LMFDB - Embedded newform 630.3.h.e.559.9

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			559.9
Root			$0.500000 - 0.422343i$ of defining polynomial
Character	$\chi$	$=$	630.559
Dual form			630.3.h.e.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -2.00000 q^{4} +(-4.91728 - 0.905717i) q^{5} +(-1.91369 + 6.73333i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+1.41421i q^{2} -2.00000 q^{4} +(-4.91728 - 0.905717i) q^{5} +(-1.91369 + 6.73333i) q^{7} -2.82843i q^{8} +(1.28088 - 6.95409i) q^{10} -17.5116 q^{11} +4.83531 q^{13} +(-9.52237 - 2.70636i) q^{14} +4.00000 q^{16} +18.0284 q^{17} -9.13350i q^{19} +(9.83457 + 1.81143i) q^{20} -24.7651i q^{22} -3.72515i q^{23} +(23.3594 + 8.90734i) q^{25} +6.83816i q^{26} +(3.82738 - 13.4667i) q^{28} -1.12582 q^{29} -57.0859i q^{31} +5.65685i q^{32} +25.4960i q^{34} +(15.5086 - 31.3765i) q^{35} +41.3624i q^{37} +12.9167 q^{38} +(-2.56176 + 13.9082i) q^{40} +11.7156i q^{41} -64.4171i q^{43} +35.0232 q^{44} +5.26816 q^{46} +77.6614 q^{47} +(-41.6756 - 25.7710i) q^{49} +(-12.5969 + 33.0351i) q^{50} -9.67062 q^{52} -77.5383i q^{53} +(86.1095 + 15.8606i) q^{55} +(19.0447 + 5.41273i) q^{56} -1.59215i q^{58} -87.0651i q^{59} -5.36957i q^{61} +80.7317 q^{62} -8.00000 q^{64} +(-23.7766 - 4.37942i) q^{65} +47.1879i q^{67} -36.0568 q^{68} +(44.3730 + 21.9325i) q^{70} +58.3047 q^{71} +53.4082 q^{73} -58.4953 q^{74} +18.2670i q^{76} +(33.5117 - 117.911i) q^{77} -74.9637 q^{79} +(-19.6691 - 3.62287i) q^{80} -16.5683 q^{82} +28.7890 q^{83} +(-88.6507 - 16.3286i) q^{85} +91.0996 q^{86} +49.5303i q^{88} +101.499i q^{89} +(-9.25327 + 32.5578i) q^{91} +7.45031i q^{92} +109.830i q^{94} +(-8.27237 + 44.9120i) q^{95} -107.830 q^{97} +(36.4457 - 58.9382i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−4.91728	−	0.905717i	−0.983457	−	0.181143i
$5$	−4.91728	−	0.905717i	−0.983457	−	0.181143i
$6$		0			0
$7$	−1.91369	+	6.73333i	−0.273384	+	0.961905i
$7$	−1.91369	+	6.73333i	−0.273384	+	0.961905i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	1.28088	−	6.95409i	0.128088	−	0.695409i
$11$	−17.5116			−1.59196			−0.795982	−	0.605321i	$-0.793045\pi$
$11$	−17.5116			−1.59196			−0.795982	+	0.605321i	$0.793045\pi$
$12$		0			0
$13$	4.83531			0.371947			0.185973	−	0.982555i	$-0.440456\pi$
$13$	4.83531			0.371947			0.185973	+	0.982555i	$0.440456\pi$
$14$	−9.52237	−	2.70636i	−0.680170	−	0.193312i
$15$		0			0
$16$	4.00000			0.250000
$17$	18.0284			1.06049			0.530247	−	0.847843i	$-0.322099\pi$
$17$	18.0284			1.06049			0.530247	+	0.847843i	$0.322099\pi$
$18$		0			0
$19$		−	9.13350i		−	0.480711i	−0.970685	−	0.240355i	$-0.922736\pi$
$19$		−	9.13350i		−	0.480711i	0.970685	−	0.240355i	$-0.0772640\pi$
$20$	9.83457	+	1.81143i	0.491728	+	0.0905717i
$21$		0			0
$22$		−	24.7651i		−	1.12569i
$23$		−	3.72515i		−	0.161963i	−0.996716	−	0.0809816i	$-0.974194\pi$
$23$		−	3.72515i		−	0.161963i	0.996716	−	0.0809816i	$-0.0258055\pi$
$24$		0			0
$25$	23.3594	+	8.90734i	0.934374	+	0.356294i
$26$			6.83816i			0.263006i
$27$		0			0
$28$	3.82738	−	13.4667i	0.136692	−	0.480952i
$29$	−1.12582			−0.0388213			−0.0194107	−	0.999812i	$-0.506179\pi$
$29$	−1.12582			−0.0388213			−0.0194107	+	0.999812i	$0.506179\pi$
$30$		0			0
$31$		−	57.0859i		−	1.84148i	−0.390175	−	0.920741i	$-0.627585\pi$
$31$		−	57.0859i		−	1.84148i	0.390175	−	0.920741i	$-0.372415\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$			25.4960i			0.749882i
$35$	15.5086	−	31.3765i	0.443104	−	0.896470i
$36$		0			0
$37$			41.3624i			1.11790i	0.829200	+	0.558952i	$0.188796\pi$
$37$			41.3624i			1.11790i	−0.829200	+	0.558952i	$0.811204\pi$
$38$	12.9167			0.339914
$39$		0			0
$40$	−2.56176	+	13.9082i	−0.0640439	+	0.347704i
$41$			11.7156i			0.285745i	0.989741	+	0.142873i	$0.0456340\pi$
$41$			11.7156i			0.285745i	−0.989741	+	0.142873i	$0.954366\pi$
$42$		0			0
$43$		−	64.4171i		−	1.49807i	−0.662529	−	0.749036i	$-0.730517\pi$
$43$		−	64.4171i		−	1.49807i	0.662529	−	0.749036i	$-0.269483\pi$
$44$	35.0232			0.795982
$45$		0			0
$46$	5.26816			0.114525
$47$	77.6614			1.65237			0.826185	−	0.563399i	$-0.190507\pi$
$47$	77.6614			1.65237			0.826185	+	0.563399i	$0.190507\pi$
$48$		0			0
$49$	−41.6756	−	25.7710i	−0.850522	−	0.525939i
$50$	−12.5969	+	33.0351i	−0.251938	+	0.660702i
$51$		0			0
$52$	−9.67062			−0.185973
$53$		−	77.5383i		−	1.46299i	−0.681849	−	0.731493i	$-0.738824\pi$
$53$		−	77.5383i		−	1.46299i	0.681849	−	0.731493i	$-0.261176\pi$
$54$		0			0
$55$	86.1095	+	15.8606i	1.56563	+	0.288374i
$56$	19.0447	+	5.41273i	0.340085	+	0.0966559i
$57$		0			0
$58$		−	1.59215i		−	0.0274508i
$59$		−	87.0651i		−	1.47568i	−0.674976	−	0.737839i	$-0.735846\pi$
$59$		−	87.0651i		−	1.47568i	0.674976	−	0.737839i	$-0.264154\pi$
$60$		0			0
$61$		−	5.36957i		−	0.0880258i	−0.999031	−	0.0440129i	$-0.985986\pi$
$61$		−	5.36957i		−	0.0880258i	0.999031	−	0.0440129i	$-0.0140143\pi$
$62$	80.7317			1.30212
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−23.7766	−	4.37942i	−0.365794	−	0.0673757i
$66$		0			0
$67$			47.1879i			0.704297i	0.935944	+	0.352149i	$0.114549\pi$
$67$			47.1879i			0.704297i	−0.935944	+	0.352149i	$0.885451\pi$
$68$	−36.0568			−0.530247
$69$		0			0
$70$	44.3730	+	21.9325i	0.633900	+	0.313322i
$71$	58.3047			0.821193			0.410597	−	0.911817i	$-0.365320\pi$
$71$	58.3047			0.821193			0.410597	+	0.911817i	$0.365320\pi$
$72$		0			0
$73$	53.4082			0.731619			0.365810	−	0.930690i	$-0.380792\pi$
$73$	53.4082			0.731619			0.365810	+	0.930690i	$0.380792\pi$
$74$	−58.4953			−0.790477
$75$		0			0
$76$			18.2670i			0.240355i
$77$	33.5117	−	117.911i	0.435217	−	1.53132i
$78$		0			0
$79$	−74.9637			−0.948907			−0.474454	−	0.880280i	$-0.657354\pi$
$79$	−74.9637			−0.948907			−0.474454	+	0.880280i	$0.657354\pi$
$80$	−19.6691	−	3.62287i	−0.245864	−	0.0452859i
$81$		0			0
$82$	−16.5683			−0.202053
$83$	28.7890			0.346855			0.173428	−	0.984847i	$-0.444516\pi$
$83$	28.7890			0.346855			0.173428	+	0.984847i	$0.444516\pi$
$84$		0			0
$85$	−88.6507	−	16.3286i	−1.04295	−	0.192101i
$86$	91.0996			1.05930
$87$		0			0
$88$			49.5303i			0.562844i
$89$			101.499i			1.14043i	0.821494	+	0.570217i	$0.193141\pi$
$89$			101.499i			1.14043i	−0.821494	+	0.570217i	$0.806859\pi$
$90$		0			0
$91$	−9.25327	+	32.5578i	−0.101684	+	0.357778i
$92$			7.45031i			0.0809816i
$93$		0			0
$94$			109.830i			1.16840i
$95$	−8.27237	+	44.9120i	−0.0870776	+	0.472758i
$96$		0			0
$97$	−107.830			−1.11165			−0.555827	−	0.831298i	$-0.687598\pi$
$97$	−107.830			−1.11165			−0.555827	+	0.831298i	$0.687598\pi$
$98$	36.4457	−	58.9382i	0.371895	−	0.601410i
$99$		0			0
$100$	−46.7187	−	17.8147i	−0.467187	−	0.178147i
$101$		−	52.6151i		−	0.520941i	−0.965482	−	0.260471i	$-0.916122\pi$
$101$		−	52.6151i		−	0.520941i	0.965482	−	0.260471i	$-0.0838777\pi$
$102$		0			0
$103$	−72.4002			−0.702915			−0.351457	−	0.936204i	$-0.614314\pi$
$103$	−72.4002			−0.702915			−0.351457	+	0.936204i	$0.614314\pi$
$104$		−	13.6763i		−	0.131503i
$105$		0			0
$106$	109.656			1.03449
$107$			173.562i			1.62207i	0.584994	+	0.811037i	$0.301097\pi$
$107$			173.562i			1.62207i	−0.584994	+	0.811037i	$0.698903\pi$
$108$		0			0
$109$	49.9966			0.458684			0.229342	−	0.973346i	$-0.426342\pi$
$109$	49.9966			0.458684			0.229342	+	0.973346i	$0.426342\pi$
$110$	−22.4302	+	121.777i	−0.203911	+	1.10707i
$111$		0			0
$112$	−7.65475	+	26.9333i	−0.0683460	+	0.240476i
$113$			70.1536i			0.620828i	0.950601	+	0.310414i	$0.100468\pi$
$113$			70.1536i			0.620828i	−0.950601	+	0.310414i	$0.899532\pi$
$114$		0			0
$115$	−3.37394	+	18.3176i	−0.0293386	+	0.159284i
$116$	2.25164			0.0194107
$117$		0			0
$118$	123.129			1.04346
$119$	−34.5007	+	121.391i	−0.289922	+	1.02009i
$120$		0			0
$121$	185.656			1.53435
$122$	7.59373			0.0622436
$123$		0			0
$124$			114.172i			0.920741i
$125$	−106.797	−	64.9569i	−0.854376	−	0.519655i
$126$		0			0
$127$		−	197.945i		−	1.55863i	−0.626635	−	0.779313i	$-0.715568\pi$
$127$		−	197.945i		−	1.55863i	0.626635	−	0.779313i	$-0.284432\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		0			0
$130$	6.19344	−	33.6252i	0.0476418	−	0.258655i
$131$		−	114.901i		−	0.877105i	−0.898706	−	0.438552i	$-0.855491\pi$
$131$		−	114.901i		−	0.877105i	0.898706	−	0.438552i	$-0.144509\pi$
$132$		0			0
$133$	61.4989	+	17.4787i	0.462398	+	0.131419i
$134$	−66.7338			−0.498013
$135$		0			0
$136$		−	50.9920i		−	0.374941i
$137$		−	95.3358i		−	0.695882i	−0.937516	−	0.347941i	$-0.886881\pi$
$137$		−	95.3358i		−	0.695882i	0.937516	−	0.347941i	$-0.113119\pi$
$138$		0			0
$139$		−	237.587i		−	1.70926i	−0.519237	−	0.854630i	$-0.673784\pi$
$139$		−	237.587i		−	1.70926i	0.519237	−	0.854630i	$-0.326216\pi$
$140$	−31.0173	+	62.7529i	−0.221552	+	0.448235i
$141$		0			0
$142$			82.4553i			0.580671i
$143$	−84.6740			−0.592126
$144$		0			0
$145$	5.53597	+	1.01967i	0.0381791	+	0.00703223i
$146$			75.5306i			0.517333i
$147$		0			0
$148$		−	82.7248i		−	0.558952i
$149$	−133.844			−0.898285			−0.449142	−	0.893460i	$-0.648270\pi$
$149$	−133.844			−0.898285			−0.449142	+	0.893460i	$0.648270\pi$
$150$		0			0
$151$	155.064			1.02691			0.513456	−	0.858116i	$-0.328365\pi$
$151$	155.064			1.02691			0.513456	+	0.858116i	$0.328365\pi$
$152$	−25.8335			−0.169957
$153$		0			0
$154$	166.752	+	47.3928i	1.08280	+	0.307745i
$155$	−51.7037	+	280.708i	−0.333572	+	1.81102i
$156$		0			0
$157$	−104.634			−0.666459			−0.333230	−	0.942846i	$-0.608138\pi$
$157$	−104.634			−0.666459			−0.333230	+	0.942846i	$0.608138\pi$
$158$		−	106.015i		−	0.670979i
$159$		0			0
$160$	5.12351	−	27.8164i	0.0320219	−	0.173852i
$161$	25.0827	+	7.12878i	0.155793	+	0.0442782i
$162$		0			0
$163$		−	130.909i		−	0.803120i	−0.915833	−	0.401560i	$-0.868468\pi$
$163$		−	130.909i		−	0.803120i	0.915833	−	0.401560i	$-0.131532\pi$
$164$		−	23.4311i		−	0.142873i
$165$		0			0
$166$			40.7138i			0.245264i
$167$	102.845			0.615838			0.307919	−	0.951413i	$-0.400367\pi$
$167$	102.845			0.615838			0.307919	+	0.951413i	$0.400367\pi$
$168$		0			0
$169$	−145.620			−0.861656
$170$	23.0922	−	125.371i	0.135836	−	0.737477i
$171$		0			0
$172$			128.834i			0.749036i
$173$	−197.432			−1.14122			−0.570612	−	0.821220i	$-0.693294\pi$
$173$	−197.432			−1.14122			−0.570612	+	0.821220i	$0.693294\pi$
$174$		0			0
$175$	−104.679	+	140.240i	−0.598163	+	0.801374i
$176$	−70.0464			−0.397991
$177$		0			0
$178$	−143.541			−0.806409
$179$	118.822			0.663809			0.331904	−	0.943313i	$-0.392309\pi$
$179$	118.822			0.663809			0.331904	+	0.943313i	$0.392309\pi$
$180$		0			0
$181$		−	14.4148i		−	0.0796399i	−0.999207	−	0.0398199i	$-0.987322\pi$
$181$		−	14.4148i		−	0.0796399i	0.999207	−	0.0398199i	$-0.0126784\pi$
$182$	−46.0436	−	13.0861i	−0.252987	−	0.0719017i
$183$		0			0
$184$	−10.5363			−0.0572626
$185$	37.4627	−	203.391i	0.202501	−	1.09941i
$186$		0			0
$187$	−315.706			−1.68827
$188$	−155.323			−0.826185
$189$		0			0
$190$	−63.5152	−	11.6989i	−0.334291	−	0.0615732i
$191$	−59.9375			−0.313809			−0.156904	−	0.987614i	$-0.550151\pi$
$191$	−59.9375			−0.313809			−0.156904	+	0.987614i	$0.550151\pi$
$192$		0			0
$193$			245.948i			1.27434i	0.770723	+	0.637171i	$0.219895\pi$
$193$			245.948i			1.27434i	−0.770723	+	0.637171i	$0.780105\pi$
$194$		−	152.495i		−	0.786058i
$195$		0			0
$196$	83.3512	+	51.5420i	0.425261	+	0.262969i
$197$		−	82.0594i		−	0.416545i	−0.978071	−	0.208273i	$-0.933216\pi$
$197$		−	82.0594i		−	0.416545i	0.978071	−	0.208273i	$-0.0667842\pi$
$198$		0			0
$199$		−	289.338i		−	1.45396i	−0.686658	−	0.726981i	$-0.740923\pi$
$199$		−	289.338i		−	1.45396i	0.686658	−	0.726981i	$-0.259077\pi$
$200$	25.1938	−	66.0702i	0.125969	−	0.330351i
$201$		0			0
$202$	74.4089			0.368361
$203$	2.15447	−	7.58051i	0.0106131	−	0.0373424i
$204$		0			0
$205$	10.6110	−	57.6087i	0.0517609	−	0.281018i
$206$		−	102.389i		−	0.497036i
$207$		0			0
$208$	19.3412			0.0929867
$209$			159.942i			0.765274i
$210$		0			0
$211$	33.6995			0.159713			0.0798567	−	0.996806i	$-0.474554\pi$
$211$	33.6995			0.159713			0.0798567	+	0.996806i	$0.474554\pi$
$212$			155.077i			0.731493i
$213$		0			0
$214$	−245.454			−1.14698
$215$	−58.3437	+	316.757i	−0.271366	+	1.47329i
$216$		0			0
$217$	384.379	+	109.245i	1.77133	+	0.503432i
$218$			70.7059i			0.324339i
$219$		0			0
$220$	−172.219	−	31.7211i	−0.782813	−	0.144187i
$221$	87.1728			0.394447
$222$		0			0
$223$	−10.7556			−0.0482313			−0.0241156	−	0.999709i	$-0.507677\pi$
$223$	−10.7556			−0.0482313			−0.0241156	+	0.999709i	$0.507677\pi$
$224$	−38.0895	−	10.8255i	−0.170042	−	0.0483279i
$225$		0			0
$226$	−99.2121			−0.438992
$227$	−416.450			−1.83458			−0.917290	−	0.398219i	$-0.869628\pi$
$227$	−416.450			−1.83458			−0.917290	+	0.398219i	$0.869628\pi$
$228$		0			0
$229$			388.469i			1.69637i	0.529700	+	0.848185i	$0.322305\pi$
$229$			388.469i			1.69637i	−0.529700	+	0.848185i	$0.677695\pi$
$230$	−25.9051	−	4.77147i	−0.112631	−	0.0207455i
$231$		0			0
$232$			3.18429i			0.0137254i
$233$			70.4036i			0.302162i	0.988521	+	0.151081i	$0.0482754\pi$
$233$			70.4036i			0.302162i	−0.988521	+	0.151081i	$0.951725\pi$
$234$		0			0
$235$	−381.883	−	70.3393i	−1.62503	−	0.299316i
$236$			174.130i			0.737839i
$237$		0			0
$238$	−171.673	−	48.7914i	−0.721315	−	0.205006i
$239$	313.133			1.31018			0.655091	−	0.755550i	$-0.272630\pi$
$239$	313.133			1.31018			0.655091	+	0.755550i	$0.272630\pi$
$240$		0			0
$241$		−	198.727i		−	0.824595i	−0.911049	−	0.412297i	$-0.864726\pi$
$241$		−	198.727i		−	0.824595i	0.911049	−	0.412297i	$-0.135274\pi$
$242$			262.557i			1.08495i
$243$		0			0
$244$			10.7391i			0.0440129i
$245$	181.589	+	164.470i	0.741181	+	0.671305i
$246$		0			0
$247$		−	44.1633i		−	0.178799i
$248$	−161.463			−0.651062
$249$		0			0
$250$	91.8629	−	151.034i	0.367452	−	0.604135i
$251$		−	300.878i		−	1.19872i	−0.800480	−	0.599359i	$-0.795422\pi$
$251$		−	300.878i		−	1.19872i	0.800480	−	0.599359i	$-0.204578\pi$
$252$		0			0
$253$			65.2334i			0.257839i
$254$	279.937			1.10211
$255$		0			0
$256$	16.0000			0.0625000
$257$	−306.052			−1.19087			−0.595433	−	0.803405i	$-0.703019\pi$
$257$	−306.052			−1.19087			−0.595433	+	0.803405i	$0.703019\pi$
$258$		0			0
$259$	−278.507	−	79.1548i	−1.07532	−	0.305617i
$260$	47.5532	+	8.75885i	0.182897	+	0.0336879i
$261$		0			0
$262$	162.494			0.620207
$263$		−	286.135i		−	1.08797i	−0.839096	−	0.543984i	$-0.816915\pi$
$263$		−	286.135i		−	1.08797i	0.839096	−	0.543984i	$-0.183085\pi$
$264$		0			0
$265$	−70.2278	+	381.278i	−0.265010	+	1.43878i
$266$	−24.7186	+	86.9726i	−0.0929270	+	0.326965i
$267$		0			0
$268$		−	94.3758i		−	0.352149i
$269$		−	188.412i		−	0.700415i	−0.936672	−	0.350208i	$-0.886111\pi$
$269$		−	188.412i		−	0.700415i	0.936672	−	0.350208i	$-0.113889\pi$
$270$		0			0
$271$		−	9.59288i		−	0.0353981i	−0.999843	−	0.0176990i	$-0.994366\pi$
$271$		−	9.59288i		−	0.0353981i	0.999843	−	0.0176990i	$-0.00563408\pi$
$272$	72.1136			0.265123
$273$		0			0
$274$	134.825			0.492063
$275$	−409.060	−	155.982i	−1.48749	−	0.567206i
$276$		0			0
$277$		−	161.066i		−	0.581464i	−0.956804	−	0.290732i	$-0.906101\pi$
$277$		−	161.066i		−	0.581464i	0.956804	−	0.290732i	$-0.0938989\pi$
$278$	335.999			1.20863
$279$		0			0
$280$	−88.7460	−	43.8651i	−0.316950	−	0.156661i
$281$	343.107			1.22102			0.610510	−	0.792008i	$-0.290964\pi$
$281$	343.107			1.22102			0.610510	+	0.792008i	$0.290964\pi$
$282$		0			0
$283$	−324.748			−1.14752			−0.573759	−	0.819024i	$-0.694516\pi$
$283$	−324.748			−1.14752			−0.573759	+	0.819024i	$0.694516\pi$
$284$	−116.609			−0.410597
$285$		0			0
$286$		−	119.747i		−	0.418696i
$287$	−78.8848	−	22.4199i	−0.274860	−	0.0781182i
$288$		0			0
$289$	36.0229			0.124647
$290$	−1.44204	+	7.82904i	−0.00497254	+	0.0269967i
$291$		0			0
$292$	−106.816			−0.365810
$293$	−100.918			−0.344429			−0.172215	−	0.985059i	$-0.555092\pi$
$293$	−100.918			−0.344429			−0.172215	+	0.985059i	$0.555092\pi$
$294$		0			0
$295$	−78.8563	+	428.124i	−0.267310	+	1.45127i
$296$	116.991			0.395238
$297$		0			0
$298$		−	189.285i		−	0.635183i
$299$		−	18.0123i		−	0.0602417i
$300$		0			0
$301$	433.742	+	123.274i	1.44100	+	0.409549i
$302$			219.293i			0.726136i
$303$		0			0
$304$		−	36.5340i		−	0.120178i
$305$	−4.86332	+	26.4037i	−0.0159453	+	0.0865696i
$306$		0			0
$307$	41.3057			0.134546			0.0672732	−	0.997735i	$-0.478570\pi$
$307$	41.3057			0.134546			0.0672732	+	0.997735i	$0.478570\pi$
$308$	−67.0235	+	235.823i	−0.217609	+	0.765659i
$309$		0			0
$310$	−396.981	−	73.1201i	−1.28058	−	0.235871i
$311$		−	470.341i		−	1.51235i	−0.654369	−	0.756176i	$-0.727066\pi$
$311$		−	470.341i		−	1.51235i	0.654369	−	0.756176i	$-0.272934\pi$
$312$		0			0
$313$	−160.220			−0.511884			−0.255942	−	0.966692i	$-0.582386\pi$
$313$	−160.220			−0.511884			−0.255942	+	0.966692i	$0.582386\pi$
$314$		−	147.975i		−	0.471258i
$315$		0			0
$316$	149.927			0.474454
$317$		−	268.766i		−	0.847843i	−0.905699	−	0.423922i	$-0.860653\pi$
$317$		−	268.766i		−	0.847843i	0.905699	−	0.423922i	$-0.139347\pi$
$318$		0			0
$319$	19.7149			0.0618021
$320$	39.3383	+	7.24574i	0.122932	+	0.0226429i
$321$		0			0
$322$	−10.0816	+	35.4723i	−0.0313094	+	0.110162i
$323$		−	164.662i		−	0.509791i
$324$		0			0
$325$	112.950	+	43.0697i	0.347537	+	0.132522i
$326$	185.133			0.567891
$327$		0			0
$328$	33.1366			0.101026
$329$	−148.620	+	522.920i	−0.451732	+	1.58942i
$330$		0			0
$331$	555.018			1.67679			0.838395	−	0.545063i	$-0.183494\pi$
$331$	555.018			1.67679			0.838395	+	0.545063i	$0.183494\pi$
$332$	−57.5780			−0.173428
$333$		0			0
$334$			145.445i			0.435463i
$335$	42.7389	−	232.036i	0.127579	−	0.692646i
$336$		0			0
$337$			47.7972i			0.141831i	0.997482	+	0.0709157i	$0.0225921\pi$
$337$			47.7972i			0.141831i	−0.997482	+	0.0709157i	$0.977408\pi$
$338$		−	205.937i		−	0.609282i
$339$		0			0
$340$	177.301	+	32.6573i	0.521475	+	0.0960507i
$341$			999.666i			2.93157i
$342$		0			0
$343$	253.279	−	231.298i	0.738422	−	0.674338i
$344$	−182.199			−0.529649
$345$		0			0
$346$		−	279.211i		−	0.806967i
$347$			283.766i			0.817771i	0.912586	+	0.408885i	$0.134082\pi$
$347$			283.766i			0.817771i	−0.912586	+	0.408885i	$0.865918\pi$
$348$		0			0
$349$		−	20.0321i		−	0.0573987i	−0.999588	−	0.0286993i	$-0.990863\pi$
$349$		−	20.0321i		−	0.0573987i	0.999588	−	0.0286993i	$-0.00913653\pi$
$350$	−198.330	−	148.038i	−0.566657	−	0.422965i
$351$		0			0
$352$		−	99.0605i		−	0.281422i
$353$	595.015			1.68559			0.842797	−	0.538231i	$-0.180907\pi$
$353$	595.015			1.68559			0.842797	+	0.538231i	$0.180907\pi$
$354$		0			0
$355$	−286.701	−	52.8076i	−0.807608	−	0.148754i
$356$		−	202.997i		−	0.570217i
$357$		0			0
$358$			168.039i			0.469384i
$359$	−588.390			−1.63897			−0.819485	−	0.573101i	$-0.805740\pi$
$359$	−588.390			−1.63897			−0.819485	+	0.573101i	$0.805740\pi$
$360$		0			0
$361$	277.579			0.768917
$362$	20.3856			0.0563139
$363$		0			0
$364$	18.5065	−	65.1155i	0.0508422	−	0.178889i
$365$	−262.623	−	48.3727i	−0.719516	−	0.132528i
$366$		0			0
$367$	662.601			1.80545			0.902726	−	0.430215i	$-0.141562\pi$
$367$	662.601			1.80545			0.902726	+	0.430215i	$0.141562\pi$
$368$		−	14.9006i		−	0.0404908i
$369$		0			0
$370$	287.638	+	52.9802i	0.777400	+	0.143190i
$371$	522.091	+	148.384i	1.40725	+	0.399957i
$372$		0			0
$373$			236.349i			0.633644i	0.948485	+	0.316822i	$0.102616\pi$
$373$			236.349i			0.633644i	−0.948485	+	0.316822i	$0.897384\pi$
$374$		−	446.476i		−	1.19378i
$375$		0			0
$376$		−	219.660i		−	0.584201i
$377$	−5.44368			−0.0144395
$378$		0			0
$379$	344.235			0.908272			0.454136	−	0.890932i	$-0.349948\pi$
$379$	344.235			0.908272			0.454136	+	0.890932i	$0.349948\pi$
$380$	16.5447	−	89.8241i	0.0435388	−	0.236379i
$381$		0			0
$382$		−	84.7644i		−	0.221896i
$383$	65.7097			0.171566			0.0857828	−	0.996314i	$-0.472661\pi$
$383$	65.7097			0.171566			0.0857828	+	0.996314i	$0.472661\pi$
$384$		0			0
$385$	−271.581	+	549.452i	−0.705406	+	1.42715i
$386$	−347.823			−0.901095
$387$		0			0
$388$	215.661			0.555827
$389$	−161.296			−0.414642			−0.207321	−	0.978273i	$-0.566474\pi$
$389$	−161.296			−0.414642			−0.207321	+	0.978273i	$0.566474\pi$
$390$		0			0
$391$		−	67.1585i		−	0.171761i
$392$	−72.8914	+	117.876i	−0.185947	+	0.300705i
$393$		0			0
$394$	116.050			0.294542
$395$	368.618	+	67.8959i	0.933209	+	0.171888i
$396$		0			0
$397$	667.752			1.68200			0.840998	−	0.541039i	$-0.181969\pi$
$397$	667.752			1.68200			0.840998	+	0.541039i	$0.181969\pi$
$398$	409.186			1.02811
$399$		0			0
$400$	93.4374	+	35.6294i	0.233594	+	0.0890734i
$401$	593.826			1.48086			0.740431	−	0.672132i	$-0.234621\pi$
$401$	593.826			1.48086			0.740431	+	0.672132i	$0.234621\pi$
$402$		0			0
$403$		−	276.028i		−	0.684933i
$404$			105.230i			0.260471i
$405$		0			0
$406$	10.7205	+	3.04687i	0.0264051	+	0.00750461i
$407$		−	724.322i		−	1.77966i
$408$		0			0
$409$			569.625i			1.39273i	0.717690	+	0.696363i	$0.245200\pi$
$409$			569.625i			1.39273i	−0.717690	+	0.696363i	$0.754800\pi$
$410$	81.4711	+	15.0062i	0.198710	+	0.0366005i
$411$		0			0
$412$	144.800			0.351457
$413$	586.238	+	166.615i	1.41946	+	0.403427i
$414$		0			0
$415$	−141.564	−	26.0747i	−0.341117	−	0.0628306i
$416$			27.3526i			0.0657515i
$417$		0			0
$418$	−226.192			−0.541130
$419$			209.456i			0.499894i	0.968260	+	0.249947i	$0.0804132\pi$
$419$			209.456i			0.499894i	−0.968260	+	0.249947i	$0.919587\pi$
$420$		0			0
$421$	−169.713			−0.403119			−0.201560	−	0.979476i	$-0.564601\pi$
$421$	−169.713			−0.403119			−0.201560	+	0.979476i	$0.564601\pi$
$422$			47.6583i			0.112934i
$423$		0			0
$424$	−219.311			−0.517244
$425$	421.132	+	160.585i	0.990898	+	0.377847i
$426$		0			0
$427$	36.1551	+	10.2757i	0.0846725	+	0.0240649i
$428$		−	347.124i		−	0.811037i
$429$		0			0
$430$	−447.962	−	82.5104i	−1.04177	−	0.191885i
$431$	−538.427			−1.24925			−0.624625	−	0.780925i	$-0.714748\pi$
$431$	−538.427			−1.24925			−0.624625	+	0.780925i	$0.714748\pi$
$432$		0			0
$433$	118.314			0.273243			0.136622	−	0.990623i	$-0.456376\pi$
$433$	118.314			0.273243			0.136622	+	0.990623i	$0.456376\pi$
$434$	−154.495	+	543.593i	−0.355980	+	1.25252i
$435$		0			0
$436$	−99.9932			−0.229342
$437$	−34.0237			−0.0778575
$438$		0			0
$439$			434.834i			0.990510i	0.868748	+	0.495255i	$0.164925\pi$
$439$			434.834i			0.990510i	−0.868748	+	0.495255i	$0.835075\pi$
$440$	44.8604	−	243.554i	0.101956	−	0.553533i
$441$		0			0
$442$			123.281i			0.278916i
$443$			555.005i			1.25283i	0.779488	+	0.626417i	$0.215479\pi$
$443$			555.005i			1.25283i	−0.779488	+	0.626417i	$0.784521\pi$
$444$		0			0
$445$	91.9291	−	499.098i	0.206582	−	1.12157i
$446$		−	15.2107i		−	0.0341047i
$447$		0			0
$448$	15.3095	−	53.8667i	0.0341730	−	0.120238i
$449$	66.8926			0.148981			0.0744906	−	0.997222i	$-0.476267\pi$
$449$	66.8926			0.148981			0.0744906	+	0.997222i	$0.476267\pi$
$450$		0			0
$451$		−	205.158i		−	0.454896i
$452$		−	140.307i		−	0.310414i
$453$		0			0
$454$		−	588.949i		−	1.29724i
$455$	74.9891	−	151.715i	0.164811	−	0.333439i
$456$		0			0
$457$		−	750.939i		−	1.64319i	−0.570070	−	0.821596i	$-0.693084\pi$
$457$		−	750.939i		−	1.64319i	0.570070	−	0.821596i	$-0.306916\pi$
$458$	−549.378			−1.19951
$459$		0			0
$460$	6.74787	−	36.6353i	0.0146693	−	0.0796419i
$461$		−	395.377i		−	0.857651i	−0.903387	−	0.428826i	$-0.858928\pi$
$461$		−	395.377i		−	0.857651i	0.903387	−	0.428826i	$-0.141072\pi$
$462$		0			0
$463$			423.981i			0.915726i	0.889023	+	0.457863i	$0.151385\pi$
$463$			423.981i			0.915726i	−0.889023	+	0.457863i	$0.848615\pi$
$464$	−4.50327			−0.00970533
$465$		0			0
$466$	−99.5658			−0.213660
$467$	584.408			1.25141			0.625705	−	0.780060i	$-0.284812\pi$
$467$	584.408			1.25141			0.625705	+	0.780060i	$0.284812\pi$
$468$		0			0
$469$	−317.732	−	90.3030i	−0.677467	−	0.192544i
$470$	99.4747	−	540.064i	0.211648	−	1.14907i
$471$		0			0
$472$	−246.257			−0.521731
$473$			1128.05i			2.38488i
$474$		0			0
$475$	81.3552	−	213.353i	0.171274	−	0.449164i
$476$	69.0014	−	242.782i	0.144961	−	0.510047i
$477$		0			0
$478$			442.837i			0.926438i
$479$		−	734.511i		−	1.53343i	−0.641990	−	0.766713i	$-0.721891\pi$
$479$		−	734.511i		−	1.53343i	0.641990	−	0.766713i	$-0.278109\pi$
$480$		0			0
$481$			200.000i			0.415801i
$482$	281.043			0.583077
$483$		0			0
$484$	−371.312			−0.767174
$485$	530.232	+	97.6638i	1.09326	+	0.201369i
$486$		0			0
$487$			91.6643i			0.188222i	0.995562	+	0.0941111i	$0.0300009\pi$
$487$			91.6643i			0.188222i	−0.995562	+	0.0941111i	$0.969999\pi$
$488$	−15.1875			−0.0311218
$489$		0			0
$490$	−232.595	+	256.806i	−0.474684	+	0.524094i
$491$	−460.086			−0.937038			−0.468519	−	0.883453i	$-0.655212\pi$
$491$	−460.086			−0.937038			−0.468519	+	0.883453i	$0.655212\pi$
$492$		0			0
$493$	−20.2967			−0.0411698
$494$	62.4564			0.126430
$495$		0			0
$496$		−	228.344i		−	0.460370i
$497$	−111.577	+	392.585i	−0.224501	+	0.789910i
$498$		0			0
$499$	−487.126			−0.976204			−0.488102	−	0.872786i	$-0.662311\pi$
$499$	−487.126			−0.976204			−0.488102	+	0.872786i	$0.662311\pi$
$500$	213.594	+	129.914i	0.427188	+	0.259828i
$501$		0			0
$502$	425.506			0.847622
$503$	−305.145			−0.606650			−0.303325	−	0.952887i	$-0.598097\pi$
$503$	−305.145			−0.606650			−0.303325	+	0.952887i	$0.598097\pi$
$504$		0			0
$505$	−47.6544	+	258.723i	−0.0943651	+	0.512323i
$506$	−92.2539			−0.182320
$507$		0			0
$508$			395.891i			0.779313i
$509$		−	800.434i		−	1.57256i	−0.617869	−	0.786281i	$-0.712004\pi$
$509$		−	800.434i		−	1.57256i	0.617869	−	0.786281i	$-0.287996\pi$
$510$		0			0
$511$	−102.207	+	359.615i	−0.200013	+	0.703748i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$		−	432.824i		−	0.842069i
$515$	356.012	+	65.5741i	0.691286	+	0.127328i
$516$		0			0
$517$	−1359.97			−2.63051
$518$	111.942	−	393.868i	0.216104	−	0.760364i
$519$		0			0
$520$	−12.3869	+	67.2503i	−0.0238209	+	0.129328i
$521$			21.4194i			0.0411121i	0.999789	+	0.0205560i	$0.00654365\pi$
$521$			21.4194i			0.0411121i	−0.999789	+	0.0205560i	$0.993456\pi$
$522$		0			0
$523$	842.290			1.61050			0.805249	−	0.592937i	$-0.202032\pi$
$523$	842.290			1.61050			0.805249	+	0.592937i	$0.202032\pi$
$524$			229.801i			0.438552i
$525$		0			0
$526$	404.657			0.769309
$527$		−	1029.17i		−	1.95288i
$528$		0			0
$529$	515.123			0.973768
$530$	−539.208	−	99.3171i	−1.01737	−	0.187391i
$531$		0			0
$532$	−122.998	−	34.9574i	−0.231199	−	0.0657093i
$533$			56.6484i			0.106282i
$534$		0			0
$535$	157.198	−	853.453i	0.293828	−	1.59524i
$536$	133.468			0.249007
$537$		0			0
$538$	266.454			0.495268
$539$	729.806	+	451.291i	1.35400	+	0.837275i
$540$		0			0
$541$	−15.6795			−0.0289824			−0.0144912	−	0.999895i	$-0.504613\pi$
$541$	−15.6795			−0.0289824			−0.0144912	+	0.999895i	$0.504613\pi$
$542$	13.5664			0.0250302
$543$		0			0
$544$			101.984i			0.187471i
$545$	−245.847	−	45.2828i	−0.451096	−	0.0830877i
$546$		0			0
$547$		−	315.792i		−	0.577317i	−0.957432	−	0.288659i	$-0.906791\pi$
$547$		−	315.792i		−	0.577317i	0.957432	−	0.288659i	$-0.0932092\pi$
$548$			190.672i			0.347941i
$549$		0			0
$550$	220.591	−	578.498i	0.401075	−	1.05181i
$551$			10.2827i			0.0186618i
$552$		0			0
$553$	143.457	−	504.756i	0.259416	−	0.912759i
$554$	227.781			0.411157
$555$		0			0
$556$			475.174i			0.854630i
$557$		−	358.421i		−	0.643484i	−0.946827	−	0.321742i	$-0.895732\pi$
$557$		−	358.421i		−	0.643484i	0.946827	−	0.321742i	$-0.104268\pi$
$558$		0			0
$559$		−	311.477i		−	0.557203i
$560$	62.0346	−	125.506i	0.110776	−	0.224118i
$561$		0			0
$562$			485.226i			0.863392i
$563$	622.834			1.10628			0.553138	−	0.833089i	$-0.313430\pi$
$563$	622.834			1.10628			0.553138	+	0.833089i	$0.313430\pi$
$564$		0			0
$565$	63.5393	−	344.965i	0.112459	−	0.610557i
$566$		−	459.263i		−	0.811418i
$567$		0			0
$568$		−	164.911i		−	0.290336i
$569$	185.789			0.326518			0.163259	−	0.986583i	$-0.447799\pi$
$569$	185.789			0.326518			0.163259	+	0.986583i	$0.447799\pi$
$570$		0			0
$571$	−486.258			−0.851589			−0.425795	−	0.904820i	$-0.640005\pi$
$571$	−486.258			−0.851589			−0.425795	+	0.904820i	$0.640005\pi$
$572$	169.348			0.296063
$573$		0			0
$574$	31.7066	−	111.560i	0.0552379	−	0.194355i
$575$	33.1812	−	87.0172i	0.0577064	−	0.151334i
$576$		0			0
$577$	270.057			0.468037			0.234018	−	0.972232i	$-0.424812\pi$
$577$	270.057			0.468037			0.234018	+	0.972232i	$0.424812\pi$
$578$			50.9440i			0.0881385i
$579$		0			0
$580$	−11.0719	−	2.03935i	−0.0190895	−	0.00351611i
$581$	−55.0932	+	193.846i	−0.0948247	+	0.333642i
$582$		0			0
$583$			1357.82i			2.32902i
$584$		−	151.061i		−	0.258666i
$585$		0			0
$586$		−	142.719i		−	0.243548i
$587$	−400.613			−0.682476			−0.341238	−	0.939977i	$-0.610846\pi$
$587$	−400.613			−0.682476			−0.341238	+	0.939977i	$0.610846\pi$
$588$		0			0
$589$	−521.395			−0.885220
$590$	−605.458	−	111.520i	−1.02620	−	0.189016i
$591$		0			0
$592$			165.450i			0.279476i
$593$	157.686			0.265912			0.132956	−	0.991122i	$-0.457553\pi$
$593$	157.686			0.265912			0.132956	+	0.991122i	$0.457553\pi$
$594$		0			0
$595$	279.596	−	565.667i	0.469909	−	0.950701i
$596$	267.689			0.449142
$597$		0			0
$598$	25.4732			0.0425973
$599$	468.940			0.782872			0.391436	−	0.920205i	$-0.371978\pi$
$599$	468.940			0.782872			0.391436	+	0.920205i	$0.371978\pi$
$600$		0			0
$601$			255.932i			0.425844i	0.977069	+	0.212922i	$0.0682980\pi$
$601$			255.932i			0.425844i	−0.977069	+	0.212922i	$0.931702\pi$
$602$	−174.336	+	613.404i	−0.289595	+	1.01894i
$603$		0			0
$604$	−310.127			−0.513456
$605$	−912.923	−	168.152i	−1.50896	−	0.277937i
$606$		0			0
$607$	−773.553			−1.27439			−0.637194	−	0.770704i	$-0.719905\pi$
$607$	−773.553			−1.27439			−0.637194	+	0.770704i	$0.719905\pi$
$608$	51.6669			0.0849785
$609$		0			0
$610$	−37.3405	−	6.87777i	−0.0612139	−	0.0112750i
$611$	375.517			0.614594
$612$		0			0
$613$		−	443.208i		−	0.723015i	−0.932369	−	0.361507i	$-0.882262\pi$
$613$		−	443.208i		−	0.723015i	0.932369	−	0.361507i	$-0.117738\pi$
$614$			58.4151i			0.0951386i
$615$		0			0
$616$	−333.504	−	94.7855i	−0.541402	−	0.153873i
$617$		−	363.298i		−	0.588813i	−0.955680	−	0.294407i	$-0.904878\pi$
$617$		−	363.298i		−	0.588813i	0.955680	−	0.294407i	$-0.0951220\pi$
$618$		0			0
$619$		−	292.211i		−	0.472069i	−0.971745	−	0.236035i	$-0.924152\pi$
$619$		−	292.211i		−	0.472069i	0.971745	−	0.236035i	$-0.0758479\pi$
$620$	103.407	−	561.415i	0.166786	−	0.905509i
$621$		0			0
$622$	665.163			1.06939
$623$	−683.425	−	194.237i	−1.09699	−	0.311777i
$624$		0			0
$625$	466.319	+	416.139i	0.746110	+	0.665823i
$626$		−	226.585i		−	0.361956i
$627$		0			0
$628$	209.268			0.333230
$629$			745.698i			1.18553i
$630$		0			0
$631$	189.221			0.299874			0.149937	−	0.988696i	$-0.452093\pi$
$631$	189.221			0.299874			0.149937	+	0.988696i	$0.452093\pi$
$632$			212.029i			0.335489i
$633$		0			0
$634$	380.093			0.599516
$635$	−179.283	+	973.354i	−0.282335	+	1.53284i
$636$		0			0
$637$	−201.514	−	124.611i	−0.316349	−	0.195621i
$638$			27.8810i			0.0437007i
$639$		0			0
$640$	−10.2470	+	55.6327i	−0.0160110	+	0.0869261i
$641$	−1162.94			−1.81425			−0.907127	−	0.420857i	$-0.861729\pi$
$641$	−1162.94			−1.81425			−0.907127	+	0.420857i	$0.861729\pi$
$642$		0			0
$643$	−1096.08			−1.70464			−0.852320	−	0.523021i	$-0.824805\pi$
$643$	−1096.08			−1.70464			−0.852320	+	0.523021i	$0.824805\pi$
$644$	−50.1654	−	14.2576i	−0.0778966	−	0.0221391i
$645$		0			0
$646$	232.868			0.360476
$647$	−262.877			−0.406302			−0.203151	−	0.979147i	$-0.565118\pi$
$647$	−262.877			−0.406302			−0.203151	+	0.979147i	$0.565118\pi$
$648$		0			0
$649$			1524.65i			2.34923i
$650$	−60.9098	+	159.735i	−0.0937074	+	0.245746i
$651$		0			0
$652$			261.817i			0.401560i
$653$			242.905i			0.371983i	0.982551	+	0.185992i	$0.0595498\pi$
$653$			242.905i			0.371983i	−0.982551	+	0.185992i	$0.940450\pi$
$654$		0			0
$655$	−104.068	+	564.999i	−0.158882	+	0.862594i
$656$			46.8622i			0.0714364i
$657$		0			0
$658$	−739.521	−	210.180i	−1.12389	−	0.319422i
$659$	−1176.49			−1.78527			−0.892634	−	0.450783i	$-0.851145\pi$
$659$	−1176.49			−1.78527			−0.892634	+	0.450783i	$0.851145\pi$
$660$		0			0
$661$		−	246.444i		−	0.372835i	−0.982471	−	0.186418i	$-0.940312\pi$
$661$		−	246.444i		−	0.372835i	0.982471	−	0.186418i	$-0.0596877\pi$
$662$			784.914i			1.18567i
$663$		0			0
$664$		−	81.4276i		−	0.122632i
$665$	−286.577	−	141.648i	−0.430943	−	0.213005i
$666$		0			0
$667$			4.19385i			0.00628763i
$668$	−205.690			−0.307919
$669$		0			0
$670$	328.149	+	60.4420i	0.489775	+	0.0902119i
$671$			94.0298i			0.140134i
$672$		0			0
$673$			76.3328i			0.113422i	0.998391	+	0.0567109i	$0.0180613\pi$
$673$			76.3328i			0.113422i	−0.998391	+	0.0567109i	$0.981939\pi$
$674$	−67.5954			−0.100290
$675$		0			0
$676$	291.240			0.430828
$677$	310.277			0.458312			0.229156	−	0.973390i	$-0.426403\pi$
$677$	310.277			0.458312			0.229156	+	0.973390i	$0.426403\pi$
$678$		0			0
$679$	206.354	−	726.058i	0.303908	−	1.06930i
$680$	−46.1843	+	250.742i	−0.0679181	+	0.368738i
$681$		0			0
$682$	−1413.74			−2.07293
$683$			157.333i			0.230356i	0.993345	+	0.115178i	$0.0367438\pi$
$683$			157.333i			0.230356i	−0.993345	+	0.115178i	$0.963256\pi$
$684$		0			0
$685$	−86.3473	+	468.793i	−0.126054	+	0.684370i
$686$	327.105	+	358.190i	0.476829	+	0.522144i
$687$		0			0
$688$		−	257.668i		−	0.374518i
$689$		−	374.921i		−	0.544153i
$690$		0			0
$691$		−	683.565i		−	0.989240i	−0.869109	−	0.494620i	$-0.835307\pi$
$691$		−	683.565i		−	0.989240i	0.869109	−	0.494620i	$-0.164693\pi$
$692$	394.863			0.570612
$693$		0			0
$694$	−401.306			−0.578251
$695$	−215.187	+	1168.28i	−0.309621	+	1.68098i
$696$		0			0
$697$			211.213i			0.303031i
$698$	28.3297			0.0405870
$699$		0			0
$700$	209.357	−	280.481i	0.299082	−	0.400687i
$701$	306.153			0.436738			0.218369	−	0.975866i	$-0.429926\pi$
$701$	306.153			0.436738			0.218369	+	0.975866i	$0.429926\pi$
$702$		0			0
$703$	377.784			0.537388
$704$	140.093			0.198995
$705$		0			0
$706$			841.478i			1.19190i
$707$	354.275	+	100.689i	0.501096	+	0.142417i
$708$		0			0
$709$	444.082			0.626350			0.313175	−	0.949695i	$-0.398607\pi$
$709$	444.082			0.626350			0.313175	+	0.949695i	$0.398607\pi$
$710$	74.6812	−	405.456i	0.105185	−	0.571065i
$711$		0			0
$712$	287.082			0.403205
$713$	−212.654			−0.298252
$714$		0			0
$715$	416.366	+	76.6907i	0.582330	+	0.107260i
$716$	−237.643			−0.331904
$717$		0			0
$718$		−	832.109i		−	1.15893i
$719$		−	672.926i		−	0.935919i	−0.883750	−	0.467960i	$-0.844989\pi$
$719$		−	672.926i		−	0.935919i	0.883750	−	0.467960i	$-0.155011\pi$
$720$		0			0
$721$	138.551	−	487.495i	0.192166	−	0.676137i
$722$			392.556i			0.543707i
$723$		0			0
$724$			28.8296i			0.0398199i
$725$	−26.2984	−	10.0280i	−0.0362736	−	0.0138318i
$726$		0			0
$727$	−675.927			−0.929748			−0.464874	−	0.885377i	$-0.653900\pi$
$727$	−675.927			−0.929748			−0.464874	+	0.885377i	$0.653900\pi$
$728$	92.0872	+	26.1722i	0.126493	+	0.0359508i
$729$		0			0
$730$	68.4094	−	371.405i	0.0937115	−	0.508775i
$731$		−	1161.34i		−	1.58870i
$732$		0			0
$733$	387.908			0.529206			0.264603	−	0.964357i	$-0.414759\pi$
$733$	387.908			0.529206			0.264603	+	0.964357i	$0.414759\pi$
$734$			937.059i			1.27665i
$735$		0			0
$736$	21.0727			0.0286313
$737$		−	826.336i		−	1.12122i
$738$		0			0
$739$	−394.643			−0.534024			−0.267012	−	0.963693i	$-0.586036\pi$
$739$	−394.643			−0.534024			−0.267012	+	0.963693i	$0.586036\pi$
$740$	−74.9253	+	406.781i	−0.101250	+	0.549705i
$741$		0			0
$742$	−209.847	+	738.348i	−0.282812	+	0.995079i
$743$			147.027i			0.197883i	0.995093	+	0.0989414i	$0.0315456\pi$
$743$			147.027i			0.197883i	−0.995093	+	0.0989414i	$0.968454\pi$
$744$		0			0
$745$	658.151	+	121.225i	0.883424	+	0.162718i
$746$	−334.248			−0.448054
$747$		0			0
$748$	631.412			0.844133
$749$	−1168.65	−	332.144i	−1.56028	−	0.443449i
$750$		0			0
$751$	103.003			0.137154			0.0685771	−	0.997646i	$-0.478154\pi$
$751$	103.003			0.137154			0.0685771	+	0.997646i	$0.478154\pi$
$752$	310.646			0.413092
$753$		0			0
$754$		−	7.69852i		−	0.0102102i
$755$	−762.492	−	140.444i	−1.00992	−	0.186018i
$756$		0			0
$757$		−	547.747i		−	0.723575i	−0.932261	−	0.361788i	$-0.882167\pi$
$757$		−	547.747i		−	0.723575i	0.932261	−	0.361788i	$-0.117833\pi$
$758$			486.822i			0.642246i
$759$		0			0
$760$	127.030	+	23.3978i	0.167145	+	0.0307866i
$761$			1223.78i			1.60813i	0.594544	+	0.804063i	$0.297332\pi$
$761$			1223.78i			1.60813i	−0.594544	+	0.804063i	$0.702668\pi$
$762$		0			0
$763$	−95.6779	+	336.644i	−0.125397	+	0.441211i
$764$	119.875			0.156904
$765$		0			0
$766$			92.9275i			0.121315i
$767$		−	420.986i		−	0.548874i
$768$		0			0
$769$			194.874i			0.253413i	0.991940	+	0.126706i	$0.0404406\pi$
$769$			194.874i			0.253413i	−0.991940	+	0.126706i	$0.959559\pi$
$770$	−777.042	−	384.074i	−1.00915	−	0.498797i
$771$		0			0
$772$		−	491.896i		−	0.637171i
$773$	−1017.59			−1.31642			−0.658209	−	0.752835i	$-0.728686\pi$
$773$	−1017.59			−1.31642			−0.658209	+	0.752835i	$0.728686\pi$
$774$		0			0
$775$	508.484	−	1333.49i	0.656108	−	1.72063i
$776$			304.990i			0.393029i
$777$		0			0
$778$		−	228.107i		−	0.293196i
$779$	107.004			0.137361
$780$		0			0
$781$	−1021.01			−1.30731
$782$	94.9765			0.121453
$783$		0			0
$784$	−166.702	−	103.084i	−0.212631	−	0.131485i
$785$	514.515	+	94.7689i	0.655434	+	0.120725i
$786$		0			0
$787$	222.094			0.282203			0.141101	−	0.989995i	$-0.454936\pi$
$787$	222.094			0.282203			0.141101	+	0.989995i	$0.454936\pi$
$788$			164.119i			0.208273i
$789$		0			0
$790$	−96.0193	+	521.304i	−0.121543	+	0.659879i
$791$	−472.367	−	134.252i	−0.597178	−	0.169724i
$792$		0			0
$793$		−	25.9636i		−	0.0327409i
$794$			944.344i			1.18935i
$795$		0			0
$796$			578.677i			0.726981i
$797$	−340.349			−0.427038			−0.213519	−	0.976939i	$-0.568493\pi$
$797$	−340.349			−0.427038			−0.213519	+	0.976939i	$0.568493\pi$
$798$		0			0
$799$	1400.11			1.75233
$800$	−50.3875	+	132.140i	−0.0629844	+	0.165176i
$801$		0			0
$802$			839.796i			1.04713i
$803$	−935.263			−1.16471
$804$		0			0
$805$	−116.882	−	57.7721i	−0.145195	−	0.0717666i
$806$	390.363			0.484321
$807$		0			0
$808$	−148.818			−0.184181
$809$	462.403			0.571573			0.285787	−	0.958293i	$-0.407745\pi$
$809$	462.403			0.571573			0.285787	+	0.958293i	$0.407745\pi$
$810$		0			0
$811$			1420.09i			1.75103i	0.483190	+	0.875516i	$0.339478\pi$
$811$			1420.09i			1.75103i	−0.483190	+	0.875516i	$0.660522\pi$
$812$	−4.30893	+	15.1610i	−0.00530656	+	0.0186712i
$813$		0			0
$814$	1024.35			1.25841
$815$	−118.566	+	643.714i	−0.145480	+	0.789833i
$816$		0			0
$817$	−588.354			−0.720140
$818$	−805.571			−0.984806
$819$		0			0
$820$	−21.2220	+	115.217i	−0.0258805	+	0.140509i
$821$	651.695			0.793782			0.396891	−	0.917866i	$-0.370089\pi$
$821$	651.695			0.793782			0.396891	+	0.917866i	$0.370089\pi$
$822$		0			0
$823$			604.705i			0.734756i	0.930072	+	0.367378i	$0.119745\pi$
$823$			604.705i			0.734756i	−0.930072	+	0.367378i	$0.880255\pi$
$824$			204.779i			0.248518i
$825$		0			0
$826$	−235.630	+	829.066i	−0.285266	+	1.00371i
$827$			504.280i			0.609771i	0.952389	+	0.304885i	$0.0986181\pi$
$827$			504.280i			0.609771i	−0.952389	+	0.304885i	$0.901382\pi$
$828$		0			0
$829$		−	814.575i		−	0.982599i	−0.870991	−	0.491300i	$-0.836522\pi$
$829$		−	814.575i		−	0.982599i	0.870991	−	0.491300i	$-0.163478\pi$
$830$	36.8752	−	200.201i	0.0444279	−	0.241206i
$831$		0			0
$832$	−38.6825			−0.0464934
$833$	−751.344	−	464.610i	−0.901973	−	0.557755i
$834$		0			0
$835$	−505.718	−	93.1484i	−0.605650	−	0.111555i
$836$		−	319.884i		−	0.382637i
$837$		0			0
$838$	−296.215			−0.353478
$839$		−	128.459i		−	0.153109i	−0.997065	−	0.0765547i	$-0.975608\pi$
$839$		−	128.459i		−	0.153109i	0.997065	−	0.0765547i	$-0.0243920\pi$
$840$		0			0
$841$	−839.733			−0.998493
$842$		−	240.011i		−	0.285048i
$843$		0			0
$844$	−67.3991			−0.0798567
$845$	716.054	+	131.890i	0.847401	+	0.156083i
$846$		0			0
$847$	−355.288	+	1250.08i	−0.419466	+	1.47590i
$848$		−	310.153i		−	0.365747i
$849$		0			0
$850$	−227.101	+	595.570i	−0.267178	+	0.700670i
$851$	154.081			0.181059
$852$		0			0
$853$	−636.175			−0.745808			−0.372904	−	0.927870i	$-0.621638\pi$
$853$	−636.175			−0.745808			−0.372904	+	0.927870i	$0.621638\pi$
$854$	−14.5320	+	51.1311i	−0.0170164	+	0.0598725i
$855$		0			0
$856$	490.907			0.573490
$857$	494.679			0.577221			0.288611	−	0.957447i	$-0.406807\pi$
$857$	494.679			0.577221			0.288611	+	0.957447i	$0.406807\pi$
$858$		0			0
$859$			745.414i			0.867770i	0.900968	+	0.433885i	$0.142858\pi$
$859$			745.414i			0.867770i	−0.900968	+	0.433885i	$0.857142\pi$
$860$	116.687	−	633.514i	0.135683	−	0.736645i
$861$		0			0
$862$		−	761.450i		−	0.883353i
$863$		−	593.451i		−	0.687661i	−0.939032	−	0.343830i	$-0.888275\pi$
$863$		−	593.451i		−	0.687661i	0.939032	−	0.343830i	$-0.111725\pi$
$864$		0			0
$865$	970.828	+	178.817i	1.12234	+	0.206725i
$866$			167.322i			0.193212i
$867$		0			0
$868$	−768.757	−	218.489i	−0.885665	−	0.251716i
$869$	1312.73			1.51063
$870$		0			0
$871$			228.168i			0.261961i
$872$		−	141.412i		−	0.162169i
$873$		0			0
$874$		−	48.1168i		−	0.0550535i
$875$	641.753	−	594.793i	0.733432	−	0.679763i
$876$		0			0
$877$		−	291.879i		−	0.332815i	−0.986057	−	0.166407i	$-0.946783\pi$
$877$		−	291.879i		−	0.332815i	0.986057	−	0.166407i	$-0.0532167\pi$
$878$	−614.948			−0.700396
$879$		0			0
$880$	344.438	+	63.4422i	0.391407	+	0.0720934i
$881$			1226.42i			1.39208i	0.718004	+	0.696039i	$0.245056\pi$
$881$			1226.42i			1.39208i	−0.718004	+	0.696039i	$0.754944\pi$
$882$		0			0
$883$		−	1132.03i		−	1.28202i	−0.767531	−	0.641012i	$-0.778515\pi$
$883$		−	1132.03i		−	1.28202i	0.767531	−	0.641012i	$-0.221485\pi$
$884$	−174.346			−0.197224
$885$		0			0
$886$	−784.896			−0.885887
$887$	−959.088			−1.08127			−0.540636	−	0.841257i	$-0.681816\pi$
$887$	−959.088			−1.08127			−0.540636	+	0.841257i	$0.681816\pi$
$888$		0			0
$889$	1332.83	+	378.806i	1.49925	+	0.426103i
$890$	705.831	+	130.007i	0.793068	+	0.146076i
$891$		0			0
$892$	21.5112			0.0241156
$893$		−	709.321i		−	0.794312i
$894$		0			0
$895$	−584.280	−	107.619i	−0.652827	−	0.120245i
$896$	76.1790	+	21.6509i	0.0850212	+	0.0241640i
$897$		0			0
$898$			94.6004i			0.105346i
$899$			64.2684i			0.0714887i
$900$		0			0
$901$		−	1397.89i		−	1.55149i
$902$	290.137			0.321660
$903$		0			0
$904$	198.424			0.219496
$905$	−13.0558	+	70.8817i	−0.0144262	+	0.0783224i
$906$		0			0
$907$			989.799i			1.09129i	0.838017	+	0.545644i	$0.183715\pi$
$907$			989.799i			1.09129i	−0.838017	+	0.545644i	$0.816285\pi$
$908$	832.900			0.917290
$909$		0			0
$910$	214.557	+	106.051i	0.235777	+	0.116539i
$911$	−994.781			−1.09197			−0.545983	−	0.837796i	$-0.683844\pi$
$911$	−994.781			−1.09197			−0.545983	+	0.837796i	$0.683844\pi$
$912$		0			0
$913$	−504.141			−0.552181
$914$	1061.99			1.16191
$915$		0			0
$916$		−	776.938i		−	0.848185i
$917$	773.665	+	219.884i	0.843691	+	0.239786i
$918$		0			0
$919$	−887.212			−0.965410			−0.482705	−	0.875783i	$-0.660346\pi$
$919$	−887.212			−0.965410			−0.482705	+	0.875783i	$0.660346\pi$
$920$	51.8101	+	9.54293i	0.0563153	+	0.0103728i
$921$		0			0
$922$	559.148			0.606451
$923$	281.921			0.305440
$924$		0			0
$925$	−368.429	+	966.199i	−0.398302	+	1.04454i
$926$	−599.600			−0.647516
$927$		0			0
$928$		−	6.36859i		−	0.00686270i
$929$		−	1224.49i		−	1.31808i	−0.752109	−	0.659039i	$-0.770963\pi$
$929$		−	1224.49i		−	1.31808i	0.752109	−	0.659039i	$-0.229037\pi$
$930$		0			0
$931$	−235.380	+	380.644i	−0.252825	+	0.408855i
$932$		−	140.807i		−	0.151081i
$933$		0			0
$934$			826.478i			0.884880i
$935$	1552.42	+	285.940i	1.66034	+	0.305819i
$936$		0			0
$937$	807.001			0.861260			0.430630	−	0.902529i	$-0.358291\pi$
$937$	807.001			0.861260			0.430630	+	0.902529i	$0.358291\pi$
$938$	127.708	−	449.341i	0.136149	−	0.479042i
$939$		0			0
$940$	763.766	+	140.679i	0.812517	+	0.149658i
$941$			1246.48i			1.32464i	0.749223	+	0.662318i	$0.230427\pi$
$941$			1246.48i			1.32464i	−0.749223	+	0.662318i	$0.769573\pi$
$942$		0			0
$943$	43.6423			0.0462802
$944$		−	348.260i		−	0.368920i
$945$		0			0
$946$	−1595.30			−1.68636
$947$			675.978i			0.713810i	0.934141	+	0.356905i	$0.116168\pi$
$947$			675.978i			0.713810i	−0.934141	+	0.356905i	$0.883832\pi$
$948$		0			0
$949$	258.245			0.272123
$950$	301.726	+	115.054i	0.317607	+	0.121109i
$951$		0			0
$952$	343.346	+	97.5828i	0.360658	+	0.102503i
$953$			1098.24i			1.15240i	0.817308	+	0.576201i	$0.195466\pi$
$953$			1098.24i			1.15240i	−0.817308	+	0.576201i	$0.804534\pi$
$954$		0			0
$955$	294.730	+	54.2864i	0.308618	+	0.0568444i
$956$	−626.267			−0.655091
$957$		0			0
$958$	1038.76			1.08430
$959$	641.928	+	182.443i	0.669372	+	0.190243i
$960$		0			0
$961$	−2297.80			−2.39105
$962$	−282.843			−0.294015
$963$		0			0
$964$			397.455i			0.412297i
$965$	222.759	−	1209.40i	0.230839	−	1.25326i
$966$		0			0
$967$		−	1345.41i		−	1.39132i	−0.718370	−	0.695661i	$-0.755111\pi$
$967$		−	1345.41i		−	1.39132i	0.718370	−	0.695661i	$-0.244889\pi$
$968$		−	525.114i		−	0.542474i
$969$		0			0
$970$	−138.118	+	749.862i	−0.142389	+	0.773054i
$971$		−	1230.36i		−	1.26710i	−0.773701	−	0.633551i	$-0.781597\pi$
$971$		−	1230.36i		−	1.26710i	0.773701	−	0.633551i	$-0.218403\pi$
$972$		0			0
$973$	1599.75	+	454.668i	1.64415	+	0.467284i
$974$	−129.633			−0.133093
$975$		0			0
$976$		−	21.4783i		−	0.0220065i
$977$		−	228.116i		−	0.233487i	−0.993162	−	0.116743i	$-0.962755\pi$
$977$		−	228.116i		−	0.233487i	0.993162	−	0.116743i	$-0.0372455\pi$
$978$		0			0
$979$		−	1777.40i		−	1.81553i
$980$	−363.179	−	328.939i	−0.370591	−	0.335652i
$981$		0			0
$982$		−	650.659i		−	0.662586i
$983$	1721.09			1.75085			0.875425	−	0.483354i	$-0.160582\pi$
$983$	1721.09			1.75085			0.875425	+	0.483354i	$0.160582\pi$
$984$		0			0
$985$	−74.3227	+	403.510i	−0.0754545	+	0.409654i
$986$		−	28.7039i		−	0.0291114i
$987$		0			0
$988$			88.3266i			0.0893994i
$989$	−239.964			−0.242633
$990$		0			0
$991$	−1911.05			−1.92841			−0.964205	−	0.265159i	$-0.914576\pi$
$991$	−1911.05			−1.92841			−0.964205	+	0.265159i	$0.914576\pi$
$992$	322.927			0.325531
$993$		0			0
$994$	−555.199	−	157.794i	−0.558550	−	0.158746i
$995$	−262.059	+	1422.76i	−0.263376	+	1.42991i
$996$		0			0
$997$	−31.3627			−0.0314571			−0.0157285	−	0.999876i	$-0.505007\pi$
$997$	−31.3627			−0.0314571			−0.0157285	+	0.999876i	$0.505007\pi$
$998$		−	688.900i		−	0.690281i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.h.e.559.9		16
3.2	odd	2		210.3.h.a.139.8	yes	16
5.4	even	2	inner	630.3.h.e.559.8		16
7.6	odd	2	inner	630.3.h.e.559.16		16
12.11	even	2		1680.3.bd.a.769.8		16
15.2	even	4		1050.3.f.e.601.9		16
15.8	even	4		1050.3.f.e.601.8		16
15.14	odd	2		210.3.h.a.139.9	yes	16
21.20	even	2		210.3.h.a.139.1	✓	16
35.34	odd	2	inner	630.3.h.e.559.1		16
60.59	even	2		1680.3.bd.a.769.10		16
84.83	odd	2		1680.3.bd.a.769.9		16
105.62	odd	4		1050.3.f.e.601.13		16
105.83	odd	4		1050.3.f.e.601.4		16
105.104	even	2		210.3.h.a.139.16	yes	16
420.419	odd	2		1680.3.bd.a.769.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.1	✓	16	21.20	even	2
210.3.h.a.139.8	yes	16	3.2	odd	2
210.3.h.a.139.9	yes	16	15.14	odd	2
210.3.h.a.139.16	yes	16	105.104	even	2
630.3.h.e.559.1		16	35.34	odd	2	inner
630.3.h.e.559.8		16	5.4	even	2	inner
630.3.h.e.559.9		16	1.1	even	1	trivial
630.3.h.e.559.16		16	7.6	odd	2	inner
1050.3.f.e.601.4		16	105.83	odd	4
1050.3.f.e.601.8		16	15.8	even	4
1050.3.f.e.601.9		16	15.2	even	4
1050.3.f.e.601.13		16	105.62	odd	4
1680.3.bd.a.769.7		16	420.419	odd	2
1680.3.bd.a.769.8		16	12.11	even	2
1680.3.bd.a.769.9		16	84.83	odd	2
1680.3.bd.a.769.10		16	60.59	even	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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(-4.91728 - 0.905717i) q^{5} +(-1.91369 + 6.73333i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(-4.91728 - 0.905717i) q^{5} +(-1.91369 + 6.73333i) q^{7} -2.82843i q^{8} +(1.28088 - 6.95409i) q^{10} -17.5116 q^{11} +4.83531 q^{13} +(-9.52237 - 2.70636i) q^{14} +4.00000 q^{16} +18.0284 q^{17} -9.13350i q^{19} +(9.83457 + 1.81143i) q^{20} -24.7651i q^{22} -3.72515i q^{23} +(23.3594 + 8.90734i) q^{25} +6.83816i q^{26} +(3.82738 - 13.4667i) q^{28} -1.12582 q^{29} -57.0859i q^{31} +5.65685i q^{32} +25.4960i q^{34} +(15.5086 - 31.3765i) q^{35} +41.3624i q^{37} +12.9167 q^{38} +(-2.56176 + 13.9082i) q^{40} +11.7156i q^{41} -64.4171i q^{43} +35.0232 q^{44} +5.26816 q^{46} +77.6614 q^{47} +(-41.6756 - 25.7710i) q^{49} +(-12.5969 + 33.0351i) q^{50} -9.67062 q^{52} -77.5383i q^{53} +(86.1095 + 15.8606i) q^{55} +(19.0447 + 5.41273i) q^{56} -1.59215i q^{58} -87.0651i q^{59} -5.36957i q^{61} +80.7317 q^{62} -8.00000 q^{64} +(-23.7766 - 4.37942i) q^{65} +47.1879i q^{67} -36.0568 q^{68} +(44.3730 + 21.9325i) q^{70} +58.3047 q^{71} +53.4082 q^{73} -58.4953 q^{74} +18.2670i q^{76} +(33.5117 - 117.911i) q^{77} -74.9637 q^{79} +(-19.6691 - 3.62287i) q^{80} -16.5683 q^{82} +28.7890 q^{83} +(-88.6507 - 16.3286i) q^{85} +91.0996 q^{86} +49.5303i q^{88} +101.499i q^{89} +(-9.25327 + 32.5578i) q^{91} +7.45031i q^{92} +109.830i q^{94} +(-8.27237 + 44.9120i) q^{95} -107.830 q^{97} +(36.4457 - 58.9382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 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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