LMFDB - Embedded newform 63.10.f.a.22.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,10,Mod(22,63)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.4472576783$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$27$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.18
Character	$\chi$	$=$	63.22
Dual form			63.10.f.a.43.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.17786 + 10.7004i) q^{2} +(-138.713 - 21.0197i) q^{3} +(179.668 - 311.194i) q^{4} +(571.192 - 989.334i) q^{5} +(-632.028 - 1614.13i) q^{6} +(-1200.50 - 2079.33i) q^{7} +10766.0 q^{8} +(18799.3 + 5831.40i) q^{9} +14115.0 q^{10} +(19722.7 + 34160.7i) q^{11} +(-31463.5 + 39390.0i) q^{12} +(61487.6 - 106500. i) q^{13} +(14833.0 - 25691.6i) q^{14} +(-100027. + 125227. i) q^{15} +(-25479.4 - 44131.6i) q^{16} -375638. q^{17} +(53741.6 + 237185. i) q^{18} +335848. q^{19} +(-205250. - 355504. i) q^{20} +(122818. + 313663. i) q^{21} +(-243688. + 422079. i) q^{22} +(-204101. + 353512. i) q^{23} +(-1.49338e6 - 226298. i) q^{24} +(324042. + 561256. i) q^{25} +1.51945e6 q^{26} +(-2.48513e6 - 1.20405e6i) q^{27} -862767. q^{28} +(-1.47383e6 - 2.55276e6i) q^{29} +(-1.95792e6 - 296693. i) q^{30} +(4.34457e6 - 7.52502e6i) q^{31} +(3.07091e6 - 5.31897e6i) q^{32} +(-2.01773e6 - 5.15308e6i) q^{33} +(-2.32064e6 - 4.01946e6i) q^{34} -2.74286e6 q^{35} +(5.19234e6 - 4.80253e6i) q^{36} -5.75180e6 q^{37} +(2.07482e6 + 3.59369e6i) q^{38} +(-1.07677e7 + 1.34804e7i) q^{39} +(6.14944e6 - 1.06512e7i) q^{40} +(5.76664e6 - 9.98811e6i) q^{41} +(-2.59756e6 + 3.25196e6i) q^{42} +(-5.56585e6 - 9.64034e6i) q^{43} +1.41741e7 q^{44} +(1.65072e7 - 1.52680e7i) q^{45} -5.04361e6 q^{46} +(591114. + 1.02384e6i) q^{47} +(2.60668e6 + 6.65718e6i) q^{48} +(-2.88240e6 + 4.99246e6i) q^{49} +(-4.00376e6 + 6.93472e6i) q^{50} +(5.21057e7 + 7.89581e6i) q^{51} +(-2.20947e7 - 3.82692e7i) q^{52} -5.26811e7 q^{53} +(-2.46906e6 - 3.40302e7i) q^{54} +4.50617e7 q^{55} +(-1.29246e7 - 2.23860e7i) q^{56} +(-4.65863e7 - 7.05943e6i) q^{57} +(1.82103e7 - 3.15411e7i) q^{58} +(-9.90739e6 + 1.71601e7i) q^{59} +(2.09982e7 + 5.36271e7i) q^{60} +(-6.42197e7 - 1.11232e8i) q^{61} +1.07361e8 q^{62} +(-1.04432e7 - 4.60906e7i) q^{63} +4.97956e7 q^{64} +(-7.02424e7 - 1.21663e8i) q^{65} +(4.26745e7 - 5.34254e7i) q^{66} +(4.33821e7 - 7.51399e7i) q^{67} +(-6.74902e7 + 1.16896e8i) q^{68} +(3.57420e7 - 4.47465e7i) q^{69} +(-1.69450e7 - 2.93496e7i) q^{70} -1.69345e8 q^{71} +(2.02393e8 + 6.27807e7i) q^{72} -4.63053e8 q^{73} +(-3.55338e7 - 6.15463e7i) q^{74} +(-3.31512e7 - 8.46646e7i) q^{75} +(6.03411e7 - 1.04514e8i) q^{76} +(4.73541e7 - 8.20197e7i) q^{77} +(-2.10766e8 - 3.19383e7i) q^{78} +(1.90054e6 + 3.29183e6i) q^{79} -5.82145e7 q^{80} +(3.19410e8 + 2.19253e8i) q^{81} +1.42502e8 q^{82} +(1.26507e8 + 2.19117e8i) q^{83} +(1.19677e8 + 1.81351e7i) q^{84} +(-2.14562e8 + 3.71632e8i) q^{85} +(6.87701e7 - 1.19113e8i) q^{86} +(1.50781e8 + 3.85079e8i) q^{87} +(2.12334e8 + 3.67773e8i) q^{88} -1.32273e8 q^{89} +(2.65352e8 + 8.23101e7i) q^{90} -2.95263e8 q^{91} +(7.33407e7 + 1.27030e8i) q^{92} +(-7.60820e8 + 9.52493e8i) q^{93} +(-7.30363e6 + 1.26503e7i) q^{94} +(1.91834e8 - 3.32265e8i) q^{95} +(-5.37777e8 + 6.73258e8i) q^{96} +(2.80121e8 + 4.85183e8i) q^{97} -7.12282e7 q^{98} +(1.71569e8 + 7.57209e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 48 q^{2} + 9 q^{3} - 6912 q^{4} - 1704 q^{5} - 540 q^{6} - 64827 q^{7} + 64650 q^{8} - 13275 q^{9} - 150009 q^{11} - 6156 q^{12} - 89478 q^{13} - 115248 q^{14} - 582588 q^{15} - 1769472 q^{16} + 924474 q^{17}+ \cdots - 5802933888 q^{99}+O(q^{100}) $ 54 * q - 48 * q^2 + 9 * q^3 - 6912 * q^4 - 1704 * q^5 - 540 * q^6 - 64827 * q^7 + 64650 * q^8 - 13275 * q^9 - 150009 * q^11 - 6156 * q^12 - 89478 * q^13 - 115248 * q^14 - 582588 * q^15 - 1769472 * q^16 + 924474 * q^17 + 3376359 * q^18 + 393930 * q^19 - 3569484 * q^20 - 540225 * q^21 + 1941084 * q^22 - 3948384 * q^23 - 529722 * q^24 - 8984061 * q^25 + 3000666 * q^26 + 9578520 * q^27 + 33191424 * q^28 - 7872498 * q^29 - 35915508 * q^30 - 1544562 * q^31 - 12651633 * q^32 + 17162955 * q^33 + 3122550 * q^34 + 8182608 * q^35 + 8496774 * q^36 - 9914616 * q^37 - 4996365 * q^38 - 5731722 * q^39 + 1981665 * q^40 - 42414849 * q^41 + 10480365 * q^42 + 785403 * q^43 + 237381888 * q^44 + 4802904 * q^45 + 27594756 * q^46 - 119882802 * q^47 - 186605055 * q^48 - 155649627 * q^49 - 155986077 * q^50 + 125783109 * q^51 - 38113875 * q^52 + 456641112 * q^53 + 107997840 * q^54 + 181700496 * q^55 - 77612325 * q^56 - 208444653 * q^57 - 106894161 * q^58 - 254205771 * q^59 + 151864524 * q^60 + 88252362 * q^61 + 475026168 * q^62 + 7087752 * q^63 + 780018066 * q^64 - 508726878 * q^65 - 903322692 * q^66 - 140145363 * q^67 - 527497665 * q^68 + 1033462602 * q^69 + 1271226492 * q^71 - 529878141 * q^72 - 1089614970 * q^73 - 1637187180 * q^74 - 1069789041 * q^75 - 355170312 * q^76 - 360171609 * q^77 + 1842021072 * q^78 - 567828360 * q^79 + 6015328602 * q^80 - 1173736791 * q^81 - 195081048 * q^82 - 3126306510 * q^83 + 295049286 * q^84 + 120736008 * q^85 - 2515127217 * q^86 + 1825753500 * q^87 + 219336660 * q^88 + 4513423020 * q^89 - 3192307821 * q^90 + 429673356 * q^91 - 3546484113 * q^92 + 80634366 * q^93 + 2125779066 * q^94 - 4867623384 * q^95 + 9060845301 * q^96 + 504276867 * q^97 + 553420896 * q^98 - 5802933888 * q^99

Character values

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

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

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 $

$2$	6.17786	+	10.7004i	0.273025	+	0.472894i	0.969635	−	0.244557i	$-0.0786424\pi$
$2$	6.17786	+	10.7004i	0.273025	+	0.472894i	−0.696610	+	0.717450i	$0.745309\pi$
$3$	−138.713	−	21.0197i	−0.988713	−	0.149824i
$3$	−138.713	−	21.0197i	−0.988713	−	0.149824i
$4$	179.668	−	311.194i	0.350914	−	0.607802i
$5$	571.192	−	989.334i	0.408712	−	0.707910i	−0.586034	−	0.810287i	$-0.699311\pi$
$5$	571.192	−	989.334i	0.408712	−	0.707910i	0.994746	+	0.102377i	$0.0326448\pi$
$6$	−632.028	−	1614.13i	−0.199093	−	0.508462i
$7$	−1200.50	−	2079.33i	−0.188982	−	0.327327i
$7$	−1200.50	−	2079.33i	−0.188982	−	0.327327i
$8$	10766.0			0.929285
$9$	18799.3	+	5831.40i	0.955106	+	0.296266i
$10$	14115.0			0.446355
$11$	19722.7	+	34160.7i	0.406161	+	0.703492i	0.994456	−	0.105155i	$-0.0335338\pi$
$11$	19722.7	+	34160.7i	0.406161	+	0.703492i	−0.588295	+	0.808647i	$0.700200\pi$
$12$	−31463.5	+	39390.0i	−0.438017	+	0.548366i
$13$	61487.6	−	106500.i	0.597093	−	1.03420i	−0.396154	−	0.918184i	$-0.629656\pi$
$13$	61487.6	−	106500.i	0.597093	−	1.03420i	0.993248	−	0.116012i	$-0.0370111\pi$
$14$	14833.0	−	25691.6i	0.103194	−	0.178737i
$15$	−100027.	+	125227.i	−0.510160	+	0.638684i
$16$	−25479.4	−	44131.6i	−0.0971962	−	0.168349i
$17$	−375638.			−1.09081			−0.545406	−	0.838172i	$-0.683624\pi$
$17$	−375638.			−1.09081			−0.545406	+	0.838172i	$0.683624\pi$
$18$	53741.6	+	237185.i	0.120666	+	0.532551i
$19$	335848.			0.591223			0.295611	−	0.955308i	$-0.404477\pi$
$19$	335848.			0.591223			0.295611	+	0.955308i	$0.404477\pi$
$20$	−205250.	−	355504.i	−0.286846	−	0.496831i
$21$	122818.	+	313663.i	0.137808	+	0.351946i
$22$	−243688.	+	422079.i	−0.221785	+	0.384142i
$23$	−204101.	+	353512.i	−0.152079	+	0.263408i	−0.931992	−	0.362480i	$-0.881930\pi$
$23$	−204101.	+	353512.i	−0.152079	+	0.263408i	0.779913	+	0.625888i	$0.215263\pi$
$24$	−1.49338e6	−	226298.i	−0.918795	−	0.139229i
$25$	324042.	+	561256.i	0.165909	+	0.287363i
$26$	1.51945e6			0.652086
$27$	−2.48513e6	−	1.20405e6i	−0.899937	−	0.436020i
$28$	−862767.			−0.265266
$29$	−1.47383e6	−	2.55276e6i	−0.386952	−	0.670221i	0.605086	−	0.796160i	$-0.293139\pi$
$29$	−1.47383e6	−	2.55276e6i	−0.386952	−	0.670221i	−0.992038	+	0.125939i	$0.959806\pi$
$30$	−1.95792e6	−	296693.i	−0.441317	−	0.0668746i
$31$	4.34457e6	−	7.52502e6i	0.844927	−	1.46346i	−0.0407570	−	0.999169i	$-0.512977\pi$
$31$	4.34457e6	−	7.52502e6i	0.844927	−	1.46346i	0.885684	−	0.464288i	$-0.153690\pi$
$32$	3.07091e6	−	5.31897e6i	0.517716	−	0.896711i
$33$	−2.01773e6	−	5.15308e6i	−0.296177	−	0.756404i
$34$	−2.32064e6	−	4.01946e6i	−0.297819	−	0.515838i
$35$	−2.74286e6			−0.308957
$36$	5.19234e6	−	4.80253e6i	0.515231	−	0.476551i
$37$	−5.75180e6			−0.504540			−0.252270	−	0.967657i	$-0.581177\pi$
$37$	−5.75180e6			−0.504540			−0.252270	+	0.967657i	$0.581177\pi$
$38$	2.07482e6	+	3.59369e6i	0.161419	+	0.279585i
$39$	−1.07677e7	+	1.34804e7i	−0.745301	+	0.933064i
$40$	6.14944e6	−	1.06512e7i	0.379810	−	0.657850i
$41$	5.76664e6	−	9.98811e6i	0.318710	−	0.552022i	−0.661509	−	0.749937i	$-0.730084\pi$
$41$	5.76664e6	−	9.98811e6i	0.318710	−	0.552022i	0.980219	+	0.197915i	$0.0634171\pi$
$42$	−2.59756e6	+	3.25196e6i	−0.128808	+	0.161259i
$43$	−5.56585e6	−	9.64034e6i	−0.248270	−	0.430016i	0.714776	−	0.699353i	$-0.246529\pi$
$43$	−5.56585e6	−	9.64034e6i	−0.248270	−	0.430016i	−0.963046	+	0.269338i	$0.913195\pi$
$44$	1.41741e7			0.570111
$45$	1.65072e7	−	1.52680e7i	0.600092	−	0.555041i
$46$	−5.04361e6			−0.166085
$47$	591114.	+	1.02384e6i	0.0176698	+	0.0306049i	0.874725	−	0.484619i	$-0.161042\pi$
$47$	591114.	+	1.02384e6i	0.0176698	+	0.0306049i	−0.857055	+	0.515224i	$0.827709\pi$
$48$	2.60668e6	+	6.65718e6i	0.0708764	+	0.181011i
$49$	−2.88240e6	+	4.99246e6i	−0.0714286	+	0.123718i
$50$	−4.00376e6	+	6.93472e6i	−0.0905948	+	0.156915i
$51$	5.21057e7	+	7.89581e6i	1.07850	+	0.163430i
$52$	−2.20947e7	−	3.82692e7i	−0.419057	−	0.725829i
$53$	−5.26811e7			−0.917094			−0.458547	−	0.888670i	$-0.651630\pi$
$53$	−5.26811e7			−0.917094			−0.458547	+	0.888670i	$0.651630\pi$
$54$	−2.46906e6	−	3.40302e7i	−0.0395148	−	0.544619i
$55$	4.50617e7			0.664012
$56$	−1.29246e7	−	2.23860e7i	−0.175618	−	0.304180i
$57$	−4.65863e7	−	7.05943e6i	−0.584549	−	0.0885794i
$58$	1.82103e7	−	3.15411e7i	0.211296	−	0.365975i
$59$	−9.90739e6	+	1.71601e7i	−0.106445	+	0.184368i	−0.914328	−	0.404975i	$-0.867280\pi$
$59$	−9.90739e6	+	1.71601e7i	−0.106445	+	0.184368i	0.807883	+	0.589343i	$0.200613\pi$
$60$	2.09982e7	+	5.36271e7i	0.209171	+	0.534200i
$61$	−6.42197e7	−	1.11232e8i	−0.593860	−	1.02860i	−0.993707	−	0.112014i	$-0.964270\pi$
$61$	−6.42197e7	−	1.11232e8i	−0.593860	−	1.02860i	0.399846	−	0.916582i	$-0.369063\pi$
$62$	1.07361e8			0.922746
$63$	−1.04432e7	−	4.60906e7i	−0.0835222	−	0.368621i
$64$	4.97956e7			0.371006
$65$	−7.02424e7	−	1.21663e8i	−0.488078	−	0.845376i
$66$	4.26745e7	−	5.34254e7i	0.276835	−	0.346578i
$67$	4.33821e7	−	7.51399e7i	0.263011	−	0.455548i	−0.704030	−	0.710170i	$-0.748618\pi$
$67$	4.33821e7	−	7.51399e7i	0.263011	−	0.455548i	0.967041	+	0.254622i	$0.0819512\pi$
$68$	−6.74902e7	+	1.16896e8i	−0.382781	+	0.662997i
$69$	3.57420e7	−	4.47465e7i	0.189827	−	0.237650i
$70$	−1.69450e7	−	2.93496e7i	−0.0843531	−	0.146104i
$71$	−1.69345e8			−0.790877			−0.395438	−	0.918492i	$-0.629407\pi$
$71$	−1.69345e8			−0.790877			−0.395438	+	0.918492i	$0.629407\pi$
$72$	2.02393e8	+	6.27807e7i	0.887565	+	0.275315i
$73$	−4.63053e8			−1.90844			−0.954218	−	0.299113i	$-0.903309\pi$
$73$	−4.63053e8			−1.90844			−0.954218	+	0.299113i	$0.903309\pi$
$74$	−3.55338e7	−	6.15463e7i	−0.137752	−	0.238594i
$75$	−3.31512e7	−	8.46646e7i	−0.120983	−	0.308977i
$76$	6.03411e7	−	1.04514e8i	0.207469	−	0.359346i
$77$	4.73541e7	−	8.20197e7i	0.153515	−	0.265895i
$78$	−2.10766e8	−	3.19383e7i	−0.644726	−	0.0976982i
$79$	1.90054e6	+	3.29183e6i	0.00548978	+	0.00950858i	0.868757	−	0.495238i	$-0.164919\pi$
$79$	1.90054e6	+	3.29183e6i	0.00548978	+	0.00950858i	−0.863267	+	0.504747i	$0.831586\pi$
$80$	−5.82145e7			−0.158901
$81$	3.19410e8	+	2.19253e8i	0.824453	+	0.565930i
$82$	1.42502e8			0.348063
$83$	1.26507e8	+	2.19117e8i	0.292593	+	0.506785i	0.974422	−	0.224726i	$-0.0721487\pi$
$83$	1.26507e8	+	2.19117e8i	0.292593	+	0.506785i	−0.681829	+	0.731511i	$0.738815\pi$
$84$	1.19677e8	+	1.81351e7i	0.262272	+	0.0397433i
$85$	−2.14562e8	+	3.71632e8i	−0.445827	+	0.772196i
$86$	6.87701e7	−	1.19113e8i	0.135568	−	0.234810i
$87$	1.50781e8	+	3.85079e8i	0.282170	+	0.720631i
$88$	2.12334e8	+	3.67773e8i	0.377439	+	0.653744i
$89$	−1.32273e8			−0.223469			−0.111734	−	0.993738i	$-0.535641\pi$
$89$	−1.32273e8			−0.223469			−0.111734	+	0.993738i	$0.535641\pi$
$90$	2.65352e8	+	8.23101e7i	0.426316	+	0.132240i
$91$	−2.95263e8			−0.451360
$92$	7.33407e7	+	1.27030e8i	0.106733	+	0.184868i
$93$	−7.60820e8	+	9.52493e8i	−1.05465	+	1.32035i
$94$	−7.30363e6	+	1.26503e7i	−0.00964858	+	0.0167118i
$95$	1.91834e8	−	3.32265e8i	0.241640	−	0.418532i
$96$	−5.37777e8	+	6.73258e8i	−0.646222	+	0.809023i
$97$	2.80121e8	+	4.85183e8i	0.321271	+	0.556459i	0.980751	−	0.195264i	$-0.0625565\pi$
$97$	2.80121e8	+	4.85183e8i	0.321271	+	0.556459i	−0.659479	+	0.751723i	$0.729223\pi$
$98$	−7.12282e7			−0.0780072
$99$	1.71569e8	+	7.57209e8i	0.179506	+	0.792241i
$100$	2.32880e8			0.232880
$101$	7.80730e8	+	1.35226e9i	0.746542	+	1.29305i	0.949471	+	0.313856i	$0.101621\pi$
$101$	7.80730e8	+	1.35226e9i	0.746542	+	1.29305i	−0.202928	+	0.979194i	$0.565046\pi$
$102$	2.37414e8	+	6.06329e8i	0.217173	+	0.554636i
$103$	8.92071e8	−	1.54511e9i	0.780965	−	1.35267i	−0.150414	−	0.988623i	$-0.548061\pi$
$103$	8.92071e8	−	1.54511e9i	0.780965	−	1.35267i	0.931380	−	0.364049i	$-0.118606\pi$
$104$	6.61974e8	−	1.14657e9i	0.554870	−	0.961062i
$105$	3.80470e8	+	5.76543e7i	0.305470	+	0.0462892i
$106$	−3.25456e8	−	5.63707e8i	−0.250390	−	0.433688i
$107$	1.12610e9			0.830521			0.415260	−	0.909703i	$-0.363690\pi$
$107$	1.12610e9			0.830521			0.415260	+	0.909703i	$0.363690\pi$
$108$	−8.21191e8	+	5.57030e8i	−0.580814	+	0.393978i
$109$	−1.88661e9			−1.28016			−0.640078	−	0.768310i	$-0.721098\pi$
$109$	−1.88661e9			−1.28016			−0.640078	+	0.768310i	$0.721098\pi$
$110$	2.78385e8	+	4.82177e8i	0.181292	+	0.314007i
$111$	7.97847e8	+	1.20901e8i	0.498845	+	0.0755923i
$112$	−6.11761e7	+	1.05960e8i	−0.0367367	+	0.0636299i
$113$	−5.99904e8	+	1.03906e9i	−0.346122	+	0.599501i	−0.985557	−	0.169344i	$-0.945835\pi$
$113$	−5.99904e8	+	1.03906e9i	−0.346122	+	0.599501i	0.639435	+	0.768845i	$0.279168\pi$
$114$	−2.12265e8	−	5.42102e8i	−0.117708	−	0.300614i
$115$	2.33161e8	+	4.03847e8i	0.124313	+	0.215316i
$116$	−1.05920e9			−0.543149
$117$	1.77697e9	−	1.64356e9i	0.876684	−	0.810868i
$118$	−2.44826e8			−0.116249
$119$	4.50954e8	+	7.81075e8i	0.206144	+	0.357052i
$120$	−1.07689e9	+	1.34819e9i	−0.474084	+	0.593520i
$121$	4.01007e8	−	6.94564e8i	0.170066	−	0.294563i
$122$	7.93481e8	−	1.37435e9i	0.324278	−	0.561666i
$123$	−1.00985e9	+	1.26426e9i	−0.397819	+	0.498040i
$124$	−1.56116e9	−	2.70401e9i	−0.592994	−	1.02710i
$125$	2.97158e9			1.08866
$126$	4.28669e8	−	3.96487e8i	0.151515	−	0.140140i
$127$	−4.08592e9			−1.39371			−0.696856	−	0.717211i	$-0.745418\pi$
$127$	−4.08592e9			−1.39371			−0.696856	+	0.717211i	$0.745418\pi$
$128$	−1.26467e9	−	2.19048e9i	−0.416422	−	0.721265i
$129$	5.69416e8	+	1.45423e9i	0.181041	+	0.462359i
$130$	8.67895e8	−	1.50324e9i	0.266515	−	0.461618i
$131$	2.69557e9	−	4.66886e9i	0.799704	−	1.38513i	−0.120104	−	0.992761i	$-0.538323\pi$
$131$	2.69557e9	−	4.66886e9i	0.799704	−	1.38513i	0.919809	−	0.392367i	$-0.128344\pi$
$132$	−1.96613e9	−	2.97937e8i	−0.563676	−	0.0854164i
$133$	−4.03185e8	−	6.98337e8i	−0.111731	−	0.193523i
$134$	1.07203e9			0.287234
$135$	−2.61069e9	+	1.77088e9i	−0.676477	+	0.458868i
$136$	−4.04411e9			−1.01367
$137$	2.93536e9	+	5.08420e9i	0.711900	+	1.23305i	0.964143	+	0.265383i	$0.0854985\pi$
$137$	2.93536e9	+	5.08420e9i	0.711900	+	1.23305i	−0.252243	+	0.967664i	$0.581168\pi$
$138$	6.99613e8	+	1.06015e8i	0.164211	+	0.0248836i
$139$	−1.98217e9	+	3.43322e9i	−0.450375	+	0.780073i	−0.998409	−	0.0563835i	$-0.982043\pi$
$139$	−1.98217e9	+	3.43322e9i	−0.450375	+	0.780073i	0.548034	+	0.836456i	$0.315376\pi$
$140$	−4.92805e8	+	8.53564e8i	−0.108417	+	0.187785i
$141$	−6.04741e7	−	1.54444e8i	−0.0128850	−	0.0329068i
$142$	−1.04619e9	−	1.81205e9i	−0.215929	−	0.374001i
$143$	4.85079e9			0.970065
$144$	−2.21647e8	−	9.78226e8i	−0.0429567	−	0.189587i
$145$	−3.36737e9			−0.632608
$146$	−2.86067e9	−	4.95483e9i	−0.521051	−	0.902487i
$147$	5.04765e8	−	6.31930e8i	0.0891582	−	0.111620i
$148$	−1.03342e9	+	1.78993e9i	−0.177050	+	0.306660i
$149$	3.46637e9	−	6.00393e9i	0.576151	−	0.997923i	−0.419764	−	0.907633i	$-0.637887\pi$
$149$	3.46637e9	−	6.00393e9i	0.576151	−	0.997923i	0.995915	−	0.0902902i	$-0.0287795\pi$
$150$	7.01138e8	−	8.77775e8i	0.113082	−	0.141570i
$151$	1.00765e9	+	1.74530e9i	0.157730	+	0.273196i	0.934050	−	0.357143i	$-0.116249\pi$
$151$	1.00765e9	+	1.74530e9i	0.157730	+	0.273196i	−0.776320	+	0.630339i	$0.782916\pi$
$152$	3.61573e9			0.549414
$153$	−7.06175e9	−	2.19050e9i	−1.04184	−	0.323170i
$154$	1.17019e9			0.167653
$155$	−4.96317e9	−	8.59646e9i	−0.690664	−	1.19626i
$156$	2.26041e9	+	5.77284e9i	0.305581	+	0.780421i
$157$	1.77203e9	−	3.06924e9i	0.232767	−	0.403165i	−0.725854	−	0.687849i	$-0.758555\pi$
$157$	1.77203e9	−	3.06924e9i	0.232767	−	0.403165i	0.958621	+	0.284684i	$0.0918886\pi$
$158$	−2.34825e7	+	4.06729e7i	−0.00299770	+	0.00519217i
$159$	7.30753e9	+	1.10734e9i	0.906742	+	0.137403i
$160$	−3.50816e9	−	6.07631e9i	−0.423194	−	0.732993i
$161$	9.80091e8			0.114961
$162$	−3.72817e8	+	4.77232e9i	−0.0425283	+	0.544392i
$163$	8.96858e9			0.995129			0.497564	−	0.867427i	$-0.334228\pi$
$163$	8.96858e9			0.995129			0.497564	+	0.867427i	$0.334228\pi$
$164$	−2.07216e9	−	3.58909e9i	−0.223680	−	0.387425i
$165$	−6.25063e9	−	9.47185e8i	−0.656517	−	0.0994849i
$166$	−1.56308e9	+	2.70734e9i	−0.159770	+	0.276730i
$167$	9.01745e9	−	1.56187e10i	0.897139	−	1.55389i	0.0660047	−	0.997819i	$-0.478975\pi$
$167$	9.01745e9	−	1.56187e10i	0.897139	−	1.55389i	0.831135	−	0.556071i	$-0.187692\pi$
$168$	1.32225e9	+	3.37689e9i	0.128063	+	0.327058i
$169$	−2.25919e9	−	3.91304e9i	−0.213041	−	0.368998i
$170$	−5.30212e9			−0.486889
$171$	6.31372e9	+	1.95846e9i	0.564680	+	0.175159i
$172$	−4.00002e9			−0.348485
$173$	−7.92408e8	−	1.37249e9i	−0.0672576	−	0.116494i	0.830436	−	0.557115i	$-0.188092\pi$
$173$	−7.92408e8	−	1.37249e9i	−0.0672576	−	0.116494i	−0.897693	+	0.440621i	$0.854758\pi$
$174$	−3.18898e9	+	3.99237e9i	−0.263742	+	0.330187i
$175$	7.78024e8	−	1.34758e9i	0.0627078	−	0.108613i
$176$	1.00504e9	−	1.74079e9i	0.0789547	−	0.136754i
$177$	1.73498e9	−	2.17207e9i	0.132866	−	0.166339i
$178$	−8.17164e8	−	1.41537e9i	−0.0610126	−	0.105677i
$179$	1.55063e10			1.12894			0.564468	−	0.825455i	$-0.309081\pi$
$179$	1.55063e10			1.12894			0.564468	+	0.825455i	$0.309081\pi$
$180$	−1.78548e9	−	7.88013e9i	−0.126774	−	0.559509i
$181$	−7.08663e9			−0.490780			−0.245390	−	0.969424i	$-0.578916\pi$
$181$	−7.08663e9			−0.490780			−0.245390	+	0.969424i	$0.578916\pi$
$182$	−1.82409e9	−	3.15942e9i	−0.123233	−	0.213445i
$183$	6.57002e9	+	1.67791e10i	0.433049	+	1.10596i
$184$	−2.19734e9	+	3.80591e9i	−0.141325	+	0.244781i
$185$	−3.28538e9	+	5.69045e9i	−0.206212	+	0.357169i
$186$	−1.48923e10	−	2.25669e9i	−0.912331	−	0.138250i
$187$	−7.40858e9	−	1.28320e10i	−0.443045	−	0.767377i
$188$	4.24817e8			0.0248023
$189$	4.79795e8	+	6.61285e9i	0.0273513	+	0.376974i
$190$	4.74048e9			0.263895
$191$	1.82255e10	+	3.15676e10i	0.990901	+	1.71629i	0.612012	+	0.790849i	$0.290360\pi$
$191$	1.82255e10	+	3.15676e10i	0.990901	+	1.71629i	0.378889	+	0.925442i	$0.376306\pi$
$192$	−6.90727e9	−	1.04669e9i	−0.366818	−	0.0555856i
$193$	−4.22872e9	+	7.32435e9i	−0.219382	+	0.379981i	−0.954619	−	0.297829i	$-0.903737\pi$
$193$	−4.22872e9	+	7.32435e9i	−0.219382	+	0.379981i	0.735237	+	0.677810i	$0.237071\pi$
$194$	−3.46109e9	+	5.99478e9i	−0.175430	+	0.303854i
$195$	7.18617e9	+	1.83527e10i	0.355911	+	0.908960i
$196$	1.03575e9	+	1.79397e9i	0.0501306	+	0.0868288i
$197$	1.70881e10			0.808342			0.404171	−	0.914684i	$-0.367560\pi$
$197$	1.70881e10			0.808342			0.404171	+	0.914684i	$0.367560\pi$
$198$	−7.04248e9	+	6.51377e9i	−0.325636	+	0.301189i
$199$	−1.16221e10			−0.525346			−0.262673	−	0.964885i	$-0.584604\pi$
$199$	−1.16221e10			−0.525346			−0.262673	+	0.964885i	$0.584604\pi$
$200$	3.48863e9	+	6.04248e9i	0.154177	+	0.267042i
$201$	−7.59706e9	+	9.51097e9i	−0.328294	+	0.411001i
$202$	−9.64647e9	+	1.67082e10i	−0.407650	+	0.706070i
$203$	−3.53868e9	+	6.12917e9i	−0.146254	+	0.253320i
$204$	1.18189e10	−	1.47964e10i	0.477794	−	0.598163i
$205$	−6.58772e9	−	1.14103e10i	−0.260521	−	0.451236i
$206$	2.20443e10			0.852893
$207$	−5.89843e9	+	5.45561e9i	−0.223290	+	0.206527i
$208$	−6.26667e9			−0.232141
$209$	6.62381e9	+	1.14728e10i	0.240132	+	0.415920i
$210$	1.73357e9	+	4.42734e9i	0.0615111	+	0.157093i
$211$	1.65123e10	−	2.86002e10i	0.573504	−	0.993339i	−0.422698	−	0.906271i	$-0.638917\pi$
$211$	1.65123e10	−	2.86002e10i	0.573504	−	0.993339i	0.996202	−	0.0870682i	$-0.0277498\pi$
$212$	−9.46512e9	+	1.63941e10i	−0.321821	+	0.557411i
$213$	2.34902e10	+	3.55958e9i	0.781950	+	0.118492i
$214$	6.95689e9	+	1.20497e10i	0.226753	+	0.392748i
$215$	−1.27167e10			−0.405883
$216$	−2.67549e10	−	1.29627e10i	−0.836298	−	0.405186i
$217$	−2.08626e10			−0.638705
$218$	−1.16552e10	−	2.01874e10i	−0.349515	−	0.605378i
$219$	6.42312e10	+	9.73324e9i	1.88689	+	0.285929i
$220$	8.09616e9	−	1.40230e10i	0.233011	−	0.403587i
$221$	−2.30971e10	+	4.00053e10i	−0.651316	+	1.12811i
$222$	3.63530e9	+	9.28416e9i	0.100450	+	0.256539i
$223$	2.30776e10	+	3.99716e10i	0.624912	+	1.08238i	0.988558	+	0.150842i	$0.0481985\pi$
$223$	2.30776e10	+	3.99716e10i	0.624912	+	1.08238i	−0.363646	+	0.931537i	$0.618468\pi$
$224$	−1.47465e10			−0.391357
$225$	2.81886e9	+	1.24409e10i	0.0733249	+	0.323616i
$226$	−1.48245e10			−0.378000
$227$	−3.32741e10	−	5.76324e10i	−0.831744	−	1.44062i	−0.896654	−	0.442731i	$-0.854010\pi$
$227$	−3.32741e10	−	5.76324e10i	−0.831744	−	1.44062i	0.0649109	−	0.997891i	$-0.479324\pi$
$228$	−1.05669e10	+	1.32290e10i	−0.258965	+	0.324206i
$229$	3.12535e10	−	5.41327e10i	0.750999	−	1.30077i	−0.196340	−	0.980536i	$-0.562906\pi$
$229$	3.12535e10	−	5.41327e10i	0.750999	−	1.30077i	0.947339	−	0.320233i	$-0.103761\pi$
$230$	−2.88087e9	+	4.98982e9i	−0.0678811	+	0.117574i
$231$	−8.29264e9	+	1.03818e10i	−0.191619	+	0.239894i
$232$	−1.58673e10	−	2.74829e10i	−0.359589	−	0.622826i
$233$	−9.85804e9			−0.219123			−0.109562	−	0.993980i	$-0.534945\pi$
$233$	−9.85804e9			−0.219123			−0.109562	+	0.993980i	$0.534945\pi$
$234$	2.85646e10	+	8.86049e9i	0.622811	+	0.193191i
$235$	1.35056e9			0.0288874
$236$	3.56008e9	+	6.16625e9i	0.0747061	+	0.129395i
$237$	−1.94435e8	−	4.96567e8i	−0.00400320	−	0.0102238i
$238$	−5.57185e9	+	9.65073e9i	−0.112565	+	0.194968i
$239$	−4.19049e10	+	7.25815e10i	−0.830758	+	1.43891i	0.0666802	+	0.997774i	$0.478759\pi$
$239$	−4.19049e10	+	7.25815e10i	−0.830758	+	1.43891i	−0.897438	+	0.441140i	$0.854574\pi$
$240$	8.07509e9	+	1.22365e9i	0.157107	+	0.0238072i
$241$	4.08605e10	+	7.07724e10i	0.780237	+	1.35141i	0.931803	+	0.362964i	$0.118235\pi$
$241$	4.08605e10	+	7.07724e10i	0.780237	+	1.35141i	−0.151566	+	0.988447i	$0.548432\pi$
$242$	9.90945e9			0.185729
$243$	−3.96975e10	−	3.71270e10i	−0.730357	−	0.683065i
$244$	−4.61530e10			−0.833577
$245$	3.29281e9	+	5.70331e9i	0.0583874	+	0.101130i
$246$	−1.97668e10	−	2.99535e9i	−0.344135	−	0.0521483i
$247$	2.06505e10	−	3.57676e10i	0.353015	−	0.611440i
$248$	4.67736e10	−	8.10142e10i	0.785178	−	1.35997i
$249$	−1.29423e10	−	3.30534e10i	−0.213361	−	0.544902i
$250$	1.83580e10	+	3.17970e10i	0.297232	+	0.514820i
$251$	2.79734e8			0.00444850			0.00222425	−	0.999998i	$-0.499292\pi$
$251$	2.79734e8			0.00444850			0.00222425	+	0.999998i	$0.499292\pi$
$252$	−1.62194e10	−	5.03114e9i	−0.253357	−	0.0785893i
$253$	−1.61016e10			−0.247074
$254$	−2.52422e10	−	4.37208e10i	−0.380518	−	0.659077i
$255$	3.75740e10	−	4.70399e10i	0.556489	−	0.696684i
$256$	2.83736e10	−	4.91446e10i	0.412891	−	0.715148i
$257$	−2.33283e10	+	4.04057e10i	−0.333567	+	0.577755i	−0.983209	−	0.182486i	$-0.941586\pi$
$257$	−2.33283e10	+	4.04057e10i	−0.333567	+	0.577755i	0.649641	+	0.760241i	$0.274919\pi$
$258$	−1.20430e10	+	1.50770e10i	−0.169218	+	0.211849i
$259$	6.90503e9	+	1.19599e10i	0.0953492	+	0.165150i
$260$	−5.04813e10			−0.685095
$261$	−1.28210e10	−	5.65846e10i	−0.171017	−	0.754773i
$262$	6.66113e10			0.873358
$263$	−2.77606e10	−	4.80828e10i	−0.357790	−	0.619711i	0.629801	−	0.776756i	$-0.283136\pi$
$263$	−2.77606e10	−	4.80828e10i	−0.357790	−	0.619711i	−0.987591	+	0.157046i	$0.949803\pi$
$264$	−2.17229e10	−	5.54779e10i	−0.275233	−	0.702915i
$265$	−3.00910e10	+	5.21192e10i	−0.374827	+	0.649219i
$266$	4.98164e9	−	8.62845e9i	0.0610106	−	0.105673i
$267$	1.83479e10	+	2.78034e9i	0.220946	+	0.0334810i
$268$	−1.55888e10	−	2.70005e10i	−0.184589	−	0.319717i
$269$	8.93139e10			1.04000			0.520000	−	0.854166i	$-0.325932\pi$
$269$	8.93139e10			1.04000			0.520000	+	0.854166i	$0.325932\pi$
$270$	−3.50775e10	−	1.69951e10i	−0.401691	−	0.194619i
$271$	1.49937e11			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$271$	1.49937e11			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$272$	9.57104e9	+	1.65775e10i	0.106023	+	0.183637i
$273$	4.09567e10	+	6.20635e9i	0.446266	+	0.0676246i
$274$	−3.62685e10	+	6.28189e10i	−0.388734	+	0.673306i
$275$	−1.27819e10	+	2.21389e10i	−0.134772	+	0.233432i
$276$	−7.50315e9	−	1.91622e10i	−0.0778310	−	0.198772i
$277$	5.25885e10	+	9.10859e10i	0.536700	+	0.929592i	0.999079	+	0.0429092i	$0.0136626\pi$
$277$	5.25885e10	+	9.10859e10i	0.536700	+	0.929592i	−0.462379	+	0.886682i	$0.653004\pi$
$278$	−4.89823e10			−0.491855
$279$	1.25556e11	−	1.16130e11i	1.24057	−	1.14743i
$280$	−2.95296e10			−0.287109
$281$	−2.51036e10	−	4.34807e10i	−0.240191	−	0.416023i	0.720577	−	0.693374i	$-0.243877\pi$
$281$	−2.51036e10	−	4.34807e10i	−0.240191	−	0.416023i	−0.960769	+	0.277351i	$0.910543\pi$
$282$	1.27901e9	−	1.60123e9i	0.0120435	−	0.0150776i
$283$	6.57855e10	−	1.13944e11i	0.609665	−	1.05597i	−0.381631	−	0.924315i	$-0.624637\pi$
$283$	6.57855e10	−	1.13944e11i	0.609665	−	1.05597i	0.991296	−	0.131655i	$-0.0420292\pi$
$284$	−3.04258e10	+	5.26991e10i	−0.277530	+	0.480696i
$285$	−3.35939e10	+	4.20571e10i	−0.301618	+	0.377605i
$286$	2.99675e10	+	5.19053e10i	0.264852	+	0.458737i
$287$	−2.76914e10			−0.240922
$288$	8.87481e10	−	8.20854e10i	0.760139	−	0.703072i
$289$	2.25161e10			0.189869
$290$	−2.08031e10	−	3.60321e10i	−0.172718	−	0.299156i
$291$	−2.86578e10	−	7.31890e10i	−0.234274	−	0.598312i
$292$	−8.31958e10	+	1.44099e11i	−0.669697	+	1.15995i
$293$	−2.24097e10	+	3.88147e10i	−0.177636	+	0.307675i	−0.941070	−	0.338211i	$-0.890178\pi$
$293$	−2.24097e10	+	3.88147e10i	−0.177636	+	0.307675i	0.763434	+	0.645885i	$0.223512\pi$
$294$	9.88025e9	+	1.49720e9i	0.0771267	+	0.0116874i
$295$	1.13180e10	+	1.96034e10i	0.0870106	+	0.150707i
$296$	−6.19238e10			−0.468862
$297$	−7.88241e9	−	1.08641e11i	−0.0587834	−	0.810193i
$298$	8.56589e10			0.629216
$299$	2.50993e10	+	4.34732e10i	0.181611	+	0.314559i
$300$	−3.23034e10	−	4.89507e9i	−0.230251	−	0.0348910i
$301$	−1.33636e10	+	2.31464e10i	−0.0938371	+	0.162531i
$302$	−1.24503e10	+	2.15645e10i	−0.0861286	+	0.149179i
$303$	−7.98728e10	−	2.03987e11i	−0.544386	−	1.39030i
$304$	−8.55720e9	−	1.48215e10i	−0.0574646	−	0.0995316i
$305$	−1.46727e11			−0.970871
$306$	−2.01874e10	−	8.90959e10i	−0.131624	−	0.580913i
$307$	−2.08567e11			−1.34006			−0.670028	−	0.742336i	$-0.733718\pi$
$307$	−2.08567e11			−1.34006			−0.670028	+	0.742336i	$0.733718\pi$
$308$	−1.70161e10	−	2.94727e10i	−0.107741	−	0.186613i
$309$	−1.56219e11	+	1.95575e11i	−0.974813	+	1.22040i
$310$	6.13235e10	−	1.06215e11i	0.377137	−	0.653221i
$311$	−1.52898e10	+	2.64828e10i	−0.0926790	+	0.160525i	−0.908638	−	0.417586i	$-0.862876\pi$
$311$	−1.52898e10	+	2.64828e10i	−0.0926790	+	0.160525i	0.815959	+	0.578110i	$0.196210\pi$
$312$	−1.15925e11	+	1.45130e11i	−0.692597	+	0.867082i
$313$	−6.20207e10	−	1.07423e11i	−0.365248	−	0.632627i	0.623568	−	0.781769i	$-0.285682\pi$
$313$	−6.20207e10	−	1.07423e11i	−0.365248	−	0.632627i	−0.988816	+	0.149142i	$0.952349\pi$
$314$	4.37893e10			0.254205
$315$	−5.15641e10	−	1.59947e10i	−0.295087	−	0.0915334i
$316$	1.36587e9			0.00770578
$317$	7.40271e10	+	1.28219e11i	0.411741	+	0.713156i	0.995080	−	0.0990725i	$-0.0315876\pi$
$317$	7.40271e10	+	1.28219e11i	0.411741	+	0.713156i	−0.583339	+	0.812229i	$0.698254\pi$
$318$	3.32959e10	+	8.50343e10i	0.182587	+	0.466307i
$319$	5.81359e10	−	1.00694e11i	0.314330	−	0.544436i
$320$	2.84429e10	−	4.92645e10i	0.151635	−	0.262639i
$321$	−1.56204e11	−	2.36703e10i	−0.821146	−	0.124432i
$322$	6.05486e9	+	1.04873e10i	0.0313872	+	0.0543642i
$323$	−1.26157e11			−0.644912
$324$	1.25618e11	−	6.00058e10i	0.633286	−	0.302511i
$325$	7.96981e10			0.396253
$326$	5.54066e10	+	9.59670e10i	0.271695	+	0.470590i
$327$	2.61697e11	+	3.96561e10i	1.26571	+	0.191798i
$328$	6.20835e10	−	1.07532e11i	0.296172	−	0.512985i
$329$	1.41926e9	−	2.45824e9i	0.00667854	−	0.0115676i
$330$	−2.84803e10	−	7.27355e10i	−0.132200	−	0.337624i
$331$	3.21305e10	+	5.56516e10i	0.147127	+	0.254831i	0.930164	−	0.367144i	$-0.119664\pi$
$331$	3.21305e10	+	5.56516e10i	0.147127	+	0.254831i	−0.783038	+	0.621974i	$0.786331\pi$
$332$	9.09172e10			0.410700
$333$	−1.08130e11	−	3.35410e10i	−0.481889	−	0.149478i
$334$	2.22834e11			0.979767
$335$	−4.95590e10	−	8.58387e10i	−0.214991	−	0.372376i
$336$	1.07131e10	−	1.34121e10i	0.0458553	−	0.0574076i
$337$	−2.24006e11	+	3.87990e11i	−0.946074	+	1.63865i	−0.192486	+	0.981300i	$0.561655\pi$
$337$	−2.24006e11	+	3.87990e11i	−0.946074	+	1.63865i	−0.753587	+	0.657348i	$0.771678\pi$
$338$	2.79139e10	−	4.83484e10i	0.116331	−	0.201491i
$339$	1.05055e11	−	1.31522e11i	0.432035	−	0.540877i
$340$	7.70998e10	+	1.33541e11i	0.312895	+	0.541949i
$341$	3.42746e11			1.37271
$342$	1.80490e10	+	7.96581e10i	0.0713403	+	0.314856i
$343$	1.38413e10			0.0539949
$344$	−5.99218e10	−	1.03788e11i	−0.230713	−	0.399607i
$345$	−2.38536e10	−	6.09196e10i	−0.0906502	−	0.231511i
$346$	9.79077e9	−	1.69581e10i	0.0367261	−	0.0636114i
$347$	−2.56999e11	+	4.45135e11i	−0.951588	+	1.64820i	−0.209597	+	0.977788i	$0.567215\pi$
$347$	−2.56999e11	+	4.45135e11i	−0.951588	+	1.64820i	−0.741991	+	0.670410i	$0.766118\pi$
$348$	1.46925e11	+	2.22642e10i	0.537018	+	0.0813767i
$349$	1.46990e11	+	2.54594e11i	0.530363	+	0.918615i	0.999372	+	0.0354222i	$0.0112776\pi$
$349$	1.46990e11	+	2.54594e11i	0.530363	+	0.918615i	−0.469010	+	0.883193i	$0.655389\pi$
$350$	1.92261e10			0.0684833
$351$	−2.81035e11	+	1.90632e11i	−0.988276	+	0.670367i
$352$	2.42266e11			0.841105
$353$	−9.38475e9	−	1.62549e10i	−0.0321689	−	0.0557182i	0.849493	−	0.527600i	$-0.176908\pi$
$353$	−9.38475e9	−	1.62549e10i	−0.0321689	−	0.0557182i	−0.881662	+	0.471882i	$0.843575\pi$
$354$	3.39604e10	+	5.14617e9i	0.114936	+	0.0174168i
$355$	−9.67283e10	+	1.67538e11i	−0.323241	+	0.559869i
$356$	−2.37653e10	+	4.11627e10i	−0.0784184	+	0.135825i
$357$	−4.61349e10	−	1.17824e11i	−0.150322	−	0.383907i
$358$	9.57957e10	+	1.65923e11i	0.308228	+	0.533867i
$359$	5.52142e11			1.75439			0.877194	−	0.480135i	$-0.159412\pi$
$359$	5.52142e11			1.75439			0.877194	+	0.480135i	$0.159412\pi$
$360$	1.77717e11	−	1.64375e11i	0.557657	−	0.515791i
$361$	−2.09894e11			−0.650456
$362$	−4.37802e10	−	7.58296e10i	−0.133995	−	0.232087i
$363$	−7.02243e10	+	8.79157e10i	−0.212279	+	0.265758i
$364$	−5.30494e10	+	9.18843e10i	−0.158389	+	0.274337i
$365$	−2.64492e11	+	4.58114e11i	−0.780000	+	1.35100i
$366$	−1.38954e11	+	1.73961e11i	−0.404769	+	0.506741i
$367$	−1.10345e11	−	1.91123e11i	−0.317508	−	0.549940i	0.662459	−	0.749098i	$-0.269513\pi$
$367$	−1.10345e11	−	1.91123e11i	−0.317508	−	0.549940i	−0.979967	+	0.199158i	$0.936179\pi$
$368$	2.08014e10			0.0591260
$369$	1.66654e11	−	1.54142e11i	0.467947	−	0.432816i
$370$	−8.11865e10			−0.225204
$371$	6.32437e10	+	1.09541e11i	0.173314	+	0.300189i
$372$	1.59715e11	+	4.07896e11i	0.432417	+	1.10435i
$373$	8.65497e10	−	1.49908e11i	0.231513	−	0.400993i	−0.726740	−	0.686912i	$-0.758966\pi$
$373$	8.65497e10	−	1.49908e11i	0.231513	−	0.400993i	0.958254	+	0.285920i	$0.0922990\pi$
$374$	9.15383e10	−	1.58549e11i	0.241925	−	0.419027i
$375$	−4.12195e11	−	6.24618e10i	−1.07637	−	0.163107i
$376$	6.36392e9	+	1.10226e10i	0.0164202	+	0.0284407i
$377$	−3.62490e11			−0.924187
$378$	−6.77958e10	+	4.59872e10i	−0.170801	+	0.115858i
$379$	3.21794e11			0.801128			0.400564	−	0.916269i	$-0.368814\pi$
$379$	3.21794e11			0.801128			0.400564	+	0.916269i	$0.368814\pi$
$380$	−6.89328e10	−	1.19395e11i	−0.169590	−	0.293738i
$381$	5.66768e11	+	8.58849e10i	1.37798	+	0.208811i
$382$	−2.25190e11	+	3.90040e11i	−0.541082	+	0.937181i
$383$	−1.52588e11	+	2.64290e11i	−0.362347	+	0.627604i	−0.988347	−	0.152220i	$-0.951358\pi$
$383$	−1.52588e11	+	2.64290e11i	−0.362347	+	0.627604i	0.625999	+	0.779823i	$0.284691\pi$
$384$	1.29383e11	+	3.30430e11i	0.303659	+	0.775513i
$385$	−5.40966e10	−	9.36981e10i	−0.125486	−	0.217349i
$386$	−1.04498e11			−0.239587
$387$	−4.84177e10	−	2.13689e11i	−0.109725	−	0.484264i
$388$	2.01315e11			0.450955
$389$	−2.33852e11	−	4.05044e11i	−0.517808	−	0.896869i	−0.999786	−	0.0206859i	$-0.993415\pi$
$389$	−2.33852e11	−	4.05044e11i	−0.517808	−	0.896869i	0.481979	−	0.876183i	$-0.339918\pi$
$390$	−1.51986e11	+	1.90275e11i	−0.332669	+	0.416477i
$391$	7.66679e10	−	1.32793e11i	0.165889	−	0.287329i
$392$	−3.10319e10	+	5.37488e10i	−0.0663775	+	0.114969i
$393$	−4.72047e11	+	5.90969e11i	−0.998203	+	1.24968i
$394$	1.05568e11	+	1.82849e11i	0.220698	+	0.382260i
$395$	4.34230e9			0.00897496
$396$	2.66464e11	+	8.26551e10i	0.544516	+	0.168904i
$397$	−4.05342e11			−0.818963			−0.409481	−	0.912318i	$-0.634290\pi$
$397$	−4.05342e11			−0.818963			−0.409481	+	0.912318i	$0.634290\pi$
$398$	−7.17996e10	−	1.24360e11i	−0.143433	−	0.248433i
$399$	4.12480e10	+	1.05343e11i	0.0814751	+	0.208079i
$400$	1.65128e10	−	2.86010e10i	0.0322515	−	0.0558613i
$401$	4.54128e11	−	7.86572e11i	0.877058	−	1.51911i	0.0225036	−	0.999747i	$-0.492836\pi$
$401$	4.54128e11	−	7.86572e11i	0.877058	−	1.51911i	0.854554	−	0.519362i	$-0.173830\pi$
$402$	−1.48704e11	−	2.25338e10i	−0.283992	−	0.0430346i
$403$	−5.34274e11	−	9.25390e11i	−1.00900	−	1.74764i
$404$	5.61089e11			1.04789
$405$	3.99359e11	−	1.90768e11i	0.737591	−	0.352336i
$406$	−8.74457e10			−0.159724
$407$	−1.13441e11	−	1.96485e11i	−0.204925	−	0.354940i
$408$	5.60969e11	+	8.50062e10i	1.00223	+	0.151873i
$409$	4.86760e11	−	8.43093e11i	0.860122	−	1.48977i	−0.0116892	−	0.999932i	$-0.503721\pi$
$409$	4.86760e11	−	8.43093e11i	0.860122	−	1.48977i	0.871811	−	0.489843i	$-0.162946\pi$
$410$	8.13960e10	−	1.40982e11i	0.142258	−	0.246397i
$411$	−3.00303e11	−	7.66942e11i	−0.519125	−	1.32579i
$412$	−3.20553e11	−	5.55215e11i	−0.548104	−	0.949344i
$413$	4.75753e10			0.0804648
$414$	−9.48166e10	−	2.94113e10i	−0.158629	−	0.0492055i
$415$	2.89039e11			0.478344
$416$	−3.77645e11	−	6.54101e11i	−0.618250	−	1.07084i
$417$	3.47117e11	−	4.34566e11i	0.562165	−	0.703791i
$418$	−8.18419e10	+	1.41754e11i	−0.131124	+	0.227114i
$419$	−2.67938e11	+	4.64082e11i	−0.424689	+	0.735583i	−0.996391	−	0.0848781i	$-0.972950\pi$
$419$	−2.67938e11	+	4.64082e11i	−0.424689	+	0.735583i	0.571702	+	0.820461i	$0.306283\pi$
$420$	8.63000e10	−	1.08041e11i	0.135328	−	0.169421i
$421$	−2.22471e11	−	3.85331e11i	−0.345147	−	0.597812i	0.640233	−	0.768180i	$-0.278838\pi$
$421$	−2.22471e11	−	3.85331e11i	−0.345147	−	0.597812i	−0.985380	+	0.170368i	$0.945504\pi$
$422$	4.08043e11			0.626325
$423$	5.14213e9	+	2.26945e10i	0.00780929	+	0.0344659i
$424$	−5.67164e11			−0.852241
$425$	−1.21722e11	−	2.10829e11i	−0.180976	−	0.313459i
$426$	1.07030e11	+	2.73345e11i	0.157458	+	0.402131i
$427$	−1.54192e11	+	2.67068e11i	−0.224458	+	0.388773i
$428$	2.02325e11	−	3.50436e11i	0.291442	−	0.504792i
$429$	−6.72866e11	−	1.01962e11i	−0.959115	−	0.145339i
$430$	−7.85618e10	−	1.36073e11i	−0.110816	−	0.191939i
$431$	−2.14904e11			−0.299984			−0.149992	−	0.988687i	$-0.547925\pi$
$431$	−2.14904e11			−0.299984			−0.149992	+	0.988687i	$0.547925\pi$
$432$	1.01832e10	+	1.40351e11i	0.0140671	+	0.193883i
$433$	−6.54739e11			−0.895102			−0.447551	−	0.894258i	$-0.647704\pi$
$433$	−6.54739e11			−0.895102			−0.447551	+	0.894258i	$0.647704\pi$
$434$	−1.28886e11	−	2.23238e11i	−0.174383	−	0.302040i
$435$	4.67096e11	+	7.07812e10i	0.625468	+	0.0947799i
$436$	−3.38964e11	+	5.87103e11i	−0.449225	+	0.778081i
$437$	−6.85467e10	+	1.18726e11i	−0.0899125	+	0.155733i
$438$	2.92662e11	+	7.47428e11i	0.379956	+	0.970366i
$439$	−2.69099e11	−	4.66093e11i	−0.345797	−	0.598938i	0.639701	−	0.768624i	$-0.279058\pi$
$439$	−2.69099e11	−	4.66093e11i	−0.345797	−	0.598938i	−0.985498	+	0.169686i	$0.945725\pi$
$440$	4.85134e11			0.617056
$441$	−8.33003e10	+	7.70466e10i	−0.104875	+	0.0970018i
$442$	−5.70762e11			−0.711303
$443$	−1.47824e11	−	2.56039e11i	−0.182359	−	0.315856i	0.760324	−	0.649544i	$-0.225040\pi$
$443$	−1.47824e11	−	2.56039e11i	−0.182359	−	0.315856i	−0.942684	+	0.333688i	$0.891707\pi$
$444$	1.80971e11	−	2.26563e11i	0.220997	−	0.276673i
$445$	−7.55534e10	+	1.30862e11i	−0.0913343	+	0.158196i
$446$	−2.85140e11	+	4.93878e11i	−0.341234	+	0.591034i
$447$	−6.07030e11	+	7.59958e11i	−0.719161	+	0.900338i
$448$	−5.97796e10	−	1.03541e11i	−0.0701136	−	0.121440i
$449$	3.33477e11			0.387219			0.193610	−	0.981079i	$-0.437980\pi$
$449$	3.33477e11			0.387219			0.193610	+	0.981079i	$0.437980\pi$
$450$	−1.15707e11	+	1.07021e11i	−0.133016	+	0.123030i
$451$	4.54934e11			0.517790
$452$	2.15567e11	+	3.73374e11i	0.242918	+	0.420747i
$453$	−1.03088e11	−	2.63276e11i	−0.115018	−	0.293744i
$454$	4.11125e11	−	7.12089e11i	0.454174	−	0.786653i
$455$	−1.68652e11	+	2.92114e11i	−0.184476	+	0.319522i
$456$	−5.01547e11	−	7.60017e10i	−0.543213	−	0.0823154i
$457$	−5.73242e11	−	9.92885e11i	−0.614774	−	1.06482i	−0.990424	−	0.138058i	$-0.955914\pi$
$457$	−5.73242e11	−	9.92885e11i	−0.614774	−	1.06482i	0.375650	−	0.926761i	$-0.377419\pi$
$458$	7.72319e11			0.820167
$459$	9.33510e11	+	4.52285e11i	0.981661	+	0.475615i
$460$	1.67567e11			0.174493
$461$	5.61751e11	+	9.72981e11i	0.579281	+	1.00334i	0.995562	+	0.0941085i	$0.0300001\pi$
$461$	5.61751e11	+	9.72981e11i	0.579281	+	1.00334i	−0.416281	+	0.909236i	$0.636667\pi$
$462$	−1.62320e11	−	2.45970e10i	−0.165761	−	0.0251185i
$463$	7.26857e11	−	1.25895e12i	0.735080	−	1.27320i	−0.219609	−	0.975588i	$-0.570478\pi$
$463$	7.26857e11	−	1.25895e12i	0.735080	−	1.27320i	0.954688	−	0.297607i	$-0.0961886\pi$
$464$	−7.51048e10	+	1.30085e11i	−0.0752206	+	0.130286i
$465$	5.07759e11	+	1.29676e12i	0.503639	+	1.28624i
$466$	−6.09016e10	−	1.05485e11i	−0.0598262	−	0.103622i
$467$	1.50099e12			1.46034			0.730169	−	0.683267i	$-0.239442\pi$
$467$	1.50099e12			1.46034			0.730169	+	0.683267i	$0.239442\pi$
$468$	−1.92203e11	−	8.48278e11i	−0.185206	−	0.817395i
$469$	−2.08321e11			−0.198817
$470$	8.34355e9	+	1.44515e10i	0.00788698	+	0.0136606i
$471$	−3.10317e11	+	3.88495e11i	−0.290544	+	0.363740i
$472$	−1.06663e11	+	1.84745e11i	−0.0989176	+	0.171330i
$473$	2.19547e11	−	3.80266e11i	0.201675	−	0.349311i
$474$	4.11226e9	−	5.14825e9i	0.00374177	−	0.00468443i
$475$	1.08829e11	+	1.88497e11i	0.0980893	+	0.169896i
$476$	3.24088e11			0.289355
$477$	−9.90371e11	−	3.07205e11i	−0.875921	−	0.271703i
$478$	−1.03553e12			−0.907272
$479$	−2.59504e11	−	4.49474e11i	−0.225234	−	0.390117i	0.731155	−	0.682211i	$-0.238981\pi$
$479$	−2.59504e11	−	4.49474e11i	−0.225234	−	0.390117i	−0.956390	+	0.292094i	$0.905648\pi$
$480$	3.58903e11	+	9.16600e11i	0.308597	+	0.788124i
$481$	−3.53664e11	+	6.12564e11i	−0.301258	+	0.521794i
$482$	−5.04860e11	+	8.74444e11i	−0.426049	+	0.737939i
$483$	−1.35951e11	−	2.06012e10i	−0.113663	−	0.0172239i
$484$	−1.44096e11	−	2.49582e11i	−0.119357	−	0.206733i
$485$	6.40011e11			0.525230
$486$	1.52027e11	−	6.54144e11i	0.123611	−	0.531875i
$487$	1.23765e12			0.997052			0.498526	−	0.866875i	$-0.333875\pi$
$487$	1.23765e12			0.997052			0.498526	+	0.866875i	$0.333875\pi$
$488$	−6.91389e11	−	1.19752e12i	−0.551865	−	0.955859i
$489$	−1.24405e12	−	1.88517e11i	−0.983897	−	0.149094i
$490$	−4.06850e10	+	7.04685e10i	−0.0318825	+	0.0552221i
$491$	3.87000e11	−	6.70304e11i	0.300500	−	0.520481i	−0.675749	−	0.737132i	$-0.736180\pi$
$491$	3.87000e11	−	6.70304e11i	0.300500	−	0.520481i	0.976249	+	0.216650i	$0.0695131\pi$
$492$	2.11993e11	+	5.41408e11i	0.163109	+	0.416564i
$493$	5.53628e11	+	9.58912e11i	0.422092	+	0.731085i
$494$	5.10302e11			0.385528
$495$	8.47131e11	+	2.62773e11i	0.634201	+	0.196724i
$496$	−4.42788e11			−0.328495
$497$	2.03298e11	+	3.52123e11i	0.149462	+	0.258875i
$498$	2.73727e11	−	3.42687e11i	0.199428	−	0.249669i
$499$	−7.25827e11	+	1.25717e12i	−0.524059	+	0.907697i	0.475548	+	0.879690i	$0.342250\pi$
$499$	−7.25827e11	+	1.25717e12i	−0.524059	+	0.907697i	−0.999608	+	0.0280079i	$0.991084\pi$
$500$	5.33898e11	−	9.24739e11i	0.382026	−	0.661689i
$501$	−1.57913e12	+	1.97696e12i	−1.11982	+	1.40194i
$502$	1.72816e9	+	2.99326e9i	0.00121455	+	0.00210367i
$503$	2.34790e12			1.63540			0.817699	−	0.575646i	$-0.195249\pi$
$503$	2.34790e12			1.63540			0.817699	+	0.575646i	$0.195249\pi$
$504$	−1.12432e11	−	4.96210e11i	−0.0776159	−	0.342553i
$505$	1.78379e12			1.22048
$506$	−9.94735e10	−	1.72293e11i	−0.0674575	−	0.116840i
$507$	2.31127e11	+	5.90275e11i	0.155352	+	0.396751i
$508$	−7.34109e11	+	1.27151e12i	−0.489073	+	0.847100i
$509$	7.07563e10	−	1.22553e11i	0.0467234	−	0.0809274i	−0.841718	−	0.539918i	$-0.818455\pi$
$509$	7.07563e10	−	1.22553e11i	0.0467234	−	0.0809274i	0.888441	+	0.458990i	$0.151789\pi$
$510$	7.35471e11	+	1.11449e11i	0.481393	+	0.0729476i
$511$	5.55895e11	+	9.62838e11i	0.360660	+	0.624682i
$512$	−5.93874e11			−0.381926
$513$	−8.34625e11	−	4.04376e11i	−0.532063	−	0.257785i
$514$	−5.76474e11			−0.364289
$515$	−1.01909e12	−	1.76511e12i	−0.638380	−	1.10571i
$516$	5.54854e11	+	8.40794e10i	0.344552	+	0.0522115i
$517$	−2.33167e10	+	4.03857e10i	−0.0143535	+	0.0248611i
$518$	−8.53166e10	+	1.47773e11i	−0.0520655	+	0.0901800i
$519$	8.10676e10	+	2.07038e11i	0.0490449	+	0.125255i
$520$	−7.56229e11	−	1.30983e12i	−0.453564	−	0.785595i
$521$	2.49536e11			0.148376			0.0741880	−	0.997244i	$-0.476364\pi$
$521$	2.49536e11			0.148376			0.0741880	+	0.997244i	$0.476364\pi$
$522$	5.26270e11	−	4.86761e11i	0.310235	−	0.286945i
$523$	−1.06477e12			−0.622298			−0.311149	−	0.950361i	$-0.600714\pi$
$523$	−1.06477e12			−0.622298			−0.311149	+	0.950361i	$0.600714\pi$
$524$	−9.68616e11	−	1.67769e12i	−0.561256	−	0.972123i
$525$	−1.36247e11	+	1.70572e11i	−0.0782729	+	0.0979920i
$526$	3.43002e11	−	5.94097e11i	0.195371	−	0.338393i
$527$	−1.63199e12	+	2.82668e12i	−0.921656	+	1.59636i
$528$	−1.76003e11	+	2.20343e11i	−0.0985524	+	0.123381i
$529$	8.17262e11	+	1.41554e12i	0.453744	+	0.785908i
$530$	−7.43593e11			−0.409349
$531$	−2.86320e11	+	2.64825e11i	−0.156288	+	0.144555i
$532$	−2.89758e11			−0.156831
$533$	−7.09153e11	−	1.22829e12i	−0.380599	−	0.659217i
$534$	8.36003e10	+	2.13506e11i	0.0444910	+	0.113625i
$535$	6.43220e11	−	1.11409e12i	0.339444	−	0.587934i
$536$	4.67051e11	−	8.08955e11i	0.244412	−	0.423334i
$537$	−2.15092e12	−	3.25938e11i	−1.11619	−	0.169142i
$538$	5.51768e11	+	9.55691e11i	0.283947	+	0.491810i
$539$	−2.27394e11			−0.116046
$540$	8.20308e10	+	1.13060e12i	0.0415150	+	0.572187i
$541$	1.22109e12			0.612858			0.306429	−	0.951893i	$-0.400866\pi$
$541$	1.22109e12			0.612858			0.306429	+	0.951893i	$0.400866\pi$
$542$	9.26289e11	+	1.60438e12i	0.461052	+	0.798565i
$543$	9.83005e11	+	1.48959e11i	0.485240	+	0.0735306i
$544$	−1.15355e12	+	1.99801e12i	−0.564731	+	0.978142i
$545$	−1.07762e12	+	1.86649e12i	−0.523215	+	0.906235i
$546$	1.86615e11	+	4.76594e11i	0.0898625	+	0.229499i
$547$	7.32832e11	+	1.26930e12i	0.349995	+	0.606209i	0.986248	−	0.165271i	$-0.0528500\pi$
$547$	7.32832e11	+	1.26930e12i	0.349995	+	0.606209i	−0.636253	+	0.771480i	$0.719517\pi$
$548$	2.10956e12			0.999264
$549$	−5.58651e11	−	2.46558e12i	−0.262461	−	1.15836i
$550$	−3.15860e11			−0.147184
$551$	−4.94984e11	−	8.57337e11i	−0.228775	−	0.396250i
$552$	3.84798e11	−	4.81740e11i	0.176403	−	0.220845i
$553$	4.56320e9	−	7.90369e9i	0.00207494	−	0.00359391i
$554$	−6.49768e11	+	1.12543e12i	−0.293065	+	0.507604i
$555$	5.75335e11	−	7.20279e11i	0.257397	−	0.322242i
$556$	7.12266e11	+	1.23368e12i	0.316086	+	0.547477i
$557$	−1.18108e12			−0.519912			−0.259956	−	0.965620i	$-0.583708\pi$
$557$	−1.18108e12			−0.519912			−0.259956	+	0.965620i	$0.583708\pi$
$558$	2.01831e12	+	6.26062e11i	0.881320	+	0.273378i
$559$	−1.36892e12			−0.592960
$560$	6.98866e10	+	1.21047e11i	0.0300295	+	0.0520126i
$561$	7.57938e11	+	1.93569e12i	0.323073	+	0.825094i
$562$	3.10173e11	−	5.37235e11i	0.131157	−	0.227170i
$563$	−1.58950e12	+	2.75309e12i	−0.666763	+	1.15487i	0.312041	+	0.950069i	$0.398987\pi$
$563$	−1.58950e12	+	2.75309e12i	−0.666763	+	1.15487i	−0.978804	+	0.204799i	$0.934346\pi$
$564$	−5.89275e10	−	8.92954e9i	−0.0245223	−	0.00371598i
$565$	6.85321e11	+	1.18701e12i	0.282928	+	0.490046i
$566$	1.62565e12			0.665815
$567$	7.24468e10	−	9.27371e11i	0.0294371	−	0.376816i
$568$	−1.82316e12			−0.734950
$569$	2.07439e12	+	3.59295e12i	0.829631	+	1.43696i	0.898328	+	0.439326i	$0.144783\pi$
$569$	2.07439e12	+	3.59295e12i	0.829631	+	1.43696i	−0.0686967	+	0.997638i	$0.521884\pi$
$570$	−6.57564e11	−	9.96436e10i	−0.260916	−	0.0395378i
$571$	−1.11962e11	+	1.93925e11i	−0.0440768	+	0.0763432i	−0.887222	−	0.461342i	$-0.847368\pi$
$571$	−1.11962e11	+	1.93925e11i	−0.0440768	+	0.0763432i	0.843145	+	0.537686i	$0.180701\pi$
$572$	8.71533e11	−	1.50954e12i	0.340410	−	0.589607i
$573$	−1.86457e12	−	4.76191e12i	−0.722575	−	1.84538i
$574$	−1.71074e11	−	2.96308e11i	−0.0657778	−	0.113930i
$575$	−2.64548e11			−0.100925
$576$	9.36125e11	+	2.90378e11i	0.354350	+	0.109916i
$577$	1.17546e12			0.441484			0.220742	−	0.975332i	$-0.429152\pi$
$577$	1.17546e12			0.441484			0.220742	+	0.975332i	$0.429152\pi$
$578$	1.39101e11	+	2.40931e11i	0.0518390	+	0.0897878i
$579$	7.40532e11	−	9.27093e11i	0.273836	−	0.342823i
$580$	−6.05009e11	+	1.04791e12i	−0.221991	+	0.384500i
$581$	3.03743e11	−	5.26099e11i	0.110590	−	0.191547i
$582$	6.06105e11	−	7.58800e11i	0.218975	−	0.274141i
$583$	−1.03901e12	−	1.79962e12i	−0.372488	−	0.645168i
$584$	−4.98522e12			−1.77348
$585$	−6.11043e11	−	2.69680e12i	−0.215710	−	0.952024i
$586$	−5.53775e11			−0.193997
$587$	8.00486e11	+	1.38648e12i	0.278280	+	0.481995i	0.970957	−	0.239252i	$-0.0769023\pi$
$587$	8.00486e11	+	1.38648e12i	0.278280	+	0.481995i	−0.692677	+	0.721248i	$0.743569\pi$
$588$	−1.05963e11	−	2.70618e11i	−0.0365557	−	0.0933595i
$589$	1.45911e12	−	2.52726e12i	0.499540	−	0.865229i
$590$	−1.39842e11	+	2.42214e11i	−0.0475122	+	0.0822935i
$591$	−2.37033e12	−	3.59187e11i	−0.799218	−	0.121109i
$592$	1.46552e11	+	2.53836e11i	0.0490394	+	0.0849388i
$593$	−5.48946e11			−0.182299			−0.0911493	−	0.995837i	$-0.529054\pi$
$593$	−5.48946e11			−0.182299			−0.0911493	+	0.995837i	$0.529054\pi$
$594$	1.11380e12	−	7.55511e11i	0.367086	−	0.249001i
$595$	1.03032e12			0.337014
$596$	−1.24559e12	−	2.15743e12i	−0.404360	−	0.700371i
$597$	1.61213e12	+	2.44293e11i	0.519416	+	0.0787094i
$598$	−3.10120e11	+	5.37143e11i	−0.0991685	+	0.171765i
$599$	7.42003e11	−	1.28519e12i	0.235497	−	0.407892i	−0.723920	−	0.689884i	$-0.757662\pi$
$599$	7.42003e11	−	1.28519e12i	0.235497	−	0.407892i	0.959417	+	0.281992i	$0.0909950\pi$
$600$	−3.56905e11	−	9.11497e11i	−0.112427	−	0.287127i
$601$	2.04551e11	+	3.54293e11i	0.0639539	+	0.110771i	0.896229	−	0.443591i	$-0.146296\pi$
$601$	2.04551e11	+	3.54293e11i	0.0639539	+	0.110771i	−0.832276	+	0.554362i	$0.812962\pi$
$602$	−3.30234e11			−0.102480
$603$	1.25373e12	−	1.15960e12i	0.386166	−	0.357175i
$604$	7.24172e11			0.221399
$605$	−4.58104e11	−	7.93460e11i	−0.139016	−	0.240783i
$606$	1.68929e12	−	2.11487e12i	0.508835	−	0.637025i
$607$	9.89523e11	−	1.71390e12i	0.295854	−	0.512434i	−0.679329	−	0.733833i	$-0.737729\pi$
$607$	9.89523e11	−	1.71390e12i	0.295854	−	0.512434i	0.975183	+	0.221400i	$0.0710626\pi$
$608$	1.03136e12	−	1.78636e12i	0.306086	−	0.530156i
$609$	6.19692e11	−	7.75810e11i	0.182557	−	0.228548i
$610$	−9.06460e11	−	1.57003e12i	−0.265072	−	0.459119i
$611$	1.45385e11			0.0422020
$612$	−1.95044e12	+	1.80401e12i	−0.562020	+	0.519827i
$613$	5.10683e12			1.46076			0.730381	−	0.683040i	$-0.239343\pi$
$613$	5.10683e12			1.46076			0.730381	+	0.683040i	$0.239343\pi$
$614$	−1.28850e12	−	2.23174e12i	−0.365869	−	0.633704i
$615$	6.73959e11	+	1.72122e12i	0.189974	+	0.485175i
$616$	5.09814e11	−	8.83023e11i	0.142659	−	0.247092i
$617$	−1.43680e12	+	2.48862e12i	−0.399130	+	0.691313i	−0.993619	−	0.112791i	$-0.964021\pi$
$617$	−1.43680e12	+	2.48862e12i	−0.399130	+	0.691313i	0.594489	+	0.804104i	$0.297354\pi$
$618$	−3.05783e12	−	4.63366e11i	−0.843266	−	0.127784i
$619$	1.00461e12	+	1.74004e12i	0.275037	+	0.476378i	0.970144	−	0.242528i	$-0.0779766\pi$
$619$	1.00461e12	+	1.74004e12i	0.275037	+	0.476378i	−0.695107	+	0.718906i	$0.744643\pi$
$620$	−3.56690e12			−0.969455
$621$	9.32861e11	−	6.32778e11i	0.251713	−	0.170742i
$622$	−3.77834e11			−0.101215
$623$	1.58794e11	+	2.75039e11i	0.0422316	+	0.0731473i
$624$	8.69265e11	+	1.31724e11i	0.229521	+	0.0347803i
$625$	1.06445e12	−	1.84368e12i	0.279039	−	0.483310i
$626$	7.66310e11	−	1.32729e12i	0.199444	−	0.345446i
$627$	−6.77651e11	−	1.73065e12i	−0.175106	−	0.447203i
$628$	−6.36754e11	−	1.10289e12i	−0.163363	−	0.282953i
$629$	2.16059e12			0.550358
$630$	−1.47406e11	−	6.50567e11i	−0.0372805	−	0.164536i
$631$	7.86052e12			1.97387			0.986936	−	0.161111i	$-0.0515076\pi$
$631$	7.86052e12			1.97387			0.986936	+	0.161111i	$0.0515076\pi$
$632$	2.04612e10	+	3.54398e10i	0.00510157	+	0.00883618i
$633$	−2.89163e12	+	3.62012e12i	−0.715857	+	0.896202i
$634$	−9.14657e11	+	1.58423e12i	−0.224831	+	0.389419i
$635$	−2.33384e12	+	4.04234e12i	−0.569626	+	0.986622i
$636$	1.65753e12	−	2.07511e12i	0.401702	−	0.502903i
$637$	3.54464e11	+	6.13949e11i	0.0852991	+	0.147742i
$638$	1.43662e12			0.343280
$639$	−3.18357e12	−	9.87516e11i	−0.755371	−	0.234310i
$640$	−2.88949e12			−0.680787
$641$	−6.60484e11	−	1.14399e12i	−0.154526	−	0.267646i	0.778360	−	0.627818i	$-0.216052\pi$
$641$	−6.60484e11	−	1.14399e12i	−0.154526	−	0.267646i	−0.932886	+	0.360171i	$0.882718\pi$
$642$	−7.11727e11	−	1.81768e12i	−0.165351	−	0.422288i
$643$	3.04440e12	−	5.27306e12i	0.702349	−	1.21650i	−0.265291	−	0.964168i	$-0.585468\pi$
$643$	3.04440e12	−	5.27306e12i	0.702349	−	1.21650i	0.967640	−	0.252335i	$-0.0811985\pi$
$644$	1.76091e11	−	3.04999e11i	0.0403414	−	0.0698734i
$645$	1.76396e12	+	2.67301e11i	0.401302	+	0.0608110i
$646$	−7.79381e11	−	1.34993e12i	−0.176077	−	0.304975i
$647$	−6.70614e12			−1.50454			−0.752269	−	0.658856i	$-0.771041\pi$
$647$	−6.70614e12			−1.50454			−0.752269	+	0.658856i	$0.771041\pi$
$648$	3.43876e12	+	2.36047e12i	0.766152	+	0.525910i
$649$	−7.81600e11			−0.172935
$650$	4.92363e11	+	8.52799e11i	0.108187	+	0.187386i
$651$	2.89391e12	+	4.38527e11i	0.631496	+	0.0956933i
$652$	1.61137e12	−	2.79097e12i	0.349205	−	0.604841i
$653$	−4.87272e11	+	8.43980e11i	−0.104873	+	0.181645i	−0.913686	−	0.406420i	$-0.866777\pi$
$653$	−4.87272e11	+	8.43980e11i	−0.104873	+	0.181645i	0.808814	+	0.588065i	$0.200110\pi$
$654$	1.19239e12	+	3.04524e12i	0.254870	+	0.650911i
$655$	−3.07937e12	−	5.33363e12i	−0.653697	−	1.13224i
$656$	−5.87722e11			−0.123910
$657$	−8.70508e12	−	2.70024e12i	−1.82276	−	0.565404i
$658$	3.50720e10			0.00729364
$659$	5.01384e11	+	8.68423e11i	0.103559	+	0.179369i	0.913148	−	0.407627i	$-0.133644\pi$
$659$	5.01384e11	+	8.68423e11i	0.103559	+	0.179369i	−0.809590	+	0.586996i	$0.800310\pi$
$660$	−1.41780e12	+	1.77498e12i	−0.290848	+	0.364121i
$661$	−4.58227e12	+	7.93672e12i	−0.933628	+	1.61709i	−0.156565	+	0.987668i	$0.550042\pi$
$661$	−4.58227e12	+	7.93672e12i	−0.933628	+	1.61709i	−0.777063	+	0.629423i	$0.783291\pi$
$662$	−3.96995e11	+	6.87615e11i	−0.0803385	+	0.139150i
$663$	4.04476e12	−	5.06374e12i	0.812983	−	1.01780i
$664$	1.36197e12	+	2.35901e12i	0.271902	+	0.470948i
$665$	−9.21185e11			−0.182662
$666$	−3.09111e11	−	1.36424e12i	−0.0608807	−	0.268694i
$667$	1.20324e12			0.235389
$668$	−3.24030e12	−	5.61236e12i	−0.629638	−	1.09057i
$669$	−2.36096e12	−	6.02965e12i	−0.455692	−	1.16379i
$670$	6.12337e11	−	1.06060e12i	0.117396	−	0.203336i
$671$	2.53317e12	−	4.38758e12i	0.482406	−	0.835552i
$672$	2.04552e12	+	3.09967e11i	0.386939	+	0.0586346i
$673$	1.19369e12	+	2.06754e12i	0.224298	+	0.388495i	0.956108	−	0.293013i	$-0.0946579\pi$
$673$	1.19369e12	+	2.06754e12i	0.224298	+	0.388495i	−0.731811	+	0.681508i	$0.761325\pi$
$674$	−5.53551e12			−1.03321
$675$	−1.29507e11	−	1.78496e12i	−0.0240119	−	0.330949i
$676$	−1.62362e12			−0.299037
$677$	2.49038e12	+	4.31347e12i	0.455635	+	0.789183i	0.998724	−	0.0504918i	$-0.0160789\pi$
$677$	2.49038e12	+	4.31347e12i	0.455635	+	0.789183i	−0.543089	+	0.839675i	$0.682746\pi$
$678$	2.05634e12	+	3.11607e11i	0.373733	+	0.0566335i
$679$	6.72569e11	−	1.16492e12i	0.121429	−	0.210322i
$680$	−2.30997e12	+	4.00098e12i	−0.414301	+	0.717590i
$681$	3.40411e12	+	8.69374e12i	0.606516	+	1.54898i
$682$	2.11744e12	+	3.66751e12i	0.374784	+	0.649144i
$683$	5.61688e12			0.987647			0.493824	−	0.869562i	$-0.335599\pi$
$683$	5.61688e12			0.987647			0.493824	+	0.869562i	$0.335599\pi$
$684$	1.74384e12	−	1.61292e12i	0.304616	−	0.281748i
$685$	6.70662e12			1.16385
$686$	8.55095e10	+	1.48107e11i	0.0147420	+	0.0255339i
$687$	−5.47311e12	+	6.85194e12i	−0.937409	+	1.17357i
$688$	−2.83629e11	+	4.91260e11i	−0.0482617	+	0.0835918i
$689$	−3.23923e12	+	5.61052e12i	−0.547590	+	0.948455i
$690$	5.04498e11	−	6.31595e11i	0.0847302	−	0.106076i
$691$	5.27930e12	+	9.14401e12i	0.880897	+	1.52576i	0.850345	+	0.526225i	$0.176393\pi$
$691$	5.27930e12	+	9.14401e12i	0.880897	+	1.52576i	0.0305515	+	0.999533i	$0.490274\pi$
$692$	−5.69482e11			−0.0944066
$693$	1.36852e12	−	1.26578e12i	0.225398	−	0.208477i
$694$	−6.35081e12			−1.03923
$695$	2.26440e12	+	3.92206e12i	0.368147	+	0.637650i
$696$	1.62331e12	+	4.14575e12i	0.262216	+	0.669671i
$697$	−2.16617e12	+	3.75192e12i	−0.347652	+	0.602151i
$698$	−1.81616e12	+	3.14569e12i	−0.289605	+	0.501610i
$699$	1.36743e12	+	2.07213e11i	0.216650	+	0.0328300i
$700$	−2.79572e11	−	4.84233e11i	−0.0440101	−	0.0762278i
$701$	−3.57511e12			−0.559188			−0.279594	−	0.960118i	$-0.590200\pi$
$701$	−3.57511e12			−0.559188			−0.279594	+	0.960118i	$0.590200\pi$
$702$	−3.77602e12	−	1.82948e12i	−0.586837	−	0.284322i
$703$	−1.93173e12			−0.298296
$704$	9.82102e11	+	1.70105e12i	0.150688	+	0.261000i
$705$	−1.87339e11	−	2.83884e10i	−0.0285613	−	0.00432802i
$706$	1.15955e11	−	2.00841e11i	0.0175659	−	0.0304250i
$707$	1.87453e12	−	3.24678e12i	0.282167	−	0.488727i
$708$	−3.64215e11	−	9.30168e11i	−0.0544764	−	0.139127i
$709$	−5.29569e10	−	9.17240e10i	−0.00787072	−	0.0136325i	0.862063	−	0.506801i	$-0.169172\pi$
$709$	−5.29569e10	−	9.17240e10i	−0.00787072	−	0.0136325i	−0.869934	+	0.493168i	$0.835839\pi$
$710$	−2.39030e12			−0.353012
$711$	1.65329e10	+	7.29671e10i	0.00242625	+	0.0107081i
$712$	−1.42405e12			−0.207666
$713$	1.77346e12	+	3.07172e12i	0.256991	+	0.445122i
$714$	9.75742e11	−	1.22156e12i	0.140505	−	0.175903i
$715$	2.77074e12	−	4.79906e12i	0.396477	−	0.686718i
$716$	2.78599e12	−	4.82548e12i	0.396160	−	0.686170i
$717$	7.33838e12	−	9.18713e12i	1.03696	−	1.29821i
$718$	3.41106e12	+	5.90812e12i	0.478993	+	0.829639i
$719$	−1.17820e12			−0.164413			−0.0822067	−	0.996615i	$-0.526197\pi$
$719$	−1.17820e12			−0.164413			−0.0822067	+	0.996615i	$0.526197\pi$
$720$	−1.09440e12	−	3.39472e11i	−0.151767	−	0.0470769i
$721$	−4.28372e12			−0.590354
$722$	−1.29670e12	−	2.24594e12i	−0.177591	−	0.307596i
$723$	−4.18024e12	−	1.06759e13i	−0.568957	−	1.45306i
$724$	−1.27324e12	+	2.20532e12i	−0.172222	+	0.298297i
$725$	9.55167e11	−	1.65440e12i	0.128398	−	0.222392i
$726$	−1.37457e12	−	2.08294e11i	−0.183633	−	0.0278267i
$727$	−2.05895e12	−	3.56621e12i	−0.273364	−	0.473480i	0.696357	−	0.717696i	$-0.254803\pi$
$727$	−2.05895e12	−	3.56621e12i	−0.273364	−	0.473480i	−0.969721	+	0.244215i	$0.921470\pi$
$728$	−3.17880e12			−0.419442
$729$	4.72615e12	+	5.98442e12i	0.619774	+	0.784780i
$730$	−6.53598e12			−0.851839
$731$	2.09075e12	+	3.62128e12i	0.270815	+	0.469066i
$732$	6.40200e12	+	9.70123e11i	0.824168	+	0.124890i
$733$	−5.45109e12	+	9.44157e12i	−0.697454	+	1.20803i	0.271892	+	0.962328i	$0.412351\pi$
$733$	−5.45109e12	+	9.44157e12i	−0.697454	+	1.20803i	−0.969346	+	0.245698i	$0.920983\pi$
$734$	1.36339e12	−	2.36146e12i	0.173375	−	0.300295i
$735$	−3.36872e11	−	8.60335e11i	−0.0425767	−	0.108736i
$736$	1.25355e12	+	2.17121e12i	0.157467	+	0.272742i
$737$	3.42244e12			0.427299
$738$	2.67894e12	+	8.30986e11i	0.332437	+	0.103119i
$739$	8.02297e12			0.989544			0.494772	−	0.869023i	$-0.335252\pi$
$739$	8.02297e12			0.989544			0.494772	+	0.869023i	$0.335252\pi$
$740$	1.18056e12	+	2.04479e12i	0.144725	+	0.250671i
$741$	−3.61630e12	+	4.52735e12i	−0.440639	+	0.551649i
$742$	−7.81421e11	+	1.35346e12i	−0.0946384	+	0.163919i
$743$	3.83082e12	−	6.63518e12i	0.461150	−	0.798736i	−0.537868	−	0.843029i	$-0.680770\pi$
$743$	3.83082e12	−	6.63518e12i	0.461150	−	0.798736i	0.999019	+	0.0442930i	$0.0141035\pi$
$744$	−8.19098e12	+	1.02545e13i	−0.980071	+	1.22698i
$745$	−3.95993e12	−	6.85879e12i	−0.470960	−	0.815726i
$746$	2.13877e12			0.252836
$747$	1.10049e12	+	4.85696e12i	0.129314	+	0.570718i
$748$	−5.32435e12			−0.621884
$749$	−1.35188e12	−	2.34153e12i	−0.156954	−	0.271852i
$750$	−1.87812e12	−	4.79652e12i	−0.216744	−	0.553542i
$751$	7.45822e12	−	1.29180e13i	0.855570	−	1.48189i	−0.0205447	−	0.999789i	$-0.506540\pi$
$751$	7.45822e12	−	1.29180e13i	0.855570	−	1.48189i	0.876115	−	0.482102i	$-0.160127\pi$
$752$	3.01224e10	−	5.21736e10i	0.00343487	−	0.00594936i
$753$	−3.88026e10	−	5.87993e9i	−0.00439829	−	0.000666492i
$754$	−2.23941e12	−	3.87877e12i	−0.252326	−	0.437042i
$755$	2.30225e12			0.257864
$756$	2.14409e12	+	1.03881e12i	0.238723	+	0.115661i
$757$	5.10347e11			0.0564852			0.0282426	−	0.999601i	$-0.491009\pi$
$757$	5.10347e11			0.0564852			0.0282426	+	0.999601i	$0.491009\pi$
$758$	1.98800e12	+	3.44332e12i	0.218728	+	0.378849i
$759$	2.23350e12	+	3.38452e11i	0.244285	+	0.0370176i
$760$	2.06528e12	−	3.57716e12i	0.224552	−	0.388936i
$761$	−8.19732e12	+	1.41982e13i	−0.886014	+	1.53462i	−0.0414675	+	0.999140i	$0.513203\pi$
$761$	−8.19732e12	+	1.41982e13i	−0.886014	+	1.53462i	−0.844547	+	0.535482i	$0.820130\pi$
$762$	2.58241e12	+	6.59521e12i	0.277478	+	0.708649i
$763$	2.26488e12	+	3.92288e12i	0.241927	+	0.419030i
$764$	1.30982e13			1.39089
$765$	−6.20075e12	+	5.73523e12i	−0.654587	+	0.605445i
$766$	−3.77066e12			−0.395720
$767$	1.21836e12	+	2.11027e12i	0.127115	+	0.220170i
$768$	−4.96878e12	+	6.22056e12i	−0.515377	+	0.645215i
$769$	−3.12810e12	+	5.41803e12i	−0.322561	+	0.558692i	−0.981016	−	0.193928i	$-0.937877\pi$
$769$	−3.12810e12	+	5.41803e12i	−0.322561	+	0.558692i	0.658455	+	0.752621i	$0.271210\pi$
$770$	6.68402e11	−	1.15771e12i	0.0685219	−	0.118683i
$771$	4.08524e12	−	5.11443e12i	0.416364	−	0.521257i
$772$	1.51953e12	+	2.63191e12i	0.153969	+	0.266681i
$773$	−5.51573e12			−0.555643			−0.277821	−	0.960633i	$-0.589612\pi$
$773$	−5.51573e12			−0.555643			−0.277821	+	0.960633i	$0.589612\pi$
$774$	1.98743e12	−	1.83822e12i	0.199048	−	0.184104i
$775$	5.63129e12			0.560725
$776$	3.01577e12	+	5.22347e12i	0.298553	+	0.517108i
$777$	−7.06422e11	−	1.80413e12i	−0.0695296	−	0.177571i
$778$	2.88941e12	−	5.00461e12i	0.282749	−	0.489736i
$779$	1.93671e12	−	3.35448e12i	0.188429	−	0.326368i
$780$	7.00239e12	+	1.06110e12i	0.677362	+	0.102644i
$781$	−3.33993e12	−	5.78492e12i	−0.321224	−	0.556376i
$782$	1.89457e12			0.181168
$783$	5.89036e11	+	8.11849e12i	0.0560034	+	0.771876i
$784$	2.93767e11			0.0277703
$785$	−2.02434e12	−	3.50625e12i	−0.190269	−	0.329556i
$786$	−9.23983e12	−	1.40015e12i	−0.863500	−	0.130850i
$787$	−5.68256e12	+	9.84249e12i	−0.528029	+	0.914574i	0.471437	+	0.881900i	$0.343736\pi$
$787$	−5.68256e12	+	9.84249e12i	−0.528029	+	0.914574i	−0.999466	+	0.0326737i	$0.989598\pi$
$788$	3.07018e12	−	5.31771e12i	0.283659	−	0.491311i
$789$	2.84006e12	+	7.25321e12i	0.260904	+	0.666321i
$790$	2.68261e10	+	4.64641e10i	0.00245039	+	0.00424420i
$791$	2.88074e12			0.261644
$792$	1.84711e12	+	8.15209e12i	0.166812	+	0.736217i
$793$	−1.57949e13			−1.41836
$794$	−2.50414e12	−	4.33730e12i	−0.223598	−	0.387282i
$795$	5.26954e12	−	6.59708e12i	0.467865	−	0.585733i
$796$	−2.08812e12	+	3.61673e12i	−0.184351	+	0.319306i
$797$	4.03888e12	−	6.99555e12i	0.354567	−	0.614129i	−0.632477	−	0.774580i	$-0.717962\pi$
$797$	4.03888e12	−	6.99555e12i	0.354567	−	0.614129i	0.987044	+	0.160451i	$0.0512949\pi$
$798$	−8.72384e11	+	1.09216e12i	−0.0761543	+	0.0953398i
$799$	−2.22045e11	−	3.84593e11i	−0.0192744	−	0.0333842i
$800$	3.98041e12			0.343576
$801$	−2.48665e12	−	7.71337e11i	−0.213436	−	0.0662061i
$802$	1.12221e13			0.957836
$803$	−9.13263e12	−	1.58182e13i	−0.775132	−	1.34257i
$804$	1.59481e12	+	4.07298e12i	0.134604	+	0.343764i
$805$	5.59820e11	−	9.69637e11i	0.0469858	−	0.0813819i
$806$	6.60134e12	−	1.14339e13i	0.550966	−	0.954300i
$807$	−1.23890e13	−	1.87735e12i	−1.02826	−	0.155817i
$808$	8.40532e12	+	1.45584e13i	0.693750	+	1.20161i
$809$	−1.40783e13			−1.15553			−0.577765	−	0.816203i	$-0.696075\pi$
$809$	−1.40783e13			−1.15553			−0.577765	+	0.816203i	$0.696075\pi$
$810$	4.50846e12	+	3.09475e12i	0.367998	+	0.252606i
$811$	−3.27789e12			−0.266073			−0.133037	−	0.991111i	$-0.542473\pi$
$811$	−3.27789e12			−0.266073			−0.133037	+	0.991111i	$0.542473\pi$
$812$	1.27157e12	+	2.20243e12i	0.102645	+	0.177787i
$813$	−2.07981e13	−	3.15163e12i	−1.66962	−	0.253004i
$814$	1.40164e12	−	2.42771e12i	0.111899	−	0.193815i
$815$	5.12278e12	−	8.87292e12i	0.406721	−	0.704461i
$816$	−9.79168e11	−	2.50069e12i	−0.0773128	−	0.197449i
$817$	−1.86928e12	−	3.23768e12i	−0.146783	−	0.254235i
$818$	1.20285e13			0.939340
$819$	−5.55076e12	−	1.72180e12i	−0.431097	−	0.133723i
$820$	−4.73441e12			−0.365682
$821$	9.97902e12	+	1.72842e13i	0.766556	+	1.32771i	0.939420	+	0.342768i	$0.111364\pi$
$821$	9.97902e12	+	1.72842e13i	0.766556	+	1.32771i	−0.172864	+	0.984946i	$0.555302\pi$
$822$	6.35133e12	−	7.95141e12i	0.485223	−	0.607465i
$823$	4.82165e12	−	8.35134e12i	0.366350	−	0.634537i	−0.622642	−	0.782507i	$-0.713941\pi$
$823$	4.82165e12	−	8.35134e12i	0.366350	−	0.634537i	0.988992	+	0.147970i	$0.0472739\pi$
$824$	9.60402e12	−	1.66346e13i	0.725739	−	1.25702i
$825$	2.23837e12	−	2.80228e12i	0.168224	−	0.210605i
$826$	2.93913e11	+	5.09073e11i	0.0219689	+	0.0380513i
$827$	2.30890e13			1.71645			0.858224	−	0.513275i	$-0.171568\pi$
$827$	2.30890e13			1.71645			0.858224	+	0.513275i	$0.171568\pi$
$828$	6.37996e11	+	2.81576e12i	0.0471717	+	0.208189i
$829$	−2.04493e13			−1.50378			−0.751888	−	0.659291i	$-0.770856\pi$
$829$	−2.04493e13			−1.50378			−0.751888	+	0.659291i	$0.770856\pi$
$830$	1.78564e12	+	3.09283e12i	0.130600	+	0.226206i
$831$	−5.38008e12	−	1.37402e13i	−0.391367	−	0.999510i
$832$	3.06181e12	−	5.30321e12i	0.221525	−	0.383693i
$833$	1.08274e12	−	1.87536e12i	0.0779151	−	0.134953i
$834$	6.79445e12	+	1.02959e12i	0.486303	+	0.0736917i
$835$	−1.03014e13	−	1.78425e13i	−0.733343	−	1.27019i
$836$	4.76035e12			0.337063
$837$	−1.98573e13	+	1.34696e13i	−1.39848	+	0.948615i
$838$	−6.62113e12			−0.463803
$839$	−5.48661e11	−	9.50308e11i	−0.0382274	−	0.0662118i	0.846279	−	0.532740i	$-0.178838\pi$
$839$	−5.48661e11	−	9.50308e11i	−0.0382274	−	0.0662118i	−0.884506	+	0.466529i	$0.845504\pi$
$840$	4.09613e12	+	6.20705e11i	0.283868	+	0.0430158i
$841$	2.90920e12	−	5.03888e12i	0.200536	−	0.347338i
$842$	2.74879e12	−	4.76104e12i	0.188468	−	0.326436i
$843$	2.56823e12	+	6.55898e12i	0.175150	+	0.447314i
$844$	−5.93347e12	−	1.02771e13i	−0.402502	−	0.697154i
$845$	−5.16173e12			−0.348289
$846$	−2.11072e11	+	1.95226e11i	−0.0141666	+	0.0131030i
$847$	−1.92564e12			−0.128558
$848$	1.34228e12	+	2.32490e12i	0.0891380	+	0.154392i
$849$	−1.15203e13	+	1.44226e13i	−0.760993	+	0.952709i
$850$	1.50397e12	−	2.60495e12i	0.0988219	−	0.171164i
$851$	1.17395e12	−	2.03333e12i	0.0767299	−	0.132900i
$852$	5.32817e12	−	6.67048e12i	0.346417	−	0.433690i
$853$	−1.25247e13	−	2.16935e13i	−0.810023	−	1.40300i	−0.912847	−	0.408302i	$-0.866121\pi$
$853$	−1.25247e13	−	2.16935e13i	−0.810023	−	1.40300i	0.102824	−	0.994700i	$-0.467212\pi$
$854$	−3.81029e12			−0.245131
$855$	5.54392e12	−	5.12771e12i	0.354788	−	0.328153i
$856$	1.21236e13			0.771790
$857$	−4.62795e12	−	8.01584e12i	−0.293072	−	0.507616i	0.681462	−	0.731853i	$-0.261344\pi$
$857$	−4.62795e12	−	8.01584e12i	−0.293072	−	0.507616i	−0.974535	+	0.224237i	$0.928011\pi$
$858$	−3.06584e12	−	7.82982e12i	−0.193133	−	0.493241i
$859$	−9.31797e12	+	1.61392e13i	−0.583919	+	1.01138i	0.411091	+	0.911594i	$0.365148\pi$
$859$	−9.31797e12	+	1.61392e13i	−0.583919	+	1.01138i	−0.995009	+	0.0997821i	$0.968185\pi$
$860$	−2.28478e12	+	3.95736e12i	−0.142430	+	0.246696i
$861$	3.84115e12	+	5.82066e11i	0.238203	+	0.0360959i
$862$	−1.32765e12	−	2.29956e12i	−0.0819031	−	0.141860i
$863$	2.03142e13			1.24667			0.623336	−	0.781954i	$-0.285777\pi$
$863$	2.03142e13			1.24667			0.623336	+	0.781954i	$0.285777\pi$
$864$	−1.40359e13	+	9.52082e12i	−0.856896	+	0.581249i
$865$	−1.81047e12			−0.109956
$866$	−4.04488e12	−	7.00594e12i	−0.244385	−	0.423288i
$867$	−3.12327e12	−	4.73283e11i	−0.187726	−	0.0284469i
$868$	−3.74835e12	+	6.49233e12i	−0.224131	+	0.388206i
$869$	−7.49674e10	+	1.29847e11i	−0.00445947	+	0.00772404i
$870$	2.12827e12	+	5.43538e12i	0.125948	+	0.321657i
$871$	−5.33492e12	−	9.24034e12i	−0.314084	−	0.544009i
$872$	−2.03112e13			−1.18963
$873$	2.43679e12	+	1.07546e13i	0.141989	+	0.626658i
$874$	−1.69389e12			−0.0981935
$875$	−3.56738e12	−	6.17889e12i	−0.205737	−	0.356348i
$876$	1.45692e13	−	1.82396e13i	0.835927	−	1.04652i
$877$	1.39186e13	−	2.41078e13i	0.794509	−	1.37613i	−0.128642	−	0.991691i	$-0.541062\pi$
$877$	1.39186e13	−	2.41078e13i	0.794509	−	1.37613i	0.923151	−	0.384439i	$-0.125605\pi$
$878$	3.32491e12	−	5.75891e12i	0.188823	−	0.327050i
$879$	3.92438e12	−	4.91304e12i	0.221728	−	0.277588i
$880$	−1.14815e12	−	1.98865e12i	−0.0645394	−	0.111786i
$881$	−2.03212e13			−1.13647			−0.568234	−	0.822867i	$-0.692373\pi$
$881$	−2.03212e13			−1.13647			−0.568234	+	0.822867i	$0.692373\pi$
$882$	−1.33904e12	−	4.15360e11i	−0.0745051	−	0.0231109i
$883$	−2.39832e13			−1.32765			−0.663825	−	0.747888i	$-0.731068\pi$
$883$	−2.39832e13			−1.32765			−0.663825	+	0.747888i	$0.731068\pi$
$884$	8.29962e12	+	1.43754e13i	0.457112	+	0.791742i
$885$	−1.15790e12	−	2.95714e12i	−0.0634490	−	0.162042i
$886$	1.82647e12	−	3.16354e12i	0.0995775	−	0.172473i
$887$	8.68697e12	−	1.50463e13i	0.471207	−	0.816155i	−0.528250	−	0.849089i	$-0.677152\pi$
$887$	8.68697e12	−	1.50463e13i	0.471207	−	0.816155i	0.999458	+	0.0329338i	$0.0104850\pi$
$888$	8.58960e12	+	1.30162e12i	0.463569	+	0.0702467i
$889$	4.90514e12	+	8.49596e12i	0.263387	+	0.456199i
$890$	−1.86703e12			−0.0997463
$891$	−1.19021e12	+	1.52355e13i	−0.0632664	+	0.809855i
$892$	1.65852e13			0.877163
$893$	1.98524e11	+	3.43854e11i	0.0104468	+	0.0180943i
$894$	−1.18820e13	−	1.80053e12i	−0.622113	−	0.0942716i
$895$	8.85708e12	−	1.53409e13i	0.461410	−	0.799185i
$896$	−3.03648e12	+	5.25934e12i	−0.157393	+	0.272612i
$897$	−2.56779e12	−	6.55786e12i	−0.132432	−	0.338218i
$898$	2.06017e12	+	3.56832e12i	0.105721	+	0.183113i
$899$	−2.56127e13			−1.30779
$900$	4.37799e12	+	1.35802e12i	0.222425	+	0.0689943i
$901$	1.97890e13			1.00038
$902$	2.81052e12	+	4.86796e12i	0.141370	+	0.244860i
$903$	2.34023e12	−	2.92980e12i	0.117129	−	0.146637i
$904$	−6.45856e12	+	1.11866e13i	−0.321646	+	0.557107i
$905$	−4.04783e12	+	7.01105e12i	−0.200587	+	0.347428i
$906$	2.18029e12	−	2.72956e12i	0.107507	−	0.134591i
$907$	1.05462e13	+	1.82665e13i	0.517442	+	0.896236i	0.999795	+	0.0202586i	$0.00644896\pi$
$907$	1.05462e13	+	1.82665e13i	0.517442	+	0.896236i	−0.482353	+	0.875977i	$0.660218\pi$
$908$	−2.39132e13			−1.16748
$909$	6.79162e12	+	2.99744e13i	0.329940	+	1.45617i
$910$	−4.16763e12			−0.201467
$911$	1.33177e13	+	2.30669e13i	0.640613	+	1.10957i	0.985296	+	0.170855i	$0.0546529\pi$
$911$	1.33177e13	+	2.30669e13i	0.640613	+	1.10957i	−0.344684	+	0.938719i	$0.612014\pi$
$912$	8.75447e11	+	2.23580e12i	0.0419038	+	0.107018i
$913$	−4.99011e12	+	8.64313e12i	−0.237680	+	0.411673i
$914$	7.08282e12	−	1.22678e13i	0.335698	−	0.581445i
$915$	2.03529e13	+	3.08417e12i	0.959912	+	0.145460i
$916$	−1.12305e13	−	1.94518e13i	−0.527073	−	0.912917i
$917$	−1.29441e13			−0.604520
$918$	9.27472e11	+	1.27830e13i	0.0431031	+	0.594076i
$919$	1.42379e13			0.658457			0.329228	−	0.944250i	$-0.393211\pi$
$919$	1.42379e13			0.658457			0.329228	+	0.944250i	$0.393211\pi$
$920$	2.51021e12	+	4.34781e12i	0.115522	+	0.200090i
$921$	2.89308e13	+	4.38402e12i	1.32493	+	0.200772i
$922$	−6.94083e12	+	1.20219e13i	−0.316317	+	0.547877i
$923$	−1.04126e13	+	1.80351e13i	−0.472227	+	0.817922i
$924$	1.74083e12	+	4.44590e12i	0.0785657	+	0.200649i
$925$	−1.86382e12	−	3.22823e12i	−0.0837079	−	0.144986i
$926$	1.79617e13			0.802781
$927$	2.57805e13	−	2.38451e13i	1.14665	−	1.06057i
$928$	−1.81040e13			−0.801326
$929$	1.30958e12	+	2.26826e12i	0.0576849	+	0.0999131i	0.893426	−	0.449211i	$-0.148295\pi$
$929$	1.30958e12	+	2.26826e12i	0.0576849	+	0.0999131i	−0.835741	+	0.549124i	$0.814961\pi$
$930$	−1.07390e13	+	1.34444e13i	−0.470749	+	0.589344i
$931$	−9.68047e11	+	1.67671e12i	−0.0422302	+	0.0731448i
$932$	−1.77118e12	+	3.06777e12i	−0.0768936	+	0.133184i
$933$	2.67755e12	−	3.35211e12i	0.115683	−	0.144827i
$934$	9.27293e12	+	1.60612e13i	0.398709	+	0.690584i
$935$	−1.69269e13			−0.724311
$936$	1.91308e13	−	1.76946e13i	0.814689	−	0.753527i
$937$	−6.56711e12			−0.278321			−0.139161	−	0.990270i	$-0.544440\pi$
$937$	−6.56711e12			−0.278321			−0.139161	+	0.990270i	$0.544440\pi$
$938$	−1.28698e12	−	2.22911e12i	−0.0542822	−	0.0940195i
$939$	6.34505e12	+	1.62046e13i	0.266342	+	0.680209i
$940$	2.42652e11	−	4.20286e11i	0.0101370	−	0.0175578i
$941$	1.49006e13	−	2.58086e13i	0.619514	−	1.07303i	−0.370061	−	0.929008i	$-0.620663\pi$
$941$	1.49006e13	−	2.58086e13i	0.619514	−	1.07303i	0.989575	−	0.144022i	$-0.0460035\pi$
$942$	−6.07413e12	−	9.20440e11i	−0.251336	−	0.0380861i
$943$	2.35395e12	+	4.07716e12i	0.0969381	+	0.167902i
$944$	1.00974e12			0.0413842
$945$	6.81638e12	+	3.30253e12i	0.278042	+	0.134711i
$946$	5.42531e12			0.220249
$947$	1.93709e13	+	3.35514e13i	0.782663	+	1.35561i	0.930385	+	0.366583i	$0.119472\pi$
$947$	1.93709e13	+	3.35514e13i	0.782663	+	1.35561i	−0.147722	+	0.989029i	$0.547194\pi$
$948$	−1.89463e11	−	2.87101e10i	−0.00761880	−	0.00115451i
$949$	−2.84720e13	+	4.93149e13i	−1.13951	+	1.97370i
$950$	−1.34465e12	+	2.32901e12i	−0.0535617	+	0.0927716i
$951$	−7.57336e12	−	1.93416e13i	−0.300245	−	0.766795i
$952$	4.85496e12	+	8.40903e12i	0.191566	+	0.331803i
$953$	−1.49808e13			−0.588326			−0.294163	−	0.955755i	$-0.595041\pi$
$953$	−1.49808e13			−0.588326			−0.294163	+	0.955755i	$0.595041\pi$
$954$	−2.83117e12	−	1.24952e13i	−0.110662	−	0.488399i
$955$	4.16411e13			1.61997
$956$	1.50580e13	+	2.60812e13i	0.583050	+	1.00987i
$957$	−1.01807e13	+	1.27456e13i	−0.392352	+	0.491196i
$958$	3.20636e12	−	5.55358e12i	0.122989	−	0.213024i
$959$	7.04780e12	−	1.22072e13i	0.269073	−	0.466048i
$960$	−4.98091e12	+	6.23574e12i	−0.189273	+	0.236956i
$961$	−2.45308e13	−	4.24886e13i	−0.927804	−	1.60700i
$962$	−8.73954e12			−0.329004
$963$	2.11700e13	+	6.56675e12i	0.793235	+	0.246055i
$964$	2.93653e13			1.09519
$965$	4.83082e12	+	8.36723e12i	0.179328	+	0.310605i
$966$	−6.19444e11	−	1.58200e12i	−0.0228879	−	0.0584532i
$967$	−2.17061e13	+	3.75961e13i	−0.798294	+	1.38269i	0.122432	+	0.992477i	$0.460931\pi$
$967$	−2.17061e13	+	3.75961e13i	−0.798294	+	1.38269i	−0.920726	+	0.390210i	$0.872403\pi$
$968$	4.31723e12	−	7.47767e12i	0.158040	−	0.273733i
$969$	1.74996e13	+	2.65179e12i	0.637633	+	0.0966234i
$970$	3.95389e12	+	6.84835e12i	0.143401	+	0.248378i
$971$	1.34442e13			0.485342			0.242671	−	0.970109i	$-0.421977\pi$
$971$	1.34442e13			0.485342			0.242671	+	0.970109i	$0.421977\pi$
$972$	−1.86861e13	+	5.68310e12i	−0.671461	+	0.204215i
$973$	9.51838e12			0.340452
$974$	7.64603e12	+	1.32433e13i	0.272220	+	0.471500i
$975$	−1.10551e13	−	1.67523e12i	−0.391781	−	0.0593683i
$976$	−3.27256e12	+	5.66824e12i	−0.115442	+	0.199951i
$977$	−1.11853e13	+	1.93734e13i	−0.392754	+	0.680270i	−0.992812	−	0.119687i	$-0.961811\pi$
$977$	−1.11853e13	+	1.93734e13i	−0.392754	+	0.680270i	0.600058	+	0.799957i	$0.295144\pi$
$978$	−5.66839e12	−	1.44765e13i	−0.198123	−	0.505985i
$979$	−2.60878e12	−	4.51854e12i	−0.0907643	−	0.157208i
$980$	2.36645e12			0.0819559
$981$	−3.54671e13	−	1.10016e13i	−1.22268	−	0.379267i
$982$	9.56333e12			0.328176
$983$	2.26475e12	+	3.92266e12i	0.0773622	+	0.133995i	0.902111	−	0.431504i	$-0.142017\pi$
$983$	2.26475e12	+	3.92266e12i	0.0773622	+	0.133995i	−0.824749	+	0.565499i	$0.808684\pi$
$984$	−1.08721e13	+	1.36110e13i	−0.369687	+	0.462821i
$985$	9.76057e12	−	1.69058e13i	0.330379	−	0.572233i
$986$	−6.84047e12	+	1.18480e13i	−0.230484	+	0.399209i
$987$	−2.48541e11	+	3.11156e11i	−0.00833626	+	0.0104364i
$988$	−7.42046e12	−	1.28526e13i	−0.247756	−	0.429126i
$989$	4.54397e12			0.151026
$990$	2.42169e12	+	1.06880e13i	0.0801234	+	0.353620i
$991$	−1.90306e13			−0.626789			−0.313394	−	0.949623i	$-0.601466\pi$
$991$	−1.90306e13			−0.626789			−0.313394	+	0.949623i	$0.601466\pi$
$992$	−2.66836e13	−	4.62173e13i	−0.874865	−	1.51531i
$993$	−3.28712e12	−	8.39495e12i	−0.107286	−	0.273997i
$994$	−2.51190e12	+	4.35073e12i	−0.0816136	+	0.141359i
$995$	−6.63844e12	+	1.14981e13i	−0.214715	+	0.371897i
$996$	−1.26113e13	−	1.91105e12i	−0.406064	−	0.0615327i
$997$	−1.30586e12	−	2.26182e12i	−0.0418571	−	0.0724987i	0.844338	−	0.535811i	$-0.179994\pi$
$997$	−1.30586e12	−	2.26182e12i	−0.0418571	−	0.0724987i	−0.886195	+	0.463312i	$0.846661\pi$
$998$	−1.79362e13			−0.572326
$999$	1.42940e13	+	6.92543e12i	0.454055	+	0.219989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.10.f.a.22.18	✓	54
9.7	even	3	inner	63.10.f.a.43.18	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.10.f.a.22.18	✓	54	1.1	even	1	trivial
63.10.f.a.43.18	yes	54	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.17786 + 10.7004i) q^{2} +(-138.713 - 21.0197i) q^{3} +(179.668 - 311.194i) q^{4} +(571.192 - 989.334i) q^{5} +(-632.028 - 1614.13i) q^{6} +(-1200.50 - 2079.33i) q^{7} +10766.0 q^{8} +(18799.3 + 5831.40i) q^{9} +14115.0 q^{10} +(19722.7 + 34160.7i) q^{11} +(-31463.5 + 39390.0i) q^{12} +(61487.6 - 106500. i) q^{13} +(14833.0 - 25691.6i) q^{14} +(-100027. + 125227. i) q^{15} +(-25479.4 - 44131.6i) q^{16} -375638. q^{17} +(53741.6 + 237185. i) q^{18} +335848. q^{19} +(-205250. - 355504. i) q^{20} +(122818. + 313663. i) q^{21} +(-243688. + 422079. i) q^{22} +(-204101. + 353512. i) q^{23} +(-1.49338e6 - 226298. i) q^{24} +(324042. + 561256. i) q^{25} +1.51945e6 q^{26} +(-2.48513e6 - 1.20405e6i) q^{27} -862767. q^{28} +(-1.47383e6 - 2.55276e6i) q^{29} +(-1.95792e6 - 296693. i) q^{30} +(4.34457e6 - 7.52502e6i) q^{31} +(3.07091e6 - 5.31897e6i) q^{32} +(-2.01773e6 - 5.15308e6i) q^{33} +(-2.32064e6 - 4.01946e6i) q^{34} -2.74286e6 q^{35} +(5.19234e6 - 4.80253e6i) q^{36} -5.75180e6 q^{37} +(2.07482e6 + 3.59369e6i) q^{38} +(-1.07677e7 + 1.34804e7i) q^{39} +(6.14944e6 - 1.06512e7i) q^{40} +(5.76664e6 - 9.98811e6i) q^{41} +(-2.59756e6 + 3.25196e6i) q^{42} +(-5.56585e6 - 9.64034e6i) q^{43} +1.41741e7 q^{44} +(1.65072e7 - 1.52680e7i) q^{45} -5.04361e6 q^{46} +(591114. + 1.02384e6i) q^{47} +(2.60668e6 + 6.65718e6i) q^{48} +(-2.88240e6 + 4.99246e6i) q^{49} +(-4.00376e6 + 6.93472e6i) q^{50} +(5.21057e7 + 7.89581e6i) q^{51} +(-2.20947e7 - 3.82692e7i) q^{52} -5.26811e7 q^{53} +(-2.46906e6 - 3.40302e7i) q^{54} +4.50617e7 q^{55} +(-1.29246e7 - 2.23860e7i) q^{56} +(-4.65863e7 - 7.05943e6i) q^{57} +(1.82103e7 - 3.15411e7i) q^{58} +(-9.90739e6 + 1.71601e7i) q^{59} +(2.09982e7 + 5.36271e7i) q^{60} +(-6.42197e7 - 1.11232e8i) q^{61} +1.07361e8 q^{62} +(-1.04432e7 - 4.60906e7i) q^{63} +4.97956e7 q^{64} +(-7.02424e7 - 1.21663e8i) q^{65} +(4.26745e7 - 5.34254e7i) q^{66} +(4.33821e7 - 7.51399e7i) q^{67} +(-6.74902e7 + 1.16896e8i) q^{68} +(3.57420e7 - 4.47465e7i) q^{69} +(-1.69450e7 - 2.93496e7i) q^{70} -1.69345e8 q^{71} +(2.02393e8 + 6.27807e7i) q^{72} -4.63053e8 q^{73} +(-3.55338e7 - 6.15463e7i) q^{74} +(-3.31512e7 - 8.46646e7i) q^{75} +(6.03411e7 - 1.04514e8i) q^{76} +(4.73541e7 - 8.20197e7i) q^{77} +(-2.10766e8 - 3.19383e7i) q^{78} +(1.90054e6 + 3.29183e6i) q^{79} -5.82145e7 q^{80} +(3.19410e8 + 2.19253e8i) q^{81} +1.42502e8 q^{82} +(1.26507e8 + 2.19117e8i) q^{83} +(1.19677e8 + 1.81351e7i) q^{84} +(-2.14562e8 + 3.71632e8i) q^{85} +(6.87701e7 - 1.19113e8i) q^{86} +(1.50781e8 + 3.85079e8i) q^{87} +(2.12334e8 + 3.67773e8i) q^{88} -1.32273e8 q^{89} +(2.65352e8 + 8.23101e7i) q^{90} -2.95263e8 q^{91} +(7.33407e7 + 1.27030e8i) q^{92} +(-7.60820e8 + 9.52493e8i) q^{93} +(-7.30363e6 + 1.26503e7i) q^{94} +(1.91834e8 - 3.32265e8i) q^{95} +(-5.37777e8 + 6.73258e8i) q^{96} +(2.80121e8 + 4.85183e8i) q^{97} -7.12282e7 q^{98} +(1.71569e8 + 7.57209e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 48 q^{2} + 9 q^{3} - 6912 q^{4} - 1704 q^{5} - 540 q^{6} - 64827 q^{7} + 64650 q^{8} - 13275 q^{9} - 150009 q^{11} - 6156 q^{12} - 89478 q^{13} - 115248 q^{14} - 582588 q^{15} - 1769472 q^{16} + 924474 q^{17}+ \cdots - 5802933888 q^{99}+O(q^{100}) \) 54 * q - 48 * q^2 + 9 * q^3 - 6912 * q^4 - 1704 * q^5 - 540 * q^6 - 64827 * q^7 + 64650 * q^8 - 13275 * q^9 - 150009 * q^11 - 6156 * q^12 - 89478 * q^13 - 115248 * q^14 - 582588 * q^15 - 1769472 * q^16 + 924474 * q^17 + 3376359 * q^18 + 393930 * q^19 - 3569484 * q^20 - 540225 * q^21 + 1941084 * q^22 - 3948384 * q^23 - 529722 * q^24 - 8984061 * q^25 + 3000666 * q^26 + 9578520 * q^27 + 33191424 * q^28 - 7872498 * q^29 - 35915508 * q^30 - 1544562 * q^31 - 12651633 * q^32 + 17162955 * q^33 + 3122550 * q^34 + 8182608 * q^35 + 8496774 * q^36 - 9914616 * q^37 - 4996365 * q^38 - 5731722 * q^39 + 1981665 * q^40 - 42414849 * q^41 + 10480365 * q^42 + 785403 * q^43 + 237381888 * q^44 + 4802904 * q^45 + 27594756 * q^46 - 119882802 * q^47 - 186605055 * q^48 - 155649627 * q^49 - 155986077 * q^50 + 125783109 * q^51 - 38113875 * q^52 + 456641112 * q^53 + 107997840 * q^54 + 181700496 * q^55 - 77612325 * q^56 - 208444653 * q^57 - 106894161 * q^58 - 254205771 * q^59 + 151864524 * q^60 + 88252362 * q^61 + 475026168 * q^62 + 7087752 * q^63 + 780018066 * q^64 - 508726878 * q^65 - 903322692 * q^66 - 140145363 * q^67 - 527497665 * q^68 + 1033462602 * q^69 + 1271226492 * q^71 - 529878141 * q^72 - 1089614970 * q^73 - 1637187180 * q^74 - 1069789041 * q^75 - 355170312 * q^76 - 360171609 * q^77 + 1842021072 * q^78 - 567828360 * q^79 + 6015328602 * q^80 - 1173736791 * q^81 - 195081048 * q^82 - 3126306510 * q^83 + 295049286 * q^84 + 120736008 * q^85 - 2515127217 * q^86 + 1825753500 * q^87 + 219336660 * q^88 + 4513423020 * q^89 - 3192307821 * q^90 + 429673356 * q^91 - 3546484113 * q^92 + 80634366 * q^93 + 2125779066 * q^94 - 4867623384 * q^95 + 9060845301 * q^96 + 504276867 * q^97 + 553420896 * q^98 - 5802933888 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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