LMFDB - Embedded newform 29.9.c.a.12.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, 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:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.3
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.0506 - 16.0506i) q^{2} +(-92.3210 - 92.3210i) q^{3} +259.242i q^{4} -266.052i q^{5} +2963.61i q^{6} -4134.50 q^{7} +(52.0309 - 52.0309i) q^{8} +10485.3i q^{9} +O(q^{10})$	\(q+(-16.0506 - 16.0506i) q^{2} +(-92.3210 - 92.3210i) q^{3} +259.242i q^{4} -266.052i q^{5} +2963.61i q^{6} -4134.50 q^{7} +(52.0309 - 52.0309i) q^{8} +10485.3i q^{9} +(-4270.28 + 4270.28i) q^{10} +(474.456 + 474.456i) q^{11} +(23933.4 - 23933.4i) q^{12} -45859.8i q^{13} +(66361.1 + 66361.1i) q^{14} +(-24562.2 + 24562.2i) q^{15} +64695.6 q^{16} +(-85408.8 - 85408.8i) q^{17} +(168295. - 168295. i) q^{18} +(-88358.4 - 88358.4i) q^{19} +68971.7 q^{20} +(381701. + 381701. i) q^{21} -15230.6i q^{22} +3107.89 q^{23} -9607.09 q^{24} +319841. q^{25} +(-736076. + 736076. i) q^{26} +(362297. - 362297. i) q^{27} -1.07184e6i q^{28} +(-673638. - 215543. i) q^{29} +788474. q^{30} +(142483. + 142483. i) q^{31} +(-1.05172e6 - 1.05172e6i) q^{32} -87604.5i q^{33} +2.74172e6i q^{34} +1.09999e6i q^{35} -2.71823e6 q^{36} +(-342942. + 342942. i) q^{37} +2.83640e6i q^{38} +(-4.23382e6 + 4.23382e6i) q^{39} +(-13842.9 - 13842.9i) q^{40} +(3.52595e6 - 3.52595e6i) q^{41} -1.22530e7i q^{42} +(360341. + 360341. i) q^{43} +(-122999. + 122999. i) q^{44} +2.78964e6 q^{45} +(-49883.4 - 49883.4i) q^{46} +(-83290.0 + 83290.0i) q^{47} +(-5.97276e6 - 5.97276e6i) q^{48} +1.13293e7 q^{49} +(-5.13364e6 - 5.13364e6i) q^{50} +1.57700e7i q^{51} +1.18888e7 q^{52} -2.78636e6 q^{53} -1.16301e7 q^{54} +(126230. - 126230. i) q^{55} +(-215122. + 215122. i) q^{56} +1.63147e7i q^{57} +(7.35268e6 + 1.42719e7i) q^{58} +5.17577e6 q^{59} +(-6.36754e6 - 6.36754e6i) q^{60} +(8.69632e6 + 8.69632e6i) q^{61} -4.57387e6i q^{62} -4.33516e7i q^{63} +1.71994e7i q^{64} -1.22011e7 q^{65} +(-1.40610e6 + 1.40610e6i) q^{66} +1.41540e7i q^{67} +(2.21415e7 - 2.21415e7i) q^{68} +(-286923. - 286923. i) q^{69} +(1.76555e7 - 1.76555e7i) q^{70} +2.78724e7i q^{71} +(545561. + 545561. i) q^{72} +(1.52324e6 - 1.52324e6i) q^{73} +1.10088e7 q^{74} +(-2.95281e7 - 2.95281e7i) q^{75} +(2.29062e7 - 2.29062e7i) q^{76} +(-1.96164e6 - 1.96164e6i) q^{77} +1.35911e8 q^{78} +(-4.23028e7 - 4.23028e7i) q^{79} -1.72124e7i q^{80} +1.89897e6 q^{81} -1.13187e8 q^{82} -5.36173e7 q^{83} +(-9.89529e7 + 9.89529e7i) q^{84} +(-2.27232e7 + 2.27232e7i) q^{85} -1.15674e7i q^{86} +(4.22917e7 + 8.20900e7i) q^{87} +49372.8 q^{88} +(-4.20612e7 - 4.20612e7i) q^{89} +(-4.47753e7 - 4.47753e7i) q^{90} +1.89608e8i q^{91} +805695. i q^{92} -2.63084e7i q^{93} +2.67370e6 q^{94} +(-2.35079e7 + 2.35079e7i) q^{95} +1.94192e8i q^{96} +(1.04497e8 - 1.04497e8i) q^{97} +(-1.81842e8 - 1.81842e8i) q^{98} +(-4.97482e6 + 4.97482e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−16.0506	−	16.0506i	−1.00316	−	1.00316i	−0.999995	−	0.00316572i	$-0.998992\pi$
$2$	−16.0506	−	16.0506i	−1.00316	−	1.00316i	−0.00316572	−	0.999995i	$-0.501008\pi$
$3$	−92.3210	−	92.3210i	−1.13976	−	1.13976i	−0.988492	−	0.151273i	$-0.951663\pi$
$3$	−92.3210	−	92.3210i	−1.13976	−	1.13976i	−0.151273	−	0.988492i	$-0.548337\pi$
$4$			259.242i			1.01266i
$5$		−	266.052i		−	0.425683i	−0.977087	−	0.212841i	$-0.931728\pi$
$5$		−	266.052i		−	0.425683i	0.977087	−	0.212841i	$-0.0682718\pi$
$6$			2963.61i			2.28673i
$7$	−4134.50			−1.72199			−0.860996	−	0.508612i	$-0.830159\pi$
$7$	−4134.50			−1.72199			−0.860996	+	0.508612i	$0.830159\pi$
$8$	52.0309	−	52.0309i	0.0127029	−	0.0127029i
$9$			10485.3i			1.59813i
$10$	−4270.28	+	4270.28i	−0.427028	+	0.427028i
$11$	474.456	+	474.456i	0.0324060	+	0.0324060i	0.723124	−	0.690718i	$-0.242705\pi$
$11$	474.456	+	474.456i	0.0324060	+	0.0324060i	−0.690718	+	0.723124i	$0.742705\pi$
$12$	23933.4	−	23933.4i	1.15420	−	1.15420i
$13$		−	45859.8i		−	1.60568i	−0.596195	−	0.802840i	$-0.703321\pi$
$13$		−	45859.8i		−	1.60568i	0.596195	−	0.802840i	$-0.296679\pi$
$14$	66361.1	+	66361.1i	1.72743	+	1.72743i
$15$	−24562.2	+	24562.2i	−0.485179	+	0.485179i
$16$	64695.6			0.987177
$17$	−85408.8	−	85408.8i	−1.02260	−	1.02260i	−0.999739	−	0.0228636i	$-0.992722\pi$
$17$	−85408.8	−	85408.8i	−1.02260	−	1.02260i	−0.0228636	−	0.999739i	$-0.507278\pi$
$18$	168295.	−	168295.i	1.60318	−	1.60318i
$19$	−88358.4	−	88358.4i	−0.678006	−	0.678006i	0.281543	−	0.959549i	$-0.409154\pi$
$19$	−88358.4	−	88358.4i	−0.678006	−	0.678006i	−0.959549	+	0.281543i	$0.909154\pi$
$20$	68971.7			0.431073
$21$	381701.	+	381701.i	1.96267	+	1.96267i
$22$		−	15230.6i		−	0.0650168i
$23$	3107.89			0.0111059			0.00555296	−	0.999985i	$-0.498232\pi$
$23$	3107.89			0.0111059			0.00555296	+	0.999985i	$0.498232\pi$
$24$	−9607.09			−0.0289565
$25$	319841.			0.818794
$26$	−736076.	+	736076.i	−1.61076	+	1.61076i
$27$	362297.	−	362297.i	0.681726	−	0.681726i
$28$		−	1.07184e6i		−	1.74380i
$29$	−673638.	−	215543.i	−0.952433	−	0.304749i
$29$	−673638.	−	215543.i	−0.952433	−	0.304749i
$30$	788474.			0.973424
$31$	142483.	+	142483.i	0.154283	+	0.154283i	0.780028	−	0.625745i	$-0.215205\pi$
$31$	142483.	+	142483.i	0.154283	+	0.154283i	−0.625745	+	0.780028i	$0.715205\pi$
$32$	−1.05172e6	−	1.05172e6i	−1.00300	−	1.00300i
$33$		−	87604.5i		−	0.0738704i
$34$			2.74172e6i			2.05167i
$35$			1.09999e6i			0.733022i
$36$	−2.71823e6			−1.61837
$37$	−342942.	+	342942.i	−0.182984	+	0.182984i	−0.792655	−	0.609671i	$-0.791302\pi$
$37$	−342942.	+	342942.i	−0.182984	+	0.182984i	0.609671	+	0.792655i	$0.291302\pi$
$38$			2.83640e6i			1.36030i
$39$	−4.23382e6	+	4.23382e6i	−1.83010	+	1.83010i
$40$	−13842.9	−	13842.9i	−0.00540739	−	0.00540739i
$41$	3.52595e6	−	3.52595e6i	1.24779	−	1.24779i	0.291093	−	0.956695i	$-0.405981\pi$
$41$	3.52595e6	−	3.52595e6i	1.24779	−	1.24779i	0.956695	−	0.291093i	$-0.0940189\pi$
$42$		−	1.22530e7i		−	3.93774i
$43$	360341.	+	360341.i	0.105400	+	0.105400i	0.757840	−	0.652440i	$-0.226255\pi$
$43$	360341.	+	360341.i	0.105400	+	0.105400i	−0.652440	+	0.757840i	$0.726255\pi$
$44$	−122999.	+	122999.i	−0.0328163	+	0.0328163i
$45$	2.78964e6			0.680296
$46$	−49883.4	−	49883.4i	−0.0111410	−	0.0111410i
$47$	−83290.0	+	83290.0i	−0.0170687	+	0.0170687i	−0.715590	−	0.698521i	$-0.753842\pi$
$47$	−83290.0	+	83290.0i	−0.0170687	+	0.0170687i	0.698521	+	0.715590i	$0.253842\pi$
$48$	−5.97276e6	−	5.97276e6i	−1.12515	−	1.12515i
$49$	1.13293e7			1.96525
$50$	−5.13364e6	−	5.13364e6i	−0.821382	−	0.821382i
$51$			1.57700e7i			2.33105i
$52$	1.18888e7			1.62601
$53$	−2.78636e6			−0.353129			−0.176564	−	0.984289i	$-0.556498\pi$
$53$	−2.78636e6			−0.353129			−0.176564	+	0.984289i	$0.556498\pi$
$54$	−1.16301e7			−1.36776
$55$	126230.	−	126230.i	0.0137947	−	0.0137947i
$56$	−215122.	+	215122.i	−0.0218742	+	0.0218742i
$57$			1.63147e7i			1.54553i
$58$	7.35268e6	+	1.42719e7i	0.649731	+	1.26116i
$59$	5.17577e6			0.427137			0.213568	−	0.976928i	$-0.431491\pi$
$59$	5.17577e6			0.427137			0.213568	+	0.976928i	$0.431491\pi$
$60$	−6.36754e6	−	6.36754e6i	−0.491322	−	0.491322i
$61$	8.69632e6	+	8.69632e6i	0.628082	+	0.628082i	0.947585	−	0.319504i	$-0.103516\pi$
$61$	8.69632e6	+	8.69632e6i	0.628082	+	0.628082i	−0.319504	+	0.947585i	$0.603516\pi$
$62$		−	4.57387e6i		−	0.309540i
$63$		−	4.33516e7i		−	2.75196i
$64$			1.71994e7i			1.02516i
$65$	−1.22011e7			−0.683511
$66$	−1.40610e6	+	1.40610e6i	−0.0741039	+	0.0741039i
$67$			1.41540e7i			0.702392i	0.936302	+	0.351196i	$0.114225\pi$
$67$			1.41540e7i			0.702392i	−0.936302	+	0.351196i	$0.885775\pi$
$68$	2.21415e7	−	2.21415e7i	1.03555	−	1.03555i
$69$	−286923.	−	286923.i	−0.0126581	−	0.0126581i
$70$	1.76555e7	−	1.76555e7i	0.735339	−	0.735339i
$71$			2.78724e7i			1.09683i	0.836205	+	0.548417i	$0.184769\pi$
$71$			2.78724e7i			1.09683i	−0.836205	+	0.548417i	$0.815231\pi$
$72$	545561.	+	545561.i	0.0203008	+	0.0203008i
$73$	1.52324e6	−	1.52324e6i	0.0536385	−	0.0536385i	−0.679779	−	0.733417i	$-0.737924\pi$
$73$	1.52324e6	−	1.52324e6i	0.0536385	−	0.0536385i	0.733417	+	0.679779i	$0.237924\pi$
$74$	1.10088e7			0.367125
$75$	−2.95281e7	−	2.95281e7i	−0.933233	−	0.933233i
$76$	2.29062e7	−	2.29062e7i	0.686591	−	0.686591i
$77$	−1.96164e6	−	1.96164e6i	−0.0558028	−	0.0558028i
$78$	1.35911e8			3.67176
$79$	−4.23028e7	−	4.23028e7i	−1.08608	−	1.08608i	−0.995928	−	0.0901477i	$-0.971266\pi$
$79$	−4.23028e7	−	4.23028e7i	−1.08608	−	1.08608i	−0.0901477	−	0.995928i	$-0.528734\pi$
$80$		−	1.72124e7i		−	0.420224i
$81$	1.89897e6			0.0441142
$82$	−1.13187e8			−2.50346
$83$	−5.36173e7			−1.12978			−0.564888	−	0.825168i	$-0.691081\pi$
$83$	−5.36173e7			−1.12978			−0.564888	+	0.825168i	$0.691081\pi$
$84$	−9.89529e7	+	9.89529e7i	−1.98752	+	1.98752i
$85$	−2.27232e7	+	2.27232e7i	−0.435304	+	0.435304i
$86$		−	1.15674e7i		−	0.211466i
$87$	4.22917e7	+	8.20900e7i	0.738207	+	1.43289i
$88$	49372.8			0.000823297
$89$	−4.20612e7	−	4.20612e7i	−0.670382	−	0.670382i	0.287422	−	0.957804i	$-0.407202\pi$
$89$	−4.20612e7	−	4.20612e7i	−0.670382	−	0.670382i	−0.957804	+	0.287422i	$0.907202\pi$
$90$	−4.47753e7	−	4.47753e7i	−0.682446	−	0.682446i
$91$			1.89608e8i			2.76497i
$92$			805695.i			0.0112465i
$93$		−	2.63084e7i		−	0.351692i
$94$	2.67370e6			0.0342454
$95$	−2.35079e7	+	2.35079e7i	−0.288615	+	0.288615i
$96$			1.94192e8i			2.28637i
$97$	1.04497e8	−	1.04497e8i	1.18037	−	1.18037i	0.200720	−	0.979649i	$-0.435672\pi$
$97$	1.04497e8	−	1.04497e8i	1.18037	−	1.18037i	0.979649	−	0.200720i	$-0.0643282\pi$
$98$	−1.81842e8	−	1.81842e8i	−1.97147	−	1.97147i
$99$	−4.97482e6	+	4.97482e6i	−0.0517889	+	0.0517889i
$100$			8.29162e7i			0.829162i
$101$	−1.08602e8	−	1.08602e8i	−1.04364	−	1.04364i	−0.999003	−	0.0446416i	$-0.985785\pi$
$101$	−1.08602e8	−	1.08602e8i	−1.04364	−	1.04364i	−0.0446416	−	0.999003i	$-0.514215\pi$
$102$	2.53118e8	−	2.53118e8i	2.33842	−	2.33842i
$103$	1.87800e8			1.66858			0.834289	−	0.551327i	$-0.185878\pi$
$103$	1.87800e8			1.66858			0.834289	+	0.551327i	$0.185878\pi$
$104$	−2.38613e6	−	2.38613e6i	−0.0203967	−	0.0203967i
$105$	1.01552e8	−	1.01552e8i	0.835473	−	0.835473i
$106$	4.47226e7	+	4.47226e7i	0.354245	+	0.354245i
$107$	−8.20994e7			−0.626333			−0.313166	−	0.949698i	$-0.601390\pi$
$107$	−8.20994e7			−0.626333			−0.313166	+	0.949698i	$0.601390\pi$
$108$	9.39225e7	+	9.39225e7i	0.690358	+	0.690358i
$109$			2.36253e8i			1.67368i	0.547451	+	0.836838i	$0.315598\pi$
$109$			2.36253e8i			1.67368i	−0.547451	+	0.836838i	$0.684402\pi$
$110$	−4.05212e6			−0.0276766
$111$	6.33214e7			0.417118
$112$	−2.67484e8			−1.69991
$113$	−3.54601e7	+	3.54601e7i	−0.217483	+	0.217483i	−0.807437	−	0.589954i	$-0.799146\pi$
$113$	−3.54601e7	+	3.54601e7i	−0.217483	+	0.217483i	0.589954	+	0.807437i	$0.299146\pi$
$114$	2.61860e8	−	2.61860e8i	1.55042	−	1.55042i
$115$		−	826860.i		−	0.00472760i
$116$	5.58778e7	−	1.74635e8i	0.308608	−	0.964493i
$117$	4.80855e8			2.56608
$118$	−8.30741e7	−	8.30741e7i	−0.428487	−	0.428487i
$119$	3.53123e8	+	3.53123e8i	1.76091	+	1.76091i
$120$			2.55598e6i			0.0123263i
$121$		−	2.13909e8i		−	0.997900i
$122$		−	2.79162e8i		−	1.26013i
$123$	−6.51038e8			−2.84437
$124$	−3.69376e7	+	3.69376e7i	−0.156236	+	0.156236i
$125$		−	1.89021e8i		−	0.774230i
$126$	−6.95818e8	+	6.95818e8i	−2.76066	+	2.76066i
$127$	1.05793e8	+	1.05793e8i	0.406668	+	0.406668i	0.880575	−	0.473907i	$-0.157157\pi$
$127$	1.05793e8	+	1.05793e8i	0.406668	+	0.406668i	−0.473907	+	0.880575i	$0.657157\pi$
$128$	6.81925e6	−	6.81925e6i	0.0254037	−	0.0254037i
$129$		−	6.65341e7i		−	0.240262i
$130$	1.95835e8	+	1.95835e8i	0.685671	+	0.685671i
$131$	−2.21245e8	+	2.21245e8i	−0.751257	+	0.751257i	−0.974714	−	0.223457i	$-0.928266\pi$
$131$	−2.21245e8	+	2.21245e8i	−0.751257	+	0.751257i	0.223457	+	0.974714i	$0.428266\pi$
$132$	2.27107e7			0.0748058
$133$	3.65318e8	+	3.65318e8i	1.16752	+	1.16752i
$134$	2.27179e8	−	2.27179e8i	0.704612	−	0.704612i
$135$	−9.63898e7	−	9.63898e7i	−0.290199	−	0.290199i
$136$	−8.88779e6			−0.0259799
$137$	−5.08894e7	−	5.08894e7i	−0.144459	−	0.144459i	0.631178	−	0.775638i	$-0.282572\pi$
$137$	−5.08894e7	−	5.08894e7i	−0.144459	−	0.144459i	−0.775638	+	0.631178i	$0.782572\pi$
$138$			9.21057e6i			0.0253963i
$139$	−2.07513e8			−0.555885			−0.277943	−	0.960598i	$-0.589652\pi$
$139$	−2.07513e8			−0.555885			−0.277943	+	0.960598i	$0.589652\pi$
$140$	−2.85164e8			−0.742305
$141$	1.53788e7			0.0389087
$142$	4.47368e8	−	4.47368e8i	1.10030	−	1.10030i
$143$	2.17585e7	−	2.17585e7i	0.0520336	−	0.0520336i
$144$			6.78354e8i			1.57764i
$145$	−5.73456e7	+	1.79223e8i	−0.129726	+	0.405434i
$146$	−4.88977e7			−0.107616
$147$	−1.04593e9	−	1.04593e9i	−2.23993	−	2.23993i
$148$	−8.89048e7	−	8.89048e7i	−0.185301	−	0.185301i
$149$		−	6.88107e8i		−	1.39608i	−0.716058	−	0.698041i	$-0.754055\pi$
$149$		−	6.88107e8i		−	1.39608i	0.716058	−	0.698041i	$-0.245945\pi$
$150$			9.47885e8i			1.87236i
$151$		−	2.09059e8i		−	0.402125i	−0.979578	−	0.201062i	$-0.935561\pi$
$151$		−	2.09059e8i		−	0.402125i	0.979578	−	0.201062i	$-0.0644394\pi$
$152$	−9.19473e6			−0.0172252
$153$	8.95538e8	−	8.95538e8i	1.63425	−	1.63425i
$154$			6.29709e7i			0.111958i
$155$	3.79079e7	−	3.79079e7i	0.0656755	−	0.0656755i
$156$	−1.09758e9	−	1.09758e9i	−1.85327	−	1.85327i
$157$	−5.45005e8	+	5.45005e8i	−0.897020	+	0.897020i	−0.995171	−	0.0981516i	$-0.968707\pi$
$157$	−5.45005e8	+	5.45005e8i	−0.897020	+	0.897020i	0.0981516	+	0.995171i	$0.468707\pi$
$158$			1.35797e9i			2.17902i
$159$	2.57239e8	+	2.57239e8i	0.402484	+	0.402484i
$160$	−2.79812e8	+	2.79812e8i	−0.426960	+	0.426960i
$161$	−1.28496e7			−0.0191243
$162$	−3.04796e7	−	3.04796e7i	−0.0442536	−	0.0442536i
$163$	4.87494e8	−	4.87494e8i	0.690588	−	0.690588i	−0.271774	−	0.962361i	$-0.587610\pi$
$163$	4.87494e8	−	4.87494e8i	0.690588	−	0.690588i	0.962361	+	0.271774i	$0.0876102\pi$
$164$	9.14073e8	+	9.14073e8i	1.26359	+	1.26359i
$165$	−2.33073e7			−0.0314454
$166$	8.60588e8	+	8.60588e8i	1.13335	+	1.13335i
$167$		−	5.94158e8i		−	0.763899i	−0.924183	−	0.381949i	$-0.875253\pi$
$167$		−	5.94158e8i		−	0.763899i	0.924183	−	0.381949i	$-0.124747\pi$
$168$	3.97205e7			0.0498629
$169$	−1.28739e9			−1.57821
$170$	7.29439e8			0.873360
$171$	9.26466e8	−	9.26466e8i	1.08354	−	1.08354i
$172$	−9.34154e7	+	9.34154e7i	−0.106735	+	0.106735i
$173$			9.65565e8i			1.07795i	0.842323	+	0.538973i	$0.181188\pi$
$173$			9.65565e8i			1.07795i	−0.842323	+	0.538973i	$0.818812\pi$
$174$	6.38785e8	−	1.99640e9i	0.696880	−	2.17796i
$175$	−1.32238e9			−1.40996
$176$	3.06952e7	+	3.06952e7i	0.0319904	+	0.0319904i
$177$	−4.77832e8	−	4.77832e8i	−0.486836	−	0.486836i
$178$			1.35021e9i			1.34500i
$179$			1.83018e9i			1.78272i	0.453300	+	0.891358i	$0.350247\pi$
$179$			1.83018e9i			1.78272i	−0.453300	+	0.891358i	$0.649753\pi$
$180$			7.23191e8i			0.688911i
$181$	−4.45536e8			−0.415115			−0.207558	−	0.978223i	$-0.566551\pi$
$181$	−4.45536e8			−0.415115			−0.207558	+	0.978223i	$0.566551\pi$
$182$	3.04331e9	−	3.04331e9i	2.77371	−	2.77371i
$183$		−	1.60570e9i		−	1.43173i
$184$	161706.	−	161706.i	0.000141077	−	0.000141077i
$185$	9.12403e7	+	9.12403e7i	0.0778932	+	0.0778932i
$186$	−4.22264e8	+	4.22264e8i	−0.352803	+	0.352803i
$187$		−	8.10454e7i		−	0.0662769i
$188$	−2.15922e7	−	2.15922e7i	−0.0172849	−	0.0172849i
$189$	−1.49792e9	+	1.49792e9i	−1.17393	+	1.17393i
$190$	7.54631e8			0.579055
$191$	−5.47198e8	−	5.47198e8i	−0.411160	−	0.411160i	0.470983	−	0.882143i	$-0.343899\pi$
$191$	−5.47198e8	−	5.47198e8i	−0.411160	−	0.411160i	−0.882143	+	0.470983i	$0.843899\pi$
$192$	1.58786e9	−	1.58786e9i	1.16845	−	1.16845i
$193$	1.13132e9	+	1.13132e9i	0.815374	+	0.815374i	0.985434	−	0.170060i	$-0.0543961\pi$
$193$	1.13132e9	+	1.13132e9i	0.815374	+	0.815374i	−0.170060	+	0.985434i	$0.554396\pi$
$194$	−3.35448e9			−2.36820
$195$	1.12642e9	+	1.12642e9i	0.779042	+	0.779042i
$196$			2.93703e9i			1.99014i
$197$	1.92557e9			1.27848			0.639241	−	0.769006i	$-0.279249\pi$
$197$	1.92557e9			1.27848			0.639241	+	0.769006i	$0.279249\pi$
$198$	1.59698e8			0.103905
$199$	1.10584e8			0.0705149			0.0352574	−	0.999378i	$-0.488775\pi$
$199$	1.10584e8			0.0705149			0.0352574	+	0.999378i	$0.488775\pi$
$200$	1.66416e7	−	1.66416e7i	0.0104010	−	0.0104010i
$201$	1.30671e9	−	1.30671e9i	0.800561	−	0.800561i
$202$			3.48625e9i			2.09389i
$203$	2.78516e9	+	8.91163e8i	1.64008	+	0.524775i
$204$	−4.08825e9			−2.36057
$205$	−9.38085e8	−	9.38085e8i	−0.531162	−	0.531162i
$206$	−3.01430e9	−	3.01430e9i	−1.67385	−	1.67385i
$207$			3.25872e7i			0.0177487i
$208$		−	2.96693e9i		−	1.58509i
$209$		−	8.38443e7i		−	0.0439429i
$210$	−3.25995e9			−1.67623
$211$	2.31984e8	−	2.31984e8i	0.117038	−	0.117038i	−0.646162	−	0.763200i	$-0.723627\pi$
$211$	2.31984e8	−	2.31984e8i	0.117038	−	0.117038i	0.763200	+	0.646162i	$0.223627\pi$
$212$		−	7.22340e8i		−	0.357601i
$213$	2.57320e9	−	2.57320e9i	1.25013	−	1.25013i
$214$	1.31774e9	+	1.31774e9i	0.628312	+	0.628312i
$215$	9.58694e7	−	9.58694e7i	0.0448669	−	0.0448669i
$216$		−	3.77013e7i		−	0.0173197i
$217$	−5.89097e8	−	5.89097e8i	−0.265673	−	0.265673i
$218$	3.79200e9	−	3.79200e9i	1.67897	−	1.67897i
$219$	−2.81254e8			−0.122271
$220$	3.27241e7	+	3.27241e7i	0.0139694	+	0.0139694i
$221$	−3.91683e9	+	3.91683e9i	−1.64197	+	1.64197i
$222$	−1.01634e9	−	1.01634e9i	−0.418436	−	0.418436i
$223$	4.95814e8			0.200493			0.100246	−	0.994963i	$-0.468037\pi$
$223$	4.95814e8			0.200493			0.100246	+	0.994963i	$0.468037\pi$
$224$	4.34834e9	+	4.34834e9i	1.72716	+	1.72716i
$225$			3.35364e9i			1.30854i
$226$	1.13831e9			0.436342
$227$	−2.14085e9			−0.806273			−0.403136	−	0.915140i	$-0.632080\pi$
$227$	−2.14085e9			−0.806273			−0.403136	+	0.915140i	$0.632080\pi$
$228$	−4.22944e9			−1.56510
$229$	1.33760e9	−	1.33760e9i	0.486389	−	0.486389i	−0.420776	−	0.907165i	$-0.638242\pi$
$229$	1.33760e9	−	1.33760e9i	0.486389	−	0.486389i	0.907165	+	0.420776i	$0.138242\pi$
$230$	−1.32716e7	+	1.32716e7i	−0.00474254	+	0.00474254i
$231$			3.62201e8i			0.127204i
$232$	−4.62649e7	+	2.38351e7i	−0.0159698	+	0.00822744i
$233$	1.76164e9			0.597714			0.298857	−	0.954298i	$-0.403395\pi$
$233$	1.76164e9			0.597714			0.298857	+	0.954298i	$0.403395\pi$
$234$	−7.71800e9	−	7.71800e9i	−2.57419	−	2.57419i
$235$	2.21595e7	+	2.21595e7i	0.00726587	+	0.00726587i
$236$			1.34178e9i			0.432546i
$237$			7.81086e9i			2.47574i
$238$		−	1.13356e10i		−	3.53296i
$239$	−3.09733e9			−0.949285			−0.474642	−	0.880179i	$-0.657423\pi$
$239$	−3.09733e9			−0.949285			−0.474642	+	0.880179i	$0.657423\pi$
$240$	−1.58906e9	+	1.58906e9i	−0.478957	+	0.478957i
$241$			3.31410e9i			0.982420i	0.871041	+	0.491210i	$0.163445\pi$
$241$			3.31410e9i			0.982420i	−0.871041	+	0.491210i	$0.836555\pi$
$242$	−3.43336e9	+	3.43336e9i	−1.00105	+	1.00105i
$243$	−2.55235e9	−	2.55235e9i	−0.732005	−	0.732005i
$244$	−2.25445e9	+	2.25445e9i	−0.636035	+	0.636035i
$245$		−	3.01418e9i		−	0.836576i
$246$	1.04495e10	+	1.04495e10i	2.85336	+	2.85336i
$247$	−4.05210e9	+	4.05210e9i	−1.08866	+	1.08866i
$248$	1.48271e7			0.00391966
$249$	4.95000e9	+	4.95000e9i	1.28768	+	1.28768i
$250$	−3.03389e9	+	3.03389e9i	−0.776677	+	0.776677i
$251$	−3.32402e9	−	3.32402e9i	−0.837470	−	0.837470i	0.151055	−	0.988525i	$-0.451733\pi$
$251$	−3.32402e9	−	3.32402e9i	−0.837470	−	0.837470i	−0.988525	+	0.151055i	$0.951733\pi$
$252$	1.12385e10			2.78681
$253$	1.47456e6	+	1.47456e6i	0.000359898	+	0.000359898i
$254$		−	3.39606e9i		−	0.815907i
$255$	4.19565e9			0.992289
$256$	4.18414e9			0.974195
$257$	−5.39380e9			−1.23641			−0.618204	−	0.786017i	$-0.712140\pi$
$257$	−5.39380e9			−1.23641			−0.618204	+	0.786017i	$0.712140\pi$
$258$	−1.06791e9	+	1.06791e9i	−0.241022	+	0.241022i
$259$	1.41789e9	−	1.41789e9i	0.315097	−	0.315097i
$260$		−	3.16303e9i		−	0.692166i
$261$	2.26004e9	−	7.06331e9i	0.487028	−	1.52211i
$262$	7.10222e9			1.50726
$263$	−1.69014e9	−	1.69014e9i	−0.353265	−	0.353265i	0.508058	−	0.861323i	$-0.330364\pi$
$263$	−1.69014e9	−	1.69014e9i	−0.353265	−	0.353265i	−0.861323	+	0.508058i	$0.830364\pi$
$264$	−4.55814e6	−	4.55814e6i	−0.000938365	−	0.000938365i
$265$			7.41316e8i			0.150321i
$266$		−	1.17271e10i		−	2.34242i
$267$			7.76627e9i			1.52815i
$268$	−3.66930e9			−0.711286
$269$	−1.84730e8	+	1.84730e8i	−0.0352801	+	0.0352801i	−0.724527	−	0.689247i	$-0.757942\pi$
$269$	−1.84730e8	+	1.84730e8i	−0.0352801	+	0.0352801i	0.689247	+	0.724527i	$0.257942\pi$
$270$			3.09422e9i			0.582233i
$271$	5.75481e9	−	5.75481e9i	1.06697	−	1.06697i	0.0693844	−	0.997590i	$-0.477896\pi$
$271$	5.75481e9	−	5.75481e9i	1.06697	−	1.06697i	0.997590	−	0.0693844i	$-0.0221035\pi$
$272$	−5.52557e9	−	5.52557e9i	−1.00949	−	1.00949i
$273$	1.75047e10	−	1.75047e10i	3.15141	−	3.15141i
$274$			1.63361e9i			0.289832i
$275$	1.51751e8	+	1.51751e8i	0.0265338	+	0.0265338i
$276$	7.43825e7	−	7.43825e7i	0.0128184	−	0.0128184i
$277$	7.31175e8			0.124195			0.0620973	−	0.998070i	$-0.480221\pi$
$277$	7.31175e8			0.124195			0.0620973	+	0.998070i	$0.480221\pi$
$278$	3.33069e9	+	3.33069e9i	0.557642	+	0.557642i
$279$	−1.49398e9	+	1.49398e9i	−0.246563	+	0.246563i
$280$	5.72336e7	+	5.72336e7i	0.00931148	+	0.00931148i
$281$	5.58383e9			0.895585			0.447792	−	0.894138i	$-0.352210\pi$
$281$	5.58383e9			0.895585			0.447792	+	0.894138i	$0.352210\pi$
$282$	−2.46839e8	−	2.46839e8i	−0.0390317	−	0.0390317i
$283$		−	1.01342e9i		−	0.157996i	−0.996875	−	0.0789979i	$-0.974828\pi$
$283$		−	1.01342e9i		−	0.157996i	0.996875	−	0.0789979i	$-0.0251720\pi$
$284$	−7.22568e9			−1.11072
$285$	4.34055e9			0.657907
$286$	−6.98472e8			−0.104396
$287$	−1.45780e10	+	1.45780e10i	−2.14868	+	2.14868i
$288$	1.10276e10	−	1.10276e10i	1.60292	−	1.60292i
$289$			7.61355e9i			1.09143i
$290$	3.79705e9	−	1.95619e9i	0.536852	−	0.276579i
$291$	−1.92946e10			−2.69069
$292$	3.94887e8	+	3.94887e8i	0.0543177	+	0.0543177i
$293$	2.20477e9	+	2.20477e9i	0.299153	+	0.299153i	0.840682	−	0.541529i	$-0.182154\pi$
$293$	2.20477e9	+	2.20477e9i	0.299153	+	0.299153i	−0.541529	+	0.840682i	$0.682154\pi$
$294$			3.35756e10i			4.49402i
$295$		−	1.37702e9i		−	0.181825i
$296$			3.56871e7i			0.00464884i
$297$	3.43788e8			0.0441840
$298$	−1.10445e10	+	1.10445e10i	−1.40049	+	1.40049i
$299$		−	1.42527e8i		−	0.0178325i
$300$	7.65491e9	−	7.65491e9i	0.945050	−	0.945050i
$301$	−1.48983e9	−	1.48983e9i	−0.181498	−	0.181498i
$302$	−3.35551e9	+	3.35551e9i	−0.403396	+	0.403396i
$303$			2.00525e10i			2.37902i
$304$	−5.71640e9	−	5.71640e9i	−0.669311	−	0.669311i
$305$	2.31367e9	−	2.31367e9i	0.267364	−	0.267364i
$306$	−2.87478e10			−3.27883
$307$	−4.66060e9	−	4.66060e9i	−0.524673	−	0.524673i	0.394306	−	0.918979i	$-0.370985\pi$
$307$	−4.66060e9	−	4.66060e9i	−0.524673	−	0.524673i	−0.918979	+	0.394306i	$0.870985\pi$
$308$	5.08539e8	−	5.08539e8i	0.0565095	−	0.0565095i
$309$	−1.73379e10	−	1.73379e10i	−1.90179	−	1.90179i
$310$	−1.21689e9			−0.131766
$311$	−4.52906e9	−	4.52906e9i	−0.484135	−	0.484135i	0.422314	−	0.906450i	$-0.361218\pi$
$311$	−4.52906e9	−	4.52906e9i	−0.484135	−	0.484135i	−0.906450	+	0.422314i	$0.861218\pi$
$312$			4.40579e8i			0.0464949i
$313$	9.00016e9			0.937719			0.468860	−	0.883273i	$-0.344665\pi$
$313$	9.00016e9			0.937719			0.468860	+	0.883273i	$0.344665\pi$
$314$	1.74953e10			1.79971
$315$	−1.15338e10			−1.17146
$316$	1.09666e10	−	1.09666e10i	1.09983	−	1.09983i
$317$	9.59424e8	−	9.59424e8i	0.0950110	−	0.0950110i	−0.658004	−	0.753015i	$-0.728599\pi$
$317$	9.59424e8	−	9.59424e8i	0.0950110	−	0.0950110i	0.753015	+	0.658004i	$0.228599\pi$
$318$		−	8.25767e9i		−	0.807512i
$319$	−2.17346e8	−	4.21877e8i	−0.0209888	−	0.0407402i
$320$	4.57593e9			0.436395
$321$	7.57950e9	+	7.57950e9i	0.713872	+	0.713872i
$322$	2.06243e8	+	2.06243e8i	0.0191847	+	0.0191847i
$323$			1.50932e10i			1.38666i
$324$			4.92292e8i			0.0446728i
$325$		−	1.46679e10i		−	1.31472i
$326$	−1.56491e10			−1.38554
$327$	2.18111e10	−	2.18111e10i	1.90760	−	1.90760i
$328$		−	3.66917e8i		−	0.0317009i
$329$	3.44363e8	−	3.44363e8i	0.0293922	−	0.0293922i
$330$	3.74096e8	+	3.74096e8i	0.0315448	+	0.0315448i
$331$	1.42515e10	−	1.42515e10i	1.18727	−	1.18727i	0.209446	−	0.977820i	$-0.432834\pi$
$331$	1.42515e10	−	1.42515e10i	1.18727	−	1.18727i	0.977820	−	0.209446i	$-0.0671662\pi$
$332$		−	1.38998e10i		−	1.14408i
$333$	−3.59585e9	−	3.59585e9i	−0.292432	−	0.292432i
$334$	−9.53657e9	+	9.53657e9i	−0.766313	+	0.766313i
$335$	3.76569e9			0.298996
$336$	2.46944e10	+	2.46944e10i	1.93750	+	1.93750i
$337$	−1.19224e10	+	1.19224e10i	−0.924366	+	0.924366i	−0.997334	−	0.0729682i	$-0.976753\pi$
$337$	−1.19224e10	+	1.19224e10i	−0.924366	+	0.924366i	0.0729682	+	0.997334i	$0.476753\pi$
$338$	2.06634e10	+	2.06634e10i	1.58320	+	1.58320i
$339$	6.54742e9			0.495760
$340$	−5.89079e9	−	5.89079e9i	−0.440817	−	0.440817i
$341$			1.35204e8i			0.00999936i
$342$	−2.97406e10			−2.17393
$343$	−2.30064e10			−1.66216
$344$	3.74978e7			0.00267776
$345$	−7.63365e7	+	7.63365e7i	−0.00538835	+	0.00538835i
$346$	1.54979e10	−	1.54979e10i	1.08135	−	1.08135i
$347$			7.79860e9i			0.537897i	0.963155	+	0.268948i	$0.0866761\pi$
$347$			7.79860e9i			0.537897i	−0.963155	+	0.268948i	$0.913324\pi$
$348$	−2.12812e10	+	1.09638e10i	−1.45104	+	0.747555i
$349$	2.44881e10			1.65064			0.825321	−	0.564664i	$-0.190994\pi$
$349$	2.44881e10			1.65064			0.825321	+	0.564664i	$0.190994\pi$
$350$	2.12250e10	+	2.12250e10i	1.41441	+	1.41441i
$351$	−1.66149e10	−	1.66149e10i	−1.09463	−	1.09463i
$352$		−	9.97991e8i		−	0.0650064i
$353$			2.68969e9i			0.173222i	0.996242	+	0.0866109i	$0.0276037\pi$
$353$			2.68969e9i			0.173222i	−0.996242	+	0.0866109i	$0.972396\pi$
$354$			1.53390e10i			0.976749i
$355$	7.41550e9			0.466903
$356$	1.09040e10	−	1.09040e10i	0.678871	−	0.678871i
$357$		−	6.52012e10i		−	4.01405i
$358$	2.93755e10	−	2.93755e10i	1.78835	−	1.78835i
$359$	8.91775e9	+	8.91775e9i	0.536881	+	0.536881i	0.922611	−	0.385731i	$-0.126051\pi$
$359$	8.91775e9	+	8.91775e9i	0.536881	+	0.536881i	−0.385731	+	0.922611i	$0.626051\pi$
$360$	1.45147e8	−	1.45147e8i	0.00864170	−	0.00864170i
$361$		−	1.36916e9i		−	0.0806170i
$362$	7.15111e9	+	7.15111e9i	0.416427	+	0.416427i
$363$	−1.97483e10	+	1.97483e10i	−1.13737	+	1.13737i
$364$	−4.91542e10			−2.79998
$365$	−4.05261e8	−	4.05261e8i	−0.0228330	−	0.0228330i
$366$	−2.57725e10	+	2.57725e10i	−1.43626	+	1.43626i
$367$	−1.74329e9	−	1.74329e9i	−0.0960959	−	0.0960959i	0.657425	−	0.753520i	$-0.271646\pi$
$367$	−1.74329e9	−	1.74329e9i	−0.0960959	−	0.0960959i	−0.753520	+	0.657425i	$0.771646\pi$
$368$	2.01067e8			0.0109635
$369$	3.69707e10	+	3.69707e10i	1.99412	+	1.99412i
$370$		−	2.92892e9i		−	0.156279i
$371$	1.15202e10			0.608085
$372$	6.82023e9			0.356145
$373$	7.78529e9			0.402198			0.201099	−	0.979571i	$-0.435549\pi$
$373$	7.78529e9			0.402198			0.201099	+	0.979571i	$0.435549\pi$
$374$	−1.30083e9	+	1.30083e9i	−0.0664864	+	0.0664864i
$375$	−1.74506e10	+	1.74506e10i	−0.882440	+	0.882440i
$376$			8.66731e6i			0.000433644i
$377$	−9.88477e9	+	3.08929e10i	−0.489329	+	1.52930i
$378$	4.80849e10			2.35527
$379$	−1.41891e10	−	1.41891e10i	−0.687697	−	0.687697i	0.274025	−	0.961723i	$-0.411645\pi$
$379$	−1.41891e10	−	1.41891e10i	−0.687697	−	0.687697i	−0.961723	+	0.274025i	$0.911645\pi$
$380$	−6.09423e9	−	6.09423e9i	−0.292270	−	0.292270i
$381$		−	1.95337e10i		−	0.927012i
$382$			1.75657e10i			0.824919i
$383$			2.03654e10i			0.946452i	0.880941	+	0.473226i	$0.156911\pi$
$383$			2.03654e10i			0.946452i	−0.880941	+	0.473226i	$0.843089\pi$
$384$	−1.25912e9			−0.0579084
$385$	−5.21898e8	+	5.21898e8i	−0.0237543	+	0.0237543i
$386$		−	3.63167e10i		−	1.63590i
$387$	−3.77829e9	+	3.77829e9i	−0.168442	+	0.168442i
$388$	2.70900e10	+	2.70900e10i	1.19532	+	1.19532i
$389$	−9.26420e9	+	9.26420e9i	−0.404585	+	0.404585i	−0.879845	−	0.475260i	$-0.842354\pi$
$389$	−9.26420e9	+	9.26420e9i	−0.404585	+	0.404585i	0.475260	+	0.879845i	$0.342354\pi$
$390$		−	3.61593e10i		−	1.56301i
$391$	−2.65441e8	−	2.65441e8i	−0.0113569	−	0.0113569i
$392$	5.89474e8	−	5.89474e8i	0.0249644	−	0.0249644i
$393$	4.08511e10			1.71251
$394$	−3.09065e10	−	3.09065e10i	−1.28252	−	1.28252i
$395$	−1.12547e10	+	1.12547e10i	−0.462324	+	0.462324i
$396$	−1.28968e9	−	1.28968e9i	−0.0524447	−	0.0524447i
$397$	−3.19385e10			−1.28574			−0.642868	−	0.765977i	$-0.722256\pi$
$397$	−3.19385e10			−1.28574			−0.642868	+	0.765977i	$0.722256\pi$
$398$	−1.77494e9	−	1.77494e9i	−0.0707378	−	0.0707378i
$399$		−	6.74530e10i		−	2.66140i
$400$	2.06923e10			0.808294
$401$	3.60308e10			1.39347			0.696733	−	0.717331i	$-0.254636\pi$
$401$	3.60308e10			1.39347			0.696733	+	0.717331i	$0.254636\pi$
$402$	−4.19468e10			−1.60618
$403$	6.53425e9	−	6.53425e9i	0.247728	−	0.247728i
$404$	2.81542e10	−	2.81542e10i	1.05686	−	1.05686i
$405$		−	5.05225e8i		−	0.0187787i
$406$	−3.03997e10	−	5.90070e10i	−1.11883	−	2.17170i
$407$	−3.25422e8			−0.0118596
$408$	8.20529e8	+	8.20529e8i	0.0296110	+	0.0296110i
$409$	1.58909e10	+	1.58909e10i	0.567880	+	0.567880i	0.931534	−	0.363654i	$-0.118471\pi$
$409$	1.58909e10	+	1.58909e10i	0.567880	+	0.567880i	−0.363654	+	0.931534i	$0.618471\pi$
$410$			3.01136e10i			1.06568i
$411$			9.39632e9i			0.329299i
$412$			4.86856e10i			1.68971i
$413$	−2.13992e10			−0.735526
$414$	5.23043e8	−	5.23043e8i	0.0178048	−	0.0178048i
$415$			1.42650e10i			0.480926i
$416$	−4.82318e10	+	4.82318e10i	−1.61050	+	1.61050i
$417$	1.91578e10	+	1.91578e10i	0.633578	+	0.633578i
$418$	−1.34575e9	+	1.34575e9i	−0.0440818	+	0.0440818i
$419$		−	5.79965e9i		−	0.188168i	−0.995564	−	0.0940840i	$-0.970008\pi$
$419$		−	5.79965e9i		−	0.188168i	0.995564	−	0.0940840i	$-0.0299922\pi$
$420$	2.63266e10	+	2.63266e10i	0.846053	+	0.846053i
$421$	−3.22064e10	+	3.22064e10i	−1.02521	+	1.02521i	−0.0255398	+	0.999674i	$0.508130\pi$
$421$	−3.22064e10	+	3.22064e10i	−1.02521	+	1.02521i	−0.999674	+	0.0255398i	$0.991870\pi$
$422$	−7.44696e9			−0.234817
$423$	−8.73323e8	−	8.73323e8i	−0.0272780	−	0.0272780i
$424$	−1.44977e8	+	1.44977e8i	−0.00448575	+	0.00448575i
$425$	−2.73173e10	−	2.73173e10i	−0.837301	−	0.837301i
$426$	−8.26028e10			−2.50817
$427$	−3.59549e10	−	3.59549e10i	−1.08155	−	1.08155i
$428$		−	2.12836e10i		−	0.634264i
$429$	−4.01753e9			−0.118612
$430$	−3.07752e9			−0.0900175
$431$	1.37157e10			0.397474			0.198737	−	0.980053i	$-0.436316\pi$
$431$	1.37157e10			0.397474			0.198737	+	0.980053i	$0.436316\pi$
$432$	2.34390e10	−	2.34390e10i	0.672984	−	0.672984i
$433$	3.88879e10	−	3.88879e10i	1.10628	−	1.10628i	0.112640	−	0.993636i	$-0.464069\pi$
$433$	3.88879e10	−	3.88879e10i	1.10628	−	1.10628i	0.993636	−	0.112640i	$-0.0359306\pi$
$434$			1.89107e10i			0.533026i
$435$	2.18402e10	−	1.12518e10i	0.609958	−	0.314242i
$436$	−6.12466e10			−1.69487
$437$	−2.74608e8	−	2.74608e8i	−0.00752987	−	0.00752987i
$438$	4.51429e9	+	4.51429e9i	0.122657	+	0.122657i
$439$			1.76099e10i			0.474130i	0.971494	+	0.237065i	$0.0761855\pi$
$439$			1.76099e10i			0.474130i	−0.971494	+	0.237065i	$0.923815\pi$
$440$		−	1.31357e7i		−	0.000350464i
$441$			1.18791e11i			3.14073i
$442$	1.25735e11			3.29432
$443$	5.00484e10	−	5.00484e10i	1.29950	−	1.29950i	0.370774	−	0.928723i	$-0.379092\pi$
$443$	5.00484e10	−	5.00484e10i	1.29950	−	1.29950i	0.928723	−	0.370774i	$-0.120908\pi$
$444$			1.64155e10i			0.422400i
$445$	−1.11905e10	+	1.11905e10i	−0.285370	+	0.285370i
$446$	−7.95809e9	−	7.95809e9i	−0.201127	−	0.201127i
$447$	−6.35267e10	+	6.35267e10i	−1.59121	+	1.59121i
$448$		−	7.11109e10i		−	1.76532i
$449$	−2.47458e10	−	2.47458e10i	−0.608858	−	0.608858i	0.333790	−	0.942648i	$-0.391672\pi$
$449$	−2.47458e10	−	2.47458e10i	−0.608858	−	0.608858i	−0.942648	+	0.333790i	$0.891672\pi$
$450$	5.38278e10	−	5.38278e10i	1.31267	−	1.31267i
$451$	3.34582e9			0.0808716
$452$	−9.19273e9	−	9.19273e9i	−0.220237	−	0.220237i
$453$	−1.93005e10	+	1.93005e10i	−0.458328	+	0.458328i
$454$	3.43618e10	+	3.43618e10i	0.808821	+	0.808821i
$455$	5.04454e10			1.17700
$456$	8.48866e8	+	8.48866e8i	0.0196327	+	0.0196327i
$457$		−	1.12541e10i		−	0.258016i	−0.991644	−	0.129008i	$-0.958821\pi$
$457$		−	1.12541e10i		−	0.258016i	0.991644	−	0.129008i	$-0.0411792\pi$
$458$	−4.29384e10			−0.975852
$459$	−6.18867e10			−1.39427
$460$	2.14357e8			0.00478746
$461$	−8.17799e9	+	8.17799e9i	−0.181068	+	0.181068i	−0.791821	−	0.610753i	$-0.790867\pi$
$461$	−8.17799e9	+	8.17799e9i	−0.181068	+	0.181068i	0.610753	+	0.791821i	$0.290867\pi$
$462$	5.81353e9	−	5.81353e9i	0.127606	−	0.127606i
$463$			9.75475e9i			0.212272i	0.994352	+	0.106136i	$0.0338479\pi$
$463$			9.75475e9i			0.212272i	−0.994352	+	0.106136i	$0.966152\pi$
$464$	−4.35814e10	−	1.39447e10i	−0.940220	−	0.300841i
$465$	−6.99939e9			−0.149709
$466$	−2.82753e10	−	2.82753e10i	−0.599604	−	0.599604i
$467$	4.15226e10	+	4.15226e10i	0.873005	+	0.873005i	0.992799	−	0.119794i	$-0.0382234\pi$
$467$	4.15226e10	+	4.15226e10i	0.873005	+	0.873005i	−0.119794	+	0.992799i	$0.538223\pi$
$468$			1.24658e11i			2.59858i
$469$		−	5.85196e10i		−	1.20951i
$470$		−	7.11344e8i		−	0.0145777i
$471$	1.00631e11			2.04478
$472$	2.69300e8	−	2.69300e8i	0.00542586	−	0.00542586i
$473$			3.41932e8i			0.00683117i
$474$	1.25369e11	−	1.25369e11i	2.48357	−	2.48357i
$475$	−2.82607e10	−	2.82607e10i	−0.555147	−	0.555147i
$476$	−9.15441e10	+	9.15441e10i	−1.78321	+	1.78321i
$477$		−	2.92159e10i		−	0.564345i
$478$	4.97140e10	+	4.97140e10i	0.952285	+	0.952285i
$479$	2.41768e10	−	2.41768e10i	0.459257	−	0.459257i	−0.439154	−	0.898412i	$-0.644722\pi$
$479$	2.41768e10	−	2.41768e10i	0.459257	−	0.459257i	0.898412	+	0.439154i	$0.144722\pi$
$480$	5.16651e10			0.973268
$481$	1.57272e10	+	1.57272e10i	0.293814	+	0.293814i
$482$	5.31932e10	−	5.31932e10i	0.985525	−	0.985525i
$483$	1.18629e9	+	1.18629e9i	0.0217972	+	0.0217972i
$484$	5.54540e10			1.01054
$485$	−2.78017e10	−	2.78017e10i	−0.502463	−	0.502463i
$486$			8.19332e10i			1.46864i
$487$	−5.99961e10			−1.06661			−0.533307	−	0.845922i	$-0.679051\pi$
$487$	−5.99961e10			−1.06661			−0.533307	+	0.845922i	$0.679051\pi$
$488$	9.04955e8			0.0159569
$489$	−9.00118e10			−1.57422
$490$	−4.83793e10	+	4.83793e10i	−0.839220	+	0.839220i
$491$	−2.33522e10	+	2.33522e10i	−0.401793	+	0.401793i	−0.878865	−	0.477071i	$-0.841698\pi$
$491$	−2.33522e10	+	2.33522e10i	−0.401793	+	0.401793i	0.477071	+	0.878865i	$0.341698\pi$
$492$		−	1.68776e11i		−	2.88039i
$493$	3.91253e10	+	7.59438e10i	0.662323	+	1.28560i
$494$	1.30077e11			2.18420
$495$	1.32356e9	+	1.32356e9i	0.0220457	+	0.0220457i
$496$	9.21804e9	+	9.21804e9i	0.152304	+	0.152304i
$497$		−	1.15238e11i		−	1.88874i
$498$		−	1.58901e11i		−	2.58350i
$499$		−	6.54031e10i		−	1.05486i	−0.849598	−	0.527432i	$-0.823155\pi$
$499$		−	6.54031e10i		−	1.05486i	0.849598	−	0.527432i	$-0.176845\pi$
$500$	4.90021e10			0.784034
$501$	−5.48532e10	+	5.48532e10i	−0.870665	+	0.870665i
$502$			1.06705e11i			1.68023i
$503$	−4.39258e9	+	4.39258e9i	−0.0686195	+	0.0686195i	−0.740584	−	0.671964i	$-0.765451\pi$
$503$	−4.39258e9	+	4.39258e9i	−0.0686195	+	0.0686195i	0.671964	+	0.740584i	$0.265451\pi$
$504$	−2.25562e9	−	2.25562e9i	−0.0349578	−	0.0349578i
$505$	−2.88938e10	+	2.88938e10i	−0.444262	+	0.444262i
$506$		−	4.73350e7i		−	0.000722071i
$507$	1.18853e11	+	1.18853e11i	1.79879	+	1.79879i
$508$	−2.74258e10	+	2.74258e10i	−0.411818	+	0.411818i
$509$	−2.25828e10			−0.336439			−0.168220	−	0.985750i	$-0.553802\pi$
$509$	−2.25828e10			−0.336439			−0.168220	+	0.985750i	$0.553802\pi$
$510$	−6.73425e10	−	6.73425e10i	−0.995426	−	0.995426i
$511$	−6.29784e9	+	6.29784e9i	−0.0923651	+	0.0923651i
$512$	−6.89035e10	−	6.89035e10i	−1.00268	−	1.00268i
$513$	−6.40239e10			−0.924428
$514$	8.65735e10	+	8.65735e10i	1.24032	+	1.24032i
$515$		−	4.99645e10i		−	0.710286i
$516$	1.72484e10			0.243305
$517$	−7.90349e7			−0.00110626
$518$	−4.55160e10			−0.632186
$519$	8.91419e10	−	8.91419e10i	1.22861	−	1.22861i
$520$	−6.34834e8	+	6.34834e8i	−0.00868254	+	0.00868254i
$521$			1.20275e11i			1.63239i	0.577776	+	0.816196i	$0.303921\pi$
$521$			1.20275e11i			1.63239i	−0.577776	+	0.816196i	$0.696079\pi$
$522$	−1.49645e11	+	7.70952e10i	−2.01549	+	1.03835i
$523$	1.28943e10			0.172341			0.0861706	−	0.996280i	$-0.472537\pi$
$523$	1.28943e10			0.172341			0.0861706	+	0.996280i	$0.472537\pi$
$524$	−5.73560e10	−	5.73560e10i	−0.760770	−	0.760770i
$525$	1.22084e11	+	1.22084e11i	1.60702	+	1.60702i
$526$			5.42556e10i			0.708764i
$527$		−	2.43386e10i		−	0.315539i
$528$		−	5.66763e9i		−	0.0729232i
$529$	−7.83013e10			−0.999877
$530$	1.18985e10	−	1.18985e10i	0.150796	−	0.150796i
$531$			5.42696e10i			0.682620i
$532$	−9.47056e10	+	9.47056e10i	−1.18230	+	1.18230i
$533$	−1.61699e11	−	1.61699e11i	−2.00355	−	2.00355i
$534$	1.24653e11	−	1.24653e11i	1.53299	−	1.53299i
$535$			2.18427e10i			0.266619i
$536$	7.36444e8	+	7.36444e8i	0.00892238	+	0.00892238i
$537$	1.68964e11	−	1.68964e11i	2.03188	−	2.03188i
$538$	5.93006e9			0.0707831
$539$	5.37526e9	+	5.37526e9i	0.0636860	+	0.0636860i
$540$	2.49883e10	−	2.49883e10i	0.293874	−	0.293874i
$541$	−6.39823e10	−	6.39823e10i	−0.746914	−	0.746914i	0.226984	−	0.973898i	$-0.427113\pi$
$541$	−6.39823e10	−	6.39823e10i	−0.746914	−	0.746914i	−0.973898	+	0.226984i	$0.927113\pi$
$542$	−1.84736e11			−2.14069
$543$	4.11323e10	+	4.11323e10i	0.473134	+	0.473134i
$544$			1.79652e11i			2.05134i
$545$	6.28556e10			0.712455
$546$	−5.61922e11			−6.32275
$547$	9.14192e10			1.02115			0.510574	−	0.859834i	$-0.329433\pi$
$547$	9.14192e10			1.02115			0.510574	+	0.859834i	$0.329433\pi$
$548$	1.31927e10	−	1.31927e10i	0.146288	−	0.146288i
$549$	−9.11837e10	+	9.11837e10i	−1.00375	+	1.00375i
$550$		−	4.87137e9i		−	0.0532354i
$551$	4.04765e10	+	7.85665e10i	0.439133	+	0.852376i
$552$	−2.98578e7			−0.000321589
$553$	1.74901e11	+	1.74901e11i	1.87021	+	1.87021i
$554$	−1.17358e10	−	1.17358e10i	−0.124587	−	0.124587i
$555$		−	1.68468e10i		−	0.177560i
$556$		−	5.37959e10i		−	0.562924i
$557$			2.05457e10i			0.213452i	0.994288	+	0.106726i	$0.0340367\pi$
$557$			2.05457e10i			0.213452i	−0.994288	+	0.106726i	$0.965963\pi$
$558$	4.79585e10			0.494685
$559$	1.65252e10	−	1.65252e10i	0.169238	−	0.169238i
$560$			7.11647e10i			0.723623i
$561$	−7.48219e9	+	7.48219e9i	−0.0755401	+	0.0755401i
$562$	−8.96236e10	−	8.96236e10i	−0.898416	−	0.898416i
$563$	−3.73674e9	+	3.73674e9i	−0.0371928	+	0.0371928i	−0.725459	−	0.688266i	$-0.758372\pi$
$563$	−3.73674e9	+	3.73674e9i	−0.0371928	+	0.0371928i	0.688266	+	0.725459i	$0.258372\pi$
$564$			3.98683e9i			0.0394014i
$565$	9.43422e9	+	9.43422e9i	0.0925790	+	0.0925790i
$566$	−1.62660e10	+	1.62660e10i	−0.158495	+	0.158495i
$567$	−7.85130e9			−0.0759642
$568$	1.45022e9	+	1.45022e9i	0.0139329	+	0.0139329i
$569$	1.20664e10	−	1.20664e10i	0.115114	−	0.115114i	−0.647203	−	0.762317i	$-0.724062\pi$
$569$	1.20664e10	−	1.20664e10i	0.115114	−	0.115114i	0.762317	+	0.647203i	$0.224062\pi$
$570$	−6.96682e10	−	6.96682e10i	−0.659987	−	0.659987i
$571$	−3.43671e9			−0.0323294			−0.0161647	−	0.999869i	$-0.505146\pi$
$571$	−3.43671e9			−0.0323294			−0.0161647	+	0.999869i	$0.505146\pi$
$572$	5.64070e9	+	5.64070e9i	0.0526925	+	0.0526925i
$573$			1.01036e11i			0.937252i
$574$	4.67972e11			4.31094
$575$	9.94032e8			0.00909345
$576$	−1.80341e11			−1.63834
$577$	−9.66135e10	+	9.66135e10i	−0.871635	+	0.871635i	−0.992651	−	0.121016i	$-0.961385\pi$
$577$	−9.66135e10	+	9.66135e10i	−0.871635	+	0.871635i	0.121016	+	0.992651i	$0.461385\pi$
$578$	1.22202e11	−	1.22202e11i	1.09488	−	1.09488i
$579$		−	2.08889e11i		−	1.85867i
$580$	−4.64620e10	−	1.48664e10i	−0.410568	−	0.131369i
$581$	2.21681e11			1.94546
$582$	3.09689e11	+	3.09689e11i	2.69919	+	2.69919i
$583$	−1.32200e9	−	1.32200e9i	−0.0114435	−	0.0114435i
$584$		−	1.58511e8i		−	0.00136273i
$585$		−	1.27932e11i		−	1.09234i
$586$		−	7.07758e10i		−	0.600197i
$587$	−1.02848e10			−0.0866254			−0.0433127	−	0.999062i	$-0.513791\pi$
$587$	−1.02848e10			−0.0866254			−0.0433127	+	0.999062i	$0.513791\pi$
$588$	2.71149e11	−	2.71149e11i	2.26829	−	2.26829i
$589$		−	2.51792e10i		−	0.209209i
$590$	−2.21020e10	+	2.21020e10i	−0.182400	+	0.182400i
$591$	−1.77771e11	−	1.77771e11i	−1.45717	−	1.45717i
$592$	−2.21868e10	+	2.21868e10i	−0.180638	+	0.180638i
$593$		−	1.27916e11i		−	1.03444i	−0.855852	−	0.517221i	$-0.826966\pi$
$593$		−	1.27916e11i		−	1.03444i	0.855852	−	0.517221i	$-0.173034\pi$
$594$	−5.51799e9	−	5.51799e9i	−0.0443236	−	0.0443236i
$595$	9.39489e10	−	9.39489e10i	0.749590	−	0.749590i
$596$	1.78386e11			1.41376
$597$	−1.02092e10	−	1.02092e10i	−0.0803704	−	0.0803704i
$598$	−2.28764e9	+	2.28764e9i	−0.0178889	+	0.0178889i
$599$	−9.09067e10	−	9.09067e10i	−0.706136	−	0.706136i	0.259584	−	0.965720i	$-0.416415\pi$
$599$	−9.09067e10	−	9.09067e10i	−0.706136	−	0.706136i	−0.965720	+	0.259584i	$0.916415\pi$
$600$	−3.07274e9			−0.0237094
$601$	−1.21242e11	−	1.21242e11i	−0.929298	−	0.929298i	0.0683622	−	0.997661i	$-0.478223\pi$
$601$	−1.21242e11	−	1.21242e11i	−0.929298	−	0.929298i	−0.997661	+	0.0683622i	$0.978223\pi$
$602$			4.78253e10i			0.364143i
$603$	−1.48409e11			−1.12251
$604$	5.41968e10			0.407217
$605$	−5.69108e10			−0.424789
$606$	3.21854e11	−	3.21854e11i	2.38654	−	2.38654i
$607$	−1.42475e11	+	1.42475e11i	−1.04951	+	1.04951i	−0.0507977	+	0.998709i	$0.516176\pi$
$607$	−1.42475e11	+	1.42475e11i	−1.04951	+	1.04951i	−0.998709	+	0.0507977i	$0.983824\pi$
$608$			1.85857e11i			1.36008i
$609$	−1.74855e11	−	3.39401e11i	−1.27119	−	2.46743i
$610$	−7.42715e10			−0.536417
$611$	3.81967e9	+	3.81967e9i	0.0274069	+	0.0274069i
$612$	2.32161e11	+	2.32161e11i	1.65494	+	1.65494i
$613$			1.24603e11i			0.882444i	0.897398	+	0.441222i	$0.145455\pi$
$613$			1.24603e11i			0.882444i	−0.897398	+	0.441222i	$0.854545\pi$
$614$			1.49611e11i			1.05266i
$615$			1.73210e11i			1.21080i
$616$	−2.04132e8			−0.00141771
$617$	−5.64245e10	+	5.64245e10i	−0.389338	+	0.389338i	−0.874451	−	0.485113i	$-0.838778\pi$
$617$	−5.64245e10	+	5.64245e10i	−0.389338	+	0.389338i	0.485113	+	0.874451i	$0.338778\pi$
$618$			5.56566e11i			3.81560i
$619$	5.83155e9	−	5.83155e9i	0.0397211	−	0.0397211i	−0.686967	−	0.726688i	$-0.741058\pi$
$619$	5.83155e9	−	5.83155e9i	0.0397211	−	0.0397211i	0.726688	+	0.686967i	$0.241058\pi$
$620$	9.82731e9	+	9.82731e9i	0.0665071	+	0.0665071i
$621$	1.12598e9	−	1.12598e9i	0.00757119	−	0.00757119i
$622$			1.45388e11i			0.971331i
$623$	1.73902e11	+	1.73902e11i	1.15439	+	1.15439i
$624$	−2.73910e11	+	2.73910e11i	−1.80663	+	1.80663i
$625$	7.46487e10			0.489218
$626$	−1.44458e11	−	1.44458e11i	−0.940683	−	0.940683i
$627$	−7.74059e9	+	7.74059e9i	−0.0500846	+	0.0500846i
$628$	−1.41288e11	−	1.41288e11i	−0.908379	−	0.908379i
$629$	5.85804e10			0.374240
$630$	1.85124e11	+	1.85124e11i	1.17517	+	1.17517i
$631$			8.93095e10i			0.563352i	0.959510	+	0.281676i	$0.0908904\pi$
$631$			8.93095e10i			0.563352i	−0.959510	+	0.281676i	$0.909110\pi$
$632$	−4.40210e9			−0.0275925
$633$	−4.28340e10			−0.266793
$634$	−3.07986e10			−0.190623
$635$	2.81463e10	−	2.81463e10i	0.173112	−	0.173112i
$636$	−6.66871e10	+	6.66871e10i	−0.407581	+	0.407581i
$637$		−	5.19560e11i		−	3.15557i
$638$	−3.28285e9	+	1.02599e10i	−0.0198138	+	0.0619242i
$639$	−2.92251e11			−1.75288
$640$	−1.81427e9	−	1.81427e9i	−0.0108139	−	0.0108139i
$641$	6.94970e10	+	6.94970e10i	0.411656	+	0.411656i	0.882315	−	0.470659i	$-0.155984\pi$
$641$	6.94970e10	+	6.94970e10i	0.411656	+	0.411656i	−0.470659	+	0.882315i	$0.655984\pi$
$642$		−	2.43311e11i		−	1.43226i
$643$			1.16083e11i			0.679089i	0.940590	+	0.339544i	$0.110273\pi$
$643$			1.16083e11i			0.679089i	−0.940590	+	0.339544i	$0.889727\pi$
$644$		−	3.33115e9i		−	0.0193665i
$645$	−1.77015e10			−0.102275
$646$	2.42254e11	−	2.42254e11i	1.39104	−	1.39104i
$647$		−	2.13768e11i		−	1.21990i	−0.792438	−	0.609952i	$-0.791189\pi$
$647$		−	2.13768e11i		−	1.21990i	0.792438	−	0.609952i	$-0.208811\pi$
$648$	9.88051e7	−	9.88051e7i	0.000560376	−	0.000560376i
$649$	2.45568e9	+	2.45568e9i	0.0138418	+	0.0138418i
$650$	−2.35428e11	+	2.35428e11i	−1.31888	+	1.31888i
$651$			1.08772e11i			0.605610i
$652$	1.26379e11	+	1.26379e11i	0.699333	+	0.699333i
$653$	−8.20802e10	+	8.20802e10i	−0.451425	+	0.451425i	−0.895827	−	0.444402i	$-0.853416\pi$
$653$	−8.20802e10	+	8.20802e10i	−0.451425	+	0.451425i	0.444402	+	0.895827i	$0.353416\pi$
$654$	−7.00161e11			−3.82725
$655$	5.88627e10	+	5.88627e10i	0.319797	+	0.319797i
$656$	2.28113e11	−	2.28113e11i	1.23179	−	1.23179i
$657$	1.59717e10	+	1.59717e10i	0.0857212	+	0.0857212i
$658$	−1.10544e10			−0.0589703
$659$	−3.63340e10	−	3.63340e10i	−0.192651	−	0.192651i	0.604190	−	0.796841i	$-0.293497\pi$
$659$	−3.63340e10	−	3.63340e10i	−0.192651	−	0.192651i	−0.796841	+	0.604190i	$0.793497\pi$
$660$		−	6.04223e9i		−	0.0318436i
$661$	−2.37093e11			−1.24197			−0.620987	−	0.783821i	$-0.713268\pi$
$661$	−2.37093e11			−1.24197			−0.620987	+	0.783821i	$0.713268\pi$
$662$	−4.57489e11			−2.38204
$663$	7.23211e11			3.74292
$664$	−2.78976e9	+	2.78976e9i	−0.0143514	+	0.0143514i
$665$	9.71935e10	−	9.71935e10i	0.496993	−	0.496993i
$666$			1.15431e11i			0.586713i
$667$	−2.09359e9	−	6.69884e8i	−0.0105776	−	0.00338451i
$668$	1.54030e11			0.773572
$669$	−4.57740e10	−	4.57740e10i	−0.228515	−	0.228515i
$670$	−6.04415e10	−	6.04415e10i	−0.299941	−	0.299941i
$671$			8.25204e9i			0.0407072i
$672$		−	8.02887e11i		−	3.93711i
$673$		−	1.28916e11i		−	0.628417i	−0.949354	−	0.314209i	$-0.898261\pi$
$673$		−	1.28916e11i		−	0.628417i	0.949354	−	0.314209i	$-0.101739\pi$
$674$	3.82723e11			1.85458
$675$	1.15878e11	−	1.15878e11i	0.558193	−	0.558193i
$676$		−	3.33746e11i		−	1.59819i
$677$	1.51323e11	−	1.51323e11i	0.720362	−	0.720362i	−0.248317	−	0.968679i	$-0.579878\pi$
$677$	1.51323e11	−	1.51323e11i	0.720362	−	0.720362i	0.968679	+	0.248317i	$0.0798775\pi$
$678$	−1.05090e11	−	1.05090e11i	−0.497327	−	0.497327i
$679$	−4.32044e11	+	4.32044e11i	−2.03258	+	2.03258i
$680$			2.36461e9i			0.0110592i
$681$	1.97645e11	+	1.97645e11i	0.918961	+	0.918961i
$682$	2.17010e9	−	2.17010e9i	0.0100310	−	0.0100310i
$683$	1.60285e10			0.0736562			0.0368281	−	0.999322i	$-0.488275\pi$
$683$	1.60285e10			0.0736562			0.0368281	+	0.999322i	$0.488275\pi$
$684$	2.40179e11	+	2.40179e11i	1.09726	+	1.09726i
$685$	−1.35392e10	+	1.35392e10i	−0.0614938	+	0.0614938i
$686$	3.69267e11	+	3.69267e11i	1.66741	+	1.66741i
$687$	−2.46976e11			−1.10874
$688$	2.33125e10	+	2.33125e10i	0.104048	+	0.104048i
$689$			1.27782e11i			0.567012i
$690$	2.45049e9			0.0108108
$691$	4.43547e10			0.194548			0.0972741	−	0.995258i	$-0.468988\pi$
$691$	4.43547e10			0.194548			0.0972741	+	0.995258i	$0.468988\pi$
$692$	−2.50315e11			−1.09160
$693$	2.05684e10	−	2.05684e10i	0.0891801	−	0.0891801i
$694$	1.25172e11	−	1.25172e11i	0.539597	−	0.539597i
$695$			5.52091e10i			0.236631i
$696$	6.47169e9	+	2.07074e9i	0.0275792	+	0.00882447i
$697$	−6.02294e11			−2.55198
$698$	−3.93048e11	−	3.93048e11i	−1.65586	−	1.65586i
$699$	−1.62636e11	−	1.62636e11i	−0.681254	−	0.681254i
$700$		−	3.42817e11i		−	1.42781i
$701$			2.83221e11i			1.17288i	0.809993	+	0.586439i	$0.199471\pi$
$701$			2.83221e11i			1.17288i	−0.809993	+	0.586439i	$0.800529\pi$
$702$			5.33357e11i			2.19619i
$703$	6.06035e10			0.248128
$704$	−8.16035e9	+	8.16035e9i	−0.0332214	+	0.0332214i
$705$		−	4.09157e9i		−	0.0165628i
$706$	4.31710e10	−	4.31710e10i	0.173769	−	0.173769i
$707$	4.49015e11	+	4.49015e11i	1.79715	+	1.79715i
$708$	1.23874e11	−	1.23874e11i	0.493000	−	0.493000i
$709$			2.21119e11i			0.875067i	0.899202	+	0.437533i	$0.144148\pi$
$709$			2.21119e11i			0.875067i	−0.899202	+	0.437533i	$0.855852\pi$
$710$	−1.19023e11	−	1.19023e11i	−0.468379	−	0.468379i
$711$	4.43558e11	−	4.43558e11i	1.73569	−	1.73569i
$712$	−4.37697e9			−0.0170315
$713$	4.42822e8	+	4.42822e8i	0.00171345	+	0.00171345i
$714$	−1.04652e12	+	1.04652e12i	−4.02674	+	4.02674i
$715$	−5.78888e9	−	5.78888e9i	−0.0221498	−	0.0221498i
$716$	−4.74459e11			−1.80529
$717$	2.85949e11	+	2.85949e11i	1.08196	+	1.08196i
$718$		−	2.86270e11i		−	1.07715i
$719$	2.97704e11			1.11396			0.556980	−	0.830526i	$-0.311960\pi$
$719$	2.97704e11			1.11396			0.556980	+	0.830526i	$0.311960\pi$
$720$	1.80477e11			0.671572
$721$	−7.76459e11			−2.87328
$722$	−2.19759e10	+	2.19759e10i	−0.0808718	+	0.0808718i
$723$	3.05961e11	−	3.05961e11i	1.11973	−	1.11973i
$724$		−	1.15502e11i		−	0.420372i
$725$	−2.15457e11	−	6.89396e10i	−0.779846	−	0.249527i
$726$	6.33942e11			2.28193
$727$	2.67974e11	+	2.67974e11i	0.959303	+	0.959303i	0.999204	−	0.0399008i	$-0.0127042\pi$
$727$	2.67974e11	+	2.67974e11i	0.959303	+	0.959303i	−0.0399008	+	0.999204i	$0.512704\pi$
$728$	9.86545e9	+	9.86545e9i	0.0351230	+	0.0351230i
$729$			4.58811e11i			1.62451i
$730$			1.30093e10i			0.0458103i
$731$		−	6.15526e10i		−	0.215564i
$732$	4.16266e11			1.44986
$733$	−2.92066e11	+	2.92066e11i	−1.01173	+	1.01173i	−0.0118020	+	0.999930i	$0.503757\pi$
$733$	−2.92066e11	+	2.92066e11i	−1.01173	+	1.01173i	−0.999930	+	0.0118020i	$0.996243\pi$
$734$			5.59615e10i			0.192799i
$735$	−2.78272e11	+	2.78272e11i	−0.953499	+	0.953499i
$736$	−3.26863e9	−	3.26863e9i	−0.0111392	−	0.0111392i
$737$	−6.71544e9	+	6.71544e9i	−0.0227617	+	0.0227617i
$738$		−	1.18680e12i		−	4.00086i
$739$	2.96199e11	+	2.96199e11i	0.993131	+	0.993131i	0.999977	−	0.00684560i	$-0.00217904\pi$
$739$	2.96199e11	+	2.96199e11i	0.993131	+	0.993131i	−0.00684560	+	0.999977i	$0.502179\pi$
$740$	−2.36533e10	+	2.36533e10i	−0.0788796	+	0.0788796i
$741$	7.48187e11			2.48163
$742$	−1.84906e11	−	1.84906e11i	−0.610007	−	0.610007i
$743$	2.36720e11	−	2.36720e11i	0.776747	−	0.776747i	−0.202529	−	0.979276i	$-0.564916\pi$
$743$	2.36720e11	−	2.36720e11i	0.776747	−	0.776747i	0.979276	+	0.202529i	$0.0649160\pi$
$744$	−1.36885e9	−	1.36885e9i	−0.00446749	−	0.00446749i
$745$	−1.83072e11			−0.594288
$746$	−1.24958e11	−	1.24958e11i	−0.403469	−	0.403469i
$747$		−	5.62194e11i		−	1.80553i
$748$	2.10103e10			0.0671161
$749$	3.39440e11			1.07854
$750$	5.60184e11			1.77046
$751$	−2.33877e11	+	2.33877e11i	−0.735239	+	0.735239i	−0.971652	−	0.236414i	$-0.924028\pi$
$751$	−2.33877e11	+	2.33877e11i	−0.735239	+	0.735239i	0.236414	+	0.971652i	$0.424028\pi$
$752$	−5.38850e9	+	5.38850e9i	−0.0168499	+	0.0168499i
$753$			6.13754e11i			1.90904i
$754$	6.54505e11	−	3.37193e11i	2.02501	−	1.04326i
$755$	−5.56205e10			−0.171178
$756$	−3.88323e11	−	3.88323e11i	−1.18879	−	1.18879i
$757$	2.70842e10	+	2.70842e10i	0.0824769	+	0.0824769i	0.747142	−	0.664665i	$-0.231426\pi$
$757$	2.70842e10	+	2.70842e10i	0.0824769	+	0.0824769i	−0.664665	+	0.747142i	$0.731426\pi$
$758$			4.55486e11i			1.37974i
$759$		−	2.72265e8i		−	0.000820398i
$760$			2.44628e9i			0.00733248i
$761$	−2.84582e10			−0.0848532			−0.0424266	−	0.999100i	$-0.513509\pi$
$761$	−2.84582e10			−0.0848532			−0.0424266	+	0.999100i	$0.513509\pi$
$762$	−3.13528e11	+	3.13528e11i	−0.929942	+	0.929942i
$763$		−	9.76789e11i		−	2.88206i
$764$	1.41856e11	−	1.41856e11i	0.416366	−	0.416366i
$765$	−2.38260e11	−	2.38260e11i	−0.695672	−	0.695672i
$766$	3.26877e11	−	3.26877e11i	0.949444	−	0.949444i
$767$		−	2.37360e11i		−	0.685845i
$768$	−3.86284e11	−	3.86284e11i	−1.11035	−	1.11035i
$769$	2.37614e11	−	2.37614e11i	0.679465	−	0.679465i	−0.280414	−	0.959879i	$-0.590472\pi$
$769$	2.37614e11	−	2.37614e11i	0.679465	−	0.679465i	0.959879	+	0.280414i	$0.0904718\pi$
$770$	1.67535e10			0.0476588
$771$	4.97961e11	+	4.97961e11i	1.40922	+	1.40922i
$772$	−2.93286e11	+	2.93286e11i	−0.825699	+	0.825699i
$773$	2.91432e11	+	2.91432e11i	0.816243	+	0.816243i	0.985561	−	0.169318i	$-0.0541566\pi$
$773$	2.91432e11	+	2.91432e11i	0.816243	+	0.816243i	−0.169318	+	0.985561i	$0.554157\pi$
$774$	1.21287e11			0.337950
$775$	4.55720e10	+	4.55720e10i	0.126326	+	0.126326i
$776$		−	1.08742e10i		−	0.0299881i
$777$	−2.61802e11			−0.718273
$778$	2.97391e11			0.811727
$779$	−6.23094e11			−1.69201
$780$	−2.92014e11	+	2.92014e11i	−0.788906	+	0.788906i
$781$	−1.32242e10	+	1.32242e10i	−0.0355440	+	0.0355440i
$782$			8.52096e9i			0.0227857i
$783$	−3.22147e11	+	1.65966e11i	−0.857053	+	0.441543i
$784$	7.32956e11			1.94005
$785$	1.45000e11	+	1.45000e11i	0.381846	+	0.381846i
$786$	−6.55684e11	−	6.55684e11i	−1.71793	−	1.71793i
$787$			8.45418e10i			0.220380i	0.993911	+	0.110190i	$0.0351460\pi$
$787$			8.45418e10i			0.220380i	−0.993911	+	0.110190i	$0.964854\pi$
$788$			4.99188e11i			1.29467i
$789$			3.12072e11i			0.805279i
$790$	3.61290e11			0.927571
$791$	1.46610e11	−	1.46610e11i	0.374505	−	0.374505i
$792$			5.17689e8i			0.00131573i
$793$	3.98812e11	−	3.98812e11i	1.00850	−	1.00850i
$794$	5.12631e11	+	5.12631e11i	1.28980	+	1.28980i
$795$	6.84390e10	−	6.84390e10i	0.171331	−	0.171331i
$796$			2.86680e10i			0.0714078i
$797$	−7.20813e10	−	7.20813e10i	−0.178644	−	0.178644i	0.612120	−	0.790765i	$-0.290317\pi$
$797$	−7.20813e10	−	7.20813e10i	−0.178644	−	0.178644i	−0.790765	+	0.612120i	$0.790317\pi$
$798$	−1.08266e12	+	1.08266e12i	−2.66981	+	2.66981i
$799$	1.42274e10			0.0349091
$800$	−3.36384e11	−	3.36384e11i	−0.821250	−	0.821250i
$801$	4.41026e11	−	4.41026e11i	1.07136	−	1.07136i
$802$	−5.78315e11	−	5.78315e11i	−1.39787	−	1.39787i
$803$	1.44542e9			0.00347642
$804$	3.38753e11	+	3.38753e11i	0.810699	+	0.810699i
$805$			3.41865e9i			0.00814088i
$806$	−2.09757e11			−0.497023
$807$	3.41090e10			0.0804219
$808$	−1.13013e10			−0.0265145
$809$	−1.49767e11	+	1.49767e11i	−0.349640	+	0.349640i	−0.859975	−	0.510335i	$-0.829521\pi$
$809$	−1.49767e11	+	1.49767e11i	−0.349640	+	0.349640i	0.510335	+	0.859975i	$0.329521\pi$
$810$	−8.10914e9	+	8.10914e9i	−0.0188380	+	0.0188380i
$811$			2.49971e10i			0.0577837i	0.999583	+	0.0288919i	$0.00919785\pi$
$811$			2.49971e10i			0.0577837i	−0.999583	+	0.0288919i	$0.990802\pi$
$812$	−2.31027e11	+	7.22028e11i	−0.531420	+	1.66085i
$813$	−1.06258e12			−2.43220
$814$	5.22320e9	+	5.22320e9i	0.0118970	+	0.0118970i
$815$	−1.29699e11	−	1.29699e11i	−0.293971	−	0.293971i
$816$			1.02025e12i			2.30116i
$817$		−	6.36783e10i		−	0.142923i
$818$		−	5.10118e11i		−	1.13935i
$819$	−1.98810e12			−4.41877
$820$	2.43191e11	−	2.43191e11i	0.537888	−	0.537888i
$821$		−	2.91396e11i		−	0.641373i	−0.947185	−	0.320686i	$-0.896086\pi$
$821$		−	2.91396e11i		−	0.641373i	0.947185	−	0.320686i	$-0.103914\pi$
$822$	1.50816e11	−	1.50816e11i	0.330340	−	0.330340i
$823$	3.15433e11	+	3.15433e11i	0.687556	+	0.687556i	0.961691	−	0.274135i	$-0.0883916\pi$
$823$	3.15433e11	+	3.15433e11i	0.687556	+	0.687556i	−0.274135	+	0.961691i	$0.588392\pi$
$824$	9.77141e9	−	9.77141e9i	0.0211957	−	0.0211957i
$825$		−	2.80195e10i		−	0.0604847i
$826$	3.43470e11	+	3.43470e11i	0.737851	+	0.737851i
$827$	3.32679e10	−	3.32679e10i	0.0711219	−	0.0711219i	−0.670651	−	0.741773i	$-0.733985\pi$
$827$	3.32679e10	−	3.32679e10i	0.0711219	−	0.0711219i	0.741773	+	0.670651i	$0.233985\pi$
$828$	−8.44797e9			−0.0179734
$829$	−4.56399e11	−	4.56399e11i	−0.966332	−	0.966332i	0.0331194	−	0.999451i	$-0.489456\pi$
$829$	−4.56399e11	−	4.56399e11i	−0.966332	−	0.966332i	−0.999451	+	0.0331194i	$0.989456\pi$
$830$	2.28961e11	−	2.28961e11i	0.482446	−	0.482446i
$831$	−6.75028e10	−	6.75028e10i	−0.141553	−	0.141553i
$832$	7.88761e11			1.64608
$833$	−9.67622e11	−	9.67622e11i	−2.00967	−	2.00967i
$834$		−	6.14986e11i		−	1.27116i
$835$	−1.58077e11			−0.325179
$836$	2.17359e10			0.0444993
$837$	1.03242e11			0.210357
$838$	−9.30877e10	+	9.30877e10i	−0.188763	+	0.188763i
$839$	4.38656e11	−	4.38656e11i	0.885271	−	0.885271i	−0.108793	−	0.994064i	$-0.534699\pi$
$839$	4.38656e11	−	4.38656e11i	0.885271	−	0.885271i	0.994064	+	0.108793i	$0.0346987\pi$
$840$		−	1.05677e10i		−	0.0212258i
$841$	4.07329e11	+	2.90396e11i	0.814256	+	0.580506i
$842$	1.03386e12			2.05691
$843$	−5.15504e11	−	5.15504e11i	−1.02076	−	1.02076i
$844$	6.01400e10	+	6.01400e10i	0.118521	+	0.118521i
$845$			3.42513e11i			0.671816i
$846$			2.80347e10i			0.0547285i
$847$			8.84406e11i			1.71837i
$848$	−1.80265e11			−0.348601
$849$	−9.35603e10	+	9.35603e10i	−0.180078	+	0.180078i
$850$			8.76915e11i			1.67989i
$851$	−1.06582e9	+	1.06582e9i	−0.00203221	+	0.00203221i
$852$	6.67082e11	+	6.67082e11i	1.26596	+	1.26596i
$853$	2.00126e9	−	2.00126e9i	0.00378014	−	0.00378014i	−0.705214	−	0.708994i	$-0.749149\pi$
$853$	2.00126e9	−	2.00126e9i	0.00378014	−	0.00378014i	0.708994	+	0.705214i	$0.249149\pi$
$854$			1.15419e12i			2.16994i
$855$	−2.46488e11	−	2.46488e11i	−0.461244	−	0.461244i
$856$	−4.27171e9	+	4.27171e9i	−0.00795621	+	0.00795621i
$857$	−9.98383e11			−1.85086			−0.925430	−	0.378918i	$-0.876296\pi$
$857$	−9.98383e11			−1.85086			−0.925430	+	0.378918i	$0.876296\pi$
$858$	6.44836e10	+	6.44836e10i	0.118987	+	0.118987i
$859$	−4.69179e11	+	4.69179e11i	−0.861720	+	0.861720i	−0.991538	−	0.129818i	$-0.958561\pi$
$859$	−4.69179e11	+	4.69179e11i	−0.861720	+	0.861720i	0.129818	+	0.991538i	$0.458561\pi$
$860$	2.48534e10	+	2.48534e10i	0.0454351	+	0.0454351i
$861$	2.69172e12			4.89798
$862$	−2.20145e11	−	2.20145e11i	−0.398730	−	0.398730i
$863$		−	3.03585e11i		−	0.547315i	−0.961827	−	0.273657i	$-0.911767\pi$
$863$		−	3.03585e11i		−	0.547315i	0.961827	−	0.273657i	$-0.0882335\pi$
$864$	−7.62071e11			−1.36754
$865$	2.56890e11			0.458863
$866$	−1.24835e12			−2.21954
$867$	7.02891e11	−	7.02891e11i	1.24397	−	1.24397i
$868$	1.52718e11	−	1.52718e11i	0.269037	−	0.269037i
$869$		−	4.01416e10i		−	0.0703907i
$870$	−5.31145e11	−	1.69950e11i	−0.927121	−	0.296650i
$871$	6.49099e11			1.12782
$872$	1.22925e10	+	1.22925e10i	0.0212605	+	0.0212605i
$873$	1.09569e12	+	1.09569e12i	1.88638	+	1.88638i
$874$			8.81523e9i			0.0151073i
$875$			7.81507e11i			1.33322i
$876$		−	7.29127e10i		−	0.123819i
$877$	−3.98502e11			−0.673647			−0.336823	−	0.941568i	$-0.609352\pi$
$877$	−3.98502e11			−0.673647			−0.336823	+	0.941568i	$0.609352\pi$
$878$	2.82648e11	−	2.82648e11i	0.475629	−	0.475629i
$879$		−	4.07094e11i		−	0.681929i
$880$	8.16652e9	−	8.16652e9i	0.0136178	−	0.0136178i
$881$	−6.03555e11	−	6.03555e11i	−1.00187	−	1.00187i	−0.999998	−	0.00187592i	$-0.999403\pi$
$881$	−6.03555e11	−	6.03555e11i	−1.00187	−	1.00187i	−0.00187592	−	0.999998i	$-0.500597\pi$
$882$	1.90667e12	−	1.90667e12i	3.15066	−	3.15066i
$883$		−	8.79709e11i		−	1.44709i	−0.690276	−	0.723546i	$-0.742511\pi$
$883$		−	8.79709e11i		−	1.44709i	0.690276	−	0.723546i	$-0.257489\pi$
$884$	−1.01541e12	−	1.01541e12i	−1.66276	−	1.66276i
$885$	−1.27128e11	+	1.27128e11i	−0.207238	+	0.207238i
$886$	−1.60661e12			−2.60721
$887$	2.09941e11	+	2.09941e11i	0.339159	+	0.339159i	0.856051	−	0.516892i	$-0.172911\pi$
$887$	2.09941e11	+	2.09941e11i	0.339159	+	0.339159i	−0.516892	+	0.856051i	$0.672911\pi$
$888$	3.29467e9	−	3.29467e9i	0.00529859	−	0.00529859i
$889$	−4.37399e11	−	4.37399e11i	−0.700279	−	0.700279i
$890$	3.59227e11			0.572544
$891$	9.00978e8	+	9.00978e8i	0.00142956	+	0.00142956i
$892$			1.28536e11i			0.203032i
$893$	1.47187e10			0.0231454
$894$	2.03928e12			3.19247
$895$	4.86923e11			0.758872
$896$	−2.81942e10	+	2.81942e10i	−0.0437449	+	0.0437449i
$897$	−1.31583e10	+	1.31583e10i	−0.0203249	+	0.0203249i
$898$			7.94368e11i			1.22156i
$899$	−6.52708e10	−	1.26693e11i	−0.0999263	−	0.193961i
$900$	−8.69403e11			−1.32511
$901$	2.37979e11	+	2.37979e11i	0.361110	+	0.361110i
$902$	−5.37023e10	−	5.37023e10i	−0.0811272	−	0.0811272i
$903$			2.75085e11i			0.413729i
$904$			3.69004e9i			0.00552532i
$905$			1.18536e11i			0.176708i
$906$	6.19569e11			0.919553
$907$	−4.66730e11	+	4.66730e11i	−0.689663	+	0.689663i	−0.962157	−	0.272494i	$-0.912151\pi$
$907$	−4.66730e11	+	4.66730e11i	−0.689663	+	0.689663i	0.272494	+	0.962157i	$0.412151\pi$
$908$		−	5.54997e11i		−	0.816482i
$909$	1.13873e12	−	1.13873e12i	1.66788	−	1.66788i
$910$	−8.09678e11	−	8.09678e11i	−1.18072	−	1.18072i
$911$	−5.16455e9	+	5.16455e9i	−0.00749823	+	0.00749823i	−0.710846	−	0.703348i	$-0.751688\pi$
$911$	−5.16455e9	+	5.16455e9i	−0.00749823	+	0.00749823i	0.703348	+	0.710846i	$0.251688\pi$
$912$			1.05549e12i			1.52572i
$913$	−2.54390e10	−	2.54390e10i	−0.0366115	−	0.0366115i
$914$	−1.80635e11	+	1.80635e11i	−0.258831	+	0.258831i
$915$	−4.27201e11			−0.609463
$916$	3.46761e11	+	3.46761e11i	0.492548	+	0.492548i
$917$	9.14739e11	−	9.14739e11i	1.29366	−	1.29366i
$918$	9.93316e11	+	9.93316e11i	1.39868	+	1.39868i
$919$	−3.39158e11			−0.475488			−0.237744	−	0.971328i	$-0.576408\pi$
$919$	−3.39158e11			−0.475488			−0.237744	+	0.971328i	$0.576408\pi$
$920$	−4.30223e7	−	4.30223e7i	−6.00540e−5	−	6.00540e-5i
$921$			8.60542e11i			1.19601i
$922$	2.62523e11			0.363281
$923$	1.27822e12			1.76116
$924$	−9.38976e10			−0.128815
$925$	−1.09687e11	+	1.09687e11i	−0.149826	+	0.149826i
$926$	1.56569e11	−	1.56569e11i	0.212943	−	0.212943i
$927$			1.96914e12i			2.66660i
$928$	4.81788e11	+	9.35171e11i	0.649627	+	1.26095i
$929$	9.13517e11			1.22646			0.613230	−	0.789904i	$-0.289870\pi$
$929$	9.13517e11			1.22646			0.613230	+	0.789904i	$0.289870\pi$
$930$	1.12344e11	+	1.12344e11i	0.150182	+	0.150182i
$931$	−1.00104e12	−	1.00104e12i	−1.33245	−	1.33245i
$932$			4.56691e11i			0.605283i
$933$			8.36255e11i			1.10360i
$934$		−	1.33292e12i		−	1.75153i
$935$	−2.15623e10			−0.0282129
$936$	2.50193e10	−	2.50193e10i	0.0325966	−	0.0325966i
$937$		−	9.17813e11i		−	1.19068i	−0.803473	−	0.595341i	$-0.797017\pi$
$937$		−	9.17813e11i		−	1.19068i	0.803473	−	0.595341i	$-0.202983\pi$
$938$	−9.39274e11	+	9.39274e11i	−1.21334	+	1.21334i
$939$	−8.30903e11	−	8.30903e11i	−1.06878	−	1.06878i
$940$	−5.74466e9	+	5.74466e9i	−0.00735788	+	0.00735788i
$941$			1.23216e12i			1.57148i	0.618554	+	0.785742i	$0.287719\pi$
$941$			1.23216e12i			1.57148i	−0.618554	+	0.785742i	$0.712281\pi$
$942$	−1.61518e12	−	1.61518e12i	−2.05125	−	2.05125i
$943$	1.09583e10	−	1.09583e10i	0.0138578	−	0.0138578i
$944$	3.34850e11			0.421660
$945$	3.98524e11	+	3.98524e11i	0.499720	+	0.499720i
$946$	5.48821e9	−	5.48821e9i	0.00685276	−	0.00685276i
$947$	−4.27620e11	−	4.27620e11i	−0.531690	−	0.531690i	0.389385	−	0.921075i	$-0.372687\pi$
$947$	−4.27620e11	−	4.27620e11i	−0.531690	−	0.531690i	−0.921075	+	0.389385i	$0.872687\pi$
$948$	−2.02490e12			−2.50709
$949$	−6.98555e10	−	6.98555e10i	−0.0861263	−	0.0861263i
$950$			9.07200e11i			1.11380i
$951$	−1.77150e11			−0.216580
$952$	3.67466e10			0.0447372
$953$	−1.61167e10			−0.0195391			−0.00976955	−	0.999952i	$-0.503110\pi$
$953$	−1.61167e10			−0.0195391			−0.00976955	+	0.999952i	$0.503110\pi$
$954$	−4.68931e11	+	4.68931e11i	−0.566129	+	0.566129i
$955$	−1.45583e11	+	1.45583e11i	−0.175024	+	0.175024i
$956$		−	8.02958e11i		−	0.961305i
$957$	−1.88825e10	+	5.90137e10i	−0.0225119	+	0.0703566i
$958$	−7.76102e11			−0.921418
$959$	2.10402e11	+	2.10402e11i	0.248758	+	0.248758i
$960$	−4.22454e11	−	4.22454e11i	−0.497387	−	0.497387i
$961$		−	8.12288e11i		−	0.952394i
$962$		−	5.04863e11i		−	0.589485i
$963$		−	8.60839e11i		−	1.00096i
$964$	−8.59152e11			−0.994860
$965$	3.00990e11	−	3.00990e11i	0.347091	−	0.347091i
$966$		−	3.80811e10i		−	0.0437322i
$967$	−3.64207e11	+	3.64207e11i	−0.416526	+	0.416526i	−0.884005	−	0.467478i	$-0.845163\pi$
$967$	−3.64207e11	+	3.64207e11i	−0.416526	+	0.416526i	0.467478	+	0.884005i	$0.345163\pi$
$968$	−1.11299e10	−	1.11299e10i	−0.0126762	−	0.0126762i
$969$	1.39341e12	−	1.39341e12i	1.58047	−	1.58047i
$970$			8.92465e11i			1.00810i
$971$	3.06817e11	+	3.06817e11i	0.345146	+	0.345146i	0.858298	−	0.513152i	$-0.171522\pi$
$971$	3.06817e11	+	3.06817e11i	0.345146	+	0.345146i	−0.513152	+	0.858298i	$0.671522\pi$
$972$	6.61674e11	−	6.61674e11i	0.741275	−	0.741275i
$973$	8.57961e11			0.957230
$974$	9.62972e11	+	9.62972e11i	1.06999	+	1.06999i
$975$	−1.35415e12	+	1.35415e12i	−1.49847	+	1.49847i
$976$	5.62614e11	+	5.62614e11i	0.620028	+	0.620028i
$977$	−4.23718e11			−0.465048			−0.232524	−	0.972591i	$-0.574698\pi$
$977$	−4.23718e11			−0.465048			−0.232524	+	0.972591i	$0.574698\pi$
$978$	1.44474e12	+	1.44474e12i	1.57919	+	1.57919i
$979$		−	3.99124e10i		−	0.0434488i
$980$	7.81402e11			0.847169
$981$	−2.47719e12			−2.67475
$982$	7.49633e11			0.806126
$983$	−1.20524e12	+	1.20524e12i	−1.29080	+	1.29080i	−0.356503	+	0.934294i	$0.616031\pi$
$983$	−1.20524e12	+	1.20524e12i	−1.29080	+	1.29080i	−0.934294	+	0.356503i	$0.883969\pi$
$984$	−3.38741e10	+	3.38741e10i	−0.0361316	+	0.0361316i
$985$		−	5.12302e11i		−	0.544228i
$986$	5.90959e11	−	1.84692e12i	0.625244	−	1.95408i
$987$	−6.35838e10			−0.0670005
$988$	−1.05047e12	−	1.05047e12i	−1.10245	−	1.10245i
$989$	1.11990e9	+	1.11990e9i	0.00117056	+	0.00117056i
$990$		−	4.24878e10i		−	0.0442307i
$991$			4.12076e11i			0.427251i	0.976916	+	0.213625i	$0.0685272\pi$
$991$			4.12076e11i			0.427251i	−0.976916	+	0.213625i	$0.931473\pi$
$992$		−	2.99705e11i		−	0.309491i
$993$	−2.63142e12			−2.70641
$994$	−1.84964e12	+	1.84964e12i	−1.89471	+	1.89471i
$995$		−	2.94211e10i		−	0.0300170i
$996$	−1.28325e12	+	1.28325e12i	−1.30398	+	1.30398i
$997$	1.15572e12	+	1.15572e12i	1.16970	+	1.16970i	0.982280	+	0.187417i	$0.0600116\pi$
$997$	1.15572e12	+	1.15572e12i	1.16970	+	1.16970i	0.187417	+	0.982280i	$0.439988\pi$
$998$	−1.04976e12	+	1.04976e12i	−1.05820	+	1.05820i
$999$			2.48493e11i			0.249490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.3	✓	38
29.17	odd	4	inner	29.9.c.a.17.3	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.3	✓	38	1.1	even	1	trivial
29.9.c.a.17.3	yes	38	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.0506 - 16.0506i) q^{2} +(-92.3210 - 92.3210i) q^{3} +259.242i q^{4} -266.052i q^{5} +2963.61i q^{6} -4134.50 q^{7} +(52.0309 - 52.0309i) q^{8} +10485.3i q^{9} +O(q^{10})\)	\(q+(-16.0506 - 16.0506i) q^{2} +(-92.3210 - 92.3210i) q^{3} +259.242i q^{4} -266.052i q^{5} +2963.61i q^{6} -4134.50 q^{7} +(52.0309 - 52.0309i) q^{8} +10485.3i q^{9} +(-4270.28 + 4270.28i) q^{10} +(474.456 + 474.456i) q^{11} +(23933.4 - 23933.4i) q^{12} -45859.8i q^{13} +(66361.1 + 66361.1i) q^{14} +(-24562.2 + 24562.2i) q^{15} +64695.6 q^{16} +(-85408.8 - 85408.8i) q^{17} +(168295. - 168295. i) q^{18} +(-88358.4 - 88358.4i) q^{19} +68971.7 q^{20} +(381701. + 381701. i) q^{21} -15230.6i q^{22} +3107.89 q^{23} -9607.09 q^{24} +319841. q^{25} +(-736076. + 736076. i) q^{26} +(362297. - 362297. i) q^{27} -1.07184e6i q^{28} +(-673638. - 215543. i) q^{29} +788474. q^{30} +(142483. + 142483. i) q^{31} +(-1.05172e6 - 1.05172e6i) q^{32} -87604.5i q^{33} +2.74172e6i q^{34} +1.09999e6i q^{35} -2.71823e6 q^{36} +(-342942. + 342942. i) q^{37} +2.83640e6i q^{38} +(-4.23382e6 + 4.23382e6i) q^{39} +(-13842.9 - 13842.9i) q^{40} +(3.52595e6 - 3.52595e6i) q^{41} -1.22530e7i q^{42} +(360341. + 360341. i) q^{43} +(-122999. + 122999. i) q^{44} +2.78964e6 q^{45} +(-49883.4 - 49883.4i) q^{46} +(-83290.0 + 83290.0i) q^{47} +(-5.97276e6 - 5.97276e6i) q^{48} +1.13293e7 q^{49} +(-5.13364e6 - 5.13364e6i) q^{50} +1.57700e7i q^{51} +1.18888e7 q^{52} -2.78636e6 q^{53} -1.16301e7 q^{54} +(126230. - 126230. i) q^{55} +(-215122. + 215122. i) q^{56} +1.63147e7i q^{57} +(7.35268e6 + 1.42719e7i) q^{58} +5.17577e6 q^{59} +(-6.36754e6 - 6.36754e6i) q^{60} +(8.69632e6 + 8.69632e6i) q^{61} -4.57387e6i q^{62} -4.33516e7i q^{63} +1.71994e7i q^{64} -1.22011e7 q^{65} +(-1.40610e6 + 1.40610e6i) q^{66} +1.41540e7i q^{67} +(2.21415e7 - 2.21415e7i) q^{68} +(-286923. - 286923. i) q^{69} +(1.76555e7 - 1.76555e7i) q^{70} +2.78724e7i q^{71} +(545561. + 545561. i) q^{72} +(1.52324e6 - 1.52324e6i) q^{73} +1.10088e7 q^{74} +(-2.95281e7 - 2.95281e7i) q^{75} +(2.29062e7 - 2.29062e7i) q^{76} +(-1.96164e6 - 1.96164e6i) q^{77} +1.35911e8 q^{78} +(-4.23028e7 - 4.23028e7i) q^{79} -1.72124e7i q^{80} +1.89897e6 q^{81} -1.13187e8 q^{82} -5.36173e7 q^{83} +(-9.89529e7 + 9.89529e7i) q^{84} +(-2.27232e7 + 2.27232e7i) q^{85} -1.15674e7i q^{86} +(4.22917e7 + 8.20900e7i) q^{87} +49372.8 q^{88} +(-4.20612e7 - 4.20612e7i) q^{89} +(-4.47753e7 - 4.47753e7i) q^{90} +1.89608e8i q^{91} +805695. i q^{92} -2.63084e7i q^{93} +2.67370e6 q^{94} +(-2.35079e7 + 2.35079e7i) q^{95} +1.94192e8i q^{96} +(1.04497e8 - 1.04497e8i) q^{97} +(-1.81842e8 - 1.81842e8i) q^{98} +(-4.97482e6 + 4.97482e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Introduction

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