LMFDB - Embedded newform 460.2.i.b.137.1

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			137.1
Root			$-2.19448 + 0.429243i$ of defining polynomial
Character	$\chi$	$=$	460.137
Dual form			460.2.i.b.413.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36693 + 2.36693i) q^{3} +(-2.19448 - 0.429243i) q^{5} +(-2.93008 + 2.93008i) q^{7} -8.20472i q^{9} +O(q^{10})$	\(q+(-2.36693 + 2.36693i) q^{3} +(-2.19448 - 0.429243i) q^{5} +(-2.93008 + 2.93008i) q^{7} -8.20472i q^{9} +1.20445i q^{11} +(2.14850 - 2.14850i) q^{13} +(6.21018 - 4.17820i) q^{15} +(-3.74895 + 3.74895i) q^{17} +5.51419 q^{19} -13.8706i q^{21} +(-0.475222 - 4.77223i) q^{23} +(4.63150 + 1.88393i) q^{25} +(12.3192 + 12.3192i) q^{27} -1.52914i q^{29} -5.73386 q^{31} +(-2.85085 - 2.85085i) q^{33} +(7.68772 - 5.17229i) q^{35} +(3.78857 - 3.78857i) q^{37} +10.1707i q^{39} -0.563145 q^{41} +(-5.82054 - 5.82054i) q^{43} +(-3.52182 + 18.0051i) q^{45} +(-4.05622 - 4.05622i) q^{47} -10.1707i q^{49} -17.7470i q^{51} +(-1.04600 - 1.04600i) q^{53} +(0.517003 - 2.64315i) q^{55} +(-13.0517 + 13.0517i) q^{57} -0.826145i q^{59} +0.187517i q^{61} +(24.0405 + 24.0405i) q^{63} +(-5.63708 + 3.79262i) q^{65} +(6.63077 - 6.63077i) q^{67} +(12.4204 + 10.1707i) q^{69} -4.26300 q^{71} +(-3.06992 + 3.06992i) q^{73} +(-15.4216 + 6.50330i) q^{75} +(-3.52914 - 3.52914i) q^{77} -11.9871 q^{79} -33.7033 q^{81} +(-1.42293 - 1.42293i) q^{83} +(9.83622 - 6.61780i) q^{85} +(3.61936 + 3.61936i) q^{87} -3.10529 q^{89} +12.5906i q^{91} +(13.5717 - 13.5717i) q^{93} +(-12.1008 - 2.36693i) q^{95} +(3.19682 - 3.19682i) q^{97} +9.88219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.36693	+	2.36693i	−1.36655	+	1.36655i	−0.501240	+	0.865308i	$0.667122\pi$
$3$	−2.36693	+	2.36693i	−1.36655	+	1.36655i	−0.865308	+	0.501240i	$0.832878\pi$
$4$		0			0
$5$	−2.19448	−	0.429243i	−0.981402	−	0.191964i
$5$	−2.19448	−	0.429243i	−0.981402	−	0.191964i
$6$		0			0
$7$	−2.93008	+	2.93008i	−1.10747	+	1.10747i	−0.113983	+	0.993483i	$0.536361\pi$
$7$	−2.93008	+	2.93008i	−1.10747	+	1.10747i	−0.993483	+	0.113983i	$0.963639\pi$
$8$		0			0
$9$		−	8.20472i		−	2.73491i
$10$		0			0
$11$			1.20445i			0.363156i	0.983377	+	0.181578i	$0.0581205\pi$
$11$			1.20445i			0.363156i	−0.983377	+	0.181578i	$0.941880\pi$
$12$		0			0
$13$	2.14850	−	2.14850i	0.595888	−	0.595888i	−0.343328	−	0.939216i	$-0.611554\pi$
$13$	2.14850	−	2.14850i	0.595888	−	0.595888i	0.939216	+	0.343328i	$0.111554\pi$
$14$		0			0
$15$	6.21018	−	4.17820i	1.60346	−	1.07881i
$16$		0			0
$17$	−3.74895	+	3.74895i	−0.909255	+	0.909255i	−0.996212	−	0.0869573i	$-0.972286\pi$
$17$	−3.74895	+	3.74895i	−0.909255	+	0.909255i	0.0869573	+	0.996212i	$0.472286\pi$
$18$		0			0
$19$	5.51419			1.26504			0.632521	−	0.774543i	$-0.282020\pi$
$19$	5.51419			1.26504			0.632521	+	0.774543i	$0.282020\pi$
$20$		0			0
$21$		−	13.8706i		−	3.02681i
$22$		0			0
$23$	−0.475222	−	4.77223i	−0.0990906	−	0.995078i
$23$	−0.475222	−	4.77223i	−0.0990906	−	0.995078i
$24$		0			0
$25$	4.63150	+	1.88393i	0.926300	+	0.376787i
$26$		0			0
$27$	12.3192	+	12.3192i	2.37084	+	2.37084i
$28$		0			0
$29$		−	1.52914i		−	0.283954i	−0.989870	−	0.141977i	$-0.954654\pi$
$29$		−	1.52914i		−	0.283954i	0.989870	−	0.141977i	$-0.0453459\pi$
$30$		0			0
$31$	−5.73386			−1.02983			−0.514916	−	0.857241i	$-0.672177\pi$
$31$	−5.73386			−1.02983			−0.514916	+	0.857241i	$0.672177\pi$
$32$		0			0
$33$	−2.85085	−	2.85085i	−0.496270	−	0.496270i
$34$		0			0
$35$	7.68772	−	5.17229i	1.29946	−	0.874276i
$36$		0			0
$37$	3.78857	−	3.78857i	0.622836	−	0.622836i	−0.323419	−	0.946256i	$-0.604832\pi$
$37$	3.78857	−	3.78857i	0.622836	−	0.622836i	0.946256	+	0.323419i	$0.104832\pi$
$38$		0			0
$39$			10.1707i			1.62862i
$40$		0			0
$41$	−0.563145			−0.0879484			−0.0439742	−	0.999033i	$-0.514002\pi$
$41$	−0.563145			−0.0879484			−0.0439742	+	0.999033i	$0.514002\pi$
$42$		0			0
$43$	−5.82054	−	5.82054i	−0.887625	−	0.887625i	0.106670	−	0.994295i	$-0.465981\pi$
$43$	−5.82054	−	5.82054i	−0.887625	−	0.887625i	−0.994295	+	0.106670i	$0.965981\pi$
$44$		0			0
$45$	−3.52182	+	18.0051i	−0.525003	+	2.68404i
$46$		0			0
$47$	−4.05622	−	4.05622i	−0.591661	−	0.591661i	0.346419	−	0.938080i	$-0.387397\pi$
$47$	−4.05622	−	4.05622i	−0.591661	−	0.591661i	−0.938080	+	0.346419i	$0.887397\pi$
$48$		0			0
$49$		−	10.1707i		−	1.45296i
$50$		0			0
$51$		−	17.7470i		−	2.48508i
$52$		0			0
$53$	−1.04600	−	1.04600i	−0.143680	−	0.143680i	0.631608	−	0.775288i	$-0.282395\pi$
$53$	−1.04600	−	1.04600i	−0.143680	−	0.143680i	−0.775288	+	0.631608i	$0.782395\pi$
$54$		0			0
$55$	0.517003	−	2.64315i	0.0697127	−	0.356402i
$56$		0			0
$57$	−13.0517	+	13.0517i	−1.72874	+	1.72874i
$58$		0			0
$59$		−	0.826145i		−	0.107555i	−0.998553	−	0.0537774i	$-0.982874\pi$
$59$		−	0.826145i		−	0.107555i	0.998553	−	0.0537774i	$-0.0171262\pi$
$60$		0			0
$61$			0.187517i			0.0240091i	0.999928	+	0.0120046i	$0.00382126\pi$
$61$			0.187517i			0.0240091i	−0.999928	+	0.0120046i	$0.996179\pi$
$62$		0			0
$63$	24.0405	+	24.0405i	3.02882	+	3.02882i
$64$		0			0
$65$	−5.63708	+	3.79262i	−0.699194	+	0.470417i
$66$		0			0
$67$	6.63077	−	6.63077i	0.810077	−	0.810077i	−0.174568	−	0.984645i	$-0.555853\pi$
$67$	6.63077	−	6.63077i	0.810077	−	0.810077i	0.984645	+	0.174568i	$0.0558529\pi$
$68$		0			0
$69$	12.4204	+	10.1707i	1.49523	+	1.22441i
$70$		0			0
$71$	−4.26300			−0.505925			−0.252963	−	0.967476i	$-0.581405\pi$
$71$	−4.26300			−0.505925			−0.252963	+	0.967476i	$0.581405\pi$
$72$		0			0
$73$	−3.06992	+	3.06992i	−0.359307	+	0.359307i	−0.863558	−	0.504250i	$-0.831769\pi$
$73$	−3.06992	+	3.06992i	−0.359307	+	0.359307i	0.504250	+	0.863558i	$0.331769\pi$
$74$		0			0
$75$	−15.4216	+	6.50330i	−1.78073	+	0.750936i
$76$		0			0
$77$	−3.52914	−	3.52914i	−0.402183	−	0.402183i
$78$		0			0
$79$	−11.9871			−1.34865			−0.674324	−	0.738435i	$-0.735565\pi$
$79$	−11.9871			−1.34865			−0.674324	+	0.738435i	$0.735565\pi$
$80$		0			0
$81$	−33.7033			−3.74481
$82$		0			0
$83$	−1.42293	−	1.42293i	−0.156187	−	0.156187i	0.624688	−	0.780875i	$-0.285226\pi$
$83$	−1.42293	−	1.42293i	−0.156187	−	0.156187i	−0.780875	+	0.624688i	$0.785226\pi$
$84$		0			0
$85$	9.83622	−	6.61780i	1.06689	−	0.717801i
$86$		0			0
$87$	3.61936	+	3.61936i	0.388037	+	0.388037i
$88$		0			0
$89$	−3.10529			−0.329160			−0.164580	−	0.986364i	$-0.552627\pi$
$89$	−3.10529			−0.329160			−0.164580	+	0.986364i	$0.552627\pi$
$90$		0			0
$91$			12.5906i			1.31985i
$92$		0			0
$93$	13.5717	−	13.5717i	1.40731	−	1.40731i
$94$		0			0
$95$	−12.1008	−	2.36693i	−1.24152	−	0.242842i
$96$		0			0
$97$	3.19682	−	3.19682i	0.324588	−	0.324588i	−0.525936	−	0.850524i	$-0.676285\pi$
$97$	3.19682	−	3.19682i	0.324588	−	0.324588i	0.850524	+	0.525936i	$0.176285\pi$
$98$		0			0
$99$	9.88219			0.993198
$100$		0			0
$101$	−7.53574			−0.749834			−0.374917	−	0.927058i	$-0.622329\pi$
$101$	−7.53574			−0.749834			−0.374917	+	0.927058i	$0.622329\pi$
$102$		0			0
$103$	5.38670	+	5.38670i	0.530768	+	0.530768i	0.920801	−	0.390033i	$-0.127536\pi$
$103$	5.38670	+	5.38670i	0.530768	+	0.530768i	−0.390033	+	0.920801i	$0.627536\pi$
$104$		0			0
$105$	−5.95386	+	30.4387i	−0.581037	+	2.97052i
$106$		0			0
$107$	−8.05004	+	8.05004i	−0.778227	+	0.778227i	−0.979529	−	0.201302i	$-0.935483\pi$
$107$	−8.05004	+	8.05004i	−0.778227	+	0.778227i	0.201302	+	0.979529i	$0.435483\pi$
$108$		0			0
$109$	−0.170213			−0.0163034			−0.00815171	−	0.999967i	$-0.502595\pi$
$109$	−0.170213			−0.0163034			−0.00815171	+	0.999967i	$0.502595\pi$
$110$		0			0
$111$			17.9345i			1.70227i
$112$		0			0
$113$	−13.0244	−	13.0244i	−1.22523	−	1.22523i	−0.965747	−	0.259486i	$-0.916447\pi$
$113$	−13.0244	−	13.0244i	−1.22523	−	1.22523i	−0.259486	−	0.965747i	$-0.583553\pi$
$114$		0			0
$115$	−1.00558	+	10.6766i	−0.0937710	+	0.995594i
$116$		0			0
$117$	−17.6279	−	17.6279i	−1.62970	−	1.62970i
$118$		0			0
$119$		−	21.9695i		−	2.01394i
$120$		0			0
$121$	9.54930			0.868118
$122$		0			0
$123$	1.33292	−	1.33292i	0.120186	−	0.120186i
$124$		0			0
$125$	−9.35508	−	6.12230i	−0.836743	−	0.547595i
$126$		0			0
$127$	9.60566	+	9.60566i	0.852365	+	0.852365i	0.990424	−	0.138059i	$-0.0440865\pi$
$127$	9.60566	+	9.60566i	0.852365	+	0.852365i	−0.138059	+	0.990424i	$0.544086\pi$
$128$		0			0
$129$	27.5537			2.42596
$130$		0			0
$131$	9.29387			0.812009			0.406005	−	0.913871i	$-0.366922\pi$
$131$	9.29387			0.812009			0.406005	+	0.913871i	$0.366922\pi$
$132$		0			0
$133$	−16.1570	+	16.1570i	−1.40099	+	1.40099i
$134$		0			0
$135$	−21.7464	−	32.3222i	−1.87163	−	2.78186i
$136$		0			0
$137$	5.61438	−	5.61438i	0.479668	−	0.479668i	−0.425357	−	0.905026i	$-0.639851\pi$
$137$	5.61438	−	5.61438i	0.479668	−	0.479668i	0.905026	+	0.425357i	$0.139851\pi$
$138$		0			0
$139$			10.2630i			0.870496i	0.900311	+	0.435248i	$0.143339\pi$
$139$			10.2630i			0.870496i	−0.900311	+	0.435248i	$0.856661\pi$
$140$		0			0
$141$	19.2016			1.61707
$142$		0			0
$143$	2.58777	+	2.58777i	0.216400	+	0.216400i
$144$		0			0
$145$	−0.656373	+	3.35567i	−0.0545088	+	0.278673i
$146$		0			0
$147$	24.0734	+	24.0734i	1.98554	+	1.98554i
$148$		0			0
$149$	4.83511			0.396108			0.198054	−	0.980191i	$-0.436538\pi$
$149$	4.83511			0.396108			0.198054	+	0.980191i	$0.436538\pi$
$150$		0			0
$151$	1.78457			0.145226			0.0726130	−	0.997360i	$-0.476866\pi$
$151$	1.78457			0.145226			0.0726130	+	0.997360i	$0.476866\pi$
$152$		0			0
$153$	30.7591	+	30.7591i	2.48673	+	2.48673i
$154$		0			0
$155$	12.5829	+	2.46122i	1.01068	+	0.197690i
$156$		0			0
$157$	10.5636	−	10.5636i	0.843066	−	0.843066i	−0.146191	−	0.989256i	$-0.546701\pi$
$157$	10.5636	−	10.5636i	0.843066	−	0.843066i	0.989256	+	0.146191i	$0.0467013\pi$
$158$		0			0
$159$	4.95164			0.392691
$160$		0			0
$161$	15.3754	+	12.5906i	1.21175	+	0.992276i
$162$		0			0
$163$	14.7764	−	14.7764i	1.15738	−	1.15738i	0.172337	−	0.985038i	$-0.444868\pi$
$163$	14.7764	−	14.7764i	1.15738	−	1.15738i	0.985038	−	0.172337i	$-0.0551319\pi$
$164$		0			0
$165$	5.03244	+	7.47986i	0.391775	+	0.582306i
$166$		0			0
$167$	−17.6279	−	17.6279i	−1.36409	−	1.36409i	−0.868637	−	0.495449i	$-0.835004\pi$
$167$	−17.6279	−	17.6279i	−1.36409	−	1.36409i	−0.495449	−	0.868637i	$-0.664996\pi$
$168$		0			0
$169$			3.76787i			0.289836i
$170$		0			0
$171$		−	45.2424i		−	3.45977i
$172$		0			0
$173$	6.57371	−	6.57371i	0.499790	−	0.499790i	−0.411583	−	0.911372i	$-0.635024\pi$
$173$	6.57371	−	6.57371i	0.499790	−	0.499790i	0.911372	+	0.411583i	$0.135024\pi$
$174$		0			0
$175$	−19.0907	+	8.05058i	−1.44312	+	0.608567i
$176$		0			0
$177$	1.95543	+	1.95543i	0.146979	+	0.146979i
$178$		0			0
$179$		−	8.56314i		−	0.640039i	−0.947411	−	0.320020i	$-0.896310\pi$
$179$		−	8.56314i		−	0.640039i	0.947411	−	0.320020i	$-0.103690\pi$
$180$		0			0
$181$		−	14.3795i		−	1.06882i	−0.845227	−	0.534408i	$-0.820535\pi$
$181$		−	14.3795i		−	1.06882i	0.845227	−	0.534408i	$-0.179465\pi$
$182$		0			0
$183$	−0.443840	−	0.443840i	−0.0328096	−	0.0328096i
$184$		0			0
$185$	−9.94015	+	6.68772i	−0.730815	+	0.491691i
$186$		0			0
$187$	−4.51543	−	4.51543i	−0.330201	−	0.330201i
$188$		0			0
$189$	−72.1926			−5.25124
$190$		0			0
$191$		−	16.4497i		−	1.19026i	−0.803630	−	0.595129i	$-0.797101\pi$
$191$		−	16.4497i		−	1.19026i	0.803630	−	0.595129i	$-0.202899\pi$
$192$		0			0
$193$	−11.1824	+	11.1824i	−0.804924	+	0.804924i	−0.983861	−	0.178936i	$-0.942734\pi$
$193$	−11.1824	+	11.1824i	−0.804924	+	0.804924i	0.178936	+	0.983861i	$0.442734\pi$
$194$		0			0
$195$	4.36571	−	22.3195i	0.312635	−	1.59833i
$196$		0			0
$197$	−12.2164	−	12.2164i	−0.870380	−	0.870380i	0.122133	−	0.992514i	$-0.461026\pi$
$197$	−12.2164	−	12.2164i	−0.870380	−	0.870380i	−0.992514	+	0.122133i	$0.961026\pi$
$198$		0			0
$199$	7.41503			0.525637			0.262819	−	0.964845i	$-0.415348\pi$
$199$	7.41503			0.525637			0.262819	+	0.964845i	$0.415348\pi$
$200$		0			0
$201$			31.3891i			2.21402i
$202$		0			0
$203$	4.48050	+	4.48050i	0.314469	+	0.314469i
$204$		0			0
$205$	1.23581	+	0.241726i	0.0863128	+	0.0168829i
$206$		0			0
$207$	−39.1548	+	3.89907i	−2.72145	+	0.271004i
$208$		0			0
$209$			6.64158i			0.459408i
$210$		0			0
$211$	−22.6110			−1.55661			−0.778304	−	0.627888i	$-0.783920\pi$
$211$	−22.6110			−1.55661			−0.778304	+	0.627888i	$0.783920\pi$
$212$		0			0
$213$	10.0902	−	10.0902i	0.691371	−	0.691371i
$214$		0			0
$215$	10.2746	+	15.2715i	0.700725	+	1.04151i
$216$		0			0
$217$	16.8007	−	16.8007i	1.14050	−	1.14050i
$218$		0			0
$219$		−	14.5326i		−	0.982022i
$220$		0			0
$221$			16.1093i			1.08363i
$222$		0			0
$223$	−15.4063	+	15.4063i	−1.03168	+	1.03168i	−0.0322013	+	0.999481i	$0.510252\pi$
$223$	−15.4063	+	15.4063i	−1.03168	+	1.03168i	−0.999481	+	0.0322013i	$0.989748\pi$
$224$		0			0
$225$	15.4572	−	38.0002i	1.03048	−	2.53335i
$226$		0			0
$227$	−12.9125	+	12.9125i	−0.857030	+	0.857030i	−0.990987	−	0.133957i	$-0.957232\pi$
$227$	−12.9125	+	12.9125i	−0.857030	+	0.857030i	0.133957	+	0.990987i	$0.457232\pi$
$228$		0			0
$229$	−2.37252			−0.156781			−0.0783904	−	0.996923i	$-0.524978\pi$
$229$	−2.37252			−0.156781			−0.0783904	+	0.996923i	$0.524978\pi$
$230$		0			0
$231$	16.7065			1.09920
$232$		0			0
$233$	−6.66394	+	6.66394i	−0.436569	+	0.436569i	−0.890856	−	0.454287i	$-0.849894\pi$
$233$	−6.66394	+	6.66394i	−0.436569	+	0.436569i	0.454287	+	0.890856i	$0.349894\pi$
$234$		0			0
$235$	7.16019	+	10.6424i	0.467080	+	0.694234i
$236$		0			0
$237$	28.3725	−	28.3725i	1.84299	−	1.84299i
$238$		0			0
$239$		−	15.8910i		−	1.02790i	−0.857819	−	0.513952i	$-0.828181\pi$
$239$		−	15.8910i		−	1.02790i	0.857819	−	0.513952i	$-0.171819\pi$
$240$		0			0
$241$		−	14.9631i		−	0.963857i	−0.876210	−	0.481929i	$-0.839936\pi$
$241$		−	14.9631i		−	0.963857i	0.876210	−	0.481929i	$-0.160064\pi$
$242$		0			0
$243$	42.8158	−	42.8158i	2.74663	−	2.74663i
$244$		0			0
$245$	−4.36571	+	22.3195i	−0.278915	+	1.42594i
$246$		0			0
$247$	11.8473	−	11.8473i	0.753823	−	0.753823i
$248$		0			0
$249$	6.73595			0.426873
$250$		0			0
$251$			19.7982i			1.24965i	0.780764	+	0.624826i	$0.214830\pi$
$251$			19.7982i			1.24965i	−0.780764	+	0.624826i	$0.785170\pi$
$252$		0			0
$253$	5.74792	−	0.572382i	0.361369	−	0.0359854i
$254$		0			0
$255$	−7.61780	+	38.9455i	−0.477045	+	2.43886i
$256$		0			0
$257$	4.38723	+	4.38723i	0.273668	+	0.273668i	0.830575	−	0.556907i	$-0.188012\pi$
$257$	4.38723	+	4.38723i	0.273668	+	0.273668i	−0.556907	+	0.830575i	$0.688012\pi$
$258$		0			0
$259$			22.2016i			1.37954i
$260$		0			0
$261$	−12.5462			−0.776588
$262$		0			0
$263$	−10.2968	−	10.2968i	−0.634930	−	0.634930i	0.314370	−	0.949301i	$-0.398207\pi$
$263$	−10.2968	−	10.2968i	−0.634930	−	0.634930i	−0.949301	+	0.314370i	$0.898207\pi$
$264$		0			0
$265$	1.84645	+	2.74443i	0.113426	+	0.168589i
$266$		0			0
$267$	7.35000	−	7.35000i	0.449813	−	0.449813i
$268$		0			0
$269$			6.51244i			0.397071i	0.980094	+	0.198535i	$0.0636184\pi$
$269$			6.51244i			0.397071i	−0.980094	+	0.198535i	$0.936382\pi$
$270$		0			0
$271$	−12.7572			−0.774942			−0.387471	−	0.921882i	$-0.626651\pi$
$271$	−12.7572			−0.774942			−0.387471	+	0.921882i	$0.626651\pi$
$272$		0			0
$273$	−29.8010	−	29.8010i	−1.80364	−	1.80364i
$274$		0			0
$275$	−2.26911	+	5.57842i	−0.136832	+	0.336391i
$276$		0			0
$277$	3.72521	+	3.72521i	0.223826	+	0.223826i	0.810107	−	0.586281i	$-0.199409\pi$
$277$	3.72521	+	3.72521i	0.223826	+	0.223826i	−0.586281	+	0.810107i	$0.699409\pi$
$278$		0			0
$279$			47.0447i			2.81650i
$280$		0			0
$281$		−	10.6124i		−	0.633082i	−0.948579	−	0.316541i	$-0.897478\pi$
$281$		−	10.6124i		−	0.633082i	0.948579	−	0.316541i	$-0.102522\pi$
$282$		0			0
$283$	−4.45265	−	4.45265i	−0.264682	−	0.264682i	0.562271	−	0.826953i	$-0.309928\pi$
$283$	−4.45265	−	4.45265i	−0.264682	−	0.264682i	−0.826953	+	0.562271i	$0.809928\pi$
$284$		0			0
$285$	34.2441	−	23.0394i	2.02845	−	1.36473i
$286$		0			0
$287$	1.65006	−	1.65006i	0.0973998	−	0.0973998i
$288$		0			0
$289$		−	11.1093i		−	0.653488i
$290$		0			0
$291$			15.1333i			0.887130i
$292$		0			0
$293$	4.73127	+	4.73127i	0.276404	+	0.276404i	0.831672	−	0.555268i	$-0.187384\pi$
$293$	4.73127	+	4.73127i	0.276404	+	0.276404i	−0.555268	+	0.831672i	$0.687384\pi$
$294$		0			0
$295$	−0.354617	+	1.81296i	−0.0206466	+	0.105555i
$296$		0			0
$297$	−14.8379	+	14.8379i	−0.860983	+	0.860983i
$298$		0			0
$299$	−11.2742	−	9.23213i	−0.652002	−	0.533908i
$300$		0			0
$301$	34.1093			1.96603
$302$		0			0
$303$	17.8366	−	17.8366i	1.02468	−	1.02468i
$304$		0			0
$305$	0.0804906	−	0.411503i	0.00460888	−	0.0235626i
$306$		0			0
$307$	7.01057	+	7.01057i	0.400114	+	0.400114i	0.878273	−	0.478159i	$-0.158696\pi$
$307$	7.01057	+	7.01057i	0.400114	+	0.400114i	−0.478159	+	0.878273i	$0.658696\pi$
$308$		0			0
$309$	−25.4999			−1.45064
$310$		0			0
$311$	−0.238730			−0.0135371			−0.00676856	−	0.999977i	$-0.502155\pi$
$311$	−0.238730			−0.0135371			−0.00676856	+	0.999977i	$0.502155\pi$
$312$		0			0
$313$	11.6957	+	11.6957i	0.661080	+	0.661080i	0.955635	−	0.294555i	$-0.0951713\pi$
$313$	11.6957	+	11.6957i	0.661080	+	0.661080i	−0.294555	+	0.955635i	$0.595171\pi$
$314$		0			0
$315$	−42.4372	−	63.0756i	−2.39106	−	3.55391i
$316$		0			0
$317$	13.3309	+	13.3309i	0.748736	+	0.748736i	0.974242	−	0.225506i	$-0.0724034\pi$
$317$	13.3309	+	13.3309i	0.748736	+	0.748736i	−0.225506	+	0.974242i	$0.572403\pi$
$318$		0			0
$319$	1.84177			0.103120
$320$		0			0
$321$		−	38.1078i		−	2.12697i
$322$		0			0
$323$	−20.6724	+	20.6724i	−1.15025	+	1.15025i
$324$		0			0
$325$	13.9984	−	5.90315i	0.776493	−	0.327448i
$326$		0			0
$327$	0.402882	−	0.402882i	0.0222794	−	0.0222794i
$328$		0			0
$329$	23.7701			1.31049
$330$		0			0
$331$	−32.8123			−1.80353			−0.901763	−	0.432230i	$-0.857727\pi$
$331$	−32.8123			−1.80353			−0.901763	+	0.432230i	$0.857727\pi$
$332$		0			0
$333$	−31.0841	−	31.0841i	−1.70340	−	1.70340i
$334$		0			0
$335$	−17.3973	+	11.7049i	−0.950517	+	0.639506i
$336$		0			0
$337$	−8.33774	+	8.33774i	−0.454186	+	0.454186i	−0.896741	−	0.442555i	$-0.854072\pi$
$337$	−8.33774	+	8.33774i	−0.454186	+	0.454186i	0.442555	+	0.896741i	$0.354072\pi$
$338$		0			0
$339$	61.6557			3.34868
$340$		0			0
$341$		−	6.90616i		−	0.373990i
$342$		0			0
$343$	9.29045	+	9.29045i	0.501637	+	0.501637i
$344$		0			0
$345$	−22.8905	−	27.6508i	−1.23238	−	1.48867i
$346$		0			0
$347$	11.1093	+	11.1093i	0.596379	+	0.596379i	0.939347	−	0.342968i	$-0.111432\pi$
$347$	11.1093	+	11.1093i	0.596379	+	0.596379i	−0.342968	+	0.939347i	$0.611432\pi$
$348$		0			0
$349$			4.72030i			0.252672i	0.991988	+	0.126336i	$0.0403217\pi$
$349$			4.72030i			0.252672i	−0.991988	+	0.126336i	$0.959678\pi$
$350$		0			0
$351$	52.9358			2.82550
$352$		0			0
$353$	−3.92348	+	3.92348i	−0.208826	+	0.208826i	−0.803768	−	0.594943i	$-0.797175\pi$
$353$	−3.92348	+	3.92348i	−0.208826	+	0.208826i	0.594943	+	0.803768i	$0.297175\pi$
$354$		0			0
$355$	9.35508	+	1.82987i	0.496516	+	0.0971192i
$356$		0			0
$357$	52.0002	+	52.0002i	2.75214	+	2.75214i
$358$		0			0
$359$	−22.0931			−1.16603			−0.583016	−	0.812461i	$-0.698127\pi$
$359$	−22.0931			−1.16603			−0.583016	+	0.812461i	$0.698127\pi$
$360$		0			0
$361$	11.4063			0.600332
$362$		0			0
$363$	−22.6025	+	22.6025i	−1.18632	+	1.18632i
$364$		0			0
$365$	8.05464	−	5.41915i	0.421599	−	0.283651i
$366$		0			0
$367$	2.53639	−	2.53639i	0.132399	−	0.132399i	−0.637802	−	0.770200i	$-0.720156\pi$
$367$	2.53639	−	2.53639i	0.132399	−	0.132399i	0.770200	+	0.637802i	$0.220156\pi$
$368$		0			0
$369$			4.62045i			0.240531i
$370$		0			0
$371$	6.12975			0.318241
$372$		0			0
$373$	−14.5069	−	14.5069i	−0.751141	−	0.751141i	0.223551	−	0.974692i	$-0.428235\pi$
$373$	−14.5069	−	14.5069i	−0.751141	−	0.751141i	−0.974692	+	0.223551i	$0.928235\pi$
$374$		0			0
$375$	36.6339	−	7.65176i	1.89177	−	0.395135i
$376$		0			0
$377$	−3.28536	−	3.28536i	−0.169205	−	0.169205i
$378$		0			0
$379$	14.9412			0.767478			0.383739	−	0.923442i	$-0.374636\pi$
$379$	14.9412			0.767478			0.383739	+	0.923442i	$0.374636\pi$
$380$		0			0
$381$	−45.4719			−2.32959
$382$		0			0
$383$	−21.0621	−	21.0621i	−1.07623	−	1.07623i	−0.996844	−	0.0793806i	$-0.974706\pi$
$383$	−21.0621	−	21.0621i	−1.07623	−	1.07623i	−0.0793806	−	0.996844i	$-0.525294\pi$
$384$		0			0
$385$	6.22977	+	9.25949i	0.317498	+	0.471907i
$386$		0			0
$387$	−47.7560	+	47.7560i	−2.42757	+	2.42757i
$388$		0			0
$389$	28.5296			1.44651			0.723255	−	0.690581i	$-0.242645\pi$
$389$	28.5296			1.44651			0.723255	+	0.690581i	$0.242645\pi$
$390$		0			0
$391$	19.6724	+	16.1093i	0.994878	+	0.814681i
$392$		0			0
$393$	−21.9979	+	21.9979i	−1.10965	+	1.10965i
$394$		0			0
$395$	26.3054	+	5.14536i	1.32357	+	0.258891i
$396$		0			0
$397$	−17.5548	−	17.5548i	−0.881051	−	0.881051i	0.112591	−	0.993641i	$-0.464085\pi$
$397$	−17.5548	−	17.5548i	−0.881051	−	0.881051i	−0.993641	+	0.112591i	$0.964085\pi$
$398$		0			0
$399$		−	76.4851i		−	3.82904i
$400$		0			0
$401$			31.2798i			1.56204i	0.624508	+	0.781018i	$0.285299\pi$
$401$			31.2798i			1.56204i	−0.624508	+	0.781018i	$0.714701\pi$
$402$		0			0
$403$	−12.3192	+	12.3192i	−0.613664	+	0.613664i
$404$		0			0
$405$	73.9613	+	14.4669i	3.67517	+	0.718867i
$406$		0			0
$407$	4.56314	+	4.56314i	0.226187	+	0.226187i
$408$		0			0
$409$			8.74143i			0.432236i	0.976367	+	0.216118i	$0.0693396\pi$
$409$			8.74143i			0.432236i	−0.976367	+	0.216118i	$0.930660\pi$
$410$		0			0
$411$			26.5777i			1.31098i
$412$		0			0
$413$	2.42067	+	2.42067i	0.119113	+	0.119113i
$414$		0			0
$415$	2.51181	+	3.73337i	0.123300	+	0.183264i
$416$		0			0
$417$	−24.2918	−	24.2918i	−1.18958	−	1.18958i
$418$		0			0
$419$	21.3220			1.04165			0.520824	−	0.853664i	$-0.325625\pi$
$419$	21.3220			1.04165			0.520824	+	0.853664i	$0.325625\pi$
$420$		0			0
$421$			14.7929i			0.720961i	0.932767	+	0.360480i	$0.117387\pi$
$421$			14.7929i			0.720961i	−0.932767	+	0.360480i	$0.882613\pi$
$422$		0			0
$423$	−33.2802	+	33.2802i	−1.61814	+	1.61814i
$424$		0			0
$425$	−24.4261	+	10.3005i	−1.18484	+	0.499647i
$426$		0			0
$427$	−0.549440	−	0.549440i	−0.0265893	−	0.0265893i
$428$		0			0
$429$	−12.2501			−0.591442
$430$		0			0
$431$		−	2.46259i		−	0.118619i	−0.998240	−	0.0593094i	$-0.981110\pi$
$431$		−	2.46259i		−	0.118619i	0.998240	−	0.0593094i	$-0.0188898\pi$
$432$		0			0
$433$	13.0512	+	13.0512i	0.627199	+	0.627199i	0.947362	−	0.320163i	$-0.103738\pi$
$433$	13.0512	+	13.0512i	0.627199	+	0.627199i	−0.320163	+	0.947362i	$0.603738\pi$
$434$		0			0
$435$	−6.38904	−	9.49622i	−0.306331	−	0.455309i
$436$		0			0
$437$	−2.62047	−	26.3150i	−0.125354	−	1.25882i
$438$		0			0
$439$		−	14.9288i		−	0.712515i	−0.934388	−	0.356258i	$-0.884053\pi$
$439$		−	14.9288i		−	0.712515i	0.934388	−	0.356258i	$-0.115947\pi$
$440$		0			0
$441$	−83.4479			−3.97371
$442$		0			0
$443$	−13.2578	+	13.2578i	−0.629897	+	0.629897i	−0.948042	−	0.318145i	$-0.896940\pi$
$443$	−13.2578	+	13.2578i	−0.629897	+	0.629897i	0.318145	+	0.948042i	$0.396940\pi$
$444$		0			0
$445$	6.81450	+	1.33292i	0.323038	+	0.0631867i
$446$		0			0
$447$	−11.4444	+	11.4444i	−0.541300	+	0.541300i
$448$		0			0
$449$		−	32.1263i		−	1.51613i	−0.652176	−	0.758067i	$-0.726144\pi$
$449$		−	32.1263i		−	1.51613i	0.652176	−	0.758067i	$-0.273856\pi$
$450$		0			0
$451$		−	0.678281i		−	0.0319390i
$452$		0			0
$453$	−4.22394	+	4.22394i	−0.198458	+	0.198458i
$454$		0			0
$455$	5.40442	−	27.6298i	0.253363	−	1.29530i
$456$		0			0
$457$	−15.1351	+	15.1351i	−0.707989	+	0.707989i	−0.966112	−	0.258123i	$-0.916896\pi$
$457$	−15.1351	+	15.1351i	−0.707989	+	0.707989i	0.258123	+	0.966112i	$0.416896\pi$
$458$		0			0
$459$	−92.3684			−4.31139
$460$		0			0
$461$	−19.6416			−0.914800			−0.457400	−	0.889261i	$-0.651219\pi$
$461$	−19.6416			−0.914800			−0.457400	+	0.889261i	$0.651219\pi$
$462$		0			0
$463$	17.4094	−	17.4094i	0.809086	−	0.809086i	−0.175410	−	0.984495i	$-0.556125\pi$
$463$	17.4094	−	17.4094i	0.809086	−	0.809086i	0.984495	+	0.175410i	$0.0561251\pi$
$464$		0			0
$465$	−35.6083	+	23.9572i	−1.65129	+	1.11099i
$466$		0			0
$467$	−28.9666	+	28.9666i	−1.34041	+	1.34041i	−0.444768	+	0.895646i	$0.646714\pi$
$467$	−28.9666	+	28.9666i	−1.34041	+	1.34041i	−0.895646	+	0.444768i	$0.853286\pi$
$468$		0			0
$469$			38.8573i			1.79426i
$470$		0			0
$471$			50.0065i			2.30418i
$472$		0			0
$473$	7.01057	−	7.01057i	0.322346	−	0.322346i
$474$		0			0
$475$	25.5390	+	10.3884i	1.17181	+	0.476651i
$476$		0			0
$477$	−8.58218	+	8.58218i	−0.392951	+	0.392951i
$478$		0			0
$479$	16.1093			0.736052			0.368026	−	0.929816i	$-0.380034\pi$
$479$	16.1093			0.736052			0.368026	+	0.929816i	$0.380034\pi$
$480$		0			0
$481$		−	16.2795i		−	0.742281i
$482$		0			0
$483$	−66.1936	+	6.59161i	−3.01191	+	0.299929i
$484$		0			0
$485$	−8.38758	+	5.64315i	−0.380860	+	0.256242i
$486$		0			0
$487$	−15.6776	−	15.6776i	−0.710422	−	0.710422i	0.256202	−	0.966623i	$-0.417529\pi$
$487$	−15.6776	−	15.6776i	−0.710422	−	0.710422i	−0.966623	+	0.256202i	$0.917529\pi$
$488$		0			0
$489$			69.9493i			3.16322i
$490$		0			0
$491$	8.24187			0.371950			0.185975	−	0.982554i	$-0.440456\pi$
$491$	8.24187			0.371950			0.185975	+	0.982554i	$0.440456\pi$
$492$		0			0
$493$	5.73267	+	5.73267i	0.258186	+	0.258186i
$494$		0			0
$495$	−21.6863	−	4.24187i	−0.974727	−	0.190658i
$496$		0			0
$497$	12.4909	−	12.4909i	0.560295	−	0.560295i
$498$		0			0
$499$		−	0.0582768i		−	0.00260883i	−0.999999	−	0.00130441i	$-0.999585\pi$
$499$		−	0.0582768i		−	0.00260883i	0.999999	−	0.00130441i	$-0.000415208\pi$
$500$		0			0
$501$	83.4479			3.72818
$502$		0			0
$503$	−15.6514	−	15.6514i	−0.697860	−	0.697860i	0.266089	−	0.963949i	$-0.414269\pi$
$503$	−15.6514	−	15.6514i	−0.697860	−	0.697860i	−0.963949	+	0.266089i	$0.914269\pi$
$504$		0			0
$505$	16.5370	+	3.23467i	0.735888	+	0.143941i
$506$		0			0
$507$	−8.91828	−	8.91828i	−0.396075	−	0.396075i
$508$		0			0
$509$			15.1367i			0.670923i	0.942054	+	0.335461i	$0.108892\pi$
$509$			15.1367i			0.670923i	−0.942054	+	0.335461i	$0.891108\pi$
$510$		0			0
$511$		−	17.9902i		−	0.795841i
$512$		0			0
$513$	67.9305	+	67.9305i	2.99921	+	2.99921i
$514$		0			0
$515$	−9.50881	−	14.1332i	−0.419008	−	0.622785i
$516$		0			0
$517$	4.88552	−	4.88552i	0.214865	−	0.214865i
$518$		0			0
$519$			31.1190i			1.36597i
$520$		0			0
$521$		−	9.22219i		−	0.404032i	−0.979382	−	0.202016i	$-0.935251\pi$
$521$		−	9.22219i		−	0.404032i	0.979382	−	0.202016i	$-0.0647492\pi$
$522$		0			0
$523$	−16.5666	−	16.5666i	−0.724409	−	0.724409i	0.245091	−	0.969500i	$-0.421182\pi$
$523$	−16.5666	−	16.5666i	−0.724409	−	0.724409i	−0.969500	+	0.245091i	$0.921182\pi$
$524$		0			0
$525$	26.1313	−	64.2416i	1.14046	−	2.80373i
$526$		0			0
$527$	21.4960	−	21.4960i	0.936380	−	0.936380i
$528$		0			0
$529$	−22.5483	+	4.53574i	−0.980362	+	0.197206i
$530$		0			0
$531$	−6.77829			−0.294153
$532$		0			0
$533$	−1.20992	+	1.20992i	−0.0524074	+	0.0524074i
$534$		0			0
$535$	21.1211	−	14.2102i	0.913145	−	0.614362i
$536$		0			0
$537$	20.2684	+	20.2684i	0.874645	+	0.874645i
$538$		0			0
$539$	12.2501			0.527651
$540$		0			0
$541$	−31.4539			−1.35231			−0.676154	−	0.736760i	$-0.736355\pi$
$541$	−31.4539			−1.35231			−0.676154	+	0.736760i	$0.736355\pi$
$542$		0			0
$543$	34.0352	+	34.0352i	1.46059	+	1.46059i
$544$		0			0
$545$	0.373528	+	0.0730627i	0.0160002	+	0.00312966i
$546$		0			0
$547$	−22.4899	−	22.4899i	−0.961600	−	0.961600i	0.0376892	−	0.999290i	$-0.488000\pi$
$547$	−22.4899	−	22.4899i	−0.961600	−	0.961600i	−0.999290	+	0.0376892i	$0.988000\pi$
$548$		0			0
$549$	1.53853			0.0656628
$550$		0			0
$551$		−	8.43196i		−	0.359214i
$552$		0			0
$553$	35.1230	−	35.1230i	1.49358	−	1.49358i
$554$		0			0
$555$	7.69829	−	39.3570i	0.326774	−	1.67061i
$556$		0			0
$557$	−0.202514	+	0.202514i	−0.00858077	+	0.00858077i	−0.711384	−	0.702803i	$-0.751931\pi$
$557$	−0.202514	+	0.202514i	−0.00858077	+	0.00858077i	0.702803	+	0.711384i	$0.251931\pi$
$558$		0			0
$559$	−25.0109			−1.05785
$560$		0			0
$561$	21.3754			0.902472
$562$		0			0
$563$	−15.7806	−	15.7806i	−0.665074	−	0.665074i	0.291498	−	0.956571i	$-0.405846\pi$
$563$	−15.7806	−	15.7806i	−0.665074	−	0.665074i	−0.956571	+	0.291498i	$0.905846\pi$
$564$		0			0
$565$	22.9912	+	34.1725i	0.967246	+	1.43765i
$566$		0			0
$567$	98.7533	−	98.7533i	4.14725	−	4.14725i
$568$		0			0
$569$	−9.01102			−0.377762			−0.188881	−	0.982000i	$-0.560486\pi$
$569$	−9.01102			−0.377762			−0.188881	+	0.982000i	$0.560486\pi$
$570$		0			0
$571$		−	14.4158i		−	0.603284i	−0.953421	−	0.301642i	$-0.902465\pi$
$571$		−	14.4158i		−	0.603284i	0.953421	−	0.301642i	$-0.0975347\pi$
$572$		0			0
$573$	38.9353	+	38.9353i	1.62655	+	1.62655i
$574$		0			0
$575$	6.78957	−	22.9979i	0.283145	−	0.959077i
$576$		0			0
$577$	−11.4455	−	11.4455i	−0.476483	−	0.476483i	0.427522	−	0.904005i	$-0.359387\pi$
$577$	−11.4455	−	11.4455i	−0.476483	−	0.476483i	−0.904005	+	0.427522i	$0.859387\pi$
$578$		0			0
$579$		−	52.9358i		−	2.19994i
$580$		0			0
$581$	8.33859			0.345943
$582$		0			0
$583$	1.25986	−	1.25986i	0.0521781	−	0.0521781i
$584$		0			0
$585$	31.1174	+	46.2507i	1.28655	+	1.91223i
$586$		0			0
$587$	8.65734	+	8.65734i	0.357327	+	0.357327i	0.862827	−	0.505500i	$-0.168692\pi$
$587$	8.65734	+	8.65734i	0.357327	+	0.357327i	−0.505500	+	0.862827i	$0.668692\pi$
$588$		0			0
$589$	−31.6176			−1.30278
$590$		0			0
$591$	57.8306			2.37883
$592$		0			0
$593$	−27.4646	+	27.4646i	−1.12784	+	1.12784i	−0.137307	+	0.990529i	$0.543845\pi$
$593$	−27.4646	+	27.4646i	−1.12784	+	1.12784i	−0.990529	+	0.137307i	$0.956155\pi$
$594$		0			0
$595$	−9.43024	+	48.2116i	−0.386602	+	1.97648i
$596$		0			0
$597$	−17.5509	+	17.5509i	−0.718309	+	0.718309i
$598$		0			0
$599$			17.8570i			0.729618i	0.931082	+	0.364809i	$0.118866\pi$
$599$			17.8570i			0.729618i	−0.931082	+	0.364809i	$0.881134\pi$
$600$		0			0
$601$	18.3074			0.746776			0.373388	−	0.927675i	$-0.378196\pi$
$601$	18.3074			0.746776			0.373388	+	0.927675i	$0.378196\pi$
$602$		0			0
$603$	−54.4036	−	54.4036i	−2.21549	−	2.21549i
$604$		0			0
$605$	−20.9558	−	4.09897i	−0.851973	−	0.166647i
$606$		0			0
$607$	−5.92142	−	5.92142i	−0.240343	−	0.240343i	0.576649	−	0.816992i	$-0.304360\pi$
$607$	−5.92142	−	5.92142i	−0.240343	−	0.240343i	−0.816992	+	0.576649i	$0.804360\pi$
$608$		0			0
$609$	−21.2100			−0.859474
$610$		0			0
$611$	−17.4296			−0.705126
$612$		0			0
$613$	−32.2730	−	32.2730i	−1.30350	−	1.30350i	−0.926019	−	0.377477i	$-0.876792\pi$
$613$	−32.2730	−	32.2730i	−1.30350	−	1.30350i	−0.377477	−	0.926019i	$-0.623208\pi$
$614$		0			0
$615$	−3.49723	+	2.35293i	−0.141022	+	0.0948793i
$616$		0			0
$617$	26.6729	−	26.6729i	1.07381	−	1.07381i	0.0767592	−	0.997050i	$-0.475543\pi$
$617$	26.6729	−	26.6729i	1.07381	−	1.07381i	0.997050	−	0.0767592i	$-0.0244573\pi$
$618$		0			0
$619$	18.7429			0.753340			0.376670	−	0.926348i	$-0.377069\pi$
$619$	18.7429			0.753340			0.376670	+	0.926348i	$0.377069\pi$
$620$		0			0
$621$	52.9358	−	64.6445i	2.12424	−	2.59409i
$622$		0			0
$623$	9.09874	−	9.09874i	0.364533	−	0.364533i
$624$		0			0
$625$	17.9016	+	17.4509i	0.716063	+	0.698035i
$626$		0			0
$627$	−15.7202	−	15.7202i	−0.627803	−	0.627803i
$628$		0			0
$629$			28.4063i			1.13263i
$630$		0			0
$631$			33.8754i			1.34856i	0.738477	+	0.674279i	$0.235545\pi$
$631$			33.8754i			1.34856i	−0.738477	+	0.674279i	$0.764455\pi$
$632$		0			0
$633$	53.5187	−	53.5187i	2.12718	−	2.12718i
$634$		0			0
$635$	−16.9563	−	25.2026i	−0.672889	−	1.00014i
$636$		0			0
$637$	−21.8518	−	21.8518i	−0.865801	−	0.865801i
$638$		0			0
$639$			34.9767i			1.38366i
$640$		0			0
$641$			14.2621i			0.563320i	0.959514	+	0.281660i	$0.0908850\pi$
$641$			14.2621i			0.563320i	−0.959514	+	0.281660i	$0.909115\pi$
$642$		0			0
$643$	−10.4930	−	10.4930i	−0.413804	−	0.413804i	0.469257	−	0.883061i	$-0.344522\pi$
$643$	−10.4930	−	10.4930i	−0.413804	−	0.413804i	−0.883061	+	0.469257i	$0.844522\pi$
$644$		0			0
$645$	−60.4660	−	11.8272i	−2.38085	−	0.465697i
$646$		0			0
$647$	17.2611	+	17.2611i	0.678603	+	0.678603i	0.959684	−	0.281081i	$-0.0906929\pi$
$647$	17.2611	+	17.2611i	0.678603	+	0.678603i	−0.281081	+	0.959684i	$0.590693\pi$
$648$		0			0
$649$	0.995052			0.0390592
$650$		0			0
$651$			79.5320i			3.11711i
$652$		0			0
$653$	24.0666	−	24.0666i	0.941800	−	0.941800i	−0.0565967	−	0.998397i	$-0.518025\pi$
$653$	24.0666	−	24.0666i	0.941800	−	0.941800i	0.998397	+	0.0565967i	$0.0180249\pi$
$654$		0			0
$655$	−20.3952	−	3.98933i	−0.796907	−	0.155876i
$656$		0			0
$657$	25.1879	+	25.1879i	0.982673	+	0.982673i
$658$		0			0
$659$	10.1280			0.394530			0.197265	−	0.980350i	$-0.436794\pi$
$659$	10.1280			0.394530			0.197265	+	0.980350i	$0.436794\pi$
$660$		0			0
$661$		−	9.46877i		−	0.368293i	−0.982899	−	0.184146i	$-0.941048\pi$
$661$		−	9.46877i		−	0.368293i	0.982899	−	0.184146i	$-0.0589520\pi$
$662$		0			0
$663$	−38.1295	−	38.1295i	−1.48083	−	1.48083i
$664$		0			0
$665$	42.3916	−	28.5210i	1.64387	−	1.10600i
$666$		0			0
$667$	−7.29740	+	0.726680i	−0.282556	+	0.0281372i
$668$		0			0
$669$		−	72.9313i		−	2.81969i
$670$		0			0
$671$	−0.225856			−0.00871906
$672$		0			0
$673$	25.6501	−	25.6501i	0.988738	−	0.988738i	−0.0111991	−	0.999937i	$-0.503565\pi$
$673$	25.6501	−	25.6501i	0.988738	−	0.988738i	0.999937	+	0.0111991i	$0.00356484\pi$
$674$		0			0
$675$	33.8479	+	80.2651i	1.30281	+	3.08940i
$676$		0			0
$677$	−6.79787	+	6.79787i	−0.261263	+	0.261263i	−0.825567	−	0.564304i	$-0.809145\pi$
$677$	−6.79787	+	6.79787i	−0.261263	+	0.261263i	0.564304	+	0.825567i	$0.309145\pi$
$678$		0			0
$679$			18.7339i			0.718940i
$680$		0			0
$681$		−	61.1258i		−	2.34235i
$682$		0			0
$683$	−11.3024	+	11.3024i	−0.432473	+	0.432473i	−0.889469	−	0.456996i	$-0.848926\pi$
$683$	−11.3024	+	11.3024i	−0.432473	+	0.432473i	0.456996	+	0.889469i	$0.348926\pi$
$684$		0			0
$685$	−14.7306	+	9.91071i	−0.562826	+	0.378669i
$686$		0			0
$687$	5.61560	−	5.61560i	0.214248	−	0.214248i
$688$		0			0
$689$	−4.49469			−0.171234
$690$		0			0
$691$	−12.6832			−0.482490			−0.241245	−	0.970464i	$-0.577556\pi$
$691$	−12.6832			−0.482490			−0.241245	+	0.970464i	$0.577556\pi$
$692$		0			0
$693$	−28.9556	+	28.9556i	−1.09993	+	1.09993i
$694$		0			0
$695$	4.40533	−	22.5220i	0.167104	−	0.854307i
$696$		0			0
$697$	2.11120	−	2.11120i	0.0799675	−	0.0799675i
$698$		0			0
$699$		−	31.5462i		−	1.19319i
$700$		0			0
$701$			36.2851i			1.37047i	0.728323	+	0.685234i	$0.240300\pi$
$701$			36.2851i			1.37047i	−0.728323	+	0.685234i	$0.759700\pi$
$702$		0			0
$703$	20.8909	−	20.8909i	0.787914	−	0.787914i
$704$		0			0
$705$	−42.1375	−	8.24216i	−1.58699	−	0.310418i
$706$		0			0
$707$	22.0803	−	22.0803i	0.830415	−	0.830415i
$708$		0			0
$709$	−7.07460			−0.265692			−0.132846	−	0.991137i	$-0.542412\pi$
$709$	−7.07460			−0.265692			−0.132846	+	0.991137i	$0.542412\pi$
$710$		0			0
$711$			98.3505i			3.68843i
$712$		0			0
$713$	2.72486	+	27.3633i	0.102047	+	1.02476i
$714$		0			0
$715$	−4.56803	−	6.78959i	−0.170835	−	0.253916i
$716$		0			0
$717$	37.6129	+	37.6129i	1.40468	+	1.40468i
$718$		0			0
$719$		−	32.8189i		−	1.22394i	−0.790882	−	0.611969i	$-0.790378\pi$
$719$		−	32.8189i		−	1.22394i	0.790882	−	0.611969i	$-0.209622\pi$
$720$		0			0
$721$	−31.5669			−1.17561
$722$		0			0
$723$	35.4166	+	35.4166i	1.31716	+	1.31716i
$724$		0			0
$725$	2.88080	−	7.08220i	0.106990	−	0.263026i
$726$		0			0
$727$	−17.8991	+	17.8991i	−0.663842	+	0.663842i	−0.956283	−	0.292441i	$-0.905532\pi$
$727$	−17.8991	+	17.8991i	−0.663842	+	0.663842i	0.292441	+	0.956283i	$0.405532\pi$
$728$		0			0
$729$			101.574i			3.76200i
$730$		0			0
$731$	43.6419			1.61415
$732$		0			0
$733$	3.44856	+	3.44856i	0.127376	+	0.127376i	0.767921	−	0.640545i	$-0.221292\pi$
$733$	3.44856	+	3.44856i	0.127376	+	0.127376i	−0.640545	+	0.767921i	$0.721292\pi$
$734$		0			0
$735$	−42.4953	−	63.1619i	−1.56746	−	2.32976i
$736$		0			0
$737$	7.98644	+	7.98644i	0.294184	+	0.294184i
$738$		0			0
$739$			0.925025i			0.0340276i	0.999855	+	0.0170138i	$0.00541592\pi$
$739$			0.925025i			0.0340276i	−0.999855	+	0.0170138i	$0.994584\pi$
$740$		0			0
$741$			56.0833i			2.06027i
$742$		0			0
$743$	27.5363	+	27.5363i	1.01021	+	1.01021i	0.999947	+	0.0102631i	$0.00326690\pi$
$743$	27.5363	+	27.5363i	1.01021	+	1.01021i	0.0102631	+	0.999947i	$0.496733\pi$
$744$		0			0
$745$	−10.6106	−	2.07544i	−0.388741	−	0.0760383i
$746$		0			0
$747$	−11.6747	+	11.6747i	−0.427156	+	0.427156i
$748$		0			0
$749$		−	47.1745i		−	1.72372i
$750$		0			0
$751$		−	50.1020i		−	1.82825i	−0.405436	−	0.914124i	$-0.632880\pi$
$751$		−	50.1020i		−	1.82825i	0.405436	−	0.914124i	$-0.367120\pi$
$752$		0			0
$753$	−46.8610	−	46.8610i	−1.70771	−	1.70771i
$754$		0			0
$755$	−3.91620	−	0.766013i	−0.142525	−	0.0278781i
$756$		0			0
$757$	6.29034	−	6.29034i	0.228626	−	0.228626i	−0.583492	−	0.812119i	$-0.698314\pi$
$757$	6.29034	−	6.29034i	0.228626	−	0.228626i	0.812119	+	0.583492i	$0.198314\pi$
$758$		0			0
$759$	−12.2501	+	14.9597i	−0.444652	+	0.543003i
$760$		0			0
$761$	−34.1370			−1.23747			−0.618733	−	0.785601i	$-0.712354\pi$
$761$	−34.1370			−1.23747			−0.618733	+	0.785601i	$0.712354\pi$
$762$		0			0
$763$	0.498736	−	0.498736i	0.0180555	−	0.0180555i
$764$		0			0
$765$	−54.2972	−	80.7035i	−1.96312	−	2.91784i
$766$		0			0
$767$	−1.77497	−	1.77497i	−0.0640906	−	0.0640906i
$768$		0			0
$769$	−49.6687			−1.79110			−0.895549	−	0.444962i	$-0.853217\pi$
$769$	−49.6687			−1.79110			−0.895549	+	0.444962i	$0.853217\pi$
$770$		0			0
$771$	−20.7686			−0.747961
$772$		0			0
$773$	6.59981	+	6.59981i	0.237379	+	0.237379i	0.815764	−	0.578385i	$-0.196317\pi$
$773$	6.59981	+	6.59981i	0.237379	+	0.237379i	−0.578385	+	0.815764i	$0.696317\pi$
$774$		0			0
$775$	−26.5564	−	10.8022i	−0.953933	−	0.388027i
$776$		0			0
$777$	−52.5496	−	52.5496i	−1.88521	−	1.88521i
$778$		0			0
$779$	−3.10529			−0.111258
$780$		0			0
$781$		−	5.13458i		−	0.183730i
$782$		0			0
$783$	18.8378	−	18.8378i	0.673208	−	0.673208i
$784$		0			0
$785$	−27.7159	+	18.6472i	−0.989224	+	0.665549i
$786$		0			0
$787$	35.9410	−	35.9410i	1.28116	−	1.28116i	0.341149	−	0.940009i	$-0.389184\pi$
$787$	35.9410	−	35.9410i	1.28116	−	1.28116i	0.940009	−	0.341149i	$-0.110816\pi$
$788$		0			0
$789$	48.7438			1.73533
$790$		0			0
$791$	76.3251			2.71381
$792$		0			0
$793$	0.402882	+	0.402882i	0.0143067	+	0.0143067i
$794$		0			0
$795$	−10.8663	−	2.12546i	−0.385387	−	0.0753823i
$796$		0			0
$797$	−36.4095	+	36.4095i	−1.28969	+	1.28969i	−0.354714	+	0.934975i	$0.615422\pi$
$797$	−36.4095	+	36.4095i	−1.28969	+	1.28969i	−0.934975	+	0.354714i	$0.884578\pi$
$798$		0			0
$799$	30.4132			1.07594
$800$		0			0
$801$			25.4780i			0.900222i
$802$		0			0
$803$	−3.69758	−	3.69758i	−0.130485	−	0.130485i
$804$		0			0
$805$	−28.3367	−	34.2296i	−0.998738	−	1.20643i
$806$		0			0
$807$	−15.4145	−	15.4145i	−0.542616	−	0.542616i
$808$		0			0
$809$			10.1631i			0.357317i	0.983911	+	0.178659i	$0.0571757\pi$
$809$			10.1631i			0.357317i	−0.983911	+	0.178659i	$0.942824\pi$
$810$		0			0
$811$	30.7370			1.07932			0.539662	−	0.841882i	$-0.318552\pi$
$811$	30.7370			1.07932			0.539662	+	0.841882i	$0.318552\pi$
$812$		0			0
$813$	30.1953	−	30.1953i	1.05900	−	1.05900i
$814$		0			0
$815$	−38.7692	+	26.0838i	−1.35802	+	0.913677i
$816$		0			0
$817$	−32.0956	−	32.0956i	−1.12288	−	1.12288i
$818$		0			0
$819$	103.302			3.60967
$820$		0			0
$821$	2.08503			0.0727681			0.0363841	−	0.999338i	$-0.488416\pi$
$821$	2.08503			0.0727681			0.0363841	+	0.999338i	$0.488416\pi$
$822$		0			0
$823$	8.13480	−	8.13480i	0.283561	−	0.283561i	−0.550966	−	0.834528i	$-0.685741\pi$
$823$	8.13480	−	8.13480i	0.283561	−	0.283561i	0.834528	+	0.550966i	$0.185741\pi$
$824$		0			0
$825$	−7.83291	−	18.5746i	−0.272707	−	0.646683i
$826$		0			0
$827$	9.63276	−	9.63276i	0.334964	−	0.334964i	−0.519504	−	0.854468i	$-0.673883\pi$
$827$	9.63276	−	9.63276i	0.334964	−	0.334964i	0.854468	+	0.519504i	$0.173883\pi$
$828$		0			0
$829$		−	13.2557i		−	0.460391i	−0.973144	−	0.230196i	$-0.926063\pi$
$829$		−	13.2557i		−	0.460391i	0.973144	−	0.230196i	$-0.0739366\pi$
$830$		0			0
$831$	−17.6346			−0.611738
$832$		0			0
$833$	38.1295	+	38.1295i	1.32111	+	1.32111i
$834$		0			0
$835$	31.1174	+	46.2507i	1.07686	+	1.60057i
$836$		0			0
$837$	−70.6367	−	70.6367i	−2.44156	−	2.44156i
$838$		0			0
$839$	2.92034			0.100821			0.0504107	−	0.998729i	$-0.483947\pi$
$839$	2.92034			0.100821			0.0504107	+	0.998729i	$0.483947\pi$
$840$		0			0
$841$	26.6617			0.919370
$842$		0			0
$843$	25.1188	+	25.1188i	0.865137	+	0.865137i
$844$		0			0
$845$	1.61733	−	8.26852i	0.0556379	−	0.284446i
$846$		0			0
$847$	−27.9802	+	27.9802i	−0.961410	+	0.961410i
$848$		0			0
$849$	21.0782			0.723403
$850$		0			0
$851$	−19.8803	−	16.2795i	−0.681488	−	0.558054i
$852$		0			0
$853$	−23.6417	+	23.6417i	−0.809477	+	0.809477i	−0.984555	−	0.175077i	$-0.943982\pi$
$853$	−23.6417	+	23.6417i	−0.809477	+	0.809477i	0.175077	+	0.984555i	$0.443982\pi$
$854$		0			0
$855$	−19.4200	+	99.2837i	−0.664150	+	3.39543i
$856$		0			0
$857$	40.2781	+	40.2781i	1.37587	+	1.37587i	0.851469	+	0.524405i	$0.175712\pi$
$857$	40.2781	+	40.2781i	1.37587	+	1.37587i	0.524405	+	0.851469i	$0.324288\pi$
$858$		0			0
$859$		−	30.1880i		−	1.03000i	−0.857190	−	0.515001i	$-0.827792\pi$
$859$		−	30.1880i		−	1.03000i	0.857190	−	0.515001i	$-0.172208\pi$
$860$		0			0
$861$			7.81115i			0.266203i
$862$		0			0
$863$	28.5619	−	28.5619i	0.972259	−	0.972259i	−0.0273665	−	0.999625i	$-0.508712\pi$
$863$	28.5619	−	28.5619i	0.972259	−	0.972259i	0.999625	+	0.0273665i	$0.00871210\pi$
$864$		0			0
$865$	−17.2476	+	11.6042i	−0.586436	+	0.394553i
$866$		0			0
$867$	26.2949	+	26.2949i	0.893023	+	0.893023i
$868$		0			0
$869$		−	14.4378i		−	0.489770i
$870$		0			0
$871$		−	28.4924i		−	0.965430i
$872$		0			0
$873$	−26.2290	−	26.2290i	−0.887718	−	0.887718i
$874$		0			0
$875$	45.3499	−	9.47229i	1.53311	−	0.320222i
$876$		0			0
$877$	2.29686	+	2.29686i	0.0775595	+	0.0775595i	0.744822	−	0.667263i	$-0.232534\pi$
$877$	2.29686	+	2.29686i	0.0775595	+	0.0775595i	−0.667263	+	0.744822i	$0.732534\pi$
$878$		0			0
$879$	−22.3972			−0.755439
$880$		0			0
$881$		−	30.8266i		−	1.03857i	−0.854600	−	0.519287i	$-0.826198\pi$
$881$		−	30.8266i		−	1.03857i	0.854600	−	0.519287i	$-0.173802\pi$
$882$		0			0
$883$	−21.4783	+	21.4783i	−0.722802	+	0.722802i	−0.969175	−	0.246373i	$-0.920761\pi$
$883$	−21.4783	+	21.4783i	−0.722802	+	0.722802i	0.246373	+	0.969175i	$0.420761\pi$
$884$		0			0
$885$	−3.45180	−	5.13050i	−0.116031	−	0.172460i
$886$		0			0
$887$	37.4043	+	37.4043i	1.25591	+	1.25591i	0.953027	+	0.302885i	$0.0979497\pi$
$887$	37.4043	+	37.4043i	1.25591	+	1.25591i	0.302885	+	0.953027i	$0.402050\pi$
$888$		0			0
$889$	−56.2907			−1.88793
$890$		0			0
$891$		−	40.5940i		−	1.35995i
$892$		0			0
$893$	−22.3668	−	22.3668i	−0.748476	−	0.748476i
$894$		0			0
$895$	−3.67567	+	18.7917i	−0.122864	+	0.628136i
$896$		0			0
$897$	48.5370	−	4.83335i	1.62060	−	0.161381i
$898$		0			0
$899$			8.76787i			0.292425i
$900$		0			0
$901$	7.84284			0.261283
$902$		0			0
$903$	−80.7344	+	80.7344i	−2.68667	+	2.68667i
$904$		0			0
$905$	−6.17229	+	31.5554i	−0.205174	+	1.04894i
$906$		0			0
$907$	14.1398	−	14.1398i	0.469503	−	0.469503i	−0.432251	−	0.901754i	$-0.642280\pi$
$907$	14.1398	−	14.1398i	0.469503	−	0.469503i	0.901754	+	0.432251i	$0.142280\pi$
$908$		0			0
$909$			61.8286i			2.05073i
$910$		0			0
$911$			33.5350i			1.11106i	0.831496	+	0.555531i	$0.187485\pi$
$911$			33.5350i			1.11106i	−0.831496	+	0.555531i	$0.812515\pi$
$912$		0			0
$913$	1.71385	−	1.71385i	0.0567201	−	0.0567201i
$914$		0			0
$915$	0.783484	+	1.16452i	0.0259012	+	0.0384977i
$916$		0			0
$917$	−27.2318	+	27.2318i	−0.899272	+	0.899272i
$918$		0			0
$919$	−16.2795			−0.537011			−0.268505	−	0.963278i	$-0.586530\pi$
$919$	−16.2795			−0.537011			−0.268505	+	0.963278i	$0.586530\pi$
$920$		0			0
$921$	−33.1871			−1.09355
$922$		0			0
$923$	−9.15907	+	9.15907i	−0.301474	+	0.301474i
$924$		0			0
$925$	24.6841	−	10.4093i	0.811610	−	0.342257i
$926$		0			0
$927$	44.1964	−	44.1964i	1.45160	−	1.45160i
$928$		0			0
$929$		−	9.62142i		−	0.315669i	−0.987466	−	0.157834i	$-0.949549\pi$
$929$		−	9.62142i		−	0.315669i	0.987466	−	0.157834i	$-0.0504512\pi$
$930$		0			0
$931$		−	56.0833i		−	1.83806i
$932$		0			0
$933$	0.565057	−	0.565057i	0.0184991	−	0.0184991i
$934$		0			0
$935$	7.97082	+	11.8473i	0.260674	+	0.387447i
$936$		0			0
$937$	38.1283	−	38.1283i	1.24560	−	1.24560i	0.287954	−	0.957644i	$-0.407025\pi$
$937$	38.1283	−	38.1283i	1.24560	−	1.24560i	0.957644	−	0.287954i	$-0.0929749\pi$
$938$		0			0
$939$	−55.3658			−1.80680
$940$		0			0
$941$			34.0464i			1.10988i	0.831890	+	0.554940i	$0.187259\pi$
$941$			34.0464i			1.10988i	−0.831890	+	0.554940i	$0.812741\pi$
$942$		0			0
$943$	0.267619	+	2.68746i	0.00871487	+	0.0875156i
$944$		0			0
$945$	158.425	+	30.9882i	5.15357	+	1.00805i
$946$		0			0
$947$	38.3100	+	38.3100i	1.24491	+	1.24491i	0.957941	+	0.286965i	$0.0926464\pi$
$947$	38.3100	+	38.3100i	1.24491	+	1.24491i	0.286965	+	0.957941i	$0.407354\pi$
$948$		0			0
$949$			13.1915i			0.428214i
$950$		0			0
$951$	−63.1065			−2.04637
$952$		0			0
$953$	22.1732	+	22.1732i	0.718259	+	0.718259i	0.968249	−	0.249989i	$-0.0804271\pi$
$953$	22.1732	+	22.1732i	0.718259	+	0.718259i	−0.249989	+	0.968249i	$0.580427\pi$
$954$		0			0
$955$	−7.06093	+	36.0986i	−0.228486	+	1.16812i
$956$		0			0
$957$	−4.35935	+	4.35935i	−0.140918	+	0.140918i
$958$		0			0
$959$			32.9011i			1.06243i
$960$		0			0
$961$	1.87717			0.0605539
$962$		0			0
$963$	66.0484	+	66.0484i	2.12838	+	2.12838i
$964$		0			0
$965$	29.3395	−	19.7395i	0.944470	−	0.635438i
$966$		0			0
$967$	−10.8753	−	10.8753i	−0.349725	−	0.349725i	0.510282	−	0.860007i	$-0.329541\pi$
$967$	−10.8753	−	10.8753i	−0.349725	−	0.349725i	−0.860007	+	0.510282i	$0.829541\pi$
$968$		0			0
$969$		−	97.8605i		−	3.14373i
$970$		0			0
$971$		−	21.3029i		−	0.683643i	−0.939765	−	0.341822i	$-0.888956\pi$
$971$		−	21.3029i		−	0.683643i	0.939765	−	0.341822i	$-0.111044\pi$
$972$		0			0
$973$	−30.0714	−	30.0714i	−0.964045	−	0.964045i
$974$		0			0
$975$	−19.1610	+	47.1057i	−0.613642	+	1.50859i
$976$		0			0
$977$	14.6294	−	14.6294i	0.468037	−	0.468037i	−0.433241	−	0.901278i	$-0.642630\pi$
$977$	14.6294	−	14.6294i	0.468037	−	0.468037i	0.901278	+	0.433241i	$0.142630\pi$
$978$		0			0
$979$		−	3.74017i		−	0.119536i
$980$		0			0
$981$			1.39655i			0.0445883i
$982$		0			0
$983$	16.3459	+	16.3459i	0.521352	+	0.521352i	0.917980	−	0.396628i	$-0.129820\pi$
$983$	16.3459	+	16.3459i	0.521352	+	0.521352i	−0.396628	+	0.917980i	$0.629820\pi$
$984$		0			0
$985$	21.5648	+	32.0524i	0.687112	+	1.02127i
$986$		0			0
$987$	−56.2621	+	56.2621i	−1.79084	+	1.79084i
$988$		0			0
$989$	−25.0109	+	30.5430i	−0.795301	+	0.971212i
$990$		0			0
$991$	−32.8362			−1.04308			−0.521538	−	0.853228i	$-0.674642\pi$
$991$	−32.8362			−1.04308			−0.521538	+	0.853228i	$0.674642\pi$
$992$		0			0
$993$	77.6644	−	77.6644i	2.46461	−	2.46461i
$994$		0			0
$995$	−16.2721	−	3.18285i	−0.515862	−	0.100903i
$996$		0			0
$997$	−40.8811	−	40.8811i	−1.29472	−	1.29472i	−0.931834	−	0.362885i	$-0.881792\pi$
$997$	−40.8811	−	40.8811i	−1.29472	−	1.29472i	−0.362885	−	0.931834i	$-0.618208\pi$
$998$		0			0
$999$	93.3443			2.95328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.i.b.137.1	✓	16
5.2	odd	4		2300.2.i.d.1793.7		16
5.3	odd	4	inner	460.2.i.b.413.2	yes	16
5.4	even	2		2300.2.i.d.1057.8		16
23.22	odd	2	inner	460.2.i.b.137.2	yes	16
115.22	even	4		2300.2.i.d.1793.8		16
115.68	even	4	inner	460.2.i.b.413.1	yes	16
115.114	odd	2		2300.2.i.d.1057.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.i.b.137.1	✓	16	1.1	even	1	trivial
460.2.i.b.137.2	yes	16	23.22	odd	2	inner
460.2.i.b.413.1	yes	16	115.68	even	4	inner
460.2.i.b.413.2	yes	16	5.3	odd	4	inner
2300.2.i.d.1057.7		16	115.114	odd	2
2300.2.i.d.1057.8		16	5.4	even	2
2300.2.i.d.1793.7		16	5.2	odd	4
2300.2.i.d.1793.8		16	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)

\(f(q)\)	\(=\)	\(q+(-2.36693 + 2.36693i) q^{3} +(-2.19448 - 0.429243i) q^{5} +(-2.93008 + 2.93008i) q^{7} -8.20472i q^{9} +O(q^{10})\)	\(q+(-2.36693 + 2.36693i) q^{3} +(-2.19448 - 0.429243i) q^{5} +(-2.93008 + 2.93008i) q^{7} -8.20472i q^{9} +1.20445i q^{11} +(2.14850 - 2.14850i) q^{13} +(6.21018 - 4.17820i) q^{15} +(-3.74895 + 3.74895i) q^{17} +5.51419 q^{19} -13.8706i q^{21} +(-0.475222 - 4.77223i) q^{23} +(4.63150 + 1.88393i) q^{25} +(12.3192 + 12.3192i) q^{27} -1.52914i q^{29} -5.73386 q^{31} +(-2.85085 - 2.85085i) q^{33} +(7.68772 - 5.17229i) q^{35} +(3.78857 - 3.78857i) q^{37} +10.1707i q^{39} -0.563145 q^{41} +(-5.82054 - 5.82054i) q^{43} +(-3.52182 + 18.0051i) q^{45} +(-4.05622 - 4.05622i) q^{47} -10.1707i q^{49} -17.7470i q^{51} +(-1.04600 - 1.04600i) q^{53} +(0.517003 - 2.64315i) q^{55} +(-13.0517 + 13.0517i) q^{57} -0.826145i q^{59} +0.187517i q^{61} +(24.0405 + 24.0405i) q^{63} +(-5.63708 + 3.79262i) q^{65} +(6.63077 - 6.63077i) q^{67} +(12.4204 + 10.1707i) q^{69} -4.26300 q^{71} +(-3.06992 + 3.06992i) q^{73} +(-15.4216 + 6.50330i) q^{75} +(-3.52914 - 3.52914i) q^{77} -11.9871 q^{79} -33.7033 q^{81} +(-1.42293 - 1.42293i) q^{83} +(9.83622 - 6.61780i) q^{85} +(3.61936 + 3.61936i) q^{87} -3.10529 q^{89} +12.5906i q^{91} +(13.5717 - 13.5717i) q^{93} +(-12.1008 - 2.36693i) q^{95} +(3.19682 - 3.19682i) q^{97} +9.88219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3}+O(q^{10}) \) 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

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Modular forms

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