LMFDB - Embedded newform 49.10.c.c.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,10,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not 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:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$-3.22311 - 5.58259i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.10.c.c.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.44622 - 9.43313i) q^{2} +(97.9084 - 169.582i) q^{3} +(196.677 - 340.655i) q^{4} +(-100.391 - 173.882i) q^{5} -2132.92 q^{6} -9861.52 q^{8} +(-9330.63 - 16161.1i) q^{9} +O(q^{10})$	\(q+(-5.44622 - 9.43313i) q^{2} +(97.9084 - 169.582i) q^{3} +(196.677 - 340.655i) q^{4} +(-100.391 - 173.882i) q^{5} -2132.92 q^{6} -9861.52 q^{8} +(-9330.63 - 16161.1i) q^{9} +(-1093.50 + 1894.01i) q^{10} +(-31932.1 + 55308.1i) q^{11} +(-38512.7 - 66706.0i) q^{12} -164679. q^{13} -39316.5 q^{15} +(-46990.7 - 81390.3i) q^{16} +(181455. - 314289. i) q^{17} +(-101633. + 176034. i) q^{18} +(218249. + 378018. i) q^{19} -78978.6 q^{20} +695638. q^{22} +(-459100. - 795184. i) q^{23} +(-965527. + 1.67234e6i) q^{24} +(956406. - 1.65654e6i) q^{25} +(896877. + 1.55344e6i) q^{26} +200076. q^{27} -3.68643e6 q^{29} +(214127. + 370878. i) q^{30} +(-1.73814e6 + 3.01055e6i) q^{31} +(-3.03639e6 + 5.25919e6i) q^{32} +(6.25285e6 + 1.08303e7i) q^{33} -3.95298e6 q^{34} -7.34049e6 q^{36} +(-9.40745e6 - 1.62942e7i) q^{37} +(2.37726e6 - 4.11754e6i) q^{38} +(-1.61234e7 + 2.79266e7i) q^{39} +(990009. + 1.71475e6i) q^{40} +2.40714e6 q^{41} -1.25306e7 q^{43} +(1.25607e7 + 2.17557e7i) q^{44} +(-1.87342e6 + 3.24486e6i) q^{45} +(-5.00072e6 + 8.66150e6i) q^{46} +(2.77255e7 + 4.80219e7i) q^{47} -1.84032e7 q^{48} -2.08352e7 q^{50} +(-3.55320e7 - 6.15432e7i) q^{51} +(-3.23886e7 + 5.60987e7i) q^{52} +(4.63444e7 - 8.02709e7i) q^{53} +(-1.08966e6 - 1.88734e6i) q^{54} +1.28228e7 q^{55} +8.54737e7 q^{57} +(2.00771e7 + 3.47746e7i) q^{58} +(1.26300e7 - 2.18758e7i) q^{59} +(-7.73267e6 + 1.33934e7i) q^{60} +(-3.46637e7 - 6.00394e7i) q^{61} +3.78653e7 q^{62} +1.80290e7 q^{64} +(1.65323e7 + 2.86347e7i) q^{65} +(6.81088e7 - 1.17968e8i) q^{66} +(1.16747e7 - 2.02211e7i) q^{67} +(-7.13762e7 - 1.23627e8i) q^{68} -1.79799e8 q^{69} -1.06194e8 q^{71} +(9.20142e7 + 1.59373e8i) q^{72} +(1.05058e8 - 1.81965e8i) q^{73} +(-1.02470e8 + 1.77484e8i) q^{74} +(-1.87280e8 - 3.24379e8i) q^{75} +1.71699e8 q^{76} +3.51247e8 q^{78} +(74803.2 + 129563. i) q^{79} +(-9.43490e6 + 1.63417e7i) q^{80} +(2.03244e8 - 3.52029e8i) q^{81} +(-1.31098e7 - 2.27069e7i) q^{82} +5.21565e8 q^{83} -7.28659e7 q^{85} +(6.82444e7 + 1.18203e8i) q^{86} +(-3.60932e8 + 6.25153e8i) q^{87} +(3.14900e8 - 5.45422e8i) q^{88} +(-1.49294e8 - 2.58584e8i) q^{89} +4.08123e7 q^{90} -3.61178e8 q^{92} +(3.40358e8 + 5.89517e8i) q^{93} +(3.01998e8 - 5.23076e8i) q^{94} +(4.38205e7 - 7.58993e7i) q^{95} +(5.94577e8 + 1.02984e9i) q^{96} -8.95983e8 q^{97} +1.19179e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 86 q^{3} + 620 q^{4} + 2238 q^{5} - 7976 q^{6} + 5232 q^{8} - 11038 q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 + 86 * q^3 + 620 * q^4 + 2238 * q^5 - 7976 * q^6 + 5232 * q^8 - 11038 * q^9	\( 4 q + 6 q^{2} + 86 q^{3} + 620 q^{4} + 2238 q^{5} - 7976 q^{6} + 5232 q^{8} - 11038 q^{9} - 43384 q^{10} - 35316 q^{11} - 52136 q^{12} - 53060 q^{13} - 614272 q^{15} + 752 q^{16} + 463920 q^{17} - 332042 q^{18} + 925426 q^{19} + 947520 q^{20} + 2355776 q^{22} - 778128 q^{23} - 3301296 q^{24} - 2081722 q^{25} + 4127424 q^{26} - 5597224 q^{27} - 20007168 q^{29} - 4095872 q^{30} - 2467260 q^{31} - 1284576 q^{32} + 15640784 q^{33} - 4493352 q^{34} - 11225432 q^{36} - 30735552 q^{37} - 3504660 q^{38} - 47417944 q^{39} + 32409984 q^{40} - 38206896 q^{41} + 8130200 q^{43} + 18650976 q^{44} - 22338298 q^{45} - 12367584 q^{46} + 82195020 q^{47} - 57612992 q^{48} - 176625252 q^{50} - 59971356 q^{51} - 33466384 q^{52} + 55189812 q^{53} - 52834472 q^{54} + 164891632 q^{55} + 63562232 q^{57} - 66558004 q^{58} + 7069218 q^{59} - 76165376 q^{60} - 44316386 q^{61} + 109820400 q^{62} + 294834304 q^{64} + 369979260 q^{65} + 83258464 q^{66} + 241921336 q^{67} - 165645816 q^{68} - 390362304 q^{69} + 412987632 q^{71} + 279147720 q^{72} + 499153188 q^{73} - 3571524 q^{74} - 813228014 q^{75} + 565023536 q^{76} + 189941920 q^{78} - 468535096 q^{79} - 249904128 q^{80} + 585745634 q^{81} - 389586092 q^{82} + 888047916 q^{83} + 346950120 q^{85} + 416830608 q^{86} - 28134340 q^{87} + 986010816 q^{88} - 636267396 q^{89} - 546485456 q^{90} - 658862976 q^{92} + 791523960 q^{93} + 152223192 q^{94} - 1104747984 q^{95} + 1714981184 q^{96} - 3265432128 q^{97} + 2818835720 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 + 86 * q^3 + 620 * q^4 + 2238 * q^5 - 7976 * q^6 + 5232 * q^8 - 11038 * q^9 - 43384 * q^10 - 35316 * q^11 - 52136 * q^12 - 53060 * q^13 - 614272 * q^15 + 752 * q^16 + 463920 * q^17 - 332042 * q^18 + 925426 * q^19 + 947520 * q^20 + 2355776 * q^22 - 778128 * q^23 - 3301296 * q^24 - 2081722 * q^25 + 4127424 * q^26 - 5597224 * q^27 - 20007168 * q^29 - 4095872 * q^30 - 2467260 * q^31 - 1284576 * q^32 + 15640784 * q^33 - 4493352 * q^34 - 11225432 * q^36 - 30735552 * q^37 - 3504660 * q^38 - 47417944 * q^39 + 32409984 * q^40 - 38206896 * q^41 + 8130200 * q^43 + 18650976 * q^44 - 22338298 * q^45 - 12367584 * q^46 + 82195020 * q^47 - 57612992 * q^48 - 176625252 * q^50 - 59971356 * q^51 - 33466384 * q^52 + 55189812 * q^53 - 52834472 * q^54 + 164891632 * q^55 + 63562232 * q^57 - 66558004 * q^58 + 7069218 * q^59 - 76165376 * q^60 - 44316386 * q^61 + 109820400 * q^62 + 294834304 * q^64 + 369979260 * q^65 + 83258464 * q^66 + 241921336 * q^67 - 165645816 * q^68 - 390362304 * q^69 + 412987632 * q^71 + 279147720 * q^72 + 499153188 * q^73 - 3571524 * q^74 - 813228014 * q^75 + 565023536 * q^76 + 189941920 * q^78 - 468535096 * q^79 - 249904128 * q^80 + 585745634 * q^81 - 389586092 * q^82 + 888047916 * q^83 + 346950120 * q^85 + 416830608 * q^86 - 28134340 * q^87 + 986010816 * q^88 - 636267396 * q^89 - 546485456 * q^90 - 658862976 * q^92 + 791523960 * q^93 + 152223192 * q^94 - 1104747984 * q^95 + 1714981184 * q^96 - 3265432128 * q^97 + 2818835720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5.44622	−	9.43313i	−0.240691	−	0.416890i	0.720220	−	0.693746i	$-0.244041\pi$
$2$	−5.44622	−	9.43313i	−0.240691	−	0.416890i	−0.960911	+	0.276856i	$0.910707\pi$
$3$	97.9084	−	169.582i	0.697870	−	1.20875i	−0.271334	−	0.962485i	$-0.587465\pi$
$3$	97.9084	−	169.582i	0.697870	−	1.20875i	0.969204	−	0.246261i	$-0.0792020\pi$
$4$	196.677	−	340.655i	0.384135	−	0.665342i
$5$	−100.391	−	173.882i	−0.0718340	−	0.124420i	0.827871	−	0.560918i	$-0.189552\pi$
$5$	−100.391	−	173.882i	−0.0718340	−	0.124420i	−0.899705	+	0.436498i	$0.856219\pi$
$6$	−2132.92			−0.671885
$7$		0			0
$7$		0			0
$8$	−9861.52			−0.851215
$9$	−9330.63	−	16161.1i	−0.474045	−	0.821070i
$10$	−1093.50	+	1894.01i	−0.0345796	+	0.0598937i
$11$	−31932.1	+	55308.1i	−0.657599	+	1.13899i	0.323637	+	0.946181i	$0.395094\pi$
$11$	−31932.1	+	55308.1i	−0.657599	+	1.13899i	−0.981236	+	0.192813i	$0.938239\pi$
$12$	−38512.7	−	66706.0i	−0.536153	−	0.928644i
$13$	−164679.			−1.59916			−0.799581	−	0.600558i	$-0.794945\pi$
$13$	−164679.			−1.59916			−0.799581	+	0.600558i	$0.794945\pi$
$14$		0			0
$15$	−39316.5			−0.200523
$16$	−46990.7	−	81390.3i	−0.179255	−	0.310480i
$17$	181455.	−	314289.i	0.526925	−	0.912661i	−0.472582	−	0.881286i	$-0.656678\pi$
$17$	181455.	−	314289.i	0.526925	−	0.912661i	0.999508	−	0.0313748i	$-0.00998856\pi$
$18$	−101633.	+	176034.i	−0.228197	+	0.395249i
$19$	218249.	+	378018.i	0.384203	+	0.665460i	0.991658	−	0.128895i	$-0.0411429\pi$
$19$	218249.	+	378018.i	0.384203	+	0.665460i	−0.607455	+	0.794354i	$0.707810\pi$
$20$	−78978.6			−0.110376
$21$		0			0
$22$	695638.			0.633113
$23$	−459100.	−	795184.i	−0.342083	−	0.592505i	0.642736	−	0.766088i	$-0.277799\pi$
$23$	−459100.	−	795184.i	−0.342083	−	0.592505i	−0.984819	+	0.173582i	$0.944466\pi$
$24$	−965527.	+	1.67234e6i	−0.594037	+	1.02890i
$25$	956406.	−	1.65654e6i	0.489680	−	0.848150i
$26$	896877.	+	1.55344e6i	0.384904	+	0.666674i
$27$	200076.			0.0724531
$28$		0			0
$29$	−3.68643e6			−0.967865			−0.483932	−	0.875105i	$-0.660792\pi$
$29$	−3.68643e6			−0.967865			−0.483932	+	0.875105i	$0.660792\pi$
$30$	214127.	+	370878.i	0.0482642	+	0.0835960i
$31$	−1.73814e6	+	3.01055e6i	−0.338032	+	0.585489i	−0.984063	−	0.177823i	$-0.943095\pi$
$31$	−1.73814e6	+	3.01055e6i	−0.338032	+	0.585489i	0.646030	+	0.763312i	$0.276428\pi$
$32$	−3.03639e6	+	5.25919e6i	−0.511898	+	0.886633i
$33$	6.25285e6	+	1.08303e7i	0.917837	+	1.58974i
$34$	−3.95298e6			−0.507305
$35$		0			0
$36$	−7.34049e6			−0.728390
$37$	−9.40745e6	−	1.62942e7i	−0.825210	−	1.42931i	−0.901759	−	0.432239i	$-0.857724\pi$
$37$	−9.40745e6	−	1.62942e7i	−0.825210	−	1.42931i	0.0765491	−	0.997066i	$-0.475610\pi$
$38$	2.37726e6	−	4.11754e6i	0.184949	−	0.320341i
$39$	−1.61234e7	+	2.79266e7i	−1.11601	+	1.93298i
$40$	990009.	+	1.71475e6i	0.0611462	+	0.105908i
$41$	2.40714e6			0.133038			0.0665188	−	0.997785i	$-0.478811\pi$
$41$	2.40714e6			0.133038			0.0665188	+	0.997785i	$0.478811\pi$
$42$		0			0
$43$	−1.25306e7			−0.558938			−0.279469	−	0.960155i	$-0.590158\pi$
$43$	−1.25306e7			−0.558938			−0.279469	+	0.960155i	$0.590158\pi$
$44$	1.25607e7	+	2.17557e7i	0.505214	+	0.875056i
$45$	−1.87342e6	+	3.24486e6i	−0.0681051	+	0.117961i
$46$	−5.00072e6	+	8.66150e6i	−0.164673	+	0.285222i
$47$	2.77255e7	+	4.80219e7i	0.828779	+	1.43549i	0.898997	+	0.437955i	$0.144297\pi$
$47$	2.77255e7	+	4.80219e7i	0.828779	+	1.43549i	−0.0702184	+	0.997532i	$0.522370\pi$
$48$	−1.84032e7			−0.500388
$49$		0			0
$50$	−2.08352e7			−0.471447
$51$	−3.55320e7	−	6.15432e7i	−0.735451	−	1.27384i
$52$	−3.23886e7	+	5.60987e7i	−0.614295	+	1.06399i
$53$	4.63444e7	−	8.02709e7i	0.806782	−	1.39739i	−0.108299	−	0.994118i	$-0.534540\pi$
$53$	4.63444e7	−	8.02709e7i	0.806782	−	1.39739i	0.915081	−	0.403269i	$-0.132126\pi$
$54$	−1.08966e6	−	1.88734e6i	−0.0174388	−	0.0302049i
$55$	1.28228e7			0.188952
$56$		0			0
$57$	8.54737e7			1.07250
$58$	2.00771e7	+	3.47746e7i	0.232957	+	0.403493i
$59$	1.26300e7	−	2.18758e7i	0.135696	−	0.235033i	−0.790167	−	0.612892i	$-0.790006\pi$
$59$	1.26300e7	−	2.18758e7i	0.135696	−	0.235033i	0.925863	+	0.377859i	$0.123339\pi$
$60$	−7.73267e6	+	1.33934e7i	−0.0770281	+	0.133417i
$61$	−3.46637e7	−	6.00394e7i	−0.320547	−	0.555203i	0.660054	−	0.751218i	$-0.270533\pi$
$61$	−3.46637e7	−	6.00394e7i	−0.320547	−	0.555203i	−0.980601	+	0.196015i	$0.937200\pi$
$62$	3.78653e7			0.325446
$63$		0			0
$64$	1.80290e7			0.134326
$65$	1.65323e7	+	2.86347e7i	0.114874	+	0.198968i
$66$	6.81088e7	−	1.17968e8i	0.441831	−	0.765273i
$67$	1.16747e7	−	2.02211e7i	0.0707796	−	0.122594i	−0.828464	−	0.560043i	$-0.810785\pi$
$67$	1.16747e7	−	2.02211e7i	0.0707796	−	0.122594i	0.899243	+	0.437449i	$0.144118\pi$
$68$	−7.13762e7	−	1.23627e8i	−0.404821	−	0.701171i
$69$	−1.79799e8			−0.954918
$70$		0			0
$71$	−1.06194e8			−0.495950			−0.247975	−	0.968766i	$-0.579765\pi$
$71$	−1.06194e8			−0.495950			−0.247975	+	0.968766i	$0.579765\pi$
$72$	9.20142e7	+	1.59373e8i	0.403514	+	0.698907i
$73$	1.05058e8	−	1.81965e8i	0.432987	−	0.749956i	−0.564142	−	0.825678i	$-0.690793\pi$
$73$	1.05058e8	−	1.81965e8i	0.432987	−	0.749956i	0.997129	+	0.0757223i	$0.0241263\pi$
$74$	−1.02470e8	+	1.77484e8i	−0.397242	+	0.688043i
$75$	−1.87280e8	−	3.24379e8i	−0.683466	−	1.18380i
$76$	1.71699e8			0.590344
$77$		0			0
$78$	3.51247e8			1.07445
$79$	74803.2	+	129563.i	0.000216072	+	0.000374248i	0.866133	−	0.499813i	$-0.166598\pi$
$79$	74803.2	+	129563.i	0.000216072	+	0.000374248i	−0.865917	+	0.500187i	$0.833265\pi$
$80$	−9.43490e6	+	1.63417e7i	−0.0257533	+	0.0446060i
$81$	2.03244e8	−	3.52029e8i	0.524608	−	0.908647i
$82$	−1.31098e7	−	2.27069e7i	−0.0320210	−	0.0554620i
$83$	5.21565e8			1.20630			0.603152	−	0.797626i	$-0.293911\pi$
$83$	5.21565e8			1.20630			0.603152	+	0.797626i	$0.293911\pi$
$84$		0			0
$85$	−7.28659e7			−0.151405
$86$	6.82444e7	+	1.18203e8i	0.134531	+	0.233015i
$87$	−3.60932e8	+	6.25153e8i	−0.675444	+	1.16990i
$88$	3.14900e8	−	5.45422e8i	0.559758	−	0.969529i
$89$	−1.49294e8	−	2.58584e8i	−0.252224	−	0.436865i	0.711914	−	0.702267i	$-0.247829\pi$
$89$	−1.49294e8	−	2.58584e8i	−0.252224	−	0.436865i	−0.964138	+	0.265402i	$0.914495\pi$
$90$	4.08123e7			0.0655692
$91$		0			0
$92$	−3.61178e8			−0.525625
$93$	3.40358e8	+	5.89517e8i	0.471805	+	0.817190i
$94$	3.01998e8	−	5.23076e8i	0.398960	−	0.691018i
$95$	4.38205e7	−	7.58993e7i	0.0551977	−	0.0956053i
$96$	5.94577e8	+	1.02984e9i	0.714476	+	1.23751i
$97$	−8.95983e8			−1.02761			−0.513803	−	0.857908i	$-0.671764\pi$
$97$	−8.95983e8			−1.02761			−0.513803	+	0.857908i	$0.671764\pi$
$98$		0			0
$99$	1.19179e9			1.24693
$100$	−3.76207e8	−	6.51609e8i	−0.376207	−	0.651609i
$101$	2.06521e7	−	3.57705e7i	0.0197478	−	0.0342042i	−0.855983	−	0.517005i	$-0.827047\pi$
$101$	2.06521e7	−	3.57705e7i	0.0197478	−	0.0342042i	0.875730	+	0.482800i	$0.160380\pi$
$102$	−3.87030e8	+	6.70356e8i	−0.354033	+	0.613203i
$103$	−2.14736e8	−	3.71933e8i	−0.187991	−	0.325610i	0.756589	−	0.653890i	$-0.226864\pi$
$103$	−2.14736e8	−	3.71933e8i	−0.187991	−	0.325610i	−0.944580	+	0.328280i	$0.893531\pi$
$104$	1.62398e9			1.36123
$105$		0			0
$106$	−1.00961e9			−0.776742
$107$	−6.16435e8	−	1.06770e9i	−0.454632	−	0.787446i	0.544035	−	0.839063i	$-0.316896\pi$
$107$	−6.16435e8	−	1.06770e9i	−0.454632	−	0.787446i	−0.998667	+	0.0516164i	$0.983563\pi$
$108$	3.93503e7	−	6.81567e7i	0.0278318	−	0.0482061i
$109$	−8.48097e8	+	1.46895e9i	−0.575475	+	0.996751i	0.420515	+	0.907285i	$0.361849\pi$
$109$	−8.48097e8	+	1.46895e9i	−0.575475	+	0.996751i	−0.995990	+	0.0894657i	$0.971484\pi$
$110$	−6.98359e7	−	1.20959e8i	−0.0454790	−	0.0787720i
$111$	−3.68428e9			−2.30356
$112$		0			0
$113$	−1.42449e9			−0.821878			−0.410939	−	0.911663i	$-0.634799\pi$
$113$	−1.42449e9			−0.821878			−0.410939	+	0.911663i	$0.634799\pi$
$114$	−4.65509e8	−	8.06285e8i	−0.258140	−	0.447112i
$115$	−9.21790e7	+	1.59659e8i	−0.0491464	+	0.0851241i
$116$	−7.25037e8	+	1.25580e9i	−0.371791	+	0.643961i
$117$	1.53656e9	+	2.66139e9i	0.758075	+	1.31302i
$118$	−2.75143e8			−0.130644
$119$		0			0
$120$	3.87721e8			0.170688
$121$	−8.60349e8	−	1.49017e9i	−0.364872	−	0.631976i
$122$	−3.77573e8	+	6.53975e8i	−0.154306	+	0.267265i
$123$	2.35680e8	−	4.08209e8i	0.0928429	−	0.160809i
$124$	6.83707e8	+	1.18422e9i	0.259700	+	0.449814i
$125$	−7.76211e8			−0.284371
$126$		0			0
$127$	−3.12858e9			−1.06716			−0.533581	−	0.845749i	$-0.679154\pi$
$127$	−3.12858e9			−1.06716			−0.533581	+	0.845749i	$0.679154\pi$
$128$	1.45644e9	+	2.52264e9i	0.479567	+	0.830634i
$129$	−1.22685e9	+	2.12497e9i	−0.390066	+	0.675614i
$130$	1.80077e8	−	3.11902e8i	0.0552985	−	0.0957797i
$131$	−3.51562e8	−	6.08923e8i	−0.104299	−	0.180651i	0.809153	−	0.587599i	$-0.199927\pi$
$131$	−3.51562e8	−	6.08923e8i	−0.104299	−	0.180651i	−0.913452	+	0.406947i	$0.866593\pi$
$132$	4.91918e9			1.41029
$133$		0			0
$134$	−2.54332e8			−0.0681442
$135$	−2.00858e7	−	3.47896e7i	−0.00520460	−	0.00901463i
$136$	−1.78942e9	+	3.09937e9i	−0.448527	+	0.776871i
$137$	1.53655e9	−	2.66139e9i	0.372653	−	0.645454i	−0.617320	−	0.786712i	$-0.711781\pi$
$137$	1.53655e9	−	2.66139e9i	0.372653	−	0.645454i	0.989973	+	0.141258i	$0.0451148\pi$
$138$	9.79225e8	+	1.69607e9i	0.229841	+	0.398095i
$139$	5.07806e9			1.15380			0.576901	−	0.816814i	$-0.304262\pi$
$139$	5.07806e9			1.15380			0.576901	+	0.816814i	$0.304262\pi$
$140$		0			0
$141$	1.08582e10			2.31352
$142$	5.78357e8	+	1.00174e9i	0.119371	+	0.206756i
$143$	5.25854e9	−	9.10807e9i	1.05161	−	1.82144i
$144$	−8.76906e8	+	1.51885e9i	−0.169950	+	0.294362i
$145$	3.70084e8	+	6.41005e8i	0.0695256	+	0.120422i
$146$	−2.28867e9			−0.416865
$147$		0			0
$148$	−7.40093e9			−1.26797
$149$	−1.06728e9	−	1.84858e9i	−0.177394	−	0.307255i	0.763593	−	0.645698i	$-0.223433\pi$
$149$	−1.06728e9	−	1.84858e9i	−0.177394	−	0.307255i	−0.940987	+	0.338442i	$0.890100\pi$
$150$	−2.03994e9	+	3.53328e9i	−0.329008	+	0.569859i
$151$	1.17649e9	−	2.03774e9i	0.184159	−	0.318972i	−0.759134	−	0.650934i	$-0.774377\pi$
$151$	1.17649e9	−	2.03774e9i	0.184159	−	0.318972i	0.943293	+	0.331962i	$0.107711\pi$
$152$	−2.15227e9	−	3.72784e9i	−0.327039	−	0.566449i
$153$	−6.77236e9			−0.999145
$154$		0			0
$155$	6.97977e8			0.0971288
$156$	6.34223e9	+	1.09851e10i	0.857396	+	1.48505i
$157$	1.49241e9	−	2.58493e9i	0.196038	−	0.339547i	−0.751203	−	0.660072i	$-0.770526\pi$
$157$	1.49241e9	−	2.58493e9i	0.196038	−	0.339547i	0.947240	+	0.320525i	$0.103859\pi$
$158$	814790.	−	1.41126e6i	0.000104013	−	0.000180156i
$159$	−9.07503e9	−	1.57184e10i	−1.12606	−	1.95039i
$160$	1.21931e9			0.147087
$161$		0			0
$162$	−4.42764e9			−0.505074
$163$	−4.60373e9	−	7.97389e9i	−0.510817	−	0.884761i	−0.999921	−	0.0125357i	$-0.996010\pi$
$163$	−4.60373e9	−	7.97389e9i	−0.510817	−	0.884761i	0.489105	−	0.872225i	$-0.337324\pi$
$164$	4.73430e8	−	8.20005e8i	0.0511044	−	0.0885155i
$165$	1.25546e9	−	2.17452e9i	0.131864	−	0.228395i
$166$	−2.84056e9	−	4.91999e9i	−0.290347	−	0.502895i
$167$	−4.95501e9			−0.492970			−0.246485	−	0.969147i	$-0.579276\pi$
$167$	−4.95501e9			−0.492970			−0.246485	+	0.969147i	$0.579276\pi$
$168$		0			0
$169$	1.65146e10			1.55732
$170$	3.96844e8	+	6.87354e8i	0.0364418	+	0.0631190i
$171$	4.07280e9	−	7.05430e9i	0.364259	−	0.630915i
$172$	−2.46448e9	+	4.26861e9i	−0.214708	+	0.371885i
$173$	−1.88773e9	−	3.26965e9i	−0.160226	−	0.277520i	0.774724	−	0.632300i	$-0.217889\pi$
$173$	−1.88773e9	−	3.26965e9i	−0.160226	−	0.277520i	−0.934950	+	0.354780i	$0.884556\pi$
$174$	7.86287e9			0.650294
$175$		0			0
$176$	6.00206e9			0.471513
$177$	−2.47316e9	−	4.28364e9i	−0.189397	−	0.328045i
$178$	−1.62617e9	+	2.81662e9i	−0.121416	+	0.210299i
$179$	9.71810e9	−	1.68322e10i	0.707526	−	1.22547i	−0.258246	−	0.966079i	$-0.583144\pi$
$179$	9.71810e9	−	1.68322e10i	0.707526	−	1.22547i	0.965772	−	0.259392i	$-0.0835223\pi$
$180$	7.36920e8	+	1.27638e9i	0.0523232	+	0.0906264i
$181$	−9.81530e9			−0.679751			−0.339875	−	0.940470i	$-0.610385\pi$
$181$	−9.81530e9			−0.679751			−0.339875	+	0.940470i	$0.610385\pi$
$182$		0			0
$183$	−1.35755e10			−0.894799
$184$	4.52742e9	+	7.84173e9i	0.291186	+	0.504349i
$185$	−1.88885e9	+	3.27158e9i	−0.118556	+	0.205345i
$186$	3.70733e9	−	6.42128e9i	0.227119	−	0.393381i
$187$	1.15885e10	+	2.00719e10i	0.693011	+	1.20033i
$188$	2.18119e10			1.27345
$189$		0			0
$190$	−9.54625e8			−0.0531424
$191$	9.22896e9	+	1.59850e10i	0.501768	+	0.869087i	0.999998	+	0.00204235i	$0.000650100\pi$
$191$	9.22896e9	+	1.59850e10i	0.501768	+	0.869087i	−0.498230	+	0.867045i	$0.666017\pi$
$192$	1.76519e9	−	3.05740e9i	0.0937424	−	0.162367i
$193$	−2.41803e9	+	4.18814e9i	−0.125445	+	0.217277i	−0.921907	−	0.387412i	$-0.873369\pi$
$193$	−2.41803e9	+	4.18814e9i	−0.125445	+	0.217277i	0.796462	+	0.604689i	$0.206703\pi$
$194$	4.87972e9	+	8.45193e9i	0.247336	+	0.428399i
$195$	6.47460e9			0.320669
$196$		0			0
$197$	2.70242e10			1.27836			0.639182	−	0.769056i	$-0.279273\pi$
$197$	2.70242e10			1.27836			0.639182	+	0.769056i	$0.279273\pi$
$198$	−6.49074e9	−	1.12423e10i	−0.300124	−	0.519830i
$199$	−8.28862e9	+	1.43563e10i	−0.374665	+	0.648939i	−0.990277	−	0.139111i	$-0.955576\pi$
$199$	−8.28862e9	+	1.43563e10i	−0.374665	+	0.648939i	0.615612	+	0.788050i	$0.288909\pi$
$200$	−9.43162e9	+	1.63360e10i	−0.416823	+	0.721958i
$201$	−2.28610e9	−	3.95964e9i	−0.0987900	−	0.171109i
$202$	−4.49904e8			−0.0190125
$203$		0			0
$204$	−2.79533e10			−1.13005
$205$	−2.41656e8	−	4.18560e8i	−0.00955662	−	0.0165526i
$206$	−2.33900e9	+	4.05126e9i	−0.0904956	+	0.156743i
$207$	−8.56738e9	+	1.48391e10i	−0.324326	+	0.561748i
$208$	7.73838e9	+	1.34033e10i	0.286659	+	0.496507i
$209$	−2.78766e10			−1.01061
$210$		0			0
$211$	−5.44866e10			−1.89243			−0.946213	−	0.323544i	$-0.895126\pi$
$211$	−5.44866e10			−1.89243			−0.946213	+	0.323544i	$0.895126\pi$
$212$	−1.82298e10	−	3.15749e10i	−0.619827	−	1.07357i
$213$	−1.03973e10	+	1.80087e10i	−0.346109	+	0.599478i
$214$	−6.71448e9	+	1.16298e10i	−0.218852	+	0.379063i
$215$	1.25796e9	+	2.17885e9i	0.0401508	+	0.0695432i
$216$	−1.97305e9			−0.0616731
$217$		0			0
$218$	1.84757e10			0.554047
$219$	−2.05721e10	−	3.56319e10i	−0.604337	−	1.04674i
$220$	2.52196e9	−	4.36816e9i	0.0725831	−	0.125718i
$221$	−2.98818e10	+	5.17568e10i	−0.842639	+	1.45949i
$222$	2.00654e10	+	3.47543e10i	0.554446	+	0.960329i
$223$	−2.05500e10			−0.556468			−0.278234	−	0.960513i	$-0.589749\pi$
$223$	−2.05500e10			−0.556468			−0.278234	+	0.960513i	$0.589749\pi$
$224$		0			0
$225$	−3.56955e10			−0.928521
$226$	7.75811e9	+	1.34374e10i	0.197819	+	0.342632i
$227$	1.97029e10	−	3.41264e10i	0.492509	−	0.853050i	−0.507454	−	0.861679i	$-0.669413\pi$
$227$	1.97029e10	−	3.41264e10i	0.492509	−	0.853050i	0.999963	+	0.00862867i	$0.00274662\pi$
$228$	1.68107e10	−	2.91170e10i	0.411984	−	0.713576i
$229$	9.12580e9	+	1.58063e10i	0.219286	+	0.379815i	0.954590	−	0.297923i	$-0.0962938\pi$
$229$	9.12580e9	+	1.58063e10i	0.219286	+	0.379815i	−0.735304	+	0.677738i	$0.762960\pi$
$230$	2.00811e9			0.0473165
$231$		0			0
$232$	3.63538e10			0.823861
$233$	2.54080e10	+	4.40080e10i	0.564767	+	0.978205i	0.997071	+	0.0764775i	$0.0243673\pi$
$233$	2.54080e10	+	4.40080e10i	0.564767	+	0.978205i	−0.432304	+	0.901728i	$0.642299\pi$
$234$	1.67368e10	−	2.89891e10i	0.364924	−	0.632067i
$235$	5.56678e9	−	9.64195e9i	0.119069	−	0.206234i
$236$	−4.96806e9	−	8.60494e9i	−0.104252	−	0.180569i
$237$	2.92955e7			0.000603160
$238$		0			0
$239$	3.80447e10			0.754230			0.377115	−	0.926166i	$-0.376916\pi$
$239$	3.80447e10			0.754230			0.377115	+	0.926166i	$0.376916\pi$
$240$	1.84751e9	+	3.19999e9i	0.0359449	+	0.0622584i
$241$	−4.90039e10	+	8.48772e10i	−0.935737	+	1.62074i	−0.162422	+	0.986721i	$0.551931\pi$
$241$	−4.90039e10	+	8.48772e10i	−0.935737	+	1.62074i	−0.773315	+	0.634022i	$0.781403\pi$
$242$	−9.37130e9	+	1.62316e10i	−0.175643	+	0.304222i
$243$	−3.78295e10	−	6.55227e10i	−0.695989	−	1.20549i
$244$	−2.72703e10			−0.492533
$245$		0			0
$246$	−5.13425e9			−0.0893859
$247$	−3.59410e10	−	6.22516e10i	−0.614403	−	1.06418i
$248$	1.71407e10	−	2.96886e10i	0.287738	−	0.498377i
$249$	5.10656e10	−	8.84482e10i	0.841843	−	1.45812i
$250$	4.22742e9	+	7.32210e9i	0.0684455	+	0.118551i
$251$	7.75125e10			1.23265			0.616325	−	0.787492i	$-0.288621\pi$
$251$	7.75125e10			1.23265			0.616325	+	0.787492i	$0.288621\pi$
$252$		0			0
$253$	5.86401e10			0.899814
$254$	1.70389e10	+	2.95123e10i	0.256856	+	0.444888i
$255$	−7.13419e9	+	1.23568e10i	−0.105661	+	0.183010i
$256$	2.04797e10	−	3.54718e10i	0.298018	−	0.516183i
$257$	5.37945e10	+	9.31748e10i	0.769199	+	1.33229i	0.937998	+	0.346641i	$0.112678\pi$
$257$	5.37945e10	+	9.31748e10i	0.769199	+	1.33229i	−0.168799	+	0.985651i	$0.553989\pi$
$258$	2.67268e10			0.375542
$259$		0			0
$260$	1.30061e10			0.176509
$261$	3.43967e10	+	5.95768e10i	0.458811	+	0.794685i
$262$	−3.82937e9	+	6.63266e9i	−0.0502078	+	0.0869624i
$263$	6.08073e9	−	1.05321e10i	0.0783708	−	0.135742i	−0.824176	−	0.566333i	$-0.808362\pi$
$263$	6.08073e9	−	1.05321e10i	0.0783708	−	0.135742i	0.902547	+	0.430591i	$0.141695\pi$
$264$	−6.16626e10	−	1.06803e11i	−0.781276	−	1.35321i
$265$	−1.86103e10			−0.231818
$266$		0			0
$267$	−5.84685e10			−0.704078
$268$	−4.59229e9	−	7.95408e9i	−0.0543779	−	0.0941853i
$269$	6.17583e10	−	1.06968e11i	0.719134	−	1.24558i	−0.242209	−	0.970224i	$-0.577872\pi$
$269$	6.17583e10	−	1.06968e11i	0.719134	−	1.24558i	0.961343	−	0.275352i	$-0.0887945\pi$
$270$	−2.18783e8	+	3.78944e8i	−0.00250540	+	0.00433948i
$271$	−6.71527e10	−	1.16312e11i	−0.756313	−	1.30997i	−0.944719	−	0.327881i	$-0.893665\pi$
$271$	−6.71527e10	−	1.16312e11i	−0.756313	−	1.30997i	0.188406	−	0.982091i	$-0.439668\pi$
$272$	−3.41068e10			−0.377817
$273$		0			0
$274$	−3.34736e10			−0.358777
$275$	6.10802e10	+	1.05794e11i	0.644025	+	1.11548i
$276$	−3.53624e10	+	6.12494e10i	−0.366818	+	0.635347i
$277$	1.08342e10	−	1.87654e10i	0.110570	−	0.191513i	−0.805430	−	0.592691i	$-0.798066\pi$
$277$	1.08342e10	−	1.87654e10i	0.110570	−	0.191513i	0.916000	+	0.401178i	$0.131399\pi$
$278$	−2.76562e10	−	4.79020e10i	−0.277710	−	0.481008i
$279$	6.48719e10			0.640970
$280$		0			0
$281$	7.73283e9			0.0739878			0.0369939	−	0.999315i	$-0.488222\pi$
$281$	7.73283e9			0.0739878			0.0369939	+	0.999315i	$0.488222\pi$
$282$	−5.91363e10	−	1.02427e11i	−0.556844	−	0.964482i
$283$	3.59800e10	−	6.23193e10i	0.333444	−	0.577542i	−0.649741	−	0.760156i	$-0.725123\pi$
$283$	3.59800e10	−	6.23193e10i	0.333444	−	0.577542i	0.983185	+	0.182614i	$0.0584559\pi$
$284$	−2.08860e10	+	3.61756e10i	−0.190512	+	0.329977i
$285$	−8.58079e9	−	1.48624e10i	−0.0770417	−	0.133440i
$286$	−1.14557e11			−1.01245
$287$		0			0
$288$	1.13326e11			0.970650
$289$	−6.55796e9	−	1.13587e10i	−0.0553004	−	0.0957831i
$290$	4.03112e9	−	6.98211e9i	0.0334684	−	0.0579690i
$291$	−8.77243e10	+	1.51943e11i	−0.717136	+	1.24212i
$292$	−4.13249e10	−	7.15769e10i	−0.332651	−	0.576169i
$293$	1.73674e11			1.37667			0.688335	−	0.725393i	$-0.258342\pi$
$293$	1.73674e11			1.37667			0.688335	+	0.725393i	$0.258342\pi$
$294$		0			0
$295$	−5.07175e9			−0.0389905
$296$	9.27718e10	+	1.60686e11i	0.702431	+	1.21665i
$297$	−6.38884e9	+	1.10658e10i	−0.0476451	+	0.0825237i
$298$	−1.16252e10	+	2.01355e10i	−0.0853943	+	0.147907i
$299$	7.56040e10	+	1.30950e11i	0.547046	+	0.947512i
$300$	−1.47335e11			−1.05017
$301$		0			0
$302$	−2.56297e10			−0.177302
$303$	−4.04404e9	−	7.00448e9i	−0.0275628	−	0.0477401i
$304$	2.05114e10	−	3.55267e10i	0.137741	−	0.238574i
$305$	−6.95986e9	+	1.20548e10i	−0.0460523	+	0.0797649i
$306$	3.68838e10	+	6.38846e10i	0.240485	+	0.416533i
$307$	2.27108e11			1.45918			0.729591	−	0.683884i	$-0.239710\pi$
$307$	2.27108e11			1.45918			0.729591	+	0.683884i	$0.239710\pi$
$308$		0			0
$309$	−8.40978e10			−0.524773
$310$	−3.80134e9	−	6.58411e9i	−0.0233781	−	0.0404920i
$311$	4.34481e10	−	7.52543e10i	0.263360	−	0.456152i	−0.703773	−	0.710425i	$-0.748503\pi$
$311$	4.34481e10	−	7.52543e10i	0.263360	−	0.456152i	0.967133	+	0.254273i	$0.0818361\pi$
$312$	1.59002e11	−	2.75399e11i	0.949962	−	1.64538i
$313$	2.62644e10	+	4.54913e10i	0.154674	+	0.267904i	0.932940	−	0.360031i	$-0.117234\pi$
$313$	2.62644e10	+	4.54913e10i	0.154674	+	0.267904i	−0.778266	+	0.627935i	$0.783900\pi$
$314$	−3.25120e10			−0.188738
$315$		0			0
$316$	5.88484e7			0.000332004
$317$	−1.31892e11	−	2.28444e11i	−0.733588	−	1.27061i	−0.955340	−	0.295508i	$-0.904511\pi$
$317$	−1.31892e11	−	2.28444e11i	−0.733588	−	1.27061i	0.221752	−	0.975103i	$-0.428822\pi$
$318$	−9.88492e10	+	1.71212e11i	−0.542065	+	0.938884i
$319$	1.17716e11	−	2.03889e11i	0.636467	−	1.10239i
$320$	−1.80995e9	−	3.13493e9i	−0.00964921	−	0.0167129i
$321$	−2.41417e11			−1.26910
$322$		0			0
$323$	1.58410e11			0.809786
$324$	−7.99469e10	−	1.38472e11i	−0.403041	−	0.698087i
$325$	−1.57500e11	+	2.72797e11i	−0.783077	+	1.35633i
$326$	−5.01458e10	+	8.68551e10i	−0.245898	+	0.425908i
$327$	1.66072e11	+	2.87645e11i	0.803213	+	1.39121i
$328$	−2.37381e10			−0.113244
$329$		0			0
$330$	−2.73501e10			−0.126954
$331$	1.05675e11	+	1.83035e11i	0.483890	+	0.838122i	0.999829	−	0.0185036i	$-0.00589020\pi$
$331$	1.05675e11	+	1.83035e11i	0.483890	+	0.838122i	−0.515939	+	0.856625i	$0.672557\pi$
$332$	1.02580e11	−	1.77674e11i	0.463384	−	0.802605i
$333$	−1.75555e11	+	3.04070e11i	−0.782373	+	1.35511i
$334$	2.69861e10	+	4.67413e10i	0.118654	+	0.205514i
$335$	−4.68813e9			−0.0203375
$336$		0			0
$337$	−3.67482e11			−1.55203			−0.776017	−	0.630712i	$-0.782763\pi$
$337$	−3.67482e11			−1.55203			−0.776017	+	0.630712i	$0.782763\pi$
$338$	−8.99421e10	−	1.55784e11i	−0.374833	−	0.649230i
$339$	−1.39470e11	+	2.41569e11i	−0.573564	+	0.993442i
$340$	−1.43311e10	+	2.48221e10i	−0.0581599	+	0.100736i
$341$	−1.11005e11	−	1.92267e11i	−0.444579	−	0.770033i
$342$	−8.87255e10			−0.350696
$343$		0			0
$344$	1.23571e11			0.475776
$345$	1.80502e10	+	3.12639e10i	0.0685956	+	0.118811i
$346$	−2.05620e10	+	3.56145e10i	−0.0771300	+	0.133593i
$347$	−2.16933e11	+	3.75739e11i	−0.803235	+	1.39124i	0.114241	+	0.993453i	$0.463556\pi$
$347$	−2.16933e11	+	3.75739e11i	−0.803235	+	1.39124i	−0.917476	+	0.397791i	$0.869777\pi$
$348$	1.41974e11	+	2.45907e11i	0.518924	+	0.898802i
$349$	1.04086e11			0.375559			0.187780	−	0.982211i	$-0.439871\pi$
$349$	1.04086e11			0.375559			0.187780	+	0.982211i	$0.439871\pi$
$350$		0			0
$351$	−3.29482e10			−0.115864
$352$	−1.93917e11	−	3.35874e11i	−0.673247	−	1.16610i
$353$	2.23445e11	−	3.87018e11i	0.765922	−	1.32662i	−0.173836	−	0.984775i	$-0.555616\pi$
$353$	2.23445e11	−	3.87018e11i	0.765922	−	1.32662i	0.939758	−	0.341841i	$-0.111050\pi$
$354$	−2.69388e10	+	4.66594e10i	−0.0911724	+	0.157915i
$355$	1.06610e10	+	1.84653e10i	0.0356261	+	0.0617062i
$356$	−1.17451e11			−0.387553
$357$		0			0
$358$	−2.11708e11			−0.681182
$359$	9.82755e10	+	1.70218e11i	0.312263	+	0.540855i	0.978852	−	0.204570i	$-0.0655797\pi$
$359$	9.82755e10	+	1.70218e11i	0.312263	+	0.540855i	−0.666589	+	0.745425i	$0.732246\pi$
$360$	1.84748e10	−	3.19993e10i	0.0579721	−	0.100411i
$361$	6.60786e10	−	1.14452e11i	0.204776	−	0.354682i
$362$	5.34563e10	+	9.25890e10i	0.163610	+	0.283381i
$363$	−3.36942e11			−1.01853
$364$		0			0
$365$	−4.21874e10			−0.124413
$366$	7.39351e10	+	1.28059e11i	0.215370	+	0.373032i
$367$	1.12759e11	−	1.95304e11i	0.324454	−	0.561971i	−0.656948	−	0.753936i	$-0.728153\pi$
$367$	1.12759e11	−	1.95304e11i	0.324454	−	0.561971i	0.981402	+	0.191965i	$0.0614861\pi$
$368$	−4.31469e10	+	7.47326e10i	−0.122641	+	0.212420i
$369$	−2.24601e10	−	3.89021e10i	−0.0630658	−	0.109233i
$370$	4.11484e10			0.114142
$371$		0			0
$372$	2.67763e11			0.724948
$373$	1.02207e11	+	1.77028e11i	0.273395	+	0.473534i	0.969729	−	0.244184i	$-0.0785200\pi$
$373$	1.02207e11	+	1.77028e11i	0.273395	+	0.473534i	−0.696334	+	0.717718i	$0.745187\pi$
$374$	1.26227e11	−	2.18632e11i	0.333603	−	0.577818i
$375$	−7.59976e10	+	1.31632e11i	−0.198454	+	0.343732i
$376$	−2.73415e11	−	4.73569e11i	−0.705469	−	1.22191i
$377$	6.07076e11			1.54777
$378$		0			0
$379$	4.03306e10			0.100406			0.0502029	−	0.998739i	$-0.484013\pi$
$379$	4.03306e10			0.100406			0.0502029	+	0.998739i	$0.484013\pi$
$380$	−1.72370e10	−	2.98554e10i	−0.0424068	−	0.0734507i
$381$	−3.06314e11	+	5.30552e11i	−0.744740	+	1.28993i
$382$	1.00526e11	−	1.74116e11i	0.241542	−	0.418363i
$383$	1.99162e11	+	3.44959e11i	0.472947	+	0.819169i	0.999521	−	0.0309608i	$-0.00985671\pi$
$383$	1.99162e11	+	3.44959e11i	0.472947	+	0.819169i	−0.526573	+	0.850130i	$0.676523\pi$
$384$	5.70393e11			1.33870
$385$		0			0
$386$	5.26764e10			0.120774
$387$	1.16918e11	+	2.02508e11i	0.264962	+	0.458927i
$388$	−1.76220e11	+	3.05221e11i	−0.394740	+	0.683710i
$389$	2.11252e11	−	3.65900e11i	0.467765	−	0.810193i	−0.531556	−	0.847023i	$-0.678393\pi$
$389$	2.11252e11	−	3.65900e11i	0.467765	−	0.810193i	0.999322	+	0.0368297i	$0.0117259\pi$
$390$	−3.52621e10	−	6.10758e10i	−0.0771823	−	0.133684i
$391$	−3.33224e11			−0.721009
$392$		0			0
$393$	−1.37683e11			−0.291149
$394$	−1.47180e11	−	2.54923e11i	−0.307691	−	0.532936i
$395$	1.50192e7	−	2.60139e7i	3.10426e−5	−	5.37674e-5i
$396$	2.34398e11	−	4.05988e11i	0.478988	−	0.829632i
$397$	−3.25499e11	−	5.63781e11i	−0.657647	−	1.13908i	−0.981223	−	0.192876i	$-0.938219\pi$
$397$	−3.25499e11	−	5.63781e11i	−0.657647	−	1.13908i	0.323576	−	0.946202i	$-0.395115\pi$
$398$	1.80567e11			0.360714
$399$		0			0
$400$	−1.79769e11			−0.351111
$401$	1.55254e11	+	2.68909e11i	0.299843	+	0.519344i	0.976100	−	0.217322i	$-0.0697322\pi$
$401$	1.55254e11	+	2.68909e11i	0.299843	+	0.519344i	−0.676257	+	0.736666i	$0.736399\pi$
$402$	−2.49012e10	+	4.31302e10i	−0.0475558	+	0.0823690i
$403$	2.86235e11	−	4.95774e11i	0.540568	−	0.936292i
$404$	−8.12361e9	−	1.40705e10i	−0.0151717	−	0.0262781i
$405$	−8.16155e10			−0.150739
$406$		0			0
$407$	1.20160e12			2.17063
$408$	3.50399e11	+	6.06910e11i	0.626026	+	1.08431i
$409$	−1.49760e11	+	2.59391e11i	−0.264630	+	0.458353i	−0.967467	−	0.252998i	$-0.918583\pi$
$409$	−1.49760e11	+	2.59391e11i	−0.264630	+	0.458353i	0.702836	+	0.711352i	$0.251917\pi$
$410$	−2.63222e9	+	4.55914e9i	−0.00460039	+	0.00796811i
$411$	−3.00883e11	−	5.21144e11i	−0.520127	−	0.900886i
$412$	−1.68935e11			−0.288856
$413$		0			0
$414$	1.86639e11			0.312249
$415$	−5.23604e10	−	9.06910e10i	−0.0866537	−	0.150089i
$416$	5.00030e11	−	8.66077e11i	0.818608	−	1.41787i
$417$	4.97185e11	−	8.61149e11i	0.805204	−	1.39465i
$418$	1.51822e11	+	2.62964e11i	0.243244	+	0.421311i
$419$	−4.35217e11			−0.689832			−0.344916	−	0.938634i	$-0.612093\pi$
$419$	−4.35217e11			−0.689832			−0.344916	+	0.938634i	$0.612093\pi$
$420$		0			0
$421$	−2.07600e11			−0.322076			−0.161038	−	0.986948i	$-0.551484\pi$
$421$	−2.07600e11			−0.322076			−0.161038	+	0.986948i	$0.551484\pi$
$422$	2.96746e11	+	5.13980e11i	0.455491	+	0.788933i
$423$	5.17392e11	−	8.96149e11i	0.785757	−	1.36097i
$424$	−4.57027e11	+	7.91594e11i	−0.686745	+	1.18948i
$425$	−3.47089e11	−	6.01176e11i	−0.516049	−	0.893824i
$426$	2.26504e11			0.333222
$427$		0			0
$428$	−4.84955e11			−0.698562
$429$	−1.02971e12	−	1.78351e12i	−1.46777	−	2.54225i
$430$	1.37023e10	−	2.37330e10i	0.0193279	−	0.0334769i
$431$	−4.30792e11	+	7.46154e11i	−0.601340	+	1.04155i	0.391279	+	0.920272i	$0.372033\pi$
$431$	−4.30792e11	+	7.46154e11i	−0.601340	+	1.04155i	−0.992618	+	0.121279i	$0.961300\pi$
$432$	−9.40170e9	−	1.62842e10i	−0.0129876	−	0.0224952i
$433$	1.45840e11			0.199379			0.0996896	−	0.995019i	$-0.468215\pi$
$433$	1.45840e11			0.199379			0.0996896	+	0.995019i	$0.468215\pi$
$434$		0			0
$435$	1.44938e11			0.194079
$436$	3.33603e11	+	5.77817e11i	0.442120	+	0.765775i
$437$	2.00396e11	−	3.47096e11i	0.262859	−	0.455285i
$438$	−2.24080e11	+	3.88118e11i	−0.290917	+	0.503884i
$439$	5.35653e10	+	9.27778e10i	0.0688324	+	0.119221i	0.898388	−	0.439203i	$-0.144739\pi$
$439$	5.35653e10	+	9.27778e10i	0.0688324	+	0.119221i	−0.829555	+	0.558425i	$0.811406\pi$
$440$	−1.26452e11			−0.160839
$441$		0			0
$442$	6.50972e11			0.811263
$443$	6.84188e10	+	1.18505e11i	0.0844031	+	0.146191i	0.905137	−	0.425121i	$-0.139768\pi$
$443$	6.84188e10	+	1.18505e11i	0.0844031	+	0.146191i	−0.820734	+	0.571311i	$0.806435\pi$
$444$	−7.24614e11	+	1.25507e12i	−0.884878	+	1.53265i
$445$	−2.99755e10	+	5.19191e10i	−0.0362365	+	0.0627635i
$446$	1.11920e11	+	1.93851e11i	0.133937	+	0.231986i
$447$	−4.17981e11			−0.495191
$448$		0			0
$449$	−7.65671e11			−0.889065			−0.444532	−	0.895763i	$-0.646630\pi$
$449$	−7.65671e11			−0.889065			−0.444532	+	0.895763i	$0.646630\pi$
$450$	1.94405e11	+	3.36720e11i	0.223487	+	0.387091i
$451$	−7.68652e10	+	1.33134e11i	−0.0874853	+	0.151529i
$452$	−2.80166e11	+	4.85261e11i	−0.315712	+	0.546830i
$453$	−2.30377e11	−	3.99024e11i	−0.257038	−	0.445202i
$454$	−4.29226e11			−0.474170
$455$		0			0
$456$	−8.42901e11			−0.912924
$457$	−2.70921e11	−	4.69249e11i	−0.290549	−	0.503246i	0.683390	−	0.730053i	$-0.260505\pi$
$457$	−2.70921e11	−	4.69249e11i	−0.290549	−	0.503246i	−0.973940	+	0.226807i	$0.927171\pi$
$458$	9.94023e10	−	1.72170e11i	0.105561	−	0.182836i
$459$	3.63047e10	−	6.28816e10i	0.0381774	−	0.0661251i
$460$	3.62591e10	+	6.28025e10i	0.0377578	+	0.0653984i
$461$	−7.10838e11			−0.733021			−0.366510	−	0.930414i	$-0.619448\pi$
$461$	−7.10838e11			−0.733021			−0.366510	+	0.930414i	$0.619448\pi$
$462$		0			0
$463$	7.96272e11			0.805280			0.402640	−	0.915358i	$-0.368093\pi$
$463$	7.96272e11			0.805280			0.402640	+	0.915358i	$0.368093\pi$
$464$	1.73228e11	+	3.00040e11i	0.173495	+	0.300502i
$465$	6.83378e10	−	1.18365e11i	0.0677833	−	0.117404i
$466$	2.76756e11	−	4.79355e11i	0.271869	−	0.470891i
$467$	8.38367e11	+	1.45209e12i	0.815658	+	1.41276i	0.908855	+	0.417113i	$0.136958\pi$
$467$	8.38367e11	+	1.45209e12i	0.815658	+	1.41276i	−0.0931969	+	0.995648i	$0.529709\pi$
$468$	1.20882e12			1.16481
$469$		0			0
$470$	−1.21272e11			−0.114635
$471$	−2.92239e11	−	5.06172e11i	−0.273617	−	0.473919i
$472$	−1.24551e11	+	2.15728e11i	−0.115507	+	0.200064i
$473$	4.00129e11	−	6.93043e11i	0.367557	−	0.636627i
$474$	−1.59550e8	−	2.76348e8i	−0.000145175	−	0.000251451i
$475$	8.34938e11			0.752546
$476$		0			0
$477$	−1.72969e12			−1.52980
$478$	−2.07200e11	−	3.58881e11i	−0.181537	−	0.314431i
$479$	−5.85644e11	+	1.01437e12i	−0.508305	+	0.880410i	0.491649	+	0.870793i	$0.336394\pi$
$479$	−5.85644e11	+	1.01437e12i	−0.508305	+	0.880410i	−0.999954	+	0.00961615i	$0.996939\pi$
$480$	1.19381e11	−	2.06773e11i	0.102647	−	0.177790i
$481$	1.54921e12	+	2.68331e12i	1.31964	+	2.28569i
$482$	1.06754e12			0.900895
$483$		0			0
$484$	−6.76844e11			−0.560641
$485$	8.99487e10	+	1.55796e11i	0.0738171	+	0.127855i
$486$	−4.12056e11	+	7.13702e11i	−0.335037	+	0.580301i
$487$	−2.24899e11	+	3.89536e11i	−0.181178	+	0.313810i	−0.942282	−	0.334820i	$-0.891324\pi$
$487$	−2.24899e11	+	3.89536e11i	−0.181178	+	0.313810i	0.761104	+	0.648630i	$0.224658\pi$
$488$	3.41837e11	+	5.92080e11i	0.272854	+	0.472597i
$489$	−1.80297e12			−1.42594
$490$		0			0
$491$	2.25034e12			1.74735			0.873677	−	0.486506i	$-0.161729\pi$
$491$	2.25034e12			1.74735			0.873677	+	0.486506i	$0.161729\pi$
$492$	−9.27056e10	−	1.60571e11i	−0.0713285	−	0.123545i
$493$	−6.68921e11	+	1.15861e12i	−0.509992	+	0.883333i
$494$	−3.91485e11	+	6.78072e11i	−0.295763	+	0.512277i
$495$	−1.19645e11	−	2.07231e11i	−0.0895716	−	0.155143i
$496$	3.26707e11			0.242376
$497$		0			0
$498$	−1.11246e12			−0.810497
$499$	−7.98560e9	−	1.38315e10i	−0.00576574	−	0.00998656i	0.863128	−	0.504985i	$-0.168502\pi$
$499$	−7.98560e9	−	1.38315e10i	−0.00576574	−	0.00998656i	−0.868894	+	0.494998i	$0.835169\pi$
$500$	−1.52663e11	+	2.64420e11i	−0.109237	+	0.189204i
$501$	−4.85137e11	+	8.40283e11i	−0.344029	+	0.595876i
$502$	−4.22150e11	−	7.31186e11i	−0.296688	−	0.513879i
$503$	1.73375e12			1.20762			0.603811	−	0.797127i	$-0.293648\pi$
$503$	1.73375e12			1.20762			0.603811	+	0.797127i	$0.293648\pi$
$504$		0			0
$505$	−8.29316e9			−0.00567425
$506$	−3.19367e11	−	5.53160e11i	−0.216577	−	0.375123i
$507$	1.61692e12	−	2.80058e12i	1.08681	−	1.88240i
$508$	−6.15320e11	+	1.06577e12i	−0.409934	+	0.710027i
$509$	−4.88730e11	−	8.46505e11i	−0.322730	−	0.558984i	0.658320	−	0.752738i	$-0.271267\pi$
$509$	−4.88730e11	−	8.46505e11i	−0.322730	−	0.558984i	−0.981050	+	0.193753i	$0.937934\pi$
$510$	1.55417e11			0.101726
$511$		0			0
$512$	1.04525e12			0.672212
$513$	4.36663e10	+	7.56322e10i	0.0278367	+	0.0482146i
$514$	5.85953e11	−	1.01490e12i	0.370279	−	0.641342i
$515$	−4.31151e10	+	7.46776e10i	−0.0270083	+	0.0467797i
$516$	4.82588e11	+	8.35866e11i	0.299676	+	0.519055i
$517$	−3.54133e12			−2.18001
$518$		0			0
$519$	−7.39300e11			−0.447268
$520$	−1.63033e11	−	2.82382e11i	−0.0977826	−	0.169364i
$521$	−2.94612e11	+	5.10282e11i	−0.175178	+	0.303418i	−0.940223	−	0.340560i	$-0.889383\pi$
$521$	−2.94612e11	+	5.10282e11i	−0.175178	+	0.303418i	0.765045	+	0.643977i	$0.222717\pi$
$522$	3.74664e11	−	6.48937e11i	0.220864	−	0.382547i
$523$	−7.16089e11	−	1.24030e12i	−0.418513	−	0.724887i	0.577277	−	0.816549i	$-0.304115\pi$
$523$	−7.16089e11	−	1.24030e12i	−0.418513	−	0.724887i	−0.995790	+	0.0916621i	$0.970782\pi$
$524$	−2.76577e11			−0.160260
$525$		0			0
$526$	−1.32468e11			−0.0754527
$527$	6.30790e11	+	1.09256e12i	0.356235	+	0.617018i
$528$	5.87652e11	−	1.01784e12i	0.329054	−	0.569939i
$529$	4.79031e11	−	8.29706e11i	0.265958	−	0.460653i
$530$	1.01356e11	+	1.75553e11i	0.0557965	+	0.0966423i
$531$	−4.71382e11			−0.257305
$532$		0			0
$533$	−3.96405e11			−0.212749
$534$	3.18432e11	+	5.51541e11i	0.169466	+	0.293523i
$535$	−1.23769e11	+	2.14374e11i	−0.0653161	+	0.113131i
$536$	−1.15130e11	+	1.99411e11i	−0.0602487	+	0.104354i
$537$	−1.90297e12	−	3.29604e12i	−0.987523	−	1.71044i
$538$	−1.34540e12			−0.692357
$539$		0			0
$540$	−1.58017e10			−0.00799708
$541$	−5.86616e11	−	1.01605e12i	−0.294419	−	0.509949i	0.680430	−	0.732813i	$-0.261793\pi$
$541$	−5.86616e11	−	1.01605e12i	−0.294419	−	0.509949i	−0.974850	+	0.222864i	$0.928460\pi$
$542$	−7.31457e11	+	1.26692e12i	−0.364076	+	0.630598i
$543$	−9.61000e11	+	1.66450e12i	−0.474378	+	0.821646i
$544$	1.10194e12	+	1.90861e12i	0.539464	+	0.934379i
$545$	3.40565e11			0.165355
$546$		0			0
$547$	2.59515e11			0.123942			0.0619712	−	0.998078i	$-0.480261\pi$
$547$	2.59515e11			0.123942			0.0619712	+	0.998078i	$0.480261\pi$
$548$	−6.04410e11	−	1.04687e12i	−0.286299	−	0.495884i
$549$	−6.46869e11	+	1.12041e12i	−0.303907	+	0.526382i
$550$	6.65312e11	−	1.15235e12i	0.310023	−	0.536975i
$551$	−8.04559e11	−	1.39354e12i	−0.371857	−	0.644075i
$552$	1.77309e12			0.812841
$553$		0			0
$554$	−2.36022e11			−0.106453
$555$	3.69869e11	+	6.40631e11i	0.165474	+	0.286609i
$556$	9.98739e11	−	1.72987e12i	0.443216	−	0.767673i
$557$	1.18326e12	−	2.04946e12i	0.520871	−	0.902175i	−0.478834	−	0.877905i	$-0.658941\pi$
$557$	1.18326e12	−	2.04946e12i	0.520871	−	0.902175i	0.999705	−	0.0242699i	$-0.00772611\pi$
$558$	−3.53307e11	−	6.11945e11i	−0.154276	−	0.267214i
$559$	2.06352e12			0.893832
$560$		0			0
$561$	4.53845e12			1.93453
$562$	−4.21147e10	−	7.29448e10i	−0.0178082	−	0.0308447i
$563$	1.21200e12	−	2.09924e12i	0.508410	−	0.880593i	−0.491542	−	0.870854i	$-0.663567\pi$
$563$	1.21200e12	−	2.09924e12i	0.508410	−	0.880593i	0.999953	−	0.00973885i	$-0.00310002\pi$
$564$	2.13557e12	−	3.69891e12i	0.888704	−	1.53928i
$565$	1.43006e11	+	2.47694e11i	0.0590388	+	0.102258i
$566$	−7.83821e11			−0.321028
$567$		0			0
$568$	1.04724e12			0.422160
$569$	1.05927e12	+	1.83471e12i	0.423645	+	0.733774i	0.996293	−	0.0860270i	$-0.0274171\pi$
$569$	1.05927e12	+	1.83471e12i	0.423645	+	0.733774i	−0.572648	+	0.819801i	$0.694084\pi$
$570$	−9.34658e10	+	1.61888e11i	−0.0370865	+	0.0642357i
$571$	3.75496e11	−	6.50378e11i	0.147823	−	0.256037i	−0.782599	−	0.622526i	$-0.786107\pi$
$571$	3.75496e11	−	6.50378e11i	0.147823	−	0.256037i	0.930423	+	0.366488i	$0.119440\pi$
$572$	−2.06847e12	−	3.58270e12i	−0.807919	−	1.39936i
$573$	3.61437e12			1.40067
$574$		0			0
$575$	−1.75634e12			−0.670045
$576$	−1.68222e11	−	2.91369e11i	−0.0636768	−	0.110291i
$577$	−2.17976e12	+	3.77545e12i	−0.818685	+	1.41800i	0.0879666	+	0.996123i	$0.471963\pi$
$577$	−2.17976e12	+	3.77545e12i	−0.818685	+	1.41800i	−0.906651	+	0.421880i	$0.861370\pi$
$578$	−7.14322e10	+	1.23724e11i	−0.0266207	+	0.0461083i
$579$	4.73490e11	+	8.20110e11i	0.175089	+	0.303262i
$580$	2.91149e11			0.106829
$581$		0			0
$582$	1.91106e12			0.690433
$583$	2.95975e12	+	5.12644e12i	1.06108	+	1.83784i
$584$	−1.03603e12	+	1.79445e12i	−0.368565	+	0.638373i
$585$	3.08513e11	−	5.34360e11i	0.108911	−	0.188640i
$586$	−9.45865e11	−	1.63829e12i	−0.331352	−	0.573919i
$587$	−2.20056e12			−0.765002			−0.382501	−	0.923955i	$-0.624937\pi$
$587$	−2.20056e12			−0.765002			−0.382501	+	0.923955i	$0.624937\pi$
$588$		0			0
$589$	−1.51739e12			−0.519492
$590$	2.76219e10	+	4.78425e10i	0.00938467	+	0.0162547i
$591$	2.64589e12	−	4.58282e12i	0.892131	−	1.54522i
$592$	−8.84126e11	+	1.53135e12i	−0.295847	+	0.512421i
$593$	1.41802e12	+	2.45608e12i	0.470907	+	0.815636i	0.999446	−	0.0332735i	$-0.0105932\pi$
$593$	1.41802e12	+	2.45608e12i	0.470907	+	0.815636i	−0.528539	+	0.848909i	$0.677260\pi$
$594$	1.39180e11			0.0458710
$595$		0			0
$596$	−8.39636e11			−0.272573
$597$	1.62305e12	+	2.81121e12i	0.522935	+	0.905750i
$598$	8.23512e11	−	1.42636e12i	0.263339	−	0.456116i
$599$	4.14643e11	−	7.18182e11i	0.131599	−	0.227937i	−0.792694	−	0.609620i	$-0.791322\pi$
$599$	4.14643e11	−	7.18182e11i	0.131599	−	0.227937i	0.924293	+	0.381683i	$0.124655\pi$
$600$	1.84687e12	+	3.19887e12i	0.581776	+	1.00767i
$601$	5.62459e12			1.75855			0.879277	−	0.476311i	$-0.158026\pi$
$601$	5.62459e12			1.75855			0.879277	+	0.476311i	$0.158026\pi$
$602$		0			0
$603$	−4.35728e11			−0.134211
$604$	−4.62778e11	−	8.01556e11i	−0.141484	−	0.245057i
$605$	−1.72743e11	+	2.99199e11i	−0.0524204	+	0.0907948i
$606$	−4.40494e10	+	7.62959e10i	−0.0132682	+	0.0229813i
$607$	2.34389e11	+	4.05973e11i	0.0700789	+	0.121380i	0.898936	−	0.438081i	$-0.144342\pi$
$607$	2.34389e11	+	4.05973e11i	0.0700789	+	0.121380i	−0.828857	+	0.559461i	$0.811008\pi$
$608$	−2.65076e12			−0.786691
$609$		0			0
$610$	1.51620e11			0.0443375
$611$	−4.56580e12	−	7.90819e12i	−1.32535	−	2.29558i
$612$	−1.33197e12	+	2.30704e12i	−0.383807	+	0.664773i
$613$	−2.79197e12	+	4.83583e12i	−0.798617	+	1.38324i	0.121900	+	0.992542i	$0.461101\pi$
$613$	−2.79197e12	+	4.83583e12i	−0.798617	+	1.38324i	−0.920517	+	0.390702i	$0.872232\pi$
$614$	−1.23688e12	−	2.14234e12i	−0.351212	−	0.608318i
$615$	−9.46405e10			−0.0266771
$616$		0			0
$617$	−3.36717e12			−0.935367			−0.467683	−	0.883896i	$-0.654911\pi$
$617$	−3.36717e12			−0.935367			−0.467683	+	0.883896i	$0.654911\pi$
$618$	4.58015e11	+	7.93306e11i	0.126308	+	0.218772i
$619$	2.83464e12	−	4.90974e12i	0.776051	−	1.34416i	−0.158151	−	0.987415i	$-0.550553\pi$
$619$	2.83464e12	−	4.90974e12i	0.776051	−	1.34416i	0.934202	−	0.356744i	$-0.116113\pi$
$620$	1.37276e11	−	2.37769e11i	0.0373106	−	0.0646239i
$621$	−9.18546e10	−	1.59097e11i	−0.0247850	−	0.0429289i
$622$	−9.46512e11			−0.253553
$623$		0			0
$624$	3.03061e12			0.800201
$625$	−1.79006e12	−	3.10047e12i	−0.469252	−	0.812769i
$626$	2.86084e11	−	4.95512e11i	0.0744576	−	0.128964i
$627$	−2.72936e12	+	4.72738e12i	−0.705272	+	1.22157i
$628$	−5.87046e11	−	1.01679e12i	−0.150610	−	0.260864i
$629$	−6.82812e12			−1.73930
$630$		0			0
$631$	−1.06685e12			−0.267899			−0.133950	−	0.990988i	$-0.542766\pi$
$631$	−1.06685e12			−0.267899			−0.133950	+	0.990988i	$0.542766\pi$
$632$	−7.37674e8	−	1.27769e9i	−0.000183924	−	0.000318565i
$633$	−5.33470e12	+	9.23998e12i	−1.32067	+	2.28746i
$634$	−1.43663e12	+	2.48831e12i	−0.353136	+	0.611650i
$635$	3.14081e11	+	5.44005e11i	0.0766585	+	0.132776i
$636$	−7.13941e12			−1.73024
$637$		0			0
$638$	−2.56442e12			−0.612768
$639$	9.90858e11	+	1.71622e12i	0.235103	+	0.407210i
$640$	2.92428e11	−	5.06500e11i	0.0688984	−	0.119336i
$641$	3.91816e12	−	6.78645e12i	0.916686	−	1.58775i	0.112273	−	0.993677i	$-0.464187\pi$
$641$	3.91816e12	−	6.78645e12i	0.916686	−	1.58775i	0.804413	−	0.594070i	$-0.202480\pi$
$642$	1.31481e12	+	2.27732e12i	0.305461	+	0.529073i
$643$	7.05971e12			1.62869			0.814343	−	0.580383i	$-0.197097\pi$
$643$	7.05971e12			1.62869			0.814343	+	0.580383i	$0.197097\pi$
$644$		0			0
$645$	4.92660e11			0.112080
$646$	−8.62734e11	−	1.49430e12i	−0.194908	−	0.337591i
$647$	−1.38657e12	+	2.40161e12i	−0.311081	+	0.538807i	−0.978597	−	0.205788i	$-0.934024\pi$
$647$	−1.38657e12	+	2.40161e12i	−0.311081	+	0.538807i	0.667516	+	0.744595i	$0.267358\pi$
$648$	−2.00429e12	+	3.47154e12i	−0.446554	+	0.773454i
$649$	8.06604e11	+	1.39708e12i	0.178468	+	0.309115i
$650$	3.43111e12			0.753919
$651$		0			0
$652$	−3.62179e12			−0.784891
$653$	−1.54782e12	−	2.68091e12i	−0.333128	−	0.576995i	0.649995	−	0.759938i	$-0.274771\pi$
$653$	−1.54782e12	−	2.68091e12i	−0.333128	−	0.576995i	−0.983123	+	0.182943i	$0.941438\pi$
$654$	1.80893e12	−	3.13315e12i	0.386653	−	0.669702i
$655$	−7.05873e10	+	1.22261e11i	−0.0149845	+	0.0259538i
$656$	−1.13113e11	−	1.95918e11i	−0.0238477	−	0.0413054i
$657$	−3.92102e12			−0.821021
$658$		0			0
$659$	−4.80261e12			−0.991958			−0.495979	−	0.868335i	$-0.665191\pi$
$659$	−4.80261e12			−0.991958			−0.495979	+	0.868335i	$0.665191\pi$
$660$	−4.93841e11	−	8.55359e11i	−0.101307	−	0.175469i
$661$	2.56694e12	−	4.44608e12i	0.523010	−	0.905879i	−0.476632	−	0.879103i	$-0.658143\pi$
$661$	2.56694e12	−	4.44608e12i	0.523010	−	0.905879i	0.999641	−	0.0267762i	$-0.00852415\pi$
$662$	1.15106e12	−	1.99369e12i	0.232936	−	0.403457i
$663$	5.85136e12	+	1.01349e13i	1.17610	+	2.03707i
$664$	−5.14342e12			−1.02682
$665$		0			0
$666$	3.82444e12			0.753241
$667$	1.69244e12	+	2.93139e12i	0.331090	+	0.573465i
$668$	−9.74538e11	+	1.68795e12i	−0.189367	+	0.327994i
$669$	−2.01202e12	+	3.48492e12i	−0.388342	+	0.672629i
$670$	2.55326e10	+	4.42238e10i	0.00489507	+	0.00847851i
$671$	4.42755e12			0.843164
$672$		0			0
$673$	4.43802e12			0.833915			0.416957	−	0.908926i	$-0.363096\pi$
$673$	4.43802e12			0.833915			0.416957	+	0.908926i	$0.363096\pi$
$674$	2.00139e12	+	3.46650e12i	0.373561	+	0.647027i
$675$	1.91353e11	−	3.31434e11i	0.0354788	−	0.0614511i
$676$	3.24805e12	−	5.62578e12i	0.598221	−	1.03615i
$677$	2.35337e12	+	4.07616e12i	0.430568	+	0.745766i	0.996922	−	0.0783962i	$-0.0249799\pi$
$677$	2.35337e12	+	4.07616e12i	0.430568	+	0.745766i	−0.566354	+	0.824162i	$0.691647\pi$
$678$	3.03834e12			0.552207
$679$		0			0
$680$	7.18569e11			0.128878
$681$	−3.85816e12	−	6.68253e12i	−0.687414	−	1.19064i
$682$	−1.20912e12	+	2.09426e12i	−0.214013	+	0.370681i
$683$	−3.06334e11	+	5.30585e11i	−0.0538644	+	0.0932958i	−0.891700	−	0.452626i	$-0.850487\pi$
$683$	−3.06334e11	+	5.30585e11i	−0.0538644	+	0.0932958i	0.837836	+	0.545922i	$0.183821\pi$
$684$	−1.60205e12	−	2.77484e12i	−0.279850	−	0.484714i
$685$	−6.17025e11			−0.107077
$686$		0			0
$687$	3.57397e12			0.612133
$688$	5.88822e11	+	1.01987e12i	0.100193	+	0.173539i
$689$	−7.63195e12	+	1.32189e13i	−1.29018	+	2.23465i
$690$	1.96611e11	−	3.40540e11i	0.0330207	−	0.0571936i
$691$	−1.34959e12	−	2.33757e12i	−0.225191	−	0.390043i	0.731185	−	0.682179i	$-0.238967\pi$
$691$	−1.34959e12	−	2.33757e12i	−0.225191	−	0.390043i	−0.956377	+	0.292136i	$0.905634\pi$
$692$	−1.48510e12			−0.246194
$693$		0			0
$694$	4.72586e12			0.773327
$695$	−5.09792e11	−	8.82986e11i	−0.0828822	−	0.143556i
$696$	3.55934e12	−	6.16496e12i	0.574948	−	0.995839i
$697$	4.36788e11	−	7.56539e11i	0.0701009	−	0.121418i
$698$	−5.66876e11	−	9.81858e11i	−0.0903938	−	0.156567i
$699$	9.95064e12			1.57654
$700$		0			0
$701$	−5.78506e12			−0.904850			−0.452425	−	0.891802i	$-0.649441\pi$
$701$	−5.78506e12			−0.904850			−0.452425	+	0.891802i	$0.649441\pi$
$702$	1.79443e11	+	3.10805e11i	0.0278875	+	0.0483026i
$703$	4.10633e12	−	7.11238e12i	0.634097	−	1.09829i
$704$	−5.75704e11	+	9.97149e11i	−0.0883329	+	0.152997i
$705$	−1.09007e12	−	1.88806e12i	−0.166189	−	0.287848i
$706$	−4.86772e12			−0.737403
$707$		0			0
$708$	−1.94566e12			−0.291016
$709$	1.86328e12	+	3.22730e12i	0.276930	+	0.479657i	0.970620	−	0.240616i	$-0.0773496\pi$
$709$	1.86328e12	+	3.22730e12i	0.276930	+	0.479657i	−0.693690	+	0.720274i	$0.744016\pi$
$710$	1.16124e11	−	2.01132e11i	0.0171498	−	0.0297043i
$711$	1.39592e9	−	2.41781e9i	0.000204856	−	0.000354820i
$712$	1.47226e12	+	2.55004e12i	0.214697	+	0.371866i
$713$	3.19192e12			0.462541
$714$		0			0
$715$	−2.11164e12			−0.302165
$716$	−3.82266e12	−	6.62104e12i	−0.543572	−	0.941494i
$717$	3.72490e12	−	6.45172e12i	0.526355	−	0.911673i
$718$	1.07046e12	−	1.85409e12i	0.150318	−	0.260358i
$719$	−6.66274e12	−	1.15402e13i	−0.929765	−	1.61040i	−0.783713	−	0.621123i	$-0.786677\pi$
$719$	−6.66274e12	−	1.15402e13i	−0.929765	−	1.61040i	−0.146052	−	0.989277i	$-0.546657\pi$
$720$	3.52134e11			0.0488328
$721$		0			0
$722$	−1.43952e12			−0.197151
$723$	9.59578e12	+	1.66204e13i	1.30605	+	2.26214i
$724$	−1.93045e12	+	3.34363e12i	−0.261116	+	0.452267i
$725$	−3.52572e12	+	6.10673e12i	−0.473944	+	0.820895i
$726$	1.83506e12	+	3.17841e12i	0.245152	+	0.424615i
$727$	−2.39852e12			−0.318448			−0.159224	−	0.987242i	$-0.550899\pi$
$727$	−2.39852e12			−0.318448			−0.159224	+	0.987242i	$0.550899\pi$
$728$		0			0
$729$	−6.81442e12			−0.893625
$730$	2.29762e11	+	3.97959e11i	0.0299451	+	0.0518664i
$731$	−2.27374e12	+	3.93823e12i	−0.294519	+	0.510121i
$732$	−2.66999e12	+	4.62456e12i	−0.343724	+	0.595348i
$733$	−3.96908e12	−	6.87464e12i	−0.507834	−	0.879594i	−0.999959	−	0.00906955i	$-0.997113\pi$
$733$	−3.96908e12	−	6.87464e12i	−0.507834	−	0.879594i	0.492125	−	0.870525i	$-0.336220\pi$
$734$	−2.45644e12			−0.312373
$735$		0			0
$736$	5.57603e12			0.700447
$737$	7.45595e11	+	1.29141e12i	0.0930892	+	0.161235i
$738$	−2.44646e11	+	4.23739e11i	−0.0303588	+	0.0525829i
$739$	1.10185e12	−	1.90847e12i	0.135902	−	0.235388i	−0.790040	−	0.613055i	$-0.789940\pi$
$739$	1.10185e12	−	1.90847e12i	0.135902	−	0.235388i	0.925941	+	0.377667i	$0.123274\pi$
$740$	7.42988e11	+	1.28689e12i	0.0910833	+	0.157761i
$741$	−1.40757e13			−1.71509
$742$		0			0
$743$	−1.09079e12			−0.131308			−0.0656540	−	0.997842i	$-0.520913\pi$
$743$	−1.09079e12			−0.131308			−0.0656540	+	0.997842i	$0.520913\pi$
$744$	−3.35645e12	−	5.81354e12i	−0.401607	−	0.695604i
$745$	−2.14290e11	+	3.71161e11i	−0.0254858	+	0.0441427i
$746$	1.11328e12	−	1.92826e12i	0.131608	−	0.227951i
$747$	−4.86652e12	−	8.42907e12i	−0.571842	−	0.990460i
$748$	9.11678e12			1.06484
$749$		0			0
$750$	1.65560e12			0.191064
$751$	1.54824e11	+	2.68162e11i	0.0177606	+	0.0307622i	0.874769	−	0.484540i	$-0.161013\pi$
$751$	1.54824e11	+	2.68162e11i	0.0177606	+	0.0307622i	−0.857009	+	0.515302i	$0.827680\pi$
$752$	2.60568e12	−	4.51317e12i	0.297126	−	0.514638i
$753$	7.58913e12	−	1.31448e13i	0.860230	−	1.48996i
$754$	−3.30627e12	−	5.72663e12i	−0.372535	−	0.645250i
$755$	−4.72437e11			−0.0529155
$756$		0			0
$757$	1.44340e12			0.159755			0.0798777	−	0.996805i	$-0.474547\pi$
$757$	1.44340e12			0.159755			0.0798777	+	0.996805i	$0.474547\pi$
$758$	−2.19649e11	−	3.80444e11i	−0.0241668	−	0.0418581i
$759$	5.74136e12	−	9.94433e12i	0.627953	−	1.08765i
$760$	−4.32137e11	+	7.48483e11i	−0.0469851	+	0.0813806i
$761$	1.13931e12	+	1.97334e12i	0.123143	+	0.213290i	0.921006	−	0.389549i	$-0.127369\pi$
$761$	1.13931e12	+	1.97334e12i	0.123143	+	0.213290i	−0.797862	+	0.602840i	$0.794036\pi$
$762$	6.67302e12			0.717010
$763$		0			0
$764$	7.26051e12			0.770987
$765$	6.79884e11	+	1.17759e12i	0.0717726	+	0.124314i
$766$	2.16937e12	−	3.75745e12i	0.227669	−	0.394334i
$767$	−2.07989e12	+	3.60247e12i	−0.217001	+	0.375856i
$768$	−4.01026e12	−	6.94598e12i	−0.415956	−	0.720457i
$769$	1.09547e13			1.12962			0.564809	−	0.825221i	$-0.308950\pi$
$769$	1.09547e13			1.12962			0.564809	+	0.825221i	$0.308950\pi$
$770$		0			0
$771$	2.10677e13			2.14720
$772$	9.51142e11	+	1.64743e12i	0.0963757	+	0.166928i
$773$	−3.76057e12	+	6.51350e12i	−0.378831	+	0.656155i	−0.990893	−	0.134655i	$-0.957007\pi$
$773$	−3.76057e12	+	6.51350e12i	−0.378831	+	0.656155i	0.612061	+	0.790810i	$0.290341\pi$
$774$	1.27353e12	−	2.20581e12i	0.127548	−	0.220920i
$775$	3.32474e12	+	5.75862e12i	0.331055	+	0.573404i
$776$	8.83576e12			0.874714
$777$		0			0
$778$	−4.60211e12			−0.450348
$779$	5.25356e11	+	9.09944e11i	0.0511135	+	0.0885311i
$780$	1.27341e12	−	2.20561e12i	0.123180	−	0.213355i
$781$	3.39101e12	−	5.87340e12i	0.326136	−	0.564885i
$782$	1.81481e12	+	3.14335e12i	0.173541	+	0.300581i
$783$	−7.37564e11			−0.0701248
$784$		0			0
$785$	−5.99298e11			−0.0563287
$786$	7.49855e11	+	1.29879e12i	0.0700770	+	0.121377i
$787$	−9.26514e11	+	1.60477e12i	−0.0860926	+	0.149117i	−0.905856	−	0.423585i	$-0.860771\pi$
$787$	−9.26514e11	+	1.60477e12i	−0.0860926	+	0.149117i	0.819764	+	0.572702i	$0.194105\pi$
$788$	5.31504e12	−	9.20592e12i	0.491065	−	0.850549i
$789$	−1.19071e12	−	2.06237e12i	−0.109385	−	0.189461i
$790$	−3.27191e8			−2.98868e−5
$791$		0			0
$792$	−1.17528e13			−1.06140
$793$	5.70838e12	+	9.88721e12i	0.512606	+	0.887859i
$794$	−3.54548e12	+	6.14096e12i	−0.316580	+	0.548332i
$795$	−1.82210e12	+	3.15598e12i	−0.161779	+	0.280209i
$796$	3.26037e12	+	5.64712e12i	0.287844	+	0.498561i
$797$	−1.84378e13			−1.61863			−0.809314	−	0.587377i	$-0.800161\pi$
$797$	−1.84378e13			−1.61863			−0.809314	+	0.587377i	$0.800161\pi$
$798$		0			0
$799$	2.01237e13			1.74682
$800$	5.80805e12	+	1.00598e13i	0.501332	+	0.868332i
$801$	−2.78601e12	+	4.82551e12i	−0.239131	+	0.414187i
$802$	1.69110e12	−	2.92907e12i	0.144339	−	0.250003i
$803$	6.70943e12	+	1.16211e13i	0.569463	+	0.986339i
$804$	−1.79850e12			−0.151795
$805$		0			0
$806$	−6.23560e12			−0.520440
$807$	−1.20933e13	−	2.09462e13i	−1.00372	−	1.73850i
$808$	−2.03661e11	+	3.52752e11i	−0.0168096	+	0.0291151i
$809$	5.17097e12	−	8.95639e12i	0.424428	−	0.735131i	−0.571939	−	0.820296i	$-0.693809\pi$
$809$	5.17097e12	−	8.95639e12i	0.424428	−	0.735131i	0.996367	+	0.0851654i	$0.0271419\pi$
$810$	4.44496e11	+	7.69890e11i	0.0362815	+	0.0628414i
$811$	−2.31795e13			−1.88153			−0.940764	−	0.339062i	$-0.889890\pi$
$811$	−2.31795e13			−1.88153			−0.940764	+	0.339062i	$0.889890\pi$
$812$		0			0
$813$	−2.62993e13			−2.11123
$814$	−6.54418e12	−	1.13349e13i	−0.522451	−	0.904912i
$815$	−9.24346e11	+	1.60101e12i	−0.0733881	+	0.127112i
$816$	−3.33935e12	+	5.78392e12i	−0.263667	+	0.456685i
$817$	−2.73479e12	−	4.73679e12i	−0.214746	−	0.371951i
$818$	3.26250e12			0.254777
$819$		0			0
$820$	−1.90113e11			−0.0146842
$821$	−5.50294e12	−	9.53138e12i	−0.422718	−	0.732169i	0.573486	−	0.819215i	$-0.305591\pi$
$821$	−5.50294e12	−	9.53138e12i	−0.422718	−	0.732169i	−0.996204	+	0.0870461i	$0.972257\pi$
$822$	−3.27735e12	+	5.67654e12i	−0.250380	+	0.433671i
$823$	−1.15059e13	+	1.99289e13i	−0.874224	+	1.51420i	−0.0166366	+	0.999862i	$0.505296\pi$
$823$	−1.15059e13	+	1.99289e13i	−0.874224	+	1.51420i	−0.857587	+	0.514339i	$0.828037\pi$
$824$	2.11762e12	+	3.66783e12i	0.160021	+	0.277164i
$825$	2.39211e13			1.79778
$826$		0			0
$827$	6.58898e12			0.489827			0.244914	−	0.969545i	$-0.421240\pi$
$827$	6.58898e12			0.489827			0.244914	+	0.969545i	$0.421240\pi$
$828$	3.37002e12	+	5.83704e12i	0.249170	+	0.431575i
$829$	6.62137e12	−	1.14686e13i	0.486915	−	0.843361i	−0.512972	−	0.858405i	$-0.671456\pi$
$829$	6.62137e12	−	1.14686e13i	0.486915	−	0.843361i	0.999887	+	0.0150444i	$0.00478896\pi$
$830$	−5.70333e11	+	9.87846e11i	−0.0417136	+	0.0722500i
$831$	−2.12152e12	−	3.67458e12i	−0.154327	−	0.267303i
$832$	−2.96899e12			−0.214810
$833$		0			0
$834$	−1.08311e13			−0.775222
$835$	4.97439e11	+	8.61590e11i	0.0354120	+	0.0613354i
$836$	−5.48270e12	+	9.49631e12i	−0.388210	+	0.672399i
$837$	−3.47760e11	+	6.02338e11i	−0.0244915	+	0.0424205i
$838$	2.37029e12	+	4.10546e12i	0.166036	+	0.287584i
$839$	−5.05558e12			−0.352243			−0.176122	−	0.984368i	$-0.556355\pi$
$839$	−5.05558e12			−0.352243			−0.176122	+	0.984368i	$0.556355\pi$
$840$		0			0
$841$	−9.17397e11			−0.0632376
$842$	1.13064e12	+	1.95832e12i	0.0775208	+	0.134270i
$843$	7.57109e11	−	1.31135e12i	0.0516338	−	0.0894324i
$844$	−1.07163e13	+	1.85612e13i	−0.726948	+	1.25911i
$845$	−1.65792e12	−	2.87160e12i	−0.111868	−	0.193762i
$846$	−1.12713e13			−0.756499
$847$		0			0
$848$	−8.71104e12			−0.578480
$849$	−7.04550e12	−	1.22032e13i	−0.465401	−	0.806098i
$850$	−3.78065e12	+	6.54828e12i	−0.248417	+	0.430271i
$851$	−8.63792e12	+	1.49613e13i	−0.564581	+	0.977883i
$852$	4.08983e12	+	7.08379e12i	0.265905	+	0.460562i
$853$	1.03049e13			0.666456			0.333228	−	0.942846i	$-0.391862\pi$
$853$	1.03049e13			0.666456			0.333228	+	0.942846i	$0.391862\pi$
$854$		0			0
$855$	−1.63549e12			−0.104665
$856$	6.07899e12	+	1.05291e13i	0.386990	+	0.670286i
$857$	8.33938e12	−	1.44442e13i	0.528105	−	0.914704i	−0.471359	−	0.881942i	$-0.656236\pi$
$857$	8.33938e12	−	1.44442e13i	0.528105	−	0.914704i	0.999463	−	0.0327624i	$-0.0104305\pi$
$858$	−1.12161e13	+	1.94268e13i	−0.706559	+	1.22380i
$859$	1.18339e13	+	2.04969e13i	0.741579	+	1.28445i	0.951776	+	0.306794i	$0.0992563\pi$
$859$	1.18339e13	+	2.04969e13i	0.741579	+	1.28445i	−0.210196	+	0.977659i	$0.567410\pi$
$860$	9.89649e11			0.0616933
$861$		0			0
$862$	9.38476e12			0.578949
$863$	−6.32140e12	−	1.09490e13i	−0.387940	−	0.671932i	0.604232	−	0.796808i	$-0.293480\pi$
$863$	−6.32140e12	−	1.09490e13i	−0.387940	−	0.671932i	−0.992172	+	0.124876i	$0.960147\pi$
$864$	−6.07508e11	+	1.05223e12i	−0.0370886	+	0.0642393i
$865$	−3.79023e11	+	6.56487e11i	−0.0230194	+	0.0398707i
$866$	−7.94274e11	−	1.37572e12i	−0.0479888	−	0.0831191i
$867$	−2.56832e12			−0.154370
$868$		0			0
$869$	−9.55450e9			−0.000568354
$870$	−7.89362e11	−	1.36722e12i	−0.0467132	−	0.0809097i
$871$	−1.92257e12	+	3.32999e12i	−0.113188	+	0.196048i
$872$	8.36353e12	−	1.44861e13i	0.489852	−	0.848449i
$873$	8.36008e12	+	1.44801e13i	0.487132	+	0.843737i
$874$	−4.36561e12			−0.253071
$875$		0			0
$876$	−1.61842e13			−0.928589
$877$	−1.10814e13	−	1.91936e13i	−0.632555	−	1.09562i	−0.987028	−	0.160551i	$-0.948673\pi$
$877$	−1.10814e13	−	1.91936e13i	−0.632555	−	1.09562i	0.354473	−	0.935066i	$-0.384660\pi$
$878$	5.83457e11	−	1.01058e12i	0.0331347	−	0.0573910i
$879$	1.70041e13	−	2.94520e13i	0.960736	−	1.66404i
$880$	−6.02553e11	−	1.04365e12i	−0.0338706	−	0.0586657i
$881$	−1.87132e13			−1.04654			−0.523272	−	0.852166i	$-0.675289\pi$
$881$	−1.87132e13			−1.04654			−0.523272	+	0.852166i	$0.675289\pi$
$882$		0			0
$883$	−1.66483e13			−0.921611			−0.460805	−	0.887501i	$-0.652439\pi$
$883$	−1.66483e13			−0.921611			−0.460805	+	0.887501i	$0.652439\pi$
$884$	1.17541e13	+	2.03588e13i	0.647375	+	1.12129i
$885$	−4.96567e11	+	8.60079e11i	−0.0272103	+	0.0471296i
$886$	7.45248e11	−	1.29081e12i	0.0406302	−	0.0703736i
$887$	7.94295e12	+	1.37576e13i	0.430849	+	0.746253i	0.996947	−	0.0780856i	$-0.0248807\pi$
$887$	7.94295e12	+	1.37576e13i	0.430849	+	0.746253i	−0.566097	+	0.824338i	$0.691547\pi$
$888$	3.63326e13			1.96082
$889$		0			0
$890$	6.53013e11			0.0348873
$891$	1.29800e13	+	2.24820e13i	0.689963	+	1.19505i
$892$	−4.04172e12	+	7.00047e12i	−0.213759	+	0.370242i
$893$	−1.21021e13	+	2.09615e13i	−0.636839	+	1.10304i
$894$	2.27642e12	+	3.94287e12i	0.119188	+	0.206440i
$895$	−3.90244e12			−0.203298
$896$		0			0
$897$	2.96091e13			1.52707
$898$	4.17001e12	+	7.22267e12i	0.213990	+	0.370642i
$899$	6.40754e12	−	1.10982e13i	0.327169	−	0.566674i
$900$	−7.02049e12	+	1.21598e13i	−0.356678	+	0.617784i
$901$	−1.68189e13	−	2.91311e13i	−0.850228	−	1.47264i
$902$	1.67450e12			0.0842278
$903$		0			0
$904$	1.40477e13			0.699595
$905$	9.85368e11	+	1.70671e12i	0.0488292	+	0.0845747i
$906$	−2.50937e12	+	4.34635e12i	−0.123733	+	0.214313i
$907$	1.82685e13	−	3.16419e13i	0.896333	−	1.55249i	0.0641877	−	0.997938i	$-0.479554\pi$
$907$	1.82685e13	−	3.16419e13i	0.896333	−	1.55249i	0.832146	−	0.554557i	$-0.187112\pi$
$908$	−7.75023e12	−	1.34238e13i	−0.378380	−	0.655374i
$909$	−7.70789e11			−0.0374454
$910$		0			0
$911$	2.09138e13			1.00600			0.503002	−	0.864286i	$-0.332229\pi$
$911$	2.09138e13			1.00600			0.503002	+	0.864286i	$0.332229\pi$
$912$	−4.01647e12	−	6.95673e12i	−0.192251	−	0.332988i
$913$	−1.66547e13	+	2.88467e13i	−0.793264	+	1.37397i
$914$	−2.95099e12	+	5.11127e12i	−0.139865	+	0.242254i
$915$	1.36286e12	+	2.36054e12i	0.0642770	+	0.111331i
$916$	7.17935e12			0.336942
$917$		0			0
$918$	−7.90894e11			−0.0367558
$919$	6.12554e11	+	1.06097e12i	0.0283286	+	0.0490665i	0.879842	−	0.475266i	$-0.157648\pi$
$919$	6.12554e11	+	1.06097e12i	0.0283286	+	0.0490665i	−0.851514	+	0.524333i	$0.824315\pi$
$920$	9.09026e11	−	1.57448e12i	0.0418342	−	0.0724589i
$921$	2.22358e13	−	3.85135e13i	1.01832	−	1.76378i
$922$	3.87138e12	+	6.70543e12i	0.176432	+	0.305589i
$923$	1.74879e13			0.793105
$924$		0			0
$925$	−3.59894e13			−1.61635
$926$	−4.33667e12	−	7.51134e12i	−0.193824	−	0.335713i
$927$	−4.00724e12	+	6.94074e12i	−0.178232	+	0.308708i
$928$	1.11934e13	−	1.93876e13i	0.495448	−	0.858141i
$929$	−4.76581e12	−	8.25463e12i	−0.209926	−	0.363602i	0.741765	−	0.670660i	$-0.233989\pi$
$929$	−4.76581e12	−	8.25463e12i	−0.209926	−	0.363602i	−0.951691	+	0.307057i	$0.900656\pi$
$930$	−1.48873e12			−0.0652594
$931$		0			0
$932$	1.99887e13			0.867788
$933$	−8.50787e12	−	1.47361e13i	−0.367581	−	0.636670i
$934$	9.13186e12	−	1.58168e13i	0.392643	−	0.680078i
$935$	2.32676e12	−	4.03007e12i	0.0995635	−	0.172449i
$936$	−1.51528e13	−	2.62454e13i	−0.645284	−	1.11767i
$937$	−9.70345e12			−0.411242			−0.205621	−	0.978632i	$-0.565921\pi$
$937$	−9.70345e12			−0.411242			−0.205621	+	0.978632i	$0.565921\pi$
$938$		0			0
$939$	1.02860e13			0.431770
$940$	−2.18972e12	−	3.79270e12i	−0.0914772	−	0.158443i
$941$	1.14813e13	−	1.98861e13i	0.477349	−	0.826793i	−0.522314	−	0.852753i	$-0.674931\pi$
$941$	1.14813e13	−	1.98861e13i	0.477349	−	0.826793i	0.999663	+	0.0259607i	$0.00826447\pi$
$942$	−3.18319e12	+	5.51346e12i	−0.131715	+	0.228137i
$943$	−1.10512e12	−	1.91412e12i	−0.0455099	−	0.0788255i
$944$	−2.37397e12			−0.0972973
$945$		0			0
$946$	−8.71676e12			−0.353871
$947$	−7.03813e12	−	1.21904e13i	−0.284369	−	0.492542i	0.688087	−	0.725628i	$-0.258451\pi$
$947$	−7.03813e12	−	1.21904e13i	−0.284369	−	0.492542i	−0.972456	+	0.233086i	$0.925117\pi$
$948$	5.76175e9	−	9.97965e9i	0.000231695	−	0.000401308i
$949$	−1.73008e13	+	2.99658e13i	−0.692416	+	1.19930i
$950$	−4.54726e12	−	7.87608e12i	−0.181131	−	0.313729i
$951$	−5.16534e13			−2.04780
$952$		0			0
$953$	9.86435e12			0.387392			0.193696	−	0.981062i	$-0.437953\pi$
$953$	9.86435e12			0.387392			0.193696	+	0.981062i	$0.437953\pi$
$954$	9.42028e12	+	1.63164e13i	0.368210	+	0.637759i
$955$	1.85301e12	−	3.20951e12i	0.0720880	−	0.124860i
$956$	7.48254e12	−	1.29601e13i	0.289727	−	0.501821i
$957$	−2.30507e13	−	3.99250e13i	−0.888342	−	1.53865i
$958$	1.27582e13			0.489378
$959$		0			0
$960$	−7.08838e11			−0.0269356
$961$	7.17752e12	+	1.24318e13i	0.271469	+	0.470197i
$962$	1.68747e13	−	2.92278e13i	0.635254	−	1.10029i
$963$	−1.15034e13	+	1.99246e13i	−0.431032	+	0.746570i
$964$	1.92759e13	+	3.33868e13i	0.718899	+	1.24517i
$965$	9.70993e11			0.0360449
$966$		0			0
$967$	−2.37375e12			−0.0873002			−0.0436501	−	0.999047i	$-0.513899\pi$
$967$	−2.37375e12			−0.0873002			−0.0436501	+	0.999047i	$0.513899\pi$
$968$	8.48435e12	+	1.46953e13i	0.310584	+	0.537948i
$969$	1.55096e13	−	2.68635e13i	0.565125	−	0.978825i
$970$	9.79761e11	−	1.69700e12i	0.0355343	−	0.0615472i
$971$	−2.22947e13	−	3.86156e13i	−0.804852	−	1.39404i	−0.916391	−	0.400284i	$-0.868911\pi$
$971$	−2.22947e13	−	3.86156e13i	−0.804852	−	1.39404i	0.111539	−	0.993760i	$-0.464422\pi$
$972$	−2.97608e13			−1.06942
$973$		0			0
$974$	4.89939e12			0.174432
$975$	3.08411e13	+	5.34184e13i	1.09297	+	1.89308i
$976$	−3.25775e12	+	5.64259e12i	−0.114919	+	0.199046i
$977$	−4.45300e11	+	7.71282e11i	−0.0156360	+	0.0270824i	−0.873738	−	0.486398i	$-0.838311\pi$
$977$	−4.45300e11	+	7.71282e11i	−0.0156360	+	0.0270824i	0.858102	+	0.513480i	$0.171644\pi$
$978$	9.81940e12	+	1.70077e13i	0.343210	+	0.594457i
$979$	1.90691e13			0.663449
$980$		0			0
$981$	3.16531e13			1.09120
$982$	−1.22558e13	−	2.12277e13i	−0.420573	−	0.728454i
$983$	−4.11897e12	+	7.13427e12i	−0.140701	+	0.243702i	−0.927761	−	0.373175i	$-0.878269\pi$
$983$	−4.11897e12	+	7.13427e12i	−0.140701	+	0.243702i	0.787060	+	0.616877i	$0.211602\pi$
$984$	−2.32416e12	+	4.02556e12i	−0.0790293	+	0.136883i
$985$	−2.71299e12	−	4.69903e12i	−0.0918300	−	0.159054i
$986$	1.45724e13			0.491003
$987$		0			0
$988$	−2.82751e13			−0.944056
$989$	5.75279e12	+	9.96413e12i	0.191203	+	0.331174i
$990$	−1.30322e12	+	2.25725e12i	−0.0431182	+	0.0746830i
$991$	−4.45112e12	+	7.70957e12i	−0.146601	+	0.253921i	−0.929969	−	0.367637i	$-0.880167\pi$
$991$	−4.45112e12	+	7.70957e12i	−0.146601	+	0.253921i	0.783368	+	0.621558i	$0.213500\pi$
$992$	−1.05554e13	−	1.82825e13i	−0.346076	−	0.599421i
$993$	4.13859e13			1.35077
$994$		0			0
$995$	3.32841e12			0.107655
$996$	−2.00869e13	−	3.47915e13i	−0.646764	−	1.12023i
$997$	−7.27252e12	+	1.25964e13i	−0.233108	+	0.403755i	−0.958721	−	0.284348i	$-0.908223\pi$
$997$	−7.27252e12	+	1.25964e13i	−0.233108	+	0.403755i	0.725613	+	0.688103i	$0.241556\pi$
$998$	−8.69827e10	+	1.50658e11i	−0.00277553	+	0.00480735i
$999$	−1.88220e12	−	3.26007e12i	−0.0597890	−	0.103558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.c.18.1		4
7.2	even	3	inner	49.10.c.c.30.1		4
7.3	odd	6		49.10.a.b.1.2		2
7.4	even	3		7.10.a.a.1.2	✓	2
7.5	odd	6		49.10.c.b.30.1		4
7.6	odd	2		49.10.c.b.18.1		4
21.11	odd	6		63.10.a.d.1.1		2
28.11	odd	6		112.10.a.e.1.2		2
35.4	even	6		175.10.a.b.1.1		2
35.18	odd	12		175.10.b.b.99.2		4
35.32	odd	12		175.10.b.b.99.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.2	✓	2	7.4	even	3
49.10.a.b.1.2		2	7.3	odd	6
49.10.c.b.18.1		4	7.6	odd	2
49.10.c.b.30.1		4	7.5	odd	6
49.10.c.c.18.1		4	1.1	even	1	trivial
49.10.c.c.30.1		4	7.2	even	3	inner
63.10.a.d.1.1		2	21.11	odd	6
112.10.a.e.1.2		2	28.11	odd	6
175.10.a.b.1.1		2	35.4	even	6
175.10.b.b.99.2		4	35.18	odd	12
175.10.b.b.99.3		4	35.32	odd	12

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.44622 - 9.43313i) q^{2} +(97.9084 - 169.582i) q^{3} +(196.677 - 340.655i) q^{4} +(-100.391 - 173.882i) q^{5} -2132.92 q^{6} -9861.52 q^{8} +(-9330.63 - 16161.1i) q^{9} +O(q^{10})\)	\(q+(-5.44622 - 9.43313i) q^{2} +(97.9084 - 169.582i) q^{3} +(196.677 - 340.655i) q^{4} +(-100.391 - 173.882i) q^{5} -2132.92 q^{6} -9861.52 q^{8} +(-9330.63 - 16161.1i) q^{9} +(-1093.50 + 1894.01i) q^{10} +(-31932.1 + 55308.1i) q^{11} +(-38512.7 - 66706.0i) q^{12} -164679. q^{13} -39316.5 q^{15} +(-46990.7 - 81390.3i) q^{16} +(181455. - 314289. i) q^{17} +(-101633. + 176034. i) q^{18} +(218249. + 378018. i) q^{19} -78978.6 q^{20} +695638. q^{22} +(-459100. - 795184. i) q^{23} +(-965527. + 1.67234e6i) q^{24} +(956406. - 1.65654e6i) q^{25} +(896877. + 1.55344e6i) q^{26} +200076. q^{27} -3.68643e6 q^{29} +(214127. + 370878. i) q^{30} +(-1.73814e6 + 3.01055e6i) q^{31} +(-3.03639e6 + 5.25919e6i) q^{32} +(6.25285e6 + 1.08303e7i) q^{33} -3.95298e6 q^{34} -7.34049e6 q^{36} +(-9.40745e6 - 1.62942e7i) q^{37} +(2.37726e6 - 4.11754e6i) q^{38} +(-1.61234e7 + 2.79266e7i) q^{39} +(990009. + 1.71475e6i) q^{40} +2.40714e6 q^{41} -1.25306e7 q^{43} +(1.25607e7 + 2.17557e7i) q^{44} +(-1.87342e6 + 3.24486e6i) q^{45} +(-5.00072e6 + 8.66150e6i) q^{46} +(2.77255e7 + 4.80219e7i) q^{47} -1.84032e7 q^{48} -2.08352e7 q^{50} +(-3.55320e7 - 6.15432e7i) q^{51} +(-3.23886e7 + 5.60987e7i) q^{52} +(4.63444e7 - 8.02709e7i) q^{53} +(-1.08966e6 - 1.88734e6i) q^{54} +1.28228e7 q^{55} +8.54737e7 q^{57} +(2.00771e7 + 3.47746e7i) q^{58} +(1.26300e7 - 2.18758e7i) q^{59} +(-7.73267e6 + 1.33934e7i) q^{60} +(-3.46637e7 - 6.00394e7i) q^{61} +3.78653e7 q^{62} +1.80290e7 q^{64} +(1.65323e7 + 2.86347e7i) q^{65} +(6.81088e7 - 1.17968e8i) q^{66} +(1.16747e7 - 2.02211e7i) q^{67} +(-7.13762e7 - 1.23627e8i) q^{68} -1.79799e8 q^{69} -1.06194e8 q^{71} +(9.20142e7 + 1.59373e8i) q^{72} +(1.05058e8 - 1.81965e8i) q^{73} +(-1.02470e8 + 1.77484e8i) q^{74} +(-1.87280e8 - 3.24379e8i) q^{75} +1.71699e8 q^{76} +3.51247e8 q^{78} +(74803.2 + 129563. i) q^{79} +(-9.43490e6 + 1.63417e7i) q^{80} +(2.03244e8 - 3.52029e8i) q^{81} +(-1.31098e7 - 2.27069e7i) q^{82} +5.21565e8 q^{83} -7.28659e7 q^{85} +(6.82444e7 + 1.18203e8i) q^{86} +(-3.60932e8 + 6.25153e8i) q^{87} +(3.14900e8 - 5.45422e8i) q^{88} +(-1.49294e8 - 2.58584e8i) q^{89} +4.08123e7 q^{90} -3.61178e8 q^{92} +(3.40358e8 + 5.89517e8i) q^{93} +(3.01998e8 - 5.23076e8i) q^{94} +(4.38205e7 - 7.58993e7i) q^{95} +(5.94577e8 + 1.02984e9i) q^{96} -8.95983e8 q^{97} +1.19179e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 86 q^{3} + 620 q^{4} + 2238 q^{5} - 7976 q^{6} + 5232 q^{8} - 11038 q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 + 86 * q^3 + 620 * q^4 + 2238 * q^5 - 7976 * q^6 + 5232 * q^8 - 11038 * q^9	\( 4 q + 6 q^{2} + 86 q^{3} + 620 q^{4} + 2238 q^{5} - 7976 q^{6} + 5232 q^{8} - 11038 q^{9} - 43384 q^{10} - 35316 q^{11} - 52136 q^{12} - 53060 q^{13} - 614272 q^{15} + 752 q^{16} + 463920 q^{17} - 332042 q^{18} + 925426 q^{19} + 947520 q^{20} + 2355776 q^{22} - 778128 q^{23} - 3301296 q^{24} - 2081722 q^{25} + 4127424 q^{26} - 5597224 q^{27} - 20007168 q^{29} - 4095872 q^{30} - 2467260 q^{31} - 1284576 q^{32} + 15640784 q^{33} - 4493352 q^{34} - 11225432 q^{36} - 30735552 q^{37} - 3504660 q^{38} - 47417944 q^{39} + 32409984 q^{40} - 38206896 q^{41} + 8130200 q^{43} + 18650976 q^{44} - 22338298 q^{45} - 12367584 q^{46} + 82195020 q^{47} - 57612992 q^{48} - 176625252 q^{50} - 59971356 q^{51} - 33466384 q^{52} + 55189812 q^{53} - 52834472 q^{54} + 164891632 q^{55} + 63562232 q^{57} - 66558004 q^{58} + 7069218 q^{59} - 76165376 q^{60} - 44316386 q^{61} + 109820400 q^{62} + 294834304 q^{64} + 369979260 q^{65} + 83258464 q^{66} + 241921336 q^{67} - 165645816 q^{68} - 390362304 q^{69} + 412987632 q^{71} + 279147720 q^{72} + 499153188 q^{73} - 3571524 q^{74} - 813228014 q^{75} + 565023536 q^{76} + 189941920 q^{78} - 468535096 q^{79} - 249904128 q^{80} + 585745634 q^{81} - 389586092 q^{82} + 888047916 q^{83} + 346950120 q^{85} + 416830608 q^{86} - 28134340 q^{87} + 986010816 q^{88} - 636267396 q^{89} - 546485456 q^{90} - 658862976 q^{92} + 791523960 q^{93} + 152223192 q^{94} - 1104747984 q^{95} + 1714981184 q^{96} - 3265432128 q^{97} + 2818835720 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 + 86 * q^3 + 620 * q^4 + 2238 * q^5 - 7976 * q^6 + 5232 * q^8 - 11038 * q^9 - 43384 * q^10 - 35316 * q^11 - 52136 * q^12 - 53060 * q^13 - 614272 * q^15 + 752 * q^16 + 463920 * q^17 - 332042 * q^18 + 925426 * q^19 + 947520 * q^20 + 2355776 * q^22 - 778128 * q^23 - 3301296 * q^24 - 2081722 * q^25 + 4127424 * q^26 - 5597224 * q^27 - 20007168 * q^29 - 4095872 * q^30 - 2467260 * q^31 - 1284576 * q^32 + 15640784 * q^33 - 4493352 * q^34 - 11225432 * q^36 - 30735552 * q^37 - 3504660 * q^38 - 47417944 * q^39 + 32409984 * q^40 - 38206896 * q^41 + 8130200 * q^43 + 18650976 * q^44 - 22338298 * q^45 - 12367584 * q^46 + 82195020 * q^47 - 57612992 * q^48 - 176625252 * q^50 - 59971356 * q^51 - 33466384 * q^52 + 55189812 * q^53 - 52834472 * q^54 + 164891632 * q^55 + 63562232 * q^57 - 66558004 * q^58 + 7069218 * q^59 - 76165376 * q^60 - 44316386 * q^61 + 109820400 * q^62 + 294834304 * q^64 + 369979260 * q^65 + 83258464 * q^66 + 241921336 * q^67 - 165645816 * q^68 - 390362304 * q^69 + 412987632 * q^71 + 279147720 * q^72 + 499153188 * q^73 - 3571524 * q^74 - 813228014 * q^75 + 565023536 * q^76 + 189941920 * q^78 - 468535096 * q^79 - 249904128 * q^80 + 585745634 * q^81 - 389586092 * q^82 + 888047916 * q^83 + 346950120 * q^85 + 416830608 * q^86 - 28134340 * q^87 + 986010816 * q^88 - 636267396 * q^89 - 546485456 * q^90 - 658862976 * q^92 + 791523960 * q^93 + 152223192 * q^94 - 1104747984 * q^95 + 1714981184 * q^96 - 3265432128 * q^97 + 2818835720 * q^99

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