LMFDB - Embedded newform 792.2.h.i.307.1

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)

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")

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);

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			307.1
Root			$-0.0131233 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	792.307
Dual form			792.2.h.i.307.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} -2.00000i q^{5} -3.02045 q^{7} +(-2.14700 - 1.84130i) q^{8} +(-0.662153 + 2.74983i) q^{10} +(-2.33205 - 2.35829i) q^{11} -1.32431 q^{13} +(4.15286 + 1.00000i) q^{14} +(2.34233 + 3.24245i) q^{16} +1.69614i q^{17} +7.04383i q^{19} +(1.82081 - 3.56155i) q^{20} +(2.42559 + 4.01454i) q^{22} +3.12311i q^{23} +1.00000 q^{25} +(1.82081 + 0.438447i) q^{26} +(-5.37874 - 2.74983i) q^{28} +1.54417 q^{29} +8.30571i q^{31} +(-2.14700 - 5.23358i) q^{32} +(0.561553 - 2.33205i) q^{34} +6.04090i q^{35} -4.66410i q^{37} +(2.33205 - 9.68466i) q^{38} +(-3.68260 + 4.29400i) q^{40} +7.73704i q^{41} -3.95548i q^{43} +(-2.00586 - 6.32270i) q^{44} +(1.03399 - 4.29400i) q^{46} -6.00000i q^{47} +2.12311 q^{49} +(-1.37491 - 0.331077i) q^{50} +(-2.35829 - 1.20565i) q^{52} +8.24621i q^{53} +(-4.71659 + 4.66410i) q^{55} +(6.48490 + 5.56155i) q^{56} +(-2.12311 - 0.511240i) q^{58} -11.9473 q^{59} +8.10887 q^{61} +(2.74983 - 11.4196i) q^{62} +(1.21922 + 7.90655i) q^{64} +2.64861i q^{65} +6.24621 q^{67} +(-1.54417 + 3.02045i) q^{68} +(2.00000 - 8.30571i) q^{70} +12.2462i q^{71} -3.08835i q^{73} +(-1.54417 + 6.41273i) q^{74} +(-6.41273 + 12.5435i) q^{76} +(7.04383 + 7.12311i) q^{77} -12.4536 q^{79} +(6.48490 - 4.68466i) q^{80} +(2.56155 - 10.6378i) q^{82} +4.71659i q^{83} +3.39228 q^{85} +(-1.30957 + 5.43845i) q^{86} +(0.664579 + 9.35726i) q^{88} -16.6114 q^{89} +4.00000 q^{91} +(-2.84329 + 5.56155i) q^{92} +(-1.98646 + 8.24948i) q^{94} +14.0877 q^{95} -13.3693 q^{97} +(-2.91909 - 0.702911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.37491	−	0.331077i	−0.972211	−	0.234107i
$2$	−1.37491	−	0.331077i	−0.972211	−	0.234107i
$3$		0			0
$3$		0			0
$4$	1.78078	+	0.910404i	0.890388	+	0.455202i
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		0			0
$7$	−3.02045			−1.14162			−0.570811	−	0.821081i	$-0.693371\pi$
$7$	−3.02045			−1.14162			−0.570811	+	0.821081i	$0.693371\pi$
$8$	−2.14700	−	1.84130i	−0.759079	−	0.650998i
$9$		0			0
$10$	−0.662153	+	2.74983i	−0.209391	+	0.869572i
$11$	−2.33205	−	2.35829i	−0.703139	−	0.711053i
$11$	−2.33205	−	2.35829i	−0.703139	−	0.711053i
$12$		0			0
$13$	−1.32431			−0.367297			−0.183648	−	0.982992i	$-0.558791\pi$
$13$	−1.32431			−0.367297			−0.183648	+	0.982992i	$0.558791\pi$
$14$	4.15286	+	1.00000i	1.10990	+	0.267261i
$15$		0			0
$16$	2.34233	+	3.24245i	0.585582	+	0.810613i
$17$			1.69614i			0.411375i	0.978618	+	0.205687i	$0.0659430\pi$
$17$			1.69614i			0.411375i	−0.978618	+	0.205687i	$0.934057\pi$
$18$		0			0
$19$			7.04383i			1.61597i	0.589206	+	0.807983i	$0.299441\pi$
$19$			7.04383i			1.61597i	−0.589206	+	0.807983i	$0.700559\pi$
$20$	1.82081	−	3.56155i	0.407145	−	0.796387i
$21$		0			0
$22$	2.42559	+	4.01454i	0.517137	+	0.855903i
$23$			3.12311i			0.651213i	0.945505	+	0.325606i	$0.105568\pi$
$23$			3.12311i			0.651213i	−0.945505	+	0.325606i	$0.894432\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.82081	+	0.438447i	0.357090	+	0.0859866i
$27$		0			0
$28$	−5.37874	−	2.74983i	−1.01649	−	0.519669i
$29$	1.54417			0.286746			0.143373	−	0.989669i	$-0.454205\pi$
$29$	1.54417			0.286746			0.143373	+	0.989669i	$0.454205\pi$
$30$		0			0
$31$			8.30571i			1.49175i	0.666086	+	0.745875i	$0.267968\pi$
$31$			8.30571i			1.49175i	−0.666086	+	0.745875i	$0.732032\pi$
$32$	−2.14700	−	5.23358i	−0.379540	−	0.925175i
$33$		0			0
$34$	0.561553	−	2.33205i	0.0963055	−	0.399943i
$35$			6.04090i			1.02110i
$36$		0			0
$37$		−	4.66410i		−	0.766773i	−0.923588	−	0.383386i	$-0.874758\pi$
$37$		−	4.66410i		−	0.766773i	0.923588	−	0.383386i	$-0.125242\pi$
$38$	2.33205	−	9.68466i	0.378308	−	1.57106i
$39$		0			0
$40$	−3.68260	+	4.29400i	−0.582270	+	0.678941i
$41$			7.73704i			1.20832i	0.796862	+	0.604161i	$0.206492\pi$
$41$			7.73704i			1.20832i	−0.796862	+	0.604161i	$0.793508\pi$
$42$		0			0
$43$		−	3.95548i		−	0.603205i	−0.953434	−	0.301603i	$-0.902478\pi$
$43$		−	3.95548i		−	0.603205i	0.953434	−	0.301603i	$-0.0975216\pi$
$44$	−2.00586	−	6.32270i	−0.302394	−	0.953183i
$45$		0			0
$46$	1.03399	−	4.29400i	0.152453	−	0.633116i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$		0			0
$49$	2.12311			0.303301
$50$	−1.37491	−	0.331077i	−0.194442	−	0.0468213i
$51$		0			0
$52$	−2.35829	−	1.20565i	−0.327037	−	0.167194i
$53$			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
$55$	−4.71659	+	4.66410i	−0.635985	+	0.628907i
$56$	6.48490	+	5.56155i	0.866582	+	0.743194i
$57$		0			0
$58$	−2.12311	−	0.511240i	−0.278777	−	0.0671291i
$59$	−11.9473			−1.55541			−0.777705	−	0.628630i	$-0.783616\pi$
$59$	−11.9473			−1.55541			−0.777705	+	0.628630i	$0.783616\pi$
$60$		0			0
$61$	8.10887			1.03823			0.519117	−	0.854703i	$-0.326261\pi$
$61$	8.10887			1.03823			0.519117	+	0.854703i	$0.326261\pi$
$62$	2.74983	−	11.4196i	0.349228	−	1.45030i
$63$		0			0
$64$	1.21922	+	7.90655i	0.152403	+	0.988318i
$65$			2.64861i			0.328520i
$66$		0			0
$67$	6.24621			0.763096			0.381548	−	0.924349i	$-0.375391\pi$
$67$	6.24621			0.763096			0.381548	+	0.924349i	$0.375391\pi$
$68$	−1.54417	+	3.02045i	−0.187259	+	0.366283i
$69$		0			0
$70$	2.00000	−	8.30571i	0.239046	−	0.992722i
$71$			12.2462i			1.45336i	0.686977	+	0.726679i	$0.258937\pi$
$71$			12.2462i			1.45336i	−0.686977	+	0.726679i	$0.741063\pi$
$72$		0			0
$73$		−	3.08835i		−	0.361464i	−0.983532	−	0.180732i	$-0.942153\pi$
$73$		−	3.08835i		−	0.361464i	0.983532	−	0.180732i	$-0.0578466\pi$
$74$	−1.54417	+	6.41273i	−0.179507	+	0.745465i
$75$		0			0
$76$	−6.41273	+	12.5435i	−0.735591	+	1.43884i
$77$	7.04383	+	7.12311i	0.802719	+	0.811753i
$78$		0			0
$79$	−12.4536			−1.40114			−0.700571	−	0.713583i	$-0.747071\pi$
$79$	−12.4536			−1.40114			−0.700571	+	0.713583i	$0.747071\pi$
$80$	6.48490	−	4.68466i	0.725034	−	0.523761i
$81$		0			0
$82$	2.56155	−	10.6378i	0.282876	−	1.17474i
$83$			4.71659i			0.517713i	0.965916	+	0.258856i	$0.0833457\pi$
$83$			4.71659i			0.517713i	−0.965916	+	0.258856i	$0.916654\pi$
$84$		0			0
$85$	3.39228			0.367945
$86$	−1.30957	+	5.43845i	−0.141214	+	0.586443i
$87$		0			0
$88$	0.664579	+	9.35726i	0.0708444	+	0.997487i
$89$	−16.6114			−1.76081			−0.880404	−	0.474225i	$-0.842728\pi$
$89$	−16.6114			−1.76081			−0.880404	+	0.474225i	$0.842728\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$	−2.84329	+	5.56155i	−0.296433	+	0.579832i
$93$		0			0
$94$	−1.98646	+	8.24948i	−0.204888	+	0.850869i
$95$	14.0877			1.44536
$96$		0			0
$97$	−13.3693			−1.35745			−0.678724	−	0.734393i	$-0.737467\pi$
$97$	−13.3693			−1.35745			−0.678724	+	0.734393i	$0.737467\pi$
$98$	−2.91909	−	0.702911i	−0.294872	−	0.0710047i
$99$		0			0
$100$	1.78078	+	0.910404i	0.178078	+	0.0910404i
$101$	−1.54417			−0.153651			−0.0768255	−	0.997045i	$-0.524478\pi$
$101$	−1.54417			−0.153651			−0.0768255	+	0.997045i	$0.524478\pi$
$102$		0			0
$103$			8.30571i			0.818386i	0.912448	+	0.409193i	$0.134190\pi$
$103$			8.30571i			0.818386i	−0.912448	+	0.409193i	$0.865810\pi$
$104$	2.84329	+	2.43845i	0.278807	+	0.239109i
$105$		0			0
$106$	2.73013	−	11.3378i	0.265174	−	1.10123i
$107$			8.10887i			0.783914i	0.919984	+	0.391957i	$0.128202\pi$
$107$			8.10887i			0.783914i	−0.919984	+	0.391957i	$0.871798\pi$
$108$		0			0
$109$	16.7984			1.60899			0.804497	−	0.593957i	$-0.202435\pi$
$109$	16.7984			1.60899			0.804497	+	0.593957i	$0.202435\pi$
$110$	8.02908	−	4.85118i	0.765542	−	0.462542i
$111$		0			0
$112$	−7.07488	−	9.79366i	−0.668514	−	0.925414i
$113$	−7.28323			−0.685149			−0.342574	−	0.939491i	$-0.611299\pi$
$113$	−7.28323			−0.685149			−0.342574	+	0.939491i	$0.611299\pi$
$114$		0			0
$115$	6.24621			0.582462
$116$	2.74983	+	1.40582i	0.255315	+	0.130527i
$117$		0			0
$118$	16.4265	+	3.95548i	1.51219	+	0.364132i
$119$		−	5.12311i		−	0.469634i
$120$		0			0
$121$	−0.123106	+	10.9993i	−0.0111914	+	0.999937i
$122$	−11.1490	−	2.68466i	−1.00938	−	0.243058i
$123$		0			0
$124$	−7.56155	+	14.7906i	−0.679047	+	1.32824i
$125$		−	12.0000i		−	1.07331i
$126$		0			0
$127$	2.27678			0.202032			0.101016	−	0.994885i	$-0.467791\pi$
$127$	2.27678			0.202032			0.101016	+	0.994885i	$0.467791\pi$
$128$	0.941346	−	11.2745i	0.0832041	−	0.996533i
$129$		0			0
$130$	0.876894	−	3.64162i	0.0769087	−	0.319391i
$131$			3.97292i			0.347116i	0.984824	+	0.173558i	$0.0555264\pi$
$131$			3.97292i			0.347116i	−0.984824	+	0.173558i	$0.944474\pi$
$132$		0			0
$133$		−	21.2755i		−	1.84482i
$134$	−8.58800	−	2.06798i	−0.741890	−	0.178646i
$135$		0			0
$136$	3.12311	−	3.64162i	0.267804	−	0.312266i
$137$	7.28323			0.622248			0.311124	−	0.950369i	$-0.399294\pi$
$137$	7.28323			0.622248			0.311124	+	0.950369i	$0.399294\pi$
$138$		0			0
$139$		−	3.95548i		−	0.335500i	−0.985830	−	0.167750i	$-0.946350\pi$
$139$		−	3.95548i		−	0.335500i	0.985830	−	0.167750i	$-0.0536501\pi$
$140$	−5.49966	+	10.7575i	−0.464806	+	0.909173i
$141$		0			0
$142$	4.05444	−	16.8375i	0.340241	−	1.41297i
$143$	3.08835	+	3.12311i	0.258261	+	0.261167i
$144$		0			0
$145$		−	3.08835i		−	0.256473i
$146$	−1.02248	+	4.24621i	−0.0846210	+	0.351419i
$147$		0			0
$148$	4.24621	−	8.30571i	0.349036	−	0.682725i
$149$	12.5435			1.02760			0.513801	−	0.857909i	$-0.328237\pi$
$149$	12.5435			1.02760			0.513801	+	0.857909i	$0.328237\pi$
$150$		0			0
$151$	−7.15640			−0.582379			−0.291190	−	0.956665i	$-0.594051\pi$
$151$	−7.15640			−0.582379			−0.291190	+	0.956665i	$0.594051\pi$
$152$	12.9698	−	15.1231i	1.05199	−	1.22665i
$153$		0			0
$154$	−7.32636	−	12.1257i	−0.590375	−	0.977117i
$155$	16.6114			1.33426
$156$		0			0
$157$		−	7.28323i		−	0.581265i	−0.956835	−	0.290633i	$-0.906134\pi$
$157$		−	7.28323i		−	0.581265i	0.956835	−	0.290633i	$-0.0938657\pi$
$158$	17.1227	+	4.12311i	1.36221	+	0.328017i
$159$		0			0
$160$	−10.4672	+	4.29400i	−0.827502	+	0.339471i
$161$		−	9.43318i		−	0.743439i
$162$		0			0
$163$	−20.4924			−1.60509			−0.802545	−	0.596591i	$-0.796521\pi$
$163$	−20.4924			−1.60509			−0.802545	+	0.596591i	$0.796521\pi$
$164$	−7.04383	+	13.7779i	−0.550031	+	1.07588i
$165$		0			0
$166$	1.56155	−	6.48490i	0.121200	−	0.503326i
$167$	−14.0877			−1.09014			−0.545068	−	0.838392i	$-0.683496\pi$
$167$	−14.0877			−1.09014			−0.545068	+	0.838392i	$0.683496\pi$
$168$		0			0
$169$	−11.2462			−0.865093
$170$	−4.66410	−	1.12311i	−0.357720	−	0.0861383i
$171$		0			0
$172$	3.60109	−	7.04383i	0.274580	−	0.537087i
$173$	−12.5435			−0.953663			−0.476832	−	0.878995i	$-0.658215\pi$
$173$	−12.5435			−0.953663			−0.476832	+	0.878995i	$0.658215\pi$
$174$		0			0
$175$	−3.02045			−0.228324
$176$	2.18423	−	13.0855i	0.164643	−	0.986353i
$177$		0			0
$178$	22.8393	+	5.49966i	1.71188	+	0.412217i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$		−	25.9396i		−	1.92808i	−0.265764	−	0.964038i	$-0.585624\pi$
$181$		−	25.9396i		−	1.92808i	0.265764	−	0.964038i	$-0.414376\pi$
$182$	−5.49966	−	1.32431i	−0.407662	−	0.0981642i
$183$		0			0
$184$	5.75058	−	6.70531i	0.423938	−	0.494322i
$185$	−9.32819			−0.685822
$186$		0			0
$187$	4.00000	−	3.95548i	0.292509	−	0.289253i
$188$	5.46242	−	10.6847i	0.398388	−	0.779259i
$189$		0			0
$190$	−19.3693	−	4.66410i	−1.40520	−	0.338369i
$191$		−	4.24621i		−	0.307245i	−0.988130	−	0.153623i	$-0.950906\pi$
$191$		−	4.24621i		−	0.307245i	0.988130	−	0.153623i	$-0.0490940\pi$
$192$		0			0
$193$		−	25.0870i		−	1.80580i	−0.429851	−	0.902900i	$-0.641434\pi$
$193$		−	25.0870i		−	1.80580i	0.429851	−	0.902900i	$-0.358566\pi$
$194$	18.3817	+	4.42627i	1.31973	+	0.317788i
$195$		0			0
$196$	3.78078	+	1.93288i	0.270055	+	0.138063i
$197$	−15.6318			−1.11372			−0.556861	−	0.830606i	$-0.687994\pi$
$197$	−15.6318			−1.11372			−0.556861	+	0.830606i	$0.687994\pi$
$198$		0			0
$199$			1.02248i			0.0724817i	0.999343	+	0.0362408i	$0.0115383\pi$
$199$			1.02248i			0.0724817i	−0.999343	+	0.0362408i	$0.988462\pi$
$200$	−2.14700	−	1.84130i	−0.151816	−	0.130200i
$201$		0			0
$202$	2.12311	+	0.511240i	0.149381	+	0.0359707i
$203$	−4.66410			−0.327355
$204$		0			0
$205$	15.4741			1.08076
$206$	2.74983	−	11.4196i	0.191590	−	0.795644i
$207$		0			0
$208$	−3.10196	−	4.29400i	−0.215082	−	0.297735i
$209$	16.6114	−	16.4265i	1.14904	−	1.13625i
$210$		0			0
$211$			7.04383i			0.484917i	0.970162	+	0.242459i	$0.0779539\pi$
$211$			7.04383i			0.484917i	−0.970162	+	0.242459i	$0.922046\pi$
$212$	−7.50738	+	14.6847i	−0.515609	+	1.00855i
$213$		0			0
$214$	2.68466	−	11.1490i	0.183519	−	0.762130i
$215$	−7.91096			−0.539523
$216$		0			0
$217$		−	25.0870i		−	1.70301i
$218$	−23.0963	−	5.56155i	−1.56428	−	0.376676i
$219$		0			0
$220$	−12.6454	+	4.01171i	−0.852553	+	0.270469i
$221$		−	2.24621i		−	0.151097i
$222$		0			0
$223$			10.3507i			0.693132i	0.938026	+	0.346566i	$0.112652\pi$
$223$			10.3507i			0.693132i	−0.938026	+	0.346566i	$0.887348\pi$
$224$	6.48490	+	15.8078i	0.433291	+	1.05620i
$225$		0			0
$226$	10.0138	+	2.41131i	0.666109	+	0.160398i
$227$		−	24.7442i		−	1.64233i	−0.570690	−	0.821166i	$-0.693324\pi$
$227$		−	24.7442i		−	1.64233i	0.570690	−	0.821166i	$-0.306676\pi$
$228$		0			0
$229$			19.2306i			1.27079i	0.772187	+	0.635396i	$0.219163\pi$
$229$			19.2306i			1.27079i	−0.772187	+	0.635396i	$0.780837\pi$
$230$	−8.58800	−	2.06798i	−0.566276	−	0.136358i
$231$		0			0
$232$	−3.31534	−	2.84329i	−0.217663	−	0.186671i
$233$			19.8188i			1.29837i	0.760629	+	0.649187i	$0.224891\pi$
$233$			19.8188i			1.29837i	−0.760629	+	0.649187i	$0.775109\pi$
$234$		0			0
$235$	−12.0000			−0.782794
$236$	−21.2755	−	10.8769i	−1.38492	−	0.708026i
$237$		0			0
$238$	−1.69614	+	7.04383i	−0.109944	+	0.456584i
$239$	7.91096			0.511718			0.255859	−	0.966714i	$-0.417642\pi$
$239$	7.91096			0.511718			0.255859	+	0.966714i	$0.417642\pi$
$240$		0			0
$241$			18.9103i			1.21812i	0.793125	+	0.609059i	$0.208453\pi$
$241$			18.9103i			1.21812i	−0.793125	+	0.609059i	$0.791547\pi$
$242$	3.81088	−	15.0823i	0.244972	−	0.969530i
$243$		0			0
$244$	14.4401	+	7.38235i	0.924432	+	0.472606i
$245$		−	4.24621i		−	0.271280i
$246$		0			0
$247$		−	9.32819i		−	0.593539i
$248$	15.2933	−	17.8324i	0.971126	−	1.13236i
$249$		0			0
$250$	−3.97292	+	16.4990i	−0.251270	+	1.04349i
$251$	16.6114			1.04850			0.524252	−	0.851563i	$-0.324345\pi$
$251$	16.6114			1.04850			0.524252	+	0.851563i	$0.324345\pi$
$252$		0			0
$253$	7.36520	−	7.28323i	0.463046	−	0.457893i
$254$	−3.13038	−	0.753789i	−0.196417	−	0.0472969i
$255$		0			0
$256$	−5.02699	+	15.1898i	−0.314187	+	0.949361i
$257$	25.9396			1.61807			0.809034	−	0.587761i	$-0.199991\pi$
$257$	25.9396			1.61807			0.809034	+	0.587761i	$0.199991\pi$
$258$		0			0
$259$			14.0877i			0.875364i
$260$	−2.41131	+	4.71659i	−0.149543	+	0.292510i
$261$		0			0
$262$	1.31534	−	5.46242i	0.0812621	−	0.337470i
$263$	−20.2644			−1.24955			−0.624777	−	0.780803i	$-0.714810\pi$
$263$	−20.2644			−1.24955			−0.624777	+	0.780803i	$0.714810\pi$
$264$		0			0
$265$	16.4924			1.01312
$266$	−7.04383	+	29.2520i	−0.431885	+	1.79356i
$267$		0			0
$268$	11.1231	+	5.68658i	0.679452	+	0.347363i
$269$			16.2462i			0.990549i	0.868737	+	0.495274i	$0.164933\pi$
$269$			16.2462i			0.990549i	−0.868737	+	0.495274i	$0.835067\pi$
$270$		0			0
$271$	−6.41273			−0.389546			−0.194773	−	0.980848i	$-0.562397\pi$
$271$	−6.41273			−0.389546			−0.194773	+	0.980848i	$0.562397\pi$
$272$	−5.49966	+	3.97292i	−0.333466	+	0.240894i
$273$		0			0
$274$	−10.0138	−	2.41131i	−0.604957	−	0.145672i
$275$	−2.33205	−	2.35829i	−0.140628	−	0.142211i
$276$		0			0
$277$	4.71659			0.283392			0.141696	−	0.989910i	$-0.454744\pi$
$277$	4.71659			0.283392			0.141696	+	0.989910i	$0.454744\pi$
$278$	−1.30957	+	5.43845i	−0.0785427	+	0.326176i
$279$		0			0
$280$	11.1231	−	12.9698i	0.664733	−	0.775094i
$281$		−	15.6829i		−	0.935562i	−0.883844	−	0.467781i	$-0.845054\pi$
$281$		−	15.6829i		−	0.935562i	0.883844	−	0.467781i	$-0.154946\pi$
$282$		0			0
$283$			14.9548i			0.888970i	0.895786	+	0.444485i	$0.146613\pi$
$283$			14.9548i			0.888970i	−0.895786	+	0.444485i	$0.853387\pi$
$284$	−11.1490	+	21.8078i	−0.661571	+	1.29405i
$285$		0			0
$286$	−3.21222	−	5.31648i	−0.189943	−	0.314370i
$287$		−	23.3693i		−	1.37945i
$288$		0			0
$289$	14.1231			0.830771
$290$	−1.02248	+	4.24621i	−0.0600421	+	0.249346i
$291$		0			0
$292$	2.81164	−	5.49966i	0.164539	−	0.321843i
$293$	−6.36679			−0.371952			−0.185976	−	0.982554i	$-0.559545\pi$
$293$	−6.36679			−0.371952			−0.185976	+	0.982554i	$0.559545\pi$
$294$		0			0
$295$			23.8947i			1.39120i
$296$	−8.58800	+	10.0138i	−0.499168	+	0.582041i
$297$		0			0
$298$	−17.2462	−	4.15286i	−0.999046	−	0.240568i
$299$		−	4.13595i		−	0.239188i
$300$		0			0
$301$			11.9473i			0.688633i
$302$	9.83943	+	2.36932i	0.566196	+	0.136339i
$303$		0			0
$304$	−22.8393	+	16.4990i	−1.30992	+	0.946281i
$305$		−	16.2177i		−	0.928625i
$306$		0			0
$307$		−	18.0431i		−	1.02978i	−0.857257	−	0.514888i	$-0.827833\pi$
$307$		−	18.0431i		−	1.02978i	0.857257	−	0.514888i	$-0.172167\pi$
$308$	6.05858	+	19.0974i	0.345220	+	1.08817i
$309$		0			0
$310$	−22.8393	−	5.49966i	−1.29718	−	0.312359i
$311$			4.87689i			0.276543i	0.990394	+	0.138272i	$0.0441547\pi$
$311$			4.87689i			0.276543i	−0.990394	+	0.138272i	$0.955845\pi$
$312$		0			0
$313$	3.12311			0.176528			0.0882642	−	0.996097i	$-0.471868\pi$
$313$	3.12311			0.176528			0.0882642	+	0.996097i	$0.471868\pi$
$314$	−2.41131	+	10.0138i	−0.136078	+	0.565112i
$315$		0			0
$316$	−22.1771	−	11.3378i	−1.24756	−	0.637803i
$317$		−	10.4924i		−	0.589313i	−0.955603	−	0.294657i	$-0.904795\pi$
$317$		−	10.4924i		−	0.589313i	0.955603	−	0.294657i	$-0.0952053\pi$
$318$		0			0
$319$	−3.60109	−	3.64162i	−0.201622	−	0.203891i
$320$	15.8131	−	2.43845i	0.883979	−	0.136313i
$321$		0			0
$322$	−3.12311	+	12.9698i	−0.174044	+	0.722779i
$323$	−11.9473			−0.664767
$324$		0			0
$325$	−1.32431			−0.0734593
$326$	28.1753	+	6.78456i	1.56049	+	0.375762i
$327$		0			0
$328$	14.2462	−	16.6114i	0.786615	−	0.917212i
$329$			18.1227i			0.999136i
$330$		0			0
$331$	18.2462			1.00290			0.501451	−	0.865186i	$-0.332800\pi$
$331$	18.2462			1.00290			0.501451	+	0.865186i	$0.332800\pi$
$332$	−4.29400	+	8.39919i	−0.235664	+	0.460965i
$333$		0			0
$334$	19.3693	+	4.66410i	1.05984	+	0.255208i
$335$		−	12.4924i		−	0.682534i
$336$		0			0
$337$			31.2637i			1.70304i	0.524322	+	0.851520i	$0.324319\pi$
$337$			31.2637i			1.70304i	−0.524322	+	0.851520i	$0.675681\pi$
$338$	15.4626	+	3.72336i	0.841053	+	0.202524i
$339$		0			0
$340$	6.04090	+	3.08835i	0.327614	+	0.167489i
$341$	19.5873	−	19.3693i	1.06071	−	1.04891i
$342$		0			0
$343$	14.7304			0.795367
$344$	−7.28323	+	8.49242i	−0.392686	+	0.457881i
$345$		0			0
$346$	17.2462	+	4.15286i	0.927162	+	0.223259i
$347$		−	20.9343i		−	1.12381i	−0.827200	−	0.561907i	$-0.810068\pi$
$347$		−	20.9343i		−	1.12381i	0.827200	−	0.561907i	$-0.189932\pi$
$348$		0			0
$349$	−15.3110			−0.819581			−0.409791	−	0.912180i	$-0.634398\pi$
$349$	−15.3110			−0.819581			−0.409791	+	0.912180i	$0.634398\pi$
$350$	4.15286	+	1.00000i	0.221979	+	0.0534522i
$351$		0			0
$352$	−7.33542	+	17.2682i	−0.390979	+	0.920399i
$353$	9.32819			0.496490			0.248245	−	0.968697i	$-0.420146\pi$
$353$	9.32819			0.496490			0.248245	+	0.968697i	$0.420146\pi$
$354$		0			0
$355$	24.4924			1.29992
$356$	−29.5812	−	15.1231i	−1.56780	−	0.801523i
$357$		0			0
$358$		0			0
$359$	36.0863			1.90456			0.952281	−	0.305224i	$-0.0987314\pi$
$359$	36.0863			1.90456			0.952281	+	0.305224i	$0.0987314\pi$
$360$		0			0
$361$	−30.6155			−1.61134
$362$	−8.58800	+	35.6647i	−0.451375	+	1.87450i
$363$		0			0
$364$	7.12311	+	3.64162i	0.373352	+	0.190873i
$365$	−6.17669			−0.323303
$366$		0			0
$367$			6.26075i			0.326809i	0.986559	+	0.163404i	$0.0522475\pi$
$367$			6.26075i			0.326809i	−0.986559	+	0.163404i	$0.947753\pi$
$368$	−10.1265	+	7.31534i	−0.527881	+	0.381339i
$369$		0			0
$370$	12.8255	+	3.08835i	0.666764	+	0.160556i
$371$		−	24.9073i		−	1.29312i
$372$		0			0
$373$	−23.5829			−1.22108			−0.610539	−	0.791986i	$-0.709047\pi$
$373$	−23.5829			−1.22108			−0.610539	+	0.791986i	$0.709047\pi$
$374$	−6.80922	+	4.11414i	−0.352097	+	0.212737i
$375$		0			0
$376$	−11.0478	+	12.8820i	−0.569747	+	0.664339i
$377$	−2.04496			−0.105321
$378$		0			0
$379$	2.24621			0.115380			0.0576901	−	0.998335i	$-0.481626\pi$
$379$	2.24621			0.115380			0.0576901	+	0.998335i	$0.481626\pi$
$380$	25.0870	+	12.8255i	1.28693	+	0.657932i
$381$		0			0
$382$	−1.40582	+	5.83817i	−0.0719281	+	0.298707i
$383$			25.3693i			1.29631i	0.761508	+	0.648156i	$0.224459\pi$
$383$			25.3693i			1.29631i	−0.761508	+	0.648156i	$0.775541\pi$
$384$		0			0
$385$	14.2462	−	14.0877i	0.726054	−	0.717974i
$386$	−8.30571	+	34.4924i	−0.422750	+	1.75562i
$387$		0			0
$388$	−23.8078	−	12.1715i	−1.20866	−	0.617913i
$389$		−	2.49242i		−	0.126371i	−0.998002	−	0.0631854i	$-0.979874\pi$
$389$		−	2.49242i		−	0.126371i	0.998002	−	0.0631854i	$-0.0201260\pi$
$390$		0			0
$391$	−5.29723			−0.267892
$392$	−4.55831	−	3.90928i	−0.230229	−	0.197448i
$393$		0			0
$394$	21.4924	+	5.17534i	1.08277	+	0.260730i
$395$			24.9073i			1.25322i
$396$		0			0
$397$			13.9923i			0.702253i	0.936328	+	0.351126i	$0.114201\pi$
$397$			13.9923i			0.702253i	−0.936328	+	0.351126i	$0.885799\pi$
$398$	0.338519	−	1.40582i	0.0169684	−	0.0704675i
$399$		0			0
$400$	2.34233	+	3.24245i	0.117116	+	0.162123i
$401$	18.6564			0.931655			0.465828	−	0.884875i	$-0.345757\pi$
$401$	18.6564			0.931655			0.465828	+	0.884875i	$0.345757\pi$
$402$		0			0
$403$		−	10.9993i		−	0.547915i
$404$	−2.74983	−	1.40582i	−0.136809	−	0.0699422i
$405$		0			0
$406$	6.41273	+	1.54417i	0.318258	+	0.0766360i
$407$	−10.9993	+	10.8769i	−0.545216	+	0.539148i
$408$		0			0
$409$			6.17669i			0.305418i	0.988271	+	0.152709i	$0.0487997\pi$
$409$			6.17669i			0.305418i	−0.988271	+	0.152709i	$0.951200\pi$
$410$	−21.2755	−	5.12311i	−1.05072	−	0.253012i
$411$		0			0
$412$	−7.56155	+	14.7906i	−0.372531	+	0.728681i
$413$	36.0863			1.77569
$414$		0			0
$415$	9.43318			0.463056
$416$	2.84329	+	6.93087i	0.139404	+	0.339814i
$417$		0			0
$418$	−28.2777	+	17.0854i	−1.38311	+	0.835676i
$419$	16.6114			0.811521			0.405761	−	0.913979i	$-0.367007\pi$
$419$	16.6114			0.811521			0.405761	+	0.913979i	$0.367007\pi$
$420$		0			0
$421$		−	7.28323i		−	0.354963i	−0.984124	−	0.177481i	$-0.943205\pi$
$421$		−	7.28323i		−	0.354963i	0.984124	−	0.177481i	$-0.0567950\pi$
$422$	2.33205	−	9.68466i	0.113522	−	0.471442i
$423$		0			0
$424$	15.1838	−	17.7046i	0.737388	−	0.859812i
$425$			1.69614i			0.0822749i
$426$		0			0
$427$	−24.4924			−1.18527
$428$	−7.38235	+	14.4401i	−0.356839	+	0.697988i
$429$		0			0
$430$	10.8769	+	2.61914i	0.524530	+	0.126306i
$431$	−28.1753			−1.35716			−0.678579	−	0.734528i	$-0.737404\pi$
$431$	−28.1753			−1.35716			−0.678579	+	0.734528i	$0.737404\pi$
$432$		0			0
$433$	−15.1231			−0.726770			−0.363385	−	0.931639i	$-0.618379\pi$
$433$	−15.1231			−0.726770			−0.363385	+	0.931639i	$0.618379\pi$
$434$	−8.30571	+	34.4924i	−0.398687	+	1.65569i
$435$		0			0
$436$	29.9142	+	15.2933i	1.43263	+	0.732417i
$437$	−21.9986			−1.05234
$438$		0			0
$439$	−23.0481			−1.10002			−0.550012	−	0.835156i	$-0.685377\pi$
$439$	−23.0481			−1.10002			−0.550012	+	0.835156i	$0.685377\pi$
$440$	18.7145	−	1.32916i	0.892180	−	0.0633651i
$441$		0			0
$442$	−0.743668	+	3.08835i	−0.0353727	+	0.146898i
$443$	4.66410			0.221598			0.110799	−	0.993843i	$-0.464659\pi$
$443$	4.66410			0.221598			0.110799	+	0.993843i	$0.464659\pi$
$444$		0			0
$445$			33.2228i			1.57491i
$446$	3.42687	−	14.2313i	0.162267	−	0.673871i
$447$		0			0
$448$	−3.68260	−	23.8813i	−0.173987	−	1.12829i
$449$	2.04496			0.0965076			0.0482538	−	0.998835i	$-0.484634\pi$
$449$	2.04496			0.0965076			0.0482538	+	0.998835i	$0.484634\pi$
$450$		0			0
$451$	18.2462	−	18.0431i	0.859181	−	0.849618i
$452$	−12.9698	−	6.63068i	−0.610048	−	0.311881i
$453$		0			0
$454$	−8.19224	+	34.0212i	−0.384481	+	1.59669i
$455$		−	8.00000i		−	0.375046i
$456$		0			0
$457$			28.1753i			1.31799i	0.752149	+	0.658993i	$0.229017\pi$
$457$			28.1753i			1.31799i	−0.752149	+	0.658993i	$0.770983\pi$
$458$	6.36679	−	26.4404i	0.297501	−	1.23548i
$459$		0			0
$460$	11.1231	+	5.68658i	0.518617	+	0.265138i
$461$	−32.8078			−1.52801			−0.764007	−	0.645208i	$-0.776771\pi$
$461$	−32.8078			−1.52801			−0.764007	+	0.645208i	$0.776771\pi$
$462$		0			0
$463$		−	34.2453i		−	1.59152i	−0.605615	−	0.795758i	$-0.707073\pi$
$463$		−	34.2453i		−	1.59152i	0.605615	−	0.795758i	$-0.292927\pi$
$464$	3.61696	+	5.00691i	0.167913	+	0.232440i
$465$		0			0
$466$	6.56155	−	27.2492i	0.303958	−	1.26229i
$467$	−4.66410			−0.215829			−0.107914	−	0.994160i	$-0.534417\pi$
$467$	−4.66410			−0.215829			−0.107914	+	0.994160i	$0.534417\pi$
$468$		0			0
$469$	−18.8664			−0.871167
$470$	16.4990	+	3.97292i	0.761041	+	0.183257i
$471$		0			0
$472$	25.6509	+	21.9986i	1.18068	+	1.01257i
$473$	−9.32819	+	9.22437i	−0.428911	+	0.424137i
$474$		0			0
$475$			7.04383i			0.323193i
$476$	4.66410	−	9.12311i	0.213778	−	0.418157i
$477$		0			0
$478$	−10.8769	−	2.61914i	−0.497498	−	0.119796i
$479$	−21.9986			−1.00514			−0.502571	−	0.864536i	$-0.667613\pi$
$479$	−21.9986			−1.00514			−0.502571	+	0.864536i	$0.667613\pi$
$480$		0			0
$481$			6.17669i			0.281633i
$482$	6.26075	−	26.0000i	0.285169	−	1.18427i
$483$		0			0
$484$	−10.2330	+	19.4752i	−0.465138	+	0.885238i
$485$			26.7386i			1.21414i
$486$		0			0
$487$		−	32.2004i		−	1.45914i	−0.683907	−	0.729569i	$-0.739721\pi$
$487$		−	32.2004i		−	1.45914i	0.683907	−	0.729569i	$-0.260279\pi$
$488$	−17.4098	−	14.9309i	−0.788102	−	0.675889i
$489$		0			0
$490$	−1.40582	+	5.83817i	−0.0635086	+	0.263742i
$491$		−	9.27015i		−	0.418356i	−0.977878	−	0.209178i	$-0.932921\pi$
$491$		−	9.27015i		−	0.418356i	0.977878	−	0.209178i	$-0.0670788\pi$
$492$		0			0
$493$			2.61914i			0.117960i
$494$	−3.08835	+	12.8255i	−0.138951	+	0.577045i
$495$		0			0
$496$	−26.9309	+	19.4547i	−1.20923	+	0.873542i
$497$		−	36.9890i		−	1.65919i
$498$		0			0
$499$	−14.7386			−0.659792			−0.329896	−	0.944017i	$-0.607014\pi$
$499$	−14.7386			−0.659792			−0.329896	+	0.944017i	$0.607014\pi$
$500$	10.9248	−	21.3693i	0.488574	−	0.955665i
$501$		0			0
$502$	−22.8393	−	5.49966i	−1.01937	−	0.245462i
$503$	28.1753			1.25628			0.628138	−	0.778102i	$-0.283817\pi$
$503$	28.1753			1.25628			0.628138	+	0.778102i	$0.283817\pi$
$504$		0			0
$505$			3.08835i			0.137430i
$506$	−12.5378	+	7.57537i	−0.557374	+	0.336766i
$507$		0			0
$508$	4.05444	+	2.07279i	0.179886	+	0.0919652i
$509$		−	10.0000i		−	0.443242i	−0.975133	−	0.221621i	$-0.928865\pi$
$509$		−	10.0000i		−	0.443242i	0.975133	−	0.221621i	$-0.0711348\pi$
$510$		0			0
$511$			9.32819i			0.412655i
$512$	11.9407	−	19.2203i	0.527707	−	0.849426i
$513$		0			0
$514$	−35.6647	−	8.58800i	−1.57310	−	0.378801i
$515$	16.6114			0.731987
$516$		0			0
$517$	−14.1498	+	13.9923i	−0.622306	+	0.615380i
$518$	4.66410	−	19.3693i	0.204929	−	0.851039i
$519$		0			0
$520$	4.87689	−	5.68658i	0.213866	−	0.249373i
$521$	−18.6564			−0.817351			−0.408675	−	0.912680i	$-0.634009\pi$
$521$	−18.6564			−0.817351			−0.408675	+	0.912680i	$0.634009\pi$
$522$		0			0
$523$			25.9541i			1.13489i	0.823410	+	0.567447i	$0.192069\pi$
$523$			25.9541i			1.13489i	−0.823410	+	0.567447i	$0.807931\pi$
$524$	−3.61696	+	7.07488i	−0.158008	+	0.309068i
$525$		0			0
$526$	27.8617	+	6.70906i	1.21483	+	0.292529i
$527$	−14.0877			−0.613668
$528$		0			0
$529$	13.2462			0.575922
$530$	−22.6757	−	5.46026i	−0.984968	−	0.237178i
$531$		0			0
$532$	19.3693	−	37.8869i	0.839766	−	1.64261i
$533$		−	10.2462i		−	0.443813i
$534$		0			0
$535$	16.2177			0.701154
$536$	−13.4106	−	11.5012i	−0.579251	−	0.496774i
$537$		0			0
$538$	5.37874	−	22.3371i	0.231894	−	0.963023i
$539$	−4.95118	−	5.00691i	−0.213263	−	0.215663i
$540$		0			0
$541$	10.0138			0.430528			0.215264	−	0.976556i	$-0.430939\pi$
$541$	10.0138			0.430528			0.215264	+	0.976556i	$0.430939\pi$
$542$	8.81695	+	2.12311i	0.378720	+	0.0911952i
$543$		0			0
$544$	8.87689	−	3.64162i	0.380594	−	0.156133i
$545$		−	33.5968i		−	1.43913i
$546$		0			0
$547$			0.867135i			0.0370760i	0.999828	+	0.0185380i	$0.00590117\pi$
$547$			0.867135i			0.0370760i	−0.999828	+	0.0185380i	$0.994099\pi$
$548$	12.9698	+	6.63068i	0.554043	+	0.283249i
$549$		0			0
$550$	2.42559	+	4.01454i	0.103427	+	0.171181i
$551$			10.8769i			0.463371i
$552$		0			0
$553$	37.6155			1.59957
$554$	−6.48490	−	1.56155i	−0.275517	−	0.0663440i
$555$		0			0
$556$	3.60109	−	7.04383i	0.152720	−	0.298725i
$557$	−28.3654			−1.20188			−0.600941	−	0.799294i	$-0.705207\pi$
$557$	−28.3654			−1.20188			−0.600941	+	0.799294i	$0.705207\pi$
$558$		0			0
$559$			5.23827i			0.221555i
$560$	−19.5873	+	14.1498i	−0.827715	+	0.597937i
$561$		0			0
$562$	−5.19224	+	21.5626i	−0.219021	+	0.909564i
$563$			38.3134i			1.61472i	0.590062	+	0.807358i	$0.299103\pi$
$563$			38.3134i			1.61472i	−0.590062	+	0.807358i	$0.700897\pi$
$564$		0			0
$565$			14.5665i			0.612816i
$566$	4.95118	−	20.5616i	0.208114	−	0.864267i
$567$		0			0
$568$	22.5490	−	26.2926i	0.946133	−	1.10321i
$569$			24.3724i			1.02174i	0.859657	+	0.510872i	$0.170677\pi$
$569$			24.3724i			1.02174i	−0.859657	+	0.510872i	$0.829323\pi$
$570$		0			0
$571$		−	10.1322i		−	0.424018i	−0.977268	−	0.212009i	$-0.931999\pi$
$571$		−	10.1322i		−	0.424018i	0.977268	−	0.212009i	$-0.0680007\pi$
$572$	2.65637	+	8.37320i	0.111068	+	0.350101i
$573$		0			0
$574$	−7.73704	+	32.1308i	−0.322938	+	1.34111i
$575$			3.12311i			0.130243i
$576$		0			0
$577$	−8.24621			−0.343294			−0.171647	−	0.985158i	$-0.554909\pi$
$577$	−8.24621			−0.343294			−0.171647	+	0.985158i	$0.554909\pi$
$578$	−19.4181	−	4.67583i	−0.807685	−	0.194489i
$579$		0			0
$580$	2.81164	−	5.49966i	0.116747	−	0.228361i
$581$		−	14.2462i		−	0.591032i
$582$		0			0
$583$	19.4470	−	19.2306i	0.805412	−	0.796448i
$584$	−5.68658	+	6.63068i	−0.235312	+	0.274380i
$585$		0			0
$586$	8.75379	+	2.10790i	0.361616	+	0.0870764i
$587$	26.5138			1.09434			0.547171	−	0.837021i	$-0.315705\pi$
$587$	26.5138			1.09434			0.547171	+	0.837021i	$0.315705\pi$
$588$		0			0
$589$	−58.5040			−2.41062
$590$	7.91096	−	32.8531i	0.325689	−	1.35254i
$591$		0			0
$592$	15.1231	−	10.9248i	0.621556	−	0.449008i
$593$			19.0752i			0.783323i	0.920109	+	0.391661i	$0.128100\pi$
$593$			19.0752i			0.783323i	−0.920109	+	0.391661i	$0.871900\pi$
$594$		0			0
$595$	−10.2462			−0.420054
$596$	22.3371	+	11.4196i	0.914965	+	0.467767i
$597$		0			0
$598$	−1.36932	+	5.68658i	−0.0559955	+	0.232541i
$599$		−	33.3693i		−	1.36343i	−0.731616	−	0.681717i	$-0.761234\pi$
$599$		−	33.3693i		−	1.36343i	0.731616	−	0.681717i	$-0.238766\pi$
$600$		0			0
$601$		−	31.2637i		−	1.27527i	−0.770338	−	0.637636i	$-0.779913\pi$
$601$		−	31.2637i		−	1.27527i	0.770338	−	0.637636i	$-0.220087\pi$
$602$	3.95548	−	16.4265i	0.161213	−	0.669496i
$603$		0			0
$604$	−12.7439	−	6.51521i	−0.518544	−	0.265100i
$605$	21.9986	+	0.246211i	0.894371	+	0.0100099i
$606$		0			0
$607$	32.8073			1.33161			0.665804	−	0.746127i	$-0.268089\pi$
$607$	32.8073			1.33161			0.665804	+	0.746127i	$0.268089\pi$
$608$	36.8645	−	15.1231i	1.49505	−	0.613323i
$609$		0			0
$610$	−5.36932	+	22.2980i	−0.217397	+	0.902820i
$611$			7.94584i			0.321454i
$612$		0			0
$613$	18.7033			0.755420			0.377710	−	0.925924i	$-0.376712\pi$
$613$	18.7033			0.755420			0.377710	+	0.925924i	$0.376712\pi$
$614$	−5.97366	+	24.8078i	−0.241077	+	1.00116i
$615$		0			0
$616$	−2.00733	−	28.2631i	−0.0808775	−	1.13875i
$617$	−11.3732			−0.457866			−0.228933	−	0.973442i	$-0.573524\pi$
$617$	−11.3732			−0.457866			−0.228933	+	0.973442i	$0.573524\pi$
$618$		0			0
$619$	24.4924			0.984434			0.492217	−	0.870473i	$-0.336187\pi$
$619$	24.4924			0.984434			0.492217	+	0.870473i	$0.336187\pi$
$620$	29.5812	+	15.1231i	1.18801	+	0.607359i
$621$		0			0
$622$	1.61463	−	6.70531i	0.0647406	−	0.268858i
$623$	50.1739			2.01018
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−4.29400	−	1.03399i	−0.171623	−	0.0413265i
$627$		0			0
$628$	6.63068	−	12.9698i	0.264593	−	0.517552i
$629$	7.91096			0.315431
$630$		0			0
$631$		−	10.3507i		−	0.412054i	−0.978546	−	0.206027i	$-0.933947\pi$
$631$		−	10.3507i		−	0.412054i	0.978546	−	0.206027i	$-0.0660534\pi$
$632$	26.7379	+	22.9309i	1.06358	+	0.912141i
$633$		0			0
$634$	−3.47380	+	14.4262i	−0.137962	+	0.572937i
$635$		−	4.55356i		−	0.180702i
$636$		0			0
$637$	−2.81164			−0.111401
$638$	3.74553	+	6.19914i	0.148287	+	0.245426i
$639$		0			0
$640$	−22.5490	−	1.88269i	−0.891326	−	0.0744200i
$641$	42.5510			1.68066			0.840332	−	0.542071i	$-0.182360\pi$
$641$	42.5510			1.68066			0.840332	+	0.542071i	$0.182360\pi$
$642$		0			0
$643$	−28.9848			−1.14305			−0.571525	−	0.820584i	$-0.693648\pi$
$643$	−28.9848			−1.14305			−0.571525	+	0.820584i	$0.693648\pi$
$644$	8.58800	−	16.7984i	0.338415	−	0.661949i
$645$		0			0
$646$	16.4265	+	3.95548i	0.646294	+	0.155626i
$647$		−	36.8769i		−	1.44978i	−0.688864	−	0.724890i	$-0.741890\pi$
$647$		−	36.8769i		−	1.44978i	0.688864	−	0.724890i	$-0.258110\pi$
$648$		0			0
$649$	27.8617	+	28.1753i	1.09367	+	1.10598i
$650$	1.82081	+	0.438447i	0.0714180	+	0.0171973i
$651$		0			0
$652$	−36.4924	−	18.6564i	−1.42915	−	0.730640i
$653$			42.9848i			1.68213i	0.540936	+	0.841063i	$0.318070\pi$
$653$			42.9848i			1.68213i	−0.540936	+	0.841063i	$0.681930\pi$
$654$		0			0
$655$	7.94584			0.310470
$656$	−25.0870	+	18.1227i	−0.979482	+	0.707572i
$657$		0			0
$658$	6.00000	−	24.9171i	0.233904	−	0.971371i
$659$			10.7575i			0.419052i	0.977803	+	0.209526i	$0.0671921\pi$
$659$			10.7575i			0.419052i	−0.977803	+	0.209526i	$0.932808\pi$
$660$		0			0
$661$			11.3732i			0.442364i	0.975233	+	0.221182i	$0.0709915\pi$
$661$			11.3732i			0.442364i	−0.975233	+	0.221182i	$0.929008\pi$
$662$	−25.0870	−	6.04090i	−0.975033	−	0.234786i
$663$		0			0
$664$	8.68466	−	10.1265i	0.337030	−	0.392985i
$665$	−42.5510			−1.65006
$666$		0			0
$667$			4.82262i			0.186732i
$668$	−25.0870	−	12.8255i	−0.970644	−	0.496232i
$669$		0			0
$670$	−4.13595	+	17.1760i	−0.159786	+	0.663567i
$671$	−18.9103	−	19.1231i	−0.730023	−	0.738239i
$672$		0			0
$673$		−	21.9986i		−	0.847985i	−0.905666	−	0.423992i	$-0.860628\pi$
$673$		−	21.9986i		−	0.847985i	0.905666	−	0.423992i	$-0.139372\pi$
$674$	10.3507	−	42.9848i	0.398693	−	1.65571i
$675$		0			0
$676$	−20.0270	−	10.2386i	−0.770269	−	0.393792i
$677$	34.5421			1.32756			0.663781	−	0.747927i	$-0.268951\pi$
$677$	34.5421			1.32756			0.663781	+	0.747927i	$0.268951\pi$
$678$		0			0
$679$	40.3813			1.54969
$680$	−7.28323	−	6.24621i	−0.279299	−	0.239531i
$681$		0			0
$682$	−33.3436	+	20.1462i	−1.27679	+	0.771439i
$683$	−49.8343			−1.90686			−0.953428	−	0.301622i	$-0.902472\pi$
$683$	−49.8343			−1.90686			−0.953428	+	0.301622i	$0.902472\pi$
$684$		0			0
$685$		−	14.5665i		−	0.556556i
$686$	−20.2530	−	4.87689i	−0.773265	−	0.186201i
$687$		0			0
$688$	12.8255	−	9.26504i	0.488966	−	0.353226i
$689$		−	10.9205i		−	0.416038i
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	−22.3371	−	11.4196i	−0.849131	−	0.434110i
$693$		0			0
$694$	−6.93087	+	28.7829i	−0.263092	+	1.09258i
$695$	−7.91096			−0.300080
$696$		0			0
$697$	−13.1231			−0.497073
$698$	21.0514	+	5.06913i	0.796806	+	0.191869i
$699$		0			0
$700$	−5.37874	−	2.74983i	−0.203297	−	0.103934i
$701$	−6.36679			−0.240470			−0.120235	−	0.992745i	$-0.538365\pi$
$701$	−6.36679			−0.240470			−0.120235	+	0.992745i	$0.538365\pi$
$702$		0			0
$703$	32.8531			1.23908
$704$	15.8027	−	21.3137i	0.595586	−	0.803292i
$705$		0			0
$706$	−12.8255	−	3.08835i	−0.482693	−	0.116231i
$707$	4.66410			0.175411
$708$		0			0
$709$			13.9923i			0.525491i	0.964865	+	0.262746i	$0.0846280\pi$
$709$			13.9923i			0.525491i	−0.964865	+	0.262746i	$0.915372\pi$
$710$	−33.6750	−	8.10887i	−1.26380	−	0.304321i
$711$		0			0
$712$	35.6647	+	30.5866i	1.33659	+	1.14628i
$713$	−25.9396			−0.971446
$714$		0			0
$715$	6.24621	−	6.17669i	0.233595	−	0.230995i
$716$		0			0
$717$		0			0
$718$	−49.6155	−	11.9473i	−1.85164	−	0.445870i
$719$			50.9848i			1.90141i	0.310091	+	0.950707i	$0.399641\pi$
$719$			50.9848i			1.90141i	−0.310091	+	0.950707i	$0.600359\pi$
$720$		0			0
$721$		−	25.0870i		−	0.934288i
$722$	42.0937	+	10.1361i	1.56657	+	0.377226i
$723$		0			0
$724$	23.6155	−	46.1927i	0.877664	−	1.71674i
$725$	1.54417			0.0573492
$726$		0			0
$727$			1.02248i			0.0379217i	0.999820	+	0.0189608i	$0.00603578\pi$
$727$			1.02248i			0.0379217i	−0.999820	+	0.0189608i	$0.993964\pi$
$728$	−8.58800	−	7.36520i	−0.318293	−	0.272973i
$729$		0			0
$730$	8.49242	+	2.04496i	0.314319	+	0.0756874i
$731$	6.70906			0.248143
$732$		0			0
$733$	−15.6371			−0.577570			−0.288785	−	0.957394i	$-0.593251\pi$
$733$	−15.6371			−0.577570			−0.288785	+	0.957394i	$0.593251\pi$
$734$	2.07279	−	8.60799i	0.0765080	−	0.317727i
$735$		0			0
$736$	16.3450	−	6.70531i	0.602486	−	0.247161i
$737$	−14.5665	−	14.7304i	−0.536563	−	0.542601i
$738$		0			0
$739$		−	35.2191i		−	1.29556i	−0.761829	−	0.647779i	$-0.775698\pi$
$739$		−	35.2191i		−	1.29556i	0.761829	−	0.647779i	$-0.224302\pi$
$740$	−16.6114	−	8.49242i	−0.610648	−	0.312188i
$741$		0			0
$742$	−8.24621	+	34.2453i	−0.302728	+	1.25719i
$743$	−15.8219			−0.580450			−0.290225	−	0.956958i	$-0.593730\pi$
$743$	−15.8219			−0.580450			−0.290225	+	0.956958i	$0.593730\pi$
$744$		0			0
$745$		−	25.0870i		−	0.919115i
$746$	32.4245	+	7.80776i	1.18715	+	0.285863i
$747$		0			0
$748$	10.7242	−	3.40221i	0.392115	−	0.124397i
$749$		−	24.4924i		−	0.894934i
$750$		0			0
$751$		−	48.8118i		−	1.78117i	−0.454819	−	0.890584i	$-0.650296\pi$
$751$		−	48.8118i		−	1.78117i	0.454819	−	0.890584i	$-0.349704\pi$
$752$	19.4547	−	14.0540i	0.709440	−	0.512496i
$753$		0			0
$754$	2.81164	+	0.677039i	0.102394	+	0.0246563i
$755$			14.3128i			0.520896i
$756$		0			0
$757$			40.5061i			1.47222i	0.676863	+	0.736109i	$0.263339\pi$
$757$			40.5061i			1.47222i	−0.676863	+	0.736109i	$0.736661\pi$
$758$	−3.08835	−	0.743668i	−0.112174	−	0.0270112i
$759$		0			0
$760$	−30.2462	−	25.9396i	−1.09715	−	0.940929i
$761$			42.8211i			1.55226i	0.630570	+	0.776132i	$0.282821\pi$
$761$			42.8211i			1.55226i	−0.630570	+	0.776132i	$0.717179\pi$
$762$		0			0
$763$	−50.7386			−1.83686
$764$	3.86577	−	7.56155i	0.139859	−	0.273567i
$765$		0			0
$766$	8.39919	−	34.8806i	0.303475	−	1.26029i
$767$	15.8219			0.571297
$768$		0			0
$769$			9.26504i			0.334106i	0.985948	+	0.167053i	$0.0534251\pi$
$769$			9.26504i			0.334106i	−0.985948	+	0.167053i	$0.946575\pi$
$770$	−24.2514	+	14.6527i	−0.873960	+	0.528048i
$771$		0			0
$772$	22.8393	−	44.6743i	0.822004	−	1.60786i
$773$			33.2311i			1.19524i	0.801780	+	0.597619i	$0.203886\pi$
$773$			33.2311i			1.19524i	−0.801780	+	0.597619i	$0.796114\pi$
$774$		0			0
$775$			8.30571i			0.298350i
$776$	28.7039	+	24.6169i	1.03041	+	0.883696i
$777$		0			0
$778$	−0.825183	+	3.42687i	−0.0295842	+	0.122859i
$779$	−54.4984			−1.95261
$780$		0			0
$781$	28.8802	−	28.5588i	1.03341	−	1.02191i
$782$	7.28323	+	1.75379i	0.260448	+	0.0627154i
$783$		0			0
$784$	4.97301	+	6.88407i	0.177608	+	0.245860i
$785$	−14.5665			−0.519899
$786$		0			0
$787$		−	30.3965i		−	1.08352i	−0.840533	−	0.541760i	$-0.817758\pi$
$787$		−	30.3965i		−	1.08352i	0.840533	−	0.541760i	$-0.182242\pi$
$788$	−27.8368	−	14.2313i	−0.991645	−	0.506968i
$789$		0			0
$790$	8.24621	−	34.2453i	0.293387	−	1.21839i
$791$	21.9986			0.782181
$792$		0			0
$793$	−10.7386			−0.381340
$794$	4.63252	−	19.2382i	0.164402	−	0.682738i
$795$		0			0
$796$	−0.930870	+	1.82081i	−0.0329938	+	0.0645368i
$797$		−	28.2462i		−	1.00053i	−0.865872	−	0.500266i	$-0.833236\pi$
$797$		−	28.2462i		−	1.00053i	0.865872	−	0.500266i	$-0.166764\pi$
$798$		0			0
$799$	10.1768			0.360031
$800$	−2.14700	−	5.23358i	−0.0759079	−	0.185035i
$801$		0			0
$802$	−25.6509	−	6.17669i	−0.905765	−	0.218107i
$803$	−7.28323	+	7.20217i	−0.257020	+	0.254159i
$804$		0			0
$805$	−18.8664			−0.664952
$806$	−3.64162	+	15.1231i	−0.128270	+	0.532689i
$807$		0			0
$808$	3.31534	+	2.84329i	0.116633	+	0.100027i
$809$			31.4830i			1.10688i	0.832888	+	0.553442i	$0.186686\pi$
$809$			31.4830i			1.10688i	−0.832888	+	0.553442i	$0.813314\pi$
$810$		0			0
$811$		−	11.8664i		−	0.416687i	−0.978056	−	0.208344i	$-0.933193\pi$
$811$		−	11.8664i		−	0.416687i	0.978056	−	0.208344i	$-0.0668072\pi$
$812$	−8.30571	−	4.24621i	−0.291473	−	0.149013i
$813$		0			0
$814$	18.7242	−	11.3132i	0.656283	−	0.396527i
$815$			40.9848i			1.43564i
$816$		0			0
$817$	27.8617			0.974759
$818$	2.04496	−	8.49242i	0.0715003	−	0.296931i
$819$		0			0
$820$	27.5559	+	14.0877i	0.962293	+	0.491962i
$821$	−31.4538			−1.09774			−0.548872	−	0.835906i	$-0.684943\pi$
$821$	−31.4538			−1.09774			−0.548872	+	0.835906i	$0.684943\pi$
$822$		0			0
$823$		−	45.6185i		−	1.59016i	−0.606504	−	0.795080i	$-0.707429\pi$
$823$		−	45.6185i		−	1.59016i	0.606504	−	0.795080i	$-0.292571\pi$
$824$	15.2933	−	17.8324i	0.532768	−	0.621220i
$825$		0			0
$826$	−49.6155	−	11.9473i	−1.72635	−	0.415701i
$827$			5.13420i			0.178534i	0.996008	+	0.0892668i	$0.0284524\pi$
$827$			5.13420i			0.178534i	−0.996008	+	0.0892668i	$0.971548\pi$
$828$		0			0
$829$			19.2306i			0.667905i	0.942590	+	0.333952i	$0.108383\pi$
$829$			19.2306i			0.667905i	−0.942590	+	0.333952i	$0.891617\pi$
$830$	−12.9698	−	3.12311i	−0.450189	−	0.108405i
$831$		0			0
$832$	−1.61463	−	10.4707i	−0.0559771	−	0.363006i
$833$			3.60109i			0.124770i
$834$		0			0
$835$			28.1753i			0.975047i
$836$	44.5360	−	14.1289i	1.54031	−	0.488658i
$837$		0			0
$838$	−22.8393	−	5.49966i	−0.788970	−	0.189982i
$839$			27.1231i			0.936394i	0.883624	+	0.468197i	$0.155096\pi$
$839$			27.1231i			0.936394i	−0.883624	+	0.468197i	$0.844904\pi$
$840$		0			0
$841$	−26.6155			−0.917777
$842$	−2.41131	+	10.0138i	−0.0830992	+	0.345099i
$843$		0			0
$844$	−6.41273	+	12.5435i	−0.220735	+	0.431765i
$845$			22.4924i			0.773763i
$846$		0			0
$847$	0.371834	−	33.2228i	0.0127764	−	1.14155i
$848$	−26.7379	+	19.3153i	−0.918185	+	0.663292i
$849$		0			0
$850$	0.561553	−	2.33205i	0.0192611	−	0.0799886i
$851$	14.5665			0.499332
$852$		0			0
$853$	43.6106			1.49320			0.746599	−	0.665274i	$-0.231685\pi$
$853$	43.6106			1.49320			0.746599	+	0.665274i	$0.231685\pi$
$854$	33.6750	+	8.10887i	1.15233	+	0.277480i
$855$		0			0
$856$	14.9309	−	17.4098i	0.510327	−	0.595053i
$857$			26.6034i			0.908755i	0.890809	+	0.454377i	$0.150138\pi$
$857$			26.6034i			0.908755i	−0.890809	+	0.454377i	$0.849862\pi$
$858$		0			0
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$	−14.0877	−	7.20217i	−0.480385	−	0.245592i
$861$		0			0
$862$	38.7386	+	9.32819i	1.31944	+	0.317719i
$863$			42.3542i			1.44175i	0.693064	+	0.720876i	$0.256260\pi$
$863$			42.3542i			1.44175i	−0.693064	+	0.720876i	$0.743740\pi$
$864$		0			0
$865$			25.0870i			0.852983i
$866$	20.7930	+	5.00691i	0.706574	+	0.170142i
$867$		0			0
$868$	22.8393	−	44.6743i	0.775216	−	1.51634i
$869$	29.0425	+	29.3693i	0.985198	+	0.996286i
$870$		0			0
$871$	−8.27190			−0.280283
$872$	−36.0661	−	30.9309i	−1.22135	−	1.04745i
$873$		0			0
$874$	30.2462	+	7.28323i	1.02309	+	0.246359i
$875$			36.2454i			1.22532i
$876$		0			0
$877$	−49.9775			−1.68762			−0.843811	−	0.536641i	$-0.819693\pi$
$877$	−49.9775			−1.68762			−0.843811	+	0.536641i	$0.819693\pi$
$878$	31.6891	+	7.63068i	1.06946	+	0.257523i
$879$		0			0
$880$	−26.1709	−	4.36846i	−0.882221	−	0.147261i
$881$	27.9846			0.942824			0.471412	−	0.881913i	$-0.343744\pi$
$881$	27.9846			0.942824			0.471412	+	0.881913i	$0.343744\pi$
$882$		0			0
$883$	22.2462			0.748645			0.374322	−	0.927299i	$-0.377875\pi$
$883$	22.2462			0.748645			0.374322	+	0.927299i	$0.377875\pi$
$884$	2.04496	−	4.00000i	0.0687794	−	0.134535i
$885$		0			0
$886$	−6.41273	−	1.54417i	−0.215440	−	0.0518775i
$887$	43.9972			1.47728			0.738641	−	0.674099i	$-0.235468\pi$
$887$	43.9972			1.47728			0.738641	+	0.674099i	$0.235468\pi$
$888$		0			0
$889$	−6.87689			−0.230644
$890$	10.9993	−	45.6786i	0.368698	−	1.53115i
$891$		0			0
$892$	−9.42329	+	18.4322i	−0.315515	+	0.617157i
$893$	42.2630			1.41428
$894$		0			0
$895$		0			0
$896$	−2.84329	+	34.0540i	−0.0949876	+	1.13766i
$897$		0			0
$898$	−2.81164	−	0.677039i	−0.0938258	−	0.0225931i
$899$			12.8255i			0.427753i
$900$		0			0
$901$	−13.9867			−0.465966
$902$	−31.0606	+	18.7669i	−1.03421	+	0.624868i
$903$		0			0
$904$	15.6371	+	13.4106i	0.520082	+	0.446031i
$905$	−51.8792			−1.72452
$906$		0			0
$907$	−18.7386			−0.622206			−0.311103	−	0.950376i	$-0.600698\pi$
$907$	−18.7386			−0.622206			−0.311103	+	0.950376i	$0.600698\pi$
$908$	22.5272	−	44.0639i	0.747593	−	1.46231i
$909$		0			0
$910$	−2.64861	+	10.9993i	−0.0878007	+	0.364624i
$911$		−	0.738634i		−	0.0244720i	−0.999925	−	0.0122360i	$-0.996105\pi$
$911$		−	0.738634i		−	0.0244720i	0.999925	−	0.0122360i	$-0.00389494\pi$
$912$		0			0
$913$	11.1231	−	10.9993i	0.368121	−	0.364024i
$914$	9.32819	−	38.7386i	0.308549	−	1.28136i
$915$		0			0
$916$	−17.5076	+	34.2453i	−0.578467	+	1.13150i
$917$		−	12.0000i		−	0.396275i
$918$		0			0
$919$	−7.57401			−0.249843			−0.124922	−	0.992167i	$-0.539868\pi$
$919$	−7.57401			−0.249843			−0.124922	+	0.992167i	$0.539868\pi$
$920$	−13.4106	−	11.5012i	−0.442135	−	0.379182i
$921$		0			0
$922$	45.1080	+	10.8619i	1.48555	+	0.357718i
$923$		−	16.2177i		−	0.533813i
$924$		0			0
$925$		−	4.66410i		−	0.153355i
$926$	−11.3378	+	47.0844i	−0.372584	+	1.54729i
$927$		0			0
$928$	−3.31534	−	8.08156i	−0.108831	−	0.265290i
$929$	2.04496			0.0670929			0.0335465	−	0.999437i	$-0.489320\pi$
$929$	2.04496			0.0670929			0.0335465	+	0.999437i	$0.489320\pi$
$930$		0			0
$931$			14.9548i			0.490124i
$932$	−18.0431	+	35.2929i	−0.591023	+	1.15606i
$933$		0			0
$934$	6.41273	+	1.54417i	0.209831	+	0.0505269i
$935$	−7.91096	−	8.00000i	−0.258716	−	0.261628i
$936$		0			0
$937$			21.9986i			0.718664i	0.933210	+	0.359332i	$0.116995\pi$
$937$			21.9986i			0.718664i	−0.933210	+	0.359332i	$0.883005\pi$
$938$	25.9396	+	6.24621i	0.846958	+	0.203946i
$939$		0			0
$940$	−21.3693	−	10.9248i	−0.696990	−	0.356329i
$941$	34.5421			1.12604			0.563020	−	0.826443i	$-0.309639\pi$
$941$	34.5421			1.12604			0.563020	+	0.826443i	$0.309639\pi$
$942$		0			0
$943$	−24.1636			−0.786875
$944$	−27.9846	−	38.7386i	−0.910820	−	1.26084i
$945$		0			0
$946$	15.8794	−	9.59437i	0.516285	−	0.311940i
$947$	−33.2228			−1.07960			−0.539799	−	0.841794i	$-0.681500\pi$
$947$	−33.2228			−1.07960			−0.539799	+	0.841794i	$0.681500\pi$
$948$		0			0
$949$			4.08992i			0.132764i
$950$	2.33205	−	9.68466i	0.0756616	−	0.314212i
$951$		0			0
$952$	−9.43318	+	10.9993i	−0.305731	+	0.356490i
$953$			54.5769i			1.76792i	0.467564	+	0.883959i	$0.345132\pi$
$953$			54.5769i			1.76792i	−0.467564	+	0.883959i	$0.654868\pi$
$954$		0			0
$955$	−8.49242			−0.274808
$956$	14.0877	+	7.20217i	0.455627	+	0.232935i
$957$		0			0
$958$	30.2462	+	7.28323i	0.977211	+	0.235311i
$959$	−21.9986			−0.710373
$960$		0			0
$961$	−37.9848			−1.22532
$962$	2.04496	−	8.49242i	0.0659321	−	0.273807i
$963$		0			0
$964$	−17.2160	+	33.6750i	−0.554490	+	1.08460i
$965$	−50.1739			−1.61516
$966$		0			0
$967$	38.1045			1.22536			0.612680	−	0.790331i	$-0.290092\pi$
$967$	38.1045			1.22536			0.612680	+	0.790331i	$0.290092\pi$
$968$	20.5173	−	23.3889i	0.659453	−	0.751746i
$969$		0			0
$970$	8.85254	−	36.7633i	0.284238	−	1.18040i
$971$	−23.3205			−0.748390			−0.374195	−	0.927350i	$-0.622081\pi$
$971$	−23.3205			−0.748390			−0.374195	+	0.927350i	$0.622081\pi$
$972$		0			0
$973$			11.9473i			0.383014i
$974$	−10.6608	+	44.2727i	−0.341594	+	1.41859i
$975$		0			0
$976$	18.9936	+	26.2926i	0.607972	+	0.841606i
$977$	61.2074			1.95820			0.979099	−	0.203382i	$-0.0651934\pi$
$977$	61.2074			1.95820			0.979099	+	0.203382i	$0.0651934\pi$
$978$		0			0
$979$	38.7386	+	39.1746i	1.23809	+	1.25203i
$980$	3.86577	−	7.56155i	0.123487	−	0.241545i
$981$		0			0
$982$	−3.06913	+	12.7457i	−0.0979399	+	0.406730i
$983$		−	22.6307i		−	0.721807i	−0.932603	−	0.360903i	$-0.882468\pi$
$983$		−	22.6307i		−	0.721807i	0.932603	−	0.360903i	$-0.117532\pi$
$984$		0			0
$985$			31.2637i			0.996143i
$986$	0.867135	−	3.60109i	0.0276152	−	0.114682i
$987$		0			0
$988$	8.49242	−	16.6114i	0.270180	−	0.528480i
$989$	12.3534			0.392815
$990$		0			0
$991$			45.6185i			1.44912i	0.689212	+	0.724559i	$0.257957\pi$
$991$			45.6185i			1.44912i	−0.689212	+	0.724559i	$0.742043\pi$
$992$	43.4686	−	17.8324i	1.38013	−	0.566178i
$993$		0			0
$994$	−12.2462	+	50.8567i	−0.388426	+	1.61308i
$995$	2.04496			0.0648296
$996$		0			0
$997$	−3.22925			−0.102271			−0.0511357	−	0.998692i	$-0.516284\pi$
$997$	−3.22925			−0.102271			−0.0511357	+	0.998692i	$0.516284\pi$
$998$	20.2644	+	4.87962i	0.641457	+	0.154462i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.h.i.307.1	✓	16
3.2	odd	2	inner	792.2.h.i.307.16	yes	16
4.3	odd	2		3168.2.h.i.2287.8		16
8.3	odd	2	inner	792.2.h.i.307.14	yes	16
8.5	even	2		3168.2.h.i.2287.10		16
11.10	odd	2	inner	792.2.h.i.307.15	yes	16
12.11	even	2		3168.2.h.i.2287.15		16
24.5	odd	2		3168.2.h.i.2287.1		16
24.11	even	2	inner	792.2.h.i.307.3	yes	16
33.32	even	2	inner	792.2.h.i.307.2	yes	16
44.43	even	2		3168.2.h.i.2287.2		16
88.21	odd	2		3168.2.h.i.2287.16		16
88.43	even	2	inner	792.2.h.i.307.4	yes	16
132.131	odd	2		3168.2.h.i.2287.9		16
264.131	odd	2	inner	792.2.h.i.307.13	yes	16
264.197	even	2		3168.2.h.i.2287.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.h.i.307.1	✓	16	1.1	even	1	trivial
792.2.h.i.307.2	yes	16	33.32	even	2	inner
792.2.h.i.307.3	yes	16	24.11	even	2	inner
792.2.h.i.307.4	yes	16	88.43	even	2	inner
792.2.h.i.307.13	yes	16	264.131	odd	2	inner
792.2.h.i.307.14	yes	16	8.3	odd	2	inner
792.2.h.i.307.15	yes	16	11.10	odd	2	inner
792.2.h.i.307.16	yes	16	3.2	odd	2	inner
3168.2.h.i.2287.1		16	24.5	odd	2
3168.2.h.i.2287.2		16	44.43	even	2
3168.2.h.i.2287.7		16	264.197	even	2
3168.2.h.i.2287.8		16	4.3	odd	2
3168.2.h.i.2287.9		16	132.131	odd	2
3168.2.h.i.2287.10		16	8.5	even	2
3168.2.h.i.2287.15		16	12.11	even	2
3168.2.h.i.2287.16		16	88.21	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.37491 - 0.331077i) q^{2} +(1.78078 + 0.910404i) q^{4} -2.00000i q^{5} -3.02045 q^{7} +(-2.14700 - 1.84130i) q^{8} +(-0.662153 + 2.74983i) q^{10} +(-2.33205 - 2.35829i) q^{11} -1.32431 q^{13} +(4.15286 + 1.00000i) q^{14} +(2.34233 + 3.24245i) q^{16} +1.69614i q^{17} +7.04383i q^{19} +(1.82081 - 3.56155i) q^{20} +(2.42559 + 4.01454i) q^{22} +3.12311i q^{23} +1.00000 q^{25} +(1.82081 + 0.438447i) q^{26} +(-5.37874 - 2.74983i) q^{28} +1.54417 q^{29} +8.30571i q^{31} +(-2.14700 - 5.23358i) q^{32} +(0.561553 - 2.33205i) q^{34} +6.04090i q^{35} -4.66410i q^{37} +(2.33205 - 9.68466i) q^{38} +(-3.68260 + 4.29400i) q^{40} +7.73704i q^{41} -3.95548i q^{43} +(-2.00586 - 6.32270i) q^{44} +(1.03399 - 4.29400i) q^{46} -6.00000i q^{47} +2.12311 q^{49} +(-1.37491 - 0.331077i) q^{50} +(-2.35829 - 1.20565i) q^{52} +8.24621i q^{53} +(-4.71659 + 4.66410i) q^{55} +(6.48490 + 5.56155i) q^{56} +(-2.12311 - 0.511240i) q^{58} -11.9473 q^{59} +8.10887 q^{61} +(2.74983 - 11.4196i) q^{62} +(1.21922 + 7.90655i) q^{64} +2.64861i q^{65} +6.24621 q^{67} +(-1.54417 + 3.02045i) q^{68} +(2.00000 - 8.30571i) q^{70} +12.2462i q^{71} -3.08835i q^{73} +(-1.54417 + 6.41273i) q^{74} +(-6.41273 + 12.5435i) q^{76} +(7.04383 + 7.12311i) q^{77} -12.4536 q^{79} +(6.48490 - 4.68466i) q^{80} +(2.56155 - 10.6378i) q^{82} +4.71659i q^{83} +3.39228 q^{85} +(-1.30957 + 5.43845i) q^{86} +(0.664579 + 9.35726i) q^{88} -16.6114 q^{89} +4.00000 q^{91} +(-2.84329 + 5.56155i) q^{92} +(-1.98646 + 8.24948i) q^{94} +14.0877 q^{95} -13.3693 q^{97} +(-2.91909 - 0.702911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 12 q^{16} + 4 q^{22} + 16 q^{25} - 24 q^{34} - 32 q^{49} + 32 q^{58} + 36 q^{64} - 32 q^{67} + 32 q^{70} + 8 q^{82} - 20 q^{88} + 64 q^{91} - 16 q^{97}+O(q^{100}) \) 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

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