LMFDB - Embedded newform 63.8.e.b.37.1

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			37.1
Root			$-5.15962 - 8.93672i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.8.e.b.46.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.4120 + 18.0342i) q^{2} +(-152.821 - 264.694i) q^{4} +(96.7016 - 167.492i) q^{5} +(612.373 + 669.733i) q^{7} +3699.23 q^{8} +(2013.72 + 3487.87i) q^{10} +(151.972 + 263.223i) q^{11} -9891.04 q^{13} +(-18454.1 + 4070.37i) q^{14} +(-18955.5 + 32831.8i) q^{16} +(6242.26 + 10811.9i) q^{17} +(-561.837 + 973.131i) q^{19} -59112.1 q^{20} -6329.35 q^{22} +(-22359.5 + 38727.8i) q^{23} +(20360.1 + 35264.8i) q^{25} +(102986. - 178377. i) q^{26} +(83690.6 - 264441. i) q^{28} -51216.6 q^{29} +(-12816.5 - 22198.9i) q^{31} +(-157979. - 273628. i) q^{32} -259978. q^{34} +(171392. - 37803.5i) q^{35} +(21054.5 - 36467.4i) q^{37} +(-11699.7 - 20264.6i) q^{38} +(357722. - 619592. i) q^{40} -787100. q^{41} -629737. q^{43} +(46449.0 - 80452.1i) q^{44} +(-465616. - 806470. i) q^{46} +(313344. - 542727. i) q^{47} +(-73540.5 + 820253. i) q^{49} -847961. q^{50} +(1.51156e6 + 2.61810e6i) q^{52} +(-268306. - 464719. i) q^{53} +58783.7 q^{55} +(2.26531e6 + 2.47750e6i) q^{56} +(533269. - 923649. i) q^{58} +(1.06004e6 + 1.83605e6i) q^{59} +(-1.35734e6 + 2.35098e6i) q^{61} +533785. q^{62} +1.72694e6 q^{64} +(-956479. + 1.65667e6i) q^{65} +(-1.88702e6 - 3.26842e6i) q^{67} +(1.90790e6 - 3.30457e6i) q^{68} +(-1.10279e6 + 3.48453e6i) q^{70} -4.31646e6 q^{71} +(355018. + 614910. i) q^{73} +(438440. + 759401. i) q^{74} +343442. q^{76} +(-83225.5 + 262971. i) q^{77} +(-1.39606e6 + 2.41804e6i) q^{79} +(3.66605e6 + 6.34978e6i) q^{80} +(8.19532e6 - 1.41947e7i) q^{82} -538991. q^{83} +2.41454e6 q^{85} +(6.55684e6 - 1.13568e7i) q^{86} +(562180. + 973724. i) q^{88} +(-1.09927e6 + 1.90400e6i) q^{89} +(-6.05701e6 - 6.62435e6i) q^{91} +1.36680e7 q^{92} +(6.52509e6 + 1.13018e7i) q^{94} +(108661. + 188207. i) q^{95} -1.16799e7 q^{97} +(-1.40269e7 - 9.86675e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	−10.4120	+	18.0342i	−0.920303	+	1.59401i	−0.121357	+	0.992609i	$0.538724\pi$
$2$	−10.4120	+	18.0342i	−0.920303	+	1.59401i	−0.798946	+	0.601402i	$0.794609\pi$
$3$		0			0
$3$		0			0
$4$	−152.821	−	264.694i	−1.19391	−	2.06792i
$5$	96.7016	−	167.492i	0.345970	−	0.599238i	−0.639559	−	0.768742i	$-0.720883\pi$
$5$	96.7016	−	167.492i	0.345970	−	0.599238i	0.985530	+	0.169504i	$0.0542166\pi$
$6$		0			0
$7$	612.373	+	669.733i	0.674797	+	0.738003i
$7$	612.373	+	669.733i	0.674797	+	0.738003i
$8$	3699.23			2.55445
$9$		0			0
$10$	2013.72	+	3487.87i	0.636794	+	1.10296i
$11$	151.972	+	263.223i	0.0344262	+	0.0596279i	0.882725	−	0.469890i	$-0.155706\pi$
$11$	151.972	+	263.223i	0.0344262	+	0.0596279i	−0.848299	+	0.529518i	$0.822373\pi$
$12$		0			0
$13$	−9891.04			−1.24865			−0.624324	−	0.781165i	$-0.714626\pi$
$13$	−9891.04			−1.24865			−0.624324	+	0.781165i	$0.714626\pi$
$14$	−18454.1	+	4070.37i	−1.79740	+	0.396448i
$15$		0			0
$16$	−18955.5	+	32831.8i	−1.15695	+	2.00390i
$17$	6242.26	+	10811.9i	0.308156	+	0.533742i	0.977959	−	0.208797i	$-0.0669548\pi$
$17$	6242.26	+	10811.9i	0.308156	+	0.533742i	−0.669803	+	0.742539i	$0.733622\pi$
$18$		0			0
$19$	−561.837	+	973.131i	−0.0187920	+	0.0325487i	−0.875268	−	0.483637i	$-0.839315\pi$
$19$	−561.837	+	973.131i	−0.0187920	+	0.0325487i	0.856476	+	0.516186i	$0.172649\pi$
$20$	−59112.1			−1.65223
$21$		0			0
$22$	−6329.35			−0.126730
$23$	−22359.5	+	38727.8i	−0.383190	+	0.663705i	−0.991516	−	0.129982i	$-0.958508\pi$
$23$	−22359.5	+	38727.8i	−0.383190	+	0.663705i	0.608326	+	0.793687i	$0.291841\pi$
$24$		0			0
$25$	20360.1	+	35264.8i	0.260610	+	0.451389i
$26$	102986.	−	178377.i	1.14913	−	1.99036i
$27$		0			0
$28$	83690.6	−	264441.i	0.720482	−	2.27654i
$29$	−51216.6			−0.389958			−0.194979	−	0.980807i	$-0.562464\pi$
$29$	−51216.6			−0.389958			−0.194979	+	0.980807i	$0.562464\pi$
$30$		0			0
$31$	−12816.5	−	22198.9i	−0.0772688	−	0.133834i	0.824802	−	0.565422i	$-0.191287\pi$
$31$	−12816.5	−	22198.9i	−0.0772688	−	0.133834i	−0.902071	+	0.431588i	$0.857953\pi$
$32$	−157979.	−	273628.i	−0.852266	−	1.47617i
$33$		0			0
$34$	−259978.			−1.13439
$35$	171392.	−	37803.5i	0.675699	−	0.149037i
$36$		0			0
$37$	21054.5	−	36467.4i	0.0683343	−	0.118358i	−0.829834	−	0.558010i	$-0.811565\pi$
$37$	21054.5	−	36467.4i	0.0683343	−	0.118358i	0.898168	+	0.439652i	$0.144898\pi$
$38$	−11699.7	−	20264.6i	−0.0345887	−	0.0599093i
$39$		0			0
$40$	357722.	−	619592.i	0.883762	−	1.53072i
$41$	−787100.			−1.78356			−0.891778	−	0.452474i	$-0.850542\pi$
$41$	−787100.			−1.78356			−0.891778	+	0.452474i	$0.850542\pi$
$42$		0			0
$43$	−629737.			−1.20787			−0.603934	−	0.797034i	$-0.706401\pi$
$43$	−629737.			−1.20787			−0.603934	+	0.797034i	$0.706401\pi$
$44$	46449.0	−	80452.1i	0.0822039	−	0.142381i
$45$		0			0
$46$	−465616.	−	806470.i	−0.705302	−	1.22162i
$47$	313344.	−	542727.i	0.440229	−	0.762498i	−0.557478	−	0.830192i	$-0.688231\pi$
$47$	313344.	−	542727.i	0.440229	−	0.762498i	0.997706	+	0.0676937i	$0.0215641\pi$
$48$		0			0
$49$	−73540.5	+	820253.i	−0.0892977	+	0.996005i
$50$	−847961.			−0.959359
$51$		0			0
$52$	1.51156e6	+	2.61810e6i	1.49078	+	2.58211i
$53$	−268306.	−	464719.i	−0.247551	−	0.428770i	0.715295	−	0.698823i	$-0.246292\pi$
$53$	−268306.	−	464719.i	−0.247551	−	0.428770i	−0.962846	+	0.270052i	$0.912959\pi$
$54$		0			0
$55$	58783.7			0.0476417
$56$	2.26531e6	+	2.47750e6i	1.72373	+	1.88519i
$57$		0			0
$58$	533269.	−	923649.i	0.358879	−	0.621597i
$59$	1.06004e6	+	1.83605e6i	0.671958	+	1.16386i	0.977348	+	0.211638i	$0.0678797\pi$
$59$	1.06004e6	+	1.83605e6i	0.671958	+	1.16386i	−0.305390	+	0.952227i	$0.598787\pi$
$60$		0			0
$61$	−1.35734e6	+	2.35098e6i	−0.765656	+	1.32616i	0.174242	+	0.984703i	$0.444252\pi$
$61$	−1.35734e6	+	2.35098e6i	−0.765656	+	1.32616i	−0.939899	+	0.341453i	$0.889081\pi$
$62$	533785.			0.284443
$63$		0			0
$64$	1.72694e6			0.823470
$65$	−956479.	+	1.65667e6i	−0.431995	+	0.748237i
$66$		0			0
$67$	−1.88702e6	−	3.26842e6i	−0.766506	−	1.32763i	−0.939447	−	0.342695i	$-0.888660\pi$
$67$	−1.88702e6	−	3.26842e6i	−0.766506	−	1.32763i	0.172941	−	0.984932i	$-0.444673\pi$
$68$	1.90790e6	−	3.30457e6i	0.735824	−	1.27448i
$69$		0			0
$70$	−1.10279e6	+	3.48453e6i	−0.384281	+	1.21423i
$71$	−4.31646e6			−1.43128			−0.715638	−	0.698472i	$-0.753864\pi$
$71$	−4.31646e6			−1.43128			−0.715638	+	0.698472i	$0.753864\pi$
$72$		0			0
$73$	355018.	+	614910.i	0.106812	+	0.185004i	0.914477	−	0.404638i	$-0.132602\pi$
$73$	355018.	+	614910.i	0.106812	+	0.185004i	−0.807665	+	0.589642i	$0.799269\pi$
$74$	438440.	+	759401.i	0.125776	+	0.217851i
$75$		0			0
$76$	343442.			0.0897442
$77$	−83225.5	+	262971.i	−0.0207749	+	0.0656434i
$78$		0			0
$79$	−1.39606e6	+	2.41804e6i	−0.318572	+	0.551783i	−0.980190	−	0.198058i	$-0.936537\pi$
$79$	−1.39606e6	+	2.41804e6i	−0.318572	+	0.551783i	0.661618	+	0.749841i	$0.269870\pi$
$80$	3.66605e6	+	6.34978e6i	0.800540	+	1.38658i
$81$		0			0
$82$	8.19532e6	−	1.41947e7i	1.64141	−	2.84301i
$83$	−538991.			−0.103468			−0.0517342	−	0.998661i	$-0.516475\pi$
$83$	−538991.			−0.103468			−0.0517342	+	0.998661i	$0.516475\pi$
$84$		0			0
$85$	2.41454e6			0.426451
$86$	6.55684e6	−	1.13568e7i	1.11160	−	1.92536i
$87$		0			0
$88$	562180.	+	973724.i	0.0879399	+	0.152316i
$89$	−1.09927e6	+	1.90400e6i	−0.165288	+	0.286287i	−0.936757	−	0.349979i	$-0.886189\pi$
$89$	−1.09927e6	+	1.90400e6i	−0.165288	+	0.286287i	0.771470	+	0.636266i	$0.219522\pi$
$90$		0			0
$91$	−6.05701e6	−	6.62435e6i	−0.842584	−	0.921507i
$92$	1.36680e7			1.82999
$93$		0			0
$94$	6.52509e6	+	1.13018e7i	0.810287	+	1.40346i
$95$	108661.	+	188207.i	0.0130029	+	0.0225218i
$96$		0			0
$97$	−1.16799e7			−1.29938			−0.649691	−	0.760198i	$-0.725102\pi$
$97$	−1.16799e7			−1.29938			−0.649691	+	0.760198i	$0.725102\pi$
$98$	−1.40269e7	−	9.86675e6i	−1.50546	−	1.05897i
$99$		0			0
$100$	6.22291e6	−	1.07784e7i	0.622291	−	1.07784i
$101$	5.79389e6	+	1.00353e7i	0.559558	+	0.969184i	0.997533	+	0.0701964i	$0.0223626\pi$
$101$	5.79389e6	+	1.00353e7i	0.559558	+	0.969184i	−0.437975	+	0.898987i	$0.644304\pi$
$102$		0			0
$103$	−4.20034e6	+	7.27521e6i	−0.378752	+	0.656017i	−0.990881	−	0.134741i	$-0.956980\pi$
$103$	−4.20034e6	+	7.27521e6i	−0.378752	+	0.656017i	0.612129	+	0.790758i	$0.290313\pi$
$104$	−3.65893e7			−3.18961
$105$		0			0
$106$	1.11744e7			0.911286
$107$	1.45109e6	−	2.51336e6i	0.114512	−	0.198341i	−0.803072	−	0.595881i	$-0.796803\pi$
$107$	1.45109e6	−	2.51336e6i	0.114512	−	0.198341i	0.917585	+	0.397541i	$0.130136\pi$
$108$		0			0
$109$	9.92983e6	+	1.71990e7i	0.734428	+	1.27207i	0.954974	+	0.296690i	$0.0958828\pi$
$109$	9.92983e6	+	1.71990e7i	0.734428	+	1.27207i	−0.220546	+	0.975377i	$0.570784\pi$
$110$	−612058.	+	1.06012e6i	−0.0438448	+	0.0759414i
$111$		0			0
$112$	−3.35964e7	+	7.41025e6i	−2.25959	+	0.498390i
$113$	−7.27288e6			−0.474167			−0.237084	−	0.971489i	$-0.576192\pi$
$113$	−7.27288e6			−0.474167			−0.237084	+	0.971489i	$0.576192\pi$
$114$		0			0
$115$	4.32440e6	+	7.49007e6i	0.265145	+	0.459244i
$116$	7.82698e6	+	1.35567e7i	0.465576	+	0.806402i
$117$		0			0
$118$	−4.41489e7			−2.47362
$119$	−3.41849e6	+	1.08016e7i	−0.185960	+	0.587587i
$120$		0			0
$121$	9.69739e6	−	1.67964e7i	0.497630	−	0.861920i
$122$	−2.82653e7	−	4.89570e7i	−1.40927	−	2.44093i
$123$		0			0
$124$	−3.91727e6	+	6.78491e6i	−0.184505	+	0.319572i
$125$	2.29850e7			1.05259
$126$		0			0
$127$	2.81015e7			1.21735			0.608676	−	0.793419i	$-0.291701\pi$
$127$	2.81015e7			1.21735			0.608676	+	0.793419i	$0.291701\pi$
$128$	2.24036e6	−	3.88042e6i	0.0944241	−	0.163547i
$129$		0			0
$130$	−1.99178e7	−	3.44986e7i	−0.795132	−	1.37721i
$131$	−9.59472e6	+	1.66185e7i	−0.372892	+	0.645867i	−0.990009	−	0.141004i	$-0.954967\pi$
$131$	−9.59472e6	+	1.66185e7i	−0.372892	+	0.645867i	0.617117	+	0.786871i	$0.288300\pi$
$132$		0			0
$133$	−995792.	+	219639.i	−0.0367018	+	0.00809521i
$134$	7.85910e7			2.82167
$135$		0			0
$136$	2.30916e7	+	3.99958e7i	0.787168	+	1.36341i
$137$	8.60460e6	+	1.49036e7i	0.285897	+	0.495187i	0.972826	−	0.231537i	$-0.0743753\pi$
$137$	8.60460e6	+	1.49036e7i	0.285897	+	0.495187i	−0.686930	+	0.726724i	$0.741042\pi$
$138$		0			0
$139$	4.17445e7			1.31840			0.659200	−	0.751968i	$-0.270895\pi$
$139$	4.17445e7			1.31840			0.659200	+	0.751968i	$0.270895\pi$
$140$	−3.61987e7	−	3.95893e7i	−1.11492	−	1.21935i
$141$		0			0
$142$	4.49431e7	−	7.78438e7i	1.31721	−	2.28147i
$143$	−1.50316e6	−	2.60355e6i	−0.0429862	−	0.0744543i
$144$		0			0
$145$	−4.95272e6	+	8.57837e6i	−0.134914	+	0.233677i
$146$	−1.47859e7			−0.393198
$147$		0			0
$148$	−1.28703e7			−0.326341
$149$	1.99889e6	−	3.46218e6i	0.0495036	−	0.0857428i	−0.840212	−	0.542258i	$-0.817569\pi$
$149$	1.99889e6	−	3.46218e6i	0.0495036	−	0.0857428i	0.889715	+	0.456516i	$0.150903\pi$
$150$		0			0
$151$	−2.86457e7	−	4.96158e7i	−0.677081	−	1.17274i	−0.975856	−	0.218415i	$-0.929911\pi$
$151$	−2.86457e7	−	4.96158e7i	−0.677081	−	1.17274i	0.298775	−	0.954323i	$-0.403422\pi$
$152$	−2.07837e6	+	3.59984e6i	−0.0480032	+	0.0831439i
$153$		0			0
$154$	−3.87593e6	−	4.23897e6i	−0.0855171	−	0.0935272i
$155$	−4.95751e6			−0.106931
$156$		0			0
$157$	1.42614e7	+	2.47014e7i	0.294112	+	0.509416i	0.974778	−	0.223177i	$-0.0716429\pi$
$157$	1.42614e7	+	2.47014e7i	0.294112	+	0.509416i	−0.680666	+	0.732594i	$0.738310\pi$
$158$	−2.90716e7	−	5.03534e7i	−0.586366	−	1.01562i
$159$		0			0
$160$	−6.11073e7			−1.17943
$161$	−3.96296e7	+	8.74098e6i	−0.748392	+	0.165071i
$162$		0			0
$163$	−1.61353e7	+	2.79472e7i	−0.291824	+	0.505454i	−0.974241	−	0.225509i	$-0.927595\pi$
$163$	−1.61353e7	+	2.79472e7i	−0.291824	+	0.505454i	0.682417	+	0.730963i	$0.260929\pi$
$164$	1.20286e8	+	2.08341e8i	2.12941	+	3.68825i
$165$		0			0
$166$	5.61199e6	−	9.72026e6i	0.0952223	−	0.164930i
$167$	−1.88088e7			−0.312502			−0.156251	−	0.987717i	$-0.549941\pi$
$167$	−1.88088e7			−0.312502			−0.156251	+	0.987717i	$0.549941\pi$
$168$		0			0
$169$	3.50841e7			0.559123
$170$	−2.51403e7	+	4.35443e7i	−0.392464	+	0.679767i
$171$		0			0
$172$	9.62371e7	+	1.66687e8i	1.44209	+	2.49778i
$173$	4.67229e7	−	8.09264e7i	0.686070	−	1.18831i	−0.287029	−	0.957922i	$-0.592668\pi$
$173$	4.67229e7	−	8.09264e7i	0.686070	−	1.18831i	0.973099	−	0.230386i	$-0.0739989\pi$
$174$		0			0
$175$	−1.11500e7	+	3.52310e7i	−0.157268	+	0.496927i
$176$	−1.15228e7			−0.159318
$177$		0			0
$178$	−2.28913e7	−	3.96489e7i	−0.304229	−	0.526941i
$179$	4.41581e7	+	7.64841e7i	0.575473	+	0.996748i	0.995990	+	0.0894634i	$0.0285152\pi$
$179$	4.41581e7	+	7.64841e7i	0.575473	+	0.996748i	−0.420517	+	0.907284i	$0.638151\pi$
$180$		0			0
$181$	−1.09260e7			−0.136958			−0.0684789	−	0.997653i	$-0.521815\pi$
$181$	−1.09260e7			−0.136958			−0.0684789	+	0.997653i	$0.521815\pi$
$182$	1.82531e8	−	4.02602e7i	2.24432	−	0.495024i
$183$		0			0
$184$	−8.27130e7	+	1.43263e8i	−0.978840	+	1.69540i
$185$	−4.07200e6	−	7.05292e6i	−0.0472832	−	0.0818969i
$186$		0			0
$187$	−1.89730e6	+	3.28621e6i	−0.0212173	+	0.0367494i
$188$	−1.91542e8			−2.10238
$189$		0			0
$190$	−4.52553e6			−0.0478666
$191$	−5.24786e7	+	9.08956e7i	−0.544961	+	0.943900i	0.453648	+	0.891181i	$0.350122\pi$
$191$	−5.24786e7	+	9.08956e7i	−0.544961	+	0.943900i	−0.998609	+	0.0527193i	$0.983211\pi$
$192$		0			0
$193$	−7.92806e6	−	1.37318e7i	−0.0793809	−	0.137492i	0.823602	−	0.567168i	$-0.191961\pi$
$193$	−7.92806e6	−	1.37318e7i	−0.0793809	−	0.137492i	−0.902983	+	0.429676i	$0.858628\pi$
$194$	1.21611e8	−	2.10637e8i	1.19582	−	2.07123i
$195$		0			0
$196$	2.28354e8	−	1.05886e8i	2.16627	−	1.00448i
$197$	−4.99805e6			−0.0465767			−0.0232883	−	0.999729i	$-0.507414\pi$
$197$	−4.99805e6			−0.0465767			−0.0232883	+	0.999729i	$0.507414\pi$
$198$		0			0
$199$	−2.75134e7	−	4.76545e7i	−0.247490	−	0.428665i	0.715339	−	0.698778i	$-0.246272\pi$
$199$	−2.75134e7	−	4.76545e7i	−0.247490	−	0.428665i	−0.962829	+	0.270112i	$0.912939\pi$
$200$	7.53168e7	+	1.30453e8i	0.665713	+	1.15305i
$201$		0			0
$202$	−2.41305e8			−2.05985
$203$	−3.13637e7	−	3.43014e7i	−0.263142	−	0.287790i
$204$		0			0
$205$	−7.61138e7	+	1.31833e8i	−0.617057	+	1.06877i
$206$	−8.74683e7	−	1.51499e8i	−0.697132	−	1.20747i
$207$		0			0
$208$	1.87489e8	−	3.24741e8i	1.44462	−	2.50216i
$209$	−341534.			−0.00258775
$210$		0			0
$211$	−5.55200e7			−0.406875			−0.203437	−	0.979088i	$-0.565211\pi$
$211$	−5.55200e7			−0.406875			−0.203437	+	0.979088i	$0.565211\pi$
$212$	−8.20055e7	+	1.42038e8i	−0.591109	+	1.02383i
$213$		0			0
$214$	3.02176e7	+	5.23385e7i	0.210772	+	0.365067i
$215$	−6.08965e7	+	1.05476e8i	−0.417886	+	0.723800i
$216$		0			0
$217$	7.01881e6	−	2.21776e7i	0.0466288	−	0.147335i
$218$	−4.13559e8			−2.70358
$219$		0			0
$220$	−8.98339e6	−	1.55597e7i	−0.0568802	−	0.0985193i
$221$	−6.17424e7	−	1.06941e8i	−0.384778	−	0.666456i
$222$		0			0
$223$	−3.31811e7			−0.200366			−0.100183	−	0.994969i	$-0.531943\pi$
$223$	−3.31811e7			−0.200366			−0.100183	+	0.994969i	$0.531943\pi$
$224$	8.65153e7	−	2.73366e8i	0.514310	−	1.62509i
$225$		0			0
$226$	7.57255e7	−	1.31160e8i	0.436378	−	0.755828i
$227$	−4.88085e6	−	8.45388e6i	−0.0276952	−	0.0479695i	0.851846	−	0.523793i	$-0.175483\pi$
$227$	−4.88085e6	−	8.45388e6i	−0.0276952	−	0.0479695i	−0.879541	+	0.475823i	$0.842150\pi$
$228$		0			0
$229$	6.85558e6	−	1.18742e7i	0.0377242	−	0.0653403i	−0.846547	−	0.532314i	$-0.821322\pi$
$229$	6.85558e6	−	1.18742e7i	0.0377242	−	0.0653403i	0.884271	+	0.466974i	$0.154656\pi$
$230$	−1.80103e8			−0.976054
$231$		0			0
$232$	−1.89462e8			−0.996127
$233$	1.14766e8	−	1.98781e8i	0.594385	−	1.02950i	−0.399249	−	0.916843i	$-0.630729\pi$
$233$	1.14766e8	−	1.98781e8i	0.594385	−	1.02950i	0.993633	−	0.112662i	$-0.0359377\pi$
$234$		0			0
$235$	−6.06016e7	−	1.04965e8i	−0.304612	−	0.527603i
$236$	3.23994e8	−	5.61174e8i	1.60452	−	2.77911i
$237$		0			0
$238$	−1.59204e8	−	1.74116e8i	−0.765481	−	0.837181i
$239$	1.18140e8			0.559764			0.279882	−	0.960034i	$-0.409705\pi$
$239$	1.18140e8			0.559764			0.279882	+	0.960034i	$0.409705\pi$
$240$		0			0
$241$	−1.10867e8	−	1.92027e8i	−0.510202	−	0.883695i	−0.999930	−	0.0118201i	$-0.996237\pi$
$241$	−1.10867e8	−	1.92027e8i	−0.510202	−	0.883695i	0.489729	−	0.871875i	$-0.337096\pi$
$242$	2.01939e8	+	3.49769e8i	0.915940	+	1.58645i
$243$		0			0
$244$	8.29720e8			3.65651
$245$	1.30274e8	+	9.16372e7i	0.565949	+	0.398098i
$246$		0			0
$247$	5.55716e6	−	9.62528e6i	0.0234646	−	0.0406419i
$248$	−4.74113e7	−	8.21188e7i	−0.197379	−	0.341871i
$249$		0			0
$250$	−2.39321e8	+	4.14516e8i	−0.968704	+	1.67784i
$251$	1.95230e8			0.779273			0.389636	−	0.920969i	$-0.372601\pi$
$251$	1.95230e8			0.779273			0.389636	+	0.920969i	$0.372601\pi$
$252$		0			0
$253$	−1.35921e7			−0.0527671
$254$	−2.92594e8	+	5.06787e8i	−1.12033	+	1.94047i
$255$		0			0
$256$	1.57178e8	+	2.72240e8i	0.585532	+	1.01417i
$257$	−2.59127e8	+	4.48821e8i	−0.952240	+	1.64933i	−0.211679	+	0.977339i	$0.567893\pi$
$257$	−2.59127e8	+	4.48821e8i	−0.952240	+	1.64933i	−0.740561	+	0.671989i	$0.765440\pi$
$258$		0			0
$259$	3.73166e7	−	8.23082e6i	0.133461	−	0.0294370i
$260$	5.84681e8			2.06306
$261$		0			0
$262$	−1.99801e8	−	3.46066e8i	−0.686347	−	1.18879i
$263$	−1.95491e8	−	3.38600e8i	−0.662646	−	1.14774i	−0.979918	−	0.199402i	$-0.936100\pi$
$263$	−1.95491e8	−	3.38600e8i	−0.662646	−	1.14774i	0.317271	−	0.948335i	$-0.397233\pi$
$264$		0			0
$265$	−1.03782e8			−0.342580
$266$	6.40722e6	−	2.02452e7i	0.0208729	−	0.0659532i
$267$		0			0
$268$	−5.76754e8	+	9.98967e8i	−1.83028	+	3.17015i
$269$	−1.79359e8	−	3.10659e8i	−0.561810	−	0.973084i	−0.997339	−	0.0729092i	$-0.976772\pi$
$269$	−1.79359e8	−	3.10659e8i	−0.561810	−	0.973084i	0.435528	−	0.900175i	$-0.356562\pi$
$270$		0			0
$271$	−9.85150e7	+	1.70633e8i	−0.300684	+	0.520799i	−0.976291	−	0.216462i	$-0.930548\pi$
$271$	−9.85150e7	+	1.70633e8i	−0.300684	+	0.520799i	0.675607	+	0.737262i	$0.263881\pi$
$272$	−4.73300e8			−1.42608
$273$		0			0
$274$	−3.58366e8			−1.05245
$275$	−6.18833e6	+	1.07185e7i	−0.0179436	+	0.0310792i
$276$		0			0
$277$	2.00995e8	+	3.48134e8i	0.568207	+	0.984164i	0.996743	+	0.0806391i	$0.0256961\pi$
$277$	2.00995e8	+	3.48134e8i	0.568207	+	0.984164i	−0.428536	+	0.903525i	$0.640971\pi$
$278$	−4.34645e8	+	7.52828e8i	−1.21333	+	2.10155i
$279$		0			0
$280$	6.34020e8	−	1.39844e8i	1.72604	−	0.380707i
$281$	−2.80445e7			−0.0754008			−0.0377004	−	0.999289i	$-0.512003\pi$
$281$	−2.80445e7			−0.0754008			−0.0377004	+	0.999289i	$0.512003\pi$
$282$		0			0
$283$	−1.03202e6	−	1.78751e6i	−0.00270667	−	0.00468809i	0.864669	−	0.502342i	$-0.167528\pi$
$283$	−1.03202e6	−	1.78751e6i	−0.00270667	−	0.00468809i	−0.867376	+	0.497654i	$0.834195\pi$
$284$	6.59646e8	+	1.14254e9i	1.70882	+	2.95977i
$285$		0			0
$286$	6.26038e7			0.158241
$287$	−4.81999e8	−	5.27147e8i	−1.20354	−	1.31627i
$288$		0			0
$289$	1.27238e8	−	2.20382e8i	0.310080	−	0.537074i
$290$	−1.03136e8	−	1.78637e8i	−0.248323	−	0.430108i
$291$		0			0
$292$	1.08509e8	−	1.87942e8i	0.255049	−	0.441758i
$293$	3.77433e8			0.876604			0.438302	−	0.898828i	$-0.355580\pi$
$293$	3.77433e8			0.876604			0.438302	+	0.898828i	$0.355580\pi$
$294$		0			0
$295$	4.10032e8			0.929909
$296$	7.78855e7	−	1.34902e8i	0.174556	−	0.302340i
$297$		0			0
$298$	4.16250e7	+	7.20967e7i	0.0911166	+	0.157819i
$299$	2.21159e8	−	3.83058e8i	0.478470	−	0.828734i
$300$		0			0
$301$	−3.85634e8	−	4.21755e8i	−0.815066	−	0.891411i
$302$	1.19304e9			2.49248
$303$		0			0
$304$	−2.12998e7	−	3.68923e7i	−0.0434828	−	0.0753145i
$305$	2.62514e8	+	4.54687e8i	0.529788	+	0.917620i
$306$		0			0
$307$	5.18232e8			1.02221			0.511105	−	0.859519i	$-0.329236\pi$
$307$	5.18232e8			1.02221			0.511105	+	0.859519i	$0.329236\pi$
$308$	8.23255e7	−	1.81583e7i	0.160549	−	0.0354118i
$309$		0			0
$310$	5.16178e7	−	8.94046e7i	0.0984087	−	0.170449i
$311$	1.41916e8	+	2.45806e8i	0.267529	+	0.463374i	0.968223	−	0.250088i	$-0.0804596\pi$
$311$	1.41916e8	+	2.45806e8i	0.267529	+	0.463374i	−0.700694	+	0.713462i	$0.747126\pi$
$312$		0			0
$313$	1.65050e7	−	2.85875e7i	0.0304236	−	0.0526952i	−0.850413	−	0.526116i	$-0.823648\pi$
$313$	1.65050e7	−	2.85875e7i	0.0304236	−	0.0526952i	0.880836	+	0.473421i	$0.156981\pi$
$314$	−5.93959e8			−1.08269
$315$		0			0
$316$	8.53387e8			1.52139
$317$	5.46589e8	−	9.46720e8i	0.963726	−	1.66922i	0.250727	−	0.968058i	$-0.419331\pi$
$317$	5.46589e8	−	9.46720e8i	0.963726	−	1.66922i	0.713000	−	0.701165i	$-0.247336\pi$
$318$		0			0
$319$	−7.78348e6	−	1.34814e7i	−0.0134248	−	0.0232524i
$320$	1.66998e8	−	2.89249e8i	0.284896	−	0.493454i
$321$		0			0
$322$	2.54989e8	−	8.05699e8i	0.425623	−	1.34486i
$323$	−1.40285e7			−0.0231635
$324$		0			0
$325$	−2.01383e8	−	3.48805e8i	−0.325410	−	0.563626i
$326$	−3.36003e8	−	5.81974e8i	−0.537133	−	0.930341i
$327$		0			0
$328$	−2.91167e9			−4.55600
$329$	5.55365e8	−	1.22495e8i	0.859791	−	0.189641i
$330$		0			0
$331$	1.60956e8	−	2.78785e8i	0.243955	−	0.422543i	−0.717882	−	0.696165i	$-0.754888\pi$
$331$	1.60956e8	−	2.78785e8i	0.243955	−	0.422543i	0.961837	+	0.273622i	$0.0882216\pi$
$332$	8.23692e7	+	1.42668e8i	0.123533	+	0.213965i
$333$		0			0
$334$	1.95838e8	−	3.39201e8i	0.287597	−	0.498132i
$335$	−7.29912e8			−1.06075
$336$		0			0
$337$	1.31007e9			1.86461			0.932307	−	0.361668i	$-0.117793\pi$
$337$	1.31007e9			1.86461			0.932307	+	0.361668i	$0.117793\pi$
$338$	−3.65297e8	+	6.32713e8i	−0.514562	+	0.891248i
$339$		0			0
$340$	−3.68993e8	−	6.39115e8i	−0.509146	−	0.881866i
$341$	3.89550e6	−	6.74721e6i	0.00532014	−	0.00921476i
$342$		0			0
$343$	−5.94384e8	+	4.53049e8i	−0.795313	+	0.606199i
$344$	−2.32954e9			−3.08543
$345$		0			0
$346$	9.72961e8	+	1.68522e9i	1.26278	+	2.18721i
$347$	8.33411e7	+	1.44351e8i	0.107079	+	0.185467i	0.914586	−	0.404392i	$-0.132517\pi$
$347$	8.33411e7	+	1.44351e8i	0.107079	+	0.185467i	−0.807506	+	0.589859i	$0.799183\pi$
$348$		0			0
$349$	7.47430e8			0.941199			0.470599	−	0.882347i	$-0.344038\pi$
$349$	7.47430e8			0.941199			0.470599	+	0.882347i	$0.344038\pi$
$350$	−5.19269e8	−	5.67907e8i	−0.647372	−	0.708010i
$351$		0			0
$352$	4.80168e7	−	8.31675e7i	0.0586805	−	0.101638i
$353$	3.08956e8	+	5.35127e8i	0.373839	+	0.647509i	0.990153	−	0.139992i	$-0.0447078\pi$
$353$	3.08956e8	+	5.35127e8i	0.373839	+	0.647509i	−0.616313	+	0.787501i	$0.711375\pi$
$354$		0			0
$355$	−4.17408e8	+	7.22972e8i	−0.495178	+	0.857674i
$356$	6.71968e8			0.789357
$357$		0			0
$358$	−1.83910e9			−2.11844
$359$	−5.08337e8	+	8.80465e8i	−0.579857	+	1.00434i	0.415638	+	0.909530i	$0.363558\pi$
$359$	−5.08337e8	+	8.80465e8i	−0.579857	+	1.00434i	−0.995495	+	0.0948120i	$0.969775\pi$
$360$		0			0
$361$	4.46305e8	+	7.73022e8i	0.499294	+	0.864802i
$362$	1.13762e8	−	1.97042e8i	0.126043	−	0.218312i
$363$		0			0
$364$	−8.27786e8	+	2.61559e9i	−0.899629	+	2.84260i
$365$	1.37323e8			0.147815
$366$		0			0
$367$	−7.38499e8	−	1.27912e9i	−0.779864	−	1.35076i	−0.932020	−	0.362407i	$-0.881955\pi$
$367$	−7.38499e8	−	1.27912e9i	−0.779864	−	1.35076i	0.152156	−	0.988356i	$-0.451378\pi$
$368$	−8.47670e8	−	1.46821e9i	−0.886664	−	1.53575i
$369$		0			0
$370$	1.69591e8			0.174060
$371$	1.46934e8	−	4.64274e8i	0.149387	−	0.472026i
$372$		0			0
$373$	8.15971e8	−	1.41330e9i	0.814130	−	1.41011i	−0.0958211	−	0.995399i	$-0.530548\pi$
$373$	8.15971e8	−	1.41330e9i	0.814130	−	1.41011i	0.909951	−	0.414716i	$-0.136119\pi$
$374$	−3.95094e7	−	6.84323e7i	−0.0390526	−	0.0676411i
$375$		0			0
$376$	1.15913e9	−	2.00767e9i	1.12454	−	1.94776i
$377$	5.06585e8			0.486920
$378$		0			0
$379$	−3.41392e8			−0.322118			−0.161059	−	0.986945i	$-0.551491\pi$
$379$	−3.41392e8			−0.322118			−0.161059	+	0.986945i	$0.551491\pi$
$380$	3.32114e7	−	5.75239e7i	0.0310488	−	0.0537781i
$381$		0			0
$382$	−1.09282e9	−	1.89282e9i	−1.00306	−	1.73735i
$383$	−1.85545e8	+	3.21374e8i	−0.168754	+	0.292290i	−0.937982	−	0.346684i	$-0.887308\pi$
$383$	−1.85545e8	+	3.21374e8i	−0.168754	+	0.292290i	0.769228	+	0.638974i	$0.220641\pi$
$384$		0			0
$385$	3.59976e7	+	3.93694e7i	0.0321485	+	0.0351597i
$386$	3.30189e8			0.292218
$387$		0			0
$388$	1.78493e9	+	3.09159e9i	1.55135	+	2.68702i
$389$	−4.74511e8	−	8.21877e8i	−0.408717	−	0.707919i	0.586029	−	0.810290i	$-0.300690\pi$
$389$	−4.74511e8	−	8.21877e8i	−0.408717	−	0.707919i	−0.994746	+	0.102371i	$0.967357\pi$
$390$		0			0
$391$	−5.58295e8			−0.472329
$392$	−2.72044e8	+	3.03431e9i	−0.228106	+	2.54424i
$393$		0			0
$394$	5.20399e7	−	9.01357e7i	0.0428647	−	0.0742438i
$395$	2.70001e8	+	4.67656e8i	0.220433	+	0.381801i
$396$		0			0
$397$	−3.81892e8	+	6.61456e8i	−0.306319	+	0.530560i	−0.977554	−	0.210685i	$-0.932431\pi$
$397$	−3.81892e8	+	6.61456e8i	−0.306319	+	0.530560i	0.671235	+	0.741244i	$0.265764\pi$
$398$	1.14588e9			0.911063
$399$		0			0
$400$	−1.54374e9			−1.20605
$401$	4.60425e8	−	7.97479e8i	0.356577	−	0.617610i	−0.630809	−	0.775938i	$-0.717277\pi$
$401$	4.60425e8	−	7.97479e8i	0.356577	−	0.617610i	0.987387	+	0.158328i	$0.0506104\pi$
$402$		0			0
$403$	1.26769e8	+	2.19570e8i	0.0964816	+	0.167111i
$404$	1.77086e9	−	3.06721e9i	1.33613	−	2.31425i
$405$		0			0
$406$	9.45158e8	−	2.08471e8i	0.700912	−	0.154598i
$407$	1.27988e7			0.00940996
$408$		0			0
$409$	4.04665e8	+	7.00900e8i	0.292458	+	0.506552i	0.974390	−	0.224863i	$-0.0721935\pi$
$409$	4.04665e8	+	7.00900e8i	0.292458	+	0.506552i	−0.681932	+	0.731415i	$0.738860\pi$
$410$	−1.58500e9	−	2.74530e9i	−1.13576	−	1.96719i
$411$		0			0
$412$	2.56760e9			1.80879
$413$	−5.80520e8	+	1.83429e9i	−0.405501	+	1.28128i
$414$		0			0
$415$	−5.21212e7	+	9.02766e7i	−0.0357970	+	0.0620022i
$416$	1.56258e9	+	2.70646e9i	1.06418	+	1.84321i
$417$		0			0
$418$	3.55607e6	−	6.15929e6i	0.00238151	−	0.00412490i
$419$	−2.33725e9			−1.55223			−0.776115	−	0.630592i	$-0.782812\pi$
$419$	−2.33725e9			−1.55223			−0.776115	+	0.630592i	$0.782812\pi$
$420$		0			0
$421$	6.85194e8			0.447534			0.223767	−	0.974643i	$-0.428164\pi$
$421$	6.85194e8			0.447534			0.223767	+	0.974643i	$0.428164\pi$
$422$	5.78076e8	−	1.00126e9i	0.374448	−	0.648563i
$423$		0			0
$424$	−9.92525e8	−	1.71910e9i	−0.632355	−	1.09527i
$425$	−2.54186e8	+	4.40263e8i	−0.160617	+	0.278196i
$426$		0			0
$427$	−2.40573e9	+	5.30624e8i	−1.49537	+	0.329829i
$428$	−8.87029e8			−0.546871
$429$		0			0
$430$	−1.26811e9	−	2.19644e9i	−0.769164	−	1.33223i
$431$	7.97694e8	+	1.38165e9i	0.479917	+	0.831240i	0.999735	−	0.0230370i	$-0.00733355\pi$
$431$	7.97694e8	+	1.38165e9i	0.479917	+	0.831240i	−0.519818	+	0.854277i	$0.674000\pi$
$432$		0			0
$433$	−3.20663e9			−1.89820			−0.949098	−	0.314981i	$-0.898002\pi$
$433$	−3.20663e9			−1.89820			−0.949098	+	0.314981i	$0.898002\pi$
$434$	3.26875e8	+	3.57493e8i	0.191941	+	0.209920i
$435$		0			0
$436$	3.03498e9	−	5.25673e9i	1.75369	−	3.03748i
$437$	−2.51248e7	−	4.35174e7i	−0.0144018	−	0.0249447i
$438$		0			0
$439$	−9.31855e8	+	1.61402e9i	−0.525681	+	0.910507i	0.473871	+	0.880594i	$0.342856\pi$
$439$	−9.31855e8	+	1.61402e9i	−0.525681	+	0.910507i	−0.999553	+	0.0299126i	$0.990477\pi$
$440$	2.17455e8			0.121698
$441$		0			0
$442$	2.57146e9			1.41645
$443$	3.99132e8	−	6.91317e8i	0.218124	−	0.377802i	−0.736110	−	0.676861i	$-0.763340\pi$
$443$	3.99132e8	−	6.91317e8i	0.218124	−	0.377802i	0.954234	+	0.299060i	$0.0966729\pi$
$444$		0			0
$445$	2.12603e8	+	3.68239e8i	0.114369	+	0.198093i
$446$	3.45483e8	−	5.98394e8i	0.184397	−	0.319386i
$447$		0			0
$448$	1.05753e9	+	1.15659e9i	0.555675	+	0.607723i
$449$	4.99626e8			0.260485			0.130242	−	0.991482i	$-0.458424\pi$
$449$	4.99626e8			0.260485			0.130242	+	0.991482i	$0.458424\pi$
$450$		0			0
$451$	−1.19617e8	−	2.07183e8i	−0.0614010	−	0.106350i
$452$	1.11145e9	+	1.92509e9i	0.566115	+	0.980541i
$453$		0			0
$454$	2.03278e8			0.101952
$455$	−1.69525e9	+	3.73916e8i	−0.843710	+	0.186095i
$456$		0			0
$457$	−1.33706e9	+	2.31585e9i	−0.655305	+	1.13502i	0.326513	+	0.945193i	$0.394126\pi$
$457$	−1.33706e9	+	2.31585e9i	−0.655305	+	1.13502i	−0.981817	+	0.189828i	$0.939207\pi$
$458$	1.42761e8	+	2.47270e8i	0.0694354	+	0.120266i
$459$		0			0
$460$	1.32172e9	−	2.28928e9i	0.633120	−	1.09660i
$461$	2.67032e9			1.26943			0.634716	−	0.772746i	$-0.281117\pi$
$461$	2.67032e9			1.26943			0.634716	+	0.772746i	$0.281117\pi$
$462$		0			0
$463$	1.72345e9			0.806983			0.403492	−	0.914983i	$-0.367796\pi$
$463$	1.72345e9			0.806983			0.403492	+	0.914983i	$0.367796\pi$
$464$	9.70835e8	−	1.68153e9i	0.451162	−	0.781435i
$465$		0			0
$466$	2.38990e9	+	4.13942e9i	1.09403	+	1.89491i
$467$	−1.41354e9	+	2.44832e9i	−0.642242	+	1.11240i	0.342689	+	0.939449i	$0.388662\pi$
$467$	−1.41354e9	+	2.44832e9i	−0.642242	+	1.11240i	−0.984931	+	0.172947i	$0.944671\pi$
$468$		0			0
$469$	1.03340e9	−	3.26529e9i	0.462557	−	1.46156i
$470$	2.52395e9			1.12134
$471$		0			0
$472$	3.92135e9	+	6.79198e9i	1.71648	+	2.97303i
$473$	−9.57023e7	−	1.65761e8i	−0.0415823	−	0.0720227i
$474$		0			0
$475$	−4.57563e7			−0.0195895
$476$	3.38153e9	−	7.45853e8i	1.43711	−	0.316978i
$477$		0			0
$478$	−1.23008e9	+	2.13056e9i	−0.515153	+	0.892271i
$479$	−1.54711e9	−	2.67967e9i	−0.643200	−	1.11405i	−0.984714	−	0.174178i	$-0.944273\pi$
$479$	−1.54711e9	−	2.67967e9i	−0.643200	−	1.11405i	0.341515	−	0.939876i	$-0.389060\pi$
$480$		0			0
$481$	−2.08251e8	+	3.60701e8i	−0.0853255	+	0.147788i
$482$	4.61740e9			1.87816
$483$		0			0
$484$	−5.92787e9			−2.37651
$485$	−1.12946e9	+	1.95628e9i	−0.449547	+	0.778638i
$486$		0			0
$487$	2.11545e8	+	3.66407e8i	0.0829949	+	0.143751i	0.904535	−	0.426399i	$-0.140218\pi$
$487$	2.11545e8	+	3.66407e8i	0.0829949	+	0.143751i	−0.821540	+	0.570151i	$0.806885\pi$
$488$	−5.02112e9	+	8.69683e9i	−1.95583	+	3.38759i
$489$		0			0
$490$	−3.00902e9	+	1.39526e9i	−1.15542	+	0.535759i
$491$	9.85934e8			0.375892			0.187946	−	0.982179i	$-0.439817\pi$
$491$	9.85934e8			0.375892			0.187946	+	0.982179i	$0.439817\pi$
$492$		0			0
$493$	−3.19707e8	−	5.53749e8i	−0.120168	−	0.208137i
$494$	1.15723e8	+	2.00437e8i	0.0431891	+	0.0748057i
$495$		0			0
$496$	9.71773e8			0.357585
$497$	−2.64328e9	−	2.89087e9i	−0.965821	−	1.05629i
$498$		0			0
$499$	2.62370e8	−	4.54437e8i	0.0945282	−	0.163728i	−0.814883	−	0.579625i	$-0.803199\pi$
$499$	2.62370e8	−	4.54437e8i	0.0945282	−	0.163728i	0.909412	+	0.415897i	$0.136532\pi$
$500$	−3.51260e9	−	6.08400e9i	−1.25671	−	2.17668i
$501$		0			0
$502$	−2.03275e9	+	3.52082e9i	−0.717167	+	1.24217i
$503$	−4.23277e9			−1.48298			−0.741492	−	0.670962i	$-0.765881\pi$
$503$	−4.23277e9			−1.48298			−0.741492	+	0.670962i	$0.765881\pi$
$504$		0			0
$505$	2.24111e9			0.774362
$506$	1.41521e8	−	2.45122e8i	0.0485618	−	0.0841114i
$507$		0			0
$508$	−4.29450e9	−	7.43829e9i	−1.45341	−	2.51739i
$509$	−1.16011e9	+	2.00938e9i	−0.389931	+	0.675381i	−0.992440	−	0.122731i	$-0.960835\pi$
$509$	−1.16011e9	+	2.00938e9i	−0.389931	+	0.675381i	0.602508	+	0.798113i	$0.294168\pi$
$510$		0			0
$511$	−1.94421e8	+	6.14322e8i	−0.0644571	+	0.203668i
$512$	−5.97263e9			−1.96662
$513$		0			0
$514$	−5.39608e9	−	9.34628e9i	−1.75270	−	3.03576i
$515$	8.12359e8	+	1.40705e9i	0.262073	+	0.453924i
$516$		0			0
$517$	1.90478e8			0.0606216
$518$	−2.40106e8	+	7.58675e8i	−0.0759013	+	0.239829i
$519$		0			0
$520$	−3.53824e9	+	6.12841e9i	−1.10351	+	1.91133i
$521$	1.37985e9	+	2.38996e9i	0.427463	+	0.740388i	0.996647	−	0.0818227i	$-0.0260741\pi$
$521$	1.37985e9	+	2.38996e9i	0.427463	+	0.740388i	−0.569184	+	0.822210i	$0.692741\pi$
$522$		0			0
$523$	−2.22280e9	+	3.85001e9i	−0.679430	+	1.17681i	0.295722	+	0.955274i	$0.404440\pi$
$523$	−2.22280e9	+	3.85001e9i	−0.679430	+	1.17681i	−0.975153	+	0.221534i	$0.928894\pi$
$524$	5.86510e9			1.78080
$525$		0			0
$526$	8.14184e9			2.43934
$527$	1.60008e8	−	2.77142e8i	0.0476217	−	0.0824832i
$528$		0			0
$529$	7.02518e8	+	1.21680e9i	0.206330	+	0.357374i
$530$	1.08058e9	−	1.87163e9i	0.315278	−	0.546077i
$531$		0			0
$532$	2.10315e8	+	2.30015e8i	0.0605591	+	0.0662315i
$533$	7.78524e9			2.22703
$534$		0			0
$535$	−2.80646e8	−	4.86092e8i	−0.0792355	−	0.137240i
$536$	−6.98054e9	−	1.20907e10i	−1.95800	−	3.39135i
$537$		0			0
$538$	7.46997e9			2.06814
$539$	−2.27086e8	+	1.05298e8i	−0.0624639	+	0.0289640i
$540$		0			0
$541$	2.67831e9	−	4.63897e9i	0.727228	−	1.25960i	−0.230822	−	0.972996i	$-0.574141\pi$
$541$	2.67831e9	−	4.63897e9i	0.727228	−	1.25960i	0.958050	−	0.286601i	$-0.0925253\pi$
$542$	−2.05148e9	−	3.55327e9i	−0.553440	−	0.958586i
$543$		0			0
$544$	1.97229e9	−	3.41611e9i	0.525261	−	0.909779i
$545$	3.84092e9			1.01636
$546$		0			0
$547$	1.36408e9			0.356357			0.178178	−	0.983998i	$-0.442980\pi$
$547$	1.36408e9			0.356357			0.178178	+	0.983998i	$0.442980\pi$
$548$	2.62993e9	−	4.55517e9i	0.682672	−	1.18242i
$549$		0			0
$550$	−1.28866e8	−	2.23203e8i	−0.0330271	−	0.0572046i
$551$	2.87754e7	−	4.98405e7i	0.00732809	−	0.0126926i
$552$		0			0
$553$	−2.47435e9	+	5.45759e8i	−0.622189	+	0.137234i
$554$	−8.37108e9			−2.09169
$555$		0			0
$556$	−6.37944e9	−	1.10495e10i	−1.57406	−	2.72635i
$557$	1.54479e9	+	2.67566e9i	0.378771	+	0.656051i	0.990884	−	0.134720i	$-0.0430135\pi$
$557$	1.54479e9	+	2.67566e9i	0.378771	+	0.656051i	−0.612113	+	0.790770i	$0.709680\pi$
$558$		0			0
$559$	6.22875e9			1.50820
$560$	−2.00766e9	+	6.34371e9i	−0.483096	+	1.52646i
$561$		0			0
$562$	2.92001e8	−	5.05760e8i	0.0693916	−	0.120190i
$563$	−9.48459e8	−	1.64278e9i	−0.223995	−	0.387971i	0.732022	−	0.681281i	$-0.238577\pi$
$563$	−9.48459e8	−	1.64278e9i	−0.223995	−	0.387971i	−0.956018	+	0.293309i	$0.905243\pi$
$564$		0			0
$565$	−7.03299e8	+	1.21815e9i	−0.164048	+	0.284139i
$566$	4.29817e7			0.00996383
$567$		0			0
$568$	−1.59676e10			−3.65612
$569$	4.17854e9	−	7.23744e9i	0.950893	−	1.64699i	0.207393	−	0.978258i	$-0.433502\pi$
$569$	4.17854e9	−	7.23744e9i	0.950893	−	1.64699i	0.743499	−	0.668737i	$-0.233165\pi$
$570$		0			0
$571$	−2.33771e9	−	4.04904e9i	−0.525491	−	0.910177i	−0.999559	−	0.0296886i	$-0.990548\pi$
$571$	−2.33771e9	−	4.04904e9i	−0.525491	−	0.910177i	0.474069	−	0.880488i	$-0.342785\pi$
$572$	−4.59429e8	+	7.95755e8i	−0.102644	+	0.177784i
$573$		0			0
$574$	1.45253e10	−	3.20379e9i	3.20577	−	0.707086i
$575$	−1.82097e9			−0.399452
$576$		0			0
$577$	3.88363e8	+	6.72664e8i	0.0841632	+	0.145775i	0.905034	−	0.425338i	$-0.139845\pi$
$577$	3.88363e8	+	6.72664e8i	0.0841632	+	0.145775i	−0.820871	+	0.571113i	$0.806512\pi$
$578$	2.64961e9	+	4.58926e9i	0.570735	+	0.988542i
$579$		0			0
$580$	3.02752e9			0.644302
$581$	−3.30064e8	−	3.60980e8i	−0.0698202	−	0.0763601i
$582$		0			0
$583$	8.15498e7	−	1.41248e8i	0.0170445	−	0.0295219i
$584$	1.31330e9	+	2.27470e9i	0.272846	+	0.472583i
$585$		0			0
$586$	−3.92985e9	+	6.80670e9i	−0.806741	+	1.39732i
$587$	−1.89326e9			−0.386347			−0.193174	−	0.981165i	$-0.561878\pi$
$587$	−1.89326e9			−0.386347			−0.193174	+	0.981165i	$0.561878\pi$
$588$		0			0
$589$	2.88032e7			0.00580814
$590$	−4.26927e9	+	7.39459e9i	−0.855798	+	1.48229i
$591$		0			0
$592$	7.98195e8	+	1.38251e9i	0.158119	+	0.273870i
$593$	2.22153e9	−	3.84780e9i	0.437483	−	0.757742i	−0.560012	−	0.828485i	$-0.689203\pi$
$593$	2.22153e9	−	3.84780e9i	0.437483	−	0.757742i	0.997495	+	0.0707423i	$0.0225368\pi$
$594$		0			0
$595$	1.47860e9	+	1.61710e9i	0.287768	+	0.314722i
$596$	−1.22189e9			−0.236412
$597$		0			0
$598$	4.60542e9	+	7.97683e9i	0.880675	+	1.52537i
$599$	1.11024e9	+	1.92299e9i	0.211068	+	0.365581i	0.952049	−	0.305945i	$-0.0989724\pi$
$599$	1.11024e9	+	1.92299e9i	0.211068	+	0.365581i	−0.740981	+	0.671526i	$0.765639\pi$
$600$		0			0
$601$	5.04814e9			0.948574			0.474287	−	0.880370i	$-0.342706\pi$
$601$	5.04814e9			0.948574			0.474287	+	0.880370i	$0.342706\pi$
$602$	1.16212e10	−	2.56326e9i	2.17103	−	0.478856i
$603$		0			0
$604$	−8.75534e9	+	1.51647e10i	−1.61675	+	2.80030i
$605$	−1.87551e9	−	3.24847e9i	−0.344330	−	0.596397i
$606$		0			0
$607$	1.41439e9	−	2.44980e9i	0.256691	−	0.444601i	−0.708663	−	0.705547i	$-0.750701\pi$
$607$	1.41439e9	−	2.44980e9i	0.256691	−	0.444601i	0.965353	+	0.260946i	$0.0840346\pi$
$608$	3.55034e8			0.0640631
$609$		0			0
$610$	−1.09332e10			−1.95026
$611$	−3.09929e9	+	5.36813e9i	−0.549691	+	0.952092i
$612$		0			0
$613$	1.60514e9	+	2.78018e9i	0.281450	+	0.487486i	0.971742	−	0.236045i	$-0.0758513\pi$
$613$	1.60514e9	+	2.78018e9i	0.281450	+	0.487486i	−0.690292	+	0.723531i	$0.742518\pi$
$614$	−5.39585e9	+	9.34589e9i	−0.940742	+	1.62941i
$615$		0			0
$616$	−3.07871e8	+	9.72793e8i	−0.0530684	+	0.167683i
$617$	−2.94679e9			−0.505070			−0.252535	−	0.967588i	$-0.581264\pi$
$617$	−2.94679e9			−0.505070			−0.252535	+	0.967588i	$0.581264\pi$
$618$		0			0
$619$	−3.20494e9	−	5.55111e9i	−0.543128	−	0.940725i	−0.998722	−	0.0505376i	$-0.983907\pi$
$619$	−3.20494e9	−	5.55111e9i	−0.543128	−	0.940725i	0.455594	−	0.890188i	$-0.349427\pi$
$620$	7.57612e8	+	1.31222e9i	0.127666	+	0.221124i
$621$		0			0
$622$	−5.91055e9			−0.984831
$623$	−1.94833e9	+	4.29738e8i	−0.322816	+	0.0712025i
$624$		0			0
$625$	6.32055e8	−	1.09475e9i	0.103556	−	0.179364i
$626$	3.43702e8	+	5.95309e8i	0.0559978	+	0.0969911i
$627$		0			0
$628$	4.35887e9	−	7.54979e9i	0.702288	−	1.21640i
$629$	5.25710e8			0.0842304
$630$		0			0
$631$	−1.37351e9			−0.217636			−0.108818	−	0.994062i	$-0.534707\pi$
$631$	−1.37351e9			−0.217636			−0.108818	+	0.994062i	$0.534707\pi$
$632$	−5.16433e9	+	8.94489e9i	−0.813776	+	1.40950i
$633$		0			0
$634$	1.13822e10	+	1.97146e10i	1.77384	+	3.07238i
$635$	2.71746e9	−	4.70677e9i	0.421167	−	0.729483i
$636$		0			0
$637$	7.27392e8	−	8.11315e9i	0.111501	−	1.24366i
$638$	3.24168e8			0.0494194
$639$		0			0
$640$	−4.33293e8	−	7.50485e8i	−0.0653358	−	0.113165i
$641$	−2.39553e9	−	4.14917e9i	−0.359251	−	0.622241i	0.628585	−	0.777741i	$-0.283634\pi$
$641$	−2.39553e9	−	4.14917e9i	−0.359251	−	0.622241i	−0.987836	+	0.155500i	$0.950301\pi$
$642$		0			0
$643$	−9.77303e9			−1.44974			−0.724871	−	0.688884i	$-0.758101\pi$
$643$	−9.77303e9			−1.44974			−0.724871	+	0.688884i	$0.758101\pi$
$644$	8.36993e9	+	9.15391e9i	1.23487	+	1.35054i
$645$		0			0
$646$	1.46066e8	−	2.52993e8i	0.0213174	−	0.0369228i
$647$	5.49025e9	+	9.50939e9i	0.796943	+	1.38035i	0.921598	+	0.388145i	$0.126884\pi$
$647$	5.49025e9	+	9.50939e9i	0.796943	+	1.38035i	−0.124656	+	0.992200i	$0.539783\pi$
$648$		0			0
$649$	−3.22194e8	+	5.58056e8i	−0.0462659	+	0.0801349i
$650$	8.38722e9			1.19790
$651$		0			0
$652$	9.86326e9			1.39365
$653$	2.11369e9	−	3.66101e9i	0.297060	−	0.514523i	−0.678402	−	0.734691i	$-0.737327\pi$
$653$	2.11369e9	−	3.66101e9i	0.297060	−	0.514523i	0.975462	+	0.220168i	$0.0706605\pi$
$654$		0			0
$655$	1.85565e9	+	3.21408e9i	0.258019	+	0.446902i
$656$	1.49199e10	−	2.58420e10i	2.06348	−	3.57406i
$657$		0			0
$658$	−3.57338e9	+	1.12910e10i	−0.488978	+	1.54504i
$659$	−1.09220e9			−0.148663			−0.0743314	−	0.997234i	$-0.523682\pi$
$659$	−1.09220e9			−0.148663			−0.0743314	+	0.997234i	$0.523682\pi$
$660$		0			0
$661$	5.74047e9	+	9.94278e9i	0.773111	+	1.33907i	0.935850	+	0.352399i	$0.114634\pi$
$661$	5.74047e9	+	9.94278e9i	0.773111	+	1.33907i	−0.162738	+	0.986669i	$0.552033\pi$
$662$	3.35177e9	+	5.80543e9i	0.449026	+	0.777735i
$663$		0			0
$664$	−1.99385e9			−0.264305
$665$	−5.95069e7	+	1.88027e8i	−0.00784678	+	0.0247938i
$666$		0			0
$667$	1.14518e9	−	1.98351e9i	0.149428	−	0.258817i
$668$	2.87438e9	+	4.97857e9i	0.373101	+	0.646230i
$669$		0			0
$670$	7.59987e9	−	1.31634e10i	0.976213	−	1.69085i
$671$	−8.25110e8			−0.105435
$672$		0			0
$673$	7.00125e9			0.885366			0.442683	−	0.896678i	$-0.354027\pi$
$673$	7.00125e9			0.885366			0.442683	+	0.896678i	$0.354027\pi$
$674$	−1.36405e10	+	2.36260e10i	−1.71601	+	2.97222i
$675$		0			0
$676$	−5.36159e9	−	9.28655e9i	−0.667545	−	1.15622i
$677$	6.16353e9	−	1.06756e10i	0.763430	−	1.32230i	−0.177642	−	0.984095i	$-0.556847\pi$
$677$	6.16353e9	−	1.06756e10i	0.763430	−	1.32230i	0.941072	−	0.338205i	$-0.109820\pi$
$678$		0			0
$679$	−7.15244e9	−	7.82239e9i	−0.876819	−	0.958948i
$680$	8.93196e9			1.08935
$681$		0			0
$682$	8.11203e7	+	1.40504e8i	0.00979229	+	0.0169607i
$683$	−6.31879e9	−	1.09445e10i	−0.758860	−	1.31438i	−0.943432	−	0.331565i	$-0.892423\pi$
$683$	−6.31879e9	−	1.09445e10i	−0.758860	−	1.31438i	0.184572	−	0.982819i	$-0.440910\pi$
$684$		0			0
$685$	3.32831e9			0.395647
$686$	−1.98161e9	−	1.54364e10i	−0.234360	−	1.82562i
$687$		0			0
$688$	1.19370e10	−	2.06754e10i	1.39744	−	2.42044i
$689$	2.65382e9	+	4.59655e9i	0.309104	+	0.535383i
$690$		0			0
$691$	2.44577e8	−	4.23619e8i	0.0281995	−	0.0488430i	−0.851581	−	0.524223i	$-0.824356\pi$
$691$	2.44577e8	−	4.23619e8i	0.0281995	−	0.0488430i	0.879781	+	0.475380i	$0.157689\pi$
$692$	−2.85610e10			−3.27644
$693$		0			0
$694$	−3.47100e9			−0.394182
$695$	4.03676e9	−	6.99187e9i	0.456127	−	0.790035i
$696$		0			0
$697$	−4.91328e9	−	8.51006e9i	−0.549613	−	0.951958i
$698$	−7.78227e9	+	1.34793e10i	−0.866188	+	1.50028i
$699$		0			0
$700$	1.10294e10	−	2.43272e9i	1.21537	−	0.268070i
$701$	1.30414e9			0.142992			0.0714959	−	0.997441i	$-0.477223\pi$
$701$	1.30414e9			0.142992			0.0714959	+	0.997441i	$0.477223\pi$
$702$		0			0
$703$	2.36584e7	+	4.09775e7i	0.00256828	+	0.00444838i
$704$	2.62447e8	+	4.54571e8i	0.0283489	+	0.0491018i
$705$		0			0
$706$	−1.28674e10			−1.37618
$707$	−3.17295e9	+	1.00257e10i	−0.337672	+	1.06696i
$708$		0			0
$709$	−4.42227e9	+	7.65959e9i	−0.465997	+	0.807131i	−0.999246	−	0.0388278i	$-0.987638\pi$
$709$	−4.42227e9	+	7.65959e9i	−0.465997	+	0.807131i	0.533249	+	0.845958i	$0.320971\pi$
$710$	−8.69214e9	−	1.50552e10i	−0.911428	−	1.57864i
$711$		0			0
$712$	−4.06647e9	+	7.04333e9i	−0.422218	+	0.731304i
$713$	1.14628e9			0.118435
$714$		0			0
$715$	−5.81432e8			−0.0594878
$716$	1.34966e10	−	2.33768e10i	1.37413	−	2.38006i
$717$		0			0
$718$	−1.05856e10	−	1.83349e10i	−1.06729	−	1.84860i
$719$	−7.53570e9	+	1.30522e10i	−0.756088	+	1.30958i	0.188743	+	0.982026i	$0.439559\pi$
$719$	−7.53570e9	+	1.30522e10i	−0.756088	+	1.30958i	−0.944832	+	0.327557i	$0.893775\pi$
$720$		0			0
$721$	−7.44462e9	+	1.64204e9i	−0.739723	+	0.163158i
$722$	−1.85878e10			−1.83801
$723$		0			0
$724$	1.66973e9	+	2.89205e9i	0.163516	+	0.283218i
$725$	−1.04278e9	−	1.80614e9i	−0.101627	−	0.176023i
$726$		0			0
$727$	−4.87633e9			−0.470677			−0.235338	−	0.971914i	$-0.575620\pi$
$727$	−4.87633e9			−0.470677			−0.235338	+	0.971914i	$0.575620\pi$
$728$	−2.24063e10	−	2.45050e10i	−2.15234	−	2.35394i
$729$		0			0
$730$	−1.42982e9	+	2.47651e9i	−0.136035	+	0.235619i
$731$	−3.93098e9	−	6.80866e9i	−0.372212	−	0.644689i
$732$		0			0
$733$	−2.55573e9	+	4.42665e9i	−0.239691	+	0.415156i	−0.960625	−	0.277847i	$-0.910379\pi$
$733$	−2.55573e9	+	4.42665e9i	−0.239691	+	0.415156i	0.720935	+	0.693003i	$0.243713\pi$
$734$	3.07571e10			2.87084
$735$		0			0
$736$	1.41293e10			1.30632
$737$	5.73549e8	−	9.93416e8i	0.0527757	−	0.0914103i
$738$		0			0
$739$	5.73949e9	+	9.94109e9i	0.523140	+	0.906105i	0.999637	+	0.0269293i	$0.00857290\pi$
$739$	5.73949e9	+	9.94109e9i	0.523140	+	0.906105i	−0.476497	+	0.879176i	$0.658094\pi$
$740$	−1.24458e9	+	2.15567e9i	−0.112904	+	0.195556i
$741$		0			0
$742$	6.84292e9	+	7.48388e9i	0.614933	+	0.672532i
$743$	3.64003e9			0.325570			0.162785	−	0.986662i	$-0.447952\pi$
$743$	3.64003e9			0.325570			0.162785	+	0.986662i	$0.447952\pi$
$744$		0			0
$745$	−3.86591e8	−	6.69596e8i	−0.0342535	−	0.0593289i
$746$	1.69918e10	+	2.94307e10i	1.49849	+	2.59546i
$747$		0			0
$748$	1.15979e9			0.101326
$749$	2.57189e9	−	5.67274e8i	0.223649	−	0.0493295i
$750$		0			0
$751$	1.86199e9	−	3.22506e9i	0.160412	−	0.277842i	−0.774604	−	0.632446i	$-0.782051\pi$
$751$	1.86199e9	−	3.22506e9i	0.160412	−	0.277842i	0.935017	+	0.354604i	$0.115384\pi$
$752$	1.18791e10	+	2.05753e10i	1.01865	+	1.76435i
$753$		0			0
$754$	−5.27459e9	+	9.13585e9i	−0.448114	+	0.776156i
$755$	−1.10803e10			−0.936998
$756$		0			0
$757$	−1.47428e10			−1.23522			−0.617611	−	0.786484i	$-0.711899\pi$
$757$	−1.47428e10			−1.23522			−0.617611	+	0.786484i	$0.711899\pi$
$758$	3.55458e9	−	6.15672e9i	0.296447	−	0.513460i
$759$		0			0
$760$	4.01963e8	+	6.96220e8i	0.0332153	+	0.0575306i
$761$	−3.67298e9	+	6.36179e9i	−0.302115	+	0.523278i	−0.976615	−	0.214997i	$-0.931026\pi$
$761$	−3.67298e9	+	6.36179e9i	−0.302115	+	0.523278i	0.674500	+	0.738275i	$0.264359\pi$
$762$		0			0
$763$	−5.43795e9	+	1.71825e10i	−0.443199	+	1.40040i
$764$	3.20793e10			2.60255
$765$		0			0
$766$	−3.86381e9	−	6.69231e9i	−0.310610	−	0.537992i
$767$	−1.04849e10	−	1.81604e10i	−0.839039	−	1.45326i
$768$		0			0
$769$	9.27906e9			0.735803			0.367902	−	0.929865i	$-0.380076\pi$
$769$	9.27906e9			0.735803			0.367902	+	0.929865i	$0.380076\pi$
$770$	−1.08480e9	+	2.39271e8i	−0.0856314	+	0.0188874i
$771$		0			0
$772$	−2.42315e9	+	4.19702e9i	−0.189548	+	0.328307i
$773$	4.84009e9	+	8.38329e9i	0.376900	+	0.652809i	0.990609	−	0.136722i	$-0.0436569\pi$
$773$	4.84009e9	+	8.38329e9i	0.376900	+	0.652809i	−0.613710	+	0.789532i	$0.710324\pi$
$774$		0			0
$775$	5.21892e8	−	9.03943e8i	0.0402740	−	0.0697566i
$776$	−4.32066e10			−3.31920
$777$		0			0
$778$	1.97625e10			1.50457
$779$	4.42222e8	−	7.65952e8i	0.0335166	−	0.0580524i
$780$		0			0
$781$	−6.55980e8	−	1.13619e9i	−0.0492734	−	0.0853440i
$782$	5.81299e9	−	1.00684e10i	0.434686	−	0.752899i
$783$		0			0
$784$	−2.55364e10	−	1.79628e10i	−1.89258	−	1.33127i
$785$	5.51638e9			0.407015
$786$		0			0
$787$	−8.05129e8	−	1.39453e9i	−0.0588781	−	0.101980i	0.835084	−	0.550123i	$-0.185419\pi$
$787$	−8.05129e8	−	1.39453e9i	−0.0588781	−	0.101980i	−0.893962	+	0.448143i	$0.852086\pi$
$788$	7.63807e8	+	1.32295e9i	0.0556086	+	0.0963169i
$789$		0			0
$790$	−1.12451e10			−0.811460
$791$	−4.45372e9	−	4.87088e9i	−0.319967	−	0.349937i
$792$		0			0
$793$	1.34255e10	−	2.32536e10i	0.956036	−	1.65590i
$794$	−7.95254e9	−	1.37742e10i	−0.563812	−	0.976551i
$795$		0			0
$796$	−8.40924e9	+	1.45652e10i	−0.590964	+	1.02358i
$797$	−1.04405e10			−0.730497			−0.365249	−	0.930910i	$-0.619016\pi$
$797$	−1.04405e10			−0.730497			−0.365249	+	0.930910i	$0.619016\pi$
$798$		0			0
$799$	7.82388e9			0.542636
$800$	6.43295e9	−	1.11422e10i	0.444217	−	0.769406i
$801$		0			0
$802$	9.58792e9	+	1.66068e10i	0.656318	+	1.13678i
$803$	−1.07906e8	+	1.86898e8i	−0.00735427	+	0.0127380i
$804$		0			0
$805$	−2.36820e9	+	7.48291e9i	−0.160005	+	0.505574i
$806$	−5.27968e9			−0.355169
$807$		0			0
$808$	2.14330e10	+	3.71230e10i	1.42936	+	2.47573i
$809$	9.81852e9	+	1.70062e10i	0.651968	+	1.12924i	0.982645	+	0.185497i	$0.0593896\pi$
$809$	9.81852e9	+	1.70062e10i	0.651968	+	1.12924i	−0.330677	+	0.943744i	$0.607277\pi$
$810$		0			0
$811$	−2.66078e10			−1.75161			−0.875803	−	0.482669i	$-0.839668\pi$
$811$	−2.66078e10			−1.75161			−0.875803	+	0.482669i	$0.839668\pi$
$812$	−4.28634e9	+	1.35438e10i	−0.280958	+	0.887755i
$813$		0			0
$814$	−1.33261e8	+	2.30815e8i	−0.00866001	+	0.0149996i
$815$	3.12062e9	+	5.40507e9i	0.201925	+	0.349744i
$816$		0			0
$817$	3.53810e8	−	6.12816e8i	0.0226983	−	0.0393145i
$818$	−1.68535e10			−1.07660
$819$		0			0
$820$	4.65272e10			2.94685
$821$	−3.57247e9	+	6.18771e9i	−0.225304	+	0.390237i	−0.956410	−	0.292026i	$-0.905671\pi$
$821$	−3.57247e9	+	6.18771e9i	−0.225304	+	0.390237i	0.731107	+	0.682263i	$0.239004\pi$
$822$		0			0
$823$	−4.17193e9	−	7.22600e9i	−0.260878	−	0.451855i	0.705597	−	0.708613i	$-0.250679\pi$
$823$	−4.17193e9	−	7.22600e9i	−0.260878	−	0.451855i	−0.966476	+	0.256759i	$0.917345\pi$
$824$	−1.55381e10	+	2.69127e10i	−0.967501	+	1.67576i
$825$		0			0
$826$	−2.70356e10	−	2.95679e10i	−1.66919	−	1.82554i
$827$	2.92874e10			1.80058			0.900288	−	0.435295i	$-0.143356\pi$
$827$	2.92874e10			1.80058			0.900288	+	0.435295i	$0.143356\pi$
$828$		0			0
$829$	4.01367e9	+	6.95188e9i	0.244681	+	0.423800i	0.962042	−	0.272902i	$-0.0879834\pi$
$829$	4.01367e9	+	6.95188e9i	0.244681	+	0.423800i	−0.717361	+	0.696702i	$0.754650\pi$
$830$	−1.08538e9	−	1.87993e9i	−0.0658881	−	0.114122i
$831$		0			0
$832$	−1.70812e10			−1.02822
$833$	−9.32756e9	+	4.32512e9i	−0.559127	+	0.259263i
$834$		0			0
$835$	−1.81884e9	+	3.15032e9i	−0.108116	+	0.187263i
$836$	5.21936e7	+	9.04020e7i	0.00308955	+	0.00535126i
$837$		0			0
$838$	2.43355e10	−	4.21504e10i	1.42852	−	2.47427i
$839$	−5.19771e9			−0.303840			−0.151920	−	0.988393i	$-0.548546\pi$
$839$	−5.19771e9			−0.303840			−0.151920	+	0.988393i	$0.548546\pi$
$840$		0			0
$841$	−1.46267e10			−0.847933
$842$	−7.13427e9	+	1.23569e10i	−0.411867	+	0.713375i
$843$		0			0
$844$	8.48462e9	+	1.46958e10i	0.485774	+	0.841384i
$845$	3.39269e9	−	5.87631e9i	0.193440	−	0.335047i
$846$		0			0
$847$	1.71875e10	−	3.79100e9i	0.971899	−	0.214369i
$848$	2.03434e10			1.14562
$849$		0			0
$850$	−5.29319e9	−	9.16808e9i	−0.295632	−	0.512050i
$851$	9.41535e8	+	1.63079e9i	0.0523701	+	0.0907076i
$852$		0			0
$853$	5.41443e9			0.298697			0.149349	−	0.988785i	$-0.452282\pi$
$853$	5.41443e9			0.298697			0.149349	+	0.988785i	$0.452282\pi$
$854$	1.54792e10	−	4.89102e10i	0.850442	−	2.68718i
$855$		0			0
$856$	5.36793e9	−	9.29752e9i	0.292515	−	0.506651i
$857$	9.54181e9	+	1.65269e10i	0.517843	+	0.896930i	0.999785	+	0.0207269i	$0.00659804\pi$
$857$	9.54181e9	+	1.65269e10i	0.517843	+	0.896930i	−0.481943	+	0.876203i	$0.660069\pi$
$858$		0			0
$859$	1.59722e10	−	2.76646e10i	0.859781	−	1.48918i	−0.0123568	−	0.999924i	$-0.503933\pi$
$859$	1.59722e10	−	2.76646e10i	0.859781	−	1.48918i	0.872138	−	0.489261i	$-0.162733\pi$
$860$	3.72251e10			1.99568
$861$		0			0
$862$	−3.32225e10			−1.76667
$863$	5.60085e9	−	9.70096e9i	0.296631	−	0.513780i	−0.678732	−	0.734386i	$-0.737470\pi$
$863$	5.60085e9	−	9.70096e9i	0.296631	−	0.513780i	0.975363	+	0.220606i	$0.0708036\pi$
$864$		0			0
$865$	−9.03635e9	−	1.56514e10i	−0.474719	−	0.822238i
$866$	3.33875e10	−	5.78289e10i	1.74692	−	3.02575i
$867$		0			0
$868$	−6.94291e9	+	1.53138e9i	−0.360348	+	0.0794809i
$869$	−8.48645e8			−0.0438689
$870$		0			0
$871$	1.86646e10	+	3.23281e10i	0.957096	+	1.65774i
$872$	3.67328e10	+	6.36230e10i	1.87606	+	3.24943i
$873$		0			0
$874$	1.04640e9			0.0530162
$875$	1.40754e10	+	1.53938e10i	0.710286	+	0.776817i
$876$		0			0
$877$	−1.36545e9	+	2.36504e9i	−0.0683563	+	0.118397i	−0.898178	−	0.439632i	$-0.855109\pi$
$877$	−1.36545e9	+	2.36504e9i	−0.0683563	+	0.118397i	0.829822	+	0.558029i	$0.188442\pi$
$878$	−1.94050e10	−	3.36105e10i	−0.967572	−	1.67588i
$879$		0			0
$880$	−1.11427e9	+	1.92998e9i	−0.0551191	+	0.0954691i
$881$	−2.77466e10			−1.36708			−0.683539	−	0.729914i	$-0.739560\pi$
$881$	−2.77466e10			−1.36708			−0.683539	+	0.729914i	$0.739560\pi$
$882$		0			0
$883$	1.21160e10			0.592240			0.296120	−	0.955151i	$-0.404307\pi$
$883$	1.21160e10			0.592240			0.296120	+	0.955151i	$0.404307\pi$
$884$	−1.88711e10	+	3.26857e10i	−0.918785	+	1.59138i
$885$		0			0
$886$	8.31156e9	+	1.43960e10i	0.401480	+	0.695384i
$887$	3.28535e9	−	5.69039e9i	0.158070	−	0.273785i	−0.776103	−	0.630606i	$-0.782806\pi$
$887$	3.28535e9	−	5.69039e9i	0.158070	−	0.273785i	0.934173	+	0.356822i	$0.116140\pi$
$888$		0			0
$889$	1.72086e10	+	1.88205e10i	0.821466	+	0.898410i
$890$	−8.85451e9			−0.421017
$891$		0			0
$892$	5.07077e9	+	8.78284e9i	0.239220	+	0.414341i
$893$	3.52096e8	+	6.09849e8i	0.0165456	+	0.0286577i
$894$		0			0
$895$	1.70806e10			0.796385
$896$	3.97078e9	−	8.75823e8i	0.184416	−	0.0406760i
$897$		0			0
$898$	−5.20212e9	+	9.01034e9i	−0.239725	+	0.415216i
$899$	6.56419e8	+	1.13695e9i	0.0301316	+	0.0521894i
$900$		0			0
$901$	3.34966e9	−	5.80179e9i	0.152568	−	0.264256i
$902$	4.98183e9			0.226030
$903$		0			0
$904$	−2.69041e10			−1.21124
$905$	−1.05656e9	+	1.83002e9i	−0.0473833	+	0.0820703i
$906$		0			0
$907$	−1.21871e9	−	2.11087e9i	−0.0542344	−	0.0939367i	0.837634	−	0.546232i	$-0.183938\pi$
$907$	−1.21871e9	−	2.11087e9i	−0.0542344	−	0.0939367i	−0.891868	+	0.452296i	$0.850605\pi$
$908$	−1.49179e9	+	2.58386e9i	−0.0661315	+	0.114543i
$909$		0			0
$910$	1.09077e10	−	3.44656e10i	0.479832	−	1.51615i
$911$	−2.15307e10			−0.943502			−0.471751	−	0.881732i	$-0.656378\pi$
$911$	−2.15307e10			−0.943502			−0.471751	+	0.881732i	$0.656378\pi$
$912$		0			0
$913$	−8.19115e7	−	1.41875e8i	−0.00356203	−	0.00616961i
$914$	−2.78430e10	−	4.82254e10i	−1.20616	−	2.08913i
$915$		0			0
$916$	−4.19071e9			−0.180158
$917$	−1.70055e10	+	3.75086e9i	−0.728279	+	0.160634i
$918$		0			0
$919$	−1.64198e10	+	2.84400e10i	−0.697853	+	1.20872i	0.271356	+	0.962479i	$0.412528\pi$
$919$	−1.64198e10	+	2.84400e10i	−0.697853	+	1.20872i	−0.969209	+	0.246238i	$0.920806\pi$
$920$	1.59970e10	+	2.77075e10i	0.677298	+	1.17311i
$921$		0			0
$922$	−2.78034e10	+	4.81570e10i	−1.16826	+	2.02349i
$923$	4.26943e10			1.78716
$924$		0			0
$925$	1.71469e9			0.0712342
$926$	−1.79446e10	+	3.10810e10i	−0.742669	+	1.28634i
$927$		0			0
$928$	8.09116e9	+	1.40143e10i	0.332348	+	0.575643i
$929$	6.42189e9	−	1.11230e10i	0.262789	−	0.455164i	−0.704193	−	0.710009i	$-0.748691\pi$
$929$	6.42189e9	−	1.11230e10i	0.262789	−	0.455164i	0.966982	+	0.254844i	$0.0820242\pi$
$930$		0			0
$931$	−7.56896e8	−	5.32413e8i	−0.0307406	−	0.0216235i
$932$	−7.01547e10			−2.83858
$933$		0			0
$934$	−2.94356e10	−	5.09840e10i	−1.18211	−	2.04748i
$935$	3.66943e8	+	6.35564e8i	0.0146811	+	0.0254284i
$936$		0			0
$937$	−2.05391e10			−0.815628			−0.407814	−	0.913065i	$-0.633709\pi$
$937$	−2.05391e10			−0.815628			−0.407814	+	0.913065i	$0.633709\pi$
$938$	4.81271e10	+	5.26350e10i	1.90405	+	2.08240i
$939$		0			0
$940$	−1.85224e10	+	3.20818e10i	−0.727361	+	1.25983i
$941$	8.06628e9	+	1.39712e10i	0.315580	+	0.546601i	0.979561	−	0.201149i	$-0.0644676\pi$
$941$	8.06628e9	+	1.39712e10i	0.315580	+	0.546601i	−0.663981	+	0.747750i	$0.731134\pi$
$942$		0			0
$943$	1.75992e10	−	3.04827e10i	0.683441	−	1.18376i
$944$	−8.03746e10			−3.10969
$945$		0			0
$946$	3.98583e9			0.153073
$947$	1.63336e9	−	2.82905e9i	0.0624965	−	0.108247i	−0.833084	−	0.553146i	$-0.813427\pi$
$947$	1.63336e9	−	2.82905e9i	0.0624965	−	0.108247i	0.895581	+	0.444899i	$0.146760\pi$
$948$		0			0
$949$	−3.51150e9	−	6.08210e9i	−0.133371	−	0.231005i
$950$	4.76416e8	−	8.25177e8i	0.0180283	−	0.0312259i
$951$		0			0
$952$	−1.26458e10	+	3.99575e10i	−0.475026	+	1.50096i
$953$	−2.56668e10			−0.960609			−0.480304	−	0.877102i	$-0.659474\pi$
$953$	−2.56668e10			−0.960609			−0.480304	+	0.877102i	$0.659474\pi$
$954$		0			0
$955$	1.01495e10	+	1.75795e10i	0.377080	+	0.653122i
$956$	−1.80543e10	−	3.12710e10i	−0.668311	−	1.15755i
$957$		0			0
$958$	6.44341e10			2.36775
$959$	−4.71220e9	+	1.48894e10i	−0.172528	+	0.545144i
$960$		0			0
$961$	1.34278e10	−	2.32576e10i	0.488059	−	0.845343i
$962$	−4.33663e9	−	7.51126e9i	−0.157051	−	0.272020i
$963$		0			0
$964$	−3.38856e10	+	5.86915e10i	−1.21827	+	2.11011i
$965$	−3.06662e9			−0.109854
$966$		0			0
$967$	−4.14546e10			−1.47428			−0.737141	−	0.675739i	$-0.763825\pi$
$967$	−4.14546e10			−1.47428			−0.737141	+	0.675739i	$0.763825\pi$
$968$	3.58729e10	−	6.21337e10i	1.27117	−	2.20173i
$969$		0			0
$970$	−2.35200e10	−	4.07378e10i	−0.827439	−	1.43317i
$971$	7.03038e9	−	1.21770e10i	0.246440	−	0.426847i	−0.716095	−	0.698003i	$-0.754072\pi$
$971$	7.03038e9	−	1.21770e10i	0.246440	−	0.426847i	0.962536	+	0.271155i	$0.0874057\pi$
$972$		0			0
$973$	2.55632e10	+	2.79576e10i	0.889653	+	0.972984i
$974$	−8.81046e9			−0.305522
$975$		0			0
$976$	−5.14580e10	−	8.91279e10i	−1.77165	−	3.06859i
$977$	−1.22458e10	−	2.12104e10i	−0.420104	−	0.727642i	0.575845	−	0.817559i	$-0.304673\pi$
$977$	−1.22458e10	−	2.12104e10i	−0.420104	−	0.727642i	−0.995949	+	0.0899169i	$0.971340\pi$
$978$		0			0
$979$	−6.68234e8			−0.0227609
$980$	4.34714e9	−	4.84869e10i	0.147541	−	1.64563i
$981$		0			0
$982$	−1.02656e10	+	1.77805e10i	−0.345934	+	0.599176i
$983$	2.87162e10	+	4.97379e10i	0.964249	+	1.67013i	0.711619	+	0.702566i	$0.247962\pi$
$983$	2.87162e10	+	4.97379e10i	0.964249	+	1.67013i	0.252630	+	0.967563i	$0.418704\pi$
$984$		0			0
$985$	−4.83319e8	+	8.37133e8i	−0.0161141	+	0.0279105i
$986$	1.33152e10			0.442363
$987$		0			0
$988$	−3.39700e9			−0.112059
$989$	1.40806e10	−	2.43883e10i	0.462843	−	0.801668i
$990$		0			0
$991$	1.22798e10	+	2.12693e10i	0.400806	+	0.694217i	0.993823	−	0.110973i	$-0.0353967\pi$
$991$	1.22798e10	+	2.12693e10i	0.400806	+	0.694217i	−0.593017	+	0.805190i	$0.702063\pi$
$992$	−4.04949e9	+	7.01392e9i	−0.131707	+	0.228123i
$993$		0			0
$994$	7.96565e10	−	1.75696e10i	2.57258	−	0.567426i
$995$	−1.06423e10			−0.342497
$996$		0			0
$997$	8.29325e9	+	1.43643e10i	0.265028	+	0.459042i	0.967571	−	0.252599i	$-0.0812855\pi$
$997$	8.29325e9	+	1.43643e10i	0.265028	+	0.459042i	−0.702543	+	0.711641i	$0.747952\pi$
$998$	5.46360e9	+	9.46324e9i	0.173989	+	0.301358i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.8.e.b.37.1		8
3.2	odd	2		7.8.c.a.2.4	✓	8
7.2	even	3		441.8.a.s.1.4		4
7.4	even	3	inner	63.8.e.b.46.1		8
7.5	odd	6		441.8.a.t.1.4		4
12.11	even	2		112.8.i.c.65.1		8
21.2	odd	6		49.8.a.f.1.1		4
21.5	even	6		49.8.a.e.1.1		4
21.11	odd	6		7.8.c.a.4.4	yes	8
21.17	even	6		49.8.c.g.18.4		8
21.20	even	2		49.8.c.g.30.4		8
84.11	even	6		112.8.i.c.81.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.c.a.2.4	✓	8	3.2	odd	2
7.8.c.a.4.4	yes	8	21.11	odd	6
49.8.a.e.1.1		4	21.5	even	6
49.8.a.f.1.1		4	21.2	odd	6
49.8.c.g.18.4		8	21.17	even	6
49.8.c.g.30.4		8	21.20	even	2
63.8.e.b.37.1		8	1.1	even	1	trivial
63.8.e.b.46.1		8	7.4	even	3	inner
112.8.i.c.65.1		8	12.11	even	2
112.8.i.c.81.1		8	84.11	even	6
441.8.a.s.1.4		4	7.2	even	3
441.8.a.t.1.4		4	7.5	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)

\(f(q)\)	\(=\)	\(q+(-10.4120 + 18.0342i) q^{2} +(-152.821 - 264.694i) q^{4} +(96.7016 - 167.492i) q^{5} +(612.373 + 669.733i) q^{7} +3699.23 q^{8} +(2013.72 + 3487.87i) q^{10} +(151.972 + 263.223i) q^{11} -9891.04 q^{13} +(-18454.1 + 4070.37i) q^{14} +(-18955.5 + 32831.8i) q^{16} +(6242.26 + 10811.9i) q^{17} +(-561.837 + 973.131i) q^{19} -59112.1 q^{20} -6329.35 q^{22} +(-22359.5 + 38727.8i) q^{23} +(20360.1 + 35264.8i) q^{25} +(102986. - 178377. i) q^{26} +(83690.6 - 264441. i) q^{28} -51216.6 q^{29} +(-12816.5 - 22198.9i) q^{31} +(-157979. - 273628. i) q^{32} -259978. q^{34} +(171392. - 37803.5i) q^{35} +(21054.5 - 36467.4i) q^{37} +(-11699.7 - 20264.6i) q^{38} +(357722. - 619592. i) q^{40} -787100. q^{41} -629737. q^{43} +(46449.0 - 80452.1i) q^{44} +(-465616. - 806470. i) q^{46} +(313344. - 542727. i) q^{47} +(-73540.5 + 820253. i) q^{49} -847961. q^{50} +(1.51156e6 + 2.61810e6i) q^{52} +(-268306. - 464719. i) q^{53} +58783.7 q^{55} +(2.26531e6 + 2.47750e6i) q^{56} +(533269. - 923649. i) q^{58} +(1.06004e6 + 1.83605e6i) q^{59} +(-1.35734e6 + 2.35098e6i) q^{61} +533785. q^{62} +1.72694e6 q^{64} +(-956479. + 1.65667e6i) q^{65} +(-1.88702e6 - 3.26842e6i) q^{67} +(1.90790e6 - 3.30457e6i) q^{68} +(-1.10279e6 + 3.48453e6i) q^{70} -4.31646e6 q^{71} +(355018. + 614910. i) q^{73} +(438440. + 759401. i) q^{74} +343442. q^{76} +(-83225.5 + 262971. i) q^{77} +(-1.39606e6 + 2.41804e6i) q^{79} +(3.66605e6 + 6.34978e6i) q^{80} +(8.19532e6 - 1.41947e7i) q^{82} -538991. q^{83} +2.41454e6 q^{85} +(6.55684e6 - 1.13568e7i) q^{86} +(562180. + 973724. i) q^{88} +(-1.09927e6 + 1.90400e6i) q^{89} +(-6.05701e6 - 6.62435e6i) q^{91} +1.36680e7 q^{92} +(6.52509e6 + 1.13018e7i) q^{94} +(108661. + 188207. i) q^{95} -1.16799e7 q^{97} +(-1.40269e7 - 9.86675e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 348 q^{4} + 252 q^{5} + 672 q^{7} + 1968 q^{8} - 4774 q^{10} - 3972 q^{11} - 2352 q^{13} - 47502 q^{14} - 57264 q^{16} + 56364 q^{17} - 41748 q^{19} - 324744 q^{20} - 305908 q^{22} + 131748 q^{23}+ \cdots - 60255006 q^{98}+O(q^{100}) \) 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

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