LMFDB - Embedded newform 605.2.m.a.282.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	16.0.3429742096000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 16x^{12} + 35x^{10} + 31x^{8} + 315x^{6} + 1296x^{4} + 3645x^{2} + 6561 $ x^16 + 5x^14 + 16x^12 + 35x^10 + 31x^8 + 315x^6 + 1296x^4 + 3645*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{U}(1)[D_{20}]$

Embedding invariants

Embedding label			282.2
Root			$-0.987975 + 1.42264i$ of defining polynomial
Character	$\chi$	$=$	605.282
Dual form			605.2.m.a.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38572 + 2.71963i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.459925 + 2.18826i) q^{5} +(-3.71282 + 5.11026i) q^{9} +O(q^{10})$	$q+(1.38572 + 2.71963i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.459925 + 2.18826i) q^{5} +(-3.71282 + 5.11026i) q^{9} +(-4.31662 - 4.31662i) q^{12} +(-6.58858 + 1.78149i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-0.477588 - 4.44656i) q^{20} +(2.84169 - 2.84169i) q^{23} +(-4.57694 - 2.01287i) q^{25} +(-9.99875 - 1.58365i) q^{27} +(8.04962 + 5.84839i) q^{31} +(3.90389 - 12.0149i) q^{36} +(-0.946968 + 1.85853i) q^{37} +(-9.47494 - 10.4749i) q^{45} +(-11.7396 + 5.98164i) q^{47} +(10.8785 + 5.54289i) q^{48} +(-4.11450 - 5.66312i) q^{49} +(-5.07493 + 0.803790i) q^{53} +(3.15430 - 1.02489i) q^{59} +(11.4312 - 7.46056i) q^{60} +(-4.70228 + 6.47214i) q^{64} +(11.4749 + 11.4749i) q^{67} +(11.6661 + 3.79056i) q^{69} +(2.42705 - 1.76336i) q^{71} +(-0.868101 - 15.2369i) q^{75} +(3.65655 + 8.16270i) q^{80} +(-3.69271 - 11.3650i) q^{81} +9.00000i q^{89} +(-3.64895 + 7.16147i) q^{92} +(-4.75094 + 29.9962i) q^{93} +(0.779856 + 4.92382i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3}+O(q^{10}) $ 16 * q + 2 * q^3	$ 16 q + 2 q^{3} - 16 q^{12} + 8 q^{15} + 16 q^{16} - 12 q^{20} + 72 q^{23} - 2 q^{25} - 22 q^{27} - 24 q^{36} + 14 q^{37} - 72 q^{45} + 24 q^{47} - 8 q^{48} + 12 q^{53} + 28 q^{60} + 104 q^{67} + 12 q^{71} - 32 q^{75} + 8 q^{81} - 36 q^{92} - 66 q^{93} + 34 q^{97}+O(q^{100}) $ 16 * q + 2 * q^3 - 16 * q^12 + 8 * q^15 + 16 * q^16 - 12 * q^20 + 72 * q^23 - 2 * q^25 - 22 * q^27 - 24 * q^36 + 14 * q^37 - 72 * q^45 + 24 * q^47 - 8 * q^48 + 12 * q^53 + 28 * q^60 + 104 * q^67 + 12 * q^71 - 32 * q^75 + 8 * q^81 - 36 * q^92 - 66 * q^93 + 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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		−0.156434	−	0.987688i	$-0.550000\pi$
$2$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$3$	1.38572	+	2.71963i	0.800047	+	1.57018i	0.821362	+	0.570408i	$0.193215\pi$
$3$	1.38572	+	2.71963i	0.800047	+	1.57018i	−0.0213149	+	0.999773i	$0.506785\pi$
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$	−0.459925	+	2.18826i	−0.205685	+	0.978618i
$5$	−0.459925	+	2.18826i	−0.205685	+	0.978618i
$6$		0			0
$7$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$7$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$8$		0			0
$9$	−3.71282	+	5.11026i	−1.23761	+	1.70342i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	−4.31662	−	4.31662i	−1.24610	−	1.24610i
$13$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$13$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$14$		0			0
$15$	−6.58858	+	1.78149i	−1.70116	+	0.459978i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$17$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$18$		0			0
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−0.477588	−	4.44656i	−0.106792	−	0.994281i
$21$		0			0
$22$		0			0
$23$	2.84169	−	2.84169i	0.592533	−	0.592533i	−0.345782	−	0.938315i	$-0.612386\pi$
$23$	2.84169	−	2.84169i	0.592533	−	0.592533i	0.938315	+	0.345782i	$0.112386\pi$
$24$		0			0
$25$	−4.57694	−	2.01287i	−0.915388	−	0.402574i
$26$		0			0
$27$	−9.99875	−	1.58365i	−1.92426	−	0.304773i
$28$		0			0
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$		0			0
$31$	8.04962	+	5.84839i	1.44575	+	1.05040i	0.986800	+	0.161942i	$0.0517756\pi$
$31$	8.04962	+	5.84839i	1.44575	+	1.05040i	0.458954	+	0.888460i	$0.348224\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$	3.90389	−	12.0149i	0.650648	−	2.00249i
$37$	−0.946968	+	1.85853i	−0.155681	+	0.305540i	−0.955652	−	0.294497i	$-0.904848\pi$
$37$	−0.946968	+	1.85853i	−0.155681	+	0.305540i	0.799972	+	0.600038i	$0.204848\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	−9.47494	−	10.4749i	−1.41244	−	1.56151i
$46$		0			0
$47$	−11.7396	+	5.98164i	−1.71240	+	0.872512i	−0.730550	+	0.682859i	$0.760736\pi$
$47$	−11.7396	+	5.98164i	−1.71240	+	0.872512i	−0.981851	+	0.189653i	$0.939264\pi$
$48$	10.8785	+	5.54289i	1.57018	+	0.800047i
$49$	−4.11450	−	5.66312i	−0.587785	−	0.809017i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.07493	+	0.803790i	−0.697095	+	0.110409i	−0.494918	−	0.868940i	$-0.664802\pi$
$53$	−5.07493	+	0.803790i	−0.697095	+	0.110409i	−0.202178	+	0.979349i	$0.564802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.15430	−	1.02489i	0.410655	−	0.133430i	−0.0964021	−	0.995342i	$-0.530733\pi$
$59$	3.15430	−	1.02489i	0.410655	−	0.133430i	0.507057	+	0.861913i	$0.330733\pi$
$60$	11.4312	−	7.46056i	1.47576	−	0.963154i
$61$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$61$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$62$		0			0
$63$		0			0
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$		0			0
$66$		0			0
$67$	11.4749	+	11.4749i	1.40189	+	1.40189i	0.794101	+	0.607785i	$0.207942\pi$
$67$	11.4749	+	11.4749i	1.40189	+	1.40189i	0.607785	+	0.794101i	$0.292058\pi$
$68$		0			0
$69$	11.6661	+	3.79056i	1.40444	+	0.456329i
$70$		0			0
$71$	2.42705	−	1.76336i	0.288038	−	0.209272i	−0.434378	−	0.900731i	$-0.643032\pi$
$71$	2.42705	−	1.76336i	0.288038	−	0.209272i	0.722416	+	0.691459i	$0.243032\pi$
$72$		0			0
$73$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$73$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$74$		0			0
$75$	−0.868101	−	15.2369i	−0.100240	−	1.75940i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	3.65655	+	8.16270i	0.408815	+	0.912617i
$81$	−3.69271	−	11.3650i	−0.410302	−	1.26278i
$82$		0			0
$83$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$83$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$			9.00000i			0.953998i	0.878904	+	0.476999i	$0.158275\pi$
$89$			9.00000i			0.953998i	−0.878904	+	0.476999i	$0.841725\pi$
$90$		0			0
$91$		0			0
$92$	−3.64895	+	7.16147i	−0.380429	+	0.746635i
$93$	−4.75094	+	29.9962i	−0.492649	+	3.11047i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.779856	+	4.92382i	0.0791824	+	0.499938i	0.995124	+	0.0986273i	$0.0314452\pi$
$97$	0.779856	+	4.92382i	0.0791824	+	0.499938i	−0.915942	+	0.401310i	$0.868555\pi$
$98$		0			0
$99$		0			0
$100$	9.94987	+	1.00000i	0.994987	+	0.100000i
$101$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$101$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$102$		0			0
$103$	−10.0174	−	5.10413i	−0.987046	−	0.502925i	−0.115536	−	0.993303i	$-0.536859\pi$
$103$	−10.0174	−	5.10413i	−0.987046	−	0.502925i	−0.871510	+	0.490378i	$0.836859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$107$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$108$	19.9975	−	3.16729i	1.92426	−	0.304773i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−6.36675			−0.604305
$112$		0			0
$113$	7.80612	+	15.3204i	0.734338	+	1.44122i	0.891206	+	0.453599i	$0.149860\pi$
$113$	7.80612	+	15.3204i	0.734338	+	1.44122i	−0.156868	+	0.987620i	$0.550140\pi$
$114$		0			0
$115$	4.91138	+	7.52531i	0.457989	+	0.701738i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	−18.9258	−	6.14936i	−1.69959	−	0.552229i
$125$	6.50972	−	9.08975i	0.582247	−	0.813012i
$126$		0			0
$127$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$127$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	8.06410	−	21.1515i	0.694047	−	1.82043i
$136$		0			0
$137$	14.1191	+	2.23625i	1.20628	+	0.191056i	0.727019	−	0.686617i	$-0.240905\pi$
$137$	14.1191	+	2.23625i	1.20628	+	0.191056i	0.479260	+	0.877673i	$0.340905\pi$
$138$		0			0
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$		0			0
$141$	−32.5357	−	23.6386i	−2.74000	−	1.99073i
$142$		0			0
$143$		0			0
$144$			25.2665i			2.10554i
$145$		0			0
$146$		0			0
$147$	9.70005	−	19.0374i	0.800047	−	1.57018i
$148$	0.652606	−	4.12039i	0.0536439	−	0.338694i
$149$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$149$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$150$		0			0
$151$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$151$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−16.5000	+	14.9248i	−1.32531	+	1.19879i
$156$		0			0
$157$	20.7596	−	10.5776i	1.65680	−	0.844181i	0.661226	−	0.750186i	$-0.270036\pi$
$157$	20.7596	−	10.5776i	1.65680	−	0.844181i	0.995573	−	0.0939948i	$-0.0299637\pi$
$158$		0			0
$159$	−9.21846	−	12.6881i	−0.731071	−	1.00623i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	25.0724	−	3.97108i	1.96382	−	0.311039i	0.965018	−	0.262184i	$-0.0844426\pi$
$163$	25.0724	−	3.97108i	1.96382	−	0.311039i	0.998806	−	0.0488556i	$-0.0155574\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$167$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$168$		0			0
$169$	12.3637	−	4.01722i	0.951057	−	0.309017i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$173$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.15831	+	7.15831i	0.538052	+	0.538052i
$178$		0			0
$179$	−19.9722	−	6.48936i	−1.49279	−	0.485037i	−0.554885	−	0.831927i	$-0.687238\pi$
$179$	−19.9722	−	6.48936i	−1.49279	−	0.485037i	−0.937906	+	0.346890i	$0.887238\pi$
$180$	24.4963	+	14.0687i	1.82584	+	1.04862i
$181$	8.04962	−	5.84839i	0.598323	−	0.434707i	−0.246960	−	0.969026i	$-0.579432\pi$
$181$	8.04962	−	5.84839i	0.598323	−	0.434707i	0.845283	+	0.534318i	$0.179432\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.63141	−	2.92699i	−0.266986	−	0.215197i
$186$		0			0
$187$		0			0
$188$	18.6332	−	18.6332i	1.35897	−	1.35897i
$189$		0			0
$190$		0			0
$191$	7.17425	+	22.0801i	0.519111	+	1.59766i	0.775676	+	0.631132i	$0.217409\pi$
$191$	7.17425	+	22.0801i	0.519111	+	1.59766i	−0.256565	+	0.966527i	$0.582591\pi$
$192$	−24.1179	−	3.81990i	−1.74056	−	0.275677i
$193$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$193$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$194$		0			0
$195$		0			0
$196$	11.3262	+	8.22899i	0.809017	+	0.587785i
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$		0			0
$199$		−	19.8997i		−	1.41066i	−0.708881	−	0.705328i	$-0.750800\pi$
$199$		−	19.8997i		−	1.41066i	0.708881	−	0.705328i	$-0.249200\pi$
$200$		0			0
$201$	−15.3065	+	47.1087i	−1.07964	+	3.32279i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.97108	+	25.0724i	0.276009	+	1.74265i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$211$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$212$	9.15632	−	4.66538i	0.628859	−	0.320420i
$213$	8.15890	+	4.15717i	0.559038	+	0.284844i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−9.26130	−	18.1763i	−0.620182	−	1.21718i	−0.960870	−	0.277000i	$-0.910660\pi$
$223$	−9.26130	−	18.1763i	−0.620182	−	1.21718i	0.340687	−	0.940177i	$-0.389340\pi$
$224$		0			0
$225$	27.2796	−	15.9159i	1.81864	−	1.06106i
$226$		0			0
$227$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$227$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$228$		0			0
$229$	17.5452	−	24.1489i	1.15942	−	1.59580i	0.446055	−	0.895005i	$-0.352828\pi$
$229$	17.5452	−	24.1489i	1.15942	−	1.59580i	0.713362	−	0.700796i	$-0.247172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$233$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$234$		0			0
$235$	−7.69002	−	28.4404i	−0.501641	−	1.85525i
$236$	−5.36641	+	3.89893i	−0.349324	+	0.253798i
$237$		0			0
$238$		0			0
$239$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$239$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$240$	−17.1326	+	21.2557i	−1.10590	+	1.37205i
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$		0			0
$243$	4.31662	−	4.31662i	0.276912	−	0.276912i
$244$		0			0
$245$	14.2847	−	6.39897i	0.912617	−	0.408815i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−21.8435	−	15.8702i	−1.37875	−	1.00172i	−0.996996	−	0.0774530i	$-0.975321\pi$
$251$	−21.8435	−	15.8702i	−1.37875	−	1.00172i	−0.381751	−	0.924265i	$-0.624679\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−14.2960	+	28.0574i	−0.891758	+	1.75017i	−0.278203	+	0.960522i	$0.589739\pi$
$257$	−14.2960	+	28.0574i	−0.891758	+	1.75017i	−0.613555	+	0.789652i	$0.710261\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$263$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$264$		0			0
$265$	0.575188	−	11.4749i	0.0353335	−	0.704900i
$266$		0			0
$267$	−24.4767	+	12.4715i	−1.49795	+	0.763243i
$268$	−28.9185	−	14.7347i	−1.76648	−	0.900067i
$269$	−7.79785	−	10.7328i	−0.475443	−	0.654392i	0.502178	−	0.864764i	$-0.332532\pi$
$269$	−7.79785	−	10.7328i	−0.475443	−	0.654392i	−0.977621	+	0.210373i	$0.932532\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−24.5330			−1.47671
$277$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$277$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$278$		0			0
$279$	−59.7735	+	19.4216i	−3.57855	+	1.16274i
$280$		0			0
$281$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$281$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$282$		0			0
$283$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$283$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$284$	−3.52671	+	4.85410i	−0.209272	+	0.288038i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	16.1680	+	5.25329i	0.951057	+	0.309017i
$290$		0			0
$291$	−12.3103	+	8.94396i	−0.721643	+	0.524304i
$292$		0			0
$293$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$293$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$294$		0			0
$295$	0.791990	+	7.37379i	0.0461114	+	0.429319i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	11.0681	+	28.4457i	0.639019	+	1.64231i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$		0			0
$309$		−	34.3166i		−	1.95220i
$310$		0			0
$311$	3.70820	−	11.4127i	0.210273	−	0.647154i	−0.789183	−	0.614159i	$-0.789495\pi$
$311$	3.70820	−	11.4127i	0.210273	−	0.647154i	0.999456	−	0.0329949i	$-0.0105045\pi$
$312$		0			0
$313$	−5.40354	+	34.1166i	−0.305426	+	1.92839i	0.0614365	+	0.998111i	$0.480432\pi$
$313$	−5.40354	+	34.1166i	−0.305426	+	1.92839i	−0.366863	+	0.930275i	$0.619568\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.55473	+	35.0712i	0.311985	+	1.96979i	0.230201	+	0.973143i	$0.426062\pi$
$317$	5.55473	+	35.0712i	0.311985	+	1.96979i	0.0817838	+	0.996650i	$0.473938\pi$
$318$		0			0
$319$		0			0
$320$	−12.0000	−	13.2665i	−0.670820	−	0.741620i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	14.0479	+	19.3353i	0.780440	+	1.07418i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−9.94987			−0.546895			−0.273447	−	0.961887i	$-0.588164\pi$
$331$	−9.94987			−0.546895			−0.273447	+	0.961887i	$0.588164\pi$
$332$		0			0
$333$	−5.98164	−	11.7396i	−0.327792	−	0.643328i
$334$		0			0
$335$	−30.3877	+	19.8325i	−1.66026	+	1.08357i
$336$		0			0
$337$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$337$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$338$		0			0
$339$	−30.8487	+	42.4595i	−1.67547	+	2.30609i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−13.6603	+	23.7851i	−0.735444	+	1.28055i
$346$		0			0
$347$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$347$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$348$		0			0
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.7414	+	13.7414i	−0.731383	+	0.731383i	−0.970894	−	0.239511i	$-0.923013\pi$
$353$	−13.7414	+	13.7414i	−0.731383	+	0.731383i	0.239511	+	0.970894i	$0.423013\pi$
$354$		0			0
$355$	2.74241	+	6.12202i	0.145552	+	0.324923i
$356$	−5.56231	−	17.1190i	−0.294802	−	0.907306i
$357$		0			0
$358$		0			0
$359$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$		0			0
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.68362	−	17.0426i	0.453282	−	0.889615i	−0.545395	−	0.838179i	$-0.683620\pi$
$367$	8.68362	−	17.0426i	0.453282	−	0.889615i	0.998676	−	0.0514358i	$-0.0163797\pi$
$368$	2.51469	−	15.8771i	0.131087	−	0.827651i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−9.50188	−	59.9925i	−0.492649	−	3.11047i
$373$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$373$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$374$		0			0
$375$	33.7414	+	5.10819i	1.74240	+	0.263786i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−17.5452	−	24.1489i	−0.901235	−	1.24044i	−0.970073	−	0.242815i	$-0.921929\pi$
$379$	−17.5452	−	24.1489i	−0.901235	−	1.24044i	0.0688378	−	0.997628i	$-0.478071\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−24.9213	+	3.94715i	−1.27342	+	0.201690i	−0.756301	−	0.654224i	$-0.772995\pi$
$383$	−24.9213	+	3.94715i	−1.27342	+	0.201690i	−0.517119	+	0.855914i	$0.672995\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−4.52646	−	8.88368i	−0.229796	−	0.451000i
$389$	34.6973	−	11.2738i	1.75922	−	0.571606i	0.762102	−	0.647456i	$-0.224167\pi$
$389$	34.6973	−	11.2738i	1.75922	−	0.571606i	0.997119	+	0.0758507i	$0.0241672\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−20.8997	−	20.8997i	−1.04893	−	1.04893i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$	−20.8997	−	20.8997i	−1.04893	−	1.04893i	−0.0501886	−	0.998740i	$-0.515982\pi$
$398$		0			0
$399$		0			0
$400$	−19.5438	+	4.24725i	−0.977191	+	0.212362i
$401$	21.4656	−	15.5957i	1.07194	−	0.778812i	0.0956827	−	0.995412i	$-0.469497\pi$
$401$	21.4656	−	15.5957i	1.07194	−	0.778812i	0.976261	+	0.216600i	$0.0694966\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	26.5679	−	2.85356i	1.32017	−	0.141794i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$		0			0
$411$	13.4834	+	41.4977i	0.665088	+	2.04693i
$412$	22.2088	+	3.51753i	1.09415	+	0.173296i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$			24.0000i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$419$			24.0000i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$420$		0			0
$421$	12.2987	−	37.8516i	0.599403	−	1.84477i	0.0679432	−	0.997689i	$-0.478356\pi$
$421$	12.2987	−	37.8516i	0.599403	−	1.84477i	0.531460	−	0.847084i	$-0.321644\pi$
$422$		0			0
$423$	13.0194	−	82.2013i	0.633025	−	3.99676i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	−36.0800	+	18.3837i	−1.73590	+	0.884485i
$433$	37.0774	+	18.8919i	1.78183	+	0.907886i	0.897467	+	0.441081i	$0.145405\pi$
$433$	37.0774	+	18.8919i	1.78183	+	0.907886i	0.884360	+	0.466805i	$0.154595\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	44.2164			2.10554
$442$		0			0
$443$	18.4531	+	36.2163i	0.876735	+	1.72069i	0.670099	+	0.742271i	$0.266252\pi$
$443$	18.4531	+	36.2163i	0.876735	+	1.72069i	0.206636	+	0.978418i	$0.433748\pi$
$444$	12.1103	−	3.93487i	0.574728	−	0.186741i
$445$	−19.6943	−	4.13933i	−0.933600	−	0.196223i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.9236	−	31.5517i	1.08183	−	1.48902i	0.224346	−	0.974510i	$-0.427976\pi$
$449$	22.9236	−	31.5517i	1.08183	−	1.48902i	0.857487	−	0.514505i	$-0.172024\pi$
$450$		0			0
$451$		0			0
$452$	−24.3166	−	24.3166i	−1.14376	−	1.14376i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$457$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$458$		0			0
$459$		0			0
$460$	−13.9929	−	11.2786i	−0.652422	−	0.525867i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−0.575188	+	0.575188i	−0.0267313	+	0.0267313i	−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−0.575188	+	0.575188i	−0.0267313	+	0.0267313i	0.693615	+	0.720346i	$0.256017\pi$
$464$		0			0
$465$	−63.4544	−	24.1923i	−2.94263	−	1.12189i
$466$		0			0
$467$	−32.2076	−	5.10118i	−1.49039	−	0.236054i	−0.642523	−	0.766267i	$-0.722112\pi$
$467$	−32.2076	−	5.10118i	−1.49039	−	0.236054i	−0.847865	+	0.530212i	$0.822112\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	57.5342	+	41.8010i	2.65103	+	1.92609i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	14.7347	−	28.9185i	0.674657	−	1.32409i
$478$		0			0
$479$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$479$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.1332	−	0.558061i	−0.505535	−	0.0253403i
$486$		0			0
$487$	33.3604	−	16.9980i	1.51170	−	0.770251i	0.515465	−	0.856911i	$-0.327619\pi$
$487$	33.3604	−	16.9980i	1.51170	−	0.770251i	0.996238	+	0.0866600i	$0.0276194\pi$
$488$		0			0
$489$	45.5433	+	62.6850i	2.05954	+	2.83471i
$490$		0			0
$491$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$491$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	39.7995			1.78705
$497$		0			0
$498$		0			0
$499$	18.9258	−	6.14936i	0.847235	−	0.275283i	0.146947	−	0.989144i	$-0.453055\pi$
$499$	18.9258	−	6.14936i	0.847235	−	0.275283i	0.700287	+	0.713861i	$0.253055\pi$
$500$	−6.76445	+	21.3130i	−0.302516	+	0.953144i
$501$		0			0
$502$		0			0
$503$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$503$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	28.0581	+	28.0581i	1.24610	+	1.24610i
$508$		0			0
$509$	−3.15430	−	1.02489i	−0.139812	−	0.0454276i	0.238275	−	0.971198i	$-0.423418\pi$
$509$	−3.15430	−	1.02489i	−0.139812	−	0.0454276i	−0.378087	+	0.925770i	$0.623418\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.7764	−	19.5732i	0.695192	−	0.862498i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.3236	−	41.0059i	−0.583718	−	1.79650i	−0.604358	−	0.796713i	$-0.706570\pi$
$521$	−13.3236	−	41.0059i	−0.583718	−	1.79650i	0.0206400	−	0.999787i	$-0.493430\pi$
$522$		0			0
$523$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$523$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$			6.84962i			0.297810i
$530$		0			0
$531$	−6.47387	+	19.9245i	−0.280942	+	0.864650i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.0272	−	63.3094i	−0.432707	−	2.73200i
$538$		0			0
$539$		0			0
$540$	−2.26650	+	45.2164i	−0.0975346	+	1.94580i
$541$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$541$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$542$		0			0
$543$	27.0600	+	13.7878i	1.16126	+	0.591689i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$547$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$548$	−28.2383	+	4.47250i	−1.20628	+	0.191056i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.92823	−	13.9321i	0.124296	−	0.591384i
$556$		0			0
$557$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$557$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$563$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$564$	76.4961	+	24.8551i	3.22107	+	1.04659i
$565$	−37.1151	+	10.0356i	−1.56145	+	0.422200i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−50.1082	+	50.1082i	−2.09330	+	2.09330i
$574$		0			0
$575$	−18.7262	+	7.28628i	−0.780935	+	0.303859i
$576$	−15.6156	−	48.0597i	−0.650648	−	2.00249i
$577$	25.8758	+	4.09833i	1.07723	+	0.170616i	0.669740	−	0.742596i	$-0.266406\pi$
$577$	25.8758	+	4.09833i	1.07723	+	0.170616i	0.407486	+	0.913212i	$0.366406\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.2795	+	26.0626i	−0.548105	+	1.07572i	0.436300	+	0.899801i	$0.356289\pi$
$587$	−13.2795	+	26.0626i	−0.548105	+	1.07572i	−0.984405	+	0.175916i	$0.943711\pi$
$588$	−6.68482	+	42.2063i	−0.275677	+	1.74056i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.30521	+	8.24078i	0.0536439	+	0.338694i
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	54.1200	−	27.5755i	2.21498	−	1.12859i
$598$		0			0
$599$	21.1603	+	29.1246i	0.864585	+	1.19000i	0.980457	+	0.196735i	$0.0630339\pi$
$599$	21.1603	+	29.1246i	0.864585	+	1.19000i	−0.115872	+	0.993264i	$0.536966\pi$
$600$		0			0
$601$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$601$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$602$		0			0
$603$	−101.244	+	16.0355i	−4.12298	+	0.653017i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$607$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$613$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.73350	−	7.73350i	−0.311339	−	0.311339i	0.534089	−	0.845428i	$-0.320655\pi$
$617$	−7.73350	−	7.73350i	−0.311339	−	0.311339i	−0.845428	+	0.534089i	$0.820655\pi$
$618$		0			0
$619$	−0.951057	−	0.309017i	−0.0382262	−	0.0124204i	0.289841	−	0.957075i	$-0.406397\pi$
$619$	−0.951057	−	0.309017i	−0.0382262	−	0.0124204i	−0.328068	+	0.944654i	$0.606397\pi$
$620$	22.1608	−	38.5862i	0.890000	−	1.54966i
$621$	−32.9135	+	23.9131i	−1.32077	+	0.959599i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	16.8967	+	18.4255i	0.675869	+	0.737022i
$626$		0			0
$627$		0			0
$628$	−32.9499	+	32.9499i	−1.31484	+	1.31484i
$629$		0			0
$630$		0			0
$631$	2.16312	+	6.65740i	0.0861124	+	0.265027i	0.984836	−	0.173489i	$-0.0555042\pi$
$631$	2.16312	+	6.65740i	0.0861124	+	0.265027i	−0.898723	+	0.438516i	$0.855504\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	25.3762	+	18.4369i	1.00623	+	0.731071i
$637$		0			0
$638$		0			0
$639$			18.9499i			0.749645i
$640$		0			0
$641$	7.17425	−	22.0801i	0.283366	−	0.872111i	−0.703518	−	0.710678i	$-0.748388\pi$
$641$	7.17425	−	22.0801i	0.283366	−	0.872111i	0.986884	−	0.161433i	$-0.0516116\pi$
$642$		0			0
$643$	1.23341	−	7.78744i	0.0486409	−	0.307106i	−0.951359	−	0.308086i	$-0.900312\pi$
$643$	1.23341	−	7.78744i	0.0486409	−	0.307106i	1.00000		0.000979141i	$0.000311670\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.78270	−	11.2555i	−0.0700851	−	0.442500i	−0.997631	−	0.0687910i	$-0.978086\pi$
$647$	−1.78270	−	11.2555i	−0.0700851	−	0.442500i	0.927546	−	0.373709i	$-0.121914\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−45.2363	+	23.0491i	−1.77159	+	0.902671i
$653$	−34.2215	−	17.4367i	−1.33919	−	0.682351i	−0.370084	−	0.928998i	$-0.620671\pi$
$653$	−34.2215	−	17.4367i	−1.33919	−	0.682351i	−0.969105	+	0.246647i	$0.920671\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−13.0000			−0.505641			−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000			−0.505641			−0.252821	+	0.967513i	$0.581358\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	36.5993	−	50.3747i	1.41501	−	1.94760i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$673$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$674$		0			0
$675$	42.5760	+	27.3744i	1.63875	+	1.05364i
$676$	−21.0344	+	15.2824i	−0.809017	+	0.587785i
$677$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$677$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	35.2164	−	35.2164i	1.34752	−	1.34752i	0.459167	−	0.888350i	$-0.348148\pi$
$683$	35.2164	−	35.2164i	1.34752	−	1.34752i	0.888350	−	0.459167i	$-0.151852\pi$
$684$		0			0
$685$	−11.3872	+	29.8678i	−0.435084	+	1.14119i
$686$		0			0
$687$	89.9887	+	14.2528i	3.43328	+	0.543779i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−13.7533	−	9.99235i	−0.523200	−	0.380127i	0.294608	−	0.955618i	$-0.404811\pi$
$691$	−13.7533	−	9.99235i	−0.523200	−	0.380127i	−0.817808	+	0.575491i	$0.804811\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$701$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	66.6913	−	60.3246i	2.51174	−	2.27195i
$706$		0			0
$707$		0			0
$708$	−18.0400	−	9.19184i	−0.677985	−	0.345450i
$709$	−11.1679	−	15.3713i	−0.419420	−	0.577282i	0.546064	−	0.837743i	$-0.316125\pi$
$709$	−11.1679	−	15.3713i	−0.419420	−	0.577282i	−0.965484	+	0.260461i	$0.916125\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	39.4938	−	6.25520i	1.47905	−	0.234259i
$714$		0			0
$715$		0			0
$716$	42.0000			1.56961
$717$		0			0
$718$		0			0
$719$	48.5039	−	15.7599i	1.80889	−	0.587744i	0.808890	−	0.587961i	$-0.200069\pi$
$719$	48.5039	−	15.7599i	1.80889	−	0.587744i	1.00000		0.000216702i	$6.89785e-5\pi$
$720$	−55.2896	−	11.6207i	−2.06052	−	0.433078i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−11.6968	+	16.0992i	−0.434707	+	0.598323i
$725$		0			0
$726$		0			0
$727$	31.4749	+	31.4749i	1.16734	+	1.16734i	0.982831	+	0.184510i	$0.0590699\pi$
$727$	31.4749	+	31.4749i	1.16734	+	1.16734i	0.184510	+	0.982831i	$0.440930\pi$
$728$		0			0
$729$	−16.3737	−	5.32015i	−0.606435	−	0.197043i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$733$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$734$		0			0
$735$	37.1975	+	29.9820i	1.37205	+	1.10590i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$739$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$740$	8.71633	+	3.32314i	0.320418	+	0.122161i
$741$		0			0
$742$		0			0
$743$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$743$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.10739	+	21.8743i	−0.259352	+	0.798205i	0.733588	+	0.679594i	$0.237844\pi$
$751$	−7.10739	+	21.8743i	−0.259352	+	0.798205i	−0.992941	+	0.118611i	$0.962156\pi$
$752$	−23.9266	+	46.9585i	−0.872512	+	1.71240i
$753$	12.8922	−	81.3979i	0.469816	−	2.96630i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.199053	+	1.25677i	0.00723470	+	0.0456781i	0.991042	−	0.133554i	$-0.0426388\pi$
$757$	0.199053	+	1.25677i	0.00723470	+	0.0456781i	−0.983807	+	0.179232i	$0.942639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$761$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$762$		0			0
$763$		0			0
$764$	−27.2925	−	37.5649i	−0.987407	−	1.35905i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	48.2358	−	7.63980i	1.74056	−	0.275677i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$	−96.1161			−3.46154
$772$		0			0
$773$	−21.5939	−	42.3804i	−0.776678	−	1.52432i	−0.849867	−	0.526998i	$-0.823318\pi$
$773$	−21.5939	−	42.3804i	−0.776678	−	1.52432i	0.0731890	−	0.997318i	$-0.476682\pi$
$774$		0			0
$775$	−25.0706	−	42.9705i	−0.900561	−	1.54355i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−26.6296	−	8.65248i	−0.951057	−	0.309017i
$785$	13.5985	+	50.2923i	0.485353	+	1.79501i
$786$		0			0
$787$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$787$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	32.0047	−	14.3368i	1.13509	−	0.508473i
$796$	12.2987	+	37.8516i	0.435917	+	1.34161i
$797$	37.2825	+	5.90497i	1.32061	+	0.209165i	0.776644	−	0.629940i	$-0.216921\pi$
$797$	37.2825	+	5.90497i	1.32061	+	0.209165i	0.543970	+	0.839105i	$0.316921\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−45.9923	−	33.4154i	−1.62506	−	1.18067i
$802$		0			0
$803$		0			0
$804$		−	99.0660i		−	3.49379i
$805$		0			0
$806$		0			0
$807$	18.3837	−	36.0800i	0.647136	−	1.27008i
$808$		0			0
$809$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$809$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$810$		0			0
$811$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$811$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.84169	+	56.6913i	−0.0995400	+	1.98581i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$821$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$822$		0			0
$823$	−55.0687	+	8.72202i	−1.91957	+	0.304030i	−0.996707	−	0.0810902i	$-0.974160\pi$
$823$	−55.0687	+	8.72202i	−1.91957	+	0.304030i	−0.922866	+	0.385121i	$0.874160\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$827$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$828$	−23.0491	−	45.2363i	−0.801010	−	1.57207i
$829$	−27.5806	+	8.96149i	−0.957915	+	0.311246i	−0.745928	−	0.666027i	$-0.767994\pi$
$829$	−27.5806	+	8.96149i	−0.957915	+	0.311246i	−0.211987	+	0.977272i	$0.567994\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−71.2243	−	71.2243i	−2.46187	−	2.46187i
$838$		0			0
$839$	−34.6973	−	11.2738i	−1.19788	−	0.389216i	−0.358901	−	0.933376i	$-0.616849\pi$
$839$	−34.6973	−	11.2738i	−1.19788	−	0.389216i	−0.838982	+	0.544160i	$0.816849\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.10432	+	28.9027i	0.106792	+	0.994281i
$846$		0			0
$847$		0			0
$848$	−14.5330	+	14.5330i	−0.499065	+	0.499065i
$849$		0			0
$850$		0			0
$851$	2.59037	+	7.97235i	0.0887968	+	0.273289i
$852$	−18.0884	−	2.86492i	−0.619699	−	0.0981507i
$853$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$853$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$857$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$858$		0			0
$859$		−	31.0000i		−	1.05771i	−0.848713	−	0.528853i	$-0.822622\pi$
$859$		−	31.0000i		−	1.05771i	0.848713	−	0.528853i	$-0.177378\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.15403	+	7.28624i	−0.0392835	+	0.248027i	−0.999514	−	0.0311832i	$-0.990072\pi$
$863$	−1.15403	+	7.28624i	−0.0392835	+	0.248027i	0.960230	+	0.279210i	$0.0900725\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	8.11728	+	51.2505i	0.275677	+	1.74056i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−28.0574	−	14.2960i	−0.949600	−	0.483845i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$877$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	57.0000			1.92038			0.960189	−	0.279350i	$-0.0901189\pi$
$881$	57.0000			1.92038			0.960189	+	0.279350i	$0.0901189\pi$
$882$		0			0
$883$	24.3653	+	47.8196i	0.819958	+	1.60926i	0.792686	+	0.609631i	$0.208682\pi$
$883$	24.3653	+	47.8196i	0.819958	+	1.60926i	0.0272727	+	0.999628i	$0.491318\pi$
$884$		0			0
$885$	−18.9565	+	12.3719i	−0.637216	+	0.415878i
$886$		0			0
$887$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$887$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	28.8496	+	28.8496i	0.965957	+	0.965957i
$893$		0			0
$894$		0			0
$895$	23.3861	−	40.7197i	0.781711	−	1.36111i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−42.0523	+	47.1336i	−1.40174	+	1.57112i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.09556	+	20.3045i	0.302347	+	0.674943i
$906$		0			0
$907$	−47.2812	−	7.48861i	−1.56995	−	0.248655i	−0.690030	−	0.723781i	$-0.742403\pi$
$907$	−47.2812	−	7.48861i	−1.56995	−	0.248655i	−0.879918	+	0.475126i	$0.842403\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.36641	−	3.89893i	−0.177797	−	0.129177i	0.495327	−	0.868706i	$-0.335048\pi$
$911$	−5.36641	−	3.89893i	−0.177797	−	0.129177i	−0.673124	+	0.739529i	$0.735048\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−18.4481	+	56.7774i	−0.609542	+	1.87598i
$917$		0			0
$918$		0			0
$919$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$919$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	8.07519	−	6.60025i	0.265511	−	0.217015i
$926$		0			0
$927$	63.2763	−	32.2409i	2.07827	−	1.05893i
$928$		0			0
$929$	31.1914	+	42.9313i	1.02336	+	1.40853i	0.909823	+	0.414996i	$0.136217\pi$
$929$	31.1914	+	42.9313i	1.02336	+	1.40853i	0.113534	+	0.993534i	$0.463783\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	36.1768	−	5.72985i	1.18438	−	0.187587i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$937$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$938$		0			0
$939$	−100.273	+	32.5805i	−3.27227	+	1.06322i
$940$	32.2044	+	49.3442i	1.05039	+	1.60943i
$941$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$941$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$942$		0			0
$943$		0			0
$944$	7.79785	−	10.7328i	0.253798	−	0.349324i
$945$		0			0
$946$		0			0
$947$	−40.1082	−	40.1082i	−1.30334	−	1.30334i	−0.926126	−	0.377215i	$-0.876882\pi$
$947$	−40.1082	−	40.1082i	−1.30334	−	1.30334i	−0.377215	−	0.926126i	$-0.623118\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−87.6834	+	63.7057i	−2.84333	+	2.06580i
$952$		0			0
$953$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$953$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$954$		0			0
$955$	−51.6165	+	5.54393i	−1.67027	+	0.179397i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	19.4513	−	51.0193i	0.627789	−	1.64664i
$961$	21.0132	+	64.6718i	0.677844	+	2.08619i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$967$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.3236	+	41.0059i	−0.427575	+	1.31594i	0.472932	+	0.881099i	$0.343196\pi$
$971$	−13.3236	+	41.0059i	−0.427575	+	1.31594i	−0.900507	+	0.434842i	$0.856804\pi$
$972$	−5.54289	+	10.8785i	−0.177788	+	0.348929i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.22344	+	58.2345i	0.295084	+	1.86309i	0.475802	+	0.879552i	$0.342158\pi$
$977$	9.22344	+	58.2345i	0.295084	+	1.86309i	−0.180718	+	0.983535i	$0.557842\pi$
$978$		0			0
$979$		0			0
$980$	−23.2164	+	21.0000i	−0.741620	+	0.670820i
$981$		0			0
$982$		0			0
$983$	−55.1174	−	28.0837i	−1.75797	−	0.895732i	−0.953306	−	0.302005i	$-0.902344\pi$
$983$	−55.1174	−	28.0837i	−1.75797	−	0.895732i	−0.804666	−	0.593727i	$-0.797656\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−59.6992			−1.89641			−0.948205	−	0.317660i	$-0.897103\pi$
$991$	−59.6992			−1.89641			−0.948205	+	0.317660i	$0.897103\pi$
$992$		0			0
$993$	−13.7878	−	27.0600i	−0.437541	−	0.858723i
$994$		0			0
$995$	43.5458	+	9.15239i	1.38049	+	0.290150i
$996$		0			0
$997$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$997$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$998$		0			0
$999$	12.4117	−	17.0833i	0.392690	−	0.540492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.a.282.2		16
5.3	odd	4	inner	605.2.m.a.403.1		16
11.2	odd	10	inner	605.2.m.a.457.2		16
11.3	even	5	inner	605.2.m.a.602.1		16
11.4	even	5	inner	605.2.m.a.112.2		16
11.5	even	5		55.2.e.b.32.1	✓	4
11.6	odd	10		55.2.e.b.32.1	✓	4
11.7	odd	10	inner	605.2.m.a.112.2		16
11.8	odd	10	inner	605.2.m.a.602.1		16
11.9	even	5	inner	605.2.m.a.457.2		16
11.10	odd	2	CM	605.2.m.a.282.2		16
33.5	odd	10		495.2.k.a.307.1		4
33.17	even	10		495.2.k.a.307.1		4
44.27	odd	10		880.2.bd.d.417.2		4
44.39	even	10		880.2.bd.d.417.2		4
55.3	odd	20	inner	605.2.m.a.118.2		16
55.8	even	20	inner	605.2.m.a.118.2		16
55.13	even	20	inner	605.2.m.a.578.2		16
55.17	even	20		275.2.e.a.43.2		4
55.18	even	20	inner	605.2.m.a.233.2		16
55.27	odd	20		275.2.e.a.43.2		4
55.28	even	20		55.2.e.b.43.1	yes	4
55.38	odd	20		55.2.e.b.43.1	yes	4
55.39	odd	10		275.2.e.a.32.2		4
55.43	even	4	inner	605.2.m.a.403.1		16
55.48	odd	20	inner	605.2.m.a.233.2		16
55.49	even	10		275.2.e.a.32.2		4
55.53	odd	20	inner	605.2.m.a.578.2		16
165.38	even	20		495.2.k.a.208.1		4
165.83	odd	20		495.2.k.a.208.1		4
220.83	odd	20		880.2.bd.d.593.2		4
220.203	even	20		880.2.bd.d.593.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.e.b.32.1	✓	4	11.5	even	5
55.2.e.b.32.1	✓	4	11.6	odd	10
55.2.e.b.43.1	yes	4	55.28	even	20
55.2.e.b.43.1	yes	4	55.38	odd	20
275.2.e.a.32.2		4	55.39	odd	10
275.2.e.a.32.2		4	55.49	even	10
275.2.e.a.43.2		4	55.17	even	20
275.2.e.a.43.2		4	55.27	odd	20
495.2.k.a.208.1		4	165.38	even	20
495.2.k.a.208.1		4	165.83	odd	20
495.2.k.a.307.1		4	33.5	odd	10
495.2.k.a.307.1		4	33.17	even	10
605.2.m.a.112.2		16	11.4	even	5	inner
605.2.m.a.112.2		16	11.7	odd	10	inner
605.2.m.a.118.2		16	55.3	odd	20	inner
605.2.m.a.118.2		16	55.8	even	20	inner
605.2.m.a.233.2		16	55.18	even	20	inner
605.2.m.a.233.2		16	55.48	odd	20	inner
605.2.m.a.282.2		16	1.1	even	1	trivial
605.2.m.a.282.2		16	11.10	odd	2	CM
605.2.m.a.403.1		16	5.3	odd	4	inner
605.2.m.a.403.1		16	55.43	even	4	inner
605.2.m.a.457.2		16	11.2	odd	10	inner
605.2.m.a.457.2		16	11.9	even	5	inner
605.2.m.a.578.2		16	55.13	even	20	inner
605.2.m.a.578.2		16	55.53	odd	20	inner
605.2.m.a.602.1		16	11.3	even	5	inner
605.2.m.a.602.1		16	11.8	odd	10	inner
880.2.bd.d.417.2		4	44.27	odd	10
880.2.bd.d.417.2		4	44.39	even	10
880.2.bd.d.593.2		4	220.83	odd	20
880.2.bd.d.593.2		4	220.203	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38572 + 2.71963i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.459925 + 2.18826i) q^{5} +(-3.71282 + 5.11026i) q^{9} +O(q^{10})\)	\(q+(1.38572 + 2.71963i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-0.459925 + 2.18826i) q^{5} +(-3.71282 + 5.11026i) q^{9} +(-4.31662 - 4.31662i) q^{12} +(-6.58858 + 1.78149i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-0.477588 - 4.44656i) q^{20} +(2.84169 - 2.84169i) q^{23} +(-4.57694 - 2.01287i) q^{25} +(-9.99875 - 1.58365i) q^{27} +(8.04962 + 5.84839i) q^{31} +(3.90389 - 12.0149i) q^{36} +(-0.946968 + 1.85853i) q^{37} +(-9.47494 - 10.4749i) q^{45} +(-11.7396 + 5.98164i) q^{47} +(10.8785 + 5.54289i) q^{48} +(-4.11450 - 5.66312i) q^{49} +(-5.07493 + 0.803790i) q^{53} +(3.15430 - 1.02489i) q^{59} +(11.4312 - 7.46056i) q^{60} +(-4.70228 + 6.47214i) q^{64} +(11.4749 + 11.4749i) q^{67} +(11.6661 + 3.79056i) q^{69} +(2.42705 - 1.76336i) q^{71} +(-0.868101 - 15.2369i) q^{75} +(3.65655 + 8.16270i) q^{80} +(-3.69271 - 11.3650i) q^{81} +9.00000i q^{89} +(-3.64895 + 7.16147i) q^{92} +(-4.75094 + 29.9962i) q^{93} +(0.779856 + 4.92382i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3}+O(q^{10}) \) 16 * q + 2 * q^3	\( 16 q + 2 q^{3} - 16 q^{12} + 8 q^{15} + 16 q^{16} - 12 q^{20} + 72 q^{23} - 2 q^{25} - 22 q^{27} - 24 q^{36} + 14 q^{37} - 72 q^{45} + 24 q^{47} - 8 q^{48} + 12 q^{53} + 28 q^{60} + 104 q^{67} + 12 q^{71} - 32 q^{75} + 8 q^{81} - 36 q^{92} - 66 q^{93} + 34 q^{97}+O(q^{100}) \) 16 * q + 2 * q^3 - 16 * q^12 + 8 * q^15 + 16 * q^16 - 12 * q^20 + 72 * q^23 - 2 * q^25 - 22 * q^27 - 24 * q^36 + 14 * q^37 - 72 * q^45 + 24 * q^47 - 8 * q^48 + 12 * q^53 + 28 * q^60 + 104 * q^67 + 12 * q^71 - 32 * q^75 + 8 * q^81 - 36 * q^92 - 66 * q^93 + 34 * q^97

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