LMFDB - Embedded newform 750.2.o.b.229.7

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:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.7
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.19782 + 0.411792i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-2.79431 + 3.84603i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.19782 + 0.411792i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-2.79431 + 3.84603i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-0.147722 - 2.23118i) q^{10} +(3.56328 - 0.914895i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(-1.15151 - 2.90838i) q^{13} +(4.42012 + 1.75005i) q^{14} +(2.23606 - 0.00733290i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.83804 + 3.34339i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(-0.583454 + 3.05857i) q^{19} +(-2.12435 + 0.697953i) q^{20} +(-2.02414 + 4.30151i) q^{21} +(-1.77230 - 3.22381i) q^{22} +(4.96567 + 0.312413i) q^{23} +(0.809017 + 0.587785i) q^{24} +(4.66085 + 1.81009i) q^{25} +(-2.53064 + 1.83862i) q^{26} +(0.844328 - 0.535827i) q^{27} +(0.595829 - 4.71647i) q^{28} +(4.66992 + 0.589948i) q^{29} +(-0.563187 - 2.16398i) q^{30} +(5.58547 + 3.07064i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(3.32873 - 1.56638i) q^{33} +(3.69545 + 0.948830i) q^{34} +(-7.72516 + 7.30223i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(4.11959 + 2.61437i) q^{37} +(3.10758 - 0.195512i) q^{38} +(-1.67609 - 2.64110i) q^{39} +(1.20433 + 1.88404i) q^{40} +(0.418715 + 6.65529i) q^{41} +(4.66975 + 0.890803i) q^{42} +(-1.46737 + 0.476776i) q^{43} +(-2.68177 + 2.51835i) q^{44} +(2.19508 - 0.426198i) q^{45} +(-0.932313 - 4.88736i) q^{46} +(-1.04661 + 1.11452i) q^{47} +(0.368125 - 0.929776i) q^{48} +(-4.82070 - 14.8366i) q^{49} +(0.594118 - 4.96458i) q^{50} +(-1.17900 + 3.62858i) q^{51} +(2.41020 + 1.99389i) q^{52} +(-11.9158 - 5.60715i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(8.20821 - 0.543447i) q^{55} +(-4.71647 + 0.595829i) q^{56} +3.11373i q^{57} +(-0.589948 - 4.66992i) q^{58} +(-2.87398 - 3.47404i) q^{59} +(-1.95594 + 1.08365i) q^{60} +(0.802804 - 12.7602i) q^{61} +(1.58512 - 6.17362i) q^{62} +(-1.18226 + 4.60460i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-1.33317 - 6.86630i) q^{65} +(-2.34499 - 2.83461i) q^{66} +(1.00929 + 7.98934i) q^{67} -3.81532i q^{68} +(4.93625 - 0.623594i) q^{69} +(8.99398 + 5.66647i) q^{70} +(-6.88173 - 6.46238i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-3.57153 - 2.95462i) q^{73} +(1.50773 - 4.64033i) q^{74} +(4.91748 + 0.904674i) q^{75} +(-0.962194 - 2.96133i) q^{76} +(-6.43818 + 16.2610i) q^{77} +(-2.14129 + 2.28025i) q^{78} +(1.55864 + 8.17069i) q^{79} +(1.52534 - 1.63503i) q^{80} +(0.728969 - 0.684547i) q^{81} +(6.34207 - 2.06066i) q^{82} +(9.17958 + 1.75110i) q^{83} +(-0.298503 - 4.74458i) q^{84} +(-5.41647 + 6.59128i) q^{85} +(0.826717 + 1.30270i) q^{86} +(4.69774 - 0.295557i) q^{87} +(3.10616 + 1.97123i) q^{88} +(7.43942 - 8.99271i) q^{89} +(-0.958701 - 2.02012i) q^{90} +(14.4034 + 3.69817i) q^{91} +(-4.50195 + 2.11846i) q^{92} +(6.06191 + 1.96963i) q^{93} +(1.33979 + 0.736555i) q^{94} +(-2.54182 + 6.48194i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(1.75674 - 13.9060i) q^{97} +(-13.1716 + 8.35896i) q^{98} +(2.97626 - 2.16238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * 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
$5$	2.19782	+	0.411792i	0.982896	+	0.184159i
$5$	2.19782	+	0.411792i	0.982896	+	0.184159i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	−2.79431	+	3.84603i	−1.05615	+	1.45366i	−0.172794	+	0.984958i	$0.555279\pi$
$7$	−2.79431	+	3.84603i	−1.05615	+	1.45366i	−0.883354	+	0.468706i	$0.844721\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	−0.147722	−	2.23118i	−0.0467137	−	0.705562i
$11$	3.56328	−	0.914895i	1.07437	−	0.275851i	0.330247	−	0.943894i	$-0.392868\pi$
$11$	3.56328	−	0.914895i	1.07437	−	0.275851i	0.744123	+	0.668043i	$0.232868\pi$
$12$	−0.770513	+	0.637424i	−0.222428	+	0.184008i
$13$	−1.15151	−	2.90838i	−0.319372	−	0.806640i	−0.997431	−	0.0716333i	$-0.977179\pi$
$13$	−1.15151	−	2.90838i	−0.319372	−	0.806640i	0.678060	−	0.735007i	$-0.262821\pi$
$14$	4.42012	+	1.75005i	1.18133	+	0.467720i
$15$	2.23606	−	0.00733290i	0.577347	−	0.00189335i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−1.83804	+	3.34339i	−0.445791	+	0.810890i	−0.999766	−	0.0216430i	$-0.993110\pi$
$17$	−1.83804	+	3.34339i	−0.445791	+	0.810890i	0.553975	+	0.832533i	$0.313110\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	−0.583454	+	3.05857i	−0.133854	+	0.701685i	0.850569	+	0.525864i	$0.176258\pi$
$19$	−0.583454	+	3.05857i	−0.133854	+	0.701685i	−0.984422	+	0.175821i	$0.943742\pi$
$20$	−2.12435	+	0.697953i	−0.475019	+	0.156067i
$21$	−2.02414	+	4.30151i	−0.441703	+	0.938666i
$22$	−1.77230	−	3.22381i	−0.377857	−	0.687319i
$23$	4.96567	+	0.312413i	1.03541	+	0.0651427i	0.571389	−	0.820680i	$-0.306405\pi$
$23$	4.96567	+	0.312413i	1.03541	+	0.0651427i	0.464025	+	0.885822i	$0.346405\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	4.66085	+	1.81009i	0.932171	+	0.362018i
$26$	−2.53064	+	1.83862i	−0.496300	+	0.360583i
$27$	0.844328	−	0.535827i	0.162491	−	0.103120i
$28$	0.595829	−	4.71647i	0.112601	−	0.891329i
$29$	4.66992	+	0.589948i	0.867182	+	0.109551i	0.546321	−	0.837576i	$-0.316028\pi$
$29$	4.66992	+	0.589948i	0.867182	+	0.109551i	0.320861	+	0.947126i	$0.396028\pi$
$30$	−0.563187	−	2.16398i	−0.102823	−	0.395087i
$31$	5.58547	+	3.07064i	1.00318	+	0.551503i	0.896619	−	0.442804i	$-0.146016\pi$
$31$	5.58547	+	3.07064i	1.00318	+	0.551503i	0.106561	+	0.994306i	$0.466016\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	3.32873	−	1.56638i	0.579458	−	0.272672i
$34$	3.69545	+	0.948830i	0.633764	+	0.162723i
$35$	−7.72516	+	7.30223i	−1.30579	+	1.23430i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	4.11959	+	2.61437i	0.677256	+	0.429800i	0.829473	−	0.558547i	$-0.188641\pi$
$37$	4.11959	+	2.61437i	0.677256	+	0.429800i	−0.152217	+	0.988347i	$0.548641\pi$
$38$	3.10758	−	0.195512i	0.504116	−	0.0317163i
$39$	−1.67609	−	2.64110i	−0.268389	−	0.422914i
$40$	1.20433	+	1.88404i	0.190421	+	0.297892i
$41$	0.418715	+	6.65529i	0.0653923	+	1.03938i	0.884740	+	0.466085i	$0.154336\pi$
$41$	0.418715	+	6.65529i	0.0653923	+	1.03938i	−0.819348	+	0.573297i	$0.805664\pi$
$42$	4.66975	+	0.890803i	0.720558	+	0.137454i
$43$	−1.46737	+	0.476776i	−0.223771	+	0.0727077i	−0.418757	−	0.908098i	$-0.637534\pi$
$43$	−1.46737	+	0.476776i	−0.223771	+	0.0727077i	0.194986	+	0.980806i	$0.437534\pi$
$44$	−2.68177	+	2.51835i	−0.404293	+	0.379656i
$45$	2.19508	−	0.426198i	0.327222	−	0.0635339i
$46$	−0.932313	−	4.88736i	−0.137462	−	0.720601i
$47$	−1.04661	+	1.11452i	−0.152663	+	0.162570i	−0.800754	−	0.598993i	$-0.795568\pi$
$47$	−1.04661	+	1.11452i	−0.152663	+	0.162570i	0.648091	+	0.761563i	$0.275568\pi$
$48$	0.368125	−	0.929776i	0.0531342	−	0.134202i
$49$	−4.82070	−	14.8366i	−0.688671	−	2.11951i
$50$	0.594118	−	4.96458i	0.0840209	−	0.702097i
$51$	−1.17900	+	3.62858i	−0.165093	+	0.508103i
$52$	2.41020	+	1.99389i	0.334235	+	0.276503i
$53$	−11.9158	−	5.60715i	−1.63676	−	0.770202i	−0.636762	−	0.771060i	$-0.719727\pi$
$53$	−11.9158	−	5.60715i	−1.63676	−	0.770202i	−1.00000		0.000858566i	$0.999727\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	8.20821	−	0.543447i	1.10679	−	0.0732784i
$56$	−4.71647	+	0.595829i	−0.630265	+	0.0796210i
$57$			3.11373i			0.412423i
$58$	−0.589948	−	4.66992i	−0.0774639	−	0.613190i
$59$	−2.87398	−	3.47404i	−0.374160	−	0.452282i	0.549501	−	0.835493i	$-0.314818\pi$
$59$	−2.87398	−	3.47404i	−0.374160	−	0.452282i	−0.923661	+	0.383212i	$0.874818\pi$
$60$	−1.95594	+	1.08365i	−0.252511	+	0.139899i
$61$	0.802804	−	12.7602i	0.102788	−	1.63378i	−0.521974	−	0.852961i	$-0.674804\pi$
$61$	0.802804	−	12.7602i	0.102788	−	1.63378i	0.624763	−	0.780815i	$-0.285196\pi$
$62$	1.58512	−	6.17362i	0.201310	−	0.784051i
$63$	−1.18226	+	4.60460i	−0.148951	+	0.580125i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−1.33317	−	6.86630i	−0.165359	−	0.851659i
$66$	−2.34499	−	2.83461i	−0.288649	−	0.348916i
$67$	1.00929	+	7.98934i	0.123304	+	0.976053i	0.925435	+	0.378905i	$0.123699\pi$
$67$	1.00929	+	7.98934i	0.123304	+	0.976053i	−0.802131	+	0.597148i	$0.796301\pi$
$68$		−	3.81532i		−	0.462675i
$69$	4.93625	−	0.623594i	0.594255	−	0.0750719i
$70$	8.99398	+	5.66647i	1.07499	+	0.677272i
$71$	−6.88173	−	6.46238i	−0.816712	−	0.766943i	0.158702	−	0.987327i	$-0.449269\pi$
$71$	−6.88173	−	6.46238i	−0.816712	−	0.766943i	−0.975413	+	0.220383i	$0.929269\pi$
$72$	0.904827	+	0.425779i	0.106635	+	0.0501786i
$73$	−3.57153	−	2.95462i	−0.418016	−	0.345813i	0.404517	−	0.914530i	$-0.367440\pi$
$73$	−3.57153	−	2.95462i	−0.418016	−	0.345813i	−0.822533	+	0.568718i	$0.807440\pi$
$74$	1.50773	−	4.64033i	0.175271	−	0.539428i
$75$	4.91748	+	0.904674i	0.567821	+	0.104463i
$76$	−0.962194	−	2.96133i	−0.110371	−	0.339688i
$77$	−6.43818	+	16.2610i	−0.733699	+	1.85311i
$78$	−2.14129	+	2.28025i	−0.242454	+	0.258187i
$79$	1.55864	+	8.17069i	0.175361	+	0.919275i	0.955794	+	0.294036i	$0.0949985\pi$
$79$	1.55864	+	8.17069i	0.175361	+	0.919275i	−0.780433	+	0.625239i	$0.785001\pi$
$80$	1.52534	−	1.63503i	0.170538	−	0.182802i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	6.34207	−	2.06066i	0.700364	−	0.227562i
$83$	9.17958	+	1.75110i	1.00759	+	0.192208i	0.664654	−	0.747151i	$-0.268579\pi$
$83$	9.17958	+	1.75110i	1.00759	+	0.192208i	0.342935	+	0.939359i	$0.388579\pi$
$84$	−0.298503	−	4.74458i	−0.0325694	−	0.517676i
$85$	−5.41647	+	6.59128i	−0.587499	+	0.714925i
$86$	0.826717	+	1.30270i	0.0891471	+	0.140473i
$87$	4.69774	−	0.295557i	0.503651	−	0.0316870i
$88$	3.10616	+	1.97123i	0.331118	+	0.210134i
$89$	7.43942	−	8.99271i	0.788577	−	0.953225i	−0.211130	−	0.977458i	$-0.567714\pi$
$89$	7.43942	−	8.99271i	0.788577	−	0.953225i	0.999706	+	0.0242326i	$0.00771423\pi$
$90$	−0.958701	−	2.02012i	−0.101056	−	0.212940i
$91$	14.4034	+	3.69817i	1.50989	+	0.387673i
$92$	−4.50195	+	2.11846i	−0.469361	+	0.220865i
$93$	6.06191	+	1.96963i	0.628591	+	0.204242i
$94$	1.33979	+	0.736555i	0.138189	+	0.0759699i
$95$	−2.54182	+	6.48194i	−0.260786	+	0.665033i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	1.75674	−	13.9060i	0.178370	−	1.41194i	−0.607877	−	0.794031i	$-0.707979\pi$
$97$	1.75674	−	13.9060i	0.178370	−	1.41194i	0.786247	−	0.617913i	$-0.212021\pi$
$98$	−13.1716	+	8.35896i	−1.33053	+	0.844382i
$99$	2.97626	−	2.16238i	0.299125	−	0.217327i
$100$	−4.95636	+	0.659188i	−0.495636	+	0.0659188i
$101$	−13.7387	−	9.98173i	−1.36705	−	0.993219i	−0.997961	−	0.0638244i	$-0.979670\pi$
$101$	−13.7387	−	9.98173i	−1.36705	−	0.993219i	−0.369088	−	0.929395i	$-0.620330\pi$
$102$	3.80779	+	0.239566i	0.377027	+	0.0237205i
$103$	−7.84022	−	14.2613i	−0.772519	−	1.40521i	−0.909959	−	0.414698i	$-0.863887\pi$
$103$	−7.84022	−	14.2613i	−0.772519	−	1.40521i	0.137440	−	0.990510i	$-0.456113\pi$
$104$	1.33186	−	2.83034i	0.130599	−	0.277538i
$105$	−6.22002	+	8.62043i	−0.607012	+	0.841268i
$106$	−2.46765	+	12.9359i	−0.239680	+	1.25644i
$107$	7.85092	+	10.8059i	0.758977	+	1.04464i	0.997298	+	0.0734561i	$0.0234029\pi$
$107$	7.85092	+	10.8059i	0.758977	+	1.04464i	−0.238321	+	0.971186i	$0.576597\pi$
$108$	−0.481754	+	0.876307i	−0.0463568	+	0.0843226i
$109$	2.56034	−	4.03445i	0.245236	−	0.386430i	−0.699305	−	0.714823i	$-0.746507\pi$
$109$	2.56034	−	4.03445i	0.245236	−	0.386430i	0.944541	+	0.328393i	$0.106507\pi$
$110$	−2.56767	−	7.81518i	−0.244818	−	0.745149i
$111$	4.53650	+	1.79613i	0.430586	+	0.170481i
$112$	1.75005	+	4.42012i	0.165364	+	0.417662i
$113$	−10.6611	+	8.81960i	−1.00291	+	0.829678i	−0.985415	−	0.170169i	$-0.945569\pi$
$113$	−10.6611	+	8.81960i	−1.00291	+	0.829678i	−0.0174934	+	0.999847i	$0.505569\pi$
$114$	3.01590	−	0.774352i	0.282465	−	0.0725247i
$115$	10.7850	+	2.73145i	1.00571	+	0.254709i
$116$	−4.37649	+	1.73277i	−0.406347	+	0.160884i
$117$	−2.14129	−	2.28025i	−0.197963	−	0.210809i
$118$	−2.65017	+	3.64764i	−0.243968	+	0.335793i
$119$	−7.72272	−	16.4116i	−0.707940	−	1.50445i
$120$	1.53603	+	1.62499i	0.140220	+	0.148341i
$121$	2.22057	−	1.22077i	0.201870	−	0.110979i
$122$	−12.5590	+	2.39575i	−1.13704	+	0.216901i
$123$	1.65837	+	6.45894i	0.149531	+	0.582383i
$124$	−6.37387			−0.572391
$125$	9.49835	+	5.89757i	0.849559	+	0.527494i
$126$	4.75396			0.423516
$127$	−2.41771	−	9.41635i	−0.214537	−	0.835566i	−0.981117	−	0.193417i	$-0.938043\pi$
$127$	−2.41771	−	9.41635i	−0.214537	−	0.835566i	0.766580	−	0.642149i	$-0.221957\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−1.35204	+	0.743288i	−0.119040	+	0.0654429i
$130$	−6.31903	+	2.99886i	−0.554216	+	0.263018i
$131$	0.974724	+	2.07139i	0.0851620	+	0.180978i	0.942872	−	0.333156i	$-0.108113\pi$
$131$	0.974724	+	2.07139i	0.0851620	+	0.180978i	−0.857710	+	0.514134i	$0.828113\pi$
$132$	−2.16238	+	2.97626i	−0.188211	+	0.259050i
$133$	−10.1330	−	10.7906i	−0.878644	−	0.935661i
$134$	7.48734	−	2.96445i	0.646808	−	0.256089i
$135$	2.07633	−	0.829965i	0.178702	−	0.0714320i
$136$	−3.69545	+	0.948830i	−0.316882	+	0.0813615i
$137$	−6.24542	+	5.16666i	−0.533582	+	0.441418i	−0.864785	−	0.502142i	$-0.832546\pi$
$137$	−6.24542	+	5.16666i	−0.533582	+	0.441418i	0.331203	+	0.943560i	$0.392546\pi$
$138$	−1.83160	−	4.62609i	−0.155916	−	0.393799i
$139$	−0.503277	−	0.199262i	−0.0426874	−	0.0169011i	0.346684	−	0.937982i	$-0.387308\pi$
$139$	−0.503277	−	0.199262i	−0.0426874	−	0.0169011i	−0.389371	+	0.921081i	$0.627308\pi$
$140$	3.25173	−	10.1206i	0.274822	−	0.855348i
$141$	−0.819228	+	1.29090i	−0.0689914	+	0.108713i
$142$	−4.54793	+	8.27266i	−0.381654	+	0.694226i
$143$	−6.76402	−	9.30988i	−0.565636	−	0.778531i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	10.0207	+	3.21963i	0.832175	+	0.267376i
$146$	−1.97360	+	4.19411i	−0.163336	+	0.347107i
$147$	−7.51541	−	13.6705i	−0.619861	−	1.12752i
$148$	−4.86950	−	0.306363i	−0.400271	−	0.0251829i
$149$	0.734920	+	0.533951i	0.0602070	+	0.0437429i	0.617482	−	0.786585i	$-0.288153\pi$
$149$	0.734920	+	0.533951i	0.0602070	+	0.0437429i	−0.557275	+	0.830328i	$0.688153\pi$
$150$	−0.346675	−	4.98797i	−0.0283059	−	0.407266i
$151$	0.180984	−	0.131492i	0.0147283	−	0.0107007i	−0.580397	−	0.814334i	$-0.697103\pi$
$151$	0.180984	−	0.131492i	0.0147283	−	0.0107007i	0.595125	+	0.803633i	$0.297103\pi$
$152$	−2.62901	+	1.66842i	−0.213240	+	0.135327i
$153$	−0.478186	+	3.78523i	−0.0386590	+	0.306018i
$154$	17.3512	+	2.19197i	1.39820	+	0.176634i
$155$	11.0114	+	9.04877i	0.884457	+	0.726814i
$156$	2.74113	+	1.50695i	0.219466	+	0.120652i
$157$	−9.55524	−	3.10468i	−0.762591	−	0.247781i	−0.0982006	−	0.995167i	$-0.531309\pi$
$157$	−9.55524	−	3.10468i	−0.762591	−	0.247781i	−0.664390	+	0.747386i	$0.731309\pi$
$158$	7.52638	−	3.54164i	0.598767	−	0.281758i
$159$	−12.7554	−	3.27504i	−1.01157	−	0.259727i
$160$	−1.96300	−	1.07080i	−0.155189	−	0.0846544i
$161$	−15.0771	+	18.2251i	−1.18825	+	1.43634i
$162$	−0.844328	−	0.535827i	−0.0663367	−	0.0420985i
$163$	−10.1065	+	0.635845i	−0.791599	+	0.0498032i	−0.453441	−	0.891286i	$-0.649804\pi$
$163$	−10.1065	+	0.635845i	−0.791599	+	0.0498032i	−0.338158	+	0.941089i	$0.609804\pi$
$164$	−3.57313	−	5.63035i	−0.279015	−	0.439657i
$165$	7.96099	−	2.07189i	0.619762	−	0.161296i
$166$	−0.586784	−	9.32667i	−0.0455433	−	0.723890i
$167$	−16.4568	−	3.13931i	−1.27347	−	0.242927i	−0.494050	−	0.869433i	$-0.664484\pi$
$167$	−16.4568	−	3.13931i	−1.27347	−	0.242927i	−0.779416	+	0.626506i	$0.784484\pi$
$168$	−4.52128	+	1.46905i	−0.348824	+	0.113340i
$169$	2.34388	−	2.20105i	0.180298	−	0.169311i
$170$	7.73123	+	3.60712i	0.592958	+	0.276653i
$171$	0.583454	+	3.05857i	0.0446178	+	0.233895i
$172$	1.05617	−	1.12471i	0.0805325	−	0.0857584i
$173$	−8.53949	+	21.5683i	−0.649245	+	1.63981i	0.113832	+	0.993500i	$0.463687\pi$
$173$	−8.53949	+	21.5683i	−0.649245	+	1.63981i	−0.763078	+	0.646307i	$0.776313\pi$
$174$	−1.45455	−	4.47665i	−0.110269	−	0.339374i
$175$	−19.9855	+	12.8678i	−1.51076	+	0.972718i
$176$	1.13683	−	3.49880i	0.0856918	−	0.263732i
$177$	−3.47404	−	2.87398i	−0.261125	−	0.216021i
$178$	−10.5603	−	4.96930i	−0.791528	−	0.372465i
$179$	9.28423	+	8.71847i	0.693936	+	0.651649i	0.949000	−	0.315275i	$-0.102097\pi$
$179$	9.28423	+	8.71847i	0.693936	+	0.651649i	−0.255064	+	0.966924i	$0.582097\pi$
$180$	−1.71824	+	1.43097i	−0.128070	+	0.106658i
$181$	12.2902	−	1.55262i	0.913526	−	0.115405i	0.345503	−	0.938418i	$-0.387708\pi$
$181$	12.2902	−	1.55262i	0.913526	−	0.115405i	0.568023	+	0.823013i	$0.307708\pi$
$182$		−	14.8706i		−	1.10228i
$183$	−1.60244	−	12.6846i	−0.118456	−	0.937674i
$184$	3.17149	+	3.83368i	0.233806	+	0.282622i
$185$	7.97755	+	7.44234i	0.586521	+	0.547172i
$186$	0.400219	−	6.36129i	0.0293455	−	0.466433i
$187$	−3.49061	+	13.5950i	−0.255259	+	0.994168i
$188$	0.380223	−	1.48087i	0.0277306	−	0.108004i
$189$	−0.298503	+	4.74458i	−0.0217129	+	0.345117i
$190$	6.91042	+	0.849975i	0.501335	+	0.0616637i
$191$	−1.70163	−	2.05692i	−0.123126	−	0.148834i	0.705348	−	0.708861i	$-0.250791\pi$
$191$	−1.70163	−	2.05692i	−0.123126	−	0.148834i	−0.828474	+	0.560027i	$0.810791\pi$
$192$	0.125333	+	0.992115i	0.00904515	+	0.0715997i
$193$		−	5.31539i		−	0.382610i	−0.981531	−	0.191305i	$-0.938728\pi$
$193$		−	5.31539i		−	0.382610i	0.981531	−	0.191305i	$-0.0612720\pi$
$194$	−13.9060	+	1.75674i	−0.998395	+	0.126127i
$195$	−2.59617	−	6.49486i	−0.185915	−	0.465107i
$196$	11.3720	+	10.6790i	0.812285	+	0.762786i
$197$	−13.0397	−	6.13604i	−0.929043	−	0.437175i	−0.0991346	−	0.995074i	$-0.531607\pi$
$197$	−13.0397	−	6.13604i	−0.929043	−	0.437175i	−0.829909	+	0.557900i	$0.811607\pi$
$198$	−2.83461	−	2.34499i	−0.201447	−	0.166651i
$199$	5.42264	−	16.6892i	0.384401	−	1.18306i	−0.552513	−	0.833504i	$-0.686331\pi$
$199$	5.42264	−	16.6892i	0.384401	−	1.18306i	0.936914	−	0.349560i	$-0.113669\pi$
$200$	1.87107	+	4.63671i	0.132305	+	0.327865i
$201$	2.48846	+	7.65871i	0.175523	+	0.540203i
$202$	−6.25147	+	15.7894i	−0.439852	+	1.11094i
$203$	−15.3181	+	16.3122i	−1.07512	+	1.14489i
$204$	−0.714919	−	3.74774i	−0.0500543	−	0.262394i
$205$	−1.82033	+	14.7996i	−0.127138	+	1.03365i
$206$	−11.8635	+	11.1405i	−0.826567	+	0.776198i
$207$	4.73197	−	1.53751i	0.328894	−	0.106864i
$208$	−3.07264	−	0.586137i	−0.213049	−	0.0406413i
$209$	0.719263	+	11.4324i	0.0497524	+	0.790793i
$210$	9.89646	+	3.88079i	0.682921	+	0.267800i
$211$	−2.16863	−	3.41722i	−0.149295	−	0.235251i	0.761447	−	0.648227i	$-0.224489\pi$
$211$	−2.16863	−	3.41722i	−0.149295	−	0.235251i	−0.910742	+	0.412976i	$0.864489\pi$
$212$	13.1432	−	0.826898i	0.902676	−	0.0567916i
$213$	−7.97077	−	5.05840i	−0.546148	−	0.346596i
$214$	8.51393	−	10.2916i	0.582001	−	0.703518i
$215$	−3.42134	+	0.443620i	−0.233334	+	0.0302546i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	−27.4173	+	12.9016i	−1.86121	+	0.875817i
$218$	−4.54443	−	1.47657i	−0.307788	−	0.100006i
$219$	−4.06191	−	2.23305i	−0.274478	−	0.150896i
$220$	−6.93110	+	4.43056i	−0.467295	+	0.298708i
$221$	11.8404	+	1.49579i	0.796470	+	0.100618i
$222$	0.611517	−	4.84066i	0.0410424	−	0.324884i
$223$	23.1688	−	14.7034i	1.55150	−	0.984612i	0.564220	−	0.825625i	$-0.309177\pi$
$223$	23.1688	−	14.7034i	1.55150	−	0.984612i	0.987281	−	0.158987i	$-0.0508229\pi$
$224$	3.84603	−	2.79431i	0.256974	−	0.186702i
$225$	4.99989	−	0.0327936i	0.333326	−	0.00218624i
$226$	11.1938	+	8.13278i	0.744601	+	0.540984i
$227$	29.3897	+	1.84904i	1.95066	+	0.122725i	0.988645	−	0.150271i	$-0.0480145\pi$
$227$	29.3897	+	1.84904i	1.95066	+	0.122725i	0.962015	+	0.272996i	$0.0880145\pi$
$228$	−1.50005	−	2.72858i	−0.0993431	−	0.180705i
$229$	−9.46268	+	20.1092i	−0.625312	+	1.32885i	0.301549	+	0.953451i	$0.402496\pi$
$229$	−9.46268	+	20.1092i	−0.625312	+	1.32885i	−0.926861	+	0.375404i	$0.877504\pi$
$230$	−0.0364847	−	11.1255i	−0.00240573	−	0.733591i
$231$	−3.27714	+	17.1794i	−0.215620	+	1.13032i
$232$	2.76672	+	3.80807i	0.181644	+	0.250012i
$233$	12.3452	−	22.4559i	0.808763	−	1.47114i	−0.0719099	−	0.997411i	$-0.522909\pi$
$233$	12.3452	−	22.4559i	0.808763	−	1.47114i	0.880673	−	0.473724i	$-0.157091\pi$
$234$	−1.67609	+	2.64110i	−0.109569	+	0.172654i
$235$	−2.75921	+	2.01854i	−0.179991	+	0.131675i
$236$	4.19212	+	1.65978i	0.272884	+	0.108042i
$237$	3.06207	+	7.73391i	0.198903	+	0.502371i
$238$	−13.9755	+	11.5615i	−0.905894	+	0.749421i
$239$	−5.67212	+	1.45635i	−0.366899	+	0.0942037i	−0.427638	−	0.903950i	$-0.640654\pi$
$239$	−5.67212	+	1.45635i	−0.366899	+	0.0942037i	0.0607390	+	0.998154i	$0.480654\pi$
$240$	1.19195	−	1.89189i	0.0769399	−	0.122121i
$241$	−8.58886	+	3.40057i	−0.553257	+	0.219050i	−0.628083	−	0.778147i	$-0.716160\pi$
$241$	−8.58886	+	3.40057i	−0.553257	+	0.219050i	0.0748253	+	0.997197i	$0.476160\pi$
$242$	−1.73465	−	1.84721i	−0.111508	−	0.118743i
$243$	0.587785	−	0.809017i	0.0377064	−	0.0518985i
$244$	5.44377	+	11.5686i	0.348502	+	0.740604i
$245$	−4.48546	−	34.5933i	−0.286565	−	2.21009i
$246$	5.84360	−	3.21255i	0.372575	−	0.204825i
$247$	9.56735	−	1.82507i	0.608756	−	0.116126i
$248$	1.58512	+	6.17362i	0.100655	+	0.392026i
$249$	9.34511			0.592222
$250$	3.35014	−	10.6666i	0.211881	−	0.674616i
$251$	17.2935			1.09156			0.545778	−	0.837930i	$-0.316234\pi$
$251$	17.2935			1.09156			0.545778	+	0.837930i	$0.316234\pi$
$252$	−1.18226	−	4.60460i	−0.0744755	−	0.290063i
$253$	17.9799	−	3.42985i	1.13039	−	0.215633i
$254$	−8.51926	+	4.68350i	−0.534546	+	0.293869i
$255$	−4.08545	+	7.48948i	−0.255841	+	0.469009i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	5.99259	−	8.24809i	0.373807	−	0.514502i	−0.580123	−	0.814529i	$-0.696996\pi$
$257$	5.99259	−	8.24809i	0.373807	−	0.514502i	0.953931	+	0.300027i	$0.0969957\pi$
$258$	1.05617	+	1.12471i	0.0657545	+	0.0700215i
$259$	−21.5663	+	8.53872i	−1.34007	+	0.530570i
$260$	4.47613	+	5.37472i	0.277598	+	0.333326i
$261$	4.55915	−	1.17059i	0.282204	−	0.0724578i
$262$	1.76391	−	1.45924i	0.108975	−	0.0901519i
$263$	3.84290	+	9.70606i	0.236963	+	0.598501i	0.998785	−	0.0492860i	$-0.0156946\pi$
$263$	3.84290	+	9.70606i	0.236963	+	0.598501i	−0.761821	+	0.647787i	$0.775695\pi$
$264$	3.42052	+	1.35428i	0.210518	+	0.0833501i
$265$	−23.8799	−	17.2304i	−1.46693	−	1.05845i
$266$	−7.93159	+	12.4982i	−0.486317	+	0.766312i
$267$	5.62258	−	10.2274i	0.344096	−	0.625909i
$268$	−4.73334	−	6.51488i	−0.289135	−	0.397960i
$269$	2.69053	−	14.1042i	0.164044	−	0.859950i	−0.801159	−	0.598451i	$-0.795783\pi$
$269$	2.69053	−	14.1042i	0.164044	−	0.859950i	0.965204	−	0.261499i	$-0.0842169\pi$
$270$	−1.32025	−	1.80470i	−0.0803480	−	0.109830i
$271$	−1.17783	+	2.50302i	−0.0715482	+	0.152048i	−0.937402	−	0.348250i	$-0.886776\pi$
$271$	−1.17783	+	2.50302i	−0.0715482	+	0.152048i	0.865854	+	0.500298i	$0.166776\pi$
$272$	1.83804	+	3.34339i	0.111448	+	0.202723i
$273$	14.8413	+	0.933732i	0.898233	+	0.0565121i
$274$	6.55752	+	4.76431i	0.396154	+	0.287823i
$275$	18.2640	+	2.18568i	1.10136	+	0.131801i
$276$	−4.02525	+	2.92452i	−0.242292	+	0.176035i
$277$	−23.5795	+	14.9640i	−1.41676	+	0.899101i	−0.999951	−	0.00989484i	$-0.996850\pi$
$277$	−23.5795	+	14.9640i	−1.41676	+	0.899101i	−0.416805	+	0.908996i	$0.636850\pi$
$278$	−0.0678414	+	0.537020i	−0.00406886	+	0.0322083i
$279$	6.32361	+	0.798858i	0.378585	+	0.0478264i
$280$	−10.6113	−	0.632679i	−0.634148	−	0.0378098i
$281$	−21.6138	−	11.8823i	−1.28937	−	0.708837i	−0.318381	−	0.947963i	$-0.603139\pi$
$281$	−21.6138	−	11.8823i	−1.28937	−	0.708837i	−0.970989	+	0.239126i	$0.923139\pi$
$282$	1.45407	+	0.472457i	0.0865889	+	0.0281344i
$283$	−7.27043	+	3.42121i	−0.432182	+	0.203370i	−0.629550	−	0.776960i	$-0.716761\pi$
$283$	−7.27043	+	3.42121i	−0.432182	+	0.203370i	0.197368	+	0.980330i	$0.436761\pi$
$284$	9.14378	+	2.34772i	0.542584	+	0.139312i
$285$	−1.28221	+	6.84342i	−0.0759514	+	0.405369i
$286$	−7.33525	+	8.86679i	−0.433742	+	0.524304i
$287$	−26.7665	−	16.9865i	−1.57997	−	1.00268i
$288$	−0.998027	+	0.0627905i	−0.0588093	+	0.00369997i
$289$	1.30922	+	2.06301i	0.0770131	+	0.121353i
$290$	0.626434	−	10.5066i	0.0367855	−	0.616968i
$291$	−0.880107	−	13.9889i	−0.0515928	−	0.820044i
$292$	4.55315	+	0.868560i	0.266453	+	0.0508287i
$293$	13.0618	−	4.24405i	0.763081	−	0.247940i	0.0984805	−	0.995139i	$-0.468602\pi$
$293$	13.0618	−	4.24405i	0.763081	−	0.247940i	0.664600	+	0.747199i	$0.268602\pi$
$294$	−11.3720	+	10.6790i	−0.663228	+	0.622813i
$295$	−4.88591	−	8.81881i	−0.284469	−	0.513451i
$296$	0.914258	+	4.79271i	0.0531402	+	0.278571i
$297$	2.51835	−	2.68177i	0.146130	−	0.155612i
$298$	0.334408	−	0.844619i	0.0193718	−	0.0489275i
$299$	−4.80940	−	14.8018i	−0.278135	−	0.856011i
$300$	−4.74505	+	1.57624i	−0.273955	+	0.0910043i
$301$	2.26657	−	6.97580i	0.130643	−	0.402078i
$302$	−0.172370	−	0.142597i	−0.00991879	−	0.00820554i
$303$	−15.3657	−	7.23055i	−0.882737	−	0.415384i
$304$	2.26981	+	2.13149i	0.130182	+	0.122249i
$305$	7.01897	−	27.7141i	0.401905	−	1.58690i
$306$	3.78523	−	0.478186i	0.216387	−	0.0273361i
$307$		−	0.442456i		−	0.0252523i	−0.999920	−	0.0126262i	$-0.995981\pi$
$307$		−	0.442456i		−	0.0252523i	0.999920	−	0.0126262i	$-0.00401914\pi$
$308$	−2.19197	−	17.3512i	−0.124899	−	0.988678i
$309$	−10.3736	−	12.5396i	−0.590136	−	0.713352i
$310$	6.02606	−	12.9158i	0.342257	−	0.733568i
$311$	0.0388648	−	0.617738i	0.00220382	−	0.0350287i	−0.996771	−	0.0802952i	$-0.974414\pi$
$311$	0.0388648	−	0.617738i	0.00220382	−	0.0350287i	0.998975	+	0.0452665i	$0.0144137\pi$
$312$	0.777913	−	3.02977i	0.0440407	−	0.171527i
$313$	8.14689	−	31.7301i	0.460490	−	1.79349i	−0.135819	−	0.990734i	$-0.543367\pi$
$313$	8.14689	−	31.7301i	0.460490	−	1.79349i	0.596309	−	0.802755i	$-0.296633\pi$
$314$	−0.630854	+	10.0271i	−0.0356012	+	0.565864i
$315$	−4.49454	+	9.63326i	−0.253239	+	0.542773i
$316$	−5.30211	−	6.40915i	−0.298267	−	0.360543i
$317$	−1.75462	−	13.8892i	−0.0985491	−	0.780097i	−0.961499	−	0.274808i	$-0.911386\pi$
$317$	−1.75462	−	13.8892i	−0.0985491	−	0.780097i	0.862950	−	0.505289i	$-0.168614\pi$
$318$			13.1692i			0.738489i
$319$	17.1800	−	2.17033i	0.961893	−	0.121515i
$320$	−0.548982	+	2.16763i	−0.0306890	+	0.121174i
$321$	9.73668	+	9.14335i	0.543448	+	0.510332i
$322$	21.4021	+	10.0711i	1.19269	+	0.561238i
$323$	−9.15358	−	7.57250i	−0.509319	−	0.421345i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	−0.102580	−	15.6399i	−0.00569010	−	0.867545i
$326$	3.12924	+	9.63082i	0.173313	+	0.533402i
$327$	1.75901	−	4.44275i	0.0972734	−	0.245684i
$328$	−4.56487	+	4.86109i	−0.252053	+	0.268409i
$329$	−1.36195	−	7.13960i	−0.0750868	−	0.393619i
$330$	−3.98661	−	7.19562i	−0.219456	−	0.396106i
$331$	−13.5957	+	12.7672i	−0.747288	+	0.701750i	−0.961429	−	0.275053i	$-0.911305\pi$
$331$	−13.5957	+	12.7672i	−0.747288	+	0.701750i	0.214142	+	0.976803i	$0.431305\pi$
$332$	−8.88772	+	2.88780i	−0.487777	+	0.158488i
$333$	4.79271	+	0.914258i	0.262639	+	0.0501010i
$334$	1.05197	+	16.7205i	0.0575610	+	0.914906i
$335$	−1.07171	+	17.9748i	−0.0585538	+	0.982067i
$336$	2.54730	+	4.01390i	0.138966	+	0.218976i
$337$	−22.6263	+	1.42352i	−1.23253	+	0.0775443i	−0.665656	−	0.746259i	$-0.731848\pi$
$337$	−22.6263	+	1.42352i	−1.23253	+	0.0775443i	−0.566876	+	0.823803i	$0.691848\pi$
$338$	−2.71479	−	1.72286i	−0.147665	−	0.0937113i
$339$	−8.81960	+	10.6611i	−0.479015	+	0.579029i
$340$	1.57112	−	8.38539i	0.0852058	−	0.454762i
$341$	22.7119	+	5.83143i	1.22992	+	0.315789i
$342$	2.81738	−	1.32576i	0.152347	−	0.0716889i
$343$	38.8835	+	12.6340i	2.09951	+	0.682173i
$344$	−1.35204	−	0.743288i	−0.0728969	−	0.0400754i
$345$	11.1058	+	0.662161i	0.597916	+	0.0356495i
$346$	23.0144	+	2.90739i	1.23726	+	0.156302i
$347$	−0.726151	+	5.74807i	−0.0389818	+	0.308573i	0.960554	+	0.278095i	$0.0897029\pi$
$347$	−0.726151	+	5.74807i	−0.0389818	+	0.308573i	−0.999535	+	0.0304780i	$0.990297\pi$
$348$	−3.97428	+	2.52215i	−0.213044	+	0.135202i
$349$	16.6779	−	12.1172i	0.892746	−	0.648618i	−0.0438467	−	0.999038i	$-0.513961\pi$
$349$	16.6779	−	12.1172i	0.892746	−	0.648618i	0.936592	+	0.350421i	$0.113961\pi$
$350$	17.4338	+	16.1575i	0.931875	+	0.863657i
$351$	−2.53064	−	1.83862i	−0.135076	−	0.0981382i
$352$	−3.67160	−	0.230998i	−0.195697	−	0.0123122i
$353$	17.0433	+	31.0017i	0.907125	+	1.65005i	0.748933	+	0.662645i	$0.230566\pi$
$353$	17.0433	+	31.0017i	0.907125	+	1.65005i	0.158192	+	0.987408i	$0.449434\pi$
$354$	−1.91973	+	4.07963i	−0.102032	+	0.216830i
$355$	−12.4637	−	17.0370i	−0.661503	−	0.904231i
$356$	−2.18694	+	11.4643i	−0.115908	+	0.607609i
$357$	−10.6612	−	14.6738i	−0.564248	−	0.776621i
$358$	6.13567	−	11.1607i	0.324280	−	0.589864i
$359$	−2.36107	+	3.72045i	−0.124613	+	0.196358i	−0.900907	−	0.434013i	$-0.857097\pi$
$359$	−2.36107	+	3.72045i	−0.124613	+	0.196358i	0.776294	+	0.630371i	$0.217097\pi$
$360$	1.81332	+	1.30839i	0.0955702	+	0.0689581i
$361$	8.65131	+	3.42529i	0.455332	+	0.180279i
$362$	−4.56029	−	11.5180i	−0.239684	−	0.605372i
$363$	1.95249	−	1.61524i	0.102479	−	0.0847781i
$364$	−14.4034	+	3.69817i	−0.754944	+	0.193837i
$365$	−6.63289	−	7.96447i	−0.347182	−	0.416879i
$366$	−11.8876	+	4.70663i	−0.621374	+	0.246020i
$367$	−8.69048	−	9.25442i	−0.453639	−	0.483077i	0.460970	−	0.887416i	$-0.347502\pi$
$367$	−8.69048	−	9.25442i	−0.453639	−	0.483077i	−0.914609	+	0.404339i	$0.867502\pi$
$368$	2.92452	−	4.02525i	0.152451	−	0.209831i
$369$	2.83929	+	6.03379i	0.147807	+	0.314107i
$370$	5.22459	−	9.57775i	0.271613	−	0.497924i
$371$	54.8617	−	30.1605i	2.84828	−	1.56585i
$372$	−6.26097	+	1.19434i	−0.324616	+	0.0619239i
$373$	5.97948	+	23.2885i	0.309606	+	1.20583i	0.912856	+	0.408282i	$0.133872\pi$
$373$	5.97948	+	23.2885i	0.309606	+	1.20583i	−0.603250	+	0.797552i	$0.706128\pi$
$374$	14.0360			0.725785
$375$	10.4352	+	4.01329i	0.538872	+	0.207245i
$376$	−1.52890			−0.0788472
$377$	−3.66166	−	14.2612i	−0.188585	−	0.734491i
$378$	4.66975	−	0.890803i	0.240186	−	0.0458180i
$379$	24.6459	−	13.5492i	1.26598	−	0.695977i	0.299836	−	0.953991i	$-0.403068\pi$
$379$	24.6459	−	13.5492i	1.26598	−	0.695977i	0.966141	+	0.258014i	$0.0830681\pi$
$380$	−0.895281	−	6.90470i	−0.0459269	−	0.354204i
$381$	−4.13933	−	8.79652i	−0.212064	−	0.450660i
$382$	−1.56912	+	2.15971i	−0.0802833	+	0.110500i
$383$	15.0130	+	15.9872i	0.767127	+	0.816908i	0.987352	−	0.158542i	$-0.0506792\pi$
$383$	15.0130	+	15.9872i	0.767127	+	0.816908i	−0.220225	+	0.975449i	$0.570679\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	−20.8461	+	33.0876i	−1.06242	+	1.68630i
$386$	−5.14840	+	1.32188i	−0.262046	+	0.0672821i
$387$	−1.18881	+	0.983469i	−0.0604306	+	0.0499925i
$388$	5.15984	+	13.0323i	0.261951	+	0.661613i
$389$	−9.43366	−	3.73505i	−0.478306	−	0.189375i	0.116586	−	0.993181i	$-0.462805\pi$
$389$	−9.43366	−	3.73505i	−0.478306	−	0.189375i	−0.594891	+	0.803806i	$0.702805\pi$
$390$	−5.64517	+	4.12981i	−0.285855	+	0.209121i
$391$	−10.1716	+	16.0279i	−0.514401	+	0.810566i
$392$	7.51541	−	13.6705i	0.379586	−	0.690464i
$393$	1.34560	+	1.85206i	0.0678765	+	0.0934240i
$394$	−2.70041	+	14.1560i	−0.136045	+	0.713171i
$395$	0.0609953	+	18.5996i	0.00306901	+	0.935846i
$396$	−1.56638	+	3.32873i	−0.0787137	+	0.167275i
$397$	−9.22636	−	16.7827i	−0.463058	−	0.842299i	0.536941	−	0.843620i	$-0.319580\pi$
$397$	−9.22636	−	16.7827i	−0.463058	−	0.842299i	−0.999999	+	0.00132060i	$0.999580\pi$
$398$	−17.5134	−	1.10185i	−0.877868	−	0.0552308i
$399$	−11.9755	−	8.70070i	−0.599524	−	0.435580i
$400$	4.02572	−	2.96539i	0.201286	−	0.148270i
$401$	4.67652	−	3.39769i	0.233534	−	0.169673i	−0.464864	−	0.885382i	$-0.653897\pi$
$401$	4.67652	−	3.39769i	0.233534	−	0.169673i	0.698398	+	0.715710i	$0.253897\pi$
$402$	6.79924	−	4.31493i	0.339115	−	0.215209i
$403$	2.49886	−	19.7805i	0.124477	−	0.985339i
$404$	16.8480	+	2.12840i	0.838220	+	0.105892i
$405$	1.88404	−	1.20433i	0.0936185	−	0.0598436i
$406$	19.6091	+	10.7802i	0.973185	+	0.535013i
$407$	17.0711	+	5.54675i	0.846184	+	0.274942i
$408$	−3.45220	+	1.62448i	−0.170909	+	0.0804239i
$409$	35.4786	+	9.10935i	1.75430	+	0.450428i	0.982627	−	0.185589i	$-0.0594194\pi$
$409$	35.4786	+	9.10935i	1.75430	+	0.450428i	0.771675	+	0.636018i	$0.219419\pi$
$410$	14.7873	−	1.91736i	0.730293	−	0.0946916i
$411$	−5.16666	+	6.24542i	−0.254853	+	0.308064i
$412$	13.7409	+	8.72022i	0.676964	+	0.429614i
$413$	21.3920	−	1.34587i	1.05263	−	0.0662261i
$414$	−2.66600	−	4.20094i	−0.131027	−	0.206465i
$415$	19.4540	+	7.62868i	0.954960	+	0.374477i
$416$	0.196412	+	3.12187i	0.00962987	+	0.153062i
$417$	−0.531701	−	0.101427i	−0.0260375	−	0.00496692i
$418$	10.8943	−	3.53978i	0.532858	−	0.173136i
$419$	0.646181	−	0.606804i	0.0315680	−	0.0296443i	−0.668603	−	0.743620i	$-0.733107\pi$
$419$	0.646181	−	0.606804i	0.0315680	−	0.0296443i	0.700171	+	0.713976i	$0.253107\pi$
$420$	1.29772	−	10.5507i	0.0633223	−	0.514820i
$421$	−6.42261	−	33.6685i	−0.313019	−	1.64090i	−0.696646	−	0.717415i	$-0.745325\pi$
$421$	−6.42261	−	33.6685i	−0.313019	−	1.64090i	0.383627	−	0.923488i	$-0.374675\pi$
$422$	−2.77055	+	2.95033i	−0.134868	+	0.143620i
$423$	−0.562827	+	1.42154i	−0.0273656	+	0.0691176i
$424$	−4.06949	−	12.5246i	−0.197632	−	0.608249i
$425$	−14.6187	+	12.2560i	−0.709110	+	0.594504i
$426$	−2.91724	+	8.97833i	−0.141341	+	0.435001i
$427$	46.8329	+	38.7435i	2.26640	+	1.87493i
$428$	−12.0856	−	5.68704i	−0.584179	−	0.274894i
$429$	−8.38871	−	7.87752i	−0.405011	−	0.380330i
$430$	1.28054	+	3.20353i	0.0617530	+	0.154488i
$431$	1.78048	−	0.224928i	0.0857629	−	0.0108344i	−0.0823346	−	0.996605i	$-0.526238\pi$
$431$	1.78048	−	0.224928i	0.0857629	−	0.0108344i	0.168098	+	0.985770i	$0.446238\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−1.93825	−	15.3428i	−0.0931464	−	0.737329i	−0.967648	−	0.252306i	$-0.918811\pi$
$433$	−1.93825	−	15.3428i	−0.0931464	−	0.737329i	0.874501	−	0.485023i	$-0.161189\pi$
$434$	19.3147	+	23.3474i	0.927133	+	1.12071i
$435$	10.4465	+	1.28491i	0.500872	+	0.0616068i
$436$	−0.300032	+	4.76887i	−0.0143689	+	0.228387i
$437$	−3.85278	+	15.0056i	−0.184303	+	0.717814i
$438$	−1.15274	+	4.48963i	−0.0550801	+	0.214523i
$439$	0.755794	−	12.0130i	0.0360721	−	0.573349i	−0.937932	−	0.346819i	$-0.887262\pi$
$439$	0.755794	−	12.0130i	0.0360721	−	0.573349i	0.974004	−	0.226530i	$-0.0727382\pi$
$440$	6.01506	+	5.61151i	0.286757	+	0.267518i
$441$	−9.94388	−	12.0201i	−0.473518	−	0.572385i
$442$	−1.49579	−	11.8404i	−0.0711473	−	0.563189i
$443$			25.2072i			1.19763i	0.800887	+	0.598816i	$0.204362\pi$
$443$			25.2072i			1.19763i	−0.800887	+	0.598816i	$0.795638\pi$
$444$	−4.84066	+	0.611517i	−0.229728	+	0.0290213i
$445$	20.0537	−	16.7009i	0.950634	−	0.791698i
$446$	−20.0033	−	18.7844i	−0.947184	−	0.889465i
$447$	0.821955	+	0.386783i	0.0388771	+	0.0182942i
$448$	−3.66299	−	3.03029i	−0.173060	−	0.143168i
$449$	−3.66429	+	11.2775i	−0.172928	+	0.532219i	−0.999533	−	0.0305647i	$-0.990269\pi$
$449$	−3.66429	+	11.2775i	−0.172928	+	0.532219i	0.826604	+	0.562783i	$0.190269\pi$
$450$	−1.27519	−	4.83466i	−0.0601128	−	0.227908i
$451$	7.58089	+	23.3316i	0.356970	+	1.09864i
$452$	5.09349	−	12.8647i	0.239577	−	0.605104i
$453$	0.153139	−	0.163076i	0.00719509	−	0.00766200i
$454$	−5.51796	−	28.9262i	−0.258971	−	1.35757i
$455$	30.1333	+	14.0591i	1.41267	+	0.659102i
$456$	−2.26981	+	2.13149i	−0.106293	+	0.0998162i
$457$	−12.8150	+	4.16384i	−0.599459	+	0.194776i	−0.592999	−	0.805203i	$-0.702056\pi$
$457$	−12.8150	+	4.16384i	−0.599459	+	0.194776i	−0.00645996	+	0.999979i	$0.502056\pi$
$458$	21.8307	+	4.16443i	1.02008	+	0.194591i
$459$	0.239566	+	3.80779i	0.0111820	+	0.177732i
$460$	−10.7669	+	2.80213i	−0.502008	+	0.130650i
$461$	−2.90187	−	4.57261i	−0.135154	−	0.212968i	0.770010	−	0.638032i	$-0.220251\pi$
$461$	−2.90187	−	4.57261i	−0.135154	−	0.212968i	−0.905163	+	0.425064i	$0.860251\pi$
$462$	17.4546	−	1.09815i	0.812063	−	0.0510907i
$463$	−0.364443	−	0.231282i	−0.0169371	−	0.0107486i	0.527331	−	0.849660i	$-0.323193\pi$
$463$	−0.364443	−	0.231282i	−0.0169371	−	0.0107486i	−0.544268	+	0.838911i	$0.683193\pi$
$464$	3.00038	−	3.62683i	0.139289	−	0.168371i
$465$	12.5119	+	6.82516i	0.580227	+	0.316509i
$466$	−24.8205	−	6.37283i	−1.14979	−	0.295216i
$467$	−6.35101	+	2.98856i	−0.293890	+	0.138294i	−0.567072	−	0.823668i	$-0.691924\pi$
$467$	−6.35101	+	2.98856i	−0.293890	+	0.138294i	0.273182	+	0.961962i	$0.411924\pi$
$468$	2.97495	+	0.966619i	0.137517	+	0.0446820i
$469$	−33.5475	−	18.4429i	−1.54908	−	0.851614i
$470$	2.64131	+	2.17053i	0.121835	+	0.100119i
$471$	−9.96775	−	1.25922i	−0.459290	−	0.0580218i
$472$	0.565094	−	4.47318i	0.0260106	−	0.205895i
$473$	−4.79244	+	3.04137i	−0.220357	+	0.139843i
$474$	6.72943	−	4.88922i	0.309093	−	0.224569i
$475$	−8.25569	+	13.1995i	−0.378797	+	0.605633i
$476$	14.6738	+	10.6612i	0.672574	+	0.488653i
$477$	−13.1432	−	0.826898i	−0.601784	−	0.0378611i
$478$	2.82120	+	5.13174i	0.129039	+	0.234720i
$479$	5.00221	−	10.6302i	0.228557	−	0.485708i	−0.757349	−	0.653011i	$-0.773506\pi$
$479$	5.00221	−	10.6302i	0.228557	−	0.485708i	0.985906	+	0.167303i	$0.0535057\pi$
$480$	−2.12888	−	0.684005i	−0.0971697	−	0.0312204i
$481$	2.85984	−	14.9918i	0.130398	−	0.683568i
$482$	5.42970	+	7.47334i	0.247316	+	0.340401i
$483$	−11.3950	+	20.7275i	−0.518492	+	0.943134i
$484$	−1.35779	+	2.13954i	−0.0617178	+	0.0972517i
$485$	9.58740	−	29.8396i	0.435342	−	1.35495i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	5.17329	+	13.0662i	0.234424	+	0.592088i	0.998599	−	0.0529216i	$-0.0168533\pi$
$487$	5.17329	+	13.0662i	0.234424	+	0.592088i	−0.764174	+	0.645010i	$0.776853\pi$
$488$	9.85134	−	8.14974i	0.445949	−	0.368921i
$489$	−9.80830	+	2.51834i	−0.443547	+	0.113883i
$490$	−32.3910	+	12.9475i	−1.46328	+	0.584911i
$491$	−15.7810	+	6.24814i	−0.712186	+	0.281975i	−0.696149	−	0.717897i	$-0.745105\pi$
$491$	−15.7810	+	6.24814i	−0.712186	+	0.281975i	−0.0160369	+	0.999871i	$0.505105\pi$
$492$	−4.56487	−	4.86109i	−0.205800	−	0.219155i
$493$	−10.5559	+	14.5290i	−0.475415	+	0.654353i
$494$	−4.14704	−	8.81290i	−0.186584	−	0.396511i
$495$	7.43175	−	3.52693i	0.334032	−	0.158524i
$496$	5.58547	−	3.07064i	0.250795	−	0.137876i
$497$	44.0842	−	8.40951i	1.97745	−	0.377218i
$498$	−2.32403	−	9.05151i	−0.104142	−	0.405608i
$499$	2.48072			0.111052			0.0555262	−	0.998457i	$-0.482316\pi$
$499$	2.48072			0.111052			0.0555262	+	0.998457i	$0.482316\pi$
$500$	−11.1646	−	0.592210i	−0.499298	−	0.0264845i
$501$	−16.7536			−0.748494
$502$	−4.30072	−	16.7502i	−0.191951	−	0.747598i
$503$	0.252767	−	0.0482179i	0.0112703	−	0.00214993i	−0.181743	−	0.983346i	$-0.558174\pi$
$503$	0.252767	−	0.0482179i	0.0112703	−	0.00214993i	0.193013	+	0.981196i	$0.438174\pi$
$504$	−4.16592	+	2.29024i	−0.185565	+	0.102015i
$505$	−26.0848	−	27.5955i	−1.16076	−	1.22799i
$506$	−7.79351	−	16.5621i	−0.346464	−	0.736273i
$507$	1.88992	−	2.60126i	0.0839345	−	0.115526i
$508$	6.65501	+	7.08687i	0.295268	+	0.314429i
$509$	2.48337	−	0.983234i	0.110073	−	0.0435811i	−0.312442	−	0.949937i	$-0.601147\pi$
$509$	2.48337	−	0.983234i	0.110073	−	0.0435811i	0.422516	+	0.906356i	$0.361147\pi$
$510$	8.27019	+	2.09454i	0.366210	+	0.0927478i
$511$	21.3435	−	5.48008i	0.944182	−	0.242425i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	1.14624	+	2.89507i	0.0506077	+	0.127820i
$514$	−9.47925	−	3.75310i	−0.418112	−	0.165542i
$515$	−11.3587	−	34.5724i	−0.500525	−	1.52344i
$516$	0.826717	−	1.30270i	0.0363942	−	0.0573480i
$517$	−2.70968	+	4.92890i	−0.119172	+	0.216773i
$518$	13.6338	+	18.7653i	0.599034	+	0.824500i
$519$	−4.34674	+	22.7864i	−0.190801	+	1.00021i
$520$	4.09270	−	5.67214i	0.179477	−	0.248740i
$521$	−1.93372	+	4.10937i	−0.0847180	+	0.180035i	−0.942697	−	0.333650i	$-0.891720\pi$
$521$	−1.93372	+	4.10937i	−0.0847180	+	0.180035i	0.857979	+	0.513684i	$0.171720\pi$
$522$	−2.26763	−	4.12480i	−0.0992515	−	0.180538i
$523$	−20.0767	−	1.26312i	−0.877894	−	0.0552324i	−0.382555	−	0.923933i	$-0.624956\pi$
$523$	−20.0767	−	1.26312i	−0.877894	−	0.0552324i	−0.495338	+	0.868700i	$0.664956\pi$
$524$	−1.85206	−	1.34560i	−0.0809075	−	0.0587828i
$525$	−17.2203	+	16.3848i	−0.751557	+	0.715093i
$526$	8.44543	−	6.13597i	0.368238	−	0.267541i
$527$	−20.5326	+	13.0304i	−0.894416	+	0.567614i
$528$	0.461083	−	3.64985i	0.0200661	−	0.158839i
$529$	1.74161	+	0.220016i	0.0757221	+	0.00956593i
$530$	−10.7504	+	27.4146i	−0.466966	+	1.19082i
$531$	−3.95104	−	2.17210i	−0.171460	−	0.0942611i
$532$	14.0780	+	4.57423i	0.610360	+	0.198318i
$533$	18.8740	−	8.88142i	0.817522	−	0.384697i
$534$	−11.3044	−	2.90248i	−0.489189	−	0.125602i
$535$	12.8052	+	26.9823i	0.553616	+	1.16655i
$536$	−5.13307	+	6.20482i	−0.221715	+	0.268007i
$537$	10.7535	+	6.82435i	0.464046	+	0.294493i
$538$	−14.3302	+	0.901582i	−0.617820	+	0.0388699i
$539$	−30.7514	−	48.4565i	−1.32456	−	2.08717i
$540$	−1.41967	+	1.72758i	−0.0610927	+	0.0743434i
$541$	−1.00769	−	16.0169i	−0.0433242	−	0.688618i	−0.958416	−	0.285374i	$-0.907882\pi$
$541$	−1.00769	−	16.0169i	−0.0433242	−	0.688618i	0.915092	−	0.403245i	$-0.132118\pi$
$542$	2.71730	+	0.518352i	0.116718	+	0.0222651i
$543$	11.7816	−	3.82808i	0.505597	−	0.164278i
$544$	2.78125	−	2.61176i	0.119245	−	0.111978i
$545$	7.28853	−	7.81268i	0.312206	−	0.334658i
$546$	−2.78647	−	14.6072i	−0.119250	−	0.625130i
$547$	1.63196	−	1.73786i	0.0697775	−	0.0743054i	−0.693133	−	0.720810i	$-0.743770\pi$
$547$	1.63196	−	1.73786i	0.0697775	−	0.0743054i	0.762910	+	0.646505i	$0.223770\pi$
$548$	2.98385	−	7.53634i	0.127464	−	0.321936i
$549$	−3.95091	−	12.1597i	−0.168621	−	0.518962i
$550$	−2.42506	−	18.2337i	−0.103405	−	0.777489i
$551$	−4.52908	+	13.9391i	−0.192945	+	0.593824i
$552$	3.83368	+	3.17149i	0.163172	+	0.134988i
$553$	−35.7801	−	16.8368i	−1.52152	−	0.715975i
$554$	20.3579	+	19.1173i	0.864924	+	0.812218i
$555$	9.23080	+	5.81567i	0.391826	+	0.246861i
$556$	0.537020	−	0.0678414i	0.0227747	−	0.00287712i
$557$			18.6840i			0.791667i	0.918322	+	0.395833i	$0.129544\pi$
$557$			18.6840i			0.791667i	−0.918322	+	0.395833i	$0.870456\pi$
$558$	−0.798858	−	6.32361i	−0.0338184	−	0.267700i
$559$	3.07634	+	3.71865i	0.130115	+	0.157282i
$560$	2.02613	+	10.4353i	0.0856195	+	0.440972i
$561$	−0.881328	+	14.0083i	−0.0372097	+	0.591431i
$562$	−6.13384	+	23.8897i	−0.258741	+	1.00773i
$563$	−1.60400	+	6.24717i	−0.0676006	+	0.263287i	−0.993396	−	0.114739i	$-0.963397\pi$
$563$	−1.60400	+	6.24717i	−0.0676006	+	0.263287i	0.925795	+	0.378026i	$0.123397\pi$
$564$	0.0960007	−	1.52589i	0.00404236	−	0.0642514i
$565$	−27.0630	+	14.9938i	−1.13855	+	0.630793i
$566$	5.12181	+	6.19120i	0.215286	+	0.260236i
$567$	0.595829	+	4.71647i	0.0250225	+	0.198073i
$568$		−	9.44037i		−	0.396109i
$569$	8.82988	−	1.11547i	0.370168	−	0.0467631i	0.0619510	−	0.998079i	$-0.480268\pi$
$569$	8.82988	−	1.11547i	0.370168	−	0.0467631i	0.308217	+	0.951316i	$0.400268\pi$
$570$	6.94729	−	0.459964i	0.290990	−	0.0192658i
$571$	−21.3820	−	20.0791i	−0.894811	−	0.840283i	0.0930443	−	0.995662i	$-0.470340\pi$
$571$	−21.3820	−	20.0791i	−0.894811	−	0.840283i	−0.987855	+	0.155379i	$0.950340\pi$
$572$	10.4124	+	4.89972i	0.435365	+	0.204867i
$573$	−2.05692	−	1.70163i	−0.0859292	−	0.0710868i
$574$	−9.79630	+	30.1499i	−0.408890	+	1.25843i
$575$	22.5788	+	10.4444i	0.941599	+	0.435563i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	11.4383	−	28.8899i	0.476183	−	1.20270i	−0.471036	−	0.882114i	$-0.656120\pi$
$577$	11.4383	−	28.8899i	0.476183	−	1.20270i	0.947219	−	0.320587i	$-0.103880\pi$
$578$	1.67260	−	1.78114i	0.0695711	−	0.0740857i
$579$	−0.996005	−	5.22124i	−0.0413925	−	0.216987i
$580$	−10.3323	+	2.00613i	−0.429025	+	0.0832999i
$581$	−32.3853	+	30.4119i	−1.34357	+	1.26170i
$582$	−13.3305	+	4.33136i	−0.552569	+	0.179540i
$583$	−47.5893	−	9.07815i	−1.97095	−	0.375979i
$584$	−0.291050	−	4.62611i	−0.0120437	−	0.191430i
$585$	−3.76720	−	5.89335i	−0.155755	−	0.243660i
$586$	−7.35906	−	11.5960i	−0.304000	−	0.479027i
$587$	−32.2867	+	2.03131i	−1.33261	+	0.0838410i	−0.713054	−	0.701109i	$-0.752689\pi$
$587$	−32.2867	+	2.03131i	−1.33261	+	0.0838410i	−0.619560	+	0.784950i	$0.712689\pi$
$588$	13.1716	+	8.35896i	0.543188	+	0.344718i
$589$	−12.6506	+	15.2920i	−0.521260	+	0.630095i
$590$	−7.32667	+	6.92556i	−0.301634	+	0.285121i
$591$	−13.9586	−	3.58395i	−0.574178	−	0.147424i
$592$	4.41477	−	2.07743i	0.181446	−	0.0853820i
$593$	−19.3390	−	6.28362i	−0.794157	−	0.258037i	−0.116284	−	0.993216i	$-0.537098\pi$
$593$	−19.3390	−	6.28362i	−0.794157	−	0.258037i	−0.677873	+	0.735179i	$0.737098\pi$
$594$	−3.22381	−	1.77230i	−0.132275	−	0.0727185i
$595$	−10.2150	−	39.2500i	−0.418774	−	1.60909i
$596$	−0.901248	−	0.113854i	−0.0369166	−	0.00466365i
$597$	2.19935	−	17.4097i	0.0900135	−	0.712530i
$598$	−13.1407	+	8.33936i	−0.537365	+	0.341022i
$599$	−23.9843	+	17.4256i	−0.979971	+	0.711991i	−0.957702	−	0.287761i	$-0.907089\pi$
$599$	−23.9843	+	17.4256i	−0.979971	+	0.711991i	−0.0222692	+	0.999752i	$0.507089\pi$
$600$	2.70676	+	4.20398i	0.110503	+	0.171627i
$601$	37.9502	+	27.5724i	1.54802	+	1.12470i	0.945044	+	0.326942i	$0.106018\pi$
$601$	37.9502	+	27.5724i	1.54802	+	1.12470i	0.602975	+	0.797760i	$0.293982\pi$
$602$	−7.32031	−	0.460555i	−0.298354	−	0.0187708i
$603$	3.87949	+	7.05676i	0.157985	+	0.287373i
$604$	−0.0952504	+	0.202417i	−0.00387568	+	0.00823625i
$605$	5.38313	−	1.76862i	0.218855	−	0.0719047i
$606$	−3.18210	+	16.6811i	−0.129264	+	0.677625i
$607$	11.4891	+	15.8133i	0.466326	+	0.641843i	0.975806	−	0.218640i	$-0.0701619\pi$
$607$	11.4891	+	15.8133i	0.466326	+	0.641843i	−0.509479	+	0.860483i	$0.670162\pi$
$608$	1.50005	−	2.72858i	0.0608350	−	0.110658i
$609$	−11.9902	+	18.8936i	−0.485868	+	0.765605i
$610$	−28.5889	+	0.0937543i	−1.15753	+	0.00379600i
$611$	4.44664	+	1.76055i	0.179892	+	0.0712242i
$612$	−1.40451	−	3.54739i	−0.0567740	−	0.143395i
$613$	24.7321	−	20.4602i	0.998922	−	0.826380i	0.0140917	−	0.999901i	$-0.495514\pi$
$613$	24.7321	−	20.4602i	0.998922	−	0.826380i	0.984830	+	0.173521i	$0.0555143\pi$
$614$	−0.428556	+	0.110034i	−0.0172951	+	0.00444063i
$615$	0.985073	+	14.8785i	0.0397220	+	0.599960i
$616$	−16.2610	+	6.43818i	−0.655174	+	0.259402i
$617$	9.17241	+	9.76762i	0.369267	+	0.393230i	0.886587	−	0.462563i	$-0.153070\pi$
$617$	9.17241	+	9.76762i	0.369267	+	0.393230i	−0.517319	+	0.855792i	$0.673070\pi$
$618$	−9.56581	+	13.1662i	−0.384793	+	0.529622i
$619$	2.96821	+	6.30778i	0.119303	+	0.253531i	0.955554	−	0.294815i	$-0.0952579\pi$
$619$	2.96821	+	6.30778i	0.119303	+	0.253531i	−0.836252	+	0.548346i	$0.815258\pi$
$620$	−14.0086	−	2.62471i	−0.562601	−	0.105411i
$621$	4.36005	−	2.39696i	0.174963	−	0.0961866i
$622$	−0.607996	+	0.115981i	−0.0243784	+	0.00465043i
$623$	13.7982	+	53.7406i	0.552815	+	2.15307i
$624$	−3.12805			−0.125222
$625$	18.4471	+	16.8732i	0.737885	+	0.674926i
$626$	−32.7593			−1.30932
$627$	2.84873	+	11.0951i	0.113767	+	0.443095i
$628$	9.86901	−	1.88261i	0.393816	−	0.0751245i
$629$	−16.3128	+	8.96805i	−0.650435	+	0.357580i
$630$	10.4484	+	1.95764i	0.416273	+	0.0779943i
$631$	−17.8976	−	38.0344i	−0.712494	−	1.51413i	−0.851794	−	0.523877i	$-0.824485\pi$
$631$	−17.8976	−	38.0344i	−0.712494	−	1.51413i	0.139300	−	0.990250i	$-0.455515\pi$
$632$	−4.88922	+	6.72943i	−0.194483	+	0.267682i
$633$	−2.77055	−	2.95033i	−0.110119	−	0.117265i
$634$	−13.0165	+	5.15360i	−0.516952	+	0.204676i
$635$	−1.43612	−	21.6911i	−0.0569905	−	0.860783i
$636$	12.7554	−	3.27504i	0.505785	−	0.129864i
$637$	−37.5994	+	31.1049i	−1.48974	+	1.23242i
$638$	−6.37463	−	16.1005i	−0.252374	−	0.637424i
$639$	−8.77744	−	3.47523i	−0.347230	−	0.137478i
$640$	2.23606	−	0.00733290i	0.0883879	−	0.000289858i
$641$	12.6372	−	19.9131i	0.499141	−	0.786521i	−0.497581	−	0.867417i	$-0.665778\pi$
$641$	12.6372	−	19.9131i	0.499141	−	0.786521i	0.996722	+	0.0808967i	$0.0257784\pi$
$642$	6.43468	−	11.7046i	0.253957	−	0.461945i
$643$	27.9696	+	38.4969i	1.10302	+	1.51817i	0.831326	+	0.555785i	$0.187582\pi$
$643$	27.9696	+	38.4969i	1.10302	+	1.51817i	0.271690	+	0.962385i	$0.412418\pi$
$644$	4.43218	−	23.2343i	0.174652	−	0.915559i
$645$	−3.27762	+	1.07686i	−0.129056	+	0.0424013i
$646$	−5.05819	+	10.7492i	−0.199012	+	0.422922i
$647$	−5.44874	−	9.91123i	−0.214212	−	0.389651i	0.747269	−	0.664522i	$-0.231365\pi$
$647$	−5.44874	−	9.91123i	−0.214212	−	0.389651i	−0.961481	+	0.274871i	$0.911365\pi$
$648$	0.998027	+	0.0627905i	0.0392062	+	0.00246664i
$649$	−13.4192	−	9.74960i	−0.526749	−	0.382705i
$650$	−15.1230	+	3.98884i	−0.593174	+	0.156455i
$651$	−24.5141	+	17.8105i	−0.960784	+	0.698050i
$652$	8.55004	−	5.42602i	0.334845	−	0.212499i
$653$	3.74581	−	29.6511i	0.146585	−	1.16034i	−0.731503	−	0.681838i	$-0.761181\pi$
$653$	3.74581	−	29.6511i	0.146585	−	1.16034i	0.878088	−	0.478500i	$-0.158819\pi$
$654$	−4.74062	−	0.598879i	−0.185373	−	0.0234180i
$655$	1.28929	+	4.95394i	0.0503766	+	0.193566i
$656$	5.84360	+	3.21255i	0.228154	+	0.125429i
$657$	−4.40839	−	1.43237i	−0.171988	−	0.0558822i
$658$	−6.57659	+	3.09471i	−0.256382	+	0.120644i
$659$	−3.67427	−	0.943392i	−0.143129	−	0.0367493i	0.176446	−	0.984310i	$-0.443540\pi$
$659$	−3.67427	−	0.943392i	−0.143129	−	0.0367493i	−0.319575	+	0.947561i	$0.603540\pi$
$660$	−5.97813	+	5.65084i	−0.232698	+	0.219959i
$661$	−14.5031	+	17.5312i	−0.564105	+	0.681886i	−0.973029	−	0.230682i	$-0.925904\pi$
$661$	−14.5031	+	17.5312i	−0.564105	+	0.681886i	0.408924	+	0.912569i	$0.365904\pi$
$662$	15.7472	+	9.99349i	0.612033	+	0.388408i
$663$	11.9109	−	0.749372i	0.462582	−	0.0291032i
$664$	5.00736	+	7.89033i	0.194323	+	0.306204i
$665$	−17.8271	−	27.8885i	−0.691306	−	1.08147i
$666$	−0.306363	−	4.86950i	−0.0118713	−	0.188689i
$667$	23.0049	+	4.38843i	0.890755	+	0.169921i
$668$	15.9336	−	5.17714i	0.616489	−	0.200309i
$669$	20.0033	−	18.7844i	0.773373	−	0.726245i
$670$	17.6766	−	3.43211i	0.682906	−	0.132594i
$671$	−8.81363	−	46.2027i	−0.340246	−	1.78363i
$672$	3.25431	−	3.46549i	0.125538	−	0.133684i
$673$	10.4010	−	26.2700i	0.400931	−	1.01263i	−0.579360	−	0.815072i	$-0.696697\pi$
$673$	10.4010	−	26.2700i	0.400931	−	1.01263i	0.980290	−	0.197563i	$-0.0633027\pi$
$674$	7.00573	+	21.5614i	0.269851	+	0.830515i
$675$	4.90519	−	0.969099i	0.188801	−	0.0373006i
$676$	−0.993592	+	3.05796i	−0.0382151	+	0.117614i
$677$	−17.5492	−	14.5180i	−0.674471	−	0.557971i	0.235893	−	0.971779i	$-0.424198\pi$
$677$	−17.5492	−	14.5180i	−0.674471	−	0.557971i	−0.910364	+	0.413808i	$0.864198\pi$
$678$	12.5195	+	5.89121i	0.480807	+	0.226251i
$679$	48.5742	+	45.6142i	1.86411	+	1.75051i
$680$	−8.51267	+	0.563604i	−0.326446	+	0.0216132i
$681$	29.2156	−	3.69078i	1.11954	−	0.141431i
$682$		−	23.4486i		−	0.897893i
$683$	2.35528	+	18.6439i	0.0901222	+	0.713391i	0.970836	+	0.239743i	$0.0770631\pi$
$683$	2.35528	+	18.6439i	0.0901222	+	0.713391i	−0.880714	+	0.473648i	$0.842937\pi$
$684$	−1.98476	−	2.39917i	−0.0758893	−	0.0917344i
$685$	−15.8539	+	8.78360i	−0.605747	+	0.335604i
$686$	2.56716	−	40.8039i	0.0980147	−	1.55790i
$687$	−5.52698	+	21.5262i	−0.210867	+	0.821274i
$688$	−0.383699	+	1.49441i	−0.0146284	+	0.0569738i
$689$	−2.58657	+	41.1124i	−0.0985406	+	1.56626i
$690$	−2.12054	−	10.9216i	−0.0807277	−	0.415777i
$691$	−16.0948	−	19.4552i	−0.612274	−	0.740112i	0.369695	−	0.929153i	$-0.379462\pi$
$691$	−16.0948	−	19.4552i	−0.612274	−	0.740112i	−0.981969	+	0.189041i	$0.939462\pi$
$692$	−2.90739	−	23.0144i	−0.110522	−	0.874875i
$693$			17.4891i			0.664358i
$694$	5.74807	−	0.726151i	0.218194	−	0.0275643i
$695$	−1.02406	−	0.645187i	−0.0388448	−	0.0244733i
$696$	3.43128	+	3.22219i	0.130062	+	0.122137i
$697$	−23.0208	−	10.8328i	−0.871975	−	0.410320i
$698$	−15.8841	−	13.1405i	−0.601223	−	0.497375i
$699$	7.91875	−	24.3714i	0.299515	−	0.921812i
$700$	11.3143	−	20.9043i	0.427641	−	0.790108i
$701$	13.4080	+	41.2656i	0.506413	+	1.55858i	0.798382	+	0.602151i	$0.205689\pi$
$701$	13.4080	+	41.2656i	0.506413	+	1.55858i	−0.291969	+	0.956428i	$0.594311\pi$
$702$	−1.15151	+	2.90838i	−0.0434610	+	0.109770i
$703$	−10.3998	+	11.0747i	−0.392237	+	0.417690i
$704$	0.689350	+	3.61370i	0.0259808	+	0.136196i
$705$	−2.33210	+	2.49981i	−0.0878319	+	0.0941483i
$706$	25.7892	−	24.2177i	0.970590	−	0.911445i
$707$	76.7801	−	24.9474i	2.88761	−	0.938242i
$708$	4.42887	+	0.844853i	0.166447	+	0.0317515i
$709$	1.80803	+	28.7378i	0.0679020	+	1.07927i	0.873505	+	0.486815i	$0.161841\pi$
$709$	1.80803	+	28.7378i	0.0679020	+	1.07927i	−0.805603	+	0.592456i	$0.798159\pi$
$710$	−13.4022	+	16.3090i	−0.502974	+	0.612067i
$711$	4.45702	+	7.02314i	0.167151	+	0.263389i
$712$	11.6480	−	0.732832i	0.436529	−	0.0274641i
$713$	26.7763	+	16.9927i	1.00278	+	0.636383i
$714$	−11.5615	+	13.9755i	−0.432678	+	0.523018i
$715$	−11.0324	−	23.2468i	−0.412588	−	0.869382i
$716$	−12.3360	−	3.16734i	−0.461018	−	0.118369i
$717$	−5.29876	+	2.49341i	−0.197886	+	0.0931180i
$718$	4.19074	+	1.36165i	0.156397	+	0.0508165i
$719$	−16.4564	−	9.04700i	−0.613722	−	0.337396i	0.144390	−	0.989521i	$-0.453878\pi$
$719$	−16.4564	−	9.04700i	−0.613722	−	0.337396i	−0.758112	+	0.652125i	$0.773878\pi$
$720$	0.816329	−	2.08173i	0.0304228	−	0.0775816i
$721$	76.7574	+	9.69671i	2.85859	+	0.361124i
$722$	1.16619	−	9.23135i	0.0434011	−	0.343555i
$723$	−7.79953	+	4.94973i	−0.290068	+	0.184082i
$724$	−10.0220	+	7.28143i	−0.372466	+	0.270612i
$725$	20.6979	+	11.2026i	0.768702	+	0.416056i
$726$	−2.05006	−	1.48945i	−0.0760848	−	0.0552788i
$727$	25.8938	+	1.62910i	0.960350	+	0.0604201i	0.535220	−	0.844712i	$-0.320229\pi$
$727$	25.8938	+	1.62910i	0.960350	+	0.0604201i	0.425129	+	0.905133i	$0.360229\pi$
$728$	7.16396	+	13.0312i	0.265514	+	0.482968i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	−6.06472	+	8.40519i	−0.224465	+	0.311090i
$731$	1.10303	−	5.78231i	0.0407972	−	0.213866i
$732$	7.51509	+	10.3436i	0.277766	+	0.382312i
$733$	1.36130	−	2.47619i	0.0502807	−	0.0914603i	−0.849972	−	0.526827i	$-0.823381\pi$
$733$	1.36130	−	2.47619i	0.0502807	−	0.0914603i	0.900253	+	0.435367i	$0.143381\pi$
$734$	−6.80244	+	10.7189i	−0.251083	+	0.395643i
$735$	−10.8881	−	33.1401i	−0.401615	−	1.22239i
$736$	−4.62609	−	1.83160i	−0.170520	−	0.0675136i
$737$	10.9058	+	27.5449i	0.401720	+	1.01463i
$738$	5.13813	−	4.25063i	0.189137	−	0.156468i
$739$	−14.5179	+	3.72756i	−0.534049	+	0.137121i	−0.506077	−	0.862488i	$-0.668905\pi$
$739$	−14.5179	+	3.72756i	−0.534049	+	0.137121i	−0.0279720	+	0.999609i	$0.508905\pi$
$740$	−10.5762	−	2.67856i	−0.388787	−	0.0984657i
$741$	9.05591	−	3.58549i	0.332677	−	0.131716i
$742$	−42.8565	−	45.6375i	−1.57331	−	1.67541i
$743$	20.3162	−	27.9628i	0.745328	−	1.02586i	−0.252967	−	0.967475i	$-0.581406\pi$
$743$	20.3162	−	27.9628i	0.745328	−	1.02586i	0.998294	−	0.0583806i	$-0.0185937\pi$
$744$	2.71386	+	5.76725i	0.0994950	+	0.211438i
$745$	1.39535	+	1.47616i	0.0511216	+	0.0540824i
$746$	21.0698	−	11.5832i	0.771421	−	0.424092i
$747$	9.17958	−	1.75110i	0.335863	−	0.0640693i
$748$	−3.49061	−	13.5950i	−0.127629	−	0.497084i
$749$	−63.4976			−2.32015
$750$	1.29208	−	11.1054i	0.0471799	−	0.405513i
$751$	−10.4832			−0.382539			−0.191270	−	0.981538i	$-0.561260\pi$
$751$	−10.4832			−0.382539			−0.191270	+	0.981538i	$0.561260\pi$
$752$	0.380223	+	1.48087i	0.0138653	+	0.0540018i
$753$	16.9872	−	3.24048i	0.619048	−	0.118090i
$754$	−12.9026	+	7.09325i	−0.469884	+	0.258321i
$755$	0.451918	−	0.214470i	0.0164470	−	0.00780534i
$756$	−2.02414	−	4.30151i	−0.0736171	−	0.156444i
$757$	7.51340	−	10.3413i	0.273079	−	0.375861i	−0.650347	−	0.759637i	$-0.725377\pi$
$757$	7.51340	−	10.3413i	0.273079	−	0.375861i	0.923426	+	0.383776i	$0.125377\pi$
$758$	−19.2527	−	20.5021i	−0.699291	−	0.744669i
$759$	17.0187	−	6.73819i	0.617741	−	0.244581i
$760$	−6.46513	+	2.58428i	−0.234515	+	0.0937418i
$761$	−22.4739	+	5.77033i	−0.814680	+	0.209174i	−0.632968	−	0.774178i	$-0.718164\pi$
$761$	−22.4739	+	5.77033i	−0.814680	+	0.209174i	−0.181711	+	0.983352i	$0.558164\pi$
$762$	−7.49076	+	6.19689i	−0.271361	+	0.224490i
$763$	8.36225	+	21.1206i	0.302734	+	0.764618i
$764$	2.48208	+	0.982727i	0.0897987	+	0.0355538i
$765$	−2.60970	+	8.12235i	−0.0943537	+	0.293664i
$766$	11.7514	−	18.5172i	0.424594	−	0.669053i
$767$	−6.79443	+	12.3590i	−0.245333	+	0.446258i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	−6.54096	+	34.2889i	−0.235873	+	1.23649i	0.645386	+	0.763857i	$0.276697\pi$
$769$	−6.54096	+	34.2889i	−0.235873	+	1.23649i	−0.881259	+	0.472634i	$0.843303\pi$
$770$	37.2323	+	11.9627i	1.34176	+	0.431105i
$771$	4.34090	−	9.22489i	0.156334	−	0.332226i
$772$	2.56071	+	4.65791i	0.0921619	+	0.167642i
$773$	11.8451	+	0.745229i	0.426038	+	0.0268040i	0.274363	−	0.961626i	$-0.411533\pi$
$773$	11.8451	+	0.745229i	0.426038	+	0.0268040i	0.151675	+	0.988430i	$0.451533\pi$
$774$	1.24822	+	0.906882i	0.0448662	+	0.0325972i
$775$	20.4749	+	24.4220i	0.735480	+	0.877264i
$776$	11.3396	−	8.23873i	0.407069	−	0.295753i
$777$	−19.5843	+	12.4286i	−0.702585	+	0.445874i
$778$	−1.27165	+	10.0662i	−0.0455909	+	0.360889i
$779$	−20.6000	−	2.60238i	−0.738071	−	0.0932400i
$780$	5.40396	+	4.44078i	0.193493	+	0.159005i
$781$	−30.4340	−	16.7312i	−1.08901	−	0.598690i
$782$	18.0539	+	5.86608i	0.645608	+	0.209771i
$783$	4.25905	−	2.00416i	0.152206	−	0.0716227i
$784$	−15.1100	−	3.87959i	−0.539643	−	0.138557i
$785$	−19.7222	−	10.7583i	−0.703917	−	0.383981i
$786$	1.45924	−	1.76391i	0.0520492	−	0.0629167i
$787$	−24.5947	−	15.6083i	−0.876705	−	0.556374i	0.0196018	−	0.999808i	$-0.493760\pi$
$787$	−24.5947	−	15.6083i	−0.876705	−	0.556374i	−0.896307	+	0.443434i	$0.853760\pi$
$788$	14.3829	−	0.904894i	0.512369	−	0.0322355i
$789$	5.59357	+	8.81405i	0.199136	+	0.313788i
$790$	18.0001	−	4.68461i	0.640414	−	0.166671i
$791$	−4.13019	−	65.6474i	−0.146853	−	2.33415i
$792$	3.61370	+	0.689350i	0.128407	+	0.0244950i
$793$	−38.0360	+	12.3586i	−1.35070	+	0.438868i
$794$	−13.9609	+	13.1102i	−0.495455	+	0.465263i
$795$	−26.6855	−	12.4505i	−0.946438	−	0.441575i
$796$	3.28817	+	17.2372i	0.116546	+	0.610957i
$797$	12.9669	−	13.8084i	0.459312	−	0.489118i	−0.457065	−	0.889433i	$-0.651099\pi$
$797$	12.9669	−	13.8084i	0.459312	−	0.489118i	0.916377	+	0.400315i	$0.131099\pi$
$798$	−5.44917	+	13.7630i	−0.192899	+	0.487206i
$799$	−1.80257	−	5.54775i	−0.0637705	−	0.196265i
$800$	−3.87339	−	3.16178i	−0.136945	−	0.111786i
$801$	3.60656	−	11.0998i	0.127431	−	0.392194i
$802$	−4.45395	−	3.68463i	−0.157274	−	0.130109i
$803$	−15.4295	−	7.26058i	−0.544496	−	0.256220i
$804$	−5.87027	−	5.51255i	−0.207028	−	0.194413i
$805$	−40.6419	+	33.8470i	−1.43244	+	1.19295i
$806$	−19.7805	+	2.49886i	−0.696740	+	0.0880187i
$807$		−	14.3586i		−	0.505445i
$808$	−2.12840	−	16.8480i	−0.0748769	−	0.592711i
$809$	27.7315	+	33.5217i	0.974989	+	1.17856i	0.983922	+	0.178599i	$0.0571564\pi$
$809$	27.7315	+	33.5217i	0.974989	+	1.17856i	−0.00893317	+	0.999960i	$0.502844\pi$
$810$	−1.63503	−	1.52534i	−0.0574493	−	0.0535950i
$811$	2.07016	−	32.9042i	0.0726930	−	1.15542i	−0.777476	−	0.628913i	$-0.783500\pi$
$811$	2.07016	−	32.9042i	0.0726930	−	1.15542i	0.850169	−	0.526510i	$-0.176500\pi$
$812$	5.56494	−	21.6740i	0.195291	−	0.760609i
$813$	−0.687950	+	2.67939i	−0.0241275	+	0.0939702i
$814$	1.12707	−	17.9142i	0.0395037	−	0.627893i
$815$	−22.4741	−	2.76429i	−0.787232	−	0.0968287i
$816$	2.43197	+	2.93975i	0.0851361	+	0.102912i
$817$	−0.602114	−	4.76622i	−0.0210653	−	0.166749i
$818$		−	36.6293i		−	1.28071i
$819$	14.7533	−	1.86378i	0.515523	−	0.0651257i
$820$	−5.53458	−	13.8459i	−0.193276	−	0.483520i
$821$	−25.1357	−	23.6040i	−0.877243	−	0.823786i	0.108140	−	0.994136i	$-0.465510\pi$
$821$	−25.1357	−	23.6040i	−0.877243	−	0.823786i	−0.985384	+	0.170349i	$0.945510\pi$
$822$	7.33411	+	3.45117i	0.255806	+	0.120373i
$823$	−26.7694	−	22.1455i	−0.933121	−	0.771945i	0.0407208	−	0.999171i	$-0.487035\pi$
$823$	−26.7694	−	22.1455i	−0.933121	−	0.771945i	−0.973842	+	0.227225i	$0.927035\pi$
$824$	5.02904	−	15.4778i	0.175195	−	0.539195i
$825$	18.3500	−	1.27537i	0.638866	−	0.0444026i
$826$	−6.62357	−	20.3853i	−0.230464	−	0.709294i
$827$	4.83203	−	12.2043i	0.168026	−	0.424386i	−0.821226	−	0.570603i	$-0.806710\pi$
$827$	4.83203	−	12.2043i	0.168026	−	0.424386i	0.989253	+	0.146217i	$0.0467097\pi$
$828$	−3.40595	+	3.62697i	−0.118365	+	0.126046i
$829$	7.11221	+	37.2835i	0.247017	+	1.29491i	0.862217	+	0.506539i	$0.169075\pi$
$829$	7.11221	+	37.2835i	0.247017	+	1.29491i	−0.615200	+	0.788371i	$0.710925\pi$
$830$	2.55100	−	20.7400i	0.0885465	−	0.719896i
$831$	−20.3579	+	19.1173i	−0.706207	+	0.663173i
$832$	2.97495	−	0.966619i	0.103138	−	0.0335115i
$833$	58.4651	+	11.1528i	2.02570	+	0.386422i
$834$	0.0339878	+	0.540220i	0.00117690	+	0.0187063i
$835$	−34.8764	−	13.6764i	−1.20695	−	0.473292i
$836$	−6.13787	−	9.67174i	−0.212283	−	0.334504i
$837$	6.36129	−	0.400219i	0.219878	−	0.0138336i
$838$	−0.748439	−	0.474974i	−0.0258544	−	0.0164077i
$839$	−29.8804	+	36.1192i	−1.03158	+	1.24697i	−0.0630715	+	0.998009i	$0.520090\pi$
$839$	−29.8804	+	36.1192i	−1.03158	+	1.24697i	−0.968513	+	0.248963i	$0.919910\pi$
$840$	−10.5419	+	1.36689i	−0.363731	+	0.0471623i
$841$	−6.62884	−	1.70200i	−0.228581	−	0.0586895i
$842$	−31.0135	+	14.5939i	−1.06880	+	0.502937i
$843$	−23.4575	−	7.62179i	−0.807918	−	0.262508i
$844$	3.54665	+	1.94979i	0.122081	+	0.0671144i
$845$	6.05780	−	3.87232i	0.208395	−	0.133212i
$846$	1.51685	+	0.191622i	0.0521503	+	0.00658812i
$847$	−1.50984	+	11.9516i	−0.0518786	+	0.410661i
$848$	−11.1191	+	7.05639i	−0.381831	+	0.242317i
$849$	−6.50059	+	4.72295i	−0.223100	+	0.162091i
$850$	15.5065	+	11.1115i	0.531868	+	0.381120i
$851$	19.6397	+	14.2691i	0.673242	+	0.489139i
$852$	9.42174	+	0.592766i	0.322784	+	0.0203078i
$853$	−15.7585	−	28.6645i	−0.539560	−	0.981455i	−0.995796	−	0.0915968i	$-0.970803\pi$
$853$	−15.7585	−	28.6645i	−0.539560	−	0.981455i	0.456237	−	0.889859i	$-0.349197\pi$
$854$	25.8795	−	54.9966i	0.885577	−	1.88195i
$855$	0.0228326	+	6.96246i	0.000780860	+	0.238111i
$856$	−2.50281	+	13.1202i	−0.0855443	+	0.448439i
$857$	23.6335	+	32.5287i	0.807304	+	1.11116i	0.991734	+	0.128313i	$0.0409563\pi$
$857$	23.6335	+	32.5287i	0.807304	+	1.11116i	−0.184429	+	0.982846i	$0.559044\pi$
$858$	−5.54385	+	10.0842i	−0.189264	+	0.344270i
$859$	9.08227	−	14.3114i	0.309883	−	0.488297i	−0.653317	−	0.757085i	$-0.726623\pi$
$859$	9.08227	−	14.3114i	0.309883	−	0.488297i	0.963200	+	0.268787i	$0.0866229\pi$
$860$	2.78443	−	2.03699i	0.0949483	−	0.0694609i
$861$	−29.4753	−	11.6701i	−1.00452	−	0.397716i
$862$	−0.660650	−	1.66861i	−0.0225018	−	0.0568331i
$863$	−15.6803	+	12.9719i	−0.533764	+	0.441568i	−0.864849	−	0.502033i	$-0.832586\pi$
$863$	−15.6803	+	12.9719i	−0.533764	+	0.441568i	0.331084	+	0.943601i	$0.392586\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	−27.6499	+	43.8868i	−0.940126	+	1.49220i
$866$	−14.3788	+	5.69296i	−0.488611	+	0.193455i
$867$	1.67260	+	1.78114i	0.0568045	+	0.0604907i
$868$	17.8105	−	24.5141i	0.604529	−	0.832063i
$869$	13.0292	+	27.6885i	0.441986	+	0.939268i
$870$	−1.35340	−	10.4379i	−0.0458846	−	0.353877i
$871$	22.0739	−	12.1352i	0.747944	−	0.411186i
$872$	4.69366	−	0.895363i	0.158947	−	0.0303208i
$873$	−3.48578	−	13.5762i	−0.117976	−	0.459485i
$874$	15.4923			0.524035
$875$	−49.2235	+	20.0514i	−1.66406	+	0.677860i
$876$	4.63526			0.156611
$877$	5.18170	+	20.1814i	0.174974	+	0.681478i	0.994157	+	0.107946i	$0.0344272\pi$
$877$	5.18170	+	20.1814i	0.174974	+	0.681478i	−0.819183	+	0.573532i	$0.805573\pi$
$878$	−11.8236	+	2.25546i	−0.399026	+	0.0761182i
$879$	12.0352	−	6.61642i	0.405938	−	0.223166i
$880$	3.93933	−	7.22161i	0.132795	−	0.243441i
$881$	1.91619	+	4.07211i	0.0645580	+	0.137193i	0.934502	−	0.355958i	$-0.115845\pi$
$881$	1.91619	+	4.07211i	0.0645580	+	0.137193i	−0.869944	+	0.493150i	$0.835845\pi$
$882$	−9.16952	+	12.6208i	−0.308754	+	0.424963i
$883$	34.0654	+	36.2759i	1.14639	+	1.22078i	0.971715	+	0.236156i	$0.0758875\pi$
$883$	34.0654	+	36.2759i	1.14639	+	1.22078i	0.174675	+	0.984626i	$0.444112\pi$
$884$	−11.0964	+	4.39337i	−0.373212	+	0.147765i
$885$	−6.45185	−	7.74707i	−0.216876	−	0.260415i
$886$	24.4153	−	6.26878i	0.820248	−	0.210604i
$887$	1.11782	−	0.924741i	0.0375327	−	0.0310498i	−0.618469	−	0.785810i	$-0.712247\pi$
$887$	1.11782	−	0.924741i	0.0375327	−	0.0310498i	0.656001	+	0.754760i	$0.272247\pi$
$888$	1.79613	+	4.53650i	0.0602741	+	0.152235i
$889$	42.9714	+	17.0136i	1.44121	+	0.570617i
$890$	−21.1633	−	15.2703i	−0.709397	−	0.511861i
$891$	1.97123	−	3.10616i	0.0660387	−	0.104060i
$892$	−13.2196	+	24.0464i	−0.442625	+	0.805132i
$893$	−2.79820	−	3.85140i	−0.0936383	−	0.128882i
$894$	0.170219	−	0.892321i	0.00569298	−	0.0298437i
$895$	16.8149	+	22.9848i	0.562060	+	0.768298i
$896$	−2.02414	+	4.30151i	−0.0676217	+	0.143703i
$897$	−7.49779	−	13.6384i	−0.250344	−	0.455374i
$898$	11.8345	+	0.744562i	0.394922	+	0.0248464i
$899$	24.2721	+	17.6347i	0.809521	+	0.588152i
$900$	−4.36564	+	2.43745i	−0.145521	+	0.0812485i
$901$	40.6486	−	29.5330i	1.35420	−	0.983885i
$902$	20.7133	−	13.1451i	0.689677	−	0.437682i
$903$	0.919293	−	7.27695i	0.0305921	−	0.242162i
$904$	−13.7272	−	1.73415i	−0.456560	−	0.0576770i
$905$	27.6511	+	1.64864i	0.919154	+	0.0548027i
$906$	−0.196037	−	0.107772i	−0.00651290	−	0.00358050i
$907$	−43.2207	−	14.0433i	−1.43512	−	0.466299i	−0.514748	−	0.857342i	$-0.672115\pi$
$907$	−43.2207	−	14.0433i	−1.43512	−	0.466299i	−0.920373	+	0.391043i	$0.872115\pi$
$908$	−26.6451	+	12.5382i	−0.884250	+	0.416096i
$909$	−16.4484	−	4.22323i	−0.545559	−	0.140076i
$910$	6.12359	−	32.6829i	0.202995	−	1.08343i
$911$	−16.7604	+	20.2599i	−0.555297	+	0.671239i	−0.971226	−	0.238158i	$-0.923456\pi$
$911$	−16.7604	+	20.2599i	−0.555297	+	0.671239i	0.415929	+	0.909397i	$0.363456\pi$
$912$	2.62901	+	1.66842i	0.0870551	+	0.0552468i
$913$	34.3115	−	2.15870i	1.13554	−	0.0714424i
$914$	7.21998	+	11.3769i	0.238816	+	0.376313i
$915$	1.70154	−	28.5384i	0.0562513	−	0.943451i
$916$	−1.39548	−	22.1805i	−0.0461080	−	0.732865i
$917$	−10.6903	−	2.03929i	−0.353026	−	0.0673432i
$918$	3.62858	−	1.17900i	0.119761	−	0.0389127i
$919$	−4.51115	+	4.23625i	−0.148809	+	0.139741i	−0.755377	−	0.655291i	$-0.772546\pi$
$919$	−4.51115	+	4.23625i	−0.148809	+	0.139741i	0.606567	+	0.795032i	$0.292546\pi$
$920$	5.39170	+	9.73174i	0.177759	+	0.320846i
$921$	−0.0829081	−	0.434619i	−0.00273191	−	0.0143212i
$922$	−3.70729	+	3.94787i	−0.122093	+	0.130016i
$923$	−10.8707	+	27.4562i	−0.357813	+	0.903732i
$924$	−5.40444	−	16.6332i	−0.177793	−	0.547191i
$925$	14.4685	+	19.6420i	0.475723	+	0.645826i
$926$	−0.133383	+	0.410511i	−0.00438324	+	0.0134902i
$927$	−12.5396	−	10.3736i	−0.411854	−	0.340715i
$928$	−4.25905	−	2.00416i	−0.139810	−	0.0657897i
$929$	−16.6318	−	15.6183i	−0.545673	−	0.512421i	0.361956	−	0.932195i	$-0.382109\pi$
$929$	−16.6318	−	15.6183i	−0.545673	−	0.512421i	−0.907628	+	0.419774i	$0.862109\pi$
$930$	3.49914	−	13.8162i	0.114741	−	0.453051i
$931$	48.1914	−	6.08799i	1.57941	−	0.199526i
$932$			25.6256i			0.839395i
$933$	−0.0775762	−	0.614079i	−0.00253973	−	0.0201040i
$934$	4.47410	+	5.40825i	0.146397	+	0.176963i
$935$	−13.2701	+	28.4421i	−0.433978	+	0.930156i
$936$	0.196412	−	3.12187i	0.00641991	−	0.102042i
$937$	8.52644	−	33.2083i	0.278547	−	1.08487i	−0.663172	−	0.748467i	$-0.730790\pi$
$937$	8.52644	−	33.2083i	0.278547	−	1.08487i	0.941719	−	0.336401i	$-0.109210\pi$
$938$	−9.52056	+	37.0801i	−0.310857	+	1.21071i
$939$	2.05697	−	32.6946i	0.0671267	−	1.06695i
$940$	1.44547	−	3.09812i	0.0471462	−	0.101050i
$941$	22.3976	+	27.0741i	0.730141	+	0.882589i	0.996695	−	0.0812307i	$-0.0258851\pi$
$941$	22.3976	+	27.0741i	0.730141	+	0.882589i	−0.266554	+	0.963820i	$0.585885\pi$
$942$	1.25922	+	9.96775i	0.0410276	+	0.324767i
$943$			33.1788i			1.08045i
$944$	−4.47318	+	0.565094i	−0.145590	+	0.0183923i
$945$	−2.60984	+	10.3048i	−0.0848980	+	0.335216i
$946$	4.13766	+	3.88552i	0.134527	+	0.126329i
$947$	−0.365892	−	0.172176i	−0.0118899	−	0.00559496i	0.419825	−	0.907605i	$-0.362091\pi$
$947$	−0.365892	−	0.172176i	−0.0118899	−	0.00559496i	−0.431715	+	0.902010i	$0.642091\pi$
$948$	−6.40915	−	5.30211i	−0.208160	−	0.172205i
$949$	−4.48053	+	13.7896i	−0.145444	+	0.447631i
$950$	14.8379	+	4.71375i	0.481404	+	0.152934i
$951$	−4.32612	−	13.3144i	−0.140284	−	0.431750i
$952$	6.67699	−	16.8641i	0.216402	−	0.546570i
$953$	−7.16004	+	7.62467i	−0.231937	+	0.246987i	−0.834400	−	0.551159i	$-0.814186\pi$
$953$	−7.16004	+	7.62467i	−0.231937	+	0.246987i	0.602464	+	0.798146i	$0.294186\pi$
$954$	2.46765	+	12.9359i	0.0798932	+	0.418815i
$955$	−2.89287	−	5.22147i	−0.0936110	−	0.168963i
$956$	4.26892	−	4.00878i	0.138067	−	0.129653i
$957$	16.4690	−	5.35110i	0.532367	−	0.172976i
$958$	−11.5403	−	2.20142i	−0.372849	−	0.0711248i
$959$	−2.41953	−	38.4573i	−0.0781307	−	1.24185i
$960$	−0.133085	+	2.23210i	−0.00429529	+	0.0720408i
$961$	5.15800	+	8.12770i	0.166387	+	0.262184i
$962$	−15.2320	+	0.958318i	−0.491100	+	0.0308974i
$963$	11.2775	+	7.15692i	0.363413	+	0.230629i
$964$	5.88824	−	7.11766i	0.189647	−	0.229244i
$965$	2.18884	−	11.6823i	0.0704611	−	0.376066i
$966$	22.9101	+	5.88232i	0.737121	+	0.189261i
$967$	−3.45287	+	1.62480i	−0.111037	+	0.0522500i	−0.480495	−	0.876997i	$-0.659543\pi$
$967$	−3.45287	+	1.62480i	−0.111037	+	0.0522500i	0.369459	+	0.929247i	$0.379543\pi$
$968$	2.40999	+	0.783052i	0.0774599	+	0.0251683i
$969$	−10.4104	−	5.72316i	−0.334430	−	0.183854i
$970$	−31.2864	−	1.86539i	−1.00455	−	0.0598941i
$971$	−59.8734	−	7.56377i	−1.92143	−	0.242733i	−0.929432	−	0.368993i	$-0.879703\pi$
$971$	−59.8734	−	7.56377i	−1.92143	−	0.242733i	−0.991997	+	0.126260i	$0.959703\pi$
$972$	−0.125333	+	0.992115i	−0.00402007	+	0.0318221i
$973$	2.17268	−	1.37882i	0.0696528	−	0.0442030i
$974$	11.3692	−	8.26021i	0.364293	−	0.264674i
$975$	−3.03139	−	15.3436i	−0.0970821	−	0.491390i
$976$	−10.3436	−	7.51509i	−0.331092	−	0.240552i
$977$	23.7785	+	1.49602i	0.760743	+	0.0478619i	0.438423	−	0.898769i	$-0.355537\pi$
$977$	23.7785	+	1.49602i	0.760743	+	0.0478619i	0.322320	+	0.946631i	$0.395537\pi$
$978$	4.87845	+	8.87387i	0.155996	+	0.283755i
$979$	18.2814	−	38.8499i	0.584275	−	1.24165i
$980$	20.5961	+	28.1535i	0.657918	+	0.899330i
$981$	0.895363	−	4.69366i	0.0285868	−	0.149857i
$982$	9.97642	+	13.7314i	0.318360	+	0.438185i
$983$	−11.5322	+	20.9770i	−0.367821	+	0.669063i	−0.993850	−	0.110736i	$-0.964679\pi$
$983$	−11.5322	+	20.9770i	−0.367821	+	0.669063i	0.626029	+	0.779800i	$0.284679\pi$
$984$	−3.57313	+	5.63035i	−0.113907	+	0.179489i
$985$	−26.1323	−	18.8556i	−0.832644	−	0.600789i
$986$	16.6977	+	6.61108i	0.531762	+	0.210540i
$987$	−2.67566	−	6.75794i	−0.0851671	−	0.215107i
$988$	−7.50470	+	6.20843i	−0.238756	+	0.197516i
$989$	−7.43540	+	1.90909i	−0.236432	+	0.0607054i
$990$	−5.26432	−	6.32115i	−0.167311	−	0.200899i
$991$	−13.5742	+	5.37442i	−0.431200	+	0.170724i	−0.573691	−	0.819072i	$-0.694489\pi$
$991$	−13.5742	+	5.37442i	−0.431200	+	0.170724i	0.142491	+	0.989796i	$0.454489\pi$
$992$	−4.36322	−	4.64635i	−0.138532	−	0.147522i
$993$	−10.9626	+	15.0887i	−0.347886	+	0.478824i
$994$	−19.1086	−	40.6078i	−0.606088	−	1.28800i
$995$	18.7905	−	34.4469i	0.595698	−	1.09204i
$996$	−8.18918	+	4.50204i	−0.259484	+	0.142653i
$997$	35.4184	−	6.75641i	1.12171	−	0.213978i	0.407021	−	0.913419i	$-0.366568\pi$
$997$	35.4184	−	6.75641i	1.12171	−	0.213978i	0.714690	+	0.699441i	$0.246568\pi$
$998$	−0.616931	−	2.40279i	−0.0195286	−	0.0760589i
$999$	4.87913			0.154369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.7	✓	280
125.119	even	50	inner	750.2.o.b.619.7	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.7	✓	280	1.1	even	1	trivial
750.2.o.b.619.7	yes	280	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)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.19782 + 0.411792i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-2.79431 + 3.84603i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.19782 + 0.411792i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-2.79431 + 3.84603i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-0.147722 - 2.23118i) q^{10} +(3.56328 - 0.914895i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(-1.15151 - 2.90838i) q^{13} +(4.42012 + 1.75005i) q^{14} +(2.23606 - 0.00733290i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.83804 + 3.34339i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(-0.583454 + 3.05857i) q^{19} +(-2.12435 + 0.697953i) q^{20} +(-2.02414 + 4.30151i) q^{21} +(-1.77230 - 3.22381i) q^{22} +(4.96567 + 0.312413i) q^{23} +(0.809017 + 0.587785i) q^{24} +(4.66085 + 1.81009i) q^{25} +(-2.53064 + 1.83862i) q^{26} +(0.844328 - 0.535827i) q^{27} +(0.595829 - 4.71647i) q^{28} +(4.66992 + 0.589948i) q^{29} +(-0.563187 - 2.16398i) q^{30} +(5.58547 + 3.07064i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(3.32873 - 1.56638i) q^{33} +(3.69545 + 0.948830i) q^{34} +(-7.72516 + 7.30223i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(4.11959 + 2.61437i) q^{37} +(3.10758 - 0.195512i) q^{38} +(-1.67609 - 2.64110i) q^{39} +(1.20433 + 1.88404i) q^{40} +(0.418715 + 6.65529i) q^{41} +(4.66975 + 0.890803i) q^{42} +(-1.46737 + 0.476776i) q^{43} +(-2.68177 + 2.51835i) q^{44} +(2.19508 - 0.426198i) q^{45} +(-0.932313 - 4.88736i) q^{46} +(-1.04661 + 1.11452i) q^{47} +(0.368125 - 0.929776i) q^{48} +(-4.82070 - 14.8366i) q^{49} +(0.594118 - 4.96458i) q^{50} +(-1.17900 + 3.62858i) q^{51} +(2.41020 + 1.99389i) q^{52} +(-11.9158 - 5.60715i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(8.20821 - 0.543447i) q^{55} +(-4.71647 + 0.595829i) q^{56} +3.11373i q^{57} +(-0.589948 - 4.66992i) q^{58} +(-2.87398 - 3.47404i) q^{59} +(-1.95594 + 1.08365i) q^{60} +(0.802804 - 12.7602i) q^{61} +(1.58512 - 6.17362i) q^{62} +(-1.18226 + 4.60460i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-1.33317 - 6.86630i) q^{65} +(-2.34499 - 2.83461i) q^{66} +(1.00929 + 7.98934i) q^{67} -3.81532i q^{68} +(4.93625 - 0.623594i) q^{69} +(8.99398 + 5.66647i) q^{70} +(-6.88173 - 6.46238i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-3.57153 - 2.95462i) q^{73} +(1.50773 - 4.64033i) q^{74} +(4.91748 + 0.904674i) q^{75} +(-0.962194 - 2.96133i) q^{76} +(-6.43818 + 16.2610i) q^{77} +(-2.14129 + 2.28025i) q^{78} +(1.55864 + 8.17069i) q^{79} +(1.52534 - 1.63503i) q^{80} +(0.728969 - 0.684547i) q^{81} +(6.34207 - 2.06066i) q^{82} +(9.17958 + 1.75110i) q^{83} +(-0.298503 - 4.74458i) q^{84} +(-5.41647 + 6.59128i) q^{85} +(0.826717 + 1.30270i) q^{86} +(4.69774 - 0.295557i) q^{87} +(3.10616 + 1.97123i) q^{88} +(7.43942 - 8.99271i) q^{89} +(-0.958701 - 2.02012i) q^{90} +(14.4034 + 3.69817i) q^{91} +(-4.50195 + 2.11846i) q^{92} +(6.06191 + 1.96963i) q^{93} +(1.33979 + 0.736555i) q^{94} +(-2.54182 + 6.48194i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(1.75674 - 13.9060i) q^{97} +(-13.1716 + 8.35896i) q^{98} +(2.97626 - 2.16238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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