LMFDB - Embedded newform 960.2.bc.e.463.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(367,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("960.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bc (of order $4$, degree $2$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.3
Root			$-1.40988 - 0.110627i$ of defining polynomial
Character	$\chi$	$=$	960.463
Dual form			960.2.bc.e.367.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{3} +(-0.849960 + 2.06823i) q^{5} +(2.08016 - 2.08016i) q^{7} -1.00000 q^{9} +(-3.33354 + 3.33354i) q^{11} -6.13735 q^{13} +(2.06823 + 0.849960i) q^{15} +(-2.33136 + 2.33136i) q^{17} +(0.834324 - 0.834324i) q^{19} +(-2.08016 - 2.08016i) q^{21} +(-2.95105 - 2.95105i) q^{23} +(-3.55514 - 3.51582i) q^{25} +1.00000i q^{27} +(0.576185 + 0.576185i) q^{29} -2.62300i q^{31} +(3.33354 + 3.33354i) q^{33} +(2.53419 + 6.07029i) q^{35} +2.07309 q^{37} +6.13735i q^{39} +10.8873i q^{41} -5.16088 q^{43} +(0.849960 - 2.06823i) q^{45} +(-8.65772 - 8.65772i) q^{47} -1.65411i q^{49} +(2.33136 + 2.33136i) q^{51} -1.58490i q^{53} +(-4.06115 - 9.72791i) q^{55} +(-0.834324 - 0.834324i) q^{57} +(2.32603 + 2.32603i) q^{59} +(-7.22499 + 7.22499i) q^{61} +(-2.08016 + 2.08016i) q^{63} +(5.21651 - 12.6934i) q^{65} +0.885549 q^{67} +(-2.95105 + 2.95105i) q^{69} -2.56877 q^{71} +(-7.35033 + 7.35033i) q^{73} +(-3.51582 + 3.55514i) q^{75} +13.8686i q^{77} -7.72612 q^{79} +1.00000 q^{81} +8.67714i q^{83} +(-2.84022 - 6.80334i) q^{85} +(0.576185 - 0.576185i) q^{87} +8.70590 q^{89} +(-12.7667 + 12.7667i) q^{91} -2.62300 q^{93} +(1.01643 + 2.43472i) q^{95} +(11.9985 - 11.9985i) q^{97} +(3.33354 - 3.33354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 4 q^{7} - 16 q^{9} - 8 q^{13} - 4 q^{15} - 8 q^{17} + 8 q^{19} - 4 q^{21} - 32 q^{25} - 12 q^{29} - 12 q^{35} - 24 q^{37} - 24 q^{43} + 8 q^{45} - 32 q^{47} + 8 q^{51} + 4 q^{55} - 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 4 * q^7 - 16 * q^9 - 8 * q^13 - 4 * q^15 - 8 * q^17 + 8 * q^19 - 4 * q^21 - 32 * q^25 - 12 * q^29 - 12 * q^35 - 24 * q^37 - 24 * q^43 + 8 * q^45 - 32 * q^47 + 8 * q^51 + 4 * q^55 - 8 * q^57 - 24 * q^59 + 40 * q^61 - 4 * q^63 - 4 * q^65 - 16 * q^67 - 8 * q^73 - 24 * q^75 - 48 * q^79 + 16 * q^81 - 8 * q^85 - 12 * q^87 + 40 * q^91 - 32 * q^93 + 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		0			0
$5$	−0.849960	+	2.06823i	−0.380114	+	0.924940i
$5$	−0.849960	+	2.06823i	−0.380114	+	0.924940i
$6$		0			0
$7$	2.08016	−	2.08016i	0.786226	−	0.786226i	−0.194647	−	0.980873i	$-0.562356\pi$
$7$	2.08016	−	2.08016i	0.786226	−	0.786226i	0.980873	+	0.194647i	$0.0623563\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−3.33354	+	3.33354i	−1.00510	+	1.00510i	−0.00511408	+	0.999987i	$0.501628\pi$
$11$	−3.33354	+	3.33354i	−1.00510	+	1.00510i	−0.999987	+	0.00511408i	$0.998372\pi$
$12$		0			0
$13$	−6.13735			−1.70220			−0.851098	−	0.525007i	$-0.824063\pi$
$13$	−6.13735			−1.70220			−0.851098	+	0.525007i	$0.824063\pi$
$14$		0			0
$15$	2.06823	+	0.849960i	0.534014	+	0.219459i
$16$		0			0
$17$	−2.33136	+	2.33136i	−0.565437	+	0.565437i	−0.930847	−	0.365410i	$-0.880929\pi$
$17$	−2.33136	+	2.33136i	−0.565437	+	0.565437i	0.365410	+	0.930847i	$0.380929\pi$
$18$		0			0
$19$	0.834324	−	0.834324i	0.191407	−	0.191407i	−0.604897	−	0.796304i	$-0.706786\pi$
$19$	0.834324	−	0.834324i	0.191407	−	0.191407i	0.796304	+	0.604897i	$0.206786\pi$
$20$		0			0
$21$	−2.08016	−	2.08016i	−0.453928	−	0.453928i
$22$		0			0
$23$	−2.95105	−	2.95105i	−0.615336	−	0.615336i	0.328996	−	0.944331i	$-0.393290\pi$
$23$	−2.95105	−	2.95105i	−0.615336	−	0.615336i	−0.944331	+	0.328996i	$0.893290\pi$
$24$		0			0
$25$	−3.55514	−	3.51582i	−0.711027	−	0.703165i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	0.576185	+	0.576185i	0.106995	+	0.106995i	0.758578	−	0.651583i	$-0.225895\pi$
$29$	0.576185	+	0.576185i	0.106995	+	0.106995i	−0.651583	+	0.758578i	$0.725895\pi$
$30$		0			0
$31$		−	2.62300i		−	0.471106i	−0.971862	−	0.235553i	$-0.924310\pi$
$31$		−	2.62300i		−	0.471106i	0.971862	−	0.235553i	$-0.0756900\pi$
$32$		0			0
$33$	3.33354	+	3.33354i	0.580295	+	0.580295i
$34$		0			0
$35$	2.53419	+	6.07029i	0.428356	+	1.02607i
$36$		0			0
$37$	2.07309			0.340814			0.170407	−	0.985374i	$-0.445492\pi$
$37$	2.07309			0.340814			0.170407	+	0.985374i	$0.445492\pi$
$38$		0			0
$39$			6.13735i			0.982763i
$40$		0			0
$41$			10.8873i			1.70031i	0.526533	+	0.850154i	$0.323492\pi$
$41$			10.8873i			1.70031i	−0.526533	+	0.850154i	$0.676508\pi$
$42$		0			0
$43$	−5.16088			−0.787027			−0.393514	−	0.919319i	$-0.628741\pi$
$43$	−5.16088			−0.787027			−0.393514	+	0.919319i	$0.628741\pi$
$44$		0			0
$45$	0.849960	−	2.06823i	0.126705	−	0.308313i
$46$		0			0
$47$	−8.65772	−	8.65772i	−1.26286	−	1.26286i	−0.949702	−	0.313156i	$-0.898614\pi$
$47$	−8.65772	−	8.65772i	−1.26286	−	1.26286i	−0.313156	−	0.949702i	$-0.601386\pi$
$48$		0			0
$49$		−	1.65411i		−	0.236302i
$50$		0			0
$51$	2.33136	+	2.33136i	0.326455	+	0.326455i
$52$		0			0
$53$		−	1.58490i		−	0.217703i	−0.994058	−	0.108851i	$-0.965283\pi$
$53$		−	1.58490i		−	0.217703i	0.994058	−	0.108851i	$-0.0347173\pi$
$54$		0			0
$55$	−4.06115	−	9.72791i	−0.547605	−	1.31171i
$56$		0			0
$57$	−0.834324	−	0.834324i	−0.110509	−	0.110509i
$58$		0			0
$59$	2.32603	+	2.32603i	0.302824	+	0.302824i	0.842118	−	0.539294i	$-0.181309\pi$
$59$	2.32603	+	2.32603i	0.302824	+	0.302824i	−0.539294	+	0.842118i	$0.681309\pi$
$60$		0			0
$61$	−7.22499	+	7.22499i	−0.925065	+	0.925065i	−0.997382	−	0.0723167i	$-0.976961\pi$
$61$	−7.22499	+	7.22499i	−0.925065	+	0.925065i	0.0723167	+	0.997382i	$0.476961\pi$
$62$		0			0
$63$	−2.08016	+	2.08016i	−0.262075	+	0.262075i
$64$		0			0
$65$	5.21651	−	12.6934i	0.647028	−	1.57443i
$66$		0			0
$67$	0.885549			0.108187			0.0540935	−	0.998536i	$-0.482773\pi$
$67$	0.885549			0.108187			0.0540935	+	0.998536i	$0.482773\pi$
$68$		0			0
$69$	−2.95105	+	2.95105i	−0.355264	+	0.355264i
$70$		0			0
$71$	−2.56877			−0.304857			−0.152428	−	0.988315i	$-0.548709\pi$
$71$	−2.56877			−0.304857			−0.152428	+	0.988315i	$0.548709\pi$
$72$		0			0
$73$	−7.35033	+	7.35033i	−0.860291	+	0.860291i	−0.991372	−	0.131081i	$-0.958155\pi$
$73$	−7.35033	+	7.35033i	−0.860291	+	0.860291i	0.131081	+	0.991372i	$0.458155\pi$
$74$		0			0
$75$	−3.51582	+	3.55514i	−0.405972	+	0.410512i
$76$		0			0
$77$			13.8686i			1.58047i
$78$		0			0
$79$	−7.72612			−0.869256			−0.434628	−	0.900610i	$-0.643120\pi$
$79$	−7.72612			−0.869256			−0.434628	+	0.900610i	$0.643120\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$			8.67714i			0.952440i	0.879326	+	0.476220i	$0.157993\pi$
$83$			8.67714i			0.952440i	−0.879326	+	0.476220i	$0.842007\pi$
$84$		0			0
$85$	−2.84022	−	6.80334i	−0.308065	−	0.737926i
$86$		0			0
$87$	0.576185	−	0.576185i	0.0617735	−	0.0617735i
$88$		0			0
$89$	8.70590			0.922823			0.461412	−	0.887186i	$-0.347343\pi$
$89$	8.70590			0.922823			0.461412	+	0.887186i	$0.347343\pi$
$90$		0			0
$91$	−12.7667	+	12.7667i	−1.33831	+	1.33831i
$92$		0			0
$93$	−2.62300			−0.271993
$94$		0			0
$95$	1.01643	+	2.43472i	0.104284	+	0.249797i
$96$		0			0
$97$	11.9985	−	11.9985i	1.21826	−	1.21826i	0.250021	−	0.968240i	$-0.419562\pi$
$97$	11.9985	−	11.9985i	1.21826	−	1.21826i	0.968240	−	0.250021i	$-0.0804375\pi$
$98$		0			0
$99$	3.33354	−	3.33354i	0.335034	−	0.335034i
$100$		0			0
$101$	−6.69380	−	6.69380i	−0.666058	−	0.666058i	0.290743	−	0.956801i	$-0.406098\pi$
$101$	−6.69380	−	6.69380i	−0.666058	−	0.666058i	−0.956801	+	0.290743i	$0.906098\pi$
$102$		0			0
$103$	13.4242	+	13.4242i	1.32272	+	1.32272i	0.911564	+	0.411158i	$0.134876\pi$
$103$	13.4242	+	13.4242i	1.32272	+	1.32272i	0.411158	+	0.911564i	$0.365124\pi$
$104$		0			0
$105$	6.07029	−	2.53419i	0.592400	−	0.247312i
$106$		0			0
$107$		−	10.9567i		−	1.05922i	−0.848240	−	0.529612i	$-0.822337\pi$
$107$		−	10.9567i		−	1.05922i	0.848240	−	0.529612i	$-0.177663\pi$
$108$		0			0
$109$	−0.643941	−	0.643941i	−0.0616784	−	0.0616784i	0.675595	−	0.737273i	$-0.263887\pi$
$109$	−0.643941	−	0.643941i	−0.0616784	−	0.0616784i	−0.737273	+	0.675595i	$0.763887\pi$
$110$		0			0
$111$		−	2.07309i		−	0.196769i
$112$		0			0
$113$	9.19571	+	9.19571i	0.865060	+	0.865060i	0.991921	−	0.126861i	$-0.0404901\pi$
$113$	9.19571	+	9.19571i	0.865060	+	0.865060i	−0.126861	+	0.991921i	$0.540490\pi$
$114$		0			0
$115$	8.61171	−	3.59517i	0.803046	−	0.335251i
$116$		0			0
$117$	6.13735			0.567398
$118$		0			0
$119$			9.69918i			0.889122i
$120$		0			0
$121$		−	11.2250i		−	1.02046i
$122$		0			0
$123$	10.8873			0.981674
$124$		0			0
$125$	10.2932	−	4.36452i	0.920656	−	0.390375i
$126$		0			0
$127$	4.80716	+	4.80716i	0.426567	+	0.426567i	0.887457	−	0.460890i	$-0.152470\pi$
$127$	4.80716	+	4.80716i	0.426567	+	0.426567i	−0.460890	+	0.887457i	$0.652470\pi$
$128$		0			0
$129$			5.16088i			0.454391i
$130$		0			0
$131$	3.53632	+	3.53632i	0.308970	+	0.308970i	0.844510	−	0.535540i	$-0.179892\pi$
$131$	3.53632	+	3.53632i	0.308970	+	0.308970i	−0.535540	+	0.844510i	$0.679892\pi$
$132$		0			0
$133$		−	3.47105i		−	0.300978i
$134$		0			0
$135$	−2.06823	−	0.849960i	−0.178005	−	0.0731529i
$136$		0			0
$137$	−7.54548	−	7.54548i	−0.644654	−	0.644654i	0.307042	−	0.951696i	$-0.400661\pi$
$137$	−7.54548	−	7.54548i	−0.644654	−	0.644654i	−0.951696	+	0.307042i	$0.900661\pi$
$138$		0			0
$139$	−2.84263	−	2.84263i	−0.241109	−	0.241109i	0.576200	−	0.817309i	$-0.304535\pi$
$139$	−2.84263	−	2.84263i	−0.241109	−	0.241109i	−0.817309	+	0.576200i	$0.804535\pi$
$140$		0			0
$141$	−8.65772	+	8.65772i	−0.729111	+	0.729111i
$142$		0			0
$143$	20.4591	−	20.4591i	1.71088	−	1.71088i
$144$		0			0
$145$	−1.68142	+	0.701948i	−0.139634	+	0.0582936i
$146$		0			0
$147$	−1.65411			−0.136429
$148$		0			0
$149$	−3.20287	+	3.20287i	−0.262389	+	0.262389i	−0.826024	−	0.563635i	$-0.809403\pi$
$149$	−3.20287	+	3.20287i	−0.262389	+	0.262389i	0.563635	+	0.826024i	$0.309403\pi$
$150$		0			0
$151$	−8.82773			−0.718390			−0.359195	−	0.933262i	$-0.616949\pi$
$151$	−8.82773			−0.718390			−0.359195	+	0.933262i	$0.616949\pi$
$152$		0			0
$153$	2.33136	−	2.33136i	0.188479	−	0.188479i
$154$		0			0
$155$	5.42497	+	2.22945i	0.435744	+	0.179074i
$156$		0			0
$157$		−	15.5186i		−	1.23852i	−0.785187	−	0.619258i	$-0.787433\pi$
$157$		−	15.5186i		−	1.23852i	0.785187	−	0.619258i	$-0.212567\pi$
$158$		0			0
$159$	−1.58490			−0.125691
$160$		0			0
$161$	−12.2773			−0.967586
$162$		0			0
$163$		−	8.65221i		−	0.677694i	−0.940842	−	0.338847i	$-0.889963\pi$
$163$		−	8.65221i		−	0.677694i	0.940842	−	0.338847i	$-0.110037\pi$
$164$		0			0
$165$	−9.72791	+	4.06115i	−0.757316	+	0.316160i
$166$		0			0
$167$	−2.86613	+	2.86613i	−0.221788	+	0.221788i	−0.809251	−	0.587463i	$-0.800127\pi$
$167$	−2.86613	+	2.86613i	−0.221788	+	0.221788i	0.587463	+	0.809251i	$0.300127\pi$
$168$		0			0
$169$	24.6671			1.89747
$170$		0			0
$171$	−0.834324	+	0.834324i	−0.0638024	+	0.0638024i
$172$		0			0
$173$	15.1143			1.14912			0.574558	−	0.818464i	$-0.305174\pi$
$173$	15.1143			1.14912			0.574558	+	0.818464i	$0.305174\pi$
$174$		0			0
$175$	−14.7087	+	0.0817750i	−1.11187	+	0.00618161i
$176$		0			0
$177$	2.32603	−	2.32603i	0.174835	−	0.174835i
$178$		0			0
$179$	−12.3666	+	12.3666i	−0.924324	+	0.924324i	−0.997331	−	0.0730070i	$-0.976740\pi$
$179$	−12.3666	+	12.3666i	−0.924324	+	0.924324i	0.0730070	+	0.997331i	$0.476740\pi$
$180$		0			0
$181$	−9.58991	−	9.58991i	−0.712813	−	0.712813i	0.254310	−	0.967123i	$-0.418152\pi$
$181$	−9.58991	−	9.58991i	−0.712813	−	0.712813i	−0.967123	+	0.254310i	$0.918152\pi$
$182$		0			0
$183$	7.22499	+	7.22499i	0.534087	+	0.534087i
$184$		0			0
$185$	−1.76205	+	4.28763i	−0.129548	+	0.315233i
$186$		0			0
$187$		−	15.5434i		−	1.13664i
$188$		0			0
$189$	2.08016	+	2.08016i	0.151309	+	0.151309i
$190$		0			0
$191$		−	14.5044i		−	1.04950i	−0.851257	−	0.524750i	$-0.824159\pi$
$191$		−	14.5044i		−	1.04950i	0.851257	−	0.524750i	$-0.175841\pi$
$192$		0			0
$193$	−1.68153	−	1.68153i	−0.121039	−	0.121039i	0.643992	−	0.765032i	$-0.277277\pi$
$193$	−1.68153	−	1.68153i	−0.121039	−	0.121039i	−0.765032	+	0.643992i	$0.777277\pi$
$194$		0			0
$195$	−12.6934	−	5.21651i	−0.908996	−	0.373562i
$196$		0			0
$197$	8.65121			0.616373			0.308187	−	0.951326i	$-0.400278\pi$
$197$	8.65121			0.616373			0.308187	+	0.951326i	$0.400278\pi$
$198$		0			0
$199$		−	22.3275i		−	1.58275i	−0.611328	−	0.791377i	$-0.709365\pi$
$199$		−	22.3275i		−	1.58275i	0.611328	−	0.791377i	$-0.290635\pi$
$200$		0			0
$201$		−	0.885549i		−	0.0624618i
$202$		0			0
$203$	2.39711			0.168244
$204$		0			0
$205$	−22.5174	−	9.25376i	−1.57268	−	0.646311i
$206$		0			0
$207$	2.95105	+	2.95105i	0.205112	+	0.205112i
$208$		0			0
$209$			5.56251i			0.384767i
$210$		0			0
$211$	−5.27613	−	5.27613i	−0.363224	−	0.363224i	0.501775	−	0.864998i	$-0.332681\pi$
$211$	−5.27613	−	5.27613i	−0.363224	−	0.363224i	−0.864998	+	0.501775i	$0.832681\pi$
$212$		0			0
$213$			2.56877i			0.176009i
$214$		0			0
$215$	4.38655	−	10.6739i	0.299160	−	0.727953i
$216$		0			0
$217$	−5.45626	−	5.45626i	−0.370395	−	0.370395i
$218$		0			0
$219$	7.35033	+	7.35033i	0.496689	+	0.496689i
$220$		0			0
$221$	14.3084	−	14.3084i	0.962484	−	0.962484i
$222$		0			0
$223$	13.8202	−	13.8202i	0.925469	−	0.925469i	−0.0719400	−	0.997409i	$-0.522919\pi$
$223$	13.8202	−	13.8202i	0.925469	−	0.925469i	0.997409	+	0.0719400i	$0.0229190\pi$
$224$		0			0
$225$	3.55514	+	3.51582i	0.237009	+	0.234388i
$226$		0			0
$227$	1.66286			0.110368			0.0551839	−	0.998476i	$-0.482425\pi$
$227$	1.66286			0.110368			0.0551839	+	0.998476i	$0.482425\pi$
$228$		0			0
$229$	−11.3744	+	11.3744i	−0.751643	+	0.751643i	−0.974786	−	0.223142i	$-0.928368\pi$
$229$	−11.3744	+	11.3744i	−0.751643	+	0.751643i	0.223142	+	0.974786i	$0.428368\pi$
$230$		0			0
$231$	13.8686			0.912486
$232$		0			0
$233$	−9.38976	+	9.38976i	−0.615143	+	0.615143i	−0.944282	−	0.329138i	$-0.893242\pi$
$233$	−9.38976	+	9.38976i	−0.615143	+	0.615143i	0.329138	+	0.944282i	$0.393242\pi$
$234$		0			0
$235$	25.2649	−	10.5474i	1.64810	−	0.688038i
$236$		0			0
$237$			7.72612i			0.501865i
$238$		0			0
$239$	8.88914			0.574991			0.287495	−	0.957782i	$-0.407177\pi$
$239$	8.88914			0.574991			0.287495	+	0.957782i	$0.407177\pi$
$240$		0			0
$241$	20.5978			1.32682			0.663411	−	0.748255i	$-0.269108\pi$
$241$	20.5978			1.32682			0.663411	+	0.748255i	$0.269108\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$	3.42109	+	1.40593i	0.218565	+	0.0898217i
$246$		0			0
$247$	−5.12054	+	5.12054i	−0.325812	+	0.325812i
$248$		0			0
$249$	8.67714			0.549891
$250$		0			0
$251$	−16.8455	+	16.8455i	−1.06328	+	1.06328i	−0.0654195	+	0.997858i	$0.520839\pi$
$251$	−16.8455	+	16.8455i	−1.06328	+	1.06328i	−0.997858	+	0.0654195i	$0.979161\pi$
$252$		0			0
$253$	19.6749			1.23695
$254$		0			0
$255$	−6.80334	+	2.84022i	−0.426042	+	0.177861i
$256$		0			0
$257$	−14.1500	+	14.1500i	−0.882653	+	0.882653i	−0.993804	−	0.111151i	$-0.964546\pi$
$257$	−14.1500	+	14.1500i	−0.882653	+	0.882653i	0.111151	+	0.993804i	$0.464546\pi$
$258$		0			0
$259$	4.31236	−	4.31236i	0.267957	−	0.267957i
$260$		0			0
$261$	−0.576185	−	0.576185i	−0.0356650	−	0.0356650i
$262$		0			0
$263$	−11.1204	−	11.1204i	−0.685712	−	0.685712i	0.275569	−	0.961281i	$-0.411134\pi$
$263$	−11.1204	−	11.1204i	−0.685712	−	0.685712i	−0.961281	+	0.275569i	$0.911134\pi$
$264$		0			0
$265$	3.27794	+	1.34710i	0.201362	+	0.0827519i
$266$		0			0
$267$		−	8.70590i		−	0.532792i
$268$		0			0
$269$	10.2902	+	10.2902i	0.627403	+	0.627403i	0.947414	−	0.320011i	$-0.103687\pi$
$269$	10.2902	+	10.2902i	0.627403	+	0.627403i	−0.320011	+	0.947414i	$0.603687\pi$
$270$		0			0
$271$			21.3325i			1.29586i	0.761702	+	0.647928i	$0.224364\pi$
$271$			21.3325i			1.29586i	−0.761702	+	0.647928i	$0.775636\pi$
$272$		0			0
$273$	12.7667	+	12.7667i	0.772674	+	0.772674i
$274$		0			0
$275$	23.5713	−	0.131048i	1.42141	−	0.00790249i
$276$		0			0
$277$	19.0041			1.14184			0.570922	−	0.821004i	$-0.306586\pi$
$277$	19.0041			1.14184			0.570922	+	0.821004i	$0.306586\pi$
$278$		0			0
$279$			2.62300i			0.157035i
$280$		0			0
$281$		−	3.86317i		−	0.230457i	−0.993339	−	0.115229i	$-0.963240\pi$
$281$		−	3.86317i		−	0.230457i	0.993339	−	0.115229i	$-0.0367600\pi$
$282$		0			0
$283$	5.89151			0.350214			0.175107	−	0.984549i	$-0.443973\pi$
$283$	5.89151			0.350214			0.175107	+	0.984549i	$0.443973\pi$
$284$		0			0
$285$	2.43472	−	1.01643i	0.144220	−	0.0602081i
$286$		0			0
$287$	22.6473	+	22.6473i	1.33683	+	1.33683i
$288$		0			0
$289$			6.12955i			0.360562i
$290$		0			0
$291$	−11.9985	−	11.9985i	−0.703364	−	0.703364i
$292$		0			0
$293$		−	4.49132i		−	0.262386i	−0.991357	−	0.131193i	$-0.958119\pi$
$293$		−	4.49132i		−	0.262386i	0.991357	−	0.131193i	$-0.0418807\pi$
$294$		0			0
$295$	−6.78780	+	2.83373i	−0.395201	+	0.164986i
$296$		0			0
$297$	−3.33354	−	3.33354i	−0.193432	−	0.193432i
$298$		0			0
$299$	18.1116	+	18.1116i	1.04742	+	1.04742i
$300$		0			0
$301$	−10.7355	+	10.7355i	−0.618781	+	0.618781i
$302$		0			0
$303$	−6.69380	+	6.69380i	−0.384549	+	0.384549i
$304$		0			0
$305$	−8.80197	−	21.0839i	−0.503999	−	1.20726i
$306$		0			0
$307$	−3.84487			−0.219438			−0.109719	−	0.993963i	$-0.534995\pi$
$307$	−3.84487			−0.219438			−0.109719	+	0.993963i	$0.534995\pi$
$308$		0			0
$309$	13.4242	−	13.4242i	0.763674	−	0.763674i
$310$		0			0
$311$	4.07103			0.230847			0.115423	−	0.993316i	$-0.463178\pi$
$311$	4.07103			0.230847			0.115423	+	0.993316i	$0.463178\pi$
$312$		0			0
$313$	1.37922	−	1.37922i	0.0779584	−	0.0779584i	−0.667052	−	0.745011i	$-0.732444\pi$
$313$	1.37922	−	1.37922i	0.0779584	−	0.0779584i	0.745011	+	0.667052i	$0.232444\pi$
$314$		0			0
$315$	−2.53419	−	6.07029i	−0.142785	−	0.342022i
$316$		0			0
$317$		−	9.80915i		−	0.550937i	−0.961310	−	0.275468i	$-0.911167\pi$
$317$		−	9.80915i		−	0.550937i	0.961310	−	0.275468i	$-0.0888330\pi$
$318$		0			0
$319$	−3.84148			−0.215081
$320$		0			0
$321$	−10.9567			−0.611543
$322$		0			0
$323$			3.89021i			0.216457i
$324$		0			0
$325$	21.8191	+	21.5778i	1.21031	+	1.19692i
$326$		0			0
$327$	−0.643941	+	0.643941i	−0.0356100	+	0.0356100i
$328$		0			0
$329$	−36.0188			−1.98578
$330$		0			0
$331$	7.17235	−	7.17235i	0.394228	−	0.394228i	−0.481963	−	0.876191i	$-0.660076\pi$
$331$	7.17235	−	7.17235i	0.394228	−	0.394228i	0.876191	+	0.481963i	$0.160076\pi$
$332$		0			0
$333$	−2.07309			−0.113605
$334$		0			0
$335$	−0.752681	+	1.83152i	−0.0411234	+	0.100066i
$336$		0			0
$337$	−25.3587	+	25.3587i	−1.38138	+	1.38138i	−0.539200	+	0.842178i	$0.681273\pi$
$337$	−25.3587	+	25.3587i	−1.38138	+	1.38138i	−0.842178	+	0.539200i	$0.818727\pi$
$338$		0			0
$339$	9.19571	−	9.19571i	0.499442	−	0.499442i
$340$		0			0
$341$	8.74390	+	8.74390i	0.473509	+	0.473509i
$342$		0			0
$343$	11.1203	+	11.1203i	0.600439	+	0.600439i
$344$		0			0
$345$	−3.59517	−	8.61171i	−0.193557	−	0.463639i
$346$		0			0
$347$		−	8.80549i		−	0.472704i	−0.971668	−	0.236352i	$-0.924048\pi$
$347$		−	8.80549i		−	0.472704i	0.971668	−	0.236352i	$-0.0759518\pi$
$348$		0			0
$349$	14.8110	+	14.8110i	0.792815	+	0.792815i	0.981951	−	0.189136i	$-0.0605687\pi$
$349$	14.8110	+	14.8110i	0.792815	+	0.792815i	−0.189136	+	0.981951i	$0.560569\pi$
$350$		0			0
$351$		−	6.13735i		−	0.327588i
$352$		0			0
$353$	−21.3226	−	21.3226i	−1.13489	−	1.13489i	−0.989353	−	0.145536i	$-0.953509\pi$
$353$	−21.3226	−	21.3226i	−1.13489	−	1.13489i	−0.145536	−	0.989353i	$-0.546491\pi$
$354$		0			0
$355$	2.18335	−	5.31280i	0.115880	−	0.281974i
$356$		0			0
$357$	9.69918			0.513335
$358$		0			0
$359$			9.38977i			0.495573i	0.968815	+	0.247787i	$0.0797032\pi$
$359$			9.38977i			0.495573i	−0.968815	+	0.247787i	$0.920297\pi$
$360$		0			0
$361$			17.6078i			0.926727i
$362$		0			0
$363$	−11.2250			−0.589161
$364$		0			0
$365$	−8.95467	−	21.4496i	−0.468709	−	1.12273i
$366$		0			0
$367$	−0.129655	−	0.129655i	−0.00676792	−	0.00676792i	0.703715	−	0.710483i	$-0.251523\pi$
$367$	−0.129655	−	0.129655i	−0.00676792	−	0.00676792i	−0.710483	+	0.703715i	$0.751523\pi$
$368$		0			0
$369$		−	10.8873i		−	0.566770i
$370$		0			0
$371$	−3.29684	−	3.29684i	−0.171164	−	0.171164i
$372$		0			0
$373$		−	2.85797i		−	0.147980i	−0.997259	−	0.0739900i	$-0.976427\pi$
$373$		−	2.85797i		−	0.147980i	0.997259	−	0.0739900i	$-0.0235733\pi$
$374$		0			0
$375$	−4.36452	−	10.2932i	−0.225383	−	0.531541i
$376$		0			0
$377$	−3.53625	−	3.53625i	−0.182126	−	0.182126i
$378$		0			0
$379$	−14.8095	−	14.8095i	−0.760713	−	0.760713i	0.215739	−	0.976451i	$-0.430784\pi$
$379$	−14.8095	−	14.8095i	−0.760713	−	0.760713i	−0.976451	+	0.215739i	$0.930784\pi$
$380$		0			0
$381$	4.80716	−	4.80716i	0.246278	−	0.246278i
$382$		0			0
$383$	−22.2921	+	22.2921i	−1.13907	+	1.13907i	−0.150458	+	0.988616i	$0.548075\pi$
$383$	−22.2921	+	22.2921i	−1.13907	+	1.13907i	−0.988616	+	0.150458i	$0.951925\pi$
$384$		0			0
$385$	−28.6834	−	11.7878i	−1.46184	−	0.600759i
$386$		0			0
$387$	5.16088			0.262342
$388$		0			0
$389$	−17.1132	+	17.1132i	−0.867671	+	0.867671i	−0.992214	−	0.124543i	$-0.960254\pi$
$389$	−17.1132	+	17.1132i	−0.867671	+	0.867671i	0.124543	+	0.992214i	$0.460254\pi$
$390$		0			0
$391$	13.7599			0.695867
$392$		0			0
$393$	3.53632	−	3.53632i	0.178384	−	0.178384i
$394$		0			0
$395$	6.56689	−	15.9794i	0.330416	−	0.804009i
$396$		0			0
$397$		−	16.2806i		−	0.817099i	−0.912736	−	0.408549i	$-0.866035\pi$
$397$		−	16.2806i		−	0.817099i	0.912736	−	0.408549i	$-0.133965\pi$
$398$		0			0
$399$	−3.47105			−0.173770
$400$		0			0
$401$	5.13860			0.256609			0.128305	−	0.991735i	$-0.459046\pi$
$401$	5.13860			0.256609			0.128305	+	0.991735i	$0.459046\pi$
$402$		0			0
$403$			16.0983i			0.801914i
$404$		0			0
$405$	−0.849960	+	2.06823i	−0.0422349	+	0.102771i
$406$		0			0
$407$	−6.91074	+	6.91074i	−0.342553	+	0.342553i
$408$		0			0
$409$	3.88999			0.192348			0.0961738	−	0.995365i	$-0.469340\pi$
$409$	3.88999			0.192348			0.0961738	+	0.995365i	$0.469340\pi$
$410$		0			0
$411$	−7.54548	+	7.54548i	−0.372191	+	0.372191i
$412$		0			0
$413$	9.67703			0.476176
$414$		0			0
$415$	−17.9463	−	7.37522i	−0.880949	−	0.362035i
$416$		0			0
$417$	−2.84263	+	2.84263i	−0.139204	+	0.139204i
$418$		0			0
$419$	−9.68913	+	9.68913i	−0.473345	+	0.473345i	−0.902995	−	0.429650i	$-0.858637\pi$
$419$	−9.68913	+	9.68913i	−0.473345	+	0.473345i	0.429650	+	0.902995i	$0.358637\pi$
$420$		0			0
$421$	−19.2867	−	19.2867i	−0.939978	−	0.939978i	0.0583197	−	0.998298i	$-0.481426\pi$
$421$	−19.2867	−	19.2867i	−0.939978	−	0.939978i	−0.998298	+	0.0583197i	$0.981426\pi$
$422$		0			0
$423$	8.65772	+	8.65772i	0.420953	+	0.420953i
$424$		0			0
$425$	16.4849	−	0.0916501i	0.799636	−	0.00444568i
$426$		0			0
$427$			30.0582i			1.45462i
$428$		0			0
$429$	−20.4591	−	20.4591i	−0.987776	−	0.987776i
$430$		0			0
$431$			4.13031i			0.198950i	0.995040	+	0.0994751i	$0.0317164\pi$
$431$			4.13031i			0.198950i	−0.995040	+	0.0994751i	$0.968284\pi$
$432$		0			0
$433$	13.3312	+	13.3312i	0.640655	+	0.640655i	0.950716	−	0.310062i	$-0.100350\pi$
$433$	13.3312	+	13.3312i	0.640655	+	0.640655i	−0.310062	+	0.950716i	$0.600350\pi$
$434$		0			0
$435$	0.701948	+	1.68142i	0.0336558	+	0.0806178i
$436$		0			0
$437$	−4.92426			−0.235559
$438$		0			0
$439$			22.0770i			1.05368i	0.849965	+	0.526839i	$0.176623\pi$
$439$			22.0770i			1.05368i	−0.849965	+	0.526839i	$0.823377\pi$
$440$		0			0
$441$			1.65411i			0.0787673i
$442$		0			0
$443$	−8.44869			−0.401409			−0.200705	−	0.979652i	$-0.564323\pi$
$443$	−8.44869			−0.401409			−0.200705	+	0.979652i	$0.564323\pi$
$444$		0			0
$445$	−7.39967	+	18.0058i	−0.350778	+	0.853556i
$446$		0			0
$447$	3.20287	+	3.20287i	0.151491	+	0.151491i
$448$		0			0
$449$		−	12.3249i		−	0.581648i	−0.956777	−	0.290824i	$-0.906071\pi$
$449$		−	12.3249i		−	0.581648i	0.956777	−	0.290824i	$-0.0939293\pi$
$450$		0			0
$451$	−36.2932	−	36.2932i	−1.70898	−	1.70898i
$452$		0			0
$453$			8.82773i			0.414763i
$454$		0			0
$455$	−15.5532	−	37.2555i	−0.729146	−	1.74657i
$456$		0			0
$457$	−10.5838	−	10.5838i	−0.495089	−	0.495089i	0.414816	−	0.909905i	$-0.363846\pi$
$457$	−10.5838	−	10.5838i	−0.495089	−	0.495089i	−0.909905	+	0.414816i	$0.863846\pi$
$458$		0			0
$459$	−2.33136	−	2.33136i	−0.108818	−	0.108818i
$460$		0			0
$461$	−6.77081	+	6.77081i	−0.315348	+	0.315348i	−0.846977	−	0.531629i	$-0.821580\pi$
$461$	−6.77081	+	6.77081i	−0.315348	+	0.315348i	0.531629	+	0.846977i	$0.321580\pi$
$462$		0			0
$463$	−11.3573	+	11.3573i	−0.527819	+	0.527819i	−0.919921	−	0.392103i	$-0.871748\pi$
$463$	−11.3573	+	11.3573i	−0.527819	+	0.527819i	0.392103	+	0.919921i	$0.371748\pi$
$464$		0			0
$465$	2.22945	−	5.42497i	0.103388	−	0.251577i
$466$		0			0
$467$	−3.11578			−0.144181			−0.0720906	−	0.997398i	$-0.522967\pi$
$467$	−3.11578			−0.144181			−0.0720906	+	0.997398i	$0.522967\pi$
$468$		0			0
$469$	1.84208	−	1.84208i	0.0850594	−	0.0850594i
$470$		0			0
$471$	−15.5186			−0.715058
$472$		0			0
$473$	17.2040	−	17.2040i	0.791042	−	0.791042i
$474$		0			0
$475$	−5.89947	+	0.0327989i	−0.270686	+	0.00150492i
$476$		0			0
$477$			1.58490i			0.0725676i
$478$		0			0
$479$	−15.3508			−0.701396			−0.350698	−	0.936489i	$-0.614056\pi$
$479$	−15.3508			−0.701396			−0.350698	+	0.936489i	$0.614056\pi$
$480$		0			0
$481$	−12.7233			−0.580132
$482$		0			0
$483$			12.2773i			0.558636i
$484$		0			0
$485$	14.6174	+	35.0138i	0.663740	+	1.58990i
$486$		0			0
$487$	−8.51351	+	8.51351i	−0.385784	+	0.385784i	−0.873181	−	0.487397i	$-0.837947\pi$
$487$	−8.51351	+	8.51351i	−0.385784	+	0.385784i	0.487397	+	0.873181i	$0.337947\pi$
$488$		0			0
$489$	−8.65221			−0.391267
$490$		0			0
$491$	6.16348	−	6.16348i	0.278154	−	0.278154i	−0.554218	−	0.832372i	$-0.686983\pi$
$491$	6.16348	−	6.16348i	0.278154	−	0.278154i	0.832372	+	0.554218i	$0.186983\pi$
$492$		0			0
$493$	−2.68659			−0.120998
$494$		0			0
$495$	4.06115	+	9.72791i	0.182535	+	0.437237i
$496$		0			0
$497$	−5.34345	+	5.34345i	−0.239686	+	0.239686i
$498$		0			0
$499$	−16.1961	+	16.1961i	−0.725037	+	0.725037i	−0.969627	−	0.244589i	$-0.921347\pi$
$499$	−16.1961	+	16.1961i	−0.725037	+	0.725037i	0.244589	+	0.969627i	$0.421347\pi$
$500$		0			0
$501$	2.86613	+	2.86613i	0.128049	+	0.128049i
$502$		0			0
$503$	−8.39462	−	8.39462i	−0.374298	−	0.374298i	0.494742	−	0.869040i	$-0.335263\pi$
$503$	−8.39462	−	8.39462i	−0.374298	−	0.374298i	−0.869040	+	0.494742i	$0.835263\pi$
$504$		0			0
$505$	19.5338	−	8.15485i	0.869242	−	0.362886i
$506$		0			0
$507$		−	24.6671i		−	1.09550i
$508$		0			0
$509$	−5.50555	−	5.50555i	−0.244029	−	0.244029i	0.574486	−	0.818515i	$-0.305202\pi$
$509$	−5.50555	−	5.50555i	−0.244029	−	0.244029i	−0.818515	+	0.574486i	$0.805202\pi$
$510$		0			0
$511$			30.5797i			1.35277i
$512$		0			0
$513$	0.834324	+	0.834324i	0.0368363	+	0.0368363i
$514$		0			0
$515$	−39.1742	+	16.3542i	−1.72622	+	0.720653i
$516$		0			0
$517$	57.7217			2.53860
$518$		0			0
$519$		−	15.1143i		−	0.663442i
$520$		0			0
$521$			39.2289i			1.71865i	0.511430	+	0.859325i	$0.329116\pi$
$521$			39.2289i			1.71865i	−0.511430	+	0.859325i	$0.670884\pi$
$522$		0			0
$523$	−16.7434			−0.732137			−0.366068	−	0.930588i	$-0.619296\pi$
$523$	−16.7434			−0.732137			−0.366068	+	0.930588i	$0.619296\pi$
$524$		0			0
$525$	0.0817750	+	14.7087i	0.00356895	+	0.641941i
$526$		0			0
$527$	6.11516	+	6.11516i	0.266381	+	0.266381i
$528$		0			0
$529$		−	5.58265i		−	0.242724i
$530$		0			0
$531$	−2.32603	−	2.32603i	−0.100941	−	0.100941i
$532$		0			0
$533$		−	66.8191i		−	2.89426i
$534$		0			0
$535$	22.6610	+	9.31276i	0.979719	+	0.402626i
$536$		0			0
$537$	12.3666	+	12.3666i	0.533659	+	0.533659i
$538$		0			0
$539$	5.51406	+	5.51406i	0.237507	+	0.237507i
$540$		0			0
$541$	3.45427	−	3.45427i	0.148511	−	0.148511i	−0.628942	−	0.777452i	$-0.716512\pi$
$541$	3.45427	−	3.45427i	0.148511	−	0.148511i	0.777452	+	0.628942i	$0.216512\pi$
$542$		0			0
$543$	−9.58991	+	9.58991i	−0.411543	+	0.411543i
$544$		0			0
$545$	1.87914	−	0.784493i	0.0804936	−	0.0336040i
$546$		0			0
$547$	18.1175			0.774647			0.387324	−	0.921944i	$-0.373400\pi$
$547$	18.1175			0.774647			0.387324	+	0.921944i	$0.373400\pi$
$548$		0			0
$549$	7.22499	−	7.22499i	0.308355	−	0.308355i
$550$		0			0
$551$	0.961451			0.0409592
$552$		0			0
$553$	−16.0715	+	16.0715i	−0.683431	+	0.683431i
$554$		0			0
$555$	4.28763	+	1.76205i	0.182000	+	0.0747947i
$556$		0			0
$557$		−	21.1776i		−	0.897324i	−0.893701	−	0.448662i	$-0.851901\pi$
$557$		−	21.1776i		−	0.897324i	0.893701	−	0.448662i	$-0.148099\pi$
$558$		0			0
$559$	31.6742			1.33967
$560$		0			0
$561$	−15.5434			−0.656241
$562$		0			0
$563$		−	44.5712i		−	1.87845i	−0.343298	−	0.939226i	$-0.611544\pi$
$563$		−	44.5712i		−	1.87845i	0.343298	−	0.939226i	$-0.388456\pi$
$564$		0			0
$565$	−26.8348	+	11.2028i	−1.12895	+	0.471307i
$566$		0			0
$567$	2.08016	−	2.08016i	0.0873584	−	0.0873584i
$568$		0			0
$569$	5.14194			0.215562			0.107781	−	0.994175i	$-0.465626\pi$
$569$	5.14194			0.215562			0.107781	+	0.994175i	$0.465626\pi$
$570$		0			0
$571$	17.4873	−	17.4873i	0.731820	−	0.731820i	−0.239160	−	0.970980i	$-0.576872\pi$
$571$	17.4873	−	17.4873i	0.731820	−	0.731820i	0.970980	+	0.239160i	$0.0768721\pi$
$572$		0			0
$573$	−14.5044			−0.605929
$574$		0			0
$575$	0.116011	+	20.8667i	0.00483801	+	0.870203i
$576$		0			0
$577$	−2.82131	+	2.82131i	−0.117453	+	0.117453i	−0.763390	−	0.645938i	$-0.776467\pi$
$577$	−2.82131	+	2.82131i	−0.117453	+	0.117453i	0.645938	+	0.763390i	$0.276467\pi$
$578$		0			0
$579$	−1.68153	+	1.68153i	−0.0698822	+	0.0698822i
$580$		0			0
$581$	18.0498	+	18.0498i	0.748833	+	0.748833i
$582$		0			0
$583$	5.28334	+	5.28334i	0.218813	+	0.218813i
$584$		0			0
$585$	−5.21651	+	12.6934i	−0.215676	+	0.524809i
$586$		0			0
$587$		−	45.9941i		−	1.89838i	−0.314702	−	0.949191i	$-0.601905\pi$
$587$		−	45.9941i		−	1.89838i	0.314702	−	0.949191i	$-0.398095\pi$
$588$		0			0
$589$	−2.18844	−	2.18844i	−0.0901729	−	0.0901729i
$590$		0			0
$591$		−	8.65121i		−	0.355863i
$592$		0			0
$593$	−7.77054	−	7.77054i	−0.319098	−	0.319098i	0.529323	−	0.848421i	$-0.322446\pi$
$593$	−7.77054	−	7.77054i	−0.319098	−	0.319098i	−0.848421	+	0.529323i	$0.822446\pi$
$594$		0			0
$595$	−20.0601	−	8.24392i	−0.822385	−	0.337968i
$596$		0			0
$597$	−22.3275			−0.913804
$598$		0			0
$599$		−	16.1877i		−	0.661413i	−0.943734	−	0.330707i	$-0.892713\pi$
$599$		−	16.1877i		−	0.661413i	0.943734	−	0.330707i	$-0.107287\pi$
$600$		0			0
$601$			14.1986i			0.579174i	0.957152	+	0.289587i	$0.0935180\pi$
$601$			14.1986i			0.579174i	−0.957152	+	0.289587i	$0.906482\pi$
$602$		0			0
$603$	−0.885549			−0.0360623
$604$		0			0
$605$	23.2159	+	9.54082i	0.943860	+	0.387889i
$606$		0			0
$607$	22.9646	+	22.9646i	0.932105	+	0.932105i	0.997837	−	0.0657320i	$-0.0209383\pi$
$607$	22.9646	+	22.9646i	0.932105	+	0.932105i	−0.0657320	+	0.997837i	$0.520938\pi$
$608$		0			0
$609$		−	2.39711i		−	0.0971359i
$610$		0			0
$611$	53.1355	+	53.1355i	2.14963	+	2.14963i
$612$		0			0
$613$			37.1155i			1.49908i	0.661958	+	0.749541i	$0.269726\pi$
$613$			37.1155i			1.49908i	−0.661958	+	0.749541i	$0.730274\pi$
$614$		0			0
$615$	−9.25376	+	22.5174i	−0.373148	+	0.907989i
$616$		0			0
$617$	1.45005	+	1.45005i	0.0583767	+	0.0583767i	0.735692	−	0.677316i	$-0.236857\pi$
$617$	1.45005	+	1.45005i	0.0583767	+	0.0583767i	−0.677316	+	0.735692i	$0.736857\pi$
$618$		0			0
$619$	13.2111	+	13.2111i	0.530998	+	0.530998i	0.920869	−	0.389872i	$-0.127481\pi$
$619$	13.2111	+	13.2111i	0.530998	+	0.530998i	−0.389872	+	0.920869i	$0.627481\pi$
$620$		0			0
$621$	2.95105	−	2.95105i	0.118421	−	0.118421i
$622$		0			0
$623$	18.1096	−	18.1096i	0.725548	−	0.725548i
$624$		0			0
$625$	0.277973	+	24.9985i	0.0111189	+	0.999938i
$626$		0			0
$627$	5.56251			0.222145
$628$		0			0
$629$	−4.83312	+	4.83312i	−0.192709	+	0.192709i
$630$		0			0
$631$	−11.6636			−0.464322			−0.232161	−	0.972677i	$-0.574580\pi$
$631$	−11.6636			−0.464322			−0.232161	+	0.972677i	$0.574580\pi$
$632$		0			0
$633$	−5.27613	+	5.27613i	−0.209707	+	0.209707i
$634$		0			0
$635$	−14.0282	+	5.85641i	−0.556692	+	0.232405i
$636$		0			0
$637$			10.1519i			0.402232i
$638$		0			0
$639$	2.56877			0.101619
$640$		0			0
$641$	−20.8880			−0.825025			−0.412512	−	0.910952i	$-0.635349\pi$
$641$	−20.8880			−0.825025			−0.412512	+	0.910952i	$0.635349\pi$
$642$		0			0
$643$			36.6130i			1.44388i	0.691957	+	0.721939i	$0.256749\pi$
$643$			36.6130i			1.44388i	−0.691957	+	0.721939i	$0.743251\pi$
$644$		0			0
$645$	−10.6739	−	4.38655i	−0.420284	−	0.172720i
$646$		0			0
$647$	−23.8735	+	23.8735i	−0.938562	+	0.938562i	−0.998219	−	0.0596566i	$-0.980999\pi$
$647$	−23.8735	+	23.8735i	−0.938562	+	0.938562i	0.0596566	+	0.998219i	$0.480999\pi$
$648$		0			0
$649$	−15.5079			−0.608737
$650$		0			0
$651$	−5.45626	+	5.45626i	−0.213848	+	0.213848i
$652$		0			0
$653$	−22.3501			−0.874627			−0.437313	−	0.899309i	$-0.644070\pi$
$653$	−22.3501			−0.874627			−0.437313	+	0.899309i	$0.644070\pi$
$654$		0			0
$655$	−10.3197	+	4.30819i	−0.403222	+	0.168335i
$656$		0			0
$657$	7.35033	−	7.35033i	0.286764	−	0.286764i
$658$		0			0
$659$	15.9700	−	15.9700i	0.622102	−	0.622102i	−0.323967	−	0.946068i	$-0.605017\pi$
$659$	15.9700	−	15.9700i	0.622102	−	0.622102i	0.946068	+	0.323967i	$0.105017\pi$
$660$		0			0
$661$	−15.1592	−	15.1592i	−0.589624	−	0.589624i	0.347906	−	0.937530i	$-0.386893\pi$
$661$	−15.1592	−	15.1592i	−0.589624	−	0.589624i	−0.937530	+	0.347906i	$0.886893\pi$
$662$		0			0
$663$	−14.3084	−	14.3084i	−0.555691	−	0.555691i
$664$		0			0
$665$	7.17893	+	2.95026i	0.278387	+	0.114406i
$666$		0			0
$667$		−	3.40070i		−	0.131676i
$668$		0			0
$669$	−13.8202	−	13.8202i	−0.534320	−	0.534320i
$670$		0			0
$671$		−	48.1696i		−	1.85957i
$672$		0			0
$673$	15.2524	+	15.2524i	0.587938	+	0.587938i	0.937073	−	0.349134i	$-0.113524\pi$
$673$	15.2524	+	15.2524i	0.587938	+	0.587938i	−0.349134	+	0.937073i	$0.613524\pi$
$674$		0			0
$675$	3.51582	−	3.55514i	0.135324	−	0.136837i
$676$		0			0
$677$	−3.95511			−0.152007			−0.0760036	−	0.997108i	$-0.524216\pi$
$677$	−3.95511			−0.152007			−0.0760036	+	0.997108i	$0.524216\pi$
$678$		0			0
$679$		−	49.9175i		−	1.91566i
$680$		0			0
$681$		−	1.66286i		−	0.0637209i
$682$		0			0
$683$	−50.9345			−1.94895			−0.974476	−	0.224490i	$-0.927928\pi$
$683$	−50.9345			−1.94895			−0.974476	+	0.224490i	$0.927928\pi$
$684$		0			0
$685$	22.0191	−	9.19242i	0.841308	−	0.351224i
$686$		0			0
$687$	11.3744	+	11.3744i	0.433962	+	0.433962i
$688$		0			0
$689$			9.72710i			0.370573i
$690$		0			0
$691$	13.5869	+	13.5869i	0.516870	+	0.516870i	0.916623	−	0.399753i	$-0.130904\pi$
$691$	13.5869	+	13.5869i	0.516870	+	0.516870i	−0.399753	+	0.916623i	$0.630904\pi$
$692$		0			0
$693$		−	13.8686i		−	0.526824i
$694$		0			0
$695$	8.29534	−	3.46309i	0.314660	−	0.131362i
$696$		0			0
$697$	−25.3822	−	25.3822i	−0.961418	−	0.961418i
$698$		0			0
$699$	9.38976	+	9.38976i	0.355153	+	0.355153i
$700$		0			0
$701$	−0.627254	+	0.627254i	−0.0236911	+	0.0236911i	−0.718853	−	0.695162i	$-0.755333\pi$
$701$	−0.627254	+	0.627254i	−0.0236911	+	0.0236911i	0.695162	+	0.718853i	$0.255333\pi$
$702$		0			0
$703$	1.72963	−	1.72963i	0.0652343	−	0.0652343i
$704$		0			0
$705$	−10.5474	−	25.2649i	−0.397239	−	0.951529i
$706$		0			0
$707$	−27.8483			−1.04734
$708$		0			0
$709$	−26.7170	+	26.7170i	−1.00338	+	1.00338i	−0.00338478	+	0.999994i	$0.501077\pi$
$709$	−26.7170	+	26.7170i	−1.00338	+	1.00338i	−0.999994	+	0.00338478i	$0.998923\pi$
$710$		0			0
$711$	7.72612			0.289752
$712$		0			0
$713$	−7.74061	+	7.74061i	−0.289888	+	0.289888i
$714$		0			0
$715$	24.9247	+	59.7036i	0.932131	+	2.23279i
$716$		0			0
$717$		−	8.88914i		−	0.331971i
$718$		0			0
$719$	−27.5794			−1.02854			−0.514269	−	0.857629i	$-0.671937\pi$
$719$	−27.5794			−1.02854			−0.514269	+	0.857629i	$0.671937\pi$
$720$		0			0
$721$	55.8488			2.07992
$722$		0			0
$723$		−	20.5978i		−	0.766041i
$724$		0			0
$725$	−0.0226510	−	4.07418i	−0.000841235	−	0.151311i
$726$		0			0
$727$	−8.11985	+	8.11985i	−0.301148	+	0.301148i	−0.841463	−	0.540315i	$-0.818305\pi$
$727$	−8.11985	+	8.11985i	−0.301148	+	0.301148i	0.540315	+	0.841463i	$0.318305\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	12.0319	−	12.0319i	0.445014	−	0.445014i
$732$		0			0
$733$	12.3271			0.455313			0.227656	−	0.973742i	$-0.426894\pi$
$733$	12.3271			0.455313			0.227656	+	0.973742i	$0.426894\pi$
$734$		0			0
$735$	1.40593	−	3.42109i	0.0518586	−	0.126189i
$736$		0			0
$737$	−2.95201	+	2.95201i	−0.108739	+	0.108739i
$738$		0			0
$739$	24.8212	−	24.8212i	0.913062	−	0.913062i	−0.0834496	−	0.996512i	$-0.526594\pi$
$739$	24.8212	−	24.8212i	0.913062	−	0.913062i	0.996512	+	0.0834496i	$0.0265938\pi$
$740$		0			0
$741$	5.12054	+	5.12054i	0.188108	+	0.188108i
$742$		0			0
$743$	26.8731	+	26.8731i	0.985877	+	0.985877i	0.999902	−	0.0140246i	$-0.00446431\pi$
$743$	26.8731	+	26.8731i	0.985877	+	0.985877i	−0.0140246	+	0.999902i	$0.504464\pi$
$744$		0			0
$745$	−3.90195	−	9.34658i	−0.142957	−	0.342432i
$746$		0			0
$747$		−	8.67714i		−	0.317480i
$748$		0			0
$749$	−22.7917	−	22.7917i	−0.832789	−	0.832789i
$750$		0			0
$751$		−	24.7594i		−	0.903484i	−0.892149	−	0.451742i	$-0.850803\pi$
$751$		−	24.7594i		−	0.903484i	0.892149	−	0.451742i	$-0.149197\pi$
$752$		0			0
$753$	16.8455	+	16.8455i	0.613883	+	0.613883i
$754$		0			0
$755$	7.50322	−	18.2578i	0.273070	−	0.664468i
$756$		0			0
$757$	−35.5014			−1.29032			−0.645160	−	0.764047i	$-0.723209\pi$
$757$	−35.5014			−1.29032			−0.645160	+	0.764047i	$0.723209\pi$
$758$		0			0
$759$		−	19.6749i		−	0.714153i
$760$		0			0
$761$			19.8569i			0.719812i	0.932989	+	0.359906i	$0.117191\pi$
$761$			19.8569i			0.719812i	−0.932989	+	0.359906i	$0.882809\pi$
$762$		0			0
$763$	−2.67900			−0.0969862
$764$		0			0
$765$	2.84022	+	6.80334i	0.102688	+	0.245975i
$766$		0			0
$767$	−14.2757	−	14.2757i	−0.515465	−	0.515465i
$768$		0			0
$769$		−	37.1951i		−	1.34129i	−0.741779	−	0.670644i	$-0.766018\pi$
$769$		−	37.1951i		−	1.34129i	0.741779	−	0.670644i	$-0.233982\pi$
$770$		0			0
$771$	14.1500	+	14.1500i	0.509600	+	0.509600i
$772$		0			0
$773$			13.2454i			0.476402i	0.971216	+	0.238201i	$0.0765578\pi$
$773$			13.2454i			0.476402i	−0.971216	+	0.238201i	$0.923442\pi$
$774$		0			0
$775$	−9.22202	+	9.32514i	−0.331265	+	0.334969i
$776$		0			0
$777$	−4.31236	−	4.31236i	−0.154705	−	0.154705i
$778$		0			0
$779$	9.08353	+	9.08353i	0.325451	+	0.325451i
$780$		0			0
$781$	8.56310	−	8.56310i	0.306412	−	0.306412i
$782$		0			0
$783$	−0.576185	+	0.576185i	−0.0205912	+	0.0205912i
$784$		0			0
$785$	32.0959	+	13.1902i	1.14555	+	0.470777i
$786$		0			0
$787$	12.0292			0.428794			0.214397	−	0.976747i	$-0.431221\pi$
$787$	12.0292			0.428794			0.214397	+	0.976747i	$0.431221\pi$
$788$		0			0
$789$	−11.1204	+	11.1204i	−0.395896	+	0.395896i
$790$		0			0
$791$	38.2571			1.36026
$792$		0			0
$793$	44.3423	−	44.3423i	1.57464	−	1.57464i
$794$		0			0
$795$	1.34710	−	3.27794i	0.0477768	−	0.116256i
$796$		0			0
$797$			45.2714i			1.60359i	0.597597	+	0.801797i	$0.296122\pi$
$797$			45.2714i			1.60359i	−0.597597	+	0.801797i	$0.703878\pi$
$798$		0			0
$799$	40.3685			1.42813
$800$		0			0
$801$	−8.70590			−0.307608
$802$		0			0
$803$		−	49.0053i		−	1.72936i
$804$		0			0
$805$	10.4352	−	25.3922i	0.367793	−	0.894958i
$806$		0			0
$807$	10.2902	−	10.2902i	0.362231	−	0.362231i
$808$		0			0
$809$	−5.16391			−0.181553			−0.0907767	−	0.995871i	$-0.528935\pi$
$809$	−5.16391			−0.181553			−0.0907767	+	0.995871i	$0.528935\pi$
$810$		0			0
$811$	−15.7171	+	15.7171i	−0.551903	+	0.551903i	−0.926990	−	0.375087i	$-0.877613\pi$
$811$	−15.7171	+	15.7171i	−0.551903	+	0.551903i	0.375087	+	0.926990i	$0.377613\pi$
$812$		0			0
$813$	21.3325			0.748163
$814$		0			0
$815$	17.8947	+	7.35404i	0.626826	+	0.257601i
$816$		0			0
$817$	−4.30585	+	4.30585i	−0.150643	+	0.150643i
$818$		0			0
$819$	12.7667	−	12.7667i	0.446103	−	0.446103i
$820$		0			0
$821$	−15.6816	−	15.6816i	−0.547293	−	0.547293i	0.378364	−	0.925657i	$-0.376487\pi$
$821$	−15.6816	−	15.6816i	−0.547293	−	0.547293i	−0.925657	+	0.378364i	$0.876487\pi$
$822$		0			0
$823$	3.65203	+	3.65203i	0.127302	+	0.127302i	0.767887	−	0.640585i	$-0.221308\pi$
$823$	3.65203	+	3.65203i	0.127302	+	0.127302i	−0.640585	+	0.767887i	$0.721308\pi$
$824$		0			0
$825$	−0.131048	−	23.5713i	−0.00456251	−	0.820649i
$826$		0			0
$827$			14.0926i			0.490046i	0.969517	+	0.245023i	$0.0787956\pi$
$827$			14.0926i			0.490046i	−0.969517	+	0.245023i	$0.921204\pi$
$828$		0			0
$829$	12.1216	+	12.1216i	0.421000	+	0.421000i	0.885548	−	0.464548i	$-0.153783\pi$
$829$	12.1216	+	12.1216i	0.421000	+	0.421000i	−0.464548	+	0.885548i	$0.653783\pi$
$830$		0			0
$831$		−	19.0041i		−	0.659244i
$832$		0			0
$833$	3.85633	+	3.85633i	0.133614	+	0.133614i
$834$		0			0
$835$	−3.49171	−	8.36390i	−0.120836	−	0.289445i
$836$		0			0
$837$	2.62300			0.0906643
$838$		0			0
$839$			14.6206i			0.504759i	0.967628	+	0.252380i	$0.0812132\pi$
$839$			14.6206i			0.504759i	−0.967628	+	0.252380i	$0.918787\pi$
$840$		0			0
$841$		−	28.3360i		−	0.977104i
$842$		0			0
$843$	−3.86317			−0.133054
$844$		0			0
$845$	−20.9661	+	51.0172i	−0.721254	+	1.75504i
$846$		0			0
$847$	−23.3498	−	23.3498i	−0.802309	−	0.802309i
$848$		0			0
$849$		−	5.89151i		−	0.202196i
$850$		0			0
$851$	−6.11779	−	6.11779i	−0.209715	−	0.209715i
$852$		0			0
$853$			13.7252i			0.469940i	0.972003	+	0.234970i	$0.0754992\pi$
$853$			13.7252i			0.469940i	−0.972003	+	0.234970i	$0.924501\pi$
$854$		0			0
$855$	−1.01643	−	2.43472i	−0.0347612	−	0.0832655i
$856$		0			0
$857$	−18.7921	−	18.7921i	−0.641927	−	0.641927i	0.309102	−	0.951029i	$-0.399972\pi$
$857$	−18.7921	−	18.7921i	−0.641927	−	0.641927i	−0.951029	+	0.309102i	$0.899972\pi$
$858$		0			0
$859$	23.1774	+	23.1774i	0.790803	+	0.790803i	0.981625	−	0.190822i	$-0.0611152\pi$
$859$	23.1774	+	23.1774i	0.790803	+	0.790803i	−0.190822	+	0.981625i	$0.561115\pi$
$860$		0			0
$861$	22.6473	−	22.6473i	0.771817	−	0.771817i
$862$		0			0
$863$	−8.96863	+	8.96863i	−0.305296	+	0.305296i	−0.843082	−	0.537786i	$-0.819261\pi$
$863$	−8.96863	+	8.96863i	−0.305296	+	0.305296i	0.537786	+	0.843082i	$0.319261\pi$
$864$		0			0
$865$	−12.8465	+	31.2597i	−0.436795	+	1.06286i
$866$		0			0
$867$	6.12955			0.208171
$868$		0			0
$869$	25.7553	−	25.7553i	0.873690	−	0.873690i
$870$		0			0
$871$	−5.43492			−0.184155
$872$		0			0
$873$	−11.9985	+	11.9985i	−0.406087	+	0.406087i
$874$		0			0
$875$	12.3327	−	30.4905i	0.416921	−	1.03077i
$876$		0			0
$877$			47.1944i			1.59364i	0.604215	+	0.796822i	$0.293487\pi$
$877$			47.1944i			1.59364i	−0.604215	+	0.796822i	$0.706513\pi$
$878$		0			0
$879$	−4.49132			−0.151489
$880$		0			0
$881$	51.5667			1.73733			0.868663	−	0.495403i	$-0.164980\pi$
$881$	51.5667			1.73733			0.868663	+	0.495403i	$0.164980\pi$
$882$		0			0
$883$			33.7083i			1.13438i	0.823589	+	0.567188i	$0.191969\pi$
$883$			33.7083i			1.13438i	−0.823589	+	0.567188i	$0.808031\pi$
$884$		0			0
$885$	2.83373	+	6.78780i	0.0952548	+	0.228170i
$886$		0			0
$887$	−4.91204	+	4.91204i	−0.164930	+	0.164930i	−0.784747	−	0.619817i	$-0.787207\pi$
$887$	−4.91204	+	4.91204i	−0.164930	+	0.164930i	0.619817	+	0.784747i	$0.287207\pi$
$888$		0			0
$889$	19.9993			0.670755
$890$		0			0
$891$	−3.33354	+	3.33354i	−0.111678	+	0.111678i
$892$		0			0
$893$	−14.4467			−0.483440
$894$		0			0
$895$	−15.0659	−	36.0881i	−0.503596	−	1.20629i
$896$		0			0
$897$	18.1116	−	18.1116i	0.604729	−	0.604729i
$898$		0			0
$899$	1.51134	−	1.51134i	0.0504059	−	0.0504059i
$900$		0			0
$901$	3.69497	+	3.69497i	0.123097	+	0.123097i
$902$		0			0
$903$	10.7355	+	10.7355i	0.357254	+	0.357254i
$904$		0			0
$905$	27.9852	−	11.6831i	0.930259	−	0.388359i
$906$		0			0
$907$		−	39.4081i		−	1.30852i	−0.756268	−	0.654262i	$-0.772979\pi$
$907$		−	39.4081i		−	1.30852i	0.756268	−	0.654262i	$-0.227021\pi$
$908$		0			0
$909$	6.69380	+	6.69380i	0.222019	+	0.222019i
$910$		0			0
$911$		−	7.29607i		−	0.241729i	−0.992669	−	0.120865i	$-0.961433\pi$
$911$		−	7.29607i		−	0.241729i	0.992669	−	0.120865i	$-0.0385667\pi$
$912$		0			0
$913$	−28.9256	−	28.9256i	−0.957298	−	0.957298i
$914$		0			0
$915$	−21.0839	+	8.80197i	−0.697012	+	0.290984i
$916$		0			0
$917$	14.7122			0.485840
$918$		0			0
$919$			52.5346i			1.73296i	0.499215	+	0.866478i	$0.333622\pi$
$919$			52.5346i			1.73296i	−0.499215	+	0.866478i	$0.666378\pi$
$920$		0			0
$921$			3.84487i			0.126693i
$922$		0			0
$923$	15.7654			0.518926
$924$		0			0
$925$	−7.37012	−	7.28862i	−0.242328	−	0.239648i
$926$		0			0
$927$	−13.4242	−	13.4242i	−0.440907	−	0.440907i
$928$		0			0
$929$			48.7878i			1.60068i	0.599549	+	0.800338i	$0.295346\pi$
$929$			48.7878i			1.60068i	−0.599549	+	0.800338i	$0.704654\pi$
$930$		0			0
$931$	−1.38007	−	1.38007i	−0.0452299	−	0.0452299i
$932$		0			0
$933$		−	4.07103i		−	0.133279i
$934$		0			0
$935$	32.1472	+	13.2112i	1.05133	+	0.432054i
$936$		0			0
$937$	29.3163	+	29.3163i	0.957722	+	0.957722i	0.999142	−	0.0414198i	$-0.0131881\pi$
$937$	29.3163	+	29.3163i	0.957722	+	0.957722i	−0.0414198	+	0.999142i	$0.513188\pi$
$938$		0			0
$939$	−1.37922	−	1.37922i	−0.0450093	−	0.0450093i
$940$		0			0
$941$	−7.65378	+	7.65378i	−0.249506	+	0.249506i	−0.820768	−	0.571262i	$-0.806454\pi$
$941$	−7.65378	+	7.65378i	−0.249506	+	0.249506i	0.571262	+	0.820768i	$0.306454\pi$
$942$		0			0
$943$	32.1289	−	32.1289i	1.04626	−	1.04626i
$944$		0			0
$945$	−6.07029	+	2.53419i	−0.197467	+	0.0824372i
$946$		0			0
$947$	−39.6694			−1.28908			−0.644541	−	0.764569i	$-0.722952\pi$
$947$	−39.6694			−1.28908			−0.644541	+	0.764569i	$0.722952\pi$
$948$		0			0
$949$	45.1116	−	45.1116i	1.46438	−	1.46438i
$950$		0			0
$951$	−9.80915			−0.318084
$952$		0			0
$953$	−8.83095	+	8.83095i	−0.286063	+	0.286063i	−0.835521	−	0.549458i	$-0.814834\pi$
$953$	−8.83095	+	8.83095i	−0.286063	+	0.286063i	0.549458	+	0.835521i	$0.314834\pi$
$954$		0			0
$955$	29.9983	+	12.3281i	0.970724	+	0.398929i
$956$		0			0
$957$			3.84148i			0.124177i
$958$		0			0
$959$	−31.3916			−1.01369
$960$		0			0
$961$	24.1198			0.778060
$962$		0			0
$963$			10.9567i			0.353075i
$964$		0			0
$965$	4.90703	−	2.04856i	0.157963	−	0.0659455i
$966$		0			0
$967$	2.42314	−	2.42314i	0.0779231	−	0.0779231i	−0.667071	−	0.744994i	$-0.732452\pi$
$967$	2.42314	−	2.42314i	0.0779231	−	0.0779231i	0.744994	+	0.667071i	$0.232452\pi$
$968$		0			0
$969$	3.89021			0.124972
$970$		0			0
$971$	−21.9788	+	21.9788i	−0.705334	+	0.705334i	−0.965550	−	0.260216i	$-0.916206\pi$
$971$	−21.9788	+	21.9788i	−0.705334	+	0.705334i	0.260216	+	0.965550i	$0.416206\pi$
$972$		0			0
$973$	−11.8263			−0.379132
$974$		0			0
$975$	21.5778	−	21.8191i	0.691044	−	0.698771i
$976$		0			0
$977$	32.7193	−	32.7193i	1.04678	−	1.04678i	0.0479337	−	0.998851i	$-0.484736\pi$
$977$	32.7193	−	32.7193i	1.04678	−	1.04678i	0.998851	−	0.0479337i	$-0.0152636\pi$
$978$		0			0
$979$	−29.0215	+	29.0215i	−0.927531	+	0.927531i
$980$		0			0
$981$	0.643941	+	0.643941i	0.0205595	+	0.0205595i
$982$		0			0
$983$	−27.7480	−	27.7480i	−0.885023	−	0.885023i	0.109017	−	0.994040i	$-0.465230\pi$
$983$	−27.7480	−	27.7480i	−0.885023	−	0.885023i	−0.994040	+	0.109017i	$0.965230\pi$
$984$		0			0
$985$	−7.35318	+	17.8927i	−0.234292	+	0.570108i
$986$		0			0
$987$			36.0188i			1.14649i
$988$		0			0
$989$	15.2300	+	15.2300i	0.484286	+	0.484286i
$990$		0			0
$991$		−	24.6172i		−	0.781991i	−0.920393	−	0.390996i	$-0.872131\pi$
$991$		−	24.6172i		−	0.781991i	0.920393	−	0.390996i	$-0.127869\pi$
$992$		0			0
$993$	−7.17235	−	7.17235i	−0.227608	−	0.227608i
$994$		0			0
$995$	46.1784	+	18.9775i	1.46395	+	0.601627i
$996$		0			0
$997$	−36.9465			−1.17011			−0.585053	−	0.810995i	$-0.698926\pi$
$997$	−36.9465			−1.17011			−0.585053	+	0.810995i	$0.698926\pi$
$998$		0			0
$999$			2.07309i			0.0655897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bc.e.463.3		16
4.3	odd	2		240.2.bc.e.43.4	yes	16
5.2	odd	4		960.2.y.e.847.7		16
8.3	odd	2		1920.2.bc.i.1183.6		16
8.5	even	2		1920.2.bc.j.1183.6		16
12.11	even	2		720.2.bd.f.523.5		16
16.3	odd	4		960.2.y.e.943.7		16
16.5	even	4		1920.2.y.i.223.2		16
16.11	odd	4		1920.2.y.j.223.2		16
16.13	even	4		240.2.y.e.163.1	✓	16
20.7	even	4		240.2.y.e.187.1	yes	16
40.27	even	4		1920.2.y.i.1567.2		16
40.37	odd	4		1920.2.y.j.1567.2		16
48.29	odd	4		720.2.z.f.163.8		16
60.47	odd	4		720.2.z.f.667.8		16
80.27	even	4		1920.2.bc.j.607.6		16
80.37	odd	4		1920.2.bc.i.607.6		16
80.67	even	4	inner	960.2.bc.e.367.3		16
80.77	odd	4		240.2.bc.e.67.4	yes	16
240.77	even	4		720.2.bd.f.307.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.1	✓	16	16.13	even	4
240.2.y.e.187.1	yes	16	20.7	even	4
240.2.bc.e.43.4	yes	16	4.3	odd	2
240.2.bc.e.67.4	yes	16	80.77	odd	4
720.2.z.f.163.8		16	48.29	odd	4
720.2.z.f.667.8		16	60.47	odd	4
720.2.bd.f.307.5		16	240.77	even	4
720.2.bd.f.523.5		16	12.11	even	2
960.2.y.e.847.7		16	5.2	odd	4
960.2.y.e.943.7		16	16.3	odd	4
960.2.bc.e.367.3		16	80.67	even	4	inner
960.2.bc.e.463.3		16	1.1	even	1	trivial
1920.2.y.i.223.2		16	16.5	even	4
1920.2.y.i.1567.2		16	40.27	even	4
1920.2.y.j.223.2		16	16.11	odd	4
1920.2.y.j.1567.2		16	40.37	odd	4
1920.2.bc.i.607.6		16	80.37	odd	4
1920.2.bc.i.1183.6		16	8.3	odd	2
1920.2.bc.j.607.6		16	80.27	even	4
1920.2.bc.j.1183.6		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{3} +(-0.849960 + 2.06823i) q^{5} +(2.08016 - 2.08016i) q^{7} -1.00000 q^{9} +(-3.33354 + 3.33354i) q^{11} -6.13735 q^{13} +(2.06823 + 0.849960i) q^{15} +(-2.33136 + 2.33136i) q^{17} +(0.834324 - 0.834324i) q^{19} +(-2.08016 - 2.08016i) q^{21} +(-2.95105 - 2.95105i) q^{23} +(-3.55514 - 3.51582i) q^{25} +1.00000i q^{27} +(0.576185 + 0.576185i) q^{29} -2.62300i q^{31} +(3.33354 + 3.33354i) q^{33} +(2.53419 + 6.07029i) q^{35} +2.07309 q^{37} +6.13735i q^{39} +10.8873i q^{41} -5.16088 q^{43} +(0.849960 - 2.06823i) q^{45} +(-8.65772 - 8.65772i) q^{47} -1.65411i q^{49} +(2.33136 + 2.33136i) q^{51} -1.58490i q^{53} +(-4.06115 - 9.72791i) q^{55} +(-0.834324 - 0.834324i) q^{57} +(2.32603 + 2.32603i) q^{59} +(-7.22499 + 7.22499i) q^{61} +(-2.08016 + 2.08016i) q^{63} +(5.21651 - 12.6934i) q^{65} +0.885549 q^{67} +(-2.95105 + 2.95105i) q^{69} -2.56877 q^{71} +(-7.35033 + 7.35033i) q^{73} +(-3.51582 + 3.55514i) q^{75} +13.8686i q^{77} -7.72612 q^{79} +1.00000 q^{81} +8.67714i q^{83} +(-2.84022 - 6.80334i) q^{85} +(0.576185 - 0.576185i) q^{87} +8.70590 q^{89} +(-12.7667 + 12.7667i) q^{91} -2.62300 q^{93} +(1.01643 + 2.43472i) q^{95} +(11.9985 - 11.9985i) q^{97} +(3.33354 - 3.33354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 4 q^{7} - 16 q^{9} - 8 q^{13} - 4 q^{15} - 8 q^{17} + 8 q^{19} - 4 q^{21} - 32 q^{25} - 12 q^{29} - 12 q^{35} - 24 q^{37} - 24 q^{43} + 8 q^{45} - 32 q^{47} + 8 q^{51} + 4 q^{55} - 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 4 * q^7 - 16 * q^9 - 8 * q^13 - 4 * q^15 - 8 * q^17 + 8 * q^19 - 4 * q^21 - 32 * q^25 - 12 * q^29 - 12 * q^35 - 24 * q^37 - 24 * q^43 + 8 * q^45 - 32 * q^47 + 8 * q^51 + 4 * q^55 - 8 * q^57 - 24 * q^59 + 40 * q^61 - 4 * q^63 - 4 * q^65 - 16 * q^67 - 8 * q^73 - 24 * q^75 - 48 * q^79 + 16 * q^81 - 8 * q^85 - 12 * q^87 + 40 * q^91 - 32 * q^93 + 8 * q^95 + 48 * q^97

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