LMFDB - Embedded newform 731.2.z.a.67.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(67,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 40]))

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

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

chi := DirichletCharacter("731.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.z (of order $42$, degree $12$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$64$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			67.10
Character	$\chi$	$=$	731.67
Dual form			731.2.z.a.611.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29990 + 1.63003i) q^{2} +(0.470647 + 3.12254i) q^{3} +(-0.522200 - 2.28791i) q^{4} +(1.19265 + 1.74929i) q^{5} +(-5.70163 - 3.29184i) q^{6} +(-0.150209 + 0.0867232i) q^{7} +(0.651331 + 0.313664i) q^{8} +(-6.66204 + 2.05497i) q^{9} +O(q^{10})$	\(q+(-1.29990 + 1.63003i) q^{2} +(0.470647 + 3.12254i) q^{3} +(-0.522200 - 2.28791i) q^{4} +(1.19265 + 1.74929i) q^{5} +(-5.70163 - 3.29184i) q^{6} +(-0.150209 + 0.0867232i) q^{7} +(0.651331 + 0.313664i) q^{8} +(-6.66204 + 2.05497i) q^{9} +(-4.40173 - 0.329864i) q^{10} +(2.27020 + 0.518158i) q^{11} +(6.89831 - 2.70739i) q^{12} +(-0.0203619 - 0.271710i) q^{13} +(0.0538960 - 0.357577i) q^{14} +(-4.90093 + 4.54740i) q^{15} +(2.87074 - 1.38247i) q^{16} +(-3.32847 + 2.43337i) q^{17} +(5.31036 - 13.5306i) q^{18} +(-4.33460 - 1.33705i) q^{19} +(3.37942 - 3.64215i) q^{20} +(-0.341492 - 0.428218i) q^{21} +(-3.79565 + 3.02693i) q^{22} +(0.898769 - 0.968643i) q^{23} +(-0.672883 + 2.18143i) q^{24} +(0.189085 - 0.481781i) q^{25} +(0.469364 + 0.320007i) q^{26} +(-5.44182 - 11.3000i) q^{27} +(0.276854 + 0.298377i) q^{28} +(0.898998 - 5.96446i) q^{29} +(-1.04165 - 13.8998i) q^{30} +(-5.99294 + 2.35206i) q^{31} +(-1.79994 + 7.88606i) q^{32} +(-0.549507 + 7.33266i) q^{33} +(0.360230 - 8.58865i) q^{34} +(-0.330851 - 0.159329i) q^{35} +(8.18048 + 14.1690i) q^{36} +(-2.20430 - 1.27265i) q^{37} +(7.81400 - 5.32749i) q^{38} +(0.838844 - 0.191461i) q^{39} +(0.228117 + 1.51346i) q^{40} +(5.66110 + 4.51457i) q^{41} +1.14191 q^{42} +(-0.844441 + 6.50284i) q^{43} -5.46459i q^{44} +(-11.5402 - 9.20301i) q^{45} +(0.410601 + 2.72416i) q^{46} +(1.10569 + 4.84433i) q^{47} +(5.66794 + 8.31334i) q^{48} +(-3.48496 + 6.03612i) q^{49} +(0.539524 + 0.934483i) q^{50} +(-9.16483 - 9.24802i) q^{51} +(-0.611015 + 0.188473i) q^{52} +(-0.308270 + 4.11357i) q^{53} +(25.4932 + 5.81867i) q^{54} +(1.80114 + 4.58923i) q^{55} +(-0.125038 + 0.00937028i) q^{56} +(2.13492 - 14.1643i) q^{57} +(8.55363 + 9.21862i) q^{58} +(-0.413358 + 0.199063i) q^{59} +(12.9633 + 8.83822i) q^{60} +(-5.98253 - 2.34797i) q^{61} +(3.95633 - 12.8261i) q^{62} +(0.822484 - 0.886427i) q^{63} +(-6.54153 - 8.20282i) q^{64} +(0.451017 - 0.359674i) q^{65} +(-11.2381 - 10.4275i) q^{66} +(8.20173 + 2.52990i) q^{67} +(7.30545 + 6.34452i) q^{68} +(3.44763 + 2.35055i) q^{69} +(0.689786 - 0.332183i) q^{70} +(6.52157 + 7.02858i) q^{71} +(-4.98376 - 0.751181i) q^{72} +(3.72772 - 0.279354i) q^{73} +(4.93984 - 1.93874i) q^{74} +(1.59337 + 0.363677i) q^{75} +(-0.795512 + 10.6154i) q^{76} +(-0.385941 + 0.119047i) q^{77} +(-0.778330 + 1.61622i) q^{78} +(0.471028 - 0.271948i) q^{79} +(5.84214 + 3.37296i) q^{80} +(15.4426 - 10.5286i) q^{81} +(-14.7178 + 3.35923i) q^{82} +(15.2785 - 2.30286i) q^{83} +(-0.801395 + 1.00492i) q^{84} +(-8.22638 - 2.92032i) q^{85} +(-9.50212 - 9.82953i) q^{86} +19.0474 q^{87} +(1.31612 + 1.04957i) q^{88} +(-10.8397 + 1.63382i) q^{89} +(30.0023 - 6.84784i) q^{90} +(0.0266221 + 0.0390475i) q^{91} +(-2.68550 - 1.55047i) q^{92} +(-10.1649 - 17.6062i) q^{93} +(-9.33368 - 4.49486i) q^{94} +(-2.83077 - 9.17713i) q^{95} +(-25.4717 - 1.90884i) q^{96} +(9.48464 + 2.16481i) q^{97} +(-5.30894 - 13.5270i) q^{98} +(-16.1889 + 1.21319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q - 24 q^{2} - 144 q^{4} - 16 q^{8} - 98 q^{9}+O(q^{10}) $ 768 * q - 24 * q^2 - 144 * q^4 - 16 * q^8 - 98 * q^9	$ 768 q - 24 q^{2} - 144 q^{4} - 16 q^{8} - 98 q^{9} - 18 q^{13} - 30 q^{15} - 160 q^{16} - 16 q^{17} - 54 q^{18} - 68 q^{19} - 50 q^{21} - 88 q^{25} - 26 q^{26} - 50 q^{32} - 36 q^{33} - 38 q^{34} + 14 q^{35} + 328 q^{36} - 44 q^{38} - 148 q^{42} + 102 q^{43} - 64 q^{47} + 298 q^{49} + 40 q^{50} - 31 q^{51} - 38 q^{52} - 28 q^{53} - 80 q^{55} - 16 q^{59} - 34 q^{60} - 64 q^{64} - 126 q^{66} + 74 q^{67} - 132 q^{68} - 28 q^{69} + 50 q^{70} + 26 q^{72} - 258 q^{76} - 112 q^{77} + 90 q^{81} + 48 q^{83} - 298 q^{84} + 36 q^{85} + 142 q^{86} + 192 q^{87} - 120 q^{89} - 188 q^{93} + 64 q^{94} + 146 q^{98}+O(q^{100}) $ 768 * q - 24 * q^2 - 144 * q^4 - 16 * q^8 - 98 * q^9 - 18 * q^13 - 30 * q^15 - 160 * q^16 - 16 * q^17 - 54 * q^18 - 68 * q^19 - 50 * q^21 - 88 * q^25 - 26 * q^26 - 50 * q^32 - 36 * q^33 - 38 * q^34 + 14 * q^35 + 328 * q^36 - 44 * q^38 - 148 * q^42 + 102 * q^43 - 64 * q^47 + 298 * q^49 + 40 * q^50 - 31 * q^51 - 38 * q^52 - 28 * q^53 - 80 * q^55 - 16 * q^59 - 34 * q^60 - 64 * q^64 - 126 * q^66 + 74 * q^67 - 132 * q^68 - 28 * q^69 + 50 * q^70 + 26 * q^72 - 258 * q^76 - 112 * q^77 + 90 * q^81 + 48 * q^83 - 298 * q^84 + 36 * q^85 + 142 * q^86 + 192 * q^87 - 120 * q^89 - 188 * q^93 + 64 * q^94 + 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−1.29990	+	1.63003i	−0.919171	+	1.15260i	0.0687479	+	0.997634i	$0.478100\pi$
$2$	−1.29990	+	1.63003i	−0.919171	+	1.15260i	−0.987919	+	0.154970i	$0.950472\pi$
$3$	0.470647	+	3.12254i	0.271728	+	1.80280i	0.542391	+	0.840126i	$0.317519\pi$
$3$	0.470647	+	3.12254i	0.271728	+	1.80280i	−0.270663	+	0.962674i	$0.587243\pi$
$4$	−0.522200	−	2.28791i	−0.261100	−	1.14395i
$5$	1.19265	+	1.74929i	0.533369	+	0.782308i	0.994468	−	0.105040i	$-0.0334972\pi$
$5$	1.19265	+	1.74929i	0.533369	+	0.782308i	−0.461099	+	0.887349i	$0.652545\pi$
$6$	−5.70163	−	3.29184i	−2.32768	−	1.34389i
$7$	−0.150209	+	0.0867232i	−0.0567737	+	0.0327783i	−0.528118	−	0.849171i	$-0.677102\pi$
$7$	−0.150209	+	0.0867232i	−0.0567737	+	0.0327783i	0.471344	+	0.881949i	$0.343769\pi$
$8$	0.651331	+	0.313664i	0.230280	+	0.110897i
$9$	−6.66204	+	2.05497i	−2.22068	+	0.684989i
$10$	−4.40173	−	0.329864i	−1.39195	−	0.104312i
$11$	2.27020	+	0.518158i	0.684491	+	0.156231i	0.550605	−	0.834766i	$-0.314397\pi$
$11$	2.27020	+	0.518158i	0.684491	+	0.156231i	0.133886	+	0.990997i	$0.457254\pi$
$12$	6.89831	−	2.70739i	1.99137	−	0.781555i
$13$	−0.0203619	−	0.271710i	−0.00564737	−	0.0753589i	0.993668	−	0.112356i	$-0.0358398\pi$
$13$	−0.0203619	−	0.271710i	−0.00564737	−	0.0753589i	−0.999315	+	0.0369973i	$0.988221\pi$
$14$	0.0538960	−	0.357577i	0.0144043	−	0.0955664i
$15$	−4.90093	+	4.54740i	−1.26541	+	1.17413i
$16$	2.87074	−	1.38247i	0.717685	−	0.345619i
$17$	−3.32847	+	2.43337i	−0.807272	+	0.590179i
$17$	−3.32847	+	2.43337i	−0.807272	+	0.590179i
$18$	5.31036	−	13.5306i	1.25166	−	3.18919i
$19$	−4.33460	−	1.33705i	−0.994426	−	0.306740i	−0.245502	−	0.969396i	$-0.578953\pi$
$19$	−4.33460	−	1.33705i	−0.994426	−	0.306740i	−0.748924	+	0.662656i	$0.769429\pi$
$20$	3.37942	−	3.64215i	0.755662	−	0.814410i
$21$	−0.341492	−	0.428218i	−0.0745197	−	0.0934448i
$22$	−3.79565	+	3.02693i	−0.809236	+	0.645344i
$23$	0.898769	−	0.968643i	0.187406	−	0.201976i	−0.632359	−	0.774675i	$-0.717913\pi$
$23$	0.898769	−	0.968643i	0.187406	−	0.201976i	0.819765	+	0.572699i	$0.194104\pi$
$24$	−0.672883	+	2.18143i	−0.137352	+	0.445283i
$25$	0.189085	−	0.481781i	0.0378170	−	0.0963561i
$26$	0.469364	+	0.320007i	0.0920499	+	0.0627586i
$27$	−5.44182	−	11.3000i	−1.04728	−	2.17470i
$28$	0.276854	+	0.298377i	0.0523204	+	0.0563880i
$29$	0.898998	−	5.96446i	0.166940	−	1.10757i	−0.735741	−	0.677263i	$-0.763166\pi$
$29$	0.898998	−	5.96446i	0.166940	−	1.10757i	0.902681	−	0.430310i	$-0.141596\pi$
$30$	−1.04165	−	13.8998i	−0.190178	−	2.53775i
$31$	−5.99294	+	2.35206i	−1.07636	+	0.422442i	−0.836275	−	0.548310i	$-0.815272\pi$
$31$	−5.99294	+	2.35206i	−1.07636	+	0.422442i	−0.240088	+	0.970751i	$0.577176\pi$
$32$	−1.79994	+	7.88606i	−0.318188	+	1.39407i
$33$	−0.549507	+	7.33266i	−0.0956569	+	1.27645i
$34$	0.360230	−	8.58865i	0.0617789	−	1.47294i
$35$	−0.330851	−	0.159329i	−0.0559240	−	0.0269316i
$36$	8.18048	+	14.1690i	1.36341	+	2.36150i
$37$	−2.20430	−	1.27265i	−0.362385	−	0.209223i	0.307742	−	0.951470i	$-0.400427\pi$
$37$	−2.20430	−	1.27265i	−0.362385	−	0.209223i	−0.670126	+	0.742247i	$0.733760\pi$
$38$	7.81400	−	5.32749i	1.26760	−	0.864234i
$39$	0.838844	−	0.191461i	0.134323	−	0.0306582i
$40$	0.228117	+	1.51346i	0.0360685	+	0.239299i
$41$	5.66110	+	4.51457i	0.884115	+	0.705058i	0.956317	−	0.292332i	$-0.0944313\pi$
$41$	5.66110	+	4.51457i	0.884115	+	0.705058i	−0.0722022	+	0.997390i	$0.523003\pi$
$42$	1.14191			0.176201
$43$	−0.844441	+	6.50284i	−0.128776	+	0.991674i
$43$	−0.844441	+	6.50284i	−0.128776	+	0.991674i
$44$		−	5.46459i		−	0.823817i
$45$	−11.5402	−	9.20301i	−1.72031	−	1.37190i
$46$	0.410601	+	2.72416i	0.0605399	+	0.401656i
$47$	1.10569	+	4.84433i	0.161281	+	0.706618i	0.989297	+	0.145914i	$0.0466123\pi$
$47$	1.10569	+	4.84433i	0.161281	+	0.706618i	−0.828016	+	0.560704i	$0.810531\pi$
$48$	5.66794	+	8.31334i	0.818097	+	1.19993i
$49$	−3.48496	+	6.03612i	−0.497851	+	0.862304i
$50$	0.539524	+	0.934483i	0.0763002	+	0.132156i
$51$	−9.16483	−	9.24802i	−1.28333	−	1.29498i
$52$	−0.611015	+	0.188473i	−0.0847326	+	0.0261365i
$53$	−0.308270	+	4.11357i	−0.0423441	+	0.565043i	0.935174	+	0.354190i	$0.115243\pi$
$53$	−0.308270	+	4.11357i	−0.0423441	+	0.565043i	−0.977518	+	0.210853i	$0.932376\pi$
$54$	25.4932	+	5.81867i	3.46919	+	0.791820i
$55$	1.80114	+	4.58923i	0.242866	+	0.618811i
$56$	−0.125038	+	0.00937028i	−0.0167089	+	0.00125216i
$57$	2.13492	−	14.1643i	0.282777	−	1.87610i
$58$	8.55363	+	9.21862i	1.12315	+	1.21046i
$59$	−0.413358	+	0.199063i	−0.0538147	+	0.0259158i	−0.460598	−	0.887609i	$-0.652365\pi$
$59$	−0.413358	+	0.199063i	−0.0538147	+	0.0259158i	0.406783	+	0.913525i	$0.366651\pi$
$60$	12.9633	+	8.83822i	1.67355	+	1.14101i
$61$	−5.98253	−	2.34797i	−0.765984	−	0.300627i	−0.0500057	−	0.998749i	$-0.515924\pi$
$61$	−5.98253	−	2.34797i	−0.765984	−	0.300627i	−0.715979	+	0.698122i	$0.754019\pi$
$62$	3.95633	−	12.8261i	0.502454	−	1.62892i
$63$	0.822484	−	0.886427i	0.103623	−	0.111679i
$64$	−6.54153	−	8.20282i	−0.817692	−	1.02535i
$65$	0.451017	−	0.359674i	0.0559418	−	0.0446121i
$66$	−11.2381	−	10.4275i	−1.38332	−	1.28353i
$67$	8.20173	+	2.52990i	1.00200	+	0.309076i	0.751996	−	0.659168i	$-0.229091\pi$
$67$	8.20173	+	2.52990i	1.00200	+	0.309076i	0.250005	+	0.968244i	$0.419568\pi$
$68$	7.30545	+	6.34452i	0.885916	+	0.769386i
$69$	3.44763	+	2.35055i	0.415046	+	0.282973i
$70$	0.689786	−	0.332183i	0.0824452	−	0.0397035i
$71$	6.52157	+	7.02858i	0.773968	+	0.834139i	0.989826	−	0.142286i	$-0.0454453\pi$
$71$	6.52157	+	7.02858i	0.773968	+	0.834139i	−0.215858	+	0.976425i	$0.569255\pi$
$72$	−4.98376	−	0.751181i	−0.587341	−	0.0885275i
$73$	3.72772	−	0.279354i	0.436296	−	0.0326959i	0.145228	−	0.989398i	$-0.453608\pi$
$73$	3.72772	−	0.279354i	0.436296	−	0.0326959i	0.291068	+	0.956702i	$0.405989\pi$
$74$	4.93984	−	1.93874i	0.574245	−	0.225374i
$75$	1.59337	+	0.363677i	0.183987	+	0.0419938i
$76$	−0.795512	+	10.6154i	−0.0912515	+	1.21767i
$77$	−0.385941	+	0.119047i	−0.0439820	+	0.0135667i
$78$	−0.778330	+	1.61622i	−0.0881286	+	0.183001i
$79$	0.471028	−	0.271948i	0.0529948	−	0.0305966i	−0.473269	−	0.880918i	$-0.656926\pi$
$79$	0.471028	−	0.271948i	0.0529948	−	0.0305966i	0.526263	+	0.850322i	$0.323593\pi$
$80$	5.84214	+	3.37296i	0.653171	+	0.377108i
$81$	15.4426	−	10.5286i	1.71585	−	1.16985i
$82$	−14.7178	+	3.35923i	−1.62531	+	0.370965i
$83$	15.2785	−	2.30286i	1.67703	−	0.252771i	0.759519	−	0.650485i	$-0.225434\pi$
$83$	15.2785	−	2.30286i	1.67703	−	0.252771i	0.917509	+	0.397714i	$0.130196\pi$
$84$	−0.801395	+	1.00492i	−0.0874394	+	0.109645i
$85$	−8.22638	−	2.92032i	−0.892276	−	0.316753i
$86$	−9.50212	−	9.82953i	−1.02464	−	1.05995i
$87$	19.0474			2.04209
$88$	1.31612	+	1.04957i	0.140299	+	0.111885i
$89$	−10.8397	+	1.63382i	−1.14901	+	0.173185i	−0.695810	−	0.718226i	$-0.744954\pi$
$89$	−10.8397	+	1.63382i	−1.14901	+	0.173185i	−0.453196	+	0.891411i	$0.649716\pi$
$90$	30.0023	−	6.84784i	3.16252	−	0.721826i
$91$	0.0266221	+	0.0390475i	0.00279076	+	0.00409329i
$92$	−2.68550	−	1.55047i	−0.279983	−	0.161648i
$93$	−10.1649	−	17.6062i	−1.05406	−	1.82568i
$94$	−9.33368	−	4.49486i	−0.962696	−	0.463610i
$95$	−2.83077	−	9.17713i	−0.290431	−	0.941553i
$96$	−25.4717	−	1.90884i	−2.59969	−	0.194820i
$97$	9.48464	+	2.16481i	0.963019	+	0.219803i	0.674997	−	0.737821i	$-0.264145\pi$
$97$	9.48464	+	2.16481i	0.963019	+	0.219803i	0.288022	+	0.957624i	$0.407002\pi$
$98$	−5.30894	−	13.5270i	−0.536284	−	1.36643i
$99$	−16.1889	+	1.21319i	−1.62705	+	0.121931i
$100$	−1.20101	−	0.181023i	−0.120101	−	0.0181023i
$101$	−1.79102	+	1.66182i	−0.178213	+	0.165358i	−0.764236	−	0.644937i	$-0.776883\pi$
$101$	−1.79102	+	1.66182i	−0.178213	+	0.165358i	0.586022	+	0.810295i	$0.300693\pi$
$102$	26.9880	−	2.91739i	2.67221	−	0.288865i
$103$	3.21367	+	2.19104i	0.316652	+	0.215890i	0.711207	−	0.702983i	$-0.248149\pi$
$103$	3.21367	+	2.19104i	0.316652	+	0.215890i	−0.394555	+	0.918872i	$0.629101\pi$
$104$	0.0719635	−	0.183360i	0.00705661	−	0.0179799i
$105$	0.341799	−	1.10808i	0.0333561	−	0.108138i
$106$	−6.30452	−	5.84974i	−0.612349	−	0.568177i
$107$	11.3716	−	9.06852i	1.09933	−	0.876687i	0.106276	−	0.994337i	$-0.466107\pi$
$107$	11.3716	−	9.06852i	1.09933	−	0.876687i	0.993055	+	0.117650i	$0.0375360\pi$
$108$	−23.0117	+	18.3513i	−2.21431	+	1.76585i
$109$	−12.0106	+	12.9444i	−1.15041	+	1.23985i	−0.183975	+	0.982931i	$0.558896\pi$
$109$	−12.0106	+	12.9444i	−1.15041	+	1.23985i	−0.966434	+	0.256915i	$0.917294\pi$
$110$	−9.82188	−	3.02965i	−0.936479	−	0.288866i
$111$	2.93646	−	7.48199i	0.278717	−	0.710159i
$112$	−0.311318	+	0.456620i	−0.0294168	+	0.0431465i
$113$	8.64922	+	17.9603i	0.813650	+	1.68956i	0.720018	+	0.693955i	$0.244133\pi$
$113$	8.64922	+	17.9603i	0.813650	+	1.68956i	0.0936319	+	0.995607i	$0.470152\pi$
$114$	20.3130	+	21.8922i	1.90248	+	2.05039i
$115$	2.76636	+	0.416961i	0.257964	+	0.0388818i
$116$	−14.1156	+	1.05782i	−1.31060	+	0.0982158i
$117$	0.694007	+	1.76830i	0.0641610	+	0.163480i
$118$	0.212848	−	0.932548i	0.0195943	−	0.0858480i
$119$	0.288936	−	0.654170i	0.0264868	−	0.0599676i
$120$	−4.61848	+	1.42461i	−0.421608	+	0.130049i
$121$	−5.02534	−	2.42008i	−0.456849	−	0.220007i
$122$	11.6040	−	6.69956i	1.05057	−	0.606549i
$123$	−11.4326	+	19.8018i	−1.03084	+	1.78547i
$124$	8.51079	+	12.4830i	0.764292	+	1.12101i
$125$	11.3888	−	2.59941i	1.01864	−	0.232498i
$126$	0.375751	+	2.49294i	0.0334745	+	0.222089i
$127$	−4.77008	+	5.98149i	−0.423276	+	0.530771i	−0.947050	−	0.321086i	$-0.895952\pi$
$127$	−4.77008	+	5.98149i	−0.423276	+	0.530771i	0.523774	+	0.851857i	$0.324524\pi$
$128$	5.69646			0.503501
$129$	−20.7028	+	0.423742i	−1.82278	+	0.0373084i
$130$			1.20271i			0.105485i
$131$	3.34456	+	2.66719i	0.292215	+	0.233034i	0.758613	−	0.651541i	$-0.225877\pi$
$131$	3.34456	+	2.66719i	0.292215	+	0.233034i	−0.466398	+	0.884575i	$0.654449\pi$
$132$	17.0634	−	2.57189i	1.48518	−	0.223855i
$133$	0.767049	−	0.175074i	0.0665116	−	0.0151808i
$134$	−14.7853	+	10.0804i	−1.27725	+	0.870816i
$135$	13.2769	−	22.9963i	1.14270	−	1.97921i
$136$	−2.93120	+	0.540906i	−0.251348	+	0.0463823i
$137$	−8.76625	−	4.22161i	−0.748952	−	0.360676i	0.0201548	−	0.999797i	$-0.493584\pi$
$137$	−8.76625	−	4.22161i	−0.748952	−	0.360676i	−0.769106	+	0.639121i	$0.779298\pi$
$138$	−8.31306	+	2.56424i	−0.707655	+	0.218283i
$139$	−9.76902	−	0.732087i	−0.828598	−	0.0620948i	−0.346324	−	0.938115i	$-0.612570\pi$
$139$	−9.76902	−	0.732087i	−0.828598	−	0.0620948i	−0.482274	+	0.876020i	$0.660189\pi$
$140$	−0.191761	+	0.840158i	−0.0162067	+	0.0710063i
$141$	−14.6062	+	5.73252i	−1.23007	+	0.482766i
$142$	−19.9342	+	1.49386i	−1.67284	+	0.125362i
$143$	0.0945634	−	0.627387i	0.00790779	−	0.0524648i
$144$	−16.2840	+	15.1094i	−1.35700	+	1.25911i
$145$	11.5058	−	5.54090i	0.955504	−	0.460146i
$146$	−4.39032	+	6.43942i	−0.363346	+	0.532930i
$147$	−20.4882	−	8.04104i	−1.68984	−	0.663214i
$148$	−1.76063	+	5.70781i	−0.144723	+	0.469179i
$149$	−4.13951	−	3.84090i	−0.339122	−	0.314659i	0.492166	−	0.870501i	$-0.336205\pi$
$149$	−4.13951	−	3.84090i	−0.339122	−	0.314659i	−0.831288	+	0.555842i	$0.812396\pi$
$150$	−2.66404	+	2.12450i	−0.217518	+	0.173464i
$151$	6.05440	+	7.59198i	0.492700	+	0.617827i	0.964565	−	0.263844i	$-0.0849904\pi$
$151$	6.05440	+	7.59198i	0.492700	+	0.617827i	−0.471865	+	0.881671i	$0.656419\pi$
$152$	−2.40388	−	2.23047i	−0.194980	−	0.180915i
$153$	17.1739	−	23.0511i	1.38843	−	1.86357i
$154$	0.307636	−	0.783844i	0.0247900	−	0.0631639i
$155$	−11.2619	−	7.67824i	−0.904578	−	0.616731i
$156$	−0.876088	−	1.81922i	−0.0701432	−	0.145654i
$157$	−13.9038	+	12.9008i	−1.10964	+	1.02960i	−0.110278	+	0.993901i	$0.535174\pi$
$157$	−13.9038	+	12.9008i	−1.10964	+	1.02960i	−0.999363	+	0.0356950i	$0.988636\pi$
$158$	−0.169008	+	1.12130i	−0.0134456	+	0.0892055i
$159$	−12.9899	+	0.973458i	−1.03017	+	0.0772002i
$160$	−15.9417	+	6.25668i	−1.26031	+	0.494634i
$161$	−0.0509994	+	0.223443i	−0.00401931	+	0.0176098i
$162$	−2.91202	+	38.8582i	−0.228790	+	3.05298i
$163$	−0.872280	−	2.82786i	−0.0683222	−	0.221495i	0.914972	−	0.403517i	$-0.132212\pi$
$163$	−0.872280	−	2.82786i	−0.0683222	−	0.221495i	−0.983295	+	0.182021i	$0.941736\pi$
$164$	7.37270	−	15.3096i	0.575711	−	1.19548i
$165$	−13.4823	+	7.78404i	−1.04960	+	0.605987i
$166$	−16.1068	+	27.8978i	−1.25013	+	2.16529i
$167$	−11.5826	−	16.9886i	−0.896292	−	1.31462i	−0.948760	−	0.315997i	$-0.897661\pi$
$167$	−11.5826	−	16.9886i	−0.896292	−	1.31462i	0.0524679	−	0.998623i	$-0.483291\pi$
$168$	−0.0881077	−	0.386025i	−0.00679766	−	0.0297825i
$169$	12.7814	−	1.92648i	0.983184	−	0.148191i
$170$	15.4537	−	9.61309i	1.18525	−	0.737291i
$171$	31.6249			2.41841
$172$	15.3189	−	1.46378i	1.16805	−	0.111612i
$173$		−	3.00284i		−	0.228302i	−0.993463	−	0.114151i	$-0.963585\pi$
$173$		−	3.00284i		−	0.228302i	0.993463	−	0.114151i	$-0.0364147\pi$
$174$	−24.7598	+	31.0478i	−1.87703	+	2.35373i
$175$	0.0133793	+	0.0887658i	0.00101138	+	0.00671007i
$176$	7.23349	−	1.65100i	0.545245	−	0.124449i
$177$	−0.816128	−	1.19704i	−0.0613439	−	0.0899750i
$178$	11.4274	−	19.7928i	0.856520	−	1.48354i
$179$	−8.24360	−	14.2783i	−0.616155	−	1.06721i	−0.990181	−	0.139794i	$-0.955356\pi$
$179$	−8.24360	−	14.2783i	−0.616155	−	1.06721i	0.374025	−	0.927419i	$-0.377977\pi$
$180$	−15.0293	+	31.2087i	−1.12022	+	2.32616i
$181$	−0.215461	−	0.698508i	−0.0160151	−	0.0519197i	0.947213	−	0.320606i	$-0.103887\pi$
$181$	−0.215461	−	0.698508i	−0.0160151	−	0.0519197i	−0.963228	+	0.268687i	$0.913410\pi$
$182$	−0.0982548	−	0.00736318i	−0.00728313	−	0.000545795i
$183$	4.51597	−	19.7858i	0.333830	−	1.46261i
$184$	0.889224	−	0.348995i	0.0655545	−	0.0257282i
$185$	−0.402710	−	5.37380i	−0.0296079	−	0.395089i
$186$	41.9121	+	6.31723i	3.07314	+	0.463202i
$187$	−8.81716	+	3.79956i	−0.644774	+	0.277851i
$188$	10.5060	−	5.05942i	0.766228	−	0.368996i
$189$	1.79739	+	1.22544i	0.130741	+	0.0891374i
$190$	18.6387	+	7.31515i	1.35219	+	0.530697i
$191$	−13.2032	−	4.07264i	−0.955347	−	0.294686i	−0.222388	−	0.974958i	$-0.571385\pi$
$191$	−13.2032	−	4.07264i	−0.955347	−	0.294686i	−0.732959	+	0.680273i	$0.761861\pi$
$192$	22.5349	−	24.2868i	1.62632	−	1.75275i
$193$	1.93425	−	1.54251i	0.139230	−	0.111032i	−0.551398	−	0.834242i	$-0.685905\pi$
$193$	1.93425	−	1.54251i	0.139230	−	0.111032i	0.690628	+	0.723210i	$0.257334\pi$
$194$	−15.8578	+	12.6462i	−1.13852	+	0.907943i
$195$	1.33537	+	1.23904i	0.0956276	+	0.0887295i
$196$	15.6299	+	4.82120i	1.11642	+	0.344371i
$197$	16.0332	+	6.29255i	1.14232	+	0.448326i	0.859645	−	0.510891i	$-0.170685\pi$
$197$	16.0332	+	6.29255i	1.14232	+	0.448326i	0.282670	+	0.959217i	$0.408780\pi$
$198$	19.0665	−	27.9655i	1.35500	−	1.98742i
$199$	3.66246	+	7.60517i	0.259625	+	0.539117i	0.989512	−	0.144451i	$-0.0461417\pi$
$199$	3.66246	+	7.60517i	0.259625	+	0.539117i	−0.729887	+	0.683568i	$0.760427\pi$
$200$	0.274274	−	0.254489i	0.0193941	−	0.0179951i
$201$	−4.03959	+	26.8009i	−0.284931	+	1.89039i
$202$	−0.380665	−	5.07962i	−0.0267835	−	0.357401i
$203$	0.382220	+	0.973880i	0.0268266	+	0.0683529i
$204$	−16.3727	+	25.7976i	−1.14632	+	1.80619i
$205$	−1.14562	+	15.2872i	−0.0800135	+	1.06771i
$206$	−7.74892	+	2.39023i	−0.539893	+	0.166535i
$207$	−3.99710	+	8.30007i	−0.277818	+	0.576895i
$208$	−0.434086	−	0.751860i	−0.0300985	−	0.0521321i
$209$	−9.14761	−	5.28138i	−0.632753	−	0.365320i
$210$	1.36190	+	1.99754i	0.0939802	+	0.137844i
$211$	21.0160	−	4.79676i	1.44680	−	0.330222i	0.574222	−	0.818700i	$-0.305305\pi$
$211$	21.0160	−	4.79676i	1.44680	−	0.330222i	0.872576	+	0.488477i	$0.162448\pi$
$212$	9.57245	−	1.44282i	0.657439	−	0.0990930i
$213$	−18.8777	+	23.6718i	−1.29348	+	1.62197i
$214$			30.3242i			2.07292i
$215$	−12.3825	+	6.27843i	−0.844480	+	0.428185i
$216$		−	9.06697i		−	0.616929i
$217$	0.696215	−	0.873027i	0.0472622	−	0.0592649i
$218$	−5.48703	−	36.4041i	−0.371629	−	2.46560i
$219$	2.62673	+	11.5085i	0.177498	+	0.777671i
$220$	9.55917	−	6.51733i	0.644479	−	0.439398i
$221$	0.728946	+	0.854832i	0.0490342	+	0.0575022i
$222$	8.37873	+	14.5124i	0.562344	+	0.974008i
$223$	−13.4980	−	6.50031i	−0.903895	−	0.435293i	−0.0766007	−	0.997062i	$-0.524407\pi$
$223$	−13.4980	−	6.50031i	−0.903895	−	0.435293i	−0.827294	+	0.561769i	$0.810121\pi$
$224$	−0.413537	−	1.34065i	−0.0276306	−	0.0895762i
$225$	−0.269648	+	3.59820i	−0.0179765	+	0.239880i
$226$	−40.5189	−	9.24818i	−2.69528	−	0.615180i
$227$	−8.59698	+	3.37407i	−0.570602	+	0.223945i	−0.633060	−	0.774103i	$-0.718201\pi$
$227$	−8.59698	+	3.37407i	−0.570602	+	0.223945i	0.0624581	+	0.998048i	$0.480106\pi$
$228$	−33.5214	+	2.51208i	−2.22001	+	0.166366i
$229$	−12.2577	−	1.84754i	−0.810008	−	0.122089i	−0.269037	−	0.963130i	$-0.586705\pi$
$229$	−12.2577	−	1.84754i	−0.810008	−	0.122089i	−0.540972	+	0.841041i	$0.681943\pi$
$230$	−4.27566	+	3.96723i	−0.281929	+	0.261591i
$231$	−0.553371	−	1.14909i	−0.0364091	−	0.0756043i
$232$	2.45638	−	3.60285i	0.161269	−	0.236539i
$233$	6.69829	+	2.62888i	0.438819	+	0.172224i	0.574457	−	0.818535i	$-0.305213\pi$
$233$	6.69829	+	2.62888i	0.438819	+	0.172224i	−0.135638	+	0.990758i	$0.543308\pi$
$234$	−3.78453	−	1.16737i	−0.247402	−	0.0763135i
$235$	−7.15546	+	7.71176i	−0.466771	+	0.503059i
$236$	0.671293	+	0.841775i	0.0436974	+	0.0547949i
$237$	1.07086	+	1.34281i	0.0695597	+	0.0872251i
$238$	0.690725	+	1.32133i	0.0447731	+	0.0856493i
$239$	−1.65587	−	0.510767i	−0.107109	−	0.0330388i	0.240737	−	0.970590i	$-0.422611\pi$
$239$	−1.65587	−	0.510767i	−0.107109	−	0.0330388i	−0.347846	+	0.937552i	$0.613087\pi$
$240$	−7.78262	+	19.8298i	−0.502366	+	1.28001i
$241$	2.17897	−	3.19596i	0.140360	−	0.205870i	−0.749622	−	0.661866i	$-0.769765\pi$
$241$	2.17897	−	3.19596i	0.140360	−	0.205870i	0.889982	+	0.455996i	$0.150717\pi$
$242$	10.4773	−	5.04558i	0.673504	−	0.324342i
$243$	14.5517	+	15.6830i	0.933491	+	1.00606i
$244$	−2.24786	+	14.9136i	−0.143904	+	0.954744i
$245$	−14.7153	+	1.10276i	−0.940125	+	0.0704527i
$246$	−17.4162	−	44.3758i	−1.11042	−	2.82930i
$247$	−0.275029	+	1.20498i	−0.0174997	+	0.0766712i
$248$	−4.64114	−	0.347805i	−0.294713	−	0.0220857i
$249$	14.3815	+	46.6238i	0.911392	+	2.95466i
$250$	−10.5672	+	21.9430i	−0.668328	+	1.38780i
$251$	8.75269	+	15.1601i	0.552465	+	0.956897i	0.998096	+	0.0616803i	$0.0196459\pi$
$251$	8.75269	+	15.1601i	0.552465	+	0.956897i	−0.445631	+	0.895217i	$0.647021\pi$
$252$	−2.45756	−	1.41888i	−0.154812	−	0.0893808i
$253$	2.54229	−	1.73331i	0.159833	−	0.108972i
$254$	−3.54935	−	15.5507i	−0.222706	−	0.975739i
$255$	5.24709	−	27.0616i	0.328586	−	1.69467i
$256$	5.67821	−	7.12025i	0.354888	−	0.445016i
$257$	18.9993			1.18514			0.592572	−	0.805518i	$-0.298113\pi$
$257$	18.9993			1.18514			0.592572	+	0.805518i	$0.298113\pi$
$258$	26.2210	−	34.2970i	1.63245	−	2.13524i
$259$	0.441474			0.0274319
$260$	−1.05842	−	0.844063i	−0.0656405	−	0.0523466i
$261$	6.26761	+	41.5829i	0.387955	+	2.57391i
$262$	−8.69521	+	1.98462i	−0.537192	+	0.122610i
$263$	15.8985	−	10.8394i	0.980341	−	0.668385i	0.0366900	−	0.999327i	$-0.488319\pi$
$263$	15.8985	−	10.8394i	0.980341	−	0.668385i	0.943651	+	0.330941i	$0.107366\pi$
$264$	−2.65790	+	4.60362i	−0.163583	+	0.283333i
$265$	−7.56351	+	4.36680i	−0.464623	+	0.268250i
$266$	−0.711715	+	1.47789i	−0.0436381	+	0.0906154i
$267$	−10.2034	−	33.0785i	−0.624435	−	2.02437i
$268$	1.50523	−	20.0859i	0.0919466	−	1.22694i
$269$	−6.80453	−	1.55309i	−0.414879	−	0.0946935i	0.00998578	−	0.999950i	$-0.496821\pi$
$269$	−6.80453	−	1.55309i	−0.414879	−	0.0946935i	−0.424865	+	0.905257i	$0.639679\pi$
$270$	20.2259	+	51.5348i	1.23091	+	3.13631i
$271$	−1.84165	−	24.5751i	−0.111872	−	1.49283i	−0.717206	−	0.696862i	$-0.754579\pi$
$271$	−1.84165	−	24.5751i	−0.111872	−	1.49283i	0.605333	−	0.795972i	$-0.293040\pi$
$272$	−6.19109	+	11.5871i	−0.375390	+	0.702571i
$273$	−0.109398	+	0.101506i	−0.00662106	+	0.00614344i
$274$	18.2766	−	8.80156i	1.10413	−	0.531722i
$275$	0.678899	−	0.995762i	0.0409392	−	0.0600467i
$276$	3.57750	−	9.11531i	0.215340	−	0.548677i
$277$	−4.17978	+	13.5505i	−0.251138	+	0.814171i	0.738954	+	0.673756i	$0.235320\pi$
$277$	−4.17978	+	13.5505i	−0.251138	+	0.814171i	−0.990093	+	0.140415i	$0.955156\pi$
$278$	13.8921	−	14.9721i	0.833194	−	0.897970i
$279$	35.0918	−	27.9848i	2.10089	−	1.67540i
$280$	−0.165517	−	0.207552i	−0.00989156	−	0.0124036i
$281$	−13.7326	−	12.7420i	−0.819219	−	0.760124i	0.154472	−	0.987997i	$-0.450632\pi$
$281$	−13.7326	−	12.7420i	−0.819219	−	0.760124i	−0.973691	+	0.227873i	$0.926823\pi$
$282$	9.64253	−	31.2603i	0.574204	−	1.86152i
$283$	17.2042	+	6.75216i	1.02268	+	0.401374i	0.816627	−	0.577166i	$-0.195841\pi$
$283$	17.2042	+	6.75216i	1.02268	+	0.401374i	0.206058	+	0.978540i	$0.433937\pi$
$284$	12.6752	−	18.5911i	0.752133	−	1.10318i
$285$	27.3237	−	13.1584i	1.61851	−	0.779435i
$286$	0.899736	+	0.969685i	0.0532025	+	0.0573387i
$287$	−1.24187	−	0.187181i	−0.0733050	−	0.0110490i
$288$	−4.21431	−	56.2361i	−0.248331	−	3.31374i
$289$	5.15742	−	16.1988i	0.303378	−	0.952870i
$290$	−5.92461	+	25.9574i	−0.347905	+	1.52427i
$291$	−2.29578	+	30.6350i	−0.134581	+	1.79586i
$292$	−2.58575	−	8.38279i	−0.151320	−	0.490566i
$293$	18.0119	+	8.67409i	1.05227	+	0.506746i	0.878352	−	0.478015i	$-0.158644\pi$
$293$	18.0119	+	8.67409i	1.05227	+	0.506746i	0.173916	+	0.984760i	$0.444358\pi$
$294$	39.7399	−	22.9438i	2.31768	−	1.33811i
$295$	−0.841211	−	0.485673i	−0.0489772	−	0.0282770i
$296$	−1.03654	−	1.52033i	−0.0602478	−	0.0883673i
$297$	−6.49879	−	28.4731i	−0.377098	−	1.65218i
$298$	11.6417	−	1.75471i	0.674388	−	0.101648i
$299$	−0.281491	−	0.224482i	−0.0162790	−	0.0129821i
$300$		−	3.83540i		−	0.221437i
$301$	−0.437104	−	1.05002i	−0.0251943	−	0.0605220i
$302$	−20.2453			−1.16499
$303$	−6.03205	−	4.81040i	−0.346532	−	0.276350i
$304$	−14.2919	+	2.15416i	−0.819699	+	0.123550i
$305$	−3.02777	−	13.2655i	−0.173369	−	0.759581i
$306$	15.2495	+	57.9582i	0.871757	+	3.31325i
$307$	−1.30165	+	2.25453i	−0.0742893	+	0.128673i	−0.900777	−	0.434282i	$-0.857002\pi$
$307$	−1.30165	+	2.25453i	−0.0742893	+	0.128673i	0.826488	+	0.562955i	$0.190335\pi$
$308$	0.473906	+	0.820830i	0.0270033	+	0.0467711i
$309$	−5.32912	+	11.0660i	−0.303163	+	0.629524i
$310$	27.1552	−	8.37626i	1.54231	−	0.475739i
$311$	12.8576	+	0.963543i	0.729087	+	0.0546375i	0.434101	−	0.900864i	$-0.357066\pi$
$311$	12.8576	+	0.963543i	0.729087	+	0.0546375i	0.294986	+	0.955502i	$0.404685\pi$
$312$	0.606419	+	0.138411i	0.0343317	+	0.00783599i
$313$	−19.6662	+	7.71841i	−1.11160	+	0.436270i	−0.848871	−	0.528600i	$-0.822717\pi$
$313$	−19.6662	+	7.71841i	−1.11160	+	0.436270i	−0.262727	+	0.964870i	$0.584622\pi$
$314$	−2.95512	−	39.4333i	−0.166767	−	2.22535i
$315$	2.53156	+	0.381571i	0.142637	+	0.0214991i
$316$	−0.868163	−	0.935657i	−0.0488380	−	0.0526348i
$317$	4.67080	+	9.69902i	0.262338	+	0.544751i	0.989980	−	0.141206i	$-0.0450980\pi$
$317$	4.67080	+	9.69902i	0.262338	+	0.544751i	−0.727642	+	0.685957i	$0.759384\pi$
$318$	15.2989	−	22.4393i	0.857917	−	1.25833i
$319$	5.13144	−	13.0747i	0.287305	−	0.732042i
$320$	6.54740	−	21.2262i	0.366011	−	1.18658i
$321$	33.6688	+	31.2401i	1.87921	+	1.74365i
$322$	−0.297924	−	0.373585i	−0.0166027	−	0.0208191i
$323$	17.6811	−	6.09737i	0.983804	−	0.339267i
$324$	−32.1526	−	29.8333i	−1.78626	−	1.65741i
$325$	−0.134755	−	0.0415664i	−0.00747486	−	0.00230569i
$326$	5.74338	+	2.25411i	0.318096	+	0.124844i
$327$	−46.0721	−	31.4114i	−2.54779	−	1.73706i
$328$	2.27118	+	4.71616i	0.125405	+	0.260407i
$329$	−0.586200	−	0.631773i	−0.0323182	−	0.0348308i
$330$	4.83756	−	32.0951i	0.266299	−	1.76678i
$331$	0.208960	+	2.78838i	0.0114855	+	0.153263i	0.999998	+	0.00212252i	$0.000675618\pi$
$331$	0.208960	+	2.78838i	0.0114855	+	0.153263i	−0.988512	+	0.151141i	$0.951705\pi$
$332$	−13.2471	−	33.7531i	−0.727031	−	1.85244i
$333$	17.3004	+	3.94870i	0.948055	+	0.216387i
$334$	42.7483	+	3.20354i	2.33908	+	0.175290i
$335$	5.35625	+	17.3645i	0.292643	+	0.948725i
$336$	−1.57233	−	0.757197i	−0.0857779	−	0.0413085i
$337$	8.67674	−	5.00952i	0.472652	−	0.272886i	−0.244697	−	0.969600i	$-0.578688\pi$
$337$	8.67674	−	5.00952i	0.472652	−	0.272886i	0.717349	+	0.696714i	$0.245355\pi$
$338$	−13.4744	+	23.3383i	−0.732909	+	1.26943i
$339$	−52.0110	+	35.4605i	−2.82485	+	1.92595i
$340$	−2.38560	+	20.3462i	−0.129377	+	1.10343i
$341$	−14.8239	+	2.23434i	−0.802759	+	0.120996i
$342$	−41.1093	+	51.5495i	−2.22294	+	2.78748i
$343$		−	2.42303i		−	0.130831i
$344$	−2.58972	+	3.97063i	−0.139628	+	0.214082i
$345$			8.83430i			0.475623i
$346$	4.89472	+	3.90341i	0.263142	+	0.209848i
$347$	−5.19419	−	34.4612i	−0.278839	−	1.84998i	−0.488968	−	0.872302i	$-0.662627\pi$
$347$	−5.19419	−	34.4612i	−0.278839	−	1.84998i	0.210129	−	0.977674i	$-0.432612\pi$
$348$	−9.94654	−	43.5786i	−0.533191	−	2.33606i
$349$	3.33572	−	2.27426i	0.178557	−	0.121738i	−0.470743	−	0.882270i	$-0.656014\pi$
$349$	3.33572	−	2.27426i	0.178557	−	0.121738i	0.649300	+	0.760532i	$0.275062\pi$
$350$	−0.162083	−	0.0935785i	−0.00866368	−	0.00500198i
$351$	−2.95954	+	1.70869i	−0.157968	+	0.0912031i
$352$	−8.17246	+	16.9703i	−0.435593	+	0.904519i
$353$	−12.5121	+	3.85946i	−0.665951	+	0.205419i	−0.609257	−	0.792973i	$-0.708532\pi$
$353$	−12.5121	+	3.85946i	−0.665951	+	0.205419i	−0.0566939	+	0.998392i	$0.518056\pi$
$354$	3.01210	+	0.225725i	0.160091	+	0.0119972i
$355$	−4.51711	+	19.7908i	−0.239744	+	1.05038i
$356$	9.39852	+	23.9470i	0.498121	+	1.26919i
$357$	2.17866	+	0.594333i	0.115307	+	0.0314554i
$358$	33.9900	+	5.12316i	1.79643	+	0.270768i
$359$	27.0932	−	25.1388i	1.42992	−	1.32677i	0.564786	−	0.825237i	$-0.308959\pi$
$359$	27.0932	−	25.1388i	1.42992	−	1.32677i	0.865136	−	0.501537i	$-0.167232\pi$
$360$	−4.62984	−	9.61395i	−0.244014	−	0.506700i
$361$	1.30256	+	0.888067i	0.0685556	+	0.0467404i
$362$	1.41867	+	0.556785i	0.0745634	+	0.0292640i
$363$	5.19163	−	16.8308i	0.272490	−	0.883390i
$364$	0.0754350	−	0.0812996i	0.00395387	−	0.00426125i
$365$	4.93453	+	6.18771i	0.258285	+	0.323879i
$366$	26.3810	+	33.0808i	1.37896	+	1.72916i
$367$	17.5287	−	18.8914i	0.914989	−	0.986124i	−0.0849582	−	0.996385i	$-0.527076\pi$
$367$	17.5287	−	18.8914i	0.914989	−	0.986124i	0.999947	+	0.0102608i	$0.00326616\pi$
$368$	1.24101	−	4.02324i	0.0646919	−	0.209726i
$369$	−46.9917	−	18.4429i	−2.44629	−	0.960099i
$370$	9.28293	+	6.32899i	0.482597	+	0.329029i
$371$	−0.310437	−	0.644630i	−0.0161171	−	0.0334675i
$372$	−34.9732	+	32.4504i	−1.81328	+	1.68248i
$373$	−33.9641	−	5.11926i	−1.75859	−	0.265065i	−0.811115	−	0.584887i	$-0.801139\pi$
$373$	−33.9641	−	5.11926i	−1.75859	−	0.265065i	−0.947478	+	0.319822i	$0.896377\pi$
$374$	5.26807	−	19.3113i	0.272405	−	0.998563i
$375$	13.4769	+	34.3385i	0.695942	+	1.77323i
$376$	−0.799326	+	3.50207i	−0.0412221	+	0.180606i
$377$	−1.63891	−	0.122819i	−0.0844082	−	0.00632552i
$378$	−4.33393	+	1.33684i	−0.222913	+	0.0687596i
$379$	1.80831	−	3.75499i	0.0928865	−	0.192881i	−0.849349	−	0.527831i	$-0.823005\pi$
$379$	1.80831	−	3.75499i	0.0928865	−	0.192881i	0.942236	+	0.334951i	$0.108720\pi$
$380$	−19.5182	+	11.2688i	−1.00126	+	0.578079i
$381$	−20.9225	−	12.0796i	−1.07189	−	0.618856i
$382$	23.8014	−	16.2275i	1.21778	−	0.830271i
$383$	7.95883	+	34.8699i	0.406677	+	1.78177i	0.599330	+	0.800502i	$0.295434\pi$
$383$	7.95883	+	34.8699i	0.406677	+	1.78177i	−0.192653	+	0.981267i	$0.561709\pi$
$384$	2.68102	+	17.7874i	0.136815	+	0.907711i
$385$	−0.668540	−	0.533143i	−0.0340719	−	0.0271715i
$386$			5.15800i			0.262535i
$387$	−7.73742	−	45.0574i	−0.393315	−	2.29040i
$388$		−	22.8304i		−	1.15904i
$389$	−22.0473	+	27.6464i	−1.11784	+	1.40173i	−0.212438	+	0.977175i	$0.568140\pi$
$389$	−22.0473	+	27.6464i	−1.11784	+	1.40173i	−0.905403	+	0.424553i	$0.860431\pi$
$390$	−3.75552	+	0.566053i	−0.190168	+	0.0286632i
$391$	−0.634459	+	5.41113i	−0.0320860	+	0.273653i
$392$	−4.16318	+	2.83841i	−0.210272	+	0.143361i
$393$	−6.75432	+	11.6988i	−0.340710	+	0.590128i
$394$	−31.0986	+	17.9548i	−1.56673	+	0.904549i
$395$	1.03749	+	0.499628i	0.0522017	+	0.0251390i
$396$	11.2295	+	36.4053i	0.564305	+	1.82943i
$397$	24.0083	+	1.79917i	1.20494	+	0.0902979i	0.662021	−	0.749486i	$-0.269699\pi$
$397$	24.0083	+	1.79917i	1.20494	+	0.0902979i	0.542921	+	0.839784i	$0.317318\pi$
$398$	−17.1575	−	3.91609i	−0.860028	−	0.196296i
$399$	0.907686	+	2.31275i	0.0454411	+	0.115782i
$400$	−0.123236	−	1.64447i	−0.00616180	−	0.0822236i
$401$	−5.22222	+	34.6471i	−0.260785	+	1.73020i	0.348556	+	0.937288i	$0.386672\pi$
$401$	−5.22222	+	34.6471i	−0.260785	+	1.73020i	−0.609341	+	0.792908i	$0.708566\pi$
$402$	−38.4352	−	41.4233i	−1.91697	−	2.06601i
$403$	0.761105	+	1.58045i	0.0379134	+	0.0787279i
$404$	4.73737	+	3.22988i	0.235693	+	0.160693i
$405$	36.8353	+	14.4568i	1.83036	+	0.718364i
$406$	−2.08430	−	0.642922i	−0.103442	−	0.0319077i
$407$	−4.34476	−	4.03135i	−0.215362	−	0.199827i
$408$	−3.06856	−	8.89820i	−0.151916	−	0.440527i
$409$	−18.6834	−	23.4283i	−0.923836	−	1.15845i	−0.987043	−	0.160453i	$-0.948704\pi$
$409$	−18.6834	−	23.4283i	−0.923836	−	1.15845i	0.0632076	−	0.998000i	$-0.479867\pi$
$410$	−23.4294	−	21.7393i	−1.15710	−	1.07363i
$411$	9.05632	−	29.3599i	0.446715	−	1.44822i
$412$	3.33472	−	8.49674i	0.164290	−	0.418604i
$413$	0.0448268	−	0.0657488i	0.00220578	−	0.00323529i
$414$	−8.33350	−	17.3047i	−0.409569	−	0.850479i
$415$	22.2502	+	23.9800i	1.09222	+	1.17713i
$416$	2.17938	+	0.328488i	0.106853	+	0.0161055i
$417$	−2.31179	−	30.8487i	−0.113209	−	1.51067i
$418$	20.4998	−	8.04558i	1.00268	−	0.393522i
$419$	30.7998	+	7.02986i	1.50467	+	0.343431i	0.893860	−	0.448346i	$-0.147987\pi$
$419$	30.7998	+	7.02986i	1.50467	+	0.343431i	0.610810	+	0.791777i	$0.290844\pi$
$420$	−2.71368	−	0.203362i	−0.132414	−	0.00992306i
$421$	35.3246	−	10.8962i	1.72161	−	0.531048i	0.732831	−	0.680410i	$-0.238198\pi$
$421$	35.3246	−	10.8962i	1.72161	−	0.531048i	0.988782	+	0.149363i	$0.0477222\pi$
$422$	−19.4999	+	40.4919i	−0.949240	+	1.97112i
$423$	−17.3211	−	30.0010i	−0.842179	−	1.45870i
$424$	−1.49107	+	2.58260i	−0.0724126	+	0.125422i
$425$	0.542987	+	2.06371i	0.0263387	+	0.100104i
$426$	−14.0466	−	61.5423i	−0.680561	−	2.98173i
$427$	1.10225	−	0.166138i	0.0533418	−	0.00803998i
$428$	−26.6862	−	21.2815i	−1.28992	−	1.02868i
$429$	2.00355			0.0967323
$430$	5.86205	−	28.3452i	0.282693	−	1.36693i
$431$		−	18.8999i		−	0.910378i	−0.890395	−	0.455189i	$-0.849572\pi$
$431$		−	18.8999i		−	0.910378i	0.890395	−	0.455189i	$-0.150428\pi$
$432$	−31.2441	−	24.9163i	−1.50323	−	1.19879i
$433$	−2.35378	+	0.354775i	−0.113115	+	0.0170494i	−0.205356	−	0.978687i	$-0.565835\pi$
$433$	−2.35378	+	0.354775i	−0.113115	+	0.0170494i	0.0922406	+	0.995737i	$0.470597\pi$
$434$	0.518045	+	2.26970i	0.0248669	+	0.108949i
$435$	22.7168	+	33.3195i	1.08919	+	1.59755i
$436$	35.8875	+	20.7196i	1.71870	+	0.992290i
$437$	−5.19093	+	2.99698i	−0.248316	+	0.143365i
$438$	−22.1736	−	10.6783i	−1.05950	−	0.510227i
$439$	5.23674	+	16.9771i	0.249936	+	0.810272i	0.990407	+	0.138184i	$0.0441264\pi$
$439$	5.23674	+	16.9771i	0.249936	+	0.810272i	−0.740471	+	0.672089i	$0.765397\pi$
$440$	−0.266340	+	3.55406i	−0.0126972	+	0.169433i
$441$	10.8129	−	47.3744i	0.514899	−	2.25592i
$442$	−2.34096	+	0.0770029i	−0.111348	+	0.00366265i
$443$	1.88887	+	25.2053i	0.0897431	+	1.19754i	0.842299	+	0.539010i	$0.181202\pi$
$443$	1.88887	+	25.2053i	0.0897431	+	1.19754i	−0.752556	+	0.658528i	$0.771179\pi$
$444$	−18.6515	−	2.81126i	−0.885162	−	0.133417i
$445$	−15.7860	−	17.0132i	−0.748328	−	0.806505i
$446$	28.1418	−	13.5524i	1.33255	−	0.641724i
$447$	10.0451	−	14.7335i	0.475118	−	0.696871i
$448$	1.69397	+	0.664835i	0.0800326	+	0.0314105i
$449$	−6.00629	+	19.4719i	−0.283455	+	0.918937i	0.696132	+	0.717914i	$0.254903\pi$
$449$	−6.00629	+	19.4719i	−0.283455	+	0.918937i	−0.979586	+	0.201023i	$0.935573\pi$
$450$	−5.51466	−	5.11685i	−0.259963	−	0.241211i
$451$	10.5126	+	13.1823i	0.495017	+	0.620731i
$452$	36.5748	−	29.1675i	1.72034	−	1.37192i
$453$	−20.8568	+	22.4783i	−0.979937	+	1.05612i
$454$	5.67543	−	18.3993i	0.266361	−	0.863521i
$455$	−0.0365547	+	0.0931399i	−0.00171371	+	0.00436647i
$456$	5.83336	−	8.55597i	0.273172	−	0.400670i
$457$	−1.61904	+	0.779691i	−0.0757357	+	0.0364724i	−0.471368	−	0.881937i	$-0.656240\pi$
$457$	−1.61904	+	0.779691i	−0.0757357	+	0.0364724i	0.395632	+	0.918409i	$0.370525\pi$
$458$	18.9453	−	17.5787i	0.885257	−	0.821398i
$459$	45.6101	+	24.3699i	2.12890	+	1.13749i
$460$	−0.490623	−	6.54690i	−0.0228754	−	0.305251i
$461$	14.9260	+	38.0309i	0.695174	+	1.77127i	0.634246	+	0.773131i	$0.281311\pi$
$461$	14.9260	+	38.0309i	0.695174	+	1.77127i	0.0609275	+	0.998142i	$0.480594\pi$
$462$	2.59237	+	0.591692i	0.120608	+	0.0275280i
$463$	1.27011	−	16.9484i	0.0590269	−	0.787659i	−0.886627	−	0.462485i	$-0.846958\pi$
$463$	1.27011	−	16.9484i	0.0590269	−	0.787659i	0.945654	−	0.325174i	$-0.105423\pi$
$464$	−5.66493	−	18.3652i	−0.262988	−	0.852585i
$465$	18.6752	−	38.7795i	0.866043	−	1.79836i
$466$	−12.9923	+	7.50110i	−0.601856	+	0.347482i
$467$	−13.2117	+	22.8833i	−0.611363	+	1.05891i	0.379647	+	0.925131i	$0.376045\pi$
$467$	−13.2117	+	22.8833i	−0.611363	+	1.05891i	−0.991011	+	0.133781i	$0.957288\pi$
$468$	3.68330	−	2.51123i	0.170261	−	0.116082i
$469$	−1.45137	+	0.331267i	−0.0670182	+	0.0152965i
$470$	−3.26896	−	21.6882i	−0.150786	−	1.00040i
$471$	−46.8270	−	37.3433i	−2.15768	−	1.72069i
$472$	−0.331672			−0.0152664
$473$	−5.28655	+	14.3252i	−0.243076	+	0.658673i
$474$	−3.58084			−0.164473
$475$	−1.46377	+	1.83551i	−0.0671625	+	0.0842191i
$476$	−1.64756	−	0.319452i	−0.0755159	−	0.0146421i
$477$	−6.39955	−	28.0383i	−0.293015	−	1.28378i
$478$	2.98503	−	2.03516i	0.136532	−	0.0930860i
$479$	−23.8380	−	13.7629i	−1.08919	−	0.628842i	−0.155827	−	0.987784i	$-0.549804\pi$
$479$	−23.8380	−	13.7629i	−1.08919	−	0.628842i	−0.933360	+	0.358942i	$0.883138\pi$
$480$	−27.0397	−	46.8341i	−1.23419	−	2.13767i
$481$	−0.300909	+	0.624845i	−0.0137203	+	0.0284905i
$482$	2.37706	+	7.70622i	0.108272	+	0.351009i
$483$	−0.721712	−	0.0540849i	−0.0328391	−	0.00246095i
$484$	−2.91268	+	12.7613i	−0.132394	+	0.580058i
$485$	7.52496	+	19.1733i	0.341691	+	0.870614i
$486$	−44.4795	+	3.33328i	−2.01763	+	0.151201i
$487$	−0.654789	+	4.34424i	−0.0296713	+	0.196856i	−0.998756	−	0.0498739i	$-0.984118\pi$
$487$	−0.654789	+	4.34424i	−0.0296713	+	0.196856i	0.969084	+	0.246730i	$0.0793562\pi$
$488$	−3.16013	−	3.40581i	−0.143052	−	0.154174i
$489$	8.41958	−	4.05466i	0.380747	−	0.183358i
$490$	17.3309	−	25.4198i	0.782932	−	1.14835i
$491$	0.408388	−	1.04055i	0.0184303	−	0.0469596i	−0.921362	−	0.388705i	$-0.872923\pi$
$491$	0.408388	−	1.04055i	0.0184303	−	0.0469596i	0.939793	+	0.341745i	$0.111018\pi$
$492$	51.2747	+	15.8161i	2.31164	+	0.713047i
$493$	11.5215	+	22.0401i	0.518900	+	0.992637i
$494$	−1.60664	−	2.01467i	−0.0722863	−	0.0906441i
$495$	−21.4300	−	26.8723i	−0.963205	−	1.20782i
$496$	−13.9525	+	15.0372i	−0.626486	+	0.675191i
$497$	−1.58914	−	0.490184i	−0.0712826	−	0.0219878i
$498$	−94.6927	−	37.1641i	−4.24328	−	1.66537i
$499$	18.9550	−	27.8019i	0.848542	−	1.24458i	−0.119259	−	0.992863i	$-0.538052\pi$
$499$	18.9550	−	27.8019i	0.848542	−	1.24458i	0.967800	−	0.251719i	$-0.0809958\pi$
$500$	−11.8944	−	24.6990i	−0.531935	−	1.10457i
$501$	47.5963	−	44.1630i	2.12645	−	1.97306i
$502$	−36.0890	−	5.43955i	−1.61073	−	0.242779i
$503$	0.657650	−	0.0492841i	0.0293232	−	0.00219747i	−0.0600604	−	0.998195i	$-0.519129\pi$
$503$	0.657650	−	0.0492841i	0.0293232	−	0.00219747i	0.0893836	+	0.995997i	$0.471510\pi$
$504$	0.813750	−	0.319373i	0.0362473	−	0.0142260i
$505$	−5.04307	−	1.15105i	−0.224414	−	0.0512210i
$506$	−0.479400	+	6.39715i	−0.0213119	+	0.284388i
$507$	12.0311	+	39.0037i	0.534318	+	1.73222i
$508$	16.1760	+	7.78996i	0.717695	+	0.345624i
$509$	7.11450	+	12.3227i	0.315345	+	0.546193i	0.979511	−	0.201392i	$-0.0645466\pi$
$509$	7.11450	+	12.3227i	0.315345	+	0.546193i	−0.664166	+	0.747585i	$0.731213\pi$
$510$	37.2905	+	43.7305i	1.65125	+	1.93642i
$511$	−0.535710	+	0.365241i	−0.0236984	+	0.0161573i
$512$	6.76024	+	29.6186i	0.298763	+	1.30897i
$513$	8.47941	+	56.2572i	0.374375	+	2.48382i
$514$	−24.6973	+	30.9694i	−1.08935	+	1.36600i
$515$			8.23480i			0.362869i
$516$	11.7805	+	47.1448i	0.518607	+	2.07544i
$517$			11.5705i			0.508871i
$518$	−0.573874	+	0.719615i	−0.0252146	+	0.0316181i
$519$	9.37650	−	1.41328i	0.411583	−	0.0620361i
$520$	0.406578	−	0.0927988i	0.0178296	−	0.00406950i
$521$	19.2999	+	28.3078i	0.845546	+	1.24019i	0.968808	+	0.247814i	$0.0797121\pi$
$521$	19.2999	+	28.3078i	0.845546	+	1.24019i	−0.123262	+	0.992374i	$0.539335\pi$
$522$	−75.9286	−	43.8374i	−3.32330	−	1.91871i
$523$	14.2320	+	24.6506i	0.622322	+	1.07789i	0.989052	+	0.147566i	$0.0471440\pi$
$523$	14.2320	+	24.6506i	0.622322	+	1.07789i	−0.366730	+	0.930327i	$0.619523\pi$
$524$	4.35577	−	9.04484i	0.190283	−	0.395126i
$525$	−0.270878	+	0.0835548i	−0.0118221	+	0.00364663i
$526$	−2.99797	+	40.0051i	−0.130718	+	1.74431i
$527$	14.2239	−	22.4118i	0.619603	−	0.976272i
$528$	8.55973	+	21.8098i	0.372514	+	0.949151i
$529$	1.58831	+	21.1945i	0.0690569	+	0.921501i
$530$	2.71384	−	18.0052i	0.117882	−	0.782094i
$531$	2.34474	−	2.17560i	0.101753	−	0.0944130i
$532$	−0.801106	−	1.66351i	−0.0347324	−	0.0721225i
$533$	1.11139	−	1.63010i	0.0481395	−	0.0706076i
$534$	67.1822	+	26.3671i	2.90726	+	1.14101i
$535$	29.4258	+	9.07666i	1.27219	+	0.392418i
$536$	4.54850	+	4.22039i	0.196465	+	0.182293i
$537$	40.7048	−	32.4610i	1.75654	−	1.40080i
$538$	11.3768	−	9.07271i	0.490489	−	0.391152i
$539$	−11.0392	+	11.8974i	−0.475493	+	0.512459i
$540$	−59.5467	−	18.3677i	−2.56248	−	0.790421i
$541$	2.14152	+	0.840485i	0.0920712	+	0.0361353i	0.410930	−	0.911667i	$-0.365204\pi$
$541$	2.14152	+	0.840485i	0.0920712	+	0.0361353i	−0.318858	+	0.947802i	$0.603299\pi$
$542$	42.4522	+	28.9434i	1.82348	+	1.24323i
$543$	2.07971	−	1.00154i	0.0892490	−	0.0429801i
$544$	−13.1987	−	30.6285i	−0.565888	−	1.31318i
$545$	−36.9680	−	5.57202i	−1.58353	−	0.238679i
$546$	−0.0232515	−	0.310270i	−0.000995073	−	0.0132783i
$547$	1.48662	−	0.583455i	0.0635633	−	0.0249468i	−0.333346	−	0.942804i	$-0.608178\pi$
$547$	1.48662	−	0.583455i	0.0635633	−	0.0249468i	0.396910	+	0.917858i	$0.370083\pi$
$548$	−5.08090	+	22.2609i	−0.217045	+	0.950938i
$549$	44.6808	+	3.34836i	1.90693	+	0.142905i
$550$	0.740617	+	2.40102i	0.0315800	+	0.102380i
$551$	−11.8716	+	24.6516i	−0.505746	+	1.05019i
$552$	1.50826	+	2.61239i	0.0641959	+	0.111191i
$553$	−0.0471684	+	0.0816981i	−0.00200581	+	0.00347416i
$554$	−16.6544	−	24.4275i	−0.707577	−	1.03783i
$555$	16.5904	−	3.78664i	0.704222	−	0.160734i
$556$	3.42643	+	22.7329i	0.145313	+	0.964090i
$557$	10.1619	−	12.7426i	0.430573	−	0.539922i	−0.518458	−	0.855103i	$-0.673494\pi$
$557$	10.1619	−	12.7426i	0.430573	−	0.539922i	0.949032	+	0.315181i	$0.102065\pi$
$558$			93.5781i			3.96148i
$559$	1.78408	+	0.0970334i	0.0754587	+	0.00410407i
$560$	−1.17006			−0.0494439
$561$	−16.0141	−	25.7437i	−0.676114	−	1.08690i
$562$	38.6209	−	5.82116i	1.62912	−	0.245551i
$563$	2.32214	+	10.1739i	0.0978664	+	0.428781i	0.999996	−	0.00268372i	$-0.000854256\pi$
$563$	2.32214	+	10.1739i	0.0978664	+	0.428781i	−0.902130	+	0.431464i	$0.857997\pi$
$564$	20.7428	+	30.4242i	0.873431	+	1.28109i
$565$	−21.1024	+	36.5504i	−0.887783	+	1.53768i
$566$	−33.3701	+	19.2662i	−1.40265	+	0.809819i
$567$	−1.40655	+	2.92073i	−0.0590695	+	0.122659i
$568$	2.04308	+	6.62351i	0.0857258	+	0.277916i
$569$	−2.45951	+	32.8198i	−0.103108	+	1.37588i	0.670357	+	0.742039i	$0.266141\pi$
$569$	−2.45951	+	32.8198i	−0.103108	+	1.37588i	−0.773465	+	0.633840i	$0.781478\pi$
$570$	−14.0696	+	61.6430i	−0.589311	+	2.58194i
$571$	12.7883	−	5.01903i	0.535173	−	0.210040i	−0.0823345	−	0.996605i	$-0.526238\pi$
$571$	12.7883	−	5.01903i	0.535173	−	0.210040i	0.617508	+	0.786565i	$0.288142\pi$
$572$	−1.48478	+	0.111269i	−0.0620820	+	0.00465240i
$573$	6.50294	−	43.1442i	0.271664	−	1.80237i
$574$	1.91942	−	1.78096i	0.0801149	−	0.0743358i
$575$	−0.296730	−	0.616165i	−0.0123745	−	0.0256959i
$576$	60.4364	+	41.2049i	2.51819	+	1.71687i
$577$	−11.5149	+	29.3395i	−0.479372	+	1.22142i	0.462852	+	0.886436i	$0.346826\pi$
$577$	−11.5149	+	29.3395i	−0.479372	+	1.22142i	−0.942224	+	0.334984i	$0.891269\pi$
$578$	19.7003	+	29.4636i	0.819426	+	1.22553i
$579$	5.72690	+	5.31379i	0.238002	+	0.220834i
$580$	−18.6854	−	23.4307i	−0.775868	−	0.972908i
$581$	−2.09525	+	1.67091i	−0.0869256	+	0.0693209i
$582$	−46.9517	−	43.5648i	−1.94621	−	1.80582i
$583$	−2.83132	+	9.17890i	−0.117261	+	0.380151i
$584$	2.51560	+	0.987300i	0.104096	+	0.0408548i
$585$	−2.26557	+	3.32299i	−0.0936699	+	0.137389i
$586$	−37.5528	+	18.0845i	−1.55129	+	0.747063i
$587$	7.66902	−	7.11581i	0.316534	−	0.293701i	−0.505864	−	0.862613i	$-0.668826\pi$
$587$	7.66902	−	7.11581i	0.316534	−	0.293701i	0.822398	+	0.568912i	$0.192636\pi$
$588$	−7.69820	+	51.0742i	−0.317468	+	2.10626i
$589$	29.1218	−	2.18238i	1.19994	−	0.0899234i
$590$	1.88515	−	0.739869i	0.0776106	−	0.0304599i
$591$	−12.1028	+	53.0258i	−0.497842	+	2.18119i
$592$	−8.08738	−	0.606065i	−0.332389	−	0.0249091i
$593$	42.9891	−	13.2604i	1.76535	−	0.544539i	0.769760	−	0.638333i	$-0.220376\pi$
$593$	42.9891	−	13.2604i	1.76535	−	0.544539i	0.995592	+	0.0937946i	$0.0298997\pi$
$594$	54.8597	+	26.4191i	2.25092	+	1.08399i
$595$	1.48893	−	0.274760i	0.0610404	−	0.0112640i
$596$	−6.62598	+	11.4765i	−0.271411	+	0.470097i
$597$	−22.0237	+	15.0155i	−0.901372	+	0.614545i
$598$	0.731823	−	0.167034i	0.0299264	−	0.00683052i
$599$	32.2543	−	4.86156i	1.31788	−	0.198638i	0.547810	−	0.836603i	$-0.315462\pi$
$599$	32.2543	−	4.86156i	1.31788	−	0.198638i	0.770066	+	0.637965i	$0.220223\pi$
$600$	0.923740	+	0.736658i	0.0377115	+	0.0300739i
$601$		−	6.31054i		−	0.257412i	−0.991683	−	0.128706i	$-0.958918\pi$
$601$		−	6.31054i		−	0.257412i	0.991683	−	0.128706i	$-0.0410824\pi$
$602$	2.27975	+	0.652430i	0.0929158	+	0.0265910i
$603$	−59.8391			−2.43684
$604$	14.2081	−	17.8164i	0.578121	−	0.724941i
$605$	−1.76004	−	11.6771i	−0.0715558	−	0.474742i
$606$	15.6822	−	3.57935i	0.637045	−	0.145401i
$607$	7.53166	+	11.0469i	0.305701	+	0.448380i	0.948092	−	0.317996i	$-0.103010\pi$
$607$	7.53166	+	11.0469i	0.305701	+	0.448380i	−0.642391	+	0.766377i	$0.722058\pi$
$608$	18.3461	−	31.7764i	0.744032	−	1.28870i
$609$	−2.86109	+	1.65185i	−0.115937	+	0.0669363i
$610$	25.5590	+	12.3085i	1.03485	+	0.498358i
$611$	1.29374	−	0.399066i	0.0523392	−	0.0161445i
$612$	−61.7070	−	27.2550i	−2.49436	−	1.10172i
$613$	4.88457	−	21.4007i	0.197286	−	0.864367i	−0.775257	−	0.631645i	$-0.782380\pi$
$613$	4.88457	−	21.4007i	0.197286	−	0.864367i	0.972543	−	0.232721i	$-0.0747630\pi$
$614$	−1.98292	−	5.05240i	−0.0800242	−	0.203898i
$615$	−48.2742	+	3.61765i	−1.94660	+	0.145878i
$616$	−0.288716	−	0.0435169i	−0.0116327	−	0.00175335i
$617$	−3.83826	−	4.13667i	−0.154523	−	0.166536i	0.651046	−	0.759038i	$-0.274331\pi$
$617$	−3.83826	−	4.13667i	−0.154523	−	0.166536i	−0.805569	+	0.592502i	$0.798140\pi$
$618$	−11.1106	−	23.0714i	−0.446934	−	0.928067i
$619$	−5.16332	+	7.57321i	−0.207532	+	0.304393i	−0.915866	−	0.401484i	$-0.868494\pi$
$619$	−5.16332	+	7.57321i	−0.207532	+	0.304393i	0.708334	+	0.705877i	$0.249447\pi$
$620$	−11.6861	+	29.7758i	−0.469326	+	1.19582i
$621$	−15.8366	−	4.88496i	−0.635503	−	0.196027i
$622$	−18.2842	+	19.7057i	−0.733131	+	0.790127i
$623$	1.48653	−	1.18547i	0.0595566	−	0.0474948i
$624$	2.14341	−	1.70931i	0.0858051	−	0.0684273i
$625$	16.2330	+	15.0620i	0.649318	+	0.602479i
$626$	12.9829	−	42.0896i	0.518902	−	1.68224i
$627$	12.1860	−	31.0495i	0.486662	−	1.24000i
$628$	36.7764	+	25.0737i	1.46754	+	1.00055i
$629$	10.4338	−	1.12789i	0.416022	−	0.0449719i
$630$	−3.91275	+	3.63051i	−0.155888	+	0.144643i
$631$	−46.3660	−	6.98856i	−1.84580	−	0.278210i	−0.869391	−	0.494125i	$-0.835489\pi$
$631$	−46.3660	−	6.98856i	−1.84580	−	0.278210i	−0.976412	+	0.215915i	$0.930727\pi$
$632$	0.392095	−	0.0293835i	0.0155967	−	0.00116881i
$633$	24.8692	+	63.3656i	0.988461	+	2.51856i
$634$	−21.8813	−	4.99426i	−0.869016	−	0.198347i
$635$	−16.1524	−	1.21046i	−0.640989	−	0.0480355i
$636$	9.01050	+	29.2113i	0.357290	+	1.15830i
$637$	1.71104	+	0.823993i	0.0677938	+	0.0326478i
$638$	14.6417	+	25.3602i	0.579672	+	1.00402i
$639$	−57.8904	−	33.4230i	−2.29011	−	1.32220i
$640$	6.79388	+	9.96479i	0.268552	+	0.393893i
$641$	22.2192	−	5.07140i	0.877608	−	0.200308i	0.240096	−	0.970749i	$-0.422821\pi$
$641$	22.2192	−	5.07140i	0.877608	−	0.200308i	0.637511	+	0.770441i	$0.279964\pi$
$642$	−94.6885	+	14.2720i	−3.73706	+	0.563271i
$643$	−10.1245	−	8.07406i	−0.399273	−	0.318410i	0.403185	−	0.915119i	$-0.367903\pi$
$643$	−10.1245	−	8.07406i	−0.399273	−	0.318410i	−0.802458	+	0.596709i	$0.796475\pi$
$644$	0.537848			0.0211942
$645$	−25.4324	−	35.7099i	−1.00140	−	1.40608i
$646$	−13.0449	+	36.7467i	−0.513244	+	1.44578i
$647$	0.908861	−	1.13968i	0.0357310	−	0.0448053i	−0.763645	−	0.645636i	$-0.776592\pi$
$647$	0.908861	−	1.13968i	0.0357310	−	0.0448053i	0.799376	+	0.600831i	$0.205164\pi$
$648$	13.3607	−	2.01380i	0.524859	−	0.0791097i
$649$	−1.04155	+	0.237727i	−0.0408845	+	0.00933161i
$650$	0.242923	−	0.165622i	0.00952822	−	0.00649623i
$651$	3.05373	+	1.76307i	0.119685	+	0.0691003i
$652$	−6.01438	+	3.47240i	−0.235541	+	0.135990i
$653$	3.62189	−	7.52092i	0.141735	−	0.294316i	−0.818002	−	0.575215i	$-0.804918\pi$
$653$	3.62189	−	7.52092i	0.141735	−	0.294316i	0.959737	+	0.280899i	$0.0906325\pi$
$654$	111.091	−	34.2670i	4.34400	−	1.33995i
$655$	−0.676828	+	9.03164i	−0.0264459	+	0.352895i
$656$	22.4928	+	5.13384i	0.878197	+	0.200443i
$657$	−24.2601	+	9.52140i	−0.946478	+	0.371465i
$658$	1.79181	−	0.134278i	0.0698521	−	0.00523469i
$659$	17.1145	+	2.57960i	0.666687	+	0.100487i	0.473662	−	0.880707i	$-0.342932\pi$
$659$	17.1145	+	2.57960i	0.666687	+	0.100487i	0.193025	+	0.981194i	$0.438170\pi$
$660$	24.8496	+	26.7815i	0.967271	+	1.04247i
$661$	−20.4782	+	9.86176i	−0.796508	+	0.383578i	−0.787448	−	0.616381i	$-0.788598\pi$
$661$	−20.4782	+	9.86176i	−0.796508	+	0.383578i	−0.00905999	+	0.999959i	$0.502884\pi$
$662$	−4.81677	−	3.28402i	−0.187209	−	0.127637i
$663$	−2.32617	+	2.67849i	−0.0903410	+	0.104024i
$664$	10.6736	+	3.29238i	0.414218	+	0.127769i
$665$	1.22108	+	1.13299i	0.0473513	+	0.0439356i
$666$	−28.9253	+	23.0672i	−1.12083	+	0.893835i
$667$	−4.96944	−	6.23148i	−0.192417	−	0.241284i
$668$	−32.8199	+	35.3715i	−1.26984	+	1.36856i
$669$	13.9447	−	45.2075i	0.539132	−	1.74782i
$670$	−35.2673	−	13.8414i	−1.36249	−	0.534739i
$671$	−12.3649	−	8.43025i	−0.477342	−	0.325446i
$672$	3.99162	−	1.92226i	0.153980	−	0.0741529i
$673$	−19.3407	−	20.8444i	−0.745530	−	0.803491i	0.240395	−	0.970675i	$-0.422723\pi$
$673$	−19.3407	−	20.8444i	−0.745530	−	0.803491i	−0.985926	+	0.167184i	$0.946532\pi$
$674$	−3.11328	+	20.6552i	−0.119919	+	0.795610i
$675$	−6.47311	+	0.485093i	−0.249150	+	0.0186712i
$676$	−11.0821	−	28.2366i	−0.426233	−	1.08602i
$677$	−34.5264	−	7.88042i	−1.32696	−	0.302869i	−0.500435	−	0.865774i	$-0.666827\pi$
$677$	−34.5264	−	7.88042i	−1.32696	−	0.302869i	−0.826522	+	0.562905i	$0.809684\pi$
$678$	9.80770	−	130.875i	0.376663	−	5.02621i
$679$	−1.61242	+	0.497365i	−0.0618789	+	0.0190871i
$680$	−4.44209	−	4.48241i	−0.170346	−	0.171893i
$681$	−14.5818	−	25.2564i	−0.558776	−	0.967829i
$682$	15.6276	−	27.0678i	0.598412	−	1.03648i
$683$	23.1653	+	33.9772i	0.886394	+	1.30010i	0.953202	+	0.302335i	$0.0977661\pi$
$683$	23.1653	+	33.9772i	0.886394	+	1.30010i	−0.0668081	+	0.997766i	$0.521282\pi$
$684$	−16.5145	−	72.3548i	−0.631448	−	2.76655i
$685$	−3.07023	−	20.3697i	−0.117307	−	0.778284i
$686$	3.94961	+	3.14971i	0.150797	+	0.120256i
$687$		−	39.1446i		−	1.49346i
$688$	6.56584	+	19.8354i	0.250320	+	0.756216i
$689$	1.12398			0.0428202
$690$	−14.4002	−	11.4838i	−0.548205	−	0.437179i
$691$	5.20716	+	34.5473i	0.198090	+	1.31424i	0.837949	+	0.545748i	$0.183754\pi$
$691$	5.20716	+	34.5473i	0.198090	+	1.31424i	−0.639860	+	0.768492i	$0.721008\pi$
$692$	−6.87022	+	1.56808i	−0.261167	+	0.0596096i
$693$	2.32651	−	1.58619i	0.0883769	−	0.0602544i
$694$	62.9247	+	36.3296i	2.38859	+	1.37905i
$695$	−10.3704	−	17.9620i	−0.393371	−	0.681338i
$696$	12.4061	+	5.97448i	0.470254	+	0.226462i
$697$	−29.8284	−	1.25108i	−1.12983	−	0.0473880i
$698$	−0.629016	+	8.39364i	−0.0238086	+	0.317704i
$699$	−5.05627	+	22.1530i	−0.191246	+	0.837902i
$700$	0.196101	−	0.0769641i	0.00741193	−	0.00290897i
$701$	−2.78012	−	37.0982i	−0.105004	−	1.40118i	−0.762143	−	0.647409i	$-0.775853\pi$
$701$	−2.78012	−	37.0982i	−0.105004	−	1.40118i	0.657139	−	0.753770i	$-0.271767\pi$
$702$	1.06190	−	7.04526i	0.0400789	−	0.265906i
$703$	7.85317	+	8.46370i	0.296188	+	0.319215i
$704$	−10.6002	−	22.0116i	−0.399511	−	0.829593i
$705$	−27.4480	−	18.7137i	−1.03375	−	0.704799i
$706$	9.97347	−	25.4120i	0.375356	−	0.956392i
$707$	0.124909	−	0.404944i	0.00469767	−	0.0152295i
$708$	−2.31253	+	2.49232i	−0.0869103	+	0.0936671i
$709$	28.2106	−	22.4972i	1.05947	−	0.844901i	0.0711780	−	0.997464i	$-0.477324\pi$
$709$	28.2106	−	22.4972i	1.05947	−	0.844901i	0.988294	+	0.152563i	$0.0487527\pi$
$710$	−26.3877	−	33.0891i	−0.990313	−	1.24181i
$711$	−2.57916	+	2.77968i	−0.0967261	+	0.104246i
$712$	−7.57270	−	2.33587i	−0.283799	−	0.0875404i
$713$	−3.10797	+	7.91897i	−0.116394	+	0.296568i
$714$	−3.80083	+	2.77870i	−0.142242	+	0.103990i
$715$	1.21027	−	0.582834i	0.0452614	−	0.0217967i
$716$	−28.3627	+	26.3167i	−1.05996	+	0.983502i
$717$	0.815562	−	5.41090i	0.0304577	−	0.202074i
$718$	5.75841	+	76.8406i	0.214902	+	2.86767i
$719$	7.46986	−	2.93171i	0.278579	−	0.109334i	−0.221938	−	0.975061i	$-0.571238\pi$
$719$	7.46986	−	2.93171i	0.278579	−	0.109334i	0.500517	+	0.865727i	$0.333143\pi$
$720$	−45.8519	−	10.4654i	−1.70880	−	0.390022i
$721$	−0.672736	−	0.0504146i	−0.0250540	−	0.00187754i
$722$	−3.14077	+	0.968800i	−0.116887	+	0.0360550i
$723$	11.0050	+	5.29975i	0.409282	+	0.197100i
$724$	−1.48561	+	0.857715i	−0.0552121	+	0.0318767i
$725$	−2.70358	−	1.56091i	−0.100408	−	0.0579707i
$726$	20.6861	+	30.3410i	0.767734	+	1.12606i
$727$	0.329640	+	1.44425i	0.0122257	+	0.0535641i	0.980673	−	0.195655i	$-0.0626832\pi$
$727$	0.329640	+	1.44425i	0.0122257	+	0.0535641i	−0.968447	+	0.249219i	$0.919826\pi$
$728$	0.00509200	+	0.0337832i	0.000188722	+	0.00125209i
$729$	−7.16243	+	8.98141i	−0.265275	+	0.332645i
$730$	−16.5006			−0.610713
$731$	−13.0131	−	23.6993i	−0.481308	−	0.876552i
$732$	−47.6262			−1.76032
$733$	18.3157	−	22.9672i	0.676508	−	0.848314i	−0.318520	−	0.947916i	$-0.603186\pi$
$733$	18.3157	−	22.9672i	0.676508	−	0.848314i	0.995027	+	0.0996025i	$0.0317571\pi$
$734$	8.00795	+	53.1293i	0.295579	+	1.96104i
$735$	−10.3691	−	45.4301i	−0.382471	−	1.67571i
$736$	6.02105	+	8.83125i	0.221939	+	0.325524i
$737$	17.3087	+	9.99317i	0.637573	+	0.368103i
$738$	91.1472	−	52.6238i	3.35517	−	1.93711i
$739$	−15.8285	−	7.62263i	−0.582263	−	0.280403i	0.119476	−	0.992837i	$-0.461878\pi$
$739$	−15.8285	−	7.62263i	−0.582263	−	0.280403i	−0.701739	+	0.712434i	$0.747593\pi$
$740$	−12.0845	+	3.72756i	−0.444233	+	0.137028i
$741$	−3.89205	−	0.291669i	−0.142978	−	0.0107147i
$742$	1.45430	+	0.331935i	0.0533892	+	0.0121857i
$743$	7.08657	−	2.78127i	0.259981	−	0.102035i	−0.231771	−	0.972770i	$-0.574452\pi$
$743$	7.08657	−	2.78127i	0.259981	−	0.102035i	0.491752	+	0.870735i	$0.336357\pi$
$744$	−1.09830	−	14.6558i	−0.0402658	−	0.537309i
$745$	1.78189	−	11.8221i	0.0652834	−	0.433127i
$746$	52.4946	−	48.7078i	1.92196	−	1.78332i
$747$	−97.0533	+	46.7384i	−3.55100	+	1.71007i
$748$	13.2974	+	18.1887i	0.486200	+	0.665045i
$749$	−0.921660	+	2.34835i	−0.0336767	+	0.0858069i
$750$	−73.4914	−	22.6691i	−2.68352	−	0.827758i
$751$	33.8883	−	36.5229i	1.23660	−	1.33274i	0.312821	−	0.949812i	$-0.398726\pi$
$751$	33.8883	−	36.5229i	1.23660	−	1.33274i	0.923779	−	0.382926i	$-0.125084\pi$
$752$	9.87130	+	12.3782i	0.359969	+	0.451387i
$753$	−43.2186	+	34.4657i	−1.57497	+	1.25600i
$754$	2.33063	−	2.51182i	0.0848765	−	0.0914751i
$755$	−6.05984	+	19.6455i	−0.220540	+	0.714973i
$756$	1.86509	−	4.75217i	0.0678327	−	0.172835i
$757$	−0.448063	−	0.305484i	−0.0162851	−	0.0111030i	0.555150	−	0.831750i	$-0.312661\pi$
$757$	−0.448063	−	0.305484i	−0.0162851	−	0.0111030i	−0.571435	+	0.820647i	$0.693613\pi$
$758$	3.77011	+	7.82871i	0.136937	+	0.284352i
$759$	6.60885	+	7.12264i	0.239886	+	0.258536i
$760$	1.03477	−	6.86525i	0.0375351	−	0.249029i
$761$	1.25969	+	16.8093i	0.0456636	+	0.609338i	0.972354	+	0.233512i	$0.0750219\pi$
$761$	1.25969	+	16.8093i	0.0456636	+	0.609338i	−0.926690	+	0.375826i	$0.877359\pi$
$762$	46.8873	−	18.4019i	1.69855	−	0.666631i
$763$	0.681526	−	2.98596i	0.0246729	−	0.108099i
$764$	−2.42312	+	32.3343i	−0.0876655	+	1.16981i
$765$	60.8056	+	2.55034i	2.19843	+	0.0922077i
$766$	−67.1847	−	32.3544i	−2.42748	−	1.16901i
$767$	0.0625042	+	0.108260i	0.00225690	+	0.00390906i
$768$	24.9057	+	14.3793i	0.898707	+	0.518869i
$769$	10.0180	−	6.83013i	0.361257	−	0.246301i	−0.369066	−	0.929403i	$-0.620322\pi$
$769$	10.0180	−	6.83013i	0.361257	−	0.246301i	0.730322	+	0.683103i	$0.239370\pi$
$770$	1.73808	−	0.396704i	0.0626359	−	0.0142962i
$771$	8.94197	+	59.3261i	0.322037	+	2.13658i
$772$	−4.53919	−	3.61988i	−0.163369	−	0.130282i
$773$	−37.5277			−1.34978			−0.674889	−	0.737919i	$-0.735809\pi$
$773$	−37.5277			−1.34978			−0.674889	+	0.737919i	$0.735809\pi$
$774$	83.5028	+	45.9582i	3.00145	+	1.65193i
$775$			3.33202i			0.119690i
$776$	5.49861	+	4.38500i	0.197389	+	0.157412i
$777$	0.207779	+	1.37852i	0.00745402	+	0.0494542i
$778$	−16.4051	−	71.8753i	−0.588151	−	2.57686i
$779$	−18.5024	−	27.1380i	−0.662917	−	0.972321i
$780$	2.13748	−	3.70222i	0.0765340	−	0.132561i
$781$	11.1633	+	19.3355i	0.399456	+	0.691878i
$782$	−7.99557	−	8.06814i	−0.285921	−	0.288516i
$783$	−72.2909	+	22.2988i	−2.58347	+	0.796894i
$784$	−1.65961	+	22.1460i	−0.0592719	+	0.790929i
$785$	−39.1496	−	8.93564i	−1.39731	−	0.318927i
$786$	−10.2894	−	26.2171i	−0.367012	−	0.935132i
$787$	−33.6209	+	2.51954i	−1.19846	+	0.0898118i	−0.658961	−	0.752177i	$-0.729004\pi$
$787$	−33.6209	+	2.51954i	−1.19846	+	0.0898118i	−0.539494	+	0.841989i	$0.681385\pi$
$788$	6.02426	−	39.9683i	0.214605	−	1.42381i
$789$	41.3290	+	44.5421i	1.47135	+	1.58574i
$790$	−2.16304	+	1.04167i	−0.0769577	+	0.0370609i
$791$	−2.85676	−	1.94771i	−0.101575	−	0.0692526i
$792$	−10.9249	−	4.28770i	−0.388199	−	0.152357i
$793$	−0.516152	+	1.67332i	−0.0183291	+	0.0594215i
$794$	−34.1412	+	36.7955i	−1.21163	+	1.30582i
$795$	−17.1952	−	21.5622i	−0.609853	−	0.764731i
$796$	15.4874	−	12.3508i	0.548936	−	0.437762i
$797$	−28.2728	−	26.2333i	−1.00147	−	0.929232i	−0.00398050	−	0.999992i	$-0.501267\pi$
$797$	−28.2728	−	26.2333i	−1.00147	−	0.929232i	−0.997493	+	0.0707601i	$0.977458\pi$
$798$	−4.94975	−	1.52679i	−0.175219	−	0.0540479i
$799$	−15.4683	−	13.4337i	−0.547229	−	0.475249i
$800$	3.45901	+	2.35831i	0.122295	+	0.0833790i
$801$	68.8570	−	33.1598i	2.43294	−	1.17164i
$802$	−49.6875	−	53.5503i	−1.75453	−	1.89093i
$803$	8.60741	+	1.29736i	0.303749	+	0.0457828i
$804$	63.4275	−	4.75323i	2.23692	−	0.167634i
$805$	−0.451692	+	0.177276i	−0.0159200	+	0.00624816i
$806$	−3.56555	−	0.813812i	−0.125591	−	0.0286653i
$807$	1.64705	−	21.9784i	0.0579790	−	0.773676i
$808$	−1.68780	+	0.520617i	−0.0593766	+	0.0183153i
$809$	9.39571	−	19.5104i	0.330336	−	0.685949i	−0.667967	−	0.744191i	$-0.732835\pi$
$809$	9.39571	−	19.5104i	0.330336	−	0.685949i	0.998302	+	0.0582420i	$0.0185495\pi$
$810$	−71.4474	+	41.2502i	−2.51040	+	1.44938i
$811$	−28.7148	−	16.5785i	−1.00831	−	0.582151i	−0.0976168	−	0.995224i	$-0.531122\pi$
$811$	−28.7148	−	16.5785i	−1.00831	−	0.582151i	−0.910698	+	0.413073i	$0.864455\pi$
$812$	2.02855	−	1.38304i	0.0711882	−	0.0485353i
$813$	75.8701	−	17.3169i	2.66088	−	0.607329i
$814$	12.2190	−	1.84172i	0.428276	−	0.0645522i
$815$	3.90644	−	4.89852i	0.136837	−	0.171588i
$816$	−39.0950	−	13.8785i	−1.36860	−	0.485845i
$817$	12.3549	−	27.0582i	0.432244	−	0.946646i
$818$	62.4754			2.18440
$819$	−0.257599	−	0.205428i	−0.00900123	−	0.00717824i
$820$	35.5740	−	5.36192i	1.24230	−	0.187246i
$821$	0.493291	−	0.112591i	0.0172160	−	0.00392944i	−0.213904	−	0.976855i	$-0.568618\pi$
$821$	0.493291	−	0.112591i	0.0172160	−	0.00392944i	0.231120	+	0.972925i	$0.425761\pi$
$822$	36.0851	+	52.9271i	1.25861	+	1.84604i
$823$	12.4875	+	7.20966i	0.435287	+	0.251313i	0.701596	−	0.712575i	$-0.252471\pi$
$823$	12.4875	+	7.20966i	0.435287	+	0.251313i	−0.266310	+	0.963888i	$0.585804\pi$
$824$	1.40591	+	2.43511i	0.0489772	+	0.0848309i
$825$	3.42883	+	1.65124i	0.119377	+	0.0574887i
$826$	0.0489019	+	0.158536i	0.00170151	+	0.00551617i
$827$	18.2250	+	1.36577i	0.633744	+	0.0474926i	0.387729	−	0.921773i	$-0.373260\pi$
$827$	18.2250	+	1.36577i	0.633744	+	0.0474926i	0.246015	+	0.969266i	$0.420879\pi$
$828$	21.0771	+	4.81071i	0.732479	+	0.167184i
$829$	−12.2646	−	31.2498i	−0.425968	−	1.08535i	−0.969311	−	0.245838i	$-0.920937\pi$
$829$	−12.2646	−	31.2498i	−0.425968	−	1.08535i	0.543343	−	0.839511i	$-0.317158\pi$
$830$	−68.0113	+	5.09674i	−2.36071	+	0.176910i
$831$	−44.2792	−	6.67402i	−1.53603	−	0.231519i
$832$	−2.09559	+	1.94443i	−0.0726517	+	0.0674109i
$833$	−3.08855	−	28.5713i	−0.107012	−	0.989935i
$834$	53.2894	+	36.3321i	1.84526	+	1.25808i
$835$	15.9041	−	40.5229i	0.550383	−	1.40235i
$836$	−7.30641	+	23.6868i	−0.252698	+	0.819226i
$837$	59.1908	+	54.9210i	2.04593	+	1.89835i
$838$	−51.4957	+	41.0665i	−1.77889	+	1.41862i
$839$	−27.9004	+	22.2499i	−0.963230	+	0.768150i	−0.972762	−	0.231804i	$-0.925537\pi$
$839$	−27.9004	+	22.2499i	−0.963230	+	0.768150i	0.00953230	+	0.999955i	$0.496966\pi$
$840$	0.570190	−	0.614519i	0.0196734	−	0.0212029i
$841$	−7.05499	−	2.17618i	−0.243276	−	0.0750406i
$842$	−28.1575	+	71.7440i	−0.970370	+	2.47246i
$843$	33.3242	−	48.8776i	1.14775	−	1.68343i
$844$	−21.9491	−	45.5777i	−0.755518	−	1.56885i
$845$	18.6137	+	20.0608i	0.640331	+	0.690112i
$846$	71.4181	+	10.7646i	2.45541	+	0.370093i
$847$	0.964728	−	0.0722964i	0.0331485	−	0.00248413i
$848$	4.80195	+	12.2352i	0.164900	+	0.420158i
$849$	−12.9868	+	56.8988i	−0.445705	+	1.95276i
$850$	−4.06973	−	1.79754i	−0.139591	−	0.0616550i
$851$	−3.21390	+	0.991358i	−0.110171	+	0.0339833i
$852$	64.0169	+	30.8289i	2.19318	+	1.05618i
$853$	28.8863	−	16.6775i	0.989048	−	0.571027i	0.0840581	−	0.996461i	$-0.473212\pi$
$853$	28.8863	−	16.6775i	0.989048	−	0.571027i	0.904989	+	0.425434i	$0.139879\pi$
$854$	−1.16201	+	2.01267i	−0.0397633	+	0.0688720i
$855$	37.7174	+	55.3212i	1.28991	+	1.89195i
$856$	10.2511	−	2.33975i	0.350376	−	0.0799710i
$857$	1.92664	+	12.7824i	0.0658129	+	0.436640i	0.997335	+	0.0729556i	$0.0232432\pi$
$857$	1.92664	+	12.7824i	0.0658129	+	0.436640i	−0.931522	+	0.363684i	$0.881519\pi$
$858$	−2.60442	+	3.26584i	−0.0889135	+	0.111494i
$859$	9.05069			0.308806			0.154403	−	0.988008i	$-0.450655\pi$
$859$	9.05069			0.308806			0.154403	+	0.988008i	$0.450655\pi$
$860$	20.8306	+	25.0514i	0.710317	+	0.854246i
$861$		−	3.96587i		−	0.135157i
$862$	30.8074	+	24.5681i	1.04931	+	0.836794i
$863$	7.60669	−	1.14652i	0.258935	−	0.0390281i	−0.0182920	−	0.999833i	$-0.505823\pi$
$863$	7.60669	−	1.14652i	0.258935	−	0.0390281i	0.277227	+	0.960805i	$0.410585\pi$
$864$	98.9079	−	22.5751i	3.36491	−	0.768020i
$865$	5.25285	−	3.58134i	0.178602	−	0.121769i
$866$	2.48139	−	4.29790i	0.0843212	−	0.146049i
$867$	53.0087	+	8.48034i	1.80027	+	0.288007i
$868$	−2.36097	−	1.13698i	−0.0801364	−	0.0385917i
$869$	1.21024	−	0.373309i	0.0410546	−	0.0126637i
$870$	−83.8414	−	6.28305i	−2.84249	−	0.213015i
$871$	0.520397	−	2.28001i	0.0176330	−	0.0772552i
$872$	−11.8831	+	4.66376i	−0.402411	+	0.157935i
$873$	−67.6356	+	5.06859i	−2.28912	+	0.171546i
$874$	1.86254	−	12.3572i	0.0630014	−	0.417987i
$875$	−1.48527	+	1.37813i	−0.0502111	+	0.0465891i
$876$	24.9586	−	12.0194i	0.843274	−	0.406100i
$877$	3.34721	−	4.90946i	0.113027	−	0.165781i	−0.765557	−	0.643368i	$-0.777536\pi$
$877$	3.34721	−	4.90946i	0.113027	−	0.165781i	0.878584	+	0.477588i	$0.158489\pi$
$878$	−34.4804	−	13.5326i	−1.16366	−	0.456702i
$879$	−18.6079	+	60.3254i	−0.627630	+	2.03473i
$880$	11.5151	+	10.6844i	0.388174	+	0.360172i
$881$	−20.5538	+	16.3911i	−0.692474	+	0.552230i	−0.905254	−	0.424870i	$-0.860320\pi$
$881$	−20.5538	+	16.3911i	−0.692474	+	0.552230i	0.212780	+	0.977100i	$0.431748\pi$
$882$	63.1658	+	79.2074i	2.12690	+	2.66705i
$883$	20.7580	+	19.2606i	0.698562	+	0.648171i	0.947281	−	0.320405i	$-0.103819\pi$
$883$	20.7580	+	19.2606i	0.698562	+	0.648171i	−0.248719	+	0.968576i	$0.580009\pi$
$884$	1.57512	−	2.11415i	0.0529770	−	0.0711067i
$885$	1.12062	−	2.85530i	0.0376693	−	0.0959797i
$886$	−43.5407	−	29.6855i	−1.46278	−	0.997304i
$887$	6.65523	+	13.8197i	0.223461	+	0.464021i	0.982314	−	0.187241i	$-0.0599544\pi$
$887$	6.65523	+	13.8197i	0.223461	+	0.464021i	−0.758853	+	0.651261i	$0.774240\pi$
$888$	4.25944	−	3.95218i	0.142937	−	0.132627i
$889$	0.197775	−	1.31215i	0.00663315	−	0.0440081i
$890$	48.2524	−	3.61601i	1.61742	−	0.121209i
$891$	40.5134	−	15.9003i	1.35725	−	0.532681i
$892$	−7.82343	+	34.2767i	−0.261948	+	1.14767i
$893$	1.68439	−	22.4766i	0.0563659	−	0.752151i
$894$	10.9583	+	35.5260i	0.366501	+	1.18817i
$895$	15.1453	−	31.4495i	0.506251	−	1.05124i
$896$	−0.855660	+	0.494015i	−0.0285856	+	0.0165039i
$897$	0.568470	−	0.984619i	0.0189807	−	0.0328755i
$898$	−23.9322	−	35.1021i	−0.798627	−	1.17137i
$899$	8.64110	+	37.8591i	0.288197	+	1.26267i
$900$	8.37316	−	1.26205i	0.279105	−	0.0420684i
$901$	−8.98378	−	14.4420i	−0.299293	−	0.481134i
$902$	−35.1529			−1.17046
$903$	3.07300	−	1.85906i	0.102263	−	0.0618658i
$904$			14.4110i			0.479304i
$905$	0.964926	−	1.20998i	0.0320752	−	0.0402211i
$906$	−9.52839	−	63.2168i	−0.316560	−	2.10024i
$907$	−6.13662	+	1.40064i	−0.203763	+	0.0465076i	−0.323184	−	0.946336i	$-0.604753\pi$
$907$	−6.13662	+	1.40064i	−0.203763	+	0.0465076i	0.119421	+	0.992844i	$0.461896\pi$
$908$	12.2089	+	17.9072i	0.405166	+	0.594270i
$909$	8.51684	−	14.7516i	0.282486	−	0.489280i
$910$	−0.104303	−	0.180658i	−0.00345761	−	0.00598876i
$911$	14.0818	−	29.2412i	0.466552	−	0.968805i	−0.526395	−	0.850240i	$-0.676457\pi$
$911$	14.0818	−	29.2412i	0.466552	−	0.968805i	0.992946	−	0.118564i	$-0.0378292\pi$
$912$	−13.4529	−	43.6133i	−0.445471	−	1.44418i
$913$	35.8784	+	2.68871i	1.18740	+	0.0889834i
$914$	0.833685	−	3.65261i	0.0275758	−	0.120818i
$915$	39.9971	−	15.6977i	1.32226	−	0.518950i
$916$	2.17394	+	29.0091i	0.0718288	+	0.958489i
$917$	−0.733690	−	0.110586i	−0.0242286	−	0.00365187i
$918$	−99.0125	+	42.6672i	−3.26790	+	1.40823i
$919$	10.7038	−	5.15466i	0.353085	−	0.170037i	−0.248930	−	0.968521i	$-0.580079\pi$
$919$	10.7038	−	5.15466i	0.353085	−	0.170037i	0.602015	+	0.798485i	$0.294365\pi$
$920$	1.67103	+	1.13929i	0.0550921	+	0.0375612i
$921$	−7.65248	−	3.00338i	−0.252158	−	0.0989646i
$922$	−81.3938	−	25.1067i	−2.68056	−	0.826844i
$923$	1.77695	−	1.91509i	0.0584889	−	0.0630361i
$924$	−2.34003	+	1.86611i	−0.0769814	+	0.0613906i
$925$	−1.02994	+	0.821349i	−0.0338642	+	0.0270058i
$926$	25.9754	+	24.1016i	0.853603	+	0.792028i
$927$	−25.9121	−	7.99282i	−0.851065	−	0.262519i
$928$	45.4180	+	17.8252i	1.49092	+	0.585142i
$929$	8.83194	−	12.9541i	0.289767	−	0.425010i	−0.653560	−	0.756874i	$-0.726725\pi$
$929$	8.83194	−	12.9541i	0.289767	−	0.425010i	0.943327	+	0.331865i	$0.107678\pi$
$930$	38.9357	+	80.8508i	1.27675	+	2.65120i
$931$	23.1765	−	21.5047i	0.759579	−	0.704786i
$932$	2.51680	−	16.6979i	0.0824404	−	0.546956i
$933$	3.04269	+	40.6018i	0.0996131	+	1.32924i
$934$	−20.1265	−	51.2815i	−0.658559	−	1.67798i
$935$	−17.1623	−	10.8923i	−0.561268	−	0.356215i
$936$	−0.102625	+	1.36943i	−0.00335440	+	0.0447614i
$937$	−15.4533	+	4.76670i	−0.504837	+	0.155721i	−0.536704	−	0.843771i	$-0.680331\pi$
$937$	−15.4533	+	4.76670i	−0.504837	+	0.155721i	0.0318674	+	0.999492i	$0.489855\pi$
$938$	1.34667	−	2.79640i	0.0439705	−	0.0913056i
$939$	−33.3569	−	57.7758i	−1.08856	−	1.88544i
$940$	21.3804	+	12.3440i	0.697350	+	0.402615i
$941$	29.3592	+	43.0621i	0.957083	+	1.40378i	0.914453	+	0.404692i	$0.132621\pi$
$941$	29.3592	+	43.0621i	0.957083	+	1.40378i	0.0426302	+	0.999091i	$0.486426\pi$
$942$	121.741	−	27.7867i	3.96655	−	0.905339i
$943$	9.46102	−	1.42602i	0.308093	−	0.0464376i
$944$	−0.911444	+	1.14291i	−0.0296650	+	0.0371987i
$945$			4.60567i			0.149823i
$946$	−16.4785	−	27.2386i	−0.535761	−	0.885603i
$947$			12.5387i			0.407454i	0.979028	+	0.203727i	$0.0653055\pi$
$947$			12.5387i			0.407454i	−0.979028	+	0.203727i	$0.934694\pi$
$948$	2.51303	−	3.15124i	0.0816194	−	0.102347i
$949$	−0.151807	−	1.00717i	−0.00492785	−	0.0326942i
$950$	−1.08917	−	4.77198i	−0.0353375	−	0.154824i
$951$	−28.0873	+	19.1496i	−0.910792	+	0.620968i
$952$	0.393383	−	0.335452i	0.0127496	−	0.0108720i
$953$	21.4923	+	37.2258i	0.696205	+	1.20586i	0.969773	+	0.244010i	$0.0784630\pi$
$953$	21.4923	+	37.2258i	0.696205	+	1.20586i	−0.273567	+	0.961853i	$0.588204\pi$
$954$	54.0220	+	26.0156i	1.74903	+	0.842287i
$955$	−8.62249	−	27.9534i	−0.279017	−	0.904552i
$956$	−0.303894	+	4.05519i	−0.00982864	+	0.131154i
$957$	43.2414	+	9.86956i	1.39779	+	0.319037i
$958$	53.4210	−	20.9662i	1.72596	−	0.677387i
$959$	1.68288	−	0.126115i	0.0543431	−	0.00407245i
$960$	69.3611	+	10.4545i	2.23862	+	0.337417i
$961$	7.65854	−	7.10609i	0.247050	−	0.229229i
$962$	−0.627362	−	1.30273i	−0.0202269	−	0.0420017i
$963$	−57.1223	+	83.7830i	−1.84074	+	2.69987i
$964$	−8.44991	−	3.31635i	−0.272153	−	0.106812i
$965$	5.00519	+	1.54390i	0.161123	+	0.0496997i
$966$	1.02632	−	1.10611i	0.0330212	−	0.0355884i
$967$	1.96619	+	2.46553i	0.0632285	+	0.0792861i	0.812440	−	0.583045i	$-0.198139\pi$
$967$	1.96619	+	2.46553i	0.0632285	+	0.0792861i	−0.749212	+	0.662331i	$0.769567\pi$
$968$	−2.51407	−	3.15254i	−0.0808052	−	0.101326i
$969$	27.3609	+	52.3403i	0.878958	+	1.68141i
$970$	−41.0347	−	12.6575i	−1.31755	−	0.406409i
$971$	−0.606596	+	1.54558i	−0.0194666	+	0.0496000i	−0.940277	−	0.340411i	$-0.889434\pi$
$971$	−0.606596	+	1.54558i	−0.0194666	+	0.0496000i	0.920810	+	0.390011i	$0.127529\pi$
$972$	28.2823	−	41.4826i	0.907156	−	1.33055i
$973$	1.53088	−	0.737235i	0.0490779	−	0.0236347i
$974$	−6.23007	−	6.71442i	−0.199624	−	0.215144i
$975$	0.0663707	−	0.440341i	0.00212556	−	0.0141022i
$976$	−20.4203	+	1.53029i	−0.653637	+	0.0489833i
$977$	−20.3803	−	51.9282i	−0.652024	−	1.66133i	−0.746158	−	0.665769i	$-0.768103\pi$
$977$	−20.3803	−	51.9282i	−0.652024	−	1.66133i	0.0941340	−	0.995560i	$-0.469992\pi$
$978$	−4.33544	+	18.9948i	−0.138632	+	0.607387i
$979$	−25.4548	−	1.90758i	−0.813540	−	0.0609664i
$980$	10.2073	+	33.0914i	0.326061	+	1.05706i
$981$	53.4149	−	110.917i	1.70541	−	3.54132i
$982$	1.16527	+	2.01831i	0.0371852	+	0.0644067i
$983$	35.5371	+	20.5173i	1.13346	+	0.654402i	0.944802	−	0.327642i	$-0.106254\pi$
$983$	35.5371	+	20.5173i	1.13346	+	0.654402i	0.188655	+	0.982043i	$0.439587\pi$
$984$	−13.6575	+	9.31152i	−0.435385	+	0.296840i
$985$	8.11440	+	35.5515i	0.258546	+	1.13277i
$986$	−50.9028	−	9.86975i	−1.62108	−	0.314317i
$987$	1.69684	−	2.12778i	0.0540111	−	0.0677278i
$988$	2.90051			0.0922774
$989$	5.53997	+	6.66251i	0.176161	+	0.211856i
$990$	71.6595			2.27749
$991$	−34.2682	−	27.3280i	−1.08857	−	0.868102i	−0.0966899	−	0.995315i	$-0.530826\pi$
$991$	−34.2682	−	27.3280i	−1.08857	−	0.868102i	−0.991875	+	0.127213i	$0.959397\pi$
$992$	−7.76151	−	51.4943i	−0.246428	−	1.63494i
$993$	−8.60849	+	1.96483i	−0.273182	+	0.0623520i
$994$	2.86474	−	1.95315i	0.0908641	−	0.0619501i
$995$	−8.93566	+	15.4770i	−0.283280	+	0.490655i
$996$	99.1608	−	57.2505i	3.14203	−	1.81405i
$997$	−20.8607	+	43.3176i	−0.660664	+	1.37188i	0.253816	+	0.967252i	$0.418314\pi$
$997$	−20.8607	+	43.3176i	−0.660664	+	1.37188i	−0.914480	+	0.404630i	$0.867400\pi$
$998$	20.6781	+	67.0369i	0.654555	+	2.12202i
$999$	−2.38565	+	31.8342i	−0.0754785	+	1.00719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.z.a.67.10	yes	768
17.16	even	2	inner	731.2.z.a.67.9	✓	768
43.9	even	21	inner	731.2.z.a.611.9	yes	768
731.611	even	42	inner	731.2.z.a.611.10	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.z.a.67.9	✓	768	17.16	even	2	inner
731.2.z.a.67.10	yes	768	1.1	even	1	trivial
731.2.z.a.611.9	yes	768	43.9	even	21	inner
731.2.z.a.611.10	yes	768	731.611	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29990 + 1.63003i) q^{2} +(0.470647 + 3.12254i) q^{3} +(-0.522200 - 2.28791i) q^{4} +(1.19265 + 1.74929i) q^{5} +(-5.70163 - 3.29184i) q^{6} +(-0.150209 + 0.0867232i) q^{7} +(0.651331 + 0.313664i) q^{8} +(-6.66204 + 2.05497i) q^{9} +O(q^{10})\)	\(q+(-1.29990 + 1.63003i) q^{2} +(0.470647 + 3.12254i) q^{3} +(-0.522200 - 2.28791i) q^{4} +(1.19265 + 1.74929i) q^{5} +(-5.70163 - 3.29184i) q^{6} +(-0.150209 + 0.0867232i) q^{7} +(0.651331 + 0.313664i) q^{8} +(-6.66204 + 2.05497i) q^{9} +(-4.40173 - 0.329864i) q^{10} +(2.27020 + 0.518158i) q^{11} +(6.89831 - 2.70739i) q^{12} +(-0.0203619 - 0.271710i) q^{13} +(0.0538960 - 0.357577i) q^{14} +(-4.90093 + 4.54740i) q^{15} +(2.87074 - 1.38247i) q^{16} +(-3.32847 + 2.43337i) q^{17} +(5.31036 - 13.5306i) q^{18} +(-4.33460 - 1.33705i) q^{19} +(3.37942 - 3.64215i) q^{20} +(-0.341492 - 0.428218i) q^{21} +(-3.79565 + 3.02693i) q^{22} +(0.898769 - 0.968643i) q^{23} +(-0.672883 + 2.18143i) q^{24} +(0.189085 - 0.481781i) q^{25} +(0.469364 + 0.320007i) q^{26} +(-5.44182 - 11.3000i) q^{27} +(0.276854 + 0.298377i) q^{28} +(0.898998 - 5.96446i) q^{29} +(-1.04165 - 13.8998i) q^{30} +(-5.99294 + 2.35206i) q^{31} +(-1.79994 + 7.88606i) q^{32} +(-0.549507 + 7.33266i) q^{33} +(0.360230 - 8.58865i) q^{34} +(-0.330851 - 0.159329i) q^{35} +(8.18048 + 14.1690i) q^{36} +(-2.20430 - 1.27265i) q^{37} +(7.81400 - 5.32749i) q^{38} +(0.838844 - 0.191461i) q^{39} +(0.228117 + 1.51346i) q^{40} +(5.66110 + 4.51457i) q^{41} +1.14191 q^{42} +(-0.844441 + 6.50284i) q^{43} -5.46459i q^{44} +(-11.5402 - 9.20301i) q^{45} +(0.410601 + 2.72416i) q^{46} +(1.10569 + 4.84433i) q^{47} +(5.66794 + 8.31334i) q^{48} +(-3.48496 + 6.03612i) q^{49} +(0.539524 + 0.934483i) q^{50} +(-9.16483 - 9.24802i) q^{51} +(-0.611015 + 0.188473i) q^{52} +(-0.308270 + 4.11357i) q^{53} +(25.4932 + 5.81867i) q^{54} +(1.80114 + 4.58923i) q^{55} +(-0.125038 + 0.00937028i) q^{56} +(2.13492 - 14.1643i) q^{57} +(8.55363 + 9.21862i) q^{58} +(-0.413358 + 0.199063i) q^{59} +(12.9633 + 8.83822i) q^{60} +(-5.98253 - 2.34797i) q^{61} +(3.95633 - 12.8261i) q^{62} +(0.822484 - 0.886427i) q^{63} +(-6.54153 - 8.20282i) q^{64} +(0.451017 - 0.359674i) q^{65} +(-11.2381 - 10.4275i) q^{66} +(8.20173 + 2.52990i) q^{67} +(7.30545 + 6.34452i) q^{68} +(3.44763 + 2.35055i) q^{69} +(0.689786 - 0.332183i) q^{70} +(6.52157 + 7.02858i) q^{71} +(-4.98376 - 0.751181i) q^{72} +(3.72772 - 0.279354i) q^{73} +(4.93984 - 1.93874i) q^{74} +(1.59337 + 0.363677i) q^{75} +(-0.795512 + 10.6154i) q^{76} +(-0.385941 + 0.119047i) q^{77} +(-0.778330 + 1.61622i) q^{78} +(0.471028 - 0.271948i) q^{79} +(5.84214 + 3.37296i) q^{80} +(15.4426 - 10.5286i) q^{81} +(-14.7178 + 3.35923i) q^{82} +(15.2785 - 2.30286i) q^{83} +(-0.801395 + 1.00492i) q^{84} +(-8.22638 - 2.92032i) q^{85} +(-9.50212 - 9.82953i) q^{86} +19.0474 q^{87} +(1.31612 + 1.04957i) q^{88} +(-10.8397 + 1.63382i) q^{89} +(30.0023 - 6.84784i) q^{90} +(0.0266221 + 0.0390475i) q^{91} +(-2.68550 - 1.55047i) q^{92} +(-10.1649 - 17.6062i) q^{93} +(-9.33368 - 4.49486i) q^{94} +(-2.83077 - 9.17713i) q^{95} +(-25.4717 - 1.90884i) q^{96} +(9.48464 + 2.16481i) q^{97} +(-5.30894 - 13.5270i) q^{98} +(-16.1889 + 1.21319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q - 24 q^{2} - 144 q^{4} - 16 q^{8} - 98 q^{9}+O(q^{10}) \) 768 * q - 24 * q^2 - 144 * q^4 - 16 * q^8 - 98 * q^9	\( 768 q - 24 q^{2} - 144 q^{4} - 16 q^{8} - 98 q^{9} - 18 q^{13} - 30 q^{15} - 160 q^{16} - 16 q^{17} - 54 q^{18} - 68 q^{19} - 50 q^{21} - 88 q^{25} - 26 q^{26} - 50 q^{32} - 36 q^{33} - 38 q^{34} + 14 q^{35} + 328 q^{36} - 44 q^{38} - 148 q^{42} + 102 q^{43} - 64 q^{47} + 298 q^{49} + 40 q^{50} - 31 q^{51} - 38 q^{52} - 28 q^{53} - 80 q^{55} - 16 q^{59} - 34 q^{60} - 64 q^{64} - 126 q^{66} + 74 q^{67} - 132 q^{68} - 28 q^{69} + 50 q^{70} + 26 q^{72} - 258 q^{76} - 112 q^{77} + 90 q^{81} + 48 q^{83} - 298 q^{84} + 36 q^{85} + 142 q^{86} + 192 q^{87} - 120 q^{89} - 188 q^{93} + 64 q^{94} + 146 q^{98}+O(q^{100}) \) 768 * q - 24 * q^2 - 144 * q^4 - 16 * q^8 - 98 * q^9 - 18 * q^13 - 30 * q^15 - 160 * q^16 - 16 * q^17 - 54 * q^18 - 68 * q^19 - 50 * q^21 - 88 * q^25 - 26 * q^26 - 50 * q^32 - 36 * q^33 - 38 * q^34 + 14 * q^35 + 328 * q^36 - 44 * q^38 - 148 * q^42 + 102 * q^43 - 64 * q^47 + 298 * q^49 + 40 * q^50 - 31 * q^51 - 38 * q^52 - 28 * q^53 - 80 * q^55 - 16 * q^59 - 34 * q^60 - 64 * q^64 - 126 * q^66 + 74 * q^67 - 132 * q^68 - 28 * q^69 + 50 * q^70 + 26 * q^72 - 258 * q^76 - 112 * q^77 + 90 * q^81 + 48 * q^83 - 298 * q^84 + 36 * q^85 + 142 * q^86 + 192 * q^87 - 120 * q^89 - 188 * q^93 + 64 * q^94 + 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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