LMFDB - Embedded newform 45.6.b.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,6,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	45.b (of order $2$, degree $1$, 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:	$7.21727189158$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-11}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 3 $ x^2 - x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$0.500000 - 1.65831i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.6.b.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+6.63325i q^{2} -12.0000 q^{4} +(45.0000 + 33.1662i) q^{5} +59.6992i q^{7} +132.665i q^{8} +(-220.000 + 298.496i) q^{10} -252.000 q^{11} +119.398i q^{13} -396.000 q^{14} -1264.00 q^{16} -689.858i q^{17} -220.000 q^{19} +(-540.000 - 397.995i) q^{20} -1671.58i q^{22} +2434.40i q^{23} +(925.000 + 2984.96i) q^{25} -792.000 q^{26} -716.391i q^{28} +6930.00 q^{29} +6752.00 q^{31} -4139.15i q^{32} +4576.00 q^{34} +(-1980.00 + 2686.47i) q^{35} -13969.6i q^{37} -1459.31i q^{38} +(-4400.00 + 5969.92i) q^{40} +198.000 q^{41} +417.895i q^{43} +3024.00 q^{44} -16148.0 q^{46} -10540.2i q^{47} +13243.0 q^{49} +(-19800.0 + 6135.76i) q^{50} -1432.78i q^{52} -5823.99i q^{53} +(-11340.0 - 8357.89i) q^{55} -7920.00 q^{56} +45968.4i q^{58} +24660.0 q^{59} -5698.00 q^{61} +44787.7i q^{62} -12992.0 q^{64} +(-3960.00 + 5372.93i) q^{65} +43640.1i q^{67} +8278.30i q^{68} +(-17820.0 - 13133.8i) q^{70} -53352.0 q^{71} -70922.7i q^{73} +92664.0 q^{74} +2640.00 q^{76} -15044.2i q^{77} +51920.0 q^{79} +(-56880.0 - 41922.1i) q^{80} +1313.38i q^{82} -61841.8i q^{83} +(22880.0 - 31043.6i) q^{85} -2772.00 q^{86} -33431.6i q^{88} +9990.00 q^{89} -7128.00 q^{91} -29212.8i q^{92} +69916.0 q^{94} +(-9900.00 - 7296.57i) q^{95} +101250. i q^{97} +87844.1i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 24 q^{4} + 90 q^{5} - 440 q^{10} - 504 q^{11} - 792 q^{14} - 2528 q^{16} - 440 q^{19} - 1080 q^{20} + 1850 q^{25} - 1584 q^{26} + 13860 q^{29} + 13504 q^{31} + 9152 q^{34} - 3960 q^{35} - 8800 q^{40}+ \cdots - 19800 q^{95}+O(q^{100}) $ 2 * q - 24 * q^4 + 90 * q^5 - 440 * q^10 - 504 * q^11 - 792 * q^14 - 2528 * q^16 - 440 * q^19 - 1080 * q^20 + 1850 * q^25 - 1584 * q^26 + 13860 * q^29 + 13504 * q^31 + 9152 * q^34 - 3960 * q^35 - 8800 * q^40 + 396 * q^41 + 6048 * q^44 - 32296 * q^46 + 26486 * q^49 - 39600 * q^50 - 22680 * q^55 - 15840 * q^56 + 49320 * q^59 - 11396 * q^61 - 25984 * q^64 - 7920 * q^65 - 35640 * q^70 - 106704 * q^71 + 185328 * q^74 + 5280 * q^76 + 103840 * q^79 - 113760 * q^80 + 45760 * q^85 - 5544 * q^86 + 19980 * q^89 - 14256 * q^91 + 139832 * q^94 - 19800 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$			6.63325i			1.17260i	0.810093	+	0.586302i	$0.199417\pi$
$2$			6.63325i			1.17260i	−0.810093	+	0.586302i	$0.800583\pi$
$3$		0			0
$3$		0			0
$4$	−12.0000			−0.375000
$5$	45.0000	+	33.1662i	0.804984	+	0.593296i
$5$	45.0000	+	33.1662i	0.804984	+	0.593296i
$6$		0			0
$7$			59.6992i			0.460494i	0.973132	+	0.230247i	$0.0739534\pi$
$7$			59.6992i			0.460494i	−0.973132	+	0.230247i	$0.926047\pi$
$8$			132.665i			0.732877i
$9$		0			0
$10$	−220.000	+	298.496i	−0.695701	+	0.943928i
$11$	−252.000			−0.627941			−0.313970	−	0.949433i	$-0.601659\pi$
$11$	−252.000			−0.627941			−0.313970	+	0.949433i	$0.601659\pi$
$12$		0			0
$13$			119.398i			0.195948i	0.995189	+	0.0979739i	$0.0312362\pi$
$13$			119.398i			0.195948i	−0.995189	+	0.0979739i	$0.968764\pi$
$14$	−396.000			−0.539977
$15$		0			0
$16$	−1264.00			−1.23438
$17$		−	689.858i		−	0.578945i	−0.957186	−	0.289473i	$-0.906520\pi$
$17$		−	689.858i		−	0.578945i	0.957186	−	0.289473i	$-0.0934799\pi$
$18$		0			0
$19$	−220.000			−0.139810			−0.0699051	−	0.997554i	$-0.522270\pi$
$19$	−220.000			−0.139810			−0.0699051	+	0.997554i	$0.522270\pi$
$20$	−540.000	−	397.995i	−0.301869	−	0.222486i
$21$		0			0
$22$		−	1671.58i		−	0.736326i
$23$			2434.40i			0.959561i	0.877388	+	0.479781i	$0.159284\pi$
$23$			2434.40i			0.959561i	−0.877388	+	0.479781i	$0.840716\pi$
$24$		0			0
$25$	925.000	+	2984.96i	0.296000	+	0.955188i
$26$	−792.000			−0.229769
$27$		0			0
$28$		−	716.391i		−	0.172685i
$29$	6930.00			1.53016			0.765082	−	0.643932i	$-0.222698\pi$
$29$	6930.00			1.53016			0.765082	+	0.643932i	$0.222698\pi$
$30$		0			0
$31$	6752.00			1.26191			0.630955	−	0.775820i	$-0.282663\pi$
$31$	6752.00			1.26191			0.630955	+	0.775820i	$0.282663\pi$
$32$		−	4139.15i		−	0.714556i
$33$		0			0
$34$	4576.00			0.678873
$35$	−1980.00	+	2686.47i	−0.273209	+	0.370690i
$36$		0			0
$37$		−	13969.6i		−	1.67757i	−0.544464	−	0.838785i	$-0.683267\pi$
$37$		−	13969.6i		−	1.67757i	0.544464	−	0.838785i	$-0.316733\pi$
$38$		−	1459.31i		−	0.163942i
$39$		0			0
$40$	−4400.00	+	5969.92i	−0.434813	+	0.589955i
$41$	198.000			0.0183952			0.00919762	−	0.999958i	$-0.497072\pi$
$41$	198.000			0.0183952			0.00919762	+	0.999958i	$0.497072\pi$
$42$		0			0
$43$			417.895i			0.0344664i	0.999851	+	0.0172332i	$0.00548577\pi$
$43$			417.895i			0.0344664i	−0.999851	+	0.0172332i	$0.994514\pi$
$44$	3024.00			0.235478
$45$		0			0
$46$	−16148.0			−1.12519
$47$		−	10540.2i		−	0.695994i	−0.937496	−	0.347997i	$-0.886862\pi$
$47$		−	10540.2i		−	0.695994i	0.937496	−	0.347997i	$-0.113138\pi$
$48$		0			0
$49$	13243.0			0.787945
$50$	−19800.0	+	6135.76i	−1.12006	+	0.347091i
$51$		0			0
$52$		−	1432.78i		−	0.0734804i
$53$		−	5823.99i		−	0.284794i	−0.989810	−	0.142397i	$-0.954519\pi$
$53$		−	5823.99i		−	0.284794i	0.989810	−	0.142397i	$-0.0454810\pi$
$54$		0			0
$55$	−11340.0	−	8357.89i	−0.505483	−	0.372555i
$56$	−7920.00			−0.337485
$57$		0			0
$58$			45968.4i			1.79428i
$59$	24660.0			0.922281			0.461140	−	0.887327i	$-0.347440\pi$
$59$	24660.0			0.922281			0.461140	+	0.887327i	$0.347440\pi$
$60$		0			0
$61$	−5698.00			−0.196064			−0.0980320	−	0.995183i	$-0.531255\pi$
$61$	−5698.00			−0.196064			−0.0980320	+	0.995183i	$0.531255\pi$
$62$			44787.7i			1.47972i
$63$		0			0
$64$	−12992.0			−0.396484
$65$	−3960.00	+	5372.93i	−0.116255	+	0.157735i
$66$		0			0
$67$			43640.1i			1.18768i	0.804583	+	0.593840i	$0.202389\pi$
$67$			43640.1i			1.18768i	−0.804583	+	0.593840i	$0.797611\pi$
$68$			8278.30i			0.217104i
$69$		0			0
$70$	−17820.0	−	13133.8i	−0.434673	−	0.320366i
$71$	−53352.0			−1.25604			−0.628022	−	0.778196i	$-0.716135\pi$
$71$	−53352.0			−1.25604			−0.628022	+	0.778196i	$0.716135\pi$
$72$		0			0
$73$		−	70922.7i		−	1.55768i	−0.627223	−	0.778840i	$-0.715808\pi$
$73$		−	70922.7i		−	1.55768i	0.627223	−	0.778840i	$-0.284192\pi$
$74$	92664.0			1.96712
$75$		0			0
$76$	2640.00			0.0524288
$77$		−	15044.2i		−	0.289163i
$78$		0			0
$79$	51920.0			0.935981			0.467990	−	0.883734i	$-0.344978\pi$
$79$	51920.0			0.935981			0.467990	+	0.883734i	$0.344978\pi$
$80$	−56880.0	−	41922.1i	−0.993653	−	0.732350i
$81$		0			0
$82$			1313.38i			0.0215703i
$83$		−	61841.8i		−	0.985342i	−0.870216	−	0.492671i	$-0.836021\pi$
$83$		−	61841.8i		−	0.985342i	0.870216	−	0.492671i	$-0.163979\pi$
$84$		0			0
$85$	22880.0	−	31043.6i	0.343486	−	0.466042i
$86$	−2772.00			−0.0404154
$87$		0			0
$88$		−	33431.6i		−	0.460204i
$89$	9990.00			0.133687			0.0668437	−	0.997763i	$-0.478707\pi$
$89$	9990.00			0.133687			0.0668437	+	0.997763i	$0.478707\pi$
$90$		0			0
$91$	−7128.00			−0.0902328
$92$		−	29212.8i		−	0.359836i
$93$		0			0
$94$	69916.0			0.816125
$95$	−9900.00	−	7296.57i	−0.112545	−	0.0829488i
$96$		0			0
$97$			101250.i			1.09261i	0.837586	+	0.546305i	$0.183966\pi$
$97$			101250.i			1.09261i	−0.837586	+	0.546305i	$0.816034\pi$
$98$			87844.1i			0.923948i
$99$		0			0
$100$	−11100.0	−	35819.5i	−0.111000	−	0.358195i
$101$	109098.			1.06418			0.532088	−	0.846689i	$-0.321408\pi$
$101$	109098.			1.06418			0.532088	+	0.846689i	$0.321408\pi$
$102$		0			0
$103$		−	70624.2i		−	0.655935i	−0.944689	−	0.327967i	$-0.893636\pi$
$103$		−	70624.2i		−	0.655935i	0.944689	−	0.327967i	$-0.106364\pi$
$104$	−15840.0			−0.143606
$105$		0			0
$106$	38632.0			0.333951
$107$			97117.4i			0.820045i	0.912075	+	0.410022i	$0.134479\pi$
$107$			97117.4i			0.820045i	−0.912075	+	0.410022i	$0.865521\pi$
$108$		0			0
$109$	−21010.0			−0.169379			−0.0846895	−	0.996407i	$-0.526990\pi$
$109$	−21010.0			−0.169379			−0.0846895	+	0.996407i	$0.526990\pi$
$110$	55440.0	−	75221.1i	0.436859	−	0.592731i
$111$		0			0
$112$		−	75459.8i		−	0.568422i
$113$			105018.i			0.773688i	0.922145	+	0.386844i	$0.126435\pi$
$113$			105018.i			0.773688i	−0.922145	+	0.386844i	$0.873565\pi$
$114$		0			0
$115$	−80740.0	+	109548.i	−0.569304	+	0.772432i
$116$	−83160.0			−0.573812
$117$		0			0
$118$			163576.i			1.08147i
$119$	41184.0			0.266601
$120$		0			0
$121$	−97547.0			−0.605690
$122$		−	37796.3i		−	0.229905i
$123$		0			0
$124$	−81024.0			−0.473216
$125$	−57375.0	+	165002.i	−0.328434	+	0.944527i
$126$		0			0
$127$			87220.6i			0.479855i	0.970791	+	0.239927i	$0.0771236\pi$
$127$			87220.6i			0.479855i	−0.970791	+	0.239927i	$0.922876\pi$
$128$		−	218632.i		−	1.17947i
$129$		0			0
$130$	−35640.0	−	26267.7i	−0.184961	−	0.136321i
$131$	−192852.			−0.981852			−0.490926	−	0.871201i	$-0.663341\pi$
$131$	−192852.			−0.981852			−0.490926	+	0.871201i	$0.663341\pi$
$132$		0			0
$133$		−	13133.8i		−	0.0643817i
$134$	−289476.			−1.39268
$135$		0			0
$136$	91520.0			0.424296
$137$		−	143570.i		−	0.653525i	−0.945106	−	0.326763i	$-0.894042\pi$
$137$		−	143570.i		−	0.653525i	0.945106	−	0.326763i	$-0.105958\pi$
$138$		0			0
$139$	−318340.			−1.39751			−0.698754	−	0.715362i	$-0.746262\pi$
$139$	−318340.			−1.39751			−0.698754	+	0.715362i	$0.746262\pi$
$140$	23760.0	−	32237.6i	0.102453	−	0.139009i
$141$		0			0
$142$		−	353897.i		−	1.47284i
$143$		−	30088.4i		−	0.123044i
$144$		0			0
$145$	311850.	+	229842.i	1.23176	+	0.907841i
$146$	470448.			1.82654
$147$		0			0
$148$			167635.i			0.629088i
$149$	−84150.0			−0.310519			−0.155260	−	0.987874i	$-0.549621\pi$
$149$	−84150.0			−0.310519			−0.155260	+	0.987874i	$0.549621\pi$
$150$		0			0
$151$	−155848.			−0.556236			−0.278118	−	0.960547i	$-0.589711\pi$
$151$	−155848.			−0.556236			−0.278118	+	0.960547i	$0.589711\pi$
$152$		−	29186.3i		−	0.102464i
$153$		0			0
$154$	99792.0			0.339074
$155$	303840.	+	223939.i	1.01582	+	0.748686i
$156$		0			0
$157$		−	356643.i		−	1.15474i	−0.816482	−	0.577371i	$-0.804079\pi$
$157$		−	356643.i		−	1.15474i	0.816482	−	0.577371i	$-0.195921\pi$
$158$			344398.i			1.09753i
$159$		0			0
$160$	137280.	−	186262.i	0.423943	−	0.575206i
$161$	−145332.			−0.441872
$162$		0			0
$163$			144890.i			0.427139i	0.976928	+	0.213570i	$0.0685090\pi$
$163$			144890.i			0.427139i	−0.976928	+	0.213570i	$0.931491\pi$
$164$	−2376.00			−0.00689822
$165$		0			0
$166$	410212.			1.15542
$167$		−	18102.1i		−	0.0502272i	−0.999685	−	0.0251136i	$-0.992005\pi$
$167$		−	18102.1i		−	0.0502272i	0.999685	−	0.0251136i	$-0.00799474\pi$
$168$		0			0
$169$	357037.			0.961604
$170$	205920.	+	151769.i	0.546482	+	0.402773i
$171$		0			0
$172$		−	5014.74i		−	0.0129249i
$173$		−	492572.i		−	1.25128i	−0.780112	−	0.625640i	$-0.784838\pi$
$173$		−	492572.i		−	1.25128i	0.780112	−	0.625640i	$-0.215162\pi$
$174$		0			0
$175$	−178200.	+	55221.8i	−0.439858	+	0.136306i
$176$	318528.			0.775115
$177$		0			0
$178$			66266.2i			0.156762i
$179$	−444420.			−1.03672			−0.518359	−	0.855163i	$-0.673457\pi$
$179$	−444420.			−1.03672			−0.518359	+	0.855163i	$0.673457\pi$
$180$		0			0
$181$	156902.			0.355985			0.177993	−	0.984032i	$-0.443040\pi$
$181$	156902.			0.355985			0.177993	+	0.984032i	$0.443040\pi$
$182$		−	47281.8i		−	0.105807i
$183$		0			0
$184$	−322960.			−0.703241
$185$	463320.	−	628633.i	0.995295	−	1.35042i
$186$		0			0
$187$			173844.i			0.363543i
$188$			126483.i			0.260998i
$189$		0			0
$190$	48400.0	−	65669.2i	0.0972661	−	0.131971i
$191$	−332352.			−0.659196			−0.329598	−	0.944121i	$-0.606913\pi$
$191$	−332352.			−0.659196			−0.329598	+	0.944121i	$0.606913\pi$
$192$		0			0
$193$		−	786120.i		−	1.51913i	−0.650430	−	0.759566i	$-0.725411\pi$
$193$		−	786120.i		−	1.51913i	0.650430	−	0.759566i	$-0.274589\pi$
$194$	−671616.			−1.28120
$195$		0			0
$196$	−158916.			−0.295480
$197$			59606.4i			0.109428i	0.998502	+	0.0547138i	$0.0174247\pi$
$197$			59606.4i			0.109428i	−0.998502	+	0.0547138i	$0.982575\pi$
$198$		0			0
$199$	−395800.			−0.708505			−0.354253	−	0.935150i	$-0.615265\pi$
$199$	−395800.			−0.708505			−0.354253	+	0.935150i	$0.615265\pi$
$200$	−396000.	+	122715.i	−0.700036	+	0.216932i
$201$		0			0
$202$			723674.i			1.24786i
$203$			413716.i			0.704631i
$204$		0			0
$205$	8910.00	+	6566.92i	0.0148079	+	0.0109138i
$206$	468468.			0.769151
$207$		0			0
$208$		−	150920.i		−	0.241873i
$209$	55440.0			0.0877925
$210$		0			0
$211$	−251548.			−0.388969			−0.194484	−	0.980906i	$-0.562303\pi$
$211$	−251548.			−0.388969			−0.194484	+	0.980906i	$0.562303\pi$
$212$			69887.9i			0.106798i
$213$		0			0
$214$	−644204.			−0.961588
$215$	−13860.0	+	18805.3i	−0.0204488	+	0.0277449i
$216$		0			0
$217$			403089.i			0.581101i
$218$		−	139365.i		−	0.198615i
$219$		0			0
$220$	136080.	+	100295.i	0.189556	+	0.139708i
$221$	82368.0			0.113443
$222$		0			0
$223$			288765.i			0.388851i	0.980917	+	0.194425i	$0.0622842\pi$
$223$			288765.i			0.388851i	−0.980917	+	0.194425i	$0.937716\pi$
$224$	247104.			0.329048
$225$		0			0
$226$	−696608.			−0.907230
$227$			1.16414e6i			1.49948i	0.661731	+	0.749741i	$0.269822\pi$
$227$			1.16414e6i			1.49948i	−0.661731	+	0.749741i	$0.730178\pi$
$228$		0			0
$229$	547670.			0.690129			0.345064	−	0.938579i	$-0.387857\pi$
$229$	547670.			0.690129			0.345064	+	0.938579i	$0.387857\pi$
$230$	−726660.	−	535569.i	−0.905757	−	0.667568i
$231$		0			0
$232$			919368.i			1.12142i
$233$			48104.3i			0.0580489i	0.999579	+	0.0290245i	$0.00924007\pi$
$233$			48104.3i			0.0580489i	−0.999579	+	0.0290245i	$0.990760\pi$
$234$		0			0
$235$	349580.	−	474311.i	0.412930	−	0.560264i
$236$	−295920.			−0.345855
$237$		0			0
$238$			273184.i			0.312617i
$239$	1.00584e6			1.13903			0.569514	−	0.821982i	$-0.307132\pi$
$239$	1.00584e6			1.13903			0.569514	+	0.821982i	$0.307132\pi$
$240$		0			0
$241$	895202.			0.992838			0.496419	−	0.868083i	$-0.334648\pi$
$241$	895202.			0.992838			0.496419	+	0.868083i	$0.334648\pi$
$242$		−	647054.i		−	0.710235i
$243$		0			0
$244$	68376.0			0.0735240
$245$	595935.	+	439221.i	0.634284	+	0.467485i
$246$		0			0
$247$		−	26267.7i		−	0.0273955i
$248$			895754.i			0.924825i
$249$		0			0
$250$	−1.09450e6	−	380583.i	−1.10756	−	0.385123i
$251$	−558252.			−0.559301			−0.279651	−	0.960102i	$-0.590219\pi$
$251$	−558252.			−0.559301			−0.279651	+	0.960102i	$0.590219\pi$
$252$		0			0
$253$		−	613469.i		−	0.602548i
$254$	−578556.			−0.562680
$255$		0			0
$256$	1.03450e6			0.986572
$257$		−	787924.i		−	0.744135i	−0.928206	−	0.372067i	$-0.878649\pi$
$257$		−	787924.i		−	0.744135i	0.928206	−	0.372067i	$-0.121351\pi$
$258$		0			0
$259$	833976.			0.772510
$260$	47520.0	−	64475.2i	0.0435956	−	0.0591506i
$261$		0			0
$262$		−	1.27924e6i		−	1.15132i
$263$		−	1.63173e6i		−	1.45465i	−0.686291	−	0.727327i	$-0.740762\pi$
$263$		−	1.63173e6i		−	1.45465i	0.686291	−	0.727327i	$-0.259238\pi$
$264$		0			0
$265$	193160.	−	262080.i	0.168967	−	0.229255i
$266$	87120.0			0.0754942
$267$		0			0
$268$		−	523682.i		−	0.445380i
$269$	1.73637e6			1.46306			0.731529	−	0.681810i	$-0.238807\pi$
$269$	1.73637e6			1.46306			0.731529	+	0.681810i	$0.238807\pi$
$270$		0			0
$271$	−1.72005e6			−1.42271			−0.711357	−	0.702831i	$-0.751919\pi$
$271$	−1.72005e6			−1.42271			−0.711357	+	0.702831i	$0.751919\pi$
$272$			871980.i			0.714635i
$273$		0			0
$274$	952336.			0.766326
$275$	−233100.	−	752211.i	−0.185871	−	0.599802i
$276$		0			0
$277$		−	1.27243e6i		−	0.996402i	−0.867062	−	0.498201i	$-0.833994\pi$
$277$		−	1.27243e6i		−	0.996402i	0.867062	−	0.498201i	$-0.166006\pi$
$278$		−	2.11163e6i		−	1.63872i
$279$		0			0
$280$	−356400.	−	262677.i	−0.271671	−	0.200229i
$281$	−1.46500e6			−1.10681			−0.553404	−	0.832913i	$-0.686671\pi$
$281$	−1.46500e6			−1.10681			−0.553404	+	0.832913i	$0.686671\pi$
$282$		0			0
$283$			1.65051e6i			1.22504i	0.790455	+	0.612521i	$0.209844\pi$
$283$			1.65051e6i			1.22504i	−0.790455	+	0.612521i	$0.790156\pi$
$284$	640224.			0.471016
$285$		0			0
$286$	199584.			0.144281
$287$			11820.5i			0.00847089i
$288$		0			0
$289$	943953.			0.664823
$290$	−1.52460e6	+	2.06858e6i	−1.06454	+	1.44437i
$291$		0			0
$292$			851072.i			0.584130i
$293$			2.38772e6i			1.62485i	0.583064	+	0.812426i	$0.301854\pi$
$293$			2.38772e6i			1.62485i	−0.583064	+	0.812426i	$0.698146\pi$
$294$		0			0
$295$	1.10970e6	+	817880.i	0.742422	+	0.547185i
$296$	1.85328e6			1.22945
$297$		0			0
$298$		−	558188.i		−	0.364116i
$299$	−290664.			−0.188024
$300$		0			0
$301$	−24948.0			−0.0158716
$302$		−	1.03378e6i		−	0.652244i
$303$		0			0
$304$	278080.			0.172578
$305$	−256410.	−	188981.i	−0.157828	−	0.116324i
$306$		0			0
$307$		−	928264.i		−	0.562115i	−0.959691	−	0.281058i	$-0.909315\pi$
$307$		−	928264.i		−	0.562115i	0.959691	−	0.281058i	$-0.0906852\pi$
$308$			180531.i			0.108436i
$309$		0			0
$310$	−1.48544e6	+	2.01545e6i	−0.877912	+	1.19115i
$311$	−568152.			−0.333092			−0.166546	−	0.986034i	$-0.553261\pi$
$311$	−568152.			−0.333092			−0.166546	+	0.986034i	$0.553261\pi$
$312$		0			0
$313$			1.72244e6i			0.993766i	0.867818	+	0.496883i	$0.165522\pi$
$313$			1.72244e6i			0.993766i	−0.867818	+	0.496883i	$0.834478\pi$
$314$	2.36570e6			1.35405
$315$		0			0
$316$	−623040.			−0.350993
$317$			131643.i			0.0735785i	0.999323	+	0.0367893i	$0.0117130\pi$
$317$			131643.i			0.0735785i	−0.999323	+	0.0367893i	$0.988287\pi$
$318$		0			0
$319$	−1.74636e6			−0.960853
$320$	−584640.	−	430896.i	−0.319164	−	0.235233i
$321$		0			0
$322$		−	964023.i		−	0.518141i
$323$			151769.i			0.0809424i
$324$		0			0
$325$	−356400.	+	110444.i	−0.187167	+	0.0580006i
$326$	−961092.			−0.500865
$327$		0			0
$328$			26267.7i			0.0134815i
$329$	629244.			0.320501
$330$		0			0
$331$	−1.58055e6			−0.792935			−0.396468	−	0.918049i	$-0.629764\pi$
$331$	−1.58055e6			−0.792935			−0.396468	+	0.918049i	$0.629764\pi$
$332$			742101.i			0.369503i
$333$		0			0
$334$	120076.			0.0588966
$335$	−1.44738e6	+	1.96381e6i	−0.704645	+	0.956063i
$336$		0			0
$337$		−	1.22885e6i		−	0.589419i	−0.955587	−	0.294709i	$-0.904777\pi$
$337$		−	1.22885e6i		−	0.589419i	0.955587	−	0.294709i	$-0.0952228\pi$
$338$			2.36832e6i			1.12758i
$339$		0			0
$340$	−274560.	+	372523.i	−0.128807	+	0.174766i
$341$	−1.70150e6			−0.792405
$342$		0			0
$343$			1.79396e6i			0.823338i
$344$	−55440.0			−0.0252596
$345$		0			0
$346$	3.26735e6			1.46726
$347$		−	3.84224e6i		−	1.71301i	−0.516137	−	0.856506i	$-0.672630\pi$
$347$		−	3.84224e6i		−	1.71301i	0.516137	−	0.856506i	$-0.327370\pi$
$348$		0			0
$349$	−1.59445e6			−0.700725			−0.350362	−	0.936614i	$-0.613942\pi$
$349$	−1.59445e6			−0.700725			−0.350362	+	0.936614i	$0.613942\pi$
$350$	−366300.	−	1.18205e6i	−0.159833	−	0.515779i
$351$		0			0
$352$			1.04307e6i			0.448699i
$353$		−	295365.i		−	0.126160i	−0.998008	−	0.0630802i	$-0.979908\pi$
$353$		−	295365.i		−	0.126160i	0.998008	−	0.0630802i	$-0.0200924\pi$
$354$		0			0
$355$	−2.40084e6	−	1.76949e6i	−1.01110	−	0.745206i
$356$	−119880.			−0.0501328
$357$		0			0
$358$		−	2.94795e6i		−	1.21566i
$359$	−1.10484e6			−0.452442			−0.226221	−	0.974076i	$-0.572637\pi$
$359$	−1.10484e6			−0.452442			−0.226221	+	0.974076i	$0.572637\pi$
$360$		0			0
$361$	−2.42770e6			−0.980453
$362$			1.04077e6i			0.417430i
$363$		0			0
$364$	85536.0			0.0338373
$365$	2.35224e6	−	3.19152e6i	0.924165	−	1.25391i
$366$		0			0
$367$			1.83760e6i			0.712174i	0.934453	+	0.356087i	$0.115889\pi$
$367$			1.83760e6i			0.712174i	−0.934453	+	0.356087i	$0.884111\pi$
$368$		−	3.07708e6i		−	1.18446i
$369$		0			0
$370$	4.16988e6	+	3.07332e6i	1.58350	+	1.16709i
$371$	347688.			0.131146
$372$		0			0
$373$		−	2.93350e6i		−	1.09173i	−0.837874	−	0.545864i	$-0.816202\pi$
$373$		−	2.93350e6i		−	1.09173i	0.837874	−	0.545864i	$-0.183798\pi$
$374$	−1.15315e6			−0.426292
$375$		0			0
$376$	1.39832e6			0.510078
$377$			827432.i			0.299832i
$378$		0			0
$379$	5.09342e6			1.82143			0.910713	−	0.413040i	$-0.135533\pi$
$379$	5.09342e6			1.82143			0.910713	+	0.413040i	$0.135533\pi$
$380$	118800.	+	87558.9i	0.0422044	+	0.0311058i
$381$		0			0
$382$		−	2.20457e6i		−	0.772976i
$383$			3.17485e6i			1.10593i	0.833205	+	0.552964i	$0.186503\pi$
$383$			3.17485e6i			1.10593i	−0.833205	+	0.552964i	$0.813497\pi$
$384$		0			0
$385$	498960.	−	676989.i	0.171559	−	0.232772i
$386$	5.21453e6			1.78134
$387$		0			0
$388$		−	1.21500e6i		−	0.409729i
$389$	−1.79991e6			−0.603083			−0.301541	−	0.953453i	$-0.597501\pi$
$389$	−1.79991e6			−0.603083			−0.301541	+	0.953453i	$0.597501\pi$
$390$		0			0
$391$	1.67939e6			0.555533
$392$			1.75688e6i			0.577467i
$393$		0			0
$394$	−395384.			−0.128315
$395$	2.33640e6	+	1.72199e6i	0.753450	+	0.555314i
$396$		0			0
$397$			4.90405e6i			1.56163i	0.624760	+	0.780817i	$0.285197\pi$
$397$			4.90405e6i			1.56163i	−0.624760	+	0.780817i	$0.714803\pi$
$398$		−	2.62544e6i		−	0.830796i
$399$		0			0
$400$	−1.16920e6	−	3.77299e6i	−0.365375	−	1.17906i
$401$	642798.			0.199624			0.0998122	−	0.995006i	$-0.468176\pi$
$401$	642798.			0.199624			0.0998122	+	0.995006i	$0.468176\pi$
$402$		0			0
$403$			806179.i			0.247268i
$404$	−1.30918e6			−0.399066
$405$		0			0
$406$	−2.74428e6			−0.826254
$407$			3.52035e6i			1.05341i
$408$		0			0
$409$	−2.05711e6			−0.608064			−0.304032	−	0.952662i	$-0.598333\pi$
$409$	−2.05711e6			−0.608064			−0.304032	+	0.952662i	$0.598333\pi$
$410$	−43560.0	+	59102.3i	−0.0127976	+	0.0173638i
$411$		0			0
$412$			847490.i			0.245975i
$413$			1.47218e6i			0.424704i
$414$		0			0
$415$	2.05106e6	−	2.78288e6i	0.584599	−	0.793185i
$416$	494208.			0.140016
$417$		0			0
$418$			367747.i			0.102946i
$419$	2.93742e6			0.817393			0.408697	−	0.912670i	$-0.365983\pi$
$419$	2.93742e6			0.817393			0.408697	+	0.912670i	$0.365983\pi$
$420$		0			0
$421$	2.71770e6			0.747303			0.373651	−	0.927569i	$-0.378106\pi$
$421$	2.71770e6			0.747303			0.373651	+	0.927569i	$0.378106\pi$
$422$		−	1.66858e6i		−	0.456106i
$423$		0			0
$424$	772640.			0.208719
$425$	2.05920e6	−	638119.i	0.553001	−	0.171368i
$426$		0			0
$427$		−	340166.i		−	0.0902862i
$428$		−	1.16541e6i		−	0.307517i
$429$		0			0
$430$	−124740.	−	91936.8i	−0.0325338	−	0.0239783i
$431$	−4.99435e6			−1.29505			−0.647524	−	0.762045i	$-0.724196\pi$
$431$	−4.99435e6			−1.29505			−0.647524	+	0.762045i	$0.724196\pi$
$432$		0			0
$433$			2.08183e6i			0.533612i	0.963750	+	0.266806i	$0.0859684\pi$
$433$			2.08183e6i			0.533612i	−0.963750	+	0.266806i	$0.914032\pi$
$434$	−2.67379e6			−0.681402
$435$		0			0
$436$	252120.			0.0635172
$437$		−	535569.i		−	0.134156i
$438$		0			0
$439$	−4.70404e6			−1.16496			−0.582478	−	0.812846i	$-0.697917\pi$
$439$	−4.70404e6			−1.16496			−0.582478	+	0.812846i	$0.697917\pi$
$440$	1.10880e6	−	1.50442e6i	0.273037	−	0.370457i
$441$		0			0
$442$			546368.i			0.133024i
$443$		−	5.70103e6i		−	1.38021i	−0.723711	−	0.690103i	$-0.757565\pi$
$443$		−	5.70103e6i		−	1.38021i	0.723711	−	0.690103i	$-0.242435\pi$
$444$		0			0
$445$	449550.	+	331331.i	0.107616	+	0.0793162i
$446$	−1.91545e6			−0.455968
$447$		0			0
$448$		−	775613.i		−	0.182579i
$449$	−6.20325e6			−1.45212			−0.726062	−	0.687630i	$-0.758651\pi$
$449$	−6.20325e6			−1.45212			−0.726062	+	0.687630i	$0.758651\pi$
$450$		0			0
$451$	−49896.0			−0.0115511
$452$		−	1.26021e6i		−	0.290133i
$453$		0			0
$454$	−7.72204e6			−1.75830
$455$	−320760.	−	236409.i	−0.0726360	−	0.0535347i
$456$		0			0
$457$			2.15371e6i			0.482388i	0.970477	+	0.241194i	$0.0775391\pi$
$457$			2.15371e6i			0.482388i	−0.970477	+	0.241194i	$0.922461\pi$
$458$			3.63283e6i			0.809248i
$459$		0			0
$460$	968880.	−	1.31458e6i	0.213489	−	0.289662i
$461$	3.85130e6			0.844024			0.422012	−	0.906590i	$-0.361324\pi$
$461$	3.85130e6			0.844024			0.422012	+	0.906590i	$0.361324\pi$
$462$		0			0
$463$			2.08213e6i			0.451394i	0.974198	+	0.225697i	$0.0724659\pi$
$463$			2.08213e6i			0.451394i	−0.974198	+	0.225697i	$0.927534\pi$
$464$	−8.75952e6			−1.88880
$465$		0			0
$466$	−319088.			−0.0680684
$467$			1.30822e6i			0.277579i	0.990322	+	0.138790i	$0.0443212\pi$
$467$			1.30822e6i			0.277579i	−0.990322	+	0.138790i	$0.955679\pi$
$468$		0			0
$469$	−2.60528e6			−0.546919
$470$	3.14622e6	+	2.31885e6i	0.656968	+	0.484204i
$471$		0			0
$472$			3.27152e6i			0.675919i
$473$		−	105309.i		−	0.0216429i
$474$		0			0
$475$	−203500.	−	656692.i	−0.0413838	−	0.133545i
$476$	−494208.			−0.0999752
$477$		0			0
$478$			6.67199e6i			1.33563i
$479$	6.76368e6			1.34693			0.673464	−	0.739220i	$-0.264806\pi$
$479$	6.76368e6			1.34693			0.673464	+	0.739220i	$0.264806\pi$
$480$		0			0
$481$	1.66795e6			0.328716
$482$			5.93810e6i			1.16421i
$483$		0			0
$484$	1.17056e6			0.227134
$485$	−3.35808e6	+	4.55625e6i	−0.648241	+	0.879534i
$486$		0			0
$487$		−	6.67193e6i		−	1.27476i	−0.770549	−	0.637381i	$-0.780018\pi$
$487$		−	6.67193e6i		−	1.27476i	0.770549	−	0.637381i	$-0.219982\pi$
$488$		−	755925.i		−	0.143691i
$489$		0			0
$490$	−2.91346e6	+	3.95299e6i	−0.548175	+	0.743764i
$491$	6.87575e6			1.28711			0.643556	−	0.765399i	$-0.277458\pi$
$491$	6.87575e6			1.28711			0.643556	+	0.765399i	$0.277458\pi$
$492$		0			0
$493$		−	4.78072e6i		−	0.885881i
$494$	174240.			0.0321241
$495$		0			0
$496$	−8.53453e6			−1.55767
$497$		−	3.18507e6i		−	0.578400i
$498$		0			0
$499$	6.94010e6			1.24771			0.623856	−	0.781539i	$-0.285565\pi$
$499$	6.94010e6			1.24771			0.623856	+	0.781539i	$0.285565\pi$
$500$	688500.	−	1.98002e6i	0.123163	−	0.354198i
$501$		0			0
$502$		−	3.70302e6i		−	0.655839i
$503$			921007.i			0.162309i	0.996702	+	0.0811546i	$0.0258607\pi$
$503$			921007.i			0.162309i	−0.996702	+	0.0811546i	$0.974139\pi$
$504$		0			0
$505$	4.90941e6	+	3.61837e6i	0.856645	+	0.631371i
$506$	4.06930e6			0.706550
$507$		0			0
$508$		−	1.04665e6i		−	0.179946i
$509$	−4.97979e6			−0.851955			−0.425977	−	0.904734i	$-0.640070\pi$
$509$	−4.97979e6			−0.851955			−0.425977	+	0.904734i	$0.640070\pi$
$510$		0			0
$511$	4.23403e6			0.717302
$512$		−	134151.i		−	0.0226161i
$513$		0			0
$514$	5.22650e6			0.872575
$515$	2.34234e6	−	3.17809e6i	0.389163	−	0.528017i
$516$		0			0
$517$			2.65614e6i			0.437043i
$518$			5.53197e6i			0.905848i
$519$		0			0
$520$	−712800.	−	525353.i	−0.115600	−	0.0852007i
$521$	147798.			0.0238547			0.0119274	−	0.999929i	$-0.496203\pi$
$521$	147798.			0.0238547			0.0119274	+	0.999929i	$0.496203\pi$
$522$		0			0
$523$		−	1.23884e7i		−	1.98043i	−0.139543	−	0.990216i	$-0.544563\pi$
$523$		−	1.23884e7i		−	1.98043i	0.139543	−	0.990216i	$-0.455437\pi$
$524$	2.31422e6			0.368194
$525$		0			0
$526$	1.08237e7			1.70573
$527$		−	4.65792e6i		−	0.730576i
$528$		0			0
$529$	510027.			0.0792417
$530$	1.73844e6	+	1.28128e6i	0.268825	+	0.198132i
$531$		0			0
$532$			157606.i			0.0241431i
$533$			23640.9i			0.00360451i
$534$		0			0
$535$	−3.22102e6	+	4.37028e6i	−0.486529	+	0.660123i
$536$	−5.78952e6			−0.870423
$537$		0			0
$538$			1.15178e7i			1.71559i
$539$	−3.33724e6			−0.494783
$540$		0			0
$541$	−9.99810e6			−1.46867			−0.734335	−	0.678787i	$-0.762506\pi$
$541$	−9.99810e6			−1.46867			−0.734335	+	0.678787i	$0.762506\pi$
$542$		−	1.14095e7i		−	1.66828i
$543$		0			0
$544$	−2.85542e6			−0.413688
$545$	−945450.	−	696823.i	−0.136348	−	0.100492i
$546$		0			0
$547$		−	1.18580e7i		−	1.69451i	−0.531189	−	0.847253i	$-0.678255\pi$
$547$		−	1.18580e7i		−	1.69451i	0.531189	−	0.847253i	$-0.321745\pi$
$548$			1.72284e6i			0.245072i
$549$		0			0
$550$	4.98960e6	−	1.54621e6i	0.703330	−	0.217953i
$551$	−1.52460e6			−0.213933
$552$		0			0
$553$			3.09958e6i			0.431013i
$554$	8.44034e6			1.16838
$555$		0			0
$556$	3.82008e6			0.524065
$557$			904550.i			0.123536i	0.998091	+	0.0617681i	$0.0196739\pi$
$557$			904550.i			0.123536i	−0.998091	+	0.0617681i	$0.980326\pi$
$558$		0			0
$559$	−49896.0			−0.00675361
$560$	2.50272e6	−	3.39569e6i	0.337242	−	0.457571i
$561$		0			0
$562$		−	9.71772e6i		−	1.29785i
$563$		−	8.68719e6i		−	1.15507i	−0.816366	−	0.577535i	$-0.804015\pi$
$563$		−	8.68719e6i		−	1.15507i	0.816366	−	0.577535i	$-0.195985\pi$
$564$		0			0
$565$	−3.48304e6	+	4.72579e6i	−0.459026	+	0.622807i
$566$	−1.09482e7			−1.43649
$567$		0			0
$568$		−	7.07794e6i		−	0.920526i
$569$	2.27007e6			0.293940			0.146970	−	0.989141i	$-0.453048\pi$
$569$	2.27007e6			0.293940			0.146970	+	0.989141i	$0.453048\pi$
$570$		0			0
$571$	1.43807e7			1.84582			0.922908	−	0.385021i	$-0.125806\pi$
$571$	1.43807e7			1.84582			0.922908	+	0.385021i	$0.125806\pi$
$572$			361061.i			0.0461414i
$573$		0			0
$574$	−78408.0			−0.00993300
$575$	−7.26660e6	+	2.25182e6i	−0.916562	+	0.284030i
$576$		0			0
$577$		−	5.63943e6i		−	0.705173i	−0.935779	−	0.352586i	$-0.885302\pi$
$577$		−	5.63943e6i		−	0.705173i	0.935779	−	0.352586i	$-0.114698\pi$
$578$			6.26148e6i			0.779574i
$579$		0			0
$580$	−3.74220e6	−	2.75811e6i	−0.461910	−	0.340440i
$581$	3.69191e6			0.453744
$582$		0			0
$583$			1.46765e6i			0.178834i
$584$	9.40896e6			1.14159
$585$		0			0
$586$	−1.58383e7			−1.90531
$587$			1.28473e6i			0.153893i	0.997035	+	0.0769464i	$0.0245170\pi$
$587$			1.28473e6i			0.153893i	−0.997035	+	0.0769464i	$0.975483\pi$
$588$		0			0
$589$	−1.48544e6			−0.176428
$590$	−5.42520e6	+	7.36092e6i	−0.641632	+	0.870566i
$591$		0			0
$592$			1.76576e7i			2.07075i
$593$			7.00943e6i			0.818552i	0.912411	+	0.409276i	$0.134219\pi$
$593$			7.00943e6i			0.818552i	−0.912411	+	0.409276i	$0.865781\pi$
$594$		0			0
$595$	1.85328e6	+	1.36592e6i	0.214609	+	0.158173i
$596$	1.00980e6			0.116445
$597$		0			0
$598$		−	1.92805e6i		−	0.220478i
$599$	8.80020e6			1.00213			0.501067	−	0.865409i	$-0.332941\pi$
$599$	8.80020e6			1.00213			0.501067	+	0.865409i	$0.332941\pi$
$600$		0			0
$601$	−1.07670e7			−1.21593			−0.607965	−	0.793964i	$-0.708014\pi$
$601$	−1.07670e7			−1.21593			−0.607965	+	0.793964i	$0.708014\pi$
$602$		−	165486.i		−	0.0186110i
$603$		0			0
$604$	1.87018e6			0.208588
$605$	−4.38962e6	−	3.23527e6i	−0.487571	−	0.359353i
$606$		0			0
$607$			1.51219e7i			1.66584i	0.553391	+	0.832921i	$0.313333\pi$
$607$			1.51219e7i			1.66584i	−0.553391	+	0.832921i	$0.686667\pi$
$608$			910613.i			0.0999021i
$609$		0			0
$610$	1.25356e6	−	1.70083e6i	0.136402	−	0.185070i
$611$	1.25849e6			0.136379
$612$		0			0
$613$			8.31622e6i			0.893871i	0.894566	+	0.446936i	$0.147485\pi$
$613$			8.31622e6i			0.893871i	−0.894566	+	0.446936i	$0.852515\pi$
$614$	6.15740e6			0.659139
$615$		0			0
$616$	1.99584e6			0.211921
$617$			1.21083e7i			1.28047i	0.768178	+	0.640237i	$0.221164\pi$
$617$			1.21083e7i			1.28047i	−0.768178	+	0.640237i	$0.778836\pi$
$618$		0			0
$619$	9.73238e6			1.02092			0.510461	−	0.859901i	$-0.329475\pi$
$619$	9.73238e6			1.02092			0.510461	+	0.859901i	$0.329475\pi$
$620$	−3.64608e6	−	2.68726e6i	−0.380932	−	0.280757i
$621$		0			0
$622$		−	3.76869e6i		−	0.390584i
$623$			596395.i			0.0615622i
$624$		0			0
$625$	−8.05437e6	+	5.52218e6i	−0.824768	+	0.565471i
$626$	−1.14254e7			−1.16529
$627$		0			0
$628$			4.27972e6i			0.433028i
$629$	−9.63706e6			−0.971220
$630$		0			0
$631$	−8.60145e6			−0.859999			−0.430000	−	0.902829i	$-0.641486\pi$
$631$	−8.60145e6			−0.859999			−0.430000	+	0.902829i	$0.641486\pi$
$632$			6.88797e6i			0.685959i
$633$		0			0
$634$	−873224.			−0.0862785
$635$	−2.89278e6	+	3.92493e6i	−0.284696	+	0.386276i
$636$		0			0
$637$			1.58119e6i			0.154396i
$638$		−	1.15840e7i		−	1.12670i
$639$		0			0
$640$	7.25120e6	−	9.83844e6i	0.699777	−	0.949459i
$641$	6.42440e6			0.617572			0.308786	−	0.951132i	$-0.400077\pi$
$641$	6.42440e6			0.617572			0.308786	+	0.951132i	$0.400077\pi$
$642$		0			0
$643$		−	3.64721e6i		−	0.347883i	−0.984756	−	0.173941i	$-0.944350\pi$
$643$		−	3.64721e6i		−	0.347883i	0.984756	−	0.173941i	$-0.0556503\pi$
$644$	1.74398e6			0.165702
$645$		0			0
$646$	−1.00672e6			−0.0949134
$647$			3.78036e6i			0.355036i	0.984118	+	0.177518i	$0.0568068\pi$
$647$			3.78036e6i			0.355036i	−0.984118	+	0.177518i	$0.943193\pi$
$648$		0			0
$649$	−6.21432e6			−0.579138
$650$	−732600.	−	2.36409e6i	−0.0680117	−	0.219473i
$651$		0			0
$652$		−	1.73868e6i		−	0.160177i
$653$		−	1.66957e7i		−	1.53223i	−0.642706	−	0.766113i	$-0.722188\pi$
$653$		−	1.66957e7i		−	1.53223i	0.642706	−	0.766113i	$-0.277812\pi$
$654$		0			0
$655$	−8.67834e6	−	6.39618e6i	−0.790375	−	0.582529i
$656$	−250272.			−0.0227066
$657$		0			0
$658$			4.17393e6i			0.375821i
$659$	1.22166e6			0.109581			0.0547907	−	0.998498i	$-0.482551\pi$
$659$	1.22166e6			0.109581			0.0547907	+	0.998498i	$0.482551\pi$
$660$		0			0
$661$	1.62789e7			1.44918			0.724589	−	0.689182i	$-0.242030\pi$
$661$	1.62789e7			1.44918			0.724589	+	0.689182i	$0.242030\pi$
$662$		−	1.04842e7i		−	0.929799i
$663$		0			0
$664$	8.20424e6			0.722135
$665$	435600.	−	591023.i	0.0381974	−	0.0518263i
$666$		0			0
$667$			1.68704e7i			1.46829i
$668$			217226.i			0.0188352i
$669$		0			0
$670$	−1.30264e7	−	9.60083e6i	−1.12108	−	0.826270i
$671$	1.43590e6			0.123117
$672$		0			0
$673$		−	1.43928e7i		−	1.22492i	−0.790503	−	0.612459i	$-0.790181\pi$
$673$		−	1.43928e7i		−	1.22492i	0.790503	−	0.612459i	$-0.209819\pi$
$674$	8.15126e6			0.691155
$675$		0			0
$676$	−4.28444e6			−0.360602
$677$			2.62429e6i			0.220059i	0.993928	+	0.110030i	$0.0350946\pi$
$677$			2.62429e6i			0.220059i	−0.993928	+	0.110030i	$0.964905\pi$
$678$		0			0
$679$	−6.04454e6			−0.503140
$680$	4.11840e6	+	3.03538e6i	0.341552	+	0.251733i
$681$		0			0
$682$		−	1.12865e7i		−	0.929177i
$683$			1.03039e7i			0.845184i	0.906320	+	0.422592i	$0.138880\pi$
$683$			1.03039e7i			0.845184i	−0.906320	+	0.422592i	$0.861120\pi$
$684$		0			0
$685$	4.76168e6	−	6.46065e6i	0.387734	−	0.526078i
$686$	−1.18998e7			−0.965449
$687$		0			0
$688$		−	528219.i		−	0.0425444i
$689$	695376.			0.0558048
$690$		0			0
$691$	4.50285e6			0.358751			0.179375	−	0.983781i	$-0.442592\pi$
$691$	4.50285e6			0.358751			0.179375	+	0.983781i	$0.442592\pi$
$692$			5.91086e6i			0.469230i
$693$		0			0
$694$	2.54865e7			2.00868
$695$	−1.43253e7	−	1.05581e7i	−1.12497	−	0.829136i
$696$		0			0
$697$		−	136592.i		−	0.0106498i
$698$		−	1.05764e7i		−	0.821672i
$699$		0			0
$700$	2.13840e6	−	662662.i	0.164947	−	0.0511148i
$701$	4.88090e6			0.375150			0.187575	−	0.982250i	$-0.439937\pi$
$701$	4.88090e6			0.375150			0.187575	+	0.982250i	$0.439937\pi$
$702$		0			0
$703$			3.07332e6i			0.234541i
$704$	3.27398e6			0.248969
$705$		0			0
$706$	1.95923e6			0.147936
$707$			6.51307e6i			0.490046i
$708$		0			0
$709$	−9.96961e6			−0.744839			−0.372420	−	0.928064i	$-0.621472\pi$
$709$	−9.96961e6			−0.744839			−0.372420	+	0.928064i	$0.621472\pi$
$710$	1.17374e7	−	1.59254e7i	0.873831	−	1.18561i
$711$		0			0
$712$			1.32532e6i			0.0979765i
$713$			1.64371e7i			1.21088i
$714$		0			0
$715$	997920.	−	1.35398e6i	0.0730013	−	0.0990482i
$716$	5.33304e6			0.388770
$717$		0			0
$718$		−	7.32868e6i		−	0.530536i
$719$	1.19167e7			0.859675			0.429838	−	0.902906i	$-0.358571\pi$
$719$	1.19167e7			0.859675			0.429838	+	0.902906i	$0.358571\pi$
$720$		0			0
$721$	4.21621e6			0.302054
$722$		−	1.61035e7i		−	1.14968i
$723$		0			0
$724$	−1.88282e6			−0.133494
$725$	6.41025e6	+	2.06858e7i	0.452929	+	1.46160i
$726$		0			0
$727$			1.38269e6i			0.0970264i	0.998823	+	0.0485132i	$0.0154483\pi$
$727$			1.38269e6i			0.0970264i	−0.998823	+	0.0485132i	$0.984552\pi$
$728$		−	945636.i		−	0.0661296i
$729$		0			0
$730$	2.11702e7	+	1.56030e7i	1.47034	+	1.08368i
$731$	288288.			0.0199541
$732$		0			0
$733$			6.09661e6i			0.419110i	0.977797	+	0.209555i	$0.0672016\pi$
$733$			6.09661e6i			0.419110i	−0.977797	+	0.209555i	$0.932798\pi$
$734$	−1.21893e7			−0.835099
$735$		0			0
$736$	1.00764e7			0.685660
$737$		−	1.09973e7i		−	0.745793i
$738$		0			0
$739$	6.16946e6			0.415562			0.207781	−	0.978175i	$-0.433376\pi$
$739$	6.16946e6			0.415562			0.207781	+	0.978175i	$0.433376\pi$
$740$	−5.55984e6	+	7.54360e6i	−0.373236	+	0.506406i
$741$		0			0
$742$			2.30630e6i			0.153782i
$743$		−	1.57574e7i		−	1.04716i	−0.851978	−	0.523578i	$-0.824597\pi$
$743$		−	1.57574e7i		−	1.04716i	0.851978	−	0.523578i	$-0.175403\pi$
$744$		0			0
$745$	−3.78675e6	−	2.79094e6i	−0.249963	−	0.184230i
$746$	1.94586e7			1.28016
$747$		0			0
$748$		−	2.08613e6i		−	0.136329i
$749$	−5.79784e6			−0.377626
$750$		0			0
$751$	−1.51816e7			−0.982243			−0.491122	−	0.871091i	$-0.663413\pi$
$751$	−1.51816e7			−0.982243			−0.491122	+	0.871091i	$0.663413\pi$
$752$			1.33229e7i			0.859118i
$753$		0			0
$754$	−5.48856e6			−0.351585
$755$	−7.01316e6	−	5.16889e6i	−0.447761	−	0.330012i
$756$		0			0
$757$			652274.i			0.0413705i	0.999786	+	0.0206852i	$0.00658478\pi$
$757$			652274.i			0.0413705i	−0.999786	+	0.0206852i	$0.993415\pi$
$758$			3.37859e7i			2.13581i
$759$		0			0
$760$	968000.	−	1.31338e6i	0.0607913	−	0.0824817i
$761$	−4.51420e6			−0.282566			−0.141283	−	0.989969i	$-0.545123\pi$
$761$	−4.51420e6			−0.282566			−0.141283	+	0.989969i	$0.545123\pi$
$762$		0			0
$763$		−	1.25428e6i		−	0.0779980i
$764$	3.98822e6			0.247199
$765$		0			0
$766$	−2.10596e7			−1.29681
$767$			2.94437e6i			0.180719i
$768$		0			0
$769$	−1.20799e7			−0.736625			−0.368312	−	0.929702i	$-0.620064\pi$
$769$	−1.20799e7			−0.736625			−0.368312	+	0.929702i	$0.620064\pi$
$770$	4.49064e6	+	3.30973e6i	0.272949	+	0.201171i
$771$		0			0
$772$			9.43344e6i			0.569674i
$773$		−	1.04245e7i		−	0.627492i	−0.949507	−	0.313746i	$-0.898416\pi$
$773$		−	1.04245e7i		−	0.627492i	0.949507	−	0.313746i	$-0.101584\pi$
$774$		0			0
$775$	6.24560e6	+	2.01545e7i	0.373525	+	1.20536i
$776$	−1.34323e7			−0.800750
$777$		0			0
$778$		−	1.19393e7i		−	0.707177i
$779$	−43560.0			−0.00257184
$780$		0			0
$781$	1.34447e7			0.788721
$782$			1.11398e7i			0.651421i
$783$		0			0
$784$	−1.67392e7			−0.972620
$785$	1.18285e7	−	1.60489e7i	0.685104	−	0.929549i
$786$		0			0
$787$		−	3.45366e7i		−	1.98766i	−0.110913	−	0.993830i	$-0.535378\pi$
$787$		−	3.45366e7i		−	1.98766i	0.110913	−	0.993830i	$-0.464622\pi$
$788$		−	715277.i		−	0.0410354i
$789$		0			0
$790$	−1.14224e7	+	1.54979e7i	−0.651163	+	0.883498i
$791$	−6.26947e6			−0.356279
$792$		0			0
$793$		−	680333.i		−	0.0384183i
$794$	−3.25298e7			−1.83118
$795$		0			0
$796$	4.74960e6			0.265689
$797$		−	2.09287e7i		−	1.16707i	−0.812089	−	0.583533i	$-0.801670\pi$
$797$		−	2.09287e7i		−	1.16707i	0.812089	−	0.583533i	$-0.198330\pi$
$798$		0			0
$799$	−7.27126e6			−0.402942
$800$	1.23552e7	−	3.82871e6i	0.682535	−	0.211508i
$801$		0			0
$802$			4.26384e6i			0.234080i
$803$			1.78725e7i			0.978131i
$804$		0			0
$805$	−6.53994e6	−	4.82012e6i	−0.355700	−	0.262161i
$806$	−5.34758e6			−0.289948
$807$		0			0
$808$			1.44735e7i			0.779910i
$809$	−2.48797e7			−1.33651			−0.668257	−	0.743930i	$-0.732959\pi$
$809$	−2.48797e7			−1.33651			−0.668257	+	0.743930i	$0.732959\pi$
$810$		0			0
$811$	−3.95415e6			−0.211106			−0.105553	−	0.994414i	$-0.533661\pi$
$811$	−3.95415e6			−0.211106			−0.105553	+	0.994414i	$0.533661\pi$
$812$		−	4.96459e6i		−	0.264237i
$813$		0			0
$814$	−2.33513e7			−1.23524
$815$	−4.80546e6	+	6.52005e6i	−0.253420	+	0.343841i
$816$		0			0
$817$		−	91936.8i		−	0.00481875i
$818$		−	1.36453e7i		−	0.713018i
$819$		0			0
$820$	−106920.	−	78803.0i	−0.00555296	−	0.00409268i
$821$	3.43550e6			0.177882			0.0889410	−	0.996037i	$-0.471652\pi$
$821$	3.43550e6			0.177882			0.0889410	+	0.996037i	$0.471652\pi$
$822$		0			0
$823$			3.94833e6i			0.203195i	0.994826	+	0.101598i	$0.0323954\pi$
$823$			3.94833e6i			0.203195i	−0.994826	+	0.101598i	$0.967605\pi$
$824$	9.36936e6			0.480720
$825$		0			0
$826$	−9.76536e6			−0.498010
$827$		−	3.38176e7i		−	1.71941i	−0.510791	−	0.859705i	$-0.670647\pi$
$827$		−	3.38176e7i		−	1.71941i	0.510791	−	0.859705i	$-0.329353\pi$
$828$		0			0
$829$	1.52015e7			0.768244			0.384122	−	0.923282i	$-0.374504\pi$
$829$	1.52015e7			0.768244			0.384122	+	0.923282i	$0.374504\pi$
$830$	1.84595e7	+	1.36052e7i	0.930091	+	0.685503i
$831$		0			0
$832$		−	1.55123e6i		−	0.0776903i
$833$		−	9.13579e6i		−	0.456177i
$834$		0			0
$835$	600380.	−	814596.i	0.0297996	−	0.0404321i
$836$	−665280.			−0.0329222
$837$		0			0
$838$			1.94846e7i			0.958478i
$839$	−2.89012e7			−1.41746			−0.708729	−	0.705481i	$-0.750731\pi$
$839$	−2.89012e7			−1.41746			−0.708729	+	0.705481i	$0.750731\pi$
$840$		0			0
$841$	2.75138e7			1.34140
$842$			1.80272e7i			0.876290i
$843$		0			0
$844$	3.01858e6			0.145863
$845$	1.60667e7	+	1.18416e7i	0.774077	+	0.570516i
$846$		0			0
$847$		−	5.82348e6i		−	0.278917i
$848$			7.36153e6i			0.351543i
$849$		0			0
$850$	4.23280e6	+	1.36592e7i	0.200946	+	0.648452i
$851$	3.40077e7			1.60973
$852$		0			0
$853$			2.02107e7i			0.951062i	0.879699	+	0.475531i	$0.157744\pi$
$853$			2.02107e7i			0.951062i	−0.879699	+	0.475531i	$0.842256\pi$
$854$	2.25641e6			0.105870
$855$		0			0
$856$	−1.28841e7			−0.600992
$857$			1.70522e7i			0.793101i	0.918013	+	0.396550i	$0.129793\pi$
$857$			1.70522e7i			0.793101i	−0.918013	+	0.396550i	$0.870207\pi$
$858$		0			0
$859$	1.95505e7			0.904015			0.452008	−	0.892014i	$-0.350708\pi$
$859$	1.95505e7			0.904015			0.452008	+	0.892014i	$0.350708\pi$
$860$	166320.	−	225663.i	0.00766829	−	0.0104043i
$861$		0			0
$862$		−	3.31288e7i		−	1.51858i
$863$			2.70896e7i			1.23816i	0.785330	+	0.619078i	$0.212493\pi$
$863$			2.70896e7i			1.23816i	−0.785330	+	0.619078i	$0.787507\pi$
$864$		0			0
$865$	1.63368e7	−	2.21657e7i	0.742379	−	1.00726i
$866$	−1.38093e7			−0.625716
$867$		0			0
$868$		−	4.83707e6i		−	0.217913i
$869$	−1.30838e7			−0.587741
$870$		0			0
$871$	−5.21057e6			−0.232723
$872$		−	2.78729e6i		−	0.124134i
$873$		0			0
$874$	3.55256e6			0.157312
$875$	−9.85050e6	−	3.42524e6i	−0.434949	−	0.151242i
$876$		0			0
$877$		−	1.98285e6i		−	0.0870545i	−0.999052	−	0.0435272i	$-0.986140\pi$
$877$		−	1.98285e6i		−	0.0870545i	0.999052	−	0.0435272i	$-0.0138595\pi$
$878$		−	3.12031e7i		−	1.36603i
$879$		0			0
$880$	1.43338e7	+	1.05644e7i	0.623955	+	0.459872i
$881$	4.22840e7			1.83542			0.917712	−	0.397247i	$-0.130034\pi$
$881$	4.22840e7			1.83542			0.917712	+	0.397247i	$0.130034\pi$
$882$		0			0
$883$		−	134502.i		−	0.00580535i	−0.999996	−	0.00290267i	$-0.999076\pi$
$883$		−	134502.i		−	0.00580535i	0.999996	−	0.00290267i	$-0.000923951\pi$
$884$	−988416.			−0.0425411
$885$		0			0
$886$	3.78164e7			1.61844
$887$			3.87668e6i			0.165444i	0.996573	+	0.0827219i	$0.0263613\pi$
$887$			3.87668e6i			0.165444i	−0.996573	+	0.0827219i	$0.973639\pi$
$888$		0			0
$889$	−5.20700e6			−0.220970
$890$	−2.19780e6	+	2.98198e6i	−0.0930065	+	0.126191i
$891$		0			0
$892$		−	3.46518e6i		−	0.145819i
$893$			2.31885e6i			0.0973070i
$894$		0			0
$895$	−1.99989e7	−	1.47397e7i	−0.834543	−	0.615081i
$896$	1.30522e7			0.543141
$897$		0			0
$898$		−	4.11477e7i		−	1.70277i
$899$	4.67914e7			1.93093
$900$		0			0
$901$	−4.01773e6			−0.164880
$902$		−	330973.i		−	0.0135449i
$903$		0			0
$904$	−1.39322e7			−0.567019
$905$	7.06059e6	+	5.20385e6i	0.286563	+	0.211205i
$906$		0			0
$907$			2.87363e7i			1.15988i	0.814660	+	0.579939i	$0.196924\pi$
$907$			2.87363e7i			1.15988i	−0.814660	+	0.579939i	$0.803076\pi$
$908$		−	1.39697e7i		−	0.562306i
$909$		0			0
$910$	1.56816e6	−	2.12768e6i	0.0627750	−	0.0851732i
$911$	−1.87675e6			−0.0749223			−0.0374611	−	0.999298i	$-0.511927\pi$
$911$	−1.87675e6			−0.0749223			−0.0374611	+	0.999298i	$0.511927\pi$
$912$		0			0
$913$			1.55841e7i			0.618736i
$914$	−1.42861e7			−0.565650
$915$		0			0
$916$	−6.57204e6			−0.258798
$917$		−	1.15131e7i		−	0.452137i
$918$		0			0
$919$	−6.76852e6			−0.264366			−0.132183	−	0.991225i	$-0.542199\pi$
$919$	−6.76852e6			−0.264366			−0.132183	+	0.991225i	$0.542199\pi$
$920$	−1.45332e7	−	1.07114e7i	−0.566098	−	0.417230i
$921$		0			0
$922$			2.55466e7i			0.989706i
$923$		−	6.37015e6i		−	0.246119i
$924$		0			0
$925$	4.16988e7	−	1.29219e7i	1.60239	−	0.496560i
$926$	−1.38113e7			−0.529306
$927$		0			0
$928$		−	2.86843e7i		−	1.09339i
$929$	−1.15356e7			−0.438530			−0.219265	−	0.975665i	$-0.570366\pi$
$929$	−1.15356e7			−0.438530			−0.219265	+	0.975665i	$0.570366\pi$
$930$		0			0
$931$	−2.91346e6			−0.110163
$932$		−	577252.i		−	0.0217684i
$933$		0			0
$934$	−8.67772e6			−0.325491
$935$	−5.76576e6	+	7.82299e6i	−0.215689	+	0.292647i
$936$		0			0
$937$		−	3.92632e7i		−	1.46096i	−0.682936	−	0.730478i	$-0.739297\pi$
$937$		−	3.92632e7i		−	1.46096i	0.682936	−	0.730478i	$-0.260703\pi$
$938$		−	1.72815e7i		−	0.641319i
$939$		0			0
$940$	−4.19496e6	+	5.69173e6i	−0.154849	+	0.210099i
$941$	−2.94919e7			−1.08575			−0.542874	−	0.839814i	$-0.682664\pi$
$941$	−2.94919e7			−1.08575			−0.542874	+	0.839814i	$0.682664\pi$
$942$		0			0
$943$			482012.i			0.0176514i
$944$	−3.11702e7			−1.13844
$945$		0			0
$946$	698544.			0.0253785
$947$			2.09628e7i			0.759581i	0.925072	+	0.379791i	$0.124004\pi$
$947$			2.09628e7i			0.759581i	−0.925072	+	0.379791i	$0.875996\pi$
$948$		0			0
$949$	8.46806e6			0.305224
$950$	4.35600e6	−	1.34987e6i	0.156595	−	0.0485268i
$951$		0			0
$952$			5.46368e6i			0.195386i
$953$		−	1.64122e7i		−	0.585375i	−0.956208	−	0.292687i	$-0.905451\pi$
$953$		−	1.64122e7i		−	0.585375i	0.956208	−	0.292687i	$-0.0945495\pi$
$954$		0			0
$955$	−1.49558e7	−	1.10229e7i	−0.530643	−	0.391099i
$956$	−1.20701e7			−0.427135
$957$		0			0
$958$			4.48652e7i			1.57941i
$959$	8.57102e6			0.300944
$960$		0			0
$961$	1.69604e7			0.592416
$962$			1.10639e7i			0.385454i
$963$		0			0
$964$	−1.07424e7			−0.372314
$965$	2.60726e7	−	3.53754e7i	0.901295	−	1.22288i
$966$		0			0
$967$			4.71911e7i			1.62291i	0.584416	+	0.811454i	$0.301324\pi$
$967$			4.71911e7i			1.62291i	−0.584416	+	0.811454i	$0.698676\pi$
$968$		−	1.29411e7i		−	0.443897i
$969$		0			0
$970$	−3.02227e7	−	2.22750e7i	−1.03135	−	0.760130i
$971$	−3.84771e7			−1.30965			−0.654823	−	0.755783i	$-0.727257\pi$
$971$	−3.84771e7			−1.30965			−0.654823	+	0.755783i	$0.727257\pi$
$972$		0			0
$973$		−	1.90047e7i		−	0.643544i
$974$	4.42566e7			1.49479
$975$		0			0
$976$	7.20227e6			0.242016
$977$			2.70184e7i			0.905572i	0.891619	+	0.452786i	$0.149570\pi$
$977$			2.70184e7i			0.905572i	−0.891619	+	0.452786i	$0.850430\pi$
$978$		0			0
$979$	−2.51748e6			−0.0839478
$980$	−7.15122e6	−	5.27065e6i	−0.237856	−	0.175307i
$981$		0			0
$982$			4.56086e7i			1.50927i
$983$			2.88475e7i			0.952192i	0.879393	+	0.476096i	$0.157949\pi$
$983$			2.88475e7i			0.952192i	−0.879393	+	0.476096i	$0.842051\pi$
$984$		0			0
$985$	−1.97692e6	+	2.68229e6i	−0.0649230	+	0.0880876i
$986$	3.17117e7			1.03879
$987$		0			0
$988$			315212.i			0.0102733i
$989$	−1.01732e6			−0.0330726
$990$		0			0
$991$	−5.21596e7			−1.68714			−0.843569	−	0.537021i	$-0.819550\pi$
$991$	−5.21596e7			−1.68714			−0.843569	+	0.537021i	$0.819550\pi$
$992$		−	2.79475e7i		−	0.901704i
$993$		0			0
$994$	2.11274e7			0.678235
$995$	−1.78110e7	−	1.31272e7i	−0.570336	−	0.420353i
$996$		0			0
$997$			9.78148e6i			0.311650i	0.987785	+	0.155825i	$0.0498036\pi$
$997$			9.78148e6i			0.311650i	−0.987785	+	0.155825i	$0.950196\pi$
$998$			4.60354e7i			1.46307i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.6.b.b.19.2		2
3.2	odd	2		5.6.b.a.4.1	✓	2
4.3	odd	2		720.6.f.f.289.2		2
5.2	odd	4		225.6.a.n.1.1		2
5.3	odd	4		225.6.a.n.1.2		2
5.4	even	2	inner	45.6.b.b.19.1		2
12.11	even	2		80.6.c.a.49.1		2
15.2	even	4		25.6.a.c.1.2		2
15.8	even	4		25.6.a.c.1.1		2
15.14	odd	2		5.6.b.a.4.2	yes	2
20.19	odd	2		720.6.f.f.289.1		2
21.20	even	2		245.6.b.a.99.1		2
24.5	odd	2		320.6.c.f.129.1		2
24.11	even	2		320.6.c.g.129.2		2
60.23	odd	4		400.6.a.t.1.2		2
60.47	odd	4		400.6.a.t.1.1		2
60.59	even	2		80.6.c.a.49.2		2
105.104	even	2		245.6.b.a.99.2		2
120.29	odd	2		320.6.c.f.129.2		2
120.59	even	2		320.6.c.g.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.6.b.a.4.1	✓	2	3.2	odd	2
5.6.b.a.4.2	yes	2	15.14	odd	2
25.6.a.c.1.1		2	15.8	even	4
25.6.a.c.1.2		2	15.2	even	4
45.6.b.b.19.1		2	5.4	even	2	inner
45.6.b.b.19.2		2	1.1	even	1	trivial
80.6.c.a.49.1		2	12.11	even	2
80.6.c.a.49.2		2	60.59	even	2
225.6.a.n.1.1		2	5.2	odd	4
225.6.a.n.1.2		2	5.3	odd	4
245.6.b.a.99.1		2	21.20	even	2
245.6.b.a.99.2		2	105.104	even	2
320.6.c.f.129.1		2	24.5	odd	2
320.6.c.f.129.2		2	120.29	odd	2
320.6.c.g.129.1		2	120.59	even	2
320.6.c.g.129.2		2	24.11	even	2
400.6.a.t.1.1		2	60.47	odd	4
400.6.a.t.1.2		2	60.23	odd	4
720.6.f.f.289.1		2	20.19	odd	2
720.6.f.f.289.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.63325i q^{2} -12.0000 q^{4} +(45.0000 + 33.1662i) q^{5} +59.6992i q^{7} +132.665i q^{8} +(-220.000 + 298.496i) q^{10} -252.000 q^{11} +119.398i q^{13} -396.000 q^{14} -1264.00 q^{16} -689.858i q^{17} -220.000 q^{19} +(-540.000 - 397.995i) q^{20} -1671.58i q^{22} +2434.40i q^{23} +(925.000 + 2984.96i) q^{25} -792.000 q^{26} -716.391i q^{28} +6930.00 q^{29} +6752.00 q^{31} -4139.15i q^{32} +4576.00 q^{34} +(-1980.00 + 2686.47i) q^{35} -13969.6i q^{37} -1459.31i q^{38} +(-4400.00 + 5969.92i) q^{40} +198.000 q^{41} +417.895i q^{43} +3024.00 q^{44} -16148.0 q^{46} -10540.2i q^{47} +13243.0 q^{49} +(-19800.0 + 6135.76i) q^{50} -1432.78i q^{52} -5823.99i q^{53} +(-11340.0 - 8357.89i) q^{55} -7920.00 q^{56} +45968.4i q^{58} +24660.0 q^{59} -5698.00 q^{61} +44787.7i q^{62} -12992.0 q^{64} +(-3960.00 + 5372.93i) q^{65} +43640.1i q^{67} +8278.30i q^{68} +(-17820.0 - 13133.8i) q^{70} -53352.0 q^{71} -70922.7i q^{73} +92664.0 q^{74} +2640.00 q^{76} -15044.2i q^{77} +51920.0 q^{79} +(-56880.0 - 41922.1i) q^{80} +1313.38i q^{82} -61841.8i q^{83} +(22880.0 - 31043.6i) q^{85} -2772.00 q^{86} -33431.6i q^{88} +9990.00 q^{89} -7128.00 q^{91} -29212.8i q^{92} +69916.0 q^{94} +(-9900.00 - 7296.57i) q^{95} +101250. i q^{97} +87844.1i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 24 q^{4} + 90 q^{5} - 440 q^{10} - 504 q^{11} - 792 q^{14} - 2528 q^{16} - 440 q^{19} - 1080 q^{20} + 1850 q^{25} - 1584 q^{26} + 13860 q^{29} + 13504 q^{31} + 9152 q^{34} - 3960 q^{35} - 8800 q^{40}+ \cdots - 19800 q^{95}+O(q^{100}) \) 2 * q - 24 * q^4 + 90 * q^5 - 440 * q^10 - 504 * q^11 - 792 * q^14 - 2528 * q^16 - 440 * q^19 - 1080 * q^20 + 1850 * q^25 - 1584 * q^26 + 13860 * q^29 + 13504 * q^31 + 9152 * q^34 - 3960 * q^35 - 8800 * q^40 + 396 * q^41 + 6048 * q^44 - 32296 * q^46 + 26486 * q^49 - 39600 * q^50 - 22680 * q^55 - 15840 * q^56 + 49320 * q^59 - 11396 * q^61 - 25984 * q^64 - 7920 * q^65 - 35640 * q^70 - 106704 * q^71 + 185328 * q^74 + 5280 * q^76 + 103840 * q^79 - 113760 * q^80 + 45760 * q^85 - 5544 * q^86 + 19980 * q^89 - 14256 * q^91 + 139832 * q^94 - 19800 * q^95

Introduction

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