LMFDB - Embedded newform 99.2.m.b.58.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(4,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("99.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			58.6
Character	$\chi$	$=$	99.58
Dual form			99.2.m.b.70.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.527858 + 0.235017i) q^{2} +(-1.46440 - 0.924946i) q^{3} +(-1.11486 - 1.23818i) q^{4} +(2.74468 - 1.22201i) q^{5} +(-0.555618 - 0.832400i) q^{6} +(1.13888 - 0.242076i) q^{7} +(-0.654602 - 2.01466i) q^{8} +(1.28895 + 2.70899i) q^{9} +1.73599 q^{10} +(-2.54741 - 2.12385i) q^{11} +(0.487356 + 2.84438i) q^{12} +(0.412487 + 3.92455i) q^{13} +(0.658057 + 0.139874i) q^{14} +(-5.14961 - 0.749167i) q^{15} +(-0.220374 + 2.09672i) q^{16} +(0.254185 + 0.184677i) q^{17} +(0.0437225 + 1.73288i) q^{18} +(1.96794 + 6.05670i) q^{19} +(-4.57300 - 2.03603i) q^{20} +(-1.89168 - 0.698904i) q^{21} +(-0.845527 - 1.71977i) q^{22} +(0.0427501 - 0.0740453i) q^{23} +(-0.904849 + 3.55574i) q^{24} +(2.69431 - 2.99234i) q^{25} +(-0.704604 + 2.16855i) q^{26} +(0.618128 - 5.15926i) q^{27} +(-1.56942 - 1.14025i) q^{28} +(7.53156 - 1.60088i) q^{29} +(-2.54219 - 1.60570i) q^{30} +(-0.682449 - 6.49307i) q^{31} +(-2.72743 + 4.72404i) q^{32} +(1.76598 + 5.46638i) q^{33} +(0.0907715 + 0.157221i) q^{34} +(2.83004 - 2.05614i) q^{35} +(1.91721 - 4.61609i) q^{36} +(-1.92922 + 5.93753i) q^{37} +(-0.384637 + 3.65957i) q^{38} +(3.02595 - 6.12865i) q^{39} +(-4.25861 - 4.72966i) q^{40} +(-5.68213 - 1.20777i) q^{41} +(-0.834284 - 0.813500i) q^{42} +(3.39229 + 5.87562i) q^{43} +(0.210303 + 5.52194i) q^{44} +(6.84817 + 5.86020i) q^{45} +(0.0399679 - 0.0290384i) q^{46} +(-0.219298 + 0.243555i) q^{47} +(2.26207 - 2.86660i) q^{48} +(-5.15638 + 2.29577i) q^{49} +(2.12546 - 0.946318i) q^{50} +(-0.201414 - 0.505549i) q^{51} +(4.39943 - 4.88606i) q^{52} +(1.96000 - 1.42402i) q^{53} +(1.53880 - 2.57808i) q^{54} +(-9.58718 - 2.71632i) q^{55} +(-1.23321 - 2.13598i) q^{56} +(2.72026 - 10.6897i) q^{57} +(4.35183 + 0.925009i) q^{58} +(-1.53634 - 1.70628i) q^{59} +(4.81350 + 7.21136i) q^{60} +(1.43070 - 13.6122i) q^{61} +(1.16575 - 3.58780i) q^{62} +(2.12373 + 2.77318i) q^{63} +(0.861321 - 0.625787i) q^{64} +(5.92799 + 10.2676i) q^{65} +(-0.352506 + 3.30051i) q^{66} +(-5.83989 + 10.1150i) q^{67} +(-0.0547189 - 0.520616i) q^{68} +(-0.131091 + 0.0688906i) q^{69} +(1.97708 - 0.420242i) q^{70} +(-7.05272 - 5.12410i) q^{71} +(4.61393 - 4.37010i) q^{72} +(0.910538 - 2.80235i) q^{73} +(-2.41378 + 2.68077i) q^{74} +(-6.71331 + 1.88989i) q^{75} +(5.30529 - 9.18904i) q^{76} +(-3.41531 - 1.80213i) q^{77} +(3.03761 - 2.52391i) q^{78} +(-8.11886 - 3.61475i) q^{79} +(1.95735 + 6.02412i) q^{80} +(-5.67722 + 6.98349i) q^{81} +(-2.71551 - 1.97293i) q^{82} +(-0.518229 + 4.93062i) q^{83} +(1.24359 + 3.12142i) q^{84} +(0.923335 + 0.196261i) q^{85} +(0.409774 + 3.89874i) q^{86} +(-12.5100 - 4.62195i) q^{87} +(-2.61129 + 6.52242i) q^{88} +2.12862 q^{89} +(2.23761 + 4.70279i) q^{90} +(1.41981 + 4.36973i) q^{91} +(-0.139342 + 0.0296180i) q^{92} +(-5.00636 + 10.1397i) q^{93} +(-0.172998 + 0.0770236i) q^{94} +(12.8027 + 14.2189i) q^{95} +(8.36354 - 4.39518i) q^{96} +(-0.0811587 - 0.0361342i) q^{97} -3.26138 q^{98} +(2.47000 - 9.63842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) $ 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.527858	+	0.235017i	0.373252	+	0.166182i	0.584785	−	0.811188i	$-0.301179\pi$
$2$	0.527858	+	0.235017i	0.373252	+	0.166182i	−0.211533	+	0.977371i	$0.567846\pi$
$3$	−1.46440	−	0.924946i	−0.845473	−	0.534018i
$3$	−1.46440	−	0.924946i	−0.845473	−	0.534018i
$4$	−1.11486	−	1.23818i	−0.557430	−	0.619089i
$5$	2.74468	−	1.22201i	1.22746	−	0.546500i	0.312450	−	0.949934i	$-0.398850\pi$
$5$	2.74468	−	1.22201i	1.22746	−	0.546500i	0.915009	+	0.403434i	$0.132184\pi$
$6$	−0.555618	−	0.832400i	−0.226830	−	0.339826i
$7$	1.13888	−	0.242076i	0.430455	−	0.0914960i	0.0124114	−	0.999923i	$-0.496049\pi$
$7$	1.13888	−	0.242076i	0.430455	−	0.0914960i	0.418044	+	0.908427i	$0.362716\pi$
$8$	−0.654602	−	2.01466i	−0.231437	−	0.712289i
$9$	1.28895	+	2.70899i	0.429650	+	0.902996i
$10$	1.73599			0.548970
$11$	−2.54741	−	2.12385i	−0.768072	−	0.640364i
$11$	−2.54741	−	2.12385i	−0.768072	−	0.640364i
$12$	0.487356	+	2.84438i	0.140688	+	0.821101i
$13$	0.412487	+	3.92455i	0.114403	+	1.08848i	0.889595	+	0.456750i	$0.150986\pi$
$13$	0.412487	+	3.92455i	0.114403	+	1.08848i	−0.775192	+	0.631726i	$0.782347\pi$
$14$	0.658057	+	0.139874i	0.175873	+	0.0373830i
$15$	−5.14961	−	0.749167i	−1.32962	−	0.193434i
$16$	−0.220374	+	2.09672i	−0.0550935	+	0.524179i
$17$	0.254185	+	0.184677i	0.0616490	+	0.0447906i	0.618183	−	0.786034i	$-0.287869\pi$
$17$	0.254185	+	0.184677i	0.0616490	+	0.0447906i	−0.556534	+	0.830825i	$0.687869\pi$
$18$	0.0437225	+	1.73288i	0.0103055	+	0.408445i
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	0.875222	+	0.483721i	$0.160715\pi$
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	−0.423746	+	0.905781i	$0.639285\pi$
$20$	−4.57300	−	2.03603i	−1.02255	−	0.455271i
$21$	−1.89168	−	0.698904i	−0.412799	−	0.152513i
$22$	−0.845527	−	1.71977i	−0.180267	−	0.366657i
$23$	0.0427501	−	0.0740453i	0.00891401	−	0.0154395i	−0.861534	−	0.507700i	$-0.830496\pi$
$23$	0.0427501	−	0.0740453i	0.00891401	−	0.0154395i	0.870448	+	0.492260i	$0.163829\pi$
$24$	−0.904849	+	3.55574i	−0.184702	+	0.725813i
$25$	2.69431	−	2.99234i	0.538862	−	0.598467i
$26$	−0.704604	+	2.16855i	−0.138184	+	0.425287i
$27$	0.618128	−	5.15926i	0.118959	−	0.992899i
$28$	−1.56942	−	1.14025i	−0.296593	−	0.215487i
$29$	7.53156	−	1.60088i	1.39858	−	0.297276i	0.553913	−	0.832575i	$-0.313134\pi$
$29$	7.53156	−	1.60088i	1.39858	−	0.297276i	0.844663	+	0.535298i	$0.179801\pi$
$30$	−2.54219	−	1.60570i	−0.464139	−	0.293160i
$31$	−0.682449	−	6.49307i	−0.122571	−	1.16619i	−0.866937	−	0.498418i	$-0.833915\pi$
$31$	−0.682449	−	6.49307i	−0.122571	−	1.16619i	0.744366	−	0.667772i	$-0.232752\pi$
$32$	−2.72743	+	4.72404i	−0.482146	+	0.835101i
$33$	1.76598	+	5.46638i	0.307418	+	0.951574i
$34$	0.0907715	+	0.157221i	0.0155672	+	0.0269632i
$35$	2.83004	−	2.05614i	0.478363	−	0.347551i
$36$	1.91721	−	4.61609i	0.319535	−	0.769349i
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	0.657694	+	0.753286i	$0.271532\pi$
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	−0.974855	+	0.222838i	$0.928468\pi$
$38$	−0.384637	+	3.65957i	−0.0623963	+	0.593661i
$39$	3.02595	−	6.12865i	0.484540	−	0.981370i
$40$	−4.25861	−	4.72966i	−0.673345	−	0.747825i
$41$	−5.68213	−	1.20777i	−0.887399	−	0.188623i	−0.258409	−	0.966036i	$-0.583198\pi$
$41$	−5.68213	−	1.20777i	−0.887399	−	0.188623i	−0.628990	+	0.777413i	$0.716532\pi$
$42$	−0.834284	−	0.813500i	−0.128733	−	0.125526i
$43$	3.39229	+	5.87562i	0.517320	+	0.896024i	0.999798	+	0.0201157i	$0.00640347\pi$
$43$	3.39229	+	5.87562i	0.517320	+	0.896024i	−0.482478	+	0.875908i	$0.660263\pi$
$44$	0.210303	+	5.52194i	0.0317043	+	0.832463i
$45$	6.84817	+	5.86020i	1.02086	+	0.873587i
$46$	0.0399679	−	0.0290384i	0.00589294	−	0.00428147i
$47$	−0.219298	+	0.243555i	−0.0319879	+	0.0355262i	−0.758926	−	0.651176i	$-0.774276\pi$
$47$	−0.219298	+	0.243555i	−0.0319879	+	0.0355262i	0.726939	+	0.686703i	$0.240942\pi$
$48$	2.26207	−	2.86660i	0.326501	−	0.413759i
$49$	−5.15638	+	2.29577i	−0.736625	+	0.327967i
$50$	2.12546	−	0.946318i	0.300586	−	0.133830i
$51$	−0.201414	−	0.505549i	−0.0282036	−	0.0707910i
$52$	4.39943	−	4.88606i	0.610091	−	0.677575i
$53$	1.96000	−	1.42402i	0.269227	−	0.195605i	−0.444978	−	0.895541i	$-0.646789\pi$
$53$	1.96000	−	1.42402i	0.269227	−	0.195605i	0.714205	+	0.699937i	$0.246789\pi$
$54$	1.53880	−	2.57808i	0.209404	−	0.350832i
$55$	−9.58718	−	2.71632i	−1.29274	−	0.366269i
$56$	−1.23321	−	2.13598i	−0.164795	−	0.285433i
$57$	2.72026	−	10.6897i	0.360308	−	1.41588i
$58$	4.35183	+	0.925009i	0.571423	+	0.121460i
$59$	−1.53634	−	1.70628i	−0.200015	−	0.222139i	0.634790	−	0.772685i	$-0.281087\pi$
$59$	−1.53634	−	1.70628i	−0.200015	−	0.222139i	−0.834805	+	0.550545i	$0.814420\pi$
$60$	4.81350	+	7.21136i	0.621420	+	0.930982i
$61$	1.43070	−	13.6122i	0.183183	−	1.74287i	−0.387656	−	0.921804i	$-0.626715\pi$
$61$	1.43070	−	13.6122i	0.183183	−	1.74287i	0.570839	−	0.821062i	$-0.306618\pi$
$62$	1.16575	−	3.58780i	0.148050	−	0.455652i
$63$	2.12373	+	2.77318i	0.267565	+	0.349388i
$64$	0.861321	−	0.625787i	0.107665	−	0.0782233i
$65$	5.92799	+	10.2676i	0.735277	+	1.27354i
$66$	−0.352506	+	3.30051i	−0.0433905	+	0.406264i
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	0.250096	+	0.968221i	$0.419538\pi$
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	−0.963552	+	0.267521i	$0.913795\pi$
$68$	−0.0547189	−	0.520616i	−0.00663564	−	0.0631339i
$69$	−0.131091	+	0.0688906i	−0.0157815	+	0.00829345i
$70$	1.97708	−	0.420242i	0.236307	−	0.0502286i
$71$	−7.05272	−	5.12410i	−0.837004	−	0.608119i	0.0845279	−	0.996421i	$-0.473062\pi$
$71$	−7.05272	−	5.12410i	−0.837004	−	0.608119i	−0.921532	+	0.388302i	$0.873062\pi$
$72$	4.61393	−	4.37010i	0.543757	−	0.515021i
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	−0.883525	−	0.468383i	$-0.844837\pi$
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	0.990096	+	0.140393i	$0.0448367\pi$
$74$	−2.41378	+	2.68077i	−0.280596	+	0.311633i
$75$	−6.71331	+	1.88989i	−0.775186	+	0.218226i
$76$	5.30529	−	9.18904i	0.608559	−	1.05405i
$77$	−3.41531	−	1.80213i	−0.389211	−	0.205372i
$78$	3.03761	−	2.52391i	0.343942	−	0.285776i
$79$	−8.11886	−	3.61475i	−0.913443	−	0.406691i	−0.104464	−	0.994529i	$-0.533313\pi$
$79$	−8.11886	−	3.61475i	−0.913443	−	0.406691i	−0.808979	+	0.587838i	$0.799979\pi$
$80$	1.95735	+	6.02412i	0.218839	+	0.673517i
$81$	−5.67722	+	6.98349i	−0.630802	+	0.775944i
$82$	−2.71551	−	1.97293i	−0.299878	−	0.217874i
$83$	−0.518229	+	4.93062i	−0.0568831	+	0.541206i	0.928558	+	0.371188i	$0.121049\pi$
$83$	−0.518229	+	4.93062i	−0.0568831	+	0.541206i	−0.985441	+	0.170018i	$0.945617\pi$
$84$	1.24359	+	3.12142i	0.135687	+	0.340575i
$85$	0.923335	+	0.196261i	0.100150	+	0.0212875i
$86$	0.409774	+	3.89874i	0.0441871	+	0.420412i
$87$	−12.5100	−	4.62195i	−1.34121	−	0.495525i
$88$	−2.61129	+	6.52242i	−0.278364	+	0.695293i
$89$	2.12862			0.225634			0.112817	−	0.993616i	$-0.464013\pi$
$89$	2.12862			0.225634			0.112817	+	0.993616i	$0.464013\pi$
$90$	2.23761	+	4.70279i	0.235865	+	0.495717i
$91$	1.41981	+	4.36973i	0.148837	+	0.458072i
$92$	−0.139342	+	0.0296180i	−0.0145274	+	0.00308789i
$93$	−5.00636	+	10.1397i	−0.519135	+	1.05144i
$94$	−0.172998	+	0.0770236i	−0.0178434	+	0.00794437i
$95$	12.8027	+	14.2189i	1.31353	+	1.45882i
$96$	8.36354	−	4.39518i	0.853600	−	0.448581i
$97$	−0.0811587	−	0.0361342i	−0.00824041	−	0.00366887i	0.402612	−	0.915371i	$-0.368102\pi$
$97$	−0.0811587	−	0.0361342i	−0.00824041	−	0.00366887i	−0.410853	+	0.911702i	$0.634769\pi$
$98$	−3.26138			−0.329449
$99$	2.47000	−	9.63842i	0.248244	−	0.968698i
$100$	−6.70883			−0.670883
$101$	−1.87869	−	0.836447i	−0.186937	−	0.0832296i	0.311134	−	0.950366i	$-0.399291\pi$
$101$	−1.87869	−	0.836447i	−0.186937	−	0.0832296i	−0.498071	+	0.867137i	$0.665958\pi$
$102$	0.0124948	−	0.314194i	0.00123717	−	0.0311098i
$103$	−2.01858	−	2.24186i	−0.198896	−	0.220897i	0.635443	−	0.772148i	$-0.280817\pi$
$103$	−2.01858	−	2.24186i	−0.198896	−	0.220897i	−0.834340	+	0.551251i	$0.814151\pi$
$104$	7.63662	−	3.40004i	0.748832	−	0.333401i
$105$	−6.04613	+	0.393387i	−0.590042	+	0.0383907i
$106$	1.36927	−	0.291048i	0.132995	−	0.0282690i
$107$	3.70600	+	11.4059i	0.358272	+	1.10265i	0.954088	+	0.299527i	$0.0968290\pi$
$107$	3.70600	+	11.4059i	0.358272	+	1.10265i	−0.595815	+	0.803121i	$0.703171\pi$
$108$	−7.07720	+	4.98650i	−0.681004	+	0.479826i
$109$	5.20013			0.498082			0.249041	−	0.968493i	$-0.419885\pi$
$109$	5.20013			0.498082			0.249041	+	0.968493i	$0.419885\pi$
$110$	−4.42228	−	3.68699i	−0.421648	−	0.351540i
$111$	8.31705	−	6.91051i	0.789420	−	0.655916i
$112$	0.256586	+	2.44125i	0.0242451	+	0.230676i
$113$	−18.8074	−	3.99763i	−1.76925	−	0.376066i	−0.795907	−	0.605419i	$-0.793005\pi$
$113$	−18.8074	−	3.99763i	−1.76925	−	0.376066i	−0.973343	+	0.229354i	$0.926339\pi$
$114$	3.94817	−	5.00332i	0.369780	−	0.468604i
$115$	0.0268512	−	0.255472i	0.00250389	−	0.0238229i
$116$	−10.3788	−	7.54065i	−0.963649	−	0.700132i
$117$	−10.0999	+	6.17597i	−0.933735	+	0.570969i
$118$	−0.409965	−	1.26174i	−0.0377403	−	0.116153i
$119$	0.334192	+	0.148792i	0.0306353	+	0.0136397i
$120$	1.86163	+	10.8651i	0.169943	+	0.991844i
$121$	1.97856	+	10.8206i	0.179869	+	0.983691i
$122$	3.95432	−	6.84907i	0.358007	−	0.620086i
$123$	7.20380	+	7.02433i	0.649544	+	0.633362i
$124$	−7.27874	+	8.08386i	−0.653650	+	0.725952i
$125$	−0.903736	+	2.78141i	−0.0808326	+	0.248777i
$126$	0.469284	+	1.96296i	0.0418071	+	0.174874i
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	0.949949	−	0.312405i	$-0.101135\pi$
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	−0.00356461	+	0.999994i	$0.501135\pi$
$128$	11.2730	−	2.39616i	0.996405	−	0.211792i
$129$	0.466954	−	11.7420i	0.0411130	−	1.03382i
$130$	0.716076	+	6.81300i	0.0628040	+	0.597540i
$131$	8.98588	−	15.5640i	0.785100	−	1.35983i	−0.143839	−	0.989601i	$-0.545945\pi$
$131$	8.98588	−	15.5640i	0.785100	−	1.35983i	0.928939	−	0.370233i	$-0.120722\pi$
$132$	4.79953	−	8.28085i	0.417745	−	0.720756i
$133$	3.70742	+	6.42144i	0.321474	+	0.556810i
$134$	−5.45983	+	3.96680i	−0.471657	+	0.342679i
$135$	−4.60810	−	14.9159i	−0.396602	−	1.28375i
$136$	0.205670	−	0.632986i	0.0176360	−	0.0542781i
$137$	1.71445	−	16.3119i	0.146475	−	1.39362i	−0.636361	−	0.771391i	$-0.719561\pi$
$137$	1.71445	−	16.3119i	0.146475	−	1.39362i	0.782836	−	0.622228i	$-0.213772\pi$
$138$	−0.0853880	+	0.00555571i	−0.00726871	+	0.000472934i
$139$	−7.96373	−	8.84461i	−0.675475	−	0.750190i	0.303798	−	0.952736i	$-0.401745\pi$
$139$	−7.96373	−	8.84461i	−0.675475	−	0.750190i	−0.979273	+	0.202546i	$0.935078\pi$
$140$	−5.70096	−	1.21178i	−0.481819	−	0.102414i
$141$	0.546416	−	0.153824i	0.0460165	−	0.0129543i
$142$	−2.51858	−	4.36231i	−0.211355	−	0.366077i
$143$	7.28438	−	10.8735i	0.609150	−	0.909287i
$144$	−5.96403	+	2.10557i	−0.497002	+	0.175464i
$145$	18.7154	−	13.5976i	1.55423	−	1.12922i
$146$	1.13923	−	1.26525i	0.0942837	−	0.104713i
$147$	9.67447	+	1.40745i	0.797937	+	0.116084i
$148$	9.50253	−	4.23080i	0.781103	−	0.347770i
$149$	−4.13993	+	1.84321i	−0.339156	+	0.151002i	−0.569246	−	0.822167i	$-0.692765\pi$
$149$	−4.13993	+	1.84321i	−0.339156	+	0.151002i	0.230090	+	0.973169i	$0.426098\pi$
$150$	−3.98783	−	0.580150i	−0.325605	−	0.0473691i
$151$	−1.96113	+	2.17806i	−0.159595	+	0.177248i	−0.817639	−	0.575732i	$-0.804717\pi$
$151$	−1.96113	+	2.17806i	−0.159595	+	0.177248i	0.658044	+	0.752979i	$0.271384\pi$
$152$	10.9140	−	7.92945i	0.885239	−	0.643164i
$153$	−0.172654	+	0.926624i	−0.0139583	+	0.0749131i
$154$	−1.37927	−	1.75393i	−0.111144	−	0.141336i
$155$	−9.80771	−	16.9874i	−0.787774	−	1.36446i
$156$	−10.9619	+	3.08593i	−0.877653	+	0.247072i
$157$	17.6591	+	3.75356i	1.40935	+	0.299567i	0.848871	−	0.528600i	$-0.177283\pi$
$157$	17.6591	+	3.75356i	1.40935	+	0.299567i	0.560481	+	0.828167i	$0.310616\pi$
$158$	−3.43607	−	3.81614i	−0.273359	−	0.303596i
$159$	−4.18737	+	0.272449i	−0.332080	+	0.0216066i
$160$	−1.71309	+	16.2989i	−0.135431	+	1.28854i
$161$	0.0307625	−	0.0946773i	0.00242443	−	0.00746161i
$162$	−4.63801	+	2.35204i	−0.364396	+	0.184794i
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	−0.387786	−	0.921749i	$-0.626760\pi$
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	0.756803	+	0.653643i	$0.226760\pi$
$164$	4.83934	+	8.38199i	0.377889	+	0.654523i
$165$	11.5270	+	12.8454i	0.897379	+	1.00001i
$166$	−1.43233	+	2.48087i	−0.111171	+	0.192553i
$167$	0.524913	+	4.99422i	0.0406190	+	0.386464i	0.995879	+	0.0906956i	$0.0289090\pi$
$167$	0.524913	+	4.99422i	0.0406190	+	0.386464i	−0.955260	+	0.295769i	$0.904424\pi$
$168$	−0.169753	+	4.26859i	−0.0130968	+	0.329329i
$169$	−2.51606	+	0.534805i	−0.193543	+	0.0411388i
$170$	0.441265	+	0.320598i	0.0338435	+	0.0245887i
$171$	−13.8709	+	13.1379i	−1.06074	+	1.00468i
$172$	3.49313	−	10.7508i	0.266349	−	0.819738i
$173$	−10.4317	+	11.5855i	−0.793104	+	0.880831i	−0.995132	−	0.0985486i	$-0.968580\pi$
$173$	−10.4317	+	11.5855i	−0.793104	+	0.880831i	0.202028	+	0.979380i	$0.435247\pi$
$174$	−5.51724	−	5.37979i	−0.418261	−	0.407841i
$175$	2.34412	−	4.06013i	0.177199	−	0.306917i
$176$	5.01449	−	4.87315i	0.377981	−	0.367327i
$177$	0.671606	+	3.91972i	0.0504810	+	0.294624i
$178$	1.12361	+	0.500263i	0.0842181	+	0.0374963i
$179$	2.17822	+	6.70387i	0.162808	+	0.501071i	0.998868	−	0.0475668i	$-0.0151467\pi$
$179$	2.17822	+	6.70387i	0.162808	+	0.501071i	−0.836060	+	0.548638i	$0.815147\pi$
$180$	−0.378783	−	15.0126i	−0.0282328	−	1.11897i
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	0.510149	−	0.860086i	$-0.329590\pi$
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	−0.660345	+	0.750962i	$0.729590\pi$
$182$	−0.277504	+	2.64028i	−0.0205700	+	0.195710i
$183$	−14.6857	+	18.6104i	−1.08560	+	1.37572i
$184$	−0.177160	−	0.0376566i	−0.0130604	−	0.00277608i
$185$	1.96063	+	18.6542i	0.144148	+	1.37148i
$186$	−5.02565	+	4.17573i	−0.368499	+	0.306180i
$187$	−0.255289	−	1.01030i	−0.0186686	−	0.0738802i
$188$	0.546051			0.0398249
$189$	−0.544960	−	6.02539i	−0.0396400	−	0.438283i
$190$	3.41633	+	10.5144i	0.247847	+	0.762795i
$191$	11.5646	−	2.45814i	0.836786	−	0.177864i	0.230461	−	0.973081i	$-0.425976\pi$
$191$	11.5646	−	2.45814i	0.836786	−	0.177864i	0.606325	+	0.795217i	$0.292643\pi$
$192$	−1.84014	+	0.119727i	−0.132801	+	0.00864058i
$193$	6.16338	−	2.74411i	0.443650	−	0.197526i	−0.172739	−	0.984968i	$-0.555262\pi$
$193$	6.16338	−	2.74411i	0.443650	−	0.197526i	0.616389	+	0.787442i	$0.288595\pi$
$194$	−0.0343481	−	0.0381474i	−0.00246605	−	0.00273882i
$195$	0.815997	−	20.5190i	0.0584348	−	1.46939i
$196$	8.59121	+	3.82505i	0.613658	+	0.273218i
$197$	−20.6474			−1.47107			−0.735534	−	0.677488i	$-0.763069\pi$
$197$	−20.6474			−1.47107			−0.735534	+	0.677488i	$0.763069\pi$
$198$	3.56900	−	4.50722i	0.253638	−	0.320314i
$199$	−13.2862			−0.941832			−0.470916	−	0.882178i	$-0.656077\pi$
$199$	−13.2862			−0.941832			−0.470916	+	0.882178i	$0.656077\pi$
$200$	−7.79224	−	3.46933i	−0.550994	−	0.245318i
$201$	17.9078	−	9.41083i	1.26312	−	0.663789i
$202$	−0.795102	−	0.883050i	−0.0559432	−	0.0621312i
$203$	8.18999	−	3.64642i	0.574824	−	0.255928i
$204$	−0.401411	+	0.813003i	−0.0281044	+	0.0569216i
$205$	−17.0715	+	3.62867i	−1.19233	+	0.253437i
$206$	−0.538646	−	1.65778i	−0.0375292	−	0.115503i
$207$	0.255690	+	0.0203688i	0.0177717	+	0.00141573i
$208$	−8.31958			−0.576859
$209$	7.85035	−	19.6085i	0.543020	−	1.35635i
$210$	−3.28395	−	1.21329i	−0.226614	−	0.0837252i
$211$	0.872292	+	8.29930i	0.0600510	+	0.571348i	0.982635	+	0.185551i	$0.0594068\pi$
$211$	0.872292	+	8.29930i	0.0600510	+	0.571348i	−0.922584	+	0.385797i	$0.873926\pi$
$212$	−3.94832	−	0.839242i	−0.271172	−	0.0576394i
$213$	5.58851	+	14.0271i	0.382918	+	0.961124i
$214$	−0.724343	+	6.89166i	−0.0495150	+	0.471104i
$215$	16.4908	+	11.9813i	1.12467	+	0.817117i
$216$	−10.7988	+	2.13194i	−0.734763	+	0.145060i
$217$	−2.34904	−	7.22960i	−0.159463	−	0.490778i
$218$	2.74493	+	1.22212i	0.185910	+	0.0827724i
$219$	−3.92541	+	3.26156i	−0.265255	+	0.220396i
$220$	7.32508	+	14.8990i	0.493857	+	1.00449i
$221$	−0.619925	+	1.07374i	−0.0417007	+	0.0722277i
$222$	6.01431	−	1.69311i	0.403654	−	0.113634i
$223$	−0.256716	+	0.285112i	−0.0171910	+	0.0190925i	−0.751679	−	0.659529i	$-0.770756\pi$
$223$	−0.256716	+	0.285112i	−0.0171910	+	0.0190925i	0.734488	+	0.678622i	$0.237422\pi$
$224$	−1.96263	+	6.04035i	−0.131134	+	0.403588i
$225$	11.5790	+	3.44189i	0.771936	+	0.229459i
$226$	−8.98811	−	6.53024i	−0.597880	−	0.434385i
$227$	−17.6204	+	3.74533i	−1.16951	+	0.248586i	−0.751422	−	0.659822i	$-0.770632\pi$
$227$	−17.6204	+	3.74533i	−1.16951	+	0.248586i	−0.418084	+	0.908408i	$0.637298\pi$
$228$	−16.2684	+	8.54934i	−1.07740	+	0.566194i
$229$	−1.40359	−	13.3543i	−0.0927521	−	0.882478i	−0.937657	−	0.347561i	$-0.887010\pi$
$229$	−1.40359	−	13.3543i	−0.0927521	−	0.882478i	0.844905	−	0.534916i	$-0.179657\pi$
$230$	0.0742139	−	0.128542i	0.00489352	−	0.00847583i
$231$	3.33452	+	5.79803i	0.219395	+	0.381482i
$232$	−8.15540	−	14.1256i	−0.535428	−	0.927389i
$233$	2.72611	−	1.98063i	0.178593	−	0.129756i	−0.494897	−	0.868952i	$-0.664794\pi$
$233$	2.72611	−	1.98063i	0.178593	−	0.129756i	0.673490	+	0.739196i	$0.264794\pi$
$234$	−6.78276	+	0.886384i	−0.443403	+	0.0579447i
$235$	−0.304276	+	0.936466i	−0.0198488	+	0.0610883i
$236$	−0.399873	+	3.80454i	−0.0260295	+	0.247654i
$237$	8.54582	+	12.8029i	0.555111	+	0.831641i
$238$	0.141437	+	0.157082i	0.00916800	+	0.0101821i
$239$	22.6899	+	4.82289i	1.46769	+	0.311967i	0.871308	−	0.490736i	$-0.163272\pi$
$239$	22.6899	+	4.82289i	1.46769	+	0.311967i	0.596379	+	0.802703i	$0.296606\pi$
$240$	2.70563	−	10.6322i	0.174648	−	0.686304i
$241$	−7.58206	−	13.1325i	−0.488404	−	0.845940i	0.511507	−	0.859279i	$-0.329087\pi$
$241$	−7.58206	−	13.1325i	−0.488404	−	0.845940i	−0.999911	+	0.0133389i	$0.995754\pi$
$242$	−1.49863	+	6.17673i	−0.0963358	+	0.397055i
$243$	14.7731	−	4.97552i	0.947694	−	0.319180i
$244$	−18.4494	+	13.4043i	−1.18110	+	0.858120i
$245$	−11.3472	+	12.6023i	−0.724944	+	0.805131i
$246$	2.15174	+	5.40086i	0.137190	+	0.344346i
$247$	−22.9581	+	10.2216i	−1.46079	+	0.650385i
$248$	−12.6346	+	5.62528i	−0.802297	+	0.357205i
$249$	5.31946	−	6.74108i	0.337107	−	0.427199i
$250$	−1.13072	+	1.25580i	−0.0715133	+	0.0794235i
$251$	0.471095	−	0.342271i	0.0297353	−	0.0216039i	−0.572818	−	0.819682i	$-0.694150\pi$
$251$	0.471095	−	0.342271i	0.0297353	−	0.0216039i	0.602554	+	0.798078i	$0.294150\pi$
$252$	1.06602	−	5.72127i	0.0671531	−	0.360406i
$253$	−0.266163	+	0.0978289i	−0.0167335	+	0.00615045i
$254$	3.80863	+	6.59673i	0.238974	+	0.413916i
$255$	−1.17060	−	1.14144i	−0.0733060	−	0.0714798i
$256$	4.43092	+	0.941821i	0.276933	+	0.0588638i
$257$	−7.34131	−	8.15335i	−0.457939	−	0.508592i	0.469313	−	0.883032i	$-0.344502\pi$
$257$	−7.34131	−	8.15335i	−0.457939	−	0.508592i	−0.927251	+	0.374440i	$0.877835\pi$
$258$	3.00605	−	6.08834i	0.187148	−	0.379044i
$259$	−0.759813	+	7.22913i	−0.0472125	+	0.449197i
$260$	6.10421	−	18.7868i	0.378567	−	1.16511i
$261$	14.0446	+	18.3394i	0.869337	+	1.13518i
$262$	8.40108	−	6.10374i	0.519020	−	0.377090i
$263$	7.19768	+	12.4668i	0.443828	+	0.768733i	0.997970	−	0.0636896i	$-0.0202868\pi$
$263$	7.19768	+	12.4668i	0.443828	+	0.768733i	−0.554142	+	0.832422i	$0.686953\pi$
$264$	9.85686	−	7.13615i	0.606648	−	0.439200i
$265$	3.63940	−	6.30363i	0.223567	−	0.387229i
$266$	0.447840	+	4.26092i	0.0274589	+	0.261254i
$267$	−3.11716	−	1.96886i	−0.190767	−	0.120492i
$268$	19.0348	−	4.04598i	1.16274	−	0.247147i
$269$	−0.395590	−	0.287413i	−0.0241195	−	0.0175239i	0.575660	−	0.817689i	$-0.304745\pi$
$269$	−0.395590	−	0.287413i	−0.0241195	−	0.0175239i	−0.599780	+	0.800165i	$0.704745\pi$
$270$	1.07307	−	8.95644i	0.0653047	−	0.545072i
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	−0.503234	−	0.864150i	$-0.667857\pi$
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	0.915060	−	0.403318i	$-0.132143\pi$
$272$	−0.443230	+	0.492257i	−0.0268748	+	0.0298475i
$273$	1.96259	−	7.71229i	0.118781	−	0.466769i
$274$	4.73856	−	8.20743i	0.286267	−	0.495829i
$275$	−13.2188	+	1.90039i	−0.797122	+	0.114598i
$276$	0.231447	+	0.0855109i	0.0139315	+	0.00514715i
$277$	2.62144	+	1.16714i	0.157507	+	0.0701267i	0.483976	−	0.875081i	$-0.339192\pi$
$277$	2.62144	+	1.16714i	0.157507	+	0.0701267i	−0.326469	+	0.945208i	$0.605859\pi$
$278$	−2.12508	−	6.54031i	−0.127454	−	0.392262i
$279$	16.7100	−	10.2180i	1.00040	−	0.611735i
$280$	−5.99497	−	4.35560i	−0.358268	−	0.260297i
$281$	−1.90013	+	18.0785i	−0.113352	+	1.07847i	0.778967	+	0.627066i	$0.215744\pi$
$281$	−1.90013	+	18.0785i	−0.113352	+	1.07847i	−0.892318	+	0.451406i	$0.850922\pi$
$282$	0.324581	+	0.0472201i	0.0193285	+	0.00281192i
$283$	20.0883	+	4.26991i	1.19413	+	0.253820i	0.761749	−	0.647873i	$-0.224341\pi$
$283$	20.0883	+	4.26991i	1.19413	+	0.253820i	0.432378	+	0.901692i	$0.357674\pi$
$284$	1.51825	+	14.4452i	0.0900916	+	0.857164i
$285$	−5.59665	−	32.6640i	−0.331517	−	1.93485i
$286$	6.40057	−	4.02770i	0.378474	−	0.238163i
$287$	−6.76362			−0.399244
$288$	−16.3129	−	1.29952i	−0.961246	−	0.0765747i
$289$	−5.22278	−	16.0741i	−0.307223	−	0.945534i
$290$	13.0747	−	2.77912i	0.767776	−	0.163196i
$291$	0.0854268	+	0.127982i	0.00500781	+	0.00750246i
$292$	−4.48493	+	1.99682i	−0.262461	+	0.116855i
$293$	0.575497	+	0.639154i	0.0336209	+	0.0373398i	0.759721	−	0.650250i	$-0.225336\pi$
$293$	0.575497	+	0.639154i	0.0336209	+	0.0373398i	−0.726100	+	0.687589i	$0.758669\pi$
$294$	4.77597	+	3.01660i	0.278540	+	0.175932i
$295$	−6.30187	−	2.80578i	−0.366909	−	0.163359i
$296$	13.2250			0.768685
$297$	−12.5321	+	11.8299i	−0.727185	+	0.686441i
$298$	−2.61848			−0.151684
$299$	0.308229	+	0.137232i	0.0178253	+	0.00793635i
$300$	9.82443	+	6.20531i	0.567214	+	0.358264i
$301$	5.28575	+	5.87042i	0.304665	+	0.338365i
$302$	−1.54708	+	0.688804i	−0.0890244	+	0.0396362i
$303$	1.97749	+	2.96258i	0.113604	+	0.170196i
$304$	−13.1329	+	2.79148i	−0.753221	+	0.160102i
$305$	−12.7075	−	39.1095i	−0.727627	−	2.23941i
$306$	−0.308910	+	0.448549i	−0.0176592	+	0.0256418i
$307$	3.48920			0.199139			0.0995696	−	0.995031i	$-0.468253\pi$
$307$	3.48920			0.199139			0.0995696	+	0.995031i	$0.468253\pi$
$308$	1.57624	+	6.23790i	0.0898144	+	0.355437i
$309$	0.882412	+	5.15005i	0.0501986	+	0.292976i
$310$	−1.18473	−	11.2719i	−0.0672880	−	0.640203i
$311$	−10.6083	−	2.25486i	−0.601542	−	0.127862i	−0.102932	−	0.994688i	$-0.532822\pi$
$311$	−10.6083	−	2.25486i	−0.601542	−	0.127862i	−0.498610	+	0.866827i	$0.666156\pi$
$312$	−14.3279	−	2.08443i	−0.811160	−	0.118008i
$313$	2.95618	−	28.1261i	0.167093	−	1.58978i	−0.514133	−	0.857710i	$-0.671886\pi$
$313$	2.95618	−	28.1261i	0.167093	−	1.58978i	0.681226	−	0.732073i	$-0.261447\pi$
$314$	8.43935	+	6.13155i	0.476260	+	0.346023i
$315$	9.21783	+	5.01627i	0.519366	+	0.282635i
$316$	4.57569	+	14.0825i	0.257403	+	0.792204i
$317$	−1.01634	−	0.452505i	−0.0570836	−	0.0254152i	0.377996	−	0.925807i	$-0.376613\pi$
$317$	−1.01634	−	0.452505i	−0.0570836	−	0.0254152i	−0.435080	+	0.900392i	$0.643280\pi$
$318$	−2.27437	−	0.840291i	−0.127540	−	0.0471212i
$319$	−22.5860	−	11.9178i	−1.26457	−	0.667267i
$320$	1.59933	−	2.77013i	0.0894055	−	0.154855i
$321$	5.12276	−	20.1307i	0.285925	−	1.12358i
$322$	0.0384890	−	0.0427464i	0.00214491	−	0.00238216i
$323$	−0.618308	+	1.90296i	−0.0344036	+	0.105883i
$324$	14.9761	−	0.756208i	0.832007	−	0.0420116i
$325$	12.8550	+	9.33967i	0.713065	+	0.518072i
$326$	3.29134	−	0.699597i	0.182291	−	0.0387471i
$327$	−7.61508	−	4.80984i	−0.421115	−	0.265985i
$328$	1.28628	+	12.2382i	0.0710230	+	0.675739i
$329$	−0.190795	+	0.330466i	−0.0105188	+	0.0182192i
$330$	3.06574	+	9.48961i	0.168763	+	0.522386i
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	0.984467	−	0.175569i	$-0.0561764\pi$
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	−0.644281	+	0.764789i	$0.722843\pi$
$332$	6.68275	−	4.85530i	0.366763	−	0.266469i
$333$	−18.5714	+	2.42694i	−1.01770	+	0.132995i
$334$	−0.896648	+	2.75960i	−0.0490624	+	0.150999i
$335$	−3.66801	+	34.8988i	−0.200405	+	1.90673i
$336$	1.88228	−	3.81230i	0.102687	−	0.207978i
$337$	9.01561	+	10.0128i	0.491112	+	0.545435i	0.936851	−	0.349728i	$-0.113726\pi$
$337$	9.01561	+	10.0128i	0.491112	+	0.545435i	−0.445740	+	0.895163i	$0.647059\pi$
$338$	−1.45381	−	0.309017i	−0.0790768	−	0.0168083i
$339$	23.8440	+	23.2500i	1.29503	+	1.26276i
$340$	−0.786384	−	1.36206i	−0.0426477	−	0.0738679i
$341$	−12.0518	+	17.9899i	−0.652642	+	0.974208i
$342$	−10.4095	+	3.67503i	−0.562882	+	0.198723i
$343$	−11.9104	+	8.65342i	−0.643102	+	0.467241i
$344$	9.61676	−	10.6805i	0.518501	−	0.575854i
$345$	−0.275619	+	0.349278i	−0.0148388	+	0.0188045i
$346$	−8.22923	+	3.66389i	−0.442406	+	0.196972i
$347$	8.89717	−	3.96128i	0.477625	−	0.212652i	−0.153781	−	0.988105i	$-0.549145\pi$
$347$	8.89717	−	3.96128i	0.477625	−	0.212652i	0.631406	+	0.775453i	$0.282478\pi$
$348$	8.22407	+	20.6424i	0.440856	+	1.10655i
$349$	−2.97107	+	3.29971i	−0.159038	+	0.176629i	−0.817397	−	0.576074i	$-0.804584\pi$
$349$	−2.97107	+	3.29971i	−0.159038	+	0.176629i	0.658360	+	0.752703i	$0.271251\pi$
$350$	2.19156	−	1.59226i	0.117144	−	0.0851100i
$351$	20.5027	+	0.297748i	1.09436	+	0.0158926i
$352$	16.9810	−	6.24142i	0.905090	−	0.332669i
$353$	−16.2618	−	28.1662i	−0.865527	−	1.49914i	−0.866523	−	0.499137i	$-0.833651\pi$
$353$	−16.2618	−	28.1662i	−0.865527	−	1.49914i	0.000996749	−	1.00000i	$-0.499683\pi$
$354$	−0.566690	+	2.22689i	−0.0301193	+	0.118358i
$355$	−25.6192	−	5.44553i	−1.35973	−	0.289019i
$356$	−2.37312	−	2.63561i	−0.125775	−	0.139687i
$357$	−0.351767	−	0.527000i	−0.0186175	−	0.0278918i
$358$	−0.425736	+	4.05061i	−0.0225008	+	0.214081i
$359$	−8.58143	+	26.4109i	−0.452911	+	1.39392i	0.420660	+	0.907218i	$0.361799\pi$
$359$	−8.58143	+	26.4109i	−0.452911	+	1.39392i	−0.873571	+	0.486697i	$0.838201\pi$
$360$	7.32347	−	17.6328i	0.385981	−	0.929330i
$361$	−17.4395	+	12.6705i	−0.917868	+	0.666870i
$362$	−0.721600	−	1.24985i	−0.0379264	−	0.0656905i
$363$	7.11107	−	17.6758i	0.373234	−	0.927737i
$364$	3.82761	−	6.62962i	0.200621	−	0.347487i
$365$	−0.925362	−	8.80424i	−0.0484357	−	0.460835i
$366$	−12.1257	+	6.37227i	−0.633822	+	0.333084i
$367$	−1.14658	+	0.243713i	−0.0598511	+	0.0127217i	−0.237740	−	0.971329i	$-0.576407\pi$
$367$	−1.14658	+	0.243713i	−0.0598511	+	0.0127217i	0.177889	+	0.984051i	$0.443073\pi$
$368$	0.145831	+	0.105952i	0.00760197	+	0.00552315i
$369$	−4.05213	−	16.9496i	−0.210945	−	0.882359i
$370$	−3.34912	+	10.3075i	−0.174112	+	0.535862i
$371$	1.88748	−	2.09626i	0.0979929	−	0.108832i
$372$	18.1361	−	5.10558i	0.940315	−	0.264712i
$373$	−10.8834	+	18.8506i	−0.563520	+	0.976046i	0.433665	+	0.901074i	$0.357220\pi$
$373$	−10.8834	+	18.8506i	−0.563520	+	0.976046i	−0.997186	+	0.0749719i	$0.976113\pi$
$374$	0.102681	−	0.593290i	0.00530951	−	0.0306783i
$375$	3.89609	−	3.23720i	0.201193	−	0.167168i
$376$	0.634233	+	0.282379i	0.0327081	+	0.0145626i
$377$	9.38942	+	28.8977i	0.483580	+	1.48831i
$378$	1.12841	−	3.30862i	0.0580392	−	0.170177i
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	0.871749	−	0.489953i	$-0.162986\pi$
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	−0.196588	+	0.980486i	$0.562986\pi$
$380$	3.33224	−	31.7041i	0.170940	−	1.62639i
$381$	−8.45100	−	21.2120i	−0.432958	−	1.08672i
$382$	6.68218	+	1.42034i	0.341890	+	0.0726709i
$383$	−0.647381	−	6.15942i	−0.0330796	−	0.314732i	−0.998533	−	0.0541542i	$-0.982754\pi$
$383$	−0.647381	−	6.15942i	−0.0330796	−	0.314732i	0.965453	−	0.260577i	$-0.0839129\pi$
$384$	−18.7246	−	6.91801i	−0.955534	−	0.353033i
$385$	−11.5762	−	0.772734i	−0.589977	−	0.0393821i
$386$	3.89830			0.198418
$387$	−11.5445	+	16.7630i	−0.586839	+	0.852114i
$388$	0.0457401	+	0.140773i	0.00232210	+	0.00714669i
$389$	0.707409	−	0.150365i	0.0358671	−	0.00762378i	−0.189943	−	0.981795i	$-0.560830\pi$
$389$	0.707409	−	0.150365i	0.0358671	−	0.00762378i	0.225810	+	0.974171i	$0.427497\pi$
$390$	5.25304	−	10.6393i	0.265998	−	0.538743i
$391$	0.0245409	−	0.0109263i	0.00124109	−	0.000552567i
$392$	8.00056	+	8.88552i	0.404089	+	0.448787i
$393$	−27.5548	+	14.4805i	−1.38996	+	0.730445i
$394$	−10.8989	−	4.85250i	−0.549079	−	0.244466i
$395$	−26.7009			−1.34347
$396$	−14.6878	+	7.68720i	−0.738089	+	0.386296i
$397$	4.08994			0.205268			0.102634	−	0.994719i	$-0.467273\pi$
$397$	4.08994			0.205268			0.102634	+	0.994719i	$0.467273\pi$
$398$	−7.01321	−	3.12248i	−0.351540	−	0.156516i
$399$	0.510332	−	12.8327i	0.0255486	−	0.642441i
$400$	5.68033	+	6.30864i	0.284016	+	0.315432i
$401$	−5.15812	+	2.29654i	−0.257584	+	0.114684i	−0.531466	−	0.847079i	$-0.678359\pi$
$401$	−5.15812	+	2.29654i	−0.257584	+	0.114684i	0.273882	+	0.961763i	$0.411692\pi$
$402$	11.6645	−	0.758940i	0.581770	−	0.0378525i
$403$	25.2009	−	5.35662i	1.25535	−	0.266832i
$404$	1.05881	+	3.25868i	0.0526777	+	0.162125i
$405$	−7.04826	+	26.1051i	−0.350231	+	1.29717i
$406$	5.18012			0.257085
$407$	17.5249	−	11.0279i	0.868677	−	0.546634i
$408$	−0.886662	+	0.736713i	−0.0438963	+	0.0364727i
$409$	−0.987666	−	9.39701i	−0.0488369	−	0.464652i	−0.991423	−	0.130690i	$-0.958281\pi$
$409$	−0.987666	−	9.39701i	−0.0488369	−	0.464652i	0.942586	−	0.333962i	$-0.108386\pi$
$410$	−9.86414	−	2.09669i	−0.487155	−	0.103548i
$411$	−17.5983	+	22.3014i	−0.868058	+	1.10005i
$412$	−0.525386	+	4.99871i	−0.0258839	+	0.246269i
$413$	−2.16276	−	1.57134i	−0.106422	−	0.0773204i
$414$	0.130181	+	0.0708435i	0.00639805	+	0.00348177i
$415$	4.60290	+	14.1663i	0.225948	+	0.695395i
$416$	−19.6648	−	8.75533i	−0.964145	−	0.429265i
$417$	3.48131	+	20.3181i	0.170480	+	0.994981i
$418$	8.75220	−	8.50551i	0.428084	−	0.416018i
$419$	−0.0757820	+	0.131258i	−0.00370219	+	0.00641238i	−0.867871	−	0.496790i	$-0.834512\pi$
$419$	−0.0757820	+	0.131258i	−0.00370219	+	0.00641238i	0.864168	+	0.503203i	$0.167845\pi$
$420$	7.22768	+	7.04762i	0.352675	+	0.343888i
$421$	11.3595	−	12.6160i	0.553630	−	0.614868i	−0.399756	−	0.916622i	$-0.630905\pi$
$421$	11.3595	−	12.6160i	0.553630	−	0.614868i	0.953386	+	0.301753i	$0.0975719\pi$
$422$	−1.49003	+	4.58585i	−0.0725337	+	0.223236i
$423$	−0.942451	−	0.280145i	−0.0458236	−	0.0136211i
$424$	−4.15194	−	3.01656i	−0.201636	−	0.146497i
$425$	1.23747	−	0.263032i	0.0600261	−	0.0127589i
$426$	−0.346686	+	8.71773i	−0.0167970	+	0.422375i
$427$	−1.66580	−	15.8490i	−0.0806135	−	0.766986i
$428$	9.99085	−	17.3047i	0.482926	−	0.836453i
$429$	−20.7247	+	9.18551i	−1.00060	+	0.443481i
$430$	5.88900	+	10.2000i	0.283993	+	0.491890i
$431$	20.5242	−	14.9117i	0.988618	−	0.718273i	0.0289998	−	0.999579i	$-0.490768\pi$
$431$	20.5242	−	14.9117i	0.988618	−	0.718273i	0.959618	+	0.281307i	$0.0907678\pi$
$432$	10.6813	+	2.43300i	0.513903	+	0.117058i
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	−0.749999	−	0.661439i	$-0.769946\pi$
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	0.995546	−	0.0942769i	$-0.0300539\pi$
$434$	0.459123	−	4.36827i	0.0220386	−	0.209684i
$435$	−39.9839	+	2.60153i	−1.91708	+	0.124734i
$436$	−5.79742	−	6.43868i	−0.277646	−	0.308357i
$437$	0.532600	+	0.113208i	0.0254777	+	0.00541545i
$438$	−2.83858	+	0.799102i	−0.135633	+	0.0381825i
$439$	19.6207	+	33.9840i	0.936443	+	1.62197i	0.772040	+	0.635574i	$0.219237\pi$
$439$	19.6207	+	33.9840i	0.936443	+	1.62197i	0.164403	+	0.986393i	$0.447430\pi$
$440$	0.803326	+	21.0930i	0.0382971	+	1.00557i
$441$	−12.8655	−	11.0094i	−0.612643	−	0.524259i
$442$	−0.579580	+	0.421089i	−0.0275678	+	0.0200292i
$443$	21.5389	−	23.9214i	1.02334	−	1.13654i	0.0327827	−	0.999463i	$-0.489563\pi$
$443$	21.5389	−	23.9214i	1.02334	−	1.13654i	0.990561	−	0.137075i	$-0.0437703\pi$
$444$	−17.8288	−	2.59374i	−0.846117	−	0.123093i
$445$	5.84239	−	2.60120i	0.276956	−	0.123309i
$446$	−0.202515	+	0.0901657i	−0.00958939	+	0.00426947i
$447$	7.76739	+	1.13000i	0.367385	+	0.0534473i
$448$	0.829451	−	0.921199i	0.0391879	−	0.0435226i
$449$	20.9085	−	15.1909i	0.986731	−	0.716902i	0.0275281	−	0.999621i	$-0.491236\pi$
$449$	20.9085	−	15.1909i	0.986731	−	0.716902i	0.959203	+	0.282719i	$0.0912364\pi$
$450$	5.30318	+	4.53810i	0.249994	+	0.213928i
$451$	11.9096	+	15.1447i	0.560799	+	0.713134i
$452$	16.0178	+	27.7437i	0.753415	+	1.30495i
$453$	4.88647	−	1.37561i	0.229586	−	0.0646318i
$454$	−10.1813	−	2.16410i	−0.477831	−	0.101566i
$455$	9.23679	+	10.2585i	0.433027	+	0.480926i
$456$	−23.3167	+	1.51709i	−1.09191	+	0.0710441i
$457$	1.32921	−	12.6466i	0.0621780	−	0.591584i	−0.918427	−	0.395590i	$-0.870540\pi$
$457$	1.32921	−	12.6466i	0.0621780	−	0.591584i	0.980605	−	0.195994i	$-0.0627932\pi$
$458$	2.39760	−	7.37904i	0.112032	−	0.344800i
$459$	1.10991	−	1.19725i	0.0518063	−	0.0558830i
$460$	−0.346255	+	0.251569i	−0.0161442	+	0.0117295i
$461$	9.51087	+	16.4733i	0.442965	+	0.767238i	0.997908	−	0.0646502i	$-0.0205932\pi$
$461$	9.51087	+	16.4733i	0.442965	+	0.767238i	−0.554943	+	0.831889i	$0.687260\pi$
$462$	0.397512	+	3.84420i	0.0184939	+	0.178849i
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	−0.467977	−	0.883741i	$-0.655017\pi$
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	0.999330	−	0.0365903i	$-0.0116497\pi$
$464$	1.69684	+	16.1443i	0.0787738	+	0.749482i
$465$	−1.35005	+	33.9481i	−0.0626069	+	1.57430i
$466$	1.90448	−	0.404810i	0.0882233	−	0.0187524i
$467$	−12.8819	−	9.35921i	−0.596101	−	0.433093i	0.248392	−	0.968660i	$-0.420098\pi$
$467$	−12.8819	−	9.35921i	−0.596101	−	0.433093i	−0.844493	+	0.535567i	$0.820098\pi$
$468$	18.9069	+	5.62012i	0.873973	+	0.259790i
$469$	−4.20232	+	12.9334i	−0.194045	+	0.597210i
$470$	−0.380700	+	0.422810i	−0.0175604	+	0.0195028i
$471$	−22.3882	−	21.8305i	−1.03159	−	1.00589i
$472$	−2.43188	+	4.21215i	−0.111936	+	0.193880i
$473$	3.83737	−	22.1723i	0.176443	−	1.01948i
$474$	1.50206	+	8.76655i	0.0689920	+	0.402661i
$475$	23.4259	+	10.4299i	1.07486	+	0.478556i
$476$	−0.188347	−	0.579671i	−0.00863285	−	0.0265692i
$477$	6.38400	+	3.47412i	0.292303	+	0.159069i
$478$	10.8436	+	7.87832i	0.495973	+	0.360346i
$479$	1.71322	−	16.3002i	0.0782789	−	0.744774i	−0.883033	−	0.469311i	$-0.844502\pi$
$479$	1.71322	−	16.3002i	0.0782789	−	0.744774i	0.961312	−	0.275463i	$-0.0888311\pi$
$480$	17.5843	−	22.2837i	0.802609	−	1.01711i
$481$	−24.0979	−	5.12217i	−1.09877	−	0.233551i
$482$	−0.915880	−	8.71402i	−0.0417172	−	0.396913i
$483$	−0.132620	+	0.110192i	−0.00603442	+	0.00501391i
$484$	11.1920	−	14.5133i	0.508728	−	0.659694i
$485$	−0.266911			−0.0121198
$486$	8.96742	+	0.845568i	0.406771	+	0.0383558i
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	0.974044	+	0.226361i	$0.0726828\pi$
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	−0.654966	+	0.755658i	$0.727317\pi$
$488$	−28.3605	+	6.02821i	−1.28382	+	0.272884i
$489$	−10.0653	+	0.654890i	−0.455167	+	0.0296151i
$490$	−8.95145	+	3.98544i	−0.404385	+	0.180044i
$491$	−29.2029	−	32.4331i	−1.31791	−	1.46368i	−0.788071	−	0.615584i	$-0.788920\pi$
$491$	−29.2029	−	32.4331i	−1.31791	−	1.46368i	−0.529836	−	0.848100i	$-0.677747\pi$
$492$	0.666143	−	16.7507i	0.0300320	−	0.755181i
$493$	2.21006	+	0.983982i	0.0995360	+	0.0443163i
$494$	−14.5209			−0.653324
$495$	−4.99890	−	29.4728i	−0.224684	−	1.32470i
$496$	13.7645			0.618045
$497$	−9.27261	−	4.12843i	−0.415933	−	0.185185i
$498$	4.39219	−	2.30817i	0.196819	−	0.103431i
$499$	−13.4519	−	14.9398i	−0.602189	−	0.668798i	0.362563	−	0.931959i	$-0.381902\pi$
$499$	−13.4519	−	14.9398i	−0.602189	−	0.668798i	−0.964752	+	0.263161i	$0.915235\pi$
$500$	4.45142	−	1.98190i	0.199074	−	0.0886333i
$501$	3.85070	−	7.79906i	0.172037	−	0.348436i
$502$	0.329111	−	0.0699546i	0.0146889	−	0.00312223i
$503$	−3.27815	−	10.0891i	−0.146165	−	0.449850i	0.850994	−	0.525176i	$-0.176000\pi$
$503$	−3.27815	−	10.0891i	−0.146165	−	0.449850i	−0.997159	+	0.0753254i	$0.976000\pi$
$504$	4.19681	−	6.09393i	0.186941	−	0.271445i
$505$	−6.17856			−0.274942
$506$	−0.163487	−	0.0109131i	−0.00726791	−	0.000485148i
$507$	4.17919	+	1.54405i	0.185604	+	0.0685736i
$508$	−2.29592	−	21.8442i	−0.101865	−	0.969179i
$509$	43.4966	+	9.24549i	1.92795	+	0.409799i	0.999239	+	0.0390051i	$0.0124189\pi$
$509$	43.4966	+	9.24549i	1.92795	+	0.409799i	0.928715	+	0.370794i	$0.120914\pi$
$510$	−0.349654	−	0.877630i	−0.0154829	−	0.0388621i
$511$	0.358610	−	3.41195i	0.0158640	−	0.150936i
$512$	−16.5301	−	12.0098i	−0.730534	−	0.530764i
$513$	32.4645	−	6.40930i	1.43334	−	0.282977i
$514$	−1.95899	−	6.02915i	−0.0864073	−	0.265934i
$515$	−8.27992	−	3.68646i	−0.364857	−	0.162445i
$516$	−15.0592	+	12.5125i	−0.662946	+	0.550831i
$517$	1.07591	−	0.154679i	0.0473187	−	0.00680275i
$518$	−2.10004	+	3.63738i	−0.0922707	+	0.159817i
$519$	25.9921	−	7.31715i	1.14093	−	0.321187i
$520$	16.8052	−	18.6641i	0.736956	−	0.818473i
$521$	5.23819	−	16.1215i	0.229489	−	0.706296i	−0.768315	−	0.640071i	$-0.778905\pi$
$521$	5.23819	−	16.1215i	0.229489	−	0.706296i	0.997805	−	0.0662243i	$-0.0210953\pi$
$522$	3.10344	+	12.9813i	0.135834	+	0.568177i
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.0931472	−	0.995652i	$-0.529693\pi$
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.975706	+	0.219085i	$0.929693\pi$
$524$	−29.2890	+	6.22557i	−1.27950	+	0.271965i
$525$	−7.18814	+	3.77748i	−0.313716	+	0.164863i
$526$	0.869448	+	8.27225i	0.0379098	+	0.360687i
$527$	1.02565	−	1.77648i	0.0446780	−	0.0773845i
$528$	−11.8506	+	2.49812i	−0.515732	+	0.108717i
$529$	11.4963	+	19.9123i	0.499841	+	0.865750i
$530$	3.40255	−	2.47210i	0.147797	−	0.107381i
$531$	2.64203	−	6.36125i	0.114654	−	0.276055i
$532$	3.81763	−	11.7495i	0.165515	−	0.509404i
$533$	2.39617	−	22.7980i	0.103790	−	0.987491i
$534$	−1.18270	−	1.77187i	−0.0511805	−	0.0766761i
$535$	24.1099	+	26.7768i	1.04236	+	1.15766i
$536$	24.2010	+	5.14409i	1.04533	+	0.222191i
$537$	3.01093	−	11.8319i	0.129931	−	0.510584i
$538$	−0.141268	−	0.244683i	−0.00609050	−	0.0105491i
$539$	18.0112	+	5.10310i	0.775799	+	0.219806i
$540$	−13.3311	+	22.3348i	−0.573680	+	0.961136i
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	−0.774216	−	0.632922i	$-0.781855\pi$
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	0.362699	+	0.931906i	$0.381855\pi$
$542$	8.48229	−	9.42053i	0.364345	−	0.404647i
$543$	1.60117	+	4.01892i	0.0687126	+	0.172469i
$544$	−1.56569	+	0.697091i	−0.0671285	+	0.0298875i
$545$	14.2727	−	6.35461i	0.611375	−	0.272202i
$546$	2.84849	−	3.60975i	0.121904	−	0.154483i
$547$	1.70348	−	1.89190i	0.0728355	−	0.0808920i	−0.705626	−	0.708585i	$-0.749334\pi$
$547$	1.70348	−	1.89190i	0.0728355	−	0.0808920i	0.778461	+	0.627693i	$0.216001\pi$
$548$	−22.1084	+	16.0627i	−0.944424	+	0.686164i
$549$	38.7194	−	13.6697i	1.65251	−	0.583409i
$550$	−7.42425	−	2.10350i	−0.316571	−	0.0896937i
$551$	24.5177	+	42.4659i	1.04449	+	1.80911i
$552$	0.224604	+	0.219008i	0.00955976	+	0.00932160i
$553$	−10.1214	−	2.15137i	−0.430407	−	0.0914857i
$554$	1.10945	+	1.23217i	0.0471360	+	0.0523498i
$555$	14.3829	−	29.1307i	0.610522	−	1.23653i
$556$	−2.07276	+	19.7210i	−0.0879048	+	0.836358i
$557$	2.98987	−	9.20189i	0.126685	−	0.389896i	−0.867519	−	0.497404i	$-0.834287\pi$
$557$	2.98987	−	9.20189i	0.126685	−	0.389896i	0.994204	+	0.107507i	$0.0342868\pi$
$558$	11.2219	−	1.46650i	0.475061	−	0.0620819i
$559$	−21.6599	+	15.7368i	−0.916117	+	0.665598i
$560$	3.68748	+	6.38690i	0.155824	+	0.269896i
$561$	−0.560625	+	1.71561i	−0.0236696	+	0.0724331i
$562$	−5.25175	+	9.09630i	−0.221532	+	0.383704i
$563$	2.50735	+	23.8558i	0.105672	+	1.00540i	0.910953	+	0.412510i	$0.135348\pi$
$563$	2.50735	+	23.8558i	0.105672	+	1.00540i	−0.805281	+	0.592893i	$0.797986\pi$
$564$	−0.799639	−	0.505068i	−0.0336709	−	0.0212672i
$565$	−56.5054	+	12.0106i	−2.37720	+	0.505290i
$566$	9.60027	+	6.97501i	0.403530	+	0.293181i
$567$	−4.77512	+	9.32766i	−0.200536	+	0.391725i
$568$	−5.70659	+	17.5631i	−0.239443	+	0.736930i
$569$	−25.1721	+	27.9565i	−1.05527	+	1.17200i	−0.0706111	+	0.997504i	$0.522495\pi$
$569$	−25.1721	+	27.9565i	−1.05527	+	1.17200i	−0.984659	+	0.174492i	$0.944172\pi$
$570$	4.72236	−	18.5572i	0.197798	−	0.777277i
$571$	7.37740	−	12.7780i	0.308735	−	0.534744i	−0.669351	−	0.742946i	$-0.733428\pi$
$571$	7.37740	−	12.7780i	0.308735	−	0.534744i	0.978086	+	0.208202i	$0.0667612\pi$
$572$	−21.5844	+	3.10307i	−0.902488	+	0.129746i
$573$	−19.2089	−	7.09695i	−0.802463	−	0.296479i
$574$	−3.57023	−	1.58957i	−0.149018	−	0.0663473i
$575$	−0.106386	−	0.327424i	−0.00443662	−	0.0136545i
$576$	2.80545	+	1.52670i	0.116894	+	0.0636126i
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	0.896226	−	0.443598i	$-0.146298\pi$
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	−0.144937	+	0.989441i	$0.546298\pi$
$578$	1.02080	−	9.71227i	0.0424597	−	0.403977i
$579$	−11.5638	−	1.68231i	−0.480576	−	0.0699143i
$580$	−37.7013	−	8.01366i	−1.56546	−	0.332749i
$581$	0.603385	+	5.74083i	0.0250326	+	0.238170i
$582$	0.0150151	+	0.0876332i	0.000622396	+	0.00363251i
$583$	−8.01732	−	0.535173i	−0.332044	−	0.0221646i
$584$	−6.24181			−0.258288
$585$	−20.1739	+	29.2933i	−0.834087	+	1.21113i
$586$	0.153568	+	0.472634i	0.00634384	+	0.0195243i
$587$	2.44553	−	0.519814i	0.100938	−	0.0214550i	−0.157166	−	0.987572i	$-0.550236\pi$
$587$	2.44553	−	0.519814i	0.100938	−	0.0214550i	0.258104	+	0.966117i	$0.416902\pi$
$588$	−9.04302	−	13.5478i	−0.372928	−	0.558703i
$589$	37.9836	−	16.9114i	1.56508	−	0.696821i
$590$	−2.66709	−	2.96210i	−0.109802	−	0.121948i
$591$	30.2361	+	19.0978i	1.24375	+	0.785577i
$592$	−12.0242	−	5.35351i	−0.494190	−	0.220028i
$593$	−10.8953			−0.447417			−0.223708	−	0.974656i	$-0.571816\pi$
$593$	−10.8953			−0.447417			−0.223708	+	0.974656i	$0.571816\pi$
$594$	−9.39539	+	3.29925i	−0.385498	+	0.135370i
$595$	1.09907			0.0450577
$596$	6.89767	+	3.07104i	0.282540	+	0.125795i
$597$	19.4563	+	12.2890i	0.796294	+	0.502955i
$598$	0.130449	+	0.144878i	0.00533445	+	0.00592451i
$599$	−33.6533	+	14.9834i	−1.37504	+	0.612205i	−0.955353	−	0.295466i	$-0.904525\pi$
$599$	−33.6533	+	14.9834i	−1.37504	+	0.612205i	−0.419682	+	0.907671i	$0.637858\pi$
$600$	8.20203	+	12.2879i	0.334846	+	0.501651i
$601$	15.1166	−	3.21313i	0.616618	−	0.131066i	0.110995	−	0.993821i	$-0.464596\pi$
$601$	15.1166	−	3.21313i	0.616618	−	0.131066i	0.505623	+	0.862755i	$0.331263\pi$
$602$	1.41047	+	4.34099i	0.0574866	+	0.176925i
$603$	−34.9287	−	2.78249i	−1.42241	−	0.113312i
$604$	4.88321			0.198695
$605$	18.6534	+	27.2813i	0.758368	+	1.10914i
$606$	0.347575	+	2.02857i	0.0141193	+	0.0824049i
$607$	2.66306	+	25.3373i	0.108090	+	1.02841i	0.905319	+	0.424733i	$0.139632\pi$
$607$	2.66306	+	25.3373i	0.108090	+	1.02841i	−0.797228	+	0.603678i	$0.793701\pi$
$608$	−33.9795	−	7.22257i	−1.37805	−	0.292914i
$609$	−15.3662	−	2.23548i	−0.622669	−	0.0905860i
$610$	2.48369	−	23.6307i	0.100562	−	0.956781i
$611$	−1.04630	−	0.760183i	−0.0423289	−	0.0307537i
$612$	1.33981	−	0.819280i	0.0541587	−	0.0331174i
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	−0.850672	−	0.525697i	$-0.823805\pi$
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	0.379211	−	0.925310i	$-0.376195\pi$
$614$	1.84180	+	0.820023i	0.0743290	+	0.0330934i
$615$	28.3559	+	10.4764i	1.14342	+	0.422450i
$616$	−1.39501	+	8.06037i	−0.0562066	+	0.324761i
$617$	−20.9464	+	36.2802i	−0.843271	+	1.46059i	0.0438437	+	0.999038i	$0.486040\pi$
$617$	−20.9464	+	36.2802i	−0.843271	+	1.46059i	−0.887115	+	0.461549i	$0.847294\pi$
$618$	−0.744564	+	2.92588i	−0.0299508	+	0.117696i
$619$	−4.00783	+	4.45115i	−0.161088	+	0.178907i	−0.818286	−	0.574812i	$-0.805075\pi$
$619$	−4.00783	+	4.45115i	−0.161088	+	0.178907i	0.657197	+	0.753719i	$0.271742\pi$
$620$	−10.0993	+	31.0823i	−0.405596	+	1.24830i
$621$	−0.355594	−	0.266328i	−0.0142695	−	0.0106874i
$622$	−5.06974	−	3.68338i	−0.203278	−	0.147690i
$623$	2.42424	−	0.515288i	0.0971251	−	0.0206446i
$624$	12.1832	+	7.69516i	0.487719	+	0.308053i
$625$	3.02291	+	28.7611i	0.120917	+	1.15044i
$626$	8.17057	−	14.1518i	0.326562	−	0.565621i
$627$	−29.6329	+	21.4535i	−1.18342	+	0.856772i
$628$	−15.0399	−	26.0498i	−0.600157	−	1.03950i
$629$	−1.58690	+	1.15295i	−0.0632739	+	0.0459712i
$630$	3.68679	+	4.81423i	0.146885	+	0.191803i
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	0.727332	+	0.686286i	$0.240760\pi$
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	−0.991813	+	0.127702i	$0.959240\pi$
$632$	−1.96786	+	18.7229i	−0.0782772	+	0.744758i
$633$	6.39902	−	12.9603i	0.254338	−	0.515127i
$634$	−0.430138	−	0.477717i	−0.0170830	−	0.0189726i
$635$	38.7416	+	8.23479i	1.53741	+	0.326788i
$636$	5.00568	+	4.88097i	0.198488	+	0.193543i
$637$	−11.1368	−	19.2895i	−0.441256	−	0.764278i
$638$	−9.12129	−	11.5990i	−0.361115	−	0.459208i
$639$	4.79053	−	25.7104i	0.189510	−	1.01709i
$640$	28.0127	−	20.3525i	1.10730	−	0.804501i
$641$	8.58963	−	9.53975i	0.339270	−	0.376798i	−0.549232	−	0.835670i	$-0.685080\pi$
$641$	8.58963	−	9.53975i	0.339270	−	0.376798i	0.888502	+	0.458872i	$0.151746\pi$
$642$	7.43514	−	9.42218i	0.293442	−	0.371864i
$643$	25.9041	−	11.5332i	1.02156	−	0.454827i	0.173558	−	0.984824i	$-0.444473\pi$
$643$	25.9041	−	11.5332i	1.02156	−	0.454827i	0.848000	+	0.529997i	$0.177807\pi$
$644$	−0.151523	+	0.0674625i	−0.00597085	+	0.00265839i
$645$	−13.0672	−	32.7986i	−0.514519	−	1.29144i
$646$	−0.773607	+	0.859177i	−0.0304372	+	0.0338039i
$647$	14.1536	−	10.2832i	0.556436	−	0.404274i	−0.273717	−	0.961810i	$-0.588253\pi$
$647$	14.1536	−	10.2832i	0.556436	−	0.404274i	0.830153	+	0.557536i	$0.188253\pi$
$648$	17.7857	+	6.86625i	0.698687	+	0.269732i
$649$	0.289810	+	7.60956i	0.0113760	+	0.298701i
$650$	4.59060	+	7.95116i	0.180058	+	0.311870i
$651$	−3.24705	+	12.7598i	−0.127262	+	0.500095i
$652$	−9.49066	−	2.01730i	−0.371683	−	0.0790036i
$653$	−19.6070	−	21.7758i	−0.767282	−	0.852152i	0.225230	−	0.974306i	$-0.427687\pi$
$653$	−19.6070	−	21.7758i	−0.767282	−	0.852152i	−0.992511	+	0.122153i	$0.961020\pi$
$654$	−2.88928	−	4.32858i	−0.112980	−	0.169261i
$655$	5.64400	−	53.6991i	0.220529	−	2.09820i
$656$	3.78455	−	11.6477i	0.147762	−	0.454764i
$657$	8.76516	−	1.14545i	0.341961	−	0.0446881i
$658$	−0.178378	+	0.129599i	−0.00695388	+	0.00505229i
$659$	−13.7935	−	23.8911i	−0.537319	−	0.930664i	−0.999047	−	0.0436422i	$-0.986104\pi$
$659$	−13.7935	−	23.8911i	−0.537319	−	0.930664i	0.461728	−	0.887021i	$-0.347229\pi$
$660$	3.05387	−	28.5934i	0.118872	−	1.11300i
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	0.416960	+	0.908925i	$0.363096\pi$
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	−0.995632	+	0.0933649i	$0.970238\pi$
$662$	0.747623	+	7.11315i	0.0290572	+	0.276461i
$663$	1.90097	−	0.998992i	0.0738277	−	0.0387976i
$664$	10.2728	−	2.18354i	0.398660	−	0.0847378i
$665$	18.0228	+	13.0943i	0.698893	+	0.507775i
$666$	−10.3734	−	3.08351i	−0.401961	−	0.119484i
$667$	0.203437	−	0.626115i	0.00787711	−	0.0242433i
$668$	5.59853	−	6.21779i	0.216613	−	0.240574i
$669$	0.639648	−	0.180070i	0.0247302	−	0.00696191i
$670$	−10.1380	+	17.5596i	−0.391666	+	0.678385i
$671$	−32.5548	+	31.6373i	−1.25677	+	1.22134i
$672$	8.46107	−	7.03017i	0.326393	−	0.271195i
$673$	8.81907	+	3.92650i	0.339950	+	0.151356i	0.569609	−	0.821916i	$-0.307094\pi$
$673$	8.81907	+	3.92650i	0.339950	+	0.151356i	−0.229659	+	0.973271i	$0.573761\pi$
$674$	2.40577	+	7.40418i	0.0926666	+	0.285198i
$675$	−13.7728	−	15.7503i	−0.530115	−	0.606229i
$676$	3.46724	+	2.51910i	0.133355	+	0.0968883i
$677$	0.0102558	−	0.0975777i	0.000394163	−	0.00375021i	−0.994323	−	0.106403i	$-0.966067\pi$
$677$	0.0102558	−	0.0975777i	0.000394163	−	0.00375021i	0.994717	+	0.102653i	$0.0327332\pi$
$678$	7.12208	+	17.8764i	0.273522	+	0.686540i
$679$	−0.101177	−	0.0215058i	−0.00388281	−	0.000825318i
$680$	−0.209018	−	1.98868i	−0.00801549	−	0.0762623i
$681$	29.2676	+	10.8132i	1.12153	+	0.414364i
$682$	−10.5896	+	6.66372i	−0.405496	+	0.255167i
$683$	30.5246			1.16799			0.583996	−	0.811756i	$-0.301488\pi$
$683$	30.5246			1.16799			0.583996	+	0.811756i	$0.301488\pi$
$684$	31.7312	+	2.52777i	1.21327	+	0.0966517i
$685$	−15.2277	−	46.8660i	−0.581820	−	1.79066i
$686$	−8.32071	+	1.76862i	−0.317686	+	0.0675263i
$687$	−10.2966	+	20.8543i	−0.392839	+	0.795642i
$688$	−13.0671	+	5.81784i	−0.498178	+	0.221803i
$689$	6.39713	+	7.10473i	0.243711	+	0.270669i
$690$	−0.227574	+	0.119594i	−0.00866358	+	0.00455286i
$691$	29.9658	+	13.3416i	1.13995	+	0.507540i	0.887838	−	0.460157i	$-0.152207\pi$
$691$	29.9658	+	13.3416i	1.13995	+	0.507540i	0.252116	+	0.967697i	$0.418873\pi$
$692$	25.9748			0.987413
$693$	0.479793	−	11.5749i	0.0182258	−	0.439694i
$694$	5.62741			0.213614
$695$	−32.6661	−	14.5439i	−1.23910	−	0.551681i
$696$	−1.12260	+	28.2288i	−0.0425522	+	1.07001i
$697$	−1.22127	−	1.35635i	−0.0462588	−	0.0513756i
$698$	−2.34379	+	1.04352i	−0.0887138	+	0.0394979i
$699$	−5.82410	+	0.378941i	−0.220288	+	0.0143329i
$700$	−7.64053	+	1.62405i	−0.288785	+	0.0613831i
$701$	−2.70365	−	8.32098i	−0.102115	−	0.314279i	0.886927	−	0.461909i	$-0.152835\pi$
$701$	−2.70365	−	8.32098i	−0.102115	−	0.314279i	−0.989043	+	0.147630i	$0.952835\pi$
$702$	10.7526	+	4.97567i	0.405829	+	0.187795i
$703$	−39.7584			−1.49952
$704$	−3.52321	−	0.235181i	−0.132786	−	0.00886373i
$705$	1.31176	−	1.08992i	0.0494039	−	0.0410489i
$706$	−1.96435	−	18.6895i	−0.0739293	−	0.703390i
$707$	−2.34208	−	0.497825i	−0.0880831	−	0.0187226i
$708$	4.10457	−	5.20151i	0.154259	−	0.195485i
$709$	−2.79884	+	26.6292i	−0.105113	+	1.00008i	0.807114	+	0.590395i	$0.201028\pi$
$709$	−2.79884	+	26.6292i	−0.105113	+	1.00008i	−0.912227	+	0.409685i	$0.865639\pi$
$710$	−12.2435	−	8.89542i	−0.459490	−	0.333839i
$711$	−0.672486	−	26.6531i	−0.0252202	−	0.999569i
$712$	−1.39340	−	4.28845i	−0.0522199	−	0.160716i
$713$	−0.509956	−	0.227047i	−0.0190980	−	0.00850298i
$714$	−0.0618286	−	0.360852i	−0.00231388	−	0.0135046i
$715$	6.70577	−	38.7459i	0.250781	−	1.44901i
$716$	5.87217	−	10.1709i	0.219453	−	0.380105i
$717$	−28.7662	−	28.0496i	−1.07429	−	1.04753i
$718$	−10.7368	+	11.9244i	−0.400694	+	0.445016i
$719$	−4.63672	+	14.2703i	−0.172920	+	0.532194i	−0.999532	−	0.0305782i	$-0.990265\pi$
$719$	−4.63672	+	14.2703i	−0.172920	+	0.532194i	0.826612	+	0.562772i	$0.190265\pi$
$720$	−13.7963	+	13.0672i	−0.514159	+	0.486987i
$721$	−2.84161	−	2.06455i	−0.105827	−	0.0768879i
$722$	−12.1834	+	2.58965i	−0.453418	+	0.0963769i
$723$	−1.04368	+	26.2443i	−0.0388150	+	0.976036i
$724$	0.434995	+	4.13870i	0.0161665	+	0.153814i
$725$	15.5020	−	26.8502i	0.575730	−	0.997193i
$726$	7.90774	−	7.65906i	0.293484	−	0.284254i
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	−0.999925	−	0.0122391i	$-0.996104\pi$
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	0.489363	−	0.872080i	$-0.337229\pi$
$728$	7.87410	−	5.72087i	0.291834	−	0.212029i
$729$	−26.2358	−	6.37816i	−0.971698	−	0.236228i
$730$	1.58069	−	4.86486i	0.0585039	−	0.180057i
$731$	−0.222818	+	2.11997i	−0.00824123	+	0.0784101i
$732$	39.4156	−	2.56455i	1.45684	−	0.0947883i
$733$	31.9441	+	35.4775i	1.17988	+	1.31039i	0.940630	+	0.339433i	$0.110235\pi$
$733$	31.9441	+	35.4775i	1.17988	+	1.31039i	0.239251	+	0.970958i	$0.423098\pi$
$734$	−0.662509	−	0.140821i	−0.0244536	−	0.00519778i
$735$	28.2733	−	7.95932i	1.04287	−	0.293584i
$736$	0.233195	+	0.403906i	0.00859570	+	0.0148882i
$737$	36.3593	−	13.3640i	1.33931	−	0.492267i
$738$	1.84450	−	9.89928i	0.0678968	−	0.364398i
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	−0.609714	−	0.792622i	$-0.708716\pi$
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	0.565416	+	0.824806i	$0.308716\pi$
$740$	20.9113	−	23.2244i	0.768716	−	0.853746i
$741$	43.0743	+	6.26646i	1.58237	+	0.230204i
$742$	1.48898	−	0.662935i	0.0546620	−	0.0243371i
$743$	−16.5901	+	7.38641i	−0.608633	+	0.270981i	−0.687823	−	0.725879i	$-0.741433\pi$
$743$	−16.5901	+	7.38641i	−0.608633	+	0.270981i	0.0791896	+	0.996860i	$0.474767\pi$
$744$	23.7052	+	3.44864i	0.869074	+	0.126433i
$745$	−9.11035	+	10.1181i	−0.333778	+	0.370698i
$746$	−10.1751	+	7.39264i	−0.372537	+	0.270664i
$747$	−14.0250	+	4.95145i	−0.513147	+	0.181164i
$748$	−0.966316	+	1.44243i	−0.0353320	+	0.0527406i
$749$	6.98177	+	12.0928i	0.255108	+	0.441860i
$750$	2.81738	−	0.793132i	0.102876	−	0.0289611i
$751$	4.29862	+	0.913700i	0.156859	+	0.0333414i	0.285672	−	0.958328i	$-0.407783\pi$
$751$	4.29862	+	0.913700i	0.156859	+	0.0333414i	−0.128813	+	0.991669i	$0.541117\pi$
$752$	−0.462338	−	0.513479i	−0.0168597	−	0.0187246i
$753$	−1.00645	+	0.0654843i	−0.0366773	+	0.00238638i
$754$	−1.83518	+	17.4605i	−0.0668332	+	0.635875i
$755$	−2.72107	+	8.37459i	−0.0990299	+	0.304783i
$756$	−6.85295	+	7.39223i	−0.249240	+	0.268853i
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	−0.366708	−	0.930336i	$-0.619515\pi$
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	0.771483	+	0.636249i	$0.219515\pi$
$758$	4.69382	+	8.12993i	0.170487	+	0.295292i
$759$	0.480256	+	0.102925i	0.0174322	+	0.00373595i
$760$	20.2655	−	35.1008i	0.735105	−	1.27324i
$761$	3.25147	+	30.9357i	0.117866	+	1.12142i	0.880321	+	0.474378i	$0.157327\pi$
$761$	3.25147	+	30.9357i	0.117866	+	1.12142i	−0.762456	+	0.647041i	$0.776006\pi$
$762$	0.524263	−	13.1830i	0.0189920	−	0.477571i
$763$	5.92230	−	1.25882i	0.214402	−	0.0455725i
$764$	−15.9365	−	11.5786i	−0.576564	−	0.418898i
$765$	0.658463	+	2.75427i	0.0238068	+	0.0995809i
$766$	1.10585	−	3.40344i	0.0399558	−	0.122971i
$767$	6.06268	−	6.73329i	0.218911	−	0.243125i
$768$	−5.61752	−	5.47757i	−0.202705	−	0.197655i
$769$	−10.9677	+	18.9966i	−0.395504	+	0.685034i	−0.993165	−	0.116715i	$-0.962764\pi$
$769$	−10.9677	+	18.9966i	−0.395504	+	0.685034i	0.597661	+	0.801749i	$0.296097\pi$
$770$	−5.92897	−	3.12850i	−0.213665	−	0.112743i
$771$	3.20922	+	18.7301i	0.115577	+	0.674549i
$772$	−10.2690	−	4.57206i	−0.369590	−	0.164552i
$773$	−3.92965	−	12.0942i	−0.141340	−	0.434999i	0.855182	−	0.518327i	$-0.173445\pi$
$773$	−3.92965	−	12.0942i	−0.141340	−	0.434999i	−0.996522	+	0.0833281i	$0.973445\pi$
$774$	−10.0335	+	6.13535i	−0.360645	+	0.220530i
$775$	−21.2682	−	15.4522i	−0.763976	−	0.555061i
$776$	−0.0196714	+	0.187160i	−0.000706160	+	0.00671867i
$777$	7.79923	−	9.88358i	0.279796	−	0.354571i
$778$	0.408750	+	0.0868824i	0.0146544	+	0.00311489i
$779$	−3.86697	−	36.7918i	−0.138549	−	1.31820i
$780$	−26.3158	+	21.8654i	−0.942258	+	0.782908i
$781$	7.08334	+	28.0321i	0.253462	+	1.00307i
$782$	0.0155220			0.000555064
$783$	−3.60390	−	39.8468i	−0.128793	−	1.42401i
$784$	−3.67724	−	11.3174i	−0.131330	−	0.404193i
$785$	53.0556	−	11.2773i	1.89363	−	0.402504i
$786$	−17.9482	+	1.16779i	−0.640191	+	0.0416536i
$787$	−15.7693	+	7.02095i	−0.562115	+	0.250270i	−0.668067	−	0.744102i	$-0.732878\pi$
$787$	−15.7693	+	7.02095i	−0.562115	+	0.250270i	0.105951	+	0.994371i	$0.466211\pi$
$788$	23.0190	+	25.5652i	0.820018	+	0.910722i
$789$	0.990772	−	24.9138i	0.0352724	−	0.886955i
$790$	−14.0943	−	6.27518i	−0.501452	−	0.223261i
$791$	−22.3870			−0.795991
$792$	−21.0350	+	1.33313i	−0.747445	+	0.0473708i
$793$	54.0120			1.91802
$794$	2.15890	+	0.961206i	0.0766166	+	0.0341119i
$795$	−11.1601	+	5.86480i	−0.395807	+	0.208003i
$796$	14.8122	+	16.4507i	0.525006	+	0.583078i
$797$	32.1582	−	14.3177i	1.13910	−	0.507161i	0.251538	−	0.967847i	$-0.419064\pi$
$797$	32.1582	−	14.3177i	1.13910	−	0.507161i	0.887563	+	0.460687i	$0.152397\pi$
$798$	3.28530	−	6.65393i	0.116298	−	0.235546i
$799$	−0.100721	+	0.0214090i	−0.00356326	+	0.000757395i
$800$	6.78739	+	20.8894i	0.239970	+	0.738553i
$801$	2.74369	+	5.76641i	0.0969434	+	0.203746i
$802$	−3.26248			−0.115202
$803$	−8.27126	+	5.20487i	−0.291887	+	0.183676i
$804$	−31.6170	−	11.6812i	−1.11504	−	0.411966i
$805$	−0.0312634	−	0.297451i	−0.00110189	−	0.0104838i
$806$	14.5614	+	3.09512i	0.512903	+	0.109021i
$807$	0.313461	+	0.786787i	0.0110344	+	0.0276962i
$808$	−0.455360	+	4.33246i	−0.0160195	+	0.152415i
$809$	15.4367	+	11.2154i	0.542725	+	0.394313i	0.825096	−	0.564992i	$-0.191121\pi$
$809$	15.4367	+	11.2154i	0.542725	+	0.394313i	−0.282371	+	0.959305i	$0.591121\pi$
$810$	−9.85563	+	12.1233i	−0.346291	+	0.425970i
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	−0.965718	−	0.259593i	$-0.916412\pi$
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	0.628698	−	0.777650i	$-0.283588\pi$
$812$	−13.6456	−	6.07542i	−0.478867	−	0.213205i
$813$	−29.2271	+	24.2843i	−1.02504	+	0.851688i
$814$	11.8424	−	1.70252i	0.415076	−	0.0596733i
$815$	8.74810	−	15.1522i	0.306433	−	0.530757i
$816$	1.10438	−	0.310898i	0.0386610	−	0.0108836i
$817$	−28.9110	+	32.1090i	−1.01147	+	1.12335i
$818$	1.68711	−	5.19240i	0.0589885	−	0.181548i
$819$	−10.0075	+	9.47861i	−0.349690	+	0.331209i
$820$	23.5253	+	17.0922i	0.821540	+	0.596884i
$821$	−33.2653	+	7.07077i	−1.16097	+	0.246771i	−0.747826	−	0.663895i	$-0.768902\pi$
$821$	−33.2653	+	7.07077i	−1.16097	+	0.246771i	−0.413143	+	0.910666i	$0.635569\pi$
$822$	−14.5306	+	7.63607i	−0.506813	+	0.266338i
$823$	−1.62605	−	15.4708i	−0.0566804	−	0.539278i	−0.985612	−	0.169026i	$-0.945938\pi$
$823$	−1.62605	−	15.4708i	−0.0566804	−	0.539278i	0.928931	−	0.370252i	$-0.120729\pi$
$824$	−3.19521	+	5.53426i	−0.111310	+	0.192795i
$825$	21.1154	+	9.44371i	0.735143	+	0.328788i
$826$	−0.772337	−	1.33773i	−0.0268730	−	0.0465455i
$827$	−12.9667	+	9.42084i	−0.450895	+	0.327595i	−0.789949	−	0.613172i	$-0.789893\pi$
$827$	−12.9667	+	9.42084i	−0.450895	+	0.327595i	0.339054	+	0.940767i	$0.389893\pi$
$828$	−0.259839	−	0.339299i	−0.00903003	−	0.0117914i
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	−0.794727	−	0.606967i	$-0.792386\pi$
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	0.999714	−	0.0239173i	$-0.00761382\pi$
$830$	−0.899644	+	8.55954i	−0.0312271	+	0.297106i
$831$	−2.75930	−	4.13386i	−0.0957191	−	0.143402i
$832$	2.81122	+	3.12217i	0.0974614	+	0.108242i
$833$	−1.73465	−	0.368711i	−0.0601021	−	0.0127751i
$834$	−2.93747	+	11.5432i	−0.101716	+	0.399709i
$835$	7.54371	+	13.0661i	0.261061	+	0.452171i
$836$	−33.0308	+	12.1406i	−1.14240	+	0.419891i
$837$	−33.9213	−	0.492616i	−1.17249	−	0.0170273i
$838$	−0.0708501	+	0.0514756i	−0.00244747	+	0.00177819i
$839$	0.995613	−	1.10574i	0.0343724	−	0.0381744i	−0.725713	−	0.687997i	$-0.758490\pi$
$839$	0.995613	−	1.10574i	0.0343724	−	0.0381744i	0.760086	+	0.649823i	$0.225157\pi$
$840$	4.75035	+	11.9234i	0.163903	+	0.411395i
$841$	27.6687	−	12.3189i	0.954095	−	0.424790i
$842$	8.96121	−	3.98979i	0.308824	−	0.137497i
$843$	19.5042	−	24.7167i	0.671759	−	0.851287i
$844$	9.30353	−	10.3326i	0.320241	−	0.355663i
$845$	−6.25224	+	4.54252i	−0.215084	+	0.156267i
$846$	−0.431641	−	0.369369i	−0.0148401	−	0.0126992i
$847$	4.87274	+	11.8444i	0.167429	+	0.406977i
$848$	2.55384	+	4.42338i	0.0876993	+	0.151900i
$849$	−25.4680	−	24.8335i	−0.874058	−	0.852283i
$850$	0.715025	+	0.151983i	0.0245252	+	0.00521298i
$851$	0.357172	+	0.396680i	0.0122437	+	0.0135980i
$852$	11.1377	−	22.5579i	0.381571	−	0.772820i
$853$	−3.95139	+	37.5950i	−0.135293	+	1.28723i	0.690532	+	0.723302i	$0.257376\pi$
$853$	−3.95139	+	37.5950i	−0.135293	+	1.28723i	−0.825825	+	0.563926i	$0.809290\pi$
$854$	2.84548	−	8.75750i	0.0973704	−	0.299675i
$855$	−22.0167	+	53.0098i	−0.752954	+	1.81290i
$856$	20.5530	−	14.9326i	0.702487	−	0.510387i
$857$	−9.91348	−	17.1706i	−0.338638	−	0.586538i	0.645539	−	0.763727i	$-0.276633\pi$
$857$	−9.91348	−	17.1706i	−0.338638	−	0.586538i	−0.984177	+	0.177189i	$0.943300\pi$
$858$	−13.0984	−	0.0220111i	−0.447173	−	0.000751447i
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	−0.700272	−	0.713876i	$-0.746938\pi$
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	0.968371	+	0.249515i	$0.0802711\pi$
$860$	−3.55001	−	33.7761i	−0.121054	−	1.15175i
$861$	9.90466	+	6.25598i	0.337550	+	0.213203i
$862$	14.3384	−	3.04772i	0.488368	−	0.103806i
$863$	−6.57548	−	4.77736i	−0.223832	−	0.162623i	0.470218	−	0.882550i	$-0.344175\pi$
$863$	−6.57548	−	4.77736i	−0.223832	−	0.162623i	−0.694050	+	0.719927i	$0.744175\pi$
$864$	22.6866	+	16.9916i	0.771815	+	0.578064i
$865$	−14.4739	+	44.5462i	−0.492128	+	1.51462i
$866$	6.39284	−	7.09997i	0.217237	−	0.241267i
$867$	−7.21940	+	28.3697i	−0.245184	+	0.963486i
$868$	−6.33269	+	10.9685i	−0.214945	+	0.372296i
$869$	13.0049	+	26.4514i	0.441159	+	0.897303i
$870$	−21.7172	−	8.02368i	−0.736283	−	0.272028i
$871$	−42.1057	−	18.7467i	−1.42670	−	0.635206i
$872$	−3.40401	−	10.4765i	−0.115274	−	0.354778i
$873$	−0.00672238	−	0.266433i	−0.000227518	−	0.00901739i
$874$	0.254531	+	0.184928i	0.00860964	+	0.00625527i
$875$	−0.355931	+	3.38646i	−0.0120327	+	0.114483i
$876$	8.41469	+	1.22417i	0.284306	+	0.0413609i
$877$	2.47817	+	0.526750i	0.0836817	+	0.0177871i	0.249562	−	0.968359i	$-0.419713\pi$
$877$	2.47817	+	0.526750i	0.0836817	+	0.0177871i	−0.165881	+	0.986146i	$0.553047\pi$
$878$	2.37009	+	22.5499i	0.0799867	+	0.761022i
$879$	−0.251576	−	1.46828i	−0.00848544	−	0.0495239i
$880$	7.80812	−	19.5030i	0.263212	−	0.657446i
$881$	−47.4109			−1.59731			−0.798657	−	0.601786i	$-0.794456\pi$
$881$	−47.4109			−1.59731			−0.798657	+	0.601786i	$0.794456\pi$
$882$	−4.20375	−	8.83503i	−0.141548	−	0.297491i
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	0.989029	+	0.147719i	$0.0471930\pi$
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	−0.713315	+	0.700844i	$0.752807\pi$
$884$	2.02061	−	0.429495i	0.0679606	−	0.0144455i
$885$	6.63329	+	9.93768i	0.222976	+	0.334051i
$886$	16.9914	−	7.56506i	0.570837	−	0.254153i
$887$	−32.0041	−	35.5441i	−1.07459	−	1.19345i	−0.980219	−	0.197918i	$-0.936582\pi$
$887$	−32.0041	−	35.5441i	−1.07459	−	1.19345i	−0.0943729	−	0.995537i	$-0.530085\pi$
$888$	−19.3667	−	12.2324i	−0.649903	−	0.410492i
$889$	14.0221	+	6.24306i	0.470288	+	0.209386i
$890$	3.69528			0.123866
$891$	29.2941	−	5.73224i	0.981388	−	0.192037i
$892$	0.639221			0.0214027
$893$	−1.90671	−	0.848920i	−0.0638055	−	0.0284080i
$894$	3.83451	+	2.42195i	0.128245	+	0.0810022i
$895$	14.1707	+	15.7382i	0.473675	+	0.526069i
$896$	12.2585	−	5.45786i	0.409529	−	0.182334i
$897$	−0.324438	−	0.486058i	−0.0108327	−	0.0162290i
$898$	14.6068	−	3.10477i	0.487435	−	0.103608i
$899$	−15.5345	−	47.8104i	−0.518106	−	1.59457i
$900$	−8.64734	−	18.1741i	−0.288245	−	0.605804i
$901$	0.761187			0.0253588
$902$	2.72730	+	10.7932i	0.0908090	+	0.359373i
$903$	−2.31064	−	13.4857i	−0.0768933	−	0.448776i
$904$	4.25749	+	40.5073i	0.141602	+	1.34725i
$905$	−7.34017	−	1.56020i	−0.243995	−	0.0518628i
$906$	2.90265	+	0.422279i	0.0964342	+	0.0140293i
$907$	−4.96075	+	47.1984i	−0.164719	+	1.56720i	0.530052	+	0.847965i	$0.322172\pi$
$907$	−4.96075	+	47.1984i	−0.164719	+	1.56720i	−0.694771	+	0.719231i	$0.744494\pi$
$908$	24.2817	+	17.6417i	0.805815	+	0.585459i
$909$	−0.155612	−	6.16749i	−0.00516133	−	0.204563i
$910$	2.46479	+	7.58583i	0.0817068	+	0.251468i
$911$	−25.9741	−	11.5644i	−0.860561	−	0.383147i	−0.0714850	−	0.997442i	$-0.522774\pi$
$911$	−25.9741	−	11.5644i	−0.860561	−	0.383147i	−0.789076	+	0.614295i	$0.789440\pi$
$912$	21.8138	+	8.05935i	0.722326	+	0.266872i
$913$	11.7920	−	11.4597i	0.390259	−	0.379259i
$914$	3.67381	−	6.36322i	0.121519	−	0.210477i
$915$	−17.5654	+	69.0258i	−0.580694	+	2.28192i
$916$	−14.9702	+	16.6261i	−0.494629	+	0.549342i
$917$	6.46615	−	19.9008i	0.213531	−	0.657181i
$918$	0.867251	−	0.371131i	0.0286236	−	0.0122491i
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.0569449	−	0.998377i	$-0.518136\pi$
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.967110	+	0.254358i	$0.918136\pi$
$920$	−0.532265	+	0.113136i	−0.0175483	+	0.00373000i
$921$	−5.10959	−	3.22732i	−0.168367	−	0.106344i
$922$	1.14887	+	10.9308i	0.0378361	+	0.359986i
$923$	17.2007	−	29.7924i	0.566167	−	0.980629i
$924$	3.46147	−	10.5927i	0.113874	−	0.348475i
$925$	12.5692	+	21.7704i	0.413272	+	0.715808i
$926$	10.6893	−	7.76621i	0.351271	−	0.255214i
$927$	3.47132	−	8.35794i	0.114013	−	0.274511i
$928$	−12.9791	+	39.9457i	−0.426061	+	1.31128i
$929$	−1.39939	+	13.3143i	−0.0459126	+	0.436829i	0.947285	+	0.320391i	$0.103814\pi$
$929$	−1.39939	+	13.3143i	−0.0459126	+	0.436829i	−0.993198	+	0.116438i	$0.962852\pi$
$930$	−8.69102	+	17.6025i	−0.284990	+	0.577207i
$931$	−24.0522	−	26.7127i	−0.788280	−	0.875473i
$932$	−5.49160	−	1.16728i	−0.179883	−	0.0382354i
$933$	13.4492	+	13.1141i	0.440307	+	0.429338i
$934$	−4.60021	−	7.96779i	−0.150523	−	0.260714i
$935$	−1.93528	−	2.46098i	−0.0632905	−	0.0804826i
$936$	19.0539	+	16.3050i	0.622795	+	0.532946i
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	−0.211934	−	0.977284i	$-0.567976\pi$
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	0.863961	+	0.503559i	$0.167976\pi$
$938$	−5.25781	+	5.83939i	−0.171674	+	0.190663i
$939$	−30.3442	+	38.4537i	−0.990245	+	1.25489i
$940$	1.49874	−	0.667281i	0.0488834	−	0.0217643i
$941$	7.58453	−	3.37685i	0.247249	−	0.110082i	−0.279371	−	0.960183i	$-0.590126\pi$
$941$	7.58453	−	3.37685i	0.247249	−	0.110082i	0.526620	+	0.850101i	$0.323459\pi$
$942$	−6.68725	−	16.7850i	−0.217883	−	0.546885i
$943$	−0.332341	+	0.369103i	−0.0108225	+	0.0120196i
$944$	3.91616	−	2.84526i	0.127460	−	0.0926053i
$945$	−8.85883	−	15.8718i	−0.288178	−	0.516311i
$946$	7.23646	−	10.8020i	0.235278	−	0.351202i
$947$	−18.9748	−	32.8653i	−0.616598	−	1.06798i	−0.990102	−	0.140351i	$-0.955177\pi$
$947$	−18.9748	−	32.8653i	−0.616598	−	1.06798i	0.373503	−	0.927629i	$-0.378156\pi$
$948$	6.32493	−	24.8548i	0.205424	−	0.807245i
$949$	11.3735	+	2.41752i	0.369201	+	0.0784761i
$950$	9.91435	+	11.0110i	0.321664	+	0.357244i
$951$	1.06979	+	1.60271i	0.0346904	+	0.0519715i
$952$	0.0810019	−	0.770681i	0.00262529	−	0.0249779i
$953$	−15.0400	+	46.2884i	−0.487194	+	1.49943i	0.341583	+	0.939852i	$0.389037\pi$
$953$	−15.0400	+	46.2884i	−0.487194	+	1.49943i	−0.828778	+	0.559578i	$0.810963\pi$
$954$	2.55336	+	3.33419i	0.0826682	+	0.107948i
$955$	28.7373	−	20.8789i	0.929918	−	0.675625i
$956$	−19.3245	−	33.4710i	−0.624998	−	1.08253i
$957$	22.0516	+	38.3432i	0.712828	+	1.23946i
$958$	4.73516	−	8.20154i	0.152986	−	0.264980i
$959$	−1.99617	−	18.9923i	−0.0644596	−	0.613292i
$960$	−4.90429	+	2.57728i	−0.158285	+	0.0831815i
$961$	−11.3716	+	2.41712i	−0.366827	+	0.0779716i
$962$	−11.5165	−	8.36721i	−0.371306	−	0.269770i
$963$	−26.1216	+	24.7411i	−0.841756	+	0.797271i
$964$	−7.80746	+	24.0289i	−0.251461	+	0.773918i
$965$	13.5632	−	15.0634i	0.436614	−	0.484909i
$966$	−0.0959015	+	0.0269976i	−0.00308558	+	0.000868635i
$967$	−5.48901	+	9.50724i	−0.176515	+	0.305732i	−0.940684	−	0.339283i	$-0.889816\pi$
$967$	−5.48901	+	9.50724i	−0.176515	+	0.305732i	0.764170	+	0.645015i	$0.223149\pi$
$968$	20.5046	−	11.0693i	0.659044	−	0.355781i
$969$	2.66559	−	2.21479i	0.0856309	−	0.0711494i
$970$	−0.140891	−	0.0627287i	−0.00452374	−	0.00201410i
$971$	4.03687	+	12.4242i	0.129549	+	0.398712i	0.994702	−	0.102796i	$-0.0327789\pi$
$971$	4.03687	+	12.4242i	0.129549	+	0.398712i	−0.865153	+	0.501508i	$0.832779\pi$
$972$	−22.6305	−	12.7447i	−0.725874	−	0.408787i
$973$	−11.2108	−	8.14510i	−0.359401	−	0.261120i
$974$	−1.37626	+	13.0942i	−0.0440981	+	0.419565i
$975$	−10.1861	−	25.5672i	−0.326217	−	0.818805i
$976$	28.2257	+	5.99955i	0.903482	+	0.192041i
$977$	1.15779	+	11.0156i	0.0370410	+	0.352421i	0.997307	+	0.0733360i	$0.0233645\pi$
$977$	1.15779	+	11.0156i	0.0370410	+	0.352421i	−0.960266	+	0.279085i	$0.909969\pi$
$978$	−5.46694	−	2.01982i	−0.174813	−	0.0645869i
$979$	−5.42247	−	4.52087i	−0.173303	−	0.144488i
$980$	28.2544			0.902554
$981$	6.70270	+	14.0871i	0.214001	+	0.449766i
$982$	−7.79262	−	23.9832i	−0.248673	−	0.765336i
$983$	25.8539	−	5.49541i	0.824611	−	0.175277i	0.223767	−	0.974643i	$-0.428165\pi$
$983$	25.8539	−	5.49541i	0.824611	−	0.175277i	0.600844	+	0.799366i	$0.294831\pi$
$984$	9.43600	−	19.1113i	0.300809	−	0.609247i
$985$	−56.6706	+	25.2314i	−1.80568	+	0.803938i
$986$	0.935344	+	1.03880i	0.0297874	+	0.0330823i
$987$	0.585063	−	0.307460i	0.0186228	−	0.00978657i
$988$	38.2512	+	17.0305i	1.21693	+	0.541814i
$989$	0.580083			0.0184456
$990$	4.28790	−	16.7322i	0.136278	−	0.531786i
$991$	−18.9911			−0.603272			−0.301636	−	0.953423i	$-0.597533\pi$
$991$	−18.9911			−0.603272			−0.301636	+	0.953423i	$0.597533\pi$
$992$	32.5349	+	14.4855i	1.03298	+	0.459914i
$993$	0.851946	−	21.4229i	0.0270357	−	0.679836i
$994$	−3.92436	−	4.35845i	−0.124473	−	0.138242i
$995$	−36.4663	+	16.2359i	−1.15606	+	0.514711i
$996$	−14.2771	+	0.928931i	−0.452388	+	0.0294343i
$997$	−21.6299	+	4.59758i	−0.685027	+	0.145607i	−0.537262	−	0.843416i	$-0.680541\pi$
$997$	−21.6299	+	4.59758i	−0.685027	+	0.145607i	−0.147765	+	0.989022i	$0.547208\pi$
$998$	−3.58956	−	11.0475i	−0.113625	−	0.349703i
$999$	29.4407	+	13.6235i	0.931463	+	0.431028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.b.58.6	yes	72
3.2	odd	2		297.2.n.b.91.4		72
9.2	odd	6		297.2.n.b.289.6		72
9.4	even	3		891.2.f.f.487.4		36
9.5	odd	6		891.2.f.e.487.6		36
9.7	even	3	inner	99.2.m.b.25.4	yes	72
11.2	odd	10		1089.2.e.o.364.11		36
11.4	even	5	inner	99.2.m.b.4.4	✓	72
11.9	even	5		1089.2.e.p.364.8		36
33.26	odd	10		297.2.n.b.37.6		72
99.4	even	15		891.2.f.f.730.4		36
99.13	odd	30		9801.2.a.co.1.8		18
99.31	even	15		9801.2.a.cm.1.11		18
99.59	odd	30		891.2.f.e.730.6		36
99.68	even	30		9801.2.a.cn.1.11		18
99.70	even	15	inner	99.2.m.b.70.6	yes	72
99.79	odd	30		1089.2.e.o.727.11		36
99.86	odd	30		9801.2.a.cp.1.8		18
99.92	odd	30		297.2.n.b.235.4		72
99.97	even	15		1089.2.e.p.727.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	11.4	even	5	inner
99.2.m.b.25.4	yes	72	9.7	even	3	inner
99.2.m.b.58.6	yes	72	1.1	even	1	trivial
99.2.m.b.70.6	yes	72	99.70	even	15	inner
297.2.n.b.37.6		72	33.26	odd	10
297.2.n.b.91.4		72	3.2	odd	2
297.2.n.b.235.4		72	99.92	odd	30
297.2.n.b.289.6		72	9.2	odd	6
891.2.f.e.487.6		36	9.5	odd	6
891.2.f.e.730.6		36	99.59	odd	30
891.2.f.f.487.4		36	9.4	even	3
891.2.f.f.730.4		36	99.4	even	15
1089.2.e.o.364.11		36	11.2	odd	10
1089.2.e.o.727.11		36	99.79	odd	30
1089.2.e.p.364.8		36	11.9	even	5
1089.2.e.p.727.8		36	99.97	even	15
9801.2.a.cm.1.11		18	99.31	even	15
9801.2.a.cn.1.11		18	99.68	even	30
9801.2.a.co.1.8		18	99.13	odd	30
9801.2.a.cp.1.8		18	99.86	odd	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.527858 + 0.235017i) q^{2} +(-1.46440 - 0.924946i) q^{3} +(-1.11486 - 1.23818i) q^{4} +(2.74468 - 1.22201i) q^{5} +(-0.555618 - 0.832400i) q^{6} +(1.13888 - 0.242076i) q^{7} +(-0.654602 - 2.01466i) q^{8} +(1.28895 + 2.70899i) q^{9} +1.73599 q^{10} +(-2.54741 - 2.12385i) q^{11} +(0.487356 + 2.84438i) q^{12} +(0.412487 + 3.92455i) q^{13} +(0.658057 + 0.139874i) q^{14} +(-5.14961 - 0.749167i) q^{15} +(-0.220374 + 2.09672i) q^{16} +(0.254185 + 0.184677i) q^{17} +(0.0437225 + 1.73288i) q^{18} +(1.96794 + 6.05670i) q^{19} +(-4.57300 - 2.03603i) q^{20} +(-1.89168 - 0.698904i) q^{21} +(-0.845527 - 1.71977i) q^{22} +(0.0427501 - 0.0740453i) q^{23} +(-0.904849 + 3.55574i) q^{24} +(2.69431 - 2.99234i) q^{25} +(-0.704604 + 2.16855i) q^{26} +(0.618128 - 5.15926i) q^{27} +(-1.56942 - 1.14025i) q^{28} +(7.53156 - 1.60088i) q^{29} +(-2.54219 - 1.60570i) q^{30} +(-0.682449 - 6.49307i) q^{31} +(-2.72743 + 4.72404i) q^{32} +(1.76598 + 5.46638i) q^{33} +(0.0907715 + 0.157221i) q^{34} +(2.83004 - 2.05614i) q^{35} +(1.91721 - 4.61609i) q^{36} +(-1.92922 + 5.93753i) q^{37} +(-0.384637 + 3.65957i) q^{38} +(3.02595 - 6.12865i) q^{39} +(-4.25861 - 4.72966i) q^{40} +(-5.68213 - 1.20777i) q^{41} +(-0.834284 - 0.813500i) q^{42} +(3.39229 + 5.87562i) q^{43} +(0.210303 + 5.52194i) q^{44} +(6.84817 + 5.86020i) q^{45} +(0.0399679 - 0.0290384i) q^{46} +(-0.219298 + 0.243555i) q^{47} +(2.26207 - 2.86660i) q^{48} +(-5.15638 + 2.29577i) q^{49} +(2.12546 - 0.946318i) q^{50} +(-0.201414 - 0.505549i) q^{51} +(4.39943 - 4.88606i) q^{52} +(1.96000 - 1.42402i) q^{53} +(1.53880 - 2.57808i) q^{54} +(-9.58718 - 2.71632i) q^{55} +(-1.23321 - 2.13598i) q^{56} +(2.72026 - 10.6897i) q^{57} +(4.35183 + 0.925009i) q^{58} +(-1.53634 - 1.70628i) q^{59} +(4.81350 + 7.21136i) q^{60} +(1.43070 - 13.6122i) q^{61} +(1.16575 - 3.58780i) q^{62} +(2.12373 + 2.77318i) q^{63} +(0.861321 - 0.625787i) q^{64} +(5.92799 + 10.2676i) q^{65} +(-0.352506 + 3.30051i) q^{66} +(-5.83989 + 10.1150i) q^{67} +(-0.0547189 - 0.520616i) q^{68} +(-0.131091 + 0.0688906i) q^{69} +(1.97708 - 0.420242i) q^{70} +(-7.05272 - 5.12410i) q^{71} +(4.61393 - 4.37010i) q^{72} +(0.910538 - 2.80235i) q^{73} +(-2.41378 + 2.68077i) q^{74} +(-6.71331 + 1.88989i) q^{75} +(5.30529 - 9.18904i) q^{76} +(-3.41531 - 1.80213i) q^{77} +(3.03761 - 2.52391i) q^{78} +(-8.11886 - 3.61475i) q^{79} +(1.95735 + 6.02412i) q^{80} +(-5.67722 + 6.98349i) q^{81} +(-2.71551 - 1.97293i) q^{82} +(-0.518229 + 4.93062i) q^{83} +(1.24359 + 3.12142i) q^{84} +(0.923335 + 0.196261i) q^{85} +(0.409774 + 3.89874i) q^{86} +(-12.5100 - 4.62195i) q^{87} +(-2.61129 + 6.52242i) q^{88} +2.12862 q^{89} +(2.23761 + 4.70279i) q^{90} +(1.41981 + 4.36973i) q^{91} +(-0.139342 + 0.0296180i) q^{92} +(-5.00636 + 10.1397i) q^{93} +(-0.172998 + 0.0770236i) q^{94} +(12.8027 + 14.2189i) q^{95} +(8.36354 - 4.39518i) q^{96} +(-0.0811587 - 0.0361342i) q^{97} -3.26138 q^{98} +(2.47000 - 9.63842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more