LMFDB - Embedded newform 430.2.t.a.109.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(9,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 2]))

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

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

chi := DirichletCharacter("430.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.t (of order $42$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$22$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.20
Character	$\chi$	$=$	430.109
Dual form			430.2.t.a.359.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 - 0.623490i) q^{2} +(1.60048 - 0.628141i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.651975 + 2.13891i) q^{5} +(0.859664 - 1.48898i) q^{6} +(0.690583 - 0.398708i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.0321915 + 0.0298693i) q^{9} +O(q^{10})$	\(q+(0.781831 - 0.623490i) q^{2} +(1.60048 - 0.628141i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.651975 + 2.13891i) q^{5} +(0.859664 - 1.48898i) q^{6} +(0.690583 - 0.398708i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.0321915 + 0.0298693i) q^{9} +(1.84332 + 1.26577i) q^{10} +(-0.931112 - 4.07947i) q^{11} +(-0.256252 - 1.70012i) q^{12} +(1.67142 - 2.45153i) q^{13} +(0.291329 - 0.742294i) q^{14} +(2.38701 + 3.01374i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(2.43414 - 0.182413i) q^{17} +(-0.00654509 + 0.0434238i) q^{18} +(4.32440 + 4.01245i) q^{19} +(2.23036 - 0.159677i) q^{20} +(0.854817 - 1.07191i) q^{21} +(-3.27148 - 2.60892i) q^{22} +(-2.04391 + 6.62619i) q^{23} +(-1.26036 - 1.16944i) q^{24} +(-4.14986 + 2.78903i) q^{25} +(-0.221731 - 2.95880i) q^{26} +(-2.27072 + 4.71521i) q^{27} +(-0.235043 - 0.761989i) q^{28} +(3.73269 - 9.51074i) q^{29} +(3.74527 + 0.867962i) q^{30} +(-10.0528 + 1.51521i) q^{31} +(-0.974928 + 0.222521i) q^{32} +(-4.05270 - 5.94422i) q^{33} +(1.78935 - 1.66028i) q^{34} +(1.30304 + 1.21715i) q^{35} +(0.0219572 + 0.0380309i) q^{36} +(3.17733 + 1.83443i) q^{37} +(5.88267 + 0.440845i) q^{38} +(1.13517 - 4.97350i) q^{39} +(1.64421 - 1.51545i) q^{40} +(-2.82776 - 3.54590i) q^{41} -1.37102i q^{42} +(-4.50292 + 4.76694i) q^{43} -4.18438 q^{44} +(-0.0848758 - 0.0493805i) q^{45} +(2.53337 + 6.45492i) q^{46} +(-10.9496 - 2.49918i) q^{47} +(-1.71452 - 0.128485i) q^{48} +(-3.18206 + 5.51150i) q^{49} +(-1.50556 + 4.76795i) q^{50} +(3.78120 - 1.82093i) q^{51} +(-2.01814 - 2.17503i) q^{52} +(2.19332 + 3.21701i) q^{53} +(1.16456 + 5.10227i) q^{54} +(8.11854 - 4.65127i) q^{55} +(-0.658856 - 0.449201i) q^{56} +(9.44148 + 3.70551i) q^{57} +(-3.01151 - 9.76309i) q^{58} +(2.16212 + 1.04122i) q^{59} +(3.46934 - 1.65654i) q^{60} +(-12.4566 - 1.87753i) q^{61} +(-6.91487 + 7.45245i) q^{62} +(-0.0103217 + 0.0334622i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(6.33332 + 1.97668i) q^{65} +(-6.87469 - 2.12056i) q^{66} +(1.14362 - 1.23253i) q^{67} +(0.363806 - 2.41370i) q^{68} +(0.890952 + 11.8889i) q^{69} +(1.77764 + 0.139168i) q^{70} +(-4.61893 + 1.42475i) q^{71} +(0.0408787 + 0.0160437i) q^{72} +(3.57761 - 5.24739i) q^{73} +(3.62788 - 0.546816i) q^{74} +(-4.88984 + 7.07047i) q^{75} +(4.87412 - 3.32312i) q^{76} +(-2.26953 - 2.44597i) q^{77} +(-2.21342 - 4.59621i) q^{78} +(1.99352 + 3.45287i) q^{79} +(0.340628 - 2.20997i) q^{80} +(-0.662582 + 8.84154i) q^{81} +(-4.42167 - 1.00922i) q^{82} +(11.7838 - 4.62481i) q^{83} +(-0.854817 - 1.07191i) q^{84} +(1.97716 + 5.08746i) q^{85} +(-0.548383 + 6.53447i) q^{86} -17.5664i q^{87} +(-3.27148 + 2.60892i) q^{88} +(-0.549133 - 1.39917i) q^{89} +(-0.0971468 + 0.0143119i) q^{90} +(0.176812 - 2.35939i) q^{91} +(6.00525 + 3.46713i) q^{92} +(-15.1375 + 8.73963i) q^{93} +(-10.1190 + 4.87305i) q^{94} +(-5.76287 + 11.8655i) q^{95} +(-1.42057 + 0.968531i) q^{96} +(10.8271 - 2.47121i) q^{97} +(0.948524 + 6.29305i) q^{98} +(0.151825 + 0.103512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 44 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 264 * q + 44 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^9	$ 264 q + 44 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{9} - 8 q^{11} + 10 q^{14} + 32 q^{15} - 44 q^{16} + 4 q^{19} - 4 q^{20} + 24 q^{21} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 46 q^{29} - 36 q^{31} + 12 q^{34} - 68 q^{35} - 134 q^{36} - 64 q^{39} - 20 q^{41} + 8 q^{44} - 70 q^{45} + 112 q^{49} - 28 q^{50} - 28 q^{51} + 68 q^{54} - 30 q^{55} + 4 q^{56} - 40 q^{59} - 4 q^{60} + 20 q^{61} + 44 q^{64} + 18 q^{65} - 44 q^{66} + 32 q^{69} - 48 q^{70} + 20 q^{71} + 40 q^{74} + 122 q^{75} + 52 q^{76} + 16 q^{79} + 4 q^{80} - 16 q^{81} - 24 q^{84} + 120 q^{85} - 14 q^{86} - 142 q^{89} - 68 q^{90} - 4 q^{94} - 22 q^{95} - 2 q^{96} - 268 q^{99}+O(q^{100}) $ 264 * q + 44 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^9 - 8 * q^11 + 10 * q^14 + 32 * q^15 - 44 * q^16 + 4 * q^19 - 4 * q^20 + 24 * q^21 + 2 * q^24 + 28 * q^25 - 12 * q^26 - 46 * q^29 - 36 * q^31 + 12 * q^34 - 68 * q^35 - 134 * q^36 - 64 * q^39 - 20 * q^41 + 8 * q^44 - 70 * q^45 + 112 * q^49 - 28 * q^50 - 28 * q^51 + 68 * q^54 - 30 * q^55 + 4 * q^56 - 40 * q^59 - 4 * q^60 + 20 * q^61 + 44 * q^64 + 18 * q^65 - 44 * q^66 + 32 * q^69 - 48 * q^70 + 20 * q^71 + 40 * q^74 + 122 * q^75 + 52 * q^76 + 16 * q^79 + 4 * q^80 - 16 * q^81 - 24 * q^84 + 120 * q^85 - 14 * q^86 - 142 * q^89 - 68 * q^90 - 4 * q^94 - 22 * q^95 - 2 * q^96 - 268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{8}{21}\right)$

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 $

$2$	0.781831	−	0.623490i	0.552838	−	0.440874i
$2$	0.781831	−	0.623490i	0.552838	−	0.440874i
$3$	1.60048	−	0.628141i	0.924036	−	0.362657i	0.144852	−	0.989453i	$-0.453729\pi$
$3$	1.60048	−	0.628141i	0.924036	−	0.362657i	0.779183	+	0.626796i	$0.215634\pi$
$4$	0.222521	−	0.974928i	0.111260	−	0.487464i
$5$	0.651975	+	2.13891i	0.291572	+	0.956549i
$5$	0.651975	+	2.13891i	0.291572	+	0.956549i
$6$	0.859664	−	1.48898i	0.350956	−	0.607874i
$7$	0.690583	−	0.398708i	0.261016	−	0.150698i	−0.363782	−	0.931484i	$-0.618515\pi$
$7$	0.690583	−	0.398708i	0.261016	−	0.150698i	0.624798	+	0.780787i	$0.285181\pi$
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$	−0.0321915	+	0.0298693i	−0.0107305	+	0.00995644i
$10$	1.84332	+	1.26577i	0.582910	+	0.400270i
$11$	−0.931112	−	4.07947i	−0.280741	−	1.23001i	−0.896846	−	0.442342i	$-0.854148\pi$
$11$	−0.931112	−	4.07947i	−0.280741	−	1.23001i	0.616106	−	0.787663i	$-0.288709\pi$
$12$	−0.256252	−	1.70012i	−0.0739737	−	0.490783i
$13$	1.67142	−	2.45153i	0.463569	−	0.679931i	−0.521272	−	0.853391i	$-0.674542\pi$
$13$	1.67142	−	2.45153i	0.463569	−	0.679931i	0.984841	+	0.173459i	$0.0554945\pi$
$14$	0.291329	−	0.742294i	0.0778609	−	0.198386i
$15$	2.38701	+	3.01374i	0.616322	+	0.778144i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	2.43414	−	0.182413i	0.590365	−	0.0442417i	0.223801	−	0.974635i	$-0.428153\pi$
$17$	2.43414	−	0.182413i	0.590365	−	0.0442417i	0.366563	+	0.930393i	$0.380534\pi$
$18$	−0.00654509	+	0.0434238i	−0.00154269	+	0.0102351i
$19$	4.32440	+	4.01245i	0.992085	+	0.920520i	0.996837	−	0.0794688i	$-0.0253224\pi$
$19$	4.32440	+	4.01245i	0.992085	+	0.920520i	−0.00475283	+	0.999989i	$0.501513\pi$
$20$	2.23036	−	0.159677i	0.498724	−	0.0357049i
$21$	0.854817	−	1.07191i	0.186536	−	0.233909i
$22$	−3.27148	−	2.60892i	−0.697482	−	0.556223i
$23$	−2.04391	+	6.62619i	−0.426185	+	1.38166i	0.447117	+	0.894476i	$0.352451\pi$
$23$	−2.04391	+	6.62619i	−0.426185	+	1.38166i	−0.873301	+	0.487181i	$0.838025\pi$
$24$	−1.26036	−	1.16944i	−0.257269	−	0.238711i
$25$	−4.14986	+	2.78903i	−0.829971	+	0.557806i
$26$	−0.221731	−	2.95880i	−0.0434851	−	0.580268i
$27$	−2.27072	+	4.71521i	−0.437001	+	0.907442i
$28$	−0.235043	−	0.761989i	−0.0444189	−	0.144002i
$29$	3.73269	−	9.51074i	0.693143	−	1.76610i	0.0520403	−	0.998645i	$-0.483428\pi$
$29$	3.73269	−	9.51074i	0.693143	−	1.76610i	0.641103	−	0.767455i	$-0.278477\pi$
$30$	3.74527	+	0.867962i	0.683790	+	0.158468i
$31$	−10.0528	+	1.51521i	−1.80553	+	0.272141i	−0.963582	−	0.267412i	$-0.913832\pi$
$31$	−10.0528	+	1.51521i	−1.80553	+	0.272141i	−0.841952	+	0.539552i	$0.818594\pi$
$32$	−0.974928	+	0.222521i	−0.172345	+	0.0393365i
$33$	−4.05270	−	5.94422i	−0.705485	−	1.03476i
$34$	1.78935	−	1.66028i	0.306871	−	0.284735i
$35$	1.30304	+	1.21715i	0.220254	+	0.205735i
$36$	0.0219572	+	0.0380309i	0.00365953	+	0.00633848i
$37$	3.17733	+	1.83443i	0.522350	+	0.301579i	0.737895	−	0.674915i	$-0.235820\pi$
$37$	3.17733	+	1.83443i	0.522350	+	0.301579i	−0.215546	+	0.976494i	$0.569153\pi$
$38$	5.88267	+	0.440845i	0.954296	+	0.0715146i
$39$	1.13517	−	4.97350i	0.181773	−	0.796398i
$40$	1.64421	−	1.51545i	0.259972	−	0.239613i
$41$	−2.82776	−	3.54590i	−0.441623	−	0.553777i	0.510347	−	0.859968i	$-0.329517\pi$
$41$	−2.82776	−	3.54590i	−0.441623	−	0.553777i	−0.951970	+	0.306191i	$0.900945\pi$
$42$		−	1.37102i		−	0.211553i
$43$	−4.50292	+	4.76694i	−0.686688	+	0.726952i
$43$	−4.50292	+	4.76694i	−0.686688	+	0.726952i
$44$	−4.18438			−0.630819
$45$	−0.0848758	−	0.0493805i	−0.0126525	−	0.00736121i
$46$	2.53337	+	6.45492i	0.373525	+	0.951726i
$47$	−10.9496	−	2.49918i	−1.59717	−	0.364543i	−0.670941	−	0.741510i	$-0.734110\pi$
$47$	−10.9496	−	2.49918i	−1.59717	−	0.364543i	−0.926227	+	0.376967i	$0.876967\pi$
$48$	−1.71452	−	0.128485i	−0.247470	−	0.0185453i
$49$	−3.18206	+	5.51150i	−0.454581	+	0.787357i
$50$	−1.50556	+	4.76795i	−0.212918	+	0.674289i
$51$	3.78120	−	1.82093i	0.529473	−	0.254981i
$52$	−2.01814	−	2.17503i	−0.279865	−	0.301623i
$53$	2.19332	+	3.21701i	0.301276	+	0.441891i	0.946787	−	0.321860i	$-0.104308\pi$
$53$	2.19332	+	3.21701i	0.301276	+	0.441891i	−0.645511	+	0.763751i	$0.723356\pi$
$54$	1.16456	+	5.10227i	0.158477	+	0.694331i
$55$	8.11854	−	4.65127i	1.09470	−	0.627178i
$56$	−0.658856	−	0.449201i	−0.0880434	−	0.0600270i
$57$	9.44148	+	3.70551i	1.25055	+	0.490806i
$58$	−3.01151	−	9.76309i	−0.395431	−	1.28196i
$59$	2.16212	+	1.04122i	0.281484	+	0.135556i	0.569299	−	0.822130i	$-0.307215\pi$
$59$	2.16212	+	1.04122i	0.281484	+	0.135556i	−0.287815	+	0.957686i	$0.592929\pi$
$60$	3.46934	−	1.65654i	0.447890	−	0.213858i
$61$	−12.4566	−	1.87753i	−1.59491	−	0.240393i	−0.709326	−	0.704881i	$-0.751001\pi$
$61$	−12.4566	−	1.87753i	−1.59491	−	0.240393i	−0.885580	+	0.464487i	$0.846239\pi$
$62$	−6.91487	+	7.45245i	−0.878189	+	0.946463i
$63$	−0.0103217	+	0.0334622i	−0.00130042	+	0.00421584i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	6.33332	+	1.97668i	0.785552	+	0.245178i
$66$	−6.87469	−	2.12056i	−0.846216	−	0.261023i
$67$	1.14362	−	1.23253i	0.139716	−	0.150578i	−0.659317	−	0.751865i	$-0.729155\pi$
$67$	1.14362	−	1.23253i	0.139716	−	0.150578i	0.799033	+	0.601287i	$0.205345\pi$
$68$	0.363806	−	2.41370i	0.0441180	−	0.292704i
$69$	0.890952	+	11.8889i	0.107258	+	1.43126i
$70$	1.77764	+	0.139168i	0.212468	+	0.0166338i
$71$	−4.61893	+	1.42475i	−0.548166	+	0.169087i	−0.556454	−	0.830879i	$-0.687838\pi$
$71$	−4.61893	+	1.42475i	−0.548166	+	0.169087i	0.00828712	+	0.999966i	$0.497362\pi$
$72$	0.0408787	+	0.0160437i	0.00481760	+	0.00189077i
$73$	3.57761	−	5.24739i	0.418727	−	0.614160i	−0.557691	−	0.830049i	$-0.688312\pi$
$73$	3.57761	−	5.24739i	0.418727	−	0.614160i	0.976418	+	0.215889i	$0.0692649\pi$
$74$	3.62788	−	0.546816i	0.421733	−	0.0635660i
$75$	−4.88984	+	7.07047i	−0.564630	+	0.816428i
$76$	4.87412	−	3.32312i	0.559100	−	0.381188i
$77$	−2.26953	−	2.44597i	−0.258637	−	0.278744i
$78$	−2.21342	−	4.59621i	−0.250620	−	0.520418i
$79$	1.99352	+	3.45287i	0.224288	+	0.388478i	0.956106	−	0.293022i	$-0.0946610\pi$
$79$	1.99352	+	3.45287i	0.224288	+	0.388478i	−0.731818	+	0.681501i	$0.761328\pi$
$80$	0.340628	−	2.20997i	0.0380834	−	0.247082i
$81$	−0.662582	+	8.84154i	−0.0736202	+	0.982393i
$82$	−4.42167	−	1.00922i	−0.488292	−	0.111449i
$83$	11.7838	−	4.62481i	1.29344	−	0.507638i	0.383947	−	0.923355i	$-0.374564\pi$
$83$	11.7838	−	4.62481i	1.29344	−	0.507638i	0.909494	+	0.415717i	$0.136469\pi$
$84$	−0.854817	−	1.07191i	−0.0932681	−	0.116955i
$85$	1.97716	+	5.08746i	0.214453	+	0.551813i
$86$	−0.548383	+	6.53447i	−0.0591337	+	0.704630i
$87$		−	17.5664i		−	1.88331i
$88$	−3.27148	+	2.60892i	−0.348741	+	0.278111i
$89$	−0.549133	−	1.39917i	−0.0582080	−	0.148312i	0.898811	−	0.438336i	$-0.144432\pi$
$89$	−0.549133	−	1.39917i	−0.0582080	−	0.148312i	−0.957019	+	0.290024i	$0.906337\pi$
$90$	−0.0971468	+	0.0143119i	−0.0102402	+	0.00150861i
$91$	0.176812	−	2.35939i	0.0185349	−	0.247332i
$92$	6.00525	+	3.46713i	0.626090	+	0.361473i
$93$	−15.1375	+	8.73963i	−1.56968	+	0.906258i
$94$	−10.1190	+	4.87305i	−1.04369	+	0.502616i
$95$	−5.76287	+	11.8655i	−0.591258	+	1.21738i
$96$	−1.42057	+	0.968531i	−0.144987	+	0.0988503i
$97$	10.8271	−	2.47121i	1.09932	−	0.250914i	0.365880	−	0.930662i	$-0.380768\pi$
$97$	10.8271	−	2.47121i	1.09932	−	0.250914i	0.733445	+	0.679749i	$0.237911\pi$
$98$	0.948524	+	6.29305i	0.0958154	+	0.635694i
$99$	0.151825	+	0.103512i	0.0152590	+	0.0104034i
$100$	1.79567	+	4.66643i	0.179567	+	0.466643i
$101$	−0.826745	+	0.255017i	−0.0822642	+	0.0253752i	−0.335614	−	0.942000i	$-0.608944\pi$
$101$	−0.826745	+	0.255017i	−0.0822642	+	0.0253752i	0.253350	+	0.967375i	$0.418468\pi$
$102$	1.82093	−	3.78120i	0.180299	−	0.374394i
$103$	−5.58338	+	0.418416i	−0.550147	+	0.0412278i	−0.346904	−	0.937901i	$-0.612767\pi$
$103$	−5.58338	+	0.418416i	−0.550147	+	0.0412278i	−0.203243	+	0.979128i	$0.565148\pi$
$104$	−2.93395	−	0.442222i	−0.287698	−	0.0433635i
$105$	2.85003	+	1.12952i	0.278134	+	0.110230i
$106$	3.72058	+	1.14765i	0.361375	+	0.111469i
$107$	12.9551	+	10.3314i	1.25242	+	0.998770i	0.999511	+	0.0312790i	$0.00995803\pi$
$107$	12.9551	+	10.3314i	1.25242	+	0.998770i	0.252907	+	0.967491i	$0.418613\pi$
$108$	4.09170	+	3.26302i	0.393724	+	0.313985i
$109$	6.18385	+	1.90746i	0.592305	+	0.182702i	0.576395	−	0.817172i	$-0.304459\pi$
$109$	6.18385	+	1.90746i	0.592305	+	0.182702i	0.0159105	+	0.999873i	$0.494935\pi$
$110$	3.44731	−	8.69834i	0.328688	−	0.829354i
$111$	6.23752	+	0.940155i	0.592039	+	0.0892356i
$112$	−0.795187	+	0.0595910i	−0.0751381	+	0.00563082i
$113$	6.86695	−	14.2594i	0.645988	−	1.34141i	−0.278588	−	0.960411i	$-0.589866\pi$
$113$	6.86695	−	14.2594i	0.645988	−	1.34141i	0.924576	−	0.380997i	$-0.124419\pi$
$114$	9.69199	−	2.98958i	0.907738	−	0.280000i
$115$	−15.5054	−	0.0516201i	−1.44589	−	0.00481360i
$116$	−8.44168	−	5.75544i	−0.783791	−	0.534379i
$117$	0.0194199	+	0.128843i	0.00179537	+	0.0119115i
$118$	2.33961	−	0.534000i	0.215378	−	0.0491586i
$119$	1.60824	−	1.09648i	0.147427	−	0.100514i
$120$	1.67960	−	3.45823i	0.153326	−	0.315692i
$121$	−5.86442	+	2.82416i	−0.533129	+	0.256742i
$122$	−10.9096	+	6.29866i	−0.987708	+	0.570254i
$123$	−6.75310	−	3.89890i	−0.608906	−	0.351552i
$124$	−0.759732	+	10.1379i	−0.0682259	+	0.910411i
$125$	−8.67109	−	7.05778i	−0.775566	−	0.631267i
$126$	0.0127935	+	0.0325973i	0.00113974	+	0.00290400i
$127$	−0.750543	+	0.598538i	−0.0665999	+	0.0531117i	−0.656224	−	0.754566i	$-0.727847\pi$
$127$	−0.750543	+	0.598538i	−0.0665999	+	0.0531117i	0.589624	+	0.807678i	$0.299276\pi$
$128$			1.00000i			0.0883883i
$129$	−4.21250	+	10.4578i	−0.370890	+	0.920762i
$130$	6.18403	−	2.40333i	0.542375	−	0.210786i
$131$	−12.5446	−	15.7304i	−1.09603	−	1.37437i	−0.920887	−	0.389830i	$-0.872534\pi$
$131$	−12.5446	−	15.7304i	−1.09603	−	1.37437i	−0.175139	−	0.984544i	$-0.556038\pi$
$132$	−6.69700	+	2.62838i	−0.582899	+	0.228771i
$133$	4.58615	+	1.04676i	0.397670	+	0.0907655i
$134$	0.125649	−	1.67667i	0.0108544	−	0.144842i
$135$	−11.5658	−	1.78267i	−0.995430	−	0.153428i
$136$	−1.22048	−	2.11393i	−0.104655	−	0.181268i
$137$	−1.46561	−	3.04338i	−0.125216	−	0.260013i	0.828932	−	0.559350i	$-0.188949\pi$
$137$	−1.46561	−	3.04338i	−0.125216	−	0.260013i	−0.954148	+	0.299336i	$0.903235\pi$
$138$	8.10920	+	8.73964i	0.690301	+	0.743967i
$139$	−0.404103	+	0.275513i	−0.0342756	+	0.0233687i	−0.580337	−	0.814377i	$-0.697079\pi$
$139$	−0.404103	+	0.275513i	−0.0342756	+	0.0233687i	0.546061	+	0.837745i	$0.316127\pi$
$140$	1.47658	−	0.999533i	0.124794	−	0.0844759i
$141$	−19.0945	+	2.87803i	−1.60804	+	0.242374i
$142$	−2.72291	+	3.99377i	−0.228501	+	0.335150i
$143$	−11.5572	−	4.53587i	−0.966462	−	0.379308i
$144$	0.0419633	−	0.0129440i	0.00349694	−	0.00107866i
$145$	22.7762	+	1.78311i	1.89146	+	0.148079i
$146$	−0.474606	−	6.33317i	−0.0392786	−	0.524137i
$147$	−1.63082	+	10.8198i	−0.134508	+	0.892402i
$148$	2.49546	−	2.68947i	0.205126	−	0.221073i
$149$	0.0626271	+	0.0193179i	0.00513061	+	0.00158259i	0.297319	−	0.954778i	$-0.403907\pi$
$149$	0.0626271	+	0.0193179i	0.00513061	+	0.00158259i	−0.292189	+	0.956361i	$0.594384\pi$
$150$	0.585334	+	8.57669i	0.0477924	+	0.700283i
$151$	8.25598	−	10.3527i	0.671862	−	0.842489i	−0.322714	−	0.946496i	$-0.604595\pi$
$151$	8.25598	−	10.3527i	0.671862	−	0.842489i	0.994576	+	0.104008i	$0.0331667\pi$
$152$	1.73881	−	5.63708i	0.141036	−	0.457228i
$153$	−0.0729098	+	0.0785781i	−0.00589441	+	0.00635266i
$154$	−3.29942	−	0.497308i	−0.265875	−	0.0400742i
$155$	−9.79508	−	20.5141i	−0.786760	−	1.64773i
$156$	−4.59621	−	2.21342i	−0.367991	−	0.177215i
$157$	6.08567	+	19.7292i	0.485689	+	1.57457i	0.784421	+	0.620228i	$0.212960\pi$
$157$	6.08567	+	19.7292i	0.485689	+	1.57457i	−0.298732	+	0.954337i	$0.596564\pi$
$158$	3.71142	+	1.45663i	0.295265	+	0.115883i
$159$	5.53110	+	3.77104i	0.438645	+	0.299063i
$160$	−1.11158	−	1.94020i	−0.0878782	−	0.153387i
$161$	1.23043	+	5.39086i	0.0969713	+	0.424859i
$162$	4.99458	+	7.32570i	0.392411	+	0.575562i
$163$	−1.05805	−	1.14031i	−0.0828730	−	0.0893158i	0.690254	−	0.723567i	$-0.257499\pi$
$163$	−1.05805	−	1.14031i	−0.0828730	−	0.0893158i	−0.773127	+	0.634251i	$0.781308\pi$
$164$	−4.08624	+	1.96783i	−0.319082	+	0.153662i
$165$	10.0719	−	12.5438i	0.784095	−	0.976537i
$166$	6.32944	−	10.9629i	0.491259	−	0.850886i
$167$	11.2357	+	0.842001i	0.869447	+	0.0651560i	0.501979	−	0.864880i	$-0.332606\pi$
$167$	11.2357	+	0.842001i	0.869447	+	0.0651560i	0.367468	+	0.930036i	$0.380225\pi$
$168$	−1.33665	−	0.305081i	−0.103124	−	0.0235375i
$169$	1.53310	+	3.90628i	0.117931	+	0.300483i
$170$	4.71779	+	2.74480i	0.361838	+	0.210516i
$171$	−0.259058			−0.0198106
$172$	3.64543	+	5.45076i	0.277962	+	0.415617i
$173$			0.974966i			0.0741253i	0.999313	+	0.0370627i	$0.0118001\pi$
$173$			0.974966i			0.0741253i	−0.999313	+	0.0370627i	$0.988200\pi$
$174$	−10.9525	−	13.7339i	−0.830303	−	1.04117i
$175$	−1.75381	+	3.58064i	−0.132576	+	0.270671i
$176$	−0.931112	+	4.07947i	−0.0701852	+	0.307501i
$177$	4.11446	+	0.308336i	0.309262	+	0.0231759i
$178$	−1.30170	−	0.751535i	−0.0975664	−	0.0563300i
$179$	3.26860	+	5.66138i	0.244307	+	0.423152i	0.961936	−	0.273273i	$-0.0881063\pi$
$179$	3.26860	+	5.66138i	0.244307	+	0.423152i	−0.717630	+	0.696425i	$0.754773\pi$
$180$	−0.0670291	+	0.0717595i	−0.00499605	+	0.00534864i
$181$	9.84311	−	9.13307i	0.731633	−	0.678856i	−0.223610	−	0.974679i	$-0.571784\pi$
$181$	9.84311	−	9.13307i	0.731633	−	0.678856i	0.955243	+	0.295823i	$0.0955938\pi$
$182$	−1.33282	−	1.95489i	−0.0987952	−	0.144906i
$183$	−21.1159	+	4.81956i	−1.56093	+	0.356272i
$184$	6.85681	−	1.03350i	0.505491	−	0.0761905i
$185$	−1.85214	+	7.99202i	−0.136172	+	0.587585i
$186$	−6.38589	+	16.2710i	−0.468236	+	1.19305i
$187$	−3.01060	−	9.76013i	−0.220157	−	0.713731i
$188$	−4.87305	+	10.1190i	−0.355403	+	0.738003i
$189$	0.311869	+	4.16160i	0.0226851	+	0.302712i
$190$	2.89243	+	12.8699i	0.209839	+	0.933682i
$191$	7.01274	+	6.50687i	0.507424	+	0.470821i	0.891848	−	0.452336i	$-0.149409\pi$
$191$	7.01274	+	6.50687i	0.507424	+	0.470821i	−0.384424	+	0.923157i	$0.625600\pi$
$192$	−0.506781	+	1.64294i	−0.0365737	+	0.118569i
$193$	11.0524	+	8.81400i	0.795570	+	0.634446i	0.934543	−	0.355850i	$-0.115809\pi$
$193$	11.0524	+	8.81400i	0.795570	+	0.634446i	−0.138973	+	0.990296i	$0.544380\pi$
$194$	6.92419	−	8.68265i	0.497128	−	0.623378i
$195$	11.3780	−	0.814578i	0.814793	−	0.0583332i
$196$	4.66524	+	4.32871i	0.333231	+	0.309193i
$197$	3.40506	−	22.5911i	0.242600	−	1.60955i	−0.453266	−	0.891376i	$-0.649741\pi$
$197$	3.40506	−	22.5911i	0.242600	−	1.60955i	0.695866	−	0.718172i	$-0.255021\pi$
$198$	0.183240	−	0.0137320i	0.0130223	−	0.000975888i
$199$	−6.02540	−	2.90168i	−0.427130	−	0.205695i	0.207953	−	0.978139i	$-0.433320\pi$
$199$	−6.02540	−	2.90168i	−0.427130	−	0.205695i	−0.635083	+	0.772444i	$0.719034\pi$
$200$	4.31339	+	2.52878i	0.305002	+	0.178811i
$201$	1.05614	−	2.69100i	0.0744942	−	0.189808i
$202$	−0.487375	+	0.714848i	−0.0342916	+	0.0502965i
$203$	−1.21428	−	8.05621i	−0.0852256	−	0.565435i
$204$	−0.933878	−	4.09159i	−0.0653845	−	0.286468i
$205$	5.74073	−	8.36017i	0.400950	−	0.583900i
$206$	−4.10438	+	3.80831i	−0.285966	+	0.265338i
$207$	−0.132123	−	0.274357i	−0.00918321	−	0.0190691i
$208$	−2.56958	+	1.48355i	−0.178168	+	0.102865i
$209$	12.3422	−	21.3773i	0.853726	−	1.47870i
$210$	2.93248	−	0.893871i	0.202361	−	0.0616830i
$211$	3.97388	−	17.4107i	0.273573	−	1.19860i	−0.632189	−	0.774814i	$-0.717843\pi$
$211$	3.97388	−	17.4107i	0.273573	−	1.19860i	0.905762	−	0.423787i	$-0.139300\pi$
$212$	3.62442	−	1.42248i	0.248926	−	0.0976963i
$213$	−6.49755	+	5.18162i	−0.445205	+	0.355039i
$214$	16.5702			1.13272
$215$	−13.1318	−	6.52340i	−0.895584	−	0.444892i
$216$	5.23348			0.356094
$217$	−6.33816	+	5.05451i	−0.430262	+	0.343123i
$218$	6.02401	−	2.36425i	0.407997	−	0.160127i
$219$	2.42978	−	10.6456i	0.164189	−	0.719360i
$220$	−2.72811	−	8.95000i	−0.183929	−	0.603409i
$221$	3.62128	−	6.27224i	0.243594	−	0.421917i
$222$	5.46287	−	3.15399i	0.366644	−	0.211682i
$223$	11.5649	+	24.0147i	0.774440	+	1.60814i	0.793687	+	0.608327i	$0.208159\pi$
$223$	11.5649	+	24.0147i	0.774440	+	1.60814i	−0.0192465	+	0.999815i	$0.506127\pi$
$224$	−0.584548	+	0.542381i	−0.0390567	+	0.0362393i
$225$	0.0502835	−	0.213736i	0.00335223	−	0.0142491i
$226$	−3.52177	−	15.4299i	−0.234265	−	1.02638i
$227$	−0.528358	−	3.50543i	−0.0350684	−	0.232663i	0.964430	−	0.264339i	$-0.0851538\pi$
$227$	−0.528358	−	3.50543i	−0.0350684	−	0.232663i	−0.999498	+	0.0316755i	$0.989916\pi$
$228$	5.71353	−	8.38021i	0.378388	−	0.554993i
$229$	−2.05395	+	5.23337i	−0.135729	+	0.345831i	−0.982537	−	0.186067i	$-0.940426\pi$
$229$	−2.05395	+	5.23337i	−0.135729	+	0.345831i	0.846808	+	0.531898i	$0.178521\pi$
$230$	−12.1548	+	9.62710i	−0.801463	+	0.634792i
$231$	−5.16874	−	2.48913i	−0.340078	−	0.163773i
$232$	−10.1884	+	0.763518i	−0.668903	+	0.0501274i
$233$	1.90756	−	12.6558i	0.124968	−	0.829111i	−0.835252	−	0.549868i	$-0.814678\pi$
$233$	1.90756	−	12.6558i	0.124968	−	0.829111i	0.960220	−	0.279244i	$-0.0900838\pi$
$234$	0.0955151	+	0.0886250i	0.00624402	+	0.00579360i
$235$	−1.79337	−	25.0497i	−0.116987	−	1.63406i
$236$	1.49623	−	1.87622i	0.0973965	−	0.122131i
$237$	5.35946	+	4.27403i	0.348135	+	0.277628i
$238$	0.573730	−	1.85999i	0.0371894	−	0.120565i
$239$	−15.3493	−	14.2421i	−0.992866	−	0.921245i	0.00402885	−	0.999992i	$-0.498718\pi$
$239$	−15.3493	−	14.2421i	−0.992866	−	0.921245i	−0.996895	+	0.0787471i	$0.974908\pi$
$240$	−0.843006	−	3.75097i	−0.0544158	−	0.242124i
$241$	1.57448	+	21.0100i	0.101421	+	1.35338i	0.783178	+	0.621797i	$0.213597\pi$
$241$	1.57448	+	21.0100i	0.101421	+	1.35338i	−0.681757	+	0.731579i	$0.738784\pi$
$242$	−2.82416	+	5.86442i	−0.181544	+	0.376979i
$243$	−0.134507	−	0.436060i	−0.00862862	−	0.0279733i
$244$	−4.60232	+	11.7265i	−0.294633	+	0.750713i
$245$	−13.8632	−	3.21278i	−0.885688	−	0.205257i
$246$	−7.71071	+	1.16220i	−0.491617	+	0.0740993i
$247$	17.0645	−	3.89487i	1.08579	−	0.247825i
$248$	5.72690	+	8.39982i	0.363659	+	0.533389i
$249$	15.9547	−	14.8038i	1.01109	−	0.938152i
$250$	−11.1798	−	0.111662i	−0.707072	−	0.00706210i
$251$	−8.10820	−	14.0438i	−0.511785	−	0.886438i	−0.999907	−	0.0136620i	$-0.995651\pi$
$251$	−8.10820	−	14.0438i	−0.511785	−	0.886438i	0.488122	−	0.872776i	$-0.337682\pi$
$252$	0.0303265	+	0.0175090i	0.00191039	+	0.00110296i
$253$	28.9344	+	2.16834i	1.81909	+	0.136322i
$254$	−0.213616	+	0.935912i	−0.0134034	+	0.0587243i
$255$	6.36004	+	6.90043i	0.398281	+	0.432122i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$		−	10.3379i		−	0.644858i	−0.946594	−	0.322429i	$-0.895501\pi$
$257$		−	10.3379i		−	0.644858i	0.946594	−	0.322429i	$-0.104499\pi$
$258$	3.22689	+	10.8027i	0.200897	+	0.672548i
$259$	2.92561			0.181789
$260$	3.33642	−	5.73468i	0.206916	−	0.355650i
$261$	0.163918	+	0.417657i	0.0101463	+	0.0258523i
$262$	−19.6155	−	4.47711i	−1.21185	−	0.276597i
$263$	−2.99861	−	0.224714i	−0.184902	−	0.0138565i	−0.0180427	−	0.999837i	$-0.505743\pi$
$263$	−2.99861	−	0.224714i	−0.184902	−	0.0138565i	−0.166859	+	0.985981i	$0.553363\pi$
$264$	−3.59716	+	6.23046i	−0.221390	+	0.383458i
$265$	−5.45091	+	6.78873i	−0.334846	+	0.417028i
$266$	4.23824	−	2.04103i	0.259863	−	0.125144i
$267$	−1.75775	−	1.89440i	−0.107573	−	0.115936i
$268$	−0.947151	−	1.38921i	−0.0578564	−	0.0848598i
$269$	−4.71148	−	20.6423i	−0.287264	−	1.25859i	−0.888263	−	0.459336i	$-0.848088\pi$
$269$	−4.71148	−	20.6423i	−0.287264	−	1.25859i	0.600999	−	0.799250i	$-0.294770\pi$
$270$	−10.1540	+	5.81744i	−0.617954	+	0.354038i
$271$	7.24964	+	4.94272i	0.440384	+	0.300249i	0.763140	−	0.646234i	$-0.223657\pi$
$271$	7.24964	+	4.94272i	0.440384	+	0.300249i	−0.322756	+	0.946482i	$0.604609\pi$
$272$	−2.27223	−	0.891783i	−0.137774	−	0.0540723i
$273$	−1.19905	−	3.88722i	−0.0725696	−	0.235265i
$274$	−3.04338	−	1.46561i	−0.183857	−	0.0885410i
$275$	15.2417	+	14.3323i	0.919111	+	0.864270i
$276$	11.7891	+	1.77692i	0.709621	+	0.106958i
$277$	−0.844668	+	0.910336i	−0.0507512	+	0.0546968i	−0.757917	−	0.652351i	$-0.773783\pi$
$277$	−0.844668	+	0.910336i	−0.0507512	+	0.0546968i	0.707166	+	0.707048i	$0.249973\pi$
$278$	−0.144161	+	0.467359i	−0.00864620	+	0.0280303i
$279$	0.278356	−	0.349047i	0.0166647	−	0.0208969i
$280$	0.531241	−	1.70210i	0.0317477	−	0.101720i
$281$	−3.21045	−	0.990293i	−0.191520	−	0.0590760i	0.197512	−	0.980301i	$-0.436714\pi$
$281$	−3.21045	−	0.990293i	−0.191520	−	0.0590760i	−0.389031	+	0.921225i	$0.627190\pi$
$282$	−13.1342	+	14.1553i	−0.782132	+	0.842938i
$283$	−2.52628	+	16.7608i	−0.150172	+	0.996323i	0.779093	+	0.626908i	$0.215680\pi$
$283$	−2.52628	+	16.7608i	−0.150172	+	0.996323i	−0.929265	+	0.369415i	$0.879558\pi$
$284$	0.361221	+	4.82016i	0.0214345	+	0.286024i
$285$	−1.77013	+	22.6104i	−0.104853	+	1.33932i
$286$	−11.8639	+	3.65952i	−0.701525	+	0.216392i
$287$	−3.36659	−	1.32129i	−0.198723	−	0.0779932i
$288$	0.0247378	−	0.0362837i	0.00145769	−	0.00213804i
$289$	−10.9184	+	1.64568i	−0.642258	+	0.0968048i
$290$	18.9189	−	12.8066i	1.11096	−	0.752032i
$291$	15.7762	−	10.7561i	0.924819	−	0.630531i
$292$	−4.31973	−	4.65556i	−0.252793	−	0.272446i
$293$	−0.241673	−	0.501839i	−0.0141187	−	0.0293177i	0.893790	−	0.448485i	$-0.148036\pi$
$293$	−0.241673	−	0.501839i	−0.0141187	−	0.0293177i	−0.907909	+	0.419167i	$0.862322\pi$
$294$	5.47101	+	9.47606i	0.319076	+	0.552655i
$295$	−0.817429	+	5.30343i	−0.0475926	+	0.308778i
$296$	0.274174	−	3.65860i	0.0159361	−	0.212652i
$297$	21.3498	+	4.87296i	1.23884	+	0.282758i
$298$	0.0610084	−	0.0239440i	0.00353412	−	0.00138704i
$299$	12.8281	+	16.0859i	0.741866	+	0.930270i
$300$	5.80511	+	6.34057i	0.335158	+	0.366073i
$301$	−1.20902	+	5.08732i	−0.0696867	+	0.293228i
$302$		−	13.2416i		−	0.761967i
$303$	−1.16300	+	0.927461i	−0.0668126	+	0.0532813i
$304$	−2.15521	−	5.49138i	−0.123610	−	0.314952i
$305$	−4.10554	−	27.8677i	−0.235082	−	1.59570i
$306$	−0.00801055	+	0.106893i	−0.000457933	+	0.00611069i
$307$	−23.3737	−	13.4948i	−1.33401	−	0.770189i	−0.348096	−	0.937459i	$-0.613172\pi$
$307$	−23.3737	−	13.4948i	−1.33401	−	0.770189i	−0.985911	+	0.167269i	$0.946505\pi$
$308$	−2.88966	+	1.66835i	−0.164654	+	0.0950628i
$309$	−8.67324	+	4.17681i	−0.493403	+	0.237611i
$310$	−20.4484	−	9.93145i	−1.16139	−	0.564068i
$311$	2.78292	−	1.89736i	0.157805	−	0.107590i	−0.481843	−	0.876258i	$-0.660032\pi$
$311$	2.78292	−	1.89736i	0.157805	−	0.107590i	0.639648	+	0.768668i	$0.279080\pi$
$312$	−4.97350	+	1.13517i	−0.281569	+	0.0642663i
$313$	−4.01640	−	26.6471i	−0.227021	−	1.50618i	−0.754322	−	0.656505i	$-0.772034\pi$
$313$	−4.01640	−	26.6471i	−0.227021	−	1.50618i	0.527301	−	0.849678i	$-0.323204\pi$
$314$	17.0590	+	11.6306i	0.962692	+	0.656352i
$315$	−0.0783022		0.000260681i	−0.00441183		1.46877e-5i
$316$	3.80990	−	1.17520i	0.214324	−	0.0661101i
$317$	−9.85579	+	20.4658i	−0.553557	+	1.14947i	0.417069	+	0.908875i	$0.363058\pi$
$317$	−9.85579	+	20.4658i	−0.553557	+	1.14947i	−0.970625	+	0.240597i	$0.922657\pi$
$318$	6.67559	−	0.500267i	0.374349	−	0.0280536i
$319$	−42.2743	−	6.37183i	−2.36691	−	0.356754i
$320$	−2.07877	−	0.823852i	−0.116207	−	0.0460548i
$321$	27.2239	+	8.39746i	1.51949	+	0.468700i
$322$	4.32313	+	3.44758i	0.240919	+	0.192126i
$323$	11.2581	+	8.97803i	0.626417	+	0.499551i
$324$	8.47242	+	2.61340i	0.470690	+	0.145189i
$325$	−0.0987785	+	14.8351i	−0.00547925	+	0.822905i
$326$	−1.53819	−	0.231845i	−0.0851924	−	0.0128407i
$327$	11.0953	−	0.831475i	0.613569	−	0.0459806i
$328$	−1.96783	+	4.08624i	−0.108655	+	0.225625i
$329$	−8.55807	+	2.63982i	−0.471822	+	0.145538i
$330$	0.0535560	−	16.0869i	0.00294816	−	0.885554i
$331$	9.00893	+	6.14219i	0.495176	+	0.337605i	0.785022	−	0.619468i	$-0.212652\pi$
$331$	9.00893	+	6.14219i	0.495176	+	0.337605i	−0.289846	+	0.957073i	$0.593604\pi$
$332$	−1.88671	−	12.5175i	−0.103546	−	0.686986i
$333$	−0.157076	+	0.0358516i	−0.00860771	+	0.00196465i
$334$	9.30943	−	6.34706i	0.509389	−	0.347296i
$335$	3.38189	+	1.64252i	0.184772	+	0.0897407i
$336$	−1.23525	+	0.594863i	−0.0673882	+	0.0324524i
$337$	12.4568	−	7.19193i	0.678565	−	0.391769i	−0.120749	−	0.992683i	$-0.538530\pi$
$337$	12.4568	−	7.19193i	0.678565	−	0.391769i	0.799314	+	0.600914i	$0.205196\pi$
$338$	3.63415	+	2.09818i	0.197672	+	0.114126i
$339$	2.03350	−	27.1352i	0.110445	−	1.47378i
$340$	5.39987	−	0.795523i	0.292849	−	0.0431433i
$341$	15.5415	+	39.5992i	0.841621	+	2.14442i
$342$	−0.202540	+	0.161520i	−0.0109521	+	0.00873400i
$343$			10.6568i			0.575412i
$344$	6.24861	+	1.98869i	0.336902	+	0.107223i
$345$	−24.8484	+	9.65695i	−1.33780	+	0.519913i
$346$	0.607881	+	0.762259i	0.0326799	+	0.0409793i
$347$	−13.8723	+	5.44448i	−0.744704	+	0.292275i	−0.707192	−	0.707021i	$-0.750039\pi$
$347$	−13.8723	+	5.44448i	−0.744704	+	0.292275i	−0.0375121	+	0.999296i	$0.511943\pi$
$348$	−17.1259	−	3.90888i	−0.918047	−	0.209538i
$349$	−0.956044	+	12.7575i	−0.0511759	+	0.682894i	0.911337	+	0.411660i	$0.135051\pi$
$349$	−0.956044	+	12.7575i	−0.0511759	+	0.682894i	−0.962513	+	0.271234i	$0.912568\pi$
$350$	0.861308	+	3.89294i	0.0460388	+	0.208086i
$351$	7.76412	+	13.4478i	0.414418	+	0.717793i
$352$	1.81553	+	3.76999i	0.0967683	+	0.200941i
$353$	21.9062	+	23.6093i	1.16595	+	1.25659i	0.960609	+	0.277904i	$0.0896397\pi$
$353$	21.9062	+	23.6093i	1.16595	+	1.25659i	0.205340	+	0.978691i	$0.434170\pi$
$354$	3.40906	−	2.32426i	0.181189	−	0.123533i
$355$	−6.05884	−	8.95057i	−0.321570	−	0.475047i
$356$	−1.48628	+	0.224021i	−0.0787728	+	0.0118731i
$357$	1.88521	−	2.76509i	0.0997759	−	0.146344i
$358$	6.08531	+	2.38831i	0.321619	+	0.126226i
$359$	−17.1801	+	5.29937i	−0.906734	+	0.279690i	−0.712835	−	0.701331i	$-0.752589\pi$
$359$	−17.1801	+	5.29937i	−0.906734	+	0.279690i	−0.193898	+	0.981022i	$0.562113\pi$
$360$	−0.00766410	+	0.0978958i	−0.000403934	+	0.00515956i
$361$	1.18075	+	15.7560i	0.0621447	+	0.829263i
$362$	2.00128	−	13.2776i	0.105185	−	0.697855i
$363$	−7.61190	+	8.20368i	−0.399521	+	0.430582i
$364$	−2.26089	−	0.697393i	−0.118503	−	0.0365533i
$365$	13.5562	+	4.23101i	0.709563	+	0.221461i
$366$	−13.5041	+	16.9336i	−0.705871	+	0.885134i
$367$	3.00272	−	9.73458i	0.156741	−	0.508141i	−0.842807	−	0.538216i	$-0.819098\pi$
$367$	3.00272	−	9.73458i	0.156741	−	0.508141i	0.999548	+	0.0300752i	$0.00957468\pi$
$368$	4.71650	−	5.08317i	0.245864	−	0.264979i
$369$	0.196944	+	0.0296845i	0.0102525	+	0.00154531i
$370$	3.53488	+	7.40320i	0.183770	+	0.384874i
$371$	2.79732	+	1.34712i	0.145230	+	0.0699389i
$372$	5.15210	+	16.7027i	0.267124	+	0.865995i
$373$	−15.5118	−	6.08794i	−0.803171	−	0.315222i	−0.0719906	−	0.997405i	$-0.522935\pi$
$373$	−15.5118	−	6.08794i	−0.803171	−	0.315222i	−0.731181	+	0.682184i	$0.761030\pi$
$374$	−8.43912	−	5.75370i	−0.436377	−	0.297517i
$375$	−18.3111	−	5.84915i	−0.945584	−	0.302049i
$376$	2.49918	+	10.9496i	0.128885	+	0.564684i
$377$	−17.0769	−	25.0473i	−0.879507	−	1.29000i
$378$	2.83854	+	3.05922i	0.145999	+	0.157349i
$379$	−15.7669	+	7.59294i	−0.809891	+	0.390023i	−0.792535	−	0.609826i	$-0.791239\pi$
$379$	−15.7669	+	7.59294i	−0.809891	+	0.390023i	−0.0173560	+	0.999849i	$0.505525\pi$
$380$	10.2857	+	8.25871i	0.527643	+	0.423663i
$381$	−0.825260	+	1.42939i	−0.0422794	+	0.0732300i
$382$	9.53975	+	0.714905i	0.488096	+	0.0365777i
$383$	−8.04255	−	1.83566i	−0.410955	−	0.0937978i	0.0120451	−	0.999927i	$-0.496166\pi$
$383$	−8.04255	−	1.83566i	−0.410955	−	0.0937978i	−0.423000	+	0.906130i	$0.639023\pi$
$384$	0.628141	+	1.60048i	0.0320547	+	0.0816740i
$385$	3.75202	−	6.44902i	0.191221	−	0.328672i
$386$	14.1366			0.719532
$387$	0.00257022	−	0.287954i	0.000130652	−	0.0146375i
$388$		−	11.1055i		−	0.563798i
$389$	10.7782	+	13.5154i	0.546474	+	0.685257i	0.975993	−	0.217801i	$-0.0698883\pi$
$389$	10.7782	+	13.5154i	0.546474	+	0.685257i	−0.429519	+	0.903058i	$0.641317\pi$
$390$	8.38777	−	7.73091i	0.424731	−	0.391470i
$391$	−3.76645	+	16.5019i	−0.190477	+	0.834536i
$392$	6.34633	+	0.475592i	0.320538	+	0.0240210i
$393$	−29.9582	−	17.2964i	−1.51119	−	0.872488i
$394$	−11.4231	−	19.7854i	−0.575489	−	0.996776i
$395$	−6.08565	+	6.51513i	−0.306202	+	0.327812i
$396$	0.134701	−	0.124984i	0.00676899	−	0.00628071i
$397$	1.14481	+	1.67913i	0.0574566	+	0.0842733i	0.853892	−	0.520450i	$-0.174236\pi$
$397$	1.14481	+	1.67913i	0.0574566	+	0.0842733i	−0.796435	+	0.604724i	$0.793284\pi$
$398$	−6.52002	+	1.48815i	−0.326819	+	0.0745943i
$399$	7.99754	−	1.20544i	0.400378	−	0.0603472i
$400$	4.94901	−	0.712275i	0.247450	−	0.0356138i
$401$	4.66662	−	11.8904i	0.233040	−	0.593776i	−0.765740	−	0.643150i	$-0.777627\pi$
$401$	4.66662	−	11.8904i	0.233040	−	0.593776i	0.998780	+	0.0493735i	$0.0157225\pi$
$402$	−0.852087	−	2.76240i	−0.0424982	−	0.137776i
$403$	−13.0879	+	27.1773i	−0.651954	+	1.35380i
$404$	0.0646552	+	0.862764i	0.00321672	+	0.0429241i
$405$	−19.3432	+	4.34726i	−0.961172	+	0.216017i
$406$	−5.97232	−	5.54151i	−0.296401	−	0.275020i
$407$	4.52505	−	14.6699i	0.224299	−	0.727158i
$408$	−3.28120	−	2.61667i	−0.162444	−	0.129544i
$409$	8.87645	−	11.1307i	0.438912	−	0.550379i	−0.512344	−	0.858780i	$-0.671223\pi$
$409$	8.87645	−	11.1307i	0.438912	−	0.550379i	0.951256	+	0.308402i	$0.0997941\pi$
$410$	−0.724197	−	10.1155i	−0.0357656	−	0.499571i
$411$	−4.25735	−	3.95024i	−0.210000	−	0.194851i
$412$	−0.834493	+	5.53650i	−0.0411125	+	0.272764i
$413$	1.90827	−	0.143005i	0.0938997	−	0.00703681i
$414$	−0.274357	−	0.132123i	−0.0134839	−	0.00649351i
$415$	17.5748	+	22.1892i	0.862712	+	1.08923i
$416$	−1.08400	+	2.76199i	−0.0531475	+	0.135418i
$417$	−0.473696	+	0.694785i	−0.0231970	+	0.0340238i
$418$	−3.67901	−	24.4086i	−0.179946	−	1.19387i
$419$	4.08569	+	17.9006i	0.199599	+	0.874500i	0.971176	+	0.238364i	$0.0766111\pi$
$419$	4.08569	+	17.9006i	0.199599	+	0.874500i	−0.771577	+	0.636136i	$0.780532\pi$
$420$	1.73539	−	2.52723i	0.0846783	−	0.123316i
$421$	−1.66403	+	1.54400i	−0.0810999	+	0.0752497i	−0.719681	−	0.694305i	$-0.755712\pi$
$421$	−1.66403	+	1.54400i	−0.0810999	+	0.0752497i	0.638581	+	0.769554i	$0.279522\pi$
$422$	−7.74849	−	16.0899i	−0.377191	−	0.783244i
$423$	0.427134	−	0.246606i	0.0207679	−	0.0119904i
$424$	1.94678	−	3.37193i	0.0945441	−	0.163755i
$425$	−9.59256	+	7.54587i	−0.465307	+	0.366028i
$426$	−1.84930	+	8.10231i	−0.0895988	+	0.392558i
$427$	−9.35091	+	3.66996i	−0.452522	+	0.177602i
$428$	12.9551	−	10.3314i	0.626209	−	0.499385i
$429$	−21.3462			−1.03060
$430$	−14.3342	+	3.08737i	−0.691255	+	0.148886i
$431$	−23.9351			−1.15291			−0.576457	−	0.817127i	$-0.695565\pi$
$431$	−23.9351			−1.15291			−0.576457	+	0.817127i	$0.695565\pi$
$432$	4.09170	−	3.26302i	0.196862	−	0.156992i
$433$	2.58873	−	1.01600i	0.124407	−	0.0488260i	−0.302321	−	0.953206i	$-0.597762\pi$
$433$	2.58873	−	1.01600i	0.124407	−	0.0488260i	0.426728	+	0.904380i	$0.359666\pi$
$434$	−1.80393	+	7.90355i	−0.0865916	+	0.379383i
$435$	37.5729	−	11.4528i	1.80148	−	0.549122i
$436$	3.23568	−	5.60435i	0.154961	−	0.268400i
$437$	−35.4260	+	20.4532i	−1.69465	+	0.978409i
$438$	−4.73772	−	9.83798i	−0.226377	−	0.470077i
$439$	−23.2144	+	21.5398i	−1.10796	+	1.02804i	−0.108541	+	0.994092i	$0.534618\pi$
$439$	−23.2144	+	21.5398i	−1.10796	+	1.02804i	−0.999424	+	0.0339488i	$0.989192\pi$
$440$	−7.71316	−	5.29644i	−0.367710	−	0.252498i
$441$	−0.0621893	−	0.272469i	−0.00296140	−	0.0129747i
$442$	−1.07945	−	7.16167i	−0.0513441	−	0.340646i
$443$	13.7628	−	20.1863i	0.653891	−	0.959082i	−0.345892	−	0.938274i	$-0.612424\pi$
$443$	13.7628	−	20.1863i	0.653891	−	0.959082i	0.999783	−	0.0208079i	$-0.00662384\pi$
$444$	2.30456	−	5.87193i	0.109370	−	0.278669i
$445$	2.63467	−	2.08677i	0.124895	−	0.0989224i
$446$	24.0147	+	11.5649i	1.13713	+	0.547612i
$447$	0.112368	−	0.00842079i	0.00531481	−	0.000398290i
$448$	−0.118849	+	0.788510i	−0.00561507	+	0.0372536i
$449$	17.0313	+	15.8027i	0.803755	+	0.745776i	0.970727	−	0.240186i	$-0.0772084\pi$
$449$	17.0313	+	15.8027i	0.803755	+	0.745776i	−0.166972	+	0.985962i	$0.553399\pi$
$450$	−0.0939492	−	0.198457i	−0.00442881	−	0.00935535i
$451$	−11.8324	+	14.8374i	−0.557168	+	0.698666i
$452$	−12.3738	−	9.86779i	−0.582015	−	0.464142i
$453$	6.71057	−	21.7551i	0.315290	−	1.02215i
$454$	−2.59869	−	2.41123i	−0.121962	−	0.113165i
$455$	5.16180	−	1.16008i	0.241989	−	0.0543855i
$456$	−0.757957	−	10.1142i	−0.0354946	−	0.473643i
$457$	13.8661	−	28.7933i	0.648630	−	1.34689i	−0.274194	−	0.961674i	$-0.588411\pi$
$457$	13.8661	−	28.7933i	0.648630	−	1.34689i	0.922825	−	0.385220i	$-0.125875\pi$
$458$	1.65711	+	5.37223i	0.0774318	+	0.251028i
$459$	−4.66713	+	11.8917i	−0.217843	+	0.555055i
$460$	−3.50060	+	15.1052i	−0.163216	+	0.704281i
$461$	−40.0721	+	6.03989i	−1.86634	+	0.281306i	−0.982470	−	0.186421i	$-0.940311\pi$
$461$	−40.0721	+	6.03989i	−1.86634	+	0.281306i	−0.883873	+	0.467727i	$0.845073\pi$
$462$	−5.59303	+	1.27657i	−0.260211	+	0.0593915i
$463$	5.13932	+	7.53800i	0.238845	+	0.350321i	0.926881	−	0.375356i	$-0.122479\pi$
$463$	5.13932	+	7.53800i	0.238845	+	0.350321i	−0.688036	+	0.725676i	$0.741527\pi$
$464$	−7.48959	+	6.94933i	−0.347696	+	0.322614i
$465$	−28.5625	−	26.6797i	−1.32456	−	1.23724i
$466$	−6.39939	−	11.0841i	−0.296446	−	0.513460i
$467$	16.7411	+	9.66550i	0.774688	+	0.447266i	0.834544	−	0.550941i	$-0.185731\pi$
$467$	16.7411	+	9.66550i	0.774688	+	0.447266i	−0.0598567	+	0.998207i	$0.519064\pi$
$468$	0.129934	+	0.00973717i	0.00600618	+	0.000450101i
$469$	0.298346	−	1.30714i	0.0137763	−	0.0603580i
$470$	−17.0203	−	18.4665i	−0.785089	−	0.851795i
$471$	22.1327	+	27.7535i	1.01982	+	1.27882i
$472$		−	2.39977i		−	0.110458i
$473$	23.6393	+	13.9309i	1.08694	+	0.640546i
$474$	6.85501			0.314861
$475$	−29.1365	−	4.59023i	−1.33687	−	0.210614i
$476$	−0.711122	−	1.81191i	−0.0325942	−	0.0830488i
$477$	−0.166696	−	0.0380473i	−0.00763250	−	0.00174207i
$478$	−20.8804	−	1.56477i	−0.955047	−	0.0715709i
$479$	9.27337	−	16.0620i	0.423711	−	0.733889i	−0.572588	−	0.819843i	$-0.694060\pi$
$479$	9.27337	−	16.0620i	0.423711	−	0.733889i	0.996299	+	0.0859540i	$0.0273938\pi$
$480$	−2.99778	−	2.40702i	−0.136829	−	0.109865i
$481$	9.80782	−	4.72320i	0.447198	−	0.215359i
$482$	14.3305	+	15.4446i	0.652738	+	0.703484i
$483$	5.35549	+	7.85506i	0.243683	+	0.357418i
$484$	1.44839	+	6.34582i	0.0658360	+	0.288447i
$485$	12.3447	+	21.5470i	0.560544	+	0.978398i
$486$	−0.377041	−	0.257062i	−0.0171029	−	0.0116606i
$487$	7.09461	+	2.78443i	0.321487	+	0.126175i	0.520597	−	0.853803i	$-0.325710\pi$
$487$	7.09461	+	2.78443i	0.321487	+	0.126175i	−0.199109	+	0.979977i	$0.563805\pi$
$488$	3.71312	+	12.0376i	0.168085	+	0.544919i
$489$	−2.40966	−	1.16043i	−0.108969	−	0.0524765i
$490$	−12.8418	+	6.13172i	−0.580135	+	0.277003i
$491$	16.4566	+	2.48043i	0.742675	+	0.111940i	0.509471	−	0.860488i	$-0.329841\pi$
$491$	16.4566	+	2.48043i	0.742675	+	0.111940i	0.233204	+	0.972428i	$0.425079\pi$
$492$	−5.30385	+	5.71620i	−0.239116	+	0.257706i
$493$	7.35099	−	23.8313i	0.331072	−	1.07331i
$494$	10.9132	−	13.6847i	0.491007	−	0.615704i
$495$	−0.122417	+	0.392227i	−0.00550225	+	0.0176293i
$496$	9.71468	+	2.99658i	0.436202	+	0.134550i
$497$	−2.62170	+	2.82552i	−0.117599	+	0.126742i
$498$	3.24387	−	21.5216i	0.145361	−	0.964408i
$499$	0.488286	+	6.51573i	0.0218587	+	0.291684i	0.997411	+	0.0719155i	$0.0229112\pi$
$499$	0.488286	+	6.51573i	0.0218587	+	0.291684i	−0.975552	+	0.219769i	$0.929470\pi$
$500$	−8.81033	+	6.88318i	−0.394010	+	0.307825i
$501$	18.5114	−	5.71002i	0.827029	−	0.255105i
$502$	−15.0954	−	5.92452i	−0.673742	−	0.264424i
$503$	−4.16965	+	6.11575i	−0.185915	+	0.272688i	−0.907869	−	0.419253i	$-0.862292\pi$
$503$	−4.16965	+	6.11575i	−0.185915	+	0.272688i	0.721954	+	0.691941i	$0.243244\pi$
$504$	0.0346269	−	0.00521916i	0.00154240	−	0.000232480i
$505$	−1.08448	−	1.60207i	−0.0482585	−	0.0712911i
$506$	23.9738	−	16.3451i	1.06576	−	0.726626i
$507$	4.90738	+	5.28890i	0.217945	+	0.234888i
$508$	0.416520	+	0.864913i	0.0184801	+	0.0383743i
$509$	−10.0053	−	17.3297i	−0.443477	−	0.768125i	0.554467	−	0.832205i	$-0.312922\pi$
$509$	−10.0053	−	17.3297i	−0.443477	−	0.768125i	−0.997945	+	0.0640801i	$0.979589\pi$
$510$	9.27483	+	1.42955i	0.410696	+	0.0633016i
$511$	0.378458	−	5.05018i	0.0167420	−	0.223407i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	−28.7391	+	11.2792i	−1.26886	+	0.497991i
$514$	−6.44556	−	8.08247i	−0.284301	−	0.356503i
$515$	−4.53518	−	11.6695i	−0.199844	−	0.514221i
$516$	9.25827	+	6.43398i	0.407573	+	0.283240i
$517$			46.9957i			2.06687i
$518$	2.28733	−	1.82409i	0.100500	−	0.0801458i
$519$	0.612416	+	1.56041i	0.0268821	+	0.0684944i
$520$	−0.966993	−	6.56378i	−0.0424054	−	0.287841i
$521$	0.0520971	−	0.695187i	0.00228241	−	0.0304567i	−0.995946	−	0.0899497i	$-0.971329\pi$
$521$	0.0520971	−	0.695187i	0.00228241	−	0.0304567i	0.998229	+	0.0594930i	$0.0189484\pi$
$522$	0.388562	+	0.224336i	0.0170069	+	0.00981893i
$523$	−33.4286	+	19.3000i	−1.46173	+	0.843931i	−0.999092	−	0.0426159i	$-0.986431\pi$
$523$	−33.4286	+	19.3000i	−1.46173	+	0.843931i	−0.462639	+	0.886547i	$0.653097\pi$
$524$	−18.1275	+	8.72973i	−0.791902	+	0.381360i
$525$	−0.557786	+	6.83237i	−0.0243438	+	0.298189i
$526$	−2.48451	+	1.69391i	−0.108330	+	0.0738581i
$527$	−24.1935	+	5.52200i	−1.05388	+	0.240542i
$528$	1.07226	+	7.11396i	0.0466640	+	0.309595i
$529$	−20.7254	−	14.1303i	−0.901103	−	0.614361i
$530$	−0.0289845	+	8.70623i	−0.00125901	+	0.378174i
$531$	−0.100702	+	0.0310626i	−0.00437011	+	0.00134800i
$532$	2.04103	−	4.23824i	0.0884898	−	0.183751i
$533$	−13.4193	+	1.00564i	−0.581253	+	0.0435589i
$534$	−2.55541	−	0.385166i	−0.110583	−	0.0166677i
$535$	−13.6514	+	34.4456i	−0.590202	+	1.48921i
$536$	−1.60667	−	0.495593i	−0.0693977	−	0.0214064i
$537$	8.78747	+	7.00777i	0.379207	+	0.302408i
$538$	−16.5539	−	13.2013i	−0.713688	−	0.569147i
$539$	25.4468	+	7.84930i	1.09607	+	0.338093i
$540$	−4.31162	+	10.8792i	−0.185543	+	0.468166i
$541$	18.9685	+	2.85905i	0.815521	+	0.122920i	0.543541	−	0.839383i	$-0.317083\pi$
$541$	18.9685	+	2.85905i	0.815521	+	0.122920i	0.271980	+	0.962303i	$0.412321\pi$
$542$	8.74973	−	0.655701i	0.375833	−	0.0281648i
$543$	10.0168	−	20.8001i	0.429863	−	0.892619i
$544$	−2.33252	+	0.719486i	−0.100006	+	0.0308477i
$545$	−0.0481741	+	14.4703i	−0.00206355	+	0.619840i
$546$	−3.36109	−	2.29155i	−0.143841	−	0.0980695i
$547$	1.70338	+	11.3012i	0.0728315	+	0.483205i	0.995277	+	0.0970775i	$0.0309495\pi$
$547$	1.70338	+	11.3012i	0.0728315	+	0.483205i	−0.922445	+	0.386128i	$0.873812\pi$
$548$	−3.29320	+	0.751652i	−0.140679	+	0.0321090i
$549$	0.457077	−	0.311630i	0.0195076	−	0.0133000i
$550$	20.8525	+	1.70237i	0.889154	+	0.0725895i
$551$	54.3030	−	26.1510i	2.31339	−	1.11407i
$552$	10.3250	−	5.96113i	0.439460	−	0.253723i
$553$	2.75337	+	1.58966i	0.117085	+	0.0675993i
$554$	−0.0928031	+	1.23837i	−0.00394283	+	0.0526134i
$555$	2.05581	+	13.9544i	0.0872641	+	0.592333i
$556$	0.178684	+	0.455279i	0.00757787	+	0.0193081i
$557$	−11.2925	+	9.00550i	−0.478480	+	0.381575i	−0.832822	−	0.553541i	$-0.813276\pi$
$557$	−11.2925	+	9.00550i	−0.478480	+	0.381575i	0.354342	+	0.935116i	$0.384705\pi$
$558$		−	0.446448i		−	0.0188996i
$559$	4.16001	+	19.0066i	0.175950	+	0.803894i
$560$	−0.645902	−	1.66198i	−0.0272943	−	0.0702314i
$561$	−10.9491	−	13.7298i	−0.462273	−	0.579672i
$562$	−3.12747	+	1.22744i	−0.131924	+	0.0517765i
$563$	15.5617	+	3.55185i	0.655847	+	0.149693i	0.537479	−	0.843277i	$-0.319377\pi$
$563$	15.5617	+	3.55185i	0.655847	+	0.149693i	0.118368	+	0.992970i	$0.462234\pi$
$564$	−1.44305	+	19.2562i	−0.0607633	+	0.810830i
$565$	34.9765	+	5.39101i	1.47147	+	0.226802i
$566$	8.47503	+	14.6792i	0.356232	+	0.617012i
$567$	3.06763	+	6.36999i	0.128828	+	0.267514i
$568$	3.28774	+	3.54334i	0.137950	+	0.148675i
$569$	10.8350	−	7.38717i	0.454227	−	0.309686i	−0.314507	−	0.949255i	$-0.601839\pi$
$569$	10.8350	−	7.38717i	0.454227	−	0.309686i	0.768734	+	0.639569i	$0.220887\pi$
$570$	12.7134	+	18.7811i	0.532505	+	0.786656i
$571$	21.9176	−	3.30355i	0.917223	−	0.138249i	0.326568	−	0.945174i	$-0.394108\pi$
$571$	21.9176	−	3.30355i	0.917223	−	0.138249i	0.590655	+	0.806924i	$0.298870\pi$
$572$	−6.99387	+	10.2581i	−0.292428	+	0.428913i
$573$	15.3110	+	6.00911i	0.639624	+	0.251034i
$574$	−3.45591	+	1.06601i	−0.144247	+	0.0444943i
$575$	−9.99873	−	33.1983i	−0.416976	−	1.38446i
$576$	−0.00328172	−	0.0437915i	−0.000136738	−	0.00182465i
$577$	−2.81642	+	18.6857i	−0.117249	+	0.777897i	0.850499	+	0.525977i	$0.176300\pi$
$577$	−2.81642	+	18.6857i	−0.117249	+	0.777897i	−0.967748	+	0.251920i	$0.918938\pi$
$578$	−7.51027	+	8.09415i	−0.312386	+	0.336672i
$579$	23.2256	+	7.16414i	0.965221	+	0.297731i
$580$	6.80659	−	21.8084i	0.282628	−	0.905544i
$581$	6.29375	−	7.89211i	0.261109	−	0.327420i
$582$	5.62807	−	18.2457i	0.233291	−	0.756311i
$583$	11.0815	−	11.9430i	0.458948	−	0.494628i
$584$	−6.28000	−	0.946557i	−0.259868	−	0.0391688i
$585$	−0.262921	+	0.125540i	−0.0108704	+	0.00519042i
$586$	−0.501839	−	0.241673i	−0.0207308	−	0.00998341i
$587$	−6.48095	−	21.0107i	−0.267497	−	0.867205i	−0.985282	−	0.170939i	$-0.945320\pi$
$587$	−6.48095	−	21.0107i	−0.267497	−	0.867205i	0.717784	−	0.696266i	$-0.245156\pi$
$588$	10.1856	+	3.99757i	0.420049	+	0.164857i
$589$	−49.5520	−	33.7840i	−2.04175	−	1.39204i
$590$	2.66754	+	4.65605i	0.109821	+	0.191686i
$591$	−8.74066	−	38.2953i	−0.359543	−	1.57526i
$592$	−2.06674	−	3.03136i	−0.0849426	−	0.124588i
$593$	−24.9353	−	26.8739i	−1.02397	−	1.10358i	−0.994576	−	0.104011i	$-0.966832\pi$
$593$	−24.9353	−	26.8739i	−1.02397	−	1.10358i	−0.0293952	−	0.999568i	$-0.509358\pi$
$594$	19.7302	−	9.50157i	0.809540	−	0.389854i
$595$	3.39381	+	2.72500i	0.139133	+	0.111714i
$596$	0.0327694	−	0.0567583i	0.00134229	−	0.00232491i
$597$	−11.4662	−	0.859272i	−0.469280	−	0.0351676i
$598$	20.0588	+	4.57828i	0.820263	+	0.187220i
$599$	−0.785058	−	2.00029i	−0.0320766	−	0.0817298i	0.913938	−	0.405854i	$-0.133026\pi$
$599$	−0.785058	−	2.00029i	−0.0320766	−	0.0817298i	−0.946015	+	0.324124i	$0.894931\pi$
$600$	8.49190	+	1.33783i	0.346680	+	0.0546168i
$601$	12.7888			0.521666			0.260833	−	0.965384i	$-0.416003\pi$
$601$	12.7888			0.521666			0.260833	+	0.965384i	$0.416003\pi$
$602$	2.22664	+	4.73124i	0.0907511	+	0.192831i
$603$			0.0738363i			0.00300685i
$604$	−8.25598	−	10.3527i	−0.335931	−	0.421244i
$605$	−9.86407	−	10.7022i	−0.401032	−	0.435106i
$606$	−0.331007	+	1.45024i	−0.0134462	+	0.0589118i
$607$	41.2425	+	3.09070i	1.67398	+	0.125447i	0.877614	−	0.479368i	$-0.159134\pi$
$607$	41.2425	+	3.09070i	1.67398	+	0.125447i	0.796366	+	0.604815i	$0.206753\pi$
$608$	−5.10883	−	2.94958i	−0.207190	−	0.119621i
$609$	−7.00385	−	12.1310i	−0.283811	−	0.491574i
$610$	−20.5850	−	19.2280i	−0.833464	−	0.778521i
$611$	−24.4283	+	22.6661i	−0.988263	+	0.916974i
$612$	0.0603840	+	0.0885671i	0.00244088	+	0.00358011i
$613$	−10.0201	+	2.28702i	−0.404707	+	0.0923717i	−0.420029	−	0.907511i	$-0.637980\pi$
$613$	−10.0201	+	2.28702i	−0.404707	+	0.0923717i	0.0153216	+	0.999883i	$0.495123\pi$
$614$	−26.6882	+	4.02259i	−1.07705	+	0.162339i
$615$	3.93654	−	16.9862i	0.158737	−	0.684951i
$616$	−1.21903	+	3.10604i	−0.0491161	+	0.125146i
$617$	8.53750	+	27.6779i	0.343707	+	1.11427i	0.948204	+	0.317663i	$0.102898\pi$
$617$	8.53750	+	27.6779i	0.343707	+	1.11427i	−0.604497	+	0.796607i	$0.706626\pi$
$618$	−4.17681	+	8.67324i	−0.168016	+	0.348889i
$619$	−0.351830	−	4.69485i	−0.0141412	−	0.188702i	−0.999801	−	0.0199560i	$-0.993647\pi$
$619$	−0.351830	−	4.69485i	−0.0141412	−	0.188702i	0.985660	−	0.168746i	$-0.0539717\pi$
$620$	−22.1794	+	4.98467i	−0.890746	+	0.200189i
$621$	−26.6027	−	24.6837i	−1.06753	−	0.990523i
$622$	0.992789	−	3.21854i	0.0398072	−	0.129052i
$623$	−0.937082	−	0.747298i	−0.0375434	−	0.0299399i
$624$	−3.18067	+	3.98844i	−0.127329	+	0.159665i
$625$	9.44261	−	23.1482i	0.377704	−	0.925926i
$626$	−19.7543	−	18.3294i	−0.789543	−	0.732588i
$627$	6.32542	−	41.9664i	0.252613	−	1.67598i
$628$	20.5888	−	1.54292i	0.821582	−	0.0615690i
$629$	8.06867	+	3.88567i	0.321719	+	0.154932i
$630$	−0.0613816	+	0.0486168i	−0.00244550	+	0.00193694i
$631$	16.3164	−	41.5736i	0.649546	−	1.65502i	−0.101555	−	0.994830i	$-0.532382\pi$
$631$	16.3164	−	41.5736i	0.649546	−	1.65502i	0.751101	−	0.660187i	$-0.229523\pi$
$632$	2.24597	−	3.29424i	0.0893401	−	0.131038i
$633$	−4.57627	−	30.3616i	−0.181890	−	1.20676i
$634$	5.05463	+	22.1458i	0.200745	+	0.879521i
$635$	−1.76955	−	1.21511i	−0.0702226	−	0.0482202i
$636$	4.90728	−	4.55329i	0.194586	−	0.180550i
$637$	8.19301	+	17.0130i	0.324619	+	0.674078i
$638$	−37.0241	+	21.3759i	−1.46580	+	0.846280i
$639$	0.106134	−	0.183829i	0.00419859	−	0.00727217i
$640$	−2.13891	+	0.651975i	−0.0845478	+	0.0257716i
$641$	1.90948	−	8.36596i	0.0754197	−	0.330435i	−0.923117	−	0.384520i	$-0.874367\pi$
$641$	1.90948	−	8.36596i	0.0754197	−	0.330435i	0.998536	+	0.0540847i	$0.0172241\pi$
$642$	26.5202	−	10.4084i	1.04667	−	0.410788i
$643$	26.9460	−	21.4887i	1.06265	−	0.847431i	0.0739336	−	0.997263i	$-0.476445\pi$
$643$	26.9460	−	21.4887i	1.06265	−	0.847431i	0.988711	+	0.149832i	$0.0478733\pi$
$644$	5.52949			0.217893
$645$	−25.1148	−	2.19190i	−0.988895	−	0.0863060i
$646$	14.3996			0.566546
$647$	−5.48756	+	4.37619i	−0.215738	+	0.172046i	−0.725396	−	0.688332i	$-0.758343\pi$
$647$	−5.48756	+	4.37619i	−0.215738	+	0.172046i	0.509658	+	0.860377i	$0.329772\pi$
$648$	8.25343	−	3.23923i	0.324225	−	0.127249i
$649$	2.23446	−	9.78979i	0.0877101	−	0.384283i
$650$	9.17233	+	11.6602i	0.359768	+	0.457349i
$651$	−6.96913	+	12.0709i	−0.273142	+	0.473095i
$652$	−1.34716	+	0.777781i	−0.0527587	+	0.0304603i
$653$	1.09632	+	2.27654i	0.0429024	+	0.0890877i	0.921318	−	0.388809i	$-0.127113\pi$
$653$	1.09632	+	2.27654i	0.0429024	+	0.0890877i	−0.878416	+	0.477897i	$0.841399\pi$
$654$	8.15620	−	7.56785i	0.318933	−	0.295926i
$655$	25.4672	−	37.0876i	0.995084	−	1.44913i
$656$	1.00922	+	4.42167i	0.0394033	+	0.172637i
$657$	0.0415674	+	0.275782i	0.00162170	+	0.0107593i
$658$	−5.04507	+	7.39976i	−0.196677	+	0.288473i
$659$	2.31563	−	5.90014i	0.0902043	−	0.229837i	−0.878651	−	0.477465i	$-0.841556\pi$
$659$	2.31563	−	5.90014i	0.0902043	−	0.229837i	0.968855	+	0.247628i	$0.0796511\pi$
$660$	−9.98814	−	12.6106i	−0.388788	−	0.490868i
$661$	−16.9149	−	8.14577i	−0.657912	−	0.316834i	0.0749736	−	0.997186i	$-0.476113\pi$
$661$	−16.9149	−	8.14577i	−0.657912	−	0.316834i	−0.732886	+	0.680352i	$0.761827\pi$
$662$	10.8731	−	0.814823i	0.422593	−	0.0316690i
$663$	1.85592	−	12.3132i	0.0720781	−	0.478207i
$664$	−9.27961	−	8.61022i	−0.360119	−	0.334141i
$665$	0.751137	+	10.4918i	0.0291278	+	0.406855i
$666$	−0.100454	+	0.125965i	−0.00389251	+	0.00488105i
$667$	55.3907	+	44.1726i	2.14474	+	1.71037i
$668$	3.32108	−	10.7667i	0.128496	−	0.416575i
$669$	33.5939	+	31.1706i	1.29881	+	1.20512i
$670$	3.66816	−	0.824396i	0.141714	−	0.0318492i
$671$	3.93917	+	52.5645i	0.152070	+	2.02923i
$672$	−0.594863	+	1.23525i	−0.0229473	+	0.0476506i
$673$	−5.05228	−	16.3791i	−0.194751	−	0.631367i	−0.999297	−	0.0374775i	$-0.988068\pi$
$673$	−5.05228	−	16.3791i	−0.194751	−	0.631367i	0.804546	−	0.593890i	$-0.202408\pi$
$674$	5.25501	−	13.3896i	0.202416	−	0.515747i
$675$	−3.72768	−	25.9005i	−0.143479	−	0.996913i
$676$	4.14949	−	0.625434i	0.159596	−	0.0240552i
$677$	−12.7471	+	2.90945i	−0.489912	+	0.111819i	−0.460339	−	0.887743i	$-0.652272\pi$
$677$	−12.7471	+	2.90945i	−0.489912	+	0.111819i	−0.0295733	+	0.999563i	$0.509415\pi$
$678$	−15.3287	−	22.4830i	−0.588693	−	0.863455i
$679$	6.49171	−	6.02343i	0.249129	−	0.231158i
$680$	3.72579	−	3.98873i	0.142877	−	0.152961i
$681$	−3.04753	−	5.27847i	−0.116782	−	0.202272i
$682$	36.8406	+	21.2699i	1.41070	+	0.814467i
$683$	15.1363	+	1.13431i	0.579174	+	0.0434031i	0.361097	−	0.932528i	$-0.382402\pi$
$683$	15.1363	+	1.13431i	0.579174	+	0.0434031i	0.218077	+	0.975932i	$0.430022\pi$
$684$	−0.0576458	+	0.252563i	−0.00220414	+	0.00965698i
$685$	5.55396	−	5.11902i	0.212206	−	0.195588i
$686$	6.64439	+	8.33180i	0.253684	+	0.318110i
$687$			9.66606i			0.368783i
$688$	6.12529	−	2.34112i	0.233524	−	0.0892545i
$689$	11.5526			0.440118
$690$	−13.4063	+	23.0429i	−0.510369	+	0.877227i
$691$	13.7036	+	34.9162i	0.521309	+	1.32827i	0.912918	+	0.408142i	$0.133823\pi$
$691$	13.7036	+	34.9162i	0.521309	+	1.32827i	−0.391609	+	0.920132i	$0.628081\pi$
$692$	0.950522	+	0.216950i	0.0361334	+	0.00824722i
$693$	0.146119	+	0.0109501i	0.00555059	+	0.000415959i
$694$	−7.45123	+	12.9059i	−0.282845	+	0.489901i
$695$	−0.852761	−	0.684711i	−0.0323471	−	0.0259726i
$696$	−15.8268	+	7.62176i	−0.599911	+	0.288902i
$697$	−7.52998	−	8.11539i	−0.285218	−	0.307392i
$698$	7.20672	+	10.5703i	0.272778	+	0.400092i
$699$	−4.89664	−	21.4536i	−0.185208	−	0.811449i
$700$	3.10060	+	2.50660i	0.117192	+	0.0947408i
$701$	−1.42581	−	0.972102i	−0.0538522	−	0.0367158i	0.536095	−	0.844158i	$-0.319899\pi$
$701$	−1.42581	−	0.972102i	−0.0538522	−	0.0367158i	−0.589947	+	0.807442i	$0.700851\pi$
$702$	14.4548	+	5.67310i	0.545562	+	0.214117i
$703$	6.37946	+	20.6817i	0.240606	+	0.780025i
$704$	3.76999	+	1.81553i	0.142087	+	0.0684255i
$705$	−18.6050	−	38.9649i	−0.700703	−	1.46750i
$706$	31.8471	+	4.80018i	1.19858	+	0.180657i
$707$	−0.469259	+	0.505740i	−0.0176483	+	0.0190203i
$708$	1.21616	−	3.94269i	0.0457060	−	0.148175i
$709$	−2.35777	+	2.95655i	−0.0885480	+	0.111036i	−0.824132	−	0.566398i	$-0.808337\pi$
$709$	−2.35777	+	2.95655i	−0.0885480	+	0.111036i	0.735584	+	0.677434i	$0.236908\pi$
$710$	−10.3176	−	3.22021i	−0.387212	−	0.120852i
$711$	−0.167309	−	0.0516080i	−0.00627458	−	0.00193545i
$712$	−1.02235	+	1.10183i	−0.0383141	+	0.0412928i
$713$	10.5069	−	69.7087i	0.393486	−	2.61061i
$714$	−0.250092	−	3.33725i	−0.00935946	−	0.124893i
$715$	2.16679	−	27.6771i	0.0810335	−	1.03506i
$716$	6.24677	−	1.92687i	0.233453	−	0.0720107i
$717$	−33.5123	−	13.1526i	−1.25154	−	0.491193i
$718$	−10.1279	+	14.8549i	−0.377969	+	0.554379i
$719$	33.7992	−	5.09441i	1.26050	−	0.189989i	0.515403	−	0.856948i	$-0.327642\pi$
$719$	33.7992	−	5.09441i	1.26050	−	0.189989i	0.745095	+	0.666959i	$0.232404\pi$
$720$	0.0550450	+	0.0813165i	0.00205141	+	0.00303049i
$721$	−3.68896	+	2.51509i	−0.137384	+	0.0936668i
$722$	10.7469	+	11.5824i	0.399957	+	0.431051i
$723$	15.7172	+	32.6371i	0.584529	+	1.21379i
$724$	−6.71379	−	11.6286i	−0.249516	−	0.432174i
$725$	11.0356	+	49.8788i	0.409853	+	1.85245i
$726$	−0.836314	+	11.1598i	−0.0310385	+	0.414180i
$727$	−26.5344	−	6.05630i	−0.984106	−	0.224616i	−0.299953	−	0.953954i	$-0.596971\pi$
$727$	−26.5344	−	6.05630i	−0.984106	−	0.224616i	−0.684153	+	0.729338i	$0.739828\pi$
$728$	−2.20246	+	0.864400i	−0.0816284	+	0.0320368i
$729$	−17.0734	−	21.4093i	−0.632347	−	0.792939i
$730$	13.2366	−	5.14421i	0.489910	−	0.190396i
$731$	−10.0912	+	12.4248i	−0.373235	+	0.459547i
$732$			21.6589i			0.800536i
$733$	23.3612	−	18.6299i	0.862865	−	0.688112i	−0.0885338	−	0.996073i	$-0.528218\pi$
$733$	23.3612	−	18.6299i	0.862865	−	0.688112i	0.951399	+	0.307961i	$0.0996467\pi$
$734$	−3.72179	−	9.48296i	−0.137374	−	0.350023i
$735$	−24.2058	+	3.56607i	−0.892845	+	0.131536i
$736$	0.518198	−	6.91487i	0.0191010	−	0.254886i
$737$	−6.09292	−	3.51775i	−0.224436	−	0.129578i
$738$	0.172485	−	0.0995841i	0.00634925	−	0.00366574i
$739$	13.5675	−	6.53377i	0.499089	−	0.240348i	−0.167365	−	0.985895i	$-0.553526\pi$
$739$	13.5675	−	6.53377i	0.499089	−	0.240348i	0.666454	+	0.745547i	$0.267811\pi$
$740$	7.37950	+	3.58409i	0.271276	+	0.131754i
$741$	24.8649	−	16.9526i	0.913434	−	0.622768i
$742$	3.02695	−	0.690881i	0.111123	−	0.0253630i
$743$	2.63218	+	17.4634i	0.0965653	+	0.640669i	0.983789	+	0.179330i	$0.0573929\pi$
$743$	2.63218	+	17.4634i	0.0965653	+	0.640669i	−0.887224	+	0.461339i	$0.847369\pi$
$744$	14.4420	+	9.84642i	0.529471	+	0.360987i
$745$	−0.000487885		0.146548i	−1.78747e−5		0.00536912i
$746$	−15.9234	+	4.91172i	−0.582997	+	0.179831i
$747$	−0.241198	+	0.500854i	−0.00882499	+	0.0183253i
$748$	−10.1853	+	0.763286i	−0.372413	+	0.0279085i
$749$	13.0658	+	1.96935i	0.477413	+	0.0719584i
$750$	−17.9631	+	6.84376i	−0.655920	+	0.249899i
$751$	−23.9029	−	7.37306i	−0.872228	−	0.269047i	−0.173847	−	0.984773i	$-0.555620\pi$
$751$	−23.9029	−	7.37306i	−0.872228	−	0.269047i	−0.698381	+	0.715726i	$0.746096\pi$
$752$	8.78092	+	7.00255i	0.320207	+	0.255357i
$753$	−21.7985	−	17.3837i	−0.794380	−	0.633497i
$754$	−28.9680	−	8.93544i	−1.05495	−	0.325410i
$755$	27.5261	+	10.9091i	1.00178	+	0.397023i
$756$	4.12665	+	0.621993i	0.150085	+	0.0226217i
$757$	−16.1106	+	1.20732i	−0.585549	+	0.0438809i	−0.364211	−	0.931316i	$-0.618661\pi$
$757$	−16.1106	+	1.20732i	−0.585549	+	0.0438809i	−0.221338	+	0.975197i	$0.571042\pi$
$758$	−7.59294	+	15.7669i	−0.275788	+	0.572679i
$759$	47.6709	−	14.7045i	1.73034	−	0.533741i
$760$	13.1909	+	0.0439147i	0.478483	+	0.00159295i
$761$	32.1717	+	21.9343i	1.16622	+	0.795116i	0.982206	−	0.187807i	$-0.0601379\pi$
$761$	32.1717	+	21.9343i	1.16622	+	0.795116i	0.184016	+	0.982923i	$0.441090\pi$
$762$	0.245997	+	1.63209i	0.00891154	+	0.0591242i
$763$	5.03098	−	1.14829i	0.182134	−	0.0415708i
$764$	7.90421	−	5.38900i	0.285964	−	0.194967i
$765$	−0.215607	−	0.104716i	−0.00779528	−	0.00378603i
$766$	−7.43243	+	3.57927i	−0.268545	+	0.129324i
$767$	6.16640	−	3.56017i	0.222656	−	0.128550i
$768$	1.48898	+	0.859664i	0.0537290	+	0.0310204i
$769$	−0.956604	+	12.7650i	−0.0344960	+	0.460318i	0.953031	+	0.302871i	$0.0979452\pi$
$769$	−0.956604	+	12.7650i	−0.0344960	+	0.460318i	−0.987528	+	0.157446i	$0.949674\pi$
$770$	−1.08745	−	7.38140i	−0.0391889	−	0.266007i
$771$	−6.49364	−	16.5455i	−0.233863	−	0.595872i
$772$	11.0524	−	8.81400i	0.397785	−	0.317223i
$773$			53.6270i			1.92883i	0.264397	+	0.964414i	$0.414827\pi$
$773$			53.6270i			1.92883i	−0.264397	+	0.964414i	$0.585173\pi$
$774$	−0.177527	−	0.226734i	−0.00638107	−	0.00814978i
$775$	37.4917	−	34.3255i	1.34674	−	1.23301i
$776$	−6.92419	−	8.68265i	−0.248564	−	0.311689i
$777$	4.68237	−	1.83770i	0.167979	−	0.0659270i
$778$	16.8534	+	3.84668i	0.604224	+	0.137910i
$779$	1.99940	−	26.6802i	0.0716360	−	0.955916i
$780$	1.73768	−	11.2740i	0.0622189	−	0.403672i
$781$	10.1130	+	17.5162i	0.361871	+	0.626778i
$782$	7.34403	+	15.2500i	0.262622	+	0.545340i
$783$	36.3692	+	39.1967i	1.29973	+	1.40077i
$784$	5.25829	−	3.58504i	0.187796	−	0.128037i
$785$	−38.2313	+	25.8797i	−1.36454	+	0.923685i
$786$	−34.2064	+	5.15579i	−1.22010	+	0.183901i
$787$	5.53148	−	8.11319i	0.197176	−	0.289204i	−0.714899	−	0.699228i	$-0.753527\pi$
$787$	5.53148	−	8.11319i	0.197176	−	0.289204i	0.912075	+	0.410024i	$0.134480\pi$
$788$	−21.2670	−	8.34667i	−0.757605	−	0.297338i
$789$	−4.94035	+	1.52390i	−0.175881	+	0.0542521i
$790$	−0.695833	+	8.88808i	−0.0247566	+	0.316224i
$791$	−0.943129	−	12.5852i	−0.0335338	−	0.447477i
$792$	0.0273871	−	0.181702i	0.000973159	−	0.00645649i
$793$	−25.4231	+	27.3996i	−0.902800	+	0.972988i
$794$	1.94197	+	0.599020i	0.0689181	+	0.0212584i
$795$	−4.45977	+	14.2891i	−0.158172	+	0.506784i
$796$	−4.16971	+	5.22865i	−0.147791	+	0.185325i
$797$	2.00963	−	6.51505i	0.0711846	−	0.230775i	−0.912988	−	0.407986i	$-0.866231\pi$
$797$	2.00963	−	6.51505i	0.0711846	−	0.230775i	0.984173	+	0.177211i	$0.0567075\pi$
$798$	5.50115	−	5.92883i	0.194739	−	0.209878i
$799$	−27.1088	−	4.08599i	−0.959039	−	0.144552i
$800$	3.42519	−	3.64253i	0.121099	−	0.128783i
$801$	0.0594696	+	0.0286391i	0.00210126	+	0.00101191i
$802$	−3.76501	−	12.2058i	−0.132947	−	0.431004i
$803$	−24.7377	−	9.70883i	−0.872974	−	0.342617i
$804$	−2.38851	−	1.62846i	−0.0842364	−	0.0574314i
$805$	−10.7283	+	6.14648i	−0.378124	+	0.216635i
$806$	6.71223	+	29.4082i	0.236428	+	1.03586i
$807$	−20.5069	−	30.0781i	−0.721877	−	1.05880i
$808$	0.588474	+	0.634224i	0.0207024	+	0.0223119i
$809$	−4.10032	+	1.97461i	−0.144160	+	0.0694236i	−0.504573	−	0.863369i	$-0.668350\pi$
$809$	−4.10032	+	1.97461i	−0.144160	+	0.0694236i	0.360413	+	0.932793i	$0.382636\pi$
$810$	−12.4127	+	15.4591i	−0.436137	+	0.543178i
$811$	−7.72148	+	13.3740i	−0.271138	+	0.469624i	−0.969153	−	0.246458i	$-0.920733\pi$
$811$	−7.72148	+	13.3740i	−0.271138	+	0.469624i	0.698016	+	0.716082i	$0.254067\pi$
$812$	−8.12442	−	0.608841i	−0.285111	−	0.0213661i
$813$	14.7076	+	3.35691i	0.515818	+	0.117732i
$814$	−5.60868	−	14.2907i	−0.196584	−	0.500888i
$815$	1.74919	−	3.00653i	0.0612715	−	0.105314i
$816$	−4.19681			−0.146918
$817$	−38.5995	+	2.54640i	−1.35043	+	0.0890872i
$818$		−	14.2367i		−	0.497775i
$819$	0.0647816	+	0.0812336i	0.00226365	+	0.00283853i
$820$	−6.87313	−	7.45711i	−0.240020	−	0.260414i
$821$	−9.90016	+	43.3754i	−0.345518	+	1.51381i	0.441714	+	0.897156i	$0.354371\pi$
$821$	−9.90016	+	43.3754i	−0.345518	+	1.51381i	−0.787232	+	0.616657i	$0.788486\pi$
$822$	−5.79147	−	0.434010i	−0.202001	−	0.0151379i
$823$	−36.7716	−	21.2301i	−1.28178	−	0.740034i	−0.304603	−	0.952479i	$-0.598524\pi$
$823$	−36.7716	−	21.2301i	−1.28178	−	0.740034i	−0.977173	+	0.212446i	$0.931857\pi$
$824$	2.79952	+	4.84891i	0.0975258	+	0.168920i
$825$	33.3967	+	13.3646i	1.16273	+	0.465294i
$826$	1.40278	−	1.30159i	0.0488090	−	0.0452881i
$827$	−19.9141	−	29.2086i	−0.692482	−	1.01568i	−0.997982	−	0.0634920i	$-0.979776\pi$
$827$	−19.9141	−	29.2086i	−0.692482	−	1.01568i	0.305501	−	0.952192i	$-0.401176\pi$
$828$	−0.296878	+	0.0677606i	−0.0103172	+	0.00235484i
$829$	22.4893	−	3.38972i	0.781085	−	0.117730i	0.253617	−	0.967305i	$-0.418380\pi$
$829$	22.4893	−	3.38972i	0.781085	−	0.117730i	0.527468	+	0.849575i	$0.323141\pi$
$830$	27.5753	+	6.39054i	0.957152	+	0.221819i
$831$	−0.780053	+	1.98754i	−0.0270597	+	0.0689471i
$832$	0.874566	+	2.83527i	0.0303201	+	0.0982954i
$833$	−6.74020	+	13.9962i	−0.233534	+	0.484939i
$834$	0.0628406	+	0.838550i	0.00217599	+	0.0290366i
$835$	5.52446	+	24.5812i	0.191182	+	0.850666i
$836$	−18.0949	−	16.7896i	−0.625825	−	0.580681i
$837$	15.6826	−	50.8416i	0.542069	−	1.75734i
$838$	14.3551	+	11.4478i	0.495890	+	0.395459i
$839$	−17.9244	+	22.4765i	−0.618818	+	0.775974i	−0.988178	−	0.153313i	$-0.951006\pi$
$839$	−17.9244	+	22.4765i	−0.618818	+	0.775974i	0.369359	+	0.929287i	$0.379577\pi$
$840$	−0.218921	−	3.05787i	−0.00755348	−	0.105506i
$841$	−55.2627	−	51.2763i	−1.90561	−	1.76815i
$842$	−0.338327	+	2.24465i	−0.0116595	+	0.0773558i
$843$	−5.76030	+	0.431675i	−0.198395	+	0.0148677i
$844$	−16.0899	−	7.74849i	−0.553837	−	0.266714i
$845$	−7.35562	+	5.82596i	−0.253041	+	0.200419i
$846$	0.180190	−	0.459117i	0.00619507	−	0.0157848i
$847$	−2.92385	+	4.28851i	−0.100465	+	0.147355i
$848$	−0.580306	−	3.85008i	−0.0199278	−	0.132212i
$849$	6.48486	+	28.4120i	0.222560	+	0.975099i
$850$	−2.79499	+	11.8805i	−0.0958674	+	0.407496i
$851$	−18.6495	+	17.3042i	−0.639295	+	0.593179i
$852$	3.60587	+	7.48766i	0.123535	+	0.256523i
$853$	−32.3045	+	18.6510i	−1.10609	+	0.638599i	−0.937813	−	0.347141i	$-0.887152\pi$
$853$	−32.3045	+	18.6510i	−1.10609	+	0.638599i	−0.168273	+	0.985740i	$0.553819\pi$
$854$	−5.02265	+	8.69949i	−0.171872	+	0.297690i
$855$	−0.168899	−	0.554101i	−0.00577624	−	0.0189499i
$856$	3.68722	−	16.1548i	0.126026	−	0.552158i
$857$	4.36588	−	1.71348i	0.149136	−	0.0585315i	−0.289599	−	0.957148i	$-0.593522\pi$
$857$	4.36588	−	1.71348i	0.149136	−	0.0585315i	0.438735	+	0.898617i	$0.355427\pi$
$858$	−16.6891	+	13.3091i	−0.569758	+	0.454367i
$859$	−27.1198			−0.925315			−0.462658	−	0.886537i	$-0.653104\pi$
$859$	−27.1198			−0.925315			−0.462658	+	0.886537i	$0.653104\pi$
$860$	−9.28195	+	11.3510i	−0.316512	+	0.387066i
$861$	−6.21810			−0.211912
$862$	−18.7132	+	14.9233i	−0.637375	+	0.508290i
$863$	17.6016	−	6.90814i	0.599167	−	0.235156i	−0.0463204	−	0.998927i	$-0.514750\pi$
$863$	17.6016	−	6.90814i	0.599167	−	0.235156i	0.645487	+	0.763771i	$0.276654\pi$
$864$	1.16456	−	5.10227i	0.0396191	−	0.173583i
$865$	−2.08536	+	0.635654i	−0.0709045	+	0.0216129i
$866$	1.39049	−	2.40839i	0.0472506	−	0.0818405i
$867$	−16.4409	+	9.49216i	−0.558362	+	0.322371i
$868$	3.51741	+	7.30398i	0.119389	+	0.247913i
$869$	12.2297	−	11.3475i	0.414864	−	0.384937i
$870$	22.2349	−	32.3805i	0.753834	−	1.09780i
$871$	−1.11011	−	4.86371i	−0.0376146	−	0.164800i
$872$	−0.964505	−	6.39907i	−0.0326623	−	0.216700i
$873$	−0.274727	+	0.402950i	−0.00929808	+	0.0136378i
$874$	−14.9448	+	38.0787i	−0.505515	+	1.28803i
$875$	−8.80210	−	1.41675i	−0.297565	−	0.0478949i
$876$	−9.83798	−	4.73772i	−0.332394	−	0.160073i
$877$	42.8462	−	3.21088i	1.44681	−	0.108424i	0.671970	−	0.740578i	$-0.265448\pi$
$877$	42.8462	−	3.21088i	1.44681	−	0.108424i	0.774842	+	0.632154i	$0.217829\pi$
$878$	−4.71990	+	31.3145i	−0.159289	+	1.05681i
$879$	−0.702017	−	0.651377i	−0.0236785	−	0.0219704i
$880$	−9.33267	+	0.668150i	−0.314604	+	0.0225233i
$881$	−12.4312	+	15.5882i	−0.418818	+	0.525181i	−0.945824	−	0.324681i	$-0.894743\pi$
$881$	−12.4312	+	15.5882i	−0.418818	+	0.525181i	0.527006	+	0.849862i	$0.323315\pi$
$882$	−0.218503	−	0.174251i	−0.00735739	−	0.00586732i
$883$	−4.88917	+	15.8503i	−0.164534	+	0.533405i	−0.999866	−	0.0163398i	$-0.994799\pi$
$883$	−4.88917	+	15.8503i	−0.164534	+	0.533405i	0.835333	+	0.549744i	$0.185275\pi$
$884$	−5.30917	−	4.92619i	−0.178567	−	0.165686i
$885$	2.02302	+	9.00147i	0.0680032	+	0.302581i
$886$	−1.82578	−	24.3633i	−0.0613382	−	0.818501i
$887$	−6.28003	+	13.0406i	−0.210863	+	0.437861i	−0.979396	−	0.201949i	$-0.935273\pi$
$887$	−6.28003	+	13.0406i	−0.210863	+	0.437861i	0.768533	+	0.639810i	$0.220987\pi$
$888$	−1.85931	−	6.02773i	−0.0623943	−	0.202277i
$889$	−0.279670	+	0.712588i	−0.00937983	+	0.0238994i
$890$	0.758790	−	3.27419i	0.0254347	−	0.109751i
$891$	36.6857	−	5.52948i	1.22902	−	0.185244i
$892$	25.9860	−	5.93113i	0.870076	−	0.198589i
$893$	−37.3227	−	54.7423i	−1.24896	−	1.83188i
$894$	0.0826023	−	0.0766437i	0.00276263	−	0.00256335i
$895$	−9.97813	+	10.6823i	−0.333532	+	0.357071i
$896$	0.398708	+	0.690583i	0.0133199	+	0.0230708i
$897$	30.6352	+	17.6872i	1.02288	+	0.590560i
$898$	23.1684	+	1.73623i	0.773140	+	0.0579388i
$899$	−23.1131	+	101.265i	−0.770867	+	3.37739i
$900$	−0.197188	−	0.0965836i	−0.00657295	−	0.00321945i
$901$	5.92567	+	7.43056i	0.197413	+	0.247548i
$902$			18.9778i			0.631890i
$903$	1.26055	+	8.90157i	0.0419483	+	0.296226i
$904$	−15.8267			−0.526388
$905$	25.9523	+	15.0990i	0.862683	+	0.501907i
$906$	−8.31757	−	21.1928i	−0.276333	−	0.704084i
$907$	−16.5837	−	3.78512i	−0.550652	−	0.125683i	−0.0618630	−	0.998085i	$-0.519704\pi$
$907$	−16.5837	−	3.78512i	−0.550652	−	0.125683i	−0.488789	+	0.872402i	$0.662561\pi$
$908$	−3.53511	−	0.264920i	−0.117317	−	0.00879168i
$909$	0.0189970	−	0.0329037i	0.000630089	−	0.00109135i
$910$	3.31236	−	4.12532i	0.109804	−	0.136753i
$911$	−25.0804	+	12.0781i	−0.830951	+	0.400165i	−0.800472	−	0.599371i	$-0.795418\pi$
$911$	−25.0804	+	12.0781i	−0.830951	+	0.400165i	−0.0304792	+	0.999535i	$0.509703\pi$
$912$	−6.89872	−	7.43505i	−0.228439	−	0.246199i
$913$	−29.8388	−	43.7655i	−0.987520	−	1.44843i
$914$	−7.11136	−	31.1569i	−0.235223	−	1.03058i
$915$	−24.0756	−	42.0227i	−0.795915	−	1.38923i
$916$	4.64511	+	3.16699i	0.153479	+	0.104640i
$917$	−14.9349	−	5.86153i	−0.493195	−	0.193565i
$918$	3.76542	+	12.2072i	0.124277	+	0.402897i
$919$	24.3524	+	11.7275i	0.803313	+	0.386855i	0.790039	−	0.613057i	$-0.210060\pi$
$919$	24.3524	+	11.7275i	0.803313	+	0.386855i	0.0132742	+	0.999912i	$0.495775\pi$
$920$	6.68103	+	13.9923i	0.220267	+	0.461312i
$921$	−45.8857	−	6.91615i	−1.51198	−	0.227895i
$922$	−27.5638	+	29.7067i	−0.907765	+	0.978338i
$923$	−4.22737	+	13.7048i	−0.139146	+	0.451099i
$924$	−3.57688	+	4.48526i	−0.117671	+	0.147554i
$925$	−18.3017	+	1.24904i	−0.601758	+	0.0410682i
$926$	8.71795	+	2.68913i	0.286490	+	0.0883703i
$927$	0.167239	−	0.180241i	0.00549286	−	0.00591989i
$928$	−1.52277	+	10.1029i	−0.0499872	+	0.331644i
$929$	2.13404	+	28.4768i	0.0700157	+	0.934295i	0.916024	+	0.401124i	$0.131380\pi$
$929$	2.13404	+	28.4768i	0.0700157	+	0.934295i	−0.846008	+	0.533170i	$0.821000\pi$
$930$	−38.9656	−	3.05055i	−1.27773	−	0.100032i
$931$	−35.8751	+	11.0660i	−1.17576	+	0.362674i
$932$	−11.9141	−	4.67592i	−0.390258	−	0.153165i
$933$	3.26219	−	4.78475i	0.106799	−	0.156646i
$934$	19.1151	−	2.88114i	0.625465	−	0.0942737i
$935$	18.9132	−	12.8028i	0.618527	−	0.418695i
$936$	0.107657	−	0.0733994i	0.00351888	−	0.00239913i
$937$	−22.5508	−	24.3040i	−0.736703	−	0.793977i	0.247899	−	0.968786i	$-0.420260\pi$
$937$	−22.5508	−	24.3040i	−0.736703	−	0.793977i	−0.984602	+	0.174809i	$0.944069\pi$
$938$	−0.581731	−	1.20798i	−0.0189942	−	0.0394419i
$939$	−23.1663	−	40.1252i	−0.756003	−	1.30944i
$940$	−24.8207	−	3.82567i	−0.809561	−	0.124780i
$941$	3.95632	−	52.7934i	0.128972	−	1.72101i	−0.439441	−	0.898272i	$-0.644823\pi$
$941$	3.95632	−	52.7934i	0.128972	−	1.72101i	0.568413	−	0.822743i	$-0.307558\pi$
$942$	34.6081	+	7.89907i	1.12759	+	0.257366i
$943$	29.2755	−	11.4898i	0.953343	−	0.374159i
$944$	−1.49623	−	1.87622i	−0.0486983	−	0.0610657i
$945$	−8.69794	+	3.38032i	−0.282944	+	0.109962i
$946$	27.1678	−	3.84721i	0.883300	−	0.125084i
$947$		−	3.35610i		−	0.109059i	−0.998512	−	0.0545293i	$-0.982634\pi$
$947$		−	3.35610i		−	0.109059i	0.998512	−	0.0545293i	$-0.0173658\pi$
$948$	5.35946	−	4.27403i	0.174067	−	0.138814i
$949$	−6.88442	−	17.5412i	−0.223478	−	0.569412i
$950$	−25.6418	+	14.5775i	−0.831929	+	0.472957i
$951$	−2.91858	+	38.9458i	−0.0946416	+	1.26290i
$952$	−1.68569	−	0.973231i	−0.0546334	−	0.0315426i
$953$	29.8924	−	17.2584i	0.968310	−	0.559054i	0.0695894	−	0.997576i	$-0.477831\pi$
$953$	29.8924	−	17.2584i	0.968310	−	0.559054i	0.898721	+	0.438522i	$0.144498\pi$
$954$	−0.154051	+	0.0741868i	−0.00498757	+	0.00240189i
$955$	−9.34547	+	19.2419i	−0.302412	+	0.622654i
$956$	−17.3006	+	11.7953i	−0.559540	+	0.381488i
$957$	−71.6614	+	16.3563i	−2.31648	+	0.528723i
$958$	−2.76425	−	18.3396i	−0.0893088	−	0.592525i
$959$	−2.22555	−	1.51735i	−0.0718667	−	0.0489979i
$960$	−3.84451	−	0.0127990i	−0.124081	−	0.000413087i
$961$	69.1400	−	21.3269i	2.23032	−	0.687963i
$962$	4.72320	−	9.80782i	0.152282	−	0.316217i
$963$	−0.725634	+	0.0543788i	−0.0233832	+	0.00175233i
$964$	20.8336	+	3.14016i	0.671006	+	0.101138i
$965$	−11.6464	+	29.3866i	−0.374912	+	0.945988i
$966$	9.08464	+	2.80224i	0.292293	+	0.0901606i
$967$	−26.7973	−	21.3701i	−0.861743	−	0.687217i	0.0893909	−	0.995997i	$-0.471508\pi$
$967$	−26.7973	−	21.3701i	−0.861743	−	0.687217i	−0.951134	+	0.308780i	$0.900079\pi$
$968$	5.08896	+	4.05831i	0.163565	+	0.130439i
$969$	23.6578	+	7.29746i	0.759997	+	0.234428i
$970$	23.0858	+	9.14932i	0.741240	+	0.293767i
$971$	−10.6399	−	1.60371i	−0.341450	−	0.0514654i	−0.0239212	−	0.999714i	$-0.507615\pi$
$971$	−10.6399	−	1.60371i	−0.341450	−	0.0514654i	−0.317529	+	0.948248i	$0.602853\pi$
$972$	−0.455058	+	0.0341019i	−0.0145960	+	0.00109382i
$973$	−0.169217	+	0.351383i	−0.00542486	+	0.0112648i
$974$	7.28285	−	2.24646i	0.233358	−	0.0719813i
$975$	9.16046	+	23.8053i	0.293370	+	0.762381i
$976$	10.4084	+	7.09632i	0.333164	+	0.227148i
$977$	−1.33301	−	8.84392i	−0.0426466	−	0.282942i	0.957335	−	0.288980i	$-0.0933161\pi$
$977$	−1.33301	−	8.84392i	−0.0426466	−	0.282942i	−0.999982	+	0.00603804i	$0.998078\pi$
$978$	−2.60747	+	0.595137i	−0.0833776	+	0.0190304i
$979$	−5.19656	+	3.54295i	−0.166083	+	0.113233i
$980$	−6.21709	+	12.8007i	−0.198597	+	0.408904i
$981$	−0.256042	+	0.123303i	−0.00817478	+	0.00393677i
$982$	14.4128	−	8.32123i	0.459931	−	0.265541i
$983$	39.3885	+	22.7410i	1.25630	+	0.725325i	0.972353	−	0.233516i	$-0.0750230\pi$
$983$	39.3885	+	22.7410i	1.25630	+	0.725325i	0.283946	+	0.958840i	$0.408356\pi$
$984$	−0.582731	+	7.77600i	−0.0185768	+	0.247890i
$985$	50.5402	−	7.44572i	1.61035	−	0.237240i
$986$	−9.11135	−	23.2153i	−0.290165	−	0.739327i
$987$	−12.0388	+	9.60064i	−0.383200	+	0.305592i
$988$		−	17.5034i		−	0.556857i
$989$	−22.3831	−	39.5804i	−0.711742	−	1.25858i
$990$	0.148840	+	0.382981i	0.00473043	+	0.0121719i
$991$	−11.4197	−	14.3198i	−0.362757	−	0.454883i	0.566639	−	0.823966i	$-0.308243\pi$
$991$	−11.4197	−	14.3198i	−0.362757	−	0.454883i	−0.929397	+	0.369083i	$0.879672\pi$
$992$	9.46358	−	3.71418i	0.300469	−	0.117925i
$993$	18.2767	+	4.17155i	0.579995	+	0.132380i
$994$	−0.288044	+	3.84368i	−0.00913619	+	0.121914i
$995$	2.27801	−	14.7796i	0.0722179	−	0.468545i
$996$	−10.8824	−	18.8488i	−0.344821	−	0.597248i
$997$	1.93705	+	4.02232i	0.0613470	+	0.127388i	0.929388	−	0.369104i	$-0.120335\pi$
$997$	1.93705	+	4.02232i	0.0613470	+	0.127388i	−0.868041	+	0.496492i	$0.834621\pi$
$998$	4.44425	+	4.78976i	0.140680	+	0.151617i
$999$	−15.8646	+	10.8163i	−0.501932	+	0.342212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.t.a.109.20	yes	264
5.4	even	2	inner	430.2.t.a.109.3	✓	264
43.15	even	21	inner	430.2.t.a.359.3	yes	264
215.144	even	42	inner	430.2.t.a.359.20	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.t.a.109.3	✓	264	5.4	even	2	inner
430.2.t.a.109.20	yes	264	1.1	even	1	trivial
430.2.t.a.359.3	yes	264	43.15	even	21	inner
430.2.t.a.359.20	yes	264	215.144	even	42	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.t (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 - 0.623490i) q^{2} +(1.60048 - 0.628141i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.651975 + 2.13891i) q^{5} +(0.859664 - 1.48898i) q^{6} +(0.690583 - 0.398708i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.0321915 + 0.0298693i) q^{9} +O(q^{10})\)	\(q+(0.781831 - 0.623490i) q^{2} +(1.60048 - 0.628141i) q^{3} +(0.222521 - 0.974928i) q^{4} +(0.651975 + 2.13891i) q^{5} +(0.859664 - 1.48898i) q^{6} +(0.690583 - 0.398708i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.0321915 + 0.0298693i) q^{9} +(1.84332 + 1.26577i) q^{10} +(-0.931112 - 4.07947i) q^{11} +(-0.256252 - 1.70012i) q^{12} +(1.67142 - 2.45153i) q^{13} +(0.291329 - 0.742294i) q^{14} +(2.38701 + 3.01374i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(2.43414 - 0.182413i) q^{17} +(-0.00654509 + 0.0434238i) q^{18} +(4.32440 + 4.01245i) q^{19} +(2.23036 - 0.159677i) q^{20} +(0.854817 - 1.07191i) q^{21} +(-3.27148 - 2.60892i) q^{22} +(-2.04391 + 6.62619i) q^{23} +(-1.26036 - 1.16944i) q^{24} +(-4.14986 + 2.78903i) q^{25} +(-0.221731 - 2.95880i) q^{26} +(-2.27072 + 4.71521i) q^{27} +(-0.235043 - 0.761989i) q^{28} +(3.73269 - 9.51074i) q^{29} +(3.74527 + 0.867962i) q^{30} +(-10.0528 + 1.51521i) q^{31} +(-0.974928 + 0.222521i) q^{32} +(-4.05270 - 5.94422i) q^{33} +(1.78935 - 1.66028i) q^{34} +(1.30304 + 1.21715i) q^{35} +(0.0219572 + 0.0380309i) q^{36} +(3.17733 + 1.83443i) q^{37} +(5.88267 + 0.440845i) q^{38} +(1.13517 - 4.97350i) q^{39} +(1.64421 - 1.51545i) q^{40} +(-2.82776 - 3.54590i) q^{41} -1.37102i q^{42} +(-4.50292 + 4.76694i) q^{43} -4.18438 q^{44} +(-0.0848758 - 0.0493805i) q^{45} +(2.53337 + 6.45492i) q^{46} +(-10.9496 - 2.49918i) q^{47} +(-1.71452 - 0.128485i) q^{48} +(-3.18206 + 5.51150i) q^{49} +(-1.50556 + 4.76795i) q^{50} +(3.78120 - 1.82093i) q^{51} +(-2.01814 - 2.17503i) q^{52} +(2.19332 + 3.21701i) q^{53} +(1.16456 + 5.10227i) q^{54} +(8.11854 - 4.65127i) q^{55} +(-0.658856 - 0.449201i) q^{56} +(9.44148 + 3.70551i) q^{57} +(-3.01151 - 9.76309i) q^{58} +(2.16212 + 1.04122i) q^{59} +(3.46934 - 1.65654i) q^{60} +(-12.4566 - 1.87753i) q^{61} +(-6.91487 + 7.45245i) q^{62} +(-0.0103217 + 0.0334622i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(6.33332 + 1.97668i) q^{65} +(-6.87469 - 2.12056i) q^{66} +(1.14362 - 1.23253i) q^{67} +(0.363806 - 2.41370i) q^{68} +(0.890952 + 11.8889i) q^{69} +(1.77764 + 0.139168i) q^{70} +(-4.61893 + 1.42475i) q^{71} +(0.0408787 + 0.0160437i) q^{72} +(3.57761 - 5.24739i) q^{73} +(3.62788 - 0.546816i) q^{74} +(-4.88984 + 7.07047i) q^{75} +(4.87412 - 3.32312i) q^{76} +(-2.26953 - 2.44597i) q^{77} +(-2.21342 - 4.59621i) q^{78} +(1.99352 + 3.45287i) q^{79} +(0.340628 - 2.20997i) q^{80} +(-0.662582 + 8.84154i) q^{81} +(-4.42167 - 1.00922i) q^{82} +(11.7838 - 4.62481i) q^{83} +(-0.854817 - 1.07191i) q^{84} +(1.97716 + 5.08746i) q^{85} +(-0.548383 + 6.53447i) q^{86} -17.5664i q^{87} +(-3.27148 + 2.60892i) q^{88} +(-0.549133 - 1.39917i) q^{89} +(-0.0971468 + 0.0143119i) q^{90} +(0.176812 - 2.35939i) q^{91} +(6.00525 + 3.46713i) q^{92} +(-15.1375 + 8.73963i) q^{93} +(-10.1190 + 4.87305i) q^{94} +(-5.76287 + 11.8655i) q^{95} +(-1.42057 + 0.968531i) q^{96} +(10.8271 - 2.47121i) q^{97} +(0.948524 + 6.29305i) q^{98} +(0.151825 + 0.103512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 44 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 264 * q + 44 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^9	\( 264 q + 44 q^{4} + 4 q^{5} - 2 q^{6} - 6 q^{9} - 8 q^{11} + 10 q^{14} + 32 q^{15} - 44 q^{16} + 4 q^{19} - 4 q^{20} + 24 q^{21} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 46 q^{29} - 36 q^{31} + 12 q^{34} - 68 q^{35} - 134 q^{36} - 64 q^{39} - 20 q^{41} + 8 q^{44} - 70 q^{45} + 112 q^{49} - 28 q^{50} - 28 q^{51} + 68 q^{54} - 30 q^{55} + 4 q^{56} - 40 q^{59} - 4 q^{60} + 20 q^{61} + 44 q^{64} + 18 q^{65} - 44 q^{66} + 32 q^{69} - 48 q^{70} + 20 q^{71} + 40 q^{74} + 122 q^{75} + 52 q^{76} + 16 q^{79} + 4 q^{80} - 16 q^{81} - 24 q^{84} + 120 q^{85} - 14 q^{86} - 142 q^{89} - 68 q^{90} - 4 q^{94} - 22 q^{95} - 2 q^{96} - 268 q^{99}+O(q^{100}) \) 264 * q + 44 * q^4 + 4 * q^5 - 2 * q^6 - 6 * q^9 - 8 * q^11 + 10 * q^14 + 32 * q^15 - 44 * q^16 + 4 * q^19 - 4 * q^20 + 24 * q^21 + 2 * q^24 + 28 * q^25 - 12 * q^26 - 46 * q^29 - 36 * q^31 + 12 * q^34 - 68 * q^35 - 134 * q^36 - 64 * q^39 - 20 * q^41 + 8 * q^44 - 70 * q^45 + 112 * q^49 - 28 * q^50 - 28 * q^51 + 68 * q^54 - 30 * q^55 + 4 * q^56 - 40 * q^59 - 4 * q^60 + 20 * q^61 + 44 * q^64 + 18 * q^65 - 44 * q^66 + 32 * q^69 - 48 * q^70 + 20 * q^71 + 40 * q^74 + 122 * q^75 + 52 * q^76 + 16 * q^79 + 4 * q^80 - 16 * q^81 - 24 * q^84 + 120 * q^85 - 14 * q^86 - 142 * q^89 - 68 * q^90 - 4 * q^94 - 22 * q^95 - 2 * q^96 - 268 * q^99

Introduction

L-functions

Modular forms

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Database

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