LMFDB - Embedded newform 460.2.i.b.137.7

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{14} + 146x^{12} - 798x^{10} + 3934x^{8} - 19950x^{6} + 91250x^{4} - 281250x^{2} + 390625 $ x^16 - 18x^14 + 146x^12 - 798x^10 + 3934x^8 - 19950x^6 + 91250x^4 - 281250*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.7
Root			$-1.06856 + 1.96422i$ of defining polynomial
Character	$\chi$	$=$	460.137
Dual form			460.2.i.b.413.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03584 - 2.03584i) q^{3} +(-1.06856 - 1.96422i) q^{5} +(0.641104 - 0.641104i) q^{7} -5.28931i q^{9} +O(q^{10})$	\(q+(2.03584 - 2.03584i) q^{3} +(-1.06856 - 1.96422i) q^{5} +(0.641104 - 0.641104i) q^{7} -5.28931i q^{9} +3.68270i q^{11} +(1.51730 - 1.51730i) q^{13} +(-6.17428 - 1.82342i) q^{15} +(0.140805 - 0.140805i) q^{17} -1.03646 q^{19} -2.61037i q^{21} +(-1.51549 - 4.55009i) q^{23} +(-2.71634 + 4.19780i) q^{25} +(-4.66067 - 4.66067i) q^{27} +4.36099i q^{29} +3.07168 q^{31} +(7.49739 + 7.49739i) q^{33} +(-1.94433 - 0.574210i) q^{35} +(3.28734 - 3.28734i) q^{37} -6.17797i q^{39} -8.10629 q^{41} +(4.71035 + 4.71035i) q^{43} +(-10.3894 + 5.65197i) q^{45} +(-1.77201 - 1.77201i) q^{47} +6.17797i q^{49} -0.573312i q^{51} +(10.0299 + 10.0299i) q^{53} +(7.23364 - 3.93520i) q^{55} +(-2.11007 + 2.11007i) q^{57} +6.32639i q^{59} -13.9583i q^{61} +(-3.39100 - 3.39100i) q^{63} +(-4.60165 - 1.35898i) q^{65} +(7.97064 - 7.97064i) q^{67} +(-12.3486 - 6.17797i) q^{69} +10.4327 q^{71} +(0.0704445 - 0.0704445i) q^{73} +(3.01602 + 14.0761i) q^{75} +(2.36099 + 2.36099i) q^{77} +9.66645 q^{79} -3.10886 q^{81} +(-5.33321 - 5.33321i) q^{83} +(-0.427031 - 0.126113i) q^{85} +(8.87829 + 8.87829i) q^{87} +8.40186 q^{89} -1.94550i q^{91} +(6.25347 - 6.25347i) q^{93} +(1.10753 + 2.03584i) q^{95} +(-7.74314 + 7.74314i) q^{97} +19.4789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3}+O(q^{10}) $ 16 * q + 4 * q^3	$ 16 q + 4 q^{3} + 12 q^{13} + 12 q^{23} + 36 q^{25} + 52 q^{27} - 8 q^{31} + 16 q^{35} - 48 q^{41} + 4 q^{47} + 24 q^{55} + 8 q^{71} - 52 q^{73} - 56 q^{75} - 64 q^{77} - 152 q^{81} + 28 q^{85} + 28 q^{87} + 84 q^{93} - 68 q^{95}+O(q^{100}) $ 16 * q + 4 * q^3 + 12 * q^13 + 12 * q^23 + 36 * q^25 + 52 * q^27 - 8 * q^31 + 16 * q^35 - 48 * q^41 + 4 * q^47 + 24 * q^55 + 8 * q^71 - 52 * q^73 - 56 * q^75 - 64 * q^77 - 152 * q^81 + 28 * q^85 + 28 * q^87 + 84 * q^93 - 68 * 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
$3$	2.03584	−	2.03584i	1.17539	−	1.17539i	0.194490	−	0.980905i	$-0.437695\pi$
$3$	2.03584	−	2.03584i	1.17539	−	1.17539i	0.980905	−	0.194490i	$-0.0623050\pi$
$4$		0			0
$5$	−1.06856	−	1.96422i	−0.477877	−	0.878427i
$5$	−1.06856	−	1.96422i	−0.477877	−	0.878427i
$6$		0			0
$7$	0.641104	−	0.641104i	0.242315	−	0.242315i	−0.575493	−	0.817807i	$-0.695190\pi$
$7$	0.641104	−	0.641104i	0.242315	−	0.242315i	0.817807	+	0.575493i	$0.195190\pi$
$8$		0			0
$9$		−	5.28931i		−	1.76310i
$10$		0			0
$11$			3.68270i			1.11038i	0.831725	+	0.555188i	$0.187354\pi$
$11$			3.68270i			1.11038i	−0.831725	+	0.555188i	$0.812646\pi$
$12$		0			0
$13$	1.51730	−	1.51730i	0.420824	−	0.420824i	−0.464664	−	0.885487i	$-0.653825\pi$
$13$	1.51730	−	1.51730i	0.420824	−	0.420824i	0.885487	+	0.464664i	$0.153825\pi$
$14$		0			0
$15$	−6.17428	−	1.82342i	−1.59419	−	0.470804i
$16$		0			0
$17$	0.140805	−	0.140805i	0.0341502	−	0.0341502i	−0.689826	−	0.723976i	$-0.742313\pi$
$17$	0.140805	−	0.140805i	0.0341502	−	0.0341502i	0.723976	+	0.689826i	$0.242313\pi$
$18$		0			0
$19$	−1.03646			−0.237781			−0.118890	−	0.992907i	$-0.537934\pi$
$19$	−1.03646			−0.237781			−0.118890	+	0.992907i	$0.537934\pi$
$20$		0			0
$21$		−	2.61037i		−	0.569630i
$22$		0			0
$23$	−1.51549	−	4.55009i	−0.316001	−	0.948759i
$23$	−1.51549	−	4.55009i	−0.316001	−	0.948759i
$24$		0			0
$25$	−2.71634	+	4.19780i	−0.543268	+	0.839559i
$26$		0			0
$27$	−4.66067	−	4.66067i	−0.896946	−	0.896946i
$28$		0			0
$29$			4.36099i			0.809816i	0.914357	+	0.404908i	$0.132696\pi$
$29$			4.36099i			0.809816i	−0.914357	+	0.404908i	$0.867304\pi$
$30$		0			0
$31$	3.07168			0.551691			0.275845	−	0.961202i	$-0.411042\pi$
$31$	3.07168			0.551691			0.275845	+	0.961202i	$0.411042\pi$
$32$		0			0
$33$	7.49739	+	7.49739i	1.30513	+	1.30513i
$34$		0			0
$35$	−1.94433	−	0.574210i	−0.328652	−	0.0970591i
$36$		0			0
$37$	3.28734	−	3.28734i	0.540435	−	0.540435i	−0.383221	−	0.923657i	$-0.625185\pi$
$37$	3.28734	−	3.28734i	0.540435	−	0.540435i	0.923657	+	0.383221i	$0.125185\pi$
$38$		0			0
$39$		−	6.17797i		−	0.989267i
$40$		0			0
$41$	−8.10629			−1.26599			−0.632995	−	0.774156i	$-0.718174\pi$
$41$	−8.10629			−1.26599			−0.632995	+	0.774156i	$0.718174\pi$
$42$		0			0
$43$	4.71035	+	4.71035i	0.718322	+	0.718322i	0.968261	−	0.249939i	$-0.0804107\pi$
$43$	4.71035	+	4.71035i	0.718322	+	0.718322i	−0.249939	+	0.968261i	$0.580411\pi$
$44$		0			0
$45$	−10.3894	+	5.65197i	−1.54876	+	0.842546i
$46$		0			0
$47$	−1.77201	−	1.77201i	−0.258474	−	0.258474i	0.565959	−	0.824433i	$-0.308506\pi$
$47$	−1.77201	−	1.77201i	−0.258474	−	0.258474i	−0.824433	+	0.565959i	$0.808506\pi$
$48$		0			0
$49$			6.17797i			0.882567i
$50$		0			0
$51$		−	0.573312i		−	0.0802798i
$52$		0			0
$53$	10.0299	+	10.0299i	1.37771	+	1.37771i	0.848475	+	0.529235i	$0.177521\pi$
$53$	10.0299	+	10.0299i	1.37771	+	1.37771i	0.529235	+	0.848475i	$0.322479\pi$
$54$		0			0
$55$	7.23364	−	3.93520i	0.975384	−	0.530623i
$56$		0			0
$57$	−2.11007	+	2.11007i	−0.279486	+	0.279486i
$58$		0			0
$59$			6.32639i			0.823626i	0.911268	+	0.411813i	$0.135104\pi$
$59$			6.32639i			0.823626i	−0.911268	+	0.411813i	$0.864896\pi$
$60$		0			0
$61$		−	13.9583i		−	1.78718i	−0.448883	−	0.893590i	$-0.648178\pi$
$61$		−	13.9583i		−	1.78718i	0.448883	−	0.893590i	$-0.351822\pi$
$62$		0			0
$63$	−3.39100	−	3.39100i	−0.427225	−	0.427225i
$64$		0			0
$65$	−4.60165	−	1.35898i	−0.570765	−	0.168561i
$66$		0			0
$67$	7.97064	−	7.97064i	0.973768	−	0.973768i	−0.0258962	−	0.999665i	$-0.508244\pi$
$67$	7.97064	−	7.97064i	0.973768	−	0.973768i	0.999665	+	0.0258962i	$0.00824393\pi$
$68$		0			0
$69$	−12.3486	−	6.17797i	−1.48659	−	0.743740i
$70$		0			0
$71$	10.4327			1.23813			0.619066	−	0.785339i	$-0.287512\pi$
$71$	10.4327			1.23813			0.619066	+	0.785339i	$0.287512\pi$
$72$		0			0
$73$	0.0704445	−	0.0704445i	0.00824490	−	0.00824490i	−0.702972	−	0.711217i	$-0.748144\pi$
$73$	0.0704445	−	0.0704445i	0.00824490	−	0.00824490i	0.711217	+	0.702972i	$0.248144\pi$
$74$		0			0
$75$	3.01602	+	14.0761i	0.348260	+	1.62537i
$76$		0			0
$77$	2.36099	+	2.36099i	0.269060	+	0.269060i
$78$		0			0
$79$	9.66645			1.08756			0.543780	−	0.839228i	$-0.316992\pi$
$79$	9.66645			1.08756			0.543780	+	0.839228i	$0.316992\pi$
$80$		0			0
$81$	−3.10886			−0.345428
$82$		0			0
$83$	−5.33321	−	5.33321i	−0.585396	−	0.585396i	0.350985	−	0.936381i	$-0.385847\pi$
$83$	−5.33321	−	5.33321i	−0.585396	−	0.585396i	−0.936381	+	0.350985i	$0.885847\pi$
$84$		0			0
$85$	−0.427031	−	0.126113i	−0.0463180	−	0.0136789i
$86$		0			0
$87$	8.87829	+	8.87829i	0.951853	+	0.951853i
$88$		0			0
$89$	8.40186			0.890595			0.445298	−	0.895383i	$-0.353098\pi$
$89$	8.40186			0.890595			0.445298	+	0.895383i	$0.353098\pi$
$90$		0			0
$91$		−	1.94550i		−	0.203943i
$92$		0			0
$93$	6.25347	−	6.25347i	0.648454	−	0.648454i
$94$		0			0
$95$	1.10753	+	2.03584i	0.113630	+	0.208873i
$96$		0			0
$97$	−7.74314	+	7.74314i	−0.786197	+	0.786197i	−0.980868	−	0.194672i	$-0.937636\pi$
$97$	−7.74314	+	7.74314i	−0.786197	+	0.786197i	0.194672	+	0.980868i	$0.437636\pi$
$98$		0			0
$99$	19.4789			1.95771
$100$		0			0
$101$	−16.7912			−1.67079			−0.835393	−	0.549653i	$-0.814760\pi$
$101$	−16.7912			−1.67079			−0.835393	+	0.549653i	$0.814760\pi$
$102$		0			0
$103$	0.859794	+	0.859794i	0.0847180	+	0.0847180i	0.748196	−	0.663478i	$-0.230920\pi$
$103$	0.859794	+	0.859794i	0.0847180	+	0.0847180i	−0.663478	+	0.748196i	$0.730920\pi$
$104$		0			0
$105$	−5.12735	+	2.78935i	−0.500378	+	0.272213i
$106$		0			0
$107$	−7.32073	+	7.32073i	−0.707721	+	0.707721i	−0.966056	−	0.258334i	$-0.916826\pi$
$107$	−7.32073	+	7.32073i	−0.707721	+	0.707721i	0.258334	+	0.966056i	$0.416826\pi$
$108$		0			0
$109$	−10.4031			−0.996432			−0.498216	−	0.867053i	$-0.666011\pi$
$109$	−10.4031			−0.996432			−0.498216	+	0.867053i	$0.666011\pi$
$110$		0			0
$111$		−	13.3850i		−	1.27045i
$112$		0			0
$113$	7.51564	+	7.51564i	0.707012	+	0.707012i	0.965906	−	0.258894i	$-0.0833579\pi$
$113$	7.51564	+	7.51564i	0.707012	+	0.707012i	−0.258894	+	0.965906i	$0.583358\pi$
$114$		0			0
$115$	−7.31799	+	7.83882i	−0.682406	+	0.730973i
$116$		0			0
$117$	−8.02547	−	8.02547i	−0.741955	−	0.741955i
$118$		0			0
$119$		−	0.180541i		−	0.0165502i
$120$		0			0
$121$	−2.56227			−0.232934
$122$		0			0
$123$	−16.5031	+	16.5031i	−1.48804	+	1.48804i
$124$		0			0
$125$	11.1480	+	0.849875i	0.997107	+	0.0760151i
$126$		0			0
$127$	15.7207	+	15.7207i	1.39499	+	1.39499i	0.813686	+	0.581304i	$0.197457\pi$
$127$	15.7207	+	15.7207i	1.39499	+	1.39499i	0.581304	+	0.813686i	$0.302543\pi$
$128$		0			0
$129$	19.1791			1.68862
$130$		0			0
$131$	−15.4698			−1.35160			−0.675800	−	0.737085i	$-0.736202\pi$
$131$	−15.4698			−1.35160			−0.675800	+	0.737085i	$0.736202\pi$
$132$		0			0
$133$	−0.664480	+	0.664480i	−0.0576177	+	0.0576177i
$134$		0			0
$135$	−4.17436	+	14.1348i	−0.359272	+	1.21653i
$136$		0			0
$137$	−12.5584	+	12.5584i	−1.07294	+	1.07294i	−0.0758178	+	0.997122i	$0.524157\pi$
$137$	−12.5584	+	12.5584i	−1.07294	+	1.07294i	−0.997122	+	0.0758178i	$0.975843\pi$
$138$		0			0
$139$		−	4.43268i		−	0.375975i	−0.982171	−	0.187987i	$-0.939804\pi$
$139$		−	4.43268i		−	0.375975i	0.982171	−	0.187987i	$-0.0601964\pi$
$140$		0			0
$141$	−7.21505			−0.607617
$142$		0			0
$143$	5.58776	+	5.58776i	0.467272	+	0.467272i
$144$		0			0
$145$	8.56596	−	4.66000i	0.711364	−	0.386992i
$146$		0			0
$147$	12.5774	+	12.5774i	1.03736	+	1.03736i
$148$		0			0
$149$	−9.63059			−0.788969			−0.394484	−	0.918903i	$-0.629077\pi$
$149$	−9.63059			−0.788969			−0.394484	+	0.918903i	$0.629077\pi$
$150$		0			0
$151$	8.54649			0.695504			0.347752	−	0.937587i	$-0.386945\pi$
$151$	8.54649			0.695504			0.347752	+	0.937587i	$0.386945\pi$
$152$		0			0
$153$	−0.744759	−	0.744759i	−0.0602102	−	0.0602102i
$154$		0			0
$155$	−3.28229	−	6.03347i	−0.263640	−	0.484620i
$156$		0			0
$157$	−12.1116	+	12.1116i	−0.966612	+	0.966612i	−0.999460	−	0.0328482i	$-0.989542\pi$
$157$	−12.1116	+	12.1116i	−0.966612	+	0.966612i	0.0328482	+	0.999460i	$0.489542\pi$
$158$		0			0
$159$	40.8385			3.23871
$160$		0			0
$161$	−3.88866	−	1.94550i	−0.306470	−	0.153327i
$162$		0			0
$163$	4.54277	−	4.54277i	0.355818	−	0.355818i	−0.506451	−	0.862269i	$-0.669043\pi$
$163$	4.54277	−	4.54277i	0.355818	−	0.355818i	0.862269	+	0.506451i	$0.169043\pi$
$164$		0			0
$165$	6.71510	−	22.7380i	0.522770	−	1.77015i
$166$		0			0
$167$	−8.02547	−	8.02547i	−0.621030	−	0.621030i	0.324765	−	0.945795i	$-0.394715\pi$
$167$	−8.02547	−	8.02547i	−0.621030	−	0.621030i	−0.945795	+	0.324765i	$0.894715\pi$
$168$		0			0
$169$			8.39559i			0.645815i
$170$		0			0
$171$			5.48217i			0.419232i
$172$		0			0
$173$	−10.2405	+	10.2405i	−0.778573	+	0.778573i	−0.979588	−	0.201015i	$-0.935576\pi$
$173$	−10.2405	+	10.2405i	−0.778573	+	0.778573i	0.201015	+	0.979588i	$0.435576\pi$
$174$		0			0
$175$	0.949769	+	4.43268i	0.0717958	+	0.335079i
$176$		0			0
$177$	12.8795	+	12.8795i	0.968085	+	0.968085i
$178$		0			0
$179$		−	16.1063i		−	1.20384i	−0.798556	−	0.601920i	$-0.794403\pi$
$179$		−	16.1063i		−	1.20384i	0.798556	−	0.601920i	$-0.205597\pi$
$180$		0			0
$181$		−	0.801442i		−	0.0595707i	−0.999556	−	0.0297853i	$-0.990518\pi$
$181$		−	0.801442i		−	0.0595707i	0.999556	−	0.0297853i	$-0.00948237\pi$
$182$		0			0
$183$	−28.4170	−	28.4170i	−2.10064	−	2.10064i
$184$		0			0
$185$	−9.96980	−	2.94433i	−0.732995	−	0.216472i
$186$		0			0
$187$	0.518541	+	0.518541i	0.0379195	+	0.0379195i
$188$		0			0
$189$	−5.97595			−0.434686
$190$		0			0
$191$		−	20.3788i		−	1.47456i	−0.675587	−	0.737280i	$-0.736110\pi$
$191$		−	20.3788i		−	1.47456i	0.675587	−	0.737280i	$-0.263890\pi$
$192$		0			0
$193$	−3.47357	+	3.47357i	−0.250033	+	0.250033i	−0.820984	−	0.570951i	$-0.806575\pi$
$193$	−3.47357	+	3.47357i	−0.250033	+	0.250033i	0.570951	+	0.820984i	$0.306575\pi$
$194$		0			0
$195$	−12.1349	+	6.60156i	−0.868999	+	0.472748i
$196$		0			0
$197$	−17.9408	−	17.9408i	−1.27823	−	1.27823i	−0.941656	−	0.336576i	$-0.890731\pi$
$197$	−17.9408	−	17.9408i	−1.27823	−	1.27823i	−0.336576	−	0.941656i	$-0.609269\pi$
$198$		0			0
$199$	−13.1210			−0.930125			−0.465062	−	0.885278i	$-0.653968\pi$
$199$	−13.1210			−0.930125			−0.465062	+	0.885278i	$0.653968\pi$
$200$		0			0
$201$		−	32.4539i		−	2.28912i
$202$		0			0
$203$	2.79585	+	2.79585i	0.196230	+	0.196230i
$204$		0			0
$205$	8.66209	+	15.9225i	0.604987	+	1.11208i
$206$		0			0
$207$	−24.0668	+	8.01587i	−1.67276	+	0.557142i
$208$		0			0
$209$		−	3.81698i		−	0.264026i
$210$		0			0
$211$	9.63644			0.663400			0.331700	−	0.943385i	$-0.392378\pi$
$211$	9.63644			0.663400			0.331700	+	0.943385i	$0.392378\pi$
$212$		0			0
$213$	21.2393	−	21.2393i	1.45529	−	1.45529i
$214$		0			0
$215$	4.21886	−	14.2855i	0.287724	−	0.974263i
$216$		0			0
$217$	1.96927	−	1.96927i	0.133683	−	0.133683i
$218$		0			0
$219$		−	0.286828i		−	0.0193820i
$220$		0			0
$221$		−	0.427286i		−	0.0287424i
$222$		0			0
$223$	13.9257	−	13.9257i	0.932537	−	0.932537i	−0.0653270	−	0.997864i	$-0.520809\pi$
$223$	13.9257	−	13.9257i	0.932537	−	0.932537i	0.997864	+	0.0653270i	$0.0208090\pi$
$224$		0			0
$225$	22.2034	+	14.3676i	1.48023	+	0.957837i
$226$		0			0
$227$	−7.31585	+	7.31585i	−0.485570	+	0.485570i	−0.906905	−	0.421335i	$-0.861562\pi$
$227$	−7.31585	+	7.31585i	−0.485570	+	0.485570i	0.421335	+	0.906905i	$0.361562\pi$
$228$		0			0
$229$	−23.0701			−1.52451			−0.762256	−	0.647275i	$-0.775908\pi$
$229$	−23.0701			−1.52451			−0.762256	+	0.647275i	$0.775908\pi$
$230$		0			0
$231$	9.61322			0.632503
$232$		0			0
$233$	−0.998760	+	0.998760i	−0.0654309	+	0.0654309i	−0.739065	−	0.673634i	$-0.764732\pi$
$233$	−0.998760	+	0.998760i	−0.0654309	+	0.0654309i	0.673634	+	0.739065i	$0.264732\pi$
$234$		0			0
$235$	−1.58711	+	5.37412i	−0.103532	+	0.350569i
$236$		0			0
$237$	19.6794	−	19.6794i	1.27831	−	1.27831i
$238$		0			0
$239$		−	12.1038i		−	0.782930i	−0.920193	−	0.391465i	$-0.871968\pi$
$239$		−	12.1038i		−	0.782930i	0.920193	−	0.391465i	$-0.128032\pi$
$240$		0			0
$241$		−	21.1246i		−	1.36075i	−0.732863	−	0.680377i	$-0.761816\pi$
$241$		−	21.1246i		−	1.36075i	0.732863	−	0.680377i	$-0.238184\pi$
$242$		0			0
$243$	7.65287	−	7.65287i	0.490932	−	0.490932i
$244$		0			0
$245$	12.1349	−	6.60156i	0.775271	−	0.421758i
$246$		0			0
$247$	−1.57263	+	1.57263i	−0.100064	+	0.100064i
$248$		0			0
$249$	−21.7151			−1.37614
$250$		0			0
$251$			11.4940i			0.725494i	0.931888	+	0.362747i	$0.118161\pi$
$251$			11.4940i			0.725494i	−0.931888	+	0.362747i	$0.881839\pi$
$252$		0			0
$253$	16.7566	−	5.58108i	1.05348	−	0.350879i
$254$		0			0
$255$	−1.12611	+	0.612621i	−0.0705199	+	0.0383638i
$256$		0			0
$257$	14.2739	+	14.2739i	0.890381	+	0.890381i	0.994559	−	0.104178i	$-0.0332211\pi$
$257$	14.2739	+	14.2739i	0.890381	+	0.890381i	−0.104178	+	0.994559i	$0.533221\pi$
$258$		0			0
$259$		−	4.21505i		−	0.261911i
$260$		0			0
$261$	23.0666			1.42779
$262$		0			0
$263$	5.00958	+	5.00958i	0.308904	+	0.308904i	0.844484	−	0.535580i	$-0.179907\pi$
$263$	5.00958	+	5.00958i	0.308904	+	0.308904i	−0.535580	+	0.844484i	$0.679907\pi$
$264$		0			0
$265$	8.98334	−	30.4185i	0.551842	−	1.86859i
$266$		0			0
$267$	17.1049	−	17.1049i	1.04680	−	1.04680i
$268$		0			0
$269$		−	1.51189i		−	0.0921817i	−0.998937	−	0.0460909i	$-0.985324\pi$
$269$		−	1.51189i		−	0.0921817i	0.998937	−	0.0460909i	$-0.0146764\pi$
$270$		0			0
$271$	−21.2314			−1.28972			−0.644858	−	0.764303i	$-0.723083\pi$
$271$	−21.2314			−1.28972			−0.644858	+	0.764303i	$0.723083\pi$
$272$		0			0
$273$	−3.96072	−	3.96072i	−0.239714	−	0.239714i
$274$		0			0
$275$	−15.4592	−	10.0035i	−0.932226	−	0.603231i
$276$		0			0
$277$	−10.7299	−	10.7299i	−0.644696	−	0.644696i	0.307010	−	0.951706i	$-0.400671\pi$
$277$	−10.7299	−	10.7299i	−0.644696	−	0.644696i	−0.951706	+	0.307010i	$0.900671\pi$
$278$		0			0
$279$		−	16.2471i		−	0.972688i
$280$		0			0
$281$			23.7522i			1.41694i	0.705742	+	0.708469i	$0.250614\pi$
$281$			23.7522i			1.41694i	−0.705742	+	0.708469i	$0.749386\pi$
$282$		0			0
$283$	3.94182	+	3.94182i	0.234317	+	0.234317i	0.814492	−	0.580175i	$-0.197016\pi$
$283$	3.94182	+	3.94182i	0.234317	+	0.234317i	−0.580175	+	0.814492i	$0.697016\pi$
$284$		0			0
$285$	6.39940	+	1.88990i	0.379068	+	0.111948i
$286$		0			0
$287$	−5.19697	+	5.19697i	−0.306768	+	0.306768i
$288$		0			0
$289$			16.9603i			0.997668i
$290$		0			0
$291$			31.5276i			1.84818i
$292$		0			0
$293$	−4.09174	−	4.09174i	−0.239042	−	0.239042i	0.577411	−	0.816453i	$-0.304063\pi$
$293$	−4.09174	−	4.09174i	−0.239042	−	0.239042i	−0.816453	+	0.577411i	$0.804063\pi$
$294$		0			0
$295$	12.4264	−	6.76016i	0.723495	−	0.393592i
$296$		0			0
$297$	17.1638	−	17.1638i	0.995947	−	0.995947i
$298$		0			0
$299$	−9.20330	−	4.60441i	−0.532241	−	0.266280i
$300$		0			0
$301$	6.03965			0.348120
$302$		0			0
$303$	−34.1842	+	34.1842i	−1.96383	+	1.96383i
$304$		0			0
$305$	−27.4173	+	14.9154i	−1.56991	+	0.854052i
$306$		0			0
$307$	−17.3468	−	17.3468i	−0.990035	−	0.990035i	0.00991588	−	0.999951i	$-0.496844\pi$
$307$	−17.3468	−	17.3468i	−0.990035	−	0.990035i	−0.999951	+	0.00991588i	$0.996844\pi$
$308$		0			0
$309$	3.50081			0.199154
$310$		0			0
$311$	−10.7566			−0.609950			−0.304975	−	0.952360i	$-0.598648\pi$
$311$	−10.7566			−0.609950			−0.304975	+	0.952360i	$0.598648\pi$
$312$		0			0
$313$	9.83073	+	9.83073i	0.555665	+	0.555665i	0.928070	−	0.372405i	$-0.121467\pi$
$313$	9.83073	+	9.83073i	0.555665	+	0.555665i	−0.372405	+	0.928070i	$0.621467\pi$
$314$		0			0
$315$	−3.03717	+	10.2842i	−0.171125	+	0.579447i
$316$		0			0
$317$	4.99087	+	4.99087i	0.280315	+	0.280315i	0.833235	−	0.552919i	$-0.186486\pi$
$317$	4.99087	+	4.99087i	0.280315	+	0.280315i	−0.552919	+	0.833235i	$0.686486\pi$
$318$		0			0
$319$	−16.0602			−0.899200
$320$		0			0
$321$			29.8077i			1.66370i
$322$		0			0
$323$	−0.145939	+	0.145939i	−0.00812025	+	0.00812025i
$324$		0			0
$325$	2.24782	+	10.4908i	0.124687	+	0.581926i
$326$		0			0
$327$	−21.1790	+	21.1790i	−1.17120	+	1.17120i
$328$		0			0
$329$	−2.27208			−0.125264
$330$		0			0
$331$	−6.00505			−0.330067			−0.165034	−	0.986288i	$-0.552773\pi$
$331$	−6.00505			−0.330067			−0.165034	+	0.986288i	$0.552773\pi$
$332$		0			0
$333$	−17.3878	−	17.3878i	−0.952843	−	0.952843i
$334$		0			0
$335$	−24.1732	−	7.13896i	−1.32073	−	0.390043i
$336$		0			0
$337$	18.1596	−	18.1596i	0.989215	−	0.989215i	−0.0107275	−	0.999942i	$-0.503415\pi$
$337$	18.1596	−	18.1596i	0.989215	−	0.989215i	0.999942	+	0.0107275i	$0.00341473\pi$
$338$		0			0
$339$	30.6013			1.66204
$340$		0			0
$341$			11.3121i			0.612584i
$342$		0			0
$343$	8.44845	+	8.44845i	0.456173	+	0.456173i
$344$		0			0
$345$	1.06032	+	30.8569i	0.0570856	+	1.66128i
$346$		0			0
$347$	−16.9603	−	16.9603i	−0.910479	−	0.910479i	0.0858306	−	0.996310i	$-0.472646\pi$
$347$	−16.9603	−	16.9603i	−0.910479	−	0.910479i	−0.996310	+	0.0858306i	$0.972646\pi$
$348$		0			0
$349$			17.2818i			0.925072i	0.886600	+	0.462536i	$0.153060\pi$
$349$			17.2818i			0.925072i	−0.886600	+	0.462536i	$0.846940\pi$
$350$		0			0
$351$	−14.1433			−0.754912
$352$		0			0
$353$	8.08174	−	8.08174i	0.430148	−	0.430148i	−0.458531	−	0.888678i	$-0.651624\pi$
$353$	8.08174	−	8.08174i	0.430148	−	0.430148i	0.888678	+	0.458531i	$0.151624\pi$
$354$		0			0
$355$	−11.1480	−	20.4921i	−0.591674	−	1.08761i
$356$		0			0
$357$	−0.367553	−	0.367553i	−0.0194530	−	0.0194530i
$358$		0			0
$359$	19.8505			1.04767			0.523835	−	0.851820i	$-0.324501\pi$
$359$	19.8505			1.04767			0.523835	+	0.851820i	$0.324501\pi$
$360$		0			0
$361$	−17.9257			−0.943460
$362$		0			0
$363$	−5.21638	+	5.21638i	−0.273789	+	0.273789i
$364$		0			0
$365$	−0.213643	−	0.0630941i	−0.0111826	−	0.00330250i
$366$		0			0
$367$	5.46914	−	5.46914i	0.285487	−	0.285487i	−0.549806	−	0.835293i	$-0.685298\pi$
$367$	5.46914	−	5.46914i	0.285487	−	0.285487i	0.835293	+	0.549806i	$0.185298\pi$
$368$		0			0
$369$			42.8766i			2.23207i
$370$		0			0
$371$	12.8604			0.667678
$372$		0			0
$373$	1.09481	+	1.09481i	0.0566873	+	0.0566873i	0.734882	−	0.678195i	$-0.237237\pi$
$373$	1.09481	+	1.09481i	0.0566873	+	0.0566873i	−0.678195	+	0.734882i	$0.737237\pi$
$374$		0			0
$375$	24.4258	−	20.9653i	1.26134	−	1.08265i
$376$		0			0
$377$	6.61694	+	6.61694i	0.340790	+	0.340790i
$378$		0			0
$379$	−19.8147			−1.01781			−0.508905	−	0.860823i	$-0.669950\pi$
$379$	−19.8147			−1.01781			−0.508905	+	0.860823i	$0.669950\pi$
$380$		0			0
$381$	64.0099			3.27933
$382$		0			0
$383$	−6.00265	−	6.00265i	−0.306721	−	0.306721i	0.536915	−	0.843636i	$-0.319590\pi$
$383$	−6.00265	−	6.00265i	−0.306721	−	0.306721i	−0.843636	+	0.536915i	$0.819590\pi$
$384$		0			0
$385$	2.11464	−	7.16039i	0.107772	−	0.364927i
$386$		0			0
$387$	24.9145	−	24.9145i	1.26648	−	1.26648i
$388$		0			0
$389$	−12.7758			−0.647761			−0.323880	−	0.946098i	$-0.604988\pi$
$389$	−12.7758			−0.647761			−0.323880	+	0.946098i	$0.604988\pi$
$390$		0			0
$391$	−0.854061	−	0.427286i	−0.0431917	−	0.0216088i
$392$		0			0
$393$	−31.4940	+	31.4940i	−1.58866	+	1.58866i
$394$		0			0
$395$	−10.3292	−	18.9871i	−0.519720	−	0.955343i
$396$		0			0
$397$	12.4084	+	12.4084i	0.622762	+	0.622762i	0.946237	−	0.323475i	$-0.104851\pi$
$397$	12.4084	+	12.4084i	0.622762	+	0.622762i	−0.323475	+	0.946237i	$0.604851\pi$
$398$		0			0
$399$			2.70555i			0.135447i
$400$		0			0
$401$		−	5.86322i		−	0.292795i	−0.989226	−	0.146397i	$-0.953232\pi$
$401$		−	5.86322i		−	0.292795i	0.989226	−	0.146397i	$-0.0467679\pi$
$402$		0			0
$403$	4.66067	−	4.66067i	0.232165	−	0.232165i
$404$		0			0
$405$	3.32201	+	6.10648i	0.165072	+	0.303434i
$406$		0			0
$407$	12.1063	+	12.1063i	0.600086	+	0.600086i
$408$		0			0
$409$		−	27.4118i		−	1.35543i	−0.735325	−	0.677714i	$-0.762971\pi$
$409$		−	27.4118i		−	1.35543i	0.735325	−	0.677714i	$-0.237029\pi$
$410$		0			0
$411$			51.1340i			2.52225i
$412$		0			0
$413$	4.05587	+	4.05587i	0.199577	+	0.199577i
$414$		0			0
$415$	−4.77673	+	16.1745i	−0.234480	+	0.793974i
$416$		0			0
$417$	−9.02423	−	9.02423i	−0.441919	−	0.441919i
$418$		0			0
$419$	−26.2153			−1.28070			−0.640351	−	0.768082i	$-0.721211\pi$
$419$	−26.2153			−1.28070			−0.640351	+	0.768082i	$0.721211\pi$
$420$		0			0
$421$			10.7215i			0.522534i	0.965267	+	0.261267i	$0.0841404\pi$
$421$			10.7215i			0.522534i	−0.965267	+	0.261267i	$0.915860\pi$
$422$		0			0
$423$	−9.37269	+	9.37269i	−0.455716	+	0.455716i
$424$		0			0
$425$	0.208596	+	0.973543i	0.0101184	+	0.0472238i
$426$		0			0
$427$	−8.94874	−	8.94874i	−0.433060	−	0.433060i
$428$		0			0
$429$	22.7516			1.09846
$430$		0			0
$431$			32.7007i			1.57513i	0.616228	+	0.787567i	$0.288660\pi$
$431$			32.7007i			1.57513i	−0.616228	+	0.787567i	$0.711340\pi$
$432$		0			0
$433$	4.99812	+	4.99812i	0.240194	+	0.240194i	0.816930	−	0.576736i	$-0.195674\pi$
$433$	4.99812	+	4.99812i	0.240194	+	0.240194i	−0.576736	+	0.816930i	$0.695674\pi$
$434$		0			0
$435$	7.95191	−	26.9260i	0.381265	−	1.29100i
$436$		0			0
$437$	1.57074	+	4.71599i	0.0751389	+	0.225597i
$438$		0			0
$439$			35.4389i			1.69141i	0.533653	+	0.845704i	$0.320819\pi$
$439$			35.4389i			1.69141i	−0.533653	+	0.845704i	$0.679181\pi$
$440$		0			0
$441$	32.6772			1.55606
$442$		0			0
$443$	15.4430	−	15.4430i	0.733721	−	0.733721i	−0.237634	−	0.971355i	$-0.576372\pi$
$443$	15.4430	−	15.4430i	0.733721	−	0.733721i	0.971355	+	0.237634i	$0.0763717\pi$
$444$		0			0
$445$	−8.97793	−	16.5031i	−0.425595	−	0.782323i
$446$		0			0
$447$	−19.6064	+	19.6064i	−0.927349	+	0.927349i
$448$		0			0
$449$			25.6660i			1.21125i	0.795749	+	0.605626i	$0.207077\pi$
$449$			25.6660i			1.21125i	−0.795749	+	0.605626i	$0.792923\pi$
$450$		0			0
$451$		−	29.8530i		−	1.40572i
$452$		0			0
$453$	17.3993	−	17.3993i	0.817491	−	0.817491i
$454$		0			0
$455$	−3.82139	+	2.07889i	−0.179149	+	0.0974598i
$456$		0			0
$457$	5.76900	−	5.76900i	0.269862	−	0.269862i	−0.559182	−	0.829045i	$-0.688885\pi$
$457$	5.76900	−	5.76900i	0.269862	−	0.269862i	0.829045	+	0.559182i	$0.188885\pi$
$458$		0			0
$459$	−1.31249			−0.0612617
$460$		0			0
$461$	−9.18302			−0.427696			−0.213848	−	0.976867i	$-0.568600\pi$
$461$	−9.18302			−0.427696			−0.213848	+	0.976867i	$0.568600\pi$
$462$		0			0
$463$	11.5786	−	11.5786i	0.538104	−	0.538104i	−0.384868	−	0.922972i	$-0.625753\pi$
$463$	11.5786	−	11.5786i	0.538104	−	0.538104i	0.922972	+	0.384868i	$0.125753\pi$
$464$		0			0
$465$	−18.9654	−	5.60096i	−0.879501	−	0.259738i
$466$		0			0
$467$	9.47482	−	9.47482i	0.438442	−	0.438442i	−0.453045	−	0.891488i	$-0.649662\pi$
$467$	9.47482	−	9.47482i	0.438442	−	0.438442i	0.891488	+	0.453045i	$0.149662\pi$
$468$		0			0
$469$		−	10.2200i		−	0.471916i
$470$		0			0
$471$			49.3147i			2.27230i
$472$		0			0
$473$	−17.3468	+	17.3468i	−0.797607	+	0.797607i
$474$		0			0
$475$	2.81538	−	4.35086i	0.129179	−	0.199631i
$476$		0			0
$477$	53.0511	−	53.0511i	2.42904	−	2.42904i
$478$		0			0
$479$	−0.427286			−0.0195232			−0.00976160	−	0.999952i	$-0.503107\pi$
$479$	−0.427286			−0.0195232			−0.00976160	+	0.999952i	$0.503107\pi$
$480$		0			0
$481$		−	9.97577i		−	0.454856i
$482$		0			0
$483$	−11.8774	+	3.95598i	−0.540442	+	0.180003i
$484$		0			0
$485$	23.4833	+	6.93520i	1.06632	+	0.314911i
$486$		0			0
$487$	−9.15631	−	9.15631i	−0.414912	−	0.414912i	0.468534	−	0.883446i	$-0.344782\pi$
$487$	−9.15631	−	9.15631i	−0.414912	−	0.414912i	−0.883446	+	0.468534i	$0.844782\pi$
$488$		0			0
$489$		−	18.4967i		−	0.836452i
$490$		0			0
$491$	42.2610			1.90721			0.953605	−	0.301061i	$-0.0973407\pi$
$491$	42.2610			1.90721			0.953605	+	0.301061i	$0.0973407\pi$
$492$		0			0
$493$	0.614048	+	0.614048i	0.0276553	+	0.0276553i
$494$		0			0
$495$	−20.8145	−	38.2610i	−0.935542	−	1.71970i
$496$		0			0
$497$	6.68843	−	6.68843i	0.300017	−	0.300017i
$498$		0			0
$499$			11.7220i			0.524748i	0.964966	+	0.262374i	$0.0845054\pi$
$499$			11.7220i			0.524748i	−0.964966	+	0.262374i	$0.915495\pi$
$500$		0			0
$501$	−32.6772			−1.45991
$502$		0			0
$503$	−14.6500	−	14.6500i	−0.653209	−	0.653209i	0.300555	−	0.953764i	$-0.402828\pi$
$503$	−14.6500	−	14.6500i	−0.653209	−	0.653209i	−0.953764	+	0.300555i	$0.902828\pi$
$504$		0			0
$505$	17.9425	+	32.9816i	0.798430	+	1.46766i
$506$		0			0
$507$	17.0921	+	17.0921i	0.759087	+	0.759087i
$508$		0			0
$509$		−	14.6453i		−	0.649139i	−0.945862	−	0.324570i	$-0.894781\pi$
$509$		−	14.6453i		−	0.649139i	0.945862	−	0.324570i	$-0.105219\pi$
$510$		0			0
$511$		−	0.0903245i		−	0.00399572i
$512$		0			0
$513$	4.83061	+	4.83061i	0.213277	+	0.213277i
$514$		0			0
$515$	0.770081	−	2.60757i	0.0339338	−	0.114903i
$516$		0			0
$517$	6.52577	−	6.52577i	0.287003	−	0.287003i
$518$		0			0
$519$			41.6962i			1.83026i
$520$		0			0
$521$		−	19.5415i		−	0.856130i	−0.903748	−	0.428065i	$-0.859195\pi$
$521$		−	19.5415i		−	0.856130i	0.903748	−	0.428065i	$-0.140805\pi$
$522$		0			0
$523$	12.6165	+	12.6165i	0.551680	+	0.551680i	0.926926	−	0.375245i	$-0.122442\pi$
$523$	12.6165	+	12.6165i	0.551680	+	0.551680i	−0.375245	+	0.926926i	$0.622442\pi$
$524$		0			0
$525$	10.9578	+	7.09066i	0.478238	+	0.309462i
$526$		0			0
$527$	0.432508	−	0.432508i	0.0188403	−	0.0188403i
$528$		0			0
$529$	−18.4066	+	13.7912i	−0.800287	+	0.599617i
$530$		0			0
$531$	33.4622			1.45214
$532$		0			0
$533$	−12.2997	+	12.2997i	−0.532758	+	0.532758i
$534$		0			0
$535$	22.2022	+	6.55686i	0.959885	+	0.283478i
$536$		0			0
$537$	−32.7899	−	32.7899i	−1.41499	−	1.41499i
$538$		0			0
$539$	−22.7516			−0.979981
$540$		0			0
$541$	5.81193			0.249874			0.124937	−	0.992165i	$-0.460127\pi$
$541$	5.81193			0.249874			0.124937	+	0.992165i	$0.460127\pi$
$542$		0			0
$543$	−1.63161	−	1.63161i	−0.0700190	−	0.0700190i
$544$		0			0
$545$	11.1163	+	20.4339i	0.476172	+	0.875293i
$546$		0			0
$547$	10.8386	+	10.8386i	0.463427	+	0.463427i	0.899777	−	0.436350i	$-0.143729\pi$
$547$	10.8386	+	10.8386i	0.463427	+	0.463427i	−0.436350	+	0.899777i	$0.643729\pi$
$548$		0			0
$549$	−73.8299			−3.15098
$550$		0			0
$551$		−	4.52000i		−	0.192559i
$552$		0			0
$553$	6.19720	−	6.19720i	0.263532	−	0.263532i
$554$		0			0
$555$	−26.2911	+	14.3028i	−1.11600	+	0.607118i
$556$		0			0
$557$	−1.86496	+	1.86496i	−0.0790209	+	0.0790209i	−0.745513	−	0.666492i	$-0.767795\pi$
$557$	−1.86496	+	1.86496i	−0.0790209	+	0.0790209i	0.666492	+	0.745513i	$0.267795\pi$
$558$		0			0
$559$	14.2940			0.604574
$560$		0			0
$561$	2.11134			0.0891407
$562$		0			0
$563$	24.5429	+	24.5429i	1.03436	+	1.03436i	0.999388	+	0.0349727i	$0.0111344\pi$
$563$	24.5429	+	24.5429i	1.03436	+	1.03436i	0.0349727	+	0.999388i	$0.488866\pi$
$564$		0			0
$565$	6.73144	−	22.7933i	0.283194	−	0.958923i
$566$		0			0
$567$	−1.99310	+	1.99310i	−0.0837023	+	0.0837023i
$568$		0			0
$569$	40.4575			1.69607			0.848033	−	0.529944i	$-0.177787\pi$
$569$	40.4575			1.69607			0.848033	+	0.529944i	$0.177787\pi$
$570$		0			0
$571$			14.9032i			0.623681i	0.950135	+	0.311840i	$0.100945\pi$
$571$			14.9032i			0.623681i	−0.950135	+	0.311840i	$0.899055\pi$
$572$		0			0
$573$	−41.4881	−	41.4881i	−1.73319	−	1.73319i
$574$		0			0
$575$	23.2169	+	5.99788i	0.968213	+	0.250129i
$576$		0			0
$577$	−9.55190	−	9.55190i	−0.397651	−	0.397651i	0.479753	−	0.877404i	$-0.340726\pi$
$577$	−9.55190	−	9.55190i	−0.397651	−	0.397651i	−0.877404	+	0.479753i	$0.840726\pi$
$578$		0			0
$579$			14.1433i			0.587775i
$580$		0			0
$581$	−6.83828			−0.283700
$582$		0			0
$583$	−36.9370	+	36.9370i	−1.52978	+	1.52978i
$584$		0			0
$585$	−7.18808	+	24.3396i	−0.297190	+	1.00632i
$586$		0			0
$587$	−12.1534	−	12.1534i	−0.501625	−	0.501625i	0.410317	−	0.911943i	$-0.365418\pi$
$587$	−12.1534	−	12.1534i	−0.501625	−	0.501625i	−0.911943	+	0.410317i	$0.865418\pi$
$588$		0			0
$589$	−3.18369			−0.131181
$590$		0			0
$591$	−73.0495			−3.00485
$592$		0			0
$593$	13.6477	−	13.6477i	0.560445	−	0.560445i	−0.368989	−	0.929434i	$-0.620296\pi$
$593$	13.6477	−	13.6477i	0.560445	−	0.560445i	0.929434	+	0.368989i	$0.120296\pi$
$594$		0			0
$595$	−0.354622	+	0.192920i	−0.0145381	+	0.00790893i
$596$		0			0
$597$	−26.7123	+	26.7123i	−1.09326	+	1.09326i
$598$		0			0
$599$			0.636527i			0.0260078i	0.999915	+	0.0130039i	$0.00413938\pi$
$599$			0.636527i			0.0260078i	−0.999915	+	0.0130039i	$0.995861\pi$
$600$		0			0
$601$	−27.8232			−1.13493			−0.567466	−	0.823397i	$-0.692076\pi$
$601$	−27.8232			−1.13493			−0.567466	+	0.823397i	$0.692076\pi$
$602$		0			0
$603$	−42.1592	−	42.1592i	−1.71685	−	1.71685i
$604$		0			0
$605$	2.73795	+	5.03287i	0.111314	+	0.204615i
$606$		0			0
$607$	−3.41225	−	3.41225i	−0.138499	−	0.138499i	0.634458	−	0.772957i	$-0.281223\pi$
$607$	−3.41225	−	3.41225i	−0.138499	−	0.138499i	−0.772957	+	0.634458i	$0.781223\pi$
$608$		0			0
$609$	11.3838			0.461296
$610$		0			0
$611$	−5.37734			−0.217544
$612$		0			0
$613$	−8.13522	−	8.13522i	−0.328578	−	0.328578i	0.523467	−	0.852046i	$-0.324638\pi$
$613$	−8.13522	−	8.13522i	−0.328578	−	0.328578i	−0.852046	+	0.523467i	$0.824638\pi$
$614$		0			0
$615$	50.0505	+	14.7811i	2.01823	+	0.596033i
$616$		0			0
$617$	−12.5389	+	12.5389i	−0.504797	+	0.504797i	−0.912925	−	0.408128i	$-0.866182\pi$
$617$	−12.5389	+	12.5389i	−0.504797	+	0.504797i	0.408128	+	0.912925i	$0.366182\pi$
$618$		0			0
$619$	−43.9838			−1.76786			−0.883928	−	0.467622i	$-0.845111\pi$
$619$	−43.9838			−1.76786			−0.883928	+	0.467622i	$0.845111\pi$
$620$		0			0
$621$	−14.1433	+	28.2696i	−0.567550	+	1.13442i
$622$		0			0
$623$	5.38647	−	5.38647i	0.215804	−	0.215804i
$624$		0			0
$625$	−10.2430	−	22.8053i	−0.409720	−	0.912211i
$626$		0			0
$627$	−7.77077	−	7.77077i	−0.310335	−	0.310335i
$628$		0			0
$629$		−	0.925746i		−	0.0369119i
$630$		0			0
$631$			8.80275i			0.350432i	0.984530	+	0.175216i	$0.0560623\pi$
$631$			8.80275i			0.350432i	−0.984530	+	0.175216i	$0.943938\pi$
$632$		0			0
$633$	19.6183	−	19.6183i	0.779756	−	0.779756i
$634$		0			0
$635$	14.0804	−	47.6777i	0.558764	−	1.89203i
$636$		0			0
$637$	9.37384	+	9.37384i	0.371405	+	0.371405i
$638$		0			0
$639$		−	55.1816i		−	2.18295i
$640$		0			0
$641$		−	28.4088i		−	1.12208i	−0.827789	−	0.561040i	$-0.810402\pi$
$641$		−	28.4088i		−	1.12208i	0.827789	−	0.561040i	$-0.189598\pi$
$642$		0			0
$643$	31.1486	+	31.1486i	1.22838	+	1.22838i	0.964576	+	0.263805i	$0.0849774\pi$
$643$	31.1486	+	31.1486i	1.22838	+	1.22838i	0.263805	+	0.964576i	$0.415023\pi$
$644$		0			0
$645$	−20.4941	−	37.6720i	−0.806954	−	1.48333i
$646$		0			0
$647$	32.5723	+	32.5723i	1.28055	+	1.28055i	0.940355	+	0.340196i	$0.110493\pi$
$647$	32.5723	+	32.5723i	1.28055	+	1.28055i	0.340196	+	0.940355i	$0.389507\pi$
$648$		0			0
$649$	−23.2982			−0.914534
$650$		0			0
$651$		−	8.01824i		−	0.314260i
$652$		0			0
$653$	−23.0858	+	23.0858i	−0.903418	+	0.903418i	−0.995730	−	0.0923122i	$-0.970574\pi$
$653$	−23.0858	+	23.0858i	−0.903418	+	0.903418i	0.0923122	+	0.995730i	$0.470574\pi$
$654$		0			0
$655$	16.5304	+	30.3860i	0.645898	+	1.18728i
$656$		0			0
$657$	−0.372603	−	0.372603i	−0.0145366	−	0.0145366i
$658$		0			0
$659$	30.7552			1.19805			0.599025	−	0.800730i	$-0.295555\pi$
$659$	30.7552			1.19805			0.599025	+	0.800730i	$0.295555\pi$
$660$		0			0
$661$		−	9.55886i		−	0.371797i	−0.982569	−	0.185898i	$-0.940481\pi$
$661$		−	9.55886i		−	0.371797i	0.982569	−	0.185898i	$-0.0595195\pi$
$662$		0			0
$663$	−0.869887	−	0.869887i	−0.0337836	−	0.0337836i
$664$		0			0
$665$	2.01523	+	0.595147i	0.0781471	+	0.0230788i
$666$		0			0
$667$	19.8429	−	6.60902i	0.768320	−	0.255902i
$668$		0			0
$669$		−	56.7012i		−	2.19220i
$670$		0			0
$671$	51.4043			1.98444
$672$		0			0
$673$	0.330200	−	0.330200i	0.0127283	−	0.0127283i	−0.700714	−	0.713442i	$-0.747135\pi$
$673$	0.330200	−	0.330200i	0.0127283	−	0.0127283i	0.713442	+	0.700714i	$0.247135\pi$
$674$		0			0
$675$	32.2245	−	6.90459i	1.24032	−	0.265758i
$676$		0			0
$677$	−9.50253	+	9.50253i	−0.365212	+	0.365212i	−0.865727	−	0.500516i	$-0.833144\pi$
$677$	−9.50253	+	9.50253i	−0.365212	+	0.365212i	0.500516	+	0.865727i	$0.333144\pi$
$678$		0			0
$679$			9.92832i			0.381014i
$680$		0			0
$681$			29.7879i			1.14147i
$682$		0			0
$683$	28.3226	−	28.3226i	1.08373	−	1.08373i	0.0875756	−	0.996158i	$-0.472088\pi$
$683$	28.3226	−	28.3226i	1.08373	−	1.08373i	0.996158	−	0.0875756i	$-0.0279119\pi$
$684$		0			0
$685$	38.0871	+	11.2481i	1.45523	+	0.429766i
$686$		0			0
$687$	−46.9670	+	46.9670i	−1.79190	+	1.79190i
$688$		0			0
$689$	30.4367			1.15955
$690$		0			0
$691$	11.6899			0.444703			0.222352	−	0.974967i	$-0.428627\pi$
$691$	11.6899			0.444703			0.222352	+	0.974967i	$0.428627\pi$
$692$		0			0
$693$	12.4880	−	12.4880i	0.474381	−	0.474381i
$694$		0			0
$695$	−8.70676	+	4.73660i	−0.330266	+	0.179670i
$696$		0			0
$697$	−1.14140	+	1.14140i	−0.0432337	+	0.0432337i
$698$		0			0
$699$			4.06663i			0.153814i
$700$		0			0
$701$		−	5.09075i		−	0.192275i	−0.995368	−	0.0961374i	$-0.969351\pi$
$701$		−	5.09075i		−	0.192275i	0.995368	−	0.0961374i	$-0.0306488\pi$
$702$		0			0
$703$	−3.40720	+	3.40720i	−0.128505	+	0.128505i
$704$		0			0
$705$	7.70975	+	14.1720i	0.290366	+	0.533747i
$706$		0			0
$707$	−10.7649	+	10.7649i	−0.404856	+	0.404856i
$708$		0			0
$709$	33.9271			1.27416			0.637080	−	0.770798i	$-0.280142\pi$
$709$	33.9271			1.27416			0.637080	+	0.770798i	$0.280142\pi$
$710$		0			0
$711$		−	51.1288i		−	1.91748i
$712$		0			0
$713$	−4.65510	−	13.9764i	−0.174335	−	0.523422i
$714$		0			0
$715$	5.00472	−	16.9465i	0.187166	−	0.633763i
$716$		0			0
$717$	−24.6414	−	24.6414i	−0.920252	−	0.920252i
$718$		0			0
$719$		−	21.1572i		−	0.789032i	−0.918889	−	0.394516i	$-0.870912\pi$
$719$		−	21.1572i		−	0.789032i	0.918889	−	0.394516i	$-0.129088\pi$
$720$		0			0
$721$	1.10243			0.0410568
$722$		0			0
$723$	−43.0063	−	43.0063i	−1.59942	−	1.59942i
$724$		0			0
$725$	−18.3066	−	11.8459i	−0.679889	−	0.439947i
$726$		0			0
$727$	13.7181	−	13.7181i	0.508776	−	0.508776i	−0.405375	−	0.914151i	$-0.632859\pi$
$727$	13.7181	−	13.7181i	0.508776	−	0.508776i	0.914151	+	0.405375i	$0.132859\pi$
$728$		0			0
$729$		−	40.4866i		−	1.49951i
$730$		0			0
$731$	1.32648			0.0490616
$732$		0			0
$733$	−30.6685	−	30.6685i	−1.13277	−	1.13277i	−0.989715	−	0.143050i	$-0.954309\pi$
$733$	−30.6685	−	30.6685i	−1.13277	−	1.13277i	−0.143050	−	0.989715i	$-0.545691\pi$
$734$		0			0
$735$	11.2650	−	38.1445i	0.415517	−	1.40698i
$736$		0			0
$737$	29.3535	+	29.3535i	1.08125	+	1.08125i
$738$		0			0
$739$			10.5711i			0.388864i	0.980916	+	0.194432i	$0.0622863\pi$
$739$			10.5711i			0.388864i	−0.980916	+	0.194432i	$0.937714\pi$
$740$		0			0
$741$			6.40323i			0.235229i
$742$		0			0
$743$	−26.7743	−	26.7743i	−0.982253	−	0.982253i	0.0175925	−	0.999845i	$-0.494400\pi$
$743$	−26.7743	−	26.7743i	−0.982253	−	0.982253i	−0.999845	+	0.0175925i	$0.994400\pi$
$744$		0			0
$745$	10.2909	+	18.9166i	0.377030	+	0.693051i
$746$		0			0
$747$	−28.2090	+	28.2090i	−1.03211	+	1.03211i
$748$		0			0
$749$			9.38669i			0.342982i
$750$		0			0
$751$		−	37.5857i		−	1.37152i	−0.727827	−	0.685760i	$-0.759470\pi$
$751$		−	37.5857i		−	1.37152i	0.727827	−	0.685760i	$-0.240530\pi$
$752$		0			0
$753$	23.3999	+	23.3999i	0.852741	+	0.852741i
$754$		0			0
$755$	−9.13248	−	16.7872i	−0.332365	−	0.610949i
$756$		0			0
$757$	−12.8355	+	12.8355i	−0.466513	+	0.466513i	−0.900783	−	0.434270i	$-0.857007\pi$
$757$	−12.8355	+	12.8355i	−0.466513	+	0.466513i	0.434270	+	0.900783i	$0.357007\pi$
$758$		0			0
$759$	22.7516	−	45.4760i	0.825831	−	1.65067i
$760$		0			0
$761$	27.5018			0.996939			0.498470	−	0.866907i	$-0.333896\pi$
$761$	27.5018			0.996939			0.498470	+	0.866907i	$0.333896\pi$
$762$		0			0
$763$	−6.66944	+	6.66944i	−0.241450	+	0.241450i
$764$		0			0
$765$	−0.667049	+	2.25870i	−0.0241172	+	0.0816633i
$766$		0			0
$767$	9.59904	+	9.59904i	0.346601	+	0.346601i
$768$		0			0
$769$	−40.2678			−1.45209			−0.726047	−	0.687645i	$-0.758644\pi$
$769$	−40.2678			−1.45209			−0.726047	+	0.687645i	$0.758644\pi$
$770$		0			0
$771$	58.1188			2.09310
$772$		0			0
$773$	−7.63820	−	7.63820i	−0.274727	−	0.274727i	0.556273	−	0.831000i	$-0.312231\pi$
$773$	−7.63820	−	7.63820i	−0.274727	−	0.274727i	−0.831000	+	0.556273i	$0.812231\pi$
$774$		0			0
$775$	−8.34374	+	12.8943i	−0.299716	+	0.463177i
$776$		0			0
$777$	−8.58119	−	8.58119i	−0.307848	−	0.307848i
$778$		0			0
$779$	8.40186			0.301028
$780$		0			0
$781$			38.4204i			1.37479i
$782$		0			0
$783$	20.3252	−	20.3252i	0.726362	−	0.726362i
$784$		0			0
$785$	36.7320	+	10.8479i	1.31102	+	0.387177i
$786$		0			0
$787$	−31.8800	+	31.8800i	−1.13640	+	1.13640i	−0.147308	+	0.989091i	$0.547061\pi$
$787$	−31.8800	+	31.8800i	−1.13640	+	1.13640i	−0.989091	+	0.147308i	$0.952939\pi$
$788$		0			0
$789$	20.3974			0.726168
$790$		0			0
$791$	9.63662			0.342639
$792$		0			0
$793$	−21.1790	−	21.1790i	−0.752088	−	0.752088i
$794$		0			0
$795$	−43.6386	−	80.2159i	−1.54770	−	2.84497i
$796$		0			0
$797$	15.8582	−	15.8582i	0.561725	−	0.561725i	−0.368072	−	0.929797i	$-0.619982\pi$
$797$	15.8582	−	15.8582i	0.561725	−	0.561725i	0.929797	+	0.368072i	$0.119982\pi$
$798$		0			0
$799$	−0.499014			−0.0176538
$800$		0			0
$801$		−	44.4400i		−	1.57021i
$802$		0			0
$803$	0.259426	+	0.259426i	0.00915494	+	0.00915494i
$804$		0			0
$805$	0.333903	+	9.71709i	0.0117685	+	0.342482i
$806$		0			0
$807$	−3.07797	−	3.07797i	−0.108350	−	0.108350i
$808$		0			0
$809$			21.1622i			0.744023i	0.928228	+	0.372012i	$0.121332\pi$
$809$			21.1622i			0.744023i	−0.928228	+	0.372012i	$0.878668\pi$
$810$		0			0
$811$	−27.4459			−0.963755			−0.481878	−	0.876238i	$-0.660045\pi$
$811$	−27.4459			−0.963755			−0.481878	+	0.876238i	$0.660045\pi$
$812$		0			0
$813$	−43.2238	+	43.2238i	−1.51592	+	1.51592i
$814$		0			0
$815$	−13.7773	−	4.06877i	−0.482597	−	0.142523i
$816$		0			0
$817$	−4.88210	−	4.88210i	−0.170803	−	0.170803i
$818$		0			0
$819$	−10.2903			−0.359573
$820$		0			0
$821$	−0.771083			−0.0269110			−0.0134555	−	0.999909i	$-0.504283\pi$
$821$	−0.771083			−0.0269110			−0.0134555	+	0.999909i	$0.504283\pi$
$822$		0			0
$823$	8.35975	−	8.35975i	0.291403	−	0.291403i	−0.546232	−	0.837634i	$-0.683938\pi$
$823$	8.35975	−	8.35975i	0.291403	−	0.291403i	0.837634	+	0.546232i	$0.183938\pi$
$824$		0			0
$825$	−51.8380	+	11.1071i	−1.80477	+	0.386699i
$826$		0			0
$827$	2.21958	−	2.21958i	0.0771824	−	0.0771824i	−0.667462	−	0.744644i	$-0.732619\pi$
$827$	2.21958	−	2.21958i	0.0771824	−	0.0771824i	0.744644	+	0.667462i	$0.232619\pi$
$828$		0			0
$829$			5.94905i			0.206619i	0.994649	+	0.103310i	$0.0329432\pi$
$829$			5.94905i			0.206619i	−0.994649	+	0.103310i	$0.967057\pi$
$830$		0			0
$831$	−43.6887			−1.51554
$832$		0			0
$833$	0.869887	+	0.869887i	0.0301398	+	0.0301398i
$834$		0			0
$835$	−7.18808	+	24.3396i	−0.248754	+	0.842305i
$836$		0			0
$837$	−14.3161	−	14.3161i	−0.494837	−	0.494837i
$838$		0			0
$839$	17.3157			0.597804			0.298902	−	0.954284i	$-0.403380\pi$
$839$	17.3157			0.597804			0.298902	+	0.954284i	$0.403380\pi$
$840$		0			0
$841$	9.98174			0.344198
$842$		0			0
$843$	48.3558	+	48.3558i	1.66546	+	1.66546i
$844$		0			0
$845$	16.4908	−	8.97124i	0.567301	−	0.308620i
$846$		0			0
$847$	−1.64268	+	1.64268i	−0.0564433	+	0.0564433i
$848$		0			0
$849$	16.0498			0.550829
$850$		0			0
$851$	−19.9396	−	9.97577i	−0.683521	−	0.341965i
$852$		0			0
$853$	−33.6940	+	33.6940i	−1.15366	+	1.15366i	−0.167849	+	0.985813i	$0.553682\pi$
$853$	−33.6940	+	33.6940i	−1.15366	+	1.15366i	−0.985813	+	0.167849i	$0.946318\pi$
$854$		0			0
$855$	10.7682	−	5.85805i	0.368265	−	0.200341i
$856$		0			0
$857$	25.8667	+	25.8667i	0.883589	+	0.883589i	0.993897	−	0.110308i	$-0.0351838\pi$
$857$	25.8667	+	25.8667i	0.883589	+	0.883589i	−0.110308	+	0.993897i	$0.535184\pi$
$858$		0			0
$859$		−	25.1384i		−	0.857711i	−0.903373	−	0.428856i	$-0.858917\pi$
$859$		−	25.1384i		−	0.857711i	0.903373	−	0.428856i	$-0.141083\pi$
$860$		0			0
$861$			21.1604i			0.721146i
$862$		0			0
$863$	−17.4031	+	17.4031i	−0.592408	+	0.592408i	−0.938281	−	0.345873i	$-0.887583\pi$
$863$	−17.4031	+	17.4031i	−0.592408	+	0.592408i	0.345873	+	0.938281i	$0.387583\pi$
$864$		0			0
$865$	31.0573	+	9.17201i	1.05598	+	0.311858i
$866$		0			0
$867$	34.5286	+	34.5286i	1.17265	+	1.17265i
$868$		0			0
$869$			35.5986i			1.20760i
$870$		0			0
$871$		−	24.1877i		−	0.819569i
$872$		0			0
$873$	40.9559	+	40.9559i	1.38615	+	1.38615i
$874$		0			0
$875$	7.69188	−	6.60216i	0.260033	−	0.223194i
$876$		0			0
$877$	−19.4764	−	19.4764i	−0.657672	−	0.657672i	0.297157	−	0.954829i	$-0.403962\pi$
$877$	−19.4764	−	19.4764i	−0.657672	−	0.657672i	−0.954829	+	0.297157i	$0.903962\pi$
$878$		0			0
$879$	−16.6603			−0.561937
$880$		0			0
$881$		−	9.42106i		−	0.317403i	−0.987327	−	0.158702i	$-0.949269\pi$
$881$		−	9.42106i		−	0.317403i	0.987327	−	0.158702i	$-0.0507308\pi$
$882$		0			0
$883$	20.4902	−	20.4902i	0.689550	−	0.689550i	−0.272583	−	0.962132i	$-0.587878\pi$
$883$	20.4902	−	20.4902i	0.689550	−	0.689550i	0.962132	+	0.272583i	$0.0878779\pi$
$884$		0			0
$885$	11.5357	−	39.0609i	0.387767	−	1.31302i
$886$		0			0
$887$	17.5682	+	17.5682i	0.589884	+	0.589884i	0.937600	−	0.347716i	$-0.113043\pi$
$887$	17.5682	+	17.5682i	0.589884	+	0.589884i	−0.347716	+	0.937600i	$0.613043\pi$
$888$		0			0
$889$	20.1573			0.676053
$890$		0			0
$891$		−	11.4490i		−	0.383555i
$892$		0			0
$893$	1.83662	+	1.83662i	0.0614601	+	0.0614601i
$894$		0			0
$895$	−31.6363	+	17.2106i	−1.05749	+	0.575287i
$896$		0			0
$897$	−28.1103	+	9.36263i	−0.938576	+	0.312609i
$898$		0			0
$899$			13.3956i			0.446768i
$900$		0			0
$901$	2.82451			0.0940980
$902$		0			0
$903$	12.2958	−	12.2958i	0.409178	−	0.409178i
$904$		0			0
$905$	−1.57421	+	0.856392i	−0.0523285	+	0.0284674i
$906$		0			0
$907$	35.9000	−	35.9000i	1.19204	−	1.19204i	0.215548	−	0.976493i	$-0.430846\pi$
$907$	35.9000	−	35.9000i	1.19204	−	1.19204i	0.976493	−	0.215548i	$-0.0691537\pi$
$908$		0			0
$909$			88.8138i			2.94577i
$910$		0			0
$911$		−	12.0034i		−	0.397689i	−0.980031	−	0.198845i	$-0.936281\pi$
$911$		−	12.0034i		−	0.397689i	0.980031	−	0.198845i	$-0.0637189\pi$
$912$		0			0
$913$	19.6406	−	19.6406i	0.650009	−	0.650009i
$914$		0			0
$915$	−25.4519	+	86.1826i	−0.841413	+	2.84911i
$916$		0			0
$917$	−9.91772	+	9.91772i	−0.327512	+	0.327512i
$918$		0			0
$919$	−9.97577			−0.329070			−0.164535	−	0.986371i	$-0.552612\pi$
$919$	−9.97577			−0.329070			−0.164535	+	0.986371i	$0.552612\pi$
$920$		0			0
$921$	−70.6308			−2.32736
$922$		0			0
$923$	15.8295	−	15.8295i	0.521035	−	0.521035i
$924$		0			0
$925$	4.87006	+	22.7291i	0.160127	+	0.747329i
$926$		0			0
$927$	4.54771	−	4.54771i	0.149367	−	0.149367i
$928$		0			0
$929$		−	5.38430i		−	0.176653i	−0.996092	−	0.0883266i	$-0.971848\pi$
$929$		−	5.38430i		−	0.176653i	0.996092	−	0.0883266i	$-0.0281519\pi$
$930$		0			0
$931$		−	6.40323i		−	0.209858i
$932$		0			0
$933$	−21.8987	+	21.8987i	−0.716932	+	0.716932i
$934$		0			0
$935$	0.464435	−	1.57263i	0.0151887	−	0.0514303i
$936$		0			0
$937$	35.2785	−	35.2785i	1.15250	−	1.15250i	0.166447	−	0.986050i	$-0.446771\pi$
$937$	35.2785	−	35.2785i	1.15250	−	1.15250i	0.986050	−	0.166447i	$-0.0532294\pi$
$938$		0			0
$939$	40.0276			1.30625
$940$		0			0
$941$		−	2.05309i		−	0.0669287i	−0.999440	−	0.0334644i	$-0.989346\pi$
$941$		−	2.05309i		−	0.0669287i	0.999440	−	0.0334644i	$-0.0106540\pi$
$942$		0			0
$943$	12.2850	+	36.8843i	0.400053	+	1.20112i
$944$		0			0
$945$	6.38569	+	11.7381i	0.207726	+	0.381840i
$946$		0			0
$947$	−28.6627	−	28.6627i	−0.931414	−	0.931414i	0.0663803	−	0.997794i	$-0.478855\pi$
$947$	−28.6627	−	28.6627i	−0.931414	−	0.931414i	−0.997794	+	0.0663803i	$0.978855\pi$
$948$		0			0
$949$		−	0.213771i		−	0.00693930i
$950$		0			0
$951$	20.3213			0.658962
$952$		0			0
$953$	−34.2531	−	34.2531i	−1.10957	−	1.10957i	−0.993207	−	0.116360i	$-0.962877\pi$
$953$	−34.2531	−	34.2531i	−1.10957	−	1.10957i	−0.116360	−	0.993207i	$-0.537123\pi$
$954$		0			0
$955$	−40.0286	+	21.7761i	−1.29529	+	0.704658i
$956$		0			0
$957$	−32.6961	+	32.6961i	−1.05691	+	1.05691i
$958$		0			0
$959$			16.1025i			0.519978i
$960$		0			0
$961$	−21.5648			−0.695637
$962$		0			0
$963$	38.7216	+	38.7216i	1.24779	+	1.24779i
$964$		0			0
$965$	10.5346	+	3.11113i	0.339121	+	0.100151i
$966$		0			0
$967$	−17.4403	−	17.4403i	−0.560841	−	0.560841i	0.368706	−	0.929546i	$-0.379801\pi$
$967$	−17.4403	−	17.4403i	−0.560841	−	0.560841i	−0.929546	+	0.368706i	$0.879801\pi$
$968$		0			0
$969$			0.594217i			0.0190890i
$970$		0			0
$971$			34.8720i			1.11910i	0.828798	+	0.559548i	$0.189025\pi$
$971$			34.8720i			1.11910i	−0.828798	+	0.559548i	$0.810975\pi$
$972$		0			0
$973$	−2.84181	−	2.84181i	−0.0911041	−	0.0911041i
$974$		0			0
$975$	25.9339	+	16.7815i	0.830549	+	0.537437i
$976$		0			0
$977$	15.1727	−	15.1727i	0.485419	−	0.485419i	−0.421438	−	0.906857i	$-0.638475\pi$
$977$	15.1727	−	15.1727i	0.485419	−	0.485419i	0.906857	+	0.421438i	$0.138475\pi$
$978$		0			0
$979$			30.9415i			0.988895i
$980$		0			0
$981$			55.0250i			1.75681i
$982$		0			0
$983$	25.9177	+	25.9177i	0.826646	+	0.826646i	0.987051	−	0.160406i	$-0.0512802\pi$
$983$	25.9177	+	25.9177i	0.826646	+	0.826646i	−0.160406	+	0.987051i	$0.551280\pi$
$984$		0			0
$985$	−16.0689	+	54.4108i	−0.511996	+	1.73367i
$986$		0			0
$987$	−4.62560	+	4.62560i	−0.147234	+	0.147234i
$988$		0			0
$989$	14.2940	−	28.5710i	0.454524	−	0.908505i
$990$		0			0
$991$	−32.4736			−1.03156			−0.515779	−	0.856722i	$-0.672497\pi$
$991$	−32.4736			−1.03156			−0.515779	+	0.856722i	$0.672497\pi$
$992$		0			0
$993$	−12.2253	+	12.2253i	−0.387959	+	0.387959i
$994$		0			0
$995$	14.0207	+	25.7726i	0.444485	+	0.817046i
$996$		0			0
$997$	22.0637	+	22.0637i	0.698766	+	0.698766i	0.964144	−	0.265378i	$-0.0854969\pi$
$997$	22.0637	+	22.0637i	0.698766	+	0.698766i	−0.265378	+	0.964144i	$0.585497\pi$
$998$		0			0
$999$	−30.6424			−0.969483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.i.b.137.7	✓	16
5.2	odd	4		2300.2.i.d.1793.2		16
5.3	odd	4	inner	460.2.i.b.413.8	yes	16
5.4	even	2		2300.2.i.d.1057.1		16
23.22	odd	2	inner	460.2.i.b.137.8	yes	16
115.22	even	4		2300.2.i.d.1793.1		16
115.68	even	4	inner	460.2.i.b.413.7	yes	16
115.114	odd	2		2300.2.i.d.1057.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.i.b.137.7	✓	16	1.1	even	1	trivial
460.2.i.b.137.8	yes	16	23.22	odd	2	inner
460.2.i.b.413.7	yes	16	115.68	even	4	inner
460.2.i.b.413.8	yes	16	5.3	odd	4	inner
2300.2.i.d.1057.1		16	5.4	even	2
2300.2.i.d.1057.2		16	115.114	odd	2
2300.2.i.d.1793.1		16	115.22	even	4
2300.2.i.d.1793.2		16	5.2	odd	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)

\(f(q)\)	\(=\)	\(q+(2.03584 - 2.03584i) q^{3} +(-1.06856 - 1.96422i) q^{5} +(0.641104 - 0.641104i) q^{7} -5.28931i q^{9} +O(q^{10})\)	\(q+(2.03584 - 2.03584i) q^{3} +(-1.06856 - 1.96422i) q^{5} +(0.641104 - 0.641104i) q^{7} -5.28931i q^{9} +3.68270i q^{11} +(1.51730 - 1.51730i) q^{13} +(-6.17428 - 1.82342i) q^{15} +(0.140805 - 0.140805i) q^{17} -1.03646 q^{19} -2.61037i q^{21} +(-1.51549 - 4.55009i) q^{23} +(-2.71634 + 4.19780i) q^{25} +(-4.66067 - 4.66067i) q^{27} +4.36099i q^{29} +3.07168 q^{31} +(7.49739 + 7.49739i) q^{33} +(-1.94433 - 0.574210i) q^{35} +(3.28734 - 3.28734i) q^{37} -6.17797i q^{39} -8.10629 q^{41} +(4.71035 + 4.71035i) q^{43} +(-10.3894 + 5.65197i) q^{45} +(-1.77201 - 1.77201i) q^{47} +6.17797i q^{49} -0.573312i q^{51} +(10.0299 + 10.0299i) q^{53} +(7.23364 - 3.93520i) q^{55} +(-2.11007 + 2.11007i) q^{57} +6.32639i q^{59} -13.9583i q^{61} +(-3.39100 - 3.39100i) q^{63} +(-4.60165 - 1.35898i) q^{65} +(7.97064 - 7.97064i) q^{67} +(-12.3486 - 6.17797i) q^{69} +10.4327 q^{71} +(0.0704445 - 0.0704445i) q^{73} +(3.01602 + 14.0761i) q^{75} +(2.36099 + 2.36099i) q^{77} +9.66645 q^{79} -3.10886 q^{81} +(-5.33321 - 5.33321i) q^{83} +(-0.427031 - 0.126113i) q^{85} +(8.87829 + 8.87829i) q^{87} +8.40186 q^{89} -1.94550i q^{91} +(6.25347 - 6.25347i) q^{93} +(1.10753 + 2.03584i) q^{95} +(-7.74314 + 7.74314i) q^{97} +19.4789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3}+O(q^{10}) \) 16 * q + 4 * q^3	\( 16 q + 4 q^{3} + 12 q^{13} + 12 q^{23} + 36 q^{25} + 52 q^{27} - 8 q^{31} + 16 q^{35} - 48 q^{41} + 4 q^{47} + 24 q^{55} + 8 q^{71} - 52 q^{73} - 56 q^{75} - 64 q^{77} - 152 q^{81} + 28 q^{85} + 28 q^{87} + 84 q^{93} - 68 q^{95}+O(q^{100}) \) 16 * q + 4 * q^3 + 12 * q^13 + 12 * q^23 + 36 * q^25 + 52 * q^27 - 8 * q^31 + 16 * q^35 - 48 * q^41 + 4 * q^47 + 24 * q^55 + 8 * q^71 - 52 * q^73 - 56 * q^75 - 64 * q^77 - 152 * q^81 + 28 * q^85 + 28 * q^87 + 84 * q^93 - 68 * q^95

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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