LMFDB - Embedded newform 128.2.g.b.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, not 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			17.1
Root			$0.500000 + 0.691860i$ of defining polynomial
Character	$\chi$	$=$	128.17
Dual form			128.2.g.b.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0794708 + 0.191860i) q^{3} +(0.707107 - 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +(1.49368 + 3.60607i) q^{11} +(-4.50504 - 1.86605i) q^{13} +0.158942i q^{15} -3.05320i q^{17} +(-3.87740 - 1.60607i) q^{19} +(0.255272 + 0.616281i) q^{21} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(-1.14288 + 0.473398i) q^{27} +(-0.931884 + 2.24977i) q^{29} -6.82843 q^{31} -0.810564 q^{33} +(0.940816 - 2.27133i) q^{35} +(3.63349 - 1.50504i) q^{37} +(0.716038 - 0.716038i) q^{39} +(-1.54266 - 1.54266i) q^{41} +(-0.748956 - 1.80814i) q^{43} +(2.09083 + 0.866048i) q^{45} +7.37109i q^{47} -3.31788i q^{49} +(0.585786 + 0.242641i) q^{51} +(1.67661 + 4.04770i) q^{53} +(2.11239 + 2.11239i) q^{55} +(0.616281 - 0.616281i) q^{57} +(10.1200 - 4.19186i) q^{59} +(1.35873 - 3.28026i) q^{61} +9.49791 q^{63} -3.73210 q^{65} +(1.99577 - 4.81822i) q^{67} +(0.0736202 - 0.0304945i) q^{69} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(-0.350801 - 0.846909i) q^{75} +(11.5832 + 4.79793i) q^{77} -9.74996i q^{79} +8.61373i q^{81} +(9.04642 + 3.74715i) q^{83} +(-0.894263 - 2.15894i) q^{85} +(-0.357582 - 0.357582i) q^{87} +(7.58323 - 7.58323i) q^{89} +(-14.4708 + 5.99402i) q^{91} +(0.542661 - 1.31010i) q^{93} -3.21215 q^{95} +3.71423 q^{97} +(-4.41664 + 10.6627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 8 q^{7} - 4 q^{11} - 8 q^{13} - 4 q^{19} + 8 q^{23} - 8 q^{25} - 8 q^{27} - 32 q^{31} - 16 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} + 8 q^{53} + 16 q^{55}+ \cdots - 28 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 8 * q^7 - 4 * q^11 - 8 * q^13 - 4 * q^19 + 8 * q^23 - 8 * q^25 - 8 * q^27 - 32 * q^31 - 16 * q^33 - 16 * q^35 - 8 * q^37 - 16 * q^39 + 8 * q^41 + 12 * q^43 + 16 * q^51 + 8 * q^53 + 16 * q^55 + 16 * q^57 + 20 * q^59 + 24 * q^61 + 40 * q^63 + 36 * q^67 + 32 * q^69 + 24 * q^71 - 32 * q^73 + 12 * q^75 + 16 * q^77 - 20 * q^83 + 8 * q^85 - 56 * q^87 - 16 * q^89 - 40 * q^91 - 16 * q^93 + 8 * q^95 + 32 * q^97 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	−0.0794708	+	0.191860i	−0.0458825	+	0.110770i	−0.945159	−	0.326610i	$-0.894094\pi$
$3$	−0.0794708	+	0.191860i	−0.0458825	+	0.110770i	0.899277	+	0.437380i	$0.144094\pi$
$4$		0			0
$5$	0.707107	−	0.292893i	0.316228	−	0.130986i	−0.218924	−	0.975742i	$-0.570255\pi$
$5$	0.707107	−	0.292893i	0.316228	−	0.130986i	0.535151	+	0.844756i	$0.320255\pi$
$6$		0			0
$7$	2.27133	−	2.27133i	0.858482	−	0.858482i	−0.132677	−	0.991159i	$-0.542357\pi$
$7$	2.27133	−	2.27133i	0.858482	−	0.858482i	0.991159	+	0.132677i	$0.0423573\pi$
$8$		0			0
$9$	2.09083	+	2.09083i	0.696942	+	0.696942i
$10$		0			0
$11$	1.49368	+	3.60607i	0.450363	+	1.08727i	0.972184	+	0.234217i	$0.0752527\pi$
$11$	1.49368	+	3.60607i	0.450363	+	1.08727i	−0.521821	+	0.853055i	$0.674747\pi$
$12$		0			0
$13$	−4.50504	−	1.86605i	−1.24947	−	0.517549i	−0.342810	−	0.939405i	$-0.611379\pi$
$13$	−4.50504	−	1.86605i	−1.24947	−	0.517549i	−0.906663	+	0.421856i	$0.861379\pi$
$14$		0			0
$15$			0.158942i			0.0410386i
$16$		0			0
$17$		−	3.05320i		−	0.740511i	−0.928930	−	0.370255i	$-0.879270\pi$
$17$		−	3.05320i		−	0.740511i	0.928930	−	0.370255i	$-0.120730\pi$
$18$		0			0
$19$	−3.87740	−	1.60607i	−0.889537	−	0.368458i	−0.109349	−	0.994003i	$-0.534877\pi$
$19$	−3.87740	−	1.60607i	−0.889537	−	0.368458i	−0.780188	+	0.625545i	$0.784877\pi$
$20$		0			0
$21$	0.255272	+	0.616281i	0.0557049	+	0.134484i
$22$		0			0
$23$	−0.271330	−	0.271330i	−0.0565763	−	0.0565763i	0.678253	−	0.734829i	$-0.262738\pi$
$23$	−0.271330	−	0.271330i	−0.0565763	−	0.0565763i	−0.734829	+	0.678253i	$0.762738\pi$
$24$		0			0
$25$	−3.12132	+	3.12132i	−0.624264	+	0.624264i
$26$		0			0
$27$	−1.14288	+	0.473398i	−0.219948	+	0.0911054i
$28$		0			0
$29$	−0.931884	+	2.24977i	−0.173047	+	0.417771i	−0.986479	−	0.163888i	$-0.947596\pi$
$29$	−0.931884	+	2.24977i	−0.173047	+	0.417771i	0.813432	+	0.581660i	$0.197596\pi$
$30$		0			0
$31$	−6.82843			−1.22642			−0.613211	−	0.789919i	$-0.710122\pi$
$31$	−6.82843			−1.22642			−0.613211	+	0.789919i	$0.710122\pi$
$32$		0			0
$33$	−0.810564			−0.141101
$34$		0			0
$35$	0.940816	−	2.27133i	0.159027	−	0.383925i
$36$		0			0
$37$	3.63349	−	1.50504i	0.597342	−	0.247427i	−0.0634640	−	0.997984i	$-0.520215\pi$
$37$	3.63349	−	1.50504i	0.597342	−	0.247427i	0.660806	+	0.750557i	$0.270215\pi$
$38$		0			0
$39$	0.716038	−	0.716038i	0.114658	−	0.114658i
$40$		0			0
$41$	−1.54266	−	1.54266i	−0.240923	−	0.240923i	0.576309	−	0.817232i	$-0.304493\pi$
$41$	−1.54266	−	1.54266i	−0.240923	−	0.240923i	−0.817232	+	0.576309i	$0.804493\pi$
$42$		0			0
$43$	−0.748956	−	1.80814i	−0.114215	−	0.275739i	0.856427	−	0.516268i	$-0.172679\pi$
$43$	−0.748956	−	1.80814i	−0.114215	−	0.275739i	−0.970642	+	0.240529i	$0.922679\pi$
$44$		0			0
$45$	2.09083	+	0.866048i	0.311682	+	0.129103i
$46$		0			0
$47$			7.37109i			1.07518i	0.843205	+	0.537592i	$0.180666\pi$
$47$			7.37109i			1.07518i	−0.843205	+	0.537592i	$0.819334\pi$
$48$		0			0
$49$		−	3.31788i		−	0.473983i
$50$		0			0
$51$	0.585786	+	0.242641i	0.0820265	+	0.0339765i
$52$		0			0
$53$	1.67661	+	4.04770i	0.230300	+	0.555994i	0.996213	−	0.0869508i	$-0.0277123\pi$
$53$	1.67661	+	4.04770i	0.230300	+	0.555994i	−0.765912	+	0.642945i	$0.777712\pi$
$54$		0			0
$55$	2.11239	+	2.11239i	0.284834	+	0.284834i
$56$		0			0
$57$	0.616281	−	0.616281i	0.0816284	−	0.0816284i
$58$		0			0
$59$	10.1200	−	4.19186i	1.31752	−	0.545734i	0.390449	−	0.920625i	$-0.372320\pi$
$59$	10.1200	−	4.19186i	1.31752	−	0.545734i	0.927069	+	0.374891i	$0.122320\pi$
$60$		0			0
$61$	1.35873	−	3.28026i	0.173967	−	0.419995i	−0.812713	−	0.582664i	$-0.802010\pi$
$61$	1.35873	−	3.28026i	0.173967	−	0.419995i	0.986681	+	0.162669i	$0.0520104\pi$
$62$		0			0
$63$	9.49791			1.19662
$64$		0			0
$65$	−3.73210			−0.462910
$66$		0			0
$67$	1.99577	−	4.81822i	0.243822	−	0.588639i	−0.753834	−	0.657065i	$-0.771798\pi$
$67$	1.99577	−	4.81822i	0.243822	−	0.588639i	0.997656	+	0.0684259i	$0.0217977\pi$
$68$		0			0
$69$	0.0736202	−	0.0304945i	0.00886283	−	0.00367110i
$70$		0			0
$71$	−6.47085	+	6.47085i	−0.767948	+	0.767948i	−0.977745	−	0.209797i	$-0.932720\pi$
$71$	−6.47085	+	6.47085i	−0.767948	+	0.767948i	0.209797	+	0.977745i	$0.432720\pi$
$72$		0			0
$73$	−2.84106	−	2.84106i	−0.332521	−	0.332521i	0.521022	−	0.853543i	$-0.325551\pi$
$73$	−2.84106	−	2.84106i	−0.332521	−	0.332521i	−0.853543	+	0.521022i	$0.825551\pi$
$74$		0			0
$75$	−0.350801	−	0.846909i	−0.0405070	−	0.0977926i
$76$		0			0
$77$	11.5832	+	4.79793i	1.32003	+	0.546775i
$78$		0			0
$79$		−	9.74996i		−	1.09696i	−0.836165	−	0.548478i	$-0.815207\pi$
$79$		−	9.74996i		−	1.09696i	0.836165	−	0.548478i	$-0.184793\pi$
$80$		0			0
$81$			8.61373i			0.957081i
$82$		0			0
$83$	9.04642	+	3.74715i	0.992974	+	0.411303i	0.819216	−	0.573485i	$-0.194409\pi$
$83$	9.04642	+	3.74715i	0.992974	+	0.411303i	0.173758	+	0.984788i	$0.444409\pi$
$84$		0			0
$85$	−0.894263	−	2.15894i	−0.0969964	−	0.234170i
$86$		0			0
$87$	−0.357582	−	0.357582i	−0.0383368	−	0.0383368i
$88$		0			0
$89$	7.58323	−	7.58323i	0.803821	−	0.803821i	−0.179869	−	0.983691i	$-0.557567\pi$
$89$	7.58323	−	7.58323i	0.803821	−	0.803821i	0.983691	+	0.179869i	$0.0575675\pi$
$90$		0			0
$91$	−14.4708	+	5.99402i	−1.51696	+	0.628344i
$92$		0			0
$93$	0.542661	−	1.31010i	0.0562713	−	0.135851i
$94$		0			0
$95$	−3.21215			−0.329559
$96$		0			0
$97$	3.71423			0.377123			0.188562	−	0.982061i	$-0.439617\pi$
$97$	3.71423			0.377123			0.188562	+	0.982061i	$0.439617\pi$
$98$		0			0
$99$	−4.41664	+	10.6627i	−0.443889	+	1.07164i
$100$		0			0
$101$	−9.04770	+	3.74768i	−0.900280	+	0.372908i	−0.784328	−	0.620347i	$-0.786992\pi$
$101$	−9.04770	+	3.74768i	−0.900280	+	0.372908i	−0.115952	+	0.993255i	$0.536992\pi$
$102$		0			0
$103$	−0.450688	+	0.450688i	−0.0444076	+	0.0444076i	−0.728962	−	0.684554i	$-0.759997\pi$
$103$	−0.450688	+	0.450688i	−0.0444076	+	0.0444076i	0.684554	+	0.728962i	$0.259997\pi$
$104$		0			0
$105$	0.361009	+	0.361009i	0.0352309	+	0.0352309i
$106$		0			0
$107$	−6.82420	−	16.4751i	−0.659720	−	1.59271i	−0.798236	−	0.602345i	$-0.794233\pi$
$107$	−6.82420	−	16.4751i	−0.659720	−	1.59271i	0.138515	−	0.990360i	$-0.455767\pi$
$108$		0			0
$109$	−7.20664	−	2.98509i	−0.690271	−	0.285920i	0.00984205	−	0.999952i	$-0.496867\pi$
$109$	−7.20664	−	2.98509i	−0.690271	−	0.285920i	−0.700113	+	0.714032i	$0.746867\pi$
$110$		0			0
$111$			0.816726i			0.0775202i
$112$		0			0
$113$			8.76744i			0.824771i	0.911009	+	0.412386i	$0.135304\pi$
$113$			8.76744i			0.824771i	−0.911009	+	0.412386i	$0.864696\pi$
$114$		0			0
$115$	−0.271330	−	0.112389i	−0.0253017	−	0.0104803i
$116$		0			0
$117$	−5.51767	−	13.3208i	−0.510109	−	1.23151i
$118$		0			0
$119$	−6.93484	−	6.93484i	−0.635715	−	0.635715i
$120$		0			0
$121$	−2.99450	+	2.99450i	−0.272227	+	0.272227i
$122$		0			0
$123$	0.418571	−	0.173378i	0.0377412	−	0.0156329i
$124$		0			0
$125$	−2.75736	+	6.65685i	−0.246626	+	0.595407i
$126$		0			0
$127$	11.4642			1.01728			0.508641	−	0.860979i	$-0.330148\pi$
$127$	11.4642			1.01728			0.508641	+	0.860979i	$0.330148\pi$
$128$		0			0
$129$	0.406429			0.0357841
$130$		0			0
$131$	−4.32211	+	10.4345i	−0.377625	+	0.911667i	0.614785	+	0.788694i	$0.289243\pi$
$131$	−4.32211	+	10.4345i	−0.377625	+	0.911667i	−0.992410	+	0.122972i	$0.960757\pi$
$132$		0			0
$133$	−12.4548	+	5.15894i	−1.07997	+	0.447337i
$134$		0			0
$135$	−0.669485	+	0.669485i	−0.0576201	+	0.0576201i
$136$		0			0
$137$	−3.42429	−	3.42429i	−0.292557	−	0.292557i	0.545533	−	0.838090i	$-0.316327\pi$
$137$	−3.42429	−	3.42429i	−0.292557	−	0.292557i	−0.838090	+	0.545533i	$0.816327\pi$
$138$		0			0
$139$	7.35745	+	17.7625i	0.624051	+	1.50659i	0.846907	+	0.531741i	$0.178462\pi$
$139$	7.35745	+	17.7625i	0.624051	+	1.50659i	−0.222856	+	0.974851i	$0.571538\pi$
$140$		0			0
$141$	−1.41421	−	0.585786i	−0.119098	−	0.0493321i
$142$		0			0
$143$		−	19.0328i		−	1.59160i
$144$		0			0
$145$			1.86377i			0.154778i
$146$		0			0
$147$	0.636568	+	0.263675i	0.0525032	+	0.0217475i
$148$		0			0
$149$	−0.931884	−	2.24977i	−0.0763429	−	0.184308i	0.881101	−	0.472929i	$-0.156803\pi$
$149$	−0.931884	−	2.24977i	−0.0763429	−	0.184308i	−0.957443	+	0.288621i	$0.906803\pi$
$150$		0			0
$151$	4.21395	+	4.21395i	0.342926	+	0.342926i	0.857466	−	0.514540i	$-0.172037\pi$
$151$	4.21395	+	4.21395i	0.342926	+	0.342926i	−0.514540	+	0.857466i	$0.672037\pi$
$152$		0			0
$153$	6.38372	−	6.38372i	0.516093	−	0.516093i
$154$		0			0
$155$	−4.82843	+	2.00000i	−0.387829	+	0.160644i
$156$		0			0
$157$	5.84401	−	14.1087i	0.466403	−	1.12600i	−0.499319	−	0.866418i	$-0.666417\pi$
$157$	5.84401	−	14.1087i	0.466403	−	1.12600i	0.965722	−	0.259578i	$-0.0835835\pi$
$158$		0			0
$159$	−0.909832			−0.0721543
$160$		0			0
$161$	−1.23256			−0.0971395
$162$		0			0
$163$	2.72369	−	6.57558i	0.213336	−	0.515039i	−0.780596	−	0.625036i	$-0.785084\pi$
$163$	2.72369	−	6.57558i	0.213336	−	0.515039i	0.993932	+	0.109997i	$0.0350842\pi$
$164$		0			0
$165$	−0.573155	+	0.237409i	−0.0446201	+	0.0184822i
$166$		0			0
$167$	−3.26355	+	3.26355i	−0.252541	+	0.252541i	−0.822012	−	0.569471i	$-0.807148\pi$
$167$	−3.26355	+	3.26355i	−0.252541	+	0.252541i	0.569471	+	0.822012i	$0.307148\pi$
$168$		0			0
$169$	7.62086	+	7.62086i	0.586220	+	0.586220i
$170$		0			0
$171$	−4.74896	−	11.4650i	−0.363162	−	0.876750i
$172$		0			0
$173$	6.86605	+	2.84401i	0.522016	+	0.216226i	0.628102	−	0.778131i	$-0.283832\pi$
$173$	6.86605	+	2.84401i	0.522016	+	0.216226i	−0.106086	+	0.994357i	$0.533832\pi$
$174$		0			0
$175$			14.1791i			1.07184i
$176$		0			0
$177$			2.27476i			0.170981i
$178$		0			0
$179$	1.79370	+	0.742977i	0.134068	+	0.0555327i	0.448709	−	0.893678i	$-0.351884\pi$
$179$	1.79370	+	0.742977i	0.134068	+	0.0555327i	−0.314641	+	0.949211i	$0.601884\pi$
$180$		0			0
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	0.970399	+	0.241506i	$0.0776415\pi$
$181$	6.12132	+	14.7782i	0.454994	+	1.09845i	−0.515405	+	0.856947i	$0.672359\pi$
$182$		0			0
$183$	0.521370	+	0.521370i	0.0385408	+	0.0385408i
$184$		0			0
$185$	2.12845	−	2.12845i	0.156487	−	0.156487i
$186$		0			0
$187$	11.0101	−	4.56052i	0.805137	−	0.333499i
$188$		0			0
$189$	−1.52062	+	3.67111i	−0.110609	+	0.267034i
$190$		0			0
$191$	6.19266			0.448085			0.224043	−	0.974579i	$-0.428075\pi$
$191$	6.19266			0.448085			0.224043	+	0.974579i	$0.428075\pi$
$192$		0			0
$193$	14.5784			1.04938			0.524688	−	0.851295i	$-0.324182\pi$
$193$	14.5784			1.04938			0.524688	+	0.851295i	$0.324182\pi$
$194$		0			0
$195$	0.296593	−	0.716038i	0.0212395	−	0.0512766i
$196$		0			0
$197$	18.5025	−	7.66398i	1.31825	−	0.546036i	0.390968	−	0.920404i	$-0.372140\pi$
$197$	18.5025	−	7.66398i	1.31825	−	0.546036i	0.927280	+	0.374368i	$0.122140\pi$
$198$		0			0
$199$	12.3777	−	12.3777i	0.877435	−	0.877435i	−0.115834	−	0.993269i	$-0.536954\pi$
$199$	12.3777	−	12.3777i	0.877435	−	0.877435i	0.993269	+	0.115834i	$0.0369540\pi$
$200$		0			0
$201$	0.765816	+	0.765816i	0.0540165	+	0.0540165i
$202$		0			0
$203$	2.99335	+	7.22658i	0.210092	+	0.507207i
$204$		0			0
$205$	−1.54266	−	0.638991i	−0.107744	−	0.0446291i
$206$		0			0
$207$		−	1.13461i		−	0.0788608i
$208$		0			0
$209$		−	16.3812i		−	1.13311i
$210$		0			0
$211$	−3.54851	−	1.46984i	−0.244290	−	0.101188i	0.257179	−	0.966364i	$-0.417207\pi$
$211$	−3.54851	−	1.46984i	−0.244290	−	0.101188i	−0.501469	+	0.865176i	$0.667207\pi$
$212$		0			0
$213$	−0.727250	−	1.75574i	−0.0498304	−	0.120301i
$214$		0			0
$215$	−1.05918	−	1.05918i	−0.0722358	−	0.0722358i
$216$		0			0
$217$	−15.5096	+	15.5096i	−1.05286	+	1.05286i
$218$		0			0
$219$	0.770865	−	0.319303i	0.0520903	−	0.0215765i
$220$		0			0
$221$	−5.69743	+	13.7548i	−0.383250	+	0.925248i
$222$		0			0
$223$	−27.5550			−1.84522			−0.922611	−	0.385732i	$-0.873949\pi$
$223$	−27.5550			−1.84522			−0.922611	+	0.385732i	$0.873949\pi$
$224$		0			0
$225$	−13.0523			−0.870152
$226$		0			0
$227$	6.02694	−	14.5503i	0.400022	−	0.965738i	−0.587638	−	0.809124i	$-0.699942\pi$
$227$	6.02694	−	14.5503i	0.400022	−	0.965738i	0.987660	−	0.156614i	$-0.0500580\pi$
$228$		0			0
$229$	18.2777	−	7.57088i	1.20783	−	0.500298i	0.314306	−	0.949322i	$-0.398228\pi$
$229$	18.2777	−	7.57088i	1.20783	−	0.500298i	0.893520	+	0.449024i	$0.148228\pi$
$230$		0			0
$231$	−1.84106	+	1.84106i	−0.121133	+	0.121133i
$232$		0			0
$233$	−6.70939	−	6.70939i	−0.439547	−	0.439547i	0.452313	−	0.891859i	$-0.350599\pi$
$233$	−6.70939	−	6.70939i	−0.439547	−	0.439547i	−0.891859	+	0.452313i	$0.850599\pi$
$234$		0			0
$235$	2.15894	+	5.21215i	0.140834	+	0.340003i
$236$		0			0
$237$	1.87062	+	0.774837i	0.121510	+	0.0503311i
$238$		0			0
$239$			26.1995i			1.69471i	0.531030	+	0.847353i	$0.321805\pi$
$239$			26.1995i			1.69471i	−0.531030	+	0.847353i	$0.678195\pi$
$240$		0			0
$241$		−	13.6734i		−	0.880781i	−0.897806	−	0.440391i	$-0.854840\pi$
$241$		−	13.6734i		−	0.880781i	0.897806	−	0.440391i	$-0.145160\pi$
$242$		0			0
$243$	−5.08128	−	2.10473i	−0.325964	−	0.135019i
$244$		0			0
$245$	−0.971786	−	2.34610i	−0.0620851	−	0.149887i
$246$		0			0
$247$	14.4708	+	14.4708i	0.920758	+	0.920758i
$248$		0			0
$249$	−1.43785	+	1.43785i	−0.0911203	+	0.0911203i
$250$		0			0
$251$	13.2054	−	5.46984i	0.833515	−	0.345253i	0.0752219	−	0.997167i	$-0.476033\pi$
$251$	13.2054	−	5.46984i	0.833515	−	0.345253i	0.758293	+	0.651913i	$0.226033\pi$
$252$		0			0
$253$	0.573155	−	1.38372i	0.0360340	−	0.0869937i
$254$		0			0
$255$	0.485281			0.0303895
$256$		0			0
$257$	−20.0656			−1.25166			−0.625828	−	0.779961i	$-0.715239\pi$
$257$	−20.0656			−1.25166			−0.625828	+	0.779961i	$0.715239\pi$
$258$		0			0
$259$	4.83441	−	11.6713i	0.300395	−	0.725219i
$260$		0			0
$261$	−6.65228	+	2.75546i	−0.411766	+	0.170559i
$262$		0			0
$263$	−4.74976	+	4.74976i	−0.292883	+	0.292883i	−0.838218	−	0.545335i	$-0.816402\pi$
$263$	−4.74976	+	4.74976i	−0.292883	+	0.292883i	0.545335	+	0.838218i	$0.316402\pi$
$264$		0			0
$265$	2.37109	+	2.37109i	0.145655	+	0.145655i
$266$		0			0
$267$	0.852270	+	2.05756i	0.0521581	+	0.125921i
$268$		0			0
$269$	−22.3818	−	9.27086i	−1.36464	−	0.565254i	−0.424313	−	0.905516i	$-0.639484\pi$
$269$	−22.3818	−	9.27086i	−1.36464	−	0.565254i	−0.940331	+	0.340262i	$0.889484\pi$
$270$		0			0
$271$			0.693146i			0.0421056i	0.999778	+	0.0210528i	$0.00670181\pi$
$271$			0.693146i			0.0421056i	−0.999778	+	0.0210528i	$0.993298\pi$
$272$		0			0
$273$		−	3.25272i		−	0.196864i
$274$		0			0
$275$	−15.9180	−	6.59344i	−0.959890	−	0.397600i
$276$		0			0
$277$	11.1898	+	27.0147i	0.672332	+	1.62315i	0.777637	+	0.628713i	$0.216418\pi$
$277$	11.1898	+	27.0147i	0.672332	+	1.62315i	−0.105305	+	0.994440i	$0.533582\pi$
$278$		0			0
$279$	−14.2771	−	14.2771i	−0.854745	−	0.854745i
$280$		0			0
$281$	−6.97958	+	6.97958i	−0.416367	+	0.416367i	−0.883949	−	0.467582i	$-0.845125\pi$
$281$	−6.97958	+	6.97958i	−0.416367	+	0.416367i	0.467582	+	0.883949i	$0.345125\pi$
$282$		0			0
$283$	−14.6079	+	6.05078i	−0.868348	+	0.359682i	−0.771967	−	0.635663i	$-0.780727\pi$
$283$	−14.6079	+	6.05078i	−0.868348	+	0.359682i	−0.0963814	+	0.995344i	$0.530727\pi$
$284$		0			0
$285$	0.255272	−	0.616281i	0.0151210	−	0.0365053i
$286$		0			0
$287$	−7.00778			−0.413656
$288$		0			0
$289$	7.67794			0.451644
$290$		0			0
$291$	−0.295173	+	0.712611i	−0.0173034	+	0.0417740i
$292$		0			0
$293$	−9.85571	+	4.08237i	−0.575777	+	0.238495i	−0.651518	−	0.758633i	$-0.725868\pi$
$293$	−9.85571	+	4.08237i	−0.575777	+	0.238495i	0.0757415	+	0.997127i	$0.475868\pi$
$294$		0			0
$295$	5.92818	−	5.92818i	0.345152	−	0.345152i
$296$		0			0
$297$	−3.41421	−	3.41421i	−0.198113	−	0.198113i
$298$		0			0
$299$	0.716038	+	1.72867i	0.0414096	+	0.0999715i
$300$		0			0
$301$	−5.80801	−	2.40576i	−0.334768	−	0.138666i
$302$		0			0
$303$		−	2.03372i		−	0.116834i
$304$		0			0
$305$		−	2.71746i		−	0.155601i
$306$		0			0
$307$	−6.96272	−	2.88406i	−0.397384	−	0.164602i	0.175037	−	0.984562i	$-0.443996\pi$
$307$	−6.96272	−	2.88406i	−0.397384	−	0.164602i	−0.572421	+	0.819960i	$0.693996\pi$
$308$		0			0
$309$	−0.0506522	−	0.122285i	−0.00288150	−	0.00695656i
$310$		0			0
$311$	−4.65020	−	4.65020i	−0.263689	−	0.263689i	0.562862	−	0.826551i	$-0.309700\pi$
$311$	−4.65020	−	4.65020i	−0.263689	−	0.263689i	−0.826551	+	0.562862i	$0.809700\pi$
$312$		0			0
$313$	−0.325668	+	0.325668i	−0.0184078	+	0.0184078i	−0.716251	−	0.697843i	$-0.754143\pi$
$313$	−0.325668	+	0.325668i	−0.0184078	+	0.0184078i	0.697843	+	0.716251i	$0.254143\pi$
$314$		0			0
$315$	6.71604	−	2.78187i	0.378406	−	0.156741i
$316$		0			0
$317$	7.92866	−	19.1415i	0.445318	−	1.07509i	−0.528738	−	0.848785i	$-0.677335\pi$
$317$	7.92866	−	19.1415i	0.445318	−	1.07509i	0.974056	−	0.226307i	$-0.0726654\pi$
$318$		0			0
$319$	−9.50477			−0.532165
$320$		0			0
$321$	3.70322			0.206694
$322$		0			0
$323$	−4.90367	+	11.8385i	−0.272847	+	0.658712i
$324$		0			0
$325$	19.8862	−	8.23714i	1.10309	−	0.456914i
$326$		0			0
$327$	1.14544	−	1.14544i	0.0633427	−	0.0633427i
$328$		0			0
$329$	16.7422	+	16.7422i	0.923026	+	0.923026i
$330$		0			0
$331$	5.91798	+	14.2873i	0.325281	+	0.785299i	0.998930	+	0.0462470i	$0.0147261\pi$
$331$	5.91798	+	14.2873i	0.325281	+	0.785299i	−0.673649	+	0.739052i	$0.735274\pi$
$332$		0			0
$333$	10.7438	+	4.45021i	0.588755	+	0.243870i
$334$		0			0
$335$		−	3.99154i		−	0.218081i
$336$		0			0
$337$			4.44955i			0.242383i	0.992629	+	0.121191i	$0.0386715\pi$
$337$			4.44955i			0.242383i	−0.992629	+	0.121191i	$0.961329\pi$
$338$		0			0
$339$	−1.68212	−	0.696756i	−0.0913600	−	0.0378426i
$340$		0			0
$341$	−10.1995	−	24.6238i	−0.552335	−	1.33345i
$342$		0			0
$343$	8.36330	+	8.36330i	0.451576	+	0.451576i
$344$		0			0
$345$	0.0431257	−	0.0431257i	0.00232181	−	0.00232181i
$346$		0			0
$347$	−7.87485	+	3.26187i	−0.422744	+	0.175106i	−0.583905	−	0.811822i	$-0.698476\pi$
$347$	−7.87485	+	3.26187i	−0.422744	+	0.175106i	0.161161	+	0.986928i	$0.448476\pi$
$348$		0			0
$349$	−12.9387	+	31.2369i	−0.692595	+	1.67207i	0.0468913	+	0.998900i	$0.485069\pi$
$349$	−12.9387	+	31.2369i	−0.692595	+	1.67207i	−0.739486	+	0.673172i	$0.764931\pi$
$350$		0			0
$351$	6.03212			0.321971
$352$		0			0
$353$	20.7013			1.10182			0.550911	−	0.834564i	$-0.314280\pi$
$353$	20.7013			1.10182			0.550911	+	0.834564i	$0.314280\pi$
$354$		0			0
$355$	−2.68031	+	6.47085i	−0.142256	+	0.343437i
$356$		0			0
$357$	1.88163	−	0.779397i	0.0995865	−	0.0412501i
$358$		0			0
$359$	19.9483	−	19.9483i	1.05283	−	1.05283i	0.0543091	−	0.998524i	$-0.482704\pi$
$359$	19.9483	−	19.9483i	1.05283	−	1.05283i	0.998524	−	0.0543091i	$-0.0172956\pi$
$360$		0			0
$361$	−0.980242	−	0.980242i	−0.0515917	−	0.0515917i
$362$		0			0
$363$	−0.336548	−	0.812498i	−0.0176642	−	0.0426451i
$364$		0			0
$365$	−2.84106	−	1.17680i	−0.148708	−	0.0615968i
$366$		0			0
$367$		−	9.14270i		−	0.477245i	−0.971112	−	0.238623i	$-0.923304\pi$
$367$		−	9.14270i		−	0.477245i	0.971112	−	0.238623i	$-0.0766959\pi$
$368$		0			0
$369$		−	6.45087i		−	0.335819i
$370$		0			0
$371$	13.0018	+	5.38552i	0.675020	+	0.279602i
$372$		0			0
$373$	−3.71974	−	8.98024i	−0.192601	−	0.464979i	0.797848	−	0.602858i	$-0.205972\pi$
$373$	−3.71974	−	8.98024i	−0.192601	−	0.464979i	−0.990449	+	0.137879i	$0.955972\pi$
$374$		0			0
$375$	−1.05805	−	1.05805i	−0.0546375	−	0.0546375i
$376$		0			0
$377$	8.39635	−	8.39635i	0.432434	−	0.432434i
$378$		0			0
$379$	7.80216	−	3.23176i	0.400770	−	0.166004i	−0.173189	−	0.984889i	$-0.555407\pi$
$379$	7.80216	−	3.23176i	0.400770	−	0.166004i	0.573959	+	0.818884i	$0.305407\pi$
$380$		0			0
$381$	−0.911069	+	2.19951i	−0.0466755	+	0.112685i
$382$		0			0
$383$	28.4633			1.45440			0.727202	−	0.686423i	$-0.240820\pi$
$383$	28.4633			1.45440			0.727202	+	0.686423i	$0.240820\pi$
$384$		0			0
$385$	9.59587			0.489051
$386$		0			0
$387$	2.21457	−	5.34644i	0.112573	−	0.271775i
$388$		0			0
$389$	−21.0834	+	8.73304i	−1.06897	+	0.442783i	−0.846628	−	0.532185i	$-0.821371\pi$
$389$	−21.0834	+	8.73304i	−1.06897	+	0.442783i	−0.222344	+	0.974968i	$0.571371\pi$
$390$		0			0
$391$	−0.828427	+	0.828427i	−0.0418954	+	0.0418954i
$392$		0			0
$393$	−1.65848	−	1.65848i	−0.0836591	−	0.0836591i
$394$		0			0
$395$	−2.85570	−	6.89426i	−0.143686	−	0.346888i
$396$		0			0
$397$	−6.46808	−	2.67916i	−0.324623	−	0.134463i	0.214420	−	0.976742i	$-0.431214\pi$
$397$	−6.46808	−	2.67916i	−0.324623	−	0.134463i	−0.539043	+	0.842278i	$0.681214\pi$
$398$		0			0
$399$		−	2.79956i		−	0.140153i
$400$		0			0
$401$			24.9871i			1.24780i	0.781505	+	0.623898i	$0.214452\pi$
$401$			24.9871i			1.24780i	−0.781505	+	0.623898i	$0.785548\pi$
$402$		0			0
$403$	30.7623	+	12.7422i	1.53238	+	0.634733i
$404$		0			0
$405$	2.52290	+	6.09083i	0.125364	+	0.302656i
$406$		0			0
$407$	10.8546	+	10.8546i	0.538041	+	0.538041i
$408$		0			0
$409$	9.19951	−	9.19951i	0.454887	−	0.454887i	−0.442086	−	0.896973i	$-0.645761\pi$
$409$	9.19951	−	9.19951i	0.454887	−	0.454887i	0.896973	+	0.442086i	$0.145761\pi$
$410$		0			0
$411$	0.929115	−	0.384852i	0.0458298	−	0.0189833i
$412$		0			0
$413$	13.4649	−	32.5071i	0.662563	−	1.59957i
$414$		0			0
$415$	7.49430			0.367881
$416$		0			0
$417$	−3.99260			−0.195519
$418$		0			0
$419$	−10.4739	+	25.2863i	−0.511685	+	1.23532i	0.431217	+	0.902248i	$0.358084\pi$
$419$	−10.4739	+	25.2863i	−0.511685	+	1.23532i	−0.942902	+	0.333070i	$0.891916\pi$
$420$		0			0
$421$	−16.6841	+	6.91080i	−0.813135	+	0.336812i	−0.750204	−	0.661206i	$-0.770045\pi$
$421$	−16.6841	+	6.91080i	−0.813135	+	0.336812i	−0.0629310	+	0.998018i	$0.520045\pi$
$422$		0			0
$423$	−15.4117	+	15.4117i	−0.749341	+	0.749341i
$424$		0			0
$425$	9.53003	+	9.53003i	0.462274	+	0.462274i
$426$		0			0
$427$	−4.36444	−	10.5367i	−0.211210	−	0.509906i
$428$		0			0
$429$	3.65162	+	1.51255i	0.176302	+	0.0730267i
$430$		0			0
$431$		−	26.5985i		−	1.28121i	−0.767872	−	0.640603i	$-0.778684\pi$
$431$		−	26.5985i		−	1.28121i	0.767872	−	0.640603i	$-0.221316\pi$
$432$		0			0
$433$			9.96788i			0.479026i	0.970893	+	0.239513i	$0.0769878\pi$
$433$			9.96788i			0.479026i	−0.970893	+	0.239513i	$0.923012\pi$
$434$		0			0
$435$	−0.357582	−	0.148115i	−0.0171447	−	0.00710158i
$436$		0			0
$437$	0.616281	+	1.48783i	0.0294807	+	0.0711727i
$438$		0			0
$439$	−17.4631	−	17.4631i	−0.833466	−	0.833466i	0.154523	−	0.987989i	$-0.450616\pi$
$439$	−17.4631	−	17.4631i	−0.833466	−	0.833466i	−0.987989	+	0.154523i	$0.950616\pi$
$440$		0			0
$441$	6.93712	−	6.93712i	0.330339	−	0.330339i
$442$		0			0
$443$	−34.7377	+	14.3888i	−1.65044	+	0.683634i	−0.997288	−	0.0735956i	$-0.976553\pi$
$443$	−34.7377	+	14.3888i	−1.65044	+	0.683634i	−0.653149	+	0.757229i	$0.726553\pi$
$444$		0			0
$445$	3.14108	−	7.58323i	0.148901	−	0.359480i
$446$		0			0
$447$	0.505697			0.0239186
$448$		0			0
$449$	−8.35000			−0.394061			−0.197030	−	0.980397i	$-0.563130\pi$
$449$	−8.35000			−0.394061			−0.197030	+	0.980397i	$0.563130\pi$
$450$		0			0
$451$	3.25870	−	7.86720i	0.153446	−	0.370452i
$452$		0			0
$453$	−1.14337	+	0.473601i	−0.0537203	+	0.0222517i
$454$		0			0
$455$	−8.47682	+	8.47682i	−0.397400	+	0.397400i
$456$		0			0
$457$	−18.0734	−	18.0734i	−0.845436	−	0.845436i	0.144123	−	0.989560i	$-0.453964\pi$
$457$	−18.0734	−	18.0734i	−0.845436	−	0.845436i	−0.989560	+	0.144123i	$0.953964\pi$
$458$		0			0
$459$	1.44538	+	3.48946i	0.0674646	+	0.162874i
$460$		0			0
$461$	26.4451	+	10.9539i	1.23167	+	0.510175i	0.901102	−	0.433607i	$-0.142759\pi$
$461$	26.4451	+	10.9539i	1.23167	+	0.510175i	0.330569	+	0.943782i	$0.392759\pi$
$462$		0			0
$463$		−	4.94169i		−	0.229660i	−0.993385	−	0.114830i	$-0.963368\pi$
$463$		−	4.94169i		−	0.229660i	0.993385	−	0.114830i	$-0.0366323\pi$
$464$		0			0
$465$		−	1.08532i		−	0.0503306i
$466$		0			0
$467$	−20.6806	−	8.56617i	−0.956983	−	0.396395i	−0.151132	−	0.988514i	$-0.548292\pi$
$467$	−20.6806	−	8.56617i	−0.956983	−	0.396395i	−0.805851	+	0.592118i	$0.798292\pi$
$468$		0			0
$469$	−6.41071	−	15.4768i	−0.296019	−	0.714653i
$470$		0			0
$471$	2.24246	+	2.24246i	0.103327	+	0.103327i
$472$		0			0
$473$	5.40158	−	5.40158i	0.248365	−	0.248365i
$474$		0			0
$475$	17.1157	−	7.08955i	0.785322	−	0.325291i
$476$		0			0
$477$	−4.95753	+	11.9685i	−0.226990	+	0.548002i
$478$		0			0
$479$	5.50637			0.251592			0.125796	−	0.992056i	$-0.459851\pi$
$479$	5.50637			0.251592			0.125796	+	0.992056i	$0.459851\pi$
$480$		0			0
$481$	−19.1775			−0.874418
$482$		0			0
$483$	0.0979527	−	0.236479i	0.00445700	−	0.0107602i
$484$		0			0
$485$	2.62636	−	1.08787i	0.119257	−	0.0493978i
$486$		0			0
$487$	−24.9561	+	24.9561i	−1.13087	+	1.13087i	−0.140837	+	0.990033i	$0.544979\pi$
$487$	−24.9561	+	24.9561i	−1.13087	+	1.13087i	−0.990033	+	0.140837i	$0.955021\pi$
$488$		0			0
$489$	1.04513	+	1.04513i	0.0472626	+	0.0472626i
$490$		0			0
$491$	−4.79438	−	11.5746i	−0.216367	−	0.522357i	0.778010	−	0.628252i	$-0.216229\pi$
$491$	−4.79438	−	11.5746i	−0.216367	−	0.522357i	−0.994377	+	0.105895i	$0.966229\pi$
$492$		0			0
$493$	6.86900	+	2.84523i	0.309364	+	0.128143i
$494$		0			0
$495$			8.83327i			0.397026i
$496$		0			0
$497$			29.3949i			1.31854i
$498$		0			0
$499$	−8.71684	−	3.61063i	−0.390219	−	0.161634i	0.178943	−	0.983859i	$-0.442732\pi$
$499$	−8.71684	−	3.61063i	−0.390219	−	0.161634i	−0.569162	+	0.822225i	$0.692732\pi$
$500$		0			0
$501$	−0.366786	−	0.885499i	−0.0163868	−	0.0395612i
$502$		0			0
$503$	−5.07960	−	5.07960i	−0.226488	−	0.226488i	0.584736	−	0.811224i	$-0.301198\pi$
$503$	−5.07960	−	5.07960i	−0.226488	−	0.226488i	−0.811224	+	0.584736i	$0.801198\pi$
$504$		0			0
$505$	−5.30002	+	5.30002i	−0.235848	+	0.235848i
$506$		0			0
$507$	−2.06777	+	0.856498i	−0.0918329	+	0.0380384i
$508$		0			0
$509$	−13.5628	+	32.7435i	−0.601161	+	1.45133i	0.271227	+	0.962515i	$0.412571\pi$
$509$	−13.5628	+	32.7435i	−0.601161	+	1.45133i	−0.872388	+	0.488815i	$0.837429\pi$
$510$		0			0
$511$	−12.9060			−0.570926
$512$		0			0
$513$	5.19173			0.229221
$514$		0			0
$515$	−0.186681	+	0.450688i	−0.00822614	+	0.0198597i
$516$		0			0
$517$	−26.5807	+	11.0101i	−1.16902	+	0.484223i
$518$		0			0
$519$	−1.09130	+	1.09130i	−0.0479028	+	0.0479028i
$520$		0			0
$521$	−17.4496	−	17.4496i	−0.764479	−	0.764479i	0.212650	−	0.977129i	$-0.431791\pi$
$521$	−17.4496	−	17.4496i	−0.764479	−	0.764479i	−0.977129	+	0.212650i	$0.931791\pi$
$522$		0			0
$523$	−16.6581	−	40.2163i	−0.728410	−	1.75854i	−0.647825	−	0.761789i	$-0.724321\pi$
$523$	−16.6581	−	40.2163i	−0.728410	−	1.75854i	−0.0805847	−	0.996748i	$-0.525679\pi$
$524$		0			0
$525$	−2.72040	−	1.12682i	−0.118728	−	0.0491787i
$526$		0			0
$527$			20.8486i			0.908179i
$528$		0			0
$529$		−	22.8528i		−	0.993598i
$530$		0			0
$531$	29.9237	+	12.3948i	1.29858	+	0.537889i
$532$		0			0
$533$	4.07107	+	9.82843i	0.176338	+	0.425716i
$534$		0			0
$535$	−9.65087	−	9.65087i	−0.417244	−	0.417244i
$536$		0			0
$537$	−0.285094	+	0.285094i	−0.0123027	+	0.0123027i
$538$		0			0
$539$	11.9645	−	4.95587i	0.515349	−	0.213464i
$540$		0			0
$541$	15.9692	−	38.5531i	0.686571	−	1.65753i	−0.0650071	−	0.997885i	$-0.520707\pi$
$541$	15.9692	−	38.5531i	0.686571	−	1.65753i	0.751578	−	0.659644i	$-0.229293\pi$
$542$		0			0
$543$	−3.32180			−0.142552
$544$		0			0
$545$	−5.97018			−0.255734
$546$		0			0
$547$	−0.383100	+	0.924886i	−0.0163802	+	0.0395453i	−0.931858	−	0.362823i	$-0.881813\pi$
$547$	−0.383100	+	0.924886i	−0.0163802	+	0.0395453i	0.915478	+	0.402368i	$0.131813\pi$
$548$		0			0
$549$	9.69932	−	4.01759i	0.413957	−	0.171467i
$550$		0			0
$551$	7.22658	−	7.22658i	0.307863	−	0.307863i
$552$		0			0
$553$	−22.1454	−	22.1454i	−0.941717	−	0.941717i
$554$		0			0
$555$	0.239213	+	0.577512i	0.0101540	+	0.0245140i
$556$		0			0
$557$	8.29127	+	3.43436i	0.351312	+	0.145518i	0.551359	−	0.834268i	$-0.314109\pi$
$557$	8.29127	+	3.43436i	0.351312	+	0.145518i	−0.200047	+	0.979786i	$0.564109\pi$
$558$		0			0
$559$			9.54333i			0.403640i
$560$		0			0
$561$			2.47482i			0.104487i
$562$		0			0
$563$	22.7143	+	9.40857i	0.957293	+	0.396524i	0.805967	−	0.591960i	$-0.201646\pi$
$563$	22.7143	+	9.40857i	0.957293	+	0.396524i	0.151326	+	0.988484i	$0.451646\pi$
$564$		0			0
$565$	2.56792	+	6.19951i	0.108033	+	0.260816i
$566$		0			0
$567$	19.5646	+	19.5646i	0.821637	+	0.821637i
$568$		0			0
$569$	−16.6413	+	16.6413i	−0.697639	+	0.697639i	−0.963901	−	0.266262i	$-0.914211\pi$
$569$	−16.6413	+	16.6413i	−0.697639	+	0.697639i	0.266262	+	0.963901i	$0.414211\pi$
$570$		0			0
$571$	−9.37532	+	3.88338i	−0.392345	+	0.162515i	−0.570129	−	0.821555i	$-0.693107\pi$
$571$	−9.37532	+	3.88338i	−0.392345	+	0.162515i	0.177785	+	0.984069i	$0.443107\pi$
$572$		0			0
$573$	−0.492136	+	1.18812i	−0.0205593	+	0.0496345i
$574$		0			0
$575$	1.69382			0.0706371
$576$		0			0
$577$	−23.0348			−0.958951			−0.479476	−	0.877555i	$-0.659173\pi$
$577$	−23.0348			−0.958951			−0.479476	+	0.877555i	$0.659173\pi$
$578$		0			0
$579$	−1.15856	+	2.79700i	−0.0481480	+	0.116239i
$580$		0			0
$581$	29.0584	−	12.0364i	1.20555	−	0.499354i
$582$		0			0
$583$	−12.0920	+	12.0920i	−0.500798	+	0.500798i
$584$		0			0
$585$	−7.80316	−	7.80316i	−0.322621	−	0.322621i
$586$		0			0
$587$	−1.02732	−	2.48018i	−0.0424022	−	0.102368i	0.901260	−	0.433280i	$-0.142644\pi$
$587$	−1.02732	−	2.48018i	−0.0424022	−	0.102368i	−0.943662	+	0.330912i	$0.892644\pi$
$588$		0			0
$589$	26.4766	+	10.9670i	1.09095	+	0.451885i
$590$		0			0
$591$			4.15894i			0.171076i
$592$		0			0
$593$			13.9339i			0.572197i	0.958200	+	0.286098i	$0.0923584\pi$
$593$			13.9339i			0.572197i	−0.958200	+	0.286098i	$0.907642\pi$
$594$		0			0
$595$	−6.93484	−	2.87250i	−0.284301	−	0.117761i
$596$		0			0
$597$	1.39112	+	3.35846i	0.0569347	+	0.137452i
$598$		0			0
$599$	7.02222	+	7.02222i	0.286920	+	0.286920i	0.835861	−	0.548941i	$-0.184969\pi$
$599$	7.02222	+	7.02222i	0.286920	+	0.286920i	−0.548941	+	0.835861i	$0.684969\pi$
$600$		0			0
$601$	24.0970	−	24.0970i	0.982938	−	0.982938i	−0.0169188	−	0.999857i	$-0.505386\pi$
$601$	24.0970	−	24.0970i	0.982938	−	0.982938i	0.999857	+	0.0169188i	$0.00538568\pi$
$602$		0			0
$603$	14.2469	−	5.90125i	0.580177	−	0.240317i
$604$		0			0
$605$	−1.24036	+	2.99450i	−0.0504278	+	0.121744i
$606$		0			0
$607$	27.8275			1.12948			0.564742	−	0.825268i	$-0.308976\pi$
$607$	27.8275			1.12948			0.564742	+	0.825268i	$0.308976\pi$
$608$		0			0
$609$	−1.62437			−0.0658229
$610$		0			0
$611$	13.7548	−	33.2070i	0.556460	−	1.34341i
$612$		0			0
$613$	−9.98279	+	4.13501i	−0.403201	+	0.167011i	−0.575062	−	0.818110i	$-0.695022\pi$
$613$	−9.98279	+	4.13501i	−0.403201	+	0.167011i	0.171861	+	0.985121i	$0.445022\pi$
$614$		0			0
$615$	0.245193	−	0.245193i	0.00988714	−	0.00988714i
$616$		0			0
$617$	23.2080	+	23.2080i	0.934318	+	0.934318i	0.997972	−	0.0636543i	$-0.0202755\pi$
$617$	23.2080	+	23.2080i	0.934318	+	0.934318i	−0.0636543	+	0.997972i	$0.520275\pi$
$618$		0			0
$619$	11.5644	+	27.9189i	0.464811	+	1.12215i	0.966399	+	0.257047i	$0.0827494\pi$
$619$	11.5644	+	27.9189i	0.464811	+	1.12215i	−0.501588	+	0.865107i	$0.667251\pi$
$620$		0			0
$621$	0.438546	+	0.181652i	0.0175982	+	0.00728943i
$622$		0			0
$623$		−	34.4481i		−	1.38013i
$624$		0			0
$625$		−	16.5563i		−	0.662254i
$626$		0			0
$627$	3.14288	+	1.30182i	0.125515	+	0.0519899i
$628$		0			0
$629$	−4.59519	−	11.0938i	−0.183222	−	0.442338i
$630$		0			0
$631$	1.34980	+	1.34980i	0.0537346	+	0.0537346i	0.733463	−	0.679729i	$-0.237903\pi$
$631$	1.34980	+	1.34980i	0.0537346	+	0.0537346i	−0.679729	+	0.733463i	$0.737903\pi$
$632$		0			0
$633$	0.564006	−	0.564006i	0.0224172	−	0.0224172i
$634$		0			0
$635$	8.10641	−	3.35778i	0.321693	−	0.133250i
$636$		0			0
$637$	−6.19133	+	14.9472i	−0.245309	+	0.592229i
$638$		0			0
$639$	−27.0588			−1.07043
$640$		0			0
$641$	41.5334			1.64047			0.820235	−	0.572027i	$-0.193843\pi$
$641$	41.5334			1.64047			0.820235	+	0.572027i	$0.193843\pi$
$642$		0			0
$643$	1.57282	−	3.79713i	0.0620261	−	0.149744i	−0.889828	−	0.456297i	$-0.849176\pi$
$643$	1.57282	−	3.79713i	0.0620261	−	0.149744i	0.951854	+	0.306553i	$0.0991755\pi$
$644$		0			0
$645$	0.287389	−	0.119040i	0.0113159	−	0.00468721i
$646$		0			0
$647$	5.84193	−	5.84193i	0.229670	−	0.229670i	−0.582885	−	0.812555i	$-0.698076\pi$
$647$	5.84193	−	5.84193i	0.229670	−	0.229670i	0.812555	+	0.582885i	$0.198076\pi$
$648$		0			0
$649$	30.2323	+	30.2323i	1.18672	+	1.18672i
$650$		0			0
$651$	−1.74311	−	4.20823i	−0.0683177	−	0.164934i
$652$		0			0
$653$	−26.0231	−	10.7791i	−1.01836	−	0.421820i	−0.189864	−	0.981810i	$-0.560805\pi$
$653$	−26.0231	−	10.7791i	−1.01836	−	0.421820i	−0.828499	+	0.559991i	$0.810805\pi$
$654$		0			0
$655$			8.64422i			0.337758i
$656$		0			0
$657$		−	11.8803i		−	0.463495i
$658$		0			0
$659$	−37.6498	−	15.5951i	−1.46663	−	0.607497i	−0.500541	−	0.865713i	$-0.666866\pi$
$659$	−37.6498	−	15.5951i	−1.46663	−	0.607497i	−0.966087	+	0.258215i	$0.916866\pi$
$660$		0			0
$661$	3.14241	+	7.58644i	0.122226	+	0.295078i	0.973136	−	0.230233i	$-0.0739488\pi$
$661$	3.14241	+	7.58644i	0.122226	+	0.295078i	−0.850910	+	0.525311i	$0.823949\pi$
$662$		0			0
$663$	−2.18621	−	2.18621i	−0.0849054	−	0.0849054i
$664$		0			0
$665$	−7.29585	+	7.29585i	−0.282921	+	0.282921i
$666$		0			0
$667$	0.863279	−	0.357582i	0.0334263	−	0.0138456i
$668$		0			0
$669$	2.18982	−	5.28670i	0.0846634	−	0.204395i
$670$		0			0
$671$	13.8584			0.534997
$672$		0			0
$673$	−5.24262			−0.202088			−0.101044	−	0.994882i	$-0.532218\pi$
$673$	−5.24262			−0.202088			−0.101044	+	0.994882i	$0.532218\pi$
$674$		0			0
$675$	2.08968	−	5.04493i	0.0804318	−	0.194179i
$676$		0			0
$677$	14.5716	−	6.03574i	0.560031	−	0.231972i	−0.0846677	−	0.996409i	$-0.526983\pi$
$677$	14.5716	−	6.03574i	0.560031	−	0.231972i	0.644699	+	0.764437i	$0.276983\pi$
$678$		0			0
$679$	8.43625	−	8.43625i	0.323754	−	0.323754i
$680$		0			0
$681$	2.31265	+	2.31265i	0.0886210	+	0.0886210i
$682$		0			0
$683$	14.9028	+	35.9785i	0.570240	+	1.37668i	0.901351	+	0.433089i	$0.142576\pi$
$683$	14.9028	+	35.9785i	0.570240	+	1.37668i	−0.331112	+	0.943592i	$0.607424\pi$
$684$		0			0
$685$	−3.42429	−	1.41839i	−0.130835	−	0.0541938i
$686$		0			0
$687$			4.10842i			0.156746i
$688$		0			0
$689$		−	21.3637i		−	0.813892i
$690$		0			0
$691$	−14.6714	−	6.07710i	−0.558127	−	0.231184i	0.0857448	−	0.996317i	$-0.472673\pi$
$691$	−14.6714	−	6.07710i	−0.558127	−	0.231184i	−0.643872	+	0.765133i	$0.722673\pi$
$692$		0			0
$693$	14.1869	+	34.2502i	0.538915	+	1.30106i
$694$		0			0
$695$	10.4050	+	10.4050i	0.394685	+	0.394685i
$696$		0			0
$697$	−4.71006	+	4.71006i	−0.178406	+	0.178406i
$698$		0			0
$699$	1.82046	−	0.754059i	0.0688561	−	0.0285211i
$700$		0			0
$701$	9.58351	−	23.1366i	0.361964	−	0.873859i	−0.633049	−	0.774112i	$-0.718197\pi$
$701$	9.58351	−	23.1366i	0.361964	−	0.873859i	0.995013	−	0.0997466i	$-0.0318032\pi$
$702$		0			0
$703$	−16.5057			−0.622524
$704$		0			0
$705$	−1.17157			−0.0441240
$706$		0			0
$707$	−12.0381	+	29.0625i	−0.452739	+	1.09301i
$708$		0			0
$709$	27.4256	−	11.3601i	1.02999	−	0.426636i	0.197282	−	0.980347i	$-0.436789\pi$
$709$	27.4256	−	11.3601i	1.02999	−	0.426636i	0.832709	+	0.553711i	$0.186789\pi$
$710$		0			0
$711$	20.3855	−	20.3855i	0.764515	−	0.764515i
$712$		0			0
$713$	1.85276	+	1.85276i	0.0693864	+	0.0693864i
$714$		0			0
$715$	−5.57457	−	13.4582i	−0.208477	−	0.503309i
$716$		0			0
$717$	−5.02663	−	2.08210i	−0.187723	−	0.0777573i
$718$		0			0
$719$			38.9976i			1.45436i	0.686445	+	0.727182i	$0.259170\pi$
$719$			38.9976i			1.45436i	−0.686445	+	0.727182i	$0.740830\pi$
$720$		0			0
$721$			2.04732i			0.0762462i
$722$		0			0
$723$	2.62337	+	1.08664i	0.0975643	+	0.0404124i
$724$		0			0
$725$	−4.11354	−	9.93095i	−0.152773	−	0.368826i
$726$		0			0
$727$	−34.9474	−	34.9474i	−1.29613	−	1.29613i	−0.930930	−	0.365198i	$-0.881001\pi$
$727$	−34.9474	−	34.9474i	−1.29613	−	1.29613i	−0.365198	−	0.930930i	$-0.618999\pi$
$728$		0			0
$729$	−17.4649	+	17.4649i	−0.646846	+	0.646846i
$730$		0			0
$731$	−5.52062	+	2.28672i	−0.204188	+	0.0845773i
$732$		0			0
$733$	−13.8093	+	33.3387i	−0.510060	+	1.23139i	0.433789	+	0.901015i	$0.357176\pi$
$733$	−13.8093	+	33.3387i	−0.510060	+	1.23139i	−0.943849	+	0.330378i	$0.892824\pi$
$734$		0			0
$735$	0.527350			0.0194516
$736$		0			0
$737$	20.3559			0.749819
$738$		0			0
$739$	−6.75096	+	16.2983i	−0.248338	+	0.599542i	−0.998063	−	0.0622080i	$-0.980186\pi$
$739$	−6.75096	+	16.2983i	−0.248338	+	0.599542i	0.749725	+	0.661750i	$0.230186\pi$
$740$		0			0
$741$	−3.92638	+	1.62636i	−0.144239	+	0.0597458i
$742$		0			0
$743$	20.6145	−	20.6145i	0.756272	−	0.756272i	−0.219370	−	0.975642i	$-0.570400\pi$
$743$	20.6145	−	20.6145i	0.756272	−	0.756272i	0.975642	+	0.219370i	$0.0704002\pi$
$744$		0			0
$745$	−1.31788	−	1.31788i	−0.0482835	−	0.0482835i
$746$		0			0
$747$	11.0799	+	26.7491i	0.405391	+	0.978700i
$748$		0			0
$749$	−52.9203	−	21.9203i	−1.93367	−	0.800951i
$750$		0			0
$751$		−	27.0344i		−	0.986499i	−0.869888	−	0.493249i	$-0.835809\pi$
$751$		−	27.0344i		−	0.986499i	0.869888	−	0.493249i	$-0.164191\pi$
$752$		0			0
$753$			2.96827i			0.108170i
$754$		0			0
$755$	4.21395	+	1.74548i	0.153361	+	0.0635244i
$756$		0			0
$757$	−19.5424	−	47.1795i	−0.710280	−	1.71477i	−0.699300	−	0.714828i	$-0.746505\pi$
$757$	−19.5424	−	47.1795i	−0.710280	−	1.71477i	−0.0109802	−	0.999940i	$-0.503495\pi$
$758$		0			0
$759$	0.219931	+	0.219931i	0.00798297	+	0.00798297i
$760$		0			0
$761$	−2.53714	+	2.53714i	−0.0919713	+	0.0919713i	−0.751596	−	0.659624i	$-0.770715\pi$
$761$	−2.53714	+	2.53714i	−0.0919713	+	0.0919713i	0.659624	+	0.751596i	$0.270715\pi$
$762$		0			0
$763$	−23.1488	+	9.58854i	−0.838042	+	0.347129i
$764$		0			0
$765$	2.64422	−	6.38372i	0.0956021	−	0.230804i
$766$		0			0
$767$	−53.4134			−1.92865
$768$		0			0
$769$	−24.0627			−0.867725			−0.433862	−	0.900979i	$-0.642850\pi$
$769$	−24.0627			−0.867725			−0.433862	+	0.900979i	$0.642850\pi$
$770$		0			0
$771$	1.59463	−	3.84977i	0.0574291	−	0.138646i
$772$		0			0
$773$	−43.4146	+	17.9829i	−1.56152	+	0.646801i	−0.985352	−	0.170534i	$-0.945451\pi$
$773$	−43.4146	+	17.9829i	−1.56152	+	0.646801i	−0.576163	+	0.817335i	$0.695451\pi$
$774$		0			0
$775$	21.3137	−	21.3137i	0.765611	−	0.765611i
$776$		0			0
$777$	1.85505	+	1.85505i	0.0665497	+	0.0665497i
$778$		0			0
$779$	3.50389	+	8.45914i	0.125540	+	0.303080i
$780$		0			0
$781$	−32.9997	−	13.6689i	−1.18082	−	0.489113i
$782$		0			0
$783$		−	3.01237i		−	0.107653i
$784$		0			0
$785$		−	11.6880i		−	0.417163i
$786$		0			0
$787$	4.62213	+	1.91455i	0.164761	+	0.0682463i	0.463540	−	0.886076i	$-0.346579\pi$
$787$	4.62213	+	1.91455i	0.164761	+	0.0682463i	−0.298778	+	0.954323i	$0.596579\pi$
$788$		0			0
$789$	−0.533819	−	1.28875i	−0.0190045	−	0.0458808i
$790$		0			0
$791$	19.9137	+	19.9137i	0.708051	+	0.708051i
$792$		0			0
$793$	−12.2423	+	12.2423i	−0.434735	+	0.434735i
$794$		0			0
$795$	−0.643348	+	0.266484i	−0.0228172	+	0.00945120i
$796$		0			0
$797$	−7.78397	+	18.7922i	−0.275722	+	0.665653i	−0.999708	−	0.0241622i	$-0.992308\pi$
$797$	−7.78397	+	18.7922i	−0.275722	+	0.665653i	0.723986	+	0.689815i	$0.242308\pi$
$798$		0			0
$799$	22.5054			0.796185
$800$		0			0
$801$	31.7104			1.12043
$802$		0			0
$803$	6.00142	−	14.4887i	0.211785	−	0.511295i
$804$		0			0
$805$	−0.871553	+	0.361009i	−0.0307182	+	0.0127239i
$806$		0			0
$807$	3.55740	−	3.55740i	0.125227	−	0.125227i
$808$		0			0
$809$	−5.79631	−	5.79631i	−0.203787	−	0.203787i	0.597833	−	0.801621i	$-0.296029\pi$
$809$	−5.79631	−	5.79631i	−0.203787	−	0.203787i	−0.801621	+	0.597833i	$0.796029\pi$
$810$		0			0
$811$	2.59457	+	6.26386i	0.0911078	+	0.219954i	0.962864	−	0.269986i	$-0.0870189\pi$
$811$	2.59457	+	6.26386i	0.0911078	+	0.219954i	−0.871757	+	0.489939i	$0.837019\pi$
$812$		0			0
$813$	−0.132987	−	0.0550849i	−0.00466405	−	0.00193191i
$814$		0			0
$815$		−	5.44739i		−	0.190814i
$816$		0			0
$817$			8.21377i			0.287363i
$818$		0			0
$819$	−42.7885	−	17.7236i	−1.49515	−	0.619311i
$820$		0			0
$821$	14.5014	+	35.0095i	0.506103	+	1.22184i	0.946110	+	0.323847i	$0.104976\pi$
$821$	14.5014	+	35.0095i	0.506103	+	1.22184i	−0.440006	+	0.897995i	$0.645024\pi$
$822$		0			0
$823$	6.84972	+	6.84972i	0.238766	+	0.238766i	0.816339	−	0.577573i	$-0.196000\pi$
$823$	6.84972	+	6.84972i	0.238766	+	0.238766i	−0.577573	+	0.816339i	$0.696000\pi$
$824$		0			0
$825$	2.53003	−	2.53003i	0.0880843	−	0.0880843i
$826$		0			0
$827$	−27.6932	+	11.4709i	−0.962987	+	0.398882i	−0.808097	−	0.589049i	$-0.799502\pi$
$827$	−27.6932	+	11.4709i	−0.962987	+	0.398882i	−0.154890	+	0.987932i	$0.549502\pi$
$828$		0			0
$829$	1.60232	−	3.86834i	0.0556509	−	0.134353i	−0.893609	−	0.448847i	$-0.851835\pi$
$829$	1.60232	−	3.86834i	0.0556509	−	0.134353i	0.949259	+	0.314494i	$0.101835\pi$
$830$		0			0
$831$	−6.07228			−0.210645
$832$		0			0
$833$	−10.1302			−0.350990
$834$		0			0
$835$	−1.35181	+	3.26355i	−0.0467811	+	0.112940i
$836$		0			0
$837$	7.80409	−	3.23256i	0.269749	−	0.111734i
$838$		0			0
$839$	−11.4718	+	11.4718i	−0.396050	+	0.396050i	−0.876837	−	0.480787i	$-0.840351\pi$
$839$	−11.4718	+	11.4718i	−0.396050	+	0.396050i	0.480787	+	0.876837i	$0.340351\pi$
$840$		0			0
$841$	16.3131	+	16.3131i	0.562519	+	0.562519i
$842$		0			0
$843$	−0.784427	−	1.89377i	−0.0270171	−	0.0652250i
$844$		0			0
$845$	7.62086	+	3.15666i	0.262165	+	0.108592i
$846$		0			0
$847$			13.6030i			0.467404i
$848$		0			0
$849$		−	3.28352i		−	0.112690i
$850$		0			0
$851$	−1.39424	−	0.577512i	−0.0477939	−	0.0197969i
$852$		0			0
$853$	−4.85275	−	11.7156i	−0.166155	−	0.401133i	0.818769	−	0.574124i	$-0.194657\pi$
$853$	−4.85275	−	11.7156i	−0.166155	−	0.401133i	−0.984924	+	0.172990i	$0.944657\pi$
$854$		0			0
$855$	−6.71604	−	6.71604i	−0.229684	−	0.229684i
$856$		0			0
$857$	−13.5307	+	13.5307i	−0.462200	+	0.462200i	−0.899376	−	0.437176i	$-0.855979\pi$
$857$	−13.5307	+	13.5307i	−0.462200	+	0.462200i	0.437176	+	0.899376i	$0.355979\pi$
$858$		0			0
$859$	50.3433	−	20.8529i	1.71769	−	0.711491i	0.717808	−	0.696241i	$-0.245145\pi$
$859$	50.3433	−	20.8529i	1.71769	−	0.711491i	0.999884	−	0.0152507i	$-0.00485464\pi$
$860$		0			0
$861$	0.556914	−	1.34451i	0.0189796	−	0.0458208i
$862$		0			0
$863$	9.50637			0.323601			0.161800	−	0.986824i	$-0.448270\pi$
$863$	9.50637			0.323601			0.161800	+	0.986824i	$0.448270\pi$
$864$		0			0
$865$	5.68802			0.193399
$866$		0			0
$867$	−0.610172	+	1.47309i	−0.0207225	+	0.0500286i
$868$		0			0
$869$	35.1591	−	14.5634i	1.19269	−	0.494028i
$870$		0			0
$871$	−17.9821	+	17.9821i	−0.609299	+	0.609299i
$872$		0			0
$873$	7.76582	+	7.76582i	0.262833	+	0.262833i
$874$		0			0
$875$	8.85704	+	21.3828i	0.299423	+	0.722870i
$876$		0			0
$877$	16.7883	+	6.95392i	0.566899	+	0.234817i	0.647677	−	0.761915i	$-0.275741\pi$
$877$	16.7883	+	6.95392i	0.566899	+	0.234817i	−0.0807782	+	0.996732i	$0.525741\pi$
$878$		0			0
$879$		−	2.21534i		−	0.0747216i
$880$		0			0
$881$		−	46.9687i		−	1.58242i	−0.611547	−	0.791208i	$-0.709453\pi$
$881$		−	46.9687i		−	1.58242i	0.611547	−	0.791208i	$-0.290547\pi$
$882$		0			0
$883$	−11.0237	−	4.56617i	−0.370978	−	0.153664i	0.189403	−	0.981900i	$-0.439345\pi$
$883$	−11.0237	−	4.56617i	−0.370978	−	0.153664i	−0.560380	+	0.828236i	$0.689345\pi$
$884$		0			0
$885$	0.666261	+	1.60850i	0.0223961	+	0.0540690i
$886$		0			0
$887$	−31.9419	−	31.9419i	−1.07250	−	1.07250i	−0.997157	−	0.0753464i	$-0.975994\pi$
$887$	−31.9419	−	31.9419i	−1.07250	−	1.07250i	−0.0753464	−	0.997157i	$-0.524006\pi$
$888$		0			0
$889$	26.0390	−	26.0390i	0.873319	−	0.873319i
$890$		0			0
$891$	−31.0617	+	12.8662i	−1.04061	+	0.431034i
$892$		0			0
$893$	11.8385	−	28.5807i	0.396160	−	0.956416i
$894$		0			0
$895$	1.48595			0.0496699
$896$		0			0
$897$	−0.388566			−0.0129738
$898$		0			0
$899$	6.36330	−	15.3624i	0.212228	−	0.512364i
$900$		0			0
$901$	12.3585	−	5.11904i	0.411720	−	0.170540i
$902$		0			0
$903$	0.923135	−	0.923135i	0.0307200	−	0.0307200i
$904$		0			0
$905$	8.65685	+	8.65685i	0.287764	+	0.287764i
$906$		0			0
$907$	−4.99616	−	12.0618i	−0.165895	−	0.400505i	0.818969	−	0.573838i	$-0.194546\pi$
$907$	−4.99616	−	12.0618i	−0.165895	−	0.400505i	−0.984863	+	0.173333i	$0.944546\pi$
$908$		0			0
$909$	−26.7529	−	11.0814i	−0.887338	−	0.367547i
$910$		0			0
$911$			13.1188i			0.434645i	0.976100	+	0.217322i	$0.0697323\pi$
$911$			13.1188i			0.434645i	−0.976100	+	0.217322i	$0.930268\pi$
$912$		0			0
$913$			38.2191i			1.26487i
$914$		0			0
$915$	0.521370	+	0.215959i	0.0172360	+	0.00713937i
$916$		0			0
$917$	13.8833	+	33.5171i	0.458465	+	1.10683i
$918$		0			0
$919$	17.2415	+	17.2415i	0.568746	+	0.568746i	0.931777	−	0.363031i	$-0.118258\pi$
$919$	17.2415	+	17.2415i	0.568746	+	0.568746i	−0.363031	+	0.931777i	$0.618258\pi$
$920$		0			0
$921$	1.10667	−	1.10667i	0.0364659	−	0.0364659i
$922$		0			0
$923$	41.2263	−	17.0765i	1.35698	−	0.562080i
$924$		0			0
$925$	−6.64357	+	16.0390i	−0.218439	+	0.527359i
$926$		0			0
$927$	−1.88462			−0.0618990
$928$		0			0
$929$	−45.9966			−1.50910			−0.754550	−	0.656242i	$-0.772145\pi$
$929$	−45.9966			−1.50910			−0.754550	+	0.656242i	$0.772145\pi$
$930$		0			0
$931$	−5.32876	+	12.8648i	−0.174643	+	0.421626i
$932$		0			0
$933$	1.26174	−	0.522630i	0.0413076	−	0.0171101i
$934$		0			0
$935$	6.44955	−	6.44955i	0.210923	−	0.210923i
$936$		0			0
$937$	−3.67273	−	3.67273i	−0.119983	−	0.119983i	0.644566	−	0.764549i	$-0.277038\pi$
$937$	−3.67273	−	3.67273i	−0.119983	−	0.119983i	−0.764549	+	0.644566i	$0.777038\pi$
$938$		0			0
$939$	−0.0366014	−	0.0883635i	−0.00119444	−	0.00288363i
$940$		0			0
$941$	41.7873	+	17.3089i	1.36223	+	0.564253i	0.939670	−	0.342083i	$-0.111132\pi$
$941$	41.7873	+	17.3089i	1.36223	+	0.564253i	0.422558	+	0.906336i	$0.361132\pi$
$942$		0			0
$943$			0.837141i			0.0272611i
$944$		0			0
$945$			3.04125i			0.0989317i
$946$		0			0
$947$	43.6427	+	18.0774i	1.41820	+	0.587436i	0.954407	−	0.298509i	$-0.0964894\pi$
$947$	43.6427	+	18.0774i	1.41820	+	0.587436i	0.463790	+	0.885945i	$0.346489\pi$
$948$		0			0
$949$	7.49753	+	18.1006i	0.243380	+	0.587571i
$950$		0			0
$951$	3.04238	+	3.04238i	0.0986559	+	0.0986559i
$952$		0			0
$953$	6.12750	−	6.12750i	0.198489	−	0.198489i	−0.600863	−	0.799352i	$-0.705176\pi$
$953$	6.12750	−	6.12750i	0.198489	−	0.198489i	0.799352	+	0.600863i	$0.205176\pi$
$954$		0			0
$955$	4.37887	−	1.81379i	0.141697	−	0.0586928i
$956$		0			0
$957$	0.755352	−	1.82358i	0.0244171	−	0.0589480i
$958$		0			0
$959$	−15.5554			−0.502310
$960$		0			0
$961$	15.6274			0.504110
$962$		0			0
$963$	20.1783	−	48.7147i	0.650237	−	1.56981i
$964$		0			0
$965$	10.3085	−	4.26991i	0.331842	−	0.137453i
$966$		0			0
$967$	−1.03516	+	1.03516i	−0.0332885	+	0.0332885i	−0.723555	−	0.690267i	$-0.757493\pi$
$967$	−1.03516	+	1.03516i	−0.0332885	+	0.0332885i	0.690267	+	0.723555i	$0.257493\pi$
$968$		0			0
$969$	−1.88163	−	1.88163i	−0.0604467	−	0.0604467i
$970$		0			0
$971$	−15.4218	−	37.2315i	−0.494909	−	1.19482i	−0.952194	−	0.305495i	$-0.901178\pi$
$971$	−15.4218	−	37.2315i	−0.494909	−	1.19482i	0.457285	−	0.889320i	$-0.348822\pi$
$972$		0			0
$973$	57.0556	+	23.6332i	1.82912	+	0.757646i
$974$		0			0
$975$			4.46997i			0.143154i
$976$		0			0
$977$		−	28.8457i		−	0.922857i	−0.887177	−	0.461429i	$-0.847337\pi$
$977$		−	28.8457i		−	0.922857i	0.887177	−	0.461429i	$-0.152663\pi$
$978$		0			0
$979$	38.6727	+	16.0187i	1.23598	+	0.511961i
$980$		0			0
$981$	−8.82653	−	21.3091i	−0.281809	−	0.680348i
$982$		0			0
$983$	40.9561	+	40.9561i	1.30630	+	1.30630i	0.924067	+	0.382231i	$0.124844\pi$
$983$	40.9561	+	40.9561i	1.30630	+	1.30630i	0.382231	+	0.924067i	$0.375156\pi$
$984$		0			0
$985$	10.8385	−	10.8385i	0.345344	−	0.345344i
$986$		0			0
$987$	−4.54266	+	1.88163i	−0.144594	+	0.0598930i
$988$		0			0
$989$	−0.287389	+	0.693818i	−0.00913843	+	0.0220621i
$990$		0			0
$991$	41.9605			1.33292			0.666460	−	0.745541i	$-0.267809\pi$
$991$	41.9605			1.33292			0.666460	+	0.745541i	$0.267809\pi$
$992$		0			0
$993$	−3.21145			−0.101912
$994$		0			0
$995$	5.12703	−	12.3777i	0.162538	−	0.392401i
$996$		0			0
$997$	−31.4380	+	13.0221i	−0.995652	+	0.412413i	−0.820201	−	0.572076i	$-0.806138\pi$
$997$	−31.4380	+	13.0221i	−0.995652	+	0.412413i	−0.175451	+	0.984488i	$0.556138\pi$
$998$		0			0
$999$	−3.44017	+	3.44017i	−0.108842	+	0.108842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.g.b.17.1		8
3.2	odd	2		1152.2.v.b.145.2		8
4.3	odd	2		32.2.g.b.13.2	yes	8
8.3	odd	2		256.2.g.d.33.1		8
8.5	even	2		256.2.g.c.33.2		8
12.11	even	2		288.2.v.b.109.1		8
16.3	odd	4		512.2.g.e.321.2		8
16.5	even	4		512.2.g.f.321.2		8
16.11	odd	4		512.2.g.h.321.1		8
16.13	even	4		512.2.g.g.321.1		8
20.3	even	4		800.2.ba.c.749.1		8
20.7	even	4		800.2.ba.d.749.2		8
20.19	odd	2		800.2.y.b.301.1		8
32.3	odd	8		512.2.g.e.193.2		8
32.5	even	8	inner	128.2.g.b.113.1		8
32.11	odd	8		256.2.g.d.225.1		8
32.13	even	8		512.2.g.f.193.2		8
32.19	odd	8		512.2.g.h.193.1		8
32.21	even	8		256.2.g.c.225.2		8
32.27	odd	8		32.2.g.b.5.2	✓	8
32.29	even	8		512.2.g.g.193.1		8
64.5	even	16		4096.2.a.q.1.4		8
64.27	odd	16		4096.2.a.k.1.4		8
64.37	even	16		4096.2.a.q.1.5		8
64.59	odd	16		4096.2.a.k.1.5		8
96.5	odd	8		1152.2.v.b.1009.2		8
96.59	even	8		288.2.v.b.37.1		8
160.27	even	8		800.2.ba.c.549.1		8
160.59	odd	8		800.2.y.b.101.1		8
160.123	even	8		800.2.ba.d.549.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.5.2	✓	8	32.27	odd	8
32.2.g.b.13.2	yes	8	4.3	odd	2
128.2.g.b.17.1		8	1.1	even	1	trivial
128.2.g.b.113.1		8	32.5	even	8	inner
256.2.g.c.33.2		8	8.5	even	2
256.2.g.c.225.2		8	32.21	even	8
256.2.g.d.33.1		8	8.3	odd	2
256.2.g.d.225.1		8	32.11	odd	8
288.2.v.b.37.1		8	96.59	even	8
288.2.v.b.109.1		8	12.11	even	2
512.2.g.e.193.2		8	32.3	odd	8
512.2.g.e.321.2		8	16.3	odd	4
512.2.g.f.193.2		8	32.13	even	8
512.2.g.f.321.2		8	16.5	even	4
512.2.g.g.193.1		8	32.29	even	8
512.2.g.g.321.1		8	16.13	even	4
512.2.g.h.193.1		8	32.19	odd	8
512.2.g.h.321.1		8	16.11	odd	4
800.2.y.b.101.1		8	160.59	odd	8
800.2.y.b.301.1		8	20.19	odd	2
800.2.ba.c.549.1		8	160.27	even	8
800.2.ba.c.749.1		8	20.3	even	4
800.2.ba.d.549.2		8	160.123	even	8
800.2.ba.d.749.2		8	20.7	even	4
1152.2.v.b.145.2		8	3.2	odd	2
1152.2.v.b.1009.2		8	96.5	odd	8
4096.2.a.k.1.4		8	64.27	odd	16
4096.2.a.k.1.5		8	64.59	odd	16
4096.2.a.q.1.4		8	64.5	even	16
4096.2.a.q.1.5		8	64.37	even	16

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0794708 + 0.191860i) q^{3} +(0.707107 - 0.292893i) q^{5} +(2.27133 - 2.27133i) q^{7} +(2.09083 + 2.09083i) q^{9} +(1.49368 + 3.60607i) q^{11} +(-4.50504 - 1.86605i) q^{13} +0.158942i q^{15} -3.05320i q^{17} +(-3.87740 - 1.60607i) q^{19} +(0.255272 + 0.616281i) q^{21} +(-0.271330 - 0.271330i) q^{23} +(-3.12132 + 3.12132i) q^{25} +(-1.14288 + 0.473398i) q^{27} +(-0.931884 + 2.24977i) q^{29} -6.82843 q^{31} -0.810564 q^{33} +(0.940816 - 2.27133i) q^{35} +(3.63349 - 1.50504i) q^{37} +(0.716038 - 0.716038i) q^{39} +(-1.54266 - 1.54266i) q^{41} +(-0.748956 - 1.80814i) q^{43} +(2.09083 + 0.866048i) q^{45} +7.37109i q^{47} -3.31788i q^{49} +(0.585786 + 0.242641i) q^{51} +(1.67661 + 4.04770i) q^{53} +(2.11239 + 2.11239i) q^{55} +(0.616281 - 0.616281i) q^{57} +(10.1200 - 4.19186i) q^{59} +(1.35873 - 3.28026i) q^{61} +9.49791 q^{63} -3.73210 q^{65} +(1.99577 - 4.81822i) q^{67} +(0.0736202 - 0.0304945i) q^{69} +(-6.47085 + 6.47085i) q^{71} +(-2.84106 - 2.84106i) q^{73} +(-0.350801 - 0.846909i) q^{75} +(11.5832 + 4.79793i) q^{77} -9.74996i q^{79} +8.61373i q^{81} +(9.04642 + 3.74715i) q^{83} +(-0.894263 - 2.15894i) q^{85} +(-0.357582 - 0.357582i) q^{87} +(7.58323 - 7.58323i) q^{89} +(-14.4708 + 5.99402i) q^{91} +(0.542661 - 1.31010i) q^{93} -3.21215 q^{95} +3.71423 q^{97} +(-4.41664 + 10.6627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 8 q^{7} - 4 q^{11} - 8 q^{13} - 4 q^{19} + 8 q^{23} - 8 q^{25} - 8 q^{27} - 32 q^{31} - 16 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} + 8 q^{53} + 16 q^{55}+ \cdots - 28 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 8 * q^7 - 4 * q^11 - 8 * q^13 - 4 * q^19 + 8 * q^23 - 8 * q^25 - 8 * q^27 - 32 * q^31 - 16 * q^33 - 16 * q^35 - 8 * q^37 - 16 * q^39 + 8 * q^41 + 12 * q^43 + 16 * q^51 + 8 * q^53 + 16 * q^55 + 16 * q^57 + 20 * q^59 + 24 * q^61 + 40 * q^63 + 36 * q^67 + 32 * q^69 + 24 * q^71 - 32 * q^73 + 12 * q^75 + 16 * q^77 - 20 * q^83 + 8 * q^85 - 56 * q^87 - 16 * q^89 - 40 * q^91 - 16 * q^93 + 8 * q^95 + 32 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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