LMFDB - Embedded newform 1264.2.n.i.767.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1264,2,Mod(735,1264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1264, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1264.735");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1264 = 2^{4} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1264.n (of order $6$, degree $2$, 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:	$10.0930908155$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			767.5
Character	$\chi$	$=$	1264.767
Dual form			1264.2.n.i.735.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.799764 - 1.38523i) q^{3} +(1.24399 - 2.15465i) q^{5} +(0.627964 - 1.08766i) q^{7} +(0.220755 - 0.382358i) q^{9} +O(q^{10})$	\(q+(-0.799764 - 1.38523i) q^{3} +(1.24399 - 2.15465i) q^{5} +(0.627964 - 1.08766i) q^{7} +(0.220755 - 0.382358i) q^{9} +(-4.25539 - 2.45685i) q^{11} +(0.756372 + 1.31008i) q^{13} -3.97960 q^{15} -5.86824i q^{17} +(4.82996 + 2.78858i) q^{19} -2.00889 q^{21} +(-2.76671 - 1.59736i) q^{23} +(-0.595025 - 1.03061i) q^{25} -5.50479 q^{27} +(3.75797 + 2.16966i) q^{29} +(-2.49981 - 1.44327i) q^{31} +7.85961i q^{33} +(-1.56236 - 2.70609i) q^{35} +(-4.96955 + 2.86917i) q^{37} +(1.20984 - 2.09550i) q^{39} -10.3606i q^{41} +(1.55506 + 2.69344i) q^{43} +(-0.549233 - 0.951300i) q^{45} +(1.56236 - 2.70609i) q^{47} +(2.71132 + 4.69615i) q^{49} +(-8.12888 + 4.69321i) q^{51} +(7.99221 + 4.61431i) q^{53} +(-10.5873 + 6.11260i) q^{55} -8.92083i q^{57} +(2.13693 + 3.70127i) q^{59} +4.46923i q^{61} +(-0.277252 - 0.480214i) q^{63} +3.76368 q^{65} +7.16896i q^{67} +5.11004i q^{69} -12.7847 q^{71} +(3.18173 - 5.51093i) q^{73} +(-0.951759 + 1.64850i) q^{75} +(-5.34447 + 3.08563i) q^{77} +(0.689399 - 8.86142i) q^{79} +(3.74027 + 6.47834i) q^{81} +(-0.643709 - 0.371646i) q^{83} +(-12.6440 - 7.30004i) q^{85} -6.94088i q^{87} -11.3878 q^{89} +1.89990 q^{91} +4.61709i q^{93} +(12.0169 - 6.93794i) q^{95} -18.4361 q^{97} +(-1.87880 + 1.08472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{9}+O(q^{10}) $ 28 * q - 20 * q^9	$ 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) $ 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times$.

$n$	$159$	$161$	$949$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.799764	−	1.38523i	−0.461744	−	0.799764i	0.537304	−	0.843389i	$-0.319443\pi$
$3$	−0.799764	−	1.38523i	−0.461744	−	0.799764i	−0.999048	+	0.0436245i	$0.986109\pi$
$4$		0			0
$5$	1.24399	−	2.15465i	0.556329	−	0.963591i	−0.441469	−	0.897276i	$-0.645543\pi$
$5$	1.24399	−	2.15465i	0.556329	−	0.963591i	0.997799	−	0.0663146i	$-0.0211241\pi$
$6$		0			0
$7$	0.627964	−	1.08766i	0.237348	−	0.411099i	−0.722604	−	0.691262i	$-0.757055\pi$
$7$	0.627964	−	1.08766i	0.237348	−	0.411099i	0.959952	+	0.280163i	$0.0903885\pi$
$8$		0			0
$9$	0.220755	−	0.382358i	0.0735849	−	0.127453i
$10$		0			0
$11$	−4.25539	−	2.45685i	−1.28305	−	0.740769i	−0.305645	−	0.952146i	$-0.598872\pi$
$11$	−4.25539	−	2.45685i	−1.28305	−	0.740769i	−0.977405	+	0.211377i	$0.932205\pi$
$12$		0			0
$13$	0.756372	+	1.31008i	0.209780	+	0.363350i	0.951645	−	0.307200i	$-0.0993919\pi$
$13$	0.756372	+	1.31008i	0.209780	+	0.363350i	−0.741865	+	0.670549i	$0.766059\pi$
$14$		0			0
$15$	−3.97960			−1.02753
$16$		0			0
$17$		−	5.86824i		−	1.42326i	−0.702555	−	0.711629i	$-0.747958\pi$
$17$		−	5.86824i		−	1.42326i	0.702555	−	0.711629i	$-0.252042\pi$
$18$		0			0
$19$	4.82996	+	2.78858i	1.10807	+	0.639744i	0.938329	−	0.345744i	$-0.112374\pi$
$19$	4.82996	+	2.78858i	1.10807	+	0.639744i	0.169741	+	0.985489i	$0.445707\pi$
$20$		0			0
$21$	−2.00889			−0.438376
$22$		0			0
$23$	−2.76671	−	1.59736i	−0.576898	−	0.333072i	0.183002	−	0.983113i	$-0.441419\pi$
$23$	−2.76671	−	1.59736i	−0.576898	−	0.333072i	−0.759900	+	0.650040i	$0.774752\pi$
$24$		0			0
$25$	−0.595025	−	1.03061i	−0.119005	−	0.206123i
$26$		0			0
$27$	−5.50479			−1.05940
$28$		0			0
$29$	3.75797	+	2.16966i	0.697837	+	0.402897i	0.806541	−	0.591178i	$-0.201337\pi$
$29$	3.75797	+	2.16966i	0.697837	+	0.402897i	−0.108704	+	0.994074i	$0.534670\pi$
$30$		0			0
$31$	−2.49981	−	1.44327i	−0.448979	−	0.259218i	0.258420	−	0.966033i	$-0.416798\pi$
$31$	−2.49981	−	1.44327i	−0.448979	−	0.259218i	−0.707399	+	0.706814i	$0.750132\pi$
$32$		0			0
$33$			7.85961i			1.36818i
$34$		0			0
$35$	−1.56236	−	2.70609i	−0.264087	−	0.457413i
$36$		0			0
$37$	−4.96955	+	2.86917i	−0.816990	+	0.471689i	−0.849377	−	0.527786i	$-0.823022\pi$
$37$	−4.96955	+	2.86917i	−0.816990	+	0.471689i	0.0323876	+	0.999475i	$0.489689\pi$
$38$		0			0
$39$	1.20984	−	2.09550i	0.193729	−	0.335549i
$40$		0			0
$41$		−	10.3606i		−	1.61806i	−0.587769	−	0.809029i	$-0.699993\pi$
$41$		−	10.3606i		−	1.61806i	0.587769	−	0.809029i	$-0.300007\pi$
$42$		0			0
$43$	1.55506	+	2.69344i	0.237144	+	0.410745i	0.959894	−	0.280365i	$-0.0904554\pi$
$43$	1.55506	+	2.69344i	0.237144	+	0.410745i	−0.722750	+	0.691110i	$0.757122\pi$
$44$		0			0
$45$	−0.549233	−	0.951300i	−0.0818749	−	0.141811i
$46$		0			0
$47$	1.56236	−	2.70609i	0.227894	−	0.394724i	−0.729290	−	0.684205i	$-0.760149\pi$
$47$	1.56236	−	2.70609i	0.227894	−	0.394724i	0.957184	+	0.289481i	$0.0934827\pi$
$48$		0			0
$49$	2.71132	+	4.69615i	0.387332	+	0.670879i
$50$		0			0
$51$	−8.12888	+	4.69321i	−1.13827	+	0.657181i
$52$		0			0
$53$	7.99221	+	4.61431i	1.09781	+	0.633824i	0.935646	−	0.352940i	$-0.114818\pi$
$53$	7.99221	+	4.61431i	1.09781	+	0.633824i	0.162168	+	0.986763i	$0.448151\pi$
$54$		0			0
$55$	−10.5873	+	6.11260i	−1.42760	+	0.824223i
$56$		0			0
$57$		−	8.92083i		−	1.18159i
$58$		0			0
$59$	2.13693	+	3.70127i	0.278205	+	0.481865i	0.970939	−	0.239328i	$-0.0769273\pi$
$59$	2.13693	+	3.70127i	0.278205	+	0.481865i	−0.692734	+	0.721193i	$0.743594\pi$
$60$		0			0
$61$			4.46923i			0.572226i	0.958196	+	0.286113i	$0.0923632\pi$
$61$			4.46923i			0.572226i	−0.958196	+	0.286113i	$0.907637\pi$
$62$		0			0
$63$	−0.277252	−	0.480214i	−0.0349304	−	0.0605013i
$64$		0			0
$65$	3.76368			0.466827
$66$		0			0
$67$			7.16896i			0.875828i	0.899017	+	0.437914i	$0.144283\pi$
$67$			7.16896i			0.875828i	−0.899017	+	0.437914i	$0.855717\pi$
$68$		0			0
$69$			5.11004i			0.615177i
$70$		0			0
$71$	−12.7847			−1.51726			−0.758630	−	0.651522i	$-0.774131\pi$
$71$	−12.7847			−1.51726			−0.758630	+	0.651522i	$0.774131\pi$
$72$		0			0
$73$	3.18173	−	5.51093i	0.372394	−	0.645005i	−0.617539	−	0.786540i	$-0.711870\pi$
$73$	3.18173	−	5.51093i	0.372394	−	0.645005i	0.989933	+	0.141535i	$0.0452037\pi$
$74$		0			0
$75$	−0.951759	+	1.64850i	−0.109900	+	0.190352i
$76$		0			0
$77$	−5.34447	+	3.08563i	−0.609058	+	0.351640i
$78$		0			0
$79$	0.689399	−	8.86142i	0.0775634	−	0.996987i
$79$	0.689399	−	8.86142i	0.0775634	−	0.996987i
$80$		0			0
$81$	3.74027	+	6.47834i	0.415586	+	0.719815i
$82$		0			0
$83$	−0.643709	−	0.371646i	−0.0706562	−	0.0407934i	0.464256	−	0.885701i	$-0.346322\pi$
$83$	−0.643709	−	0.371646i	−0.0706562	−	0.0407934i	−0.534912	+	0.844908i	$0.679655\pi$
$84$		0			0
$85$	−12.6440	−	7.30004i	−1.37144	−	0.791800i
$86$		0			0
$87$		−	6.94088i		−	0.744140i
$88$		0			0
$89$	−11.3878			−1.20710			−0.603552	−	0.797323i	$-0.706249\pi$
$89$	−11.3878			−1.20710			−0.603552	+	0.797323i	$0.706249\pi$
$90$		0			0
$91$	1.89990			0.199163
$92$		0			0
$93$			4.61709i			0.478770i
$94$		0			0
$95$	12.0169	−	6.93794i	1.23290	−	0.711817i
$96$		0			0
$97$	−18.4361			−1.87190			−0.935951	−	0.352129i	$-0.885458\pi$
$97$	−18.4361			−1.87190			−0.935951	+	0.352129i	$0.885458\pi$
$98$		0			0
$99$	−1.87880	+	1.08472i	−0.188826	+	0.109019i
$100$		0			0
$101$	−6.12660			−0.609619			−0.304810	−	0.952413i	$-0.598593\pi$
$101$	−6.12660			−0.609619			−0.304810	+	0.952413i	$0.598593\pi$
$102$		0			0
$103$	−2.99947	−	5.19523i	−0.295546	−	0.511901i	0.679566	−	0.733615i	$-0.262168\pi$
$103$	−2.99947	−	5.19523i	−0.295546	−	0.511901i	−0.975112	+	0.221714i	$0.928835\pi$
$104$		0			0
$105$	−2.49904	+	4.32847i	−0.243882	+	0.422415i
$106$		0			0
$107$	−5.03195	−	8.71558i	−0.486457	−	0.842567i	0.513422	−	0.858136i	$-0.328377\pi$
$107$	−5.03195	−	8.71558i	−0.486457	−	0.842567i	−0.999879	+	0.0155687i	$0.995044\pi$
$108$		0			0
$109$	7.40344	−	4.27438i	0.709121	−	0.409411i	−0.101614	−	0.994824i	$-0.532401\pi$
$109$	7.40344	−	4.27438i	0.709121	−	0.409411i	0.810736	+	0.585412i	$0.199067\pi$
$110$		0			0
$111$	7.94894	+	4.58932i	0.754480	+	0.435599i
$112$		0			0
$113$	−8.54045	+	4.93083i	−0.803418	+	0.463854i	−0.844665	−	0.535295i	$-0.820200\pi$
$113$	−8.54045	+	4.93083i	−0.803418	+	0.463854i	0.0412468	+	0.999149i	$0.486867\pi$
$114$		0			0
$115$	−6.88351	+	3.97420i	−0.641891	+	0.370596i
$116$		0			0
$117$	0.667891			0.0617465
$118$		0			0
$119$	−6.38268	−	3.68504i	−0.585100	−	0.337807i
$120$		0			0
$121$	6.57225	+	11.3835i	0.597478	+	1.03486i
$122$		0			0
$123$	−14.3519	+	8.28606i	−1.29407	+	0.747129i
$124$		0			0
$125$	9.47908			0.847835
$126$		0			0
$127$	4.68776	−	8.11944i	0.415972	−	0.720484i	−0.579558	−	0.814931i	$-0.696775\pi$
$127$	4.68776	−	8.11944i	0.415972	−	0.720484i	0.995530	+	0.0944467i	$0.0301082\pi$
$128$		0			0
$129$	2.48736	−	4.30823i	0.219000	−	0.379318i
$130$		0			0
$131$		−	12.3540i		−	1.07937i	−0.841867	−	0.539685i	$-0.818543\pi$
$131$		−	12.3540i		−	1.07937i	0.841867	−	0.539685i	$-0.181457\pi$
$132$		0			0
$133$	6.06608	−	3.50226i	0.525996	−	0.303684i
$134$		0			0
$135$	−6.84791	+	11.8609i	−0.589374	+	1.02083i
$136$		0			0
$137$			6.33495i			0.541231i	0.962688	+	0.270616i	$0.0872272\pi$
$137$			6.33495i			0.541231i	−0.962688	+	0.270616i	$0.912773\pi$
$138$		0			0
$139$	1.71794	−	2.97555i	0.145713	−	0.252383i	−0.783925	−	0.620855i	$-0.786786\pi$
$139$	1.71794	−	2.97555i	0.145713	−	0.252383i	0.929639	+	0.368472i	$0.120119\pi$
$140$		0			0
$141$	−4.99808			−0.420915
$142$		0			0
$143$		−	7.43318i		−	0.621594i
$144$		0			0
$145$	9.34976	−	5.39808i	0.776455	−	0.448286i
$146$		0			0
$147$	4.33684	−	7.51162i	0.357696	−	0.619548i
$148$		0			0
$149$	4.13499	+	2.38734i	0.338752	+	0.195578i	0.659720	−	0.751512i	$-0.270675\pi$
$149$	4.13499	+	2.38734i	0.338752	+	0.195578i	−0.320968	+	0.947090i	$0.604008\pi$
$150$		0			0
$151$	20.0960	+	11.6024i	1.63539	+	0.944190i	0.982393	+	0.186826i	$0.0598202\pi$
$151$	20.0960	+	11.6024i	1.63539	+	0.944190i	0.652993	+	0.757364i	$0.273513\pi$
$152$		0			0
$153$	−2.24377	−	1.29544i	−0.181398	−	0.104730i
$154$		0			0
$155$	−6.21948	+	3.59082i	−0.499561	+	0.288422i
$156$		0			0
$157$		−	9.39569i		−	0.749858i	−0.927054	−	0.374929i	$-0.877667\pi$
$157$		−	9.39569i		−	0.749858i	0.927054	−	0.374929i	$-0.122333\pi$
$158$		0			0
$159$		−	14.7614i		−	1.17066i
$160$		0			0
$161$	−3.47478	+	2.00617i	−0.273851	+	0.158108i
$162$		0			0
$163$	−6.15897	−	3.55588i	−0.482407	−	0.278518i	0.239012	−	0.971017i	$-0.423177\pi$
$163$	−6.15897	−	3.55588i	−0.482407	−	0.278518i	−0.721419	+	0.692499i	$0.756510\pi$
$164$		0			0
$165$	16.9348	+	9.77728i	1.31837	+	0.761160i
$166$		0			0
$167$	20.9032	+	12.0685i	1.61754	+	0.933885i	0.987555	+	0.157274i	$0.0502707\pi$
$167$	20.9032	+	12.0685i	1.61754	+	0.933885i	0.629981	+	0.776611i	$0.283063\pi$
$168$		0			0
$169$	5.35580	−	9.27652i	0.411985	−	0.713578i
$170$		0			0
$171$	2.13247	−	1.23118i	0.163074	−	0.0941510i
$172$		0			0
$173$		−	7.84122i		−	0.596157i	−0.954541	−	0.298078i	$-0.903654\pi$
$173$		−	7.84122i		−	0.596157i	0.954541	−	0.298078i	$-0.0963457\pi$
$174$		0			0
$175$	−1.49462			−0.112982
$176$		0			0
$177$	3.41808	−	5.92029i	0.256919	−	0.444996i
$178$		0			0
$179$			21.9474i			1.64043i	0.572058	+	0.820213i	$0.306145\pi$
$179$			21.9474i			1.64043i	−0.572058	+	0.820213i	$0.693855\pi$
$180$		0			0
$181$	4.60075	−	7.96873i	0.341971	−	0.592311i	−0.642828	−	0.766011i	$-0.722239\pi$
$181$	4.60075	−	7.96873i	0.341971	−	0.592311i	0.984799	+	0.173700i	$0.0555722\pi$
$182$		0			0
$183$	6.19092	−	3.57433i	0.457646	−	0.264222i
$184$		0			0
$185$			14.2769i			1.04966i
$186$		0			0
$187$	−14.4174	+	24.9717i	−1.05431	+	1.82611i
$188$		0			0
$189$	−3.45681	+	5.98737i	−0.251446	+	0.435517i
$190$		0			0
$191$	8.32727			0.602540			0.301270	−	0.953539i	$-0.402589\pi$
$191$	8.32727			0.602540			0.301270	+	0.953539i	$0.402589\pi$
$192$		0			0
$193$	−5.91276	+	3.41374i	−0.425610	+	0.245726i	−0.697475	−	0.716609i	$-0.745693\pi$
$193$	−5.91276	+	3.41374i	−0.425610	+	0.245726i	0.271865	+	0.962336i	$0.412360\pi$
$194$		0			0
$195$	−3.01006	−	5.21357i	−0.215555	−	0.373352i
$196$		0			0
$197$	0.875331	+	0.505372i	0.0623647	+	0.0360063i	0.530858	−	0.847461i	$-0.321870\pi$
$197$	0.875331	+	0.505372i	0.0623647	+	0.0360063i	−0.468493	+	0.883467i	$0.655203\pi$
$198$		0			0
$199$	21.4489			1.52047			0.760236	−	0.649647i	$-0.225083\pi$
$199$	21.4489			1.52047			0.760236	+	0.649647i	$0.225083\pi$
$200$		0			0
$201$	9.93067	−	5.73348i	0.700456	−	0.404408i
$202$		0			0
$203$	4.71974	−	2.72494i	0.331261	−	0.191253i
$204$		0			0
$205$	−22.3236	−	12.8885i	−1.55915	−	0.900174i
$206$		0			0
$207$	−1.22153	+	0.705248i	−0.0849019	+	0.0490182i
$208$		0			0
$209$	−13.7023	−	23.7330i	−0.947806	−	1.64165i
$210$		0			0
$211$	1.45019	−	2.51180i	0.0998349	−	0.172919i	−0.811781	−	0.583962i	$-0.801502\pi$
$211$	1.45019	−	2.51180i	0.0998349	−	0.172919i	0.911616	+	0.411042i	$0.134835\pi$
$212$		0			0
$213$	10.2247	+	17.7097i	0.700585	+	1.21345i
$214$		0			0
$215$	7.73790			0.527720
$216$		0			0
$217$	−3.13958	+	1.81264i	−0.213129	+	0.123050i
$218$		0			0
$219$	−10.1785			−0.687803
$220$		0			0
$221$	7.68784	−	4.43858i	0.517140	−	0.298571i
$222$		0			0
$223$		−	18.1270i		−	1.21388i	−0.794749	−	0.606938i	$-0.792398\pi$
$223$		−	18.1270i		−	1.21388i	0.794749	−	0.606938i	$-0.207602\pi$
$224$		0			0
$225$	−0.525418			−0.0350279
$226$		0			0
$227$	29.7346			1.97355			0.986776	−	0.162091i	$-0.0518238\pi$
$227$	29.7346			1.97355			0.986776	+	0.162091i	$0.0518238\pi$
$228$		0			0
$229$		−	0.705620i		−	0.0466287i	−0.999728	−	0.0233143i	$-0.992578\pi$
$229$		−	0.705620i		−	0.0466287i	0.999728	−	0.0233143i	$-0.00742186\pi$
$230$		0			0
$231$	8.54862	+	4.93555i	0.562458	+	0.324735i
$232$		0			0
$233$	14.9527	+	8.63297i	0.979587	+	0.565565i	0.902145	−	0.431432i	$-0.141992\pi$
$233$	14.9527	+	8.63297i	0.979587	+	0.565565i	0.0774412	+	0.996997i	$0.475325\pi$
$234$		0			0
$235$	−3.88713	−	6.73270i	−0.253568	−	0.439193i
$236$		0			0
$237$	−12.8265	+	6.13207i	−0.833169	+	0.398321i
$238$		0			0
$239$	13.7459	−	7.93621i	0.889150	−	0.513351i	0.0154856	−	0.999880i	$-0.495071\pi$
$239$	13.7459	−	7.93621i	0.889150	−	0.513351i	0.873664	+	0.486529i	$0.161737\pi$
$240$		0			0
$241$	6.79655	−	11.7720i	0.437804	−	0.758299i	−0.559716	−	0.828685i	$-0.689090\pi$
$241$	6.79655	−	11.7720i	0.437804	−	0.758299i	0.997520	+	0.0703855i	$0.0224229\pi$
$242$		0			0
$243$	−2.27452	+	3.93958i	−0.145910	+	0.252724i
$244$		0			0
$245$	13.4914			0.861937
$246$		0			0
$247$			8.43682i			0.536822i
$248$		0			0
$249$			1.18892i			0.0753444i
$250$		0			0
$251$	7.62733			0.481433			0.240716	−	0.970595i	$-0.422618\pi$
$251$	7.62733			0.481433			0.240716	+	0.970595i	$0.422618\pi$
$252$		0			0
$253$	7.84895	+	13.5948i	0.493459	+	0.854697i
$254$		0			0
$255$			23.3532i			1.46244i
$256$		0			0
$257$	−6.59842	−	11.4288i	−0.411598	−	0.712909i	0.583466	−	0.812137i	$-0.301696\pi$
$257$	−6.59842	−	11.4288i	−0.411598	−	0.712909i	−0.995065	+	0.0992280i	$0.968363\pi$
$258$		0			0
$259$			7.20695i			0.447818i
$260$		0			0
$261$	1.65918	−	0.957927i	0.102701	−	0.0592942i
$262$		0			0
$263$	5.26644	+	3.04058i	0.324743	+	0.187490i	0.653505	−	0.756923i	$-0.273298\pi$
$263$	5.26644	+	3.04058i	0.324743	+	0.187490i	−0.328762	+	0.944413i	$0.606631\pi$
$264$		0			0
$265$	19.8845	−	11.4803i	1.22149	−	0.705229i
$266$		0			0
$267$	9.10756	+	15.7747i	0.557373	+	0.965399i
$268$		0			0
$269$	1.21431	−	2.10325i	0.0740380	−	0.128238i	−0.826630	−	0.562746i	$-0.809745\pi$
$269$	1.21431	−	2.10325i	0.0740380	−	0.128238i	0.900668	+	0.434509i	$0.143078\pi$
$270$		0			0
$271$	7.40299	+	12.8224i	0.449700	+	0.778903i	0.998366	−	0.0571385i	$-0.0181976\pi$
$271$	7.40299	+	12.8224i	0.449700	+	0.778903i	−0.548666	+	0.836041i	$0.684864\pi$
$272$		0			0
$273$	−1.51947	−	2.63180i	−0.0919625	−	0.159284i
$274$		0			0
$275$			5.84756i			0.352621i
$276$		0			0
$277$	−0.856206	+	1.48299i	−0.0514444	+	0.0891044i	−0.890601	−	0.454786i	$-0.849716\pi$
$277$	−0.856206	+	1.48299i	−0.0514444	+	0.0891044i	0.839156	+	0.543890i	$0.183049\pi$
$278$		0			0
$279$	−1.10369	+	0.637215i	−0.0660762	+	0.0381491i
$280$		0			0
$281$	−4.46455	−	7.73284i	−0.266333	−	0.461302i	0.701579	−	0.712592i	$-0.252479\pi$
$281$	−4.46455	−	7.73284i	−0.266333	−	0.461302i	−0.967912	+	0.251289i	$0.919145\pi$
$282$		0			0
$283$			9.53790i			0.566969i	0.958977	+	0.283485i	$0.0914905\pi$
$283$			9.53790i			0.566969i	−0.958977	+	0.283485i	$0.908510\pi$
$284$		0			0
$285$	−19.2213	−	11.0974i	−1.13857	−	0.657355i
$286$		0			0
$287$	−11.2689	−	6.50610i	−0.665182	−	0.384043i
$288$		0			0
$289$	−17.4363			−1.02566
$290$		0			0
$291$	14.7445	+	25.5383i	0.864340	+	1.49708i
$292$		0			0
$293$	−22.5797	−	13.0364i	−1.31912	−	0.761595i	−0.335534	−	0.942028i	$-0.608917\pi$
$293$	−22.5797	−	13.0364i	−1.31912	−	0.761595i	−0.983587	+	0.180433i	$0.942250\pi$
$294$		0			0
$295$	10.6333			0.619094
$296$		0			0
$297$	23.4251	+	13.5245i	1.35926	+	0.784769i
$298$		0			0
$299$		−	4.83279i		−	0.279488i
$300$		0			0
$301$	3.90608			0.225142
$302$		0			0
$303$	4.89983	+	8.48676i	0.281488	+	0.487552i
$304$		0			0
$305$	9.62964	+	5.55967i	0.551392	+	0.318346i
$306$		0			0
$307$	−4.89247	+	8.47401i	−0.279228	+	0.483637i	−0.971193	−	0.238294i	$-0.923412\pi$
$307$	−4.89247	+	8.47401i	−0.279228	+	0.483637i	0.691965	+	0.721931i	$0.256745\pi$
$308$		0			0
$309$	−4.79773	+	8.30992i	−0.272933	+	0.472735i
$310$		0			0
$311$	15.9967	−	27.7072i	0.907092	−	1.57113i	0.0890072	−	0.996031i	$-0.471631\pi$
$311$	15.9967	−	27.7072i	0.907092	−	1.57113i	0.818085	−	0.575098i	$-0.195036\pi$
$312$		0			0
$313$	2.47265	+	4.28275i	0.139762	+	0.242076i	0.927407	−	0.374055i	$-0.122033\pi$
$313$	2.47265	+	4.28275i	0.139762	+	0.242076i	−0.787644	+	0.616130i	$0.788699\pi$
$314$		0			0
$315$	−1.37959			−0.0777313
$316$		0			0
$317$	−14.5745			−0.818586			−0.409293	−	0.912403i	$-0.634225\pi$
$317$	−14.5745			−0.818586			−0.409293	+	0.912403i	$0.634225\pi$
$318$		0			0
$319$	−10.6611	−	18.4656i	−0.596907	−	1.03387i
$320$		0			0
$321$	−8.04874	+	13.9408i	−0.449237	+	0.778101i
$322$		0			0
$323$	16.3641	−	28.3434i	0.910521	−	1.57707i
$324$		0			0
$325$	0.900121	−	1.55906i	0.0499297	−	0.0864808i
$326$		0			0
$327$	−11.8420	−	6.83699i	−0.654865	−	0.378087i
$328$		0			0
$329$	−1.96221	−	3.39865i	−0.108180	−	0.187374i
$330$		0			0
$331$	−22.0554			−1.21227			−0.606136	−	0.795361i	$-0.707281\pi$
$331$	−22.0554			−1.21227			−0.606136	+	0.795361i	$0.707281\pi$
$332$		0			0
$333$			2.53353i			0.138837i
$334$		0			0
$335$	15.4466	+	8.91812i	0.843940	+	0.487249i
$336$		0			0
$337$	9.99329			0.544369			0.272185	−	0.962245i	$-0.412254\pi$
$337$	9.99329			0.544369			0.272185	+	0.962245i	$0.412254\pi$
$338$		0			0
$339$	13.6607	+	7.88701i	0.741947	+	0.428363i
$340$		0			0
$341$	7.09179	+	12.2833i	0.384042	+	0.665180i
$342$		0			0
$343$	15.6019			0.842426
$344$		0			0
$345$	11.0104	+	6.35684i	0.592779	+	0.342241i
$346$		0			0
$347$	−20.5963	−	11.8913i	−1.10567	−	0.638357i	−0.167963	−	0.985793i	$-0.553719\pi$
$347$	−20.5963	−	11.8913i	−1.10567	−	0.638357i	−0.937704	+	0.347436i	$0.887052\pi$
$348$		0			0
$349$		−	25.3574i		−	1.35735i	−0.734438	−	0.678676i	$-0.762554\pi$
$349$		−	25.3574i		−	1.35735i	0.734438	−	0.678676i	$-0.237446\pi$
$350$		0			0
$351$	−4.16367	−	7.21169i	−0.222240	−	0.384932i
$352$		0			0
$353$	−23.2632	+	13.4310i	−1.23818	+	0.714861i	−0.968721	−	0.248153i	$-0.920177\pi$
$353$	−23.2632	+	13.4310i	−1.23818	+	0.714861i	−0.269454	+	0.963013i	$0.586843\pi$
$354$		0			0
$355$	−15.9040	+	27.5465i	−0.844096	+	1.46202i
$356$		0			0
$357$			11.7887i			0.623922i
$358$		0			0
$359$	7.70165	+	13.3396i	0.406477	+	0.704039i	0.994492	−	0.104811i	$-0.0334237\pi$
$359$	7.70165	+	13.3396i	0.406477	+	0.704039i	−0.588015	+	0.808850i	$0.700090\pi$
$360$		0			0
$361$	6.05237	+	10.4830i	0.318546	+	0.551738i
$362$		0			0
$363$	10.5125	−	18.2082i	0.551763	−	0.955682i
$364$		0			0
$365$	−7.91609	−	13.7111i	−0.414347	−	0.717671i
$366$		0			0
$367$	32.1403	−	18.5562i	1.67771	−	0.968628i	0.714598	−	0.699536i	$-0.246610\pi$
$367$	32.1403	−	18.5562i	1.67771	−	0.968628i	0.963115	−	0.269092i	$-0.0867235\pi$
$368$		0			0
$369$	−3.96147	−	2.28716i	−0.206226	−	0.119065i
$370$		0			0
$371$	10.0376	−	5.79523i	0.521128	−	0.300873i
$372$		0			0
$373$		−	7.66306i		−	0.396778i	−0.980123	−	0.198389i	$-0.936429\pi$
$373$		−	7.66306i		−	0.396778i	0.980123	−	0.198389i	$-0.0635709\pi$
$374$		0			0
$375$	−7.58103	−	13.1307i	−0.391483	−	0.678068i
$376$		0			0
$377$			6.56430i			0.338079i
$378$		0			0
$379$	−0.0184117	−	0.0318899i	−0.000945744	−	0.00163808i	0.865552	−	0.500819i	$-0.166968\pi$
$379$	−0.0184117	−	0.0318899i	−0.000945744	−	0.00163808i	−0.866498	+	0.499181i	$0.833634\pi$
$380$		0			0
$381$	−14.9964			−0.768290
$382$		0			0
$383$		−	25.9853i		−	1.32779i	−0.747827	−	0.663893i	$-0.768903\pi$
$383$		−	25.9853i		−	1.32779i	0.747827	−	0.663893i	$-0.231097\pi$
$384$		0			0
$385$			15.3540i			0.782511i
$386$		0			0
$387$	1.37314			0.0698008
$388$		0			0
$389$	18.8051	−	32.5715i	0.953458	−	1.65144i	0.215602	−	0.976481i	$-0.430829\pi$
$389$	18.8051	−	32.5715i	0.953458	−	1.65144i	0.737857	−	0.674957i	$-0.235838\pi$
$390$		0			0
$391$	−9.37369	+	16.2357i	−0.474048	+	0.821075i
$392$		0			0
$393$	−17.1131	+	9.88025i	−0.863242	+	0.498393i
$394$		0			0
$395$	−18.2357	−	12.5089i	−0.917537	−	0.629393i
$396$		0			0
$397$	6.29638	+	10.9056i	0.316006	+	0.547339i	0.979651	−	0.200709i	$-0.0643247\pi$
$397$	6.29638	+	10.9056i	0.316006	+	0.547339i	−0.663645	+	0.748048i	$0.730991\pi$
$398$		0			0
$399$	−9.70287	−	5.60196i	−0.485751	−	0.280449i
$400$		0			0
$401$	30.1681	+	17.4176i	1.50652	+	0.869792i	0.999971	+	0.00758312i	$0.00241381\pi$
$401$	30.1681	+	17.4176i	1.50652	+	0.869792i	0.506553	+	0.862209i	$0.330920\pi$
$402$		0			0
$403$		−	4.36659i		−	0.217515i
$404$		0			0
$405$	18.6114			0.924810
$406$		0			0
$407$	28.1965			1.39765
$408$		0			0
$409$			30.5738i			1.51178i	0.654699	+	0.755889i	$0.272795\pi$
$409$			30.5738i			1.51178i	−0.654699	+	0.755889i	$0.727205\pi$
$410$		0			0
$411$	8.77537	−	5.06646i	0.432857	−	0.249910i
$412$		0			0
$413$	5.36766			0.264125
$414$		0			0
$415$	−1.60154	+	0.924647i	−0.0786163	+	0.0453891i
$416$		0			0
$417$	−5.49577			−0.269129
$418$		0			0
$419$	−0.607161	−	1.05163i	−0.0296617	−	0.0513756i	0.850813	−	0.525468i	$-0.176110\pi$
$419$	−0.607161	−	1.05163i	−0.0296617	−	0.0513756i	−0.880475	+	0.474092i	$0.842776\pi$
$420$		0			0
$421$	−3.22994	+	5.59442i	−0.157418	+	0.272655i	−0.933937	−	0.357438i	$-0.883650\pi$
$421$	−3.22994	+	5.59442i	−0.157418	+	0.272655i	0.776519	+	0.630094i	$0.216984\pi$
$422$		0			0
$423$	−0.689797	−	1.19476i	−0.0335391	−	0.0580914i
$424$		0			0
$425$	−6.04789	+	3.49175i	−0.293366	+	0.169375i
$426$		0			0
$427$	4.86102	+	2.80651i	0.235241	+	0.135817i
$428$		0			0
$429$	−10.2967	+	5.94479i	−0.497129	+	0.287017i
$430$		0			0
$431$	−19.7196	+	11.3851i	−0.949859	+	0.548401i	−0.893037	−	0.449983i	$-0.851430\pi$
$431$	−19.7196	+	11.3851i	−0.949859	+	0.548401i	−0.0568216	+	0.998384i	$0.518097\pi$
$432$		0			0
$433$	−22.8873			−1.09989			−0.549947	−	0.835199i	$-0.685352\pi$
$433$	−22.8873			−1.09989			−0.549947	+	0.835199i	$0.685352\pi$
$434$		0			0
$435$	−14.9552	−	8.63439i	−0.717047	−	0.413987i
$436$		0			0
$437$	−8.90873	−	15.4304i	−0.426162	−	0.738135i
$438$		0			0
$439$	−32.7844	+	18.9281i	−1.56471	+	0.903388i	−0.567945	+	0.823067i	$0.692261\pi$
$439$	−32.7844	+	18.9281i	−1.56471	+	0.903388i	−0.996769	+	0.0803211i	$0.974405\pi$
$440$		0			0
$441$	2.39415			0.114007
$442$		0			0
$443$	14.1260	−	24.4669i	0.671146	−	1.16246i	−0.306434	−	0.951892i	$-0.599136\pi$
$443$	14.1260	−	24.4669i	0.671146	−	1.16246i	0.977579	−	0.210567i	$-0.0675309\pi$
$444$		0			0
$445$	−14.1663	+	24.5368i	−0.671548	+	1.16315i
$446$		0			0
$447$		−	7.63723i		−	0.361229i
$448$		0			0
$449$	−5.91741	+	3.41642i	−0.279260	+	0.161231i	−0.633088	−	0.774080i	$-0.718213\pi$
$449$	−5.91741	+	3.41642i	−0.279260	+	0.161231i	0.353829	+	0.935310i	$0.384880\pi$
$450$		0			0
$451$	−25.4545	+	44.0886i	−1.19861	+	2.07605i
$452$		0			0
$453$		−	37.1168i		−	1.74390i
$454$		0			0
$455$	2.36345	−	4.09362i	0.110800	−	0.191912i
$456$		0			0
$457$	−17.8846			−0.836606			−0.418303	−	0.908308i	$-0.637375\pi$
$457$	−17.8846			−0.836606			−0.418303	+	0.908308i	$0.637375\pi$
$458$		0			0
$459$			32.3035i			1.50780i
$460$		0			0
$461$	−5.52965	+	3.19255i	−0.257542	+	0.148692i	−0.623213	−	0.782052i	$-0.714173\pi$
$461$	−5.52965	+	3.19255i	−0.257542	+	0.148692i	0.365671	+	0.930744i	$0.380840\pi$
$462$		0			0
$463$	10.9650	−	18.9919i	0.509586	−	0.882629i	−0.490352	−	0.871524i	$-0.663132\pi$
$463$	10.9650	−	18.9919i	0.509586	−	0.882629i	0.999938	−	0.0111044i	$-0.00353472\pi$
$464$		0			0
$465$	9.94824	+	5.74362i	0.461338	+	0.266354i
$466$		0			0
$467$	13.8872	+	8.01777i	0.642623	+	0.371018i	0.785624	−	0.618704i	$-0.212342\pi$
$467$	13.8872	+	8.01777i	0.642623	+	0.371018i	−0.143002	+	0.989722i	$0.545675\pi$
$468$		0			0
$469$	7.79743	+	4.50185i	0.360052	+	0.207876i
$470$		0			0
$471$	−13.0152	+	7.51434i	−0.599709	+	0.346242i
$472$		0			0
$473$		−	15.2822i		−	0.702675i
$474$		0			0
$475$		−	6.63710i		−	0.304531i
$476$		0			0
$477$	3.52863	−	2.03726i	0.161565	−	0.0932796i
$478$		0			0
$479$	−7.66581	−	4.42586i	−0.350260	−	0.202223i	0.314540	−	0.949244i	$-0.398150\pi$
$479$	−7.66581	−	4.42586i	−0.350260	−	0.202223i	−0.664800	+	0.747022i	$0.731483\pi$
$480$		0			0
$481$	−7.51767	−	4.34033i	−0.342776	−	0.197902i
$482$		0			0
$483$	5.55801	+	3.20892i	0.252898	+	0.146011i
$484$		0			0
$485$	−22.9343	+	39.7234i	−1.04139	+	1.80375i
$486$		0			0
$487$	−18.4508	+	10.6525i	−0.836083	+	0.482713i	−0.855931	−	0.517090i	$-0.827015\pi$
$487$	−18.4508	+	10.6525i	−0.836083	+	0.482713i	0.0198476	+	0.999803i	$0.493682\pi$
$488$		0			0
$489$			11.3755i			0.514416i
$490$		0			0
$491$	43.7491			1.97437			0.987184	−	0.159588i	$-0.0510166\pi$
$491$	43.7491			1.97437			0.987184	+	0.159588i	$0.0510166\pi$
$492$		0			0
$493$	12.7321	−	22.0527i	0.573426	−	0.993203i
$494$		0			0
$495$			5.39754i			0.242601i
$496$		0			0
$497$	−8.02830	+	13.9054i	−0.360118	+	0.623743i
$498$		0			0
$499$	1.12589	−	0.650033i	0.0504017	−	0.0290995i	−0.474587	−	0.880208i	$-0.657403\pi$
$499$	1.12589	−	0.650033i	0.0504017	−	0.0290995i	0.524989	+	0.851109i	$0.324069\pi$
$500$		0			0
$501$		−	38.6077i		−	1.72486i
$502$		0			0
$503$	−2.31168	+	4.00395i	−0.103073	+	0.178528i	−0.912949	−	0.408073i	$-0.866201\pi$
$503$	−2.31168	+	4.00395i	−0.103073	+	0.178528i	0.809876	+	0.586601i	$0.199534\pi$
$504$		0			0
$505$	−7.62143	+	13.2007i	−0.339149	+	0.587424i
$506$		0			0
$507$	−17.1335			−0.760926
$508$		0			0
$509$	−5.18949	+	2.99615i	−0.230020	+	0.132802i	−0.610581	−	0.791954i	$-0.709064\pi$
$509$	−5.18949	+	2.99615i	−0.230020	+	0.132802i	0.380561	+	0.924756i	$0.375731\pi$
$510$		0			0
$511$	−3.99603	−	6.92132i	−0.176774	−	0.306181i
$512$		0			0
$513$	−26.5879	−	15.3506i	−1.17389	−	0.677744i
$514$		0			0
$515$	−14.9252			−0.657684
$516$		0			0
$517$	−13.2969	+	7.67699i	−0.584798	+	0.337633i
$518$		0			0
$519$	−10.8619	+	6.27113i	−0.476785	+	0.275272i
$520$		0			0
$521$	13.1587	+	7.59717i	0.576492	+	0.332838i	0.759738	−	0.650229i	$-0.225327\pi$
$521$	13.1587	+	7.59717i	0.576492	+	0.332838i	−0.183246	+	0.983067i	$0.558660\pi$
$522$		0			0
$523$	0.775854	−	0.447939i	0.0339257	−	0.0195870i	−0.482941	−	0.875653i	$-0.660432\pi$
$523$	0.775854	−	0.447939i	0.0339257	−	0.0195870i	0.516867	+	0.856066i	$0.327098\pi$
$524$		0			0
$525$	1.19534	+	2.07039i	0.0521689	+	0.0903593i
$526$		0			0
$527$	−8.46944	+	14.6695i	−0.368935	+	0.639013i
$528$		0			0
$529$	−6.39689	−	11.0797i	−0.278126	−	0.481728i
$530$		0			0
$531$	1.88695			0.0818867
$532$		0			0
$533$	13.5732	−	7.83649i	0.587921	−	0.339436i
$534$		0			0
$535$	−25.0388			−1.08252
$536$		0			0
$537$	30.4023	−	17.5527i	1.31195	−	0.757457i
$538$		0			0
$539$		−	26.6453i		−	1.14769i
$540$		0			0
$541$	27.9158			1.20019			0.600097	−	0.799927i	$-0.295129\pi$
$541$	27.9158			1.20019			0.600097	+	0.799927i	$0.295129\pi$
$542$		0			0
$543$	−14.7181			−0.631612
$544$		0			0
$545$		−	21.2692i		−	0.911071i
$546$		0			0
$547$	−16.8598	−	9.73401i	−0.720873	−	0.416196i	0.0942011	−	0.995553i	$-0.469970\pi$
$547$	−16.8598	−	9.73401i	−0.720873	−	0.416196i	−0.815074	+	0.579357i	$0.803304\pi$
$548$		0			0
$549$	1.70885	+	0.986602i	0.0729317	+	0.0421072i
$550$		0			0
$551$	12.1006	+	20.9588i	0.515502	+	0.892875i
$552$		0			0
$553$	−9.20534	−	6.31448i	−0.391451	−	0.268519i
$554$		0			0
$555$	19.7768	−	11.4182i	0.839479	−	0.484674i
$556$		0			0
$557$	−0.534520	+	0.925815i	−0.0226483	+	0.0392281i	−0.877127	−	0.480258i	$-0.840543\pi$
$557$	−0.534520	+	0.925815i	−0.0226483	+	0.0392281i	0.854479	+	0.519486i	$0.173876\pi$
$558$		0			0
$559$	−2.35240	+	4.07448i	−0.0994961	+	0.172332i
$560$		0			0
$561$	46.1221			1.94728
$562$		0			0
$563$		−	11.6057i		−	0.489124i	−0.969634	−	0.244562i	$-0.921356\pi$
$563$		−	11.6057i		−	0.489124i	0.969634	−	0.244562i	$-0.0786442\pi$
$564$		0			0
$565$			24.5356i			1.03222i
$566$		0			0
$567$	9.39502			0.394554
$568$		0			0
$569$	−2.70790	−	4.69023i	−0.113521	−	0.196625i	0.803666	−	0.595080i	$-0.202880\pi$
$569$	−2.70790	−	4.69023i	−0.113521	−	0.196625i	−0.917188	+	0.398455i	$0.869546\pi$
$570$		0			0
$571$			9.62001i			0.402585i	0.979531	+	0.201292i	$0.0645142\pi$
$571$			9.62001i			0.402585i	−0.979531	+	0.201292i	$0.935486\pi$
$572$		0			0
$573$	−6.65985	−	11.5352i	−0.278219	−	0.481890i
$574$		0			0
$575$			3.80187i			0.158549i
$576$		0			0
$577$	35.5405	−	20.5193i	1.47957	−	0.854230i	0.479837	−	0.877358i	$-0.340696\pi$
$577$	35.5405	−	20.5193i	1.47957	−	0.854230i	0.999733	+	0.0231283i	$0.00736264\pi$
$578$		0			0
$579$	9.45763	+	5.46037i	0.393046	+	0.226925i
$580$		0			0
$581$	−0.808452	+	0.466760i	−0.0335402	+	0.0193645i
$582$		0			0
$583$	−22.6733	−	39.2714i	−0.939034	−	1.62645i
$584$		0			0
$585$	0.830850	−	1.43907i	0.0343514	−	0.0594984i
$586$		0			0
$587$	1.82990	+	3.16948i	0.0755280	+	0.130818i	0.901316	−	0.433163i	$-0.142602\pi$
$587$	1.82990	+	3.16948i	0.0755280	+	0.130818i	−0.825788	+	0.563981i	$0.809269\pi$
$588$		0			0
$589$	−8.04933	−	13.9419i	−0.331667	−	0.574464i
$590$		0			0
$591$		−	1.61671i		−	0.0665028i
$592$		0			0
$593$	13.1793	−	22.8271i	0.541207	−	0.937398i	−0.457628	−	0.889144i	$-0.651301\pi$
$593$	13.1793	−	22.8271i	0.541207	−	0.937398i	0.998835	−	0.0482545i	$-0.0153659\pi$
$594$		0			0
$595$	−15.8800	+	9.16832i	−0.651016	+	0.375864i
$596$		0			0
$597$	−17.1541	−	29.7117i	−0.702069	−	1.21602i
$598$		0			0
$599$			11.0439i			0.451241i	0.974215	+	0.225620i	$0.0724409\pi$
$599$			11.0439i			0.451241i	−0.974215	+	0.225620i	$0.927559\pi$
$600$		0			0
$601$	19.8447	+	11.4573i	0.809481	+	0.467354i	0.846776	−	0.531950i	$-0.178541\pi$
$601$	19.8447	+	11.4573i	0.809481	+	0.467354i	−0.0372944	+	0.999304i	$0.511874\pi$
$602$		0			0
$603$	2.74111	+	1.58258i	0.111627	+	0.0644477i
$604$		0			0
$605$	32.7033			1.32958
$606$		0			0
$607$	−18.1055	−	31.3597i	−0.734880	−	1.27285i	−0.954776	−	0.297326i	$-0.903905\pi$
$607$	−18.1055	−	31.3597i	−0.734880	−	1.27285i	0.219896	−	0.975523i	$-0.429428\pi$
$608$		0			0
$609$	−7.54935	−	4.35862i	−0.305915	−	0.176620i
$610$		0			0
$611$	4.72691			0.191230
$612$		0			0
$613$	22.7267	+	13.1212i	0.917921	+	0.529962i	0.882971	−	0.469427i	$-0.155540\pi$
$613$	22.7267	+	13.1212i	0.917921	+	0.529962i	0.0349498	+	0.999389i	$0.488873\pi$
$614$		0			0
$615$			41.2311i			1.66260i
$616$		0			0
$617$	−8.58060			−0.345442			−0.172721	−	0.984971i	$-0.555256\pi$
$617$	−8.58060			−0.345442			−0.172721	+	0.984971i	$0.555256\pi$
$618$		0			0
$619$	−9.39085	−	16.2654i	−0.377450	−	0.653763i	0.613240	−	0.789896i	$-0.289866\pi$
$619$	−9.39085	−	16.2654i	−0.377450	−	0.653763i	−0.990690	+	0.136134i	$0.956532\pi$
$620$		0			0
$621$	15.2301	+	8.79313i	0.611164	+	0.352856i
$622$		0			0
$623$	−7.15113	+	12.3861i	−0.286504	+	0.496239i
$624$		0			0
$625$	14.7670	−	25.5772i	0.590681	−	1.02309i
$626$		0			0
$627$	−21.9172	+	37.9616i	−0.875287	+	1.51604i
$628$		0			0
$629$	16.8370	+	29.1626i	0.671335	+	1.16279i
$630$		0			0
$631$	−8.39663			−0.334264			−0.167132	−	0.985934i	$-0.553451\pi$
$631$	−8.39663			−0.334264			−0.167132	+	0.985934i	$0.553451\pi$
$632$		0			0
$633$	−4.63923			−0.184393
$634$		0			0
$635$	−11.6631	−	20.2010i	−0.462835	−	0.801653i
$636$		0			0
$637$	−4.10154	+	7.10408i	−0.162509	+	0.281474i
$638$		0			0
$639$	−2.82227	+	4.88832i	−0.111647	+	0.193379i
$640$		0			0
$641$	−21.2079	+	36.7332i	−0.837662	+	1.45087i	0.0541821	+	0.998531i	$0.482745\pi$
$641$	−21.2079	+	36.7332i	−0.837662	+	1.45087i	−0.891844	+	0.452343i	$0.850588\pi$
$642$		0			0
$643$	−1.74713	−	1.00871i	−0.0689001	−	0.0397795i	0.465154	−	0.885230i	$-0.345999\pi$
$643$	−1.74713	−	1.00871i	−0.0689001	−	0.0397795i	−0.534054	+	0.845450i	$0.679332\pi$
$644$		0			0
$645$	−6.18850	−	10.7188i	−0.243672	−	0.422052i
$646$		0			0
$647$	23.9679			0.942276			0.471138	−	0.882059i	$-0.343843\pi$
$647$	23.9679			0.942276			0.471138	+	0.882059i	$0.343843\pi$
$648$		0			0
$649$		−	21.0005i		−	0.824342i
$650$		0			0
$651$	5.02185	+	2.89937i	0.196822	+	0.113635i
$652$		0			0
$653$	−10.3308			−0.404276			−0.202138	−	0.979357i	$-0.564789\pi$
$653$	−10.3308			−0.404276			−0.202138	+	0.979357i	$0.564789\pi$
$654$		0			0
$655$	−26.6185	−	15.3682i	−1.04007	−	0.600485i
$656$		0			0
$657$	−1.40476	−	2.43312i	−0.0548051	−	0.0949252i
$658$		0			0
$659$	−10.8615			−0.423103			−0.211552	−	0.977367i	$-0.567852\pi$
$659$	−10.8615			−0.423103			−0.211552	+	0.977367i	$0.567852\pi$
$660$		0			0
$661$	29.0289	+	16.7598i	1.12909	+	0.651882i	0.943707	−	0.330784i	$-0.107313\pi$
$661$	29.0289	+	16.7598i	1.12909	+	0.651882i	0.185386	+	0.982666i	$0.440646\pi$
$662$		0			0
$663$	−12.2969	−	7.09963i	−0.477573	−	0.275727i
$664$		0			0
$665$		−	17.4271i		−	0.675794i
$666$		0			0
$667$	−6.93146	−	12.0056i	−0.268387	−	0.464861i
$668$		0			0
$669$	−25.1101	+	14.4973i	−0.970814	+	0.560500i
$670$		0			0
$671$	10.9802	−	19.0183i	0.423887	−	0.734194i
$672$		0			0
$673$			0.830289i			0.0320053i	0.999872	+	0.0160026i	$0.00509402\pi$
$673$			0.830289i			0.0320053i	−0.999872	+	0.0160026i	$0.994906\pi$
$674$		0			0
$675$	3.27549	+	5.67331i	0.126074	+	0.218366i
$676$		0			0
$677$	15.0455	+	26.0595i	0.578244	+	1.00155i	0.995681	+	0.0928417i	$0.0295950\pi$
$677$	15.0455	+	26.0595i	0.578244	+	1.00155i	−0.417437	+	0.908706i	$0.637072\pi$
$678$		0			0
$679$	−11.5772	+	20.0523i	−0.444292	+	0.769537i
$680$		0			0
$681$	−23.7806	−	41.1893i	−0.911276	−	1.57838i
$682$		0			0
$683$	−7.41739	+	4.28243i	−0.283818	+	0.163863i	−0.635151	−	0.772388i	$-0.719062\pi$
$683$	−7.41739	+	4.28243i	−0.283818	+	0.163863i	0.351332	+	0.936251i	$0.385729\pi$
$684$		0			0
$685$	13.6496	+	7.88061i	0.521525	+	0.301103i
$686$		0			0
$687$	−0.977447	+	0.564329i	−0.0372919	+	0.0215305i
$688$		0			0
$689$			13.9605i			0.531854i
$690$		0			0
$691$	−3.27447	−	5.67155i	−0.124567	−	0.215756i	0.796997	−	0.603984i	$-0.206421\pi$
$691$	−3.27447	−	5.67155i	−0.124567	−	0.215756i	−0.921564	+	0.388228i	$0.873087\pi$
$692$		0			0
$693$			2.72467i			0.103502i
$694$		0			0
$695$	−4.27419	−	7.40312i	−0.162129	−	0.280816i
$696$		0			0
$697$	−60.7987			−2.30291
$698$		0			0
$699$		−	27.6174i		−	1.04458i
$700$		0			0
$701$		−	2.07234i		−	0.0782712i	−0.999234	−	0.0391356i	$-0.987540\pi$
$701$		−	2.07234i		−	0.0782712i	0.999234	−	0.0391356i	$-0.0124604\pi$
$702$		0			0
$703$	−32.0037			−1.20704
$704$		0			0
$705$	−6.21757	+	10.7691i	−0.234167	+	0.405589i
$706$		0			0
$707$	−3.84728	+	6.66369i	−0.144692	+	0.250614i
$708$		0			0
$709$	−25.3139	+	14.6150i	−0.950682	+	0.548877i	−0.893293	−	0.449475i	$-0.851611\pi$
$709$	−25.3139	+	14.6150i	−0.950682	+	0.548877i	−0.0573894	+	0.998352i	$0.518278\pi$
$710$		0			0
$711$	−3.23605	−	2.21980i	−0.121361	−	0.0832489i
$712$		0			0
$713$	4.61083	+	7.98619i	0.172677	+	0.299085i
$714$		0			0
$715$	−16.0159	−	9.24681i	−0.598962	−	0.345811i
$716$		0			0
$717$	−21.9870	−	12.6942i	−0.821119	−	0.474074i
$718$		0			0
$719$		−	7.35317i		−	0.274227i	−0.990555	−	0.137114i	$-0.956217\pi$
$719$		−	7.35317i		−	0.274227i	0.990555	−	0.137114i	$-0.0437825\pi$
$720$		0			0
$721$	−7.53422			−0.280589
$722$		0			0
$723$	−21.7426			−0.808614
$724$		0			0
$725$		−	5.16402i		−	0.191787i
$726$		0			0
$727$	−3.82108	+	2.20610i	−0.141716	+	0.0818197i	−0.569182	−	0.822212i	$-0.692740\pi$
$727$	−3.82108	+	2.20610i	−0.141716	+	0.0818197i	0.427466	+	0.904032i	$0.359407\pi$
$728$		0			0
$729$	29.7179			1.10066
$730$		0			0
$731$	15.8057	−	9.12545i	0.584596	−	0.337517i
$732$		0			0
$733$	−35.6474			−1.31667			−0.658333	−	0.752727i	$-0.728738\pi$
$733$	−35.6474			−1.31667			−0.658333	+	0.752727i	$0.728738\pi$
$734$		0			0
$735$	−10.7900	−	18.6888i	−0.397994	−	0.689346i
$736$		0			0
$737$	17.6131	−	30.5067i	0.648786	−	1.12373i
$738$		0			0
$739$	5.73838	+	9.93917i	0.211090	+	0.365618i	0.952056	−	0.305924i	$-0.0989654\pi$
$739$	5.73838	+	9.93917i	0.211090	+	0.365618i	−0.740966	+	0.671543i	$0.765632\pi$
$740$		0			0
$741$	11.6870	−	6.74747i	0.429331	−	0.247874i
$742$		0			0
$743$	−37.9957	−	21.9368i	−1.39393	−	0.804784i	−0.400180	−	0.916437i	$-0.631052\pi$
$743$	−37.9957	−	21.9368i	−1.39393	−	0.804784i	−0.993747	+	0.111652i	$0.964386\pi$
$744$		0			0
$745$	10.2878	−	5.93965i	0.376915	−	0.217612i
$746$		0			0
$747$	−0.284203	+	0.164085i	−0.0103985	+	0.00600355i
$748$		0			0
$749$	−12.6395			−0.461838
$750$		0			0
$751$	4.87521	+	2.81470i	0.177899	+	0.102710i	0.586305	−	0.810090i	$-0.300582\pi$
$751$	4.87521	+	2.81470i	0.177899	+	0.102710i	−0.408406	+	0.912800i	$0.633915\pi$
$752$		0			0
$753$	−6.10007	−	10.5656i	−0.222299	−	0.385033i
$754$		0			0
$755$	49.9984	−	28.8666i	1.81963	−	1.05056i
$756$		0			0
$757$	−41.0634			−1.49247			−0.746237	−	0.665680i	$-0.768142\pi$
$757$	−41.0634			−1.49247			−0.746237	+	0.665680i	$0.768142\pi$
$758$		0			0
$759$	12.5546	−	21.7452i	0.455704	−	0.789302i
$760$		0			0
$761$	−3.20422	+	5.54987i	−0.116153	+	0.201183i	−0.918240	−	0.396024i	$-0.870390\pi$
$761$	−3.20422	+	5.54987i	−0.116153	+	0.201183i	0.802087	+	0.597207i	$0.203723\pi$
$762$		0			0
$763$		−	10.7366i		−	0.388692i
$764$		0			0
$765$	−5.58246	+	3.22303i	−0.201834	+	0.116529i
$766$		0			0
$767$	−3.23263	+	5.59908i	−0.116724	+	0.202171i
$768$		0			0
$769$			35.0115i			1.26255i	0.775560	+	0.631274i	$0.217468\pi$
$769$			35.0115i			1.26255i	−0.775560	+	0.631274i	$0.782532\pi$
$770$		0			0
$771$	−10.5544	+	18.2807i	−0.380106	+	0.658363i
$772$		0			0
$773$	36.8946			1.32701			0.663504	−	0.748173i	$-0.269069\pi$
$773$	36.8946			1.32701			0.663504	+	0.748173i	$0.269069\pi$
$774$		0			0
$775$			3.43512i			0.123393i
$776$		0			0
$777$	9.98329	−	5.76386i	0.358149	−	0.206777i
$778$		0			0
$779$	28.8915	−	50.0415i	1.03514	−	1.79292i
$780$		0			0
$781$	54.4037	+	31.4100i	1.94672	+	1.12394i
$782$		0			0
$783$	−20.6868	−	11.9435i	−0.739287	−	0.426828i
$784$		0			0
$785$	−20.2445	−	11.6882i	−0.722556	−	0.417168i
$786$		0			0
$787$	−20.0793	+	11.5928i	−0.715750	+	0.413239i	−0.813187	−	0.582003i	$-0.802269\pi$
$787$	−20.0793	+	11.5928i	−0.715750	+	0.413239i	0.0974361	+	0.995242i	$0.468936\pi$
$788$		0			0
$789$		−	9.72699i		−	0.346290i
$790$		0			0
$791$			12.3855i			0.440379i
$792$		0			0
$793$	−5.85502	+	3.38040i	−0.207918	+	0.120042i
$794$		0			0
$795$	−31.8058	−	18.3631i	−1.12803	−	0.651271i
$796$		0			0
$797$	−1.90860	−	1.10193i	−0.0676061	−	0.0390324i	0.465816	−	0.884882i	$-0.345761\pi$
$797$	−1.90860	−	1.10193i	−0.0676061	−	0.0390324i	−0.533422	+	0.845849i	$0.679094\pi$
$798$		0			0
$799$	−15.8800	−	9.16832i	−0.561794	−	0.324352i
$800$		0			0
$801$	−2.51391	+	4.35422i	−0.0888246	+	0.153849i
$802$		0			0
$803$	−27.0791	+	15.6341i	−0.955600	+	0.551716i
$804$		0			0
$805$			9.98261i			0.351841i
$806$		0			0
$807$	−3.88466			−0.136746
$808$		0			0
$809$	8.60892	−	14.9111i	0.302673	−	0.524246i	−0.674067	−	0.738670i	$-0.735454\pi$
$809$	8.60892	−	14.9111i	0.302673	−	0.524246i	0.976741	+	0.214424i	$0.0687875\pi$
$810$		0			0
$811$			49.4249i			1.73554i	0.496964	+	0.867771i	$0.334448\pi$
$811$			49.4249i			1.73554i	−0.496964	+	0.867771i	$0.665552\pi$
$812$		0			0
$813$	11.8413	−	20.5097i	0.415292	−	0.719308i
$814$		0			0
$815$	−15.3234	+	8.84696i	−0.536755	+	0.309896i
$816$		0			0
$817$			17.3456i			0.606846i
$818$		0			0
$819$	0.419411	−	0.726441i	0.0146554	−	0.0253839i
$820$		0			0
$821$	0.260209	−	0.450696i	0.00908137	−	0.0157294i	−0.861449	−	0.507844i	$-0.830443\pi$
$821$	0.260209	−	0.450696i	0.00908137	−	0.0157294i	0.870530	+	0.492115i	$0.163776\pi$
$822$		0			0
$823$	31.5290			1.09903			0.549516	−	0.835483i	$-0.314812\pi$
$823$	31.5290			1.09903			0.549516	+	0.835483i	$0.314812\pi$
$824$		0			0
$825$	8.10022	−	4.67667i	0.282014	−	0.162821i
$826$		0			0
$827$	−18.5882	−	32.1958i	−0.646376	−	1.11956i	−0.983982	−	0.178269i	$-0.942950\pi$
$827$	−18.5882	−	32.1958i	−0.646376	−	1.11956i	0.337605	−	0.941288i	$-0.390383\pi$
$828$		0			0
$829$	33.5666	+	19.3797i	1.16582	+	0.673085i	0.952691	−	0.303940i	$-0.0983022\pi$
$829$	33.5666	+	19.3797i	1.16582	+	0.673085i	0.213126	+	0.977025i	$0.431636\pi$
$830$		0			0
$831$	2.73905			0.0950167
$832$		0			0
$833$	27.5582	−	15.9107i	0.954833	−	0.551273i
$834$		0			0
$835$	52.0067	−	30.0261i	1.79977	−	1.03910i
$836$		0			0
$837$	13.7609	+	7.94488i	0.475648	+	0.274615i
$838$		0			0
$839$	3.64833	−	2.10636i	0.125954	−	0.0727197i	−0.435699	−	0.900092i	$-0.643499\pi$
$839$	3.64833	−	2.10636i	0.125954	−	0.0727197i	0.561653	+	0.827373i	$0.310165\pi$
$840$		0			0
$841$	−5.08511	−	8.80767i	−0.175349	−	0.303713i
$842$		0			0
$843$	−7.14118	+	12.3689i	−0.245955	+	0.426007i
$844$		0			0
$845$	−13.3251	−	23.0798i	−0.458398	−	0.793969i
$846$		0			0
$847$	16.5085			0.567240
$848$		0			0
$849$	13.2122	−	7.62807i	0.453442	−	0.261795i
$850$		0			0
$851$	18.3324			0.628426
$852$		0			0
$853$	−18.6941	+	10.7931i	−0.640074	+	0.369547i	−0.784643	−	0.619948i	$-0.787154\pi$
$853$	−18.6941	+	10.7931i	−0.640074	+	0.369547i	0.144569	+	0.989495i	$0.453821\pi$
$854$		0			0
$855$		−	6.12633i		−	0.209516i
$856$		0			0
$857$	−3.92712			−0.134148			−0.0670739	−	0.997748i	$-0.521366\pi$
$857$	−3.92712			−0.134148			−0.0670739	+	0.997748i	$0.521366\pi$
$858$		0			0
$859$	6.23215			0.212638			0.106319	−	0.994332i	$-0.466093\pi$
$859$	6.23215			0.212638			0.106319	+	0.994332i	$0.466093\pi$
$860$		0			0
$861$			20.8134i			0.709318i
$862$		0			0
$863$	14.5687	+	8.41122i	0.495923	+	0.286321i	0.727028	−	0.686607i	$-0.240901\pi$
$863$	14.5687	+	8.41122i	0.495923	+	0.286321i	−0.231105	+	0.972929i	$0.574234\pi$
$864$		0			0
$865$	−16.8951	−	9.75440i	−0.574451	−	0.331660i
$866$		0			0
$867$	13.9449	+	24.1533i	0.473594	+	0.820289i
$868$		0			0
$869$	−24.7049	+	36.0151i	−0.838055	+	1.22173i
$870$		0			0
$871$	−9.39188	+	5.42240i	−0.318232	+	0.183731i
$872$		0			0
$873$	−4.06986	+	7.04920i	−0.137744	+	0.238579i
$874$		0			0
$875$	5.95252	−	10.3101i	0.201232	−	0.348544i
$876$		0			0
$877$	−6.00127			−0.202648			−0.101324	−	0.994853i	$-0.532308\pi$
$877$	−6.00127			−0.202648			−0.101324	+	0.994853i	$0.532308\pi$
$878$		0			0
$879$			41.7042i			1.40665i
$880$		0			0
$881$			56.8171i			1.91422i	0.289731	+	0.957108i	$0.406434\pi$
$881$			56.8171i			1.91422i	−0.289731	+	0.957108i	$0.593566\pi$
$882$		0			0
$883$	−38.3854			−1.29177			−0.645887	−	0.763433i	$-0.723512\pi$
$883$	−38.3854			−1.29177			−0.645887	+	0.763433i	$0.723512\pi$
$884$		0			0
$885$	−8.50413	−	14.7296i	−0.285863	−	0.495129i
$886$		0			0
$887$			14.4549i			0.485349i	0.970108	+	0.242674i	$0.0780247\pi$
$887$			14.4549i			0.485349i	−0.970108	+	0.242674i	$0.921975\pi$
$888$		0			0
$889$	−5.88749	−	10.1974i	−0.197460	−	0.342011i
$890$		0			0
$891$		−	36.7572i		−	1.23141i
$892$		0			0
$893$	15.0923	−	8.71355i	0.505045	−	0.291588i
$894$		0			0
$895$	47.2891	+	27.3024i	1.58070	+	0.912617i
$896$		0			0
$897$	−6.69454	+	3.86509i	−0.223524	+	0.129052i
$898$		0			0
$899$	−6.26281	−	10.8475i	−0.208876	−	0.361784i
$900$		0			0
$901$	27.0779	−	46.9002i	0.902095	−	1.56247i
$902$		0			0
$903$	−3.12394	−	5.41082i	−0.103958	−	0.180061i
$904$		0			0
$905$	−11.4466	−	19.8261i	−0.380497	−	0.659040i
$906$		0			0
$907$			0.611849i			0.0203161i	0.999948	+	0.0101581i	$0.00323346\pi$
$907$			0.611849i			0.0203161i	−0.999948	+	0.0101581i	$0.996767\pi$
$908$		0			0
$909$	−1.35247	+	2.34256i	−0.0448588	+	0.0776977i
$910$		0			0
$911$	−45.8511	+	26.4721i	−1.51911	+	0.877060i	−0.519367	+	0.854552i	$0.673832\pi$
$911$	−45.8511	+	26.4721i	−1.51911	+	0.877060i	−0.999747	+	0.0225089i	$0.992835\pi$
$912$		0			0
$913$	1.82616	+	3.16300i	0.0604370	+	0.104680i
$914$		0			0
$915$		−	17.7857i		−	0.587978i
$916$		0			0
$917$	−13.4370	−	7.75784i	−0.443728	−	0.256186i
$918$		0			0
$919$	49.9799	+	28.8559i	1.64868	+	0.951868i	0.977596	+	0.210491i	$0.0675063\pi$
$919$	49.9799	+	28.8559i	1.64868	+	0.951868i	0.671089	+	0.741377i	$0.265827\pi$
$920$		0			0
$921$	15.6513			0.515728
$922$		0			0
$923$	−9.66996	−	16.7489i	−0.318291	−	0.551295i
$924$		0			0
$925$	5.91402	+	3.41446i	0.194452	+	0.112267i
$926$		0			0
$927$	−2.64858			−0.0869909
$928$		0			0
$929$	35.6099	+	20.5594i	1.16832	+	0.674532i	0.953285	−	0.302074i	$-0.0976789\pi$
$929$	35.6099	+	20.5594i	1.16832	+	0.674532i	0.215039	+	0.976606i	$0.431012\pi$
$930$		0			0
$931$			30.2430i			0.991174i
$932$		0			0
$933$	−51.1745			−1.67538
$934$		0			0
$935$	35.8702	+	62.1291i	1.17308	+	2.03184i
$936$		0			0
$937$	−39.0785	−	22.5620i	−1.27664	−	0.737068i	−0.300410	−	0.953810i	$-0.597124\pi$
$937$	−39.0785	−	22.5620i	−1.27664	−	0.737068i	−0.976229	+	0.216742i	$0.930457\pi$
$938$		0			0
$939$	3.95507	−	6.85038i	0.129069	−	0.223554i
$940$		0			0
$941$	−7.42322	+	12.8574i	−0.241990	+	0.419139i	−0.961281	−	0.275570i	$-0.911133\pi$
$941$	−7.42322	+	12.8574i	−0.241990	+	0.419139i	0.719291	+	0.694709i	$0.244467\pi$
$942$		0			0
$943$	−16.5496	+	28.6648i	−0.538930	+	0.933455i
$944$		0			0
$945$	8.60048	+	14.8965i	0.279773	+	0.484582i
$946$		0			0
$947$	−47.6215			−1.54749			−0.773746	−	0.633496i	$-0.781619\pi$
$947$	−47.6215			−1.54749			−0.773746	+	0.633496i	$0.781619\pi$
$948$		0			0
$949$	9.62631			0.312483
$950$		0			0
$951$	11.6562	+	20.1891i	0.377977	+	0.654676i
$952$		0			0
$953$	−28.5480	+	49.4465i	−0.924759	+	1.60173i	−0.132811	+	0.991141i	$0.542400\pi$
$953$	−28.5480	+	49.4465i	−0.924759	+	1.60173i	−0.791948	+	0.610588i	$0.790933\pi$
$954$		0			0
$955$	10.3590	−	17.9424i	0.335211	−	0.580602i
$956$		0			0
$957$	−17.0527	+	29.5362i	−0.551236	+	0.954769i
$958$		0			0
$959$	6.89030	+	3.97812i	0.222499	+	0.128460i
$960$		0			0
$961$	−11.3340	−	19.6310i	−0.365612	−	0.633258i
$962$		0			0
$963$	−4.44330			−0.143183
$964$		0			0
$965$			16.9866i			0.546819i
$966$		0			0
$967$	30.7929	+	17.7783i	0.990232	+	0.571711i	0.905344	−	0.424680i	$-0.139613\pi$
$967$	30.7929	+	17.7783i	0.990232	+	0.571711i	0.0848885	+	0.996390i	$0.472947\pi$
$968$		0			0
$969$	−52.3496			−1.68171
$970$		0			0
$971$	−20.3224	−	11.7331i	−0.652176	−	0.376534i	0.137113	−	0.990555i	$-0.456218\pi$
$971$	−20.3224	−	11.7331i	−0.652176	−	0.376534i	−0.789289	+	0.614021i	$0.789551\pi$
$972$		0			0
$973$	−2.15760	−	3.73708i	−0.0691695	−	0.119805i
$974$		0			0
$975$	−2.87954			−0.0922190
$976$		0			0
$977$	−30.0060	−	17.3240i	−0.959978	−	0.554243i	−0.0638116	−	0.997962i	$-0.520326\pi$
$977$	−30.0060	−	17.3240i	−0.959978	−	0.554243i	−0.896166	+	0.443718i	$0.853659\pi$
$978$		0			0
$979$	48.4596	+	27.9782i	1.54878	+	0.894186i
$980$		0			0
$981$		−	3.77436i		−	0.120506i
$982$		0			0
$983$	−14.8683	−	25.7527i	−0.474225	−	0.821382i	0.525339	−	0.850893i	$-0.323938\pi$
$983$	−14.8683	−	25.7527i	−0.474225	−	0.821382i	−0.999564	+	0.0295107i	$0.990605\pi$
$984$		0			0
$985$	2.17781	−	1.25736i	0.0693907	−	0.0400627i
$986$		0			0
$987$	−3.13861	+	5.43624i	−0.0999032	+	0.173037i
$988$		0			0
$989$		−	9.93593i		−	0.315944i
$990$		0			0
$991$	−5.58029	−	9.66534i	−0.177264	−	0.307030i	0.763679	−	0.645597i	$-0.223391\pi$
$991$	−5.58029	−	9.66534i	−0.177264	−	0.307030i	−0.940942	+	0.338567i	$0.890058\pi$
$992$		0			0
$993$	17.6391	+	30.5518i	0.559759	+	0.969531i
$994$		0			0
$995$	26.6822	−	46.2150i	0.845883	−	1.46511i
$996$		0			0
$997$	27.2327	+	47.1685i	0.862469	+	1.49384i	0.869539	+	0.493865i	$0.164416\pi$
$997$	27.2327	+	47.1685i	0.862469	+	1.49384i	−0.00706980	+	0.999975i	$0.502250\pi$
$998$		0			0
$999$	27.3564	−	15.7942i	0.865517	−	0.499706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1264.2.n.i.767.5	yes	28
4.3	odd	2	inner	1264.2.n.i.767.10	yes	28
79.24	odd	6	inner	1264.2.n.i.735.10	yes	28
316.103	even	6	inner	1264.2.n.i.735.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1264.2.n.i.735.5	✓	28	316.103	even	6	inner
1264.2.n.i.735.10	yes	28	79.24	odd	6	inner
1264.2.n.i.767.5	yes	28	1.1	even	1	trivial
1264.2.n.i.767.10	yes	28	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.799764 - 1.38523i) q^{3} +(1.24399 - 2.15465i) q^{5} +(0.627964 - 1.08766i) q^{7} +(0.220755 - 0.382358i) q^{9} +O(q^{10})\)	\(q+(-0.799764 - 1.38523i) q^{3} +(1.24399 - 2.15465i) q^{5} +(0.627964 - 1.08766i) q^{7} +(0.220755 - 0.382358i) q^{9} +(-4.25539 - 2.45685i) q^{11} +(0.756372 + 1.31008i) q^{13} -3.97960 q^{15} -5.86824i q^{17} +(4.82996 + 2.78858i) q^{19} -2.00889 q^{21} +(-2.76671 - 1.59736i) q^{23} +(-0.595025 - 1.03061i) q^{25} -5.50479 q^{27} +(3.75797 + 2.16966i) q^{29} +(-2.49981 - 1.44327i) q^{31} +7.85961i q^{33} +(-1.56236 - 2.70609i) q^{35} +(-4.96955 + 2.86917i) q^{37} +(1.20984 - 2.09550i) q^{39} -10.3606i q^{41} +(1.55506 + 2.69344i) q^{43} +(-0.549233 - 0.951300i) q^{45} +(1.56236 - 2.70609i) q^{47} +(2.71132 + 4.69615i) q^{49} +(-8.12888 + 4.69321i) q^{51} +(7.99221 + 4.61431i) q^{53} +(-10.5873 + 6.11260i) q^{55} -8.92083i q^{57} +(2.13693 + 3.70127i) q^{59} +4.46923i q^{61} +(-0.277252 - 0.480214i) q^{63} +3.76368 q^{65} +7.16896i q^{67} +5.11004i q^{69} -12.7847 q^{71} +(3.18173 - 5.51093i) q^{73} +(-0.951759 + 1.64850i) q^{75} +(-5.34447 + 3.08563i) q^{77} +(0.689399 - 8.86142i) q^{79} +(3.74027 + 6.47834i) q^{81} +(-0.643709 - 0.371646i) q^{83} +(-12.6440 - 7.30004i) q^{85} -6.94088i q^{87} -11.3878 q^{89} +1.89990 q^{91} +4.61709i q^{93} +(12.0169 - 6.93794i) q^{95} -18.4361 q^{97} +(-1.87880 + 1.08472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{9}+O(q^{10}) \) 28 * q - 20 * q^9	\( 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) \) 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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