LMFDB - Embedded newform 460.2.i.a.137.3

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			137.3
Root			$-0.386289 - 0.386289i$ of defining polynomial
Character	$\chi$	$=$	460.137
Dual form			460.2.i.a.413.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{3} +(0.386289 - 2.20245i) q^{5} +(-0.386289 + 0.386289i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{3} +(0.386289 - 2.20245i) q^{5} +(-0.386289 + 0.386289i) q^{7} +1.00000i q^{9} -0.772577i q^{11} +(2.70156 - 2.70156i) q^{13} +(1.81616 + 2.58874i) q^{15} +(4.79119 - 4.79119i) q^{17} +5.95005 q^{19} -0.772577i q^{21} +(-2.82899 + 3.87257i) q^{23} +(-4.70156 - 1.70156i) q^{25} +(-4.00000 - 4.00000i) q^{27} +2.29844i q^{29} +9.10469 q^{31} +(0.772577 + 0.772577i) q^{33} +(0.701562 + 1.00000i) q^{35} +(4.79119 - 4.79119i) q^{37} +5.40312i q^{39} +7.70156 q^{41} +(4.13389 + 4.13389i) q^{43} +(2.20245 + 0.386289i) q^{45} +(-6.40312 - 6.40312i) q^{47} +6.70156i q^{49} +9.58237i q^{51} +(-5.56376 - 5.56376i) q^{53} +(-1.70156 - 0.298438i) q^{55} +(-5.95005 + 5.95005i) q^{57} +3.70156i q^{59} -7.49521i q^{61} +(-0.386289 - 0.386289i) q^{63} +(-4.90647 - 6.99364i) q^{65} +(-6.33634 + 6.33634i) q^{67} +(-1.04358 - 6.70156i) q^{69} +2.29844 q^{71} +(-2.40312 + 2.40312i) q^{73} +(6.40312 - 3.00000i) q^{75} +(0.298438 + 0.298438i) q^{77} -13.2147 q^{79} +5.00000 q^{81} +(0.386289 + 0.386289i) q^{83} +(-8.70156 - 12.4031i) q^{85} +(-2.29844 - 2.29844i) q^{87} -16.8470 q^{89} +2.08717i q^{91} +(-9.10469 + 9.10469i) q^{93} +(2.29844 - 13.1047i) q^{95} +(-10.6260 + 10.6260i) q^{97} +0.772577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

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

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	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		0			0
$5$	0.386289	−	2.20245i	0.172754	−	0.984965i
$5$	0.386289	−	2.20245i	0.172754	−	0.984965i
$6$		0			0
$7$	−0.386289	+	0.386289i	−0.146003	+	0.146003i	−0.776330	−	0.630327i	$-0.782921\pi$
$7$	−0.386289	+	0.386289i	−0.146003	+	0.146003i	0.630327	+	0.776330i	$0.282921\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	0.772577i		−	0.232941i	−0.993194	−	0.116470i	$-0.962842\pi$
$11$		−	0.772577i		−	0.232941i	0.993194	−	0.116470i	$-0.0371580\pi$
$12$		0			0
$13$	2.70156	−	2.70156i	0.749279	−	0.749279i	−0.225065	−	0.974344i	$-0.572260\pi$
$13$	2.70156	−	2.70156i	0.749279	−	0.749279i	0.974344	+	0.225065i	$0.0722595\pi$
$14$		0			0
$15$	1.81616	+	2.58874i	0.468931	+	0.668409i
$16$		0			0
$17$	4.79119	−	4.79119i	1.16203	−	1.16203i	0.178004	−	0.984030i	$-0.443036\pi$
$17$	4.79119	−	4.79119i	1.16203	−	1.16203i	0.984030	−	0.178004i	$-0.0569639\pi$
$18$		0			0
$19$	5.95005			1.36504			0.682518	−	0.730869i	$-0.260885\pi$
$19$	5.95005			1.36504			0.682518	+	0.730869i	$0.260885\pi$
$20$		0			0
$21$		−	0.772577i		−	0.168590i
$22$		0			0
$23$	−2.82899	+	3.87257i	−0.589885	+	0.807487i
$23$	−2.82899	+	3.87257i	−0.589885	+	0.807487i
$24$		0			0
$25$	−4.70156	−	1.70156i	−0.940312	−	0.340312i
$26$		0			0
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$			2.29844i			0.426809i	0.976964	+	0.213405i	$0.0684553\pi$
$29$			2.29844i			0.426809i	−0.976964	+	0.213405i	$0.931545\pi$
$30$		0			0
$31$	9.10469			1.63525			0.817625	−	0.575751i	$-0.195290\pi$
$31$	9.10469			1.63525			0.817625	+	0.575751i	$0.195290\pi$
$32$		0			0
$33$	0.772577	+	0.772577i	0.134488	+	0.134488i
$34$		0			0
$35$	0.701562	+	1.00000i	0.118586	+	0.169031i
$36$		0			0
$37$	4.79119	−	4.79119i	0.787666	−	0.787666i	−0.193445	−	0.981111i	$-0.561966\pi$
$37$	4.79119	−	4.79119i	0.787666	−	0.787666i	0.981111	+	0.193445i	$0.0619661\pi$
$38$		0			0
$39$			5.40312i			0.865192i
$40$		0			0
$41$	7.70156			1.20278			0.601391	−	0.798955i	$-0.294613\pi$
$41$	7.70156			1.20278			0.601391	+	0.798955i	$0.294613\pi$
$42$		0			0
$43$	4.13389	+	4.13389i	0.630413	+	0.630413i	0.948172	−	0.317759i	$-0.102930\pi$
$43$	4.13389	+	4.13389i	0.630413	+	0.630413i	−0.317759	+	0.948172i	$0.602930\pi$
$44$		0			0
$45$	2.20245	+	0.386289i	0.328322	+	0.0575845i
$46$		0			0
$47$	−6.40312	−	6.40312i	−0.933992	−	0.933992i	0.0639608	−	0.997952i	$-0.479627\pi$
$47$	−6.40312	−	6.40312i	−0.933992	−	0.933992i	−0.997952	+	0.0639608i	$0.979627\pi$
$48$		0			0
$49$			6.70156i			0.957366i
$50$		0			0
$51$			9.58237i			1.34180i
$52$		0			0
$53$	−5.56376	−	5.56376i	−0.764242	−	0.764242i	0.212844	−	0.977086i	$-0.431727\pi$
$53$	−5.56376	−	5.56376i	−0.764242	−	0.764242i	−0.977086	+	0.212844i	$0.931727\pi$
$54$		0			0
$55$	−1.70156	−	0.298438i	−0.229439	−	0.0402414i
$56$		0			0
$57$	−5.95005	+	5.95005i	−0.788104	+	0.788104i
$58$		0			0
$59$			3.70156i			0.481902i	0.970537	+	0.240951i	$0.0774594\pi$
$59$			3.70156i			0.481902i	−0.970537	+	0.240951i	$0.922541\pi$
$60$		0			0
$61$		−	7.49521i		−	0.959663i	−0.877361	−	0.479831i	$-0.840698\pi$
$61$		−	7.49521i		−	0.959663i	0.877361	−	0.479831i	$-0.159302\pi$
$62$		0			0
$63$	−0.386289	−	0.386289i	−0.0486678	−	0.0486678i
$64$		0			0
$65$	−4.90647	−	6.99364i	−0.608573	−	0.867454i
$66$		0			0
$67$	−6.33634	+	6.33634i	−0.774107	+	0.774107i	−0.978822	−	0.204714i	$-0.934373\pi$
$67$	−6.33634	+	6.33634i	−0.774107	+	0.774107i	0.204714	+	0.978822i	$0.434373\pi$
$68$		0			0
$69$	−1.04358	−	6.70156i	−0.125633	−	0.806773i
$70$		0			0
$71$	2.29844			0.272774			0.136387	−	0.990656i	$-0.456451\pi$
$71$	2.29844			0.272774			0.136387	+	0.990656i	$0.456451\pi$
$72$		0			0
$73$	−2.40312	+	2.40312i	−0.281264	+	0.281264i	−0.833613	−	0.552349i	$-0.813732\pi$
$73$	−2.40312	+	2.40312i	−0.281264	+	0.281264i	0.552349	+	0.833613i	$0.313732\pi$
$74$		0			0
$75$	6.40312	−	3.00000i	0.739369	−	0.346410i
$76$		0			0
$77$	0.298438	+	0.298438i	0.0340102	+	0.0340102i
$78$		0			0
$79$	−13.2147			−1.48677			−0.743385	−	0.668864i	$-0.766781\pi$
$79$	−13.2147			−1.48677			−0.743385	+	0.668864i	$0.766781\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	0.386289	+	0.386289i	0.0424007	+	0.0424007i	0.727989	−	0.685589i	$-0.240455\pi$
$83$	0.386289	+	0.386289i	0.0424007	+	0.0424007i	−0.685589	+	0.727989i	$0.740455\pi$
$84$		0			0
$85$	−8.70156	−	12.4031i	−0.943817	−	1.34531i
$86$		0			0
$87$	−2.29844	−	2.29844i	−0.246418	−	0.246418i
$88$		0			0
$89$	−16.8470			−1.78578			−0.892890	−	0.450275i	$-0.851326\pi$
$89$	−16.8470			−1.78578			−0.892890	+	0.450275i	$0.851326\pi$
$90$		0			0
$91$			2.08717i			0.218794i
$92$		0			0
$93$	−9.10469	+	9.10469i	−0.944112	+	0.944112i
$94$		0			0
$95$	2.29844	−	13.1047i	0.235815	−	1.34451i
$96$		0			0
$97$	−10.6260	+	10.6260i	−1.07890	+	1.07890i	−0.0822943	+	0.996608i	$0.526225\pi$
$97$	−10.6260	+	10.6260i	−1.07890	+	1.07890i	−0.996608	+	0.0822943i	$0.973775\pi$
$98$		0			0
$99$	0.772577			0.0776469
$100$		0			0
$101$	−7.10469			−0.706943			−0.353471	−	0.935445i	$-0.614999\pi$
$101$	−7.10469			−0.706943			−0.353471	+	0.935445i	$0.614999\pi$
$102$		0			0
$103$	−1.81616	−	1.81616i	−0.178952	−	0.178952i	0.611947	−	0.790899i	$-0.290387\pi$
$103$	−1.81616	−	1.81616i	−0.178952	−	0.178952i	−0.790899	+	0.611947i	$0.790387\pi$
$104$		0			0
$105$	−1.70156	−	0.298438i	−0.166055	−	0.0291246i
$106$		0			0
$107$	8.42351	−	8.42351i	0.814331	−	0.814331i	−0.170949	−	0.985280i	$-0.554683\pi$
$107$	8.42351	−	8.42351i	0.814331	−	0.814331i	0.985280	+	0.170949i	$0.0546833\pi$
$108$		0			0
$109$	10.8970			1.04374			0.521870	−	0.853025i	$-0.325235\pi$
$109$	10.8970			1.04374			0.521870	+	0.853025i	$0.325235\pi$
$110$		0			0
$111$			9.58237i			0.909519i
$112$		0			0
$113$	−8.42351	−	8.42351i	−0.792417	−	0.792417i	0.189470	−	0.981887i	$-0.439323\pi$
$113$	−8.42351	−	8.42351i	−0.792417	−	0.792417i	−0.981887	+	0.189470i	$0.939323\pi$
$114$		0			0
$115$	7.43634	+	7.72664i	0.693442	+	0.720513i
$116$		0			0
$117$	2.70156	+	2.70156i	0.249760	+	0.249760i
$118$		0			0
$119$			3.70156i			0.339322i
$120$		0			0
$121$	10.4031			0.945739
$122$		0			0
$123$	−7.70156	+	7.70156i	−0.694426	+	0.694426i
$124$		0			0
$125$	−5.56376	+	9.69766i	−0.497638	+	0.867385i
$126$		0			0
$127$	6.70156	+	6.70156i	0.594667	+	0.594667i	0.938889	−	0.344221i	$-0.111857\pi$
$127$	6.70156	+	6.70156i	0.594667	+	0.594667i	−0.344221	+	0.938889i	$0.611857\pi$
$128$		0			0
$129$	−8.26778			−0.727938
$130$		0			0
$131$	11.4031			0.996296			0.498148	−	0.867092i	$-0.334014\pi$
$131$	11.4031			0.996296			0.498148	+	0.867092i	$0.334014\pi$
$132$		0			0
$133$	−2.29844	+	2.29844i	−0.199300	+	0.199300i
$134$		0			0
$135$	−10.3550	+	7.26464i	−0.891212	+	0.625241i
$136$		0			0
$137$	−1.81616	+	1.81616i	−0.155165	+	0.155165i	−0.780420	−	0.625255i	$-0.784995\pi$
$137$	−1.81616	+	1.81616i	−0.155165	+	0.155165i	0.625255	+	0.780420i	$0.284995\pi$
$138$		0			0
$139$			3.70156i			0.313962i	0.987602	+	0.156981i	$0.0501762\pi$
$139$			3.70156i			0.313962i	−0.987602	+	0.156981i	$0.949824\pi$
$140$		0			0
$141$	12.8062			1.07848
$142$		0			0
$143$	−2.08717	−	2.08717i	−0.174538	−	0.174538i
$144$		0			0
$145$	5.06219	+	0.887861i	0.420392	+	0.0737328i
$146$		0			0
$147$	−6.70156	−	6.70156i	−0.552736	−	0.552736i
$148$		0			0
$149$	8.26778			0.677323			0.338662	−	0.940908i	$-0.390026\pi$
$149$	8.26778			0.677323			0.338662	+	0.940908i	$0.390026\pi$
$150$		0			0
$151$	−15.4031			−1.25349			−0.626744	−	0.779225i	$-0.715613\pi$
$151$	−15.4031			−1.25349			−0.626744	+	0.779225i	$0.715613\pi$
$152$		0			0
$153$	4.79119	+	4.79119i	0.387344	+	0.387344i
$154$		0			0
$155$	3.51704	−	20.0526i	0.282495	−	1.61066i
$156$		0			0
$157$	6.33634	−	6.33634i	0.505695	−	0.505695i	−0.407507	−	0.913202i	$-0.633602\pi$
$157$	6.33634	−	6.33634i	0.505695	−	0.505695i	0.913202	+	0.407507i	$0.133602\pi$
$158$		0			0
$159$	11.1275			0.882470
$160$		0			0
$161$	−0.403124	−	2.58874i	−0.0317706	−	0.204021i
$162$		0			0
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	−0.875268	−	0.483638i	$-0.839315\pi$
$163$	−5.00000	+	5.00000i	−0.391630	+	0.391630i	0.483638	+	0.875268i	$0.339315\pi$
$164$		0			0
$165$	2.00000	−	1.40312i	0.155700	−	0.109233i
$166$		0			0
$167$	2.70156	+	2.70156i	0.209053	+	0.209053i	0.803865	−	0.594812i	$-0.202773\pi$
$167$	2.70156	+	2.70156i	0.209053	+	0.209053i	−0.594812	+	0.803865i	$0.702773\pi$
$168$		0			0
$169$		−	1.59688i		−	0.122837i
$170$		0			0
$171$			5.95005i			0.455012i
$172$		0			0
$173$	8.40312	−	8.40312i	0.638878	−	0.638878i	−0.311401	−	0.950279i	$-0.600798\pi$
$173$	8.40312	−	8.40312i	0.638878	−	0.638878i	0.950279	+	0.311401i	$0.100798\pi$
$174$		0			0
$175$	2.47345	−	1.15887i	0.186976	−	0.0876020i
$176$		0			0
$177$	−3.70156	−	3.70156i	−0.278226	−	0.278226i
$178$		0			0
$179$			10.0000i			0.747435i	0.927543	+	0.373718i	$0.121917\pi$
$179$			10.0000i			0.747435i	−0.927543	+	0.373718i	$0.878083\pi$
$180$		0			0
$181$			26.6600i			1.98162i	0.135266	+	0.990809i	$0.456811\pi$
$181$			26.6600i			1.98162i	−0.135266	+	0.990809i	$0.543189\pi$
$182$		0			0
$183$	7.49521	+	7.49521i	0.554062	+	0.554062i
$184$		0			0
$185$	−8.70156	−	12.4031i	−0.639752	−	0.911896i
$186$		0			0
$187$	−3.70156	−	3.70156i	−0.270685	−	0.270685i
$188$		0			0
$189$	3.09031			0.224787
$190$		0			0
$191$		−	24.3422i		−	1.76134i	−0.473729	−	0.880671i	$-0.657092\pi$
$191$		−	24.3422i		−	1.76134i	0.473729	−	0.880671i	$-0.342908\pi$
$192$		0			0
$193$	−1.29844	+	1.29844i	−0.0934636	+	0.0934636i	−0.752293	−	0.658829i	$-0.771052\pi$
$193$	−1.29844	+	1.29844i	−0.0934636	+	0.0934636i	0.658829	+	0.752293i	$0.271052\pi$
$194$		0			0
$195$	11.9001	+	2.08717i	0.852184	+	0.149465i
$196$		0			0
$197$	12.4031	+	12.4031i	0.883686	+	0.883686i	0.993907	−	0.110221i	$-0.0351559\pi$
$197$	12.4031	+	12.4031i	0.883686	+	0.883686i	−0.110221	+	0.993907i	$0.535156\pi$
$198$		0			0
$199$	−3.09031			−0.219066			−0.109533	−	0.993983i	$-0.534936\pi$
$199$	−3.09031			−0.219066			−0.109533	+	0.993983i	$0.534936\pi$
$200$		0			0
$201$		−	12.6727i		−	0.893862i
$202$		0			0
$203$	−0.887861	−	0.887861i	−0.0623156	−	0.0623156i
$204$		0			0
$205$	2.97503	−	16.9623i	0.207785	−	1.18470i
$206$		0			0
$207$	−3.87257	−	2.82899i	−0.269162	−	0.196628i
$208$		0			0
$209$		−	4.59688i		−	0.317973i
$210$		0			0
$211$	−6.29844			−0.433602			−0.216801	−	0.976216i	$-0.569562\pi$
$211$	−6.29844			−0.433602			−0.216801	+	0.976216i	$0.569562\pi$
$212$		0			0
$213$	−2.29844	+	2.29844i	−0.157486	+	0.157486i
$214$		0			0
$215$	10.7016	−	7.50781i	0.729840	−	0.512028i
$216$		0			0
$217$	−3.51704	+	3.51704i	−0.238752	+	0.238752i
$218$		0			0
$219$		−	4.80625i		−	0.324776i
$220$		0			0
$221$		−	25.8874i		−	1.74137i
$222$		0			0
$223$	−10.1047	+	10.1047i	−0.676660	+	0.676660i	−0.959243	−	0.282583i	$-0.908809\pi$
$223$	−10.1047	+	10.1047i	−0.676660	+	0.676660i	0.282583	+	0.959243i	$0.408809\pi$
$224$		0			0
$225$	1.70156	−	4.70156i	0.113437	−	0.313437i
$226$		0			0
$227$	−11.3985	+	11.3985i	−0.756547	+	0.756547i	−0.975692	−	0.219145i	$-0.929673\pi$
$227$	−11.3985	+	11.3985i	−0.756547	+	0.756547i	0.219145	+	0.975692i	$0.429673\pi$
$228$		0			0
$229$	12.4421			0.822198			0.411099	−	0.911591i	$-0.365145\pi$
$229$	12.4421			0.822198			0.411099	+	0.911591i	$0.365145\pi$
$230$		0			0
$231$	−0.596876			−0.0392715
$232$		0			0
$233$	−6.40312	+	6.40312i	−0.419483	+	0.419483i	−0.885025	−	0.465543i	$-0.845859\pi$
$233$	−6.40312	+	6.40312i	−0.419483	+	0.419483i	0.465543	+	0.885025i	$0.345859\pi$
$234$		0			0
$235$	−16.5760	+	11.6291i	−1.08130	+	0.758599i
$236$		0			0
$237$	13.2147	−	13.2147i	0.858387	−	0.858387i
$238$		0			0
$239$		−	7.10469i		−	0.459564i	−0.973242	−	0.229782i	$-0.926199\pi$
$239$		−	7.10469i		−	0.459564i	0.973242	−	0.229782i	$-0.0738013\pi$
$240$		0			0
$241$			10.3550i			0.667021i	0.942746	+	0.333510i	$0.108233\pi$
$241$			10.3550i			0.667021i	−0.942746	+	0.333510i	$0.891767\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$		0			0
$245$	14.7598	+	2.58874i	0.942972	+	0.165388i
$246$		0			0
$247$	16.0744	−	16.0744i	1.02279	−	1.02279i
$248$		0			0
$249$	−0.772577			−0.0489601
$250$		0			0
$251$		−	2.08717i		−	0.131741i	−0.997828	−	0.0658704i	$-0.979018\pi$
$251$		−	2.08717i		−	0.131741i	0.997828	−	0.0658704i	$-0.0209824\pi$
$252$		0			0
$253$	2.99186	+	2.18561i	0.188097	+	0.137408i
$254$		0			0
$255$	21.1047	+	3.70156i	1.32163	+	0.231801i
$256$		0			0
$257$	1.59688	+	1.59688i	0.0996104	+	0.0996104i	0.755156	−	0.655545i	$-0.227561\pi$
$257$	1.59688	+	1.59688i	0.0996104	+	0.0996104i	−0.655545	+	0.755156i	$0.727561\pi$
$258$		0			0
$259$			3.70156i			0.230004i
$260$		0			0
$261$	−2.29844			−0.142270
$262$		0			0
$263$	−4.01861	−	4.01861i	−0.247798	−	0.247798i	0.572268	−	0.820066i	$-0.306064\pi$
$263$	−4.01861	−	4.01861i	−0.247798	−	0.247798i	−0.820066	+	0.572268i	$0.806064\pi$
$264$		0			0
$265$	−14.4031	+	10.1047i	−0.884777	+	0.620726i
$266$		0			0
$267$	16.8470	−	16.8470i	1.03102	−	1.03102i
$268$		0			0
$269$			10.8953i			0.664299i	0.943227	+	0.332149i	$0.107774\pi$
$269$			10.8953i			0.664299i	−0.943227	+	0.332149i	$0.892226\pi$
$270$		0			0
$271$	6.89531			0.418860			0.209430	−	0.977824i	$-0.432839\pi$
$271$	6.89531			0.418860			0.209430	+	0.977824i	$0.432839\pi$
$272$		0			0
$273$	−2.08717	−	2.08717i	−0.126321	−	0.126321i
$274$		0			0
$275$	−1.31459	+	3.63232i	−0.0792727	+	0.219037i
$276$		0			0
$277$	21.5078	+	21.5078i	1.29228	+	1.29228i	0.933374	+	0.358905i	$0.116850\pi$
$277$	21.5078	+	21.5078i	1.29228	+	1.29228i	0.358905	+	0.933374i	$0.383150\pi$
$278$		0			0
$279$			9.10469i			0.545083i
$280$		0			0
$281$			20.4793i			1.22169i	0.791748	+	0.610847i	$0.209171\pi$
$281$			20.4793i			1.22169i	−0.791748	+	0.610847i	$0.790829\pi$
$282$		0			0
$283$	1.70088	+	1.70088i	0.101107	+	0.101107i	0.755851	−	0.654744i	$-0.227224\pi$
$283$	1.70088	+	1.70088i	0.101107	+	0.101107i	−0.654744	+	0.755851i	$0.727224\pi$
$284$		0			0
$285$	10.8062	+	15.4031i	0.640107	+	0.912402i
$286$		0			0
$287$	−2.97503	+	2.97503i	−0.175610	+	0.175610i
$288$		0			0
$289$		−	28.9109i		−	1.70064i
$290$		0			0
$291$		−	21.2519i		−	1.24581i
$292$		0			0
$293$	1.70088	+	1.70088i	0.0993663	+	0.0993663i	0.755042	−	0.655676i	$-0.227616\pi$
$293$	1.70088	+	1.70088i	0.0993663	+	0.0993663i	−0.655676	+	0.755042i	$0.727616\pi$
$294$		0			0
$295$	8.15250	+	1.42987i	0.474657	+	0.0832503i
$296$		0			0
$297$	−3.09031	+	3.09031i	−0.179318	+	0.179318i
$298$		0			0
$299$	2.81930	+	18.1047i	0.163045	+	1.04702i
$300$		0			0
$301$	−3.19375			−0.184085
$302$		0			0
$303$	7.10469	−	7.10469i	0.408154	−	0.408154i
$304$		0			0
$305$	−16.5078	−	2.89531i	−0.945234	−	0.165785i
$306$		0			0
$307$	−5.29844	−	5.29844i	−0.302398	−	0.302398i	0.539553	−	0.841951i	$-0.318593\pi$
$307$	−5.29844	−	5.29844i	−0.302398	−	0.302398i	−0.841951	+	0.539553i	$0.818593\pi$
$308$		0			0
$309$	3.63232			0.206635
$310$		0			0
$311$	−31.4031			−1.78071			−0.890354	−	0.455269i	$-0.849543\pi$
$311$	−31.4031			−1.78071			−0.890354	+	0.455269i	$0.849543\pi$
$312$		0			0
$313$	4.79119	+	4.79119i	0.270814	+	0.270814i	0.829428	−	0.558614i	$-0.188667\pi$
$313$	4.79119	+	4.79119i	0.270814	+	0.270814i	−0.558614	+	0.829428i	$0.688667\pi$
$314$		0			0
$315$	−1.00000	+	0.701562i	−0.0563436	+	0.0395285i
$316$		0			0
$317$	−8.10469	−	8.10469i	−0.455205	−	0.455205i	0.441873	−	0.897078i	$-0.354314\pi$
$317$	−8.10469	−	8.10469i	−0.455205	−	0.455205i	−0.897078	+	0.441873i	$0.854314\pi$
$318$		0			0
$319$	1.77572			0.0994213
$320$		0			0
$321$			16.8470i			0.940309i
$322$		0			0
$323$	28.5078	−	28.5078i	1.58622	−	1.58622i
$324$		0			0
$325$	−17.2984	+	8.10469i	−0.959545	+	0.449567i
$326$		0			0
$327$	−10.8970	+	10.8970i	−0.602603	+	0.602603i
$328$		0			0
$329$	4.94691			0.272732
$330$		0			0
$331$	17.7016			0.972966			0.486483	−	0.873690i	$-0.338280\pi$
$331$	17.7016			0.972966			0.486483	+	0.873690i	$0.338280\pi$
$332$		0			0
$333$	4.79119	+	4.79119i	0.262555	+	0.262555i
$334$		0			0
$335$	11.5078	+	16.4031i	0.628739	+	0.896198i
$336$		0			0
$337$	5.67905	−	5.67905i	0.309357	−	0.309357i	−0.535303	−	0.844660i	$-0.679803\pi$
$337$	5.67905	−	5.67905i	0.309357	−	0.309357i	0.844660	+	0.535303i	$0.179803\pi$
$338$		0			0
$339$	16.8470			0.915004
$340$		0			0
$341$		−	7.03407i		−	0.380916i
$342$		0			0
$343$	−5.29276	−	5.29276i	−0.285782	−	0.285782i
$344$		0			0
$345$	−15.1630	−	0.290300i	−0.816347	−	0.0156292i
$346$		0			0
$347$	−19.5078	−	19.5078i	−1.04723	−	1.04723i	−0.998828	−	0.0484064i	$-0.984586\pi$
$347$	−19.5078	−	19.5078i	−1.04723	−	1.04723i	−0.0484064	−	0.998828i	$-0.515414\pi$
$348$		0			0
$349$		−	21.7016i		−	1.16166i	−0.814026	−	0.580829i	$-0.802728\pi$
$349$		−	21.7016i		−	1.16166i	0.814026	−	0.580829i	$-0.197272\pi$
$350$		0			0
$351$	−21.6125			−1.15359
$352$		0			0
$353$	7.29844	−	7.29844i	0.388457	−	0.388457i	−0.485680	−	0.874137i	$-0.661428\pi$
$353$	7.29844	−	7.29844i	0.388457	−	0.388457i	0.874137	+	0.485680i	$0.161428\pi$
$354$		0			0
$355$	0.887861	−	5.06219i	0.0471227	−	0.268673i
$356$		0			0
$357$	−3.70156	−	3.70156i	−0.195907	−	0.195907i
$358$		0			0
$359$	1.31459			0.0693813			0.0346907	−	0.999398i	$-0.488955\pi$
$359$	1.31459			0.0693813			0.0346907	+	0.999398i	$0.488955\pi$
$360$		0			0
$361$	16.4031			0.863322
$362$		0			0
$363$	−10.4031	+	10.4031i	−0.546022	+	0.546022i
$364$		0			0
$365$	4.36446	+	6.22106i	0.228446	+	0.325625i
$366$		0			0
$367$	−16.4607	+	16.4607i	−0.859243	+	0.859243i	−0.991249	−	0.132006i	$-0.957858\pi$
$367$	−16.4607	+	16.4607i	−0.859243	+	0.859243i	0.132006	+	0.991249i	$0.457858\pi$
$368$		0			0
$369$			7.70156i			0.400927i
$370$		0			0
$371$	4.29844			0.223164
$372$		0			0
$373$	18.8937	+	18.8937i	0.978281	+	0.978281i	0.999769	−	0.0214883i	$-0.00684047\pi$
$373$	18.8937	+	18.8937i	0.978281	+	0.978281i	−0.0214883	+	0.999769i	$0.506840\pi$
$374$		0			0
$375$	−4.13389	−	15.2614i	−0.213473	−	0.788096i
$376$		0			0
$377$	6.20937	+	6.20937i	0.319799	+	0.319799i
$378$		0			0
$379$	−23.5696			−1.21069			−0.605346	−	0.795963i	$-0.706965\pi$
$379$	−23.5696			−1.21069			−0.605346	+	0.795963i	$0.706965\pi$
$380$		0			0
$381$	−13.4031			−0.686663
$382$		0			0
$383$	−14.6041	−	14.6041i	−0.746236	−	0.746236i	0.227534	−	0.973770i	$-0.426934\pi$
$383$	−14.6041	−	14.6041i	−0.746236	−	0.746236i	−0.973770	+	0.227534i	$0.926934\pi$
$384$		0			0
$385$	0.772577	−	0.542011i	0.0393742	−	0.0276234i
$386$		0			0
$387$	−4.13389	+	4.13389i	−0.210138	+	0.210138i
$388$		0			0
$389$	−12.9032			−0.654221			−0.327110	−	0.944986i	$-0.606075\pi$
$389$	−12.9032			−0.654221			−0.327110	+	0.944986i	$0.606075\pi$
$390$		0			0
$391$	5.00000	+	32.1084i	0.252861	+	1.62379i
$392$		0			0
$393$	−11.4031	+	11.4031i	−0.575212	+	0.575212i
$394$		0			0
$395$	−5.10469	+	29.1047i	−0.256845	+	1.46442i
$396$		0			0
$397$	−0.701562	−	0.701562i	−0.0352104	−	0.0352104i	0.689282	−	0.724493i	$-0.257926\pi$
$397$	−0.701562	−	0.701562i	−0.0352104	−	0.0352104i	−0.724493	+	0.689282i	$0.757926\pi$
$398$		0			0
$399$		−	4.59688i		−	0.230132i
$400$		0			0
$401$			8.80980i			0.439940i	0.975507	+	0.219970i	$0.0705960\pi$
$401$			8.80980i			0.439940i	−0.975507	+	0.219970i	$0.929404\pi$
$402$		0			0
$403$	24.5969	−	24.5969i	1.22526	−	1.22526i
$404$		0			0
$405$	1.93144	−	11.0122i	0.0959742	−	0.547203i
$406$		0			0
$407$	−3.70156	−	3.70156i	−0.183480	−	0.183480i
$408$		0			0
$409$		−	21.7016i		−	1.07307i	−0.843877	−	0.536537i	$-0.819732\pi$
$409$		−	21.7016i		−	1.07307i	0.843877	−	0.536537i	$-0.180268\pi$
$410$		0			0
$411$		−	3.63232i		−	0.179169i
$412$		0			0
$413$	−1.42987	−	1.42987i	−0.0703594	−	0.0703594i
$414$		0			0
$415$	1.00000	−	0.701562i	0.0490881	−	0.0344383i
$416$		0			0
$417$	−3.70156	−	3.70156i	−0.181266	−	0.181266i
$418$		0			0
$419$	−36.7843			−1.79703			−0.898516	−	0.438940i	$-0.855354\pi$
$419$	−36.7843			−1.79703			−0.898516	+	0.438940i	$0.855354\pi$
$420$		0			0
$421$		−	8.80980i		−	0.429363i	−0.976684	−	0.214682i	$-0.931129\pi$
$421$		−	8.80980i		−	0.429363i	0.976684	−	0.214682i	$-0.0688714\pi$
$422$		0			0
$423$	6.40312	−	6.40312i	0.311331	−	0.311331i
$424$		0			0
$425$	−30.6786	+	14.3736i	−1.48813	+	0.697220i
$426$		0			0
$427$	2.89531	+	2.89531i	0.140114	+	0.140114i
$428$		0			0
$429$	4.17433			0.201539
$430$		0			0
$431$		−	30.0617i		−	1.44802i	−0.689789	−	0.724011i	$-0.742297\pi$
$431$		−	30.0617i		−	1.44802i	0.689789	−	0.724011i	$-0.257703\pi$
$432$		0			0
$433$	−9.96866	−	9.96866i	−0.479063	−	0.479063i	0.425769	−	0.904832i	$-0.360004\pi$
$433$	−9.96866	−	9.96866i	−0.479063	−	0.479063i	−0.904832	+	0.425769i	$0.860004\pi$
$434$		0			0
$435$	−5.95005	+	4.17433i	−0.285283	+	0.200144i
$436$		0			0
$437$	−16.8326	+	23.0420i	−0.805214	+	1.10225i
$438$		0			0
$439$		−	24.8062i		−	1.18394i	−0.805961	−	0.591969i	$-0.798351\pi$
$439$		−	24.8062i		−	1.18394i	0.805961	−	0.591969i	$-0.201649\pi$
$440$		0			0
$441$	−6.70156			−0.319122
$442$		0			0
$443$	4.70156	−	4.70156i	0.223378	−	0.223378i	−0.586541	−	0.809919i	$-0.699511\pi$
$443$	4.70156	−	4.70156i	0.223378	−	0.223378i	0.809919	+	0.586541i	$0.199511\pi$
$444$		0			0
$445$	−6.50781	+	37.1047i	−0.308500	+	1.75893i
$446$		0			0
$447$	−8.26778	+	8.26778i	−0.391053	+	0.391053i
$448$		0			0
$449$			27.3141i			1.28903i	0.764592	+	0.644515i	$0.222941\pi$
$449$			27.3141i			1.28903i	−0.764592	+	0.644515i	$0.777059\pi$
$450$		0			0
$451$		−	5.95005i		−	0.280177i
$452$		0			0
$453$	15.4031	−	15.4031i	0.723702	−	0.723702i
$454$		0			0
$455$	4.59688	+	0.806248i	0.215505	+	0.0377975i
$456$		0			0
$457$	−24.7285	+	24.7285i	−1.15675	+	1.15675i	−0.171581	+	0.985170i	$0.554887\pi$
$457$	−24.7285	+	24.7285i	−1.15675	+	1.15675i	−0.985170	+	0.171581i	$0.945113\pi$
$458$		0			0
$459$	−38.3295			−1.78907
$460$		0			0
$461$	−6.59688			−0.307247			−0.153624	−	0.988129i	$-0.549094\pi$
$461$	−6.59688			−0.307247			−0.153624	+	0.988129i	$0.549094\pi$
$462$		0			0
$463$	−1.00000	+	1.00000i	−0.0464739	+	0.0464739i	−0.729962	−	0.683488i	$-0.760462\pi$
$463$	−1.00000	+	1.00000i	−0.0464739	+	0.0464739i	0.683488	+	0.729962i	$0.260462\pi$
$464$		0			0
$465$	16.5356	+	23.5696i	0.766819	+	1.09302i
$466$		0			0
$467$	12.8284	−	12.8284i	0.593628	−	0.593628i	−0.344982	−	0.938609i	$-0.612115\pi$
$467$	12.8284	−	12.8284i	0.593628	−	0.593628i	0.938609	+	0.344982i	$0.112115\pi$
$468$		0			0
$469$		−	4.89531i		−	0.226045i
$470$		0			0
$471$			12.6727i			0.583926i
$472$		0			0
$473$	3.19375	−	3.19375i	0.146849	−	0.146849i
$474$		0			0
$475$	−27.9745	−	10.1244i	−1.28356	−	0.464539i
$476$		0			0
$477$	5.56376	−	5.56376i	0.254747	−	0.254747i
$478$		0			0
$479$	18.0807			0.826129			0.413065	−	0.910702i	$-0.364458\pi$
$479$	18.0807			0.826129			0.413065	+	0.910702i	$0.364458\pi$
$480$		0			0
$481$		−	25.8874i		−	1.18036i
$482$		0			0
$483$	2.99186	+	2.18561i	0.136134	+	0.0994488i
$484$		0			0
$485$	19.2984	+	27.5078i	0.876297	+	1.24907i
$486$		0			0
$487$	22.1047	+	22.1047i	1.00166	+	1.00166i	0.999999	+	0.00166033i	$0.000528500\pi$
$487$	22.1047	+	22.1047i	1.00166	+	1.00166i	0.00166033	+	0.999999i	$0.499472\pi$
$488$		0			0
$489$		−	10.0000i		−	0.452216i
$490$		0			0
$491$	−42.7172			−1.92780			−0.963900	−	0.266265i	$-0.914210\pi$
$491$	−42.7172			−1.92780			−0.963900	+	0.266265i	$0.914210\pi$
$492$		0			0
$493$	11.0122	+	11.0122i	0.495967	+	0.495967i
$494$		0			0
$495$	0.298438	−	1.70156i	0.0134138	−	0.0764795i
$496$		0			0
$497$	−0.887861	+	0.887861i	−0.0398260	+	0.0398260i
$498$		0			0
$499$			19.7016i			0.881963i	0.897516	+	0.440982i	$0.145370\pi$
$499$			19.7016i			0.881963i	−0.897516	+	0.440982i	$0.854630\pi$
$500$		0			0
$501$	−5.40312			−0.241394
$502$		0			0
$503$	22.4108	+	22.4108i	0.999247	+	0.999247i	1.00000		0.000752539i	$-0.000239541\pi$
$503$	22.4108	+	22.4108i	0.999247	+	0.999247i	−0.000752539		1.00000i	$0.500240\pi$
$504$		0			0
$505$	−2.74446	+	15.6477i	−0.122127	+	0.696314i
$506$		0			0
$507$	1.59688	+	1.59688i	0.0709197	+	0.0709197i
$508$		0			0
$509$		−	33.6125i		−	1.48985i	−0.667149	−	0.744924i	$-0.732486\pi$
$509$		−	33.6125i		−	1.48985i	0.667149	−	0.744924i	$-0.267514\pi$
$510$		0			0
$511$		−	1.85660i		−	0.0821311i
$512$		0			0
$513$	−23.8002	−	23.8002i	−1.05080	−	1.05080i
$514$		0			0
$515$	−4.70156	+	3.29844i	−0.207176	+	0.145347i
$516$		0			0
$517$	−4.94691	+	4.94691i	−0.217565	+	0.217565i
$518$		0			0
$519$			16.8062i			0.737712i
$520$		0			0
$521$			42.7344i			1.87223i	0.351697	+	0.936114i	$0.385605\pi$
$521$			42.7344i			1.87223i	−0.351697	+	0.936114i	$0.614395\pi$
$522$		0			0
$523$	−30.0213	−	30.0213i	−1.31274	−	1.31274i	−0.919389	−	0.393349i	$-0.871316\pi$
$523$	−30.0213	−	30.0213i	−1.31274	−	1.31274i	−0.393349	−	0.919389i	$-0.628684\pi$
$524$		0			0
$525$	−1.31459	+	3.63232i	−0.0573733	+	0.158527i
$526$		0			0
$527$	43.6222	−	43.6222i	1.90022	−	1.90022i
$528$		0			0
$529$	−6.99364	−	21.9109i	−0.304071	−	0.952649i
$530$		0			0
$531$	−3.70156			−0.160634
$532$		0			0
$533$	20.8062	−	20.8062i	0.901219	−	0.901219i
$534$		0			0
$535$	−15.2984	−	21.8062i	−0.661409	−	0.942766i
$536$		0			0
$537$	−10.0000	−	10.0000i	−0.431532	−	0.431532i
$538$		0			0
$539$	5.17748			0.223010
$540$		0			0
$541$	−24.8062			−1.06650			−0.533252	−	0.845956i	$-0.679030\pi$
$541$	−24.8062			−1.06650			−0.533252	+	0.845956i	$0.679030\pi$
$542$		0			0
$543$	−26.6600	−	26.6600i	−1.14409	−	1.14409i
$544$		0			0
$545$	4.20937	−	24.0000i	0.180310	−	1.02805i
$546$		0			0
$547$	−9.89531	−	9.89531i	−0.423093	−	0.423093i	0.463174	−	0.886267i	$-0.346710\pi$
$547$	−9.89531	−	9.89531i	−0.423093	−	0.423093i	−0.886267	+	0.463174i	$0.846710\pi$
$548$		0			0
$549$	7.49521			0.319888
$550$		0			0
$551$			13.6758i			0.582610i
$552$		0			0
$553$	5.10469	−	5.10469i	0.217073	−	0.217073i
$554$		0			0
$555$	21.1047	+	3.70156i	0.895844	+	0.157123i
$556$		0			0
$557$	−5.33320	+	5.33320i	−0.225975	+	0.225975i	−0.811009	−	0.585034i	$-0.801081\pi$
$557$	−5.33320	+	5.33320i	−0.225975	+	0.225975i	0.585034	+	0.811009i	$0.301081\pi$
$558$		0			0
$559$	22.3359			0.944709
$560$		0			0
$561$	7.40312			0.312560
$562$		0			0
$563$	18.0059	+	18.0059i	0.758857	+	0.758857i	0.976114	−	0.217257i	$-0.0697110\pi$
$563$	18.0059	+	18.0059i	0.758857	+	0.758857i	−0.217257	+	0.976114i	$0.569711\pi$
$564$		0			0
$565$	−21.8062	+	15.2984i	−0.917396	+	0.643610i
$566$		0			0
$567$	−1.93144	+	1.93144i	−0.0811130	+	0.0811130i
$568$		0			0
$569$	−0.772577			−0.0323881			−0.0161941	−	0.999869i	$-0.505155\pi$
$569$	−0.772577			−0.0323881			−0.0161941	+	0.999869i	$0.505155\pi$
$570$		0			0
$571$		−	18.8533i		−	0.788986i	−0.918899	−	0.394493i	$-0.870920\pi$
$571$		−	18.8533i		−	0.788986i	0.918899	−	0.394493i	$-0.129080\pi$
$572$		0			0
$573$	24.3422	+	24.3422i	1.01691	+	1.01691i
$574$		0			0
$575$	19.8901	−	13.3934i	0.829474	−	0.558545i
$576$		0			0
$577$	23.2094	+	23.2094i	0.966219	+	0.966219i	0.999448	−	0.0332289i	$-0.0105790\pi$
$577$	23.2094	+	23.2094i	0.966219	+	0.966219i	−0.0332289	+	0.999448i	$0.510579\pi$
$578$		0			0
$579$		−	2.59688i		−	0.107922i
$580$		0			0
$581$	−0.298438			−0.0123813
$582$		0			0
$583$	−4.29844	+	4.29844i	−0.178023	+	0.178023i
$584$		0			0
$585$	6.99364	−	4.90647i	0.289151	−	0.202858i
$586$		0			0
$587$	5.00000	+	5.00000i	0.206372	+	0.206372i	0.802723	−	0.596351i	$-0.203384\pi$
$587$	5.00000	+	5.00000i	0.206372	+	0.206372i	−0.596351	+	0.802723i	$0.703384\pi$
$588$		0			0
$589$	54.1734			2.23217
$590$		0			0
$591$	−24.8062			−1.02039
$592$		0			0
$593$	−23.0000	+	23.0000i	−0.944497	+	0.944497i	−0.998539	−	0.0540419i	$-0.982790\pi$
$593$	−23.0000	+	23.0000i	−0.944497	+	0.944497i	0.0540419	+	0.998539i	$0.482790\pi$
$594$		0			0
$595$	8.15250	+	1.42987i	0.334220	+	0.0586190i
$596$		0			0
$597$	3.09031	−	3.09031i	0.126478	−	0.126478i
$598$		0			0
$599$			22.0000i			0.898896i	0.893307	+	0.449448i	$0.148379\pi$
$599$			22.0000i			0.898896i	−0.893307	+	0.449448i	$0.851621\pi$
$600$		0			0
$601$	−2.50781			−0.102296			−0.0511479	−	0.998691i	$-0.516288\pi$
$601$	−2.50781			−0.102296			−0.0511479	+	0.998691i	$0.516288\pi$
$602$		0			0
$603$	−6.33634	−	6.33634i	−0.258036	−	0.258036i
$604$		0			0
$605$	4.01861	−	22.9123i	0.163380	−	0.931519i
$606$		0			0
$607$	5.59688	+	5.59688i	0.227170	+	0.227170i	0.811509	−	0.584339i	$-0.198646\pi$
$607$	5.59688	+	5.59688i	0.227170	+	0.227170i	−0.584339	+	0.811509i	$0.698646\pi$
$608$		0			0
$609$	1.77572			0.0719558
$610$		0			0
$611$	−34.5969			−1.39964
$612$		0			0
$613$	11.6291	+	11.6291i	0.469695	+	0.469695i	0.901816	−	0.432121i	$-0.142235\pi$
$613$	11.6291	+	11.6291i	0.469695	+	0.469695i	−0.432121	+	0.901816i	$0.642235\pi$
$614$		0			0
$615$	13.9873	+	19.9373i	0.564021	+	0.803950i
$616$		0			0
$617$	−10.1992	+	10.1992i	−0.410605	+	0.410605i	−0.881949	−	0.471344i	$-0.843769\pi$
$617$	−10.1992	+	10.1992i	−0.410605	+	0.410605i	0.471344	+	0.881949i	$0.343769\pi$
$618$		0			0
$619$	11.6695			0.469038			0.234519	−	0.972111i	$-0.424648\pi$
$619$	11.6695			0.469038			0.234519	+	0.972111i	$0.424648\pi$
$620$		0			0
$621$	26.8062	−	4.17433i	1.07570	−	0.167510i
$622$		0			0
$623$	6.50781	−	6.50781i	0.260730	−	0.260730i
$624$		0			0
$625$	19.2094	+	16.0000i	0.768375	+	0.640000i
$626$		0			0
$627$	4.59688	+	4.59688i	0.183582	+	0.183582i
$628$		0			0
$629$		−	45.9109i		−	1.83059i
$630$		0			0
$631$		−	18.6227i		−	0.741359i	−0.928761	−	0.370680i	$-0.879125\pi$
$631$		−	18.6227i		−	0.741359i	0.928761	−	0.370680i	$-0.120875\pi$
$632$		0			0
$633$	6.29844	−	6.29844i	0.250340	−	0.250340i
$634$		0			0
$635$	17.3486	−	12.1711i	0.688458	−	0.482996i
$636$		0			0
$637$	18.1047	+	18.1047i	0.717334	+	0.717334i
$638$		0			0
$639$			2.29844i			0.0909248i
$640$		0			0
$641$			14.7598i			0.582979i	0.956574	+	0.291489i	$0.0941508\pi$
$641$			14.7598i			0.582979i	−0.956574	+	0.291489i	$0.905849\pi$
$642$		0			0
$643$	19.7816	+	19.7816i	0.780110	+	0.780110i	0.979849	−	0.199739i	$-0.0640094\pi$
$643$	19.7816	+	19.7816i	0.780110	+	0.780110i	−0.199739	+	0.979849i	$0.564009\pi$
$644$		0			0
$645$	−3.19375	+	18.2094i	−0.125754	+	0.716993i
$646$		0			0
$647$	6.10469	+	6.10469i	0.240000	+	0.240000i	0.816850	−	0.576850i	$-0.195718\pi$
$647$	6.10469	+	6.10469i	0.240000	+	0.240000i	−0.576850	+	0.816850i	$0.695718\pi$
$648$		0			0
$649$	2.85974			0.112255
$650$		0			0
$651$		−	7.03407i		−	0.275687i
$652$		0			0
$653$	−16.1047	+	16.1047i	−0.630225	+	0.630225i	−0.948124	−	0.317899i	$-0.897023\pi$
$653$	−16.1047	+	16.1047i	−0.630225	+	0.630225i	0.317899	+	0.948124i	$0.397023\pi$
$654$		0			0
$655$	4.40490	−	25.1148i	0.172114	−	0.981316i
$656$		0			0
$657$	−2.40312	−	2.40312i	−0.0937548	−	0.0937548i
$658$		0			0
$659$	25.3454			0.987315			0.493658	−	0.869656i	$-0.335660\pi$
$659$	25.3454			0.987315			0.493658	+	0.869656i	$0.335660\pi$
$660$		0			0
$661$		−	18.9342i		−	0.736454i	−0.929736	−	0.368227i	$-0.879965\pi$
$661$		−	18.9342i		−	0.736454i	0.929736	−	0.368227i	$-0.120035\pi$
$662$		0			0
$663$	25.8874	+	25.8874i	1.00538	+	1.00538i
$664$		0			0
$665$	4.17433	+	5.95005i	0.161874	+	0.230733i
$666$		0			0
$667$	−8.90087	−	6.50226i	−0.344643	−	0.251768i
$668$		0			0
$669$		−	20.2094i		−	0.781339i
$670$		0			0
$671$	−5.79063			−0.223545
$672$		0			0
$673$	−12.1047	+	12.1047i	−0.466601	+	0.466601i	−0.900812	−	0.434210i	$-0.857028\pi$
$673$	−12.1047	+	12.1047i	−0.466601	+	0.466601i	0.434210	+	0.900812i	$0.357028\pi$
$674$		0			0
$675$	12.0000	+	25.6125i	0.461880	+	0.985825i
$676$		0			0
$677$	10.9718	−	10.9718i	0.421681	−	0.421681i	−0.464101	−	0.885782i	$-0.653623\pi$
$677$	10.9718	−	10.9718i	0.421681	−	0.421681i	0.885782	+	0.464101i	$0.153623\pi$
$678$		0			0
$679$		−	8.20937i		−	0.315047i
$680$		0			0
$681$		−	22.7971i		−	0.873585i
$682$		0			0
$683$	25.2094	−	25.2094i	0.964610	−	0.964610i	−0.0347850	−	0.999395i	$-0.511075\pi$
$683$	25.2094	−	25.2094i	0.964610	−	0.964610i	0.999395	+	0.0347850i	$0.0110746\pi$
$684$		0			0
$685$	3.29844	+	4.70156i	0.126027	+	0.179637i
$686$		0			0
$687$	−12.4421	+	12.4421i	−0.474696	+	0.474696i
$688$		0			0
$689$	−30.0617			−1.14526
$690$		0			0
$691$	−26.2094			−0.997052			−0.498526	−	0.866875i	$-0.666125\pi$
$691$	−26.2094			−0.997052			−0.498526	+	0.866875i	$0.666125\pi$
$692$		0			0
$693$	−0.298438	+	0.298438i	−0.0113367	+	0.0113367i
$694$		0			0
$695$	8.15250	+	1.42987i	0.309242	+	0.0542381i
$696$		0			0
$697$	36.8996	−	36.8996i	1.39767	−	1.39767i
$698$		0			0
$699$		−	12.8062i		−	0.484377i
$700$		0			0
$701$			6.18062i			0.233439i	0.993165	+	0.116719i	$0.0372378\pi$
$701$			6.18062i			0.233439i	−0.993165	+	0.116719i	$0.962762\pi$
$702$		0			0
$703$	28.5078	−	28.5078i	1.07519	−	1.07519i
$704$		0			0
$705$	4.94691	−	28.2051i	0.186311	−	1.06227i
$706$		0			0
$707$	2.74446	−	2.74446i	0.103216	−	0.103216i
$708$		0			0
$709$	−43.9681			−1.65126			−0.825628	−	0.564214i	$-0.809179\pi$
$709$	−43.9681			−1.65126			−0.825628	+	0.564214i	$0.809179\pi$
$710$		0			0
$711$		−	13.2147i		−	0.495590i
$712$		0			0
$713$	−25.7571	+	35.2586i	−0.964610	+	1.32044i
$714$		0			0
$715$	−5.40312	+	3.79063i	−0.202065	+	0.141761i
$716$		0			0
$717$	7.10469	+	7.10469i	0.265329	+	0.265329i
$718$		0			0
$719$			38.5078i			1.43610i	0.695992	+	0.718050i	$0.254965\pi$
$719$			38.5078i			1.43610i	−0.695992	+	0.718050i	$0.745035\pi$
$720$		0			0
$721$	1.40312			0.0522551
$722$		0			0
$723$	−10.3550	−	10.3550i	−0.385105	−	0.385105i
$724$		0			0
$725$	3.91093	−	10.8062i	0.145248	−	0.401334i
$726$		0			0
$727$	−8.96552	+	8.96552i	−0.332513	+	0.332513i	−0.853540	−	0.521027i	$-0.825549\pi$
$727$	−8.96552	+	8.96552i	−0.332513	+	0.332513i	0.521027	+	0.853540i	$0.325549\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	39.6125			1.46512
$732$		0			0
$733$	−33.7689	−	33.7689i	−1.24728	−	1.24728i	−0.956916	−	0.290366i	$-0.906223\pi$
$733$	−33.7689	−	33.7689i	−1.24728	−	1.24728i	−0.290366	−	0.956916i	$-0.593777\pi$
$734$		0			0
$735$	−17.3486	+	12.1711i	−0.639912	+	0.448938i
$736$		0			0
$737$	4.89531	+	4.89531i	0.180321	+	0.180321i
$738$		0			0
$739$			8.29844i			0.305263i	0.988283	+	0.152631i	$0.0487748\pi$
$739$			8.29844i			0.305263i	−0.988283	+	0.152631i	$0.951225\pi$
$740$		0			0
$741$			32.1489i			1.18102i
$742$		0			0
$743$	24.8438	+	24.8438i	0.911430	+	0.911430i	0.996385	−	0.0849545i	$-0.0270745\pi$
$743$	24.8438	+	24.8438i	0.911430	+	0.911430i	−0.0849545	+	0.996385i	$0.527074\pi$
$744$		0			0
$745$	3.19375	−	18.2094i	0.117010	−	0.667140i
$746$		0			0
$747$	−0.386289	+	0.386289i	−0.0141336	+	0.0141336i
$748$		0			0
$749$			6.50781i			0.237790i
$750$		0			0
$751$		−	30.0617i		−	1.09697i	−0.836161	−	0.548484i	$-0.815205\pi$
$751$		−	30.0617i		−	1.09697i	0.836161	−	0.548484i	$-0.184795\pi$
$752$		0			0
$753$	2.08717	+	2.08717i	0.0760605	+	0.0760605i
$754$		0			0
$755$	−5.95005	+	33.9246i	−0.216545	+	1.23464i
$756$		0			0
$757$	32.7657	−	32.7657i	1.19089	−	1.19089i	0.214073	−	0.976818i	$-0.431327\pi$
$757$	32.7657	−	32.7657i	1.19089	−	1.19089i	0.976818	−	0.214073i	$-0.0686730\pi$
$758$		0			0
$759$	−5.17748	+	0.806248i	−0.187930	+	0.0292650i
$760$		0			0
$761$	−6.50781			−0.235908			−0.117954	−	0.993019i	$-0.537634\pi$
$761$	−6.50781			−0.235908			−0.117954	+	0.993019i	$0.537634\pi$
$762$		0			0
$763$	−4.20937	+	4.20937i	−0.152390	+	0.152390i
$764$		0			0
$765$	12.4031	−	8.70156i	0.448436	−	0.314606i
$766$		0			0
$767$	10.0000	+	10.0000i	0.361079	+	0.361079i
$768$		0			0
$769$	41.7312			1.50487			0.752434	−	0.658668i	$-0.228880\pi$
$769$	41.7312			1.50487			0.752434	+	0.658668i	$0.228880\pi$
$770$		0			0
$771$	−3.19375			−0.115020
$772$		0			0
$773$	−9.54193	−	9.54193i	−0.343200	−	0.343200i	0.514369	−	0.857569i	$-0.328026\pi$
$773$	−9.54193	−	9.54193i	−0.343200	−	0.343200i	−0.857569	+	0.514369i	$0.828026\pi$
$774$		0			0
$775$	−42.8062	−	15.4922i	−1.53765	−	0.556496i
$776$		0			0
$777$	−3.70156	−	3.70156i	−0.132793	−	0.132793i
$778$		0			0
$779$	45.8247			1.64184
$780$		0			0
$781$		−	1.77572i		−	0.0635403i
$782$		0			0
$783$	9.19375	−	9.19375i	0.328558	−	0.328558i
$784$		0			0
$785$	−11.5078	−	16.4031i	−0.410731	−	0.585453i
$786$		0			0
$787$	−0.386289	+	0.386289i	−0.0137697	+	0.0137697i	−0.713958	−	0.700188i	$-0.753099\pi$
$787$	−0.386289	+	0.386289i	−0.0137697	+	0.0137697i	0.700188	+	0.713958i	$0.253099\pi$
$788$		0			0
$789$	8.03722			0.286133
$790$		0			0
$791$	6.50781			0.231391
$792$		0			0
$793$	−20.2488	−	20.2488i	−0.719055	−	0.719055i
$794$		0			0
$795$	4.29844	−	24.5078i	0.152450	−	0.869202i
$796$		0			0
$797$	−6.87835	+	6.87835i	−0.243644	+	0.243644i	−0.818356	−	0.574712i	$-0.805114\pi$
$797$	−6.87835	+	6.87835i	−0.243644	+	0.243644i	0.574712	+	0.818356i	$0.305114\pi$
$798$		0			0
$799$	−61.3571			−2.17066
$800$		0			0
$801$		−	16.8470i		−	0.595260i
$802$		0			0
$803$	1.85660	+	1.85660i	0.0655180	+	0.0655180i
$804$		0			0
$805$	−5.85728	−	0.112139i	−0.206442	−	0.00395240i
$806$		0			0
$807$	−10.8953	−	10.8953i	−0.383533	−	0.383533i
$808$		0			0
$809$		−	35.9109i		−	1.26256i	−0.775555	−	0.631281i	$-0.782530\pi$
$809$		−	35.9109i		−	1.26256i	0.775555	−	0.631281i	$-0.217470\pi$
$810$		0			0
$811$	32.5078			1.14150			0.570752	−	0.821123i	$-0.306652\pi$
$811$	32.5078			1.14150			0.570752	+	0.821123i	$0.306652\pi$
$812$		0			0
$813$	−6.89531	+	6.89531i	−0.241829	+	0.241829i
$814$		0			0
$815$	9.08080	+	12.9437i	0.318087	+	0.453398i
$816$		0			0
$817$	24.5969	+	24.5969i	0.860536	+	0.860536i
$818$		0			0
$819$	−2.08717			−0.0729315
$820$		0			0
$821$	−15.0156			−0.524049			−0.262024	−	0.965061i	$-0.584390\pi$
$821$	−15.0156			−0.524049			−0.262024	+	0.965061i	$0.584390\pi$
$822$		0			0
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	−0.971018	−	0.239004i	$-0.923179\pi$
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	0.239004	+	0.971018i	$0.423179\pi$
$824$		0			0
$825$	−2.31773	−	4.94691i	−0.0806931	−	0.172229i
$826$		0			0
$827$	−25.5011	+	25.5011i	−0.886760	+	0.886760i	−0.994210	−	0.107451i	$-0.965731\pi$
$827$	−25.5011	+	25.5011i	−0.886760	+	0.886760i	0.107451	+	0.994210i	$0.465731\pi$
$828$		0			0
$829$		−	31.3141i		−	1.08758i	−0.839221	−	0.543791i	$-0.816988\pi$
$829$		−	31.3141i		−	1.08758i	0.839221	−	0.543791i	$-0.183012\pi$
$830$		0			0
$831$	−43.0156			−1.49220
$832$		0			0
$833$	32.1084	+	32.1084i	1.11249	+	1.11249i
$834$		0			0
$835$	6.99364	−	4.90647i	0.242025	−	0.169795i
$836$		0			0
$837$	−36.4187	−	36.4187i	−1.25882	−	1.25882i
$838$		0			0
$839$	29.5197			1.01913			0.509567	−	0.860431i	$-0.329806\pi$
$839$	29.5197			1.01913			0.509567	+	0.860431i	$0.329806\pi$
$840$		0			0
$841$	23.7172			0.817834
$842$		0			0
$843$	−20.4793	−	20.4793i	−0.705346	−	0.705346i
$844$		0			0
$845$	−3.51704	−	0.616855i	−0.120990	−	0.0212205i
$846$		0			0
$847$	−4.01861	+	4.01861i	−0.138081	+	0.138081i
$848$		0			0
$849$	−3.40175			−0.116748
$850$		0			0
$851$	5.00000	+	32.1084i	0.171398	+	1.10066i
$852$		0			0
$853$	−18.4031	+	18.4031i	−0.630111	+	0.630111i	−0.948096	−	0.317985i	$-0.896994\pi$
$853$	−18.4031	+	18.4031i	−0.630111	+	0.630111i	0.317985	+	0.948096i	$0.396994\pi$
$854$		0			0
$855$	13.1047	+	2.29844i	0.448171	+	0.0786049i
$856$		0			0
$857$	−8.19375	−	8.19375i	−0.279893	−	0.279893i	0.553173	−	0.833066i	$-0.313417\pi$
$857$	−8.19375	−	8.19375i	−0.279893	−	0.279893i	−0.833066	+	0.553173i	$0.813417\pi$
$858$		0			0
$859$		−	43.1047i		−	1.47071i	−0.677681	−	0.735356i	$-0.737015\pi$
$859$		−	43.1047i		−	1.47071i	0.677681	−	0.735356i	$-0.262985\pi$
$860$		0			0
$861$		−	5.95005i		−	0.202777i
$862$		0			0
$863$	5.29844	−	5.29844i	0.180361	−	0.180361i	−0.611152	−	0.791513i	$-0.709294\pi$
$863$	5.29844	−	5.29844i	0.180361	−	0.180361i	0.791513	+	0.611152i	$0.209294\pi$
$864$		0			0
$865$	−15.2614	−	21.7535i	−0.518904	−	0.739641i
$866$		0			0
$867$	28.9109	+	28.9109i	0.981867	+	0.981867i
$868$		0			0
$869$			10.2094i			0.346329i
$870$		0			0
$871$			34.2360i			1.16004i
$872$		0			0
$873$	−10.6260	−	10.6260i	−0.359634	−	0.359634i
$874$		0			0
$875$	−1.59688	−	5.89531i	−0.0539843	−	0.199298i
$876$		0			0
$877$	19.8062	+	19.8062i	0.668809	+	0.668809i	0.957440	−	0.288631i	$-0.0932001\pi$
$877$	19.8062	+	19.8062i	0.668809	+	0.668809i	−0.288631	+	0.957440i	$0.593200\pi$
$878$		0			0
$879$	−3.40175			−0.114738
$880$		0			0
$881$		−	27.1211i		−	0.913733i	−0.889535	−	0.456866i	$-0.848972\pi$
$881$		−	27.1211i		−	0.913733i	0.889535	−	0.456866i	$-0.151028\pi$
$882$		0			0
$883$	−26.1047	+	26.1047i	−0.878493	+	0.878493i	−0.993379	−	0.114886i	$-0.963350\pi$
$883$	−26.1047	+	26.1047i	−0.878493	+	0.878493i	0.114886	+	0.993379i	$0.463350\pi$
$884$		0			0
$885$	−9.58237	+	6.72263i	−0.322108	+	0.225979i
$886$		0			0
$887$	21.5078	+	21.5078i	0.722162	+	0.722162i	0.969045	−	0.246884i	$-0.0794065\pi$
$887$	21.5078	+	21.5078i	0.722162	+	0.722162i	−0.246884	+	0.969045i	$0.579407\pi$
$888$		0			0
$889$	−5.17748			−0.173647
$890$		0			0
$891$		−	3.86289i		−	0.129412i
$892$		0			0
$893$	−38.0989	−	38.0989i	−1.27493	−	1.27493i
$894$		0			0
$895$	22.0245	+	3.86289i	0.736197	+	0.129122i
$896$		0			0
$897$	−20.9240	−	15.2854i	−0.698632	−	0.510364i
$898$		0			0
$899$			20.9266i			0.697940i
$900$		0			0
$901$	−53.3141			−1.77615
$902$		0			0
$903$	3.19375	−	3.19375i	0.106281	−	0.106281i
$904$		0			0
$905$	58.7172	+	10.2984i	1.95183	+	0.342332i
$906$		0			0
$907$	−6.56691	+	6.56691i	−0.218051	+	0.218051i	−0.807676	−	0.589626i	$-0.799275\pi$
$907$	−6.56691	+	6.56691i	−0.218051	+	0.218051i	0.589626	+	0.807676i	$0.299275\pi$
$908$		0			0
$909$		−	7.10469i		−	0.235648i
$910$		0			0
$911$			37.7875i			1.25196i	0.779841	+	0.625978i	$0.215300\pi$
$911$			37.7875i			1.25196i	−0.779841	+	0.625978i	$0.784700\pi$
$912$		0			0
$913$	0.298438	−	0.298438i	0.00987685	−	0.00987685i
$914$		0			0
$915$	19.4031	−	13.6125i	0.641448	−	0.450015i
$916$		0			0
$917$	−4.40490	+	4.40490i	−0.145463	+	0.145463i
$918$		0			0
$919$	18.0807			0.596428			0.298214	−	0.954499i	$-0.403609\pi$
$919$	18.0807			0.596428			0.298214	+	0.954499i	$0.403609\pi$
$920$		0			0
$921$	10.5969			0.349179
$922$		0			0
$923$	6.20937	−	6.20937i	0.204384	−	0.204384i
$924$		0			0
$925$	−30.6786	+	14.3736i	−1.00870	+	0.472600i
$926$		0			0
$927$	1.81616	−	1.81616i	0.0596505	−	0.0596505i
$928$		0			0
$929$			54.7172i			1.79521i	0.440798	+	0.897606i	$0.354695\pi$
$929$			54.7172i			1.79521i	−0.440798	+	0.897606i	$0.645305\pi$
$930$		0			0
$931$			39.8746i			1.30684i
$932$		0			0
$933$	31.4031	−	31.4031i	1.02809	−	1.02809i
$934$		0			0
$935$	−9.58237	+	6.72263i	−0.313377	+	0.219854i
$936$		0			0
$937$	−15.2614	+	15.2614i	−0.498569	+	0.498569i	−0.910992	−	0.412423i	$-0.864682\pi$
$937$	−15.2614	+	15.2614i	−0.498569	+	0.498569i	0.412423	+	0.910992i	$0.364682\pi$
$938$		0			0
$939$	−9.58237			−0.312709
$940$		0			0
$941$		−	20.4793i		−	0.667607i	−0.942643	−	0.333804i	$-0.891668\pi$
$941$		−	20.4793i		−	0.667607i	0.942643	−	0.333804i	$-0.108332\pi$
$942$		0			0
$943$	−21.7876	+	29.8249i	−0.709503	+	0.971231i
$944$		0			0
$945$	1.19375	−	6.80625i	0.0388327	−	0.221407i
$946$		0			0
$947$	−34.4031	−	34.4031i	−1.11795	−	1.11795i	−0.992042	−	0.125910i	$-0.959815\pi$
$947$	−34.4031	−	34.4031i	−1.11795	−	1.11795i	−0.125910	−	0.992042i	$-0.540185\pi$
$948$		0			0
$949$			12.9844i			0.421491i
$950$		0			0
$951$	16.2094			0.525625
$952$		0			0
$953$	14.2583	+	14.2583i	0.461871	+	0.461871i	0.899268	−	0.437397i	$-0.144100\pi$
$953$	14.2583	+	14.2583i	0.461871	+	0.461871i	−0.437397	+	0.899268i	$0.644100\pi$
$954$		0			0
$955$	−53.6125	−	9.40312i	−1.73486	−	0.304278i
$956$		0			0
$957$	−1.77572	+	1.77572i	−0.0574009	+	0.0574009i
$958$		0			0
$959$		−	1.40312i		−	0.0453092i
$960$		0			0
$961$	51.8953			1.67404
$962$		0			0
$963$	8.42351	+	8.42351i	0.271444	+	0.271444i
$964$		0			0
$965$	2.35817	+	3.36131i	0.0759122	+	0.108205i
$966$		0			0
$967$	−3.00000	−	3.00000i	−0.0964735	−	0.0964735i	0.657223	−	0.753696i	$-0.271731\pi$
$967$	−3.00000	−	3.00000i	−0.0964735	−	0.0964735i	−0.753696	+	0.657223i	$0.771731\pi$
$968$		0			0
$969$			57.0156i			1.83161i
$970$		0			0
$971$		−	18.3922i		−	0.590233i	−0.955461	−	0.295116i	$-0.904642\pi$
$971$		−	18.3922i		−	0.590233i	0.955461	−	0.295116i	$-0.0953584\pi$
$972$		0			0
$973$	−1.42987	−	1.42987i	−0.0458396	−	0.0458396i
$974$		0			0
$975$	9.19375	−	25.4031i	0.294436	−	0.813551i
$976$		0			0
$977$	−2.47345	+	2.47345i	−0.0791328	+	0.0791328i	−0.745565	−	0.666433i	$-0.767820\pi$
$977$	−2.47345	+	2.47345i	−0.0791328	+	0.0791328i	0.666433	+	0.745565i	$0.267820\pi$
$978$		0			0
$979$			13.0156i			0.415981i
$980$		0			0
$981$			10.8970i			0.347913i
$982$		0			0
$983$	25.7317	+	25.7317i	0.820712	+	0.820712i	0.986210	−	0.165498i	$-0.0529231\pi$
$983$	25.7317	+	25.7317i	0.820712	+	0.820712i	−0.165498	+	0.986210i	$0.552923\pi$
$984$		0			0
$985$	32.1084	−	22.5261i	1.02306	−	0.717740i
$986$		0			0
$987$	−4.94691	+	4.94691i	−0.157462	+	0.157462i
$988$		0			0
$989$	−27.7035	+	4.31406i	−0.880921	+	0.137179i
$990$		0			0
$991$	27.4922			0.873318			0.436659	−	0.899627i	$-0.356162\pi$
$991$	27.4922			0.873318			0.436659	+	0.899627i	$0.356162\pi$
$992$		0			0
$993$	−17.7016	+	17.7016i	−0.561742	+	0.561742i
$994$		0			0
$995$	−1.19375	+	6.80625i	−0.0378445	+	0.215773i
$996$		0			0
$997$	−1.29844	−	1.29844i	−0.0411219	−	0.0411219i	0.686247	−	0.727369i	$-0.259257\pi$
$997$	−1.29844	−	1.29844i	−0.0411219	−	0.0411219i	−0.727369	+	0.686247i	$0.759257\pi$
$998$		0			0
$999$	−38.3295			−1.21269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.i.a.137.3	yes	8
5.2	odd	4		2300.2.i.c.1793.2		8
5.3	odd	4	inner	460.2.i.a.413.2	yes	8
5.4	even	2		2300.2.i.c.1057.3		8
23.22	odd	2	inner	460.2.i.a.137.2	✓	8
115.22	even	4		2300.2.i.c.1793.3		8
115.68	even	4	inner	460.2.i.a.413.3	yes	8
115.114	odd	2		2300.2.i.c.1057.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.i.a.137.2	✓	8	23.22	odd	2	inner
460.2.i.a.137.3	yes	8	1.1	even	1	trivial
460.2.i.a.413.2	yes	8	5.3	odd	4	inner
460.2.i.a.413.3	yes	8	115.68	even	4	inner
2300.2.i.c.1057.2		8	115.114	odd	2
2300.2.i.c.1057.3		8	5.4	even	2
2300.2.i.c.1793.2		8	5.2	odd	4
2300.2.i.c.1793.3		8	115.22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(0.386289 - 2.20245i) q^{5} +(-0.386289 + 0.386289i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{3} +(0.386289 - 2.20245i) q^{5} +(-0.386289 + 0.386289i) q^{7} +1.00000i q^{9} -0.772577i q^{11} +(2.70156 - 2.70156i) q^{13} +(1.81616 + 2.58874i) q^{15} +(4.79119 - 4.79119i) q^{17} +5.95005 q^{19} -0.772577i q^{21} +(-2.82899 + 3.87257i) q^{23} +(-4.70156 - 1.70156i) q^{25} +(-4.00000 - 4.00000i) q^{27} +2.29844i q^{29} +9.10469 q^{31} +(0.772577 + 0.772577i) q^{33} +(0.701562 + 1.00000i) q^{35} +(4.79119 - 4.79119i) q^{37} +5.40312i q^{39} +7.70156 q^{41} +(4.13389 + 4.13389i) q^{43} +(2.20245 + 0.386289i) q^{45} +(-6.40312 - 6.40312i) q^{47} +6.70156i q^{49} +9.58237i q^{51} +(-5.56376 - 5.56376i) q^{53} +(-1.70156 - 0.298438i) q^{55} +(-5.95005 + 5.95005i) q^{57} +3.70156i q^{59} -7.49521i q^{61} +(-0.386289 - 0.386289i) q^{63} +(-4.90647 - 6.99364i) q^{65} +(-6.33634 + 6.33634i) q^{67} +(-1.04358 - 6.70156i) q^{69} +2.29844 q^{71} +(-2.40312 + 2.40312i) q^{73} +(6.40312 - 3.00000i) q^{75} +(0.298438 + 0.298438i) q^{77} -13.2147 q^{79} +5.00000 q^{81} +(0.386289 + 0.386289i) q^{83} +(-8.70156 - 12.4031i) q^{85} +(-2.29844 - 2.29844i) q^{87} -16.8470 q^{89} +2.08717i q^{91} +(-9.10469 + 9.10469i) q^{93} +(2.29844 - 13.1047i) q^{95} +(-10.6260 + 10.6260i) q^{97} +0.772577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3}+O(q^{10}) \) 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

L-functions

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