LMFDB - Embedded newform 460.2.i.a.413.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(137,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("460.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.i (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.11574317056.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 45x^{4} + 4 $ x^8 + 45*x^4 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			413.4
Root			$-1.83051 + 1.83051i$ of defining polynomial
Character	$\chi$	$=$	460.413
Dual form			460.2.i.a.137.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{3} +(1.83051 - 1.28422i) q^{5} +(-1.83051 - 1.83051i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{3} +(1.83051 - 1.28422i) q^{5} +(-1.83051 - 1.83051i) q^{7} -1.00000i q^{9} +3.66103i q^{11} +(-3.70156 - 3.70156i) q^{13} +(-3.11473 - 0.546295i) q^{15} +(-0.737925 - 0.737925i) q^{17} +4.75362 q^{19} +3.66103i q^{21} +(-3.53710 + 3.23866i) q^{23} +(1.70156 - 4.70156i) q^{25} +(-4.00000 + 4.00000i) q^{27} -8.70156i q^{29} -10.1047 q^{31} +(3.66103 - 3.66103i) q^{33} +(-5.70156 - 1.00000i) q^{35} +(-0.737925 - 0.737925i) q^{37} +7.40312i q^{39} +1.29844 q^{41} +(7.86835 - 7.86835i) q^{43} +(-1.28422 - 1.83051i) q^{45} +(6.40312 - 6.40312i) q^{47} -0.298438i q^{49} +1.47585i q^{51} +(-2.92310 + 2.92310i) q^{53} +(4.70156 + 6.70156i) q^{55} +(-4.75362 - 4.75362i) q^{57} +2.70156i q^{59} +12.0757i q^{61} +(-1.83051 + 1.83051i) q^{63} +(-11.5294 - 2.02214i) q^{65} +(-6.58413 - 6.58413i) q^{67} +(6.77576 + 0.298438i) q^{69} +8.70156 q^{71} +(10.4031 + 10.4031i) q^{73} +(-6.40312 + 3.00000i) q^{75} +(6.70156 - 6.70156i) q^{77} +7.70532 q^{79} +5.00000 q^{81} +(1.83051 - 1.83051i) q^{83} +(-2.29844 - 0.403124i) q^{85} +(-8.70156 + 8.70156i) q^{87} +13.9348 q^{89} +13.5515i q^{91} +(10.1047 + 10.1047i) q^{93} +(8.70156 - 6.10469i) q^{95} +(8.25161 + 8.25161i) q^{97} +3.66103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3}+O(q^{10}) $ 8 * q - 8 * q^3	$ 8 q - 8 q^{3} - 4 q^{13} - 14 q^{23} - 12 q^{25} - 32 q^{27} - 4 q^{31} - 20 q^{35} + 36 q^{41} + 12 q^{55} + 44 q^{71} + 32 q^{73} + 28 q^{77} + 40 q^{81} - 44 q^{85} - 44 q^{87} + 4 q^{93} + 44 q^{95}+O(q^{100}) $ 8 * q - 8 * q^3 - 4 * q^13 - 14 * q^23 - 12 * q^25 - 32 * q^27 - 4 * q^31 - 20 * q^35 + 36 * q^41 + 12 * q^55 + 44 * q^71 + 32 * q^73 + 28 * q^77 + 40 * q^81 - 44 * q^85 - 44 * q^87 + 4 * q^93 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$		0			0
$5$	1.83051	−	1.28422i	0.818631	−	0.574320i
$5$	1.83051	−	1.28422i	0.818631	−	0.574320i
$6$		0			0
$7$	−1.83051	−	1.83051i	−0.691869	−	0.691869i	0.270774	−	0.962643i	$-0.412720\pi$
$7$	−1.83051	−	1.83051i	−0.691869	−	0.691869i	−0.962643	+	0.270774i	$0.912720\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			3.66103i			1.10384i	0.833897	+	0.551921i	$0.186105\pi$
$11$			3.66103i			1.10384i	−0.833897	+	0.551921i	$0.813895\pi$
$12$		0			0
$13$	−3.70156	−	3.70156i	−1.02663	−	1.02663i	−0.999636	−	0.0269930i	$-0.991407\pi$
$13$	−3.70156	−	3.70156i	−1.02663	−	1.02663i	−0.0269930	−	0.999636i	$-0.508593\pi$
$14$		0			0
$15$	−3.11473	−	0.546295i	−0.804221	−	0.141053i
$16$		0			0
$17$	−0.737925	−	0.737925i	−0.178973	−	0.178973i	0.611935	−	0.790908i	$-0.290391\pi$
$17$	−0.737925	−	0.737925i	−0.178973	−	0.178973i	−0.790908	+	0.611935i	$0.790391\pi$
$18$		0			0
$19$	4.75362			1.09055			0.545277	−	0.838256i	$-0.316424\pi$
$19$	4.75362			1.09055			0.545277	+	0.838256i	$0.316424\pi$
$20$		0			0
$21$			3.66103i			0.798902i
$22$		0			0
$23$	−3.53710	+	3.23866i	−0.737536	+	0.675308i
$23$	−3.53710	+	3.23866i	−0.737536	+	0.675308i
$24$		0			0
$25$	1.70156	−	4.70156i	0.340312	−	0.940312i
$26$		0			0
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$		−	8.70156i		−	1.61584i	−0.589293	−	0.807920i	$-0.700593\pi$
$29$		−	8.70156i		−	1.61584i	0.589293	−	0.807920i	$-0.299407\pi$
$30$		0			0
$31$	−10.1047			−1.81486			−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−10.1047			−1.81486			−0.907428	+	0.420208i	$0.861957\pi$
$32$		0			0
$33$	3.66103	−	3.66103i	0.637303	−	0.637303i
$34$		0			0
$35$	−5.70156	−	1.00000i	−0.963740	−	0.169031i
$36$		0			0
$37$	−0.737925	−	0.737925i	−0.121314	−	0.121314i	0.643843	−	0.765157i	$-0.277339\pi$
$37$	−0.737925	−	0.737925i	−0.121314	−	0.121314i	−0.765157	+	0.643843i	$0.777339\pi$
$38$		0			0
$39$			7.40312i			1.18545i
$40$		0			0
$41$	1.29844			0.202782			0.101391	−	0.994847i	$-0.467671\pi$
$41$	1.29844			0.202782			0.101391	+	0.994847i	$0.467671\pi$
$42$		0			0
$43$	7.86835	−	7.86835i	1.19991	−	1.19991i	0.225720	−	0.974192i	$-0.427527\pi$
$43$	7.86835	−	7.86835i	1.19991	−	1.19991i	0.974192	−	0.225720i	$-0.0724734\pi$
$44$		0			0
$45$	−1.28422	−	1.83051i	−0.191440	−	0.272877i
$46$		0			0
$47$	6.40312	−	6.40312i	0.933992	−	0.933992i	−0.0639608	−	0.997952i	$-0.520373\pi$
$47$	6.40312	−	6.40312i	0.933992	−	0.933992i	0.997952	+	0.0639608i	$0.0203732\pi$
$48$		0			0
$49$		−	0.298438i		−	0.0426340i
$50$		0			0
$51$			1.47585i			0.206660i
$52$		0			0
$53$	−2.92310	+	2.92310i	−0.401519	+	0.401519i	−0.878768	−	0.477249i	$-0.841634\pi$
$53$	−2.92310	+	2.92310i	−0.401519	+	0.401519i	0.477249	+	0.878768i	$0.341634\pi$
$54$		0			0
$55$	4.70156	+	6.70156i	0.633959	+	0.903638i
$56$		0			0
$57$	−4.75362	−	4.75362i	−0.629632	−	0.629632i
$58$		0			0
$59$			2.70156i			0.351713i	0.984416	+	0.175857i	$0.0562695\pi$
$59$			2.70156i			0.351713i	−0.984416	+	0.175857i	$0.943730\pi$
$60$		0			0
$61$			12.0757i			1.54613i	0.634326	+	0.773066i	$0.281278\pi$
$61$			12.0757i			1.54613i	−0.634326	+	0.773066i	$0.718722\pi$
$62$		0			0
$63$	−1.83051	+	1.83051i	−0.230623	+	0.230623i
$64$		0			0
$65$	−11.5294	−	2.02214i	−1.43004	−	0.250816i
$66$		0			0
$67$	−6.58413	−	6.58413i	−0.804380	−	0.804380i	0.179397	−	0.983777i	$-0.442585\pi$
$67$	−6.58413	−	6.58413i	−0.804380	−	0.804380i	−0.983777	+	0.179397i	$0.942585\pi$
$68$		0			0
$69$	6.77576	+	0.298438i	0.815706	+	0.0359277i
$70$		0			0
$71$	8.70156			1.03269			0.516343	−	0.856382i	$-0.327293\pi$
$71$	8.70156			1.03269			0.516343	+	0.856382i	$0.327293\pi$
$72$		0			0
$73$	10.4031	+	10.4031i	1.21759	+	1.21759i	0.968472	+	0.249121i	$0.0801418\pi$
$73$	10.4031	+	10.4031i	1.21759	+	1.21759i	0.249121	+	0.968472i	$0.419858\pi$
$74$		0			0
$75$	−6.40312	+	3.00000i	−0.739369	+	0.346410i
$76$		0			0
$77$	6.70156	−	6.70156i	0.763714	−	0.763714i
$78$		0			0
$79$	7.70532			0.866916			0.433458	−	0.901174i	$-0.357293\pi$
$79$	7.70532			0.866916			0.433458	+	0.901174i	$0.357293\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	1.83051	−	1.83051i	0.200925	−	0.200925i	−0.599471	−	0.800396i	$-0.704622\pi$
$83$	1.83051	−	1.83051i	0.200925	−	0.200925i	0.800396	+	0.599471i	$0.204622\pi$
$84$		0			0
$85$	−2.29844	−	0.403124i	−0.249301	−	0.0437250i
$86$		0			0
$87$	−8.70156	+	8.70156i	−0.932905	+	0.932905i
$88$		0			0
$89$	13.9348			1.47708			0.738542	−	0.674208i	$-0.235515\pi$
$89$	13.9348			1.47708			0.738542	+	0.674208i	$0.235515\pi$
$90$		0			0
$91$			13.5515i			1.42059i
$92$		0			0
$93$	10.1047	+	10.1047i	1.04781	+	1.04781i
$94$		0			0
$95$	8.70156	−	6.10469i	0.892761	−	0.626328i
$96$		0			0
$97$	8.25161	+	8.25161i	0.837824	+	0.837824i	0.988572	−	0.150748i	$-0.0481683\pi$
$97$	8.25161	+	8.25161i	0.837824	+	0.837824i	−0.150748	+	0.988572i	$0.548168\pi$
$98$		0			0
$99$	3.66103			0.367947
$100$		0			0
$101$	12.1047			1.20446			0.602231	−	0.798322i	$-0.294279\pi$
$101$	12.1047			1.20446			0.602231	+	0.798322i	$0.294279\pi$
$102$		0			0
$103$	3.11473	−	3.11473i	0.306904	−	0.306904i	−0.536804	−	0.843707i	$-0.680368\pi$
$103$	3.11473	−	3.11473i	0.306904	−	0.306904i	0.843707	+	0.536804i	$0.180368\pi$
$104$		0			0
$105$	4.70156	+	6.70156i	0.458825	+	0.654005i
$106$		0			0
$107$	−6.96739	−	6.96739i	−0.673563	−	0.673563i	0.284973	−	0.958536i	$-0.408015\pi$
$107$	−6.96739	−	6.96739i	−0.673563	−	0.673563i	−0.958536	+	0.284973i	$0.908015\pi$
$108$		0			0
$109$	−18.6884			−1.79002			−0.895012	−	0.446042i	$-0.852833\pi$
$109$	−18.6884			−1.79002			−0.895012	+	0.446042i	$0.852833\pi$
$110$		0			0
$111$			1.47585i			0.140081i
$112$		0			0
$113$	6.96739	−	6.96739i	0.655437	−	0.655437i	−0.298860	−	0.954297i	$-0.596606\pi$
$113$	6.96739	−	6.96739i	0.655437	−	0.655437i	0.954297	+	0.298860i	$0.0966064\pi$
$114$		0			0
$115$	−2.31556	+	10.4708i	−0.215927	+	0.976410i
$116$		0			0
$117$	−3.70156	+	3.70156i	−0.342210	+	0.342210i
$118$		0			0
$119$			2.70156i			0.247652i
$120$		0			0
$121$	−2.40312			−0.218466
$122$		0			0
$123$	−1.29844	−	1.29844i	−0.117076	−	0.117076i
$124$		0			0
$125$	−2.92310	−	10.7915i	−0.261450	−	0.965217i
$126$		0			0
$127$	0.298438	−	0.298438i	0.0264821	−	0.0264821i	−0.693742	−	0.720224i	$-0.744039\pi$
$127$	0.298438	−	0.298438i	0.0264821	−	0.0264821i	0.720224	+	0.693742i	$0.244039\pi$
$128$		0			0
$129$	−15.7367			−1.38554
$130$		0			0
$131$	−1.40312			−0.122592			−0.0612958	−	0.998120i	$-0.519523\pi$
$131$	−1.40312			−0.122592			−0.0612958	+	0.998120i	$0.519523\pi$
$132$		0			0
$133$	−8.70156	−	8.70156i	−0.754521	−	0.754521i
$134$		0			0
$135$	−2.18518	+	12.4589i	−0.188070	+	1.07229i
$136$		0			0
$137$	3.11473	+	3.11473i	0.266110	+	0.266110i	0.827530	−	0.561421i	$-0.189745\pi$
$137$	3.11473	+	3.11473i	0.266110	+	0.266110i	−0.561421	+	0.827530i	$0.689745\pi$
$138$		0			0
$139$			2.70156i			0.229144i	0.993415	+	0.114572i	$0.0365496\pi$
$139$			2.70156i			0.229144i	−0.993415	+	0.114572i	$0.963450\pi$
$140$		0			0
$141$	−12.8062			−1.07848
$142$		0			0
$143$	13.5515	−	13.5515i	1.13324	−	1.13324i
$144$		0			0
$145$	−11.1747	−	15.9283i	−0.928009	−	1.32278i
$146$		0			0
$147$	−0.298438	+	0.298438i	−0.0246147	+	0.0246147i
$148$		0			0
$149$	15.7367			1.28920			0.644600	−	0.764520i	$-0.277024\pi$
$149$	15.7367			1.28920			0.644600	+	0.764520i	$0.277024\pi$
$150$		0			0
$151$	−2.59688			−0.211331			−0.105665	−	0.994402i	$-0.533697\pi$
$151$	−2.59688			−0.211331			−0.105665	+	0.994402i	$0.533697\pi$
$152$		0			0
$153$	−0.737925	+	0.737925i	−0.0596577	+	0.0596577i
$154$		0			0
$155$	−18.4968	+	12.9766i	−1.48570	+	1.04231i
$156$		0			0
$157$	6.58413	+	6.58413i	0.525471	+	0.525471i	0.919219	−	0.393748i	$-0.128822\pi$
$157$	6.58413	+	6.58413i	0.525471	+	0.525471i	−0.393748	+	0.919219i	$0.628822\pi$
$158$		0			0
$159$	5.84621			0.463634
$160$		0			0
$161$	12.4031	+	0.546295i	0.977503	+	0.0430541i
$162$		0			0
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	0.483638	−	0.875268i	$-0.339315\pi$
$163$	−5.00000	−	5.00000i	−0.391630	−	0.391630i	−0.875268	+	0.483638i	$0.839315\pi$
$164$		0			0
$165$	2.00000	−	11.4031i	0.155700	−	0.887732i
$166$		0			0
$167$	−3.70156	+	3.70156i	−0.286435	+	0.286435i	−0.835669	−	0.549233i	$-0.814920\pi$
$167$	−3.70156	+	3.70156i	−0.286435	+	0.286435i	0.549233	+	0.835669i	$0.314920\pi$
$168$		0			0
$169$			14.4031i			1.10793i
$170$		0			0
$171$		−	4.75362i		−	0.363518i
$172$		0			0
$173$	−4.40312	−	4.40312i	−0.334763	−	0.334763i	0.519629	−	0.854392i	$-0.326070\pi$
$173$	−4.40312	−	4.40312i	−0.334763	−	0.334763i	−0.854392	+	0.519629i	$0.826070\pi$
$174$		0			0
$175$	−11.7210	+	5.49154i	−0.886025	+	0.415122i
$176$		0			0
$177$	2.70156	−	2.70156i	0.203062	−	0.203062i
$178$		0			0
$179$		−	10.0000i		−	0.747435i	−0.927543	−	0.373718i	$-0.878083\pi$
$179$		−	10.0000i		−	0.747435i	0.927543	−	0.373718i	$-0.121917\pi$
$180$		0			0
$181$		−	9.12397i		−	0.678180i	−0.940754	−	0.339090i	$-0.889881\pi$
$181$		−	9.12397i		−	0.678180i	0.940754	−	0.339090i	$-0.110119\pi$
$182$		0			0
$183$	12.0757	−	12.0757i	0.892659	−	0.892659i
$184$		0			0
$185$	−2.29844	−	0.403124i	−0.168985	−	0.0296383i
$186$		0			0
$187$	2.70156	−	2.70156i	0.197558	−	0.197558i
$188$		0			0
$189$	14.6441			1.06520
$190$		0			0
$191$		−	1.85911i		−	0.134520i	−0.997735	−	0.0672602i	$-0.978574\pi$
$191$		−	1.85911i		−	0.134520i	0.997735	−	0.0672602i	$-0.0214258\pi$
$192$		0			0
$193$	−7.70156	−	7.70156i	−0.554371	−	0.554371i	0.373329	−	0.927699i	$-0.378216\pi$
$193$	−7.70156	−	7.70156i	−0.554371	−	0.554371i	−0.927699	+	0.373329i	$0.878216\pi$
$194$		0			0
$195$	9.50723	+	13.5515i	0.680827	+	0.970445i
$196$		0			0
$197$	−0.403124	+	0.403124i	−0.0287214	+	0.0287214i	−0.721322	−	0.692600i	$-0.756465\pi$
$197$	−0.403124	+	0.403124i	−0.0287214	+	0.0287214i	0.692600	+	0.721322i	$0.256465\pi$
$198$		0			0
$199$	−14.6441			−1.03809			−0.519047	−	0.854746i	$-0.673713\pi$
$199$	−14.6441			−1.03809			−0.519047	+	0.854746i	$0.673713\pi$
$200$		0			0
$201$			13.1683i			0.928818i
$202$		0			0
$203$	−15.9283	+	15.9283i	−1.11795	+	1.11795i
$204$		0			0
$205$	2.37681	−	1.66748i	0.166004	−	0.116462i
$206$		0			0
$207$	3.23866	+	3.53710i	0.225103	+	0.245845i
$208$		0			0
$209$			17.4031i			1.20380i
$210$		0			0
$211$	−12.7016			−0.874412			−0.437206	−	0.899361i	$-0.644032\pi$
$211$	−12.7016			−0.874412			−0.437206	+	0.899361i	$0.644032\pi$
$212$		0			0
$213$	−8.70156	−	8.70156i	−0.596221	−	0.596221i
$214$		0			0
$215$	4.29844	−	24.5078i	0.293151	−	1.67142i
$216$		0			0
$217$	18.4968	+	18.4968i	1.25564	+	1.25564i
$218$		0			0
$219$		−	20.8062i		−	1.40596i
$220$		0			0
$221$			5.46295i			0.367478i
$222$		0			0
$223$	9.10469	+	9.10469i	0.609695	+	0.609695i	0.942866	−	0.333171i	$-0.108119\pi$
$223$	9.10469	+	9.10469i	0.609695	+	0.609695i	−0.333171	+	0.942866i	$0.608119\pi$
$224$		0			0
$225$	−4.70156	−	1.70156i	−0.313437	−	0.113437i
$226$		0			0
$227$	4.59058	+	4.59058i	0.304688	+	0.304688i	0.842845	−	0.538157i	$-0.180879\pi$
$227$	4.59058	+	4.59058i	0.304688	+	0.304688i	−0.538157	+	0.842845i	$0.680879\pi$
$228$		0			0
$229$	−11.3663			−0.751109			−0.375555	−	0.926800i	$-0.622548\pi$
$229$	−11.3663			−0.751109			−0.375555	+	0.926800i	$0.622548\pi$
$230$		0			0
$231$	−13.4031			−0.881861
$232$		0			0
$233$	6.40312	+	6.40312i	0.419483	+	0.419483i	0.885025	−	0.465543i	$-0.154141\pi$
$233$	6.40312	+	6.40312i	0.419483	+	0.419483i	−0.465543	+	0.885025i	$0.654141\pi$
$234$		0			0
$235$	3.49799	−	19.9440i	0.228184	−	1.30100i
$236$		0			0
$237$	−7.70532	−	7.70532i	−0.500514	−	0.500514i
$238$		0			0
$239$		−	12.1047i		−	0.782987i	−0.920181	−	0.391494i	$-0.871959\pi$
$239$		−	12.1047i		−	0.782987i	0.920181	−	0.391494i	$-0.128041\pi$
$240$		0			0
$241$		−	2.18518i		−	0.140760i	−0.997520	−	0.0703799i	$-0.977579\pi$
$241$		−	2.18518i		−	0.140760i	0.997520	−	0.0703799i	$-0.0224211\pi$
$242$		0			0
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$		0			0
$245$	−0.383260	−	0.546295i	−0.0244856	−	0.0349015i
$246$		0			0
$247$	−17.5958	−	17.5958i	−1.11959	−	1.11959i
$248$		0			0
$249$	−3.66103			−0.232008
$250$		0			0
$251$		−	13.5515i		−	0.855364i	−0.903929	−	0.427682i	$-0.859330\pi$
$251$		−	13.5515i		−	0.855364i	0.903929	−	0.427682i	$-0.140670\pi$
$252$		0			0
$253$	−11.8568	−	12.9494i	−0.745432	−	0.814123i
$254$		0			0
$255$	1.89531	+	2.70156i	0.118689	+	0.169178i
$256$		0			0
$257$	14.4031	−	14.4031i	0.898442	−	0.898442i	−0.0968562	−	0.995298i	$-0.530879\pi$
$257$	14.4031	−	14.4031i	0.898442	−	0.898442i	0.995298	+	0.0968562i	$0.0308787\pi$
$258$		0			0
$259$			2.70156i			0.167867i
$260$		0			0
$261$	−8.70156			−0.538613
$262$		0			0
$263$	4.39895	−	4.39895i	0.271251	−	0.271251i	−0.558353	−	0.829604i	$-0.688566\pi$
$263$	4.39895	−	4.39895i	0.271251	−	0.271251i	0.829604	+	0.558353i	$0.188566\pi$
$264$		0			0
$265$	−1.59688	+	9.10469i	−0.0980953	+	0.559296i
$266$		0			0
$267$	−13.9348	−	13.9348i	−0.852795	−	0.852795i
$268$		0			0
$269$		−	30.1047i		−	1.83552i	−0.397141	−	0.917758i	$-0.629998\pi$
$269$		−	30.1047i		−	1.83552i	0.397141	−	0.917758i	$-0.370002\pi$
$270$		0			0
$271$	26.1047			1.58575			0.792873	−	0.609386i	$-0.208584\pi$
$271$	26.1047			1.58575			0.792873	+	0.609386i	$0.208584\pi$
$272$		0			0
$273$	13.5515	−	13.5515i	0.820175	−	0.820175i
$274$		0			0
$275$	17.2125	+	6.22947i	1.03796	+	0.375651i
$276$		0			0
$277$	−10.5078	+	10.5078i	−0.631353	+	0.631353i	−0.948407	−	0.317054i	$-0.897306\pi$
$277$	−10.5078	+	10.5078i	−0.631353	+	0.631353i	0.317054	+	0.948407i	$0.397306\pi$
$278$		0			0
$279$			10.1047i			0.604952i
$280$		0			0
$281$			20.1642i			1.20290i	0.798911	+	0.601449i	$0.205410\pi$
$281$			20.1642i			1.20290i	−0.798911	+	0.601449i	$0.794590\pi$
$282$		0			0
$283$	−15.3820	+	15.3820i	−0.914367	+	0.914367i	−0.996612	−	0.0822450i	$-0.973791\pi$
$283$	−15.3820	+	15.3820i	−0.914367	+	0.914367i	0.0822450	+	0.996612i	$0.473791\pi$
$284$		0			0
$285$	−14.8062	−	2.59688i	−0.877046	−	0.153826i
$286$		0			0
$287$	−2.37681	−	2.37681i	−0.140299	−	0.140299i
$288$		0			0
$289$		−	15.9109i		−	0.935937i
$290$		0			0
$291$		−	16.5032i		−	0.967436i
$292$		0			0
$293$	−15.3820	+	15.3820i	−0.898628	+	0.898628i	−0.995315	−	0.0966867i	$-0.969175\pi$
$293$	−15.3820	+	15.3820i	−0.898628	+	0.898628i	0.0966867	+	0.995315i	$0.469175\pi$
$294$		0			0
$295$	3.46940	+	4.94525i	0.201996	+	0.287923i
$296$		0			0
$297$	−14.6441	−	14.6441i	−0.849738	−	0.849738i
$298$		0			0
$299$	25.0809	+	1.10469i	1.45047	+	0.0638857i
$300$		0			0
$301$	−28.8062			−1.66036
$302$		0			0
$303$	−12.1047	−	12.1047i	−0.695396	−	0.695396i
$304$		0			0
$305$	15.5078	+	22.1047i	0.887975	+	1.26571i
$306$		0			0
$307$	−11.7016	+	11.7016i	−0.667843	+	0.667843i	−0.957216	−	0.289373i	$-0.906553\pi$
$307$	−11.7016	+	11.7016i	−0.667843	+	0.667843i	0.289373	+	0.957216i	$0.406553\pi$
$308$		0			0
$309$	−6.22947			−0.354382
$310$		0			0
$311$	−18.5969			−1.05453			−0.527266	−	0.849700i	$-0.676783\pi$
$311$	−18.5969			−1.05453			−0.527266	+	0.849700i	$0.676783\pi$
$312$		0			0
$313$	−0.737925	+	0.737925i	−0.0417100	+	0.0417100i	−0.727654	−	0.685944i	$-0.759389\pi$
$313$	−0.737925	+	0.737925i	−0.0417100	+	0.0417100i	0.685944	+	0.727654i	$0.259389\pi$
$314$		0			0
$315$	−1.00000	+	5.70156i	−0.0563436	+	0.321247i
$316$		0			0
$317$	11.1047	−	11.1047i	0.623701	−	0.623701i	−0.322775	−	0.946476i	$-0.604616\pi$
$317$	11.1047	−	11.1047i	0.623701	−	0.623701i	0.946476	+	0.322775i	$0.104616\pi$
$318$		0			0
$319$	31.8567			1.78363
$320$		0			0
$321$			13.9348i			0.777764i
$322$		0			0
$323$	−3.50781	−	3.50781i	−0.195180	−	0.195180i
$324$		0			0
$325$	−23.7016	+	11.1047i	−1.31473	+	0.615977i
$326$		0			0
$327$	18.6884	+	18.6884i	1.03347	+	1.03347i
$328$		0			0
$329$	−23.4420			−1.29240
$330$		0			0
$331$	11.2984			0.621018			0.310509	−	0.950570i	$-0.399500\pi$
$331$	11.2984			0.621018			0.310509	+	0.950570i	$0.399500\pi$
$332$		0			0
$333$	−0.737925	+	0.737925i	−0.0404380	+	0.0404380i
$334$		0			0
$335$	−20.5078	−	3.59688i	−1.12046	−	0.196518i
$336$		0			0
$337$	15.1904	+	15.1904i	0.827474	+	0.827474i	0.987167	−	0.159693i	$-0.0510503\pi$
$337$	15.1904	+	15.1904i	0.827474	+	0.827474i	−0.159693	+	0.987167i	$0.551050\pi$
$338$		0			0
$339$	−13.9348			−0.756833
$340$		0			0
$341$		−	36.9935i		−	2.00331i
$342$		0			0
$343$	−13.3599	+	13.3599i	−0.721366	+	0.721366i
$344$		0			0
$345$	12.7864	−	8.15527i	0.688396	−	0.439065i
$346$		0			0
$347$	12.5078	−	12.5078i	0.671454	−	0.671454i	−0.286597	−	0.958051i	$-0.592524\pi$
$347$	12.5078	−	12.5078i	0.671454	−	0.671454i	0.958051	+	0.286597i	$0.0925240\pi$
$348$		0			0
$349$			15.2984i			0.818907i	0.912331	+	0.409453i	$0.134281\pi$
$349$			15.2984i			0.818907i	−0.912331	+	0.409453i	$0.865719\pi$
$350$		0			0
$351$	29.6125			1.58060
$352$		0			0
$353$	13.7016	+	13.7016i	0.729261	+	0.729261i	0.970472	−	0.241212i	$-0.0775449\pi$
$353$	13.7016	+	13.7016i	0.729261	+	0.729261i	−0.241212	+	0.970472i	$0.577545\pi$
$354$		0			0
$355$	15.9283	−	11.1747i	0.845388	−	0.593092i
$356$		0			0
$357$	2.70156	−	2.70156i	0.142982	−	0.142982i
$358$		0			0
$359$	−17.2125			−0.908444			−0.454222	−	0.890889i	$-0.650083\pi$
$359$	−17.2125			−0.908444			−0.454222	+	0.890889i	$0.650083\pi$
$360$		0			0
$361$	3.59688			0.189309
$362$		0			0
$363$	2.40312	+	2.40312i	0.126131	+	0.126131i
$364$		0			0
$365$	32.4030	+	5.68317i	1.69605	+	0.297471i
$366$		0			0
$367$	15.7653	+	15.7653i	0.822942	+	0.822942i	0.986529	−	0.163587i	$-0.0523065\pi$
$367$	15.7653	+	15.7653i	0.822942	+	0.822942i	−0.163587	+	0.986529i	$0.552307\pi$
$368$		0			0
$369$		−	1.29844i		−	0.0675940i
$370$		0			0
$371$	10.7016			0.555597
$372$		0			0
$373$	7.48509	−	7.48509i	0.387563	−	0.387563i	−0.486254	−	0.873817i	$-0.661637\pi$
$373$	7.48509	−	7.48509i	0.387563	−	0.387563i	0.873817	+	0.486254i	$0.161637\pi$
$374$		0			0
$375$	−7.86835	+	13.7146i	−0.406320	+	0.708217i
$376$		0			0
$377$	−32.2094	+	32.2094i	−1.65887	+	1.65887i
$378$		0			0
$379$	5.52014			0.283550			0.141775	−	0.989899i	$-0.454719\pi$
$379$	5.52014			0.283550			0.141775	+	0.989899i	$0.454719\pi$
$380$		0			0
$381$	−0.596876			−0.0305789
$382$		0			0
$383$	−22.3208	+	22.3208i	−1.14054	+	1.14054i	−0.152190	+	0.988351i	$0.548633\pi$
$383$	−22.3208	+	22.3208i	−1.14054	+	1.14054i	−0.988351	+	0.152190i	$0.951367\pi$
$384$		0			0
$385$	3.66103	−	20.8736i	0.186583	−	1.06382i
$386$		0			0
$387$	−7.86835	−	7.86835i	−0.399971	−	0.399971i
$388$		0			0
$389$	−37.7029			−1.91161			−0.955806	−	0.293999i	$-0.905014\pi$
$389$	−37.7029			−1.91161			−0.955806	+	0.293999i	$0.905014\pi$
$390$		0			0
$391$	5.00000	+	0.220225i	0.252861	+	0.0111372i
$392$		0			0
$393$	1.40312	+	1.40312i	0.0707783	+	0.0707783i
$394$		0			0
$395$	14.1047	−	9.89531i	0.709684	−	0.497887i
$396$		0			0
$397$	5.70156	−	5.70156i	0.286153	−	0.286153i	−0.549404	−	0.835557i	$-0.685145\pi$
$397$	5.70156	−	5.70156i	0.286153	−	0.286153i	0.835557	+	0.549404i	$0.185145\pi$
$398$		0			0
$399$			17.4031i			0.871246i
$400$		0			0
$401$			5.13688i			0.256523i	0.991740	+	0.128262i	$0.0409397\pi$
$401$			5.13688i			0.256523i	−0.991740	+	0.128262i	$0.959060\pi$
$402$		0			0
$403$	37.4031	+	37.4031i	1.86318	+	1.86318i
$404$		0			0
$405$	9.15257	−	6.42110i	0.454795	−	0.319067i
$406$		0			0
$407$	2.70156	−	2.70156i	0.133911	−	0.133911i
$408$		0			0
$409$			15.2984i			0.756459i	0.925712	+	0.378230i	$0.123467\pi$
$409$			15.2984i			0.756459i	−0.925712	+	0.378230i	$0.876533\pi$
$410$		0			0
$411$		−	6.22947i		−	0.307277i
$412$		0			0
$413$	4.94525	−	4.94525i	0.243340	−	0.243340i
$414$		0			0
$415$	1.00000	−	5.70156i	0.0490881	−	0.279879i
$416$		0			0
$417$	2.70156	−	2.70156i	0.132296	−	0.132296i
$418$		0			0
$419$	13.2255			0.646106			0.323053	−	0.946381i	$-0.395291\pi$
$419$	13.2255			0.646106			0.323053	+	0.946381i	$0.395291\pi$
$420$		0			0
$421$		−	5.13688i		−	0.250356i	−0.992134	−	0.125178i	$-0.960050\pi$
$421$		−	5.13688i		−	0.250356i	0.992134	−	0.125178i	$-0.0399502\pi$
$422$		0			0
$423$	−6.40312	−	6.40312i	−0.311331	−	0.311331i
$424$		0			0
$425$	−4.72502	+	2.21377i	−0.229197	+	0.107384i
$426$		0			0
$427$	22.1047	−	22.1047i	1.06972	−	1.06972i
$428$		0			0
$429$	−27.1030			−1.30855
$430$		0			0
$431$		−	21.6401i		−	1.04237i	−0.853445	−	0.521183i	$-0.825491\pi$
$431$		−	21.6401i		−	1.04237i	0.853445	−	0.521183i	$-0.174509\pi$
$432$		0			0
$433$	−0.354665	+	0.354665i	−0.0170441	+	0.0170441i	−0.715577	−	0.698533i	$-0.753836\pi$
$433$	−0.354665	+	0.354665i	−0.0170441	+	0.0170441i	0.698533	+	0.715577i	$0.253836\pi$
$434$		0			0
$435$	−4.75362	+	27.1030i	−0.227918	+	1.29949i
$436$		0			0
$437$	−16.8140	+	15.3954i	−0.804323	+	0.736460i
$438$		0			0
$439$		−	0.806248i		−	0.0384801i	−0.999815	−	0.0192401i	$-0.993875\pi$
$439$		−	0.806248i		−	0.0384801i	0.999815	−	0.0192401i	$-0.00612468\pi$
$440$		0			0
$441$	−0.298438			−0.0142113
$442$		0			0
$443$	−1.70156	−	1.70156i	−0.0808437	−	0.0808437i	0.665529	−	0.746372i	$-0.268206\pi$
$443$	−1.70156	−	1.70156i	−0.0808437	−	0.0808437i	−0.746372	+	0.665529i	$0.768206\pi$
$444$		0			0
$445$	25.5078	−	17.8953i	1.20919	−	0.848319i
$446$		0			0
$447$	−15.7367	−	15.7367i	−0.744320	−	0.744320i
$448$		0			0
$449$			30.3141i			1.43061i	0.698813	+	0.715304i	$0.253712\pi$
$449$			30.3141i			1.43061i	−0.698813	+	0.715304i	$0.746288\pi$
$450$		0			0
$451$			4.75362i			0.223839i
$452$		0			0
$453$	2.59688	+	2.59688i	0.122012	+	0.122012i
$454$		0			0
$455$	17.4031	+	24.8062i	0.815871	+	1.16293i
$456$		0			0
$457$	0.0285948	+	0.0285948i	0.00133761	+	0.00133761i	0.707775	−	0.706438i	$-0.249699\pi$
$457$	0.0285948	+	0.0285948i	0.00133761	+	0.00133761i	−0.706438	+	0.707775i	$0.749699\pi$
$458$		0			0
$459$	5.90340			0.275547
$460$		0			0
$461$	−19.4031			−0.903694			−0.451847	−	0.892096i	$-0.649235\pi$
$461$	−19.4031			−0.903694			−0.451847	+	0.892096i	$0.649235\pi$
$462$		0			0
$463$	−1.00000	−	1.00000i	−0.0464739	−	0.0464739i	0.683488	−	0.729962i	$-0.260462\pi$
$463$	−1.00000	−	1.00000i	−0.0464739	−	0.0464739i	−0.729962	+	0.683488i	$0.760462\pi$
$464$		0			0
$465$	31.4734	+	5.52014i	1.45954	+	0.255990i
$466$		0			0
$467$	−9.53583	−	9.53583i	−0.441266	−	0.441266i	0.451172	−	0.892437i	$-0.351006\pi$
$467$	−9.53583	−	9.53583i	−0.441266	−	0.441266i	−0.892437	+	0.451172i	$0.851006\pi$
$468$		0			0
$469$			24.1047i			1.11305i
$470$		0			0
$471$		−	13.1683i		−	0.606761i
$472$		0			0
$473$	28.8062	+	28.8062i	1.32451	+	1.32451i
$474$		0			0
$475$	8.08857	−	22.3494i	0.371129	−	1.02546i
$476$		0			0
$477$	2.92310	+	2.92310i	0.133840	+	0.133840i
$478$		0			0
$479$	38.7955			1.77261			0.886305	−	0.463102i	$-0.153264\pi$
$479$	38.7955			1.77261			0.886305	+	0.463102i	$0.153264\pi$
$480$		0			0
$481$			5.46295i			0.249089i
$482$		0			0
$483$	−11.8568	−	12.9494i	−0.539504	−	0.589219i
$484$		0			0
$485$	25.7016	+	4.50781i	1.16705	+	0.204689i
$486$		0			0
$487$	2.89531	−	2.89531i	0.131199	−	0.131199i	−0.638458	−	0.769657i	$-0.720427\pi$
$487$	2.89531	−	2.89531i	0.131199	−	0.131199i	0.769657	+	0.638458i	$0.220427\pi$
$488$		0			0
$489$			10.0000i			0.452216i
$490$		0			0
$491$	27.7172			1.25086			0.625429	−	0.780281i	$-0.284924\pi$
$491$	27.7172			1.25086			0.625429	+	0.780281i	$0.284924\pi$
$492$		0			0
$493$	−6.42110	+	6.42110i	−0.289192	+	0.289192i
$494$		0			0
$495$	6.70156	−	4.70156i	0.301213	−	0.211320i
$496$		0			0
$497$	−15.9283	−	15.9283i	−0.714483	−	0.714483i
$498$		0			0
$499$		−	13.2984i		−	0.595320i	−0.954672	−	0.297660i	$-0.903794\pi$
$499$		−	13.2984i		−	0.595320i	0.954672	−	0.297660i	$-0.0962061\pi$
$500$		0			0
$501$	7.40312			0.330747
$502$		0			0
$503$	−11.0117	+	11.0117i	−0.490986	+	0.490986i	−0.908617	−	0.417630i	$-0.862861\pi$
$503$	−11.0117	+	11.0117i	−0.490986	+	0.490986i	0.417630	+	0.908617i	$0.362861\pi$
$504$		0			0
$505$	22.1578	−	15.5451i	0.986009	−	0.691747i
$506$		0			0
$507$	14.4031	−	14.4031i	0.639665	−	0.639665i
$508$		0			0
$509$		−	17.6125i		−	0.780660i	−0.920675	−	0.390330i	$-0.872361\pi$
$509$		−	17.6125i		−	0.780660i	0.920675	−	0.390330i	$-0.127639\pi$
$510$		0			0
$511$		−	38.0861i		−	1.68483i
$512$		0			0
$513$	−19.0145	+	19.0145i	−0.839509	+	0.839509i
$514$		0			0
$515$	1.70156	−	9.70156i	0.0749798	−	0.427502i
$516$		0			0
$517$	23.4420	+	23.4420i	1.03098	+	1.03098i
$518$		0			0
$519$			8.80625i			0.386551i
$520$		0			0
$521$			8.47183i			0.371158i	0.982629	+	0.185579i	$0.0594160\pi$
$521$			8.47183i			0.371158i	−0.982629	+	0.185579i	$0.940584\pi$
$522$		0			0
$523$	−13.3313	+	13.3313i	−0.582937	+	0.582937i	−0.935709	−	0.352772i	$-0.885239\pi$
$523$	−13.3313	+	13.3313i	−0.582937	+	0.582937i	0.352772	+	0.935709i	$0.385239\pi$
$524$		0			0
$525$	17.2125	+	6.22947i	0.751217	+	0.271876i
$526$		0			0
$527$	7.45650	+	7.45650i	0.324810	+	0.324810i
$528$		0			0
$529$	2.02214	−	22.9109i	0.0879193	−	0.996128i
$530$		0			0
$531$	2.70156			0.117238
$532$		0			0
$533$	−4.80625	−	4.80625i	−0.208182	−	0.208182i
$534$		0			0
$535$	−21.7016	−	3.80625i	−0.938240	−	0.164558i
$536$		0			0
$537$	−10.0000	+	10.0000i	−0.431532	+	0.431532i
$538$		0			0
$539$	1.09259			0.0470612
$540$		0			0
$541$	0.806248			0.0346633			0.0173317	−	0.999850i	$-0.494483\pi$
$541$	0.806248			0.0346633			0.0173317	+	0.999850i	$0.494483\pi$
$542$		0			0
$543$	−9.12397	+	9.12397i	−0.391547	+	0.391547i
$544$		0			0
$545$	−34.2094	+	24.0000i	−1.46537	+	1.02805i
$546$		0			0
$547$	−29.1047	+	29.1047i	−1.24443	+	1.24443i	−0.286281	+	0.958146i	$0.592419\pi$
$547$	−29.1047	+	29.1047i	−1.24443	+	1.24443i	−0.958146	+	0.286281i	$0.907581\pi$
$548$		0			0
$549$	12.0757			0.515377
$550$		0			0
$551$		−	41.3639i		−	1.76216i
$552$		0			0
$553$	−14.1047	−	14.1047i	−0.599792	−	0.599792i
$554$		0			0
$555$	1.89531	+	2.70156i	0.0804516	+	0.114675i
$556$		0			0
$557$	21.6115	+	21.6115i	0.915709	+	0.915709i	0.996714	−	0.0810050i	$-0.0258130\pi$
$557$	21.6115	+	21.6115i	0.915709	+	0.915709i	−0.0810050	+	0.996714i	$0.525813\pi$
$558$		0			0
$559$	−58.2504			−2.46373
$560$		0			0
$561$	−5.40312			−0.228120
$562$		0			0
$563$	−8.44324	+	8.44324i	−0.355840	+	0.355840i	−0.862277	−	0.506437i	$-0.830962\pi$
$563$	−8.44324	+	8.44324i	−0.355840	+	0.355840i	0.506437	+	0.862277i	$0.330962\pi$
$564$		0			0
$565$	3.80625	−	21.7016i	0.160130	−	0.912992i
$566$		0			0
$567$	−9.15257	−	9.15257i	−0.384372	−	0.384372i
$568$		0			0
$569$	−3.66103			−0.153478			−0.0767391	−	0.997051i	$-0.524451\pi$
$569$	−3.66103			−0.153478			−0.0767391	+	0.997051i	$0.524451\pi$
$570$		0			0
$571$			42.4565i			1.77675i	0.459120	+	0.888374i	$0.348165\pi$
$571$			42.4565i			1.77675i	−0.459120	+	0.888374i	$0.651835\pi$
$572$		0			0
$573$	−1.85911	+	1.85911i	−0.0776654	+	0.0776654i
$574$		0			0
$575$	9.20817	+	22.1407i	0.384007	+	0.923330i
$576$		0			0
$577$	−15.2094	+	15.2094i	−0.633174	+	0.633174i	−0.948863	−	0.315688i	$-0.897765\pi$
$577$	−15.2094	+	15.2094i	−0.633174	+	0.633174i	0.315688	+	0.948863i	$0.397765\pi$
$578$		0			0
$579$			15.4031i			0.640132i
$580$		0			0
$581$	−6.70156			−0.278028
$582$		0			0
$583$	−10.7016	−	10.7016i	−0.443213	−	0.443213i
$584$		0			0
$585$	−2.02214	+	11.5294i	−0.0836054	+	0.476681i
$586$		0			0
$587$	5.00000	−	5.00000i	0.206372	−	0.206372i	−0.596351	−	0.802723i	$-0.703384\pi$
$587$	5.00000	−	5.00000i	0.206372	−	0.206372i	0.802723	+	0.596351i	$0.203384\pi$
$588$		0			0
$589$	−48.0338			−1.97920
$590$		0			0
$591$	0.806248			0.0331646
$592$		0			0
$593$	−23.0000	−	23.0000i	−0.944497	−	0.944497i	0.0540419	−	0.998539i	$-0.482790\pi$
$593$	−23.0000	−	23.0000i	−0.944497	−	0.944497i	−0.998539	+	0.0540419i	$0.982790\pi$
$594$		0			0
$595$	3.46940	+	4.94525i	0.142231	+	0.202735i
$596$		0			0
$597$	14.6441	+	14.6441i	0.599344	+	0.599344i
$598$		0			0
$599$		−	22.0000i		−	0.898896i	−0.893307	−	0.449448i	$-0.851621\pi$
$599$		−	22.0000i		−	0.898896i	0.893307	−	0.449448i	$-0.148379\pi$
$600$		0			0
$601$	29.5078			1.20365			0.601824	−	0.798628i	$-0.294441\pi$
$601$	29.5078			1.20365			0.601824	+	0.798628i	$0.294441\pi$
$602$		0			0
$603$	−6.58413	+	6.58413i	−0.268127	+	0.268127i
$604$		0			0
$605$	−4.39895	+	3.08614i	−0.178843	+	0.125469i
$606$		0			0
$607$	18.4031	−	18.4031i	0.746960	−	0.746960i	−0.226947	−	0.973907i	$-0.572875\pi$
$607$	18.4031	−	18.4031i	0.746960	−	0.746960i	0.973907	+	0.226947i	$0.0728745\pi$
$608$		0			0
$609$	31.8567			1.29090
$610$		0			0
$611$	−47.4031			−1.91773
$612$		0			0
$613$	19.9440	−	19.9440i	0.805531	−	0.805531i	−0.178422	−	0.983954i	$-0.557099\pi$
$613$	19.9440	−	19.9440i	0.805531	−	0.805531i	0.983954	+	0.178422i	$0.0570994\pi$
$614$		0			0
$615$	−4.04429	−	0.709330i	−0.163081	−	0.0286029i
$616$		0			0
$617$	−24.8893	−	24.8893i	−1.00200	−	1.00200i	−0.999998	−	0.00200628i	$-0.999361\pi$
$617$	−24.8893	−	24.8893i	−1.00200	−	1.00200i	−0.00200628	−	0.999998i	$-0.500639\pi$
$618$		0			0
$619$	−15.0274			−0.604001			−0.302001	−	0.953308i	$-0.597654\pi$
$619$	−15.0274			−0.604001			−0.302001	+	0.953308i	$0.597654\pi$
$620$		0			0
$621$	1.19375	−	27.1030i	0.0479036	−	1.08761i
$622$		0			0
$623$	−25.5078	−	25.5078i	−1.02195	−	1.02195i
$624$		0			0
$625$	−19.2094	−	16.0000i	−0.768375	−	0.640000i
$626$		0			0
$627$	17.4031	−	17.4031i	0.695014	−	0.695014i
$628$		0			0
$629$			1.08907i			0.0434239i
$630$		0			0
$631$			17.9219i			0.713459i	0.934208	+	0.356729i	$0.116108\pi$
$631$			17.9219i			0.713459i	−0.934208	+	0.356729i	$0.883892\pi$
$632$		0			0
$633$	12.7016	+	12.7016i	0.504842	+	0.504842i
$634$		0			0
$635$	0.163035	−	0.929554i	0.00646985	−	0.0368882i
$636$		0			0
$637$	−1.10469	+	1.10469i	−0.0437693	+	0.0437693i
$638$		0			0
$639$		−	8.70156i		−	0.344228i
$640$		0			0
$641$			0.383260i			0.0151378i	0.999971	+	0.00756892i	$0.00240929\pi$
$641$			0.383260i			0.0151378i	−0.999971	+	0.00756892i	$0.997591\pi$
$642$		0			0
$643$	23.4134	−	23.4134i	0.923335	−	0.923335i	−0.0739284	−	0.997264i	$-0.523554\pi$
$643$	23.4134	−	23.4134i	0.923335	−	0.923335i	0.997264	+	0.0739284i	$0.0235536\pi$
$644$		0			0
$645$	−28.8062	+	20.2094i	−1.13424	+	0.795743i
$646$		0			0
$647$	−13.1047	+	13.1047i	−0.515198	+	0.515198i	−0.916115	−	0.400916i	$-0.868692\pi$
$647$	−13.1047	+	13.1047i	−0.515198	+	0.515198i	0.400916	+	0.916115i	$0.368692\pi$
$648$		0			0
$649$	−9.89049			−0.388236
$650$		0			0
$651$		−	36.9935i		−	1.44989i
$652$		0			0
$653$	3.10469	+	3.10469i	0.121496	+	0.121496i	0.765240	−	0.643745i	$-0.222620\pi$
$653$	3.10469	+	3.10469i	0.121496	+	0.121496i	−0.643745	+	0.765240i	$0.722620\pi$
$654$		0			0
$655$	−2.56844	+	1.80192i	−0.100357	+	0.0704068i
$656$		0			0
$657$	10.4031	−	10.4031i	0.405865	−	0.405865i
$658$		0			0
$659$	26.3365			1.02593			0.512963	−	0.858411i	$-0.328548\pi$
$659$	26.3365			1.02593			0.512963	+	0.858411i	$0.328548\pi$
$660$		0			0
$661$		−	27.4863i		−	1.06909i	−0.845139	−	0.534547i	$-0.820482\pi$
$661$		−	27.4863i		−	1.06909i	0.845139	−	0.534547i	$-0.179518\pi$
$662$		0			0
$663$	5.46295	−	5.46295i	0.212163	−	0.212163i
$664$		0			0
$665$	−27.1030	−	4.75362i	−1.05101	−	0.184337i
$666$		0			0
$667$	28.1814	+	30.7783i	1.09119	+	1.19174i
$668$		0			0
$669$		−	18.2094i		−	0.704015i
$670$		0			0
$671$	−44.2094			−1.70668
$672$		0			0
$673$	7.10469	+	7.10469i	0.273866	+	0.273866i	0.830654	−	0.556789i	$-0.187967\pi$
$673$	7.10469	+	7.10469i	0.273866	+	0.273866i	−0.556789	+	0.830654i	$0.687967\pi$
$674$		0			0
$675$	12.0000	+	25.6125i	0.461880	+	0.985825i
$676$		0			0
$677$	28.5503	+	28.5503i	1.09728	+	1.09728i	0.994728	+	0.102549i	$0.0326999\pi$
$677$	28.5503	+	28.5503i	1.09728	+	1.09728i	0.102549	+	0.994728i	$0.467300\pi$
$678$		0			0
$679$		−	30.2094i		−	1.15933i
$680$		0			0
$681$		−	9.18116i		−	0.351823i
$682$		0			0
$683$	−13.2094	−	13.2094i	−0.505443	−	0.505443i	0.407682	−	0.913124i	$-0.366337\pi$
$683$	−13.2094	−	13.2094i	−0.505443	−	0.505443i	−0.913124	+	0.407682i	$0.866337\pi$
$684$		0			0
$685$	9.70156	+	1.70156i	0.370678	+	0.0650133i
$686$		0			0
$687$	11.3663	+	11.3663i	0.433653	+	0.433653i
$688$		0			0
$689$	21.6401			0.824422
$690$		0			0
$691$	12.2094			0.464466			0.232233	−	0.972660i	$-0.425397\pi$
$691$	12.2094			0.464466			0.232233	+	0.972660i	$0.425397\pi$
$692$		0			0
$693$	−6.70156	−	6.70156i	−0.254571	−	0.254571i
$694$		0			0
$695$	3.46940	+	4.94525i	0.131602	+	0.187584i
$696$		0			0
$697$	−0.958149	−	0.958149i	−0.0362925	−	0.0362925i
$698$		0			0
$699$		−	12.8062i		−	0.484377i
$700$		0			0
$701$		−	29.2882i		−	1.10620i	−0.833115	−	0.553100i	$-0.813445\pi$
$701$		−	29.2882i		−	1.10620i	0.833115	−	0.553100i	$-0.186555\pi$
$702$		0			0
$703$	−3.50781	−	3.50781i	−0.132300	−	0.132300i
$704$		0			0
$705$	−23.4420	+	16.4460i	−0.882877	+	0.619393i
$706$		0			0
$707$	−22.1578	−	22.1578i	−0.833330	−	0.833330i
$708$		0			0
$709$	−44.2584			−1.66216			−0.831080	−	0.556153i	$-0.812277\pi$
$709$	−44.2584			−1.66216			−0.831080	+	0.556153i	$0.812277\pi$
$710$		0			0
$711$		−	7.70532i		−	0.288972i
$712$		0			0
$713$	35.7413	−	32.7257i	1.33852	−	1.22559i
$714$		0			0
$715$	7.40312	−	42.2094i	0.276861	−	1.57854i
$716$		0			0
$717$	−12.1047	+	12.1047i	−0.452058	+	0.452058i
$718$		0			0
$719$		−	6.49219i		−	0.242118i	−0.992645	−	0.121059i	$-0.961371\pi$
$719$		−	6.49219i		−	0.242118i	0.992645	−	0.121059i	$-0.0386290\pi$
$720$		0			0
$721$	−11.4031			−0.424675
$722$		0			0
$723$	−2.18518	+	2.18518i	−0.0812677	+	0.0812677i
$724$		0			0
$725$	−40.9109	−	14.8062i	−1.51939	−	0.549890i
$726$		0			0
$727$	27.8410	+	27.8410i	1.03256	+	1.03256i	0.999452	+	0.0331127i	$0.0105420\pi$
$727$	27.8410	+	27.8410i	1.03256	+	1.03256i	0.0331127	+	0.999452i	$0.489458\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−11.6125			−0.429504
$732$		0			0
$733$	−19.3691	+	19.3691i	−0.715415	+	0.715415i	−0.967663	−	0.252247i	$-0.918830\pi$
$733$	−19.3691	+	19.3691i	−0.715415	+	0.715415i	0.252247	+	0.967663i	$0.418830\pi$
$734$		0			0
$735$	−0.163035	+	0.929554i	−0.00601364	+	0.0342871i
$736$		0			0
$737$	24.1047	−	24.1047i	0.887908	−	0.887908i
$738$		0			0
$739$		−	14.7016i		−	0.540806i	−0.962747	−	0.270403i	$-0.912843\pi$
$739$		−	14.7016i		−	0.540806i	0.962747	−	0.270403i	$-0.0871569\pi$
$740$		0			0
$741$			35.1916i			1.29280i
$742$		0			0
$743$	12.2387	−	12.2387i	0.448995	−	0.448995i	−0.446026	−	0.895020i	$-0.647161\pi$
$743$	12.2387	−	12.2387i	0.448995	−	0.448995i	0.895020	+	0.446026i	$0.147161\pi$
$744$		0			0
$745$	28.8062	−	20.2094i	1.05538	−	0.740414i
$746$		0			0
$747$	−1.83051	−	1.83051i	−0.0669750	−	0.0669750i
$748$		0			0
$749$			25.5078i			0.932035i
$750$		0			0
$751$		−	21.6401i		−	0.789658i	−0.918755	−	0.394829i	$-0.870804\pi$
$751$		−	21.6401i		−	0.789658i	0.918755	−	0.394829i	$-0.129196\pi$
$752$		0			0
$753$	−13.5515	+	13.5515i	−0.493845	+	0.493845i
$754$		0			0
$755$	−4.75362	+	3.33496i	−0.173002	+	0.121372i
$756$		0			0
$757$	−8.82650	−	8.82650i	−0.320805	−	0.320805i	0.528271	−	0.849076i	$-0.322840\pi$
$757$	−8.82650	−	8.82650i	−0.320805	−	0.320805i	−0.849076	+	0.528271i	$0.822840\pi$
$758$		0			0
$759$	−1.09259	+	24.8062i	−0.0396585	+	0.900410i
$760$		0			0
$761$	25.5078			0.924657			0.462329	−	0.886709i	$-0.347014\pi$
$761$	25.5078			0.924657			0.462329	+	0.886709i	$0.347014\pi$
$762$		0			0
$763$	34.2094	+	34.2094i	1.23846	+	1.23846i
$764$		0			0
$765$	−0.403124	+	2.29844i	−0.0145750	+	0.0831002i
$766$		0			0
$767$	10.0000	−	10.0000i	0.361079	−	0.361079i
$768$		0			0
$769$	−36.6675			−1.32226			−0.661131	−	0.750270i	$-0.729923\pi$
$769$	−36.6675			−1.32226			−0.661131	+	0.750270i	$0.729923\pi$
$770$		0			0
$771$	−28.8062			−1.03743
$772$		0			0
$773$	−33.4955	+	33.4955i	−1.20475	+	1.20475i	−0.232046	+	0.972705i	$0.574542\pi$
$773$	−33.4955	+	33.4955i	−1.20475	+	1.20475i	−0.972705	+	0.232046i	$0.925458\pi$
$774$		0			0
$775$	−17.1938	+	47.5078i	−0.617618	+	1.70653i
$776$		0			0
$777$	2.70156	−	2.70156i	0.0969180	−	0.0969180i
$778$		0			0
$779$	6.17228			0.221145
$780$		0			0
$781$			31.8567i			1.13992i
$782$		0			0
$783$	34.8062	+	34.8062i	1.24387	+	1.24387i
$784$		0			0
$785$	20.5078	+	3.59688i	0.731955	+	0.128378i
$786$		0			0
$787$	−1.83051	−	1.83051i	−0.0652508	−	0.0652508i	0.673728	−	0.738979i	$-0.264692\pi$
$787$	−1.83051	−	1.83051i	−0.0652508	−	0.0652508i	−0.738979	+	0.673728i	$0.764692\pi$
$788$		0			0
$789$	−8.79790			−0.313214
$790$		0			0
$791$	−25.5078			−0.906953
$792$		0			0
$793$	44.6989	−	44.6989i	1.58730	−	1.58730i
$794$		0			0
$795$	10.7016	−	7.50781i	0.379545	−	0.266275i
$796$		0			0
$797$	14.2894	+	14.2894i	0.506158	+	0.506158i	0.913345	−	0.407187i	$-0.133490\pi$
$797$	14.2894	+	14.2894i	0.506158	+	0.506158i	−0.407187	+	0.913345i	$0.633490\pi$
$798$		0			0
$799$	−9.45004			−0.334319
$800$		0			0
$801$		−	13.9348i		−	0.492361i
$802$		0			0
$803$	−38.0861	+	38.0861i	−1.34403	+	1.34403i
$804$		0			0
$805$	23.4057	−	14.9283i	0.824941	−	0.526155i
$806$		0			0
$807$	−30.1047	+	30.1047i	−1.05974	+	1.05974i
$808$		0			0
$809$		−	8.91093i		−	0.313292i	−0.987655	−	0.156646i	$-0.949932\pi$
$809$		−	8.91093i		−	0.313292i	0.987655	−	0.156646i	$-0.0500681\pi$
$810$		0			0
$811$	0.492189			0.0172831			0.00864155	−	0.999963i	$-0.497249\pi$
$811$	0.492189			0.0172831			0.00864155	+	0.999963i	$0.497249\pi$
$812$		0			0
$813$	−26.1047	−	26.1047i	−0.915531	−	0.915531i
$814$		0			0
$815$	−15.5737	−	2.73147i	−0.545522	−	0.0956793i
$816$		0			0
$817$	37.4031	−	37.4031i	1.30857	−	1.30857i
$818$		0			0
$819$	13.5515			0.473528
$820$		0			0
$821$	49.0156			1.71066			0.855328	−	0.518086i	$-0.173355\pi$
$821$	49.0156			1.71066			0.855328	+	0.518086i	$0.173355\pi$
$822$		0			0
$823$	−21.0000	−	21.0000i	−0.732014	−	0.732014i	0.239004	−	0.971018i	$-0.423179\pi$
$823$	−21.0000	−	21.0000i	−0.732014	−	0.732014i	−0.971018	+	0.239004i	$0.923179\pi$
$824$		0			0
$825$	−10.9831	−	23.4420i	−0.382382	−	0.816146i
$826$		0			0
$827$	−3.63243	−	3.63243i	−0.126312	−	0.126312i	0.641125	−	0.767437i	$-0.278468\pi$
$827$	−3.63243	−	3.63243i	−0.126312	−	0.126312i	−0.767437	+	0.641125i	$0.778468\pi$
$828$		0			0
$829$		−	26.3141i		−	0.913925i	−0.889486	−	0.456963i	$-0.848937\pi$
$829$		−	26.3141i		−	0.913925i	0.889486	−	0.456963i	$-0.151063\pi$
$830$		0			0
$831$	21.0156			0.729024
$832$		0			0
$833$	−0.220225	+	0.220225i	−0.00763033	+	0.00763033i
$834$		0			0
$835$	−2.02214	+	11.5294i	−0.0699792	+	0.398991i
$836$		0			0
$837$	40.4187	−	40.4187i	1.39708	−	1.39708i
$838$		0			0
$839$	−0.766519			−0.0264632			−0.0132316	−	0.999912i	$-0.504212\pi$
$839$	−0.766519			−0.0264632			−0.0132316	+	0.999912i	$0.504212\pi$
$840$		0			0
$841$	−46.7172			−1.61094
$842$		0			0
$843$	20.1642	−	20.1642i	0.694494	−	0.694494i
$844$		0			0
$845$	18.4968	+	26.3651i	0.636308	+	0.906988i
$846$		0			0
$847$	4.39895	+	4.39895i	0.151150	+	0.151150i
$848$		0			0
$849$	30.7641			1.05582
$850$		0			0
$851$	5.00000	+	0.220225i	0.171398	+	0.00754920i
$852$		0			0
$853$	−5.59688	−	5.59688i	−0.191633	−	0.191633i	0.604768	−	0.796402i	$-0.293266\pi$
$853$	−5.59688	−	5.59688i	−0.191633	−	0.191633i	−0.796402	+	0.604768i	$0.793266\pi$
$854$		0			0
$855$	−6.10469	−	8.70156i	−0.208776	−	0.297587i
$856$		0			0
$857$	−33.8062	+	33.8062i	−1.15480	+	1.15480i	−0.169221	+	0.985578i	$0.554125\pi$
$857$	−33.8062	+	33.8062i	−1.15480	+	1.15480i	−0.985578	+	0.169221i	$0.945875\pi$
$858$		0			0
$859$			23.8953i			0.815298i	0.913139	+	0.407649i	$0.133651\pi$
$859$			23.8953i			0.815298i	−0.913139	+	0.407649i	$0.866349\pi$
$860$		0			0
$861$			4.75362i			0.162003i
$862$		0			0
$863$	11.7016	+	11.7016i	0.398326	+	0.398326i	0.877642	−	0.479316i	$-0.159115\pi$
$863$	11.7016	+	11.7016i	0.398326	+	0.398326i	−0.479316	+	0.877642i	$0.659115\pi$
$864$		0			0
$865$	−13.7146	−	2.40540i	−0.466309	−	0.0817862i
$866$		0			0
$867$	−15.9109	+	15.9109i	−0.540364	+	0.540364i
$868$		0			0
$869$			28.2094i			0.956937i
$870$		0			0
$871$			48.7431i			1.65160i
$872$		0			0
$873$	8.25161	−	8.25161i	0.279275	−	0.279275i
$874$		0			0
$875$	−14.4031	+	25.1047i	−0.486914	+	0.848693i
$876$		0			0
$877$	−5.80625	+	5.80625i	−0.196063	+	0.196063i	−0.798310	−	0.602247i	$-0.794272\pi$
$877$	−5.80625	+	5.80625i	−0.196063	+	0.196063i	0.602247	+	0.798310i	$0.294272\pi$
$878$		0			0
$879$	30.7641			1.03765
$880$		0			0
$881$			58.1932i			1.96058i	0.197568	+	0.980289i	$0.436696\pi$
$881$			58.1932i			1.96058i	−0.197568	+	0.980289i	$0.563304\pi$
$882$		0			0
$883$	−6.89531	−	6.89531i	−0.232046	−	0.232046i	0.581500	−	0.813546i	$-0.302466\pi$
$883$	−6.89531	−	6.89531i	−0.232046	−	0.232046i	−0.813546	+	0.581500i	$0.802466\pi$
$884$		0			0
$885$	1.47585	−	8.41464i	0.0496101	−	0.282855i
$886$		0			0
$887$	−10.5078	+	10.5078i	−0.352818	+	0.352818i	−0.861157	−	0.508339i	$-0.830260\pi$
$887$	−10.5078	+	10.5078i	−0.352818	+	0.352818i	0.508339	+	0.861157i	$0.330260\pi$
$888$		0			0
$889$	−1.09259			−0.0366443
$890$		0			0
$891$			18.3051i			0.613245i
$892$		0			0
$893$	30.4380	−	30.4380i	1.01857	−	1.01857i
$894$		0			0
$895$	−12.8422	−	18.3051i	−0.429267	−	0.611873i
$896$		0			0
$897$	−23.9762	−	26.1856i	−0.800542	−	0.874311i
$898$		0			0
$899$			87.9266i			2.93251i
$900$		0			0
$901$	4.31406			0.143722
$902$		0			0
$903$	28.8062	+	28.8062i	0.958612	+	0.958612i
$904$		0			0
$905$	−11.7172	−	16.7016i	−0.389492	−	0.555179i
$906$		0			0
$907$	−31.1187	−	31.1187i	−1.03328	−	1.03328i	−0.999427	−	0.0338539i	$-0.989222\pi$
$907$	−31.1187	−	31.1187i	−1.03328	−	1.03328i	−0.0338539	−	0.999427i	$-0.510778\pi$
$908$		0			0
$909$		−	12.1047i		−	0.401487i
$910$		0			0
$911$		−	14.9702i		−	0.495984i	−0.968762	−	0.247992i	$-0.920229\pi$
$911$		−	14.9702i		−	0.495984i	0.968762	−	0.247992i	$-0.0797707\pi$
$912$		0			0
$913$	6.70156	+	6.70156i	0.221789	+	0.221789i
$914$		0			0
$915$	6.59688	−	37.6125i	0.218086	−	1.24343i
$916$		0			0
$917$	2.56844	+	2.56844i	0.0848173	+	0.0848173i
$918$		0			0
$919$	38.7955			1.27974			0.639872	−	0.768481i	$-0.278987\pi$
$919$	38.7955			1.27974			0.639872	+	0.768481i	$0.278987\pi$
$920$		0			0
$921$	23.4031			0.771159
$922$		0			0
$923$	−32.2094	−	32.2094i	−1.06018	−	1.06018i
$924$		0			0
$925$	−4.72502	+	2.21377i	−0.155358	+	0.0727884i
$926$		0			0
$927$	−3.11473	−	3.11473i	−0.102301	−	0.102301i
$928$		0			0
$929$			15.7172i			0.515664i	0.966190	+	0.257832i	$0.0830081\pi$
$929$			15.7172i			0.515664i	−0.966190	+	0.257832i	$0.916992\pi$
$930$		0			0
$931$		−	1.41866i		−	0.0464947i
$932$		0			0
$933$	18.5969	+	18.5969i	0.608834	+	0.608834i
$934$		0			0
$935$	1.47585	−	8.41464i	0.0482654	−	0.275188i
$936$		0			0
$937$	−13.7146	−	13.7146i	−0.448035	−	0.448035i	0.446666	−	0.894701i	$-0.352611\pi$
$937$	−13.7146	−	13.7146i	−0.448035	−	0.448035i	−0.894701	+	0.446666i	$0.852611\pi$
$938$		0			0
$939$	1.47585			0.0481625
$940$		0			0
$941$		−	20.1642i		−	0.657336i	−0.944446	−	0.328668i	$-0.893400\pi$
$941$		−	20.1642i		−	0.657336i	0.944446	−	0.328668i	$-0.106600\pi$
$942$		0			0
$943$	−4.59270	+	4.20520i	−0.149559	+	0.136940i
$944$		0			0
$945$	26.8062	−	18.8062i	0.872007	−	0.611767i
$946$		0			0
$947$	−21.5969	+	21.5969i	−0.701804	+	0.701804i	−0.964798	−	0.262993i	$-0.915290\pi$
$947$	−21.5969	+	21.5969i	−0.701804	+	0.701804i	0.262993	+	0.964798i	$0.415290\pi$
$948$		0			0
$949$		−	77.0156i		−	2.50003i
$950$		0			0
$951$	−22.2094			−0.720188
$952$		0			0
$953$	−14.4811	+	14.4811i	−0.469088	+	0.469088i	−0.901619	−	0.432531i	$-0.857621\pi$
$953$	−14.4811	+	14.4811i	−0.469088	+	0.469088i	0.432531	+	0.901619i	$0.357621\pi$
$954$		0			0
$955$	−2.38750	−	3.40312i	−0.0772578	−	0.110123i
$956$		0			0
$957$	−31.8567	−	31.8567i	−1.02978	−	1.02978i
$958$		0			0
$959$		−	11.4031i		−	0.368226i
$960$		0			0
$961$	71.1047			2.29370
$962$		0			0
$963$	−6.96739	+	6.96739i	−0.224521	+	0.224521i
$964$		0			0
$965$	−23.9883	−	4.20732i	−0.772211	−	0.135439i
$966$		0			0
$967$	−3.00000	+	3.00000i	−0.0964735	+	0.0964735i	−0.753696	−	0.657223i	$-0.771731\pi$
$967$	−3.00000	+	3.00000i	−0.0964735	+	0.0964735i	0.657223	+	0.753696i	$0.271731\pi$
$968$		0			0
$969$			7.01562i			0.225374i
$970$		0			0
$971$		−	6.61273i		−	0.212212i	−0.994355	−	0.106106i	$-0.966162\pi$
$971$		−	6.61273i		−	0.212212i	0.994355	−	0.106106i	$-0.0338384\pi$
$972$		0			0
$973$	4.94525	−	4.94525i	0.158537	−	0.158537i
$974$		0			0
$975$	34.8062	+	12.5969i	1.11469	+	0.403423i
$976$		0			0
$977$	11.7210	+	11.7210i	0.374988	+	0.374988i	0.869290	−	0.494302i	$-0.164576\pi$
$977$	11.7210	+	11.7210i	0.374988	+	0.374988i	−0.494302	+	0.869290i	$0.664576\pi$
$978$		0			0
$979$			51.0156i			1.63047i
$980$		0			0
$981$			18.6884i			0.596675i
$982$		0			0
$983$	28.1670	−	28.1670i	0.898389	−	0.898389i	−0.0969047	−	0.995294i	$-0.530894\pi$
$983$	28.1670	−	28.1670i	0.898389	−	0.898389i	0.995294	+	0.0969047i	$0.0308942\pi$
$984$		0			0
$985$	−0.220225	+	1.25562i	−0.00701694	+	0.0400075i
$986$		0			0
$987$	23.4420	+	23.4420i	0.746168	+	0.746168i
$988$		0			0
$989$	−2.34821	+	53.3141i	−0.0746689	+	1.69529i
$990$		0			0
$991$	59.5078			1.89033			0.945164	−	0.326596i	$-0.105902\pi$
$991$	59.5078			1.89033			0.945164	+	0.326596i	$0.105902\pi$
$992$		0			0
$993$	−11.2984	−	11.2984i	−0.358545	−	0.358545i
$994$		0			0
$995$	−26.8062	+	18.8062i	−0.849815	+	0.596198i
$996$		0			0
$997$	−7.70156	+	7.70156i	−0.243911	+	0.243911i	−0.818466	−	0.574555i	$-0.805175\pi$
$997$	−7.70156	+	7.70156i	−0.243911	+	0.243911i	0.574555	+	0.818466i	$0.305175\pi$
$998$		0			0
$999$	5.90340			0.186775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.i.a.413.4	yes	8
5.2	odd	4	inner	460.2.i.a.137.1	✓	8
5.3	odd	4		2300.2.i.c.1057.1		8
5.4	even	2		2300.2.i.c.1793.4		8
23.22	odd	2	inner	460.2.i.a.413.1	yes	8
115.22	even	4	inner	460.2.i.a.137.4	yes	8
115.68	even	4		2300.2.i.c.1057.4		8
115.114	odd	2		2300.2.i.c.1793.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.i.a.137.1	✓	8	5.2	odd	4	inner
460.2.i.a.137.4	yes	8	115.22	even	4	inner
460.2.i.a.413.1	yes	8	23.22	odd	2	inner
460.2.i.a.413.4	yes	8	1.1	even	1	trivial
2300.2.i.c.1057.1		8	5.3	odd	4
2300.2.i.c.1057.4		8	115.68	even	4
2300.2.i.c.1793.1		8	115.114	odd	2
2300.2.i.c.1793.4		8	5.4	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{3} +(1.83051 - 1.28422i) q^{5} +(-1.83051 - 1.83051i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{3} +(1.83051 - 1.28422i) q^{5} +(-1.83051 - 1.83051i) q^{7} -1.00000i q^{9} +3.66103i q^{11} +(-3.70156 - 3.70156i) q^{13} +(-3.11473 - 0.546295i) q^{15} +(-0.737925 - 0.737925i) q^{17} +4.75362 q^{19} +3.66103i q^{21} +(-3.53710 + 3.23866i) q^{23} +(1.70156 - 4.70156i) q^{25} +(-4.00000 + 4.00000i) q^{27} -8.70156i q^{29} -10.1047 q^{31} +(3.66103 - 3.66103i) q^{33} +(-5.70156 - 1.00000i) q^{35} +(-0.737925 - 0.737925i) q^{37} +7.40312i q^{39} +1.29844 q^{41} +(7.86835 - 7.86835i) q^{43} +(-1.28422 - 1.83051i) q^{45} +(6.40312 - 6.40312i) q^{47} -0.298438i q^{49} +1.47585i q^{51} +(-2.92310 + 2.92310i) q^{53} +(4.70156 + 6.70156i) q^{55} +(-4.75362 - 4.75362i) q^{57} +2.70156i q^{59} +12.0757i q^{61} +(-1.83051 + 1.83051i) q^{63} +(-11.5294 - 2.02214i) q^{65} +(-6.58413 - 6.58413i) q^{67} +(6.77576 + 0.298438i) q^{69} +8.70156 q^{71} +(10.4031 + 10.4031i) q^{73} +(-6.40312 + 3.00000i) q^{75} +(6.70156 - 6.70156i) q^{77} +7.70532 q^{79} +5.00000 q^{81} +(1.83051 - 1.83051i) q^{83} +(-2.29844 - 0.403124i) q^{85} +(-8.70156 + 8.70156i) q^{87} +13.9348 q^{89} +13.5515i q^{91} +(10.1047 + 10.1047i) q^{93} +(8.70156 - 6.10469i) q^{95} +(8.25161 + 8.25161i) q^{97} +3.66103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3}+O(q^{10}) \) 8 * q - 8 * q^3	\( 8 q - 8 q^{3} - 4 q^{13} - 14 q^{23} - 12 q^{25} - 32 q^{27} - 4 q^{31} - 20 q^{35} + 36 q^{41} + 12 q^{55} + 44 q^{71} + 32 q^{73} + 28 q^{77} + 40 q^{81} - 44 q^{85} - 44 q^{87} + 4 q^{93} + 44 q^{95}+O(q^{100}) \) 8 * q - 8 * q^3 - 4 * q^13 - 14 * q^23 - 12 * q^25 - 32 * q^27 - 4 * q^31 - 20 * q^35 + 36 * q^41 + 12 * q^55 + 44 * q^71 + 32 * q^73 + 28 * q^77 + 40 * q^81 - 44 * q^85 - 44 * q^87 + 4 * q^93 + 44 * q^95

Introduction

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