476$		−	20.1378i		−	0.923016i
$477$		0			0
$478$	17.6824	+	10.2089i	0.808774	+	0.466946i
$479$	−37.7575	−	21.7993i	−1.72518	−	0.996036i	−0.907068	−	0.420984i	$-0.861685\pi$
$479$	−37.7575	−	21.7993i	−1.72518	−	0.996036i	−0.818117	−	0.575052i	$-0.804982\pi$
$480$		0			0
$481$	0.769380			0.0350807
$482$	−2.57982	−	1.48946i	−0.117507	−	0.0678429i
$483$		0			0
$484$	−6.26135	+	10.8450i	−0.284607	+	0.492953i
$485$	0.701450	+	1.21495i	0.0318512	+	0.0551679i
$486$		0			0
$487$			18.8798i			0.855523i	0.903892	+	0.427762i	$0.140698\pi$
$487$			18.8798i			0.855523i	−0.903892	+	0.427762i	$0.859302\pi$
$488$	−15.6536	+	27.1128i	−0.708605	+	1.22734i
$489$		0			0
$490$			0.419393i			0.0189463i
$491$	−24.0044	+	13.8589i	−1.08330	+	0.625445i	−0.931785	−	0.363010i	$-0.881749\pi$
$491$	−24.0044	+	13.8589i	−1.08330	+	0.625445i	−0.151517	+	0.988455i	$0.548416\pi$
$492$		0			0
$493$	17.7301	−	10.2365i	0.798524	−	0.461028i
$494$	−0.420532	−	1.18340i	−0.0189206	−	0.0532435i
$495$		0			0
$496$	4.10592	+	2.37055i	0.184361	+	0.106441i
$497$	38.6892			1.73545
$498$		0			0
$499$	−8.59319	−	14.8838i	−0.384684	−	0.666292i	0.607041	−	0.794670i	$-0.292356\pi$
$499$	−8.59319	−	14.8838i	−0.384684	−	0.666292i	−0.991725	+	0.128378i	$0.959023\pi$
$500$		−	1.62584i		−	0.0727097i
$501$		0			0
$502$	−7.17085	+	4.14009i	−0.320050	+	0.184781i
$503$	30.9064	−	17.8438i	1.37805	−	0.795617i	0.386124	−	0.922447i	$-0.373814\pi$
$503$	30.9064	−	17.8438i	1.37805	−	0.795617i	0.991924	+	0.126830i	$0.0404804\pi$
$504$		0			0
$505$	0.189226			0.00842043
$506$	−8.20551	−	14.2124i	−0.364779	−	0.631816i
$507$		0			0
$508$	21.6891	−	12.5222i	0.962299	−	0.555584i
$509$	−28.6898			−1.27165			−0.635826	−	0.771832i	$-0.719341\pi$
$509$	−28.6898			−1.27165			−0.635826	+	0.771832i	$0.719341\pi$
$510$		0			0
$511$	17.6054			0.778816
$512$	14.5292			0.642105
$513$		0			0
$514$	−13.8101			−0.609136
$515$	−0.193460			−0.00852486
$516$		0			0
$517$	1.10105			0.0484243
$518$	3.93529	−	2.27204i	0.172907	−	0.0998276i
$519$		0			0
$520$	−0.0542627	−	0.0939857i	−0.00237958	−	0.00412155i
$521$	−19.0866			−0.836198			−0.418099	−	0.908402i	$-0.637303\pi$
$521$	−19.0866			−0.836198			−0.418099	+	0.908402i	$0.637303\pi$
$522$		0			0
$523$	6.44315	−	3.71996i	0.281739	−	0.162662i	−0.352471	−	0.935823i	$-0.614659\pi$
$523$	6.44315	−	3.71996i	0.281739	−	0.162662i	0.634211	+	0.773160i	$0.281325\pi$
$524$	−12.7381	+	7.35435i	−0.556467	+	0.321276i
$525$		0			0
$526$			5.82985i			0.254194i
$527$	6.47747	+	11.2193i	0.282163	+	0.488721i
$528$		0			0
$529$	−6.30053			−0.273936
$530$	−0.184673	−	0.106621i	−0.00802167	−	0.00463132i
$531$		0			0
$532$	17.9744	+	15.3173i	0.779288	+	0.664090i
$533$	−3.59911	+	2.07794i	−0.155895	+	0.0900058i
$534$		0			0
$535$	1.26004	−	0.727486i	0.0544764	−	0.0314520i
$536$			25.8088i			1.11477i
$537$		0			0
$538$	−7.53936	+	13.0585i	−0.325045	+	0.562994i
$539$		−	24.8707i		−	1.07126i
$540$		0			0
$541$	5.10236	+	8.83755i	0.219368	+	0.379956i	0.954615	−	0.297843i	$-0.0962672\pi$
$541$	5.10236	+	8.83755i	0.219368	+	0.379956i	−0.735247	+	0.677799i	$0.762934\pi$
$542$	1.46157	−	2.53152i	0.0627799	−	0.108738i
$543$		0			0
$544$	18.7046	+	10.7991i	0.801954	+	0.463008i
$545$	1.35714			0.0581335
$546$		0			0
$547$	28.7808	+	16.6166i	1.23058	+	0.710474i	0.967150	−	0.254206i	$-0.0818141\pi$
$547$	28.7808	+	16.6166i	1.23058	+	0.710474i	0.263426	+	0.964680i	$0.415147\pi$
$548$	−16.6019	−	9.58514i	−0.709200	−	0.409457i
$549$		0			0
$550$		−	15.1242i		−	0.644899i
$551$	−4.34919	+	23.6115i	−0.185282	+	1.00588i
$552$		0			0
$553$	−3.37366	+	1.94779i	−0.143463	+	0.0828283i
$554$	5.72977	+	9.92425i	0.243434	+	0.421641i
$555$		0			0
$556$	−15.4615			−0.655712
$557$	22.7991	−	13.1631i	0.966030	−	0.557738i	0.0680066	−	0.997685i	$-0.478336\pi$
$557$	22.7991	−	13.1631i	0.966030	−	0.557738i	0.898024	+	0.439947i	$0.145003\pi$
$558$		0			0
$559$		−	4.50228i		−	0.190426i
$560$	0.448491	+	0.258936i	0.0189522	+	0.0109421i
$561$		0			0
$562$	6.08731	−	10.5435i	0.256778	−	0.444752i
$563$	5.84768	−	10.1285i	0.246450	−	0.426864i	−0.716088	−	0.698010i	$-0.754069\pi$
$563$	5.84768	−	10.1285i	0.246450	−	0.426864i	0.962538	+	0.271146i	$0.0874025\pi$
$564$		0			0
$565$		−	0.606811i		−	0.0255287i
$566$	11.0378	+	19.1180i	0.463953	+	0.803590i
$567$		0			0
$568$	−13.2329	+	22.9201i	−0.555241	+	0.961706i
$569$	−9.05101	−	15.6768i	−0.379438	−	0.657206i	0.611543	−	0.791211i	$-0.290549\pi$
$569$	−9.05101	−	15.6768i	−0.379438	−	0.657206i	−0.990981	+	0.134006i	$0.957216\pi$
$570$		0			0
$571$	4.87651	−	8.44636i	0.204076	−	0.353469i	−0.745762	−	0.666212i	$-0.767914\pi$
$571$	4.87651	−	8.44636i	0.204076	−	0.353469i	0.949838	+	0.312743i	$0.101248\pi$
$572$	1.39055	+	2.40850i	0.0581418	+	0.100705i
$573$		0			0
$574$	−12.2727	+	21.2569i	−0.512251	+	0.887244i
$575$	−23.3853	−	13.5015i	−0.975236	−	0.563053i
$576$		0			0
$577$	−25.3878			−1.05691			−0.528454	−	0.848962i	$-0.677228\pi$
$577$	−25.3878			−1.05691			−0.528454	+	0.848962i	$0.677228\pi$
$578$	−1.10074	−	1.90655i	−0.0457850	−	0.0793019i
$579$		0			0
$580$			0.896531i			0.0372264i
$581$	−25.6687	−	14.8198i	−1.06492	−	0.614830i
$582$		0			0
$583$	10.9514	+	6.32278i	0.453560	+	0.261863i
$584$	−6.02160	+	10.4297i	−0.249176	+	0.431585i
$585$		0			0
$586$	9.71765	−	16.8315i	0.401433	−	0.695302i
$587$			19.1724i			0.791331i	0.918395	+	0.395666i	$0.129486\pi$
$587$			19.1724i			0.791331i	−0.918395	+	0.395666i	$0.870514\pi$
$588$		0			0
$589$	−14.9409	−	2.75209i	−0.615630	−	0.113398i
$590$	0.152081	+	0.0878040i	0.00626107	+	0.00361483i
$591$		0			0
$592$		−	2.51148i		−	0.103221i
$593$	2.09357	−	1.20873i	0.0859728	−	0.0496364i	−0.456397	−	0.889776i	$-0.650860\pi$
$593$	2.09357	−	1.20873i	0.0859728	−	0.0496364i	0.542370	+	0.840140i	$0.317527\pi$
$594$		0			0
$595$	0.707537	+	1.22549i	0.0290062	+	0.0502402i
$596$	22.5685	−	13.0299i	0.924440	−	0.533726i
$597$		0			0
$598$	−1.55960			−0.0637769
$599$	32.1864			1.31510			0.657550	−	0.753411i	$-0.271593\pi$
$599$	32.1864			1.31510			0.657550	+	0.753411i	$0.271593\pi$
$600$		0			0
$601$	23.2325	−	13.4133i	0.947675	−	0.547140i	0.0553168	−	0.998469i	$-0.482383\pi$
$601$	23.2325	−	13.4133i	0.947675	−	0.547140i	0.892358	+	0.451329i	$0.149050\pi$
$602$	−13.2956	−	23.0286i	−0.541887	−	0.938577i
$603$		0			0
$604$	1.10327	−	0.636974i	0.0448915	−	0.0259181i
$605$		−	0.879962i		−	0.0357755i
$606$		0			0
$607$	−21.3827	−	12.3453i	−0.867897	−	0.501081i	−0.00124816	−	0.999999i	$-0.500397\pi$
$607$	−21.3827	−	12.3453i	−0.867897	−	0.501081i	−0.866649	+	0.498919i	$0.833731\pi$
$608$	−23.8661	+	8.48107i	−0.967899	+	0.343953i
$609$		0			0
$610$		−	0.950670i		−	0.0384915i
$611$	0.0523187	−	0.0906187i	0.00211659	−	0.00366604i
$612$		0			0
$613$	−1.93026	+	3.34330i	−0.0779624	+	0.135035i	−0.902371	−	0.430961i	$-0.858175\pi$
$613$	−1.93026	+	3.34330i	−0.0779624	+	0.135035i	0.824408	+	0.565996i	$0.191508\pi$
$614$	−5.79792	−	3.34743i	−0.233985	−	0.135091i
$615$		0			0
$616$	32.9179	+	19.0052i	1.32630	+	0.765740i
$617$		−	21.4855i		−	0.864972i	−0.901641	−	0.432486i	$-0.857636\pi$
$617$		−	21.4855i		−	0.864972i	0.901641	−	0.432486i	$-0.142364\pi$
$618$		0			0
$619$	−16.6647	−	28.8640i	−0.669809	−	1.16014i	−0.977957	−	0.208805i	$-0.933042\pi$
$619$	−16.6647	−	28.8640i	−0.669809	−	1.16014i	0.308148	−	0.951339i	$-0.400291\pi$
$620$	−0.567310			−0.0227837
$621$		0			0
$622$	−0.0683909	−	0.0394855i	−0.00274223	−	0.00158322i
$623$	9.31361	−	16.1316i	0.373142	−	0.646301i
$624$		0			0
$625$	−12.4143	−	21.5022i	−0.496571	−	0.860087i
$626$	0.783887	−	1.35773i	0.0313304	−	0.0542659i
$627$		0			0
$628$	−11.3599	−	19.6758i	−0.453308	−	0.785152i
$629$	3.43127	−	5.94314i	0.136814	−	0.236969i
$630$		0			0
$631$	−10.5833	−	18.3308i	−0.421313	−	0.729736i	0.574755	−	0.818325i	$-0.305097\pi$
$631$	−10.5833	−	18.3308i	−0.421313	−	0.729736i	−0.996068	+	0.0885897i	$0.971764\pi$
$632$		−	2.66482i		−	0.106001i
$633$		0			0
$634$	−3.40994	+	5.90620i	−0.135426	+	0.234565i
$635$	−0.879929	+	1.52408i	−0.0349189	+	0.0604813i
$636$		0			0
$637$	−2.04690	−	1.18178i	−0.0811011	−	0.0468238i
$638$			16.6989i			0.661118i
$639$		0			0
$640$	−0.993312	+	0.573489i	−0.0392641	+	0.0226691i
$641$	30.3002			1.19679			0.598393	−	0.801203i	$-0.295806\pi$
$641$	30.3002			1.19679			0.598393	+	0.801203i	$0.295806\pi$
$642$		0			0
$643$	−4.26242	−	7.38272i	−0.168093	−	0.291146i	0.769656	−	0.638459i	$-0.220428\pi$
$643$	−4.26242	−	7.38272i	−0.168093	−	0.291146i	−0.937749	+	0.347313i	$0.887094\pi$
$644$	25.3975	−	14.6633i	1.00080	−	0.577814i
$645$		0			0
$646$	−11.0167	−	2.02926i	−0.433447	−	0.0798402i
$647$			30.0725i			1.18227i	0.806572	+	0.591135i	$0.201320\pi$
$647$			30.0725i			1.18227i	−0.806572	+	0.591135i	$0.798680\pi$
$648$		0			0
$649$	−9.01863	−	5.20691i	−0.354012	−	0.204389i
$650$	−1.24475	−	0.718657i	−0.0488231	−	0.0281881i
$651$		0			0
$652$	−5.91922			−0.231814
$653$	38.8242	+	22.4151i	1.51931	+	0.877173i	0.999741	+	0.0227422i	$0.00723970\pi$
$653$	38.8242	+	22.4151i	1.51931	+	0.877173i	0.519566	+	0.854430i	$0.326094\pi$
$654$		0			0
$655$	0.516786	−	0.895099i	0.0201925	−	0.0349744i
$656$	6.78300	+	11.7485i	0.264832	+	0.458702i
$657$		0			0
$658$		−	0.618004i		−	0.0240923i
$659$	−3.85903	+	6.68403i	−0.150326	+	0.260373i	−0.931347	−	0.364132i	$-0.881366\pi$
$659$	−3.85903	+	6.68403i	−0.150326	+	0.260373i	0.781021	+	0.624505i	$0.214699\pi$
$660$		0			0
$661$		−	5.46052i		−	0.212389i	−0.994345	−	0.106195i	$-0.966133\pi$
$661$		−	5.46052i		−	0.212389i	0.994345	−	0.106195i	$-0.0338667\pi$
$662$	4.54011	−	2.62123i	0.176456	−	0.101877i
$663$		0			0
$664$	17.5590	−	10.1377i	0.681422	−	0.393419i
$665$	−1.63200	−	0.300612i	−0.0632863	−	0.0116572i
$666$		0			0
$667$	25.8202	+	14.9073i	0.999762	+	0.577213i
$668$	−14.5706			−0.563753
$669$		0			0
$670$	−0.391854	−	0.678711i	−0.0151386	−	0.0262209i
$671$			56.3762i			2.17638i
$672$		0			0
$673$	−7.25030	+	4.18596i	−0.279478	+	0.161357i	−0.633187	−	0.773999i	$-0.718254\pi$
$673$	−7.25030	+	4.18596i	−0.279478	+	0.161357i	0.353709	+	0.935356i	$0.384920\pi$
$674$	8.45029	−	4.87878i	0.325493	−	0.187924i
$675$		0			0
$676$	−19.5212			−0.750816
$677$	−18.8962	−	32.7292i	−0.726241	−	1.25789i	−0.958461	−	0.285223i	$-0.907932\pi$
$677$	−18.8962	−	32.7292i	−0.726241	−	1.25789i	0.232220	−	0.972663i	$-0.425401\pi$
$678$		0			0
$679$	−40.4395	+	23.3478i	−1.55193	+	0.896005i
$680$	−0.968000			−0.0371211
$681$		0			0
$682$	−10.5668			−0.404624
$683$	−6.09850			−0.233352			−0.116676	−	0.993170i	$-0.537224\pi$
$683$	−6.09850			−0.233352			−0.116676	+	0.993170i	$0.537224\pi$
$684$		0			0
$685$	1.34708			0.0514694
$686$	3.26900			0.124811
$687$		0			0
$688$	−14.6967			−0.560308
$689$	1.04075	−	0.600879i	0.0396495	−	0.0228916i
$690$		0			0
$691$	−16.5151	−	28.6050i	−0.628265	−	1.08819i	−0.987900	−	0.155094i	$-0.950432\pi$
$691$	−16.5151	−	28.6050i	−0.628265	−	1.08819i	0.359635	−	0.933093i	$-0.382901\pi$
$692$	6.82681			0.259516
$693$		0			0
$694$	4.10889	−	2.37227i	0.155971	−	0.0900500i
$695$	0.940909	−	0.543234i	0.0356907	−	0.0206060i
$696$		0			0
$697$			37.0688i			1.40408i
$698$	2.14797	+	3.72040i	0.0813020	+	0.140819i
$699$		0			0
$700$	27.0270			1.02153
$701$	−5.80129	−	3.34938i	−0.219112	−	0.126504i	0.386427	−	0.922320i	$-0.373709\pi$
$701$	−5.80129	−	3.34938i	−0.219112	−	0.126504i	−0.605539	+	0.795816i	$0.707042\pi$
$702$		0			0
$703$	2.69475	+	7.58314i	0.101634	+	0.286004i
$704$	−4.92512	+	2.84352i	−0.185622	+	0.107169i
$705$		0			0
$706$	7.62856	−	4.40435i	0.287105	−	0.165760i
$707$			6.29838i			0.236875i
$708$		0			0
$709$	−10.9246	+	18.9219i	−0.410280	+	0.710627i	−0.994920	−	0.100666i	$-0.967903\pi$
$709$	−10.9246	+	18.9219i	−0.410280	+	0.710627i	0.584640	+	0.811293i	$0.301236\pi$
$710$		−	0.803658i		−	0.0301608i
$711$		0			0
$712$	6.37110	+	11.0351i	0.238767	+	0.413557i
$713$	−9.43308	+	16.3386i	−0.353272	+	0.611885i
$714$		0			0
$715$	−0.169244	−	0.0977131i	−0.00632937	−	0.00365426i
$716$	−7.64264			−0.285619
$717$		0			0
$718$	9.11469	+	5.26237i	0.340157	+	0.196390i
$719$	−20.5211	−	11.8479i	−0.765309	−	0.441851i	0.0658895	−	0.997827i	$-0.479012\pi$
$719$	−20.5211	−	11.8479i	−0.765309	−	0.441851i	−0.831199	+	0.555975i	$0.812345\pi$
$720$		0			0
$721$		−	6.43932i		−	0.239813i
$722$	10.1908	−	8.28966i	0.379263	−	0.308509i
$723$		0			0
$724$	−16.6751	+	9.62735i	−0.619723	+	0.357798i
$725$	13.7384	+	23.7956i	0.510232	+	0.883748i
$726$		0			0
$727$	−18.4719			−0.685085			−0.342542	−	0.939502i	$-0.611288\pi$
$727$	−18.4719			−0.685085			−0.342542	+	0.939502i	$0.611288\pi$
$728$	3.12832	−	1.80613i	0.115943	−	0.0669398i
$729$		0			0
$730$		−	0.365702i		−	0.0135352i
$731$	−34.7783	−	20.0792i	−1.28632	−	0.742657i
$732$		0			0
$733$	−20.4287	+	35.3835i	−0.754550	+	1.30692i	0.191048	+	0.981581i	$0.438811\pi$
$733$	−20.4287	+	35.3835i	−0.754550	+	1.30692i	−0.945598	+	0.325338i	$0.894522\pi$
$734$	2.65002	−	4.58997i	0.0978140	−	0.169419i
$735$		0			0
$736$			31.4533i			1.15938i
$737$	23.2375	+	40.2486i	0.855965	+	1.48257i
$738$		0			0
$739$	1.64367	−	2.84692i	0.0604633	−	0.104726i	−0.834209	−	0.551448i	$-0.814076\pi$
$739$	1.64367	−	2.84692i	0.0604633	−	0.104726i	0.894673	+	0.446722i	$0.147409\pi$
$740$	0.150259	+	0.260256i	0.00552362	+	0.00956720i
$741$		0			0
$742$	3.54888	−	6.14684i	0.130283	−	0.225658i
$743$	16.8680	+	29.2162i	0.618826	+	1.07184i	0.989700	+	0.143156i	$0.0457249\pi$
$743$	16.8680	+	29.2162i	0.618826	+	1.07184i	−0.370874	+	0.928683i	$0.620942\pi$
$744$		0			0
$745$	−0.915604	+	1.58587i	−0.0335451	+	0.0581018i
$746$	11.3186	+	6.53477i	0.414402	+	0.239255i
$747$		0			0
$748$	24.8062			0.907005
$749$	24.2144	+	41.9405i	0.884774	+	1.53247i
$750$		0			0
$751$			39.6120i			1.44546i	0.691129	+	0.722731i	$0.257114\pi$
$751$			39.6120i			1.44546i	−0.691129	+	0.722731i	$0.742886\pi$
$752$	−0.295805	−	0.170783i	−0.0107869	−	0.00622782i
$753$		0			0
$754$	1.37435	+	0.793483i	0.0500510	+	0.0288969i
$755$	−0.0447598	+	0.0775263i	−0.00162898	+	0.00282147i
$756$		0			0
$757$	2.10833	−	3.65174i	0.0766287	−	0.132725i	−0.825165	−	0.564892i	$-0.808918\pi$
$757$	2.10833	−	3.65174i	0.0766287	−	0.132725i	0.901793	+	0.432167i	$0.142251\pi$
$758$			17.0886i			0.620686i
$759$		0			0
$760$	0.736284	−	0.864006i	0.0267078	−	0.0313408i
$761$	6.65646	+	3.84311i	0.241297	+	0.139313i	0.615773	−	0.787924i	$-0.288844\pi$
$761$	6.65646	+	3.84311i	0.241297	+	0.139313i	−0.374476	+	0.927237i	$0.622177\pi$
$762$		0			0
$763$			45.1724i			1.63535i
$764$	19.6119	−	11.3229i	0.709534	−	0.409650i
$765$		0			0
$766$	−7.91354	−	13.7067i	−0.285928	−	0.495242i
$767$	−0.857076	+	0.494833i	−0.0309472	+	0.0178674i
$768$		0			0
$769$	−17.6975			−0.638190			−0.319095	−	0.947723i	$-0.603379\pi$
$769$	−17.6975			−0.638190			−0.319095	+	0.947723i	$0.603379\pi$
$770$	−1.15422			−0.0415951
$771$		0			0
$772$	17.5942	−	10.1580i	0.633230	−	0.365596i
$773$	0.137641	+	0.238402i	0.00495061	+	0.00857471i	0.868490	−	0.495707i	$-0.165091\pi$
$773$	0.137641	+	0.238402i	0.00495061	+	0.00857471i	−0.863539	+	0.504281i	$0.831757\pi$
$774$		0			0
$775$	−15.0575	+	8.69343i	−0.540880	+	0.312277i
$776$		−	31.9427i		−	1.14668i
$777$		0			0
$778$	−2.26993	−	1.31054i	−0.0813808	−	0.0469852i
$779$	−33.0864	−	28.1954i	−1.18544	−	1.01020i
$780$		0			0
$781$			47.6582i			1.70534i
$782$	−6.95550	+	12.0473i	−0.248728	+	0.430810i
$783$		0			0
$784$	−3.85766	+	6.68166i	−0.137774	+	0.238631i
$785$	1.38261	+	0.798250i	0.0493475	+	0.0284908i
$786$		0			0
$787$	11.1612	+	6.44390i	0.397853	+	0.229700i	0.685557	−	0.728019i	$-0.259559\pi$
$787$	11.1612	+	6.44390i	0.397853	+	0.229700i	−0.287704	+	0.957719i	$0.592892\pi$
$788$			32.5948i			1.16114i
$789$		0			0
$790$	0.0404598	+	0.0700783i	0.00143949	+	0.00249328i
$791$	20.1977			0.718148
$792$		0			0
$793$	4.63986	+	2.67882i	0.164766	+	0.0951278i
$794$	2.44620	−	4.23694i	0.0868123	−	0.150363i
$795$		0			0
$796$	−3.81886	−	6.61445i	−0.135356	−	0.234443i
$797$	−24.8067	+	42.9665i	−0.878699	+	1.52195i	−0.0259298	+	0.999664i	$0.508255\pi$
$797$	−24.8067	+	42.9665i	−0.878699	+	1.52195i	−0.852769	+	0.522288i	$0.825079\pi$
$798$		0			0
$799$	−0.466661	−	0.808280i	−0.0165093	−	0.0285949i
$800$	−14.4935	+	25.1035i	−0.512423	+	0.887543i
$801$		0			0
$802$	4.37537	+	7.57837i	0.154500	+	0.267602i
$803$			21.6867i			0.765306i
$804$		0			0
$805$	−1.03038	+	1.78467i	−0.0363161	+	0.0629013i
$806$	−0.502102	+	0.869667i	−0.0176858	+	0.0306327i
$807$		0			0
$808$	−3.73126	−	2.15425i	−0.131265	−	0.0757861i
$809$		−	23.6970i		−	0.833142i	−0.909103	−	0.416571i	$-0.863232\pi$
$809$		−	23.6970i		−	0.833142i	0.909103	−	0.416571i	$-0.136768\pi$
$810$		0			0
$811$	35.4486	−	20.4662i	1.24477	−	0.718667i	0.274707	−	0.961528i	$-0.411419\pi$
$811$	35.4486	−	20.4662i	1.24477	−	0.718667i	0.970061	+	0.242861i	$0.0780860\pi$
$812$	−29.8411			−1.04722
$813$		0			0
$814$	2.79875	+	4.84757i	0.0980960	+	0.169907i
$815$	0.360215	−	0.207970i	0.0126178	−	0.00728487i
$816$		0			0
$817$	44.3753	−	15.7692i	1.55249	−	0.551695i
$818$		−	16.7126i		−	0.584342i
$819$		0			0
$820$	−1.40580	−	0.811639i	−0.0490927	−	0.0283437i
$821$	−45.2151	−	26.1049i	−1.57802	−	0.911068i	−0.995136	−	0.0985109i	$-0.968592\pi$
$821$	−45.2151	−	26.1049i	−1.57802	−	0.911068i	−0.582881	−	0.812558i	$-0.698075\pi$
$822$		0			0
$823$	−13.7069			−0.477794			−0.238897	−	0.971045i	$-0.576786\pi$
$823$	−13.7069			−0.477794			−0.238897	+	0.971045i	$0.576786\pi$
$824$	3.81476	+	2.20245i	0.132893	+	0.0767260i
$825$		0			0
$826$	−2.92256	+	5.06202i	−0.101689	+	0.176130i
$827$	5.42239	+	9.39185i	0.188555	+	0.326587i	0.944769	−	0.327738i	$-0.106286\pi$
$827$	5.42239	+	9.39185i	0.188555	+	0.326587i	−0.756214	+	0.654325i	$0.772953\pi$
$828$		0			0
$829$			44.0349i			1.52939i	0.644390	+	0.764697i	$0.277111\pi$
$829$			44.0349i			1.52939i	−0.644390	+	0.764697i	$0.722889\pi$
$830$	−0.307840	+	0.533194i	−0.0106853	+	0.0185074i
$831$		0			0
$832$			0.540461i			0.0187371i
$833$	−18.2575	+	10.5410i	−0.632584	+	0.365223i
$834$		0			0
$835$	0.886694	−	0.511933i	0.0306853	−	0.0177162i
$836$	−18.8682	+	22.1412i	−0.652571	+	0.765771i
$837$		0			0
$838$	−16.1499	−	9.32416i	−0.557890	−	0.322098i
$839$	41.1382			1.42025			0.710124	−	0.704077i	$-0.248639\pi$
$839$	41.1382			1.42025			0.710124	+	0.704077i	$0.248639\pi$
$840$		0			0
$841$	−0.668844	−	1.15847i	−0.0230636	−	0.0399473i
$842$			18.3539i			0.632518i
$843$		0			0
$844$	21.1013	−	12.1829i	0.726337	−	0.419351i
$845$	1.18797	−	0.685872i	0.0408672	−	0.0235947i
$846$		0			0
$847$	29.2896			1.00640
$848$	−1.96144	−	3.39731i	−0.0673561	−	0.116664i
$849$		0			0
$850$	−11.1026	+	6.41012i	−0.380818	+	0.219865i
$851$	9.99386			0.342585
$852$		0			0
$853$	−12.4985			−0.427942			−0.213971	−	0.976840i	$-0.568640\pi$
$853$	−12.4985			−0.427942			−0.213971	+	0.976840i	$0.568640\pi$
$854$	31.6431			1.08280
$855$		0			0
$856$	−33.1284			−1.13230
$857$	−4.84208			−0.165402			−0.0827012	−	0.996574i	$-0.526355\pi$
$857$	−4.84208			−0.165402			−0.0827012	+	0.996574i	$0.526355\pi$
$858$		0			0
$859$	14.1040			0.481222			0.240611	−	0.970622i	$-0.422652\pi$
$859$	14.1040			0.481222			0.240611	+	0.970622i	$0.422652\pi$
$860$	1.52297	−	0.879289i	0.0519330	−	0.0299835i
$861$		0			0
$862$	−5.84432	−	10.1227i	−0.199058	−	0.344779i
$863$	37.3291			1.27070			0.635348	−	0.772226i	$-0.280857\pi$
$863$	37.3291			1.27070			0.635348	+	0.772226i	$0.280857\pi$
$864$		0			0
$865$	−0.415446	+	0.239858i	−0.0141256	+	0.00815541i
$866$	−9.01576	+	5.20525i	−0.306368	+	0.176882i
$867$		0			0
$868$		−	18.8829i		−	0.640928i
$869$	−2.39932	−	4.15575i	−0.0813915	−	0.140974i
$870$		0			0
$871$	4.41670			0.149654
$872$	−26.7609	−	15.4504i	−0.906239	−	0.523217i
$873$		0			0
$874$	−5.46249	−	15.3717i	−0.184772	−	0.519956i
$875$	−3.29324	+	1.90135i	−0.111332	+	0.0642774i
$876$		0			0
$877$	14.6584	−	8.46303i	0.494979	−	0.285776i	−0.231659	−	0.972797i	$-0.574415\pi$
$877$	14.6584	−	8.46303i	0.494979	−	0.285776i	0.726638	+	0.687021i	$0.241082\pi$
$878$		−	10.3524i		−	0.349377i
$879$		0			0
$880$	−0.318963	+	0.552461i	−0.0107523	+	0.0186234i
$881$			11.2468i			0.378913i	0.981889	+	0.189457i	$0.0606727\pi$
$881$			11.2468i			0.378913i	−0.981889	+	0.189457i	$0.939327\pi$
$882$		0			0
$883$	−2.49791	−	4.32650i	−0.0840613	−	0.145598i	0.820930	−	0.571030i	$-0.193456\pi$
$883$	−2.49791	−	4.32650i	−0.0840613	−	0.145598i	−0.904991	+	0.425431i	$0.860122\pi$
$884$	1.17872	−	2.04160i	0.0396445	−	0.0686663i
$885$		0			0
$886$	−8.32842	−	4.80841i	−0.279799	−	0.161542i
$887$	28.6123			0.960708			0.480354	−	0.877075i	$-0.340508\pi$
$887$	28.6123			0.960708			0.480354	+	0.877075i	$0.340508\pi$
$888$		0			0
$889$	−50.7291	−	29.2885i	−1.70140	−	0.982303i
$890$	−0.335089	−	0.193464i	−0.0112322	−	0.00648493i
$891$		0			0
$892$		−	12.4863i		−	0.418072i
$893$	1.07640	+	0.198271i	0.0360203	+	0.00663488i
$894$		0			0
$895$	0.465094	−	0.268522i	0.0155464	−	0.00897570i
$896$	−19.0886	−	33.0624i	−0.637705	−	1.10454i
$897$		0			0
$898$	23.4405			0.782219
$899$	16.6252	−	9.59858i	0.554483	−	0.320131i
$900$		0			0
$901$		−	10.7192i		−	0.357107i
$902$	−26.1847	−	15.1177i	−0.871854	−	0.503365i
$903$		0			0
$904$	−6.90826	+	11.9655i	−0.229765	+	0.397965i
$905$	0.676508	−	1.17175i	0.0224879	−	0.0389502i
$906$		0			0
$907$			23.8243i			0.791074i	0.918450	+	0.395537i	$0.129442\pi$
$907$			23.8243i			0.791074i	−0.918450	+	0.395537i	$0.870558\pi$
$908$	−21.9192	−	37.9651i	−0.727413	−	1.25992i
$909$		0			0
$910$	−0.0548448	+	0.0949940i	−0.00181809	+	0.00314902i
$911$	−20.4314	−	35.3881i	−0.676921	−	1.17246i	−0.975903	−	0.218203i	$-0.929981\pi$
$911$	−20.4314	−	35.3881i	−0.676921	−	1.17246i	0.298982	−	0.954259i	$-0.403353\pi$
$912$		0			0
$913$	18.2554	−	31.6192i	0.604165	−	1.04644i
$914$	−12.0545	−	20.8790i	−0.398728	−	0.690617i
$915$		0			0
$916$	−14.0785	+	24.3847i	−0.465168	+	0.805694i
$917$	29.7934	+	17.2012i	0.983864	+	0.568034i
$918$		0			0
$919$	−48.0310			−1.58440			−0.792198	−	0.610264i	$-0.791063\pi$
$919$	−48.0310			−1.58440			−0.792198	+	0.610264i	$0.791063\pi$
$920$	−0.704845	−	1.22083i	−0.0232381	−	0.0402495i
$921$		0			0
$922$		−	8.43530i		−	0.277802i
$923$	3.92235	+	2.26457i	0.129106	+	0.0745392i
$924$		0			0
$925$	7.97630	+	4.60512i	0.262259	+	0.151415i
$926$	5.45946	−	9.45606i	0.179409	−	0.310746i
$927$		0			0
$928$	16.0026	−	27.7173i	0.525310	−	0.909864i
$929$		−	13.4620i		−	0.441675i	−0.975311	−	0.220838i	$-0.929121\pi$
$929$		−	13.4620i		−	0.441675i	0.975311	−	0.220838i	$-0.0708791\pi$
$930$		0			0
$931$	4.47855	−	24.3137i	0.146779	−	0.796851i
$932$	27.1587	+	15.6801i	0.889612	+	0.513618i
$933$		0			0
$934$			0.697552i			0.0228246i
$935$	−1.50958	+	0.871559i	−0.0493687	+	0.0285030i
$936$		0			0
$937$	7.39153	+	12.8025i	0.241471	+	0.418240i	0.961133	−	0.276084i	$-0.0890369\pi$
$937$	7.39153	+	12.8025i	0.241471	+	0.418240i	−0.719663	+	0.694324i	$0.755704\pi$
$938$	22.5909	−	13.0429i	0.737619	−	0.425864i
$939$		0			0
$940$	0.0408711			0.00133307
$941$	−19.7804			−0.644823			−0.322412	−	0.946600i	$-0.604494\pi$
$941$	−19.7804			−0.644823			−0.322412	+	0.946600i	$0.604494\pi$
$942$		0			0
$943$	−46.7506	+	26.9915i	−1.52241	+	0.878963i
$944$	1.61528	+	2.79774i	0.0525727	+	0.0910587i
$945$		0			0
$946$	28.3672	−	16.3778i	0.922296	−	0.532488i
$947$			30.6712i			0.996680i	0.866982	+	0.498340i	$0.166057\pi$
$947$			30.6712i			0.996680i	−0.866982	+	0.498340i	$0.833943\pi$
$948$		0			0
$949$	1.78485	+	1.03048i	0.0579388	+	0.0334510i
$950$	2.72348	−	14.7856i	0.0883612	−	0.479707i
$951$		0			0
$952$		−	32.2199i		−	1.04425i
$953$	−20.9938	+	36.3623i	−0.680055	+	1.17789i	0.294908	+	0.955526i	$0.404711\pi$
$953$	−20.9938	+	36.3623i	−0.680055	+	1.17789i	−0.974964	+	0.222365i	$0.928622\pi$
$954$		0			0
$955$	−0.795657	+	1.37812i	−0.0257468	+	0.0445948i
$956$	−38.9237	−	22.4726i	−1.25888	−	0.726816i
$957$		0			0
$958$	−26.1056	−	15.0721i	−0.843435	−	0.486957i
$959$			44.8377i			1.44788i
$960$		0			0
$961$	−9.42618	−	16.3266i	−0.304070	−	0.526665i
$962$	0.531951			0.0171508
$963$		0			0
$964$	5.67887	+	3.27870i	0.182904	+	0.105600i
$965$	−0.713799	+	1.23634i	−0.0229780	+	0.0397991i
$966$		0			0
$967$	16.7605	+	29.0301i	0.538982	+	0.933545i	0.998959	+	0.0456140i	$0.0145244\pi$
$967$	16.7605	+	29.0301i	0.538982	+	0.933545i	−0.459977	+	0.887931i	$0.652142\pi$
$968$	−10.0180	+	17.3516i	−0.321989	+	0.557702i
$969$		0			0
$970$	0.484984	+	0.840017i	0.0155719	+	0.0269713i
$971$	15.4529	−	26.7652i	0.495907	−	0.858936i	−0.504082	−	0.863656i	$-0.668169\pi$
$971$	15.4529	−	26.7652i	0.495907	−	0.858936i	0.999989	+	0.00471955i	$0.00150229\pi$
$972$		0			0
$973$	18.0816	+	31.3182i	0.579668	+	1.00401i
$974$			13.0535i			0.418261i
$975$		0			0
$976$	8.74444	−	15.1458i	0.279903	−	0.484806i
$977$	−18.1095	+	31.3666i	−0.579375	+	1.00351i	0.416176	+	0.909284i	$0.363370\pi$
$977$	−18.1095	+	31.3666i	−0.579375	+	1.00351i	−0.995551	+	0.0942233i	$0.969963\pi$
$978$		0			0
$979$	19.8713	+	11.4727i	0.635090	+	0.366669i
$980$		−	0.923198i		−	0.0294905i
$981$		0			0
$982$	−16.5967	+	9.58210i	−0.529621	+	0.305777i
$983$	15.5150			0.494852			0.247426	−	0.968907i	$-0.420415\pi$
$983$	15.5150			0.494852			0.247426	+	0.968907i	$0.420415\pi$
$984$		0			0
$985$	−1.14521	−	1.98356i	−0.0364894	−	0.0632015i
$986$	12.2586	−	7.07753i	0.390395	−	0.225395i
$987$		0			0
$988$	0.925704	+	2.60497i	0.0294506	+	0.0828752i
$989$		−	58.4824i		−	1.85963i
$990$		0			0
$991$	−3.23093	−	1.86538i	−0.102634	−	0.0592558i	0.447804	−	0.894132i	$-0.352206\pi$
$991$	−3.23093	−	1.86538i	−0.102634	−	0.0592558i	−0.550438	+	0.834876i	$0.685539\pi$
$992$	17.5390	+	10.1261i	0.556864	+	0.321506i
$993$		0			0
$994$	26.7498			0.848451
$995$	0.464794	+	0.268349i	0.0147350	+	0.00850723i
$996$		0			0
$997$	20.3507	−	35.2484i	0.644512	−	1.11633i	−0.339903	−	0.940461i	$-0.610394\pi$
$997$	20.3507	−	35.2484i	0.644512	−	1.11633i	0.984414	−	0.175866i	$-0.0562726\pi$
$998$	−5.94135	−	10.2907i	−0.188070	−	0.325747i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.t.a.179.11		36
3.2	odd	2		171.2.t.a.122.8	yes	36
9.2	odd	6		513.2.k.a.8.11		36
9.7	even	3		171.2.k.a.65.8	yes	36
19.12	odd	6		513.2.k.a.449.11		36
57.50	even	6		171.2.k.a.50.8	✓	36
171.88	odd	6		171.2.t.a.164.8	yes	36
171.164	even	6	inner	513.2.t.a.278.11		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.8	✓	36	57.50	even	6
171.2.k.a.65.8	yes	36	9.7	even	3
171.2.t.a.122.8	yes	36	3.2	odd	2
171.2.t.a.164.8	yes	36	171.88	odd	6
513.2.k.a.8.11		36	9.2	odd	6
513.2.k.a.449.11		36	19.12	odd	6
513.2.t.a.179.11		36	1.1	even	1	trivial
513.2.t.a.278.11		36	171.164	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.691402 q^{2} -1.52196 q^{4} +(0.0926192 - 0.0534737i) q^{5} +(1.77987 + 3.08283i) q^{7} -2.43509 q^{8} +(0.0640371 - 0.0369718i) q^{10} +(-3.79750 + 2.19249i) q^{11} +0.416721i q^{13} +(1.23061 + 2.13148i) q^{14} +1.36030 q^{16} +(3.21900 + 1.85849i) q^{17} +(-4.10727 + 1.45956i) q^{19} +(-0.140963 + 0.0813850i) q^{20} +(-2.62560 + 1.51589i) q^{22} +5.41300i q^{23} +(-2.49428 + 4.32022i) q^{25} +0.288122i q^{26} +(-2.70890 - 4.69195i) q^{28} +(2.75398 - 4.77004i) q^{29} +(3.01840 + 1.74267i) q^{31} +5.81070 q^{32} +(2.22562 + 1.28496i) q^{34} +(0.329701 + 0.190353i) q^{35} -1.84627i q^{37} +(-2.83978 + 1.00914i) q^{38} +(-0.225536 + 0.130213i) q^{40} +(4.98642 + 8.63673i) q^{41} -10.8041 q^{43} +(5.77965 - 3.33688i) q^{44} +3.74256i q^{46} +(-0.217456 - 0.125549i) q^{47} +(-2.83590 + 4.91192i) q^{49} +(-1.72455 + 2.98701i) q^{50} -0.634234i q^{52} +(-1.44192 - 2.49748i) q^{53} +(-0.234481 + 0.406133i) q^{55} +(-4.33416 - 7.50698i) q^{56} +(1.90411 - 3.29802i) q^{58} +(1.18744 + 2.05671i) q^{59} +(6.42834 - 11.1342i) q^{61} +(2.08693 + 1.20489i) q^{62} +1.29694 q^{64} +(0.0222836 + 0.0385964i) q^{65} -10.5987i q^{67} +(-4.89919 - 2.82855i) q^{68} +(0.227956 + 0.131610i) q^{70} +(5.43426 - 9.41241i) q^{71} +(2.47284 - 4.28309i) q^{73} -1.27652i q^{74} +(6.25111 - 2.22140i) q^{76} +(-13.5181 - 7.80470i) q^{77} +1.09434i q^{79} +(0.125990 - 0.0727401i) q^{80} +(3.44762 + 5.97145i) q^{82} +(-7.21082 + 4.16317i) q^{83} +0.397521 q^{85} -7.46996 q^{86} +(9.24726 - 5.33891i) q^{88} +(-2.61637 - 4.53168i) q^{89} +(-1.28468 + 0.741711i) q^{91} -8.23838i q^{92} +(-0.150350 - 0.0868045i) q^{94} +(-0.302364 + 0.354814i) q^{95} +13.1177i q^{97} +(-1.96075 + 3.39611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

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