LMFDB - Embedded newform 630.3.h.e.559.6

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			559.6
Root			$0.500000 - 0.971291i$ of defining polynomial
Character	$\chi$	$=$	630.559
Dual form			630.3.h.e.559.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.00000 q^{4} +(2.40341 + 4.38447i) q^{5} +(6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q-1.41421i q^{2} -2.00000 q^{4} +(2.40341 + 4.38447i) q^{5} +(6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +(6.20058 - 3.39894i) q^{10} -2.88097 q^{11} +13.8145 q^{13} +(1.20663 - 9.82568i) q^{14} +4.00000 q^{16} -24.1754 q^{17} +6.53403i q^{19} +(-4.80682 - 8.76895i) q^{20} +4.07430i q^{22} +28.8420i q^{23} +(-13.4472 + 21.0754i) q^{25} -19.5367i q^{26} +(-13.8956 - 1.70644i) q^{28} +32.9589 q^{29} -2.43276i q^{31} -5.65685i q^{32} +34.1892i q^{34} +(12.9575 + 32.5131i) q^{35} +50.9799i q^{37} +9.24052 q^{38} +(-12.4012 + 6.79788i) q^{40} +21.5225i q^{41} -13.5554i q^{43} +5.76193 q^{44} +40.7887 q^{46} +40.7305 q^{47} +(47.5440 + 11.8560i) q^{49} +(29.8051 + 19.0172i) q^{50} -27.6291 q^{52} -17.2758i q^{53} +(-6.92415 - 12.6315i) q^{55} +(-2.41326 + 19.6514i) q^{56} -46.6109i q^{58} +1.47488i q^{59} -111.568i q^{61} -3.44045 q^{62} -8.00000 q^{64} +(33.2020 + 60.5694i) q^{65} +120.293i q^{67} +48.3508 q^{68} +(45.9805 - 18.3247i) q^{70} +90.3855 q^{71} -21.4890 q^{73} +72.0964 q^{74} -13.0681i q^{76} +(-20.0164 - 2.45809i) q^{77} -66.1324 q^{79} +(9.61365 + 17.5379i) q^{80} +30.4375 q^{82} +78.5172 q^{83} +(-58.1035 - 105.996i) q^{85} -19.1703 q^{86} -8.14861i q^{88} +90.9724i q^{89} +(95.9807 + 11.7868i) q^{91} -57.6840i q^{92} -57.6016i q^{94} +(-28.6483 + 15.7040i) q^{95} -44.1972 q^{97} +(16.7669 - 67.2374i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.40341	+	4.38447i	0.480682	+	0.876895i
$5$	2.40341	+	4.38447i	0.480682	+	0.876895i
$6$		0			0
$7$	6.94781	+	0.853218i	0.992544	+	0.121888i
$7$	6.94781	+	0.853218i	0.992544	+	0.121888i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	6.20058	−	3.39894i	0.620058	−	0.339894i
$11$	−2.88097			−0.261906			−0.130953	−	0.991389i	$-0.541804\pi$
$11$	−2.88097			−0.261906			−0.130953	+	0.991389i	$0.541804\pi$
$12$		0			0
$13$	13.8145			1.06266			0.531328	−	0.847166i	$-0.321693\pi$
$13$	13.8145			1.06266			0.531328	+	0.847166i	$0.321693\pi$
$14$	1.20663	−	9.82568i	0.0861880	−	0.701834i
$15$		0			0
$16$	4.00000			0.250000
$17$	−24.1754			−1.42208			−0.711041	−	0.703150i	$-0.751776\pi$
$17$	−24.1754			−1.42208			−0.711041	+	0.703150i	$0.751776\pi$
$18$		0			0
$19$			6.53403i			0.343896i	0.985106	+	0.171948i	$0.0550062\pi$
$19$			6.53403i			0.343896i	−0.985106	+	0.171948i	$0.944994\pi$
$20$	−4.80682	−	8.76895i	−0.240341	−	0.438447i
$21$		0			0
$22$			4.07430i			0.185196i
$23$			28.8420i			1.25400i	0.779019	+	0.627000i	$0.215717\pi$
$23$			28.8420i			1.25400i	−0.779019	+	0.627000i	$0.784283\pi$
$24$		0			0
$25$	−13.4472	+	21.0754i	−0.537889	+	0.843016i
$26$		−	19.5367i		−	0.751411i
$27$		0			0
$28$	−13.8956	−	1.70644i	−0.496272	−	0.0609441i
$29$	32.9589			1.13651			0.568257	−	0.822851i	$-0.307618\pi$
$29$	32.9589			1.13651			0.568257	+	0.822851i	$0.307618\pi$
$30$		0			0
$31$		−	2.43276i		−	0.0784762i	−0.999230	−	0.0392381i	$-0.987507\pi$
$31$		−	2.43276i		−	0.0784762i	0.999230	−	0.0392381i	$-0.0124931\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$			34.1892i			1.00556i
$35$	12.9575	+	32.5131i	0.370215	+	0.928946i
$36$		0			0
$37$			50.9799i			1.37783i	0.724840	+	0.688917i	$0.241914\pi$
$37$			50.9799i			1.37783i	−0.724840	+	0.688917i	$0.758086\pi$
$38$	9.24052			0.243171
$39$		0			0
$40$	−12.4012	+	6.79788i	−0.310029	+	0.169947i
$41$			21.5225i			0.524940i	0.964940	+	0.262470i	$0.0845371\pi$
$41$			21.5225i			0.524940i	−0.964940	+	0.262470i	$0.915463\pi$
$42$		0			0
$43$		−	13.5554i		−	0.315243i	−0.987500	−	0.157621i	$-0.949617\pi$
$43$		−	13.5554i		−	0.315243i	0.987500	−	0.157621i	$-0.0503826\pi$
$44$	5.76193			0.130953
$45$		0			0
$46$	40.7887			0.886712
$47$	40.7305			0.866605			0.433303	−	0.901248i	$-0.357348\pi$
$47$	40.7305			0.866605			0.433303	+	0.901248i	$0.357348\pi$
$48$		0			0
$49$	47.5440	+	11.8560i	0.970287	+	0.241959i
$50$	29.8051	+	19.0172i	0.596102	+	0.380345i
$51$		0			0
$52$	−27.6291			−0.531328
$53$		−	17.2758i		−	0.325959i	−0.986629	−	0.162979i	$-0.947890\pi$
$53$		−	17.2758i		−	0.325959i	0.986629	−	0.162979i	$-0.0521104\pi$
$54$		0			0
$55$	−6.92415	−	12.6315i	−0.125894	−	0.229664i
$56$	−2.41326	+	19.6514i	−0.0430940	+	0.350917i
$57$		0			0
$58$		−	46.6109i		−	0.803636i
$59$			1.47488i			0.0249980i	0.999922	+	0.0124990i	$0.00397867\pi$
$59$			1.47488i			0.0249980i	−0.999922	+	0.0124990i	$0.996021\pi$
$60$		0			0
$61$		−	111.568i		−	1.82898i	−0.404609	−	0.914490i	$-0.632592\pi$
$61$		−	111.568i		−	1.82898i	0.404609	−	0.914490i	$-0.367408\pi$
$62$	−3.44045			−0.0554911
$63$		0			0
$64$	−8.00000			−0.125000
$65$	33.2020	+	60.5694i	0.510800	+	0.931837i
$66$		0			0
$67$			120.293i			1.79542i	0.440590	+	0.897709i	$0.354769\pi$
$67$			120.293i			1.79542i	−0.440590	+	0.897709i	$0.645231\pi$
$68$	48.3508			0.711041
$69$		0			0
$70$	45.9805	−	18.3247i	0.656864	−	0.261782i
$71$	90.3855			1.27304			0.636518	−	0.771262i	$-0.280374\pi$
$71$	90.3855			1.27304			0.636518	+	0.771262i	$0.280374\pi$
$72$		0			0
$73$	−21.4890			−0.294370			−0.147185	−	0.989109i	$-0.547021\pi$
$73$	−21.4890			−0.294370			−0.147185	+	0.989109i	$0.547021\pi$
$74$	72.0964			0.974276
$75$		0			0
$76$		−	13.0681i		−	0.171948i
$77$	−20.0164	−	2.45809i	−0.259953	−	0.0319233i
$78$		0			0
$79$	−66.1324			−0.837119			−0.418559	−	0.908189i	$-0.637465\pi$
$79$	−66.1324			−0.837119			−0.418559	+	0.908189i	$0.637465\pi$
$80$	9.61365	+	17.5379i	0.120171	+	0.219224i
$81$		0			0
$82$	30.4375			0.371189
$83$	78.5172			0.945990			0.472995	−	0.881065i	$-0.343173\pi$
$83$	78.5172			0.945990			0.472995	+	0.881065i	$0.343173\pi$
$84$		0			0
$85$	−58.1035	−	105.996i	−0.683570	−	1.24702i
$86$	−19.1703			−0.222910
$87$		0			0
$88$		−	8.14861i		−	0.0925978i
$89$			90.9724i			1.02216i	0.859533	+	0.511081i	$0.170755\pi$
$89$			90.9724i			1.02216i	−0.859533	+	0.511081i	$0.829245\pi$
$90$		0			0
$91$	95.9807	+	11.7868i	1.05473	+	0.129525i
$92$		−	57.6840i		−	0.627000i
$93$		0			0
$94$		−	57.6016i		−	0.612783i
$95$	−28.6483	+	15.7040i	−0.301561	+	0.165305i
$96$		0			0
$97$	−44.1972			−0.455642			−0.227821	−	0.973703i	$-0.573160\pi$
$97$	−44.1972			−0.455642			−0.227821	+	0.973703i	$0.573160\pi$
$98$	16.7669	−	67.2374i	0.171091	−	0.686096i
$99$		0			0
$100$	26.8944	−	42.1508i	0.268944	−	0.421508i
$101$		−	180.052i		−	1.78269i	−0.453326	−	0.891345i	$-0.649763\pi$
$101$		−	180.052i		−	1.78269i	0.453326	−	0.891345i	$-0.350237\pi$
$102$		0			0
$103$	107.208			1.04086			0.520428	−	0.853906i	$-0.325772\pi$
$103$	107.208			1.04086			0.520428	+	0.853906i	$0.325772\pi$
$104$			39.0734i			0.375706i
$105$		0			0
$106$	−24.4317			−0.230488
$107$		−	33.1521i		−	0.309833i	−0.987928	−	0.154917i	$-0.950489\pi$
$107$		−	33.1521i		−	0.309833i	0.987928	−	0.154917i	$-0.0495109\pi$
$108$		0			0
$109$	108.819			0.998338			0.499169	−	0.866505i	$-0.333639\pi$
$109$	108.819			0.998338			0.499169	+	0.866505i	$0.333639\pi$
$110$	−17.8637	+	9.79223i	−0.162397	+	0.0890203i
$111$		0			0
$112$	27.7912	+	3.41287i	0.248136	+	0.0304721i
$113$			157.658i			1.39520i	0.716488	+	0.697600i	$0.245749\pi$
$113$			157.658i			1.39520i	−0.716488	+	0.697600i	$0.754251\pi$
$114$		0			0
$115$	−126.457	+	69.3192i	−1.09963	+	0.602776i
$116$	−65.9178			−0.568257
$117$		0			0
$118$	2.08580			0.0176763
$119$	−167.966	−	20.6269i	−1.41148	−	0.173335i
$120$		0			0
$121$	−112.700			−0.931405
$122$	−157.781			−1.29328
$123$		0			0
$124$			4.86553i			0.0392381i
$125$	−124.724	−	8.30611i	−0.997790	−	0.0664489i
$126$		0			0
$127$			28.2047i			0.222085i	0.993816	+	0.111042i	$0.0354189\pi$
$127$			28.2047i			0.222085i	−0.993816	+	0.111042i	$0.964581\pi$
$128$			11.3137i			0.0883883i
$129$		0			0
$130$	85.6581	−	46.9547i	0.658908	−	0.361190i
$131$		−	157.620i		−	1.20321i	−0.798795	−	0.601604i	$-0.794529\pi$
$131$		−	157.620i		−	1.20321i	0.798795	−	0.601604i	$-0.205471\pi$
$132$		0			0
$133$	−5.57495	+	45.3972i	−0.0419169	+	0.341332i
$134$	170.120			1.26955
$135$		0			0
$136$		−	68.3784i		−	0.502782i
$137$		−	244.855i		−	1.78726i	−0.448800	−	0.893632i	$-0.648148\pi$
$137$		−	244.855i		−	1.78726i	0.448800	−	0.893632i	$-0.351852\pi$
$138$		0			0
$139$			238.245i			1.71399i	0.515325	+	0.856995i	$0.327671\pi$
$139$			238.245i			1.71399i	−0.515325	+	0.856995i	$0.672329\pi$
$140$	−25.9151	−	65.0262i	−0.185108	−	0.464473i
$141$		0			0
$142$		−	127.824i		−	0.900172i
$143$	−39.7992			−0.278316
$144$		0			0
$145$	79.2138	+	144.507i	0.546302	+	0.996603i
$146$			30.3900i			0.208151i
$147$		0			0
$148$		−	101.960i		−	0.688917i
$149$	−10.8398			−0.0727503			−0.0363751	−	0.999338i	$-0.511581\pi$
$149$	−10.8398			−0.0727503			−0.0363751	+	0.999338i	$0.511581\pi$
$150$		0			0
$151$	−112.999			−0.748340			−0.374170	−	0.927360i	$-0.622072\pi$
$151$	−112.999			−0.748340			−0.374170	+	0.927360i	$0.622072\pi$
$152$	−18.4810			−0.121586
$153$		0			0
$154$	−3.47627	+	28.3075i	−0.0225732	+	0.183815i
$155$	10.6664	−	5.84693i	0.0688154	−	0.0377222i
$156$		0			0
$157$	103.693			0.660462			0.330231	−	0.943900i	$-0.392873\pi$
$157$	103.693			0.660462			0.330231	+	0.943900i	$0.392873\pi$
$158$			93.5253i			0.591932i
$159$		0			0
$160$	24.8023	−	13.5958i	0.155015	−	0.0849735i
$161$	−24.6085	+	200.389i	−0.152848	+	1.24465i
$162$		0			0
$163$			199.576i			1.22439i	0.790706	+	0.612196i	$0.209713\pi$
$163$			199.576i			1.22439i	−0.790706	+	0.612196i	$0.790287\pi$
$164$		−	43.0451i		−	0.262470i
$165$		0			0
$166$		−	111.040i		−	0.668916i
$167$	87.0777			0.521424			0.260712	−	0.965417i	$-0.416043\pi$
$167$	87.0777			0.521424			0.260712	+	0.965417i	$0.416043\pi$
$168$		0			0
$169$	21.8411			0.129237
$170$	−149.902	+	82.1707i	−0.881774	+	0.483357i
$171$		0			0
$172$			27.1109i			0.157621i
$173$	106.597			0.616166			0.308083	−	0.951359i	$-0.400313\pi$
$173$	106.597			0.616166			0.308083	+	0.951359i	$0.400313\pi$
$174$		0			0
$175$	−111.411	+	134.954i	−0.636632	+	0.771168i
$176$	−11.5239			−0.0654765
$177$		0			0
$178$	128.654			0.722778
$179$	−275.881			−1.54123			−0.770617	−	0.637298i	$-0.780052\pi$
$179$	−275.881			−1.54123			−0.770617	+	0.637298i	$0.780052\pi$
$180$		0			0
$181$		−	186.431i		−	1.03000i	−0.857189	−	0.515002i	$-0.827791\pi$
$181$		−	186.431i		−	1.03000i	0.857189	−	0.515002i	$-0.172209\pi$
$182$	16.6690	−	135.737i	0.0915882	−	0.745808i
$183$		0			0
$184$	−81.5775			−0.443356
$185$	−223.520	+	122.526i	−1.20822	+	0.662301i
$186$		0			0
$187$	69.6485			0.372452
$188$	−81.4609			−0.433303
$189$		0			0
$190$	22.2088	+	40.5148i	0.116888	+	0.213236i
$191$	177.076			0.927102			0.463551	−	0.886070i	$-0.346575\pi$
$191$	177.076			0.927102			0.463551	+	0.886070i	$0.346575\pi$
$192$		0			0
$193$		−	153.453i		−	0.795092i	−0.917582	−	0.397546i	$-0.869862\pi$
$193$		−	153.453i		−	0.795092i	0.917582	−	0.397546i	$-0.130138\pi$
$194$			62.5043i			0.322187i
$195$		0			0
$196$	−95.0881	−	23.7120i	−0.485143	−	0.120979i
$197$			214.041i			1.08650i	0.839570	+	0.543252i	$0.182807\pi$
$197$			214.041i			1.08650i	−0.839570	+	0.543252i	$0.817193\pi$
$198$		0			0
$199$		−	178.176i		−	0.895359i	−0.894194	−	0.447679i	$-0.852251\pi$
$199$		−	178.176i		−	0.895359i	0.894194	−	0.447679i	$-0.147749\pi$
$200$	−59.6102	−	38.0345i	−0.298051	−	0.190172i
$201$		0			0
$202$	−254.631			−1.26055
$203$	228.992	+	28.1211i	1.12804	+	0.138528i
$204$		0			0
$205$	−94.3650	+	51.7275i	−0.460317	+	0.252329i
$206$		−	151.615i		−	0.735996i
$207$		0			0
$208$	55.2581			0.265664
$209$		−	18.8243i		−	0.0900686i
$210$		0			0
$211$	−398.012			−1.88631			−0.943156	−	0.332350i	$-0.892158\pi$
$211$	−398.012			−1.88631			−0.943156	+	0.332350i	$0.892158\pi$
$212$			34.5517i			0.162979i
$213$		0			0
$214$	−46.8842			−0.219085
$215$	59.4335	−	32.5793i	0.276435	−	0.151532i
$216$		0			0
$217$	2.07568	−	16.9024i	0.00956533	−	0.0778911i
$218$		−	153.893i		−	0.705932i
$219$		0			0
$220$	13.8483	+	25.2631i	0.0629468	+	0.114832i
$221$	−333.972			−1.51118
$222$		0			0
$223$	6.96741			0.0312440			0.0156220	−	0.999878i	$-0.495027\pi$
$223$	6.96741			0.0312440			0.0156220	+	0.999878i	$0.495027\pi$
$224$	4.82653	−	39.3027i	0.0215470	−	0.175459i
$225$		0			0
$226$	222.961			0.986555
$227$	−242.118			−1.06660			−0.533299	−	0.845927i	$-0.679048\pi$
$227$	−242.118			−1.06660			−0.533299	+	0.845927i	$0.679048\pi$
$228$		0			0
$229$		−	225.586i		−	0.985093i	−0.870286	−	0.492547i	$-0.836066\pi$
$229$		−	225.586i		−	0.985093i	0.870286	−	0.492547i	$-0.163934\pi$
$230$	98.0322	+	178.837i	0.426227	+	0.777553i
$231$		0			0
$232$			93.2218i			0.401818i
$233$		−	435.850i		−	1.87060i	−0.353856	−	0.935300i	$-0.615130\pi$
$233$		−	435.850i		−	1.87060i	0.353856	−	0.935300i	$-0.384870\pi$
$234$		0			0
$235$	97.8921	+	178.582i	0.416562	+	0.759922i
$236$		−	2.94977i		−	0.0124990i
$237$		0			0
$238$	−29.1708	+	237.540i	−0.122566	+	0.998066i
$239$	−194.711			−0.814690			−0.407345	−	0.913274i	$-0.633545\pi$
$239$	−194.711			−0.814690			−0.407345	+	0.913274i	$0.633545\pi$
$240$		0			0
$241$		−	245.810i		−	1.01996i	−0.860186	−	0.509980i	$-0.829653\pi$
$241$		−	245.810i		−	1.01996i	0.860186	−	0.509980i	$-0.170347\pi$
$242$			159.382i			0.658603i
$243$		0			0
$244$			223.136i			0.914490i
$245$	62.2857	+	236.950i	0.254227	+	0.967144i
$246$		0			0
$247$			90.2645i			0.365443i
$248$	6.88089			0.0277455
$249$		0			0
$250$	−11.7466	+	176.386i	−0.0469864	+	0.705544i
$251$		−	147.023i		−	0.585749i	−0.956151	−	0.292875i	$-0.905388\pi$
$251$		−	147.023i		−	0.585749i	0.956151	−	0.292875i	$-0.0946118\pi$
$252$		0			0
$253$		−	83.0928i		−	0.328430i
$254$	39.8875			0.157038
$255$		0			0
$256$	16.0000			0.0625000
$257$	421.734			1.64099			0.820495	−	0.571654i	$-0.193698\pi$
$257$	421.734			1.64099			0.820495	+	0.571654i	$0.193698\pi$
$258$		0			0
$259$	−43.4969	+	354.198i	−0.167942	+	1.36756i
$260$	−66.4040	−	121.139i	−0.255400	−	0.465919i
$261$		0			0
$262$	−222.909			−0.850796
$263$			68.6354i			0.260971i	0.991450	+	0.130486i	$0.0416536\pi$
$263$			68.6354i			0.260971i	−0.991450	+	0.130486i	$0.958346\pi$
$264$		0			0
$265$	75.7454	−	41.5209i	0.285832	−	0.156683i
$266$	64.2013	+	7.88417i	0.241358	+	0.0296397i
$267$		0			0
$268$		−	240.586i		−	0.897709i
$269$		−	93.2991i		−	0.346837i	−0.984848	−	0.173418i	$-0.944519\pi$
$269$		−	93.2991i		−	0.346837i	0.984848	−	0.173418i	$-0.0554813\pi$
$270$		0			0
$271$		−	288.317i		−	1.06390i	−0.846776	−	0.531949i	$-0.821460\pi$
$271$		−	288.317i		−	1.06390i	0.846776	−	0.531949i	$-0.178540\pi$
$272$	−96.7016			−0.355521
$273$		0			0
$274$	−346.278			−1.26379
$275$	38.7410	−	60.7175i	0.140876	−	0.220791i
$276$		0			0
$277$		−	385.440i		−	1.39148i	−0.718294	−	0.695740i	$-0.755077\pi$
$277$		−	385.440i		−	1.39148i	0.718294	−	0.695740i	$-0.244923\pi$
$278$	336.929			1.21197
$279$		0			0
$280$	−91.9610	+	36.6494i	−0.328432	+	0.130891i
$281$	−243.958			−0.868179			−0.434090	−	0.900870i	$-0.642930\pi$
$281$	−243.958			−0.868179			−0.434090	+	0.900870i	$0.642930\pi$
$282$		0			0
$283$	−501.435			−1.77185			−0.885927	−	0.463825i	$-0.846477\pi$
$283$	−501.435			−1.77185			−0.885927	+	0.463825i	$0.846477\pi$
$284$	−180.771			−0.636518
$285$		0			0
$286$			56.2846i			0.196799i
$287$	−18.3634	+	149.534i	−0.0639840	+	0.521026i
$288$		0			0
$289$	295.450			1.02232
$290$	204.364	−	112.025i	0.704705	−	0.386294i
$291$		0			0
$292$	42.9780			0.147185
$293$	−337.308			−1.15122			−0.575611	−	0.817724i	$-0.695236\pi$
$293$	−337.308			−1.15122			−0.575611	+	0.817724i	$0.695236\pi$
$294$		0			0
$295$	−6.46659	+	3.54476i	−0.0219207	+	0.0120161i
$296$	−144.193			−0.487138
$297$		0			0
$298$			15.3298i			0.0514422i
$299$			398.438i			1.33257i
$300$		0			0
$301$	11.5657	−	94.1806i	0.0384244	−	0.312892i
$302$			159.805i			0.529156i
$303$		0			0
$304$			26.1361i			0.0859741i
$305$	489.166	−	268.143i	1.60382	−	0.879159i
$306$		0			0
$307$	−112.285			−0.365751			−0.182875	−	0.983136i	$-0.558540\pi$
$307$	−112.285			−0.365751			−0.182875	+	0.983136i	$0.558540\pi$
$308$	40.0328	+	4.91618i	0.129977	+	0.0159616i
$309$		0			0
$310$	−8.26881	−	15.0846i	−0.0266736	−	0.0486598i
$311$		−	146.478i		−	0.470990i	−0.971876	−	0.235495i	$-0.924329\pi$
$311$		−	146.478i		−	0.470990i	0.971876	−	0.235495i	$-0.0756711\pi$
$312$		0			0
$313$	139.927			0.447052			0.223526	−	0.974698i	$-0.428243\pi$
$313$	139.927			0.447052			0.223526	+	0.974698i	$0.428243\pi$
$314$		−	146.643i		−	0.467017i
$315$		0			0
$316$	132.265			0.418559
$317$		−	39.7776i		−	0.125481i	−0.998030	−	0.0627407i	$-0.980016\pi$
$317$		−	39.7776i		−	0.125481i	0.998030	−	0.0627407i	$-0.0199841\pi$
$318$		0			0
$319$	−94.9535			−0.297660
$320$	−19.2273	−	35.0758i	−0.0600853	−	0.109612i
$321$		0			0
$322$	283.392	+	34.8017i	0.880100	+	0.108080i
$323$		−	157.963i		−	0.489049i
$324$		0			0
$325$	−185.767	+	291.147i	−0.571591	+	0.895836i
$326$	282.243			0.865775
$327$		0			0
$328$	−60.8749			−0.185594
$329$	282.987	+	34.7519i	0.860144	+	0.105629i
$330$		0			0
$331$	−13.6736			−0.0413101			−0.0206550	−	0.999787i	$-0.506575\pi$
$331$	−13.6736			−0.0413101			−0.0206550	+	0.999787i	$0.506575\pi$
$332$	−157.034			−0.472995
$333$		0			0
$334$		−	123.147i		−	0.368702i
$335$	−527.421	+	289.114i	−1.57439	+	0.863026i
$336$		0			0
$337$		−	364.873i		−	1.08271i	−0.840795	−	0.541354i	$-0.817912\pi$
$337$		−	364.873i		−	1.08271i	0.840795	−	0.541354i	$-0.182088\pi$
$338$		−	30.8880i		−	0.0913846i
$339$		0			0
$340$	116.207	+	211.993i	0.341785	+	0.623508i
$341$			7.00871i			0.0205534i
$342$		0			0
$343$	320.211	+	122.938i	0.933560	+	0.358421i
$344$	38.3406			0.111455
$345$		0			0
$346$		−	150.751i		−	0.435695i
$347$			469.783i			1.35384i	0.736056	+	0.676920i	$0.236686\pi$
$347$			469.783i			1.35384i	−0.736056	+	0.676920i	$0.763314\pi$
$348$		0			0
$349$			26.7504i			0.0766487i	0.999265	+	0.0383244i	$0.0122020\pi$
$349$			26.7504i			0.0766487i	−0.999265	+	0.0383244i	$0.987798\pi$
$350$	190.854	+	157.558i	0.545298	+	0.450167i
$351$		0			0
$352$			16.2972i			0.0462989i
$353$	−473.408			−1.34110			−0.670550	−	0.741864i	$-0.733942\pi$
$353$	−473.408			−1.34110			−0.670550	+	0.741864i	$0.733942\pi$
$354$		0			0
$355$	217.234	+	396.293i	0.611926	+	1.11632i
$356$		−	181.945i		−	0.511081i
$357$		0			0
$358$			390.155i			1.08982i
$359$	98.8174			0.275257			0.137629	−	0.990484i	$-0.456052\pi$
$359$	98.8174			0.275257			0.137629	+	0.990484i	$0.456052\pi$
$360$		0			0
$361$	318.306			0.881735
$362$	−263.653			−0.728323
$363$		0			0
$364$	−191.961	−	23.5736i	−0.527366	−	0.0647626i
$365$	−51.6469	−	94.2179i	−0.141498	−	0.258131i
$366$		0			0
$367$	331.526			0.903341			0.451671	−	0.892185i	$-0.350828\pi$
$367$	331.526			0.903341			0.451671	+	0.892185i	$0.350828\pi$
$368$			115.368i			0.313500i
$369$		0			0
$370$	173.277	+	316.105i	0.468317	+	0.854338i
$371$	14.7400	−	120.029i	0.0397306	−	0.323529i
$372$		0			0
$373$		−	416.519i		−	1.11667i	−0.829614	−	0.558337i	$-0.811440\pi$
$373$		−	416.519i		−	1.11667i	0.829614	−	0.558337i	$-0.188560\pi$
$374$		−	98.4979i		−	0.263363i
$375$		0			0
$376$			115.203i			0.306391i
$377$	455.311			1.20772
$378$		0			0
$379$	560.942			1.48006			0.740028	−	0.672576i	$-0.234812\pi$
$379$	560.942			1.48006			0.740028	+	0.672576i	$0.234812\pi$
$380$	57.2966	−	31.4079i	0.150780	−	0.0826525i
$381$		0			0
$382$		−	250.424i		−	0.655560i
$383$	−135.702			−0.354314			−0.177157	−	0.984183i	$-0.556690\pi$
$383$	−135.702			−0.354314			−0.177157	+	0.984183i	$0.556690\pi$
$384$		0			0
$385$	−37.3302	−	93.6692i	−0.0969616	−	0.243297i
$386$	−217.015			−0.562215
$387$		0			0
$388$	88.3945			0.227821
$389$	703.375			1.80816			0.904081	−	0.427361i	$-0.140557\pi$
$389$	703.375			1.80816			0.904081	+	0.427361i	$0.140557\pi$
$390$		0			0
$391$		−	697.267i		−	1.78329i
$392$	−33.5338	+	134.475i	−0.0855454	+	0.343048i
$393$		0			0
$394$	302.700			0.768274
$395$	−158.943	−	289.956i	−0.402388	−	0.734065i
$396$		0			0
$397$	2.16495			0.00545326			0.00272663	−	0.999996i	$-0.499132\pi$
$397$	2.16495			0.00545326			0.00272663	+	0.999996i	$0.499132\pi$
$398$	−251.979			−0.633114
$399$		0			0
$400$	−53.7889	+	84.3016i	−0.134472	+	0.210754i
$401$	227.907			0.568347			0.284174	−	0.958773i	$-0.408281\pi$
$401$	227.907			0.568347			0.284174	+	0.958773i	$0.408281\pi$
$402$		0			0
$403$		−	33.6075i		−	0.0833932i
$404$			360.103i			0.891345i
$405$		0			0
$406$	39.7693	−	323.844i	0.0979538	−	0.797644i
$407$		−	146.871i		−	0.360863i
$408$		0			0
$409$			219.271i			0.536116i	0.963403	+	0.268058i	$0.0863818\pi$
$409$			219.271i			0.536116i	−0.963403	+	0.268058i	$0.913618\pi$
$410$	73.1538	+	133.452i	0.178424	+	0.325493i
$411$		0			0
$412$	−214.416			−0.520428
$413$	−1.25840	+	10.2472i	−0.00304697	+	0.0248117i
$414$		0			0
$415$	188.709	+	344.257i	0.454721	+	0.829534i
$416$		−	78.1468i		−	0.187853i
$417$		0			0
$418$	−26.6216			−0.0636881
$419$		−	636.723i		−	1.51963i	−0.650141	−	0.759813i	$-0.725290\pi$
$419$		−	636.723i		−	1.51963i	0.650141	−	0.759813i	$-0.274710\pi$
$420$		0			0
$421$	816.589			1.93964			0.969821	−	0.243819i	$-0.0784003\pi$
$421$	816.589			1.93964			0.969821	+	0.243819i	$0.0784003\pi$
$422$			562.874i			1.33382i
$423$		0			0
$424$	48.8634			0.115244
$425$	325.092	−	509.506i	0.764922	−	1.19884i
$426$		0			0
$427$	95.1916	−	775.151i	0.222931	−	1.81534i
$428$			66.3043i			0.154917i
$429$		0			0
$430$	−46.0741	−	84.0516i	−0.107149	−	0.195469i
$431$	288.911			0.670328			0.335164	−	0.942160i	$-0.391208\pi$
$431$	288.911			0.670328			0.335164	+	0.942160i	$0.391208\pi$
$432$		0			0
$433$	114.744			0.264997			0.132498	−	0.991183i	$-0.457700\pi$
$433$	114.744			0.264997			0.132498	+	0.991183i	$0.457700\pi$
$434$	−23.9036	−	2.93545i	−0.0550773	−	0.00676371i
$435$		0			0
$436$	−217.638			−0.499169
$437$	−188.454			−0.431246
$438$		0			0
$439$		−	637.443i		−	1.45203i	−0.687677	−	0.726017i	$-0.741369\pi$
$439$		−	637.443i		−	1.45203i	0.687677	−	0.726017i	$-0.258631\pi$
$440$	35.7273	−	19.5845i	0.0811985	−	0.0445101i
$441$		0			0
$442$			472.307i			1.06857i
$443$			184.901i			0.417384i	0.977981	+	0.208692i	$0.0669207\pi$
$443$			184.901i			0.417384i	−0.977981	+	0.208692i	$0.933079\pi$
$444$		0			0
$445$	−398.866	+	218.644i	−0.896328	+	0.491335i
$446$		−	9.85341i		−	0.0220928i
$447$		0			0
$448$	−55.5825	−	6.82574i	−0.124068	−	0.0152360i
$449$	313.278			0.697723			0.348862	−	0.937174i	$-0.386568\pi$
$449$	313.278			0.697723			0.348862	+	0.937174i	$0.386568\pi$
$450$		0			0
$451$		−	62.0057i		−	0.137485i
$452$		−	315.315i		−	0.697600i
$453$		0			0
$454$			342.406i			0.754198i
$455$	179.002	+	449.153i	0.393411	+	0.987150i
$456$		0			0
$457$		−	174.826i		−	0.382551i	−0.981536	−	0.191275i	$-0.938738\pi$
$457$		−	174.826i		−	0.382551i	0.981536	−	0.191275i	$-0.0612623\pi$
$458$	−319.027			−0.696566
$459$		0			0
$460$	252.914	−	138.638i	0.549813	−	0.301388i
$461$		−	379.263i		−	0.822695i	−0.911479	−	0.411348i	$-0.865058\pi$
$461$		−	379.263i		−	0.822695i	0.911479	−	0.411348i	$-0.134942\pi$
$462$		0			0
$463$			403.499i			0.871489i	0.900071	+	0.435744i	$0.143515\pi$
$463$			403.499i			0.871489i	−0.900071	+	0.435744i	$0.856485\pi$
$464$	131.836			0.284128
$465$		0			0
$466$	−616.385			−1.32271
$467$	807.901			1.72998			0.864991	−	0.501788i	$-0.167324\pi$
$467$	807.901			1.72998			0.864991	+	0.501788i	$0.167324\pi$
$468$		0			0
$469$	−102.636	+	835.772i	−0.218840	+	1.78203i
$470$	252.553	−	138.440i	0.537346	−	0.294554i
$471$		0			0
$472$	−4.17160			−0.00883815
$473$			39.0528i			0.0825640i
$474$		0			0
$475$	−137.707	−	87.8645i	−0.289910	−	0.184978i
$476$	335.932	+	41.2538i	0.705740	+	0.0866675i
$477$		0			0
$478$			275.363i			0.576073i
$479$			439.564i			0.917671i	0.888521	+	0.458835i	$0.151733\pi$
$479$			439.564i			0.917671i	−0.888521	+	0.458835i	$0.848267\pi$
$480$		0			0
$481$			704.263i			1.46416i
$482$	−347.628			−0.721220
$483$		0			0
$484$	225.400			0.465703
$485$	−106.224	−	193.782i	−0.219019	−	0.399550i
$486$		0			0
$487$			37.9665i			0.0779599i	0.999240	+	0.0389799i	$0.0124108\pi$
$487$			37.9665i			0.0779599i	−0.999240	+	0.0389799i	$0.987589\pi$
$488$	315.561			0.646642
$489$		0			0
$490$	335.098	−	88.0853i	0.683874	−	0.179766i
$491$	7.32753			0.0149237			0.00746184	−	0.999972i	$-0.497625\pi$
$491$	7.32753			0.0149237			0.00746184	+	0.999972i	$0.497625\pi$
$492$		0			0
$493$	−796.794			−1.61622
$494$	127.653			0.258408
$495$		0			0
$496$		−	9.73105i		−	0.0196191i
$497$	627.981	+	77.1185i	1.26354	+	0.155168i
$498$		0			0
$499$	−397.886			−0.797366			−0.398683	−	0.917089i	$-0.630533\pi$
$499$	−397.886			−0.797366			−0.398683	+	0.917089i	$0.630533\pi$
$500$	249.447	+	16.6122i	0.498895	+	0.0332244i
$501$		0			0
$502$	−207.922			−0.414187
$503$	−70.5081			−0.140175			−0.0700876	−	0.997541i	$-0.522328\pi$
$503$	−70.5081			−0.140175			−0.0700876	+	0.997541i	$0.522328\pi$
$504$		0			0
$505$	789.432	−	432.738i	1.56323	−	0.856908i
$506$	−117.511			−0.232235
$507$		0			0
$508$		−	56.4095i		−	0.111042i
$509$			505.073i			0.992285i	0.868241	+	0.496143i	$0.165251\pi$
$509$			505.073i			0.992285i	−0.868241	+	0.496143i	$0.834749\pi$
$510$		0			0
$511$	−149.301	−	18.3348i	−0.292175	−	0.0358802i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$		−	596.422i		−	1.16035i
$515$	257.665	+	470.051i	0.500321	+	0.912721i
$516$		0			0
$517$	−117.343			−0.226969
$518$	500.912	+	61.5139i	0.967012	+	0.118753i
$519$		0			0
$520$	−171.316	+	93.9094i	−0.329454	+	0.180595i
$521$		−	214.185i		−	0.411104i	−0.978646	−	0.205552i	$-0.934101\pi$
$521$		−	214.185i		−	0.411104i	0.978646	−	0.205552i	$-0.0658990\pi$
$522$		0			0
$523$	121.732			0.232757			0.116379	−	0.993205i	$-0.462871\pi$
$523$	121.732			0.232757			0.116379	+	0.993205i	$0.462871\pi$
$524$			315.240i			0.601604i
$525$		0			0
$526$	97.0651			0.184534
$527$			58.8130i			0.111600i
$528$		0			0
$529$	−302.861			−0.572515
$530$	−58.7195	−	107.120i	−0.110791	−	0.202114i
$531$		0			0
$532$	11.1499	−	90.7944i	0.0209585	−	0.170666i
$533$			297.324i			0.557830i
$534$		0			0
$535$	145.355	−	79.6783i	0.271691	−	0.148931i
$536$	−340.240			−0.634776
$537$		0			0
$538$	−131.945			−0.245251
$539$	−136.973	−	34.1567i	−0.254124	−	0.0633705i
$540$		0			0
$541$	600.626			1.11021			0.555107	−	0.831779i	$-0.312677\pi$
$541$	600.626			1.11021			0.555107	+	0.831779i	$0.312677\pi$
$542$	−407.741			−0.752290
$543$		0			0
$544$			136.757i			0.251391i
$545$	261.537	+	477.113i	0.479884	+	0.875437i
$546$		0			0
$547$			1045.16i			1.91071i	0.295457	+	0.955356i	$0.404528\pi$
$547$			1045.16i			1.91071i	−0.295457	+	0.955356i	$0.595472\pi$
$548$			489.711i			0.893632i
$549$		0			0
$550$	−85.8676	−	54.7880i	−0.156123	−	0.0996146i
$551$			215.354i			0.390843i
$552$		0			0
$553$	−459.475	−	56.4253i	−0.830877	−	0.102035i
$554$	−545.094			−0.983924
$555$		0			0
$556$		−	476.489i		−	0.856995i
$557$		−	601.731i		−	1.08031i	−0.841566	−	0.540154i	$-0.818366\pi$
$557$		−	601.731i		−	1.08031i	0.841566	−	0.540154i	$-0.181634\pi$
$558$		0			0
$559$		−	187.262i		−	0.334995i
$560$	51.8301	+	130.052i	0.0925538	+	0.232236i
$561$		0			0
$562$			345.009i			0.613896i
$563$	−363.871			−0.646308			−0.323154	−	0.946346i	$-0.604743\pi$
$563$	−363.871			−0.646308			−0.323154	+	0.946346i	$0.604743\pi$
$564$		0			0
$565$	−691.245	+	378.916i	−1.22344	+	0.670648i
$566$			709.136i			1.25289i
$567$		0			0
$568$			255.649i			0.450086i
$569$	−902.900			−1.58682			−0.793410	−	0.608688i	$-0.791696\pi$
$569$	−902.900			−1.58682			−0.793410	+	0.608688i	$0.791696\pi$
$570$		0			0
$571$	−847.207			−1.48372			−0.741862	−	0.670552i	$-0.766057\pi$
$571$	−847.207			−1.48372			−0.741862	+	0.670552i	$0.766057\pi$
$572$	79.5984			0.139158
$573$		0			0
$574$	211.474	+	25.9698i	0.368421	+	0.0452435i
$575$	−607.856	−	387.845i	−1.05714	−	0.674512i
$576$		0			0
$577$	−306.535			−0.531256			−0.265628	−	0.964076i	$-0.585579\pi$
$577$	−306.535			−0.531256			−0.265628	+	0.964076i	$0.585579\pi$
$578$		−	417.829i		−	0.722888i
$579$		0			0
$580$	−158.428	−	289.015i	−0.273151	−	0.498301i
$581$	545.522	+	66.9923i	0.938937	+	0.115305i
$582$		0			0
$583$			49.7711i			0.0853707i
$584$		−	60.7801i		−	0.104075i
$585$		0			0
$586$			477.025i			0.814037i
$587$	467.524			0.796463			0.398232	−	0.917285i	$-0.369624\pi$
$587$	467.524			0.796463			0.398232	+	0.917285i	$0.369624\pi$
$588$		0			0
$589$	15.8958			0.0269877
$590$	5.01304	+	9.14514i	0.00849668	+	0.0155002i
$591$		0			0
$592$			203.920i			0.344459i
$593$	−744.542			−1.25555			−0.627775	−	0.778395i	$-0.716034\pi$
$593$	−744.542			−1.25555			−0.627775	+	0.778395i	$0.716034\pi$
$594$		0			0
$595$	−313.254	−	786.017i	−0.526477	−	1.32104i
$596$	21.6796			0.0363751
$597$		0			0
$598$	563.477			0.942269
$599$	276.145			0.461011			0.230505	−	0.973071i	$-0.425962\pi$
$599$	276.145			0.461011			0.230505	+	0.973071i	$0.425962\pi$
$600$		0			0
$601$		−	779.606i		−	1.29718i	−0.761137	−	0.648591i	$-0.775359\pi$
$601$		−	779.606i		−	1.29718i	0.761137	−	0.648591i	$-0.224641\pi$
$602$	−133.191	−	16.3564i	−0.221248	−	0.0271702i
$603$		0			0
$604$	225.999			0.374170
$605$	−270.865	−	494.130i	−0.447710	−	0.816744i
$606$		0			0
$607$	567.539			0.934990			0.467495	−	0.883996i	$-0.345157\pi$
$607$	567.539			0.934990			0.467495	+	0.883996i	$0.345157\pi$
$608$	36.9621			0.0607929
$609$		0			0
$610$	−379.212	−	691.785i	−0.621659	−	1.13407i
$611$	562.672			0.920903
$612$		0			0
$613$			801.088i			1.30683i	0.756999	+	0.653416i	$0.226665\pi$
$613$			801.088i			1.30683i	−0.756999	+	0.653416i	$0.773335\pi$
$614$			158.796i			0.258625i
$615$		0			0
$616$	6.95253	−	56.6149i	0.0112866	−	0.0919074i
$617$		−	71.2583i		−	0.115492i	−0.998331	−	0.0577458i	$-0.981609\pi$
$617$		−	71.2583i		−	0.115492i	0.998331	−	0.0577458i	$-0.0183913\pi$
$618$		0			0
$619$			821.793i			1.32761i	0.747904	+	0.663807i	$0.231060\pi$
$619$			821.793i			1.32761i	−0.747904	+	0.663807i	$0.768940\pi$
$620$	−21.3328	+	11.6939i	−0.0344077	+	0.0188611i
$621$		0			0
$622$	−207.151			−0.333040
$623$	−77.6193	+	632.059i	−0.124590	+	1.01454i
$624$		0			0
$625$	−263.345	−	566.811i	−0.421351	−	0.906897i
$626$		−	197.887i		−	0.316114i
$627$		0			0
$628$	−207.385			−0.330231
$629$		−	1232.46i		−	1.95939i
$630$		0			0
$631$	−916.907			−1.45310			−0.726551	−	0.687113i	$-0.758878\pi$
$631$	−916.907			−1.45310			−0.726551	+	0.687113i	$0.758878\pi$
$632$		−	187.051i		−	0.295966i
$633$		0			0
$634$	−56.2540			−0.0887287
$635$	−123.663	+	67.7876i	−0.194745	+	0.106752i
$636$		0			0
$637$	656.798	+	163.785i	1.03108	+	0.257119i
$638$			134.285i			0.210477i
$639$		0			0
$640$	−49.6047	+	27.1915i	−0.0775073	+	0.0424867i
$641$	−737.240			−1.15014			−0.575070	−	0.818104i	$-0.695025\pi$
$641$	−737.240			−1.15014			−0.575070	+	0.818104i	$0.695025\pi$
$642$		0			0
$643$	256.297			0.398596			0.199298	−	0.979939i	$-0.436134\pi$
$643$	256.297			0.398596			0.199298	+	0.979939i	$0.436134\pi$
$644$	49.2170	−	400.777i	0.0764239	−	0.622325i
$645$		0			0
$646$	−223.393			−0.345810
$647$	−689.147			−1.06514			−0.532571	−	0.846385i	$-0.678774\pi$
$647$	−689.147			−1.06514			−0.532571	+	0.846385i	$0.678774\pi$
$648$		0			0
$649$		−	4.24910i		−	0.00654714i
$650$	411.743	+	262.714i	0.633451	+	0.404176i
$651$		0			0
$652$		−	399.152i		−	0.612196i
$653$		−	395.775i		−	0.606087i	−0.952977	−	0.303044i	$-0.901997\pi$
$653$		−	395.775i		−	0.606087i	0.952977	−	0.303044i	$-0.0980028\pi$
$654$		0			0
$655$	691.081	−	378.826i	1.05509	−	0.578361i
$656$			86.0902i			0.131235i
$657$		0			0
$658$	49.1467	−	400.205i	0.0746910	−	0.608214i
$659$	47.8147			0.0725565			0.0362782	−	0.999342i	$-0.488450\pi$
$659$	47.8147			0.0725565			0.0362782	+	0.999342i	$0.488450\pi$
$660$		0			0
$661$			89.9129i			0.136026i	0.997684	+	0.0680128i	$0.0216659\pi$
$661$			89.9129i			0.136026i	−0.997684	+	0.0680128i	$0.978334\pi$
$662$			19.3374i			0.0292106i
$663$		0			0
$664$			222.080i			0.334458i
$665$	−212.442	+	84.6649i	−0.319461	+	0.127316i
$666$		0			0
$667$			950.600i			1.42519i
$668$	−174.155			−0.260712
$669$		0			0
$670$	408.868	+	745.886i	0.610251	+	1.11326i
$671$			321.423i			0.479021i
$672$		0			0
$673$		−	833.478i		−	1.23845i	−0.785213	−	0.619226i	$-0.787447\pi$
$673$		−	833.478i		−	1.23845i	0.785213	−	0.619226i	$-0.212553\pi$
$674$	−516.008			−0.765590
$675$		0			0
$676$	−43.6822			−0.0646187
$677$	44.1092			0.0651540			0.0325770	−	0.999469i	$-0.489629\pi$
$677$	44.1092			0.0651540			0.0325770	+	0.999469i	$0.489629\pi$
$678$		0			0
$679$	−307.074	−	37.7099i	−0.452244	−	0.0555373i
$680$	299.803	−	164.341i	0.440887	−	0.241679i
$681$		0			0
$682$	9.91182			0.0145335
$683$			130.146i			0.190550i	0.995451	+	0.0952750i	$0.0303731\pi$
$683$			130.146i			0.190550i	−0.995451	+	0.0952750i	$0.969627\pi$
$684$		0			0
$685$	1073.56	−	588.488i	1.56724	−	0.859107i
$686$	173.861	−	452.847i	0.253442	−	0.660127i
$687$		0			0
$688$		−	54.2218i		−	0.0788107i
$689$		−	238.657i		−	0.346382i
$690$		0			0
$691$			714.724i			1.03433i	0.855885	+	0.517167i	$0.173013\pi$
$691$			714.724i			1.03433i	−0.855885	+	0.517167i	$0.826987\pi$
$692$	−213.194			−0.308083
$693$		0			0
$694$	664.373			0.957310
$695$	−1044.58	+	572.600i	−1.50299	+	0.823885i
$696$		0			0
$697$		−	520.316i		−	0.746508i
$698$	37.8308			0.0541988
$699$		0			0
$700$	222.821	−	269.909i	0.318316	−	0.385584i
$701$	−463.854			−0.661704			−0.330852	−	0.943683i	$-0.607336\pi$
$701$	−463.854			−0.661704			−0.330852	+	0.943683i	$0.607336\pi$
$702$		0			0
$703$	−333.104			−0.473832
$704$	23.0477			0.0327383
$705$		0			0
$706$			669.500i			0.948301i
$707$	153.623	−	1250.96i	0.217289	−	1.76940i
$708$		0			0
$709$	−970.049			−1.36819			−0.684097	−	0.729391i	$-0.739803\pi$
$709$	−970.049			−1.36819			−0.684097	+	0.729391i	$0.739803\pi$
$710$	560.443	−	307.215i	0.789356	−	0.432697i
$711$		0			0
$712$	−257.309			−0.361389
$713$	70.1657			0.0984092
$714$		0			0
$715$	−95.6539	−	174.499i	−0.133782	−	0.244054i
$716$	551.762			0.770617
$717$		0			0
$718$		−	139.749i		−	0.194636i
$719$			1369.36i			1.90453i	0.305266	+	0.952267i	$0.401255\pi$
$719$			1369.36i			1.90453i	−0.305266	+	0.952267i	$0.598745\pi$
$720$		0			0
$721$	744.861	+	91.4719i	1.03309	+	0.126868i
$722$		−	450.153i		−	0.623481i
$723$		0			0
$724$			372.862i			0.515002i
$725$	−443.205	+	694.622i	−0.611318	+	0.958099i
$726$		0			0
$727$	1106.85			1.52249			0.761246	−	0.648463i	$-0.224588\pi$
$727$	1106.85			1.52249			0.761246	+	0.648463i	$0.224588\pi$
$728$	−33.3381	+	271.474i	−0.0457941	+	0.372904i
$729$		0			0
$730$	−133.244	+	73.0398i	−0.182526	+	0.100054i
$731$			327.708i			0.448301i
$732$		0			0
$733$	297.353			0.405665			0.202833	−	0.979213i	$-0.434985\pi$
$733$	297.353			0.405665			0.202833	+	0.979213i	$0.434985\pi$
$734$		−	468.849i		−	0.638759i
$735$		0			0
$736$	163.155			0.221678
$737$		−	346.560i		−	0.470231i
$738$		0			0
$739$	604.951			0.818608			0.409304	−	0.912398i	$-0.365772\pi$
$739$	604.951			0.818608			0.409304	+	0.912398i	$0.365772\pi$
$740$	447.040	−	245.051i	0.604108	−	0.331150i
$741$		0			0
$742$	−169.747	−	20.8456i	−0.228769	−	0.0280938i
$743$		−	733.877i		−	0.987722i	−0.869541	−	0.493861i	$-0.835585\pi$
$743$		−	733.877i		−	0.987722i	0.869541	−	0.493861i	$-0.164415\pi$
$744$		0			0
$745$	−26.0525	−	47.5268i	−0.0349698	−	0.0637943i
$746$	−589.047			−0.789608
$747$		0			0
$748$	−139.297			−0.186226
$749$	28.2860	−	230.335i	0.0377650	−	0.307523i
$750$		0			0
$751$	−71.0036			−0.0945455			−0.0472727	−	0.998882i	$-0.515053\pi$
$751$	−71.0036			−0.0945455			−0.0472727	+	0.998882i	$0.515053\pi$
$752$	162.922			0.216651
$753$		0			0
$754$		−	643.908i		−	0.853989i
$755$	−271.584	−	495.443i	−0.359714	−	0.656216i
$756$		0			0
$757$			708.172i			0.935497i	0.883861	+	0.467749i	$0.154935\pi$
$757$			708.172i			0.935497i	−0.883861	+	0.467749i	$0.845065\pi$
$758$		−	793.291i		−	1.04656i
$759$		0			0
$760$	−44.4175	−	81.0296i	−0.0584441	−	0.106618i
$761$		−	797.652i		−	1.04816i	−0.851668	−	0.524081i	$-0.824409\pi$
$761$		−	797.652i		−	1.04816i	0.851668	−	0.524081i	$-0.175591\pi$
$762$		0			0
$763$	756.052	+	92.8462i	0.990894	+	0.121686i
$764$	−354.153			−0.463551
$765$		0			0
$766$			191.912i			0.250538i
$767$			20.3748i			0.0265643i
$768$		0			0
$769$		−	261.829i		−	0.340480i	−0.985403	−	0.170240i	$-0.945546\pi$
$769$		−	261.829i		−	0.340480i	0.985403	−	0.170240i	$-0.0544543\pi$
$770$	−132.468	+	52.7929i	−0.172037	+	0.0685622i
$771$		0			0
$772$			306.906i			0.397546i
$773$	643.514			0.832489			0.416245	−	0.909253i	$-0.363346\pi$
$773$	643.514			0.832489			0.416245	+	0.909253i	$0.363346\pi$
$774$		0			0
$775$	51.2715	+	32.7139i	0.0661567	+	0.0422115i
$776$		−	125.009i		−	0.161094i
$777$		0			0
$778$		−	994.722i		−	1.27856i
$779$	−140.629			−0.180525
$780$		0			0
$781$	−260.398			−0.333416
$782$	−986.084			−1.26098
$783$		0			0
$784$	190.176	+	47.4239i	0.242572	+	0.0604897i
$785$	249.216	+	454.637i	0.317473	+	0.579156i
$786$		0			0
$787$	−919.663			−1.16857			−0.584284	−	0.811549i	$-0.698625\pi$
$787$	−919.663			−1.16857			−0.584284	+	0.811549i	$0.698625\pi$
$788$		−	428.082i		−	0.543252i
$789$		0			0
$790$	−410.059	+	224.780i	−0.519062	+	0.284531i
$791$	−134.516	+	1095.37i	−0.170058	+	1.38480i
$792$		0			0
$793$		−	1541.26i		−	1.94358i
$794$		−	3.06170i		−	0.00385604i
$795$		0			0
$796$			356.353i			0.447679i
$797$	−246.244			−0.308964			−0.154482	−	0.987996i	$-0.549371\pi$
$797$	−246.244			−0.308964			−0.154482	+	0.987996i	$0.549371\pi$
$798$		0			0
$799$	−984.675			−1.23238
$800$	119.220	+	76.0690i	0.149026	+	0.0950862i
$801$		0			0
$802$		−	322.309i		−	0.401882i
$803$	61.9091			0.0770973
$804$		0			0
$805$	−937.743	+	373.721i	−1.16490	+	0.464250i
$806$	−47.5281			−0.0589679
$807$		0			0
$808$	509.263			0.630276
$809$	609.838			0.753817			0.376908	−	0.926251i	$-0.376987\pi$
$809$	609.838			0.753817			0.376908	+	0.926251i	$0.376987\pi$
$810$		0			0
$811$			605.726i			0.746888i	0.927653	+	0.373444i	$0.121823\pi$
$811$			605.726i			0.746888i	−0.927653	+	0.373444i	$0.878177\pi$
$812$	−457.984	−	56.2422i	−0.564020	−	0.0692638i
$813$		0			0
$814$	−207.707			−0.255169
$815$	−875.035	+	479.663i	−1.07366	+	0.588543i
$816$		0			0
$817$	88.5717			0.108411
$818$	310.097			0.379091
$819$		0			0
$820$	188.730	−	103.455i	0.230159	−	0.126165i
$821$	−890.751			−1.08496			−0.542480	−	0.840069i	$-0.682514\pi$
$821$	−890.751			−1.08496			−0.542480	+	0.840069i	$0.682514\pi$
$822$		0			0
$823$		−	317.029i		−	0.385211i	−0.981276	−	0.192606i	$-0.938306\pi$
$823$		−	317.029i		−	0.385211i	0.981276	−	0.192606i	$-0.0616938\pi$
$824$			303.230i			0.367998i
$825$		0			0
$826$	14.4918	+	1.77964i	0.0175445	+	0.00215453i
$827$		−	90.7251i		−	0.109704i	−0.998494	−	0.0548520i	$-0.982531\pi$
$827$		−	90.7251i		−	0.109704i	0.998494	−	0.0548520i	$-0.0174687\pi$
$828$		0			0
$829$		−	1366.86i		−	1.64880i	−0.566007	−	0.824400i	$-0.691513\pi$
$829$		−	1366.86i		−	1.64880i	0.566007	−	0.824400i	$-0.308487\pi$
$830$	486.852	−	266.875i	0.586569	−	0.321536i
$831$		0			0
$832$	−110.516			−0.132832
$833$	−1149.40	−	286.623i	−1.37983	−	0.344085i
$834$		0			0
$835$	209.284	+	381.790i	0.250639	+	0.457234i
$836$			37.6487i			0.0450343i
$837$		0			0
$838$	−900.463			−1.07454
$839$		−	73.5993i		−	0.0877227i	−0.999038	−	0.0438613i	$-0.986034\pi$
$839$		−	73.5993i		−	0.0877227i	0.999038	−	0.0438613i	$-0.0139660\pi$
$840$		0			0
$841$	245.289			0.291663
$842$		−	1154.83i		−	1.37153i
$843$		0			0
$844$	796.024			0.943156
$845$	52.4932	+	95.7618i	0.0621221	+	0.113328i
$846$		0			0
$847$	−783.018	−	96.1576i	−0.924460	−	0.113527i
$848$		−	69.1033i		−	0.0814897i
$849$		0			0
$850$	−720.550	−	459.749i	−0.847706	−	0.540882i
$851$	−1470.36			−1.72780
$852$		0			0
$853$	−822.046			−0.963711			−0.481856	−	0.876251i	$-0.660037\pi$
$853$	−822.046			−0.963711			−0.481856	+	0.876251i	$0.660037\pi$
$854$	−1096.23	−	134.621i	−1.28364	−	0.157636i
$855$		0			0
$856$	93.7684			0.109543
$857$	625.685			0.730087			0.365044	−	0.930990i	$-0.381054\pi$
$857$	625.685			0.730087			0.365044	+	0.930990i	$0.381054\pi$
$858$		0			0
$859$		−	1396.65i		−	1.62590i	−0.582332	−	0.812951i	$-0.697860\pi$
$859$		−	1396.65i		−	1.62590i	0.582332	−	0.812951i	$-0.302140\pi$
$860$	−118.867	+	65.1586i	−0.138217	+	0.0757659i
$861$		0			0
$862$		−	408.582i		−	0.473993i
$863$			601.569i			0.697068i	0.937296	+	0.348534i	$0.113320\pi$
$863$			601.569i			0.697068i	−0.937296	+	0.348534i	$0.886680\pi$
$864$		0			0
$865$	256.196	+	467.371i	0.296180	+	0.540313i
$866$		−	162.272i		−	0.187381i
$867$		0			0
$868$	−4.15135	+	33.8047i	−0.00478267	+	0.0389456i
$869$	190.525			0.219246
$870$		0			0
$871$			1661.79i			1.90791i
$872$			307.786i			0.352966i
$873$		0			0
$874$			266.515i			0.304937i
$875$	−859.469	−	164.126i	−0.982251	−	0.187572i
$876$		0			0
$877$			570.762i			0.650812i	0.945574	+	0.325406i	$0.105501\pi$
$877$			570.762i			0.650812i	−0.945574	+	0.325406i	$0.894499\pi$
$878$	−901.480			−1.02674
$879$		0			0
$880$	−27.6966	−	50.5261i	−0.0314734	−	0.0574160i
$881$			1095.44i			1.24341i	0.783253	+	0.621703i	$0.213559\pi$
$881$			1095.44i			1.24341i	−0.783253	+	0.621703i	$0.786441\pi$
$882$		0			0
$883$			305.870i			0.346399i	0.984887	+	0.173199i	$0.0554105\pi$
$883$			305.870i			0.346399i	−0.984887	+	0.173199i	$0.944590\pi$
$884$	667.943			0.755592
$885$		0			0
$886$	261.490			0.295135
$887$	637.527			0.718745			0.359372	−	0.933194i	$-0.382991\pi$
$887$	637.527			0.718745			0.359372	+	0.933194i	$0.382991\pi$
$888$		0			0
$889$	−24.0648	+	195.961i	−0.0270695	+	0.220429i
$890$	309.210	+	564.082i	0.347427	+	0.633800i
$891$		0			0
$892$	−13.9348			−0.0156220
$893$			266.134i			0.298022i
$894$		0			0
$895$	−663.056	−	1209.59i	−0.740845	−	1.35150i
$896$	−9.65306	+	78.6055i	−0.0107735	+	0.0877293i
$897$		0			0
$898$		−	443.042i		−	0.493365i
$899$		−	80.1812i		−	0.0891893i
$900$		0			0
$901$			417.650i			0.463541i
$902$	−87.6893			−0.0972166
$903$		0			0
$904$	−445.923			−0.493278
$905$	817.401	−	448.070i	0.903206	−	0.495105i
$906$		0			0
$907$		−	785.727i		−	0.866292i	−0.901324	−	0.433146i	$-0.857403\pi$
$907$		−	785.727i		−	0.866292i	0.901324	−	0.433146i	$-0.142597\pi$
$908$	484.235			0.533299
$909$		0			0
$910$	635.199	−	253.147i	0.698020	−	0.278184i
$911$	909.376			0.998217			0.499109	−	0.866539i	$-0.333661\pi$
$911$	909.376			0.998217			0.499109	+	0.866539i	$0.333661\pi$
$912$		0			0
$913$	−226.205			−0.247761
$914$	−247.241			−0.270504
$915$		0			0
$916$			451.173i			0.492547i
$917$	134.484	−	1095.11i	0.146657	−	1.19424i
$918$		0			0
$919$	−270.279			−0.294101			−0.147050	−	0.989129i	$-0.546978\pi$
$919$	−270.279			−0.294101			−0.147050	+	0.989129i	$0.546978\pi$
$920$	−196.064	−	357.674i	−0.213113	−	0.388776i
$921$		0			0
$922$	−536.358			−0.581733
$923$	1248.63			1.35280
$924$		0			0
$925$	−1074.42	−	685.538i	−1.16154	−	0.741122i
$926$	570.634			0.616235
$927$		0			0
$928$		−	186.444i		−	0.200909i
$929$			1053.28i			1.13378i	0.823795	+	0.566889i	$0.191853\pi$
$929$			1053.28i			1.13378i	−0.823795	+	0.566889i	$0.808147\pi$
$930$		0			0
$931$	−77.4674	+	310.654i	−0.0832088	+	0.333678i
$932$			871.699i			0.935300i
$933$		0			0
$934$		−	1142.55i		−	1.22328i
$935$	167.394	+	305.372i	0.179031	+	0.326601i
$936$		0			0
$937$	1012.18			1.08024			0.540119	−	0.841589i	$-0.318379\pi$
$937$	1012.18			1.08024			0.540119	+	0.841589i	$0.318379\pi$
$938$	1181.96	+	145.149i	1.26009	+	0.154743i
$939$		0			0
$940$	−195.784	−	357.163i	−0.208281	−	0.379961i
$941$			1384.55i			1.47136i	0.677331	+	0.735679i	$0.263137\pi$
$941$			1384.55i			1.47136i	−0.677331	+	0.735679i	$0.736863\pi$
$942$		0			0
$943$	−620.753			−0.658275
$944$			5.89954i			0.00624951i
$945$		0			0
$946$	55.2290			0.0583816
$947$			1216.79i			1.28489i	0.766332	+	0.642444i	$0.222080\pi$
$947$			1216.79i			1.28489i	−0.766332	+	0.642444i	$0.777920\pi$
$948$		0			0
$949$	−296.860			−0.312814
$950$	−124.259	+	194.748i	−0.130799	+	0.204997i
$951$		0			0
$952$	58.3416	−	475.080i	0.0612832	−	0.499033i
$953$		−	30.5870i		−	0.0320955i	−0.999871	−	0.0160478i	$-0.994892\pi$
$953$		−	30.5870i		−	0.0320955i	0.999871	−	0.0160478i	$-0.00510838\pi$
$954$		0			0
$955$	425.588	+	776.387i	0.445642	+	0.812971i
$956$	389.422			0.407345
$957$		0			0
$958$	621.638			0.648891
$959$	208.915	−	1701.21i	0.217847	−	1.77394i
$960$		0			0
$961$	955.082			0.993841
$962$	995.978			1.03532
$963$		0			0
$964$			491.620i			0.509980i
$965$	672.810	−	368.810i	0.697212	−	0.382187i
$966$		0			0
$967$			1878.59i			1.94270i	0.237650	+	0.971351i	$0.423623\pi$
$967$			1878.59i			1.94270i	−0.237650	+	0.971351i	$0.576377\pi$
$968$		−	318.764i		−	0.329301i
$969$		0			0
$970$	−274.049	+	150.224i	−0.282524	+	0.154870i
$971$		−	712.009i		−	0.733274i	−0.930364	−	0.366637i	$-0.880509\pi$
$971$		−	712.009i		−	0.733274i	0.930364	−	0.366637i	$-0.119491\pi$
$972$		0			0
$973$	−203.274	+	1655.28i	−0.208915	+	1.70121i
$974$	53.6927			0.0551260
$975$		0			0
$976$		−	446.271i		−	0.457245i
$977$		−	750.938i		−	0.768616i	−0.923205	−	0.384308i	$-0.874440\pi$
$977$		−	750.938i		−	0.768616i	0.923205	−	0.384308i	$-0.125560\pi$
$978$		0			0
$979$		−	262.089i		−	0.267710i
$980$	−124.571	−	473.901i	−0.127114	−	0.483572i
$981$		0			0
$982$		−	10.3627i		−	0.0105526i
$983$	1525.09			1.55147			0.775735	−	0.631059i	$-0.217379\pi$
$983$	1525.09			1.55147			0.775735	+	0.631059i	$0.217379\pi$
$984$		0			0
$985$	−938.458	+	514.429i	−0.952749	+	0.522263i
$986$			1126.84i			1.14284i
$987$		0			0
$988$		−	180.529i		−	0.182722i
$989$	390.966			0.395314
$990$		0			0
$991$	1259.84			1.27128			0.635641	−	0.771985i	$-0.280736\pi$
$991$	1259.84			1.27128			0.635641	+	0.771985i	$0.280736\pi$
$992$	−13.7618			−0.0138728
$993$		0			0
$994$	109.062	−	888.099i	0.109720	−	0.893460i
$995$	781.210	−	428.231i	0.785135	−	0.430383i
$996$		0			0
$997$	1406.62			1.41086			0.705428	−	0.708781i	$-0.250755\pi$
$997$	1406.62			1.41086			0.705428	+	0.708781i	$0.250755\pi$
$998$			562.695i			0.563823i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.h.e.559.6		16
3.2	odd	2		210.3.h.a.139.14	yes	16
5.4	even	2	inner	630.3.h.e.559.11		16
7.6	odd	2	inner	630.3.h.e.559.3		16
12.11	even	2		1680.3.bd.a.769.3		16
15.2	even	4		1050.3.f.e.601.2		16
15.8	even	4		1050.3.f.e.601.15		16
15.14	odd	2		210.3.h.a.139.3	✓	16
21.20	even	2		210.3.h.a.139.11	yes	16
35.34	odd	2	inner	630.3.h.e.559.14		16
60.59	even	2		1680.3.bd.a.769.13		16
84.83	odd	2		1680.3.bd.a.769.14		16
105.62	odd	4		1050.3.f.e.601.6		16
105.83	odd	4		1050.3.f.e.601.11		16
105.104	even	2		210.3.h.a.139.6	yes	16
420.419	odd	2		1680.3.bd.a.769.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.h.a.139.3	✓	16	15.14	odd	2
210.3.h.a.139.6	yes	16	105.104	even	2
210.3.h.a.139.11	yes	16	21.20	even	2
210.3.h.a.139.14	yes	16	3.2	odd	2
630.3.h.e.559.3		16	7.6	odd	2	inner
630.3.h.e.559.6		16	1.1	even	1	trivial
630.3.h.e.559.11		16	5.4	even	2	inner
630.3.h.e.559.14		16	35.34	odd	2	inner
1050.3.f.e.601.2		16	15.2	even	4
1050.3.f.e.601.6		16	105.62	odd	4
1050.3.f.e.601.11		16	105.83	odd	4
1050.3.f.e.601.15		16	15.8	even	4
1680.3.bd.a.769.3		16	12.11	even	2
1680.3.bd.a.769.4		16	420.419	odd	2
1680.3.bd.a.769.13		16	60.59	even	2
1680.3.bd.a.769.14		16	84.83	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(2.40341 + 4.38447i) q^{5} +(6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(2.40341 + 4.38447i) q^{5} +(6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +(6.20058 - 3.39894i) q^{10} -2.88097 q^{11} +13.8145 q^{13} +(1.20663 - 9.82568i) q^{14} +4.00000 q^{16} -24.1754 q^{17} +6.53403i q^{19} +(-4.80682 - 8.76895i) q^{20} +4.07430i q^{22} +28.8420i q^{23} +(-13.4472 + 21.0754i) q^{25} -19.5367i q^{26} +(-13.8956 - 1.70644i) q^{28} +32.9589 q^{29} -2.43276i q^{31} -5.65685i q^{32} +34.1892i q^{34} +(12.9575 + 32.5131i) q^{35} +50.9799i q^{37} +9.24052 q^{38} +(-12.4012 + 6.79788i) q^{40} +21.5225i q^{41} -13.5554i q^{43} +5.76193 q^{44} +40.7887 q^{46} +40.7305 q^{47} +(47.5440 + 11.8560i) q^{49} +(29.8051 + 19.0172i) q^{50} -27.6291 q^{52} -17.2758i q^{53} +(-6.92415 - 12.6315i) q^{55} +(-2.41326 + 19.6514i) q^{56} -46.6109i q^{58} +1.47488i q^{59} -111.568i q^{61} -3.44045 q^{62} -8.00000 q^{64} +(33.2020 + 60.5694i) q^{65} +120.293i q^{67} +48.3508 q^{68} +(45.9805 - 18.3247i) q^{70} +90.3855 q^{71} -21.4890 q^{73} +72.0964 q^{74} -13.0681i q^{76} +(-20.0164 - 2.45809i) q^{77} -66.1324 q^{79} +(9.61365 + 17.5379i) q^{80} +30.4375 q^{82} +78.5172 q^{83} +(-58.1035 - 105.996i) q^{85} -19.1703 q^{86} -8.14861i q^{88} +90.9724i q^{89} +(95.9807 + 11.7868i) q^{91} -57.6840i q^{92} -57.6016i q^{94} +(-28.6483 + 15.7040i) q^{95} -44.1972 q^{97} +(16.7669 - 67.2374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 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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