LMFDB - Embedded newform 350.2.x.a.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(3,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("350.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.x (of order $60$, degree $16$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$20$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.14
Character	$\chi$	$=$	350.3
Dual form			350.2.x.a.117.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.544639 - 0.838671i) q^{2} +(-0.327039 + 0.851967i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80326 + 1.32222i) q^{5} +(0.536401 + 0.738293i) q^{6} +(2.28229 - 1.33834i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.61054 + 1.45014i) q^{9} +O(q^{10})$	\(q+(0.544639 - 0.838671i) q^{2} +(-0.327039 + 0.851967i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80326 + 1.32222i) q^{5} +(0.536401 + 0.738293i) q^{6} +(2.28229 - 1.33834i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.61054 + 1.45014i) q^{9} +(0.126777 + 2.23247i) q^{10} +(3.49679 + 3.88358i) q^{11} +(0.911329 - 0.0477607i) q^{12} +(0.360985 + 0.183931i) q^{13} +(0.120595 - 2.64300i) q^{14} +(-0.536746 - 1.96873i) q^{15} +(-0.669131 + 0.743145i) q^{16} +(2.15222 - 2.65777i) q^{17} +(2.09335 - 0.560912i) q^{18} +(-1.38042 - 0.614601i) q^{19} +(1.94136 + 1.10957i) q^{20} +(0.393825 + 2.38212i) q^{21} +(5.16154 - 0.817507i) q^{22} +(6.59771 + 4.28460i) q^{23} +(0.456290 - 0.790317i) q^{24} +(1.50349 - 4.76860i) q^{25} +(0.350864 - 0.202572i) q^{26} +(-4.20152 + 2.14078i) q^{27} +(-2.15093 - 1.54062i) q^{28} +(0.214451 - 0.295167i) q^{29} +(-1.94345 - 0.622096i) q^{30} +(-4.84281 + 0.509000i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-4.45227 + 1.70907i) q^{33} +(-1.05681 - 3.25252i) q^{34} +(-2.34598 + 5.43106i) q^{35} +(0.669701 - 2.06113i) q^{36} +(0.269961 + 5.15116i) q^{37} +(-1.26728 + 0.822979i) q^{38} +(-0.274760 + 0.247395i) q^{39} +(1.98790 - 1.02384i) q^{40} +(-4.77457 + 1.55135i) q^{41} +(2.21231 + 0.967108i) q^{42} +(-9.07822 - 9.07822i) q^{43} +(2.12555 - 4.77407i) q^{44} +(-4.82162 - 0.485494i) q^{45} +(7.18674 - 3.19974i) q^{46} +(6.99870 - 5.66743i) q^{47} +(-0.414303 - 0.813115i) q^{48} +(3.41768 - 6.10897i) q^{49} +(-3.18042 - 3.85810i) q^{50} +(1.56047 + 2.70281i) q^{51} +(0.0212035 - 0.404588i) q^{52} +(2.98438 + 1.14560i) q^{53} +(-0.492902 + 4.68965i) q^{54} +(-11.4406 - 2.37960i) q^{55} +(-2.46355 + 0.964837i) q^{56} +(0.975071 - 0.975071i) q^{57} +(-0.130749 - 0.340613i) q^{58} +(-11.5852 - 2.46251i) q^{59} +(-1.58021 + 1.29110i) q^{60} +(1.24686 + 5.86601i) q^{61} +(-2.21070 + 4.33875i) q^{62} +(5.61650 + 1.15418i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-0.894147 + 0.145624i) q^{65} +(-0.991537 + 4.66481i) q^{66} +(-5.90736 - 4.78369i) q^{67} +(-3.30338 - 0.885137i) q^{68} +(-5.80805 + 4.21980i) q^{69} +(3.27715 + 4.92547i) q^{70} +(0.0239513 + 0.0174017i) q^{71} +(-1.36386 - 1.68423i) q^{72} +(5.81327 + 0.304661i) q^{73} +(4.46716 + 2.57912i) q^{74} +(3.57098 + 2.84045i) q^{75} +1.51105i q^{76} +(13.1783 + 4.18355i) q^{77} +(0.0578378 + 0.365174i) q^{78} +(-11.6460 - 1.22404i) q^{79} +(0.224019 - 2.22482i) q^{80} +(0.229789 + 2.18630i) q^{81} +(-1.29934 + 4.84922i) q^{82} +(2.26432 - 14.2964i) q^{83} +(2.01600 - 1.32867i) q^{84} +(-0.366868 + 7.63834i) q^{85} +(-12.5580 + 2.66928i) q^{86} +(0.181338 + 0.279236i) q^{87} +(-2.84622 - 4.38279i) q^{88} +(1.20623 - 0.256391i) q^{89} +(-3.03321 + 3.77933i) q^{90} +(1.07003 - 0.0633379i) q^{91} +(1.23065 - 7.77001i) q^{92} +(1.15014 - 4.29238i) q^{93} +(-0.941346 - 8.95631i) q^{94} +(3.30189 - 0.716922i) q^{95} +(-0.907581 - 0.0953906i) q^{96} +(-0.869979 - 5.49283i) q^{97} +(-3.26201 - 6.19349i) q^{98} +11.3255i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 320 * q + 12 * q^5 - 8 * q^7	$ 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98}+O(q^{100}) $ 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.544639	−	0.838671i	0.385118	−	0.593030i
$2$	0.544639	−	0.838671i	0.385118	−	0.593030i
$3$	−0.327039	+	0.851967i	−0.188816	+	0.491883i	−0.995011	−	0.0997673i	$-0.968190\pi$
$3$	−0.327039	+	0.851967i	−0.188816	+	0.491883i	0.806194	+	0.591651i	$0.201523\pi$
$4$	−0.406737	−	0.913545i	−0.203368	−	0.456773i
$5$	−1.80326	+	1.32222i	−0.806442	+	0.591313i
$5$	−1.80326	+	1.32222i	−0.806442	+	0.591313i
$6$	0.536401	+	0.738293i	0.218985	+	0.301407i
$7$	2.28229	−	1.33834i	0.862624	−	0.505846i
$7$	2.28229	−	1.33834i	0.862624	−	0.505846i
$8$	−0.987688	−	0.156434i	−0.349201	−	0.0553079i
$9$	1.61054	+	1.45014i	0.536847	+	0.483379i
$10$	0.126777	+	2.23247i	0.0400904	+	0.705969i
$11$	3.49679	+	3.88358i	1.05432	+	1.17094i	0.984859	+	0.173360i	$0.0554623\pi$
$11$	3.49679	+	3.88358i	1.05432	+	1.17094i	0.0694642	+	0.997584i	$0.477871\pi$
$12$	0.911329	−	0.0477607i	0.263078	−	0.0137873i
$13$	0.360985	+	0.183931i	0.100119	+	0.0510133i	0.503333	−	0.864093i	$-0.332107\pi$
$13$	0.360985	+	0.183931i	0.100119	+	0.0510133i	−0.403214	+	0.915106i	$0.632107\pi$
$14$	0.120595	−	2.64300i	0.0322303	−	0.706372i
$15$	−0.536746	−	1.96873i	−0.138587	−	0.508325i
$16$	−0.669131	+	0.743145i	−0.167283	+	0.185786i
$17$	2.15222	−	2.65777i	0.521989	−	0.644603i	−0.446167	−	0.894950i	$-0.647211\pi$
$17$	2.15222	−	2.65777i	0.521989	−	0.644603i	0.968156	+	0.250347i	$0.0805446\pi$
$18$	2.09335	−	0.560912i	0.493408	−	0.132208i
$19$	−1.38042	−	0.614601i	−0.316689	−	0.140999i	0.242235	−	0.970217i	$-0.422119\pi$
$19$	−1.38042	−	0.614601i	−0.316689	−	0.140999i	−0.558925	+	0.829218i	$0.688786\pi$
$20$	1.94136	+	1.10957i	0.434100	+	0.248107i
$21$	0.393825	+	2.38212i	0.0859397	+	0.519822i
$22$	5.16154	−	0.817507i	1.10044	−	0.174293i
$23$	6.59771	+	4.28460i	1.37572	+	0.893401i	0.999452	−	0.0331104i	$-0.0105413\pi$
$23$	6.59771	+	4.28460i	1.37572	+	0.893401i	0.376266	+	0.926512i	$0.377208\pi$
$24$	0.456290	−	0.790317i	0.0931398	−	0.161323i
$25$	1.50349	−	4.76860i	0.300699	−	0.953719i
$26$	0.350864	−	0.202572i	0.0688101	−	0.0397275i
$27$	−4.20152	+	2.14078i	−0.808584	+	0.411994i
$28$	−2.15093	−	1.54062i	−0.406487	−	0.291150i
$29$	0.214451	−	0.295167i	0.0398226	−	0.0548111i	−0.788641	−	0.614853i	$-0.789215\pi$
$29$	0.214451	−	0.295167i	0.0398226	−	0.0548111i	0.828464	+	0.560042i	$0.189215\pi$
$30$	−1.94345	−	0.622096i	−0.354824	−	0.113579i
$31$	−4.84281	+	0.509000i	−0.869795	+	0.0914191i	−0.528902	−	0.848683i	$-0.677396\pi$
$31$	−4.84281	+	0.509000i	−0.869795	+	0.0914191i	−0.340893	+	0.940102i	$0.610729\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−4.45227	+	1.70907i	−0.775041	+	0.297510i
$34$	−1.05681	−	3.25252i	−0.181241	−	0.557803i
$35$	−2.34598	+	5.43106i	−0.396543	+	0.918016i
$36$	0.669701	−	2.06113i	0.111617	−	0.343521i
$37$	0.269961	+	5.15116i	0.0443813	+	0.846846i	0.926610	+	0.376024i	$0.122709\pi$
$37$	0.269961	+	5.15116i	0.0443813	+	0.846846i	−0.882228	+	0.470822i	$0.843958\pi$
$38$	−1.26728	+	0.822979i	−0.205580	+	0.133505i
$39$	−0.274760	+	0.247395i	−0.0439967	+	0.0396148i
$40$	1.98790	−	1.02384i	0.314314	−	0.161884i
$41$	−4.77457	+	1.55135i	−0.745662	+	0.242280i	−0.657114	−	0.753791i	$-0.728223\pi$
$41$	−4.77457	+	1.55135i	−0.745662	+	0.242280i	−0.0885487	+	0.996072i	$0.528223\pi$
$42$	2.21231	+	0.967108i	0.341367	+	0.149228i
$43$	−9.07822	−	9.07822i	−1.38441	−	1.38441i	−0.836599	−	0.547816i	$-0.815459\pi$
$43$	−9.07822	−	9.07822i	−1.38441	−	1.38441i	−0.547816	−	0.836599i	$-0.684541\pi$
$44$	2.12555	−	4.77407i	0.320439	−	0.719719i
$45$	−4.82162	−	0.485494i	−0.718765	−	0.0723732i
$46$	7.18674	−	3.19974i	1.05963	−	0.471776i
$47$	6.99870	−	5.66743i	1.02086	−	0.826680i	0.0358861	−	0.999356i	$-0.488575\pi$
$47$	6.99870	−	5.66743i	1.02086	−	0.826680i	0.984979	+	0.172676i	$0.0552413\pi$
$48$	−0.414303	−	0.813115i	−0.0597994	−	0.117363i
$49$	3.41768	−	6.10897i	0.488240	−	0.872710i
$50$	−3.18042	−	3.85810i	−0.449779	−	0.545618i
$51$	1.56047	+	2.70281i	0.218509	+	0.378469i
$52$	0.0212035	−	0.404588i	0.00294040	−	0.0561062i
$53$	2.98438	+	1.14560i	0.409937	+	0.157360i	0.554592	−	0.832122i	$-0.312874\pi$
$53$	2.98438	+	1.14560i	0.409937	+	0.157360i	−0.144656	+	0.989482i	$0.546207\pi$
$54$	−0.492902	+	4.68965i	−0.0670755	+	0.638180i
$55$	−11.4406	−	2.37960i	−1.54264	−	0.320865i
$56$	−2.46355	+	0.964837i	−0.329206	+	0.128932i
$57$	0.975071	−	0.975071i	0.129151	−	0.129151i
$58$	−0.130749	−	0.340613i	−0.0171682	−	0.0447247i
$59$	−11.5852	−	2.46251i	−1.50827	−	0.320592i	−0.621723	−	0.783237i	$-0.713567\pi$
$59$	−11.5852	−	2.46251i	−1.50827	−	0.320592i	−0.886543	+	0.462646i	$0.846900\pi$
$60$	−1.58021	+	1.29110i	−0.204005	+	0.166680i
$61$	1.24686	+	5.86601i	0.159644	+	0.751066i	0.983010	+	0.183554i	$0.0587604\pi$
$61$	1.24686	+	5.86601i	0.159644	+	0.751066i	−0.823366	+	0.567511i	$0.807906\pi$
$62$	−2.21070	+	4.33875i	−0.280759	+	0.551021i
$63$	5.61650	+	1.15418i	0.707613	+	0.145413i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−0.894147	+	0.145624i	−0.110905	+	0.0180625i
$66$	−0.991537	+	4.66481i	−0.122050	+	0.574199i
$67$	−5.90736	−	4.78369i	−0.721699	−	0.584421i	0.196517	−	0.980500i	$-0.437037\pi$
$67$	−5.90736	−	4.78369i	−0.721699	−	0.584421i	−0.918216	+	0.396080i	$0.870370\pi$
$68$	−3.30338	−	0.885137i	−0.400593	−	0.107339i
$69$	−5.80805	+	4.21980i	−0.699207	+	0.508004i
$70$	3.27715	+	4.92547i	0.391695	+	0.588706i
$71$	0.0239513	+	0.0174017i	0.00284250	+	0.00206520i	0.589206	−	0.807983i	$-0.299441\pi$
$71$	0.0239513	+	0.0174017i	0.00284250	+	0.00206520i	−0.586363	+	0.810048i	$0.699441\pi$
$72$	−1.36386	−	1.68423i	−0.160733	−	0.198488i
$73$	5.81327	+	0.304661i	0.680392	+	0.0356579i	0.389402	−	0.921068i	$-0.372682\pi$
$73$	5.81327	+	0.304661i	0.680392	+	0.0356579i	0.290991	+	0.956726i	$0.406015\pi$
$74$	4.46716	+	2.57912i	0.519297	+	0.299816i
$75$	3.57098	+	2.84045i	0.412342	+	0.327986i
$76$			1.51105i			0.173330i
$77$	13.1783	+	4.18355i	1.50180	+	0.476759i
$78$	0.0578378	+	0.365174i	0.00654884	+	0.0413478i
$79$	−11.6460	−	1.22404i	−1.31028	−	0.137716i	−0.576496	−	0.817100i	$-0.695580\pi$
$79$	−11.6460	−	1.22404i	−1.31028	−	0.137716i	−0.733782	+	0.679384i	$0.762247\pi$
$80$	0.224019	−	2.22482i	0.0250461	−	0.248742i
$81$	0.229789	+	2.18630i	0.0255321	+	0.242922i
$82$	−1.29934	+	4.84922i	−0.143489	+	0.535507i
$83$	2.26432	−	14.2964i	0.248542	−	1.56923i	−0.475651	−	0.879634i	$-0.657788\pi$
$83$	2.26432	−	14.2964i	0.248542	−	1.56923i	0.724193	−	0.689597i	$-0.242212\pi$
$84$	2.01600	−	1.32867i	0.219963	−	0.144970i
$85$	−0.366868	+	7.63834i	−0.0397924	+	0.828494i
$86$	−12.5580	+	2.66928i	−1.35416	+	0.287836i
$87$	0.181338	+	0.279236i	0.0194415	+	0.0299373i
$88$	−2.84622	−	4.38279i	−0.303408	−	0.467207i
$89$	1.20623	−	0.256391i	0.127860	−	0.0271774i	−0.143537	−	0.989645i	$-0.545848\pi$
$89$	1.20623	−	0.256391i	0.127860	−	0.0271774i	0.271397	+	0.962468i	$0.412514\pi$
$90$	−3.03321	+	3.77933i	−0.319729	+	0.398377i
$91$	1.07003	−	0.0633379i	0.112170	−	0.00663962i
$92$	1.23065	−	7.77001i	0.128304	−	0.810080i
$93$	1.15014	−	4.29238i	0.119264	−	0.445099i
$94$	−0.941346	−	8.95631i	−0.0970924	−	0.923772i
$95$	3.30189	−	0.716922i	0.338766	−	0.0735547i
$96$	−0.907581	−	0.0953906i	−0.0926296	−	0.00973576i
$97$	−0.869979	−	5.49283i	−0.0883330	−	0.557712i	−0.991672	−	0.128786i	$-0.958892\pi$
$97$	−0.869979	−	5.49283i	−0.0883330	−	0.557712i	0.903339	−	0.428926i	$-0.141108\pi$
$98$	−3.26201	−	6.19349i	−0.329513	−	0.625637i
$99$			11.3255i			1.13826i
$100$	−4.96786	+	0.566052i	−0.496786	+	0.0566052i
$101$	10.2430	+	5.91380i	1.01922	+	0.588445i	0.913877	−	0.405991i	$-0.133074\pi$
$101$	10.2430	+	5.91380i	1.01922	+	0.588445i	0.105340	+	0.994436i	$0.466407\pi$
$102$	3.11666	+	0.163337i	0.308595	+	0.0161728i
$103$	7.01876	+	8.66745i	0.691579	+	0.854029i	0.995108	−	0.0987932i	$-0.0314982\pi$
$103$	7.01876	+	8.66745i	0.691579	+	0.854029i	−0.303529	+	0.952822i	$0.598165\pi$
$104$	−0.327768	−	0.238137i	−0.0321403	−	0.0233513i
$105$	−3.85985	−	3.77487i	−0.376683	−	0.368389i
$106$	2.58619	−	1.87898i	0.251193	−	0.182502i
$107$	−8.61831	−	2.30927i	−0.833163	−	0.223245i	−0.183070	−	0.983100i	$-0.558603\pi$
$107$	−8.61831	−	2.30927i	−0.833163	−	0.223245i	−0.650093	+	0.759854i	$0.725270\pi$
$108$	3.66462	+	2.96755i	0.352628	+	0.285552i
$109$	0.0997782	−	0.469419i	0.00955701	−	0.0449622i	−0.973111	−	0.230338i	$-0.926017\pi$
$109$	0.0997782	−	0.469419i	0.00955701	−	0.0449622i	0.982668	+	0.185376i	$0.0593502\pi$
$110$	−8.22667	+	8.29884i	−0.784382	+	0.791263i
$111$	−4.47691	−	1.45464i	−0.424929	−	0.138068i
$112$	−0.532567	+	2.59160i	−0.0503228	+	0.244883i
$113$	8.42139	−	16.5279i	0.792217	−	1.55481i	−0.0392425	−	0.999230i	$-0.512494\pi$
$113$	8.42139	−	16.5279i	0.792217	−	1.55481i	0.831460	−	0.555585i	$-0.187506\pi$
$114$	−0.286702	−	1.34882i	−0.0268521	−	0.126329i
$115$	−17.5626	+	0.997338i	−1.63772	+	0.0930022i
$116$	−0.356873	−	0.0758558i	−0.0331349	−	0.00704303i
$117$	0.314656	+	0.819707i	0.0290900	+	0.0757819i
$118$	−8.37499	+	8.37499i	−0.770981	+	0.770981i
$119$	1.35498	−	8.94619i	0.124211	−	0.820096i
$120$	0.222160	+	2.02846i	0.0202803	+	0.185172i
$121$	−1.70484	+	16.2204i	−0.154985	+	1.47458i
$122$	5.59874	+	2.14915i	0.506886	+	0.194575i
$123$	0.239772	−	4.57513i	0.0216195	−	0.412525i
$124$	2.43474	+	4.21710i	0.218647	+	0.378707i
$125$	3.59392	+	10.5870i	0.321450	+	0.946927i
$126$	4.02694	−	4.08179i	0.358748	−	0.363634i
$127$	−4.16746	−	8.17910i	−0.369802	−	0.725777i	0.628858	−	0.777520i	$-0.283523\pi$
$127$	−4.16746	−	8.17910i	−0.369802	−	0.725777i	−0.998660	+	0.0517424i	$0.983523\pi$
$128$	0.777146	−	0.629320i	0.0686906	−	0.0556246i
$129$	10.7033	−	4.76540i	0.942371	−	0.419570i
$130$	−0.364856	+	0.829207i	−0.0320000	+	0.0727263i
$131$	−0.184727	+	0.414904i	−0.0161397	+	0.0362503i	−0.921435	−	0.388531i	$-0.872982\pi$
$131$	−0.184727	+	0.414904i	−0.0161397	+	0.0362503i	0.905296	+	0.424782i	$0.139649\pi$
$132$	3.37221	+	3.37221i	0.293513	+	0.293513i
$133$	−3.97306	+	0.444774i	−0.344508	+	0.0385668i
$134$	−7.22932	+	2.34895i	−0.624518	+	0.202918i
$135$	4.74587	−	9.41571i	0.408459	−	0.810375i
$136$	−2.54149	+	2.28836i	−0.217931	+	0.196226i
$137$	−14.2520	+	9.25535i	−1.21763	+	0.790738i	−0.983401	−	0.181444i	$-0.941923\pi$
$137$	−14.2520	+	9.25535i	−1.21763	+	0.790738i	−0.234228	+	0.972182i	$0.575256\pi$
$138$	0.375727	+	7.16931i	0.0319840	+	0.610292i
$139$	−3.81794	+	11.7504i	−0.323833	+	0.996656i	0.648131	+	0.761528i	$0.275551\pi$
$139$	−3.81794	+	11.7504i	−0.323833	+	0.996656i	−0.971965	+	0.235127i	$0.924449\pi$
$140$	5.91571	−	0.0658474i	0.499969	−	0.00556512i
$141$	2.53962	+	7.81613i	0.213874	+	0.658237i
$142$	0.0276391	−	0.0106097i	0.00231942	−	0.000890343i
$143$	0.547979	+	2.04508i	0.0458243	+	0.171019i
$144$	−2.15533	+	0.226534i	−0.179610	+	0.0188778i
$145$	0.00356262	+	0.815813i	0.000295859	+	0.0677496i
$146$	3.42165	−	4.70949i	0.283177	−	0.389760i
$147$	4.08692	+	4.90962i	0.337084	+	0.404939i
$148$	4.59602	−	2.34179i	0.377790	−	0.192494i
$149$	5.04059	−	2.91018i	0.412941	−	0.238412i	−0.279112	−	0.960259i	$-0.590040\pi$
$149$	5.04059	−	2.91018i	0.412941	−	0.238412i	0.692053	+	0.721847i	$0.256707\pi$
$150$	4.32710	−	1.44786i	0.353306	−	0.118217i
$151$	7.20031	−	12.4713i	0.585953	−	1.01490i	−0.408803	−	0.912623i	$-0.634054\pi$
$151$	7.20031	−	12.4713i	0.585953	−	1.01490i	0.994756	−	0.102278i	$-0.0326130\pi$
$152$	1.26728	+	0.822979i	0.102790	+	0.0667524i
$153$	7.32036	−	1.15943i	0.591816	−	0.0937345i
$154$	10.6860	−	8.77369i	0.861103	−	0.707004i
$155$	8.05985	−	7.32110i	0.647382	−	0.588045i
$156$	0.337761	+	0.150381i	0.0270425	+	0.0120401i
$157$	4.17748	−	1.11935i	0.333399	−	0.0893340i	−0.0882361	−	0.996100i	$-0.528123\pi$
$157$	4.17748	−	1.11935i	0.333399	−	0.0893340i	0.421635	+	0.906766i	$0.361456\pi$
$158$	−7.36944	+	9.10050i	−0.586281	+	0.723997i
$159$	−1.95202	+	2.16794i	−0.154805	+	0.171929i
$160$	−1.74388	−	1.39960i	−0.137866	−	0.110648i
$161$	20.7921	+	0.948703i	1.63865	+	0.0747683i
$162$	1.95873	+	0.998025i	0.153893	+	0.0784122i
$163$	11.1491	−	0.584300i	0.873265	−	0.0457659i	0.389564	−	0.920999i	$-0.372626\pi$
$163$	11.1491	−	0.584300i	0.873265	−	0.0457659i	0.483701	+	0.875233i	$0.339292\pi$
$164$	3.35922	+	3.73079i	0.262311	+	0.291326i
$165$	5.76885	−	8.96875i	0.449104	−	0.698217i
$166$	−10.7567	−	9.68539i	−0.834883	−	0.751732i
$167$	−0.893588	−	0.141530i	−0.0691479	−	0.0109520i	0.121765	−	0.992559i	$-0.461145\pi$
$167$	−0.893588	−	0.141530i	−0.0691479	−	0.0109520i	−0.190913	+	0.981607i	$0.561145\pi$
$168$	−0.0163302	−	2.41440i	−0.00125990	−	0.186275i
$169$	−7.54473	−	10.3844i	−0.580364	−	0.798802i
$170$	6.20624	+	4.46782i	0.475997	+	0.342666i
$171$	−1.33196	−	2.99164i	−0.101858	−	0.228776i
$172$	−4.60092	+	11.9858i	−0.350817	+	0.913909i
$173$	6.66270	−	10.2597i	0.506556	−	0.780027i	−0.489189	−	0.872178i	$-0.662707\pi$
$173$	6.66270	−	10.2597i	0.506556	−	0.780027i	0.995745	+	0.0921502i	$0.0293740\pi$
$174$	0.332951			0.0252410
$175$	−2.95061	−	12.8955i	−0.223045	−	0.974808i
$176$	−5.22588			−0.393915
$177$	5.88680	−	9.06488i	0.442479	−	0.681358i
$178$	0.441930	−	1.15127i	0.0331240	−	0.0862910i
$179$	0.656531	+	1.47459i	0.0490714	+	0.110216i	0.936418	−	0.350888i	$-0.114120\pi$
$179$	0.656531	+	1.47459i	0.0490714	+	0.110216i	−0.887346	+	0.461104i	$0.847453\pi$
$180$	1.51761	+	4.60224i	0.113116	+	0.343031i
$181$	−0.230710	−	0.317545i	−0.0171485	−	0.0236029i	0.800357	−	0.599524i	$-0.204643\pi$
$181$	−0.230710	−	0.317545i	−0.0171485	−	0.0236029i	−0.817505	+	0.575921i	$0.804643\pi$
$182$	0.529663	−	0.931903i	0.0392612	−	0.0690772i
$183$	−5.40542	−	0.856134i	−0.399580	−	0.0632873i
$184$	−5.84622	−	5.26396i	−0.430989	−	0.388064i
$185$	−7.29775	−	8.93194i	−0.536542	−	0.656689i
$186$	−2.97348	−	3.30239i	−0.218026	−	0.242143i
$187$	17.8475	−	0.935348i	1.30514	−	0.0683994i
$188$	−8.02408	−	4.08848i	−0.585216	−	0.298183i
$189$	−6.72399	+	10.5090i	−0.489098	+	0.764415i
$190$	1.19707	−	3.15966i	0.0868449	−	0.229226i
$191$	−4.05568	+	4.50429i	−0.293458	+	0.325919i	−0.871787	−	0.489885i	$-0.837039\pi$
$191$	−4.05568	+	4.50429i	−0.293458	+	0.325919i	0.578328	+	0.815804i	$0.303705\pi$
$192$	−0.574305	+	0.709208i	−0.0414469	+	0.0511827i
$193$	5.33518	−	1.42956i	0.384035	−	0.102902i	−0.0616360	−	0.998099i	$-0.519632\pi$
$193$	5.33518	−	1.42956i	0.384035	−	0.102902i	0.445671	+	0.895197i	$0.352965\pi$
$194$	−5.08050	−	2.26198i	−0.364759	−	0.162401i
$195$	0.168354	−	0.809408i	0.0120561	−	0.0579629i
$196$	−6.97091	−	0.637464i	−0.497922	−	0.0455332i
$197$	−12.9845	+	2.05654i	−0.925104	+	0.146522i	−0.600771	−	0.799421i	$-0.705140\pi$
$197$	−12.9845	+	2.05654i	−0.925104	+	0.146522i	−0.324333	+	0.945943i	$0.605140\pi$
$198$	9.49837	+	6.16831i	0.675020	+	0.438363i
$199$	−9.80716	+	16.9865i	−0.695211	+	1.20414i	0.274898	+	0.961473i	$0.411356\pi$
$199$	−9.80716	+	16.9865i	−0.695211	+	1.20414i	−0.970109	+	0.242668i	$0.921977\pi$
$200$	−2.23096	+	4.47469i	−0.157752	+	0.316408i
$201$	6.00748	−	3.46842i	0.423735	−	0.244644i
$202$	10.5385	−	5.36962i	0.741485	−	0.377805i
$203$	0.0944052	−	0.960665i	0.00662595	−	0.0674254i
$204$	1.83444	−	2.52489i	0.128437	−	0.176778i
$205$	6.55857	−	9.11050i	0.458070	−	0.636305i
$206$	11.0918	−	1.16580i	0.772804	−	0.0812250i
$207$	4.41262	+	16.4681i	0.306698	+	1.14461i
$208$	−0.378234	+	0.145190i	−0.0262258	+	0.0100671i
$209$	−2.44018	−	7.51010i	−0.168791	−	0.519484i
$210$	−5.26810	+	1.18120i	−0.363533	+	0.0815107i
$211$	7.22739	−	22.2436i	0.497554	−	1.53131i	−0.315384	−	0.948964i	$-0.602133\pi$
$211$	7.22739	−	22.2436i	0.497554	−	1.53131i	0.812938	−	0.582350i	$-0.197867\pi$
$212$	−0.167303	−	3.19233i	−0.0114904	−	0.219250i
$213$	−0.0226587	+	0.0147147i	−0.00155255	+	0.00100824i
$214$	−6.63058	+	5.97020i	−0.453257	+	0.408115i
$215$	28.3737	+	4.36703i	1.93507	+	0.297829i
$216$	4.48469	−	1.45716i	0.305144	−	0.0991474i
$217$	−10.3715	+	7.64303i	−0.704062	+	0.518843i
$218$	−0.339345	−	0.339345i	−0.0229833	−	0.0229833i
$219$	−2.16073	+	4.85308i	−0.146009	+	0.327941i
$220$	2.47942	+	11.4193i	0.167163	+	0.769892i
$221$	1.26576	−	0.563554i	0.0851445	−	0.0379088i
$222$	−3.65826	+	2.96240i	−0.245526	+	0.198823i
$223$	−7.77854	−	15.2662i	−0.520890	−	1.02230i	−0.990251	−	0.139297i	$-0.955516\pi$
$223$	−7.77854	−	15.2662i	−0.520890	−	1.02230i	0.469361	−	0.883006i	$-0.344484\pi$
$224$	1.88344	+	1.85813i	0.125843	+	0.124152i
$225$	9.33656	−	5.49975i	0.622438	−	0.366650i
$226$	−9.27485	−	16.0645i	−0.616954	−	1.06860i
$227$	−1.15225	+	21.9862i	−0.0764772	+	1.45927i	0.643591	+	0.765369i	$0.277444\pi$
$227$	−1.15225	+	21.9862i	−0.0764772	+	1.45927i	−0.720068	+	0.693903i	$0.755890\pi$
$228$	−1.28737	−	0.494175i	−0.0852581	−	0.0327275i
$229$	2.49208	−	23.7105i	0.164681	−	1.56684i	−0.530301	−	0.847809i	$-0.677921\pi$
$229$	2.49208	−	23.7105i	0.164681	−	1.56684i	0.694983	−	0.719027i	$-0.255412\pi$
$230$	−8.72881	+	15.2724i	−0.575561	+	1.00703i
$231$	−7.87405	+	9.85925i	−0.518075	+	0.648691i
$232$	−0.257985	+	0.257985i	−0.0169376	+	0.0169376i
$233$	4.50440	+	11.7344i	0.295093	+	0.768743i	0.998329	+	0.0577868i	$0.0184044\pi$
$233$	4.50440	+	11.7344i	0.295093	+	0.768743i	−0.703236	+	0.710956i	$0.748262\pi$
$234$	0.858838	+	0.182552i	0.0561440	+	0.0119338i
$235$	−5.12691	+	19.4736i	−0.334442	+	1.27032i
$236$	2.46251	+	11.5852i	0.160296	+	0.754133i
$237$	4.85155	−	9.52170i	0.315142	−	0.618501i
$238$	−6.76493	−	6.00882i	−0.438505	−	0.389494i
$239$	−5.55667	−	1.80547i	−0.359431	−	0.116786i	0.123734	−	0.992315i	$-0.460513\pi$
$239$	−5.55667	−	1.80547i	−0.359431	−	0.116786i	−0.483165	+	0.875529i	$0.660513\pi$
$240$	1.82221	+	0.918460i	0.117623	+	0.0592864i
$241$	4.54562	−	21.3855i	0.292809	−	1.37756i	−0.548113	−	0.836404i	$-0.684654\pi$
$241$	4.54562	−	21.3855i	0.292809	−	1.37756i	0.840922	−	0.541156i	$-0.182013\pi$
$242$	12.6751	+	10.2641i	0.814785	+	0.659800i
$243$	−15.6022	−	4.18060i	−1.00088	−	0.268186i
$244$	4.85172	−	3.52498i	0.310600	−	0.225664i
$245$	1.91440	+	15.5350i	0.122307	+	0.992492i
$246$	−3.70644	−	2.69288i	−0.236314	−	0.171692i
$247$	−0.385266	−	0.475764i	−0.0245139	−	0.0302721i
$248$	4.86282	+	0.254849i	0.308789	+	0.0161830i
$249$	11.4395	+	6.60461i	0.724950	+	0.418550i
$250$	10.8364	+	2.75196i	0.685352	+	0.174049i
$251$			22.2173i			1.40234i	0.712993	+	0.701171i	$0.247339\pi$
$251$			22.2173i			1.40234i	−0.712993	+	0.701171i	$0.752661\pi$
$252$	−1.23004	−	5.60038i	−0.0774855	−	0.352791i
$253$	6.43122	+	40.6051i	0.404327	+	2.55282i
$254$	−9.12933	−	0.959531i	−0.572825	−	0.0602063i
$255$	−6.38763	−	2.81060i	−0.400009	−	0.176006i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	3.64212	−	13.5926i	0.227189	−	0.847882i	−0.754326	−	0.656500i	$-0.772036\pi$
$257$	3.64212	−	13.5926i	0.227189	−	0.847882i	0.981516	−	0.191382i	$-0.0612969\pi$
$258$	1.83282	−	11.5719i	0.114106	−	0.720438i
$259$	7.51015	+	11.3951i	0.466658	+	0.708059i
$260$	0.496717	+	0.757613i	0.0308051	+	0.0469851i
$261$	0.773415	−	0.164394i	0.0478732	−	0.0101758i
$262$	0.247358	+	0.380898i	0.0152818	+	0.0235320i
$263$	−0.775940	−	1.19484i	−0.0478465	−	0.0736772i	0.813938	−	0.580952i	$-0.197320\pi$
$263$	−0.775940	−	1.19484i	−0.0478465	−	0.0736772i	−0.861784	+	0.507275i	$0.830653\pi$
$264$	4.66481	−	0.991537i	0.287099	−	0.0610249i
$265$	−6.89635	+	1.88019i	−0.423639	+	0.115499i
$266$	−1.79086	+	3.57433i	−0.109805	+	0.219156i
$267$	−0.176046	+	1.11151i	−0.0107739	+	0.0680235i
$268$	−1.96738	+	7.34235i	−0.120177	+	0.448505i
$269$	1.63313	+	15.5382i	0.0995739	+	0.947382i	0.924253	+	0.381781i	$0.124689\pi$
$269$	1.63313	+	15.5382i	0.0995739	+	0.947382i	−0.824679	+	0.565601i	$0.808644\pi$
$270$	−5.31189	−	9.10838i	−0.323272	−	0.554318i
$271$	−20.7432	−	2.18020i	−1.26006	−	0.132437i	−0.549151	−	0.835723i	$-0.685049\pi$
$271$	−20.7432	−	2.18020i	−1.26006	−	0.132437i	−0.710907	+	0.703286i	$0.751715\pi$
$272$	0.534991	+	3.37780i	0.0324386	+	0.204809i
$273$	−0.295982	+	0.932348i	−0.0179136	+	0.0564283i
$274$			16.9935i			1.02662i
$275$	23.7766	−	10.8358i	1.43379	−	0.653426i
$276$	6.21732	+	3.58957i	0.374239	+	0.216067i
$277$	−13.0045	−	0.681537i	−0.781365	−	0.0409496i	−0.342518	−	0.939511i	$-0.611280\pi$
$277$	−13.0045	−	0.681537i	−0.781365	−	0.0409496i	−0.438847	+	0.898562i	$0.644613\pi$
$278$	7.77532	+	9.60172i	0.466333	+	0.575873i
$279$	−8.53767	−	6.20298i	−0.511137	−	0.371363i
$280$	3.16670	−	4.99720i	0.189247	−	0.298640i
$281$	3.81661	−	2.77293i	0.227680	−	0.165419i	−0.468097	−	0.883677i	$-0.655060\pi$
$281$	3.81661	−	2.77293i	0.227680	−	0.165419i	0.695777	+	0.718258i	$0.255060\pi$
$282$	7.93833	+	2.12707i	0.472721	+	0.126665i
$283$	−1.95718	−	1.58489i	−0.116342	−	0.0942121i	0.569384	−	0.822072i	$-0.307182\pi$
$283$	−1.95718	−	1.58489i	−0.116342	−	0.0942121i	−0.685726	+	0.727860i	$0.740515\pi$
$284$	0.00615533	−	0.0289585i	0.000365251	−	0.00171837i
$285$	−0.469053	+	3.04756i	−0.0277843	+	0.180522i
$286$	2.01360	+	0.654259i	0.119067	+	0.0386872i
$287$	−8.82070	+	9.93064i	−0.520670	+	0.586187i
$288$	−0.983887	+	1.93099i	−0.0579761	+	0.113785i
$289$	1.10281	+	5.18833i	0.0648714	+	0.305196i
$290$	0.686139	+	0.441336i	0.0402914	+	0.0259161i
$291$	4.96423	+	1.05518i	0.291008	+	0.0618557i
$292$	−2.08615	−	5.43461i	−0.122083	−	0.318036i
$293$	1.61078	−	1.61078i	0.0941030	−	0.0941030i	−0.658488	−	0.752591i	$-0.728804\pi$
$293$	1.61078	−	1.61078i	0.0941030	−	0.0941030i	0.752591	+	0.658488i	$0.228804\pi$
$294$	6.34345	−	0.753609i	0.369958	−	0.0439514i
$295$	24.1471	−	10.8776i	1.40590	−	0.633318i
$296$	0.539182	−	5.12997i	0.0313393	−	0.298174i
$297$	−23.0058	−	8.83109i	−1.33493	−	0.512432i
$298$	0.304615	−	5.81239i	0.0176458	−	0.336703i
$299$	1.59360	+	2.76020i	0.0921604	+	0.159627i
$300$	1.14243	−	4.41757i	0.0659581	−	0.255048i
$301$	−32.8689	−	8.56934i	−1.89453	−	0.493929i
$302$	−6.53775	−	12.8310i	−0.376205	−	0.738344i
$303$	−8.38823	+	6.79266i	−0.481891	+	0.390228i
$304$	1.38042	−	0.614601i	0.0791724	−	0.0352498i
$305$	−10.0045	−	8.92933i	−0.572858	−	0.511292i
$306$	3.01457	−	6.77084i	0.172332	−	0.387063i
$307$	−7.12925	−	7.12925i	−0.406888	−	0.406888i	0.473764	−	0.880652i	$-0.342895\pi$
$307$	−7.12925	−	7.12925i	−0.406888	−	0.406888i	−0.880652	+	0.473764i	$0.842895\pi$
$308$	−1.53822	−	13.7405i	−0.0876481	−	0.782940i
$309$	−9.67979	+	3.14515i	−0.550664	+	0.178922i
$310$	−1.75029	−	10.7469i	−0.0994095	−	0.610384i
$311$	−15.6068	+	14.0525i	−0.884983	+	0.796842i	−0.980075	−	0.198626i	$-0.936352\pi$
$311$	−15.6068	+	14.0525i	−0.884983	+	0.796842i	0.0950926	+	0.995468i	$0.469685\pi$
$312$	0.310078	−	0.201367i	0.0175547	−	0.0114002i
$313$	1.35378	+	25.8317i	0.0765202	+	1.46009i	0.719651	+	0.694336i	$0.244302\pi$
$313$	1.35378	+	25.8317i	0.0765202	+	1.46009i	−0.643130	+	0.765757i	$0.722365\pi$
$314$	1.33645	−	4.11317i	0.0754202	−	0.232120i
$315$	−11.6541	+	5.34494i	−0.656633	+	0.301153i
$316$	3.61864	+	11.1370i	0.203564	+	0.626506i
$317$	−25.4685	+	9.77644i	−1.43045	+	0.549100i	−0.945553	−	0.325470i	$-0.894478\pi$
$317$	−25.4685	+	9.77644i	−1.43045	+	0.549100i	−0.484901	+	0.874569i	$0.661144\pi$
$318$	0.755040	+	2.81785i	0.0423406	+	0.158017i
$319$	1.89620	−	0.199298i	0.106167	−	0.0111586i
$320$	−2.12359	+	0.700263i	−0.118712	+	0.0391459i
$321$	4.78595	−	6.58729i	0.267125	−	0.367667i
$322$	12.1199	−	16.9211i	0.675413	−	0.942974i
$323$	−4.60442	+	2.34607i	−0.256197	+	0.130539i
$324$	1.90382	−	1.09917i	0.105768	−	0.0610650i
$325$	1.41983	−	1.44485i	0.0787581	−	0.0801460i
$326$	5.58220	−	9.66866i	0.309170	−	0.535497i
$327$	0.367298	+	0.238526i	0.0203116	+	0.0131905i
$328$	4.95847	−	0.785345i	0.273786	−	0.0433634i
$329$	8.38808	−	22.3014i	0.462450	−	1.22951i
$330$	−4.37989	−	9.72290i	−0.241105	−	0.535228i
$331$	−18.8360	−	8.38633i	−1.03532	−	0.460954i	−0.182526	−	0.983201i	$-0.558427\pi$
$331$	−18.8360	−	8.38633i	−1.03532	−	0.460954i	−0.852794	+	0.522247i	$0.825094\pi$
$332$	−13.9814	+	3.74630i	−0.767328	+	0.205605i
$333$	−7.03511	+	8.68764i	−0.385522	+	0.476080i
$334$	−0.605380	+	0.672343i	−0.0331249	+	0.0367890i
$335$	16.9776	+	0.815430i	0.927584	+	0.0445517i
$336$	−2.03378	−	1.30128i	−0.110952	−	0.0709908i
$337$	−14.4462	−	7.36070i	−0.786934	−	0.400963i	0.0138591	−	0.999904i	$-0.495588\pi$
$337$	−14.4462	−	7.36070i	−0.786934	−	0.400963i	−0.800793	+	0.598941i	$0.795588\pi$
$338$	−12.8183	+	0.671777i	−0.697222	+	0.0365398i
$339$	11.3271	+	12.5800i	0.615204	+	0.683253i
$340$	7.12719	−	2.77164i	0.386526	−	0.150313i
$341$	−18.9111	−	17.0276i	−1.02409	−	0.922096i
$342$	−3.23444	−	0.512284i	−0.174898	−	0.0277012i
$343$	−0.375762	−	18.5164i	−0.0202892	−	0.999794i
$344$	7.54630	+	10.3866i	0.406869	+	0.560008i
$345$	4.89395	−	15.2889i	0.263481	−	0.823126i
$346$	−4.97571	−	11.1756i	−0.267496	−	0.600805i
$347$	2.87846	−	7.49865i	0.154524	−	0.402549i	−0.834363	−	0.551215i	$-0.814165\pi$
$347$	2.87846	−	7.49865i	0.154524	−	0.402549i	0.988887	+	0.148666i	$0.0474979\pi$
$348$	0.181338	−	0.279236i	0.00972075	−	0.0149686i
$349$	20.3833			1.09109			0.545547	−	0.838080i	$-0.316322\pi$
$349$	20.3833			1.09109			0.545547	+	0.838080i	$0.316322\pi$
$350$	−12.4221	−	4.54881i	−0.663989	−	0.243144i
$351$	−1.91044			−0.101972
$352$	−2.84622	+	4.38279i	−0.151704	+	0.233603i
$353$	−11.3884	+	29.6679i	−0.606146	+	1.57906i	0.195135	+	0.980776i	$0.437485\pi$
$353$	−11.3884	+	29.6679i	−0.606146	+	1.57906i	−0.801281	+	0.598288i	$0.795848\pi$
$354$	−4.39626	−	9.87417i	−0.233659	−	0.524806i
$355$	−0.0661992		0.000289089i	−0.00351349		1.53433e-5i
$356$	−0.724841	−	0.997658i	−0.0384165	−	0.0528758i
$357$	7.17873	+	4.08015i	0.379939	+	0.215945i
$358$	1.59427	+	0.252508i	0.0842598	+	0.0133454i
$359$	4.94708	+	4.45437i	0.261097	+	0.235093i	0.789273	−	0.614042i	$-0.210457\pi$
$359$	4.94708	+	4.45437i	0.261097	+	0.235093i	−0.528177	+	0.849135i	$0.677124\pi$
$360$	4.68631	+	1.23378i	0.246990	+	0.0650262i
$361$	−11.1857	−	12.4229i	−0.588719	−	0.653839i
$362$	−0.391969	+	0.0205422i	−0.0206014	+	0.00107968i
$363$	−13.2617	−	6.75718i	−0.696060	−	0.354660i
$364$	−0.493084	−	0.951764i	−0.0258446	−	0.0498860i
$365$	−10.8857	+	7.13702i	−0.569782	+	0.373569i
$366$	−3.66202	+	4.06708i	−0.191417	+	0.212590i
$367$	11.8428	−	14.6246i	0.618189	−	0.763400i	−0.367856	−	0.929883i	$-0.619908\pi$
$367$	11.8428	−	14.6246i	0.618189	−	0.763400i	0.986044	+	0.166483i	$0.0532412\pi$
$368$	−7.59881	+	2.03609i	−0.396115	+	0.106139i
$369$	−9.93932	−	4.42527i	−0.517420	−	0.230370i
$370$	−11.4656	+	1.25573i	−0.596068	+	0.0652822i
$371$	8.34443	−	1.37954i	0.433221	−	0.0716223i
$372$	−4.38909	+	0.695163i	−0.227564	+	0.0360425i
$373$	19.8012	+	12.8591i	1.02527	+	0.665817i	0.943684	−	0.330849i	$-0.107335\pi$
$373$	19.8012	+	12.8591i	1.02527	+	0.665817i	0.0815847	+	0.996666i	$0.474002\pi$
$374$	8.93600	−	15.4776i	0.462070	−	0.800328i
$375$	−10.1951	−	0.400456i	−0.526472	−	0.0206795i
$376$	−7.79911	+	4.50282i	−0.402209	+	0.232215i
$377$	0.131704	−	0.0671065i	0.00678310	−	0.00345616i
$378$	5.15141	+	11.3628i	0.264960	+	0.584440i
$379$	4.53491	−	6.24176i	0.232943	−	0.320618i	−0.676504	−	0.736439i	$-0.736506\pi$
$379$	4.53491	−	6.24176i	0.232943	−	0.320618i	0.909446	+	0.415821i	$0.136506\pi$
$380$	−1.99794	−	2.72483i	−0.102492	−	0.139781i
$381$	8.33124	−	0.875649i	0.426822	−	0.0448609i
$382$	1.56873	+	5.85459i	0.0802633	+	0.299547i
$383$	−27.3491	+	10.4984i	−1.39748	+	0.536441i	−0.936405	−	0.350922i	$-0.885868\pi$
$383$	−27.3491	+	10.4984i	−1.39748	+	0.536441i	−0.461072	+	0.887363i	$0.652535\pi$
$384$	0.282003	+	0.867915i	0.0143909	+	0.0442906i
$385$	−29.2954	+	9.88046i	−1.49303	+	0.503555i
$386$	1.70682	−	5.25306i	0.0868749	−	0.267374i
$387$	−1.45618	−	27.7855i	−0.0740216	−	1.41242i
$388$	−4.66410	+	3.02890i	−0.236784	+	0.153769i
$389$	6.98318	−	6.28768i	0.354061	−	0.318798i	−0.472837	−	0.881150i	$-0.656770\pi$
$389$	6.98318	−	6.28768i	0.354061	−	0.318798i	0.826898	+	0.562352i	$0.190103\pi$
$390$	−0.587135	−	0.582029i	−0.0297307	−	0.0294722i
$391$	25.5872	−	8.31378i	1.29400	−	0.420446i
$392$	−4.33125	+	5.49911i	−0.218761	+	0.277747i
$393$	−0.293071	−	0.293071i	−0.0147835	−	0.0147835i
$394$	−5.34708	+	12.0097i	−0.269382	+	0.605042i
$395$	22.6192	−	13.1913i	1.13810	−	0.663724i
$396$	10.3464	−	4.60650i	0.519924	−	0.231485i
$397$	4.42102	−	3.58007i	0.221885	−	0.179679i	−0.511932	−	0.859026i	$-0.671070\pi$
$397$	4.42102	−	3.58007i	0.221885	−	0.179679i	0.733817	+	0.679347i	$0.237737\pi$
$398$	8.90472	+	17.4765i	0.446353	+	0.876018i
$399$	0.920414	−	3.53037i	0.0460783	−	0.176740i
$400$	2.53772	+	4.30813i	0.126886	+	0.215406i
$401$	15.7315	+	27.2478i	0.785595	+	1.36069i	0.928643	+	0.370974i	$0.120976\pi$
$401$	15.7315	+	27.2478i	0.785595	+	1.36069i	−0.143048	+	0.989716i	$0.545690\pi$
$402$	0.363046	−	6.92734i	0.0181071	−	0.345504i
$403$	−1.84180	−	0.707003i	−0.0917468	−	0.0352183i
$404$	1.23632	−	11.7628i	0.0615093	−	0.585222i
$405$	−3.30512	−	3.63863i	−0.164233	−	0.180805i
$406$	−0.754264	−	0.602390i	−0.0374335	−	0.0298961i
$407$	−19.0610	+	19.0610i	−0.944817	+	0.944817i
$408$	−1.11844	−	2.91365i	−0.0553712	−	0.144247i
$409$	−5.96527	−	1.26796i	−0.294963	−	0.0626964i	0.0580531	−	0.998313i	$-0.481511\pi$
$409$	−5.96527	−	1.26796i	−0.294963	−	0.0626964i	−0.353017	+	0.935617i	$0.614844\pi$
$410$	−4.06865	−	10.4624i	−0.200936	−	0.516702i
$411$	−3.22429	−	15.1691i	−0.159042	−	0.748236i
$412$	5.06332	−	9.93733i	0.249452	−	0.489577i
$413$	−29.7365	+	9.88482i	−1.46324	+	0.486400i
$414$	16.2146	+	5.26845i	0.796905	+	0.258930i
$415$	14.8197	+	28.7740i	0.727471	+	1.41246i
$416$	−0.0842340	+	0.396290i	−0.00412991	+	0.0194297i
$417$	−8.76234	−	7.09560i	−0.429093	−	0.347473i
$418$	−7.62751	−	2.04379i	−0.373074	−	0.0999649i
$419$	−3.63168	+	2.63857i	−0.177419	+	0.128903i	−0.672951	−	0.739687i	$-0.734973\pi$
$419$	−3.63168	+	2.63857i	−0.177419	+	0.128903i	0.495531	+	0.868590i	$0.334973\pi$
$420$	−1.87857	+	5.06153i	−0.0916649	+	0.246977i
$421$	20.5128	+	14.9034i	0.999734	+	0.726349i	0.962031	−	0.272940i	$-0.0879959\pi$
$421$	20.5128	+	14.9034i	0.999734	+	0.726349i	0.0377031	+	0.999289i	$0.487996\pi$
$422$	−14.7188	−	18.1761i	−0.716498	−	0.884801i
$423$	19.4903	+	1.02144i	0.947649	+	0.0496642i
$424$	−2.76843	−	1.59835i	−0.134447	−	0.0776229i
$425$	−9.43797	−	14.2590i	−0.457809	−	0.691662i
$426$			0.0270174i			0.00130900i
$427$	10.6964	+	11.7192i	0.517636	+	0.567132i
$428$	1.39576	+	8.81248i	0.0674666	+	0.425967i
$429$	−1.92155	−	0.201964i	−0.0927735	−	0.00975089i
$430$	19.1159	−	21.4178i	0.921853	−	1.03286i
$431$	2.60374	+	24.7729i	0.125418	+	1.19327i	0.858385	+	0.513006i	$0.171468\pi$
$431$	2.60374	+	24.7729i	0.125418	+	1.19327i	−0.732968	+	0.680264i	$0.761865\pi$
$432$	1.22046	−	4.55481i	0.0587192	−	0.219143i
$433$	−0.493648	+	3.11677i	−0.0237232	+	0.149783i	−0.996707	−	0.0810928i	$-0.974159\pi$
$433$	−0.493648	+	3.11677i	−0.0237232	+	0.149783i	0.972983	+	0.230875i	$0.0741590\pi$
$434$	0.761270	+	12.8609i	0.0365421	+	0.617345i
$435$	−0.696211	−	0.263768i	−0.0333807	−	0.0126467i
$436$	−0.469419	+	0.0997782i	−0.0224811	+	0.00477851i
$437$	−6.47427	−	9.96950i	−0.309706	−	0.476906i
$438$	2.89332	+	4.45532i	0.138248	+	0.212883i
$439$	29.6762	−	6.30788i	1.41637	−	0.301059i	0.564769	−	0.825249i	$-0.308965\pi$
$439$	29.6762	−	6.30788i	1.41637	−	0.301059i	0.851601	+	0.524190i	$0.175632\pi$
$440$	10.9275	+	4.14000i	0.520946	+	0.197367i
$441$	14.3632	−	4.88264i	0.683960	−	0.232507i
$442$	0.216748	−	1.36849i	0.0103096	−	0.0650926i
$443$	5.99160	−	22.3610i	0.284670	−	1.06240i	−0.664411	−	0.747368i	$-0.731317\pi$
$443$	5.99160	−	22.3610i	0.284670	−	1.06240i	0.949080	−	0.315034i	$-0.102016\pi$
$444$	0.492047	+	4.68151i	0.0233515	+	0.222175i
$445$	−1.83613	+	2.05723i	−0.0870411	+	0.0975220i
$446$	−17.0398	−	1.79096i	−0.806860	−	0.0848044i
$447$	0.830910	+	5.24616i	0.0393007	+	0.248135i
$448$	2.58416	−	0.567574i	0.122090	−	0.0268153i
$449$			40.7160i			1.92151i	0.277405	+	0.960753i	$0.410526\pi$
$449$			40.7160i			1.92151i	−0.277405	+	0.960753i	$0.589474\pi$
$450$	0.472581	−	10.8257i	0.0222777	−	0.510327i
$451$	−22.7205	−	13.1177i	−1.06987	−	0.617687i
$452$	−18.5243	−	0.970816i	−0.871309	−	0.0456634i
$453$	8.27035	+	10.2130i	0.388575	+	0.479850i
$454$	17.8116	+	12.9409i	0.835939	+	0.607345i
$455$	−1.84580	+	1.52903i	−0.0865327	+	0.0716821i
$456$	−1.11560	+	0.810531i	−0.0522428	+	0.0379566i
$457$	13.3315	+	3.57218i	0.623623	+	0.167099i	0.556774	−	0.830664i	$-0.312039\pi$
$457$	13.3315	+	3.57218i	0.623623	+	0.167099i	0.0668490	+	0.997763i	$0.478705\pi$
$458$	−18.5280	−	15.0037i	−0.865758	−	0.701077i
$459$	−3.35289	+	15.7741i	−0.156499	+	0.736272i
$460$	8.05445	+	15.6385i	0.375541	+	0.729151i
$461$	31.1929	+	10.1352i	1.45280	+	0.472042i	0.925861	−	0.377863i	$-0.123341\pi$
$461$	31.1929	+	10.1352i	1.45280	+	0.472042i	0.526935	+	0.849906i	$0.323341\pi$
$462$	3.98015	+	11.9735i	0.185173	+	0.557056i
$463$	−5.54453	+	10.8818i	−0.257676	+	0.505718i	−0.983212	−	0.182466i	$-0.941592\pi$
$463$	−5.54453	+	10.8818i	−0.257676	+	0.505718i	0.725536	+	0.688184i	$0.241592\pi$
$464$	0.0758558	+	0.356873i	0.00352152	+	0.0165674i
$465$	3.60145	+	9.26101i	0.167013	+	0.429469i
$466$	12.2945	+	2.61328i	0.569533	+	0.121058i
$467$	−2.78657	−	7.25927i	−0.128947	−	0.335919i	0.853874	−	0.520480i	$-0.174247\pi$
$467$	−2.78657	−	7.25927i	−0.128947	−	0.335919i	−0.982821	+	0.184561i	$0.940914\pi$
$468$	0.620857	−	0.620857i	0.0286991	−	0.0286991i
$469$	−19.8845	−	3.01168i	−0.918182	−	0.139066i
$470$	13.5397	+	14.9059i	0.624538	+	0.687557i
$471$	−0.412549	+	3.92515i	−0.0190093	+	0.180861i
$472$	11.0574	+	4.24452i	0.508956	+	0.195370i
$473$	3.51135	−	67.0006i	0.161452	−	3.08069i
$474$	−5.34323	−	9.25474i	−0.245423	−	0.425084i
$475$	−5.00624	+	5.65860i	−0.229702	+	0.259634i
$476$	−8.72387	+	2.40091i	−0.399858	+	0.110046i
$477$	3.14520	+	6.17280i	0.144009	+	0.282633i
$478$	−4.54057	+	3.67688i	−0.207681	+	0.168177i
$479$	−1.11408	+	0.496019i	−0.0509035	+	0.0226637i	−0.432030	−	0.901859i	$-0.642203\pi$
$479$	−1.11408	+	0.496019i	−0.0509035	+	0.0226637i	0.381127	+	0.924523i	$0.375536\pi$
$480$	1.76273	−	1.02800i	0.0804573	−	0.0469217i
$481$	−0.850007	+	1.90915i	−0.0387570	+	0.0870496i
$482$	−15.4597	−	15.4597i	−0.704168	−	0.704168i
$483$	−7.60811	+	17.4040i	−0.346181	+	0.791907i
$484$	15.5115	−	5.04000i	0.705069	−	0.229091i
$485$	8.83150	+	8.75470i	0.401018	+	0.397531i
$486$	−12.0037	+	10.8082i	−0.544500	+	0.490270i
$487$	−5.91075	+	3.83849i	−0.267842	+	0.173938i	−0.671571	−	0.740940i	$-0.734380\pi$
$487$	−5.91075	+	3.83849i	−0.267842	+	0.173938i	0.403730	+	0.914878i	$0.367714\pi$
$488$	−0.313862	−	5.98884i	−0.0142079	−	0.271102i
$489$	−3.14839	+	9.68976i	−0.142375	+	0.438186i
$490$	14.0714	+	6.85539i	0.635680	+	0.309695i
$491$	−2.18353	−	6.72023i	−0.0985415	−	0.303280i	0.889619	−	0.456704i	$-0.150970\pi$
$491$	−2.18353	−	6.72023i	−0.0985415	−	0.303280i	−0.988160	+	0.153424i	$0.950970\pi$
$492$	−4.27711	+	1.64183i	−0.192827	+	0.0740194i
$493$	−0.322939	−	1.20522i	−0.0145444	−	0.0542805i
$494$	−0.608840	+	0.0639916i	−0.0273930	+	0.00287912i
$495$	−14.9748	−	20.4228i	−0.673065	−	0.917938i
$496$	2.86221	−	3.93950i	0.128517	−	0.176889i
$497$	0.0779532	+	0.00766052i	0.00349668	+	0.000343621i
$498$	11.7695	−	5.99686i	0.527404	−	0.268726i
$499$	−13.3946	+	7.73340i	−0.599626	+	0.346194i	−0.768895	−	0.639376i	$-0.779193\pi$
$499$	−13.3946	+	7.73340i	−0.599626	+	0.346194i	0.169268	+	0.985570i	$0.445860\pi$
$500$	8.20989	−	7.58931i	0.367158	−	0.339404i
$501$	0.412818	−	0.715021i	0.0184433	−	0.0319448i
$502$	18.6330	+	12.1004i	0.831631	+	0.540067i
$503$	8.70720	−	1.37908i	0.388235	−	0.0614903i	0.0407339	−	0.999170i	$-0.487030\pi$
$503$	8.70720	−	1.37908i	0.388235	−	0.0614903i	0.347501	+	0.937680i	$0.387030\pi$
$504$	−5.36680	−	2.01858i	−0.239056	−	0.0899148i
$505$	−26.2901	+	2.87933i	−1.16990	+	0.128129i
$506$	37.5570	+	16.7215i	1.66961	+	0.743359i
$507$	11.3146	−	3.03174i	0.502500	−	0.134644i
$508$	−5.77692	+	7.13390i	−0.256309	+	0.316516i
$509$	24.9988	−	27.7640i	1.10805	−	1.23062i	0.137301	−	0.990529i	$-0.456157\pi$
$509$	24.9988	−	27.7640i	1.10805	−	1.23062i	0.970751	−	0.240087i	$-0.0771760\pi$
$510$	−5.83612	+	3.82636i	−0.258428	+	0.169434i
$511$	13.6753	−	7.08483i	0.604960	−	0.313414i
$512$	−0.891007	−	0.453990i	−0.0393773	−	0.0200637i
$513$	7.11559	−	0.372912i	0.314161	−	0.0164645i
$514$	−9.41605	−	10.4576i	−0.415324	−	0.461264i
$515$	−24.1169	−	6.34935i	−1.06272	−	0.279786i
$516$	−8.70683	−	7.83966i	−0.383297	−	0.345122i
$517$	46.4829	+	7.36217i	2.04432	+	0.323788i
$518$	13.6471	−	0.0923040i	0.599619	−	0.00405561i
$519$	6.56192	+	9.03171i	0.288036	+	0.396448i
$520$	0.905919	−	0.00395611i	0.0397272	−	0.000173487i
$521$	1.08952	+	2.44711i	0.0477328	+	0.107210i	0.935838	−	0.352431i	$-0.114645\pi$
$521$	1.08952	+	2.44711i	0.0477328	+	0.107210i	−0.888105	+	0.459641i	$0.847978\pi$
$522$	0.283359	−	0.738176i	0.0124023	−	0.0323091i
$523$	−7.51406	+	11.5706i	−0.328567	+	0.505949i	−0.963891	−	0.266297i	$-0.914200\pi$
$523$	−7.51406	+	11.5706i	−0.328567	+	0.505949i	0.635324	+	0.772246i	$0.280867\pi$
$524$	0.454169			0.0198405
$525$	11.9515	+	1.70352i	0.521606	+	0.0743476i
$526$	−1.42469			−0.0621193
$527$	−9.06998	+	13.9665i	−0.395095	+	0.608392i
$528$	1.70907	−	4.45227i	0.0743776	−	0.193760i
$529$	15.8170	+	35.5256i	0.687696	+	1.54459i
$530$	−2.17916	+	6.80779i	−0.0946568	+	0.295711i
$531$	−15.0875	−	20.7661i	−0.654741	−	0.901174i
$532$	2.02231	+	3.44866i	0.0876782	+	0.149518i
$533$	−2.00889	−	0.318177i	−0.0870147	−	0.0137818i
$534$	0.836312	+	0.753019i	0.0361908	+	0.0325863i
$535$	18.5944	−	7.23104i	0.803906	−	0.312625i
$536$	5.08630	+	5.64891i	0.219695	+	0.243996i
$537$	−1.47102	+	0.0770927i	−0.0634790	+	0.00332680i
$538$	13.9209	+	7.09306i	0.600173	+	0.305804i
$539$	35.6756	−	8.08896i	1.53666	−	0.348416i
$540$	−10.5320	−	0.505850i	−0.453225	−	0.0217683i
$541$	−11.3630	+	12.6199i	−0.488532	+	0.542570i	−0.936125	−	0.351668i	$-0.885615\pi$
$541$	−11.3630	+	12.6199i	−0.488532	+	0.542570i	0.447593	+	0.894237i	$0.352281\pi$
$542$	−13.1260	+	16.2093i	−0.563810	+	0.696248i
$543$	0.345989	−	0.0927074i	0.0148478	−	0.00397846i
$544$	3.12424	+	1.39100i	0.133951	+	0.0596387i
$545$	0.440747	+	0.978413i	0.0188795	+	0.0419106i
$546$	0.620730	+	0.756024i	0.0265648	+	0.0323549i
$547$	−3.94661	+	0.625081i	−0.168745	+	0.0267266i	−0.240235	−	0.970715i	$-0.577225\pi$
$547$	−3.94661	+	0.625081i	−0.168745	+	0.0267266i	0.0714902	+	0.997441i	$0.477225\pi$
$548$	14.2520	+	9.25535i	0.608815	+	0.395369i
$549$	−6.49841	+	11.2556i	−0.277345	+	0.480376i
$550$	3.86198	−	25.8424i	0.164675	−	1.10192i
$551$	−0.477442	+	0.275651i	−0.0203397	+	0.0117431i
$552$	6.39667	−	3.25926i	0.272260	−	0.138723i
$553$	−28.2177	+	12.7927i	−1.19994	+	0.544002i
$554$	−7.65434	+	10.5353i	−0.325202	+	0.447602i
$555$	9.99637	−	3.29635i	0.424322	−	0.139922i
$556$	12.2874	−	1.29146i	0.521103	−	0.0547701i
$557$	−6.92243	−	25.8349i	−0.293313	−	1.09466i	−0.942548	−	0.334071i	$-0.891577\pi$
$557$	−6.92243	−	25.8349i	−0.293313	−	1.09466i	0.649235	−	0.760588i	$-0.275089\pi$
$558$	−9.85221	+	3.78191i	−0.417077	+	0.160101i
$559$	−1.60733	−	4.94687i	−0.0679830	−	0.209230i
$560$	−2.46629	−	5.37749i	−0.104220	−	0.227240i
$561$	−5.03995	+	15.5114i	−0.212787	+	0.654891i
$562$	−0.246899	−	4.71112i	−0.0104148	−	0.198727i
$563$	34.1590	−	22.1831i	1.43963	−	0.934906i	0.440316	−	0.897843i	$-0.354866\pi$
$563$	34.1590	−	22.1831i	1.43963	−	0.934906i	0.999313	−	0.0370635i	$-0.0118004\pi$
$564$	6.10744	−	5.49916i	0.257169	−	0.231556i
$565$	6.66749	+	40.9390i	0.280503	+	1.72232i
$566$	−2.39516	+	0.778234i	−0.100676	+	0.0327116i
$567$	3.45046	+	4.68222i	0.144906	+	0.196635i
$568$	−0.0209342	−	0.0209342i	−0.000878381	−	0.000878381i
$569$	12.5390	−	28.1631i	0.525663	−	1.18066i	−0.434361	−	0.900739i	$-0.643026\pi$
$569$	12.5390	−	28.1631i	0.525663	−	1.18066i	0.960024	−	0.279919i	$-0.0903077\pi$
$570$	2.30043	+	2.05320i	0.0963546	+	0.0859991i
$571$	15.0604	−	6.70532i	0.630258	−	0.280609i	−0.0666423	−	0.997777i	$-0.521229\pi$
$571$	15.0604	−	6.70532i	0.630258	−	0.280609i	0.696900	+	0.717168i	$0.254562\pi$
$572$	1.64539	−	1.33241i	0.0687974	−	0.0557110i
$573$	−2.51114	−	4.92838i	−0.104904	−	0.205886i
$574$	3.52444	+	12.8063i	0.147107	+	0.534524i
$575$	30.3512	−	25.0199i	1.26573	−	1.04340i
$576$	1.08360	+	1.87685i	0.0451500	+	0.0782020i
$577$	2.04931	−	39.1032i	0.0853139	−	1.62789i	−0.535926	−	0.844265i	$-0.680037\pi$
$577$	2.04931	−	39.1032i	0.0853139	−	1.62789i	0.621240	−	0.783621i	$-0.286629\pi$
$578$	4.95194	+	1.90087i	0.205974	+	0.0790658i
$579$	−0.526879	+	5.01292i	−0.0218964	+	0.208330i
$580$	0.743833	−	0.335076i	0.0308860	−	0.0139133i
$581$	−13.9656	−	35.6589i	−0.579391	−	1.47938i
$582$	3.58866	−	3.58866i	0.148755	−	0.148755i
$583$	5.98675	+	15.5960i	0.247946	+	0.645921i
$584$	−5.69404	−	1.21031i	−0.235621	−	0.0500828i
$585$	−1.65124	−	1.06210i	−0.0682702	−	0.0439125i
$586$	−0.473621	−	2.22821i	−0.0195651	−	0.0920466i
$587$	−12.2118	+	23.9671i	−0.504036	+	0.989226i	0.489096	+	0.872230i	$0.337327\pi$
$587$	−12.2118	+	23.9671i	−0.504036	+	0.989226i	−0.993132	+	0.116997i	$0.962673\pi$
$588$	2.82286	−	5.73051i	0.116413	−	0.236322i
$589$	6.99794	+	2.27377i	0.288345	+	0.0936889i
$590$	4.02875	−	26.1758i	0.165861	−	1.07764i
$591$	2.49433	−	11.7349i	0.102603	−	0.482709i
$592$	−4.00870	−	3.24618i	−0.164757	−	0.133417i
$593$	−22.5595	−	6.04480i	−0.926407	−	0.248230i	−0.236085	−	0.971732i	$-0.575864\pi$
$593$	−22.5595	−	6.04480i	−0.926407	−	0.248230i	−0.690322	+	0.723502i	$0.742531\pi$
$594$	−19.9362	+	14.4845i	−0.817993	+	0.594307i
$595$	9.38541	+	17.9239i	0.384764	+	0.734807i
$596$	−4.70878	−	3.42113i	−0.192879	−	0.140135i
$597$	−11.2646	−	13.9106i	−0.461030	−	0.569324i
$598$	3.18284	+	0.166805i	0.130156	+	0.00682118i
$599$	27.0239	+	15.6022i	1.10417	+	0.637490i	0.937312	−	0.348491i	$-0.113306\pi$
$599$	27.0239	+	15.6022i	1.10417	+	0.637490i	0.166854	+	0.985982i	$0.446639\pi$
$600$	−3.08267	−	3.36410i	−0.125850	−	0.137339i
$601$		−	23.6239i		−	0.963639i	−0.876271	−	0.481819i	$-0.839976\pi$
$601$		−	23.6239i		−	0.963639i	0.876271	−	0.481819i	$-0.160024\pi$
$602$	−25.0885	+	22.8990i	−1.02253	+	0.933292i
$603$	−2.57705	−	16.2708i	−0.104945	−	0.662599i
$604$	−14.3217	−	1.50527i	−0.582743	−	0.0612488i
$605$	−18.3726	−	31.5038i	−0.746954	−	1.28081i
$606$	1.12824	+	10.7345i	0.0458317	+	0.436060i
$607$	−3.64124	+	13.5893i	−0.147794	+	0.551573i	0.851822	+	0.523832i	$0.175498\pi$
$607$	−3.64124	+	13.5893i	−0.147794	+	0.551573i	−0.999615	+	0.0277411i	$0.991169\pi$
$608$	0.236381	−	1.49245i	0.00958652	−	0.0605269i
$609$	0.787580	+	0.394605i	0.0319144	+	0.0159902i
$610$	−12.9376	+	3.52725i	−0.523829	+	0.142814i
$611$	3.56884	−	0.758581i	0.144380	−	0.0306889i
$612$	−4.03665	−	6.21590i	−0.163172	−	0.251263i
$613$	18.3348	+	28.2331i	0.740535	+	1.14032i	0.985315	+	0.170746i	$0.0546177\pi$
$613$	18.3348	+	28.2331i	0.740535	+	1.14032i	−0.244780	+	0.969579i	$0.578716\pi$
$614$	−9.86196	+	2.09622i	−0.397996	+	0.0845967i
$615$	5.61693	+	8.56718i	0.226497	+	0.345462i
$616$	−12.3616	−	6.19357i	−0.498061	−	0.249546i
$617$	−1.71126	+	10.8045i	−0.0688928	+	0.434972i	0.929000	+	0.370081i	$0.120670\pi$
$617$	−1.71126	+	10.8045i	−0.0688928	+	0.434972i	−0.997892	+	0.0648911i	$0.979330\pi$
$618$	−2.63424	+	9.83113i	−0.105965	+	0.395466i
$619$	−3.03218	−	28.8493i	−0.121874	−	1.15955i	−0.868981	−	0.494846i	$-0.835224\pi$
$619$	−3.03218	−	28.8493i	−0.121874	−	1.15955i	0.747107	−	0.664704i	$-0.231442\pi$
$620$	−9.96639	−	4.38528i	−0.400260	−	0.176117i
$621$	−36.8928	−	3.87759i	−1.48046	−	0.155603i
$622$	3.28529	+	20.7425i	0.131728	+	0.831699i
$623$	2.40981	−	2.19950i	0.0965472	−	0.0881211i
$624$		−	0.369725i		−	0.0148009i
$625$	−20.4790	−	14.3391i	−0.819160	−	0.573565i
$626$	22.4016	+	12.9336i	0.895348	+	0.516929i
$627$	7.19639	+	0.377147i	0.287396	+	0.0150618i
$628$	−2.72171	−	3.36103i	−0.108608	−	0.134120i
$629$	14.2716	+	10.3689i	0.569046	+	0.413436i
$630$	−1.86462	+	12.6850i	−0.0742884	+	0.505383i
$631$	6.20389	−	4.50739i	0.246973	−	0.179436i	−0.457411	−	0.889255i	$-0.651223\pi$
$631$	6.20389	−	4.50739i	0.246973	−	0.179436i	0.704384	+	0.709819i	$0.251223\pi$
$632$	11.3111	+	3.03081i	0.449933	+	0.120559i
$633$	16.5872	+	13.4320i	0.659282	+	0.533876i
$634$	−5.67193	+	26.6843i	−0.225261	+	1.05977i
$635$	18.3295	+	9.23876i	0.727385	+	0.366629i
$636$	2.77447	+	0.901480i	0.110015	+	0.0357460i
$637$	2.35736	−	1.57663i	0.0934020	−	0.0624683i
$638$	0.865596	−	1.69883i	0.0342693	−	0.0672573i
$639$	0.0133398	+	0.0627589i	0.000527715	+	0.00248270i
$640$	−0.569299	+	2.16238i	−0.0225035	+	0.0854757i
$641$	6.04533	+	1.28497i	0.238776	+	0.0507534i	0.325745	−	0.945458i	$-0.394385\pi$
$641$	6.04533	+	1.28497i	0.238776	+	0.0507534i	−0.0869691	+	0.996211i	$0.527718\pi$
$642$	−2.91795	−	7.60153i	−0.115162	−	0.300008i
$643$	−7.72460	+	7.72460i	−0.304628	+	0.304628i	−0.842822	−	0.538193i	$-0.819107\pi$
$643$	−7.72460	+	7.72460i	−0.304628	+	0.304628i	0.538193	+	0.842822i	$0.319107\pi$
$644$	−7.59024	−	19.3804i	−0.299097	−	0.763696i
$645$	−12.9999	+	22.7453i	−0.511870	+	0.895595i
$646$	−0.540168	+	5.13936i	−0.0212526	+	0.202205i
$647$	28.1619	+	10.8104i	1.10716	+	0.424999i	0.842148	−	0.539246i	$-0.181291\pi$
$647$	28.1619	+	10.8104i	1.10716	+	0.424999i	0.265012	+	0.964245i	$0.414624\pi$
$648$	0.115052	−	2.19533i	0.00451968	−	0.0862406i
$649$	−30.9477	−	53.6030i	−1.21480	−	2.10410i
$650$	−0.438459	−	1.97769i	−0.0171978	−	0.0775716i
$651$	−3.11972	−	11.3357i	−0.122272	−	0.444282i
$652$	−5.06853	−	9.94756i	−0.198499	−	0.389576i
$653$	−4.55987	+	3.69251i	−0.178441	+	0.144499i	−0.714380	−	0.699758i	$-0.753291\pi$
$653$	−4.55987	+	3.69251i	−0.178441	+	0.144499i	0.535939	+	0.844257i	$0.319958\pi$
$654$	0.400090	−	0.178132i	0.0156448	−	0.00696549i
$655$	−0.215481	−	0.992429i	−0.00841954	−	0.0387774i
$656$	2.04193	−	4.58625i	0.0797240	−	0.179063i
$657$	8.92072	+	8.92072i	0.348030	+	0.348030i
$658$	−14.1350	−	19.1810i	−0.551041	−	0.747754i
$659$	−26.7071	+	8.67766i	−1.04036	+	0.338034i	−0.778879	−	0.627175i	$-0.784211\pi$
$659$	−26.7071	+	8.67766i	−1.04036	+	0.338034i	−0.261482	+	0.965208i	$0.584211\pi$
$660$	−10.5398	−	1.62219i	−0.410260	−	0.0631435i
$661$	−6.44350	+	5.80175i	−0.250623	+	0.225662i	−0.784861	−	0.619672i	$-0.787265\pi$
$661$	−6.44350	+	5.80175i	−0.250623	+	0.225662i	0.534238	+	0.845334i	$0.320599\pi$
$662$	−17.2922	+	11.2297i	−0.672080	+	0.436454i
$663$	0.0661750	+	1.26269i	0.00257002	+	0.0490389i
$664$	−4.47289	+	13.7661i	−0.173582	+	0.534230i
$665$	6.57637	−	6.05528i	0.255021	−	0.234814i
$666$	3.45447	+	10.6318i	0.133858	+	0.411973i
$667$	2.67956	−	1.02859i	0.103753	−	0.0398270i
$668$	0.234160	+	0.873899i	0.00905994	+	0.0338122i
$669$	15.5502	−	1.63439i	0.601206	−	0.0631893i
$670$	9.93053	−	13.7945i	0.383650	−	0.532927i
$671$	−18.4211	+	25.3545i	−0.711140	+	0.978800i
$672$	−2.19903	+	0.996945i	−0.0848293	+	0.0384580i
$673$	−0.848552	+	0.432359i	−0.0327093	+	0.0166662i	−0.470269	−	0.882523i	$-0.655843\pi$
$673$	−0.848552	+	0.432359i	−0.0327093	+	0.0166662i	0.437559	+	0.899190i	$0.355843\pi$
$674$	−14.0412	+	8.10667i	−0.540845	+	0.312257i
$675$	3.89156	+	23.2540i	0.149786	+	0.895048i
$676$	−6.41793	+	11.1162i	−0.246843	+	0.427545i
$677$	5.45122	+	3.54006i	0.209507	+	0.136056i	0.645127	−	0.764075i	$-0.276804\pi$
$677$	5.45122	+	3.54006i	0.209507	+	0.136056i	−0.435620	+	0.900131i	$0.643471\pi$
$678$	16.7197	−	2.64814i	0.642115	−	0.101701i
$679$	−9.33683	−	11.3719i	−0.358315	−	0.436413i
$680$	1.55725	−	7.48691i	0.0597178	−	0.287110i
$681$	−18.3546	−	8.17202i	−0.703352	−	0.313152i
$682$	−24.5802	+	6.58626i	−0.941226	+	0.252201i
$683$	20.1776	−	24.9173i	0.772076	−	0.953434i	−0.227718	−	0.973727i	$-0.573127\pi$
$683$	20.1776	−	24.9173i	0.772076	−	0.953434i	0.999794	+	0.0202930i	$0.00645992\pi$
$684$	−2.19124	+	2.43362i	−0.0837841	+	0.0930517i
$685$	13.4625	−	35.5340i	0.514375	−	1.35768i
$686$	−15.7339	−	9.76964i	−0.600721	−	0.373007i
$687$	19.3856	+	9.87744i	0.739606	+	0.376848i
$688$	12.8209	−	0.671917i	0.488794	−	0.0256166i
$689$	0.866607	+	0.962465i	0.0330151	+	0.0366670i
$690$	−10.1569	−	12.4313i	−0.386667	−	0.473253i
$691$	37.6831	+	33.9301i	1.43353	+	1.29076i	0.893460	+	0.449143i	$0.148271\pi$
$691$	37.6831	+	33.9301i	1.43353	+	1.29076i	0.540075	+	0.841617i	$0.318396\pi$
$692$	−12.0826	−	1.91370i	−0.459313	−	0.0727480i
$693$	15.1574	+	25.8481i	0.575782	+	0.981887i
$694$	−4.72118	−	6.49814i	−0.179213	−	0.246666i
$695$	−8.65182	−	26.2372i	−0.328182	−	0.995232i
$696$	−0.135423	−	0.304166i	−0.00513321	−	0.0115294i
$697$	−6.15278	+	16.0285i	−0.233053	+	0.607124i
$698$	11.1015	−	17.0949i	0.420200	−	0.647051i
$699$	−11.4704			−0.433850
$700$	−10.5805	+	7.94059i	−0.399906	+	0.300126i
$701$	26.6062			1.00490			0.502451	−	0.864606i	$-0.332432\pi$
$701$	26.6062			1.00490			0.502451	+	0.864606i	$0.332432\pi$
$702$	−1.04050	+	1.60223i	−0.0392712	+	0.0604724i
$703$	2.79325	−	7.27667i	0.105350	−	0.274445i
$704$	2.12555	+	4.77407i	0.0801099	+	0.179930i
$705$	−14.9142	−	10.7366i	−0.561701	−	0.404364i
$706$	18.6790	+	25.7095i	0.702994	+	0.967588i
$707$	31.2922	−	0.211649i	1.17686	−	0.00795989i
$708$	−10.6756	−	1.69084i	−0.401212	−	0.0635457i
$709$	−15.1800	−	13.6681i	−0.570098	−	0.513318i	0.332901	−	0.942962i	$-0.391973\pi$
$709$	−15.1800	−	13.6681i	−0.570098	−	0.513318i	−0.902999	+	0.429644i	$0.858639\pi$
$710$	−0.0358122	+	0.0556768i	−0.00134401	+	0.00208951i
$711$	−16.9813	−	18.8597i	−0.636850	−	0.707294i
$712$	−1.23148	+	0.0645393i	−0.0461518	+	0.00241871i
$713$	−34.1323	−	17.3913i	−1.27827	−	0.651309i
$714$	7.33172	−	3.79838i	0.274383	−	0.142151i
$715$	−3.69219	−	2.96327i	−0.138080	−	0.110820i
$716$	1.08007	−	1.19954i	0.0403642	−	0.0448290i
$717$	3.35545	−	4.14364i	0.125312	−	0.154747i
$718$	6.43012	−	1.72295i	0.239970	−	0.0642998i
$719$	−17.4137	−	7.75309i	−0.649422	−	0.289141i	0.0554651	−	0.998461i	$-0.482336\pi$
$719$	−17.4137	−	7.75309i	−0.649422	−	0.289141i	−0.704887	+	0.709319i	$0.749003\pi$
$720$	3.58709	−	3.25830i	0.133683	−	0.121430i
$721$	27.6188	+	10.3881i	1.02858	+	0.386873i
$722$	−16.5109	+	2.61507i	−0.614472	+	0.0973228i
$723$	16.7331	+	10.8666i	0.622312	+	0.404134i
$724$	−0.196253	+	0.339921i	−0.00729370	+	0.0126331i
$725$	−1.08510	−	1.46641i	−0.0402998	−	0.0544612i
$726$	−12.8899	+	7.44199i	−0.478389	+	0.276198i
$727$	3.12251	−	1.59100i	0.115807	−	0.0590068i	−0.395127	−	0.918626i	$-0.629299\pi$
$727$	3.12251	−	1.59100i	0.115807	−	0.0590068i	0.510934	+	0.859620i	$0.329299\pi$
$728$	−1.06677	−	0.104832i	−0.0395371	−	0.00388534i
$729$	4.78782	−	6.58987i	0.177327	−	0.244069i
$730$	0.0568429	+	13.0166i	0.00210385	+	0.481766i
$731$	−43.6661	+	4.58949i	−1.61505	+	0.169748i
$732$	1.41646	+	5.28632i	0.0523540	+	0.195388i
$733$	−25.0907	+	9.63140i	−0.926744	+	0.355744i	−0.774482	−	0.632596i	$-0.781989\pi$
$733$	−25.0907	+	9.63140i	−0.926744	+	0.355744i	−0.152263	+	0.988340i	$0.548656\pi$
$734$	−5.81520	−	17.8973i	−0.214643	−	0.660603i
$735$	−13.8614	−	3.44954i	−0.511284	−	0.127238i
$736$	−2.43100	+	7.48183i	−0.0896077	+	0.275784i
$737$	−2.07898	−	39.6693i	−0.0765802	−	1.46124i
$738$	−9.12468	+	5.92564i	−0.335884	+	0.218126i
$739$	8.52172	−	7.67299i	0.313477	−	0.282256i	−0.497340	−	0.867556i	$-0.665690\pi$
$739$	8.52172	−	7.67299i	0.313477	−	0.282256i	0.810817	+	0.585300i	$0.199023\pi$
$740$	−5.19147	+	10.2998i	−0.190842	+	0.378627i
$741$	0.531332	−	0.172640i	0.0195190	−	0.00634210i
$742$	3.38772	−	7.74958i	0.124367	−	0.284496i
$743$	−4.91784	−	4.91784i	−0.180418	−	0.180418i	0.611120	−	0.791538i	$-0.290719\pi$
$743$	−4.91784	−	4.91784i	−0.180418	−	0.180418i	−0.791538	+	0.611120i	$0.790719\pi$
$744$	−1.80746	+	4.05961i	−0.0662645	+	0.148833i
$745$	−5.24160	+	11.9126i	−0.192037	+	0.436442i
$746$	21.5690	−	9.60315i	0.789698	−	0.351596i
$747$	24.3785	−	19.7413i	0.891963	−	0.722297i
$748$	−8.11372	−	15.9241i	−0.296667	−	0.582242i
$749$	−22.7601	+	6.26383i	−0.831634	+	0.228875i
$750$	−5.88850	+	8.33222i	−0.215017	+	0.304250i
$751$	−12.5487	−	21.7350i	−0.457909	−	0.793122i	0.540941	−	0.841061i	$-0.318068\pi$
$751$	−12.5487	−	21.7350i	−0.457909	−	0.793122i	−0.998850	+	0.0479383i	$0.984735\pi$
$752$	−0.471319	+	8.99330i	−0.0171872	+	0.327952i
$753$	−18.9284	−	7.26593i	−0.689789	−	0.264785i
$754$	0.0154509	−	0.147005i	0.000562687	−	0.00535361i
$755$	3.50571	+	32.0094i	0.127586	+	1.16494i
$756$	12.3353	+	1.86829i	0.448631	+	0.0679490i
$757$	−9.90281	+	9.90281i	−0.359924	+	0.359924i	−0.863785	−	0.503861i	$-0.831912\pi$
$757$	−9.90281	+	9.90281i	−0.359924	+	0.359924i	0.503861	+	0.863785i	$0.331912\pi$
$758$	−2.76490	−	7.20280i	−0.100426	−	0.261618i
$759$	−36.6975	−	7.80029i	−1.33203	−	0.283133i
$760$	−3.37339	+	0.191567i	−0.122366	+	0.00694886i
$761$	−8.35548	−	39.3095i	−0.302886	−	1.42497i	−0.821622	−	0.570032i	$-0.806931\pi$
$761$	−8.35548	−	39.3095i	−0.302886	−	1.42497i	0.518736	−	0.854934i	$-0.326403\pi$
$762$	3.80314	−	7.46408i	0.137773	−	0.270395i
$763$	−0.400521	−	1.20489i	−0.0144998	−	0.0436199i
$764$	5.76446	+	1.87299i	0.208551	+	0.0677623i
$765$	−11.6675	+	11.7699i	−0.421839	+	0.425540i
$766$	−6.09075	+	28.6547i	−0.220068	+	1.03534i
$767$	−3.72916	−	3.01981i	−0.134652	−	0.109039i
$768$	0.881485	+	0.236193i	0.0318078	+	0.00852288i
$769$	24.2107	−	17.5901i	0.873059	−	0.634315i	−0.0583467	−	0.998296i	$-0.518583\pi$
$769$	24.2107	−	17.5901i	0.873059	−	0.634315i	0.931406	+	0.363982i	$0.118583\pi$
$770$	−7.66895	+	29.9504i	−0.276370	+	1.07934i
$771$	10.3893	+	7.54827i	0.374162	+	0.271844i
$772$	−3.47598	−	4.29248i	−0.125103	−	0.154490i
$773$	−52.4196	−	2.74719i	−1.88540	−	0.0988097i	−0.925432	−	0.378914i	$-0.876297\pi$
$773$	−52.4196	−	2.74719i	−1.88540	−	0.0988097i	−0.959969	+	0.280105i	$0.909631\pi$
$774$	−24.0960	−	13.9118i	−0.866112	−	0.500050i
$775$	−4.85393	+	23.8587i	−0.174358	+	0.857030i
$776$			5.56130i			0.199639i
$777$	−12.1644	+	2.67174i	−0.436395	+	0.0958481i
$778$	−1.46998	−	9.28110i	−0.0527014	−	0.332744i
$779$	7.54436	+	0.792944i	0.270305	+	0.0284102i
$780$	−0.807907	+	0.175417i	−0.0289277	+	0.00628093i
$781$	0.0161721	+	0.153867i	0.000578682	+	0.00550579i
$782$	6.96325	−	25.9872i	0.249005	−	0.929301i
$783$	−0.269134	+	1.69924i	−0.00961806	+	0.0607260i
$784$	2.25297	+	6.62753i	0.0804633	+	0.236697i
$785$	−6.05306	+	7.54201i	−0.216043	+	0.269186i
$786$	−0.405408	+	0.0861722i	−0.0144604	+	0.00307366i
$787$	4.93358	+	7.59704i	0.175863	+	0.270805i	0.915600	−	0.402091i	$-0.131717\pi$
$787$	4.93358	+	7.59704i	0.175863	+	0.270805i	−0.739737	+	0.672897i	$0.765050\pi$
$788$	7.15999	+	11.0254i	0.255064	+	0.392764i
$789$	1.27173	−	0.270315i	0.0452748	−	0.00962345i
$790$	1.25620	−	26.1546i	0.0446935	−	0.930537i
$791$	−2.89996	−	48.9921i	−0.103111	−	1.74196i
$792$	1.77170	−	11.1861i	0.0629546	−	0.397480i
$793$	−0.628844	+	2.34688i	−0.0223309	+	0.0833401i
$794$	−0.594641	−	5.65763i	−0.0211030	−	0.200782i
$795$	0.653521	−	6.49035i	0.0231780	−	0.230189i
$796$	19.5069	+	2.05026i	0.691403	+	0.0726694i
$797$	3.64742	+	23.0289i	0.129198	+	0.815726i	0.964141	+	0.265390i	$0.0855006\pi$
$797$	3.64742	+	23.0289i	0.129198	+	0.815726i	−0.834943	+	0.550337i	$0.814499\pi$
$798$	−2.45953	−	2.69470i	−0.0870663	−	0.0953914i
$799$		−	30.7984i		−	1.08957i
$800$	4.99524	+	0.218061i	0.176608	+	0.00770962i
$801$	2.31448	+	1.33626i	0.0817781	+	0.0472146i
$802$	31.4199	+	1.64665i	1.10948	+	0.0581452i
$803$	19.1446	+	23.6417i	0.675600	+	0.834296i
$804$	−5.61203	−	4.07738i	−0.197921	−	0.143798i
$805$	−38.7480	+	25.7809i	−1.36569	+	0.908658i
$806$	−1.59606	+	1.15961i	−0.0562188	+	0.0408454i
$807$	−13.7721	−	3.69024i	−0.484803	−	0.129902i
$808$	−9.19178	−	7.44335i	−0.323366	−	0.261856i
$809$	−1.53653	+	7.22879i	−0.0540214	+	0.254151i	−0.996869	−	0.0790744i	$-0.974804\pi$
$809$	−1.53653	+	7.22879i	−0.0540214	+	0.254151i	0.942847	+	0.333225i	$0.108137\pi$
$810$	−4.85171	+	0.790169i	−0.170472	+	0.0277637i
$811$	21.1639	+	6.87658i	0.743167	+	0.241470i	0.656038	−	0.754728i	$-0.272231\pi$
$811$	21.1639	+	6.87658i	0.743167	+	0.241470i	0.0871284	+	0.996197i	$0.472231\pi$
$812$	−0.916009	+	0.304494i	−0.0321456	+	0.0106856i
$813$	8.64129	−	16.9595i	0.303063	−	0.594795i
$814$	5.60452	+	26.3672i	0.196438	+	0.924170i
$815$	−19.3322	+	15.7952i	−0.677176	+	0.553280i
$816$	−3.05274	−	0.648879i	−0.106867	−	0.0227153i
$817$	6.95224	+	18.1112i	0.243228	+	0.633631i
$818$	−4.31231	+	4.31231i	−0.150777	+	0.150777i
$819$	1.81518	+	1.44969i	0.0634277	+	0.0506563i
$820$	−10.9905	−	2.28598i	−0.383804	−	0.0798298i
$821$	−4.96194	+	47.2097i	−0.173173	+	1.64763i	0.470550	+	0.882373i	$0.344055\pi$
$821$	−4.96194	+	47.2097i	−0.173173	+	1.64763i	−0.643723	+	0.765258i	$0.722611\pi$
$822$	−14.4779	−	5.55756i	−0.504976	−	0.193842i
$823$	2.04199	−	38.9635i	0.0711794	−	1.35818i	−0.696596	−	0.717464i	$-0.745303\pi$
$823$	2.04199	−	38.9635i	0.0711794	−	1.35818i	0.767775	−	0.640719i	$-0.221364\pi$
$824$	−5.57646	−	9.65871i	−0.194265	−	0.336477i
$825$	1.45588	+	23.8007i	0.0506873	+	0.828633i
$826$	−7.90554	+	30.3228i	−0.275069	+	1.05506i
$827$	−1.79040	−	3.51386i	−0.0622583	−	0.122189i	0.857780	−	0.514016i	$-0.171843\pi$
$827$	−1.79040	−	3.51386i	−0.0622583	−	0.122189i	−0.920039	+	0.391828i	$0.871843\pi$
$828$	13.2496	−	10.7293i	0.460456	−	0.372870i
$829$	10.2732	−	4.57394i	0.356804	−	0.158859i	−0.220503	−	0.975386i	$-0.570770\pi$
$829$	10.2732	−	4.57394i	0.356804	−	0.158859i	0.577308	+	0.816527i	$0.304103\pi$
$830$	32.2033	+	3.24259i	1.11779	+	0.112552i
$831$	4.83363	−	10.8565i	0.167677	−	0.376608i
$832$	0.286479	+	0.286479i	0.00993189	+	0.00993189i
$833$	−8.88062	−	22.2312i	−0.307695	−	0.770266i
$834$	−10.7232	+	3.48417i	−0.371313	+	0.120647i
$835$	1.79850	−	0.926299i	0.0622398	−	0.0320559i
$836$	−5.86831	+	5.28385i	−0.202960	+	0.182746i
$837$	19.2575	−	12.5060i	0.665638	−	0.432270i
$838$	0.234936	+	4.48285i	0.00811574	+	0.154858i
$839$	8.79475	−	27.0674i	0.303628	−	0.934472i	−0.676557	−	0.736390i	$-0.736529\pi$
$839$	8.79475	−	27.0674i	0.303628	−	0.934472i	0.980185	−	0.198082i	$-0.0634712\pi$
$840$	3.22181	+	4.33221i	0.111163	+	0.149475i
$841$	8.92036	+	27.4540i	0.307599	+	0.946691i
$842$	23.6712	−	9.08651i	0.815762	−	0.313142i
$843$	1.11426	+	4.15848i	0.0383772	+	0.143226i
$844$	−23.2602	+	2.44475i	−0.800649	+	0.0841516i
$845$	27.3356	+	8.75007i	0.940372	+	0.301012i
$846$	11.4718	−	15.7896i	0.394409	−	0.542857i
$847$	17.8176	+	39.3013i	0.612219	+	1.35041i
$848$	−2.84829	+	1.45128i	−0.0978106	+	0.0498370i
$849$	1.99035	−	1.14913i	0.0683087	−	0.0394380i
$850$	−17.0989	+	0.149343i	−0.586487	+	0.00512242i
$851$	−20.2896	+	35.1425i	−0.695517	+	1.20467i
$852$	0.0226587	+	0.0147147i	0.000776273	+	0.000504118i
$853$	10.2904	−	1.62984i	0.352336	−	0.0558045i	0.0222420	−	0.999753i	$-0.492920\pi$
$853$	10.2904	−	1.62984i	0.352336	−	0.0558045i	0.330094	+	0.943948i	$0.392920\pi$
$854$	15.6542	−	2.58804i	0.535677	−	0.0885609i
$855$	6.35746	+	3.63356i	0.217421	+	0.124265i
$856$	8.15095	+	3.62904i	0.278594	+	0.124038i
$857$	7.46112	−	1.99920i	0.254867	−	0.0682914i	−0.129123	−	0.991629i	$-0.541216\pi$
$857$	7.46112	−	1.99920i	0.254867	−	0.0682914i	0.383990	+	0.923337i	$0.374550\pi$
$858$	−1.21593	+	1.50155i	−0.0415113	+	0.0512622i
$859$	−26.5669	+	29.5055i	−0.906451	+	1.00672i	0.0934873	+	0.995620i	$0.470199\pi$
$859$	−26.5669	+	29.5055i	−0.906451	+	1.00672i	−0.999938	+	0.0110955i	$0.996468\pi$
$860$	−7.55116	−	27.6969i	−0.257492	−	0.944458i
$861$	−5.57586	−	10.7627i	−0.190025	−	0.366790i
$862$	22.1944	+	11.3086i	0.755945	+	0.385173i
$863$	−3.31836	+	0.173908i	−0.112958	+	0.00591989i	−0.108731	−	0.994071i	$-0.534679\pi$
$863$	−3.31836	+	0.173908i	−0.112958	+	0.00591989i	−0.00422697	+	0.999991i	$0.501345\pi$
$864$	−3.15527	−	3.50429i	−0.107345	−	0.119218i
$865$	1.55089	+	27.3104i	0.0527320	+	0.928580i
$866$	2.34509	+	2.11152i	0.0796893	+	0.0717525i
$867$	−4.78095	−	0.757229i	−0.162370	−	0.0257168i
$868$	11.2007	+	6.36612i	0.380177	+	0.216080i
$869$	−35.9700	−	49.5085i	−1.22020	−	1.67946i
$870$	−0.600398	+	0.440233i	−0.0203554	+	0.0149253i
$871$	−1.25260	−	2.81339i	−0.0424428	−	0.0953280i
$872$	−0.171983	+	0.448031i	−0.00582408	+	0.0151723i
$873$	6.56423	−	10.1080i	0.222165	−	0.342105i
$874$	−11.8873			−0.402093
$875$	22.3713	+	19.3526i	0.756289	+	0.654237i
$876$	5.31236			0.179488
$877$	10.4101	−	16.0302i	0.351525	−	0.541301i	−0.618036	−	0.786149i	$-0.712072\pi$
$877$	10.4101	−	16.0302i	0.351525	−	0.541301i	0.969561	+	0.244849i	$0.0787383\pi$
$878$	10.8726	−	28.3241i	0.366933	−	0.955893i
$879$	0.845544	+	1.89912i	0.0285195	+	0.0640558i
$880$	9.42361	−	6.90973i	0.317670	−	0.232927i
$881$	−22.3215	−	30.7229i	−0.752031	−	1.03508i	−0.997835	−	0.0657623i	$-0.979052\pi$
$881$	−22.3215	−	30.7229i	−0.752031	−	1.03508i	0.245804	−	0.969319i	$-0.420948\pi$
$882$	3.72781	−	14.7052i	0.125522	−	0.495151i
$883$	28.1868	+	4.46435i	0.948562	+	0.150237i	0.611500	−	0.791245i	$-0.290567\pi$
$883$	28.1868	+	4.46435i	0.948562	+	0.150237i	0.337063	+	0.941482i	$0.390567\pi$
$884$	−1.02967	−	0.927115i	−0.0346314	−	0.0311822i
$885$	1.37028	+	24.1299i	0.0460616	+	0.811119i
$886$	−15.4902	−	17.2036i	−0.520404	−	0.577968i
$887$	30.6040	−	1.60389i	1.02758	−	0.0538533i	0.468914	−	0.883244i	$-0.344646\pi$
$887$	30.6040	−	1.60389i	1.02758	−	0.0538533i	0.558669	+	0.829391i	$0.311312\pi$
$888$	4.19423	+	2.13707i	0.140749	+	0.0717153i
$889$	−20.4578	−	13.0896i	−0.686132	−	0.439010i
$890$	0.725307	+	2.66036i	0.0243124	+	0.0891754i
$891$	−7.68714	+	8.53743i	−0.257529	+	0.286015i
$892$	−10.7826	+	13.3154i	−0.361028	+	0.445832i
$893$	−13.1443	+	3.52201i	−0.439858	+	0.117860i
$894$	4.85234	+	2.16040i	0.162287	+	0.0722547i
$895$	−3.13363	−	1.79100i	−0.104746	−	0.0598665i
$896$	0.931425	−	2.47638i	0.0311167	−	0.0827300i
$897$	−2.87277	+	0.455002i	−0.0959190	+	0.0151921i
$898$	34.1473	+	22.1755i	1.13951	+	0.740006i
$899$	−0.888307	+	1.53859i	−0.0296267	+	0.0513149i
$900$	−8.82179	−	6.29243i	−0.294060	−	0.209748i
$901$	9.46777	−	5.46622i	0.315417	−	0.182106i
$902$	−23.3759	+	11.9106i	−0.778331	+	0.396580i
$903$	18.0502	−	25.2007i	0.600673	−	0.838626i
$904$	−10.9032	+	15.0070i	−0.362636	+	0.499126i
$905$	0.835892	+	0.267568i	0.0277860	+	0.00889426i
$906$	13.0697	−	1.37368i	0.434213	−	0.0456376i
$907$	2.61461	+	9.75786i	0.0868168	+	0.324005i	0.995652	−	0.0931506i	$-0.0296938\pi$
$907$	2.61461	+	9.75786i	0.0868168	+	0.324005i	−0.908835	+	0.417155i	$0.863027\pi$
$908$	20.5540	−	7.88995i	0.682109	−	0.261837i
$909$	7.92096	+	24.3782i	0.262722	+	0.808574i
$910$	0.277056	+	2.38079i	0.00918431	+	0.0789225i
$911$	−14.7660	+	45.4451i	−0.489220	+	1.50566i	0.336555	+	0.941664i	$0.390738\pi$
$911$	−14.7660	+	45.4451i	−0.489220	+	1.50566i	−0.825775	+	0.564000i	$0.809262\pi$
$912$	0.0721691	+	1.37707i	0.00238976	+	0.0455993i
$913$	63.4390	−	41.1978i	2.09953	−	1.36345i
$914$	10.2568	−	9.23523i	0.339264	−	0.305474i
$915$	10.8794	−	5.60329i	0.359661	−	0.185239i
$916$	−22.6743	+	7.36731i	−0.749179	+	0.243423i
$917$	0.133683	+	1.19416i	0.00441460	+	0.0394346i
$918$	11.4032	+	11.4032i	0.376360	+	0.376360i
$919$	−17.9831	+	40.3907i	−0.593207	+	1.33237i	0.328509	+	0.944501i	$0.393454\pi$
$919$	−17.9831	+	40.3907i	−0.593207	+	1.33237i	−0.921716	+	0.387864i	$0.873213\pi$
$920$	17.5023	+	1.76233i	0.577035	+	0.0581023i
$921$	8.40543	−	3.74234i	0.276968	−	0.123314i
$922$	25.4889	−	20.6405i	0.839433	−	0.679759i
$923$	0.00544537	+	0.0106871i	0.000179237	+	0.000351771i
$924$	12.2095	+	3.18319i	0.401664	+	0.104719i
$925$	24.9697	+	6.45741i	0.820998	+	0.212318i
$926$	6.10644	+	10.5767i	0.200670	+	0.347571i
$927$	−1.26499	+	24.1375i	−0.0415477	+	0.792778i
$928$	0.340613	+	0.130749i	0.0111812	+	0.00429205i
$929$	−3.46644	+	32.9810i	−0.113730	+	1.08207i	0.777614	+	0.628742i	$0.216430\pi$
$929$	−3.46644	+	32.9810i	−0.113730	+	1.08207i	−0.891344	+	0.453328i	$0.850237\pi$
$930$	9.72843	+	2.02348i	0.319008	+	0.0663525i
$931$	−8.47240	+	6.33241i	−0.277672	+	0.207536i
$932$	8.88776	−	8.88776i	0.291128	−	0.291128i
$933$	−6.86818	−	17.8922i	−0.224854	−	0.585765i
$934$	−7.60581	−	1.61666i	−0.248870	−	0.0528989i
$935$	−30.9470	+	25.2849i	−1.01207	+	0.826905i
$936$	−0.182552	−	0.858838i	−0.00596689	−	0.0280720i
$937$	−17.9256	+	35.1810i	−0.585604	+	1.14931i	0.388125	+	0.921607i	$0.373123\pi$
$937$	−17.9256	+	35.1810i	−0.585604	+	1.14931i	−0.973730	+	0.227707i	$0.926877\pi$
$938$	−13.3557	+	15.0363i	−0.436079	+	0.490952i
$939$	−22.4505	−	7.29460i	−0.732644	−	0.238050i
$940$	19.8754	−	3.23698i	0.648263	−	0.105579i
$941$	−1.63490	+	7.69159i	−0.0532961	+	0.250739i	−0.996728	−	0.0808276i	$-0.974244\pi$
$941$	−1.63490	+	7.69159i	−0.0532961	+	0.250739i	0.943432	+	0.331566i	$0.107577\pi$
$942$	3.06721	+	2.48378i	0.0999352	+	0.0809259i
$943$	−38.1481	−	10.2218i	−1.24227	−	0.332866i
$944$	9.58202	−	6.96175i	0.311868	−	0.226586i
$945$	−1.77001	−	27.8410i	−0.0575785	−	0.905666i
$946$	−54.2790	−	39.4360i	−1.76476	−	1.28218i
$947$	7.43765	+	9.18474i	0.241691	+	0.298464i	0.883529	−	0.468377i	$-0.155161\pi$
$947$	7.43765	+	9.18474i	0.241691	+	0.298464i	−0.641838	+	0.766841i	$0.721828\pi$
$948$	−10.6718	−	0.559286i	−0.346604	−	0.0181648i
$949$	2.04247	+	1.17922i	0.0663013	+	0.0382791i
$950$	2.01911	+	7.28048i	0.0655086	+	0.236210i
$951$		−	24.8956i		−	0.807295i
$952$	−2.73779	+	8.62408i	−0.0887322	+	0.279508i
$953$	−1.09758	−	6.92986i	−0.0355542	−	0.224480i	0.963513	−	0.267661i	$-0.0862508\pi$
$953$	−1.09758	−	6.92986i	−0.0355542	−	0.224480i	−0.999067	+	0.0431810i	$0.986251\pi$
$954$	6.88995	+	0.724163i	0.223070	+	0.0234456i
$955$	1.35781	−	13.4849i	0.0439376	−	0.436360i
$956$	0.610721	+	5.81062i	0.0197521	+	0.187929i
$957$	−0.450335	+	1.68067i	−0.0145573	+	0.0543285i
$958$	−0.190773	+	1.20449i	−0.00616360	+	0.0389155i
$959$	−20.1403	+	40.1974i	−0.650365	+	1.29804i
$960$	0.0978964	−	2.03824i	0.00315959	−	0.0657840i
$961$	−7.12881	+	1.51528i	−0.229962	+	0.0488799i
$962$	1.13820	+	1.75267i	0.0366970	+	0.0565084i
$963$	−10.5314	−	16.2169i	−0.339369	−	0.522583i
$964$	−21.3855	+	4.54562i	−0.688780	+	0.146405i
$965$	−7.73054	+	9.63213i	−0.248855	+	0.310069i
$966$	10.4525	+	15.8596i	0.336304	+	0.510273i
$967$	−0.275885	+	1.74187i	−0.00887188	+	0.0560148i	−0.991727	−	0.128364i	$-0.959027\pi$
$967$	−0.275885	+	1.74187i	−0.00887188	+	0.0560148i	0.982855	+	0.184379i	$0.0590274\pi$
$968$	4.22128	−	15.7540i	0.135677	−	0.506354i
$969$	−0.492947	−	4.69007i	−0.0158357	−	0.150667i
$970$	12.1523	−	2.63857i	0.390187	−	0.0847193i
$971$	−23.1870	−	2.43705i	−0.744107	−	0.0782088i	−0.275115	−	0.961411i	$-0.588716\pi$
$971$	−23.1870	−	2.43705i	−0.744107	−	0.0782088i	−0.468992	+	0.883203i	$0.655383\pi$
$972$	2.52682	+	15.9537i	0.0810479	+	0.511716i
$973$	7.01243	+	31.9275i	0.224808	+	1.02355i
$974$			7.04776i			0.225825i
$975$	0.766625	+	1.68217i	0.0245517	+	0.0538727i
$976$	−5.19361	−	2.99853i	−0.166243	−	0.0959806i
$977$	−42.4190	−	2.22308i	−1.35710	−	0.0711227i	−0.640153	−	0.768248i	$-0.721129\pi$
$977$	−42.4190	−	2.22308i	−1.35710	−	0.0711227i	−0.716950	+	0.697125i	$0.754462\pi$
$978$	6.41178	+	7.91788i	0.205026	+	0.253186i
$979$	5.21364	+	3.78793i	0.166629	+	0.121063i
$980$	13.4132	−	8.06753i	0.428470	−	0.257708i
$981$	0.841420	−	0.611327i	0.0268645	−	0.0195182i
$982$	−6.82529	−	1.82883i	−0.217804	−	0.0583604i
$983$	9.72754	+	7.87721i	0.310260	+	0.251244i	0.771785	−	0.635883i	$-0.219364\pi$
$983$	9.72754	+	7.87721i	0.310260	+	0.251244i	−0.461525	+	0.887127i	$0.652697\pi$
$984$	−0.952528	+	4.48129i	−0.0303655	+	0.142858i
$985$	20.6952	−	20.8767i	0.659403	−	0.665187i
$986$	−1.18667	−	0.385573i	−0.0377913	−	0.0122791i
$987$	16.2568	+	14.4398i	0.517459	+	0.459624i
$988$	−0.277930	+	0.545468i	−0.00884213	+	0.0173537i
$989$	−20.9989	−	98.7920i	−0.667726	−	3.14140i
$990$	−25.2839	+	1.43581i	−0.803574	+	0.0456331i
$991$	−13.7017	−	2.91239i	−0.435249	−	0.0925151i	−0.0149240	−	0.999889i	$-0.504751\pi$
$991$	−13.7017	−	2.91239i	−0.435249	−	0.0925151i	−0.420325	+	0.907374i	$0.638084\pi$
$992$	−1.74507	−	4.54606i	−0.0554060	−	0.144338i
$993$	13.3050	−	13.3050i	0.422221	−	0.422221i
$994$	0.0488810	−	0.0612049i	0.00155041	−	0.00194130i
$995$	−4.77495	−	43.5983i	−0.151376	−	1.38216i
$996$	1.38074	−	13.1369i	0.0437504	−	0.416257i
$997$	13.7254	+	5.26870i	0.434689	+	0.166861i	0.565865	−	0.824498i	$-0.308542\pi$
$997$	13.7254	+	5.26870i	0.434689	+	0.166861i	−0.131177	+	0.991359i	$0.541875\pi$
$998$	−0.809469	+	15.4456i	−0.0256233	+	0.488922i
$999$	−12.1618	−	21.0648i	−0.384781	−	0.666461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.x.a.3.14	✓	320
7.5	odd	6	inner	350.2.x.a.103.7	yes	320
25.17	odd	20	inner	350.2.x.a.17.7	yes	320
175.117	even	60	inner	350.2.x.a.117.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.x.a.3.14	✓	320	1.1	even	1	trivial
350.2.x.a.17.7	yes	320	25.17	odd	20	inner
350.2.x.a.103.7	yes	320	7.5	odd	6	inner
350.2.x.a.117.14	yes	320	175.117	even	60	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.544639 - 0.838671i) q^{2} +(-0.327039 + 0.851967i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80326 + 1.32222i) q^{5} +(0.536401 + 0.738293i) q^{6} +(2.28229 - 1.33834i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.61054 + 1.45014i) q^{9} +O(q^{10})\)	\(q+(0.544639 - 0.838671i) q^{2} +(-0.327039 + 0.851967i) q^{3} +(-0.406737 - 0.913545i) q^{4} +(-1.80326 + 1.32222i) q^{5} +(0.536401 + 0.738293i) q^{6} +(2.28229 - 1.33834i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(1.61054 + 1.45014i) q^{9} +(0.126777 + 2.23247i) q^{10} +(3.49679 + 3.88358i) q^{11} +(0.911329 - 0.0477607i) q^{12} +(0.360985 + 0.183931i) q^{13} +(0.120595 - 2.64300i) q^{14} +(-0.536746 - 1.96873i) q^{15} +(-0.669131 + 0.743145i) q^{16} +(2.15222 - 2.65777i) q^{17} +(2.09335 - 0.560912i) q^{18} +(-1.38042 - 0.614601i) q^{19} +(1.94136 + 1.10957i) q^{20} +(0.393825 + 2.38212i) q^{21} +(5.16154 - 0.817507i) q^{22} +(6.59771 + 4.28460i) q^{23} +(0.456290 - 0.790317i) q^{24} +(1.50349 - 4.76860i) q^{25} +(0.350864 - 0.202572i) q^{26} +(-4.20152 + 2.14078i) q^{27} +(-2.15093 - 1.54062i) q^{28} +(0.214451 - 0.295167i) q^{29} +(-1.94345 - 0.622096i) q^{30} +(-4.84281 + 0.509000i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-4.45227 + 1.70907i) q^{33} +(-1.05681 - 3.25252i) q^{34} +(-2.34598 + 5.43106i) q^{35} +(0.669701 - 2.06113i) q^{36} +(0.269961 + 5.15116i) q^{37} +(-1.26728 + 0.822979i) q^{38} +(-0.274760 + 0.247395i) q^{39} +(1.98790 - 1.02384i) q^{40} +(-4.77457 + 1.55135i) q^{41} +(2.21231 + 0.967108i) q^{42} +(-9.07822 - 9.07822i) q^{43} +(2.12555 - 4.77407i) q^{44} +(-4.82162 - 0.485494i) q^{45} +(7.18674 - 3.19974i) q^{46} +(6.99870 - 5.66743i) q^{47} +(-0.414303 - 0.813115i) q^{48} +(3.41768 - 6.10897i) q^{49} +(-3.18042 - 3.85810i) q^{50} +(1.56047 + 2.70281i) q^{51} +(0.0212035 - 0.404588i) q^{52} +(2.98438 + 1.14560i) q^{53} +(-0.492902 + 4.68965i) q^{54} +(-11.4406 - 2.37960i) q^{55} +(-2.46355 + 0.964837i) q^{56} +(0.975071 - 0.975071i) q^{57} +(-0.130749 - 0.340613i) q^{58} +(-11.5852 - 2.46251i) q^{59} +(-1.58021 + 1.29110i) q^{60} +(1.24686 + 5.86601i) q^{61} +(-2.21070 + 4.33875i) q^{62} +(5.61650 + 1.15418i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-0.894147 + 0.145624i) q^{65} +(-0.991537 + 4.66481i) q^{66} +(-5.90736 - 4.78369i) q^{67} +(-3.30338 - 0.885137i) q^{68} +(-5.80805 + 4.21980i) q^{69} +(3.27715 + 4.92547i) q^{70} +(0.0239513 + 0.0174017i) q^{71} +(-1.36386 - 1.68423i) q^{72} +(5.81327 + 0.304661i) q^{73} +(4.46716 + 2.57912i) q^{74} +(3.57098 + 2.84045i) q^{75} +1.51105i q^{76} +(13.1783 + 4.18355i) q^{77} +(0.0578378 + 0.365174i) q^{78} +(-11.6460 - 1.22404i) q^{79} +(0.224019 - 2.22482i) q^{80} +(0.229789 + 2.18630i) q^{81} +(-1.29934 + 4.84922i) q^{82} +(2.26432 - 14.2964i) q^{83} +(2.01600 - 1.32867i) q^{84} +(-0.366868 + 7.63834i) q^{85} +(-12.5580 + 2.66928i) q^{86} +(0.181338 + 0.279236i) q^{87} +(-2.84622 - 4.38279i) q^{88} +(1.20623 - 0.256391i) q^{89} +(-3.03321 + 3.77933i) q^{90} +(1.07003 - 0.0633379i) q^{91} +(1.23065 - 7.77001i) q^{92} +(1.15014 - 4.29238i) q^{93} +(-0.941346 - 8.95631i) q^{94} +(3.30189 - 0.716922i) q^{95} +(-0.907581 - 0.0953906i) q^{96} +(-0.869979 - 5.49283i) q^{97} +(-3.26201 - 6.19349i) q^{98} +11.3255i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 320 * q + 12 * q^5 - 8 * q^7	\( 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98}+O(q^{100}) \) 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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