LMFDB - Embedded newform 570.2.bi.a.443.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.17
Character	$\chi$	$=$	570.443
Dual form			570.2.bi.a.377.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(1.48522 - 0.891129i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.13591 - 1.92606i) q^{5} +(-1.55724 + 0.758292i) q^{6} +(-1.01991 - 3.80635i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.41178 - 2.64705i) q^{9} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(1.48522 - 0.891129i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.13591 - 1.92606i) q^{5} +(-1.55724 + 0.758292i) q^{6} +(-1.01991 - 3.80635i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.41178 - 2.64705i) q^{9} +(0.963721 + 2.01773i) q^{10} +(-0.467885 + 0.270133i) q^{11} +(1.61740 - 0.619684i) q^{12} +(5.33483 + 2.48767i) q^{13} +(0.684282 + 3.88076i) q^{14} +(-3.40345 - 1.84839i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-5.65287 - 0.494562i) q^{17} +(-1.63711 + 2.51393i) q^{18} +(-3.81136 + 2.11507i) q^{19} +(-0.784197 - 2.09405i) q^{20} +(-4.90674 - 4.74441i) q^{21} +(0.489648 - 0.228327i) q^{22} +(-1.96647 - 2.80841i) q^{23} +(-1.66526 + 0.476360i) q^{24} +(-2.41941 + 4.37566i) q^{25} +(-5.09772 - 2.94317i) q^{26} +(-0.262057 - 5.18954i) q^{27} +(-0.343448 - 3.92563i) q^{28} +(1.48373 + 1.24500i) q^{29} +(3.22940 + 2.13798i) q^{30} +(-2.35545 + 4.07976i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-0.454190 + 0.818154i) q^{33} +(5.58825 + 0.985360i) q^{34} +(-6.17274 + 6.28808i) q^{35} +(1.84999 - 2.36168i) q^{36} +(4.99612 - 4.99612i) q^{37} +(3.98120 - 1.77484i) q^{38} +(10.1403 - 1.05927i) q^{39} +(0.598705 + 2.15443i) q^{40} +(1.91970 - 5.27433i) q^{41} +(4.47457 + 5.15401i) q^{42} +(4.80690 - 6.86497i) q^{43} +(-0.507685 + 0.184782i) q^{44} +(-6.70203 + 0.287645i) q^{45} +(1.71422 + 2.96911i) q^{46} +(-0.270716 - 3.09430i) q^{47} +(1.70044 - 0.329411i) q^{48} +(-7.38592 + 4.26427i) q^{49} +(2.79157 - 4.14815i) q^{50} +(-8.83649 + 4.30290i) q^{51} +(4.82181 + 3.37626i) q^{52} +(5.68234 + 8.11522i) q^{53} +(-0.191238 + 5.19263i) q^{54} +(1.05177 + 0.594327i) q^{55} +3.94063i q^{56} +(-3.77593 + 6.53776i) q^{57} +(-1.36958 - 1.36958i) q^{58} +(-3.68971 + 3.09603i) q^{59} +(-3.03077 - 2.41131i) q^{60} +(1.84789 - 10.4799i) q^{61} +(2.70206 - 3.85895i) q^{62} +(-11.5155 - 2.67397i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.26849 - 13.1010i) q^{65} +(0.523768 - 0.775456i) q^{66} +(8.36870 - 0.732166i) q^{67} +(-5.48111 - 1.46866i) q^{68} +(-5.42331 - 2.41874i) q^{69} +(6.69729 - 5.72617i) q^{70} +(-0.213572 + 0.0376584i) q^{71} +(-2.04878 + 2.19146i) q^{72} +(-3.65687 - 7.84218i) q^{73} +(-5.41254 + 4.54166i) q^{74} +(0.305912 + 8.65485i) q^{75} +(-4.12074 + 1.42110i) q^{76} +(1.50542 + 1.50542i) q^{77} +(-10.1940 + 0.171460i) q^{78} +(-0.573661 + 1.57612i) q^{79} +(-0.408656 - 2.19841i) q^{80} +(-5.01376 - 7.47410i) q^{81} +(-2.37208 + 5.08694i) q^{82} +(-0.132816 - 0.495677i) q^{83} +(-4.00834 - 5.52438i) q^{84} +(5.46860 + 11.4495i) q^{85} +(-5.38693 + 6.41990i) q^{86} +(3.31312 + 0.526905i) q^{87} +(0.521858 - 0.139831i) q^{88} +(12.0104 - 4.37142i) q^{89} +(6.70160 + 0.297571i) q^{90} +(4.02792 - 22.8435i) q^{91} +(-1.44892 - 3.10722i) q^{92} +(0.137221 + 8.15837i) q^{93} +3.10612i q^{94} +(8.40312 + 4.93839i) q^{95} +(-1.72268 + 0.179954i) q^{96} +(0.162180 - 1.85372i) q^{97} +(7.72947 - 3.60431i) q^{98} +(0.0545073 + 1.61988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	1.48522	−	0.891129i	0.857494	−	0.514494i
$3$	1.48522	−	0.891129i	0.857494	−	0.514494i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−1.13591	−	1.92606i	−0.507995	−	0.861360i
$5$	−1.13591	−	1.92606i	−0.507995	−	0.861360i
$6$	−1.55724	+	0.758292i	−0.635740	+	0.309571i
$7$	−1.01991	−	3.80635i	−0.385489	−	1.43867i	−0.837394	−	0.546600i	$-0.815922\pi$
$7$	−1.01991	−	3.80635i	−0.385489	−	1.43867i	0.451905	−	0.892066i	$-0.350745\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	1.41178	−	2.64705i	0.470593	−	0.882350i
$10$	0.963721	+	2.01773i	0.304755	+	0.638063i
$11$	−0.467885	+	0.270133i	−0.141073	+	0.0814483i	−0.568875	−	0.822424i	$-0.692621\pi$
$11$	−0.467885	+	0.270133i	−0.141073	+	0.0814483i	0.427802	+	0.903872i	$0.359288\pi$
$12$	1.61740	−	0.619684i	0.466904	−	0.178887i
$13$	5.33483	+	2.48767i	1.47962	+	0.689957i	0.983932	−	0.178546i	$-0.0571393\pi$
$13$	5.33483	+	2.48767i	1.47962	+	0.689957i	0.495685	+	0.868502i	$0.334917\pi$
$14$	0.684282	+	3.88076i	0.182882	+	1.03718i
$15$	−3.40345	−	1.84839i	−0.878767	−	0.477251i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−5.65287	−	0.494562i	−1.37102	−	0.119949i	−0.622272	−	0.782801i	$-0.713790\pi$
$17$	−5.65287	−	0.494562i	−1.37102	−	0.119949i	−0.748750	+	0.662853i	$0.769346\pi$
$18$	−1.63711	+	2.51393i	−0.385871	+	0.592540i
$19$	−3.81136	+	2.11507i	−0.874387	+	0.485230i
$19$	−3.81136	+	2.11507i	−0.874387	+	0.485230i
$20$	−0.784197	−	2.09405i	−0.175352	−	0.468243i
$21$	−4.90674	−	4.74441i	−1.07074	−	1.03532i
$22$	0.489648	−	0.228327i	0.104393	−	0.0486794i
$23$	−1.96647	−	2.80841i	−0.410038	−	0.585594i	0.560017	−	0.828481i	$-0.310795\pi$
$23$	−1.96647	−	2.80841i	−0.410038	−	0.585594i	−0.970055	+	0.242887i	$0.921906\pi$
$24$	−1.66526	+	0.476360i	−0.339919	+	0.0972366i
$25$	−2.41941	+	4.37566i	−0.483883	+	0.875133i
$26$	−5.09772	−	2.94317i	−0.999745	−	0.577203i
$27$	−0.262057	−	5.18954i	−0.0504329	−	0.998727i
$28$	−0.343448	−	3.92563i	−0.0649056	−	0.741874i
$29$	1.48373	+	1.24500i	0.275522	+	0.231190i	0.770069	−	0.637960i	$-0.220222\pi$
$29$	1.48373	+	1.24500i	0.275522	+	0.231190i	−0.494547	+	0.869151i	$0.664666\pi$
$30$	3.22940	+	2.13798i	0.589605	+	0.390340i
$31$	−2.35545	+	4.07976i	−0.423052	+	0.732747i	−0.996236	−	0.0866791i	$-0.972375\pi$
$31$	−2.35545	+	4.07976i	−0.423052	+	0.732747i	0.573184	+	0.819426i	$0.305708\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	−0.454190	+	0.818154i	−0.0790643	+	0.142422i
$34$	5.58825	+	0.985360i	0.958377	+	0.168988i
$35$	−6.17274	+	6.28808i	−1.04338	+	1.06288i
$36$	1.84999	−	2.36168i	0.308331	−	0.393614i
$37$	4.99612	−	4.99612i	0.821356	−	0.821356i	−0.164946	−	0.986303i	$-0.552745\pi$
$37$	4.99612	−	4.99612i	0.821356	−	0.821356i	0.986303	+	0.164946i	$0.0527450\pi$
$38$	3.98120	−	1.77484i	0.645836	−	0.287917i
$39$	10.1403	−	1.05927i	1.62374	−	0.169619i
$40$	0.598705	+	2.15443i	0.0946635	+	0.340645i
$41$	1.91970	−	5.27433i	0.299806	−	0.823711i	−0.694725	−	0.719275i	$-0.744474\pi$
$41$	1.91970	−	5.27433i	0.299806	−	0.823711i	0.994532	−	0.104436i	$-0.0333038\pi$
$42$	4.47457	+	5.15401i	0.690441	+	0.795281i
$43$	4.80690	−	6.86497i	0.733046	−	1.04690i	−0.263565	−	0.964642i	$-0.584898\pi$
$43$	4.80690	−	6.86497i	0.733046	−	1.04690i	0.996611	−	0.0822564i	$-0.0262126\pi$
$44$	−0.507685	+	0.184782i	−0.0765364	+	0.0278570i
$45$	−6.70203	+	0.287645i	−0.999080	+	0.0428796i
$46$	1.71422	+	2.96911i	0.252748	+	0.437772i
$47$	−0.270716	−	3.09430i	−0.0394880	−	0.451350i	−0.990040	−	0.140785i	$-0.955037\pi$
$47$	−0.270716	−	3.09430i	−0.0394880	−	0.451350i	0.950552	−	0.310565i	$-0.100518\pi$
$48$	1.70044	−	0.329411i	0.245437	−	0.0475464i
$49$	−7.38592	+	4.26427i	−1.05513	+	0.609181i
$50$	2.79157	−	4.14815i	0.394788	−	0.586637i
$51$	−8.83649	+	4.30290i	−1.23736	+	0.602526i
$52$	4.82181	+	3.37626i	0.668664	+	0.468204i
$53$	5.68234	+	8.11522i	0.780530	+	1.11471i	0.990568	+	0.137019i	$0.0437521\pi$
$53$	5.68234	+	8.11522i	0.780530	+	1.11471i	−0.210039	+	0.977693i	$0.567359\pi$
$54$	−0.191238	+	5.19263i	−0.0260242	+	0.706628i
$55$	1.05177	+	0.594327i	0.141820	+	0.0801390i
$56$			3.94063i			0.526588i
$57$	−3.77593	+	6.53776i	−0.500134	+	0.865948i
$58$	−1.36958	−	1.36958i	−0.179834	−	0.179834i
$59$	−3.68971	+	3.09603i	−0.480359	+	0.403069i	−0.850556	−	0.525884i	$-0.823735\pi$
$59$	−3.68971	+	3.09603i	−0.480359	+	0.403069i	0.370197	+	0.928953i	$0.379290\pi$
$60$	−3.03077	−	2.41131i	−0.391271	−	0.311299i
$61$	1.84789	−	10.4799i	0.236599	−	1.34182i	−0.602622	−	0.798027i	$-0.705877\pi$
$61$	1.84789	−	10.4799i	0.236599	−	1.34182i	0.839221	−	0.543791i	$-0.183012\pi$
$62$	2.70206	−	3.85895i	0.343163	−	0.490087i
$63$	−11.5155	−	2.67397i	−1.45082	−	0.336889i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−1.26849	−	13.1010i	−0.157336	−	1.62498i
$66$	0.523768	−	0.775456i	0.0644714	−	0.0954520i
$67$	8.36870	−	0.732166i	1.02240	−	0.0894484i	0.436394	−	0.899756i	$-0.356255\pi$
$67$	8.36870	−	0.732166i	1.02240	−	0.0894484i	0.586005	+	0.810307i	$0.300700\pi$
$68$	−5.48111	−	1.46866i	−0.664682	−	0.178101i
$69$	−5.42331	−	2.41874i	−0.652889	−	0.291182i
$70$	6.69729	−	5.72617i	0.800479	−	0.684408i
$71$	−0.213572	+	0.0376584i	−0.0253463	+	0.00446924i	−0.186307	−	0.982492i	$-0.559652\pi$
$71$	−0.213572	+	0.0376584i	−0.0253463	+	0.00446924i	0.160961	+	0.986961i	$0.448541\pi$
$72$	−2.04878	+	2.19146i	−0.241451	+	0.258266i
$73$	−3.65687	−	7.84218i	−0.428004	−	0.917857i	−0.995525	−	0.0944986i	$-0.969875\pi$
$73$	−3.65687	−	7.84218i	−0.428004	−	0.917857i	0.567521	−	0.823359i	$-0.307903\pi$
$74$	−5.41254	+	4.54166i	−0.629196	+	0.527958i
$75$	0.305912	+	8.65485i	0.0353237	+	0.999376i
$76$	−4.12074	+	1.42110i	−0.472681	+	0.163011i
$77$	1.50542	+	1.50542i	0.171559	+	0.171559i
$78$	−10.1940	+	0.171460i	−1.15424	+	0.0194140i
$79$	−0.573661	+	1.57612i	−0.0645419	+	0.177327i	−0.967771	−	0.251831i	$-0.918967\pi$
$79$	−0.573661	+	1.57612i	−0.0645419	+	0.177327i	0.903229	+	0.429158i	$0.141190\pi$
$80$	−0.408656	−	2.19841i	−0.0456891	−	0.245790i
$81$	−5.01376	−	7.47410i	−0.557085	−	0.830456i
$82$	−2.37208	+	5.08694i	−0.261952	+	0.561759i
$83$	−0.132816	−	0.495677i	−0.0145785	−	0.0544076i	0.958253	−	0.285920i	$-0.0922992\pi$
$83$	−0.132816	−	0.495677i	−0.0145785	−	0.0544076i	−0.972832	+	0.231513i	$0.925633\pi$
$84$	−4.00834	−	5.52438i	−0.437346	−	0.602760i
$85$	5.46860	+	11.4495i	0.593153	+	1.24188i
$86$	−5.38693	+	6.41990i	−0.580888	+	0.692275i
$87$	3.31312	+	0.526905i	0.355204	+	0.0564901i
$88$	0.521858	−	0.139831i	0.0556302	−	0.0149061i
$89$	12.0104	−	4.37142i	1.27310	−	0.463369i	0.384953	−	0.922936i	$-0.374218\pi$
$89$	12.0104	−	4.37142i	1.27310	−	0.463369i	0.888143	+	0.459567i	$0.151995\pi$
$90$	6.70160	+	0.297571i	0.706411	+	0.0313667i
$91$	4.02792	−	22.8435i	0.422240	−	2.39464i
$92$	−1.44892	−	3.10722i	−0.151060	−	0.323950i
$93$	0.137221	+	8.15837i	0.0142292	+	0.845984i
$94$			3.10612i			0.320371i
$95$	8.40312	+	4.93839i	0.862141	+	0.506668i
$96$	−1.72268	+	0.179954i	−0.175820	+	0.0183665i
$97$	0.162180	−	1.85372i	0.0164668	−	0.188217i	−0.983506	−	0.180874i	$-0.942107\pi$
$97$	0.162180	−	1.85372i	0.0164668	−	0.188217i	0.999973	−	0.00734241i	$-0.00233718\pi$
$98$	7.72947	−	3.60431i	0.780795	−	0.364091i
$99$	0.0545073	+	1.61988i	0.00547819	+	0.162804i
$100$	−3.14248	+	3.88906i	−0.314248	+	0.388906i
$101$	2.24632	+	6.17172i	0.223517	+	0.614109i	0.999869	−	0.0161910i	$-0.00515399\pi$
$101$	2.24632	+	6.17172i	0.223517	+	0.614109i	−0.776351	+	0.630300i	$0.782932\pi$
$102$	9.17789	−	3.51637i	0.908746	−	0.348173i
$103$	−3.42695	+	12.7895i	−0.337667	+	1.26019i	0.563281	+	0.826265i	$0.309539\pi$
$103$	−3.42695	+	12.7895i	−0.337667	+	1.26019i	−0.900948	+	0.433926i	$0.857128\pi$
$104$	−4.50920	−	3.78366i	−0.442163	−	0.371019i
$105$	−3.56440	+	14.8399i	−0.347850	+	1.44823i
$106$	−4.95343	−	8.57959i	−0.481120	−	0.833324i
$107$	12.1917	−	3.26677i	1.17862	−	0.315810i	0.384241	−	0.923233i	$-0.374463\pi$
$107$	12.1917	−	3.26677i	1.17862	−	0.315810i	0.794379	+	0.607422i	$0.207796\pi$
$108$	0.643078	−	5.15621i	0.0618802	−	0.496156i
$109$	−12.5307	+	2.20951i	−1.20023	+	0.211633i	−0.737797	−	0.675023i	$-0.764134\pi$
$109$	−12.5307	+	2.20951i	−1.20023	+	0.211633i	−0.462431	+	0.886655i	$0.653023\pi$
$110$	−0.995967	−	0.683733i	−0.0949618	−	0.0651914i
$111$	2.96817	−	11.8725i	0.281726	−	1.12689i
$112$	0.343448	−	3.92563i	0.0324528	−	0.370937i
$113$	3.07124	−	3.07124i	0.288918	−	0.288918i	−0.547734	−	0.836652i	$-0.684510\pi$
$113$	3.07124	−	3.07124i	0.288918	−	0.288918i	0.836652	+	0.547734i	$0.184510\pi$
$114$	4.33136	−	6.18379i	0.405669	−	0.579165i
$115$	−3.17543	+	6.97765i	−0.296111	+	0.650669i
$116$	1.24500	+	1.48373i	0.115595	+	0.137761i
$117$	14.1166	−	10.6095i	1.30508	−	0.980852i
$118$	3.94551	−	2.76267i	0.363213	−	0.254325i
$119$	3.88293	+	22.0212i	0.355948	+	2.01868i
$120$	2.80908	+	2.66628i	0.256433	+	0.243397i
$121$	−5.35406	+	9.27350i	−0.486732	+	0.843045i
$122$	−2.75425	+	10.2790i	−0.249358	+	0.930617i
$123$	−1.84892	−	9.54425i	−0.166712	−	0.860576i
$124$	−3.02811	+	3.60876i	−0.271932	+	0.324076i
$125$	11.1760	−	0.310432i	0.999614	−	0.0277659i
$126$	11.2386	+	3.66744i	1.00122	+	0.326722i
$127$	−0.0615101	+	0.131909i	−0.00545813	+	0.0117050i	−0.909018	−	0.416757i	$-0.863167\pi$
$127$	−0.0615101	+	0.131909i	−0.00545813	+	0.0117050i	0.903560	+	0.428462i	$0.140944\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	1.02175	−	14.4796i	0.0899604	−	1.27486i
$130$	0.121834	+	13.1617i	0.0106856	+	1.15436i
$131$	3.73368	+	4.44963i	0.326213	+	0.388766i	0.904079	−	0.427366i	$-0.140559\pi$
$131$	3.73368	+	4.44963i	0.326213	+	0.388766i	−0.577865	+	0.816132i	$0.696114\pi$
$132$	−0.589361	+	0.726856i	−0.0512973	+	0.0632647i
$133$	11.9379	+	12.3502i	1.03515	+	1.07090i
$134$	−8.40067			−0.725707
$135$	−9.69769	+	6.39959i	−0.834644	+	0.550789i
$136$	5.33225	+	1.94078i	0.457236	+	0.166420i
$137$	9.00973	−	6.30868i	0.769753	−	0.538987i	−0.121447	−	0.992598i	$-0.538753\pi$
$137$	9.00973	−	6.30868i	0.769753	−	0.538987i	0.891200	+	0.453611i	$0.149864\pi$
$138$	5.19186	+	2.88221i	0.441961	+	0.245350i
$139$	−2.70873	−	7.44217i	−0.229751	−	0.631236i	0.770227	−	0.637769i	$-0.220143\pi$
$139$	−2.70873	−	7.44217i	−0.229751	−	0.631236i	−0.999979	+	0.00653302i	$0.997920\pi$
$140$	−7.17087	+	5.12067i	−0.606049	+	0.432775i
$141$	−3.15949	−	4.35448i	−0.266077	−	0.366713i
$142$	0.216041	−	0.0189011i	0.0181298	−	0.00158615i
$143$	−3.16809	+	0.277172i	−0.264929	+	0.0231783i
$144$	2.23198	−	2.00456i	0.185999	−	0.167047i
$145$	0.712554	−	4.27196i	0.0591744	−	0.354767i
$146$	2.95946	+	8.13105i	0.244927	+	0.672931i
$147$	−7.16974	+	12.9152i	−0.591350	+	1.06523i
$148$	5.78778	−	4.05265i	0.475753	−	0.333126i
$149$	6.51695	+	2.37197i	0.533889	+	0.194320i	0.594874	−	0.803819i	$-0.297202\pi$
$149$	6.51695	+	2.37197i	0.533889	+	0.194320i	−0.0609850	+	0.998139i	$0.519424\pi$
$150$	0.449571	−	8.64858i	0.0367074	−	0.706153i
$151$	−17.3539			−1.41224			−0.706120	−	0.708092i	$-0.749556\pi$
$151$	−17.3539			−1.41224			−0.706120	+	0.708092i	$0.749556\pi$
$152$	4.22891	−	1.05654i	0.343010	−	0.0856971i
$153$	−9.28973	+	14.2652i	−0.751030	+	1.15327i
$154$	−1.36849	−	1.63090i	−0.110276	−	0.131422i
$155$	10.5335	−	0.0975055i	0.846067	−	0.00783183i
$156$	10.1701	+	0.717658i	0.814263	+	0.0574586i
$157$	13.3594	+	9.35435i	1.06620	+	0.746559i	0.968589	−	0.248666i	$-0.0799922\pi$
$157$	13.3594	+	9.35435i	1.06620	+	0.746559i	0.0976072	+	0.995225i	$0.468881\pi$
$158$	0.708846	−	1.52012i	0.0563927	−	0.120935i
$159$	15.6713	+	6.98922i	1.24281	+	0.554282i
$160$	0.215497	+	2.22566i	0.0170365	+	0.175954i
$161$	−8.68418	+	10.3494i	−0.684410	+	0.815648i
$162$	4.34327	+	7.88264i	0.341240	+	0.619319i
$163$	3.36527	−	12.5594i	0.263588	−	0.983725i	−0.699520	−	0.714613i	$-0.746603\pi$
$163$	3.36527	−	12.5594i	0.263588	−	0.983725i	0.963109	−	0.269113i	$-0.0867304\pi$
$164$	2.80641	−	4.86084i	0.219144	−	0.379568i
$165$	2.09173	−	0.0545535i	0.162841	−	0.00424698i
$166$	0.0891098	+	0.505367i	0.00691626	+	0.0392241i
$167$	4.75543	−	3.32979i	0.367986	−	0.257667i	−0.374927	−	0.927054i	$-0.622332\pi$
$167$	4.75543	−	3.32979i	0.367986	−	0.257667i	0.742913	+	0.669387i	$0.233443\pi$
$168$	3.51161	+	5.85271i	0.270926	+	0.451546i
$169$	13.9157	+	16.5841i	1.07044	+	1.27570i
$170$	−4.44990	−	11.8826i	−0.341291	−	0.911353i
$171$	0.217892	+	13.0749i	0.0166626	+	0.999861i
$172$	5.92596	−	5.92596i	0.451851	−	0.451851i
$173$	−1.35787	+	15.5206i	−0.103237	+	1.18001i	0.751064	+	0.660229i	$0.229541\pi$
$173$	−1.35787	+	15.5206i	−0.103237	+	1.18001i	−0.854302	+	0.519778i	$0.826015\pi$
$174$	−3.25459	−	0.813658i	−0.246730	−	0.0616832i
$175$	19.1229	+	4.74636i	1.44556	+	0.358791i
$176$	−0.532059	+	0.0938164i	−0.0401055	+	0.00707167i
$177$	−2.72108	+	7.88631i	−0.204529	+	0.592771i
$178$	−12.3457	+	3.30801i	−0.925346	+	0.247946i
$179$	−6.76261	−	11.7132i	−0.505461	−	0.875484i	−0.999980	−	0.00631754i	$-0.997989\pi$
$179$	−6.76261	−	11.7132i	−0.505461	−	0.875484i	0.494519	−	0.869167i	$-0.335344\pi$
$180$	−6.65016	−	0.880521i	−0.495674	−	0.0656302i
$181$	18.5743	+	15.5857i	1.38062	+	1.15848i	0.968983	+	0.247128i	$0.0794867\pi$
$181$	18.5743	+	15.5857i	1.38062	+	1.15848i	0.411635	+	0.911349i	$0.364958\pi$
$182$	−6.00353	+	22.4055i	−0.445011	+	1.66080i
$183$	−6.59443	−	17.2118i	−0.487474	−	1.27233i
$184$	1.17259	+	3.22168i	0.0864448	+	0.237505i
$185$	−15.2980	−	3.94768i	−1.12473	−	0.290239i
$186$	0.574350	−	8.13929i	0.0421134	−	0.596802i
$187$	2.77849	−	1.29563i	0.203183	−	0.0947459i
$188$	0.270716	−	3.09430i	0.0197440	−	0.225675i
$189$	−19.4859	+	6.29034i	−1.41739	+	0.457555i
$190$	−7.94073	−	5.65197i	−0.576081	−	0.410037i
$191$			9.73152i			0.704148i	0.935972	+	0.352074i	$0.114523\pi$
$191$			9.73152i			0.704148i	−0.935972	+	0.352074i	$0.885477\pi$
$192$	1.73181	−	0.0291284i	0.124982	−	0.00210216i
$193$	−2.95417	−	6.33523i	−0.212646	−	0.456020i	0.770835	−	0.637035i	$-0.219839\pi$
$193$	−2.95417	−	6.33523i	−0.212646	−	0.456020i	−0.983480	+	0.181015i	$0.942062\pi$
$194$	−0.323125	+	1.83253i	−0.0231990	+	0.131568i
$195$	−13.5587	−	18.3275i	−0.970955	−	1.31246i
$196$	−8.01420	+	2.91693i	−0.572443	+	0.208352i
$197$	15.9410	−	4.27137i	1.13575	−	0.304322i	0.358507	−	0.933527i	$-0.383286\pi$
$197$	15.9410	−	4.27137i	1.13575	−	0.304322i	0.777239	+	0.629205i	$0.216619\pi$
$198$	0.0868823	−	1.61847i	0.00617445	−	0.115020i
$199$	16.4235	−	19.5727i	1.16423	−	1.38747i	0.257226	−	0.966351i	$-0.417192\pi$
$199$	16.4235	−	19.5727i	1.16423	−	1.38747i	0.907003	−	0.421123i	$-0.138364\pi$
$200$	3.46948	−	3.60038i	0.245329	−	0.254585i
$201$	11.7769	−	8.54502i	0.830681	−	0.602719i
$202$	−1.69987	−	6.34402i	−0.119603	−	0.446363i
$203$	3.22563	−	6.91738i	0.226395	−	0.485505i
$204$	−9.44943	+	2.70309i	−0.661593	+	0.189254i
$205$	−12.3393	+	2.29371i	−0.861812	+	0.160200i
$206$	4.52859	−	12.4422i	0.315522	−	0.866889i
$207$	−10.2102	+	1.24049i	−0.709660	+	0.0862204i
$208$	4.16227	+	4.16227i	0.288601	+	0.288601i
$209$	1.21193	−	2.01918i	0.0838309	−	0.139670i
$210$	4.84422	−	14.4728i	0.334283	−	0.998717i
$211$	−0.877461	+	0.736277i	−0.0604069	+	0.0506874i	−0.672491	−	0.740105i	$-0.734776\pi$
$211$	−0.877461	+	0.736277i	−0.0604069	+	0.0506874i	0.612084	+	0.790792i	$0.290331\pi$
$212$	4.18682	+	8.97866i	0.287552	+	0.616657i
$213$	−0.283643	+	0.246251i	−0.0194349	+	0.0168728i
$214$	−12.4301	+	2.19176i	−0.849702	+	0.149825i
$215$	−18.6826	−	1.46039i	−1.27414	−	0.0995977i
$216$	−1.09002	+	5.08054i	−0.0741667	+	0.345687i
$217$	17.9314	+	4.80469i	1.21726	+	0.326164i
$218$	12.6756	−	1.10897i	0.858502	−	0.0751092i
$219$	−12.4197	−	8.38865i	−0.839243	−	0.566852i
$220$	0.932586	+	0.767935i	0.0628750	+	0.0517742i
$221$	−28.9268	−	16.7009i	−1.94583	−	1.12342i
$222$	−3.99163	+	11.5687i	−0.267901	+	0.776438i
$223$	12.0675	−	17.2341i	0.808096	−	1.15408i	−0.177359	−	0.984146i	$-0.556755\pi$
$223$	12.0675	−	17.2341i	0.808096	−	1.15408i	0.985455	−	0.169935i	$-0.0543558\pi$
$224$	−0.684282	+	3.88076i	−0.0457205	+	0.259294i
$225$	8.16693	+	12.5818i	0.544462	+	0.838785i
$226$	−3.32723	+	2.79187i	−0.221324	+	0.185713i
$227$	−16.1379	−	16.1379i	−1.07111	−	1.07111i	−0.997270	−	0.0738373i	$-0.976475\pi$
$227$	−16.1379	−	16.1379i	−1.07111	−	1.07111i	−0.0738373	−	0.997270i	$-0.523525\pi$
$228$	−4.85383	+	5.78276i	−0.321453	+	0.382972i
$229$			3.29214i			0.217551i	0.994066	+	0.108775i	$0.0346929\pi$
$229$			3.29214i			0.217551i	−0.994066	+	0.108775i	$0.965307\pi$
$230$	3.77149	−	6.67434i	0.248685	−	0.440093i
$231$	3.57742	+	0.894364i	0.235377	+	0.0588448i
$232$	−1.11094	−	1.58659i	−0.0729371	−	0.104165i
$233$	23.4908	+	16.4484i	1.53893	+	1.07757i	0.966189	+	0.257836i	$0.0830094\pi$
$233$	23.4908	+	16.4484i	1.53893	+	1.07757i	0.572743	+	0.819735i	$0.305879\pi$
$234$	−14.9876	+	9.33882i	−0.979768	+	0.610498i
$235$	−5.65229	+	4.03626i	−0.368715	+	0.263297i
$236$	−4.17128	+	2.40829i	−0.271527	+	0.156766i
$237$	0.552511	+	2.85210i	0.0358895	+	0.185264i
$238$	−1.94888	−	22.2758i	−0.126327	−	1.44393i
$239$	−0.526737	−	0.912335i	−0.0340718	−	0.0590140i	0.848487	−	0.529217i	$-0.177514\pi$
$239$	−0.526737	−	0.912335i	−0.0340718	−	0.0590140i	−0.882558	+	0.470203i	$0.844181\pi$
$240$	−2.56601	−	2.90096i	−0.165635	−	0.187256i
$241$	−4.73866	+	1.72473i	−0.305244	+	0.111100i	−0.490101	−	0.871666i	$-0.663040\pi$
$241$	−4.73866	+	1.72473i	−0.305244	+	0.111100i	0.184857	+	0.982765i	$0.440818\pi$
$242$	6.14192	−	8.77157i	0.394818	−	0.563858i
$243$	−14.1069	−	6.63280i	−0.904961	−	0.425494i
$244$	3.63964	−	9.99983i	0.233004	−	0.640174i
$245$	16.6030	+	9.38191i	1.06073	+	0.599388i
$246$	1.01005	+	9.66908i	0.0643986	+	0.616478i
$247$	−25.5946	+	1.80210i	−1.62854	+	0.114665i
$248$	3.33111	−	3.33111i	0.211526	−	0.211526i
$249$	−0.638974	−	0.617835i	−0.0404933	−	0.0391537i
$250$	−11.1606	−	0.664804i	−0.705856	−	0.0420459i
$251$	−20.0005	−	3.52664i	−1.26242	−	0.222599i	−0.497922	−	0.867222i	$-0.665904\pi$
$251$	−20.0005	−	3.52664i	−1.26242	−	0.222599i	−0.764501	+	0.644622i	$0.777015\pi$
$252$	−10.8762	−	4.63300i	−0.685137	−	0.291851i
$253$	1.67873	+	0.782804i	0.105541	+	0.0492145i
$254$	0.0727726	−	0.126046i	0.00456616	−	0.00790882i
$255$	18.3251	+	12.1319i	1.14756	+	0.759729i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.10926	+	12.6789i	0.0691937	+	0.790888i	0.948943	+	0.315449i	$0.102155\pi$
$257$	1.10926	+	12.6789i	0.0691937	+	0.790888i	−0.879749	+	0.475439i	$0.842289\pi$
$258$	−2.27984	+	14.3354i	−0.141937	+	0.892485i
$259$	−24.1126	−	13.9214i	−1.49828	−	0.865033i
$260$	1.02575	−	13.1222i	0.0636141	−	0.813806i
$261$	5.39027	−	2.16985i	0.333649	−	0.134310i
$262$	−3.33166	−	4.75811i	−0.205831	−	0.293957i
$263$	1.78274	−	0.831305i	0.109928	−	0.0512604i	−0.366876	−	0.930270i	$-0.619573\pi$
$263$	1.78274	−	0.831305i	0.109928	−	0.0512604i	0.476805	+	0.879009i	$0.341795\pi$
$264$	0.650468	−	0.672723i	0.0400335	−	0.0414033i
$265$	9.17577	−	20.1627i	0.563663	−	1.23858i
$266$	−10.8161	−	13.3437i	−0.663179	−	0.818153i
$267$	13.9426	−	17.1953i	0.853272	−	1.05234i
$268$	8.36870	+	0.732166i	0.511200	+	0.0447242i
$269$	23.3897	+	8.51314i	1.42609	+	0.519056i	0.935809	−	0.352507i	$-0.114671\pi$
$269$	23.3897	+	8.51314i	1.42609	+	0.519056i	0.490284	+	0.871563i	$0.336893\pi$
$270$	10.2185	−	5.53003i	0.621881	−	0.336547i
$271$	2.26449	+	12.8426i	0.137558	+	0.780131i	0.973044	+	0.230619i	$0.0740751\pi$
$271$	2.26449	+	12.8426i	0.137558	+	0.780131i	−0.835486	+	0.549512i	$0.814814\pi$
$272$	−5.14281	−	2.39813i	−0.311828	−	0.145408i
$273$	−14.3741	−	37.5170i	−0.869960	−	2.27063i
$274$	−9.52528	+	5.49942i	−0.575443	+	0.332232i
$275$	−0.0500069	−	2.70087i	−0.00301553	−	0.162869i
$276$	−4.92091	−	3.32374i	−0.296204	−	0.200066i
$277$	−30.1582	−	8.08087i	−1.81203	−	0.485533i	−0.816284	−	0.577651i	$-0.803970\pi$
$277$	−30.1582	−	8.08087i	−1.81203	−	0.485533i	−0.995748	+	0.0921184i	$0.970636\pi$
$278$	2.04979	+	7.64993i	0.122938	+	0.458812i
$279$	7.47397	+	11.9947i	0.447455	+	0.718106i
$280$	7.58988	−	4.47620i	0.453582	−	0.267504i
$281$	11.9492	+	2.10697i	0.712831	+	0.125691i	0.518292	−	0.855203i	$-0.326568\pi$
$281$	11.9492	+	2.10697i	0.712831	+	0.125691i	0.194539	+	0.980895i	$0.437679\pi$
$282$	2.76795	+	4.61328i	0.164829	+	0.274717i
$283$	−24.5707	−	2.14965i	−1.46057	−	0.127784i	−0.671008	−	0.741450i	$-0.734139\pi$
$283$	−24.5707	−	2.14965i	−1.46057	−	0.127784i	−0.789566	+	0.613666i	$0.789694\pi$
$284$	−0.216866			−0.0128687
$285$	16.8812	−	0.153653i	0.999959	−	0.00910162i
$286$	3.18019			0.188049
$287$	−22.0339	−	1.92771i	−1.30062	−	0.113789i
$288$	−2.39820	+	1.80240i	−0.141315	+	0.106207i
$289$	14.9686	+	2.63936i	0.880505	+	0.155257i
$290$	−1.08217	+	4.19360i	−0.0635471	+	0.246257i
$291$	−1.41103	−	2.89771i	−0.0827161	−	0.169867i
$292$	−2.23953	−	8.35805i	−0.131059	−	0.489118i
$293$	−21.3272	−	5.71459i	−1.24595	−	0.333850i	−0.425177	−	0.905110i	$-0.639788\pi$
$293$	−21.3272	−	5.71459i	−1.24595	−	0.333850i	−0.820769	+	0.571260i	$0.806455\pi$
$294$	8.26809	−	12.2412i	0.482205	−	0.713919i
$295$	10.1543	+	3.58978i	0.591208	+	0.209005i
$296$	−6.11897	+	3.53279i	−0.355658	+	0.205339i
$297$	1.52448	+	2.35732i	0.0884594	+	0.136785i
$298$	−6.28541	−	2.93094i	−0.364104	−	0.169785i
$299$	−3.50438	−	19.8744i	−0.202664	−	1.14936i
$300$	−1.20163	+	8.57648i	−0.0693764	+	0.495164i
$301$	−31.0331	−	11.2951i	−1.78872	−	0.651040i
$302$	17.2879	+	1.51249i	0.994805	+	0.0870341i
$303$	8.83609	+	7.16462i	0.507620	+	0.411597i
$304$	−4.30491	+	0.683950i	−0.246903	+	0.0392272i
$305$	−22.2840	+	8.34511i	−1.27598	+	0.477840i
$306$	10.4977	−	13.4013i	0.600112	−	0.766100i
$307$	1.92059	−	0.895587i	0.109614	−	0.0511139i	−0.367038	−	0.930206i	$-0.619628\pi$
$307$	1.92059	−	0.895587i	0.109614	−	0.0511139i	0.476652	+	0.879092i	$0.341850\pi$
$308$	1.22114	+	1.74397i	0.0695808	+	0.0993717i
$309$	6.30735	+	22.0492i	0.358813	+	1.25433i
$310$	−10.5019	−	0.820917i	−0.596466	−	0.0466249i
$311$	25.6407	+	14.8036i	1.45395	+	0.839437i	0.998702	−	0.0509286i	$-0.0162181\pi$
$311$	25.6407	+	14.8036i	1.45395	+	0.839437i	0.455246	+	0.890366i	$0.349551\pi$
$312$	−10.0689	−	1.60131i	−0.570039	−	0.0906565i
$313$	0.0440209	+	0.503162i	0.00248821	+	0.0284404i	0.997337	−	0.0729267i	$-0.0232339\pi$
$313$	0.0440209	+	0.503162i	0.00248821	+	0.0284404i	−0.994849	+	0.101367i	$0.967678\pi$
$314$	−12.4933	−	10.4831i	−0.705037	−	0.591596i
$315$	7.93034	+	25.2169i	0.446824	+	1.42081i
$316$	−0.838636	+	1.45256i	−0.0471769	+	0.0817129i
$317$	−24.0748	−	11.2263i	−1.35217	−	0.630529i	−0.394636	−	0.918837i	$-0.629129\pi$
$317$	−24.0748	−	11.2263i	−1.35217	−	0.630529i	−0.957538	+	0.288308i	$0.906907\pi$
$318$	−15.0025	−	8.32847i	−0.841297	−	0.467037i
$319$	−1.03053	−	0.181710i	−0.0576986	−	0.0101738i
$320$	−0.0206978	−	2.23597i	−0.00115704	−	0.124995i
$321$	15.1964	−	15.7163i	0.848178	−	0.877198i
$322$	9.55315	−	9.55315i	0.532376	−	0.532376i
$323$	22.5912	−	10.0712i	1.25701	−	0.560379i
$324$	−3.63973	−	8.23118i	−0.202207	−	0.457288i
$325$	−23.7924	+	17.3247i	−1.31976	+	0.961003i
$326$	−4.44709	+	12.2183i	−0.246301	+	0.676707i
$327$	−16.6420	+	14.4481i	−0.920305	+	0.798983i
$328$	−3.21938	+	4.59775i	−0.177761	+	0.253868i
$329$	−11.5019	+	4.18634i	−0.634119	+	0.230800i
$330$	−2.08853	−	0.127961i	−0.114970	−	0.00704401i
$331$	4.81975	+	8.34804i	0.264917	+	0.458850i	0.967542	−	0.252711i	$-0.0813221\pi$
$331$	4.81975	+	8.34804i	0.264917	+	0.458850i	−0.702625	+	0.711561i	$0.747989\pi$
$332$	−0.0447251	−	0.511210i	−0.00245461	−	0.0280563i
$333$	−6.17157	−	20.2784i	−0.338200	−	1.11125i
$334$	−5.02755	+	2.90266i	−0.275095	+	0.158826i
$335$	−10.9163	−	15.2869i	−0.596421	−	0.835215i
$336$	−2.98815	−	6.13650i	−0.163017	−	0.334773i
$337$	10.1127	+	7.08101i	0.550875	+	0.385727i	0.815617	−	0.578592i	$-0.196398\pi$
$337$	10.1127	+	7.08101i	0.550875	+	0.385727i	−0.264742	+	0.964319i	$0.585287\pi$
$338$	−12.4173	−	17.7338i	−0.675414	−	0.964591i
$339$	1.82461	−	7.29834i	0.0990990	−	0.396392i
$340$	3.39733	+	12.2252i	0.184246	+	0.663005i
$341$		−	2.54515i		−	0.137827i
$342$	0.922488	−	13.0441i	0.0498825	−	0.705345i
$343$	4.25916	+	4.25916i	0.229973	+	0.229973i
$344$	−6.41990	+	5.38693i	−0.346138	+	0.290444i
$345$	1.50175	+	13.1931i	0.0808518	+	0.710292i
$346$	2.70541	−	15.3432i	0.145444	−	0.824853i
$347$	−7.88082	+	11.2550i	−0.423065	+	0.604199i	−0.972943	−	0.231046i	$-0.925785\pi$
$347$	−7.88082	+	11.2550i	−0.423065	+	0.604199i	0.549878	+	0.835245i	$0.314674\pi$
$348$	3.17129	+	1.09422i	0.169999	+	0.0586562i
$349$	13.1316	+	7.58155i	0.702920	+	0.405831i	0.808434	−	0.588587i	$-0.200315\pi$
$349$	13.1316	+	7.58155i	0.702920	+	0.405831i	−0.105514	+	0.994418i	$0.533649\pi$
$350$	−18.6365	−	6.39497i	−0.996161	−	0.341825i
$351$	11.5119	−	28.3372i	0.614457	−	1.51253i
$352$	0.538211	−	0.0470874i	0.0286867	−	0.00250977i
$353$	0.599899	+	0.160742i	0.0319294	+	0.00855546i	0.274748	−	0.961516i	$-0.411405\pi$
$353$	0.599899	+	0.160742i	0.0319294	+	0.00855546i	−0.242819	+	0.970072i	$0.578072\pi$
$354$	3.39806	−	7.61914i	0.180605	−	0.404953i
$355$	0.315131	+	0.368575i	0.0167254	+	0.0195619i
$356$	12.5870	−	2.21943i	0.667109	−	0.117629i
$357$	25.3908	+	29.2462i	1.34382	+	1.54787i
$358$	5.71600	+	12.2580i	0.302100	+	0.647856i
$359$	28.0170	−	23.5091i	1.47868	−	1.24076i	0.571106	−	0.820876i	$-0.306515\pi$
$359$	28.0170	−	23.5091i	1.47868	−	1.24076i	0.907577	−	0.419886i	$-0.137930\pi$
$360$	6.54812	+	1.45677i	0.345116	+	0.0767785i
$361$	10.0530	−	16.1226i	0.529104	−	0.848557i
$362$	−17.1453	−	17.1453i	−0.901135	−	0.901135i
$363$	0.311911	+	18.5444i	0.0163711	+	0.973327i
$364$	7.93345	−	21.7970i	0.415826	−	1.14247i
$365$	−10.9506	+	15.9514i	−0.573182	+	0.834932i
$366$	5.06924	+	17.7210i	0.264973	+	0.926292i
$367$	−8.55955	+	18.3560i	−0.446805	+	0.958176i	0.545928	+	0.837832i	$0.316177\pi$
$367$	−8.55955	+	18.3560i	−0.446805	+	0.958176i	−0.992732	+	0.120343i	$0.961600\pi$
$368$	−0.887345	−	3.31162i	−0.0462561	−	0.172630i
$369$	−11.2512	−	12.5277i	−0.585715	−	0.652167i
$370$	14.8957	+	5.26596i	0.774390	+	0.273764i
$371$	25.0939	−	29.9058i	1.30281	−	1.55263i
$372$	−1.28155	+	8.05826i	−0.0664453	+	0.417801i
$373$	8.56098	−	2.29391i	0.443271	−	0.118774i	−0.0302782	−	0.999542i	$-0.509639\pi$
$373$	8.56098	−	2.29391i	0.443271	−	0.118774i	0.473549	+	0.880767i	$0.342973\pi$
$374$	−2.88084	+	1.04854i	−0.148965	+	0.0542187i
$375$	16.3223	−	10.4203i	0.842878	−	0.538104i
$376$	−0.539371	+	3.05893i	−0.0278160	+	0.157752i
$377$	4.81831	+	10.3329i	0.248155	+	0.532171i
$378$	19.9600	−	4.56809i	1.02663	−	0.234957i
$379$		−	11.1017i		−	0.570257i	−0.958489	−	0.285128i	$-0.907964\pi$
$379$		−	11.1017i		−	0.570257i	0.958489	−	0.285128i	$-0.0920362\pi$
$380$	7.41791	+	6.32255i	0.380531	+	0.324340i
$381$	0.0261915	+	0.250727i	0.00134183	+	0.0128452i
$382$	0.848158	−	9.69449i	0.0433955	−	0.496013i
$383$	−5.86919	+	2.73685i	−0.299902	+	0.139846i	−0.566745	−	0.823894i	$-0.691797\pi$
$383$	−5.86919	+	2.73685i	−0.299902	+	0.139846i	0.266843	+	0.963740i	$0.414020\pi$
$384$	−1.72775	−	0.121919i	−0.0881691	−	0.00622166i
$385$	1.18951	−	4.60956i	0.0606230	−	0.234925i
$386$	2.39077	+	6.56860i	0.121687	+	0.334333i
$387$	−11.3856	−	22.4159i	−0.578765	−	1.13947i
$388$	0.481611	−	1.79740i	0.0244501	−	0.0912489i
$389$	22.3140	+	18.7237i	1.13136	+	0.949328i	0.999122	−	0.0418897i	$-0.0133378\pi$
$389$	22.3140	+	18.7237i	1.13136	+	0.949328i	0.132242	+	0.991217i	$0.457782\pi$
$390$	11.9097	+	19.4395i	0.603072	+	0.984356i
$391$	9.72727	+	16.8481i	0.491929	+	0.852046i
$392$	8.23793	−	2.20735i	0.416078	−	0.111488i
$393$	9.51054	+	3.28150i	0.479743	+	0.165530i
$394$	−16.2526	+	2.86577i	−0.818793	+	0.144375i
$395$	3.68733	−	0.685427i	0.185530	−	0.0344876i
$396$	−0.227611	+	1.60474i	−0.0114379	+	0.0806412i
$397$	−0.0651989	+	0.745226i	−0.00327224	+	0.0374018i	−0.997655	−	0.0684395i	$-0.978198\pi$
$397$	−0.0651989	+	0.745226i	−0.00327224	+	0.0374018i	0.994383	+	0.105841i	$0.0337536\pi$
$398$	−18.0669	+	18.0669i	−0.905610	+	0.905610i
$399$	28.7361	+	7.70459i	1.43861	+	0.385712i
$400$	−3.77007	+	3.28429i	−0.188503	+	0.164215i
$401$	−12.3873	−	14.7627i	−0.618594	−	0.737212i	0.362234	−	0.932087i	$-0.382014\pi$
$401$	−12.3873	−	14.7627i	−0.618594	−	0.737212i	−0.980828	+	0.194876i	$0.937570\pi$
$402$	−12.4769	+	7.48608i	−0.622290	+	0.373372i
$403$	−22.7151	+	15.9053i	−1.13152	+	0.792298i
$404$	1.14049	+	6.46803i	0.0567414	+	0.321796i
$405$	−8.70038	+	18.1467i	−0.432325	+	0.901718i
$406$	−3.81624	+	6.60993i	−0.189397	+	0.328045i
$407$	−0.987989	+	3.68723i	−0.0489728	+	0.182769i
$408$	9.64907	−	1.86923i	0.477700	−	0.0925406i
$409$	−23.2021	+	27.6512i	−1.14727	+	1.36726i	−0.227986	+	0.973664i	$0.573214\pi$
$409$	−23.2021	+	27.6512i	−1.14727	+	1.36726i	−0.919283	+	0.393598i	$0.871230\pi$
$410$	12.4922	−	1.20955i	0.616947	−	0.0597352i
$411$	7.75961	−	17.3986i	0.382754	−	0.858211i
$412$	−5.59577	+	12.0002i	−0.275684	+	0.591206i
$413$	15.5478	+	10.8867i	0.765056	+	0.535698i
$414$	10.2795	−	0.345894i	0.505210	−	0.0169998i
$415$	−0.803836	+	0.818857i	−0.0394588	+	0.0401961i
$416$	−3.78366	−	4.50920i	−0.185509	−	0.221082i
$417$	−10.6550	−	8.63946i	−0.521777	−	0.423076i
$418$	−1.38330	+	1.90587i	−0.0676594	+	0.0932194i
$419$	−18.6260			−0.909940			−0.454970	−	0.890507i	$-0.650350\pi$
$419$	−18.6260			−0.909940			−0.454970	+	0.890507i	$0.650350\pi$
$420$	−6.08717	+	13.9955i	−0.297024	+	0.682911i
$421$	23.2256	+	8.45342i	1.13195	+	0.411995i	0.838998	−	0.544134i	$-0.183142\pi$
$421$	23.2256	+	8.45342i	1.13195	+	0.411995i	0.292947	+	0.956129i	$0.405364\pi$
$422$	0.938292	−	0.656999i	0.0456754	−	0.0319822i
$423$	−8.57295	−	3.65186i	−0.416831	−	0.177560i
$424$	−3.38835	−	9.30940i	−0.164553	−	0.452105i
$425$	15.8407	−	23.5385i	0.768385	−	1.14179i
$426$	0.304026	−	0.220593i	0.0147301	−	0.0106878i
$427$	−41.7750	+	3.65484i	−2.02163	+	0.176870i
$428$	12.5738	−	1.10006i	0.607777	−	0.0531736i
$429$	−4.45833	+	3.23484i	−0.215250	+	0.156180i
$430$	18.4842	+	3.08312i	0.891386	+	0.148681i
$431$	−0.641549	−	1.76264i	−0.0309024	−	0.0849035i	0.923282	−	0.384123i	$-0.125496\pi$
$431$	−0.641549	−	1.76264i	−0.0309024	−	0.0849035i	−0.954184	+	0.299219i	$0.903274\pi$
$432$	1.52867	−	4.96620i	0.0735484	−	0.238936i
$433$	−21.5772	+	15.1085i	−1.03694	+	0.726070i	−0.962535	−	0.271158i	$-0.912593\pi$
$433$	−21.5772	+	15.1085i	−1.03694	+	0.726070i	−0.0744008	+	0.997228i	$0.523704\pi$
$434$	−17.4444	−	6.34923i	−0.837357	−	0.304773i
$435$	−2.74856	−	6.97979i	−0.131784	−	0.334655i
$436$	−12.7241			−0.609372
$437$	13.4349	+	6.54466i	0.642679	+	0.313074i
$438$	11.6413	+	9.43917i	0.556242	+	0.451021i
$439$	5.79376	+	6.90474i	0.276521	+	0.329545i	0.886374	−	0.462969i	$-0.153216\pi$
$439$	5.79376	+	6.90474i	0.276521	+	0.329545i	−0.609853	+	0.792514i	$0.708772\pi$
$440$	−0.862108	−	0.846293i	−0.0410994	−	0.0403455i
$441$	0.860440	+	25.5711i	0.0409733	+	1.21767i
$442$	27.3611	+	19.1585i	1.30144	+	0.911276i
$443$	−10.5975	+	22.7265i	−0.503504	+	1.07977i	0.476203	+	0.879335i	$0.342013\pi$
$443$	−10.5975	+	22.7265i	−0.503504	+	1.07977i	−0.979707	+	0.200433i	$0.935765\pi$
$444$	4.98472	−	11.1767i	0.236564	−	0.530425i
$445$	−22.0623	−	18.1671i	−1.04585	−	0.861205i
$446$	−13.5236	+	16.1168i	−0.640360	+	0.763152i
$447$	11.7929	−	2.28453i	0.557783	−	0.108054i
$448$	1.01991	−	3.80635i	0.0481862	−	0.179833i
$449$	2.52683	−	4.37659i	0.119248	−	0.206544i	−0.800222	−	0.599704i	$-0.795285\pi$
$449$	2.52683	−	4.37659i	0.119248	−	0.206544i	0.919470	+	0.393160i	$0.128618\pi$
$450$	−7.03928	−	13.2457i	−0.331835	−	0.624408i
$451$	0.526574	+	2.98635i	0.0247954	+	0.140622i
$452$	3.55789	−	2.49126i	0.167349	−	0.117179i
$453$	−25.7744	+	15.4646i	−1.21099	+	0.726588i
$454$	14.6699	+	17.4830i	0.688495	+	0.820516i
$455$	−48.5732	+	18.1901i	−2.27715	+	0.852766i
$456$	5.33937	−	5.33771i	0.250039	−	0.249961i
$457$	5.05214	−	5.05214i	0.236329	−	0.236329i	−0.578999	−	0.815328i	$-0.696557\pi$
$457$	5.05214	−	5.05214i	0.236329	−	0.236329i	0.815328	+	0.578999i	$0.196557\pi$
$458$	0.286929	−	3.27961i	0.0134073	−	0.153246i
$459$	−1.08517	+	29.4654i	−0.0506516	+	1.37533i
$460$	−4.33885	+	6.32023i	−0.202300	+	0.294682i
$461$	−13.3490	+	2.35378i	−0.621723	+	0.109627i	−0.475632	−	0.879645i	$-0.657781\pi$
$461$	−13.3490	+	2.35378i	−0.621723	+	0.109627i	−0.146091	+	0.989271i	$0.546669\pi$
$462$	−3.48585	−	1.20275i	−0.162177	−	0.0559571i
$463$	25.3442	−	6.79095i	1.17784	−	0.315602i	0.383773	−	0.923427i	$-0.374625\pi$
$463$	25.3442	−	6.79095i	1.17784	−	0.315602i	0.794071	+	0.607825i	$0.207958\pi$
$464$	0.968436	+	1.67738i	0.0449585	+	0.0778704i
$465$	15.5576	−	9.53148i	0.721469	−	0.442012i
$466$	−21.9678	−	18.4332i	−1.01764	−	0.853900i
$467$	4.33348	−	16.1728i	0.200530	−	0.748387i	−0.790236	−	0.612803i	$-0.790042\pi$
$467$	4.33348	−	16.1728i	0.200530	−	0.748387i	0.990766	−	0.135585i	$-0.0432913\pi$
$468$	15.7445	−	7.99703i	0.727788	−	0.369663i
$469$	−11.3222	−	31.1075i	−0.522810	−	1.43641i
$470$	5.98257	−	3.52827i	0.275955	−	0.162747i
$471$	28.1776	+	1.98836i	1.29836	+	0.0916187i
$472$	4.36530	−	2.03557i	0.200929	−	0.0936948i
$473$	−0.394619	+	4.51052i	−0.0181446	+	0.207394i
$474$	−0.301832	−	2.88940i	−0.0138636	−	0.132714i
$475$	−0.0335660	−	21.7945i	−0.00154011	−	0.999999i
$476$			22.3609i			1.02491i
$477$	29.5036	−	3.58455i	1.35088	−	0.164125i
$478$	0.445217	+	0.954771i	0.0203638	+	0.0436702i
$479$	2.68352	−	15.2190i	0.122613	−	0.695373i	−0.860084	−	0.510152i	$-0.829589\pi$
$479$	2.68352	−	15.2190i	0.122613	−	0.695373i	0.982697	−	0.185220i	$-0.0592999\pi$
$480$	2.30341	+	3.11357i	0.105136	+	0.142114i
$481$	39.0822	−	14.2247i	1.78199	−	0.648592i
$482$	4.87095	−	1.30517i	0.221866	−	0.0594488i
$483$	−3.67530	+	23.1099i	−0.167232	+	1.05154i
$484$	−6.88304	+	8.20289i	−0.312866	+	0.372859i
$485$	−3.75460	+	1.79329i	−0.170487	+	0.0814293i
$486$	13.4752	+	7.83706i	0.611246	+	0.355496i
$487$	−2.09257	−	7.80956i	−0.0948232	−	0.353885i	0.902169	−	0.431382i	$-0.141974\pi$
$487$	−2.09257	−	7.80956i	−0.0948232	−	0.353885i	−0.996993	+	0.0774969i	$0.975307\pi$
$488$	−4.49733	+	9.64457i	−0.203585	+	0.436589i
$489$	−6.19383	−	21.6524i	−0.280095	−	0.979153i
$490$	−15.7221	−	10.7933i	−0.710253	−	0.487589i
$491$	−10.5402	+	28.9589i	−0.475671	+	1.30690i	0.437463	+	0.899237i	$0.355877\pi$
$491$	−10.5402	+	28.9589i	−0.475671	+	1.30690i	−0.913134	+	0.407660i	$0.866345\pi$
$492$	−0.163493	−	9.72031i	−0.00737082	−	0.438226i
$493$	−7.77160	−	7.77160i	−0.350015	−	0.350015i
$494$	25.6543	+	0.435468i	1.15424	+	0.0195926i
$495$	3.05808	−	1.94503i	0.137450	−	0.0874225i
$496$	−3.60876	+	3.02811i	−0.162038	+	0.135966i
$497$	0.361165	+	0.774521i	0.0162005	+	0.0347420i
$498$	0.582695	+	0.671174i	0.0261112	+	0.0300760i
$499$	−8.25635	+	1.45582i	−0.369605	+	0.0651713i	−0.355366	−	0.934727i	$-0.615644\pi$
$499$	−8.25635	+	1.45582i	−0.369605	+	0.0651713i	−0.0142391	+	0.999899i	$0.504533\pi$
$500$	11.0601	+	1.63498i	0.494625	+	0.0731186i
$501$	4.09561	−	9.18319i	0.182978	−	0.410274i
$502$	19.6171	+	5.25638i	0.875553	+	0.234604i
$503$	−42.9410	+	3.75685i	−1.91464	+	0.167510i	−0.981431	−	0.191816i	$-0.938562\pi$
$503$	−42.9410	+	3.75685i	−1.91464	+	0.167510i	−0.933212	+	0.359326i	$0.883007\pi$
$504$	10.4310	+	5.56329i	0.464635	+	0.247809i
$505$	9.33548	−	11.3371i	0.415424	−	0.504493i
$506$	−1.60411	−	0.926136i	−0.0713116	−	0.0411718i
$507$	35.4465	+	12.2304i	1.57423	+	0.543170i
$508$	−0.0834813	+	0.119224i	−0.00370388	+	0.00528969i
$509$	−7.35153	+	41.6926i	−0.325851	+	1.84799i	0.177778	+	0.984071i	$0.443109\pi$
$509$	−7.35153	+	41.6926i	−0.325851	+	1.84799i	−0.503628	+	0.863920i	$0.668002\pi$
$510$	−17.1980	−	13.6829i	−0.761541	−	0.605888i
$511$	−26.1204	+	21.9176i	−1.15550	+	0.969579i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	11.9750	+	19.2250i	0.528710	+	0.848802i
$514$		−	12.7273i		−	0.561378i
$515$	28.5261	−	7.92728i	1.25701	−	0.349318i
$516$	3.52058	−	14.0822i	0.154985	−	0.619933i
$517$	0.962537	+	1.37465i	0.0423323	+	0.0604568i
$518$	22.8075	+	15.9700i	1.00210	+	0.701680i
$519$	11.8141	+	24.2615i	0.518580	+	1.06496i
$520$	−2.16552	+	12.9829i	−0.0949643	+	0.569337i
$521$	−13.3719	+	7.72028i	−0.585835	+	0.338232i	−0.763449	−	0.645868i	$-0.776495\pi$
$521$	−13.3719	+	7.72028i	−0.585835	+	0.338232i	0.177614	+	0.984100i	$0.443162\pi$
$522$	−5.55887	+	1.69180i	−0.243305	+	0.0740481i
$523$	0.0782775	+	0.894716i	0.00342284	+	0.0391232i	0.997714	−	0.0675773i	$-0.0215269\pi$
$523$	0.0782775	+	0.894716i	0.00342284	+	0.0391232i	−0.994291	+	0.106701i	$0.965971\pi$
$524$	2.90429	+	5.03037i	0.126874	+	0.219753i
$525$	32.6314	−	9.99157i	1.42415	−	0.436068i
$526$	−1.84841	+	0.672765i	−0.0805944	+	0.0293340i
$527$	15.3328	−	21.8974i	0.667905	−	0.953868i
$528$	−0.706624	+	0.613472i	−0.0307519	+	0.0266979i
$529$	3.84629	−	10.5676i	0.167230	−	0.459461i
$530$	−10.8982	+	19.2863i	−0.473385	+	0.837741i
$531$	2.98631	+	14.1378i	0.129595	+	0.613527i
$532$	9.61198	+	14.2356i	0.416732	+	0.617191i
$533$	23.3621	−	23.3621i	1.01192	−	1.01192i
$534$	−15.3882	+	15.9147i	−0.665913	+	0.688697i
$535$	−20.1407	−	19.7713i	−0.870760	−	0.854787i
$536$	−8.27304	−	1.45876i	−0.357341	−	0.0630089i
$537$	−20.4819	−	11.3703i	−0.883861	−	0.490666i
$538$	−22.5587	−	10.5193i	−0.972575	−	0.453519i
$539$	2.30384	−	3.99037i	0.0992335	−	0.171877i
$540$	−10.6616	+	4.61838i	−0.458804	+	0.198744i
$541$	0.598588	+	0.502275i	0.0257353	+	0.0215945i	0.655565	−	0.755139i	$-0.272431\pi$
$541$	0.598588	+	0.502275i	0.0257353	+	0.0215945i	−0.629829	+	0.776734i	$0.716875\pi$
$542$	−1.13657	−	12.9911i	−0.0488199	−	0.558014i
$543$	41.4759	+	6.59614i	1.77990	+	0.283068i
$544$	4.91423	+	2.83723i	0.210696	+	0.121645i
$545$	18.4895	+	21.6252i	0.792001	+	0.926320i
$546$	11.0496	+	38.6271i	0.472878	+	1.65309i
$547$	−10.4111	−	14.8686i	−0.445147	−	0.635736i	0.532390	−	0.846499i	$-0.321294\pi$
$547$	−10.4111	−	14.8686i	−0.445147	−	0.635736i	−0.977537	+	0.210763i	$0.932405\pi$
$548$	9.96834	−	4.64831i	0.425826	−	0.198566i
$549$	−25.1321	−	19.6868i	−1.07261	−	0.840213i
$550$	−0.185580	+	2.69495i	−0.00791315	+	0.114913i
$551$	−8.28829	−	1.60695i	−0.353093	−	0.0684583i
$552$	4.61250	+	3.73998i	0.196321	+	0.159184i
$553$	6.58435	+	0.576056i	0.279995	+	0.0244964i
$554$	29.3392	+	10.6786i	1.24650	+	0.453690i
$555$	−26.2388	+	7.76928i	−1.11377	+	0.329787i
$556$	−1.37526	−	7.79947i	−0.0583239	−	0.330771i
$557$	−33.8302	−	15.7753i	−1.43343	−	0.668419i	−0.458045	−	0.888929i	$-0.651450\pi$
$557$	−33.8302	−	15.7753i	−1.43343	−	0.668419i	−0.975385	+	0.220509i	$0.929228\pi$
$558$	−6.40012	−	12.6005i	−0.270939	−	0.533421i
$559$	42.7218	−	24.6655i	1.80694	−	1.04324i
$560$	−7.95113	+	3.79766i	−0.335996	+	0.160481i
$561$	2.97210	−	4.40029i	0.125482	−	0.185781i
$562$	−11.7201	−	3.14040i	−0.494384	−	0.132470i
$563$	0.297346	+	1.10971i	0.0125317	+	0.0467688i	0.971909	−	0.235359i	$-0.0756265\pi$
$563$	0.297346	+	1.10971i	0.0125317	+	0.0467688i	−0.959377	+	0.282128i	$0.908960\pi$
$564$	−2.35534	−	4.83697i	−0.0991779	−	0.203673i
$565$	−9.40404	−	2.42673i	−0.395631	−	0.102093i
$566$	24.2898	+	4.28295i	1.02098	+	0.180026i
$567$	−23.3355	+	26.7070i	−0.979998	+	1.12159i
$568$	0.216041	+	0.0189011i	0.00906488	+	0.000793075i
$569$	22.1912			0.930305			0.465152	−	0.885231i	$-0.346000\pi$
$569$	22.1912			0.930305			0.465152	+	0.885231i	$0.346000\pi$
$570$	−16.8304	−	1.31823i	−0.704948	−	0.0552145i
$571$	6.09318			0.254992			0.127496	−	0.991839i	$-0.459306\pi$
$571$	6.09318			0.254992			0.127496	+	0.991839i	$0.459306\pi$
$572$	−3.16809	−	0.277172i	−0.132465	−	0.0115891i
$573$	8.67204	+	14.4535i	0.362280	+	0.603803i
$574$	21.7820	+	3.84075i	0.909163	+	0.160310i
$575$	17.0464	−	1.80991i	0.710883	−	0.0754785i
$576$	2.54616	−	1.58652i	0.106090	−	0.0661052i
$577$	−1.72749	−	6.44708i	−0.0719164	−	0.268396i	0.920600	−	0.390507i	$-0.127700\pi$
$577$	−1.72749	−	6.44708i	−0.0719164	−	0.268396i	−0.992516	+	0.122111i	$0.961034\pi$
$578$	−14.6816	−	3.93392i	−0.610673	−	0.163629i
$579$	−10.0331	−	6.77669i	−0.416962	−	0.281630i
$580$	1.44355	−	4.08333i	0.0599400	−	0.169551i
$581$	−1.75126	+	1.01109i	−0.0726546	+	0.0419471i
$582$	1.15311	+	3.00966i	0.0477979	+	0.124755i
$583$	−4.85088	−	2.26200i	−0.200903	−	0.0936825i
$584$	1.50256	+	8.52143i	0.0621763	+	0.352619i
$585$	−36.4698	−	15.1379i	−1.50784	−	0.625877i
$586$	20.7479	+	7.55163i	0.857089	+	0.311955i
$587$	−19.6341	−	1.71776i	−0.810386	−	0.0708996i	−0.325573	−	0.945517i	$-0.605557\pi$
$587$	−19.6341	−	1.71776i	−0.810386	−	0.0708996i	−0.484814	+	0.874617i	$0.661113\pi$
$588$	−9.30352	+	11.4740i	−0.383670	+	0.473179i
$589$	0.348510	−	20.5314i	0.0143601	−	0.845982i
$590$	−9.80282	−	4.46113i	−0.403576	−	0.183662i
$591$	19.8695	−	20.5494i	0.817324	−	0.845289i
$592$	6.40359	−	2.98604i	0.263186	−	0.122726i
$593$	15.5545	+	22.2142i	0.638747	+	0.912226i	0.999793	−	0.0203221i	$-0.00646916\pi$
$593$	15.5545	+	22.2142i	0.638747	+	0.912226i	−0.361046	+	0.932548i	$0.617580\pi$
$594$	−1.31323	−	2.48121i	−0.0538823	−	0.101805i
$595$	38.0035	−	32.4929i	1.55799	−	1.33208i
$596$	6.00605	+	3.46759i	0.246017	+	0.142038i
$597$	6.95070	−	43.7053i	0.284473	−	1.78874i
$598$	1.75889	+	20.1042i	0.0719262	+	0.822120i
$599$	8.70265	+	7.30239i	0.355581	+	0.298368i	0.803026	−	0.595944i	$-0.203222\pi$
$599$	8.70265	+	7.30239i	0.355581	+	0.298368i	−0.447446	+	0.894311i	$0.647666\pi$
$600$	1.94455	−	8.43912i	0.0793860	−	0.344526i
$601$	−12.8669	+	22.2862i	−0.524852	+	0.909071i	0.474729	+	0.880132i	$0.342546\pi$
$601$	−12.8669	+	22.2862i	−0.524852	+	0.909071i	−0.999581	+	0.0289390i	$0.990787\pi$
$602$	29.9306	+	13.9569i	1.21988	+	0.568839i
$603$	9.87667	−	23.1860i	0.402209	−	0.944208i
$604$	−17.0903	−	3.01347i	−0.695393	−	0.122616i
$605$	23.9430	−	0.221635i	0.973423	−	0.00901073i
$606$	−8.17803	−	7.90748i	−0.332210	−	0.321219i
$607$	−15.7383	+	15.7383i	−0.638798	+	0.638798i	−0.950259	−	0.311461i	$-0.899182\pi$
$607$	−15.7383	+	15.7383i	−0.638798	+	0.638798i	0.311461	+	0.950259i	$0.399182\pi$
$608$	4.34813	−	0.306150i	0.176340	−	0.0124160i
$609$	−1.37350	−	13.1483i	−0.0556570	−	0.532797i
$610$	22.9265	−	6.37118i	0.928269	−	0.257961i
$611$	6.25338	−	17.1810i	0.252985	−	0.695069i
$612$	−11.6257	+	12.4354i	−0.469942	+	0.502669i
$613$	−10.5104	+	15.0104i	−0.424510	+	0.606263i	−0.973255	−	0.229727i	$-0.926217\pi$
$613$	−10.5104	+	15.0104i	−0.424510	+	0.606263i	0.548745	+	0.835990i	$0.315106\pi$
$614$	−1.99134	+	0.724789i	−0.0803640	+	0.0292501i
$615$	−16.2826	+	14.4026i	−0.656577	+	0.580767i
$616$	−1.06449	−	1.84376i	−0.0428897	−	0.0742872i
$617$	−1.59734	−	18.2577i	−0.0643065	−	0.735027i	−0.958079	−	0.286505i	$-0.907506\pi$
$617$	−1.59734	−	18.2577i	−0.0643065	−	0.735027i	0.893772	−	0.448521i	$-0.148049\pi$
$618$	−4.36164	−	22.5150i	−0.175451	−	0.905687i
$619$	9.47538	−	5.47061i	0.380848	−	0.219883i	−0.297339	−	0.954772i	$-0.596099\pi$
$619$	9.47538	−	5.47061i	0.380848	−	0.219883i	0.678187	+	0.734889i	$0.262766\pi$
$620$	10.3904	+	1.73309i	0.417287	+	0.0696026i
$621$	−14.0590	+	10.9410i	−0.564170	+	0.439049i
$622$	−24.2529	−	16.9820i	−0.972451	−	0.680918i
$623$	−28.8886	−	41.2572i	−1.15740	−	1.65294i
$624$	9.89102	+	2.47278i	0.395958	+	0.0989905i
$625$	−13.2929	−	21.1731i	−0.531715	−	0.846923i
$626$		−	0.505084i		−	0.0201872i
$627$	0.000631181	−	4.07893i	2.52069e−5	−	0.162897i
$628$	11.5321	+	11.5321i	0.460180	+	0.460180i
$629$	−30.7133	+	25.7715i	−1.22462	+	1.02758i
$630$	−5.70236	−	25.8121i	−0.227188	−	1.02838i
$631$	−3.97599	+	22.5489i	−0.158282	+	0.897659i	0.797443	+	0.603395i	$0.206186\pi$
$631$	−3.97599	+	22.5489i	−0.158282	+	0.897659i	−0.955724	+	0.294264i	$0.904925\pi$
$632$	0.962043	−	1.37394i	0.0382680	−	0.0546524i
$633$	−0.647108	+	1.87547i	−0.0257202	+	0.0745431i
$634$	23.0047	+	13.2818i	0.913635	+	0.527487i
$635$	0.323934	−	0.0313645i	0.0128549	−	0.00124466i
$636$	14.2195	+	9.60433i	0.563840	+	0.380836i
$637$	−50.0108	+	4.37538i	−1.98150	+	0.173359i
$638$	1.01077	+	0.270836i	0.0400168	+	0.0107225i
$639$	−0.201832	+	0.618501i	−0.00798435	+	0.0244675i
$640$	−0.174259	+	2.22927i	−0.00688818	+	0.0881195i
$641$	−10.5572	+	1.86152i	−0.416984	+	0.0735255i	−0.378204	−	0.925722i	$-0.623458\pi$
$641$	−10.5572	+	1.86152i	−0.416984	+	0.0735255i	−0.0387797	+	0.999248i	$0.512347\pi$
$642$	−16.5083	+	14.3320i	−0.651531	+	0.565641i
$643$	1.28256	+	2.75046i	0.0505792	+	0.108467i	0.929973	−	0.367627i	$-0.119830\pi$
$643$	1.28256	+	2.75046i	0.0505792	+	0.108467i	−0.879394	+	0.476095i	$0.842052\pi$
$644$	−10.3494	+	8.68418i	−0.407824	+	0.342205i
$645$	−29.0492	+	14.4796i	−1.14381	+	0.570132i
$646$	−23.3830	+	8.06397i	−0.919990	+	0.317273i
$647$	10.1217	+	10.1217i	0.397923	+	0.397923i	0.877500	−	0.479577i	$-0.159210\pi$
$647$	10.1217	+	10.1217i	0.397923	+	0.397923i	−0.479577	+	0.877500i	$0.659210\pi$
$648$	2.90848	+	8.51708i	0.114256	+	0.334583i
$649$	0.890017	−	2.44530i	0.0349362	−	0.0959865i
$650$	25.2118	−	15.1852i	0.988888	−	0.595611i
$651$	30.9137	−	8.84311i	1.21160	−	0.346589i
$652$	5.49506	−	11.7842i	0.215203	−	0.461504i
$653$	−5.32876	−	19.8872i	−0.208530	−	0.778246i	−0.988344	−	0.152235i	$-0.951353\pi$
$653$	−5.32876	−	19.8872i	−0.208530	−	0.778246i	0.779814	−	0.626011i	$-0.215314\pi$
$654$	17.8379	−	12.9427i	0.697518	−	0.506100i
$655$	4.32912	−	12.2457i	0.169153	−	0.478478i
$656$	3.60785	−	4.29967i	0.140863	−	0.167874i
$657$	−25.9213	−	1.39150i	−1.01129	−	0.0542877i
$658$	11.8230	−	3.16796i	0.460907	−	0.123500i
$659$	27.5638	−	10.0324i	1.07373	−	0.390807i	0.256161	−	0.966634i	$-0.417542\pi$
$659$	27.5638	−	10.0324i	1.07373	−	0.390807i	0.817571	+	0.575827i	$0.195320\pi$
$660$	2.06943	+	0.309501i	0.0805524	+	0.0120473i
$661$	0.479316	−	2.71834i	0.0186432	−	0.105731i	−0.974066	−	0.226263i	$-0.927349\pi$
$661$	0.479316	−	2.71834i	0.0186432	−	0.105731i	0.992709	+	0.120532i	$0.0384601\pi$
$662$	−4.07382	−	8.73635i	−0.158334	−	0.339548i
$663$	−57.8454	+	0.972942i	−2.24653	+	0.0377859i
$664$			0.513163i			0.0199146i
$665$	10.2268	−	37.0219i	0.396579	−	1.43565i
$666$	4.38070	+	20.7391i	0.169749	+	0.803624i
$667$	0.578753	−	6.61518i	0.0224094	−	0.256141i
$668$	5.26140	−	2.45343i	0.203570	−	0.0949261i
$669$	2.56505	−	36.3502i	0.0991707	−	1.40538i
$670$	9.54241	+	16.1802i	0.368655	+	0.625095i
$671$	1.96638	+	5.40258i	0.0759112	+	0.208564i
$672$	2.44194	+	6.37358i	0.0942000	+	0.245866i
$673$	2.74657	−	10.2504i	0.105873	−	0.395122i	−0.892570	−	0.450909i	$-0.851100\pi$
$673$	2.74657	−	10.2504i	0.105873	−	0.395122i	0.998443	+	0.0557866i	$0.0177666\pi$
$674$	−9.45709	−	7.93544i	−0.364274	−	0.305662i
$675$	23.3417	+	11.4090i	0.898423	+	0.439131i
$676$	10.8245	+	18.7486i	0.416326	+	0.721098i
$677$	19.1734	−	5.13751i	0.736895	−	0.197450i	0.129197	−	0.991619i	$-0.458760\pi$
$677$	19.1734	−	5.13751i	0.736895	−	0.197450i	0.607698	+	0.794168i	$0.292093\pi$
$678$	−2.45376	+	7.11155i	−0.0942359	+	0.273117i
$679$	−7.22132	+	1.27331i	−0.277129	+	0.0488653i
$680$	−2.31890	−	12.4748i	−0.0889258	−	0.478386i
$681$	−38.3493	−	9.58742i	−1.46955	−	0.367391i
$682$	−0.221824	+	2.53546i	−0.00849409	+	0.0970878i
$683$	3.91138	−	3.91138i	0.149665	−	0.149665i	−0.628303	−	0.777968i	$-0.716250\pi$
$683$	3.91138	−	3.91138i	0.149665	−	0.149665i	0.777968	+	0.628303i	$0.216250\pi$
$684$	−2.05585	+	12.9141i	−0.0786073	+	0.493782i
$685$	−22.3851	−	10.1872i	−0.855292	−	0.389232i
$686$	−3.87175	−	4.61417i	−0.147824	−	0.176170i
$687$	2.93372	+	4.88956i	0.111928	+	0.186548i
$688$	6.86497	−	4.80690i	0.261724	−	0.183261i
$689$	10.1263	+	57.4292i	0.385782	+	2.18788i
$690$	−0.346187	−	13.2738i	−0.0131791	−	0.505324i
$691$	7.45546	−	12.9132i	0.283619	−	0.491243i	−0.688654	−	0.725090i	$-0.741798\pi$
$691$	7.45546	−	12.9132i	0.283619	−	0.491243i	0.972273	+	0.233847i	$0.0751316\pi$
$692$	−4.03236	+	15.0490i	−0.153287	+	0.572076i
$693$	6.11026	−	1.85961i	0.232109	−	0.0706407i
$694$	8.83177	−	10.5253i	0.335249	−	0.399535i
$695$	−11.2572	+	13.6708i	−0.427009	+	0.518563i
$696$	−3.06386	−	1.36645i	−0.116135	−	0.0517952i
$697$	−13.4603	+	28.8657i	−0.509844	+	1.09336i
$698$	−12.4209	−	8.69720i	−0.470137	−	0.329194i
$699$	49.5467	+	3.49627i	1.87403	+	0.132241i
$700$	18.0082	+	7.99491i	0.680645	+	0.302179i
$701$	−3.73702	−	4.45360i	−0.141145	−	0.168210i	0.690841	−	0.723007i	$-0.257241\pi$
$701$	−3.73702	−	4.45360i	−0.141145	−	0.168210i	−0.831986	+	0.554797i	$0.812796\pi$
$702$	−13.9378	+	27.2261i	−0.526048	+	1.02758i
$703$	−8.47489	+	29.6091i	−0.319637	+	1.11673i
$704$	−0.540267			−0.0203621
$705$	−4.79809	+	11.0317i	−0.180706	+	0.415477i
$706$	−0.583607	−	0.212415i	−0.0219643	−	0.00799436i
$707$	21.2007	−	14.8449i	0.797334	−	0.558300i
$708$	−4.04918	+	7.29399i	−0.152178	+	0.274125i
$709$	10.4948	+	28.8342i	0.394140	+	1.08289i	0.965093	+	0.261909i	$0.0843519\pi$
$709$	10.4948	+	28.8342i	0.394140	+	1.08289i	−0.570952	+	0.820983i	$0.693426\pi$
$710$	−0.281808	−	0.394638i	−0.0105761	−	0.0148105i
$711$	3.36219	+	3.74364i	0.126092	+	0.140398i
$712$	−12.7325	+	1.11395i	−0.477172	+	0.0417471i
$713$	16.0896	−	1.40766i	0.602560	−	0.0527172i
$714$	−22.7452	−	31.3479i	−0.851216	−	1.17317i
$715$	4.13252	+	5.78709i	0.154547	+	0.216425i
$716$	−4.62590	−	12.7095i	−0.172878	−	0.474978i
$717$	−1.59533	−	0.885631i	−0.0595787	−	0.0330745i
$718$	−29.9594	+	20.9778i	−1.11807	+	0.782884i
$719$	−43.8056	−	15.9439i	−1.63367	−	0.594608i	−0.647757	−	0.761847i	$-0.724293\pi$
$719$	−43.8056	−	15.9439i	−1.63367	−	0.594608i	−0.985916	+	0.167239i	$0.946515\pi$
$720$	−6.39623	−	2.02193i	−0.238374	−	0.0753530i
$721$	52.1767			1.94316
$722$	−11.4199	+	15.1851i	−0.425005	+	0.565129i
$723$	−5.50102	+	6.78437i	−0.204585	+	0.252314i
$724$	15.5857	+	18.5743i	0.579238	+	0.690309i
$725$	−9.03745	+	3.48014i	−0.335642	+	0.129249i
$726$	1.30552	−	18.5010i	0.0484526	−	0.686636i
$727$	−3.63385	−	2.54445i	−0.134772	−	0.0943685i	0.504246	−	0.863560i	$-0.331770\pi$
$727$	−3.63385	−	2.54445i	−0.134772	−	0.0943685i	−0.639018	+	0.769191i	$0.720659\pi$
$728$	−9.80299	+	21.0226i	−0.363323	+	0.779149i
$729$	−26.8627	+	2.71991i	−0.994913	+	0.100737i
$730$	12.2992	−	14.9363i	0.455214	−	0.552815i
$731$	−30.5679	+	36.4294i	−1.13060	+	1.34739i
$732$	−3.50546	−	18.0954i	−0.129565	−	0.668824i
$733$	−5.71316	+	21.3218i	−0.211020	+	0.787538i	0.776509	+	0.630106i	$0.216988\pi$
$733$	−5.71316	+	21.3218i	−0.211020	+	0.787538i	−0.987530	+	0.157433i	$0.949678\pi$
$734$	10.1268	−	17.5401i	0.373787	−	0.647418i
$735$	33.0196	−	0.861169i	1.21795	−	0.0317647i
$736$	0.595342	+	3.37635i	0.0219446	+	0.124454i
$737$	−3.71781	+	2.60324i	−0.136947	+	0.0958914i
$738$	10.1165	+	13.4607i	0.372395	+	0.495494i
$739$	13.0289	+	15.5273i	0.479276	+	0.571179i	0.950456	−	0.310858i	$-0.100616\pi$
$739$	13.0289	+	15.5273i	0.479276	+	0.571179i	−0.471180	+	0.882037i	$0.656172\pi$
$740$	−14.3800	−	6.54416i	−0.528621	−	0.240568i
$741$	−36.4078	+	25.4846i	−1.33747	+	0.936200i
$742$	−27.6049	+	27.6049i	−1.01341	+	1.01341i
$743$	−3.13457	+	35.8283i	−0.114996	+	1.31441i	0.691156	+	0.722706i	$0.257102\pi$
$743$	−3.13457	+	35.8283i	−0.114996	+	1.31441i	−0.806152	+	0.591709i	$0.798454\pi$
$744$	1.97900	−	7.91590i	0.0725535	−	0.290211i
$745$	−2.83411	−	15.2464i	−0.103834	−	0.558584i
$746$	−8.72833	+	1.53904i	−0.319567	+	0.0563483i
$747$	−1.49959	−	0.348215i	−0.0548671	−	0.0127405i
$748$	2.96126	−	0.793468i	0.108274	−	0.0290120i
$749$	−24.8689	−	43.0743i	−0.908691	−	1.57390i
$750$	−17.1683	+	8.95811i	−0.626899	+	0.327104i
$751$	21.0713	+	17.6810i	0.768904	+	0.645187i	0.940428	−	0.339993i	$-0.110425\pi$
$751$	21.0713	+	17.6810i	0.768904	+	0.645187i	−0.171524	+	0.985180i	$0.554869\pi$
$752$	0.803922	−	3.00028i	0.0293160	−	0.109409i
$753$	−32.8480	+	12.5852i	−1.19705	+	0.458631i
$754$	−3.89940	−	10.7135i	−0.142008	−	0.390163i
$755$	19.7125	+	33.4246i	0.717411	+	1.21645i
$756$	−20.2822	+	2.81108i	−0.737657	+	0.102238i
$757$	22.5497	−	10.5151i	0.819584	−	0.382178i	0.0328423	−	0.999461i	$-0.489544\pi$
$757$	22.5497	−	10.5151i	0.819584	−	0.382178i	0.786742	+	0.617282i	$0.211766\pi$
$758$	−0.967578	+	11.0595i	−0.0351440	+	0.401698i
$759$	3.19087	−	0.333325i	0.115821	−	0.0120989i
$760$	−6.83864	−	6.94500i	−0.248063	−	0.251922i
$761$			14.7009i			0.532907i	0.963848	+	0.266453i	$0.0858518\pi$
$761$			14.7009i			0.532907i	−0.963848	+	0.266453i	$0.914148\pi$
$762$	−0.00423951	−	0.252056i	−0.000153581	−	0.00913103i
$763$	21.1904	+	45.4429i	0.767144	+	1.64514i
$764$	−1.68986	+	9.58368i	−0.0611370	+	0.346725i
$765$	38.0280	+	1.68855i	1.37490	+	0.0610497i
$766$	6.08539	−	2.21490i	0.219874	−	0.0800276i
$767$	−27.3859	+	7.33803i	−0.988848	+	0.264961i
$768$	1.71055	+	0.272039i	0.0617243	+	0.00981636i
$769$	−6.78043	+	8.08060i	−0.244509	+	0.291394i	−0.874316	−	0.485358i	$-0.838689\pi$
$769$	−6.78043	+	8.08060i	−0.244509	+	0.291394i	0.629807	+	0.776751i	$0.283134\pi$
$770$	−1.58673	+	4.48835i	−0.0571818	+	0.161749i
$771$	12.9460	+	17.8425i	0.466240	+	0.642582i
$772$	−1.80918	−	6.75197i	−0.0651140	−	0.243009i
$773$	20.0659	−	43.0315i	0.721721	−	1.54773i	−0.110863	−	0.993836i	$-0.535362\pi$
$773$	20.0659	−	43.0315i	0.721721	−	1.54773i	0.832584	−	0.553899i	$-0.186861\pi$
$774$	9.38864	+	23.3230i	0.337468	+	0.838326i
$775$	−12.1529	−	20.1773i	−0.436544	−	0.724790i
$776$	−0.636431	+	1.74858i	−0.0228466	+	0.0627704i
$777$	−48.2183	+	0.811017i	−1.72982	+	0.0290951i
$778$	−20.5972	−	20.5972i	−0.738446	−	0.738446i
$779$	3.83889	+	24.1627i	0.137543	+	0.865717i
$780$	−10.1701	−	20.4035i	−0.364149	−	0.730563i
$781$	0.0897541	−	0.0753127i	0.00321166	−	0.00269490i
$782$	−8.22184	−	17.6318i	−0.294012	−	0.630512i
$783$	6.07214	−	8.02614i	0.217001	−	0.286831i
$784$	−8.39896	+	1.48096i	−0.299963	+	0.0528916i
$785$	2.84195	−	36.3567i	0.101434	−	1.29763i
$786$	−9.18835	−	4.09791i	−0.327738	−	0.146168i
$787$	−22.9446	−	6.14799i	−0.817888	−	0.219152i	−0.174465	−	0.984663i	$-0.555820\pi$
$787$	−22.9446	−	6.14799i	−0.817888	−	0.219152i	−0.643423	+	0.765511i	$0.722486\pi$
$788$	16.4405	−	1.43836i	0.585668	−	0.0512393i
$789$	1.90697	−	2.82332i	0.0678898	−	0.100513i
$790$	−3.73304	+	0.361447i	−0.132815	+	0.0128597i
$791$	−14.8226	−	8.55783i	−0.527031	−	0.304281i
$792$	0.366607	−	1.57880i	0.0130268	−	0.0561000i
$793$	35.9289	−	51.3117i	1.27587	−	1.82213i
$794$	0.129902	−	0.736708i	0.00461003	−	0.0261448i
$795$	−4.33949	−	38.1229i	−0.153906	−	1.35208i
$796$	19.5727	−	16.4235i	0.693737	−	0.582115i
$797$	−24.2492	−	24.2492i	−0.858951	−	0.858951i	0.132264	−	0.991215i	$-0.457775\pi$
$797$	−24.2492	−	24.2492i	−0.858951	−	0.858951i	−0.991215	+	0.132264i	$0.957775\pi$
$798$	−27.9553	−	10.1798i	−0.989606	−	0.360361i
$799$			17.6255i			0.623547i
$800$	4.04197	−	2.94321i	0.142905	−	0.104058i
$801$	5.38462	−	37.9635i	0.190256	−	1.34138i
$802$	11.0535	+	15.7861i	0.390314	+	0.557427i
$803$	3.82943	+	2.68139i	0.135138	+	0.0946243i
$804$	13.0818	−	6.37016i	0.461361	−	0.224658i
$805$	29.7980	+	4.97025i	1.05024	+	0.175178i
$806$	24.0149	−	13.8650i	0.845888	−	0.488373i
$807$	42.3252	−	8.19929i	1.48992	−	0.288629i
$808$	−0.572422	−	6.54282i	−0.0201377	−	0.230175i
$809$	7.82424	+	13.5520i	0.275086	+	0.476462i	0.970157	−	0.242479i	$-0.0779605\pi$
$809$	7.82424	+	13.5520i	0.275086	+	0.476462i	−0.695071	+	0.718941i	$0.744627\pi$
$810$	10.2489	−	17.3194i	0.360108	−	0.608541i
$811$	16.7815	−	6.10798i	0.589280	−	0.214480i	−0.0301328	−	0.999546i	$-0.509593\pi$
$811$	16.7815	−	6.10798i	0.589280	−	0.214480i	0.619413	+	0.785066i	$0.287371\pi$
$812$	4.37782	−	6.25217i	0.153631	−	0.219408i
$813$	14.8077	+	17.0561i	0.519327	+	0.598185i
$814$	1.30559	−	3.58709i	0.0457610	−	0.125727i
$815$	−28.0127	+	7.78460i	−0.981243	+	0.272683i
$816$	−9.77526	+	1.02114i	−0.342203	+	0.0357472i
$817$	−3.80098	+	36.3318i	−0.132979	+	1.27109i
$818$	25.5237	−	25.5237i	0.892417	−	0.892417i
$819$	−54.7813	−	42.9120i	−1.91421	−	1.49947i
$820$	−12.5501	+	0.116173i	−0.438269	+	0.00405694i
$821$	−49.1610	−	8.66841i	−1.71573	−	0.302530i	−0.772586	−	0.634910i	$-0.781037\pi$
$821$	−49.1610	−	8.66841i	−1.71573	−	0.302530i	−0.943145	+	0.332381i	$0.892148\pi$
$822$	−9.24648	+	16.6561i	−0.322508	+	0.580949i
$823$	36.2498	+	16.9035i	1.26359	+	0.589220i	0.934797	−	0.355183i	$-0.115581\pi$
$823$	36.2498	+	16.9035i	1.26359	+	0.589220i	0.328790	+	0.944403i	$0.393359\pi$
$824$	6.62036	−	11.4668i	0.230631	−	0.399465i
$825$	−2.48110	−	3.96684i	−0.0863807	−	0.138108i
$826$	−14.5398	−	12.2003i	−0.505903	−	0.424503i
$827$	4.21057	+	48.1270i	0.146416	+	1.67354i	0.613781	+	0.789476i	$0.289648\pi$
$827$	4.21057	+	48.1270i	0.146416	+	1.67354i	−0.467366	+	0.884064i	$0.654797\pi$
$828$	−10.2705	−	0.551340i	−0.356926	−	0.0191604i
$829$	25.0598	+	14.4683i	0.870362	+	0.502504i	0.867469	−	0.497492i	$-0.165746\pi$
$829$	25.0598	+	14.4683i	0.870362	+	0.502504i	0.00289374	+	0.999996i	$0.499079\pi$
$830$	0.872146	−	0.745682i	0.0302726	−	0.0258830i
$831$	−51.9928	+	14.8730i	−1.80361	+	0.515937i
$832$	3.37626	+	4.82181i	0.117051	+	0.167166i
$833$	43.8606	−	20.4525i	1.51968	−	0.708638i
$834$	9.86147	+	9.53522i	0.341475	+	0.330178i
$835$	−11.8151	−	5.37690i	−0.408879	−	0.186075i
$836$	1.54414	−	1.77806i	0.0534054	−	0.0614955i
$837$	21.7894	+	11.1546i	0.753151	+	0.385559i
$838$	18.5551	+	1.62336i	0.640976	+	0.0560781i
$839$	34.9337	+	12.7148i	1.20605	+	0.438965i	0.865330	−	0.501202i	$-0.167109\pi$
$839$	34.9337	+	12.7148i	1.20605	+	0.438965i	0.340715	+	0.940167i	$0.389331\pi$
$840$	7.28380	−	13.4117i	0.251315	−	0.462748i
$841$	−4.38436	−	24.8649i	−0.151185	−	0.857412i
$842$	−22.4004	−	10.4455i	−0.771970	−	0.359976i
$843$	19.6249	−	7.51898i	0.675916	−	0.258967i
$844$	−0.991983	+	0.572722i	−0.0341455	+	0.0197139i
$845$	16.1349	−	45.6405i	0.555058	−	1.57008i
$846$	8.22205	+	4.38515i	0.282680	+	0.150765i
$847$	40.7588	+	10.9213i	1.40049	+	0.375260i
$848$	2.56408	+	9.56929i	0.0880510	+	0.328611i
$849$	−38.4085	+	18.7029i	−1.31818	+	0.641882i
$850$	−17.8319	+	22.0683i	−0.611629	+	0.756937i
$851$	−23.8559	−	4.20643i	−0.817769	−	0.144195i
$852$	−0.322095	+	0.193256i	−0.0110348	+	0.00662084i
$853$	−12.0005	−	1.04991i	−0.410890	−	0.0359482i	−0.120163	−	0.992754i	$-0.538342\pi$
$853$	−12.0005	−	1.04991i	−0.410890	−	0.0359482i	−0.290727	+	0.956806i	$0.593897\pi$
$854$	41.9346			1.43497
$855$	24.9355	−	15.2716i	0.852776	−	0.522277i
$856$	−12.6218			−0.431405
$857$	33.1762	+	2.90254i	1.13328	+	0.0991488i	0.638321	−	0.769770i	$-0.279629\pi$
$857$	33.1762	+	2.90254i	1.13328	+	0.0991488i	0.494955	+	0.868919i	$0.335185\pi$
$858$	4.72330	−	2.83396i	0.161251	−	0.0967499i
$859$	−35.9836	−	6.34488i	−1.22775	−	0.216485i	−0.478089	−	0.878312i	$-0.658670\pi$
$859$	−35.9836	−	6.34488i	−1.22775	−	0.216485i	−0.749657	+	0.661827i	$0.769781\pi$
$860$	−18.1451	−	4.68239i	−0.618744	−	0.159668i
$861$	−34.4430	+	16.7719i	−1.17382	+	0.571586i
$862$	0.485484	+	1.81185i	0.0165356	+	0.0617119i
$863$	−3.05665	−	0.819026i	−0.104049	−	0.0278800i	0.206419	−	0.978464i	$-0.433819\pi$
$863$	−3.05665	−	0.819026i	−0.104049	−	0.0278800i	−0.310468	+	0.950584i	$0.600486\pi$
$864$	−1.95569	+	4.81407i	−0.0665339	+	0.163778i
$865$	31.4360	−	15.0146i	1.06885	−	0.510513i
$866$	22.8119	−	13.1705i	0.775181	−	0.447551i
$867$	24.5837	−	9.41889i	0.834906	−	0.319882i
$868$	16.8246	+	7.84545i	0.571065	+	0.266292i
$869$	−0.157356	−	0.892408i	−0.00533792	−	0.0302729i
$870$	2.12978	+	7.19279i	0.0722062	+	0.243858i
$871$	46.4670	+	16.9126i	1.57447	+	0.573062i
$872$	12.6756	+	1.10897i	0.429251	+	0.0375546i
$873$	−4.67793	−	3.04634i	−0.158324	−	0.103103i
$874$	−12.8134	−	7.69069i	−0.433419	−	0.260141i
$875$	−12.5801	−	42.2233i	−0.425287	−	1.42741i
$876$	−10.7743	−	10.4179i	−0.364030	−	0.351987i
$877$	36.1506	−	16.8573i	1.22072	−	0.569230i	0.297949	−	0.954582i	$-0.403698\pi$
$877$	36.1506	−	16.8573i	1.22072	−	0.569230i	0.922770	+	0.385351i	$0.125920\pi$
$878$	−5.16993	−	7.38342i	−0.174477	−	0.249178i
$879$	−36.7680	+	10.5178i	−1.24016	+	0.354756i
$880$	0.785068	+	0.918211i	0.0264646	+	0.0309529i
$881$	16.5954	+	9.58136i	0.559113	+	0.322804i	0.752789	−	0.658261i	$-0.228708\pi$
$881$	16.5954	+	9.58136i	0.559113	+	0.322804i	−0.193676	+	0.981065i	$0.562041\pi$
$882$	1.37150	−	25.5488i	0.0461809	−	0.860273i
$883$	3.84878	+	43.9917i	0.129522	+	1.48044i	0.731453	+	0.681892i	$0.238843\pi$
$883$	3.84878	+	43.9917i	0.129522	+	1.48044i	−0.601931	+	0.798548i	$0.705602\pi$
$884$	−25.5873	−	21.4703i	−0.860592	−	0.722123i
$885$	18.2804	−	3.71719i	0.614489	−	0.124952i
$886$	12.5380	−	21.7164i	0.421221	−	0.729576i
$887$	0.584959	+	0.272771i	0.0196410	+	0.00915875i	0.432414	−	0.901675i	$-0.357662\pi$
$887$	0.584959	+	0.272771i	0.0196410	+	0.00915875i	−0.412773	+	0.910834i	$0.635440\pi$
$888$	−5.93987	+	10.6998i	−0.199329	+	0.359061i
$889$	0.564826	+	0.0995940i	0.0189436	+	0.00334028i
$890$	20.3950	+	20.0209i	0.683642	+	0.671101i
$891$	4.36487	+	2.14263i	0.146229	+	0.0717809i
$892$	14.8768	−	14.8768i	0.498112	−	0.498112i
$893$	7.57644	+	11.2209i	0.253536	+	0.375493i
$894$	−11.9471	+	1.24802i	−0.399570	+	0.0417400i
$895$	−14.8786	+	26.3303i	−0.497336	+	0.880126i
$896$	−1.34777	+	3.70298i	−0.0450259	+	0.123708i
$897$	−22.9154	−	26.3950i	−0.765123	−	0.881303i
$898$	−2.89866	+	4.13971i	−0.0967294	+	0.138144i
$899$	−8.57415	+	3.12074i	−0.285964	+	0.104082i
$900$	5.85806	+	13.8088i	0.195269	+	0.460294i
$901$	−28.1080	−	48.6846i	−0.936415	−	1.62192i
$902$	−0.264293	−	3.02088i	−0.00879999	−	0.100584i
$903$	−56.1565	+	10.8787i	−1.86877	+	0.362021i
$904$	−3.76148	+	2.17169i	−0.125105	+	0.0722294i
$905$	8.92023	−	53.4792i	0.296518	−	1.77771i
$906$	27.0242	−	13.1593i	0.897818	−	0.437189i
$907$	−38.5427	−	26.9879i	−1.27979	−	0.896118i	−0.281798	−	0.959474i	$-0.590931\pi$
$907$	−38.5427	−	26.9879i	−1.27979	−	0.896118i	−0.997991	+	0.0633558i	$0.979820\pi$
$908$	−13.0904	−	18.6950i	−0.434420	−	0.620415i
$909$	19.5082	+	2.76697i	0.647045	+	0.0917747i
$910$	49.9738	−	13.8875i	1.65661	−	0.460365i
$911$		−	9.53352i		−	0.315860i	−0.987450	−	0.157930i	$-0.949518\pi$
$911$		−	9.53352i		−	0.315860i	0.987450	−	0.157930i	$-0.0504820\pi$
$912$	−5.78426	+	4.85205i	−0.191536	+	0.160667i
$913$	0.196042	+	0.196042i	0.00648803	+	0.00648803i
$914$	−5.47324	+	4.59259i	−0.181039	+	0.151909i
$915$	−25.6602	+	32.2523i	−0.848299	+	1.06623i
$916$	−0.571674	+	3.24212i	−0.0188886	+	0.107123i
$917$	13.1288	−	18.7499i	0.433552	−	0.619177i
$918$	3.64912	−	29.2587i	0.120439	−	0.965680i
$919$	−19.0442	−	10.9952i	−0.628209	−	0.362697i	0.151849	−	0.988404i	$-0.451477\pi$
$919$	−19.0442	−	10.9952i	−0.628209	−	0.362697i	−0.780058	+	0.625707i	$0.784811\pi$
$920$	4.87318	−	5.91803i	0.160664	−	0.195112i
$921$	2.05443	−	3.04164i	0.0676957	−	0.100226i
$922$	13.5033	−	1.18139i	0.444708	−	0.0389069i
$923$	−1.23305	−	0.330395i	−0.0405864	−	0.0108751i
$924$	3.36776	+	1.50199i	0.110791	+	0.0494118i
$925$	9.77366	+	33.9490i	0.321356	+	1.11624i
$926$	−25.8396	+	4.55622i	−0.849142	+	0.149727i
$927$	29.0165	+	27.1273i	0.953027	+	0.890978i
$928$	−0.818558	−	1.75540i	−0.0268705	−	0.0576239i
$929$	−22.9131	+	19.2263i	−0.751753	+	0.630796i	−0.935966	−	0.352091i	$-0.885471\pi$
$929$	−22.9131	+	19.2263i	−0.751753	+	0.630796i	0.184213	+	0.982886i	$0.441026\pi$
$930$	−16.3292	+	8.13927i	−0.535454	+	0.266897i
$931$	19.1312	−	31.8744i	0.627001	−	1.04464i
$932$	20.2777	+	20.2777i	0.664217	+	0.664217i
$933$	51.2741	−	0.862414i	1.67864	−	0.0282342i
$934$	−5.72655	+	15.7336i	−0.187378	+	0.514818i
$935$	−5.65158	−	3.87981i	−0.184826	−	0.126883i
$936$	−16.3815	+	6.59438i	−0.535447	+	0.215544i
$937$	21.7462	−	46.6348i	0.710417	−	1.52349i	−0.135847	−	0.990730i	$-0.543376\pi$
$937$	21.7462	−	46.6348i	0.710417	−	1.52349i	0.846264	−	0.532764i	$-0.178847\pi$
$938$	8.56792	+	31.9759i	0.279752	+	1.04405i
$939$	0.513763	+	0.708079i	0.0167660	+	0.0231073i
$940$	−6.26731	+	2.99343i	−0.204417	+	0.0976349i
$941$	−1.65556	+	1.97302i	−0.0539697	+	0.0643186i	−0.792354	−	0.610062i	$-0.791145\pi$
$941$	−1.65556	+	1.97302i	−0.0539697	+	0.0643186i	0.738384	+	0.674380i	$0.235589\pi$
$942$	−27.8971	−	4.43664i	−0.908937	−	0.144553i
$943$	−18.5875	+	4.98051i	−0.605293	+	0.162188i
$944$	−4.52610	+	1.64737i	−0.147312	+	0.0536172i
$945$	34.2499	+	30.3858i	1.11415	+	0.988451i
$946$	0.786236	−	4.45896i	0.0255627	−	0.144973i
$947$	13.4805	+	28.9091i	0.438059	+	0.939420i	0.994121	+	0.108279i	$0.0345341\pi$
$947$	13.4805	+	28.9091i	0.438059	+	0.939420i	−0.556062	+	0.831141i	$0.687688\pi$
$948$	0.0488563	+	2.90471i	0.00158678	+	0.0943406i
$949$		−	50.9338i		−	1.65338i
$950$	−1.86607	+	21.7145i	−0.0605435	+	0.704510i
$951$	−45.7605	+	4.78023i	−1.48388	+	0.155010i
$952$	1.94888	−	22.2758i	0.0631637	−	0.721964i
$953$	−32.5716	+	15.1884i	−1.05510	+	0.492001i	−0.871192	−	0.490943i	$-0.836652\pi$
$953$	−32.5716	+	15.1884i	−1.05510	+	0.492001i	−0.183907	+	0.982944i	$0.558875\pi$
$954$	−29.7038	+	0.999499i	−0.961695	+	0.0323600i
$955$	18.7435	−	11.0541i	0.606525	−	0.357704i
$956$	−0.360309	−	0.989941i	−0.0116532	−	0.0320170i
$957$	−1.69250	+	0.648455i	−0.0547106	+	0.0209616i
$958$	−3.99973	+	14.9272i	−0.129225	+	0.482275i
$959$	−33.2022	−	27.8599i	−1.07215	−	0.899644i
$960$	−2.02328	−	3.30247i	−0.0653011	−	0.106587i
$961$	4.40368	+	7.62740i	0.142054	+	0.246045i
$962$	−40.1732	+	10.7644i	−1.29524	+	0.347057i
$963$	8.56474	−	36.8841i	0.275995	−	1.18857i
$964$	−4.96617	+	0.875670i	−0.159950	+	0.0282034i
$965$	−8.84636	+	12.8862i	−0.284774	+	0.414820i
$966$	5.67548	−	22.7016i	0.182605	−	0.730414i
$967$	−2.50831	+	28.6701i	−0.0806618	+	0.921969i	0.842787	+	0.538247i	$0.180913\pi$
$967$	−2.50831	+	28.6701i	−0.0806618	+	0.921969i	−0.923449	+	0.383721i	$0.874642\pi$
$968$	7.57178	−	7.57178i	0.243366	−	0.243366i
$969$	24.5782	−	35.0897i	0.789564	−	1.12724i
$970$	3.89661	−	1.45923i	0.125112	−	0.0468532i
$971$	15.6307	+	18.6279i	0.501612	+	0.597797i	0.956131	−	0.292939i	$-0.0946334\pi$
$971$	15.6307	+	18.6279i	0.501612	+	0.597797i	−0.454519	+	0.890737i	$0.650189\pi$
$972$	−12.7409	−	8.98168i	−0.408663	−	0.288088i
$973$	−25.5648	+	17.9007i	−0.819571	+	0.573870i
$974$	1.40395	+	7.96222i	0.0449856	+	0.255126i
$975$	−19.8984	+	46.9332i	−0.637260	+	1.50306i
$976$	5.32080	−	9.21590i	0.170315	−	0.294994i
$977$	−11.2101	+	41.8366i	−0.358642	+	1.33847i	0.517196	+	0.855867i	$0.326976\pi$
$977$	−11.2101	+	41.8366i	−0.358642	+	1.33847i	−0.875839	+	0.482604i	$0.839691\pi$
$978$	4.28313	+	22.1098i	0.136960	+	0.706993i
$979$	−4.43860	+	5.28972i	−0.141858	+	0.169060i
$980$	14.7216	+	12.1225i	0.470264	+	0.387237i
$981$	−11.8420	+	36.2889i	−0.378085	+	1.15861i
$982$	13.0240	−	27.9301i	0.415612	−	0.891284i
$983$	9.77077	+	6.84157i	0.311639	+	0.218212i	0.718923	−	0.695089i	$-0.244635\pi$
$983$	9.77077	+	6.84157i	0.311639	+	0.218212i	−0.407284	+	0.913302i	$0.633524\pi$
$984$	−0.684311	+	9.69758i	−0.0218150	+	0.309147i
$985$	−26.3344	−	25.8513i	−0.839084	−	0.823692i
$986$	7.06469	+	8.41937i	0.224986	+	0.268127i
$987$	−13.3523	+	16.4673i	−0.425008	+	0.524160i
$988$	−25.5187	−	2.66973i	−0.811857	−	0.0849353i
$989$	−28.7323			−0.913634
$990$	−3.21596	+	1.67110i	−0.102210	+	0.0531110i
$991$	−25.1838	−	9.16614i	−0.799989	−	0.291172i	−0.0905070	−	0.995896i	$-0.528849\pi$
$991$	−25.1838	−	9.16614i	−0.799989	−	0.291172i	−0.709482	+	0.704724i	$0.751071\pi$
$992$	3.85895	−	2.70206i	0.122522	−	0.0857906i
$993$	14.5976	+	8.10370i	0.463240	+	0.257163i
$994$	−0.292287	−	0.803051i	−0.00927077	−	0.0254712i
$995$	−56.3539	−	9.39971i	−1.78654	−	0.297991i
$996$	−0.521981	−	0.719405i	−0.0165396	−	0.0227952i
$997$	−24.6609	+	2.15755i	−0.781018	+	0.0683303i	−0.470689	−	0.882299i	$-0.655995\pi$
$997$	−24.6609	+	2.15755i	−0.781018	+	0.0683303i	−0.310329	+	0.950629i	$0.600439\pi$
$998$	8.35181	−	0.730689i	0.264372	−	0.0231296i
$999$	−27.2368	−	24.6183i	−0.861735	−	0.778888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.443.17	yes	480
3.2	odd	2	inner	570.2.bi.a.443.22	yes	480
5.2	odd	4	inner	570.2.bi.a.557.27	yes	480
15.2	even	4	inner	570.2.bi.a.557.12	yes	480
19.16	even	9	inner	570.2.bi.a.263.12	✓	480
57.35	odd	18	inner	570.2.bi.a.263.27	yes	480
95.92	odd	36	inner	570.2.bi.a.377.22	yes	480
285.92	even	36	inner	570.2.bi.a.377.17	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.263.12	✓	480	19.16	even	9	inner
570.2.bi.a.263.27	yes	480	57.35	odd	18	inner
570.2.bi.a.377.17	yes	480	285.92	even	36	inner
570.2.bi.a.377.22	yes	480	95.92	odd	36	inner
570.2.bi.a.443.17	yes	480	1.1	even	1	trivial
570.2.bi.a.443.22	yes	480	3.2	odd	2	inner
570.2.bi.a.557.12	yes	480	15.2	even	4	inner
570.2.bi.a.557.27	yes	480	5.2	odd	4	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(1.48522 - 0.891129i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.13591 - 1.92606i) q^{5} +(-1.55724 + 0.758292i) q^{6} +(-1.01991 - 3.80635i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.41178 - 2.64705i) q^{9} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(1.48522 - 0.891129i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-1.13591 - 1.92606i) q^{5} +(-1.55724 + 0.758292i) q^{6} +(-1.01991 - 3.80635i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.41178 - 2.64705i) q^{9} +(0.963721 + 2.01773i) q^{10} +(-0.467885 + 0.270133i) q^{11} +(1.61740 - 0.619684i) q^{12} +(5.33483 + 2.48767i) q^{13} +(0.684282 + 3.88076i) q^{14} +(-3.40345 - 1.84839i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-5.65287 - 0.494562i) q^{17} +(-1.63711 + 2.51393i) q^{18} +(-3.81136 + 2.11507i) q^{19} +(-0.784197 - 2.09405i) q^{20} +(-4.90674 - 4.74441i) q^{21} +(0.489648 - 0.228327i) q^{22} +(-1.96647 - 2.80841i) q^{23} +(-1.66526 + 0.476360i) q^{24} +(-2.41941 + 4.37566i) q^{25} +(-5.09772 - 2.94317i) q^{26} +(-0.262057 - 5.18954i) q^{27} +(-0.343448 - 3.92563i) q^{28} +(1.48373 + 1.24500i) q^{29} +(3.22940 + 2.13798i) q^{30} +(-2.35545 + 4.07976i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-0.454190 + 0.818154i) q^{33} +(5.58825 + 0.985360i) q^{34} +(-6.17274 + 6.28808i) q^{35} +(1.84999 - 2.36168i) q^{36} +(4.99612 - 4.99612i) q^{37} +(3.98120 - 1.77484i) q^{38} +(10.1403 - 1.05927i) q^{39} +(0.598705 + 2.15443i) q^{40} +(1.91970 - 5.27433i) q^{41} +(4.47457 + 5.15401i) q^{42} +(4.80690 - 6.86497i) q^{43} +(-0.507685 + 0.184782i) q^{44} +(-6.70203 + 0.287645i) q^{45} +(1.71422 + 2.96911i) q^{46} +(-0.270716 - 3.09430i) q^{47} +(1.70044 - 0.329411i) q^{48} +(-7.38592 + 4.26427i) q^{49} +(2.79157 - 4.14815i) q^{50} +(-8.83649 + 4.30290i) q^{51} +(4.82181 + 3.37626i) q^{52} +(5.68234 + 8.11522i) q^{53} +(-0.191238 + 5.19263i) q^{54} +(1.05177 + 0.594327i) q^{55} +3.94063i q^{56} +(-3.77593 + 6.53776i) q^{57} +(-1.36958 - 1.36958i) q^{58} +(-3.68971 + 3.09603i) q^{59} +(-3.03077 - 2.41131i) q^{60} +(1.84789 - 10.4799i) q^{61} +(2.70206 - 3.85895i) q^{62} +(-11.5155 - 2.67397i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.26849 - 13.1010i) q^{65} +(0.523768 - 0.775456i) q^{66} +(8.36870 - 0.732166i) q^{67} +(-5.48111 - 1.46866i) q^{68} +(-5.42331 - 2.41874i) q^{69} +(6.69729 - 5.72617i) q^{70} +(-0.213572 + 0.0376584i) q^{71} +(-2.04878 + 2.19146i) q^{72} +(-3.65687 - 7.84218i) q^{73} +(-5.41254 + 4.54166i) q^{74} +(0.305912 + 8.65485i) q^{75} +(-4.12074 + 1.42110i) q^{76} +(1.50542 + 1.50542i) q^{77} +(-10.1940 + 0.171460i) q^{78} +(-0.573661 + 1.57612i) q^{79} +(-0.408656 - 2.19841i) q^{80} +(-5.01376 - 7.47410i) q^{81} +(-2.37208 + 5.08694i) q^{82} +(-0.132816 - 0.495677i) q^{83} +(-4.00834 - 5.52438i) q^{84} +(5.46860 + 11.4495i) q^{85} +(-5.38693 + 6.41990i) q^{86} +(3.31312 + 0.526905i) q^{87} +(0.521858 - 0.139831i) q^{88} +(12.0104 - 4.37142i) q^{89} +(6.70160 + 0.297571i) q^{90} +(4.02792 - 22.8435i) q^{91} +(-1.44892 - 3.10722i) q^{92} +(0.137221 + 8.15837i) q^{93} +3.10612i q^{94} +(8.40312 + 4.93839i) q^{95} +(-1.72268 + 0.179954i) q^{96} +(0.162180 - 1.85372i) q^{97} +(7.72947 - 3.60431i) q^{98} +(0.0545073 + 1.61988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more