LMFDB - Embedded newform 276.2.m.a.7.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(7,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 19]))

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

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

chi := DirichletCharacter("276.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.m (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.9
Character	$\chi$	$=$	276.7
Dual form			276.2.m.a.79.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.723978 - 1.21485i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.951711 + 1.75905i) q^{4} +(-2.68981 + 1.22840i) q^{5} +(-0.630583 + 1.26585i) q^{6} +(0.0149354 - 0.00438542i) q^{7} +(2.82599 - 0.117329i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.723978 - 1.21485i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.951711 + 1.75905i) q^{4} +(-2.68981 + 1.22840i) q^{5} +(-0.630583 + 1.26585i) q^{6} +(0.0149354 - 0.00438542i) q^{7} +(2.82599 - 0.117329i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(3.43968 + 2.37838i) q^{10} +(0.950206 + 1.09660i) q^{11} +(1.99434 - 0.150383i) q^{12} +(6.18777 + 1.81689i) q^{13} +(-0.0161405 - 0.0149692i) q^{14} +(2.48762 + 1.59869i) q^{15} +(-2.18849 - 3.34821i) q^{16} +(-0.419359 - 0.0602947i) q^{17} +(1.40582 - 0.153888i) q^{18} +(0.900853 + 6.26557i) q^{19} +(0.399116 - 5.90059i) q^{20} +(-0.0117639 - 0.0101935i) q^{21} +(0.644269 - 1.94827i) q^{22} +(-2.79657 + 3.89605i) q^{23} +(-1.62655 - 2.31394i) q^{24} +(2.45184 - 2.82957i) q^{25} +(-2.27256 - 8.83259i) q^{26} +(0.989821 - 0.142315i) q^{27} +(-0.00649998 + 0.0304457i) q^{28} +(0.122320 - 0.850755i) q^{29} +(0.141189 - 4.17950i) q^{30} +(-1.51311 + 2.35444i) q^{31} +(-2.48314 + 5.08272i) q^{32} +(0.408795 - 1.39223i) q^{33} +(0.230358 + 0.553109i) q^{34} +(-0.0347863 + 0.0301425i) q^{35} +(-1.20473 - 1.59644i) q^{36} +(4.06116 + 1.85467i) q^{37} +(6.95952 - 5.63054i) q^{38} +(-1.81689 - 6.18777i) q^{39} +(-7.45727 + 3.78703i) q^{40} +(-2.76678 - 6.05839i) q^{41} +(-0.00386672 + 0.0216712i) q^{42} +(2.19248 - 1.40902i) q^{43} +(-2.83329 + 0.627815i) q^{44} -2.95704i q^{45} +(6.75776 + 0.576746i) q^{46} +6.84887i q^{47} +(-1.63350 + 3.65126i) q^{48} +(-5.88857 + 3.78435i) q^{49} +(-5.21257 - 0.930060i) q^{50} +(0.175999 + 0.385385i) q^{51} +(-9.08497 + 9.15542i) q^{52} +(3.67235 + 12.5069i) q^{53} +(-0.889500 - 1.09945i) q^{54} +(-3.90293 - 1.78241i) q^{55} +(0.0416927 - 0.0141455i) q^{56} +(4.78390 - 4.14527i) q^{57} +(-1.12209 + 0.467328i) q^{58} +(1.75231 - 5.96783i) q^{59} +(-5.17967 + 2.85434i) q^{60} +(-0.357133 + 0.555710i) q^{61} +(3.95575 + 0.133631i) q^{62} +(-0.00221526 + 0.0154075i) q^{63} +(7.97247 - 0.663140i) q^{64} +(-18.8758 + 2.71393i) q^{65} +(-1.98731 + 0.511320i) q^{66} +(-5.13984 + 5.93169i) q^{67} +(0.505169 - 0.680289i) q^{68} +(4.78950 + 0.246257i) q^{69} +(0.0618031 + 0.0204375i) q^{70} +(7.24911 + 6.28139i) q^{71} +(-1.06723 + 2.61935i) q^{72} +(-2.20132 - 15.3105i) q^{73} +(-0.687051 - 6.27644i) q^{74} +(-3.70595 - 0.532835i) q^{75} +(-11.8788 - 4.37837i) q^{76} +(0.0190007 + 0.0122110i) q^{77} +(-6.20181 + 6.68706i) q^{78} +(-8.81861 - 2.58938i) q^{79} +(9.99957 + 6.31772i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-5.35694 + 7.74736i) q^{82} +(5.51200 - 12.0696i) q^{83} +(0.0291267 - 0.0109920i) q^{84} +(1.20206 - 0.352957i) q^{85} +(-3.29905 - 1.64343i) q^{86} +(-0.781832 + 0.357051i) q^{87} +(2.81394 + 2.98749i) q^{88} +(-4.02629 - 6.26503i) q^{89} +(-3.59235 + 2.14083i) q^{90} +0.100384 q^{91} +(-4.19182 - 8.62721i) q^{92} +2.79873 q^{93} +(8.32034 - 4.95843i) q^{94} +(-10.1197 - 15.7466i) q^{95} +(5.61834 - 0.658974i) q^{96} +(-8.57609 + 3.91657i) q^{97} +(8.86061 + 4.41393i) q^{98} +(-1.39223 + 0.408795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^6 - 4 * q^8 + 24 * q^9	$ 240 q - 4 q^{2} - 4 q^{6} - 4 q^{8} + 24 q^{9} - 8 q^{16} + 4 q^{18} + 4 q^{24} + 24 q^{25} - 40 q^{26} + 32 q^{29} + 36 q^{32} - 22 q^{34} - 22 q^{36} - 110 q^{38} - 22 q^{40} - 16 q^{41} - 110 q^{42} - 154 q^{44} - 88 q^{46} - 56 q^{48} - 40 q^{49} - 142 q^{50} - 70 q^{52} - 18 q^{54} - 110 q^{56} - 46 q^{58} - 22 q^{60} + 40 q^{62} - 48 q^{64} - 16 q^{69} - 72 q^{70} + 4 q^{72} + 22 q^{74} + 110 q^{76} - 192 q^{77} + 198 q^{80} - 24 q^{81} + 172 q^{82} - 200 q^{85} + 220 q^{86} + 176 q^{88} - 88 q^{89} + 154 q^{92} - 16 q^{93} + 126 q^{94} - 44 q^{96} - 88 q^{97} + 228 q^{98}+O(q^{100}) $ 240 * q - 4 * q^2 - 4 * q^6 - 4 * q^8 + 24 * q^9 - 8 * q^16 + 4 * q^18 + 4 * q^24 + 24 * q^25 - 40 * q^26 + 32 * q^29 + 36 * q^32 - 22 * q^34 - 22 * q^36 - 110 * q^38 - 22 * q^40 - 16 * q^41 - 110 * q^42 - 154 * q^44 - 88 * q^46 - 56 * q^48 - 40 * q^49 - 142 * q^50 - 70 * q^52 - 18 * q^54 - 110 * q^56 - 46 * q^58 - 22 * q^60 + 40 * q^62 - 48 * q^64 - 16 * q^69 - 72 * q^70 + 4 * q^72 + 22 * q^74 + 110 * q^76 - 192 * q^77 + 198 * q^80 - 24 * q^81 + 172 * q^82 - 200 * q^85 + 220 * q^86 + 176 * q^88 - 88 * q^89 + 154 * q^92 - 16 * q^93 + 126 * q^94 - 44 * q^96 - 88 * q^97 + 228 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.723978	−	1.21485i	−0.511930	−	0.859027i
$2$	−0.723978	−	1.21485i	−0.511930	−	0.859027i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$4$	−0.951711	+	1.75905i	−0.475855	+	0.879524i
$5$	−2.68981	+	1.22840i	−1.20292	+	0.549356i	−0.913104	−	0.407726i	$-0.866322\pi$
$5$	−2.68981	+	1.22840i	−1.20292	+	0.549356i	−0.289817	+	0.957082i	$0.593594\pi$
$6$	−0.630583	+	1.26585i	−0.257434	+	0.516779i
$7$	0.0149354	−	0.00438542i	0.00564504	−	0.00165753i	−0.278909	−	0.960318i	$-0.589973\pi$
$7$	0.0149354	−	0.00438542i	0.00564504	−	0.00165753i	0.284554	+	0.958660i	$0.408155\pi$
$8$	2.82599	−	0.117329i	0.999139	−	0.0414820i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	3.43968	+	2.37838i	1.08772	+	0.752110i
$11$	0.950206	+	1.09660i	0.286498	+	0.330636i	0.880695	−	0.473683i	$-0.157076\pi$
$11$	0.950206	+	1.09660i	0.286498	+	0.330636i	−0.594198	+	0.804319i	$0.702530\pi$
$12$	1.99434	−	0.150383i	0.575716	−	0.0434118i
$13$	6.18777	+	1.81689i	1.71618	+	0.503916i	0.984147	−	0.177355i	$-0.0567541\pi$
$13$	6.18777	+	1.81689i	1.71618	+	0.503916i	0.732032	+	0.681270i	$0.238572\pi$
$14$	−0.0161405	−	0.0149692i	−0.00431373	−	0.00400070i
$15$	2.48762	+	1.59869i	0.642300	+	0.412781i
$16$	−2.18849	−	3.34821i	−0.547124	−	0.837052i
$17$	−0.419359	−	0.0602947i	−0.101709	−	0.0146236i	0.0912722	−	0.995826i	$-0.470907\pi$
$17$	−0.419359	−	0.0602947i	−0.101709	−	0.0146236i	−0.192982	+	0.981202i	$0.561816\pi$
$18$	1.40582	−	0.153888i	0.331354	−	0.0362717i
$19$	0.900853	+	6.26557i	0.206670	+	1.43742i	0.783924	+	0.620856i	$0.213215\pi$
$19$	0.900853	+	6.26557i	0.206670	+	1.43742i	−0.577255	+	0.816564i	$0.695876\pi$
$20$	0.399116	−	5.90059i	0.0892451	−	1.31941i
$21$	−0.0117639	−	0.0101935i	−0.00256710	−	0.00222440i
$22$	0.644269	−	1.94827i	0.137359	−	0.415372i
$23$	−2.79657	+	3.89605i	−0.583124	+	0.812383i
$23$	−2.79657	+	3.89605i	−0.583124	+	0.812383i
$24$	−1.62655	−	2.31394i	−0.332018	−	0.472332i
$25$	2.45184	−	2.82957i	0.490367	−	0.565914i
$26$	−2.27256	−	8.83259i	−0.445686	−	1.73221i
$27$	0.989821	−	0.142315i	0.190491	−	0.0273885i
$28$	−0.00649998	+	0.0304457i	−0.00122838	+	0.00575369i
$29$	0.122320	−	0.850755i	0.0227143	−	0.157981i	−0.975307	−	0.220852i	$-0.929116\pi$
$29$	0.122320	−	0.850755i	0.0227143	−	0.157981i	0.998022	+	0.0628704i	$0.0200255\pi$
$30$	0.141189	−	4.17950i	0.0257775	−	0.763068i
$31$	−1.51311	+	2.35444i	−0.271762	+	0.422870i	−0.950131	−	0.311851i	$-0.899051\pi$
$31$	−1.51311	+	2.35444i	−0.271762	+	0.422870i	0.678369	+	0.734722i	$0.262687\pi$
$32$	−2.48314	+	5.08272i	−0.438961	+	0.898506i
$33$	0.408795	−	1.39223i	0.0711621	−	0.242356i
$34$	0.230358	+	0.553109i	0.0395060	+	0.0948574i
$35$	−0.0347863	+	0.0301425i	−0.00587996	+	0.00509501i
$36$	−1.20473	−	1.59644i	−0.200788	−	0.266073i
$37$	4.06116	+	1.85467i	0.667651	+	0.304906i	0.720255	−	0.693709i	$-0.244025\pi$
$37$	4.06116	+	1.85467i	0.667651	+	0.304906i	−0.0526039	+	0.998615i	$0.516752\pi$
$38$	6.95952	−	5.63054i	1.12898	−	0.913394i
$39$	−1.81689	−	6.18777i	−0.290936	−	0.990836i
$40$	−7.45727	+	3.78703i	−1.17910	+	0.598782i
$41$	−2.76678	−	6.05839i	−0.432098	−	0.946162i	−0.992982	−	0.118268i	$-0.962266\pi$
$41$	−2.76678	−	6.05839i	−0.432098	−	0.946162i	0.560884	−	0.827894i	$-0.310461\pi$
$42$	−0.00386672	+	0.0216712i	−0.000596648	+	0.00334394i
$43$	2.19248	−	1.40902i	0.334350	−	0.214874i	−0.362683	−	0.931912i	$-0.618139\pi$
$43$	2.19248	−	1.40902i	0.334350	−	0.214874i	0.697033	+	0.717039i	$0.254503\pi$
$44$	−2.83329	+	0.627815i	−0.427134	+	0.0946467i
$45$		−	2.95704i		−	0.440809i
$46$	6.75776	+	0.576746i	0.996378	+	0.0850366i
$47$			6.84887i			0.999010i	0.866311	+	0.499505i	$0.166485\pi$
$47$			6.84887i			0.999010i	−0.866311	+	0.499505i	$0.833515\pi$
$48$	−1.63350	+	3.65126i	−0.235776	+	0.527013i
$49$	−5.88857	+	3.78435i	−0.841224	+	0.540622i
$50$	−5.21257	−	0.930060i	−0.737169	−	0.131530i
$51$	0.175999	+	0.385385i	0.0246448	+	0.0539647i
$52$	−9.08497	+	9.15542i	−1.25986	+	1.26963i
$53$	3.67235	+	12.5069i	0.504436	+	1.71795i	0.679755	+	0.733439i	$0.262086\pi$
$53$	3.67235	+	12.5069i	0.504436	+	1.71795i	−0.175320	+	0.984512i	$0.556096\pi$
$54$	−0.889500	−	1.09945i	−0.121046	−	0.149616i
$55$	−3.90293	−	1.78241i	−0.526271	−	0.240340i
$56$	0.0416927	−	0.0141455i	0.00557142	−	0.00189027i
$57$	4.78390	−	4.14527i	0.633642	−	0.549054i
$58$	−1.12209	+	0.467328i	−0.147338	+	0.0613631i
$59$	1.75231	−	5.96783i	0.228132	−	0.776946i	−0.763268	−	0.646082i	$-0.776407\pi$
$59$	1.75231	−	5.96783i	0.228132	−	0.776946i	0.991400	−	0.130864i	$-0.0417752\pi$
$60$	−5.17967	+	2.85434i	−0.668692	+	0.368494i
$61$	−0.357133	+	0.555710i	−0.0457262	+	0.0711513i	−0.863364	−	0.504582i	$-0.831647\pi$
$61$	−0.357133	+	0.555710i	−0.0457262	+	0.0711513i	0.817638	+	0.575733i	$0.195283\pi$
$62$	3.95575	+	0.133631i	0.502380	+	0.0169711i
$63$	−0.00221526	+	0.0154075i	−0.000279096	+	0.00194116i
$64$	7.97247	−	0.663140i	0.996558	−	0.0828925i
$65$	−18.8758	+	2.71393i	−2.34126	+	0.336622i
$66$	−1.98731	+	0.511320i	−0.244620	+	0.0629391i
$67$	−5.13984	+	5.93169i	−0.627932	+	0.724672i	−0.977193	−	0.212354i	$-0.931887\pi$
$67$	−5.13984	+	5.93169i	−0.627932	+	0.724672i	0.349261	+	0.937025i	$0.386433\pi$
$68$	0.505169	−	0.680289i	0.0612608	−	0.0824971i
$69$	4.78950	+	0.246257i	0.576589	+	0.0296459i
$70$	0.0618031	+	0.0204375i	0.00738688	+	0.00244275i
$71$	7.24911	+	6.28139i	0.860311	+	0.745463i	0.968592	−	0.248657i	$-0.0799892\pi$
$71$	7.24911	+	6.28139i	0.860311	+	0.745463i	−0.108281	+	0.994120i	$0.534535\pi$
$72$	−1.06723	+	2.61935i	−0.125775	+	0.308694i
$73$	−2.20132	−	15.3105i	−0.257645	−	1.79196i	−0.549495	−	0.835497i	$-0.685180\pi$
$73$	−2.20132	−	15.3105i	−0.257645	−	1.79196i	0.291850	−	0.956464i	$-0.405729\pi$
$74$	−0.687051	−	6.27644i	−0.0798681	−	0.729621i
$75$	−3.70595	−	0.532835i	−0.427926	−	0.0615265i
$76$	−11.8788	−	4.37837i	−1.36259	−	0.502233i
$77$	0.0190007	+	0.0122110i	0.00216533	+	0.00139157i
$78$	−6.20181	+	6.68706i	−0.702216	+	0.757161i
$79$	−8.81861	−	2.58938i	−0.992172	−	0.291328i	−0.254932	−	0.966959i	$-0.582053\pi$
$79$	−8.81861	−	2.58938i	−0.992172	−	0.291328i	−0.737240	+	0.675631i	$0.763871\pi$
$80$	9.99957	+	6.31772i	1.11799	+	0.706342i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−5.35694	+	7.74736i	−0.591575	+	0.855552i
$83$	5.51200	−	12.0696i	0.605021	−	1.32481i	−0.320907	−	0.947111i	$-0.603988\pi$
$83$	5.51200	−	12.0696i	0.605021	−	1.32481i	0.925928	−	0.377700i	$-0.123285\pi$
$84$	0.0291267	−	0.0109920i	0.00317798	−	0.00119933i
$85$	1.20206	−	0.352957i	0.130382	−	0.0382836i
$86$	−3.29905	−	1.64343i	−0.355746	−	0.177215i
$87$	−0.781832	+	0.357051i	−0.0838211	+	0.0382798i
$88$	2.81394	+	2.98749i	0.299967	+	0.318467i
$89$	−4.02629	−	6.26503i	−0.426786	−	0.664092i	0.559558	−	0.828791i	$-0.310971\pi$
$89$	−4.02629	−	6.26503i	−0.426786	−	0.664092i	−0.986344	+	0.164699i	$0.947335\pi$
$90$	−3.59235	+	2.14083i	−0.378667	+	0.225663i
$91$	0.100384			0.0105231
$92$	−4.19182	−	8.62721i	−0.437027	−	0.899448i
$93$	2.79873			0.290215
$94$	8.32034	−	4.95843i	0.858177	−	0.511423i
$95$	−10.1197	−	15.7466i	−1.03826	−	1.61557i
$96$	5.61834	−	0.658974i	0.573420	−	0.0672563i
$97$	−8.57609	+	3.91657i	−0.870770	+	0.397668i	−0.800125	−	0.599834i	$-0.795233\pi$
$97$	−8.57609	+	3.91657i	−0.870770	+	0.397668i	−0.0706459	+	0.997501i	$0.522506\pi$
$98$	8.86061	+	4.41393i	0.895057	+	0.445874i
$99$	−1.39223	+	0.408795i	−0.139924	+	0.0410855i
$100$	2.64391	+	7.00583i	0.264391	+	0.700583i
$101$	−3.22439	+	7.06043i	−0.320839	+	0.702539i	−0.999490	−	0.0319212i	$-0.989837\pi$
$101$	−3.22439	+	7.06043i	−0.320839	+	0.702539i	0.678651	+	0.734460i	$0.262565\pi$
$102$	0.340764	−	0.492823i	0.0337407	−	0.0487967i
$103$	8.30428	+	9.58365i	0.818245	+	0.944305i	0.999232	−	0.0391801i	$-0.0124746\pi$
$103$	8.30428	+	9.58365i	0.818245	+	0.944305i	−0.180987	+	0.983486i	$0.557929\pi$
$104$	17.6998	+	4.40852i	1.73560	+	0.432291i
$105$	0.0441644	+	0.0129678i	0.00431000	+	0.00126553i
$106$	12.5352	−	13.5160i	1.21753	−	1.31279i
$107$	5.73147	+	3.68339i	0.554082	+	0.356087i	0.787524	−	0.616284i	$-0.211363\pi$
$107$	5.73147	+	3.68339i	0.554082	+	0.356087i	−0.233442	+	0.972371i	$0.574999\pi$
$108$	−0.691685	+	1.87659i	−0.0665574	+	0.180574i
$109$	10.0095	+	1.43915i	0.958738	+	0.137846i	0.603881	−	0.797075i	$-0.293620\pi$
$109$	10.0095	+	1.43915i	0.958738	+	0.137846i	0.354857	+	0.934921i	$0.384529\pi$
$110$	0.660282	+	6.03189i	0.0629555	+	0.575119i
$111$	−0.635382	−	4.41918i	−0.0603078	−	0.419450i
$112$	−0.0473692	−	0.0404092i	−0.00447597	−	0.00381831i
$113$	6.22373	+	5.39289i	0.585479	+	0.507321i	0.896477	−	0.443090i	$-0.146118\pi$
$113$	6.22373	+	5.39289i	0.585479	+	0.507321i	−0.310998	+	0.950411i	$0.600663\pi$
$114$	−8.49931	−	2.81062i	−0.796033	−	0.263239i
$115$	2.73635	−	13.9149i	0.255166	−	1.29758i
$116$	1.38010	+	1.02484i	0.128139	+	0.0951539i
$117$	−4.22320	+	4.87383i	−0.390435	+	0.450586i
$118$	−8.51865	+	2.19179i	−0.784205	+	0.201770i
$119$	−0.00652769		0.000938540i	−0.000598392		8.60359e-5i
$120$	7.21756	+	4.22603i	0.658870	+	0.385782i
$121$	1.26583	−	8.80405i	0.115076	−	0.800368i
$122$	0.933659	+	0.0315404i	0.0845295	+	0.00285553i
$123$	−3.60081	+	5.60297i	−0.324674	+	0.505203i
$124$	−2.70153	−	4.90238i	−0.242605	−	0.440246i
$125$	1.04632	−	3.56343i	0.0935855	−	0.318723i
$126$	0.0203215	−	0.00846346i	0.00181038	−	0.000753985i
$127$	7.42443	−	6.43331i	0.658812	−	0.570864i	−0.259976	−	0.965615i	$-0.583715\pi$
$127$	7.42443	−	6.43331i	0.658812	−	0.570864i	0.918788	+	0.394751i	$0.129169\pi$
$128$	−6.57751	−	9.20524i	−0.581375	−	0.813636i
$129$	−2.37069	−	1.08266i	−0.208727	−	0.0953226i
$130$	16.9627	+	20.9664i	1.48773	+	1.83888i
$131$	3.40084	+	11.5822i	0.297133	+	1.01194i	0.963809	+	0.266593i	$0.0858981\pi$
$131$	3.40084	+	11.5822i	0.297133	+	1.01194i	−0.666677	+	0.745347i	$0.732284\pi$
$132$	2.05994	+	2.04409i	0.179295	+	0.177915i
$133$	0.0409317	+	0.0896279i	0.00354923	+	0.00777173i
$134$	10.9272	+	1.94971i	0.943970	+	0.168429i
$135$	−2.48762	+	1.59869i	−0.214100	+	0.137594i
$136$	−1.19218	−	0.121190i	−0.102229	−	0.0103919i
$137$			8.69445i			0.742817i	0.928470	+	0.371409i	$0.121125\pi$
$137$			8.69445i			0.742817i	−0.928470	+	0.371409i	$0.878875\pi$
$138$	−3.16833	−	5.99680i	−0.269706	−	0.510482i
$139$		−	17.1083i		−	1.45111i	−0.688165	−	0.725554i	$-0.741584\pi$
$139$		−	17.1083i		−	1.45111i	0.688165	−	0.725554i	$-0.258416\pi$
$140$	−0.0199156	−	0.0898777i	−0.00168318	−	0.00759605i
$141$	5.76164	−	3.70278i	0.485217	−	0.311830i
$142$	2.38273	−	13.3541i	0.199954	−	1.12066i
$143$	3.88726	+	8.51191i	0.325069	+	0.711802i
$144$	3.95477	−	0.599829i	0.329564	−	0.0499857i
$145$	0.716046	+	2.43863i	0.0594644	+	0.202517i
$146$	−17.0062	+	13.7588i	−1.40745	+	1.13868i
$147$	6.36720	+	2.90780i	0.525158	+	0.239832i
$148$	−7.12751	+	5.37867i	−0.585877	+	0.442124i
$149$	5.50106	−	4.76670i	0.450665	−	0.390503i	−0.399743	−	0.916627i	$-0.630901\pi$
$149$	5.50106	−	4.76670i	0.450665	−	0.390503i	0.850408	+	0.526124i	$0.176355\pi$
$150$	2.03571	+	4.88792i	0.166215	+	0.399097i
$151$	6.40594	−	21.8166i	0.521308	−	1.77541i	−0.103497	−	0.994630i	$-0.533003\pi$
$151$	6.40594	−	21.8166i	0.521308	−	1.77541i	0.624804	−	0.780781i	$-0.285179\pi$
$152$	3.28094	+	17.6008i	0.266119	+	1.42761i
$153$	0.229054	−	0.356415i	0.0185179	−	0.0288144i
$154$	0.00107842	−	0.0319235i	8.69016e−5	−	0.00257247i
$155$	1.17779	−	8.19171i	0.0946023	−	0.657974i
$156$	12.6137	+	2.69297i	1.00991	+	0.215610i
$157$	−17.6729	+	2.54098i	−1.41045	+	0.202792i	−0.805086	−	0.593158i	$-0.797881\pi$
$157$	−17.6729	+	2.54098i	−1.41045	+	0.202792i	−0.605363	+	0.795950i	$0.706972\pi$
$158$	3.23879	+	12.5879i	0.257664	+	1.00144i
$159$	8.53603	−	9.85110i	0.676951	−	0.781243i
$160$	0.435591	−	16.7218i	0.0344365	−	1.32198i
$161$	−0.0246819	+	0.0704530i	−0.00194521	+	0.00555248i
$162$	−0.444016	+	1.34270i	−0.0348852	+	0.105493i
$163$	−2.09886	−	1.81867i	−0.164395	−	0.142449i	0.568778	−	0.822491i	$-0.307416\pi$
$163$	−2.09886	−	1.81867i	−0.164395	−	0.142449i	−0.733173	+	0.680042i	$0.761962\pi$
$164$	13.2902	+	0.898948i	1.03779	+	0.0701960i
$165$	0.610626	+	4.24700i	0.0475372	+	0.330628i
$166$	−18.6533	+	2.04189i	−1.44778	+	0.158481i
$167$	−13.3308	−	1.91668i	−1.03157	−	0.148317i	−0.394318	−	0.918974i	$-0.629019\pi$
$167$	−13.3308	−	1.91668i	−1.03157	−	0.148317i	−0.637250	+	0.770657i	$0.719928\pi$
$168$	−0.0344407	−	0.0274265i	−0.00265716	−	0.00211600i
$169$	24.0511	+	15.4567i	1.85009	+	1.18898i
$170$	−1.29906	−	1.20479i	−0.0996331	−	0.0924032i
$171$	−6.07359	−	1.78337i	−0.464459	−	0.136377i
$172$	0.391929	+	5.19766i	0.0298843	+	0.396318i
$173$	5.93055	+	6.84421i	0.450891	+	0.520356i	0.934998	−	0.354653i	$-0.115401\pi$
$173$	5.93055	+	6.84421i	0.450891	+	0.520356i	−0.484107	+	0.875009i	$0.660855\pi$
$174$	0.999791	+	0.691310i	0.0757940	+	0.0524080i
$175$	0.0242102	−	0.0530130i	0.00183012	−	0.00400740i
$176$	1.59211	−	5.58138i	0.120010	−	0.420712i
$177$	−5.96783	+	1.75231i	−0.448570	+	0.131712i
$178$	−4.69611	+	9.42708i	−0.351989	+	0.706590i
$179$	4.30217	−	1.96473i	0.321559	−	0.146851i	−0.248095	−	0.968736i	$-0.579804\pi$
$179$	4.30217	−	1.96473i	0.321559	−	0.146851i	0.569654	+	0.821885i	$0.307077\pi$
$180$	5.20156	+	2.81424i	0.387702	+	0.209761i
$181$	−10.2753	−	15.9887i	−0.763759	−	1.18843i	−0.977375	−	0.211515i	$-0.932160\pi$
$181$	−10.2753	−	15.9887i	−0.763759	−	1.18843i	0.213616	−	0.976918i	$-0.431476\pi$
$182$	−0.0726762	−	0.121952i	−0.00538711	−	0.00903967i
$183$	0.660573			0.0488310
$184$	−7.44596	+	11.3383i	−0.548923	+	0.835873i
$185$	−13.2020			−0.970634
$186$	−2.02622	−	3.40003i	−0.148570	−	0.249302i
$187$	−0.332358	−	0.517160i	−0.0243044	−	0.0378185i
$188$	−12.0475	−	6.51814i	−0.878653	−	0.475384i
$189$	0.0141592	−	0.00646630i	0.00102993	−	0.000470354i
$190$	−11.8033	+	23.6941i	−0.856299	+	1.71895i
$191$	1.17356	−	0.344588i	0.0849157	−	0.0249335i	−0.238999	−	0.971020i	$-0.576819\pi$
$191$	1.17356	−	0.344588i	0.0849157	−	0.0249335i	0.323914	+	0.946086i	$0.395001\pi$
$192$	−4.86811	−	6.34835i	−0.351326	−	0.458152i
$193$	2.70845	−	5.93068i	0.194959	−	0.426900i	−0.786754	−	0.617266i	$-0.788240\pi$
$193$	2.70845	−	5.93068i	0.194959	−	0.426900i	0.981713	+	0.190366i	$0.0609675\pi$
$194$	10.9669	+	7.58314i	0.787381	+	0.544437i
$195$	12.4881	+	14.4121i	0.894294	+	1.03207i
$196$	−1.05264	−	13.9599i	−0.0751888	−	0.997135i
$197$	−5.15884	−	1.51477i	−0.367552	−	0.107923i	0.0927403	−	0.995690i	$-0.470437\pi$
$197$	−5.15884	−	1.51477i	−0.367552	−	0.107923i	−0.460293	+	0.887767i	$0.652256\pi$
$198$	1.50457	+	1.39539i	0.106925	+	0.0991658i
$199$	1.50277	+	0.965769i	0.106528	+	0.0684616i	0.592820	−	0.805335i	$-0.298014\pi$
$199$	1.50277	+	0.965769i	0.106528	+	0.0684616i	−0.486292	+	0.873796i	$0.661651\pi$
$200$	6.59688	−	8.28401i	0.466470	−	0.585768i
$201$	7.76887	+	1.11699i	0.547974	+	0.0787867i
$202$	10.9117	−	1.19446i	0.767747	−	0.0840416i
$203$	−0.00190402	−	0.0132428i	−0.000133636	−	0.000929459i
$204$	−0.845410	−	0.0571836i	−0.0591906	−	0.00400365i
$205$	14.8842	+	12.8973i	1.03956	+	0.900783i
$206$	5.63056	−	17.0268i	0.392300	−	1.18631i
$207$	−2.38224	−	4.16232i	−0.165577	−	0.289302i
$208$	−7.45856	−	24.6942i	−0.517158	−	1.71223i
$209$	−6.01480	+	6.94145i	−0.416053	+	0.480150i
$210$	−0.0162201	−	0.0630414i	−0.00111929	−	0.00435027i
$211$	3.08291	−	0.443255i	0.212236	−	0.0305149i	−0.0353766	−	0.999374i	$-0.511263\pi$
$211$	3.08291	−	0.443255i	0.212236	−	0.0305149i	0.247613	+	0.968859i	$0.420354\pi$
$212$	−25.4952	−	5.44308i	−1.75102	−	0.373833i
$213$	1.36508	−	9.49431i	0.0935334	−	0.650539i
$214$	0.325300	−	9.62955i	0.0222371	−	0.658263i
$215$	−4.16653	+	6.48324i	−0.284155	+	0.442153i
$216$	2.78053	−	0.518315i	0.189191	−	0.0352669i
$217$	−0.0122736	+	0.0418000i	−0.000833186	+	0.00283757i
$218$	−5.49832	−	13.2020i	−0.372393	−	0.894149i
$219$	−11.6899	+	10.1294i	−0.789931	+	0.684479i
$220$	6.84980	−	5.16910i	0.461814	−	0.348501i
$221$	−2.48535	−	1.13502i	−0.167183	−	0.0763497i
$222$	−4.90863	+	3.97128i	−0.329445	+	0.266535i
$223$	5.44880	+	18.5569i	0.364879	+	1.24266i	0.913585	+	0.406647i	$0.133302\pi$
$223$	5.44880	+	18.5569i	0.364879	+	1.24266i	−0.548707	+	0.836015i	$0.684880\pi$
$224$	−0.0147968	+	0.0868018i	−0.000988650	+	0.00579969i
$225$	1.55534	+	3.40571i	0.103689	+	0.227048i
$226$	2.04570	−	11.4652i	0.136078	−	0.762655i
$227$	−19.1748	+	12.3229i	−1.27268	+	0.817900i	−0.989966	−	0.141306i	$-0.954870\pi$
$227$	−19.1748	+	12.3229i	−1.27268	+	0.817900i	−0.282711	+	0.959205i	$0.591234\pi$
$228$	2.73884	+	12.3602i	0.181384	+	0.818574i
$229$			4.72477i			0.312221i	0.987740	+	0.156111i	$0.0498957\pi$
$229$			4.72477i			0.312221i	−0.987740	+	0.156111i	$0.950104\pi$
$230$	−18.8856	+	6.74988i	−1.24528	+	0.445074i
$231$		−	0.0225862i		−	0.00148606i
$232$	0.245858	−	2.41858i	0.0161413	−	0.158787i
$233$	22.2753	−	14.3155i	1.45930	−	0.937836i	0.460563	−	0.887627i	$-0.347647\pi$
$233$	22.2753	−	14.3155i	1.45930	−	0.937836i	0.998739	−	0.0502095i	$-0.0159889\pi$
$234$	8.97846	+	1.60199i	0.586941	+	0.104726i
$235$	−8.41313	−	18.4222i	−0.548812	−	1.20173i
$236$	8.83001	+	8.76206i	0.574785	+	0.570361i
$237$	2.58938	+	8.81861i	0.168198	+	0.572831i
$238$	0.00586609	+	0.00725067i	0.000380242	+	0.000469991i
$239$	−13.7700	−	6.28853i	−0.890704	−	0.406771i	−0.0831313	−	0.996539i	$-0.526492\pi$
$239$	−13.7700	−	6.28853i	−0.890704	−	0.406771i	−0.807573	+	0.589768i	$0.799219\pi$
$240$	−0.0913747	−	11.8278i	−0.00589821	−	0.763480i
$241$	−23.1351	+	20.0467i	−1.49026	+	1.29132i	−0.635747	+	0.771897i	$0.719308\pi$
$241$	−23.1351	+	20.0467i	−1.49026	+	1.29132i	−0.854517	+	0.519424i	$0.826147\pi$
$242$	−11.6120	+	4.83615i	−0.746449	+	0.310880i
$243$	−0.281733	+	0.959493i	−0.0180732	+	0.0615515i
$244$	−0.637632	−	1.15709i	−0.0408202	−	0.0740750i
$245$	11.1905	−	17.4127i	0.714933	−	1.11246i
$246$	9.41367	+	0.318007i	0.600194	+	0.0202754i
$247$	−5.80960	+	40.4067i	−0.369656	+	2.57101i
$248$	−3.99979	+	6.83117i	−0.253987	+	0.433779i
$249$	−13.1336	+	1.88833i	−0.832309	+	0.119668i
$250$	−5.08654	+	1.30873i	−0.321701	+	0.0827713i
$251$	−11.5443	+	13.3228i	−0.728667	+	0.840927i	−0.992321	−	0.123691i	$-0.960527\pi$
$251$	−11.5443	+	13.3228i	−0.728667	+	0.840927i	0.263654	+	0.964617i	$0.415072\pi$
$252$	−0.0249941	−	0.0185602i	−0.00157448	−	0.00116918i
$253$	−6.92971	+	0.635347i	−0.435667	+	0.0399439i
$254$	−13.1906	−	4.36198i	−0.827653	−	0.273695i
$255$	−0.946811	−	0.820416i	−0.0592916	−	0.0513765i
$256$	−6.42099	+	14.6551i	−0.401312	+	0.915942i
$257$	−2.37295	−	16.5042i	−0.148021	−	1.02951i	−0.919455	−	0.393196i	$-0.871369\pi$
$257$	−2.37295	−	16.5042i	−0.148021	−	1.02951i	0.771434	−	0.636309i	$-0.219540\pi$
$258$	0.401063	+	3.66385i	0.0249691	+	0.228101i
$259$	0.0687884	+	0.00989029i	0.00427431	+	0.000614552i
$260$	13.1904	−	35.7863i	0.818032	−	2.21937i
$261$	0.723060	+	0.464683i	0.0447563	+	0.0287631i
$262$	11.6085	−	12.5168i	0.717173	−	0.773288i
$263$	27.3124	+	8.01965i	1.68416	+	0.494513i	0.977124	−	0.212669i	$-0.0682155\pi$
$263$	27.3124	+	8.01965i	1.68416	+	0.494513i	0.707032	+	0.707182i	$0.250034\pi$
$264$	0.991904	−	3.98239i	0.0610475	−	0.245099i
$265$	−25.2413	−	29.1300i	−1.55056	−	1.78944i
$266$	0.0792506	−	0.114614i	0.00485917	−	0.00702746i
$267$	−3.09370	+	6.77427i	−0.189332	+	0.414578i
$268$	−5.54249	−	14.6865i	−0.338561	−	0.897119i
$269$	12.4451	−	3.65422i	0.758794	−	0.222802i	0.120625	−	0.992698i	$-0.461510\pi$
$269$	12.4451	−	3.65422i	0.758794	−	0.222802i	0.638169	+	0.769896i	$0.279692\pi$
$270$	3.74315	+	1.86466i	0.227801	+	0.113479i
$271$	−13.9661	+	6.37811i	−0.848381	+	0.387443i	−0.791671	−	0.610948i	$-0.790788\pi$
$271$	−13.9661	+	6.37811i	−0.848381	+	0.387443i	−0.0567105	+	0.998391i	$0.518061\pi$
$272$	0.715885	+	1.53605i	0.0434069	+	0.0931370i
$273$	−0.0542719	−	0.0844487i	−0.00328469	−	0.00511107i
$274$	10.5624	−	6.29460i	0.638100	−	0.380270i
$275$	5.43264			0.327601
$276$	−4.99140	+	8.19060i	−0.300447	+	0.493016i
$277$	10.5624			0.634633			0.317317	−	0.948320i	$-0.397218\pi$
$277$	10.5624			0.634633			0.317317	+	0.948320i	$0.397218\pi$
$278$	−20.7840	+	12.3860i	−1.24654	+	0.742866i
$279$	−1.51311	−	2.35444i	−0.0905874	−	0.140957i
$280$	−0.0947693	+	0.0892639i	−0.00566355	+	0.00533454i
$281$	9.94197	−	4.54034i	0.593088	−	0.270854i	−0.0961762	−	0.995364i	$-0.530661\pi$
$281$	9.94197	−	4.54034i	0.593088	−	0.270854i	0.689264	+	0.724510i	$0.257934\pi$
$282$	−8.66961	−	4.31878i	−0.516268	−	0.257180i
$283$	9.45395	−	2.77593i	0.561979	−	0.165012i	0.0116086	−	0.999933i	$-0.496305\pi$
$283$	9.45395	−	2.77593i	0.561979	−	0.165012i	0.550370	+	0.834921i	$0.314487\pi$
$284$	−17.9483	+	6.77346i	−1.06504	+	0.401931i
$285$	−7.77575	+	17.0265i	−0.460596	+	1.00856i
$286$	7.52638	−	10.8849i	0.445044	−	0.643636i
$287$	−0.0678914	−	0.0783508i	−0.00400750	−	0.00462490i
$288$	−3.59187	−	4.37018i	−0.211653	−	0.257515i
$289$	−16.1392	−	4.73888i	−0.949362	−	0.278758i
$290$	2.44416	−	2.63540i	0.143526	−	0.154756i
$291$	7.93142	+	5.09721i	0.464948	+	0.298804i
$292$	29.0270	+	10.6990i	1.69867	+	0.626109i
$293$	5.91887	+	0.851005i	0.345784	+	0.0497162i	0.313019	−	0.949747i	$-0.398660\pi$
$293$	5.91887	+	0.851005i	0.345784	+	0.0497162i	0.0327649	+	0.999463i	$0.489569\pi$
$294$	−1.07718	−	9.84037i	−0.0628223	−	0.573902i
$295$	2.61747	+	18.2049i	0.152395	+	1.05993i
$296$	11.6944	+	4.76480i	0.679725	+	0.276948i
$297$	1.09660	+	0.950206i	0.0636310	+	0.0551365i
$298$	−9.77346	−	3.23197i	−0.566161	−	0.187223i
$299$	−24.3832	+	19.0268i	−1.41012	+	1.10035i
$300$	4.46427	−	6.01183i	0.257745	−	0.347093i
$301$	0.0265663	−	0.0306592i	0.00153126	−	0.00176717i
$302$	−31.1416	+	8.01252i	−1.79200	+	0.461069i
$303$	7.68285	−	1.10463i	0.441368	−	0.0634592i
$304$	19.0069	−	16.7284i	1.09012	−	0.959440i
$305$	0.277989	−	1.93346i	0.0159176	−	0.110709i
$306$	−0.598820	−	0.0202290i	−0.0342323	−	0.00115641i
$307$	−2.78122	+	4.32767i	−0.158733	+	0.246993i	−0.911506	−	0.411287i	$-0.865079\pi$
$307$	−2.78122	+	4.32767i	−0.158733	+	0.246993i	0.752773	+	0.658280i	$0.228716\pi$
$308$	−0.0395629	+	0.0218018i	−0.00225431	+	0.00124227i
$309$	3.57265	−	12.1673i	0.203241	−	0.692175i
$310$	−10.8044	+	4.49978i	−0.613647	+	0.255571i
$311$	11.4380	−	9.91107i	0.648589	−	0.562005i	−0.267212	−	0.963638i	$-0.586102\pi$
$311$	11.4380	−	9.91107i	0.648589	−	0.562005i	0.915801	+	0.401632i	$0.131557\pi$
$312$	−5.86053	−	17.2734i	−0.331787	−	0.977915i
$313$	0.593548	+	0.271064i	0.0335493	+	0.0153214i	0.432119	−	0.901817i	$-0.357766\pi$
$313$	0.593548	+	0.271064i	0.0335493	+	0.0153214i	−0.398570	+	0.917138i	$0.630493\pi$
$314$	15.8817	+	19.6302i	0.896255	+	1.10780i
$315$	−0.0129678	−	0.0441644i	−0.000730655	−	0.00248838i
$316$	12.9476	−	13.0480i	0.728360	−	0.734008i
$317$	−5.40490	−	11.8351i	−0.303569	−	0.664724i	0.694954	−	0.719054i	$-0.255425\pi$
$317$	−5.40490	−	11.8351i	−0.303569	−	0.664724i	−0.998523	+	0.0543305i	$0.982698\pi$
$318$	−18.1475	−	3.23799i	−1.01766	−	0.181577i
$319$	1.04916	−	0.674256i	0.0587419	−	0.0377511i
$320$	−20.6299	+	11.5771i	−1.15324	+	0.647178i
$321$		−	6.81301i		−	0.380265i
$322$	0.103459	−	0.0210217i	0.00576554	−	0.00117149i
$323$		−	2.68184i		−	0.149221i
$324$	1.95264	−	0.432676i	0.108480	−	0.0240376i
$325$	20.3124	−	13.0540i	1.12673	−	0.724106i
$326$	−0.689880	+	3.86647i	−0.0382089	+	0.214144i
$327$	−4.20086	−	9.19860i	−0.232308	−	0.508684i
$328$	−8.52971	−	16.7964i	−0.470974	−	0.927423i
$329$	0.0300352	+	0.102290i	0.00165589	+	0.00563945i
$330$	4.71738	−	3.81655i	0.259683	−	0.210094i
$331$	21.7940	+	9.95299i	1.19791	+	0.547066i	0.911602	−	0.411073i	$-0.134846\pi$
$331$	21.7940	+	9.95299i	1.19791	+	0.547066i	0.286304	+	0.958139i	$0.407573\pi$
$332$	15.9852	+	21.1826i	0.877300	+	1.16255i
$333$	−3.37414	+	2.92371i	−0.184902	+	0.160218i
$334$	7.32273	+	17.5825i	0.400682	+	0.962072i
$335$	6.53874	−	22.2689i	0.357250	−	1.21668i
$336$	−0.00838466	+	0.0616964i	−0.000457421	+	0.00336582i
$337$	4.42690	−	6.88839i	0.241148	−	0.375234i	−0.699491	−	0.714641i	$-0.746590\pi$
$337$	4.42690	−	6.88839i	0.241148	−	0.375234i	0.940640	+	0.339407i	$0.110226\pi$
$338$	1.36507	−	40.4088i	0.0742498	−	2.19795i
$339$	1.17199	−	8.15135i	0.0636536	−	0.442721i
$340$	−0.523147	+	2.45040i	−0.0283716	+	0.132892i
$341$	−4.01964	+	0.577936i	−0.217675	+	0.0312970i
$342$	2.23063	+	8.66961i	0.120619	+	0.468799i
$343$	−0.142706	+	0.164692i	−0.00770542	+	0.00889253i
$344$	6.03061	−	4.23912i	0.325149	−	0.228558i
$345$	−13.1854	+	5.22103i	−0.709877	+	0.281091i
$346$	4.02109	−	12.1598i	0.216175	−	0.653713i
$347$	8.00171	+	6.93352i	0.429554	+	0.372211i	0.842637	−	0.538483i	$-0.181002\pi$
$347$	8.00171	+	6.93352i	0.429554	+	0.372211i	−0.413082	+	0.910694i	$0.635548\pi$
$348$	0.116009	−	1.71509i	0.00621872	−	0.0919383i
$349$	2.56379	+	17.8316i	0.137237	+	0.954502i	0.935785	+	0.352571i	$0.114693\pi$
$349$	2.56379	+	17.8316i	0.137237	+	0.954502i	−0.798548	+	0.601931i	$0.794398\pi$
$350$	−0.0819304	+	0.00896852i	−0.00437936	+	0.000479388i
$351$	6.38336	+	0.917788i	0.340718	+	0.0489879i
$352$	−7.93318	+	2.10663i	−0.422840	+	0.112284i
$353$	14.0122	+	9.00510i	0.745794	+	0.479293i	0.857523	−	0.514446i	$-0.172002\pi$
$353$	14.0122	+	9.00510i	0.745794	+	0.479293i	−0.111729	+	0.993739i	$0.535639\pi$
$354$	6.44938	+	5.98137i	0.342781	+	0.317906i
$355$	−27.2148	−	7.99098i	−1.44441	−	0.424117i
$356$	14.8524	−	1.11994i	0.787173	−	0.0593567i
$357$	0.00431869	+	0.00498403i	0.000228569	+	0.000263783i
$358$	−5.50153	−	3.80405i	−0.290765	−	0.201051i
$359$	9.31943	−	20.4067i	0.491861	−	1.07702i	−0.487169	−	0.873308i	$-0.661970\pi$
$359$	9.31943	−	20.4067i	0.491861	−	1.07702i	0.979030	−	0.203717i	$-0.0653022\pi$
$360$	−0.346945	−	8.35656i	−0.0182856	−	0.440429i
$361$	−20.2155	+	5.93580i	−1.06397	+	0.312410i
$362$	−11.9848	+	24.0585i	−0.629905	+	1.26448i
$363$	−8.09080	+	3.69494i	−0.424657	+	0.193934i
$364$	−0.0955369	+	0.176581i	−0.00500749	+	0.00925536i
$365$	24.7285	+	38.4784i	1.29435	+	2.01405i
$366$	−0.478241	−	0.802496i	−0.0249980	−	0.0419471i
$367$	27.9211			1.45747			0.728734	−	0.684797i	$-0.240109\pi$
$367$	27.9211			1.45747			0.728734	+	0.684797i	$0.240109\pi$
$368$	19.1651	+	0.837001i	0.999048	+	0.0436317i
$369$	6.66027			0.346720
$370$	9.55800	+	16.0385i	0.496897	+	0.833801i
$371$	0.109696	+	0.170690i	0.00569512	+	0.00886177i
$372$	−2.66358	+	4.92310i	−0.138100	+	0.255251i
$373$	−1.15446	+	0.527222i	−0.0597754	+	0.0272985i	−0.445078	−	0.895492i	$-0.646824\pi$
$373$	−1.15446	+	0.527222i	−0.0597754	+	0.0272985i	0.385303	+	0.922790i	$0.374097\pi$
$374$	−0.387650	+	0.778177i	−0.0200449	+	0.0402386i
$375$	−3.56343	+	1.04632i	−0.184015	+	0.0540316i
$376$	0.803569	+	19.3549i	0.0414409	+	0.998151i
$377$	2.30262	−	5.04203i	0.118591	−	0.259678i
$378$	−0.0181066	−	0.0125198i	−0.000931301	−	0.000643951i
$379$	−8.20530	−	9.46942i	−0.421478	−	0.486411i	0.504809	−	0.863231i	$-0.331563\pi$
$379$	−8.20530	−	9.46942i	−0.421478	−	0.486411i	−0.926287	+	0.376820i	$0.877018\pi$
$380$	37.3301	−	2.81487i	1.91499	−	0.144400i
$381$	−9.42599	−	2.76772i	−0.482908	−	0.141795i
$382$	−1.26825	−	1.17622i	−0.0648895	−	0.0601807i
$383$	−25.1907	−	16.1891i	−1.28718	−	0.827223i	−0.295428	−	0.955365i	$-0.595462\pi$
$383$	−25.1907	−	16.1891i	−1.28718	−	0.827223i	−0.991756	+	0.128142i	$0.959099\pi$
$384$	−4.18787	+	10.5101i	−0.213711	+	0.536340i
$385$	−0.0661083	−	0.00950494i	−0.00336919	−	0.000484417i
$386$	−9.16574	+	1.00333i	−0.466524	+	0.0510681i
$387$	0.370902	+	2.57968i	0.0188540	+	0.131132i
$388$	1.27253	−	18.8132i	0.0646027	−	0.955095i
$389$	25.6851	+	22.2563i	1.30229	+	1.12844i	0.983558	+	0.180594i	$0.0578021\pi$
$389$	25.6851	+	22.2563i	1.30229	+	1.12844i	0.318731	+	0.947845i	$0.396743\pi$
$390$	8.46734	−	25.6052i	0.428761	−	1.29657i
$391$	1.40768	−	1.46522i	0.0711892	−	0.0740996i
$392$	−16.1970	+	11.3855i	−0.818074	+	0.575052i
$393$	7.90493	−	9.12277i	0.398751	−	0.460183i
$394$	1.89467	+	7.36387i	0.0954522	+	0.370987i
$395$	26.9012	−	3.86781i	1.35355	−	0.194611i
$396$	0.605909	−	2.83805i	0.0304481	−	0.142617i
$397$	−1.42261	+	9.89450i	−0.0713990	+	0.496591i	0.922474	+	0.386060i	$0.126164\pi$
$397$	−1.42261	+	9.89450i	−0.0713990	+	0.496591i	−0.993873	+	0.110531i	$0.964745\pi$
$398$	0.0852923	−	2.52483i	0.00427532	−	0.126558i
$399$	0.0532705	−	0.0828905i	0.00266686	−	0.00414971i
$400$	−14.8398	−	2.01676i	−0.741991	−	0.100838i
$401$	2.72323	−	9.27445i	0.135991	−	0.463144i	−0.863133	−	0.504976i	$-0.831501\pi$
$401$	2.72323	−	9.27445i	0.135991	−	0.463144i	0.999125	+	0.0418321i	$0.0133194\pi$
$402$	−4.26751	−	10.2467i	−0.212844	−	0.511057i
$403$	−13.6405	+	11.8196i	−0.679483	+	0.588776i
$404$	−9.35095	−	12.3913i	−0.465227	−	0.616492i
$405$	2.68981	+	1.22840i	0.133658	+	0.0610395i
$406$	−0.0147095	+	0.0119006i	−0.000730018	+	0.000590615i
$407$	1.82512	+	6.21578i	0.0904677	+	0.308105i
$408$	0.542590	+	1.06844i	0.0268622	+	0.0528959i
$409$	2.44698	+	5.35814i	0.120996	+	0.264943i	0.960432	−	0.278515i	$-0.0898421\pi$
$409$	2.44698	+	5.35814i	0.120996	+	0.264943i	−0.839436	+	0.543458i	$0.817115\pi$
$410$	4.89234	−	27.4194i	0.241616	−	1.35415i
$411$	7.31424	−	4.70058i	0.360785	−	0.231862i
$412$	−24.7614	+	5.48676i	−1.21991	+	0.270313i
$413$		−	0.0968164i		−	0.00476402i
$414$	−3.33190	+	5.90749i	−0.163754	+	0.290337i
$415$			39.2359i			1.92602i
$416$	−24.5999	+	26.9391i	−1.20611	+	1.32080i
$417$	−14.3924	+	9.24945i	−0.704800	+	0.452947i
$418$	12.7874	+	2.28161i	0.625452	+	0.111597i
$419$	−2.81140	−	6.15611i	−0.137346	−	0.300746i	0.828444	−	0.560072i	$-0.189227\pi$
$419$	−2.81140	−	6.15611i	−0.137346	−	0.300746i	−0.965790	+	0.259327i	$0.916499\pi$
$420$	−0.0648427	+	0.0653456i	−0.00316400	+	0.00318854i
$421$	7.18065	+	24.4550i	0.349963	+	1.19187i	0.926973	+	0.375128i	$0.122401\pi$
$421$	7.18065	+	24.4550i	0.349963	+	1.19187i	−0.577010	+	0.816737i	$0.695781\pi$
$422$	−2.77045	−	3.42436i	−0.134863	−	0.166695i
$423$	−6.22995	−	2.84512i	−0.302911	−	0.138335i
$424$	11.8454	+	34.9134i	0.575266	+	1.69555i
$425$	−1.19881	+	1.03877i	−0.0581507	+	0.0503878i
$426$	−12.5224	+	5.21532i	−0.606714	+	0.252683i
$427$	−0.00289689	+	0.00986590i	−0.000140190	+	0.000477444i
$428$	−11.9340	+	6.57640i	−0.576849	+	0.317882i
$429$	5.05906	−	7.87205i	0.244254	−	0.380066i
$430$	10.8926	+	0.367969i	0.525289	+	0.0177450i
$431$	−2.46075	+	17.1149i	−0.118530	+	0.824395i	0.840646	+	0.541585i	$0.182176\pi$
$431$	−2.46075	+	17.1149i	−0.118530	+	0.824395i	−0.959176	+	0.282810i	$0.908734\pi$
$432$	−2.64272	−	3.00267i	−0.127148	−	0.144466i
$433$	4.42431	−	0.636119i	0.212619	−	0.0305700i	−0.0351823	−	0.999381i	$-0.511201\pi$
$433$	4.42431	−	0.636119i	0.212619	−	0.0305700i	0.247801	+	0.968811i	$0.420292\pi$
$434$	0.0596665	−	0.0153518i	0.00286408	−	0.000736909i
$435$	1.66438	−	1.92080i	0.0798010	−	0.0920953i
$436$	−12.0577	+	16.2376i	−0.577459	+	0.777638i
$437$	−26.9303	−	14.0123i	−1.28825	−	0.670300i
$438$	20.7689	+	6.86802i	0.992375	+	0.328167i
$439$	−24.7502	−	21.4462i	−1.18126	−	1.02357i	−0.999188	−	0.0402864i	$-0.987173\pi$
$439$	−24.7502	−	21.4462i	−1.18126	−	1.02357i	−0.182076	−	0.983285i	$-0.558282\pi$
$440$	−11.2388	−	4.57915i	−0.535788	−	0.218302i
$441$	−0.996169	−	6.92851i	−0.0474366	−	0.329929i
$442$	0.420461	+	3.84105i	0.0199993	+	0.182700i
$443$	5.66781	+	0.814908i	0.269286	+	0.0387174i	0.275635	−	0.961262i	$-0.411112\pi$
$443$	5.66781	+	0.814908i	0.269286	+	0.0387174i	−0.00634920	+	0.999980i	$0.502021\pi$
$444$	8.37824	+	3.08811i	0.397614	+	0.146555i
$445$	18.5259	+	11.9059i	0.878213	+	0.564393i
$446$	18.5990	−	20.0543i	0.880688	−	0.949597i
$447$	−6.98410	−	2.05072i	−0.330337	−	0.0969956i
$448$	0.116164	−	0.0448668i	0.00548821	−	0.00211976i
$449$	−3.74565	−	4.32271i	−0.176768	−	0.204001i	0.660451	−	0.750869i	$-0.270365\pi$
$449$	−3.74565	−	4.32271i	−0.176768	−	0.204001i	−0.837219	+	0.546868i	$0.815820\pi$
$450$	3.01139	−	4.35516i	0.141958	−	0.205304i
$451$	4.01460	−	8.79076i	0.189040	−	0.413941i
$452$	−15.4095	+	5.81536i	−0.724804	+	0.273532i
$453$	−21.8166	+	6.40594i	−1.02503	+	0.300977i
$454$	28.8526	+	14.3730i	1.35412	+	0.674556i
$455$	−0.270015	+	0.123312i	−0.0126585	+	0.00578095i
$456$	13.0329	−	12.2758i	0.610321	−	0.574866i
$457$	7.72687	+	12.0232i	0.361448	+	0.562424i	0.973584	−	0.228329i	$-0.0733261\pi$
$457$	7.72687	+	12.0232i	0.361448	+	0.562424i	−0.612136	+	0.790752i	$0.709690\pi$
$458$	5.73987	−	3.42063i	0.268207	−	0.159836i
$459$	−0.423671			−0.0197753
$460$	21.8728	+	18.0564i	1.01983	+	0.841882i
$461$	−5.63734			−0.262557			−0.131279	−	0.991346i	$-0.541908\pi$
$461$	−5.63734			−0.262557			−0.131279	+	0.991346i	$0.541908\pi$
$462$	−0.0274388	+	0.0163519i	−0.00127657	+	0.000760759i
$463$	−5.48010	−	8.52719i	−0.254682	−	0.396292i	0.690244	−	0.723576i	$-0.257503\pi$
$463$	−5.48010	−	8.52719i	−0.254682	−	0.396292i	−0.944926	+	0.327284i	$0.893867\pi$
$464$	−3.11620	+	1.45232i	−0.144666	+	0.0674222i
$465$	−7.52806	+	3.43795i	−0.349106	+	0.159431i
$466$	−33.5179	−	16.6970i	−1.55269	−	0.773473i
$467$	10.9225	−	3.20712i	0.505431	−	0.148408i	−0.0190694	−	0.999818i	$-0.506070\pi$
$467$	10.9225	−	3.20712i	0.505431	−	0.148408i	0.524500	+	0.851410i	$0.324252\pi$
$468$	−4.55403	−	12.0673i	−0.210510	−	0.557810i
$469$	−0.0507524	+	0.111132i	−0.00234353	+	0.00513161i
$470$	−16.2892	+	23.5579i	−0.751366	+	1.08665i
$471$	11.6923	+	13.4936i	0.538752	+	0.621753i
$472$	4.25183	−	17.0707i	0.195706	−	0.785741i
$473$	3.62843	+	1.06540i	0.166836	+	0.0489873i
$474$	8.83862	−	9.53019i	0.405971	−	0.437736i
$475$	19.9376	+	12.8131i	0.914800	+	0.587906i
$476$	0.00456154	−	0.0123757i	0.000209078	−	0.000567241i
$477$	−12.9022	−	1.85506i	−0.590751	−	0.0849372i
$478$	2.32955	+	21.2812i	0.106551	+	0.973377i
$479$	−5.94657	−	41.3593i	−0.271706	−	1.88976i	−0.430729	−	0.902481i	$-0.641744\pi$
$479$	−5.94657	−	41.3593i	−0.271706	−	1.88976i	0.159024	−	0.987275i	$-0.449165\pi$
$480$	−14.3028	+	8.67407i	−0.652831	+	0.395915i
$481$	21.7598	+	18.8550i	0.992162	+	0.859713i
$482$	41.1030	+	13.5923i	1.87219	+	0.619111i
$483$	0.0726129	−	0.0173260i	0.00330400	−	0.000788362i
$484$	14.2820	+	10.6056i	0.649183	+	0.482071i
$485$	18.2570	−	21.0697i	0.829007	−	0.956725i
$486$	1.36961	−	0.352390i	0.0621266	−	0.0159847i
$487$	−12.5249	+	1.80080i	−0.567556	+	0.0816023i	−0.420119	−	0.907469i	$-0.638012\pi$
$487$	−12.5249	+	1.80080i	−0.567556	+	0.0816023i	−0.147437	+	0.989071i	$0.547103\pi$
$488$	−0.944054	+	1.61233i	−0.0427353	+	0.0729869i
$489$	−0.395234	+	2.74892i	−0.0178731	+	0.124310i
$490$	−29.2555	−	0.988291i	−1.32163	−	0.0446465i
$491$	7.82846	−	12.1813i	0.353293	−	0.549735i	−0.618435	−	0.785836i	$-0.712233\pi$
$491$	7.82846	−	12.1813i	0.353293	−	0.549735i	0.971729	+	0.236100i	$0.0758694\pi$
$492$	−6.42896	−	11.6664i	−0.289840	−	0.525962i
$493$	−0.102592	+	0.349396i	−0.00462051	+	0.0157360i
$494$	53.2940	−	22.1958i	2.39781	−	0.998635i
$495$	3.24267	−	2.80979i	0.145747	−	0.126291i
$496$	11.1946	−	0.0864830i	0.502652	−	0.00388320i
$497$	0.135815	+	0.0620244i	0.00609211	+	0.00278217i
$498$	11.8025	+	14.5882i	0.528882	+	0.653714i
$499$	−1.34502	−	4.58072i	−0.0602114	−	0.205061i	0.923893	−	0.382650i	$-0.124989\pi$
$499$	−1.34502	−	4.58072i	−0.0602114	−	0.205061i	−0.984105	+	0.177589i	$0.943170\pi$
$500$	5.27245	+	5.23187i	0.235791	+	0.233977i
$501$	5.59476	+	12.2508i	0.249955	+	0.547326i
$502$	24.5430	+	4.37911i	1.09541	+	0.195449i
$503$	32.3175	−	20.7692i	1.44096	−	0.926052i	0.441378	−	0.897321i	$-0.354490\pi$
$503$	32.3175	−	20.7692i	1.44096	−	0.926052i	0.999587	−	0.0287304i	$-0.00914644\pi$
$504$	−0.00445256	+	0.0438013i	−0.000198333	+	0.00195106i
$505$		−	22.9521i		−	1.02135i
$506$	5.78881	+	7.95856i	0.257344	+	0.353801i
$507$		−	28.5896i		−	1.26971i
$508$	4.25058	+	19.1826i	0.188589	+	0.851089i
$509$	−16.9245	+	10.8767i	−0.750167	+	0.482103i	−0.859012	−	0.511956i	$-0.828921\pi$
$509$	−16.9245	+	10.8767i	−0.750167	+	0.482103i	0.108845	+	0.994059i	$0.465285\pi$
$510$	−0.311210	+	1.74419i	−0.0137806	+	0.0772342i
$511$	−0.100021	−	0.219014i	−0.00442465	−	0.00968863i
$512$	22.4523	−	2.80943i	0.992262	−	0.124160i
$513$	1.78337	+	6.07359i	0.0787376	+	0.268156i
$514$	−18.3322	+	14.8315i	−0.808597	+	0.654189i
$515$	−34.1095	−	15.5773i	−1.50304	−	0.686417i
$516$	4.16065	−	3.13978i	0.183163	−	0.138221i
$517$	−7.51045	+	6.50784i	−0.330309	+	0.286214i
$518$	−0.0377862	−	0.0907278i	−0.00166023	−	0.00398635i
$519$	2.55142	−	8.68935i	0.111995	−	0.381420i
$520$	−53.0245	+	9.88423i	−2.32528	+	0.433452i
$521$	13.5322	−	21.0565i	0.592857	−	0.922503i	−0.407102	−	0.913383i	$-0.633461\pi$
$521$	13.5322	−	21.0565i	0.592857	−	0.922503i	0.999958	−	0.00912026i	$-0.00290311\pi$
$522$	0.0410386	−	1.21483i	0.00179621	−	0.0531716i
$523$	3.33361	−	23.1858i	0.145769	−	1.01384i	−0.777279	−	0.629157i	$-0.783400\pi$
$523$	3.33361	−	23.1858i	0.145769	−	1.01384i	0.923047	−	0.384687i	$-0.125690\pi$
$524$	−23.6102	−	5.04066i	−1.03142	−	0.220202i
$525$	−0.0576864	+	0.00829405i	−0.00251764	+	0.000361982i
$526$	−10.0309	−	38.9865i	−0.437370	−	1.69989i
$527$	0.776495	−	0.896123i	0.0338247	−	0.0390357i
$528$	−5.55612	+	1.67815i	−0.241799	+	0.0730322i
$529$	−7.35843	−	21.7911i	−0.319932	−	0.947441i
$530$	−17.1144	+	51.7539i	−0.743402	+	2.24805i
$531$	4.70060	+	4.07309i	0.203988	+	0.176757i
$532$	−0.196615	−	0.0132990i	−0.00852434	−	0.000576587i
$533$	−6.11272	−	42.5149i	−0.264771	−	1.84152i
$534$	10.4695	−	1.14604i	0.453059	−	0.0495941i
$535$	−19.9412	−	2.86712i	−0.862135	−	0.123956i
$536$	−13.8292	+	17.3660i	−0.597330	+	0.750096i
$537$	−3.97877	−	2.55700i	−0.171696	−	0.110343i
$538$	−13.4493	−	12.4734i	−0.579842	−	0.537765i
$539$	−9.74526	−	2.86147i	−0.419758	−	0.123252i
$540$	−0.444687	−	5.89733i	−0.0191363	−	0.253781i
$541$	−18.2864	−	21.1036i	−0.786193	−	0.907315i	0.211348	−	0.977411i	$-0.432215\pi$
$541$	−18.2864	−	21.1036i	−0.786193	−	0.907315i	−0.997540	+	0.0700962i	$0.977669\pi$
$542$	17.8596	+	12.3491i	0.767136	+	0.530439i
$543$	−7.89531	+	17.2883i	−0.338820	+	0.741913i
$544$	1.34779	−	1.98176i	0.0577859	−	0.0849673i
$545$	−28.6916	+	8.42461i	−1.22901	+	0.360871i
$546$	−0.0633007	+	0.127071i	−0.00270902	+	0.00543814i
$547$	30.1126	−	13.7520i	1.28752	−	0.587991i	0.350271	−	0.936649i	$-0.386090\pi$
$547$	30.1126	−	13.7520i	1.28752	−	0.587991i	0.937250	+	0.348657i	$0.113362\pi$
$548$	−15.2940	−	8.27460i	−0.653325	−	0.353473i
$549$	−0.357133	−	0.555710i	−0.0152421	−	0.0237171i
$550$	−3.93312	−	6.59984i	−0.167709	−	0.281418i
$551$	5.44066			0.231780
$552$	13.5640	+	0.133975i	0.577322	+	0.00570236i
$553$	−0.143065			−0.00608373
$554$	−7.64695	−	12.8317i	−0.324888	−	0.545167i
$555$	7.13756	+	11.1063i	0.302973	+	0.471435i
$556$	30.0943	+	16.2822i	1.27628	+	0.690517i
$557$	−12.6935	+	5.79691i	−0.537839	+	0.245623i	−0.665766	−	0.746161i	$-0.731895\pi$
$557$	−12.6935	+	5.79691i	−0.537839	+	0.245623i	0.127927	+	0.991784i	$0.459168\pi$
$558$	−1.76483	+	3.54276i	−0.0747113	+	0.149977i
$559$	16.1266	−	4.73520i	0.682083	−	0.200278i
$560$	0.177053	+	0.0505051i	0.00748185	+	0.00213423i
$561$	−0.255376	+	0.559195i	−0.0107820	+	0.0236092i
$562$	−12.7136	−	8.79087i	−0.536291	−	0.370820i
$563$	0.515268	+	0.594651i	0.0217160	+	0.0250616i	0.766504	−	0.642240i	$-0.221995\pi$
$563$	0.515268	+	0.594651i	0.0217160	+	0.0250616i	−0.744788	+	0.667301i	$0.767449\pi$
$564$	1.02995	+	13.6590i	0.0433688	+	0.575146i
$565$	−23.3653	−	6.86067i	−0.982985	−	0.288630i
$566$	−10.2168	−	9.47539i	−0.429443	−	0.398280i
$567$	−0.0130949	−	0.00841555i	−0.000549932	−	0.000353420i
$568$	21.2229	+	16.9006i	0.890493	+	0.709134i
$569$	−29.1298	−	4.18823i	−1.22118	−	0.175580i	−0.498580	−	0.866844i	$-0.666145\pi$
$569$	−29.1298	−	4.18823i	−1.22118	−	0.175580i	−0.722602	+	0.691264i	$0.757054\pi$
$570$	26.3141	−	2.88048i	1.10218	−	0.120650i
$571$	−4.78589	−	33.2866i	−0.200283	−	1.39300i	−0.803443	−	0.595382i	$-0.797001\pi$
$571$	−4.78589	−	33.2866i	−0.200283	−	1.39300i	0.603160	−	0.797620i	$-0.293908\pi$
$572$	−18.6724	−	1.26300i	−0.780732	−	0.0528088i
$573$	−0.924359	−	0.800962i	−0.0386157	−	0.0334607i
$574$	−0.0460324	+	0.139202i	−0.00192136	+	0.00581018i
$575$	4.16742	+	17.4656i	0.173794	+	0.728364i
$576$	−2.70867	+	7.52749i	−0.112861	+	0.313645i
$577$	17.9605	−	20.7275i	0.747705	−	0.862898i	−0.246639	−	0.969108i	$-0.579326\pi$
$577$	17.9605	−	20.7275i	0.747705	−	0.862898i	0.994344	+	0.106210i	$0.0338715\pi$
$578$	5.92738	+	23.0375i	0.246546	+	0.958232i
$579$	−6.45351	+	0.927874i	−0.268199	+	0.0385611i
$580$	−4.97113	−	1.06131i	−0.206415	−	0.0440685i
$581$	0.0293935	−	0.204436i	0.00121945	−	0.00848145i
$582$	0.450162	−	13.3257i	0.0186598	−	0.552369i
$583$	−10.2255	+	15.9112i	−0.423497	+	0.658974i
$584$	−8.01728	−	43.0091i	−0.331757	−	1.77973i
$585$	5.37262	−	18.2975i	0.222130	−	0.756507i
$586$	−3.25129	−	7.80663i	−0.134310	−	0.322489i
$587$	−18.8445	+	16.3288i	−0.777795	+	0.673963i	−0.950401	−	0.311028i	$-0.899327\pi$
$587$	−18.8445	+	16.3288i	−0.777795	+	0.673963i	0.172606	+	0.984991i	$0.444781\pi$
$588$	−11.1747	+	8.43282i	−0.460837	+	0.347764i
$589$	−16.1150	−	7.35948i	−0.664007	−	0.303242i
$590$	20.2212	−	16.3598i	0.832493	−	0.673522i
$591$	1.51477	+	5.15884i	0.0623094	+	0.212206i
$592$	−2.67801	−	17.6566i	−0.110065	−	0.725680i
$593$	−8.51293	−	18.6407i	−0.349584	−	0.765483i	−0.999983	−	0.00588955i	$-0.998125\pi$
$593$	−8.51293	−	18.6407i	−0.349584	−	0.765483i	0.650398	−	0.759593i	$-0.274602\pi$
$594$	0.360444	−	2.02013i	0.0147892	−	0.0828868i
$595$	0.0164054	−	0.0105431i	0.000672555	−	0.000432225i
$596$	3.14943	+	14.2131i	0.129006	+	0.582193i
$597$		−	1.78634i		−	0.0731101i
$598$	40.7676	+	15.8469i	1.66711	+	0.648028i
$599$		−	1.56257i		−	0.0638447i	−0.999490	−	0.0319223i	$-0.989837\pi$
$599$		−	1.56257i		−	0.0638447i	0.999490	−	0.0319223i	$-0.0101629\pi$
$600$	−10.5355	−	1.07097i	−0.430110	−	0.0437223i
$601$	14.4716	−	9.30036i	0.590311	−	0.379370i	−0.211117	−	0.977461i	$-0.567710\pi$
$601$	14.4716	−	9.30036i	0.590311	−	0.379370i	0.801428	+	0.598091i	$0.204074\pi$
$602$	−0.0564797	−	0.0100775i	−0.00230194	−	0.000410727i
$603$	−3.26049	−	7.13948i	−0.132777	−	0.290742i
$604$	32.2799	+	32.0315i	1.31345	+	1.30334i
$605$	7.41002	+	25.2362i	0.301260	+	1.02600i
$606$	−6.90417	−	8.53377i	−0.280463	−	0.346661i
$607$	43.6570	+	19.9375i	1.77198	+	0.809237i	0.980084	+	0.198581i	$0.0636334\pi$
$607$	43.6570	+	19.9375i	1.77198	+	0.809237i	0.791897	+	0.610655i	$0.209094\pi$
$608$	−34.0831	−	10.9795i	−1.38225	−	0.445278i
$609$	−0.0101111	+	0.00876134i	−0.000409723	+	0.000355027i
$610$	−2.55011	+	1.06207i	−0.103251	+	0.0430018i
$611$	−12.4437	+	42.3792i	−0.503417	+	1.71448i
$612$	0.408957	+	0.742120i	0.0165311	+	0.0299984i
$613$	18.0815	−	28.1353i	0.730303	−	1.13637i	−0.255228	−	0.966881i	$-0.582151\pi$
$613$	18.0815	−	28.1353i	0.730303	−	1.13637i	0.985531	−	0.169493i	$-0.0542131\pi$
$614$	7.27100	+	0.245625i	0.293434	+	0.00991261i
$615$	2.80284	−	19.4942i	0.113021	−	0.786081i
$616$	0.0551285	+	0.0322789i	0.00222119	+	0.00130055i
$617$	5.08452	−	0.731043i	0.204695	−	0.0294307i	−0.0392045	−	0.999231i	$-0.512482\pi$
$617$	5.08452	−	0.731043i	0.204695	−	0.0294307i	0.243900	+	0.969801i	$0.421573\pi$
$618$	−17.3680	+	4.46865i	−0.698642	+	0.179756i
$619$	−14.5755	+	16.8210i	−0.585837	+	0.676092i	−0.968849	−	0.247651i	$-0.920341\pi$
$619$	−14.5755	+	16.8210i	−0.585837	+	0.676092i	0.383012	+	0.923743i	$0.374887\pi$
$620$	13.2887	+	9.86792i	0.533686	+	0.396305i
$621$	−2.21364	+	4.25439i	−0.0888301	+	0.170723i
$622$	−20.3213	−	6.72001i	−0.814810	−	0.269448i
$623$	−0.0876089	−	0.0759136i	−0.00350998	−	0.00304141i
$624$	−16.7417	+	19.6252i	−0.670204	+	0.785638i
$625$	4.22708	+	29.4000i	0.169083	+	1.17600i
$626$	−0.100414	−	0.917315i	−0.00401335	−	0.0366633i
$627$	9.09137	+	1.30714i	0.363074	+	0.0522022i
$628$	12.3498	−	33.5057i	0.492809	−	1.33702i
$629$	−1.59126	−	1.02264i	−0.0634476	−	0.0407753i
$630$	−0.0442646	+	0.0477280i	−0.00176354	+	0.00190153i
$631$	−15.2034	−	4.46413i	−0.605238	−	0.177714i	−0.0352662	−	0.999378i	$-0.511228\pi$
$631$	−15.2034	−	4.46413i	−0.605238	−	0.177714i	−0.569972	+	0.821664i	$0.693046\pi$
$632$	−25.2251	−	6.28289i	−1.00340	−	0.249920i
$633$	−2.03964	−	2.35386i	−0.0810682	−	0.0935577i
$634$	−10.4648	+	15.1345i	−0.415610	+	0.601066i
$635$	−12.0677	+	26.4245i	−0.478892	+	1.04863i
$636$	9.20472	+	24.3907i	0.364991	+	0.967153i
$637$	−43.3129	+	12.7178i	−1.71612	+	0.503898i
$638$	−1.57869	−	0.786427i	−0.0625010	−	0.0311349i
$639$	−8.72514	+	3.98464i	−0.345161	+	0.157630i
$640$	29.0000	+	16.6806i	1.14632	+	0.659358i
$641$	7.86569	+	12.2392i	0.310676	+	0.483421i	0.961119	−	0.276134i	$-0.0890532\pi$
$641$	7.86569	+	12.2392i	0.310676	+	0.483421i	−0.650443	+	0.759555i	$0.725417\pi$
$642$	−8.27677	+	4.93247i	−0.326658	+	0.194669i
$643$	18.6471			0.735371			0.367686	−	0.929950i	$-0.380150\pi$
$643$	18.6471			0.735371			0.367686	+	0.929950i	$0.380150\pi$
$644$	−0.100440	−	0.110468i	−0.00395790	−	0.00435303i
$645$	7.70664			0.303449
$646$	−3.25803	+	1.94159i	−0.128185	+	0.0763910i
$647$	−21.7624	−	33.8629i	−0.855567	−	1.33129i	−0.942201	−	0.335048i	$-0.891247\pi$
$647$	−21.7624	−	33.8629i	−0.855567	−	1.33129i	0.0866338	−	0.996240i	$-0.472389\pi$
$648$	−1.93930	−	2.05891i	−0.0761830	−	0.0808816i
$649$	8.20936	−	3.74909i	0.322246	−	0.147165i
$650$	−30.5644	−	15.2257i	−1.19883	−	0.597201i
$651$	0.0418000	−	0.0122736i	0.00163827	−	0.000481040i
$652$	5.19663	−	1.96114i	0.203516	−	0.0768042i
$653$	−12.7578	+	27.9357i	−0.499251	+	1.09321i	0.477461	+	0.878653i	$0.341557\pi$
$653$	−12.7578	+	27.9357i	−0.499251	+	1.09321i	−0.976712	+	0.214554i	$0.931170\pi$
$654$	−8.13357	+	11.7630i	−0.318048	+	0.459970i
$655$	−23.3751	−	26.9764i	−0.913342	−	1.05405i
$656$	−14.2297	+	22.5225i	−0.555576	+	0.879356i
$657$	14.8414	+	4.35783i	0.579018	+	0.170015i
$658$	0.102522	−	0.110544i	0.00399674	−	0.00430946i
$659$	−11.3831	−	7.31549i	−0.443424	−	0.284971i	0.299815	−	0.953997i	$-0.403075\pi$
$659$	−11.3831	−	7.31549i	−0.443424	−	0.284971i	−0.743239	+	0.669026i	$0.766711\pi$
$660$	−8.05181	−	2.96779i	−0.313416	−	0.115521i
$661$	21.3570	+	3.07067i	0.830691	+	0.119435i	0.544525	−	0.838745i	$-0.316710\pi$
$661$	21.3570	+	3.07067i	0.830691	+	0.119435i	0.286166	+	0.958180i	$0.407619\pi$
$662$	−3.68702	−	33.6821i	−0.143300	−	1.30909i
$663$	0.388840	+	2.70444i	0.0151013	+	0.105032i
$664$	14.1608	−	34.7553i	0.549544	−	1.34877i
$665$	−0.220197	−	0.190802i	−0.00853889	−	0.00739899i
$666$	5.99466	+	1.98236i	0.232288	+	0.0768150i
$667$	2.97251	+	2.85576i	0.115096	+	0.110575i
$668$	16.0586	−	21.6254i	0.621325	−	0.836711i
$669$	12.6652	−	14.6164i	0.489666	−	0.565104i
$670$	−31.7873	+	8.17864i	−1.22805	+	0.315968i
$671$	−0.948739	+	0.136408i	−0.0366257	+	0.00526597i
$672$	0.0810221	−	0.0344808i	0.00312549	−	0.00133013i
$673$	−6.74782	+	46.9321i	−0.260109	+	1.80910i	0.271862	+	0.962336i	$0.412361\pi$
$673$	−6.74782	+	46.9321i	−0.260109	+	1.80910i	−0.531971	+	0.846763i	$0.678548\pi$
$674$	−11.5733	−	0.390963i	−0.445788	−	0.0150593i
$675$	2.02419	−	3.14970i	0.0779111	−	0.121232i
$676$	−50.0788	+	27.5967i	−1.92611	+	1.06141i
$677$	8.98562	−	30.6022i	0.345346	−	1.17614i	−0.585484	−	0.810684i	$-0.699095\pi$
$677$	8.98562	−	30.6022i	0.345346	−	1.17614i	0.930829	−	0.365455i	$-0.119086\pi$
$678$	−10.7511	+	4.47762i	−0.412895	+	0.171962i
$679$	−0.110911	+	0.0961052i	−0.00425638	+	0.00368818i
$680$	3.35561	−	1.13849i	0.128682	−	0.0436592i
$681$	20.7334	+	9.46861i	0.794504	+	0.362838i
$682$	3.61223	+	4.46483i	0.138320	+	0.170967i
$683$	2.14130	+	7.29260i	0.0819346	+	0.279044i	0.990262	−	0.139216i	$-0.0444583\pi$
$683$	2.14130	+	7.29260i	0.0819346	+	0.279044i	−0.908327	+	0.418260i	$0.862640\pi$
$684$	8.91733	−	8.98648i	0.340963	−	0.343607i
$685$	−10.6802	−	23.3865i	−0.408071	−	0.893551i
$686$	0.303392	+	0.0541331i	0.0115836	+	0.00206681i
$687$	3.97473	−	2.55440i	0.151645	−	0.0974565i
$688$	−9.51592	−	4.25724i	−0.362791	−	0.162306i
$689$			84.0619i			3.20250i
$690$	15.8887	+	12.2383i	0.604872	+	0.465905i
$691$		−	24.4954i		−	0.931849i	−0.884824	−	0.465925i	$-0.845722\pi$
$691$		−	24.4954i		−	0.931849i	0.884824	−	0.465925i	$-0.154278\pi$
$692$	−17.6835	+	3.91840i	−0.672224	+	0.148955i
$693$	−0.0190007	+	0.0122110i	−0.000721777	+	0.000463858i
$694$	2.63011	−	14.7406i	0.0998376	−	0.559545i
$695$	21.0158	+	46.0182i	0.797174	+	1.74557i
$696$	−2.16756	+	1.10075i	−0.0821611	+	0.0417240i
$697$	0.794983	+	2.70746i	0.0301121	+	0.102552i
$698$	19.8065	−	16.0243i	0.749687	−	0.606528i
$699$	−24.0858	−	10.9996i	−0.911010	−	0.416045i
$700$	0.0702112	+	0.0930399i	0.00265373	+	0.00351658i
$701$	6.57056	−	5.69342i	0.248167	−	0.215038i	−0.521891	−	0.853012i	$-0.674773\pi$
$701$	6.57056	−	5.69342i	0.248167	−	0.215038i	0.770057	+	0.637975i	$0.220228\pi$
$702$	−3.50644	−	8.41927i	−0.132342	−	0.317765i
$703$	−7.96206	+	27.1163i	−0.300295	+	1.02271i
$704$	8.30268	+	8.11246i	0.312919	+	0.305750i
$705$	−10.9492	+	17.0374i	−0.412373	+	0.641664i
$706$	0.795289	−	23.5422i	0.0299311	−	0.886022i
$707$	−0.0171945	+	0.119590i	−0.000646666	+	0.00449766i
$708$	2.59725	−	12.1654i	0.0976105	−	0.457204i
$709$	5.22323	−	0.750988i	0.196163	−	0.0282039i	−0.0435331	−	0.999052i	$-0.513861\pi$
$709$	5.22323	−	0.750988i	0.196163	−	0.0282039i	0.239696	+	0.970848i	$0.422952\pi$
$710$	9.99509	+	38.8471i	0.375109	+	1.45791i
$711$	6.01877	−	6.94603i	0.225721	−	0.260496i
$712$	−12.1133	−	17.2325i	−0.453967	−	0.645817i
$713$	−4.94152	−	12.4795i	−0.185061	−	0.467361i
$714$	0.00292820	−	0.00885488i	0.000109585	−	0.000331385i
$715$	−20.9120	−	18.1204i	−0.782065	−	0.677663i
$716$	−0.638358	+	9.43757i	−0.0238566	+	0.352699i
$717$	2.15435	+	14.9839i	0.0804558	+	0.559582i
$718$	−31.5381	+	3.45232i	−1.17699	+	0.128840i
$719$	−38.0449	−	5.47004i	−1.41884	−	0.203998i	−0.610173	−	0.792268i	$-0.708900\pi$
$719$	−38.0449	−	5.47004i	−1.41884	−	0.203998i	−0.808664	+	0.588271i	$0.799809\pi$
$720$	−9.90077	+	6.47145i	−0.368980	+	0.241177i
$721$	0.166056	+	0.106718i	0.00618424	+	0.00397437i
$722$	21.8466	+	20.2613i	0.813048	+	0.754048i
$723$	29.3721	+	8.62444i	1.09236	+	0.320746i
$724$	37.9041	−	2.85815i	1.40869	−	0.106222i
$725$	−2.10736	−	2.43202i	−0.0782654	−	0.0903231i
$726$	10.3464	+	7.15403i	0.383989	+	0.265511i
$727$	−8.60712	+	18.8470i	−0.319220	+	0.698995i	−0.999421	−	0.0340310i	$-0.989166\pi$
$727$	−8.60712	+	18.8470i	−0.319220	+	0.698995i	0.680200	+	0.733026i	$0.261893\pi$
$728$	0.283686	−	0.0117780i	0.0105141	−	0.000436521i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	28.8424	−	57.8989i	1.06751	−	2.14294i
$731$	−1.00439	+	0.458690i	−0.0371488	+	0.0169653i
$732$	−0.628675	+	1.16198i	−0.0232365	+	0.0429480i
$733$	−14.6774	−	22.8385i	−0.542122	−	0.843559i	0.456819	−	0.889560i	$-0.348989\pi$
$733$	−14.6774	−	22.8385i	−0.542122	−	0.843559i	−0.998941	+	0.0460008i	$0.985352\pi$
$734$	−20.2143	−	33.9199i	−0.746122	−	1.25200i
$735$	−20.6985			−0.763477
$736$	−12.8583	−	23.8886i	−0.473962	−	0.880545i
$737$	−11.3886			−0.419504
$738$	−4.82189	−	8.09121i	−0.177496	−	0.297842i
$739$	5.60813	+	8.72642i	0.206298	+	0.321007i	0.928950	−	0.370206i	$-0.120713\pi$
$739$	5.60813	+	8.72642i	0.206298	+	0.321007i	−0.722651	+	0.691213i	$0.757077\pi$
$740$	12.5645	−	23.2230i	0.461881	−	0.853695i
$741$	37.1332	−	16.9581i	1.36412	−	0.622973i
$742$	0.127945	−	0.256839i	0.00469700	−	0.00942887i
$743$	−8.97622	+	2.63565i	−0.329305	+	0.0966928i	−0.442206	−	0.896913i	$-0.645804\pi$
$743$	−8.97622	+	2.63565i	−0.329305	+	0.0966928i	0.112901	+	0.993606i	$0.463986\pi$
$744$	7.90919	−	0.328371i	0.289965	−	0.0120387i
$745$	−8.94144	+	19.5790i	−0.327589	+	0.717320i
$746$	1.47630	+	1.02079i	0.0540510	+	0.0373738i
$747$	8.68913	+	10.0278i	0.317919	+	0.366898i
$748$	1.22602	−	0.0924477i	0.0448276	−	0.00338022i
$749$	0.101755	+	0.0298779i	0.00371804	+	0.00109171i
$750$	3.85096	+	3.57151i	0.140617	+	0.130413i
$751$	31.9260	+	20.5176i	1.16500	+	0.748699i	0.972570	−	0.232612i	$-0.0747273\pi$
$751$	31.9260	+	20.5176i	1.16500	+	0.748699i	0.192429	+	0.981311i	$0.438364\pi$
$752$	22.9314	−	14.9887i	0.836224	−	0.546582i
$753$	17.4491	+	2.50881i	0.635882	+	0.0914260i
$754$	−7.79235	+	0.852991i	−0.283781	+	0.0310641i
$755$	9.56869	+	66.5517i	0.348240	+	2.42206i
$756$	−0.00210095	+	0.0310608i	−7.64110e−5	+	0.00112967i
$757$	−7.46438	−	6.46792i	−0.271297	−	0.235081i	0.508577	−	0.861016i	$-0.330172\pi$
$757$	−7.46438	−	6.46792i	−0.271297	−	0.235081i	−0.779875	+	0.625936i	$0.784717\pi$
$758$	−5.56344	+	16.8238i	−0.202073	+	0.611070i
$759$	4.28097	+	5.48615i	0.155389	+	0.199135i
$760$	−30.4458	−	43.3125i	−1.10439	−	1.57111i
$761$	4.74910	−	5.48075i	0.172155	−	0.198677i	−0.663115	−	0.748517i	$-0.730766\pi$
$761$	4.74910	−	5.48075i	0.172155	−	0.198677i	0.835270	+	0.549840i	$0.185311\pi$
$762$	3.46186	+	13.4549i	0.125410	+	0.487420i
$763$	0.155807	−	0.0224017i	0.00564059	−	0.000810995i
$764$	−0.510742	+	2.39229i	−0.0184780	+	0.0865501i
$765$	−0.178294	+	1.24006i	−0.00644622	+	0.0448344i
$766$	−1.42975	+	42.3234i	−0.0516588	+	1.52921i
$767$	21.6858	−	33.7438i	0.783030	−	1.21842i
$768$	15.8001	−	2.52145i	0.570136	−	0.0909849i
$769$	6.10885	−	20.8048i	0.220291	−	0.750241i	−0.772981	−	0.634430i	$-0.781235\pi$
$769$	6.10885	−	20.8048i	0.220291	−	0.750241i	0.993271	−	0.115811i	$-0.0369468\pi$
$770$	0.0363139	+	0.0871929i	0.00130866	+	0.00314221i
$771$	−12.6013	+	10.9191i	−0.453826	+	0.393242i
$772$	7.85469	+	10.4086i	0.282696	+	0.374613i
$773$	35.3612	+	16.1489i	1.27185	+	0.580836i	0.932957	−	0.359987i	$-0.117219\pi$
$773$	35.3612	+	16.1489i	1.27185	+	0.580836i	0.338897	+	0.940824i	$0.389946\pi$
$774$	2.86539	−	2.31822i	0.102994	−	0.0833267i
$775$	2.95216	+	10.0541i	0.106045	+	0.361156i
$776$	−23.7765	+	12.0744i	−0.853525	+	0.433446i
$777$	−0.0288696	−	0.0632156i	−0.00103569	−	0.00226785i
$778$	8.44253	−	47.3166i	0.302680	−	1.69638i
$779$	35.4668	−	22.7931i	1.27073	−	0.816649i
$780$	−37.2366	+	8.25110i	−1.33329	+	0.295437i
$781$			13.9180i			0.498023i
$782$	−2.79915	−	0.649321i	−0.100097	−	0.0232197i
$783$		−	0.859503i		−	0.0307161i
$784$	25.5579	+	11.4341i	0.912782	+	0.408361i
$785$	44.4154	−	28.5441i	1.58525	−	1.01878i
$786$	−16.8058	−	2.99859i	−0.599442	−	0.106956i
$787$	−17.4468	−	38.2031i	−0.621910	−	1.36179i	−0.914122	−	0.405439i	$-0.867119\pi$
$787$	−17.4468	−	38.2031i	−0.621910	−	1.36179i	0.292212	−	0.956353i	$-0.405609\pi$
$788$	7.57428	−	7.63302i	0.269823	−	0.271915i
$789$	−8.01965	−	27.3124i	−0.285507	−	0.972348i
$790$	−24.1747	−	29.8807i	−0.860097	−	1.06311i
$791$	0.116604	+	0.0532511i	0.00414595	+	0.00189339i
$792$	−3.88646	+	1.31860i	−0.138100	+	0.0468544i
$793$	−3.21952	+	2.78973i	−0.114329	+	0.0990663i
$794$	13.0503	−	5.43514i	0.463136	−	0.192886i
$795$	−10.8593	+	36.9832i	−0.385138	+	1.31166i
$796$	−3.12903	+	1.72430i	−0.110906	+	0.0611163i
$797$	9.10616	−	14.1695i	0.322557	−	0.501908i	−0.641672	−	0.766979i	$-0.721759\pi$
$797$	9.10616	−	14.1695i	0.322557	−	0.501908i	0.964229	+	0.265071i	$0.0853954\pi$
$798$	−0.139266	−	0.00470460i	−0.00492996	−	0.000166541i
$799$	0.412950	−	2.87213i	0.0146091	−	0.101609i
$800$	8.29365	+	19.4882i	0.293225	+	0.689012i
$801$	7.37146	−	1.05986i	0.260458	−	0.0374482i
$802$	−13.2386	+	3.40620i	−0.467471	+	0.120277i
$803$	14.6978	−	16.9621i	0.518672	−	0.598580i
$804$	−9.35856	+	12.6027i	−0.330051	+	0.444465i
$805$	−0.0201545	−	0.219825i	−0.000710353	−	0.00774780i
$806$	24.2345	+	8.01405i	0.853622	+	0.282283i
$807$	−9.80248	−	8.49390i	−0.345064	−	0.298999i
$808$	−8.28371	+	20.3310i	−0.291420	+	0.715244i
$809$	6.34366	+	44.1211i	0.223031	+	1.55122i	0.726478	+	0.687189i	$0.241156\pi$
$809$	6.34366	+	44.1211i	0.223031	+	1.55122i	−0.503447	+	0.864026i	$0.667935\pi$
$810$	−0.455052	−	4.15705i	−0.0159889	−	0.146064i
$811$	7.36296	+	1.05863i	0.258549	+	0.0371737i	0.270370	−	0.962756i	$-0.412854\pi$
$811$	7.36296	+	1.05863i	0.258549	+	0.0371737i	−0.0118216	+	0.999930i	$0.503763\pi$
$812$	0.0251067	+	0.00925401i	0.000881073	+	0.000324752i
$813$	12.9163	+	8.30078i	0.452993	+	0.291121i
$814$	6.22988	−	6.71733i	0.218357	−	0.235442i
$815$	7.87958	+	2.31365i	0.276010	+	0.0810437i
$816$	0.905175	−	1.43269i	0.0316875	−	0.0501543i
$817$	10.8034	+	12.4678i	0.377964	+	0.436194i
$818$	4.73777	−	6.85189i	0.165652	−	0.239571i
$819$	−0.0417012	+	0.0913129i	−0.00145716	+	0.00319073i
$820$	−36.8523	+	13.9076i	−1.28694	+	0.485674i
$821$	−26.6862	+	7.83578i	−0.931356	+	0.273471i	−0.712004	−	0.702175i	$-0.752212\pi$
$821$	−26.6862	+	7.83578i	−0.931356	+	0.273471i	−0.219352	+	0.975646i	$0.570394\pi$
$822$	−11.0058	−	5.48257i	−0.383873	−	0.191227i
$823$	16.8508	−	7.69549i	0.587381	−	0.268248i	−0.0994764	−	0.995040i	$-0.531717\pi$
$823$	16.8508	−	7.69549i	0.587381	−	0.268248i	0.686858	+	0.726792i	$0.258990\pi$
$824$	24.5923	+	26.1090i	0.856713	+	0.909550i
$825$	−2.93711	−	4.57023i	−0.102257	−	0.159115i
$826$	−0.117617	+	0.0700930i	−0.00409243	+	0.00243885i
$827$	36.4148			1.26627			0.633133	−	0.774043i	$-0.281769\pi$
$827$	36.4148			1.26627			0.633133	+	0.774043i	$0.281769\pi$
$828$	9.58893	−	0.229139i	0.333238	−	0.00796313i
$829$	6.00574			0.208588			0.104294	−	0.994547i	$-0.466742\pi$
$829$	6.00574			0.208588			0.104294	+	0.994547i	$0.466742\pi$
$830$	47.6657	−	28.4060i	1.65450	−	0.985985i
$831$	−5.71047	−	8.88566i	−0.198094	−	0.308240i
$832$	50.5367	+	10.3818i	1.75204	+	0.359923i
$833$	2.69760	−	1.23195i	0.0934663	−	0.0426846i
$834$	21.6565	+	10.7882i	0.749902	+	0.373565i
$835$	38.2118	−	11.2200i	1.32237	−	0.388284i
$836$	−6.48599	−	17.1866i	−0.224323	−	0.594410i
$837$	−1.16263	+	2.54581i	−0.0401865	+	0.0879962i
$838$	−5.44334	+	7.87231i	−0.188037	+	0.271944i
$839$	20.8181	+	24.0254i	0.718720	+	0.829447i	0.991153	−	0.132728i	$-0.0423735\pi$
$839$	20.8181	+	24.0254i	0.718720	+	0.829447i	−0.272432	+	0.962175i	$0.587828\pi$
$840$	0.126330	+	0.0314653i	0.00435879	+	0.00108565i
$841$	27.1165	+	7.96212i	0.935051	+	0.274556i
$842$	24.5105	−	26.4283i	0.844688	−	0.910780i
$843$	−9.19461	−	5.90902i	−0.316679	−	0.203517i
$844$	−2.15433	+	5.84483i	−0.0741550	+	0.201187i
$845$	−83.6800	−	12.0314i	−2.87868	−	0.413891i
$846$	1.05396	+	9.62825i	0.0362358	+	0.331026i
$847$	−0.0197038	−	0.137043i	−0.000677030	−	0.00470885i
$848$	33.8387	−	39.6670i	1.16202	−	1.36217i
$849$	−7.44645	−	6.45238i	−0.255561	−	0.221445i
$850$	2.12986	+	0.704319i	0.0730536	+	0.0241580i
$851$	−18.5832	+	10.6358i	−0.637024	+	0.364590i
$852$	15.4018	+	11.4371i	0.527656	+	0.391827i
$853$	−15.8252	+	18.2632i	−0.541843	+	0.625320i	−0.958963	−	0.283531i	$-0.908494\pi$
$853$	−15.8252	+	18.2632i	−0.541843	+	0.625320i	0.417120	+	0.908851i	$0.363040\pi$
$854$	0.0140829	−	0.00362342i	0.000481905	−	0.000123991i
$855$	18.5275	−	2.66385i	0.633628	−	0.0911019i
$856$	16.6292	+	9.73677i	0.568376	+	0.332796i
$857$	5.48437	−	38.1446i	0.187343	−	1.30300i	−0.651511	−	0.758639i	$-0.725865\pi$
$857$	5.48437	−	38.1446i	0.187343	−	1.30300i	0.838854	−	0.544357i	$-0.183226\pi$
$858$	−13.2260	−	0.446793i	−0.451528	−	0.0152533i
$859$	12.7876	−	19.8979i	0.436307	−	0.678907i	−0.551573	−	0.834127i	$-0.685972\pi$
$859$	12.7876	−	19.8979i	0.436307	−	0.678907i	0.987880	+	0.155220i	$0.0496086\pi$
$860$	−7.43900	−	13.4993i	−0.253668	−	0.460322i
$861$	−0.0292081	+	0.0994735i	−0.000995408	+	0.00339005i
$862$	22.5735	−	9.40137i	0.768856	−	0.320212i
$863$	11.3738	−	9.85541i	0.387167	−	0.335482i	−0.439430	−	0.898277i	$-0.644819\pi$
$863$	11.3738	−	9.85541i	0.387167	−	0.335482i	0.826597	+	0.562795i	$0.190274\pi$
$864$	−1.73452	+	5.38437i	−0.0590095	+	0.183180i
$865$	−24.3595	−	11.1246i	−0.828247	−	0.378248i
$866$	−3.97589	−	4.91432i	−0.135106	−	0.166996i
$867$	4.73888	+	16.1392i	0.160941	+	0.548114i
$868$	−0.0618473	−	0.0613714i	−0.00209924	−	0.00208308i
$869$	−5.54000	−	12.1309i	−0.187932	−	0.411513i
$870$	−3.53845	−	0.631354i	−0.119965	−	0.0214049i
$871$	−42.5814	+	27.3654i	−1.44282	+	0.927242i
$872$	28.4557	+	2.89263i	0.963631	+	0.0979567i
$873$		−	9.42809i		−	0.319093i
$874$	2.47411	+	42.8608i	0.0836879	+	1.44979i
$875$		−	0.0578096i		−	0.00195432i
$876$	−6.69262	−	30.2033i	−0.226123	−	1.02048i
$877$	11.1222	−	7.14782i	0.375571	−	0.241365i	−0.339214	−	0.940709i	$-0.610161\pi$
$877$	11.1222	−	7.14782i	0.375571	−	0.241365i	0.714785	+	0.699344i	$0.246525\pi$
$878$	−8.13523	+	45.5943i	−0.274551	+	1.53873i
$879$	−2.48407	−	5.43936i	−0.0837856	−	0.183465i
$880$	2.57367	+	16.9686i	0.0867583	+	0.572012i
$881$	12.2185	+	41.6123i	0.411651	+	1.40195i	0.861003	+	0.508600i	$0.169837\pi$
$881$	12.2185	+	41.6123i	0.411651	+	1.40195i	−0.449352	+	0.893355i	$0.648345\pi$
$882$	−7.69588	+	6.22629i	−0.259134	+	0.209650i
$883$	45.8628	+	20.9449i	1.54341	+	0.704850i	0.991626	−	0.129139i	$-0.0412214\pi$
$883$	45.8628	+	20.9449i	1.54341	+	0.704850i	0.551780	+	0.833989i	$0.313949\pi$
$884$	4.36188	−	3.29163i	0.146706	−	0.110710i
$885$	13.8998	−	12.0443i	0.467238	−	0.404864i
$886$	−3.11338	−	7.47550i	−0.104596	−	0.251144i
$887$	3.36062	−	11.4452i	0.112839	−	0.384293i	−0.883637	−	0.468172i	$-0.844913\pi$
$887$	3.36062	−	11.4452i	0.112839	−	0.384293i	0.996476	+	0.0838792i	$0.0267310\pi$
$888$	−2.31408	−	12.4140i	−0.0776555	−	0.416587i
$889$	0.0826738	−	0.128643i	0.00277279	−	0.00431455i
$890$	1.05147	−	31.1258i	0.0352455	−	1.04334i
$891$	0.206499	−	1.43624i	0.00691799	−	0.0481157i
$892$	−37.8281	−	8.07611i	−1.26658	−	0.270408i
$893$	−42.9121	+	6.16983i	−1.43600	+	0.206465i
$894$	2.56503	+	9.96929i	0.0857874	+	0.333423i
$895$	−9.15856	+	10.5695i	−0.306137	+	0.353301i
$896$	−0.138606	−	0.108638i	−0.00463051	−	0.00362935i
$897$	29.1889	+	10.2258i	0.974590	+	0.341430i
$898$	−2.53966	+	7.67993i	−0.0847496	+	0.256283i
$899$	1.81797	+	1.57528i	0.0606327	+	0.0525385i
$900$	−7.47104	−	0.505342i	−0.249035	−	0.0168447i
$901$	−0.785933	−	5.46629i	−0.0261832	−	0.182108i
$902$	−13.5859	+	1.48719i	−0.452362	+	0.0495178i
$903$	−0.0401550	−	0.00577341i	−0.00133627	−	0.000192127i
$904$	18.2210	+	14.5101i	0.606020	+	0.482597i
$905$	47.2792	+	30.3845i	1.57161	+	1.01002i
$906$	23.5770	+	21.8661i	0.783293	+	0.726453i
$907$	−14.2563	−	4.18602i	−0.473371	−	0.138994i	0.0363407	−	0.999339i	$-0.488430\pi$
$907$	−14.2563	−	4.18602i	−0.473371	−	0.138994i	−0.509712	+	0.860345i	$0.670248\pi$
$908$	−3.42770	−	45.4572i	−0.113752	−	1.50855i
$909$	−5.08293	−	5.86602i	−0.168590	−	0.194564i
$910$	0.345291	+	0.238752i	0.0114463	+	0.00791457i
$911$	−18.0333	+	39.4874i	−0.597470	+	1.30828i	0.333352	+	0.942802i	$0.391820\pi$
$911$	−18.0333	+	39.4874i	−0.597470	+	1.30828i	−0.930822	+	0.365474i	$0.880907\pi$
$912$	−24.3487	−	6.94558i	−0.806268	−	0.229991i
$913$	18.4730	−	5.42417i	0.611368	−	0.179514i
$914$	9.01232	−	18.0915i	0.298101	−	0.598415i
$915$	−1.77682	+	0.811446i	−0.0587398	+	0.0268256i
$916$	−8.31109	−	4.49661i	−0.274606	−	0.148572i
$917$	0.101585	+	0.158070i	0.00335465	+	0.00521993i
$918$	0.306729	+	0.514696i	0.0101236	+	0.0169875i
$919$	−52.6265			−1.73599			−0.867994	−	0.496575i	$-0.834591\pi$
$919$	−52.6265			−1.73599			−0.867994	+	0.496575i	$0.834591\pi$
$920$	6.10027	−	39.6446i	0.201120	−	1.30704i
$921$	5.14431			0.169511
$922$	4.08131	+	6.84851i	0.134411	+	0.225544i
$923$	33.4432	+	52.0386i	1.10080	+	1.71287i
$924$	0.0397302	+	0.0214955i	0.00130703	+	0.000707150i
$925$	15.2052	−	6.94400i	0.499945	−	0.228317i
$926$	−6.39177	+	12.8310i	−0.210047	+	0.421652i
$927$	−12.1673	+	3.57265i	−0.399627	+	0.117341i
$928$	4.02041	+	2.73426i	0.131976	+	0.0897565i
$929$	−11.9947	+	26.2647i	−0.393533	+	0.861717i	0.604352	+	0.796717i	$0.293432\pi$
$929$	−11.9947	+	26.2647i	−0.393533	+	0.861717i	−0.997885	+	0.0649996i	$0.979295\pi$
$930$	9.62674	+	6.65645i	0.315673	+	0.218274i
$931$	−29.0159	−	33.4861i	−0.950957	−	1.09746i
$932$	3.98194	+	52.8074i	0.130433	+	1.72976i
$933$	−14.5216	−	4.26392i	−0.475415	−	0.139594i
$934$	−11.8038	−	10.9472i	−0.386232	−	0.358204i
$935$	1.52926	+	0.982795i	0.0500121	+	0.0321408i
$936$	−11.3629	+	14.2689i	−0.371407	+	0.466394i
$937$	42.2194	+	6.07024i	1.37925	+	0.198306i	0.791714	−	0.610892i	$-0.209189\pi$
$937$	42.2194	+	6.07024i	1.37925	+	0.198306i	0.587535	+	0.809198i	$0.300098\pi$
$938$	0.171753	−	0.0188009i	0.00560792	−	0.000613872i
$939$	−0.0928624	−	0.645872i	−0.00303045	−	0.0210772i
$940$	40.4124	+	2.73349i	1.31811	+	0.0891568i
$941$	−23.7589	−	20.5872i	−0.774520	−	0.671125i	0.175093	−	0.984552i	$-0.443977\pi$
$941$	−23.7589	−	20.5872i	−0.774520	−	0.671125i	−0.949612	+	0.313427i	$0.898523\pi$
$942$	7.92773	−	23.9734i	0.258299	−	0.781097i
$943$	31.3413	+	6.16320i	1.02061	+	0.200701i
$944$	−23.8165	+	7.19346i	−0.775160	+	0.234127i
$945$	−0.0301425	+	0.0347863i	−0.000980536	+	0.00113160i
$946$	−1.33260	−	5.17933i	−0.0433267	−	0.168394i
$947$	−6.78608	+	0.975690i	−0.220518	+	0.0317057i	−0.251688	−	0.967808i	$-0.580986\pi$
$947$	−6.78608	+	0.975690i	−0.220518	+	0.0317057i	0.0311702	+	0.999514i	$0.490077\pi$
$948$	−17.9767	−	3.83793i	−0.583856	−	0.124650i
$949$	14.1963	−	98.7376i	0.460832	−	3.20516i
$950$	1.13160	−	33.4976i	0.0367138	−	1.08681i
$951$	−7.03419	+	10.9454i	−0.228099	+	0.354929i
$952$	−0.0183371	+	0.00341819i	−0.000594308	+	0.000110784i
$953$	−11.2703	+	38.3830i	−0.365080	+	1.24335i	0.548314	+	0.836272i	$0.315270\pi$
$953$	−11.2703	+	38.3830i	−0.365080	+	1.24335i	−0.913394	+	0.407076i	$0.866548\pi$
$954$	7.08730	+	17.0172i	0.229460	+	0.550953i
$955$	−2.73336	+	2.36847i	−0.0884496	+	0.0766420i
$956$	24.1668	−	18.2371i	0.781611	−	0.589831i
$957$	−1.13444	−	0.518082i	−0.0366713	−	0.0167472i
$958$	−45.9401	+	37.1674i	−1.48426	+	1.20083i
$959$	0.0381288	+	0.129855i	0.00123124	+	0.00419323i
$960$	20.8926	+	11.0959i	0.674306	+	0.358119i
$961$	9.62396	+	21.0735i	0.310450	+	0.679792i
$962$	7.15230	−	40.0855i	0.230599	−	1.29241i
$963$	−5.73147	+	3.68339i	−0.184694	+	0.118696i
$964$	−13.2451	−	59.7744i	−0.426597	−	1.92520i
$965$			19.2795i			0.620629i
$966$	−0.0736187	−	0.0756700i	−0.00236864	−	0.00243464i
$967$			42.0031i			1.35073i	0.737485	+	0.675364i	$0.236013\pi$
$967$			42.0031i			1.35073i	−0.737485	+	0.675364i	$0.763987\pi$
$968$	2.54426	−	25.0287i	0.0817757	−	0.804453i
$969$	−2.25611	+	1.44991i	−0.0724766	+	0.0465779i
$970$	−38.8141	−	6.92547i	−1.24625	−	0.222363i
$971$	−7.94977	−	17.4076i	−0.255120	−	0.558636i	0.738126	−	0.674663i	$-0.235711\pi$
$971$	−7.94977	−	17.4076i	−0.255120	−	0.558636i	−0.993246	+	0.116028i	$0.962984\pi$
$972$	−1.41967	−	1.40874i	−0.0455358	−	0.0451854i
$973$	−0.0750271	−	0.255519i	−0.00240526	−	0.00819155i
$974$	11.2554	+	13.9121i	0.360648	+	0.445772i
$975$	−21.9635	−	10.0304i	−0.703393	−	0.321229i
$976$	2.64221	−	0.0204122i	0.0845752	−	0.000653380i
$977$	−11.4135	+	9.88984i	−0.365150	+	0.316404i	−0.818039	−	0.575163i	$-0.804939\pi$
$977$	−11.4135	+	9.88984i	−0.365150	+	0.316404i	0.452889	+	0.891567i	$0.350393\pi$
$978$	3.62566	−	1.51001i	0.115936	−	0.0482847i
$979$	3.04440	−	10.3683i	0.0972996	−	0.331372i
$980$	19.9797	+	36.2564i	0.638228	+	1.15817i
$981$	−5.46720	+	8.50713i	−0.174554	+	0.271612i
$982$	−20.4661	−	0.691374i	−0.653099	−	0.0220626i
$983$	0.463793	−	3.22575i	0.0147927	−	0.102885i	−0.981087	−	0.193565i	$-0.937995\pi$
$983$	0.463793	−	3.22575i	0.0147927	−	0.102885i	0.995880	+	0.0906798i	$0.0289040\pi$
$984$	−9.51848	+	16.2564i	−0.303438	+	0.518236i
$985$	15.7371	−	2.26265i	0.501425	−	0.0720940i
$986$	0.498738	−	0.128322i	0.0158830	−	0.00408659i
$987$	0.0698139	−	0.0805695i	0.00222220	−	0.00256456i
$988$	−65.5482	−	48.6748i	−2.08537	−	1.54855i
$989$	−0.641797	+	12.4824i	−0.0204080	+	0.396918i
$990$	−5.76110	−	1.90513i	−0.183100	−	0.0605489i
$991$	−20.2006	−	17.5039i	−0.641692	−	0.556029i	0.272071	−	0.962277i	$-0.412291\pi$
$991$	−20.2006	−	17.5039i	−0.641692	−	0.556029i	−0.913763	+	0.406248i	$0.866837\pi$
$992$	−8.20970	−	13.5371i	−0.260658	−	0.429804i
$993$	−3.40974	−	23.7153i	−0.108205	−	0.752581i
$994$	−0.0229766	−	0.209898i	−0.000728772	−	0.00665757i
$995$	−5.22851	−	0.751746i	−0.165755	−	0.0238320i
$996$	9.17774	−	24.8998i	0.290808	−	0.788980i
$997$	−8.81700	−	5.66634i	−0.279237	−	0.179455i	0.393524	−	0.919314i	$-0.371256\pi$
$997$	−8.81700	−	5.66634i	−0.279237	−	0.179455i	−0.672762	+	0.739859i	$0.734892\pi$
$998$	−4.59111	+	4.95034i	−0.145329	+	0.156700i
$999$	4.28377	+	1.25783i	0.135533	+	0.0397960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.m.a.7.9	✓	240
3.2	odd	2		828.2.u.c.559.16		240
4.3	odd	2	inner	276.2.m.a.7.21	yes	240
12.11	even	2		828.2.u.c.559.4		240
23.10	odd	22	inner	276.2.m.a.79.21	yes	240
69.56	even	22		828.2.u.c.631.4		240
92.79	even	22	inner	276.2.m.a.79.9	yes	240
276.263	odd	22		828.2.u.c.631.16		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.m.a.7.9	✓	240	1.1	even	1	trivial
276.2.m.a.7.21	yes	240	4.3	odd	2	inner
276.2.m.a.79.9	yes	240	92.79	even	22	inner
276.2.m.a.79.21	yes	240	23.10	odd	22	inner
828.2.u.c.559.4		240	12.11	even	2
828.2.u.c.559.16		240	3.2	odd	2
828.2.u.c.631.4		240	69.56	even	22
828.2.u.c.631.16		240	276.263	odd	22

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.m (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.723978 - 1.21485i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.951711 + 1.75905i) q^{4} +(-2.68981 + 1.22840i) q^{5} +(-0.630583 + 1.26585i) q^{6} +(0.0149354 - 0.00438542i) q^{7} +(2.82599 - 0.117329i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.723978 - 1.21485i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.951711 + 1.75905i) q^{4} +(-2.68981 + 1.22840i) q^{5} +(-0.630583 + 1.26585i) q^{6} +(0.0149354 - 0.00438542i) q^{7} +(2.82599 - 0.117329i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(3.43968 + 2.37838i) q^{10} +(0.950206 + 1.09660i) q^{11} +(1.99434 - 0.150383i) q^{12} +(6.18777 + 1.81689i) q^{13} +(-0.0161405 - 0.0149692i) q^{14} +(2.48762 + 1.59869i) q^{15} +(-2.18849 - 3.34821i) q^{16} +(-0.419359 - 0.0602947i) q^{17} +(1.40582 - 0.153888i) q^{18} +(0.900853 + 6.26557i) q^{19} +(0.399116 - 5.90059i) q^{20} +(-0.0117639 - 0.0101935i) q^{21} +(0.644269 - 1.94827i) q^{22} +(-2.79657 + 3.89605i) q^{23} +(-1.62655 - 2.31394i) q^{24} +(2.45184 - 2.82957i) q^{25} +(-2.27256 - 8.83259i) q^{26} +(0.989821 - 0.142315i) q^{27} +(-0.00649998 + 0.0304457i) q^{28} +(0.122320 - 0.850755i) q^{29} +(0.141189 - 4.17950i) q^{30} +(-1.51311 + 2.35444i) q^{31} +(-2.48314 + 5.08272i) q^{32} +(0.408795 - 1.39223i) q^{33} +(0.230358 + 0.553109i) q^{34} +(-0.0347863 + 0.0301425i) q^{35} +(-1.20473 - 1.59644i) q^{36} +(4.06116 + 1.85467i) q^{37} +(6.95952 - 5.63054i) q^{38} +(-1.81689 - 6.18777i) q^{39} +(-7.45727 + 3.78703i) q^{40} +(-2.76678 - 6.05839i) q^{41} +(-0.00386672 + 0.0216712i) q^{42} +(2.19248 - 1.40902i) q^{43} +(-2.83329 + 0.627815i) q^{44} -2.95704i q^{45} +(6.75776 + 0.576746i) q^{46} +6.84887i q^{47} +(-1.63350 + 3.65126i) q^{48} +(-5.88857 + 3.78435i) q^{49} +(-5.21257 - 0.930060i) q^{50} +(0.175999 + 0.385385i) q^{51} +(-9.08497 + 9.15542i) q^{52} +(3.67235 + 12.5069i) q^{53} +(-0.889500 - 1.09945i) q^{54} +(-3.90293 - 1.78241i) q^{55} +(0.0416927 - 0.0141455i) q^{56} +(4.78390 - 4.14527i) q^{57} +(-1.12209 + 0.467328i) q^{58} +(1.75231 - 5.96783i) q^{59} +(-5.17967 + 2.85434i) q^{60} +(-0.357133 + 0.555710i) q^{61} +(3.95575 + 0.133631i) q^{62} +(-0.00221526 + 0.0154075i) q^{63} +(7.97247 - 0.663140i) q^{64} +(-18.8758 + 2.71393i) q^{65} +(-1.98731 + 0.511320i) q^{66} +(-5.13984 + 5.93169i) q^{67} +(0.505169 - 0.680289i) q^{68} +(4.78950 + 0.246257i) q^{69} +(0.0618031 + 0.0204375i) q^{70} +(7.24911 + 6.28139i) q^{71} +(-1.06723 + 2.61935i) q^{72} +(-2.20132 - 15.3105i) q^{73} +(-0.687051 - 6.27644i) q^{74} +(-3.70595 - 0.532835i) q^{75} +(-11.8788 - 4.37837i) q^{76} +(0.0190007 + 0.0122110i) q^{77} +(-6.20181 + 6.68706i) q^{78} +(-8.81861 - 2.58938i) q^{79} +(9.99957 + 6.31772i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-5.35694 + 7.74736i) q^{82} +(5.51200 - 12.0696i) q^{83} +(0.0291267 - 0.0109920i) q^{84} +(1.20206 - 0.352957i) q^{85} +(-3.29905 - 1.64343i) q^{86} +(-0.781832 + 0.357051i) q^{87} +(2.81394 + 2.98749i) q^{88} +(-4.02629 - 6.26503i) q^{89} +(-3.59235 + 2.14083i) q^{90} +0.100384 q^{91} +(-4.19182 - 8.62721i) q^{92} +2.79873 q^{93} +(8.32034 - 4.95843i) q^{94} +(-10.1197 - 15.7466i) q^{95} +(5.61834 - 0.658974i) q^{96} +(-8.57609 + 3.91657i) q^{97} +(8.86061 + 4.41393i) q^{98} +(-1.39223 + 0.408795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^6 - 4 * q^8 + 24 * q^9	\( 240 q - 4 q^{2} - 4 q^{6} - 4 q^{8} + 24 q^{9} - 8 q^{16} + 4 q^{18} + 4 q^{24} + 24 q^{25} - 40 q^{26} + 32 q^{29} + 36 q^{32} - 22 q^{34} - 22 q^{36} - 110 q^{38} - 22 q^{40} - 16 q^{41} - 110 q^{42} - 154 q^{44} - 88 q^{46} - 56 q^{48} - 40 q^{49} - 142 q^{50} - 70 q^{52} - 18 q^{54} - 110 q^{56} - 46 q^{58} - 22 q^{60} + 40 q^{62} - 48 q^{64} - 16 q^{69} - 72 q^{70} + 4 q^{72} + 22 q^{74} + 110 q^{76} - 192 q^{77} + 198 q^{80} - 24 q^{81} + 172 q^{82} - 200 q^{85} + 220 q^{86} + 176 q^{88} - 88 q^{89} + 154 q^{92} - 16 q^{93} + 126 q^{94} - 44 q^{96} - 88 q^{97} + 228 q^{98}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^6 - 4 * q^8 + 24 * q^9 - 8 * q^16 + 4 * q^18 + 4 * q^24 + 24 * q^25 - 40 * q^26 + 32 * q^29 + 36 * q^32 - 22 * q^34 - 22 * q^36 - 110 * q^38 - 22 * q^40 - 16 * q^41 - 110 * q^42 - 154 * q^44 - 88 * q^46 - 56 * q^48 - 40 * q^49 - 142 * q^50 - 70 * q^52 - 18 * q^54 - 110 * q^56 - 46 * q^58 - 22 * q^60 + 40 * q^62 - 48 * q^64 - 16 * q^69 - 72 * q^70 + 4 * q^72 + 22 * q^74 + 110 * q^76 - 192 * q^77 + 198 * q^80 - 24 * q^81 + 172 * q^82 - 200 * q^85 + 220 * q^86 + 176 * q^88 - 88 * q^89 + 154 * q^92 - 16 * q^93 + 126 * q^94 - 44 * q^96 - 88 * q^97 + 228 * q^98

Introduction

L-functions

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