LMFDB - Embedded newform 1184.2.y.a.529.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1184,2,Mod(529,1184)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1184, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1184.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1184 = 2^{5} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1184.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.45428759932$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.13
Character	$\chi$	$=$	1184.529
Dual form			1184.2.y.a.1137.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.727471 - 0.420006i) q^{3} +(0.249638 - 0.432386i) q^{5} +(-0.235288 + 0.407531i) q^{7} +(-1.14719 - 1.98699i) q^{9} -1.14772i q^{11} +(-3.10587 + 5.37952i) q^{13} +(-0.363209 + 0.209699i) q^{15} +(-0.363464 + 0.209846i) q^{17} +(-1.39615 + 2.41820i) q^{19} +(0.342330 - 0.197644i) q^{21} -7.74213i q^{23} +(2.37536 + 4.11425i) q^{25} +4.44734i q^{27} -5.48269 q^{29} +7.40664i q^{31} +(-0.482049 + 0.834933i) q^{33} +(0.117474 + 0.203470i) q^{35} +(-5.34584 + 2.90207i) q^{37} +(4.51886 - 2.60896i) q^{39} +(1.51018 - 2.61571i) q^{41} +1.44686 q^{43} -1.14553 q^{45} +0.412916 q^{47} +(3.38928 + 5.87040i) q^{49} +0.352546 q^{51} +(-6.89691 + 3.98194i) q^{53} +(-0.496258 - 0.286515i) q^{55} +(2.03131 - 1.17278i) q^{57} +(5.73102 + 9.92641i) q^{59} +(2.66975 - 4.62415i) q^{61} +1.07968 q^{63} +(1.55069 + 2.68587i) q^{65} +(-8.66568 - 5.00313i) q^{67} +(-3.25174 + 5.63217i) q^{69} +(-2.85626 + 4.94719i) q^{71} -5.09043 q^{73} -3.99066i q^{75} +(0.467731 + 0.270045i) q^{77} +(-5.88163 - 3.39576i) q^{79} +(-1.57366 + 2.72567i) q^{81} +(-11.4936 + 6.63581i) q^{83} +0.209542i q^{85} +(3.98850 + 2.30276i) q^{87} +(-10.0474 + 5.80087i) q^{89} +(-1.46155 - 2.53147i) q^{91} +(3.11083 - 5.38811i) q^{93} +(0.697063 + 1.20735i) q^{95} -8.36880i q^{97} +(-2.28051 + 1.31665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) $ 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1184\mathbb{Z}\right)^\times$.

$n$	$223$	$705$	$741$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	−0.727471	−	0.420006i	−0.420006	−	0.242490i	0.275074	−	0.961423i	$-0.411298\pi$
$3$	−0.727471	−	0.420006i	−0.420006	−	0.242490i	−0.695080	+	0.718933i	$0.744631\pi$
$4$		0			0
$5$	0.249638	−	0.432386i	0.111642	−	0.193369i	−0.804791	−	0.593559i	$-0.797722\pi$
$5$	0.249638	−	0.432386i	0.111642	−	0.193369i	0.916432	+	0.400190i	$0.131056\pi$
$6$		0			0
$7$	−0.235288	+	0.407531i	−0.0889305	+	0.154032i	−0.907059	−	0.421003i	$-0.861678\pi$
$7$	−0.235288	+	0.407531i	−0.0889305	+	0.154032i	0.818129	+	0.575035i	$0.195012\pi$
$8$		0			0
$9$	−1.14719	−	1.98699i	−0.382397	−	0.662331i
$10$		0			0
$11$		−	1.14772i		−	0.346051i	−0.984917	−	0.173025i	$-0.944646\pi$
$11$		−	1.14772i		−	0.346051i	0.984917	−	0.173025i	$-0.0553542\pi$
$12$		0			0
$13$	−3.10587	+	5.37952i	−0.861413	+	1.49201i	0.00915271	+	0.999958i	$0.497087\pi$
$13$	−3.10587	+	5.37952i	−0.861413	+	1.49201i	−0.870565	+	0.492053i	$0.836247\pi$
$14$		0			0
$15$	−0.363209	+	0.209699i	−0.0937801	+	0.0541440i
$16$		0			0
$17$	−0.363464	+	0.209846i	−0.0881530	+	0.0508952i	−0.543428	−	0.839455i	$-0.682874\pi$
$17$	−0.363464	+	0.209846i	−0.0881530	+	0.0508952i	0.455276	+	0.890351i	$0.349541\pi$
$18$		0			0
$19$	−1.39615	+	2.41820i	−0.320298	+	0.554773i	−0.980549	−	0.196272i	$-0.937116\pi$
$19$	−1.39615	+	2.41820i	−0.320298	+	0.554773i	0.660251	+	0.751045i	$0.270450\pi$
$20$		0			0
$21$	0.342330	−	0.197644i	0.0747026	−	0.0431296i
$22$		0			0
$23$		−	7.74213i		−	1.61435i	−0.590315	−	0.807173i	$-0.700997\pi$
$23$		−	7.74213i		−	1.61435i	0.590315	−	0.807173i	$-0.299003\pi$
$24$		0			0
$25$	2.37536	+	4.11425i	0.475072	+	0.822849i
$26$		0			0
$27$			4.44734i			0.855891i
$28$		0			0
$29$	−5.48269			−1.01811			−0.509055	−	0.860734i	$-0.670005\pi$
$29$	−5.48269			−1.01811			−0.509055	+	0.860734i	$0.670005\pi$
$30$		0			0
$31$			7.40664i			1.33027i	0.746722	+	0.665136i	$0.231626\pi$
$31$			7.40664i			1.33027i	−0.746722	+	0.665136i	$0.768374\pi$
$32$		0			0
$33$	−0.482049	+	0.834933i	−0.0839139	+	0.145343i
$34$		0			0
$35$	0.117474	+	0.203470i	0.0198567	+	0.0343928i
$36$		0			0
$37$	−5.34584	+	2.90207i	−0.878851	+	0.477097i
$37$	−5.34584	+	2.90207i	−0.878851	+	0.477097i
$38$		0			0
$39$	4.51886	−	2.60896i	0.723596	−	0.417769i
$40$		0			0
$41$	1.51018	−	2.61571i	0.235851	−	0.408505i	−0.723669	−	0.690147i	$-0.757546\pi$
$41$	1.51018	−	2.61571i	0.235851	−	0.408505i	0.959520	+	0.281642i	$0.0908791\pi$
$42$		0			0
$43$	1.44686			0.220644			0.110322	−	0.993896i	$-0.464812\pi$
$43$	1.44686			0.220644			0.110322	+	0.993896i	$0.464812\pi$
$44$		0			0
$45$	−1.14553			−0.170765
$46$		0			0
$47$	0.412916			0.0602300			0.0301150	−	0.999546i	$-0.490413\pi$
$47$	0.412916			0.0602300			0.0301150	+	0.999546i	$0.490413\pi$
$48$		0			0
$49$	3.38928	+	5.87040i	0.484183	+	0.838629i
$50$		0			0
$51$	0.352546			0.0493663
$52$		0			0
$53$	−6.89691	+	3.98194i	−0.947364	+	0.546961i	−0.892261	−	0.451520i	$-0.850882\pi$
$53$	−6.89691	+	3.98194i	−0.947364	+	0.546961i	−0.0551030	+	0.998481i	$0.517549\pi$
$54$		0			0
$55$	−0.496258	−	0.286515i	−0.0669154	−	0.0386336i
$56$		0			0
$57$	2.03131	−	1.17278i	0.269054	−	0.155338i
$58$		0			0
$59$	5.73102	+	9.92641i	0.746115	+	1.29231i	0.949672	+	0.313246i	$0.101416\pi$
$59$	5.73102	+	9.92641i	0.746115	+	1.29231i	−0.203557	+	0.979063i	$0.565250\pi$
$60$		0			0
$61$	2.66975	−	4.62415i	0.341827	−	0.592061i	−0.642945	−	0.765912i	$-0.722288\pi$
$61$	2.66975	−	4.62415i	0.341827	−	0.592061i	0.984772	+	0.173851i	$0.0556211\pi$
$62$		0			0
$63$	1.07968			0.136027
$64$		0			0
$65$	1.55069	+	2.68587i	0.192339	+	0.333141i
$66$		0			0
$67$	−8.66568	−	5.00313i	−1.05868	−	0.611230i	−0.133614	−	0.991033i	$-0.542658\pi$
$67$	−8.66568	−	5.00313i	−1.05868	−	0.611230i	−0.925067	+	0.379803i	$0.875992\pi$
$68$		0			0
$69$	−3.25174	+	5.63217i	−0.391463	+	0.678034i
$70$		0			0
$71$	−2.85626	+	4.94719i	−0.338976	+	0.587123i	−0.984240	−	0.176836i	$-0.943414\pi$
$71$	−2.85626	+	4.94719i	−0.338976	+	0.587123i	0.645265	+	0.763959i	$0.276747\pi$
$72$		0			0
$73$	−5.09043			−0.595790			−0.297895	−	0.954599i	$-0.596285\pi$
$73$	−5.09043			−0.595790			−0.297895	+	0.954599i	$0.596285\pi$
$74$		0			0
$75$		−	3.99066i		−	0.460802i
$76$		0			0
$77$	0.467731	+	0.270045i	0.0533029	+	0.0307744i
$78$		0			0
$79$	−5.88163	−	3.39576i	−0.661735	−	0.382053i	0.131203	−	0.991356i	$-0.458116\pi$
$79$	−5.88163	−	3.39576i	−0.661735	−	0.382053i	−0.792938	+	0.609303i	$0.791449\pi$
$80$		0			0
$81$	−1.57366	+	2.72567i	−0.174852	+	0.302852i
$82$		0			0
$83$	−11.4936	+	6.63581i	−1.26158	+	0.728375i	−0.973381	−	0.229194i	$-0.926391\pi$
$83$	−11.4936	+	6.63581i	−1.26158	+	0.728375i	−0.288202	+	0.957570i	$0.593058\pi$
$84$		0			0
$85$			0.209542i			0.0227281i
$86$		0			0
$87$	3.98850	+	2.30276i	0.427612	+	0.246882i
$88$		0			0
$89$	−10.0474	+	5.80087i	−1.06502	+	0.614891i	−0.926817	−	0.375512i	$-0.877467\pi$
$89$	−10.0474	+	5.80087i	−1.06502	+	0.614891i	−0.138206	+	0.990404i	$0.544134\pi$
$90$		0			0
$91$	−1.46155	−	2.53147i	−0.153212	−	0.265370i
$92$		0			0
$93$	3.11083	−	5.38811i	0.322578	−	0.558721i
$94$		0			0
$95$	0.697063	+	1.20735i	0.0715172	+	0.123871i
$96$		0			0
$97$		−	8.36880i		−	0.849723i	−0.905258	−	0.424861i	$-0.860323\pi$
$97$		−	8.36880i		−	0.849723i	0.905258	−	0.424861i	$-0.139677\pi$
$98$		0			0
$99$	−2.28051	+	1.31665i	−0.229200	+	0.132329i
$100$		0			0
$101$			4.99152i			0.496675i	0.968674	+	0.248337i	$0.0798841\pi$
$101$			4.99152i			0.496675i	−0.968674	+	0.248337i	$0.920116\pi$
$102$		0			0
$103$			8.16774i			0.804791i	0.915466	+	0.402396i	$0.131822\pi$
$103$			8.16774i			0.804791i	−0.915466	+	0.402396i	$0.868178\pi$
$104$		0			0
$105$		−	0.197358i		−	0.0192602i
$106$		0			0
$107$	9.89318	+	5.71183i	0.956410	+	0.552183i	0.895066	−	0.445933i	$-0.147128\pi$
$107$	9.89318	+	5.71183i	0.956410	+	0.552183i	0.0613436	+	0.998117i	$0.480461\pi$
$108$		0			0
$109$	4.53724	+	7.85873i	0.434589	+	0.752729i	0.997262	−	0.0739498i	$-0.0235605\pi$
$109$	4.53724	+	7.85873i	0.434589	+	0.752729i	−0.562673	+	0.826679i	$0.690227\pi$
$110$		0			0
$111$	5.10783	+	0.134115i	0.484814	+	0.0127296i
$112$		0			0
$113$	6.36432	−	3.67444i	0.598705	−	0.345663i	−0.169827	−	0.985474i	$-0.554321\pi$
$113$	6.36432	−	3.67444i	0.598705	−	0.345663i	0.768532	+	0.639811i	$0.220987\pi$
$114$		0			0
$115$	−3.34759	−	1.93273i	−0.312164	−	0.180228i
$116$		0			0
$117$	14.2521			1.31761
$118$		0			0
$119$		−	0.197497i		−	0.0181045i
$120$		0			0
$121$	9.68274			0.880249
$122$		0			0
$123$	−2.19723	+	1.26857i	−0.198117	+	0.114383i
$124$		0			0
$125$	4.86830			0.435434
$126$		0			0
$127$	−3.31142	−	5.73554i	−0.293841	−	0.508947i	0.680874	−	0.732401i	$-0.261600\pi$
$127$	−3.31142	−	5.73554i	−0.293841	−	0.508947i	−0.974715	+	0.223454i	$0.928267\pi$
$128$		0			0
$129$	−1.05255	−	0.607689i	−0.0926718	−	0.0535041i
$130$		0			0
$131$	0.266884	+	0.462257i	0.0233178	+	0.0403876i	0.877449	−	0.479670i	$-0.159244\pi$
$131$	0.266884	+	0.462257i	0.0233178	+	0.0403876i	−0.854131	+	0.520058i	$0.825910\pi$
$132$		0			0
$133$	−0.656993	−	1.13795i	−0.0569685	−	0.0986724i
$134$		0			0
$135$	1.92297	+	1.11023i	0.165503	+	0.0955530i
$136$		0			0
$137$	−5.65304			−0.482972			−0.241486	−	0.970404i	$-0.577635\pi$
$137$	−5.65304			−0.482972			−0.241486	+	0.970404i	$0.577635\pi$
$138$		0			0
$139$	−17.4673	+	10.0847i	−1.48156	+	0.855376i	−0.999781	−	0.0209193i	$-0.993341\pi$
$139$	−17.4673	+	10.0847i	−1.48156	+	0.855376i	−0.481774	+	0.876296i	$0.660007\pi$
$140$		0			0
$141$	−0.300385	−	0.173427i	−0.0252969	−	0.0146052i
$142$		0			0
$143$	6.17418	+	3.56467i	0.516311	+	0.298092i
$144$		0			0
$145$	−1.36869	+	2.37064i	−0.113663	+	0.196871i
$146$		0			0
$147$		−	5.69406i		−	0.469639i
$148$		0			0
$149$		−	22.0781i		−	1.80871i	−0.426783	−	0.904354i	$-0.640353\pi$
$149$		−	22.0781i		−	1.80871i	0.426783	−	0.904354i	$-0.359647\pi$
$150$		0			0
$151$	−4.93283	+	8.54392i	−0.401428	+	0.695294i	−0.993899	−	0.110298i	$-0.964819\pi$
$151$	−4.93283	+	8.54392i	−0.401428	+	0.695294i	0.592470	+	0.805592i	$0.298153\pi$
$152$		0			0
$153$	0.833925	+	0.481467i	0.0674189	+	0.0389243i
$154$		0			0
$155$	3.20252	+	1.84898i	0.257233	+	0.148514i
$156$		0			0
$157$	−1.42690	+	0.823821i	−0.113879	+	0.0657481i	−0.555858	−	0.831278i	$-0.687610\pi$
$157$	−1.42690	+	0.823821i	−0.113879	+	0.0657481i	0.441979	+	0.897026i	$0.354277\pi$
$158$		0			0
$159$	6.68974			0.530531
$160$		0			0
$161$	3.15515	+	1.82163i	0.248661	+	0.143564i
$162$		0			0
$163$	−10.1821	−	17.6358i	−0.797520	−	1.38134i	−0.921227	−	0.389026i	$-0.872812\pi$
$163$	−10.1821	−	17.6358i	−0.797520	−	1.38134i	0.123707	−	0.992319i	$-0.460522\pi$
$164$		0			0
$165$	0.240675	+	0.416862i	0.0187366	+	0.0324527i
$166$		0			0
$167$	−5.22741	−	3.01805i	−0.404509	−	0.233544i	0.283919	−	0.958848i	$-0.408365\pi$
$167$	−5.22741	−	3.01805i	−0.404509	−	0.233544i	−0.688428	+	0.725305i	$0.741699\pi$
$168$		0			0
$169$	−12.7928	−	22.1578i	−0.984064	−	1.70445i
$170$		0			0
$171$	6.40659			0.489924
$172$		0			0
$173$	2.78685	−	1.60899i	0.211880	−	0.122329i	−0.390305	−	0.920686i	$-0.627630\pi$
$173$	2.78685	−	1.60899i	0.211880	−	0.122329i	0.602185	+	0.798357i	$0.294297\pi$
$174$		0			0
$175$	−2.23558			−0.168994
$176$		0			0
$177$		−	9.62824i		−	0.723703i
$178$		0			0
$179$	9.92175			0.741586			0.370793	−	0.928715i	$-0.379086\pi$
$179$	9.92175			0.741586			0.370793	+	0.928715i	$0.379086\pi$
$180$		0			0
$181$	11.4409	+	6.60542i	0.850397	+	0.490977i	0.860785	−	0.508969i	$-0.169973\pi$
$181$	11.4409	+	6.60542i	0.850397	+	0.490977i	−0.0103880	+	0.999946i	$0.503307\pi$
$182$		0			0
$183$	−3.88433	+	2.24262i	−0.287138	+	0.165779i
$184$		0			0
$185$	−0.0797136	+	3.03593i	−0.00586066	+	0.223206i
$186$		0			0
$187$	0.240845	+	0.417155i	0.0176123	+	0.0305054i
$188$		0			0
$189$	−1.81243	−	1.04640i	−0.131835	−	0.0761148i
$190$		0			0
$191$		−	12.1287i		−	0.877599i	−0.898585	−	0.438800i	$-0.855404\pi$
$191$		−	12.1287i		−	0.877599i	0.898585	−	0.438800i	$-0.144596\pi$
$192$		0			0
$193$		−	10.8801i		−	0.783167i	−0.920143	−	0.391584i	$-0.871927\pi$
$193$		−	10.8801i		−	0.783167i	0.920143	−	0.391584i	$-0.128073\pi$
$194$		0			0
$195$		−	2.60519i		−	0.186561i
$196$		0			0
$197$	14.2206	−	8.21024i	1.01317	−	0.584956i	0.101054	−	0.994881i	$-0.467779\pi$
$197$	14.2206	−	8.21024i	1.01317	−	0.584956i	0.912119	+	0.409925i	$0.134445\pi$
$198$		0			0
$199$			0.188747i			0.0133799i	0.999978	+	0.00668996i	$0.00212950\pi$
$199$			0.188747i			0.0133799i	−0.999978	+	0.00668996i	$0.997871\pi$
$200$		0			0
$201$	4.20269	+	7.27927i	0.296435	+	0.513440i
$202$		0			0
$203$	1.29001	−	2.23436i	0.0905409	−	0.156822i
$204$		0			0
$205$	−0.753997	−	1.30596i	−0.0526615	−	0.0912123i
$206$		0			0
$207$	−15.3836	+	8.88170i	−1.06923	+	0.617321i
$208$		0			0
$209$	2.77541	+	1.60239i	0.191979	+	0.110839i
$210$		0			0
$211$		−	8.56666i		−	0.589753i	−0.955535	−	0.294877i	$-0.904721\pi$
$211$		−	8.56666i		−	0.589753i	0.955535	−	0.294877i	$-0.0952786\pi$
$212$		0			0
$213$	4.15569	−	2.39929i	0.284743	−	0.164397i
$214$		0			0
$215$	0.361191	−	0.625602i	0.0246330	−	0.0426657i
$216$		0			0
$217$	−3.01843	−	1.74269i	−0.204904	−	0.118302i
$218$		0			0
$219$	3.70314	+	2.13801i	0.250235	+	0.144473i
$220$		0			0
$221$		−	2.60702i		−	0.175367i
$222$		0			0
$223$	0.300028			0.0200913			0.0100457	−	0.999950i	$-0.496802\pi$
$223$	0.300028			0.0200913			0.0100457	+	0.999950i	$0.496802\pi$
$224$		0			0
$225$	5.44999	−	9.43965i	0.363332	−	0.629310i
$226$		0			0
$227$	7.13138	−	12.3519i	0.473327	−	0.819826i	−0.526207	−	0.850356i	$-0.676386\pi$
$227$	7.13138	−	12.3519i	0.473327	−	0.819826i	0.999534	+	0.0305307i	$0.00971974\pi$
$228$		0			0
$229$	−17.1515	−	9.90243i	−1.13340	−	0.654371i	−0.188615	−	0.982051i	$-0.560400\pi$
$229$	−17.1515	−	9.90243i	−1.13340	−	0.654371i	−0.944789	+	0.327680i	$0.893733\pi$
$230$		0			0
$231$	−0.226840	−	0.392899i	−0.0149250	−	0.0258509i
$232$		0			0
$233$	−12.5136			−0.819792			−0.409896	−	0.912132i	$-0.634435\pi$
$233$	−12.5136			−0.819792			−0.409896	+	0.912132i	$0.634435\pi$
$234$		0			0
$235$	0.103080	−	0.178539i	0.00672417	−	0.0116466i
$236$		0			0
$237$	2.85248	+	4.94063i	0.185288	+	0.320929i
$238$		0			0
$239$	16.6694	−	9.62406i	1.07825	−	0.622529i	0.147827	−	0.989013i	$-0.452772\pi$
$239$	16.6694	−	9.62406i	1.07825	−	0.622529i	0.930424	+	0.366484i	$0.119439\pi$
$240$		0			0
$241$	23.8525	+	13.7713i	1.53648	+	0.887085i	0.999041	+	0.0437793i	$0.0139398\pi$
$241$	23.8525	+	13.7713i	1.53648	+	0.887085i	0.537435	+	0.843305i	$0.319393\pi$
$242$		0			0
$243$	13.8441	−	7.99290i	0.888101	−	0.512745i
$244$		0			0
$245$	3.38437			0.216220
$246$		0			0
$247$	−8.67250	−	15.0212i	−0.551818	−	0.955777i
$248$		0			0
$249$	11.1483			0.706496
$250$		0			0
$251$	11.6728			0.736782			0.368391	−	0.929671i	$-0.379909\pi$
$251$	11.6728			0.736782			0.368391	+	0.929671i	$0.379909\pi$
$252$		0			0
$253$	−8.88579			−0.558645
$254$		0			0
$255$	0.0880089	−	0.152436i	0.00551133	−	0.00954591i
$256$		0			0
$257$	−14.2286	+	8.21487i	−0.887554	+	0.512430i	−0.873142	−	0.487467i	$-0.837921\pi$
$257$	−14.2286	+	8.21487i	−0.887554	+	0.512430i	−0.0144125	+	0.999896i	$0.504588\pi$
$258$		0			0
$259$	0.0751314	−	2.86141i	0.00466844	−	0.177800i
$260$		0			0
$261$	6.28969	+	10.8941i	0.389322	+	0.674325i
$262$		0			0
$263$	−4.66110	+	8.07326i	−0.287416	+	0.497818i	−0.973192	−	0.229994i	$-0.926129\pi$
$263$	−4.66110	+	8.07326i	−0.287416	+	0.497818i	0.685776	+	0.727812i	$0.259463\pi$
$264$		0			0
$265$			3.97617i			0.244254i
$266$		0			0
$267$	9.74560			0.596421
$268$		0			0
$269$		−	19.2317i		−	1.17258i	−0.810103	−	0.586288i	$-0.800589\pi$
$269$		−	19.2317i		−	1.17258i	0.810103	−	0.586288i	$-0.199411\pi$
$270$		0			0
$271$	−7.72293	−	13.3765i	−0.469135	−	0.812565i	0.530243	−	0.847846i	$-0.322101\pi$
$271$	−7.72293	−	13.3765i	−0.469135	−	0.812565i	−0.999377	+	0.0352809i	$0.988767\pi$
$272$		0			0
$273$			2.45543i			0.148609i
$274$		0			0
$275$	4.72200	−	2.72625i	0.284747	−	0.164399i
$276$		0			0
$277$	−0.229440	+	0.397402i	−0.0137857	+	0.0238776i	−0.872836	−	0.488014i	$-0.837722\pi$
$277$	−0.229440	+	0.397402i	−0.0137857	+	0.0238776i	0.859050	+	0.511891i	$0.171055\pi$
$278$		0			0
$279$	14.7169	−	8.49683i	0.881080	−	0.508692i
$280$		0			0
$281$	−8.44006	+	4.87287i	−0.503492	+	0.290691i	−0.730154	−	0.683282i	$-0.760552\pi$
$281$	−8.44006	+	4.87287i	−0.503492	+	0.290691i	0.226663	+	0.973973i	$0.427219\pi$
$282$		0			0
$283$	5.24831	−	9.09033i	0.311979	−	0.540364i	−0.666811	−	0.745227i	$-0.732341\pi$
$283$	5.24831	−	9.09033i	0.311979	−	0.540364i	0.978791	+	0.204862i	$0.0656747\pi$
$284$		0			0
$285$		−	1.17108i		−	0.0693689i
$286$		0			0
$287$	0.710654	+	1.23089i	0.0419486	+	0.0726571i
$288$		0			0
$289$	−8.41193	+	14.5699i	−0.494819	+	0.857052i
$290$		0			0
$291$	−3.51494	+	6.08806i	−0.206050	+	0.356888i
$292$		0			0
$293$	−8.07314	−	4.66103i	−0.471638	−	0.272300i	0.245287	−	0.969450i	$-0.421118\pi$
$293$	−8.07314	−	4.66103i	−0.471638	−	0.272300i	−0.716925	+	0.697150i	$0.754451\pi$
$294$		0			0
$295$	5.72272			0.333190
$296$		0			0
$297$	5.10430			0.296181
$298$		0			0
$299$	41.6489	+	24.0460i	2.40862	+	1.39062i
$300$		0			0
$301$	−0.340429	+	0.589640i	−0.0196220	+	0.0339863i
$302$		0			0
$303$	2.09647	−	3.63119i	0.120439	−	0.208606i
$304$		0			0
$305$	−1.33294	−	2.30873i	−0.0763241	−	0.132197i
$306$		0			0
$307$		−	20.0139i		−	1.14225i	−0.820862	−	0.571126i	$-0.806507\pi$
$307$		−	20.0139i		−	1.14225i	0.820862	−	0.571126i	$-0.193493\pi$
$308$		0			0
$309$	3.43050	−	5.94179i	0.195154	−	0.338017i
$310$		0			0
$311$	25.0811	−	14.4806i	1.42222	−	0.821120i	0.425732	−	0.904849i	$-0.360016\pi$
$311$	25.0811	−	14.4806i	1.42222	−	0.821120i	0.996489	+	0.0837295i	$0.0266832\pi$
$312$		0			0
$313$	2.49143	−	1.43843i	0.140824	−	0.0813046i	−0.427933	−	0.903811i	$-0.640758\pi$
$313$	2.49143	−	1.43843i	0.140824	−	0.0813046i	0.568757	+	0.822506i	$0.307425\pi$
$314$		0			0
$315$	0.269529	−	0.466838i	0.0151863	−	0.0263034i
$316$		0			0
$317$	−7.46736	+	4.31129i	−0.419409	+	0.242146i	−0.694824	−	0.719179i	$-0.744518\pi$
$317$	−7.46736	+	4.31129i	−0.419409	+	0.242146i	0.275415	+	0.961325i	$0.411185\pi$
$318$		0			0
$319$			6.29259i			0.352317i
$320$		0			0
$321$	−4.79800	−	8.31038i	−0.267798	−	0.463840i
$322$		0			0
$323$		−	1.17190i		−	0.0652065i
$324$		0			0
$325$	−29.5102			−1.63693
$326$		0			0
$327$		−	7.62266i		−	0.421534i
$328$		0			0
$329$	−0.0971542	+	0.168276i	−0.00535628	+	0.00927735i
$330$		0			0
$331$	4.15111	+	7.18994i	0.228166	+	0.395195i	0.957265	−	0.289214i	$-0.0933939\pi$
$331$	4.15111	+	7.18994i	0.228166	+	0.395195i	−0.729099	+	0.684408i	$0.760061\pi$
$332$		0			0
$333$	11.8991	+	7.29292i	0.652066	+	0.399650i
$334$		0			0
$335$	−4.32657	+	2.49795i	−0.236386	+	0.136477i
$336$		0			0
$337$	−10.8934	+	18.8680i	−0.593402	+	1.02780i	0.400368	+	0.916354i	$0.368882\pi$
$337$	−10.8934	+	18.8680i	−0.593402	+	1.02780i	−0.993770	+	0.111448i	$0.964451\pi$
$338$		0			0
$339$	−6.17315			−0.335279
$340$		0			0
$341$	8.50074			0.460341
$342$		0			0
$343$	−6.48386			−0.350095
$344$		0			0
$345$	1.62351	+	2.81201i	0.0874071	+	0.151394i
$346$		0			0
$347$	1.00199			0.0537898			0.0268949	−	0.999638i	$-0.491438\pi$
$347$	1.00199			0.0537898			0.0268949	+	0.999638i	$0.491438\pi$
$348$		0			0
$349$	16.2509	−	9.38245i	0.869890	−	0.502231i	0.00257815	−	0.999997i	$-0.499179\pi$
$349$	16.2509	−	9.38245i	0.869890	−	0.502231i	0.867312	+	0.497766i	$0.165846\pi$
$350$		0			0
$351$	−23.9246	−	13.8128i	−1.27700	−	0.737275i
$352$		0			0
$353$	−21.8311	+	12.6042i	−1.16195	+	0.670855i	−0.951772	−	0.306808i	$-0.900739\pi$
$353$	−21.8311	+	12.6042i	−1.16195	+	0.670855i	−0.210183	+	0.977662i	$0.567406\pi$
$354$		0			0
$355$	1.42606	+	2.47001i	0.0756875	+	0.131095i
$356$		0			0
$357$	−0.0829498	+	0.143673i	−0.00439017	+	0.00760400i
$358$		0			0
$359$	−33.6660			−1.77682			−0.888412	−	0.459047i	$-0.848191\pi$
$359$	−33.6660			−1.77682			−0.888412	+	0.459047i	$0.848191\pi$
$360$		0			0
$361$	5.60155	+	9.70216i	0.294818	+	0.510640i
$362$		0			0
$363$	−7.04391	−	4.06680i	−0.369710	−	0.213452i
$364$		0			0
$365$	−1.27077	+	2.20103i	−0.0665149	+	0.115207i
$366$		0			0
$367$	−13.2260	+	22.9081i	−0.690392	+	1.19579i	0.281318	+	0.959615i	$0.409229\pi$
$367$	−13.2260	+	22.9081i	−0.690392	+	1.19579i	−0.971710	+	0.236179i	$0.924105\pi$
$368$		0			0
$369$	−6.92986			−0.360754
$370$		0			0
$371$		−	3.74760i		−	0.194566i
$372$		0			0
$373$	−11.5090	−	6.64475i	−0.595916	−	0.344052i	0.171517	−	0.985181i	$-0.445133\pi$
$373$	−11.5090	−	6.64475i	−0.595916	−	0.344052i	−0.767433	+	0.641129i	$0.778466\pi$
$374$		0			0
$375$	−3.54155	−	2.04471i	−0.182885	−	0.105589i
$376$		0			0
$377$	17.0285	−	29.4942i	0.877013	−	1.51903i
$378$		0			0
$379$	21.9072	−	12.6481i	1.12530	−	0.649691i	0.182550	−	0.983197i	$-0.441565\pi$
$379$	21.9072	−	12.6481i	1.12530	−	0.649691i	0.942748	+	0.333506i	$0.108232\pi$
$380$		0			0
$381$			5.56325i			0.285014i
$382$		0			0
$383$	20.1182	+	11.6152i	1.02799	+	0.593510i	0.916408	−	0.400245i	$-0.131075\pi$
$383$	20.1182	+	11.6152i	1.02799	+	0.593510i	0.111582	+	0.993755i	$0.464408\pi$
$384$		0			0
$385$	0.233527	−	0.134827i	0.0119016	−	0.00687141i
$386$		0			0
$387$	−1.65982	−	2.87490i	−0.0843736	−	0.146139i
$388$		0			0
$389$	−6.88172	+	11.9195i	−0.348917	+	0.604342i	−0.986057	−	0.166406i	$-0.946784\pi$
$389$	−6.88172	+	11.9195i	−0.348917	+	0.604342i	0.637140	+	0.770748i	$0.280117\pi$
$390$		0			0
$391$	1.62466	+	2.81399i	0.0821624	+	0.142309i
$392$		0			0
$393$		−	0.448372i		−	0.0226174i
$394$		0			0
$395$	−2.93656	+	1.69542i	−0.147754	+	0.0853059i
$396$		0			0
$397$		−	7.87786i		−	0.395378i	−0.980265	−	0.197689i	$-0.936656\pi$
$397$		−	7.87786i		−	0.395378i	0.980265	−	0.197689i	$-0.0633437\pi$
$398$		0			0
$399$			1.10376i			0.0552573i
$400$		0			0
$401$		−	28.1711i		−	1.40680i	−0.710795	−	0.703399i	$-0.751665\pi$
$401$		−	28.1711i		−	1.40680i	0.710795	−	0.703399i	$-0.248335\pi$
$402$		0			0
$403$	−39.8442	−	23.0040i	−1.98478	−	1.14591i
$404$		0			0
$405$	0.785693	+	1.36086i	0.0390414	+	0.0676217i
$406$		0			0
$407$	3.33076	+	6.13553i	0.165100	+	0.304127i
$408$		0			0
$409$	−30.1621	+	17.4141i	−1.49142	+	0.861070i	−0.999952	−	0.00982636i	$-0.996872\pi$
$409$	−30.1621	+	17.4141i	−1.49142	+	0.861070i	−0.491466	+	0.870897i	$0.663539\pi$
$410$		0			0
$411$	4.11242	+	2.37431i	0.202851	+	0.117116i
$412$		0			0
$413$	−5.39376			−0.265409
$414$		0			0
$415$			6.62621i			0.325268i
$416$		0			0
$417$	16.9426			0.829682
$418$		0			0
$419$	−6.67879	+	3.85600i	−0.326280	+	0.188378i	−0.654188	−	0.756332i	$-0.726990\pi$
$419$	−6.67879	+	3.85600i	−0.326280	+	0.188378i	0.327908	+	0.944710i	$0.393656\pi$
$420$		0			0
$421$	12.1517			0.592237			0.296118	−	0.955151i	$-0.404308\pi$
$421$	12.1517			0.592237			0.296118	+	0.955151i	$0.404308\pi$
$422$		0			0
$423$	−0.473694	−	0.820461i	−0.0230318	−	0.0398922i
$424$		0			0
$425$	−1.72672	−	0.996921i	−0.0837581	−	0.0483578i
$426$		0			0
$427$	1.25632	+	2.17601i	0.0607976	+	0.105305i
$428$		0			0
$429$	−2.99436	−	5.18638i	−0.144569	−	0.250401i
$430$		0			0
$431$	−0.881212	−	0.508768i	−0.0424465	−	0.0245065i	0.478627	−	0.878019i	$-0.341135\pi$
$431$	−0.881212	−	0.508768i	−0.0424465	−	0.0245065i	−0.521073	+	0.853512i	$0.674468\pi$
$432$		0			0
$433$	20.6777			0.993707			0.496854	−	0.867834i	$-0.334489\pi$
$433$	20.6777			0.993707			0.496854	+	0.867834i	$0.334489\pi$
$434$		0			0
$435$	1.99136	−	1.14971i	0.0954784	−	0.0551245i
$436$		0			0
$437$	18.7220	+	10.8092i	0.895595	+	0.517072i
$438$		0			0
$439$	27.5320	+	15.8956i	1.31403	+	0.758655i	0.982761	−	0.184881i	$-0.0591900\pi$
$439$	27.5320	+	15.8956i	1.31403	+	0.758655i	0.331269	+	0.943536i	$0.392523\pi$
$440$		0			0
$441$	7.77630	−	13.4689i	0.370300	−	0.641378i
$442$		0			0
$443$			22.1773i			1.05368i	0.849965	+	0.526839i	$0.176623\pi$
$443$			22.1773i			1.05368i	−0.849965	+	0.526839i	$0.823377\pi$
$444$		0			0
$445$			5.79248i			0.274590i
$446$		0			0
$447$	−9.27292	+	16.0612i	−0.438594	+	0.759668i
$448$		0			0
$449$	23.2259	+	13.4095i	1.09610	+	0.632833i	0.935194	−	0.354136i	$-0.115225\pi$
$449$	23.2259	+	13.4095i	1.09610	+	0.632833i	0.160906	+	0.986970i	$0.448558\pi$
$450$		0			0
$451$	−3.00210	−	1.73326i	−0.141363	−	0.0816162i
$452$		0			0
$453$	7.17698	−	4.14363i	0.337204	−	0.194685i
$454$		0			0
$455$	−1.45943			−0.0684191
$456$		0			0
$457$	21.9187	+	12.6548i	1.02532	+	0.591966i	0.915639	−	0.402001i	$-0.131685\pi$
$457$	21.9187	+	12.6548i	1.02532	+	0.591966i	0.109676	+	0.993967i	$0.465019\pi$
$458$		0			0
$459$	−0.933257	−	1.61645i	−0.0435607	−	0.0754493i
$460$		0			0
$461$	0.344353	+	0.596437i	0.0160381	+	0.0277788i	0.873933	−	0.486046i	$-0.161561\pi$
$461$	0.344353	+	0.596437i	0.0160381	+	0.0277788i	−0.857895	+	0.513825i	$0.828228\pi$
$462$		0			0
$463$	16.9919	+	9.81026i	0.789679	+	0.455922i	0.839850	−	0.542819i	$-0.182643\pi$
$463$	16.9919	+	9.81026i	0.789679	+	0.455922i	−0.0501704	+	0.998741i	$0.515976\pi$
$464$		0			0
$465$	−1.55316	−	2.69016i	−0.0720262	−	0.124753i
$466$		0			0
$467$	−21.6680			−1.00268			−0.501338	−	0.865252i	$-0.667159\pi$
$467$	−21.6680			−1.00268			−0.501338	+	0.865252i	$0.667159\pi$
$468$		0			0
$469$	4.07786	−	2.35435i	0.188298	−	0.108714i
$470$		0			0
$471$	1.38404			0.0637731
$472$		0			0
$473$		−	1.66059i		−	0.0763540i
$474$		0			0
$475$	−13.2654			−0.608659
$476$		0			0
$477$	15.8242	+	9.13608i	0.724538	+	0.418312i
$478$		0			0
$479$	9.04166	−	5.22020i	0.413124	−	0.238517i	−0.279007	−	0.960289i	$-0.590005\pi$
$479$	9.04166	−	5.22020i	0.413124	−	0.238517i	0.692131	+	0.721772i	$0.256672\pi$
$480$		0			0
$481$	0.991756	−	37.7715i	0.0452202	−	1.72223i
$482$		0			0
$483$	−1.53019	−	2.65036i	−0.0696260	−	0.120596i
$484$		0			0
$485$	−3.61855	−	2.08917i	−0.164310	−	0.0948643i
$486$		0			0
$487$		−	6.64519i		−	0.301122i	−0.988601	−	0.150561i	$-0.951892\pi$
$487$		−	6.64519i		−	0.301122i	0.988601	−	0.150561i	$-0.0481080\pi$
$488$		0			0
$489$			17.1061i			0.773563i
$490$		0			0
$491$			10.5764i			0.477304i	0.971105	+	0.238652i	$0.0767056\pi$
$491$			10.5764i			0.477304i	−0.971105	+	0.238652i	$0.923294\pi$
$492$		0			0
$493$	1.99276	−	1.15052i	0.0897494	−	0.0518168i
$494$		0			0
$495$			1.31475i			0.0590935i
$496$		0			0
$497$	−1.34409	−	2.32803i	−0.0602905	−	0.104426i
$498$		0			0
$499$	−15.5770	+	26.9801i	−0.697322	+	1.20780i	0.272070	+	0.962278i	$0.412292\pi$
$499$	−15.5770	+	26.9801i	−0.697322	+	1.20780i	−0.969392	+	0.245519i	$0.921041\pi$
$500$		0			0
$501$	2.53519	+	4.39108i	0.113264	+	0.196179i
$502$		0			0
$503$	−29.1988	+	16.8580i	−1.30191	+	0.751659i	−0.980732	−	0.195359i	$-0.937413\pi$
$503$	−29.1988	+	16.8580i	−1.30191	+	0.751659i	−0.321180	+	0.947018i	$0.604079\pi$
$504$		0			0
$505$	2.15826	+	1.24607i	0.0960414	+	0.0554495i
$506$		0			0
$507$			21.4922i			0.954504i
$508$		0			0
$509$	−6.62597	+	3.82551i	−0.293691	+	0.169563i	−0.639605	−	0.768704i	$-0.720902\pi$
$509$	−6.62597	+	3.82551i	−0.293691	+	0.169563i	0.345914	+	0.938266i	$0.387569\pi$
$510$		0			0
$511$	1.19772	−	2.07451i	0.0529839	−	0.0917707i
$512$		0			0
$513$	−10.7545	−	6.20914i	−0.474825	−	0.274140i
$514$		0			0
$515$	3.53162	+	2.03898i	0.155622	+	0.0898481i
$516$		0			0
$517$		−	0.473912i		−	0.0208426i
$518$		0			0
$519$	−2.70314			−0.118655
$520$		0			0
$521$	6.90920	−	11.9671i	0.302697	−	0.524287i	−0.674049	−	0.738687i	$-0.735446\pi$
$521$	6.90920	−	11.9671i	0.302697	−	0.524287i	0.976746	+	0.214400i	$0.0687795\pi$
$522$		0			0
$523$	−21.1550	+	36.6416i	−0.925045	+	1.60223i	−0.133557	+	0.991041i	$0.542640\pi$
$523$	−21.1550	+	36.6416i	−0.925045	+	1.60223i	−0.791488	+	0.611185i	$0.790693\pi$
$524$		0			0
$525$	1.62632	+	0.938954i	0.0709783	+	0.0409793i
$526$		0			0
$527$	−1.55425	−	2.69205i	−0.0677044	−	0.117267i
$528$		0			0
$529$	−36.9405			−1.60611
$530$		0			0
$531$	13.1491	−	22.7750i	0.570624	−	0.988350i
$532$		0			0
$533$	9.38084	+	16.2481i	0.406329	+	0.703783i
$534$		0			0
$535$	4.93943	−	2.85178i	0.213550	−	0.123293i
$536$		0			0
$537$	−7.21779	−	4.16719i	−0.311470	−	0.179828i
$538$		0			0
$539$	6.73758	−	3.88994i	0.290208	−	0.167552i
$540$		0			0
$541$	−34.1336			−1.46752			−0.733758	−	0.679411i	$-0.762236\pi$
$541$	−34.1336			−1.46752			−0.733758	+	0.679411i	$0.762236\pi$
$542$		0			0
$543$	−5.54862	−	9.61050i	−0.238114	−	0.412426i
$544$		0			0
$545$	4.53067			0.194073
$546$		0			0
$547$	−27.0461			−1.15641			−0.578204	−	0.815892i	$-0.696246\pi$
$547$	−27.0461			−1.15641			−0.578204	+	0.815892i	$0.696246\pi$
$548$		0			0
$549$	−12.2509			−0.522854
$550$		0			0
$551$	7.65464	−	13.2582i	0.326099	−	0.564819i
$552$		0			0
$553$	2.76775	−	1.59796i	0.117697	−	0.0679523i
$554$		0			0
$555$	1.33310	−	2.17507i	0.0565868	−	0.0923267i
$556$		0			0
$557$	15.0179	+	26.0119i	0.636331	+	1.10216i	0.986231	+	0.165371i	$0.0528820\pi$
$557$	15.0179	+	26.0119i	0.636331	+	1.10216i	−0.349901	+	0.936787i	$0.613785\pi$
$558$		0			0
$559$	−4.49376	+	7.78341i	−0.190066	+	0.329203i
$560$		0			0
$561$		−	0.404624i		−	0.0170832i
$562$		0			0
$563$	−40.5799			−1.71024			−0.855119	−	0.518432i	$-0.826516\pi$
$563$	−40.5799			−1.71024			−0.855119	+	0.518432i	$0.826516\pi$
$564$		0			0
$565$		−	3.66912i		−	0.154361i
$566$		0			0
$567$	−0.740528	−	1.28263i	−0.0310993	−	0.0538655i
$568$		0			0
$569$			16.5430i			0.693518i	0.937954	+	0.346759i	$0.112718\pi$
$569$			16.5430i			0.693518i	−0.937954	+	0.346759i	$0.887282\pi$
$570$		0			0
$571$	−1.47508	+	0.851636i	−0.0617300	+	0.0356399i	−0.530547	−	0.847655i	$-0.678014\pi$
$571$	−1.47508	+	0.851636i	−0.0617300	+	0.0356399i	0.468817	+	0.883295i	$0.344680\pi$
$572$		0			0
$573$	−5.09411	+	8.82325i	−0.212809	+	0.368597i
$574$		0			0
$575$	31.8530	−	18.3904i	1.32836	−	0.766931i
$576$		0			0
$577$	0.231740	−	0.133795i	0.00964747	−	0.00556997i	−0.495169	−	0.868797i	$-0.664894\pi$
$577$	0.231740	−	0.133795i	0.00964747	−	0.00556997i	0.504816	+	0.863227i	$0.331560\pi$
$578$		0			0
$579$	−4.56971	+	7.91496i	−0.189910	+	0.328935i
$580$		0			0
$581$		−	6.24531i		−	0.259099i
$582$		0			0
$583$	4.57015	+	7.91573i	0.189276	+	0.327836i
$584$		0			0
$585$	3.55786	−	6.16240i	0.147100	−	0.254784i
$586$		0			0
$587$	21.4047	−	37.0741i	0.883468	−	1.53021i	0.0360094	−	0.999351i	$-0.488535\pi$
$587$	21.4047	−	37.0741i	0.883468	−	1.53021i	0.847459	−	0.530861i	$-0.178131\pi$
$588$		0			0
$589$	−17.9107	−	10.3408i	−0.737998	−	0.426084i
$590$		0			0
$591$	−13.7934			−0.567384
$592$		0			0
$593$	−16.0993			−0.661121			−0.330560	−	0.943785i	$-0.607238\pi$
$593$	−16.0993			−0.661121			−0.330560	+	0.943785i	$0.607238\pi$
$594$		0			0
$595$	−0.0853949	−	0.0493028i	−0.00350085	−	0.00202122i
$596$		0			0
$597$	0.0792748	−	0.137308i	0.00324450	−	0.00561964i
$598$		0			0
$599$	4.37997	−	7.58634i	0.178961	−	0.309969i	−0.762564	−	0.646913i	$-0.776060\pi$
$599$	4.37997	−	7.58634i	0.178961	−	0.309969i	0.941525	+	0.336943i	$0.109393\pi$
$600$		0			0
$601$	−22.3879	−	38.7770i	−0.913223	−	1.58175i	−0.809483	−	0.587144i	$-0.800252\pi$
$601$	−22.3879	−	38.7770i	−0.913223	−	1.58175i	−0.103740	−	0.994604i	$-0.533081\pi$
$602$		0			0
$603$			22.9582i			0.934930i
$604$		0			0
$605$	2.41718	−	4.18668i	0.0982723	−	0.170213i
$606$		0			0
$607$	13.6542	−	7.88328i	0.554208	−	0.319972i	−0.196609	−	0.980482i	$-0.562993\pi$
$607$	13.6542	−	7.88328i	0.554208	−	0.319972i	0.750818	+	0.660510i	$0.229660\pi$
$608$		0			0
$609$	−1.87689	+	1.08362i	−0.0760554	+	0.0439106i
$610$		0			0
$611$	−1.28246	+	2.22129i	−0.0518829	+	0.0898638i
$612$		0			0
$613$	−27.4452	+	15.8455i	−1.10850	+	0.639993i	−0.938441	−	0.345441i	$-0.887729\pi$
$613$	−27.4452	+	15.8455i	−1.10850	+	0.639993i	−0.170060	+	0.985434i	$0.554396\pi$
$614$		0			0
$615$			1.26673i			0.0510796i
$616$		0			0
$617$	21.4334	+	37.1238i	0.862878	+	1.49455i	0.869139	+	0.494568i	$0.164674\pi$
$617$	21.4334	+	37.1238i	0.862878	+	1.49455i	−0.00626123	+	0.999980i	$0.501993\pi$
$618$		0			0
$619$			26.9176i			1.08191i	0.841052	+	0.540954i	$0.181937\pi$
$619$			26.9176i			1.08191i	−0.841052	+	0.540954i	$0.818063\pi$
$620$		0			0
$621$	34.4319			1.38170
$622$		0			0
$623$		−	5.45950i		−	0.218730i
$624$		0			0
$625$	−10.6615	+	18.4663i	−0.426460	+	0.738650i
$626$		0			0
$627$	−1.34602	−	2.33138i	−0.0537549	−	0.0931063i
$628$		0			0
$629$	1.33403	−	2.17660i	0.0531914	−	0.0867867i
$630$		0			0
$631$	4.29512	−	2.47979i	0.170986	−	0.0987189i	−0.412065	−	0.911155i	$-0.635192\pi$
$631$	4.29512	−	2.47979i	0.170986	−	0.0987189i	0.583051	+	0.812436i	$0.301859\pi$
$632$		0			0
$633$	−3.59805	+	6.23200i	−0.143009	+	0.247700i
$634$		0			0
$635$	−3.30662			−0.131219
$636$		0			0
$637$	−42.1066			−1.66832
$638$		0			0
$639$	13.1067			0.518493
$640$		0			0
$641$	19.5007	+	33.7763i	0.770233	+	1.33408i	0.937435	+	0.348160i	$0.113194\pi$
$641$	19.5007	+	33.7763i	0.770233	+	1.33408i	−0.167202	+	0.985923i	$0.553473\pi$
$642$		0			0
$643$	−15.4140			−0.607869			−0.303935	−	0.952693i	$-0.598300\pi$
$643$	−15.4140			−0.607869			−0.303935	+	0.952693i	$0.598300\pi$
$644$		0			0
$645$	−0.525512	+	0.303405i	−0.0206920	+	0.0119466i
$646$		0			0
$647$	15.7881	+	9.11524i	0.620693	+	0.358357i	0.777139	−	0.629329i	$-0.216670\pi$
$647$	15.7881	+	9.11524i	0.620693	+	0.358357i	−0.156446	+	0.987687i	$0.550004\pi$
$648$		0			0
$649$	11.3927	−	6.57760i	0.447204	−	0.258193i
$650$		0			0
$651$	1.46388	+	2.53552i	0.0573740	+	0.0993747i
$652$		0			0
$653$	4.36624	−	7.56254i	0.170864	−	0.295945i	−0.767858	−	0.640620i	$-0.778677\pi$
$653$	4.36624	−	7.56254i	0.170864	−	0.295945i	0.938722	+	0.344675i	$0.112011\pi$
$654$		0			0
$655$	0.266498			0.0104129
$656$		0			0
$657$	5.83969	+	10.1146i	0.227828	+	0.394610i
$658$		0			0
$659$	20.8602	+	12.0437i	0.812599	+	0.469154i	0.847858	−	0.530224i	$-0.177892\pi$
$659$	20.8602	+	12.0437i	0.812599	+	0.469154i	−0.0352586	+	0.999378i	$0.511225\pi$
$660$		0			0
$661$	14.7957	−	25.6269i	0.575486	−	0.996771i	−0.420502	−	0.907291i	$-0.638146\pi$
$661$	14.7957	−	25.6269i	0.575486	−	0.996771i	0.995989	−	0.0894800i	$-0.0285205\pi$
$662$		0			0
$663$	−1.09496	+	1.89653i	−0.0425248	+	0.0736551i
$664$		0			0
$665$	−0.656042			−0.0254402
$666$		0			0
$667$			42.4477i			1.64358i
$668$		0			0
$669$	−0.218262	−	0.126013i	−0.00843848	−	0.00487196i
$670$		0			0
$671$	−5.30722	−	3.06413i	−0.204883	−	0.118289i
$672$		0			0
$673$	0.475568	−	0.823709i	0.0183318	−	0.0317516i	−0.856714	−	0.515792i	$-0.827498\pi$
$673$	0.475568	−	0.823709i	0.0183318	−	0.0317516i	0.875046	+	0.484040i	$0.160831\pi$
$674$		0			0
$675$	−18.2975	+	10.5640i	−0.704269	+	0.406610i
$676$		0			0
$677$			38.9665i			1.49760i	0.662794	+	0.748802i	$0.269370\pi$
$677$			38.9665i			1.49760i	−0.662794	+	0.748802i	$0.730630\pi$
$678$		0			0
$679$	3.41054	+	1.96908i	0.130885	+	0.0755662i
$680$		0			0
$681$	−10.3757	+	5.99044i	−0.397600	+	0.229554i
$682$		0			0
$683$	−23.8499	−	41.3092i	−0.912589	−	1.58065i	−0.810393	−	0.585887i	$-0.800746\pi$
$683$	−23.8499	−	41.3092i	−0.912589	−	1.58065i	−0.102196	−	0.994764i	$-0.532587\pi$
$684$		0			0
$685$	−1.41121	+	2.44429i	−0.0539197	+	0.0933917i
$686$		0			0
$687$	8.31815	+	14.4075i	0.317357	+	0.549679i
$688$		0			0
$689$		−	49.4695i		−	1.88464i
$690$		0			0
$691$	−2.28449	+	1.31895i	−0.0869061	+	0.0501753i	−0.542823	−	0.839847i	$-0.682645\pi$
$691$	−2.28449	+	1.31895i	−0.0869061	+	0.0501753i	0.455917	+	0.890022i	$0.349311\pi$
$692$		0			0
$693$		−	1.23917i		−	0.0470722i
$694$		0			0
$695$			10.0701i			0.381982i
$696$		0			0
$697$			1.26762i			0.0480146i
$698$		0			0
$699$	9.10327	+	5.25577i	0.344317	+	0.198792i
$700$		0			0
$701$	−6.38945	−	11.0668i	−0.241326	−	0.417989i	0.719766	−	0.694217i	$-0.244249\pi$
$701$	−6.38945	−	11.0668i	−0.241326	−	0.417989i	−0.961092	+	0.276228i	$0.910916\pi$
$702$		0			0
$703$	0.445813	−	16.9790i	0.0168142	−	0.640376i
$704$		0			0
$705$	−0.149975	+	0.0865880i	−0.00564838	+	0.00326109i
$706$		0			0
$707$	−2.03420	−	1.17444i	−0.0765038	−	0.0441695i
$708$		0			0
$709$	−30.4902			−1.14508			−0.572542	−	0.819875i	$-0.694043\pi$
$709$	−30.4902			−1.14508			−0.572542	+	0.819875i	$0.694043\pi$
$710$		0			0
$711$			15.5823i			0.584383i
$712$		0			0
$713$	57.3431			2.14752
$714$		0			0
$715$	3.08262	−	1.77975i	0.115284	−	0.0665590i
$716$		0			0
$717$	−16.1686			−0.603829
$718$		0			0
$719$	−18.5708	−	32.1655i	−0.692572	−	1.19957i	−0.970992	−	0.239111i	$-0.923144\pi$
$719$	−18.5708	−	32.1655i	−0.692572	−	1.19957i	0.278420	−	0.960459i	$-0.410189\pi$
$720$		0			0
$721$	−3.32860	−	1.92177i	−0.123964	−	0.0715705i
$722$		0			0
$723$	−11.5680	−	20.0364i	−0.430219	−	0.745161i
$724$		0			0
$725$	−13.0234	−	22.5571i	−0.483676	−	0.837751i
$726$		0			0
$727$	4.90169	+	2.82999i	0.181794	+	0.104959i	0.588135	−	0.808763i	$-0.299862\pi$
$727$	4.90169	+	2.82999i	0.181794	+	0.104959i	−0.406341	+	0.913721i	$0.633196\pi$
$728$		0			0
$729$	−3.98627			−0.147640
$730$		0			0
$731$	−0.525882	+	0.303618i	−0.0194504	+	0.0112297i
$732$		0			0
$733$	5.84844	+	3.37660i	0.216017	+	0.124718i	0.604105	−	0.796905i	$-0.293531\pi$
$733$	5.84844	+	3.37660i	0.216017	+	0.124718i	−0.388088	+	0.921622i	$0.626864\pi$
$734$		0			0
$735$	−2.46203	−	1.42146i	−0.0908134	−	0.0524312i
$736$		0			0
$737$	−5.74220	+	9.94577i	−0.211517	+	0.366357i
$738$		0			0
$739$		−	32.3100i		−	1.18854i	−0.804265	−	0.594271i	$-0.797441\pi$
$739$		−	32.3100i		−	1.18854i	0.804265	−	0.594271i	$-0.202559\pi$
$740$		0			0
$741$			14.5700i			0.535242i
$742$		0			0
$743$	−24.3834	+	42.2333i	−0.894540	+	1.54939i	−0.0601677	+	0.998188i	$0.519164\pi$
$743$	−24.3834	+	42.2333i	−0.894540	+	1.54939i	−0.834373	+	0.551201i	$0.814170\pi$
$744$		0			0
$745$	−9.54626	−	5.51153i	−0.349748	−	0.201927i
$746$		0			0
$747$	26.3706	+	15.2251i	0.964851	+	0.557057i
$748$		0			0
$749$	−4.65549	+	2.68785i	−0.170108	+	0.0982119i
$750$		0			0
$751$	40.5687			1.48037			0.740186	−	0.672402i	$-0.234737\pi$
$751$	40.5687			1.48037			0.740186	+	0.672402i	$0.234737\pi$
$752$		0			0
$753$	−8.49164	−	4.90265i	−0.309452	−	0.178662i
$754$		0			0
$755$	2.46285	+	4.26577i	0.0896321	+	0.155247i
$756$		0			0
$757$	11.7022	+	20.2688i	0.425324	+	0.736682i	0.996451	−	0.0841796i	$-0.0268270\pi$
$757$	11.7022	+	20.2688i	0.425324	+	0.736682i	−0.571127	+	0.820862i	$0.693494\pi$
$758$		0			0
$759$	6.46416	+	3.73208i	0.234634	+	0.135466i
$760$		0			0
$761$	−14.1234	−	24.4625i	−0.511974	−	0.886764i	−0.999904	−	0.0138815i	$-0.995581\pi$
$761$	−14.1234	−	24.4625i	−0.511974	−	0.886764i	0.487930	−	0.872883i	$-0.337752\pi$
$762$		0			0
$763$	−4.27023			−0.154593
$764$		0			0
$765$	0.416359	−	0.240385i	0.0150535	−	0.00869114i
$766$		0			0
$767$	−71.1991			−2.57085
$768$		0			0
$769$			8.06031i			0.290662i	0.989383	+	0.145331i	$0.0464247\pi$
$769$			8.06031i			0.290662i	−0.989383	+	0.145331i	$0.953575\pi$
$770$		0			0
$771$	13.8012			0.497037
$772$		0			0
$773$	−24.6510	−	14.2323i	−0.886635	−	0.511899i	−0.0137947	−	0.999905i	$-0.504391\pi$
$773$	−24.6510	−	14.2323i	−0.886635	−	0.511899i	−0.872840	+	0.488006i	$0.837724\pi$
$774$		0			0
$775$	−30.4727	+	17.5934i	−1.09461	+	0.631975i
$776$		0			0
$777$	−1.25647	+	2.05004i	−0.0450755	+	0.0735448i
$778$		0			0
$779$	4.21687	+	7.30383i	0.151085	+	0.261687i
$780$		0			0
$781$	5.67799	+	3.27819i	0.203174	+	0.117303i
$782$		0			0
$783$		−	24.3834i		−	0.871391i
$784$		0			0
$785$			0.822628i			0.0293609i
$786$		0			0
$787$			22.8308i			0.813829i	0.913466	+	0.406915i	$0.133395\pi$
$787$			22.8308i			0.813829i	−0.913466	+	0.406915i	$0.866605\pi$
$788$		0			0
$789$	6.78163	−	3.91537i	0.241432	−	0.139391i
$790$		0			0
$791$			3.45821i			0.122960i
$792$		0			0
$793$	16.5838	+	28.7240i	0.588908	+	1.02002i
$794$		0			0
$795$	1.67001	−	2.89255i	0.0592293	−	0.102588i
$796$		0			0
$797$	25.8463	+	44.7671i	0.915523	+	1.58573i	0.806134	+	0.591733i	$0.201556\pi$
$797$	25.8463	+	44.7671i	0.915523	+	1.58573i	0.109388	+	0.993999i	$0.465111\pi$
$798$		0			0
$799$	−0.150080	+	0.0866489i	−0.00530946	+	0.00306542i
$800$		0			0
$801$	23.0526	+	13.3094i	0.814523	+	0.470265i
$802$		0			0
$803$			5.84239i			0.206173i
$804$		0			0
$805$	1.57529	−	0.909496i	0.0555218	−	0.0320555i
$806$		0			0
$807$	−8.07741	+	13.9905i	−0.284338	+	0.492488i
$808$		0			0
$809$	−5.03875	−	2.90912i	−0.177153	−	0.102279i	0.408801	−	0.912623i	$-0.365947\pi$
$809$	−5.03875	−	2.90912i	−0.177153	−	0.102279i	−0.585954	+	0.810344i	$0.699280\pi$
$810$		0			0
$811$	−21.5536	−	12.4440i	−0.756850	−	0.436967i	0.0713139	−	0.997454i	$-0.477281\pi$
$811$	−21.5536	−	12.4440i	−0.756850	−	0.436967i	−0.828163	+	0.560487i	$0.810614\pi$
$812$		0			0
$813$			12.9747i			0.455042i
$814$		0			0
$815$	−10.1673			−0.356145
$816$		0			0
$817$	−2.02003	+	3.49879i	−0.0706719	+	0.122407i
$818$		0			0
$819$	−3.35334	+	5.80816i	−0.117175	+	0.202954i
$820$		0			0
$821$	48.4345	+	27.9637i	1.69038	+	0.975939i	0.954209	+	0.299140i	$0.0966996\pi$
$821$	48.4345	+	27.9637i	1.69038	+	0.975939i	0.736167	+	0.676800i	$0.236634\pi$
$822$		0			0
$823$	−24.7431	−	42.8563i	−0.862489	−	1.49388i	−0.869519	−	0.493900i	$-0.835571\pi$
$823$	−24.7431	−	42.8563i	−0.862489	−	1.49388i	0.00702958	−	0.999975i	$-0.497762\pi$
$824$		0			0
$825$	−4.58016			−0.159461
$826$		0			0
$827$	−0.104098	+	0.180303i	−0.00361985	+	0.00626976i	−0.867830	−	0.496862i	$-0.834486\pi$
$827$	−0.104098	+	0.180303i	−0.00361985	+	0.00626976i	0.864210	+	0.503132i	$0.167819\pi$
$828$		0			0
$829$	1.32569	+	2.29616i	0.0460431	+	0.0797490i	0.888128	−	0.459595i	$-0.152006\pi$
$829$	1.32569	+	2.29616i	0.0460431	+	0.0797490i	−0.842085	+	0.539344i	$0.818672\pi$
$830$		0			0
$831$	0.333822	−	0.192732i	0.0115802	−	0.00668581i
$832$		0			0
$833$	−2.46376	−	1.42245i	−0.0853643	−	0.0492851i
$834$		0			0
$835$	−2.60992	+	1.50684i	−0.0903201	+	0.0521463i
$836$		0			0
$837$	−32.9398			−1.13857
$838$		0			0
$839$	−3.80615	−	6.59245i	−0.131403	−	0.227597i	0.792815	−	0.609463i	$-0.208615\pi$
$839$	−3.80615	−	6.59245i	−0.131403	−	0.227597i	−0.924218	+	0.381866i	$0.875282\pi$
$840$		0			0
$841$	1.05986			0.0365470
$842$		0			0
$843$	8.18653			0.281959
$844$		0			0
$845$	−12.7743			−0.439450
$846$		0			0
$847$	−2.27823	+	3.94601i	−0.0782809	+	0.135587i
$848$		0			0
$849$	−7.63598	+	4.40864i	−0.262066	+	0.151304i
$850$		0			0
$851$	22.4682	+	41.3882i	0.770199	+	1.41877i
$852$		0			0
$853$	−0.326333	−	0.565225i	−0.0111734	−	0.0193529i	0.860385	−	0.509645i	$-0.170223\pi$
$853$	−0.326333	−	0.565225i	−0.0111734	−	0.0193529i	−0.871558	+	0.490292i	$0.836890\pi$
$854$		0			0
$855$	1.59933	−	2.77012i	0.0546959	−	0.0947360i
$856$		0			0
$857$		−	25.0754i		−	0.856560i	−0.903646	−	0.428280i	$-0.859120\pi$
$857$		−	25.0754i		−	0.856560i	0.903646	−	0.428280i	$-0.140880\pi$
$858$		0			0
$859$	45.7376			1.56055			0.780273	−	0.625439i	$-0.215080\pi$
$859$	45.7376			1.56055			0.780273	+	0.625439i	$0.215080\pi$
$860$		0			0
$861$		−	1.19392i		−	0.0406885i
$862$		0			0
$863$	27.9001	+	48.3245i	0.949732	+	1.64498i	0.745988	+	0.665960i	$0.231978\pi$
$863$	27.9001	+	48.3245i	0.949732	+	1.64498i	0.203744	+	0.979024i	$0.434689\pi$
$864$		0			0
$865$		−	1.60666i		−	0.0546281i
$866$		0			0
$867$	12.2389	−	7.06611i	0.415654	−	0.239978i
$868$		0			0
$869$	−3.89738	+	6.75046i	−0.132210	+	0.228994i
$870$		0			0
$871$	53.8289	−	31.0781i	1.82392	−	1.05304i
$872$		0			0
$873$	−16.6287	+	9.60061i	−0.562797	+	0.324931i
$874$		0			0
$875$	−1.14545	+	1.98398i	−0.0387234	+	0.0670708i
$876$		0			0
$877$		−	55.1352i		−	1.86178i	−0.365295	−	0.930892i	$-0.619032\pi$
$877$		−	55.1352i		−	1.86178i	0.365295	−	0.930892i	$-0.380968\pi$
$878$		0			0
$879$	3.91532	+	6.78153i	0.132060	+	0.228735i
$880$		0			0
$881$	−9.75254	+	16.8919i	−0.328571	+	0.569102i	−0.982229	−	0.187688i	$-0.939900\pi$
$881$	−9.75254	+	16.8919i	−0.328571	+	0.569102i	0.653657	+	0.756791i	$0.273234\pi$
$882$		0			0
$883$	23.1064	−	40.0215i	0.777592	−	1.34683i	−0.155733	−	0.987799i	$-0.549774\pi$
$883$	23.1064	−	40.0215i	0.777592	−	1.34683i	0.933326	−	0.359031i	$-0.116893\pi$
$884$		0			0
$885$	−4.16311	−	2.40357i	−0.139942	−	0.0807953i
$886$		0			0
$887$	34.7080			1.16538			0.582690	−	0.812695i	$-0.302000\pi$
$887$	34.7080			1.16538			0.582690	+	0.812695i	$0.302000\pi$
$888$		0			0
$889$	3.11654			0.104526
$890$		0			0
$891$	3.12830	+	1.80613i	0.104802	+	0.0605075i
$892$		0			0
$893$	−0.576492	+	0.998513i	−0.0192916	+	0.0334140i
$894$		0			0
$895$	2.47685	−	4.29002i	0.0827918	−	0.143400i
$896$		0			0
$897$	−20.1989	−	34.9856i	−0.674423	−	1.16813i
$898$		0			0
$899$		−	40.6083i		−	1.35436i
$900$		0			0
$901$	1.67119	−	2.89458i	0.0556753	−	0.0964325i
$902$		0			0
$903$	0.495304	−	0.285964i	0.0164827	−	0.00951628i
$904$		0			0
$905$	5.71218	−	3.29793i	0.189879	−	0.109627i
$906$		0			0
$907$	−2.24528	+	3.88894i	−0.0745534	+	0.129130i	−0.900892	−	0.434043i	$-0.857086\pi$
$907$	−2.24528	+	3.88894i	−0.0745534	+	0.129130i	0.826339	+	0.563174i	$0.190420\pi$
$908$		0			0
$909$	9.91811	−	5.72622i	0.328963	−	0.189927i
$910$		0			0
$911$			24.3620i			0.807150i	0.914947	+	0.403575i	$0.132233\pi$
$911$			24.3620i			0.807150i	−0.914947	+	0.403575i	$0.867767\pi$
$912$		0			0
$913$	7.61606	+	13.1914i	0.252055	+	0.436571i
$914$		0			0
$915$			2.23937i			0.0740314i
$916$		0			0
$917$	−0.251179			−0.00829465
$918$		0			0
$919$			3.85794i			0.127262i	0.997974	+	0.0636308i	$0.0202680\pi$
$919$			3.85794i			0.127262i	−0.997974	+	0.0636308i	$0.979732\pi$
$920$		0			0
$921$	−8.40594	+	14.5595i	−0.276985	+	0.479752i
$922$		0			0
$923$	−17.7423	−	30.7306i	−0.583996	−	1.01151i
$924$		0			0
$925$	−24.6381	−	15.1007i	−0.810096	−	0.496507i
$926$		0			0
$927$	16.2292	−	9.36996i	0.533038	−	0.307750i
$928$		0			0
$929$	−4.55848	+	7.89552i	−0.149559	+	0.259044i	−0.931064	−	0.364855i	$-0.881119\pi$
$929$	−4.55848	+	7.89552i	−0.149559	+	0.259044i	0.781506	+	0.623898i	$0.214452\pi$
$930$		0			0
$931$	−18.9277			−0.620331
$932$		0			0
$933$	−24.3277			−0.796454
$934$		0			0
$935$	0.240496			0.00786505
$936$		0			0
$937$	15.6460	+	27.0996i	0.511132	+	0.885307i	0.999917	+	0.0129024i	$0.00410709\pi$
$937$	15.6460	+	27.0996i	0.511132	+	0.885307i	−0.488785	+	0.872405i	$0.662560\pi$
$938$		0			0
$939$	−2.41659			−0.0788623
$940$		0			0
$941$	19.8092	−	11.4369i	0.645763	−	0.372831i	−0.141068	−	0.990000i	$-0.545054\pi$
$941$	19.8092	−	11.4369i	0.645763	−	0.372831i	0.786831	+	0.617169i	$0.211720\pi$
$942$		0			0
$943$	−20.2512	−	11.6920i	−0.659469	−	0.380744i
$944$		0			0
$945$	−0.904901	+	0.522445i	−0.0294364	+	0.0169951i
$946$		0			0
$947$	1.61262	+	2.79314i	0.0524030	+	0.0907647i	0.891037	−	0.453931i	$-0.149979\pi$
$947$	1.61262	+	2.79314i	0.0524030	+	0.0907647i	−0.838634	+	0.544695i	$0.816645\pi$
$948$		0			0
$949$	15.8102	−	27.3841i	0.513221	−	0.888925i
$950$		0			0
$951$	7.24306			0.234872
$952$		0			0
$953$	18.6742	+	32.3447i	0.604917	+	1.04775i	0.992065	+	0.125729i	$0.0401269\pi$
$953$	18.6742	+	32.3447i	0.604917	+	1.04775i	−0.387148	+	0.922018i	$0.626540\pi$
$954$		0			0
$955$	−5.24426	−	3.02778i	−0.169700	−	0.0979765i
$956$		0			0
$957$	2.64292	−	4.57768i	0.0854336	−	0.147975i
$958$		0			0
$959$	1.33009	−	2.30379i	0.0429509	−	0.0743932i
$960$		0			0
$961$	−23.8583			−0.769622
$962$		0			0
$963$		−	26.2102i		−	0.844613i
$964$		0			0
$965$	−4.70440	−	2.71609i	−0.151440	−	0.0874340i
$966$		0			0
$967$	−24.7361	−	14.2814i	−0.795460	−	0.459259i	0.0464213	−	0.998922i	$-0.485218\pi$
$967$	−24.7361	−	14.2814i	−0.795460	−	0.459259i	−0.841881	+	0.539663i	$0.818552\pi$
$968$		0			0
$969$	−0.492206	+	0.852526i	−0.0158119	+	0.0273871i
$970$		0			0
$971$	33.1378	−	19.1321i	1.06344	−	0.613979i	0.137060	−	0.990563i	$-0.456235\pi$
$971$	33.1378	−	19.1321i	1.06344	−	0.613979i	0.926382	+	0.376584i	$0.122901\pi$
$972$		0			0
$973$		−	9.49126i		−	0.304276i
$974$		0			0
$975$	21.4678	+	12.3945i	0.687521	+	0.396941i
$976$		0			0
$977$	9.69869	−	5.59954i	0.310288	−	0.179145i	−0.336767	−	0.941588i	$-0.609333\pi$
$977$	9.69869	−	5.59954i	0.310288	−	0.179145i	0.647056	+	0.762443i	$0.276000\pi$
$978$		0			0
$979$	6.65778	+	11.5316i	0.212784	+	0.368552i
$980$		0			0
$981$	10.4102	−	18.0309i	0.332371	−	0.575683i
$982$		0			0
$983$	−9.97280	−	17.2734i	−0.318083	−	0.550936i	0.662005	−	0.749499i	$-0.269706\pi$
$983$	−9.97280	−	17.2734i	−0.318083	−	0.550936i	−0.980088	+	0.198564i	$0.936372\pi$
$984$		0			0
$985$		−	8.19836i		−	0.261221i
$986$		0			0
$987$	0.141354	−	0.0816106i	0.00449934	−	0.00259769i
$988$		0			0
$989$		−	11.2018i		−	0.356196i
$990$		0			0
$991$			36.3527i			1.15478i	0.816467	+	0.577391i	$0.195929\pi$
$991$			36.3527i			1.15478i	−0.816467	+	0.577391i	$0.804071\pi$
$992$		0			0
$993$		−	6.97396i		−	0.221312i
$994$		0			0
$995$	0.0816115	+	0.0471184i	0.00258726	+	0.00149375i
$996$		0			0
$997$	9.16192	+	15.8689i	0.290161	+	0.502574i	0.973848	−	0.227202i	$-0.0729578\pi$
$997$	9.16192	+	15.8689i	0.290161	+	0.502574i	−0.683687	+	0.729776i	$0.739624\pi$
$998$		0			0
$999$	−12.9065	−	23.7748i	−0.408343	−	0.752200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1184.2.y.a.529.13		72
4.3	odd	2		296.2.q.a.85.34	yes	72
8.3	odd	2		296.2.q.a.85.28	✓	72
8.5	even	2	inner	1184.2.y.a.529.24		72
37.27	even	6	inner	1184.2.y.a.1137.24		72
148.27	odd	6		296.2.q.a.101.28	yes	72
296.27	odd	6		296.2.q.a.101.34	yes	72
296.101	even	6	inner	1184.2.y.a.1137.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.28	✓	72	8.3	odd	2
296.2.q.a.85.34	yes	72	4.3	odd	2
296.2.q.a.101.28	yes	72	148.27	odd	6
296.2.q.a.101.34	yes	72	296.27	odd	6
1184.2.y.a.529.13		72	1.1	even	1	trivial
1184.2.y.a.529.24		72	8.5	even	2	inner
1184.2.y.a.1137.13		72	296.101	even	6	inner
1184.2.y.a.1137.24		72	37.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1184 = 2^{5} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1184.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.727471 - 0.420006i) q^{3} +(0.249638 - 0.432386i) q^{5} +(-0.235288 + 0.407531i) q^{7} +(-1.14719 - 1.98699i) q^{9} -1.14772i q^{11} +(-3.10587 + 5.37952i) q^{13} +(-0.363209 + 0.209699i) q^{15} +(-0.363464 + 0.209846i) q^{17} +(-1.39615 + 2.41820i) q^{19} +(0.342330 - 0.197644i) q^{21} -7.74213i q^{23} +(2.37536 + 4.11425i) q^{25} +4.44734i q^{27} -5.48269 q^{29} +7.40664i q^{31} +(-0.482049 + 0.834933i) q^{33} +(0.117474 + 0.203470i) q^{35} +(-5.34584 + 2.90207i) q^{37} +(4.51886 - 2.60896i) q^{39} +(1.51018 - 2.61571i) q^{41} +1.44686 q^{43} -1.14553 q^{45} +0.412916 q^{47} +(3.38928 + 5.87040i) q^{49} +0.352546 q^{51} +(-6.89691 + 3.98194i) q^{53} +(-0.496258 - 0.286515i) q^{55} +(2.03131 - 1.17278i) q^{57} +(5.73102 + 9.92641i) q^{59} +(2.66975 - 4.62415i) q^{61} +1.07968 q^{63} +(1.55069 + 2.68587i) q^{65} +(-8.66568 - 5.00313i) q^{67} +(-3.25174 + 5.63217i) q^{69} +(-2.85626 + 4.94719i) q^{71} -5.09043 q^{73} -3.99066i q^{75} +(0.467731 + 0.270045i) q^{77} +(-5.88163 - 3.39576i) q^{79} +(-1.57366 + 2.72567i) q^{81} +(-11.4936 + 6.63581i) q^{83} +0.209542i q^{85} +(3.98850 + 2.30276i) q^{87} +(-10.0474 + 5.80087i) q^{89} +(-1.46155 - 2.53147i) q^{91} +(3.11083 - 5.38811i) q^{93} +(0.697063 + 1.20735i) q^{95} -8.36880i q^{97} +(-2.28051 + 1.31665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) \) 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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