LMFDB - Embedded newform 750.2.o.a.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.3
Character	$\chi$	$=$	750.229
Dual form			750.2.o.a.619.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.20346 + 1.88459i) q^{5} +(0.425779 + 0.904827i) q^{6} +(-2.69851 + 3.71418i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.20346 + 1.88459i) q^{5} +(0.425779 + 0.904827i) q^{6} +(-2.69851 + 3.71418i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(2.12467 + 0.696977i) q^{10} +(2.44813 - 0.628572i) q^{11} +(0.770513 - 0.637424i) q^{12} +(-0.630953 - 1.59361i) q^{13} +(4.26859 + 1.69005i) q^{14} +(0.829011 - 2.07671i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.35429 + 2.46344i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(1.38561 - 7.26362i) q^{19} +(0.146696 - 2.23125i) q^{20} +(1.95474 - 4.15404i) q^{21} +(-1.21765 - 2.21489i) q^{22} +(-5.08310 - 0.319802i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-2.10335 - 4.53607i) q^{25} +(-1.38663 + 1.00744i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(0.575402 - 4.55478i) q^{28} +(-7.86132 - 0.993116i) q^{29} +(-2.21764 - 0.286508i) q^{30} +(-2.16936 - 1.19262i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-2.28698 + 1.07617i) q^{33} +(2.72284 + 0.699107i) q^{34} +(-3.75214 - 9.55547i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(6.67096 + 4.23352i) q^{37} +(-7.38001 + 0.464311i) q^{38} +(0.918389 + 1.44715i) q^{39} +(-2.19763 + 0.412802i) q^{40} +(0.0681357 + 1.08299i) q^{41} +(-4.50966 - 0.860264i) q^{42} +(3.81979 - 1.24112i) q^{43} +(-1.84249 + 1.73022i) q^{44} +(-0.425189 + 2.19527i) q^{45} +(0.954362 + 5.00294i) q^{46} +(4.92695 - 5.24667i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-4.35006 - 13.3881i) q^{49} +(-3.87048 + 3.16534i) q^{50} +(0.868696 - 2.67357i) q^{51} +(1.32063 + 1.09252i) q^{52} +(0.0107615 + 0.00506399i) q^{53} +(0.728969 + 0.684547i) q^{54} +(-1.76163 + 5.37018i) q^{55} +(-4.55478 + 0.575402i) q^{56} +7.39460i q^{57} +(0.993116 + 7.86132i) q^{58} +(-5.99536 - 7.24715i) q^{59} +(0.273997 + 2.21922i) q^{60} +(-0.353961 + 5.62605i) q^{61} +(-0.615650 + 2.39780i) q^{62} +(-1.14173 + 4.44675i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(3.76262 + 0.728760i) q^{65} +(1.61111 + 1.94750i) q^{66} +(-0.686466 - 5.43394i) q^{67} -2.81116i q^{68} +(5.05299 - 0.638341i) q^{69} +(-8.32214 + 6.01061i) q^{70} +(-0.276150 - 0.259322i) q^{71} +(0.904827 + 0.425779i) q^{72} +(4.29556 + 3.55360i) q^{73} +(2.44151 - 7.51421i) q^{74} +(2.91607 + 4.06159i) q^{75} +(2.28506 + 7.03268i) q^{76} +(-4.27166 + 10.7890i) q^{77} +(1.17329 - 1.24943i) q^{78} +(-0.554414 - 2.90634i) q^{79} +(0.946363 + 2.02593i) q^{80} +(0.728969 - 0.684547i) q^{81} +(1.03202 - 0.335323i) q^{82} +(-16.2402 - 3.09798i) q^{83} +(0.288270 + 4.58192i) q^{84} +(-3.01273 - 5.51693i) q^{85} +(-2.15208 - 3.39113i) q^{86} +(7.90817 - 0.497540i) q^{87} +(2.13407 + 1.35432i) q^{88} +(-6.03518 + 7.29528i) q^{89} +(2.23204 - 0.134111i) q^{90} +(7.62158 + 1.95689i) q^{91} +(4.60842 - 2.16856i) q^{92} +(2.35441 + 0.764995i) q^{93} +(-6.30712 - 3.46737i) q^{94} +(12.0214 + 11.3528i) q^{95} +(0.992115 + 0.125333i) q^{96} +(1.14923 - 9.09706i) q^{97} +(-11.8857 + 7.54289i) q^{98} +(2.04482 - 1.48565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	−1.20346	+	1.88459i	−0.538205	+	0.842814i
$5$	−1.20346	+	1.88459i	−0.538205	+	0.842814i
$6$	0.425779	+	0.904827i	0.173824	+	0.369394i
$7$	−2.69851	+	3.71418i	−1.01994	+	1.40383i	−0.107696	+	0.994184i	$0.534347\pi$
$7$	−2.69851	+	3.71418i	−1.01994	+	1.40383i	−0.912245	+	0.409645i	$0.865653\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	2.12467	+	0.696977i	0.671880	+	0.220403i
$11$	2.44813	−	0.628572i	0.738138	−	0.189522i	0.139141	−	0.990273i	$-0.455566\pi$
$11$	2.44813	−	0.628572i	0.738138	−	0.189522i	0.598997	+	0.800751i	$0.295566\pi$
$12$	0.770513	−	0.637424i	0.222428	−	0.184008i
$13$	−0.630953	−	1.59361i	−0.174995	−	0.441987i	0.815634	−	0.578568i	$-0.196388\pi$
$13$	−0.630953	−	1.59361i	−0.174995	−	0.441987i	−0.990629	+	0.136582i	$0.956388\pi$
$14$	4.26859	+	1.69005i	1.14083	+	0.451686i
$15$	0.829011	−	2.07671i	0.214050	−	0.536205i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−1.35429	+	2.46344i	−0.328463	+	0.597471i	−0.988046	−	0.154160i	$-0.950733\pi$
$17$	−1.35429	+	2.46344i	−0.328463	+	0.597471i	0.659583	+	0.751631i	$0.270733\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	1.38561	−	7.26362i	0.317881	−	1.66639i	−0.361324	−	0.932440i	$-0.617675\pi$
$19$	1.38561	−	7.26362i	0.317881	−	1.66639i	0.679205	−	0.733949i	$-0.262325\pi$
$20$	0.146696	−	2.23125i	0.0328022	−	0.498923i
$21$	1.95474	−	4.15404i	0.426560	−	0.906487i
$22$	−1.21765	−	2.21489i	−0.259604	−	0.472217i
$23$	−5.08310	−	0.319802i	−1.05990	−	0.0666833i	−0.476743	−	0.879043i	$-0.658183\pi$
$23$	−5.08310	−	0.319802i	−1.05990	−	0.0666833i	−0.583157	+	0.812359i	$0.698183\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	−2.10335	−	4.53607i	−0.420670	−	0.907214i
$26$	−1.38663	+	1.00744i	−0.271940	+	0.197576i
$27$	−0.844328	+	0.535827i	−0.162491	+	0.103120i
$28$	0.575402	−	4.55478i	0.108741	−	0.860772i
$29$	−7.86132	−	0.993116i	−1.45981	−	0.184417i	−0.645017	−	0.764168i	$-0.723150\pi$
$29$	−7.86132	−	0.993116i	−1.45981	−	0.184417i	−0.814794	+	0.579751i	$0.803150\pi$
$30$	−2.21764	−	0.286508i	−0.404883	−	0.0523089i
$31$	−2.16936	−	1.19262i	−0.389629	−	0.214200i	0.274883	−	0.961478i	$-0.411361\pi$
$31$	−2.16936	−	1.19262i	−0.389629	−	0.214200i	−0.664512	+	0.747277i	$0.731361\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	−2.28698	+	1.07617i	−0.398112	+	0.187337i
$34$	2.72284	+	0.699107i	0.466963	+	0.119896i
$35$	−3.75214	−	9.55547i	−0.634228	−	1.61517i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	6.67096	+	4.23352i	1.09670	+	0.695986i	0.955794	−	0.294037i	$-0.0949990\pi$
$37$	6.67096	+	4.23352i	1.09670	+	0.695986i	0.140904	+	0.990023i	$0.454999\pi$
$38$	−7.38001	+	0.464311i	−1.19720	+	0.0753211i
$39$	0.918389	+	1.44715i	0.147060	+	0.231729i
$40$	−2.19763	+	0.412802i	−0.347476	+	0.0652698i
$41$	0.0681357	+	1.08299i	0.0106410	+	0.169134i	0.999758	+	0.0220023i	$0.00700411\pi$
$41$	0.0681357	+	1.08299i	0.0106410	+	0.169134i	−0.989117	+	0.147132i	$0.952996\pi$
$42$	−4.50966	−	0.860264i	−0.695856	−	0.132742i
$43$	3.81979	−	1.24112i	0.582512	−	0.189270i	−0.00291345	−	0.999996i	$-0.500927\pi$
$43$	3.81979	−	1.24112i	0.582512	−	0.189270i	0.585426	+	0.810726i	$0.300927\pi$
$44$	−1.84249	+	1.73022i	−0.277766	+	0.260840i
$45$	−0.425189	+	2.19527i	−0.0633834	+	0.327252i
$46$	0.954362	+	5.00294i	0.140713	+	0.737643i
$47$	4.92695	−	5.24667i	0.718670	−	0.765305i	−0.261126	−	0.965305i	$-0.584094\pi$
$47$	4.92695	−	5.24667i	0.718670	−	0.765305i	0.979796	+	0.199999i	$0.0640940\pi$
$48$	−0.368125	+	0.929776i	−0.0531342	+	0.134202i
$49$	−4.35006	−	13.3881i	−0.621438	−	1.91259i
$50$	−3.87048	+	3.16534i	−0.547368	+	0.447647i
$51$	0.868696	−	2.67357i	0.121642	−	0.374375i
$52$	1.32063	+	1.09252i	0.183139	+	0.151506i
$53$	0.0107615	+	0.00506399i	0.00147821	+	0.000695593i	0.426518	−	0.904479i	$-0.359740\pi$
$53$	0.0107615	+	0.00506399i	0.00147821	+	0.000695593i	−0.425040	+	0.905175i	$0.639740\pi$
$54$	0.728969	+	0.684547i	0.0992001	+	0.0931551i
$55$	−1.76163	+	5.37018i	−0.237538	+	0.724114i
$56$	−4.55478	+	0.575402i	−0.608658	+	0.0768914i
$57$			7.39460i			0.979438i
$58$	0.993116	+	7.86132i	0.130403	+	1.03224i
$59$	−5.99536	−	7.24715i	−0.780530	−	0.943498i	0.218951	−	0.975736i	$-0.429737\pi$
$59$	−5.99536	−	7.24715i	−0.780530	−	0.943498i	−0.999480	+	0.0322377i	$0.989737\pi$
$60$	0.273997	+	2.21922i	0.0353729	+	0.286500i
$61$	−0.353961	+	5.62605i	−0.0453201	+	0.720342i	0.908111	+	0.418730i	$0.137525\pi$
$61$	−0.353961	+	5.62605i	−0.0453201	+	0.720342i	−0.953431	+	0.301612i	$0.902475\pi$
$62$	−0.615650	+	2.39780i	−0.0781877	+	0.304521i
$63$	−1.14173	+	4.44675i	−0.143845	+	0.560237i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	3.76262	+	0.728760i	0.466696	+	0.0903915i
$66$	1.61111	+	1.94750i	0.198314	+	0.239720i
$67$	−0.686466	−	5.43394i	−0.0838652	−	0.663862i	−0.976873	−	0.213820i	$-0.931409\pi$
$67$	−0.686466	−	5.43394i	−0.0838652	−	0.663862i	0.893008	−	0.450041i	$-0.148591\pi$
$68$		−	2.81116i		−	0.340903i
$69$	5.05299	−	0.638341i	0.608309	−	0.0768473i
$70$	−8.32214	+	6.01061i	−0.994686	+	0.718405i
$71$	−0.276150	−	0.259322i	−0.0327730	−	0.0307759i	0.667988	−	0.744172i	$-0.267156\pi$
$71$	−0.276150	−	0.259322i	−0.0327730	−	0.0307759i	−0.700761	+	0.713396i	$0.747156\pi$
$72$	0.904827	+	0.425779i	0.106635	+	0.0501786i
$73$	4.29556	+	3.55360i	0.502757	+	0.415917i	0.853925	−	0.520395i	$-0.174215\pi$
$73$	4.29556	+	3.55360i	0.502757	+	0.415917i	−0.351168	+	0.936312i	$0.614215\pi$
$74$	2.44151	−	7.51421i	0.283820	−	0.873509i
$75$	2.91607	+	4.06159i	0.336718	+	0.468993i
$76$	2.28506	+	7.03268i	0.262114	+	0.806704i
$77$	−4.27166	+	10.7890i	−0.486801	+	1.22952i
$78$	1.17329	−	1.24943i	0.132849	−	0.141470i
$79$	−0.554414	−	2.90634i	−0.0623764	−	0.326989i	0.937397	−	0.348262i	$-0.113228\pi$
$79$	−0.554414	−	2.90634i	−0.0623764	−	0.326989i	−0.999774	+	0.0212733i	$0.993228\pi$
$80$	0.946363	+	2.02593i	0.105807	+	0.226506i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	1.03202	−	0.335323i	0.113967	−	0.0370302i
$83$	−16.2402	−	3.09798i	−1.78259	−	0.340047i	−0.812530	−	0.582919i	$-0.801910\pi$
$83$	−16.2402	−	3.09798i	−1.78259	−	0.340047i	−0.970058	+	0.242872i	$0.921910\pi$
$84$	0.288270	+	4.58192i	0.0314528	+	0.499929i
$85$	−3.01273	−	5.51693i	−0.326777	−	0.598395i
$86$	−2.15208	−	3.39113i	−0.232064	−	0.365675i
$87$	7.90817	−	0.497540i	0.847845	−	0.0533419i
$88$	2.13407	+	1.35432i	0.227492	+	0.144371i
$89$	−6.03518	+	7.29528i	−0.639728	+	0.773298i	−0.986342	−	0.164710i	$-0.947331\pi$
$89$	−6.03518	+	7.29528i	−0.639728	+	0.773298i	0.346614	+	0.938008i	$0.387331\pi$
$90$	2.23204	−	0.134111i	0.235278	−	0.0141365i
$91$	7.62158	+	1.95689i	0.798958	+	0.205138i
$92$	4.60842	−	2.16856i	0.480461	−	0.226088i
$93$	2.35441	+	0.764995i	0.244141	+	0.0793262i
$94$	−6.30712	−	3.46737i	−0.650530	−	0.357632i
$95$	12.0214	+	11.3528i	1.23337	+	1.16477i
$96$	0.992115	+	0.125333i	0.101257	+	0.0127918i
$97$	1.14923	−	9.09706i	0.116686	−	0.923666i	−0.819724	−	0.572759i	$-0.805873\pi$
$97$	1.14923	−	9.09706i	0.116686	−	0.923666i	0.936410	−	0.350907i	$-0.114127\pi$
$98$	−11.8857	+	7.54289i	−1.20064	+	0.761947i
$99$	2.04482	−	1.48565i	0.205512	−	0.149313i
$100$	4.02845	+	2.96169i	0.402845	+	0.296169i
$101$	−1.28189	−	0.931344i	−0.127552	−	0.0926722i	0.522180	−	0.852835i	$-0.325119\pi$
$101$	−1.28189	−	0.931344i	−0.127552	−	0.0926722i	−0.649732	+	0.760163i	$0.725119\pi$
$102$	−2.80561	−	0.176514i	−0.277797	−	0.0174775i
$103$	−4.73958	−	8.62127i	−0.467005	−	0.849479i	−0.999994	−	0.00335677i	$-0.998932\pi$
$103$	−4.73958	−	8.62127i	−0.467005	−	0.849479i	0.532990	−	0.846122i	$-0.321068\pi$
$104$	0.729771	−	1.55084i	0.0715600	−	0.152073i
$105$	5.47620	+	8.68313i	0.534422	+	0.847387i
$106$	0.00222861	−	0.0116828i	0.000216462	−	0.00113473i
$107$	−8.52868	−	11.7387i	−0.824498	−	1.13482i	−0.988922	−	0.148435i	$-0.952576\pi$
$107$	−8.52868	−	11.7387i	−0.824498	−	1.13482i	0.164424	−	0.986390i	$-0.447424\pi$
$108$	0.481754	−	0.876307i	0.0463568	−	0.0843226i
$109$	10.7800	−	16.9866i	1.03254	−	1.62702i	0.290241	−	0.956953i	$-0.406264\pi$
$109$	10.7800	−	16.9866i	1.03254	−	1.62702i	0.742299	−	0.670069i	$-0.233736\pi$
$110$	5.63956	+	0.370779i	0.537711	+	0.0353524i
$111$	−7.34608	−	2.90852i	−0.697259	−	0.276064i
$112$	1.69005	+	4.26859i	0.159695	+	0.403343i
$113$	−4.78060	+	3.95486i	−0.449721	+	0.372041i	−0.834537	−	0.550952i	$-0.814265\pi$
$113$	−4.78060	+	3.95486i	−0.449721	+	0.372041i	0.384816	+	0.922993i	$0.374265\pi$
$114$	7.16228	−	1.83896i	0.670809	−	0.172235i
$115$	6.72003	−	9.19469i	0.626646	−	0.857409i
$116$	7.36737	−	2.91695i	0.684043	−	0.270832i
$117$	−1.17329	−	1.24943i	−0.108471	−	0.115510i
$118$	−5.52848	+	7.60930i	−0.508938	+	0.700493i
$119$	−5.49510	−	11.6777i	−0.503735	−	1.07049i
$120$	2.08136	−	0.817286i	0.190001	−	0.0746077i
$121$	−4.04115	+	2.22164i	−0.367378	+	0.201968i
$122$	5.53733	−	1.05630i	0.501326	−	0.0956330i
$123$	−0.269860	−	1.05104i	−0.0243325	−	0.0947687i
$124$	2.47557			0.222313
$125$	11.0799	+	1.49505i	0.991019	+	0.133721i
$126$	4.59098			0.408997
$127$	2.62327	+	10.2170i	0.232778	+	0.906609i	0.972349	+	0.233531i	$0.0750281\pi$
$127$	2.62327	+	10.2170i	0.232778	+	0.906609i	−0.739572	+	0.673078i	$0.764972\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−3.51957	+	1.93490i	−0.309881	+	0.170358i
$130$	−0.229861	−	3.82565i	−0.0201602	−	0.335531i
$131$	3.97108	+	8.43897i	0.346955	+	0.737316i	0.999796	−	0.0201782i	$-0.00642336\pi$
$131$	3.97108	+	8.43897i	0.346955	+	0.737316i	−0.652842	+	0.757494i	$0.726423\pi$
$132$	1.48565	−	2.04482i	0.129309	−	0.177979i
$133$	23.2393	+	24.7474i	2.01510	+	2.14587i
$134$	−5.09251	+	2.01627i	−0.439926	+	0.174179i
$135$	0.00630506	−	2.23606i	0.000542653	−	0.192449i
$136$	−2.72284	+	0.699107i	−0.233482	+	0.0599479i
$137$	−17.4649	+	14.4482i	−1.49213	+	1.23440i	−0.586769	+	0.809754i	$0.699600\pi$
$137$	−17.4649	+	14.4482i	−1.49213	+	1.23440i	−0.905361	+	0.424643i	$0.860400\pi$
$138$	−1.87491	−	4.73549i	−0.159603	−	0.403112i
$139$	−5.92686	−	2.34661i	−0.502710	−	0.199037i	0.103063	−	0.994675i	$-0.467136\pi$
$139$	−5.92686	−	2.34661i	−0.502710	−	0.199037i	−0.605772	+	0.795638i	$0.707136\pi$
$140$	7.89141	+	6.56591i	0.666946	+	0.554921i
$141$	−3.85655	+	6.07695i	−0.324780	+	0.511772i
$142$	−0.182500	+	0.331965i	−0.0153150	+	0.0278579i
$143$	−2.54635	−	3.50475i	−0.212936	−	0.293082i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	11.3324	−	13.6202i	0.941107	−	1.13109i
$146$	2.37369	−	5.04435i	0.196448	−	0.417473i
$147$	6.78170	+	12.3359i	0.559345	+	1.01744i
$148$	−7.88532	−	0.496102i	−0.648169	−	0.0407793i
$149$	10.2459	+	7.44409i	0.839377	+	0.609843i	0.922197	−	0.386721i	$-0.126392\pi$
$149$	10.2459	+	7.44409i	0.839377	+	0.609843i	−0.0828193	+	0.996565i	$0.526392\pi$
$150$	3.20880	−	3.83453i	0.261997	−	0.313088i
$151$	−6.83109	+	4.96308i	−0.555906	+	0.403890i	−0.829958	−	0.557825i	$-0.811636\pi$
$151$	−6.83109	+	4.96308i	−0.555906	+	0.403890i	0.274052	+	0.961715i	$0.411636\pi$
$152$	6.24347	−	3.96222i	0.506412	−	0.321379i
$153$	−0.352332	+	2.78899i	−0.0284843	+	0.225477i
$154$	11.5124	+	1.45435i	0.927692	+	0.117195i
$155$	4.85834	−	2.65308i	0.390231	−	0.213101i
$156$	−1.50196	−	0.825710i	−0.120253	−	0.0661097i
$157$	−3.26579	−	1.06112i	−0.260639	−	0.0846866i	0.175783	−	0.984429i	$-0.443754\pi$
$157$	−3.26579	−	1.06112i	−0.260639	−	0.0846866i	−0.436421	+	0.899742i	$0.643754\pi$
$158$	−2.67715	+	1.25977i	−0.212983	+	0.100222i
$159$	−0.0115198	−	0.00295778i	−0.000913581	−	0.000234568i
$160$	1.72693	−	1.42046i	0.136526	−	0.112297i
$161$	14.9046	−	18.0166i	1.17465	−	1.41991i
$162$	−0.844328	−	0.535827i	−0.0663367	−	0.0420985i
$163$	−3.57440	+	0.224882i	−0.279969	+	0.0176141i	−0.202154	−	0.979354i	$-0.564794\pi$
$163$	−3.57440	+	0.224882i	−0.279969	+	0.0176141i	−0.0778146	+	0.996968i	$0.524794\pi$
$164$	−0.581440	−	0.916203i	−0.0454029	−	0.0715435i
$165$	0.724158	−	5.60515i	0.0563756	−	0.436360i
$166$	1.03812	+	16.5004i	0.0805734	+	1.28068i
$167$	−7.76739	−	1.48171i	−0.601059	−	0.114658i	−0.122133	−	0.992514i	$-0.538974\pi$
$167$	−7.76739	−	1.48171i	−0.601059	−	0.114658i	−0.478925	+	0.877856i	$0.658974\pi$
$168$	4.36628	−	1.41869i	0.336866	−	0.109454i
$169$	7.33511	−	6.88813i	0.564240	−	0.529856i
$170$	−4.59437	+	4.29008i	−0.352372	+	0.329034i
$171$	−1.38561	−	7.26362i	−0.105960	−	0.555463i
$172$	−2.74939	+	2.92780i	−0.209639	+	0.223243i
$173$	−6.66971	+	16.8458i	−0.507089	+	1.28076i	0.420546	+	0.907271i	$0.361839\pi$
$173$	−6.66971	+	16.8458i	−0.507089	+	1.28076i	−0.927635	+	0.373489i	$0.878161\pi$
$174$	−2.44859	−	7.53599i	−0.185627	−	0.571302i
$175$	22.5237	+	4.42841i	1.70263	+	0.334756i
$176$	0.781051	−	2.40383i	0.0588739	−	0.181195i
$177$	7.24715	+	5.99536i	0.544729	+	0.450639i
$178$	8.56697	+	4.03131i	0.642122	+	0.302160i
$179$	6.75169	+	6.34026i	0.504645	+	0.473893i	0.894554	−	0.446960i	$-0.147493\pi$
$179$	6.75169	+	6.34026i	0.504645	+	0.473893i	−0.389909	+	0.920854i	$0.627493\pi$
$180$	−0.684984	−	2.12857i	−0.0510557	−	0.158654i
$181$	−7.54250	+	0.952840i	−0.560630	+	0.0708240i	−0.400541	−	0.916279i	$-0.631178\pi$
$181$	−7.54250	+	0.952840i	−0.560630	+	0.0708240i	−0.160088	+	0.987103i	$0.551178\pi$
$182$		−	7.86879i		−	0.583273i
$183$	−0.706525	−	5.59272i	−0.0522279	−	0.413426i
$184$	−3.24650	−	3.92434i	−0.239335	−	0.289306i
$185$	−16.0067	+	7.47712i	−1.17684	+	0.549729i
$186$	0.155443	−	2.47069i	0.0113976	−	0.181160i
$187$	−1.76702	+	6.88207i	−0.129217	+	0.503267i
$188$	−1.78992	+	6.97127i	−0.130543	+	0.508432i
$189$	0.288270	−	4.58192i	0.0209686	−	0.333286i
$190$	8.00654	−	14.4671i	0.580855	−	1.04955i
$191$	−0.499712	−	0.604048i	−0.0361579	−	0.0437073i	0.752124	−	0.659021i	$-0.229029\pi$
$191$	−0.499712	−	0.604048i	−0.0361579	−	0.0437073i	−0.788282	+	0.615314i	$0.789029\pi$
$192$	−0.125333	−	0.992115i	−0.00904515	−	0.0715997i
$193$		−	21.0791i		−	1.51731i	−0.651495	−	0.758653i	$-0.725858\pi$
$193$		−	21.0791i		−	1.51731i	0.651495	−	0.758653i	$-0.274142\pi$
$194$	−9.09706	+	1.14923i	−0.653131	+	0.0825096i
$195$	−3.83253	−	0.0108067i	−0.274453	−	0.000773881i
$196$	10.2618	+	9.63644i	0.732983	+	0.688317i
$197$	23.0541	+	10.8484i	1.64254	+	0.772919i	0.999978	+	0.00668396i	$0.00212759\pi$
$197$	23.0541	+	10.8484i	1.64254	+	0.772919i	0.642560	+	0.766236i	$0.277872\pi$
$198$	−1.94750	−	1.61111i	−0.138403	−	0.114497i
$199$	−0.680112	+	2.09317i	−0.0482119	+	0.148381i	−0.972264	−	0.233885i	$-0.924856\pi$
$199$	−0.680112	+	2.09317i	−0.0482119	+	0.148381i	0.924052	+	0.382266i	$0.124856\pi$
$200$	1.86681	−	4.63843i	0.132003	−	0.327986i
$201$	1.69253	+	5.20906i	0.119382	+	0.367419i
$202$	−0.583292	+	1.47323i	−0.0410403	+	0.103656i
$203$	24.9025	−	26.5184i	1.74781	−	1.86123i
$204$	0.526759	+	2.76136i	0.0368805	+	0.193334i
$205$	−2.12298	−	1.17493i	−0.148275	−	0.0820604i
$206$	−7.17173	+	6.73470i	−0.499678	+	0.469229i
$207$	−4.84388	+	1.57387i	−0.336673	+	0.109392i
$208$	−1.68361	−	0.321165i	−0.116737	−	0.0222688i
$209$	−1.17356	−	18.6532i	−0.0811769	−	1.29027i
$210$	7.04846	−	7.46356i	0.486390	−	0.515035i
$211$	3.95773	+	6.23638i	0.272461	+	0.429330i	0.952814	−	0.303555i	$-0.0981735\pi$
$211$	3.95773	+	6.23638i	0.272461	+	0.429330i	−0.680353	+	0.732885i	$0.738173\pi$
$212$	−0.0118700		0.000746797i	−0.000815235		5.12902e-5i
$213$	0.319851	+	0.202984i	0.0219158	+	0.0139082i
$214$	−9.24893	+	11.1800i	−0.632244	+	0.764251i
$215$	−2.25797	+	8.69238i	−0.153992	+	0.592815i
$216$	−0.968583	−	0.248690i	−0.0659037	−	0.0169212i
$217$	10.2836	−	4.83911i	0.698099	−	0.328501i
$218$	−19.1338	−	6.21696i	−1.29591	−	0.421066i
$219$	−4.88535	−	2.68574i	−0.330121	−	0.181486i
$220$	−1.04337	−	5.55459i	−0.0703441	−	0.374491i
$221$	4.78024	+	0.603885i	0.321554	+	0.0406217i
$222$	−0.990246	+	7.83861i	−0.0664610	+	0.526093i
$223$	−22.5439	+	14.3068i	−1.50965	+	0.958053i	−0.514733	+	0.857350i	$0.672109\pi$
$223$	−22.5439	+	14.3068i	−1.50965	+	0.958053i	−0.994917	+	0.100702i	$0.967891\pi$
$224$	3.71418	−	2.69851i	0.248164	−	0.180302i
$225$	−3.62548	−	3.44324i	−0.241699	−	0.229549i
$226$	5.01949	+	3.64687i	0.333892	+	0.242587i
$227$	−6.36355	−	0.400361i	−0.422364	−	0.0265729i	−0.149813	−	0.988714i	$-0.547867\pi$
$227$	−6.36355	−	0.400361i	−0.422364	−	0.0265729i	−0.272551	+	0.962141i	$0.587867\pi$
$228$	−3.56237	−	6.47994i	−0.235924	−	0.429144i
$229$	−9.10460	+	19.3483i	−0.601649	+	1.27857i	0.339510	+	0.940603i	$0.389739\pi$
$229$	−9.10460	+	19.3483i	−0.601649	+	1.27857i	−0.941158	+	0.337966i	$0.890261\pi$
$230$	−10.5770	−	4.22228i	−0.697428	−	0.278409i
$231$	2.17435	−	11.3983i	0.143061	−	0.749954i
$232$	−4.65750	−	6.41049i	−0.305780	−	0.420869i
$233$	10.6185	−	19.3150i	0.695642	−	1.26537i	−0.258500	−	0.966011i	$-0.583228\pi$
$233$	10.6185	−	19.3150i	0.695642	−	1.26537i	0.954141	−	0.299356i	$-0.0967719\pi$
$234$	−0.918389	+	1.44715i	−0.0600370	+	0.0946031i
$235$	3.95841	+	15.5995i	0.258218	+	1.01760i
$236$	8.74512	+	3.46244i	0.569259	+	0.225385i
$237$	1.08919	+	2.75097i	0.0707503	+	0.178695i
$238$	−9.94422	+	8.22658i	−0.644588	+	0.533250i
$239$	9.50536	−	2.44056i	0.614850	−	0.157867i	0.0715943	−	0.997434i	$-0.477191\pi$
$239$	9.50536	−	2.44056i	0.614850	−	0.157867i	0.543256	+	0.839567i	$0.317191\pi$
$240$	−1.30922	−	1.81272i	−0.0845099	−	0.117010i
$241$	9.70437	−	3.84223i	0.625114	−	0.247500i	−0.0341443	−	0.999417i	$-0.510871\pi$
$241$	9.70437	−	3.84223i	0.625114	−	0.247500i	0.659258	+	0.751917i	$0.270871\pi$
$242$	3.15684	+	3.36169i	0.202929	+	0.216098i
$243$	−0.587785	+	0.809017i	−0.0377064	+	0.0518985i
$244$	−2.40019	−	5.10067i	−0.153657	−	0.326537i
$245$	30.4662	+	7.91404i	1.94642	+	0.505609i
$246$	−0.950904	+	0.522764i	−0.0606274	+	0.0333302i
$247$	−12.4496	+	2.37489i	−0.792149	+	0.151111i
$248$	−0.615650	−	2.39780i	−0.0390938	−	0.152260i
$249$	16.5330			1.04774
$250$	−1.30739	−	11.1036i	−0.0826865	−	0.702256i
$251$	−1.48310			−0.0936126			−0.0468063	−	0.998904i	$-0.514904\pi$
$251$	−1.48310			−0.0936126			−0.0468063	+	0.998904i	$0.514904\pi$
$252$	−1.14173	−	4.44675i	−0.0719223	−	0.280119i
$253$	−12.6451	+	2.41218i	−0.794990	+	0.151653i
$254$	9.24360	−	5.08171i	0.579995	−	0.318855i
$255$	3.99314	+	4.85468i	0.250060	+	0.304012i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	−17.6392	+	24.2782i	−1.10030	+	1.51444i	−0.265317	+	0.964161i	$0.585477\pi$
$257$	−17.6392	+	24.2782i	−1.10030	+	1.51444i	−0.834984	+	0.550274i	$0.814523\pi$
$258$	2.74939	+	2.92780i	0.171170	+	0.182277i
$259$	−33.7257	+	13.3529i	−2.09561	+	0.829712i
$260$	−3.64829	+	1.17404i	−0.226258	+	0.0728108i
$261$	−7.67486	+	1.97057i	−0.475062	+	0.121975i
$262$	7.18628	−	5.94500i	0.443970	−	0.367284i
$263$	−9.77802	−	24.6965i	−0.602938	−	1.52285i	−0.835058	−	0.550161i	$-0.814566\pi$
$263$	−9.77802	−	24.6965i	−0.602938	−	1.52285i	0.232120	−	0.972687i	$-0.425434\pi$
$264$	−2.35004	−	0.930447i	−0.144635	−	0.0572651i
$265$	−0.0224947	+	0.0141867i	−0.00138184	+	0.000871484i
$266$	18.1905	−	28.6636i	1.11533	−	1.75748i
$267$	4.56128	−	8.29694i	0.279146	−	0.507764i
$268$	3.21938	+	4.43109i	0.196655	+	0.270672i
$269$	−1.31427	+	6.88965i	−0.0801325	+	0.420069i	0.919503	+	0.393082i	$0.128591\pi$
$269$	−1.31427	+	6.88965i	−0.0801325	+	0.420069i	−0.999636	+	0.0269869i	$0.991409\pi$
$270$	−2.16738	+	0.549978i	−0.131902	+	0.0334706i
$271$	8.13182	−	17.2810i	0.493973	−	1.04975i	−0.490048	−	0.871695i	$-0.663021\pi$
$271$	8.13182	−	17.2810i	0.493973	−	1.04975i	0.984021	−	0.178051i	$-0.0569792\pi$
$272$	1.35429	+	2.46344i	0.0821156	+	0.149368i
$273$	−7.85326	−	0.494085i	−0.475301	−	0.0299034i
$274$	18.3377	+	13.3231i	1.10782	+	0.804878i
$275$	−8.00051	−	9.78276i	−0.482449	−	0.589923i
$276$	−4.12045	+	2.99368i	−0.248022	+	0.180198i
$277$	−8.26526	+	5.24529i	−0.496611	+	0.315159i	−0.760438	−	0.649411i	$-0.775015\pi$
$277$	−8.26526	+	5.24529i	−0.496611	+	0.315159i	0.263826	+	0.964570i	$0.415015\pi$
$278$	−0.798936	+	6.32423i	−0.0479170	+	0.379302i
$279$	−2.45605	−	0.310272i	−0.147040	−	0.0185755i
$280$	4.39712	−	9.27636i	0.262778	−	0.554369i
$281$	10.4511	+	5.74552i	0.623458	+	0.342749i	0.761970	−	0.647612i	$-0.224232\pi$
$281$	10.4511	+	5.74552i	0.623458	+	0.342749i	−0.138513	+	0.990361i	$0.544232\pi$
$282$	6.84512	+	2.22411i	0.407621	+	0.132444i
$283$	14.4279	−	6.78925i	0.857649	−	0.403579i	0.0538993	−	0.998546i	$-0.482835\pi$
$283$	14.4279	−	6.78925i	0.857649	−	0.403579i	0.803750	+	0.594967i	$0.202835\pi$
$284$	0.366922	+	0.0942095i	0.0217728	+	0.00559031i
$285$	−13.9358	−	8.89913i	−0.825484	−	0.527139i
$286$	−2.76139	+	3.33795i	−0.163284	+	0.197377i
$287$	−4.20627	−	2.66938i	−0.248288	−	0.157569i
$288$	−0.998027	+	0.0627905i	−0.0588093	+	0.00369997i
$289$	4.87462	+	7.68118i	0.286743	+	0.451834i
$290$	−16.0105	−	7.58920i	−0.940171	−	0.445653i
$291$	0.575749	+	9.15127i	0.0337510	+	0.536457i
$292$	−5.47619	−	1.04464i	−0.320469	−	0.0611328i
$293$	−25.2355	+	8.19949i	−1.47427	+	0.479020i	−0.932396	−	0.361439i	$-0.882285\pi$
$293$	−25.2355	+	8.19949i	−1.47427	+	0.479020i	−0.541875	+	0.840459i	$0.682285\pi$
$294$	10.2618	−	9.63644i	0.598478	−	0.562009i
$295$	20.8731	−	2.57711i	1.21528	−	0.150045i
$296$	1.48048	+	7.76096i	0.0860513	+	0.451097i
$297$	−1.73022	+	1.84249i	−0.100397	+	0.106912i
$298$	4.66216	−	11.7753i	0.270072	−	0.682124i
$299$	2.69756	+	8.30224i	0.156004	+	0.480131i
$300$	−4.51206	−	2.15438i	−0.260504	−	0.124383i
$301$	−5.69798	+	17.5366i	−0.328426	+	1.01079i
$302$	6.50598	+	5.38221i	0.374377	+	0.309712i
$303$	1.43370	+	0.674646i	0.0823637	+	0.0387574i
$304$	−5.39043	−	5.06195i	−0.309162	−	0.290323i
$305$	−10.1768	−	7.43782i	−0.582723	−	0.425888i
$306$	2.78899	−	0.352332i	0.159436	−	0.0201415i
$307$			10.1211i			0.577640i	0.957383	+	0.288820i	$0.0932629\pi$
$307$			10.1211i			0.577640i	−0.957383	+	0.288820i	$0.906737\pi$
$308$	−1.45435	−	11.5124i	−0.0828692	−	0.655977i
$309$	6.27109	+	7.58045i	0.356750	+	0.431237i
$310$	−3.77795	−	4.04591i	−0.214573	−	0.229792i
$311$	−1.00059	+	15.9040i	−0.0567385	+	0.901833i	0.861986	+	0.506933i	$0.169221\pi$
$311$	−1.00059	+	15.9040i	−0.0567385	+	0.901833i	−0.918724	+	0.394900i	$0.870779\pi$
$312$	−0.426246	+	1.66012i	−0.0241314	+	0.0939857i
$313$	2.17040	−	8.45315i	0.122678	−	0.477800i	−0.877320	−	0.479907i	$-0.840671\pi$
$313$	2.17040	−	8.45315i	0.122678	−	0.477800i	0.999998	+	0.00210647i	$0.000670510\pi$
$314$	−0.215614	+	3.42708i	−0.0121678	+	0.193401i
$315$	−7.00626	−	7.50319i	−0.394758	−	0.422757i
$316$	1.88598	+	2.27975i	0.106094	+	0.128246i
$317$	−1.27534	−	10.0953i	−0.0716301	−	0.567011i	−0.986560	−	0.163398i	$-0.947754\pi$
$317$	−1.27534	−	10.0953i	−0.0716301	−	0.567011i	0.914930	−	0.403613i	$-0.132246\pi$
$318$			0.0118935i			0.000666953i
$319$	−19.8698	+	2.51013i	−1.11249	+	0.140541i
$320$	−1.80530	−	1.31942i	−0.100920	−	0.0737580i
$321$	10.5772	+	9.93268i	0.590363	+	0.554388i
$322$	−21.1572	−	9.95581i	−1.17904	−	0.554816i
$323$	16.0170	+	13.2504i	0.891207	+	0.737271i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	−5.90159	+	6.21396i	−0.327361	+	0.344688i
$326$	1.10673	+	3.40618i	0.0612964	+	0.188651i
$327$	−7.40612	+	18.7057i	−0.409559	+	1.03443i
$328$	−0.742821	+	0.791024i	−0.0410154	+	0.0436770i
$329$	6.19165	+	32.4578i	0.341357	+	1.78946i
$330$	−5.60915	+	0.692537i	−0.308773	+	0.0381229i
$331$	14.7408	−	13.8426i	0.810229	−	0.760856i	−0.163989	−	0.986462i	$-0.552436\pi$
$331$	14.7408	−	13.8426i	0.810229	−	0.760856i	0.974219	+	0.225606i	$0.0724362\pi$
$332$	15.7238	−	5.10898i	0.862957	−	0.280392i
$333$	7.76096	+	1.48048i	0.425298	+	0.0811299i
$334$	0.496513	+	7.89185i	0.0271680	+	0.431823i
$335$	11.0669	+	5.24585i	0.604648	+	0.286611i
$336$	−2.45997	−	3.87629i	−0.134202	−	0.211469i
$337$	−31.5472	+	1.98478i	−1.71849	+	0.108118i	−0.891186	−	0.453639i	$-0.850126\pi$
$337$	−31.5472	+	1.98478i	−1.71849	+	0.108118i	−0.827302	+	0.561757i	$0.810126\pi$
$338$	−8.49590	−	5.39166i	−0.462116	−	0.293268i
$339$	3.95486	−	4.78060i	0.214798	−	0.259646i
$340$	5.29788	+	3.38313i	0.287318	+	0.183476i
$341$	−6.06052	−	1.55608i	−0.328196	−	0.0842663i
$342$	−6.69083	+	3.14847i	−0.361799	+	0.170250i
$343$	30.9006	+	10.0402i	1.66848	+	0.542121i
$344$	3.51957	+	1.93490i	0.189762	+	0.104323i
$345$	−4.87808	+	10.2910i	−0.262627	+	0.554051i
$346$	17.9752	+	2.27080i	0.966354	+	0.122079i
$347$	0.629828	−	4.98560i	0.0338110	−	0.267641i	−0.966143	−	0.258008i	$-0.916934\pi$
$347$	0.629828	−	4.98560i	0.0338110	−	0.267641i	0.999954	−	0.00963277i	$-0.00306625\pi$
$348$	−6.69029	+	4.24579i	−0.358637	+	0.227598i
$349$	−26.5125	+	19.2624i	−1.41918	+	1.03109i	−0.427273	+	0.904123i	$0.640526\pi$
$349$	−26.5125	+	19.2624i	−1.41918	+	1.03109i	−0.991906	+	0.126971i	$0.959474\pi$
$350$	−1.31213	−	22.9174i	−0.0701364	−	1.22498i
$351$	1.38663	+	1.00744i	0.0740127	+	0.0537734i
$352$	−2.52255	−	0.158705i	−0.134452	−	0.00845901i
$353$	−9.52204	−	17.3205i	−0.506807	−	0.921879i	−0.998688	−	0.0512162i	$-0.983690\pi$
$353$	−9.52204	−	17.3205i	−0.506807	−	0.921879i	0.491880	−	0.870663i	$-0.336310\pi$
$354$	4.00471	−	8.51045i	0.212848	−	0.452325i
$355$	0.821053	−	0.208345i	0.0435770	−	0.0110578i
$356$	1.77414	−	9.30037i	0.0940293	−	0.492919i
$357$	7.58594	+	10.4412i	0.401491	+	0.552604i
$358$	4.46199	−	8.11633i	0.235824	−	0.428962i
$359$	−2.86973	+	4.52196i	−0.151458	+	0.238660i	−0.911582	−	0.411118i	$-0.865138\pi$
$359$	−2.86973	+	4.52196i	−0.151458	+	0.238660i	0.760124	+	0.649778i	$0.225138\pi$
$360$	−1.89135	+	1.19282i	−0.0996827	+	0.0628670i
$361$	−33.1745	−	13.1347i	−1.74603	−	0.691301i
$362$	2.79865	+	7.06858i	0.147094	+	0.371516i
$363$	3.55328	−	2.93953i	0.186499	−	0.154285i
$364$	−7.62158	+	1.95689i	−0.399479	+	0.102569i
$365$	−11.8666	+	3.81874i	−0.621127	+	0.199882i
$366$	−5.24131	+	2.07518i	−0.273968	+	0.108472i
$367$	−21.2911	−	22.6728i	−1.11139	−	1.18351i	−0.981396	−	0.191993i	$-0.938505\pi$
$367$	−21.2911	−	22.6728i	−1.11139	−	1.18351i	−0.129992	−	0.991515i	$-0.541495\pi$
$368$	−2.99368	+	4.12045i	−0.156056	+	0.214793i
$369$	0.462025	+	0.981852i	0.0240520	+	0.0511132i
$370$	11.2229	+	13.6443i	0.583452	+	0.709335i
$371$	−0.0478487	+	0.0263050i	−0.00248418	+	0.00136569i
$372$	−2.43172	+	0.463876i	−0.126079	+	0.0240509i
$373$	−1.51793	−	5.91196i	−0.0785956	−	0.306110i	0.917116	−	0.398620i	$-0.130511\pi$
$373$	−1.51793	−	5.91196i	−0.0785956	−	0.306110i	−0.995712	+	0.0925105i	$0.970511\pi$
$374$	7.10530			0.367406
$375$	−11.1638	+	0.607606i	−0.576497	+	0.0313766i
$376$	7.19739			0.371177
$377$	3.37749	+	13.1545i	0.173950	+	0.677489i
$378$	−4.50966	+	0.860264i	−0.231952	+	0.0442472i
$379$	−11.3913	+	6.26243i	−0.585133	+	0.321679i	−0.746678	−	0.665186i	$-0.768352\pi$
$379$	−11.3913	+	6.26243i	−0.585133	+	0.321679i	0.161545	+	0.986865i	$0.448352\pi$
$380$	−16.0037	−	4.15719i	−0.820972	−	0.213259i
$381$	−4.49127	−	9.54444i	−0.230095	−	0.488977i
$382$	−0.460797	+	0.634233i	−0.0235764	+	0.0324502i
$383$	−24.1359	−	25.7021i	−1.23328	−	1.31331i	−0.933180	−	0.359408i	$-0.882979\pi$
$383$	−24.1359	−	25.7021i	−1.23328	−	1.31331i	−0.300104	−	0.953906i	$-0.597021\pi$
$384$	−0.929776	+	0.368125i	−0.0474475	+	0.0187858i
$385$	−15.1920	−	21.0345i	−0.774257	−	1.07202i
$386$	−20.4168	+	5.24215i	−1.03919	+	0.266819i
$387$	3.09466	−	2.56013i	0.157310	−	0.130139i
$388$	3.37547	+	8.52546i	0.171363	+	0.432814i
$389$	−10.8681	−	4.30300i	−0.551037	−	0.218171i	0.0760724	−	0.997102i	$-0.475762\pi$
$389$	−10.8681	−	4.30300i	−0.551037	−	0.218171i	−0.627109	+	0.778931i	$0.715762\pi$
$390$	0.942644	+	3.71481i	0.0477327	+	0.188107i
$391$	7.67179	−	12.0888i	0.387979	−	0.611357i
$392$	6.78170	−	12.3359i	0.342527	−	0.623055i
$393$	−5.48204	−	7.54539i	−0.276532	−	0.380614i
$394$	4.77429	−	25.0277i	0.240525	−	1.26088i
$395$	6.14447	+	2.45283i	0.309162	+	0.123415i
$396$	−1.07617	+	2.28698i	−0.0540797	+	0.114925i
$397$	13.1939	+	23.9996i	0.662181	+	1.20450i	0.967649	+	0.252301i	$0.0811872\pi$
$397$	13.1939	+	23.9996i	0.662181	+	1.20450i	−0.305468	+	0.952202i	$0.598813\pi$
$398$	2.19655	+	0.138195i	0.110103	+	0.00692709i
$399$	−27.4649	−	19.9544i	−1.37496	−	0.998970i
$400$	−4.95696	−	0.654631i	−0.247848	−	0.0327315i
$401$	−10.2757	+	7.46577i	−0.513146	+	0.372823i	−0.814016	−	0.580843i	$-0.802723\pi$
$401$	−10.2757	+	7.46577i	−0.513146	+	0.372823i	0.300870	+	0.953665i	$0.402723\pi$
$402$	4.62449	−	2.93479i	0.230649	−	0.146374i
$403$	−0.531795	+	4.20959i	−0.0264906	+	0.209695i
$404$	1.57200	+	0.198590i	0.0782101	+	0.00988023i
$405$	0.412802	+	2.19763i	0.0205123	+	0.109201i
$406$	−31.8783	−	17.5253i	−1.58209	−	0.869764i
$407$	18.9924	+	6.17101i	0.941419	+	0.305886i
$408$	2.54361	−	1.19693i	0.125928	−	0.0592570i
$409$	−25.5077	−	6.54926i	−1.26127	−	0.323840i	−0.441882	−	0.897073i	$-0.645689\pi$
$409$	−25.5077	−	6.54926i	−1.26127	−	0.323840i	−0.819392	+	0.573233i	$0.805689\pi$
$410$	−0.610050	+	2.34848i	−0.0301282	+	0.115983i
$411$	14.4482	−	17.4649i	0.712680	−	0.861482i
$412$	8.30665	+	5.27156i	0.409239	+	0.259711i
$413$	43.0958	−	2.71136i	2.12060	−	0.133417i
$414$	2.72905	+	4.30029i	0.134125	+	0.211348i
$415$	25.3828	−	26.8777i	1.24600	−	1.31937i
$416$	0.107621	+	1.71058i	0.00527655	+	0.0838683i
$417$	6.26159	+	1.19446i	0.306631	+	0.0584930i
$418$	−17.7753	+	5.77556i	−0.869420	+	0.282492i
$419$	−1.65442	+	1.55360i	−0.0808235	+	0.0758983i	−0.723906	−	0.689898i	$-0.757655\pi$
$419$	−1.65442	+	1.55360i	−0.0808235	+	0.0758983i	0.643083	+	0.765797i	$0.277655\pi$
$420$	−8.98196	−	4.97091i	−0.438275	−	0.242555i
$421$	4.36067	+	22.8594i	0.212526	+	1.11410i	0.915326	+	0.402713i	$0.131933\pi$
$421$	4.36067	+	22.8594i	0.212526	+	1.11410i	−0.702801	+	0.711387i	$0.748067\pi$
$422$	5.05621	−	5.38431i	0.246132	−	0.262104i
$423$	2.64953	−	6.69196i	0.128825	−	0.325374i
$424$	0.00367528	+	0.0113114i	0.000178488	+	0.000549328i
$425$	14.0229	+	0.961666i	0.680208	+	0.0466477i
$426$	0.117063	−	0.360282i	0.00567171	−	0.0174557i
$427$	−19.9410	−	16.4966i	−0.965013	−	0.798328i
$428$	13.1289	+	6.17799i	0.634610	+	0.298625i
$429$	3.15797	+	2.96553i	0.152468	+	0.143177i
$430$	8.98083	+	0.0253234i	0.433094	+	0.00122120i
$431$	−32.2934	+	4.07960i	−1.55552	+	0.196508i	−0.855570	−	0.517686i	$-0.826793\pi$
$431$	−32.2934	+	4.07960i	−1.55552	+	0.196508i	−0.699948	+	0.714194i	$0.746793\pi$
$432$			1.00000i			0.0481125i
$433$	3.39502	+	26.8744i	0.163154	+	1.29150i	0.834769	+	0.550600i	$0.185601\pi$
$433$	3.39502	+	26.8744i	0.163154	+	1.29150i	−0.671615	+	0.740900i	$0.734399\pi$
$434$	−7.24452	−	8.75712i	−0.347748	−	0.420355i
$435$	−8.57954	+	15.5024i	−0.411357	+	0.743284i
$436$	−1.26325	+	20.0788i	−0.0604988	+	0.961600i
$437$	−9.36611	+	36.4786i	−0.448042	+	1.74501i
$438$	−1.38643	+	5.39979i	−0.0662462	+	0.258012i
$439$	2.37136	−	37.6917i	0.113179	−	1.79893i	−0.375874	−	0.926671i	$-0.622657\pi$
$439$	2.37136	−	37.6917i	0.113179	−	1.79893i	0.489053	−	0.872254i	$-0.337343\pi$
$440$	−5.12061	+	2.39196i	−0.244115	+	0.114032i
$441$	−8.97308	−	10.8466i	−0.427290	−	0.516504i
$442$	−0.603885	−	4.78024i	−0.0287239	−	0.227373i
$443$			27.7288i			1.31744i	0.752389	+	0.658718i	$0.228901\pi$
$443$			27.7288i			1.31744i	−0.752389	+	0.658718i	$0.771099\pi$
$444$	7.83861	−	0.990246i	0.372004	−	0.0469950i
$445$	−6.48548	−	20.1534i	−0.307441	−	0.955365i
$446$	19.4637	+	18.2777i	0.921635	+	0.865473i
$447$	−11.4593	−	5.39234i	−0.542007	−	0.255049i
$448$	−3.53741	−	2.92640i	−0.167127	−	0.138259i
$449$	8.42199	−	25.9202i	0.397458	−	1.22325i	−0.529572	−	0.848265i	$-0.677647\pi$
$449$	8.42199	−	25.9202i	0.397458	−	1.22325i	0.927030	−	0.374986i	$-0.122353\pi$
$450$	−2.43344	+	4.36788i	−0.114713	+	0.205904i
$451$	0.847540	+	2.60846i	0.0399091	+	0.122828i
$452$	2.28400	−	5.76874i	0.107431	−	0.271339i
$453$	5.78011	−	6.15519i	0.271573	−	0.289196i
$454$	1.19477	+	6.26320i	0.0560733	+	0.293946i
$455$	−12.8602	+	12.0085i	−0.602896	+	0.562967i
$456$	−5.39043	+	5.06195i	−0.252430	+	0.237048i
$457$	−0.647827	+	0.210492i	−0.0303041	+	0.00984639i	−0.324130	−	0.946013i	$-0.605071\pi$
$457$	−0.647827	+	0.210492i	−0.0303041	+	0.00984639i	0.293826	+	0.955859i	$0.405071\pi$
$458$	21.0046	+	4.00684i	0.981481	+	0.187228i
$459$	−0.176514	−	2.80561i	−0.00823897	−	0.130955i
$460$	−1.45923	+	11.2948i	−0.0680369	+	0.526621i
$461$	3.28225	+	5.17200i	0.152870	+	0.240884i	0.912128	−	0.409905i	$-0.134438\pi$
$461$	3.28225	+	5.17200i	0.152870	+	0.240884i	−0.759258	+	0.650789i	$0.774438\pi$
$462$	−11.5810	+	0.728612i	−0.538795	+	0.0338981i
$463$	33.0010	+	20.9431i	1.53369	+	0.973308i	0.991072	+	0.133326i	$0.0425658\pi$
$463$	33.0010	+	20.9431i	1.53369	+	0.973308i	0.542615	+	0.839981i	$0.317434\pi$
$464$	−5.05082	+	6.10540i	−0.234479	+	0.283436i
$465$	−4.27515	+	3.51645i	−0.198255	+	0.163072i
$466$	−21.3489	−	5.48146i	−0.988968	−	0.253924i
$467$	14.9455	−	7.03283i	0.691596	−	0.325440i	−0.0476611	−	0.998864i	$-0.515177\pi$
$467$	14.9455	−	7.03283i	0.691596	−	0.325440i	0.739257	+	0.673423i	$0.235177\pi$
$468$	1.63008	+	0.529645i	0.0753504	+	0.0244828i
$469$	22.0351	+	12.1139i	1.01749	+	0.559367i
$470$	14.1250	−	7.71347i	0.651535	−	0.355796i
$471$	3.40678	+	0.430376i	0.156976	+	0.0198307i
$472$	1.17884	−	9.33144i	0.0542603	−	0.429515i
$473$	8.57119	−	5.43944i	0.394104	−	0.250106i
$474$	2.39368	−	1.73911i	0.109945	−	0.0798798i
$475$	−35.8627	+	8.99271i	−1.64549	+	0.412614i
$476$	10.4412	+	7.58594i	0.478569	+	0.347701i
$477$	0.0118700		0.000746797i	0.000543490		3.41935e-5i
$478$	−4.72777	−	8.59978i	−0.216243	−	0.393345i
$479$	−0.555018	+	1.17947i	−0.0253594	+	0.0538915i	−0.917105	−	0.398645i	$-0.869481\pi$
$479$	−0.555018	+	1.17947i	−0.0253594	+	0.0538915i	0.891746	+	0.452536i	$0.149481\pi$
$480$	−1.43018	+	1.71889i	−0.0652783	+	0.0784564i
$481$	2.53750	−	13.3020i	0.115700	−	0.606520i
$482$	−6.13490	−	8.44397i	−0.279437	−	0.384612i
$483$	−11.2646	+	20.4903i	−0.512559	+	0.932341i
$484$	2.47100	−	3.89368i	0.112318	−	0.176985i
$485$	15.7612	+	13.1138i	0.715677	+	0.595467i
$486$	0.929776	+	0.368125i	0.0421755	+	0.0166985i
$487$	−14.0358	−	35.4504i	−0.636024	−	1.60641i	−0.786354	−	0.617776i	$-0.788034\pi$
$487$	−14.0358	−	35.4504i	−0.636024	−	1.60641i	0.150330	−	0.988636i	$-0.451966\pi$
$488$	−4.34352	+	3.59327i	−0.196622	+	0.162660i
$489$	3.46895	−	0.890675i	0.156871	−	0.0402777i
$490$	0.0887570	−	31.4772i	0.00400963	−	1.42200i
$491$	26.9789	−	10.6817i	1.21754	−	0.482058i	0.330524	−	0.943798i	$-0.392775\pi$
$491$	26.9789	−	10.6817i	1.21754	−	0.482058i	0.887015	+	0.461740i	$0.152775\pi$
$492$	0.742821	+	0.791024i	0.0334889	+	0.0356621i
$493$	13.0930	−	18.0209i	0.589677	−	0.811621i
$494$	5.39637	+	11.4679i	0.242794	+	0.515964i
$495$	0.338969	+	5.64156i	0.0152355	+	0.253569i
$496$	−2.16936	+	1.19262i	−0.0974072	+	0.0535501i
$497$	1.70837	−	0.325888i	0.0766307	−	0.0146181i
$498$	−4.11159	−	16.0136i	−0.184245	−	0.717586i
$499$	−9.35758			−0.418903			−0.209451	−	0.977819i	$-0.567168\pi$
$499$	−9.35758			−0.418903			−0.209451	+	0.977819i	$0.567168\pi$
$500$	−10.4297	+	4.02768i	−0.466429	+	0.180123i
$501$	7.90745			0.353279
$502$	0.368833	+	1.43651i	0.0164618	+	0.0641145i
$503$	−20.0580	+	3.82626i	−0.894340	+	0.170605i	−0.614009	−	0.789299i	$-0.710444\pi$
$503$	−20.0580	+	3.82626i	−0.894340	+	0.170605i	−0.280331	+	0.959903i	$0.590444\pi$
$504$	−4.02311	+	2.21172i	−0.179203	+	0.0985179i
$505$	3.29790	−	1.29499i	0.146755	−	0.0576262i
$506$	5.48111	+	11.6479i	0.243665	+	0.517814i
$507$	−5.91448	+	8.14059i	−0.262671	+	0.361536i
$508$	−7.22085	−	7.68943i	−0.320373	−	0.341163i
$509$	−13.0633	+	5.17211i	−0.579019	+	0.229250i	−0.639333	−	0.768930i	$-0.720790\pi$
$509$	−13.0633	+	5.17211i	−0.579019	+	0.229250i	0.0603146	+	0.998179i	$0.480790\pi$
$510$	3.70911	−	5.07499i	0.164242	−	0.224725i
$511$	−24.7903	+	6.36507i	−1.09666	+	0.281574i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	2.72213	+	6.87532i	0.120185	+	0.303553i
$514$	27.9022	+	11.0473i	1.23071	+	0.487274i
$515$	21.9515	+	1.44322i	0.967297	+	0.0635959i
$516$	2.15208	−	3.39113i	0.0947398	−	0.149286i
$517$	8.76389	−	15.9415i	0.385435	−	0.701104i
$518$	21.3207	+	29.3454i	0.936777	+	1.28936i
$519$	3.39499	−	17.7972i	0.149024	−	0.781209i
$520$	2.04445	+	3.24170i	0.0896550	+	0.142158i
$521$	9.49787	−	20.1840i	0.416109	−	0.884277i	−0.581392	−	0.813624i	$-0.697492\pi$
$521$	9.49787	−	20.1840i	0.416109	−	0.884277i	0.997501	−	0.0706530i	$-0.0225083\pi$
$522$	3.81732	+	6.94368i	0.167080	+	0.303917i
$523$	−41.2213	−	2.59342i	−1.80248	−	0.113402i	−0.874266	−	0.485448i	$-0.838657\pi$
$523$	−41.2213	−	2.59342i	−1.80248	−	0.113402i	−0.928215	+	0.372045i	$0.878657\pi$
$524$	−7.54539	−	5.48204i	−0.329622	−	0.239484i
$525$	−22.9545	−	0.129452i	−1.00182	−	0.00564974i
$526$	−21.4889	+	15.6126i	−0.936960	+	0.680741i
$527$	5.87587	−	3.72894i	0.255957	−	0.162435i
$528$	−0.316784	+	2.50760i	−0.0137863	+	0.109129i
$529$	2.91702	+	0.368506i	0.126827	+	0.0160220i
$530$	0.0193352	+	0.0182598i	0.000839868	+	0.000793157i
$531$	−8.24220	−	4.53119i	−0.357681	−	0.196637i
$532$	−32.2869	−	10.4907i	−1.39981	−	0.454827i
$533$	1.68286	−	0.791895i	0.0728929	−	0.0343008i
$534$	−9.17062	−	2.35462i	−0.396852	−	0.101894i
$535$	32.3866	−	1.94593i	1.40020	−	0.0841297i
$536$	3.49125	−	4.22020i	0.150799	−	0.182285i
$537$	−7.82015	−	4.96282i	−0.337464	−	0.214161i
$538$	7.00004	−	0.440405i	0.301793	−	0.0189872i
$539$	−19.0649	−	30.0415i	−0.821184	−	1.29398i
$540$	1.07170	+	1.96251i	0.0461188	+	0.0844530i
$541$	1.18434	+	18.8246i	0.0509188	+	0.809332i	0.937766	+	0.347268i	$0.112891\pi$
$541$	1.18434	+	18.8246i	0.0509188	+	0.809332i	−0.886847	+	0.462063i	$0.847109\pi$
$542$	−18.7604	−	3.57874i	−0.805828	−	0.153720i
$543$	7.23036	−	2.34929i	0.310284	−	0.100818i
$544$	2.04925	−	1.92437i	0.0878607	−	0.0825067i
$545$	19.0394	+	40.7587i	0.815558	+	1.74591i
$546$	1.47446	+	7.72941i	0.0631012	+	0.330788i
$547$	26.4343	−	28.1497i	1.13025	−	1.20360i	0.153744	−	0.988111i	$-0.450867\pi$
$547$	26.4343	−	28.1497i	1.13025	−	1.20360i	0.976507	−	0.215485i	$-0.0691331\pi$
$548$	8.34414	−	21.0749i	0.356444	−	0.900275i
$549$	1.74198	+	5.36127i	0.0743460	+	0.228814i
$550$	−7.48577	+	10.1820i	−0.319194	+	0.434163i
$551$	−18.1063	+	55.7256i	−0.771356	+	2.37399i
$552$	3.92434	+	3.24650i	0.167031	+	0.138180i
$553$	12.2908	+	5.78359i	0.522656	+	0.245943i
$554$	7.13599	+	6.70114i	0.303179	+	0.284704i
$555$	14.3221	−	10.3440i	0.607939	−	0.439080i
$556$	6.32423	−	0.798936i	0.268207	−	0.0338824i
$557$		−	31.6055i		−	1.33917i	−0.742737	−	0.669583i	$-0.766473\pi$
$557$		−	31.6055i		−	1.33917i	0.742737	−	0.669583i	$-0.233527\pi$
$558$	0.310272	+	2.45605i	0.0131348	+	0.103973i
$559$	−4.38797	−	5.30415i	−0.185591	−	0.224341i
$560$	−10.0784	−	1.95203i	−0.425892	−	0.0824885i
$561$	0.446145	−	7.09128i	0.0188363	−	0.299394i
$562$	2.96594	−	11.5516i	0.125111	−	0.487274i
$563$	−7.41116	+	28.8646i	−0.312343	+	1.21650i	0.597610	+	0.801787i	$0.296117\pi$
$563$	−7.41116	+	28.8646i	−0.312343	+	1.21650i	−0.909954	+	0.414710i	$0.863883\pi$
$564$	0.451928	−	7.18318i	0.0190296	−	0.302467i
$565$	−1.70000	−	13.7690i	−0.0715194	−	0.579266i
$566$	−10.1640	−	12.2862i	−0.427226	−	0.516427i
$567$	0.575402	+	4.55478i	0.0241646	+	0.191283i
$568$		−	0.378823i		−	0.0158951i
$569$	7.80170	−	0.985585i	0.327064	−	0.0413179i	0.0399134	−	0.999203i	$-0.487292\pi$
$569$	7.80170	−	0.985585i	0.327064	−	0.0413179i	0.287151	+	0.957885i	$0.407292\pi$
$570$	−5.15386	+	15.7111i	−0.215872	+	0.658065i
$571$	4.70268	+	4.41611i	0.196801	+	0.184809i	0.776682	−	0.629892i	$-0.216901\pi$
$571$	4.70268	+	4.41611i	0.196801	+	0.184809i	−0.579881	+	0.814701i	$0.696901\pi$
$572$	3.91981	+	1.84452i	0.163895	+	0.0771233i
$573$	0.604048	+	0.499712i	0.0252345	+	0.0208758i
$574$	−1.53946	+	4.73797i	−0.0642558	+	0.197759i
$575$	9.24090	+	23.7300i	0.385372	+	0.989608i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	16.1025	−	40.6703i	0.670356	−	1.69313i	−0.0492900	−	0.998785i	$-0.515696\pi$
$577$	16.1025	−	40.6703i	0.670356	−	1.69313i	0.719646	−	0.694341i	$-0.244304\pi$
$578$	6.22759	−	6.63171i	0.259034	−	0.275843i
$579$	3.94982	+	20.7057i	0.164149	+	0.860500i
$580$	−3.36912	+	17.3949i	−0.139895	+	0.722284i
$581$	55.3307	−	51.9590i	2.29550	−	2.15562i
$582$	8.72058	−	2.83349i	0.361480	−	0.117452i
$583$	0.0295287	+	0.00563290i	0.00122295	+	0.000233291i
$584$	0.350053	+	5.56393i	0.0144853	+	0.230237i
$585$	3.76667	−	0.707529i	0.155733	−	0.0292527i
$586$	14.2177	+	22.4035i	0.587328	+	0.925480i
$587$	−1.49652	+	0.0941530i	−0.0617680	+	0.00388611i	−0.0936444	−	0.995606i	$-0.529852\pi$
$587$	−1.49652	+	0.0941530i	−0.0617680	+	0.00388611i	0.0318765	+	0.999492i	$0.489852\pi$
$588$	−11.8857	−	7.54289i	−0.490158	−	0.311063i
$589$	−11.6686	+	14.1049i	−0.480797	+	0.581183i
$590$	−7.68707	−	19.5764i	−0.316472	−	0.805949i
$591$	−24.6786	−	6.33638i	−1.01514	−	0.260644i
$592$	7.14895	−	3.36404i	0.293820	−	0.138261i
$593$	−15.5806	−	5.06243i	−0.639817	−	0.207889i	−0.0288979	−	0.999582i	$-0.509200\pi$
$593$	−15.5806	−	5.06243i	−0.639817	−	0.207889i	−0.610919	+	0.791693i	$0.709200\pi$
$594$	2.21489	+	1.21765i	0.0908782	+	0.0499607i
$595$	28.6208	+	3.69766i	1.17334	+	0.151589i
$596$	−12.5648	−	1.58730i	−0.514673	−	0.0650183i
$597$	0.275845	−	2.18353i	0.0112896	−	0.0893661i
$598$	7.37056	−	4.67750i	0.301404	−	0.191277i
$599$	35.0104	−	25.4365i	1.43048	−	1.03931i	0.440558	−	0.897724i	$-0.354781\pi$
$599$	35.0104	−	25.4365i	1.43048	−	1.03931i	0.989926	−	0.141583i	$-0.0452193\pi$
$600$	−0.964589	+	4.90607i	−0.0393792	+	0.200290i
$601$	−12.6886	−	9.21882i	−0.517580	−	0.376044i	0.298112	−	0.954531i	$-0.403643\pi$
$601$	−12.6886	−	9.21882i	−0.517580	−	0.376044i	−0.815691	+	0.578487i	$0.803643\pi$
$602$	18.4027	+	1.15780i	0.750036	+	0.0471883i
$603$	−2.63863	−	4.79965i	−0.107453	−	0.195457i
$604$	3.59515	−	7.64008i	0.146285	−	0.310871i
$605$	0.676499	−	10.2896i	0.0275036	−	0.418331i
$606$	0.296905	−	1.55643i	0.0120610	−	0.0632257i
$607$	24.0289	+	33.0729i	0.975301	+	1.34239i	0.939323	+	0.343035i	$0.111455\pi$
$607$	24.0289	+	33.0729i	0.975301	+	1.34239i	0.0359787	+	0.999353i	$0.488545\pi$
$608$	−3.56237	+	6.47994i	−0.144473	+	0.262796i
$609$	−19.4923	+	30.7150i	−0.789869	+	1.24463i
$610$	−4.67328	+	11.7068i	−0.189215	+	0.473995i
$611$	−11.4698	−	4.54121i	−0.464018	−	0.183718i
$612$	−1.03486	−	2.61375i	−0.0418316	−	0.105655i
$613$	23.7812	−	19.6735i	0.960514	−	0.794607i	−0.0182000	−	0.999834i	$-0.505794\pi$
$613$	23.7812	−	19.6735i	0.960514	−	0.794607i	0.978714	+	0.205228i	$0.0657935\pi$
$614$	9.80310	−	2.51701i	0.395621	−	0.101578i
$615$	2.30554	+	0.756308i	0.0929682	+	0.0304973i
$616$	−10.7890	+	4.27166i	−0.434701	+	0.172110i
$617$	1.96726	+	2.09492i	0.0791989	+	0.0843383i	0.767347	−	0.641232i	$-0.221576\pi$
$617$	1.96726	+	2.09492i	0.0791989	+	0.0843383i	−0.688148	+	0.725570i	$0.741576\pi$
$618$	5.78274	−	7.95926i	0.232616	−	0.320168i
$619$	2.29967	+	4.88706i	0.0924317	+	0.196427i	0.945697	−	0.325050i	$-0.105381\pi$
$619$	2.29967	+	4.88706i	0.0924317	+	0.196427i	−0.853265	+	0.521477i	$0.825381\pi$
$620$	−2.97926	+	4.66544i	−0.119650	+	0.187369i
$621$	4.46316	−	2.45365i	0.179101	−	0.0984614i
$622$	15.6532	−	2.98600i	0.627635	−	0.119728i
$623$	−10.8100	−	42.1021i	−0.433093	−	1.68679i
$624$	1.71397			0.0686136
$625$	−16.1518	+	19.0819i	−0.646074	+	0.763275i
$626$	−8.72733			−0.348814
$627$	4.64804	+	18.1029i	0.185625	+	0.722961i
$628$	3.37303	−	0.643441i	0.134599	−	0.0256761i
$629$	−19.4634	+	10.7001i	−0.776056	+	0.426640i
$630$	−5.52508	+	8.65211i	−0.220124	+	0.344708i
$631$	14.6738	+	31.1835i	0.584156	+	1.24139i	0.950445	+	0.310893i	$0.100628\pi$
$631$	14.6738	+	31.1835i	0.584156	+	1.24139i	−0.366289	+	0.930501i	$0.619372\pi$
$632$	1.73911	−	2.39368i	0.0691780	−	0.0952153i
$633$	−5.05621	−	5.38431i	−0.200966	−	0.214007i
$634$	−9.46102	+	3.74588i	−0.375745	+	0.148768i
$635$	−22.4118	−	7.35196i	−0.889385	−	0.291754i
$636$	0.0115198	−	0.00295778i	0.000456790	−	0.000117284i
$637$	−18.5907	+	15.3796i	−0.736590	+	0.609361i
$638$	7.37268	+	18.6213i	0.291887	+	0.737223i
$639$	−0.352221	−	0.139454i	−0.0139337	−	0.00551672i
$640$	−0.829011	+	2.07671i	−0.0327695	+	0.0820893i
$641$	19.5411	−	30.7919i	0.771829	−	1.21621i	−0.199833	−	0.979830i	$-0.564040\pi$
$641$	19.5411	−	30.7919i	0.771829	−	1.21621i	0.971661	−	0.236377i	$-0.0759601\pi$
$642$	6.99017	−	12.7151i	0.275880	−	0.501824i
$643$	11.6996	+	16.1032i	0.461389	+	0.635047i	0.974796	−	0.223098i	$-0.0716170\pi$
$643$	11.6996	+	16.1032i	0.461389	+	0.635047i	−0.513407	+	0.858145i	$0.671617\pi$
$644$	−4.38146	+	22.9684i	−0.172654	+	0.905082i
$645$	0.589184	−	8.96151i	0.0231991	−	0.352859i
$646$	8.85084	−	18.8090i	0.348232	−	0.740030i
$647$	−6.06274	−	11.0281i	−0.238351	−	0.433559i	0.729895	−	0.683560i	$-0.239569\pi$
$647$	−6.06274	−	11.0281i	−0.238351	−	0.433559i	−0.968246	+	0.250001i	$0.919569\pi$
$648$	0.998027	+	0.0627905i	0.0392062	+	0.00246664i
$649$	−19.2328	−	13.9734i	−0.754952	−	0.548505i
$650$	7.48640	+	4.17083i	0.293641	+	0.163594i
$651$	−9.19473	+	6.68036i	−0.360370	+	0.261824i
$652$	3.02393	−	1.91905i	0.118426	−	0.0751557i
$653$	2.18021	−	17.2581i	0.0853182	−	0.675363i	−0.890220	−	0.455531i	$-0.849449\pi$
$653$	2.18021	−	17.2581i	0.0853182	−	0.675363i	0.975538	−	0.219831i	$-0.0705507\pi$
$654$	19.9599	+	2.52152i	0.780492	+	0.0985991i
$655$	−20.6830	−	2.67215i	−0.808153	−	0.104409i
$656$	0.950904	+	0.522764i	0.0371266	+	0.0204105i
$657$	5.30208	+	1.72275i	0.206854	+	0.0672108i
$658$	29.8983	−	14.0691i	1.16556	−	0.548469i
$659$	29.3313	+	7.53100i	1.14259	+	0.293366i	0.772118	−	0.635479i	$-0.219197\pi$
$659$	29.3313	+	7.53100i	1.14259	+	0.293366i	0.370468	+	0.928845i	$0.379197\pi$
$660$	2.06572	+	5.26070i	0.0804080	+	0.204772i
$661$	18.7290	−	22.6395i	0.728474	−	0.880574i	−0.268090	−	0.963394i	$-0.586393\pi$
$661$	18.7290	−	22.6395i	0.728474	−	0.880574i	0.996565	+	0.0828197i	$0.0263926\pi$
$662$	−17.0736	−	10.8352i	−0.663583	−	0.421123i
$663$	−4.80872	+	0.302539i	−0.186755	+	0.0117497i
$664$	−8.85882	−	13.9593i	−0.343789	−	0.541725i
$665$	−74.6063	+	14.0140i	−2.89311	+	0.543440i
$666$	−0.496102	−	7.88532i	−0.0192236	−	0.305550i
$667$	39.6423	+	7.56218i	1.53496	+	0.292809i
$668$	7.52043	−	2.44354i	0.290974	−	0.0945433i
$669$	19.4637	−	18.2777i	0.752512	−	0.706655i
$670$	2.32882	−	12.0238i	0.0899700	−	0.464519i
$671$	2.66984	+	13.9958i	0.103068	+	0.540301i
$672$	−3.14274	+	3.34668i	−0.121234	+	0.129101i
$673$	0.342372	−	0.864732i	0.0131975	−	0.0333330i	−0.923028	−	0.384732i	$-0.874294\pi$
$673$	0.342372	−	0.864732i	0.0131975	−	0.0333330i	0.936226	+	0.351399i	$0.114294\pi$
$674$	9.76791	+	30.0625i	0.376246	+	1.15797i
$675$	4.20646	+	2.70290i	0.161907	+	0.104035i
$676$	−3.10943	+	9.56983i	−0.119593	+	0.368071i
$677$	−5.01610	−	4.14968i	−0.192784	−	0.159485i	0.536024	−	0.844203i	$-0.319926\pi$
$677$	−5.01610	−	4.14968i	−0.192784	−	0.159485i	−0.728809	+	0.684717i	$0.759926\pi$
$678$	−5.61394	−	2.64172i	−0.215602	−	0.101455i
$679$	30.6869	+	28.8169i	1.17766	+	1.10589i
$680$	1.95931	−	5.97278i	0.0751362	−	0.229046i
$681$	6.32586	−	0.799142i	0.242407	−	0.0306232i
$682$			6.25710i			0.239597i
$683$	1.22195	+	9.67273i	0.0467566	+	0.370117i	0.998081	+	0.0619247i	$0.0197239\pi$
$683$	1.22195	+	9.67273i	0.0467566	+	0.370117i	−0.951324	+	0.308192i	$0.900276\pi$
$684$	4.71349	+	5.69764i	0.180225	+	0.217855i
$685$	−6.21059	−	50.3022i	−0.237294	−	1.92195i
$686$	2.04012	−	32.4267i	0.0778920	−	1.23806i
$687$	5.31783	−	20.7116i	0.202888	−	0.790196i
$688$	0.998829	−	3.89018i	0.0380800	−	0.148312i
$689$	0.00127999	−	0.0203448i	4.87635e−5	−	0.000775074i
$690$	11.1809	+	2.16555i	0.425648	+	0.0824412i
$691$	−6.51184	−	7.87146i	−0.247722	−	0.299444i	0.631966	−	0.774996i	$-0.282248\pi$
$691$	−6.51184	−	7.87146i	−0.247722	−	0.299444i	−0.879688	+	0.475552i	$0.842248\pi$
$692$	−2.27080	−	17.9752i	−0.0863228	−	0.683316i
$693$			11.6039i			0.440794i
$694$	−4.98560	+	0.629828i	−0.189251	+	0.0239080i
$695$	11.5552	−	8.34563i	0.438312	−	0.316568i
$696$	5.77621	+	5.42422i	0.218946	+	0.205604i
$697$	−2.76014	−	1.29882i	−0.104548	−	0.0491965i
$698$	25.2506	+	20.8891i	0.955751	+	0.790666i
$699$	−6.81116	+	20.9626i	−0.257622	+	0.792878i
$700$	−21.8711	+	6.97023i	−0.826649	+	0.263450i
$701$	−6.39297	−	19.6755i	−0.241459	−	0.743135i	−0.996199	−	0.0871102i	$-0.972237\pi$
$701$	−6.39297	−	19.6755i	−0.241459	−	0.743135i	0.754740	−	0.656025i	$-0.227763\pi$
$702$	0.630953	−	1.59361i	0.0238138	−	0.0601468i
$703$	39.9940	−	42.5893i	1.50840	−	1.60629i
$704$	0.473613	+	2.48276i	0.0178499	+	0.0935727i
$705$	−6.81134	−	14.5814i	−0.256530	−	0.549168i
$706$	−14.4083	+	13.5303i	−0.542265	+	0.509221i
$707$	6.91836	−	2.24791i	0.260192	−	0.0845414i
$708$	−9.23901	−	1.76244i	−0.347223	−	0.0662364i
$709$	3.06984	+	48.7937i	0.115290	+	1.83248i	0.453319	+	0.891348i	$0.350240\pi$
$709$	3.06984	+	48.7937i	0.115290	+	1.83248i	−0.338029	+	0.941136i	$0.609760\pi$
$710$	−0.405987	−	0.743445i	−0.0152364	−	0.0279010i
$711$	−1.58537	−	2.49815i	−0.0594562	−	0.0936880i
$712$	−9.44939	+	0.594506i	−0.354131	+	0.0222800i
$713$	10.6457	+	6.75596i	0.398684	+	0.253013i
$714$	8.22658	−	9.94422i	0.307872	−	0.372153i
$715$	9.66945	−	0.580982i	0.361617	−	0.0217275i
$716$	−8.97100	−	2.30336i	−0.335262	−	0.0860806i
$717$	−8.87967	+	4.17846i	−0.331618	+	0.156047i
$718$	5.09357	+	1.65500i	0.190090	+	0.0617641i
$719$	−6.79122	−	3.73350i	−0.253270	−	0.139236i	0.350062	−	0.936727i	$-0.386160\pi$
$719$	−6.79122	−	3.73350i	−0.253270	−	0.139236i	−0.603332	+	0.797490i	$0.706160\pi$
$720$	1.62570	+	1.53528i	0.0605863	+	0.0572167i
$721$	44.8108	+	5.66091i	1.66884	+	0.210823i
$722$	−4.47190	+	35.3987i	−0.166427	+	1.31740i
$723$	−8.81252	+	5.59259i	−0.327741	+	0.207991i
$724$	6.15051	−	4.46861i	0.228582	−	0.166074i
$725$	12.0303	+	37.7484i	0.446793	+	1.40194i
$726$	−3.73084	−	2.71061i	−0.138465	−	0.100600i
$727$	5.43439	+	0.341903i	0.201550	+	0.0126805i	0.163245	−	0.986586i	$-0.447804\pi$
$727$	5.43439	+	0.341903i	0.201550	+	0.0126805i	0.0383055	+	0.999266i	$0.487804\pi$
$728$	3.79082	+	6.89547i	0.140497	+	0.255563i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	6.64987	+	10.5441i	0.246123	+	0.390256i
$731$	−2.11565	+	11.0906i	−0.0782503	+	0.410202i
$732$	3.31345	+	4.56057i	0.122469	+	0.168564i
$733$	5.42800	−	9.87349i	0.200488	−	0.364686i	−0.756882	−	0.653552i	$-0.773278\pi$
$733$	5.42800	−	9.87349i	0.200488	−	0.364686i	0.957370	+	0.288866i	$0.0932782\pi$
$734$	−16.6656	+	26.2607i	−0.615137	+	0.969301i
$735$	−31.4095	−	2.06505i	−1.15856	−	0.0761706i
$736$	4.73549	+	1.87491i	0.174553	+	0.0691103i
$737$	−5.09618	−	12.8715i	−0.187720	−	0.474127i
$738$	0.836105	−	0.691686i	0.0307774	−	0.0254613i
$739$	−8.14121	+	2.09031i	−0.299479	+	0.0768932i	−0.395440	−	0.918492i	$-0.629408\pi$
$739$	−8.14121	+	2.09031i	−0.299479	+	0.0768932i	0.0959604	+	0.995385i	$0.469408\pi$
$740$	10.4246	−	14.2635i	0.383217	−	0.524338i
$741$	11.7841	−	4.66565i	0.432899	−	0.171397i
$742$	0.0373781	+	0.0398036i	0.00137219	+	0.00146124i
$743$	−16.7177	+	23.0099i	−0.613311	+	0.844151i	−0.996845	−	0.0793765i	$-0.974707\pi$
$743$	−16.7177	+	23.0099i	−0.613311	+	0.844151i	0.383533	+	0.923527i	$0.374707\pi$
$744$	1.05405	+	2.23997i	0.0386433	+	0.0821212i
$745$	−26.3596	+	10.3506i	−0.965742	+	0.379218i
$746$	−5.34873	+	2.94049i	−0.195831	+	0.107659i
$747$	−16.2402	+	3.09798i	−0.594196	+	0.113349i
$748$	−1.76702	−	6.88207i	−0.0646085	−	0.251633i
$749$	66.6145			2.43404
$750$	3.36485	+	10.6620i	0.122867	+	0.389320i
$751$	−47.7358			−1.74191			−0.870953	−	0.491367i	$-0.836497\pi$
$751$	−47.7358			−1.74191			−0.870953	+	0.491367i	$0.836497\pi$
$752$	−1.78992	−	6.97127i	−0.0652716	−	0.254216i
$753$	1.45683	−	0.277906i	0.0530899	−	0.0101274i
$754$	11.9012	−	6.54276i	0.433418	−	0.238273i
$755$	−1.13239	−	18.8467i	−0.0412119	−	0.685901i
$756$	1.95474	+	4.15404i	0.0710934	+	0.151081i
$757$	−24.4046	+	33.5901i	−0.887000	+	1.22085i	0.0874320	+	0.996170i	$0.472134\pi$
$757$	−24.4046	+	33.5901i	−0.887000	+	1.22085i	−0.974432	+	0.224681i	$0.927866\pi$
$758$	8.89859	+	9.47603i	0.323211	+	0.344185i
$759$	11.9691	−	4.73891i	0.434452	−	0.172012i
$760$	−0.0466234	+	16.5348i	−0.00169121	+	0.599779i
$761$	−14.4407	+	3.70775i	−0.523477	+	0.134406i	−0.501176	−	0.865345i	$-0.667099\pi$
$761$	−14.4407	+	3.70775i	−0.523477	+	0.134406i	−0.0223007	+	0.999751i	$0.507099\pi$
$762$	−8.12765	+	6.72378i	−0.294434	+	0.243577i
$763$	34.0013	+	85.8776i	1.23093	+	3.10898i
$764$	0.728903	+	0.288593i	0.0263708	+	0.0104409i
$765$	−4.83208	−	4.02045i	−0.174704	−	0.145360i
$766$	−18.8923	+	29.7694i	−0.682605	+	1.07561i
$767$	−7.76630	+	14.1269i	−0.280425	+	0.510091i
$768$	0.587785	+	0.809017i	0.0212099	+	0.0291929i
$769$	−5.10795	+	26.7768i	−0.184197	+	0.965596i	0.763351	+	0.645984i	$0.223553\pi$
$769$	−5.10795	+	26.7768i	−0.184197	+	0.965596i	−0.947548	+	0.319612i	$0.896447\pi$
$770$	−16.5956	+	19.9458i	−0.598062	+	0.718797i
$771$	12.7774	−	27.1535i	0.460169	−	0.977908i
$772$	10.1549	+	18.4717i	0.365484	+	0.664812i
$773$	1.02510	+	0.0644939i	0.0368703	+	0.00231968i	0.0812150	−	0.996697i	$-0.474120\pi$
$773$	1.02510	+	0.0644939i	0.0368703	+	0.00231968i	−0.0443446	+	0.999016i	$0.514120\pi$
$774$	−3.24931	−	2.36076i	−0.116794	−	0.0848557i
$775$	−0.846867	+	12.3489i	−0.0304203	+	0.443584i
$776$	7.41817	−	5.38962i	0.266297	−	0.193476i
$777$	30.6262	−	19.4360i	1.09871	−	0.697263i
$778$	−1.46502	+	11.5968i	−0.0525234	+	0.415766i
$779$	7.96081	+	1.00568i	0.285226	+	0.0360324i
$780$	3.36368	−	1.83687i	0.120439	−	0.0657703i
$781$	−0.839054	−	0.461274i	−0.0300237	−	0.0165057i
$782$	−13.6169	−	4.42440i	−0.486939	−	0.158216i
$783$	7.16967	−	3.37379i	0.256223	−	0.120569i
$784$	−13.6348	−	3.50083i	−0.486959	−	0.125030i
$785$	5.93004	−	4.87766i	0.211652	−	0.174091i
$786$	−5.94500	+	7.18628i	−0.212051	+	0.256326i
$787$	−25.9121	−	16.4443i	−0.923667	−	0.586177i	−0.0132696	−	0.999912i	$-0.504224\pi$
$787$	−25.9121	−	16.4443i	−0.923667	−	0.586177i	−0.910397	+	0.413735i	$0.864224\pi$
$788$	−25.4287	+	1.59984i	−0.905862	+	0.0569920i
$789$	14.2325	+	22.4268i	0.506690	+	0.798415i
$790$	0.847704	−	6.56142i	0.0301599	−	0.233445i
$791$	−1.78855	−	28.4282i	−0.0635936	−	1.01079i
$792$	2.48276	+	0.473613i	0.0882212	+	0.0168291i
$793$	9.18904	−	2.98570i	0.326312	−	0.106025i
$794$	19.9644	−	18.7478i	0.708509	−	0.665335i
$795$	0.0194379	−	0.0181505i	0.000689391	−	0.000643733i
$796$	−0.412406	−	2.16191i	−0.0146173	−	0.0766267i
$797$	26.7944	−	28.5332i	0.949107	−	1.01070i	−0.0508213	−	0.998708i	$-0.516184\pi$
$797$	26.7944	−	28.5332i	0.949107	−	1.01070i	0.999928	−	0.0119884i	$-0.00381612\pi$
$798$	−12.4973	+	31.5645i	−0.442398	+	1.11737i
$799$	6.25234	+	19.2427i	0.221192	+	0.680759i
$800$	0.598682	+	4.96403i	0.0211666	+	0.175505i
$801$	−2.92580	+	9.00468i	−0.103378	+	0.318165i
$802$	9.78669	+	8.09625i	0.345580	+	0.285889i
$803$	12.7498	+	5.99958i	0.449929	+	0.211721i
$804$	−3.99266	−	3.74935i	−0.140810	−	0.132230i
$805$	16.0167	+	49.7714i	0.564514	+	1.75421i
$806$	4.20959	−	0.531795i	0.148277	−	0.0187317i
$807$		−	7.01388i		−	0.246900i
$808$	−0.198590	−	1.57200i	−0.00698638	−	0.0553029i
$809$	27.6513	+	33.4247i	0.972169	+	1.17515i	0.984528	+	0.175227i	$0.0560659\pi$
$809$	27.6513	+	33.4247i	0.972169	+	1.17515i	−0.0123592	+	0.999924i	$0.503934\pi$
$810$	2.02593	−	0.946363i	0.0711840	−	0.0332518i
$811$	−0.683701	+	10.8671i	−0.0240080	+	0.381596i	0.967615	+	0.252430i	$0.0812299\pi$
$811$	−0.683701	+	10.8671i	−0.0240080	+	0.381596i	−0.991623	+	0.129166i	$0.958770\pi$
$812$	−9.04685	+	35.2352i	−0.317482	+	1.23651i
$813$	−4.74965	+	18.4987i	−0.166577	+	0.648776i
$814$	1.25391	−	19.9304i	0.0439497	−	0.698560i
$815$	3.87785	−	7.00692i	0.135835	−	0.245442i
$816$	−1.79190	−	2.16603i	−0.0627290	−	0.0758264i
$817$	−3.72232	−	29.4652i	−0.130228	−	1.03086i
$818$			26.3351i			0.920784i
$819$	7.80674	−	0.986221i	0.272790	−	0.0344613i
$820$	2.42641	+	0.00684179i	0.0847339	+	0.000238926i
$821$	−3.95705	−	3.71592i	−0.138102	−	0.129686i	0.612418	−	0.790534i	$-0.290197\pi$
$821$	−3.95705	−	3.71592i	−0.138102	−	0.129686i	−0.750520	+	0.660848i	$0.770197\pi$
$822$	−20.5094	−	9.65098i	−0.715347	−	0.336617i
$823$	13.5156	+	11.1811i	0.471123	+	0.389747i	0.842467	−	0.538748i	$-0.181103\pi$
$823$	13.5156	+	11.1811i	0.471123	+	0.389747i	−0.371343	+	0.928496i	$0.621103\pi$
$824$	3.04017	−	9.35667i	0.105909	−	0.325955i
$825$	9.69191	+	8.11034i	0.337429	+	0.282366i
$826$	−13.3437	−	41.0675i	−0.464285	−	1.42892i
$827$	−7.21201	+	18.2155i	−0.250786	+	0.633414i	−0.999568	−	0.0294034i	$-0.990639\pi$
$827$	−7.21201	+	18.2155i	−0.250786	+	0.633414i	0.748781	+	0.662817i	$0.230639\pi$
$828$	3.48650	−	3.71275i	0.121164	−	0.129027i
$829$	−4.78895	−	25.1045i	−0.166327	−	0.871917i	−0.963407	−	0.268043i	$-0.913623\pi$
$829$	−4.78895	−	25.1045i	−0.166327	−	0.871917i	0.797080	−	0.603874i	$-0.206377\pi$
$830$	−32.3458	−	17.9012i	−1.12274	−	0.621359i
$831$	7.13599	−	6.70114i	0.247545	−	0.232460i
$832$	1.63008	−	0.529645i	0.0565128	−	0.0183621i
$833$	38.8720	+	7.41523i	1.34684	+	0.256923i
$834$	−0.400258	−	6.36192i	−0.0138598	−	0.220295i
$835$	12.1402	−	12.8552i	0.420128	−	0.444871i
$836$	10.0147	+	15.7806i	0.346364	+	0.545782i
$837$	2.47069	−	0.155443i	0.0853995	−	0.00537288i
$838$	1.91623	+	1.21607i	0.0661950	+	0.0420086i
$839$	6.46348	−	7.81300i	0.223144	−	0.269735i	−0.647046	−	0.762451i	$-0.723996\pi$
$839$	6.46348	−	7.81300i	0.223144	−	0.269735i	0.870190	+	0.492716i	$0.163996\pi$
$840$	−2.58101	+	9.93599i	−0.0890534	+	0.342824i
$841$	32.7252	+	8.40241i	1.12846	+	0.289738i
$842$	21.0568	−	9.90857i	0.725665	−	0.341472i
$843$	−11.3425	−	3.68542i	−0.390658	−	0.126932i
$844$	−6.47258	−	3.55833i	−0.222795	−	0.122483i
$845$	4.15375	+	22.1133i	0.142893	+	0.760720i
$846$	−7.14063	−	0.902072i	−0.245500	−	0.0310139i
$847$	2.65351	−	21.0047i	0.0911757	−	0.721730i
$848$	0.0100420	−	0.00637284i	0.000344843	−	0.000218844i
$849$	−12.9002	+	9.37251i	−0.442732	+	0.321664i
$850$	−2.55589	−	13.8215i	−0.0876663	−	0.474072i
$851$	−32.5553	−	23.6528i	−1.11598	−	0.810807i
$852$	−0.378076	−	0.0237865i	−0.0129527	−	0.000814913i
$853$	−19.5324	−	35.5294i	−0.668778	−	1.21650i	−0.965217	−	0.261451i	$-0.915799\pi$
$853$	−19.5324	−	35.5294i	−0.668778	−	1.21650i	0.296439	−	0.955052i	$-0.404201\pi$
$854$	−11.0192	+	23.4171i	−0.377071	+	0.801316i
$855$	15.3565	+	6.13020i	0.525180	+	0.209648i
$856$	2.71888	−	14.2528i	0.0929292	−	0.487152i
$857$	2.62272	+	3.60986i	0.0895903	+	0.123310i	0.851459	−	0.524421i	$-0.175718\pi$
$857$	2.62272	+	3.60986i	0.0895903	+	0.123310i	−0.761869	+	0.647731i	$0.775718\pi$
$858$	2.08701	−	3.79626i	0.0712493	−	0.129602i
$859$	−2.36066	+	3.71981i	−0.0805448	+	0.126918i	−0.882212	−	0.470852i	$-0.843947\pi$
$859$	−2.36066	+	3.71981i	−0.0805448	+	0.126918i	0.801667	+	0.597770i	$0.203947\pi$
$860$	−2.20891	−	8.70497i	−0.0753233	−	0.296837i
$861$	4.63196	+	1.83392i	0.157857	+	0.0624999i
$862$	11.9825	+	30.2643i	0.408125	+	1.03081i
$863$	18.3721	−	15.1988i	0.625395	−	0.517372i	−0.269875	−	0.962895i	$-0.586982\pi$
$863$	18.3721	−	15.1988i	0.625395	−	0.517372i	0.895270	+	0.445523i	$0.146982\pi$
$864$	0.968583	−	0.248690i	0.0329519	−	0.00846060i
$865$	−23.7206	−	32.8430i	−0.806525	−	1.11669i
$866$	25.1858	−	9.97175i	0.855847	−	0.338854i
$867$	−6.22759	−	6.63171i	−0.211500	−	0.225225i
$868$	−6.68036	+	9.19473i	−0.226746	+	0.312090i
$869$	−3.18412	−	6.76659i	−0.108014	−	0.229541i
$870$	17.1490	+	4.45470i	0.581406	+	0.151029i
$871$	−8.22643	+	4.52252i	−0.278742	+	0.153240i
$872$	19.7622	−	3.76983i	0.669231	−	0.127663i
$873$	−2.28033	−	8.88129i	−0.0771774	−	0.300586i
$874$	37.6618			1.27393
$875$	−35.4522	+	37.1185i	−1.19850	+	1.25483i
$876$	5.57493			0.188360
$877$	1.08083	+	4.20954i	0.0364969	+	0.142146i	0.984220	−	0.176946i	$-0.0566219\pi$
$877$	1.08083	+	4.20954i	0.0364969	+	0.142146i	−0.947724	+	0.319093i	$0.896622\pi$
$878$	−37.0972	+	7.07668i	−1.25197	+	0.238826i
$879$	23.2520	−	12.7829i	0.784271	−	0.431157i
$880$	3.59026	+	4.36488i	0.121028	+	0.147140i
$881$	1.20122	+	2.55273i	0.0404702	+	0.0860035i	0.924040	−	0.382296i	$-0.124867\pi$
$881$	1.20122	+	2.55273i	0.0404702	+	0.0860035i	−0.883570	+	0.468300i	$0.844867\pi$
$882$	−8.27431	+	11.3886i	−0.278611	+	0.383475i
$883$	11.1112	+	11.8322i	0.373921	+	0.398185i	0.888214	−	0.459429i	$-0.151946\pi$
$883$	11.1112	+	11.8322i	0.373921	+	0.398185i	−0.514294	+	0.857614i	$0.671946\pi$
$884$	−4.47988	+	1.77371i	−0.150675	+	0.0596563i
$885$	−20.0205	+	6.44269i	−0.672981	+	0.216569i
$886$	26.8577	−	6.89588i	0.902302	−	0.231672i
$887$	21.2922	−	17.6144i	0.714921	−	0.591434i	−0.207217	−	0.978295i	$-0.566441\pi$
$887$	21.2922	−	17.6144i	0.714921	−	0.591434i	0.922138	+	0.386861i	$0.126441\pi$
$888$	−2.90852	−	7.34608i	−0.0976035	−	0.246518i
$889$	−45.0266	−	17.8273i	−1.51014	−	0.597908i
$890$	−17.9074	+	11.2937i	−0.600258	+	0.378565i
$891$	1.35432	−	2.13407i	0.0453714	−	0.0714939i
$892$	12.8630	−	23.3977i	0.430685	−	0.783414i
$893$	−31.2830	−	43.0573i	−1.04685	−	1.44086i
$894$	−2.37312	+	12.4403i	−0.0793689	+	0.416066i
$895$	−20.0742	+	5.09389i	−0.671006	+	0.170270i
$896$	−1.95474	+	4.15404i	−0.0653034	+	0.138777i
$897$	−4.20547	−	7.64971i	−0.140416	−	0.255417i
$898$	−27.2004	−	1.71130i	−0.907688	−	0.0571069i
$899$	15.8697	+	11.5300i	0.529282	+	0.384546i
$900$	4.83583	+	1.27074i	0.161194	+	0.0423580i
$901$	−0.0270490	+	0.0196523i	−0.000901133	+	0.000654712i
$902$	2.31573	−	1.46961i	0.0771055	−	0.0489327i
$903$	2.31103	−	18.2936i	0.0769061	−	0.608774i
$904$	−6.15551	−	0.777622i	−0.204729	−	0.0258633i
$905$	7.28142	−	15.3612i	0.242043	−	0.510624i
$906$	−7.39927	−	4.06778i	−0.245824	−	0.135143i
$907$	42.5468	+	13.8243i	1.41274	+	0.459028i	0.913289	−	0.407312i	$-0.133534\pi$
$907$	42.5468	+	13.8243i	1.41274	+	0.459028i	0.499454	+	0.866340i	$0.333534\pi$
$908$	5.76930	−	2.71483i	0.191461	−	0.0900947i
$909$	−1.53472	−	0.394049i	−0.0509034	−	0.0130698i
$910$	14.8294	+	9.46980i	0.491591	+	0.313921i
$911$	−24.7847	+	29.9596i	−0.821155	+	0.992606i	0.178807	+	0.983884i	$0.442776\pi$
$911$	−24.7847	+	29.9596i	−0.821155	+	0.992606i	−0.999962	+	0.00872200i	$0.997224\pi$
$912$	6.24347	+	3.96222i	0.206742	+	0.131202i
$913$	−41.7053	+	2.62387i	−1.38024	+	0.0868375i
$914$	0.364987	+	0.575127i	0.0120727	+	0.0190235i
$915$	11.3903	+	5.39913i	0.376550	+	0.178490i
$916$	−1.34267	−	21.3412i	−0.0443632	−	0.705132i
$917$	−42.0599	−	8.02335i	−1.38894	−	0.264954i
$918$	−2.67357	+	0.868696i	−0.0882410	+	0.0286712i
$919$	−32.4280	+	30.4519i	−1.06970	+	1.00452i	−0.0697245	+	0.997566i	$0.522212\pi$
$919$	−32.4280	+	30.4519i	−1.06970	+	1.00452i	−0.999976	+	0.00694919i	$0.997788\pi$
$920$	11.3028	−	1.39551i	0.372643	−	0.0460086i
$921$	−1.89650	−	9.94180i	−0.0624918	−	0.327593i
$922$	4.19325	−	4.46536i	0.138097	−	0.147059i
$923$	−0.239020	+	0.603695i	−0.00786743	+	0.0198709i
$924$	3.58579	+	11.0359i	0.117964	+	0.363055i
$925$	5.17218	−	39.1645i	0.170060	−	1.28772i
$926$	12.0781	−	37.1726i	0.396911	−	1.22157i
$927$	−7.58045	−	6.27109i	−0.248975	−	0.205970i
$928$	7.16967	+	3.37379i	0.235356	+	0.110750i
$929$	26.9536	+	25.3111i	0.884319	+	0.830431i	0.986403	−	0.164345i	$-0.0525511\pi$
$929$	26.9536	+	25.3111i	0.884319	+	0.830431i	−0.102084	+	0.994776i	$0.532551\pi$
$930$	4.46916	+	3.26633i	0.146550	+	0.107107i
$931$	−103.274	+	13.0465i	−3.38466	+	0.427582i
$932$			22.0414i			0.721989i
$933$	−1.99724	−	15.8098i	−0.0653867	−	0.517589i
$934$	−10.5287	−	12.7270i	−0.344509	−	0.416440i
$935$	−10.8433	−	11.6124i	−0.354615	−	0.379767i
$936$	0.107621	−	1.71058i	0.00351770	−	0.0559122i
$937$	0.220917	−	0.860416i	0.00721705	−	0.0281086i	−0.964873	−	0.262718i	$-0.915381\pi$
$937$	0.220917	−	0.860416i	0.00721705	−	0.0281086i	0.972090	+	0.234609i	$0.0753811\pi$
$938$	6.25341	−	24.3554i	0.204181	−	0.795232i
$939$	−0.547994	+	8.71011i	−0.0178831	+	0.284244i
$940$	−10.9839	−	11.7629i	−0.358254	−	0.383664i
$941$	−23.6587	−	28.5984i	−0.771251	−	0.932282i	0.227892	−	0.973686i	$-0.426817\pi$
$941$	−23.6587	−	28.5984i	−0.771251	−	0.932282i	−0.999142	+	0.0414047i	$0.986817\pi$
$942$	−0.430376	−	3.40678i	−0.0140224	−	0.110999i
$943$		−	5.52672i		−	0.179975i
$944$	−9.33144	+	1.17884i	−0.303713	+	0.0383678i
$945$	8.28811	+	6.05745i	0.269612	+	0.197049i
$946$	−7.40012	−	6.94918i	−0.240599	−	0.225937i
$947$	36.9015	+	17.3645i	1.19914	+	0.564271i	0.918453	−	0.395529i	$-0.129439\pi$
$947$	36.9015	+	17.3645i	1.19914	+	0.564271i	0.280683	+	0.959800i	$0.409439\pi$
$948$	−2.27975	−	1.88598i	−0.0740429	−	0.0612536i
$949$	2.95273	−	9.08758i	0.0958498	−	0.294995i
$950$	17.6289	+	32.4996i	0.571956	+	1.05443i
$951$	3.14443	+	9.67755i	0.101965	+	0.313816i
$952$	4.75101	−	11.9997i	0.153981	−	0.388912i
$953$	18.5699	−	19.7749i	0.601538	−	0.640573i	−0.354069	−	0.935219i	$-0.615202\pi$
$953$	18.5699	−	19.7749i	0.601538	−	0.640573i	0.955606	+	0.294647i	$0.0952020\pi$
$954$	−0.00222861	−	0.0116828i	−7.21540e−5	−	0.000378245i
$955$	1.73977	−	0.214801i	0.0562975	−	0.00695081i
$956$	−7.15386	+	6.71792i	−0.231372	+	0.217273i
$957$	19.0475	−	6.18889i	0.615717	−	0.200059i
$958$	1.28044	+	0.244258i	0.0413693	+	0.00789161i
$959$	−6.53411	−	103.857i	−0.210997	−	3.35371i
$960$	2.02056	+	0.957773i	0.0652134	+	0.0309120i
$961$	−13.3268	−	20.9997i	−0.429898	−	0.677411i
$962$	−13.5152	+	0.850302i	−0.435747	+	0.0274148i
$963$	−12.2511	−	7.77477i	−0.394785	−	0.250538i
$964$	−6.65300	+	8.04209i	−0.214279	+	0.259018i
$965$	39.7254	+	25.3679i	1.27881	+	0.816622i
$966$	22.6480	+	5.81501i	0.728686	+	0.187095i
$967$	−43.7351	+	20.5802i	−1.40643	+	0.661814i	−0.971147	−	0.238482i	$-0.923350\pi$
$967$	−43.7351	+	20.5802i	−1.40643	+	0.661814i	−0.435279	+	0.900296i	$0.643350\pi$
$968$	−4.38587	−	1.42505i	−0.140967	−	0.0458030i
$969$	−18.2161	−	10.0144i	−0.585186	−	0.321709i
$970$	8.78216	−	18.5273i	0.281978	−	0.594875i
$971$	−25.6155	−	3.23600i	−0.822042	−	0.103848i	−0.296949	−	0.954893i	$-0.595969\pi$
$971$	−25.6155	−	3.23600i	−0.822042	−	0.103848i	−0.525092	+	0.851045i	$0.675969\pi$
$972$	0.125333	−	0.992115i	0.00402007	−	0.0318221i
$973$	24.7094	−	15.6811i	0.792148	−	0.502712i
$974$	−30.8461	+	22.4110i	−0.988373	+	0.718095i
$975$	4.63268	−	7.20974i	0.148364	−	0.230896i
$976$	4.56057	+	3.31345i	0.145980	+	0.106061i
$977$	−45.7533	−	2.87856i	−1.46378	−	0.0920931i	−0.689200	−	0.724571i	$-0.742038\pi$
$977$	−45.7533	−	2.87856i	−1.46378	−	0.0920931i	−0.774578	+	0.632478i	$0.782038\pi$
$978$	−1.72539	−	3.13847i	−0.0551718	−	0.100357i
$979$	−10.1893	+	21.6533i	−0.325651	+	0.692043i
$980$	−30.5104	+	7.74210i	−0.974619	+	0.247312i
$981$	3.76983	−	19.7622i	0.120361	−	0.630957i
$982$	−17.0555	−	23.4748i	−0.544262	−	0.749113i
$983$	−13.1497	+	23.9193i	−0.419411	+	0.762906i	−0.998633	−	0.0522635i	$-0.983356\pi$
$983$	−13.1497	+	23.9193i	−0.419411	+	0.762906i	0.579222	+	0.815170i	$0.303356\pi$
$984$	0.581440	−	0.916203i	0.0185356	−	0.0292075i
$985$	−48.1896	+	30.3918i	−1.53545	+	0.968364i
$986$	−20.7108	−	8.20000i	−0.659567	−	0.261141i
$987$	−12.1640	−	30.7227i	−0.387183	−	0.977913i
$988$	9.76556	−	8.07877i	0.310684	−	0.257020i
$989$	−19.8133	+	5.08719i	−0.630026	+	0.161763i
$990$	5.38002	−	1.73132i	0.170988	−	0.0550249i
$991$	−1.34060	+	0.530783i	−0.0425857	+	0.0168609i	−0.389321	−	0.921102i	$-0.627290\pi$
$991$	−1.34060	+	0.530783i	−0.0425857	+	0.0168609i	0.346735	+	0.937963i	$0.387290\pi$
$992$	1.69465	+	1.80462i	0.0538051	+	0.0572966i
$993$	−11.8859	+	16.3595i	−0.377187	+	0.519154i
$994$	−0.740503	−	1.57365i	−0.0234873	−	0.0499131i
$995$	−3.12627	−	3.80079i	−0.0991096	−	0.120493i
$996$	−14.4880	+	7.96483i	−0.459069	+	0.252375i
$997$	42.8532	−	8.17469i	1.35717	−	0.258895i	0.543106	−	0.839664i	$-0.317248\pi$
$997$	42.8532	−	8.17469i	1.35717	−	0.258895i	0.814068	+	0.580769i	$0.197248\pi$
$998$	2.32714	+	9.06360i	0.0736642	+	0.286903i
$999$	−7.90091			−0.249974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.229.3	✓	240
125.119	even	50	inner	750.2.o.a.619.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.229.3	✓	240	1.1	even	1	trivial
750.2.o.a.619.3	yes	240	125.119	even	50	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.20346 + 1.88459i) q^{5} +(0.425779 + 0.904827i) q^{6} +(-2.69851 + 3.71418i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-1.20346 + 1.88459i) q^{5} +(0.425779 + 0.904827i) q^{6} +(-2.69851 + 3.71418i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(2.12467 + 0.696977i) q^{10} +(2.44813 - 0.628572i) q^{11} +(0.770513 - 0.637424i) q^{12} +(-0.630953 - 1.59361i) q^{13} +(4.26859 + 1.69005i) q^{14} +(0.829011 - 2.07671i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.35429 + 2.46344i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(1.38561 - 7.26362i) q^{19} +(0.146696 - 2.23125i) q^{20} +(1.95474 - 4.15404i) q^{21} +(-1.21765 - 2.21489i) q^{22} +(-5.08310 - 0.319802i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-2.10335 - 4.53607i) q^{25} +(-1.38663 + 1.00744i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(0.575402 - 4.55478i) q^{28} +(-7.86132 - 0.993116i) q^{29} +(-2.21764 - 0.286508i) q^{30} +(-2.16936 - 1.19262i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-2.28698 + 1.07617i) q^{33} +(2.72284 + 0.699107i) q^{34} +(-3.75214 - 9.55547i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(6.67096 + 4.23352i) q^{37} +(-7.38001 + 0.464311i) q^{38} +(0.918389 + 1.44715i) q^{39} +(-2.19763 + 0.412802i) q^{40} +(0.0681357 + 1.08299i) q^{41} +(-4.50966 - 0.860264i) q^{42} +(3.81979 - 1.24112i) q^{43} +(-1.84249 + 1.73022i) q^{44} +(-0.425189 + 2.19527i) q^{45} +(0.954362 + 5.00294i) q^{46} +(4.92695 - 5.24667i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-4.35006 - 13.3881i) q^{49} +(-3.87048 + 3.16534i) q^{50} +(0.868696 - 2.67357i) q^{51} +(1.32063 + 1.09252i) q^{52} +(0.0107615 + 0.00506399i) q^{53} +(0.728969 + 0.684547i) q^{54} +(-1.76163 + 5.37018i) q^{55} +(-4.55478 + 0.575402i) q^{56} +7.39460i q^{57} +(0.993116 + 7.86132i) q^{58} +(-5.99536 - 7.24715i) q^{59} +(0.273997 + 2.21922i) q^{60} +(-0.353961 + 5.62605i) q^{61} +(-0.615650 + 2.39780i) q^{62} +(-1.14173 + 4.44675i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(3.76262 + 0.728760i) q^{65} +(1.61111 + 1.94750i) q^{66} +(-0.686466 - 5.43394i) q^{67} -2.81116i q^{68} +(5.05299 - 0.638341i) q^{69} +(-8.32214 + 6.01061i) q^{70} +(-0.276150 - 0.259322i) q^{71} +(0.904827 + 0.425779i) q^{72} +(4.29556 + 3.55360i) q^{73} +(2.44151 - 7.51421i) q^{74} +(2.91607 + 4.06159i) q^{75} +(2.28506 + 7.03268i) q^{76} +(-4.27166 + 10.7890i) q^{77} +(1.17329 - 1.24943i) q^{78} +(-0.554414 - 2.90634i) q^{79} +(0.946363 + 2.02593i) q^{80} +(0.728969 - 0.684547i) q^{81} +(1.03202 - 0.335323i) q^{82} +(-16.2402 - 3.09798i) q^{83} +(0.288270 + 4.58192i) q^{84} +(-3.01273 - 5.51693i) q^{85} +(-2.15208 - 3.39113i) q^{86} +(7.90817 - 0.497540i) q^{87} +(2.13407 + 1.35432i) q^{88} +(-6.03518 + 7.29528i) q^{89} +(2.23204 - 0.134111i) q^{90} +(7.62158 + 1.95689i) q^{91} +(4.60842 - 2.16856i) q^{92} +(2.35441 + 0.764995i) q^{93} +(-6.30712 - 3.46737i) q^{94} +(12.0214 + 11.3528i) q^{95} +(0.992115 + 0.125333i) q^{96} +(1.14923 - 9.09706i) q^{97} +(-11.8857 + 7.54289i) q^{98} +(2.04482 - 1.48565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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