LMFDB - Embedded newform 783.2.bf.a.4.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(4,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(126)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.bf (of order $126$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$88$ over $\Q(\zeta_{126})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{126}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	783.4
Dual form			783.2.bf.a.196.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.91602 - 1.23750i) q^{2} +(0.932239 + 1.45977i) q^{3} +(1.31716 + 2.91914i) q^{4} +(1.16159 + 0.489651i) q^{5} +(0.0202736 - 3.95060i) q^{6} +(1.07427 - 2.38083i) q^{7} +(0.408806 - 2.71225i) q^{8} +(-1.26186 + 2.72171i) q^{9} +(-1.61969 - 2.37565i) q^{10} +(3.16148 + 2.79002i) q^{11} +(-3.03336 + 4.64409i) q^{12} +(1.51730 + 0.927204i) q^{13} +(-5.00459 + 3.23231i) q^{14} +(0.368101 + 2.15213i) q^{15} +(0.0984645 - 0.111574i) q^{16} +(1.58489 + 0.915038i) q^{17} +(5.78587 - 3.65331i) q^{18} +(1.16821 - 0.0875453i) q^{19} +(0.100646 + 4.03579i) q^{20} +(4.47694 - 0.651311i) q^{21} +(-2.60482 - 9.25807i) q^{22} +(0.133714 - 0.260818i) q^{23} +(4.34037 - 1.93170i) q^{24} +(-2.38165 - 2.44179i) q^{25} +(-1.75977 - 3.65420i) q^{26} +(-5.14943 + 0.695255i) q^{27} +8.36494 q^{28} +(-4.96346 + 2.08904i) q^{29} +(1.95796 - 4.57905i) q^{30} +(-2.71354 - 3.58237i) q^{31} +(-5.60747 + 1.57770i) q^{32} +(-1.12554 + 7.21601i) q^{33} +(-1.90433 - 3.71453i) q^{34} +(2.41363 - 2.23953i) q^{35} +(-9.60712 - 0.0986057i) q^{36} +(11.1695 - 4.38371i) q^{37} +(-2.34665 - 1.27792i) q^{38} +(0.0609826 + 3.07929i) q^{39} +(1.80292 - 2.95035i) q^{40} +(2.56463 + 7.04626i) q^{41} +(-9.38390 - 4.29227i) q^{42} +(2.27847 + 5.40518i) q^{43} +(-3.98027 + 12.9037i) q^{44} +(-2.79845 + 2.54364i) q^{45} +(-0.578960 + 0.334263i) q^{46} +(-0.109086 + 0.539616i) q^{47} +(0.254665 + 0.0397221i) q^{48} +(0.117525 + 0.133172i) q^{49} +(1.54159 + 7.62581i) q^{50} +(0.141752 + 3.16661i) q^{51} +(-0.708098 + 5.65049i) q^{52} +(-0.547609 + 2.39923i) q^{53} +(10.7268 + 5.04028i) q^{54} +(2.30621 + 4.78888i) q^{55} +(-6.01823 - 3.88699i) q^{56} +(1.21685 + 1.62371i) q^{57} +(12.0953 + 2.13963i) q^{58} +(-0.931502 + 5.28281i) q^{59} +(-5.79750 + 3.90924i) q^{60} +(-9.20291 - 4.15251i) q^{61} +(0.766025 + 10.2219i) q^{62} +(5.12434 + 5.92812i) q^{63} +(12.4120 + 3.82861i) q^{64} +(1.30848 + 1.81998i) q^{65} +(11.0864 - 12.4332i) q^{66} +(0.0515777 - 0.153513i) q^{67} +(-0.583557 + 5.83177i) q^{68} +(0.505387 - 0.0479535i) q^{69} +(-7.39598 + 1.30411i) q^{70} +(11.4917 - 1.73210i) q^{71} +(6.86611 + 4.53514i) q^{72} +(4.97438 + 5.36111i) q^{73} +(-26.8259 - 5.42296i) q^{74} +(1.34418 - 5.75299i) q^{75} +(1.79428 + 3.29485i) q^{76} +(10.0388 - 4.52970i) q^{77} +(3.69377 - 5.97545i) q^{78} +(-1.81922 - 2.97702i) q^{79} +(0.169008 - 0.0813898i) q^{80} +(-5.81541 - 6.86884i) q^{81} +(3.80585 - 16.6745i) q^{82} +(-6.01639 - 6.16830i) q^{83} +(7.79812 + 12.2109i) q^{84} +(1.39295 + 1.83894i) q^{85} +(2.32329 - 13.1760i) q^{86} +(-7.67665 - 5.29803i) q^{87} +(8.85968 - 7.43415i) q^{88} +(0.325490 + 1.05521i) q^{89} +(8.50965 - 1.41059i) q^{90} +(3.83750 - 2.61636i) q^{91} +(0.937486 + 0.0467880i) q^{92} +(2.69977 - 7.30077i) q^{93} +(0.876785 - 0.898923i) q^{94} +(1.39985 + 0.470324i) q^{95} +(-7.53058 - 6.71483i) q^{96} +(15.1877 + 4.27316i) q^{97} +(-0.0603804 - 0.400598i) q^{98} +(-11.5830 + 5.08401i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) $ 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.91602	−	1.23750i	−1.35483	−	0.875043i	−0.356587	−	0.934262i	$-0.616060\pi$
$2$	−1.91602	−	1.23750i	−1.35483	−	0.875043i	−0.998245	+	0.0592187i	$0.981139\pi$
$3$	0.932239	+	1.45977i	0.538228	+	0.842799i
$3$	0.932239	+	1.45977i	0.538228	+	0.842799i
$4$	1.31716	+	2.91914i	0.658582	+	1.45957i
$5$	1.16159	+	0.489651i	0.519479	+	0.218979i	0.632424	−	0.774623i	$-0.282060\pi$
$5$	1.16159	+	0.489651i	0.519479	+	0.218979i	−0.112945	+	0.993601i	$0.536028\pi$
$6$	0.0202736	−	3.95060i	0.00827665	−	1.61282i
$7$	1.07427	−	2.38083i	0.406036	−	0.899867i	−0.589701	−	0.807622i	$-0.700754\pi$
$7$	1.07427	−	2.38083i	0.406036	−	0.899867i	0.995736	−	0.0922456i	$-0.0294045\pi$
$8$	0.408806	−	2.71225i	0.144535	−	0.958926i
$9$	−1.26186	+	2.72171i	−0.420620	+	0.907237i
$10$	−1.61969	−	2.37565i	−0.512191	−	0.751246i
$11$	3.16148	+	2.79002i	0.953222	+	0.841224i	0.987408	−	0.158192i	$-0.0505664\pi$
$11$	3.16148	+	2.79002i	0.953222	+	0.841224i	−0.0341860	+	0.999415i	$0.510884\pi$
$12$	−3.03336	+	4.64409i	−0.875655	+	1.34063i
$13$	1.51730	+	0.927204i	0.420824	+	0.257160i	0.715745	−	0.698361i	$-0.246087\pi$
$13$	1.51730	+	0.927204i	0.420824	+	0.257160i	−0.294922	+	0.955521i	$0.595294\pi$
$14$	−5.00459	+	3.23231i	−1.33753	+	0.863871i
$15$	0.368101	+	2.15213i	0.0950432	+	0.555677i
$16$	0.0984645	−	0.111574i	0.0246161	−	0.0278935i
$17$	1.58489	+	0.915038i	0.384393	+	0.221929i	0.679728	−	0.733464i	$-0.262098\pi$
$17$	1.58489	+	0.915038i	0.384393	+	0.221929i	−0.295335	+	0.955394i	$0.595431\pi$
$18$	5.78587	−	3.65331i	1.36374	−	0.861092i
$19$	1.16821	−	0.0875453i	0.268006	−	0.0200843i	0.0599506	−	0.998201i	$-0.480906\pi$
$19$	1.16821	−	0.0875453i	0.268006	−	0.0200843i	0.208055	+	0.978117i	$0.433287\pi$
$20$	0.100646	+	4.03579i	0.0225052	+	0.902430i
$21$	4.47694	−	0.651311i	0.976947	−	0.142128i
$22$	−2.60482	−	9.25807i	−0.555349	−	1.97383i
$23$	0.133714	−	0.260818i	0.0278812	−	0.0543843i	−0.875516	−	0.483190i	$-0.839478\pi$
$23$	0.133714	−	0.260818i	0.0278812	−	0.0543843i	0.903397	+	0.428805i	$0.141065\pi$
$24$	4.34037	−	1.93170i	0.885975	−	0.394307i
$25$	−2.38165	−	2.44179i	−0.476330	−	0.488357i
$26$	−1.75977	−	3.65420i	−0.345119	−	0.716648i
$27$	−5.14943	+	0.695255i	−0.991008	+	0.133802i
$28$	8.36494			1.58083
$29$	−4.96346	+	2.08904i	−0.921691	+	0.387925i
$29$	−4.96346	+	2.08904i	−0.921691	+	0.387925i
$30$	1.95796	−	4.57905i	0.357474	−	0.836015i
$31$	−2.71354	−	3.58237i	−0.487366	−	0.643412i	0.485649	−	0.874154i	$-0.338583\pi$
$31$	−2.71354	−	3.58237i	−0.487366	−	0.643412i	−0.973015	+	0.230741i	$0.925885\pi$
$32$	−5.60747	+	1.57770i	−0.991271	+	0.278900i
$33$	−1.12554	+	7.21601i	−0.195931	+	1.25615i
$34$	−1.90433	−	3.71453i	−0.326590	−	0.637037i
$35$	2.41363	−	2.23953i	0.407979	−	0.378549i
$36$	−9.60712	−	0.0986057i	−1.60119	−	0.0164343i
$37$	11.1695	−	4.38371i	1.83626	−	0.720677i	0.857878	−	0.513853i	$-0.171782\pi$
$37$	11.1695	−	4.38371i	1.83626	−	0.720677i	0.978378	−	0.206824i	$-0.0663129\pi$
$38$	−2.34665	−	1.27792i	−0.380678	−	0.207306i
$39$	0.0609826	+	3.07929i	0.00976503	+	0.493081i
$40$	1.80292	−	2.95035i	0.285067	−	0.466492i
$41$	2.56463	+	7.04626i	0.400528	+	1.10044i	0.962025	+	0.272962i	$0.0880034\pi$
$41$	2.56463	+	7.04626i	0.400528	+	1.10044i	−0.561497	+	0.827479i	$0.689774\pi$
$42$	−9.38390	−	4.29227i	−1.44797	−	0.662312i
$43$	2.27847	+	5.40518i	0.347464	+	0.824282i	0.997903	+	0.0647236i	$0.0206166\pi$
$43$	2.27847	+	5.40518i	0.347464	+	0.824282i	−0.650439	+	0.759558i	$0.725415\pi$
$44$	−3.98027	+	12.9037i	−0.600048	+	1.94531i
$45$	−2.79845	+	2.54364i	−0.417169	+	0.379183i
$46$	−0.578960	+	0.334263i	−0.0853630	+	0.0492843i
$47$	−0.109086	+	0.539616i	−0.0159118	+	0.0787111i	−0.987338	−	0.158631i	$-0.949292\pi$
$47$	−0.109086	+	0.539616i	−0.0159118	+	0.0787111i	0.971426	+	0.237342i	$0.0762762\pi$
$48$	0.254665	+	0.0397221i	0.0367577	+	0.00573340i
$49$	0.117525	+	0.133172i	0.0167893	+	0.0190246i
$50$	1.54159	+	7.62581i	0.218014	+	1.07845i
$51$	0.141752	+	3.16661i	0.0198493	+	0.443415i
$52$	−0.708098	+	5.65049i	−0.0981955	+	0.783582i
$53$	−0.547609	+	2.39923i	−0.0752199	+	0.329560i	−0.998512	−	0.0545397i	$-0.982631\pi$
$53$	−0.547609	+	2.39923i	−0.0752199	+	0.329560i	0.923292	+	0.384099i	$0.125488\pi$
$54$	10.7268	+	5.04028i	1.45973	+	0.685896i
$55$	2.30621	+	4.78888i	0.310969	+	0.645733i
$56$	−6.01823	−	3.88699i	−0.804220	−	0.519420i
$57$	1.21685	+	1.62371i	0.161175	+	0.215065i
$58$	12.0953	+	2.13963i	1.58819	+	0.280947i
$59$	−0.931502	+	5.28281i	−0.121271	+	0.687763i	0.862182	+	0.506599i	$0.169098\pi$
$59$	−0.931502	+	5.28281i	−0.121271	+	0.687763i	−0.983453	+	0.181164i	$0.942013\pi$
$60$	−5.79750	+	3.90924i	−0.748454	+	0.504681i
$61$	−9.20291	−	4.15251i	−1.17831	−	0.531675i	−0.275329	−	0.961350i	$-0.588787\pi$
$61$	−9.20291	−	4.15251i	−1.17831	−	0.531675i	−0.902983	+	0.429676i	$0.858628\pi$
$62$	0.766025	+	10.2219i	0.0972853	+	1.29818i
$63$	5.12434	+	5.92812i	0.645606	+	0.746873i
$64$	12.4120	+	3.82861i	1.55151	+	0.478576i
$65$	1.30848	+	1.81998i	0.162296	+	0.225741i
$66$	11.0864	−	12.4332i	1.36464	−	1.53042i
$67$	0.0515777	−	0.153513i	0.00630122	−	0.0187546i	−0.944730	−	0.327848i	$-0.893676\pi$
$67$	0.0515777	−	0.153513i	0.00630122	−	0.0187546i	0.951032	+	0.309094i	$0.100026\pi$
$68$	−0.583557	+	5.83177i	−0.0707666	+	0.707206i
$69$	0.505387	−	0.0479535i	0.0608415	−	0.00577292i
$70$	−7.39598	+	1.30411i	−0.883989	+	0.155871i
$71$	11.4917	−	1.73210i	1.36381	−	0.205562i	0.573973	−	0.818874i	$-0.305401\pi$
$71$	11.4917	−	1.73210i	1.36381	−	0.205562i	0.789841	+	0.613312i	$0.210163\pi$
$72$	6.86611	+	4.53514i	0.809178	+	0.534471i
$73$	4.97438	+	5.36111i	0.582207	+	0.627470i	0.953626	−	0.300995i	$-0.0973189\pi$
$73$	4.97438	+	5.36111i	0.582207	+	0.627470i	−0.371418	+	0.928466i	$0.621128\pi$
$74$	−26.8259	−	5.42296i	−3.11844	−	0.630407i
$75$	1.34418	−	5.75299i	0.155213	−	0.664299i
$76$	1.79428	+	3.29485i	0.205818	+	0.377946i
$77$	10.0388	−	4.52970i	1.14403	−	0.516207i
$78$	3.69377	−	5.97545i	0.418237	−	0.676586i
$79$	−1.81922	−	2.97702i	−0.204678	−	0.334941i	0.734356	−	0.678764i	$-0.237484\pi$
$79$	−1.81922	−	2.97702i	−0.204678	−	0.334941i	−0.939034	+	0.343823i	$0.888278\pi$
$80$	0.169008	−	0.0813898i	0.0188956	−	0.00909965i
$81$	−5.81541	−	6.86884i	−0.646157	−	0.763205i
$82$	3.80585	−	16.6745i	0.420286	−	1.84139i
$83$	−6.01639	−	6.16830i	−0.660384	−	0.677058i	0.300572	−	0.953759i	$-0.402822\pi$
$83$	−6.01639	−	6.16830i	−0.660384	−	0.677058i	−0.960956	+	0.276701i	$0.910759\pi$
$84$	7.79812	+	12.2109i	0.850845	+	1.33232i
$85$	1.39295	+	1.83894i	0.151086	+	0.199461i
$86$	2.32329	−	13.1760i	0.250527	−	1.42081i
$87$	−7.67665	−	5.29803i	−0.823023	−	0.568008i
$88$	8.85968	−	7.43415i	0.944445	−	0.792484i
$89$	0.325490	+	1.05521i	0.0345018	+	0.111852i	0.971186	−	0.238324i	$-0.0765980\pi$
$89$	0.325490	+	1.05521i	0.0345018	+	0.111852i	−0.936684	+	0.350176i	$0.886122\pi$
$90$	8.50965	−	1.41059i	0.896995	−	0.148689i
$91$	3.83750	−	2.61636i	0.402279	−	0.274269i
$92$	0.937486	+	0.0467880i	0.0977397	+	0.00487798i
$93$	2.69977	−	7.30077i	0.279953	−	0.757054i
$94$	0.876785	−	0.898923i	0.0904334	−	0.0927168i
$95$	1.39985	+	0.470324i	0.143621	+	0.0482542i
$96$	−7.53058	−	6.71483i	−0.768587	−	0.685330i
$97$	15.1877	+	4.27316i	1.54208	+	0.433874i	0.933190	−	0.359382i	$-0.117013\pi$
$97$	15.1877	+	4.27316i	1.54208	+	0.433874i	0.608888	+	0.793256i	$0.291616\pi$
$98$	−0.0603804	−	0.400598i	−0.00609934	−	0.0404665i
$99$	−11.5830	+	5.08401i	−1.16413	+	0.510962i
$100$	3.99088	−	10.1686i	0.399088	−	1.01686i
$101$	−2.74892	+	3.62908i	−0.273528	+	0.361107i	−0.913179	−	0.407558i	$-0.866380\pi$
$101$	−2.74892	+	3.62908i	−0.273528	+	0.361107i	0.639651	+	0.768665i	$0.279079\pi$
$102$	3.64708	−	6.24272i	0.361115	−	0.618121i
$103$	−3.25361	+	1.77182i	−0.320588	+	0.174583i	−0.630514	−	0.776178i	$-0.717156\pi$
$103$	−3.25361	+	1.77182i	−0.320588	+	0.174583i	0.309926	+	0.950761i	$0.399696\pi$
$104$	3.13509	−	3.73626i	0.307421	−	0.366370i
$105$	5.51928	+	1.43558i	0.538626	+	0.140098i
$106$	4.01827	−	3.91931i	0.390289	−	0.380677i
$107$	−0.475897	+	0.596756i	−0.0460067	+	0.0576906i	−0.804303	−	0.594220i	$-0.797461\pi$
$107$	−0.475897	+	0.596756i	−0.0460067	+	0.0576906i	0.758296	+	0.651911i	$0.226032\pi$
$108$	−8.81219	−	14.1161i	−0.847953	−	1.35832i
$109$	−6.34220	+	3.05424i	−0.607472	+	0.292543i	−0.712221	−	0.701956i	$-0.752310\pi$
$109$	−6.34220	+	3.05424i	−0.607472	+	0.292543i	0.104749	+	0.994499i	$0.466596\pi$
$110$	1.50750	−	12.0295i	0.143734	−	1.14697i
$111$	16.8119	+	12.2183i	1.59571	+	1.15971i
$112$	−0.159860	−	0.354287i	−0.0151054	−	0.0334770i
$113$	12.3074	−	3.46276i	1.15778	−	0.325749i	0.362497	−	0.931985i	$-0.381924\pi$
$113$	12.3074	−	3.46276i	1.15778	−	0.325749i	0.795285	+	0.606235i	$0.207321\pi$
$114$	−0.322172	−	4.61690i	−0.0301742	−	0.432413i
$115$	0.283030	−	0.237490i	0.0263927	−	0.0221461i
$116$	−12.6359	−	11.7374i	−1.17321	−	1.08979i
$117$	−4.43820	+	2.95965i	−0.410312	+	0.273620i
$118$	8.32225	−	8.96925i	0.766125	−	0.825686i
$119$	3.88115	−	2.79035i	0.355784	−	0.255791i
$120$	5.98759	−	0.118579i	0.546590	−	0.0108247i
$121$	0.842950	+	6.72658i	0.0766318	+	0.611508i
$122$	12.4943	+	19.3449i	1.13118	+	1.75140i
$123$	−7.89508	+	10.3126i	−0.711875	+	0.929853i
$124$	6.88324	−	12.6398i	0.618134	−	1.13508i
$125$	−3.87358	−	9.86971i	−0.346463	−	0.882774i
$126$	−2.48230	−	17.6998i	−0.221141	−	1.57682i
$127$	14.4903	+	5.68701i	1.28580	+	0.504640i	0.907114	−	0.420884i	$-0.138280\pi$
$127$	14.4903	+	5.68701i	1.28580	+	0.504640i	0.378688	+	0.925524i	$0.376375\pi$
$128$	−11.5551	−	13.7709i	−1.02134	−	1.21718i
$129$	−5.76624	+	8.36497i	−0.507689	+	0.736494i
$130$	−0.254848	−	5.10635i	−0.0223516	−	0.447857i
$131$	4.66247	+	2.39031i	0.407362	+	0.208842i	0.647780	−	0.761827i	$-0.275697\pi$
$131$	4.66247	+	2.39031i	0.407362	+	0.208842i	−0.240419	+	0.970669i	$0.577285\pi$
$132$	−22.5470	+	6.21906i	−1.96247	+	0.541300i
$133$	1.04654	−	2.87535i	0.0907468	−	0.249325i
$134$	−0.288796	+	0.230307i	−0.0249482	+	0.0198955i
$135$	−6.32196	−	1.71382i	−0.544107	−	0.147502i
$136$	3.12973	−	3.92455i	0.268372	−	0.336528i
$137$	−3.23258	−	5.28988i	−0.276178	−	0.451945i	0.684737	−	0.728791i	$-0.259917\pi$
$137$	−3.23258	−	5.28988i	−0.276178	−	0.451945i	−0.960914	+	0.276846i	$0.910711\pi$
$138$	−1.02768	−	0.533536i	−0.0874816	−	0.0454176i
$139$	−8.53135	+	16.6410i	−0.723619	+	1.41147i	0.180232	+	0.983624i	$0.442315\pi$
$139$	−8.53135	+	16.6410i	−0.723619	+	1.41147i	−0.903851	+	0.427848i	$0.859272\pi$
$140$	9.71663	+	4.09590i	0.821205	+	0.346167i
$141$	−0.889410	+	0.343811i	−0.0749018	+	0.0289541i
$142$	−24.1618	−	10.9022i	−2.02761	−	0.914895i
$143$	2.21000	+	7.16464i	0.184809	+	0.599138i
$144$	0.179423	+	0.408783i	0.0149519	+	0.0340652i
$145$	−6.78840	−	0.00375806i	−0.563746	−	0.000312090i
$146$	−2.89666	−	16.4278i	−0.239729	−	1.35957i
$147$	−0.0848393	+	0.295708i	−0.00699743	+	0.0243896i
$148$	27.5087	+	26.8313i	2.26120	+	2.20552i
$149$	11.7326	+	1.17403i	0.961176	+	0.0961801i	0.567772	−	0.823186i	$-0.307805\pi$
$149$	11.7326	+	1.17403i	0.961176	+	0.0961801i	0.393404	+	0.919366i	$0.371298\pi$
$150$	−9.69480	+	9.35944i	−0.791577	+	0.764195i
$151$	5.15414	−	2.17265i	0.419438	−	0.176808i	−0.168522	−	0.985698i	$-0.553900\pi$
$151$	5.15414	−	2.17265i	0.419438	−	0.176808i	0.587960	+	0.808890i	$0.299931\pi$
$152$	0.240127	−	3.20427i	0.0194769	−	0.259901i
$153$	−4.49038	+	3.15897i	−0.363026	+	0.255387i
$154$	−24.8401	−	3.74405i	−2.00168	−	0.301704i
$155$	−1.39791	−	5.48993i	−0.112283	−	0.440962i
$156$	−8.90853	+	4.23394i	−0.713254	+	0.338987i
$157$	−7.32455	−	1.29152i	−0.584563	−	0.103074i	−0.126457	−	0.991972i	$-0.540361\pi$
$157$	−7.32455	−	1.29152i	−0.584563	−	0.103074i	−0.458106	+	0.888898i	$0.651472\pi$
$158$	−0.198393	+	7.95532i	−0.0157833	+	0.632891i
$159$	−4.01283	+	1.43727i	−0.318238	+	0.113983i
$160$	−7.28610	−	0.913067i	−0.576017	−	0.0721843i
$161$	−0.477318	−	0.598538i	−0.0376179	−	0.0471714i
$162$	2.64228	+	20.3574i	0.207597	+	1.59943i
$163$	−4.01387	+	3.20095i	−0.314391	+	0.250718i	−0.767953	−	0.640507i	$-0.778724\pi$
$163$	−4.01387	+	3.20095i	−0.314391	+	0.250718i	0.453562	+	0.891225i	$0.350153\pi$
$164$	−17.1910	+	16.7676i	−1.34239	+	1.30933i
$165$	−4.84074	+	7.83092i	−0.376851	+	0.609636i
$166$	3.89427	+	19.2639i	0.302254	+	1.49517i
$167$	−6.07990	−	21.6092i	−0.470477	−	1.67217i	−0.712318	−	0.701857i	$-0.752354\pi$
$167$	−6.07990	−	21.6092i	−0.470477	−	1.67217i	0.241841	−	0.970316i	$-0.422249\pi$
$168$	0.0636793	−	12.4088i	0.00491297	−	0.957363i
$169$	−4.48824	−	8.75464i	−0.345249	−	0.673434i
$170$	−0.393225	−	5.24722i	−0.0301590	−	0.402444i
$171$	−1.23585	+	3.29000i	−0.0945076	+	0.251593i
$172$	−12.7773	+	13.7707i	−0.974262	+	1.05000i
$173$	−0.0160017	−	0.0907504i	−0.00121659	−	0.00689963i	0.984193	−	0.177097i	$-0.0566706\pi$
$173$	−0.0160017	−	0.0907504i	−0.00121659	−	0.00689963i	−0.985410	+	0.170197i	$0.945559\pi$
$174$	8.15232	+	19.6510i	0.618026	+	1.48974i
$175$	−8.37201	+	3.04716i	−0.632864	+	0.230344i
$176$	0.622587	−	0.0780203i	0.0469293	−	0.00588100i
$177$	−8.58008	+	3.56506i	−0.644918	+	0.267966i
$178$	0.682177	−	2.42460i	0.0511313	−	0.181732i
$179$	−10.4493	−	9.69554i	−0.781018	−	0.724679i	0.185117	−	0.982716i	$-0.440734\pi$
$179$	−10.4493	−	9.69554i	−0.781018	−	0.724679i	−0.966135	+	0.258038i	$0.916924\pi$
$180$	−11.1112	−	4.81868i	−0.828184	−	0.359163i
$181$	−15.6563	−	10.6743i	−1.16372	−	0.793412i	−0.181918	−	0.983314i	$-0.558231\pi$
$181$	−15.6563	−	10.6743i	−1.16372	−	0.793412i	−0.981803	+	0.189902i	$0.939183\pi$
$182$	−10.5905	+	0.264110i	−0.785019	+	0.0195771i
$183$	−2.51760	−	17.3053i	−0.186106	−	1.27924i
$184$	−0.652741	−	0.469289i	−0.0481207	−	0.0345964i
$185$	15.1209	+	0.377091i	1.11171	+	0.0277243i
$186$	−14.2075	+	10.6475i	−1.04175	+	0.780710i
$187$	2.45763	+	7.31476i	0.179720	+	0.534908i
$188$	−1.71890	+	0.392327i	−0.125363	+	0.0286134i
$189$	−3.87659	+	13.0068i	−0.281981	+	0.946104i
$190$	−2.10011	−	2.63346i	−0.152358	−	0.191051i
$191$	7.60227	−	20.8871i	0.550081	−	1.51134i	−0.283519	−	0.958967i	$-0.591502\pi$
$191$	7.60227	−	20.8871i	0.550081	−	1.51134i	0.833600	−	0.552369i	$-0.186276\pi$
$192$	5.98210	+	21.6879i	0.431721	+	1.56519i
$193$	−11.2915	+	5.09493i	−0.812781	+	0.366741i	−0.774538	−	0.632528i	$-0.782017\pi$
$193$	−11.2915	+	5.09493i	−0.812781	+	0.366741i	−0.0382434	+	0.999268i	$0.512176\pi$
$194$	−23.8120	−	26.9822i	−1.70960	−	1.93721i
$195$	−1.43694	+	3.60673i	−0.102901	+	0.258283i
$196$	−0.233948	+	0.518481i	−0.0167105	+	0.0370344i
$197$	−19.9730	+	18.5323i	−1.42302	+	1.32037i	−0.547831	+	0.836589i	$0.684546\pi$
$197$	−19.9730	+	18.5323i	−1.42302	+	1.32037i	−0.875189	+	0.483781i	$0.839263\pi$
$198$	28.4847	+	4.59285i	2.02432	+	0.326399i
$199$	12.1277	−	8.26854i	0.859712	−	0.586141i	−0.0512253	−	0.998687i	$-0.516313\pi$
$199$	12.1277	−	8.26854i	0.859712	−	0.586141i	0.910937	+	0.412546i	$0.135360\pi$
$200$	−7.59638	+	5.46142i	−0.537145	+	0.386181i
$201$	0.272177	−	0.0678194i	0.0191979	−	0.00478361i
$202$	9.75797	−	3.55161i	0.686568	−	0.249890i
$203$	−0.358457	+	14.0613i	−0.0251587	+	0.986911i
$204$	−9.05706	+	4.58474i	−0.634121	+	0.320996i
$205$	−0.471163	+	9.44064i	−0.0329074	+	0.659363i
$206$	8.42662	+	0.631488i	0.587110	+	0.0439978i
$207$	0.541143	+	0.693046i	0.0376120	+	0.0481700i
$208$	0.252852	−	0.0779945i	0.0175321	−	0.00540795i
$209$	3.93753	+	2.98256i	0.272365	+	0.206308i
$210$	−8.79853	−	9.58070i	−0.607156	−	0.661131i
$211$	17.2401	−	15.2145i	1.18686	−	1.04741i	0.188999	−	0.981977i	$-0.439476\pi$
$211$	17.2401	−	15.2145i	1.18686	−	1.04741i	0.997857	−	0.0654299i	$-0.0208419\pi$
$212$	−7.72497	+	1.56164i	−0.530553	+	0.107254i
$213$	13.2415	+	15.1605i	0.907291	+	1.03878i
$214$	1.65031	−	0.554476i	0.112813	−	0.0379032i
$215$			7.39425i			0.504284i
$216$	−0.219411	+	14.2508i	−0.0149290	+	0.969642i
$217$	−11.4441	+	2.61203i	−0.776874	+	0.177316i
$218$	15.9314	+	1.99646i	1.07901	+	0.135218i
$219$	−3.18868	+	12.2593i	−0.215471	+	0.828406i
$220$	−10.9418	+	13.0399i	−0.737693	+	0.879148i
$221$	1.55633	+	2.85791i	0.104690	+	0.192244i
$222$	−17.0918	−	44.2151i	−1.14713	−	2.96752i
$223$	−0.0138671	−	0.556052i	−0.000928608	−	0.0372360i	0.999051	−	0.0435444i	$-0.0138650\pi$
$223$	−0.0138671	−	0.556052i	−0.000928608	−	0.0372360i	−0.999980	+	0.00630837i	$0.997992\pi$
$224$	−2.26771	+	15.0453i	−0.151518	+	1.00526i
$225$	9.65115	−	3.40097i	0.643410	−	0.226731i
$226$	−27.8664	−	8.59565i	−1.85365	−	0.571774i
$227$	1.46682	+	0.0732061i	0.0973565	+	0.00485886i	0.0984649	−	0.995141i	$-0.468607\pi$
$227$	1.46682	+	0.0732061i	0.0973565	+	0.00485886i	−0.00110841	+	0.999999i	$0.500353\pi$
$228$	−3.13703	+	5.69083i	−0.207755	+	0.376884i
$229$	−13.8555	−	13.5143i	−0.915597	−	0.893048i	0.0789987	−	0.996875i	$-0.474828\pi$
$229$	−13.8555	−	13.5143i	−0.915597	−	0.893048i	−0.994595	+	0.103827i	$0.966891\pi$
$230$	−0.836186	+	0.104788i	−0.0551365	+	0.00690950i
$231$	15.9709	+	10.4316i	1.05081	+	0.686352i
$232$	3.63690	+	14.3162i	0.238775	+	0.939902i
$233$	−8.00273	+	13.8611i	−0.524276	+	0.908073i	0.475324	+	0.879811i	$0.342331\pi$
$233$	−8.00273	+	13.8611i	−0.524276	+	0.908073i	−0.999601	+	0.0282623i	$0.991003\pi$
$234$	12.1663	−	0.178490i	0.795333	−	0.0116682i
$235$	−0.390936	+	0.573398i	−0.0255019	+	0.0374044i
$236$	−16.6482	+	4.23915i	−1.08370	+	0.275945i
$237$	2.64982	−	5.43094i	0.172124	−	0.352778i
$238$	−10.8894	+	0.543468i	−0.705856	+	0.0352278i
$239$	−8.17813	−	2.08241i	−0.528999	−	0.134700i	−0.0271112	−	0.999632i	$-0.508631\pi$
$239$	−8.17813	−	2.08241i	−0.528999	−	0.134700i	−0.501888	+	0.864933i	$0.667361\pi$
$240$	0.276366	+	0.170838i	0.0178393	+	0.0110275i
$241$	−19.8349	+	12.1208i	−1.27768	+	0.780772i	−0.984517	−	0.175291i	$-0.943913\pi$
$241$	−19.8349	+	12.1208i	−1.27768	+	0.780772i	−0.293161	+	0.956063i	$0.594707\pi$
$242$	6.70902	−	13.9314i	0.431272	−	0.895546i
$243$	4.60558	−	14.8926i	0.295448	−	0.955359i
$244$		−	32.3341i		−	2.06998i
$245$	0.0713080	+	0.212238i	0.00455570	+	0.0135594i
$246$	27.8889	−	9.98896i	1.77813	−	0.636873i
$247$	1.85370	+	0.950336i	0.117948	+	0.0604685i
$248$	−10.8256	+	5.89531i	−0.687426	+	0.374352i
$249$	3.39559	−	14.5329i	0.215187	−	0.920983i
$250$	−4.79189	+	23.7041i	−0.303066	+	1.49918i
$251$	−22.5894	+	1.69284i	−1.42583	+	0.106851i	−0.765166	−	0.643833i	$-0.777343\pi$
$251$	−22.5894	+	1.69284i	−1.42583	+	0.106851i	−0.660662	+	0.750684i	$0.729724\pi$
$252$	−10.5554	+	22.7669i	−0.664928	+	1.43418i
$253$	1.15042	−	0.451507i	0.0723264	−	0.0283860i
$254$	−20.7260	−	28.8281i	−1.30046	−	1.80884i
$255$	−1.38588	+	3.74771i	−0.0867870	+	0.234691i
$256$	1.86823	+	14.9081i	0.116764	+	0.931758i
$257$	6.02042	+	0.602434i	0.375544	+	0.0375788i	0.285551	−	0.958364i	$-0.407823\pi$
$257$	6.02042	+	0.602434i	0.375544	+	0.0375788i	0.0899930	+	0.995942i	$0.471316\pi$
$258$	21.3999	−	8.89175i	1.33230	−	0.553576i
$259$	1.56222	−	31.3019i	0.0970713	−	1.94501i
$260$	−3.58929	+	6.21683i	−0.222598	+	0.385551i
$261$	0.577441	−	16.1452i	0.0357427	−	0.999361i
$262$	−5.97539	−	10.3497i	−0.369161	−	0.639405i
$263$	−2.08420	+	1.06851i	−0.128517	+	0.0658869i	−0.519278	−	0.854605i	$-0.673799\pi$
$263$	−2.08420	+	1.06851i	−0.128517	+	0.0658869i	0.390761	+	0.920492i	$0.372212\pi$
$264$	19.1115	+	6.00270i	1.17623	+	0.369440i
$265$	−1.81088	+	2.51878i	−0.111242	+	0.154728i
$266$	−5.56344	+	4.21414i	−0.341117	+	0.258386i
$267$	−1.23693	+	1.45885i	−0.0756991	+	0.0892802i
$268$	0.516062	−	0.0516398i	0.0315235	−	0.00315440i
$269$	−12.2314	−	9.75419i	−0.745760	−	0.594723i	0.175131	−	0.984545i	$-0.443965\pi$
$269$	−12.2314	−	9.75419i	−0.745760	−	0.594723i	−0.920890	+	0.389822i	$0.872537\pi$
$270$	9.99215	+	11.1071i	0.608103	+	0.675958i
$271$	−3.61347	+	7.50344i	−0.219503	+	0.455802i	−0.981420	−	0.191873i	$-0.938544\pi$
$271$	−3.61347	+	7.50344i	−0.219503	+	0.455802i	0.761917	+	0.647674i	$0.224258\pi$
$272$	0.258150	−	0.0867338i	0.0156526	−	0.00525901i
$273$	7.39676	+	3.16280i	0.447672	+	0.191421i
$274$	−0.352526	+	14.1358i	−0.0212969	+	0.853977i
$275$	−0.716904	−	14.3645i	−0.0432309	−	0.866214i
$276$	0.805661	+	1.41213i	0.0484951	+	0.0850004i
$277$	−7.80682	−	1.57818i	−0.469066	−	0.0948238i	−0.0421430	−	0.999112i	$-0.513419\pi$
$277$	−7.80682	−	1.57818i	−0.469066	−	0.0948238i	−0.426923	+	0.904288i	$0.640403\pi$
$278$	36.9395	−	21.3270i	2.21548	−	1.27911i
$279$	13.1743	−	2.86501i	0.788723	−	0.171524i
$280$	−5.08745	−	7.46192i	−0.304033	−	0.445935i
$281$	−22.2599	−	12.1221i	−1.32792	−	0.723145i	−0.350921	−	0.936405i	$-0.614132\pi$
$281$	−22.2599	−	12.1221i	−1.32792	−	0.723145i	−0.976995	+	0.213260i	$0.931592\pi$
$282$	2.12959	+	0.441894i	0.126815	+	0.0263144i
$283$	1.71410	−	1.75738i	0.101893	−	0.104465i	−0.663012	−	0.748608i	$-0.730722\pi$
$283$	1.71410	−	1.75738i	0.101893	−	0.104465i	0.764905	+	0.644143i	$0.222786\pi$
$284$	20.1927	+	31.2644i	1.19822	+	1.85520i
$285$	0.618427	+	2.48191i	0.0366325	+	0.147016i
$286$	4.63182	−	16.4625i	0.273886	−	0.973447i
$287$	19.5310	+	1.46365i	1.15288	+	0.0863964i
$288$	2.78182	−	17.2528i	0.163920	−	1.01663i
$289$	−6.82541	−	11.8220i	−0.401495	−	0.695409i
$290$	13.0021	+	8.40784i	0.763508	+	0.493725i
$291$	7.92074	+	26.1542i	0.464322	+	1.53319i
$292$	−9.09772	+	21.5824i	−0.532404	+	1.26301i
$293$	6.87166	−	26.9867i	0.401446	−	1.57658i	−0.362935	−	0.931815i	$-0.618225\pi$
$293$	6.87166	−	26.9867i	0.401446	−	1.57658i	0.764381	−	0.644765i	$-0.223045\pi$
$294$	0.528492	−	0.461594i	0.0308223	−	0.0269207i
$295$	−3.66876	+	5.68035i	−0.213603	+	0.330723i
$296$	−7.32356	−	32.0866i	−0.425673	−	1.86500i
$297$	−18.2196	−	12.1690i	−1.05721	−	0.706117i
$298$	−21.0271	−	16.7686i	−1.21807	−	0.971378i
$299$	0.444715	−	0.271760i	0.0257185	−	0.0157163i
$300$	18.5643	−	3.65379i	1.07181	−	0.210952i
$301$	15.3165	+	0.381969i	0.882827	+	0.0220163i
$302$	−12.5641	−	2.21539i	−0.722982	−	0.127481i
$303$	−7.86027	−	0.629625i	−0.451561	−	0.0361710i
$304$	0.105260	−	0.138962i	0.00603705	−	0.00797001i
$305$	−8.65672	−	9.32973i	−0.495683	−	0.534219i
$306$	12.5129	−	0.495808i	0.715314	−	0.0283435i
$307$	13.7409	+	7.93332i	0.784235	+	0.452778i	0.837929	−	0.545779i	$-0.183766\pi$
$307$	13.7409	+	7.93332i	0.784235	+	0.452778i	−0.0536939	+	0.998557i	$0.517100\pi$
$308$	26.4456	+	23.3384i	1.50688	+	1.32983i
$309$	−5.61960	−	3.09777i	−0.319688	−	0.176226i
$310$	−4.11536	+	12.2487i	−0.233737	+	0.695681i
$311$	3.96084	+	1.33077i	0.224599	+	0.0754611i	0.428543	−	0.903521i	$-0.359027\pi$
$311$	3.96084	+	1.33077i	0.224599	+	0.0754611i	−0.203945	+	0.978982i	$0.565376\pi$
$312$	8.37673	+	1.09343i	0.474239	+	0.0619034i
$313$	26.2079	−	11.0476i	1.48136	−	0.624446i	0.509599	−	0.860412i	$-0.329794\pi$
$313$	26.2079	−	11.0476i	1.48136	−	0.624446i	0.971761	+	0.235966i	$0.0758255\pi$
$314$	12.4358	+	11.5387i	0.701790	+	0.651166i
$315$	3.04967	+	9.39518i	0.171829	+	0.529359i
$316$	6.29412	−	9.23178i	0.354072	−	0.519328i
$317$	7.55139	−	3.87137i	0.424128	−	0.217438i	−0.231003	−	0.972953i	$-0.574201\pi$
$317$	7.55139	−	3.87137i	0.424128	−	0.217438i	0.655131	+	0.755515i	$0.272613\pi$
$318$	9.46729	+	2.21202i	0.530899	+	0.124044i
$319$	−21.5203	−	7.24371i	−1.20491	−	0.405570i
$320$	12.5430	+	10.5248i	0.701176	+	0.588357i
$321$	−1.31478	−	0.138381i	−0.0733837	−	0.00772370i
$322$	0.173862	+	1.73749i	0.00968896	+	0.0968266i
$323$	1.93160	+	0.930207i	0.107477	+	0.0517581i
$324$	12.3912	−	26.0234i	0.688402	−	1.44574i
$325$	−1.34965	−	5.91320i	−0.0748651	−	0.328005i
$326$	11.6518	−	1.16594i	0.645336	−	0.0645756i
$327$	−10.3709	−	6.41087i	−0.573514	−	0.354522i
$328$	20.1597	−	4.07537i	1.11313	−	0.225024i
$329$	1.16754	+	0.839407i	0.0643688	+	0.0462780i
$330$	18.9657	−	9.01380i	1.04403	−	0.496193i
$331$	−4.32297	−	5.15191i	−0.237612	−	0.283175i	0.634040	−	0.773300i	$-0.281395\pi$
$331$	−4.32297	−	5.15191i	−0.237612	−	0.283175i	−0.871652	+	0.490125i	$0.836951\pi$
$332$	10.0815	−	25.6873i	0.553295	−	1.40977i
$333$	−2.16319	+	35.9318i	−0.118542	+	1.96905i
$334$	−15.0922	+	48.9276i	−0.825807	+	2.67720i
$335$	0.135080	−	0.153064i	0.00738021	−	0.00836280i
$336$	0.368150	−	0.563640i	0.0200842	−	0.0307491i
$337$	2.38363	−	3.90064i	0.129845	−	0.212482i	−0.781729	−	0.623619i	$-0.785662\pi$
$337$	2.38363	−	3.90064i	0.129845	−	0.212482i	0.911574	+	0.411137i	$0.134868\pi$
$338$	−2.23428	+	22.3283i	−0.121529	+	1.21450i
$339$	16.5283	+	14.7379i	0.897693	+	0.800450i
$340$	−3.53339	+	6.48839i	−0.191625	+	0.351882i
$341$	1.41609	−	18.8964i	0.0766857	−	1.02330i
$342$	6.43928	−	4.77435i	0.348196	−	0.258168i
$343$	17.9148	−	5.52598i	0.967308	−	0.298375i
$344$	15.5917	−	3.97012i	0.840646	−	0.214055i
$345$	0.610533	+	0.191761i	0.0328700	+	0.0103241i
$346$	−0.0816438	+	0.193682i	−0.00438920	+	0.0104124i
$347$	−3.28231	−	2.75418i	−0.176204	−	0.147852i	0.550421	−	0.834888i	$-0.314467\pi$
$347$	−3.28231	−	2.75418i	−0.176204	−	0.147852i	−0.726624	+	0.687035i	$0.758912\pi$
$348$	5.35426	−	29.3875i	0.287019	−	1.57534i
$349$	−19.6366	−	7.14715i	−1.05113	−	0.382578i	−0.242038	−	0.970267i	$-0.577816\pi$
$349$	−19.6366	−	7.14715i	−1.05113	−	0.382578i	−0.809087	+	0.587688i	$0.800038\pi$
$350$	19.8118	+	4.52191i	1.05899	+	0.241706i
$351$	−8.45788	−	3.71966i	−0.451448	−	0.198541i
$352$	−22.1297	−	10.6571i	−1.17952	−	0.568026i
$353$	6.88326	−	10.6574i	0.366359	−	0.567234i	−0.607520	−	0.794305i	$-0.707835\pi$
$353$	6.88326	−	10.6574i	0.366359	−	0.567234i	0.973878	+	0.227070i	$0.0729148\pi$
$354$	20.8514	+	3.78709i	1.10824	+	0.201282i
$355$	14.1968	+	3.61494i	0.753486	+	0.191861i
$356$	−2.65158	+	2.34004i	−0.140534	+	0.124022i
$357$	7.69143	+	3.06431i	0.407074	+	0.162180i
$358$	8.02289	+	31.5079i	0.424023	+	1.66524i
$359$	13.0295	+	5.11370i	0.687671	+	0.269891i	0.683341	−	0.730100i	$-0.260526\pi$
$359$	13.0295	+	5.11370i	0.687671	+	0.269891i	0.00433018	+	0.999991i	$0.498622\pi$
$360$	5.75496	+	8.62997i	0.303313	+	0.454839i
$361$	−17.4307	+	2.62726i	−0.917407	+	0.138277i
$362$	16.7884	+	39.8267i	0.882377	+	2.09325i
$363$	−9.03344	+	7.50130i	−0.474133	+	0.393716i
$364$	12.6921	+	7.75600i	0.665249	+	0.406525i
$365$	3.15312	+	8.66312i	0.165042	+	0.453448i
$366$	−16.5915	+	36.2728i	−0.867250	+	1.89601i
$367$	−6.35288	−	1.78742i	−0.331618	−	0.0933028i	0.100984	−	0.994888i	$-0.467801\pi$
$367$	−6.35288	−	1.78742i	−0.331618	−	0.0933028i	−0.432601	+	0.901585i	$0.642404\pi$
$368$	−0.0159344	−	0.0406003i	−0.000830639	−	0.00211643i
$369$	−22.4141	−	1.91123i	−1.16683	−	0.0994945i
$370$	−28.5053	−	19.4346i	−1.48192	−	1.01036i
$371$	5.12387	+	3.88118i	0.266018	+	0.201501i
$372$	24.8680	−	1.73531i	1.28934	−	0.0899718i
$373$	0.872919	−	1.21416i	0.0451980	−	0.0628667i	−0.788730	−	0.614739i	$-0.789261\pi$
$373$	0.872919	−	1.21416i	0.0451980	−	0.0628667i	0.833928	+	0.551873i	$0.186087\pi$
$374$	4.34313	−	17.0566i	0.224578	−	0.881974i
$375$	10.7964	−	14.8555i	0.557525	−	0.767133i
$376$	1.41898	+	0.516466i	0.0731783	+	0.0266347i
$377$	−9.46803	−	1.43244i	−0.487628	−	0.0737742i
$378$	23.5235	−	20.1240i	1.20992	−	1.03507i
$379$	26.3640	+	6.01740i	1.35423	+	0.309093i	0.837209	−	0.546883i	$-0.184186\pi$
$379$	26.3640	+	6.01740i	1.35423	+	0.309093i	0.517016	+	0.855976i	$0.327043\pi$
$380$	0.470890	+	4.70584i	0.0241562	+	0.241404i
$381$	5.20665	+	26.4541i	0.266745	+	1.35528i
$382$	−40.4138	+	30.6123i	−2.06775	+	1.56626i
$383$	28.7101	−	1.43286i	1.46702	−	0.0732158i	0.699679	−	0.714458i	$-0.253326\pi$
$383$	28.7101	−	1.43286i	1.46702	−	0.0732158i	0.767339	+	0.641242i	$0.221580\pi$
$384$	9.33017	−	29.7056i	0.476128	−	1.51591i
$385$	13.8790	−	0.346120i	0.707339	−	0.0176399i
$386$	27.9398	+	4.21124i	1.42210	+	0.214347i
$387$	−17.5864	−	0.619241i	−0.893969	−	0.0314778i
$388$	7.53078	+	49.9635i	0.382317	+	2.53651i
$389$	−19.1881	+	3.38338i	−0.972875	+	0.171544i	−0.637424	−	0.770513i	$-0.720000\pi$
$389$	−19.1881	+	3.38338i	−0.972875	+	0.171544i	−0.335451	+	0.942058i	$0.608889\pi$
$390$	7.21653	−	5.13236i	0.365423	−	0.259887i
$391$	0.450580	−	0.291015i	0.0227868	−	0.0147173i
$392$	0.409241	−	0.264316i	0.0206698	−	0.0133500i
$393$	0.857232	+	9.03447i	0.0432416	+	0.455729i
$394$	61.2024	−	10.7916i	3.08333	−	0.543675i
$395$	−0.655485	−	4.34886i	−0.0329810	−	0.218815i
$396$	−30.0976	−	27.1158i	−1.51246	−	1.36262i
$397$	−26.7340	−	4.02950i	−1.34174	−	0.202235i	−0.561376	−	0.827561i	$-0.689728\pi$
$397$	−26.7340	−	4.02950i	−1.34174	−	0.202235i	−0.780364	+	0.625326i	$0.784966\pi$
$398$	−33.4693	+	0.834672i	−1.67766	+	0.0418383i
$399$	5.17298	−	1.15280i	0.258973	−	0.0577123i
$400$	−0.506948	+	0.0253007i	−0.0253474	+	0.00126504i
$401$	−13.5494	+	10.2633i	−0.676627	+	0.512525i	−0.885039	−	0.465516i	$-0.845869\pi$
$401$	−13.5494	+	10.2633i	−0.676627	+	0.512525i	0.208412	+	0.978041i	$0.433170\pi$
$402$	−0.605423	−	0.206875i	−0.0301958	−	0.0103180i
$403$	−0.795671	−	7.95154i	−0.0396352	−	0.396094i
$404$	−14.2145	−	3.24438i	−0.707200	−	0.161414i
$405$	−3.39179	−	10.8263i	−0.168539	−	0.537963i
$406$	18.0877	−	26.4982i	0.897676	−	1.31508i
$407$	47.5429	+	17.3042i	2.35661	+	0.857737i
$408$	8.64660	+	0.910063i	0.428071	+	0.0450548i
$409$	6.12045	−	24.0365i	0.302637	−	1.18853i	−0.614162	−	0.789180i	$-0.710506\pi$
$409$	6.12045	−	24.0365i	0.302637	−	1.18853i	0.916799	−	0.399349i	$-0.130764\pi$
$410$	12.5855	−	17.5054i	0.621555	−	0.864530i
$411$	4.70848	−	9.65025i	0.232252	−	0.476012i
$412$	−9.45773	−	7.16395i	−0.465949	−	0.352943i
$413$	11.5768	+	7.89291i	0.569656	+	0.388385i
$414$	−0.179199	−	1.99755i	−0.00880714	−	0.0981744i
$415$	−3.96826	−	10.1110i	−0.194794	−	0.496327i
$416$	−9.97107	−	2.80543i	−0.488872	−	0.137547i
$417$	−32.2453	+	3.05958i	−1.57906	+	0.149828i
$418$	−3.85348	−	10.5873i	−0.188480	−	0.517844i
$419$	−0.0112006	−	0.00684457i	−0.000547187	−	0.000334379i	0.521162	−	0.853458i	$-0.325499\pi$
$419$	−0.0112006	−	0.00684457i	−0.000547187	−	0.000334379i	−0.521709	+	0.853124i	$0.674705\pi$
$420$	3.07914	+	18.0024i	0.150247	+	0.878428i
$421$	1.08769	+	2.58029i	0.0530105	+	0.125756i	0.945834	−	0.324652i	$-0.105247\pi$
$421$	1.08769	+	2.58029i	0.0530105	+	0.125756i	−0.892823	+	0.450407i	$0.851279\pi$
$422$	−51.8603	+	7.81668i	−2.52452	+	0.380510i
$423$	−1.33103	−	0.977820i	−0.0647168	−	0.0475433i
$424$	6.28345	+	2.46607i	0.305151	+	0.119763i
$425$	−1.54033	−	6.04927i	−0.0747172	−	0.293433i
$426$	−6.60983	−	45.4342i	−0.320247	−	2.20129i
$427$	−19.7728	+	17.4496i	−0.956873	+	0.844446i
$428$	−2.36885	−	0.603182i	−0.114502	−	0.0291559i
$429$	−8.39849	+	9.90525i	−0.405483	+	0.478230i
$430$	9.15038	−	14.1676i	0.441270	−	0.683220i
$431$	−9.45010	−	4.55093i	−0.455195	−	0.219210i	0.192214	−	0.981353i	$-0.438433\pi$
$431$	−9.45010	−	4.55093i	−0.455195	−	0.219210i	−0.647409	+	0.762143i	$0.724147\pi$
$432$	−0.429464	+	0.643000i	−0.0206626	+	0.0309363i
$433$	36.8983	+	8.42180i	1.77322	+	0.404726i	0.979156	−	0.203108i	$-0.0651043\pi$
$433$	36.8983	+	8.42180i	1.77322	+	0.404726i	0.794064	+	0.607834i	$0.207961\pi$
$434$	25.1595	+	9.15730i	1.20769	+	0.439564i
$435$	−6.32293	−	9.91301i	−0.303161	−	0.475293i
$436$	−17.2695	−	14.4908i	−0.827057	−	0.693983i
$437$	0.133372	−	0.316396i	0.00638006	−	0.0151353i
$438$	21.2804	−	19.5431i	1.01682	−	0.933805i
$439$	28.5214	−	7.26245i	1.36125	−	0.346618i	0.504976	−	0.863134i	$-0.331501\pi$
$439$	28.5214	−	7.26245i	1.36125	−	0.346618i	0.856278	+	0.516516i	$0.172771\pi$
$440$	13.9315	−	4.29728i	0.664156	−	0.204865i
$441$	−0.510756	+	0.151824i	−0.0243217	+	0.00722973i
$442$	0.554686	−	7.40177i	0.0263837	−	0.352066i
$443$	−13.9688	+	25.6511i	−0.663679	+	1.21872i	0.300579	+	0.953757i	$0.402820\pi$
$443$	−13.9688	+	25.6511i	−0.663679	+	1.21872i	−0.964259	+	0.264963i	$0.914640\pi$
$444$	−13.5228	+	65.1696i	−0.641763	+	3.09281i
$445$	−0.138600	+	1.38510i	−0.00657028	+	0.0656600i
$446$	−0.661544	+	1.08257i	−0.0313250	+	0.0512611i
$447$	9.22382	+	18.2214i	0.436272	+	0.861845i
$448$	22.4491	−	25.4380i	1.06062	−	1.20183i
$449$	−1.40460	+	4.55361i	−0.0662874	+	0.214898i	−0.982656	−	0.185437i	$-0.940630\pi$
$449$	−1.40460	+	4.55361i	−0.0662874	+	0.214898i	0.916369	+	0.400335i	$0.131106\pi$
$450$	−22.7005	−	5.42695i	−1.07011	−	0.255829i
$451$	−11.5512	+	29.4320i	−0.543925	+	1.38590i
$452$	26.3191	+	31.3659i	1.23795	+	1.47533i
$453$	7.97646	+	5.49843i	0.374767	+	0.258339i
$454$	−2.71987	−	1.95546i	−0.127650	−	0.0917741i
$455$	5.73871	−	1.16010i	0.269035	−	0.0543865i
$456$	4.90136	−	2.63662i	0.229527	−	0.123471i
$457$	−19.9573	+	1.99703i	−0.933561	+	0.0934169i	−0.554713	−	0.832042i	$-0.687172\pi$
$457$	−19.9573	+	1.99703i	−0.933561	+	0.0934169i	−0.378848	+	0.925459i	$0.623680\pi$
$458$	9.82355	+	43.0398i	0.459024	+	2.01112i
$459$	−8.79748	−	3.61002i	−0.410631	−	0.168501i
$460$	1.06606	+	0.513389i	0.0497055	+	0.0239369i
$461$	0.263069	+	2.62898i	0.0122523	+	0.122444i	0.999272	−	0.0381573i	$-0.0121488\pi$
$461$	0.263069	+	2.62898i	0.0122523	+	0.122444i	−0.987019	+	0.160601i	$0.948657\pi$
$462$	−17.6915	−	39.7513i	−0.823082	−	1.84940i
$463$	18.9172	+	15.8734i	0.879155	+	0.737699i	0.966005	−	0.258523i	$-0.0832357\pi$
$463$	18.9172	+	15.8734i	0.879155	+	0.737699i	−0.0868503	+	0.996221i	$0.527680\pi$
$464$	−0.255643	+	0.759488i	−0.0118679	+	0.0352584i
$465$	6.71085	−	7.15855i	0.311208	−	0.331970i
$466$	32.4865	−	16.6549i	1.50491	−	0.771522i
$467$	−1.54731	+	2.26949i	−0.0716009	+	0.105019i	−0.860369	−	0.509672i	$-0.829767\pi$
$467$	−1.54731	+	2.26949i	−0.0716009	+	0.105019i	0.788768	+	0.614691i	$0.210719\pi$
$468$	−14.4855	−	9.05737i	−0.669591	−	0.418677i
$469$	−0.310080	−	0.287712i	−0.0143182	−	0.0132853i
$470$	1.45862	−	0.614861i	0.0672812	−	0.0283614i
$471$	−4.94291	−	11.8962i	−0.227757	−	0.548147i
$472$	13.9475	+	4.68611i	0.641986	+	0.215696i
$473$	−7.87722	+	23.4454i	−0.362195	+	1.07802i
$474$	−11.7979	+	7.12665i	−0.541895	+	0.327338i
$475$	−2.99604	−	2.64402i	−0.137468	−	0.121316i
$476$	13.2575	+	7.65424i	0.607658	+	0.350832i
$477$	−5.83900	−	4.51793i	−0.267350	−	0.206862i
$478$	13.0925	+	14.1104i	0.598837	+	0.645393i
$479$	17.1058	−	22.5828i	0.781586	−	1.03184i	−0.216865	−	0.976201i	$-0.569583\pi$
$479$	17.1058	−	22.5828i	0.781586	−	1.03184i	0.998451	−	0.0556349i	$-0.0177183\pi$
$480$	−5.45952	−	11.4872i	−0.249192	−	0.524318i
$481$	21.0121	+	3.70500i	0.958070	+	0.168934i
$482$	53.0036	+	1.32183i	2.41425	+	0.0602076i
$483$	0.428753	−	1.25475i	0.0195090	−	0.0570933i
$484$	−18.5255	+	11.3207i	−0.842068	+	0.514577i
$485$	15.5495	+	12.4003i	0.706068	+	0.563070i
$486$	−27.2539	+	22.8351i	−1.23626	+	1.03582i
$487$	−2.38820	−	10.4634i	−0.108220	−	0.474142i	−0.999775	−	0.0212292i	$-0.993242\pi$
$487$	−2.38820	−	10.4634i	−0.108220	−	0.474142i	0.891555	−	0.452913i	$-0.149615\pi$
$488$	−15.0249	+	23.2630i	−0.680144	+	1.05307i
$489$	−8.41454	−	2.87528i	−0.380519	−	0.130024i
$490$	0.126016	−	0.494895i	0.00569282	−	0.0223571i
$491$	10.8812	−	25.8133i	0.491063	−	1.16494i	−0.468505	−	0.883461i	$-0.655207\pi$
$491$	10.8812	−	25.8133i	0.491063	−	1.16494i	0.959568	−	0.281478i	$-0.0908246\pi$
$492$	−40.5029	−	9.46346i	−1.82601	−	0.426646i
$493$	−9.77810	−	1.23085i	−0.440383	−	0.0554348i
$494$	−2.37569	−	4.11482i	−0.106887	−	0.185134i
$495$	−15.9441	+	0.233913i	−0.716633	+	0.0105136i
$496$	−0.666886	−	0.0499762i	−0.0299441	−	0.00224400i
$497$	8.22137	−	29.2205i	0.368779	−	1.31072i
$498$	−24.4904	+	23.6433i	−1.09744	+	1.05948i
$499$	−15.4653	−	23.9449i	−0.692320	−	1.07192i	−0.992991	−	0.118193i	$-0.962290\pi$
$499$	−15.4653	−	23.9449i	−0.692320	−	1.07192i	0.300671	−	0.953728i	$-0.402789\pi$
$500$	23.7089	−	24.3075i	1.06029	−	1.08707i
$501$	25.8766	−	29.0202i	1.15608	−	1.29653i
$502$	45.3766	+	24.7108i	2.02526	+	1.10290i
$503$	−23.8084	−	34.9205i	−1.06156	−	1.55703i	−0.807525	−	0.589833i	$-0.799194\pi$
$503$	−23.8084	−	34.9205i	−1.06156	−	1.55703i	−0.254038	−	0.967194i	$-0.581759\pi$
$504$	18.1734	−	11.4750i	0.809509	−	0.511139i
$505$	−4.97010	+	2.86949i	−0.221166	+	0.127691i
$506$	−2.76297	−	0.558547i	−0.122829	−	0.0248304i
$507$	8.59565	−	14.7132i	0.381746	−	0.653437i
$508$	2.48490	+	49.7898i	0.110250	+	2.20906i
$509$	0.670388	−	26.8817i	0.0297144	−	1.19151i	−0.787922	−	0.615776i	$-0.788843\pi$
$509$	0.670388	−	26.8817i	0.0297144	−	1.19151i	0.817636	−	0.575736i	$-0.195284\pi$
$510$	7.29316	−	5.46568i	0.322947	−	0.242024i
$511$	18.1077	−	6.08386i	0.801037	−	0.269134i
$512$	−0.730300	+	1.51648i	−0.0322750	+	0.0670197i
$513$	−5.95475	+	1.26301i	−0.262909	+	0.0557634i
$514$	−10.7898	−	8.60454i	−0.475916	−	0.379530i
$515$	−4.64694	+	0.464996i	−0.204768	+	0.0204902i
$516$	−32.0136	−	5.81440i	−1.40932	−	0.255965i
$517$	−1.85041	+	1.40163i	−0.0813811	+	0.0616438i
$518$	−41.7293	+	58.0420i	−1.83348	+	2.55022i
$519$	0.117557	−	0.107960i	0.00516020	−	0.00473892i
$520$	5.47115	−	2.80490i	0.239926	−	0.123003i
$521$	−2.12458	−	3.67988i	−0.0930796	−	0.161219i	0.815726	−	0.578439i	$-0.196338\pi$
$521$	−2.12458	−	3.67988i	−0.0930796	−	0.161219i	−0.908805	+	0.417220i	$0.863004\pi$
$522$	−21.0860	+	30.2199i	−0.922910	+	1.32269i
$523$	−8.95295	+	15.5070i	−0.391485	+	0.678073i	−0.992646	−	0.121056i	$-0.961372\pi$
$523$	−8.95295	+	15.5070i	−0.391485	+	0.678073i	0.601160	+	0.799128i	$0.294705\pi$
$524$	−0.836397	+	16.7588i	−0.0365382	+	0.732112i
$525$	−12.2529	−	9.38053i	−0.534759	−	0.409400i
$526$	5.31564	+	0.531910i	0.231773	+	0.0231924i
$527$	−1.02266	−	8.16066i	−0.0445479	−	0.355484i
$528$	0.694292	+	0.836101i	0.0302152	+	0.0363866i
$529$	13.3760	+	18.6048i	0.581563	+	0.808905i
$530$	6.58668	−	2.58508i	0.286107	−	0.112289i
$531$	−13.2029	−	9.20145i	−0.572955	−	0.399309i
$532$	9.77201	−	0.732311i	0.423671	−	0.0317497i
$533$	−2.64200	+	13.0692i	−0.114438	+	0.566091i
$534$	4.17532	−	1.26449i	0.180684	−	0.0547197i
$535$	−0.844999	+	0.460162i	−0.0365325	+	0.0198945i
$536$	−0.395281	−	0.202649i	−0.0170736	−	0.00875310i
$537$	4.41202	−	24.2921i	0.190393	−	1.04828i
$538$	11.3648	+	33.8255i	0.489970	+	1.45832i
$539$			0.748919i			0.0322582i
$540$	−3.32417	−	20.7120i	−0.143050	−	0.891304i
$541$	−3.72594	+	7.73698i	−0.160190	+	0.332639i	−0.965580	−	0.260107i	$-0.916242\pi$
$541$	−3.72594	+	7.73698i	−0.160190	+	0.332639i	0.805389	+	0.592746i	$0.201956\pi$
$542$	16.2090	−	9.90510i	0.696235	−	0.425461i
$543$	0.986596	−	32.8055i	0.0423389	−	1.40782i
$544$	−10.3309	−	2.63057i	−0.442934	−	0.112785i
$545$	−8.86254	+	0.442311i	−0.379630	+	0.0189465i
$546$	−10.2584	−	15.2135i	−0.439019	−	0.651076i
$547$	32.9090	−	8.37967i	1.40709	−	0.358289i	0.533849	−	0.845580i	$-0.320745\pi$
$547$	32.9090	−	8.37967i	1.40709	−	0.358289i	0.873240	+	0.487291i	$0.162015\pi$
$548$	11.1840	−	16.4040i	0.477758	−	0.700743i
$549$	22.9147	−	19.8078i	0.977977	−	0.845375i
$550$	−16.4025	+	28.4099i	−0.699404	+	1.21140i
$551$	−5.61548	+	2.87496i	−0.239227	+	0.122478i
$552$	0.0765436	−	1.39034i	0.00325791	−	0.0591769i
$553$	−9.04210	+	1.13312i	−0.384509	+	0.0481853i
$554$	13.0050	+	12.6848i	0.552531	+	0.538924i
$555$	13.5458	+	22.4246i	0.574987	+	0.951869i
$556$	−59.8145	−	2.98522i	−2.53670	−	0.126602i
$557$	−32.8379	−	10.1291i	−1.39139	−	0.429186i	−0.493627	−	0.869673i	$-0.664329\pi$
$557$	−32.8379	−	10.1291i	−1.39139	−	0.429186i	−0.897759	+	0.440488i	$0.854806\pi$
$558$	−28.7877	−	10.8137i	−1.21868	−	0.457781i
$559$	−1.55457	+	10.3139i	−0.0657513	+	0.436231i
$560$	−0.0122152	−	0.489812i	−0.000516184	−	0.0206983i
$561$	−8.38678	+	10.4067i	−0.354090	+	0.439370i
$562$	27.6494	+	50.7729i	1.16632	+	2.14172i
$563$	16.1734	−	19.2748i	0.681630	−	0.812335i	−0.308687	−	0.951164i	$-0.599889\pi$
$563$	16.1734	−	19.2748i	0.681630	−	0.812335i	0.990316	+	0.138829i	$0.0443339\pi$
$564$	−2.17513	−	2.14345i	−0.0915895	−	0.0902556i
$565$	15.9917	+	2.00402i	0.672775	+	0.0843097i
$566$	−5.45901	+	1.24598i	−0.229459	+	0.0523726i
$567$	−22.6008	+	6.46649i	−0.949146	+	0.271567i
$568$		−	31.8765i		−	1.33751i
$569$	−29.5567	+	9.93051i	−1.23908	+	0.416309i	−0.860591	−	0.509297i	$-0.829905\pi$
$569$	−29.5567	+	9.93051i	−1.23908	+	0.416309i	−0.378489	+	0.925606i	$0.623556\pi$
$570$	1.88644	−	5.52070i	0.0790143	−	0.231237i
$571$	15.8991	−	3.21406i	0.665355	−	0.134504i	0.146293	−	0.989241i	$-0.453266\pi$
$571$	15.8991	−	3.21406i	0.665355	−	0.134504i	0.519061	+	0.854737i	$0.326282\pi$
$572$	−18.0036	+	15.8883i	−0.752770	+	0.664323i
$573$	37.5775	−	8.37416i	1.56982	−	0.349836i
$574$	−35.6106	−	26.9740i	−1.48636	−	1.12587i
$575$	−0.955321	+	0.294678i	−0.0398396	+	0.0122889i
$576$	−26.0826	+	28.9508i	−1.08678	+	1.20628i
$577$	22.5815	+	1.69225i	0.940081	+	0.0704493i	0.535948	−	0.844251i	$-0.319954\pi$
$577$	22.5815	+	1.69225i	0.940081	+	0.0704493i	0.404133	+	0.914700i	$0.367573\pi$
$578$	−1.55201	+	31.0976i	−0.0645553	+	1.29349i
$579$	−17.9638	−	11.7333i	−0.746551	−	0.487621i
$580$	−8.93047	−	19.8212i	−0.370818	−	0.823031i
$581$	−21.1489	+	7.69755i	−0.877402	+	0.319348i
$582$	17.1894	−	59.9139i	0.712525	−	2.48351i
$583$	−8.42517	+	6.05728i	−0.348935	+	0.250867i
$584$	16.5742	−	11.3001i	0.685847	−	0.467602i
$585$	−6.60457	+	1.26473i	−0.273065	+	0.0522901i
$586$	−46.5622	+	43.2034i	−1.92347	+	1.78472i
$587$	−5.16442	+	11.4455i	−0.213158	+	0.472407i	−0.986949	−	0.161034i	$-0.948517\pi$
$587$	−5.16442	+	11.4455i	−0.213158	+	0.472407i	0.773790	+	0.633442i	$0.218358\pi$
$588$	−0.974959	+	0.141838i	−0.0402066	+	0.00584932i
$589$	−3.48360	−	3.94740i	−0.143539	−	0.162650i
$590$	14.0588	−	6.34359i	0.578793	−	0.261161i
$591$	−45.6725	−	11.8796i	−1.87872	−	0.488660i
$592$	0.610693	−	1.67787i	0.0250993	−	0.0689598i
$593$	−16.2166	−	20.3349i	−0.665934	−	0.835055i	0.328041	−	0.944664i	$-0.393612\pi$
$593$	−16.2166	−	20.3349i	−0.665934	−	0.835055i	−0.993975	+	0.109609i	$0.965040\pi$
$594$	19.8501	+	45.8628i	0.814457	+	1.88177i
$595$	5.87460	−	1.34084i	0.240835	−	0.0549691i
$596$	12.0267	+	35.7956i	0.492632	+	1.46624i
$597$	23.3761	+	9.99544i	0.956721	+	0.409086i
$598$	−1.18839	−	0.0296365i	−0.0485967	−	0.00121193i
$599$	14.3097	+	10.2880i	0.584678	+	0.420355i	0.836932	−	0.547306i	$-0.184347\pi$
$599$	14.3097	+	10.2880i	0.584678	+	0.420355i	−0.252255	+	0.967661i	$0.581172\pi$
$600$	−15.0541	−	5.99762i	−0.614580	−	0.244852i
$601$	18.0787	−	0.450856i	0.737447	−	0.0183908i	0.345551	−	0.938400i	$-0.387692\pi$
$601$	18.0787	−	0.450856i	0.737447	−	0.0183908i	0.391897	+	0.920009i	$0.371819\pi$
$602$	−28.8740	−	19.6860i	−1.17682	−	0.802341i
$603$	0.352735	+	0.334092i	0.0143645	+	0.0136053i
$604$	13.1311	+	12.1839i	0.534297	+	0.495755i
$605$	−2.31452	+	8.22628i	−0.0940985	+	0.334446i
$606$	14.2813	+	10.9334i	0.580138	+	0.444141i
$607$	5.44394	−	0.682214i	0.220963	−	0.0276902i	−0.0130892	−	0.999914i	$-0.504167\pi$
$607$	5.44394	−	0.682214i	0.220963	−	0.0276902i	0.234052	+	0.972224i	$0.424801\pi$
$608$	−6.41259	+	2.33399i	−0.260065	+	0.0946559i
$609$	−20.8605	+	12.5852i	−0.845309	+	0.509980i
$610$	5.04095	+	28.5886i	0.204102	+	1.15752i
$611$	−0.665850	+	0.717615i	−0.0269374	+	0.0290316i
$612$	−15.1360	−	8.94716i	−0.611837	−	0.361667i
$613$	−1.36355	−	18.1953i	−0.0550733	−	0.734902i	−0.954572	−	0.297979i	$-0.903687\pi$
$613$	−1.36355	−	18.1953i	−0.0550733	−	0.734902i	0.899499	−	0.436923i	$-0.143932\pi$
$614$	−16.5104	−	32.2048i	−0.666306	−	1.29968i
$615$	−14.2204	+	8.11314i	−0.573422	+	0.327153i
$616$	−8.18174	−	29.0796i	−0.329652	−	1.17165i
$617$	3.54141	+	17.5183i	0.142572	+	0.705262i	0.985829	+	0.167752i	$0.0536508\pi$
$617$	3.54141	+	17.5183i	0.142572	+	0.705262i	−0.843258	+	0.537510i	$0.819365\pi$
$618$	6.93379	+	12.8896i	0.278918	+	0.518497i
$619$	−28.6955	+	27.9888i	−1.15337	+	1.12496i	−0.162982	+	0.986629i	$0.552111\pi$
$619$	−28.6955	+	27.9888i	−1.15337	+	1.12496i	−0.990386	+	0.138334i	$0.955825\pi$
$620$	14.1846	−	11.3118i	0.569666	−	0.454294i
$621$	−0.507214	+	1.43603i	−0.0203538	+	0.0576259i
$622$	−5.94223	−	7.45132i	−0.238262	−	0.298771i
$623$	2.86194	+	0.358647i	0.114661	+	0.0143689i
$624$	0.349573	+	0.296396i	0.0139941	+	0.0118654i
$625$	−0.0919780	+	3.68820i	−0.00367912	+	0.147528i
$626$	−63.8863	−	11.2649i	−2.55341	−	0.450235i
$627$	−0.683140	+	8.52835i	−0.0272820	+	0.340589i
$628$	−5.87753	−	23.0825i	−0.234539	−	0.921092i
$629$	21.7137	+	3.27282i	0.865783	+	0.130496i
$630$	5.78329	−	21.7753i	0.230412	−	0.867550i
$631$	−1.92632	+	25.7049i	−0.0766855	+	1.02330i	0.817596	+	0.575792i	$0.195306\pi$
$631$	−1.92632	+	25.7049i	−0.0766855	+	1.02330i	−0.894282	+	0.447505i	$0.852313\pi$
$632$	−8.81814	+	3.71716i	−0.350767	+	0.147861i
$633$	38.2815	+	10.9831i	1.52155	+	0.436537i
$634$	−19.2594	−	1.92720i	−0.764890	−	0.0765388i
$635$	14.0471	+	13.7011i	0.557441	+	0.543713i
$636$	−9.48115	−	9.82087i	−0.375952	−	0.389423i
$637$	0.0548433	+	0.311032i	0.00217297	+	0.0123235i
$638$	32.2694	+	40.5105i	1.27756	+	1.60383i
$639$	−9.78668	+	33.4627i	−0.387155	+	1.32377i
$640$	−6.67940	−	21.6541i	−0.264026	−	0.855953i
$641$	−45.4736	−	20.5185i	−1.79610	−	0.810431i	−0.968459	−	0.249173i	$-0.919841\pi$
$641$	−45.4736	−	20.5185i	−1.79610	−	0.810431i	−0.827641	−	0.561258i	$-0.810317\pi$
$642$	2.34789	+	1.89218i	0.0926640	+	0.0746782i
$643$	−12.6925	−	5.35036i	−0.500545	−	0.210997i	0.123561	−	0.992337i	$-0.460569\pi$
$643$	−12.6925	−	5.35036i	−0.500545	−	0.210997i	−0.624106	+	0.781339i	$0.714537\pi$
$644$	1.11851	−	2.18173i	0.0440753	−	0.0859721i
$645$	−10.7939	+	6.89321i	−0.425010	+	0.271420i
$646$	−2.54985	−	4.17264i	−0.100322	−	0.164170i
$647$	17.5494	−	22.0063i	0.689939	−	0.865157i	−0.306288	−	0.951939i	$-0.599087\pi$
$647$	17.5494	−	22.0063i	0.689939	−	0.865157i	0.996227	+	0.0867824i	$0.0276585\pi$
$648$	−21.0074	+	12.9648i	−0.825249	+	0.509307i
$649$	−17.6841	+	14.1026i	−0.694161	+	0.553575i
$650$	−4.73162	+	13.0000i	−0.185589	+	0.509903i
$651$	−14.4816	−	14.2707i	−0.567578	−	0.559312i
$652$	−14.6309	−	7.50085i	−0.572992	−	0.293756i
$653$	0.555853	+	11.1376i	0.0217522	+	0.435847i	0.985568	+	0.169278i	$0.0541437\pi$
$653$	0.555853	+	11.1376i	0.0217522	+	0.435847i	−0.963816	+	0.266568i	$0.914110\pi$
$654$	11.9375	+	25.1174i	0.466793	+	0.982167i
$655$	4.24546	+	5.05954i	0.165884	+	0.197692i
$656$	1.03870	+	0.407661i	0.0405546	+	0.0159165i
$657$	−20.8684	+	6.77385i	−0.814152	+	0.264273i
$658$	−1.19828	−	3.05316i	−0.0467136	−	0.119024i
$659$	18.1460	−	33.3216i	0.706867	−	1.29803i	−0.238221	−	0.971211i	$-0.576564\pi$
$659$	18.1460	−	33.3216i	0.706867	−	1.29803i	0.945088	−	0.326815i	$-0.105975\pi$
$660$	−29.2356	−	3.81618i	−1.13799	−	0.148544i
$661$	2.97551	+	4.60699i	0.115734	+	0.179191i	0.893101	−	0.449856i	$-0.148525\pi$
$661$	2.97551	+	4.60699i	0.115734	+	0.179191i	−0.777367	+	0.629047i	$0.783445\pi$
$662$	1.90742	+	15.2208i	0.0741339	+	0.591575i
$663$	−2.72101	+	4.93614i	−0.105675	+	0.191704i
$664$	−19.1895	+	13.7963i	−0.744697	+	0.535401i
$665$	2.62357	−	2.82754i	0.101738	−	0.109647i
$666$	48.6103	−	66.1692i	1.88361	−	2.56400i
$667$	−0.118823	+	1.57389i	−0.00460085	+	0.0609413i
$668$	55.0721	−	46.2110i	2.13080	−	1.78796i
$669$	0.798781	−	0.538616i	0.0308827	−	0.0208241i
$670$	−0.448233	+	0.126113i	−0.0173168	+	0.00487218i
$671$	−17.5092	−	38.8044i	−0.675936	−	1.49803i
$672$	−24.0767	+	10.7155i	−0.928780	+	0.413358i
$673$	3.35183	−	26.7470i	0.129204	−	1.03102i	−0.783212	−	0.621755i	$-0.786420\pi$
$673$	3.35183	−	26.7470i	0.129204	−	1.03102i	0.912416	−	0.409265i	$-0.134215\pi$
$674$	−9.39414	+	4.52398i	−0.361849	+	0.174257i
$675$	13.9618	+	10.9180i	0.537390	+	0.420232i
$676$	19.6442	−	24.6331i	0.755547	−	0.947426i
$677$	−8.73355	+	8.51847i	−0.335658	+	0.327391i	−0.846606	−	0.532220i	$-0.821358\pi$
$677$	−8.73355	+	8.51847i	−0.335658	+	0.327391i	0.510948	+	0.859611i	$0.329294\pi$
$678$	−13.4305	−	48.6918i	−0.515794	−	1.87000i
$679$	26.4893	−	31.5688i	1.01657	−	1.21150i
$680$	5.55712	−	3.02625i	0.213106	−	0.116051i
$681$	1.26057	+	2.20947i	0.0483050	+	0.0846671i
$682$	−26.0976	+	34.4536i	−0.999327	+	1.31930i
$683$	3.50728	−	8.93641i	0.134202	−	0.341942i	−0.847937	−	0.530097i	$-0.822155\pi$
$683$	3.50728	−	8.93641i	0.134202	−	0.341942i	0.982139	+	0.188155i	$0.0602507\pi$
$684$	−11.2318	+	0.725866i	−0.429457	+	0.0277542i
$685$	−1.16473	−	7.72750i	−0.0445022	−	0.295253i
$686$	−41.1636	−	11.5816i	−1.57163	−	0.442189i
$687$	6.81110	−	32.8244i	0.259860	−	1.25233i
$688$	0.827425	+	0.278000i	0.0315453	+	0.0105987i
$689$	−3.05546	+	3.13261i	−0.116404	+	0.119343i
$690$	−0.932491	−	1.12295i	−0.0354993	−	0.0427501i
$691$	−47.1239	−	2.35186i	−1.79268	−	0.0894689i	−0.874352	−	0.485292i	$-0.838713\pi$
$691$	−47.1239	−	2.35186i	−1.79268	−	0.0894689i	−0.918327	+	0.395823i	$0.870459\pi$
$692$	0.243836	−	0.166245i	0.00926925	−	0.00631967i
$693$	−0.339103	+	33.0387i	−0.0128815	+	1.25504i
$694$	2.88068	+	9.33893i	0.109349	+	0.354501i
$695$	−18.0582	+	15.1526i	−0.684987	+	0.574772i
$696$	−17.5079	+	18.6551i	−0.663633	+	0.707121i
$697$	−2.38294	+	13.5143i	−0.0902601	+	0.511890i
$698$	28.7797	+	37.9944i	1.08933	+	1.43811i
$699$	−27.6945	+	1.23974i	−1.04750	+	0.0468912i
$700$	−19.9224	−	20.4254i	−0.752995	−	0.772008i
$701$	−3.03672	+	13.3047i	−0.114695	+	0.502512i	0.884648	+	0.466260i	$0.154399\pi$
$701$	−3.03672	+	13.3047i	−0.114695	+	0.502512i	−0.999343	+	0.0362520i	$0.988458\pi$
$702$	11.6024	+	17.5936i	0.437905	+	0.664026i
$703$	12.6646	−	6.09893i	0.477653	−	0.230026i
$704$	28.5585	+	46.7340i	1.07634	+	1.76135i
$705$	−1.20148	−	0.0361333i	−0.0452502	−	0.00136086i
$706$	−26.3769	+	11.9017i	−0.992709	+	0.447927i
$707$	5.68712	+	10.4433i	0.213886	+	0.392761i
$708$	−21.7083	−	20.3506i	−0.815847	−	0.764824i
$709$	22.2848	+	4.50497i	0.836923	+	0.169188i	0.597642	−	0.801763i	$-0.296104\pi$
$709$	22.2848	+	4.50497i	0.836923	+	0.169188i	0.239281	+	0.970950i	$0.423088\pi$
$710$	−22.7278	−	24.4948i	−0.852960	−	0.919273i
$711$	10.3982	−	1.19480i	0.389963	−	0.0448085i
$712$	2.99506	−	0.451433i	0.112245	−	0.0169182i
$713$	−1.29718	+	0.228728i	−0.0485799	+	0.00856595i
$714$	−10.9449	−	15.3894i	−0.409602	−	0.575935i
$715$	−0.941063	+	9.40450i	−0.0351937	+	0.351708i
$716$	14.5391	−	43.2736i	0.543353	−	1.61721i
$717$	−4.58413	−	13.8795i	−0.171197	−	0.518339i
$718$	−18.6366	−	25.9220i	−0.695512	−	0.967399i
$719$	20.6833	+	6.37996i	0.771357	+	0.237932i	0.655359	−	0.755317i	$-0.272517\pi$
$719$	20.6833	+	6.37996i	0.771357	+	0.237932i	0.115998	+	0.993249i	$0.462993\pi$
$720$	0.00825519	+	0.562692i	0.000307653	+	0.0209703i
$721$	0.723145	+	9.64970i	0.0269313	+	0.359373i
$722$	36.6489	+	16.5366i	1.36393	+	0.615429i
$723$	−36.1845	−	17.6549i	−1.34572	−	0.656591i
$724$	10.5377	−	59.7625i	0.391632	−	2.22106i
$725$	16.9222	+	7.14435i	0.628475	+	0.265334i
$726$	26.5911	−	3.19378i	0.986888	−	0.118532i
$727$	38.4759	+	24.8504i	1.42699	+	0.921649i	0.999847	+	0.0174660i	$0.00555989\pi$
$727$	38.4759	+	24.8504i	1.42699	+	0.921649i	0.427145	+	0.904183i	$0.359519\pi$
$728$	−5.52744	−	11.4779i	−0.204861	−	0.425398i
$729$	26.0332	−	7.16034i	0.964194	−	0.265198i
$730$	4.67915	−	20.5007i	0.173183	−	0.758765i
$731$	−1.33481	+	10.6515i	−0.0493697	+	0.393960i
$732$	47.2004	−	30.1431i	1.74458	−	1.11412i
$733$	0.740802	+	3.66453i	0.0273621	+	0.135353i	0.991514	−	0.129997i	$-0.0414967\pi$
$733$	0.740802	+	3.66453i	0.0273621	+	0.135353i	−0.964152	+	0.265350i	$0.914513\pi$
$734$	9.96033	+	11.2864i	0.367642	+	0.416589i
$735$	−0.243342	+	0.301949i	−0.00897581	+	0.0111376i
$736$	−0.338303	+	1.67349i	−0.0124700	+	0.0616857i
$737$	0.591368	−	0.341426i	0.0217833	−	0.0125766i
$738$	40.5807	+	31.3993i	1.49380	+	1.15583i
$739$	−3.55517	+	11.5256i	−0.130779	+	0.423975i	−0.997152	−	0.0754228i	$-0.975969\pi$
$739$	−3.55517	+	11.5256i	−0.130779	+	0.423975i	0.866373	+	0.499398i	$0.166446\pi$
$740$	18.8159	+	44.6366i	0.691686	+	1.64087i
$741$	0.340818	+	3.59192i	0.0125202	+	0.131952i
$742$	−5.01449	−	13.7772i	−0.184088	−	0.505777i
$743$	−22.0798	+	36.1320i	−0.810029	+	1.32555i	0.132417	+	0.991194i	$0.457726\pi$
$743$	−22.0798	+	36.1320i	−0.810029	+	1.32555i	−0.942446	+	0.334359i	$0.891480\pi$
$744$	−18.6978	−	10.3071i	−0.685496	−	0.377875i
$745$	13.0537	+	7.10864i	0.478249	+	0.260440i
$746$	−3.17505	+	1.24612i	−0.116247	+	0.0456235i
$747$	24.3802	−	8.59132i	0.892023	−	0.314340i
$748$	−18.1157	+	16.8089i	−0.662375	+	0.614594i
$749$	0.909530	+	1.77410i	0.0332335	+	0.0648244i
$750$	−39.0698	+	15.1028i	−1.42663	+	0.551478i
$751$	11.1334	−	3.13246i	0.406264	−	0.114305i	−0.0616094	−	0.998100i	$-0.519623\pi$
$751$	11.1334	−	3.13246i	0.406264	−	0.114305i	0.467874	+	0.883795i	$0.345020\pi$
$752$	0.0494660	+	0.0653042i	0.00180384	+	0.00238140i
$753$	−23.5298	−	31.3972i	−0.857475	−	1.14418i
$754$	16.3683	+	14.4612i	0.596099	+	0.526647i
$755$	7.05083			0.256606
$756$	−43.0747	+	5.81577i	−1.56661	+	0.211518i
$757$	18.4483	+	38.3083i	0.670515	+	1.39234i	0.907178	+	0.420747i	$0.138232\pi$
$757$	18.4483	+	38.3083i	0.670515	+	1.39234i	−0.236663	+	0.971592i	$0.576054\pi$
$758$	−43.0674	−	44.1548i	−1.56428	−	1.60378i
$759$	1.73156	+	1.25844i	0.0628518	+	0.0456784i
$760$	1.84790	−	3.60447i	0.0670305	−	0.130748i
$761$	5.30974	+	18.8719i	0.192478	+	0.684107i	0.996042	+	0.0888885i	$0.0283315\pi$
$761$	5.30974	+	18.8719i	0.192478	+	0.684107i	−0.803564	+	0.595219i	$0.797065\pi$
$762$	22.7608	−	57.1299i	0.824538	−	2.06960i
$763$	0.458387	+	18.3807i	0.0165947	+	0.665427i
$764$	70.9856	−	5.31964i	2.56817	−	0.192458i
$765$	−6.76277	+	1.47070i	−0.244509	+	0.0531733i
$766$	−56.7824	−	32.7833i	−2.05163	−	1.18451i
$767$	−6.31161	+	7.15192i	−0.227899	+	0.258241i
$768$	−20.0208	+	16.6251i	−0.722438	+	0.599907i
$769$	−35.5428	+	22.9560i	−1.28171	+	0.827813i	−0.991620	−	0.129187i	$-0.958763\pi$
$769$	−35.5428	+	22.9560i	−1.28171	+	0.827813i	−0.290086	+	0.957001i	$0.593684\pi$
$770$	−27.0208	−	16.5120i	−0.973761	−	0.595053i
$771$	4.73306	+	9.35005i	0.170457	+	0.336734i
$772$	−29.7456	−	26.2506i	−1.07057	−	0.944780i
$773$	3.03245	+	4.44779i	0.109070	+	0.159976i	0.876893	−	0.480686i	$-0.159612\pi$
$773$	3.03245	+	4.44779i	0.109070	+	0.159976i	−0.767823	+	0.640662i	$0.778660\pi$
$774$	32.9297	+	22.9497i	1.18363	+	0.824909i
$775$	−2.28468	+	15.1578i	−0.0820680	+	0.544486i
$776$	17.7987	−	39.4460i	0.638937	−	1.41603i
$777$	47.1500	−	26.9004i	1.69150	−	0.965047i
$778$	40.9517	+	17.2626i	1.46819	+	0.618894i
$779$	3.61289	+	8.00699i	0.129445	+	0.286880i
$780$	−12.4212	+	0.556032i	−0.444751	+	0.0199091i
$781$	41.1634	+	26.5861i	1.47294	+	0.951327i
$782$	−1.22345			−0.0437506
$783$	24.1066	−	14.2082i	0.861498	−	0.507761i
$784$	0.0264306			0.000943949
$785$	−7.87573	−	5.08669i	−0.281097	−	0.181552i
$786$	9.53766	−	18.3711i	0.340197	−	0.655274i
$787$	1.16511	+	2.58215i	0.0415317	+	0.0920437i	0.931109	−	0.364741i	$-0.118842\pi$
$787$	1.16511	+	2.58215i	0.0415317	+	0.0920437i	−0.889577	+	0.456784i	$0.849001\pi$
$788$	−80.4060	−	33.8940i	−2.86435	−	1.20742i
$789$	−3.50274	−	2.04635i	−0.124701	−	0.0728520i
$790$	−4.12578	+	9.14368i	−0.146789	+	0.325317i
$791$	4.97722	−	33.0217i	0.176970	−	1.17412i
$792$	9.05392	+	33.4944i	0.321717	+	1.19017i
$793$	−10.1134	−	14.8336i	−0.359136	−	0.526756i
$794$	46.2364	+	40.8039i	1.64087	+	1.44807i
$795$	−5.36502	−	0.295365i	−0.190278	−	0.0104755i
$796$	40.1112	+	24.5114i	1.42170	+	0.868785i
$797$	9.81099	−	6.33661i	0.347523	−	0.224454i	−0.357051	−	0.934085i	$-0.616218\pi$
$797$	9.81099	−	6.33661i	0.347523	−	0.224454i	0.704574	+	0.709631i	$0.251138\pi$
$798$	−11.3381	−	4.19276i	−0.401366	−	0.148422i
$799$	−0.666658	+	0.755416i	−0.0235847	+	0.0267247i
$800$	17.2075	+	9.93473i	0.608375	+	0.351246i
$801$	−3.28270	−	0.445642i	−0.115989	−	0.0157460i
$802$	38.6619	−	2.89731i	1.36520	−	0.102307i
$803$	0.768794	+	30.8277i	0.0271302	+	1.08789i
$804$	0.556476	+	0.705192i	0.0196254	+	0.0248702i
$805$	−0.261373	−	0.928974i	−0.00921218	−	0.0327420i
$806$	−8.31549	+	16.2200i	−0.292901	+	0.571324i
$807$	2.83633	−	26.9482i	0.0998434	−	0.948622i
$808$	8.71920	+	8.93935i	0.306740	+	0.314485i
$809$	7.46175	+	15.4945i	0.262341	+	0.544757i	0.989981	−	0.141203i	$-0.0450969\pi$
$809$	7.46175	+	15.4945i	0.262341	+	0.544757i	−0.727640	+	0.685960i	$0.759383\pi$
$810$	−6.89879	+	24.9408i	−0.242399	+	0.876329i
$811$	13.0166			0.457074			0.228537	−	0.973535i	$-0.426606\pi$
$811$	13.0166			0.457074			0.228537	+	0.973535i	$0.426606\pi$
$812$	−41.5190	+	17.4747i	−1.45703	+	0.613241i
$813$	−14.3219	+	1.72017i	−0.502292	+	0.0603289i
$814$	−69.6793	−	91.9894i	−2.44226	−	3.22423i
$815$	−6.22982	+	1.75280i	−0.218221	+	0.0613979i
$816$	0.367269	+	0.295983i	0.0128570	+	0.0103615i
$817$	3.13493	+	6.11492i	0.109677	+	0.213934i
$818$	−41.4720	+	38.4804i	−1.45004	+	1.34544i
$819$	2.27859	+	13.7461i	0.0796203	+	0.480326i
$820$	−28.1791	+	11.0595i	−0.984057	+	0.386214i
$821$	−4.70298	−	2.56111i	−0.164135	−	0.0893833i	0.394094	−	0.919070i	$-0.371059\pi$
$821$	−4.70298	−	2.56111i	−0.164135	−	0.0893833i	−0.558229	+	0.829687i	$0.688519\pi$
$822$	−20.9637	+	12.6634i	−0.731193	+	0.441686i
$823$	29.0966	−	47.6145i	1.01424	−	1.65974i	0.308571	−	0.951201i	$-0.400149\pi$
$823$	29.0966	−	47.6145i	1.01424	−	1.65974i	0.705674	−	0.708537i	$-0.250645\pi$
$824$	3.47553	+	9.54895i	0.121076	+	0.332653i
$825$	20.3006	−	14.4377i	0.706776	−	0.502656i
$826$	−12.4139	−	29.4492i	−0.431934	−	1.02467i
$827$	2.26200	−	7.33324i	0.0786576	−	0.255002i	−0.907700	−	0.419620i	$-0.862163\pi$
$827$	2.26200	−	7.33324i	0.0786576	−	0.255002i	0.986357	+	0.164619i	$0.0526394\pi$
$828$	−1.31032	+	2.49252i	−0.0455368	+	0.0866212i
$829$	−4.55654	+	2.63072i	−0.158255	+	0.0913687i	−0.577036	−	0.816719i	$-0.695791\pi$
$829$	−4.55654	+	2.63072i	−0.158255	+	0.0913687i	0.418781	+	0.908087i	$0.362458\pi$
$830$	−4.90902	+	24.2835i	−0.170395	+	0.842894i
$831$	−4.97404	−	12.8674i	−0.172547	−	0.446366i
$832$	15.2829	+	17.3176i	0.529840	+	0.600381i
$833$	0.0644070	+	0.318603i	0.00223157	+	0.0110389i
$834$	65.5689	+	34.0413i	2.27047	+	1.17875i
$835$	3.51864	−	28.0781i	0.121768	−	0.971683i
$836$	−3.52013	+	15.4227i	−0.121746	+	0.533405i
$837$	16.4638	+	16.5606i	0.569073	+	0.572416i
$838$	0.0129905	+	0.0269751i	0.000448750	+	0.000931840i
$839$	−37.4015	−	24.1565i	−1.29124	−	0.833974i	−0.298522	−	0.954403i	$-0.596494\pi$
$839$	−37.4015	−	24.1565i	−1.29124	−	0.833974i	−0.992722	+	0.120429i	$0.961573\pi$
$840$	6.14997	−	14.3828i	0.212194	−	0.496254i
$841$	20.2718	−	20.7377i	0.699029	−	0.715093i
$842$	1.10908	−	6.28991i	0.0382214	−	0.216765i
$843$	−3.05607	−	43.7951i	−0.105257	−	1.50838i
$844$	67.1211	+	30.2862i	2.31040	+	1.04249i
$845$	−0.926776	−	12.3670i	−0.0318821	−	0.425437i
$846$	1.34023	+	3.52067i	0.0460779	+	0.121043i
$847$	16.9204	+	5.21924i	0.581391	+	0.179335i
$848$	0.213771	+	0.297338i	0.00734094	+	0.0102106i
$849$	4.16332	+	0.863895i	0.142885	+	0.0296488i
$850$	−4.53465	+	13.4967i	−0.155537	+	0.462933i
$851$	0.350165	−	3.49937i	0.0120035	−	0.119957i
$852$	−26.8144	+	58.6226i	−0.918647	+	2.00838i
$853$	−32.2595	+	5.68823i	−1.10455	+	0.194761i	−0.696046	−	0.717997i	$-0.745059\pi$
$853$	−32.2595	+	5.68823i	−1.10455	+	0.194761i	−0.408500	+	0.912758i	$0.633948\pi$
$854$	59.4790	−	8.96502i	2.03533	−	0.306777i
$855$	−3.04650	+	3.21650i	−0.104188	+	0.110002i
$856$	1.42400	+	1.53471i	0.0486714	+	0.0524553i
$857$	15.0948	+	3.05147i	0.515627	+	0.104236i	0.448982	−	0.893541i	$-0.351787\pi$
$857$	15.0948	+	3.05147i	0.515627	+	0.104236i	0.0666444	+	0.997777i	$0.478771\pi$
$858$	28.3494	−	8.58556i	0.967833	−	0.293106i
$859$	−22.3448	−	41.0319i	−0.762394	−	1.39999i	−0.911556	−	0.411177i	$-0.865118\pi$
$859$	−22.3448	−	41.0319i	−0.762394	−	1.39999i	0.149162	−	0.988813i	$-0.452342\pi$
$860$	−21.5848	+	9.73945i	−0.736037	+	0.332112i
$861$	16.0710	+	29.8753i	0.547698	+	1.01815i
$862$	12.4748	+	20.4142i	0.424894	+	0.695309i
$863$	2.25635	−	1.08660i	0.0768069	−	0.0369883i	−0.395086	−	0.918644i	$-0.629285\pi$
$863$	2.25635	−	1.08660i	0.0768069	−	0.0369883i	0.471893	+	0.881656i	$0.343571\pi$
$864$	27.7784	−	12.0229i	0.945040	−	0.409026i
$865$	0.0258486	−	0.113250i	0.000878878	−	0.00385062i
$866$	−60.2760	−	61.7980i	−2.04826	−	2.09998i
$867$	10.8944	−	20.9844i	0.369994	−	0.712668i
$868$	−22.6986	−	29.9663i	−0.770441	−	1.01712i
$869$	2.55453	−	14.4875i	0.0866565	−	0.491454i
$870$	−0.152472	+	26.8182i	−0.00516927	+	0.909221i
$871$	0.220597	−	0.185103i	0.00747464	−	0.00627197i
$872$	5.69114	+	18.4502i	0.192726	+	0.624803i
$873$	−30.7951	+	35.9444i	−1.04226	+	1.21653i
$874$	−0.647084	+	0.441174i	−0.0218879	+	0.0149229i
$875$	−27.6593	−	1.38042i	−0.935056	−	0.0466667i
$876$	−39.9865	+	6.83932i	−1.35102	+	0.231079i
$877$	28.0776	−	28.7865i	0.948113	−	0.972052i	−0.0515329	−	0.998671i	$-0.516411\pi$
$877$	28.0776	−	28.7865i	0.948113	−	0.972052i	0.999646	+	0.0266194i	$0.00847420\pi$
$878$	−63.6349	−	21.3802i	−2.14758	−	0.721547i
$879$	45.8004	−	15.1270i	1.54481	−	0.510221i
$880$	0.761394	+	0.214223i	0.0256666	+	0.00722146i
$881$	6.08642	+	40.3807i	0.205057	+	1.36046i	0.820214	+	0.572057i	$0.193855\pi$
$881$	6.08642	+	40.3807i	0.205057	+	1.36046i	−0.615157	+	0.788405i	$0.710907\pi$
$882$	1.16650	+	0.341161i	0.0392782	+	0.0114875i
$883$	−6.70450	+	17.0828i	−0.225624	+	0.574882i	−0.998196	−	0.0600465i	$-0.980875\pi$
$883$	−6.70450	+	17.0828i	−0.225624	+	0.574882i	0.772571	+	0.634928i	$0.218970\pi$
$884$	−6.29267	+	8.30748i	−0.211645	+	0.279411i
$885$	−11.7122	−	0.0601042i	−0.393700	−	0.00202038i
$886$	58.5078	−	31.8616i	1.96561	−	1.07041i
$887$	0.644606	−	0.768212i	0.0216438	−	0.0257940i	−0.755114	−	0.655594i	$-0.772419\pi$
$887$	0.644606	−	0.768212i	0.0216438	−	0.0257940i	0.776758	+	0.629799i	$0.216863\pi$
$888$	40.0118	−	40.6031i	1.34271	−	1.36255i
$889$	29.1062	−	28.3894i	0.976191	−	0.952150i
$890$	1.97962	−	2.48236i	0.0663570	−	0.0832090i
$891$	0.778918	−	37.9408i	0.0260947	−	1.27107i
$892$	1.60493	−	0.772892i	0.0537369	−	0.0258783i
$893$	−0.0801943	+	0.639935i	−0.00268360	+	0.0214146i
$894$	4.87597	−	46.3271i	0.163077	−	1.54941i
$895$	−7.39037	−	16.3787i	−0.247033	−	0.547481i
$896$	−45.1994	+	12.7171i	−1.51000	+	0.424849i
$897$	0.811288	+	0.395837i	0.0270881	+	0.0132166i
$898$	8.32634	−	6.98663i	0.277854	−	0.233147i
$899$	20.9522	+	12.1123i	0.698796	+	0.403966i
$900$	22.6400	+	23.6934i	0.754668	+	0.789780i
$901$	−3.06329	+	3.30144i	−0.102053	+	0.109987i
$902$	58.5544	−	42.0977i	1.94965	−	1.40170i
$903$	13.7210	+	22.7146i	0.456607	+	0.755896i
$904$	−4.36055	−	34.7964i	−0.145030	−	1.15731i
$905$	−12.9595	−	20.0652i	−0.430788	−	0.666991i
$906$	−8.47878	−	20.4060i	−0.281688	−	0.677943i
$907$	−6.27189	+	11.5171i	−0.208255	+	0.382420i	−0.961281	−	0.275571i	$-0.911133\pi$
$907$	−6.27189	+	11.5171i	−0.208255	+	0.382420i	0.753026	+	0.657991i	$0.228593\pi$
$908$	1.71835	+	4.37828i	0.0570254	+	0.145298i
$909$	−6.40854	−	12.0612i	−0.212558	−	0.400043i
$910$	−12.4311	−	4.87885i	−0.412087	−	0.161732i
$911$	9.91323	+	11.8141i	0.328440	+	0.391420i	0.904843	−	0.425746i	$-0.139988\pi$
$911$	9.91323	+	11.8141i	0.328440	+	0.391420i	−0.576403	+	0.817166i	$0.695544\pi$
$912$	0.300979	+	0.0241091i	0.00996643	+	0.000798333i
$913$	−1.81100	−	36.2868i	−0.0599353	−	1.20092i
$914$	40.7099	+	20.8707i	1.34656	+	0.690342i
$915$	5.54913	−	21.3344i	0.183449	−	0.705292i
$916$	21.2000	−	58.2466i	0.700468	−	1.92452i
$917$	10.6996	−	8.53269i	0.353334	−	0.281774i
$918$	12.3888	+	17.8037i	0.408890	+	0.587611i
$919$	−8.06760	+	10.1164i	−0.266125	+	0.333711i	−0.896882	−	0.442270i	$-0.854173\pi$
$919$	−8.06760	+	10.1164i	−0.266125	+	0.333711i	0.630756	+	0.775981i	$0.282745\pi$
$920$	−0.528430	−	0.864737i	−0.0174218	−	0.0285095i
$921$	1.22898	+	27.4543i	0.0404964	+	0.904651i
$922$	2.74931	−	5.36273i	0.0905437	−	0.176612i
$923$	19.0424	+	8.02704i	0.626788	+	0.264213i
$924$	−9.41507	+	60.3615i	−0.309733	+	1.98575i
$925$	−37.3060	−	16.8331i	−1.22661	−	0.553469i
$926$	−16.6024	−	53.8237i	−0.545589	−	1.76876i
$927$	−0.716780	−	11.0912i	−0.0235421	−	0.364282i
$928$	24.5366	−	19.5451i	0.805453	−	0.641598i
$929$	3.07646	+	17.4475i	0.100936	+	0.572434i	0.992766	+	0.120064i	$0.0383101\pi$
$929$	3.07646	+	17.4475i	0.100936	+	0.572434i	−0.891831	+	0.452370i	$0.850579\pi$
$930$	−21.7168	+	5.41127i	−0.712123	+	0.177443i
$931$	0.148953	+	0.145284i	0.00488172	+	0.00476150i
$932$	−51.0034	−	5.10366i	−1.67067	−	0.167176i
$933$	1.74983	+	7.02251i	0.0572868	+	0.229907i
$934$	5.77316	−	2.43359i	0.188904	−	0.0796296i
$935$	−0.726924	+	9.70013i	−0.0237730	+	0.317228i
$936$	6.21296	+	13.2475i	0.203077	+	0.433006i
$937$	10.3534	+	1.56052i	0.338229	+	0.0509799i	0.315961	−	0.948772i	$-0.397673\pi$
$937$	10.3534	+	1.56052i	0.338229	+	0.0509799i	0.0222682	+	0.999752i	$0.492911\pi$
$938$	0.238077	+	0.934986i	0.00777348	+	0.0305284i
$939$	40.5590	+	27.9586i	1.32359	+	0.912395i
$940$	−2.18876	−	0.385937i	−0.0713893	−	0.0125879i
$941$	−1.38985	+	55.7311i	−0.0453077	+	1.81678i	0.394725	+	0.918799i	$0.370840\pi$
$941$	−1.38985	+	55.7311i	−0.0453077	+	1.81678i	−0.440032	+	0.897982i	$0.645033\pi$
$942$	−5.25075	+	28.9102i	−0.171079	+	0.941944i
$943$	2.18072	+	0.273279i	0.0710139	+	0.00889920i
$944$	0.497704	+	0.624101i	0.0161989	+	0.0203127i
$945$	−10.8718	+	13.2104i	−0.353660	+	0.429733i
$946$	44.1065	−	35.1738i	1.43403	−	1.14360i
$947$	42.0017	−	40.9673i	1.36487	−	1.33126i	0.471550	−	0.881840i	$-0.343695\pi$
$947$	42.0017	−	40.9673i	1.36487	−	1.33126i	0.893322	−	0.449418i	$-0.148369\pi$
$948$	19.3439	+	0.581750i	0.628261	+	0.0188944i
$949$	2.57680	+	12.7467i	0.0836464	+	0.413775i
$950$	2.46851	+	8.77359i	0.0800889	+	0.284653i
$951$	12.6910	+	7.41426i	0.411534	+	0.240424i
$952$	−5.98151	−	11.6674i	−0.193862	−	0.378141i
$953$	0.800087	+	10.6764i	0.0259174	+	0.345843i	0.995055	+	0.0993236i	$0.0316679\pi$
$953$	0.800087	+	10.6764i	0.0259174	+	0.345843i	−0.969138	+	0.246519i	$0.920713\pi$
$954$	5.59673	+	15.8822i	0.181201	+	0.514206i
$955$	19.0581	−	20.5397i	0.616706	−	0.664651i
$956$	−4.69311	−	26.6159i	−0.151786	−	0.860821i
$957$	−9.48794	−	38.1676i	−0.306702	−	1.23378i
$958$	−60.7214	+	22.1008i	−1.96182	+	0.714044i
$959$	−16.0669	+	2.01345i	−0.518828	+	0.0650176i
$960$	−3.67077	+	28.1216i	−0.118474	+	0.907621i
$961$	2.92598	−	10.3996i	0.0943865	−	0.335470i
$962$	−35.6747	−	33.1013i	−1.15020	−	1.06723i
$963$	−1.02368	−	2.04828i	−0.0329876	−	0.0660048i
$964$	−61.5082	−	41.9356i	−1.98105	−	1.35065i
$965$	−15.6108	+	0.389310i	−0.502531	+	0.0125323i
$966$	−2.37426	+	1.87356i	−0.0763905	+	0.0602807i
$967$	10.2532	+	7.37154i	0.329720	+	0.237053i	0.736444	−	0.676498i	$-0.236503\pi$
$967$	10.2532	+	7.37154i	0.329720	+	0.237053i	−0.406724	+	0.913551i	$0.633329\pi$
$968$	18.5888	+	0.463576i	0.597466	+	0.0148999i
$969$	0.442819	+	3.68686i	0.0142254	+	0.118439i
$970$	−14.4479	−	43.0018i	−0.463893	−	1.38071i
$971$	−35.5298	+	8.10945i	−1.14021	+	0.260245i	−0.750613	−	0.660743i	$-0.770242\pi$
$971$	−35.5298	+	8.10945i	−1.14021	+	0.260245i	−0.389593	+	0.920987i	$0.627384\pi$
$972$	49.5397	−	6.17164i	1.58899	−	0.197955i
$973$	30.4544	+	38.1886i	0.976322	+	1.22427i
$974$	−8.37259	+	23.0035i	−0.268275	+	0.737080i
$975$	7.37372	−	7.48270i	0.236148	−	0.239638i
$976$	−1.36947	+	0.617929i	−0.0438357	+	0.0197794i
$977$	−13.0654	−	14.8049i	−0.418000	−	0.473651i	0.502397	−	0.864637i	$-0.332452\pi$
$977$	−13.0654	−	14.8049i	−0.418000	−	0.473651i	−0.920397	+	0.390986i	$0.872134\pi$
$978$	12.5643	+	15.9221i	0.401762	+	0.509132i
$979$	−1.91504	+	4.24416i	−0.0612048	+	0.135644i
$980$	−0.525626	+	0.487710i	−0.0167905	+	0.0155793i
$981$	−0.309785	−	21.1156i	−0.00989067	−	0.674171i
$982$	−52.7926	+	35.9934i	−1.68468	+	1.14860i
$983$	0.523868	−	0.376635i	0.0167088	−	0.0120128i	−0.575358	−	0.817901i	$-0.695137\pi$
$983$	0.523868	−	0.376635i	0.0167088	−	0.0120128i	0.592067	+	0.805889i	$0.298312\pi$
$984$	24.7427	+	25.6293i	0.788769	+	0.817032i
$985$	−32.2748	+	11.7471i	−1.02836	+	0.374293i
$986$	17.2119	+	14.4587i	0.548138	+	0.460459i
$987$	−0.136912	+	2.48687i	−0.00435795	+	0.0791581i
$988$	−0.332534	+	6.66295i	−0.0105793	+	0.211977i
$989$	1.71443	+	0.128479i	0.0545157	+	0.00408539i
$990$	30.8387	+	19.2826i	0.980117	+	0.612840i
$991$	−8.90951	+	2.74822i	−0.283020	+	0.0873001i	−0.433015	−	0.901387i	$-0.642550\pi$
$991$	−8.90951	+	2.74822i	−0.283020	+	0.0873001i	0.149995	+	0.988687i	$0.452074\pi$
$992$	20.8680	+	15.8069i	0.662560	+	0.501869i
$993$	3.49057	−	11.1134i	0.110770	−	0.352672i
$994$	−51.9126	+	45.8132i	−1.64657	+	1.45310i
$995$	18.1361	−	3.66630i	0.574954	−	0.116230i
$996$	46.8960	−	9.22999i	1.48596	−	0.292463i
$997$	−9.51486	+	3.19682i	−0.301339	+	0.101244i	−0.465107	−	0.885254i	$-0.653984\pi$
$997$	−9.51486	+	3.19682i	−0.301339	+	0.101244i	0.163769	+	0.986499i	$0.447635\pi$
$998$			65.0172i			2.05808i
$999$	−54.4688	+	30.3393i	−1.72332	+	0.959892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.bf.a.4.11	✓	3168
27.7	even	9	inner	783.2.bf.a.439.11	yes	3168
29.22	even	14	inner	783.2.bf.a.544.11	yes	3168
783.196	even	126	inner	783.2.bf.a.196.11	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.bf.a.4.11	✓	3168	1.1	even	1	trivial
783.2.bf.a.196.11	yes	3168	783.196	even	126	inner
783.2.bf.a.439.11	yes	3168	27.7	even	9	inner
783.2.bf.a.544.11	yes	3168	29.22	even	14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.bf (of order \(126\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91602 - 1.23750i) q^{2} +(0.932239 + 1.45977i) q^{3} +(1.31716 + 2.91914i) q^{4} +(1.16159 + 0.489651i) q^{5} +(0.0202736 - 3.95060i) q^{6} +(1.07427 - 2.38083i) q^{7} +(0.408806 - 2.71225i) q^{8} +(-1.26186 + 2.72171i) q^{9} +(-1.61969 - 2.37565i) q^{10} +(3.16148 + 2.79002i) q^{11} +(-3.03336 + 4.64409i) q^{12} +(1.51730 + 0.927204i) q^{13} +(-5.00459 + 3.23231i) q^{14} +(0.368101 + 2.15213i) q^{15} +(0.0984645 - 0.111574i) q^{16} +(1.58489 + 0.915038i) q^{17} +(5.78587 - 3.65331i) q^{18} +(1.16821 - 0.0875453i) q^{19} +(0.100646 + 4.03579i) q^{20} +(4.47694 - 0.651311i) q^{21} +(-2.60482 - 9.25807i) q^{22} +(0.133714 - 0.260818i) q^{23} +(4.34037 - 1.93170i) q^{24} +(-2.38165 - 2.44179i) q^{25} +(-1.75977 - 3.65420i) q^{26} +(-5.14943 + 0.695255i) q^{27} +8.36494 q^{28} +(-4.96346 + 2.08904i) q^{29} +(1.95796 - 4.57905i) q^{30} +(-2.71354 - 3.58237i) q^{31} +(-5.60747 + 1.57770i) q^{32} +(-1.12554 + 7.21601i) q^{33} +(-1.90433 - 3.71453i) q^{34} +(2.41363 - 2.23953i) q^{35} +(-9.60712 - 0.0986057i) q^{36} +(11.1695 - 4.38371i) q^{37} +(-2.34665 - 1.27792i) q^{38} +(0.0609826 + 3.07929i) q^{39} +(1.80292 - 2.95035i) q^{40} +(2.56463 + 7.04626i) q^{41} +(-9.38390 - 4.29227i) q^{42} +(2.27847 + 5.40518i) q^{43} +(-3.98027 + 12.9037i) q^{44} +(-2.79845 + 2.54364i) q^{45} +(-0.578960 + 0.334263i) q^{46} +(-0.109086 + 0.539616i) q^{47} +(0.254665 + 0.0397221i) q^{48} +(0.117525 + 0.133172i) q^{49} +(1.54159 + 7.62581i) q^{50} +(0.141752 + 3.16661i) q^{51} +(-0.708098 + 5.65049i) q^{52} +(-0.547609 + 2.39923i) q^{53} +(10.7268 + 5.04028i) q^{54} +(2.30621 + 4.78888i) q^{55} +(-6.01823 - 3.88699i) q^{56} +(1.21685 + 1.62371i) q^{57} +(12.0953 + 2.13963i) q^{58} +(-0.931502 + 5.28281i) q^{59} +(-5.79750 + 3.90924i) q^{60} +(-9.20291 - 4.15251i) q^{61} +(0.766025 + 10.2219i) q^{62} +(5.12434 + 5.92812i) q^{63} +(12.4120 + 3.82861i) q^{64} +(1.30848 + 1.81998i) q^{65} +(11.0864 - 12.4332i) q^{66} +(0.0515777 - 0.153513i) q^{67} +(-0.583557 + 5.83177i) q^{68} +(0.505387 - 0.0479535i) q^{69} +(-7.39598 + 1.30411i) q^{70} +(11.4917 - 1.73210i) q^{71} +(6.86611 + 4.53514i) q^{72} +(4.97438 + 5.36111i) q^{73} +(-26.8259 - 5.42296i) q^{74} +(1.34418 - 5.75299i) q^{75} +(1.79428 + 3.29485i) q^{76} +(10.0388 - 4.52970i) q^{77} +(3.69377 - 5.97545i) q^{78} +(-1.81922 - 2.97702i) q^{79} +(0.169008 - 0.0813898i) q^{80} +(-5.81541 - 6.86884i) q^{81} +(3.80585 - 16.6745i) q^{82} +(-6.01639 - 6.16830i) q^{83} +(7.79812 + 12.2109i) q^{84} +(1.39295 + 1.83894i) q^{85} +(2.32329 - 13.1760i) q^{86} +(-7.67665 - 5.29803i) q^{87} +(8.85968 - 7.43415i) q^{88} +(0.325490 + 1.05521i) q^{89} +(8.50965 - 1.41059i) q^{90} +(3.83750 - 2.61636i) q^{91} +(0.937486 + 0.0467880i) q^{92} +(2.69977 - 7.30077i) q^{93} +(0.876785 - 0.898923i) q^{94} +(1.39985 + 0.470324i) q^{95} +(-7.53058 - 6.71483i) q^{96} +(15.1877 + 4.27316i) q^{97} +(-0.0603804 - 0.400598i) q^{98} +(-11.5830 + 5.08401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) \) 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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