LMFDB - Embedded newform 792.2.f.g.397.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(397,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("792.397");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.578281160704.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 2x^{8} - 2x^{7} - 3x^{6} - 6x^{5} - 6x^{4} - 8x^{3} + 16x^{2} + 32 $ x^10 + 2x^8 - 2x^7 - 3x^6 - 6x^5 - 6x^4 - 8x^3 + 16*x^2 + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			397.10
Root			$1.41363 - 0.0406696i$ of defining polynomial
Character	$\chi$	$=$	792.397
Dual form			792.2.f.g.397.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29865 + 0.559929i) q^{2} +(1.37296 + 1.45430i) q^{4} -2.51595i q^{5} +1.47743 q^{7} +(0.968683 + 2.65738i) q^{8} +(1.40875 - 3.26733i) q^{10} +1.00000i q^{11} +3.47743i q^{13} +(1.91866 + 0.827257i) q^{14} +(-0.229967 + 3.99338i) q^{16} +3.31475 q^{17} -7.13195i q^{19} +(3.65894 - 3.45430i) q^{20} +(-0.559929 + 1.29865i) q^{22} +6.45332 q^{23} -1.33001 q^{25} +(-1.94712 + 4.51595i) q^{26} +(2.02845 + 2.14863i) q^{28} +1.41480i q^{29} +0.636125 q^{31} +(-2.53466 + 5.05722i) q^{32} +(4.30469 + 1.85603i) q^{34} -3.71715i q^{35} -6.97588i q^{37} +(3.99338 - 9.26187i) q^{38} +(6.68583 - 2.43716i) q^{40} -6.72955 q^{41} -3.21471i q^{43} +(-1.45430 + 1.37296i) q^{44} +(8.38057 + 3.61340i) q^{46} -0.862328 q^{47} -4.81719 q^{49} +(-1.72721 - 0.744712i) q^{50} +(-5.05722 + 4.77437i) q^{52} +13.2515i q^{53} +2.51595 q^{55} +(1.43116 + 3.92610i) q^{56} +(-0.792187 + 1.83732i) q^{58} -2.63236i q^{59} +6.45993i q^{61} +(0.826100 + 0.356185i) q^{62} +(-6.12331 + 5.14831i) q^{64} +8.74905 q^{65} +7.66426i q^{67} +(4.55102 + 4.82064i) q^{68} +(2.08134 - 4.82726i) q^{70} -12.2900 q^{71} -13.2440 q^{73} +(3.90600 - 9.05920i) q^{74} +(10.3720 - 9.79187i) q^{76} +1.47743i q^{77} -16.3409 q^{79} +(10.0472 + 0.578585i) q^{80} +(-8.73930 - 3.76807i) q^{82} -13.8040i q^{83} -8.33976i q^{85} +(1.80001 - 4.17477i) q^{86} +(-2.65738 + 0.968683i) q^{88} +1.04979 q^{89} +5.13767i q^{91} +(8.86014 + 9.38505i) q^{92} +(-1.11986 - 0.482842i) q^{94} -17.9436 q^{95} +16.2110 q^{97} +(-6.25582 - 2.69729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{4} + 10 q^{10} + 12 q^{14} + 4 q^{17} - 12 q^{20} + 12 q^{23} - 6 q^{25} + 20 q^{26} - 12 q^{28} - 4 q^{31} + 20 q^{32} - 8 q^{38} + 20 q^{40} - 4 q^{41} - 4 q^{44} + 2 q^{46} + 4 q^{47} - 6 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) $ 10 * q - 4 * q^4 + 10 * q^10 + 12 * q^14 + 4 * q^17 - 12 * q^20 + 12 * q^23 - 6 * q^25 + 20 * q^26 - 12 * q^28 - 4 * q^31 + 20 * q^32 - 8 * q^38 + 20 * q^40 - 4 * q^41 - 4 * q^44 + 2 * q^46 + 4 * q^47 - 6 * q^49 + 6 * q^50 - 20 * q^52 - 8 * q^55 + 8 * q^56 + 36 * q^58 - 22 * q^62 - 16 * q^64 - 16 * q^65 + 28 * q^68 + 28 * q^70 + 12 * q^71 - 4 * q^73 + 14 * q^74 + 44 * q^76 + 16 * q^79 + 56 * q^80 - 4 * q^82 + 20 * q^86 - 12 * q^88 + 4 * q^89 + 36 * q^92 - 24 * q^95 - 20 * q^97 - 24 * q^98

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 $

$2$	1.29865	+	0.559929i	0.918281	+	0.395930i
$2$	1.29865	+	0.559929i	0.918281	+	0.395930i
$3$		0			0
$3$		0			0
$4$	1.37296	+	1.45430i	0.686480	+	0.727149i
$5$		−	2.51595i		−	1.12517i	−0.826740	−	0.562584i	$-0.809807\pi$
$5$		−	2.51595i		−	1.12517i	0.826740	−	0.562584i	$-0.190193\pi$
$6$		0			0
$7$	1.47743			0.558417			0.279209	−	0.960230i	$-0.409928\pi$
$7$	1.47743			0.558417			0.279209	+	0.960230i	$0.409928\pi$
$8$	0.968683	+	2.65738i	0.342481	+	0.939525i
$9$		0			0
$10$	1.40875	−	3.26733i	0.445487	−	1.03322i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$		0			0
$13$			3.47743i			0.964466i	0.876043	+	0.482233i	$0.160174\pi$
$13$			3.47743i			0.964466i	−0.876043	+	0.482233i	$0.839826\pi$
$14$	1.91866	+	0.827257i	0.512784	+	0.221094i
$15$		0			0
$16$	−0.229967	+	3.99338i	−0.0574917	+	0.998346i
$17$	3.31475			0.803946			0.401973	−	0.915652i	$-0.368325\pi$
$17$	3.31475			0.803946			0.401973	+	0.915652i	$0.368325\pi$
$18$		0			0
$19$		−	7.13195i		−	1.63618i	−0.575090	−	0.818090i	$-0.695033\pi$
$19$		−	7.13195i		−	1.63618i	0.575090	−	0.818090i	$-0.304967\pi$
$20$	3.65894	−	3.45430i	0.818165	−	0.772405i
$21$		0			0
$22$	−0.559929	+	1.29865i	−0.119377	+	0.276872i
$23$	6.45332			1.34561			0.672805	−	0.739820i	$-0.265089\pi$
$23$	6.45332			1.34561			0.672805	+	0.739820i	$0.265089\pi$
$24$		0			0
$25$	−1.33001			−0.266002
$26$	−1.94712	+	4.51595i	−0.381861	+	0.885651i
$27$		0			0
$28$	2.02845	+	2.14863i	0.383342	+	0.406052i
$29$			1.41480i			0.262722i	0.991335	+	0.131361i	$0.0419346\pi$
$29$			1.41480i			0.262722i	−0.991335	+	0.131361i	$0.958065\pi$
$30$		0			0
$31$	0.636125			0.114251			0.0571257	−	0.998367i	$-0.481806\pi$
$31$	0.636125			0.114251			0.0571257	+	0.998367i	$0.481806\pi$
$32$	−2.53466	+	5.05722i	−0.448068	+	0.893999i
$33$		0			0
$34$	4.30469	+	1.85603i	0.738248	+	0.318306i
$35$		−	3.71715i		−	0.628313i
$36$		0			0
$37$		−	6.97588i		−	1.14683i	−0.819266	−	0.573414i	$-0.805619\pi$
$37$		−	6.97588i		−	1.14683i	0.819266	−	0.573414i	$-0.194381\pi$
$38$	3.99338	−	9.26187i	0.647812	−	1.50247i
$39$		0			0
$40$	6.68583	−	2.43716i	1.05712	−	0.385349i
$41$	−6.72955			−1.05098			−0.525490	−	0.850800i	$-0.676118\pi$
$41$	−6.72955			−1.05098			−0.525490	+	0.850800i	$0.676118\pi$
$42$		0			0
$43$		−	3.21471i		−	0.490239i	−0.969493	−	0.245119i	$-0.921173\pi$
$43$		−	3.21471i		−	0.490239i	0.969493	−	0.245119i	$-0.0788271\pi$
$44$	−1.45430	+	1.37296i	−0.219244	+	0.206981i
$45$		0			0
$46$	8.38057	+	3.61340i	1.23565	+	0.532767i
$47$	−0.862328			−0.125783			−0.0628917	−	0.998020i	$-0.520032\pi$
$47$	−0.862328			−0.125783			−0.0628917	+	0.998020i	$0.520032\pi$
$48$		0			0
$49$	−4.81719			−0.688170
$50$	−1.72721	−	0.744712i	−0.244265	−	0.105318i
$51$		0			0
$52$	−5.05722	+	4.77437i	−0.701311	+	0.662086i
$53$			13.2515i			1.82023i	0.414353	+	0.910116i	$0.364008\pi$
$53$			13.2515i			1.82023i	−0.414353	+	0.910116i	$0.635992\pi$
$54$		0			0
$55$	2.51595			0.339251
$56$	1.43116	+	3.92610i	0.191247	+	0.524647i
$57$		0			0
$58$	−0.792187	+	1.83732i	−0.104019	+	0.241252i
$59$		−	2.63236i		−	0.342704i	−0.985210	−	0.171352i	$-0.945186\pi$
$59$		−	2.63236i		−	0.342704i	0.985210	−	0.171352i	$-0.0548136\pi$
$60$		0			0
$61$			6.45993i			0.827110i	0.910479	+	0.413555i	$0.135713\pi$
$61$			6.45993i			0.827110i	−0.910479	+	0.413555i	$0.864287\pi$
$62$	0.826100	+	0.356185i	0.104915	+	0.0452355i
$63$		0			0
$64$	−6.12331	+	5.14831i	−0.765413	+	0.643539i
$65$	8.74905			1.08519
$66$		0			0
$67$			7.66426i			0.936339i	0.883639	+	0.468169i	$0.155086\pi$
$67$			7.66426i			0.936339i	−0.883639	+	0.468169i	$0.844914\pi$
$68$	4.55102	+	4.82064i	0.551892	+	0.584589i
$69$		0			0
$70$	2.08134	−	4.82726i	0.248768	−	0.576968i
$71$	−12.2900			−1.45856			−0.729278	−	0.684218i	$-0.760144\pi$
$71$	−12.2900			−1.45856			−0.729278	+	0.684218i	$0.760144\pi$
$72$		0			0
$73$	−13.2440			−1.55009			−0.775045	−	0.631905i	$-0.782273\pi$
$73$	−13.2440			−1.55009			−0.775045	+	0.631905i	$0.782273\pi$
$74$	3.90600	−	9.05920i	0.454063	−	1.05311i
$75$		0			0
$76$	10.3720	−	9.79187i	1.18975	−	1.12320i
$77$			1.47743i			0.168369i
$78$		0			0
$79$	−16.3409			−1.83850			−0.919249	−	0.393676i	$-0.871203\pi$
$79$	−16.3409			−1.83850			−0.919249	+	0.393676i	$0.871203\pi$
$80$	10.0472	+	0.578585i	1.12331	+	0.0646878i
$81$		0			0
$82$	−8.73930	−	3.76807i	−0.965094	−	0.416114i
$83$		−	13.8040i		−	1.51518i	−0.652730	−	0.757591i	$-0.726376\pi$
$83$		−	13.8040i		−	1.51518i	0.652730	−	0.757591i	$-0.273624\pi$
$84$		0			0
$85$		−	8.33976i		−	0.904574i
$86$	1.80001	−	4.17477i	0.194100	−	0.450177i
$87$		0			0
$88$	−2.65738	+	0.968683i	−0.283277	+	0.103262i
$89$	1.04979			0.111277			0.0556387	−	0.998451i	$-0.482280\pi$
$89$	1.04979			0.111277			0.0556387	+	0.998451i	$0.482280\pi$
$90$		0			0
$91$			5.13767i			0.538574i
$92$	8.86014	+	9.38505i	0.923734	+	0.978459i
$93$		0			0
$94$	−1.11986	−	0.482842i	−0.115505	−	0.0498014i
$95$	−17.9436			−1.84098
$96$		0			0
$97$	16.2110			1.64598			0.822989	−	0.568057i	$-0.192305\pi$
$97$	16.2110			1.64598			0.822989	+	0.568057i	$0.192305\pi$
$98$	−6.25582	−	2.69729i	−0.631934	−	0.272467i
$99$		0			0
$100$	−1.82605	−	1.93423i	−0.182605	−	0.193423i
$101$			8.63460i			0.859175i	0.903025	+	0.429588i	$0.141341\pi$
$101$			8.63460i			0.859175i	−0.903025	+	0.429588i	$0.858659\pi$
$102$		0			0
$103$	−4.95487			−0.488217			−0.244109	−	0.969748i	$-0.578495\pi$
$103$	−4.95487			−0.488217			−0.244109	+	0.969748i	$0.578495\pi$
$104$	−9.24085	+	3.36853i	−0.906140	+	0.330312i
$105$		0			0
$106$	−7.41989	+	17.2090i	−0.720684	+	1.67148i
$107$		−	6.34666i		−	0.613554i	−0.951781	−	0.306777i	$-0.900749\pi$
$107$		−	6.34666i		−	0.613554i	0.951781	−	0.306777i	$-0.0992507\pi$
$108$		0			0
$109$			7.94246i			0.760750i	0.924832	+	0.380375i	$0.124205\pi$
$109$			7.94246i			0.760750i	−0.924832	+	0.380375i	$0.875795\pi$
$110$	3.26733	+	1.40875i	0.311528	+	0.134319i
$111$		0			0
$112$	−0.339760	+	5.89996i	−0.0321043	+	0.557493i
$113$	−4.88248			−0.459305			−0.229653	−	0.973273i	$-0.573759\pi$
$113$	−4.88248			−0.459305			−0.229653	+	0.973273i	$0.573759\pi$
$114$		0			0
$115$		−	16.2362i		−	1.51404i
$116$	−2.05754	+	1.94246i	−0.191038	+	0.180353i
$117$		0			0
$118$	1.47394	−	3.41850i	0.135687	−	0.314699i
$119$	4.89733			0.448937
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−3.61710	+	8.38916i	−0.327477	+	0.759519i
$123$		0			0
$124$	0.873373	+	0.925115i	0.0784312	+	0.0830778i
$125$		−	9.23351i		−	0.825871i
$126$		0			0
$127$	−4.12017			−0.365606			−0.182803	−	0.983150i	$-0.558517\pi$
$127$	−4.12017			−0.365606			−0.182803	+	0.983150i	$0.558517\pi$
$128$	−10.8347	+	3.25721i	−0.957661	+	0.287900i
$129$		0			0
$130$	11.3619	+	4.89885i	0.996506	+	0.429657i
$131$		−	13.3015i		−	1.16216i	−0.813847	−	0.581080i	$-0.802630\pi$
$131$		−	13.3015i		−	1.16216i	0.813847	−	0.581080i	$-0.197370\pi$
$132$		0			0
$133$		−	10.5370i		−	0.913671i
$134$	−4.29144	+	9.95316i	−0.370724	+	0.859822i
$135$		0			0
$136$	3.21095	+	8.80855i	0.275336	+	0.755327i
$137$	6.84444			0.584760			0.292380	−	0.956302i	$-0.405553\pi$
$137$	6.84444			0.584760			0.292380	+	0.956302i	$0.405553\pi$
$138$		0			0
$139$		−	12.1966i		−	1.03450i	−0.855834	−	0.517250i	$-0.826956\pi$
$139$		−	12.1966i		−	1.03450i	0.855834	−	0.517250i	$-0.173044\pi$
$140$	5.40584	−	5.10349i	0.456877	−	0.431324i
$141$		0			0
$142$	−15.9604	−	6.88153i	−1.33936	−	0.577485i
$143$	−3.47743			−0.290798
$144$		0			0
$145$	3.55956			0.295606
$146$	−17.1992	−	7.41569i	−1.42342	−	0.613727i
$147$		0			0
$148$	10.1450	−	9.57760i	0.833915	−	0.787274i
$149$			3.04004i			0.249050i	0.992216	+	0.124525i	$0.0397407\pi$
$149$			3.04004i			0.249050i	−0.992216	+	0.124525i	$0.960259\pi$
$150$		0			0
$151$	−1.83669			−0.149468			−0.0747339	−	0.997204i	$-0.523811\pi$
$151$	−1.83669			−0.149468			−0.0747339	+	0.997204i	$0.523811\pi$
$152$	18.9523	−	6.90860i	1.53723	−	0.560361i
$153$		0			0
$154$	−0.827257	+	1.91866i	−0.0666623	+	0.154610i
$155$		−	1.60046i		−	0.128552i
$156$		0			0
$157$			10.0560i			0.802558i	0.915956	+	0.401279i	$0.131434\pi$
$157$			10.0560i			0.802558i	−0.915956	+	0.401279i	$0.868566\pi$
$158$	−21.2211	−	9.14976i	−1.68826	−	0.727916i
$159$		0			0
$160$	12.7237	+	6.37707i	1.00590	+	0.504152i
$161$	9.53434			0.751411
$162$		0			0
$163$		−	12.8934i		−	1.00989i	−0.863152	−	0.504945i	$-0.831513\pi$
$163$		−	12.8934i		−	1.00989i	0.863152	−	0.504945i	$-0.168487\pi$
$164$	−9.23940	−	9.78678i	−0.721476	−	0.764219i
$165$		0			0
$166$	7.72924	−	17.9264i	0.599905	−	1.39136i
$167$	−4.47434			−0.346235			−0.173117	−	0.984901i	$-0.555384\pi$
$167$	−4.47434			−0.346235			−0.173117	+	0.984901i	$0.555384\pi$
$168$		0			0
$169$	0.907463			0.0698048
$170$	4.66967	−	10.8304i	0.358148	−	0.830653i
$171$		0			0
$172$	4.67515	−	4.41366i	0.356477	−	0.336539i
$173$		−	0.182807i		−	0.0138986i	−0.999976	−	0.00694928i	$-0.997788\pi$
$173$		−	0.182807i		−	0.0138986i	0.999976	−	0.00694928i	$-0.00221204\pi$
$174$		0			0
$175$	−1.96500			−0.148540
$176$	−3.99338	−	0.229967i	−0.301013	−	0.0173344i
$177$		0			0
$178$	1.36330	+	0.587808i	0.102184	+	0.0440580i
$179$			20.0915i			1.50171i	0.660469	+	0.750853i	$0.270358\pi$
$179$			20.0915i			1.50171i	−0.660469	+	0.750853i	$0.729642\pi$
$180$		0			0
$181$		−	7.63413i		−	0.567440i	−0.958907	−	0.283720i	$-0.908431\pi$
$181$		−	7.63413i		−	0.567440i	0.958907	−	0.283720i	$-0.0915686\pi$
$182$	−2.87673	+	6.67201i	−0.213238	+	0.494563i
$183$		0			0
$184$	6.25122	+	17.1489i	0.460846	+	1.26423i
$185$	−17.5510			−1.29037
$186$		0			0
$187$			3.31475i			0.242399i
$188$	−1.18394	−	1.25408i	−0.0863478	−	0.0914633i
$189$		0			0
$190$	−23.3024	−	10.0472i	−1.69053	−	0.728898i
$191$	22.9943			1.66381			0.831906	−	0.554917i	$-0.187250\pi$
$191$	22.9943			1.66381			0.831906	+	0.554917i	$0.187250\pi$
$192$		0			0
$193$	0.735278			0.0529265			0.0264632	−	0.999650i	$-0.491576\pi$
$193$	0.735278			0.0529265			0.0264632	+	0.999650i	$0.491576\pi$
$194$	21.0524	+	9.07701i	1.51147	+	0.651692i
$195$		0			0
$196$	−6.61381	−	7.00564i	−0.472415	−	0.500403i
$197$		−	11.1665i		−	0.795579i	−0.917477	−	0.397789i	$-0.869777\pi$
$197$		−	11.1665i		−	0.795579i	0.917477	−	0.397789i	$-0.130223\pi$
$198$		0			0
$199$	−18.1315			−1.28531			−0.642655	−	0.766156i	$-0.722167\pi$
$199$	−18.1315			−1.28531			−0.642655	+	0.766156i	$0.722167\pi$
$200$	−1.28836	−	3.53434i	−0.0911008	−	0.249916i
$201$		0			0
$202$	−4.83476	+	11.2133i	−0.340173	+	0.788964i
$203$			2.09027i			0.146708i
$204$		0			0
$205$			16.9312i			1.18253i
$206$	−6.43461	−	2.77437i	−0.448321	−	0.193300i
$207$		0			0
$208$	−13.8867	−	0.799694i	−0.962871	−	0.0554488i
$209$	7.13195			0.493327
$210$		0			0
$211$			18.4180i			1.26795i	0.773355	+	0.633973i	$0.218577\pi$
$211$			18.4180i			1.26795i	−0.773355	+	0.633973i	$0.781423\pi$
$212$	−19.2716	+	18.1938i	−1.32358	+	1.24955i
$213$		0			0
$214$	3.55368	−	8.24206i	0.242924	−	0.563415i
$215$	−8.08805			−0.551601
$216$		0			0
$217$	0.939831			0.0637999
$218$	−4.44721	+	10.3144i	−0.301203	+	0.698582i
$219$		0			0
$220$	3.45430	+	3.65894i	0.232889	+	0.246686i
$221$			11.5268i			0.775379i
$222$		0			0
$223$	14.5654			0.975368			0.487684	−	0.873020i	$-0.337842\pi$
$223$	14.5654			0.975368			0.487684	+	0.873020i	$0.337842\pi$
$224$	−3.74478	+	7.47171i	−0.250209	+	0.499224i
$225$		0			0
$226$	−6.34061	−	2.73384i	−0.421771	−	0.181853i
$227$			7.15145i			0.474658i	0.971429	+	0.237329i	$0.0762720\pi$
$227$			7.15145i			0.474658i	−0.971429	+	0.237329i	$0.923728\pi$
$228$		0			0
$229$			6.48500i			0.428541i	0.976774	+	0.214271i	$0.0687374\pi$
$229$			6.48500i			0.428541i	−0.976774	+	0.214271i	$0.931263\pi$
$230$	9.09114	−	21.0851i	0.599452	−	1.39031i
$231$		0			0
$232$	−3.75965	+	1.37049i	−0.246833	+	0.0899772i
$233$	−11.4786			−0.751988			−0.375994	−	0.926622i	$-0.622699\pi$
$233$	−11.4786			−0.751988			−0.375994	+	0.926622i	$0.622699\pi$
$234$		0			0
$235$			2.16957i			0.141527i
$236$	3.82824	−	3.61412i	0.249197	−	0.235259i
$237$		0			0
$238$	6.35989	+	2.74215i	0.412250	+	0.177747i
$239$	−0.112036			−0.00724698			−0.00362349	−	0.999993i	$-0.501153\pi$
$239$	−0.112036			−0.00724698			−0.00362349	+	0.999993i	$0.501153\pi$
$240$		0			0
$241$	2.93937			0.189341			0.0946706	−	0.995509i	$-0.469820\pi$
$241$	2.93937			0.189341			0.0946706	+	0.995509i	$0.469820\pi$
$242$	−1.29865	−	0.559929i	−0.0834801	−	0.0359936i
$243$		0			0
$244$	−9.39467	+	8.86922i	−0.601432	+	0.567794i
$245$			12.1198i			0.774307i
$246$		0			0
$247$	24.8009			1.57804
$248$	0.616203	+	1.69042i	0.0391289	+	0.107342i
$249$		0			0
$250$	5.17011	−	11.9911i	0.326987	−	0.758381i
$251$		−	31.2199i		−	1.97058i	−0.170882	−	0.985291i	$-0.554662\pi$
$251$		−	31.2199i		−	1.97058i	0.170882	−	0.985291i	$-0.445338\pi$
$252$		0			0
$253$			6.45332i			0.405717i
$254$	−5.35064	−	2.30700i	−0.335729	−	0.144754i
$255$		0			0
$256$	−15.8942	−	1.83669i	−0.993389	−	0.114793i
$257$	−7.09741			−0.442725			−0.221362	−	0.975192i	$-0.571050\pi$
$257$	−7.09741			−0.442725			−0.221362	+	0.975192i	$0.571050\pi$
$258$		0			0
$259$		−	10.3064i		−	0.640409i
$260$	12.0121	+	12.7237i	0.744958	+	0.789092i
$261$		0			0
$262$	7.44791	−	17.2740i	0.460133	−	1.06719i
$263$	−16.3863			−1.01042			−0.505211	−	0.862996i	$-0.668585\pi$
$263$	−16.3863			−1.01042			−0.505211	+	0.862996i	$0.668585\pi$
$264$		0			0
$265$	33.3401			2.04807
$266$	5.89996	−	13.6838i	0.361749	−	0.839007i
$267$		0			0
$268$	−11.1461	+	10.5227i	−0.680858	+	0.642777i
$269$		−	17.1262i		−	1.04420i	−0.852883	−	0.522102i	$-0.825148\pi$
$269$		−	17.1262i		−	1.04420i	0.852883	−	0.522102i	$-0.174852\pi$
$270$		0			0
$271$	19.5142			1.18540			0.592702	−	0.805422i	$-0.298061\pi$
$271$	19.5142			1.18540			0.592702	+	0.805422i	$0.298061\pi$
$272$	−0.762283	+	13.2371i	−0.0462202	+	0.802616i
$273$		0			0
$274$	8.88850	+	3.83240i	0.536974	+	0.231524i
$275$		−	1.33001i		−	0.0802027i
$276$		0			0
$277$			10.5618i			0.634596i	0.948326	+	0.317298i	$0.102776\pi$
$277$			10.5618i			0.634596i	−0.948326	+	0.317298i	$0.897224\pi$
$278$	6.82922	−	15.8390i	0.409589	−	0.949962i
$279$		0			0
$280$	9.87787	−	3.60074i	0.590315	−	0.215185i
$281$	11.5994			0.691961			0.345981	−	0.938242i	$-0.387546\pi$
$281$	11.5994			0.691961			0.345981	+	0.938242i	$0.387546\pi$
$282$		0			0
$283$			21.6234i			1.28538i	0.766128	+	0.642688i	$0.222181\pi$
$283$			21.6234i			1.28538i	−0.766128	+	0.642688i	$0.777819\pi$
$284$	−16.8737	−	17.8733i	−1.00127	−	1.06059i
$285$		0			0
$286$	−4.51595	−	1.94712i	−0.267034	−	0.115135i
$287$	−9.94246			−0.586885
$288$		0			0
$289$	−6.01240			−0.353671
$290$	4.62261	+	1.99310i	0.271449	+	0.117039i
$291$		0			0
$292$	−18.1834	−	19.2607i	−1.06411	−	1.12715i
$293$			20.1305i			1.17604i	0.808848	+	0.588018i	$0.200092\pi$
$293$			20.1305i			1.17604i	−0.808848	+	0.588018i	$0.799908\pi$
$294$		0			0
$295$	−6.62289			−0.385600
$296$	18.5376	−	6.75742i	1.07747	−	0.392767i
$297$		0			0
$298$	−1.70221	+	3.94793i	−0.0986062	+	0.228698i
$299$			22.4410i			1.29780i
$300$		0			0
$301$		−	4.74952i		−	0.273758i
$302$	−2.38521	−	1.02842i	−0.137253	−	0.0591787i
$303$		0			0
$304$	28.4806	+	1.64011i	1.63347	+	0.0940668i
$305$	16.2529			0.930637
$306$		0			0
$307$			2.24089i			0.127894i	0.997953	+	0.0639471i	$0.0203689\pi$
$307$			2.24089i			0.127894i	−0.997953	+	0.0639471i	$0.979631\pi$
$308$	−2.14863	+	2.02845i	−0.122429	+	0.115582i
$309$		0			0
$310$	0.896143	−	2.07843i	0.0508975	−	0.118047i
$311$	15.6919			0.889807			0.444904	−	0.895578i	$-0.353238\pi$
$311$	15.6919			0.889807			0.444904	+	0.895578i	$0.353238\pi$
$312$		0			0
$313$	−12.1167			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$313$	−12.1167			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$314$	−5.63066	+	13.0592i	−0.317756	+	0.736973i
$315$		0			0
$316$	−22.4354	−	23.7646i	−1.26209	−	1.33686i
$317$			11.8958i			0.668132i	0.942550	+	0.334066i	$0.108421\pi$
$317$			11.8958i			0.668132i	−0.942550	+	0.334066i	$0.891579\pi$
$318$		0			0
$319$	−1.41480			−0.0792135
$320$	12.9529	+	15.4059i	0.724089	+	0.861218i
$321$		0			0
$322$	12.3817	+	5.33855i	0.690007	+	0.297506i
$323$		−	23.6407i		−	1.31540i
$324$		0			0
$325$		−	4.62502i		−	0.256550i
$326$	7.21939	−	16.7440i	0.399845	−	0.927362i
$327$		0			0
$328$	−6.51880	−	17.8830i	−0.359941	−	0.987421i
$329$	−1.27403			−0.0702396
$330$		0			0
$331$		−	24.7692i		−	1.36144i	−0.732544	−	0.680719i	$-0.761667\pi$
$331$		−	24.7692i		−	1.36144i	0.732544	−	0.680719i	$-0.238333\pi$
$332$	20.0751	−	18.9523i	1.10176	−	1.04014i
$333$		0			0
$334$	−5.81058	−	2.50531i	−0.317941	−	0.137085i
$335$	19.2829			1.05354
$336$		0			0
$337$	−11.2285			−0.611654			−0.305827	−	0.952087i	$-0.598933\pi$
$337$	−11.2285			−0.611654			−0.305827	+	0.952087i	$0.598933\pi$
$338$	1.17847	+	0.508115i	0.0641004	+	0.0276378i
$339$		0			0
$340$	12.1285	−	11.4501i	0.657760	−	0.620972i
$341$			0.636125i			0.0344481i
$342$		0			0
$343$	−17.4591			−0.942703
$344$	8.54270	−	3.11403i	0.460591	−	0.167898i
$345$		0			0
$346$	0.102359	−	0.237401i	0.00550285	−	0.0127628i
$347$		−	16.0230i		−	0.860160i	−0.902791	−	0.430080i	$-0.858485\pi$
$347$		−	16.0230i		−	0.860160i	0.902791	−	0.430080i	$-0.141515\pi$
$348$		0			0
$349$			9.27513i			0.496486i	0.968698	+	0.248243i	$0.0798532\pi$
$349$			9.27513i			0.496486i	−0.968698	+	0.248243i	$0.920147\pi$
$350$	−2.55184	−	1.10026i	−0.136402	−	0.0588115i
$351$		0			0
$352$	−5.05722	−	2.53466i	−0.269551	−	0.135098i
$353$	9.58150			0.509972			0.254986	−	0.966945i	$-0.417929\pi$
$353$	9.58150			0.509972			0.254986	+	0.966945i	$0.417929\pi$
$354$		0			0
$355$			30.9211i			1.64112i
$356$	1.44132	+	1.52671i	0.0763897	+	0.0809153i
$357$		0			0
$358$	−11.2498	+	26.0917i	−0.594570	+	1.37899i
$359$	7.80501			0.411932			0.205966	−	0.978559i	$-0.433966\pi$
$359$	7.80501			0.411932			0.205966	+	0.978559i	$0.433966\pi$
$360$		0			0
$361$	−31.8647			−1.67709
$362$	4.27457	−	9.91402i	0.224666	−	0.521069i
$363$		0			0
$364$	−7.47171	+	7.05381i	−0.391624	+	0.369720i
$365$			33.3212i			1.74411i
$366$		0			0
$367$	31.4393			1.64112			0.820558	−	0.571563i	$-0.193663\pi$
$367$	31.4393			1.64112			0.820558	+	0.571563i	$0.193663\pi$
$368$	−1.48405	+	25.7706i	−0.0773614	+	1.34338i
$369$		0			0
$370$	−22.7925	−	9.82731i	−1.18493	−	0.510897i
$371$			19.5782i			1.01645i
$372$		0			0
$373$		−	32.0424i		−	1.65909i	−0.558437	−	0.829547i	$-0.688599\pi$
$373$		−	32.0424i		−	1.65909i	0.558437	−	0.829547i	$-0.311401\pi$
$374$	−1.85603	+	4.30469i	−0.0959729	+	0.222590i
$375$		0			0
$376$	−0.835322	−	2.29153i	−0.0430785	−	0.118177i
$377$	−4.91987			−0.253386
$378$		0			0
$379$			11.4465i			0.587965i	0.955811	+	0.293983i	$0.0949808\pi$
$379$			11.4465i			0.587965i	−0.955811	+	0.293983i	$0.905019\pi$
$380$	−24.6359	−	26.0954i	−1.26379	−	1.33867i
$381$		0			0
$382$	29.8615	+	12.8752i	1.52785	+	0.658752i
$383$	6.82520			0.348751			0.174376	−	0.984679i	$-0.444209\pi$
$383$	6.82520			0.348751			0.174376	+	0.984679i	$0.444209\pi$
$384$		0			0
$385$	3.71715			0.189443
$386$	0.954865	+	0.411703i	0.0486014	+	0.0209552i
$387$		0			0
$388$	22.2571	+	23.5756i	1.12993	+	1.19687i
$389$			6.65984i			0.337667i	0.985645	+	0.168834i	$0.0540000\pi$
$389$			6.65984i			0.337667i	−0.985645	+	0.168834i	$0.946000\pi$
$390$		0			0
$391$	21.3912			1.08180
$392$	−4.66633	−	12.8011i	−0.235685	−	0.646553i
$393$		0			0
$394$	6.25244	−	14.5013i	0.314993	−	0.730565i
$395$			41.1130i			2.06862i
$396$		0			0
$397$		−	2.42189i		−	0.121551i	−0.998151	−	0.0607757i	$-0.980643\pi$
$397$		−	2.42189i		−	0.121551i	0.998151	−	0.0607757i	$-0.0193574\pi$
$398$	−23.5464	−	10.1524i	−1.18028	−	0.508892i
$399$		0			0
$400$	0.305858	−	5.31125i	0.0152929	−	0.265562i
$401$	9.09122			0.453994			0.226997	−	0.973895i	$-0.427109\pi$
$401$	9.09122			0.453994			0.226997	+	0.973895i	$0.427109\pi$
$402$		0			0
$403$			2.21208i			0.110192i
$404$	−12.5573	+	11.8550i	−0.624748	+	0.589806i
$405$		0			0
$406$	−1.17040	+	2.71452i	−0.0580861	+	0.134719i
$407$	6.97588			0.345782
$408$		0			0
$409$	9.08013			0.448984			0.224492	−	0.974476i	$-0.427928\pi$
$409$	9.08013			0.448984			0.224492	+	0.974476i	$0.427928\pi$
$410$	−9.48029	+	21.9877i	−0.468198	+	1.08589i
$411$		0			0
$412$	−6.80283	−	7.20585i	−0.335151	−	0.355007i
$413$		−	3.88914i		−	0.191372i
$414$		0			0
$415$	−34.7301			−1.70483
$416$	−17.5862	−	8.81410i	−0.862232	−	0.432147i
$417$		0			0
$418$	9.26187	+	3.99338i	0.453013	+	0.195323i
$419$		−	2.99512i		−	0.146321i	−0.997320	−	0.0731607i	$-0.976691\pi$
$419$		−	2.99512i		−	0.146321i	0.997320	−	0.0731607i	$-0.0233086\pi$
$420$		0			0
$421$			26.6646i			1.29955i	0.760126	+	0.649776i	$0.225137\pi$
$421$			26.6646i			1.29955i	−0.760126	+	0.649776i	$0.774863\pi$
$422$	−10.3128	+	23.9184i	−0.502017	+	1.16433i
$423$		0			0
$424$	−35.2142	+	12.8365i	−1.71015	+	0.623395i
$425$	−4.40866			−0.213851
$426$		0			0
$427$			9.54412i			0.461872i
$428$	9.22993	−	8.71370i	0.446146	−	0.421193i
$429$		0			0
$430$	−10.5035	−	4.52874i	−0.506524	−	0.218395i
$431$	−19.5700			−0.942656			−0.471328	−	0.881958i	$-0.656225\pi$
$431$	−19.5700			−0.942656			−0.471328	+	0.881958i	$0.656225\pi$
$432$		0			0
$433$	−6.49028			−0.311903			−0.155951	−	0.987765i	$-0.549844\pi$
$433$	−6.49028			−0.311903			−0.155951	+	0.987765i	$0.549844\pi$
$434$	1.22051	+	0.526239i	0.0585862	+	0.0252603i
$435$		0			0
$436$	−11.5507	+	10.9047i	−0.553179	+	0.522239i
$437$		−	46.0247i		−	2.20166i
$438$		0			0
$439$	25.3338			1.20912			0.604559	−	0.796560i	$-0.293349\pi$
$439$	25.3338			1.20912			0.604559	+	0.796560i	$0.293349\pi$
$440$	2.43716	+	6.68583i	0.116187	+	0.318735i
$441$		0			0
$442$	−6.45421	+	14.9693i	−0.306995	+	0.712016i
$443$			1.46196i			0.0694597i	0.999397	+	0.0347299i	$0.0110571\pi$
$443$			1.46196i			0.0694597i	−0.999397	+	0.0347299i	$0.988943\pi$
$444$		0			0
$445$		−	2.64122i		−	0.125206i
$446$	18.9152	+	8.15556i	0.895662	+	0.386177i
$447$		0			0
$448$	−9.04677	+	7.60628i	−0.427420	+	0.359363i
$449$	6.00066			0.283188			0.141594	−	0.989925i	$-0.454777\pi$
$449$	6.00066			0.283188			0.141594	+	0.989925i	$0.454777\pi$
$450$		0			0
$451$		−	6.72955i		−	0.316882i
$452$	−6.70345	−	7.10059i	−0.315304	−	0.333983i
$453$		0			0
$454$	−4.00430	+	9.28719i	−0.187931	+	0.435869i
$455$	12.9261			0.605986
$456$		0			0
$457$	17.5689			0.821837			0.410919	−	0.911672i	$-0.365208\pi$
$457$	17.5689			0.821837			0.410919	+	0.911672i	$0.365208\pi$
$458$	−3.63114	+	8.42172i	−0.169672	+	0.393521i
$459$		0			0
$460$	23.6123	−	22.2917i	1.10093	−	1.03936i
$461$			26.1231i			1.21668i	0.793678	+	0.608338i	$0.208163\pi$
$461$			26.1231i			1.21668i	−0.793678	+	0.608338i	$0.791837\pi$
$462$		0			0
$463$	20.3258			0.944619			0.472310	−	0.881433i	$-0.343420\pi$
$463$	20.3258			0.944619			0.472310	+	0.881433i	$0.343420\pi$
$464$	−5.64983	−	0.325357i	−0.262287	−	0.0151043i
$465$		0			0
$466$	−14.9066	−	6.42720i	−0.690537	−	0.297734i
$467$		−	1.29764i		−	0.0600478i	−0.999549	−	0.0300239i	$-0.990442\pi$
$467$		−	1.29764i		−	0.0600478i	0.999549	−	0.0300239i	$-0.00955833\pi$
$468$		0			0
$469$			11.3234i			0.522868i
$470$	−1.21481	+	2.81751i	−0.0560349	+	0.129962i
$471$		0			0
$472$	6.99518	−	2.54992i	0.321979	−	0.117370i
$473$	3.21471			0.147813
$474$		0			0
$475$			9.48557i			0.435228i
$476$	6.72383	+	7.12217i	0.308186	+	0.326444i
$477$		0			0
$478$	−0.145495	−	0.0627320i	−0.00665476	−	0.00286929i
$479$	28.5133			1.30281			0.651404	−	0.758731i	$-0.274180\pi$
$479$	28.5133			1.30281			0.651404	+	0.758731i	$0.274180\pi$
$480$		0			0
$481$	24.2582			1.10608
$482$	3.81719	+	1.64584i	0.173868	+	0.0749658i
$483$		0			0
$484$	−1.37296	−	1.45430i	−0.0624072	−	0.0661045i
$485$		−	40.7861i		−	1.85200i
$486$		0			0
$487$	−6.03364			−0.273410			−0.136705	−	0.990612i	$-0.543651\pi$
$487$	−6.03364			−0.273410			−0.136705	+	0.990612i	$0.543651\pi$
$488$	−17.1665	+	6.25763i	−0.777090	+	0.283270i
$489$		0			0
$490$	−6.78624	+	15.7394i	−0.306571	+	0.711031i
$491$		−	4.15408i		−	0.187471i	−0.995597	−	0.0937354i	$-0.970119\pi$
$491$		−	4.15408i		−	0.187471i	0.995597	−	0.0937354i	$-0.0298808\pi$
$492$		0			0
$493$			4.68971i			0.211214i
$494$	32.2075	+	13.8867i	1.44909	+	0.624793i
$495$		0			0
$496$	−0.146288	+	2.54029i	−0.00656850	+	0.114062i
$497$	−18.1577			−0.814482
$498$		0			0
$499$		−	30.1028i		−	1.34759i	−0.738920	−	0.673793i	$-0.764664\pi$
$499$		−	30.1028i		−	1.34759i	0.738920	−	0.673793i	$-0.235336\pi$
$500$	13.4283	−	12.6772i	0.600531	−	0.566943i
$501$		0			0
$502$	17.4809	−	40.5436i	0.780212	−	1.80955i
$503$	−14.0368			−0.625869			−0.312935	−	0.949775i	$-0.601312\pi$
$503$	−14.0368			−0.625869			−0.312935	+	0.949775i	$0.601312\pi$
$504$		0			0
$505$	21.7242			0.966716
$506$	−3.61340	+	8.38057i	−0.160635	+	0.372562i
$507$		0			0
$508$	−5.65683	−	5.99196i	−0.250981	−	0.265850i
$509$		−	16.9844i		−	0.752821i	−0.926453	−	0.376411i	$-0.877158\pi$
$509$		−	16.9844i		−	0.752821i	0.926453	−	0.376411i	$-0.122842\pi$
$510$		0			0
$511$	−19.5671			−0.865597
$512$	−19.6126	−	11.2849i	−0.866760	−	0.498725i
$513$		0			0
$514$	−9.21702	−	3.97405i	−0.406546	−	0.175288i
$515$			12.4662i			0.549326i
$516$		0			0
$517$		−	0.862328i		−	0.0379251i
$518$	5.77085	−	13.3844i	0.253557	−	0.588075i
$519$		0			0
$520$	8.47506	+	23.2495i	0.371656	+	1.01956i
$521$	3.66607			0.160613			0.0803066	−	0.996770i	$-0.474410\pi$
$521$	3.66607			0.160613			0.0803066	+	0.996770i	$0.474410\pi$
$522$		0			0
$523$		−	2.91807i		−	0.127598i	−0.997963	−	0.0637990i	$-0.979678\pi$
$523$		−	2.91807i		−	0.127598i	0.997963	−	0.0637990i	$-0.0203217\pi$
$524$	19.3444	−	18.2624i	0.845063	−	0.797799i
$525$		0			0
$526$	−21.2800	−	9.17516i	−0.927851	−	0.400056i
$527$	2.10860			0.0918519
$528$		0			0
$529$	18.6453			0.810666
$530$	43.2970	+	18.6681i	1.88070	+	0.810890i
$531$		0			0
$532$	15.3239	−	14.4668i	0.664375	−	0.627217i
$533$		−	23.4016i		−	1.01363i
$534$		0			0
$535$	−15.9679			−0.690352
$536$	−20.3668	+	7.42424i	−0.879713	+	0.320678i
$537$		0			0
$538$	9.58947	−	22.2409i	0.413431	−	0.958873i
$539$		−	4.81719i		−	0.207491i
$540$		0			0
$541$			16.4673i			0.707984i	0.935248	+	0.353992i	$0.115176\pi$
$541$			16.4673i			0.707984i	−0.935248	+	0.353992i	$0.884824\pi$
$542$	25.3420	+	10.9266i	1.08853	+	0.469337i
$543$		0			0
$544$	−8.40176	+	16.7635i	−0.360223	+	0.718727i
$545$	19.9828			0.855971
$546$		0			0
$547$			25.9536i			1.10969i	0.831952	+	0.554847i	$0.187223\pi$
$547$			25.9536i			1.10969i	−0.831952	+	0.554847i	$0.812777\pi$
$548$	9.39714	+	9.95386i	0.401426	+	0.425208i
$549$		0			0
$550$	0.744712	−	1.72721i	0.0317546	−	0.0736486i
$551$	10.0903			0.429860
$552$		0			0
$553$	−24.1426			−1.02665
$554$	−5.91385	+	13.7160i	−0.251255	+	0.582737i
$555$		0			0
$556$	17.7375	−	16.7454i	0.752236	−	0.710163i
$557$			13.0152i			0.551473i	0.961233	+	0.275737i	$0.0889217\pi$
$557$			13.0152i			0.551473i	−0.961233	+	0.275737i	$0.911078\pi$
$558$		0			0
$559$	11.1789			0.472819
$560$	14.8440	+	0.854821i	0.627274	+	0.0361228i
$561$		0			0
$562$	15.0635	+	6.49483i	0.635415	+	0.273968i
$563$			27.9837i			1.17937i	0.807632	+	0.589687i	$0.200749\pi$
$563$			27.9837i			1.17937i	−0.807632	+	0.589687i	$0.799251\pi$
$564$		0			0
$565$			12.2841i			0.516795i
$566$	−12.1076	+	28.0811i	−0.508918	+	1.18034i
$567$		0			0
$568$	−11.9051	−	32.6592i	−0.499528	−	1.37035i
$569$	10.6048			0.444574			0.222287	−	0.974981i	$-0.428648\pi$
$569$	10.6048			0.444574			0.222287	+	0.974981i	$0.428648\pi$
$570$		0			0
$571$		−	1.82472i		−	0.0763622i	−0.999271	−	0.0381811i	$-0.987844\pi$
$571$		−	1.82472i		−	0.0763622i	0.999271	−	0.0381811i	$-0.0121564\pi$
$572$	−4.77437	−	5.05722i	−0.199627	−	0.211453i
$573$		0			0
$574$	−12.9117	−	5.56707i	−0.538925	−	0.232365i
$575$	−8.58298			−0.357935
$576$		0			0
$577$	23.3377			0.971560			0.485780	−	0.874081i	$-0.338536\pi$
$577$	23.3377			0.971560			0.485780	+	0.874081i	$0.338536\pi$
$578$	−7.80798	−	3.36652i	−0.324769	−	0.140029i
$579$		0			0
$580$	4.88714	+	5.17667i	0.202927	+	0.214949i
$581$		−	20.3944i		−	0.846103i
$582$		0			0
$583$	−13.2515			−0.548821
$584$	−12.8292	−	35.1943i	−0.530877	−	1.45635i
$585$		0			0
$586$	−11.2716	+	26.1424i	−0.465627	+	1.07993i
$587$			30.3967i			1.25461i	0.778775	+	0.627303i	$0.215841\pi$
$587$			30.3967i			1.25461i	−0.778775	+	0.627303i	$0.784159\pi$
$588$		0			0
$589$		−	4.53681i		−	0.186936i
$590$	−8.60079	−	3.70835i	−0.354089	−	0.152670i
$591$		0			0
$592$	27.8574	+	1.60422i	1.14493	+	0.0659331i
$593$	−39.3809			−1.61718			−0.808590	−	0.588373i	$-0.799769\pi$
$593$	−39.3809			−1.61718			−0.808590	+	0.588373i	$0.799769\pi$
$594$		0			0
$595$		−	12.3214i		−	0.505130i
$596$	−4.42113	+	4.17385i	−0.181096	+	0.170968i
$597$		0			0
$598$	−12.5654	+	29.1429i	−0.513835	+	1.19174i
$599$	35.9183			1.46758			0.733792	−	0.679374i	$-0.237749\pi$
$599$	35.9183			1.46758			0.733792	+	0.679374i	$0.237749\pi$
$600$		0			0
$601$	13.8292			0.564104			0.282052	−	0.959399i	$-0.408985\pi$
$601$	13.8292			0.564104			0.282052	+	0.959399i	$0.408985\pi$
$602$	2.65939	−	6.16794i	0.108389	−	0.251386i
$603$		0			0
$604$	−2.52170	−	2.67110i	−0.102607	−	0.108685i
$605$			2.51595i			0.102288i
$606$		0			0
$607$	19.7004			0.799615			0.399807	−	0.916599i	$-0.369077\pi$
$607$	19.7004			0.799615			0.399807	+	0.916599i	$0.369077\pi$
$608$	36.0679	+	18.0770i	1.46274	+	0.733121i
$609$		0			0
$610$	21.1067	+	9.10046i	0.854586	+	0.368467i
$611$		−	2.99869i		−	0.121314i
$612$		0			0
$613$		−	31.7465i		−	1.28223i	−0.767445	−	0.641114i	$-0.778472\pi$
$613$		−	31.7465i		−	1.28223i	0.767445	−	0.641114i	$-0.221528\pi$
$614$	−1.25474	+	2.91012i	−0.0506371	+	0.117443i
$615$		0			0
$616$	−3.92610	+	1.43116i	−0.158187	+	0.0576632i
$617$	27.5402			1.10873			0.554363	−	0.832275i	$-0.312962\pi$
$617$	27.5402			1.10873			0.554363	+	0.832275i	$0.312962\pi$
$618$		0			0
$619$		−	19.6108i		−	0.788224i	−0.919063	−	0.394112i	$-0.871052\pi$
$619$		−	19.6108i		−	0.788224i	0.919063	−	0.394112i	$-0.128948\pi$
$620$	2.32754	−	2.19736i	0.0934764	−	0.0882483i
$621$		0			0
$622$	20.3782	+	8.78636i	0.817093	+	0.352301i
$623$	1.55099			0.0621392
$624$		0			0
$625$	−29.8811			−1.19525
$626$	−15.7353	−	6.78449i	−0.628908	−	0.271163i
$627$		0			0
$628$	−14.6244	+	13.8065i	−0.583579	+	0.550939i
$629$		−	23.1233i		−	0.921988i
$630$		0			0
$631$	17.6518			0.702705			0.351353	−	0.936243i	$-0.385722\pi$
$631$	17.6518			0.702705			0.351353	+	0.936243i	$0.385722\pi$
$632$	−15.8292	−	43.4240i	−0.629651	−	1.72731i
$633$		0			0
$634$	−6.66078	+	15.4484i	−0.264533	+	0.613533i
$635$			10.3662i			0.411368i
$636$		0			0
$637$		−	16.7515i		−	0.663717i
$638$	−1.83732	−	0.792187i	−0.0727403	−	0.0313630i
$639$		0			0
$640$	8.19499	+	27.2596i	0.323936	+	1.07753i
$641$	−16.7617			−0.662047			−0.331024	−	0.943622i	$-0.607394\pi$
$641$	−16.7617			−0.662047			−0.331024	+	0.943622i	$0.607394\pi$
$642$		0			0
$643$			22.1367i			0.872984i	0.899708	+	0.436492i	$0.143779\pi$
$643$			22.1367i			0.872984i	−0.899708	+	0.436492i	$0.856221\pi$
$644$	13.0903	+	13.8658i	0.515829	+	0.546388i
$645$		0			0
$646$	13.2371	−	30.7008i	0.520806	−	1.20791i
$647$	−22.7792			−0.895544			−0.447772	−	0.894148i	$-0.647782\pi$
$647$	−22.7792			−0.895544			−0.447772	+	0.894148i	$0.647782\pi$
$648$		0			0
$649$	2.63236			0.103329
$650$	2.58969	−	6.00627i	0.101576	−	0.235585i
$651$		0			0
$652$	18.7509	−	17.7021i	0.734340	−	0.693268i
$653$		−	35.9327i		−	1.40615i	−0.711114	−	0.703077i	$-0.751809\pi$
$653$		−	35.9327i		−	1.40615i	0.711114	−	0.703077i	$-0.248191\pi$
$654$		0			0
$655$	−33.4660			−1.30762
$656$	1.54757	−	26.8737i	0.0604226	−	1.04924i
$657$		0			0
$658$	−1.65451	−	0.713367i	−0.0644997	−	0.0278099i
$659$			1.49362i			0.0581831i	0.999577	+	0.0290916i	$0.00926144\pi$
$659$			1.49362i			0.0581831i	−0.999577	+	0.0290916i	$0.990739\pi$
$660$		0			0
$661$		−	44.3160i		−	1.72369i	−0.507170	−	0.861846i	$-0.669308\pi$
$661$		−	44.3160i		−	1.72369i	0.507170	−	0.861846i	$-0.330692\pi$
$662$	13.8690	−	32.1664i	0.539034	−	1.25018i
$663$		0			0
$664$	36.6823	−	13.3717i	1.42355	−	0.518921i
$665$	−26.5105			−1.02803
$666$		0			0
$667$			9.13015i			0.353521i
$668$	−6.14308	−	6.50702i	−0.237683	−	0.251764i
$669$		0			0
$670$	25.0417	+	10.7971i	0.967444	+	0.417127i
$671$	−6.45993			−0.249383
$672$		0			0
$673$	−33.8921			−1.30644			−0.653222	−	0.757166i	$-0.726583\pi$
$673$	−33.8921			−1.30644			−0.653222	+	0.757166i	$0.726583\pi$
$674$	−14.5818	−	6.28715i	−0.561671	−	0.242172i
$675$		0			0
$676$	1.24591	+	1.31972i	0.0479196	+	0.0507585i
$677$		−	7.57568i		−	0.291157i	−0.989347	−	0.145578i	$-0.953496\pi$
$677$		−	7.57568i		−	0.291157i	0.989347	−	0.145578i	$-0.0465043\pi$
$678$		0			0
$679$	23.9507			0.919143
$680$	22.1619	−	8.07858i	0.849870	−	0.309800i
$681$		0			0
$682$	−0.356185	+	0.826100i	−0.0136390	+	0.0316330i
$683$		−	16.1346i		−	0.617374i	−0.951164	−	0.308687i	$-0.900110\pi$
$683$		−	16.1346i		−	0.617374i	0.951164	−	0.308687i	$-0.0998896\pi$
$684$		0			0
$685$		−	17.2203i		−	0.657953i
$686$	−22.6732	−	9.77586i	−0.865666	−	0.373244i
$687$		0			0
$688$	12.8376	+	0.739276i	0.489428	+	0.0281847i
$689$	−46.0812			−1.75555
$690$		0			0
$691$		−	10.5531i		−	0.401457i	−0.979647	−	0.200729i	$-0.935669\pi$
$691$		−	10.5531i		−	0.401457i	0.979647	−	0.200729i	$-0.0643309\pi$
$692$	0.265856	−	0.250987i	0.0101063	−	0.00954108i
$693$		0			0
$694$	8.97175	−	20.8082i	0.340563	−	0.789869i
$695$	−30.6860			−1.16399
$696$		0			0
$697$	−22.3068			−0.844931
$698$	−5.19341	+	12.0451i	−0.196574	+	0.455914i
$699$		0			0
$700$	−2.69787	−	2.85770i	−0.101970	−	0.108011i
$701$			43.8782i			1.65726i	0.559800	+	0.828628i	$0.310878\pi$
$701$			43.8782i			1.65726i	−0.559800	+	0.828628i	$0.689122\pi$
$702$		0			0
$703$	−49.7516			−1.87642
$704$	−5.14831	−	6.12331i	−0.194034	−	0.230781i
$705$		0			0
$706$	12.4430	+	5.36496i	0.468297	+	0.201913i
$707$			12.7570i			0.479778i
$708$		0			0
$709$		−	4.31359i		−	0.162000i	−0.996714	−	0.0810002i	$-0.974189\pi$
$709$		−	4.31359i		−	0.162000i	0.996714	−	0.0810002i	$-0.0258115\pi$
$710$	−17.3136	+	40.1555i	−0.649768	+	1.50701i
$711$		0			0
$712$	1.01691	+	2.78969i	0.0381104	+	0.104548i
$713$	4.10511			0.153738
$714$		0			0
$715$			8.74905i			0.327196i
$716$	−29.2190	+	27.5848i	−1.09196	+	1.03089i
$717$		0			0
$718$	10.1359	+	4.37025i	0.378270	+	0.163096i
$719$	0.793243			0.0295830			0.0147915	−	0.999891i	$-0.495292\pi$
$719$	0.793243			0.0295830			0.0147915	+	0.999891i	$0.495292\pi$
$720$		0			0
$721$	−7.32048			−0.272629
$722$	−41.3809	−	17.8420i	−1.54004	−	0.664009i
$723$		0			0
$724$	11.1023	−	10.4813i	0.412614	−	0.389536i
$725$		−	1.88170i		−	0.0698845i
$726$		0			0
$727$	−38.5654			−1.43031			−0.715155	−	0.698966i	$-0.753644\pi$
$727$	−38.5654			−1.43031			−0.715155	+	0.698966i	$0.753644\pi$
$728$	−13.6527	+	4.97678i	−0.506004	+	0.184452i
$729$		0			0
$730$	−18.6575	+	43.2724i	−0.690546	+	1.60158i
$731$		−	10.6560i		−	0.394125i
$732$		0			0
$733$		−	35.3659i		−	1.30627i	−0.757242	−	0.653134i	$-0.773454\pi$
$733$		−	35.3659i		−	1.30627i	0.757242	−	0.653134i	$-0.226546\pi$
$734$	40.8284	+	17.6038i	1.50701	+	0.649766i
$735$		0			0
$736$	−16.3569	+	32.6359i	−0.602925	+	1.20297i
$737$	−7.66426			−0.282317
$738$		0			0
$739$			41.6624i			1.53258i	0.642497	+	0.766288i	$0.277899\pi$
$739$			41.6624i			1.53258i	−0.642497	+	0.766288i	$0.722101\pi$
$740$	−24.0968	−	25.5244i	−0.885816	−	0.938294i
$741$		0			0
$742$	−10.9624	+	25.4251i	−0.402442	+	0.933385i
$743$	−33.2692			−1.22053			−0.610264	−	0.792198i	$-0.708937\pi$
$743$	−33.2692			−1.22053			−0.610264	+	0.792198i	$0.708937\pi$
$744$		0			0
$745$	7.64859			0.280223
$746$	17.9415	−	41.6118i	0.656885	−	1.52351i
$747$		0			0
$748$	−4.82064	+	4.55102i	−0.176260	+	0.166402i
$749$		−	9.37676i		−	0.342619i
$750$		0			0
$751$	−3.69284			−0.134754			−0.0673768	−	0.997728i	$-0.521463\pi$
$751$	−3.69284			−0.134754			−0.0673768	+	0.997728i	$0.521463\pi$
$752$	0.198307	−	3.44361i	0.00723150	−	0.125575i
$753$		0			0
$754$	−6.38916	−	2.75478i	−0.232680	−	0.100323i
$755$			4.62103i			0.168176i
$756$		0			0
$757$		−	19.2210i		−	0.698600i	−0.937011	−	0.349300i	$-0.886419\pi$
$757$		−	19.2210i		−	0.698600i	0.937011	−	0.349300i	$-0.113581\pi$
$758$	−6.40920	+	14.8649i	−0.232793	+	0.539917i
$759$		0			0
$760$	−17.3817	−	47.6830i	−0.630500	−	1.72964i
$761$	9.79341			0.355011			0.177505	−	0.984120i	$-0.443197\pi$
$761$	9.79341			0.355011			0.177505	+	0.984120i	$0.443197\pi$
$762$		0			0
$763$			11.7345i			0.424816i
$764$	31.5703	+	33.4406i	1.14217	+	1.20984i
$765$		0			0
$766$	8.86351	+	3.82163i	0.320252	+	0.138081i
$767$	9.15386			0.330527
$768$		0			0
$769$	−48.2853			−1.74121			−0.870606	−	0.491981i	$-0.836273\pi$
$769$	−48.2853			−1.74121			−0.870606	+	0.491981i	$0.836273\pi$
$770$	4.82726	+	2.08134i	0.173962	+	0.0750063i
$771$		0			0
$772$	1.00951	+	1.06931i	0.0363329	+	0.0384854i
$773$		−	21.0475i		−	0.757025i	−0.925596	−	0.378513i	$-0.876436\pi$
$773$		−	21.0475i		−	0.757025i	0.925596	−	0.378513i	$-0.123564\pi$
$774$		0			0
$775$	−0.846053			−0.0303911
$776$	15.7033	+	43.0788i	0.563717	+	1.54644i
$777$		0			0
$778$	−3.72904	+	8.64877i	−0.133692	+	0.310073i
$779$			47.9948i			1.71959i
$780$		0			0
$781$		−	12.2900i		−	0.439771i
$782$	27.7795	+	11.9775i	0.993394	+	0.428316i
$783$		0			0
$784$	1.10779	−	19.2369i	0.0395641	−	0.687032i
$785$	25.3005			0.903012
$786$		0			0
$787$		−	18.2077i		−	0.649034i	−0.945880	−	0.324517i	$-0.894798\pi$
$787$		−	18.2077i		−	0.649034i	0.945880	−	0.324517i	$-0.105202\pi$
$788$	16.2394	−	15.3311i	0.578504	−	0.546149i
$789$		0			0
$790$	−23.0204	+	53.3912i	−0.819027	+	1.89957i
$791$	−7.21354			−0.256484
$792$		0			0
$793$	−22.4640			−0.797719
$794$	1.35609	−	3.14518i	0.0481258	−	0.111618i
$795$		0			0
$796$	−24.8939	−	26.3687i	−0.882339	−	0.934612i
$797$			40.2274i			1.42493i	0.701709	+	0.712463i	$0.252421\pi$
$797$			40.2274i			1.42493i	−0.701709	+	0.712463i	$0.747579\pi$
$798$		0			0
$799$	−2.85840			−0.101123
$800$	3.37112	−	6.72617i	0.119187	−	0.237806i
$801$		0			0
$802$	11.8063	+	5.09044i	0.416894	+	0.179750i
$803$		−	13.2440i		−	0.467370i
$804$		0			0
$805$		−	23.9879i		−	0.845464i
$806$	−1.23861	+	2.87271i	−0.0436281	+	0.101187i
$807$		0			0
$808$	−22.9454	+	8.36419i	−0.807216	+	0.294251i
$809$	−27.8044			−0.977552			−0.488776	−	0.872409i	$-0.662556\pi$
$809$	−27.8044			−0.977552			−0.488776	+	0.872409i	$0.662556\pi$
$810$		0			0
$811$		−	7.59987i		−	0.266868i	−0.991058	−	0.133434i	$-0.957400\pi$
$811$		−	7.59987i		−	0.266868i	0.991058	−	0.133434i	$-0.0426004\pi$
$812$	−3.03988	+	2.86985i	−0.106679	+	0.100712i
$813$		0			0
$814$	9.05920	+	3.90600i	0.317525	+	0.136905i
$815$	−32.4392			−1.13629
$816$		0			0
$817$	−22.9271			−0.802119
$818$	11.7919	+	5.08423i	0.412293	+	0.177766i
$819$		0			0
$820$	−24.6231	+	23.2459i	−0.859874	+	0.811781i
$821$		−	26.6456i		−	0.929937i	−0.885327	−	0.464968i	$-0.846066\pi$
$821$		−	26.6456i		−	0.929937i	0.885327	−	0.464968i	$-0.153934\pi$
$822$		0			0
$823$	35.5588			1.23950			0.619751	−	0.784799i	$-0.287234\pi$
$823$	35.5588			1.23950			0.619751	+	0.784799i	$0.287234\pi$
$824$	−4.79969	−	13.1669i	−0.167205	−	0.458692i
$825$		0			0
$826$	2.17764	−	5.05061i	0.0757698	−	0.175733i
$827$			3.03188i			0.105429i	0.998610	+	0.0527145i	$0.0167873\pi$
$827$			3.03188i			0.105429i	−0.998610	+	0.0527145i	$0.983213\pi$
$828$		0			0
$829$			35.0569i			1.21758i	0.793332	+	0.608789i	$0.208344\pi$
$829$			35.0569i			1.21758i	−0.793332	+	0.608789i	$0.791656\pi$
$830$	−45.1021	−	19.4464i	−1.56552	−	0.674994i
$831$		0			0
$832$	−17.9029	−	21.2934i	−0.620672	−	0.738215i
$833$	−15.9678			−0.553252
$834$		0			0
$835$			11.2572i			0.389572i
$836$	9.79187	+	10.3720i	0.338659	+	0.358722i
$837$		0			0
$838$	1.67706	−	3.88960i	0.0579329	−	0.134364i
$839$	6.41520			0.221477			0.110739	−	0.993850i	$-0.464678\pi$
$839$	6.41520			0.221477			0.110739	+	0.993850i	$0.464678\pi$
$840$		0			0
$841$	26.9983			0.930977
$842$	−14.9303	+	34.6278i	−0.514531	+	1.19335i
$843$		0			0
$844$	−26.7852	+	25.2871i	−0.921985	+	0.870419i
$845$		−	2.28313i		−	0.0785421i
$846$		0			0
$847$	−1.47743			−0.0507652
$848$	−52.9183	−	3.04740i	−1.81722	−	0.104648i
$849$		0			0
$850$	−5.72529	−	2.46854i	−0.196376	−	0.0846701i
$851$		−	45.0176i		−	1.54318i
$852$		0			0
$853$			10.5605i			0.361585i	0.983521	+	0.180793i	$0.0578663\pi$
$853$			10.5605i			0.361585i	−0.983521	+	0.180793i	$0.942134\pi$
$854$	−5.34403	+	12.3944i	−0.182869	+	0.424128i
$855$		0			0
$856$	16.8655	−	6.14790i	0.576450	−	0.210131i
$857$	5.03900			0.172129			0.0860644	−	0.996290i	$-0.472571\pi$
$857$	5.03900			0.172129			0.0860644	+	0.996290i	$0.472571\pi$
$858$		0			0
$859$			24.5174i			0.836521i	0.908327	+	0.418261i	$0.137360\pi$
$859$			24.5174i			0.836521i	−0.908327	+	0.418261i	$0.862640\pi$
$860$	−11.1046	−	11.7624i	−0.378663	−	0.401096i
$861$		0			0
$862$	−25.4145	−	10.9578i	−0.865623	−	0.373225i
$863$	−17.8155			−0.606448			−0.303224	−	0.952919i	$-0.598063\pi$
$863$	−17.8155			−0.606448			−0.303224	+	0.952919i	$0.598063\pi$
$864$		0			0
$865$	−0.459934			−0.0156382
$866$	−8.42857	−	3.63409i	−0.286414	−	0.123492i
$867$		0			0
$868$	1.29035	+	1.36679i	0.0437973	+	0.0463920i
$869$		−	16.3409i		−	0.554328i
$870$		0			0
$871$	−26.6520			−0.903067
$872$	−21.1061	+	7.69373i	−0.714743	+	0.260542i
$873$		0			0
$874$	25.7706	−	59.7698i	0.871703	−	2.02174i
$875$		−	13.6419i		−	0.461180i
$876$		0			0
$877$			22.4071i			0.756634i	0.925676	+	0.378317i	$0.123497\pi$
$877$			22.4071i			0.756634i	−0.925676	+	0.378317i	$0.876503\pi$
$878$	32.8997	+	14.1852i	1.11031	+	0.478726i
$879$		0			0
$880$	−0.578585	+	10.0472i	−0.0195041	+	0.338690i
$881$	12.0016			0.404345			0.202172	−	0.979350i	$-0.435200\pi$
$881$	12.0016			0.404345			0.202172	+	0.979350i	$0.435200\pi$
$882$		0			0
$883$		−	27.9363i		−	0.940130i	−0.882632	−	0.470065i	$-0.844230\pi$
$883$		−	27.9363i		−	0.940130i	0.882632	−	0.470065i	$-0.155770\pi$
$884$	−16.7635	+	15.8259i	−0.563816	+	0.532282i
$885$		0			0
$886$	−0.818593	+	1.89857i	−0.0275012	+	0.0637836i
$887$	48.6903			1.63486			0.817430	−	0.576028i	$-0.195398\pi$
$887$	48.6903			1.63486			0.817430	+	0.576028i	$0.195398\pi$
$888$		0			0
$889$	−6.08728			−0.204161
$890$	1.47890	−	3.43001i	0.0495727	−	0.114974i
$891$		0			0
$892$	19.9976	+	21.1824i	0.669570	+	0.709238i
$893$			6.15008i			0.205804i
$894$		0			0
$895$	50.5492			1.68967
$896$	−16.0075	+	4.81232i	−0.534774	+	0.160768i
$897$		0			0
$898$	7.79272	+	3.35994i	0.260047	+	0.112123i
$899$			0.899988i			0.0300163i
$900$		0			0
$901$			43.9254i			1.46337i
$902$	3.76807	−	8.73930i	0.125463	−	0.290987i
$903$		0			0
$904$	−4.72958	−	12.9746i	−0.157303	−	0.431529i
$905$	−19.2071			−0.638465
$906$		0			0
$907$		−	48.2773i		−	1.60302i	−0.597981	−	0.801510i	$-0.704030\pi$
$907$		−	48.2773i		−	1.60302i	0.597981	−	0.801510i	$-0.295970\pi$
$908$	−10.4003	+	9.81864i	−0.345147	+	0.325843i
$909$		0			0
$910$	16.7865	+	7.23772i	0.556466	+	0.239928i
$911$	−43.1688			−1.43025			−0.715123	−	0.698998i	$-0.753630\pi$
$911$	−43.1688			−1.43025			−0.715123	+	0.698998i	$0.753630\pi$
$912$		0			0
$913$	13.8040			0.456844
$914$	22.8157	+	9.83732i	0.754677	+	0.325390i
$915$		0			0
$916$	−9.43113	+	8.90364i	−0.311613	+	0.294185i
$917$		−	19.6521i		−	0.648970i
$918$		0			0
$919$	36.1457			1.19234			0.596168	−	0.802860i	$-0.296689\pi$
$919$	36.1457			1.19234			0.596168	+	0.802860i	$0.296689\pi$
$920$	43.1458	−	15.7278i	1.42247	−	0.518529i
$921$		0			0
$922$	−14.6271	+	33.9247i	−0.481718	+	1.11725i
$923$		−	42.7377i		−	1.40673i
$924$		0			0
$925$			9.27801i			0.305059i
$926$	26.3960	+	11.3810i	0.867426	+	0.374003i
$927$		0			0
$928$	−7.15495	−	3.58603i	−0.234873	−	0.117717i
$929$	−26.1901			−0.859269			−0.429634	−	0.903003i	$-0.641358\pi$
$929$	−26.1901			−0.859269			−0.429634	+	0.903003i	$0.641358\pi$
$930$		0			0
$931$			34.3560i			1.12597i
$932$	−15.7597	−	16.6933i	−0.516225	−	0.546808i
$933$		0			0
$934$	0.726588	−	1.68518i	0.0237747	−	0.0551407i
$935$	8.33976			0.272739
$936$		0			0
$937$	−14.6547			−0.478749			−0.239375	−	0.970927i	$-0.576942\pi$
$937$	−14.6547			−0.478749			−0.239375	+	0.970927i	$0.576942\pi$
$938$	−6.34032	+	14.7051i	−0.207019	+	0.480139i
$939$		0			0
$940$	−3.15521	+	2.97874i	−0.102912	+	0.0971557i
$941$		−	5.50159i		−	0.179347i	−0.995971	−	0.0896734i	$-0.971418\pi$
$941$		−	5.50159i		−	0.179347i	0.995971	−	0.0896734i	$-0.0285823\pi$
$942$		0			0
$943$	−43.4279			−1.41421
$944$	10.5120	+	0.605356i	0.342137	+	0.0197026i
$945$		0			0
$946$	4.17477	+	1.80001i	0.135733	+	0.0585233i
$947$			1.00019i			0.0325019i	0.999868	+	0.0162509i	$0.00517306\pi$
$947$			1.00019i			0.0325019i	−0.999868	+	0.0162509i	$0.994827\pi$
$948$		0			0
$949$		−	46.0551i		−	1.49501i
$950$	−5.31125	+	12.3184i	−0.172320	+	0.399661i
$951$		0			0
$952$	4.74396	+	13.0140i	0.153753	+	0.421788i
$953$	−55.6770			−1.80356			−0.901778	−	0.432200i	$-0.857737\pi$
$953$	−55.6770			−1.80356			−0.901778	+	0.432200i	$0.857737\pi$
$954$		0			0
$955$		−	57.8526i		−	1.87207i
$956$	−0.153820	−	0.162933i	−0.00497490	−	0.00526964i
$957$		0			0
$958$	37.0287	+	15.9654i	1.19634	+	0.515820i
$959$	10.1122			0.326540
$960$		0			0
$961$	−30.5953			−0.986947
$962$	31.5028	+	13.5829i	1.01569	+	0.437929i
$963$		0			0
$964$	4.03563	+	4.27471i	0.129979	+	0.137679i
$965$		−	1.84992i		−	0.0595511i
$966$		0			0
$967$	−25.9869			−0.835682			−0.417841	−	0.908520i	$-0.637213\pi$
$967$	−25.9869			−0.835682			−0.417841	+	0.908520i	$0.637213\pi$
$968$	−0.968683	−	2.65738i	−0.0311347	−	0.0854113i
$969$		0			0
$970$	22.8373	−	52.9667i	0.733262	−	1.70066i
$971$		−	16.0587i		−	0.515349i	−0.966232	−	0.257675i	$-0.917044\pi$
$971$		−	16.0587i		−	0.515349i	0.966232	−	0.257675i	$-0.0829563\pi$
$972$		0			0
$973$		−	18.0196i		−	0.577683i
$974$	−7.83556	−	3.37841i	−0.251068	−	0.108251i
$975$		0			0
$976$	−25.7970	−	1.48557i	−0.825742	−	0.0475519i
$977$	5.40488			0.172918			0.0864588	−	0.996255i	$-0.472445\pi$
$977$	5.40488			0.172918			0.0864588	+	0.996255i	$0.472445\pi$
$978$		0			0
$979$			1.04979i			0.0335514i
$980$	−17.6258	+	16.6400i	−0.563037	+	0.531546i
$981$		0			0
$982$	2.32599	−	5.39467i	0.0742252	−	0.172151i
$983$	36.4792			1.16350			0.581752	−	0.813366i	$-0.302367\pi$
$983$	36.4792			1.16350			0.581752	+	0.813366i	$0.302367\pi$
$984$		0			0
$985$	−28.0943			−0.895159
$986$	−2.62590	+	6.09027i	−0.0836258	+	0.193954i
$987$		0			0
$988$	34.0506	+	36.0679i	1.08329	+	1.14747i
$989$		−	20.7455i		−	0.659670i
$990$		0			0
$991$	48.2714			1.53339			0.766696	−	0.642010i	$-0.221899\pi$
$991$	48.2714			1.53339			0.766696	+	0.642010i	$0.221899\pi$
$992$	−1.61236	+	3.21702i	−0.0511924	+	0.102141i
$993$		0			0
$994$	−23.5804	−	10.1670i	−0.747924	−	0.322478i
$995$			45.6181i			1.44619i
$996$		0			0
$997$		−	8.78994i		−	0.278380i	−0.990266	−	0.139190i	$-0.955550\pi$
$997$		−	8.78994i		−	0.278380i	0.990266	−	0.139190i	$-0.0444499\pi$
$998$	16.8554	−	39.0929i	0.533549	−	1.23746i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.f.g.397.10		10
3.2	odd	2		88.2.c.a.45.1	✓	10
4.3	odd	2		3168.2.f.g.1585.2		10
8.3	odd	2		3168.2.f.g.1585.9		10
8.5	even	2	inner	792.2.f.g.397.9		10
12.11	even	2		352.2.c.a.177.5		10
24.5	odd	2		88.2.c.a.45.2	yes	10
24.11	even	2		352.2.c.a.177.6		10
33.2	even	10		968.2.o.h.565.4		40
33.5	odd	10		968.2.o.g.245.10		40
33.8	even	10		968.2.o.h.493.8		40
33.14	odd	10		968.2.o.g.493.3		40
33.17	even	10		968.2.o.h.245.1		40
33.20	odd	10		968.2.o.g.565.7		40
33.26	odd	10		968.2.o.g.269.6		40
33.29	even	10		968.2.o.h.269.5		40
33.32	even	2		968.2.c.d.485.10		10
48.5	odd	4		2816.2.a.r.1.3		5
48.11	even	4		2816.2.a.q.1.3		5
48.29	odd	4		2816.2.a.o.1.3		5
48.35	even	4		2816.2.a.p.1.3		5
132.131	odd	2		3872.2.c.f.1937.5		10
264.5	odd	10		968.2.o.g.245.7		40
264.29	even	10		968.2.o.h.269.8		40
264.53	odd	10		968.2.o.g.565.10		40
264.101	even	10		968.2.o.h.565.1		40
264.125	odd	10		968.2.o.g.269.3		40
264.131	odd	2		3872.2.c.f.1937.6		10
264.149	even	10		968.2.o.h.245.4		40
264.173	even	10		968.2.o.h.493.5		40
264.197	even	2		968.2.c.d.485.9		10
264.245	odd	10		968.2.o.g.493.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.1	✓	10	3.2	odd	2
88.2.c.a.45.2	yes	10	24.5	odd	2
352.2.c.a.177.5		10	12.11	even	2
352.2.c.a.177.6		10	24.11	even	2
792.2.f.g.397.9		10	8.5	even	2	inner
792.2.f.g.397.10		10	1.1	even	1	trivial
968.2.c.d.485.9		10	264.197	even	2
968.2.c.d.485.10		10	33.32	even	2
968.2.o.g.245.7		40	264.5	odd	10
968.2.o.g.245.10		40	33.5	odd	10
968.2.o.g.269.3		40	264.125	odd	10
968.2.o.g.269.6		40	33.26	odd	10
968.2.o.g.493.3		40	33.14	odd	10
968.2.o.g.493.6		40	264.245	odd	10
968.2.o.g.565.7		40	33.20	odd	10
968.2.o.g.565.10		40	264.53	odd	10
968.2.o.h.245.1		40	33.17	even	10
968.2.o.h.245.4		40	264.149	even	10
968.2.o.h.269.5		40	33.29	even	10
968.2.o.h.269.8		40	264.29	even	10
968.2.o.h.493.5		40	264.173	even	10
968.2.o.h.493.8		40	33.8	even	10
968.2.o.h.565.1		40	264.101	even	10
968.2.o.h.565.4		40	33.2	even	10
2816.2.a.o.1.3		5	48.29	odd	4
2816.2.a.p.1.3		5	48.35	even	4
2816.2.a.q.1.3		5	48.11	even	4
2816.2.a.r.1.3		5	48.5	odd	4
3168.2.f.g.1585.2		10	4.3	odd	2
3168.2.f.g.1585.9		10	8.3	odd	2
3872.2.c.f.1937.5		10	132.131	odd	2
3872.2.c.f.1937.6		10	264.131	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.29865 + 0.559929i) q^{2} +(1.37296 + 1.45430i) q^{4} -2.51595i q^{5} +1.47743 q^{7} +(0.968683 + 2.65738i) q^{8} +(1.40875 - 3.26733i) q^{10} +1.00000i q^{11} +3.47743i q^{13} +(1.91866 + 0.827257i) q^{14} +(-0.229967 + 3.99338i) q^{16} +3.31475 q^{17} -7.13195i q^{19} +(3.65894 - 3.45430i) q^{20} +(-0.559929 + 1.29865i) q^{22} +6.45332 q^{23} -1.33001 q^{25} +(-1.94712 + 4.51595i) q^{26} +(2.02845 + 2.14863i) q^{28} +1.41480i q^{29} +0.636125 q^{31} +(-2.53466 + 5.05722i) q^{32} +(4.30469 + 1.85603i) q^{34} -3.71715i q^{35} -6.97588i q^{37} +(3.99338 - 9.26187i) q^{38} +(6.68583 - 2.43716i) q^{40} -6.72955 q^{41} -3.21471i q^{43} +(-1.45430 + 1.37296i) q^{44} +(8.38057 + 3.61340i) q^{46} -0.862328 q^{47} -4.81719 q^{49} +(-1.72721 - 0.744712i) q^{50} +(-5.05722 + 4.77437i) q^{52} +13.2515i q^{53} +2.51595 q^{55} +(1.43116 + 3.92610i) q^{56} +(-0.792187 + 1.83732i) q^{58} -2.63236i q^{59} +6.45993i q^{61} +(0.826100 + 0.356185i) q^{62} +(-6.12331 + 5.14831i) q^{64} +8.74905 q^{65} +7.66426i q^{67} +(4.55102 + 4.82064i) q^{68} +(2.08134 - 4.82726i) q^{70} -12.2900 q^{71} -13.2440 q^{73} +(3.90600 - 9.05920i) q^{74} +(10.3720 - 9.79187i) q^{76} +1.47743i q^{77} -16.3409 q^{79} +(10.0472 + 0.578585i) q^{80} +(-8.73930 - 3.76807i) q^{82} -13.8040i q^{83} -8.33976i q^{85} +(1.80001 - 4.17477i) q^{86} +(-2.65738 + 0.968683i) q^{88} +1.04979 q^{89} +5.13767i q^{91} +(8.86014 + 9.38505i) q^{92} +(-1.11986 - 0.482842i) q^{94} -17.9436 q^{95} +16.2110 q^{97} +(-6.25582 - 2.69729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{4} + 10 q^{10} + 12 q^{14} + 4 q^{17} - 12 q^{20} + 12 q^{23} - 6 q^{25} + 20 q^{26} - 12 q^{28} - 4 q^{31} + 20 q^{32} - 8 q^{38} + 20 q^{40} - 4 q^{41} - 4 q^{44} + 2 q^{46} + 4 q^{47} - 6 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 10 * q - 4 * q^4 + 10 * q^10 + 12 * q^14 + 4 * q^17 - 12 * q^20 + 12 * q^23 - 6 * q^25 + 20 * q^26 - 12 * q^28 - 4 * q^31 + 20 * q^32 - 8 * q^38 + 20 * q^40 - 4 * q^41 - 4 * q^44 + 2 * q^46 + 4 * q^47 - 6 * q^49 + 6 * q^50 - 20 * q^52 - 8 * q^55 + 8 * q^56 + 36 * q^58 - 22 * q^62 - 16 * q^64 - 16 * q^65 + 28 * q^68 + 28 * q^70 + 12 * q^71 - 4 * q^73 + 14 * q^74 + 44 * q^76 + 16 * q^79 + 56 * q^80 - 4 * q^82 + 20 * q^86 - 12 * q^88 + 4 * q^89 + 36 * q^92 - 24 * q^95 - 20 * q^97 - 24 * q^98

Introduction

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