LMFDB - Embedded newform 630.3.h.e.559.3

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			559.3
Root			$0.500000 - 0.442923i$ of defining polynomial
Character	$\chi$	$=$	630.559
Dual form			630.3.h.e.559.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.00000 q^{4} +(-2.40341 - 4.38447i) q^{5} +(-6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q-1.41421i q^{2} -2.00000 q^{4} +(-2.40341 - 4.38447i) q^{5} +(-6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +(-6.20058 + 3.39894i) q^{10} -2.88097 q^{11} -13.8145 q^{13} +(1.20663 + 9.82568i) q^{14} +4.00000 q^{16} +24.1754 q^{17} -6.53403i q^{19} +(4.80682 + 8.76895i) q^{20} +4.07430i q^{22} +28.8420i q^{23} +(-13.4472 + 21.0754i) q^{25} +19.5367i q^{26} +(13.8956 - 1.70644i) q^{28} +32.9589 q^{29} +2.43276i q^{31} -5.65685i q^{32} -34.1892i q^{34} +(20.4394 + 28.4118i) q^{35} +50.9799i q^{37} -9.24052 q^{38} +(12.4012 - 6.79788i) q^{40} -21.5225i q^{41} -13.5554i q^{43} +5.76193 q^{44} +40.7887 q^{46} -40.7305 q^{47} +(47.5440 - 11.8560i) q^{49} +(29.8051 + 19.0172i) q^{50} +27.6291 q^{52} -17.2758i q^{53} +(6.92415 + 12.6315i) q^{55} +(-2.41326 - 19.6514i) q^{56} -46.6109i q^{58} -1.47488i q^{59} +111.568i q^{61} +3.44045 q^{62} -8.00000 q^{64} +(33.2020 + 60.5694i) q^{65} +120.293i q^{67} -48.3508 q^{68} +(40.1804 - 28.9056i) q^{70} +90.3855 q^{71} +21.4890 q^{73} +72.0964 q^{74} +13.0681i q^{76} +(20.0164 - 2.45809i) q^{77} -66.1324 q^{79} +(-9.61365 - 17.5379i) q^{80} -30.4375 q^{82} -78.5172 q^{83} +(-58.1035 - 105.996i) q^{85} -19.1703 q^{86} -8.14861i q^{88} -90.9724i q^{89} +(95.9807 - 11.7868i) q^{91} -57.6840i q^{92} +57.6016i q^{94} +(-28.6483 + 15.7040i) q^{95} +44.1972 q^{97} +(-16.7669 - 67.2374i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.678307\pi$
$13$	−13.8145			−1.06266			−0.531328	+	0.847166i	$0.678307\pi$
$14$	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	$-0.248224\pi$
$17$	24.1754			1.42208			0.711041	+	0.703150i	$0.248224\pi$
$18$		0			0
$19$		−	6.53403i		−	0.343896i	−0.985106	−	0.171948i	$-0.944994\pi$
$19$		−	6.53403i		−	0.343896i	0.985106	−	0.171948i	$-0.0550062\pi$
$20$	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	$0.0124931\pi$
$31$			2.43276i			0.0784762i	−0.999230	+	0.0392381i	$0.987507\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$		−	34.1892i		−	1.00556i
$35$	20.4394	+	28.4118i	0.583982	+	0.811767i
$36$		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	$-0.915463\pi$
$41$		−	21.5225i		−	0.524940i	0.964940	−	0.262470i	$-0.0845371\pi$
$42$		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	$-0.642652\pi$
$47$	−40.7305			−0.866605			−0.433303	+	0.901248i	$0.642652\pi$
$48$		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	$-0.996021\pi$
$59$		−	1.47488i		−	0.0249980i	0.999922	−	0.0124990i	$-0.00397867\pi$
$60$		0			0
$61$			111.568i			1.82898i	0.404609	+	0.914490i	$0.367408\pi$
$61$			111.568i			1.82898i	−0.404609	+	0.914490i	$0.632592\pi$
$62$	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
$70$	40.1804	−	28.9056i	0.574006	−	0.412937i
$71$	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	$-0.452979\pi$
$73$	21.4890			0.294370			0.147185	+	0.989109i	$0.452979\pi$
$74$	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	$-0.656827\pi$
$83$	−78.5172			−0.945990			−0.472995	+	0.881065i	$0.656827\pi$
$84$		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	$-0.829245\pi$
$89$		−	90.9724i		−	1.02216i	0.859533	−	0.511081i	$-0.170755\pi$
$90$		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	$-0.426840\pi$
$97$	44.1972			0.455642			0.227821	+	0.973703i	$0.426840\pi$
$98$	−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	$0.350237\pi$
$101$			180.052i			1.78269i	−0.453326	+	0.891345i	$0.649763\pi$
$102$		0			0
$103$	−107.208			−1.04086			−0.520428	−	0.853906i	$-0.674228\pi$
$103$	−107.208			−1.04086			−0.520428	+	0.853906i	$0.674228\pi$
$104$		−	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	$0.205471\pi$
$131$			157.620i			1.20321i	−0.798795	+	0.601604i	$0.794529\pi$
$132$		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	$-0.672329\pi$
$139$		−	238.245i		−	1.71399i	0.515325	−	0.856995i	$-0.327671\pi$
$140$	−40.8787	−	56.8237i	−0.291991	−	0.405883i
$141$		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	$-0.607127\pi$
$157$	−103.693			−0.660462			−0.330231	+	0.943900i	$0.607127\pi$
$158$			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	$-0.583957\pi$
$167$	−87.0777			−0.521424			−0.260712	+	0.965417i	$0.583957\pi$
$168$		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	$-0.599687\pi$
$173$	−106.597			−0.616166			−0.308083	+	0.951359i	$0.599687\pi$
$174$		0			0
$175$	75.4468	−	157.901i	0.431124	−	0.902292i
$176$	−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	$0.172209\pi$
$181$			186.431i			1.03000i	−0.857189	+	0.515002i	$0.827791\pi$
$182$	−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	$0.147749\pi$
$199$			178.176i			0.895359i	−0.894194	+	0.447679i	$0.852251\pi$
$200$	−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	$-0.504973\pi$
$223$	−6.96741			−0.0312440			−0.0156220	+	0.999878i	$0.504973\pi$
$224$	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	$-0.320952\pi$
$227$	242.118			1.06660			0.533299	+	0.845927i	$0.320952\pi$
$228$		0			0
$229$			225.586i			0.985093i	0.870286	+	0.492547i	$0.163934\pi$
$229$			225.586i			0.985093i	−0.870286	+	0.492547i	$0.836066\pi$
$230$	−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	$0.170347\pi$
$241$			245.810i			1.01996i	−0.860186	+	0.509980i	$0.829653\pi$
$242$			159.382i			0.658603i
$243$		0			0
$244$		−	223.136i		−	0.914490i
$245$	−166.250	−	179.961i	−0.678572	−	0.734534i
$246$		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	$0.0946118\pi$
$251$			147.023i			0.585749i	−0.956151	+	0.292875i	$0.905388\pi$
$252$		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	$-0.806302\pi$
$257$	−421.734			−1.64099			−0.820495	+	0.571654i	$0.806302\pi$
$258$		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	$0.0554813\pi$
$269$			93.2991i			0.346837i	−0.984848	+	0.173418i	$0.944519\pi$
$270$		0			0
$271$			288.317i			1.06390i	0.846776	+	0.531949i	$0.178540\pi$
$271$			288.317i			1.06390i	−0.846776	+	0.531949i	$0.821460\pi$
$272$	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
$280$	−80.3608	+	57.8112i	−0.287003	+	0.206469i
$281$	−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	$-0.153523\pi$
$283$	501.435			1.77185			0.885927	+	0.463825i	$0.153523\pi$
$284$	−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	$-0.304764\pi$
$293$	337.308			1.15122			0.575611	+	0.817724i	$0.304764\pi$
$294$		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	$-0.441460\pi$
$307$	112.285			0.365751			0.182875	+	0.983136i	$0.441460\pi$
$308$	−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	$0.0756711\pi$
$311$			146.478i			0.470990i	−0.971876	+	0.235495i	$0.924329\pi$
$312$		0			0
$313$	−139.927			−0.447052			−0.223526	−	0.974698i	$-0.571757\pi$
$313$	−139.927			−0.447052			−0.223526	+	0.974698i	$0.571757\pi$
$314$			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	$-0.987798\pi$
$349$		−	26.7504i		−	0.0766487i	0.999265	−	0.0383244i	$-0.0122020\pi$
$350$	−223.306	−	106.698i	−0.638017	−	0.304851i
$351$		0			0
$352$			16.2972i			0.0462989i
$353$	473.408			1.34110			0.670550	−	0.741864i	$-0.266058\pi$
$353$	473.408			1.34110			0.670550	+	0.741864i	$0.266058\pi$
$354$		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	$-0.649172\pi$
$367$	−331.526			−0.903341			−0.451671	+	0.892185i	$0.649172\pi$
$368$			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	$-0.443310\pi$
$383$	135.702			0.354314			0.177157	+	0.984183i	$0.443310\pi$
$384$		0			0
$385$	−58.8851	−	81.8536i	−0.152948	−	0.212607i
$386$	−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	$-0.500868\pi$
$397$	−2.16495			−0.00545326			−0.00272663	+	0.999996i	$0.500868\pi$
$398$	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	$-0.913618\pi$
$409$		−	219.271i		−	0.536116i	0.963403	−	0.268058i	$-0.0863818\pi$
$410$	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	$0.274710\pi$
$419$			636.723i			1.51963i	−0.650141	+	0.759813i	$0.725290\pi$
$420$		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	$-0.542300\pi$
$433$	−114.744			−0.264997			−0.132498	+	0.991183i	$0.542300\pi$
$434$	−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	$0.258631\pi$
$439$			637.443i			1.45203i	−0.687677	+	0.726017i	$0.741369\pi$
$440$	−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
$455$	−282.360	−	392.496i	−0.620571	−	0.862629i
$456$		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	$0.134942\pi$
$461$			379.263i			0.822695i	−0.911479	+	0.411348i	$0.865058\pi$
$462$		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	$-0.832676\pi$
$467$	−807.901			−1.72998			−0.864991	+	0.501788i	$0.832676\pi$
$468$		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	$-0.848267\pi$
$479$		−	439.564i		−	0.917671i	0.888521	−	0.458835i	$-0.151733\pi$
$480$		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
$490$	−254.503	+	235.113i	−0.519394	+	0.479823i
$491$	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	$-0.477672\pi$
$503$	70.5081			0.140175			0.0700876	+	0.997541i	$0.477672\pi$
$504$		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	$-0.834749\pi$
$509$		−	505.073i		−	0.992285i	0.868241	−	0.496143i	$-0.165251\pi$
$510$		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	$0.0658990\pi$
$521$			214.185i			0.411104i	−0.978646	+	0.205552i	$0.934101\pi$
$522$		0			0
$523$	−121.732			−0.232757			−0.116379	−	0.993205i	$-0.537129\pi$
$523$	−121.732			−0.232757			−0.116379	+	0.993205i	$0.537129\pi$
$524$		−	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
$560$	81.7574	+	113.647i	0.145995	+	0.202942i
$561$		0			0
$562$			345.009i			0.613896i
$563$	363.871			0.646308			0.323154	−	0.946346i	$-0.395257\pi$
$563$	363.871			0.646308			0.323154	+	0.946346i	$0.395257\pi$
$564$		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	$-0.414421\pi$
$577$	306.535			0.531256			0.265628	+	0.964076i	$0.414421\pi$
$578$		−	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	$-0.630376\pi$
$587$	−467.524			−0.796463			−0.398232	+	0.917285i	$0.630376\pi$
$588$		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	$-0.283966\pi$
$593$	744.542			1.25555			0.627775	+	0.778395i	$0.283966\pi$
$594$		0			0
$595$	494.130	+	686.868i	0.830470	+	1.15440i
$596$	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	$0.224641\pi$
$601$			779.606i			1.29718i	−0.761137	+	0.648591i	$0.775359\pi$
$602$	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	$-0.654843\pi$
$607$	−567.539			−0.934990			−0.467495	+	0.883996i	$0.654843\pi$
$608$	−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	$-0.768940\pi$
$619$		−	821.793i		−	1.32761i	0.747904	−	0.663807i	$-0.231060\pi$
$620$	−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	$-0.563866\pi$
$643$	−256.297			−0.398596			−0.199298	+	0.979939i	$0.563866\pi$
$644$	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	$-0.321226\pi$
$647$	689.147			1.06514			0.532571	+	0.846385i	$0.321226\pi$
$648$		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	$-0.978334\pi$
$661$		−	89.9129i		−	0.136026i	0.997684	−	0.0680128i	$-0.0216659\pi$
$662$			19.3374i			0.0292106i
$663$		0			0
$664$		−	222.080i		−	0.334458i
$665$	185.644	−	133.551i	0.279164	−	0.200829i
$666$		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	$-0.510371\pi$
$677$	−44.1092			−0.0651540			−0.0325770	+	0.999469i	$0.510371\pi$
$678$		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	$-0.826987\pi$
$691$		−	714.724i		−	1.03433i	0.855885	−	0.517167i	$-0.173013\pi$
$692$	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
$700$	−150.894	+	315.802i	−0.215562	+	0.451146i
$701$	−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	$-0.598745\pi$
$719$		−	1369.36i		−	1.90453i	0.305266	−	0.952267i	$-0.401255\pi$
$720$		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	$-0.775412\pi$
$727$	−1106.85			−1.52249			−0.761246	+	0.648463i	$0.775412\pi$
$728$	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	$-0.565015\pi$
$733$	−297.353			−0.405665			−0.202833	+	0.979213i	$0.565015\pi$
$734$			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	$0.175591\pi$
$761$			797.652i			1.04816i	−0.851668	+	0.524081i	$0.824409\pi$
$762$		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	$0.0544543\pi$
$769$			261.829i			0.340480i	−0.985403	+	0.170240i	$0.945546\pi$
$770$	−115.758	+	83.2761i	−0.150336	+	0.108151i
$771$		0			0
$772$			306.906i			0.397546i
$773$	−643.514			−0.832489			−0.416245	−	0.909253i	$-0.636654\pi$
$773$	−643.514			−0.832489			−0.416245	+	0.909253i	$0.636654\pi$
$774$		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	$-0.301375\pi$
$787$	919.663			1.16857			0.584284	+	0.811549i	$0.301375\pi$
$788$		−	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	$-0.450629\pi$
$797$	246.244			0.308964			0.154482	+	0.987996i	$0.450629\pi$
$798$		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
$805$	−819.454	+	589.512i	−1.01796	+	0.732313i
$806$	−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	$-0.878177\pi$
$811$		−	605.726i		−	0.746888i	0.927653	−	0.373444i	$-0.121823\pi$
$812$	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	$0.308487\pi$
$829$			1366.86i			1.64880i	−0.566007	+	0.824400i	$0.691513\pi$
$830$	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	$0.0139660\pi$
$839$			73.5993i			0.0877227i	−0.999038	+	0.0438613i	$0.986034\pi$
$840$		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	$-0.339963\pi$
$853$	822.046			0.963711			0.481856	+	0.876251i	$0.339963\pi$
$854$	−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	$-0.618946\pi$
$857$	−625.685			−0.730087			−0.365044	+	0.930990i	$0.618946\pi$
$858$		0			0
$859$			1396.65i			1.62590i	0.582332	+	0.812951i	$0.302140\pi$
$859$			1396.65i			1.62590i	−0.582332	+	0.812951i	$0.697860\pi$
$860$	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
$875$	−873.643	+	48.7073i	−0.998449	+	0.0556654i
$876$		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	$-0.786441\pi$
$881$		−	1095.44i		−	1.24341i	0.783253	−	0.621703i	$-0.213559\pi$
$882$		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	$-0.617009\pi$
$887$	−637.527			−0.718745			−0.359372	+	0.933194i	$0.617009\pi$
$888$		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
$910$	−555.073	+	399.317i	−0.609971	+	0.438810i
$911$	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	$-0.808147\pi$
$929$		−	1053.28i		−	1.13378i	0.823795	−	0.566889i	$-0.191853\pi$
$930$		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	$-0.681621\pi$
$937$	−1012.18			−1.08024			−0.540119	+	0.841589i	$0.681621\pi$
$938$	−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	$-0.736863\pi$
$941$		−	1384.55i		−	1.47136i	0.677331	−	0.735679i	$-0.263137\pi$
$942$		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	$0.119491\pi$
$971$			712.009i			0.733274i	−0.930364	+	0.366637i	$0.880509\pi$
$972$		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
$980$	332.500	+	359.922i	0.339286	+	0.367267i
$981$		0			0
$982$		−	10.3627i		−	0.0105526i
$983$	−1525.09			−1.55147			−0.775735	−	0.631059i	$-0.782621\pi$
$983$	−1525.09			−1.55147			−0.775735	+	0.631059i	$0.782621\pi$
$984$		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	$-0.749245\pi$
$997$	−1406.62			−1.41086			−0.705428	+	0.708781i	$0.749245\pi$
$998$			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.559.3		16
3.2	odd	2		210.3.h.a.139.11	yes	16
5.4	even	2	inner	630.3.h.e.559.14		16
7.6	odd	2	inner	630.3.h.e.559.6		16
12.11	even	2		1680.3.bd.a.769.14		16
15.2	even	4		1050.3.f.e.601.6		16
15.8	even	4		1050.3.f.e.601.11		16
15.14	odd	2		210.3.h.a.139.6	yes	16
21.20	even	2		210.3.h.a.139.14	yes	16
35.34	odd	2	inner	630.3.h.e.559.11		16
60.59	even	2		1680.3.bd.a.769.4		16
84.83	odd	2		1680.3.bd.a.769.3		16
105.62	odd	4		1050.3.f.e.601.2		16
105.83	odd	4		1050.3.f.e.601.15		16
105.104	even	2		210.3.h.a.139.3	✓	16
420.419	odd	2		1680.3.bd.a.769.13		16

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

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(-2.40341 - 4.38447i) q^{5} +(-6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(-2.40341 - 4.38447i) q^{5} +(-6.94781 + 0.853218i) q^{7} +2.82843i q^{8} +(-6.20058 + 3.39894i) q^{10} -2.88097 q^{11} -13.8145 q^{13} +(1.20663 + 9.82568i) q^{14} +4.00000 q^{16} +24.1754 q^{17} -6.53403i q^{19} +(4.80682 + 8.76895i) q^{20} +4.07430i q^{22} +28.8420i q^{23} +(-13.4472 + 21.0754i) q^{25} +19.5367i q^{26} +(13.8956 - 1.70644i) q^{28} +32.9589 q^{29} +2.43276i q^{31} -5.65685i q^{32} -34.1892i q^{34} +(20.4394 + 28.4118i) q^{35} +50.9799i q^{37} -9.24052 q^{38} +(12.4012 - 6.79788i) q^{40} -21.5225i q^{41} -13.5554i q^{43} +5.76193 q^{44} +40.7887 q^{46} -40.7305 q^{47} +(47.5440 - 11.8560i) q^{49} +(29.8051 + 19.0172i) q^{50} +27.6291 q^{52} -17.2758i q^{53} +(6.92415 + 12.6315i) q^{55} +(-2.41326 - 19.6514i) q^{56} -46.6109i q^{58} -1.47488i q^{59} +111.568i q^{61} +3.44045 q^{62} -8.00000 q^{64} +(33.2020 + 60.5694i) q^{65} +120.293i q^{67} -48.3508 q^{68} +(40.1804 - 28.9056i) q^{70} +90.3855 q^{71} +21.4890 q^{73} +72.0964 q^{74} +13.0681i q^{76} +(20.0164 - 2.45809i) q^{77} -66.1324 q^{79} +(-9.61365 - 17.5379i) q^{80} -30.4375 q^{82} -78.5172 q^{83} +(-58.1035 - 105.996i) q^{85} -19.1703 q^{86} -8.14861i q^{88} -90.9724i q^{89} +(95.9807 - 11.7868i) q^{91} -57.6840i q^{92} +57.6016i q^{94} +(-28.6483 + 15.7040i) q^{95} +44.1972 q^{97} +(-16.7669 - 67.2374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 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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