LMFDB - Embedded newform 792.2.h.i.307.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(307,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.3342602057661458415616.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 20x^{14} + 164x^{12} - 666x^{10} + 1300x^{8} - 924x^{6} + 273x^{4} + 404x^{2} + 64 $ x^16 - 20x^14 + 164x^12 - 666x^10 + 1300x^8 - 924x^6 + 273x^4 + 404*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.8
Root			$-0.946412 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	792.307
Dual form			792.2.h.i.307.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.927153 + 1.06789i) q^{2} +(-0.280776 - 1.98019i) q^{4} +2.00000i q^{5} -0.936426 q^{7} +(2.37495 + 1.53610i) q^{8} +(-2.13578 - 1.85431i) q^{10} +(3.09218 - 1.19935i) q^{11} -4.27156 q^{13} +(0.868210 - 1.00000i) q^{14} +(-3.84233 + 1.11198i) q^{16} +3.33513i q^{17} +2.89560i q^{19} +(3.96039 - 0.561553i) q^{20} +(-1.58614 + 4.41409i) q^{22} +5.12311i q^{23} +1.00000 q^{25} +(3.96039 - 4.56155i) q^{26} +(0.262926 + 1.85431i) q^{28} -6.60421 q^{29} -1.73642i q^{31} +(2.37495 - 5.13416i) q^{32} +(-3.56155 - 3.09218i) q^{34} -1.87285i q^{35} -6.18435i q^{37} +(-3.09218 - 2.68466i) q^{38} +(-3.07221 + 4.74990i) q^{40} +1.46228i q^{41} +10.3128i q^{43} +(-3.24316 - 5.78636i) q^{44} +(-5.47091 - 4.74990i) q^{46} +6.00000i q^{47} -6.12311 q^{49} +(-0.927153 + 1.06789i) q^{50} +(1.19935 + 8.45851i) q^{52} +8.24621i q^{53} +(2.39871 + 6.18435i) q^{55} +(-2.22397 - 1.43845i) q^{56} +(6.12311 - 7.05256i) q^{58} -9.65719 q^{59} -9.06897 q^{61} +(1.85431 + 1.60993i) q^{62} +(3.28078 + 7.29634i) q^{64} -8.54312i q^{65} -10.2462 q^{67} +(6.60421 - 0.936426i) q^{68} +(2.00000 + 1.73642i) q^{70} +4.24621i q^{71} -13.2084i q^{73} +(6.60421 + 5.73384i) q^{74} +(5.73384 - 0.813015i) q^{76} +(-2.89560 + 1.12311i) q^{77} +3.86098 q^{79} +(-2.22397 - 7.68466i) q^{80} +(-1.56155 - 1.35576i) q^{82} +2.39871i q^{83} -6.67026 q^{85} +(-11.0129 - 9.56155i) q^{86} +(9.18609 + 1.90150i) q^{88} -3.47284 q^{89} +4.00000 q^{91} +(10.1447 - 1.43845i) q^{92} +(-6.40734 - 5.56292i) q^{94} -5.79119 q^{95} +11.3693 q^{97} +(5.67705 - 6.53880i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 12 q^{16} + 4 q^{22} + 16 q^{25} - 24 q^{34} - 32 q^{49} + 32 q^{58} + 36 q^{64} - 32 q^{67} + 32 q^{70} + 8 q^{82} - 20 q^{88} + 64 q^{91} - 16 q^{97}+O(q^{100}) $ 16 * q + 12 * q^4 - 12 * q^16 + 4 * q^22 + 16 * q^25 - 24 * q^34 - 32 * q^49 + 32 * q^58 + 36 * q^64 - 32 * q^67 + 32 * q^70 + 8 * q^82 - 20 * q^88 + 64 * q^91 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.927153	+	1.06789i	−0.655596	+	0.755112i
$2$	−0.927153	+	1.06789i	−0.655596	+	0.755112i
$3$		0			0
$3$		0			0
$4$	−0.280776	−	1.98019i	−0.140388	−	0.990097i
$5$			2.00000i			0.894427i	0.894427	+	0.447214i	$0.147584\pi$
$5$			2.00000i			0.894427i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	−0.936426			−0.353936			−0.176968	−	0.984217i	$-0.556629\pi$
$7$	−0.936426			−0.353936			−0.176968	+	0.984217i	$0.556629\pi$
$8$	2.37495	+	1.53610i	0.839672	+	0.543094i
$9$		0			0
$10$	−2.13578	−	1.85431i	−0.675393	−	0.586383i
$11$	3.09218	−	1.19935i	0.932326	−	0.361618i
$11$	3.09218	−	1.19935i	0.932326	−	0.361618i
$12$		0			0
$13$	−4.27156			−1.18472			−0.592359	−	0.805674i	$-0.701803\pi$
$13$	−4.27156			−1.18472			−0.592359	+	0.805674i	$0.701803\pi$
$14$	0.868210	−	1.00000i	0.232039	−	0.267261i
$15$		0			0
$16$	−3.84233	+	1.11198i	−0.960582	+	0.277996i
$17$			3.33513i			0.808888i	0.914563	+	0.404444i	$0.132535\pi$
$17$			3.33513i			0.808888i	−0.914563	+	0.404444i	$0.867465\pi$
$18$		0			0
$19$			2.89560i			0.664295i	0.943227	+	0.332148i	$0.107773\pi$
$19$			2.89560i			0.664295i	−0.943227	+	0.332148i	$0.892227\pi$
$20$	3.96039	−	0.561553i	0.885569	−	0.125567i
$21$		0			0
$22$	−1.58614	+	4.41409i	−0.338167	+	0.941086i
$23$			5.12311i			1.06824i	0.845408	+	0.534121i	$0.179357\pi$
$23$			5.12311i			1.06824i	−0.845408	+	0.534121i	$0.820643\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	3.96039	−	4.56155i	0.776696	−	0.894594i
$27$		0			0
$28$	0.262926	+	1.85431i	0.0496884	+	0.350431i
$29$	−6.60421			−1.22637			−0.613185	−	0.789939i	$-0.710112\pi$
$29$	−6.60421			−1.22637			−0.613185	+	0.789939i	$0.710112\pi$
$30$		0			0
$31$		−	1.73642i		−	0.311870i	−0.987767	−	0.155935i	$-0.950161\pi$
$31$		−	1.73642i		−	0.311870i	0.987767	−	0.155935i	$-0.0498391\pi$
$32$	2.37495	−	5.13416i	0.419836	−	0.907600i
$33$		0			0
$34$	−3.56155	−	3.09218i	−0.610801	−	0.530304i
$35$		−	1.87285i		−	0.316570i
$36$		0			0
$37$		−	6.18435i		−	1.01670i	−0.861150	−	0.508351i	$-0.830255\pi$
$37$		−	6.18435i		−	1.01670i	0.861150	−	0.508351i	$-0.169745\pi$
$38$	−3.09218	−	2.68466i	−0.501617	−	0.435509i
$39$		0			0
$40$	−3.07221	+	4.74990i	−0.485758	+	0.751025i
$41$			1.46228i			0.228370i	0.993460	+	0.114185i	$0.0364256\pi$
$41$			1.46228i			0.228370i	−0.993460	+	0.114185i	$0.963574\pi$
$42$		0			0
$43$			10.3128i			1.57269i	0.617788	+	0.786345i	$0.288029\pi$
$43$			10.3128i			1.57269i	−0.617788	+	0.786345i	$0.711971\pi$
$44$	−3.24316	−	5.78636i	−0.488925	−	0.872326i
$45$		0			0
$46$	−5.47091	−	4.74990i	−0.806642	−	0.700335i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$		0			0
$49$	−6.12311			−0.874729
$50$	−0.927153	+	1.06789i	−0.131119	+	0.151022i
$51$		0			0
$52$	1.19935	+	8.45851i	0.166320	+	1.17298i
$53$			8.24621i			1.13270i	0.824163	+	0.566352i	$0.191646\pi$
$53$			8.24621i			1.13270i	−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$	2.39871	+	6.18435i	0.323441	+	0.833898i
$56$	−2.22397	−	1.43845i	−0.297190	−	0.192221i
$57$		0			0
$58$	6.12311	−	7.05256i	0.804003	−	0.926047i
$59$	−9.65719			−1.25726			−0.628630	−	0.777705i	$-0.716384\pi$
$59$	−9.65719			−1.25726			−0.628630	+	0.777705i	$0.716384\pi$
$60$		0			0
$61$	−9.06897			−1.16116			−0.580581	−	0.814202i	$-0.697175\pi$
$61$	−9.06897			−1.16116			−0.580581	+	0.814202i	$0.697175\pi$
$62$	1.85431	+	1.60993i	0.235497	+	0.204461i
$63$		0			0
$64$	3.28078	+	7.29634i	0.410097	+	0.912042i
$65$		−	8.54312i		−	1.05964i
$66$		0			0
$67$	−10.2462			−1.25177			−0.625887	−	0.779914i	$-0.715263\pi$
$67$	−10.2462			−1.25177			−0.625887	+	0.779914i	$0.715263\pi$
$68$	6.60421	−	0.936426i	0.800878	−	0.113558i
$69$		0			0
$70$	2.00000	+	1.73642i	0.239046	+	0.207542i
$71$			4.24621i			0.503933i	0.967736	+	0.251966i	$0.0810772\pi$
$71$			4.24621i			0.503933i	−0.967736	+	0.251966i	$0.918923\pi$
$72$		0			0
$73$		−	13.2084i		−	1.54593i	−0.634450	−	0.772964i	$-0.718773\pi$
$73$		−	13.2084i		−	1.54593i	0.634450	−	0.772964i	$-0.281227\pi$
$74$	6.60421	+	5.73384i	0.767723	+	0.666545i
$75$		0			0
$76$	5.73384	−	0.813015i	0.657716	−	0.0932592i
$77$	−2.89560	+	1.12311i	−0.329984	+	0.127990i
$78$		0			0
$79$	3.86098			0.434395			0.217197	−	0.976128i	$-0.430308\pi$
$79$	3.86098			0.434395			0.217197	+	0.976128i	$0.430308\pi$
$80$	−2.22397	−	7.68466i	−0.248647	−	0.859171i
$81$		0			0
$82$	−1.56155	−	1.35576i	−0.172445	−	0.149718i
$83$			2.39871i			0.263292i	0.991297	+	0.131646i	$0.0420262\pi$
$83$			2.39871i			0.263292i	−0.991297	+	0.131646i	$0.957974\pi$
$84$		0			0
$85$	−6.67026			−0.723492
$86$	−11.0129	−	9.56155i	−1.18756	−	1.03105i
$87$		0			0
$88$	9.18609	+	1.90150i	0.979241	+	0.202700i
$89$	−3.47284			−0.368120			−0.184060	−	0.982915i	$-0.558924\pi$
$89$	−3.47284			−0.368120			−0.184060	+	0.982915i	$0.558924\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	10.1447	−	1.43845i	1.05766	−	0.149968i
$93$		0			0
$94$	−6.40734	−	5.56292i	−0.660866	−	0.573771i
$95$	−5.79119			−0.594164
$96$		0			0
$97$	11.3693			1.15438			0.577190	−	0.816610i	$-0.304149\pi$
$97$	11.3693			1.15438			0.577190	+	0.816610i	$0.304149\pi$
$98$	5.67705	−	6.53880i	0.573469	−	0.660519i
$99$		0			0
$100$	−0.280776	−	1.98019i	−0.0280776	−	0.198019i
$101$	6.60421			0.657143			0.328571	−	0.944479i	$-0.393433\pi$
$101$	6.60421			0.657143			0.328571	+	0.944479i	$0.393433\pi$
$102$		0			0
$103$		−	1.73642i		−	0.171095i	−0.996334	−	0.0855473i	$-0.972736\pi$
$103$		−	1.73642i		−	0.171095i	0.996334	−	0.0855473i	$-0.0272639\pi$
$104$	−10.1447	−	6.56155i	−0.994773	−	0.643413i
$105$		0			0
$106$	−8.80604	−	7.64550i	−0.855319	−	0.742596i
$107$			9.06897i			0.876730i	0.898797	+	0.438365i	$0.144442\pi$
$107$			9.06897i			0.876730i	−0.898797	+	0.438365i	$0.855558\pi$
$108$		0			0
$109$	1.34700			0.129019			0.0645096	−	0.997917i	$-0.479452\pi$
$109$	1.34700			0.129019			0.0645096	+	0.997917i	$0.479452\pi$
$110$	−8.82817	−	3.17228i	−0.841733	−	0.302465i
$111$		0			0
$112$	3.59806	−	1.04129i	0.339985	−	0.0983927i
$113$	−15.8415			−1.49025			−0.745124	−	0.666926i	$-0.767610\pi$
$113$	−15.8415			−1.49025			−0.745124	+	0.666926i	$0.767610\pi$
$114$		0			0
$115$	−10.2462			−0.955464
$116$	1.85431	+	13.0776i	0.172168	+	1.21422i
$117$		0			0
$118$	8.95369	−	10.3128i	0.824254	−	0.949372i
$119$		−	3.12311i		−	0.286295i
$120$		0			0
$121$	8.12311	−	7.41722i	0.738464	−	0.674293i
$122$	8.40832	−	9.68466i	0.761253	−	0.876808i
$123$		0			0
$124$	−3.43845	+	0.487546i	−0.308782	+	0.0437829i
$125$			12.0000i			1.07331i
$126$		0			0
$127$	16.1498			1.43306			0.716532	−	0.697554i	$-0.245728\pi$
$127$	16.1498			1.43306			0.716532	+	0.697554i	$0.245728\pi$
$128$	−10.8335	−	3.26131i	−0.957552	−	0.288262i
$129$		0			0
$130$	9.12311	+	7.92077i	0.800149	+	0.694698i
$131$		−	12.8147i		−	1.11962i	−0.828620	−	0.559812i	$-0.810873\pi$
$131$		−	12.8147i		−	1.11962i	0.828620	−	0.559812i	$-0.189127\pi$
$132$		0			0
$133$		−	2.71151i		−	0.235118i
$134$	9.49980	−	10.9418i	0.820658	−	0.945229i
$135$		0			0
$136$	−5.12311	+	7.92077i	−0.439303	+	0.679201i
$137$	15.8415			1.35343			0.676717	−	0.736243i	$-0.263402\pi$
$137$	15.8415			1.35343			0.676717	+	0.736243i	$0.263402\pi$
$138$		0			0
$139$			10.3128i			0.874722i	0.899286	+	0.437361i	$0.144087\pi$
$139$			10.3128i			0.874722i	−0.899286	+	0.437361i	$0.855913\pi$
$140$	−3.70861	+	0.525853i	−0.313435	+	0.0444427i
$141$		0			0
$142$	−4.53448	−	3.93689i	−0.380526	−	0.330376i
$143$	−13.2084	+	5.12311i	−1.10454	+	0.428416i
$144$		0			0
$145$		−	13.2084i		−	1.09690i
$146$	14.1051	+	12.2462i	1.16735	+	1.01350i
$147$		0			0
$148$	−12.2462	+	1.73642i	−1.00663	+	0.142733i
$149$	0.813015			0.0666048			0.0333024	−	0.999445i	$-0.489398\pi$
$149$	0.813015			0.0666048			0.0333024	+	0.999445i	$0.489398\pi$
$150$		0			0
$151$	20.9472			1.70466			0.852330	−	0.523004i	$-0.175189\pi$
$151$	20.9472			1.70466			0.852330	+	0.523004i	$0.175189\pi$
$152$	−4.44793	+	6.87689i	−0.360775	+	0.557790i
$153$		0			0
$154$	1.48531	−	4.13347i	0.119689	−	0.333084i
$155$	3.47284			0.278945
$156$		0			0
$157$			15.8415i			1.26429i	0.774849	+	0.632146i	$0.217826\pi$
$157$			15.8415i			1.26429i	−0.774849	+	0.632146i	$0.782174\pi$
$158$	−3.57972	+	4.12311i	−0.284787	+	0.328017i
$159$		0			0
$160$	10.2683	+	4.74990i	0.811782	+	0.375513i
$161$		−	4.79741i		−	0.378089i
$162$		0			0
$163$	12.4924			0.978482			0.489241	−	0.872149i	$-0.337274\pi$
$163$	12.4924			0.978482			0.489241	+	0.872149i	$0.337274\pi$
$164$	2.89560	−	0.410574i	0.226108	−	0.0320604i
$165$		0			0
$166$	−2.56155	−	2.22397i	−0.198815	−	0.172613i
$167$	5.79119			0.448136			0.224068	−	0.974574i	$-0.428066\pi$
$167$	5.79119			0.448136			0.224068	+	0.974574i	$0.428066\pi$
$168$		0			0
$169$	5.24621			0.403555
$170$	6.18435	−	7.12311i	0.474318	−	0.546317i
$171$		0			0
$172$	20.4214	−	2.89560i	1.55711	−	0.220787i
$173$	−0.813015			−0.0618124			−0.0309062	−	0.999522i	$-0.509839\pi$
$173$	−0.813015			−0.0618124			−0.0309062	+	0.999522i	$0.509839\pi$
$174$		0			0
$175$	−0.936426			−0.0707872
$176$	−10.5475	+	8.04676i	−0.795048	+	0.606547i
$177$		0			0
$178$	3.21985	−	3.70861i	0.241338	−	0.277972i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$		−	8.89586i		−	0.661224i	−0.943767	−	0.330612i	$-0.892745\pi$
$181$		−	8.89586i		−	0.661224i	0.943767	−	0.330612i	$-0.107255\pi$
$182$	−3.70861	+	4.27156i	−0.274900	+	0.316629i
$183$		0			0
$184$	−7.86962	+	12.1671i	−0.580156	+	0.896972i
$185$	12.3687			0.909365
$186$		0			0
$187$	4.00000	+	10.3128i	0.292509	+	0.754148i
$188$	11.8812	−	1.68466i	0.866523	−	0.122866i
$189$		0			0
$190$	5.36932	−	6.18435i	0.389531	−	0.448660i
$191$		−	12.2462i		−	0.886105i	−0.896496	−	0.443052i	$-0.853896\pi$
$191$		−	12.2462i		−	0.886105i	0.896496	−	0.443052i	$-0.146104\pi$
$192$		0			0
$193$			1.62603i			0.117044i	0.998286	+	0.0585221i	$0.0186388\pi$
$193$			1.62603i			0.117044i	−0.998286	+	0.0585221i	$0.981361\pi$
$194$	−10.5411	+	12.1412i	−0.756806	+	0.871686i
$195$		0			0
$196$	1.71922	+	12.1249i	0.122802	+	0.866067i
$197$	12.3954			0.883135			0.441568	−	0.897228i	$-0.354423\pi$
$197$	12.3954			0.883135			0.441568	+	0.897228i	$0.354423\pi$
$198$		0			0
$199$			14.1051i			0.999886i	0.866058	+	0.499943i	$0.166646\pi$
$199$			14.1051i			0.999886i	−0.866058	+	0.499943i	$0.833354\pi$
$200$	2.37495	+	1.53610i	0.167934	+	0.108619i
$201$		0			0
$202$	−6.12311	+	7.05256i	−0.430820	+	0.496217i
$203$	6.18435			0.434056
$204$		0			0
$205$	−2.92456			−0.204260
$206$	1.85431	+	1.60993i	0.129196	+	0.112169i
$207$		0			0
$208$	16.4127	−	4.74990i	1.13802	−	0.329346i
$209$	3.47284	+	8.95369i	0.240221	+	0.619340i
$210$		0			0
$211$			2.89560i			0.199341i	0.995020	+	0.0996705i	$0.0317789\pi$
$211$			2.89560i			0.199341i	−0.995020	+	0.0996705i	$0.968221\pi$
$212$	16.3291	−	2.31534i	1.12149	−	0.159018i
$213$		0			0
$214$	−9.68466	−	8.40832i	−0.662030	−	0.574781i
$215$	−20.6256			−1.40666
$216$		0			0
$217$			1.62603i			0.110382i
$218$	−1.24887	+	1.43845i	−0.0845844	+	0.0974239i
$219$		0			0
$220$	11.5727	−	6.48632i	0.780232	−	0.437308i
$221$		−	14.2462i		−	0.958304i
$222$		0			0
$223$			26.4738i			1.77282i	0.462902	+	0.886409i	$0.346808\pi$
$223$			26.4738i			1.77282i	−0.462902	+	0.886409i	$0.653192\pi$
$224$	−2.22397	+	4.80776i	−0.148595	+	0.321232i
$225$		0			0
$226$	14.6875	−	16.9170i	0.977000	−	1.12530i
$227$			26.9764i			1.79048i	0.445581	+	0.895242i	$0.352997\pi$
$227$			26.9764i			1.79048i	−0.445581	+	0.895242i	$0.647003\pi$
$228$		0			0
$229$		−	25.4987i		−	1.68500i	−0.538693	−	0.842502i	$-0.681082\pi$
$229$		−	25.4987i		−	1.68500i	0.538693	−	0.842502i	$-0.318918\pi$
$230$	9.49980	−	10.9418i	0.626398	−	0.721482i
$231$		0			0
$232$	−15.6847	−	10.1447i	−1.02975	−	0.666035i
$233$		−	2.28343i		−	0.149592i	−0.997199	−	0.0747961i	$-0.976169\pi$
$233$		−	2.28343i		−	0.149592i	0.997199	−	0.0747961i	$-0.0238306\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	2.71151	+	19.1231i	0.176504	+	1.24481i
$237$		0			0
$238$	3.33513	+	2.89560i	0.216184	+	0.187694i
$239$	20.6256			1.33416			0.667081	−	0.744986i	$-0.267544\pi$
$239$	20.6256			1.33416			0.667081	+	0.744986i	$0.267544\pi$
$240$		0			0
$241$		−	28.0429i		−	1.80640i	−0.429221	−	0.903199i	$-0.641212\pi$
$241$		−	28.0429i		−	1.80640i	0.429221	−	0.903199i	$-0.358788\pi$
$242$	0.389414	+	15.5515i	0.0250325	+	0.999687i
$243$		0			0
$244$	2.54635	+	17.9583i	0.163014	+	1.14966i
$245$		−	12.2462i		−	0.782382i
$246$		0			0
$247$		−	12.3687i		−	0.787002i
$248$	2.66732	−	4.12391i	0.169375	−	0.261869i
$249$		0			0
$250$	−12.8147	−	11.1258i	−0.810471	−	0.703659i
$251$	3.47284			0.219204			0.109602	−	0.993976i	$-0.465042\pi$
$251$	3.47284			0.219204			0.109602	+	0.993976i	$0.465042\pi$
$252$		0			0
$253$	6.14441	+	15.8415i	0.386296	+	0.995949i
$254$	−14.9733	+	17.2462i	−0.939511	+	1.08212i
$255$		0			0
$256$	13.5270	−	8.54521i	0.845437	−	0.534076i
$257$	−8.89586			−0.554909			−0.277454	−	0.960739i	$-0.589491\pi$
$257$	−8.89586			−0.554909			−0.277454	+	0.960739i	$0.589491\pi$
$258$		0			0
$259$			5.79119i			0.359847i
$260$	−16.9170	+	2.39871i	−1.04915	+	0.148761i
$261$		0			0
$262$	13.6847	+	11.8812i	0.845441	+	0.734020i
$263$	32.2080			1.98603			0.993016	−	0.117984i	$-0.0376430\pi$
$263$	32.2080			1.98603			0.993016	+	0.117984i	$0.0376430\pi$
$264$		0			0
$265$	−16.4924			−1.01312
$266$	2.89560	+	2.51398i	0.177540	+	0.154142i
$267$		0			0
$268$	2.87689	+	20.2895i	0.175734	+	1.23938i
$269$			0.246211i			0.0150118i	0.999972	+	0.00750588i	$0.00238922\pi$
$269$			0.246211i			0.0150118i	−0.999972	+	0.00750588i	$0.997611\pi$
$270$		0			0
$271$	5.73384			0.348306			0.174153	−	0.984719i	$-0.444281\pi$
$271$	5.73384			0.348306			0.174153	+	0.984719i	$0.444281\pi$
$272$	−3.70861	−	12.8147i	−0.224868	−	0.777004i
$273$		0			0
$274$	−14.6875	+	16.9170i	−0.887306	+	1.02199i
$275$	3.09218	−	1.19935i	0.186465	−	0.0723237i
$276$		0			0
$277$	−2.39871			−0.144124			−0.0720621	−	0.997400i	$-0.522958\pi$
$277$	−2.39871			−0.144124			−0.0720621	+	0.997400i	$0.522958\pi$
$278$	−11.0129	−	9.56155i	−0.660513	−	0.573464i
$279$		0			0
$280$	2.87689	−	4.44793i	0.171927	−	0.265815i
$281$			24.1671i			1.44169i	0.693098	+	0.720843i	$0.256245\pi$
$281$			24.1671i			1.44169i	−0.693098	+	0.720843i	$0.743755\pi$
$282$		0			0
$283$		−	17.7300i		−	1.05394i	−0.849884	−	0.526971i	$-0.823328\pi$
$283$		−	17.7300i		−	1.05394i	0.849884	−	0.526971i	$-0.176672\pi$
$284$	8.40832	−	1.19224i	0.498942	−	0.0707462i
$285$		0			0
$286$	6.77530	−	18.8550i	0.400632	−	1.11492i
$287$		−	1.36932i		−	0.0808282i
$288$		0			0
$289$	5.87689			0.345700
$290$	14.1051	+	12.2462i	0.828281	+	0.719122i
$291$		0			0
$292$	−26.1552	+	3.70861i	−1.53062	+	0.217030i
$293$	−27.2298			−1.59078			−0.795392	−	0.606095i	$-0.792735\pi$
$293$	−27.2298			−1.59078			−0.795392	+	0.606095i	$0.792735\pi$
$294$		0			0
$295$		−	19.3144i		−	1.12453i
$296$	9.49980	−	14.6875i	0.552165	−	0.853695i
$297$		0			0
$298$	−0.753789	+	0.868210i	−0.0436658	+	0.0502941i
$299$		−	21.8836i		−	1.26556i
$300$		0			0
$301$		−	9.65719i		−	0.556631i
$302$	−19.4213	+	22.3693i	−1.11757	+	1.28721i
$303$		0			0
$304$	−3.21985	−	11.1258i	−0.184671	−	0.638110i
$305$		−	18.1379i		−	1.03858i
$306$		0			0
$307$			4.52162i			0.258063i	0.991641	+	0.129031i	$0.0411868\pi$
$307$			4.52162i			0.258063i	−0.991641	+	0.129031i	$0.958813\pi$
$308$	3.03698	+	5.41850i	0.173048	+	0.308747i
$309$		0			0
$310$	−3.21985	+	3.70861i	−0.182875	+	0.210635i
$311$		−	13.1231i		−	0.744143i	−0.928204	−	0.372072i	$-0.878648\pi$
$311$		−	13.1231i		−	0.744143i	0.928204	−	0.372072i	$-0.121352\pi$
$312$		0			0
$313$	−5.12311			−0.289575			−0.144788	−	0.989463i	$-0.546250\pi$
$313$	−5.12311			−0.289575			−0.144788	+	0.989463i	$0.546250\pi$
$314$	−16.9170	−	14.6875i	−0.954683	−	0.828865i
$315$		0			0
$316$	−1.08407	−	7.64550i	−0.0609839	−	0.430093i
$317$		−	22.4924i		−	1.26330i	−0.775254	−	0.631650i	$-0.782378\pi$
$317$		−	22.4924i		−	1.26330i	0.775254	−	0.631650i	$-0.217622\pi$
$318$		0			0
$319$	−20.4214	+	7.92077i	−1.14338	+	0.443478i
$320$	−14.5927	+	6.56155i	−0.815755	+	0.366802i
$321$		0			0
$322$	5.12311	+	4.44793i	0.285500	+	0.247874i
$323$	−9.65719			−0.537341
$324$		0			0
$325$	−4.27156			−0.236943
$326$	−11.5824	+	13.3405i	−0.641489	+	0.738864i
$327$		0			0
$328$	−2.24621	+	3.47284i	−0.124026	+	0.191756i
$329$		−	5.61856i		−	0.309761i
$330$		0			0
$331$	1.75379			0.0963969			0.0481985	−	0.998838i	$-0.484652\pi$
$331$	1.75379			0.0963969			0.0481985	+	0.998838i	$0.484652\pi$
$332$	4.74990	−	0.673500i	0.260685	−	0.0369631i
$333$		0			0
$334$	−5.36932	+	6.18435i	−0.293796	+	0.338393i
$335$		−	20.4924i		−	1.11962i
$336$		0			0
$337$			24.7908i			1.35044i	0.737616	+	0.675220i	$0.235951\pi$
$337$			24.7908i			1.35044i	−0.737616	+	0.675220i	$0.764049\pi$
$338$	−4.86404	+	5.60237i	−0.264569	+	0.304729i
$339$		0			0
$340$	1.87285	+	13.2084i	0.101570	+	0.716327i
$341$	−2.08258	−	5.36932i	−0.112778	−	0.290765i
$342$		0			0
$343$	12.2888			0.663534
$344$	−15.8415	+	24.4924i	−0.854119	+	1.32054i
$345$		0			0
$346$	0.753789	−	0.868210i	0.0405239	−	0.0466753i
$347$		−	20.5366i		−	1.10246i	−0.834352	−	0.551232i	$-0.814158\pi$
$347$		−	20.5366i		−	1.10246i	0.834352	−	0.551232i	$-0.185842\pi$
$348$		0			0
$349$	−31.7738			−1.70081			−0.850405	−	0.526128i	$-0.823643\pi$
$349$	−31.7738			−1.70081			−0.850405	+	0.526128i	$0.823643\pi$
$350$	0.868210	−	1.00000i	0.0464078	−	0.0534522i
$351$		0			0
$352$	1.18609	−	18.7241i	0.0632190	−	0.998000i
$353$	−12.3687			−0.658320			−0.329160	−	0.944274i	$-0.606765\pi$
$353$	−12.3687			−0.658320			−0.329160	+	0.944274i	$0.606765\pi$
$354$		0			0
$355$	−8.49242			−0.450731
$356$	0.975092	+	6.87689i	0.0516798	+	0.364475i
$357$		0			0
$358$		0			0
$359$	9.04325			0.477284			0.238642	−	0.971108i	$-0.423298\pi$
$359$	9.04325			0.477284			0.238642	+	0.971108i	$0.423298\pi$
$360$		0			0
$361$	10.6155			0.558712
$362$	9.49980	+	8.24782i	0.499298	+	0.433496i
$363$		0			0
$364$	−1.12311	−	7.92077i	−0.0588667	−	0.415161i
$365$	26.4168			1.38272
$366$		0			0
$367$		−	29.9467i		−	1.56320i	−0.623778	−	0.781602i	$-0.714403\pi$
$367$		−	29.9467i		−	1.56320i	0.623778	−	0.781602i	$-0.285597\pi$
$368$	−5.69681	−	19.6847i	−0.296967	−	1.02613i
$369$		0			0
$370$	−11.4677	+	13.2084i	−0.596176	+	0.686673i
$371$		−	7.72197i		−	0.400905i
$372$		0			0
$373$	11.9935			0.621001			0.310501	−	0.950573i	$-0.399503\pi$
$373$	11.9935			0.621001			0.310501	+	0.950573i	$0.399503\pi$
$374$	−14.7216	−	5.28999i	−0.761234	−	0.273539i
$375$		0			0
$376$	−9.21662	+	14.2497i	−0.475311	+	0.734872i
$377$	28.2102			1.45290
$378$		0			0
$379$	−14.2462			−0.731779			−0.365889	−	0.930658i	$-0.619235\pi$
$379$	−14.2462			−0.731779			−0.365889	+	0.930658i	$0.619235\pi$
$380$	1.62603	+	11.4677i	0.0834136	+	0.588279i
$381$		0			0
$382$	13.0776	+	11.3541i	0.669108	+	0.580927i
$383$		−	0.630683i		−	0.0322264i	−0.999870	−	0.0161132i	$-0.994871\pi$
$383$		−	0.630683i		−	0.0322264i	0.999870	−	0.0161132i	$-0.00512921\pi$
$384$		0			0
$385$	−2.24621	−	5.79119i	−0.114478	−	0.295146i
$386$	−1.73642	−	1.50758i	−0.0883815	−	0.0767337i
$387$		0			0
$388$	−3.19224	−	22.5134i	−0.162061	−	1.14295i
$389$		−	30.4924i		−	1.54603i	−0.634389	−	0.773014i	$-0.718748\pi$
$389$		−	30.4924i		−	1.54603i	0.634389	−	0.773014i	$-0.281252\pi$
$390$		0			0
$391$	−17.0862			−0.864088
$392$	−14.5421	−	9.40572i	−0.734485	−	0.475061i
$393$		0			0
$394$	−11.4924	+	13.2369i	−0.578980	+	0.666866i
$395$			7.72197i			0.388534i
$396$		0			0
$397$			18.5531i			0.931151i	0.885008	+	0.465576i	$0.154153\pi$
$397$			18.5531i			0.931151i	−0.885008	+	0.465576i	$0.845847\pi$
$398$	−15.0627	−	13.0776i	−0.755026	−	0.655521i
$399$		0			0
$400$	−3.84233	+	1.11198i	−0.192116	+	0.0555991i
$401$	−24.7374			−1.23533			−0.617664	−	0.786442i	$-0.711921\pi$
$401$	−24.7374			−1.23533			−0.617664	+	0.786442i	$0.711921\pi$
$402$		0			0
$403$			7.41722i			0.369478i
$404$	−1.85431	−	13.0776i	−0.0922551	−	0.650635i
$405$		0			0
$406$	−5.73384	+	6.60421i	−0.284566	+	0.327761i
$407$	−7.41722	−	19.1231i	−0.367658	−	0.947897i
$408$		0			0
$409$			26.4168i			1.30623i	0.757260	+	0.653114i	$0.226538\pi$
$409$			26.4168i			1.30623i	−0.757260	+	0.653114i	$0.773462\pi$
$410$	2.71151	−	3.12311i	0.133912	−	0.154239i
$411$		0			0
$412$	−3.43845	+	0.487546i	−0.169400	+	0.0240197i
$413$	9.04325			0.444989
$414$		0			0
$415$	−4.79741			−0.235496
$416$	−10.1447	+	21.9309i	−0.497387	+	1.07525i
$417$		0			0
$418$	−12.7814	−	4.59283i	−0.625159	−	0.224642i
$419$	3.47284			0.169659			0.0848297	−	0.996395i	$-0.472965\pi$
$419$	3.47284			0.169659			0.0848297	+	0.996395i	$0.472965\pi$
$420$		0			0
$421$			15.8415i			0.772070i	0.922484	+	0.386035i	$0.126156\pi$
$421$			15.8415i			0.772070i	−0.922484	+	0.386035i	$0.873844\pi$
$422$	−3.09218	−	2.68466i	−0.150525	−	0.130687i
$423$		0			0
$424$	−12.6670	+	19.5843i	−0.615165	+	0.951100i
$425$			3.33513i			0.161778i
$426$		0			0
$427$	8.49242			0.410977
$428$	17.9583	−	2.54635i	0.868048	−	0.123083i
$429$		0			0
$430$	19.1231	−	22.0259i	0.922198	−	1.06218i
$431$	11.5824			0.557904			0.278952	−	0.960305i	$-0.410013\pi$
$431$	11.5824			0.557904			0.278952	+	0.960305i	$0.410013\pi$
$432$		0			0
$433$	−6.87689			−0.330482			−0.165241	−	0.986253i	$-0.552840\pi$
$433$	−6.87689			−0.330482			−0.165241	+	0.986253i	$0.552840\pi$
$434$	−1.73642	−	1.50758i	−0.0833508	−	0.0723660i
$435$		0			0
$436$	−0.378206	−	2.66732i	−0.0181128	−	0.127741i
$437$	−14.8344			−0.709628
$438$		0			0
$439$	−30.3115			−1.44669			−0.723344	−	0.690488i	$-0.757396\pi$
$439$	−30.3115			−1.44669			−0.723344	+	0.690488i	$0.757396\pi$
$440$	−3.80299	+	18.3722i	−0.181301	+	0.875860i
$441$		0			0
$442$	15.2134	+	13.2084i	0.723627	+	0.628260i
$443$	−6.18435			−0.293827			−0.146914	−	0.989149i	$-0.546934\pi$
$443$	−6.18435			−0.293827			−0.146914	+	0.989149i	$0.546934\pi$
$444$		0			0
$445$		−	6.94568i		−	0.329257i
$446$	−28.2711	−	24.5453i	−1.33868	−	1.16225i
$447$		0			0
$448$	−3.07221	−	6.83248i	−0.145148	−	0.322804i
$449$	−28.2102			−1.33132			−0.665662	−	0.746253i	$-0.731851\pi$
$449$	−28.2102			−1.33132			−0.665662	+	0.746253i	$0.731851\pi$
$450$		0			0
$451$	1.75379	+	4.52162i	0.0825827	+	0.212915i
$452$	4.44793	+	31.3693i	0.209213	+	1.47549i
$453$		0			0
$454$	−28.8078	−	25.0112i	−1.35202	−	1.17383i
$455$			8.00000i			0.375046i
$456$		0			0
$457$			11.5824i			0.541801i	0.962607	+	0.270900i	$0.0873214\pi$
$457$			11.5824i			0.541801i	−0.962607	+	0.270900i	$0.912679\pi$
$458$	27.2298	+	23.6412i	1.27237	+	1.10468i
$459$		0			0
$460$	2.87689	+	20.2895i	0.134136	+	0.946002i
$461$	31.3950			1.46221			0.731105	−	0.682265i	$-0.239005\pi$
$461$	31.3950			1.46221			0.731105	+	0.682265i	$0.239005\pi$
$462$		0			0
$463$		−	7.15944i		−	0.332728i	−0.986064	−	0.166364i	$-0.946797\pi$
$463$		−	7.15944i		−	0.332728i	0.986064	−	0.166364i	$-0.0532026\pi$
$464$	25.3755	−	7.34376i	1.17803	−	0.340926i
$465$		0			0
$466$	2.43845	+	2.11708i	0.112959	+	0.0980720i
$467$	6.18435			0.286178			0.143089	−	0.989710i	$-0.454297\pi$
$467$	6.18435			0.286178			0.143089	+	0.989710i	$0.454297\pi$
$468$		0			0
$469$	9.59482			0.443048
$470$	11.1258	−	12.8147i	0.513196	−	0.591097i
$471$		0			0
$472$	−22.9354	−	14.8344i	−1.05569	−	0.682810i
$473$	12.3687	+	31.8890i	0.568714	+	1.46626i
$474$		0			0
$475$			2.89560i			0.132859i
$476$	−6.18435	+	0.876894i	−0.283459	+	0.0401924i
$477$		0			0
$478$	−19.1231	+	22.0259i	−0.874670	+	1.00744i
$479$	−14.8344			−0.677803			−0.338901	−	0.940822i	$-0.610055\pi$
$479$	−14.8344			−0.677803			−0.338901	+	0.940822i	$0.610055\pi$
$480$		0			0
$481$			26.4168i			1.20450i
$482$	29.9467	+	26.0000i	1.36403	+	1.18427i
$483$		0			0
$484$	−16.9683	−	14.0027i	−0.771287	−	0.636488i
$485$			22.7386i			1.03251i
$486$		0			0
$487$			21.0508i			0.953903i	0.878930	+	0.476952i	$0.158258\pi$
$487$			21.0508i			0.953903i	−0.878930	+	0.476952i	$0.841742\pi$
$488$	−21.5384	−	13.9309i	−0.974995	−	0.630621i
$489$		0			0
$490$	13.0776	+	11.3541i	0.590786	+	0.512926i
$491$			29.9009i			1.34941i	0.738088	+	0.674705i	$0.235729\pi$
$491$			29.9009i			1.34941i	−0.738088	+	0.674705i	$0.764271\pi$
$492$		0			0
$493$		−	22.0259i		−	0.991996i
$494$	13.2084	+	11.4677i	0.594274	+	0.515955i
$495$		0			0
$496$	1.93087	+	6.67190i	0.0866986	+	0.299577i
$497$		−	3.97626i		−	0.178360i
$498$		0			0
$499$	34.7386			1.55511			0.777557	−	0.628812i	$-0.216458\pi$
$499$	34.7386			1.55511			0.777557	+	0.628812i	$0.216458\pi$
$500$	23.7623	−	3.36932i	1.06268	−	0.150680i
$501$		0			0
$502$	−3.21985	+	3.70861i	−0.143709	+	0.165523i
$503$	−11.5824			−0.516433			−0.258216	−	0.966087i	$-0.583135\pi$
$503$	−11.5824			−0.516433			−0.258216	+	0.966087i	$0.583135\pi$
$504$		0			0
$505$			13.2084i			0.587767i
$506$	−22.6138	−	8.12598i	−1.00531	−	0.361244i
$507$		0			0
$508$	−4.53448	−	31.9797i	−0.201185	−	1.41887i
$509$			10.0000i			0.443242i	0.975133	+	0.221621i	$0.0711348\pi$
$509$			10.0000i			0.443242i	−0.975133	+	0.221621i	$0.928865\pi$
$510$		0			0
$511$			12.3687i			0.547159i
$512$	−3.41624	+	22.3680i	−0.150978	+	0.988537i
$513$		0			0
$514$	8.24782	−	9.49980i	0.363796	−	0.419018i
$515$	3.47284			0.153032
$516$		0			0
$517$	7.19612	+	18.5531i	0.316485	+	0.815962i
$518$	−6.18435	−	5.36932i	−0.271725	−	0.235914i
$519$		0			0
$520$	13.1231	−	20.2895i	0.575486	−	0.889752i
$521$	24.7374			1.08377			0.541883	−	0.840454i	$-0.317712\pi$
$521$	24.7374			1.08377			0.541883	+	0.840454i	$0.317712\pi$
$522$		0			0
$523$		−	25.1473i		−	1.09961i	−0.835292	−	0.549806i	$-0.814702\pi$
$523$		−	25.1473i		−	1.09961i	0.835292	−	0.549806i	$-0.185298\pi$
$524$	−25.3755	+	3.59806i	−1.10854	+	0.157182i
$525$		0			0
$526$	−29.8617	+	34.3946i	−1.30203	+	1.49968i
$527$	5.79119			0.252268
$528$		0			0
$529$	−3.24621			−0.141140
$530$	15.2910	−	17.6121i	0.664198	−	0.765020i
$531$		0			0
$532$	−5.36932	+	0.761329i	−0.232789	+	0.0330078i
$533$		−	6.24621i		−	0.270553i
$534$		0			0
$535$	−18.1379			−0.784172
$536$	−24.3342	−	15.7392i	−1.05108	−	0.679831i
$537$		0			0
$538$	−0.262926	−	0.228275i	−0.0113356	−	0.00984165i
$539$	−18.9337	+	7.34376i	−0.815533	+	0.316318i
$540$		0			0
$541$	14.6875			0.631466			0.315733	−	0.948848i	$-0.397750\pi$
$541$	14.6875			0.631466			0.315733	+	0.948848i	$0.397750\pi$
$542$	−5.31614	+	6.12311i	−0.228348	+	0.263010i
$543$		0			0
$544$	17.1231	+	7.92077i	0.734147	+	0.339600i
$545$			2.69400i			0.115398i
$546$		0			0
$547$		−	23.5212i		−	1.00570i	−0.864375	−	0.502848i	$-0.832286\pi$
$547$		−	23.5212i		−	1.00570i	0.864375	−	0.502848i	$-0.167714\pi$
$548$	−4.44793	−	31.3693i	−0.190006	−	1.34003i
$549$		0			0
$550$	−1.58614	+	4.41409i	−0.0676333	+	0.188217i
$551$		−	19.1231i		−	0.814672i
$552$		0			0
$553$	−3.61553			−0.153748
$554$	2.22397	−	2.56155i	0.0944873	−	0.108830i
$555$		0			0
$556$	20.4214	−	2.89560i	0.866059	−	0.122801i
$557$	−42.0643			−1.78232			−0.891160	−	0.453689i	$-0.850108\pi$
$557$	−42.0643			−1.78232			−0.891160	+	0.453689i	$0.850108\pi$
$558$		0			0
$559$		−	44.0518i		−	1.86319i
$560$	2.08258	+	7.19612i	0.0880051	+	0.304091i
$561$		0			0
$562$	−25.8078	−	22.4066i	−1.08863	−	0.945164i
$563$		−	0.295294i		−	0.0124452i	−0.999981	−	0.00622258i	$-0.998019\pi$
$563$		−	0.295294i		−	0.0124452i	0.999981	−	0.00622258i	$-0.00198072\pi$
$564$		0			0
$565$		−	31.6831i		−	1.33292i
$566$	18.9337	+	16.4384i	0.795844	+	0.690959i
$567$		0			0
$568$	−6.52262	+	10.0845i	−0.273683	+	0.423138i
$569$		−	34.5830i		−	1.44980i	−0.688856	−	0.724898i	$-0.741887\pi$
$569$		−	34.5830i		−	1.44980i	0.688856	−	0.724898i	$-0.258113\pi$
$570$		0			0
$571$		−	16.1040i		−	0.673932i	−0.941517	−	0.336966i	$-0.890599\pi$
$571$		−	16.1040i		−	0.673932i	0.941517	−	0.336966i	$-0.109401\pi$
$572$	13.8533	+	24.7168i	0.579238	+	1.03346i
$573$		0			0
$574$	1.46228	+	1.26957i	0.0610344	+	0.0529906i
$575$			5.12311i			0.213648i
$576$		0			0
$577$	8.24621			0.343294			0.171647	−	0.985158i	$-0.445091\pi$
$577$	8.24621			0.343294			0.171647	+	0.985158i	$0.445091\pi$
$578$	−5.44878	+	6.27587i	−0.226639	+	0.261042i
$579$		0			0
$580$	−26.1552	+	3.70861i	−1.08604	+	0.153992i
$581$		−	2.24621i		−	0.0931885i
$582$		0			0
$583$	9.89012	+	25.4987i	0.409607	+	1.05605i
$584$	20.2895	−	31.3693i	0.839585	−	1.29807i
$585$		0			0
$586$	25.2462	−	29.0785i	1.04291	−	1.20122i
$587$	41.3403			1.70630			0.853148	−	0.521669i	$-0.174690\pi$
$587$	41.3403			1.70630			0.853148	+	0.521669i	$0.174690\pi$
$588$		0			0
$589$	5.02797			0.207174
$590$	20.6256	+	17.9074i	0.849144	+	0.737235i
$591$		0			0
$592$	6.87689	+	23.7623i	0.282639	+	0.976625i
$593$		−	17.4968i		−	0.718508i	−0.933240	−	0.359254i	$-0.883031\pi$
$593$		−	17.4968i		−	0.718508i	0.933240	−	0.359254i	$-0.116969\pi$
$594$		0			0
$595$	6.24621			0.256070
$596$	−0.228275	−	1.60993i	−0.00935052	−	0.0659452i
$597$		0			0
$598$	23.3693	+	20.2895i	0.955642	+	0.829698i
$599$			8.63068i			0.352640i	0.984333	+	0.176320i	$0.0564194\pi$
$599$			8.63068i			0.352640i	−0.984333	+	0.176320i	$0.943581\pi$
$600$		0			0
$601$		−	24.7908i		−	1.01124i	−0.862757	−	0.505619i	$-0.831264\pi$
$601$		−	24.7908i		−	1.01124i	0.862757	−	0.505619i	$-0.168736\pi$
$602$	10.3128	+	8.95369i	0.420319	+	0.364925i
$603$		0			0
$604$	−5.88148	−	41.4795i	−0.239314	−	1.68778i
$605$	14.8344	+	16.2462i	0.603106	+	0.660502i
$606$		0			0
$607$	−43.8826			−1.78114			−0.890569	−	0.454848i	$-0.849694\pi$
$607$	−43.8826			−1.78114			−0.890569	+	0.454848i	$0.849694\pi$
$608$	14.8665	+	6.87689i	0.602914	+	0.278895i
$609$		0			0
$610$	19.3693	+	16.8166i	0.784241	+	0.680886i
$611$		−	25.6294i		−	1.03685i
$612$		0			0
$613$	25.1035			1.01392			0.506960	−	0.861969i	$-0.330769\pi$
$613$	25.1035			1.01392			0.506960	+	0.861969i	$0.330769\pi$
$614$	−4.82860	−	4.19224i	−0.194866	−	0.169185i
$615$		0			0
$616$	−8.60210	−	1.78061i	−0.346588	−	0.0717429i
$617$	40.5790			1.63365			0.816824	−	0.576888i	$-0.195733\pi$
$617$	40.5790			1.63365			0.816824	+	0.576888i	$0.195733\pi$
$618$		0			0
$619$	−8.49242			−0.341339			−0.170670	−	0.985328i	$-0.554593\pi$
$619$	−8.49242			−0.341339			−0.170670	+	0.985328i	$0.554593\pi$
$620$	−0.975092	−	6.87689i	−0.0391606	−	0.276183i
$621$		0			0
$622$	14.0140	+	12.1671i	0.561911	+	0.487857i
$623$	3.25206			0.130291
$624$		0			0
$625$	−19.0000			−0.760000
$626$	4.74990	−	5.47091i	0.189844	−	0.218662i
$627$		0			0
$628$	31.3693	−	4.44793i	1.25177	−	0.177492i
$629$	20.6256			0.822398
$630$		0			0
$631$		−	26.4738i		−	1.05391i	−0.849894	−	0.526953i	$-0.823334\pi$
$631$		−	26.4738i		−	1.05391i	0.849894	−	0.526953i	$-0.176666\pi$
$632$	9.16965	+	5.93087i	0.364749	+	0.235917i
$633$		0			0
$634$	24.0194	+	20.8539i	0.953933	+	0.828214i
$635$			32.2996i			1.28177i
$636$		0			0
$637$	26.1552			1.03631
$638$	10.4752	−	29.1515i	0.414718	−	1.15412i
$639$		0			0
$640$	6.52262	−	21.6669i	0.257829	−	0.856460i
$641$	−5.42302			−0.214197			−0.107098	−	0.994248i	$-0.534156\pi$
$641$	−5.42302			−0.214197			−0.107098	+	0.994248i	$0.534156\pi$
$642$		0			0
$643$	36.9848			1.45854			0.729270	−	0.684226i	$-0.239860\pi$
$643$	36.9848			1.45854			0.729270	+	0.684226i	$0.239860\pi$
$644$	−9.49980	+	1.34700i	−0.374345	+	0.0530792i
$645$		0			0
$646$	8.95369	−	10.3128i	0.352278	−	0.405752i
$647$			45.1231i			1.77397i	0.461796	+	0.886986i	$0.347205\pi$
$647$			45.1231i			1.77397i	−0.461796	+	0.886986i	$0.652795\pi$
$648$		0			0
$649$	−29.8617	+	11.5824i	−1.17218	+	0.454648i
$650$	3.96039	−	4.56155i	0.155339	−	0.178919i
$651$		0			0
$652$	−3.50758	−	24.7374i	−0.137367	−	0.968792i
$653$			22.9848i			0.899466i	0.893163	+	0.449733i	$0.148481\pi$
$653$			22.9848i			0.899466i	−0.893163	+	0.449733i	$0.851519\pi$
$654$		0			0
$655$	25.6294			1.00142
$656$	−1.62603	−	5.61856i	−0.0634858	−	0.219368i
$657$		0			0
$658$	6.00000	+	5.20926i	0.233904	+	0.203078i
$659$			0.525853i			0.0204843i	0.999948	+	0.0102422i	$0.00326024\pi$
$659$			0.525853i			0.0204843i	−0.999948	+	0.0102422i	$0.996740\pi$
$660$		0			0
$661$			40.5790i			1.57834i	0.614176	+	0.789169i	$0.289489\pi$
$661$			40.5790i			1.57834i	−0.614176	+	0.789169i	$0.710511\pi$
$662$	−1.62603	+	1.87285i	−0.0631974	+	0.0727905i
$663$		0			0
$664$	−3.68466	+	5.69681i	−0.142992	+	0.221079i
$665$	5.42302			0.210296
$666$		0			0
$667$		−	33.8340i		−	1.31006i
$668$	−1.62603	−	11.4677i	−0.0629130	−	0.443698i
$669$		0			0
$670$	21.8836	+	18.9996i	0.845439	+	0.734019i
$671$	−28.0429	+	10.8769i	−1.08258	+	0.419898i
$672$		0			0
$673$			14.8344i			0.571826i	0.958256	+	0.285913i	$0.0922968\pi$
$673$			14.8344i			0.571826i	−0.958256	+	0.285913i	$0.907703\pi$
$674$	−26.4738	−	22.9848i	−1.01973	−	0.885343i
$675$		0			0
$676$	−1.47301	−	10.3885i	−0.0566543	−	0.399558i
$677$	15.6475			0.601381			0.300690	−	0.953722i	$-0.402783\pi$
$677$	15.6475			0.601381			0.300690	+	0.953722i	$0.402783\pi$
$678$		0			0
$679$	−10.6465			−0.408576
$680$	−15.8415	−	10.2462i	−0.607496	−	0.392924i
$681$		0			0
$682$	7.66471	+	2.75421i	0.293497	+	0.105464i
$683$	−10.4185			−0.398654			−0.199327	−	0.979933i	$-0.563876\pi$
$683$	−10.4185			−0.398654			−0.199327	+	0.979933i	$0.563876\pi$
$684$		0			0
$685$			31.6831i			1.21055i
$686$	−11.3936	+	13.1231i	−0.435010	+	0.501043i
$687$		0			0
$688$	−11.4677	−	39.6252i	−0.437201	−	1.51070i
$689$		−	35.2242i		−	1.34193i
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	0.228275	+	1.60993i	0.00867773	+	0.0612002i
$693$		0			0
$694$	21.9309	+	19.0406i	0.832484	+	0.722771i
$695$	−20.6256			−0.782375
$696$		0			0
$697$	−4.87689			−0.184726
$698$	29.4591	−	33.9309i	1.11504	−	1.28430i
$699$		0			0
$700$	0.262926	+	1.85431i	0.00993769	+	0.0700861i
$701$	−27.2298			−1.02846			−0.514228	−	0.857653i	$-0.671922\pi$
$701$	−27.2298			−1.02846			−0.514228	+	0.857653i	$0.671922\pi$
$702$		0			0
$703$	17.9074			0.675390
$704$	18.8956	+	18.6267i	0.712155	+	0.702022i
$705$		0			0
$706$	11.4677	−	13.2084i	0.431592	−	0.497105i
$707$	−6.18435			−0.232586
$708$		0			0
$709$			18.5531i			0.696775i	0.937351	+	0.348387i	$0.113271\pi$
$709$			18.5531i			0.696775i	−0.937351	+	0.348387i	$0.886729\pi$
$710$	7.87377	−	9.06897i	0.295497	−	0.340352i
$711$		0			0
$712$	−8.24782	−	5.33464i	−0.309100	−	0.199924i
$713$	8.89586			0.333153
$714$		0			0
$715$	−10.2462	−	26.4168i	−0.383187	−	0.987933i
$716$		0			0
$717$		0			0
$718$	−8.38447	+	9.65719i	−0.312906	+	0.360403i
$719$			14.9848i			0.558840i	0.960169	+	0.279420i	$0.0901422\pi$
$719$			14.9848i			0.558840i	−0.960169	+	0.279420i	$0.909858\pi$
$720$		0			0
$721$			1.62603i			0.0605565i
$722$	−9.84221	+	11.3362i	−0.366289	+	0.421890i
$723$		0			0
$724$	−17.6155	+	2.49775i	−0.654676	+	0.0928281i
$725$	−6.60421			−0.245274
$726$		0			0
$727$			14.1051i			0.523130i	0.965186	+	0.261565i	$0.0842386\pi$
$727$			14.1051i			0.523130i	−0.965186	+	0.261565i	$0.915761\pi$
$728$	9.49980	+	6.14441i	0.352086	+	0.227727i
$729$		0			0
$730$	−24.4924	+	28.2102i	−0.906505	+	1.04411i
$731$	−34.3946			−1.27213
$732$		0			0
$733$	37.6229			1.38963			0.694816	−	0.719187i	$-0.255486\pi$
$733$	37.6229			1.38963			0.694816	+	0.719187i	$0.255486\pi$
$734$	31.9797	+	27.7651i	1.18039	+	1.02483i
$735$		0			0
$736$	26.3029	+	12.1671i	0.969536	+	0.448486i
$737$	−31.6831	+	12.2888i	−1.16706	+	0.452665i
$738$		0			0
$739$		−	14.4780i		−	0.532581i	−0.963893	−	0.266290i	$-0.914202\pi$
$739$		−	14.4780i		−	0.532581i	0.963893	−	0.266290i	$-0.0857980\pi$
$740$	−3.47284	−	24.4924i	−0.127664	−	0.900359i
$741$		0			0
$742$	8.24621	+	7.15944i	0.302728	+	0.262831i
$743$	−41.2513			−1.51336			−0.756681	−	0.653784i	$-0.773180\pi$
$743$	−41.2513			−1.51336			−0.756681	+	0.653784i	$0.773180\pi$
$744$		0			0
$745$			1.62603i			0.0595731i
$746$	−11.1198	+	12.8078i	−0.407126	+	0.468926i
$747$		0			0
$748$	19.2983	−	10.8164i	0.705614	−	0.395486i
$749$		−	8.49242i		−	0.310306i
$750$		0			0
$751$			24.5236i			0.894881i	0.894314	+	0.447440i	$0.147664\pi$
$751$			24.5236i			0.894881i	−0.894314	+	0.447440i	$0.852336\pi$
$752$	−6.67190	−	23.0540i	−0.243299	−	0.840692i
$753$		0			0
$754$	−26.1552	+	30.1254i	−0.952516	+	1.09710i
$755$			41.8944i			1.52469i
$756$		0			0
$757$		−	22.7872i		−	0.828216i	−0.910228	−	0.414108i	$-0.864094\pi$
$757$		−	22.7872i		−	0.828216i	0.910228	−	0.414108i	$-0.135906\pi$
$758$	13.2084	−	15.2134i	0.479751	−	0.552575i
$759$		0			0
$760$	−13.7538	−	8.89586i	−0.498902	−	0.322687i
$761$			29.1950i			1.05832i	0.848522	+	0.529160i	$0.177493\pi$
$761$			29.1950i			1.05832i	−0.848522	+	0.529160i	$0.822507\pi$
$762$		0			0
$763$	−1.26137			−0.0456645
$764$	−24.2499	+	3.43845i	−0.877329	+	0.124399i
$765$		0			0
$766$	0.673500	+	0.584739i	0.0243345	+	0.0211275i
$767$	41.2513			1.48950
$768$		0			0
$769$			39.6252i			1.42892i	0.699675	+	0.714461i	$0.253328\pi$
$769$			39.6252i			1.42892i	−0.699675	+	0.714461i	$0.746672\pi$
$770$	8.26693	+	2.97061i	0.297920	+	0.107053i
$771$		0			0
$772$	3.21985	−	0.456551i	0.115885	−	0.0164316i
$773$			49.2311i			1.77072i	0.464908	+	0.885359i	$0.346087\pi$
$773$			49.2311i			1.77072i	−0.464908	+	0.885359i	$0.653913\pi$
$774$		0			0
$775$		−	1.73642i		−	0.0623741i
$776$	27.0016	+	17.4644i	0.969300	+	0.626937i
$777$		0			0
$778$	32.5625	+	28.2711i	1.16742	+	1.01357i
$779$	−4.23417			−0.151705
$780$		0			0
$781$	5.09271	+	13.1300i	0.182231	+	0.469830i
$782$	15.8415	−	18.2462i	0.566492	−	0.652483i
$783$		0			0
$784$	23.5270	−	6.80879i	0.840250	−	0.243171i
$785$	−31.6831			−1.13082
$786$		0			0
$787$		−	48.3120i		−	1.72214i	−0.508489	−	0.861069i	$-0.669796\pi$
$787$		−	48.3120i		−	1.72214i	0.508489	−	0.861069i	$-0.330204\pi$
$788$	−3.48033	−	24.5453i	−0.123982	−	0.874389i
$789$		0			0
$790$	−8.24621	−	7.15944i	−0.293387	−	0.254722i
$791$	14.8344			0.527452
$792$		0			0
$793$	38.7386			1.37565
$794$	−19.8126	−	17.2015i	−0.703123	−	0.610459i
$795$		0			0
$796$	27.9309	−	3.96039i	0.989983	−	0.140372i
$797$			11.7538i			0.416341i	0.978093	+	0.208170i	$0.0667508\pi$
$797$			11.7538i			0.416341i	−0.978093	+	0.208170i	$0.933249\pi$
$798$		0			0
$799$	−20.0108			−0.707931
$800$	2.37495	−	5.13416i	0.0839672	−	0.181520i
$801$		0			0
$802$	22.9354	−	26.4168i	0.809875	−	0.932810i
$803$	−15.8415	−	40.8427i	−0.559036	−	1.44131i
$804$		0			0
$805$	9.59482			0.338173
$806$	−7.92077	−	6.87689i	−0.278997	−	0.242228i
$807$		0			0
$808$	15.6847	+	10.1447i	0.551784	+	0.356891i
$809$			48.1541i			1.69301i	0.532382	+	0.846504i	$0.321297\pi$
$809$			48.1541i			1.69301i	−0.532382	+	0.846504i	$0.678703\pi$
$810$		0			0
$811$			30.9384i			1.08640i	0.839605	+	0.543198i	$0.182787\pi$
$811$			30.9384i			1.08640i	−0.839605	+	0.543198i	$0.817213\pi$
$812$	−1.73642	−	12.2462i	−0.0609364	−	0.429758i
$813$		0			0
$814$	27.2983	+	9.80926i	0.956804	+	0.343815i
$815$			24.9848i			0.875181i
$816$		0			0
$817$	−29.8617			−1.04473
$818$	−28.2102	−	24.4924i	−0.986348	−	0.856357i
$819$		0			0
$820$	0.821147	+	5.79119i	0.0286757	+	0.202237i
$821$	−28.8559			−1.00708			−0.503538	−	0.863973i	$-0.667969\pi$
$821$	−28.8559			−1.00708			−0.503538	+	0.863973i	$0.667969\pi$
$822$		0			0
$823$		−	47.7384i		−	1.66406i	−0.554734	−	0.832028i	$-0.687180\pi$
$823$		−	47.7384i		−	1.66406i	0.554734	−	0.832028i	$-0.312820\pi$
$824$	2.66732	−	4.12391i	0.0929205	−	0.143663i
$825$		0			0
$826$	−8.38447	+	9.65719i	−0.291733	+	0.336017i
$827$		−	51.7846i		−	1.80073i	−0.435140	−	0.900363i	$-0.643301\pi$
$827$		−	51.7846i		−	1.80073i	0.435140	−	0.900363i	$-0.356699\pi$
$828$		0			0
$829$		−	25.4987i		−	0.885608i	−0.896618	−	0.442804i	$-0.853984\pi$
$829$		−	25.4987i		−	0.885608i	0.896618	−	0.442804i	$-0.146016\pi$
$830$	4.44793	−	5.12311i	0.154390	−	0.177826i
$831$		0			0
$832$	−14.0140	−	31.1667i	−0.485849	−	1.08051i
$833$		−	20.4214i		−	0.707558i
$834$		0			0
$835$			11.5824i			0.400825i
$836$	16.7549	−	9.39088i	0.579482	−	0.324790i
$837$		0			0
$838$	−3.21985	+	3.70861i	−0.111228	+	0.128112i
$839$		−	18.8769i		−	0.651703i	−0.945421	−	0.325851i	$-0.894349\pi$
$839$		−	18.8769i		−	0.651703i	0.945421	−	0.325851i	$-0.105651\pi$
$840$		0			0
$841$	14.6155			0.503984
$842$	−16.9170	−	14.6875i	−0.582999	−	0.506166i
$843$		0			0
$844$	5.73384	−	0.813015i	0.197367	−	0.0279851i
$845$			10.4924i			0.360950i
$846$		0			0
$847$	−7.60669	+	6.94568i	−0.261369	+	0.238656i
$848$	−9.16965	−	31.6847i	−0.314887	−	1.08806i
$849$		0			0
$850$	−3.56155	−	3.09218i	−0.122160	−	0.106061i
$851$	31.6831			1.08608
$852$		0			0
$853$	17.3815			0.595132			0.297566	−	0.954701i	$-0.403825\pi$
$853$	17.3815			0.595132			0.297566	+	0.954701i	$0.403825\pi$
$854$	−7.87377	+	9.06897i	−0.269435	+	0.310334i
$855$		0			0
$856$	−13.9309	+	21.5384i	−0.476147	+	0.736166i
$857$			11.0571i			0.377703i	0.982006	+	0.188852i	$0.0604765\pi$
$857$			11.0571i			0.377703i	−0.982006	+	0.188852i	$0.939523\pi$
$858$		0			0
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$	5.79119	+	40.8427i	0.197478	+	1.39273i
$861$		0			0
$862$	−10.7386	+	12.3687i	−0.365759	+	0.421280i
$863$			48.3542i			1.64599i	0.568045	+	0.822997i	$0.307700\pi$
$863$			48.3542i			1.64599i	−0.568045	+	0.822997i	$0.692300\pi$
$864$		0			0
$865$		−	1.62603i		−	0.0552867i
$866$	6.37593	−	7.34376i	0.216663	−	0.249551i
$867$		0			0
$868$	3.21985	−	0.456551i	0.109289	−	0.0154963i
$869$	11.9388	−	4.63068i	0.404998	−	0.157085i
$870$		0			0
$871$	43.7673			1.48300
$872$	3.19906	+	2.06913i	0.108334	+	0.0700696i
$873$		0			0
$874$	13.7538	−	15.8415i	0.465229	−	0.535848i
$875$		−	11.2371i		−	0.379884i
$876$		0			0
$877$	50.1423			1.69318			0.846592	−	0.532243i	$-0.178651\pi$
$877$	50.1423			1.69318			0.846592	+	0.532243i	$0.178651\pi$
$878$	28.1034	−	32.3693i	0.948443	−	1.09241i
$879$		0			0
$880$	−16.0935	−	21.0950i	−0.542512	−	0.711112i
$881$	−37.1061			−1.25014			−0.625068	−	0.780570i	$-0.714929\pi$
$881$	−37.1061			−1.25014			−0.625068	+	0.780570i	$0.714929\pi$
$882$		0			0
$883$	5.75379			0.193630			0.0968152	−	0.995302i	$-0.469134\pi$
$883$	5.75379			0.193630			0.0968152	+	0.995302i	$0.469134\pi$
$884$	−28.2102	+	4.00000i	−0.948813	+	0.134535i
$885$		0			0
$886$	5.73384	−	6.60421i	0.192632	−	0.221873i
$887$	29.6689			0.996184			0.498092	−	0.867124i	$-0.334034\pi$
$887$	29.6689			0.996184			0.498092	+	0.867124i	$0.334034\pi$
$888$		0			0
$889$	−15.1231			−0.507213
$890$	7.41722	+	6.43971i	0.248626	+	0.215859i
$891$		0			0
$892$	52.4233	−	7.43323i	1.75526	−	0.248883i
$893$	−17.3736			−0.581384
$894$		0			0
$895$		0			0
$896$	10.1447	+	3.05398i	0.338912	+	0.102026i
$897$		0			0
$898$	26.1552	−	30.1254i	0.872810	−	1.00530i
$899$			11.4677i			0.382468i
$900$		0			0
$901$	−27.5022			−0.916231
$902$	−6.45463	−	2.31938i	−0.214916	−	0.0772270i
$903$		0			0
$904$	−37.6229	−	24.3342i	−1.25132	−	0.809345i
$905$	17.7917			0.591417
$906$		0			0
$907$	30.7386			1.02066			0.510330	−	0.859979i	$-0.329523\pi$
$907$	30.7386			1.02066			0.510330	+	0.859979i	$0.329523\pi$
$908$	53.4184	−	7.57432i	1.77275	−	0.251363i
$909$		0			0
$910$	−8.54312	−	7.41722i	−0.283202	−	0.245878i
$911$		−	48.7386i		−	1.61478i	−0.590016	−	0.807391i	$-0.700879\pi$
$911$		−	48.7386i		−	1.61478i	0.590016	−	0.807391i	$-0.299121\pi$
$912$		0			0
$913$	2.87689	+	7.41722i	0.0952113	+	0.245474i
$914$	−12.3687	−	10.7386i	−0.409120	−	0.355202i
$915$		0			0
$916$	−50.4924	+	7.15944i	−1.66832	+	0.236555i
$917$			12.0000i			0.396275i
$918$		0			0
$919$	−33.2360			−1.09636			−0.548178	−	0.836362i	$-0.684678\pi$
$919$	−33.2360			−1.09636			−0.548178	+	0.836362i	$0.684678\pi$
$920$	−24.3342	−	15.7392i	−0.802276	−	0.518907i
$921$		0			0
$922$	−29.1080	+	33.5264i	−0.958619	+	1.10413i
$923$		−	18.1379i		−	0.597018i
$924$		0			0
$925$		−	6.18435i		−	0.203340i
$926$	7.64550	+	6.63790i	0.251247	+	0.218135i
$927$		0			0
$928$	−15.6847	+	33.9071i	−0.514874	+	1.11305i
$929$	−28.2102			−0.925548			−0.462774	−	0.886476i	$-0.653146\pi$
$929$	−28.2102			−0.925548			−0.462774	+	0.886476i	$0.653146\pi$
$930$		0			0
$931$		−	17.7300i		−	0.581078i
$932$	−4.52162	+	0.641132i	−0.148111	+	0.0210010i
$933$		0			0
$934$	−5.73384	+	6.60421i	−0.187617	+	0.216096i
$935$	−20.6256	+	8.00000i	−0.674530	+	0.261628i
$936$		0			0
$937$		−	14.8344i		−	0.484620i	−0.970199	−	0.242310i	$-0.922095\pi$
$937$		−	14.8344i		−	0.484620i	0.970199	−	0.242310i	$-0.0779051\pi$
$938$	−8.89586	+	10.2462i	−0.290460	+	0.334551i
$939$		0			0
$940$	3.36932	+	23.7623i	0.109895	+	0.775041i
$941$	15.6475			0.510092			0.255046	−	0.966929i	$-0.417909\pi$
$941$	15.6475			0.510092			0.255046	+	0.966929i	$0.417909\pi$
$942$		0			0
$943$	−7.49141			−0.243954
$944$	37.1061	−	10.7386i	1.20770	−	0.349513i
$945$		0			0
$946$	−45.5217	−	16.3576i	−1.48004	−	0.531831i
$947$	−6.94568			−0.225704			−0.112852	−	0.993612i	$-0.535999\pi$
$947$	−6.94568			−0.225704			−0.112852	+	0.993612i	$0.535999\pi$
$948$		0			0
$949$			56.4205i			1.83149i
$950$	−3.09218	−	2.68466i	−0.100323	−	0.0871018i
$951$		0			0
$952$	4.79741	−	7.41722i	0.155485	−	0.240393i
$953$		−	43.9473i		−	1.42359i	−0.702386	−	0.711796i	$-0.747882\pi$
$953$		−	43.9473i		−	1.42359i	0.702386	−	0.711796i	$-0.252118\pi$
$954$		0			0
$955$	24.4924			0.792556
$956$	−5.79119	−	40.8427i	−0.187300	−	1.32095i
$957$		0			0
$958$	13.7538	−	15.8415i	0.444365	−	0.511817i
$959$	−14.8344			−0.479029
$960$		0			0
$961$	27.9848			0.902737
$962$	−28.2102	−	24.4924i	−0.909535	−	0.789667i
$963$		0			0
$964$	−55.5303	+	7.87377i	−1.78851	+	0.253597i
$965$	−3.25206			−0.104687
$966$		0			0
$967$	−26.7963			−0.861712			−0.430856	−	0.902421i	$-0.641788\pi$
$967$	−26.7963			−0.861712			−0.430856	+	0.902421i	$0.641788\pi$
$968$	30.6856	−	5.13760i	0.986272	−	0.165129i
$969$		0			0
$970$	−24.2824	−	21.0822i	−0.779659	−	0.676908i
$971$	30.9218			0.992327			0.496163	−	0.868229i	$-0.334742\pi$
$971$	30.9218			0.992327			0.496163	+	0.868229i	$0.334742\pi$
$972$		0			0
$973$		−	9.65719i		−	0.309595i
$974$	−22.4799	−	19.5173i	−0.720304	−	0.625375i
$975$		0			0
$976$	34.8460	−	10.0845i	1.11539	−	0.322798i
$977$	−30.1604			−0.964918			−0.482459	−	0.875919i	$-0.660256\pi$
$977$	−30.1604			−0.964918			−0.482459	+	0.875919i	$0.660256\pi$
$978$		0			0
$979$	−10.7386	+	4.16516i	−0.343208	+	0.133119i
$980$	−24.2499	+	3.43845i	−0.774633	+	0.109837i
$981$		0			0
$982$	−31.9309	−	27.7227i	−1.01895	−	0.884667i
$983$			47.3693i			1.51085i	0.655237	+	0.755423i	$0.272569\pi$
$983$			47.3693i			1.51085i	−0.655237	+	0.755423i	$0.727431\pi$
$984$		0			0
$985$			24.7908i			0.789900i
$986$	23.5212	+	20.4214i	0.749068	+	0.650349i
$987$		0			0
$988$	−24.4924	+	3.47284i	−0.779208	+	0.110486i
$989$	−52.8336			−1.68001
$990$		0			0
$991$			47.7384i			1.51646i	0.651987	+	0.758230i	$0.273936\pi$
$991$			47.7384i			1.51646i	−0.651987	+	0.758230i	$0.726064\pi$
$992$	−8.91506	−	4.12391i	−0.283053	−	0.130934i
$993$		0			0
$994$	4.24621	+	3.68660i	0.134682	+	0.116932i
$995$	−28.2102			−0.894325
$996$		0			0
$997$	−28.0281			−0.887657			−0.443829	−	0.896112i	$-0.646380\pi$
$997$	−28.0281			−0.887657			−0.443829	+	0.896112i	$0.646380\pi$
$998$	−32.2080	+	37.0970i	−1.01953	+	1.17429i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.h.i.307.8	yes	16
3.2	odd	2	inner	792.2.h.i.307.9	yes	16
4.3	odd	2		3168.2.h.i.2287.13		16
8.3	odd	2	inner	792.2.h.i.307.11	yes	16
8.5	even	2		3168.2.h.i.2287.3		16
11.10	odd	2	inner	792.2.h.i.307.10	yes	16
12.11	even	2		3168.2.h.i.2287.6		16
24.5	odd	2		3168.2.h.i.2287.12		16
24.11	even	2	inner	792.2.h.i.307.6	yes	16
33.32	even	2	inner	792.2.h.i.307.7	yes	16
44.43	even	2		3168.2.h.i.2287.11		16
88.21	odd	2		3168.2.h.i.2287.5		16
88.43	even	2	inner	792.2.h.i.307.5	✓	16
132.131	odd	2		3168.2.h.i.2287.4		16
264.131	odd	2	inner	792.2.h.i.307.12	yes	16
264.197	even	2		3168.2.h.i.2287.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.h.i.307.5	✓	16	88.43	even	2	inner
792.2.h.i.307.6	yes	16	24.11	even	2	inner
792.2.h.i.307.7	yes	16	33.32	even	2	inner
792.2.h.i.307.8	yes	16	1.1	even	1	trivial
792.2.h.i.307.9	yes	16	3.2	odd	2	inner
792.2.h.i.307.10	yes	16	11.10	odd	2	inner
792.2.h.i.307.11	yes	16	8.3	odd	2	inner
792.2.h.i.307.12	yes	16	264.131	odd	2	inner
3168.2.h.i.2287.3		16	8.5	even	2
3168.2.h.i.2287.4		16	132.131	odd	2
3168.2.h.i.2287.5		16	88.21	odd	2
3168.2.h.i.2287.6		16	12.11	even	2
3168.2.h.i.2287.11		16	44.43	even	2
3168.2.h.i.2287.12		16	24.5	odd	2
3168.2.h.i.2287.13		16	4.3	odd	2
3168.2.h.i.2287.14		16	264.197	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927153 + 1.06789i) q^{2} +(-0.280776 - 1.98019i) q^{4} +2.00000i q^{5} -0.936426 q^{7} +(2.37495 + 1.53610i) q^{8} +(-2.13578 - 1.85431i) q^{10} +(3.09218 - 1.19935i) q^{11} -4.27156 q^{13} +(0.868210 - 1.00000i) q^{14} +(-3.84233 + 1.11198i) q^{16} +3.33513i q^{17} +2.89560i q^{19} +(3.96039 - 0.561553i) q^{20} +(-1.58614 + 4.41409i) q^{22} +5.12311i q^{23} +1.00000 q^{25} +(3.96039 - 4.56155i) q^{26} +(0.262926 + 1.85431i) q^{28} -6.60421 q^{29} -1.73642i q^{31} +(2.37495 - 5.13416i) q^{32} +(-3.56155 - 3.09218i) q^{34} -1.87285i q^{35} -6.18435i q^{37} +(-3.09218 - 2.68466i) q^{38} +(-3.07221 + 4.74990i) q^{40} +1.46228i q^{41} +10.3128i q^{43} +(-3.24316 - 5.78636i) q^{44} +(-5.47091 - 4.74990i) q^{46} +6.00000i q^{47} -6.12311 q^{49} +(-0.927153 + 1.06789i) q^{50} +(1.19935 + 8.45851i) q^{52} +8.24621i q^{53} +(2.39871 + 6.18435i) q^{55} +(-2.22397 - 1.43845i) q^{56} +(6.12311 - 7.05256i) q^{58} -9.65719 q^{59} -9.06897 q^{61} +(1.85431 + 1.60993i) q^{62} +(3.28078 + 7.29634i) q^{64} -8.54312i q^{65} -10.2462 q^{67} +(6.60421 - 0.936426i) q^{68} +(2.00000 + 1.73642i) q^{70} +4.24621i q^{71} -13.2084i q^{73} +(6.60421 + 5.73384i) q^{74} +(5.73384 - 0.813015i) q^{76} +(-2.89560 + 1.12311i) q^{77} +3.86098 q^{79} +(-2.22397 - 7.68466i) q^{80} +(-1.56155 - 1.35576i) q^{82} +2.39871i q^{83} -6.67026 q^{85} +(-11.0129 - 9.56155i) q^{86} +(9.18609 + 1.90150i) q^{88} -3.47284 q^{89} +4.00000 q^{91} +(10.1447 - 1.43845i) q^{92} +(-6.40734 - 5.56292i) q^{94} -5.79119 q^{95} +11.3693 q^{97} +(5.67705 - 6.53880i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 12 q^{16} + 4 q^{22} + 16 q^{25} - 24 q^{34} - 32 q^{49} + 32 q^{58} + 36 q^{64} - 32 q^{67} + 32 q^{70} + 8 q^{82} - 20 q^{88} + 64 q^{91} - 16 q^{97}+O(q^{100}) \) 16 * q + 12 * q^4 - 12 * q^16 + 4 * q^22 + 16 * q^25 - 24 * q^34 - 32 * q^49 + 32 * q^58 + 36 * q^64 - 32 * q^67 + 32 * q^70 + 8 * q^82 - 20 * q^88 + 64 * q^91 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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