LMFDB - Embedded newform 630.3.h.e.559.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(559,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("630.559");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.h (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:	$17.1662566547$
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} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 $ x^16 - 8x^15 + 96x^14 - 532x^13 + 3236x^12 - 12864x^11 + 49526x^10 - 141436x^9 + 362298x^8 - 722060x^7 + 1208164x^6 - 1570812x^5 + 1591101x^4 - 1183860x^3 + 619650x^2 - 202500*x + 33750
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.4
Root			$0.500000 + 3.55177i$ of defining polynomial
Character	$\chi$	$=$	630.559
Dual form			630.3.h.e.559.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.00000 q^{4} +(-1.38028 + 4.80571i) q^{5} +(-5.24961 + 4.63050i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q-1.41421i q^{2} -2.00000 q^{4} +(-1.38028 + 4.80571i) q^{5} +(-5.24961 + 4.63050i) q^{7} +2.82843i q^{8} +(6.79630 + 1.95201i) q^{10} -11.7671 q^{11} +24.8280 q^{13} +(6.54852 + 7.42407i) q^{14} +4.00000 q^{16} -7.26100 q^{17} -23.0050i q^{19} +(2.76057 - 9.61141i) q^{20} +16.6412i q^{22} -26.4223i q^{23} +(-21.1896 - 13.2665i) q^{25} -35.1122i q^{26} +(10.4992 - 9.26101i) q^{28} -57.0861 q^{29} +10.2222i q^{31} -5.65685i q^{32} +10.2686i q^{34} +(-15.0069 - 31.6195i) q^{35} +14.2196i q^{37} -32.5340 q^{38} +(-13.5926 - 3.90403i) q^{40} -16.2271i q^{41} -82.3114i q^{43} +23.5342 q^{44} -37.3668 q^{46} +51.6631 q^{47} +(6.11686 - 48.6167i) q^{49} +(-18.7616 + 29.9667i) q^{50} -49.6561 q^{52} +64.8273i q^{53} +(16.2419 - 56.5491i) q^{55} +(-13.0970 - 14.8481i) q^{56} +80.7320i q^{58} -81.7685i q^{59} -13.1240i q^{61} +14.4564 q^{62} -8.00000 q^{64} +(-34.2697 + 119.316i) q^{65} +22.4035i q^{67} +14.5220 q^{68} +(-44.7167 + 21.2230i) q^{70} -91.5022 q^{71} -71.9256 q^{73} +20.1096 q^{74} +46.0100i q^{76} +(61.7726 - 54.4875i) q^{77} +45.2802 q^{79} +(-5.52113 + 19.2228i) q^{80} -22.9486 q^{82} -17.7328 q^{83} +(10.0222 - 34.8943i) q^{85} -116.406 q^{86} -33.2823i q^{88} -77.5800i q^{89} +(-130.338 + 114.966i) q^{91} +52.8446i q^{92} -73.0627i q^{94} +(110.555 + 31.7534i) q^{95} -6.15741 q^{97} +(-68.7544 - 8.65055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4}+O(q^{10}) $ 16 * q - 32 * q^4	$ 16 q - 32 q^{4} - 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{25} - 64 q^{29} + 8 q^{35} + 192 q^{44} - 176 q^{46} + 224 q^{49} + 96 q^{50} + 32 q^{56} - 128 q^{64} - 368 q^{65} - 56 q^{70} + 384 q^{71} - 224 q^{74} - 608 q^{79} - 440 q^{85} - 416 q^{86} + 224 q^{91} + 560 q^{95}+O(q^{100}) $ 16 * q - 32 * q^4 - 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^25 - 64 * q^29 + 8 * q^35 + 192 * q^44 - 176 * q^46 + 224 * q^49 + 96 * q^50 + 32 * q^56 - 128 * q^64 - 368 * q^65 - 56 * q^70 + 384 * q^71 - 224 * q^74 - 608 * q^79 - 440 * q^85 - 416 * q^86 + 224 * q^91 + 560 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	−1.38028	+	4.80571i	−0.276057	+	0.961141i
$5$	−1.38028	+	4.80571i	−0.276057	+	0.961141i
$6$		0			0
$7$	−5.24961	+	4.63050i	−0.749945	+	0.661501i
$7$	−5.24961	+	4.63050i	−0.749945	+	0.661501i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	6.79630	+	1.95201i	0.679630	+	0.195201i
$11$	−11.7671			−1.06973			−0.534867	−	0.844936i	$-0.679638\pi$
$11$	−11.7671			−1.06973			−0.534867	+	0.844936i	$0.679638\pi$
$12$		0			0
$13$	24.8280			1.90985			0.954925	−	0.296848i	$-0.0959354\pi$
$13$	24.8280			1.90985			0.954925	+	0.296848i	$0.0959354\pi$
$14$	6.54852	+	7.42407i	0.467752	+	0.530291i
$15$		0			0
$16$	4.00000			0.250000
$17$	−7.26100			−0.427118			−0.213559	−	0.976930i	$-0.568506\pi$
$17$	−7.26100			−0.427118			−0.213559	+	0.976930i	$0.568506\pi$
$18$		0			0
$19$		−	23.0050i		−	1.21079i	−0.795925	−	0.605395i	$-0.793015\pi$
$19$		−	23.0050i		−	1.21079i	0.795925	−	0.605395i	$-0.206985\pi$
$20$	2.76057	−	9.61141i	0.138028	−	0.480571i
$21$		0			0
$22$			16.6412i			0.756417i
$23$		−	26.4223i		−	1.14880i	−0.818576	−	0.574398i	$-0.805236\pi$
$23$		−	26.4223i		−	1.14880i	0.818576	−	0.574398i	$-0.194764\pi$
$24$		0			0
$25$	−21.1896	−	13.2665i	−0.847586	−	0.530659i
$26$		−	35.1122i		−	1.35047i
$27$		0			0
$28$	10.4992	−	9.26101i	0.374972	−	0.330750i
$29$	−57.0861			−1.96849			−0.984243	−	0.176819i	$-0.943419\pi$
$29$	−57.0861			−1.96849			−0.984243	+	0.176819i	$0.943419\pi$
$30$		0			0
$31$			10.2222i			0.329749i	0.986315	+	0.164874i	$0.0527219\pi$
$31$			10.2222i			0.329749i	−0.986315	+	0.164874i	$0.947278\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$			10.2686i			0.302018i
$35$	−15.0069	−	31.6195i	−0.428768	−	0.903414i
$36$		0			0
$37$			14.2196i			0.384314i	0.981364	+	0.192157i	$0.0615482\pi$
$37$			14.2196i			0.384314i	−0.981364	+	0.192157i	$0.938452\pi$
$38$	−32.5340			−0.856158
$39$		0			0
$40$	−13.5926	−	3.90403i	−0.339815	−	0.0976007i
$41$		−	16.2271i		−	0.395782i	−0.980224	−	0.197891i	$-0.936591\pi$
$41$		−	16.2271i		−	0.395782i	0.980224	−	0.197891i	$-0.0634093\pi$
$42$		0			0
$43$		−	82.3114i		−	1.91422i	−0.289725	−	0.957110i	$-0.593564\pi$
$43$		−	82.3114i		−	1.91422i	0.289725	−	0.957110i	$-0.406436\pi$
$44$	23.5342			0.534867
$45$		0			0
$46$	−37.3668			−0.812321
$47$	51.6631			1.09922			0.549608	−	0.835423i	$-0.314777\pi$
$47$	51.6631			1.09922			0.549608	+	0.835423i	$0.314777\pi$
$48$		0			0
$49$	6.11686	−	48.6167i	0.124834	−	0.992178i
$50$	−18.7616	+	29.9667i	−0.375232	+	0.599333i
$51$		0			0
$52$	−49.6561			−0.954925
$53$			64.8273i			1.22316i	0.791184	+	0.611579i	$0.209465\pi$
$53$			64.8273i			1.22316i	−0.791184	+	0.611579i	$0.790535\pi$
$54$		0			0
$55$	16.2419	−	56.5491i	0.295307	−	1.02817i
$56$	−13.0970	−	14.8481i	−0.233876	−	0.265145i
$57$		0			0
$58$			80.7320i			1.39193i
$59$		−	81.7685i		−	1.38591i	−0.720982	−	0.692953i	$-0.756309\pi$
$59$		−	81.7685i		−	1.38591i	0.720982	−	0.692953i	$-0.243691\pi$
$60$		0			0
$61$		−	13.1240i		−	0.215148i	−0.994197	−	0.107574i	$-0.965692\pi$
$61$		−	13.1240i		−	0.215148i	0.994197	−	0.107574i	$-0.0343083\pi$
$62$	14.4564			0.233168
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−34.2697	+	119.316i	−0.527226	+	1.83564i
$66$		0			0
$67$			22.4035i			0.334381i	0.985925	+	0.167190i	$0.0534695\pi$
$67$			22.4035i			0.334381i	−0.985925	+	0.167190i	$0.946531\pi$
$68$	14.5220			0.213559
$69$		0			0
$70$	−44.7167	+	21.2230i	−0.638810	+	0.303185i
$71$	−91.5022			−1.28876			−0.644382	−	0.764704i	$-0.722885\pi$
$71$	−91.5022			−1.28876			−0.644382	+	0.764704i	$0.722885\pi$
$72$		0			0
$73$	−71.9256			−0.985282			−0.492641	−	0.870233i	$-0.663968\pi$
$73$	−71.9256			−0.985282			−0.492641	+	0.870233i	$0.663968\pi$
$74$	20.1096			0.271751
$75$		0			0
$76$			46.0100i			0.605395i
$77$	61.7726	−	54.4875i	0.802242	−	0.707630i
$78$		0			0
$79$	45.2802			0.573167			0.286584	−	0.958055i	$-0.407480\pi$
$79$	45.2802			0.573167			0.286584	+	0.958055i	$0.407480\pi$
$80$	−5.52113	+	19.2228i	−0.0690141	+	0.240285i
$81$		0			0
$82$	−22.9486			−0.279860
$83$	−17.7328			−0.213648			−0.106824	−	0.994278i	$-0.534068\pi$
$83$	−17.7328			−0.213648			−0.106824	+	0.994278i	$0.534068\pi$
$84$		0			0
$85$	10.0222	−	34.8943i	0.117909	−	0.410521i
$86$	−116.406			−1.35356
$87$		0			0
$88$		−	33.2823i		−	0.378208i
$89$		−	77.5800i		−	0.871686i	−0.900023	−	0.435843i	$-0.856450\pi$
$89$		−	77.5800i		−	0.871686i	0.900023	−	0.435843i	$-0.143550\pi$
$90$		0			0
$91$	−130.338	+	114.966i	−1.43228	+	1.26337i
$92$			52.8446i			0.574398i
$93$		0			0
$94$		−	73.0627i		−	0.777263i
$95$	110.555	+	31.7534i	1.16374	+	0.334247i
$96$		0			0
$97$	−6.15741			−0.0634785			−0.0317392	−	0.999496i	$-0.510105\pi$
$97$	−6.15741			−0.0634785			−0.0317392	+	0.999496i	$0.510105\pi$
$98$	−68.7544	−	8.65055i	−0.701576	−	0.0882709i
$99$		0			0
$100$	42.3793	+	26.5329i	0.423793	+	0.265329i
$101$			142.983i			1.41568i	0.706374	+	0.707839i	$0.250330\pi$
$101$			142.983i			1.41568i	−0.706374	+	0.707839i	$0.749670\pi$
$102$		0			0
$103$	14.5292			0.141060			0.0705302	−	0.997510i	$-0.477531\pi$
$103$	14.5292			0.141060			0.0705302	+	0.997510i	$0.477531\pi$
$104$			70.2243i			0.675234i
$105$		0			0
$106$	91.6797			0.864903
$107$		−	78.4228i		−	0.732923i	−0.930433	−	0.366462i	$-0.880569\pi$
$107$		−	78.4228i		−	0.732923i	0.930433	−	0.366462i	$-0.119431\pi$
$108$		0			0
$109$	−74.7424			−0.685710			−0.342855	−	0.939388i	$-0.611394\pi$
$109$	−74.7424			−0.685710			−0.342855	+	0.939388i	$0.611394\pi$
$110$	−79.9726	−	22.9695i	−0.727023	−	0.208814i
$111$		0			0
$112$	−20.9985	+	18.5220i	−0.187486	+	0.165375i
$113$		−	85.2417i		−	0.754351i	−0.926142	−	0.377175i	$-0.876895\pi$
$113$		−	85.2417i		−	0.754351i	0.926142	−	0.377175i	$-0.123105\pi$
$114$		0			0
$115$	126.978	+	36.4702i	1.10415	+	0.317132i
$116$	114.172			0.984243
$117$		0			0
$118$	−115.638			−0.979984
$119$	38.1175	−	33.6221i	0.320315	−	0.282539i
$120$		0			0
$121$	17.4642			0.144332
$122$	−18.5602			−0.152133
$123$		0			0
$124$		−	20.4444i		−	0.164874i
$125$	93.0025	−	83.5197i	0.744020	−	0.668158i
$126$		0			0
$127$			66.7734i			0.525775i	0.964827	+	0.262887i	$0.0846747\pi$
$127$			66.7734i			0.525775i	−0.964827	+	0.262887i	$0.915325\pi$
$128$			11.3137i			0.0883883i
$129$		0			0
$130$	168.739	+	48.4647i	1.29799	+	0.372805i
$131$		−	28.8330i		−	0.220099i	−0.993926	−	0.110049i	$-0.964899\pi$
$131$		−	28.8330i		−	0.220099i	0.993926	−	0.110049i	$-0.0351009\pi$
$132$		0			0
$133$	106.525	+	120.767i	0.800939	+	0.908026i
$134$	31.6834			0.236443
$135$		0			0
$136$		−	20.5372i		−	0.151009i
$137$		−	119.450i		−	0.871897i	−0.899972	−	0.435948i	$-0.856413\pi$
$137$		−	119.450i		−	0.871897i	0.899972	−	0.435948i	$-0.143587\pi$
$138$		0			0
$139$			200.948i			1.44567i	0.691021	+	0.722834i	$0.257161\pi$
$139$			200.948i			1.44567i	−0.691021	+	0.722834i	$0.742839\pi$
$140$	30.0138	+	63.2390i	0.214384	+	0.451707i
$141$		0			0
$142$			129.404i			0.911293i
$143$	−292.154			−2.04303
$144$		0			0
$145$	78.7950	−	274.339i	0.543414	−	1.89199i
$146$			101.718i			0.696700i
$147$		0			0
$148$		−	28.4392i		−	0.192157i
$149$	5.70484			0.0382875			0.0191438	−	0.999817i	$-0.493906\pi$
$149$	5.70484			0.0382875			0.0191438	+	0.999817i	$0.493906\pi$
$150$		0			0
$151$	−216.490			−1.43371			−0.716854	−	0.697223i	$-0.754419\pi$
$151$	−216.490			−1.43371			−0.716854	+	0.697223i	$0.754419\pi$
$152$	65.0680			0.428079
$153$		0			0
$154$	−77.0570	−	87.3597i	−0.500370	−	0.567271i
$155$	−49.1250	−	14.1095i	−0.316935	−	0.0910293i
$156$		0			0
$157$	−108.287			−0.689726			−0.344863	−	0.938653i	$-0.612075\pi$
$157$	−108.287			−0.689726			−0.344863	+	0.938653i	$0.612075\pi$
$158$		−	64.0359i		−	0.405290i
$159$		0			0
$160$	27.1852	+	7.80806i	0.169907	+	0.0488004i
$161$	122.349	+	138.707i	0.759929	+	0.861533i
$162$		0			0
$163$		−	234.395i		−	1.43800i	−0.695008	−	0.719002i	$-0.744599\pi$
$163$		−	234.395i		−	1.43800i	0.695008	−	0.719002i	$-0.255401\pi$
$164$			32.4542i			0.197891i
$165$		0			0
$166$			25.0779i			0.151072i
$167$	−41.8830			−0.250796			−0.125398	−	0.992106i	$-0.540021\pi$
$167$	−41.8830			−0.250796			−0.125398	+	0.992106i	$0.540021\pi$
$168$		0			0
$169$	447.432			2.64753
$170$	−49.3479	−	14.1736i	−0.290282	−	0.0833740i
$171$		0			0
$172$			164.623i			0.957110i
$173$	−13.0301			−0.0753183			−0.0376592	−	0.999291i	$-0.511990\pi$
$173$	−13.0301			−0.0753183			−0.0376592	+	0.999291i	$0.511990\pi$
$174$		0			0
$175$	172.668	−	28.4749i	0.986673	−	0.162714i
$176$	−47.0683			−0.267434
$177$		0			0
$178$	−109.715			−0.616375
$179$	24.1573			0.134957			0.0674786	−	0.997721i	$-0.478505\pi$
$179$	24.1573			0.134957			0.0674786	+	0.997721i	$0.478505\pi$
$180$		0			0
$181$			43.5107i			0.240390i	0.992750	+	0.120195i	$0.0383521\pi$
$181$			43.5107i			0.240390i	−0.992750	+	0.120195i	$0.961648\pi$
$182$	162.587	+	184.325i	0.893335	+	1.01278i
$183$		0			0
$184$	74.7335			0.406160
$185$	−68.3353	−	19.6271i	−0.369380	−	0.106092i
$186$		0			0
$187$	85.4408			0.456903
$188$	−103.326			−0.549608
$189$		0			0
$190$	44.9061	−	156.349i	0.236348	−	0.822889i
$191$	246.572			1.29095			0.645477	−	0.763780i	$-0.276659\pi$
$191$	246.572			1.29095			0.645477	+	0.763780i	$0.276659\pi$
$192$		0			0
$193$		−	161.875i		−	0.838733i	−0.907817	−	0.419366i	$-0.862252\pi$
$193$		−	161.875i		−	0.838733i	0.907817	−	0.419366i	$-0.137748\pi$
$194$			8.70789i			0.0448860i
$195$		0			0
$196$	−12.2337	+	97.2334i	−0.0624170	+	0.496089i
$197$			44.8380i			0.227604i	0.993503	+	0.113802i	$0.0363029\pi$
$197$			44.8380i			0.227604i	−0.993503	+	0.113802i	$0.963697\pi$
$198$		0			0
$199$		−	114.767i		−	0.576718i	−0.957522	−	0.288359i	$-0.906890\pi$
$199$		−	114.767i		−	0.576718i	0.957522	−	0.288359i	$-0.0931097\pi$
$200$	37.5232	−	59.9333i	0.187616	−	0.299667i
$201$		0			0
$202$	202.209			1.00104
$203$	299.680	−	264.338i	1.47626	−	1.30216i
$204$		0			0
$205$	77.9826	+	22.3980i	0.380403	+	0.109258i
$206$		−	20.5474i		−	0.0997448i
$207$		0			0
$208$	99.3122			0.477462
$209$			270.702i			1.29522i
$210$		0			0
$211$	−219.602			−1.04077			−0.520384	−	0.853932i	$-0.674211\pi$
$211$	−219.602			−1.04077			−0.520384	+	0.853932i	$0.674211\pi$
$212$		−	129.655i		−	0.611579i
$213$		0			0
$214$	−110.907			−0.518255
$215$	395.565	+	113.613i	1.83984	+	0.528433i
$216$		0			0
$217$	−47.3340	−	53.6626i	−0.218129	−	0.247293i
$218$			105.702i			0.484870i
$219$		0			0
$220$	−32.4838	+	113.098i	−0.147654	+	0.514083i
$221$	−180.277			−0.815731
$222$		0			0
$223$	−3.57102			−0.0160136			−0.00800678	−	0.999968i	$-0.502549\pi$
$223$	−3.57102			−0.0160136			−0.00800678	+	0.999968i	$0.502549\pi$
$224$	26.1941	+	29.6963i	0.116938	+	0.132573i
$225$		0			0
$226$	−120.550			−0.533407
$227$	−68.0647			−0.299844			−0.149922	−	0.988698i	$-0.547902\pi$
$227$	−68.0647			−0.299844			−0.149922	+	0.988698i	$0.547902\pi$
$228$		0			0
$229$			180.019i			0.786109i	0.919515	+	0.393054i	$0.128582\pi$
$229$			180.019i			0.786109i	−0.919515	+	0.393054i	$0.871418\pi$
$230$	51.5767	−	179.574i	0.224247	−	0.780755i
$231$		0			0
$232$		−	161.464i		−	0.695965i
$233$			115.207i			0.494449i	0.968958	+	0.247225i	$0.0795185\pi$
$233$			115.207i			0.494449i	−0.968958	+	0.247225i	$0.920481\pi$
$234$		0			0
$235$	−71.3097	+	248.278i	−0.303446	+	1.05650i
$236$			163.537i			0.692953i
$237$		0			0
$238$	−47.5488	−	53.9062i	−0.199785	−	0.226497i
$239$	−15.6873			−0.0656374			−0.0328187	−	0.999461i	$-0.510448\pi$
$239$	−15.6873			−0.0656374			−0.0328187	+	0.999461i	$0.510448\pi$
$240$		0			0
$241$			303.442i			1.25909i	0.776962	+	0.629547i	$0.216760\pi$
$241$			303.442i			1.25909i	−0.776962	+	0.629547i	$0.783240\pi$
$242$		−	24.6981i		−	0.102058i
$243$		0			0
$244$			26.2481i			0.107574i
$245$	225.195	+	96.5007i	0.919162	+	0.393880i
$246$		0			0
$247$		−	571.170i		−	2.31243i
$248$	−28.9128			−0.116584
$249$		0			0
$250$	−118.115	−	131.525i	−0.472459	−	0.526101i
$251$			80.5241i			0.320813i	0.987051	+	0.160407i	$0.0512805\pi$
$251$			80.5241i			0.320813i	−0.987051	+	0.160407i	$0.948719\pi$
$252$		0			0
$253$			310.913i			1.22891i
$254$	94.4318			0.371779
$255$		0			0
$256$	16.0000			0.0625000
$257$	−39.1012			−0.152145			−0.0760723	−	0.997102i	$-0.524238\pi$
$257$	−39.1012			−0.152145			−0.0760723	+	0.997102i	$0.524238\pi$
$258$		0			0
$259$	−65.8439	−	74.6474i	−0.254224	−	0.288214i
$260$	68.5394	−	238.633i	0.263613	−	0.917818i
$261$		0			0
$262$	−40.7760			−0.155633
$263$		−	79.1644i		−	0.301005i	−0.988610	−	0.150503i	$-0.951911\pi$
$263$		−	79.1644i		−	0.301005i	0.988610	−	0.150503i	$-0.0480892\pi$
$264$		0			0
$265$	−311.541	−	89.4801i	−1.17563	−	0.337661i
$266$	170.791	−	150.649i	0.642071	−	0.566349i
$267$		0			0
$268$		−	44.8070i		−	0.167190i
$269$			53.2775i			0.198058i	0.995085	+	0.0990288i	$0.0315736\pi$
$269$			53.2775i			0.198058i	−0.995085	+	0.0990288i	$0.968426\pi$
$270$		0			0
$271$		−	237.638i		−	0.876892i	−0.898757	−	0.438446i	$-0.855529\pi$
$271$		−	237.638i		−	0.876892i	0.898757	−	0.438446i	$-0.144471\pi$
$272$	−29.0440			−0.106779
$273$		0			0
$274$	−168.928			−0.616524
$275$	249.340	+	156.108i	0.906692	+	0.567664i
$276$		0			0
$277$		−	168.185i		−	0.607167i	−0.952805	−	0.303583i	$-0.901817\pi$
$277$		−	168.185i		−	0.607167i	0.952805	−	0.303583i	$-0.0981831\pi$
$278$	284.183			1.02224
$279$		0			0
$280$	89.4335	−	42.4459i	0.319405	−	0.151593i
$281$	−128.175			−0.456140			−0.228070	−	0.973645i	$-0.573242\pi$
$281$	−128.175			−0.456140			−0.228070	+	0.973645i	$0.573242\pi$
$282$		0			0
$283$	72.7293			0.256994			0.128497	−	0.991710i	$-0.458985\pi$
$283$	72.7293			0.256994			0.128497	+	0.991710i	$0.458985\pi$
$284$	183.004			0.644382
$285$		0			0
$286$			413.168i			1.44464i
$287$	75.1396	+	85.1859i	0.261810	+	0.296815i
$288$		0			0
$289$	−236.278			−0.817570
$290$	−387.974	−	111.433i	−1.33784	−	0.384252i
$291$		0			0
$292$	143.851			0.492641
$293$	273.216			0.932477			0.466238	−	0.884659i	$-0.345609\pi$
$293$	273.216			0.932477			0.466238	+	0.884659i	$0.345609\pi$
$294$		0			0
$295$	392.955	+	112.864i	1.33205	+	0.382589i
$296$	−40.2191			−0.135875
$297$		0			0
$298$		−	8.06786i		−	0.0270734i
$299$		−	656.014i		−	2.19403i
$300$		0			0
$301$	381.143	+	432.103i	1.26626	+	1.43556i
$302$			306.163i			1.01379i
$303$		0			0
$304$		−	92.0201i		−	0.302698i
$305$	63.0703	+	18.1149i	0.206788	+	0.0593931i
$306$		0			0
$307$	336.086			1.09474			0.547372	−	0.836889i	$-0.315628\pi$
$307$	336.086			1.09474			0.547372	+	0.836889i	$0.315628\pi$
$308$	−123.545	+	108.975i	−0.401121	+	0.353815i
$309$		0			0
$310$	−19.9539	+	69.4732i	−0.0643674	+	0.224107i
$311$			497.276i			1.59896i	0.600693	+	0.799480i	$0.294891\pi$
$311$			497.276i			1.59896i	−0.600693	+	0.799480i	$0.705109\pi$
$312$		0			0
$313$	−252.024			−0.805188			−0.402594	−	0.915379i	$-0.631891\pi$
$313$	−252.024			−0.805188			−0.402594	+	0.915379i	$0.631891\pi$
$314$			153.141i			0.487710i
$315$		0			0
$316$	−90.5604			−0.286584
$317$			270.203i			0.852377i	0.904634	+	0.426188i	$0.140144\pi$
$317$			270.203i			0.852377i	−0.904634	+	0.426188i	$0.859856\pi$
$318$		0			0
$319$	671.737			2.10576
$320$	11.0423	−	38.4457i	0.0345071	−	0.120143i
$321$		0			0
$322$	196.161	−	173.027i	0.609196	−	0.537351i
$323$			167.040i			0.517150i
$324$		0			0
$325$	−526.097	−	329.380i	−1.61876	−	1.01348i
$326$	−331.484			−1.01682
$327$		0			0
$328$	45.8971			0.139930
$329$	−271.211	+	239.226i	−0.824351	+	0.727132i
$330$		0			0
$331$	−306.813			−0.926926			−0.463463	−	0.886116i	$-0.653393\pi$
$331$	−306.813			−0.926926			−0.463463	+	0.886116i	$0.653393\pi$
$332$	35.4656			0.106824
$333$		0			0
$334$			59.2315i			0.177340i
$335$	−107.665	−	30.9232i	−0.321387	−	0.0923080i
$336$		0			0
$337$			485.903i			1.44185i	0.693014	+	0.720924i	$0.256282\pi$
$337$			485.903i			1.44185i	−0.693014	+	0.720924i	$0.743718\pi$
$338$		−	632.764i		−	1.87208i
$339$		0			0
$340$	−20.0445	+	69.7885i	−0.0589543	+	0.205260i
$341$		−	120.286i		−	0.352744i
$342$		0			0
$343$	193.009	+	283.543i	0.562708	+	0.826656i
$344$	232.812			0.676779
$345$		0			0
$346$			18.4273i			0.0532581i
$347$			8.02712i			0.0231329i	0.999933	+	0.0115665i	$0.00368180\pi$
$347$			8.02712i			0.0231329i	−0.999933	+	0.0115665i	$0.996318\pi$
$348$		0			0
$349$		−	649.899i		−	1.86217i	−0.364798	−	0.931087i	$-0.618862\pi$
$349$		−	649.899i		−	1.86217i	0.364798	−	0.931087i	$-0.381138\pi$
$350$	−40.2696	−	244.189i	−0.115056	−	0.697683i
$351$		0			0
$352$			66.5647i			0.189104i
$353$	−396.496			−1.12322			−0.561608	−	0.827403i	$-0.689817\pi$
$353$	−396.496			−1.12322			−0.561608	+	0.827403i	$0.689817\pi$
$354$		0			0
$355$	126.299	−	439.733i	0.355772	−	1.23868i
$356$			155.160i			0.435843i
$357$		0			0
$358$		−	34.1636i		−	0.0954291i
$359$	−398.981			−1.11137			−0.555684	−	0.831394i	$-0.687543\pi$
$359$	−398.981			−1.11137			−0.555684	+	0.831394i	$0.687543\pi$
$360$		0			0
$361$	−168.231			−0.466014
$362$	61.5334			0.169982
$363$		0			0
$364$	260.675	−	229.933i	0.716141	−	0.631683i
$365$	99.2777	−	345.653i	0.271994	−	0.946996i
$366$		0			0
$367$	−506.200			−1.37929			−0.689646	−	0.724147i	$-0.742234\pi$
$367$	−506.200			−1.37929			−0.689646	+	0.724147i	$0.742234\pi$
$368$		−	105.689i		−	0.287199i
$369$		0			0
$370$	−27.7569	+	96.6406i	−0.0750186	+	0.261191i
$371$	−300.183	−	340.318i	−0.809119	−	0.917300i
$372$		0			0
$373$			278.751i			0.747322i	0.927565	+	0.373661i	$0.121898\pi$
$373$			278.751i			0.747322i	−0.927565	+	0.373661i	$0.878102\pi$
$374$		−	120.832i		−	0.323079i
$375$		0			0
$376$			146.125i			0.388631i
$377$	−1417.34			−3.75951
$378$		0			0
$379$	−515.959			−1.36137			−0.680685	−	0.732576i	$-0.738318\pi$
$379$	−515.959			−1.36137			−0.680685	+	0.732576i	$0.738318\pi$
$380$	−221.111	−	63.5069i	−0.581870	−	0.167123i
$381$		0			0
$382$		−	348.706i		−	0.912842i
$383$	238.715			0.623276			0.311638	−	0.950201i	$-0.399122\pi$
$383$	238.715			0.623276			0.311638	+	0.950201i	$0.399122\pi$
$384$		0			0
$385$	176.587	+	372.069i	0.458669	+	0.966414i
$386$	−228.926			−0.593073
$387$		0			0
$388$	12.3148			0.0317392
$389$	170.748			0.438941			0.219471	−	0.975619i	$-0.429567\pi$
$389$	170.748			0.438941			0.219471	+	0.975619i	$0.429567\pi$
$390$		0			0
$391$			191.852i			0.490671i
$392$	137.509	+	17.3011i	0.350788	+	0.0441355i
$393$		0			0
$394$	63.4105			0.160940
$395$	−62.4995	+	217.603i	−0.158227	+	0.550895i
$396$		0			0
$397$	80.7184			0.203321			0.101660	−	0.994819i	$-0.467584\pi$
$397$	80.7184			0.203321			0.101660	+	0.994819i	$0.467584\pi$
$398$	−162.305			−0.407801
$399$		0			0
$400$	−84.7586	−	53.0659i	−0.211896	−	0.132665i
$401$	−469.375			−1.17051			−0.585255	−	0.810849i	$-0.699006\pi$
$401$	−469.375			−1.17051			−0.585255	+	0.810849i	$0.699006\pi$
$402$		0			0
$403$			253.798i			0.629770i
$404$		−	285.967i		−	0.707839i
$405$		0			0
$406$	−373.830	−	423.812i	−0.920763	−	1.04387i
$407$		−	167.323i		−	0.411114i
$408$		0			0
$409$			671.238i			1.64117i	0.571525	+	0.820585i	$0.306352\pi$
$409$			671.238i			1.64117i	−0.571525	+	0.820585i	$0.693648\pi$
$410$	31.6755	−	110.284i	0.0772573	−	0.268985i
$411$		0			0
$412$	−29.0584			−0.0705302
$413$	378.629	+	429.253i	0.916778	+	1.03935i
$414$		0			0
$415$	24.4763	−	85.2185i	0.0589789	−	0.205346i
$416$		−	140.449i		−	0.337617i
$417$		0			0
$418$	382.830			0.915862
$419$		−	16.1628i		−	0.0385747i	−0.999814	−	0.0192874i	$-0.993860\pi$
$419$		−	16.1628i		−	0.0385747i	0.999814	−	0.0192874i	$-0.00613974\pi$
$420$		0			0
$421$	−463.356			−1.10061			−0.550304	−	0.834964i	$-0.685488\pi$
$421$	−463.356			−1.10061			−0.550304	+	0.834964i	$0.685488\pi$
$422$			310.564i			0.735934i
$423$		0			0
$424$	−183.359			−0.432451
$425$	153.858	+	96.3279i	0.362019	+	0.226654i
$426$		0			0
$427$	60.7709	+	68.8961i	0.142321	+	0.161349i
$428$			156.846i			0.366462i
$429$		0			0
$430$	160.673	−	559.413i	0.373658	−	1.30096i
$431$	−425.457			−0.987140			−0.493570	−	0.869706i	$-0.664308\pi$
$431$	−425.457			−0.987140			−0.493570	+	0.869706i	$0.664308\pi$
$432$		0			0
$433$	−480.947			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$433$	−480.947			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$434$	−75.8904	+	66.9404i	−0.174863	+	0.154240i
$435$		0			0
$436$	149.485			0.342855
$437$	−607.845			−1.39095
$438$		0			0
$439$			73.3796i			0.167152i	0.996501	+	0.0835759i	$0.0266341\pi$
$439$			73.3796i			0.167152i	−0.996501	+	0.0835759i	$0.973366\pi$
$440$	159.945	+	45.9390i	0.363512	+	0.104407i
$441$		0			0
$442$			254.950i			0.576809i
$443$		−	72.4361i		−	0.163513i	−0.996652	−	0.0817563i	$-0.973947\pi$
$443$		−	72.4361i		−	0.163513i	0.996652	−	0.0817563i	$-0.0260529\pi$
$444$		0			0
$445$	372.827	+	107.082i	0.837813	+	0.240635i
$446$			5.05019i			0.0113233i
$447$		0			0
$448$	41.9969	−	37.0440i	0.0937431	−	0.0826876i
$449$	721.760			1.60748			0.803742	−	0.594978i	$-0.202839\pi$
$449$	721.760			1.60748			0.803742	+	0.594978i	$0.202839\pi$
$450$		0			0
$451$			190.945i			0.423382i
$452$			170.483i			0.377175i
$453$		0			0
$454$			96.2580i			0.212022i
$455$	−372.592	−	785.050i	−0.818883	−	1.72539i
$456$		0			0
$457$			622.396i			1.36192i	0.732322	+	0.680958i	$0.238436\pi$
$457$			622.396i			1.36192i	−0.732322	+	0.680958i	$0.761564\pi$
$458$	254.585			0.555863
$459$		0			0
$460$	−253.956	−	72.9405i	−0.552077	−	0.158566i
$461$		−	600.196i		−	1.30194i	−0.759102	−	0.650971i	$-0.774362\pi$
$461$		−	600.196i		−	1.30194i	0.759102	−	0.650971i	$-0.225638\pi$
$462$		0			0
$463$		−	127.513i		−	0.275406i	−0.990474	−	0.137703i	$-0.956028\pi$
$463$		−	127.513i		−	0.275406i	0.990474	−	0.137703i	$-0.0439720\pi$
$464$	−228.344			−0.492122
$465$		0			0
$466$	162.927			0.349628
$467$	−11.4438			−0.0245048			−0.0122524	−	0.999925i	$-0.503900\pi$
$467$	−11.4438			−0.0245048			−0.0122524	+	0.999925i	$0.503900\pi$
$468$		0			0
$469$	−103.740	−	117.610i	−0.221193	−	0.250767i
$470$	351.118	+	100.847i	0.747060	+	0.214569i
$471$		0			0
$472$	231.276			0.489992
$473$			968.566i			2.04771i
$474$		0			0
$475$	−305.195	+	487.468i	−0.642517	+	1.02625i
$476$	−76.2349	+	67.2442i	−0.160157	+	0.141269i
$477$		0			0
$478$			22.1853i			0.0464127i
$479$		−	205.867i		−	0.429784i	−0.976638	−	0.214892i	$-0.931060\pi$
$479$		−	205.867i		−	0.429784i	0.976638	−	0.214892i	$-0.0689400\pi$
$480$		0			0
$481$			353.045i			0.733981i
$482$	429.131			0.890314
$483$		0			0
$484$	−34.9284			−0.0721662
$485$	8.49897	−	29.5907i	0.0175236	−	0.0610118i
$486$		0			0
$487$		−	603.451i		−	1.23912i	−0.784950	−	0.619559i	$-0.787311\pi$
$487$		−	603.451i		−	1.23912i	0.784950	−	0.619559i	$-0.212689\pi$
$488$	37.1204			0.0760664
$489$		0			0
$490$	136.473	−	318.473i	0.278515	−	0.649946i
$491$	522.576			1.06431			0.532154	−	0.846647i	$-0.321383\pi$
$491$	522.576			1.06431			0.532154	+	0.846647i	$0.321383\pi$
$492$		0			0
$493$	414.503			0.840776
$494$	−807.756			−1.63513
$495$		0			0
$496$			40.8888i			0.0824372i
$497$	480.351	−	423.701i	0.966501	−	0.852518i
$498$		0			0
$499$	124.569			0.249636			0.124818	−	0.992180i	$-0.460165\pi$
$499$	124.569			0.249636			0.124818	+	0.992180i	$0.460165\pi$
$500$	−186.005	+	167.039i	−0.372010	+	0.334079i
$501$		0			0
$502$	113.878			0.226849
$503$	33.8355			0.0672673			0.0336337	−	0.999434i	$-0.489292\pi$
$503$	33.8355			0.0672673			0.0336337	+	0.999434i	$0.489292\pi$
$504$		0			0
$505$	−687.137	−	197.358i	−1.36067	−	0.390807i
$506$	439.698			0.868968
$507$		0			0
$508$		−	133.547i		−	0.262887i
$509$		−	630.938i		−	1.23956i	−0.784774	−	0.619782i	$-0.787221\pi$
$509$		−	630.938i		−	1.23956i	0.784774	−	0.619782i	$-0.212779\pi$
$510$		0			0
$511$	377.582	−	333.052i	0.738907	−	0.651765i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$			55.2974i			0.107582i
$515$	−20.0544	+	69.8232i	−0.0389406	+	0.135579i
$516$		0			0
$517$	−607.924			−1.17587
$518$	−105.567	+	93.1174i	−0.203798	+	0.179763i
$519$		0			0
$520$	−337.477	−	96.9294i	−0.648995	−	0.186403i
$521$		−	492.821i		−	0.945914i	−0.881086	−	0.472957i	$-0.843187\pi$
$521$		−	492.821i		−	0.945914i	0.881086	−	0.472957i	$-0.156813\pi$
$522$		0			0
$523$	−331.944			−0.634692			−0.317346	−	0.948310i	$-0.602792\pi$
$523$	−331.944			−0.634692			−0.317346	+	0.948310i	$0.602792\pi$
$524$			57.6659i			0.110049i
$525$		0			0
$526$	−111.955			−0.212843
$527$		−	74.2235i		−	0.140842i
$528$		0			0
$529$	−169.138			−0.319731
$530$	−126.544	+	440.586i	−0.238762	+	0.831294i
$531$		0			0
$532$	−213.050	−	241.535i	−0.400469	−	0.454013i
$533$		−	402.887i		−	0.755885i
$534$		0			0
$535$	376.877	+	108.246i	0.704443	+	0.202328i
$536$	−63.3667			−0.118221
$537$		0			0
$538$	75.3457			0.140048
$539$	−71.9776	+	572.077i	−0.133539	+	1.06137i
$540$		0			0
$541$	−96.8104			−0.178947			−0.0894735	−	0.995989i	$-0.528518\pi$
$541$	−96.8104			−0.178947			−0.0894735	+	0.995989i	$0.528518\pi$
$542$	−336.071			−0.620057
$543$		0			0
$544$			41.0744i			0.0755045i
$545$	103.166	−	359.190i	0.189295	−	0.659065i
$546$		0			0
$547$		−	772.034i		−	1.41140i	−0.708512	−	0.705699i	$-0.750633\pi$
$547$		−	772.034i		−	1.41140i	0.708512	−	0.705699i	$-0.249367\pi$
$548$			238.900i			0.435948i
$549$		0			0
$550$	220.770	−	352.620i	0.401399	−	0.641128i
$551$			1313.27i			2.38343i
$552$		0			0
$553$	−237.704	+	209.670i	−0.429844	+	0.379150i
$554$	−237.850			−0.429332
$555$		0			0
$556$		−	401.896i		−	0.722834i
$557$			42.3682i			0.0760650i	0.999277	+	0.0380325i	$0.0121090\pi$
$557$			42.3682i			0.0760650i	−0.999277	+	0.0380325i	$0.987891\pi$
$558$		0			0
$559$		−	2043.63i		−	3.65587i
$560$	−60.0276	−	126.478i	−0.107192	−	0.225854i
$561$		0			0
$562$			181.267i			0.322540i
$563$	−370.393			−0.657891			−0.328946	−	0.944349i	$-0.606693\pi$
$563$	−370.393			−0.657891			−0.328946	+	0.944349i	$0.606693\pi$
$564$		0			0
$565$	409.646	+	117.658i	0.725038	+	0.208244i
$566$		−	102.855i		−	0.181722i
$567$		0			0
$568$		−	258.807i		−	0.455647i
$569$	419.012			0.736401			0.368201	−	0.929746i	$-0.379974\pi$
$569$	419.012			0.736401			0.368201	+	0.929746i	$0.379974\pi$
$570$		0			0
$571$	−113.210			−0.198266			−0.0991329	−	0.995074i	$-0.531607\pi$
$571$	−113.210			−0.198266			−0.0991329	+	0.995074i	$0.531607\pi$
$572$	584.307			1.02152
$573$		0			0
$574$	120.471	−	106.263i	0.209880	−	0.185128i
$575$	−350.531	+	559.879i	−0.609618	+	0.973702i
$576$		0			0
$577$	−604.749			−1.04809			−0.524046	−	0.851690i	$-0.675578\pi$
$577$	−604.749			−1.04809			−0.524046	+	0.851690i	$0.675578\pi$
$578$			334.147i			0.578109i
$579$		0			0
$580$	−157.590	+	548.678i	−0.271707	+	0.945997i
$581$	93.0902	−	82.1117i	0.160224	−	0.141328i
$582$		0			0
$583$		−	762.829i		−	1.30845i
$584$		−	203.436i		−	0.348350i
$585$		0			0
$586$		−	386.385i		−	0.659360i
$587$	458.151			0.780496			0.390248	−	0.920710i	$-0.372389\pi$
$587$	458.151			0.780496			0.390248	+	0.920710i	$0.372389\pi$
$588$		0			0
$589$	235.162			0.399257
$590$	159.613	−	555.723i	0.270531	−	0.941903i
$591$		0			0
$592$			56.8784i			0.0960784i
$593$	780.457			1.31612			0.658059	−	0.752967i	$-0.271378\pi$
$593$	780.457			1.31612			0.658059	+	0.752967i	$0.271378\pi$
$594$		0			0
$595$	108.965	+	229.589i	0.183135	+	0.385864i
$596$	−11.4097			−0.0191438
$597$		0			0
$598$	−927.744			−1.55141
$599$	11.7391			0.0195977			0.00979887	−	0.999952i	$-0.496881\pi$
$599$	11.7391			0.0195977			0.00979887	+	0.999952i	$0.496881\pi$
$600$		0			0
$601$			182.878i			0.304290i	0.988358	+	0.152145i	$0.0486181\pi$
$601$			182.878i			0.304290i	−0.988358	+	0.152145i	$0.951382\pi$
$602$	611.086	−	539.018i	1.01509	−	0.895379i
$603$		0			0
$604$	432.980			0.716854
$605$	−24.1056	+	83.9279i	−0.0398439	+	0.138724i
$606$		0			0
$607$	777.171			1.28035			0.640174	−	0.768230i	$-0.278862\pi$
$607$	777.171			1.28035			0.640174	+	0.768230i	$0.278862\pi$
$608$	−130.136			−0.214040
$609$		0			0
$610$	25.6183	−	89.1949i	0.0419973	−	0.146221i
$611$	1282.69			2.09934
$612$		0			0
$613$			106.169i			0.173196i	0.996243	+	0.0865978i	$0.0275995\pi$
$613$			106.169i			0.173196i	−0.996243	+	0.0865978i	$0.972400\pi$
$614$		−	475.298i		−	0.774101i
$615$		0			0
$616$	154.114	+	174.719i	0.250185	+	0.283635i
$617$		−	680.569i		−	1.10303i	−0.834165	−	0.551515i	$-0.814050\pi$
$617$		−	680.569i		−	1.10303i	0.834165	−	0.551515i	$-0.185950\pi$
$618$		0			0
$619$			861.054i			1.39104i	0.718507	+	0.695520i	$0.244826\pi$
$619$			861.054i			1.39104i	−0.718507	+	0.695520i	$0.755174\pi$
$620$	98.2499	+	28.2191i	0.158468	+	0.0455147i
$621$		0			0
$622$	703.255			1.13063
$623$	359.235	+	407.265i	0.576621	+	0.653716i
$624$		0			0
$625$	273.002	+	562.223i	0.436803	+	0.899557i
$626$			356.416i			0.569354i
$627$		0			0
$628$	216.574			0.344863
$629$		−	103.249i		−	0.164147i
$630$		0			0
$631$	−489.247			−0.775352			−0.387676	−	0.921796i	$-0.626722\pi$
$631$	−489.247			−0.775352			−0.387676	+	0.921796i	$0.626722\pi$
$632$			128.072i			0.202645i
$633$		0			0
$634$	382.125			0.602721
$635$	−320.893	−	92.1661i	−0.505344	−	0.145144i
$636$		0			0
$637$	151.870	−	1207.06i	0.238414	−	1.89491i
$638$		−	949.980i		−	1.48900i
$639$		0			0
$640$	−54.3704	−	15.6161i	−0.0849537	−	0.0244002i
$641$	−962.813			−1.50205			−0.751024	−	0.660275i	$-0.770440\pi$
$641$	−962.813			−1.50205			−0.751024	+	0.660275i	$0.770440\pi$
$642$		0			0
$643$	581.069			0.903684			0.451842	−	0.892098i	$-0.350767\pi$
$643$	581.069			0.903684			0.451842	+	0.892098i	$0.350767\pi$
$644$	−244.697	−	277.414i	−0.379964	−	0.430766i
$645$		0			0
$646$	236.230			0.365681
$647$	−339.036			−0.524012			−0.262006	−	0.965066i	$-0.584384\pi$
$647$	−339.036			−0.524012			−0.262006	+	0.965066i	$0.584384\pi$
$648$		0			0
$649$			962.177i			1.48255i
$650$	−465.814	+	744.014i	−0.716637	+	1.14464i
$651$		0			0
$652$			468.789i			0.719002i
$653$			289.383i			0.443159i	0.975142	+	0.221580i	$0.0711213\pi$
$653$			289.383i			0.443159i	−0.975142	+	0.221580i	$0.928879\pi$
$654$		0			0
$655$	138.563	+	39.7976i	0.211546	+	0.0607598i
$656$		−	64.9083i		−	0.0989456i
$657$		0			0
$658$	338.317	+	383.551i	0.514160	+	0.582904i
$659$	−62.6627			−0.0950875			−0.0475438	−	0.998869i	$-0.515139\pi$
$659$	−62.6627			−0.0950875			−0.0475438	+	0.998869i	$0.515139\pi$
$660$		0			0
$661$			148.826i			0.225153i	0.993643	+	0.112577i	$0.0359104\pi$
$661$			148.826i			0.225153i	−0.993643	+	0.112577i	$0.964090\pi$
$662$			433.899i			0.655436i
$663$		0			0
$664$		−	50.1559i		−	0.0755360i
$665$	−727.407	+	345.234i	−1.09385	+	0.519149i
$666$		0			0
$667$			1508.35i			2.26139i
$668$	83.7660			0.125398
$669$		0			0
$670$	−43.7320	+	152.261i	−0.0652716	+	0.227255i
$671$			154.432i			0.230152i
$672$		0			0
$673$			833.049i			1.23781i	0.785464	+	0.618907i	$0.212424\pi$
$673$			833.049i			1.23781i	−0.785464	+	0.618907i	$0.787576\pi$
$674$	687.170			1.01954
$675$		0			0
$676$	−894.864			−1.32376
$677$	391.042			0.577611			0.288805	−	0.957388i	$-0.406742\pi$
$677$	391.042			0.577611			0.288805	+	0.957388i	$0.406742\pi$
$678$		0			0
$679$	32.3240	−	28.5119i	0.0476053	−	0.0419910i
$680$	98.6959	+	28.3472i	0.145141	+	0.0416870i
$681$		0			0
$682$	−170.110			−0.249427
$683$		−	992.775i		−	1.45355i	−0.686875	−	0.726775i	$-0.741018\pi$
$683$		−	992.775i		−	1.45355i	0.686875	−	0.726775i	$-0.258982\pi$
$684$		0			0
$685$	574.041	+	164.875i	0.838016	+	0.240693i
$686$	400.990	−	272.956i	0.584534	−	0.397894i
$687$		0			0
$688$		−	329.246i		−	0.478555i
$689$			1609.54i			2.33605i
$690$		0			0
$691$		−	697.871i		−	1.00994i	−0.863136	−	0.504972i	$-0.831503\pi$
$691$		−	697.871i		−	1.00994i	0.863136	−	0.504972i	$-0.168497\pi$
$692$	26.0601			0.0376592
$693$		0			0
$694$	11.3521			0.0163574
$695$	−965.697	−	277.365i	−1.38949	−	0.399086i
$696$		0			0
$697$			117.825i			0.169046i
$698$	−919.095			−1.31676
$699$		0			0
$700$	−345.336	+	56.9498i	−0.493337	+	0.0813568i
$701$	222.920			0.318003			0.159002	−	0.987278i	$-0.449172\pi$
$701$	222.920			0.318003			0.159002	+	0.987278i	$0.449172\pi$
$702$		0			0
$703$	327.122			0.465323
$704$	94.1367			0.133717
$705$		0			0
$706$			560.729i			0.794234i
$707$	−662.085	−	750.608i	−0.936472	−	1.06168i
$708$		0			0
$709$	−267.679			−0.377544			−0.188772	−	0.982021i	$-0.560451\pi$
$709$	−267.679			−0.377544			−0.188772	+	0.982021i	$0.560451\pi$
$710$	−621.876	−	178.614i	−0.875882	−	0.251568i
$711$		0			0
$712$	219.429			0.308187
$713$	270.094			0.378814
$714$		0			0
$715$	403.255	−	1404.00i	0.563992	−	1.96364i
$716$	−48.3147			−0.0674786
$717$		0			0
$718$			564.244i			0.785856i
$719$			217.258i			0.302167i	0.988521	+	0.151083i	$0.0482762\pi$
$719$			217.258i			0.302167i	−0.988521	+	0.151083i	$0.951724\pi$
$720$		0			0
$721$	−76.2728	+	67.2776i	−0.105787	+	0.0933115i
$722$			237.915i			0.329522i
$723$		0			0
$724$		−	87.0213i		−	0.120195i
$725$	1209.63	+	757.331i	1.66846	+	1.04459i
$726$		0			0
$727$	−771.678			−1.06146			−0.530728	−	0.847543i	$-0.678081\pi$
$727$	−771.678			−1.06146			−0.530728	+	0.847543i	$0.678081\pi$
$728$	−325.174	−	368.650i	−0.446668	−	0.506388i
$729$		0			0
$730$	−488.828	−	140.400i	−0.669627	−	0.192329i
$731$			597.664i			0.817598i
$732$		0			0
$733$	1103.98			1.50611			0.753053	−	0.657960i	$-0.228580\pi$
$733$	1103.98			1.50611			0.753053	+	0.657960i	$0.228580\pi$
$734$			715.875i			0.975306i
$735$		0			0
$736$	−149.467			−0.203080
$737$		−	263.624i		−	0.357699i
$738$		0			0
$739$	264.136			0.357423			0.178712	−	0.983901i	$-0.442807\pi$
$739$	264.136			0.357423			0.178712	+	0.983901i	$0.442807\pi$
$740$	136.671	+	39.2541i	0.184690	+	0.0530461i
$741$		0			0
$742$	−481.283	+	424.523i	−0.648629	+	0.572134i
$743$			1069.03i			1.43880i	0.694595	+	0.719401i	$0.255583\pi$
$743$			1069.03i			1.43880i	−0.694595	+	0.719401i	$0.744417\pi$
$744$		0			0
$745$	−7.87429	+	27.4158i	−0.0105695	+	0.0367997i
$746$	394.213			0.528436
$747$		0			0
$748$	−170.882			−0.228451
$749$	363.137	+	411.689i	0.484829	+	0.549652i
$750$		0			0
$751$	987.190			1.31450			0.657250	−	0.753673i	$-0.271720\pi$
$751$	987.190			1.31450			0.657250	+	0.753673i	$0.271720\pi$
$752$	206.653			0.274804
$753$		0			0
$754$			2004.42i			2.65838i
$755$	298.817	−	1040.39i	0.395785	−	1.37800i
$756$		0			0
$757$			1173.09i			1.54966i	0.632169	+	0.774830i	$0.282165\pi$
$757$			1173.09i			1.54966i	−0.632169	+	0.774830i	$0.717835\pi$
$758$			729.677i			0.962634i
$759$		0			0
$760$	−89.8123	+	312.698i	−0.118174	+	0.411445i
$761$		−	271.712i		−	0.357045i	−0.983936	−	0.178523i	$-0.942868\pi$
$761$		−	271.712i		−	0.357045i	0.983936	−	0.178523i	$-0.0571318\pi$
$762$		0			0
$763$	392.369	−	346.095i	0.514245	−	0.453598i
$764$	−493.144			−0.645477
$765$		0			0
$766$		−	337.594i		−	0.440723i
$767$		−	2030.15i		−	2.64687i
$768$		0			0
$769$		−	1031.82i		−	1.34177i	−0.741563	−	0.670883i	$-0.765915\pi$
$769$		−	1031.82i		−	1.34177i	0.741563	−	0.670883i	$-0.234085\pi$
$770$	526.185	−	249.732i	0.683358	−	0.324328i
$771$		0			0
$772$			323.751i			0.419366i
$773$	−877.988			−1.13582			−0.567910	−	0.823091i	$-0.692248\pi$
$773$	−877.988			−1.13582			−0.567910	+	0.823091i	$0.692248\pi$
$774$		0			0
$775$	135.613	−	216.605i	0.174984	−	0.279490i
$776$		−	17.4158i		−	0.0224430i
$777$		0			0
$778$		−	241.474i		−	0.310378i
$779$	−373.304			−0.479210
$780$		0			0
$781$	1076.71			1.37863
$782$	271.320			0.346957
$783$		0			0
$784$	24.4675	−	194.467i	0.0312085	−	0.248044i
$785$	149.467	−	520.396i	0.190403	−	0.662924i
$786$		0			0
$787$	−142.727			−0.181356			−0.0906780	−	0.995880i	$-0.528903\pi$
$787$	−142.727			−0.181356			−0.0906780	+	0.995880i	$0.528903\pi$
$788$		−	89.6759i		−	0.113802i
$789$		0			0
$790$	307.738	+	88.3876i	0.389541	+	0.111883i
$791$	394.712	+	447.486i	0.499004	+	0.565721i
$792$		0			0
$793$		−	325.844i		−	0.410901i
$794$		−	114.153i		−	0.143770i
$795$		0			0
$796$			229.534i			0.288359i
$797$	317.415			0.398262			0.199131	−	0.979973i	$-0.436188\pi$
$797$	317.415			0.398262			0.199131	+	0.979973i	$0.436188\pi$
$798$		0			0
$799$	−375.126			−0.469495
$800$	−75.0465	+	119.867i	−0.0938081	+	0.149833i
$801$		0			0
$802$			663.796i			0.827676i
$803$	846.354			1.05399
$804$		0			0
$805$	−835.460	+	396.517i	−1.03784	+	0.492567i
$806$	358.924			0.445315
$807$		0			0
$808$	−404.418			−0.500518
$809$	1392.39			1.72112			0.860560	−	0.509350i	$-0.170114\pi$
$809$	1392.39			1.72112			0.860560	+	0.509350i	$0.170114\pi$
$810$		0			0
$811$		−	1087.46i		−	1.34089i	−0.741958	−	0.670447i	$-0.766102\pi$
$811$		−	1087.46i		−	1.34089i	0.741958	−	0.670447i	$-0.233898\pi$
$812$	−599.360	+	528.675i	−0.738128	+	0.651078i
$813$		0			0
$814$	−236.631			−0.290701
$815$	1126.43	+	323.531i	1.38212	+	0.396970i
$816$		0			0
$817$	−1893.58			−2.31772
$818$	949.274			1.16048
$819$		0			0
$820$	−155.965	−	44.7959i	−0.190201	−	0.0546292i
$821$	−172.333			−0.209906			−0.104953	−	0.994477i	$-0.533469\pi$
$821$	−172.333			−0.209906			−0.104953	+	0.994477i	$0.533469\pi$
$822$		0			0
$823$		−	215.439i		−	0.261773i	−0.991397	−	0.130886i	$-0.958218\pi$
$823$		−	215.439i		−	0.261773i	0.991397	−	0.130886i	$-0.0417823\pi$
$824$			41.0948i			0.0498724i
$825$		0			0
$826$	607.055	−	535.463i	0.734934	−	0.648260i
$827$			797.435i			0.964250i	0.876102	+	0.482125i	$0.160135\pi$
$827$			797.435i			0.964250i	−0.876102	+	0.482125i	$0.839865\pi$
$828$		0			0
$829$		−	389.170i		−	0.469445i	−0.972062	−	0.234723i	$-0.924582\pi$
$829$		−	389.170i		−	0.469445i	0.972062	−	0.234723i	$-0.0754182\pi$
$830$	−120.517	−	34.6146i	−0.145201	−	0.0417044i
$831$		0			0
$832$	−198.624			−0.238731
$833$	−44.4146	+	353.006i	−0.0533188	+	0.423777i
$834$		0			0
$835$	57.8104	−	201.277i	0.0692340	−	0.241051i
$836$		−	541.404i		−	0.647612i
$837$		0			0
$838$	−22.8577			−0.0272764
$839$			280.262i			0.334043i	0.985953	+	0.167021i	$0.0534149\pi$
$839$			280.262i			0.334043i	−0.985953	+	0.167021i	$0.946585\pi$
$840$		0			0
$841$	2417.83			2.87494
$842$			655.285i			0.778248i
$843$		0			0
$844$	439.204			0.520384
$845$	−617.582	+	2150.23i	−0.730867	+	2.54465i
$846$		0			0
$847$	−91.6804	+	80.8681i	−0.108241	+	0.0954760i
$848$			259.309i			0.305789i
$849$		0			0
$850$	136.228	−	217.588i	0.160268	−	0.255986i
$851$	375.715			0.441498
$852$		0			0
$853$	245.874			0.288246			0.144123	−	0.989560i	$-0.453964\pi$
$853$	245.874			0.288246			0.144123	+	0.989560i	$0.453964\pi$
$854$	97.4339	−	85.9431i	0.114091	−	0.100636i
$855$		0			0
$856$	221.813			0.259127
$857$	798.850			0.932147			0.466074	−	0.884746i	$-0.345668\pi$
$857$	798.850			0.932147			0.466074	+	0.884746i	$0.345668\pi$
$858$		0			0
$859$			1274.93i			1.48420i	0.670287	+	0.742102i	$0.266171\pi$
$859$			1274.93i			1.48420i	−0.670287	+	0.742102i	$0.733829\pi$
$860$	−791.129	−	227.226i	−0.919918	−	0.264216i
$861$		0			0
$862$			601.688i			0.698013i
$863$		−	736.114i		−	0.852971i	−0.904494	−	0.426486i	$-0.859751\pi$
$863$		−	736.114i		−	0.852971i	0.904494	−	0.426486i	$-0.140249\pi$
$864$		0			0
$865$	17.9852	−	62.6187i	0.0207921	−	0.0723915i
$866$			680.162i			0.785407i
$867$		0			0
$868$	94.6680	+	107.325i	0.109064	+	0.123647i
$869$	−532.816			−0.613137
$870$		0			0
$871$			556.236i			0.638617i
$872$		−	211.404i		−	0.242435i
$873$		0			0
$874$			859.623i			0.983551i
$875$	−101.488	+	869.094i	−0.115987	+	0.993251i
$876$		0			0
$877$		−	1103.15i		−	1.25787i	−0.777457	−	0.628936i	$-0.783491\pi$
$877$		−	1103.15i		−	1.25787i	0.777457	−	0.628936i	$-0.216509\pi$
$878$	103.774			0.118194
$879$		0			0
$880$	64.9676	−	226.197i	0.0738268	−	0.257042i
$881$		−	269.425i		−	0.305817i	−0.988240	−	0.152909i	$-0.951136\pi$
$881$		−	269.425i		−	0.305817i	0.988240	−	0.152909i	$-0.0488640\pi$
$882$		0			0
$883$		−	1077.49i		−	1.22026i	−0.792302	−	0.610129i	$-0.791118\pi$
$883$		−	1077.49i		−	1.22026i	0.792302	−	0.610129i	$-0.208882\pi$
$884$	360.553			0.407865
$885$		0			0
$886$	−102.440			−0.115621
$887$	−500.908			−0.564721			−0.282361	−	0.959308i	$-0.591117\pi$
$887$	−500.908			−0.564721			−0.282361	+	0.959308i	$0.591117\pi$
$888$		0			0
$889$	−309.194	−	350.534i	−0.347800	−	0.394302i
$890$	151.437	−	527.257i	0.170154	−	0.592423i
$891$		0			0
$892$	7.14204			0.00800678
$893$		−	1188.51i		−	1.33092i
$894$		0			0
$895$	−33.3439	+	116.093i	−0.0372558	+	0.129713i
$896$	−52.3882	−	59.3926i	−0.0584689	−	0.0662864i
$897$		0			0
$898$		−	1020.72i		−	1.13666i
$899$		−	583.546i		−	0.649106i
$900$		0			0
$901$		−	470.712i		−	0.522433i
$902$	270.038			0.299376
$903$		0			0
$904$	241.100			0.266703
$905$	−209.100	−	60.0570i	−0.231049	−	0.0663614i
$906$		0			0
$907$		−	789.727i		−	0.870702i	−0.900261	−	0.435351i	$-0.856624\pi$
$907$		−	789.727i		−	0.870702i	0.900261	−	0.435351i	$-0.143376\pi$
$908$	136.129			0.149922
$909$		0			0
$910$	−1110.23	+	526.924i	−1.22003	+	0.579038i
$911$	−885.912			−0.972461			−0.486231	−	0.873830i	$-0.661629\pi$
$911$	−885.912			−0.972461			−0.486231	+	0.873830i	$0.661629\pi$
$912$		0			0
$913$	208.663			0.228547
$914$	880.200			0.963020
$915$		0			0
$916$		−	360.038i		−	0.393054i
$917$	133.511	+	151.362i	0.145596	+	0.165062i
$918$		0			0
$919$	−1411.37			−1.53577			−0.767883	−	0.640590i	$-0.778690\pi$
$919$	−1411.37			−1.53577			−0.767883	+	0.640590i	$0.778690\pi$
$920$	−103.153	+	359.147i	−0.112123	+	0.390378i
$921$		0			0
$922$	−848.805			−0.920613
$923$	−2271.82			−2.46134
$924$		0			0
$925$	188.644	−	301.308i	0.203939	−	0.325739i
$926$	−180.331			−0.194742
$927$		0			0
$928$			322.928i			0.347983i
$929$		−	1394.66i		−	1.50125i	−0.660727	−	0.750627i	$-0.729752\pi$
$929$		−	1394.66i		−	1.50125i	0.660727	−	0.750627i	$-0.270248\pi$
$930$		0			0
$931$	−1118.43	−	140.719i	−1.20132	−	0.151148i
$932$		−	230.413i		−	0.247225i
$933$		0			0
$934$			16.1839i			0.0173275i
$935$	−117.933	+	410.604i	−0.126131	+	0.439148i
$936$		0			0
$937$	448.660			0.478826			0.239413	−	0.970918i	$-0.423045\pi$
$937$	448.660			0.478826			0.239413	+	0.970918i	$0.423045\pi$
$938$	−166.325	+	146.710i	−0.177319	+	0.156407i
$939$		0			0
$940$	142.619	−	496.556i	0.151723	−	0.528251i
$941$		−	1061.98i		−	1.12856i	−0.825583	−	0.564281i	$-0.809153\pi$
$941$		−	1061.98i		−	1.12856i	0.825583	−	0.564281i	$-0.190847\pi$
$942$		0			0
$943$	−428.757			−0.454673
$944$		−	327.074i		−	0.346477i
$945$		0			0
$946$	1369.76			1.44795
$947$			470.708i			0.497051i	0.968625	+	0.248526i	$0.0799460\pi$
$947$			470.708i			0.497051i	−0.968625	+	0.248526i	$0.920054\pi$
$948$		0			0
$949$	−1785.77			−1.88174
$950$	689.384	+	431.611i	0.725667	+	0.454328i
$951$		0			0
$952$	95.0977	+	107.812i	0.0998925	+	0.113248i
$953$			625.282i			0.656119i	0.944657	+	0.328060i	$0.106395\pi$
$953$			625.282i			0.656119i	−0.944657	+	0.328060i	$0.893605\pi$
$954$		0			0
$955$	−340.339	+	1184.95i	−0.356376	+	1.24079i
$956$	31.3747			0.0328187
$957$		0			0
$958$	−291.139			−0.303903
$959$	553.113	+	627.065i	0.576760	+	0.653874i
$960$		0			0
$961$	856.506			0.891266
$962$	499.281			0.519003
$963$		0			0
$964$		−	606.884i		−	0.629547i
$965$	777.926	+	223.434i	0.806141	+	0.231538i
$966$		0			0
$967$			593.257i			0.613503i	0.951790	+	0.306751i	$0.0992420\pi$
$967$			593.257i			0.613503i	−0.951790	+	0.306751i	$0.900758\pi$
$968$			49.3963i			0.0510292i
$969$		0			0
$970$	−41.8476	−	12.0194i	−0.0431418	−	0.0123911i
$971$		−	1633.10i		−	1.68187i	−0.541133	−	0.840937i	$-0.682004\pi$
$971$		−	1633.10i		−	1.68187i	0.541133	−	0.840937i	$-0.317996\pi$
$972$		0			0
$973$	−930.490	−	1054.90i	−0.956311	−	1.08417i
$974$	−853.408			−0.876189
$975$		0			0
$976$		−	52.4962i		−	0.0537871i
$977$			1137.81i			1.16459i	0.812977	+	0.582296i	$0.197846\pi$
$977$			1137.81i			1.16459i	−0.812977	+	0.582296i	$0.802154\pi$
$978$		0			0
$979$			912.891i			0.932472i
$980$	−450.389	−	193.001i	−0.459581	−	0.196940i
$981$		0			0
$982$		−	739.034i		−	0.752580i
$983$	746.446			0.759355			0.379677	−	0.925119i	$-0.376035\pi$
$983$	746.446			0.759355			0.379677	+	0.925119i	$0.376035\pi$
$984$		0			0
$985$	−215.478	−	61.8891i	−0.218760	−	0.0628315i
$986$		−	586.195i		−	0.594518i
$987$		0			0
$988$			1142.34i			1.15621i
$989$	−2174.86			−2.19905
$990$		0			0
$991$	−765.218			−0.772168			−0.386084	−	0.922464i	$-0.626172\pi$
$991$	−765.218			−0.772168			−0.386084	+	0.922464i	$0.626172\pi$
$992$	57.8256			0.0582919
$993$		0			0
$994$	−599.204	−	679.319i	−0.602821	−	0.683420i
$995$	551.536	+	158.411i	0.554308	+	0.159207i
$996$		0			0
$997$	1799.05			1.80446			0.902230	−	0.431255i	$-0.141929\pi$
$997$	1799.05			1.80446			0.902230	+	0.431255i	$0.141929\pi$
$998$		−	176.167i		−	0.176520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.h.e.559.4		16
3.2	odd	2		210.3.h.a.139.10	yes	16
5.4	even	2	inner	630.3.h.e.559.13		16
7.6	odd	2	inner	630.3.h.e.559.5		16
12.11	even	2		1680.3.bd.a.769.11		16
15.2	even	4		1050.3.f.e.601.5		16
15.8	even	4		1050.3.f.e.601.12		16
15.14	odd	2		210.3.h.a.139.7	yes	16
21.20	even	2		210.3.h.a.139.15	yes	16
35.34	odd	2	inner	630.3.h.e.559.12		16
60.59	even	2		1680.3.bd.a.769.5		16
84.83	odd	2		1680.3.bd.a.769.6		16
105.62	odd	4		1050.3.f.e.601.1		16
105.83	odd	4		1050.3.f.e.601.16		16
105.104	even	2		210.3.h.a.139.2	✓	16
420.419	odd	2		1680.3.bd.a.769.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.2	✓	16	105.104	even	2
210.3.h.a.139.7	yes	16	15.14	odd	2
210.3.h.a.139.10	yes	16	3.2	odd	2
210.3.h.a.139.15	yes	16	21.20	even	2
630.3.h.e.559.4		16	1.1	even	1	trivial
630.3.h.e.559.5		16	7.6	odd	2	inner
630.3.h.e.559.12		16	35.34	odd	2	inner
630.3.h.e.559.13		16	5.4	even	2	inner
1050.3.f.e.601.1		16	105.62	odd	4
1050.3.f.e.601.5		16	15.2	even	4
1050.3.f.e.601.12		16	15.8	even	4
1050.3.f.e.601.16		16	105.83	odd	4
1680.3.bd.a.769.5		16	60.59	even	2
1680.3.bd.a.769.6		16	84.83	odd	2
1680.3.bd.a.769.11		16	12.11	even	2
1680.3.bd.a.769.12		16	420.419	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(-1.38028 + 4.80571i) q^{5} +(-5.24961 + 4.63050i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(-1.38028 + 4.80571i) q^{5} +(-5.24961 + 4.63050i) q^{7} +2.82843i q^{8} +(6.79630 + 1.95201i) q^{10} -11.7671 q^{11} +24.8280 q^{13} +(6.54852 + 7.42407i) q^{14} +4.00000 q^{16} -7.26100 q^{17} -23.0050i q^{19} +(2.76057 - 9.61141i) q^{20} +16.6412i q^{22} -26.4223i q^{23} +(-21.1896 - 13.2665i) q^{25} -35.1122i q^{26} +(10.4992 - 9.26101i) q^{28} -57.0861 q^{29} +10.2222i q^{31} -5.65685i q^{32} +10.2686i q^{34} +(-15.0069 - 31.6195i) q^{35} +14.2196i q^{37} -32.5340 q^{38} +(-13.5926 - 3.90403i) q^{40} -16.2271i q^{41} -82.3114i q^{43} +23.5342 q^{44} -37.3668 q^{46} +51.6631 q^{47} +(6.11686 - 48.6167i) q^{49} +(-18.7616 + 29.9667i) q^{50} -49.6561 q^{52} +64.8273i q^{53} +(16.2419 - 56.5491i) q^{55} +(-13.0970 - 14.8481i) q^{56} +80.7320i q^{58} -81.7685i q^{59} -13.1240i q^{61} +14.4564 q^{62} -8.00000 q^{64} +(-34.2697 + 119.316i) q^{65} +22.4035i q^{67} +14.5220 q^{68} +(-44.7167 + 21.2230i) q^{70} -91.5022 q^{71} -71.9256 q^{73} +20.1096 q^{74} +46.0100i q^{76} +(61.7726 - 54.4875i) q^{77} +45.2802 q^{79} +(-5.52113 + 19.2228i) q^{80} -22.9486 q^{82} -17.7328 q^{83} +(10.0222 - 34.8943i) q^{85} -116.406 q^{86} -33.2823i q^{88} -77.5800i q^{89} +(-130.338 + 114.966i) q^{91} +52.8446i q^{92} -73.0627i q^{94} +(110.555 + 31.7534i) q^{95} -6.15741 q^{97} +(-68.7544 - 8.65055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 16 * q - 32 * q^4	\( 16 q - 32 q^{4} - 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{25} - 64 q^{29} + 8 q^{35} + 192 q^{44} - 176 q^{46} + 224 q^{49} + 96 q^{50} + 32 q^{56} - 128 q^{64} - 368 q^{65} - 56 q^{70} + 384 q^{71} - 224 q^{74} - 608 q^{79} - 440 q^{85} - 416 q^{86} + 224 q^{91} + 560 q^{95}+O(q^{100}) \) 16 * q - 32 * q^4 - 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^25 - 64 * q^29 + 8 * q^35 + 192 * q^44 - 176 * q^46 + 224 * q^49 + 96 * q^50 + 32 * q^56 - 128 * q^64 - 368 * q^65 - 56 * q^70 + 384 * q^71 - 224 * q^74 - 608 * q^79 - 440 * q^85 - 416 * q^86 + 224 * q^91 + 560 * q^95

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