LMFDB - Embedded newform 45.6.b.b.19.1

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-6.63325i q^{2} -12.0000 q^{4} +(45.0000 - 33.1662i) q^{5} -59.6992i q^{7} -132.665i q^{8} +(-220.000 - 298.496i) q^{10} -252.000 q^{11} -119.398i q^{13} -396.000 q^{14} -1264.00 q^{16} +689.858i q^{17} -220.000 q^{19} +(-540.000 + 397.995i) q^{20} +1671.58i q^{22} -2434.40i q^{23} +(925.000 - 2984.96i) q^{25} -792.000 q^{26} +716.391i q^{28} +6930.00 q^{29} +6752.00 q^{31} +4139.15i q^{32} +4576.00 q^{34} +(-1980.00 - 2686.47i) q^{35} +13969.6i q^{37} +1459.31i q^{38} +(-4400.00 - 5969.92i) q^{40} +198.000 q^{41} -417.895i q^{43} +3024.00 q^{44} -16148.0 q^{46} +10540.2i q^{47} +13243.0 q^{49} +(-19800.0 - 6135.76i) q^{50} +1432.78i q^{52} +5823.99i q^{53} +(-11340.0 + 8357.89i) q^{55} -7920.00 q^{56} -45968.4i q^{58} +24660.0 q^{59} -5698.00 q^{61} -44787.7i q^{62} -12992.0 q^{64} +(-3960.00 - 5372.93i) q^{65} -43640.1i q^{67} -8278.30i q^{68} +(-17820.0 + 13133.8i) q^{70} -53352.0 q^{71} +70922.7i q^{73} +92664.0 q^{74} +2640.00 q^{76} +15044.2i q^{77} +51920.0 q^{79} +(-56880.0 + 41922.1i) q^{80} -1313.38i q^{82} +61841.8i q^{83} +(22880.0 + 31043.6i) q^{85} -2772.00 q^{86} +33431.6i q^{88} +9990.00 q^{89} -7128.00 q^{91} +29212.8i q^{92} +69916.0 q^{94} +(-9900.00 + 7296.57i) q^{95} -101250. i q^{97} -87844.1i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.800583\pi$
$2$		−	6.63325i		−	1.17260i	0.810093	−	0.586302i	$-0.199417\pi$
$3$		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	$-0.926047\pi$
$7$		−	59.6992i		−	0.460494i	0.973132	−	0.230247i	$-0.0739534\pi$
$8$		−	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	$-0.968764\pi$
$13$		−	119.398i		−	0.195948i	0.995189	−	0.0979739i	$-0.0312362\pi$
$14$	−396.000			−0.539977
$15$		0			0
$16$	−1264.00			−1.23438
$17$			689.858i			0.578945i	0.957186	+	0.289473i	$0.0934799\pi$
$17$			689.858i			0.578945i	−0.957186	+	0.289473i	$0.906520\pi$
$18$		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	$-0.840716\pi$
$23$		−	2434.40i		−	0.959561i	0.877388	−	0.479781i	$-0.159284\pi$
$24$		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	$0.316733\pi$
$37$			13969.6i			1.67757i	−0.544464	+	0.838785i	$0.683267\pi$
$38$			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	$-0.994514\pi$
$43$		−	417.895i		−	0.0344664i	0.999851	−	0.0172332i	$-0.00548577\pi$
$44$	3024.00			0.235478
$45$		0			0
$46$	−16148.0			−1.12519
$47$			10540.2i			0.695994i	0.937496	+	0.347997i	$0.113138\pi$
$47$			10540.2i			0.695994i	−0.937496	+	0.347997i	$0.886862\pi$
$48$		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	$0.0454810\pi$
$53$			5823.99i			0.284794i	−0.989810	+	0.142397i	$0.954519\pi$
$54$		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	$-0.797611\pi$
$67$		−	43640.1i		−	1.18768i	0.804583	−	0.593840i	$-0.202389\pi$
$68$		−	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	$0.284192\pi$
$73$			70922.7i			1.55768i	−0.627223	+	0.778840i	$0.715808\pi$
$74$	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	$0.163979\pi$
$83$			61841.8i			0.985342i	−0.870216	+	0.492671i	$0.836021\pi$
$84$		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	$-0.816034\pi$
$97$		−	101250.i		−	1.09261i	0.837586	−	0.546305i	$-0.183966\pi$
$98$		−	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	$0.106364\pi$
$103$			70624.2i			0.655935i	−0.944689	+	0.327967i	$0.893636\pi$
$104$	−15840.0			−0.143606
$105$		0			0
$106$	38632.0			0.333951
$107$		−	97117.4i		−	0.820045i	−0.912075	−	0.410022i	$-0.865521\pi$
$107$		−	97117.4i		−	0.820045i	0.912075	−	0.410022i	$-0.134479\pi$
$108$		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	$-0.873565\pi$
$113$		−	105018.i		−	0.773688i	0.922145	−	0.386844i	$-0.126435\pi$
$114$		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	$-0.922876\pi$
$127$		−	87220.6i		−	0.479855i	0.970791	−	0.239927i	$-0.0771236\pi$
$128$			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	$0.105958\pi$
$137$			143570.i			0.653525i	−0.945106	+	0.326763i	$0.894042\pi$
$138$		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	$0.195921\pi$
$157$			356643.i			1.15474i	−0.816482	+	0.577371i	$0.804079\pi$
$158$		−	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	$-0.931491\pi$
$163$		−	144890.i		−	0.427139i	0.976928	−	0.213570i	$-0.0685090\pi$
$164$	−2376.00			−0.00689822
$165$		0			0
$166$	410212.			1.15542
$167$			18102.1i			0.0502272i	0.999685	+	0.0251136i	$0.00799474\pi$
$167$			18102.1i			0.0502272i	−0.999685	+	0.0251136i	$0.992005\pi$
$168$		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	$0.215162\pi$
$173$			492572.i			1.25128i	−0.780112	+	0.625640i	$0.784838\pi$
$174$		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	$0.274589\pi$
$193$			786120.i			1.51913i	−0.650430	+	0.759566i	$0.725411\pi$
$194$	−671616.			−1.28120
$195$		0			0
$196$	−158916.			−0.295480
$197$		−	59606.4i		−	0.109428i	−0.998502	−	0.0547138i	$-0.982575\pi$
$197$		−	59606.4i		−	0.109428i	0.998502	−	0.0547138i	$-0.0174247\pi$
$198$		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	$-0.937716\pi$
$223$		−	288765.i		−	0.388851i	0.980917	−	0.194425i	$-0.0622842\pi$
$224$	247104.			0.329048
$225$		0			0
$226$	−696608.			−0.907230
$227$		−	1.16414e6i		−	1.49948i	−0.661731	−	0.749741i	$-0.730178\pi$
$227$		−	1.16414e6i		−	1.49948i	0.661731	−	0.749741i	$-0.269822\pi$
$228$		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	$-0.990760\pi$
$233$		−	48104.3i		−	0.0580489i	0.999579	−	0.0290245i	$-0.00924007\pi$
$234$		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	$0.121351\pi$
$257$			787924.i			0.744135i	−0.928206	+	0.372067i	$0.878649\pi$
$258$		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	$0.259238\pi$
$263$			1.63173e6i			1.45465i	−0.686291	+	0.727327i	$0.740762\pi$
$264$		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	$0.166006\pi$
$277$			1.27243e6i			0.996402i	−0.867062	+	0.498201i	$0.833994\pi$
$278$			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	$-0.790156\pi$
$283$		−	1.65051e6i		−	1.22504i	0.790455	−	0.612521i	$-0.209844\pi$
$284$	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	$-0.698146\pi$
$293$		−	2.38772e6i		−	1.62485i	0.583064	−	0.812426i	$-0.301854\pi$
$294$		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	$0.0906852\pi$
$307$			928264.i			0.562115i	−0.959691	+	0.281058i	$0.909315\pi$
$308$		−	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	$-0.834478\pi$
$313$		−	1.72244e6i		−	0.993766i	0.867818	−	0.496883i	$-0.165522\pi$
$314$	2.36570e6			1.35405
$315$		0			0
$316$	−623040.			−0.350993
$317$		−	131643.i		−	0.0735785i	−0.999323	−	0.0367893i	$-0.988287\pi$
$317$		−	131643.i		−	0.0735785i	0.999323	−	0.0367893i	$-0.0117130\pi$
$318$		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	$0.0952228\pi$
$337$			1.22885e6i			0.589419i	−0.955587	+	0.294709i	$0.904777\pi$
$338$		−	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	$0.327370\pi$
$347$			3.84224e6i			1.71301i	−0.516137	+	0.856506i	$0.672630\pi$
$348$		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	$0.0200924\pi$
$353$			295365.i			0.126160i	−0.998008	+	0.0630802i	$0.979908\pi$
$354$		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	$-0.884111\pi$
$367$		−	1.83760e6i		−	0.712174i	0.934453	−	0.356087i	$-0.115889\pi$
$368$			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	$0.183798\pi$
$373$			2.93350e6i			1.09173i	−0.837874	+	0.545864i	$0.816202\pi$
$374$	−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	$-0.813497\pi$
$383$		−	3.17485e6i		−	1.10593i	0.833205	−	0.552964i	$-0.186503\pi$
$384$		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	$-0.714803\pi$
$397$		−	4.90405e6i		−	1.56163i	0.624760	−	0.780817i	$-0.285197\pi$
$398$			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	$-0.914032\pi$
$433$		−	2.08183e6i		−	0.533612i	0.963750	−	0.266806i	$-0.0859684\pi$
$434$	−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	$0.242435\pi$
$443$			5.70103e6i			1.38021i	−0.723711	+	0.690103i	$0.757565\pi$
$444$		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	$-0.922461\pi$
$457$		−	2.15371e6i		−	0.482388i	0.970477	−	0.241194i	$-0.0775391\pi$
$458$		−	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	$-0.927534\pi$
$463$		−	2.08213e6i		−	0.451394i	0.974198	−	0.225697i	$-0.0724659\pi$
$464$	−8.75952e6			−1.88880
$465$		0			0
$466$	−319088.			−0.0680684
$467$		−	1.30822e6i		−	0.277579i	−0.990322	−	0.138790i	$-0.955679\pi$
$467$		−	1.30822e6i		−	0.277579i	0.990322	−	0.138790i	$-0.0443212\pi$
$468$		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	$0.219982\pi$
$487$			6.67193e6i			1.27476i	−0.770549	+	0.637381i	$0.780018\pi$
$488$			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	$-0.974139\pi$
$503$		−	921007.i		−	0.162309i	0.996702	−	0.0811546i	$-0.0258607\pi$
$504$		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	$0.455437\pi$
$523$			1.23884e7i			1.98043i	−0.139543	+	0.990216i	$0.544563\pi$
$524$	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	$0.321745\pi$
$547$			1.18580e7i			1.69451i	−0.531189	+	0.847253i	$0.678255\pi$
$548$		−	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	$-0.980326\pi$
$557$		−	904550.i		−	0.123536i	0.998091	−	0.0617681i	$-0.0196739\pi$
$558$		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	$0.195985\pi$
$563$			8.68719e6i			1.15507i	−0.816366	+	0.577535i	$0.804015\pi$
$564$		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	$0.114698\pi$
$577$			5.63943e6i			0.705173i	−0.935779	+	0.352586i	$0.885302\pi$
$578$		−	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	$-0.975483\pi$
$587$		−	1.28473e6i		−	0.153893i	0.997035	−	0.0769464i	$-0.0245170\pi$
$588$		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	$-0.865781\pi$
$593$		−	7.00943e6i		−	0.818552i	0.912411	−	0.409276i	$-0.134219\pi$
$594$		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	$-0.686667\pi$
$607$		−	1.51219e7i		−	1.66584i	0.553391	−	0.832921i	$-0.313333\pi$
$608$		−	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	$-0.852515\pi$
$613$		−	8.31622e6i		−	0.893871i	0.894566	−	0.446936i	$-0.147485\pi$
$614$	6.15740e6			0.659139
$615$		0			0
$616$	1.99584e6			0.211921
$617$		−	1.21083e7i		−	1.28047i	−0.768178	−	0.640237i	$-0.778836\pi$
$617$		−	1.21083e7i		−	1.28047i	0.768178	−	0.640237i	$-0.221164\pi$
$618$		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	$0.0556503\pi$
$643$			3.64721e6i			0.347883i	−0.984756	+	0.173941i	$0.944350\pi$
$644$	1.74398e6			0.165702
$645$		0			0
$646$	−1.00672e6			−0.0949134
$647$		−	3.78036e6i		−	0.355036i	−0.984118	−	0.177518i	$-0.943193\pi$
$647$		−	3.78036e6i		−	0.355036i	0.984118	−	0.177518i	$-0.0568068\pi$
$648$		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	$0.277812\pi$
$653$			1.66957e7i			1.53223i	−0.642706	+	0.766113i	$0.722188\pi$
$654$		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	$0.209819\pi$
$673$			1.43928e7i			1.22492i	−0.790503	+	0.612459i	$0.790181\pi$
$674$	8.15126e6			0.691155
$675$		0			0
$676$	−4.28444e6			−0.360602
$677$		−	2.62429e6i		−	0.220059i	−0.993928	−	0.110030i	$-0.964905\pi$
$677$		−	2.62429e6i		−	0.220059i	0.993928	−	0.110030i	$-0.0350946\pi$
$678$		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	$-0.861120\pi$
$683$		−	1.03039e7i		−	0.845184i	0.906320	−	0.422592i	$-0.138880\pi$
$684$		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	$-0.984552\pi$
$727$		−	1.38269e6i		−	0.0970264i	0.998823	−	0.0485132i	$-0.0154483\pi$
$728$			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	$-0.932798\pi$
$733$		−	6.09661e6i		−	0.419110i	0.977797	−	0.209555i	$-0.0672016\pi$
$734$	−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	$0.175403\pi$
$743$			1.57574e7i			1.04716i	−0.851978	+	0.523578i	$0.824597\pi$
$744$		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	$-0.993415\pi$
$757$		−	652274.i		−	0.0413705i	0.999786	−	0.0206852i	$-0.00658478\pi$
$758$		−	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	$0.101584\pi$
$773$			1.04245e7i			0.627492i	−0.949507	+	0.313746i	$0.898416\pi$
$774$		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	$0.464622\pi$
$787$			3.45366e7i			1.98766i	−0.110913	+	0.993830i	$0.535378\pi$
$788$			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	$0.198330\pi$
$797$			2.09287e7i			1.16707i	−0.812089	+	0.583533i	$0.801670\pi$
$798$		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	$-0.967605\pi$
$823$		−	3.94833e6i		−	0.203195i	0.994826	−	0.101598i	$-0.0323954\pi$
$824$	9.36936e6			0.480720
$825$		0			0
$826$	−9.76536e6			−0.498010
$827$			3.38176e7i			1.71941i	0.510791	+	0.859705i	$0.329353\pi$
$827$			3.38176e7i			1.71941i	−0.510791	+	0.859705i	$0.670647\pi$
$828$		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	$-0.842256\pi$
$853$		−	2.02107e7i		−	0.951062i	0.879699	−	0.475531i	$-0.157744\pi$
$854$	2.25641e6			0.105870
$855$		0			0
$856$	−1.28841e7			−0.600992
$857$		−	1.70522e7i		−	0.793101i	−0.918013	−	0.396550i	$-0.870207\pi$
$857$		−	1.70522e7i		−	0.793101i	0.918013	−	0.396550i	$-0.129793\pi$
$858$		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	$-0.787507\pi$
$863$		−	2.70896e7i		−	1.23816i	0.785330	−	0.619078i	$-0.212493\pi$
$864$		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	$0.0138595\pi$
$877$			1.98285e6i			0.0870545i	−0.999052	+	0.0435272i	$0.986140\pi$
$878$			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	$0.000923951\pi$
$883$			134502.i			0.00580535i	−0.999996	+	0.00290267i	$0.999076\pi$
$884$	−988416.			−0.0425411
$885$		0			0
$886$	3.78164e7			1.61844
$887$		−	3.87668e6i		−	0.165444i	−0.996573	−	0.0827219i	$-0.973639\pi$
$887$		−	3.87668e6i		−	0.165444i	0.996573	−	0.0827219i	$-0.0263613\pi$
$888$		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	$-0.803076\pi$
$907$		−	2.87363e7i		−	1.15988i	0.814660	−	0.579939i	$-0.196924\pi$
$908$			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	$0.260703\pi$
$937$			3.92632e7i			1.46096i	−0.682936	+	0.730478i	$0.739297\pi$
$938$			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	$-0.875996\pi$
$947$		−	2.09628e7i		−	0.759581i	0.925072	−	0.379791i	$-0.124004\pi$
$948$		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	$0.0945495\pi$
$953$			1.64122e7i			0.585375i	−0.956208	+	0.292687i	$0.905451\pi$
$954$		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	$-0.698676\pi$
$967$		−	4.71911e7i		−	1.62291i	0.584416	−	0.811454i	$-0.301324\pi$
$968$			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	$-0.850430\pi$
$977$		−	2.70184e7i		−	0.905572i	0.891619	−	0.452786i	$-0.149570\pi$
$978$		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	$-0.842051\pi$
$983$		−	2.88475e7i		−	0.952192i	0.879393	−	0.476096i	$-0.157949\pi$
$984$		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	$-0.950196\pi$
$997$		−	9.78148e6i		−	0.311650i	0.987785	−	0.155825i	$-0.0498036\pi$
$998$		−	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.19.1		2
3.2	odd	2		5.6.b.a.4.2	yes	2
4.3	odd	2		720.6.f.f.289.1		2
5.2	odd	4		225.6.a.n.1.2		2
5.3	odd	4		225.6.a.n.1.1		2
5.4	even	2	inner	45.6.b.b.19.2		2
12.11	even	2		80.6.c.a.49.2		2
15.2	even	4		25.6.a.c.1.1		2
15.8	even	4		25.6.a.c.1.2		2
15.14	odd	2		5.6.b.a.4.1	✓	2
20.19	odd	2		720.6.f.f.289.2		2
21.20	even	2		245.6.b.a.99.2		2
24.5	odd	2		320.6.c.f.129.2		2
24.11	even	2		320.6.c.g.129.1		2
60.23	odd	4		400.6.a.t.1.1		2
60.47	odd	4		400.6.a.t.1.2		2
60.59	even	2		80.6.c.a.49.1		2
105.104	even	2		245.6.b.a.99.1		2
120.29	odd	2		320.6.c.f.129.1		2
120.59	even	2		320.6.c.g.129.2		2

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

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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