LMFDB - Embedded newform 756.2.e.a.323.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (of order $2$, degree $1$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.11
Character	$\chi$	$=$	756.323
Dual form			756.2.e.a.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.310394 - 1.37973i) q^{2} +(-1.80731 + 0.856520i) q^{4} +1.05392i q^{5} -1.00000i q^{7} +(1.74275 + 2.22774i) q^{8} +O(q^{10})$	\(q+(-0.310394 - 1.37973i) q^{2} +(-1.80731 + 0.856520i) q^{4} +1.05392i q^{5} -1.00000i q^{7} +(1.74275 + 2.22774i) q^{8} +(1.45413 - 0.327131i) q^{10} -2.97924 q^{11} +0.985148 q^{13} +(-1.37973 + 0.310394i) q^{14} +(2.53275 - 3.09600i) q^{16} +6.35564i q^{17} +1.26888i q^{19} +(-0.902706 - 1.90477i) q^{20} +(0.924740 + 4.11055i) q^{22} -2.66217 q^{23} +3.88925 q^{25} +(-0.305784 - 1.35924i) q^{26} +(0.856520 + 1.80731i) q^{28} +5.12873i q^{29} +8.41216i q^{31} +(-5.05779 - 2.53353i) q^{32} +(8.76907 - 1.97275i) q^{34} +1.05392 q^{35} +8.91591 q^{37} +(1.75072 - 0.393854i) q^{38} +(-2.34787 + 1.83672i) q^{40} +4.54486i q^{41} +0.646087i q^{43} +(5.38442 - 2.55178i) q^{44} +(0.826321 + 3.67307i) q^{46} -4.64851 q^{47} -1.00000 q^{49} +(-1.20720 - 5.36611i) q^{50} +(-1.78047 + 0.843799i) q^{52} +2.57717i q^{53} -3.13989i q^{55} +(2.22774 - 1.74275i) q^{56} +(7.07627 - 1.59193i) q^{58} +13.7573 q^{59} +4.89018 q^{61} +(11.6065 - 2.61109i) q^{62} +(-1.92568 + 7.76478i) q^{64} +1.03827i q^{65} +8.21439i q^{67} +(-5.44374 - 11.4866i) q^{68} +(-0.327131 - 1.45413i) q^{70} -0.583871 q^{71} -12.4131 q^{73} +(-2.76745 - 12.3015i) q^{74} +(-1.08683 - 2.29327i) q^{76} +2.97924i q^{77} -15.1046i q^{79} +(3.26294 + 2.66932i) q^{80} +(6.27068 - 1.41070i) q^{82} -4.73179 q^{83} -6.69835 q^{85} +(0.891426 - 0.200542i) q^{86} +(-5.19206 - 6.63699i) q^{88} -1.74631i q^{89} -0.985148i q^{91} +(4.81136 - 2.28020i) q^{92} +(1.44287 + 6.41369i) q^{94} -1.33731 q^{95} +3.00594 q^{97} +(0.310394 + 1.37973i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.310394	−	1.37973i	−0.219482	−	0.975617i
$2$	−0.310394	−	1.37973i	−0.219482	−	0.975617i
$3$		0			0
$3$		0			0
$4$	−1.80731	+	0.856520i	−0.903655	+	0.428260i
$5$			1.05392i			0.471328i	0.971835	+	0.235664i	$0.0757266\pi$
$5$			1.05392i			0.471328i	−0.971835	+	0.235664i	$0.924273\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.74275	+	2.22774i	0.616154	+	0.787626i
$9$		0			0
$10$	1.45413	−	0.327131i	0.459836	−	0.103448i
$11$	−2.97924			−0.898276			−0.449138	−	0.893462i	$-0.648269\pi$
$11$	−2.97924			−0.898276			−0.449138	+	0.893462i	$0.648269\pi$
$12$		0			0
$13$	0.985148			0.273231			0.136615	−	0.990624i	$-0.456378\pi$
$13$	0.985148			0.273231			0.136615	+	0.990624i	$0.456378\pi$
$14$	−1.37973	+	0.310394i	−0.368748	+	0.0829563i
$15$		0			0
$16$	2.53275	−	3.09600i	0.633186	−	0.773999i
$17$			6.35564i			1.54147i	0.637156	+	0.770735i	$0.280111\pi$
$17$			6.35564i			1.54147i	−0.637156	+	0.770735i	$0.719889\pi$
$18$		0			0
$19$			1.26888i			0.291102i	0.989351	+	0.145551i	$0.0464955\pi$
$19$			1.26888i			0.291102i	−0.989351	+	0.145551i	$0.953504\pi$
$20$	−0.902706	−	1.90477i	−0.201851	−	0.425919i
$21$		0			0
$22$	0.924740	+	4.11055i	0.197155	+	0.876373i
$23$	−2.66217			−0.555100			−0.277550	−	0.960711i	$-0.589522\pi$
$23$	−2.66217			−0.555100			−0.277550	+	0.960711i	$0.589522\pi$
$24$		0			0
$25$	3.88925			0.777849
$26$	−0.305784	−	1.35924i	−0.0599692	−	0.266569i
$27$		0			0
$28$	0.856520	+	1.80731i	0.161867	+	0.341550i
$29$			5.12873i			0.952382i	0.879342	+	0.476191i	$0.157983\pi$
$29$			5.12873i			0.952382i	−0.879342	+	0.476191i	$0.842017\pi$
$30$		0			0
$31$			8.41216i			1.51087i	0.655224	+	0.755435i	$0.272574\pi$
$31$			8.41216i			1.51087i	−0.655224	+	0.755435i	$0.727426\pi$
$32$	−5.05779	−	2.53353i	−0.894099	−	0.447869i
$33$		0			0
$34$	8.76907	−	1.97275i	1.50388	−	0.338324i
$35$	1.05392			0.178145
$36$		0			0
$37$	8.91591			1.46577			0.732883	−	0.680355i	$-0.238174\pi$
$37$	8.91591			1.46577			0.732883	+	0.680355i	$0.238174\pi$
$38$	1.75072	−	0.393854i	0.284004	−	0.0638916i
$39$		0			0
$40$	−2.34787	+	1.83672i	−0.371231	+	0.290411i
$41$			4.54486i			0.709788i	0.934907	+	0.354894i	$0.115483\pi$
$41$			4.54486i			0.709788i	−0.934907	+	0.354894i	$0.884517\pi$
$42$		0			0
$43$			0.646087i			0.0985273i	0.998786	+	0.0492637i	$0.0156875\pi$
$43$			0.646087i			0.0985273i	−0.998786	+	0.0492637i	$0.984313\pi$
$44$	5.38442	−	2.55178i	0.811732	−	0.384696i
$45$		0			0
$46$	0.826321	+	3.67307i	0.121834	+	0.541565i
$47$	−4.64851			−0.678055			−0.339027	−	0.940777i	$-0.610098\pi$
$47$	−4.64851			−0.678055			−0.339027	+	0.940777i	$0.610098\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−1.20720	−	5.36611i	−0.170724	−	0.758883i
$51$		0			0
$52$	−1.78047	+	0.843799i	−0.246907	+	0.117014i
$53$			2.57717i			0.354002i	0.984211	+	0.177001i	$0.0566396\pi$
$53$			2.57717i			0.354002i	−0.984211	+	0.177001i	$0.943360\pi$
$54$		0			0
$55$		−	3.13989i		−	0.423383i
$56$	2.22774	−	1.74275i	0.297695	−	0.232884i
$57$		0			0
$58$	7.07627	−	1.59193i	0.929159	−	0.209030i
$59$	13.7573			1.79104			0.895521	−	0.445019i	$-0.146803\pi$
$59$	13.7573			1.79104			0.895521	+	0.445019i	$0.146803\pi$
$60$		0			0
$61$	4.89018			0.626124			0.313062	−	0.949733i	$-0.398645\pi$
$61$	4.89018			0.626124			0.313062	+	0.949733i	$0.398645\pi$
$62$	11.6065	−	2.61109i	1.47403	−	0.331608i
$63$		0			0
$64$	−1.92568	+	7.76478i	−0.240709	+	0.970597i
$65$			1.03827i			0.128782i
$66$		0			0
$67$			8.21439i			1.00355i	0.864999	+	0.501774i	$0.167319\pi$
$67$			8.21439i			1.00355i	−0.864999	+	0.501774i	$0.832681\pi$
$68$	−5.44374	−	11.4866i	−0.660150	−	1.39296i
$69$		0			0
$70$	−0.327131	−	1.45413i	−0.0390997	−	0.173802i
$71$	−0.583871			−0.0692927			−0.0346464	−	0.999400i	$-0.511030\pi$
$71$	−0.583871			−0.0692927			−0.0346464	+	0.999400i	$0.511030\pi$
$72$		0			0
$73$	−12.4131			−1.45284			−0.726422	−	0.687249i	$-0.758818\pi$
$73$	−12.4131			−1.45284			−0.726422	+	0.687249i	$0.758818\pi$
$74$	−2.76745	−	12.3015i	−0.321709	−	1.43003i
$75$		0			0
$76$	−1.08683	−	2.29327i	−0.124667	−	0.263056i
$77$			2.97924i			0.339516i
$78$		0			0
$79$		−	15.1046i		−	1.69940i	−0.527269	−	0.849699i	$-0.676784\pi$
$79$		−	15.1046i		−	1.69940i	0.527269	−	0.849699i	$-0.323216\pi$
$80$	3.26294	+	2.66932i	0.364808	+	0.298439i
$81$		0			0
$82$	6.27068	−	1.41070i	0.692481	−	0.155786i
$83$	−4.73179			−0.519382			−0.259691	−	0.965692i	$-0.583621\pi$
$83$	−4.73179			−0.519382			−0.259691	+	0.965692i	$0.583621\pi$
$84$		0			0
$85$	−6.69835			−0.726538
$86$	0.891426	−	0.200542i	0.0961249	−	0.0216250i
$87$		0			0
$88$	−5.19206	−	6.63699i	−0.553476	−	0.707505i
$89$		−	1.74631i		−	0.185108i	−0.995708	−	0.0925541i	$-0.970497\pi$
$89$		−	1.74631i		−	0.185108i	0.995708	−	0.0925541i	$-0.0295031\pi$
$90$		0			0
$91$		−	0.985148i		−	0.103272i
$92$	4.81136	−	2.28020i	0.501619	−	0.237727i
$93$		0			0
$94$	1.44287	+	6.41369i	0.148821	+	0.661521i
$95$	−1.33731			−0.137205
$96$		0			0
$97$	3.00594			0.305207			0.152604	−	0.988287i	$-0.451234\pi$
$97$	3.00594			0.305207			0.152604	+	0.988287i	$0.451234\pi$
$98$	0.310394	+	1.37973i	0.0313545	+	0.139374i
$99$		0			0
$100$	−7.02908	+	3.33122i	−0.702908	+	0.333122i
$101$			1.53513i			0.152751i	0.997079	+	0.0763757i	$0.0243348\pi$
$101$			1.53513i			0.152751i	−0.997079	+	0.0763757i	$0.975665\pi$
$102$		0			0
$103$		−	11.6910i		−	1.15195i	−0.817468	−	0.575974i	$-0.804623\pi$
$103$		−	11.6910i		−	1.15195i	0.817468	−	0.575974i	$-0.195377\pi$
$104$	1.71686	+	2.19466i	0.168352	+	0.215204i
$105$		0			0
$106$	3.55581	−	0.799940i	0.345370	−	0.0776970i
$107$	−15.7149			−1.51922			−0.759611	−	0.650378i	$-0.774610\pi$
$107$	−15.7149			−1.51922			−0.759611	+	0.650378i	$0.774610\pi$
$108$		0			0
$109$	−7.34105			−0.703145			−0.351573	−	0.936161i	$-0.614353\pi$
$109$	−7.34105			−0.703145			−0.351573	+	0.936161i	$0.614353\pi$
$110$	−4.33220	+	0.974604i	−0.413059	+	0.0929249i
$111$		0			0
$112$	−3.09600	−	2.53275i	−0.292544	−	0.239322i
$113$			4.35118i			0.409324i	0.978833	+	0.204662i	$0.0656096\pi$
$113$			4.35118i			0.409324i	−0.978833	+	0.204662i	$0.934390\pi$
$114$		0			0
$115$		−	2.80572i		−	0.261635i
$116$	−4.39286	−	9.26921i	−0.407867	−	0.860625i
$117$		0			0
$118$	−4.27017	−	18.9813i	−0.393101	−	1.74737i
$119$	6.35564			0.582621
$120$		0			0
$121$	−2.12410			−0.193100
$122$	−1.51788	−	6.74713i	−0.137423	−	0.610857i
$123$		0			0
$124$	−7.20519	−	15.2034i	−0.647045	−	1.36531i
$125$			9.36858i			0.837951i
$126$		0			0
$127$			20.4265i			1.81255i	0.422684	+	0.906277i	$0.361088\pi$
$127$			20.4265i			1.81255i	−0.422684	+	0.906277i	$0.638912\pi$
$128$	11.3110	+	0.246771i	0.999762	+	0.0218117i
$129$		0			0
$130$	1.43253	−	0.322273i	0.125641	−	0.0282652i
$131$	17.1791			1.50094			0.750471	−	0.660903i	$-0.229827\pi$
$131$	17.1791			1.50094			0.750471	+	0.660903i	$0.229827\pi$
$132$		0			0
$133$	1.26888			0.110026
$134$	11.3336	−	2.54970i	0.979078	−	0.220260i
$135$		0			0
$136$	−14.1587	+	11.0763i	−1.21410	+	0.949782i
$137$		−	16.2830i		−	1.39115i	−0.718452	−	0.695577i	$-0.755149\pi$
$137$		−	16.2830i		−	1.39115i	0.718452	−	0.695577i	$-0.244851\pi$
$138$		0			0
$139$		−	1.05732i		−	0.0896804i	−0.998994	−	0.0448402i	$-0.985722\pi$
$139$		−	1.05732i		−	0.0896804i	0.998994	−	0.0448402i	$-0.0142779\pi$
$140$	−1.90477	+	0.902706i	−0.160982	+	0.0762926i
$141$		0			0
$142$	0.181230	+	0.805584i	0.0152085	+	0.0676031i
$143$	−2.93500			−0.245437
$144$		0			0
$145$	−5.40529			−0.448885
$146$	3.85295	+	17.1267i	0.318873	+	1.41742i
$147$		0			0
$148$	−16.1138	+	7.63666i	−1.32455	+	0.627729i
$149$			6.71787i			0.550349i	0.961394	+	0.275175i	$0.0887357\pi$
$149$			6.71787i			0.550349i	−0.961394	+	0.275175i	$0.911264\pi$
$150$		0			0
$151$			4.96946i			0.404409i	0.979343	+	0.202205i	$0.0648106\pi$
$151$			4.96946i			0.404409i	−0.979343	+	0.202205i	$0.935189\pi$
$152$	−2.82675	+	2.21134i	−0.229280	+	0.179364i
$153$		0			0
$154$	4.11055	−	0.924740i	0.331238	−	0.0745177i
$155$	−8.86577			−0.712116
$156$		0			0
$157$	14.3997			1.14922			0.574609	−	0.818428i	$-0.305154\pi$
$157$	14.3997			1.14922			0.574609	+	0.818428i	$0.305154\pi$
$158$	−20.8402	+	4.68837i	−1.65796	+	0.372987i
$159$		0			0
$160$	2.67014	−	5.33052i	0.211093	−	0.421415i
$161$			2.66217i			0.209808i
$162$		0			0
$163$		−	2.22595i		−	0.174350i	−0.996193	−	0.0871749i	$-0.972216\pi$
$163$		−	2.22595i		−	0.174350i	0.996193	−	0.0871749i	$-0.0277839\pi$
$164$	−3.89277	−	8.21398i	−0.303974	−	0.641404i
$165$		0			0
$166$	1.46872	+	6.52860i	0.113995	+	0.506717i
$167$	12.4976			0.967094			0.483547	−	0.875318i	$-0.339348\pi$
$167$	12.4976			0.967094			0.483547	+	0.875318i	$0.339348\pi$
$168$		0			0
$169$	−12.0295			−0.925345
$170$	2.07913	+	9.24192i	0.159462	+	0.708823i
$171$		0			0
$172$	−0.553387	−	1.16768i	−0.0421953	−	0.0890348i
$173$			16.1418i			1.22724i	0.789603	+	0.613619i	$0.210287\pi$
$173$			16.1418i			1.22724i	−0.789603	+	0.613619i	$0.789713\pi$
$174$		0			0
$175$		−	3.88925i		−	0.293999i
$176$	−7.54567	+	9.22373i	−0.568776	+	0.695265i
$177$		0			0
$178$	−2.40943	+	0.542043i	−0.180595	+	0.0406279i
$179$	−14.5759			−1.08945			−0.544727	−	0.838613i	$-0.683367\pi$
$179$	−14.5759			−1.08945			−0.544727	+	0.838613i	$0.683367\pi$
$180$		0			0
$181$	1.95874			0.145592			0.0727960	−	0.997347i	$-0.476808\pi$
$181$	1.95874			0.145592			0.0727960	+	0.997347i	$0.476808\pi$
$182$	−1.35924	+	0.305784i	−0.100753	+	0.0226662i
$183$		0			0
$184$	−4.63948	−	5.93062i	−0.342027	−	0.437211i
$185$			9.39668i			0.690857i
$186$		0			0
$187$		−	18.9350i		−	1.38466i
$188$	8.40130	−	3.98154i	0.612728	−	0.290384i
$189$		0			0
$190$	0.415092	+	1.84512i	0.0301139	+	0.133859i
$191$	−26.2224			−1.89739			−0.948694	−	0.316194i	$-0.897595\pi$
$191$	−26.2224			−1.89739			−0.948694	+	0.316194i	$0.897595\pi$
$192$		0			0
$193$	−23.4000			−1.68437			−0.842186	−	0.539187i	$-0.818732\pi$
$193$	−23.4000			−1.68437			−0.842186	+	0.539187i	$0.818732\pi$
$194$	−0.933027	−	4.14739i	−0.0669874	−	0.297765i
$195$		0			0
$196$	1.80731	−	0.856520i	0.129094	−	0.0611800i
$197$		−	16.5377i		−	1.17826i	−0.808036	−	0.589132i	$-0.799470\pi$
$197$		−	16.5377i		−	1.17826i	0.808036	−	0.589132i	$-0.200530\pi$
$198$		0			0
$199$		−	1.20608i		−	0.0854964i	−0.999086	−	0.0427482i	$-0.986389\pi$
$199$		−	1.20608i		−	0.0854964i	0.999086	−	0.0427482i	$-0.0136113\pi$
$200$	6.77797	+	8.66424i	0.479275	+	0.612654i
$201$		0			0
$202$	2.11807	−	0.476496i	0.149027	−	0.0335261i
$203$	5.12873			0.359966
$204$		0			0
$205$	−4.78993			−0.334543
$206$	−16.1304	+	3.62881i	−1.12386	+	0.252831i
$207$		0			0
$208$	2.49513	−	3.05002i	0.173006	−	0.211481i
$209$		−	3.78032i		−	0.261490i
$210$		0			0
$211$			9.33019i			0.642317i	0.947025	+	0.321159i	$0.104072\pi$
$211$			9.33019i			0.642317i	−0.947025	+	0.321159i	$0.895928\pi$
$212$	−2.20740	−	4.65776i	−0.151605	−	0.319896i
$213$		0			0
$214$	4.87783	+	21.6824i	0.333441	+	1.48218i
$215$	−0.680926			−0.0464387
$216$		0			0
$217$	8.41216			0.571055
$218$	2.27862	+	10.1287i	0.154328	+	0.686000i
$219$		0			0
$220$	2.68938	+	5.67476i	0.181318	+	0.382592i
$221$			6.26125i			0.421177i
$222$		0			0
$223$		−	2.92491i		−	0.195866i	−0.995193	−	0.0979332i	$-0.968777\pi$
$223$		−	2.92491i		−	0.195866i	0.995193	−	0.0979332i	$-0.0312231\pi$
$224$	−2.53353	+	5.05779i	−0.169278	+	0.337938i
$225$		0			0
$226$	6.00345	−	1.35058i	0.399344	−	0.0898393i
$227$	23.0959			1.53293			0.766466	−	0.642285i	$-0.222013\pi$
$227$	23.0959			1.53293			0.766466	+	0.642285i	$0.222013\pi$
$228$		0			0
$229$	9.08386			0.600278			0.300139	−	0.953895i	$-0.402967\pi$
$229$	9.08386			0.600278			0.300139	+	0.953895i	$0.402967\pi$
$230$	−3.87113	+	0.870879i	−0.255255	+	0.0574240i
$231$		0			0
$232$	−11.4255	+	8.93807i	−0.750120	+	0.586813i
$233$		−	29.4595i		−	1.92996i	−0.262330	−	0.964978i	$-0.584491\pi$
$233$		−	29.4595i		−	1.92996i	0.262330	−	0.964978i	$-0.415509\pi$
$234$		0			0
$235$		−	4.89917i		−	0.319586i
$236$	−24.8636	+	11.7834i	−1.61849	+	0.767032i
$237$		0			0
$238$	−1.97275	−	8.76907i	−0.127875	−	0.568414i
$239$	17.3719			1.12369			0.561846	−	0.827242i	$-0.310091\pi$
$239$	17.3719			1.12369			0.561846	+	0.827242i	$0.310091\pi$
$240$		0			0
$241$	−11.8341			−0.762299			−0.381150	−	0.924513i	$-0.624472\pi$
$241$	−11.8341			−0.762299			−0.381150	+	0.924513i	$0.624472\pi$
$242$	0.659310	+	2.93069i	0.0423820	+	0.188392i
$243$		0			0
$244$	−8.83808	+	4.18854i	−0.565800	+	0.268144i
$245$		−	1.05392i		−	0.0673326i
$246$		0			0
$247$			1.25004i			0.0795381i
$248$	−18.7401	+	14.6603i	−1.19000	+	0.930928i
$249$		0			0
$250$	12.9261	−	2.90795i	0.817519	−	0.183915i
$251$	−22.4110			−1.41457			−0.707284	−	0.706930i	$-0.750080\pi$
$251$	−22.4110			−1.41457			−0.707284	+	0.706930i	$0.750080\pi$
$252$		0			0
$253$	7.93125			0.498633
$254$	28.1830	−	6.34025i	1.76836	−	0.397823i
$255$		0			0
$256$	−3.17040	−	15.6827i	−0.198150	−	0.980172i
$257$		−	20.2382i		−	1.26242i	−0.775611	−	0.631211i	$-0.782558\pi$
$257$		−	20.2382i		−	1.26242i	0.775611	−	0.631211i	$-0.217442\pi$
$258$		0			0
$259$		−	8.91591i		−	0.554008i
$260$	−0.889299	−	1.87648i	−0.0551520	−	0.116374i
$261$		0			0
$262$	−5.33228	−	23.7025i	−0.329429	−	1.46434i
$263$	25.1291			1.54952			0.774762	−	0.632253i	$-0.217870\pi$
$263$	25.1291			1.54952			0.774762	+	0.632253i	$0.217870\pi$
$264$		0			0
$265$	−2.71614			−0.166851
$266$	−0.393854	−	1.75072i	−0.0241488	−	0.107343i
$267$		0			0
$268$	−7.03579	−	14.8460i	−0.429779	−	0.906861i
$269$		−	4.09135i		−	0.249454i	−0.992191	−	0.124727i	$-0.960195\pi$
$269$		−	4.09135i		−	0.249454i	0.992191	−	0.124727i	$-0.0398055\pi$
$270$		0			0
$271$		−	2.36584i		−	0.143715i	−0.997415	−	0.0718573i	$-0.977107\pi$
$271$		−	2.36584i		−	0.143715i	0.997415	−	0.0718573i	$-0.0228926\pi$
$272$	19.6770	+	16.0972i	1.19310	+	0.976038i
$273$		0			0
$274$	−22.4662	+	5.05416i	−1.35723	+	0.305333i
$275$	−11.5870			−0.698723
$276$		0			0
$277$	20.9260			1.25732			0.628661	−	0.777679i	$-0.283603\pi$
$277$	20.9260			1.25732			0.628661	+	0.777679i	$0.283603\pi$
$278$	−1.45881	+	0.328185i	−0.0874937	+	0.0196832i
$279$		0			0
$280$	1.83672	+	2.34787i	0.109765	+	0.140312i
$281$			12.7122i			0.758348i	0.925325	+	0.379174i	$0.123792\pi$
$281$			12.7122i			0.758348i	−0.925325	+	0.379174i	$0.876208\pi$
$282$		0			0
$283$			18.4751i			1.09823i	0.835747	+	0.549115i	$0.185035\pi$
$283$			18.4751i			1.09823i	−0.835747	+	0.549115i	$0.814965\pi$
$284$	1.05524	−	0.500097i	0.0626168	−	0.0296753i
$285$		0			0
$286$	0.911006	+	4.04950i	0.0538689	+	0.239452i
$287$	4.54486			0.268275
$288$		0			0
$289$	−23.3942			−1.37613
$290$	1.67777	+	7.45784i	0.0985220	+	0.437939i
$291$		0			0
$292$	22.4343	−	10.6321i	1.31287	−	0.622195i
$293$		−	26.8597i		−	1.56916i	−0.620028	−	0.784579i	$-0.712879\pi$
$293$		−	26.8597i		−	1.56916i	0.620028	−	0.784579i	$-0.287121\pi$
$294$		0			0
$295$			14.4991i			0.844169i
$296$	15.5382	+	19.8623i	0.903137	+	1.15448i
$297$		0			0
$298$	9.26885	−	2.08519i	0.536930	−	0.120792i
$299$	−2.62263			−0.151671
$300$		0			0
$301$	0.646087			0.0372398
$302$	6.85652	−	1.54249i	0.394548	−	0.0887605i
$303$		0			0
$304$	3.92846	+	3.21376i	0.225313	+	0.184322i
$305$			5.15387i			0.295110i
$306$		0			0
$307$		−	16.6518i		−	0.950370i	−0.879886	−	0.475185i	$-0.842381\pi$
$307$		−	16.6518i		−	0.950370i	0.879886	−	0.475185i	$-0.157619\pi$
$308$	−2.55178	−	5.38442i	−0.145401	−	0.306806i
$309$		0			0
$310$	2.75188	+	12.2324i	0.156296	+	0.694752i
$311$	9.01174			0.511009			0.255505	−	0.966808i	$-0.417758\pi$
$311$	9.01174			0.511009			0.255505	+	0.966808i	$0.417758\pi$
$312$		0			0
$313$	−2.50866			−0.141798			−0.0708988	−	0.997484i	$-0.522587\pi$
$313$	−2.50866			−0.141798			−0.0708988	+	0.997484i	$0.522587\pi$
$314$	−4.46957	−	19.8677i	−0.252233	−	1.12120i
$315$		0			0
$316$	12.9374	+	27.2987i	0.727784	+	1.53567i
$317$		−	22.1219i		−	1.24249i	−0.783616	−	0.621246i	$-0.786627\pi$
$317$		−	22.1219i		−	1.24249i	0.783616	−	0.621246i	$-0.213373\pi$
$318$		0			0
$319$		−	15.2797i		−	0.855501i
$320$	−8.18347	−	2.02951i	−0.457470	−	0.113453i
$321$		0			0
$322$	3.67307	−	0.826321i	0.204692	−	0.0460491i
$323$	−8.06458			−0.448725
$324$		0			0
$325$	3.83148			0.212533
$326$	−3.07121	+	0.690922i	−0.170099	+	0.0382666i
$327$		0			0
$328$	−10.1248	+	7.92054i	−0.559047	+	0.437338i
$329$			4.64851i			0.256281i
$330$		0			0
$331$			18.4307i			1.01304i	0.862228	+	0.506520i	$0.169068\pi$
$331$			18.4307i			1.01304i	−0.862228	+	0.506520i	$0.830932\pi$
$332$	8.55182	−	4.05288i	0.469342	−	0.222431i
$333$		0			0
$334$	−3.87918	−	17.2433i	−0.212259	−	0.943513i
$335$	−8.65733			−0.473001
$336$		0			0
$337$	−24.7708			−1.34935			−0.674675	−	0.738115i	$-0.735716\pi$
$337$	−24.7708			−1.34935			−0.674675	+	0.738115i	$0.735716\pi$
$338$	3.73388	+	16.5974i	0.203096	+	0.902782i
$339$		0			0
$340$	12.1060	−	5.73728i	0.656540	−	0.311147i
$341$		−	25.0619i		−	1.35718i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−1.43932	+	1.12597i	−0.0776027	+	0.0607080i
$345$		0			0
$346$	22.2713	−	5.01031i	1.19731	−	0.269356i
$347$	27.1358			1.45673			0.728364	−	0.685191i	$-0.240281\pi$
$347$	27.1358			1.45673			0.728364	+	0.685191i	$0.240281\pi$
$348$		0			0
$349$	12.5396			0.671232			0.335616	−	0.941999i	$-0.391056\pi$
$349$	12.5396			0.671232			0.335616	+	0.941999i	$0.391056\pi$
$350$	−5.36611	+	1.20720i	−0.286831	+	0.0645275i
$351$		0			0
$352$	15.0684	+	7.54799i	0.803148	+	0.402309i
$353$		−	24.6724i		−	1.31318i	−0.754247	−	0.656590i	$-0.771998\pi$
$353$		−	24.6724i		−	1.31318i	0.754247	−	0.656590i	$-0.228002\pi$
$354$		0			0
$355$		−	0.615355i		−	0.0326596i
$356$	1.49575	+	3.15612i	0.0792744	+	0.167274i
$357$		0			0
$358$	4.52427	+	20.1108i	0.239115	+	1.06289i
$359$	−22.8525			−1.20611			−0.603054	−	0.797700i	$-0.706050\pi$
$359$	−22.8525			−1.20611			−0.603054	+	0.797700i	$0.706050\pi$
$360$		0			0
$361$	17.3899			0.915260
$362$	−0.607981	−	2.70253i	−0.0319548	−	0.142042i
$363$		0			0
$364$	0.843799	+	1.78047i	0.0442271	+	0.0933219i
$365$		−	13.0824i		−	0.684767i
$366$		0			0
$367$			20.3116i			1.06026i	0.847917	+	0.530128i	$0.177856\pi$
$367$			20.3116i			1.06026i	−0.847917	+	0.530128i	$0.822144\pi$
$368$	−6.74259	+	8.24206i	−0.351482	+	0.429647i
$369$		0			0
$370$	12.9649	−	2.91667i	0.674012	−	0.151631i
$371$	2.57717			0.133800
$372$		0			0
$373$	29.4192			1.52327			0.761635	−	0.648007i	$-0.224397\pi$
$373$	29.4192			1.52327			0.761635	+	0.648007i	$0.224397\pi$
$374$	−26.1252	+	5.87731i	−1.35090	+	0.303909i
$375$		0			0
$376$	−8.10117	−	10.3557i	−0.417786	−	0.534053i
$377$			5.05256i			0.260220i
$378$		0			0
$379$			18.5441i			0.952546i	0.879298	+	0.476273i	$0.158013\pi$
$379$			18.5441i			0.952546i	−0.879298	+	0.476273i	$0.841987\pi$
$380$	2.41693	−	1.14543i	0.123986	−	0.0587593i
$381$		0			0
$382$	8.13929	+	36.1799i	0.416442	+	1.85112i
$383$	37.8089			1.93194			0.965972	−	0.258648i	$-0.0832771\pi$
$383$	37.8089			1.93194			0.965972	+	0.258648i	$0.0832771\pi$
$384$		0			0
$385$	−3.13989			−0.160024
$386$	7.26324	+	32.2857i	0.369689	+	1.64330i
$387$		0			0
$388$	−5.43267	+	2.57465i	−0.275802	+	0.130708i
$389$		−	8.06117i		−	0.408718i	−0.978896	−	0.204359i	$-0.934489\pi$
$389$		−	8.06117i		−	0.408718i	0.978896	−	0.204359i	$-0.0655109\pi$
$390$		0			0
$391$		−	16.9198i		−	0.855670i
$392$	−1.74275	−	2.22774i	−0.0880219	−	0.112518i
$393$		0			0
$394$	−22.8176	+	5.13322i	−1.14953	+	0.258608i
$395$	15.9191			0.800974
$396$		0			0
$397$	27.5806			1.38423			0.692115	−	0.721787i	$-0.256679\pi$
$397$	27.5806			1.38423			0.692115	+	0.721787i	$0.256679\pi$
$398$	−1.66406	+	0.374359i	−0.0834117	+	0.0187649i
$399$		0			0
$400$	9.85048	−	12.0411i	0.492524	−	0.602055i
$401$			7.24355i			0.361725i	0.983508	+	0.180863i	$0.0578890\pi$
$401$			7.24355i			0.361725i	−0.983508	+	0.180863i	$0.942111\pi$
$402$		0			0
$403$			8.28723i			0.412816i
$404$	−1.31487	−	2.77446i	−0.0654173	−	0.138035i
$405$		0			0
$406$	−1.59193	−	7.07627i	−0.0790061	−	0.351189i
$407$	−26.5627			−1.31666
$408$		0			0
$409$	26.4380			1.30728			0.653638	−	0.756807i	$-0.273242\pi$
$409$	26.4380			1.30728			0.653638	+	0.756807i	$0.273242\pi$
$410$	1.48677	+	6.60881i	0.0734262	+	0.326386i
$411$		0			0
$412$	10.0136	+	21.1292i	0.493333	+	1.04096i
$413$		−	13.7573i		−	0.676950i
$414$		0			0
$415$		−	4.98694i		−	0.244799i
$416$	−4.98267	−	2.49590i	−0.244296	−	0.122372i
$417$		0			0
$418$	−5.21582	+	1.17339i	−0.255114	+	0.0573923i
$419$	−20.3362			−0.993487			−0.496744	−	0.867897i	$-0.665471\pi$
$419$	−20.3362			−0.993487			−0.496744	+	0.867897i	$0.665471\pi$
$420$		0			0
$421$	13.6537			0.665442			0.332721	−	0.943025i	$-0.392033\pi$
$421$	13.6537			0.665442			0.332721	+	0.943025i	$0.392033\pi$
$422$	12.8732	−	2.89604i	0.626655	−	0.140977i
$423$		0			0
$424$	−5.74128	+	4.49136i	−0.278821	+	0.218120i
$425$			24.7187i			1.19903i
$426$		0			0
$427$		−	4.89018i		−	0.236653i
$428$	28.4018	−	13.4602i	1.37285	−	0.650622i
$429$		0			0
$430$	0.211355	+	0.939494i	0.0101925	+	0.0453064i
$431$	16.9782			0.817811			0.408906	−	0.912577i	$-0.365911\pi$
$431$	16.9782			0.817811			0.408906	+	0.912577i	$0.365911\pi$
$432$		0			0
$433$	0.624418			0.0300076			0.0150038	−	0.999887i	$-0.495224\pi$
$433$	0.624418			0.0300076			0.0150038	+	0.999887i	$0.495224\pi$
$434$	−2.61109	−	11.6065i	−0.125336	−	0.557131i
$435$		0			0
$436$	13.2676	−	6.28776i	0.635401	−	0.301129i
$437$		−	3.37798i		−	0.161591i
$438$		0			0
$439$			22.8786i			1.09194i	0.837806	+	0.545969i	$0.183838\pi$
$439$			22.8786i			1.09194i	−0.837806	+	0.545969i	$0.816162\pi$
$440$	6.99487	−	5.47203i	0.333467	−	0.260869i
$441$		0			0
$442$	8.63883	−	1.94345i	0.410907	−	0.0924407i
$443$	0.212425			0.0100926			0.00504630	−	0.999987i	$-0.498394\pi$
$443$	0.212425			0.0100926			0.00504630	+	0.999987i	$0.498394\pi$
$444$		0			0
$445$	1.84047			0.0872467
$446$	−4.03558	+	0.907874i	−0.191090	+	0.0429891i
$447$		0			0
$448$	7.76478	+	1.92568i	0.366851	+	0.0909796i
$449$		−	17.6011i		−	0.830650i	−0.909673	−	0.415325i	$-0.863668\pi$
$449$		−	17.6011i		−	0.830650i	0.909673	−	0.415325i	$-0.136332\pi$
$450$		0			0
$451$		−	13.5402i		−	0.637585i
$452$	−3.72687	−	7.86393i	−0.175297	−	0.369888i
$453$		0			0
$454$	−7.16885	−	31.8662i	−0.336451	−	1.49555i
$455$	1.03827			0.0486748
$456$		0			0
$457$	8.56351			0.400584			0.200292	−	0.979736i	$-0.435811\pi$
$457$	8.56351			0.400584			0.200292	+	0.979736i	$0.435811\pi$
$458$	−2.81958	−	12.5333i	−0.131750	−	0.585641i
$459$		0			0
$460$	2.40315	+	5.07081i	0.112048	+	0.236428i
$461$		−	33.2233i		−	1.54736i	−0.633575	−	0.773681i	$-0.718413\pi$
$461$		−	33.2233i		−	1.54736i	0.633575	−	0.773681i	$-0.281587\pi$
$462$		0			0
$463$		−	10.8819i		−	0.505723i	−0.967502	−	0.252862i	$-0.918628\pi$
$463$		−	10.8819i		−	0.505723i	0.967502	−	0.252862i	$-0.0813717\pi$
$464$	15.8785	+	12.9898i	0.737143	+	0.603035i
$465$		0			0
$466$	−40.6462	+	9.14406i	−1.88290	+	0.423590i
$467$	41.7776			1.93324			0.966618	−	0.256224i	$-0.0824783\pi$
$467$	41.7776			1.93324			0.966618	+	0.256224i	$0.0824783\pi$
$468$		0			0
$469$	8.21439			0.379305
$470$	−6.75953	+	1.52067i	−0.311794	+	0.0701434i
$471$		0			0
$472$	23.9754	+	30.6476i	1.10356	+	1.41067i
$473$		−	1.92485i		−	0.0885047i
$474$		0			0
$475$			4.93501i			0.226434i
$476$	−11.4866	+	5.44374i	−0.526488	+	0.249513i
$477$		0			0
$478$	−5.39212	−	23.9685i	−0.246630	−	1.09629i
$479$	8.46943			0.386978			0.193489	−	0.981102i	$-0.438020\pi$
$479$	8.46943			0.386978			0.193489	+	0.981102i	$0.438020\pi$
$480$		0			0
$481$	8.78349			0.400493
$482$	3.67323	+	16.3278i	0.167311	+	0.743712i
$483$		0			0
$484$	3.83892	−	1.81934i	0.174496	−	0.0826972i
$485$			3.16803i			0.143853i
$486$		0			0
$487$			23.1496i			1.04901i	0.851408	+	0.524504i	$0.175749\pi$
$487$			23.1496i			1.04901i	−0.851408	+	0.524504i	$0.824251\pi$
$488$	8.52234	+	10.8941i	0.385788	+	0.493151i
$489$		0			0
$490$	−1.45413	+	0.327131i	−0.0656908	+	0.0147783i
$491$	−6.91483			−0.312062			−0.156031	−	0.987752i	$-0.549870\pi$
$491$	−6.91483			−0.312062			−0.156031	+	0.987752i	$0.549870\pi$
$492$		0			0
$493$	−32.5964			−1.46807
$494$	1.72472	−	0.388005i	0.0775987	−	0.0174572i
$495$		0			0
$496$	26.0440	+	21.3059i	1.16941	+	0.956662i
$497$			0.583871i			0.0261902i
$498$		0			0
$499$			7.58869i			0.339717i	0.985468	+	0.169858i	$0.0543310\pi$
$499$			7.58869i			0.339717i	−0.985468	+	0.169858i	$0.945669\pi$
$500$	−8.02438	−	16.9319i	−0.358861	−	0.757219i
$501$		0			0
$502$	6.95623	+	30.9211i	0.310472	+	1.38008i
$503$	−19.2293			−0.857390			−0.428695	−	0.903449i	$-0.641027\pi$
$503$	−19.2293			−0.857390			−0.428695	+	0.903449i	$0.641027\pi$
$504$		0			0
$505$	−1.61791			−0.0719961
$506$	−2.46181	−	10.9430i	−0.109441	−	0.486475i
$507$		0			0
$508$	−17.4957	−	36.9170i	−0.776245	−	1.63792i
$509$			23.2826i			1.03198i	0.856593	+	0.515992i	$0.172577\pi$
$509$			23.2826i			1.03198i	−0.856593	+	0.515992i	$0.827423\pi$
$510$		0			0
$511$			12.4131i			0.549123i
$512$	−20.6539	+	9.24212i	−0.912782	+	0.408448i
$513$		0			0
$514$	−27.9232	+	6.28181i	−1.23164	+	0.277079i
$515$	12.3214			0.542945
$516$		0			0
$517$	13.8490			0.609080
$518$	−12.3015	+	2.76745i	−0.540499	+	0.121595i
$519$		0			0
$520$	−2.31300	+	1.80944i	−0.101432	+	0.0793492i
$521$			29.5778i			1.29583i	0.761714	+	0.647914i	$0.224358\pi$
$521$			29.5778i			1.29583i	−0.761714	+	0.647914i	$0.775642\pi$
$522$		0			0
$523$		−	35.2794i		−	1.54266i	−0.636434	−	0.771331i	$-0.719591\pi$
$523$		−	35.2794i		−	1.54266i	0.636434	−	0.771331i	$-0.280409\pi$
$524$	−31.0479	+	14.7142i	−1.35633	+	0.642794i
$525$		0			0
$526$	−7.79991	−	34.6713i	−0.340092	−	1.51174i
$527$	−53.4647			−2.32896
$528$		0			0
$529$	−15.9129			−0.691864
$530$	0.843075	+	3.74754i	0.0366208	+	0.162783i
$531$		0			0
$532$	−2.29327	+	1.08683i	−0.0994258	+	0.0471199i
$533$			4.47736i			0.193936i
$534$		0			0
$535$		−	16.5623i		−	0.716052i
$536$	−18.2996	+	14.3156i	−0.790420	+	0.618340i
$537$		0			0
$538$	−5.64496	+	1.26993i	−0.243371	+	0.0547506i
$539$	2.97924			0.128325
$540$		0			0
$541$	−12.4892			−0.536955			−0.268477	−	0.963286i	$-0.586520\pi$
$541$	−12.4892			−0.536955			−0.268477	+	0.963286i	$0.586520\pi$
$542$	−3.26422	+	0.734343i	−0.140210	+	0.0315427i
$543$		0			0
$544$	16.1022	−	32.1455i	0.690376	−	1.37823i
$545$		−	7.73690i		−	0.331412i
$546$		0			0
$547$			28.2389i			1.20741i	0.797209	+	0.603703i	$0.206309\pi$
$547$			28.2389i			1.20741i	−0.797209	+	0.603703i	$0.793691\pi$
$548$	13.9468	+	29.4285i	0.595776	+	1.25712i
$549$		0			0
$550$	3.59654	+	15.9870i	0.153357	+	0.681686i
$551$	−6.50777			−0.277240
$552$		0			0
$553$	−15.1046			−0.642312
$554$	−6.49531	−	28.8723i	−0.275959	−	1.22666i
$555$		0			0
$556$	0.905613	+	1.91090i	0.0384065	+	0.0810402i
$557$			44.4589i			1.88378i	0.335918	+	0.941891i	$0.390953\pi$
$557$			44.4589i			1.88378i	−0.335918	+	0.941891i	$0.609047\pi$
$558$		0			0
$559$			0.636491i			0.0269207i
$560$	2.66932	−	3.26294i	0.112799	−	0.137884i
$561$		0			0
$562$	17.5395	−	3.94580i	0.739857	−	0.166444i
$563$	−9.21017			−0.388162			−0.194081	−	0.980985i	$-0.562173\pi$
$563$	−9.21017			−0.388162			−0.194081	+	0.980985i	$0.562173\pi$
$564$		0			0
$565$	−4.58581			−0.192926
$566$	25.4906	−	5.73456i	1.07145	−	0.241041i
$567$		0			0
$568$	−1.01754	−	1.30071i	−0.0426950	−	0.0545768i
$569$			26.5427i			1.11273i	0.830939	+	0.556363i	$0.187804\pi$
$569$			26.5427i			1.11273i	−0.830939	+	0.556363i	$0.812196\pi$
$570$		0			0
$571$		−	16.7288i		−	0.700077i	−0.936735	−	0.350039i	$-0.886168\pi$
$571$		−	16.7288i		−	0.700077i	0.936735	−	0.350039i	$-0.113832\pi$
$572$	5.30445	−	2.51388i	0.221790	−	0.105111i
$573$		0			0
$574$	−1.41070	−	6.27068i	−0.0588814	−	0.261733i
$575$	−10.3538			−0.431785
$576$		0			0
$577$	−29.4646			−1.22663			−0.613314	−	0.789839i	$-0.710164\pi$
$577$	−29.4646			−1.22663			−0.613314	+	0.789839i	$0.710164\pi$
$578$	7.26141	+	32.2777i	0.302035	+	1.34257i
$579$		0			0
$580$	9.76903	−	4.62974i	0.405637	−	0.192239i
$581$			4.73179i			0.196308i
$582$		0			0
$583$		−	7.67803i		−	0.317992i
$584$	−21.6329	−	27.6532i	−0.895175	−	1.14430i
$585$		0			0
$586$	−37.0591	+	8.33708i	−1.53090	+	0.344402i
$587$	−19.5265			−0.805943			−0.402972	−	0.915212i	$-0.632023\pi$
$587$	−19.5265			−0.805943			−0.402972	+	0.915212i	$0.632023\pi$
$588$		0			0
$589$	−10.6741			−0.439817
$590$	20.0048	−	4.50043i	0.823585	−	0.185280i
$591$		0			0
$592$	22.5817	−	27.6036i	0.928103	−	1.13450i
$593$			1.64809i			0.0676788i	0.999427	+	0.0338394i	$0.0107735\pi$
$593$			1.64809i			0.0676788i	−0.999427	+	0.0338394i	$0.989227\pi$
$594$		0			0
$595$			6.69835i			0.274606i
$596$	−5.75399	−	12.1413i	−0.235693	−	0.497326i
$597$		0			0
$598$	0.814049	+	3.61852i	0.0332889	+	0.147972i
$599$	5.92633			0.242143			0.121072	−	0.992644i	$-0.461367\pi$
$599$	5.92633			0.242143			0.121072	+	0.992644i	$0.461367\pi$
$600$		0			0
$601$	−33.0438			−1.34788			−0.673941	−	0.738785i	$-0.735400\pi$
$601$	−33.0438			−1.34788			−0.673941	+	0.738785i	$0.735400\pi$
$602$	−0.200542	−	0.891426i	−0.00817346	−	0.0363318i
$603$		0			0
$604$	−4.25645	−	8.98137i	−0.173192	−	0.365447i
$605$		−	2.23864i		−	0.0910137i
$606$		0			0
$607$			17.4880i			0.709815i	0.934901	+	0.354907i	$0.115488\pi$
$607$			17.4880i			0.709815i	−0.934901	+	0.354907i	$0.884512\pi$
$608$	3.21475	−	6.41775i	0.130375	−	0.260274i
$609$		0			0
$610$	7.11096	−	1.59973i	0.287914	−	0.0647713i
$611$	−4.57947			−0.185265
$612$		0			0
$613$	21.6723			0.875336			0.437668	−	0.899137i	$-0.355805\pi$
$613$	21.6723			0.875336			0.437668	+	0.899137i	$0.355805\pi$
$614$	−22.9750	+	5.16863i	−0.927197	+	0.208589i
$615$		0			0
$616$	−6.63699	+	5.19206i	−0.267412	+	0.209194i
$617$		−	6.28958i		−	0.253209i	−0.991953	−	0.126604i	$-0.959592\pi$
$617$		−	6.28958i		−	0.253209i	0.991953	−	0.126604i	$-0.0404079\pi$
$618$		0			0
$619$		−	35.8504i		−	1.44095i	−0.693481	−	0.720475i	$-0.743924\pi$
$619$		−	35.8504i		−	1.44095i	0.693481	−	0.720475i	$-0.256076\pi$
$620$	16.0232	−	7.59371i	0.643507	−	0.304971i
$621$		0			0
$622$	−2.79719	−	12.4338i	−0.112157	−	0.498549i
$623$	−1.74631			−0.0699643
$624$		0			0
$625$	9.57248			0.382899
$626$	0.778673	+	3.46127i	0.0311220	+	0.138340i
$627$		0			0
$628$	−26.0247	+	12.3336i	−1.03850	+	0.492165i
$629$			56.6663i			2.25943i
$630$		0			0
$631$		−	30.9763i		−	1.23315i	−0.787298	−	0.616573i	$-0.788520\pi$
$631$		−	30.9763i		−	1.23315i	0.787298	−	0.616573i	$-0.211480\pi$
$632$	33.6491	−	26.3234i	1.33849	−	1.04709i
$633$		0			0
$634$	−30.5223	+	6.86652i	−1.21220	+	0.272704i
$635$	−21.5279			−0.854309
$636$		0			0
$637$	−0.985148			−0.0390330
$638$	−21.0819	+	4.74274i	−0.834641	+	0.187767i
$639$		0			0
$640$	−0.260078	+	11.9209i	−0.0102805	+	0.471216i
$641$		−	4.95455i		−	0.195693i	−0.995202	−	0.0978466i	$-0.968805\pi$
$641$		−	4.95455i		−	0.195693i	0.995202	−	0.0978466i	$-0.0311954\pi$
$642$		0			0
$643$		−	4.37251i		−	0.172435i	−0.996276	−	0.0862175i	$-0.972522\pi$
$643$		−	4.37251i		−	0.172435i	0.996276	−	0.0862175i	$-0.0274780\pi$
$644$	−2.28020	−	4.81136i	−0.0898525	−	0.189594i
$645$		0			0
$646$	2.50320	+	11.1269i	0.0984870	+	0.437784i
$647$	31.7458			1.24805			0.624027	−	0.781402i	$-0.285495\pi$
$647$	31.7458			1.24805			0.624027	+	0.781402i	$0.285495\pi$
$648$		0			0
$649$	−40.9862			−1.60885
$650$	−1.18927	−	5.28641i	−0.0466470	−	0.207350i
$651$		0			0
$652$	1.90657	+	4.02298i	0.0746671	+	0.157552i
$653$			0.116763i			0.00456930i	0.999997	+	0.00228465i	$0.000727227\pi$
$653$			0.116763i			0.00456930i	−0.999997	+	0.00228465i	$0.999273\pi$
$654$		0			0
$655$			18.1054i			0.707437i
$656$	14.0709	+	11.5110i	0.549375	+	0.449428i
$657$		0			0
$658$	6.41369	−	1.44287i	0.250032	−	0.0562489i
$659$	−3.95369			−0.154014			−0.0770069	−	0.997031i	$-0.524536\pi$
$659$	−3.95369			−0.154014			−0.0770069	+	0.997031i	$0.524536\pi$
$660$		0			0
$661$	38.7062			1.50550			0.752749	−	0.658307i	$-0.228727\pi$
$661$	38.7062			1.50550			0.752749	+	0.658307i	$0.228727\pi$
$662$	25.4293	−	5.72077i	0.988339	−	0.222344i
$663$		0			0
$664$	−8.24631	−	10.5412i	−0.320019	−	0.409079i
$665$			1.33731i			0.0518585i
$666$		0			0
$667$		−	13.6535i		−	0.528667i
$668$	−22.5871	+	10.7045i	−0.873920	+	0.414168i
$669$		0			0
$670$	2.68719	+	11.9448i	0.103815	+	0.461467i
$671$	−14.5690			−0.562432
$672$		0			0
$673$	−6.45012			−0.248634			−0.124317	−	0.992243i	$-0.539674\pi$
$673$	−6.45012			−0.248634			−0.124317	+	0.992243i	$0.539674\pi$
$674$	7.68870	+	34.1770i	0.296158	+	1.31645i
$675$		0			0
$676$	21.7410	−	10.3035i	0.836193	−	0.396288i
$677$			30.4104i			1.16877i	0.811478	+	0.584384i	$0.198664\pi$
$677$			30.4104i			1.16877i	−0.811478	+	0.584384i	$0.801336\pi$
$678$		0			0
$679$		−	3.00594i		−	0.115358i
$680$	−11.6735	−	14.9222i	−0.447659	−	0.572241i
$681$		0			0
$682$	−34.5786	+	7.77906i	−1.32408	+	0.297876i
$683$	16.9861			0.649953			0.324977	−	0.945722i	$-0.394644\pi$
$683$	16.9861			0.649953			0.324977	+	0.945722i	$0.394644\pi$
$684$		0			0
$685$	17.1611			0.655690
$686$	1.37973	−	0.310394i	0.0526783	−	0.0118509i
$687$		0			0
$688$	2.00028	+	1.63637i	0.0762601	+	0.0623862i
$689$			2.53890i			0.0967243i
$690$		0			0
$691$		−	2.74292i		−	0.104346i	−0.998638	−	0.0521729i	$-0.983385\pi$
$691$		−	2.74292i		−	0.104346i	0.998638	−	0.0521729i	$-0.0166147\pi$
$692$	−13.8258	−	29.1732i	−0.525577	−	1.10900i
$693$		0			0
$694$	−8.42280	−	37.4401i	−0.319725	−	1.42121i
$695$	1.11433			0.0422689
$696$		0			0
$697$	−28.8855			−1.09412
$698$	−3.89223	−	17.3013i	−0.147323	−	0.654865i
$699$		0			0
$700$	3.33122	+	7.02908i	0.125908	+	0.265674i
$701$		−	8.97421i		−	0.338951i	−0.985534	−	0.169476i	$-0.945793\pi$
$701$		−	8.97421i		−	0.338951i	0.985534	−	0.169476i	$-0.0542074\pi$
$702$		0			0
$703$			11.3133i			0.426688i
$704$	5.73706	−	23.1332i	0.216223	−	0.871864i
$705$		0			0
$706$	−34.0413	+	7.65818i	−1.28116	+	0.288219i
$707$	1.53513			0.0577346
$708$		0			0
$709$	3.13240			0.117640			0.0588200	−	0.998269i	$-0.481266\pi$
$709$	3.13240			0.117640			0.0588200	+	0.998269i	$0.481266\pi$
$710$	−0.849023	+	0.191002i	−0.0318633	+	0.00716820i
$711$		0			0
$712$	3.89032	−	3.04337i	0.145796	−	0.114055i
$713$		−	22.3946i		−	0.838684i
$714$		0			0
$715$		−	3.09326i		−	0.115681i
$716$	26.3432	−	12.4846i	0.984491	−	0.466570i
$717$		0			0
$718$	7.09328	+	31.5303i	0.264719	+	1.17670i
$719$	29.4070			1.09670			0.548348	−	0.836250i	$-0.315257\pi$
$719$	29.4070			1.09670			0.548348	+	0.836250i	$0.315257\pi$
$720$		0			0
$721$	−11.6910			−0.435395
$722$	−5.39773	−	23.9934i	−0.200883	−	0.892942i
$723$		0			0
$724$	−3.54005	+	1.67770i	−0.131565	+	0.0623512i
$725$			19.9469i			0.740809i
$726$		0			0
$727$		−	11.0639i		−	0.410338i	−0.978727	−	0.205169i	$-0.934226\pi$
$727$		−	11.0639i		−	0.410338i	0.978727	−	0.205169i	$-0.0657743\pi$
$728$	2.19466	−	1.71686i	0.0813394	−	0.0636312i
$729$		0			0
$730$	−18.0502	+	4.06071i	−0.668070	+	0.150294i
$731$	−4.10630			−0.151877
$732$		0			0
$733$	−22.1305			−0.817410			−0.408705	−	0.912667i	$-0.634019\pi$
$733$	−22.1305			−0.817410			−0.408705	+	0.912667i	$0.634019\pi$
$734$	28.0245	−	6.30460i	1.03440	−	0.232707i
$735$		0			0
$736$	13.4647	+	6.74467i	0.496315	+	0.248612i
$737$		−	24.4727i		−	0.901463i
$738$		0			0
$739$		−	5.76011i		−	0.211889i	−0.994372	−	0.105944i	$-0.966213\pi$
$739$		−	5.76011i		−	0.211889i	0.994372	−	0.105944i	$-0.0337866\pi$
$740$	−8.04844	−	16.9827i	−0.295867	−	0.624297i
$741$		0			0
$742$	−0.799940	−	3.55581i	−0.0293667	−	0.130538i
$743$	−51.9086			−1.90434			−0.952170	−	0.305567i	$-0.901154\pi$
$743$	−51.9086			−1.90434			−0.952170	+	0.305567i	$0.901154\pi$
$744$		0			0
$745$	−7.08011			−0.259395
$746$	−9.13155	−	40.5906i	−0.334330	−	1.48613i
$747$		0			0
$748$	16.2182	+	34.2214i	0.592997	+	1.25126i
$749$			15.7149i			0.574212i
$750$		0			0
$751$		−	36.7888i		−	1.34244i	−0.741257	−	0.671221i	$-0.765770\pi$
$751$		−	36.7888i		−	1.34244i	0.741257	−	0.671221i	$-0.234230\pi$
$752$	−11.7735	+	14.3918i	−0.429335	+	0.524814i
$753$		0			0
$754$	6.97117	−	1.56828i	0.253875	−	0.0571136i
$755$	−5.23743			−0.190610
$756$		0			0
$757$	32.2356			1.17162			0.585812	−	0.810447i	$-0.300776\pi$
$757$	32.2356			1.17162			0.585812	+	0.810447i	$0.300776\pi$
$758$	25.5858	−	5.75597i	0.929319	−	0.209066i
$759$		0			0
$760$	−2.33058	−	2.97917i	−0.0845392	−	0.108066i
$761$			13.8150i			0.500793i	0.968143	+	0.250396i	$0.0805609\pi$
$761$			13.8150i			0.500793i	−0.968143	+	0.250396i	$0.919439\pi$
$762$		0			0
$763$			7.34105i			0.265764i
$764$	47.3921	−	22.4600i	1.71459	−	0.812576i
$765$		0			0
$766$	−11.7357	−	52.1660i	−0.424026	−	1.88484i
$767$	13.5529			0.489368
$768$		0			0
$769$	−47.3420			−1.70720			−0.853599	−	0.520931i	$-0.825585\pi$
$769$	−47.3420			−1.70720			−0.853599	+	0.520931i	$0.825585\pi$
$770$	0.974604	+	4.33220i	0.0351223	+	0.156122i
$771$		0			0
$772$	42.2912	−	20.0426i	1.52209	−	0.721349i
$773$		−	12.7984i		−	0.460325i	−0.973152	−	0.230163i	$-0.926074\pi$
$773$		−	12.7984i		−	0.460325i	0.973152	−	0.230163i	$-0.0739259\pi$
$774$		0			0
$775$			32.7170i			1.17523i
$776$	5.23859	+	6.69647i	0.188055	+	0.240389i
$777$		0			0
$778$	−11.1222	+	2.50214i	−0.398752	+	0.0897061i
$779$	−5.76690			−0.206621
$780$		0			0
$781$	1.73949			0.0622440
$782$	−23.3447	+	5.25180i	−0.834806	+	0.187804i
$783$		0			0
$784$	−2.53275	+	3.09600i	−0.0904552	+	0.110571i
$785$			15.1761i			0.541660i
$786$		0			0
$787$			35.5078i			1.26572i	0.774267	+	0.632858i	$0.218119\pi$
$787$			35.5078i			1.26572i	−0.774267	+	0.632858i	$0.781881\pi$
$788$	14.1649	+	29.8888i	0.504604	+	1.06475i
$789$		0			0
$790$	−4.94118	−	21.9640i	−0.175799	−	0.781444i
$791$	4.35118			0.154710
$792$		0			0
$793$	4.81755			0.171076
$794$	−8.56086	−	38.0538i	−0.303813	−	1.35048i
$795$		0			0
$796$	1.03303	+	2.17975i	0.0366147	+	0.0772593i
$797$		−	30.3922i		−	1.07655i	−0.842770	−	0.538273i	$-0.819077\pi$
$797$		−	30.3922i		−	1.07655i	0.842770	−	0.538273i	$-0.180923\pi$
$798$		0			0
$799$		−	29.5442i		−	1.04520i
$800$	−19.6710	−	9.85351i	−0.695475	−	0.348374i
$801$		0			0
$802$	9.99414	−	2.24835i	0.352905	−	0.0793922i
$803$	36.9817			1.30505
$804$		0			0
$805$	−2.80572			−0.0988886
$806$	11.4341	−	2.57231i	0.402750	−	0.0906056i
$807$		0			0
$808$	−3.41988	+	2.67535i	−0.120311	+	0.0941183i
$809$			41.0141i			1.44198i	0.692946	+	0.720989i	$0.256312\pi$
$809$			41.0141i			1.44198i	−0.692946	+	0.720989i	$0.743688\pi$
$810$		0			0
$811$			46.2839i			1.62525i	0.582788	+	0.812624i	$0.301962\pi$
$811$			46.2839i			1.62525i	−0.582788	+	0.812624i	$0.698038\pi$
$812$	−9.26921	+	4.39286i	−0.325286	+	0.154159i
$813$		0			0
$814$	8.24489	+	36.6493i	0.288983	+	1.28456i
$815$	2.34598			0.0821760
$816$		0			0
$817$	−0.819810			−0.0286815
$818$	−8.20621	−	36.4773i	−0.286923	−	1.27540i
$819$		0			0
$820$	8.65690	−	4.10267i	0.302312	−	0.143272i
$821$			4.65424i			0.162434i	0.996696	+	0.0812170i	$0.0258807\pi$
$821$			4.65424i			0.162434i	−0.996696	+	0.0812170i	$0.974119\pi$
$822$		0			0
$823$		−	24.1740i		−	0.842654i	−0.906909	−	0.421327i	$-0.861564\pi$
$823$		−	24.1740i		−	0.842654i	0.906909	−	0.421327i	$-0.138436\pi$
$824$	26.0445	−	20.3744i	0.907303	−	0.709776i
$825$		0			0
$826$	−18.9813	+	4.27017i	−0.660444	+	0.148578i
$827$	36.6008			1.27273			0.636367	−	0.771386i	$-0.280436\pi$
$827$	36.6008			1.27273			0.636367	+	0.771386i	$0.280436\pi$
$828$		0			0
$829$	−37.1578			−1.29054			−0.645272	−	0.763953i	$-0.723256\pi$
$829$	−37.1578			−1.29054			−0.645272	+	0.763953i	$0.723256\pi$
$830$	−6.88064	+	1.54792i	−0.238830	+	0.0537290i
$831$		0			0
$832$	−1.89708	+	7.64946i	−0.0657693	+	0.265197i
$833$		−	6.35564i		−	0.220210i
$834$		0			0
$835$			13.1715i			0.455819i
$836$	3.23792	+	6.83221i	0.111986	+	0.236297i
$837$		0			0
$838$	6.31223	+	28.0584i	0.218052	+	0.969263i
$839$	3.38158			0.116745			0.0583726	−	0.998295i	$-0.481409\pi$
$839$	3.38158			0.116745			0.0583726	+	0.998295i	$0.481409\pi$
$840$		0			0
$841$	2.69611			0.0929694
$842$	−4.23803	−	18.8384i	−0.146052	−	0.649216i
$843$		0			0
$844$	−7.99150	−	16.8626i	−0.275079	−	0.580433i
$845$		−	12.6781i		−	0.436141i
$846$		0			0
$847$			2.12410i			0.0729851i
$848$	7.97893	+	6.52733i	0.273997	+	0.224149i
$849$		0			0
$850$	34.1051	−	7.67253i	1.16979	−	0.263166i
$851$	−23.7356			−0.813647
$852$		0			0
$853$	28.2168			0.966124			0.483062	−	0.875586i	$-0.339525\pi$
$853$	28.2168			0.966124			0.483062	+	0.875586i	$0.339525\pi$
$854$	−6.74713	+	1.51788i	−0.230882	+	0.0519409i
$855$		0			0
$856$	−27.3872	−	35.0089i	−0.936074	−	1.19658i
$857$			17.3707i			0.593373i	0.954975	+	0.296686i	$0.0958816\pi$
$857$			17.3707i			0.593373i	−0.954975	+	0.296686i	$0.904118\pi$
$858$		0			0
$859$			45.9940i			1.56930i	0.619941	+	0.784648i	$0.287156\pi$
$859$			45.9940i			1.56930i	−0.619941	+	0.784648i	$0.712844\pi$
$860$	1.23064	−	0.583227i	0.0419646	−	0.0198879i
$861$		0			0
$862$	−5.26993	−	23.4253i	−0.179495	−	0.797870i
$863$	1.05635			0.0359586			0.0179793	−	0.999838i	$-0.494277\pi$
$863$	1.05635			0.0359586			0.0179793	+	0.999838i	$0.494277\pi$
$864$		0			0
$865$	−17.0122			−0.578432
$866$	−0.193816	−	0.861528i	−0.00658613	−	0.0292759i
$867$		0			0
$868$	−15.2034	+	7.20519i	−0.516037	+	0.244560i
$869$			45.0002i			1.52653i
$870$		0			0
$871$			8.09239i			0.274200i
$872$	−12.7936	−	16.3540i	−0.433246	−	0.553816i
$873$		0			0
$874$	−4.66071	+	1.04851i	−0.157651	+	0.0354663i
$875$	9.36858			0.316716
$876$		0			0
$877$	4.34738			0.146801			0.0734003	−	0.997303i	$-0.476615\pi$
$877$	4.34738			0.146801			0.0734003	+	0.997303i	$0.476615\pi$
$878$	31.5663	−	7.10139i	1.06531	−	0.239660i
$879$		0			0
$880$	−9.72110	−	7.95255i	−0.327698	−	0.268080i
$881$			58.0353i			1.95526i	0.210331	+	0.977630i	$0.432546\pi$
$881$			58.0353i			1.95526i	−0.210331	+	0.977630i	$0.567454\pi$
$882$		0			0
$883$		−	37.8799i		−	1.27476i	−0.770550	−	0.637379i	$-0.780018\pi$
$883$		−	37.8799i		−	1.27476i	0.770550	−	0.637379i	$-0.219982\pi$
$884$	−5.36289	−	11.3160i	−0.180373	−	0.380599i
$885$		0			0
$886$	−0.0659353	−	0.293089i	−0.00221514	−	0.00984650i
$887$	4.92085			0.165226			0.0826130	−	0.996582i	$-0.473673\pi$
$887$	4.92085			0.165226			0.0826130	+	0.996582i	$0.473673\pi$
$888$		0			0
$889$	20.4265			0.685081
$890$	−0.571272	−	2.53935i	−0.0191491	−	0.0851194i
$891$		0			0
$892$	2.50524	+	5.28622i	0.0838818	+	0.176996i
$893$		−	5.89842i		−	0.197383i
$894$		0			0
$895$		−	15.3619i		−	0.513491i
$896$	0.246771	−	11.3110i	0.00824404	−	0.377875i
$897$		0			0
$898$	−24.2848	+	5.46329i	−0.810396	+	0.182312i
$899$	−43.1437			−1.43892
$900$		0			0
$901$	−16.3796			−0.545684
$902$	−18.6819	+	4.20281i	−0.622039	+	0.139938i
$903$		0			0
$904$	−9.69331	+	7.58300i	−0.322395	+	0.252207i
$905$			2.06436i			0.0686216i
$906$		0			0
$907$		−	40.3942i		−	1.34127i	−0.741789	−	0.670633i	$-0.766022\pi$
$907$		−	40.3942i		−	1.34127i	0.741789	−	0.670633i	$-0.233978\pi$
$908$	−41.7416	+	19.7821i	−1.38524	+	0.656494i
$909$		0			0
$910$	−0.322273	−	1.43253i	−0.0106832	−	0.0474880i
$911$	24.4159			0.808934			0.404467	−	0.914553i	$-0.367457\pi$
$911$	24.4159			0.808934			0.404467	+	0.914553i	$0.367457\pi$
$912$		0			0
$913$	14.0972			0.466548
$914$	−2.65806	−	11.8153i	−0.0879209	−	0.390817i
$915$		0			0
$916$	−16.4174	+	7.78051i	−0.542445	+	0.257075i
$917$		−	17.1791i		−	0.567303i
$918$		0			0
$919$			0.922920i			0.0304443i	0.999884	+	0.0152222i	$0.00484555\pi$
$919$			0.922920i			0.0304443i	−0.999884	+	0.0152222i	$0.995154\pi$
$920$	6.25042	−	4.88965i	0.206070	−	0.161207i
$921$		0			0
$922$	−45.8392	+	10.3123i	−1.50963	+	0.339618i
$923$	−0.575199			−0.0189329
$924$		0			0
$925$	34.6762			1.14015
$926$	−15.0140	+	3.37767i	−0.493392	+	0.110997i
$927$		0			0
$928$	12.9938	−	25.9400i	0.426542	−	0.851524i
$929$			18.1210i			0.594530i	0.954795	+	0.297265i	$0.0960744\pi$
$929$			18.1210i			0.594530i	−0.954795	+	0.297265i	$0.903926\pi$
$930$		0			0
$931$		−	1.26888i		−	0.0415860i
$932$	25.2327	+	53.2425i	0.826523	+	1.74402i
$933$		0			0
$934$	−12.9675	−	57.6418i	−0.424310	−	1.88610i
$935$	19.9560			0.652632
$936$		0			0
$937$	58.1414			1.89940			0.949699	−	0.313165i	$-0.101389\pi$
$937$	58.1414			1.89940			0.949699	+	0.313165i	$0.101389\pi$
$938$	−2.54970	−	11.3336i	−0.0832506	−	0.370057i
$939$		0			0
$940$	4.19624	+	8.85432i	0.136866	+	0.288796i
$941$			11.4151i			0.372121i	0.982538	+	0.186061i	$0.0595721\pi$
$941$			11.4151i			0.372121i	−0.982538	+	0.186061i	$0.940428\pi$
$942$		0			0
$943$		−	12.0992i		−	0.394004i
$944$	34.8436	−	42.5924i	1.13406	−	1.38627i
$945$		0			0
$946$	−2.65577	+	0.597462i	−0.0863467	+	0.0194252i
$947$	−53.1805			−1.72813			−0.864067	−	0.503377i	$-0.832091\pi$
$947$	−53.1805			−1.72813			−0.864067	+	0.503377i	$0.832091\pi$
$948$		0			0
$949$	−12.2287			−0.396962
$950$	6.80898	−	1.53180i	0.220912	−	0.0496981i
$951$		0			0
$952$	11.0763	+	14.1587i	0.358984	+	0.458887i
$953$		−	32.5256i		−	1.05361i	−0.849987	−	0.526803i	$-0.823391\pi$
$953$		−	32.5256i		−	1.05361i	0.849987	−	0.526803i	$-0.176609\pi$
$954$		0			0
$955$		−	27.6364i		−	0.894293i
$956$	−31.3963	+	14.8793i	−1.01543	+	0.481232i
$957$		0			0
$958$	−2.62886	−	11.6855i	−0.0849347	−	0.377542i
$959$	−16.2830			−0.525807
$960$		0			0
$961$	−39.7645			−1.28273
$962$	−2.72634	−	12.1188i	−0.0879008	−	0.390727i
$963$		0			0
$964$	21.3878	−	10.1361i	0.688856	−	0.326462i
$965$		−	24.6618i		−	0.793892i
$966$		0			0
$967$		−	34.1888i		−	1.09944i	−0.835350	−	0.549719i	$-0.814735\pi$
$967$		−	34.1888i		−	1.09944i	0.835350	−	0.549719i	$-0.185265\pi$
$968$	−3.70177	−	4.73196i	−0.118980	−	0.152091i
$969$		0			0
$970$	4.37103	−	0.983338i	0.140345	−	0.0315731i
$971$	−14.1172			−0.453041			−0.226521	−	0.974006i	$-0.572735\pi$
$971$	−14.1172			−0.453041			−0.226521	+	0.974006i	$0.572735\pi$
$972$		0			0
$973$	−1.05732			−0.0338960
$974$	31.9402	−	7.18549i	1.02343	−	0.230238i
$975$		0			0
$976$	12.3856	−	15.1400i	0.396453	−	0.484619i
$977$		−	23.3492i		−	0.747007i	−0.927629	−	0.373504i	$-0.878156\pi$
$977$		−	23.3492i		−	0.747007i	0.927629	−	0.373504i	$-0.121844\pi$
$978$		0			0
$979$			5.20267i			0.166278i
$980$	0.902706	+	1.90477i	0.0288359	+	0.0608455i
$981$		0			0
$982$	2.14632	+	9.54060i	0.0684919	+	0.304453i
$983$	27.3413			0.872052			0.436026	−	0.899934i	$-0.356386\pi$
$983$	27.3413			0.872052			0.436026	+	0.899934i	$0.356386\pi$
$984$		0			0
$985$	17.4295			0.555350
$986$	10.1177	+	44.9742i	0.322214	+	1.43227i
$987$		0			0
$988$	−1.07068	−	2.25921i	−0.0340630	−	0.0718750i
$989$		−	1.71999i		−	0.0546926i
$990$		0			0
$991$			27.2385i			0.865259i	0.901572	+	0.432629i	$0.142414\pi$
$991$			27.2385i			0.865259i	−0.901572	+	0.432629i	$0.857586\pi$
$992$	21.3124	−	42.5470i	0.676671	−	1.35087i
$993$		0			0
$994$	0.805584	−	0.181230i	0.0255516	−	0.00574827i
$995$	1.27111			0.0402969
$996$		0			0
$997$	56.6550			1.79428			0.897141	−	0.441744i	$-0.145640\pi$
$997$	56.6550			1.79428			0.897141	+	0.441744i	$0.145640\pi$
$998$	10.4704	−	2.35549i	0.331433	−	0.0745616i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.a.323.11	✓	24
3.2	odd	2	inner	756.2.e.a.323.14	yes	24
4.3	odd	2	inner	756.2.e.a.323.13	yes	24
12.11	even	2	inner	756.2.e.a.323.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.a.323.11	✓	24	1.1	even	1	trivial
756.2.e.a.323.12	yes	24	12.11	even	2	inner
756.2.e.a.323.13	yes	24	4.3	odd	2	inner
756.2.e.a.323.14	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.310394 - 1.37973i) q^{2} +(-1.80731 + 0.856520i) q^{4} +1.05392i q^{5} -1.00000i q^{7} +(1.74275 + 2.22774i) q^{8} +O(q^{10})\)	\(q+(-0.310394 - 1.37973i) q^{2} +(-1.80731 + 0.856520i) q^{4} +1.05392i q^{5} -1.00000i q^{7} +(1.74275 + 2.22774i) q^{8} +(1.45413 - 0.327131i) q^{10} -2.97924 q^{11} +0.985148 q^{13} +(-1.37973 + 0.310394i) q^{14} +(2.53275 - 3.09600i) q^{16} +6.35564i q^{17} +1.26888i q^{19} +(-0.902706 - 1.90477i) q^{20} +(0.924740 + 4.11055i) q^{22} -2.66217 q^{23} +3.88925 q^{25} +(-0.305784 - 1.35924i) q^{26} +(0.856520 + 1.80731i) q^{28} +5.12873i q^{29} +8.41216i q^{31} +(-5.05779 - 2.53353i) q^{32} +(8.76907 - 1.97275i) q^{34} +1.05392 q^{35} +8.91591 q^{37} +(1.75072 - 0.393854i) q^{38} +(-2.34787 + 1.83672i) q^{40} +4.54486i q^{41} +0.646087i q^{43} +(5.38442 - 2.55178i) q^{44} +(0.826321 + 3.67307i) q^{46} -4.64851 q^{47} -1.00000 q^{49} +(-1.20720 - 5.36611i) q^{50} +(-1.78047 + 0.843799i) q^{52} +2.57717i q^{53} -3.13989i q^{55} +(2.22774 - 1.74275i) q^{56} +(7.07627 - 1.59193i) q^{58} +13.7573 q^{59} +4.89018 q^{61} +(11.6065 - 2.61109i) q^{62} +(-1.92568 + 7.76478i) q^{64} +1.03827i q^{65} +8.21439i q^{67} +(-5.44374 - 11.4866i) q^{68} +(-0.327131 - 1.45413i) q^{70} -0.583871 q^{71} -12.4131 q^{73} +(-2.76745 - 12.3015i) q^{74} +(-1.08683 - 2.29327i) q^{76} +2.97924i q^{77} -15.1046i q^{79} +(3.26294 + 2.66932i) q^{80} +(6.27068 - 1.41070i) q^{82} -4.73179 q^{83} -6.69835 q^{85} +(0.891426 - 0.200542i) q^{86} +(-5.19206 - 6.63699i) q^{88} -1.74631i q^{89} -0.985148i q^{91} +(4.81136 - 2.28020i) q^{92} +(1.44287 + 6.41369i) q^{94} -1.33731 q^{95} +3.00594 q^{97} +(0.310394 + 1.37973i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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