LMFDB - Embedded newform 13.10.c.a.3.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,10,Mod(3,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.3"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	13.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.69546587013$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 3193 x^{16} + 896 x^{15} + 6827472 x^{14} + 3327136 x^{13} + 8054385232 x^{12} + \cdots + 15\!\cdots\!00 $ x^18 - 3x^17 + 3193x^16 + 896x^15 + 6827472x^14 + 3327136x^13 + 8054385232x^12 + 694281600x^11 + 6899832636736x^10 - 1285276575488x^9 + 3495304064394496x^8 - 764853454571520x^7 + 1234658135287256064x^6 + 1254918535240499200x^5 + 146439647836867215360x^4 + 1052079877442940928000x^3 + 12856821885420326502400x^2 + 44600611845158952960000*x + 152210992401321984000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.4
Root			$7.02454 - 12.1669i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.10.c.a.9.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.02454 - 10.4348i) q^{2} +(-96.9066 - 167.847i) q^{3} +(183.410 - 317.675i) q^{4} -26.3134 q^{5} +(-1167.64 + 2022.40i) q^{6} +(-1348.09 + 2334.97i) q^{7} -10589.0 q^{8} +(-8940.28 + 15485.0i) q^{9} +(158.526 + 274.576i) q^{10} +(-2396.88 - 4151.52i) q^{11} -71094.5 q^{12} +(-30488.9 + 98361.2i) q^{13} +32486.6 q^{14} +(2549.95 + 4416.64i) q^{15} +(-30112.1 - 52155.7i) q^{16} +(126241. - 218655. i) q^{17} +215444. q^{18} +(278673. - 482675. i) q^{19} +(-4826.14 + 8359.13i) q^{20} +522557. q^{21} +(-28880.2 + 50022.0i) q^{22} +(-153504. - 265876. i) q^{23} +(1.02614e6 + 1.77733e6i) q^{24} -1.95243e6 q^{25} +(1.21006e6 - 274435. i) q^{26} -349336. q^{27} +(494508. + 856512. i) q^{28} +(-2.77950e6 - 4.81424e6i) q^{29} +(30724.5 - 53216.4i) q^{30} -3.02375e6 q^{31} +(-3.07360e6 + 5.32363e6i) q^{32} +(-464547. + 804619. i) q^{33} -3.04217e6 q^{34} +(35473.0 - 61441.1i) q^{35} +(3.27947e6 + 5.68021e6i) q^{36} +(7.14141e6 + 1.23693e7i) q^{37} -6.71550e6 q^{38} +(1.94642e7 - 4.41438e6i) q^{39} +278632. q^{40} +(-1.16889e7 - 2.02457e7i) q^{41} +(-3.14817e6 - 5.45279e6i) q^{42} +(2.14972e7 - 3.72342e7i) q^{43} -1.75845e6 q^{44} +(235250. - 407464. i) q^{45} +(-1.84958e6 + 3.20356e6i) q^{46} +2.42805e7 q^{47} +(-5.83613e6 + 1.01085e7i) q^{48} +(1.65421e7 + 2.86517e7i) q^{49} +(1.17625e7 + 2.03733e7i) q^{50} -4.89343e7 q^{51} +(2.56549e7 + 2.77260e7i) q^{52} -6.28700e7 q^{53} +(2.10459e6 + 3.64525e6i) q^{54} +(63070.2 + 109241. i) q^{55} +(1.42749e7 - 2.47249e7i) q^{56} -1.08021e8 q^{57} +(-3.34905e7 + 5.80072e7i) q^{58} +(4.66839e7 - 8.08590e7i) q^{59} +1.87074e6 q^{60} +(-1.07150e7 + 1.85589e7i) q^{61} +(1.82167e7 + 3.15522e7i) q^{62} +(-2.41047e7 - 4.17506e7i) q^{63} +4.32333e7 q^{64} +(802268. - 2.58822e6i) q^{65} +1.11947e7 q^{66} +(9.99675e7 + 1.73149e8i) q^{67} +(-4.63076e7 - 8.02071e7i) q^{68} +(-2.97510e7 + 5.15303e7i) q^{69} -854835. q^{70} +(1.27929e8 - 2.21579e8i) q^{71} +(9.46684e7 - 1.63970e8i) q^{72} +1.64695e7 q^{73} +(8.60475e7 - 1.49039e8i) q^{74} +(1.89204e8 + 3.27710e8i) q^{75} +(-1.02223e8 - 1.77055e8i) q^{76} +1.29249e7 q^{77} +(-1.63326e8 - 1.76511e8i) q^{78} -1.39500e8 q^{79} +(792354. + 1.37240e6i) q^{80} +(2.09825e8 + 3.63427e8i) q^{81} +(-1.40840e8 + 2.43942e8i) q^{82} +3.64688e8 q^{83} +(9.58421e7 - 1.66003e8i) q^{84} +(-3.32183e6 + 5.75358e6i) q^{85} -5.18042e8 q^{86} +(-5.38704e8 + 9.33064e8i) q^{87} +(2.53805e7 + 4.39603e7i) q^{88} +(-5.80652e8 - 1.00572e9i) q^{89} -5.66909e6 q^{90} +(-1.88568e8 - 2.03791e8i) q^{91} -1.12616e8 q^{92} +(2.93021e8 + 5.07527e8i) q^{93} +(-1.46279e8 - 2.53363e8i) q^{94} +(-7.33284e6 + 1.27009e7i) q^{95} +1.19141e9 q^{96} +(-1.89552e8 + 3.28314e8i) q^{97} +(1.99317e8 - 3.45227e8i) q^{98} +8.57151e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 15 q^{2} + 161 q^{3} - 1793 q^{4} - 2280 q^{5} + 2118 q^{6} - 1939 q^{7} - 14478 q^{8} - 33654 q^{9} + 46923 q^{10} - 5433 q^{11} + 8712 q^{12} - 212524 q^{13} - 9900 q^{14} - 347428 q^{15} + 400127 q^{16}+ \cdots + 2262149268 q^{99}+O(q^{100}) $ 18 * q + 15 * q^2 + 161 * q^3 - 1793 * q^4 - 2280 * q^5 + 2118 * q^6 - 1939 * q^7 - 14478 * q^8 - 33654 * q^9 + 46923 * q^10 - 5433 * q^11 + 8712 * q^12 - 212524 * q^13 - 9900 * q^14 - 347428 * q^15 + 400127 * q^16 + 248589 * q^17 - 38738 * q^18 - 311001 * q^19 + 927069 * q^20 + 1553030 * q^21 + 1857242 * q^22 + 591609 * q^23 - 4492800 * q^24 + 7008998 * q^25 - 3801525 * q^26 - 11603482 * q^27 + 2697168 * q^28 + 11014155 * q^29 - 6597836 * q^30 - 23148076 * q^31 - 11868417 * q^32 + 14131427 * q^33 + 21859862 * q^34 + 21112794 * q^35 + 10792871 * q^36 - 29215749 * q^37 + 14572188 * q^38 - 71569875 * q^39 + 27322222 * q^40 + 3328377 * q^41 + 39828306 * q^42 + 6074381 * q^43 + 31824624 * q^44 + 32857342 * q^45 + 36693338 * q^46 - 45575052 * q^47 - 30270064 * q^48 + 10293266 * q^49 - 49601730 * q^50 - 136587494 * q^51 - 35278230 * q^52 - 29480016 * q^53 + 152965386 * q^54 - 18710998 * q^55 - 7665444 * q^56 + 523363230 * q^57 - 163479359 * q^58 - 32715855 * q^59 - 188638416 * q^60 - 220502845 * q^61 - 59980476 * q^62 + 166572574 * q^63 - 924604030 * q^64 + 128091756 * q^65 - 48128076 * q^66 + 112659045 * q^67 - 238942419 * q^68 + 86003951 * q^69 + 2040150992 * q^70 - 236450709 * q^71 + 995206683 * q^72 - 211881220 * q^73 - 455580507 * q^74 + 968954813 * q^75 - 365789708 * q^76 - 2399230890 * q^77 - 441111970 * q^78 - 817519096 * q^79 + 580424625 * q^80 + 176914851 * q^81 + 941792217 * q^82 + 2225691456 * q^83 - 1819004068 * q^84 + 1812284636 * q^85 + 291320076 * q^86 + 69564799 * q^87 + 3178375740 * q^88 - 1154379039 * q^89 - 10225809510 * q^90 - 1658338903 * q^91 - 4545506592 * q^92 + 3136878060 * q^93 + 2755131560 * q^94 + 1779441012 * q^95 + 5906965568 * q^96 - 3616470111 * q^97 + 8263323501 * q^98 + 2262149268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

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

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 $

$2$	−6.02454	−	10.4348i	−0.266250	−	0.461158i	0.701641	−	0.712531i	$-0.252451\pi$
$2$	−6.02454	−	10.4348i	−0.266250	−	0.461158i	−0.967890	+	0.251373i	$0.919118\pi$
$3$	−96.9066	−	167.847i	−0.690729	−	1.19638i	−0.971599	−	0.236632i	$-0.923956\pi$
$3$	−96.9066	−	167.847i	−0.690729	−	1.19638i	0.280870	−	0.959746i	$-0.409377\pi$
$4$	183.410	−	317.675i	0.358222	−	0.620459i
$5$	−26.3134			−0.0188284			−0.00941419	−	0.999956i	$-0.502997\pi$
$5$	−26.3134			−0.0188284			−0.00941419	+	0.999956i	$0.502997\pi$
$6$	−1167.64	+	2022.40i	−0.367813	+	0.637070i
$7$	−1348.09	+	2334.97i	−0.212217	+	0.367570i	−0.952408	−	0.304826i	$-0.901402\pi$
$7$	−1348.09	+	2334.97i	−0.212217	+	0.367570i	0.740191	+	0.672396i	$0.234735\pi$
$8$	−10589.0			−0.914005
$9$	−8940.28	+	15485.0i	−0.454213	+	0.786721i
$10$	158.526	+	274.576i	0.00501305	+	0.00868285i
$11$	−2396.88	−	4151.52i	−0.0493605	−	0.0854948i	0.840290	−	0.542138i	$-0.182385\pi$
$11$	−2396.88	−	4151.52i	−0.0493605	−	0.0854948i	−0.889650	+	0.456643i	$0.849052\pi$
$12$	−71094.5			−0.989738
$13$	−30488.9	+	98361.2i	−0.296071	+	0.955166i
$13$	−30488.9	+	98361.2i	−0.296071	+	0.955166i
$14$	32486.6			0.226010
$15$	2549.95	+	4416.64i	0.0130053	+	0.0225258i
$16$	−30112.1	−	52155.7i	−0.114869	−	0.198958i
$17$	126241.	−	218655.i	0.366589	−	0.634951i	−0.622441	−	0.782667i	$-0.713859\pi$
$17$	126241.	−	218655.i	0.366589	−	0.634951i	0.989030	+	0.147716i	$0.0471922\pi$
$18$	215444.			0.483737
$19$	278673.	−	482675.i	0.490573	−	0.849697i	−0.509369	−	0.860548i	$-0.670121\pi$
$19$	278673.	−	482675.i	0.490573	−	0.849697i	0.999941	+	0.0108519i	$0.00345433\pi$
$20$	−4826.14	+	8359.13i	−0.00674474	+	0.0116822i
$21$	522557.			0.586337
$22$	−28880.2	+	50022.0i	−0.0262844	+	0.0455259i
$23$	−153504.	−	265876.i	−0.114378	−	0.198109i	0.803153	−	0.595773i	$-0.203154\pi$
$23$	−153504.	−	265876.i	−0.114378	−	0.198109i	−0.917531	+	0.397664i	$0.869821\pi$
$24$	1.02614e6	+	1.77733e6i	0.631330	+	1.09350i
$25$	−1.95243e6			−0.999645
$26$	1.21006e6	−	274435.i	0.519311	−	0.117777i
$27$	−349336.			−0.126505
$28$	494508.	+	856512.i	0.152041	+	0.263343i
$29$	−2.77950e6	−	4.81424e6i	−0.729754	−	1.26397i	−0.956987	−	0.290130i	$-0.906301\pi$
$29$	−2.77950e6	−	4.81424e6i	−0.729754	−	1.26397i	0.227234	−	0.973840i	$-0.427032\pi$
$30$	30724.5	−	53216.4i	0.00692532	−	0.0119950i
$31$	−3.02375e6			−0.588055			−0.294027	−	0.955797i	$-0.594996\pi$
$31$	−3.02375e6			−0.588055			−0.294027	+	0.955797i	$0.594996\pi$
$32$	−3.07360e6	+	5.32363e6i	−0.518170	+	0.897497i
$33$	−464547.	+	804619.i	−0.0681894	+	0.118108i
$34$	−3.04217e6			−0.390417
$35$	35473.0	−	61441.1i	0.00399569	−	0.00692074i
$36$	3.27947e6	+	5.68021e6i	0.325419	+	0.563642i
$37$	7.14141e6	+	1.23693e7i	0.626436	+	1.08502i	0.988261	+	0.152773i	$0.0488202\pi$
$37$	7.14141e6	+	1.23693e7i	0.626436	+	1.08502i	−0.361826	+	0.932246i	$0.617846\pi$
$38$	−6.71550e6			−0.522459
$39$	1.94642e7	−	4.41438e6i	1.34724	−	0.305548i
$40$	278632.			0.0172092
$41$	−1.16889e7	−	2.02457e7i	−0.646018	−	1.11894i	−0.984065	−	0.177807i	$-0.943100\pi$
$41$	−1.16889e7	−	2.02457e7i	−0.646018	−	1.11894i	0.338047	−	0.941129i	$-0.390234\pi$
$42$	−3.14817e6	−	5.45279e6i	−0.156112	−	0.270394i
$43$	2.14972e7	−	3.72342e7i	0.958900	−	1.66086i	0.233719	−	0.972304i	$-0.424910\pi$
$43$	2.14972e7	−	3.72342e7i	0.958900	−	1.66086i	0.725181	−	0.688559i	$-0.241756\pi$
$44$	−1.75845e6			−0.0707281
$45$	235250.	−	407464.i	0.00855210	−	0.0148127i
$46$	−1.84958e6	+	3.20356e6i	−0.0609063	+	0.105493i
$47$	2.42805e7			0.725802			0.362901	−	0.931828i	$-0.381786\pi$
$47$	2.42805e7			0.725802			0.362901	+	0.931828i	$0.381786\pi$
$48$	−5.83613e6	+	1.01085e7i	−0.158686	+	0.274853i
$49$	1.65421e7	+	2.86517e7i	0.409928	+	0.710017i
$50$	1.17625e7	+	2.03733e7i	0.266155	+	0.460994i
$51$	−4.89343e7			−1.01285
$52$	2.56549e7	+	2.77260e7i	0.486582	+	0.525862i
$53$	−6.28700e7			−1.09446			−0.547232	−	0.836981i	$-0.684319\pi$
$53$	−6.28700e7			−1.09446			−0.547232	+	0.836981i	$0.684319\pi$
$54$	2.10459e6	+	3.64525e6i	0.0336818	+	0.0583386i
$55$	63070.2	+	109241.i	0.000929377	+	0.00160973i
$56$	1.42749e7	−	2.47249e7i	0.193967	−	0.335961i
$57$	−1.08021e8			−1.35541
$58$	−3.34905e7	+	5.80072e7i	−0.388593	+	0.673063i
$59$	4.66839e7	−	8.08590e7i	0.501572	−	0.868748i	−0.498426	−	0.866932i	$-0.666089\pi$
$59$	4.66839e7	−	8.08590e7i	0.501572	−	0.868748i	0.999998	−	0.00181634i	$-0.000578159\pi$
$60$	1.87074e6			0.0186352
$61$	−1.07150e7	+	1.85589e7i	−0.0990851	+	0.171620i	−0.911306	−	0.411729i	$-0.864925\pi$
$61$	−1.07150e7	+	1.85589e7i	−0.0990851	+	0.171620i	0.812221	+	0.583350i	$0.198258\pi$
$62$	1.82167e7	+	3.15522e7i	0.156569	+	0.271186i
$63$	−2.41047e7	−	4.17506e7i	−0.192783	−	0.333910i
$64$	4.32333e7			0.322113
$65$	802268.	−	2.58822e6i	0.00557454	−	0.0179842i
$66$	1.11947e7			0.0726216
$67$	9.99675e7	+	1.73149e8i	0.606069	+	1.04974i	0.991882	+	0.127165i	$0.0405879\pi$
$67$	9.99675e7	+	1.73149e8i	0.606069	+	1.04974i	−0.385812	+	0.922577i	$0.626079\pi$
$68$	−4.63076e7	−	8.02071e7i	−0.262641	−	0.454907i
$69$	−2.97510e7	+	5.15303e7i	−0.158009	+	0.273679i
$70$	−854835.			−0.00425541
$71$	1.27929e8	−	2.21579e8i	0.597455	−	1.03482i	−0.395741	−	0.918362i	$-0.629512\pi$
$71$	1.27929e8	−	2.21579e8i	0.597455	−	1.03482i	0.993195	−	0.116460i	$-0.0371545\pi$
$72$	9.46684e7	−	1.63970e8i	0.415154	−	0.719067i
$73$	1.64695e7			0.0678779			0.0339389	−	0.999424i	$-0.489195\pi$
$73$	1.64695e7			0.0678779			0.0339389	+	0.999424i	$0.489195\pi$
$74$	8.60475e7	−	1.49039e8i	0.333577	−	0.577771i
$75$	1.89204e8	+	3.27710e8i	0.690484	+	1.19595i
$76$	−1.02223e8	−	1.77055e8i	−0.351468	−	0.608760i
$77$	1.29249e7			0.0419004
$78$	−1.63326e8	−	1.76511e8i	−0.499609	−	0.539940i
$79$	−1.39500e8			−0.402950			−0.201475	−	0.979494i	$-0.564573\pi$
$79$	−1.39500e8			−0.402950			−0.201475	+	0.979494i	$0.564573\pi$
$80$	792354.	+	1.37240e6i	0.00216279	+	0.00374606i
$81$	2.09825e8	+	3.63427e8i	0.541594	+	0.938068i
$82$	−1.40840e8	+	2.43942e8i	−0.344004	+	0.595833i
$83$	3.64688e8			0.843472			0.421736	−	0.906719i	$-0.361421\pi$
$83$	3.64688e8			0.843472			0.421736	+	0.906719i	$0.361421\pi$
$84$	9.58421e7	−	1.66003e8i	0.210039	−	0.363798i
$85$	−3.32183e6	+	5.75358e6i	−0.00690227	+	0.0119551i
$86$	−5.18042e8			−1.02123
$87$	−5.38704e8	+	9.33064e8i	−1.00812	+	1.74612i
$88$	2.53805e7	+	4.39603e7i	0.0451157	+	0.0781427i
$89$	−5.80652e8	−	1.00572e9i	−0.980981	−	1.69911i	−0.658589	−	0.752503i	$-0.728846\pi$
$89$	−5.80652e8	−	1.00572e9i	−0.980981	−	1.69911i	−0.322392	−	0.946606i	$-0.604487\pi$
$90$	−5.66909e6			−0.00910797
$91$	−1.88568e8	−	2.03791e8i	−0.288259	−	0.311529i
$92$	−1.12616e8			−0.163891
$93$	2.93021e8	+	5.07527e8i	0.406187	+	0.703536i
$94$	−1.46279e8	−	2.53363e8i	−0.193244	−	0.334709i
$95$	−7.33284e6	+	1.27009e7i	−0.00923668	+	0.0159984i
$96$	1.19141e9			1.43166
$97$	−1.89552e8	+	3.28314e8i	−0.217399	+	0.376545i	−0.954012	−	0.299769i	$-0.903090\pi$
$97$	−1.89552e8	+	3.28314e8i	−0.217399	+	0.376545i	0.736613	+	0.676314i	$0.236424\pi$
$98$	1.99317e8	−	3.45227e8i	0.218287	−	0.378083i
$99$	8.57151e7			0.0896807
$100$	−3.58095e8	+	6.20239e8i	−0.358095	+	0.620239i
$101$	−1.30677e8	−	2.26339e8i	−0.124955	−	0.216428i	0.796761	−	0.604295i	$-0.206545\pi$
$101$	−1.30677e8	−	2.26339e8i	−0.124955	−	0.216428i	−0.921715	+	0.387867i	$0.873212\pi$
$102$	2.94806e8	+	5.10620e8i	0.269672	+	0.467086i
$103$	−6.34912e8			−0.555836			−0.277918	−	0.960605i	$-0.589644\pi$
$103$	−6.34912e8			−0.555836			−0.277918	+	0.960605i	$0.589644\pi$
$104$	3.22846e8	−	1.04154e9i	0.270611	−	0.873027i
$105$	−1.37503e7			−0.0110398
$106$	3.78763e8	+	6.56036e8i	0.291401	+	0.504721i
$107$	7.71569e7	+	1.33640e8i	0.0569046	+	0.0985617i	0.893074	−	0.449909i	$-0.148544\pi$
$107$	7.71569e7	+	1.33640e8i	0.0569046	+	0.0985617i	−0.836170	+	0.548471i	$0.815210\pi$
$108$	−6.40716e7	+	1.10975e8i	−0.0453167	+	0.0784909i
$109$	1.27321e9			0.863937			0.431968	−	0.901889i	$-0.357819\pi$
$109$	1.27321e9			0.863937			0.431968	+	0.901889i	$0.357819\pi$
$110$	759938.	−	1.31625e6i	0.000494893	−	0.000857179i
$111$	1.38410e9	−	2.39733e9i	0.865395	−	1.49891i
$112$	1.62376e8			0.0975081
$113$	8.39651e8	−	1.45432e9i	0.484447	−	0.839086i	−0.515394	−	0.856953i	$-0.672354\pi$
$113$	8.39651e8	−	1.45432e9i	0.484447	−	0.839086i	0.999840	+	0.0178674i	$0.00568769\pi$
$114$	6.50777e8	+	1.12718e9i	0.360878	+	0.625058i
$115$	4.03921e6	+	6.99612e6i	0.00215356	+	0.00373007i
$116$	−2.03915e9			−1.04566
$117$	−1.25055e9	−	1.35150e9i	−0.616969	−	0.666775i
$118$	−1.12500e9			−0.534174
$119$	3.40369e8	+	5.89536e8i	0.155593	+	0.269494i
$120$	−2.70013e7	−	4.67676e7i	−0.0118869	−	0.0205887i
$121$	1.16748e9	−	2.02214e9i	0.495127	−	0.857585i
$122$	2.58212e8			0.105525
$123$	−2.26545e9	+	3.92388e9i	−0.892447	+	1.54576i
$124$	−5.54585e8	+	9.60569e8i	−0.210654	+	0.364864i
$125$	1.02769e8			0.0376501
$126$	−2.90440e8	+	5.03056e8i	−0.102657	+	0.177807i
$127$	1.99093e9	+	3.44839e9i	0.679107	+	1.17625i	0.975250	+	0.221105i	$0.0709663\pi$
$127$	1.99093e9	+	3.44839e9i	0.679107	+	1.17625i	−0.296143	+	0.955144i	$0.595700\pi$
$128$	1.31322e9	+	2.27457e9i	0.432408	+	0.748952i
$129$	−8.33287e9			−2.64936
$130$	−3.18409e7	+	7.22134e6i	−0.00977778	+	0.00221755i
$131$	2.65654e8			0.0788126			0.0394063	−	0.999223i	$-0.487453\pi$
$131$	2.65654e8			0.0788126			0.0394063	+	0.999223i	$0.487453\pi$
$132$	1.70405e8	+	2.95150e8i	0.0488539	+	0.0846175i
$133$	7.51354e8	+	1.30138e9i	0.208215	+	0.360639i
$134$	1.20452e9	−	2.08628e9i	0.322731	−	0.558987i
$135$	9.19223e6			0.00238187
$136$	−1.33676e9	+	2.31534e9i	−0.335064	+	0.580348i
$137$	3.26965e9	−	5.66321e9i	0.792974	−	1.37347i	−0.131143	−	0.991363i	$-0.541865\pi$
$137$	3.26965e9	−	5.66321e9i	0.792974	−	1.37347i	0.924117	−	0.382108i	$-0.124802\pi$
$138$	7.16946e8			0.168279
$139$	2.03670e9	−	3.52767e9i	0.462765	−	0.801533i	−0.536332	−	0.844007i	$-0.680191\pi$
$139$	2.03670e9	−	3.52767e9i	0.462765	−	0.801533i	0.999098	+	0.0424738i	$0.0135239\pi$
$140$	−1.30122e7	−	2.25378e7i	−0.00286269	−	0.00495833i
$141$	−2.35294e9	−	4.07542e9i	−0.501332	−	0.868333i
$142$	−3.08284e9			−0.636288
$143$	4.81427e8	−	1.09185e8i	0.0962760	−	0.0218349i
$144$	1.07684e9			0.208699
$145$	7.31383e7	+	1.26679e8i	0.0137401	+	0.0237985i
$146$	−9.92213e7	−	1.71856e8i	−0.0180725	−	0.0313024i
$147$	3.20607e9	−	5.55308e9i	0.566299	−	0.980858i
$148$	5.23922e9			0.897613
$149$	−4.96569e9	+	8.60083e9i	−0.825356	+	1.42956i	0.0762906	+	0.997086i	$0.475692\pi$
$149$	−4.96569e9	+	8.60083e9i	−0.825356	+	1.42956i	−0.901647	+	0.432473i	$0.857641\pi$
$150$	2.27973e9	−	3.94861e9i	0.367682	−	0.636845i
$151$	9.12112e9			1.42775			0.713874	−	0.700274i	$-0.246939\pi$
$151$	9.12112e9			1.42775			0.713874	+	0.700274i	$0.246939\pi$
$152$	−2.95086e9	+	5.11103e9i	−0.448386	+	0.776627i
$153$	2.25726e9	+	3.90968e9i	0.333019	+	0.576806i
$154$	−7.78665e7	−	1.34869e8i	−0.0111560	−	0.0193227i
$155$	7.95652e7			0.0110721
$156$	2.16759e9	−	6.99294e9i	0.293033	−	0.945364i
$157$	−9.65195e9			−1.26785			−0.633923	−	0.773396i	$-0.718557\pi$
$157$	−9.65195e9			−1.26785			−0.633923	+	0.773396i	$0.718557\pi$
$158$	8.40421e8	+	1.45565e9i	0.107285	+	0.185823i
$159$	6.09252e9	+	1.05525e10i	0.755979	+	1.30939i
$160$	8.08770e7	−	1.40083e8i	0.00975630	−	0.0168984i
$161$	8.27750e8			0.0970918
$162$	2.52819e9	−	4.37896e9i	0.288398	−	0.499520i
$163$	2.07830e9	−	3.59972e9i	0.230602	−	0.399415i	−0.727383	−	0.686231i	$-0.759264\pi$
$163$	2.07830e9	−	3.59972e9i	0.230602	−	0.399415i	0.957985	+	0.286817i	$0.0925971\pi$
$164$	−8.57540e9			−0.925672
$165$	1.22238e7	−	2.11723e7i	0.00128390	−	0.00222377i
$166$	−2.19708e9	−	3.80546e9i	−0.224574	−	0.388974i
$167$	−1.23010e9	−	2.13060e9i	−0.122382	−	0.211972i	0.798325	−	0.602227i	$-0.205720\pi$
$167$	−1.23010e9	−	2.13060e9i	−0.122382	−	0.211972i	−0.920707	+	0.390256i	$0.872387\pi$
$168$	−5.53334e9			−0.535915
$169$	−8.74536e9	−	5.99785e9i	−0.824683	−	0.565595i
$170$	8.00500e7			0.00735091
$171$	4.98283e9	+	8.63051e9i	0.445649	+	0.771887i
$172$	−7.88558e9	−	1.36582e10i	−0.686998	−	1.18992i
$173$	−9.36260e9	+	1.62165e10i	−0.794674	+	1.37642i	0.128371	+	0.991726i	$0.459025\pi$
$173$	−9.36260e9	+	1.62165e10i	−0.794674	+	1.37642i	−0.923046	+	0.384690i	$0.874308\pi$
$174$	1.29818e10			1.07365
$175$	2.63206e9	−	4.55887e9i	0.212141	−	0.367440i
$176$	−1.44350e8	+	2.50022e8i	−0.0113399	+	0.0196413i
$177$	−1.80959e10			−1.38580
$178$	−6.99632e9	+	1.21180e10i	−0.522372	+	0.904774i
$179$	9.22318e9	+	1.59750e10i	0.671494	+	1.16306i	0.977481	+	0.211026i	$0.0676803\pi$
$179$	9.22318e9	+	1.59750e10i	0.671494	+	1.16306i	−0.305987	+	0.952036i	$0.598986\pi$
$180$	−8.62942e7	−	1.49466e8i	−0.00612710	−	0.0106125i
$181$	9.10014e9			0.630223			0.315112	−	0.949055i	$-0.397958\pi$
$181$	9.10014e9			0.630223			0.315112	+	0.949055i	$0.397958\pi$
$182$	−9.90481e8	+	3.19542e9i	−0.0669152	+	0.215877i
$183$	4.15342e9			0.273764
$184$	1.62545e9	+	2.81535e9i	0.104542	+	0.181073i
$185$	−1.87915e8	−	3.25479e8i	−0.0117948	−	0.0204291i
$186$	3.53063e9	−	6.11524e9i	0.216294	−	0.374632i
$187$	−1.21034e9			−0.0723800
$188$	4.45329e9	−	7.71332e9i	0.259998	−	0.450330i
$189$	4.70938e8	−	8.15688e8i	0.0268464	−	0.0464992i
$190$	1.76708e8			0.00983705
$191$	2.41655e9	−	4.18559e9i	0.131385	−	0.227565i	−0.792826	−	0.609448i	$-0.791391\pi$
$191$	2.41655e9	−	4.18559e9i	0.131385	−	0.227565i	0.924211	+	0.381883i	$0.124724\pi$
$192$	−4.18959e9	−	7.25659e9i	−0.222493	−	0.385369i
$193$	−1.43871e10	−	2.49192e10i	−0.746389	−	1.29278i	−0.949543	−	0.313637i	$-0.898452\pi$
$193$	−1.43871e10	−	2.49192e10i	−0.746389	−	1.29278i	0.203154	−	0.979147i	$-0.434881\pi$
$194$	4.56787e9			0.231529
$195$	−5.12171e8	+	1.16158e8i	−0.0253664	+	0.00575296i
$196$	1.21359e10			0.587382
$197$	5.27479e9	+	9.13621e9i	0.249521	+	0.432183i	0.963393	−	0.268093i	$-0.0863934\pi$
$197$	5.27479e9	+	9.13621e9i	0.249521	+	0.432183i	−0.713872	+	0.700276i	$0.753060\pi$
$198$	−5.16394e8	−	8.94421e8i	−0.0238775	−	0.0413570i
$199$	−5.31470e9	+	9.20533e9i	−0.240237	+	0.416103i	−0.960782	−	0.277306i	$-0.910559\pi$
$199$	−5.31470e9	+	9.20533e9i	−0.240237	+	0.416103i	0.720545	+	0.693409i	$0.243892\pi$
$200$	2.06743e10			0.913681
$201$	1.93750e10	−	3.35585e10i	0.837259	−	1.45018i
$202$	−1.57454e9	+	2.72717e9i	−0.0665382	+	0.115248i
$203$	1.49881e10			0.619463
$204$	−8.97502e9	+	1.55452e10i	−0.362827	+	0.628435i
$205$	3.07574e8	+	5.32734e8i	0.0121635	+	0.0210677i
$206$	3.82506e9	+	6.62519e9i	0.147991	+	0.256328i
$207$	5.48946e9			0.207809
$208$	6.04818e9	−	1.37169e9i	0.224047	−	0.0508127i
$209$	−2.67178e9			−0.0968595
$210$	8.28391e7	+	1.43482e8i	0.00293933	+	0.00509107i
$211$	2.71457e9	+	4.70178e9i	0.0942824	+	0.163302i	0.909309	−	0.416122i	$-0.136611\pi$
$211$	2.71457e9	+	4.70178e9i	0.0942824	+	0.163302i	−0.815026	+	0.579424i	$0.803278\pi$
$212$	−1.15310e10	+	1.99722e10i	−0.392062	+	0.679071i
$213$	−4.95885e10			−1.65072
$214$	9.29670e8	−	1.61024e9i	0.0303017	−	0.0524841i
$215$	−5.65665e8	+	9.79760e8i	−0.0180545	+	0.0312713i
$216$	3.69911e9			0.115626
$217$	4.07630e9	−	7.06035e9i	0.124795	−	0.216151i
$218$	−7.67053e9	−	1.32857e10i	−0.230023	−	0.398411i
$219$	−1.59601e9	−	2.76436e9i	−0.0468852	−	0.0812076i
$220$	4.62708e7			0.00133169
$221$	1.76583e10	+	1.90838e10i	0.497947	+	0.538144i
$222$	−3.33543e10			−0.921644
$223$	−1.35606e10	−	2.34877e10i	−0.367204	−	0.636016i	0.621923	−	0.783078i	$-0.286352\pi$
$223$	−1.35606e10	−	2.34877e10i	−0.367204	−	0.636016i	−0.989127	+	0.147062i	$0.953018\pi$
$224$	−8.28701e9	−	1.43535e10i	−0.219929	−	0.380927i
$225$	1.74553e10	−	3.02335e10i	0.454052	−	0.786442i
$226$	−2.02341e10			−0.515935
$227$	−2.77233e10	+	4.80182e10i	−0.692994	+	1.20030i	0.277859	+	0.960622i	$0.410375\pi$
$227$	−2.77233e10	+	4.80182e10i	−0.692994	+	1.20030i	−0.970852	+	0.239678i	$0.922958\pi$
$228$	−1.98121e10	+	3.43156e10i	−0.485538	+	0.840977i
$229$	1.70044e10			0.408603			0.204301	−	0.978908i	$-0.434508\pi$
$229$	1.70044e10			0.408603			0.204301	+	0.978908i	$0.434508\pi$
$230$	4.86688e7	−	8.42968e7i	0.00114677	−	0.00198626i
$231$	−1.25251e9	−	2.16941e9i	−0.0289418	−	0.0501287i
$232$	2.94321e10	+	5.09779e10i	0.666999	+	1.15528i
$233$	4.36994e10			0.971346			0.485673	−	0.874141i	$-0.338575\pi$
$233$	4.36994e10			0.971346			0.485673	+	0.874141i	$0.338575\pi$
$234$	−6.56866e9	+	2.11914e10i	−0.143221	+	0.462049i
$235$	−6.38905e8			−0.0136657
$236$	−1.71246e10	−	2.96606e10i	−0.359349	−	0.622410i
$237$	1.35184e10	+	2.34146e10i	0.278329	+	0.482080i
$238$	4.10113e9	−	7.10337e9i	0.0828529	−	0.143505i
$239$	−6.61075e10			−1.31057			−0.655285	−	0.755382i	$-0.727451\pi$
$239$	−6.61075e10			−1.31057			−0.655285	+	0.755382i	$0.727451\pi$
$240$	1.53569e8	−	2.65989e8i	0.00298780	−	0.00517503i
$241$	−5.19128e9	+	8.99156e9i	−0.0991283	+	0.171695i	−0.911324	−	0.411690i	$-0.864939\pi$
$241$	−5.19128e9	+	8.99156e9i	−0.0991283	+	0.171695i	0.812196	+	0.583385i	$0.198272\pi$
$242$	−2.81342e10			−0.527310
$243$	3.72288e10	−	6.44821e10i	0.684937	−	1.18635i
$244$	3.93048e9	+	6.80778e9i	0.0709890	+	0.122956i
$245$	−4.35279e8	−	7.53926e8i	−0.00771828	−	0.0133685i
$246$	5.45933e10			0.950455
$247$	3.89801e10	+	4.21268e10i	0.666357	+	0.720149i
$248$	3.20184e10			0.537485
$249$	−3.53407e10	−	6.12119e10i	−0.582611	−	1.00911i
$250$	−6.19134e8	−	1.07237e9i	−0.0100243	−	0.0173626i
$251$	3.60007e10	−	6.23551e10i	0.572506	−	0.991609i	−0.423802	−	0.905755i	$-0.639305\pi$
$251$	3.60007e10	−	6.23551e10i	0.572506	−	0.991609i	0.996308	−	0.0858540i	$-0.0273619\pi$
$252$	−1.76842e10			−0.276237
$253$	−7.35860e8	+	1.27455e9i	−0.0112915	+	0.0195575i
$254$	2.39888e10	−	4.15499e10i	0.361624	−	0.626352i
$255$	1.28763e9			0.0190704
$256$	2.68909e10	−	4.65763e10i	0.391313	−	0.677775i
$257$	−3.64070e10	−	6.30588e10i	−0.520579	−	0.901669i	−0.999714	−	0.0239275i	$-0.992383\pi$
$257$	−3.64070e10	−	6.30588e10i	−0.520579	−	0.901669i	0.479135	−	0.877741i	$-0.340950\pi$
$258$	5.02017e10	+	8.69519e10i	0.705391	+	1.22177i
$259$	−3.85092e10			−0.531760
$260$	−6.75070e8	−	7.29566e8i	−0.00916155	−	0.00990112i
$261$	9.93982e10			1.32586
$262$	−1.60044e9	−	2.77205e9i	−0.0209838	−	0.0363450i
$263$	−3.98676e10	−	6.90528e10i	−0.513830	−	0.889980i	−0.999871	−	0.0160439i	$-0.994893\pi$
$263$	−3.98676e10	−	6.90528e10i	−0.513830	−	0.889980i	0.486041	−	0.873936i	$-0.338440\pi$
$264$	4.91907e9	−	8.52009e9i	0.0623255	−	0.107951i
$265$	1.65433e9			0.0206070
$266$	9.05313e9	−	1.56805e10i	0.110874	−	0.192040i
$267$	−1.12538e11	+	1.94921e11i	−1.35518	+	2.34725i
$268$	7.33401e10			0.868430
$269$	5.66265e9	−	9.80800e9i	0.0659378	−	0.114208i	−0.831172	−	0.556016i	$-0.812329\pi$
$269$	5.66265e9	−	9.80800e9i	0.0659378	−	0.114208i	0.897110	+	0.441808i	$0.145663\pi$
$270$	−5.53790e7	−	9.59192e7i	−0.000634173	−	0.00109842i
$271$	2.99294e10	+	5.18393e10i	0.337083	+	0.583845i	0.983883	−	0.178815i	$-0.0572264\pi$
$271$	2.99294e10	+	5.18393e10i	0.337083	+	0.583845i	−0.646800	+	0.762660i	$0.723893\pi$
$272$	−1.52055e10			−0.168438
$273$	−1.59322e10	+	5.13994e10i	−0.173597	+	0.560049i
$274$	−7.87927e10			−0.844517
$275$	4.67975e9	+	8.10556e9i	0.0493430	+	0.0854645i
$276$	1.09133e10	+	1.89023e10i	0.113205	+	0.196076i
$277$	−9.35415e10	+	1.62019e11i	−0.954653	+	1.65351i	−0.219492	+	0.975614i	$0.570440\pi$
$277$	−9.35415e10	+	1.62019e11i	−0.954653	+	1.65351i	−0.735161	+	0.677893i	$0.762893\pi$
$278$	−4.90808e10			−0.492844
$279$	2.70331e10	−	4.68228e10i	0.267102	−	0.462635i
$280$	−3.75623e8	+	6.50598e8i	−0.00365208	+	0.00632560i
$281$	4.65792e10			0.445670			0.222835	−	0.974856i	$-0.428469\pi$
$281$	4.65792e10			0.445670			0.222835	+	0.974856i	$0.428469\pi$
$282$	−2.83508e10	+	4.91051e10i	−0.266959	+	0.462387i
$283$	−8.91511e10	−	1.54414e11i	−0.826205	−	1.43103i	−0.900995	−	0.433829i	$-0.857162\pi$
$283$	−8.91511e10	−	1.54414e11i	−0.826205	−	1.43103i	0.0747904	−	0.997199i	$-0.476171\pi$
$284$	−4.69267e10	−	8.12794e10i	−0.428043	−	0.741392i
$285$	2.84240e9			0.0255202
$286$	−4.03970e9	−	4.36581e9i	−0.0357028	−	0.0385849i
$287$	6.30307e10			0.548383
$288$	−5.49577e10	−	9.51895e10i	−0.470720	−	0.815310i
$289$	2.74205e10	+	4.74937e10i	0.231225	+	0.400493i
$290$	8.81250e8	−	1.52637e9i	0.00731658	−	0.0126727i
$291$	7.34755e10			0.600654
$292$	3.02067e9	−	5.23196e9i	0.0243154	−	0.0421154i
$293$	−5.62499e10	+	9.74277e10i	−0.445880	+	0.772286i	−0.998113	−	0.0614035i	$-0.980442\pi$
$293$	−5.62499e10	+	9.74277e10i	−0.445880	+	0.772286i	0.552233	+	0.833689i	$0.313776\pi$
$294$	−7.72605e10			−0.603107
$295$	−1.22842e9	+	2.12768e9i	−0.00944379	+	0.0163571i
$296$	−7.56202e10	−	1.30978e11i	−0.572566	−	0.991713i
$297$	8.37316e8	+	1.45027e9i	0.00624432	+	0.0108155i
$298$	1.19664e11			0.879003
$299$	3.08321e10	−	6.99254e9i	0.223091	−	0.0505958i
$300$	1.38807e11			0.989387
$301$	5.79604e10	+	1.00390e11i	0.406989	+	0.704925i
$302$	−5.49506e10	−	9.51772e10i	−0.380138	−	0.658418i
$303$	−2.53269e10	+	4.38674e10i	−0.172620	+	0.298986i
$304$	−3.35657e10			−0.225406
$305$	2.81949e8	−	4.88350e8i	0.00186561	−	0.00323133i
$306$	2.71979e10	−	4.71081e10i	0.177333	−	0.307149i
$307$	−1.02041e11			−0.655620			−0.327810	−	0.944744i	$-0.606311\pi$
$307$	−1.02041e11			−0.655620			−0.327810	+	0.944744i	$0.606311\pi$
$308$	2.37055e9	−	4.10591e9i	0.0150097	−	0.0259975i
$309$	6.15272e10	+	1.06568e11i	0.383932	+	0.664989i
$310$	−4.79344e8	−	8.30248e8i	−0.00294795	−	0.00510599i
$311$	2.13525e11			1.29428			0.647138	−	0.762373i	$-0.275966\pi$
$311$	2.13525e11			1.29428			0.647138	+	0.762373i	$0.275966\pi$
$312$	−2.06106e11	+	4.67437e10i	−1.23139	+	0.279272i
$313$	1.60400e10			0.0944614			0.0472307	−	0.998884i	$-0.484960\pi$
$313$	1.60400e10			0.0944614			0.0472307	+	0.998884i	$0.484960\pi$
$314$	5.81486e10	+	1.00716e11i	0.337564	+	0.584678i
$315$	6.34278e8	+	1.09860e9i	0.00362979	+	0.00628699i
$316$	−2.55856e10	+	4.43155e10i	−0.144346	+	0.250014i
$317$	2.71859e11			1.51209			0.756044	−	0.654521i	$-0.227130\pi$
$317$	2.71859e11			1.51209			0.756044	+	0.654521i	$0.227130\pi$
$318$	7.34092e10	−	1.27149e11i	0.402558	−	0.697251i
$319$	−1.33243e10	+	2.30783e10i	−0.0720419	+	0.124780i
$320$	−1.13762e9			−0.00606487
$321$	1.49540e10	−	2.59011e10i	0.0786114	−	0.136159i
$322$	−4.98681e9	−	8.63742e9i	−0.0258507	−	0.0447747i
$323$	−7.03597e10	−	1.21867e11i	−0.359677	−	0.622979i
$324$	1.53935e11			0.776044
$325$	5.95275e10	−	1.92044e11i	0.295966	−	0.954827i
$326$	−5.00831e10			−0.245591
$327$	−1.23383e11	−	2.13705e11i	−0.596746	−	1.03359i
$328$	1.23773e11	+	2.14381e11i	0.590464	+	1.02271i
$329$	−3.27325e10	+	5.66943e10i	−0.154027	+	0.266783i
$330$	−2.94572e8			−0.00136735
$331$	9.25009e10	−	1.60216e11i	0.423565	−	0.733636i	−0.572720	−	0.819751i	$-0.694112\pi$
$331$	9.25009e10	−	1.60216e11i	0.423565	−	0.733636i	0.996285	+	0.0861147i	$0.0274451\pi$
$332$	6.68874e10	−	1.15852e11i	0.302150	−	0.523340i
$333$	−2.55385e11			−1.13814
$334$	−1.48216e10	+	2.56718e10i	−0.0651683	+	0.112875i
$335$	−2.63049e9	−	4.55614e9i	−0.0114113	−	0.0197649i
$336$	−1.57353e10	−	2.72543e10i	−0.0673517	−	0.116657i
$337$	−1.53099e11			−0.646603			−0.323302	−	0.946296i	$-0.604793\pi$
$337$	−1.53099e11			−0.646603			−0.323302	+	0.946296i	$0.604793\pi$
$338$	−9.89965e9	+	1.27390e11i	−0.0412567	+	0.530899i
$339$	−3.25471e11			−1.33849
$340$	1.21851e9	+	2.11052e9i	0.00494510	+	0.00856516i
$341$	7.24756e9	+	1.25531e10i	0.0290267	+	0.0502756i
$342$	6.00385e10	−	1.03990e11i	0.237308	−	0.411029i
$343$	−1.98002e11			−0.772407
$344$	−2.27633e11	+	3.94272e11i	−0.876439	+	1.51804i
$345$	7.82852e8	−	1.35594e9i	0.00297505	−	0.00515293i
$346$	2.25622e11			0.846327
$347$	−7.18658e10	+	1.24475e11i	−0.266097	+	0.460893i	−0.967850	−	0.251526i	$-0.919067\pi$
$347$	−7.18658e10	+	1.24475e11i	−0.266097	+	0.460893i	0.701754	+	0.712420i	$0.252401\pi$
$348$	1.97607e11	+	3.42266e11i	0.722265	+	1.25100i
$349$	−4.13187e10	−	7.15661e10i	−0.149084	−	0.258222i	0.781805	−	0.623523i	$-0.214299\pi$
$349$	−4.13187e10	−	7.15661e10i	−0.149084	−	0.258222i	−0.930889	+	0.365301i	$0.880966\pi$
$350$	−6.34279e10			−0.225930
$351$	1.06509e10	−	3.43611e10i	0.0374544	−	0.120833i
$352$	2.94682e10			0.102308
$353$	1.82229e11	+	3.15630e11i	0.624643	+	1.08191i	0.988610	+	0.150501i	$0.0480887\pi$
$353$	1.82229e11	+	3.15630e11i	0.624643	+	1.08191i	−0.363967	+	0.931412i	$0.618578\pi$
$354$	1.09020e11	+	1.88828e11i	0.368969	+	0.639074i
$355$	−3.36624e9	+	5.83050e9i	−0.0112491	+	0.0194840i
$356$	−4.25989e11			−1.40564
$357$	6.59680e10	−	1.14260e11i	0.214945	−	0.372295i
$358$	1.11131e11	−	1.92484e11i	0.357570	−	0.619329i
$359$	2.21213e11			0.702887			0.351443	−	0.936209i	$-0.385691\pi$
$359$	2.21213e11			0.702887			0.351443	+	0.936209i	$0.385691\pi$
$360$	−2.49105e9	+	4.31463e9i	−0.00781667	+	0.0135389i
$361$	6.02688e9	+	1.04389e10i	0.0186771	+	0.0323498i
$362$	−5.48242e10	−	9.49583e10i	−0.167797	−	0.290633i
$363$	−4.52548e11			−1.36799
$364$	−9.93246e10	+	2.25263e10i	−0.296552	+	0.0672563i
$365$	−4.33370e8			−0.00127803
$366$	−2.50225e10	−	4.33402e10i	−0.0728895	−	0.126248i
$367$	−2.84117e11	−	4.92105e11i	−0.817523	−	1.41599i	−0.907502	−	0.420048i	$-0.862013\pi$
$367$	−2.84117e11	−	4.92105e11i	−0.817523	−	1.41599i	0.0899786	−	0.995944i	$-0.471320\pi$
$368$	−9.24464e9	+	1.60122e10i	−0.0262769	+	0.0455130i
$369$	4.18007e11			1.17372
$370$	−2.26421e9	+	3.92172e9i	−0.00628070	+	0.0108785i
$371$	8.47547e10	−	1.46799e11i	0.232264	−	0.402292i
$372$	2.14972e11			0.582020
$373$	6.51036e10	−	1.12763e11i	0.174147	−	0.301631i	−0.765719	−	0.643175i	$-0.777617\pi$
$373$	6.51036e10	−	1.12763e11i	0.174147	−	0.301631i	0.939866	+	0.341544i	$0.110950\pi$
$374$	7.29172e9	+	1.26296e10i	0.0192712	+	0.0333786i
$375$	−9.95897e9	−	1.72494e10i	−0.0260060	−	0.0450437i
$376$	−2.57106e11			−0.663387
$377$	5.58279e11	−	1.26614e11i	1.42336	−	0.322810i
$378$	−1.13487e10			−0.0285913
$379$	2.33809e11	+	4.04968e11i	0.582082	+	1.00820i	0.995232	+	0.0975326i	$0.0310950\pi$
$379$	2.33809e11	+	4.04968e11i	0.582082	+	1.00820i	−0.413150	+	0.910663i	$0.635572\pi$
$380$	2.68983e9	+	4.65892e9i	0.00661757	+	0.0114620i
$381$	3.85868e11	−	6.68343e11i	0.938159	−	1.62494i
$382$	−5.82344e10			−0.139925
$383$	−1.50174e11	+	2.60108e11i	−0.356615	+	0.617675i	−0.987393	−	0.158288i	$-0.949402\pi$
$383$	−1.50174e11	+	2.60108e11i	−0.356615	+	0.617675i	0.630778	+	0.775963i	$0.282736\pi$
$384$	2.54520e11	−	4.40841e11i	0.597353	−	1.03465i
$385$	−3.40098e8			−0.000788917
$386$	−1.73351e11	+	3.00253e11i	−0.397452	+	0.688407i
$387$	3.84381e11	+	6.65768e11i	0.871090	+	1.50877i
$388$	6.95315e10	+	1.20432e11i	0.155754	+	0.269774i
$389$	−4.38367e11			−0.970655			−0.485327	−	0.874333i	$-0.661300\pi$
$389$	−4.38367e11			−0.970655			−0.485327	+	0.874333i	$0.661300\pi$
$390$	4.29768e9	+	4.64461e9i	0.00940682	+	0.0101662i
$391$	−7.75137e10			−0.167719
$392$	−1.75164e11	−	3.03392e11i	−0.374677	−	0.648959i
$393$	−2.57436e10	−	4.45893e10i	−0.0544381	−	0.0942896i
$394$	6.35564e10	−	1.10083e11i	0.132870	−	0.230137i
$395$	3.67071e9			0.00758689
$396$	1.57210e10	−	2.72296e10i	0.0321256	−	0.0556432i
$397$	1.48211e11	−	2.56709e11i	0.299449	−	0.518660i	−0.676561	−	0.736386i	$-0.736531\pi$
$397$	1.48211e11	−	2.56709e11i	0.299449	−	0.518660i	0.976010	+	0.217726i	$0.0698639\pi$
$398$	1.28075e11			0.255852
$399$	1.45622e11	−	2.52225e11i	0.287641	−	0.498208i
$400$	5.87919e10	+	1.01831e11i	0.114828	+	0.198888i
$401$	2.87623e11	+	4.98177e11i	0.555486	+	0.962131i	0.997866	+	0.0653026i	$0.0208013\pi$
$401$	2.87623e11	+	4.98177e11i	0.555486	+	0.962131i	−0.442379	+	0.896828i	$0.645865\pi$
$402$	−4.66903e11			−0.891680
$403$	9.21907e10	−	2.97419e11i	0.174106	−	0.561690i
$404$	−9.58696e10			−0.179046
$405$	−5.52121e9	−	9.56301e9i	−0.0101973	−	0.0176623i
$406$	−9.02967e10	−	1.56398e11i	−0.164932	−	0.285670i
$407$	3.42342e10	−	5.92954e10i	0.0618423	−	0.107114i
$408$	5.18163e11			0.925755
$409$	−2.63363e11	+	4.56158e11i	−0.465371	+	0.806047i	−0.999218	−	0.0395343i	$-0.987413\pi$
$409$	−2.63363e11	+	4.56158e11i	−0.465371	+	0.806047i	0.533847	+	0.845581i	$0.320746\pi$
$410$	3.70599e9	−	6.41895e9i	0.00647704	−	0.0112186i
$411$	−1.26740e12			−2.19092
$412$	−1.16449e11	+	2.01696e11i	−0.199113	+	0.344873i
$413$	1.25869e11	+	2.18011e11i	0.212884	+	0.368726i
$414$	−3.30715e10	−	5.72815e10i	−0.0553290	−	0.0958326i
$415$	−9.59621e9			−0.0158812
$416$	−4.29928e11	−	4.64635e11i	−0.703843	−	0.760662i
$417$	−7.89480e11			−1.27858
$418$	1.60963e10	+	2.78795e10i	0.0257888	+	0.0446675i
$419$	2.05621e11	+	3.56146e11i	0.325915	+	0.564502i	0.981697	−	0.190449i	$-0.0609943\pi$
$419$	2.05621e11	+	3.56146e11i	0.325915	+	0.564502i	−0.655782	+	0.754950i	$0.727661\pi$
$420$	−2.52194e9	+	4.36812e9i	−0.00395469	+	0.00684972i
$421$	1.35755e11			0.210614			0.105307	−	0.994440i	$-0.466417\pi$
$421$	1.35755e11			0.210614			0.105307	+	0.994440i	$0.466417\pi$
$422$	3.27081e10	−	5.66521e10i	0.0502053	−	0.0869582i
$423$	−2.17075e11	+	3.75985e11i	−0.329669	+	0.571003i
$424$	6.65728e11			1.00035
$425$	−2.46477e11	+	4.26910e11i	−0.366459	+	0.634726i
$426$	2.98748e11	+	5.17447e11i	0.439503	+	0.761241i
$427$	−2.88897e10	−	5.00384e10i	−0.0420550	−	0.0728414i
$428$	5.66053e10			0.0815380
$429$	−6.49798e10	−	7.02253e10i	−0.0926233	−	0.100100i
$430$	1.36315e10			0.0192280
$431$	3.90747e11	+	6.76793e11i	0.545441	+	0.944731i	0.998579	+	0.0532906i	$0.0169710\pi$
$431$	3.90747e11	+	6.76793e11i	0.545441	+	0.944731i	−0.453138	+	0.891440i	$0.649696\pi$
$432$	1.05192e10	+	1.82199e10i	0.0145314	+	0.0251691i
$433$	−7.54874e10	+	1.30748e11i	−0.103200	+	0.178747i	−0.913001	−	0.407957i	$-0.866241\pi$
$433$	−7.54874e10	+	1.30748e11i	−0.103200	+	0.178747i	0.809801	+	0.586704i	$0.199575\pi$
$434$	−9.82313e10			−0.132906
$435$	1.41752e10	−	2.45521e10i	0.0189813	−	0.0328766i
$436$	2.33520e11	−	4.04468e11i	0.309481	−	0.536037i
$437$	−1.71109e11			−0.224443
$438$	−1.92304e10	+	3.33080e10i	−0.0249663	+	0.0432430i
$439$	−5.30423e11	−	9.18720e11i	−0.681604	−	1.18057i	−0.974491	−	0.224426i	$-0.927949\pi$
$439$	−5.30423e11	−	9.18720e11i	−0.681604	−	1.18057i	0.292887	−	0.956147i	$-0.405384\pi$
$440$	−6.67848e8	−	1.15675e9i	−0.000849456	−	0.00147130i
$441$	−5.91564e11			−0.744780
$442$	9.27524e10	−	2.99232e11i	0.115591	−	0.372913i
$443$	4.09294e11			0.504916			0.252458	−	0.967608i	$-0.418761\pi$
$443$	4.09294e11			0.504916			0.252458	+	0.967608i	$0.418761\pi$
$444$	−5.07715e11	−	8.79388e11i	−0.620007	−	1.07388i
$445$	1.52789e10	+	2.64639e10i	0.0184703	+	0.0319915i
$446$	−1.63393e11	+	2.83005e11i	−0.195536	+	0.338678i
$447$	1.92483e12			2.28039
$448$	−5.82826e10	+	1.00948e11i	−0.0683578	+	0.118399i
$449$	4.03097e11	−	6.98185e11i	0.468060	−	0.810703i	−0.531274	−	0.847200i	$-0.678287\pi$
$449$	4.03097e11	−	6.98185e11i	0.468060	−	0.810703i	0.999334	+	0.0364970i	$0.0116199\pi$
$450$	−4.20641e11			−0.483565
$451$	−5.60336e10	+	9.70530e10i	−0.0637755	+	0.110462i
$452$	−3.08000e11	−	5.33472e11i	−0.347079	−	0.601159i
$453$	−8.83897e11	−	1.53095e12i	−0.986188	−	1.70813i
$454$	6.68082e11			0.738037
$455$	4.96189e9	+	5.36244e9i	0.00542745	+	0.00586558i
$456$	1.14383e12			1.23885
$457$	7.27703e11	+	1.26042e12i	0.780425	+	1.35174i	0.931694	+	0.363243i	$0.118331\pi$
$457$	7.27703e11	+	1.26042e12i	0.780425	+	1.35174i	−0.151269	+	0.988493i	$0.548336\pi$
$458$	−1.02444e11	−	1.77438e11i	−0.108790	−	0.188430i
$459$	−4.41004e10	+	7.63841e10i	−0.0463752	+	0.0803241i
$460$	2.96332e9			0.00308581
$461$	−2.23044e11	+	3.86324e11i	−0.230005	+	0.398380i	−0.957809	−	0.287405i	$-0.907208\pi$
$461$	−2.23044e11	+	3.86324e11i	−0.230005	+	0.398380i	0.727804	+	0.685785i	$0.240541\pi$
$462$	−1.50916e10	+	2.61393e10i	−0.0154115	+	0.0266935i
$463$	1.26062e12			1.27488			0.637442	−	0.770498i	$-0.279993\pi$
$463$	1.26062e12			1.27488			0.637442	+	0.770498i	$0.279993\pi$
$464$	−1.67393e11	+	2.89934e11i	−0.167652	+	0.290381i
$465$	−7.71039e9	−	1.33548e10i	−0.00764783	−	0.0132464i
$466$	−2.63269e11	−	4.55995e11i	−0.258620	−	0.447944i
$467$	9.09200e11			0.884573			0.442286	−	0.896874i	$-0.354167\pi$
$467$	9.09200e11			0.884573			0.442286	+	0.896874i	$0.354167\pi$
$468$	−6.58700e11	+	1.49389e11i	−0.634718	+	0.143951i
$469$	−5.39063e11			−0.514472
$470$	3.84911e9	+	6.66685e9i	0.00363848	+	0.00630203i
$471$	9.35338e11	+	1.62005e12i	0.875739	+	1.51682i
$472$	−4.94335e11	+	8.56213e11i	−0.458440	+	0.794041i
$473$	−2.06104e11			−0.189327
$474$	1.62885e11	−	2.82125e11i	0.148210	−	0.256707i
$475$	−5.44090e11	+	9.42391e11i	−0.490399	+	0.849395i
$476$	2.49708e11			0.222947
$477$	5.62075e11	−	9.73543e11i	0.497121	−	0.861038i
$478$	3.98267e11	+	6.89819e11i	0.348939	+	0.604379i
$479$	−3.71124e11	−	6.42806e11i	−0.322114	−	0.557918i	0.658810	−	0.752309i	$-0.271060\pi$
$479$	−3.71124e11	−	6.42806e11i	−0.322114	−	0.557918i	−0.980924	+	0.194391i	$0.937727\pi$
$480$	−3.13501e10			−0.0269558
$481$	−1.43439e12	+	3.25312e11i	−1.22184	+	0.277107i
$482$	1.25100e11			0.105572
$483$	−8.02145e10	−	1.38936e11i	−0.0670642	−	0.116159i
$484$	−4.28256e11	−	7.41761e11i	−0.354731	−	0.614412i
$485$	4.98778e9	−	8.63909e9i	0.00409326	−	0.00708973i
$486$	−8.97145e11			−0.729457
$487$	6.37095e11	−	1.10348e12i	0.513244	−	0.888964i	−0.486638	−	0.873604i	$-0.661777\pi$
$487$	6.37095e11	−	1.10348e12i	0.513244	−	0.888964i	0.999882	−	0.0153606i	$-0.00488961\pi$
$488$	1.13461e11	−	1.96520e11i	0.0905643	−	0.156862i
$489$	−8.05603e11			−0.637134
$490$	−5.24472e9	+	9.08412e9i	−0.00410998	+	0.00711869i
$491$	−8.01293e11	−	1.38788e12i	−0.622192	−	1.07767i	−0.989077	−	0.147402i	$-0.952909\pi$
$491$	−8.01293e11	−	1.38788e12i	−0.622192	−	1.07767i	0.366884	−	0.930267i	$-0.380425\pi$
$492$	8.31013e11	+	1.43936e12i	0.639389	+	1.10745i
$493$	−1.40355e12			−1.07008
$494$	2.04748e11	−	6.60545e11i	0.154685	−	0.499035i
$495$	−2.25546e9			−0.00168854
$496$	9.10514e10	+	1.57706e11i	0.0675490	+	0.116998i
$497$	3.44920e11	+	5.97418e11i	0.253580	+	0.439213i
$498$	−4.25823e11	+	7.37548e11i	−0.310240	+	0.537351i
$499$	−9.66345e11			−0.697718			−0.348859	−	0.937175i	$-0.613431\pi$
$499$	−9.66345e11			−0.697718			−0.348859	+	0.937175i	$0.613431\pi$
$500$	1.88488e10	−	3.26471e10i	0.0134871	−	0.0233603i
$501$	−2.38410e11	+	4.12939e11i	−0.169066	+	0.292830i
$502$	−8.67552e11			−0.609718
$503$	1.35182e12	−	2.34143e12i	0.941595	−	1.63089i	0.179166	−	0.983819i	$-0.442660\pi$
$503$	1.35182e12	−	2.34143e12i	0.941595	−	1.63089i	0.762429	−	0.647072i	$-0.224007\pi$
$504$	2.55244e11	+	4.42095e11i	0.176205	+	0.305196i
$505$	3.43856e9	+	5.95575e9i	0.00235269	+	0.00407498i
$506$	1.77329e10			0.0120255
$507$	−1.59239e11	+	2.04911e12i	−0.107032	+	1.37731i
$508$	1.46062e12			0.973086
$509$	−4.50817e11	−	7.80838e11i	−0.297694	−	0.515621i	0.677914	−	0.735141i	$-0.262884\pi$
$509$	−4.50817e11	−	7.80838e11i	−0.297694	−	0.515621i	−0.975608	+	0.219520i	$0.929551\pi$
$510$	−7.75737e9	−	1.34362e10i	−0.00507749	−	0.00879447i
$511$	−2.22025e10	+	3.84558e10i	−0.0144048	+	0.0249499i
$512$	6.96719e11			0.448067
$513$	−9.73503e10	+	1.68616e11i	−0.0620596	+	0.107490i
$514$	−4.38671e11	+	7.59801e11i	−0.277208	+	0.480138i
$515$	1.67067e10			0.0104655
$516$	−1.52833e12	+	2.64714e12i	−0.949060	+	1.64382i
$517$	−5.81975e10	−	1.00801e11i	−0.0358259	−	0.0620523i
$518$	2.32000e11	+	4.01836e11i	0.141581	+	0.245225i
$519$	3.62919e12			2.19562
$520$	−8.49519e9	+	2.74066e10i	−0.00509516	+	0.0164377i
$521$	−2.75454e12			−1.63787			−0.818934	−	0.573887i	$-0.805435\pi$
$521$	−2.75454e12			−1.63787			−0.818934	+	0.573887i	$0.805435\pi$
$522$	−5.98828e11	−	1.03720e12i	−0.353009	−	0.611429i
$523$	−2.31618e11	−	4.01174e11i	−0.135368	−	0.234464i	0.790370	−	0.612630i	$-0.209888\pi$
$523$	−2.31618e11	−	4.01174e11i	−0.135368	−	0.234464i	−0.925738	+	0.378166i	$0.876555\pi$
$524$	4.87235e10	−	8.43917e10i	0.0282324	−	0.0489000i
$525$	−1.02026e12			−0.586129
$526$	−4.80368e11	+	8.32022e11i	−0.273614	+	0.473914i
$527$	−3.81720e11	+	6.61159e11i	−0.215574	+	0.373386i
$528$	5.59540e10			0.0313313
$529$	8.53450e11	−	1.47822e12i	0.473835	−	0.820707i
$530$	−9.96655e9	−	1.72626e10i	−0.00548660	−	0.00950308i
$531$	8.34735e11	+	1.44580e12i	0.455642	+	0.789194i
$532$	5.51223e11			0.298349
$533$	2.34777e12	−	5.32461e11i	1.26004	−	0.285769i
$534$	2.71196e12			1.44327
$535$	−2.03026e9	−	3.51652e9i	−0.00107142	−	0.00185576i
$536$	−1.05855e12	−	1.83347e12i	−0.553951	−	0.959471i
$537$	1.78757e12	−	3.09617e12i	0.927641	−	1.60672i
$538$	−1.36459e11			−0.0702237
$539$	7.92988e10	−	1.37350e11i	0.0404685	−	0.0700935i
$540$	1.68594e9	−	2.92014e9i	0.000853240	−	0.00147786i
$541$	9.80985e11			0.492351			0.246175	−	0.969225i	$-0.420826\pi$
$541$	9.80985e11			0.492351			0.246175	+	0.969225i	$0.420826\pi$
$542$	3.60622e11	−	6.24616e11i	0.179496	−	0.310897i
$543$	−8.81864e11	−	1.52743e12i	−0.435314	−	0.753985i
$544$	7.76027e11	+	1.34412e12i	0.379911	+	0.658025i
$545$	−3.35026e10			−0.0162665
$546$	6.32327e11	−	1.43408e11i	0.304491	−	0.0690569i
$547$	−6.89509e11			−0.329304			−0.164652	−	0.986352i	$-0.552650\pi$
$547$	−6.89509e11			−0.329304			−0.164652	+	0.986352i	$0.552650\pi$
$548$	−1.19937e12	−	2.07737e12i	−0.568122	−	0.984016i
$549$	−1.91590e11	−	3.31844e11i	−0.0900116	−	0.155905i
$550$	5.63867e10	−	9.76646e10i	0.0262751	−	0.0455098i
$551$	−3.09829e12			−1.43199
$552$	3.15033e11	−	5.45653e11i	0.144421	−	0.250144i
$553$	1.88059e11	−	3.25727e11i	0.0855126	−	0.148112i
$554$	2.25418e12			1.01670
$555$	−3.64205e10	+	6.30821e10i	−0.0162940	+	0.0282220i
$556$	−7.47102e11	−	1.29402e12i	−0.331546	−	0.574254i
$557$	4.34598e11	+	7.52746e11i	0.191311	+	0.331360i	0.945685	−	0.325085i	$-0.105393\pi$
$557$	4.34598e11	+	7.52746e11i	0.191311	+	0.331360i	−0.754374	+	0.656445i	$0.772059\pi$
$558$	−6.51449e11			−0.284464
$559$	3.00697e12	+	3.24972e12i	1.30250	+	1.40764i
$560$	−4.27267e9			−0.00183592
$561$	1.17290e11	+	2.03151e11i	0.0499950	+	0.0865938i
$562$	−2.80618e11	−	4.86045e11i	−0.118659	−	0.205524i
$563$	−3.14793e11	+	5.45238e11i	−0.132050	+	0.228717i	−0.924467	−	0.381263i	$-0.875489\pi$
$563$	−3.14793e11	+	5.45238e11i	−0.132050	+	0.228717i	0.792417	+	0.609980i	$0.208823\pi$
$564$	−1.72621e12			−0.718354
$565$	−2.20941e10	+	3.82681e10i	−0.00912134	+	0.0157986i
$566$	−1.07419e12	+	1.86055e12i	−0.439953	+	0.762022i
$567$	−1.13145e12			−0.459741
$568$	−1.35463e12	+	2.34629e12i	−0.546077	+	0.945833i
$569$	4.79727e11	+	8.30911e11i	0.191862	+	0.332314i	0.945867	−	0.324554i	$-0.105214\pi$
$569$	4.79727e11	+	8.30911e11i	0.191862	+	0.332314i	−0.754005	+	0.656868i	$0.771881\pi$
$570$	−1.71242e10	−	2.96599e10i	−0.00679474	−	0.0117688i
$571$	9.04385e10			0.0356034			0.0178017	−	0.999842i	$-0.494333\pi$
$571$	9.04385e10			0.0356034			0.0178017	+	0.999842i	$0.494333\pi$
$572$	5.36130e10	−	1.72963e11i	0.0209406	−	0.0675570i
$573$	−9.36719e11			−0.363006
$574$	−3.79731e11	−	6.57714e11i	−0.146007	−	0.252891i
$575$	2.99706e11	+	5.19105e11i	0.114338	+	0.198039i
$576$	−3.86518e11	+	6.69469e11i	−0.146308	+	0.253413i
$577$	3.87397e11			0.145501			0.0727504	−	0.997350i	$-0.476822\pi$
$577$	3.87397e11			0.145501			0.0727504	+	0.997350i	$0.476822\pi$
$578$	3.30392e11	−	5.72255e11i	0.123127	−	0.213262i
$579$	−2.78841e12	+	4.82967e12i	−1.03111	+	1.78593i
$580$	5.36571e10			0.0196880
$581$	−4.91635e11	+	8.51536e11i	−0.178999	+	0.310035i
$582$	−4.42656e11	−	7.66703e11i	−0.159924	−	0.276996i
$583$	1.50692e11	+	2.61006e11i	0.0540233	+	0.0935711i
$584$	−1.74395e11			−0.0620407
$585$	3.29062e10	+	3.55626e10i	0.0116165	+	0.0125543i
$586$	1.35552e12			0.474861
$587$	−7.12519e11	−	1.23412e12i	−0.247699	−	0.429028i	0.715188	−	0.698932i	$-0.246341\pi$
$587$	−7.12519e11	−	1.23412e12i	−0.247699	−	0.429028i	−0.962887	+	0.269905i	$0.913008\pi$
$588$	−1.17605e12	−	2.03698e12i	−0.405722	−	0.702731i
$589$	−8.42636e11	+	1.45949e12i	−0.288484	+	0.499668i
$590$	2.96026e10			0.0100576
$591$	1.02232e12	−	1.77072e12i	0.344703	−	0.597043i
$592$	4.30086e11	−	7.44931e11i	0.143916	−	0.249269i
$593$	−5.67301e11			−0.188394			−0.0941970	−	0.995554i	$-0.530028\pi$
$593$	−5.67301e11			−0.188394			−0.0941970	+	0.995554i	$0.530028\pi$
$594$	1.00889e10	−	1.74745e10i	0.00332510	−	0.00575924i
$595$	−8.95628e9	−	1.55127e10i	−0.00292955	−	0.00507414i
$596$	1.82151e12	+	3.15495e12i	0.591322	+	1.02420i
$597$	2.06012e12			0.663755
$598$	−2.58715e11	−	2.79600e11i	−0.0827306	−	0.0894091i
$599$	−2.10161e12			−0.667008			−0.333504	−	0.942749i	$-0.608231\pi$
$599$	−2.10161e12			−0.667008			−0.333504	+	0.942749i	$0.608231\pi$
$600$	−2.00347e12	−	3.47011e12i	−0.631106	−	1.09311i
$601$	−2.79940e11	−	4.84870e11i	−0.0875246	−	0.151597i	0.818940	−	0.573880i	$-0.194562\pi$
$601$	−2.79940e11	−	4.84870e11i	−0.0875246	−	0.151597i	−0.906464	+	0.422283i	$0.861229\pi$
$602$	6.98370e11	−	1.20961e12i	0.216721	−	0.375372i
$603$	−3.57495e12			−1.10114
$604$	1.67290e12	−	2.89755e12i	0.511451	−	0.885860i
$605$	−3.07205e10	+	5.32095e10i	−0.00932244	+	0.0161469i
$606$	6.10331e11			0.183840
$607$	2.63614e12	−	4.56594e12i	0.788170	−	1.36515i	−0.138916	−	0.990304i	$-0.544362\pi$
$607$	2.63614e12	−	4.56594e12i	0.788170	−	1.36515i	0.927087	−	0.374847i	$-0.122305\pi$
$608$	1.71306e12	+	2.96710e12i	0.508400	+	0.880575i
$609$	−1.45245e12	−	2.51572e12i	−0.427881	−	0.741112i
$610$	−6.79445e9			−0.00198687
$611$	−7.40287e11	+	2.38826e12i	−0.214889	+	0.693261i
$612$	1.65601e12			0.477180
$613$	3.29005e12	+	5.69853e12i	0.941087	+	1.63001i	0.763402	+	0.645924i	$0.223528\pi$
$613$	3.29005e12	+	5.69853e12i	0.941087	+	1.63001i	0.177686	+	0.984087i	$0.443139\pi$
$614$	6.14750e11	+	1.06478e12i	0.174559	+	0.302344i
$615$	5.96119e10	−	1.03251e11i	0.0168033	−	0.0291042i
$616$	−1.36861e11			−0.0382972
$617$	−1.97484e11	+	3.42053e11i	−0.0548592	+	0.0950189i	−0.892151	−	0.451738i	$-0.850804\pi$
$617$	−1.97484e11	+	3.42053e11i	−0.0548592	+	0.0950189i	0.837292	+	0.546757i	$0.184138\pi$
$618$	7.41347e11	−	1.28405e12i	0.204443	−	0.354106i
$619$	−4.24633e12			−1.16253			−0.581267	−	0.813713i	$-0.697443\pi$
$619$	−4.24633e12			−1.16253			−0.581267	+	0.813713i	$0.697443\pi$
$620$	1.45930e10	−	2.52759e10i	0.00396628	−	0.00686979i
$621$	5.36243e10	+	9.28800e10i	0.0144694	+	0.0250617i
$622$	−1.28639e12	−	2.22809e12i	−0.344601	−	0.596866i
$623$	3.13109e12			0.832722
$624$	−8.16344e11	−	8.82244e11i	−0.215547	−	0.232948i
$625$	3.81064e12			0.998937
$626$	−9.66336e10	−	1.67374e11i	−0.0251503	−	0.0435616i
$627$	2.58913e11	+	4.48451e11i	0.0669037	+	0.115881i
$628$	−1.77026e12	+	3.06619e12i	−0.454171	+	0.786647i
$629$	3.60615e12			0.918578
$630$	7.64247e9	−	1.32371e10i	0.00193286	−	0.00334782i
$631$	2.04974e12	−	3.55025e12i	0.514714	−	0.891511i	−0.485140	−	0.874436i	$-0.661231\pi$
$631$	2.04974e12	−	3.55025e12i	0.514714	−	0.891511i	0.999854	−	0.0170746i	$-0.00543528\pi$
$632$	1.47716e12			0.368298
$633$	5.26120e11	−	9.11267e11i	0.130247	−	0.225595i
$634$	−1.63783e12	−	2.83680e12i	−0.402593	−	0.697311i
$635$	−5.23881e10	−	9.07389e10i	−0.0127865	−	0.0221468i
$636$	4.46971e12			1.08323
$637$	−3.32257e12	+	7.53540e11i	−0.799552	+	0.181334i
$638$	3.21091e11			0.0767246
$639$	2.28743e12	+	3.96195e12i	0.542744	+	0.940060i
$640$	−3.45554e10	−	5.98517e10i	−0.00814153	−	0.0141015i
$641$	8.42548e9	−	1.45934e10i	0.00197121	−	0.00341424i	−0.865038	−	0.501706i	$-0.832706\pi$
$641$	8.42548e9	−	1.45934e10i	0.00197121	−	0.00341424i	0.867009	+	0.498292i	$0.166039\pi$
$642$	−3.60365e11			−0.0837210
$643$	1.22238e12	−	2.11723e12i	0.282006	−	0.488449i	−0.689873	−	0.723931i	$-0.742333\pi$
$643$	1.22238e12	−	2.11723e12i	0.282006	−	0.488449i	0.971879	+	0.235482i	$0.0756668\pi$
$644$	1.51817e11	−	2.62956e11i	0.0347805	−	0.0602415i
$645$	2.19267e11			0.0498831
$646$	−8.47770e11	+	1.46838e12i	−0.191528	+	0.331736i
$647$	−9.94023e11	−	1.72170e12i	−0.223012	−	0.386267i	0.732709	−	0.680542i	$-0.238255\pi$
$647$	−9.94023e11	−	1.72170e12i	−0.223012	−	0.386267i	−0.955721	+	0.294274i	$0.904922\pi$
$648$	−2.22183e12	−	3.84831e12i	−0.495020	−	0.857399i
$649$	−4.47583e11			−0.0990313
$650$	−2.36257e12	+	5.35817e11i	−0.519127	+	0.117735i
$651$	−1.58008e12			−0.344798
$652$	−7.62360e11	−	1.32045e12i	−0.165214	−	0.286158i
$653$	1.76677e12	+	3.06013e12i	0.380251	+	0.658614i	0.991098	−	0.133134i	$-0.0425042\pi$
$653$	1.76677e12	+	3.06013e12i	0.380251	+	0.658614i	−0.610847	+	0.791749i	$0.709171\pi$
$654$	−1.48665e12	+	2.57495e12i	−0.317767	+	0.550389i
$655$	−6.99027e9			−0.00148391
$656$	−7.03952e11	+	1.21928e12i	−0.148414	+	0.257061i
$657$	−1.47242e11	+	2.55031e11i	−0.0308310	+	0.0534009i
$658$	7.88792e11			0.164039
$659$	−1.23577e12	+	2.14042e12i	−0.255243	+	0.442093i	−0.964961	−	0.262392i	$-0.915489\pi$
$659$	−1.23577e12	+	2.14042e12i	−0.255243	+	0.442093i	0.709719	+	0.704485i	$0.248822\pi$
$660$	−4.48394e9	−	7.76642e9i	−0.000919840	−	0.00159321i
$661$	−1.55213e12	−	2.68837e12i	−0.316244	−	0.547751i	0.663457	−	0.748214i	$-0.269089\pi$
$661$	−1.55213e12	−	2.68837e12i	−0.316244	−	0.547751i	−0.979701	+	0.200464i	$0.935755\pi$
$662$	−2.22910e12			−0.451096
$663$	1.49195e12	−	4.81323e12i	0.299877	−	0.967444i
$664$	−3.86168e12			−0.770938
$665$	−1.97707e10	−	3.42439e10i	−0.00392035	−	0.00679025i
$666$	1.53858e12	+	2.66489e12i	0.303030	+	0.524863i
$667$	−8.53328e11	+	1.47801e12i	−0.166936	+	0.289141i
$668$	−9.02452e11			−0.175360
$669$	−2.62822e12	+	4.55222e12i	−0.507277	+	0.878629i
$670$	−3.16950e10	+	5.48973e10i	−0.00607651	+	0.0105248i
$671$	1.02730e11			0.0195635
$672$	−1.60613e12	+	2.78190e12i	−0.303822	+	0.526235i
$673$	−6.89414e10	−	1.19410e11i	−0.0129543	−	0.0224374i	0.859476	−	0.511177i	$-0.170790\pi$
$673$	−6.89414e10	−	1.19410e11i	−0.0129543	−	0.0224374i	−0.872430	+	0.488739i	$0.837457\pi$
$674$	9.22352e11	+	1.59756e12i	0.172158	+	0.298186i
$675$	6.82054e11			0.126460
$676$	−3.50935e12	+	1.67812e12i	−0.646348	+	0.309074i
$677$	−4.78263e12			−0.875020			−0.437510	−	0.899213i	$-0.644140\pi$
$677$	−4.78263e12			−0.875020			−0.437510	+	0.899213i	$0.644140\pi$
$678$	1.96081e12	+	3.39623e12i	0.356371	+	0.617253i
$679$	−5.11069e11	−	8.85198e11i	−0.0922711	−	0.159818i
$680$	3.51748e10	−	6.09245e10i	0.00630872	−	0.0109270i
$681$	1.07463e13			1.91468
$682$	8.73264e10	−	1.51254e11i	0.0154567	−	0.0267717i
$683$	−3.78418e12	+	6.55439e12i	−0.665393	+	1.15250i	0.313785	+	0.949494i	$0.398403\pi$
$683$	−3.78418e12	+	6.55439e12i	−0.665393	+	1.15250i	−0.979178	+	0.203001i	$0.934930\pi$
$684$	3.65560e12			0.638566
$685$	−8.60359e10	+	1.49018e11i	−0.0149304	+	0.0258602i
$686$	1.19287e12	+	2.06612e12i	0.205653	+	0.356202i
$687$	−1.64784e12	−	2.85414e12i	−0.282234	−	0.488843i
$688$	−2.58930e12			−0.440590
$689$	1.91684e12	−	6.18397e12i	0.324040	−	1.04540i
$690$	−1.88653e10			−0.00316842
$691$	−4.43933e12	−	7.68915e12i	−0.740742	−	1.28300i	−0.952158	−	0.305606i	$-0.901141\pi$
$691$	−4.43933e12	−	7.68915e12i	−0.740742	−	1.28300i	0.211417	−	0.977396i	$-0.432192\pi$
$692$	3.43439e12	+	5.94853e12i	0.569340	+	0.986126i
$693$	−1.15552e11	+	2.00142e11i	−0.0190317	+	0.0329639i
$694$	1.73183e12			0.283393
$695$	−5.35926e10	+	9.28252e10i	−0.00871312	+	0.0150916i
$696$	5.70433e12	−	9.88018e12i	0.921431	−	1.59597i
$697$	−5.90244e12			−0.947292
$698$	−4.97853e11	+	8.62306e11i	−0.0793874	+	0.137503i
$699$	−4.23476e12	−	7.33482e12i	−0.670937	−	1.16210i
$700$	−9.65493e11	−	1.67228e12i	−0.151987	−	0.263250i
$701$	−9.16142e12			−1.43295			−0.716476	−	0.697612i	$-0.754246\pi$
$701$	−9.16142e12			−1.43295			−0.716476	+	0.697612i	$0.754246\pi$
$702$	−4.22718e11	+	9.58701e10i	−0.0656952	+	0.0148993i
$703$	7.96047e12			1.22925
$704$	−1.03625e11	−	1.79484e11i	−0.0158997	−	0.0275390i
$705$	6.19141e10	+	1.07238e11i	0.00943927	+	0.0163493i
$706$	2.19569e12	−	3.80305e12i	0.332622	−	0.576118i
$707$	7.04659e11			0.106070
$708$	−3.31897e12	+	5.74863e12i	−0.496425	+	0.859834i
$709$	1.99925e12	−	3.46280e12i	0.297138	−	0.514659i	−0.678342	−	0.734747i	$-0.737301\pi$
$709$	1.99925e12	−	3.46280e12i	0.297138	−	0.514659i	0.975480	+	0.220088i	$0.0706344\pi$
$710$	8.11202e10			0.0119803
$711$	1.24717e12	−	2.16015e12i	0.183025	−	0.317009i
$712$	6.14850e12	+	1.06495e13i	0.896622	+	1.55300i
$713$	4.64156e11	+	8.03942e11i	0.0672607	+	0.116499i
$714$	−1.58971e12			−0.228916
$715$	−1.26680e10	+	2.87303e9i	−0.00181272	+	0.000411115i
$716$	6.76649e12			0.962176
$717$	6.40625e12	+	1.10960e13i	0.905248	+	1.56794i
$718$	−1.33271e12	−	2.30831e12i	−0.187143	−	0.324142i
$719$	5.57631e12	−	9.65845e12i	0.778156	−	1.34781i	−0.154847	−	0.987938i	$-0.549488\pi$
$719$	5.57631e12	−	9.65845e12i	0.778156	−	1.34781i	0.933003	−	0.359868i	$-0.117178\pi$
$720$	−2.83355e10			−0.00392947
$721$	8.55922e11	−	1.48250e12i	0.117958	−	0.204308i
$722$	7.26184e10	−	1.25779e11i	0.00994556	−	0.0172262i
$723$	2.01228e12			0.273883
$724$	1.66906e12	−	2.89089e12i	0.225760	−	0.391028i
$725$	5.42679e12	+	9.39948e12i	0.729495	+	1.26352i
$726$	2.72639e12	+	4.72225e12i	0.364228	+	0.630862i
$727$	−1.01837e13			−1.35207			−0.676036	−	0.736869i	$-0.736304\pi$
$727$	−1.01837e13			−1.35207			−0.676036	+	0.736869i	$0.736304\pi$
$728$	1.99675e12	+	2.15794e12i	0.263470	+	0.284739i
$729$	−6.17091e12			−0.809236
$730$	2.61085e9	+	4.52213e9i	0.000340275	+	0.000589373i
$731$	−5.42764e12	−	9.40094e12i	−0.703044	−	1.21771i
$732$	7.61778e11	−	1.31944e12i	0.0980683	−	0.169859i
$733$	1.13836e13			1.45651			0.728254	−	0.685307i	$-0.240332\pi$
$733$	1.13836e13			1.45651			0.728254	+	0.685307i	$0.240332\pi$
$734$	−3.42335e12	+	5.92942e12i	−0.435331	+	0.754015i
$735$	−8.43629e10	+	1.46121e11i	−0.0106625	+	0.0184680i
$736$	1.88724e12			0.237070
$737$	4.79220e11	−	8.30034e11i	0.0598317	−	0.103632i
$738$	−2.51830e12	−	4.36182e12i	−0.312503	−	0.541270i
$739$	5.65502e12	+	9.79479e12i	0.697484	+	1.20808i	0.969336	+	0.245739i	$0.0790306\pi$
$739$	5.65502e12	+	9.79479e12i	0.697484	+	1.20808i	−0.271852	+	0.962339i	$0.587636\pi$
$740$	−1.37862e11			−0.0169006
$741$	3.29344e12	−	1.06251e13i	0.401298	−	1.29464i
$742$	−2.04243e12			−0.247360
$743$	−5.20665e12	−	9.01819e12i	−0.626771	−	1.08560i	−0.988195	−	0.153198i	$-0.951043\pi$
$743$	−5.20665e12	−	9.01819e12i	−0.626771	−	1.08560i	0.361424	−	0.932402i	$-0.382291\pi$
$744$	−3.10279e12	−	5.37419e12i	−0.371257	−	0.643035i
$745$	1.30664e11	−	2.26317e11i	0.0155401	−	0.0269163i
$746$	−1.56888e12			−0.185466
$747$	−3.26042e12	+	5.64721e12i	−0.383116	+	0.663577i
$748$	−2.21987e11	+	3.84494e11i	−0.0259281	+	0.0449088i
$749$	−4.16059e11			−0.0483044
$750$	−1.19996e11	+	2.07840e11i	−0.0138482	+	0.0239857i
$751$	1.89234e12	+	3.27762e12i	0.217079	+	0.375992i	0.953914	−	0.300081i	$-0.0970136\pi$
$751$	1.89234e12	+	3.27762e12i	0.217079	+	0.375992i	−0.736834	+	0.676073i	$0.763680\pi$
$752$	−7.31138e11	−	1.26637e12i	−0.0833718	−	0.144404i
$753$	−1.39548e13			−1.58179
$754$	−4.68457e12	−	5.06274e12i	−0.527836	−	0.570446i
$755$	−2.40008e11			−0.0268822
$756$	−1.72749e11	−	2.99210e11i	−0.0192339	−	0.0333141i
$757$	2.52840e12	+	4.37932e12i	0.279843	+	0.484703i	0.971346	−	0.237671i	$-0.0763842\pi$
$757$	2.52840e12	+	4.37932e12i	0.279843	+	0.484703i	−0.691502	+	0.722374i	$0.743051\pi$
$758$	2.81718e12	−	4.87950e12i	0.309958	−	0.536863i
$759$	2.85239e11			0.0311975
$760$	7.76472e10	−	1.34489e11i	0.00844238	−	0.0146226i
$761$	6.40170e12	−	1.10881e13i	0.691933	−	1.19846i	−0.279270	−	0.960213i	$-0.590092\pi$
$761$	6.40170e12	−	1.10881e13i	0.691933	−	1.19846i	0.971204	−	0.238251i	$-0.0765742\pi$
$762$	−9.29871e12			−0.999138
$763$	−1.71641e12	+	2.97291e12i	−0.183342	+	0.317557i
$764$	−8.86438e11	−	1.53536e12i	−0.0941300	−	0.163038i
$765$	−5.93962e10	−	1.02877e11i	−0.00627021	−	0.0108603i
$766$	3.61891e12			0.379794
$767$	6.53004e12	+	7.05719e12i	0.681298	+	0.736296i
$768$	−1.04236e13			−1.08117
$769$	8.53888e12	+	1.47898e13i	0.880506	+	1.52508i	0.850780	+	0.525522i	$0.176130\pi$
$769$	8.53888e12	+	1.47898e13i	0.880506	+	1.52508i	0.0297260	+	0.999558i	$0.490537\pi$
$770$	2.04894e9	+	3.54886e9i	0.000210049	+	0.000363815i
$771$	−7.05617e12	+	1.22216e13i	−0.719158	+	1.24562i
$772$	−1.05549e13			−1.06949
$773$	−2.57109e12	+	4.45326e12i	−0.259006	+	0.448612i	−0.965976	−	0.258632i	$-0.916728\pi$
$773$	−2.57109e12	+	4.45326e12i	−0.259006	+	0.448612i	0.706970	+	0.707244i	$0.250062\pi$
$774$	4.63144e12	−	8.02190e12i	0.463855	−	0.803420i
$775$	5.90366e12			0.587846
$776$	2.00717e12	−	3.47651e12i	0.198703	−	0.344164i
$777$	3.73180e12	+	6.46366e12i	0.367302	+	0.636186i
$778$	2.64096e12	+	4.57428e12i	0.258436	+	0.447625i
$779$	−1.30295e13			−1.26767
$780$	−5.70368e10	+	1.84008e11i	−0.00551734	+	0.0177997i
$781$	−1.22652e12			−0.117963
$782$	4.66984e11	+	8.08841e11i	0.0446552	+	0.0773451i
$783$	9.70980e11	+	1.68179e12i	0.0923171	+	0.159898i
$784$	9.96234e11	−	1.72553e12i	0.0941758	−	0.163117i
$785$	2.53976e11			0.0238715
$786$	−3.10187e11	+	5.37260e11i	−0.0289883	+	0.0502092i
$787$	−8.92384e12	+	1.54565e13i	−0.829212	+	1.43624i	0.0694452	+	0.997586i	$0.477877\pi$
$787$	−8.92384e12	+	1.54565e13i	−0.829212	+	1.43624i	−0.898657	+	0.438652i	$0.855456\pi$
$788$	3.86980e12			0.357536
$789$	−7.72687e12	+	1.33833e13i	−0.709835	+	1.22947i
$790$	−2.21144e10	−	3.83032e10i	−0.00202001	−	0.00349875i
$791$	2.26386e12	+	3.92112e12i	0.205615	+	0.356136i
$792$	−9.07635e11			−0.0819687
$793$	−1.49879e12	−	1.61978e12i	−0.134590	−	0.145455i
$794$	−3.57161e12			−0.318913
$795$	−1.60315e11	−	2.77674e11i	−0.0142338	−	0.0246538i
$796$	1.94954e12	+	3.37670e12i	0.172117	+	0.298115i
$797$	9.73888e12	−	1.68682e13i	0.854961	−	1.48084i	−0.0217194	−	0.999764i	$-0.506914\pi$
$797$	9.73888e12	−	1.68682e13i	0.854961	−	1.48084i	0.876681	−	0.481073i	$-0.159753\pi$
$798$	−3.50923e12			−0.306337
$799$	3.06519e12	−	5.30907e12i	0.266071	−	0.460848i
$800$	6.00100e12	−	1.03940e13i	0.517987	−	0.897179i
$801$	2.07648e13			1.78230
$802$	3.46559e12	−	6.00258e12i	0.295796	−	0.512334i
$803$	−3.94755e10	−	6.83735e10i	−0.00335048	−	0.00580321i
$804$	−7.10714e12	−	1.23099e13i	−0.599850	−	1.03897i
$805$	−2.17810e10			−0.00182808
$806$	−3.65892e12	+	8.29823e11i	−0.305383	+	0.0692593i
$807$	−2.19499e12			−0.182181
$808$	1.38373e12	+	2.39669e12i	0.114209	+	0.197816i
$809$	−1.85098e12	−	3.20599e12i	−0.151926	−	0.263144i	0.780009	−	0.625768i	$-0.215214\pi$
$809$	−1.85098e12	−	3.20599e12i	−0.151926	−	0.263144i	−0.931936	+	0.362624i	$0.881881\pi$
$810$	−6.65255e10	+	1.15226e11i	−0.00543007	+	0.00940516i
$811$	3.82292e12			0.310314			0.155157	−	0.987890i	$-0.450412\pi$
$811$	3.82292e12			0.310314			0.155157	+	0.987890i	$0.450412\pi$
$812$	2.74897e12	−	4.76136e12i	0.221905	−	0.384352i
$813$	5.80072e12	−	1.00471e13i	0.465666	−	0.806557i
$814$	−8.24982e11			−0.0658620
$815$	−5.46872e10	+	9.47209e10i	−0.00434186	+	0.00752033i
$816$	1.47351e12	+	2.55220e12i	0.116345	+	0.201516i
$817$	−1.19813e13	−	2.07523e13i	−0.940820	−	1.62955i
$818$	6.34656e12			0.495620
$819$	4.84156e12	−	1.09804e12i	0.376017	−	0.0852786i
$820$	2.25648e11			0.0174289
$821$	−9.60510e12	−	1.66365e13i	−0.737833	−	1.27796i	−0.953469	−	0.301490i	$-0.902516\pi$
$821$	−9.60510e12	−	1.66365e13i	−0.737833	−	1.27796i	0.215637	−	0.976474i	$-0.430817\pi$
$822$	7.63553e12	+	1.32251e13i	0.583332	+	1.01036i
$823$	−5.15137e11	+	8.92243e11i	−0.0391402	+	0.0677929i	−0.884932	−	0.465720i	$-0.845795\pi$
$823$	−5.15137e11	+	8.92243e11i	−0.0391402	+	0.0677929i	0.845792	+	0.533513i	$0.179129\pi$
$824$	6.72307e12			0.508037
$825$	9.06997e11	−	1.57096e12i	0.0681652	−	0.118066i
$826$	1.51660e12	−	2.62683e12i	0.113360	−	0.196346i
$827$	−2.42705e13			−1.80428			−0.902141	−	0.431441i	$-0.858005\pi$
$827$	−2.42705e13			−1.80428			−0.902141	+	0.431441i	$0.858005\pi$
$828$	1.00682e12	−	1.74387e12i	0.0744417	−	0.128937i
$829$	3.95279e12	+	6.84642e12i	0.290675	+	0.503464i	0.973970	−	0.226679i	$-0.0727868\pi$
$829$	3.95279e12	+	6.84642e12i	0.290675	+	0.503464i	−0.683294	+	0.730143i	$0.739453\pi$
$830$	5.78128e10	+	1.00135e11i	0.00422836	+	0.00732374i
$831$	3.62592e13			2.63763
$832$	−1.31814e12	+	4.25248e12i	−0.0953685	+	0.307672i
$833$	8.35314e12			0.601101
$834$	4.75625e12	+	8.23807e12i	0.340422	+	0.589628i
$835$	3.23683e10	+	5.60635e10i	0.00230425	+	0.00399109i
$836$	−4.90031e11	+	8.48758e11i	−0.0346972	+	0.0600974i
$837$	1.05630e12			0.0743916
$838$	2.47755e12	−	4.29123e12i	0.173550	−	0.300597i
$839$	−2.83505e12	+	4.91045e12i	−0.197529	+	0.342131i	−0.947727	−	0.319083i	$-0.896625\pi$
$839$	−2.83505e12	+	4.91045e12i	−0.197529	+	0.342131i	0.750197	+	0.661214i	$0.229958\pi$
$840$	1.45601e11			0.0100904
$841$	−8.19770e12	+	1.41988e13i	−0.565080	+	0.978748i
$842$	−8.17864e11	−	1.41658e12i	−0.0560759	−	0.0971264i
$843$	−4.51383e12	−	7.81818e12i	−0.307837	−	0.533190i
$844$	1.99152e12			0.135096
$845$	2.30120e11	+	1.57824e11i	0.0155274	+	0.0106492i
$846$	5.23111e12			0.351097
$847$	3.14776e12	+	5.45208e12i	0.210148	+	0.363988i
$848$	1.89315e12	+	3.27903e12i	0.125720	+	0.217753i
$849$	−1.72787e13	+	2.99275e13i	−1.14137	+	1.97691i
$850$	5.93963e12			0.390278
$851$	2.19247e12	−	3.79746e12i	0.143301	−	0.248205i
$852$	−9.09501e12	+	1.57530e13i	−0.591324	+	1.02420i
$853$	−2.15853e13			−1.39601			−0.698004	−	0.716094i	$-0.745928\pi$
$853$	−2.15853e13			−1.39601			−0.698004	+	0.716094i	$0.745928\pi$
$854$	−3.48094e11	+	6.02917e11i	−0.0223943	+	0.0387880i
$855$	−1.31115e11	−	2.27098e11i	−0.00839085	−	0.0145334i
$856$	−8.17012e11	−	1.41511e12i	−0.0520112	−	0.0900860i
$857$	−3.77284e12			−0.238921			−0.119461	−	0.992839i	$-0.538117\pi$
$857$	−3.77284e12			−0.238921			−0.119461	+	0.992839i	$0.538117\pi$
$858$	−3.41315e11	+	1.10113e12i	−0.0215012	+	0.0693657i
$859$	3.98337e12			0.249621			0.124811	−	0.992181i	$-0.460168\pi$
$859$	3.98337e12			0.249621			0.124811	+	0.992181i	$0.460168\pi$
$860$	2.07497e11	+	3.59395e11i	0.0129351	+	0.0224042i
$861$	−6.10809e12	−	1.05795e13i	−0.378784	−	0.656073i
$862$	4.70814e12	−	8.15473e12i	0.290447	−	0.503068i
$863$	−2.30035e13			−1.41171			−0.705856	−	0.708355i	$-0.749438\pi$
$863$	−2.30035e13			−1.41171			−0.705856	+	0.708355i	$0.749438\pi$
$864$	1.07372e12	−	1.85973e12i	0.0655509	−	0.113537i
$865$	2.46362e11	−	4.26712e11i	0.0149624	−	0.0259157i
$866$	1.81911e12			0.109908
$867$	5.31445e12	−	9.20490e12i	0.319428	−	0.553265i
$868$	−1.49527e12	−	2.58988e12i	−0.0894087	−	0.154860i
$869$	3.34364e11	+	5.79135e11i	0.0198898	+	0.0344501i
$870$	−3.41596e11			−0.0202151
$871$	−2.00790e13	+	4.55381e12i	−1.18212	+	0.268098i
$872$	−1.34820e13			−0.789643
$873$	−3.38930e12	−	5.87045e12i	−0.197491	−	0.342064i
$874$	1.03085e12	+	1.78549e12i	0.0597580	+	0.103504i
$875$	−1.38542e11	+	2.39962e11i	−0.00798997	+	0.0138390i
$876$	−1.17089e12			−0.0671813
$877$	8.98012e12	−	1.55540e13i	0.512606	−	0.887860i	−0.487287	−	0.873242i	$-0.662013\pi$
$877$	8.98012e12	−	1.55540e13i	0.512606	−	0.887860i	0.999893	−	0.0146179i	$-0.00465319\pi$
$878$	−6.39111e12	+	1.10697e13i	−0.362954	+	0.628654i
$879$	2.18040e13			1.23193
$880$	3.79835e9	−	6.57894e9i	0.000213513	−	0.000369815i
$881$	8.96850e11	+	1.55339e12i	0.0501566	+	0.0868738i	0.890014	−	0.455934i	$-0.150695\pi$
$881$	8.96850e11	+	1.55339e12i	0.0501566	+	0.0868738i	−0.839857	+	0.542808i	$0.817361\pi$
$882$	3.56390e12	+	6.17286e12i	0.198297	+	0.343461i
$883$	2.83251e13			1.56801			0.784005	−	0.620754i	$-0.213173\pi$
$883$	2.83251e13			1.56801			0.784005	+	0.620754i	$0.213173\pi$
$884$	9.30113e12	−	2.10945e12i	0.512272	−	0.116180i
$885$	4.76166e11			0.0260924
$886$	−2.46581e12	−	4.27091e12i	−0.134434	−	0.232846i
$887$	1.57128e12	+	2.72154e12i	0.0852309	+	0.147624i	0.905490	−	0.424368i	$-0.139504\pi$
$887$	1.57128e12	+	2.72154e12i	0.0852309	+	0.147624i	−0.820259	+	0.571993i	$0.806171\pi$
$888$	−1.46562e13	+	2.53853e13i	−0.790975	+	1.37001i
$889$	−1.07358e13			−0.576471
$890$	1.84097e11	−	3.18866e11i	0.00983541	−	0.0170354i
$891$	1.00585e12	−	1.74218e12i	0.0534666	−	0.0926069i
$892$	−9.94859e12			−0.526162
$893$	6.76632e12	−	1.17196e13i	0.356058	−	0.616711i
$894$	−1.15962e13	−	2.00853e13i	−0.607153	−	1.05162i
$895$	−2.42694e11	−	4.20358e11i	−0.0126431	−	0.0218985i
$896$	−7.08139e12			−0.367056
$897$	−4.16151e12	−	4.49745e12i	−0.214627	−	0.231953i
$898$	−9.71390e12			−0.498483
$899$	8.40451e12	+	1.45570e13i	0.429135	+	0.743284i
$900$	−6.40295e12	−	1.10902e13i	−0.325303	−	0.563442i
$901$	−7.93675e12	+	1.37469e13i	−0.401219	+	0.694931i
$902$	1.35031e12			0.0679208
$903$	1.12335e13	−	1.94570e13i	0.562238	−	0.973825i
$904$	−8.89104e12	+	1.53997e13i	−0.442787	+	0.766929i
$905$	−2.39456e11			−0.0118661
$906$	−1.06501e13	+	1.84466e13i	−0.525144	+	0.909577i
$907$	−7.71044e12	−	1.33549e13i	−0.378309	−	0.655250i	0.612508	−	0.790465i	$-0.290161\pi$
$907$	−7.71044e12	−	1.33549e13i	−0.378309	−	0.655250i	−0.990816	+	0.135215i	$0.956828\pi$
$908$	1.01695e13	+	1.76140e13i	0.496491	+	0.859948i
$909$	4.67315e12			0.227024
$910$	2.60630e10	−	8.40826e10i	0.00125990	−	0.00406462i
$911$	3.52370e13			1.69499			0.847493	−	0.530806i	$-0.178111\pi$
$911$	3.52370e13			1.69499			0.847493	+	0.530806i	$0.178111\pi$
$912$	3.25274e12	+	5.63391e12i	0.155694	+	0.269670i
$913$	−8.74114e11	−	1.51401e12i	−0.0416342	−	0.0721125i
$914$	8.76815e12	−	1.51869e13i	0.415576	−	0.719798i
$915$	−1.09291e11			−0.00515453
$916$	3.11877e12	−	5.40187e12i	0.146371	−	0.253521i
$917$	−3.58127e11	+	6.20294e11i	−0.0167253	+	0.0289691i
$918$	1.06274e12			0.0493895
$919$	6.46942e12	−	1.12054e13i	0.299189	−	0.518210i	−0.676762	−	0.736202i	$-0.736617\pi$
$919$	6.46942e12	−	1.12054e13i	0.299189	−	0.518210i	0.975951	+	0.217992i	$0.0699506\pi$
$920$	−4.27711e10	−	7.40817e10i	−0.00196836	−	0.00340930i
$921$	9.88845e12	+	1.71273e13i	0.452856	+	0.784369i
$922$	5.37496e12			0.244955
$923$	1.78944e13	+	1.93389e13i	0.811537	+	0.877049i
$924$	−9.18888e11			−0.0414705
$925$	−1.39431e13	−	2.41502e13i	−0.626214	−	1.08463i
$926$	−7.59468e12	−	1.31544e13i	−0.339437	−	0.587923i
$927$	5.67630e12	−	9.83163e12i	0.252468	−	0.437287i
$928$	3.41723e13			1.51255
$929$	−1.89370e13	+	3.27999e13i	−0.834144	+	1.44478i	0.0605812	+	0.998163i	$0.480705\pi$
$929$	−1.89370e13	+	3.27999e13i	−0.834144	+	1.44478i	−0.894725	+	0.446617i	$0.852629\pi$
$930$	−9.29032e10	+	1.60913e11i	−0.00407246	+	0.00705372i
$931$	1.84393e13			0.804398
$932$	8.01490e12	−	1.38822e13i	0.347958	−	0.602680i
$933$	−2.06920e13	−	3.58396e13i	−0.893994	−	1.54844i
$934$	−5.47752e12	−	9.48734e12i	−0.235517	−	0.407928i
$935$	3.18481e10			0.00136280
$936$	1.32420e13	+	1.43110e13i	0.563913	+	0.609436i
$937$	7.79793e12			0.330484			0.165242	−	0.986253i	$-0.447159\pi$
$937$	7.79793e12			0.330484			0.165242	+	0.986253i	$0.447159\pi$
$938$	3.24761e12	+	5.62502e12i	0.136978	+	0.237253i
$939$	−1.55438e12	−	2.69227e12i	−0.0652473	−	0.113012i
$940$	−1.17181e11	+	2.02964e11i	−0.00489534	+	0.00847899i
$941$	−2.87425e13			−1.19501			−0.597505	−	0.801866i	$-0.703841\pi$
$941$	−2.87425e13			−1.19501			−0.597505	+	0.801866i	$0.703841\pi$
$942$	1.12700e13	−	1.95202e13i	0.466330	−	0.807708i
$943$	−3.58856e12	+	6.21558e12i	−0.147781	+	0.255964i
$944$	−5.62301e12			−0.230460
$945$	−1.23920e10	+	2.14636e10i	−0.000505473	+	0.000875505i
$946$	1.24169e12	+	2.15066e12i	0.0504082	+	0.0873096i
$947$	1.58428e13	+	2.74405e13i	0.640114	+	1.10871i	0.985407	+	0.170215i	$0.0544461\pi$
$947$	1.58428e13	+	2.74405e13i	0.640114	+	1.10871i	−0.345293	+	0.938495i	$0.612221\pi$
$948$	9.91765e12			0.398815
$949$	−5.02137e11	+	1.61996e12i	−0.0200967	+	0.0648346i
$950$	1.31116e13			0.522274
$951$	−2.63449e13	−	4.56308e13i	−1.04444	−	1.80903i
$952$	−3.60416e12	−	6.24258e12i	−0.142212	−	0.246319i
$953$	1.85175e13	−	3.20732e13i	0.727217	−	1.25958i	−0.230838	−	0.972992i	$-0.574147\pi$
$953$	1.85175e13	−	3.20732e13i	0.727217	−	1.25958i	0.958055	−	0.286584i	$-0.0925198\pi$
$954$	−1.35450e13			−0.529433
$955$	−6.35878e10	+	1.10137e11i	−0.00247376	+	0.00428469i
$956$	−1.21248e13	+	2.10007e13i	−0.469475	+	0.813155i
$957$	5.16484e12			0.199046
$958$	−4.47171e12	+	7.74523e12i	−0.171526	+	0.297091i
$959$	8.81561e12	+	1.52691e13i	0.336565	+	0.582947i
$960$	1.10243e11	+	1.90946e11i	0.00418918	+	0.00725587i
$961$	−1.72966e13			−0.654192
$962$	1.20361e13	+	1.30078e13i	0.453105	+	0.489682i
$963$	−2.75922e12			−0.103387
$964$	1.90426e12	+	3.29828e12i	0.0710199	+	0.123010i
$965$	3.78574e11	+	6.55710e11i	0.0140533	+	0.0243410i
$966$	−9.66511e11	+	1.67405e12i	−0.0357116	+	0.0618543i
$967$	−3.53275e12			−0.129925			−0.0649627	−	0.997888i	$-0.520693\pi$
$967$	−3.53275e12			−0.129925			−0.0649627	+	0.997888i	$0.520693\pi$
$968$	−1.23625e13	+	2.14124e13i	−0.452549	+	0.783838i
$969$	−1.36366e13	+	2.36194e13i	−0.496879	+	0.860619i
$970$	−1.20196e11			−0.00435932
$971$	−6.73610e12	+	1.16673e13i	−0.243177	+	0.421194i	−0.961617	−	0.274394i	$-0.911523\pi$
$971$	−6.73610e12	+	1.16673e13i	−0.243177	+	0.421194i	0.718441	+	0.695588i	$0.244856\pi$
$972$	−1.36562e13	−	2.36533e13i	−0.490719	−	0.849951i
$973$	5.49133e12	+	9.51127e12i	0.196413	+	0.340197i
$974$	−1.53528e13			−0.546604
$975$	−3.80026e13	+	8.61878e12i	−1.34677	+	0.305439i
$976$	1.29061e12			0.0455271
$977$	−6.20621e12	−	1.07495e13i	−0.217922	−	0.377452i	0.736251	−	0.676709i	$-0.236594\pi$
$977$	−6.20621e12	−	1.07495e13i	−0.217922	−	0.377452i	−0.954172	+	0.299257i	$0.903261\pi$
$978$	4.85339e12	+	8.40631e12i	0.169637	+	0.293820i
$979$	−2.78350e12	+	4.82117e12i	−0.0968434	+	0.167738i
$980$	−3.19338e11			−0.0110594
$981$	−1.13829e13	+	1.97157e13i	−0.392412	+	0.679677i
$982$	−9.65485e12	+	1.67227e13i	−0.331317	+	0.573858i
$983$	1.24049e13			0.423743			0.211871	−	0.977298i	$-0.432044\pi$
$983$	1.24049e13			0.423743			0.211871	+	0.977298i	$0.432044\pi$
$984$	2.39888e13	−	4.15499e13i	0.815701	−	1.41284i
$985$	−1.38798e11	−	2.40405e11i	−0.00469808	−	0.00813731i
$986$	8.45572e12	+	1.46457e13i	0.284908	+	0.493475i
$987$	1.26880e13			0.425564
$988$	2.05320e13	−	4.65654e12i	0.685527	−	0.155474i
$989$	−1.31996e13			−0.438709
$990$	1.35881e10	+	2.35353e10i	0.000449574	+	0.000778685i
$991$	1.88843e13	+	3.27085e13i	0.621969	+	1.07728i	0.989119	+	0.147120i	$0.0470005\pi$
$991$	1.88843e13	+	3.27085e13i	0.621969	+	1.07728i	−0.367149	+	0.930162i	$0.619666\pi$
$992$	9.29379e12	−	1.60973e13i	0.304712	−	0.527777i
$993$	−3.58558e13			−1.17028
$994$	4.15597e12	−	7.19834e12i	0.135031	−	0.233880i
$995$	1.39848e11	−	2.42224e11i	0.00452327	−	0.00783454i
$996$	−2.59273e13			−0.834816
$997$	1.36307e13	−	2.36090e13i	0.436908	−	0.756746i	−0.560542	−	0.828126i	$-0.689407\pi$
$997$	1.36307e13	−	2.36090e13i	0.436908	−	0.756746i	0.997449	+	0.0713801i	$0.0227403\pi$
$998$	5.82178e12	+	1.00836e13i	0.185767	+	0.321758i
$999$	−2.49475e12	−	4.32104e12i	−0.0792469	−	0.137260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.c.a.3.4	✓	18
13.3	even	3		169.10.a.c.1.6		9
13.9	even	3	inner	13.10.c.a.9.4	yes	18
13.10	even	6		169.10.a.d.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.4	✓	18	1.1	even	1	trivial
13.10.c.a.9.4	yes	18	13.9	even	3	inner
169.10.a.c.1.6		9	13.3	even	3
169.10.a.d.1.4		9	13.10	even	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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	13.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.02454 - 10.4348i) q^{2} +(-96.9066 - 167.847i) q^{3} +(183.410 - 317.675i) q^{4} -26.3134 q^{5} +(-1167.64 + 2022.40i) q^{6} +(-1348.09 + 2334.97i) q^{7} -10589.0 q^{8} +(-8940.28 + 15485.0i) q^{9} +(158.526 + 274.576i) q^{10} +(-2396.88 - 4151.52i) q^{11} -71094.5 q^{12} +(-30488.9 + 98361.2i) q^{13} +32486.6 q^{14} +(2549.95 + 4416.64i) q^{15} +(-30112.1 - 52155.7i) q^{16} +(126241. - 218655. i) q^{17} +215444. q^{18} +(278673. - 482675. i) q^{19} +(-4826.14 + 8359.13i) q^{20} +522557. q^{21} +(-28880.2 + 50022.0i) q^{22} +(-153504. - 265876. i) q^{23} +(1.02614e6 + 1.77733e6i) q^{24} -1.95243e6 q^{25} +(1.21006e6 - 274435. i) q^{26} -349336. q^{27} +(494508. + 856512. i) q^{28} +(-2.77950e6 - 4.81424e6i) q^{29} +(30724.5 - 53216.4i) q^{30} -3.02375e6 q^{31} +(-3.07360e6 + 5.32363e6i) q^{32} +(-464547. + 804619. i) q^{33} -3.04217e6 q^{34} +(35473.0 - 61441.1i) q^{35} +(3.27947e6 + 5.68021e6i) q^{36} +(7.14141e6 + 1.23693e7i) q^{37} -6.71550e6 q^{38} +(1.94642e7 - 4.41438e6i) q^{39} +278632. q^{40} +(-1.16889e7 - 2.02457e7i) q^{41} +(-3.14817e6 - 5.45279e6i) q^{42} +(2.14972e7 - 3.72342e7i) q^{43} -1.75845e6 q^{44} +(235250. - 407464. i) q^{45} +(-1.84958e6 + 3.20356e6i) q^{46} +2.42805e7 q^{47} +(-5.83613e6 + 1.01085e7i) q^{48} +(1.65421e7 + 2.86517e7i) q^{49} +(1.17625e7 + 2.03733e7i) q^{50} -4.89343e7 q^{51} +(2.56549e7 + 2.77260e7i) q^{52} -6.28700e7 q^{53} +(2.10459e6 + 3.64525e6i) q^{54} +(63070.2 + 109241. i) q^{55} +(1.42749e7 - 2.47249e7i) q^{56} -1.08021e8 q^{57} +(-3.34905e7 + 5.80072e7i) q^{58} +(4.66839e7 - 8.08590e7i) q^{59} +1.87074e6 q^{60} +(-1.07150e7 + 1.85589e7i) q^{61} +(1.82167e7 + 3.15522e7i) q^{62} +(-2.41047e7 - 4.17506e7i) q^{63} +4.32333e7 q^{64} +(802268. - 2.58822e6i) q^{65} +1.11947e7 q^{66} +(9.99675e7 + 1.73149e8i) q^{67} +(-4.63076e7 - 8.02071e7i) q^{68} +(-2.97510e7 + 5.15303e7i) q^{69} -854835. q^{70} +(1.27929e8 - 2.21579e8i) q^{71} +(9.46684e7 - 1.63970e8i) q^{72} +1.64695e7 q^{73} +(8.60475e7 - 1.49039e8i) q^{74} +(1.89204e8 + 3.27710e8i) q^{75} +(-1.02223e8 - 1.77055e8i) q^{76} +1.29249e7 q^{77} +(-1.63326e8 - 1.76511e8i) q^{78} -1.39500e8 q^{79} +(792354. + 1.37240e6i) q^{80} +(2.09825e8 + 3.63427e8i) q^{81} +(-1.40840e8 + 2.43942e8i) q^{82} +3.64688e8 q^{83} +(9.58421e7 - 1.66003e8i) q^{84} +(-3.32183e6 + 5.75358e6i) q^{85} -5.18042e8 q^{86} +(-5.38704e8 + 9.33064e8i) q^{87} +(2.53805e7 + 4.39603e7i) q^{88} +(-5.80652e8 - 1.00572e9i) q^{89} -5.66909e6 q^{90} +(-1.88568e8 - 2.03791e8i) q^{91} -1.12616e8 q^{92} +(2.93021e8 + 5.07527e8i) q^{93} +(-1.46279e8 - 2.53363e8i) q^{94} +(-7.33284e6 + 1.27009e7i) q^{95} +1.19141e9 q^{96} +(-1.89552e8 + 3.28314e8i) q^{97} +(1.99317e8 - 3.45227e8i) q^{98} +8.57151e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 15 q^{2} + 161 q^{3} - 1793 q^{4} - 2280 q^{5} + 2118 q^{6} - 1939 q^{7} - 14478 q^{8} - 33654 q^{9} + 46923 q^{10} - 5433 q^{11} + 8712 q^{12} - 212524 q^{13} - 9900 q^{14} - 347428 q^{15} + 400127 q^{16}+ \cdots + 2262149268 q^{99}+O(q^{100}) \) 18 * q + 15 * q^2 + 161 * q^3 - 1793 * q^4 - 2280 * q^5 + 2118 * q^6 - 1939 * q^7 - 14478 * q^8 - 33654 * q^9 + 46923 * q^10 - 5433 * q^11 + 8712 * q^12 - 212524 * q^13 - 9900 * q^14 - 347428 * q^15 + 400127 * q^16 + 248589 * q^17 - 38738 * q^18 - 311001 * q^19 + 927069 * q^20 + 1553030 * q^21 + 1857242 * q^22 + 591609 * q^23 - 4492800 * q^24 + 7008998 * q^25 - 3801525 * q^26 - 11603482 * q^27 + 2697168 * q^28 + 11014155 * q^29 - 6597836 * q^30 - 23148076 * q^31 - 11868417 * q^32 + 14131427 * q^33 + 21859862 * q^34 + 21112794 * q^35 + 10792871 * q^36 - 29215749 * q^37 + 14572188 * q^38 - 71569875 * q^39 + 27322222 * q^40 + 3328377 * q^41 + 39828306 * q^42 + 6074381 * q^43 + 31824624 * q^44 + 32857342 * q^45 + 36693338 * q^46 - 45575052 * q^47 - 30270064 * q^48 + 10293266 * q^49 - 49601730 * q^50 - 136587494 * q^51 - 35278230 * q^52 - 29480016 * q^53 + 152965386 * q^54 - 18710998 * q^55 - 7665444 * q^56 + 523363230 * q^57 - 163479359 * q^58 - 32715855 * q^59 - 188638416 * q^60 - 220502845 * q^61 - 59980476 * q^62 + 166572574 * q^63 - 924604030 * q^64 + 128091756 * q^65 - 48128076 * q^66 + 112659045 * q^67 - 238942419 * q^68 + 86003951 * q^69 + 2040150992 * q^70 - 236450709 * q^71 + 995206683 * q^72 - 211881220 * q^73 - 455580507 * q^74 + 968954813 * q^75 - 365789708 * q^76 - 2399230890 * q^77 - 441111970 * q^78 - 817519096 * q^79 + 580424625 * q^80 + 176914851 * q^81 + 941792217 * q^82 + 2225691456 * q^83 - 1819004068 * q^84 + 1812284636 * q^85 + 291320076 * q^86 + 69564799 * q^87 + 3178375740 * q^88 - 1154379039 * q^89 - 10225809510 * q^90 - 1658338903 * q^91 - 4545506592 * q^92 + 3136878060 * q^93 + 2755131560 * q^94 + 1779441012 * q^95 + 5906965568 * q^96 - 3616470111 * q^97 + 8263323501 * q^98 + 2262149268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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