LMFDB - Embedded newform 630.6.g.h.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,6,Mod(379,630)]

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, 0]))

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

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

chi := DirichletCharacter("630.379");

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.g (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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 1831x^{8} + 1077303x^{6} + 232401393x^{4} + 12760557696x^{2} + 187121995776 $ x^10 + 1831x^8 + 1077303x^6 + 232401393x^4 + 12760557696x^2 + 187121995776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{6}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.2
Root			$6.91835i$ of defining polynomial
Character	$\chi$	$=$	630.379
Dual form			630.6.g.h.379.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000i q^{2} -16.0000 q^{4} +(-30.1818 + 47.0538i) q^{5} +49.0000i q^{7} +64.0000i q^{8} +(188.215 + 120.727i) q^{10} -337.260 q^{11} -24.3276i q^{13} +196.000 q^{14} +256.000 q^{16} -1445.07i q^{17} +1197.44 q^{19} +(482.908 - 752.861i) q^{20} +1349.04i q^{22} -2247.26i q^{23} +(-1303.12 - 2840.33i) q^{25} -97.3103 q^{26} -784.000i q^{28} +1182.78 q^{29} +10458.6 q^{31} -1024.00i q^{32} -5780.27 q^{34} +(-2305.64 - 1478.91i) q^{35} +825.831i q^{37} -4789.75i q^{38} +(-3011.44 - 1931.63i) q^{40} -2843.58 q^{41} -9617.84i q^{43} +5396.16 q^{44} -8989.03 q^{46} +10435.0i q^{47} -2401.00 q^{49} +(-11361.3 + 5212.48i) q^{50} +389.241i q^{52} +33934.4i q^{53} +(10179.1 - 15869.4i) q^{55} -3136.00 q^{56} -4731.12i q^{58} +18857.8 q^{59} -26489.1 q^{61} -41834.6i q^{62} -4096.00 q^{64} +(1144.71 + 734.250i) q^{65} +10647.5i q^{67} +23121.1i q^{68} +(-5915.63 + 9222.55i) q^{70} -47989.5 q^{71} +37699.4i q^{73} +3303.32 q^{74} -19159.0 q^{76} -16525.7i q^{77} -62335.6 q^{79} +(-7726.53 + 12045.8i) q^{80} +11374.3i q^{82} -369.796i q^{83} +(67995.9 + 43614.7i) q^{85} -38471.4 q^{86} -21584.6i q^{88} +115397. q^{89} +1192.05 q^{91} +35956.1i q^{92} +41739.9 q^{94} +(-36140.8 + 56344.0i) q^{95} +136508. i q^{97} +9604.00i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 160 q^{4} + 66 q^{5} - 416 q^{10} - 1496 q^{11} + 1960 q^{14} + 2560 q^{16} + 512 q^{19} - 1056 q^{20} - 4170 q^{25} - 3648 q^{26} + 15424 q^{29} + 824 q^{31} - 6240 q^{34} + 5096 q^{35} + 6656 q^{40}+ \cdots - 215316 q^{95}+O(q^{100}) $ 10 * q - 160 * q^4 + 66 * q^5 - 416 * q^10 - 1496 * q^11 + 1960 * q^14 + 2560 * q^16 + 512 * q^19 - 1056 * q^20 - 4170 * q^25 - 3648 * q^26 + 15424 * q^29 + 824 * q^31 - 6240 * q^34 + 5096 * q^35 + 6656 * q^40 - 14964 * q^41 + 23936 * q^44 + 27616 * q^46 - 24010 * q^49 - 20496 * q^50 + 73936 * q^55 - 31360 * q^56 + 159192 * q^59 + 19508 * q^61 - 40960 * q^64 - 150936 * q^65 + 12936 * q^70 + 123856 * q^71 + 115200 * q^74 - 8192 * q^76 - 301824 * q^79 + 16896 * q^80 + 388812 * q^85 - 165344 * q^86 + 537900 * q^89 + 44688 * q^91 - 473616 * q^94 - 215316 * q^95

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
$5$	−30.1818	+	47.0538i	−0.539908	+	0.841724i
$5$	−30.1818	+	47.0538i	−0.539908	+	0.841724i
$6$		0			0
$7$			49.0000i			0.377964i
$7$			49.0000i			0.377964i
$8$			64.0000i			0.353553i
$9$		0			0
$10$	188.215	+	120.727i	0.595189	+	0.381773i
$11$	−337.260			−0.840394			−0.420197	−	0.907433i	$-0.638039\pi$
$11$	−337.260			−0.840394			−0.420197	+	0.907433i	$0.638039\pi$
$12$		0			0
$13$		−	24.3276i		−	0.0399246i	−0.999801	−	0.0199623i	$-0.993645\pi$
$13$		−	24.3276i		−	0.0399246i	0.999801	−	0.0199623i	$-0.00635462\pi$
$14$	196.000			0.267261
$15$		0			0
$16$	256.000			0.250000
$17$		−	1445.07i		−	1.21273i	−0.795185	−	0.606367i	$-0.792626\pi$
$17$		−	1445.07i		−	1.21273i	0.795185	−	0.606367i	$-0.207374\pi$
$18$		0			0
$19$	1197.44			0.760973			0.380486	−	0.924786i	$-0.375757\pi$
$19$	1197.44			0.760973			0.380486	+	0.924786i	$0.375757\pi$
$20$	482.908	−	752.861i	0.269954	−	0.420862i
$21$		0			0
$22$			1349.04i			0.594248i
$23$		−	2247.26i		−	0.885795i	−0.896572	−	0.442898i	$-0.853950\pi$
$23$		−	2247.26i		−	0.885795i	0.896572	−	0.442898i	$-0.146050\pi$
$24$		0			0
$25$	−1303.12	−	2840.33i	−0.416999	−	0.908907i
$26$	−97.3103			−0.0282310
$27$		0			0
$28$		−	784.000i		−	0.188982i
$29$	1182.78			0.261162			0.130581	−	0.991438i	$-0.458316\pi$
$29$	1182.78			0.261162			0.130581	+	0.991438i	$0.458316\pi$
$30$		0			0
$31$	10458.6			1.95466			0.977330	−	0.211721i	$-0.0679068\pi$
$31$	10458.6			1.95466			0.977330	+	0.211721i	$0.0679068\pi$
$32$		−	1024.00i		−	0.176777i
$33$		0			0
$34$	−5780.27			−0.857533
$35$	−2305.64	−	1478.91i	−0.318142	−	0.204066i
$36$		0			0
$37$			825.831i			0.0991715i	0.998770	+	0.0495857i	$0.0157901\pi$
$37$			825.831i			0.0991715i	−0.998770	+	0.0495857i	$0.984210\pi$
$38$		−	4789.75i		−	0.538089i
$39$		0			0
$40$	−3011.44	−	1931.63i	−0.297594	−	0.190886i
$41$	−2843.58			−0.264183			−0.132092	−	0.991238i	$-0.542169\pi$
$41$	−2843.58			−0.264183			−0.132092	+	0.991238i	$0.542169\pi$
$42$		0			0
$43$		−	9617.84i		−	0.793244i	−0.917982	−	0.396622i	$-0.870182\pi$
$43$		−	9617.84i		−	0.793244i	0.917982	−	0.396622i	$-0.129818\pi$
$44$	5396.16			0.420197
$45$		0			0
$46$	−8989.03			−0.626352
$47$			10435.0i			0.689043i	0.938778	+	0.344522i	$0.111959\pi$
$47$			10435.0i			0.689043i	−0.938778	+	0.344522i	$0.888041\pi$
$48$		0			0
$49$	−2401.00			−0.142857
$50$	−11361.3	+	5212.48i	−0.642694	+	0.294863i
$51$		0			0
$52$			389.241i			0.0199623i
$53$			33934.4i			1.65940i	0.558212	+	0.829698i	$0.311488\pi$
$53$			33934.4i			1.65940i	−0.558212	+	0.829698i	$0.688512\pi$
$54$		0			0
$55$	10179.1	−	15869.4i	0.453735	−	0.707380i
$56$	−3136.00			−0.133631
$57$		0			0
$58$		−	4731.12i		−	0.184669i
$59$	18857.8			0.705281			0.352640	−	0.935759i	$-0.385284\pi$
$59$	18857.8			0.705281			0.352640	+	0.935759i	$0.385284\pi$
$60$		0			0
$61$	−26489.1			−0.911470			−0.455735	−	0.890115i	$-0.650624\pi$
$61$	−26489.1			−0.911470			−0.455735	+	0.890115i	$0.650624\pi$
$62$		−	41834.6i		−	1.38215i
$63$		0			0
$64$	−4096.00			−0.125000
$65$	1144.71	+	734.250i	0.0336055	+	0.0215556i
$66$		0			0
$67$			10647.5i			0.289774i	0.989448	+	0.144887i	$0.0462819\pi$
$67$			10647.5i			0.289774i	−0.989448	+	0.144887i	$0.953718\pi$
$68$			23121.1i			0.606367i
$69$		0			0
$70$	−5915.63	+	9222.55i	−0.144296	+	0.224960i
$71$	−47989.5			−1.12980			−0.564899	−	0.825160i	$-0.691085\pi$
$71$	−47989.5			−1.12980			−0.564899	+	0.825160i	$0.691085\pi$
$72$		0			0
$73$			37699.4i			0.827993i	0.910278	+	0.413997i	$0.135868\pi$
$73$			37699.4i			0.827993i	−0.910278	+	0.413997i	$0.864132\pi$
$74$	3303.32			0.0701248
$75$		0			0
$76$	−19159.0			−0.380486
$77$		−	16525.7i		−	0.317639i
$78$		0			0
$79$	−62335.6			−1.12375			−0.561874	−	0.827223i	$-0.689919\pi$
$79$	−62335.6			−1.12375			−0.561874	+	0.827223i	$0.689919\pi$
$80$	−7726.53	+	12045.8i	−0.134977	+	0.210431i
$81$		0			0
$82$			11374.3i			0.186806i
$83$		−	369.796i		−	0.00589205i	−0.999996	−	0.00294603i	$-0.999062\pi$
$83$		−	369.796i		−	0.00589205i	0.999996	−	0.00294603i	$-0.000937750\pi$
$84$		0			0
$85$	67995.9	+	43614.7i	1.02079	+	0.654765i
$86$	−38471.4			−0.560908
$87$		0			0
$88$		−	21584.6i		−	0.297124i
$89$	115397.			1.54425			0.772126	−	0.635469i	$-0.219193\pi$
$89$	115397.			1.54425			0.772126	+	0.635469i	$0.219193\pi$
$90$		0			0
$91$	1192.05			0.0150901
$92$			35956.1i			0.442898i
$93$		0			0
$94$	41739.9			0.487227
$95$	−36140.8	+	56344.0i	−0.410855	+	0.640529i
$96$		0			0
$97$			136508.i			1.47309i	0.676390	+	0.736544i	$0.263543\pi$
$97$			136508.i			1.47309i	−0.676390	+	0.736544i	$0.736457\pi$
$98$			9604.00i			0.101015i
$99$		0			0
$100$	20849.9	+	45445.4i	0.208499	+	0.454454i
$101$	−55976.1			−0.546008			−0.273004	−	0.962013i	$-0.588017\pi$
$101$	−55976.1			−0.546008			−0.273004	+	0.962013i	$0.588017\pi$
$102$		0			0
$103$			165176.i			1.53410i	0.641585	+	0.767052i	$0.278277\pi$
$103$			165176.i			1.53410i	−0.641585	+	0.767052i	$0.721723\pi$
$104$	1556.97			0.0141155
$105$		0			0
$106$	135737.			1.17337
$107$			99801.0i			0.842705i	0.906897	+	0.421352i	$0.138444\pi$
$107$			99801.0i			0.842705i	−0.906897	+	0.421352i	$0.861556\pi$
$108$		0			0
$109$	−225386.			−1.81703			−0.908514	−	0.417855i	$-0.862782\pi$
$109$	−225386.			−1.81703			−0.908514	+	0.417855i	$0.862782\pi$
$110$	−63477.4	−	40716.4i	−0.500193	−	0.320839i
$111$		0			0
$112$			12544.0i			0.0944911i
$113$			104503.i			0.769895i	0.922938	+	0.384948i	$0.125781\pi$
$113$			104503.i			0.769895i	−0.922938	+	0.384948i	$0.874219\pi$
$114$		0			0
$115$	105742.	+	67826.2i	0.745595	+	0.478248i
$116$	−18924.5			−0.130581
$117$		0			0
$118$		−	75431.4i		−	0.498709i
$119$	70808.3			0.458371
$120$		0			0
$121$	−47306.9			−0.293738
$122$			105956.i			0.644507i
$123$		0			0
$124$	−167338.			−0.977330
$125$	172979.	+	24409.5i	0.990190	+	0.139728i
$126$		0			0
$127$		−	245433.i		−	1.35028i	−0.737689	−	0.675141i	$-0.764083\pi$
$127$		−	245433.i		−	1.35028i	0.737689	−	0.675141i	$-0.235917\pi$
$128$			16384.0i			0.0883883i
$129$		0			0
$130$	2937.00	−	4578.82i	0.0152421	−	0.0237627i
$131$	101703.			0.517792			0.258896	−	0.965905i	$-0.416641\pi$
$131$	101703.			0.517792			0.258896	+	0.965905i	$0.416641\pi$
$132$		0			0
$133$			58674.5i			0.287621i
$134$	42589.9			0.204901
$135$		0			0
$136$	92484.3			0.428766
$137$			63654.7i			0.289754i	0.989450	+	0.144877i	$0.0462786\pi$
$137$			63654.7i			0.289754i	−0.989450	+	0.144877i	$0.953721\pi$
$138$		0			0
$139$	−277917.			−1.22005			−0.610025	−	0.792382i	$-0.708841\pi$
$139$	−277917.			−1.22005			−0.610025	+	0.792382i	$0.708841\pi$
$140$	36890.2	+	23662.5i	0.159071	+	0.102033i
$141$		0			0
$142$			191958.i			0.798888i
$143$			8204.71i			0.0335524i
$144$		0			0
$145$	−35698.4	+	55654.4i	−0.141003	+	0.219826i
$146$	150797.			0.585480
$147$		0			0
$148$		−	13213.3i		−	0.0495857i
$149$	456393.			1.68412			0.842060	−	0.539384i	$-0.181343\pi$
$149$	456393.			1.68412			0.842060	+	0.539384i	$0.181343\pi$
$150$		0			0
$151$	318099.			1.13532			0.567662	−	0.823262i	$-0.307848\pi$
$151$	318099.			1.13532			0.567662	+	0.823262i	$0.307848\pi$
$152$			76636.1i			0.269045i
$153$		0			0
$154$	−66102.9			−0.224605
$155$	−315661.	+	492119.i	−1.05534	+	1.64528i
$156$		0			0
$157$		−	392920.i		−	1.27220i	−0.771607	−	0.636099i	$-0.780547\pi$
$157$		−	392920.i		−	1.27220i	0.771607	−	0.636099i	$-0.219453\pi$
$158$			249342.i			0.794609i
$159$		0			0
$160$	48183.1	+	30906.1i	0.148797	+	0.0954431i
$161$	110116.			0.334799
$162$		0			0
$163$		−	56353.1i		−	0.166130i	−0.996544	−	0.0830652i	$-0.973529\pi$
$163$		−	56353.1i		−	0.166130i	0.996544	−	0.0830652i	$-0.0264710\pi$
$164$	45497.2			0.132092
$165$		0			0
$166$	−1479.18			−0.00416631
$167$			312776.i			0.867845i	0.900950	+	0.433922i	$0.142871\pi$
$167$			312776.i			0.867845i	−0.900950	+	0.433922i	$0.857129\pi$
$168$		0			0
$169$	370701.			0.998406
$170$	174459.	−	271984.i	0.462989	−	0.721806i
$171$		0			0
$172$			153885.i			0.396622i
$173$		−	307297.i		−	0.780626i	−0.920682	−	0.390313i	$-0.872367\pi$
$173$		−	307297.i		−	0.780626i	0.920682	−	0.390313i	$-0.127633\pi$
$174$		0			0
$175$	139176.	−	63852.9i	0.343535	−	0.157611i
$176$	−86338.5			−0.210098
$177$		0			0
$178$		−	461587.i		−	1.09195i
$179$	−804792.			−1.87738			−0.938688	−	0.344768i	$-0.887958\pi$
$179$	−804792.			−1.87738			−0.938688	+	0.344768i	$0.887958\pi$
$180$		0			0
$181$	−518678.			−1.17680			−0.588399	−	0.808571i	$-0.700241\pi$
$181$	−518678.			−1.17680			−0.588399	+	0.808571i	$0.700241\pi$
$182$		−	4768.21i		−	0.0106703i
$183$		0			0
$184$	143825.			0.313176
$185$	−38858.5	−	24925.0i	−0.0834750	−	0.0535435i
$186$		0			0
$187$			487363.i			1.01917i
$188$		−	166960.i		−	0.344522i
$189$		0			0
$190$	225376.	+	144563.i	0.452923	+	0.290519i
$191$	204063.			0.404744			0.202372	−	0.979309i	$-0.435135\pi$
$191$	204063.			0.404744			0.202372	+	0.979309i	$0.435135\pi$
$192$		0			0
$193$			873491.i			1.68797i	0.536365	+	0.843986i	$0.319797\pi$
$193$			873491.i			1.68797i	−0.536365	+	0.843986i	$0.680203\pi$
$194$	546032.			1.04163
$195$		0			0
$196$	38416.0			0.0714286
$197$		−	114332.i		−	0.209895i	−0.994478	−	0.104948i	$-0.966532\pi$
$197$		−	114332.i		−	0.209895i	0.994478	−	0.104948i	$-0.0334675\pi$
$198$		0			0
$199$	262148.			0.469261			0.234630	−	0.972085i	$-0.424612\pi$
$199$	262148.			0.469261			0.234630	+	0.972085i	$0.424612\pi$
$200$	181781.	−	83399.7i	0.321347	−	0.147431i
$201$		0			0
$202$			223904.i			0.386086i
$203$			57956.3i			0.0987098i
$204$		0			0
$205$	85824.2	−	133801.i	0.142635	−	0.222369i
$206$	660705.			1.08478
$207$		0			0
$208$		−	6227.86i		−	0.00998115i
$209$	−403848.			−0.639517
$210$		0			0
$211$	878765.			1.35883			0.679417	−	0.733752i	$-0.262233\pi$
$211$	878765.			1.35883			0.679417	+	0.733752i	$0.262233\pi$
$212$		−	542950.i		−	0.829698i
$213$		0			0
$214$	399204.			0.595882
$215$	452556.	+	290284.i	0.667692	+	0.428279i
$216$		0			0
$217$			512474.i			0.738792i
$218$			901546.i			1.28483i
$219$		0			0
$220$	−162866.	+	253910.i	−0.226868	+	0.353690i
$221$	−35155.0			−0.0484179
$222$		0			0
$223$		−	540539.i		−	0.727888i	−0.931421	−	0.363944i	$-0.881430\pi$
$223$		−	540539.i		−	0.727888i	0.931421	−	0.363944i	$-0.118570\pi$
$224$	50176.0			0.0668153
$225$		0			0
$226$	418011.			0.544398
$227$			135234.i			0.174189i	0.996200	+	0.0870947i	$0.0277583\pi$
$227$			135234.i			0.174189i	−0.996200	+	0.0870947i	$0.972242\pi$
$228$		0			0
$229$	118878.			0.149800			0.0749000	−	0.997191i	$-0.476136\pi$
$229$	118878.			0.149800			0.0749000	+	0.997191i	$0.476136\pi$
$230$	271305.	−	422968.i	0.338172	−	0.527215i
$231$		0			0
$232$			75698.0i			0.0923346i
$233$			659512.i			0.795854i	0.917417	+	0.397927i	$0.130270\pi$
$233$			659512.i			0.795854i	−0.917417	+	0.397927i	$0.869730\pi$
$234$		0			0
$235$	−491005.	−	314946.i	−0.579984	−	0.372020i
$236$	−301726.			−0.352640
$237$		0			0
$238$		−	283233.i		−	0.324117i
$239$	467946.			0.529908			0.264954	−	0.964261i	$-0.414643\pi$
$239$	467946.			0.529908			0.264954	+	0.964261i	$0.414643\pi$
$240$		0			0
$241$	−215104.			−0.238564			−0.119282	−	0.992860i	$-0.538059\pi$
$241$	−215104.			−0.238564			−0.119282	+	0.992860i	$0.538059\pi$
$242$			189228.i			0.207704i
$243$		0			0
$244$	423826.			0.455735
$245$	72466.4	−	112976.i	0.0771297	−	0.120246i
$246$		0			0
$247$		−	29130.8i		−	0.0303815i
$248$			669353.i			0.691077i
$249$		0			0
$250$	97638.1	−	691916.i	0.0988028	−	0.700170i
$251$	874948.			0.876593			0.438297	−	0.898830i	$-0.355582\pi$
$251$	874948.			0.876593			0.438297	+	0.898830i	$0.355582\pi$
$252$		0			0
$253$			757910.i			0.744417i
$254$	−981734.			−0.954793
$255$		0			0
$256$	65536.0			0.0625000
$257$			227843.i			0.215180i	0.994195	+	0.107590i	$0.0343134\pi$
$257$			227843.i			0.215180i	−0.994195	+	0.107590i	$0.965687\pi$
$258$		0			0
$259$	−40465.7			−0.0374833
$260$	−18315.3	−	11748.0i	−0.0168027	−	0.0107778i
$261$		0			0
$262$		−	406812.i		−	0.366134i
$263$			1.56138e6i			1.39194i	0.718073	+	0.695968i	$0.245024\pi$
$263$			1.56138e6i			1.39194i	−0.718073	+	0.695968i	$0.754976\pi$
$264$		0			0
$265$	−1.59674e6	−	1.02420e6i	−1.39675	−	0.895921i
$266$	234698.			0.203379
$267$		0			0
$268$		−	170360.i		−	0.144887i
$269$	−1.58500e6			−1.33551			−0.667756	−	0.744380i	$-0.732745\pi$
$269$	−1.58500e6			−1.33551			−0.667756	+	0.744380i	$0.732745\pi$
$270$		0			0
$271$	477067.			0.394599			0.197300	−	0.980343i	$-0.436783\pi$
$271$	477067.			0.394599			0.197300	+	0.980343i	$0.436783\pi$
$272$		−	369937.i		−	0.303184i
$273$		0			0
$274$	254619.			0.204887
$275$	439490.	+	957930.i	0.350443	+	0.763840i
$276$		0			0
$277$		−	138751.i		−	0.108652i	−0.998523	−	0.0543258i	$-0.982699\pi$
$277$		−	138751.i		−	0.108652i	0.998523	−	0.0543258i	$-0.0173010\pi$
$278$			1.11167e6i			0.862706i
$279$		0			0
$280$	94650.0	−	147561.i	0.0721482	−	0.112480i
$281$	2.51115e6			1.89717			0.948585	−	0.316522i	$-0.102515\pi$
$281$	2.51115e6			1.89717			0.948585	+	0.316522i	$0.102515\pi$
$282$		0			0
$283$			2.29079e6i			1.70027i	0.526563	+	0.850136i	$0.323480\pi$
$283$			2.29079e6i			1.70027i	−0.526563	+	0.850136i	$0.676520\pi$
$284$	767833.			0.564899
$285$		0			0
$286$	32818.9			0.0237251
$287$		−	139335.i		−	0.0998519i
$288$		0			0
$289$	−668362.			−0.470725
$290$	222617.	+	142794.i	0.155440	+	0.0997044i
$291$		0			0
$292$		−	603190.i		−	0.413997i
$293$		−	446400.i		−	0.303777i	−0.988398	−	0.151888i	$-0.951465\pi$
$293$		−	446400.i		−	0.303777i	0.988398	−	0.151888i	$-0.0485354\pi$
$294$		0			0
$295$	−569163.	+	887333.i	−0.380787	+	0.593652i
$296$	−52853.2			−0.0350624
$297$		0			0
$298$		−	1.82557e6i		−	1.19085i
$299$	−54670.4			−0.0353650
$300$		0			0
$301$	471274.			0.299818
$302$		−	1.27240e6i		−	0.802795i
$303$		0			0
$304$	306544.			0.190243
$305$	799488.	−	1.24641e6i	0.492110	−	0.767207i
$306$		0			0
$307$		−	132928.i		−	0.0804956i	−0.999190	−	0.0402478i	$-0.987185\pi$
$307$		−	132928.i		−	0.0804956i	0.999190	−	0.0402478i	$-0.0128147\pi$
$308$			264412.i			0.158819i
$309$		0			0
$310$	1.96848e6	+	1.26264e6i	1.16339	+	0.746236i
$311$	1.02347e6			0.600029			0.300015	−	0.953935i	$-0.403008\pi$
$311$	1.02347e6			0.600029			0.300015	+	0.953935i	$0.403008\pi$
$312$		0			0
$313$			2.03277e6i			1.17281i	0.810018	+	0.586404i	$0.199457\pi$
$313$			2.03277e6i			1.17281i	−0.810018	+	0.586404i	$0.800543\pi$
$314$	−1.57168e6			−0.899580
$315$		0			0
$316$	997370.			0.561874
$317$			2.42685e6i			1.35642i	0.734866	+	0.678212i	$0.237245\pi$
$317$			2.42685e6i			1.35642i	−0.734866	+	0.678212i	$0.762755\pi$
$318$		0			0
$319$	−398904.			−0.219479
$320$	123625.	−	192732.i	0.0674885	−	0.105216i
$321$		0			0
$322$		−	440463.i		−	0.236739i
$323$		−	1.73038e6i		−	0.922858i
$324$		0			0
$325$	−69098.5	+	31701.8i	−0.0362878	+	0.0166485i
$326$	−225412.			−0.117472
$327$		0			0
$328$		−	181989.i		−	0.0934029i
$329$	−511314.			−0.260434
$330$		0			0
$331$	552981.			0.277422			0.138711	−	0.990333i	$-0.455704\pi$
$331$	552981.			0.277422			0.138711	+	0.990333i	$0.455704\pi$
$332$			5916.73i			0.00294603i
$333$		0			0
$334$	1.25110e6			0.613659
$335$	−501005.	−	321360.i	−0.243910	−	0.156452i
$336$		0			0
$337$			202099.i			0.0969371i	0.998825	+	0.0484685i	$0.0154341\pi$
$337$			202099.i			0.0969371i	−0.998825	+	0.0484685i	$0.984566\pi$
$338$		−	1.48280e6i		−	0.705980i
$339$		0			0
$340$	−1.08793e6	−	697835.i	−0.510394	−	0.327382i
$341$	−3.52728e6			−1.64268
$342$		0			0
$343$		−	117649.i		−	0.0539949i
$344$	615542.			0.280454
$345$		0			0
$346$	−1.22919e6			−0.551986
$347$		−	1.04617e6i		−	0.466419i	−0.972426	−	0.233210i	$-0.925077\pi$
$347$		−	1.04617e6i		−	0.466419i	0.972426	−	0.233210i	$-0.0749229\pi$
$348$		0			0
$349$	2.72359e6			1.19696			0.598479	−	0.801139i	$-0.295772\pi$
$349$	2.72359e6			1.19696			0.598479	+	0.801139i	$0.295772\pi$
$350$	−255412.	−	556706.i	−0.111448	−	0.242916i
$351$		0			0
$352$			345354.i			0.148562i
$353$			1.73711e6i			0.741979i	0.928637	+	0.370989i	$0.120981\pi$
$353$			1.73711e6i			0.741979i	−0.928637	+	0.370989i	$0.879019\pi$
$354$		0			0
$355$	1.44841e6	−	2.25809e6i	0.609987	−	0.950978i
$356$	−1.84635e6			−0.772126
$357$		0			0
$358$			3.21917e6i			1.32751i
$359$	1.68699e6			0.690837			0.345419	−	0.938449i	$-0.387737\pi$
$359$	1.68699e6			0.690837			0.345419	+	0.938449i	$0.387737\pi$
$360$		0			0
$361$	−1.04224e6			−0.420920
$362$			2.07471e6i			0.832121i
$363$		0			0
$364$	−19072.8			−0.00754504
$365$	−1.77390e6	−	1.13783e6i	−0.696942	−	0.447040i
$366$		0			0
$367$			3.25743e6i			1.26244i	0.775605	+	0.631219i	$0.217445\pi$
$367$			3.25743e6i			1.26244i	−0.775605	+	0.631219i	$0.782555\pi$
$368$		−	575298.i		−	0.221449i
$369$		0			0
$370$	−99700.2	+	155434.i	−0.0378610	+	0.0590258i
$371$	−1.66278e6			−0.627193
$372$		0			0
$373$		−	3.36622e6i		−	1.25277i	−0.779514	−	0.626384i	$-0.784534\pi$
$373$		−	3.36622e6i		−	1.25277i	0.779514	−	0.626384i	$-0.215466\pi$
$374$	1.94945e6			0.720665
$375$		0			0
$376$	−667838.			−0.243614
$377$		−	28774.2i		−	0.0104268i
$378$		0			0
$379$	−4.98342e6			−1.78209			−0.891044	−	0.453917i	$-0.850026\pi$
$379$	−4.98342e6			−1.78209			−0.891044	+	0.453917i	$0.850026\pi$
$380$	578253.	−	901505.i	0.205428	−	0.320265i
$381$		0			0
$382$		−	816252.i		−	0.286197i
$383$		−	1.14076e6i		−	0.397374i	−0.980063	−	0.198687i	$-0.936332\pi$
$383$		−	1.14076e6i		−	0.397374i	0.980063	−	0.198687i	$-0.0636677\pi$
$384$		0			0
$385$	777598.	+	498776.i	0.267364	+	0.171496i
$386$	3.49396e6			1.19358
$387$		0			0
$388$		−	2.18413e6i		−	0.736544i
$389$	−4.58469e6			−1.53616			−0.768080	−	0.640354i	$-0.778788\pi$
$389$	−4.58469e6			−1.53616			−0.768080	+	0.640354i	$0.778788\pi$
$390$		0			0
$391$	−3.24744e6			−1.07423
$392$		−	153664.i		−	0.0505076i
$393$		0			0
$394$	−457329.			−0.148418
$395$	1.88140e6	−	2.93313e6i	0.606720	−	0.945885i
$396$		0			0
$397$		−	4.12709e6i		−	1.31422i	−0.753795	−	0.657110i	$-0.771779\pi$
$397$		−	4.12709e6i		−	1.31422i	0.753795	−	0.657110i	$-0.228221\pi$
$398$		−	1.04859e6i		−	0.331817i
$399$		0			0
$400$	−333599.	−	727126.i	−0.104250	−	0.227227i
$401$	−2.33931e6			−0.726487			−0.363243	−	0.931694i	$-0.618331\pi$
$401$	−2.33931e6			−0.726487			−0.363243	+	0.931694i	$0.618331\pi$
$402$		0			0
$403$		−	254434.i		−	0.0780390i
$404$	895617.			0.273004
$405$		0			0
$406$	231825.			0.0697984
$407$		−	278520.i		−	0.0833431i
$408$		0			0
$409$	−5.04134e6			−1.49018			−0.745088	−	0.666966i	$-0.767592\pi$
$409$	−5.04134e6			−1.49018			−0.745088	+	0.666966i	$0.767592\pi$
$410$	−535204.	−	343297.i	−0.157239	−	0.100858i
$411$		0			0
$412$		−	2.64282e6i		−	0.767052i
$413$			924034.i			0.266571i
$414$		0			0
$415$	17400.3	+	11161.1i	0.00495948	+	0.00318117i
$416$	−24911.4			−0.00705774
$417$		0			0
$418$			1.61539e6i			0.452207i
$419$	66941.5			0.0186277			0.00931387	−	0.999957i	$-0.497035\pi$
$419$	66941.5			0.0186277			0.00931387	+	0.999957i	$0.497035\pi$
$420$		0			0
$421$	670296.			0.184315			0.0921576	−	0.995744i	$-0.470624\pi$
$421$	670296.			0.184315			0.0921576	+	0.995744i	$0.470624\pi$
$422$		−	3.51506e6i		−	0.960841i
$423$		0			0
$424$	−2.17180e6			−0.586685
$425$	−4.10447e6	+	1.88310e6i	−1.10226	+	0.505709i
$426$		0			0
$427$		−	1.29797e6i		−	0.344503i
$428$		−	1.59682e6i		−	0.421352i
$429$		0			0
$430$	1.16113e6	−	1.81022e6i	0.302839	−	0.472130i
$431$	365337.			0.0947329			0.0473664	−	0.998878i	$-0.484917\pi$
$431$	365337.			0.0947329			0.0473664	+	0.998878i	$0.484917\pi$
$432$		0			0
$433$		−	1.30294e6i		−	0.333967i	−0.985960	−	0.166984i	$-0.946597\pi$
$433$		−	1.30294e6i		−	0.333967i	0.985960	−	0.166984i	$-0.0534027\pi$
$434$	2.04989e6			0.522405
$435$		0			0
$436$	3.60618e6			0.908514
$437$		−	2.69095e6i		−	0.674066i
$438$		0			0
$439$	−5.16315e6			−1.27865			−0.639327	−	0.768935i	$-0.720787\pi$
$439$	−5.16315e6			−1.27865			−0.639327	+	0.768935i	$0.720787\pi$
$440$	1.01564e6	+	651462.i	0.250096	+	0.160420i
$441$		0			0
$442$			140620.i			0.0342367i
$443$			7.64624e6i			1.85114i	0.378579	+	0.925569i	$0.376413\pi$
$443$			7.64624e6i			1.85114i	−0.378579	+	0.925569i	$0.623587\pi$
$444$		0			0
$445$	−3.48288e6	+	5.42985e6i	−0.833754	+	1.29983i
$446$	−2.16216e6			−0.514695
$447$		0			0
$448$		−	200704.i		−	0.0472456i
$449$	4.83346e6			1.13147			0.565734	−	0.824588i	$-0.308593\pi$
$449$	4.83346e6			1.13147			0.565734	+	0.824588i	$0.308593\pi$
$450$		0			0
$451$	959024.			0.222018
$452$		−	1.67204e6i		−	0.384948i
$453$		0			0
$454$	540936.			0.123170
$455$	−35978.2	+	56090.6i	−0.00814726	+	0.0127017i
$456$		0			0
$457$			3.51870e6i			0.788119i	0.919085	+	0.394060i	$0.128930\pi$
$457$			3.51870e6i			0.788119i	−0.919085	+	0.394060i	$0.871070\pi$
$458$		−	475511.i		−	0.105925i
$459$		0			0
$460$	−1.69187e6	−	1.08522e6i	−0.372798	−	0.239124i
$461$	−3.55938e6			−0.780049			−0.390024	−	0.920805i	$-0.627533\pi$
$461$	−3.55938e6			−0.780049			−0.390024	+	0.920805i	$0.627533\pi$
$462$		0			0
$463$			4.39317e6i			0.952413i	0.879333	+	0.476207i	$0.157989\pi$
$463$			4.39317e6i			0.952413i	−0.879333	+	0.476207i	$0.842011\pi$
$464$	302792.			0.0652904
$465$		0			0
$466$	2.63805e6			0.562754
$467$		−	7.46723e6i		−	1.58441i	−0.610256	−	0.792205i	$-0.708933\pi$
$467$		−	7.46723e6i		−	1.58441i	0.610256	−	0.792205i	$-0.291067\pi$
$468$		0			0
$469$	−521727.			−0.109524
$470$	−1.25978e6	+	1.96402e6i	−0.263058	+	0.410111i
$471$		0			0
$472$			1.20690e6i			0.249354i
$473$			3.24371e6i			0.666637i
$474$		0			0
$475$	−1.56041e6	−	3.40113e6i	−0.317325	−	0.691654i
$476$	−1.13293e6			−0.229185
$477$		0			0
$478$		−	1.87178e6i		−	0.374702i
$479$	−5.07249e6			−1.01014			−0.505070	−	0.863078i	$-0.668534\pi$
$479$	−5.07249e6			−1.01014			−0.505070	+	0.863078i	$0.668534\pi$
$480$		0			0
$481$	20090.5			0.00395938
$482$			860414.i			0.168690i
$483$		0			0
$484$	756910.			0.146869
$485$	−6.42322e6	−	4.12005e6i	−1.23993	−	0.795332i
$486$		0			0
$487$			8.40987e6i			1.60682i	0.595428	+	0.803409i	$0.296983\pi$
$487$			8.40987e6i			1.60682i	−0.595428	+	0.803409i	$0.703017\pi$
$488$		−	1.69530e6i		−	0.322253i
$489$		0			0
$490$	−451905.	−	289866.i	−0.0850270	−	0.0545389i
$491$	1.07319e6			0.200896			0.100448	−	0.994942i	$-0.467972\pi$
$491$	1.07319e6			0.200896			0.100448	+	0.994942i	$0.467972\pi$
$492$		0			0
$493$		−	1.70920e6i		−	0.316720i
$494$	−116523.			−0.0214830
$495$		0			0
$496$	2.67741e6			0.488665
$497$		−	2.35149e6i		−	0.427023i
$498$		0			0
$499$	−4.34278e6			−0.780758			−0.390379	−	0.920654i	$-0.627656\pi$
$499$	−4.34278e6			−0.780758			−0.390379	+	0.920654i	$0.627656\pi$
$500$	−2.76766e6	−	390553.i	−0.495095	−	0.0698642i
$501$		0			0
$502$		−	3.49979e6i		−	0.619845i
$503$		−	1.03452e6i		−	0.182313i	−0.995837	−	0.0911564i	$-0.970944\pi$
$503$		−	1.03452e6i		−	0.182313i	0.995837	−	0.0911564i	$-0.0290563\pi$
$504$		0			0
$505$	1.68946e6	−	2.63389e6i	0.294794	−	0.459588i
$506$	3.03164e6			0.526382
$507$		0			0
$508$			3.92693e6i			0.675141i
$509$	−1.12485e6			−0.192442			−0.0962208	−	0.995360i	$-0.530675\pi$
$509$	−1.12485e6			−0.192442			−0.0962208	+	0.995360i	$0.530675\pi$
$510$		0			0
$511$	−1.84727e6			−0.312952
$512$		−	262144.i		−	0.0441942i
$513$		0			0
$514$	911371.			0.152155
$515$	−7.77218e6	−	4.98532e6i	−1.29129	−	0.828275i
$516$		0			0
$517$		−	3.51930e6i		−	0.579068i
$518$			161863.i			0.0265047i
$519$		0			0
$520$	−46992.0	+	73261.1i	−0.00762106	+	0.0118813i
$521$	193877.			0.0312919			0.0156460	−	0.999878i	$-0.495020\pi$
$521$	193877.			0.0312919			0.0156460	+	0.999878i	$0.495020\pi$
$522$		0			0
$523$			6.31332e6i			1.00926i	0.863336	+	0.504630i	$0.168371\pi$
$523$			6.31332e6i			1.00926i	−0.863336	+	0.504630i	$0.831629\pi$
$524$	−1.62725e6			−0.258896
$525$		0			0
$526$	6.24552e6			0.984247
$527$		−	1.51134e7i		−	2.37048i
$528$		0			0
$529$	1.38617e6			0.215367
$530$	−4.09680e6	+	6.38697e6i	−0.633512	+	0.987654i
$531$		0			0
$532$		−	938792.i		−	0.143810i
$533$			69177.3i			0.0105474i
$534$		0			0
$535$	−4.69602e6	−	3.01217e6i	−0.709325	−	0.454983i
$536$	−681439.			−0.102451
$537$		0			0
$538$			6.33999e6i			0.944349i
$539$	809761.			0.120056
$540$		0			0
$541$	−4.19872e6			−0.616770			−0.308385	−	0.951262i	$-0.599789\pi$
$541$	−4.19872e6			−0.616770			−0.308385	+	0.951262i	$0.599789\pi$
$542$		−	1.90827e6i		−	0.279024i
$543$		0			0
$544$	−1.47975e6			−0.214383
$545$	6.80256e6	−	1.06053e7i	0.981028	−	1.52944i
$546$		0			0
$547$			6.84530e6i			0.978192i	0.872230	+	0.489096i	$0.162673\pi$
$547$			6.84530e6i			0.978192i	−0.872230	+	0.489096i	$0.837327\pi$
$548$		−	1.01848e6i		−	0.144877i
$549$		0			0
$550$	3.83172e6	−	1.75796e6i	0.540116	−	0.247801i
$551$	1.41631e6			0.198737
$552$		0			0
$553$		−	3.05445e6i		−	0.424736i
$554$	−555003.			−0.0768283
$555$		0			0
$556$	4.44667e6			0.610025
$557$			9.43023e6i			1.28791i	0.765065	+	0.643953i	$0.222707\pi$
$557$			9.43023e6i			1.28791i	−0.765065	+	0.643953i	$0.777293\pi$
$558$		0			0
$559$	−233979.			−0.0316699
$560$	−590243.	−	378600.i	−0.0795354	−	0.0510165i
$561$		0			0
$562$		−	1.00446e7i		−	1.34150i
$563$			1.27111e7i			1.69010i	0.534685	+	0.845052i	$0.320430\pi$
$563$			1.27111e7i			1.69010i	−0.534685	+	0.845052i	$0.679570\pi$
$564$		0			0
$565$	−4.91725e6	−	3.15408e6i	−0.648039	−	0.415673i
$566$	9.16315e6			1.20227
$567$		0			0
$568$		−	3.07133e6i		−	0.399444i
$569$	7.92638e6			1.02635			0.513173	−	0.858285i	$-0.328470\pi$
$569$	7.92638e6			1.02635			0.513173	+	0.858285i	$0.328470\pi$
$570$		0			0
$571$	1.10620e6			0.141985			0.0709927	−	0.997477i	$-0.477383\pi$
$571$	1.10620e6			0.141985			0.0709927	+	0.997477i	$0.477383\pi$
$572$		−	131275.i		−	0.0167762i
$573$		0			0
$574$	−557341.			−0.0706059
$575$	−6.38297e6	+	2.92845e6i	−0.805106	+	0.369376i
$576$		0			0
$577$		−	4.53166e6i		−	0.566654i	−0.959023	−	0.283327i	$-0.908562\pi$
$577$		−	4.53166e6i		−	0.566654i	0.959023	−	0.283327i	$-0.0914381\pi$
$578$			2.67345e6i			0.332853i
$579$		0			0
$580$	571175.	−	890470.i	0.0705016	−	0.109913i
$581$	18120.0			0.00222699
$582$		0			0
$583$		−	1.14447e7i		−	1.39455i
$584$	−2.41276e6			−0.292740
$585$		0			0
$586$	−1.78560e6			−0.214803
$587$			201145.i			0.0240943i	0.999927	+	0.0120472i	$0.00383482\pi$
$587$			201145.i			0.0240943i	−0.999927	+	0.0120472i	$0.996165\pi$
$588$		0			0
$589$	1.25236e7			1.48744
$590$	3.54933e6	+	2.27665e6i	0.419775	+	0.269257i
$591$		0			0
$592$			211413.i			0.0247929i
$593$		−	1.56210e7i		−	1.82420i	−0.409973	−	0.912098i	$-0.634462\pi$
$593$		−	1.56210e7i		−	1.82420i	0.409973	−	0.912098i	$-0.365538\pi$
$594$		0			0
$595$	−2.13712e6	+	3.33180e6i	−0.247478	+	0.385821i
$596$	−7.30228e6			−0.842060
$597$		0			0
$598$			218681.i			0.0250069i
$599$	−2.80468e6			−0.319386			−0.159693	−	0.987167i	$-0.551050\pi$
$599$	−2.80468e6			−0.319386			−0.159693	+	0.987167i	$0.551050\pi$
$600$		0			0
$601$	7.57493e6			0.855446			0.427723	−	0.903910i	$-0.359316\pi$
$601$	7.57493e6			0.855446			0.427723	+	0.903910i	$0.359316\pi$
$602$		−	1.88510e6i		−	0.212003i
$603$		0			0
$604$	−5.08958e6			−0.567662
$605$	1.42781e6	−	2.22597e6i	0.158592	−	0.247247i
$606$		0			0
$607$		−	1.71170e7i		−	1.88562i	−0.333324	−	0.942812i	$-0.608170\pi$
$607$		−	1.71170e7i		−	1.88562i	0.333324	−	0.942812i	$-0.391830\pi$
$608$		−	1.22618e6i		−	0.134522i
$609$		0			0
$610$	−4.98565e6	−	3.19795e6i	−0.542497	−	0.347974i
$611$	253858.			0.0275098
$612$		0			0
$613$		−	1.57603e7i		−	1.69400i	−0.531590	−	0.847002i	$-0.678405\pi$
$613$		−	1.57603e7i		−	1.69400i	0.531590	−	0.847002i	$-0.321595\pi$
$614$	−531714.			−0.0569190
$615$		0			0
$616$	1.05765e6			0.112302
$617$			1.16536e7i			1.23239i	0.787594	+	0.616194i	$0.211326\pi$
$617$			1.16536e7i			1.23239i	−0.787594	+	0.616194i	$0.788674\pi$
$618$		0			0
$619$	9.20111e6			0.965192			0.482596	−	0.875843i	$-0.339694\pi$
$619$	9.20111e6			0.965192			0.482596	+	0.875843i	$0.339694\pi$
$620$	5.05057e6	−	7.87391e6i	0.527668	−	0.822642i
$621$		0			0
$622$		−	4.09386e6i		−	0.424285i
$623$			5.65444e6i			0.583673i
$624$		0			0
$625$	−6.36938e6	+	7.40260e6i	−0.652224	+	0.758026i
$626$	8.13108e6			0.829301
$627$		0			0
$628$			6.28672e6i			0.636099i
$629$	1.19338e6			0.120269
$630$		0			0
$631$	1.50421e7			1.50395			0.751976	−	0.659191i	$-0.229101\pi$
$631$	1.50421e7			1.50395			0.751976	+	0.659191i	$0.229101\pi$
$632$		−	3.98948e6i		−	0.397305i
$633$		0			0
$634$	9.70742e6			0.959137
$635$	1.15486e7	+	7.40761e6i	1.13656	+	0.729028i
$636$		0			0
$637$			58410.5i			0.00570351i
$638$			1.59562e6i			0.155195i
$639$		0			0
$640$	−770930.	−	494498.i	−0.0743986	−	0.0477216i
$641$	1.15445e7			1.10976			0.554879	−	0.831931i	$-0.312765\pi$
$641$	1.15445e7			1.10976			0.554879	+	0.831931i	$0.312765\pi$
$642$		0			0
$643$			4.82038e6i			0.459784i	0.973216	+	0.229892i	$0.0738373\pi$
$643$			4.82038e6i			0.459784i	−0.973216	+	0.229892i	$0.926163\pi$
$644$	−1.76185e6			−0.167400
$645$		0			0
$646$	−6.92152e6			−0.652559
$647$			7.53202e6i			0.707377i	0.935363	+	0.353688i	$0.115073\pi$
$647$			7.53202e6i			0.707377i	−0.935363	+	0.353688i	$0.884927\pi$
$648$		0			0
$649$	−6.35999e6			−0.592713
$650$	126807.	+	276394.i	0.0117723	+	0.0256593i
$651$		0			0
$652$			901650.i			0.0830652i
$653$		−	4.07749e6i		−	0.374205i	−0.982340	−	0.187103i	$-0.940090\pi$
$653$		−	4.07749e6i		−	0.374205i	0.982340	−	0.187103i	$-0.0599097\pi$
$654$		0			0
$655$	−3.06958e6	+	4.78551e6i	−0.279560	+	0.435838i
$656$	−727956.			−0.0660458
$657$		0			0
$658$			2.04525e6i			0.184155i
$659$	−1.52918e7			−1.37165			−0.685826	−	0.727765i	$-0.740559\pi$
$659$	−1.52918e7			−1.37165			−0.685826	+	0.727765i	$0.740559\pi$
$660$		0			0
$661$	2.03724e7			1.81359			0.906796	−	0.421570i	$-0.138521\pi$
$661$	2.03724e7			1.81359			0.906796	+	0.421570i	$0.138521\pi$
$662$		−	2.21193e6i		−	0.196167i
$663$		0			0
$664$	23666.9			0.00208315
$665$	−2.76086e6	−	1.77090e6i	−0.242097	−	0.155289i
$666$		0			0
$667$		−	2.65802e6i		−	0.231336i
$668$		−	5.00442e6i		−	0.433922i
$669$		0			0
$670$	−1.28544e6	+	2.00402e6i	−0.110628	+	0.172470i
$671$	8.93371e6			0.765994
$672$		0			0
$673$			4.09627e6i			0.348619i	0.984691	+	0.174309i	$0.0557692\pi$
$673$			4.09627e6i			0.348619i	−0.984691	+	0.174309i	$0.944231\pi$
$674$	808397.			0.0685449
$675$		0			0
$676$	−5.93122e6			−0.499203
$677$			7.73865e6i			0.648924i	0.945899	+	0.324462i	$0.105183\pi$
$677$			7.73865e6i			0.648924i	−0.945899	+	0.324462i	$0.894817\pi$
$678$		0			0
$679$	−6.68889e6			−0.556775
$680$	−2.79134e6	+	4.35174e6i	−0.231494	+	0.360903i
$681$		0			0
$682$			1.41091e7i			1.16155i
$683$			2.24027e7i			1.83759i	0.394734	+	0.918795i	$0.370837\pi$
$683$			2.24027e7i			1.83759i	−0.394734	+	0.918795i	$0.629163\pi$
$684$		0			0
$685$	−2.99520e6	−	1.92121e6i	−0.243893	−	0.156440i
$686$	−470596.			−0.0381802
$687$		0			0
$688$		−	2.46217e6i		−	0.198311i
$689$	825541.			0.0662507
$690$		0			0
$691$	−2.60639e6			−0.207656			−0.103828	−	0.994595i	$-0.533109\pi$
$691$	−2.60639e6			−0.207656			−0.103828	+	0.994595i	$0.533109\pi$
$692$			4.91675e6i			0.390313i
$693$		0			0
$694$	−4.18466e6			−0.329808
$695$	8.38802e6	−	1.30770e7i	0.658715	−	1.02695i
$696$		0			0
$697$			4.10916e6i			0.320384i
$698$		−	1.08944e7i		−	0.846377i
$699$		0			0
$700$	−2.22682e6	+	1.02165e6i	−0.171767	+	0.0788054i
$701$	5.34202e6			0.410592			0.205296	−	0.978700i	$-0.434184\pi$
$701$	5.34202e6			0.410592			0.205296	+	0.978700i	$0.434184\pi$
$702$		0			0
$703$			988882.i			0.0754668i
$704$	1.38142e6			0.105049
$705$		0			0
$706$	6.94846e6			0.524658
$707$		−	2.74283e6i		−	0.206372i
$708$		0			0
$709$	1.78376e7			1.33266			0.666332	−	0.745656i	$-0.267864\pi$
$709$	1.78376e7			1.33266			0.666332	+	0.745656i	$0.267864\pi$
$710$	−9.03236e6	−	5.79364e6i	−0.672443	−	0.431326i
$711$		0			0
$712$			7.38539e6i			0.545976i
$713$		−	2.35033e7i		−	1.73143i
$714$		0			0
$715$	−386063.	−	247633.i	−0.0282418	−	0.0181152i
$716$	1.28767e7			0.938688
$717$		0			0
$718$		−	6.74795e6i		−	0.488496i
$719$	−1.93072e7			−1.39283			−0.696414	−	0.717640i	$-0.745222\pi$
$719$	−1.93072e7			−1.39283			−0.696414	+	0.717640i	$0.745222\pi$
$720$		0			0
$721$	−8.09364e6			−0.579837
$722$			4.16896e6i			0.297636i
$723$		0			0
$724$	8.29885e6			0.588399
$725$	−1.54131e6	−	3.35949e6i	−0.108904	−	0.237372i
$726$		0			0
$727$			2.11119e7i			1.48147i	0.671800	+	0.740733i	$0.265522\pi$
$727$			2.11119e7i			1.48147i	−0.671800	+	0.740733i	$0.734478\pi$
$728$			76291.3i			0.00533515i
$729$		0			0
$730$	−4.55134e6	+	7.09559e6i	−0.316105	+	0.492812i
$731$	−1.38984e7			−0.961994
$732$		0			0
$733$			2.35579e7i			1.61948i	0.586786	+	0.809742i	$0.300393\pi$
$733$			2.35579e7i			1.61948i	−0.586786	+	0.809742i	$0.699607\pi$
$734$	1.30297e7			0.892678
$735$		0			0
$736$	−2.30119e6			−0.156588
$737$		−	3.59097e6i		−	0.243525i
$738$		0			0
$739$	8.49978e6			0.572528			0.286264	−	0.958151i	$-0.407587\pi$
$739$	8.49978e6			0.572528			0.286264	+	0.958151i	$0.407587\pi$
$740$	621736.	+	398801.i	0.0417375	+	0.0267717i
$741$		0			0
$742$			6.65114e6i			0.443492i
$743$		−	5.28179e6i		−	0.351001i	−0.984479	−	0.175501i	$-0.943846\pi$
$743$		−	5.28179e6i		−	0.351001i	0.984479	−	0.175501i	$-0.0561544\pi$
$744$		0			0
$745$	−1.37747e7	+	2.14750e7i	−0.909270	+	1.41756i
$746$	−1.34649e7			−0.885841
$747$		0			0
$748$		−	7.79781e6i		−	0.509587i
$749$	−4.89025e6			−0.318512
$750$		0			0
$751$	1.72132e7			1.11368			0.556842	−	0.830619i	$-0.312013\pi$
$751$	1.72132e7			1.11368			0.556842	+	0.830619i	$0.312013\pi$
$752$			2.67135e6i			0.172261i
$753$		0			0
$754$	−115097.			−0.00737284
$755$	−9.60079e6	+	1.49678e7i	−0.612970	+	0.955629i
$756$		0			0
$757$		−	1.95610e7i		−	1.24066i	−0.784343	−	0.620328i	$-0.787000\pi$
$757$		−	1.95610e7i		−	1.24066i	0.784343	−	0.620328i	$-0.213000\pi$
$758$			1.99337e7i			1.26013i
$759$		0			0
$760$	−3.60602e6	−	2.31301e6i	−0.226461	−	0.145259i
$761$	2.65917e7			1.66450			0.832250	−	0.554401i	$-0.187052\pi$
$761$	2.65917e7			1.66450			0.832250	+	0.554401i	$0.187052\pi$
$762$		0			0
$763$		−	1.10439e7i		−	0.686772i
$764$	−3.26501e6			−0.202372
$765$		0			0
$766$	−4.56306e6			−0.280986
$767$		−	458766.i		−	0.0281581i
$768$		0			0
$769$	−3.32124e6			−0.202528			−0.101264	−	0.994860i	$-0.532289\pi$
$769$	−3.32124e6			−0.202528			−0.101264	+	0.994860i	$0.532289\pi$
$770$	1.99510e6	−	3.11039e6i	0.121266	−	0.189055i
$771$		0			0
$772$		−	1.39759e7i		−	0.843986i
$773$			3.03574e7i			1.82732i	0.406476	+	0.913662i	$0.366758\pi$
$773$			3.03574e7i			1.82732i	−0.406476	+	0.913662i	$0.633242\pi$
$774$		0			0
$775$	−1.36289e7	−	2.97061e7i	−0.815091	−	1.77660i
$776$	−8.73651e6			−0.520815
$777$		0			0
$778$			1.83388e7i			1.08623i
$779$	−3.40501e6			−0.201036
$780$		0			0
$781$	1.61849e7			0.949475
$782$			1.29898e7i			0.759599i
$783$		0			0
$784$	−614656.			−0.0357143
$785$	1.84884e7	+	1.18590e7i	1.07084	+	0.686870i
$786$		0			0
$787$			1.37541e7i			0.791583i	0.918340	+	0.395792i	$0.129530\pi$
$787$			1.37541e7i			0.791583i	−0.918340	+	0.395792i	$0.870470\pi$
$788$			1.82932e6i			0.104948i
$789$		0			0
$790$	−1.17325e7	−	7.52560e6i	−0.668842	−	0.429016i
$791$	−5.12064e6			−0.290993
$792$		0			0
$793$			644416.i			0.0363901i
$794$	−1.65084e7			−0.929294
$795$		0			0
$796$	−4.19437e6			−0.234630
$797$			2.68171e6i			0.149543i	0.997201	+	0.0747715i	$0.0238227\pi$
$797$			2.68171e6i			0.149543i	−0.997201	+	0.0747715i	$0.976177\pi$
$798$		0			0
$799$	1.50792e7			0.835627
$800$	−2.90850e6	+	1.33440e6i	−0.160674	+	0.0737157i
$801$		0			0
$802$			9.35726e6i			0.513704i
$803$		−	1.27145e7i		−	0.695840i
$804$		0			0
$805$	−3.32349e6	+	5.18136e6i	−0.180761	+	0.281809i
$806$	−1.01773e6			−0.0551819
$807$		0			0
$808$		−	3.58247e6i		−	0.193043i
$809$	3.35759e7			1.80367			0.901834	−	0.432083i	$-0.142221\pi$
$809$	3.35759e7			1.80367			0.901834	+	0.432083i	$0.142221\pi$
$810$		0			0
$811$	5.24303e6			0.279917			0.139959	−	0.990157i	$-0.455303\pi$
$811$	5.24303e6			0.279917			0.139959	+	0.990157i	$0.455303\pi$
$812$		−	927300.i		−	0.0493549i
$813$		0			0
$814$	−1.11408e6			−0.0589325
$815$	2.65163e6	+	1.70084e6i	0.139836	+	0.0896951i
$816$		0			0
$817$		−	1.15168e7i		−	0.603637i
$818$			2.01653e7i			1.05371i
$819$		0			0
$820$	−1.37319e6	+	2.14082e6i	−0.0713173	+	0.111185i
$821$	1.95688e7			1.01323			0.506614	−	0.862173i	$-0.330897\pi$
$821$	1.95688e7			1.01323			0.506614	+	0.862173i	$0.330897\pi$
$822$		0			0
$823$			6.20206e6i			0.319181i	0.987183	+	0.159590i	$0.0510173\pi$
$823$			6.20206e6i			0.319181i	−0.987183	+	0.159590i	$0.948983\pi$
$824$	−1.05713e7			−0.542388
$825$		0			0
$826$	3.69614e6			0.188494
$827$		−	2.30838e7i		−	1.17366i	−0.809710	−	0.586831i	$-0.800375\pi$
$827$		−	2.30838e7i		−	1.17366i	0.809710	−	0.586831i	$-0.199625\pi$
$828$		0			0
$829$	−2.73598e7			−1.38270			−0.691348	−	0.722522i	$-0.742983\pi$
$829$	−2.73598e7			−1.38270			−0.691348	+	0.722522i	$0.742983\pi$
$830$	44644.3	−	69601.2i	0.00224942	−	0.00350688i
$831$		0			0
$832$			99645.8i			0.00499058i
$833$			3.46961e6i			0.173248i
$834$		0			0
$835$	−1.47173e7	−	9.44013e6i	−0.730486	−	0.468556i
$836$	6.46156e6			0.319758
$837$		0			0
$838$		−	267766.i		−	0.0131718i
$839$	1.15303e7			0.565504			0.282752	−	0.959193i	$-0.408753\pi$
$839$	1.15303e7			0.565504			0.282752	+	0.959193i	$0.408753\pi$
$840$		0			0
$841$	−1.91122e7			−0.931795
$842$		−	2.68118e6i		−	0.130331i
$843$		0			0
$844$	−1.40602e7			−0.679417
$845$	−1.11884e7	+	1.74429e7i	−0.539047	+	0.840382i
$846$		0			0
$847$		−	2.31804e6i		−	0.111023i
$848$			8.68720e6i			0.414849i
$849$		0			0
$850$	7.53239e6	+	1.64179e7i	0.357590	+	0.779418i
$851$	1.85586e6			0.0878456
$852$		0			0
$853$			1.31074e7i			0.616800i	0.951257	+	0.308400i	$0.0997936\pi$
$853$			1.31074e7i			0.616800i	−0.951257	+	0.308400i	$0.900206\pi$
$854$	−5.19186e6			−0.243601
$855$		0			0
$856$	−6.38726e6			−0.297941
$857$			3.48607e7i			1.62138i	0.585477	+	0.810689i	$0.300907\pi$
$857$			3.48607e7i			1.62138i	−0.585477	+	0.810689i	$0.699093\pi$
$858$		0			0
$859$	−2.14838e7			−0.993410			−0.496705	−	0.867919i	$-0.665457\pi$
$859$	−2.14838e7			−0.993410			−0.496705	+	0.867919i	$0.665457\pi$
$860$	−7.24090e6	−	4.64454e6i	−0.333846	−	0.214139i
$861$		0			0
$862$		−	1.46135e6i		−	0.0669863i
$863$		−	3.37660e6i		−	0.154331i	−0.997018	−	0.0771654i	$-0.975413\pi$
$863$		−	3.37660e6i		−	0.154331i	0.997018	−	0.0771654i	$-0.0245870\pi$
$864$		0			0
$865$	1.44595e7	+	9.27477e6i	0.657072	+	0.421466i
$866$	−5.21175e6			−0.236151
$867$		0			0
$868$		−	8.19958e6i		−	0.369396i
$869$	2.10233e7			0.944390
$870$		0			0
$871$	259028.			0.0115691
$872$		−	1.44247e7i		−	0.642416i
$873$		0			0
$874$	−1.07638e7			−0.476637
$875$	−1.19607e6	+	8.47597e6i	−0.0528123	+	0.374257i
$876$		0			0
$877$			1.58283e7i			0.694921i	0.937695	+	0.347461i	$0.112956\pi$
$877$			1.58283e7i			0.694921i	−0.937695	+	0.347461i	$0.887044\pi$
$878$			2.06526e7i			0.904145i
$879$		0			0
$880$	2.60585e6	−	4.06255e6i	0.113434	−	0.176845i
$881$	1.50941e7			0.655191			0.327596	−	0.944818i	$-0.393762\pi$
$881$	1.50941e7			0.655191			0.327596	+	0.944818i	$0.393762\pi$
$882$		0			0
$883$			4.20608e7i			1.81542i	0.419603	+	0.907708i	$0.362169\pi$
$883$			4.20608e7i			1.81542i	−0.419603	+	0.907708i	$0.637831\pi$
$884$	562480.			0.0242090
$885$		0			0
$886$	3.05850e7			1.30895
$887$			2.83691e7i			1.21070i	0.795959	+	0.605351i	$0.206967\pi$
$887$			2.83691e7i			1.21070i	−0.795959	+	0.605351i	$0.793033\pi$
$888$		0			0
$889$	1.20262e7			0.510358
$890$	2.17194e7	+	1.39315e7i	0.919122	+	0.589553i
$891$		0			0
$892$			8.64862e6i			0.363944i
$893$			1.24952e7i			0.524343i
$894$		0			0
$895$	2.42901e7	−	3.78685e7i	1.01361	−	1.58023i
$896$	−802816.			−0.0334077
$897$		0			0
$898$		−	1.93338e7i		−	0.800068i
$899$	1.23703e7			0.510482
$900$		0			0
$901$	4.90374e7			2.01241
$902$		−	3.83610e6i		−	0.156990i
$903$		0			0
$904$	−6.68818e6			−0.272199
$905$	1.56546e7	−	2.44058e7i	0.635362	−	0.990539i
$906$		0			0
$907$			1.00151e7i			0.404236i	0.979361	+	0.202118i	$0.0647825\pi$
$907$			1.00151e7i			0.404236i	−0.979361	+	0.202118i	$0.935217\pi$
$908$		−	2.16375e6i		−	0.0870947i
$909$		0			0
$910$	224362.	+	143913.i	0.00898145	+	0.00576098i
$911$	2.06987e7			0.826317			0.413158	−	0.910659i	$-0.364426\pi$
$911$	2.06987e7			0.826317			0.413158	+	0.910659i	$0.364426\pi$
$912$		0			0
$913$			124717.i			0.00495164i
$914$	1.40748e7			0.557284
$915$		0			0
$916$	−1.90204e6			−0.0749000
$917$			4.98345e6i			0.195707i
$918$		0			0
$919$	−6.79248e6			−0.265301			−0.132651	−	0.991163i	$-0.542349\pi$
$919$	−6.79248e6			−0.265301			−0.132651	+	0.991163i	$0.542349\pi$
$920$	−4.34088e6	+	6.76749e6i	−0.169086	+	0.263608i
$921$		0			0
$922$			1.42375e7i			0.551578i
$923$			1.16747e6i			0.0451067i
$924$		0			0
$925$	2.34564e6	−	1.07616e6i	0.0901377	−	0.0413544i
$926$	1.75727e7			0.673458
$927$		0			0
$928$		−	1.21117e6i		−	0.0461673i
$929$	−2.18354e7			−0.830085			−0.415042	−	0.909802i	$-0.636233\pi$
$929$	−2.18354e7			−0.830085			−0.415042	+	0.909802i	$0.636233\pi$
$930$		0			0
$931$	−2.87505e6			−0.108710
$932$		−	1.05522e7i		−	0.397927i
$933$		0			0
$934$	−2.98689e7			−1.12035
$935$	−2.29323e7	−	1.47095e7i	−0.857864	−	0.550260i
$936$		0			0
$937$		−	3.76114e7i		−	1.39949i	−0.714391	−	0.699747i	$-0.753296\pi$
$937$		−	3.76114e7i		−	1.39949i	0.714391	−	0.699747i	$-0.246704\pi$
$938$			2.08691e6i			0.0774455i
$939$		0			0
$940$	7.85608e6	+	5.03913e6i	0.289992	+	0.186010i
$941$	−3.13453e7			−1.15398			−0.576989	−	0.816752i	$-0.695773\pi$
$941$	−3.13453e7			−1.15398			−0.576989	+	0.816752i	$0.695773\pi$
$942$		0			0
$943$			6.39025e6i			0.234012i
$944$	4.82761e6			0.176320
$945$		0			0
$946$	1.29748e7			0.471383
$947$		−	2.16274e6i		−	0.0783664i	−0.999232	−	0.0391832i	$-0.987524\pi$
$947$		−	2.16274e6i		−	0.0783664i	0.999232	−	0.0391832i	$-0.0124756\pi$
$948$		0			0
$949$	917134.			0.0330573
$950$	−1.36045e7	+	6.24163e6i	−0.489073	+	0.224382i
$951$		0			0
$952$			4.53173e6i			0.162058i
$953$		−	2.60248e7i		−	0.928230i	−0.885775	−	0.464115i	$-0.846372\pi$
$953$		−	2.60248e7i		−	0.928230i	0.885775	−	0.464115i	$-0.153628\pi$
$954$		0			0
$955$	−6.15898e6	+	9.60194e6i	−0.218525	+	0.340683i
$956$	−7.48713e6			−0.264954
$957$		0			0
$958$			2.02899e7i			0.714278i
$959$	−3.11908e6			−0.109517
$960$		0			0
$961$	8.07542e7			2.82070
$962$		−	80361.9i		−	0.00279971i
$963$		0			0
$964$	3.44166e6			0.119282
$965$	−4.11011e7	−	2.63635e7i	−1.42081	−	0.911349i
$966$		0			0
$967$			3.85997e7i			1.32745i	0.747977	+	0.663725i	$0.231025\pi$
$967$			3.85997e7i			1.32745i	−0.747977	+	0.663725i	$0.768975\pi$
$968$		−	3.02764e6i		−	0.103852i
$969$		0			0
$970$	−1.64802e7	+	2.56929e7i	−0.562384	+	0.876765i
$971$	−1.98202e7			−0.674621			−0.337310	−	0.941393i	$-0.609517\pi$
$971$	−1.98202e7			−0.674621			−0.337310	+	0.941393i	$0.609517\pi$
$972$		0			0
$973$		−	1.36179e7i		−	0.461136i
$974$	3.36395e7			1.13619
$975$		0			0
$976$	−6.78121e6			−0.227868
$977$			6.29461e6i			0.210976i	0.994421	+	0.105488i	$0.0336404\pi$
$977$			6.29461e6i			0.210976i	−0.994421	+	0.105488i	$0.966360\pi$
$978$		0			0
$979$	−3.89187e7			−1.29778
$980$	−1.15946e6	+	1.80762e6i	−0.0385649	+	0.0601231i
$981$		0			0
$982$		−	4.29275e6i		−	0.142055i
$983$		−	3.54716e7i		−	1.17084i	−0.810731	−	0.585419i	$-0.800930\pi$
$983$		−	3.54716e7i		−	1.17084i	0.810731	−	0.585419i	$-0.199070\pi$
$984$		0			0
$985$	5.37977e6	+	3.45075e6i	0.176674	+	0.113324i
$986$	−6.83679e6			−0.223955
$987$		0			0
$988$			466093.i			0.0151908i
$989$	−2.16138e7			−0.702652
$990$		0			0
$991$	−1.49772e7			−0.484446			−0.242223	−	0.970221i	$-0.577877\pi$
$991$	−1.49772e7			−0.484446			−0.242223	+	0.970221i	$0.577877\pi$
$992$		−	1.07097e7i		−	0.345538i
$993$		0			0
$994$	−9.40595e6			−0.301951
$995$	−7.91210e6	+	1.23351e7i	−0.253358	+	0.394988i
$996$		0			0
$997$		−	3.79210e7i		−	1.20821i	−0.796905	−	0.604104i	$-0.793531\pi$
$997$		−	3.79210e7i		−	1.20821i	0.796905	−	0.604104i	$-0.206469\pi$
$998$			1.73711e7i			0.552079i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.6.g.h.379.2		10
3.2	odd	2		70.6.c.d.29.9	yes	10
5.4	even	2	inner	630.6.g.h.379.7		10
12.11	even	2		560.6.g.d.449.4		10
15.2	even	4		350.6.a.y.1.4		5
15.8	even	4		350.6.a.z.1.2		5
15.14	odd	2		70.6.c.d.29.2	✓	10
60.59	even	2		560.6.g.d.449.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.c.d.29.2	✓	10	15.14	odd	2
70.6.c.d.29.9	yes	10	3.2	odd	2
350.6.a.y.1.4		5	15.2	even	4
350.6.a.z.1.2		5	15.8	even	4
560.6.g.d.449.4		10	12.11	even	2
560.6.g.d.449.7		10	60.59	even	2
630.6.g.h.379.2		10	1.1	even	1	trivial
630.6.g.h.379.7		10	5.4	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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -16.0000 q^{4} +(-30.1818 + 47.0538i) q^{5} +49.0000i q^{7} +64.0000i q^{8} +(188.215 + 120.727i) q^{10} -337.260 q^{11} -24.3276i q^{13} +196.000 q^{14} +256.000 q^{16} -1445.07i q^{17} +1197.44 q^{19} +(482.908 - 752.861i) q^{20} +1349.04i q^{22} -2247.26i q^{23} +(-1303.12 - 2840.33i) q^{25} -97.3103 q^{26} -784.000i q^{28} +1182.78 q^{29} +10458.6 q^{31} -1024.00i q^{32} -5780.27 q^{34} +(-2305.64 - 1478.91i) q^{35} +825.831i q^{37} -4789.75i q^{38} +(-3011.44 - 1931.63i) q^{40} -2843.58 q^{41} -9617.84i q^{43} +5396.16 q^{44} -8989.03 q^{46} +10435.0i q^{47} -2401.00 q^{49} +(-11361.3 + 5212.48i) q^{50} +389.241i q^{52} +33934.4i q^{53} +(10179.1 - 15869.4i) q^{55} -3136.00 q^{56} -4731.12i q^{58} +18857.8 q^{59} -26489.1 q^{61} -41834.6i q^{62} -4096.00 q^{64} +(1144.71 + 734.250i) q^{65} +10647.5i q^{67} +23121.1i q^{68} +(-5915.63 + 9222.55i) q^{70} -47989.5 q^{71} +37699.4i q^{73} +3303.32 q^{74} -19159.0 q^{76} -16525.7i q^{77} -62335.6 q^{79} +(-7726.53 + 12045.8i) q^{80} +11374.3i q^{82} -369.796i q^{83} +(67995.9 + 43614.7i) q^{85} -38471.4 q^{86} -21584.6i q^{88} +115397. q^{89} +1192.05 q^{91} +35956.1i q^{92} +41739.9 q^{94} +(-36140.8 + 56344.0i) q^{95} +136508. i q^{97} +9604.00i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 160 q^{4} + 66 q^{5} - 416 q^{10} - 1496 q^{11} + 1960 q^{14} + 2560 q^{16} + 512 q^{19} - 1056 q^{20} - 4170 q^{25} - 3648 q^{26} + 15424 q^{29} + 824 q^{31} - 6240 q^{34} + 5096 q^{35} + 6656 q^{40}+ \cdots - 215316 q^{95}+O(q^{100}) \) 10 * q - 160 * q^4 + 66 * q^5 - 416 * q^10 - 1496 * q^11 + 1960 * q^14 + 2560 * q^16 + 512 * q^19 - 1056 * q^20 - 4170 * q^25 - 3648 * q^26 + 15424 * q^29 + 824 * q^31 - 6240 * q^34 + 5096 * q^35 + 6656 * q^40 - 14964 * q^41 + 23936 * q^44 + 27616 * q^46 - 24010 * q^49 - 20496 * q^50 + 73936 * q^55 - 31360 * q^56 + 159192 * q^59 + 19508 * q^61 - 40960 * q^64 - 150936 * q^65 + 12936 * q^70 + 123856 * q^71 + 115200 * q^74 - 8192 * q^76 - 301824 * q^79 + 16896 * q^80 + 388812 * q^85 - 165344 * q^86 + 537900 * q^89 + 44688 * q^91 - 473616 * q^94 - 215316 * q^95

Introduction

L-functions

Modular forms

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