LMFDB - Embedded newform 630.6.b.b.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,6,Mod(251,630)]

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([1, 0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("630.251");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	630.b (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:	$101.041806482$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.1
Character	$\chi$	$=$	630.251
Dual form			630.6.b.b.251.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} -16.0000 q^{4} +25.0000 q^{5} +(-124.893 + 34.7652i) q^{7} +64.0000i q^{8} -100.000i q^{10} -250.926i q^{11} +257.140i q^{13} +(139.061 + 499.574i) q^{14} +256.000 q^{16} -1652.74 q^{17} +117.851i q^{19} -400.000 q^{20} -1003.70 q^{22} -3228.81i q^{23} +625.000 q^{25} +1028.56 q^{26} +(1998.30 - 556.244i) q^{28} -1172.64i q^{29} +6328.52i q^{31} -1024.00i q^{32} +6610.97i q^{34} +(-3122.34 + 869.131i) q^{35} +8379.92 q^{37} +471.404 q^{38} +1600.00i q^{40} -14627.5 q^{41} -15895.7 q^{43} +4014.82i q^{44} -12915.2 q^{46} +16810.9 q^{47} +(14389.8 - 8683.90i) q^{49} -2500.00i q^{50} -4114.25i q^{52} -2337.18i q^{53} -6273.15i q^{55} +(-2224.98 - 7993.18i) q^{56} -4690.55 q^{58} +9243.24 q^{59} +19645.3i q^{61} +25314.1 q^{62} -4096.00 q^{64} +6428.51i q^{65} +46708.5 q^{67} +26443.9 q^{68} +(3476.52 + 12489.3i) q^{70} +36402.7i q^{71} +26899.4i q^{73} -33519.7i q^{74} -1885.62i q^{76} +(8723.50 + 31339.0i) q^{77} -37598.8 q^{79} +6400.00 q^{80} +58509.9i q^{82} +90834.3 q^{83} -41318.6 q^{85} +63582.8i q^{86} +16059.3 q^{88} +57741.9 q^{89} +(-8939.55 - 32115.2i) q^{91} +51660.9i q^{92} -67243.4i q^{94} +2946.27i q^{95} +24079.1i q^{97} +(-34735.6 - 57559.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 384 q^{4} + 600 q^{5} - 196 q^{7} + 6144 q^{16} - 9600 q^{20} + 15000 q^{25} - 3872 q^{26} + 3136 q^{28} - 4900 q^{35} - 33512 q^{37} - 10208 q^{38} + 44968 q^{41} + 8016 q^{43} - 1312 q^{46} + 47240 q^{47}+ \cdots + 257936 q^{98}+O(q^{100}) $ 24 * q - 384 * q^4 + 600 * q^5 - 196 * q^7 + 6144 * q^16 - 9600 * q^20 + 15000 * q^25 - 3872 * q^26 + 3136 * q^28 - 4900 * q^35 - 33512 * q^37 - 10208 * q^38 + 44968 * q^41 + 8016 * q^43 - 1312 * q^46 + 47240 * q^47 - 31724 * q^49 + 35168 * q^58 - 110400 * q^59 + 20320 * q^62 - 98304 * q^64 - 92032 * q^67 + 107212 * q^77 + 90632 * q^79 + 153600 * q^80 - 211664 * q^83 + 286888 * q^89 - 173684 * q^91 + 257936 * q^98

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−16.0000			−0.500000
$5$	25.0000			0.447214
$5$	25.0000			0.447214
$6$		0			0
$7$	−124.893	+	34.7652i	−0.963373	+	0.268164i
$7$	−124.893	+	34.7652i	−0.963373	+	0.268164i
$8$			64.0000i			0.353553i
$9$		0			0
$10$		−	100.000i		−	0.316228i
$11$		−	250.926i		−	0.625265i	−0.949874	−	0.312632i	$-0.898789\pi$
$11$		−	250.926i		−	0.625265i	0.949874	−	0.312632i	$-0.101211\pi$
$12$		0			0
$13$			257.140i			0.422000i	0.977486	+	0.211000i	$0.0676719\pi$
$13$			257.140i			0.422000i	−0.977486	+	0.211000i	$0.932328\pi$
$14$	139.061	+	499.574i	0.189620	+	0.681208i
$15$		0			0
$16$	256.000			0.250000
$17$	−1652.74			−1.38702			−0.693511	−	0.720446i	$-0.743937\pi$
$17$	−1652.74			−1.38702			−0.693511	+	0.720446i	$0.743937\pi$
$18$		0			0
$19$			117.851i			0.0748944i	0.999299	+	0.0374472i	$0.0119226\pi$
$19$			117.851i			0.0748944i	−0.999299	+	0.0374472i	$0.988077\pi$
$20$	−400.000			−0.223607
$21$		0			0
$22$	−1003.70			−0.442129
$23$		−	3228.81i		−	1.27269i	−0.771405	−	0.636344i	$-0.780446\pi$
$23$		−	3228.81i		−	1.27269i	0.771405	−	0.636344i	$-0.219554\pi$
$24$		0			0
$25$	625.000			0.200000
$26$	1028.56			0.298399
$27$		0			0
$28$	1998.30	−	556.244i	0.481687	−	0.134082i
$29$		−	1172.64i		−	0.258922i	−0.991585	−	0.129461i	$-0.958675\pi$
$29$		−	1172.64i		−	0.258922i	0.991585	−	0.129461i	$-0.0413247\pi$
$30$		0			0
$31$			6328.52i			1.18276i	0.806392	+	0.591382i	$0.201417\pi$
$31$			6328.52i			1.18276i	−0.806392	+	0.591382i	$0.798583\pi$
$32$		−	1024.00i		−	0.176777i
$33$		0			0
$34$			6610.97i			0.980772i
$35$	−3122.34	+	869.131i	−0.430834	+	0.119927i
$36$		0			0
$37$	8379.92			1.00632			0.503159	−	0.864194i	$-0.332171\pi$
$37$	8379.92			1.00632			0.503159	+	0.864194i	$0.332171\pi$
$38$	471.404			0.0529583
$39$		0			0
$40$			1600.00i			0.158114i
$41$	−14627.5			−1.35897			−0.679485	−	0.733690i	$-0.737797\pi$
$41$	−14627.5			−1.35897			−0.679485	+	0.733690i	$0.737797\pi$
$42$		0			0
$43$	−15895.7			−1.31102			−0.655508	−	0.755188i	$-0.727546\pi$
$43$	−15895.7			−1.31102			−0.655508	+	0.755188i	$0.727546\pi$
$44$			4014.82i			0.312632i
$45$		0			0
$46$	−12915.2			−0.899927
$47$	16810.9			1.11006			0.555028	−	0.831831i	$-0.312707\pi$
$47$	16810.9			1.11006			0.555028	+	0.831831i	$0.312707\pi$
$48$		0			0
$49$	14389.8	−	8683.90i	0.856176	−	0.516684i
$50$		−	2500.00i		−	0.141421i
$51$		0			0
$52$		−	4114.25i		−	0.211000i
$53$		−	2337.18i		−	0.114289i	−0.998366	−	0.0571444i	$-0.981800\pi$
$53$		−	2337.18i		−	0.114289i	0.998366	−	0.0571444i	$-0.0181995\pi$
$54$		0			0
$55$		−	6273.15i		−	0.279627i
$56$	−2224.98	−	7993.18i	−0.0948102	−	0.340604i
$57$		0			0
$58$	−4690.55			−0.183085
$59$	9243.24			0.345696			0.172848	−	0.984949i	$-0.444703\pi$
$59$	9243.24			0.345696			0.172848	+	0.984949i	$0.444703\pi$
$60$		0			0
$61$			19645.3i			0.675979i	0.941150	+	0.337990i	$0.109747\pi$
$61$			19645.3i			0.675979i	−0.941150	+	0.337990i	$0.890253\pi$
$62$	25314.1			0.836340
$63$		0			0
$64$	−4096.00			−0.125000
$65$			6428.51i			0.188724i
$66$		0			0
$67$	46708.5			1.27118			0.635592	−	0.772025i	$-0.280756\pi$
$67$	46708.5			1.27118			0.635592	+	0.772025i	$0.280756\pi$
$68$	26443.9			0.693511
$69$		0			0
$70$	3476.52	+	12489.3i	0.0848009	+	0.304645i
$71$			36402.7i			0.857014i	0.903538	+	0.428507i	$0.140960\pi$
$71$			36402.7i			0.857014i	−0.903538	+	0.428507i	$0.859040\pi$
$72$		0			0
$73$			26899.4i			0.590793i	0.955375	+	0.295397i	$0.0954518\pi$
$73$			26899.4i			0.590793i	−0.955375	+	0.295397i	$0.904548\pi$
$74$		−	33519.7i		−	0.711575i
$75$		0			0
$76$		−	1885.62i		−	0.0374472i
$77$	8723.50	+	31339.0i	0.167673	+	0.602363i
$78$		0			0
$79$	−37598.8			−0.677807			−0.338903	−	0.940821i	$-0.610056\pi$
$79$	−37598.8			−0.677807			−0.338903	+	0.940821i	$0.610056\pi$
$80$	6400.00			0.111803
$81$		0			0
$82$			58509.9i			0.960937i
$83$	90834.3			1.44729			0.723643	−	0.690174i	$-0.242466\pi$
$83$	90834.3			1.44729			0.723643	+	0.690174i	$0.242466\pi$
$84$		0			0
$85$	−41318.6			−0.620295
$86$			63582.8i			0.927029i
$87$		0			0
$88$	16059.3			0.221064
$89$	57741.9			0.772709			0.386354	−	0.922350i	$-0.373734\pi$
$89$	57741.9			0.772709			0.386354	+	0.922350i	$0.373734\pi$
$90$		0			0
$91$	−8939.55	−	32115.2i	−0.113165	−	0.406543i
$92$			51660.9i			0.636344i
$93$		0			0
$94$		−	67243.4i		−	0.784929i
$95$			2946.27i			0.0334938i
$96$		0			0
$97$			24079.1i			0.259843i	0.991524	+	0.129921i	$0.0414725\pi$
$97$			24079.1i			0.259843i	−0.991524	+	0.129921i	$0.958527\pi$
$98$	−34735.6	−	57559.0i	−0.365351	−	0.605408i
$99$		0			0
$100$	−10000.0			−0.100000
$101$	46941.1			0.457878			0.228939	−	0.973441i	$-0.426474\pi$
$101$	46941.1			0.457878			0.228939	+	0.973441i	$0.426474\pi$
$102$		0			0
$103$		−	15891.2i		−	0.147593i	−0.997273	−	0.0737964i	$-0.976489\pi$
$103$		−	15891.2i		−	0.147593i	0.997273	−	0.0737964i	$-0.0235115\pi$
$104$	−16457.0			−0.149199
$105$		0			0
$106$	−9348.74			−0.0808143
$107$		−	32260.0i		−	0.272398i	−0.990681	−	0.136199i	$-0.956511\pi$
$107$		−	32260.0i		−	0.272398i	0.990681	−	0.136199i	$-0.0434887\pi$
$108$		0			0
$109$	−82838.0			−0.667826			−0.333913	−	0.942604i	$-0.608369\pi$
$109$	−82838.0			−0.667826			−0.333913	+	0.942604i	$0.608369\pi$
$110$	−25092.6			−0.197726
$111$		0			0
$112$	−31972.7	+	8899.90i	−0.240843	+	0.0670410i
$113$			218676.i			1.61104i	0.592571	+	0.805518i	$0.298113\pi$
$113$			218676.i			1.61104i	−0.592571	+	0.805518i	$0.701887\pi$
$114$		0			0
$115$		−	80720.1i		−	0.569164i
$116$			18762.2i			0.129461i
$117$		0			0
$118$		−	36973.0i		−	0.244444i
$119$	206417.	−	57458.0i	1.33622	−	0.371949i
$120$		0			0
$121$	98087.2			0.609044
$122$	78581.1			0.477990
$123$		0			0
$124$		−	101256.i		−	0.591382i
$125$	15625.0			0.0894427
$126$		0			0
$127$	86791.1			0.477492			0.238746	−	0.971082i	$-0.423264\pi$
$127$	86791.1			0.477492			0.238746	+	0.971082i	$0.423264\pi$
$128$			16384.0i			0.0883883i
$129$		0			0
$130$	25714.0			0.133448
$131$	222644.			1.13353			0.566766	−	0.823879i	$-0.308195\pi$
$131$	222644.			1.13353			0.566766	+	0.823879i	$0.308195\pi$
$132$		0			0
$133$	−4097.12	−	14718.8i	−0.0200840	−	0.0721512i
$134$		−	186834.i		−	0.898863i
$135$		0			0
$136$		−	105776.i		−	0.490386i
$137$		−	218091.i		−	0.992743i	−0.868110	−	0.496372i	$-0.834665\pi$
$137$		−	218091.i		−	0.992743i	0.868110	−	0.496372i	$-0.165335\pi$
$138$		0			0
$139$			407509.i			1.78896i	0.447110	+	0.894479i	$0.352453\pi$
$139$			407509.i			1.78896i	−0.447110	+	0.894479i	$0.647547\pi$
$140$	49957.4	−	13906.1i	0.215417	−	0.0599633i
$141$		0			0
$142$	145611.			0.606000
$143$	64523.2			0.263861
$144$		0			0
$145$		−	29315.9i		−	0.115793i
$146$	107598.			0.417754
$147$		0			0
$148$	−134079.			−0.503159
$149$		−	17290.9i		−	0.0638048i	−0.999491	−	0.0319024i	$-0.989843\pi$
$149$		−	17290.9i		−	0.0638048i	0.999491	−	0.0319024i	$-0.0101566\pi$
$150$		0			0
$151$	−261712.			−0.934074			−0.467037	−	0.884238i	$-0.654679\pi$
$151$	−261712.			−0.934074			−0.467037	+	0.884238i	$0.654679\pi$
$152$	−7542.46			−0.0264792
$153$		0			0
$154$	125356.	−	34894.0i	0.425935	−	0.118563i
$155$			158213.i			0.528948i
$156$		0			0
$157$		−	221963.i		−	0.718672i	−0.933208	−	0.359336i	$-0.883003\pi$
$157$		−	221963.i		−	0.718672i	0.933208	−	0.359336i	$-0.116997\pi$
$158$			150395.i			0.479282i
$159$		0			0
$160$		−	25600.0i		−	0.0790569i
$161$	112250.	+	403257.i	0.341289	+	1.22607i
$162$		0			0
$163$	112138.			0.330586			0.165293	−	0.986245i	$-0.447143\pi$
$163$	112138.			0.330586			0.165293	+	0.986245i	$0.447143\pi$
$164$	234040.			0.679485
$165$		0			0
$166$		−	363337.i		−	1.02339i
$167$	680406.			1.88789			0.943945	−	0.330102i	$-0.107083\pi$
$167$	680406.			1.88789			0.943945	+	0.330102i	$0.107083\pi$
$168$		0			0
$169$	305172.			0.821916
$170$			165274.i			0.438615i
$171$		0			0
$172$	254331.			0.655508
$173$	457211.			1.16145			0.580726	−	0.814099i	$-0.302769\pi$
$173$	457211.			1.16145			0.580726	+	0.814099i	$0.302769\pi$
$174$		0			0
$175$	−78058.4	+	21728.3i	−0.192675	+	0.0536328i
$176$		−	64237.0i		−	0.156316i
$177$		0			0
$178$		−	230967.i		−	0.546388i
$179$			430235.i			1.00363i	0.864975	+	0.501815i	$0.167334\pi$
$179$			430235.i			1.00363i	−0.864975	+	0.501815i	$0.832666\pi$
$180$		0			0
$181$		−	612200.i		−	1.38898i	−0.719501	−	0.694491i	$-0.755630\pi$
$181$		−	612200.i		−	1.38898i	0.719501	−	0.694491i	$-0.244370\pi$
$182$	−128461.	+	35758.2i	−0.287469	+	0.0800198i
$183$		0			0
$184$	206644.			0.449963
$185$	209498.			0.450040
$186$		0			0
$187$			414716.i			0.867255i
$188$	−268974.			−0.555028
$189$		0			0
$190$	11785.1			0.0236837
$191$			48454.8i			0.0961067i	0.998845	+	0.0480534i	$0.0153018\pi$
$191$			48454.8i			0.0961067i	−0.998845	+	0.0480534i	$0.984698\pi$
$192$		0			0
$193$	203700.			0.393639			0.196819	−	0.980440i	$-0.436939\pi$
$193$	203700.			0.393639			0.196819	+	0.980440i	$0.436939\pi$
$194$	96316.4			0.183737
$195$		0			0
$196$	−230236.	+	138942.i	−0.428088	+	0.258342i
$197$		−	761950.i		−	1.39882i	−0.714722	−	0.699409i	$-0.753447\pi$
$197$		−	761950.i		−	1.39882i	0.714722	−	0.699409i	$-0.246553\pi$
$198$		0			0
$199$		−	828377.i		−	1.48284i	−0.671040	−	0.741422i	$-0.734152\pi$
$199$		−	828377.i		−	1.48284i	0.671040	−	0.741422i	$-0.265848\pi$
$200$			40000.0i			0.0707107i
$201$		0			0
$202$		−	187765.i		−	0.323769i
$203$	40767.0	+	146455.i	0.0694335	+	0.249438i
$204$		0			0
$205$	−365687.			−0.607750
$206$	−63565.0			−0.104364
$207$		0			0
$208$			65827.9i			0.105500i
$209$	29571.9			0.0468288
$210$		0			0
$211$	650544.			1.00594			0.502968	−	0.864305i	$-0.332241\pi$
$211$	650544.			1.00594			0.502968	+	0.864305i	$0.332241\pi$
$212$			37395.0i			0.0571444i
$213$		0			0
$214$	−129040.			−0.192615
$215$	−397392.			−0.586304
$216$		0			0
$217$	−220013.	−	790391.i	−0.317175	−	1.13944i
$218$			331352.i			0.472225i
$219$		0			0
$220$			100370.i			0.139813i
$221$		−	424987.i		−	0.585322i
$222$		0			0
$223$		−	872212.i		−	1.17452i	−0.809399	−	0.587259i	$-0.800207\pi$
$223$		−	872212.i		−	1.17452i	0.809399	−	0.587259i	$-0.199793\pi$
$224$	35599.6	+	127891.i	0.0474051	+	0.170302i
$225$		0			0
$226$	874705.			1.13918
$227$	685709.			0.883233			0.441617	−	0.897204i	$-0.354405\pi$
$227$	685709.			0.883233			0.441617	+	0.897204i	$0.354405\pi$
$228$		0			0
$229$		−	541865.i		−	0.682815i	−0.939915	−	0.341407i	$-0.889096\pi$
$229$		−	541865.i		−	0.682815i	0.939915	−	0.341407i	$-0.110904\pi$
$230$	−322881.			−0.402460
$231$		0			0
$232$	75048.8			0.0915427
$233$		−	925562.i		−	1.11690i	−0.829537	−	0.558452i	$-0.811396\pi$
$233$		−	925562.i		−	1.11690i	0.829537	−	0.558452i	$-0.188604\pi$
$234$		0			0
$235$	420271.			0.496432
$236$	−147892.			−0.172848
$237$		0			0
$238$	−229832.	−	825667.i	−0.263008	−	0.944850i
$239$			655469.i			0.742262i	0.928580	+	0.371131i	$0.121030\pi$
$239$			655469.i			0.742262i	−0.928580	+	0.371131i	$0.878970\pi$
$240$		0			0
$241$			418245.i			0.463861i	0.972732	+	0.231930i	$0.0745042\pi$
$241$			418245.i			0.463861i	−0.972732	+	0.231930i	$0.925496\pi$
$242$		−	392349.i		−	0.430659i
$243$		0			0
$244$		−	314324.i		−	0.337990i
$245$	359744.	−	217098.i	0.382894	−	0.231068i
$246$		0			0
$247$	−30304.2			−0.0316054
$248$	−405025.			−0.418170
$249$		0			0
$250$		−	62500.0i		−	0.0632456i
$251$	−626694.			−0.627872			−0.313936	−	0.949444i	$-0.601648\pi$
$251$	−626694.			−0.627872			−0.313936	+	0.949444i	$0.601648\pi$
$252$		0			0
$253$	−810191.			−0.795767
$254$		−	347164.i		−	0.337638i
$255$		0			0
$256$	65536.0			0.0625000
$257$	−74024.8			−0.0699108			−0.0349554	−	0.999389i	$-0.511129\pi$
$257$	−74024.8			−0.0699108			−0.0349554	+	0.999389i	$0.511129\pi$
$258$		0			0
$259$	−1.04660e6	+	291330.i	−0.969461	+	0.269858i
$260$		−	102856.i		−	0.0943620i
$261$		0			0
$262$		−	890577.i		−	0.801528i
$263$			2.12162e6i			1.89138i	0.325074	+	0.945689i	$0.394611\pi$
$263$			2.12162e6i			1.89138i	−0.325074	+	0.945689i	$0.605389\pi$
$264$		0			0
$265$		−	58429.6i		−	0.0511115i
$266$	−58875.3	+	16388.5i	−0.0510186	+	0.0142015i
$267$		0			0
$268$	−747335.			−0.635592
$269$	781904.			0.658829			0.329414	−	0.944185i	$-0.393149\pi$
$269$	781904.			0.658829			0.329414	+	0.944185i	$0.393149\pi$
$270$		0			0
$271$			1.53480e6i			1.26949i	0.772723	+	0.634743i	$0.218894\pi$
$271$			1.53480e6i			1.26949i	−0.772723	+	0.634743i	$0.781106\pi$
$272$	−423102.			−0.346755
$273$		0			0
$274$	−872365.			−0.701975
$275$		−	156829.i		−	0.125053i
$276$		0			0
$277$	63027.3			0.0493548			0.0246774	−	0.999695i	$-0.492144\pi$
$277$	63027.3			0.0493548			0.0246774	+	0.999695i	$0.492144\pi$
$278$	1.63004e6			1.26498
$279$		0			0
$280$	−55624.4	−	199830.i	−0.0424004	−	0.152323i
$281$			1.12630e6i			0.850916i	0.904978	+	0.425458i	$0.139887\pi$
$281$			1.12630e6i			0.850916i	−0.904978	+	0.425458i	$0.860113\pi$
$282$		0			0
$283$			178391.i			0.132406i	0.997806	+	0.0662029i	$0.0210885\pi$
$283$			178391.i			0.132406i	−0.997806	+	0.0662029i	$0.978912\pi$
$284$		−	582443.i		−	0.428507i
$285$		0			0
$286$		−	258093.i		−	0.186578i
$287$	1.82688e6	−	508528.i	1.30920	−	0.364427i
$288$		0			0
$289$	1.31170e6			0.923828
$290$	−117264.			−0.0818783
$291$		0			0
$292$		−	430390.i		−	0.295397i
$293$	−887427.			−0.603898			−0.301949	−	0.953324i	$-0.597637\pi$
$293$	−887427.			−0.603898			−0.301949	+	0.953324i	$0.597637\pi$
$294$		0			0
$295$	231081.			0.154600
$296$			536315.i			0.355787i
$297$		0			0
$298$	−69163.8			−0.0451168
$299$	830256.			0.537074
$300$		0			0
$301$	1.98527e6	−	552618.i	1.26300	−	0.351567i
$302$			1.04685e6i			0.660490i
$303$		0			0
$304$			30169.8i			0.0187236i
$305$			491132.i			0.302307i
$306$		0			0
$307$		−	559597.i		−	0.338867i	−0.985542	−	0.169434i	$-0.945806\pi$
$307$		−	559597.i		−	0.338867i	0.985542	−	0.169434i	$-0.0541938\pi$
$308$	−139576.	−	501424.i	−0.0838367	−	0.301182i
$309$		0			0
$310$	632852.			0.374023
$311$	1.69108e6			0.991430			0.495715	−	0.868485i	$-0.334906\pi$
$311$	1.69108e6			0.991430			0.495715	+	0.868485i	$0.334906\pi$
$312$		0			0
$313$			128607.i			0.0741998i	0.999312	+	0.0370999i	$0.0118120\pi$
$313$			128607.i			0.0741998i	−0.999312	+	0.0370999i	$0.988188\pi$
$314$	−887851.			−0.508178
$315$		0			0
$316$	601580.			0.338903
$317$		−	429305.i		−	0.239949i	−0.992777	−	0.119974i	$-0.961719\pi$
$317$		−	429305.i		−	0.239949i	0.992777	−	0.119974i	$-0.0382812\pi$
$318$		0			0
$319$	−294245.			−0.161895
$320$	−102400.			−0.0559017
$321$		0			0
$322$	1.61303e6	−	449001.i	0.866966	−	0.241328i
$323$		−	194777.i		−	0.103880i
$324$		0			0
$325$			160713.i			0.0843999i
$326$		−	448553.i		−	0.233760i
$327$		0			0
$328$		−	936158.i		−	0.480468i
$329$	−2.09957e6	+	584434.i	−1.06940	+	0.297677i
$330$		0			0
$331$	1.28096e6			0.642638			0.321319	−	0.946971i	$-0.395874\pi$
$331$	1.28096e6			0.642638			0.321319	+	0.946971i	$0.395874\pi$
$332$	−1.45335e6			−0.723643
$333$		0			0
$334$		−	2.72162e6i		−	1.33494i
$335$	1.16771e6			0.568491
$336$		0			0
$337$	−2.74480e6			−1.31655			−0.658273	−	0.752779i	$-0.728713\pi$
$337$	−2.74480e6			−1.31655			−0.658273	+	0.752779i	$0.728713\pi$
$338$		−	1.22069e6i		−	0.581183i
$339$		0			0
$340$	661097.			0.310147
$341$	1.58799e6			0.739540
$342$		0			0
$343$	−1.49529e6	+	1.58483e6i	−0.686261	+	0.727355i
$344$		−	1.01732e6i		−	0.463514i
$345$		0			0
$346$		−	1.82884e6i		−	0.821271i
$347$		−	1.96460e6i		−	0.875892i	−0.899001	−	0.437946i	$-0.855706\pi$
$347$		−	1.96460e6i		−	0.875892i	0.899001	−	0.437946i	$-0.144294\pi$
$348$		0			0
$349$			1.32426e6i			0.581982i	0.956726	+	0.290991i	$0.0939850\pi$
$349$			1.32426e6i			0.581982i	−0.956726	+	0.290991i	$0.906015\pi$
$350$	86913.1	+	312234.i	0.0379241	+	0.136242i
$351$		0			0
$352$	−256948.			−0.110532
$353$	4.26988e6			1.82381			0.911903	−	0.410407i	$-0.134613\pi$
$353$	4.26988e6			1.82381			0.911903	+	0.410407i	$0.134613\pi$
$354$		0			0
$355$			910068.i			0.383268i
$356$	−923870.			−0.386354
$357$		0			0
$358$	1.72094e6			0.709674
$359$			2.14957e6i			0.880271i	0.897931	+	0.440135i	$0.145070\pi$
$359$			2.14957e6i			0.880271i	−0.897931	+	0.440135i	$0.854930\pi$
$360$		0			0
$361$	2.46221e6			0.994391
$362$	−2.44880e6			−0.982159
$363$		0			0
$364$	143033.	+	513843.i	0.0565825	+	0.203272i
$365$			672485.i			0.264211i
$366$		0			0
$367$			3.00711e6i			1.16542i	0.812679	+	0.582712i	$0.198008\pi$
$367$			3.00711e6i			1.16542i	−0.812679	+	0.582712i	$0.801992\pi$
$368$		−	826574.i		−	0.318172i
$369$		0			0
$370$		−	837992.i		−	0.318226i
$371$	81252.8	+	291899.i	0.0306481	+	0.110103i
$372$		0			0
$373$	−3.59913e6			−1.33945			−0.669723	−	0.742611i	$-0.733587\pi$
$373$	−3.59913e6			−1.33945			−0.669723	+	0.742611i	$0.733587\pi$
$374$	1.65887e6			0.613242
$375$		0			0
$376$			1.07589e6i			0.392464i
$377$	301532.			0.109265
$378$		0			0
$379$	−2.67563e6			−0.956817			−0.478408	−	0.878138i	$-0.658786\pi$
$379$	−2.67563e6			−0.956817			−0.478408	+	0.878138i	$0.658786\pi$
$380$		−	47140.4i		−	0.0167469i
$381$		0			0
$382$	193819.			0.0679577
$383$	−2.95549e6			−1.02951			−0.514757	−	0.857336i	$-0.672118\pi$
$383$	−2.95549e6			−1.02951			−0.514757	+	0.857336i	$0.672118\pi$
$384$		0			0
$385$	218088.	+	783475.i	0.0749858	+	0.269385i
$386$		−	814800.i		−	0.278345i
$387$		0			0
$388$		−	385266.i		−	0.129921i
$389$		−	892541.i		−	0.299057i	−0.988757	−	0.149529i	$-0.952224\pi$
$389$		−	892541.i		−	0.299057i	0.988757	−	0.149529i	$-0.0477756\pi$
$390$		0			0
$391$			5.33639e6i			1.76525i
$392$	555770.	+	920944.i	0.182675	+	0.302704i
$393$		0			0
$394$	−3.04780e6			−0.989113
$395$	−939969.			−0.303124
$396$		0			0
$397$			5.77515e6i			1.83902i	0.393066	+	0.919510i	$0.371415\pi$
$397$			5.77515e6i			1.83902i	−0.393066	+	0.919510i	$0.628585\pi$
$398$	−3.31351e6			−1.04853
$399$		0			0
$400$	160000.			0.0500000
$401$			1.74154e6i			0.540843i	0.962742	+	0.270422i	$0.0871631\pi$
$401$			1.74154e6i			0.540843i	−0.962742	+	0.270422i	$0.912837\pi$
$402$		0			0
$403$	−1.62732e6			−0.499126
$404$	−751058.			−0.228939
$405$		0			0
$406$	585819.	−	163068.i	0.176380	−	0.0490969i
$407$		−	2.10274e6i		−	0.629216i
$408$		0			0
$409$			383019.i			0.113217i	0.998396	+	0.0566085i	$0.0180287\pi$
$409$			383019.i			0.113217i	−0.998396	+	0.0566085i	$0.981971\pi$
$410$			1.46275e6i			0.429744i
$411$		0			0
$412$			254260.i			0.0737964i
$413$	−1.15442e6	+	321344.i	−0.333034	+	0.0927031i
$414$		0			0
$415$	2.27086e6			0.647246
$416$	263312.			0.0745997
$417$		0			0
$418$		−	118287.i		−	0.0331130i
$419$	−2.56608e6			−0.714060			−0.357030	−	0.934093i	$-0.616211\pi$
$419$	−2.56608e6			−0.714060			−0.357030	+	0.934093i	$0.616211\pi$
$420$		0			0
$421$	−2.66217e6			−0.732034			−0.366017	−	0.930608i	$-0.619279\pi$
$421$	−2.66217e6			−0.732034			−0.366017	+	0.930608i	$0.619279\pi$
$422$		−	2.60217e6i		−	0.711304i
$423$		0			0
$424$	149580.			0.0404072
$425$	−1.03296e6			−0.277404
$426$		0			0
$427$	−682973.	−	2.45357e6i	−0.181273	−	0.651220i
$428$			516160.i			0.136199i
$429$		0			0
$430$			1.58957e6i			0.414580i
$431$			108661.i			0.0281761i	0.999901	+	0.0140881i	$0.00448452\pi$
$431$			108661.i			0.0281761i	−0.999901	+	0.0140881i	$0.995515\pi$
$432$		0			0
$433$			5.80622e6i			1.48824i	0.668044	+	0.744121i	$0.267132\pi$
$433$			5.80622e6i			1.48824i	−0.668044	+	0.744121i	$0.732868\pi$
$434$	−3.16156e6	+	880051.i	−0.805708	+	0.224276i
$435$		0			0
$436$	1.32541e6			0.333913
$437$	380518.			0.0953172
$438$		0			0
$439$			7.58694e6i			1.87891i	0.342677	+	0.939453i	$0.388666\pi$
$439$			7.58694e6i			1.87891i	−0.342677	+	0.939453i	$0.611334\pi$
$440$	401482.			0.0988630
$441$		0			0
$442$	−1.69995e6			−0.413885
$443$		−	1.62606e6i		−	0.393667i	−0.980437	−	0.196833i	$-0.936934\pi$
$443$		−	1.62606e6i		−	0.393667i	0.980437	−	0.196833i	$-0.0630658\pi$
$444$		0			0
$445$	1.44355e6			0.345566
$446$	−3.48885e6			−0.830510
$447$		0			0
$448$	511564.	−	142398.i	0.120422	−	0.0335205i
$449$		−	3.92915e6i		−	0.919778i	−0.887976	−	0.459889i	$-0.847889\pi$
$449$		−	3.92915e6i		−	0.919778i	0.887976	−	0.459889i	$-0.152111\pi$
$450$		0			0
$451$			3.67041e6i			0.849716i
$452$		−	3.49882e6i		−	0.805518i
$453$		0			0
$454$		−	2.74284e6i		−	0.624540i
$455$	−223489.	−	802879.i	−0.0506089	−	0.181812i
$456$		0			0
$457$	3.27250e6			0.732975			0.366487	−	0.930423i	$-0.380560\pi$
$457$	3.27250e6			0.732975			0.366487	+	0.930423i	$0.380560\pi$
$458$	−2.16746e6			−0.482823
$459$		0			0
$460$			1.29152e6i			0.284582i
$461$	−2.27791e6			−0.499212			−0.249606	−	0.968348i	$-0.580301\pi$
$461$	−2.27791e6			−0.499212			−0.249606	+	0.968348i	$0.580301\pi$
$462$		0			0
$463$	1.74893e6			0.379159			0.189579	−	0.981865i	$-0.439288\pi$
$463$	1.74893e6			0.379159			0.189579	+	0.981865i	$0.439288\pi$
$464$		−	300195.i		−	0.0647305i
$465$		0			0
$466$	−3.70225e6			−0.789770
$467$	−2.56896e6			−0.545086			−0.272543	−	0.962144i	$-0.587865\pi$
$467$	−2.56896e6			−0.545086			−0.272543	+	0.962144i	$0.587865\pi$
$468$		0			0
$469$	−5.83358e6	+	1.62383e6i	−1.22462	+	0.340886i
$470$		−	1.68109e6i		−	0.351031i
$471$		0			0
$472$			591567.i			0.122222i
$473$			3.98864e6i			0.819732i
$474$		0			0
$475$			73656.8i			0.0149789i
$476$	−3.30267e6	+	919329.i	−0.668110	+	0.185975i
$477$		0			0
$478$	2.62188e6			0.524859
$479$	−431057.			−0.0858412			−0.0429206	−	0.999078i	$-0.513666\pi$
$479$	−431057.			−0.0858412			−0.0429206	+	0.999078i	$0.513666\pi$
$480$		0			0
$481$			2.15482e6i			0.424666i
$482$	1.67298e6			0.327999
$483$		0			0
$484$	−1.56939e6			−0.304522
$485$			601978.i			0.116205i
$486$		0			0
$487$	−4.46936e6			−0.853930			−0.426965	−	0.904268i	$-0.640417\pi$
$487$	−4.46936e6			−0.853930			−0.426965	+	0.904268i	$0.640417\pi$
$488$	−1.25730e6			−0.238995
$489$		0			0
$490$	−868390.	−	1.43898e6i	−0.163390	−	0.270747i
$491$			8.72553e6i			1.63338i	0.577074	+	0.816692i	$0.304194\pi$
$491$			8.72553e6i			1.63338i	−0.577074	+	0.816692i	$0.695806\pi$
$492$		0			0
$493$			1.93807e6i			0.359130i
$494$			121217.i			0.0223484i
$495$		0			0
$496$			1.62010e6i			0.295691i
$497$	−1.26555e6	−	4.54646e6i	−0.229820	−	0.825624i
$498$		0			0
$499$	−4.39068e6			−0.789370			−0.394685	−	0.918816i	$-0.629146\pi$
$499$	−4.39068e6			−0.789370			−0.394685	+	0.918816i	$0.629146\pi$
$500$	−250000.			−0.0447214
$501$		0			0
$502$			2.50677e6i			0.443972i
$503$	−6.08246e6			−1.07191			−0.535956	−	0.844246i	$-0.680049\pi$
$503$	−6.08246e6			−1.07191			−0.535956	+	0.844246i	$0.680049\pi$
$504$		0			0
$505$	1.17353e6			0.204769
$506$			3.24076e6i			0.562693i
$507$		0			0
$508$	−1.38866e6			−0.238746
$509$	1.05519e7			1.80525			0.902624	−	0.430429i	$-0.141638\pi$
$509$	1.05519e7			1.80525			0.902624	+	0.430429i	$0.141638\pi$
$510$		0			0
$511$	−935164.	−	3.35956e6i	−0.158429	−	0.569154i
$512$		−	262144.i		−	0.0441942i
$513$		0			0
$514$			296099.i			0.0494344i
$515$		−	397281.i		−	0.0660055i
$516$		0			0
$517$		−	4.21828e6i		−	0.694079i
$518$	1.16532e6	+	4.18639e6i	0.190819	+	0.685512i
$519$		0			0
$520$	−411425.			−0.0667240
$521$	−9.28639e6			−1.49883			−0.749415	−	0.662100i	$-0.769665\pi$
$521$	−9.28639e6			−1.49883			−0.749415	+	0.662100i	$0.769665\pi$
$522$		0			0
$523$			2.11426e6i			0.337990i	0.985617	+	0.168995i	$0.0540522\pi$
$523$			2.11426e6i			0.337990i	−0.985617	+	0.168995i	$0.945948\pi$
$524$	−3.56231e6			−0.566766
$525$		0			0
$526$	8.48648e6			1.33741
$527$		−	1.04594e7i		−	1.64052i
$528$		0			0
$529$	−3.98884e6			−0.619737
$530$	−233718.			−0.0361413
$531$		0			0
$532$	65553.9	+	235501.i	0.0100420	+	0.0360756i
$533$		−	3.76132e6i		−	0.573485i
$534$		0			0
$535$		−	806499.i		−	0.121820i
$536$			2.98934e6i			0.449431i
$537$		0			0
$538$		−	3.12761e6i		−	0.465862i
$539$	−2.17902e6	−	3.61076e6i	−0.323064	−	0.535337i
$540$		0			0
$541$	−8.45504e6			−1.24200			−0.621001	−	0.783810i	$-0.713274\pi$
$541$	−8.45504e6			−1.24200			−0.621001	+	0.783810i	$0.713274\pi$
$542$	6.13919e6			0.897663
$543$		0			0
$544$			1.69241e6i			0.245193i
$545$	−2.07095e6			−0.298661
$546$		0			0
$547$	1.35037e7			1.92968			0.964839	−	0.262842i	$-0.0846598\pi$
$547$	1.35037e7			1.92968			0.964839	+	0.262842i	$0.0846598\pi$
$548$			3.48946e6i			0.496372i
$549$		0			0
$550$	−627315.			−0.0884258
$551$	138196.			0.0193918
$552$		0			0
$553$	4.69584e6	−	1.30713e6i	0.652981	−	0.181763i
$554$		−	252109.i		−	0.0348991i
$555$		0			0
$556$		−	6.52014e6i		−	0.894479i
$557$		−	3.34565e6i		−	0.456923i	−0.973553	−	0.228461i	$-0.926631\pi$
$557$		−	3.34565e6i		−	0.456923i	0.973553	−	0.228461i	$-0.0733695\pi$
$558$		0			0
$559$		−	4.08742e6i		−	0.553248i
$560$	−799318.	+	222498.i	−0.107708	+	0.0299816i
$561$		0			0
$562$	4.50518e6			0.601688
$563$	8.21303e6			1.09202			0.546012	−	0.837777i	$-0.316145\pi$
$563$	8.21303e6			1.09202			0.546012	+	0.837777i	$0.316145\pi$
$564$		0			0
$565$			5.46691e6i			0.720478i
$566$	713564.			0.0936250
$567$		0			0
$568$	−2.32977e6			−0.303000
$569$			8.77528e6i			1.13627i	0.822937	+	0.568133i	$0.192334\pi$
$569$			8.77528e6i			1.13627i	−0.822937	+	0.568133i	$0.807666\pi$
$570$		0			0
$571$	683364.			0.0877126			0.0438563	−	0.999038i	$-0.486036\pi$
$571$	683364.			0.0877126			0.0438563	+	0.999038i	$0.486036\pi$
$572$	−1.03237e6			−0.131931
$573$		0			0
$574$	−2.03411e6	−	7.30750e6i	−0.257688	−	0.925741i
$575$		−	2.01800e6i		−	0.254538i
$576$		0			0
$577$			1.99601e6i			0.249588i	0.992183	+	0.124794i	$0.0398269\pi$
$577$			1.99601e6i			0.249588i	−0.992183	+	0.124794i	$0.960173\pi$
$578$		−	5.24682e6i		−	0.653245i
$579$		0			0
$580$			469055.i			0.0578967i
$581$	−1.13446e7	+	3.15788e6i	−1.39428	+	0.388110i
$582$		0			0
$583$	−586460.			−0.0714607
$584$	−1.72156e6			−0.208877
$585$		0			0
$586$			3.54971e6i			0.427020i
$587$	6.98045e6			0.836157			0.418079	−	0.908411i	$-0.362704\pi$
$587$	6.98045e6			0.836157			0.418079	+	0.908411i	$0.362704\pi$
$588$		0			0
$589$	−745822.			−0.0885823
$590$		−	924324.i		−	0.109319i
$591$		0			0
$592$	2.14526e6			0.251580
$593$	105524.			0.0123230			0.00616148	−	0.999981i	$-0.498039\pi$
$593$	105524.			0.0123230			0.00616148	+	0.999981i	$0.498039\pi$
$594$		0			0
$595$	5.16042e6	−	1.43645e6i	0.597575	−	0.166341i
$596$			276655.i			0.0319024i
$597$		0			0
$598$		−	3.32103e6i		−	0.379769i
$599$			1.58816e6i			0.180854i	0.995903	+	0.0904268i	$0.0288231\pi$
$599$			1.58816e6i			0.180854i	−0.995903	+	0.0904268i	$0.971177\pi$
$600$		0			0
$601$			644521.i			0.0727865i	0.999338	+	0.0363932i	$0.0115869\pi$
$601$			644521.i			0.0727865i	−0.999338	+	0.0363932i	$0.988413\pi$
$602$	−2.21047e6	−	7.94107e6i	−0.248596	−	0.893075i
$603$		0			0
$604$	4.18739e6			0.467037
$605$	2.45218e6			0.272373
$606$		0			0
$607$			1.11241e7i			1.22544i	0.790299	+	0.612722i	$0.209925\pi$
$607$			1.11241e7i			1.22544i	−0.790299	+	0.612722i	$0.790075\pi$
$608$	120679.			0.0132396
$609$		0			0
$610$	1.96453e6			0.213763
$611$			4.32275e6i			0.468443i
$612$		0			0
$613$	−396382.			−0.0426052			−0.0213026	−	0.999773i	$-0.506781\pi$
$613$	−396382.			−0.0426052			−0.0213026	+	0.999773i	$0.506781\pi$
$614$	−2.23839e6			−0.239615
$615$		0			0
$616$	−2.00570e6	+	558304.i	−0.212968	+	0.0592815i
$617$		−	1.10297e7i		−	1.16641i	−0.812325	−	0.583205i	$-0.801798\pi$
$617$		−	1.10297e7i		−	1.16641i	0.812325	−	0.583205i	$-0.198202\pi$
$618$		0			0
$619$		−	5.83730e6i		−	0.612330i	−0.951979	−	0.306165i	$-0.900954\pi$
$619$		−	5.83730e6i		−	0.612330i	0.951979	−	0.306165i	$-0.0990458\pi$
$620$		−	2.53141e6i		−	0.264474i
$621$		0			0
$622$		−	6.76430e6i		−	0.701047i
$623$	−7.21158e6	+	2.00741e6i	−0.744407	+	0.207213i
$624$		0			0
$625$	390625.			0.0400000
$626$	514427.			0.0524672
$627$		0			0
$628$			3.55140e6i			0.359336i
$629$	−1.38499e7			−1.39579
$630$		0			0
$631$	1.24844e6			0.124822			0.0624112	−	0.998051i	$-0.480121\pi$
$631$	1.24844e6			0.124822			0.0624112	+	0.998051i	$0.480121\pi$
$632$		−	2.40632e6i		−	0.239641i
$633$		0			0
$634$	−1.71722e6			−0.169669
$635$	2.16978e6			0.213541
$636$		0			0
$637$	2.23298e6	+	3.70019e6i	0.218040	+	0.361306i
$638$			1.17698e6i			0.114477i
$639$		0			0
$640$			409600.i			0.0395285i
$641$			1.44761e7i			1.39158i	0.718247	+	0.695789i	$0.244945\pi$
$641$			1.44761e7i			1.39158i	−0.718247	+	0.695789i	$0.755055\pi$
$642$		0			0
$643$		−	1.34882e7i		−	1.28655i	−0.765634	−	0.643276i	$-0.777575\pi$
$643$		−	1.34882e7i		−	1.28655i	0.765634	−	0.643276i	$-0.222425\pi$
$644$	−1.79600e6	−	6.45211e6i	−0.170645	−	0.613037i
$645$		0			0
$646$	−779110.			−0.0734543
$647$	5.98310e6			0.561908			0.280954	−	0.959721i	$-0.409349\pi$
$647$	5.98310e6			0.561908			0.280954	+	0.959721i	$0.409349\pi$
$648$		0			0
$649$		−	2.31937e6i		−	0.216151i
$650$	642851.			0.0596797
$651$		0			0
$652$	−1.79421e6			−0.165293
$653$		−	1.23357e7i		−	1.13209i	−0.824375	−	0.566044i	$-0.808473\pi$
$653$		−	1.23357e7i		−	1.13209i	0.824375	−	0.566044i	$-0.191527\pi$
$654$		0			0
$655$	5.56611e6			0.506931
$656$	−3.74463e6			−0.339742
$657$		0			0
$658$	2.33773e6	+	8.39826e6i	0.210489	+	0.756179i
$659$			9.01551e6i			0.808680i	0.914609	+	0.404340i	$0.132499\pi$
$659$			9.01551e6i			0.808680i	−0.914609	+	0.404340i	$0.867501\pi$
$660$		0			0
$661$		−	1.47810e7i		−	1.31583i	−0.753092	−	0.657915i	$-0.771439\pi$
$661$		−	1.47810e7i		−	1.31583i	0.753092	−	0.657915i	$-0.228561\pi$
$662$		−	5.12385e6i		−	0.454414i
$663$		0			0
$664$			5.81339e6i			0.511693i
$665$	−102428.	−	367970.i	−0.00898182	−	0.0322670i
$666$		0			0
$667$	−3.78622e6			−0.329527
$668$	−1.08865e7			−0.943945
$669$		0			0
$670$		−	4.67085e6i		−	0.401984i
$671$	4.92951e6			0.422666
$672$		0			0
$673$	−1.73688e7			−1.47819			−0.739097	−	0.673599i	$-0.764747\pi$
$673$	−1.73688e7			−1.47819			−0.739097	+	0.673599i	$0.764747\pi$
$674$			1.09792e7i			0.930938i
$675$		0			0
$676$	−4.88275e6			−0.410958
$677$	−3.84201e6			−0.322171			−0.161086	−	0.986940i	$-0.551500\pi$
$677$	−3.84201e6			−0.322171			−0.161086	+	0.986940i	$0.551500\pi$
$678$		0			0
$679$	−837116.	−	3.00732e6i	−0.0696805	−	0.250326i
$680$		−	2.64439e6i		−	0.219307i
$681$		0			0
$682$		−	6.35196e6i		−	0.522934i
$683$		−	1.53924e7i		−	1.26257i	−0.775552	−	0.631284i	$-0.782528\pi$
$683$		−	1.53924e7i		−	1.26257i	0.775552	−	0.631284i	$-0.217472\pi$
$684$		0			0
$685$		−	5.45228e6i		−	0.443968i
$686$	6.33931e6	+	5.98115e6i	0.514318	+	0.485260i
$687$		0			0
$688$	−4.06930e6			−0.327754
$689$	600985.			0.0482298
$690$		0			0
$691$			2.18384e6i			0.173990i	0.996209	+	0.0869952i	$0.0277265\pi$
$691$			2.18384e6i			0.173990i	−0.996209	+	0.0869952i	$0.972274\pi$
$692$	−7.31538e6			−0.580726
$693$		0			0
$694$	−7.85840e6			−0.619349
$695$			1.01877e7i			0.800047i
$696$		0			0
$697$	2.41755e7			1.88492
$698$	5.29704e6			0.411524
$699$		0			0
$700$	1.24893e6	−	347652.i	0.0963373	−	0.0268164i
$701$			7.56984e6i			0.581824i	0.956750	+	0.290912i	$0.0939588\pi$
$701$			7.56984e6i			0.581824i	−0.956750	+	0.290912i	$0.906041\pi$
$702$		0			0
$703$			987582.i			0.0753676i
$704$			1.02779e6i			0.0781581i
$705$		0			0
$706$		−	1.70795e7i		−	1.28963i
$707$	−5.86264e6	+	1.63192e6i	−0.441108	+	0.122786i
$708$		0			0
$709$	−7.94088e6			−0.593271			−0.296636	−	0.954991i	$-0.595865\pi$
$709$	−7.94088e6			−0.593271			−0.296636	+	0.954991i	$0.595865\pi$
$710$	3.64027e6			0.271012
$711$		0			0
$712$			3.69548e6i			0.273194i
$713$	2.04336e7			1.50529
$714$		0			0
$715$	1.61308e6			0.118002
$716$		−	6.88377e6i		−	0.501815i
$717$		0			0
$718$	8.59829e6			0.622445
$719$	−6.60018e6			−0.476139			−0.238069	−	0.971248i	$-0.576515\pi$
$719$	−6.60018e6			−0.476139			−0.238069	+	0.971248i	$0.576515\pi$
$720$		0			0
$721$	552463.	+	1.98471e6i	0.0395790	+	0.142187i
$722$		−	9.84884e6i		−	0.703141i
$723$		0			0
$724$			9.79519e6i			0.694491i
$725$		−	732898.i		−	0.0517844i
$726$		0			0
$727$			1.48905e7i			1.04490i	0.852670	+	0.522450i	$0.174982\pi$
$727$			1.48905e7i			1.04490i	−0.852670	+	0.522450i	$0.825018\pi$
$728$	2.05537e6	−	572131.i	0.143735	−	0.0400099i
$729$		0			0
$730$	2.68994e6			0.186825
$731$	2.62715e7			1.81841
$732$		0			0
$733$		−	2.92924e6i		−	0.201370i	−0.994918	−	0.100685i	$-0.967897\pi$
$733$		−	2.92924e6i		−	0.201370i	0.994918	−	0.100685i	$-0.0321035\pi$
$734$	1.20284e7			0.824079
$735$		0			0
$736$	−3.30630e6			−0.224982
$737$		−	1.17204e7i		−	0.794827i
$738$		0			0
$739$	−1.34133e7			−0.903490			−0.451745	−	0.892147i	$-0.649198\pi$
$739$	−1.34133e7			−0.903490			−0.451745	+	0.892147i	$0.649198\pi$
$740$	−3.35197e6			−0.225020
$741$		0			0
$742$	1.16760e6	−	325011.i	0.0778544	−	0.0216715i
$743$			1.84546e7i			1.22640i	0.789926	+	0.613202i	$0.210119\pi$
$743$			1.84546e7i			1.22640i	−0.789926	+	0.613202i	$0.789881\pi$
$744$		0			0
$745$		−	432274.i		−	0.0285344i
$746$			1.43965e7i			0.947131i
$747$		0			0
$748$		−	6.63546e6i		−	0.433628i
$749$	1.12153e6	+	4.02906e6i	0.0730474	+	0.262421i
$750$		0			0
$751$	−7.69435e6			−0.497819			−0.248910	−	0.968527i	$-0.580072\pi$
$751$	−7.69435e6			−0.497819			−0.248910	+	0.968527i	$0.580072\pi$
$752$	4.30358e6			0.277514
$753$		0			0
$754$		−	1.20613e6i		−	0.0772619i
$755$	−6.54280e6			−0.417731
$756$		0			0
$757$	2.98178e7			1.89119			0.945596	−	0.325343i	$-0.105480\pi$
$757$	2.98178e7			1.89119			0.945596	+	0.325343i	$0.105480\pi$
$758$			1.07025e7i			0.676571i
$759$		0			0
$760$	−188562.			−0.0118418
$761$	−989967.			−0.0619668			−0.0309834	−	0.999520i	$-0.509864\pi$
$761$	−989967.			−0.0619668			−0.0309834	+	0.999520i	$0.509864\pi$
$762$		0			0
$763$	1.03459e7	−	2.87989e6i	0.643366	−	0.179087i
$764$		−	775277.i		−	0.0480534i
$765$		0			0
$766$			1.18219e7i			0.727976i
$767$			2.37681e6i			0.145883i
$768$		0			0
$769$		−	2.70691e7i		−	1.65066i	−0.564648	−	0.825332i	$-0.690988\pi$
$769$		−	2.70691e7i		−	1.65066i	0.564648	−	0.825332i	$-0.309012\pi$
$770$	3.13390e6	−	872350.i	0.190484	−	0.0530230i
$771$		0			0
$772$	−3.25920e6			−0.196819
$773$	7.03911e6			0.423710			0.211855	−	0.977301i	$-0.432049\pi$
$773$	7.03911e6			0.423710			0.211855	+	0.977301i	$0.432049\pi$
$774$		0			0
$775$			3.95533e6i			0.236553i
$776$	−1.54106e6			−0.0918684
$777$		0			0
$778$	−3.57016e6			−0.211465
$779$		−	1.72386e6i		−	0.101779i
$780$		0			0
$781$	9.13439e6			0.535861
$782$	2.13455e7			1.24822
$783$		0			0
$784$	3.68378e6	−	2.22308e6i	0.214044	−	0.129171i
$785$		−	5.54907e6i		−	0.321400i
$786$		0			0
$787$		−	2.34090e7i		−	1.34725i	−0.739076	−	0.673623i	$-0.764737\pi$
$787$		−	2.34090e7i		−	1.34725i	0.739076	−	0.673623i	$-0.235263\pi$
$788$			1.21912e7i			0.699409i
$789$		0			0
$790$			3.75988e6i			0.214341i
$791$	−7.60233e6	−	2.73112e7i	−0.432022	−	1.55203i
$792$		0			0
$793$	−5.05159e6			−0.285263
$794$	2.31006e7			1.30038
$795$		0			0
$796$			1.32540e7i			0.741422i
$797$	3.71917e6			0.207396			0.103698	−	0.994609i	$-0.466932\pi$
$797$	3.71917e6			0.207396			0.103698	+	0.994609i	$0.466932\pi$
$798$		0			0
$799$	−2.77840e7			−1.53967
$800$		−	640000.i		−	0.0353553i
$801$		0			0
$802$	6.96614e6			0.382434
$803$	6.74976e6			0.369402
$804$		0			0
$805$	2.80626e6	+	1.00814e7i	0.152629	+	0.548317i
$806$			6.50927e6i			0.352935i
$807$		0			0
$808$			3.00423e6i			0.161884i
$809$			2.99575e7i			1.60929i	0.593757	+	0.804645i	$0.297644\pi$
$809$			2.99575e7i			1.60929i	−0.593757	+	0.804645i	$0.702356\pi$
$810$		0			0
$811$		−	2.53853e7i		−	1.35528i	−0.735393	−	0.677641i	$-0.763003\pi$
$811$		−	2.53853e7i		−	1.35528i	0.735393	−	0.677641i	$-0.236997\pi$
$812$	−652272.	−	2.34328e6i	−0.0347167	−	0.124719i
$813$		0			0
$814$	−8.41096e6			−0.444923
$815$	2.80345e6			0.147843
$816$		0			0
$817$		−	1.87332e6i		−	0.0981878i
$818$	1.53208e6			0.0800565
$819$		0			0
$820$	5.85099e6			0.303875
$821$			4.22769e6i			0.218900i	0.993992	+	0.109450i	$0.0349089\pi$
$821$			4.22769e6i			0.218900i	−0.993992	+	0.109450i	$0.965091\pi$
$822$		0			0
$823$	−2.93521e7			−1.51056			−0.755282	−	0.655400i	$-0.772500\pi$
$823$	−2.93521e7			−1.51056			−0.755282	+	0.655400i	$0.772500\pi$
$824$	1.01704e6			0.0521819
$825$		0			0
$826$	1.28537e6	+	4.61768e6i	0.0655510	+	0.235491i
$827$			6.82203e6i			0.346856i	0.984847	+	0.173428i	$0.0554845\pi$
$827$			6.82203e6i			0.346856i	−0.984847	+	0.173428i	$0.944516\pi$
$828$		0			0
$829$		−	3.86069e7i		−	1.95110i	−0.219785	−	0.975548i	$-0.570535\pi$
$829$		−	3.86069e7i		−	1.95110i	0.219785	−	0.975548i	$-0.429465\pi$
$830$		−	9.08343e6i		−	0.457672i
$831$		0			0
$832$		−	1.05325e6i		−	0.0527499i
$833$	−2.37826e7	+	1.43523e7i	−1.18753	+	0.716652i
$834$		0			0
$835$	1.70101e7			0.844290
$836$	−473150.			−0.0234144
$837$		0			0
$838$			1.02643e7i			0.504917i
$839$	2.42201e7			1.18788			0.593938	−	0.804511i	$-0.297572\pi$
$839$	2.42201e7			1.18788			0.593938	+	0.804511i	$0.297572\pi$
$840$		0			0
$841$	1.91361e7			0.932959
$842$			1.06487e7i			0.517626i
$843$		0			0
$844$	−1.04087e7			−0.502968
$845$	7.62930e6			0.367572
$846$		0			0
$847$	−1.22504e7	+	3.41002e6i	−0.586737	+	0.163324i
$848$		−	598319.i		−	0.0285722i
$849$		0			0
$850$			4.13186e6i			0.196154i
$851$		−	2.70571e7i		−	1.28073i
$852$		0			0
$853$		−	3.76643e7i		−	1.77238i	−0.463320	−	0.886191i	$-0.653342\pi$
$853$		−	3.76643e7i		−	1.77238i	0.463320	−	0.886191i	$-0.346658\pi$
$854$	−9.81426e6	+	2.73189e6i	−0.460482	+	0.128180i
$855$		0			0
$856$	2.06464e6			0.0963074
$857$	2.10162e7			0.977467			0.488734	−	0.872433i	$-0.337459\pi$
$857$	2.10162e7			0.977467			0.488734	+	0.872433i	$0.337459\pi$
$858$		0			0
$859$			2.70614e7i			1.25132i	0.780098	+	0.625658i	$0.215169\pi$
$859$			2.70614e7i			1.25132i	−0.780098	+	0.625658i	$0.784831\pi$
$860$	6.35828e6			0.293152
$861$		0			0
$862$	434645.			0.0199235
$863$			2.02727e7i			0.926583i	0.886206	+	0.463292i	$0.153332\pi$
$863$			2.02727e7i			0.926583i	−0.886206	+	0.463292i	$0.846668\pi$
$864$		0			0
$865$	1.14303e7			0.519417
$866$	2.32249e7			1.05235
$867$		0			0
$868$	3.52020e6	+	1.26463e7i	0.158587	+	0.569722i
$869$			9.43450e6i			0.423809i
$870$		0			0
$871$			1.20106e7i			0.536439i
$872$		−	5.30164e6i		−	0.236112i
$873$		0			0
$874$		−	1.52207e6i		−	0.0673995i
$875$	−1.95146e6	+	543207.i	−0.0861667	+	0.0239853i
$876$		0			0
$877$	4.00096e7			1.75657			0.878285	−	0.478138i	$-0.158688\pi$
$877$	4.00096e7			1.75657			0.878285	+	0.478138i	$0.158688\pi$
$878$	3.03477e7			1.32859
$879$		0			0
$880$		−	1.60593e6i		−	0.0699067i
$881$	8.08763e6			0.351060			0.175530	−	0.984474i	$-0.443836\pi$
$881$	8.08763e6			0.351060			0.175530	+	0.984474i	$0.443836\pi$
$882$		0			0
$883$	3.10207e6			0.133891			0.0669453	−	0.997757i	$-0.478675\pi$
$883$	3.10207e6			0.133891			0.0669453	+	0.997757i	$0.478675\pi$
$884$			6.79979e6i			0.292661i
$885$		0			0
$886$	−6.50426e6			−0.278364
$887$	4.62219e7			1.97260			0.986300	−	0.164963i	$-0.0527506\pi$
$887$	4.62219e7			1.97260			0.986300	+	0.164963i	$0.0527506\pi$
$888$		0			0
$889$	−1.08396e7	+	3.01731e6i	−0.460003	+	0.128046i
$890$		−	5.77419e6i		−	0.244352i
$891$		0			0
$892$			1.39554e7i			0.587259i
$893$			1.98118e6i			0.0831370i
$894$		0			0
$895$			1.07559e7i			0.448837i
$896$	−569594.	−	2.04625e6i	−0.0237026	−	0.0851510i
$897$		0			0
$898$	−1.57166e7			−0.650381
$899$	7.42106e6			0.306243
$900$		0			0
$901$			3.86277e6i			0.158521i
$902$	1.46817e7			0.600840
$903$		0			0
$904$	−1.39953e7			−0.569588
$905$		−	1.53050e7i		−	0.621172i
$906$		0			0
$907$	2.20005e7			0.888004			0.444002	−	0.896026i	$-0.353558\pi$
$907$	2.20005e7			0.888004			0.444002	+	0.896026i	$0.353558\pi$
$908$	−1.09714e7			−0.441617
$909$		0			0
$910$	−3.21152e6	+	893955.i	−0.128560	+	0.0357859i
$911$		−	2.23313e7i		−	0.891492i	−0.895160	−	0.445746i	$-0.852939\pi$
$911$		−	2.23313e7i		−	0.891492i	0.895160	−	0.445746i	$-0.147061\pi$
$912$		0			0
$913$		−	2.27927e7i		−	0.904937i
$914$		−	1.30900e7i		−	0.518292i
$915$		0			0
$916$			8.66985e6i			0.341407i
$917$	−2.78068e7	+	7.74029e6i	−1.09201	+	0.303972i
$918$		0			0
$919$	−1.05602e6			−0.0412462			−0.0206231	−	0.999787i	$-0.506565\pi$
$919$	−1.05602e6			−0.0412462			−0.0206231	+	0.999787i	$0.506565\pi$
$920$	5.16609e6			0.201230
$921$		0			0
$922$			9.11165e6i			0.352996i
$923$	−9.36061e6			−0.361660
$924$		0			0
$925$	5.23745e6			0.201264
$926$		−	6.99574e6i		−	0.268106i
$927$		0			0
$928$	−1.20078e6			−0.0457713
$929$	−3.87822e7			−1.47432			−0.737162	−	0.675716i	$-0.763835\pi$
$929$	−3.87822e7			−1.47432			−0.737162	+	0.675716i	$0.763835\pi$
$930$		0			0
$931$	1.02341e6	+	1.69585e6i	0.0386967	+	0.0641228i
$932$			1.48090e7i			0.558452i
$933$		0			0
$934$			1.02758e7i			0.385434i
$935$			1.03679e7i			0.387848i
$936$		0			0
$937$		−	3.16361e7i		−	1.17716i	−0.808440	−	0.588579i	$-0.799688\pi$
$937$		−	3.16361e7i		−	1.17716i	0.808440	−	0.588579i	$-0.200312\pi$
$938$	6.49532e6	+	2.33343e7i	0.241043	+	0.865941i
$939$		0			0
$940$	−6.72434e6			−0.248216
$941$	2.56952e7			0.945972			0.472986	−	0.881070i	$-0.343176\pi$
$941$	2.56952e7			0.945972			0.472986	+	0.881070i	$0.343176\pi$
$942$		0			0
$943$			4.72293e7i			1.72955i
$944$	2.36627e6			0.0864240
$945$		0			0
$946$	1.59546e7			0.579638
$947$		−	3.15439e7i		−	1.14299i	−0.820607	−	0.571493i	$-0.806364\pi$
$947$		−	3.15439e7i		−	1.14299i	0.820607	−	0.571493i	$-0.193636\pi$
$948$		0			0
$949$	−6.91692e6			−0.249314
$950$	294627.			0.0105917
$951$		0			0
$952$	3.67731e6	+	1.32107e7i	0.131504	+	0.472425i
$953$		−	4.31186e7i		−	1.53792i	−0.639299	−	0.768958i	$-0.720775\pi$
$953$		−	4.31186e7i		−	1.53792i	0.639299	−	0.768958i	$-0.279225\pi$
$954$		0			0
$955$			1.21137e6i			0.0429802i
$956$		−	1.04875e7i		−	0.371131i
$957$		0			0
$958$			1.72423e6i			0.0606989i
$959$	7.58200e6	+	2.72382e7i	0.266218	+	0.956382i
$960$		0			0
$961$	−1.14210e7			−0.398930
$962$	8.61927e6			0.300284
$963$		0			0
$964$		−	6.69192e6i		−	0.231930i
$965$	5.09250e6			0.176041
$966$		0			0
$967$	1.47439e7			0.507044			0.253522	−	0.967330i	$-0.418411\pi$
$967$	1.47439e7			0.507044			0.253522	+	0.967330i	$0.418411\pi$
$968$			6.27758e6i			0.215330i
$969$		0			0
$970$	2.40791e6			0.0821696
$971$	−7.88048e6			−0.268228			−0.134114	−	0.990966i	$-0.542819\pi$
$971$	−7.88048e6			−0.268228			−0.134114	+	0.990966i	$0.542819\pi$
$972$		0			0
$973$	−1.41672e7	−	5.08952e7i	−0.479734	−	1.72343i
$974$			1.78774e7i			0.603820i
$975$		0			0
$976$			5.02919e6i			0.168995i
$977$		−	3.16243e7i		−	1.05995i	−0.848014	−	0.529974i	$-0.822202\pi$
$977$		−	3.16243e7i		−	1.05995i	0.848014	−	0.529974i	$-0.177798\pi$
$978$		0			0
$979$		−	1.44889e7i		−	0.483147i
$980$	−5.75590e6	+	3.47356e6i	−0.191447	+	0.115534i
$981$		0			0
$982$	3.49021e7			1.15498
$983$	2.88301e7			0.951618			0.475809	−	0.879549i	$-0.342155\pi$
$983$	2.88301e7			0.951618			0.475809	+	0.879549i	$0.342155\pi$
$984$		0			0
$985$		−	1.90488e7i		−	0.625570i
$986$	7.75227e6			0.253943
$987$		0			0
$988$	484868.			0.0158027
$989$			5.13241e7i			1.66852i
$990$		0			0
$991$	−4.63270e6			−0.149848			−0.0749238	−	0.997189i	$-0.523871\pi$
$991$	−4.63270e6			−0.149848			−0.0749238	+	0.997189i	$0.523871\pi$
$992$	6.48041e6			0.209085
$993$		0			0
$994$	−1.81858e7	+	5.06220e6i	−0.583805	+	0.162507i
$995$		−	2.07094e7i		−	0.663148i
$996$		0			0
$997$			2.04363e7i			0.651125i	0.945521	+	0.325562i	$0.105554\pi$
$997$			2.04363e7i			0.651125i	−0.945521	+	0.325562i	$0.894446\pi$
$998$			1.75627e7i			0.558169i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.6.b.b.251.1	yes	24
3.2	odd	2		630.6.b.a.251.13	yes	24
7.6	odd	2		630.6.b.a.251.1	✓	24
21.20	even	2	inner	630.6.b.b.251.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.6.b.a.251.1	✓	24	7.6	odd	2
630.6.b.a.251.13	yes	24	3.2	odd	2
630.6.b.b.251.1	yes	24	1.1	even	1	trivial
630.6.b.b.251.13	yes	24	21.20	even	2	inner

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	630.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -16.0000 q^{4} +25.0000 q^{5} +(-124.893 + 34.7652i) q^{7} +64.0000i q^{8} -100.000i q^{10} -250.926i q^{11} +257.140i q^{13} +(139.061 + 499.574i) q^{14} +256.000 q^{16} -1652.74 q^{17} +117.851i q^{19} -400.000 q^{20} -1003.70 q^{22} -3228.81i q^{23} +625.000 q^{25} +1028.56 q^{26} +(1998.30 - 556.244i) q^{28} -1172.64i q^{29} +6328.52i q^{31} -1024.00i q^{32} +6610.97i q^{34} +(-3122.34 + 869.131i) q^{35} +8379.92 q^{37} +471.404 q^{38} +1600.00i q^{40} -14627.5 q^{41} -15895.7 q^{43} +4014.82i q^{44} -12915.2 q^{46} +16810.9 q^{47} +(14389.8 - 8683.90i) q^{49} -2500.00i q^{50} -4114.25i q^{52} -2337.18i q^{53} -6273.15i q^{55} +(-2224.98 - 7993.18i) q^{56} -4690.55 q^{58} +9243.24 q^{59} +19645.3i q^{61} +25314.1 q^{62} -4096.00 q^{64} +6428.51i q^{65} +46708.5 q^{67} +26443.9 q^{68} +(3476.52 + 12489.3i) q^{70} +36402.7i q^{71} +26899.4i q^{73} -33519.7i q^{74} -1885.62i q^{76} +(8723.50 + 31339.0i) q^{77} -37598.8 q^{79} +6400.00 q^{80} +58509.9i q^{82} +90834.3 q^{83} -41318.6 q^{85} +63582.8i q^{86} +16059.3 q^{88} +57741.9 q^{89} +(-8939.55 - 32115.2i) q^{91} +51660.9i q^{92} -67243.4i q^{94} +2946.27i q^{95} +24079.1i q^{97} +(-34735.6 - 57559.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 384 q^{4} + 600 q^{5} - 196 q^{7} + 6144 q^{16} - 9600 q^{20} + 15000 q^{25} - 3872 q^{26} + 3136 q^{28} - 4900 q^{35} - 33512 q^{37} - 10208 q^{38} + 44968 q^{41} + 8016 q^{43} - 1312 q^{46} + 47240 q^{47}+ \cdots + 257936 q^{98}+O(q^{100}) \) 24 * q - 384 * q^4 + 600 * q^5 - 196 * q^7 + 6144 * q^16 - 9600 * q^20 + 15000 * q^25 - 3872 * q^26 + 3136 * q^28 - 4900 * q^35 - 33512 * q^37 - 10208 * q^38 + 44968 * q^41 + 8016 * q^43 - 1312 * q^46 + 47240 * q^47 - 31724 * q^49 + 35168 * q^58 - 110400 * q^59 + 20320 * q^62 - 98304 * q^64 - 92032 * q^67 + 107212 * q^77 + 90632 * q^79 + 153600 * q^80 - 211664 * q^83 + 286888 * q^89 - 173684 * q^91 + 257936 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more