LMFDB - Embedded newform 1890.2.d.e.1889.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1889,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1890.1889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.d (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 3 x^{14} + 5 x^{12} + 15 x^{11} - 12 x^{10} + 381 x^{9} - 1356 x^{8} + 1905 x^{7} + \cdots + 390625 $ x^16 - 3x^15 + 3x^14 + 5x^12 + 15x^11 - 12x^10 + 381x^9 - 1356x^8 + 1905x^7 - 300x^6 + 1875x^5 + 3125x^4 + 46875x^2 - 234375*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1889.6
Root			$-2.23107 + 0.149392i$ of defining polynomial
Character	$\chi$	$=$	1890.1889
Dual form			1890.2.d.e.1889.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-0.986159 + 2.00686i) q^{5} +(2.28525 + 1.33328i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.986159 + 2.00686i) q^{5} +(2.28525 + 1.33328i) q^{7} -1.00000 q^{8} +(0.986159 - 2.00686i) q^{10} +4.42292i q^{11} +1.99638 q^{13} +(-2.28525 - 1.33328i) q^{14} +1.00000 q^{16} +4.94340i q^{17} +0.802373i q^{19} +(-0.986159 + 2.00686i) q^{20} -4.42292i q^{22} +6.49971 q^{23} +(-3.05498 - 3.95817i) q^{25} -1.99638 q^{26} +(2.28525 + 1.33328i) q^{28} -0.868528i q^{29} -2.53442i q^{31} -1.00000 q^{32} -4.94340i q^{34} +(-4.92933 + 3.27135i) q^{35} +6.08271i q^{37} -0.802373i q^{38} +(0.986159 - 2.00686i) q^{40} -9.63304 q^{41} +2.62489i q^{43} +4.42292i q^{44} -6.49971 q^{46} -8.97616i q^{47} +(3.44473 + 6.09375i) q^{49} +(3.05498 + 3.95817i) q^{50} +1.99638 q^{52} +12.0619 q^{53} +(-8.87618 - 4.36170i) q^{55} +(-2.28525 - 1.33328i) q^{56} +0.868528i q^{58} -5.08660 q^{59} +2.53442i q^{62} +1.00000 q^{64} +(-1.96875 + 4.00645i) q^{65} -9.54054i q^{67} +4.94340i q^{68} +(4.92933 - 3.27135i) q^{70} +4.38125i q^{71} +10.2589 q^{73} -6.08271i q^{74} +0.802373i q^{76} +(-5.89699 + 10.1075i) q^{77} -2.84201 q^{79} +(-0.986159 + 2.00686i) q^{80} +9.63304 q^{82} +3.21135i q^{83} +(-9.92072 - 4.87498i) q^{85} -2.62489i q^{86} -4.42292i q^{88} -17.7283 q^{89} +(4.56222 + 2.66173i) q^{91} +6.49971 q^{92} +8.97616i q^{94} +(-1.61025 - 0.791267i) q^{95} -11.1133 q^{97} +(-3.44473 - 6.09375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} - 6 q^{25} - 16 q^{32} - q^{35} - 8 q^{46} + 2 q^{49} + 6 q^{50} - 16 q^{53} + 16 q^{64} - 40 q^{65} + q^{70} - 14 q^{77} - 8 q^{79} - 44 q^{85} - 40 q^{91} + 8 q^{92} - 36 q^{95} - 2 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 - 6 * q^25 - 16 * q^32 - q^35 - 8 * q^46 + 2 * q^49 + 6 * q^50 - 16 * q^53 + 16 * q^64 - 40 * q^65 + q^70 - 14 * q^77 - 8 * q^79 - 44 * q^85 - 40 * q^91 + 8 * q^92 - 36 * q^95 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.986159	+	2.00686i	−0.441024	+	0.897495i
$5$	−0.986159	+	2.00686i	−0.441024	+	0.897495i
$6$		0			0
$7$	2.28525	+	1.33328i	0.863743	+	0.503932i
$7$	2.28525	+	1.33328i	0.863743	+	0.503932i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.986159	−	2.00686i	0.311851	−	0.634625i
$11$			4.42292i			1.33356i	0.745254	+	0.666780i	$0.232328\pi$
$11$			4.42292i			1.33356i	−0.745254	+	0.666780i	$0.767672\pi$
$12$		0			0
$13$	1.99638			0.553695			0.276848	−	0.960914i	$-0.410710\pi$
$13$	1.99638			0.553695			0.276848	+	0.960914i	$0.410710\pi$
$14$	−2.28525	−	1.33328i	−0.610759	−	0.356334i
$15$		0			0
$16$	1.00000			0.250000
$17$			4.94340i			1.19895i	0.800393	+	0.599475i	$0.204624\pi$
$17$			4.94340i			1.19895i	−0.800393	+	0.599475i	$0.795376\pi$
$18$		0			0
$19$			0.802373i			0.184077i	0.995755	+	0.0920384i	$0.0293383\pi$
$19$			0.802373i			0.184077i	−0.995755	+	0.0920384i	$0.970662\pi$
$20$	−0.986159	+	2.00686i	−0.220512	+	0.448748i
$21$		0			0
$22$		−	4.42292i		−	0.942970i
$23$	6.49971			1.35528			0.677642	−	0.735392i	$-0.263002\pi$
$23$	6.49971			1.35528			0.677642	+	0.735392i	$0.263002\pi$
$24$		0			0
$25$	−3.05498	−	3.95817i	−0.610996	−	0.791634i
$26$	−1.99638			−0.391522
$27$		0			0
$28$	2.28525	+	1.33328i	0.431872	+	0.251966i
$29$		−	0.868528i		−	0.161282i	−0.996743	−	0.0806408i	$-0.974303\pi$
$29$		−	0.868528i		−	0.161282i	0.996743	−	0.0806408i	$-0.0256967\pi$
$30$		0			0
$31$		−	2.53442i		−	0.455196i	−0.973755	−	0.227598i	$-0.926913\pi$
$31$		−	2.53442i		−	0.455196i	0.973755	−	0.227598i	$-0.0730872\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		−	4.94340i		−	0.847786i
$35$	−4.92933	+	3.27135i	−0.833208	+	0.552959i
$36$		0			0
$37$			6.08271i			0.999992i	0.866028	+	0.499996i	$0.166665\pi$
$37$			6.08271i			0.999992i	−0.866028	+	0.499996i	$0.833335\pi$
$38$		−	0.802373i		−	0.130162i
$39$		0			0
$40$	0.986159	−	2.00686i	0.155925	−	0.317313i
$41$	−9.63304			−1.50443			−0.752214	−	0.658919i	$-0.771014\pi$
$41$	−9.63304			−1.50443			−0.752214	+	0.658919i	$0.771014\pi$
$42$		0			0
$43$			2.62489i			0.400292i	0.979766	+	0.200146i	$0.0641416\pi$
$43$			2.62489i			0.400292i	−0.979766	+	0.200146i	$0.935858\pi$
$44$			4.42292i			0.666780i
$45$		0			0
$46$	−6.49971			−0.958330
$47$		−	8.97616i		−	1.30931i	−0.755929	−	0.654654i	$-0.772814\pi$
$47$		−	8.97616i		−	1.30931i	0.755929	−	0.654654i	$-0.227186\pi$
$48$		0			0
$49$	3.44473	+	6.09375i	0.492104	+	0.870536i
$50$	3.05498	+	3.95817i	0.432039	+	0.559770i
$51$		0			0
$52$	1.99638			0.276848
$53$	12.0619			1.65683			0.828417	−	0.560112i	$-0.189242\pi$
$53$	12.0619			1.65683			0.828417	+	0.560112i	$0.189242\pi$
$54$		0			0
$55$	−8.87618	−	4.36170i	−1.19686	−	0.588132i
$56$	−2.28525	−	1.33328i	−0.305379	−	0.178167i
$57$		0			0
$58$			0.868528i			0.114043i
$59$	−5.08660			−0.662219			−0.331109	−	0.943592i	$-0.607423\pi$
$59$	−5.08660			−0.662219			−0.331109	+	0.943592i	$0.607423\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$			2.53442i			0.321872i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.96875	+	4.00645i	−0.244193	+	0.496939i
$66$		0			0
$67$		−	9.54054i		−	1.16556i	−0.812629	−	0.582781i	$-0.801964\pi$
$67$		−	9.54054i		−	1.16556i	0.812629	−	0.582781i	$-0.198036\pi$
$68$			4.94340i			0.599475i
$69$		0			0
$70$	4.92933	−	3.27135i	0.589167	−	0.391001i
$71$			4.38125i			0.519959i	0.965614	+	0.259979i	$0.0837157\pi$
$71$			4.38125i			0.519959i	−0.965614	+	0.259979i	$0.916284\pi$
$72$		0			0
$73$	10.2589			1.20071			0.600357	−	0.799732i	$-0.295025\pi$
$73$	10.2589			1.20071			0.600357	+	0.799732i	$0.295025\pi$
$74$		−	6.08271i		−	0.707101i
$75$		0			0
$76$			0.802373i			0.0920384i
$77$	−5.89699	+	10.1075i	−0.672024	+	1.15185i
$78$		0			0
$79$	−2.84201			−0.319751			−0.159876	−	0.987137i	$-0.551109\pi$
$79$	−2.84201			−0.319751			−0.159876	+	0.987137i	$0.551109\pi$
$80$	−0.986159	+	2.00686i	−0.110256	+	0.224374i
$81$		0			0
$82$	9.63304			1.06379
$83$			3.21135i			0.352491i	0.984346	+	0.176246i	$0.0563953\pi$
$83$			3.21135i			0.352491i	−0.984346	+	0.176246i	$0.943605\pi$
$84$		0			0
$85$	−9.92072	−	4.87498i	−1.07605	−	0.528766i
$86$		−	2.62489i		−	0.283049i
$87$		0			0
$88$		−	4.42292i		−	0.471485i
$89$	−17.7283			−1.87920			−0.939599	−	0.342279i	$-0.888801\pi$
$89$	−17.7283			−1.87920			−0.939599	+	0.342279i	$0.888801\pi$
$90$		0			0
$91$	4.56222	+	2.66173i	0.478251	+	0.279025i
$92$	6.49971			0.677642
$93$		0			0
$94$			8.97616i			0.925820i
$95$	−1.61025	−	0.791267i	−0.165208	−	0.0811823i
$96$		0			0
$97$	−11.1133			−1.12839			−0.564193	−	0.825643i	$-0.690813\pi$
$97$	−11.1133			−1.12839			−0.564193	+	0.825643i	$0.690813\pi$
$98$	−3.44473	−	6.09375i	−0.347970	−	0.615562i
$99$		0			0
$100$	−3.05498	−	3.95817i	−0.305498	−	0.395817i
$101$	3.71609			0.369764			0.184882	−	0.982761i	$-0.440810\pi$
$101$	3.71609			0.369764			0.184882	+	0.982761i	$0.440810\pi$
$102$		0			0
$103$	−11.5813			−1.14114			−0.570570	−	0.821249i	$-0.693278\pi$
$103$	−11.5813			−1.14114			−0.570570	+	0.821249i	$0.693278\pi$
$104$	−1.99638			−0.195761
$105$		0			0
$106$	−12.0619			−1.17156
$107$	6.95197			0.672072			0.336036	−	0.941849i	$-0.390914\pi$
$107$	6.95197			0.672072			0.336036	+	0.941849i	$0.390914\pi$
$108$		0			0
$109$	14.5142			1.39021			0.695104	−	0.718910i	$-0.255358\pi$
$109$	14.5142			1.39021			0.695104	+	0.718910i	$0.255358\pi$
$110$	8.87618	+	4.36170i	0.846311	+	0.415872i
$111$		0			0
$112$	2.28525	+	1.33328i	0.215936	+	0.125983i
$113$	−18.5142			−1.74167			−0.870834	−	0.491577i	$-0.836421\pi$
$113$	−18.5142			−1.74167			−0.870834	+	0.491577i	$0.836421\pi$
$114$		0			0
$115$	−6.40975	+	13.0440i	−0.597712	+	1.21636i
$116$		−	0.868528i		−	0.0806408i
$117$		0			0
$118$	5.08660			0.468259
$119$	−6.59093	+	11.2969i	−0.604190	+	1.03559i
$120$		0			0
$121$	−8.56222			−0.778384
$122$		0			0
$123$		0			0
$124$		−	2.53442i		−	0.227598i
$125$	10.9562	−	2.22754i	0.979951	−	0.199237i
$126$		0			0
$127$			14.0184i			1.24393i	0.783046	+	0.621964i	$0.213665\pi$
$127$			14.0184i			1.24393i	−0.783046	+	0.621964i	$0.786335\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	1.96875	−	4.00645i	0.172670	−	0.351389i
$131$	−5.61623			−0.490692			−0.245346	−	0.969436i	$-0.578902\pi$
$131$	−5.61623			−0.490692			−0.245346	+	0.969436i	$0.578902\pi$
$132$		0			0
$133$	−1.06979	+	1.83362i	−0.0927623	+	0.158995i
$134$			9.54054i			0.824177i
$135$		0			0
$136$		−	4.94340i		−	0.423893i
$137$	10.4517			0.892947			0.446474	−	0.894797i	$-0.352680\pi$
$137$	10.4517			0.892947			0.446474	+	0.894797i	$0.352680\pi$
$138$		0			0
$139$		−	3.61044i		−	0.306234i	−0.988208	−	0.153117i	$-0.951069\pi$
$139$		−	3.61044i		−	0.306234i	0.988208	−	0.153117i	$-0.0489311\pi$
$140$	−4.92933	+	3.27135i	−0.416604	+	0.276480i
$141$		0			0
$142$		−	4.38125i		−	0.367666i
$143$			8.82982i			0.738386i
$144$		0			0
$145$	1.74302	+	0.856507i	0.144750	+	0.0711290i
$146$	−10.2589			−0.849033
$147$		0			0
$148$			6.08271i			0.499996i
$149$		−	20.9503i		−	1.71631i	−0.513387	−	0.858157i	$-0.671609\pi$
$149$		−	20.9503i		−	1.71631i	0.513387	−	0.858157i	$-0.328391\pi$
$150$		0			0
$151$	15.9514			1.29811			0.649053	−	0.760743i	$-0.275165\pi$
$151$	15.9514			1.29811			0.649053	+	0.760743i	$0.275165\pi$
$152$		−	0.802373i		−	0.0650810i
$153$		0			0
$154$	5.89699	−	10.1075i	0.475193	−	0.814484i
$155$	5.08623	+	2.49934i	0.408536	+	0.200752i
$156$		0			0
$157$	−2.48842			−0.198597			−0.0992987	−	0.995058i	$-0.531660\pi$
$157$	−2.48842			−0.198597			−0.0992987	+	0.995058i	$0.531660\pi$
$158$	2.84201			0.226098
$159$		0			0
$160$	0.986159	−	2.00686i	0.0779627	−	0.158656i
$161$	14.8535	+	8.66593i	1.17062	+	0.682971i
$162$		0			0
$163$			24.5596i			1.92365i	0.273657	+	0.961827i	$0.411767\pi$
$163$			24.5596i			1.92365i	−0.273657	+	0.961827i	$0.588233\pi$
$164$	−9.63304			−0.752214
$165$		0			0
$166$		−	3.21135i		−	0.249249i
$167$			14.5965i			1.12951i	0.825259	+	0.564755i	$0.191029\pi$
$167$			14.5965i			1.12951i	−0.825259	+	0.564755i	$0.808971\pi$
$168$		0			0
$169$	−9.01448			−0.693421
$170$	9.92072	+	4.87498i	0.760884	+	0.373894i
$171$		0			0
$172$			2.62489i			0.200146i
$173$			16.0108i			1.21728i	0.793448	+	0.608638i	$0.208284\pi$
$173$			16.0108i			1.21728i	−0.793448	+	0.608638i	$0.791716\pi$
$174$		0			0
$175$	−1.70405	−	13.1185i	−0.128814	−	0.991669i
$176$			4.42292i			0.333390i
$177$		0			0
$178$	17.7283			1.32879
$179$		−	12.1593i		−	0.908832i	−0.890789	−	0.454416i	$-0.849848\pi$
$179$		−	12.1593i		−	0.908832i	0.890789	−	0.454416i	$-0.150152\pi$
$180$		0			0
$181$		−	6.18898i		−	0.460023i	−0.973188	−	0.230012i	$-0.926124\pi$
$181$		−	6.18898i		−	0.460023i	0.973188	−	0.230012i	$-0.0738765\pi$
$182$	−4.56222	−	2.66173i	−0.338174	−	0.197300i
$183$		0			0
$184$	−6.49971			−0.479165
$185$	−12.2072	−	5.99852i	−0.897488	−	0.441020i
$186$		0			0
$187$	−21.8643			−1.59887
$188$		−	8.97616i		−	0.654654i
$189$		0			0
$190$	1.61025	+	0.791267i	0.116820	+	0.0574045i
$191$			11.5897i			0.838598i	0.907848	+	0.419299i	$0.137724\pi$
$191$			11.5897i			0.838598i	−0.907848	+	0.419299i	$0.862276\pi$
$192$		0			0
$193$			25.7269i			1.85187i	0.377688	+	0.925933i	$0.376719\pi$
$193$			25.7269i			1.85187i	−0.377688	+	0.925933i	$0.623281\pi$
$194$	11.1133			0.797890
$195$		0			0
$196$	3.44473	+	6.09375i	0.246052	+	0.435268i
$197$	−8.34172			−0.594323			−0.297161	−	0.954827i	$-0.596040\pi$
$197$	−8.34172			−0.594323			−0.297161	+	0.954827i	$0.596040\pi$
$198$		0			0
$199$			12.2326i			0.867148i	0.901118	+	0.433574i	$0.142748\pi$
$199$			12.2326i			0.867148i	−0.901118	+	0.433574i	$0.857252\pi$
$200$	3.05498	+	3.95817i	0.216020	+	0.279885i
$201$		0			0
$202$	−3.71609			−0.261463
$203$	1.15799	−	1.98480i	0.0812750	−	0.139306i
$204$		0			0
$205$	9.49971	−	19.3322i	0.663489	−	1.35022i
$206$	11.5813			0.806907
$207$		0			0
$208$	1.99638			0.138424
$209$	−3.54883			−0.245478
$210$		0			0
$211$	3.65770			0.251807			0.125903	−	0.992043i	$-0.459817\pi$
$211$	3.65770			0.251807			0.125903	+	0.992043i	$0.459817\pi$
$212$	12.0619			0.828417
$213$		0			0
$214$	−6.95197			−0.475227
$215$	−5.26779	−	2.58856i	−0.359260	−	0.176538i
$216$		0			0
$217$	3.37910	−	5.79179i	0.229388	−	0.393172i
$218$	−14.5142			−0.983025
$219$		0			0
$220$	−8.87618	−	4.36170i	−0.598432	−	0.294066i
$221$			9.86889i			0.663853i
$222$		0			0
$223$	−17.9662			−1.20311			−0.601554	−	0.798832i	$-0.705452\pi$
$223$	−17.9662			−1.20311			−0.601554	+	0.798832i	$0.705452\pi$
$224$	−2.28525	−	1.33328i	−0.152690	−	0.0890835i
$225$		0			0
$226$	18.5142			1.23155
$227$		−	9.94995i		−	0.660401i	−0.943911	−	0.330201i	$-0.892884\pi$
$227$		−	9.94995i		−	0.660401i	0.943911	−	0.330201i	$-0.107116\pi$
$228$		0			0
$229$		−	5.06885i		−	0.334959i	−0.985876	−	0.167479i	$-0.946437\pi$
$229$		−	5.06885i		−	0.334959i	0.985876	−	0.167479i	$-0.0535628\pi$
$230$	6.40975	−	13.0440i	0.422646	−	0.860097i
$231$		0			0
$232$			0.868528i			0.0570217i
$233$	−3.70573			−0.242771			−0.121385	−	0.992605i	$-0.538734\pi$
$233$	−3.70573			−0.242771			−0.121385	+	0.992605i	$0.538734\pi$
$234$		0			0
$235$	18.0139	+	8.85192i	1.17510	+	0.577436i
$236$	−5.08660			−0.331109
$237$		0			0
$238$	6.59093	−	11.2969i	0.427227	−	0.732269i
$239$		−	19.5121i		−	1.26213i	−0.775729	−	0.631066i	$-0.782618\pi$
$239$		−	19.5121i		−	1.26213i	0.775729	−	0.631066i	$-0.217382\pi$
$240$		0			0
$241$			10.3723i			0.668136i	0.942549	+	0.334068i	$0.108422\pi$
$241$			10.3723i			0.668136i	−0.942549	+	0.334068i	$0.891578\pi$
$242$	8.56222			0.550400
$243$		0			0
$244$		0			0
$245$	−15.6264	+	0.903683i	−0.998332	+	0.0577342i
$246$		0			0
$247$			1.60184i			0.101923i
$248$			2.53442i			0.160936i
$249$		0			0
$250$	−10.9562	+	2.22754i	−0.692930	+	0.140882i
$251$	3.00867			0.189906			0.0949528	−	0.995482i	$-0.469730\pi$
$251$	3.00867			0.189906			0.0949528	+	0.995482i	$0.469730\pi$
$252$		0			0
$253$			28.7477i			1.80735i
$254$		−	14.0184i		−	0.879590i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	16.8150i		−	1.04889i	−0.851444	−	0.524446i	$-0.824273\pi$
$257$		−	16.8150i		−	1.04889i	0.851444	−	0.524446i	$-0.175727\pi$
$258$		0			0
$259$	−8.10996	+	13.9005i	−0.503928	+	0.863736i
$260$	−1.96875	+	4.00645i	−0.122096	+	0.248470i
$261$		0			0
$262$	5.61623			0.346972
$263$	10.6247			0.655149			0.327574	−	0.944825i	$-0.393769\pi$
$263$	10.6247			0.655149			0.327574	+	0.944825i	$0.393769\pi$
$264$		0			0
$265$	−11.8950	+	24.2066i	−0.730703	+	1.48700i
$266$	1.06979	−	1.83362i	0.0655929	−	0.112427i
$267$		0			0
$268$		−	9.54054i		−	0.582781i
$269$	−10.4408			−0.636589			−0.318295	−	0.947992i	$-0.603110\pi$
$269$	−10.4408			−0.636589			−0.318295	+	0.947992i	$0.603110\pi$
$270$		0			0
$271$			10.3733i			0.630131i	0.949070	+	0.315066i	$0.102027\pi$
$271$			10.3733i			0.630131i	−0.949070	+	0.315066i	$0.897973\pi$
$272$			4.94340i			0.299738i
$273$		0			0
$274$	−10.4517			−0.631409
$275$	17.5067	−	13.5119i	1.05569	−	0.814800i
$276$		0			0
$277$		−	13.6646i		−	0.821028i	−0.911854	−	0.410514i	$-0.865349\pi$
$277$		−	13.6646i		−	0.821028i	0.911854	−	0.410514i	$-0.134651\pi$
$278$			3.61044i			0.216540i
$279$		0			0
$280$	4.92933	−	3.27135i	0.294584	−	0.195501i
$281$			14.6521i			0.874070i	0.899445	+	0.437035i	$0.143971\pi$
$281$			14.6521i			0.874070i	−0.899445	+	0.437035i	$0.856029\pi$
$282$		0			0
$283$	2.74253			0.163027			0.0815133	−	0.996672i	$-0.474025\pi$
$283$	2.74253			0.163027			0.0815133	+	0.996672i	$0.474025\pi$
$284$			4.38125i			0.259979i
$285$		0			0
$286$		−	8.82982i		−	0.522118i
$287$	−22.0139	−	12.8435i	−1.29944	−	0.758130i
$288$		0			0
$289$	−7.43720			−0.437482
$290$	−1.74302	−	0.856507i	−0.102353	−	0.0502958i
$291$		0			0
$292$	10.2589			0.600357
$293$		−	16.8150i		−	0.982343i	−0.871063	−	0.491171i	$-0.836569\pi$
$293$		−	16.8150i		−	0.982343i	0.871063	−	0.491171i	$-0.163431\pi$
$294$		0			0
$295$	5.01620	−	10.2081i	0.292054	−	0.594338i
$296$		−	6.08271i		−	0.353551i
$297$		0			0
$298$			20.9503i			1.21362i
$299$	12.9759			0.750414
$300$		0			0
$301$	−3.49971	+	5.99852i	−0.201720	+	0.345749i
$302$	−15.9514			−0.917899
$303$		0			0
$304$			0.802373i			0.0460192i
$305$		0			0
$306$		0			0
$307$	8.68239			0.495530			0.247765	−	0.968820i	$-0.420304\pi$
$307$	8.68239			0.495530			0.247765	+	0.968820i	$0.420304\pi$
$308$	−5.89699	+	10.1075i	−0.336012	+	0.575927i
$309$		0			0
$310$	−5.08623	−	2.49934i	−0.288879	−	0.141953i
$311$	12.8195			0.726927			0.363464	−	0.931608i	$-0.381594\pi$
$311$	12.8195			0.726927			0.363464	+	0.931608i	$0.381594\pi$
$312$		0			0
$313$	30.0317			1.69749			0.848746	−	0.528800i	$-0.177358\pi$
$313$	30.0317			1.69749			0.848746	+	0.528800i	$0.177358\pi$
$314$	2.48842			0.140430
$315$		0			0
$316$	−2.84201			−0.159876
$317$	28.2457			1.58643			0.793217	−	0.608939i	$-0.208405\pi$
$317$	28.2457			1.58643			0.793217	+	0.608939i	$0.208405\pi$
$318$		0			0
$319$	3.84143			0.215079
$320$	−0.986159	+	2.00686i	−0.0551280	+	0.112187i
$321$		0			0
$322$	−14.8535	−	8.66593i	−0.827751	−	0.482934i
$323$	−3.96645			−0.220699
$324$		0			0
$325$	−6.09889	−	7.90200i	−0.338306	−	0.438324i
$326$		−	24.5596i		−	1.36023i
$327$		0			0
$328$	9.63304			0.531896
$329$	11.9677	−	20.5128i	0.659802	−	1.13091i
$330$		0			0
$331$	−26.4662			−1.45471			−0.727356	−	0.686261i	$-0.759251\pi$
$331$	−26.4662			−1.45471			−0.727356	+	0.686261i	$0.759251\pi$
$332$			3.21135i			0.176246i
$333$		0			0
$334$		−	14.5965i		−	0.798684i
$335$	19.1465	+	9.40849i	1.04609	+	0.514041i
$336$		0			0
$337$		−	17.8106i		−	0.970206i	−0.874457	−	0.485103i	$-0.838782\pi$
$337$		−	17.8106i		−	0.970206i	0.874457	−	0.485103i	$-0.161218\pi$
$338$	9.01448			0.490323
$339$		0			0
$340$	−9.92072	−	4.87498i	−0.538026	−	0.264383i
$341$	11.2096			0.607031
$342$		0			0
$343$	−0.252610	+	18.5185i	−0.0136397	+	0.999907i
$344$		−	2.62489i		−	0.141525i
$345$		0			0
$346$		−	16.0108i		−	0.860744i
$347$	−12.3299			−0.661903			−0.330951	−	0.943648i	$-0.607370\pi$
$347$	−12.3299			−0.661903			−0.330951	+	0.943648i	$0.607370\pi$
$348$		0			0
$349$		−	24.8216i		−	1.32867i	−0.747436	−	0.664334i	$-0.768715\pi$
$349$		−	24.8216i		−	1.32867i	0.747436	−	0.664334i	$-0.231285\pi$
$350$	1.70405	+	13.1185i	0.0910851	+	0.701216i
$351$		0			0
$352$		−	4.42292i		−	0.235742i
$353$		−	26.0671i		−	1.38741i	−0.720258	−	0.693707i	$-0.755976\pi$
$353$		−	26.0671i		−	1.38741i	0.720258	−	0.693707i	$-0.244024\pi$
$354$		0			0
$355$	−8.79256	−	4.32061i	−0.466660	−	0.229314i
$356$	−17.7283			−0.939599
$357$		0			0
$358$			12.1593i			0.642642i
$359$		−	3.13662i		−	0.165544i	−0.996568	−	0.0827722i	$-0.973623\pi$
$359$		−	3.13662i		−	0.165544i	0.996568	−	0.0827722i	$-0.0263774\pi$
$360$		0			0
$361$	18.3562			0.966116
$362$			6.18898i			0.325286i
$363$		0			0
$364$	4.56222	+	2.66173i	0.239125	+	0.139513i
$365$	−10.1169	+	20.5882i	−0.529543	+	1.07764i
$366$		0			0
$367$	−26.6408			−1.39064			−0.695318	−	0.718702i	$-0.744736\pi$
$367$	−26.6408			−1.39064			−0.695318	+	0.718702i	$0.744736\pi$
$368$	6.49971			0.338821
$369$		0			0
$370$	12.2072	+	5.99852i	0.634620	+	0.311848i
$371$	27.5645	+	16.0819i	1.43108	+	0.834932i
$372$		0			0
$373$		−	6.20467i		−	0.321265i	−0.987014	−	0.160633i	$-0.948647\pi$
$373$		−	6.20467i		−	0.321265i	0.987014	−	0.160633i	$-0.0513535\pi$
$374$	21.8643			1.13057
$375$		0			0
$376$			8.97616i			0.462910i
$377$		−	1.73391i		−	0.0893009i
$378$		0			0
$379$	−16.9994			−0.873202			−0.436601	−	0.899655i	$-0.643818\pi$
$379$	−16.9994			−0.873202			−0.436601	+	0.899655i	$0.643818\pi$
$380$	−1.61025	−	0.791267i	−0.0826041	−	0.0405911i
$381$		0			0
$382$		−	11.5897i		−	0.592979i
$383$			2.36486i			0.120839i	0.998173	+	0.0604194i	$0.0192438\pi$
$383$			2.36486i			0.120839i	−0.998173	+	0.0604194i	$0.980756\pi$
$384$		0			0
$385$	−14.4689	−	21.8020i	−0.737405	−	1.11113i
$386$		−	25.7269i		−	1.30947i
$387$		0			0
$388$	−11.1133			−0.564193
$389$		−	4.51340i		−	0.228839i	−0.993433	−	0.114419i	$-0.963499\pi$
$389$		−	4.51340i		−	0.228839i	0.993433	−	0.114419i	$-0.0365007\pi$
$390$		0			0
$391$			32.1307i			1.62492i
$392$	−3.44473	−	6.09375i	−0.173985	−	0.307781i
$393$		0			0
$394$	8.34172			0.420250
$395$	2.80267	−	5.70352i	0.141018	−	0.286975i
$396$		0			0
$397$	−9.28535			−0.466018			−0.233009	−	0.972475i	$-0.574857\pi$
$397$	−9.28535			−0.466018			−0.233009	+	0.972475i	$0.574857\pi$
$398$		−	12.2326i		−	0.613166i
$399$		0			0
$400$	−3.05498	−	3.95817i	−0.152749	−	0.197908i
$401$		−	11.9276i		−	0.595634i	−0.954623	−	0.297817i	$-0.903741\pi$
$401$		−	11.9276i		−	0.595634i	0.954623	−	0.297817i	$-0.0962586\pi$
$402$		0			0
$403$		−	5.05966i		−	0.252040i
$404$	3.71609			0.184882
$405$		0			0
$406$	−1.15799	+	1.98480i	−0.0574701	+	0.0985041i
$407$	−26.9034			−1.33355
$408$		0			0
$409$		−	24.2728i		−	1.20021i	−0.799920	−	0.600106i	$-0.795125\pi$
$409$		−	24.2728i		−	1.20021i	0.799920	−	0.600106i	$-0.204875\pi$
$410$	−9.49971	+	19.3322i	−0.469157	+	0.954748i
$411$		0			0
$412$	−11.5813			−0.570570
$413$	−11.6241	−	6.78186i	−0.571987	−	0.333714i
$414$		0			0
$415$	−6.44473	−	3.16690i	−0.316359	−	0.155457i
$416$	−1.99638			−0.0978804
$417$		0			0
$418$	3.54883			0.173579
$419$	36.4542			1.78091			0.890453	−	0.455076i	$-0.150388\pi$
$419$	36.4542			1.78091			0.890453	+	0.455076i	$0.150388\pi$
$420$		0			0
$421$	−24.2306			−1.18093			−0.590464	−	0.807064i	$-0.701055\pi$
$421$	−24.2306			−1.18093			−0.590464	+	0.807064i	$0.701055\pi$
$422$	−3.65770			−0.178054
$423$		0			0
$424$	−12.0619			−0.585779
$425$	19.5668	−	15.1020i	0.949130	−	0.732554i
$426$		0			0
$427$		0			0
$428$	6.95197			0.336036
$429$		0			0
$430$	5.26779	+	2.58856i	0.254035	+	0.124831i
$431$		−	30.8639i		−	1.48666i	−0.668925	−	0.743330i	$-0.733245\pi$
$431$		−	30.8639i		−	1.48666i	0.668925	−	0.743330i	$-0.266755\pi$
$432$		0			0
$433$	40.5673			1.94954			0.974769	−	0.223214i	$-0.0716548\pi$
$433$	40.5673			1.94954			0.974769	+	0.223214i	$0.0716548\pi$
$434$	−3.37910	+	5.79179i	−0.162202	+	0.278015i
$435$		0			0
$436$	14.5142			0.695104
$437$			5.21519i			0.249476i
$438$		0			0
$439$			19.0325i			0.908373i	0.890907	+	0.454186i	$0.150070\pi$
$439$			19.0325i			0.908373i	−0.890907	+	0.454186i	$0.849930\pi$
$440$	8.87618	+	4.36170i	0.423155	+	0.207936i
$441$		0			0
$442$		−	9.86889i		−	0.469415i
$443$	38.6499			1.83631			0.918156	−	0.396220i	$-0.129678\pi$
$443$	38.6499			1.83631			0.918156	+	0.396220i	$0.129678\pi$
$444$		0			0
$445$	17.4829	−	35.5782i	0.828771	−	1.68657i
$446$	17.9662			0.850726
$447$		0			0
$448$	2.28525	+	1.33328i	0.107968	+	0.0629915i
$449$		−	1.93019i		−	0.0910911i	−0.998962	−	0.0455456i	$-0.985497\pi$
$449$		−	1.93019i		−	0.0910911i	0.998962	−	0.0455456i	$-0.0145026\pi$
$450$		0			0
$451$		−	42.6062i		−	2.00625i
$452$	−18.5142			−0.870834
$453$		0			0
$454$			9.94995i			0.466974i
$455$	−9.84079	+	6.53085i	−0.461344	+	0.306171i
$456$		0			0
$457$		−	9.72759i		−	0.455038i	−0.973774	−	0.227519i	$-0.926939\pi$
$457$		−	9.72759i		−	0.455038i	0.973774	−	0.227519i	$-0.0730613\pi$
$458$			5.06885i			0.236852i
$459$		0			0
$460$	−6.40975	+	13.0440i	−0.298856	+	0.608180i
$461$	6.96384			0.324338			0.162169	−	0.986763i	$-0.448151\pi$
$461$	6.96384			0.324338			0.162169	+	0.986763i	$0.448151\pi$
$462$		0			0
$463$			29.1014i			1.35246i	0.736691	+	0.676229i	$0.236387\pi$
$463$			29.1014i			1.35246i	−0.736691	+	0.676229i	$0.763613\pi$
$464$		−	0.868528i		−	0.0403204i
$465$		0			0
$466$	3.70573			0.171665
$467$		−	8.09160i		−	0.374434i	−0.982319	−	0.187217i	$-0.940053\pi$
$467$		−	8.09160i		−	0.374434i	0.982319	−	0.187217i	$-0.0599468\pi$
$468$		0			0
$469$	12.7202	−	21.8025i	0.587365	−	1.00675i
$470$	−18.0139	−	8.85192i	−0.830919	−	0.408309i
$471$		0			0
$472$	5.08660			0.234130
$473$	−11.6097			−0.533813
$474$		0			0
$475$	3.17593	−	2.45123i	0.145721	−	0.112470i
$476$	−6.59093	+	11.2969i	−0.302095	+	0.517793i
$477$		0			0
$478$			19.5121i			0.892462i
$479$	−6.95331			−0.317705			−0.158852	−	0.987302i	$-0.550779\pi$
$479$	−6.95331			−0.317705			−0.158852	+	0.987302i	$0.550779\pi$
$480$		0			0
$481$			12.1434i			0.553691i
$482$		−	10.3723i		−	0.472444i
$483$		0			0
$484$	−8.56222			−0.389192
$485$	10.9595	−	22.3029i	0.497645	−	1.01272i
$486$		0			0
$487$		−	12.8957i		−	0.584361i	−0.956363	−	0.292180i	$-0.905619\pi$
$487$		−	12.8957i		−	0.584361i	0.956363	−	0.292180i	$-0.0943808\pi$
$488$		0			0
$489$		0			0
$490$	15.6264	−	0.903683i	0.705927	−	0.0408242i
$491$			28.7345i			1.29677i	0.761313	+	0.648384i	$0.224555\pi$
$491$			28.7345i			1.29677i	−0.761313	+	0.648384i	$0.775445\pi$
$492$		0			0
$493$	4.29348			0.193369
$494$		−	1.60184i		−	0.0720701i
$495$		0			0
$496$		−	2.53442i		−	0.113799i
$497$	−5.84143	+	10.0122i	−0.262024	+	0.449111i
$498$		0			0
$499$	7.09548			0.317637			0.158819	−	0.987308i	$-0.449231\pi$
$499$	7.09548			0.317637			0.158819	+	0.987308i	$0.449231\pi$
$500$	10.9562	−	2.22754i	0.489976	−	0.0996185i
$501$		0			0
$502$	−3.00867			−0.134283
$503$			1.68879i			0.0752995i	0.999291	+	0.0376498i	$0.0119871\pi$
$503$			1.68879i			0.0752995i	−0.999291	+	0.0376498i	$0.988013\pi$
$504$		0			0
$505$	−3.66465	+	7.45767i	−0.163075	+	0.331862i
$506$		−	28.7477i		−	1.27799i
$507$		0			0
$508$			14.0184i			0.621964i
$509$	12.2688			0.543805			0.271903	−	0.962325i	$-0.412347\pi$
$509$	12.2688			0.543805			0.271903	+	0.962325i	$0.412347\pi$
$510$		0			0
$511$	23.4442	+	13.6780i	1.03711	+	0.605079i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			16.8150i			0.741678i
$515$	11.4210	−	23.2421i	0.503270	−	1.02417i
$516$		0			0
$517$	39.7008			1.74604
$518$	8.10996	−	13.9005i	0.356331	−	0.610754i
$519$		0			0
$520$	1.96875	−	4.00645i	0.0863352	−	0.175694i
$521$	43.9477			1.92538			0.962692	−	0.270600i	$-0.0872222\pi$
$521$	43.9477			1.92538			0.962692	+	0.270600i	$0.0872222\pi$
$522$		0			0
$523$	41.6371			1.82066			0.910331	−	0.413881i	$-0.135827\pi$
$523$	41.6371			1.82066			0.910331	+	0.413881i	$0.135827\pi$
$524$	−5.61623			−0.245346
$525$		0			0
$526$	−10.6247			−0.463260
$527$	12.5287			0.545757
$528$		0			0
$529$	19.2462			0.836793
$530$	11.8950	−	24.2066i	0.516685	−	1.05147i
$531$		0			0
$532$	−1.06979	+	1.83362i	−0.0463812	+	0.0794976i
$533$	−19.2312			−0.832995
$534$		0			0
$535$	−6.85575	+	13.9516i	−0.296400	+	0.603182i
$536$			9.54054i			0.412089i
$537$		0			0
$538$	10.4408			0.450137
$539$	−26.9522	+	15.2358i	−1.16091	+	0.656251i
$540$		0			0
$541$	−4.51419			−0.194080			−0.0970401	−	0.995280i	$-0.530938\pi$
$541$	−4.51419			−0.194080			−0.0970401	+	0.995280i	$0.530938\pi$
$542$		−	10.3733i		−	0.445570i
$543$		0			0
$544$		−	4.94340i		−	0.211947i
$545$	−14.3133	+	29.1280i	−0.613114	+	1.24770i
$546$		0			0
$547$		−	15.7493i		−	0.673393i	−0.941613	−	0.336696i	$-0.890690\pi$
$547$		−	15.7493i		−	0.673393i	0.941613	−	0.336696i	$-0.109310\pi$
$548$	10.4517			0.446474
$549$		0			0
$550$	−17.5067	+	13.5119i	−0.746487	+	0.576151i
$551$	0.696883			0.0296882
$552$		0			0
$553$	−6.49470	−	3.78919i	−0.276183	−	0.161133i
$554$			13.6646i			0.580554i
$555$		0			0
$556$		−	3.61044i		−	0.153117i
$557$	20.6097			0.873260			0.436630	−	0.899641i	$-0.356172\pi$
$557$	20.6097			0.873260			0.436630	+	0.899641i	$0.356172\pi$
$558$		0			0
$559$			5.24027i			0.221640i
$560$	−4.92933	+	3.27135i	−0.208302	+	0.138240i
$561$		0			0
$562$		−	14.6521i		−	0.618061i
$563$		−	2.83129i		−	0.119325i	−0.998219	−	0.0596623i	$-0.980998\pi$
$563$		−	2.83129i		−	0.119325i	0.998219	−	0.0596623i	$-0.0190024\pi$
$564$		0			0
$565$	18.2579	−	37.1554i	0.768117	−	1.56314i
$566$	−2.74253			−0.115277
$567$		0			0
$568$		−	4.38125i		−	0.183833i
$569$		−	33.8430i		−	1.41877i	−0.704821	−	0.709385i	$-0.748973\pi$
$569$		−	33.8430i		−	1.41877i	0.704821	−	0.709385i	$-0.251027\pi$
$570$		0			0
$571$	1.24682			0.0521776			0.0260888	−	0.999660i	$-0.491695\pi$
$571$	1.24682			0.0521776			0.0260888	+	0.999660i	$0.491695\pi$
$572$			8.82982i			0.369193i
$573$		0			0
$574$	22.0139	+	12.8435i	0.918842	+	0.536079i
$575$	−19.8565	−	25.7269i	−0.828073	−	1.07289i
$576$		0			0
$577$	11.0276			0.459086			0.229543	−	0.973299i	$-0.426277\pi$
$577$	11.0276			0.459086			0.229543	+	0.973299i	$0.426277\pi$
$578$	7.43720			0.309347
$579$		0			0
$580$	1.74302	+	0.856507i	0.0723748	+	0.0355645i
$581$	−4.28163	+	7.33873i	−0.177632	+	0.304462i
$582$		0			0
$583$			53.3489i			2.20949i
$584$	−10.2589			−0.424516
$585$		0			0
$586$			16.8150i			0.694621i
$587$		−	32.9312i		−	1.35922i	−0.733576	−	0.679608i	$-0.762150\pi$
$587$		−	32.9312i		−	1.35922i	0.733576	−	0.679608i	$-0.237850\pi$
$588$		0			0
$589$	2.03355			0.0837910
$590$	−5.01620	+	10.2081i	−0.206514	+	0.420261i
$591$		0			0
$592$			6.08271i			0.249998i
$593$		−	9.75849i		−	0.400733i	−0.979721	−	0.200367i	$-0.935787\pi$
$593$		−	9.75849i		−	0.400733i	0.979721	−	0.200367i	$-0.0642133\pi$
$594$		0			0
$595$	−16.1716	−	24.3676i	−0.662971	−	0.998975i
$596$		−	20.9503i		−	0.858157i
$597$		0			0
$598$	−12.9759			−0.530623
$599$		−	12.4704i		−	0.509525i	−0.967004	−	0.254762i	$-0.918003\pi$
$599$		−	12.4704i		−	0.509525i	0.967004	−	0.254762i	$-0.0819972\pi$
$600$		0			0
$601$		−	37.8365i		−	1.54338i	−0.635997	−	0.771692i	$-0.719411\pi$
$601$		−	37.8365i		−	1.54338i	0.635997	−	0.771692i	$-0.280589\pi$
$602$	3.49971	−	5.99852i	0.142638	−	0.244482i
$603$		0			0
$604$	15.9514			0.649053
$605$	8.44371	−	17.1832i	0.343286	−	0.698596i
$606$		0			0
$607$	−13.8652			−0.562772			−0.281386	−	0.959595i	$-0.590794\pi$
$607$	−13.8652			−0.562772			−0.281386	+	0.959595i	$0.590794\pi$
$608$		−	0.802373i		−	0.0325405i
$609$		0			0
$610$		0			0
$611$		−	17.9198i		−	0.724957i
$612$		0			0
$613$		−	34.2028i		−	1.38144i	−0.723124	−	0.690718i	$-0.757294\pi$
$613$		−	34.2028i		−	1.38144i	0.723124	−	0.690718i	$-0.242706\pi$
$614$	−8.68239			−0.350393
$615$		0			0
$616$	5.89699	−	10.1075i	0.237596	−	0.407242i
$617$	4.19096			0.168722			0.0843609	−	0.996435i	$-0.473115\pi$
$617$	4.19096			0.168722			0.0843609	+	0.996435i	$0.473115\pi$
$618$		0			0
$619$			40.2376i			1.61729i	0.588300	+	0.808643i	$0.299797\pi$
$619$			40.2376i			1.61729i	−0.588300	+	0.808643i	$0.700203\pi$
$620$	5.08623	+	2.49934i	0.204268	+	0.100376i
$621$		0			0
$622$	−12.8195			−0.514015
$623$	−40.5136	−	23.6368i	−1.62314	−	0.946988i
$624$		0			0
$625$	−6.33419	+	24.1843i	−0.253368	+	0.967370i
$626$	−30.0317			−1.20031
$627$		0			0
$628$	−2.48842			−0.0992987
$629$	−30.0693			−1.19894
$630$		0			0
$631$	1.79398			0.0714172			0.0357086	−	0.999362i	$-0.488631\pi$
$631$	1.79398			0.0714172			0.0357086	+	0.999362i	$0.488631\pi$
$632$	2.84201			0.113049
$633$		0			0
$634$	−28.2457			−1.12178
$635$	−28.1329	−	13.8243i	−1.11642	−	0.548602i
$636$		0			0
$637$	6.87698	+	12.1654i	0.272476	+	0.482012i
$638$	−3.84143			−0.152084
$639$		0			0
$640$	0.986159	−	2.00686i	0.0389814	−	0.0793281i
$641$			22.1085i			0.873234i	0.899647	+	0.436617i	$0.143823\pi$
$641$			22.1085i			0.873234i	−0.899647	+	0.436617i	$0.856177\pi$
$642$		0			0
$643$	12.2925			0.484770			0.242385	−	0.970180i	$-0.422070\pi$
$643$	12.2925			0.484770			0.242385	+	0.970180i	$0.422070\pi$
$644$	14.8535	+	8.66593i	0.585308	+	0.341486i
$645$		0			0
$646$	3.96645			0.156058
$647$			41.3405i			1.62526i	0.582777	+	0.812632i	$0.301966\pi$
$647$			41.3405i			1.62526i	−0.582777	+	0.812632i	$0.698034\pi$
$648$		0			0
$649$		−	22.4976i		−	0.883109i
$650$	6.09889	+	7.90200i	0.239218	+	0.309942i
$651$		0			0
$652$			24.5596i			0.961827i
$653$	48.4175			1.89473			0.947363	−	0.320163i	$-0.103738\pi$
$653$	48.4175			1.89473			0.947363	+	0.320163i	$0.103738\pi$
$654$		0			0
$655$	5.53849	−	11.2710i	0.216407	−	0.440394i
$656$	−9.63304			−0.376107
$657$		0			0
$658$	−11.9677	+	20.5128i	−0.466551	+	0.799671i
$659$			49.1059i			1.91290i	0.291903	+	0.956448i	$0.405711\pi$
$659$			49.1059i			1.91290i	−0.291903	+	0.956448i	$0.594289\pi$
$660$		0			0
$661$		−	48.5857i		−	1.88976i	−0.327413	−	0.944881i	$-0.606177\pi$
$661$		−	48.5857i		−	1.88976i	0.327413	−	0.944881i	$-0.393823\pi$
$662$	26.4662			1.02864
$663$		0			0
$664$		−	3.21135i		−	0.124625i
$665$	−2.62484	−	3.95516i	−0.101787	−	0.153374i
$666$		0			0
$667$		−	5.64518i		−	0.218582i
$668$			14.5965i			0.564755i
$669$		0			0
$670$	−19.1465	−	9.40849i	−0.739695	−	0.363482i
$671$		0			0
$672$		0			0
$673$		−	11.3935i		−	0.439186i	−0.975592	−	0.219593i	$-0.929527\pi$
$673$		−	11.3935i		−	0.439186i	0.975592	−	0.219593i	$-0.0704729\pi$
$674$			17.8106i			0.686039i
$675$		0			0
$676$	−9.01448			−0.346711
$677$			24.7141i			0.949841i	0.880029	+	0.474921i	$0.157523\pi$
$677$			24.7141i			0.949841i	−0.880029	+	0.474921i	$0.842477\pi$
$678$		0			0
$679$	−25.3967	−	14.8172i	−0.974636	−	0.568630i
$680$	9.92072	+	4.87498i	0.380442	+	0.186947i
$681$		0			0
$682$	−11.2096			−0.429236
$683$	−40.9659			−1.56752			−0.783758	−	0.621067i	$-0.786700\pi$
$683$	−40.9659			−1.56752			−0.783758	+	0.621067i	$0.786700\pi$
$684$		0			0
$685$	−10.3070	+	20.9751i	−0.393811	+	0.801416i
$686$	0.252610	−	18.5185i	0.00964470	−	0.707041i
$687$		0			0
$688$			2.62489i			0.100073i
$689$	24.0802			0.917381
$690$		0			0
$691$		−	0.782333i		−	0.0297614i	−0.999889	−	0.0148807i	$-0.995263\pi$
$691$		−	0.782333i		−	0.0297614i	0.999889	−	0.0148807i	$-0.00473684\pi$
$692$			16.0108i			0.608638i
$693$		0			0
$694$	12.3299			0.468036
$695$	7.24566	+	3.56047i	0.274844	+	0.135056i
$696$		0			0
$697$		−	47.6200i		−	1.80373i
$698$			24.8216i			0.939510i
$699$		0			0
$700$	−1.70405	−	13.1185i	−0.0644069	−	0.495834i
$701$			39.2726i			1.48331i	0.670783	+	0.741654i	$0.265958\pi$
$701$			39.2726i			1.48331i	−0.670783	+	0.741654i	$0.734042\pi$
$702$		0			0
$703$	−4.88060			−0.184075
$704$			4.42292i			0.166695i
$705$		0			0
$706$			26.0671i			0.981049i
$707$	8.49218	+	4.95458i	0.319381	+	0.186336i
$708$		0			0
$709$	−6.83017			−0.256512			−0.128256	−	0.991741i	$-0.540938\pi$
$709$	−6.83017			−0.256512			−0.128256	+	0.991741i	$0.540938\pi$
$710$	8.79256	+	4.32061i	0.329979	+	0.162150i
$711$		0			0
$712$	17.7283			0.664396
$713$		−	16.4730i		−	0.616919i
$714$		0			0
$715$	−17.7202	−	8.70760i	−0.662698	−	0.325646i
$716$		−	12.1593i		−	0.454416i
$717$		0			0
$718$			3.13662i			0.117058i
$719$	−8.58616			−0.320210			−0.160105	−	0.987100i	$-0.551183\pi$
$719$	−8.58616			−0.320210			−0.160105	+	0.987100i	$0.551183\pi$
$720$		0			0
$721$	−26.4662	−	15.4411i	−0.985651	−	0.575057i
$722$	−18.3562			−0.683147
$723$		0			0
$724$		−	6.18898i		−	0.230012i
$725$	−3.43778	+	2.65334i	−0.127676	+	0.0985424i
$726$		0			0
$727$	−16.6570			−0.617775			−0.308887	−	0.951099i	$-0.599957\pi$
$727$	−16.6570			−0.617775			−0.308887	+	0.951099i	$0.599957\pi$
$728$	−4.56222	−	2.66173i	−0.169087	−	0.0986502i
$729$		0			0
$730$	10.1169	−	20.5882i	0.374444	−	0.762003i
$731$	−12.9759			−0.479930
$732$		0			0
$733$	28.6946			1.05986			0.529930	−	0.848041i	$-0.322218\pi$
$733$	28.6946			1.05986			0.529930	+	0.848041i	$0.322218\pi$
$734$	26.6408			0.983328
$735$		0			0
$736$	−6.49971			−0.239583
$737$	42.1970			1.55435
$738$		0			0
$739$	20.9994			0.772476			0.386238	−	0.922399i	$-0.373774\pi$
$739$	20.9994			0.772476			0.386238	+	0.922399i	$0.373774\pi$
$740$	−12.2072	−	5.99852i	−0.448744	−	0.220510i
$741$		0			0
$742$	−27.5645	−	16.0819i	−1.01193	−	0.590386i
$743$	−28.2786			−1.03744			−0.518721	−	0.854943i	$-0.673592\pi$
$743$	−28.2786			−1.03744			−0.518721	+	0.854943i	$0.673592\pi$
$744$		0			0
$745$	42.0443	+	20.6603i	1.54038	+	0.756936i
$746$			6.20467i			0.227169i
$747$		0			0
$748$	−21.8643			−0.799437
$749$	15.8870	+	9.26892i	0.580498	+	0.338679i
$750$		0			0
$751$	−20.6360			−0.753018			−0.376509	−	0.926413i	$-0.622876\pi$
$751$	−20.6360			−0.753018			−0.376509	+	0.926413i	$0.622876\pi$
$752$		−	8.97616i		−	0.327327i
$753$		0			0
$754$			1.73391i			0.0631453i
$755$	−15.7306	+	32.0122i	−0.572496	+	1.16504i
$756$		0			0
$757$		−	22.7869i		−	0.828205i	−0.910230	−	0.414103i	$-0.864095\pi$
$757$		−	22.7869i		−	0.828205i	0.910230	−	0.414103i	$-0.135905\pi$
$758$	16.9994			0.617447
$759$		0			0
$760$	1.61025	+	0.791267i	0.0584099	+	0.0287023i
$761$	−19.1834			−0.695397			−0.347698	−	0.937606i	$-0.613037\pi$
$761$	−19.1834			−0.695397			−0.347698	+	0.937606i	$0.613037\pi$
$762$		0			0
$763$	33.1685	+	19.3515i	1.20078	+	0.700570i
$764$			11.5897i			0.419299i
$765$		0			0
$766$		−	2.36486i		−	0.0854459i
$767$	−10.1548			−0.366668
$768$		0			0
$769$			30.8381i			1.11205i	0.831165	+	0.556025i	$0.187674\pi$
$769$			30.8381i			1.11205i	−0.831165	+	0.556025i	$0.812326\pi$
$770$	14.4689	+	21.8020i	0.521424	+	0.785690i
$771$		0			0
$772$			25.7269i			0.925933i
$773$			41.9966i			1.51051i	0.655430	+	0.755256i	$0.272487\pi$
$773$			41.9966i			1.51051i	−0.655430	+	0.755256i	$0.727513\pi$
$774$		0			0
$775$	−10.0317	+	7.74261i	−0.360348	+	0.278123i
$776$	11.1133			0.398945
$777$		0			0
$778$			4.51340i			0.161813i
$779$		−	7.72929i		−	0.276930i
$780$		0			0
$781$	−19.3779			−0.693396
$782$		−	32.1307i		−	1.14899i
$783$		0			0
$784$	3.44473	+	6.09375i	0.123026	+	0.217634i
$785$	2.45398	−	4.99391i	0.0875862	−	0.178240i
$786$		0			0
$787$	−13.6871			−0.487892			−0.243946	−	0.969789i	$-0.578442\pi$
$787$	−13.6871			−0.487892			−0.243946	+	0.969789i	$0.578442\pi$
$788$	−8.34172			−0.297161
$789$		0			0
$790$	−2.80267	+	5.70352i	−0.0997146	+	0.202922i
$791$	−42.3095	−	24.6846i	−1.50435	−	0.877683i
$792$		0			0
$793$		0			0
$794$	9.28535			0.329525
$795$		0			0
$796$			12.2326i			0.433574i
$797$		−	25.5765i		−	0.905965i	−0.891519	−	0.452983i	$-0.850360\pi$
$797$		−	25.5765i		−	0.905965i	0.891519	−	0.452983i	$-0.149640\pi$
$798$		0			0
$799$	44.3727			1.56979
$800$	3.05498	+	3.95817i	0.108010	+	0.139942i
$801$		0			0
$802$			11.9276i			0.421177i
$803$			45.3743i			1.60122i
$804$		0			0
$805$	−32.0392	+	21.2628i	−1.12923	+	0.749417i
$806$			5.05966i			0.178219i
$807$		0			0
$808$	−3.71609			−0.130731
$809$			24.6907i			0.868078i	0.900894	+	0.434039i	$0.142912\pi$
$809$			24.6907i			0.868078i	−0.900894	+	0.434039i	$0.857088\pi$
$810$		0			0
$811$			37.4090i			1.31361i	0.754061	+	0.656804i	$0.228092\pi$
$811$			37.4090i			1.31361i	−0.754061	+	0.656804i	$0.771908\pi$
$812$	1.15799	−	1.98480i	0.0406375	−	0.0696529i
$813$		0			0
$814$	26.9034			0.942962
$815$	−49.2877	−	24.2197i	−1.72647	−	0.848378i
$816$		0			0
$817$	−2.10614			−0.0736845
$818$			24.2728i			0.848678i
$819$		0			0
$820$	9.49971	−	19.3322i	0.331744	−	0.675109i
$821$			8.13183i			0.283803i	0.989881	+	0.141901i	$0.0453216\pi$
$821$			8.13183i			0.283803i	−0.989881	+	0.141901i	$0.954678\pi$
$822$		0			0
$823$			43.5569i			1.51830i	0.650918	+	0.759148i	$0.274384\pi$
$823$			43.5569i			1.51830i	−0.650918	+	0.759148i	$0.725616\pi$
$824$	11.5813			0.403454
$825$		0			0
$826$	11.6241	+	6.78186i	0.404456	+	0.235971i
$827$	−34.2489			−1.19095			−0.595475	−	0.803374i	$-0.703036\pi$
$827$	−34.2489			−1.19095			−0.595475	+	0.803374i	$0.703036\pi$
$828$		0			0
$829$			45.1596i			1.56846i	0.620471	+	0.784229i	$0.286941\pi$
$829$			45.1596i			1.56846i	−0.620471	+	0.784229i	$0.713059\pi$
$830$	6.44473	+	3.16690i	0.223700	+	0.109925i
$831$		0			0
$832$	1.99638			0.0692119
$833$	−30.1239	+	17.0287i	−1.04373	+	0.590009i
$834$		0			0
$835$	−29.2931	−	14.3945i	−1.01373	−	0.498141i
$836$	−3.54883			−0.122739
$837$		0			0
$838$	−36.4542			−1.25929
$839$	−9.18761			−0.317192			−0.158596	−	0.987344i	$-0.550697\pi$
$839$	−9.18761			−0.317192			−0.158596	+	0.987344i	$0.550697\pi$
$840$		0			0
$841$	28.2457			0.973988
$842$	24.2306			0.835042
$843$		0			0
$844$	3.65770			0.125903
$845$	8.88971	−	18.0908i	0.305815	−	0.622343i
$846$		0			0
$847$	−19.5668	−	11.4158i	−0.672323	−	0.392253i
$848$	12.0619			0.414208
$849$		0			0
$850$	−19.5668	+	15.1020i	−0.671136	+	0.517994i
$851$			39.5359i			1.35527i
$852$		0			0
$853$	13.3119			0.455790			0.227895	−	0.973686i	$-0.426816\pi$
$853$	13.3119			0.455790			0.227895	+	0.973686i	$0.426816\pi$
$854$		0			0
$855$		0			0
$856$	−6.95197			−0.237613
$857$			38.1060i			1.30168i	0.759217	+	0.650838i	$0.225582\pi$
$857$			38.1060i			1.30168i	−0.759217	+	0.650838i	$0.774418\pi$
$858$		0			0
$859$		−	11.1947i		−	0.381957i	−0.981594	−	0.190979i	$-0.938834\pi$
$859$		−	11.1947i		−	0.381957i	0.981594	−	0.190979i	$-0.0611662\pi$
$860$	−5.26779	−	2.58856i	−0.179630	−	0.0882691i
$861$		0			0
$862$			30.8639i			1.05123i
$863$	9.40307			0.320084			0.160042	−	0.987110i	$-0.448837\pi$
$863$	9.40307			0.320084			0.160042	+	0.987110i	$0.448837\pi$
$864$		0			0
$865$	−32.1314	−	15.7892i	−1.09250	−	0.536848i
$866$	−40.5673			−1.37853
$867$		0			0
$868$	3.37910	−	5.79179i	0.114694	−	0.196586i
$869$		−	12.5700i		−	0.426407i
$870$		0			0
$871$		−	19.0465i		−	0.645367i
$872$	−14.5142			−0.491512
$873$		0			0
$874$		−	5.21519i		−	0.176406i
$875$	28.0076	+	9.51719i	0.946828	+	0.321740i
$876$		0			0
$877$		−	6.99899i		−	0.236339i	−0.992993	−	0.118170i	$-0.962297\pi$
$877$		−	6.99899i		−	0.236339i	0.992993	−	0.118170i	$-0.0377027\pi$
$878$		−	19.0325i		−	0.642316i
$879$		0			0
$880$	−8.87618	−	4.36170i	−0.299216	−	0.147033i
$881$	−4.60774			−0.155239			−0.0776193	−	0.996983i	$-0.524732\pi$
$881$	−4.60774			−0.155239			−0.0776193	+	0.996983i	$0.524732\pi$
$882$		0			0
$883$		−	22.5582i		−	0.759144i	−0.925162	−	0.379572i	$-0.876071\pi$
$883$		−	22.5582i		−	0.759144i	0.925162	−	0.379572i	$-0.123929\pi$
$884$			9.86889i			0.331927i
$885$		0			0
$886$	−38.6499			−1.29847
$887$			5.26116i			0.176653i	0.996092	+	0.0883263i	$0.0281518\pi$
$887$			5.26116i			0.176653i	−0.996092	+	0.0883263i	$0.971848\pi$
$888$		0			0
$889$	−18.6904	+	32.0354i	−0.626856	+	1.07443i
$890$	−17.4829	+	35.5782i	−0.586029	+	1.19259i
$891$		0			0
$892$	−17.9662			−0.601554
$893$	7.20222			0.241013
$894$		0			0
$895$	24.4021	+	11.9911i	0.815673	+	0.400817i
$896$	−2.28525	−	1.33328i	−0.0763448	−	0.0445417i
$897$		0			0
$898$			1.93019i			0.0644112i
$899$	−2.20122			−0.0734147
$900$		0			0
$901$			59.6269i			1.98646i
$902$			42.6062i			1.41863i
$903$		0			0
$904$	18.5142			0.615773
$905$	12.4204	+	6.10332i	0.412869	+	0.202881i
$906$		0			0
$907$			46.4322i			1.54176i	0.636982	+	0.770879i	$0.280182\pi$
$907$			46.4322i			1.54176i	−0.636982	+	0.770879i	$0.719818\pi$
$908$		−	9.94995i		−	0.330201i
$909$		0			0
$910$	9.84079	−	6.53085i	0.326219	−	0.216496i
$911$		−	1.24463i		−	0.0412364i	−0.999787	−	0.0206182i	$-0.993437\pi$
$911$		−	1.24463i		−	0.0412364i	0.999787	−	0.0206182i	$-0.00656344\pi$
$912$		0			0
$913$	−14.2035			−0.470069
$914$			9.72759i			0.321760i
$915$		0			0
$916$		−	5.06885i		−	0.167479i
$917$	−12.8345	−	7.48800i	−0.423832	−	0.247276i
$918$		0			0
$919$	−31.0434			−1.02403			−0.512014	−	0.858977i	$-0.671101\pi$
$919$	−31.0434			−1.02403			−0.512014	+	0.858977i	$0.671101\pi$
$920$	6.40975	−	13.0440i	0.211323	−	0.430048i
$921$		0			0
$922$	−6.96384			−0.229342
$923$			8.74662i			0.287899i
$924$		0			0
$925$	24.0764	−	18.5826i	0.791627	−	0.610991i
$926$		−	29.1014i		−	0.956332i
$927$		0			0
$928$			0.868528i			0.0285108i
$929$	−42.3486			−1.38941			−0.694707	−	0.719293i	$-0.744466\pi$
$929$	−42.3486			−1.38941			−0.694707	+	0.719293i	$0.744466\pi$
$930$		0			0
$931$	−4.88946	+	2.76396i	−0.160246	+	0.0905850i
$932$	−3.70573			−0.121385
$933$		0			0
$934$			8.09160i			0.264765i
$935$	21.5616	−	43.8785i	0.705141	−	1.43498i
$936$		0			0
$937$	17.4513			0.570109			0.285054	−	0.958511i	$-0.407988\pi$
$937$	17.4513			0.570109			0.285054	+	0.958511i	$0.407988\pi$
$938$	−12.7202	+	21.8025i	−0.415330	+	0.711877i
$939$		0			0
$940$	18.0139	+	8.85192i	0.587549	+	0.288718i
$941$	−24.2805			−0.791522			−0.395761	−	0.918354i	$-0.629519\pi$
$941$	−24.2805			−0.791522			−0.395761	+	0.918354i	$0.629519\pi$
$942$		0			0
$943$	−62.6120			−2.03893
$944$	−5.08660			−0.165555
$945$		0			0
$946$	11.6097			0.377463
$947$	15.2969			0.497083			0.248541	−	0.968621i	$-0.420049\pi$
$947$	15.2969			0.497083			0.248541	+	0.968621i	$0.420049\pi$
$948$		0			0
$949$	20.4806			0.664830
$950$	−3.17593	+	2.45123i	−0.103041	+	0.0795285i
$951$		0			0
$952$	6.59093	−	11.2969i	0.213613	−	0.366135i
$953$	26.3449			0.853396			0.426698	−	0.904394i	$-0.359677\pi$
$953$	26.3449			0.853396			0.426698	+	0.904394i	$0.359677\pi$
$954$		0			0
$955$	−23.2588	−	11.4292i	−0.752638	−	0.369842i
$956$		−	19.5121i		−	0.631066i
$957$		0			0
$958$	6.95331			0.224651
$959$	23.8847	+	13.9350i	0.771277	+	0.449985i
$960$		0			0
$961$	24.5767			0.792797
$962$		−	12.1434i		−	0.391519i
$963$		0			0
$964$			10.3723i			0.334068i
$965$	−51.6304	−	25.3709i	−1.66204	−	0.816717i
$966$		0			0
$967$		−	11.8117i		−	0.379839i	−0.981800	−	0.189919i	$-0.939177\pi$
$967$		−	11.8117i		−	0.379839i	0.981800	−	0.189919i	$-0.0608226\pi$
$968$	8.56222			0.275200
$969$		0			0
$970$	−10.9595	+	22.3029i	−0.351888	+	0.716102i
$971$	31.0440			0.996249			0.498125	−	0.867105i	$-0.334022\pi$
$971$	31.0440			0.996249			0.498125	+	0.867105i	$0.334022\pi$
$972$		0			0
$973$	4.81373	−	8.25077i	0.154321	−	0.264507i
$974$			12.8957i			0.413206i
$975$		0			0
$976$		0			0
$977$	12.7677			0.408474			0.204237	−	0.978922i	$-0.434529\pi$
$977$	12.7677			0.408474			0.204237	+	0.978922i	$0.434529\pi$
$978$		0			0
$979$		−	78.4109i		−	2.50602i
$980$	−15.6264	+	0.903683i	−0.499166	+	0.0288671i
$981$		0			0
$982$		−	28.7345i		−	0.916954i
$983$		−	11.8725i		−	0.378673i	−0.981912	−	0.189336i	$-0.939366\pi$
$983$		−	11.8725i		−	0.378673i	0.981912	−	0.189336i	$-0.0606336\pi$
$984$		0			0
$985$	8.22626	−	16.7407i	0.262111	−	0.533402i
$986$	−4.29348			−0.136732
$987$		0			0
$988$			1.60184i			0.0509613i
$989$			17.0610i			0.542509i
$990$		0			0
$991$	24.5498			0.779850			0.389925	−	0.920847i	$-0.372501\pi$
$991$	24.5498			0.779850			0.389925	+	0.920847i	$0.372501\pi$
$992$			2.53442i			0.0804680i
$993$		0			0
$994$	5.84143	−	10.0122i	0.185279	−	0.317569i
$995$	−24.5492	−	12.0633i	−0.778261	−	0.382433i
$996$		0			0
$997$	44.5345			1.41042			0.705210	−	0.708998i	$-0.250853\pi$
$997$	44.5345			1.41042			0.705210	+	0.708998i	$0.250853\pi$
$998$	−7.09548			−0.224604
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.d.e.1889.6	yes	16
3.2	odd	2		1890.2.d.f.1889.11	yes	16
5.4	even	2		1890.2.d.f.1889.5	yes	16
7.6	odd	2	inner	1890.2.d.e.1889.11	yes	16
15.14	odd	2	inner	1890.2.d.e.1889.12	yes	16
21.20	even	2		1890.2.d.f.1889.6	yes	16
35.34	odd	2		1890.2.d.f.1889.12	yes	16
105.104	even	2	inner	1890.2.d.e.1889.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.d.e.1889.5	✓	16	105.104	even	2	inner
1890.2.d.e.1889.6	yes	16	1.1	even	1	trivial
1890.2.d.e.1889.11	yes	16	7.6	odd	2	inner
1890.2.d.e.1889.12	yes	16	15.14	odd	2	inner
1890.2.d.f.1889.5	yes	16	5.4	even	2
1890.2.d.f.1889.6	yes	16	21.20	even	2
1890.2.d.f.1889.11	yes	16	3.2	odd	2
1890.2.d.f.1889.12	yes	16	35.34	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.986159 + 2.00686i) q^{5} +(2.28525 + 1.33328i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.986159 + 2.00686i) q^{5} +(2.28525 + 1.33328i) q^{7} -1.00000 q^{8} +(0.986159 - 2.00686i) q^{10} +4.42292i q^{11} +1.99638 q^{13} +(-2.28525 - 1.33328i) q^{14} +1.00000 q^{16} +4.94340i q^{17} +0.802373i q^{19} +(-0.986159 + 2.00686i) q^{20} -4.42292i q^{22} +6.49971 q^{23} +(-3.05498 - 3.95817i) q^{25} -1.99638 q^{26} +(2.28525 + 1.33328i) q^{28} -0.868528i q^{29} -2.53442i q^{31} -1.00000 q^{32} -4.94340i q^{34} +(-4.92933 + 3.27135i) q^{35} +6.08271i q^{37} -0.802373i q^{38} +(0.986159 - 2.00686i) q^{40} -9.63304 q^{41} +2.62489i q^{43} +4.42292i q^{44} -6.49971 q^{46} -8.97616i q^{47} +(3.44473 + 6.09375i) q^{49} +(3.05498 + 3.95817i) q^{50} +1.99638 q^{52} +12.0619 q^{53} +(-8.87618 - 4.36170i) q^{55} +(-2.28525 - 1.33328i) q^{56} +0.868528i q^{58} -5.08660 q^{59} +2.53442i q^{62} +1.00000 q^{64} +(-1.96875 + 4.00645i) q^{65} -9.54054i q^{67} +4.94340i q^{68} +(4.92933 - 3.27135i) q^{70} +4.38125i q^{71} +10.2589 q^{73} -6.08271i q^{74} +0.802373i q^{76} +(-5.89699 + 10.1075i) q^{77} -2.84201 q^{79} +(-0.986159 + 2.00686i) q^{80} +9.63304 q^{82} +3.21135i q^{83} +(-9.92072 - 4.87498i) q^{85} -2.62489i q^{86} -4.42292i q^{88} -17.7283 q^{89} +(4.56222 + 2.66173i) q^{91} +6.49971 q^{92} +8.97616i q^{94} +(-1.61025 - 0.791267i) q^{95} -11.1133 q^{97} +(-3.44473 - 6.09375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} - 6 q^{25} - 16 q^{32} - q^{35} - 8 q^{46} + 2 q^{49} + 6 q^{50} - 16 q^{53} + 16 q^{64} - 40 q^{65} + q^{70} - 14 q^{77} - 8 q^{79} - 44 q^{85} - 40 q^{91} + 8 q^{92} - 36 q^{95} - 2 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 - 6 * q^25 - 16 * q^32 - q^35 - 8 * q^46 + 2 * q^49 + 6 * q^50 - 16 * q^53 + 16 * q^64 - 40 * q^65 + q^70 - 14 * q^77 - 8 * q^79 - 44 * q^85 - 40 * q^91 + 8 * q^92 - 36 * q^95 - 2 * q^98

Introduction

L-functions

Modular forms

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Database

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