LMFDB - Embedded newform 63.8.e.b.46.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,8,Mod(37,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.37"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.6802566055$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 103x^{6} - 378x^{5} + 9744x^{4} - 22680x^{3} + 149400x^{2} + 216000x + 810000 $ x^8 - x^7 + 103x^6 - 378x^5 + 9744x^4 - 22680x^3 + 149400x^2 + 216000x + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$2.57145 - 4.45388i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.8.e.b.37.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.69038 - 6.39193i) q^{2} +(36.7621 - 63.6739i) q^{4} +(-145.409 - 251.857i) q^{5} +(358.327 - 833.753i) q^{7} -1487.40 q^{8} +(-1073.23 + 1858.89i) q^{10} +(1596.44 - 2765.12i) q^{11} +5186.70 q^{13} +(-6651.66 + 786.465i) q^{14} +(783.535 + 1357.12i) q^{16} +(-1224.56 + 2120.99i) q^{17} +(-16159.1 - 27988.4i) q^{19} -21382.2 q^{20} -23565.9 q^{22} +(31470.7 + 54508.9i) q^{23} +(-3225.30 + 5586.38i) q^{25} +(-19140.9 - 33153.0i) q^{26} +(-39915.4 - 53466.7i) q^{28} -141752. q^{29} +(-141188. + 244545. i) q^{31} +(-89410.7 + 154864. i) q^{32} +18076.3 q^{34} +(-262090. + 30988.5i) q^{35} +(65683.8 + 113768. i) q^{37} +(-119267. + 206576. i) q^{38} +(216283. + 374612. i) q^{40} +65254.0 q^{41} -257876. q^{43} +(-117377. - 203303. i) q^{44} +(232278. - 402317. i) q^{46} +(63728.7 + 110381. i) q^{47} +(-566746. - 597513. i) q^{49} +47610.4 q^{50} +(190674. - 330257. i) q^{52} +(395323. - 684719. i) q^{53} -928551. q^{55} +(-532978. + 1.24013e6i) q^{56} +(523119. + 906068. i) q^{58} +(607173. - 1.05165e6i) q^{59} +(-381042. - 659985. i) q^{61} +2.08415e6 q^{62} +1.52042e6 q^{64} +(-754195. - 1.30630e6i) q^{65} +(1.72143e6 - 2.98160e6i) q^{67} +(90034.6 + 155944. i) q^{68} +(1.16529e6 + 1.56090e6i) q^{70} +3.99576e6 q^{71} +(384669. - 666266. i) q^{73} +(484797. - 839693. i) q^{74} -2.37617e6 q^{76} +(-1.73338e6 - 2.32186e6i) q^{77} +(2.91690e6 + 5.05222e6i) q^{79} +(227867. - 394677. i) q^{80} +(-240812. - 417099. i) q^{82} -1.39747e6 q^{83} +712248. q^{85} +(951662. + 1.64833e6i) q^{86} +(-2.37455e6 + 4.11285e6i) q^{88} +(808509. + 1.40038e6i) q^{89} +(1.85854e6 - 4.32443e6i) q^{91} +4.62772e6 q^{92} +(470367. - 814699. i) q^{94} +(-4.69937e6 + 8.13955e6i) q^{95} -5.68544e6 q^{97} +(-1.72775e6 + 5.82765e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 348 q^{4} + 252 q^{5} + 672 q^{7} + 1968 q^{8} - 4774 q^{10} - 3972 q^{11} - 2352 q^{13} - 47502 q^{14} - 57264 q^{16} + 56364 q^{17} - 41748 q^{19} - 324744 q^{20} - 305908 q^{22} + 131748 q^{23}+ \cdots - 60255006 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 - 348 * q^4 + 252 * q^5 + 672 * q^7 + 1968 * q^8 - 4774 * q^10 - 3972 * q^11 - 2352 * q^13 - 47502 * q^14 - 57264 * q^16 + 56364 * q^17 - 41748 * q^19 - 324744 * q^20 - 305908 * q^22 + 131748 * q^23 + 68016 * q^25 + 113652 * q^26 + 681548 * q^28 - 68112 * q^29 - 401212 * q^31 - 453408 * q^32 + 164220 * q^34 - 40404 * q^35 + 5396 * q^37 + 31794 * q^38 + 443688 * q^40 - 820848 * q^41 + 93088 * q^43 - 1465836 * q^44 - 1379202 * q^46 + 1470084 * q^47 - 2793784 * q^49 - 2791056 * q^50 + 5269768 * q^52 - 642372 * q^53 - 6126680 * q^55 + 6195168 * q^56 + 1972220 * q^58 + 752220 * q^59 - 1325772 * q^61 + 6032628 * q^62 - 1731712 * q^64 - 4868808 * q^65 + 290916 * q^67 + 2453556 * q^68 + 11665990 * q^70 - 6755520 * q^71 - 6706588 * q^73 + 3616878 * q^74 + 5846008 * q^76 + 5310564 * q^77 - 3946244 * q^79 + 10695888 * q^80 + 17563252 * q^82 - 19084128 * q^83 + 14012136 * q^85 + 23237832 * q^86 + 8043336 * q^88 + 16165212 * q^89 - 2414720 * q^91 + 38885256 * q^92 - 5720442 * q^94 - 3268452 * q^95 + 3066224 * q^97 - 60255006 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−3.69038	−	6.39193i	−0.326187	−	0.564972i	0.655565	−	0.755139i	$-0.272431\pi$
$2$	−3.69038	−	6.39193i	−0.326187	−	0.564972i	−0.981752	+	0.190167i	$0.939097\pi$
$3$		0			0
$3$		0			0
$4$	36.7621	−	63.6739i	0.287204	−	0.497452i
$5$	−145.409	−	251.857i	−0.520233	−	0.901069i	−0.999723	−	0.0235223i	$-0.992512\pi$
$5$	−145.409	−	251.857i	−0.520233	−	0.901069i	0.479491	−	0.877547i	$-0.340821\pi$
$6$		0			0
$7$	358.327	−	833.753i	0.394854	−	0.918744i
$7$	358.327	−	833.753i	0.394854	−	0.918744i
$8$	−1487.40			−1.02710
$9$		0			0
$10$	−1073.23	+	1858.89i	−0.339386	+	0.587834i
$11$	1596.44	−	2765.12i	0.361642	−	0.626382i	−0.626589	−	0.779350i	$-0.715550\pi$
$11$	1596.44	−	2765.12i	0.361642	−	0.626382i	0.988231	+	0.152967i	$0.0488830\pi$
$12$		0			0
$13$	5186.70			0.654771			0.327385	−	0.944891i	$-0.393832\pi$
$13$	5186.70			0.654771			0.327385	+	0.944891i	$0.393832\pi$
$14$	−6651.66	+	786.465i	−0.647861	+	0.0766004i
$15$		0			0
$16$	783.535	+	1357.12i	0.0478232	+	0.0828322i
$17$	−1224.56	+	2120.99i	−0.0604515	+	0.104705i	−0.894667	−	0.446733i	$-0.852587\pi$
$17$	−1224.56	+	2120.99i	−0.0604515	+	0.104705i	0.834216	+	0.551438i	$0.185921\pi$
$18$		0			0
$19$	−16159.1	−	27988.4i	−0.540480	−	0.936139i	−0.998876	−	0.0473912i	$-0.984909\pi$
$19$	−16159.1	−	27988.4i	−0.540480	−	0.936139i	0.458396	−	0.888748i	$-0.348424\pi$
$20$	−21382.2			−0.597652
$21$		0			0
$22$	−23565.9			−0.471851
$23$	31470.7	+	54508.9i	0.539335	+	0.934156i	0.998940	+	0.0460327i	$0.0146578\pi$
$23$	31470.7	+	54508.9i	0.539335	+	0.934156i	−0.459604	+	0.888124i	$0.652009\pi$
$24$		0			0
$25$	−3225.30	+	5586.38i	−0.0412838	+	0.0715057i
$26$	−19140.9	−	33153.0i	−0.213578	−	0.369927i
$27$		0			0
$28$	−39915.4	−	53466.7i	−0.343627	−	0.460288i
$29$	−141752.			−1.07928			−0.539642	−	0.841895i	$-0.681440\pi$
$29$	−141752.			−1.07928			−0.539642	+	0.841895i	$0.681440\pi$
$30$		0			0
$31$	−141188.	+	244545.i	−0.851200	+	1.47432i	0.0289267	+	0.999582i	$0.490791\pi$
$31$	−141188.	+	244545.i	−0.851200	+	1.47432i	−0.880126	+	0.474739i	$0.842542\pi$
$32$	−89410.7	+	154864.i	−0.482353	+	0.835460i
$33$		0			0
$34$	18076.3			0.0788740
$35$	−262090.	+	30988.5i	−1.03327	+	0.122169i
$36$		0			0
$37$	65683.8	+	113768.i	0.213183	+	0.369244i	0.952709	−	0.303884i	$-0.0982836\pi$
$37$	65683.8	+	113768.i	0.213183	+	0.369244i	−0.739526	+	0.673128i	$0.764950\pi$
$38$	−119267.	+	206576.i	−0.352595	+	0.610713i
$39$		0			0
$40$	216283.	+	374612.i	0.534332	+	0.925491i
$41$	65254.0			0.147864			0.0739322	−	0.997263i	$-0.476445\pi$
$41$	65254.0			0.147864			0.0739322	+	0.997263i	$0.476445\pi$
$42$		0			0
$43$	−257876.			−0.494620			−0.247310	−	0.968936i	$-0.579547\pi$
$43$	−257876.			−0.494620			−0.247310	+	0.968936i	$0.579547\pi$
$44$	−117377.	−	203303.i	−0.207730	−	0.359799i
$45$		0			0
$46$	232278.	−	402317.i	0.351848	−	0.609419i
$47$	63728.7	+	110381.i	0.0895349	+	0.155079i	0.907315	−	0.420452i	$-0.138129\pi$
$47$	63728.7	+	110381.i	0.0895349	+	0.155079i	−0.817780	+	0.575531i	$0.804795\pi$
$48$		0			0
$49$	−566746.	−	597513.i	−0.688180	−	0.725540i
$50$	47610.4			0.0538650
$51$		0			0
$52$	190674.	−	330257.i	0.188053	−	0.325717i
$53$	395323.	−	684719.i	0.364743	−	0.631753i	−0.623992	−	0.781431i	$-0.714490\pi$
$53$	395323.	−	684719.i	0.364743	−	0.631753i	0.988735	+	0.149678i	$0.0478237\pi$
$54$		0			0
$55$	−928551.			−0.752552
$56$	−532978.	+	1.24013e6i	−0.405556	+	0.943644i
$57$		0			0
$58$	523119.	+	906068.i	0.352048	+	0.609765i
$59$	607173.	−	1.05165e6i	0.384884	−	0.666639i	−0.606869	−	0.794802i	$-0.707575\pi$
$59$	607173.	−	1.05165e6i	0.384884	−	0.666639i	0.991753	+	0.128163i	$0.0409080\pi$
$60$		0			0
$61$	−381042.	−	659985.i	−0.214941	−	0.372288i	0.738314	−	0.674458i	$-0.235622\pi$
$61$	−381042.	−	659985.i	−0.214941	−	0.372288i	−0.953254	+	0.302169i	$0.902289\pi$
$62$	2.08415e6			1.11060
$63$		0			0
$64$	1.52042e6			0.724995
$65$	−754195.	−	1.30630e6i	−0.340633	−	0.589994i
$66$		0			0
$67$	1.72143e6	−	2.98160e6i	0.699241	−	1.21112i	−0.269488	−	0.963004i	$-0.586855\pi$
$67$	1.72143e6	−	2.98160e6i	0.699241	−	1.21112i	0.968730	−	0.248118i	$-0.0798121\pi$
$68$	90034.6	+	155944.i	0.0347239	+	0.0601435i
$69$		0			0
$70$	1.16529e6	+	1.56090e6i	0.406061	+	0.543918i
$71$	3.99576e6			1.32494			0.662469	−	0.749089i	$-0.269509\pi$
$71$	3.99576e6			1.32494			0.662469	+	0.749089i	$0.269509\pi$
$72$		0			0
$73$	384669.	−	666266.i	0.115733	−	0.200455i	−0.802340	−	0.596868i	$-0.796412\pi$
$73$	384669.	−	666266.i	0.115733	−	0.200455i	0.918073	+	0.396412i	$0.129745\pi$
$74$	484797.	−	839693.i	0.139075	−	0.240885i
$75$		0			0
$76$	−2.37617e6			−0.620913
$77$	−1.73338e6	−	2.32186e6i	−0.432689	−	0.579586i
$78$		0			0
$79$	2.91690e6	+	5.05222e6i	0.665620	+	1.15289i	0.979117	+	0.203299i	$0.0651663\pi$
$79$	2.91690e6	+	5.05222e6i	0.665620	+	1.15289i	−0.313496	+	0.949589i	$0.601500\pi$
$80$	227867.	−	394677.i	0.0497584	−	0.0861840i
$81$		0			0
$82$	−240812.	−	417099.i	−0.0482314	−	0.0835393i
$83$	−1.39747e6			−0.268267			−0.134134	−	0.990963i	$-0.542825\pi$
$83$	−1.39747e6			−0.268267			−0.134134	+	0.990963i	$0.542825\pi$
$84$		0			0
$85$	712248.			0.125795
$86$	951662.	+	1.64833e6i	0.161339	+	0.279447i
$87$		0			0
$88$	−2.37455e6	+	4.11285e6i	−0.371443	+	0.643359i
$89$	808509.	+	1.40038e6i	0.121568	+	0.210562i	0.920386	−	0.391010i	$-0.127874\pi$
$89$	808509.	+	1.40038e6i	0.121568	+	0.210562i	−0.798818	+	0.601573i	$0.794541\pi$
$90$		0			0
$91$	1.85854e6	−	4.32443e6i	0.258539	−	0.601567i
$92$	4.62772e6			0.619598
$93$		0			0
$94$	470367.	−	814699.i	0.0584102	−	0.101170i
$95$	−4.69937e6	+	8.13955e6i	−0.562351	+	0.974020i
$96$		0			0
$97$	−5.68544e6			−0.632504			−0.316252	−	0.948675i	$-0.602424\pi$
$97$	−5.68544e6			−0.632504			−0.316252	+	0.948675i	$0.602424\pi$
$98$	−1.72775e6	+	5.82765e6i	−0.185435	+	0.625464i
$99$		0			0
$100$	237138.	+	410735.i	0.0237138	+	0.0410735i
$101$	5.04402e6	−	8.73650e6i	0.487138	−	0.843748i	−0.512752	−	0.858537i	$-0.671374\pi$
$101$	5.04402e6	−	8.73650e6i	0.487138	−	0.843748i	0.999891	+	0.0147883i	$0.00470742\pi$
$102$		0			0
$103$	−4.66877e6	−	8.08655e6i	−0.420991	−	0.729177i	0.575046	−	0.818121i	$-0.304984\pi$
$103$	−4.66877e6	−	8.08655e6i	−0.420991	−	0.729177i	−0.996037	+	0.0889438i	$0.971651\pi$
$104$	−7.71471e6			−0.672517
$105$		0			0
$106$	−5.83557e6			−0.475897
$107$	−7.20247e6	−	1.24750e7i	−0.568379	−	0.984462i	−0.996726	−	0.0808474i	$-0.974237\pi$
$107$	−7.20247e6	−	1.24750e7i	−0.568379	−	0.984462i	0.428347	−	0.903614i	$-0.359096\pi$
$108$		0			0
$109$	−4.27999e6	+	7.41316e6i	−0.316556	+	0.548291i	−0.979767	−	0.200142i	$-0.935860\pi$
$109$	−4.27999e6	+	7.41316e6i	−0.316556	+	0.548291i	0.663211	+	0.748432i	$0.269193\pi$
$110$	3.42671e6	+	5.93523e6i	0.245472	+	0.425171i
$111$		0			0
$112$	1.41227e6	−	166981.i	0.0949848	−	0.0112306i
$113$	−1.15607e7			−0.753722			−0.376861	−	0.926270i	$-0.622997\pi$
$113$	−1.15607e7			−0.753722			−0.376861	+	0.926270i	$0.622997\pi$
$114$		0			0
$115$	9.15227e6	−	1.58522e7i	0.561160	−	0.971957i
$116$	−5.21110e6	+	9.02589e6i	−0.309975	+	0.536892i
$117$		0			0
$118$	−8.96280e6			−0.502177
$119$	1.32959e6	+	1.78099e6i	0.0723276	+	0.0968827i
$120$		0			0
$121$	4.64633e6	+	8.04768e6i	0.238430	+	0.412973i
$122$	−2.81238e6	+	4.87119e6i	−0.140222	+	0.242871i
$123$		0			0
$124$	1.03807e7	+	1.79800e7i	0.488936	+	0.846862i
$125$	−2.08443e7			−0.954556
$126$		0			0
$127$	2.65100e7			1.14841			0.574204	−	0.818712i	$-0.305312\pi$
$127$	2.65100e7			1.14841			0.574204	+	0.818712i	$0.305312\pi$
$128$	5.83363e6	+	1.01041e7i	0.245869	+	0.425857i
$129$		0			0
$130$	−5.56654e6	+	9.64152e6i	−0.222220	+	0.384896i
$131$	2.27287e6	+	3.93672e6i	0.0883333	+	0.152998i	0.906807	−	0.421547i	$-0.138513\pi$
$131$	2.27287e6	+	3.93672e6i	0.0883333	+	0.152998i	−0.818473	+	0.574544i	$0.805179\pi$
$132$		0			0
$133$	−2.91257e7	+	3.44370e6i	−1.07348	+	0.126924i
$134$	−2.54109e7			−0.912334
$135$		0			0
$136$	1.82141e6	−	3.15477e6i	0.0620899	−	0.107543i
$137$	2.46771e7	−	4.27420e7i	0.819922	−	1.42015i	−0.0858166	−	0.996311i	$-0.527350\pi$
$137$	2.46771e7	−	4.27420e7i	0.819922	−	1.42015i	0.905739	−	0.423836i	$-0.139317\pi$
$138$		0			0
$139$	−4.41231e7			−1.39352			−0.696761	−	0.717303i	$-0.745376\pi$
$139$	−4.41231e7			−1.39352			−0.696761	+	0.717303i	$0.745376\pi$
$140$	−7.66185e6	+	1.78275e7i	−0.235985	+	0.549089i
$141$		0			0
$142$	−1.47459e7	−	2.55406e7i	−0.432177	−	0.748553i
$143$	8.28026e6	−	1.43418e7i	0.236793	−	0.410137i
$144$		0			0
$145$	2.06121e7	+	3.57011e7i	0.561479	+	0.972509i
$146$	−5.67830e6			−0.151002
$147$		0			0
$148$	9.65872e6			0.244908
$149$	1.11368e7	+	1.92894e7i	0.275808	+	0.477714i	0.970339	−	0.241750i	$-0.0777212\pi$
$149$	1.11368e7	+	1.92894e7i	0.275808	+	0.477714i	−0.694531	+	0.719463i	$0.744388\pi$
$150$		0			0
$151$	3.47581e7	−	6.02027e7i	0.821554	−	1.42297i	−0.0829702	−	0.996552i	$-0.526441\pi$
$151$	3.47581e7	−	6.02027e7i	0.821554	−	1.42297i	0.904524	−	0.426422i	$-0.140226\pi$
$152$	2.40351e7	+	4.16300e7i	0.555129	+	0.961511i
$153$		0			0
$154$	−8.44432e6	+	1.96482e7i	−0.186313	+	0.433511i
$155$	8.21202e7			1.77129
$156$		0			0
$157$	6.14609e6	−	1.06453e7i	0.126751	−	0.219538i	−0.795665	−	0.605737i	$-0.792879\pi$
$157$	6.14609e6	−	1.06453e7i	0.126751	−	0.219538i	0.922416	+	0.386198i	$0.126212\pi$
$158$	2.15289e7	−	3.72892e7i	0.434233	−	0.752114i
$159$		0			0
$160$	5.20047e7			1.00374
$161$	5.67237e7	−	6.70678e6i	1.07121	−	0.126655i
$162$		0			0
$163$	8.80901e6	+	1.52577e7i	0.159320	+	0.275950i	0.934624	−	0.355638i	$-0.115736\pi$
$163$	8.80901e6	+	1.52577e7i	0.159320	+	0.275950i	−0.775304	+	0.631589i	$0.782403\pi$
$164$	2.39888e6	−	4.15498e6i	0.0424673	−	0.0735555i
$165$		0			0
$166$	5.15718e6	+	8.93250e6i	0.0875053	+	0.151564i
$167$	−1.13558e8			−1.88673			−0.943367	−	0.331751i	$-0.892361\pi$
$167$	−1.13558e8			−1.88673			−0.943367	+	0.331751i	$0.892361\pi$
$168$		0			0
$169$	−3.58467e7			−0.571275
$170$	−2.62847e6	−	4.55264e6i	−0.0410328	−	0.0710709i
$171$		0			0
$172$	−9.48008e6	+	1.64200e7i	−0.142057	+	0.246050i
$173$	−1.08140e7	−	1.87304e7i	−0.158791	−	0.275034i	0.775642	−	0.631173i	$-0.217426\pi$
$173$	−1.08140e7	−	1.87304e7i	−0.158791	−	0.275034i	−0.934433	+	0.356139i	$0.884093\pi$
$174$		0			0
$175$	3.50195e6	+	4.69086e6i	0.0493943	+	0.0661636i
$176$	5.00348e6			0.0691795
$177$		0			0
$178$	5.96742e6	−	1.03359e7i	0.0793079	−	0.137365i
$179$	5.41432e7	−	9.37787e7i	0.705599	−	1.22213i	−0.260875	−	0.965372i	$-0.584011\pi$
$179$	5.41432e7	−	9.37787e7i	0.705599	−	1.22213i	0.966475	−	0.256761i	$-0.0826555\pi$
$180$		0			0
$181$	6.56731e7			0.823214			0.411607	−	0.911361i	$-0.364968\pi$
$181$	6.56731e7			0.823214			0.411607	+	0.911361i	$0.364968\pi$
$182$	−3.45002e7	+	4.07915e6i	−0.424200	+	0.0501557i
$183$		0			0
$184$	−4.68096e7	−	8.10767e7i	−0.553953	−	0.959475i
$185$	1.91021e7	−	3.30858e7i	0.221809	−	0.384185i
$186$		0			0
$187$	3.90986e6	+	6.77208e6i	0.0437236	+	0.0757315i
$188$	9.37121e6			0.102859
$189$		0			0
$190$	6.93699e7			0.733726
$191$	−7.23000e6	−	1.25227e7i	−0.0750795	−	0.130042i	0.826041	−	0.563610i	$-0.190588\pi$
$191$	−7.23000e6	−	1.25227e7i	−0.0750795	−	0.130042i	−0.901121	+	0.433568i	$0.857254\pi$
$192$		0			0
$193$	3.11856e7	−	5.40150e7i	0.312251	−	0.540834i	−0.666599	−	0.745417i	$-0.732250\pi$
$193$	3.11856e7	−	5.40150e7i	0.312251	−	0.540834i	0.978849	+	0.204583i	$0.0655838\pi$
$194$	2.09815e7	+	3.63410e7i	0.206314	+	0.357347i
$195$		0			0
$196$	−5.88808e7	+	1.41211e7i	−0.558570	+	0.133959i
$197$	1.35525e7			0.126296			0.0631478	−	0.998004i	$-0.479886\pi$
$197$	1.35525e7			0.126296			0.0631478	+	0.998004i	$0.479886\pi$
$198$		0			0
$199$	1.48623e7	−	2.57423e7i	0.133691	−	0.231559i	−0.791406	−	0.611291i	$-0.790650\pi$
$199$	1.48623e7	−	2.57423e7i	0.133691	−	0.231559i	0.925097	+	0.379732i	$0.123984\pi$
$200$	4.79732e6	−	8.30920e6i	0.0424027	−	0.0734437i
$201$		0			0
$202$	−7.44575e7			−0.635593
$203$	−5.07936e7	+	1.18186e8i	−0.426160	+	0.991585i
$204$		0			0
$205$	−9.48855e6	−	1.64346e7i	−0.0769239	−	0.133236i
$206$	−3.44591e7	+	5.96850e7i	−0.274643	+	0.475696i
$207$		0			0
$208$	4.06396e6	+	7.03899e6i	0.0313132	+	0.0542361i
$209$	−1.03188e8			−0.781841
$210$		0			0
$211$	−1.45624e8			−1.06719			−0.533597	−	0.845739i	$-0.679160\pi$
$211$	−1.45624e8			−1.06719			−0.533597	+	0.845739i	$0.679160\pi$
$212$	−2.90658e7	−	5.03435e7i	−0.209511	−	0.362884i
$213$		0			0
$214$	−5.31597e7	+	9.20754e7i	−0.370796	+	0.642237i
$215$	3.74976e7	+	6.49478e7i	0.257317	+	0.445687i
$216$		0			0
$217$	1.53298e8	+	2.05343e8i	1.01842	+	1.36418i
$218$	6.31792e7			0.413025
$219$		0			0
$220$	−3.41355e7	+	5.91245e7i	−0.216136	+	0.374359i
$221$	−6.35140e6	+	1.10010e7i	−0.0395819	+	0.0685579i
$222$		0			0
$223$	−2.01327e8			−1.21573			−0.607863	−	0.794042i	$-0.707973\pi$
$223$	−2.01327e8			−1.21573			−0.607863	+	0.794042i	$0.707973\pi$
$224$	9.70800e7	+	1.30039e8i	0.577114	+	0.773043i
$225$		0			0
$226$	4.26636e7	+	7.38955e7i	0.245854	+	0.425832i
$227$	−1.53854e8	+	2.66483e8i	−0.873010	+	1.51210i	−0.0141421	+	0.999900i	$0.504502\pi$
$227$	−1.53854e8	+	2.66483e8i	−0.873010	+	1.51210i	−0.858868	+	0.512197i	$0.828832\pi$
$228$		0			0
$229$	−9.26335e7	−	1.60446e8i	−0.509734	−	0.882886i	−0.999936	−	0.0112769i	$-0.996410\pi$
$229$	−9.26335e7	−	1.60446e8i	−0.509734	−	0.882886i	0.490202	−	0.871609i	$-0.336923\pi$
$230$	−1.35102e8			−0.732172
$231$		0			0
$232$	2.10842e8			1.10854
$233$	−1.24551e8	−	2.15729e8i	−0.645062	−	1.11728i	−0.984287	−	0.176576i	$-0.943498\pi$
$233$	−1.24551e8	−	2.15729e8i	−0.645062	−	1.11728i	0.339225	−	0.940705i	$-0.389835\pi$
$234$		0			0
$235$	1.85335e7	−	3.21010e7i	0.0931580	−	0.161354i
$236$	−4.46420e7	−	7.73221e7i	−0.221081	−	0.382923i
$237$		0			0
$238$	6.47724e6	−	1.50712e7i	0.0311437	−	0.0724650i
$239$	−3.36485e6			−0.0159431			−0.00797156	−	0.999968i	$-0.502537\pi$
$239$	−3.36485e6			−0.0159431			−0.00797156	+	0.999968i	$0.502537\pi$
$240$		0			0
$241$	−1.09274e8	+	1.89269e8i	−0.502873	+	0.871001i	0.497122	+	0.867681i	$0.334390\pi$
$241$	−1.09274e8	+	1.89269e8i	−0.502873	+	0.871001i	−0.999994	+	0.00332052i	$0.998943\pi$
$242$	3.42935e7	−	5.93981e7i	0.155546	−	0.269413i
$243$		0			0
$244$	−5.60317e7			−0.246928
$245$	−6.80774e7	+	2.29623e8i	−0.295748	+	0.997547i
$246$		0			0
$247$	−8.38124e7	−	1.45167e8i	−0.353891	−	0.612957i
$248$	2.10003e8	−	3.63736e8i	0.874270	−	1.51428i
$249$		0			0
$250$	7.69233e7	+	1.33235e8i	0.311364	+	0.539298i
$251$	−3.10664e8			−1.24003			−0.620017	−	0.784588i	$-0.712874\pi$
$251$	−3.10664e8			−1.24003			−0.620017	+	0.784588i	$0.712874\pi$
$252$		0			0
$253$	2.00965e8			0.780185
$254$	−9.78319e7	−	1.69450e8i	−0.374596	−	0.648818i
$255$		0			0
$256$	1.40364e8	−	2.43117e8i	0.522896	−	0.905682i
$257$	1.48074e8	+	2.56472e8i	0.544144	+	0.942486i	0.998660	+	0.0517471i	$0.0164790\pi$
$257$	1.48074e8	+	2.56472e8i	0.544144	+	0.942486i	−0.454516	+	0.890739i	$0.650188\pi$
$258$		0			0
$259$	1.18391e8	−	1.39980e7i	0.423417	−	0.0500630i
$260$	−1.10903e8			−0.391325
$261$		0			0
$262$	1.67755e7	−	2.90560e7i	0.0576263	−	0.0998118i
$263$	1.29723e8	−	2.24687e8i	0.439717	−	0.761612i	−0.557951	−	0.829874i	$-0.688412\pi$
$263$	1.29723e8	−	2.24687e8i	0.439717	−	0.761612i	0.997667	+	0.0682625i	$0.0217455\pi$
$264$		0			0
$265$	−2.29935e8			−0.759004
$266$	1.29497e8	+	1.73461e8i	0.421865	+	0.565087i
$267$		0			0
$268$	−1.26567e8	−	2.19220e8i	−0.401650	−	0.695679i
$269$	7.32285e7	−	1.26835e8i	0.229376	−	0.397290i	−0.728248	−	0.685314i	$-0.759665\pi$
$269$	7.32285e7	−	1.26835e8i	0.229376	−	0.397290i	0.957623	+	0.288024i	$0.0929983\pi$
$270$		0			0
$271$	1.25786e8	+	2.17867e8i	0.383918	+	0.664965i	0.991618	−	0.129201i	$-0.0412413\pi$
$271$	1.25786e8	+	2.17867e8i	0.383918	+	0.664965i	−0.607701	+	0.794166i	$0.707908\pi$
$272$	−3.83793e6			−0.0115639
$273$		0			0
$274$	−3.64272e8			−1.06979
$275$	1.02980e7	+	1.78367e7i	0.0298599	+	0.0517189i
$276$		0			0
$277$	2.32652e8	−	4.02966e8i	0.657701	−	1.13917i	−0.323508	−	0.946225i	$-0.604862\pi$
$277$	2.32652e8	−	4.02966e8i	0.657701	−	1.13917i	0.981209	−	0.192946i	$-0.0618043\pi$
$278$	1.62831e8	+	2.82032e8i	0.454549	+	0.787302i
$279$		0			0
$280$	3.89834e8	−	4.60924e7i	1.06127	−	0.125480i
$281$	5.58490e8			1.50156			0.750781	−	0.660551i	$-0.229677\pi$
$281$	5.58490e8			1.50156			0.750781	+	0.660551i	$0.229677\pi$
$282$		0			0
$283$	−3.76398e7	+	6.51940e7i	−0.0987176	+	0.170984i	−0.911154	−	0.412066i	$-0.864807\pi$
$283$	−3.76398e7	+	6.51940e7i	−0.0987176	+	0.170984i	0.812437	+	0.583050i	$0.198141\pi$
$284$	1.46893e8	−	2.54426e8i	0.380528	−	0.659094i
$285$		0			0
$286$	−1.22229e8			−0.308955
$287$	2.33823e7	−	5.44058e7i	0.0583849	−	0.135850i
$288$		0			0
$289$	2.02170e8	+	3.50169e8i	0.492691	+	0.853366i
$290$	1.52133e8	−	2.63502e8i	0.366294	−	0.634440i
$291$		0			0
$292$	−2.82825e7	−	4.89867e7i	−0.0664780	−	0.115143i
$293$	5.90696e8			1.37192			0.685958	−	0.727641i	$-0.259383\pi$
$293$	5.90696e8			1.37192			0.685958	+	0.727641i	$0.259383\pi$
$294$		0			0
$295$	−3.53155e8			−0.800918
$296$	−9.76984e7	−	1.69219e8i	−0.218961	−	0.379251i
$297$		0			0
$298$	8.21978e7	−	1.42371e8i	0.179930	−	0.311648i
$299$	1.63229e8	+	2.82721e8i	0.353141	+	0.611658i
$300$		0			0
$301$	−9.24041e7	+	2.15005e8i	−0.195303	+	0.454429i
$302$	−5.13082e8			−1.07192
$303$		0			0
$304$	2.53225e7	−	4.38598e7i	0.0516950	−	0.0895384i
$305$	−1.10814e8	+	1.91936e8i	−0.223638	+	0.387353i
$306$		0			0
$307$	6.49771e8			1.28167			0.640835	−	0.767679i	$-0.278588\pi$
$307$	6.49771e8			1.28167			0.640835	+	0.767679i	$0.278588\pi$
$308$	−2.11564e8	+	2.50145e7i	−0.412586	+	0.0487825i
$309$		0			0
$310$	−3.03055e8	−	5.24907e8i	−0.577771	−	1.00073i
$311$	2.24291e7	−	3.88483e7i	0.0422815	−	0.0732336i	−0.844110	−	0.536170i	$-0.819871\pi$
$311$	2.24291e7	−	3.88483e7i	0.0422815	−	0.0732336i	0.886392	+	0.462936i	$0.153204\pi$
$312$		0			0
$313$	−2.86009e6	−	4.95383e6i	−0.00527200	−	0.00913137i	0.863377	−	0.504559i	$-0.168345\pi$
$313$	−2.86009e6	−	4.95383e6i	−0.00527200	−	0.00913137i	−0.868649	+	0.495427i	$0.835011\pi$
$314$	−9.07257e7			−0.165378
$315$		0			0
$316$	4.28926e8			0.764676
$317$	−1.39838e8	−	2.42207e8i	−0.246558	−	0.427050i	0.716011	−	0.698089i	$-0.245966\pi$
$317$	−1.39838e8	−	2.42207e8i	−0.246558	−	0.427050i	−0.962568	+	0.271039i	$0.912633\pi$
$318$		0			0
$319$	−2.26299e8	+	3.91961e8i	−0.390314	+	0.676044i
$320$	−2.21084e8	−	3.82929e8i	−0.377166	−	0.653271i
$321$		0			0
$322$	−2.52202e8	−	3.37824e8i	−0.420971	−	0.563890i
$323$	7.91509e7			0.130691
$324$		0			0
$325$	−1.67287e7	+	2.89749e7i	−0.0270314	+	0.0468198i
$326$	6.50172e7	−	1.12613e8i	0.103936	−	0.180023i
$327$		0			0
$328$	−9.70591e7			−0.151872
$329$	1.14867e8	−	1.35813e7i	0.177831	−	0.0210260i
$330$		0			0
$331$	4.38853e8	+	7.60115e8i	0.665152	+	1.15208i	0.979244	+	0.202684i	$0.0649666\pi$
$331$	4.38853e8	+	7.60115e8i	0.665152	+	1.15208i	−0.314092	+	0.949392i	$0.601700\pi$
$332$	−5.13738e7	+	8.89821e7i	−0.0770475	+	0.133450i
$333$		0			0
$334$	4.19073e8	+	7.25856e8i	0.615428	+	1.06595i
$335$	−1.00125e9			−1.45507
$336$		0			0
$337$	1.05320e8			0.149902			0.0749508	−	0.997187i	$-0.476120\pi$
$337$	1.05320e8			0.149902			0.0749508	+	0.997187i	$0.476120\pi$
$338$	1.32288e8	+	2.29129e8i	0.186342	+	0.322755i
$339$		0			0
$340$	2.61838e7	−	4.53516e7i	0.0361290	−	0.0625772i
$341$	4.50796e8	+	7.80802e8i	0.615659	+	1.06635i
$342$		0			0
$343$	−7.01259e8	+	2.58421e8i	−0.938316	+	0.345779i
$344$	3.83566e8			0.508025
$345$		0			0
$346$	−7.98157e7	+	1.38245e8i	−0.103591	+	0.179425i
$347$	1.79512e8	−	3.10925e8i	0.230644	−	0.399486i	−0.727354	−	0.686262i	$-0.759250\pi$
$347$	1.79512e8	−	3.10925e8i	0.230644	−	0.399486i	0.957998	+	0.286776i	$0.0925835\pi$
$348$		0			0
$349$	−1.99439e8			−0.251142			−0.125571	−	0.992085i	$-0.540076\pi$
$349$	−1.99439e8			−0.251142			−0.125571	+	0.992085i	$0.540076\pi$
$350$	1.70601e7	−	3.96953e7i	0.0212688	−	0.0494881i
$351$		0			0
$352$	2.85478e8	+	4.94463e8i	0.348878	+	0.604274i
$353$	−8.23100e8	+	1.42565e9i	−0.995958	+	1.72505i	−0.420191	+	0.907436i	$0.638037\pi$
$353$	−8.23100e8	+	1.42565e9i	−0.995958	+	1.72505i	−0.575767	+	0.817614i	$0.695297\pi$
$354$		0			0
$355$	−5.81022e8	−	1.00636e9i	−0.689276	−	1.19386i
$356$	1.18890e8			0.139660
$357$		0			0
$358$	−7.99236e8			−0.920629
$359$	1.20711e7	+	2.09077e7i	0.0137694	+	0.0238493i	0.872828	−	0.488028i	$-0.162284\pi$
$359$	1.20711e7	+	2.09077e7i	0.0137694	+	0.0238493i	−0.859059	+	0.511877i	$0.828950\pi$
$360$		0			0
$361$	−7.52977e7	+	1.30419e8i	−0.0842377	+	0.145904i
$362$	−2.42359e8	−	4.19778e8i	−0.268522	−	0.465093i
$363$		0			0
$364$	−2.07029e8	−	2.77315e8i	−0.224997	−	0.301383i
$365$	−2.23738e8			−0.240832
$366$		0			0
$367$	7.76929e8	−	1.34568e9i	0.820447	−	1.42106i	−0.0849034	−	0.996389i	$-0.527058\pi$
$367$	7.76929e8	−	1.34568e9i	0.820447	−	1.42106i	0.905350	−	0.424666i	$-0.139609\pi$
$368$	−4.93168e7	+	8.54192e7i	−0.0515855	+	0.0893487i
$369$		0			0
$370$	−2.81976e8			−0.289405
$371$	−4.29232e8	−	5.74955e8i	−0.436399	−	0.584555i
$372$		0			0
$373$	−7.61551e8	−	1.31905e9i	−0.759833	−	1.31607i	−0.942935	−	0.332976i	$-0.891947\pi$
$373$	−7.61551e8	−	1.31905e9i	−0.759833	−	1.31607i	0.183102	−	0.983094i	$-0.441386\pi$
$374$	2.88578e7	−	4.99832e7i	0.0285241	−	0.0494053i
$375$		0			0
$376$	−9.47903e7	−	1.64182e8i	−0.0919616	−	0.159282i
$377$	−7.35224e8			−0.706684
$378$		0			0
$379$	9.32142e8			0.879518			0.439759	−	0.898116i	$-0.355064\pi$
$379$	9.32142e8			0.879518			0.439759	+	0.898116i	$0.355064\pi$
$380$	3.45518e8	+	5.98455e8i	0.323019	+	0.559485i
$381$		0			0
$382$	−5.33629e7	+	9.24273e7i	−0.0489799	+	0.0848357i
$383$	−8.77369e8	−	1.51965e9i	−0.797970	−	1.38213i	−0.920936	−	0.389714i	$-0.872574\pi$
$383$	−8.77369e8	−	1.51965e9i	−0.797970	−	1.38213i	0.122965	−	0.992411i	$-0.460760\pi$
$384$		0			0
$385$	−3.32725e8	+	7.74182e8i	−0.297148	+	0.691402i
$386$	−4.60347e8			−0.407408
$387$		0			0
$388$	−2.09009e8	+	3.62014e8i	−0.181658	+	0.314640i
$389$	−4.60335e8	+	7.97323e8i	−0.396506	+	0.686769i	−0.993292	−	0.115632i	$-0.963111\pi$
$389$	−4.60335e8	+	7.97323e8i	−0.396506	+	0.686769i	0.596786	+	0.802400i	$0.296444\pi$
$390$		0			0
$391$	−1.54151e8			−0.130415
$392$	8.42980e8	+	8.88744e8i	0.706832	+	0.745204i
$393$		0			0
$394$	−5.00140e7	−	8.66268e7i	−0.0411960	−	0.0713535i
$395$	8.48289e8	−	1.46928e9i	0.692555	−	1.19954i
$396$		0			0
$397$	4.67778e8	+	8.10215e8i	0.375209	+	0.649881i	0.990358	−	0.138530i	$-0.0442377\pi$
$397$	4.67778e8	+	8.10215e8i	0.375209	+	0.649881i	−0.615149	+	0.788410i	$0.710904\pi$
$398$	−2.19391e8			−0.174433
$399$		0			0
$400$	−1.01085e7			−0.00789730
$401$	9.74458e8	+	1.68781e9i	0.754671	+	1.30713i	0.945538	+	0.325513i	$0.105537\pi$
$401$	9.74458e8	+	1.68781e9i	0.754671	+	1.30713i	−0.190867	+	0.981616i	$0.561130\pi$
$402$		0			0
$403$	−7.32299e8	+	1.26838e9i	−0.557341	+	0.965342i
$404$	−3.70858e8	−	6.42345e8i	−0.279816	−	0.484656i
$405$		0			0
$406$	9.42885e8	−	1.11483e8i	0.699226	−	0.0826736i
$407$	4.19442e8			0.308384
$408$		0			0
$409$	1.50260e8	−	2.60258e8i	0.108596	−	0.188093i	−0.806606	−	0.591089i	$-0.798698\pi$
$409$	1.50260e8	−	2.60258e8i	0.108596	−	0.188093i	0.915202	+	0.402997i	$0.132031\pi$
$410$	−7.00328e7	+	1.21300e8i	−0.0501831	+	0.0869197i
$411$		0			0
$412$	−6.86536e8			−0.483641
$413$	−6.59253e8	−	8.83069e8i	−0.460497	−	0.616836i
$414$		0			0
$415$	2.03205e8	+	3.51961e8i	0.139561	+	0.241727i
$416$	−4.63747e8	+	8.03233e8i	−0.315831	+	0.547034i
$417$		0			0
$418$	3.80804e8	+	6.59573e8i	0.255026	+	0.441719i
$419$	7.41204e8			0.492253			0.246127	−	0.969238i	$-0.420842\pi$
$419$	7.41204e8			0.492253			0.246127	+	0.969238i	$0.420842\pi$
$420$		0			0
$421$	2.25657e9			1.47388			0.736940	−	0.675958i	$-0.236270\pi$
$421$	2.25657e9			1.47388			0.736940	+	0.675958i	$0.236270\pi$
$422$	5.37407e8	+	9.30817e8i	0.348105	+	0.602935i
$423$		0			0
$424$	−5.88005e8	+	1.01845e9i	−0.374628	+	0.648875i
$425$	−7.89912e6	−	1.36817e7i	−0.00499134	−	0.00864526i
$426$		0			0
$427$	−6.86802e8	+	8.12046e7i	−0.426908	+	0.0504758i
$428$	−1.05911e9			−0.652964
$429$		0			0
$430$	2.76761e8	−	4.79364e8i	0.167867	−	0.290754i
$431$	1.09503e7	−	1.89664e7i	0.00658802	−	0.0114108i	−0.862713	−	0.505695i	$-0.831236\pi$
$431$	1.09503e7	−	1.89664e7i	0.00658802	−	0.0114108i	0.869301	+	0.494284i	$0.164570\pi$
$432$		0			0
$433$	1.42535e9			0.843749			0.421875	−	0.906654i	$-0.361372\pi$
$433$	1.42535e9			0.843749			0.421875	+	0.906654i	$0.361372\pi$
$434$	7.46808e8	−	1.73767e9i	0.438525	−	1.02036i
$435$		0			0
$436$	3.14683e8	+	5.45047e8i	0.181832	+	0.314943i
$437$	1.01708e9	−	1.76163e9i	0.583000	−	1.00979i
$438$		0			0
$439$	−1.25618e9	−	2.17576e9i	−0.708640	−	1.22740i	−0.965362	−	0.260915i	$-0.915976\pi$
$439$	−1.25618e9	−	2.17576e9i	−0.708640	−	1.22740i	0.256722	−	0.966485i	$-0.417357\pi$
$440$	1.38113e9			0.772948
$441$		0			0
$442$	9.37564e7			0.0516444
$443$	−7.35054e8	−	1.27315e9i	−0.401704	−	0.695772i	0.592228	−	0.805771i	$-0.298249\pi$
$443$	−7.35054e8	−	1.27315e9i	−0.401704	−	0.695772i	−0.993932	+	0.109999i	$0.964915\pi$
$444$		0			0
$445$	2.35130e8	−	4.07257e8i	0.126487	−	0.219083i
$446$	7.42975e8	+	1.28687e9i	0.396554	+	0.686852i
$447$		0			0
$448$	5.44810e8	−	1.26766e9i	0.286267	−	0.666085i
$449$	2.83997e9			1.48064			0.740322	−	0.672252i	$-0.234673\pi$
$449$	2.83997e9			1.48064			0.740322	+	0.672252i	$0.234673\pi$
$450$		0			0
$451$	1.04174e8	−	1.80435e8i	0.0534740	−	0.0926197i
$452$	−4.24998e8	+	7.36117e8i	−0.216472	+	0.374941i
$453$		0			0
$454$	2.27113e9			1.13906
$455$	−1.35938e9	+	1.60728e8i	−0.676554	+	0.0799929i
$456$		0			0
$457$	2.06011e8	+	3.56821e8i	0.100968	+	0.174882i	0.912084	−	0.410004i	$-0.134473\pi$
$457$	2.06011e8	+	3.56821e8i	0.100968	+	0.174882i	−0.811116	+	0.584886i	$0.801139\pi$
$458$	−6.83706e8	+	1.18421e9i	−0.332537	+	0.575971i
$459$		0			0
$460$	−6.72914e8	−	1.16552e9i	−0.322335	−	0.558300i
$461$	4.14604e9			1.97097			0.985484	−	0.169766i	$-0.0543011\pi$
$461$	4.14604e9			1.97097			0.985484	+	0.169766i	$0.0543011\pi$
$462$		0			0
$463$	−2.49603e9			−1.16873			−0.584367	−	0.811490i	$-0.698657\pi$
$463$	−2.49603e9			−1.16873			−0.584367	+	0.811490i	$0.698657\pi$
$464$	−1.11068e8	−	1.92375e8i	−0.0516148	−	0.0893995i
$465$		0			0
$466$	−9.19282e8	+	1.59224e9i	−0.420822	+	0.728885i
$467$	−1.36711e9	−	2.36791e9i	−0.621148	−	1.07586i	−0.989272	−	0.146084i	$-0.953333\pi$
$467$	−1.36711e9	−	2.36791e9i	−0.621148	−	1.07586i	0.368124	−	0.929777i	$-0.380000\pi$
$468$		0			0
$469$	−1.86908e9	−	2.50364e9i	−0.836612	−	1.12064i
$470$	−2.73583e8			−0.121548
$471$		0			0
$472$	−9.03111e8	+	1.56423e9i	−0.395316	+	0.684707i
$473$	−4.11684e8	+	7.13058e8i	−0.178875	+	0.309821i
$474$		0			0
$475$	2.08472e8			0.0892524
$476$	1.62281e8	−	1.91874e7i	0.0689673	−	0.00815441i
$477$		0			0
$478$	1.24176e7	+	2.15079e7i	0.00520044	+	0.00900742i
$479$	6.08065e8	−	1.05320e9i	0.252799	−	0.437861i	−0.711496	−	0.702690i	$-0.751982\pi$
$479$	6.08065e8	−	1.05320e9i	0.252799	−	0.437861i	0.964295	+	0.264829i	$0.0853155\pi$
$480$		0			0
$481$	3.40682e8	+	5.90079e8i	0.139586	+	0.241770i
$482$	1.61306e9			0.656122
$483$		0			0
$484$	6.83236e8			0.273913
$485$	8.26717e8	+	1.43192e9i	0.329049	+	0.569930i
$486$		0			0
$487$	1.19069e9	−	2.06233e9i	0.467140	−	0.809110i	−0.532155	−	0.846647i	$-0.678618\pi$
$487$	1.19069e9	−	2.06233e9i	0.467140	−	0.809110i	0.999295	+	0.0375368i	$0.0119511\pi$
$488$	5.66764e8	+	9.81663e8i	0.220766	+	0.382378i
$489$		0			0
$490$	1.71896e9	−	4.12250e8i	0.660056	−	0.158297i
$491$	−4.90402e9			−1.86968			−0.934839	−	0.355072i	$-0.884456\pi$
$491$	−4.90402e9			−1.86968			−0.934839	+	0.355072i	$0.884456\pi$
$492$		0			0
$493$	1.73583e8	−	3.00655e8i	0.0652444	−	0.113007i
$494$	−6.18600e8	+	1.07145e9i	−0.230869	+	0.399877i
$495$		0			0
$496$	−4.42503e8			−0.162828
$497$	1.43179e9	−	3.33148e9i	0.523158	−	1.21728i
$498$		0			0
$499$	1.45354e9	+	2.51760e9i	0.523690	+	0.907057i	0.999620	+	0.0275740i	$0.00877819\pi$
$499$	1.45354e9	+	2.51760e9i	0.523690	+	0.907057i	−0.475930	+	0.879483i	$0.657888\pi$
$500$	−7.66280e8	+	1.32724e9i	−0.274153	+	0.474846i
$501$		0			0
$502$	1.14647e9	+	1.98575e9i	0.404483	+	0.700585i
$503$	7.90853e7			0.0277082			0.0138541	−	0.999904i	$-0.495590\pi$
$503$	7.90853e7			0.0277082			0.0138541	+	0.999904i	$0.495590\pi$
$504$		0			0
$505$	−2.93379e9			−1.01370
$506$	−7.41636e8	−	1.28455e9i	−0.254486	−	0.440783i
$507$		0			0
$508$	9.74563e8	−	1.68799e9i	0.329828	−	0.571278i
$509$	−1.69924e9	−	2.94316e9i	−0.571138	−	0.989241i	−0.996449	−	0.0841935i	$-0.973169\pi$
$509$	−1.69924e9	−	2.94316e9i	−0.571138	−	0.989241i	0.425311	−	0.905047i	$-0.360165\pi$
$510$		0			0
$511$	−4.17664e8	−	5.59460e8i	−0.138469	−	0.185480i
$512$	−5.78577e8			−0.190509
$513$		0			0
$514$	1.09290e9	−	1.89296e9i	0.354986	−	0.614853i
$515$	−1.35777e9	+	2.35172e9i	−0.438026	+	0.758684i
$516$		0			0
$517$	4.06957e8			0.129518
$518$	−5.26381e8	−	7.05086e8i	−0.166397	−	0.222889i
$519$		0			0
$520$	1.12179e9	+	1.94300e9i	0.349865	+	0.605984i
$521$	−1.79657e9	+	3.11176e9i	−0.556561	+	0.963992i	0.441219	+	0.897399i	$0.354546\pi$
$521$	−1.79657e9	+	3.11176e9i	−0.556561	+	0.963992i	−0.997780	+	0.0665929i	$0.978787\pi$
$522$		0			0
$523$	−1.09639e9	−	1.89900e9i	−0.335126	−	0.580456i	0.648383	−	0.761315i	$-0.275446\pi$
$523$	−1.09639e9	−	1.89900e9i	−0.335126	−	0.580456i	−0.983509	+	0.180859i	$0.942112\pi$
$524$	3.34222e8			0.101479
$525$		0			0
$526$	−1.91492e9			−0.573719
$527$	−3.45785e8	−	5.98917e8i	−0.102913	−	0.178250i
$528$		0			0
$529$	−2.78397e8	+	4.82198e8i	−0.0817655	+	0.141622i
$530$	8.48547e8	+	1.46973e9i	0.247577	+	0.428816i
$531$		0			0
$532$	−8.51448e8	+	1.98114e9i	−0.245170	+	0.570460i
$533$	3.38453e8			0.0968173
$534$		0			0
$535$	−2.09461e9	+	3.62798e9i	−0.591379	+	1.02430i
$536$	−2.56046e9	+	4.43485e9i	−0.718193	+	1.24395i
$537$		0			0
$538$	−1.08097e9			−0.299277
$539$	−2.55697e9	+	6.13224e8i	−0.703340	+	0.168678i
$540$		0			0
$541$	2.39445e8	+	4.14730e8i	0.0650152	+	0.112610i	0.896701	−	0.442637i	$-0.145957\pi$
$541$	2.39445e8	+	4.14730e8i	0.0650152	+	0.112610i	−0.831686	+	0.555247i	$0.812624\pi$
$542$	9.28394e8	−	1.60803e9i	0.250458	−	0.433806i
$543$		0			0
$544$	−2.18977e8	−	3.79279e8i	−0.0583179	−	0.101010i
$545$	2.48940e9			0.658730
$546$		0			0
$547$	−1.52985e9			−0.399664			−0.199832	−	0.979830i	$-0.564040\pi$
$547$	−1.52985e9			−0.399664			−0.199832	+	0.979830i	$0.564040\pi$
$548$	−1.81437e9	−	3.14258e9i	−0.470970	−	0.815744i
$549$		0			0
$550$	7.60072e7	−	1.31648e8i	0.0194798	−	0.0337401i
$551$	2.29058e9	+	3.96741e9i	0.583332	+	1.01036i
$552$		0			0
$553$	5.25751e9	−	6.21626e8i	1.32203	−	0.156312i
$554$	−3.43431e9			−0.858134
$555$		0			0
$556$	−1.62206e9	+	2.80949e9i	−0.400226	+	0.693211i
$557$	2.45884e8	−	4.25884e8i	0.0602889	−	0.104423i	−0.834306	−	0.551302i	$-0.814131\pi$
$557$	2.45884e8	−	4.25884e8i	0.0602889	−	0.104423i	0.894595	+	0.446879i	$0.147464\pi$
$558$		0			0
$559$	−1.33753e9			−0.323863
$560$	−2.47412e8	−	3.31408e8i	−0.0595337	−	0.0797453i
$561$		0			0
$562$	−2.06104e9	−	3.56983e9i	−0.489790	−	0.848341i
$563$	−5.62247e8	+	9.73840e8i	−0.132785	+	0.229990i	−0.924749	−	0.380578i	$-0.875725\pi$
$563$	−5.62247e8	+	9.73840e8i	−0.132785	+	0.229990i	0.791964	+	0.610567i	$0.209058\pi$
$564$		0			0
$565$	1.68104e9	+	2.91165e9i	0.392111	+	0.679156i
$566$	5.55621e8			0.128801
$567$		0			0
$568$	−5.94331e9			−1.36085
$569$	1.53913e9	+	2.66585e9i	0.350253	+	0.606656i	0.986294	−	0.164999i	$-0.0527622\pi$
$569$	1.53913e9	+	2.66585e9i	0.350253	+	0.606656i	−0.636041	+	0.771656i	$0.719429\pi$
$570$		0			0
$571$	−4.59821e8	+	7.96433e8i	−0.103362	+	0.179029i	−0.913068	−	0.407807i	$-0.866293\pi$
$571$	−4.59821e8	+	7.96433e8i	−0.103362	+	0.179029i	0.809706	+	0.586836i	$0.199627\pi$
$572$	−6.08801e8	−	1.05447e9i	−0.136016	−	0.235586i
$573$		0			0
$574$	−4.34047e8	+	5.13200e7i	−0.0957956	+	0.0113265i
$575$	−4.06010e8			−0.0890633
$576$		0			0
$577$	−2.43160e9	+	4.21166e9i	−0.526959	+	0.912720i	0.472547	+	0.881305i	$0.343335\pi$
$577$	−2.43160e9	+	4.21166e9i	−0.526959	+	0.912720i	−0.999506	+	0.0314146i	$0.989999\pi$
$578$	1.49217e9	−	2.58452e9i	0.321419	−	0.556714i
$579$		0			0
$580$	3.03097e9			0.645036
$581$	−5.00750e8	+	1.16514e9i	−0.105927	+	0.246469i
$582$		0			0
$583$	−1.26222e9	−	2.18623e9i	−0.263812	−	0.456936i
$584$	−5.72158e8	+	9.91007e8i	−0.118870	+	0.205888i
$585$		0			0
$586$	−2.17990e9	−	3.77569e9i	−0.447501	−	0.775095i
$587$	−1.16578e9			−0.237894			−0.118947	−	0.992901i	$-0.537952\pi$
$587$	−1.16578e9			−0.237894			−0.118947	+	0.992901i	$0.537952\pi$
$588$		0			0
$589$	9.12588e9			1.84023
$590$	1.30328e9	+	2.25734e9i	0.261249	+	0.452496i
$591$		0			0
$592$	−1.02931e8	+	1.78282e8i	−0.0203902	+	0.0353168i
$593$	−1.67754e9	−	2.90559e9i	−0.330356	−	0.572193i	0.652226	−	0.758025i	$-0.273835\pi$
$593$	−1.67754e9	−	2.90559e9i	−0.330356	−	0.572193i	−0.982582	+	0.185832i	$0.940502\pi$
$594$		0			0
$595$	2.55218e8	−	5.93839e8i	0.0496709	−	0.115574i
$596$	1.63765e9			0.316853
$597$		0			0
$598$	1.20476e9	−	2.08670e9i	0.230380	−	0.399030i
$599$	−1.16072e9	+	2.01043e9i	−0.220666	+	0.382205i	−0.955010	−	0.296572i	$-0.904156\pi$
$599$	−1.16072e9	+	2.01043e9i	−0.220666	+	0.382205i	0.734344	+	0.678777i	$0.237490\pi$
$600$		0			0
$601$	4.38113e9			0.823238			0.411619	−	0.911356i	$-0.364964\pi$
$601$	4.38113e9			0.823238			0.411619	+	0.911356i	$0.364964\pi$
$602$	1.71530e9	−	2.02810e8i	0.320445	−	0.0378881i
$603$		0			0
$604$	−2.55556e9	−	4.42636e9i	−0.471908	−	0.817368i
$605$	1.35124e9	−	2.34042e9i	0.248078	−	0.429684i
$606$		0			0
$607$	−2.16431e9	−	3.74869e9i	−0.392788	−	0.680329i	0.600028	−	0.799979i	$-0.295156\pi$
$607$	−2.16431e9	−	3.74869e9i	−0.392788	−	0.680329i	−0.992816	+	0.119650i	$0.961823\pi$
$608$	5.77919e9			1.04281
$609$		0			0
$610$	1.63579e9			0.291792
$611$	3.30542e8	+	5.72515e8i	0.0586249	+	0.101541i
$612$		0			0
$613$	−9.51623e8	+	1.64826e9i	−0.166860	+	0.289011i	−0.937314	−	0.348485i	$-0.886696\pi$
$613$	−9.51623e8	+	1.64826e9i	−0.166860	+	0.289011i	0.770454	+	0.637496i	$0.220030\pi$
$614$	−2.39791e9	−	4.15329e9i	−0.418064	−	0.724108i
$615$		0			0
$616$	2.57823e9	+	3.45354e9i	0.444416	+	0.595294i
$617$	8.11496e9			1.39088			0.695438	−	0.718586i	$-0.255210\pi$
$617$	8.11496e9			1.39088			0.695438	+	0.718586i	$0.255210\pi$
$618$		0			0
$619$	2.30171e9	−	3.98668e9i	0.390062	−	0.675608i	−0.602395	−	0.798198i	$-0.705787\pi$
$619$	2.30171e9	−	3.98668e9i	0.390062	−	0.675608i	0.992457	+	0.122590i	$0.0391201\pi$
$620$	3.01891e9	−	5.22891e9i	0.508721	−	0.881131i
$621$		0			0
$622$	−3.31087e8			−0.0551666
$623$	1.45728e9	−	1.72303e8i	0.241455	−	0.0285486i
$624$		0			0
$625$	3.28293e9	+	5.68620e9i	0.537875	+	0.931627i
$626$	−2.11097e7	+	3.65631e7i	−0.00343931	+	0.00595706i
$627$		0			0
$628$	−4.51887e8	−	7.82691e8i	−0.0728066	−	0.126105i
$629$	−3.21734e8			−0.0515490
$630$		0			0
$631$	3.73470e9			0.591770			0.295885	−	0.955224i	$-0.404385\pi$
$631$	3.73470e9			0.591770			0.295885	+	0.955224i	$0.404385\pi$
$632$	−4.33861e9	−	7.51469e9i	−0.683660	−	1.18413i
$633$		0			0
$634$	−1.03211e9	+	1.78767e9i	−0.160848	+	0.278596i
$635$	−3.85480e9	−	6.67671e9i	−0.597439	−	1.03479i
$636$		0			0
$637$	−2.93954e9	−	3.09912e9i	−0.450600	−	0.475062i
$638$	3.34051e9			0.509262
$639$		0			0
$640$	1.69653e9	−	2.93847e9i	0.255818	−	0.443090i
$641$	−3.64484e9	+	6.31304e9i	−0.546607	+	0.946750i	0.451897	+	0.892070i	$0.350747\pi$
$641$	−3.64484e9	+	6.31304e9i	−0.546607	+	0.946750i	−0.998504	+	0.0546804i	$0.982586\pi$
$642$		0			0
$643$	4.01680e9			0.595856			0.297928	−	0.954588i	$-0.403704\pi$
$643$	4.01680e9			0.595856			0.297928	+	0.954588i	$0.403704\pi$
$644$	1.65824e9	−	3.85838e9i	0.244651	−	0.569252i
$645$		0			0
$646$	−2.92097e8	−	5.05927e8i	−0.0426298	−	0.0738370i
$647$	1.77143e9	−	3.06820e9i	0.257133	−	0.445368i	−0.708339	−	0.705872i	$-0.750555\pi$
$647$	1.77143e9	−	3.06820e9i	0.257133	−	0.445368i	0.965473	+	0.260504i	$0.0838887\pi$
$648$		0			0
$649$	−1.93863e9	−	3.35781e9i	−0.278381	−	0.482169i
$650$	2.46941e8			0.0352692
$651$		0			0
$652$	1.29535e9			0.183030
$653$	5.59905e9	+	9.69783e9i	0.786897	+	1.36295i	0.927859	+	0.372931i	$0.121647\pi$
$653$	5.59905e9	+	9.69783e9i	0.786897	+	1.36295i	−0.140962	+	0.990015i	$0.545020\pi$
$654$		0			0
$655$	6.60993e8	−	1.14487e9i	0.0919078	−	0.159189i
$656$	5.11288e7	+	8.85577e7i	0.00707135	+	0.0122479i
$657$		0			0
$658$	−5.10713e8	−	6.84099e8i	−0.0698853	−	0.0936113i
$659$	−8.68249e9			−1.18180			−0.590902	−	0.806743i	$-0.701228\pi$
$659$	−8.68249e9			−1.18180			−0.590902	+	0.806743i	$0.701228\pi$
$660$		0			0
$661$	−5.17499e9	+	8.96335e9i	−0.696955	+	1.20716i	0.272562	+	0.962138i	$0.412129\pi$
$661$	−5.17499e9	+	8.96335e9i	−0.696955	+	1.20716i	−0.969517	+	0.245023i	$0.921204\pi$
$662$	3.23907e9	−	5.61023e9i	0.433928	−	0.751585i
$663$		0			0
$664$	2.07860e9			0.275538
$665$	5.10246e9	+	6.83474e9i	0.672828	+	0.901252i
$666$		0			0
$667$	−4.46103e9	−	7.72673e9i	−0.582096	−	1.00822i
$668$	−4.17464e9	+	7.23069e9i	−0.541878	+	0.938560i
$669$		0			0
$670$	3.69499e9	+	6.39991e9i	0.474626	+	0.822076i
$671$	−2.43325e9			−0.310926
$672$		0			0
$673$	1.94227e9			0.245617			0.122808	−	0.992430i	$-0.460810\pi$
$673$	1.94227e9			0.245617			0.122808	+	0.992430i	$0.460810\pi$
$674$	−3.88671e8	−	6.73198e8i	−0.0488959	−	0.0846902i
$675$		0			0
$676$	−1.31780e9	+	2.28250e9i	−0.164073	+	0.284182i
$677$	2.69675e9	+	4.67091e9i	0.334027	+	0.578551i	0.983297	−	0.182006i	$-0.0582592\pi$
$677$	2.69675e9	+	4.67091e9i	0.334027	+	0.578551i	−0.649271	+	0.760557i	$0.724926\pi$
$678$		0			0
$679$	−2.03725e9	+	4.74026e9i	−0.249747	+	0.581109i
$680$	−1.05940e9			−0.129205
$681$		0			0
$682$	3.32722e9	−	5.76292e9i	0.401640	−	0.695660i
$683$	5.57579e9	−	9.65754e9i	0.669628	−	1.15983i	−0.308380	−	0.951263i	$-0.599787\pi$
$683$	5.57579e9	−	9.65754e9i	0.669628	−	1.15983i	0.978008	−	0.208567i	$-0.0668798\pi$
$684$		0			0
$685$	−1.43531e10			−1.70620
$686$	4.23972e9	+	3.52873e9i	0.501422	+	0.417334i
$687$		0			0
$688$	−2.02055e8	−	3.49970e8i	−0.0236543	−	0.0409705i
$689$	2.05042e9	−	3.55143e9i	0.238823	−	0.413653i
$690$		0			0
$691$	2.14163e9	+	3.70942e9i	0.246929	+	0.427693i	0.962672	−	0.270670i	$-0.0872453\pi$
$691$	2.14163e9	+	3.70942e9i	0.246929	+	0.427693i	−0.715743	+	0.698363i	$0.753912\pi$
$692$	−1.59019e9			−0.182422
$693$		0			0
$694$	−2.64988e9			−0.300932
$695$	6.41591e9	+	1.11127e10i	0.724956	+	1.25566i
$696$		0			0
$697$	−7.99072e7	+	1.38403e8i	−0.00893863	+	0.0154822i
$698$	7.36005e8	+	1.27480e9i	0.0819194	+	0.141888i
$699$		0			0
$700$	4.27424e8	−	5.05369e7i	0.0470995	−	0.00556885i
$701$	9.26658e8			0.101603			0.0508015	−	0.998709i	$-0.483822\pi$
$701$	9.26658e8			0.101603			0.0508015	+	0.998709i	$0.483822\pi$
$702$		0			0
$703$	2.12278e9	−	3.67677e9i	0.230442	−	0.399138i
$704$	2.42727e9	−	4.20416e9i	0.262189	−	0.454124i
$705$		0			0
$706$	1.21502e10			1.29947
$707$	−5.47668e9	−	7.33600e9i	−0.582840	−	0.780713i
$708$		0			0
$709$	2.79426e9	+	4.83980e9i	0.294446	+	0.509995i	0.974856	−	0.222837i	$-0.0715317\pi$
$709$	2.79426e9	+	4.83980e9i	0.294446	+	0.509995i	−0.680410	+	0.732831i	$0.738198\pi$
$710$	−4.28839e9	+	7.42770e9i	−0.449666	+	0.778843i
$711$		0			0
$712$	−1.20258e9	−	2.08293e9i	−0.124863	−	0.216269i
$713$	−1.77731e10			−1.83633
$714$		0			0
$715$	−4.81611e9			−0.492749
$716$	−3.98084e9	−	6.89501e9i	−0.405302	−	0.702004i
$717$		0			0
$718$	8.90938e7	−	1.54315e8i	0.00898281	−	0.0155587i
$719$	6.60046e9	+	1.14323e10i	0.662252	+	1.14705i	0.980023	+	0.198886i	$0.0637324\pi$
$719$	6.60046e9	+	1.14323e10i	0.662252	+	1.14705i	−0.317771	+	0.948168i	$0.602934\pi$
$720$		0			0
$721$	−8.41514e9	+	9.94971e8i	−0.836157	+	0.0988637i
$722$	1.11151e9			0.109909
$723$		0			0
$724$	2.41428e9	−	4.18166e9i	0.236431	−	0.409510i
$725$	4.57192e8	−	7.91880e8i	0.0445570	−	0.0771749i
$726$		0			0
$727$	−7.32749e9			−0.707269			−0.353635	−	0.935384i	$-0.615054\pi$
$727$	−7.32749e9			−0.707269			−0.353635	+	0.935384i	$0.615054\pi$
$728$	−2.76439e9	+	6.43217e9i	−0.265546	+	0.617871i
$729$		0			0
$730$	8.25679e8	+	1.43012e9i	0.0785563	+	0.136064i
$731$	3.15784e8	−	5.46953e8i	0.0299005	−	0.0517892i
$732$		0			0
$733$	6.96170e9	+	1.20580e10i	0.652907	+	1.13087i	0.982414	+	0.186715i	$0.0597841\pi$
$733$	6.96170e9	+	1.20580e10i	0.652907	+	1.13087i	−0.329507	+	0.944153i	$0.606883\pi$
$734$	−1.14687e10			−1.07048
$735$		0			0
$736$	−1.12553e10			−1.04060
$737$	−5.49632e9	−	9.51991e9i	−0.505750	−	0.875985i
$738$		0			0
$739$	−1.47710e9	+	2.55841e9i	−0.134634	+	0.233193i	−0.925458	−	0.378851i	$-0.876319\pi$
$739$	−1.47710e9	+	2.55841e9i	−0.134634	+	0.233193i	0.790824	+	0.612044i	$0.209653\pi$
$740$	−1.40447e9	−	2.43261e9i	−0.127409	−	0.220679i
$741$		0			0
$742$	−2.09105e9	+	4.86543e9i	−0.187910	+	0.437227i
$743$	5.39743e9			0.482754			0.241377	−	0.970431i	$-0.422401\pi$
$743$	5.39743e9			0.482754			0.241377	+	0.970431i	$0.422401\pi$
$744$		0			0
$745$	3.23878e9	−	5.60973e9i	0.286969	−	0.497044i
$746$	−5.62083e9	+	9.73557e9i	−0.495695	+	0.858569i
$747$		0			0
$748$	5.74940e8			0.0502304
$749$	−1.29819e10	+	1.53493e9i	−1.12889	+	0.133476i
$750$		0			0
$751$	−5.61607e8	−	9.72733e8i	−0.0483830	−	0.0838019i	0.840820	−	0.541315i	$-0.182073\pi$
$751$	−5.61607e8	−	9.72733e8i	−0.0483830	−	0.0838019i	−0.889203	+	0.457513i	$0.848740\pi$
$752$	−9.98674e7	+	1.72975e8i	−0.00856370	+	0.0148328i
$753$		0			0
$754$	2.71326e9	+	4.69950e9i	0.230511	+	0.399257i
$755$	−2.02166e10			−1.70960
$756$		0			0
$757$	9.72000e9			0.814387			0.407193	−	0.913342i	$-0.366507\pi$
$757$	9.72000e9			0.814387			0.407193	+	0.913342i	$0.366507\pi$
$758$	−3.43996e9	−	5.95819e9i	−0.286887	−	0.496904i
$759$		0			0
$760$	6.98986e9	−	1.21068e10i	0.577592	−	1.00042i
$761$	9.55634e9	+	1.65521e10i	0.786041	+	1.36146i	0.928375	+	0.371644i	$0.121206\pi$
$761$	9.55634e9	+	1.65521e10i	0.786041	+	1.36146i	−0.142334	+	0.989819i	$0.545461\pi$
$762$		0			0
$763$	4.64711e9	+	6.22480e9i	0.378745	+	0.507328i
$764$	−1.06316e9			−0.0862526
$765$		0			0
$766$	−6.47566e9	+	1.12162e10i	−0.520575	+	0.901662i
$767$	3.14922e9	−	5.45461e9i	0.252011	−	0.436496i
$768$		0			0
$769$	−1.69816e10			−1.34660			−0.673298	−	0.739371i	$-0.735123\pi$
$769$	−1.69816e10			−1.34660			−0.673298	+	0.739371i	$0.735123\pi$
$770$	6.17640e9	−	7.30272e8i	0.487549	−	0.0576458i
$771$		0			0
$772$	−2.29290e9	−	3.97142e9i	−0.179359	−	0.310660i
$773$	8.18943e9	−	1.41845e10i	0.637713	−	1.10455i	−0.348220	−	0.937413i	$-0.613214\pi$
$773$	8.18943e9	−	1.41845e10i	0.637713	−	1.10455i	0.985933	−	0.167139i	$-0.0534529\pi$
$774$		0			0
$775$	−9.10746e8	−	1.57746e9i	−0.0702816	−	0.121731i
$776$	8.45655e9			0.649646
$777$		0			0
$778$	6.79524e9			0.517341
$779$	−1.05445e9	−	1.82636e9i	−0.0799178	−	0.138422i
$780$		0			0
$781$	6.37901e9	−	1.10488e10i	0.479153	−	0.829918i
$782$	5.68874e8	+	9.85319e8i	0.0425395	+	0.0736806i
$783$		0			0
$784$	3.66834e8	−	1.23732e9i	0.0271871	−	0.0917011i
$785$	−3.57480e9			−0.263759
$786$		0			0
$787$	6.77582e9	−	1.17361e10i	0.495508	−	0.858245i	−0.504479	−	0.863424i	$-0.668315\pi$
$787$	6.77582e9	−	1.17361e10i	0.495508	−	0.858245i	0.999987	+	0.00517934i	$0.00164864\pi$
$788$	4.98220e8	−	8.62942e8i	0.0362726	−	0.0628260i
$789$		0			0
$790$	−1.25220e10			−0.903609
$791$	−4.14253e9	+	9.63880e9i	−0.297610	+	0.692477i
$792$		0			0
$793$	−1.97635e9	−	3.42314e9i	−0.140737	−	0.243763i
$794$	3.45256e9	−	5.98001e9i	0.244776	−	0.423965i
$795$		0			0
$796$	−1.09274e9	−	1.89269e9i	−0.0767931	−	0.133010i
$797$	5.21891e7			0.00365153			0.00182577	−	0.999998i	$-0.499419\pi$
$797$	5.21891e7			0.00365153			0.00182577	+	0.999998i	$0.499419\pi$
$798$		0			0
$799$	−3.12157e8			−0.0216501
$800$	−5.76753e8	−	9.98965e8i	−0.0398267	−	0.0689819i
$801$		0			0
$802$	7.19225e9	−	1.24573e10i	0.492328	−	0.852736i
$803$	−1.22820e9	−	2.12731e9i	−0.0837078	−	0.144986i
$804$		0			0
$805$	−9.93731e9	−	1.33110e10i	−0.671403	−	0.899344i
$806$	1.08099e10			0.727189
$807$		0			0
$808$	−7.50250e9	+	1.29947e10i	−0.500341	+	0.866616i
$809$	6.80229e9	−	1.17819e10i	0.451685	−	0.782341i	−0.546806	−	0.837259i	$-0.684157\pi$
$809$	6.80229e9	−	1.17819e10i	0.451685	−	0.782341i	0.998491	+	0.0549185i	$0.0174899\pi$
$810$		0			0
$811$	−3.10614e9			−0.204479			−0.102239	−	0.994760i	$-0.532601\pi$
$811$	−3.10614e9			−0.204479			−0.102239	+	0.994760i	$0.532601\pi$
$812$	5.65809e9	+	7.57900e9i	0.370871	+	0.496782i
$813$		0			0
$814$	−1.54790e9	−	2.68104e9i	−0.100591	−	0.174228i
$815$	2.56183e9	−	4.43721e9i	0.165767	−	0.287117i
$816$		0			0
$817$	4.16705e9	+	7.21754e9i	0.267332	+	0.463033i
$818$	−2.21807e9			−0.141690
$819$		0			0
$820$	−1.39528e9			−0.0883715
$821$	5.28866e9	+	9.16022e9i	0.333537	+	0.577704i	0.983203	−	0.182517i	$-0.0584243\pi$
$821$	5.28866e9	+	9.16022e9i	0.333537	+	0.577704i	−0.649665	+	0.760220i	$0.725091\pi$
$822$		0			0
$823$	−5.14054e9	+	8.90368e9i	−0.321447	+	0.556762i	−0.980787	−	0.195083i	$-0.937503\pi$
$823$	−5.14054e9	+	8.90368e9i	−0.321447	+	0.556762i	0.659340	+	0.751845i	$0.270836\pi$
$824$	6.94435e9	+	1.20280e10i	0.432401	+	0.748940i
$825$		0			0
$826$	−3.21162e9	+	7.47277e9i	−0.198287	+	0.461372i
$827$	−1.76194e9			−0.108323			−0.0541617	−	0.998532i	$-0.517249\pi$
$827$	−1.76194e9			−0.108323			−0.0541617	+	0.998532i	$0.517249\pi$
$828$		0			0
$829$	9.25086e9	−	1.60230e10i	0.563951	−	0.976792i	−0.433196	−	0.901300i	$-0.642614\pi$
$829$	9.25086e9	−	1.60230e10i	0.563951	−	0.976792i	0.997146	−	0.0754917i	$-0.0240526\pi$
$830$	1.49981e9	−	2.59774e9i	0.0910462	−	0.157697i
$831$		0			0
$832$	7.88599e9			0.474706
$833$	1.96133e9	−	4.70376e8i	0.117569	−	0.0281960i
$834$		0			0
$835$	1.65124e10	+	2.86004e10i	0.981541	+	1.70008i
$836$	−3.79342e9	+	6.57040e9i	−0.224548	+	0.388929i
$837$		0			0
$838$	−2.73533e9	−	4.73772e9i	−0.160567	−	0.278109i
$839$	1.91428e10			1.11902			0.559512	−	0.828822i	$-0.310988\pi$
$839$	1.91428e10			1.11902			0.559512	+	0.828822i	$0.310988\pi$
$840$		0			0
$841$	2.84370e9			0.164854
$842$	−8.32762e9	−	1.44239e10i	−0.480760	−	0.832701i
$843$		0			0
$844$	−5.35344e9	+	9.27243e9i	−0.306503	+	0.530878i
$845$	5.21244e9	+	9.02822e9i	0.297196	+	0.514759i
$846$		0			0
$847$	8.37469e9	−	9.90188e8i	0.473562	−	0.0559920i
$848$	1.23900e9			0.0697726
$849$		0			0
$850$	−5.83015e7	+	1.00981e8i	−0.00325622	+	0.00563994i
$851$	−4.13423e9	+	7.16070e9i	−0.229954	+	0.398292i
$852$		0			0
$853$	7.28376e9			0.401822			0.200911	−	0.979609i	$-0.435610\pi$
$853$	7.28376e9			0.401822			0.200911	+	0.979609i	$0.435610\pi$
$854$	3.05362e9	+	4.09032e9i	0.167769	+	0.224726i
$855$		0			0
$856$	1.07130e10	+	1.85554e10i	0.583784	+	1.01114i
$857$	1.38663e10	−	2.40172e10i	0.752539	−	1.30344i	−0.194049	−	0.980992i	$-0.562162\pi$
$857$	1.38663e10	−	2.40172e10i	0.752539	−	1.30344i	0.946588	−	0.322444i	$-0.104504\pi$
$858$		0			0
$859$	−9.92987e8	−	1.71990e9i	−0.0534524	−	0.0925823i	0.838061	−	0.545576i	$-0.183689\pi$
$859$	−9.92987e8	−	1.71990e9i	−0.0534524	−	0.0925823i	−0.891514	+	0.452994i	$0.850356\pi$
$860$	5.51397e9			0.295611
$861$		0			0
$862$	−1.61643e8			−0.00859570
$863$	−4.84554e9	−	8.39271e9i	−0.256628	−	0.444493i	0.708708	−	0.705501i	$-0.249278\pi$
$863$	−4.84554e9	−	8.39271e9i	−0.256628	−	0.444493i	−0.965336	+	0.261009i	$0.915945\pi$
$864$		0			0
$865$	−3.14492e9	+	5.44716e9i	−0.165216	+	0.286163i
$866$	−5.26008e9	−	9.11073e9i	−0.275220	−	0.476695i
$867$		0			0
$868$	1.87106e10	−	2.21226e9i	0.971108	−	0.114820i
$869$	1.86266e10			0.962865
$870$		0			0
$871$	8.92853e9	−	1.54647e10i	0.457843	−	0.793007i
$872$	6.36608e9	−	1.10264e10i	0.325135	−	0.563151i
$873$		0			0
$874$	−1.50136e10			−0.760668
$875$	−7.46907e9	+	1.73790e10i	−0.376911	+	0.876993i
$876$		0			0
$877$	−4.03240e9	−	6.98431e9i	−0.201867	−	0.349643i	0.747263	−	0.664528i	$-0.231367\pi$
$877$	−4.03240e9	−	6.98431e9i	−0.201867	−	0.349643i	−0.949130	+	0.314885i	$0.898034\pi$
$878$	−9.27156e9	+	1.60588e10i	−0.462298	+	0.800723i
$879$		0			0
$880$	−7.27553e8	−	1.26016e9i	−0.0359894	−	0.0623355i
$881$	−3.72296e10			−1.83431			−0.917156	−	0.398529i	$-0.869521\pi$
$881$	−3.72296e10			−1.83431			−0.917156	+	0.398529i	$0.869521\pi$
$882$		0			0
$883$	1.71532e10			0.838458			0.419229	−	0.907880i	$-0.362300\pi$
$883$	1.71532e10			0.838458			0.419229	+	0.907880i	$0.362300\pi$
$884$	4.66982e8	+	8.08837e8i	0.0227362	+	0.0393802i
$885$		0			0
$886$	−5.42526e9	+	9.39683e9i	−0.262061	+	0.453903i
$887$	−1.09654e10	−	1.89927e10i	−0.527586	−	0.913806i	−0.999483	−	0.0321523i	$-0.989764\pi$
$887$	−1.09654e10	−	1.89927e10i	−0.527586	−	0.913806i	0.471897	−	0.881654i	$-0.343569\pi$
$888$		0			0
$889$	9.49925e9	−	2.21028e10i	0.453454	−	1.05509i
$890$	−3.47088e9			−0.165034
$891$		0			0
$892$	−7.40122e9	+	1.28193e10i	−0.349162	+	0.604766i
$893$	2.05960e9	−	3.56733e9i	0.0967837	−	0.167634i
$894$		0			0
$895$	−3.14917e10			−1.46830
$896$	1.05147e10	−	1.24321e9i	0.488336	−	0.0577389i
$897$		0			0
$898$	−1.04806e10	−	1.81529e10i	−0.482967	−	0.836523i
$899$	2.00136e10	−	3.46646e10i	0.918686	−	1.59121i
$900$		0			0
$901$	9.68190e8	+	1.67695e9i	0.0440985	+	0.0763808i
$902$	−1.53777e9			−0.0697700
$903$		0			0
$904$	1.71955e10			0.774150
$905$	−9.54949e9	−	1.65402e10i	−0.428263	−	0.741773i
$906$		0			0
$907$	1.25298e9	−	2.17022e9i	0.0557593	−	0.0965779i	−0.836798	−	0.547511i	$-0.815575\pi$
$907$	1.25298e9	−	2.17022e9i	0.0557593	−	0.0965779i	0.892558	+	0.450933i	$0.148909\pi$
$908$	1.13120e10	+	1.95930e10i	0.501464	+	0.868562i
$909$		0			0
$910$	6.04401e9	+	8.09594e9i	0.265877	+	0.356141i
$911$	8.68527e9			0.380600			0.190300	−	0.981726i	$-0.439054\pi$
$911$	8.68527e9			0.380600			0.190300	+	0.981726i	$0.439054\pi$
$912$		0			0
$913$	−2.23097e9	+	3.86416e9i	−0.0970167	+	0.168038i
$914$	1.52052e9	−	2.63361e9i	0.0658688	−	0.114088i
$915$		0			0
$916$	−1.36216e10			−0.585591
$917$	4.09669e9	−	4.84375e8i	0.175445	−	0.0207438i
$918$		0			0
$919$	−3.34164e9	−	5.78789e9i	−0.142022	−	0.245989i	0.786236	−	0.617926i	$-0.212027\pi$
$919$	−3.34164e9	−	5.78789e9i	−0.142022	−	0.245989i	−0.928258	+	0.371937i	$0.878694\pi$
$920$	−1.36131e10	+	2.35786e10i	−0.576369	+	0.998300i
$921$		0			0
$922$	−1.53005e10	−	2.65012e10i	−0.642904	−	1.11354i
$923$	2.07248e10			0.867531
$924$		0			0
$925$	−8.47400e8			−0.0352040
$926$	9.21129e9	+	1.59544e10i	0.381226	+	0.660302i
$927$		0			0
$928$	1.26741e10	−	2.19522e10i	0.520596	−	0.901698i
$929$	−6.08895e9	−	1.05464e10i	−0.249165	−	0.431567i	0.714129	−	0.700014i	$-0.246823\pi$
$929$	−6.08895e9	−	1.05464e10i	−0.249165	−	0.431567i	−0.963294	+	0.268447i	$0.913490\pi$
$930$		0			0
$931$	−7.56533e9	+	2.55176e10i	−0.307259	+	1.03637i
$932$	−1.83151e10			−0.741059
$933$		0			0
$934$	−1.00903e10	+	1.74770e10i	−0.405221	+	0.701863i
$935$	1.13706e9	−	1.96945e9i	0.0454929	−	0.0787960i
$936$		0			0
$937$	4.28141e10			1.70019			0.850097	−	0.526626i	$-0.176543\pi$
$937$	4.28141e10			1.70019			0.850097	+	0.526626i	$0.176543\pi$
$938$	−9.10543e9	+	2.11864e10i	−0.360239	+	0.838201i
$939$		0			0
$940$	−1.36266e9	−	2.36020e9i	−0.0535107	−	0.0926833i
$941$	−1.97417e10	+	3.41937e10i	−0.772363	+	1.33777i	0.163902	+	0.986477i	$0.447592\pi$
$941$	−1.97417e10	+	3.41937e10i	−0.772363	+	1.33777i	−0.936265	+	0.351295i	$0.885741\pi$
$942$		0			0
$943$	2.05359e9	+	3.55692e9i	0.0797485	+	0.138129i
$944$	1.90297e9			0.0736256
$945$		0			0
$946$	6.07709e9			0.233387
$947$	5.55513e9	+	9.62176e9i	0.212554	+	0.368154i	0.952513	−	0.304498i	$-0.0984885\pi$
$947$	5.55513e9	+	9.62176e9i	0.212554	+	0.368154i	−0.739959	+	0.672652i	$0.765155\pi$
$948$		0			0
$949$	1.99516e9	−	3.45572e9i	0.0757786	−	0.131252i
$950$	−7.69341e8	−	1.33254e9i	−0.0291129	−	0.0504251i
$951$		0			0
$952$	−1.97764e9	−	2.64905e9i	−0.0742879	−	0.0995085i
$953$	3.33302e10			1.24742			0.623711	−	0.781655i	$-0.285624\pi$
$953$	3.33302e10			1.24742			0.623711	+	0.781655i	$0.285624\pi$
$954$		0			0
$955$	−2.10262e9	+	3.64184e9i	−0.0781176	+	0.135304i
$956$	−1.23699e8	+	2.14253e8i	−0.00457893	+	0.00793095i
$957$		0			0
$958$	−8.97597e9			−0.329839
$959$	−2.67938e10	−	3.58903e10i	−0.981001	−	1.31405i
$960$		0			0
$961$	−2.61117e10	−	4.52268e10i	−0.949082	−	1.64386i
$962$	2.51450e9	−	4.35524e9i	0.0910622	−	0.157724i
$963$		0			0
$964$	8.03431e9	+	1.39158e10i	0.288854	+	0.500311i
$965$	−1.81387e10			−0.649772
$966$		0			0
$967$	−5.24781e10			−1.86632			−0.933158	−	0.359466i	$-0.882959\pi$
$967$	−5.24781e10			−1.86632			−0.933158	+	0.359466i	$0.882959\pi$
$968$	−6.91097e9	−	1.19702e10i	−0.244892	−	0.424166i
$969$		0			0
$970$	6.10180e9	−	1.05686e10i	0.214663	−	0.371807i
$971$	1.74484e10	+	3.02216e10i	0.611630	+	1.05937i	0.990966	+	0.134115i	$0.0428192\pi$
$971$	1.74484e10	+	3.02216e10i	0.611630	+	1.05937i	−0.379336	+	0.925259i	$0.623847\pi$
$972$		0			0
$973$	−1.58105e10	+	3.67878e10i	−0.550238	+	1.28029i
$974$	−1.75764e10			−0.609499
$975$		0			0
$976$	5.97120e8	−	1.03424e9i	0.0205583	−	0.0356080i
$977$	−2.82223e10	+	4.88824e10i	−0.968191	+	1.67696i	−0.267404	+	0.963585i	$0.586166\pi$
$977$	−2.82223e10	+	4.88824e10i	−0.968191	+	1.67696i	−0.700787	+	0.713371i	$0.747168\pi$
$978$		0			0
$979$	5.16295e9			0.175857
$980$	1.21183e10	+	1.27762e10i	0.411292	+	0.433620i
$981$		0			0
$982$	1.80977e10	+	3.13461e10i	0.609864	+	1.05632i
$983$	−4.20622e7	+	7.28538e7i	−0.00141239	+	0.00244633i	−0.866731	−	0.498776i	$-0.833783\pi$
$983$	−4.20622e7	+	7.28538e7i	−0.00141239	+	0.00244633i	0.865318	+	0.501223i	$0.167116\pi$
$984$		0			0
$985$	−1.97066e9	−	3.41329e9i	−0.0657031	−	0.113801i
$986$	−2.56235e9			−0.0851274
$987$		0			0
$988$	−1.23245e10			−0.406556
$989$	−8.11554e9	−	1.40565e10i	−0.266766	−	0.462052i
$990$		0			0
$991$	−6.49617e9	+	1.12517e10i	−0.212031	+	0.367249i	−0.952350	−	0.305007i	$-0.901341\pi$
$991$	−6.49617e9	+	1.12517e10i	−0.212031	+	0.367249i	0.740319	+	0.672256i	$0.234674\pi$
$992$	−2.52474e10	−	4.37298e10i	−0.821157	−	1.42229i
$993$		0			0
$994$	−2.65785e10	+	3.14253e9i	−0.858376	+	0.101491i
$995$	−8.64449e9			−0.278201
$996$		0			0
$997$	1.11340e8	−	1.92846e8i	0.00355808	−	0.00616278i	−0.864241	−	0.503078i	$-0.832201\pi$
$997$	1.11340e8	−	1.92846e8i	0.00355808	−	0.00616278i	0.867799	+	0.496915i	$0.165534\pi$
$998$	1.07282e10	−	1.85818e10i	0.341641	−	0.591740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.8.e.b.46.2		8
3.2	odd	2		7.8.c.a.4.3	yes	8
7.2	even	3	inner	63.8.e.b.37.2		8
7.3	odd	6		441.8.a.t.1.3		4
7.4	even	3		441.8.a.s.1.3		4
12.11	even	2		112.8.i.c.81.4		8
21.2	odd	6		7.8.c.a.2.3	✓	8
21.5	even	6		49.8.c.g.30.3		8
21.11	odd	6		49.8.a.f.1.2		4
21.17	even	6		49.8.a.e.1.2		4
21.20	even	2		49.8.c.g.18.3		8
84.23	even	6		112.8.i.c.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.c.a.2.3	✓	8	21.2	odd	6
7.8.c.a.4.3	yes	8	3.2	odd	2
49.8.a.e.1.2		4	21.17	even	6
49.8.a.f.1.2		4	21.11	odd	6
49.8.c.g.18.3		8	21.20	even	2
49.8.c.g.30.3		8	21.5	even	6
63.8.e.b.37.2		8	7.2	even	3	inner
63.8.e.b.46.2		8	1.1	even	1	trivial
112.8.i.c.65.4		8	84.23	even	6
112.8.i.c.81.4		8	12.11	even	2
441.8.a.s.1.3		4	7.4	even	3
441.8.a.t.1.3		4	7.3	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.69038 - 6.39193i) q^{2} +(36.7621 - 63.6739i) q^{4} +(-145.409 - 251.857i) q^{5} +(358.327 - 833.753i) q^{7} -1487.40 q^{8} +(-1073.23 + 1858.89i) q^{10} +(1596.44 - 2765.12i) q^{11} +5186.70 q^{13} +(-6651.66 + 786.465i) q^{14} +(783.535 + 1357.12i) q^{16} +(-1224.56 + 2120.99i) q^{17} +(-16159.1 - 27988.4i) q^{19} -21382.2 q^{20} -23565.9 q^{22} +(31470.7 + 54508.9i) q^{23} +(-3225.30 + 5586.38i) q^{25} +(-19140.9 - 33153.0i) q^{26} +(-39915.4 - 53466.7i) q^{28} -141752. q^{29} +(-141188. + 244545. i) q^{31} +(-89410.7 + 154864. i) q^{32} +18076.3 q^{34} +(-262090. + 30988.5i) q^{35} +(65683.8 + 113768. i) q^{37} +(-119267. + 206576. i) q^{38} +(216283. + 374612. i) q^{40} +65254.0 q^{41} -257876. q^{43} +(-117377. - 203303. i) q^{44} +(232278. - 402317. i) q^{46} +(63728.7 + 110381. i) q^{47} +(-566746. - 597513. i) q^{49} +47610.4 q^{50} +(190674. - 330257. i) q^{52} +(395323. - 684719. i) q^{53} -928551. q^{55} +(-532978. + 1.24013e6i) q^{56} +(523119. + 906068. i) q^{58} +(607173. - 1.05165e6i) q^{59} +(-381042. - 659985. i) q^{61} +2.08415e6 q^{62} +1.52042e6 q^{64} +(-754195. - 1.30630e6i) q^{65} +(1.72143e6 - 2.98160e6i) q^{67} +(90034.6 + 155944. i) q^{68} +(1.16529e6 + 1.56090e6i) q^{70} +3.99576e6 q^{71} +(384669. - 666266. i) q^{73} +(484797. - 839693. i) q^{74} -2.37617e6 q^{76} +(-1.73338e6 - 2.32186e6i) q^{77} +(2.91690e6 + 5.05222e6i) q^{79} +(227867. - 394677. i) q^{80} +(-240812. - 417099. i) q^{82} -1.39747e6 q^{83} +712248. q^{85} +(951662. + 1.64833e6i) q^{86} +(-2.37455e6 + 4.11285e6i) q^{88} +(808509. + 1.40038e6i) q^{89} +(1.85854e6 - 4.32443e6i) q^{91} +4.62772e6 q^{92} +(470367. - 814699. i) q^{94} +(-4.69937e6 + 8.13955e6i) q^{95} -5.68544e6 q^{97} +(-1.72775e6 + 5.82765e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 348 q^{4} + 252 q^{5} + 672 q^{7} + 1968 q^{8} - 4774 q^{10} - 3972 q^{11} - 2352 q^{13} - 47502 q^{14} - 57264 q^{16} + 56364 q^{17} - 41748 q^{19} - 324744 q^{20} - 305908 q^{22} + 131748 q^{23}+ \cdots - 60255006 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 - 348 * q^4 + 252 * q^5 + 672 * q^7 + 1968 * q^8 - 4774 * q^10 - 3972 * q^11 - 2352 * q^13 - 47502 * q^14 - 57264 * q^16 + 56364 * q^17 - 41748 * q^19 - 324744 * q^20 - 305908 * q^22 + 131748 * q^23 + 68016 * q^25 + 113652 * q^26 + 681548 * q^28 - 68112 * q^29 - 401212 * q^31 - 453408 * q^32 + 164220 * q^34 - 40404 * q^35 + 5396 * q^37 + 31794 * q^38 + 443688 * q^40 - 820848 * q^41 + 93088 * q^43 - 1465836 * q^44 - 1379202 * q^46 + 1470084 * q^47 - 2793784 * q^49 - 2791056 * q^50 + 5269768 * q^52 - 642372 * q^53 - 6126680 * q^55 + 6195168 * q^56 + 1972220 * q^58 + 752220 * q^59 - 1325772 * q^61 + 6032628 * q^62 - 1731712 * q^64 - 4868808 * q^65 + 290916 * q^67 + 2453556 * q^68 + 11665990 * q^70 - 6755520 * q^71 - 6706588 * q^73 + 3616878 * q^74 + 5846008 * q^76 + 5310564 * q^77 - 3946244 * q^79 + 10695888 * q^80 + 17563252 * q^82 - 19084128 * q^83 + 14012136 * q^85 + 23237832 * q^86 + 8043336 * q^88 + 16165212 * q^89 - 2414720 * q^91 + 38885256 * q^92 - 5720442 * q^94 - 3268452 * q^95 + 3066224 * q^97 - 60255006 * q^98

Introduction

L-functions

Modular forms

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