LMFDB - Embedded newform 693.2.m.k.190.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.6
Character	$\chi$	$=$	693.190
Dual form			693.2.m.k.631.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.727975 - 0.528905i) q^{2} +(-0.367826 + 1.13205i) q^{4} +(-0.650418 - 0.472557i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.887104 + 2.73023i) q^{8} +O(q^{10})$	\(q+(0.727975 - 0.528905i) q^{2} +(-0.367826 + 1.13205i) q^{4} +(-0.650418 - 0.472557i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.887104 + 2.73023i) q^{8} -0.723426 q^{10} +(3.31060 + 0.199849i) q^{11} +(-2.38421 + 1.73223i) q^{13} +(-0.278062 - 0.855786i) q^{14} +(0.163856 + 0.119049i) q^{16} +(2.67299 + 1.94204i) q^{17} +(2.45327 + 7.55040i) q^{19} +(0.774200 - 0.562489i) q^{20} +(2.51574 - 1.60551i) q^{22} +7.53481 q^{23} +(-1.34535 - 4.14056i) q^{25} +(-0.819462 + 2.52205i) q^{26} +(0.962982 + 0.699647i) q^{28} +(0.0724492 - 0.222976i) q^{29} +(-3.22308 + 2.34171i) q^{31} -5.55921 q^{32} +2.97302 q^{34} +(-0.650418 + 0.472557i) q^{35} +(-0.165770 + 0.510186i) q^{37} +(5.77936 + 4.19895i) q^{38} +(0.713197 - 2.19500i) q^{40} +(1.47849 + 4.55032i) q^{41} +3.16645 q^{43} +(-1.44396 + 3.67426i) q^{44} +(5.48516 - 3.98520i) q^{46} +(3.40270 + 10.4724i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-3.16935 - 2.30267i) q^{50} +(-1.08400 - 3.33622i) q^{52} +(9.49116 - 6.89573i) q^{53} +(-2.05883 - 1.69443i) q^{55} +2.87073 q^{56} +(-0.0651917 - 0.200640i) q^{58} +(1.62342 - 4.99638i) q^{59} +(-2.95649 - 2.14802i) q^{61} +(-1.10778 + 3.40941i) q^{62} +(-4.37468 + 3.17839i) q^{64} +2.36931 q^{65} -13.6736 q^{67} +(-3.18169 + 2.31163i) q^{68} +(-0.223551 + 0.688019i) q^{70} +(-8.36286 - 6.07597i) q^{71} +(2.75315 - 8.47332i) q^{73} +(0.149164 + 0.459079i) q^{74} -9.44983 q^{76} +(1.21310 - 3.08681i) q^{77} +(6.77674 - 4.92359i) q^{79} +(-0.0503180 - 0.154863i) q^{80} +(3.48299 + 2.53054i) q^{82} +(-5.87535 - 4.26869i) q^{83} +(-0.820837 - 2.52628i) q^{85} +(2.30509 - 1.67475i) q^{86} +(2.39121 + 9.21597i) q^{88} -8.03460 q^{89} +(0.910689 + 2.80281i) q^{91} +(-2.77150 + 8.52980i) q^{92} +(8.01600 + 5.82396i) q^{94} +(1.97234 - 6.07023i) q^{95} +(-15.5907 + 11.3273i) q^{97} -0.899827 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.727975	−	0.528905i	0.514756	−	0.373992i	−0.299869	−	0.953981i	$-0.596943\pi$
$2$	0.727975	−	0.528905i	0.514756	−	0.373992i	0.814625	+	0.579988i	$0.196943\pi$
$3$		0			0
$3$		0			0
$4$	−0.367826	+	1.13205i	−0.183913	+	0.566027i
$5$	−0.650418	−	0.472557i	−0.290876	−	0.211334i	0.432771	−	0.901504i	$-0.357536\pi$
$5$	−0.650418	−	0.472557i	−0.290876	−	0.211334i	−0.723647	+	0.690170i	$0.757536\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.887104	+	2.73023i	0.313639	+	0.965280i
$9$		0			0
$10$	−0.723426			−0.228767
$11$	3.31060	+	0.199849i	0.998183	+	0.0602567i
$11$	3.31060	+	0.199849i	0.998183	+	0.0602567i
$12$		0			0
$13$	−2.38421	+	1.73223i	−0.661262	+	0.480435i	−0.867089	−	0.498154i	$-0.834012\pi$
$13$	−2.38421	+	1.73223i	−0.661262	+	0.480435i	0.205827	+	0.978588i	$0.434012\pi$
$14$	−0.278062	−	0.855786i	−0.0743152	−	0.228719i
$15$		0			0
$16$	0.163856	+	0.119049i	0.0409641	+	0.0297621i
$17$	2.67299	+	1.94204i	0.648295	+	0.471014i	0.862690	−	0.505733i	$-0.168778\pi$
$17$	2.67299	+	1.94204i	0.648295	+	0.471014i	−0.214395	+	0.976747i	$0.568778\pi$
$18$		0			0
$19$	2.45327	+	7.55040i	0.562819	+	1.73218i	0.674344	+	0.738418i	$0.264427\pi$
$19$	2.45327	+	7.55040i	0.562819	+	1.73218i	−0.111524	+	0.993762i	$0.535573\pi$
$20$	0.774200	−	0.562489i	0.173116	−	0.125776i
$21$		0			0
$22$	2.51574	−	1.60551i	0.536357	−	0.342295i
$23$	7.53481			1.57112			0.785558	−	0.618788i	$-0.212376\pi$
$23$	7.53481			1.57112			0.785558	+	0.618788i	$0.212376\pi$
$24$		0			0
$25$	−1.34535	−	4.14056i	−0.269070	−	0.828113i
$26$	−0.819462	+	2.52205i	−0.160710	+	0.494614i
$27$		0			0
$28$	0.962982	+	0.699647i	0.181986	+	0.132221i
$29$	0.0724492	−	0.222976i	0.0134535	−	0.0414055i	−0.944104	−	0.329647i	$-0.893070\pi$
$29$	0.0724492	−	0.222976i	0.0134535	−	0.0414055i	0.957558	+	0.288241i	$0.0930704\pi$
$30$		0			0
$31$	−3.22308	+	2.34171i	−0.578882	+	0.420583i	−0.838321	−	0.545177i	$-0.816462\pi$
$31$	−3.22308	+	2.34171i	−0.578882	+	0.420583i	0.259439	+	0.965760i	$0.416462\pi$
$32$	−5.55921			−0.982738
$33$		0			0
$34$	2.97302			0.509869
$35$	−0.650418	+	0.472557i	−0.109941	+	0.0798766i
$36$		0			0
$37$	−0.165770	+	0.510186i	−0.0272523	+	0.0838741i	−0.963758	−	0.266779i	$-0.914040\pi$
$37$	−0.165770	+	0.510186i	−0.0272523	+	0.0838741i	0.936505	+	0.350653i	$0.114040\pi$
$38$	5.77936	+	4.19895i	0.937537	+	0.681160i
$39$		0			0
$40$	0.713197	−	2.19500i	0.112766	−	0.347059i
$41$	1.47849	+	4.55032i	0.230901	+	0.710641i	0.997639	+	0.0686803i	$0.0218788\pi$
$41$	1.47849	+	4.55032i	0.230901	+	0.710641i	−0.766737	+	0.641961i	$0.778121\pi$
$42$		0			0
$43$	3.16645			0.482878			0.241439	−	0.970416i	$-0.422381\pi$
$43$	3.16645			0.482878			0.241439	+	0.970416i	$0.422381\pi$
$44$	−1.44396	+	3.67426i	−0.217686	+	0.553916i
$45$		0			0
$46$	5.48516	−	3.98520i	0.808742	−	0.587586i
$47$	3.40270	+	10.4724i	0.496334	+	1.52756i	0.814867	+	0.579648i	$0.196810\pi$
$47$	3.40270	+	10.4724i	0.496334	+	1.52756i	−0.318533	+	0.947912i	$0.603190\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−3.16935	−	2.30267i	−0.448213	−	0.325646i
$51$		0			0
$52$	−1.08400	−	3.33622i	−0.150324	−	0.462650i
$53$	9.49116	−	6.89573i	1.30371	−	0.947201i	0.303726	−	0.952759i	$-0.401769\pi$
$53$	9.49116	−	6.89573i	1.30371	−	0.947201i	0.999985	+	0.00555811i	$0.00176921\pi$
$54$		0			0
$55$	−2.05883	−	1.69443i	−0.277613	−	0.228477i
$56$	2.87073			0.383617
$57$		0			0
$58$	−0.0651917	−	0.200640i	−0.00856010	−	0.0263453i
$59$	1.62342	−	4.99638i	0.211352	−	0.650474i	−0.788041	−	0.615623i	$-0.788904\pi$
$59$	1.62342	−	4.99638i	0.211352	−	0.650474i	0.999393	−	0.0348508i	$-0.0110956\pi$
$60$		0			0
$61$	−2.95649	−	2.14802i	−0.378540	−	0.275025i	0.382203	−	0.924078i	$-0.375165\pi$
$61$	−2.95649	−	2.14802i	−0.378540	−	0.275025i	−0.760743	+	0.649053i	$0.775165\pi$
$62$	−1.10778	+	3.40941i	−0.140689	+	0.432995i
$63$		0			0
$64$	−4.37468	+	3.17839i	−0.546835	+	0.397299i
$65$	2.36931			0.293877
$66$		0			0
$67$	−13.6736			−1.67050			−0.835250	−	0.549871i	$-0.814677\pi$
$67$	−13.6736			−1.67050			−0.835250	+	0.549871i	$0.814677\pi$
$68$	−3.18169	+	2.31163i	−0.385836	+	0.280326i
$69$		0			0
$70$	−0.223551	+	0.688019i	−0.0267195	+	0.0822340i
$71$	−8.36286	−	6.07597i	−0.992489	−	0.721085i	−0.0320239	−	0.999487i	$-0.510195\pi$
$71$	−8.36286	−	6.07597i	−0.992489	−	0.721085i	−0.960465	+	0.278402i	$0.910195\pi$
$72$		0			0
$73$	2.75315	−	8.47332i	0.322232	−	0.991727i	−0.650443	−	0.759555i	$-0.725417\pi$
$73$	2.75315	−	8.47332i	0.322232	−	0.991727i	0.972675	−	0.232172i	$-0.0745832\pi$
$74$	0.149164	+	0.459079i	0.0173400	+	0.0533669i
$75$		0			0
$76$	−9.44983			−1.08397
$77$	1.21310	−	3.08681i	0.138245	−	0.351775i
$78$		0			0
$79$	6.77674	−	4.92359i	0.762442	−	0.553947i	−0.137216	−	0.990541i	$-0.543815\pi$
$79$	6.77674	−	4.92359i	0.762442	−	0.553947i	0.899658	+	0.436594i	$0.143815\pi$
$80$	−0.0503180	−	0.154863i	−0.00562572	−	0.0173142i
$81$		0			0
$82$	3.48299	+	2.53054i	0.384632	+	0.279452i
$83$	−5.87535	−	4.26869i	−0.644904	−	0.468550i	0.216628	−	0.976254i	$-0.430494\pi$
$83$	−5.87535	−	4.26869i	−0.644904	−	0.468550i	−0.861531	+	0.507704i	$0.830494\pi$
$84$		0			0
$85$	−0.820837	−	2.52628i	−0.0890323	−	0.274013i
$86$	2.30509	−	1.67475i	0.248565	−	0.180593i
$87$		0			0
$88$	2.39121	+	9.21597i	0.254904	+	0.982425i
$89$	−8.03460			−0.851666			−0.425833	−	0.904802i	$-0.640019\pi$
$89$	−8.03460			−0.851666			−0.425833	+	0.904802i	$0.640019\pi$
$90$		0			0
$91$	0.910689	+	2.80281i	0.0954661	+	0.293814i
$92$	−2.77150	+	8.52980i	−0.288949	+	0.889293i
$93$		0			0
$94$	8.01600	+	5.82396i	0.826787	+	0.600696i
$95$	1.97234	−	6.07023i	0.202357	−	0.622792i
$96$		0			0
$97$	−15.5907	+	11.3273i	−1.58299	+	1.15011i	−0.669829	+	0.742516i	$0.733632\pi$
$97$	−15.5907	+	11.3273i	−1.58299	+	1.15011i	−0.913163	+	0.407595i	$0.866368\pi$
$98$	−0.899827			−0.0908963
$99$		0			0
$100$	5.18219			0.518219
$101$	13.9793	−	10.1566i	1.39099	−	1.01062i	0.395239	−	0.918578i	$-0.370662\pi$
$101$	13.9793	−	10.1566i	1.39099	−	1.01062i	0.995755	−	0.0920385i	$-0.0293383\pi$
$102$		0			0
$103$	4.43665	−	13.6546i	0.437156	−	1.34543i	−0.453704	−	0.891152i	$-0.649898\pi$
$103$	4.43665	−	13.6546i	0.437156	−	1.34543i	0.890861	−	0.454277i	$-0.150102\pi$
$104$	−6.84443	−	4.97277i	−0.671152	−	0.487620i
$105$		0			0
$106$	3.26214	−	10.0398i	0.316847	−	0.975156i
$107$	−4.73420	−	14.5704i	−0.457672	−	1.40857i	−0.867969	−	0.496618i	$-0.834575\pi$
$107$	−4.73420	−	14.5704i	−0.457672	−	1.40857i	0.410297	−	0.911952i	$-0.365425\pi$
$108$		0			0
$109$	−5.50237			−0.527032			−0.263516	−	0.964655i	$-0.584882\pi$
$109$	−5.50237			−0.527032			−0.263516	+	0.964655i	$0.584882\pi$
$110$	−2.39497	−	0.144576i	−0.228352	−	0.0137848i
$111$		0			0
$112$	0.163856	−	0.119049i	0.0154830	−	0.0112490i
$113$	2.06880	+	6.36710i	0.194616	+	0.598967i	0.999981	+	0.00618714i	$0.00196944\pi$
$113$	2.06880	+	6.36710i	0.194616	+	0.598967i	−0.805365	+	0.592780i	$0.798031\pi$
$114$		0			0
$115$	−4.90078	−	3.56062i	−0.457000	−	0.332030i
$116$	0.225772	+	0.164033i	0.0209624	+	0.0152300i
$117$		0			0
$118$	−1.46080	−	4.49588i	−0.134478	−	0.413880i
$119$	2.67299	−	1.94204i	0.245032	−	0.178026i
$120$		0			0
$121$	10.9201	+	1.32324i	0.992738	+	0.120294i
$122$	−3.28835			−0.297713
$123$		0			0
$124$	−1.46540	−	4.51004i	−0.131597	−	0.405014i
$125$	−2.32380	+	7.15192i	−0.207847	+	0.639687i
$126$		0			0
$127$	9.33897	+	6.78516i	0.828700	+	0.602086i	0.919191	−	0.393812i	$-0.128844\pi$
$127$	9.33897	+	6.78516i	0.828700	+	0.602086i	−0.0904914	+	0.995897i	$0.528844\pi$
$128$	1.93219	−	5.94666i	0.170783	−	0.525616i
$129$		0			0
$130$	1.72480	−	1.25314i	0.151275	−	0.109908i
$131$	−21.2008			−1.85232			−0.926161	−	0.377128i	$-0.876912\pi$
$131$	−21.2008			−1.85232			−0.926161	+	0.377128i	$0.876912\pi$
$132$		0			0
$133$	7.93896			0.688395
$134$	−9.95407	+	7.23205i	−0.859900	+	0.624754i
$135$		0			0
$136$	−2.93099	+	9.02065i	−0.251330	+	0.773514i
$137$	0.659483	+	0.479143i	0.0563435	+	0.0409359i	0.615601	−	0.788058i	$-0.288914\pi$
$137$	0.659483	+	0.479143i	0.0563435	+	0.0409359i	−0.559257	+	0.828994i	$0.688914\pi$
$138$		0			0
$139$	2.86540	−	8.81880i	0.243040	−	0.748001i	−0.752912	−	0.658121i	$-0.771352\pi$
$139$	2.86540	−	8.81880i	0.243040	−	0.748001i	0.995953	−	0.0898801i	$-0.0286484\pi$
$140$	−0.295718	−	0.910127i	−0.0249927	−	0.0769198i
$141$		0			0
$142$	−9.30157			−0.780570
$143$	−8.23936	+	5.25824i	−0.689010	+	0.439716i
$144$		0			0
$145$	−0.152491	+	0.110791i	−0.0126637	+	0.00920070i
$146$	−2.47736	−	7.62452i	−0.205028	−	0.631010i
$147$		0			0
$148$	−0.516583	−	0.375320i	−0.0424629	−	0.0308511i
$149$	5.62143	+	4.08421i	0.460526	+	0.334592i	0.793738	−	0.608260i	$-0.208132\pi$
$149$	5.62143	+	4.08421i	0.460526	+	0.334592i	−0.333212	+	0.942852i	$0.608132\pi$
$150$		0			0
$151$	4.33498	+	13.3417i	0.352776	+	1.08573i	0.957288	+	0.289136i	$0.0933681\pi$
$151$	4.33498	+	13.3417i	0.352776	+	1.08573i	−0.604512	+	0.796596i	$0.706632\pi$
$152$	−18.4380	+	13.3960i	−1.49552	+	1.08656i
$153$		0			0
$154$	−0.749523	−	2.88874i	−0.0603983	−	0.232781i
$155$	3.20294			0.257266
$156$		0			0
$157$	0.226627	+	0.697487i	0.0180868	+	0.0556655i	0.959693	−	0.281052i	$-0.0906833\pi$
$157$	0.226627	+	0.697487i	0.0180868	+	0.0556655i	−0.941606	+	0.336717i	$0.890683\pi$
$158$	2.32919	−	7.16850i	0.185300	−	0.570295i
$159$		0			0
$160$	3.61581	+	2.62704i	0.285855	+	0.207686i
$161$	2.32838	−	7.16603i	0.183502	−	0.564762i
$162$		0			0
$163$	−2.39758	+	1.74195i	−0.187793	+	0.136440i	−0.677710	−	0.735330i	$-0.737027\pi$
$163$	−2.39758	+	1.74195i	−0.187793	+	0.136440i	0.489916	+	0.871769i	$0.337027\pi$
$164$	−5.69504			−0.444708
$165$		0			0
$166$	−6.53485			−0.507203
$167$	6.50456	−	4.72584i	0.503338	−	0.365697i	−0.306952	−	0.951725i	$-0.599309\pi$
$167$	6.50456	−	4.72584i	0.503338	−	0.365697i	0.810291	+	0.586028i	$0.199309\pi$
$168$		0			0
$169$	−1.33338	+	4.10371i	−0.102567	+	0.315670i
$170$	−1.93371	−	1.40492i	−0.148309	−	0.107753i
$171$		0			0
$172$	−1.16470	+	3.58458i	−0.0888077	+	0.273322i
$173$	−1.59317	−	4.90326i	−0.121126	−	0.372788i	0.872049	−	0.489418i	$-0.162791\pi$
$173$	−1.59317	−	4.90326i	−0.121126	−	0.372788i	−0.993175	+	0.116630i	$0.962791\pi$
$174$		0			0
$175$	−4.35365			−0.329105
$176$	0.518671	+	0.426868i	0.0390963	+	0.0321764i
$177$		0			0
$178$	−5.84899	+	4.24954i	−0.438400	+	0.318516i
$179$	−1.85804	−	5.71844i	−0.138876	−	0.427417i	0.857297	−	0.514823i	$-0.172142\pi$
$179$	−1.85804	−	5.71844i	−0.138876	−	0.427417i	−0.996173	+	0.0874061i	$0.972142\pi$
$180$		0			0
$181$	−1.98246	−	1.44034i	−0.147355	−	0.107060i	0.511665	−	0.859185i	$-0.329029\pi$
$181$	−1.98246	−	1.44034i	−0.147355	−	0.107060i	−0.659020	+	0.752125i	$0.729029\pi$
$182$	2.14538	+	1.55871i	0.159026	+	0.115539i
$183$		0			0
$184$	6.68416	+	20.5717i	0.492763	+	1.51657i
$185$	0.348911	−	0.253499i	0.0256525	−	0.0186376i
$186$		0			0
$187$	8.46107	+	6.96351i	0.618735	+	0.509222i
$188$	−13.1069			−0.955922
$189$		0			0
$190$	−1.77476	−	5.46215i	−0.128755	−	0.396266i
$191$	6.57422	−	20.2334i	0.475694	−	1.46404i	−0.369325	−	0.929300i	$-0.620411\pi$
$191$	6.57422	−	20.2334i	0.475694	−	1.46404i	0.845019	−	0.534736i	$-0.179589\pi$
$192$		0			0
$193$	6.79512	+	4.93695i	0.489124	+	0.355369i	0.804847	−	0.593482i	$-0.202247\pi$
$193$	6.79512	+	4.93695i	0.489124	+	0.355369i	−0.315723	+	0.948851i	$0.602247\pi$
$194$	−5.35856	+	16.4920i	−0.384722	+	1.18405i
$195$		0			0
$196$	0.962982	−	0.699647i	0.0687844	−	0.0499748i
$197$	−10.9646			−0.781194			−0.390597	−	0.920562i	$-0.627731\pi$
$197$	−10.9646			−0.781194			−0.390597	+	0.920562i	$0.627731\pi$
$198$		0			0
$199$	6.26130			0.443852			0.221926	−	0.975064i	$-0.428766\pi$
$199$	6.26130			0.443852			0.221926	+	0.975064i	$0.428766\pi$
$200$	10.1112	−	7.34622i	0.714970	−	0.519456i
$201$		0			0
$202$	4.80474	−	14.7875i	0.338060	−	1.04044i
$203$	−0.189674	−	0.137807i	−0.0133125	−	0.00967212i
$204$		0			0
$205$	1.18865	−	3.65828i	0.0830188	−	0.255506i
$206$	−3.99222	−	12.2868i	−0.278151	−	0.856061i
$207$		0			0
$208$	−0.596888			−0.0413867
$209$	6.61286	+	25.4866i	0.457421	+	1.76295i
$210$		0			0
$211$	−13.5270	+	9.82796i	−0.931239	+	0.676585i	−0.946296	−	0.323302i	$-0.895207\pi$
$211$	−13.5270	+	9.82796i	−0.931239	+	0.676585i	0.0150571	+	0.999887i	$0.495207\pi$
$212$	4.31523	+	13.2809i	0.296371	+	0.912138i
$213$		0			0
$214$	−11.1527	−	8.10293i	−0.762384	−	0.553905i
$215$	−2.05951	−	1.49632i	−0.140458	−	0.102049i
$216$		0			0
$217$	1.23111	+	3.78896i	0.0835730	+	0.257211i
$218$	−4.00559	+	2.91023i	−0.271293	+	0.197106i
$219$		0			0
$220$	2.67548	−	1.70745i	0.180381	−	0.115116i
$221$	−9.73704			−0.654984
$222$		0			0
$223$	4.04713	+	12.4558i	0.271016	+	0.834101i	0.990246	+	0.139329i	$0.0444947\pi$
$223$	4.04713	+	12.4558i	0.271016	+	0.834101i	−0.719230	+	0.694772i	$0.755505\pi$
$224$	−1.71789	+	5.28712i	−0.114781	+	0.353261i
$225$		0			0
$226$	4.87363	+	3.54090i	0.324189	+	0.235537i
$227$	4.91414	−	15.1242i	0.326163	−	1.00383i	−0.644750	−	0.764393i	$-0.723039\pi$
$227$	4.91414	−	15.1242i	0.326163	−	1.00383i	0.970913	−	0.239432i	$-0.0769613\pi$
$228$		0			0
$229$	−7.29405	+	5.29944i	−0.482004	+	0.350197i	−0.802101	−	0.597188i	$-0.796285\pi$
$229$	−7.29405	+	5.29944i	−0.482004	+	0.350197i	0.320097	+	0.947385i	$0.396285\pi$
$230$	−5.45088			−0.359420
$231$		0			0
$232$	0.673044			0.0441875
$233$	2.05652	−	1.49415i	0.134727	−	0.0978850i	−0.518381	−	0.855150i	$-0.673465\pi$
$233$	2.05652	−	1.49415i	0.134727	−	0.0978850i	0.653108	+	0.757265i	$0.273465\pi$
$234$		0			0
$235$	2.73564	−	8.41942i	0.178453	−	0.549222i
$236$	5.05903	+	3.67560i	0.329315	+	0.239261i
$237$		0			0
$238$	0.918715	−	2.82751i	0.0595514	−	0.183281i
$239$	−5.92537	−	18.2364i	−0.383281	−	1.17962i	−0.937720	−	0.347392i	$-0.887067\pi$
$239$	−5.92537	−	18.2364i	−0.383281	−	1.17962i	0.554439	−	0.832224i	$-0.312933\pi$
$240$		0			0
$241$	−7.50063			−0.483158			−0.241579	−	0.970381i	$-0.577665\pi$
$241$	−7.50063			−0.483158			−0.241579	+	0.970381i	$0.577665\pi$
$242$	8.64945	−	4.81242i	0.556008	−	0.309354i
$243$		0			0
$244$	3.51914	−	2.55681i	0.225290	−	0.163683i
$245$	0.248438	+	0.764613i	0.0158721	+	0.0488493i
$246$		0			0
$247$	−18.9282	−	13.7521i	−1.20437	−	0.875026i
$248$	−9.25259	−	6.72240i	−0.587540	−	0.426873i
$249$		0			0
$250$	2.09102	+	6.43549i	0.132248	+	0.407016i
$251$	11.8847	−	8.63475i	0.750157	−	0.545021i	−0.145719	−	0.989326i	$-0.546549\pi$
$251$	11.8847	−	8.63475i	0.750157	−	0.545021i	0.895875	+	0.444305i	$0.146549\pi$
$252$		0			0
$253$	24.9447	+	1.50582i	1.56826	+	0.0946703i
$254$	10.3872			0.651754
$255$		0			0
$256$	−5.08059	−	15.6365i	−0.317537	−	0.977279i
$257$	−6.41213	+	19.7345i	−0.399978	+	1.23101i	0.525038	+	0.851079i	$0.324051\pi$
$257$	−6.41213	+	19.7345i	−0.399978	+	1.23101i	−0.925016	+	0.379927i	$0.875949\pi$
$258$		0			0
$259$	0.433990	+	0.315312i	0.0269668	+	0.0195926i
$260$	−0.871496	+	2.68219i	−0.0540479	+	0.166342i
$261$		0			0
$262$	−15.4337	+	11.2132i	−0.953495	+	0.692754i
$263$	27.3462			1.68624			0.843118	−	0.537729i	$-0.180717\pi$
$263$	27.3462			1.68624			0.843118	+	0.537729i	$0.180717\pi$
$264$		0			0
$265$	−9.43185			−0.579394
$266$	5.77936	−	4.19895i	0.354356	−	0.257454i
$267$		0			0
$268$	5.02952	−	15.4793i	0.307227	−	0.945547i
$269$	−1.27748	−	0.928141i	−0.0778891	−	0.0565898i	0.548159	−	0.836374i	$-0.315329\pi$
$269$	−1.27748	−	0.928141i	−0.0778891	−	0.0565898i	−0.626048	+	0.779784i	$0.715329\pi$
$270$		0			0
$271$	4.66658	−	14.3622i	0.283474	−	0.872444i	−0.703377	−	0.710817i	$-0.748326\pi$
$271$	4.66658	−	14.3622i	0.283474	−	0.872444i	0.986852	−	0.161628i	$-0.0516744\pi$
$272$	0.206789	+	0.636431i	0.0125384	+	0.0385893i
$273$		0			0
$274$	0.733509			0.0443129
$275$	−3.62643	−	13.9766i	−0.218682	−	0.842821i
$276$		0			0
$277$	13.1342	−	9.54256i	0.789158	−	0.573357i	−0.118555	−	0.992947i	$-0.537826\pi$
$277$	13.1342	−	9.54256i	0.789158	−	0.573357i	0.907714	+	0.419590i	$0.137826\pi$
$278$	−2.57837	−	7.93540i	−0.154640	−	0.475933i
$279$		0			0
$280$	−1.86717	−	1.35658i	−0.111585	−	0.0810713i
$281$	13.8234	+	10.0433i	0.824633	+	0.599131i	0.918036	−	0.396498i	$-0.129774\pi$
$281$	13.8234	+	10.0433i	0.824633	+	0.599131i	−0.0934030	+	0.995628i	$0.529774\pi$
$282$		0			0
$283$	−0.0355451	−	0.109397i	−0.00211294	−	0.00650296i	0.949994	−	0.312267i	$-0.101088\pi$
$283$	−0.0355451	−	0.109397i	−0.00211294	−	0.00650296i	−0.952107	+	0.305764i	$0.901088\pi$
$284$	9.95440	−	7.23230i	0.590685	−	0.429158i
$285$		0			0
$286$	−3.21694	+	8.18571i	−0.190222	+	0.484031i
$287$	4.78449			0.282420
$288$		0			0
$289$	−1.87994	−	5.78587i	−0.110585	−	0.340345i
$290$	−0.0524116	+	0.161306i	−0.00307772	+	0.00947224i
$291$		0			0
$292$	8.57956	+	6.23342i	0.502081	+	0.364783i
$293$	−5.76629	+	17.7468i	−0.336870	+	1.03678i	0.628923	+	0.777467i	$0.283496\pi$
$293$	−5.76629	+	17.7468i	−0.336870	+	1.03678i	−0.965793	+	0.259313i	$0.916504\pi$
$294$		0			0
$295$	−3.41698	+	2.48258i	−0.198944	+	0.144541i
$296$	−1.53998			−0.0895094
$297$		0			0
$298$	6.25243			0.362193
$299$	−17.9646	+	13.0520i	−1.03892	+	0.754819i
$300$		0			0
$301$	0.978486	−	3.01147i	0.0563990	−	0.173578i
$302$	10.2123	+	7.41964i	0.587649	+	0.426952i
$303$		0			0
$304$	−0.496880	+	1.52924i	−0.0284980	+	0.0877078i
$305$	0.907897	+	2.79422i	0.0519860	+	0.159996i
$306$		0			0
$307$	13.9263			0.794817			0.397408	−	0.917642i	$-0.369910\pi$
$307$	13.9263			0.794817			0.397408	+	0.917642i	$0.369910\pi$
$308$	3.04822	+	2.50870i	0.173689	+	0.142947i
$309$		0			0
$310$	2.33166	−	1.69405i	0.132429	−	0.0962156i
$311$	3.13862	+	9.65969i	0.177975	+	0.547751i	0.999757	−	0.0220516i	$-0.00701980\pi$
$311$	3.13862	+	9.65969i	0.177975	+	0.547751i	−0.821782	+	0.569802i	$0.807020\pi$
$312$		0			0
$313$	−3.89853	−	2.83245i	−0.220358	−	0.160099i	0.472130	−	0.881529i	$-0.343485\pi$
$313$	−3.89853	−	2.83245i	−0.220358	−	0.160099i	−0.692488	+	0.721430i	$0.743485\pi$
$314$	0.533884	+	0.387889i	0.0301288	+	0.0218899i
$315$		0			0
$316$	3.08110	+	9.48265i	0.173325	+	0.533441i
$317$	6.53134	−	4.74530i	0.366837	−	0.266523i	−0.389061	−	0.921212i	$-0.627201\pi$
$317$	6.53134	−	4.74530i	0.366837	−	0.266523i	0.755898	+	0.654689i	$0.227201\pi$
$318$		0			0
$319$	0.284412	−	0.723704i	0.0159240	−	0.0405196i
$320$	4.34734			0.243024
$321$		0			0
$322$	−2.09514	−	6.44819i	−0.116758	−	0.359343i
$323$	−8.10560	+	24.9465i	−0.451008	+	1.38806i
$324$		0			0
$325$	10.3800	+	7.54153i	0.575780	+	0.418329i
$326$	−0.824058	+	2.53619i	−0.0456403	+	0.140467i
$327$		0			0
$328$	−11.1118	+	8.07322i	−0.613548	+	0.445769i
$329$	11.0114			0.607076
$330$		0			0
$331$	0.776780			0.0426957			0.0213479	−	0.999772i	$-0.493204\pi$
$331$	0.776780			0.0426957			0.0213479	+	0.999772i	$0.493204\pi$
$332$	6.99350	−	5.08107i	0.383818	−	0.278860i
$333$		0			0
$334$	2.23564	−	6.88059i	0.122329	−	0.376489i
$335$	8.89358	+	6.46156i	0.485908	+	0.353033i
$336$		0			0
$337$	0.0647699	−	0.199341i	0.00352824	−	0.0108588i	−0.949277	−	0.314441i	$-0.898183\pi$
$337$	0.0647699	−	0.199341i	0.00352824	−	0.0108588i	0.952805	+	0.303583i	$0.0981828\pi$
$338$	1.19981	+	3.69263i	0.0652610	+	0.200853i
$339$		0			0
$340$	3.16180			0.171473
$341$	−11.1383	+	7.10832i	−0.603173	+	0.384937i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	2.80897	+	8.64511i	0.151449	+	0.466113i
$345$		0			0
$346$	−3.75315	−	2.72682i	−0.201770	−	0.146595i
$347$	18.4431	+	13.3997i	0.990079	+	0.719334i	0.959938	−	0.280211i	$-0.0904045\pi$
$347$	18.4431	+	13.3997i	0.990079	+	0.719334i	0.0301406	+	0.999546i	$0.490405\pi$
$348$		0			0
$349$	−4.33532	−	13.3427i	−0.232064	−	0.714220i	−0.997497	−	0.0707048i	$-0.977475\pi$
$349$	−4.33532	−	13.3427i	−0.232064	−	0.714220i	0.765433	−	0.643516i	$-0.222525\pi$
$350$	−3.16935	+	2.30267i	−0.169409	+	0.123083i
$351$		0			0
$352$	−18.4043	−	1.11100i	−0.980953	−	0.0592166i
$353$	22.3703			1.19065			0.595327	−	0.803484i	$-0.297023\pi$
$353$	22.3703			1.19065			0.595327	+	0.803484i	$0.297023\pi$
$354$		0			0
$355$	2.56812	+	7.90385i	0.136301	+	0.419493i
$356$	2.95534	−	9.09559i	0.156633	−	0.482065i
$357$		0			0
$358$	−4.37712	−	3.18016i	−0.231338	−	0.168077i
$359$	0.834999	−	2.56986i	0.0440695	−	0.135632i	−0.926601	−	0.376046i	$-0.877283\pi$
$359$	0.834999	−	2.56986i	0.0440695	−	0.135632i	0.970670	+	0.240414i	$0.0772833\pi$
$360$		0			0
$361$	−35.6186	+	25.8784i	−1.87466	+	1.36202i
$362$	−2.20499			−0.115892
$363$		0			0
$364$	−3.50791			−0.183864
$365$	−5.79482	+	4.21018i	−0.303315	+	0.220371i
$366$		0			0
$367$	8.73963	−	26.8978i	0.456205	−	1.40405i	−0.413509	−	0.910500i	$-0.635697\pi$
$367$	8.73963	−	26.8978i	0.456205	−	1.40405i	0.869715	−	0.493555i	$-0.164303\pi$
$368$	1.23463	+	0.897008i	0.0643593	+	0.0467598i
$369$		0			0
$370$	0.119922	−	0.369082i	0.00623445	−	0.0191877i
$371$	−3.62530	−	11.1575i	−0.188216	−	0.579270i
$372$		0			0
$373$	8.53857			0.442110			0.221055	−	0.975261i	$-0.429050\pi$
$373$	8.53857			0.442110			0.221055	+	0.975261i	$0.429050\pi$
$374$	9.84249	+	0.594156i	0.508943	+	0.0307231i
$375$		0			0
$376$	−25.5735	+	18.5802i	−1.31885	+	0.958203i
$377$	0.213511	+	0.657120i	0.0109964	+	0.0338434i
$378$		0			0
$379$	−28.0587	−	20.3858i	−1.44128	−	1.04715i	−0.987773	−	0.155897i	$-0.950173\pi$
$379$	−28.0587	−	20.3858i	−1.44128	−	1.04715i	−0.453506	−	0.891253i	$-0.649827\pi$
$380$	6.14634	+	4.46558i	0.315301	+	0.229079i
$381$		0			0
$382$	−5.91566	−	18.2065i	−0.302672	−	0.931528i
$383$	10.2885	−	7.47507i	0.525720	−	0.381958i	−0.293034	−	0.956102i	$-0.594665\pi$
$383$	10.2885	−	7.47507i	0.525720	−	0.381958i	0.818754	+	0.574144i	$0.194665\pi$
$384$		0			0
$385$	−2.24771	+	1.43446i	−0.114554	+	0.0731068i
$386$	7.55786			0.384685
$387$		0			0
$388$	−7.08842	−	21.8159i	−0.359860	−	1.10754i
$389$	−0.768678	+	2.36575i	−0.0389735	+	0.119948i	−0.968650	−	0.248428i	$-0.920086\pi$
$389$	−0.768678	+	2.36575i	−0.0389735	+	0.119948i	0.929677	+	0.368376i	$0.120086\pi$
$390$		0			0
$391$	20.1404	+	14.6329i	1.01855	+	0.740017i
$392$	0.887104	−	2.73023i	0.0448055	−	0.137897i
$393$		0			0
$394$	−7.98194	+	5.79922i	−0.402124	+	0.292160i
$395$	−6.73439			−0.338844
$396$		0			0
$397$	19.1634			0.961781			0.480891	−	0.876781i	$-0.340313\pi$
$397$	19.1634			0.961781			0.480891	+	0.876781i	$0.340313\pi$
$398$	4.55807	−	3.31163i	0.228476	−	0.165997i
$399$		0			0
$400$	0.272484	−	0.838619i	0.0136242	−	0.0419310i
$401$	−7.41873	−	5.39002i	−0.370474	−	0.269165i	0.386934	−	0.922108i	$-0.373534\pi$
$401$	−7.41873	−	5.39002i	−0.370474	−	0.269165i	−0.757407	+	0.652943i	$0.773534\pi$
$402$		0			0
$403$	3.62813	−	11.1663i	0.180730	−	0.556231i
$404$	6.35582	+	19.5612i	0.316214	+	0.973206i
$405$		0			0
$406$	−0.210965			−0.0104700
$407$	−0.650756	+	1.65589i	−0.0322568	+	0.0820795i
$408$		0			0
$409$	23.9765	−	17.4200i	1.18556	−	0.861361i	0.192774	−	0.981243i	$-0.438252\pi$
$409$	23.9765	−	17.4200i	1.18556	−	0.861361i	0.992788	+	0.119882i	$0.0382516\pi$
$410$	−1.06958	−	3.29182i	−0.0528227	−	0.162572i
$411$		0			0
$412$	13.8258	+	10.0451i	0.681150	+	0.494884i
$413$	−4.25018	−	3.08794i	−0.209138	−	0.151947i
$414$		0			0
$415$	1.80424	+	5.55287i	0.0885666	+	0.272580i
$416$	13.2543	−	9.62984i	0.649847	−	0.472142i
$417$		0			0
$418$	18.2940	+	15.0561i	0.894789	+	0.736415i
$419$	−31.7616			−1.55166			−0.775828	−	0.630944i	$-0.782668\pi$
$419$	−31.7616			−1.55166			−0.775828	+	0.630944i	$0.782668\pi$
$420$		0			0
$421$	1.83822	+	5.65747i	0.0895895	+	0.275728i	0.985806	−	0.167889i	$-0.0536950\pi$
$421$	1.83822	+	5.65747i	0.0895895	+	0.275728i	−0.896216	+	0.443617i	$0.853695\pi$
$422$	−4.64928	+	14.3090i	−0.226324	+	0.696552i
$423$		0			0
$424$	27.2465	+	19.7958i	1.32321	+	0.961367i
$425$	4.44503	−	13.6804i	0.215616	−	0.663597i
$426$		0			0
$427$	−2.95649	+	2.14802i	−0.143075	+	0.103950i
$428$	18.2358			0.881460
$429$		0			0
$430$	−2.29069			−0.110467
$431$	9.13425	−	6.63642i	0.439981	−	0.319665i	−0.345646	−	0.938365i	$-0.612340\pi$
$431$	9.13425	−	6.63642i	0.439981	−	0.319665i	0.785628	+	0.618700i	$0.212340\pi$
$432$		0			0
$433$	5.31293	−	16.3515i	0.255323	−	0.785804i	−0.738443	−	0.674316i	$-0.764438\pi$
$433$	5.31293	−	16.3515i	0.255323	−	0.785804i	0.993766	−	0.111488i	$-0.0355616\pi$
$434$	2.90022	+	2.10713i	0.139215	+	0.101145i
$435$		0			0
$436$	2.02392	−	6.22898i	0.0969281	−	0.298314i
$437$	18.4849	+	56.8908i	0.884254	+	2.72146i
$438$		0			0
$439$	−33.6983			−1.60833			−0.804167	−	0.594404i	$-0.797388\pi$
$439$	−33.6983			−1.60833			−0.804167	+	0.594404i	$0.797388\pi$
$440$	2.79978	−	7.12422i	0.133474	−	0.339634i
$441$		0			0
$442$	−7.08832	+	5.14997i	−0.337157	+	0.244959i
$443$	0.427271	+	1.31500i	0.0203002	+	0.0624777i	0.960693	−	0.277611i	$-0.0895428\pi$
$443$	0.427271	+	1.31500i	0.0203002	+	0.0624777i	−0.940393	+	0.340089i	$0.889543\pi$
$444$		0			0
$445$	5.22585	+	3.79680i	0.247729	+	0.179986i
$446$	9.53414	+	6.92696i	0.451455	+	0.328001i
$447$		0			0
$448$	1.67098	+	5.14274i	0.0789463	+	0.242972i
$449$	−17.3559	+	12.6098i	−0.819076	+	0.595094i	−0.916448	−	0.400154i	$-0.868956\pi$
$449$	−17.3559	+	12.6098i	−0.819076	+	0.595094i	0.0973716	+	0.995248i	$0.468956\pi$
$450$		0			0
$451$	3.98531	+	15.3598i	0.187661	+	0.723263i
$452$	−7.96886			−0.374823
$453$		0			0
$454$	−4.42187	−	13.6091i	−0.207529	−	0.638708i
$455$	0.732158	−	2.25335i	0.0343241	−	0.105639i
$456$		0			0
$457$	2.86665	+	2.08274i	0.134096	+	0.0974266i	0.652811	−	0.757521i	$-0.273589\pi$
$457$	2.86665	+	2.08274i	0.134096	+	0.0974266i	−0.518715	+	0.854947i	$0.673589\pi$
$458$	−2.50699	+	7.71572i	−0.117144	+	0.360532i
$459$		0			0
$460$	5.83345	−	4.23825i	0.271986	−	0.197609i
$461$	20.0540			0.934006			0.467003	−	0.884256i	$-0.345334\pi$
$461$	20.0540			0.934006			0.467003	+	0.884256i	$0.345334\pi$
$462$		0			0
$463$	−9.80547			−0.455699			−0.227849	−	0.973696i	$-0.573169\pi$
$463$	−9.80547			−0.455699			−0.227849	+	0.973696i	$0.573169\pi$
$464$	0.0384162	−	0.0279110i	0.00178343	−	0.00129574i
$465$		0			0
$466$	0.706833	−	2.17541i	0.0327434	−	0.100774i
$467$	−14.6630	−	10.6533i	−0.678520	−	0.492974i	0.194346	−	0.980933i	$-0.437742\pi$
$467$	−14.6630	−	10.6533i	−0.678520	−	0.492974i	−0.872867	+	0.487959i	$0.837742\pi$
$468$		0			0
$469$	−4.22538	+	13.0044i	−0.195110	+	0.600487i
$470$	−2.46160	−	7.57602i	−0.113545	−	0.349456i
$471$		0			0
$472$	15.0814			0.694178
$473$	10.4828	+	0.632811i	0.482001	+	0.0290967i
$474$		0			0
$475$	27.9624	−	20.3159i	1.28300	−	0.932155i
$476$	1.21530	+	3.74030i	0.0557030	+	0.171436i
$477$		0			0
$478$	−13.9589	−	10.1417i	−0.638464	−	0.463871i
$479$	−31.2418	−	22.6985i	−1.42747	−	1.03712i	−0.990480	−	0.137654i	$-0.956044\pi$
$479$	−31.2418	−	22.6985i	−1.42747	−	1.03712i	−0.436992	−	0.899465i	$-0.643956\pi$
$480$		0			0
$481$	−0.488531	−	1.50354i	−0.0222751	−	0.0685557i
$482$	−5.46028	+	3.96712i	−0.248709	+	0.180698i
$483$		0			0
$484$	−5.51468	+	11.8754i	−0.250667	+	0.539792i
$485$	15.4932			0.703511
$486$		0			0
$487$	5.07760	+	15.6272i	0.230088	+	0.708138i	0.997735	+	0.0672654i	$0.0214274\pi$
$487$	5.07760	+	15.6272i	0.230088	+	0.708138i	−0.767647	+	0.640873i	$0.778573\pi$
$488$	3.24185	−	9.97740i	0.146752	−	0.451656i
$489$		0			0
$490$	0.585264	+	0.425219i	0.0264395	+	0.0192094i
$491$	8.06058	−	24.8079i	0.363769	−	1.11957i	−0.586979	−	0.809602i	$-0.699683\pi$
$491$	8.06058	−	24.8079i	0.363769	−	1.11957i	0.950748	−	0.309964i	$-0.100317\pi$
$492$		0			0
$493$	0.626683	−	0.455312i	0.0282244	−	0.0205062i
$494$	−21.0528			−0.947210
$495$		0			0
$496$	−0.806899			−0.0362308
$497$	−8.36286	+	6.07597i	−0.375125	+	0.272545i
$498$		0			0
$499$	−10.1147	+	31.1299i	−0.452797	+	1.39357i	0.420904	+	0.907105i	$0.361713\pi$
$499$	−10.1147	+	31.1299i	−0.452797	+	1.39357i	−0.873702	+	0.486462i	$0.838287\pi$
$500$	−7.24159	−	5.26133i	−0.323854	−	0.235294i
$501$		0			0
$502$	4.08482	−	12.5718i	0.182314	−	0.561106i
$503$	5.76094	+	17.7304i	0.256868	+	0.790558i	0.993456	+	0.114216i	$0.0364356\pi$
$503$	5.76094	+	17.7304i	0.256868	+	0.790558i	−0.736588	+	0.676342i	$0.763564\pi$
$504$		0			0
$505$	−13.8920			−0.618184
$506$	18.9556	−	12.0972i	0.842678	−	0.537786i
$507$		0			0
$508$	−11.1163	+	8.07645i	−0.493205	+	0.358335i
$509$	7.38282	+	22.7220i	0.327238	+	1.00713i	0.970420	+	0.241422i	$0.0776137\pi$
$509$	7.38282	+	22.7220i	0.327238	+	1.00713i	−0.643182	+	0.765713i	$0.722386\pi$
$510$		0			0
$511$	−7.20783	−	5.23680i	−0.318856	−	0.231662i
$512$	−1.85168	−	1.34533i	−0.0818337	−	0.0594557i
$513$		0			0
$514$	5.76981	+	17.7577i	0.254496	+	0.783257i
$515$	−9.33826	+	6.78464i	−0.411493	+	0.298967i
$516$		0			0
$517$	9.17206	+	35.3500i	0.403387	+	1.55469i
$518$	0.482705			0.0212088
$519$		0			0
$520$	2.10183	+	6.46876i	0.0921713	+	0.283674i
$521$	11.1315	−	34.2591i	0.487678	−	1.50092i	−0.340385	−	0.940286i	$-0.610557\pi$
$521$	11.1315	−	34.2591i	0.487678	−	1.50092i	0.828064	−	0.560634i	$-0.189443\pi$
$522$		0			0
$523$	−22.9277	−	16.6579i	−1.00256	−	0.728401i	−0.0399225	−	0.999203i	$-0.512711\pi$
$523$	−22.9277	−	16.6579i	−1.00256	−	0.728401i	−0.962635	+	0.270802i	$0.912711\pi$
$524$	7.79821	−	24.0004i	0.340666	−	1.04846i
$525$		0			0
$526$	19.9073	−	14.4635i	0.868001	−	0.630640i
$527$	−13.1629			−0.573387
$528$		0			0
$529$	33.7733			1.46841
$530$	−6.86615	+	4.98855i	−0.298247	+	0.216689i
$531$		0			0
$532$	−2.92016	+	8.98732i	−0.126605	+	0.389650i
$533$	−11.4073	−	8.28785i	−0.494103	−	0.358987i
$534$		0			0
$535$	−3.80611	+	11.7140i	−0.164553	+	0.506441i
$536$	−12.1299	−	37.3321i	−0.523933	−	1.61250i
$537$		0			0
$538$	−1.42087			−0.0612581
$539$	−2.56086	−	2.10760i	−0.110304	−	0.0907808i
$540$		0			0
$541$	−20.8075	+	15.1175i	−0.894582	+	0.649952i	−0.937069	−	0.349145i	$-0.886472\pi$
$541$	−20.8075	+	15.1175i	−0.894582	+	0.649952i	0.0424864	+	0.999097i	$0.486472\pi$
$542$	−4.19911	−	12.9235i	−0.180367	−	0.555114i
$543$		0			0
$544$	−14.8597	−	10.7962i	−0.637104	−	0.462883i
$545$	3.57884	+	2.60018i	0.153301	+	0.111380i
$546$		0			0
$547$	10.2533	+	31.5563i	0.438398	+	1.34925i	0.889564	+	0.456810i	$0.151008\pi$
$547$	10.2533	+	31.5563i	0.438398	+	1.34925i	−0.451166	+	0.892440i	$0.648992\pi$
$548$	−0.784990	+	0.570329i	−0.0335331	+	0.0243632i
$549$		0			0
$550$	−10.0323	−	8.25659i	−0.427777	−	0.352062i
$551$	1.86129			0.0792937
$552$		0			0
$553$	−2.58848	−	7.96653i	−0.110073	−	0.338771i
$554$	4.51427	−	13.8935i	0.191793	−	0.590278i
$555$		0			0
$556$	8.92938	+	6.48757i	0.378690	+	0.275134i
$557$	−10.0097	+	30.8066i	−0.424123	+	1.30532i	0.479709	+	0.877428i	$0.340742\pi$
$557$	−10.0097	+	30.8066i	−0.424123	+	1.30532i	−0.903832	+	0.427888i	$0.859258\pi$
$558$		0			0
$559$	−7.54948	+	5.48502i	−0.319309	+	0.231992i
$560$	−0.162832			−0.00688092
$561$		0			0
$562$	15.3750			0.648555
$563$	−28.0446	+	20.3756i	−1.18194	+	0.858728i	−0.992389	−	0.123143i	$-0.960702\pi$
$563$	−28.0446	+	20.3756i	−1.18194	+	0.858728i	−0.189549	+	0.981871i	$0.560702\pi$
$564$		0			0
$565$	1.66323	−	5.11890i	0.0699727	−	0.215354i
$566$	−0.0837365	−	0.0608381i	−0.00351971	−	0.00255722i
$567$		0			0
$568$	9.17005	−	28.2225i	0.384767	−	1.18419i
$569$	5.70625	+	17.5620i	0.239218	+	0.736239i	0.996534	+	0.0831893i	$0.0265106\pi$
$569$	5.70625	+	17.5620i	0.239218	+	0.736239i	−0.757315	+	0.653049i	$0.773489\pi$
$570$		0			0
$571$	14.2034			0.594394			0.297197	−	0.954816i	$-0.403948\pi$
$571$	14.2034			0.594394			0.297197	+	0.954816i	$0.403948\pi$
$572$	−2.92196	−	11.2615i	−0.122173	−	0.470867i
$573$		0			0
$574$	3.48299	−	2.53054i	0.145377	−	0.105623i
$575$	−10.1370	−	31.1984i	−0.422740	−	1.30106i
$576$		0			0
$577$	−13.6734	−	9.93428i	−0.569229	−	0.413569i	0.265596	−	0.964084i	$-0.414431\pi$
$577$	−13.6734	−	9.93428i	−0.569229	−	0.413569i	−0.834825	+	0.550515i	$0.814431\pi$
$578$	−4.42873	−	3.21766i	−0.184211	−	0.133837i
$579$		0			0
$580$	−0.0693313	−	0.213380i	−0.00287882	−	0.00886011i
$581$	−5.87535	+	4.26869i	−0.243751	+	0.177095i
$582$		0			0
$583$	32.7995	−	20.9322i	1.35842	−	0.866923i
$584$	25.5764			1.05836
$585$		0			0
$586$	5.18866	+	15.9691i	0.214342	+	0.659676i
$587$	−10.7356	+	33.0409i	−0.443107	+	1.36374i	0.441440	+	0.897291i	$0.354468\pi$
$587$	−10.7356	+	33.0409i	−0.443107	+	1.36374i	−0.884547	+	0.466451i	$0.845532\pi$
$588$		0			0
$589$	−25.5879	−	18.5907i	−1.05433	−	0.766016i
$590$	−1.17443	+	3.61452i	−0.0483504	+	0.148807i
$591$		0			0
$592$	−0.0878993	+	0.0638626i	−0.00361264	+	0.00262474i
$593$	−2.43045			−0.0998068			−0.0499034	−	0.998754i	$-0.515891\pi$
$593$	−2.43045			−0.0998068			−0.0499034	+	0.998754i	$0.515891\pi$
$594$		0			0
$595$	−2.65628			−0.108897
$596$	−6.69126	+	4.86148i	−0.274084	+	0.199134i
$597$		0			0
$598$	−6.17449	+	19.0031i	−0.252494	+	0.777096i
$599$	−13.5264	−	9.82750i	−0.552674	−	0.401541i	0.276097	−	0.961130i	$-0.410959\pi$
$599$	−13.5264	−	9.82750i	−0.552674	−	0.401541i	−0.828770	+	0.559589i	$0.810959\pi$
$600$		0			0
$601$	0.132866	−	0.408920i	0.00541972	−	0.0166802i	−0.948310	−	0.317345i	$-0.897209\pi$
$601$	0.132866	−	0.408920i	0.00541972	−	0.0166802i	0.953730	+	0.300665i	$0.0972086\pi$
$602$	−0.880468	−	2.70980i	−0.0358852	−	0.110443i
$603$		0			0
$604$	−16.6980			−0.679433
$605$	−6.47734	−	6.02103i	−0.263341	−	0.244790i
$606$		0			0
$607$	−9.33931	+	6.78541i	−0.379071	+	0.275411i	−0.760962	−	0.648796i	$-0.775273\pi$
$607$	−9.33931	+	6.78541i	−0.379071	+	0.275411i	0.381891	+	0.924207i	$0.375273\pi$
$608$	−13.6383	−	41.9742i	−0.553104	−	1.70228i
$609$		0			0
$610$	2.13880	+	1.55393i	0.0865976	+	0.0629168i
$611$	−26.2534	−	19.0742i	−1.06210	−	0.771660i
$612$		0			0
$613$	−5.56380	−	17.1236i	−0.224720	−	0.691616i	−0.998320	−	0.0579424i	$-0.981546\pi$
$613$	−5.56380	−	17.1236i	−0.224720	−	0.691616i	0.773600	−	0.633674i	$-0.218454\pi$
$614$	10.1380	−	7.36570i	0.409137	−	0.297255i
$615$		0			0
$616$	9.50383	+	0.573712i	0.382920	+	0.0231155i
$617$	−32.1061			−1.29254			−0.646272	−	0.763107i	$-0.723673\pi$
$617$	−32.1061			−1.29254			−0.646272	+	0.763107i	$0.723673\pi$
$618$		0			0
$619$	−0.0866156	−	0.266575i	−0.00348137	−	0.0107146i	0.949301	−	0.314369i	$-0.101793\pi$
$619$	−0.0866156	−	0.266575i	−0.00348137	−	0.0107146i	−0.952782	+	0.303655i	$0.901793\pi$
$620$	−1.17813	+	3.62590i	−0.0473147	+	0.145620i
$621$		0			0
$622$	7.39390	+	5.37198i	0.296468	+	0.215397i
$623$	−2.48283	+	7.64136i	−0.0994724	+	0.306144i
$624$		0			0
$625$	−12.7197	+	9.24143i	−0.508790	+	0.369657i
$626$	−4.33613			−0.173307
$627$		0			0
$628$	−0.872952			−0.0348346
$629$	−1.43390	+	1.04179i	−0.0571734	+	0.0415389i
$630$		0			0
$631$	9.37415	−	28.8507i	0.373179	−	1.14853i	−0.571520	−	0.820588i	$-0.693646\pi$
$631$	9.37415	−	28.8507i	0.373179	−	1.14853i	0.944699	−	0.327938i	$-0.106354\pi$
$632$	19.4542	+	14.1343i	0.773845	+	0.562231i
$633$		0			0
$634$	2.24484	−	6.90892i	0.0891542	−	0.274388i
$635$	−2.86787	−	8.82639i	−0.113808	−	0.350264i
$636$		0			0
$637$	2.94705			0.116766
$638$	−0.175726	−	0.677265i	−0.00695706	−	0.0268132i
$639$		0			0
$640$	−4.06686	+	2.95475i	−0.160757	+	0.116797i
$641$	−1.21458	−	3.73810i	−0.0479731	−	0.147646i	0.924200	−	0.381908i	$-0.124733\pi$
$641$	−1.21458	−	3.73810i	−0.0479731	−	0.147646i	−0.972174	+	0.234262i	$0.924733\pi$
$642$		0			0
$643$	11.1032	+	8.06695i	0.437867	+	0.318129i	0.784787	−	0.619766i	$-0.212772\pi$
$643$	11.1032	+	8.06695i	0.437867	+	0.318129i	−0.346920	+	0.937895i	$0.612772\pi$
$644$	7.25588	+	5.27171i	0.285922	+	0.207734i
$645$		0			0
$646$	7.29364	+	22.4475i	0.286964	+	0.883185i
$647$	−1.62640	+	1.18165i	−0.0639403	+	0.0464553i	−0.619296	−	0.785157i	$-0.712582\pi$
$647$	−1.62640	+	1.18165i	−0.0639403	+	0.0464553i	0.555356	+	0.831613i	$0.312582\pi$
$648$		0			0
$649$	6.37303	−	16.2166i	0.250163	−	0.636556i
$650$	11.5452			0.452838
$651$		0			0
$652$	−1.09008	−	3.35493i	−0.0426909	−	0.131389i
$653$	0.245776	−	0.756421i	0.00961797	−	0.0296011i	−0.946132	−	0.323780i	$-0.895046\pi$
$653$	0.245776	−	0.756421i	0.00961797	−	0.0296011i	0.955750	+	0.294179i	$0.0950462\pi$
$654$		0			0
$655$	13.7894	+	10.0186i	0.538796	+	0.391458i
$656$	−0.299450	+	0.921611i	−0.0116915	+	0.0359829i
$657$		0			0
$658$	8.01600	−	5.82396i	0.312496	−	0.227042i
$659$	21.9135			0.853628			0.426814	−	0.904340i	$-0.359636\pi$
$659$	21.9135			0.853628			0.426814	+	0.904340i	$0.359636\pi$
$660$		0			0
$661$	−19.4952			−0.758276			−0.379138	−	0.925340i	$-0.623779\pi$
$661$	−19.4952			−0.758276			−0.379138	+	0.925340i	$0.623779\pi$
$662$	0.565477	−	0.410843i	0.0219779	−	0.0159679i
$663$		0			0
$664$	6.44245	−	19.8278i	0.250015	−	0.769468i
$665$	−5.16364	−	3.75161i	−0.200237	−	0.145481i
$666$		0			0
$667$	0.545891	−	1.68008i	0.0211370	−	0.0650529i
$668$	2.95735	+	9.10180i	0.114423	+	0.352159i
$669$		0			0
$670$	9.89186			0.382156
$671$	−9.35847	−	7.70207i	−0.361280	−	0.297335i
$672$		0			0
$673$	5.66917	−	4.11889i	0.218530	−	0.158772i	−0.473134	−	0.880990i	$-0.656878\pi$
$673$	5.66917	−	4.11889i	0.218530	−	0.158772i	0.691665	+	0.722219i	$0.256878\pi$
$674$	−0.0582818	−	0.179373i	−0.00224493	−	0.00690918i
$675$		0			0
$676$	−4.15517	−	3.01891i	−0.159814	−	0.116112i
$677$	−4.73782	−	3.44223i	−0.182089	−	0.132296i	0.493007	−	0.870026i	$-0.335898\pi$
$677$	−4.73782	−	3.44223i	−0.182089	−	0.132296i	−0.675096	+	0.737730i	$0.735898\pi$
$678$		0			0
$679$	5.95510	+	18.3279i	0.228536	+	0.703361i
$680$	6.16913	−	4.48214i	0.236576	−	0.171882i
$681$		0			0
$682$	−4.34879	+	11.0658i	−0.166524	+	0.423731i
$683$	−34.2255			−1.30960			−0.654802	−	0.755801i	$-0.727248\pi$
$683$	−34.2255			−1.30960			−0.654802	+	0.755801i	$0.727248\pi$
$684$		0			0
$685$	−0.202518	−	0.623286i	−0.00773782	−	0.0238145i
$686$	−0.278062	+	0.855786i	−0.0106165	+	0.0326741i
$687$		0			0
$688$	0.518842	+	0.376961i	0.0197807	+	0.0143715i
$689$	−10.6839	+	32.8818i	−0.407026	+	1.25270i
$690$		0			0
$691$	−12.1422	+	8.82184i	−0.461912	+	0.335598i	−0.794281	−	0.607551i	$-0.792152\pi$
$691$	−12.1422	+	8.82184i	−0.461912	+	0.335598i	0.332369	+	0.943149i	$0.392152\pi$
$692$	6.13676			0.233285
$693$		0			0
$694$	20.5133			0.778675
$695$	−6.03109	+	4.38184i	−0.228772	+	0.166213i
$696$		0			0
$697$	−4.88492	+	15.0342i	−0.185030	+	0.569463i
$698$	−10.2130	−	7.42021i	−0.386570	−	0.280859i
$699$		0			0
$700$	1.60139	−	4.92856i	0.0605267	−	0.186282i
$701$	−3.70534	−	11.4039i	−0.139949	−	0.430718i	0.856378	−	0.516349i	$-0.172709\pi$
$701$	−3.70534	−	11.4039i	−0.139949	−	0.430718i	−0.996327	+	0.0856309i	$0.972709\pi$
$702$		0			0
$703$	−4.25878			−0.160623
$704$	−15.1180	+	9.64810i	−0.569781	+	0.363626i
$705$		0			0
$706$	16.2851	−	11.8318i	0.612896	−	0.445295i
$707$	−5.33963	−	16.4337i	−0.200817	−	0.618052i
$708$		0			0
$709$	−32.0008	−	23.2499i	−1.20181	−	0.873169i	−0.207352	−	0.978266i	$-0.566485\pi$
$709$	−32.0008	−	23.2499i	−1.20181	−	0.873169i	−0.994462	+	0.105098i	$0.966485\pi$
$710$	6.04991	+	4.39552i	0.227049	+	0.164961i
$711$		0			0
$712$	−7.12752	−	21.9363i	−0.267115	−	0.822096i
$713$	−24.2853	+	17.6443i	−0.909492	+	0.660784i
$714$		0			0
$715$	7.84385	+	0.473505i	0.293343	+	0.0177081i
$716$	7.15702			0.267470
$717$		0			0
$718$	−0.751355	−	2.31243i	−0.0280403	−	0.0862992i
$719$	13.7145	−	42.2089i	0.511465	−	1.57413i	−0.278158	−	0.960535i	$-0.589724\pi$
$719$	13.7145	−	42.2089i	0.511465	−	1.57413i	0.789623	−	0.613592i	$-0.210276\pi$
$720$		0			0
$721$	−11.6153	−	8.43902i	−0.432577	−	0.314285i
$722$	−12.2422	+	37.6777i	−0.455609	+	1.40222i
$723$		0			0
$724$	2.35975	−	1.71446i	0.0876994	−	0.0637173i
$725$	−1.02071			−0.0379084
$726$		0			0
$727$	−45.1325			−1.67387			−0.836935	−	0.547302i	$-0.815655\pi$
$727$	−45.1325			−1.67387			−0.836935	+	0.547302i	$0.815655\pi$
$728$	−6.84443	+	4.97277i	−0.253671	+	0.184303i
$729$		0			0
$730$	−1.99170	+	6.12982i	−0.0737161	+	0.226875i
$731$	8.46387	+	6.14936i	0.313048	+	0.227442i
$732$		0			0
$733$	4.26354	−	13.1218i	0.157478	−	0.484666i	−0.840926	−	0.541150i	$-0.817989\pi$
$733$	4.26354	−	13.1218i	0.157478	−	0.484666i	0.998404	+	0.0564840i	$0.0179890\pi$
$734$	−7.86416	−	24.2034i	−0.290271	−	0.893364i
$735$		0			0
$736$	−41.8876			−1.54400
$737$	−45.2679	−	2.73266i	−1.66746	−	0.100659i
$738$		0			0
$739$	13.5472	−	9.84263i	0.498342	−	0.362067i	−0.310041	−	0.950723i	$-0.600343\pi$
$739$	13.5472	−	9.84263i	0.498342	−	0.362067i	0.808383	+	0.588656i	$0.200343\pi$
$740$	0.158635	+	0.488230i	0.00583156	+	0.0179477i
$741$		0			0
$742$	−8.54040	−	6.20496i	−0.313528	−	0.227791i
$743$	−8.81274	−	6.40283i	−0.323308	−	0.234897i	0.414278	−	0.910151i	$-0.364034\pi$
$743$	−8.81274	−	6.40283i	−0.323308	−	0.234897i	−0.737586	+	0.675253i	$0.764034\pi$
$744$		0			0
$745$	−1.72626	−	5.31289i	−0.0632454	−	0.194649i
$746$	6.21587	−	4.51609i	0.227579	−	0.165346i
$747$		0			0
$748$	−10.9953	+	7.01702i	−0.402027	+	0.256568i
$749$	−15.3202			−0.559788
$750$		0			0
$751$	−8.37184	−	25.7659i	−0.305493	−	0.940210i	−0.979493	−	0.201479i	$-0.935425\pi$
$751$	−8.37184	−	25.7659i	−0.305493	−	0.940210i	0.674000	−	0.738731i	$-0.264575\pi$
$752$	−0.689173	+	2.12106i	−0.0251316	+	0.0773470i
$753$		0			0
$754$	0.502985	+	0.365440i	0.0183176	+	0.0133086i
$755$	3.48516	−	10.7262i	0.126838	−	0.390367i
$756$		0			0
$757$	−24.4567	+	17.7688i	−0.888894	+	0.645820i	−0.935590	−	0.353090i	$-0.885131\pi$
$757$	−24.4567	+	17.7688i	−0.888894	+	0.645820i	0.0466951	+	0.998909i	$0.485131\pi$
$758$	−31.2082			−1.13353
$759$		0			0
$760$	18.3227			0.664636
$761$	31.2246	−	22.6860i	1.13189	−	0.822367i	0.145922	−	0.989296i	$-0.453385\pi$
$761$	31.2246	−	22.6860i	1.13189	−	0.822367i	0.985969	+	0.166930i	$0.0533853\pi$
$762$		0			0
$763$	−1.70033	+	5.23307i	−0.0615560	+	0.189450i
$764$	20.4871	+	14.8847i	0.741197	+	0.538511i
$765$		0			0
$766$	3.53621	−	10.8833i	0.127768	−	0.393231i
$767$	4.78431	+	14.7246i	0.172751	+	0.531674i
$768$		0			0
$769$	40.5122			1.46091			0.730454	−	0.682962i	$-0.239309\pi$
$769$	40.5122			1.46091			0.730454	+	0.682962i	$0.239309\pi$
$770$	−0.877587	+	2.23308i	−0.0316261	+	0.0804746i
$771$		0			0
$772$	−8.08831	+	5.87650i	−0.291105	+	0.211500i
$773$	6.85839	+	21.1079i	0.246679	+	0.759200i	0.995356	+	0.0962647i	$0.0306895\pi$
$773$	6.85839	+	21.1079i	0.246679	+	0.759200i	−0.748677	+	0.662935i	$0.769310\pi$
$774$		0			0
$775$	14.0322	+	10.1950i	0.504050	+	0.366214i
$776$	−44.7565	−	32.5175i	−1.60667	−	1.16731i
$777$		0			0
$778$	0.691677	+	2.12876i	0.0247978	+	0.0763199i
$779$	−30.7296	+	22.3264i	−1.10100	+	0.799925i
$780$		0			0
$781$	−26.4718	−	21.7864i	−0.947235	−	0.779579i
$782$	22.4012			0.801064
$783$		0			0
$784$	−0.0625875	−	0.192625i	−0.00223527	−	0.00687945i
$785$	0.182200	−	0.560753i	0.00650298	−	0.0200141i
$786$		0			0
$787$	−12.1985	−	8.86271i	−0.434829	−	0.315922i	0.348748	−	0.937217i	$-0.386607\pi$
$787$	−12.1985	−	8.86271i	−0.434829	−	0.315922i	−0.783577	+	0.621295i	$0.786607\pi$
$788$	4.03306	−	12.4125i	0.143672	−	0.442176i
$789$		0			0
$790$	−4.90247	+	3.56185i	−0.174422	+	0.126725i
$791$	6.69477			0.238039
$792$		0			0
$793$	10.7698			0.382446
$794$	13.9505	−	10.1356i	0.495083	−	0.359699i
$795$		0			0
$796$	−2.30307	+	7.08813i	−0.0816302	+	0.251232i
$797$	18.5731	+	13.4942i	0.657894	+	0.477988i	0.865951	−	0.500129i	$-0.166714\pi$
$797$	18.5731	+	13.4942i	0.657894	+	0.477988i	−0.208057	+	0.978117i	$0.566714\pi$
$798$		0			0
$799$	−11.2425	+	34.6008i	−0.397731	+	1.22409i
$800$	7.47908	+	23.0183i	0.264426	+	0.813818i
$801$		0			0
$802$	−8.25146			−0.291369
$803$	10.8079	−	27.5015i	0.381404	−	0.970508i
$804$		0			0
$805$	−4.90078	+	3.56062i	−0.172730	+	0.125495i
$806$	−3.26469	−	10.0477i	−0.114994	−	0.353915i
$807$		0			0
$808$	40.1308	+	29.1568i	1.41180	+	1.02573i
$809$	22.3327	+	16.2257i	0.785176	+	0.570464i	0.906528	−	0.422146i	$-0.138723\pi$
$809$	22.3327	+	16.2257i	0.785176	+	0.570464i	−0.121352	+	0.992610i	$0.538723\pi$
$810$		0			0
$811$	−15.4600	−	47.5810i	−0.542874	−	1.67079i	−0.725992	−	0.687703i	$-0.758619\pi$
$811$	−15.4600	−	47.5810i	−0.542874	−	1.67079i	0.183118	−	0.983091i	$-0.441381\pi$
$812$	0.225772	−	0.164033i	0.00792303	−	0.00575642i
$813$		0			0
$814$	0.402075	+	1.54964i	0.0140927	+	0.0543148i
$815$	2.38260			0.0834589
$816$		0			0
$817$	7.76815	+	23.9079i	0.271773	+	0.836432i
$818$	8.24081	−	25.3626i	0.288133	−	0.886783i
$819$		0			0
$820$	3.70416	+	2.69123i	0.129355	+	0.0939817i
$821$	8.39576	−	25.8395i	0.293014	−	0.901804i	−0.690867	−	0.722982i	$-0.742771\pi$
$821$	8.39576	−	25.8395i	0.293014	−	0.901804i	0.983881	−	0.178823i	$-0.0572289\pi$
$822$		0			0
$823$	−14.0981	+	10.2429i	−0.491429	+	0.357044i	−0.805734	−	0.592278i	$-0.798229\pi$
$823$	−14.0981	+	10.2429i	−0.491429	+	0.357044i	0.314305	+	0.949322i	$0.398229\pi$
$824$	41.2159			1.43583
$825$		0			0
$826$	−4.72725			−0.164482
$827$	24.6382	−	17.9007i	0.856754	−	0.622468i	−0.0702459	−	0.997530i	$-0.522378\pi$
$827$	24.6382	−	17.9007i	0.856754	−	0.622468i	0.927000	+	0.375061i	$0.122378\pi$
$828$		0			0
$829$	8.47131	−	26.0720i	0.294221	−	0.905518i	−0.689262	−	0.724513i	$-0.742065\pi$
$829$	8.47131	−	26.0720i	0.294221	−	0.905518i	0.983482	−	0.181005i	$-0.0579351\pi$
$830$	4.25039	+	3.08809i	0.147533	+	0.107189i
$831$		0			0
$832$	4.92446	−	15.1559i	0.170725	−	0.525437i
$833$	−1.02099	−	3.14229i	−0.0353752	−	0.108874i
$834$		0			0
$835$	−6.46391			−0.223693
$836$	−31.2846	−	1.88854i	−1.08200	−	0.0653164i
$837$		0			0
$838$	−23.1217	+	16.7989i	−0.798725	+	0.580308i
$839$	9.06745	+	27.9067i	0.313043	+	0.963448i	0.976552	+	0.215280i	$0.0690663\pi$
$839$	9.06745	+	27.9067i	0.313043	+	0.963448i	−0.663509	+	0.748168i	$0.730934\pi$
$840$		0			0
$841$	23.4170	+	17.0135i	0.807484	+	0.586671i
$842$	4.33045	+	3.14625i	0.149237	+	0.108427i
$843$		0			0
$844$	−6.15017	−	18.9283i	−0.211698	−	0.651539i
$845$	2.80649	−	2.03903i	0.0965461	−	0.0701449i
$846$		0			0
$847$	4.63298	−	9.97675i	0.159191	−	0.342805i
$848$	2.37611			0.0815960
$849$		0			0
$850$	−3.99976	−	12.3100i	−0.137191	−	0.422229i
$851$	−1.24904	+	3.84415i	−0.0428166	+	0.131776i
$852$		0			0
$853$	15.7817	+	11.4661i	0.540356	+	0.392591i	0.824217	−	0.566274i	$-0.191616\pi$
$853$	15.7817	+	11.4661i	0.540356	+	0.392591i	−0.283861	+	0.958865i	$0.591616\pi$
$854$	−1.01616	+	3.12741i	−0.0347721	+	0.107018i
$855$		0			0
$856$	35.5807	−	25.8509i	1.21612	−	0.883564i
$857$	−10.9432			−0.373811			−0.186906	−	0.982378i	$-0.559846\pi$
$857$	−10.9432			−0.373811			−0.186906	+	0.982378i	$0.559846\pi$
$858$		0			0
$859$	−15.3191			−0.522680			−0.261340	−	0.965247i	$-0.584164\pi$
$859$	−15.3191			−0.522680			−0.261340	+	0.965247i	$0.584164\pi$
$860$	2.45146	−	1.78109i	0.0835942	−	0.0607347i
$861$		0			0
$862$	3.13947	−	9.66230i	0.106931	−	0.329099i
$863$	10.8904	+	7.91234i	0.370714	+	0.269339i	0.757507	−	0.652827i	$-0.226417\pi$
$863$	10.8904	+	7.91234i	0.370714	+	0.269339i	−0.386793	+	0.922167i	$0.626417\pi$
$864$		0			0
$865$	−1.28084	+	3.94203i	−0.0435500	+	0.134033i
$866$	−4.78072	−	14.7135i	−0.162456	−	0.499987i
$867$		0			0
$868$	−4.74214			−0.160959
$869$	23.4190	−	14.9457i	0.794436	−	0.506998i
$870$		0			0
$871$	32.6008	−	23.6859i	1.10464	−	0.802566i
$872$	−4.88118	−	15.0227i	−0.165297	−	0.508733i
$873$		0			0
$874$	43.5464	+	31.6383i	1.47298	+	1.07018i
$875$	6.08378	+	4.42013i	0.205669	+	0.149428i
$876$		0			0
$877$	0.995286	+	3.06318i	0.0336084	+	0.103436i	0.966453	−	0.256842i	$-0.0826819\pi$
$877$	0.995286	+	3.06318i	0.0336084	+	0.103436i	−0.932845	+	0.360278i	$0.882682\pi$
$878$	−24.5316	+	17.8232i	−0.827900	+	0.601504i
$879$		0			0
$880$	−0.135633	−	0.522744i	−0.00457220	−	0.0176217i
$881$	19.3721			0.652661			0.326331	−	0.945256i	$-0.394188\pi$
$881$	19.3721			0.652661			0.326331	+	0.945256i	$0.394188\pi$
$882$		0			0
$883$	−0.906186	−	2.78895i	−0.0304956	−	0.0938557i	0.934650	−	0.355568i	$-0.115713\pi$
$883$	−0.906186	−	2.78895i	−0.0304956	−	0.0938557i	−0.965146	+	0.261713i	$0.915713\pi$
$884$	3.58154	−	11.0228i	0.120460	−	0.370738i
$885$		0			0
$886$	1.00655	+	0.731305i	0.0338159	+	0.0245687i
$887$	−2.37525	+	7.31027i	−0.0797531	+	0.245455i	−0.982981	−	0.183706i	$-0.941191\pi$
$887$	−2.37525	+	7.31027i	−0.0797531	+	0.245455i	0.903228	+	0.429161i	$0.141191\pi$
$888$		0			0
$889$	9.33897	−	6.78516i	0.313219	−	0.227567i
$890$	5.81244			0.194833
$891$		0			0
$892$	−15.5893			−0.521967
$893$	−70.7232	+	51.3834i	−2.36666	+	1.71948i
$894$		0			0
$895$	−1.49379	+	4.59741i	−0.0499318	+	0.153674i
$896$	−5.05853	−	3.67524i	−0.168994	−	0.122781i
$897$		0			0
$898$	−5.96529	+	18.3593i	−0.199064	+	0.612656i
$899$	0.288634	+	0.888323i	0.00962647	+	0.0296272i
$900$		0			0
$901$	38.7615			1.29133
$902$	11.0251	+	9.07368i	0.367095	+	0.302121i
$903$		0			0
$904$	−15.5484	+	11.2966i	−0.517132	+	0.375718i
$905$	0.608787	+	1.87365i	0.0202368	+	0.0622824i
$906$		0			0
$907$	10.3348	+	7.50870i	0.343163	+	0.249322i	0.745995	−	0.665951i	$-0.231974\pi$
$907$	10.3348	+	7.50870i	0.343163	+	0.249322i	−0.402832	+	0.915274i	$0.631974\pi$
$908$	15.3138	+	11.1261i	0.508206	+	0.369233i
$909$		0			0
$910$	−0.658816	−	2.02763i	−0.0218395	−	0.0672152i
$911$	8.96644	−	6.51450i	0.297071	−	0.215835i	−0.429258	−	0.903182i	$-0.641225\pi$
$911$	8.96644	−	6.51450i	0.297071	−	0.215835i	0.726329	+	0.687347i	$0.241225\pi$
$912$		0			0
$913$	−18.5978	−	15.3061i	−0.615499	−	0.506558i
$914$	3.18843			0.105464
$915$		0			0
$916$	−3.31630	−	10.2065i	−0.109574	−	0.337233i
$917$	−6.55141	+	20.1632i	−0.216346	+	0.665846i
$918$		0			0
$919$	−10.9640	−	7.96579i	−0.361668	−	0.262767i	0.392079	−	0.919931i	$-0.371756\pi$
$919$	−10.9640	−	7.96579i	−0.361668	−	0.262767i	−0.753748	+	0.657164i	$0.771756\pi$
$920$	5.37380	−	16.5389i	0.177169	−	0.545270i
$921$		0			0
$922$	14.5988	−	10.6066i	0.480786	−	0.349311i
$923$	30.4638			1.00273
$924$		0			0
$925$	2.33548			0.0767900
$926$	−7.13814	+	5.18616i	−0.234574	+	0.170428i
$927$		0			0
$928$	−0.402760	+	1.23957i	−0.0132212	+	0.0406908i
$929$	34.8014	+	25.2847i	1.14180	+	0.829565i	0.987369	−	0.158439i	$-0.0506461\pi$
$929$	34.8014	+	25.2847i	1.14180	+	0.829565i	0.154429	+	0.988004i	$0.450646\pi$
$930$		0			0
$931$	2.45327	−	7.55040i	0.0804027	−	0.247454i
$932$	0.935014	+	2.87768i	0.0306274	+	0.0942615i
$933$		0			0
$934$	−16.3088			−0.533641
$935$	−2.21259	−	8.52753i	−0.0723593	−	0.278880i
$936$		0			0
$937$	2.07500	−	1.50757i	0.0677872	−	0.0492503i	−0.553376	−	0.832932i	$-0.686661\pi$
$937$	2.07500	−	1.50757i	0.0677872	−	0.0492503i	0.621163	+	0.783682i	$0.286661\pi$
$938$	3.80211	+	11.7017i	0.124143	+	0.382074i
$939$		0			0
$940$	8.52499	+	6.19377i	0.278055	+	0.202018i
$941$	13.4006	+	9.73609i	0.436847	+	0.317388i	0.784381	−	0.620280i	$-0.212981\pi$
$941$	13.4006	+	9.73609i	0.436847	+	0.317388i	−0.347534	+	0.937667i	$0.612981\pi$
$942$		0			0
$943$	11.1401	+	34.2858i	0.362773	+	1.11650i
$944$	0.860820	−	0.625423i	0.0280173	−	0.0203558i
$945$		0			0
$946$	7.96594	−	5.08375i	0.258995	−	0.165287i
$947$	−46.5682			−1.51326			−0.756632	−	0.653841i	$-0.773157\pi$
$947$	−46.5682			−1.51326			−0.756632	+	0.653841i	$0.773157\pi$
$948$		0			0
$949$	8.11366	+	24.9713i	0.263381	+	0.810602i
$950$	9.61076	−	29.5789i	0.311814	−	0.959666i
$951$		0			0
$952$	7.67342	+	5.57507i	0.248697	+	0.180689i
$953$	12.3450	−	37.9940i	0.399894	−	1.23075i	−0.525190	−	0.850985i	$-0.676006\pi$
$953$	12.3450	−	37.9940i	0.399894	−	1.23075i	0.925084	−	0.379763i	$-0.123994\pi$
$954$		0			0
$955$	−13.8374	+	10.0535i	−0.447768	+	0.325323i
$956$	22.8241			0.738185
$957$		0			0
$958$	−34.7486			−1.12268
$959$	0.659483	−	0.479143i	0.0212958	−	0.0154723i
$960$		0			0
$961$	−4.67486	+	14.3877i	−0.150802	+	0.464121i
$962$	−1.15087	−	0.836156i	−0.0371056	−	0.0269588i
$963$		0			0
$964$	2.75893	−	8.49111i	0.0888592	−	0.273480i
$965$	−2.08669	−	6.42216i	−0.0671728	−	0.206737i
$966$		0			0
$967$	35.2572			1.13380			0.566898	−	0.823788i	$-0.308143\pi$
$967$	35.2572			1.13380			0.566898	+	0.823788i	$0.308143\pi$
$968$	6.07454	+	30.9882i	0.195243	+	0.996000i
$969$		0			0
$970$	11.2787	−	8.19445i	0.362137	−	0.263108i
$971$	−10.7637	−	33.1271i	−0.345422	−	1.06310i	−0.961357	−	0.275304i	$-0.911222\pi$
$971$	−10.7637	−	33.1271i	−0.345422	−	1.06310i	0.615935	−	0.787797i	$-0.288778\pi$
$972$		0			0
$973$	−7.50172	−	5.45032i	−0.240494	−	0.174729i
$974$	11.9617	+	8.69068i	0.383278	+	0.278467i
$975$		0			0
$976$	−0.228721	−	0.703932i	−0.00732119	−	0.0225323i
$977$	−18.7803	+	13.6447i	−0.600834	+	0.436532i	−0.846175	−	0.532905i	$-0.821100\pi$
$977$	−18.7803	+	13.6447i	−0.600834	+	0.436532i	0.245341	+	0.969437i	$0.421100\pi$
$978$		0			0
$979$	−26.5993	−	1.60571i	−0.850118	−	0.0513186i
$980$	−0.956964			−0.0305691
$981$		0			0
$982$	−7.25313	−	22.3228i	−0.231457	−	0.712350i
$983$	15.7217	−	48.3863i	0.501444	−	1.54328i	−0.305225	−	0.952280i	$-0.598732\pi$
$983$	15.7217	−	48.3863i	0.501444	−	1.54328i	0.806668	−	0.591004i	$-0.201268\pi$
$984$		0			0
$985$	7.13156	+	5.18138i	0.227230	+	0.165093i
$986$	0.215393	−	0.662912i	0.00685952	−	0.0211114i
$987$		0			0
$988$	22.5304	−	16.3693i	0.716788	−	0.520777i
$989$	23.8586			0.758658
$990$		0			0
$991$	−49.0338			−1.55761			−0.778805	−	0.627266i	$-0.784174\pi$
$991$	−49.0338			−1.55761			−0.778805	+	0.627266i	$0.784174\pi$
$992$	17.9178	−	13.0180i	0.568890	−	0.413323i
$993$		0			0
$994$	−2.87434	+	8.84632i	−0.0911686	+	0.280588i
$995$	−4.07247	−	2.95882i	−0.129106	−	0.0938009i
$996$		0			0
$997$	−1.43407	+	4.41361i	−0.0454175	+	0.139781i	−0.971194	−	0.238291i	$-0.923413\pi$
$997$	−1.43407	+	4.41361i	−0.0454175	+	0.139781i	0.925776	+	0.378072i	$0.123413\pi$
$998$	9.10151	+	28.0116i	0.288103	+	0.886691i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.190.6	yes	32
3.2	odd	2	inner	693.2.m.k.190.3	✓	32
11.2	odd	10		7623.2.a.db.1.11		16
11.4	even	5	inner	693.2.m.k.631.6	yes	32
11.9	even	5		7623.2.a.dc.1.6		16
33.2	even	10		7623.2.a.db.1.6		16
33.20	odd	10		7623.2.a.dc.1.11		16
33.26	odd	10	inner	693.2.m.k.631.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.190.3	✓	32	3.2	odd	2	inner
693.2.m.k.190.6	yes	32	1.1	even	1	trivial
693.2.m.k.631.3	yes	32	33.26	odd	10	inner
693.2.m.k.631.6	yes	32	11.4	even	5	inner
7623.2.a.db.1.6		16	33.2	even	10
7623.2.a.db.1.11		16	11.2	odd	10
7623.2.a.dc.1.6		16	11.9	even	5
7623.2.a.dc.1.11		16	33.20	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.727975 - 0.528905i) q^{2} +(-0.367826 + 1.13205i) q^{4} +(-0.650418 - 0.472557i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.887104 + 2.73023i) q^{8} +O(q^{10})\)	\(q+(0.727975 - 0.528905i) q^{2} +(-0.367826 + 1.13205i) q^{4} +(-0.650418 - 0.472557i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.887104 + 2.73023i) q^{8} -0.723426 q^{10} +(3.31060 + 0.199849i) q^{11} +(-2.38421 + 1.73223i) q^{13} +(-0.278062 - 0.855786i) q^{14} +(0.163856 + 0.119049i) q^{16} +(2.67299 + 1.94204i) q^{17} +(2.45327 + 7.55040i) q^{19} +(0.774200 - 0.562489i) q^{20} +(2.51574 - 1.60551i) q^{22} +7.53481 q^{23} +(-1.34535 - 4.14056i) q^{25} +(-0.819462 + 2.52205i) q^{26} +(0.962982 + 0.699647i) q^{28} +(0.0724492 - 0.222976i) q^{29} +(-3.22308 + 2.34171i) q^{31} -5.55921 q^{32} +2.97302 q^{34} +(-0.650418 + 0.472557i) q^{35} +(-0.165770 + 0.510186i) q^{37} +(5.77936 + 4.19895i) q^{38} +(0.713197 - 2.19500i) q^{40} +(1.47849 + 4.55032i) q^{41} +3.16645 q^{43} +(-1.44396 + 3.67426i) q^{44} +(5.48516 - 3.98520i) q^{46} +(3.40270 + 10.4724i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(-3.16935 - 2.30267i) q^{50} +(-1.08400 - 3.33622i) q^{52} +(9.49116 - 6.89573i) q^{53} +(-2.05883 - 1.69443i) q^{55} +2.87073 q^{56} +(-0.0651917 - 0.200640i) q^{58} +(1.62342 - 4.99638i) q^{59} +(-2.95649 - 2.14802i) q^{61} +(-1.10778 + 3.40941i) q^{62} +(-4.37468 + 3.17839i) q^{64} +2.36931 q^{65} -13.6736 q^{67} +(-3.18169 + 2.31163i) q^{68} +(-0.223551 + 0.688019i) q^{70} +(-8.36286 - 6.07597i) q^{71} +(2.75315 - 8.47332i) q^{73} +(0.149164 + 0.459079i) q^{74} -9.44983 q^{76} +(1.21310 - 3.08681i) q^{77} +(6.77674 - 4.92359i) q^{79} +(-0.0503180 - 0.154863i) q^{80} +(3.48299 + 2.53054i) q^{82} +(-5.87535 - 4.26869i) q^{83} +(-0.820837 - 2.52628i) q^{85} +(2.30509 - 1.67475i) q^{86} +(2.39121 + 9.21597i) q^{88} -8.03460 q^{89} +(0.910689 + 2.80281i) q^{91} +(-2.77150 + 8.52980i) q^{92} +(8.01600 + 5.82396i) q^{94} +(1.97234 - 6.07023i) q^{95} +(-15.5907 + 11.3273i) q^{97} -0.899827 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more