LMFDB - Embedded newform 930.2.bn.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.15286 - 0.604297i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.63601 + 2.37347i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.15286 - 0.604297i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.63601 + 2.37347i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(1.75431 - 1.38651i) q^{10} +(-3.73823 - 0.794585i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(2.57746 - 0.270902i) q^{13} +(-3.46959 + 0.737484i) q^{14} +(-1.42770 + 1.72095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.847184 + 3.98569i) q^{17} +(0.994522 - 0.104528i) q^{18} +(-0.100372 + 0.954980i) q^{19} +(0.0905513 + 2.23423i) q^{20} +(3.24044 - 1.44274i) q^{21} +(2.84011 - 2.55724i) q^{22} +(6.06438 + 1.97044i) q^{23} +(0.669131 - 0.743145i) q^{24} +(4.26965 + 2.60194i) q^{25} +(-1.29583 + 2.24444i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.44274 - 3.24044i) q^{28} +(-1.63664 - 1.18909i) q^{29} +(-0.553096 - 2.16658i) q^{30} +(4.46139 - 3.33106i) q^{31} -1.00000i q^{32} +(-2.24636 + 3.09185i) q^{33} +(-3.72245 - 1.65734i) q^{34} +(-4.24069 - 6.70270i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.42783 + 2.55641i) q^{37} +(-0.713598 - 0.642526i) q^{38} +(0.800866 - 2.46481i) q^{39} +(-1.86076 - 1.23999i) q^{40} +(0.895624 - 0.398758i) q^{41} +(-0.737484 + 3.46959i) q^{42} +(7.32843 + 0.770249i) q^{43} +(0.399481 + 3.80081i) q^{44} +(0.991467 + 2.00424i) q^{45} +(-5.15867 + 3.74800i) q^{46} +(3.27323 + 4.50522i) q^{47} +(0.207912 + 0.978148i) q^{48} +(0.583471 + 5.55135i) q^{49} +(-4.61465 + 1.92484i) q^{50} +(3.98569 + 0.847184i) q^{51} +(-1.05412 - 2.36760i) q^{52} +(8.05010 - 7.24834i) q^{53} +(0.309017 - 0.951057i) q^{54} +(7.56773 + 3.96963i) q^{55} +(1.77355 + 3.07188i) q^{56} +(0.831592 + 0.480120i) q^{57} +(1.92399 - 0.625141i) q^{58} +(2.52400 + 1.12376i) q^{59} +(2.07790 + 0.826022i) q^{60} +10.9547 q^{61} +(0.0725482 + 5.56729i) q^{62} -3.54710i q^{63} +(0.809017 + 0.587785i) q^{64} +(-5.71263 - 0.974336i) q^{65} +(-1.18098 - 3.63469i) q^{66} +(8.83808 + 5.10267i) q^{67} +(3.52882 - 2.03736i) q^{68} +(4.26669 - 4.73864i) q^{69} +(7.91521 + 0.508959i) q^{70} +(5.99516 + 6.65830i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-3.02301 + 14.2222i) q^{73} +(0.534435 - 5.08480i) q^{74} +(4.11361 - 2.84222i) q^{75} +(0.939257 - 0.199645i) q^{76} +(-7.96808 - 10.9671i) q^{77} +(1.52334 + 2.09670i) q^{78} +(-15.8867 + 3.37683i) q^{79} +(2.09690 - 0.776536i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.203833 + 0.958959i) q^{82} +(-2.46240 - 5.53064i) q^{83} +(-2.37347 - 2.63601i) q^{84} +(0.584665 - 9.09259i) q^{85} +(-4.93068 + 5.47608i) q^{86} +(-1.75197 + 1.01150i) q^{87} +(-3.30973 - 1.91087i) q^{88} +(0.674266 + 2.07518i) q^{89} +(-2.20424 - 0.375951i) q^{90} +(7.43719 + 5.40344i) q^{91} -6.37647i q^{92} +(-1.22847 - 5.43055i) q^{93} -5.56876 q^{94} +(0.793180 - 1.99529i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(9.40728 - 3.05661i) q^{97} +(-4.83409 - 2.79097i) q^{98} +(1.91087 + 3.30973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−2.15286	−	0.604297i	−0.962790	−	0.270250i
$5$	−2.15286	−	0.604297i	−0.962790	−	0.270250i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	2.63601	+	2.37347i	0.996318	+	0.897089i	0.994691	−	0.102910i	$-0.0328153\pi$
$7$	2.63601	+	2.37347i	0.996318	+	0.897089i	0.00162753	+	0.999999i	$0.499482\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	1.75431	−	1.38651i	0.554761	−	0.438452i
$11$	−3.73823	−	0.794585i	−1.12712	−	0.239576i	−0.393624	−	0.919272i	$-0.628779\pi$
$11$	−3.73823	−	0.794585i	−1.12712	−	0.239576i	−0.733495	+	0.679695i	$0.762112\pi$
$12$	−0.994522	−	0.104528i	−0.287094	−	0.0301748i
$13$	2.57746	−	0.270902i	0.714859	−	0.0751347i	0.259885	−	0.965640i	$-0.416315\pi$
$13$	2.57746	−	0.270902i	0.714859	−	0.0751347i	0.454974	+	0.890505i	$0.349649\pi$
$14$	−3.46959	+	0.737484i	−0.927287	+	0.197101i
$15$	−1.42770	+	1.72095i	−0.368631	+	0.444347i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.847184	+	3.98569i	0.205472	+	0.966671i	0.953124	+	0.302580i	$0.0978479\pi$
$17$	0.847184	+	3.98569i	0.205472	+	0.966671i	−0.747652	+	0.664091i	$0.768819\pi$
$18$	0.994522	−	0.104528i	0.234411	−	0.0246376i
$19$	−0.100372	+	0.954980i	−0.0230270	+	0.219087i	0.976957	+	0.213436i	$0.0684655\pi$
$19$	−0.100372	+	0.954980i	−0.0230270	+	0.219087i	−0.999984	+	0.00565128i	$0.998201\pi$
$20$	0.0905513	+	2.23423i	0.0202479	+	0.499590i
$21$	3.24044	−	1.44274i	0.707122	−	0.314831i
$22$	2.84011	−	2.55724i	0.605513	−	0.545206i
$23$	6.06438	+	1.97044i	1.26451	+	0.410865i	0.863100	−	0.505033i	$-0.168520\pi$
$23$	6.06438	+	1.97044i	1.26451	+	0.410865i	0.401412	+	0.915898i	$0.368520\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	4.26965	+	2.60194i	0.853930	+	0.520388i
$26$	−1.29583	+	2.24444i	−0.254133	+	0.440171i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	1.44274	−	3.24044i	0.272652	−	0.612385i
$29$	−1.63664	−	1.18909i	−0.303916	−	0.220808i	0.425365	−	0.905022i	$-0.360146\pi$
$29$	−1.63664	−	1.18909i	−0.303916	−	0.220808i	−0.729282	+	0.684214i	$0.760146\pi$
$30$	−0.553096	−	2.16658i	−0.100981	−	0.395562i
$31$	4.46139	−	3.33106i	0.801289	−	0.598277i
$31$	4.46139	−	3.33106i	0.801289	−	0.598277i
$32$		−	1.00000i		−	0.176777i
$33$	−2.24636	+	3.09185i	−0.391042	+	0.538223i
$34$	−3.72245	−	1.65734i	−0.638395	−	0.284232i
$35$	−4.24069	−	6.70270i	−0.716807	−	1.13296i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−4.42783	+	2.55641i	−0.727930	+	0.420271i	−0.817664	−	0.575695i	$-0.804732\pi$
$37$	−4.42783	+	2.55641i	−0.727930	+	0.420271i	0.0897343	+	0.995966i	$0.471398\pi$
$38$	−0.713598	−	0.642526i	−0.115761	−	0.104232i
$39$	0.800866	−	2.46481i	0.128241	−	0.394686i
$40$	−1.86076	−	1.23999i	−0.294212	−	0.196060i
$41$	0.895624	−	0.398758i	0.139873	−	0.0622755i	−0.335607	−	0.942002i	$-0.608941\pi$
$41$	0.895624	−	0.398758i	0.139873	−	0.0622755i	0.475480	+	0.879727i	$0.342275\pi$
$42$	−0.737484	+	3.46959i	−0.113796	+	0.535369i
$43$	7.32843	+	0.770249i	1.11757	+	0.117462i	0.645256	−	0.763966i	$-0.276751\pi$
$43$	7.32843	+	0.770249i	1.11757	+	0.117462i	0.472318	+	0.881428i	$0.343417\pi$
$44$	0.399481	+	3.80081i	0.0602240	+	0.572993i
$45$	0.991467	+	2.00424i	0.147799	+	0.298775i
$46$	−5.15867	+	3.74800i	−0.760605	+	0.552612i
$47$	3.27323	+	4.50522i	0.477450	+	0.657154i	0.978012	−	0.208547i	$-0.0668734\pi$
$47$	3.27323	+	4.50522i	0.477450	+	0.657154i	−0.500562	+	0.865701i	$0.666873\pi$
$48$	0.207912	+	0.978148i	0.0300095	+	0.141183i
$49$	0.583471	+	5.55135i	0.0833529	+	0.793050i
$50$	−4.61465	+	1.92484i	−0.652610	+	0.272213i
$51$	3.98569	+	0.847184i	0.558108	+	0.118629i
$52$	−1.05412	−	2.36760i	−0.146180	−	0.328327i
$53$	8.05010	−	7.24834i	1.10577	−	0.995636i	0.105767	−	0.994391i	$-0.466270\pi$
$53$	8.05010	−	7.24834i	1.10577	−	0.995636i	0.999999	−	0.00124535i	$-0.000396408\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	7.56773	+	3.96963i	1.02043	+	0.535265i
$56$	1.77355	+	3.07188i	0.237001	+	0.410497i
$57$	0.831592	+	0.480120i	0.110147	+	0.0635935i
$58$	1.92399	−	0.625141i	0.252632	−	0.0820850i
$59$	2.52400	+	1.12376i	0.328597	+	0.146301i	0.564403	−	0.825499i	$-0.309106\pi$
$59$	2.52400	+	1.12376i	0.328597	+	0.146301i	−0.235806	+	0.971800i	$0.575773\pi$
$60$	2.07790	+	0.826022i	0.268256	+	0.106639i
$61$	10.9547			1.40260			0.701300	−	0.712866i	$-0.252603\pi$
$61$	10.9547			1.40260			0.701300	+	0.712866i	$0.252603\pi$
$62$	0.0725482	+	5.56729i	0.00921363	+	0.707047i
$63$		−	3.54710i		−	0.446893i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−5.71263	−	0.974336i	−0.708564	−	0.120851i
$66$	−1.18098	−	3.63469i	−0.145369	−	0.447400i
$67$	8.83808	+	5.10267i	1.07974	+	0.623390i	0.930827	−	0.365459i	$-0.119088\pi$
$67$	8.83808	+	5.10267i	1.07974	+	0.623390i	0.148917	+	0.988850i	$0.452421\pi$
$68$	3.52882	−	2.03736i	0.427932	−	0.247067i
$69$	4.26669	−	4.73864i	0.513649	−	0.570465i
$70$	7.91521	+	0.508959i	0.946049	+	0.0608322i
$71$	5.99516	+	6.65830i	0.711495	+	0.790195i	0.985162	−	0.171630i	$-0.0549033\pi$
$71$	5.99516	+	6.65830i	0.711495	+	0.790195i	−0.273667	+	0.961825i	$0.588237\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	−3.02301	+	14.2222i	−0.353817	+	1.66458i	0.336967	+	0.941517i	$0.390599\pi$
$73$	−3.02301	+	14.2222i	−0.353817	+	1.66458i	−0.690784	+	0.723061i	$0.742734\pi$
$74$	0.534435	−	5.08480i	0.0621267	−	0.591097i
$75$	4.11361	−	2.84222i	0.474999	−	0.328191i
$76$	0.939257	−	0.199645i	0.107740	−	0.0229009i
$77$	−7.96808	−	10.9671i	−0.908047	−	1.24982i
$78$	1.52334	+	2.09670i	0.172484	+	0.237404i
$79$	−15.8867	+	3.37683i	−1.78739	+	0.379923i	−0.978208	−	0.207628i	$-0.933426\pi$
$79$	−15.8867	+	3.37683i	−1.78739	+	0.379923i	−0.809187	+	0.587551i	$0.800092\pi$
$80$	2.09690	−	0.776536i	0.234441	−	0.0868193i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−0.203833	+	0.958959i	−0.0225096	+	0.105899i
$83$	−2.46240	−	5.53064i	−0.270283	−	0.607066i	0.726504	−	0.687162i	$-0.241144\pi$
$83$	−2.46240	−	5.53064i	−0.270283	−	0.607066i	−0.996787	+	0.0800962i	$0.974477\pi$
$84$	−2.37347	−	2.63601i	−0.258967	−	0.287612i
$85$	0.584665	−	9.09259i	0.0634159	−	0.986230i
$86$	−4.93068	+	5.47608i	−0.531689	+	0.590501i
$87$	−1.75197	+	1.01150i	−0.187831	+	0.108444i
$88$	−3.30973	−	1.91087i	−0.352818	−	0.203700i
$89$	0.674266	+	2.07518i	0.0714720	+	0.219968i	0.980412	−	0.196960i	$-0.0631068\pi$
$89$	0.674266	+	2.07518i	0.0714720	+	0.219968i	−0.908940	+	0.416928i	$0.863107\pi$
$90$	−2.20424	−	0.375951i	−0.232347	−	0.0396287i
$91$	7.43719	+	5.40344i	0.779630	+	0.566434i
$92$		−	6.37647i		−	0.664793i
$93$	−1.22847	−	5.43055i	−0.127386	−	0.563122i
$94$	−5.56876			−0.574373
$95$	0.793180	−	1.99529i	0.0813785	−	0.204712i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	9.40728	−	3.05661i	0.955164	−	0.310352i	0.210352	−	0.977626i	$-0.432539\pi$
$97$	9.40728	−	3.05661i	0.955164	−	0.310352i	0.744812	+	0.667274i	$0.232539\pi$
$98$	−4.83409	−	2.79097i	−0.488317	−	0.281930i
$99$	1.91087	+	3.30973i	0.192050	+	0.332640i
$100$	1.15520	−	4.86472i	0.115520	−	0.486472i
$101$	−2.10885	+	6.49036i	−0.209838	+	0.645815i	0.789642	+	0.613568i	$0.210266\pi$
$101$	−2.10885	+	6.49036i	−0.209838	+	0.645815i	−0.999480	+	0.0322471i	$0.989734\pi$
$102$	−3.02811	+	2.72653i	−0.299828	+	0.269966i
$103$	−3.77527	−	8.47939i	−0.371988	−	0.835499i	−0.998429	−	0.0560302i	$-0.982156\pi$
$103$	−3.77527	−	8.47939i	−0.371988	−	0.835499i	0.626441	−	0.779469i	$-0.284511\pi$
$104$	2.53502	+	0.538836i	0.248580	+	0.0528372i
$105$	−7.84807	+	1.14783i	−0.765893	+	0.112017i
$106$	1.13230	+	10.7731i	0.109979	+	1.04638i
$107$	0.352301	+	1.65745i	0.0340582	+	0.160231i	0.991890	−	0.127097i	$-0.0405661\pi$
$107$	0.352301	+	1.65745i	0.0340582	+	0.160231i	−0.957832	+	0.287329i	$0.907233\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	4.92269	−	3.57654i	0.471508	−	0.342571i	−0.326521	−	0.945190i	$-0.605876\pi$
$109$	4.92269	−	3.57654i	0.471508	−	0.342571i	0.798029	+	0.602619i	$0.205876\pi$
$110$	−7.65970	+	3.78913i	−0.730324	+	0.361280i
$111$	0.534435	+	5.08480i	0.0507263	+	0.482628i
$112$	−3.52767	−	0.370773i	−0.333334	−	0.0350348i
$113$	0.997531	−	4.69302i	0.0938399	−	0.441482i	−0.905995	−	0.423289i	$-0.860875\pi$
$113$	0.997531	−	4.69302i	0.0938399	−	0.441482i	0.999835	−	0.0181927i	$-0.00579122\pi$
$114$	−0.877223	+	0.390565i	−0.0821595	+	0.0365798i
$115$	−11.8651	−	7.90677i	−1.10642	−	0.737310i
$116$	−0.625141	+	1.92399i	−0.0580429	+	0.178638i
$117$	−1.92598	−	1.73416i	−0.178057	−	0.160323i
$118$	−2.39271	+	1.38143i	−0.220267	+	0.127171i
$119$	−7.22674	+	12.5171i	−0.662474	+	1.14744i
$120$	−1.88963	+	1.19554i	−0.172499	+	0.109137i
$121$	3.29398	+	1.46658i	0.299453	+	0.133325i
$122$	−6.43898	+	8.86250i	−0.582958	+	0.802373i
$123$		−	0.980383i		−	0.0883981i
$124$	−4.54668	−	3.21368i	−0.408304	−	0.288597i
$125$	−7.61964	−	8.18176i	−0.681521	−	0.731799i
$126$	2.86967	+	2.08493i	0.255650	+	0.185741i
$127$	−6.38162	+	14.3334i	−0.566277	+	1.27188i	0.372716	+	0.927945i	$0.378426\pi$
$127$	−6.38162	+	14.3334i	−0.566277	+	1.27188i	−0.938994	+	0.343934i	$0.888240\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	3.68440	−	6.38156i	0.324393	−	0.561865i
$130$	4.14605	−	4.04891i	0.363633	−	0.355113i
$131$	−8.55997	+	9.50681i	−0.747888	+	0.830614i	−0.990211	−	0.139582i	$-0.955424\pi$
$131$	−8.55997	+	9.50681i	−0.747888	+	0.830614i	0.242322	+	0.970196i	$0.422091\pi$
$132$	3.63469	+	1.18098i	0.316359	+	0.102791i
$133$	−2.53120	+	2.27911i	−0.219483	+	0.197624i
$134$	−9.32304	+	4.15089i	−0.805388	+	0.358582i
$135$	2.23423	−	0.0905513i	0.192292	−	0.00779342i
$136$	−0.425925	+	4.05241i	−0.0365228	+	0.347491i
$137$	−12.3666	+	1.29979i	−1.05655	+	0.111048i	−0.616839	−	0.787089i	$-0.711587\pi$
$137$	−12.3666	+	1.29979i	−1.05655	+	0.111048i	−0.439715	+	0.898137i	$0.644920\pi$
$138$	1.32574	+	6.23713i	0.112855	+	0.530940i
$139$	12.7429	−	9.25828i	1.08084	−	0.785277i	0.103012	−	0.994680i	$-0.467152\pi$
$139$	12.7429	−	9.25828i	1.08084	−	0.785277i	0.977829	+	0.209403i	$0.0671520\pi$
$140$	−5.06420	+	6.10438i	−0.428003	+	0.515915i
$141$	5.44707	−	1.15781i	0.458726	−	0.0975052i
$142$	−8.91054	+	0.936536i	−0.747756	+	0.0785923i
$143$	−9.85039	−	1.03532i	−0.823731	−	0.0865776i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	2.80490	+	3.54896i	0.232934	+	0.294725i
$146$	−9.72909	−	10.8052i	−0.805185	−	0.894249i
$147$	5.30873	+	1.72491i	0.437857	+	0.142268i
$148$	3.79956	+	3.42114i	0.312322	+	0.281216i
$149$	1.89497	+	3.28219i	0.155242	+	0.268888i	0.933147	−	0.359494i	$-0.117051\pi$
$149$	1.89497	+	3.28219i	0.155242	+	0.268888i	−0.777905	+	0.628382i	$0.783717\pi$
$150$	−0.118519	+	4.99860i	−0.00967705	+	0.408134i
$151$	−4.84455	−	14.9100i	−0.394244	−	1.21336i	−0.929549	−	0.368700i	$-0.879803\pi$
$151$	−4.84455	−	14.9100i	−0.394244	−	1.21336i	0.535304	−	0.844659i	$-0.320197\pi$
$152$	−0.390565	+	0.877223i	−0.0316790	+	0.0711522i
$153$	2.39507	−	3.29652i	0.193630	−	0.266508i
$154$	13.5561			1.09238
$155$	−11.6177	+	4.47533i	−0.933158	+	0.359467i
$156$	−2.59166			−0.207499
$157$	1.76864	−	2.43433i	0.141153	−	0.194281i	−0.732587	−	0.680673i	$-0.761687\pi$
$157$	1.76864	−	2.43433i	0.141153	−	0.194281i	0.873740	+	0.486392i	$0.161687\pi$
$158$	6.60607	−	14.8375i	0.525550	−	1.18041i
$159$	−3.34742	−	10.3023i	−0.265468	−	0.817025i
$160$	−0.604297	+	2.15286i	−0.0477739	+	0.170199i
$161$	11.3090	+	19.5878i	0.891274	+	1.54373i
$162$	−0.743145	−	0.669131i	−0.0583870	−	0.0525719i
$163$	−22.0479	−	7.16379i	−1.72692	−	0.561111i	−0.733923	−	0.679233i	$-0.762313\pi$
$163$	−22.0479	−	7.16379i	−1.72692	−	0.561111i	−0.992999	+	0.118122i	$0.962313\pi$
$164$	−0.656004	−	0.728566i	−0.0512253	−	0.0568915i
$165$	6.70451	−	5.29887i	0.521946	−	0.412517i
$166$	5.92174	+	1.25870i	0.459616	+	0.0976944i
$167$	15.0497	+	1.58179i	1.16458	+	0.122402i	0.667028	−	0.745032i	$-0.267566\pi$
$167$	15.0497	+	1.58179i	1.16458	+	0.122402i	0.497551	+	0.867435i	$0.334233\pi$
$168$	3.52767	−	0.370773i	0.272166	−	0.0286058i
$169$	−6.14600	+	1.30637i	−0.472770	+	0.100490i
$170$	7.01240	+	5.81750i	0.537827	+	0.446182i
$171$	0.776851	−	0.564415i	0.0594073	−	0.0431619i
$172$	−1.53206	−	7.20777i	−0.116818	−	0.549587i
$173$	−15.4290	+	1.62166i	−1.17305	+	0.123292i	−0.670939	−	0.741512i	$-0.734109\pi$
$173$	−15.4290	+	1.62166i	−1.17305	+	0.123292i	−0.502108	+	0.864805i	$0.667442\pi$
$174$	0.211461	−	2.01192i	0.0160308	−	0.152523i
$175$	5.07921	+	16.9926i	0.383952	+	1.28452i
$176$	3.49134	−	1.55444i	0.263169	−	0.117171i
$177$	2.05321	−	1.84872i	0.154328	−	0.138958i
$178$	−2.07518	−	0.674266i	−0.155541	−	0.0505384i
$179$	14.7750	−	16.4092i	1.10433	−	1.22648i	0.132407	−	0.991195i	$-0.457730\pi$
$179$	14.7750	−	16.4092i	1.10433	−	1.22648i	0.971925	−	0.235289i	$-0.0756038\pi$
$180$	1.59977	−	1.56229i	0.119240	−	0.116446i
$181$	−2.91133	+	5.04258i	−0.216398	+	0.374812i	−0.953704	−	0.300747i	$-0.902764\pi$
$181$	−2.91133	+	5.04258i	−0.216398	+	0.374812i	0.737306	+	0.675558i	$0.236097\pi$
$182$	−8.74294	+	2.84075i	−0.648070	+	0.210571i
$183$	4.45566	−	10.0076i	0.329372	−	0.739781i
$184$	5.15867	+	3.74800i	0.380302	+	0.276306i
$185$	11.0773	−	2.82788i	0.814422	−	0.207910i
$186$	5.11548	+	2.19815i	0.375085	+	0.161176i
$187$		−	15.5726i		−	1.13878i
$188$	3.27323	−	4.50522i	0.238725	−	0.328577i
$189$	−3.24044	−	1.44274i	−0.235707	−	0.104944i
$190$	1.14800	+	1.81450i	0.0832849	+	0.131637i
$191$	0.794705	−	1.37647i	0.0575028	−	0.0995978i	−0.835841	−	0.548972i	$-0.815020\pi$
$191$	0.794705	−	1.37647i	0.0575028	−	0.0995978i	0.893344	+	0.449374i	$0.148353\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−4.54972	−	4.09659i	−0.327496	−	0.294879i	0.488937	−	0.872319i	$-0.337385\pi$
$193$	−4.54972	−	4.09659i	−0.327496	−	0.294879i	−0.816433	+	0.577440i	$0.804052\pi$
$194$	−3.05661	+	9.40728i	−0.219452	+	0.675403i
$195$	−3.21364	+	4.82245i	−0.230133	+	0.345343i
$196$	5.09935	−	2.27038i	0.364239	−	0.162170i
$197$	−1.74852	+	8.22614i	−0.124577	+	0.586088i	0.870931	+	0.491406i	$0.163517\pi$
$197$	−1.74852	+	8.22614i	−0.124577	+	0.586088i	−0.995508	+	0.0946821i	$0.969817\pi$
$198$	−3.80081	−	0.399481i	−0.270112	−	0.0283899i
$199$	−1.34704	−	12.8162i	−0.0954892	−	0.908519i	−0.932460	−	0.361272i	$-0.882343\pi$
$199$	−1.34704	−	12.8162i	−0.0954892	−	0.908519i	0.836971	−	0.547247i	$-0.184324\pi$
$200$	3.25664	+	3.79398i	0.230279	+	0.268275i
$201$	8.25629	−	5.99855i	0.582354	−	0.423105i
$202$	−4.01126	−	5.52103i	−0.282232	−	0.388458i
$203$	−1.49193	−	7.01897i	−0.104713	−	0.492635i
$204$	−0.425925	−	4.05241i	−0.0298207	−	0.283725i
$205$	−2.16913	+	0.317248i	−0.151498	+	0.0221576i
$206$	9.07902	+	1.92980i	0.632565	+	0.134456i
$207$	−2.59354	−	5.82520i	−0.180264	−	0.404879i
$208$	−1.92598	+	1.73416i	−0.133542	+	0.120242i
$209$	1.13403	−	3.49018i	0.0784423	−	0.241421i
$210$	3.68436	−	7.02390i	0.254245	−	0.484695i
$211$	−1.67648	−	2.90376i	−0.115414	−	0.199903i	0.802531	−	0.596610i	$-0.203486\pi$
$211$	−1.67648	−	2.90376i	−0.115414	−	0.199903i	−0.917945	+	0.396707i	$0.870153\pi$
$212$	−9.38120	−	5.41624i	−0.644303	−	0.371989i
$213$	8.52111	−	2.76868i	0.583857	−	0.189707i
$214$	−1.54798	−	0.689205i	−0.105818	−	0.0471131i
$215$	−15.3116	−	6.08678i	−1.04425	−	0.415115i
$216$	−1.00000			−0.0680414
$217$	19.6665	+	1.80828i	1.33505	+	0.122754i
$218$			6.08478i			0.412113i
$219$	11.7630	+	8.54633i	0.794871	+	0.577508i
$220$	1.43679	−	8.42403i	0.0968682	−	0.567948i
$221$	3.26331	+	10.0434i	0.219514	+	0.675595i
$222$	−4.42783	−	2.55641i	−0.297176	−	0.171575i
$223$	−9.06237	+	5.23216i	−0.606861	+	0.350371i	−0.771736	−	0.635943i	$-0.780611\pi$
$223$	−9.06237	+	5.23216i	−0.606861	+	0.350371i	0.164875	+	0.986315i	$0.447278\pi$
$224$	2.37347	−	2.63601i	0.158584	−	0.176126i
$225$	−0.923337	−	4.91401i	−0.0615558	−	0.327600i
$226$	3.21040	+	3.56551i	0.213552	+	0.237174i
$227$	−4.51007	−	10.1298i	−0.299344	−	0.672337i	0.699773	−	0.714366i	$-0.253285\pi$
$227$	−4.51007	−	10.1298i	−0.299344	−	0.672337i	−0.999116	+	0.0420285i	$0.986618\pi$
$228$	0.199645	−	0.939257i	0.0132218	−	0.0622038i
$229$	−0.970050	+	9.22940i	−0.0641027	+	0.609896i	0.914564	+	0.404441i	$0.132534\pi$
$229$	−0.970050	+	9.22940i	−0.0641027	+	0.609896i	−0.978667	+	0.205455i	$0.934133\pi$
$230$	13.3708	−	4.95156i	0.881646	−	0.326496i
$231$	−13.2599	+	2.81847i	−0.872436	+	0.185442i
$232$	−1.18909	−	1.63664i	−0.0780675	−	0.107451i
$233$	16.1218	+	22.1897i	1.05617	+	1.45370i	0.883331	+	0.468749i	$0.155295\pi$
$233$	16.1218	+	22.1897i	1.05617	+	1.45370i	0.172842	+	0.984949i	$0.444705\pi$
$234$	2.53502	−	0.538836i	0.165720	−	0.0352248i
$235$	−4.32434	−	11.6771i	−0.282089	−	0.761732i
$236$	0.288798	−	2.74773i	0.0187991	−	0.178862i
$237$	−3.37683	+	15.8867i	−0.219348	+	1.03195i
$238$	−5.87876	−	13.2039i	−0.381063	−	0.855882i
$239$	−3.23329	−	3.59094i	−0.209144	−	0.232278i	0.629441	−	0.777048i	$-0.283284\pi$
$239$	−3.23329	−	3.59094i	−0.209144	−	0.232278i	−0.838586	+	0.544770i	$0.816617\pi$
$240$	0.143486	−	2.23146i	0.00926197	−	0.144040i
$241$	−4.70320	+	5.22343i	−0.302960	+	0.336471i	−0.875331	−	0.483523i	$-0.839357\pi$
$241$	−4.70320	+	5.22343i	−0.302960	+	0.336471i	0.572372	+	0.819994i	$0.306023\pi$
$242$	−3.12264	+	1.80286i	−0.200731	+	0.115892i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−3.38517	−	10.4185i	−0.216714	−	0.666976i
$245$	2.09853	−	12.3039i	0.134070	−	0.786067i
$246$	0.793146	+	0.576254i	0.0505692	+	0.0367406i
$247$			2.48861i			0.158347i
$248$	5.27239	−	1.78939i	0.334797	−	0.113626i
$249$	−6.05403			−0.383659
$250$	11.0979	−	1.35530i	0.701892	−	0.0857167i
$251$	−24.0963	−	10.7284i	−1.52095	−	0.677169i	−0.535095	−	0.844792i	$-0.679724\pi$
$251$	−24.0963	−	10.7284i	−1.52095	−	0.677169i	−0.985851	+	0.167623i	$0.946391\pi$
$252$	−3.37349	+	1.09611i	−0.212510	+	0.0690487i
$253$	−21.1044	−	12.1846i	−1.32682	−	0.766040i
$254$	−7.84491	−	13.5878i	−0.492233	−	0.852573i
$255$	−8.06869	−	4.23241i	−0.505281	−	0.265044i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.68301	−	6.01741i	0.416875	−	0.375356i	−0.433834	−	0.900993i	$-0.642840\pi$
$257$	6.68301	−	6.01741i	0.416875	−	0.375356i	0.850709	+	0.525637i	$0.176173\pi$
$258$	2.99716	+	6.73173i	0.186595	+	0.419099i
$259$	−17.7394	−	3.77062i	−1.10227	−	0.234295i
$260$	0.838651	+	5.73412i	0.0520109	+	0.355615i
$261$	0.211461	+	2.01192i	0.0130891	+	0.124534i
$262$	−2.65975	−	12.5131i	−0.164320	−	0.773063i
$263$	−7.33808	−	10.1000i	−0.452485	−	0.622792i	0.520444	−	0.853896i	$-0.325766\pi$
$263$	−7.33808	−	10.1000i	−0.452485	−	0.622792i	−0.972929	+	0.231103i	$0.925766\pi$
$264$	−3.09185	+	2.24636i	−0.190290	+	0.138254i
$265$	−21.7109	+	10.7400i	−1.33369	+	0.659756i
$266$	−0.356031	−	3.38741i	−0.0218297	−	0.207696i
$267$	2.17002	+	0.228078i	0.132803	+	0.0139581i
$268$	2.12181	−	9.98233i	0.129610	−	0.609768i
$269$	1.37293	−	0.611269i	0.0837092	−	0.0372697i	−0.364455	−	0.931221i	$-0.618745\pi$
$269$	1.37293	−	0.611269i	0.0837092	−	0.0372697i	0.448164	+	0.893951i	$0.352078\pi$
$270$	−1.23999	+	1.86076i	−0.0754635	+	0.113242i
$271$	4.10944	−	12.6476i	0.249631	−	0.768285i	−0.745209	−	0.666831i	$-0.767650\pi$
$271$	4.10944	−	12.6476i	0.249631	−	0.768285i	0.994840	−	0.101454i	$-0.0323495\pi$
$272$	−3.02811	−	2.72653i	−0.183606	−	0.165320i
$273$	7.96126	−	4.59644i	0.481838	−	0.278189i
$274$	6.21738	−	10.7688i	0.375606	−	0.650568i
$275$	−13.8935	−	13.1192i	−0.837808	−	0.791120i
$276$	−5.82520	−	2.59354i	−0.350636	−	0.156113i
$277$	12.0152	−	16.5375i	0.721923	−	0.993642i	−0.277534	−	0.960716i	$-0.589517\pi$
$277$	12.0152	−	16.5375i	0.721923	−	0.993642i	0.999458	−	0.0329267i	$-0.0104828\pi$
$278$			15.7511i			0.944690i
$279$	−5.46072	−	1.08654i	−0.326925	−	0.0650496i
$280$	−1.96189	−	7.68509i	−0.117245	−	0.459272i
$281$	9.46391	+	6.87594i	0.564570	+	0.410184i	0.833129	−	0.553079i	$-0.186547\pi$
$281$	9.46391	+	6.87594i	0.564570	+	0.410184i	−0.268559	+	0.963263i	$0.586547\pi$
$282$	−2.26502	+	5.08731i	−0.134880	+	0.302945i
$283$	−4.80469	+	1.56114i	−0.285609	+	0.0928000i	−0.448318	−	0.893874i	$-0.647977\pi$
$283$	−4.80469	+	1.56114i	−0.285609	+	0.0928000i	0.162709	+	0.986674i	$0.447977\pi$
$284$	4.47981	−	7.75926i	0.265828	−	0.460428i
$285$	−1.50017	−	1.53616i	−0.0888625	−	0.0909944i
$286$	6.62750	−	7.36059i	0.391892	−	0.435241i
$287$	3.30731	+	1.07461i	0.195225	+	0.0634323i
$288$	−0.743145	+	0.669131i	−0.0437902	+	0.0394289i
$289$	0.362301	−	0.161307i	0.0213118	−	0.00948862i
$290$	−4.51985	+	0.183185i	−0.265415	+	0.0107570i
$291$	1.03393	−	9.83721i	0.0606102	−	0.576668i
$292$	14.4602	−	1.51983i	0.846222	−	0.0889415i
$293$	2.88074	+	13.5528i	0.168295	+	0.791765i	0.978602	+	0.205760i	$0.0659666\pi$
$293$	2.88074	+	13.5528i	0.168295	+	0.791765i	−0.810308	+	0.586005i	$0.800700\pi$
$294$	−4.51588	+	3.28098i	−0.263371	+	0.191350i
$295$	−4.75475	−	3.94454i	−0.276832	−	0.229660i
$296$	−5.00109	+	1.06301i	−0.290682	+	0.0617864i
$297$	3.80081	−	0.399481i	0.220545	−	0.0231802i
$298$	−3.76919	−	0.396157i	−0.218343	−	0.0229488i
$299$	16.1645	+	3.43587i	0.934818	+	0.198702i
$300$	−3.97428	−	3.03398i	−0.229455	−	0.175167i
$301$	17.4896	+	19.4242i	1.00809	+	1.11959i
$302$	14.9100	+	4.84455i	0.857974	+	0.278773i
$303$	5.07149	+	4.56639i	0.291350	+	0.262333i
$304$	−0.480120	−	0.831592i	−0.0275368	−	0.0476951i
$305$	−23.5839	−	6.61986i	−1.35041	−	0.379052i
$306$	1.25916	+	3.87530i	0.0719814	+	0.221536i
$307$	−8.16908	+	18.3481i	−0.466234	+	1.04718i	0.515495	+	0.856893i	$0.327608\pi$
$307$	−8.16908	+	18.3481i	−0.466234	+	1.04718i	−0.981729	+	0.190286i	$0.939058\pi$
$308$	−7.96808	+	10.9671i	−0.454024	+	0.624910i
$309$	−9.28185			−0.528026
$310$	3.20811	−	12.0295i	0.182208	−	0.683228i
$311$	−31.9577			−1.81216			−0.906078	−	0.423111i	$-0.860938\pi$
$311$	−31.9577			−1.81216			−0.906078	+	0.423111i	$0.860938\pi$
$312$	1.52334	−	2.09670i	0.0862421	−	0.118702i
$313$	−6.96147	+	15.6357i	−0.393486	+	0.883783i	0.602818	+	0.797879i	$0.294045\pi$
$313$	−6.96147	+	15.6357i	−0.393486	+	0.883783i	−0.996303	+	0.0859043i	$0.972622\pi$
$314$	0.929831	+	2.86173i	0.0524734	+	0.161497i
$315$	−2.14350	+	7.63643i	−0.120773	+	0.430264i
$316$	8.12082	+	14.0657i	0.456832	+	0.791256i
$317$	−9.60374	−	8.64725i	−0.539400	−	0.485678i	0.353810	−	0.935317i	$-0.384886\pi$
$317$	−9.60374	−	8.64725i	−0.539400	−	0.485678i	−0.893210	+	0.449639i	$0.851553\pi$
$318$	10.3023	+	3.34742i	0.577724	+	0.187714i
$319$	5.17330	+	5.74553i	0.289649	+	0.321688i
$320$	−1.38651	−	1.75431i	−0.0775081	−	0.0980688i
$321$	1.65745	+	0.352301i	0.0925097	+	0.0196635i
$322$	−22.4941	−	2.36422i	−1.25355	−	0.131753i
$323$	−3.89128	+	0.408990i	−0.216517	+	0.0227568i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	11.7097	+	5.54974i	0.649539	+	0.307844i
$326$	18.7550	−	13.6263i	1.03875	−	0.754693i
$327$	−1.26510	−	5.95181i	−0.0699600	−	0.329136i
$328$	0.975012	−	0.102478i	0.0538360	−	0.00565839i
$329$	−2.06475	+	19.6447i	−0.113833	+	1.08305i
$330$	0.346064	+	8.53867i	0.0190502	+	0.470038i
$331$	−10.7664	+	4.79349i	−0.591772	+	0.263474i	−0.680698	−	0.732564i	$-0.738323\pi$
$331$	−10.7664	+	4.79349i	−0.591772	+	0.263474i	0.0889256	+	0.996038i	$0.471657\pi$
$332$	−4.49902	+	4.05094i	−0.246916	+	0.222324i
$333$	4.86257	+	1.57995i	0.266467	+	0.0865805i
$334$	−10.1257	+	11.2457i	−0.554052	+	0.615337i
$335$	−15.9437	−	16.3262i	−0.871096	−	0.891995i
$336$	−1.77355	+	3.07188i	−0.0967551	+	0.167585i
$337$	30.7450	−	9.98965i	1.67479	−	0.544171i	0.690897	−	0.722953i	$-0.257216\pi$
$337$	30.7450	−	9.98965i	1.67479	−	0.544171i	0.983889	+	0.178782i	$0.0572158\pi$
$338$	2.55565	−	5.74009i	0.139009	−	0.312220i
$339$	−3.88155	−	2.82011i	−0.210817	−	0.153167i
$340$	−8.82824	+	2.25372i	−0.478779	+	0.122225i
$341$	−19.3245	+	8.90733i	−1.04648	+	0.482359i
$342$			0.960240i			0.0519238i
$343$	2.95658	−	4.06939i	0.159640	−	0.219726i
$344$	6.73173	+	2.99716i	0.362950	+	0.161596i
$345$	−12.0492	+	7.62330i	−0.648705	+	0.410425i
$346$	7.75701	−	13.4355i	0.417019	−	0.722299i
$347$	15.9592	−	9.21404i	0.856734	−	0.494635i	−0.00618355	−	0.999981i	$-0.501968\pi$
$347$	15.9592	−	9.21404i	0.856734	−	0.494635i	0.862917	+	0.505346i	$0.168635\pi$
$348$	1.50338	+	1.35365i	0.0805896	+	0.0725632i
$349$	7.29594	−	22.4546i	0.390543	−	1.20197i	−0.541836	−	0.840484i	$-0.682271\pi$
$349$	7.29594	−	22.4546i	0.390543	−	1.20197i	0.932379	−	0.361482i	$-0.117729\pi$
$350$	−16.7328	−	5.87886i	−0.894407	−	0.314238i
$351$	−2.36760	+	1.05412i	−0.126373	+	0.0562649i
$352$	−0.794585	+	3.73823i	−0.0423515	+	0.199248i
$353$	35.1482	+	3.69423i	1.87075	+	0.196624i	0.970885	−	0.239545i	$-0.0769981\pi$
$353$	35.1482	+	3.69423i	1.87075	+	0.196624i	0.899865	+	0.436168i	$0.143665\pi$
$354$	0.288798	+	2.74773i	0.0153494	+	0.146040i
$355$	−8.88318	−	17.9573i	−0.471470	−	0.953073i
$356$	1.76525	−	1.28253i	0.0935581	−	0.0679739i
$357$	8.49554	+	11.6931i	0.449632	+	0.618865i
$358$	4.59086	+	21.5983i	0.242635	+	1.14151i
$359$	2.08568	+	19.8439i	0.110078	+	1.04732i	0.900529	+	0.434796i	$0.143180\pi$
$359$	2.08568	+	19.8439i	0.110078	+	1.04732i	−0.790451	+	0.612526i	$0.790154\pi$
$360$	0.323596	+	2.21253i	0.0170550	+	0.116611i
$361$	17.6829	+	3.75861i	0.930679	+	0.197822i
$362$	−2.36829	−	5.31927i	−0.124475	−	0.279575i
$363$	2.67957	−	2.41269i	0.140641	−	0.126634i
$364$	2.84075	−	8.74294i	0.148896	−	0.458255i
$365$	15.1025	−	28.7916i	0.790503	−	1.50702i
$366$	5.47733	+	9.48701i	0.286304	+	0.495894i
$367$	−32.5612	−	18.7992i	−1.69968	−	0.981311i	−0.946055	−	0.324007i	$-0.894970\pi$
$367$	−32.5612	−	18.7992i	−1.69968	−	0.981311i	−0.753625	−	0.657304i	$-0.771697\pi$
$368$	−6.06438	+	1.97044i	−0.316128	+	0.102716i
$369$	−0.895624	−	0.398758i	−0.0466243	−	0.0207585i
$370$	−4.22330	+	10.6239i	−0.219559	+	0.552312i
$371$	38.4239			1.99487
$372$	−4.78514	+	2.84647i	−0.248098	+	0.147583i
$373$			27.5395i			1.42594i	0.701194	+	0.712970i	$0.252651\pi$
$373$			27.5395i			1.42594i	−0.701194	+	0.712970i	$0.747349\pi$
$374$	12.5985	+	9.15332i	0.651451	+	0.473307i
$375$	−10.5736	+	3.63306i	−0.546018	+	0.187611i
$376$	1.72084	+	5.29620i	0.0887456	+	0.273131i
$377$	−4.54050	−	2.62146i	−0.233848	−	0.135012i
$378$	3.07188	−	1.77355i	0.158000	−	0.0912216i
$379$	14.9912	−	16.6494i	0.770045	−	0.855221i	−0.222771	−	0.974871i	$-0.571510\pi$
$379$	14.9912	−	16.6494i	0.770045	−	0.855221i	0.992816	+	0.119649i	$0.0381770\pi$
$380$	−2.14274	−	0.137781i	−0.109920	−	0.00706801i
$381$	10.4985	+	11.6598i	0.537856	+	0.597350i
$382$	0.646471	+	1.45200i	0.0330764	+	0.0742907i
$383$	0.551706	−	2.59557i	0.0281909	−	0.132628i	−0.961802	−	0.273747i	$-0.911737\pi$
$383$	0.551706	−	2.59557i	0.0281909	−	0.132628i	0.989993	+	0.141120i	$0.0450702\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	10.5268	+	28.4258i	0.536495	+	1.44871i
$386$	5.98847	−	1.27289i	0.304805	−	0.0647883i
$387$	−4.33127	−	5.96148i	−0.220171	−	0.303039i
$388$	−5.81402	−	8.00231i	−0.295162	−	0.406256i
$389$	−14.9928	+	3.18681i	−0.760164	+	0.161578i	−0.571656	−	0.820494i	$-0.693699\pi$
$389$	−14.9928	+	3.18681i	−0.760164	+	0.161578i	−0.188509	+	0.982072i	$0.560365\pi$
$390$	−2.01251	−	5.43445i	−0.101908	−	0.275184i
$391$	−2.71590	+	25.8401i	−0.137349	+	1.30679i
$392$	−1.16055	+	5.45995i	−0.0586166	+	0.275769i
$393$	5.20325	+	11.6867i	0.262469	+	0.589516i
$394$	−5.62733	−	6.24978i	−0.283501	−	0.314859i
$395$	36.2425	+	2.33044i	1.82356	+	0.117257i
$396$	2.55724	−	2.84011i	0.128506	−	0.142721i
$397$	−7.32872	+	4.23124i	−0.367818	+	0.212360i	−0.672505	−	0.740093i	$-0.734782\pi$
$397$	−7.32872	+	4.23124i	−0.367818	+	0.212360i	0.304687	+	0.952453i	$0.401448\pi$
$398$	11.1603	+	6.44341i	0.559416	+	0.322979i
$399$	1.05253	+	3.23937i	0.0526926	+	0.162171i
$400$	−4.98360	+	0.404626i	−0.249180	+	0.0202313i
$401$	10.0731	+	7.31854i	0.503027	+	0.365470i	0.810172	−	0.586192i	$-0.199374\pi$
$401$	10.0731	+	7.31854i	0.503027	+	0.365470i	−0.307145	+	0.951663i	$0.599374\pi$
$402$			10.2053i			0.508996i
$403$	10.5967	−	9.79429i	0.527858	−	0.487888i
$404$	6.82437			0.339525
$405$	0.826022	−	2.07790i	0.0410454	−	0.103252i
$406$	6.55540	+	2.91865i	0.325339	+	0.144850i
$407$	18.5835	−	6.03815i	0.921150	−	0.299300i
$408$	3.52882	+	2.03736i	0.174703	+	0.100865i
$409$	−17.3018	−	29.9676i	−0.855519	−	1.48180i	−0.876163	−	0.482016i	$-0.839905\pi$
$409$	−17.3018	−	29.9676i	−0.855519	−	1.48180i	0.0206434	−	0.999787i	$-0.493429\pi$
$410$	1.01832	−	1.94133i	0.0502913	−	0.0958756i
$411$	−3.84255	+	11.8262i	−0.189539	+	0.583342i
$412$	−6.89776	+	6.21077i	−0.339828	+	0.305983i
$413$	3.98608	+	8.95288i	0.196142	+	0.440543i
$414$	6.23713	+	1.32574i	0.306538	+	0.0651567i
$415$	1.95906	+	13.3947i	0.0961666	+	0.657521i
$416$	−0.270902	−	2.57746i	−0.0132821	−	0.126370i
$417$	−3.27484	−	15.4069i	−0.160370	−	0.754481i
$418$	2.15705	+	2.96892i	0.105505	+	0.145215i
$419$	5.72944	−	4.16268i	0.279902	−	0.203360i	−0.438973	−	0.898500i	$-0.644658\pi$
$419$	5.72944	−	4.16268i	0.279902	−	0.203360i	0.718874	+	0.695140i	$0.244658\pi$
$420$	3.51684	+	7.10926i	0.171604	+	0.346896i
$421$	2.14546	+	20.4127i	0.104564	+	0.994855i	0.913467	+	0.406913i	$0.133395\pi$
$421$	2.14546	+	20.4127i	0.104564	+	0.994855i	−0.808903	+	0.587942i	$0.799938\pi$
$422$	3.33460	+	0.350481i	0.162326	+	0.0170611i
$423$	1.15781	−	5.44707i	0.0562946	−	0.264845i
$424$	9.89596	−	4.40597i	0.480590	−	0.213973i
$425$	−6.75333	+	19.2218i	−0.327585	+	0.932395i
$426$	−2.76868	+	8.52111i	−0.134143	+	0.412849i
$427$	28.8766	+	26.0006i	1.39744	+	1.25826i
$428$	1.46746	−	0.847238i	0.0709323	−	0.0409528i
$429$	−4.95232	+	8.57768i	−0.239100	+	0.414134i
$430$	13.9243	−	8.80966i	0.671488	−	0.424840i
$431$	7.35277	+	3.27366i	0.354170	+	0.157687i	0.576107	−	0.817374i	$-0.304571\pi$
$431$	7.35277	+	3.27366i	0.354170	+	0.157687i	−0.221937	+	0.975061i	$0.571238\pi$
$432$	0.587785	−	0.809017i	0.0282798	−	0.0389238i
$433$			23.2127i			1.11553i	0.829998	+	0.557766i	$0.188341\pi$
$433$			23.2127i			1.11553i	−0.829998	+	0.557766i	$0.811659\pi$
$434$	−13.0226	+	14.8476i	−0.625104	+	0.712709i
$435$	4.38299	−	1.11891i	0.210148	−	0.0536477i
$436$	−4.92269	−	3.57654i	−0.235754	−	0.171285i
$437$	−2.49043	+	5.59359i	−0.119133	+	0.267578i
$438$	−13.8283	+	4.49307i	−0.660740	+	0.214687i
$439$	−9.33652	+	16.1713i	−0.445608	+	0.771816i	−0.998094	−	0.0617063i	$-0.980346\pi$
$439$	−9.33652	+	16.1713i	−0.445608	+	0.771816i	0.552486	+	0.833522i	$0.313679\pi$
$440$	5.97066	+	6.11390i	0.284640	+	0.291469i
$441$	3.73504	−	4.14818i	0.177859	−	0.197533i
$442$	−10.0434	−	3.26331i	−0.477718	−	0.155220i
$443$	19.2773	−	17.3574i	0.915894	−	0.824675i	−0.0690385	−	0.997614i	$-0.521993\pi$
$443$	19.2773	−	17.3574i	0.915894	−	0.824675i	0.984932	+	0.172939i	$0.0553265\pi$
$444$	4.67079	−	2.07957i	0.221666	−	0.0986920i
$445$	−0.197580	−	4.87503i	−0.00936620	−	0.231099i
$446$	1.09382	−	10.4070i	0.0517939	−	0.492786i
$447$	3.76919	−	0.396157i	0.178276	−	0.0187376i
$448$	0.737484	+	3.46959i	0.0348428	+	0.163923i
$449$	1.26537	−	0.919342i	0.0597163	−	0.0433864i	−0.557527	−	0.830159i	$-0.688250\pi$
$449$	1.26537	−	0.919342i	0.0597163	−	0.0433864i	0.617243	+	0.786773i	$0.288250\pi$
$450$	4.51824	+	2.14138i	0.212992	+	0.100946i
$451$	−3.66489	+	0.778997i	−0.172573	+	0.0366815i
$452$	−4.77158	+	0.501513i	−0.224436	+	0.0235892i
$453$	−15.5914	−	1.63872i	−0.732549	−	0.0769940i
$454$	10.8461	+	2.30541i	0.509033	+	0.108198i
$455$	−12.7460	−	16.1271i	−0.597541	−	0.756052i
$456$	0.642526	+	0.713598i	0.0300890	+	0.0334173i
$457$	6.34751	+	2.06243i	0.296924	+	0.0964765i	0.453691	−	0.891159i	$-0.350107\pi$
$457$	6.34751	+	2.06243i	0.296924	+	0.0964765i	−0.156767	+	0.987636i	$0.550107\pi$
$458$	−6.89656	−	6.20969i	−0.322255	−	0.290160i
$459$	−2.03736	−	3.52882i	−0.0950960	−	0.164711i
$460$	−3.85328	+	13.7277i	−0.179660	+	0.640056i
$461$	2.60926	+	8.03049i	0.121526	+	0.374017i	0.993252	−	0.115976i	$-0.0369994\pi$
$461$	2.60926	+	8.03049i	0.121526	+	0.374017i	−0.871727	+	0.489993i	$0.836999\pi$
$462$	5.51377	−	12.3841i	0.256524	−	0.576161i
$463$	−20.8067	+	28.6380i	−0.966970	+	1.33092i	−0.0234067	+	0.999726i	$0.507451\pi$
$463$	−20.8067	+	28.6380i	−0.966970	+	1.33092i	−0.943563	+	0.331193i	$0.892549\pi$
$464$	2.02300			0.0939153
$465$	−0.636939	+	12.4336i	−0.0295373	+	0.576594i
$466$	−27.4280			−1.27058
$467$	23.5113	−	32.3605i	1.08797	−	1.49746i	0.237541	−	0.971377i	$-0.423659\pi$
$467$	23.5113	−	32.3605i	1.08797	−	1.49746i	0.850431	−	0.526087i	$-0.176341\pi$
$468$	−1.05412	+	2.36760i	−0.0487268	+	0.109442i
$469$	11.1862	+	34.4277i	0.516532	+	1.58972i
$470$	11.9888	+	3.36518i	0.553001	+	0.155224i
$471$	−1.50450	−	2.60587i	−0.0693236	−	0.120072i
$472$	2.05321	+	1.84872i	0.0945065	+	0.0850940i
$473$	−26.7833	−	8.70242i	−1.23150	−	0.400138i
$474$	−10.8678	−	12.0699i	−0.499173	−	0.554388i
$475$	−2.91335	+	3.81627i	−0.133674	+	0.175102i
$476$	14.1376	+	3.00505i	0.647997	+	0.137736i
$477$	−10.7731	−	1.13230i	−0.493268	−	0.0518446i
$478$	4.80561	−	0.505090i	0.219804	−	0.0231023i
$479$	−16.9992	+	3.61330i	−0.776715	+	0.165096i	−0.579180	−	0.815200i	$-0.696627\pi$
$479$	−16.9992	+	3.61330i	−0.776715	+	0.165096i	−0.197535	+	0.980296i	$0.563294\pi$
$480$	1.72095	+	1.42770i	0.0785503	+	0.0651654i
$481$	−10.7200	+	7.78854i	−0.488790	+	0.355127i
$482$	−1.46137	−	6.87523i	−0.0665638	−	0.313158i
$483$	22.4941	−	2.36422i	1.02352	−	0.107576i
$484$	0.376900	−	3.58596i	0.0171318	−	0.162998i
$485$	−22.0997	+	0.895679i	−1.00350	+	0.0406707i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	3.58833	−	3.23095i	0.162603	−	0.146408i	−0.583813	−	0.811888i	$-0.698440\pi$
$487$	3.58833	−	3.23095i	0.162603	−	0.146408i	0.746416	+	0.665480i	$0.231773\pi$
$488$	10.4185	+	3.38517i	0.471623	+	0.153240i
$489$	−15.5121	+	17.2280i	−0.701482	+	0.779075i
$490$	8.72058	+	8.92980i	0.393956	+	0.403407i
$491$	6.29101	−	10.8963i	0.283909	−	0.491745i	−0.688435	−	0.725298i	$-0.741702\pi$
$491$	6.29101	−	10.8963i	0.283909	−	0.491745i	0.972344	+	0.233553i	$0.0750352\pi$
$492$	−0.932399	+	0.302955i	−0.0420358	+	0.0136583i
$493$	3.35280	−	7.53051i	0.151002	−	0.339157i
$494$	−2.01333	−	1.46277i	−0.0905841	−	0.0658132i
$495$	−2.11379	−	8.28012i	−0.0950078	−	0.372164i
$496$	−1.65139	+	5.31723i	−0.0741496	+	0.238751i
$497$			31.7807i			1.42556i
$498$	3.55847	−	4.89782i	0.159459	−	0.219476i
$499$	−38.3517	−	17.0753i	−1.71686	−	0.764394i	−0.997569	−	0.0696815i	$-0.977802\pi$
$499$	−38.3517	−	17.0753i	−1.71686	−	0.764394i	−0.719288	−	0.694712i	$-0.755532\pi$
$500$	−5.42672	+	9.77501i	−0.242690	+	0.437152i
$501$	7.56629	−	13.1052i	0.338037	−	0.585497i
$502$	22.8429	−	13.1883i	1.01953	−	0.588625i
$503$	28.4392	+	25.6067i	1.26804	+	1.14175i	0.983074	+	0.183210i	$0.0586489\pi$
$503$	28.4392	+	25.6067i	1.26804	+	1.14175i	0.284966	+	0.958538i	$0.408018\pi$
$504$	1.09611	−	3.37349i	0.0488248	−	0.150267i
$505$	8.46216	−	12.6985i	0.376561	−	0.565076i
$506$	22.2624	−	9.91186i	0.989684	−	0.440636i
$507$	−1.30637	+	6.14600i	−0.0580181	+	0.272954i
$508$	15.6039	+	1.64003i	0.692309	+	0.0727646i
$509$	0.801770	+	7.62833i	0.0355378	+	0.338120i	0.997816	+	0.0660528i	$0.0210406\pi$
$509$	0.801770	+	7.62833i	0.0355378	+	0.338120i	−0.962278	+	0.272067i	$0.912293\pi$
$510$	8.16675	−	4.03996i	0.361630	−	0.178892i
$511$	−41.7246	+	30.3147i	−1.84579	+	1.34104i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−0.199645	−	0.939257i	−0.00881455	−	0.0414692i
$514$	0.940011	+	8.94361i	0.0414621	+	0.394486i
$515$	3.00357	+	20.5364i	0.132353	+	0.904940i
$516$	−7.20777	−	1.53206i	−0.317304	−	0.0674451i
$517$	−8.65631	−	19.4424i	−0.380704	−	0.855076i
$518$	13.4774	−	12.1351i	0.592164	−	0.533187i
$519$	−4.79410	+	14.7547i	−0.210437	+	0.647660i
$520$	−5.13195	−	2.69195i	−0.225051	−	0.118050i
$521$	−13.5929	−	23.5437i	−0.595518	−	1.03147i	−0.993474	−	0.114062i	$-0.963614\pi$
$521$	−13.5929	−	23.5437i	−0.595518	−	1.03147i	0.397956	−	0.917405i	$-0.369720\pi$
$522$	−1.75197	−	1.01150i	−0.0766815	−	0.0442721i
$523$	−1.32762	+	0.431370i	−0.0580528	+	0.0188625i	−0.337899	−	0.941182i	$-0.609716\pi$
$523$	−1.32762	+	0.431370i	−0.0580528	+	0.0188625i	0.279847	+	0.960045i	$0.409716\pi$
$524$	11.6867	+	5.20325i	0.510535	+	0.227305i
$525$	17.5895	+	2.27144i	0.767667	+	0.0991338i
$526$	12.4843			0.544341
$527$	17.0562	+	14.9597i	0.742980	+	0.651654i
$528$		−	3.82174i		−	0.166320i
$529$	14.2867	+	10.3799i	0.621163	+	0.451301i
$530$	4.07248	−	23.8773i	0.176897	−	1.03717i
$531$	−0.853771	−	2.62764i	−0.0370505	−	0.114030i
$532$	2.94974	+	1.70304i	0.127888	+	0.0738359i
$533$	2.20041	−	1.27041i	0.0953104	−	0.0550275i
$534$	−1.46002	+	1.62152i	−0.0631814	+	0.0701700i
$535$	0.243133	−	3.78115i	0.0105116	−	0.163473i
$536$	6.82871	+	7.58405i	0.294955	+	0.327581i
$537$	−8.98108	−	20.1718i	−0.387562	−	0.870479i
$538$	−0.312462	+	1.47002i	−0.0134712	+	0.0633771i
$539$	2.22987	−	21.2158i	0.0960475	−	0.913831i
$540$	−0.776536	−	2.09690i	−0.0334168	−	0.0902362i
$541$	−23.3093	+	4.95455i	−1.00215	+	0.213013i	−0.679633	−	0.733552i	$-0.737861\pi$
$541$	−23.3093	+	4.95455i	−1.00215	+	0.213013i	−0.322513	+	0.946565i	$0.604528\pi$
$542$	7.81662	+	10.7587i	0.335753	+	0.462124i
$543$	3.42248	+	4.71063i	0.146873	+	0.202153i
$544$	3.98569	−	0.847184i	0.170885	−	0.0363227i
$545$	−12.7592	+	4.72505i	−0.546543	+	0.202399i
$546$	−0.960917	+	9.14251i	−0.0411235	+	0.391264i
$547$	−9.65588	+	45.4273i	−0.412856	+	1.94233i	−0.0897722	+	0.995962i	$0.528614\pi$
$547$	−9.65588	+	45.4273i	−0.412856	+	1.94233i	−0.323083	+	0.946370i	$0.604719\pi$
$548$	5.05768	+	11.3597i	0.216053	+	0.485263i
$549$	−7.33009	−	8.14090i	−0.312841	−	0.347445i
$550$	18.7801	−	3.52876i	0.800785	−	0.150467i
$551$	1.29983	−	1.44361i	0.0553746	−	0.0614997i
$552$	5.52219	−	3.18824i	0.235040	−	0.135700i
$553$	−49.8923	−	28.8054i	−2.12164	−	1.22493i
$554$	6.31677	+	19.4410i	0.268374	+	0.825969i
$555$	1.92217	−	11.2699i	0.0815914	−	0.478379i
$556$	−12.7429	−	9.25828i	−0.540421	−	0.392639i
$557$			12.5466i			0.531616i	0.964026	+	0.265808i	$0.0856387\pi$
$557$			12.5466i			0.531616i	−0.964026	+	0.265808i	$0.914361\pi$
$558$	4.08876	−	3.77916i	0.173091	−	0.159985i
$559$	19.0974			0.807734
$560$	7.37054	+	2.92998i	0.311462	+	0.123814i
$561$	−14.2262	−	6.33393i	−0.600632	−	0.267419i
$562$	−11.1255	+	3.61489i	−0.469301	+	0.152485i
$563$	−17.8879	−	10.3276i	−0.753886	−	0.435256i	0.0732104	−	0.997317i	$-0.476676\pi$
$563$	−17.8879	−	10.3276i	−0.753886	−	0.435256i	−0.827096	+	0.562060i	$0.810009\pi$
$564$	−2.78438	−	4.82268i	−0.117243	−	0.203072i
$565$	−4.98352	+	9.50062i	−0.209658	+	0.399694i
$566$	1.56114	−	4.80469i	0.0656195	−	0.201956i
$567$	−2.63601	+	2.37347i	−0.110702	+	0.0996766i
$568$	3.64421	+	8.18502i	0.152908	+	0.343436i
$569$	5.32775	+	1.13245i	0.223351	+	0.0474747i	0.318228	−	0.948014i	$-0.396912\pi$
$569$	5.32775	+	1.13245i	0.223351	+	0.0474747i	−0.0948767	+	0.995489i	$0.530246\pi$
$570$	2.12456	−	0.310730i	0.0889880	−	0.0130151i
$571$	−0.271192	−	2.58022i	−0.0113490	−	0.107979i	0.987381	−	0.158364i	$-0.0506219\pi$
$571$	−0.271192	−	2.58022i	−0.0113490	−	0.107979i	−0.998730	+	0.0503849i	$0.983955\pi$
$572$	2.05929	+	9.68821i	0.0861033	+	0.405084i
$573$	−0.934232	−	1.28586i	−0.0390281	−	0.0537176i
$574$	−2.81337	+	2.04403i	−0.117428	+	0.0853163i
$575$	20.7658	+	24.1922i	0.865996	+	1.00889i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	43.4825	+	4.57020i	1.81020	+	0.190260i	0.948419	−	0.317018i	$-0.102682\pi$
$577$	43.4825	+	4.57020i	1.81020	+	0.190260i	0.861782	+	0.507278i	$0.169348\pi$
$578$	−0.0824551	+	0.387921i	−0.00342968	+	0.0161354i
$579$	−5.59296	+	2.49015i	−0.232435	+	0.103487i
$580$	2.50850	−	3.76431i	0.104160	−	0.156304i
$581$	6.63592	−	20.4233i	0.275304	−	0.847299i
$582$	7.35074	+	6.61864i	0.304698	+	0.274351i
$583$	−35.8525	+	20.6995i	−1.48486	+	0.857284i
$584$	−7.26995	+	12.5919i	−0.300833	+	0.521057i
$585$	3.09842	+	4.89727i	0.128104	+	0.202477i
$586$	−12.6577	−	5.63558i	−0.522886	−	0.232804i
$587$	13.1895	−	18.1539i	0.544391	−	0.749290i	−0.444847	−	0.895607i	$-0.646742\pi$
$587$	13.1895	−	18.1539i	0.544391	−	0.749290i	0.989238	+	0.146317i	$0.0467419\pi$
$588$		−	5.58193i		−	0.230195i
$589$	2.73330	+	4.59489i	0.112624	+	0.189329i
$590$	5.98597	−	1.52813i	0.246439	−	0.0629120i
$591$	6.80376	+	4.94322i	0.279869	+	0.203337i
$592$	2.07957	−	4.67079i	0.0854697	−	0.191968i
$593$	−14.7714	+	4.79952i	−0.606589	+	0.197093i	−0.596177	−	0.802853i	$-0.703314\pi$
$593$	−14.7714	+	4.79952i	−0.606589	+	0.197093i	−0.0104119	+	0.999946i	$0.503314\pi$
$594$	−1.91087	+	3.30973i	−0.0784040	+	0.135800i
$595$	23.1222	−	22.5805i	0.947919	−	0.925709i
$596$	2.53597	−	2.81648i	0.103877	−	0.115368i
$597$	−12.2561	−	3.98225i	−0.501609	−	0.162983i
$598$	−12.2809	+	11.0578i	−0.502205	+	0.452187i
$599$	15.1969	−	6.76612i	0.620930	−	0.276456i	−0.0720629	−	0.997400i	$-0.522958\pi$
$599$	15.1969	−	6.76612i	0.620930	−	0.276456i	0.692993	+	0.720944i	$0.256292\pi$
$600$	4.79057	−	1.43193i	0.195574	−	0.0584584i
$601$	4.16504	−	39.6277i	0.169895	−	1.61645i	−0.494577	−	0.869134i	$-0.664677\pi$
$601$	4.16504	−	39.6277i	0.169895	−	1.61645i	0.664473	−	0.747313i	$-0.268656\pi$
$602$	−25.9947	+	2.73215i	−1.05946	+	0.111354i
$603$	−2.12181	−	9.98233i	−0.0864068	−	0.406512i
$604$	−12.6832	+	9.21489i	−0.516072	+	0.374948i
$605$	−6.20525	−	5.14788i	−0.252279	−	0.209291i
$606$	−6.67524	+	1.41887i	−0.271163	+	0.0576375i
$607$	16.3319	−	1.71655i	0.662892	−	0.0696728i	0.232894	−	0.972502i	$-0.425181\pi$
$607$	16.3319	−	1.71655i	0.662892	−	0.0696728i	0.429999	+	0.902829i	$0.358514\pi$
$608$	0.954980	+	0.100372i	0.0387296	+	0.00407064i
$609$	−7.01897	−	1.49193i	−0.284423	−	0.0604560i
$610$	19.2178	−	15.1887i	0.778108	−	0.614973i
$611$	9.65710	+	10.7253i	0.390685	+	0.433899i
$612$	−3.87530	−	1.25916i	−0.156650	−	0.0508985i
$613$	−0.303993	−	0.273716i	−0.0122782	−	0.0110553i	0.662969	−	0.748647i	$-0.269296\pi$
$613$	−0.303993	−	0.273716i	−0.0122782	−	0.0110553i	−0.675247	+	0.737592i	$0.735963\pi$
$614$	−10.0422	−	17.3936i	−0.405271	−	0.701950i
$615$	−0.592442	+	2.11063i	−0.0238896	+	0.0851088i
$616$	−4.18907	−	12.8926i	−0.168782	−	0.519459i
$617$	−6.40436	+	14.3844i	−0.257830	+	0.579095i	−0.995360	−	0.0962186i	$-0.969325\pi$
$617$	−6.40436	+	14.3844i	−0.257830	+	0.579095i	0.737530	+	0.675314i	$0.235992\pi$
$618$	5.45573	−	7.50917i	0.219462	−	0.302063i
$619$	−33.2039			−1.33458			−0.667288	−	0.744800i	$-0.732545\pi$
$619$	−33.2039			−1.33458			−0.667288	+	0.744800i	$0.732545\pi$
$620$	7.84636	+	9.66616i	0.315117	+	0.388202i
$621$	−6.37647			−0.255879
$622$	18.7843	−	25.8543i	0.753181	−	1.03666i
$623$	−3.14801	+	7.07054i	−0.126122	+	0.283275i
$624$	0.800866	+	2.46481i	0.0320603	+	0.0986715i
$625$	11.4598	+	22.2187i	0.458393	+	0.888749i
$626$	−8.55771	−	14.8224i	−0.342035	−	0.592422i
$627$	−2.72719	−	2.45557i	−0.108913	−	0.0980660i
$628$	−2.86173	−	0.929831i	−0.114195	−	0.0371043i
$629$	−13.9402	−	15.4822i	−0.555833	−	0.617315i
$630$	−4.91808	−	6.22271i	−0.195941	−	0.247919i
$631$	−8.90785	−	1.89342i	−0.354616	−	0.0753759i	0.0271594	−	0.999631i	$-0.491354\pi$
$631$	−8.90785	−	1.89342i	−0.354616	−	0.0753759i	−0.381775	+	0.924255i	$0.624687\pi$
$632$	−16.1527	−	1.69771i	−0.642518	−	0.0675314i
$633$	−3.33460	+	0.350481i	−0.132538	+	0.0139304i
$634$	12.6407	−	2.68687i	0.502027	−	0.106709i
$635$	22.4004	−	27.0014i	0.888931	−	1.07152i
$636$	−8.76366	+	6.36717i	−0.347502	+	0.252475i
$637$	3.00774	+	14.1503i	0.119171	+	0.560656i
$638$	−7.68902	+	0.808149i	−0.304411	+	0.0319949i
$639$	0.936536	−	8.91054i	0.0370488	−	0.352496i
$640$	2.23423	−	0.0905513i	0.0883158	−	0.00357936i
$641$	35.9423	−	16.0026i	1.41964	−	0.632063i	0.453773	−	0.891117i	$-0.350078\pi$
$641$	35.9423	−	16.0026i	1.41964	−	0.632063i	0.965863	+	0.259054i	$0.0834109\pi$
$642$	−1.25924	+	1.13383i	−0.0496983	+	0.0447485i
$643$	−30.7031	−	9.97603i	−1.21081	−	0.393416i	−0.367083	−	0.930188i	$-0.619643\pi$
$643$	−30.7031	−	9.97603i	−1.21081	−	0.393416i	−0.843727	+	0.536772i	$0.819643\pi$
$644$	15.1344	−	16.8084i	0.596379	−	0.662345i
$645$	−11.7884	+	11.5122i	−0.464166	+	0.453291i
$646$	1.95636	−	3.38851i	0.0769719	−	0.133319i
$647$	18.5689	−	6.03340i	0.730019	−	0.237198i	0.0796574	−	0.996822i	$-0.474617\pi$
$647$	18.5689	−	6.03340i	0.730019	−	0.237198i	0.650362	+	0.759625i	$0.274617\pi$
$648$	−0.406737	+	0.913545i	−0.0159781	+	0.0358875i
$649$	−8.54237	−	6.20639i	−0.335317	−	0.243622i
$650$	−11.3726	+	6.21132i	−0.446071	+	0.243628i
$651$	9.65102	−	17.2307i	0.378253	−	0.675325i
$652$			23.1825i			0.907897i
$653$	−17.1557	+	23.6127i	−0.671353	+	0.924038i	−0.999790	−	0.0204881i	$-0.993478\pi$
$653$	−17.1557	+	23.6127i	−0.671353	+	0.924038i	0.328437	+	0.944526i	$0.393478\pi$
$654$	5.55872	+	2.47490i	0.217363	+	0.0967763i
$655$	24.1734	−	15.2941i	0.944533	−	0.597590i
$656$	−0.490191	+	0.849036i	−0.0191388	+	0.0331493i
$657$	12.5919	−	7.26995i	0.491257	−	0.283628i
$658$	−14.6793	−	13.2173i	−0.572259	−	0.515264i
$659$	8.51892	−	26.2185i	0.331850	−	1.02133i	−0.636403	−	0.771357i	$-0.719579\pi$
$659$	8.51892	−	26.2185i	0.331850	−	1.02133i	0.968253	−	0.249972i	$-0.0804215\pi$
$660$	−7.11134	−	4.73893i	−0.276808	−	0.184463i
$661$	19.1538	−	8.52782i	0.744996	−	0.331694i	0.00110944	−	0.999999i	$-0.499647\pi$
$661$	19.1538	−	8.52782i	0.744996	−	0.331694i	0.743887	+	0.668306i	$0.232980\pi$
$662$	2.45029	−	11.5277i	0.0952332	−	0.448037i
$663$	10.5025	+	1.10385i	0.407881	+	0.0428701i
$664$	−0.632819	−	6.02087i	−0.0245581	−	0.233655i
$665$	6.82659	−	3.37701i	0.264724	−	0.130955i
$666$	−4.13635	+	3.00524i	−0.160280	+	0.116451i
$667$	−7.58219	−	10.4360i	−0.293583	−	0.404083i
$668$	−3.14624	−	14.8019i	−0.121732	−	0.572703i
$669$	1.09382	+	10.4070i	0.0422895	+	0.402358i
$670$	22.5796	−	3.30241i	0.872327	−	0.127583i
$671$	−40.9510	−	8.70440i	−1.58090	−	0.336030i
$672$	−1.44274	−	3.24044i	−0.0556548	−	0.125003i
$673$	4.27867	−	3.85253i	0.164931	−	0.148504i	−0.582533	−	0.812807i	$-0.697938\pi$
$673$	4.27867	−	3.85253i	0.164931	−	0.148504i	0.747463	+	0.664303i	$0.231272\pi$
$674$	−9.98965	+	30.7450i	−0.384787	+	1.18425i
$675$	−4.86472	−	1.15520i	−0.187243	−	0.0444635i
$676$	3.14165	+	5.44151i	0.120833	+	0.209289i
$677$	1.59712	+	0.922096i	0.0613822	+	0.0354390i	0.530377	−	0.847762i	$-0.322050\pi$
$677$	1.59712	+	0.922096i	0.0613822	+	0.0354390i	−0.468995	+	0.883201i	$0.655384\pi$
$678$	4.56304	−	1.48262i	0.175242	−	0.0569397i
$679$	32.0525	+	14.2707i	1.23006	+	0.547658i
$680$	3.36582	−	8.46690i	0.129073	−	0.324691i
$681$	−11.0884			−0.424909
$682$	4.15248	−	20.8695i	0.159007	−	0.799133i
$683$			45.4799i			1.74024i	0.492841	+	0.870119i	$0.335958\pi$
$683$			45.4799i			1.74024i	−0.492841	+	0.870119i	$0.664042\pi$
$684$	−0.776851	−	0.564415i	−0.0297036	−	0.0215810i
$685$	27.4092	+	4.67486i	1.04725	+	0.178617i
$686$	1.55437	+	4.78385i	0.0593460	+	0.182648i
$687$	8.03693	+	4.64012i	0.306628	+	0.177032i
$688$	−6.38156	+	3.68440i	−0.243295	+	0.140466i
$689$	18.7852	−	20.8631i	0.715660	−	0.794821i
$690$	0.914933	−	14.2288i	0.0348309	−	0.541683i
$691$	−10.0992	−	11.2163i	−0.384191	−	0.426687i	0.519767	−	0.854308i	$-0.326019\pi$
$691$	−10.0992	−	11.2163i	−0.384191	−	0.426687i	−0.903958	+	0.427621i	$0.859352\pi$
$692$	6.31012	+	14.1728i	0.239875	+	0.538768i
$693$	−2.81847	+	13.2599i	−0.107065	+	0.503701i
$694$	−1.92626	+	18.3271i	−0.0731197	+	0.695688i
$695$	−33.0286	+	12.2313i	−1.25284	+	0.463960i
$696$	−1.97879	+	0.420605i	−0.0750059	+	0.0159430i
$697$	2.34808	+	3.23186i	0.0889399	+	0.122415i
$698$	13.8777	+	19.1010i	0.525279	+	0.722984i
$699$	26.8287	−	5.70261i	1.01475	−	0.215692i
$700$	14.5914	−	10.0816i	0.551503	−	0.381050i
$701$	3.12797	−	29.7607i	0.118142	−	1.12404i	−0.761419	−	0.648259i	$-0.775497\pi$
$701$	3.12797	−	29.7607i	0.118142	−	1.12404i	0.879561	−	0.475785i	$-0.157836\pi$
$702$	0.538836	−	2.53502i	0.0203371	−	0.0956783i
$703$	−1.99689	−	4.48508i	−0.0753140	−	0.169158i
$704$	−2.55724	−	2.84011i	−0.0963798	−	0.107041i
$705$	−12.4265	−	0.799037i	−0.468007	−	0.0300935i
$706$	−23.6483	+	26.2641i	−0.890015	+	0.988462i
$707$	−20.9636	+	12.1034i	−0.788419	+	0.455194i
$708$	−2.39271	−	1.38143i	−0.0899235	−	0.0519173i
$709$	−0.449913	−	1.38469i	−0.0168968	−	0.0520031i	0.942253	−	0.334903i	$-0.108704\pi$
$709$	−0.449913	−	1.38469i	−0.0168968	−	0.0520031i	−0.959149	+	0.282900i	$0.908704\pi$
$710$	19.7491	+	3.36838i	0.741172	+	0.126413i
$711$	13.1398	+	9.54659i	0.492779	+	0.358025i
$712$			2.18197i			0.0817728i
$713$	33.6192	−	11.4100i	1.25905	−	0.427306i
$714$	−14.4535			−0.540908
$715$	20.5809	+	8.18146i	0.769683	+	0.305969i
$716$	−20.1718	−	8.98108i	−0.753857	−	0.335639i
$717$	−4.59558	+	1.49320i	−0.171625	+	0.0557644i
$718$	−17.2800	−	9.97661i	−0.644884	−	0.372324i
$719$	5.96380	+	10.3296i	0.222412	+	0.385229i	0.955540	−	0.294862i	$-0.0952736\pi$
$719$	5.96380	+	10.3296i	0.222412	+	0.385229i	−0.733128	+	0.680091i	$0.761940\pi$
$720$	−1.98018	−	1.03870i	−0.0737969	−	0.0387100i
$721$	10.1740	−	31.3123i	0.378898	−	1.16613i
$722$	−13.4345	+	12.0965i	−0.499981	+	0.450185i
$723$	2.85888	+	6.42115i	0.106323	+	0.238805i
$724$	5.69543	+	1.21060i	0.211669	+	0.0449916i
$725$	−3.89395	−	9.33543i	−0.144617	−	0.346709i
$726$	0.376900	+	3.58596i	0.0139881	+	0.133087i
$727$	−6.45536	−	30.3701i	−0.239416	−	1.12636i	−0.919457	−	0.393190i	$-0.871371\pi$
$727$	−6.45536	−	30.3701i	−0.239416	−	1.12636i	0.680041	−	0.733174i	$-0.261962\pi$
$728$	5.40344	+	7.43719i	0.200265	+	0.275641i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	14.4158	+	29.1415i	0.533554	+	1.07857i
$731$	3.13855	+	29.8613i	0.116084	+	1.10446i
$732$	−10.8946	−	1.14507i	−0.402678	−	0.0423231i
$733$	−4.41513	+	20.7715i	−0.163076	+	0.767214i	0.818250	+	0.574863i	$0.194945\pi$
$733$	−4.41513	+	20.7715i	−0.163076	+	0.767214i	−0.981326	+	0.192351i	$0.938389\pi$
$734$	34.3479	−	15.2927i	1.26780	−	0.564462i
$735$	−10.3866	−	6.92155i	−0.383116	−	0.255305i
$736$	1.97044	−	6.06438i	0.0726313	−	0.223536i
$737$	−28.9843	−	26.0976i	−1.06765	−	0.961316i
$738$	0.849036	−	0.490191i	0.0312535	−	0.0180442i
$739$	2.51628	−	4.35833i	0.0925629	−	0.160324i	−0.816026	−	0.578015i	$-0.803827\pi$
$739$	2.51628	−	4.35833i	0.0925629	−	0.160324i	0.908589	+	0.417692i	$0.137161\pi$
$740$	−6.11256	−	9.66131i	−0.224702	−	0.355157i
$741$	2.27346	+	1.01221i	0.0835177	+	0.0371845i
$742$	−22.5850	+	31.0856i	−0.829121	+	1.14119i
$743$		−	38.6295i		−	1.41718i	−0.705621	−	0.708590i	$-0.749332\pi$
$743$		−	38.6295i		−	1.41718i	0.705621	−	0.708590i	$-0.250668\pi$
$744$	0.509790	−	5.54438i	0.0186898	−	0.203267i
$745$	−2.09620	−	8.21124i	−0.0767990	−	0.300837i
$746$	−22.2799	−	16.1873i	−0.815726	−	0.592659i
$747$	−2.46240	+	5.53064i	−0.0900944	+	0.202355i
$748$	−14.8104	+	4.81219i	−0.541521	+	0.175951i
$749$	−3.00524	+	5.20522i	−0.109809	+	0.190195i
$750$	3.27579	−	10.6897i	0.119615	−	0.390332i
$751$	17.1492	−	19.0461i	0.625782	−	0.695001i	−0.344001	−	0.938969i	$-0.611783\pi$
$751$	17.1492	−	19.0461i	0.625782	−	0.695001i	0.969783	+	0.243968i	$0.0784492\pi$
$752$	−5.29620	−	1.72084i	−0.193133	−	0.0627526i
$753$	−19.6017	+	17.6495i	−0.714326	+	0.643182i
$754$	4.78964	−	2.13249i	0.174429	−	0.0776606i
$755$	1.41960	+	35.0268i	0.0516646	+	1.27475i
$756$	−0.370773	+	3.52767i	−0.0134849	+	0.128300i
$757$	38.0600	−	4.00026i	1.38331	−	0.145392i	0.616546	−	0.787319i	$-0.288531\pi$
$757$	38.0600	−	4.00026i	1.38331	−	0.145392i	0.766766	+	0.641926i	$0.221865\pi$
$758$	4.65804	+	21.9144i	0.169188	+	0.795966i
$759$	−19.7151	+	14.3239i	−0.715614	+	0.519924i
$760$	1.37094	−	1.65253i	0.0497291	−	0.0599434i
$761$	5.51856	−	1.17301i	0.200048	−	0.0425215i	−0.106798	−	0.994281i	$-0.534060\pi$
$761$	5.51856	−	1.17301i	0.200048	−	0.0425215i	0.306846	+	0.951759i	$0.400726\pi$
$762$	−15.6039	+	1.64003i	−0.565268	+	0.0594121i
$763$	21.4651	+	2.25607i	0.777088	+	0.0816753i
$764$	−1.55468	−	0.330457i	−0.0562463	−	0.0119555i
$765$	−7.14833	+	5.64964i	−0.258448	+	0.204263i
$766$	1.77558	+	1.97198i	0.0641542	+	0.0712505i
$767$	6.80994	+	2.21268i	0.245893	+	0.0798953i
$768$	−0.743145	−	0.669131i	−0.0268159	−	0.0241452i
$769$	−5.13463	−	8.89345i	−0.185160	−	0.320706i	0.758471	−	0.651707i	$-0.225947\pi$
$769$	−5.13463	−	8.89345i	−0.185160	−	0.320706i	−0.943630	+	0.331001i	$0.892614\pi$
$770$	−29.1845	−	8.19191i	−1.05174	−	0.295216i
$771$	−2.77895	−	8.55273i	−0.100081	−	0.308019i
$772$	−2.49015	+	5.59296i	−0.0896223	+	0.201295i
$773$	27.9877	−	38.5218i	1.00665	−	1.38553i	0.0854940	−	0.996339i	$-0.472753\pi$
$773$	27.9877	−	38.5218i	1.00665	−	1.38553i	0.921155	−	0.389195i	$-0.127247\pi$
$774$	7.36879			0.264866
$775$	27.7158	−	2.61422i	0.995581	−	0.0939056i
$776$	9.89140			0.355080
$777$	−10.6599	+	14.6721i	−0.382421	+	0.526357i
$778$	6.23435	−	14.0026i	0.223512	−	0.502017i
$779$	0.290909	+	0.895327i	0.0104229	+	0.0320784i
$780$	5.57949	+	1.56613i	0.199778	+	0.0560765i
$781$	−17.1207	−	29.6539i	−0.612626	−	1.06110i
$782$	−19.3087	−	17.3856i	−0.690477	−	0.621708i
$783$	1.92399	+	0.625141i	0.0687576	+	0.0223407i
$784$	−3.73504	−	4.14818i	−0.133394	−	0.148149i
$785$	−5.27871	+	4.17200i	−0.188405	+	0.148905i
$786$	−12.5131	−	2.65975i	−0.446328	−	0.0948700i
$787$	10.2010	+	1.07217i	0.363626	+	0.0382187i	0.284580	−	0.958652i	$-0.408146\pi$
$787$	10.2010	+	1.07217i	0.363626	+	0.0382187i	0.0790463	+	0.996871i	$0.474813\pi$
$788$	8.36384	−	0.879075i	0.297950	−	0.0313158i
$789$	−12.2115	+	2.59563i	−0.434740	+	0.0924068i
$790$	−23.1882	+	27.9510i	−0.824999	+	0.994453i
$791$	13.7683	−	10.0032i	0.489543	−	0.355674i
$792$	0.794585	+	3.73823i	0.0282343	+	0.132832i
$793$	28.2352	−	2.96764i	1.00266	−	0.105384i
$794$	0.884570	−	8.41612i	0.0313922	−	0.298677i
$795$	0.980895	+	24.2023i	0.0347888	+	0.858367i
$796$	−11.7727	+	5.24155i	−0.417272	+	0.185782i
$797$	−12.2633	+	11.0419i	−0.434388	+	0.391125i	−0.857109	−	0.515135i	$-0.827742\pi$
$797$	−12.2633	+	11.0419i	−0.434388	+	0.391125i	0.422721	+	0.906260i	$0.361075\pi$
$798$	−3.23937	−	1.05253i	−0.114672	−	0.0372593i
$799$	−15.1834	+	16.8628i	−0.537149	+	0.596564i
$800$	2.60194	−	4.26965i	0.0919924	−	0.150955i
$801$	1.09099	−	1.88964i	0.0385481	−	0.0667672i
$802$	−11.8416	+	3.84758i	−0.418143	+	0.135863i
$803$	22.6014	−	50.7636i	0.797587	−	1.79141i
$804$	−8.25629	−	5.99855i	−0.291177	−	0.211552i
$805$	−12.5099	−	49.0038i	−0.440917	−	1.72716i
$806$	1.69518	+	14.3298i	0.0597102	+	0.504746i
$807$		−	1.50286i		−	0.0529032i
$808$	−4.01126	+	5.52103i	−0.141116	+	0.194229i
$809$	20.2378	+	9.01044i	0.711522	+	0.316790i	0.730389	−	0.683032i	$-0.239339\pi$
$809$	20.2378	+	9.01044i	0.711522	+	0.316790i	−0.0188663	+	0.999822i	$0.506006\pi$
$810$	1.19554	+	1.88963i	0.0420069	+	0.0663947i
$811$	8.22213	−	14.2411i	0.288718	−	0.500074i	−0.684786	−	0.728744i	$-0.740104\pi$
$811$	8.22213	−	14.2411i	0.288718	−	0.500074i	0.973504	+	0.228670i	$0.0734377\pi$
$812$	−6.21441	+	3.58789i	−0.218083	+	0.125910i
$813$	−9.88266	−	8.89839i	−0.346600	−	0.312080i
$814$	−6.03815	+	18.5835i	−0.211637	+	0.651352i
$815$	43.1370	+	28.7461i	1.51102	+	1.00693i
$816$	−3.72245	+	1.65734i	−0.130312	+	0.0580186i
$817$	−1.47114	+	6.92119i	−0.0514688	+	0.242142i
$818$	34.4140	+	3.61706i	1.20326	+	0.126468i
$819$	−0.960917	−	9.14251i	−0.0335772	−	0.319465i
$820$	0.972017	+	1.96493i	0.0339443	+	0.0686182i
$821$	−24.1951	+	17.5788i	−0.844416	+	0.613504i	−0.923601	−	0.383356i	$-0.874768\pi$
$821$	−24.1951	+	17.5788i	−0.844416	+	0.613504i	0.0791850	+	0.996860i	$0.474768\pi$
$822$	−7.30897	−	10.0599i	−0.254930	−	0.350881i
$823$	−4.90931	−	23.0965i	−0.171128	−	0.805093i	−0.977040	−	0.213058i	$-0.931658\pi$
$823$	−4.90931	−	23.0965i	−0.171128	−	0.805093i	0.805912	−	0.592036i	$-0.201676\pi$
$824$	−0.970217	−	9.23100i	−0.0337991	−	0.321577i
$825$	−17.6360	+	7.35624i	−0.614007	+	0.256111i
$826$	−9.58599	−	2.03757i	−0.333539	−	0.0708960i
$827$	−8.08044	−	18.1490i	−0.280984	−	0.631101i	0.716825	−	0.697253i	$-0.245595\pi$
$827$	−8.08044	−	18.1490i	−0.280984	−	0.631101i	−0.997810	+	0.0661516i	$0.978928\pi$
$828$	−4.73864	+	4.26669i	−0.164679	+	0.148278i
$829$	−2.11547	+	6.51074i	−0.0734732	+	0.226127i	−0.981049	−	0.193762i	$-0.937931\pi$
$829$	−2.11547	+	6.51074i	−0.0734732	+	0.226127i	0.907575	+	0.419889i	$0.137931\pi$
$830$	−11.9881	−	6.28831i	−0.416112	−	0.218270i
$831$	−10.2207	−	17.7028i	−0.354554	−	0.614105i
$832$	2.24444	+	1.29583i	0.0778120	+	0.0449248i
$833$	−21.6316	+	7.02855i	−0.749492	+	0.243525i
$834$	14.3894	+	6.40656i	0.498263	+	0.221841i
$835$	−31.4441	−	12.4998i	−1.08817	−	0.432575i
$836$	−3.66979			−0.126922
$837$	−3.21368	+	4.54668i	−0.111081	+	0.157156i
$838$			7.08198i			0.244643i
$839$	−23.5034	−	17.0762i	−0.811428	−	0.589537i	0.102816	−	0.994700i	$-0.467215\pi$
$839$	−23.5034	−	17.0762i	−0.811428	−	0.589537i	−0.914244	+	0.405163i	$0.867215\pi$
$840$	−7.81865	−	1.33354i	−0.269769	−	0.0460113i
$841$	−7.69683	−	23.6884i	−0.265408	−	0.816842i
$842$	−17.7753	−	10.2626i	−0.612578	−	0.353672i
$843$	10.1308	−	5.84902i	0.348923	−	0.201451i
$844$	−2.24357	+	2.49174i	−0.0772270	+	0.0857693i
$845$	14.0210	+	0.901565i	0.482335	+	0.0310148i
$846$	3.72623	+	4.13839i	0.128110	+	0.142281i
$847$	5.20209	+	11.6841i	0.178746	+	0.401470i
$848$	−2.25220	+	10.5958i	−0.0773408	+	0.363860i
$849$	−0.528072	+	5.02427i	−0.0181234	+	0.172433i
$850$	−11.5813	−	16.7619i	−0.397234	−	0.574927i
$851$	−31.8893	+	6.77828i	−1.09315	+	0.232356i
$852$	−5.26634	−	7.24849i	−0.180422	−	0.248329i
$853$	−9.77861	−	13.4591i	−0.334813	−	0.460831i	0.608104	−	0.793857i	$-0.291930\pi$
$853$	−9.77861	−	13.4591i	−0.334813	−	0.460831i	−0.942918	+	0.333026i	$0.891930\pi$
$854$	−38.0081	+	8.07888i	−1.30061	+	0.276454i
$855$	−2.01353	+	0.745661i	−0.0688612	+	0.0255011i
$856$	−0.177121	+	1.68519i	−0.00605387	+	0.0575987i
$857$	5.79016	−	27.2406i	0.197788	−	0.930520i	−0.761516	−	0.648146i	$-0.775545\pi$
$857$	5.79016	−	27.2406i	0.197788	−	0.930520i	0.959304	−	0.282374i	$-0.0911219\pi$
$858$	−4.02858	−	9.04835i	−0.137534	−	0.308905i
$859$	1.45509	+	1.61604i	0.0496470	+	0.0551386i	0.767457	−	0.641101i	$-0.221522\pi$
$859$	1.45509	+	1.61604i	0.0496470	+	0.0551386i	−0.717810	+	0.696239i	$0.754855\pi$
$860$	−1.05732	+	16.4432i	−0.0360542	+	0.560707i
$861$	2.32691	−	2.58430i	0.0793010	−	0.0880727i
$862$	−6.97030	+	4.02430i	−0.237409	+	0.137068i
$863$	−39.3078	−	22.6944i	−1.33805	−	0.772526i	−0.351536	−	0.936175i	$-0.614340\pi$
$863$	−39.3078	−	22.6944i	−1.33805	−	0.772526i	−0.986519	+	0.163649i	$0.947674\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	34.1966	+	5.83251i	1.16272	+	0.198311i
$866$	−18.7795	−	13.6441i	−0.638153	−	0.463645i
$867$		−	0.396587i		−	0.0134688i
$868$	−4.35750	−	19.2627i	−0.147903	−	0.653819i
$869$	62.0713			2.10563
$870$	−1.67104	+	4.20360i	−0.0566536	+	0.142515i
$871$	24.1621	+	10.7577i	0.818703	+	0.364510i
$872$	5.78697	−	1.88030i	0.195971	−	0.0636750i
$873$	−8.56620	−	4.94570i	−0.289922	−	0.167387i
$874$	−3.06147	−	5.30263i	−0.103556	−	0.179364i
$875$	−0.666252	−	39.6522i	−0.0225234	−	1.34049i
$876$	4.49307	−	13.8283i	0.151807	−	0.467214i
$877$	−20.2643	+	18.2460i	−0.684275	+	0.616124i	−0.936136	−	0.351639i	$-0.885624\pi$
$877$	−20.2643	+	18.2460i	−0.684275	+	0.616124i	0.251860	+	0.967764i	$0.418958\pi$
$878$	−7.59501	−	17.0587i	−0.256319	−	0.575702i
$879$	13.5528	+	2.88074i	0.457126	+	0.0971650i
$880$	−8.45572	+	1.23670i	−0.285042	+	0.0416892i
$881$	−1.83840	−	17.4912i	−0.0619374	−	0.589295i	−0.980841	−	0.194812i	$-0.937590\pi$
$881$	−1.83840	−	17.4912i	−0.0619374	−	0.589295i	0.918903	−	0.394483i	$-0.129076\pi$
$882$	1.16055	+	5.45995i	0.0390777	+	0.183846i
$883$	−30.5627	−	42.0659i	−1.02852	−	1.41563i	−0.906057	−	0.423156i	$-0.860922\pi$
$883$	−30.5627	−	42.0659i	−1.02852	−	1.41563i	−0.122459	−	0.992474i	$-0.539078\pi$
$884$	8.54346	−	6.20719i	0.287348	−	0.208770i
$885$	−5.53745	+	2.73929i	−0.186139	+	0.0920801i
$886$	2.71149	+	25.7981i	0.0910943	+	0.866705i
$887$	−21.6247	−	2.27285i	−0.726086	−	0.0763147i	−0.265728	−	0.964048i	$-0.585612\pi$
$887$	−21.6247	−	2.27285i	−0.726086	−	0.0763147i	−0.460358	+	0.887733i	$0.652279\pi$
$888$	−1.06301	+	5.00109i	−0.0356724	+	0.167825i
$889$	−50.8419	+	22.6363i	−1.70518	+	0.759196i
$890$	4.06012	+	2.70563i	0.136095	+	0.0906928i
$891$	1.18098	−	3.63469i	0.0395644	−	0.121767i
$892$	7.77651	+	7.00200i	0.260377	+	0.234444i
$893$	−4.63094	+	2.67367i	−0.154968	+	0.0894710i
$894$	−1.89497	+	3.28219i	−0.0633774	+	0.109773i
$895$	−41.7245	+	26.3984i	−1.39470	+	0.882402i
$896$	−3.24044	−	1.44274i	−0.108255	−	0.0481984i
$897$	9.71352	−	13.3695i	0.324325	−	0.446395i
$898$			1.56408i			0.0521940i
$899$	−11.2626	+	0.146765i	−0.375629	+	0.00489488i
$900$	−4.38817	+	2.39666i	−0.146272	+	0.0798886i
$901$	35.7095	+	25.9445i	1.18966	+	0.864336i
$902$	1.52395	−	3.42284i	0.0507419	−	0.113968i
$903$	24.8586	−	8.07704i	0.827242	−	0.268787i
$904$	2.39893	−	4.15507i	0.0797872	−	0.138196i
$905$	9.31492	−	9.09667i	0.309638	−	0.302384i
$906$	10.4902	−	11.6505i	0.348512	−	0.387062i
$907$	−6.06611	−	1.97100i	−0.201422	−	0.0654460i	0.206569	−	0.978432i	$-0.433770\pi$
$907$	−6.06611	−	1.97100i	−0.201422	−	0.0654460i	−0.407991	+	0.912986i	$0.633770\pi$
$908$	−8.24031	+	7.41960i	−0.273464	+	0.246228i
$909$	6.23437	−	2.77572i	0.206781	−	0.0920649i
$910$	20.5390	−	0.832427i	0.680862	−	0.0275947i
$911$	−1.12826	+	10.7346i	−0.0373808	+	0.355654i	0.959804	+	0.280671i	$0.0905570\pi$
$911$	−1.12826	+	10.7346i	−0.0373808	+	0.355654i	−0.997185	+	0.0749833i	$0.976110\pi$
$912$	−0.954980	+	0.100372i	−0.0316225	+	0.00332366i
$913$	4.81044	+	22.6314i	0.159202	+	0.748989i
$914$	−5.39951	+	3.92298i	−0.178600	+	0.129761i
$915$	−15.6400	+	18.8524i	−0.517042	+	0.623242i
$916$	9.07745	−	1.92947i	0.299927	−	0.0637515i
$917$	−45.1283	+	4.74318i	−1.49027	+	0.156634i
$918$	4.05241	+	0.425925i	0.133749	+	0.0140576i
$919$	3.52653	+	0.749587i	0.116330	+	0.0247266i	0.265709	−	0.964053i	$-0.414394\pi$
$919$	3.52653	+	0.749587i	0.116330	+	0.0247266i	−0.149379	+	0.988780i	$0.547727\pi$
$920$	−8.84102	−	11.1863i	−0.291480	−	0.368801i
$921$	13.4391	+	14.9257i	0.442834	+	0.491817i
$922$	−8.03049	−	2.60926i	−0.264470	−	0.0859315i
$923$	17.2560	+	15.5374i	0.567989	+	0.511420i
$924$	6.77805	+	11.7399i	0.222982	+	0.386215i
$925$	−25.5569	−	0.605966i	−0.840305	−	0.0199240i
$926$	−10.9387	−	33.6660i	−0.359469	−	1.10633i
$927$	−3.77527	+	8.47939i	−0.123996	+	0.278500i
$928$	−1.18909	+	1.63664i	−0.0390337	+	0.0537253i
$929$	6.31711			0.207258			0.103629	−	0.994616i	$-0.466955\pi$
$929$	6.31711			0.207258			0.103629	+	0.994616i	$0.466955\pi$
$930$	−9.68461	−	7.82358i	−0.317571	−	0.256545i
$931$	−5.35999			−0.175667
$932$	16.1218	−	22.1897i	0.528087	−	0.726849i
$933$	−12.9984	+	29.1948i	−0.425548	+	0.955795i
$934$	12.3606	+	38.0420i	0.404451	+	1.24477i
$935$	−9.41045	+	33.5256i	−0.307755	+	1.09640i
$936$	−1.29583	−	2.24444i	−0.0423555	−	0.0733619i
$937$	−35.4180	−	31.8905i	−1.15706	−	1.04182i	−0.998516	−	0.0544664i	$-0.982654\pi$
$937$	−35.4180	−	31.8905i	−1.15706	−	1.04182i	−0.158541	−	0.987352i	$-0.550679\pi$
$938$	−34.4277	−	11.1862i	−1.12410	−	0.365243i
$939$	11.4525	+	12.7192i	0.373737	+	0.415077i
$940$	−9.76932	+	7.72112i	−0.318640	+	0.251835i
$941$	0.377805	+	0.0803049i	0.0123161	+	0.00261786i	0.214066	−	0.976819i	$-0.431329\pi$
$941$	0.377805	+	0.0803049i	0.0123161	+	0.00261786i	−0.201750	+	0.979437i	$0.564663\pi$
$942$	2.99251	+	0.314526i	0.0975014	+	0.0102478i
$943$	6.21714	−	0.653447i	0.202458	−	0.0212792i
$944$	−2.70249	+	0.574431i	−0.0879584	+	0.0186961i
$945$	6.10438	+	5.06420i	0.198576	+	0.164739i
$946$	22.7832	−	16.5530i	0.740747	−	0.538184i
$947$	10.6242	+	49.9829i	0.345240	+	1.62422i	0.717823	+	0.696226i	$0.245139\pi$
$947$	10.6242	+	49.9829i	0.345240	+	1.62422i	−0.372583	+	0.927999i	$0.621528\pi$
$948$	16.1527	−	1.69771i	0.524614	−	0.0551392i
$949$	−3.93889	+	37.4760i	−0.127862	+	1.21652i
$950$	−1.37500	−	4.60010i	−0.0446109	−	0.149247i
$951$	−11.8058	+	5.25630i	−0.382831	+	0.170447i
$952$	−10.7410	+	9.67126i	−0.348119	+	0.313447i
$953$	−4.11743	−	1.33783i	−0.133377	−	0.0433367i	0.241568	−	0.970384i	$-0.422338\pi$
$953$	−4.11743	−	1.33783i	−0.133377	−	0.0433367i	−0.374945	+	0.927047i	$0.622338\pi$
$954$	7.24834	−	8.05010i	0.234674	−	0.260632i
$955$	−2.54269	+	2.48311i	−0.0822795	+	0.0803517i
$956$	−2.41604	+	4.18471i	−0.0781404	+	0.135343i
$957$	7.35298	−	2.38913i	0.237688	−	0.0772295i
$958$	7.06868	−	15.8765i	0.228379	−	0.512947i
$959$	−35.6836	−	25.9257i	−1.15228	−	0.837184i
$960$	−2.16658	+	0.553096i	−0.0699262	+	0.0178511i
$961$	8.80802	−	29.7224i	0.284130	−	0.958786i
$962$		−	13.2507i		−	0.427219i
$963$	0.995988	−	1.37086i	0.0320953	−	0.0441753i
$964$	6.42115	+	2.85888i	0.206811	+	0.0920783i
$965$	7.31938	+	11.5688i	0.235619	+	0.372412i
$966$	−11.3090	+	19.5878i	−0.363861	+	0.630226i
$967$	1.29686	−	0.748741i	0.0417042	−	0.0240779i	−0.479003	−	0.877813i	$-0.659002\pi$
$967$	1.29686	−	0.748741i	0.0417042	−	0.0240779i	0.520707	+	0.853735i	$0.325668\pi$
$968$	2.67957	+	2.41269i	0.0861246	+	0.0775469i
$969$	−1.20910	+	3.72122i	−0.0388418	+	0.119543i
$970$	12.2653	−	18.4055i	0.393814	−	0.590965i
$971$	37.7508	−	16.8077i	1.21148	−	0.539386i	0.301273	−	0.953538i	$-0.402589\pi$
$971$	37.7508	−	16.8077i	1.21148	−	0.539386i	0.910208	+	0.414152i	$0.135922\pi$
$972$	0.207912	−	0.978148i	0.00666877	−	0.0313741i
$973$	55.5648	+	5.84010i	1.78133	+	0.187225i
$974$	0.504724	+	4.80212i	0.0161724	+	0.153870i
$975$	9.83271	−	8.44009i	0.314899	−	0.270299i
$976$	−8.86250	+	6.43898i	−0.283682	+	0.206107i
$977$	17.2038	+	23.6789i	0.550397	+	0.757557i	0.990066	−	0.140603i	$-0.0449042\pi$
$977$	17.2038	+	23.6789i	0.550397	+	0.757557i	−0.439669	+	0.898160i	$0.644904\pi$
$978$	−4.81991	−	22.6759i	−0.154124	−	0.725095i
$979$	−0.871655	−	8.29325i	−0.0278582	−	0.265053i
$980$	−12.3502	+	1.80629i	−0.394512	+	0.0576999i
$981$	−5.95181	−	1.26510i	−0.190027	−	0.0403914i
$982$	5.11757	+	11.4942i	0.163308	+	0.366796i
$983$	25.7001	−	23.1405i	0.819705	−	0.738066i	−0.148314	−	0.988940i	$-0.547385\pi$
$983$	25.7001	−	23.1405i	0.819705	−	0.738066i	0.968020	+	0.250874i	$0.0807181\pi$
$984$	0.302955	−	0.932399i	0.00965785	−	0.0297238i
$985$	8.73535	−	16.6531i	0.278331	−	0.530613i
$986$	4.12158	+	7.13879i	0.131258	+	0.227345i
$987$	17.1066	+	9.87647i	0.544508	+	0.314372i
$988$	2.36681	−	0.769024i	0.0752984	−	0.0244659i
$989$	42.9247	+	19.1113i	1.36492	+	0.607704i
$990$	7.94122	+	3.15684i	0.252388	+	0.100331i
$991$	15.3649			0.488082			0.244041	−	0.969765i	$-0.421527\pi$
$991$	15.3649			0.488082			0.244041	+	0.969765i	$0.421527\pi$
$992$	−3.33106	−	4.46139i	−0.105761	−	0.141649i
$993$			11.7852i			0.373993i
$994$	−25.7111	−	18.6802i	−0.815507	−	0.592501i
$995$	−4.84481	+	28.4056i	−0.153591	+	0.900519i
$996$	1.87080	+	5.75773i	0.0592786	+	0.182441i
$997$	9.31556	+	5.37834i	0.295027	+	0.170334i	0.640207	−	0.768203i	$-0.278849\pi$
$997$	9.31556	+	5.37834i	0.295027	+	0.170334i	−0.345180	+	0.938537i	$0.612182\pi$
$998$	36.3567	−	20.9906i	1.15085	−	0.664445i
$999$	3.42114	−	3.79956i	0.108240	−	0.120213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.a.19.1	✓	112
5.4	even	2	inner	930.2.bn.a.19.12	yes	112
31.18	even	15	inner	930.2.bn.a.49.12	yes	112
155.49	even	30	inner	930.2.bn.a.49.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.a.19.1	✓	112	1.1	even	1	trivial
930.2.bn.a.19.12	yes	112	5.4	even	2	inner
930.2.bn.a.49.1	yes	112	155.49	even	30	inner
930.2.bn.a.49.12	yes	112	31.18	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.15286 - 0.604297i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.63601 + 2.37347i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.15286 - 0.604297i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.63601 + 2.37347i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(1.75431 - 1.38651i) q^{10} +(-3.73823 - 0.794585i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(2.57746 - 0.270902i) q^{13} +(-3.46959 + 0.737484i) q^{14} +(-1.42770 + 1.72095i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.847184 + 3.98569i) q^{17} +(0.994522 - 0.104528i) q^{18} +(-0.100372 + 0.954980i) q^{19} +(0.0905513 + 2.23423i) q^{20} +(3.24044 - 1.44274i) q^{21} +(2.84011 - 2.55724i) q^{22} +(6.06438 + 1.97044i) q^{23} +(0.669131 - 0.743145i) q^{24} +(4.26965 + 2.60194i) q^{25} +(-1.29583 + 2.24444i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.44274 - 3.24044i) q^{28} +(-1.63664 - 1.18909i) q^{29} +(-0.553096 - 2.16658i) q^{30} +(4.46139 - 3.33106i) q^{31} -1.00000i q^{32} +(-2.24636 + 3.09185i) q^{33} +(-3.72245 - 1.65734i) q^{34} +(-4.24069 - 6.70270i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.42783 + 2.55641i) q^{37} +(-0.713598 - 0.642526i) q^{38} +(0.800866 - 2.46481i) q^{39} +(-1.86076 - 1.23999i) q^{40} +(0.895624 - 0.398758i) q^{41} +(-0.737484 + 3.46959i) q^{42} +(7.32843 + 0.770249i) q^{43} +(0.399481 + 3.80081i) q^{44} +(0.991467 + 2.00424i) q^{45} +(-5.15867 + 3.74800i) q^{46} +(3.27323 + 4.50522i) q^{47} +(0.207912 + 0.978148i) q^{48} +(0.583471 + 5.55135i) q^{49} +(-4.61465 + 1.92484i) q^{50} +(3.98569 + 0.847184i) q^{51} +(-1.05412 - 2.36760i) q^{52} +(8.05010 - 7.24834i) q^{53} +(0.309017 - 0.951057i) q^{54} +(7.56773 + 3.96963i) q^{55} +(1.77355 + 3.07188i) q^{56} +(0.831592 + 0.480120i) q^{57} +(1.92399 - 0.625141i) q^{58} +(2.52400 + 1.12376i) q^{59} +(2.07790 + 0.826022i) q^{60} +10.9547 q^{61} +(0.0725482 + 5.56729i) q^{62} -3.54710i q^{63} +(0.809017 + 0.587785i) q^{64} +(-5.71263 - 0.974336i) q^{65} +(-1.18098 - 3.63469i) q^{66} +(8.83808 + 5.10267i) q^{67} +(3.52882 - 2.03736i) q^{68} +(4.26669 - 4.73864i) q^{69} +(7.91521 + 0.508959i) q^{70} +(5.99516 + 6.65830i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-3.02301 + 14.2222i) q^{73} +(0.534435 - 5.08480i) q^{74} +(4.11361 - 2.84222i) q^{75} +(0.939257 - 0.199645i) q^{76} +(-7.96808 - 10.9671i) q^{77} +(1.52334 + 2.09670i) q^{78} +(-15.8867 + 3.37683i) q^{79} +(2.09690 - 0.776536i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.203833 + 0.958959i) q^{82} +(-2.46240 - 5.53064i) q^{83} +(-2.37347 - 2.63601i) q^{84} +(0.584665 - 9.09259i) q^{85} +(-4.93068 + 5.47608i) q^{86} +(-1.75197 + 1.01150i) q^{87} +(-3.30973 - 1.91087i) q^{88} +(0.674266 + 2.07518i) q^{89} +(-2.20424 - 0.375951i) q^{90} +(7.43719 + 5.40344i) q^{91} -6.37647i q^{92} +(-1.22847 - 5.43055i) q^{93} -5.56876 q^{94} +(0.793180 - 1.99529i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(9.40728 - 3.05661i) q^{97} +(-4.83409 - 2.79097i) q^{98} +(1.91087 + 3.30973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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