LMFDB - Embedded newform 320.2.o.e.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,2,Mod(223,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("320.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.1
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	320.223
Dual form			320.2.o.e.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18890 - 2.18890i) q^{3} +(0.456850 + 2.18890i) q^{5} +(1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +O(q^{10})$	\(q+(-2.18890 - 2.18890i) q^{3} +(0.456850 + 2.18890i) q^{5} +(1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +0.913701 q^{11} +(1.73205 - 1.73205i) q^{13} +(3.79129 - 5.79129i) q^{15} +(3.00000 - 3.00000i) q^{17} +3.46410i q^{19} -7.84190i q^{21} +(3.79129 - 3.79129i) q^{23} +(-4.58258 + 2.00000i) q^{25} +(7.84190 - 7.84190i) q^{27} +5.29150 q^{29} +7.58258i q^{31} +(-2.00000 - 2.00000i) q^{33} +(-3.10260 + 4.73930i) q^{35} +(5.19615 + 5.19615i) q^{37} -7.58258 q^{39} +1.58258 q^{41} +(-0.361500 - 0.361500i) q^{43} +(-14.4086 + 3.00725i) q^{45} +(-3.79129 - 3.79129i) q^{47} -0.582576i q^{49} -13.1334 q^{51} +(-2.64575 + 2.64575i) q^{53} +(0.417424 + 2.00000i) q^{55} +(7.58258 - 7.58258i) q^{57} +5.29150i q^{59} +6.20520i q^{61} +(-11.7913 + 11.7913i) q^{63} +(4.58258 + 3.00000i) q^{65} +(0.361500 - 0.361500i) q^{67} -16.5975 q^{69} +4.41742i q^{71} +(-8.58258 - 8.58258i) q^{73} +(14.4086 + 5.65300i) q^{75} +(1.63670 + 1.63670i) q^{77} +12.0000 q^{79} -14.5826 q^{81} +(-3.10260 - 3.10260i) q^{83} +(7.93725 + 5.19615i) q^{85} +(-11.5826 - 11.5826i) q^{87} -15.1652i q^{89} +6.20520 q^{91} +(16.5975 - 16.5975i) q^{93} +(-7.58258 + 1.58258i) q^{95} +(-8.58258 + 8.58258i) q^{97} +6.01450i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^7	$ 8 q - 4 q^{7} + 12 q^{15} + 24 q^{17} + 12 q^{23} - 16 q^{33} - 24 q^{39} - 24 q^{41} - 12 q^{47} + 40 q^{55} + 24 q^{57} - 76 q^{63} - 32 q^{73} + 96 q^{79} - 80 q^{81} - 56 q^{87} - 24 q^{95} - 32 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 + 12 * q^15 + 24 * q^17 + 12 * q^23 - 16 * q^33 - 24 * q^39 - 24 * q^41 - 12 * q^47 + 40 * q^55 + 24 * q^57 - 76 * q^63 - 32 * q^73 + 96 * q^79 - 80 * q^81 - 56 * q^87 - 24 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−2.18890	−	2.18890i	−1.26376	−	1.26376i	−0.949255	−	0.314508i	$-0.898161\pi$
$3$	−2.18890	−	2.18890i	−1.26376	−	1.26376i	−0.314508	−	0.949255i	$-0.601839\pi$
$4$		0			0
$5$	0.456850	+	2.18890i	0.204310	+	0.978906i
$5$	0.456850	+	2.18890i	0.204310	+	0.978906i
$6$		0			0
$7$	1.79129	+	1.79129i	0.677043	+	0.677043i	0.959330	−	0.282287i	$-0.0910930\pi$
$7$	1.79129	+	1.79129i	0.677043	+	0.677043i	−0.282287	+	0.959330i	$0.591093\pi$
$8$		0			0
$9$			6.58258i			2.19419i
$10$		0			0
$11$	0.913701			0.275491			0.137746	−	0.990468i	$-0.456014\pi$
$11$	0.913701			0.275491			0.137746	+	0.990468i	$0.456014\pi$
$12$		0			0
$13$	1.73205	−	1.73205i	0.480384	−	0.480384i	−0.424870	−	0.905254i	$-0.639680\pi$
$13$	1.73205	−	1.73205i	0.480384	−	0.480384i	0.905254	+	0.424870i	$0.139680\pi$
$14$		0			0
$15$	3.79129	−	5.79129i	0.978906	−	1.49530i
$16$		0			0
$17$	3.00000	−	3.00000i	0.727607	−	0.727607i	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	3.00000	−	3.00000i	0.727607	−	0.727607i	0.970143	+	0.242536i	$0.0779791\pi$
$18$		0			0
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$		−	7.84190i		−	1.71124i
$22$		0			0
$23$	3.79129	−	3.79129i	0.790538	−	0.790538i	−0.191043	−	0.981582i	$-0.561187\pi$
$23$	3.79129	−	3.79129i	0.790538	−	0.790538i	0.981582	+	0.191043i	$0.0611871\pi$
$24$		0			0
$25$	−4.58258	+	2.00000i	−0.916515	+	0.400000i
$26$		0			0
$27$	7.84190	−	7.84190i	1.50918	−	1.50918i
$28$		0			0
$29$	5.29150			0.982607			0.491304	−	0.870988i	$-0.336521\pi$
$29$	5.29150			0.982607			0.491304	+	0.870988i	$0.336521\pi$
$30$		0			0
$31$			7.58258i			1.36187i	0.732343	+	0.680935i	$0.238427\pi$
$31$			7.58258i			1.36187i	−0.732343	+	0.680935i	$0.761573\pi$
$32$		0			0
$33$	−2.00000	−	2.00000i	−0.348155	−	0.348155i
$34$		0			0
$35$	−3.10260	+	4.73930i	−0.524435	+	0.801088i
$36$		0			0
$37$	5.19615	+	5.19615i	0.854242	+	0.854242i	0.990652	−	0.136410i	$-0.0435565\pi$
$37$	5.19615	+	5.19615i	0.854242	+	0.854242i	−0.136410	+	0.990652i	$0.543557\pi$
$38$		0			0
$39$	−7.58258			−1.21418
$40$		0			0
$41$	1.58258			0.247157			0.123578	−	0.992335i	$-0.460563\pi$
$41$	1.58258			0.247157			0.123578	+	0.992335i	$0.460563\pi$
$42$		0			0
$43$	−0.361500	−	0.361500i	−0.0551282	−	0.0551282i	0.679005	−	0.734133i	$-0.262411\pi$
$43$	−0.361500	−	0.361500i	−0.0551282	−	0.0551282i	−0.734133	+	0.679005i	$0.762411\pi$
$44$		0			0
$45$	−14.4086	+	3.00725i	−2.14791	+	0.448295i
$46$		0			0
$47$	−3.79129	−	3.79129i	−0.553016	−	0.553016i	0.374294	−	0.927310i	$-0.377885\pi$
$47$	−3.79129	−	3.79129i	−0.553016	−	0.553016i	−0.927310	+	0.374294i	$0.877885\pi$
$48$		0			0
$49$		−	0.582576i		−	0.0832251i
$50$		0			0
$51$	−13.1334			−1.83904
$52$		0			0
$53$	−2.64575	+	2.64575i	−0.363422	+	0.363422i	−0.865071	−	0.501649i	$-0.832727\pi$
$53$	−2.64575	+	2.64575i	−0.363422	+	0.363422i	0.501649	+	0.865071i	$0.332727\pi$
$54$		0			0
$55$	0.417424	+	2.00000i	0.0562855	+	0.269680i
$56$		0			0
$57$	7.58258	−	7.58258i	1.00434	−	1.00434i
$58$		0			0
$59$			5.29150i			0.688895i	0.938806	+	0.344447i	$0.111934\pi$
$59$			5.29150i			0.688895i	−0.938806	+	0.344447i	$0.888066\pi$
$60$		0			0
$61$			6.20520i			0.794495i	0.917712	+	0.397247i	$0.130035\pi$
$61$			6.20520i			0.794495i	−0.917712	+	0.397247i	$0.869965\pi$
$62$		0			0
$63$	−11.7913	+	11.7913i	−1.48556	+	1.48556i
$64$		0			0
$65$	4.58258	+	3.00000i	0.568399	+	0.372104i
$66$		0			0
$67$	0.361500	−	0.361500i	0.0441643	−	0.0441643i	−0.684680	−	0.728844i	$-0.740058\pi$
$67$	0.361500	−	0.361500i	0.0441643	−	0.0441643i	0.728844	+	0.684680i	$0.240058\pi$
$68$		0			0
$69$	−16.5975			−1.99811
$70$		0			0
$71$			4.41742i			0.524252i	0.965034	+	0.262126i	$0.0844236\pi$
$71$			4.41742i			0.524252i	−0.965034	+	0.262126i	$0.915576\pi$
$72$		0			0
$73$	−8.58258	−	8.58258i	−1.00451	−	1.00451i	−0.999990	−	0.00452474i	$-0.998560\pi$
$73$	−8.58258	−	8.58258i	−1.00451	−	1.00451i	−0.00452474	−	0.999990i	$-0.501440\pi$
$74$		0			0
$75$	14.4086	+	5.65300i	1.66376	+	0.652753i
$76$		0			0
$77$	1.63670	+	1.63670i	0.186519	+	0.186519i
$78$		0			0
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$		0			0
$81$	−14.5826			−1.62029
$82$		0			0
$83$	−3.10260	−	3.10260i	−0.340555	−	0.340555i	0.516021	−	0.856576i	$-0.327413\pi$
$83$	−3.10260	−	3.10260i	−0.340555	−	0.340555i	−0.856576	+	0.516021i	$0.827413\pi$
$84$		0			0
$85$	7.93725	+	5.19615i	0.860916	+	0.563602i
$86$		0			0
$87$	−11.5826	−	11.5826i	−1.24178	−	1.24178i
$88$		0			0
$89$		−	15.1652i		−	1.60750i	−0.594965	−	0.803751i	$-0.702834\pi$
$89$		−	15.1652i		−	1.60750i	0.594965	−	0.803751i	$-0.297166\pi$
$90$		0			0
$91$	6.20520			0.650482
$92$		0			0
$93$	16.5975	−	16.5975i	1.72108	−	1.72108i
$94$		0			0
$95$	−7.58258	+	1.58258i	−0.777956	+	0.162369i
$96$		0			0
$97$	−8.58258	+	8.58258i	−0.871429	+	0.871429i	−0.992628	−	0.121200i	$-0.961326\pi$
$97$	−8.58258	+	8.58258i	−0.871429	+	0.871429i	0.121200	+	0.992628i	$0.461326\pi$
$98$		0			0
$99$			6.01450i			0.604480i
$100$		0			0
$101$		−	17.5112i		−	1.74243i	−0.490901	−	0.871215i	$-0.663332\pi$
$101$		−	17.5112i		−	1.74243i	0.490901	−	0.871215i	$-0.336668\pi$
$102$		0			0
$103$	−3.37386	+	3.37386i	−0.332437	+	0.332437i	−0.853511	−	0.521075i	$-0.825531\pi$
$103$	−3.37386	+	3.37386i	−0.332437	+	0.332437i	0.521075	+	0.853511i	$0.325531\pi$
$104$		0			0
$105$	17.1652	−	3.58258i	1.67515	−	0.349624i
$106$		0			0
$107$	0.361500	−	0.361500i	0.0349475	−	0.0349475i	−0.689417	−	0.724365i	$-0.742133\pi$
$107$	0.361500	−	0.361500i	0.0349475	−	0.0349475i	0.724365	+	0.689417i	$0.242133\pi$
$108$		0			0
$109$	−9.66930			−0.926151			−0.463076	−	0.886319i	$-0.653254\pi$
$109$	−9.66930			−0.926151			−0.463076	+	0.886319i	$0.653254\pi$
$110$		0			0
$111$		−	22.7477i		−	2.15912i
$112$		0			0
$113$	4.58258	+	4.58258i	0.431092	+	0.431092i	0.889000	−	0.457907i	$-0.151401\pi$
$113$	4.58258	+	4.58258i	0.431092	+	0.431092i	−0.457907	+	0.889000i	$0.651401\pi$
$114$		0			0
$115$	10.0308	+	6.56670i	0.935377	+	0.612348i
$116$		0			0
$117$	11.4014	+	11.4014i	1.05406	+	1.05406i
$118$		0			0
$119$	10.7477			0.985243
$120$		0			0
$121$	−10.1652			−0.924105
$122$		0			0
$123$	−3.46410	−	3.46410i	−0.312348	−	0.312348i
$124$		0			0
$125$	−6.47135	−	9.11710i	−0.578815	−	0.815459i
$126$		0			0
$127$	5.79129	+	5.79129i	0.513894	+	0.513894i	0.915717	−	0.401823i	$-0.131623\pi$
$127$	5.79129	+	5.79129i	0.513894	+	0.513894i	−0.401823	+	0.915717i	$0.631623\pi$
$128$		0			0
$129$			1.58258i			0.139338i
$130$		0			0
$131$	−6.01450			−0.525490			−0.262745	−	0.964865i	$-0.584628\pi$
$131$	−6.01450			−0.525490			−0.262745	+	0.964865i	$0.584628\pi$
$132$		0			0
$133$	−6.20520	+	6.20520i	−0.538059	+	0.538059i
$134$		0			0
$135$	20.7477	+	13.5826i	1.78568	+	1.16900i
$136$		0			0
$137$	−6.16515	+	6.16515i	−0.526724	+	0.526724i	−0.919594	−	0.392870i	$-0.871482\pi$
$137$	−6.16515	+	6.16515i	−0.526724	+	0.526724i	0.392870	+	0.919594i	$0.371482\pi$
$138$		0			0
$139$		−	22.8027i		−	1.93410i	−0.254585	−	0.967050i	$-0.581939\pi$
$139$		−	22.8027i		−	1.93410i	0.254585	−	0.967050i	$-0.418061\pi$
$140$		0			0
$141$			16.5975i			1.39776i
$142$		0			0
$143$	1.58258	−	1.58258i	0.132342	−	0.132342i
$144$		0			0
$145$	2.41742	+	11.5826i	0.200756	+	0.961881i
$146$		0			0
$147$	−1.27520	+	1.27520i	−0.105177	+	0.105177i
$148$		0			0
$149$	0.913701			0.0748533			0.0374266	−	0.999299i	$-0.488084\pi$
$149$	0.913701			0.0748533			0.0374266	+	0.999299i	$0.488084\pi$
$150$		0			0
$151$			14.7477i			1.20015i	0.799943	+	0.600077i	$0.204863\pi$
$151$			14.7477i			1.20015i	−0.799943	+	0.600077i	$0.795137\pi$
$152$		0			0
$153$	19.7477	+	19.7477i	1.59651	+	1.59651i
$154$		0			0
$155$	−16.5975	+	3.46410i	−1.33314	+	0.278243i
$156$		0			0
$157$	4.47315	+	4.47315i	0.356996	+	0.356996i	0.862705	−	0.505708i	$-0.168769\pi$
$157$	4.47315	+	4.47315i	0.356996	+	0.356996i	−0.505708	+	0.862705i	$0.668769\pi$
$158$		0			0
$159$	11.5826			0.918558
$160$		0			0
$161$	13.5826			1.07046
$162$		0			0
$163$	−0.361500	−	0.361500i	−0.0283149	−	0.0283149i	0.692808	−	0.721122i	$-0.256374\pi$
$163$	−0.361500	−	0.361500i	−0.0283149	−	0.0283149i	−0.721122	+	0.692808i	$0.756374\pi$
$164$		0			0
$165$	3.46410	−	5.29150i	0.269680	−	0.411943i
$166$		0			0
$167$	−15.7913	−	15.7913i	−1.22197	−	1.22197i	−0.966932	−	0.255035i	$-0.917913\pi$
$167$	−15.7913	−	15.7913i	−1.22197	−	1.22197i	−0.255035	−	0.966932i	$-0.582087\pi$
$168$		0			0
$169$			7.00000i			0.538462i
$170$		0			0
$171$	−22.8027			−1.74377
$172$		0			0
$173$	−8.66025	+	8.66025i	−0.658427	+	0.658427i	−0.955008	−	0.296581i	$-0.904154\pi$
$173$	−8.66025	+	8.66025i	−0.658427	+	0.658427i	0.296581	+	0.955008i	$0.404154\pi$
$174$		0			0
$175$	−11.7913	−	4.62614i	−0.891338	−	0.349703i
$176$		0			0
$177$	11.5826	−	11.5826i	0.870600	−	0.870600i
$178$		0			0
$179$		−	19.1479i		−	1.43118i	−0.698520	−	0.715591i	$-0.746157\pi$
$179$		−	19.1479i		−	1.43118i	0.698520	−	0.715591i	$-0.253843\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$		0			0
$183$	13.5826	−	13.5826i	1.00405	−	1.00405i
$184$		0			0
$185$	−9.00000	+	13.7477i	−0.661693	+	1.01075i
$186$		0			0
$187$	2.74110	−	2.74110i	0.200449	−	0.200449i
$188$		0			0
$189$	28.0942			2.04355
$190$		0			0
$191$		−	4.41742i		−	0.319634i	−0.987147	−	0.159817i	$-0.948910\pi$
$191$		−	4.41742i		−	0.319634i	0.987147	−	0.159817i	$-0.0510903\pi$
$192$		0			0
$193$	−4.16515	−	4.16515i	−0.299814	−	0.299814i	0.541127	−	0.840941i	$-0.317998\pi$
$193$	−4.16515	−	4.16515i	−0.299814	−	0.299814i	−0.840941	+	0.541127i	$0.817998\pi$
$194$		0			0
$195$	−3.46410	−	16.5975i	−0.248069	−	1.18857i
$196$		0			0
$197$	−2.64575	−	2.64575i	−0.188502	−	0.188502i	0.606546	−	0.795048i	$-0.292554\pi$
$197$	−2.64575	−	2.64575i	−0.188502	−	0.188502i	−0.795048	+	0.606546i	$0.792554\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$	−1.58258			−0.111626
$202$		0			0
$203$	9.47860	+	9.47860i	0.665268	+	0.665268i
$204$		0			0
$205$	0.723000	+	3.46410i	0.0504965	+	0.241943i
$206$		0			0
$207$	24.9564	+	24.9564i	1.73459	+	1.73459i
$208$		0			0
$209$			3.16515i			0.218938i
$210$		0			0
$211$	23.5257			1.61958			0.809788	−	0.586722i	$-0.199582\pi$
$211$	23.5257			1.61958			0.809788	+	0.586722i	$0.199582\pi$
$212$		0			0
$213$	9.66930	−	9.66930i	0.662530	−	0.662530i
$214$		0			0
$215$	0.626136	−	0.956439i	0.0427022	−	0.0652286i
$216$		0			0
$217$	−13.5826	+	13.5826i	−0.922045	+	0.922045i
$218$		0			0
$219$			37.5728i			2.53894i
$220$		0			0
$221$		−	10.3923i		−	0.699062i
$222$		0			0
$223$	1.37386	−	1.37386i	0.0920007	−	0.0920007i	−0.659609	−	0.751609i	$-0.729278\pi$
$223$	1.37386	−	1.37386i	0.0920007	−	0.0920007i	0.751609	+	0.659609i	$0.229278\pi$
$224$		0			0
$225$	−13.1652	−	30.1652i	−0.877677	−	2.01101i
$226$		0			0
$227$	11.8582	−	11.8582i	0.787057	−	0.787057i	−0.193954	−	0.981011i	$-0.562131\pi$
$227$	11.8582	−	11.8582i	0.787057	−	0.787057i	0.981011	+	0.193954i	$0.0621312\pi$
$228$		0			0
$229$	3.46410			0.228914			0.114457	−	0.993428i	$-0.463487\pi$
$229$	3.46410			0.228914			0.114457	+	0.993428i	$0.463487\pi$
$230$		0			0
$231$		−	7.16515i		−	0.471432i
$232$		0			0
$233$	−12.1652	−	12.1652i	−0.796966	−	0.796966i	0.185650	−	0.982616i	$-0.440561\pi$
$233$	−12.1652	−	12.1652i	−0.796966	−	0.796966i	−0.982616	+	0.185650i	$0.940561\pi$
$234$		0			0
$235$	6.56670	−	10.0308i	0.428364	−	0.654338i
$236$		0			0
$237$	−26.2668	−	26.2668i	−1.70621	−	1.70621i
$238$		0			0
$239$	−15.1652			−0.980952			−0.490476	−	0.871455i	$-0.663177\pi$
$239$	−15.1652			−0.980952			−0.490476	+	0.871455i	$0.663177\pi$
$240$		0			0
$241$	16.7477			1.07882			0.539408	−	0.842045i	$-0.318648\pi$
$241$	16.7477			1.07882			0.539408	+	0.842045i	$0.318648\pi$
$242$		0			0
$243$	8.39410	+	8.39410i	0.538482	+	0.538482i
$244$		0			0
$245$	1.27520	−	0.266150i	0.0814696	−	0.0170037i
$246$		0			0
$247$	6.00000	+	6.00000i	0.381771	+	0.381771i
$248$		0			0
$249$			13.5826i			0.860761i
$250$		0			0
$251$	12.9427			0.816936			0.408468	−	0.912773i	$-0.366063\pi$
$251$	12.9427			0.816936			0.408468	+	0.912773i	$0.366063\pi$
$252$		0			0
$253$	3.46410	−	3.46410i	0.217786	−	0.217786i
$254$		0			0
$255$	−6.00000	−	28.7477i	−0.375735	−	1.80025i
$256$		0			0
$257$	7.74773	−	7.74773i	0.483290	−	0.483290i	−0.422891	−	0.906181i	$-0.638985\pi$
$257$	7.74773	−	7.74773i	0.483290	−	0.483290i	0.906181	+	0.422891i	$0.138985\pi$
$258$		0			0
$259$			18.6156i			1.15672i
$260$		0			0
$261$			34.8317i			2.15603i
$262$		0			0
$263$	14.2087	−	14.2087i	0.876147	−	0.876147i	−0.116987	−	0.993133i	$-0.537324\pi$
$263$	14.2087	−	14.2087i	0.876147	−	0.876147i	0.993133	+	0.116987i	$0.0373235\pi$
$264$		0			0
$265$	−7.00000	−	4.58258i	−0.430007	−	0.281505i
$266$		0			0
$267$	−33.1950	+	33.1950i	−2.03150	+	2.03150i
$268$		0			0
$269$	−13.3241			−0.812385			−0.406193	−	0.913788i	$-0.633144\pi$
$269$	−13.3241			−0.812385			−0.406193	+	0.913788i	$0.633144\pi$
$270$		0			0
$271$			18.7477i			1.13884i	0.822046	+	0.569422i	$0.192833\pi$
$271$			18.7477i			1.13884i	−0.822046	+	0.569422i	$0.807167\pi$
$272$		0			0
$273$	−13.5826	−	13.5826i	−0.822055	−	0.822055i
$274$		0			0
$275$	−4.18710	+	1.82740i	−0.252492	+	0.110196i
$276$		0			0
$277$	−21.7937	−	21.7937i	−1.30945	−	1.30945i	−0.921808	−	0.387646i	$-0.873288\pi$
$277$	−21.7937	−	21.7937i	−1.30945	−	1.30945i	−0.387646	−	0.921808i	$-0.626712\pi$
$278$		0			0
$279$	−49.9129			−2.98821
$280$		0			0
$281$	16.7477			0.999086			0.499543	−	0.866289i	$-0.333501\pi$
$281$	16.7477			0.999086			0.499543	+	0.866289i	$0.333501\pi$
$282$		0			0
$283$	−22.4412	−	22.4412i	−1.33399	−	1.33399i	−0.901765	−	0.432226i	$-0.857728\pi$
$283$	−22.4412	−	22.4412i	−1.33399	−	1.33399i	−0.432226	−	0.901765i	$-0.642272\pi$
$284$		0			0
$285$	20.0616	+	13.1334i	1.18835	+	0.777956i
$286$		0			0
$287$	2.83485	+	2.83485i	0.167336	+	0.167336i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$	37.5728			2.20256
$292$		0			0
$293$	−18.1389	+	18.1389i	−1.05968	+	1.05968i	−0.0615814	+	0.998102i	$0.519614\pi$
$293$	−18.1389	+	18.1389i	−1.05968	+	1.05968i	−0.998102	+	0.0615814i	$0.980386\pi$
$294$		0			0
$295$	−11.5826	+	2.41742i	−0.674364	+	0.140748i
$296$		0			0
$297$	7.16515	−	7.16515i	0.415764	−	0.415764i
$298$		0			0
$299$		−	13.1334i		−	0.759525i
$300$		0			0
$301$		−	1.29510i		−	0.0746484i
$302$		0			0
$303$	−38.3303	+	38.3303i	−2.20202	+	2.20202i
$304$		0			0
$305$	−13.5826	+	2.83485i	−0.777736	+	0.162323i
$306$		0			0
$307$	−6.56670	+	6.56670i	−0.374782	+	0.374782i	−0.869215	−	0.494434i	$-0.835375\pi$
$307$	−6.56670	+	6.56670i	−0.374782	+	0.374782i	0.494434	+	0.869215i	$0.335375\pi$
$308$		0			0
$309$	14.7701			0.840242
$310$		0			0
$311$			19.5826i			1.11043i	0.831708	+	0.555213i	$0.187363\pi$
$311$			19.5826i			1.11043i	−0.831708	+	0.555213i	$0.812637\pi$
$312$		0			0
$313$	−6.58258	−	6.58258i	−0.372069	−	0.372069i	0.496161	−	0.868230i	$-0.334742\pi$
$313$	−6.58258	−	6.58258i	−0.372069	−	0.372069i	−0.868230	+	0.496161i	$0.834742\pi$
$314$		0			0
$315$	−31.1968	−	20.4231i	−1.75774	−	1.15071i
$316$		0			0
$317$	14.1425	+	14.1425i	0.794320	+	0.794320i	0.982193	−	0.187874i	$-0.0601596\pi$
$317$	14.1425	+	14.1425i	0.794320	+	0.794320i	−0.187874	+	0.982193i	$0.560160\pi$
$318$		0			0
$319$	4.83485			0.270700
$320$		0			0
$321$	−1.58258			−0.0883308
$322$		0			0
$323$	10.3923	+	10.3923i	0.578243	+	0.578243i
$324$		0			0
$325$	−4.47315	+	11.4014i	−0.248126	+	0.632433i
$326$		0			0
$327$	21.1652	+	21.1652i	1.17044	+	1.17044i
$328$		0			0
$329$		−	13.5826i		−	0.748832i
$330$		0			0
$331$	−9.66930			−0.531473			−0.265737	−	0.964046i	$-0.585615\pi$
$331$	−9.66930			−0.531473			−0.265737	+	0.964046i	$0.585615\pi$
$332$		0			0
$333$	−34.2041	+	34.2041i	−1.87437	+	1.87437i
$334$		0			0
$335$	0.956439	+	0.626136i	0.0522559	+	0.0342095i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$		−	20.0616i		−	1.08960i
$340$		0			0
$341$			6.92820i			0.375183i
$342$		0			0
$343$	13.5826	−	13.5826i	0.733390	−	0.733390i
$344$		0			0
$345$	−7.58258	−	36.3303i	−0.408232	−	1.95596i
$346$		0			0
$347$	1.27520	−	1.27520i	0.0684564	−	0.0684564i	−0.672050	−	0.740506i	$-0.734586\pi$
$347$	1.27520	−	1.27520i	0.0684564	−	0.0684564i	0.740506	+	0.672050i	$0.234586\pi$
$348$		0			0
$349$	−10.3923			−0.556287			−0.278144	−	0.960539i	$-0.589719\pi$
$349$	−10.3923			−0.556287			−0.278144	+	0.960539i	$0.589719\pi$
$350$		0			0
$351$		−	27.1652i		−	1.44997i
$352$		0			0
$353$	24.1652	+	24.1652i	1.28618	+	1.28618i	0.937088	+	0.349093i	$0.113510\pi$
$353$	24.1652	+	24.1652i	1.28618	+	1.28618i	0.349093	+	0.937088i	$0.386490\pi$
$354$		0			0
$355$	−9.66930	+	2.01810i	−0.513193	+	0.107110i
$356$		0			0
$357$	−23.5257	−	23.5257i	−1.24511	−	1.24511i
$358$		0			0
$359$	−27.1652			−1.43372			−0.716861	−	0.697216i	$-0.754422\pi$
$359$	−27.1652			−1.43372			−0.716861	+	0.697216i	$0.754422\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		0			0
$363$	22.2505	+	22.2505i	1.16785	+	1.16785i
$364$		0			0
$365$	14.8655	−	22.7074i	0.778094	−	1.18856i
$366$		0			0
$367$	−16.5390	−	16.5390i	−0.863330	−	0.863330i	0.128394	−	0.991723i	$-0.459018\pi$
$367$	−16.5390	−	16.5390i	−0.863330	−	0.863330i	−0.991723	+	0.128394i	$0.959018\pi$
$368$		0			0
$369$			10.4174i			0.542309i
$370$		0			0
$371$	−9.47860			−0.492105
$372$		0			0
$373$	5.19615	−	5.19615i	0.269047	−	0.269047i	−0.559669	−	0.828716i	$-0.689072\pi$
$373$	5.19615	−	5.19615i	0.269047	−	0.269047i	0.828716	+	0.559669i	$0.189072\pi$
$374$		0			0
$375$	−5.79129	+	34.1216i	−0.299061	+	1.76203i
$376$		0			0
$377$	9.16515	−	9.16515i	0.472029	−	0.472029i
$378$		0			0
$379$			10.3923i			0.533817i	0.963722	+	0.266908i	$0.0860021\pi$
$379$			10.3923i			0.533817i	−0.963722	+	0.266908i	$0.913998\pi$
$380$		0			0
$381$		−	25.3531i		−	1.29888i
$382$		0			0
$383$	17.3739	−	17.3739i	0.887763	−	0.887763i	−0.106545	−	0.994308i	$-0.533979\pi$
$383$	17.3739	−	17.3739i	0.887763	−	0.887763i	0.994308	+	0.106545i	$0.0339788\pi$
$384$		0			0
$385$	−2.83485	+	4.33030i	−0.144477	+	0.220693i
$386$		0			0
$387$	2.37960	−	2.37960i	0.120962	−	0.120962i
$388$		0			0
$389$	35.5547			1.80270			0.901348	−	0.433096i	$-0.142579\pi$
$389$	35.5547			1.80270			0.901348	+	0.433096i	$0.142579\pi$
$390$		0			0
$391$		−	22.7477i		−	1.15040i
$392$		0			0
$393$	13.1652	+	13.1652i	0.664094	+	0.664094i
$394$		0			0
$395$	5.48220	+	26.2668i	0.275840	+	1.32163i
$396$		0			0
$397$	7.93725	+	7.93725i	0.398359	+	0.398359i	0.877654	−	0.479295i	$-0.159107\pi$
$397$	7.93725	+	7.93725i	0.398359	+	0.398359i	−0.479295	+	0.877654i	$0.659107\pi$
$398$		0			0
$399$	27.1652			1.35996
$400$		0			0
$401$	−24.3303			−1.21500			−0.607499	−	0.794321i	$-0.707827\pi$
$401$	−24.3303			−1.21500			−0.607499	+	0.794321i	$0.707827\pi$
$402$		0			0
$403$	13.1334	+	13.1334i	0.654222	+	0.654222i
$404$		0			0
$405$	−6.66205	−	31.9198i	−0.331040	−	1.58611i
$406$		0			0
$407$	4.74773	+	4.74773i	0.235336	+	0.235336i
$408$		0			0
$409$		−	16.4174i		−	0.811789i	−0.913920	−	0.405895i	$-0.866960\pi$
$409$		−	16.4174i		−	0.811789i	0.913920	−	0.405895i	$-0.133040\pi$
$410$		0			0
$411$	26.9898			1.33131
$412$		0			0
$413$	−9.47860	+	9.47860i	−0.466412	+	0.466412i
$414$		0			0
$415$	5.37386	−	8.20871i	0.263793	−	0.402950i
$416$		0			0
$417$	−49.9129	+	49.9129i	−2.44424	+	2.44424i
$418$		0			0
$419$		−	20.9753i		−	1.02471i	−0.858773	−	0.512355i	$-0.828773\pi$
$419$		−	20.9753i		−	1.02471i	0.858773	−	0.512355i	$-0.171227\pi$
$420$		0			0
$421$			13.1334i			0.640083i	0.947404	+	0.320042i	$0.103697\pi$
$421$			13.1334i			0.640083i	−0.947404	+	0.320042i	$0.896303\pi$
$422$		0			0
$423$	24.9564	−	24.9564i	1.21342	−	1.21342i
$424$		0			0
$425$	−7.74773	+	19.7477i	−0.375820	+	0.957905i
$426$		0			0
$427$	−11.1153	+	11.1153i	−0.537907	+	0.537907i
$428$		0			0
$429$	−6.92820			−0.334497
$430$		0			0
$431$			10.7477i			0.517700i	0.965918	+	0.258850i	$0.0833435\pi$
$431$			10.7477i			0.517700i	−0.965918	+	0.258850i	$0.916656\pi$
$432$		0			0
$433$	−5.41742	−	5.41742i	−0.260345	−	0.260345i	0.564849	−	0.825194i	$-0.308934\pi$
$433$	−5.41742	−	5.41742i	−0.260345	−	0.260345i	−0.825194	+	0.564849i	$0.808934\pi$
$434$		0			0
$435$	20.0616	−	30.6446i	0.961881	−	1.46930i
$436$		0			0
$437$	13.1334	+	13.1334i	0.628256	+	0.628256i
$438$		0			0
$439$	25.4955			1.21683			0.608416	−	0.793618i	$-0.291805\pi$
$439$	25.4955			1.21683			0.608416	+	0.793618i	$0.291805\pi$
$440$		0			0
$441$	3.83485			0.182612
$442$		0			0
$443$	14.4086	+	14.4086i	0.684574	+	0.684574i	0.961027	−	0.276454i	$-0.0891592\pi$
$443$	14.4086	+	14.4086i	0.684574	+	0.684574i	−0.276454	+	0.961027i	$0.589159\pi$
$444$		0			0
$445$	33.1950	−	6.92820i	1.57359	−	0.328428i
$446$		0			0
$447$	−2.00000	−	2.00000i	−0.0945968	−	0.0945968i
$448$		0			0
$449$		−	19.5826i		−	0.924159i	−0.886839	−	0.462079i	$-0.847103\pi$
$449$		−	19.5826i		−	0.924159i	0.886839	−	0.462079i	$-0.152897\pi$
$450$		0			0
$451$	1.44600			0.0680895
$452$		0			0
$453$	32.2813	−	32.2813i	1.51671	−	1.51671i
$454$		0			0
$455$	2.83485	+	13.5826i	0.132900	+	0.636761i
$456$		0			0
$457$	12.5826	−	12.5826i	0.588588	−	0.588588i	−0.348661	−	0.937249i	$-0.613364\pi$
$457$	12.5826	−	12.5826i	0.588588	−	0.588588i	0.937249	+	0.348661i	$0.113364\pi$
$458$		0			0
$459$		−	47.0514i		−	2.19617i
$460$		0			0
$461$			3.65480i			0.170221i	0.996372	+	0.0851106i	$0.0271243\pi$
$461$			3.65480i			0.170221i	−0.996372	+	0.0851106i	$0.972876\pi$
$462$		0			0
$463$	−12.2087	+	12.2087i	−0.567387	+	0.567387i	−0.931396	−	0.364009i	$-0.881408\pi$
$463$	−12.2087	+	12.2087i	−0.567387	+	0.567387i	0.364009	+	0.931396i	$0.381408\pi$
$464$		0			0
$465$	43.9129	+	28.7477i	2.03641	+	1.33314i
$466$		0			0
$467$	−16.2360	+	16.2360i	−0.751313	+	0.751313i	−0.974724	−	0.223411i	$-0.928281\pi$
$467$	−16.2360	+	16.2360i	−0.751313	+	0.751313i	0.223411	+	0.974724i	$0.428281\pi$
$468$		0			0
$469$	1.29510			0.0598022
$470$		0			0
$471$		−	19.5826i		−	0.902317i
$472$		0			0
$473$	−0.330303	−	0.330303i	−0.0151873	−	0.0151873i
$474$		0			0
$475$	−6.92820	−	15.8745i	−0.317888	−	0.728372i
$476$		0			0
$477$	−17.4159	−	17.4159i	−0.797417	−	0.797417i
$478$		0			0
$479$	33.4955			1.53045			0.765223	−	0.643765i	$-0.222629\pi$
$479$	33.4955			1.53045			0.765223	+	0.643765i	$0.222629\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$	−29.7309	−	29.7309i	−1.35280	−	1.35280i
$484$		0			0
$485$	−22.7074	−	14.8655i	−1.03109	−	0.675006i
$486$		0			0
$487$	−13.3739	−	13.3739i	−0.606028	−	0.606028i	0.335878	−	0.941906i	$-0.390967\pi$
$487$	−13.3739	−	13.3739i	−0.606028	−	0.606028i	−0.941906	+	0.335878i	$0.890967\pi$
$488$		0			0
$489$			1.58258i			0.0715665i
$490$		0			0
$491$	−27.1805			−1.22664			−0.613320	−	0.789835i	$-0.710166\pi$
$491$	−27.1805			−1.22664			−0.613320	+	0.789835i	$0.710166\pi$
$492$		0			0
$493$	15.8745	−	15.8745i	0.714952	−	0.714952i
$494$		0			0
$495$	−13.1652	+	2.74773i	−0.591730	+	0.123501i
$496$		0			0
$497$	−7.91288	+	7.91288i	−0.354941	+	0.354941i
$498$		0			0
$499$			24.2487i			1.08552i	0.839887	+	0.542761i	$0.182621\pi$
$499$			24.2487i			1.08552i	−0.839887	+	0.542761i	$0.817379\pi$
$500$		0			0
$501$			69.1311i			3.08855i
$502$		0			0
$503$	−14.5390	+	14.5390i	−0.648263	+	0.648263i	−0.952573	−	0.304310i	$-0.901574\pi$
$503$	−14.5390	+	14.5390i	−0.648263	+	0.648263i	0.304310	+	0.952573i	$0.401574\pi$
$504$		0			0
$505$	38.3303	−	8.00000i	1.70568	−	0.355995i
$506$		0			0
$507$	15.3223	−	15.3223i	0.680488	−	0.680488i
$508$		0			0
$509$	−3.84550			−0.170449			−0.0852244	−	0.996362i	$-0.527161\pi$
$509$	−3.84550			−0.170449			−0.0852244	+	0.996362i	$0.527161\pi$
$510$		0			0
$511$		−	30.7477i		−	1.36020i
$512$		0			0
$513$	27.1652	+	27.1652i	1.19937	+	1.19937i
$514$		0			0
$515$	−8.92640	−	5.84370i	−0.393344	−	0.257504i
$516$		0			0
$517$	−3.46410	−	3.46410i	−0.152351	−	0.152351i
$518$		0			0
$519$	37.9129			1.66419
$520$		0			0
$521$	−14.8348			−0.649927			−0.324963	−	0.945727i	$-0.605352\pi$
$521$	−14.8348			−0.649927			−0.324963	+	0.945727i	$0.605352\pi$
$522$		0			0
$523$	−23.8872	−	23.8872i	−1.04451	−	1.04451i	−0.998962	−	0.0455529i	$-0.985495\pi$
$523$	−23.8872	−	23.8872i	−1.04451	−	1.04451i	−0.0455529	−	0.998962i	$-0.514505\pi$
$524$		0			0
$525$	15.6838	+	35.9361i	0.684497	+	1.56838i
$526$		0			0
$527$	22.7477	+	22.7477i	0.990907	+	0.990907i
$528$		0			0
$529$		−	5.74773i		−	0.249901i
$530$		0			0
$531$	−34.8317			−1.51157
$532$		0			0
$533$	2.74110	−	2.74110i	0.118730	−	0.118730i
$534$		0			0
$535$	0.956439	+	0.626136i	0.0413505	+	0.0270702i
$536$		0			0
$537$	−41.9129	+	41.9129i	−1.80867	+	1.80867i
$538$		0			0
$539$		−	0.532300i		−	0.0229278i
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−15.1652	+	15.1652i	−0.650799	+	0.650799i
$544$		0			0
$545$	−4.41742	−	21.1652i	−0.189222	−	0.906615i
$546$		0			0
$547$	−23.1642	+	23.1642i	−0.990430	+	0.990430i	−0.999955	−	0.00952449i	$-0.996968\pi$
$547$	−23.1642	+	23.1642i	−0.990430	+	0.990430i	0.00952449	+	0.999955i	$0.496968\pi$
$548$		0			0
$549$	−40.8462			−1.74327
$550$		0			0
$551$			18.3303i			0.780897i
$552$		0			0
$553$	21.4955	+	21.4955i	0.914080	+	0.914080i
$554$		0			0
$555$	49.7925	−	10.3923i	2.11357	−	0.441129i
$556$		0			0
$557$	20.8800	+	20.8800i	0.884712	+	0.884712i	0.994009	−	0.109297i	$-0.0348599\pi$
$557$	20.8800	+	20.8800i	0.884712	+	0.884712i	−0.109297	+	0.994009i	$0.534860\pi$
$558$		0			0
$559$	−1.25227			−0.0529655
$560$		0			0
$561$	−12.0000			−0.506640
$562$		0			0
$563$	11.6675	+	11.6675i	0.491727	+	0.491727i	0.908850	−	0.417123i	$-0.136962\pi$
$563$	11.6675	+	11.6675i	0.491727	+	0.491727i	−0.417123	+	0.908850i	$0.636962\pi$
$564$		0			0
$565$	−7.93725	+	12.1244i	−0.333923	+	0.510075i
$566$		0			0
$567$	−26.1216	−	26.1216i	−1.09700	−	1.09700i
$568$		0			0
$569$			22.7477i			0.953634i	0.879002	+	0.476817i	$0.158210\pi$
$569$			22.7477i			0.953634i	−0.879002	+	0.476817i	$0.841790\pi$
$570$		0			0
$571$	8.22330			0.344135			0.172067	−	0.985085i	$-0.444955\pi$
$571$	8.22330			0.344135			0.172067	+	0.985085i	$0.444955\pi$
$572$		0			0
$573$	−9.66930	+	9.66930i	−0.403941	+	0.403941i
$574$		0			0
$575$	−9.79129	+	24.9564i	−0.408325	+	1.04076i
$576$		0			0
$577$	15.7477	−	15.7477i	0.655586	−	0.655586i	−0.298746	−	0.954333i	$-0.596568\pi$
$577$	15.7477	−	15.7477i	0.655586	−	0.655586i	0.954333	+	0.298746i	$0.0965684\pi$
$578$		0			0
$579$			18.2342i			0.757788i
$580$		0			0
$581$		−	11.1153i		−	0.461141i
$582$		0			0
$583$	−2.41742	+	2.41742i	−0.100119	+	0.100119i
$584$		0			0
$585$	−19.7477	+	30.1652i	−0.816468	+	1.24718i
$586$		0			0
$587$	4.54860	−	4.54860i	0.187741	−	0.187741i	−0.606978	−	0.794719i	$-0.707618\pi$
$587$	4.54860	−	4.54860i	0.187741	−	0.187741i	0.794719	+	0.606978i	$0.207618\pi$
$588$		0			0
$589$	−26.2668			−1.08231
$590$		0			0
$591$			11.5826i			0.476444i
$592$		0			0
$593$	−18.1652	−	18.1652i	−0.745953	−	0.745953i	0.227763	−	0.973717i	$-0.426859\pi$
$593$	−18.1652	−	18.1652i	−0.745953	−	0.745953i	−0.973717	+	0.227763i	$0.926859\pi$
$594$		0			0
$595$	4.91010	+	23.5257i	0.201295	+	0.964460i
$596$		0			0
$597$	8.75560	+	8.75560i	0.358343	+	0.358343i
$598$		0			0
$599$	5.66970			0.231658			0.115829	−	0.993269i	$-0.463048\pi$
$599$	5.66970			0.231658			0.115829	+	0.993269i	$0.463048\pi$
$600$		0			0
$601$	24.7477			1.00948			0.504740	−	0.863271i	$-0.331588\pi$
$601$	24.7477			1.00948			0.504740	+	0.863271i	$0.331588\pi$
$602$		0			0
$603$	2.37960	+	2.37960i	0.0969049	+	0.0969049i
$604$		0			0
$605$	−4.64395	−	22.2505i	−0.188803	−	0.904612i
$606$		0			0
$607$	7.37386	+	7.37386i	0.299296	+	0.299296i	0.840738	−	0.541442i	$-0.182121\pi$
$607$	7.37386	+	7.37386i	0.299296	+	0.299296i	−0.541442	+	0.840738i	$0.682121\pi$
$608$		0			0
$609$		−	41.4955i		−	1.68148i
$610$		0			0
$611$	−13.1334			−0.531321
$612$		0			0
$613$	8.66025	−	8.66025i	0.349784	−	0.349784i	−0.510245	−	0.860029i	$-0.670445\pi$
$613$	8.66025	−	8.66025i	0.349784	−	0.349784i	0.860029	+	0.510245i	$0.170445\pi$
$614$		0			0
$615$	6.00000	−	9.16515i	0.241943	−	0.369575i
$616$		0			0
$617$	3.00000	−	3.00000i	0.120775	−	0.120775i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	3.00000	−	3.00000i	0.120775	−	0.120775i	0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$		−	2.01810i		−	0.0811143i	−0.999177	−	0.0405572i	$-0.987087\pi$
$619$		−	2.01810i		−	0.0811143i	0.999177	−	0.0405572i	$-0.0129133\pi$
$620$		0			0
$621$		−	59.4618i		−	2.38612i
$622$		0			0
$623$	27.1652	−	27.1652i	1.08835	−	1.08835i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$		0			0
$627$	6.92820	−	6.92820i	0.276686	−	0.276686i
$628$		0			0
$629$	31.1769			1.24310
$630$		0			0
$631$		−	17.0780i		−	0.679866i	−0.940450	−	0.339933i	$-0.889596\pi$
$631$		−	17.0780i		−	0.679866i	0.940450	−	0.339933i	$-0.110404\pi$
$632$		0			0
$633$	−51.4955	−	51.4955i	−2.04676	−	2.04676i
$634$		0			0
$635$	−10.0308	+	15.3223i	−0.398060	+	0.608047i
$636$		0			0
$637$	−1.00905	−	1.00905i	−0.0399800	−	0.0399800i
$638$		0			0
$639$	−29.0780			−1.15031
$640$		0			0
$641$	−19.9129			−0.786511			−0.393256	−	0.919429i	$-0.628651\pi$
$641$	−19.9129			−0.786511			−0.393256	+	0.919429i	$0.628651\pi$
$642$		0			0
$643$	10.7538	+	10.7538i	0.424089	+	0.424089i	0.886609	−	0.462520i	$-0.153055\pi$
$643$	10.7538	+	10.7538i	0.424089	+	0.424089i	−0.462520	+	0.886609i	$0.653055\pi$
$644$		0			0
$645$	−3.46410	+	0.723000i	−0.136399	+	0.0284681i
$646$		0			0
$647$	−32.5390	−	32.5390i	−1.27924	−	1.27924i	−0.941093	−	0.338148i	$-0.890200\pi$
$647$	−32.5390	−	32.5390i	−1.27924	−	1.27924i	−0.338148	−	0.941093i	$-0.609800\pi$
$648$		0			0
$649$			4.83485i			0.189784i
$650$		0			0
$651$	59.4618			2.33049
$652$		0			0
$653$	−4.47315	+	4.47315i	−0.175048	+	0.175048i	−0.789193	−	0.614145i	$-0.789501\pi$
$653$	−4.47315	+	4.47315i	−0.175048	+	0.175048i	0.614145	+	0.789193i	$0.289501\pi$
$654$		0			0
$655$	−2.74773	−	13.1652i	−0.107363	−	0.514405i
$656$		0			0
$657$	56.4955	−	56.4955i	2.20410	−	2.20410i
$658$		0			0
$659$		−	38.4865i		−	1.49922i	−0.661879	−	0.749611i	$-0.730241\pi$
$659$		−	38.4865i		−	1.49922i	0.661879	−	0.749611i	$-0.269759\pi$
$660$		0			0
$661$		−	37.9542i		−	1.47625i	−0.674665	−	0.738124i	$-0.735712\pi$
$661$		−	37.9542i		−	1.47625i	0.674665	−	0.738124i	$-0.264288\pi$
$662$		0			0
$663$	−22.7477	+	22.7477i	−0.883449	+	0.883449i
$664$		0			0
$665$	−16.4174	−	10.7477i	−0.636640	−	0.416779i
$666$		0			0
$667$	20.0616	−	20.0616i	0.776789	−	0.776789i
$668$		0			0
$669$	−6.01450			−0.232534
$670$		0			0
$671$			5.66970i			0.218876i
$672$		0			0
$673$	−9.41742	−	9.41742i	−0.363015	−	0.363015i	0.501907	−	0.864922i	$-0.332632\pi$
$673$	−9.41742	−	9.41742i	−0.363015	−	0.363015i	−0.864922	+	0.501907i	$0.832632\pi$
$674$		0			0
$675$	−20.2523	+	51.6199i	−0.779512	+	1.98685i
$676$		0			0
$677$	2.45505	+	2.45505i	0.0943553	+	0.0943553i	0.752709	−	0.658354i	$-0.228747\pi$
$677$	2.45505	+	2.45505i	0.0943553	+	0.0943553i	−0.658354	+	0.752709i	$0.728747\pi$
$678$		0			0
$679$	−30.7477			−1.17999
$680$		0			0
$681$	−51.9129			−1.98931
$682$		0			0
$683$	32.8335	+	32.8335i	1.25634	+	1.25634i	0.952828	+	0.303512i	$0.0981592\pi$
$683$	32.8335	+	32.8335i	1.25634	+	1.25634i	0.303512	+	0.952828i	$0.401841\pi$
$684$		0			0
$685$	−16.3115	−	10.6784i	−0.623229	−	0.407999i
$686$		0			0
$687$	−7.58258	−	7.58258i	−0.289293	−	0.289293i
$688$		0			0
$689$			9.16515i			0.349164i
$690$		0			0
$691$	−15.1515			−0.576391			−0.288195	−	0.957572i	$-0.593055\pi$
$691$	−15.1515			−0.576391			−0.288195	+	0.957572i	$0.593055\pi$
$692$		0			0
$693$	−10.7737	+	10.7737i	−0.409259	+	0.409259i
$694$		0			0
$695$	49.9129	−	10.4174i	1.89330	−	0.395155i
$696$		0			0
$697$	4.74773	−	4.74773i	0.179833	−	0.179833i
$698$		0			0
$699$			53.2566i			2.01435i
$700$		0			0
$701$			25.1624i			0.950371i	0.879886	+	0.475186i	$0.157619\pi$
$701$			25.1624i			0.950371i	−0.879886	+	0.475186i	$0.842381\pi$
$702$		0			0
$703$	−18.0000	+	18.0000i	−0.678883	+	0.678883i
$704$		0			0
$705$	−36.3303	+	7.58258i	−1.36828	+	0.285576i
$706$		0			0
$707$	31.3676	−	31.3676i	1.17970	−	1.17970i
$708$		0			0
$709$	36.6591			1.37676			0.688381	−	0.725349i	$-0.258322\pi$
$709$	36.6591			1.37676			0.688381	+	0.725349i	$0.258322\pi$
$710$		0			0
$711$			78.9909i			2.96239i
$712$		0			0
$713$	28.7477	+	28.7477i	1.07661	+	1.07661i
$714$		0			0
$715$	4.18710	+	2.74110i	0.156589	+	0.102511i
$716$		0			0
$717$	33.1950	+	33.1950i	1.23969	+	1.23969i
$718$		0			0
$719$	−51.8258			−1.93277			−0.966387	−	0.257091i	$-0.917236\pi$
$719$	−51.8258			−1.93277			−0.966387	+	0.257091i	$0.917236\pi$
$720$		0			0
$721$	−12.0871			−0.450148
$722$		0			0
$723$	−36.6591	−	36.6591i	−1.36337	−	1.36337i
$724$		0			0
$725$	−24.2487	+	10.5830i	−0.900575	+	0.393043i
$726$		0			0
$727$	16.9564	+	16.9564i	0.628880	+	0.628880i	0.947786	−	0.318907i	$-0.103316\pi$
$727$	16.9564	+	16.9564i	0.628880	+	0.628880i	−0.318907	+	0.947786i	$0.603316\pi$
$728$		0			0
$729$			7.00000i			0.259259i
$730$		0			0
$731$	−2.16900			−0.0802234
$732$		0			0
$733$	−14.1425	+	14.1425i	−0.522364	+	0.522364i	−0.918285	−	0.395921i	$-0.870425\pi$
$733$	−14.1425	+	14.1425i	−0.522364	+	0.522364i	0.395921	+	0.918285i	$0.370425\pi$
$734$		0			0
$735$	−3.37386	−	2.20871i	−0.124447	−	0.0814696i
$736$		0			0
$737$	0.330303	−	0.330303i	0.0121669	−	0.0121669i
$738$		0			0
$739$			29.7309i			1.09367i	0.837241	+	0.546835i	$0.184167\pi$
$739$			29.7309i			1.09367i	−0.837241	+	0.546835i	$0.815833\pi$
$740$		0			0
$741$		−	26.2668i		−	0.964935i
$742$		0			0
$743$	−21.7913	+	21.7913i	−0.799445	+	0.799445i	−0.983008	−	0.183563i	$-0.941237\pi$
$743$	−21.7913	+	21.7913i	−0.799445	+	0.799445i	0.183563	+	0.983008i	$0.441237\pi$
$744$		0			0
$745$	0.417424	+	2.00000i	0.0152932	+	0.0732743i
$746$		0			0
$747$	20.4231	−	20.4231i	0.747243	−	0.747243i
$748$		0			0
$749$	1.29510			0.0473220
$750$		0			0
$751$		−	41.0780i		−	1.49896i	−0.662028	−	0.749479i	$-0.730304\pi$
$751$		−	41.0780i		−	1.49896i	0.662028	−	0.749479i	$-0.269696\pi$
$752$		0			0
$753$	−28.3303	−	28.3303i	−1.03241	−	1.03241i
$754$		0			0
$755$	−32.2813	+	6.73750i	−1.17484	+	0.245203i
$756$		0			0
$757$	−27.2759	−	27.2759i	−0.991358	−	0.991358i	0.00860486	−	0.999963i	$-0.497261\pi$
$757$	−27.2759	−	27.2759i	−0.991358	−	0.991358i	−0.999963	+	0.00860486i	$0.997261\pi$
$758$		0			0
$759$	−15.1652			−0.550460
$760$		0			0
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$	−17.3205	−	17.3205i	−0.627044	−	0.627044i
$764$		0			0
$765$	−34.2041	+	52.2476i	−1.23665	+	1.88902i
$766$		0			0
$767$	9.16515	+	9.16515i	0.330934	+	0.330934i
$768$		0			0
$769$			17.4955i			0.630902i	0.948942	+	0.315451i	$0.102156\pi$
$769$			17.4955i			0.630902i	−0.948942	+	0.315451i	$0.897844\pi$
$770$		0			0
$771$	−33.9180			−1.22153
$772$		0			0
$773$	−31.4630	+	31.4630i	−1.13164	+	1.13164i	−0.141740	+	0.989904i	$0.545270\pi$
$773$	−31.4630	+	31.4630i	−1.13164	+	1.13164i	−0.989904	+	0.141740i	$0.954730\pi$
$774$		0			0
$775$	−15.1652	−	34.7477i	−0.544748	−	1.24818i
$776$		0			0
$777$	40.7477	−	40.7477i	1.46182	−	1.46182i
$778$		0			0
$779$			5.48220i			0.196420i
$780$		0			0
$781$			4.03620i			0.144427i
$782$		0			0
$783$	41.4955	−	41.4955i	1.48293	−	1.48293i
$784$		0			0
$785$	−7.74773	+	11.8348i	−0.276528	+	0.422404i
$786$		0			0
$787$	−18.9771	+	18.9771i	−0.676461	+	0.676461i	−0.959198	−	0.282737i	$-0.908758\pi$
$787$	−18.9771	+	18.9771i	−0.676461	+	0.676461i	0.282737	+	0.959198i	$0.408758\pi$
$788$		0			0
$789$	−62.2029			−2.21448
$790$		0			0
$791$			16.4174i			0.583736i
$792$		0			0
$793$	10.7477	+	10.7477i	0.381663	+	0.381663i
$794$		0			0
$795$	5.29150	+	25.3531i	0.187670	+	0.899182i
$796$		0			0
$797$	3.17805	+	3.17805i	0.112572	+	0.112572i	0.761149	−	0.648577i	$-0.224635\pi$
$797$	3.17805	+	3.17805i	0.112572	+	0.112572i	−0.648577	+	0.761149i	$0.724635\pi$
$798$		0			0
$799$	−22.7477			−0.804757
$800$		0			0
$801$	99.8258			3.52717
$802$		0			0
$803$	−7.84190	−	7.84190i	−0.276735	−	0.276735i
$804$		0			0
$805$	6.20520	+	29.7309i	0.218705	+	1.04788i
$806$		0			0
$807$	29.1652	+	29.1652i	1.02666	+	1.02666i
$808$		0			0
$809$		−	6.33030i		−	0.222562i	−0.993789	−	0.111281i	$-0.964505\pi$
$809$		−	6.33030i		−	0.222562i	0.993789	−	0.111281i	$-0.0354953\pi$
$810$		0			0
$811$	−49.7925			−1.74845			−0.874226	−	0.485519i	$-0.838631\pi$
$811$	−49.7925			−1.74845			−0.874226	+	0.485519i	$0.838631\pi$
$812$		0			0
$813$	41.0369	−	41.0369i	1.43923	−	1.43923i
$814$		0			0
$815$	0.626136	−	0.956439i	0.0219326	−	0.0335026i
$816$		0			0
$817$	1.25227	−	1.25227i	0.0438115	−	0.0438115i
$818$		0			0
$819$			40.8462i			1.42728i
$820$		0			0
$821$		−	17.8528i		−	0.623067i	−0.950235	−	0.311534i	$-0.899157\pi$
$821$		−	17.8528i		−	0.623067i	0.950235	−	0.311534i	$-0.100843\pi$
$822$		0			0
$823$	7.79129	−	7.79129i	0.271587	−	0.271587i	−0.558152	−	0.829739i	$-0.688489\pi$
$823$	7.79129	−	7.79129i	0.271587	−	0.271587i	0.829739	+	0.558152i	$0.188489\pi$
$824$		0			0
$825$	13.1652	+	5.16515i	0.458352	+	0.179827i
$826$		0			0
$827$	32.6428	−	32.6428i	1.13510	−	1.13510i	0.145786	−	0.989316i	$-0.453429\pi$
$827$	32.6428	−	32.6428i	1.13510	−	1.13510i	0.989316	−	0.145786i	$-0.0465710\pi$
$828$		0			0
$829$	−23.5257			−0.817082			−0.408541	−	0.912740i	$-0.633962\pi$
$829$	−23.5257			−0.817082			−0.408541	+	0.912740i	$0.633962\pi$
$830$		0			0
$831$			95.4083i			3.30968i
$832$		0			0
$833$	−1.74773	−	1.74773i	−0.0605552	−	0.0605552i
$834$		0			0
$835$	27.3513	−	41.7798i	0.946531	−	1.44585i
$836$		0			0
$837$	59.4618	+	59.4618i	2.05530	+	2.05530i
$838$		0			0
$839$	6.33030			0.218546			0.109273	−	0.994012i	$-0.465148\pi$
$839$	6.33030			0.218546			0.109273	+	0.994012i	$0.465148\pi$
$840$		0			0
$841$	−1.00000			−0.0344828
$842$		0			0
$843$	−36.6591	−	36.6591i	−1.26261	−	1.26261i
$844$		0			0
$845$	−15.3223	+	3.19795i	−0.527103	+	0.110013i
$846$		0			0
$847$	−18.2087	−	18.2087i	−0.625659	−	0.625659i
$848$		0			0
$849$			98.2432i			3.37170i
$850$		0			0
$851$	39.4002			1.35062
$852$		0			0
$853$	26.5529	−	26.5529i	0.909153	−	0.909153i	−0.0870511	−	0.996204i	$-0.527744\pi$
$853$	26.5529	−	26.5529i	0.909153	−	0.909153i	0.996204	+	0.0870511i	$0.0277443\pi$
$854$		0			0
$855$	−10.4174	−	49.9129i	−0.356268	−	1.70698i
$856$		0			0
$857$	2.66970	−	2.66970i	0.0911951	−	0.0911951i	−0.660038	−	0.751233i	$-0.729460\pi$
$857$	2.66970	−	2.66970i	0.0911951	−	0.0911951i	0.751233	+	0.660038i	$0.229460\pi$
$858$		0			0
$859$		−	29.7309i		−	1.01441i	−0.861827	−	0.507203i	$-0.830679\pi$
$859$		−	29.7309i		−	1.01441i	0.861827	−	0.507203i	$-0.169321\pi$
$860$		0			0
$861$		−	12.4104i		−	0.422946i
$862$		0			0
$863$	−17.7042	+	17.7042i	−0.602657	+	0.602657i	−0.941017	−	0.338360i	$-0.890128\pi$
$863$	−17.7042	+	17.7042i	−0.602657	+	0.602657i	0.338360	+	0.941017i	$0.390128\pi$
$864$		0			0
$865$	−22.9129	−	15.0000i	−0.779061	−	0.510015i
$866$		0			0
$867$	−2.18890	+	2.18890i	−0.0743390	+	0.0743390i
$868$		0			0
$869$	10.9644			0.371942
$870$		0			0
$871$		−	1.25227i		−	0.0424316i
$872$		0			0
$873$	−56.4955	−	56.4955i	−1.91208	−	1.91208i
$874$		0			0
$875$	4.73930	−	27.9234i	0.160218	−	0.943984i
$876$		0			0
$877$	−35.6501	−	35.6501i	−1.20382	−	1.20382i	−0.972996	−	0.230821i	$-0.925859\pi$
$877$	−35.6501	−	35.6501i	−1.20382	−	1.20382i	−0.230821	−	0.972996i	$-0.574141\pi$
$878$		0			0
$879$	79.4083			2.67838
$880$		0			0
$881$	−46.4174			−1.56384			−0.781921	−	0.623377i	$-0.785760\pi$
$881$	−46.4174			−1.56384			−0.781921	+	0.623377i	$0.785760\pi$
$882$		0			0
$883$	−14.2179	−	14.2179i	−0.478471	−	0.478471i	0.426172	−	0.904642i	$-0.359862\pi$
$883$	−14.2179	−	14.2179i	−0.478471	−	0.478471i	−0.904642	+	0.426172i	$0.859862\pi$
$884$		0			0
$885$	30.6446	+	20.0616i	1.03011	+	0.674364i
$886$		0			0
$887$	0.956439	+	0.956439i	0.0321141	+	0.0321141i	0.722981	−	0.690867i	$-0.242771\pi$
$887$	0.956439	+	0.956439i	0.0321141	+	0.0321141i	−0.690867	+	0.722981i	$0.742771\pi$
$888$		0			0
$889$			20.7477i			0.695856i
$890$		0			0
$891$	−13.3241			−0.446374
$892$		0			0
$893$	13.1334	−	13.1334i	0.439493	−	0.439493i
$894$		0			0
$895$	41.9129	−	8.74773i	1.40099	−	0.292404i
$896$		0			0
$897$	−28.7477	+	28.7477i	−0.959859	+	0.959859i
$898$		0			0
$899$			40.1232i			1.33818i
$900$		0			0
$901$			15.8745i			0.528857i
$902$		0			0
$903$	−2.83485	+	2.83485i	−0.0943379	+	0.0943379i
$904$		0			0
$905$	15.1652	−	3.16515i	0.504107	−	0.105213i
$906$		0			0
$907$	12.7719	−	12.7719i	0.424084	−	0.424084i	−0.462523	−	0.886607i	$-0.653056\pi$
$907$	12.7719	−	12.7719i	0.424084	−	0.424084i	0.886607	+	0.462523i	$0.153056\pi$
$908$		0			0
$909$	115.269			3.82323
$910$		0			0
$911$		−	40.4174i		−	1.33909i	−0.742772	−	0.669545i	$-0.766489\pi$
$911$		−	40.4174i		−	1.33909i	0.742772	−	0.669545i	$-0.233511\pi$
$912$		0			0
$913$	−2.83485	−	2.83485i	−0.0938198	−	0.0938198i
$914$		0			0
$915$	35.9361	+	23.5257i	1.18801	+	0.777736i
$916$		0			0
$917$	−10.7737	−	10.7737i	−0.355779	−	0.355779i
$918$		0			0
$919$	5.66970			0.187026			0.0935130	−	0.995618i	$-0.470190\pi$
$919$	5.66970			0.187026			0.0935130	+	0.995618i	$0.470190\pi$
$920$		0			0
$921$	28.7477			0.947270
$922$		0			0
$923$	7.65120	+	7.65120i	0.251842	+	0.251842i
$924$		0			0
$925$	−34.2041	−	13.4195i	−1.12462	−	0.441229i
$926$		0			0
$927$	−22.2087	−	22.2087i	−0.729430	−	0.729430i
$928$		0			0
$929$			25.9129i			0.850174i	0.905153	+	0.425087i	$0.139756\pi$
$929$			25.9129i			0.850174i	−0.905153	+	0.425087i	$0.860244\pi$
$930$		0			0
$931$	2.01810			0.0661406
$932$		0			0
$933$	42.8643	−	42.8643i	1.40331	−	1.40331i
$934$		0			0
$935$	7.25227	+	4.74773i	0.237175	+	0.155267i
$936$		0			0
$937$	15.8348	−	15.8348i	0.517302	−	0.517302i	−0.399452	−	0.916754i	$-0.630800\pi$
$937$	15.8348	−	15.8348i	0.517302	−	0.517302i	0.916754	+	0.399452i	$0.130800\pi$
$938$		0			0
$939$			28.8172i			0.940414i
$940$		0			0
$941$		−	3.27340i		−	0.106710i	−0.998576	−	0.0533549i	$-0.983009\pi$
$941$		−	3.27340i		−	0.106710i	0.998576	−	0.0533549i	$-0.0169915\pi$
$942$		0			0
$943$	6.00000	−	6.00000i	0.195387	−	0.195387i
$944$		0			0
$945$	12.8348	+	61.4955i	0.417518	+	2.00045i
$946$		0			0
$947$	30.2831	−	30.2831i	0.984069	−	0.984069i	−0.0158061	−	0.999875i	$-0.505031\pi$
$947$	30.2831	−	30.2831i	0.984069	−	0.984069i	0.999875	+	0.0158061i	$0.00503144\pi$
$948$		0			0
$949$	−29.7309			−0.965106
$950$		0			0
$951$		−	61.9129i		−	2.00766i
$952$		0			0
$953$	34.9129	+	34.9129i	1.13094	+	1.13094i	0.990021	+	0.140918i	$0.0450053\pi$
$953$	34.9129	+	34.9129i	1.13094	+	1.13094i	0.140918	+	0.990021i	$0.454995\pi$
$954$		0			0
$955$	9.66930	−	2.01810i	0.312891	−	0.0653042i
$956$		0			0
$957$	−10.5830	−	10.5830i	−0.342100	−	0.342100i
$958$		0			0
$959$	−22.0871			−0.713230
$960$		0			0
$961$	−26.4955			−0.854692
$962$		0			0
$963$	2.37960	+	2.37960i	0.0766816	+	0.0766816i
$964$		0			0
$965$	7.21425	−	11.0200i	0.232235	−	0.354745i
$966$		0			0
$967$	4.20871	+	4.20871i	0.135343	+	0.135343i	0.771533	−	0.636190i	$-0.219490\pi$
$967$	4.20871	+	4.20871i	0.135343	+	0.135343i	−0.636190	+	0.771533i	$0.719490\pi$
$968$		0			0
$969$		−	45.4955i		−	1.46152i
$970$		0			0
$971$	−0.532300			−0.0170823			−0.00854116	−	0.999964i	$-0.502719\pi$
$971$	−0.532300			−0.0170823			−0.00854116	+	0.999964i	$0.502719\pi$
$972$		0			0
$973$	40.8462	−	40.8462i	1.30947	−	1.30947i
$974$		0			0
$975$	34.7477	−	15.1652i	1.11282	−	0.485674i
$976$		0			0
$977$	19.4174	−	19.4174i	0.621218	−	0.621218i	−0.324625	−	0.945843i	$-0.605238\pi$
$977$	19.4174	−	19.4174i	0.621218	−	0.621218i	0.945843	+	0.324625i	$0.105238\pi$
$978$		0			0
$979$		−	13.8564i		−	0.442853i
$980$		0			0
$981$		−	63.6489i		−	2.03215i
$982$		0			0
$983$	23.7042	−	23.7042i	0.756045	−	0.756045i	−0.219555	−	0.975600i	$-0.570460\pi$
$983$	23.7042	−	23.7042i	0.756045	−	0.756045i	0.975600	+	0.219555i	$0.0704604\pi$
$984$		0			0
$985$	4.58258	−	7.00000i	0.146013	−	0.223039i
$986$		0			0
$987$	−29.7309	+	29.7309i	−0.946345	+	0.946345i
$988$		0			0
$989$	−2.74110			−0.0871620
$990$		0			0
$991$			30.7477i			0.976734i	0.872638	+	0.488367i	$0.162407\pi$
$991$			30.7477i			0.976734i	−0.872638	+	0.488367i	$0.837593\pi$
$992$		0			0
$993$	21.1652	+	21.1652i	0.671656	+	0.671656i
$994$		0			0
$995$	−1.82740	−	8.75560i	−0.0579325	−	0.277571i
$996$		0			0
$997$	14.1425	+	14.1425i	0.447896	+	0.447896i	0.894655	−	0.446758i	$-0.147422\pi$
$997$	14.1425	+	14.1425i	0.447896	+	0.447896i	−0.446758	+	0.894655i	$0.647422\pi$
$998$		0			0
$999$	81.4955			2.57840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.o.e.223.1	✓	8
4.3	odd	2		320.2.o.f.223.4	yes	8
5.2	odd	4		320.2.o.f.287.1	yes	8
5.3	odd	4		1600.2.o.e.607.4		8
5.4	even	2		1600.2.o.l.543.4		8
8.3	odd	2		320.2.o.f.223.1	yes	8
8.5	even	2	inner	320.2.o.e.223.4	yes	8
16.3	odd	4		1280.2.n.n.1023.1		8
16.5	even	4		1280.2.n.p.1023.1		8
16.11	odd	4		1280.2.n.n.1023.4		8
16.13	even	4		1280.2.n.p.1023.4		8
20.3	even	4		1600.2.o.l.607.1		8
20.7	even	4	inner	320.2.o.e.287.4	yes	8
20.19	odd	2		1600.2.o.e.543.1		8
40.3	even	4		1600.2.o.l.607.4		8
40.13	odd	4		1600.2.o.e.607.1		8
40.19	odd	2		1600.2.o.e.543.4		8
40.27	even	4	inner	320.2.o.e.287.1	yes	8
40.29	even	2		1600.2.o.l.543.1		8
40.37	odd	4		320.2.o.f.287.4	yes	8
80.27	even	4		1280.2.n.p.767.1		8
80.37	odd	4		1280.2.n.n.767.4		8
80.67	even	4		1280.2.n.p.767.4		8
80.77	odd	4		1280.2.n.n.767.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
320.2.o.e.223.1	✓	8	1.1	even	1	trivial
320.2.o.e.223.4	yes	8	8.5	even	2	inner
320.2.o.e.287.1	yes	8	40.27	even	4	inner
320.2.o.e.287.4	yes	8	20.7	even	4	inner
320.2.o.f.223.1	yes	8	8.3	odd	2
320.2.o.f.223.4	yes	8	4.3	odd	2
320.2.o.f.287.1	yes	8	5.2	odd	4
320.2.o.f.287.4	yes	8	40.37	odd	4
1280.2.n.n.767.1		8	80.77	odd	4
1280.2.n.n.767.4		8	80.37	odd	4
1280.2.n.n.1023.1		8	16.3	odd	4
1280.2.n.n.1023.4		8	16.11	odd	4
1280.2.n.p.767.1		8	80.27	even	4
1280.2.n.p.767.4		8	80.67	even	4
1280.2.n.p.1023.1		8	16.5	even	4
1280.2.n.p.1023.4		8	16.13	even	4
1600.2.o.e.543.1		8	20.19	odd	2
1600.2.o.e.543.4		8	40.19	odd	2
1600.2.o.e.607.1		8	40.13	odd	4
1600.2.o.e.607.4		8	5.3	odd	4
1600.2.o.l.543.1		8	40.29	even	2
1600.2.o.l.543.4		8	5.4	even	2
1600.2.o.l.607.1		8	20.3	even	4
1600.2.o.l.607.4		8	40.3	even	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18890 - 2.18890i) q^{3} +(0.456850 + 2.18890i) q^{5} +(1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +O(q^{10})\)	\(q+(-2.18890 - 2.18890i) q^{3} +(0.456850 + 2.18890i) q^{5} +(1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +0.913701 q^{11} +(1.73205 - 1.73205i) q^{13} +(3.79129 - 5.79129i) q^{15} +(3.00000 - 3.00000i) q^{17} +3.46410i q^{19} -7.84190i q^{21} +(3.79129 - 3.79129i) q^{23} +(-4.58258 + 2.00000i) q^{25} +(7.84190 - 7.84190i) q^{27} +5.29150 q^{29} +7.58258i q^{31} +(-2.00000 - 2.00000i) q^{33} +(-3.10260 + 4.73930i) q^{35} +(5.19615 + 5.19615i) q^{37} -7.58258 q^{39} +1.58258 q^{41} +(-0.361500 - 0.361500i) q^{43} +(-14.4086 + 3.00725i) q^{45} +(-3.79129 - 3.79129i) q^{47} -0.582576i q^{49} -13.1334 q^{51} +(-2.64575 + 2.64575i) q^{53} +(0.417424 + 2.00000i) q^{55} +(7.58258 - 7.58258i) q^{57} +5.29150i q^{59} +6.20520i q^{61} +(-11.7913 + 11.7913i) q^{63} +(4.58258 + 3.00000i) q^{65} +(0.361500 - 0.361500i) q^{67} -16.5975 q^{69} +4.41742i q^{71} +(-8.58258 - 8.58258i) q^{73} +(14.4086 + 5.65300i) q^{75} +(1.63670 + 1.63670i) q^{77} +12.0000 q^{79} -14.5826 q^{81} +(-3.10260 - 3.10260i) q^{83} +(7.93725 + 5.19615i) q^{85} +(-11.5826 - 11.5826i) q^{87} -15.1652i q^{89} +6.20520 q^{91} +(16.5975 - 16.5975i) q^{93} +(-7.58258 + 1.58258i) q^{95} +(-8.58258 + 8.58258i) q^{97} +6.01450i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^7	\( 8 q - 4 q^{7} + 12 q^{15} + 24 q^{17} + 12 q^{23} - 16 q^{33} - 24 q^{39} - 24 q^{41} - 12 q^{47} + 40 q^{55} + 24 q^{57} - 76 q^{63} - 32 q^{73} + 96 q^{79} - 80 q^{81} - 56 q^{87} - 24 q^{95} - 32 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 + 12 * q^15 + 24 * q^17 + 12 * q^23 - 16 * q^33 - 24 * q^39 - 24 * q^41 - 12 * q^47 + 40 * q^55 + 24 * q^57 - 76 * q^63 - 32 * q^73 + 96 * q^79 - 80 * q^81 - 56 * q^87 - 24 * q^95 - 32 * q^97

Introduction

L-functions

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