LMFDB - Embedded newform 98.12.c.l.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,12,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	98.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:	$75.2976316948$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 101803 x^{6} + 6576400 x^{5} + 8539617914 x^{4} + 333205096780 x^{3} + \cdots + 33\!\cdots\!81 $ x^8 - x^7 + 101803x^6 + 6576400x^5 + 8539617914x^4 + 333205096780x^3 + 195840371083183x^2 - 5894448091672309x + 3315283474489744081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$152.619 + 264.344i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.12.c.l.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.0000 + 27.7128i) q^{2} +(271.738 + 470.665i) q^{3} +(-512.000 - 886.810i) q^{4} +(-3667.11 + 6351.63i) q^{5} -17391.3 q^{6} +32768.0 q^{8} +(-59110.0 + 102381. i) q^{9} +O(q^{10})$	\(q+(-16.0000 + 27.7128i) q^{2} +(271.738 + 470.665i) q^{3} +(-512.000 - 886.810i) q^{4} +(-3667.11 + 6351.63i) q^{5} -17391.3 q^{6} +32768.0 q^{8} +(-59110.0 + 102381. i) q^{9} +(-117348. - 203252. i) q^{10} +(-24115.9 - 41769.9i) q^{11} +(278260. - 481961. i) q^{12} +1.82289e6 q^{13} -3.98598e6 q^{15} +(-524288. + 908093. i) q^{16} +(-3.35793e6 - 5.81611e6i) q^{17} +(-1.89152e6 - 3.27621e6i) q^{18} +(8.95659e6 - 1.55133e7i) q^{19} +7.51025e6 q^{20} +1.54342e6 q^{22} +(1.04379e7 - 1.80789e7i) q^{23} +(8.90432e6 + 1.54227e7i) q^{24} +(-2.48139e6 - 4.29789e6i) q^{25} +(-2.91663e7 + 5.05174e7i) q^{26} +3.20255e7 q^{27} +2.38808e7 q^{29} +(6.37757e7 - 1.10463e8i) q^{30} +(-5.14984e7 - 8.91978e7i) q^{31} +(-1.67772e7 - 2.90590e7i) q^{32} +(1.31064e7 - 2.27010e7i) q^{33} +2.14908e8 q^{34} +1.21057e8 q^{36} +(2.60667e8 - 4.51488e8i) q^{37} +(2.86611e8 + 4.96425e8i) q^{38} +(4.95349e8 + 8.57970e8i) q^{39} +(-1.20164e8 + 2.08130e8i) q^{40} +1.25858e9 q^{41} -1.03048e9 q^{43} +(-2.46947e7 + 4.27724e7i) q^{44} +(-4.33526e8 - 7.50889e8i) q^{45} +(3.34012e8 + 5.78526e8i) q^{46} +(7.99740e8 - 1.38519e9i) q^{47} -5.69877e8 q^{48} +1.58809e8 q^{50} +(1.82496e9 - 3.16092e9i) q^{51} +(-9.33320e8 - 1.61656e9i) q^{52} +(-2.29236e9 - 3.97049e9i) q^{53} +(-5.12408e8 + 8.87516e8i) q^{54} +3.53743e8 q^{55} +9.73540e9 q^{57} +(-3.82093e8 + 6.61804e8i) q^{58} +(-2.88236e9 - 4.99240e9i) q^{59} +(2.04082e9 + 3.53481e9i) q^{60} +(-2.91537e9 + 5.04957e9i) q^{61} +3.29590e9 q^{62} +1.07374e9 q^{64} +(-6.68475e9 + 1.15783e10i) q^{65} +(4.19406e8 + 7.26432e8i) q^{66} +(-7.79178e9 - 1.34958e10i) q^{67} +(-3.43852e9 + 5.95570e9i) q^{68} +1.13455e10 q^{69} -7.49669e8 q^{71} +(-1.93692e9 + 3.35484e9i) q^{72} +(-5.51048e9 - 9.54443e9i) q^{73} +(8.34133e9 + 1.44476e10i) q^{74} +(1.34858e9 - 2.33580e9i) q^{75} -1.83431e10 q^{76} -3.17024e10 q^{78} +(-1.78570e10 + 3.09292e10i) q^{79} +(-3.84525e9 - 6.66016e9i) q^{80} +(1.91737e10 + 3.32098e10i) q^{81} +(-2.01373e10 + 3.48788e10i) q^{82} +3.77864e10 q^{83} +4.92557e10 q^{85} +(1.64876e10 - 2.85574e10i) q^{86} +(6.48933e9 + 1.12398e10i) q^{87} +(-7.90229e8 - 1.36872e9i) q^{88} +(-8.88627e9 + 1.53915e10i) q^{89} +2.77457e10 q^{90} -2.13768e10 q^{92} +(2.79882e10 - 4.84769e10i) q^{93} +(2.55917e10 + 4.43261e10i) q^{94} +(6.56897e10 + 1.13778e11i) q^{95} +(9.11803e9 - 1.57929e10i) q^{96} +8.79572e10 q^{97} +5.70196e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{2} - 266 q^{3} - 4096 q^{4} - 7504 q^{5} + 17024 q^{6} + 262144 q^{8} - 123520 q^{9}+O(q^{10}) $ 8 * q - 128 * q^2 - 266 * q^3 - 4096 * q^4 - 7504 * q^5 + 17024 * q^6 + 262144 * q^8 - 123520 * q^9	\( 8 q - 128 q^{2} - 266 q^{3} - 4096 q^{4} - 7504 q^{5} + 17024 q^{6} + 262144 q^{8} - 123520 q^{9} - 240128 q^{10} + 213026 q^{11} - 272384 q^{12} + 2609712 q^{13} + 2275500 q^{15} - 4194304 q^{16} - 8854244 q^{17} - 3952640 q^{18} - 7232806 q^{19} + 15368192 q^{20} - 13633664 q^{22} - 10649134 q^{23} - 8716288 q^{24} - 119407256 q^{25} - 41755392 q^{26} - 19012196 q^{27} - 221414576 q^{29} - 36408000 q^{30} - 486231270 q^{31} - 134217728 q^{32} - 489871116 q^{33} + 566671616 q^{34} + 252968960 q^{36} + 463131040 q^{37} - 231449792 q^{38} + 493924396 q^{39} - 245891072 q^{40} + 1617723408 q^{41} + 2926896352 q^{43} + 218138624 q^{44} - 2871035832 q^{45} - 340772288 q^{46} + 894091254 q^{47} + 557842432 q^{48} + 7642064384 q^{50} + 6950287158 q^{51} - 1336172544 q^{52} - 1448863512 q^{53} + 304195136 q^{54} + 25123348964 q^{55} + 18014730520 q^{57} + 3542633216 q^{58} - 14386900738 q^{59} - 1165056000 q^{60} - 10854402216 q^{61} + 31118801280 q^{62} + 8589934592 q^{64} + 5495584080 q^{65} - 15675875712 q^{66} + 19629545546 q^{67} - 9066745856 q^{68} + 92767078992 q^{69} + 1474804928 q^{71} - 4047503360 q^{72} - 21420158732 q^{73} + 14820193280 q^{74} - 63738659600 q^{75} + 14812786688 q^{76} - 31611161344 q^{78} - 60246238086 q^{79} - 7868514304 q^{80} + 100835656724 q^{81} - 25883574528 q^{82} + 139893582304 q^{83} + 109585554592 q^{85} - 46830341632 q^{86} + 77636109684 q^{87} + 6980435968 q^{88} - 126354105612 q^{89} + 183746293248 q^{90} + 21809426432 q^{92} - 213975312128 q^{93} + 28610920128 q^{94} + 368499346550 q^{95} - 8925478912 q^{96} + 538182884176 q^{97} + 393415805736 q^{99}+O(q^{100}) \) 8 * q - 128 * q^2 - 266 * q^3 - 4096 * q^4 - 7504 * q^5 + 17024 * q^6 + 262144 * q^8 - 123520 * q^9 - 240128 * q^10 + 213026 * q^11 - 272384 * q^12 + 2609712 * q^13 + 2275500 * q^15 - 4194304 * q^16 - 8854244 * q^17 - 3952640 * q^18 - 7232806 * q^19 + 15368192 * q^20 - 13633664 * q^22 - 10649134 * q^23 - 8716288 * q^24 - 119407256 * q^25 - 41755392 * q^26 - 19012196 * q^27 - 221414576 * q^29 - 36408000 * q^30 - 486231270 * q^31 - 134217728 * q^32 - 489871116 * q^33 + 566671616 * q^34 + 252968960 * q^36 + 463131040 * q^37 - 231449792 * q^38 + 493924396 * q^39 - 245891072 * q^40 + 1617723408 * q^41 + 2926896352 * q^43 + 218138624 * q^44 - 2871035832 * q^45 - 340772288 * q^46 + 894091254 * q^47 + 557842432 * q^48 + 7642064384 * q^50 + 6950287158 * q^51 - 1336172544 * q^52 - 1448863512 * q^53 + 304195136 * q^54 + 25123348964 * q^55 + 18014730520 * q^57 + 3542633216 * q^58 - 14386900738 * q^59 - 1165056000 * q^60 - 10854402216 * q^61 + 31118801280 * q^62 + 8589934592 * q^64 + 5495584080 * q^65 - 15675875712 * q^66 + 19629545546 * q^67 - 9066745856 * q^68 + 92767078992 * q^69 + 1474804928 * q^71 - 4047503360 * q^72 - 21420158732 * q^73 + 14820193280 * q^74 - 63738659600 * q^75 + 14812786688 * q^76 - 31611161344 * q^78 - 60246238086 * q^79 - 7868514304 * q^80 + 100835656724 * q^81 - 25883574528 * q^82 + 139893582304 * q^83 + 109585554592 * q^85 - 46830341632 * q^86 + 77636109684 * q^87 + 6980435968 * q^88 - 126354105612 * q^89 + 183746293248 * q^90 + 21809426432 * q^92 - 213975312128 * q^93 + 28610920128 * q^94 + 368499346550 * q^95 - 8925478912 * q^96 + 538182884176 * q^97 + 393415805736 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−16.0000	+	27.7128i	−0.353553	+	0.612372i
$2$	−16.0000	+	27.7128i	−0.353553	+	0.612372i
$3$	271.738	+	470.665i	0.645631	+	1.11826i	0.984156	+	0.177307i	$0.0567387\pi$
$3$	271.738	+	470.665i	0.645631	+	1.11826i	−0.338525	+	0.940957i	$0.609928\pi$
$4$	−512.000	−	886.810i	−0.250000	−	0.433013i
$5$	−3667.11	+	6351.63i	−0.524795	+	0.908971i	0.474789	+	0.880100i	$0.342525\pi$
$5$	−3667.11	+	6351.63i	−0.524795	+	0.908971i	−0.999583	+	0.0288710i	$0.990809\pi$
$6$	−17391.3			−0.913059
$7$		0			0
$7$		0			0
$8$	32768.0			0.353553
$9$	−59110.0	+	102381.i	−0.333678	+	0.577946i
$10$	−117348.	−	203252.i	−0.371086	−	0.642740i
$11$	−24115.9	−	41769.9i	−0.0451485	−	0.0781995i	0.842568	−	0.538590i	$-0.181043\pi$
$11$	−24115.9	−	41769.9i	−0.0451485	−	0.0781995i	−0.887717	+	0.460390i	$0.847709\pi$
$12$	278260.	−	481961.i	0.322815	−	0.559132i
$13$	1.82289e6			1.36167			0.680836	−	0.732436i	$-0.261617\pi$
$13$	1.82289e6			1.36167			0.680836	+	0.732436i	$0.261617\pi$
$14$		0			0
$15$	−3.98598e6			−1.35529
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−3.35793e6	−	5.81611e6i	−0.573592	−	0.993490i	−0.996193	−	0.0871746i	$-0.972216\pi$
$17$	−3.35793e6	−	5.81611e6i	−0.573592	−	0.993490i	0.422601	−	0.906316i	$-0.361117\pi$
$18$	−1.89152e6	−	3.27621e6i	−0.235946	−	0.408670i
$19$	8.95659e6	−	1.55133e7i	0.829847	−	1.43734i	−0.0683108	−	0.997664i	$-0.521761\pi$
$19$	8.95659e6	−	1.55133e7i	0.829847	−	1.43734i	0.898158	−	0.439673i	$-0.144906\pi$
$20$	7.51025e6			0.524795
$21$		0			0
$22$	1.54342e6			0.0638496
$23$	1.04379e7	−	1.80789e7i	0.338150	−	0.585693i	−0.645935	−	0.763393i	$-0.723532\pi$
$23$	1.04379e7	−	1.80789e7i	0.338150	−	0.585693i	0.984085	+	0.177700i	$0.0568656\pi$
$24$	8.90432e6	+	1.54227e7i	0.228265	+	0.395366i
$25$	−2.48139e6	−	4.29789e6i	−0.0508188	−	0.0880207i
$26$	−2.91663e7	+	5.05174e7i	−0.481423	+	0.833850i
$27$	3.20255e7			0.429531
$28$		0			0
$29$	2.38808e7			0.216202			0.108101	−	0.994140i	$-0.465523\pi$
$29$	2.38808e7			0.216202			0.108101	+	0.994140i	$0.465523\pi$
$30$	6.37757e7	−	1.10463e8i	0.479169	−	0.829944i
$31$	−5.14984e7	−	8.91978e7i	−0.323076	−	0.559583i	0.658045	−	0.752978i	$-0.271383\pi$
$31$	−5.14984e7	−	8.91978e7i	−0.323076	−	0.559583i	−0.981121	+	0.193395i	$0.938050\pi$
$32$	−1.67772e7	−	2.90590e7i	−0.0883883	−	0.153093i
$33$	1.31064e7	−	2.27010e7i	0.0582985	−	0.100976i
$34$	2.14908e8			0.811182
$35$		0			0
$36$	1.21057e8			0.333678
$37$	2.60667e8	−	4.51488e8i	0.617982	−	1.07038i	−0.371871	−	0.928284i	$-0.621284\pi$
$37$	2.60667e8	−	4.51488e8i	0.617982	−	1.07038i	0.989853	−	0.142092i	$-0.0453830\pi$
$38$	2.86611e8	+	4.96425e8i	0.586790	+	1.01635i
$39$	4.95349e8	+	8.57970e8i	0.879136	+	1.52271i
$40$	−1.20164e8	+	2.08130e8i	−0.185543	+	0.321370i
$41$	1.25858e9			1.69656			0.848281	−	0.529546i	$-0.177638\pi$
$41$	1.25858e9			1.69656			0.848281	+	0.529546i	$0.177638\pi$
$42$		0			0
$43$	−1.03048e9			−1.06896			−0.534480	−	0.845181i	$-0.679492\pi$
$43$	−1.03048e9			−1.06896			−0.534480	+	0.845181i	$0.679492\pi$
$44$	−2.46947e7	+	4.27724e7i	−0.0225743	+	0.0390998i
$45$	−4.33526e8	−	7.50889e8i	−0.350224	−	0.606606i
$46$	3.34012e8	+	5.78526e8i	0.239108	+	0.414147i
$47$	7.99740e8	−	1.38519e9i	0.508640	−	0.880991i	−0.491310	−	0.870985i	$-0.663482\pi$
$47$	7.99740e8	−	1.38519e9i	0.508640	−	0.880991i	0.999950	−	0.0100058i	$-0.00318499\pi$
$48$	−5.69877e8			−0.322815
$49$		0			0
$50$	1.58809e8			0.0718686
$51$	1.82496e9	−	3.16092e9i	0.740657	−	1.28286i
$52$	−9.33320e8	−	1.61656e9i	−0.340418	−	0.589621i
$53$	−2.29236e9	−	3.97049e9i	−0.752949	−	1.30415i	−0.946387	−	0.323034i	$-0.895297\pi$
$53$	−2.29236e9	−	3.97049e9i	−0.752949	−	1.30415i	0.193438	−	0.981113i	$-0.438036\pi$
$54$	−5.12408e8	+	8.87516e8i	−0.151862	+	0.263033i
$55$	3.53743e8			0.0947748
$56$		0			0
$57$	9.73540e9			2.14310
$58$	−3.82093e8	+	6.61804e8i	−0.0764390	+	0.132396i
$59$	−2.88236e9	−	4.99240e9i	−0.524883	−	0.909124i	−0.999580	−	0.0289746i	$-0.990776\pi$
$59$	−2.88236e9	−	4.99240e9i	−0.524883	−	0.909124i	0.474697	−	0.880149i	$-0.342558\pi$
$60$	2.04082e9	+	3.53481e9i	0.338823	+	0.586859i
$61$	−2.91537e9	+	5.04957e9i	−0.441957	+	0.765491i	−0.997835	−	0.0657725i	$-0.979049\pi$
$61$	−2.91537e9	+	5.04957e9i	−0.441957	+	0.765491i	0.555878	+	0.831264i	$0.312382\pi$
$62$	3.29590e9			0.456898
$63$		0			0
$64$	1.07374e9			0.125000
$65$	−6.68475e9	+	1.15783e10i	−0.714598	+	1.23772i
$66$	4.19406e8	+	7.26432e8i	0.0412233	+	0.0714008i
$67$	−7.79178e9	−	1.34958e10i	−0.705059	−	1.22120i	−0.966670	−	0.256025i	$-0.917587\pi$
$67$	−7.79178e9	−	1.34958e10i	−0.705059	−	1.22120i	0.261611	−	0.965173i	$-0.415746\pi$
$68$	−3.43852e9	+	5.95570e9i	−0.286796	+	0.496745i
$69$	1.13455e10			0.873279
$70$		0			0
$71$	−7.49669e8			−0.0493116			−0.0246558	−	0.999696i	$-0.507849\pi$
$71$	−7.49669e8			−0.0493116			−0.0246558	+	0.999696i	$0.507849\pi$
$72$	−1.93692e9	+	3.35484e9i	−0.117973	+	0.204335i
$73$	−5.51048e9	−	9.54443e9i	−0.311110	−	0.538858i	0.667493	−	0.744616i	$-0.267367\pi$
$73$	−5.51048e9	−	9.54443e9i	−0.311110	−	0.538858i	−0.978603	+	0.205758i	$0.934034\pi$
$74$	8.34133e9	+	1.44476e10i	0.436979	+	0.756870i
$75$	1.34858e9	−	2.33580e9i	0.0656203	−	0.113658i
$76$	−1.83431e10			−0.829847
$77$		0			0
$78$	−3.17024e10			−1.24329
$79$	−1.78570e10	+	3.09292e10i	−0.652918	+	1.13089i	0.329493	+	0.944158i	$0.393122\pi$
$79$	−1.78570e10	+	3.09292e10i	−0.652918	+	1.13089i	−0.982411	+	0.186730i	$0.940211\pi$
$80$	−3.84525e9	−	6.66016e9i	−0.131199	−	0.227243i
$81$	1.91737e10	+	3.32098e10i	0.610996	+	1.05828i
$82$	−2.01373e10	+	3.48788e10i	−0.599825	+	1.03893i
$83$	3.77864e10			1.05295			0.526473	−	0.850192i	$-0.323514\pi$
$83$	3.77864e10			1.05295			0.526473	+	0.850192i	$0.323514\pi$
$84$		0			0
$85$	4.92557e10			1.20407
$86$	1.64876e10	−	2.85574e10i	0.377934	−	0.654601i
$87$	6.48933e9	+	1.12398e10i	0.139587	+	0.241771i
$88$	−7.90229e8	−	1.36872e9i	−0.0159624	−	0.0276477i
$89$	−8.88627e9	+	1.53915e10i	−0.168684	+	0.292170i	−0.937957	−	0.346750i	$-0.887285\pi$
$89$	−8.88627e9	+	1.53915e10i	−0.168684	+	0.292170i	0.769273	+	0.638920i	$0.220618\pi$
$90$	2.77457e10			0.495292
$91$		0			0
$92$	−2.13768e10			−0.338150
$93$	2.79882e10	−	4.84769e10i	0.417175	−	0.722568i
$94$	2.55917e10	+	4.43261e10i	0.359663	+	0.622955i
$95$	6.56897e10	+	1.13778e11i	0.870999	+	1.50861i
$96$	9.11803e9	−	1.57929e10i	0.114132	−	0.197683i
$97$	8.79572e10			1.03998			0.519992	−	0.854171i	$-0.325935\pi$
$97$	8.79572e10			1.03998			0.519992	+	0.854171i	$0.325935\pi$
$98$		0			0
$99$	5.70196e9			0.0602602
$100$	−2.54094e9	+	4.40104e9i	−0.0254094	+	0.0440104i
$101$	3.29398e10	+	5.70534e10i	0.311856	+	0.540150i	0.978764	−	0.204990i	$-0.0657161\pi$
$101$	3.29398e10	+	5.70534e10i	0.311856	+	0.540150i	−0.666908	+	0.745140i	$0.732383\pi$
$102$	5.83987e10	+	1.01149e11i	0.523724	+	0.907116i
$103$	2.10495e10	−	3.64589e10i	0.178911	−	0.309884i	−0.762597	−	0.646874i	$-0.776076\pi$
$103$	2.10495e10	−	3.64589e10i	0.178911	−	0.309884i	0.941508	+	0.336991i	$0.109409\pi$
$104$	5.97325e10			0.481423
$105$		0			0
$106$	1.46711e11			1.06483
$107$	−1.17144e11	+	2.02899e11i	−0.807436	+	1.39852i	0.107199	+	0.994238i	$0.465812\pi$
$107$	−1.17144e11	+	2.02899e11i	−0.807436	+	1.39852i	−0.914634	+	0.404282i	$0.867522\pi$
$108$	−1.63970e10	−	2.84005e10i	−0.107383	−	0.185993i
$109$	−2.24935e10	−	3.89598e10i	−0.140027	−	0.242533i	0.787480	−	0.616341i	$-0.211385\pi$
$109$	−2.24935e10	−	3.89598e10i	−0.140027	−	0.242533i	−0.927506	+	0.373807i	$0.878052\pi$
$110$	−5.65989e9	+	9.80321e9i	−0.0335080	+	0.0580375i
$111$	2.83332e11			1.59595
$112$		0			0
$113$	7.01436e10			0.358143			0.179071	−	0.983836i	$-0.442691\pi$
$113$	7.01436e10			0.358143			0.179071	+	0.983836i	$0.442691\pi$
$114$	−1.55766e11	+	2.69795e11i	−0.757700	+	1.31237i
$115$	7.65538e10	+	1.32595e11i	0.354918	+	0.614737i
$116$	−1.22270e10	−	2.11777e10i	−0.0540505	−	0.0936182i
$117$	−1.07751e11	+	1.86630e11i	−0.454359	+	0.786973i
$118$	1.84471e11			0.742296
$119$		0			0
$120$	−1.30613e11			−0.479169
$121$	1.41493e11	−	2.45073e11i	0.495923	−	0.858964i
$122$	−9.32919e10	−	1.61586e11i	−0.312511	−	0.541284i
$123$	3.42005e11	+	5.92369e11i	1.09535	+	1.89721i
$124$	−5.27343e10	+	9.13385e10i	−0.161538	+	0.279792i
$125$	−3.21718e11			−0.942912
$126$		0			0
$127$	−4.04128e11			−1.08542			−0.542711	−	0.839920i	$-0.682602\pi$
$127$	−4.04128e11			−1.08542			−0.542711	+	0.839920i	$0.682602\pi$
$128$	−1.71799e10	+	2.97564e10i	−0.0441942	+	0.0765466i
$129$	−2.80020e11	−	4.85008e11i	−0.690153	−	1.19538i
$130$	−2.13912e11	−	3.70506e11i	−0.505297	−	0.875200i
$131$	−3.39520e11	+	5.88066e11i	−0.768907	+	1.33179i	0.169250	+	0.985573i	$0.445866\pi$
$131$	−3.39520e11	+	5.88066e11i	−0.768907	+	1.33179i	−0.938156	+	0.346212i	$0.887468\pi$
$132$	−2.68420e10			−0.0582985
$133$		0			0
$134$	4.98674e11			0.997104
$135$	−1.17441e11	+	2.03414e11i	−0.225416	+	0.390432i
$136$	−1.10033e11	−	1.90582e11i	−0.202795	−	0.351252i
$137$	4.25961e10	+	7.37785e10i	0.0754061	+	0.130607i	0.901263	−	0.433273i	$-0.142641\pi$
$137$	4.25961e10	+	7.37785e10i	0.0754061	+	0.130607i	−0.825857	+	0.563880i	$0.809308\pi$
$138$	−1.81528e11	+	3.14415e11i	−0.308751	+	0.534772i
$139$	1.00319e11			0.163984			0.0819922	−	0.996633i	$-0.473872\pi$
$139$	1.00319e11			0.163984			0.0819922	+	0.996633i	$0.473872\pi$
$140$		0			0
$141$	8.69280e11			1.31357
$142$	1.19947e10	−	2.07754e10i	0.0174343	−	0.0301970i
$143$	−4.39606e10	−	7.61421e10i	−0.0614774	−	0.106482i
$144$	−6.19813e10	−	1.07355e11i	−0.0834194	−	0.144487i
$145$	−8.75736e10	+	1.51682e11i	−0.113462	+	0.196521i
$146$	3.52671e11			0.439976
$147$		0			0
$148$	−5.33845e11			−0.617982
$149$	−6.22902e11	+	1.07890e12i	−0.694857	+	1.20353i	0.275372	+	0.961338i	$0.411199\pi$
$149$	−6.22902e11	+	1.07890e12i	−0.694857	+	1.20353i	−0.970229	+	0.242190i	$0.922134\pi$
$150$	4.31544e10	+	7.47457e10i	0.0464006	+	0.0803682i
$151$	8.88615e9	+	1.53913e10i	0.00921172	+	0.0159552i	0.870595	−	0.492001i	$-0.163734\pi$
$151$	8.88615e9	+	1.53913e10i	0.00921172	+	0.0159552i	−0.861383	+	0.507956i	$0.830401\pi$
$152$	2.93490e11	−	5.08339e11i	0.293395	−	0.508175i
$153$	7.93949e11			0.765579
$154$		0			0
$155$	7.55401e11			0.678193
$156$	5.07238e11	−	8.78562e11i	0.439568	−	0.761354i
$157$	1.44394e11	+	2.50097e11i	0.120809	+	0.209248i	0.920087	−	0.391714i	$-0.128118\pi$
$157$	1.44394e11	+	2.50097e11i	0.120809	+	0.209248i	−0.799278	+	0.600962i	$0.794784\pi$
$158$	−5.71423e11	−	9.89734e11i	−0.461683	−	0.799659i
$159$	1.24585e12	−	2.15787e12i	0.972254	−	1.68399i
$160$	2.46096e11			0.185543
$161$		0			0
$162$	−1.22712e12			−0.864079
$163$	1.40718e12	−	2.43732e12i	0.957898	−	1.65913i	0.230306	−	0.973118i	$-0.426027\pi$
$163$	1.40718e12	−	2.43732e12i	0.957898	−	1.65913i	0.727592	−	0.686010i	$-0.240639\pi$
$164$	−6.44393e11	−	1.11612e12i	−0.424141	−	0.734633i
$165$	9.61255e10	+	1.66494e11i	0.0611895	+	0.105983i
$166$	−6.04582e11	+	1.04717e12i	−0.372272	+	0.644795i
$167$	7.61477e11			0.453645			0.226823	−	0.973936i	$-0.427166\pi$
$167$	7.61477e11			0.453645			0.226823	+	0.973936i	$0.427166\pi$
$168$		0			0
$169$	1.53077e12			0.854148
$170$	−7.88091e11	+	1.36501e12i	−0.425704	+	0.737340i
$171$	1.05885e12	+	1.83398e12i	0.553803	+	0.959214i
$172$	5.27603e11	+	9.13836e11i	0.267240	+	0.462873i
$173$	9.63093e11	−	1.66813e12i	0.472514	−	0.818418i	−0.526991	−	0.849871i	$-0.676680\pi$
$173$	9.63093e11	−	1.66813e12i	0.472514	−	0.818418i	0.999505	+	0.0314523i	$0.0100132\pi$
$174$	−4.15317e11			−0.197405
$175$		0			0
$176$	5.05747e10			0.0225743
$177$	1.56650e12	−	2.71325e12i	0.677761	−	1.17392i
$178$	−2.84361e11	−	4.92527e11i	−0.119278	−	0.206595i
$179$	1.78409e11	+	3.09013e11i	0.0725646	+	0.125686i	0.900025	−	0.435839i	$-0.143548\pi$
$179$	1.78409e11	+	3.09013e11i	0.0725646	+	0.125686i	−0.827460	+	0.561525i	$0.810215\pi$
$180$	−4.43931e11	+	7.68910e11i	−0.175112	+	0.303303i
$181$	−3.24944e12			−1.24330			−0.621651	−	0.783295i	$-0.713538\pi$
$181$	−3.24944e12			−1.24330			−0.621651	+	0.783295i	$0.713538\pi$
$182$		0			0
$183$	−3.16887e12			−1.14136
$184$	3.42028e11	−	5.92411e11i	0.119554	−	0.207074i
$185$	1.91179e12	+	3.31131e12i	0.648627	+	1.12346i
$186$	8.95621e11	+	1.55126e12i	0.294987	+	0.510933i
$187$	−1.61959e11	+	2.80521e11i	−0.0517937	+	0.0897092i
$188$	−1.63787e12			−0.508640
$189$		0			0
$190$	−4.20414e12			−1.23178
$191$	5.09614e11	−	8.82677e11i	0.145063	−	0.251257i	−0.784333	−	0.620340i	$-0.786995\pi$
$191$	5.09614e11	−	8.82677e11i	0.145063	−	0.251257i	0.929397	+	0.369083i	$0.120328\pi$
$192$	2.91777e11	+	5.05372e11i	0.0807038	+	0.139783i
$193$	−3.57744e12	−	6.19631e12i	−0.961628	−	1.66559i	−0.718414	−	0.695616i	$-0.755132\pi$
$193$	−3.57744e12	−	6.19631e12i	−0.961628	−	1.66559i	−0.243214	−	0.969973i	$-0.578202\pi$
$194$	−1.40732e12	+	2.43754e12i	−0.367690	+	0.636858i
$195$	−7.26601e12			−1.84546
$196$		0			0
$197$	6.77238e11			0.162621			0.0813106	−	0.996689i	$-0.474089\pi$
$197$	6.77238e11			0.162621			0.0813106	+	0.996689i	$0.474089\pi$
$198$	−9.12313e10	+	1.58017e11i	−0.0213052	+	0.0369017i
$199$	−1.21493e12	−	2.10432e12i	−0.275968	−	0.477991i	0.694411	−	0.719579i	$-0.255665\pi$
$199$	−1.21493e12	−	2.10432e12i	−0.275968	−	0.477991i	−0.970379	+	0.241588i	$0.922332\pi$
$200$	−8.13101e10	−	1.40833e11i	−0.0179672	−	0.0311200i
$201$	4.23465e12	−	7.33463e12i	0.910415	−	1.57689i
$202$	−2.10815e12			−0.441030
$203$		0			0
$204$	−3.73752e12			−0.740657
$205$	−4.61536e12	+	7.99404e12i	−0.890347	+	1.54213i
$206$	6.73585e11	+	1.16668e12i	0.126509	+	0.219121i
$207$	1.23397e12	+	2.13729e12i	0.225666	+	0.390865i
$208$	−9.55720e11	+	1.65536e12i	−0.170209	+	0.294810i
$209$	−8.63985e11			−0.149865
$210$		0			0
$211$	4.18828e12			0.689418			0.344709	−	0.938710i	$-0.387978\pi$
$211$	4.18828e12			0.689418			0.344709	+	0.938710i	$0.387978\pi$
$212$	−2.34738e12	+	4.06578e12i	−0.376475	+	0.652073i
$213$	−2.03714e11	−	3.52843e11i	−0.0318371	−	0.0551434i
$214$	−3.74860e12	−	6.49276e12i	−0.570943	−	0.988903i
$215$	3.77887e12	−	6.54520e12i	0.560984	−	0.971653i
$216$	1.04941e12			0.151862
$217$		0			0
$218$	1.43958e12			0.198028
$219$	2.99482e12	−	5.18718e12i	0.401724	−	0.695806i
$220$	−1.81116e11	−	3.13703e11i	−0.0236937	−	0.0410387i
$221$	−6.12115e12	−	1.06021e13i	−0.781044	−	1.35281i
$222$	−4.53332e12	+	7.85194e12i	−0.564254	+	0.977317i
$223$	−2.85623e12			−0.346830			−0.173415	−	0.984849i	$-0.555480\pi$
$223$	−2.85623e12			−0.346830			−0.173415	+	0.984849i	$0.555480\pi$
$224$		0			0
$225$	5.86699e11			0.0678284
$226$	−1.12230e12	+	1.94388e12i	−0.126623	+	0.219317i
$227$	6.36517e12	+	1.10248e13i	0.700919	+	1.21403i	0.968144	+	0.250394i	$0.0805600\pi$
$227$	6.36517e12	+	1.10248e13i	0.700919	+	1.21403i	−0.267225	+	0.963634i	$0.586107\pi$
$228$	−4.98452e12	−	8.63345e12i	−0.535775	−	0.927989i
$229$	8.64561e12	−	1.49746e13i	0.907194	−	1.57131i	0.0892503	−	0.996009i	$-0.471553\pi$
$229$	8.64561e12	−	1.49746e13i	0.907194	−	1.57131i	0.817944	−	0.575298i	$-0.195114\pi$
$230$	−4.89944e12			−0.501930
$231$		0			0
$232$	7.82526e11			0.0764390
$233$	−2.46241e12	+	4.26502e12i	−0.234911	+	0.406877i	−0.959247	−	0.282570i	$-0.908813\pi$
$233$	−2.46241e12	+	4.26502e12i	−0.234911	+	0.406877i	0.724336	+	0.689447i	$0.242146\pi$
$234$	−3.44803e12	−	5.97217e12i	−0.321280	−	0.556474i
$235$	5.86548e12	+	1.01593e13i	0.533863	+	0.924678i
$236$	−2.95154e12	+	5.11221e12i	−0.262441	+	0.454562i
$237$	−1.94097e13			−1.68618
$238$		0			0
$239$	1.35641e13			1.12513			0.562564	−	0.826754i	$-0.309815\pi$
$239$	1.35641e13			1.12513			0.562564	+	0.826754i	$0.309815\pi$
$240$	2.08980e12	−	3.61964e12i	0.169412	−	0.293430i
$241$	−9.51393e12	−	1.64786e13i	−0.753818	−	1.30565i	−0.945960	−	0.324283i	$-0.894877\pi$
$241$	−9.51393e12	−	1.64786e13i	−0.753818	−	1.30565i	0.192142	−	0.981367i	$-0.438456\pi$
$242$	4.52777e12	+	7.84232e12i	0.350671	+	0.607379i
$243$	−7.58385e12	+	1.31356e13i	−0.574190	+	0.994526i
$244$	5.97068e12			0.441957
$245$		0			0
$246$	−2.18883e13			−1.54906
$247$	1.63269e13	−	2.82790e13i	1.12998	−	1.95718i
$248$	−1.68750e12	−	2.92283e12i	−0.114224	−	0.197843i
$249$	1.02680e13	+	1.77847e13i	0.679814	+	1.17747i
$250$	5.14750e12	−	8.91572e12i	0.333370	−	0.577413i
$251$	2.28213e13			1.44589			0.722944	−	0.690906i	$-0.242788\pi$
$251$	2.28213e13			1.44589			0.722944	+	0.690906i	$0.242788\pi$
$252$		0			0
$253$	−1.00688e12			−0.0610679
$254$	6.46605e12	−	1.11995e13i	0.383755	−	0.664682i
$255$	1.33847e13	+	2.31829e13i	0.777386	+	1.34647i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−7.41460e12	+	1.28425e13i	−0.412530	+	0.714523i	−0.995166	−	0.0982104i	$-0.968688\pi$
$257$	−7.41460e12	+	1.28425e13i	−0.412530	+	0.714523i	0.582636	+	0.812734i	$0.302022\pi$
$258$	1.79213e13			0.976023
$259$		0			0
$260$	1.36904e13			0.714598
$261$	−1.41159e12	+	2.44495e12i	−0.0721417	+	0.124953i
$262$	−1.08646e13	−	1.88181e13i	−0.543699	−	0.941714i
$263$	−1.81665e12	−	3.14652e12i	−0.0890254	−	0.154196i	0.818074	−	0.575113i	$-0.195042\pi$
$263$	−1.81665e12	−	3.14652e12i	−0.0890254	−	0.154196i	−0.907099	+	0.420916i	$0.861709\pi$
$264$	4.29471e11	−	7.43866e11i	0.0206116	−	0.0357004i
$265$	3.36254e13			1.58058
$266$		0			0
$267$	−9.65896e12			−0.435631
$268$	−7.97879e12	+	1.38197e13i	−0.352530	+	0.610599i
$269$	5.35700e12	+	9.27859e12i	0.231891	+	0.401647i	0.958365	−	0.285547i	$-0.0921754\pi$
$269$	5.35700e12	+	9.27859e12i	0.231891	+	0.401647i	−0.726474	+	0.687194i	$0.758842\pi$
$270$	−3.75812e12	−	6.50925e12i	−0.159393	−	0.276077i
$271$	1.12716e13	−	1.95229e13i	0.468439	−	0.811361i	−0.530910	−	0.847428i	$-0.678150\pi$
$271$	1.12716e13	−	1.95229e13i	0.468439	−	0.811361i	0.999349	+	0.0360675i	$0.0114831\pi$
$272$	7.04210e12			0.286796
$273$		0			0
$274$	−2.72615e12			−0.106640
$275$	−1.19682e11	+	2.07295e11i	−0.00458879	+	0.00794801i
$276$	−5.80889e12	−	1.00613e13i	−0.218320	−	0.378141i
$277$	1.45924e13	+	2.52748e13i	0.537636	+	0.931213i	0.999031	+	0.0440178i	$0.0140158\pi$
$277$	1.45924e13	+	2.52748e13i	0.537636	+	0.931213i	−0.461395	+	0.887195i	$0.652651\pi$
$278$	−1.60511e12	+	2.78013e12i	−0.0579772	+	0.100420i
$279$	1.21763e13			0.431212
$280$		0			0
$281$	1.40962e13			0.479975			0.239987	−	0.970776i	$-0.422857\pi$
$281$	1.40962e13			0.479975			0.239987	+	0.970776i	$0.422857\pi$
$282$	−1.39085e13	+	2.40902e13i	−0.464419	+	0.804397i
$283$	−4.60359e12	−	7.97366e12i	−0.150755	−	0.261115i	0.780750	−	0.624843i	$-0.214837\pi$
$283$	−4.60359e12	−	7.97366e12i	−0.150755	−	0.261115i	−0.931505	+	0.363728i	$0.881504\pi$
$284$	3.83831e11	+	6.64814e11i	0.0123279	+	0.0213525i
$285$	−3.57008e13	+	6.18356e13i	−1.12469	+	1.94801i
$286$	2.81348e12			0.0869422
$287$		0			0
$288$	3.96680e12			0.117973
$289$	−5.41549e12	+	9.37991e12i	−0.158016	+	0.273691i
$290$	−2.80235e12	−	4.85382e12i	−0.0802295	−	0.138962i
$291$	2.39013e13	+	4.13983e13i	0.671446	+	1.16298i
$292$	−5.64273e12	+	9.77350e12i	−0.155555	+	0.269429i
$293$	4.53137e12			0.122591			0.0612954	−	0.998120i	$-0.480477\pi$
$293$	4.53137e12			0.122591			0.0612954	+	0.998120i	$0.480477\pi$
$294$		0			0
$295$	4.22798e13			1.10182
$296$	8.54152e12	−	1.47944e13i	0.218490	−	0.378435i
$297$	−7.72323e11	−	1.33770e12i	−0.0193927	−	0.0335892i
$298$	−1.99329e13	−	3.45248e13i	−0.491338	−	0.851023i
$299$	1.90271e13	−	3.29559e13i	0.460449	−	0.797521i
$300$	−2.76188e12			−0.0656203
$301$		0			0
$302$	−5.68714e11			−0.0130273
$303$	−1.79020e13	+	3.10072e13i	−0.402687	+	0.697474i
$304$	9.39167e12	+	1.62668e13i	0.207462	+	0.359334i
$305$	−2.13820e13	−	3.70347e13i	−0.463873	−	0.803451i
$306$	−1.27032e13	+	2.20026e13i	−0.270673	+	0.468819i
$307$	2.58128e13			0.540224			0.270112	−	0.962829i	$-0.412939\pi$
$307$	2.58128e13			0.540224			0.270112	+	0.962829i	$0.412939\pi$
$308$		0			0
$309$	2.28799e13			0.462042
$310$	−1.20864e13	+	2.09343e13i	−0.239778	+	0.415307i
$311$	−3.07286e13	−	5.32235e13i	−0.598909	−	1.03734i	−0.992982	−	0.118262i	$-0.962268\pi$
$311$	−3.07286e13	−	5.32235e13i	−0.598909	−	1.03734i	0.394073	−	0.919079i	$-0.371066\pi$
$312$	1.62316e13	+	2.81140e13i	0.310822	+	0.538359i
$313$	−4.79028e12	+	8.29700e12i	−0.0901295	+	0.156109i	−0.907565	−	0.419911i	$-0.862061\pi$
$313$	−4.79028e12	+	8.29700e12i	−0.0901295	+	0.156109i	0.817436	+	0.576019i	$0.195395\pi$
$314$	−9.24120e12			−0.170850
$315$		0			0
$316$	3.65711e13			0.652918
$317$	−3.51662e13	+	6.09097e13i	−0.617021	+	1.06871i	0.373005	+	0.927829i	$0.378327\pi$
$317$	−3.51662e13	+	6.09097e13i	−0.617021	+	1.06871i	−0.990026	+	0.140882i	$0.955006\pi$
$318$	3.98670e13	+	6.90517e13i	0.687488	+	1.19076i
$319$	−5.75906e11	−	9.97499e11i	−0.00976120	−	0.0169069i
$320$	−3.93753e12	+	6.82001e12i	−0.0655993	+	0.113621i
$321$	−1.27330e14			−2.08522
$322$		0			0
$323$	−1.20303e14			−1.90397
$324$	1.96339e13	−	3.40069e13i	0.305498	−	0.529138i
$325$	−4.52330e12	−	7.83458e12i	−0.0691985	−	0.119855i
$326$	4.50299e13	+	7.79941e13i	0.677336	+	1.17318i
$327$	1.22247e13	−	2.11738e13i	0.180811	−	0.313174i
$328$	4.12412e13			0.599825
$329$		0			0
$330$	−6.15203e12			−0.0865350
$331$	2.70651e12	−	4.68781e12i	0.0374417	−	0.0648509i	−0.846697	−	0.532075i	$-0.821412\pi$
$331$	2.70651e12	−	4.68781e12i	0.0374417	−	0.0648509i	0.884139	+	0.467224i	$0.154746\pi$
$332$	−1.93466e13	−	3.35093e13i	−0.263236	−	0.455939i
$333$	3.08160e13	+	5.33749e13i	0.412414	+	0.714321i
$334$	−1.21836e13	+	2.11027e13i	−0.160388	+	0.277800i
$335$	1.14293e14			1.48004
$336$		0			0
$337$	−2.77737e12			−0.0348072			−0.0174036	−	0.999849i	$-0.505540\pi$
$337$	−2.77737e12			−0.0348072			−0.0174036	+	0.999849i	$0.505540\pi$
$338$	−2.44923e13	+	4.24220e13i	−0.301987	+	0.523057i
$339$	1.90607e13	+	3.30141e13i	0.231228	+	0.400499i
$340$	−2.52189e13	−	4.36805e13i	−0.301018	−	0.521378i
$341$	−2.48386e12	+	4.30217e12i	−0.0291728	+	0.0505287i
$342$	−6.77663e13			−0.783195
$343$		0			0
$344$	−3.37666e13			−0.377934
$345$	−4.16052e13	+	7.20623e13i	−0.458292	+	0.793786i
$346$	3.08190e13	+	5.33800e13i	0.334118	+	0.578709i
$347$	−2.22782e12	−	3.85870e12i	−0.0237721	−	0.0411745i	0.853895	−	0.520446i	$-0.174234\pi$
$347$	−2.22782e12	−	3.85870e12i	−0.0237721	−	0.0411745i	−0.877667	+	0.479271i	$0.840901\pi$
$348$	6.64507e12	−	1.15096e13i	0.0697933	−	0.120886i
$349$	−4.25296e13			−0.439695			−0.219848	−	0.975534i	$-0.570556\pi$
$349$	−4.25296e13			−0.439695			−0.219848	+	0.975534i	$0.570556\pi$
$350$		0			0
$351$	5.83790e13			0.584881
$352$	−8.09195e11	+	1.40157e12i	−0.00798121	+	0.0138239i
$353$	2.21765e13	+	3.84108e13i	0.215343	+	0.372986i	0.953379	−	0.301776i	$-0.0975796\pi$
$353$	2.21765e13	+	3.84108e13i	0.215343	+	0.372986i	−0.738035	+	0.674762i	$0.764246\pi$
$354$	5.01279e13	+	8.68240e13i	0.479249	+	0.830084i
$355$	2.74912e12	−	4.76162e12i	0.0258784	−	0.0448228i
$356$	1.81991e13			0.168684
$357$		0			0
$358$	−1.14182e13			−0.102622
$359$	5.69725e13	−	9.86792e13i	0.504250	−	0.873386i	−0.495738	−	0.868472i	$-0.665102\pi$
$359$	5.69725e13	−	9.86792e13i	0.504250	−	0.873386i	0.999988	−	0.00491416i	$-0.00156423\pi$
$360$	−1.42058e13	−	2.46051e13i	−0.123823	−	0.214468i
$361$	−1.02196e14	−	1.77009e14i	−0.877292	−	1.51951i
$362$	5.19910e13	−	9.00511e13i	0.439573	−	0.761364i
$363$	1.53796e14			1.28073
$364$		0			0
$365$	8.08302e13			0.653075
$366$	5.07020e13	−	8.78184e13i	0.403533	−	0.698939i
$367$	4.73329e13	+	8.19830e13i	0.371108	+	0.642777i	0.989736	−	0.142906i	$-0.0456448\pi$
$367$	4.73329e13	+	8.19830e13i	0.371108	+	0.642777i	−0.618629	+	0.785684i	$0.712311\pi$
$368$	1.09449e13	+	1.89571e13i	0.0845375	+	0.146423i
$369$	−7.43947e13	+	1.28855e14i	−0.566105	+	0.980522i
$370$	−1.22354e14			−0.917298
$371$		0			0
$372$	−5.73198e13			−0.417175
$373$	1.11323e14	−	1.92817e14i	0.798335	−	1.38276i	−0.122365	−	0.992485i	$-0.539048\pi$
$373$	1.11323e14	−	1.92817e14i	0.798335	−	1.38276i	0.920700	−	0.390272i	$-0.127619\pi$
$374$	−5.18269e12	−	8.97669e12i	−0.0366236	−	0.0634340i
$375$	−8.74233e13	−	1.51422e14i	−0.608772	−	1.05442i
$376$	2.62059e13	−	4.53899e13i	0.179831	−	0.311477i
$377$	4.35321e13			0.294396
$378$		0			0
$379$	−5.21543e13			−0.342590			−0.171295	−	0.985220i	$-0.554795\pi$
$379$	−5.21543e13			−0.342590			−0.171295	+	0.985220i	$0.554795\pi$
$380$	6.72662e13	−	1.16509e14i	0.435499	−	0.754307i
$381$	−1.09817e14	−	1.90209e14i	−0.700781	−	1.21379i
$382$	1.63076e13	+	2.82457e13i	0.102575	+	0.177666i
$383$	3.99715e13	−	6.92326e13i	0.247832	−	0.429257i	−0.715092	−	0.699030i	$-0.753615\pi$
$383$	3.99715e13	−	6.92326e13i	0.247832	−	0.429257i	0.962924	+	0.269773i	$0.0869486\pi$
$384$	−1.86737e13			−0.114132
$385$		0			0
$386$	2.28956e14			1.35995
$387$	6.09114e13	−	1.05502e14i	0.356688	−	0.617801i
$388$	−4.50341e13	−	7.80013e13i	−0.259996	−	0.450326i
$389$	1.13471e13	+	1.96537e13i	0.0645893	+	0.111872i	0.896512	−	0.443020i	$-0.146093\pi$
$389$	1.13471e13	+	1.96537e13i	0.0645893	+	0.111872i	−0.831922	+	0.554892i	$0.812760\pi$
$390$	1.16256e14	−	2.01362e14i	0.652470	−	1.13011i
$391$	−1.40199e14			−0.775840
$392$		0			0
$393$	−3.69043e14			−1.98572
$394$	−1.08358e13	+	1.87682e13i	−0.0574953	+	0.0995848i
$395$	−1.30967e14	−	2.26842e14i	−0.685296	−	1.18697i
$396$	−2.91940e12	−	5.05655e12i	−0.0150650	−	0.0260934i
$397$	2.43291e13	−	4.21392e13i	0.123816	−	0.214456i	−0.797453	−	0.603381i	$-0.793820\pi$
$397$	2.43291e13	−	4.21392e13i	0.123816	−	0.214456i	0.921270	+	0.388925i	$0.127153\pi$
$398$	7.77555e13			0.390278
$399$		0			0
$400$	5.20384e12			0.0254094
$401$	−9.64251e13	+	1.67013e14i	−0.464404	+	0.804372i	−0.999174	−	0.0406258i	$-0.987065\pi$
$401$	−9.64251e13	+	1.67013e14i	−0.464404	+	0.804372i	0.534770	+	0.844998i	$0.320398\pi$
$402$	1.35509e14	+	2.34708e14i	0.643761	+	1.11503i
$403$	−9.38759e13	−	1.62598e14i	−0.439923	−	0.761968i
$404$	3.37304e13	−	5.84227e13i	0.155928	−	0.270075i
$405$	−2.81249e14			−1.28259
$406$		0			0
$407$	−2.51448e13			−0.111604
$408$	5.98003e13	−	1.03577e14i	0.261862	−	0.453558i
$409$	6.61963e13	+	1.14655e14i	0.285993	+	0.495354i	0.972849	−	0.231439i	$-0.0743433\pi$
$409$	6.61963e13	+	1.14655e14i	0.285993	+	0.495354i	−0.686857	+	0.726793i	$0.741010\pi$
$410$	−1.47691e14	−	2.55809e14i	−0.629570	−	1.09045i
$411$	−2.31500e13	+	4.00969e13i	−0.0973689	+	0.168648i
$412$	−4.31095e13			−0.178911
$413$		0			0
$414$	−7.89738e13			−0.319140
$415$	−1.38567e14	+	2.40005e14i	−0.552580	+	0.957097i
$416$	−3.05830e13	−	5.29714e13i	−0.120356	−	0.208462i
$417$	2.72606e13	+	4.72167e13i	0.105873	+	0.183378i
$418$	1.38238e13	−	2.39435e13i	0.0529854	−	0.0917735i
$419$	−4.29093e14			−1.62321			−0.811605	−	0.584207i	$-0.801406\pi$
$419$	−4.29093e14			−1.62321			−0.811605	+	0.584207i	$0.801406\pi$
$420$		0			0
$421$	2.06975e13			0.0762724			0.0381362	−	0.999273i	$-0.487858\pi$
$421$	2.06975e13			0.0762724			0.0381362	+	0.999273i	$0.487858\pi$
$422$	−6.70126e13	+	1.16069e14i	−0.243746	+	0.422181i
$423$	9.45452e13	+	1.63757e14i	0.339444	+	0.587934i
$424$	−7.51161e13	−	1.30105e14i	−0.266208	−	0.461085i
$425$	−1.66647e13	+	2.88640e13i	−0.0582985	+	0.100976i
$426$	1.30377e13			0.0450244
$427$		0			0
$428$	2.39910e14			0.807436
$429$	2.38916e13	−	4.13814e13i	0.0793834	−	0.137496i
$430$	1.20924e14	+	2.09446e14i	0.396676	+	0.687062i
$431$	1.11477e14	+	1.93085e14i	0.361046	+	0.625349i	0.988133	−	0.153599i	$-0.0490866\pi$
$431$	1.11477e14	+	1.93085e14i	0.361046	+	0.625349i	−0.627088	+	0.778949i	$0.715753\pi$
$432$	−1.67906e13	+	2.90821e13i	−0.0536914	+	0.0929963i
$433$	3.45887e14			1.09207			0.546035	−	0.837762i	$-0.316136\pi$
$433$	3.45887e14			1.09207			0.546035	+	0.837762i	$0.316136\pi$
$434$		0			0
$435$	−9.51884e13			−0.293017
$436$	−2.30333e13	+	3.98949e13i	−0.0700133	+	0.121267i
$437$	−1.86976e14	−	3.23851e14i	−0.561225	−	0.972071i
$438$	9.58342e13	+	1.65990e14i	0.284062	+	0.492009i
$439$	−1.53324e14	+	2.65565e14i	−0.448803	+	0.777350i	−0.998308	−	0.0581402i	$-0.981483\pi$
$439$	−1.53324e14	+	2.65565e14i	−0.448803	+	0.777350i	0.549505	+	0.835490i	$0.314816\pi$
$440$	1.15914e13			0.0335080
$441$		0			0
$442$	3.91753e14			1.10456
$443$	9.90194e13	−	1.71507e14i	0.275740	−	0.477596i	−0.694581	−	0.719414i	$-0.744410\pi$
$443$	9.90194e13	−	1.71507e14i	0.275740	−	0.477596i	0.970322	+	0.241818i	$0.0777437\pi$
$444$	−1.45066e14	−	2.51262e14i	−0.398988	−	0.691068i
$445$	−6.51739e13	−	1.12885e14i	−0.177049	−	0.306658i
$446$	4.56997e13	−	7.91543e13i	0.122623	−	0.212389i
$447$	−6.77066e14			−1.79448
$448$		0			0
$449$	−2.07366e14			−0.536270			−0.268135	−	0.963381i	$-0.586407\pi$
$449$	−2.07366e14			−0.536270			−0.268135	+	0.963381i	$0.586407\pi$
$450$	−9.38718e12	+	1.62591e13i	−0.0239809	+	0.0415362i
$451$	−3.03518e13	−	5.25708e13i	−0.0765973	−	0.132670i
$452$	−3.59135e13	−	6.22040e13i	−0.0895357	−	0.155080i
$453$	−4.82942e12	+	8.36480e12i	−0.0118947	+	0.0206023i
$454$	−4.07371e14			−0.991249
$455$		0			0
$456$	3.19010e14			0.757700
$457$	2.68599e13	−	4.65227e13i	0.0630326	−	0.109176i	−0.832787	−	0.553594i	$-0.813256\pi$
$457$	2.68599e13	−	4.65227e13i	0.0630326	−	0.109176i	0.895820	+	0.444418i	$0.146589\pi$
$458$	2.76659e14	+	4.79188e14i	0.641483	+	1.11108i
$459$	−1.07539e14	−	1.86264e14i	−0.246376	−	0.426735i
$460$	7.83911e13	−	1.35777e14i	0.177459	−	0.307368i
$461$	4.54319e14			1.01626			0.508132	−	0.861279i	$-0.330336\pi$
$461$	4.54319e14			1.01626			0.508132	+	0.861279i	$0.330336\pi$
$462$		0			0
$463$	−7.25051e14			−1.58370			−0.791850	−	0.610715i	$-0.790882\pi$
$463$	−7.25051e14			−1.58370			−0.791850	+	0.610715i	$0.790882\pi$
$464$	−1.25204e13	+	2.16860e13i	−0.0270253	+	0.0468091i
$465$	2.05272e14	+	3.55541e14i	0.437862	+	0.758400i
$466$	−7.87972e13	−	1.36481e14i	−0.166107	−	0.287706i
$467$	−3.61955e14	+	6.26924e14i	−0.754069	+	1.30609i	0.191766	+	0.981441i	$0.438578\pi$
$467$	−3.61955e14	+	6.26924e14i	−0.754069	+	1.30609i	−0.945836	+	0.324646i	$0.894755\pi$
$468$	2.20674e14			0.454359
$469$		0			0
$470$	−3.75391e14			−0.754997
$471$	−7.84747e13	+	1.35922e14i	−0.155996	+	0.270194i
$472$	−9.44492e13	−	1.63591e14i	−0.185574	−	0.321424i
$473$	2.48508e13	+	4.30429e13i	0.0482619	+	0.0835921i
$474$	3.10555e14	−	5.37897e14i	0.596153	−	1.03257i
$475$	−8.88991e13			−0.168687
$476$		0			0
$477$	5.42006e14			1.00497
$478$	−2.17025e14	+	3.75899e14i	−0.397793	+	0.688997i
$479$	2.39438e13	+	4.14719e13i	0.0433858	+	0.0751465i	0.886903	−	0.461956i	$-0.152852\pi$
$479$	2.39438e13	+	4.14719e13i	0.0433858	+	0.0751465i	−0.843517	+	0.537102i	$0.819519\pi$
$480$	6.68737e13	+	1.15829e14i	0.119792	+	0.207486i
$481$	4.75167e14	−	8.23013e14i	0.841489	−	1.45750i
$482$	6.08892e14			1.06606
$483$		0			0
$484$	−2.89777e14			−0.495923
$485$	−3.22549e14	+	5.58671e14i	−0.545778	+	0.945316i
$486$	−2.42683e14	−	4.20340e14i	−0.406013	−	0.703236i
$487$	3.13073e14	+	5.42259e14i	0.517889	+	0.897010i	0.999784	+	0.0207813i	$0.00661537\pi$
$487$	3.13073e14	+	5.42259e14i	0.517889	+	0.897010i	−0.481895	+	0.876229i	$0.660051\pi$
$488$	−9.55309e13	+	1.65464e14i	−0.156255	+	0.270642i
$489$	1.52954e15			2.47379
$490$		0			0
$491$	5.32442e14			0.842024			0.421012	−	0.907055i	$-0.361675\pi$
$491$	5.32442e14			0.842024			0.421012	+	0.907055i	$0.361675\pi$
$492$	3.50213e14	−	6.06586e14i	0.547676	−	0.948603i
$493$	−8.01901e13	−	1.38893e14i	−0.124012	−	0.214795i
$494$	5.22461e14	+	9.04928e14i	0.799016	+	1.38394i
$495$	−2.09097e13	+	3.62167e13i	−0.0316242	+	0.0547748i
$496$	1.08000e14			0.161538
$497$		0			0
$498$	−6.57153e14			−0.961402
$499$	1.65784e14	−	2.87146e14i	0.239878	−	0.415480i	−0.720801	−	0.693142i	$-0.756226\pi$
$499$	1.65784e14	−	2.87146e14i	0.239878	−	0.415480i	0.960679	+	0.277662i	$0.0895594\pi$
$500$	1.64720e14	+	2.85303e14i	0.235728	+	0.408293i
$501$	2.06923e14	+	3.58400e14i	0.292887	+	0.507296i
$502$	−3.65141e14	+	6.32442e14i	−0.511199	+	0.885422i
$503$	4.32412e14			0.598789			0.299395	−	0.954129i	$-0.403215\pi$
$503$	4.32412e14			0.598789			0.299395	+	0.954129i	$0.403215\pi$
$504$		0			0
$505$	−4.83176e14			−0.654641
$506$	1.61100e13	−	2.79033e13i	0.0215907	−	0.0373963i
$507$	4.15969e14	+	7.20480e14i	0.551464	+	0.955164i
$508$	2.06914e14	+	3.58385e14i	0.271355	+	0.470001i
$509$	−2.50583e14	+	4.34023e14i	−0.325090	+	0.563073i	−0.981531	−	0.191305i	$-0.938728\pi$
$509$	−2.50583e14	+	4.34023e14i	−0.325090	+	0.563073i	0.656440	+	0.754378i	$0.272061\pi$
$510$	−8.56618e14			−1.09939
$511$		0			0
$512$	3.51844e13			0.0441942
$513$	2.86839e14	−	4.96820e14i	0.356445	−	0.617382i
$514$	−2.37267e14	−	4.10959e14i	−0.291703	−	0.505244i
$515$	1.54382e14	+	2.67398e14i	0.187783	+	0.325250i
$516$	−2.86740e14	+	4.96649e14i	−0.345076	+	0.597690i
$517$	−7.71458e13			−0.0918574
$518$		0			0
$519$	1.04684e15			1.22028
$520$	−2.19046e14	+	3.79399e14i	−0.252648	+	0.437600i
$521$	2.41341e14	+	4.18015e14i	0.275438	+	0.477073i	0.970246	−	0.242123i	$-0.0778438\pi$
$521$	2.41341e14	+	4.18015e14i	0.275438	+	0.477073i	−0.694807	+	0.719196i	$0.744510\pi$
$522$	−4.51710e13	−	7.82384e13i	−0.0510119	−	0.0883552i
$523$	9.49008e13	−	1.64373e14i	0.106050	−	0.183684i	−0.808117	−	0.589022i	$-0.799513\pi$
$523$	9.49008e13	−	1.64373e14i	0.106050	−	0.183684i	0.914167	+	0.405338i	$0.132846\pi$
$524$	6.95337e14			0.768907
$525$		0			0
$526$	1.16265e14			0.125901
$527$	−3.45856e14	+	5.99040e14i	−0.370627	+	0.641945i
$528$	1.37431e13	+	2.38037e13i	0.0145746	+	0.0252440i
$529$	2.58506e14	+	4.47746e14i	0.271309	+	0.469922i
$530$	−5.38006e14	+	9.31854e14i	−0.558818	+	0.967901i
$531$	6.81505e14			0.700566
$532$		0			0
$533$	2.29426e15			2.31016
$534$	1.54543e14	−	2.67677e14i	0.154019	−	0.266768i
$535$	−8.59158e14	−	1.48811e15i	−0.847476	−	1.46787i
$536$	−2.55321e14	−	4.42229e14i	−0.249276	−	0.431759i
$537$	−9.69611e13	+	1.67941e14i	−0.0936998	+	0.162293i
$538$	−3.42848e14			−0.327943
$539$		0			0
$540$	2.40519e14			0.225416
$541$	1.13858e14	−	1.97207e14i	0.105627	−	0.182952i	−0.808367	−	0.588679i	$-0.799648\pi$
$541$	1.13858e14	−	1.97207e14i	0.105627	−	0.182952i	0.913994	+	0.405727i	$0.132982\pi$
$542$	3.60690e14	+	6.24734e14i	0.331237	+	0.573719i
$543$	−8.82998e14	−	1.52940e15i	−0.802713	−	1.39034i
$544$	−1.12674e14	+	1.95156e14i	−0.101398	+	0.175626i
$545$	3.29944e14			0.293941
$546$		0			0
$547$	−7.92435e13			−0.0691884			−0.0345942	−	0.999401i	$-0.511014\pi$
$547$	−7.92435e13			−0.0691884			−0.0345942	+	0.999401i	$0.511014\pi$
$548$	4.36184e13	−	7.55492e13i	0.0377030	−	0.0653036i
$549$	−3.44655e14	−	5.96960e14i	−0.294942	−	0.510854i
$550$	−3.82981e12	−	6.63343e12i	−0.00324476	−	0.00562009i
$551$	2.13891e14	−	3.70469e14i	0.179415	−	0.310755i
$552$	3.71769e14			0.308751
$553$		0			0
$554$	−9.33914e14			−0.760332
$555$	−1.03901e15	+	1.79962e15i	−0.837547	+	1.45067i
$556$	−5.13634e13	−	8.89640e13i	−0.0409961	−	0.0710073i
$557$	1.05189e15	+	1.82193e15i	0.831320	+	1.43989i	0.896992	+	0.442047i	$0.145748\pi$
$557$	1.05189e15	+	1.82193e15i	0.831320	+	1.43989i	−0.0656717	+	0.997841i	$0.520919\pi$
$558$	−1.94820e14	+	3.37439e14i	−0.152457	+	0.264062i
$559$	−1.87844e15			−1.45557
$560$		0			0
$561$	−1.76042e14			−0.133758
$562$	−2.25540e14	+	3.90646e14i	−0.169697	+	0.293923i
$563$	−4.53717e14	−	7.85860e14i	−0.338056	−	0.585530i	0.646011	−	0.763328i	$-0.276436\pi$
$563$	−4.53717e14	−	7.85860e14i	−0.338056	−	0.585530i	−0.984067	+	0.177798i	$0.943103\pi$
$564$	−4.45072e14	−	7.70887e14i	−0.328394	−	0.568794i
$565$	−2.57224e14	+	4.45526e14i	−0.187951	+	0.325541i
$566$	2.94630e14			0.213200
$567$		0			0
$568$	−2.45652e13			−0.0174343
$569$	6.59225e14	−	1.14181e15i	0.463357	−	0.802559i	−0.535768	−	0.844365i	$-0.679978\pi$
$569$	6.59225e14	−	1.14181e15i	0.463357	−	0.802559i	0.999126	+	0.0418064i	$0.0133113\pi$
$570$	−1.14243e15	−	1.97874e15i	−0.795273	−	1.37745i
$571$	−5.27818e14	−	9.14207e14i	−0.363903	−	0.630298i	0.624697	−	0.780868i	$-0.285223\pi$
$571$	−5.27818e14	−	9.14207e14i	−0.363903	−	0.630298i	−0.988599	+	0.150569i	$0.951889\pi$
$572$	−4.50157e13	+	7.79695e13i	−0.0307387	+	0.0532410i
$573$	5.53927e14			0.374629
$574$		0			0
$575$	−1.03602e14			−0.0687375
$576$	−6.34688e13	+	1.09931e14i	−0.0417097	+	0.0722433i
$577$	2.07738e14	+	3.59813e14i	0.135223	+	0.234212i	0.925682	−	0.378301i	$-0.123492\pi$
$577$	2.07738e14	+	3.59813e14i	0.135223	+	0.234212i	−0.790460	+	0.612514i	$0.790158\pi$
$578$	−1.73296e14	−	3.00157e14i	−0.111734	−	0.193529i
$579$	1.94426e15	−	3.36755e15i	1.24171	−	2.15071i
$580$	1.79351e14			0.113462
$581$		0			0
$582$	−1.52969e15			−0.949568
$583$	−1.10565e14	+	1.91504e14i	−0.0679891	+	0.117761i
$584$	−1.80567e14	−	3.12752e14i	−0.109994	−	0.190515i
$585$	−7.90271e14	−	1.36879e15i	−0.476890	−	0.825998i
$586$	−7.25019e13	+	1.25577e14i	−0.0433424	+	0.0750712i
$587$	1.07334e15			0.635663			0.317831	−	0.948147i	$-0.397045\pi$
$587$	1.07334e15			0.635663			0.317831	+	0.948147i	$0.397045\pi$
$588$		0			0
$589$	−1.84500e15			−1.07241
$590$	−6.76477e14	+	1.17169e15i	−0.389553	+	0.674726i
$591$	1.84032e14	+	3.18752e14i	0.104993	+	0.181854i
$592$	2.73329e14	+	4.73419e14i	0.154496	+	0.267594i
$593$	−1.89360e14	+	3.27982e14i	−0.106044	+	0.183674i	−0.914164	−	0.405343i	$-0.867152\pi$
$593$	−1.89360e14	+	3.27982e14i	−0.106044	+	0.183674i	0.808120	+	0.589018i	$0.200485\pi$
$594$	4.94287e13			0.0274254
$595$		0			0
$596$	1.27570e15			0.694857
$597$	6.60286e14	−	1.14365e15i	0.356347	−	0.617212i
$598$	6.08868e14	+	1.05459e15i	0.325587	+	0.563932i
$599$	−2.11397e14	−	3.66151e14i	−0.112009	−	0.194005i	0.804571	−	0.593856i	$-0.202395\pi$
$599$	−2.11397e14	−	3.66151e14i	−0.112009	−	0.194005i	−0.916580	+	0.399851i	$0.869062\pi$
$600$	4.41901e13	−	7.65395e13i	0.0232003	−	0.0401841i
$601$	1.03977e15			0.540913			0.270457	−	0.962732i	$-0.412825\pi$
$601$	1.03977e15			0.540913			0.270457	+	0.962732i	$0.412825\pi$
$602$		0			0
$603$	1.84229e15			0.941049
$604$	9.09942e12	−	1.57607e13i	0.00460586	−	0.00797758i
$605$	1.03774e15	+	1.79742e15i	0.520516	+	0.901560i
$606$	−5.72865e14	−	9.92231e14i	−0.284743	−	0.493189i
$607$	−1.40054e15	+	2.42582e15i	−0.689857	+	1.19487i	0.282026	+	0.959407i	$0.408993\pi$
$607$	−1.40054e15	+	2.42582e15i	−0.689857	+	1.19487i	−0.971884	+	0.235461i	$0.924340\pi$
$608$	−6.01067e14			−0.293395
$609$		0			0
$610$	1.36845e15			0.656015
$611$	1.45784e15	−	2.52505e15i	0.692601	−	1.19962i
$612$	−4.06502e14	−	7.04082e14i	−0.191395	−	0.331505i
$613$	1.96527e15	+	3.40394e15i	0.917041	+	1.58836i	0.803885	+	0.594784i	$0.202762\pi$
$613$	1.96527e15	+	3.40394e15i	0.917041	+	1.58836i	0.113155	+	0.993577i	$0.463904\pi$
$614$	−4.13005e14	+	7.15345e14i	−0.190998	+	0.330818i
$615$	−5.01668e15			−2.29934
$616$		0			0
$617$	−5.56217e14			−0.250424			−0.125212	−	0.992130i	$-0.539961\pi$
$617$	−5.56217e14			−0.250424			−0.125212	+	0.992130i	$0.539961\pi$
$618$	−3.66078e14	+	6.34066e14i	−0.163357	+	0.282942i
$619$	1.37005e15	+	2.37299e15i	0.605950	+	1.04954i	0.991901	+	0.127017i	$0.0405402\pi$
$619$	1.37005e15	+	2.37299e15i	0.605950	+	1.04954i	−0.385951	+	0.922519i	$0.626126\pi$
$620$	−3.86766e14	−	6.69898e14i	−0.169548	−	0.293666i
$621$	3.34278e14	−	5.78987e14i	0.145246	−	0.251573i
$622$	1.96663e15			0.846985
$623$		0			0
$624$	−1.03882e15			−0.439568
$625$	1.30094e15	−	2.25329e15i	0.545654	−	0.945100i
$626$	−1.53289e14	−	2.65504e14i	−0.0637312	−	0.110386i
$627$	−2.34778e14	−	4.06647e14i	−0.0967577	−	0.167589i
$628$	1.47859e14	−	2.56100e14i	0.0604047	−	0.104624i
$629$	−3.50121e15			−1.41788
$630$		0			0
$631$	−3.78645e15			−1.50685			−0.753427	−	0.657532i	$-0.771600\pi$
$631$	−3.78645e15			−1.50685			−0.753427	+	0.657532i	$0.771600\pi$
$632$	−5.85137e14	+	1.01349e15i	−0.230842	+	0.399829i
$633$	1.13812e15	+	1.97128e15i	0.445109	+	0.770952i
$634$	−1.12532e15	−	1.94911e15i	−0.436300	−	0.755693i
$635$	1.48198e15	−	2.56687e15i	0.569624	−	0.986617i
$636$	−2.55149e15			−0.972254
$637$		0			0
$638$	3.68580e13			0.0138044
$639$	4.43129e13	−	7.67522e13i	0.0164542	−	0.0284994i
$640$	−1.26001e14	−	2.18240e14i	−0.0463857	−	0.0803424i
$641$	2.14598e15	+	3.71694e15i	0.783259	+	1.35665i	0.930033	+	0.367475i	$0.119778\pi$
$641$	2.14598e15	+	3.71694e15i	0.783259	+	1.35665i	−0.146774	+	0.989170i	$0.546889\pi$
$642$	2.03727e15	−	3.52866e15i	0.737237	−	1.27693i
$643$	−1.31472e15			−0.471707			−0.235854	−	0.971789i	$-0.575789\pi$
$643$	−1.31472e15			−0.471707			−0.235854	+	0.971789i	$0.575789\pi$
$644$		0			0
$645$	4.10746e15			1.44875
$646$	1.92484e15	−	3.33392e15i	0.673157	−	1.16594i
$647$	1.64822e15	+	2.85481e15i	0.571535	+	0.989927i	0.996409	+	0.0846745i	$0.0269851\pi$
$647$	1.64822e15	+	2.85481e15i	0.571535	+	0.989927i	−0.424874	+	0.905252i	$0.639682\pi$
$648$	6.28284e14	+	1.08822e15i	0.216020	+	0.374157i
$649$	−1.39021e14	+	2.40792e14i	−0.0473954	+	0.0820912i
$650$	2.89491e14			0.0978614
$651$		0			0
$652$	−2.88191e15			−0.957898
$653$	−8.30281e14	+	1.43809e15i	−0.273654	+	0.473983i	−0.969795	−	0.243922i	$-0.921566\pi$
$653$	−8.30281e14	+	1.43809e15i	−0.273654	+	0.473983i	0.696140	+	0.717906i	$0.254899\pi$
$654$	3.91190e14	+	6.77560e14i	0.127853	+	0.221447i
$655$	−2.49012e15	−	4.31301e15i	−0.807036	−	1.39783i
$656$	−6.59859e14	+	1.14291e15i	−0.212070	+	0.367317i
$657$	1.30290e15			0.415241
$658$		0			0
$659$	−5.53221e15			−1.73392			−0.866960	−	0.498378i	$-0.833929\pi$
$659$	−5.53221e15			−1.73392			−0.866960	+	0.498378i	$0.833929\pi$
$660$	9.84325e13	−	1.70490e14i	0.0305948	−	0.0529917i
$661$	2.37193e14	+	4.10829e14i	0.0731127	+	0.126635i	0.900264	−	0.435344i	$-0.143373\pi$
$661$	2.37193e14	+	4.10829e14i	0.0731127	+	0.126635i	−0.827151	+	0.561979i	$0.810040\pi$
$662$	8.66082e13	+	1.50010e14i	0.0264753	+	0.0458565i
$663$	3.32670e15	−	5.76201e15i	1.00853	−	1.74683i
$664$	1.23818e15			0.372272
$665$		0			0
$666$	−1.97222e15			−0.583241
$667$	2.49265e14	−	4.31739e14i	0.0731087	−	0.126628i
$668$	−3.89876e14	−	6.75286e14i	−0.113411	−	0.196434i
$669$	−7.76148e14	−	1.34433e15i	−0.223924	−	0.387848i
$670$	−1.82869e15	+	3.16739e15i	−0.523275	+	0.906339i
$671$	2.81227e14			0.0798147
$672$		0			0
$673$	4.91801e14			0.137312			0.0686558	−	0.997640i	$-0.478129\pi$
$673$	4.91801e14			0.137312			0.0686558	+	0.997640i	$0.478129\pi$
$674$	4.44379e13	−	7.69688e13i	0.0123062	−	0.0213150i
$675$	−7.94676e13	−	1.37642e14i	−0.0218283	−	0.0378077i
$676$	−7.83755e14	−	1.35750e15i	−0.213537	−	0.369857i
$677$	6.78122e14	−	1.17454e15i	0.183261	−	0.317417i	−0.759728	−	0.650241i	$-0.774668\pi$
$677$	6.78122e14	−	1.17454e15i	0.183261	−	0.317417i	0.942989	+	0.332823i	$0.108001\pi$
$678$	−1.21988e15			−0.327006
$679$		0			0
$680$	1.61401e15			0.425704
$681$	−3.45932e15	+	5.99172e15i	−0.905070	+	1.56763i
$682$	−7.94834e13	−	1.37669e14i	−0.0206283	−	0.0357292i
$683$	1.45514e15	+	2.52038e15i	0.374620	+	0.648862i	0.990270	−	0.139158i	$-0.0444397\pi$
$683$	1.45514e15	+	2.52038e15i	0.374620	+	0.648862i	−0.615650	+	0.788020i	$0.711106\pi$
$684$	1.08426e15	−	1.87799e15i	0.276901	−	0.479607i
$685$	−6.24818e14			−0.158291
$686$		0			0
$687$	9.39737e15			2.34285
$688$	5.40266e14	−	9.35768e14i	0.133620	−	0.231436i
$689$	−4.17872e15	−	7.23776e15i	−1.02527	−	1.77582i
$690$	−1.33137e15	−	2.30599e15i	−0.324062	−	0.561291i
$691$	−4.36664e12	+	7.56324e12i	−0.00105443	+	0.00182633i	−0.866552	−	0.499087i	$-0.833669\pi$
$691$	−4.36664e12	+	7.56324e12i	−0.00105443	+	0.00182633i	0.865498	+	0.500913i	$0.167002\pi$
$692$	−1.97241e15			−0.472514
$693$		0			0
$694$	1.42580e14			0.0336188
$695$	−3.67882e14	+	6.37190e14i	−0.0860581	+	0.149057i
$696$	2.12642e14	+	3.68307e14i	0.0493513	+	0.0854790i
$697$	−4.22623e15	−	7.32005e15i	−0.973135	−	1.68552i
$698$	6.80474e14	−	1.17862e15i	0.155456	−	0.269257i
$699$	−2.67653e15			−0.606662
$700$		0			0
$701$	−3.88857e15			−0.867643			−0.433821	−	0.900999i	$-0.642835\pi$
$701$	−3.88857e15			−0.867643			−0.433821	+	0.900999i	$0.642835\pi$
$702$	−9.34063e14	+	1.61785e15i	−0.206787	+	0.358165i
$703$	−4.66937e15	−	8.08759e15i	−1.02566	−	1.77650i
$704$	−2.58942e13	−	4.48501e13i	−0.00564356	−	0.00977494i
$705$	−3.18775e15	+	5.52135e15i	−0.689357	+	1.19400i
$706$	−1.41929e15			−0.304541
$707$		0			0
$708$	−3.20818e15			−0.677761
$709$	−9.52940e14	+	1.65054e15i	−0.199761	+	0.345997i	−0.948451	−	0.316924i	$-0.897350\pi$
$709$	−9.52940e14	+	1.65054e15i	−0.199761	+	0.345997i	0.748690	+	0.662921i	$0.230683\pi$
$710$	8.79719e13	+	1.52372e14i	0.0182988	+	0.0316945i
$711$	−2.11105e15	−	3.65645e15i	−0.435728	−	0.754704i
$712$	−2.91185e14	+	5.04348e14i	−0.0596389	+	0.103298i
$713$	−2.15013e15			−0.436992
$714$		0			0
$715$	6.44835e14			0.129052
$716$	1.82691e14	−	3.16430e14i	0.0362823	−	0.0628428i
$717$	3.68588e15	+	6.38413e15i	0.726417	+	1.25819i
$718$	1.82312e15	+	3.15774e15i	0.356558	+	0.617577i
$719$	−4.17626e14	+	7.23350e14i	−0.0810548	+	0.140391i	−0.903703	−	0.428159i	$-0.859162\pi$
$719$	−4.17626e14	+	7.23350e14i	−0.0810548	+	0.140391i	0.822648	+	0.568550i	$0.192496\pi$
$720$	9.09170e14			0.175112
$721$		0			0
$722$	6.54054e15			1.24068
$723$	5.17060e15	−	8.95574e15i	0.973375	−	1.68594i
$724$	1.66371e15	+	2.88164e15i	0.310825	+	0.538365i
$725$	−5.92575e13	−	1.02637e14i	−0.0109871	−	0.0190303i
$726$	−2.46074e15	+	4.26212e15i	−0.452807	+	0.784285i
$727$	3.30709e14			0.0603958			0.0301979	−	0.999544i	$-0.490386\pi$
$727$	3.30709e14			0.0603958			0.0301979	+	0.999544i	$0.490386\pi$
$728$		0			0
$729$	−1.45017e15			−0.260865
$730$	−1.29328e15	+	2.24003e15i	−0.230897	+	0.399925i
$731$	3.46027e15	+	5.99336e15i	0.613146	+	1.06200i
$732$	1.62246e15	+	2.81019e15i	0.285341	+	0.494225i
$733$	−5.53730e15	+	9.59089e15i	−0.966554	+	1.67412i	−0.261175	+	0.965291i	$0.584110\pi$
$733$	−5.53730e15	+	9.59089e15i	−0.966554	+	1.67412i	−0.705379	+	0.708830i	$0.749223\pi$
$734$	−3.02931e15			−0.524825
$735$		0			0
$736$	−7.00474e14			−0.119554
$737$	−3.75812e14	+	6.50925e14i	−0.0636647	+	0.110271i
$738$	−2.38063e15	−	4.12337e15i	−0.400296	−	0.693334i
$739$	2.45965e14	+	4.26025e14i	0.0410516	+	0.0711034i	0.885821	−	0.464027i	$-0.153596\pi$
$739$	2.45965e14	+	4.26025e14i	0.0410516	+	0.0711034i	−0.844770	+	0.535130i	$0.820263\pi$
$740$	1.95767e15	−	3.39079e15i	0.324314	−	0.561728i
$741$	1.77466e16			2.91820
$742$		0			0
$743$	−1.54271e15			−0.249945			−0.124973	−	0.992160i	$-0.539884\pi$
$743$	−1.54271e15			−0.249945			−0.124973	+	0.992160i	$0.539884\pi$
$744$	9.17116e14	−	1.58849e15i	0.147494	−	0.255466i
$745$	−4.56851e15	−	7.91289e15i	−0.729315	−	1.26321i
$746$	3.56233e15	+	6.17013e15i	0.564508	+	0.977757i
$747$	−2.23355e15	+	3.86863e15i	−0.351344	+	0.608546i
$748$	3.31692e14			0.0517937
$749$		0			0
$750$	5.59509e15			0.860934
$751$	−2.85390e15	+	4.94310e15i	−0.435933	+	0.755057i	−0.997371	−	0.0724610i	$-0.976915\pi$
$751$	−2.85390e15	+	4.94310e15i	−0.435933	+	0.755057i	0.561439	+	0.827518i	$0.310248\pi$
$752$	8.38588e14	+	1.45248e15i	0.127160	+	0.220248i
$753$	6.20142e15	+	1.07412e16i	0.933510	+	1.61689i
$754$	−6.96513e14	+	1.20640e15i	−0.104085	+	0.180280i
$755$	−1.30346e14			−0.0193370
$756$		0			0
$757$	6.10745e15			0.892962			0.446481	−	0.894793i	$-0.352677\pi$
$757$	6.10745e15			0.892962			0.446481	+	0.894793i	$0.352677\pi$
$758$	8.34468e14	−	1.44534e15i	0.121124	−	0.209792i
$759$	−2.73607e14	−	4.73900e14i	−0.0394273	−	0.0682900i
$760$	2.15252e15	+	3.72827e15i	0.307944	+	0.533376i
$761$	5.53570e15	−	9.58812e15i	0.786244	−	1.36181i	−0.142009	−	0.989865i	$-0.545356\pi$
$761$	5.53570e15	−	9.58812e15i	0.786244	−	1.36181i	0.928253	−	0.371949i	$-0.121310\pi$
$762$	7.02829e15			0.991055
$763$		0			0
$764$	−1.04369e15			−0.145063
$765$	−2.91150e15	+	5.04287e15i	−0.401772	+	0.695889i
$766$	1.27909e15	+	2.21544e15i	0.175244	+	0.303531i
$767$	−5.25423e15	−	9.10059e15i	−0.714718	−	1.23793i
$768$	2.98779e14	−	5.17501e14i	0.0403519	−	0.0698916i
$769$	4.18888e15			0.561699			0.280849	−	0.959752i	$-0.409384\pi$
$769$	4.18888e15			0.561699			0.280849	+	0.959752i	$0.409384\pi$
$770$		0			0
$771$	−8.05933e15			−1.06537
$772$	−3.66330e15	+	6.34502e15i	−0.480814	+	0.832794i
$773$	−5.41511e15	−	9.37925e15i	−0.705700	−	1.22231i	−0.966438	−	0.256899i	$-0.917299\pi$
$773$	−5.41511e15	−	9.37925e15i	−0.705700	−	1.22231i	0.260738	−	0.965410i	$-0.416034\pi$
$774$	1.94916e15	+	3.37605e15i	0.252216	+	0.436851i
$775$	−2.55575e14	+	4.42668e14i	−0.0328366	+	0.0568747i
$776$	2.88218e15			0.367690
$777$		0			0
$778$	−7.26212e14			−0.0913431
$779$	1.12726e16	−	1.95247e16i	1.40789	−	2.43853i
$780$	3.72020e15	+	6.44357e15i	0.461366	+	0.799109i
$781$	1.80789e13	+	3.13136e13i	0.00222634	+	0.00385614i
$782$	2.24318e15	−	3.88530e15i	0.274301	−	0.475103i
$783$	7.64794e14			0.0928656
$784$		0			0
$785$	−2.11803e15			−0.253600
$786$	5.90468e15	−	1.02272e16i	0.702057	−	1.21600i
$787$	−1.54134e15	−	2.66968e15i	−0.181986	−	0.315209i	0.760571	−	0.649255i	$-0.224919\pi$
$787$	−1.54134e15	−	2.66968e15i	−0.181986	−	0.315209i	−0.942557	+	0.334046i	$0.891586\pi$
$788$	−3.46746e14	−	6.00582e14i	−0.0406553	−	0.0704171i
$789$	9.87305e14	−	1.71006e15i	0.114955	−	0.199108i
$790$	8.38190e15			0.969155
$791$		0			0
$792$	1.86842e14			0.0213052
$793$	−5.31440e15	+	9.20481e15i	−0.601800	+	1.04235i
$794$	7.78530e14	+	1.34845e15i	0.0875513	+	0.151643i
$795$	9.13731e15	+	1.58263e16i	1.02047	+	1.76750i
$796$	−1.24409e15	+	2.15482e15i	−0.137984	+	0.238996i
$797$	1.25665e16			1.38418			0.692092	−	0.721809i	$-0.256689\pi$
$797$	1.25665e16			1.38418			0.692092	+	0.721809i	$0.256689\pi$
$798$		0			0
$799$	−1.07419e16			−1.16701
$800$	−8.32615e13	+	1.44213e14i	−0.00898358	+	0.0155600i
$801$	−1.05053e15	−	1.81958e15i	−0.112572	−	0.194981i
$802$	−3.08560e15	−	5.34442e15i	−0.328383	−	0.568777i
$803$	−2.65780e14	+	4.60345e14i	−0.0280923	+	0.0486573i
$804$	−8.67257e15			−0.910415
$805$		0			0
$806$	6.00806e15			0.622145
$807$	−2.91140e15	+	5.04270e15i	−0.299432	+	0.518631i
$808$	1.07937e15	+	1.86953e15i	0.110258	+	0.190972i
$809$	1.62040e15	+	2.80662e15i	0.164402	+	0.284752i	0.936443	−	0.350821i	$-0.114097\pi$
$809$	1.62040e15	+	2.80662e15i	0.164402	+	0.284752i	−0.772041	+	0.635573i	$0.780764\pi$
$810$	4.49998e15	−	7.79419e15i	0.453464	−	0.785423i
$811$	1.25754e15			0.125866			0.0629328	−	0.998018i	$-0.479955\pi$
$811$	1.25754e15			0.125866			0.0629328	+	0.998018i	$0.479955\pi$
$812$		0			0
$813$	1.22517e16			1.20975
$814$	4.02317e14	−	6.96834e14i	0.0394579	−	0.0683432i
$815$	1.03206e16	+	1.78758e16i	1.00540	+	1.74140i
$816$	1.91361e15	+	3.31447e15i	0.185164	+	0.320714i
$817$	−9.22955e15	+	1.59860e16i	−0.887073	+	1.53645i
$818$	−4.23656e15			−0.404455
$819$		0			0
$820$	9.45225e15			0.890347
$821$	−9.13860e15	+	1.58285e16i	−0.855051	+	1.48099i	0.0215461	+	0.999768i	$0.493141\pi$
$821$	−9.13860e15	+	1.58285e16i	−0.855051	+	1.48099i	−0.876597	+	0.481224i	$0.840192\pi$
$822$	−7.40799e14	−	1.28310e15i	−0.0688502	−	0.119252i
$823$	2.21039e15	+	3.82850e15i	0.204065	+	0.353451i	0.949834	−	0.312753i	$-0.101251\pi$
$823$	2.21039e15	+	3.82850e15i	0.204065	+	0.353451i	−0.745769	+	0.666204i	$0.767918\pi$
$824$	6.89751e14	−	1.19468e15i	0.0632547	−	0.109560i
$825$	−1.30088e14			−0.0118506
$826$		0			0
$827$	1.42765e16			1.28334			0.641668	−	0.766982i	$-0.278243\pi$
$827$	1.42765e16			1.28334			0.641668	+	0.766982i	$0.278243\pi$
$828$	1.26358e15	−	2.18859e15i	0.112833	−	0.195432i
$829$	−3.51984e15	−	6.09655e15i	−0.312229	−	0.540797i	0.666616	−	0.745402i	$-0.267742\pi$
$829$	−3.51984e15	−	6.09655e15i	−0.312229	−	0.540797i	−0.978845	+	0.204605i	$0.934409\pi$
$830$	−4.43414e15	−	7.68016e15i	−0.390733	−	0.676770i
$831$	−7.93063e15	+	1.37363e16i	−0.694228	+	1.20244i
$832$	1.95731e15			0.170209
$833$		0			0
$834$	−1.74468e15			−0.149728
$835$	−2.79242e15	+	4.83662e15i	−0.238071	+	0.412350i
$836$	4.42360e14	+	7.66190e14i	0.0374664	+	0.0648936i
$837$	−1.64926e15	−	2.85660e15i	−0.138771	−	0.240359i
$838$	6.86549e15	−	1.18914e16i	0.573891	−	0.994009i
$839$	−8.54484e15			−0.709599			−0.354799	−	0.934942i	$-0.615451\pi$
$839$	−8.54484e15			−0.709599			−0.354799	+	0.934942i	$0.615451\pi$
$840$		0			0
$841$	−1.16302e16			−0.953257
$842$	−3.31161e14	+	5.73587e14i	−0.0269664	+	0.0467071i
$843$	3.83049e15	+	6.63460e15i	0.309886	+	0.536739i
$844$	−2.14440e15	−	3.71421e15i	−0.172355	−	0.298527i
$845$	−5.61351e15	+	9.72289e15i	−0.448252	+	0.776396i
$846$	−6.05090e15			−0.480046
$847$		0			0
$848$	4.80743e15			0.376475
$849$	2.50195e15	−	4.33350e15i	0.194664	−	0.337168i
$850$	−5.33269e14	−	9.23649e14i	−0.0412233	−	0.0714008i
$851$	−5.44161e15	−	9.42515e15i	−0.417941	−	0.723895i
$852$	−2.08603e14	+	3.61311e14i	−0.0159185	+	0.0275717i
$853$	−3.53834e15			−0.268275			−0.134137	−	0.990963i	$-0.542826\pi$
$853$	−3.53834e15			−0.268275			−0.134137	+	0.990963i	$0.542826\pi$
$854$		0			0
$855$	−1.55317e16			−1.16253
$856$	−3.83856e15	+	6.64858e15i	−0.285472	+	0.494451i
$857$	1.32869e15	+	2.30135e15i	0.0981812	+	0.170055i	0.910932	−	0.412557i	$-0.135364\pi$
$857$	1.32869e15	+	2.30135e15i	0.0981812	+	0.170055i	−0.812751	+	0.582612i	$0.802031\pi$
$858$	7.64531e14	+	1.32421e15i	0.0561326	+	0.0972244i
$859$	5.56134e15	−	9.63252e15i	0.405711	−	0.702712i	−0.588693	−	0.808357i	$-0.700357\pi$
$859$	5.56134e15	−	9.63252e15i	0.405711	−	0.702712i	0.994404	+	0.105645i	$0.0336906\pi$
$860$	−7.73913e15			−0.560984
$861$		0			0
$862$	−7.13456e15			−0.510595
$863$	−1.21561e15	+	2.10549e15i	−0.0864437	+	0.149725i	−0.906005	−	0.423266i	$-0.860884\pi$
$863$	−1.21561e15	+	2.10549e15i	−0.0864437	+	0.149725i	0.819562	+	0.572991i	$0.194217\pi$
$864$	−5.37298e14	−	9.30628e14i	−0.0379656	−	0.0657583i
$865$	7.06355e15	+	1.22344e16i	0.495946	+	0.859003i
$866$	−5.53419e15	+	9.58550e15i	−0.386105	+	0.668754i
$867$	−5.88639e15			−0.408079
$868$		0			0
$869$	1.72255e15			0.117913
$870$	1.52301e15	−	2.63794e15i	0.103597	−	0.179436i
$871$	−1.42036e16	−	2.46013e16i	−0.960059	−	1.66287i
$872$	−7.37066e14	−	1.27664e15i	−0.0495069	−	0.0857485i
$873$	−5.19915e15	+	9.00519e15i	−0.347019	+	0.601055i
$874$	1.19664e16			0.793692
$875$		0			0
$876$	−6.13339e15			−0.401724
$877$	−1.20004e16	+	2.07853e16i	−0.781085	+	1.35288i	0.150225	+	0.988652i	$0.452000\pi$
$877$	−1.20004e16	+	2.07853e16i	−0.781085	+	1.35288i	−0.931310	+	0.364228i	$0.881333\pi$
$878$	−4.90638e15	−	8.49809e15i	−0.317352	−	0.549670i
$879$	1.23135e15	+	2.13276e15i	0.0791483	+	0.137089i
$880$	−1.85463e14	+	3.21232e14i	−0.0118468	+	0.0205193i
$881$	−2.29807e16			−1.45880			−0.729398	−	0.684089i	$-0.760200\pi$
$881$	−2.29807e16			−1.45880			−0.729398	+	0.684089i	$0.760200\pi$
$882$		0			0
$883$	−2.90107e16			−1.81875			−0.909376	−	0.415974i	$-0.863441\pi$
$883$	−2.90107e16			−1.81875			−0.909376	+	0.415974i	$0.863441\pi$
$884$	−6.26805e15	+	1.08566e16i	−0.390522	+	0.676404i
$885$	1.14890e16	+	1.98996e16i	0.711370	+	1.23213i
$886$	3.16862e15	+	5.48821e15i	0.194978	+	0.337711i
$887$	9.00978e15	−	1.56054e16i	0.550978	−	0.954322i	−0.447226	−	0.894421i	$-0.647588\pi$
$887$	9.00978e15	−	1.56054e16i	0.550978	−	0.954322i	0.998204	−	0.0599012i	$-0.0190786\pi$
$888$	9.28424e15			0.564254
$889$		0			0
$890$	4.17113e15			0.250385
$891$	9.24782e14	−	1.60177e15i	0.0551711	−	0.0955592i
$892$	1.46239e15	+	2.53294e15i	0.0867076	+	0.150182i
$893$	−1.43259e16	−	2.48132e16i	−0.844187	−	1.46218i
$894$	1.08331e16	−	1.87634e16i	0.634446	−	1.09889i
$895$	−2.61698e15			−0.152326
$896$		0			0
$897$	2.06816e16			1.18912
$898$	3.31786e15	−	5.74671e15i	0.189600	−	0.328397i
$899$	−1.22982e15	−	2.13011e15i	−0.0698496	−	0.120983i
$900$	−3.00390e14	−	5.20290e14i	−0.0169571	−	0.0293705i
$901$	−1.53952e16	+	2.66653e16i	−0.863771	+	1.49610i
$902$	1.94251e15			0.108325
$903$		0			0
$904$	2.29846e15			0.126623
$905$	1.19161e16	−	2.06392e16i	0.652478	−	1.13012i
$906$	−1.54541e14	−	2.67673e14i	−0.00841085	−	0.0145680i
$907$	−1.13720e16	−	1.96969e16i	−0.615174	−	1.06551i	−0.990354	−	0.138560i	$-0.955753\pi$
$907$	−1.13720e16	−	1.96969e16i	−0.615174	−	1.06551i	0.375180	−	0.926952i	$-0.377581\pi$
$908$	6.51794e15	−	1.12894e16i	0.350460	−	0.607014i
$909$	−7.78829e15			−0.416237
$910$		0			0
$911$	−3.36472e15			−0.177663			−0.0888317	−	0.996047i	$-0.528313\pi$
$911$	−3.36472e15			−0.177663			−0.0888317	+	0.996047i	$0.528313\pi$
$912$	−5.10415e15	+	8.84065e15i	−0.267887	+	0.463994i
$913$	−9.11252e14	−	1.57834e15i	−0.0475389	−	0.0823398i
$914$	8.59517e14	+	1.48873e15i	0.0445708	+	0.0771989i
$915$	1.16206e16	−	2.01275e16i	0.598981	−	1.03747i
$916$	−1.77062e16			−0.907194
$917$		0			0
$918$	6.88253e15			0.348428
$919$	1.79742e16	−	3.11322e16i	0.904510	−	1.56666i	0.0829360	−	0.996555i	$-0.473570\pi$
$919$	1.79742e16	−	3.11322e16i	0.904510	−	1.56666i	0.821574	−	0.570102i	$-0.193096\pi$
$920$	2.50851e15	+	4.34487e15i	0.125483	+	0.217342i
$921$	7.01433e15	+	1.21492e16i	0.348785	+	0.604114i
$922$	−7.26911e15	+	1.25905e16i	−0.359303	+	0.622332i
$923$	−1.36657e15			−0.0671461
$924$		0			0
$925$	−2.58726e15			−0.125620
$926$	1.16008e16	−	2.00932e16i	0.559923	−	0.969815i
$927$	2.48848e15	+	4.31017e15i	0.119397	+	0.206802i
$928$	−4.00653e14	−	6.93952e14i	−0.0191097	−	0.0330990i
$929$	1.91078e16	−	3.30958e16i	0.905994	−	1.56923i	0.0864167	−	0.996259i	$-0.472458\pi$
$929$	1.91078e16	−	3.30958e16i	0.905994	−	1.56923i	0.819577	−	0.572969i	$-0.194208\pi$
$930$	−1.31374e16			−0.619231
$931$		0			0
$932$	5.04302e15			0.234911
$933$	1.67003e16	−	2.89257e16i	0.773348	−	1.33948i
$934$	−1.15825e16	−	2.00616e16i	−0.533207	−	0.923542i
$935$	−1.18785e15	−	2.05741e15i	−0.0543621	−	0.0941579i
$936$	−3.53079e15	+	6.11550e15i	−0.160640	+	0.278237i
$937$	2.12364e16			0.960535			0.480268	−	0.877122i	$-0.340540\pi$
$937$	2.12364e16			0.960535			0.480268	+	0.877122i	$0.340540\pi$
$938$		0			0
$939$	−5.20681e15			−0.232761
$940$	6.00625e15	−	1.04031e16i	0.266932	−	0.462339i
$941$	1.30780e15	+	2.26518e15i	0.0577828	+	0.100083i	0.893470	−	0.449123i	$-0.148264\pi$
$941$	1.30780e15	+	2.26518e15i	0.0577828	+	0.100083i	−0.835687	+	0.549206i	$0.814930\pi$
$942$	−2.51119e15	−	4.34951e15i	−0.110306	−	0.191056i
$943$	1.31369e16	−	2.27538e16i	0.573692	−	0.993664i
$944$	6.04475e15			0.262441
$945$		0			0
$946$	−1.59045e15			−0.0682527
$947$	−2.83119e14	+	4.90377e14i	−0.0120794	+	0.0209221i	−0.872002	−	0.489502i	$-0.837178\pi$
$947$	−2.83119e14	+	4.90377e14i	−0.0120794	+	0.0209221i	0.859923	+	0.510425i	$0.170512\pi$
$948$	9.93777e15	+	1.72127e16i	0.421544	+	0.730136i
$949$	−1.00450e16	−	1.73985e16i	−0.423629	−	0.733747i
$950$	1.42239e15	−	2.46364e15i	0.0596400	−	0.103299i
$951$	−3.82241e16			−1.59347
$952$		0			0
$953$	2.88196e16			1.18762			0.593809	−	0.804606i	$-0.297624\pi$
$953$	2.88196e16			1.18762			0.593809	+	0.804606i	$0.297624\pi$
$954$	−8.67209e15	+	1.50205e16i	−0.355310	+	0.615415i
$955$	3.73762e15	+	6.47376e15i	0.152257	+	0.263717i
$956$	−6.94481e15	−	1.20288e16i	−0.281282	−	0.487194i
$957$	3.12992e14	−	5.42118e14i	0.0126043	−	0.0218312i
$958$	−1.53240e15			−0.0613568
$959$		0			0
$960$	−4.27992e15			−0.169412
$961$	7.40008e15	−	1.28173e16i	0.291244	−	0.504450i
$962$	1.52053e16	+	2.63364e16i	0.595022	+	1.03061i
$963$	−1.38487e16	−	2.39867e16i	−0.538846	−	0.933309i
$964$	−9.74227e15	+	1.68741e16i	−0.376909	+	0.652825i
$965$	5.24755e16			2.01863
$966$		0			0
$967$	1.83108e16			0.696407			0.348203	−	0.937419i	$-0.386792\pi$
$967$	1.83108e16			0.696407			0.348203	+	0.937419i	$0.386792\pi$
$968$	4.63643e15	−	8.03054e15i	0.175335	−	0.303690i
$969$	−3.26908e16	−	5.66222e16i	−1.22926	−	2.12915i
$970$	−1.03216e16	−	1.78775e16i	−0.385924	−	0.668439i
$971$	1.63293e16	−	2.82832e16i	0.607103	−	1.05153i	−0.384613	−	0.923078i	$-0.625665\pi$
$971$	1.63293e16	−	2.82832e16i	0.607103	−	1.05153i	0.991715	−	0.128455i	$-0.0410017\pi$
$972$	1.55317e16			0.574190
$973$		0			0
$974$	−2.00367e16			−0.732406
$975$	2.45831e15	−	4.25791e15i	0.0893533	−	0.154764i
$976$	−3.05699e15	−	5.29486e15i	−0.110489	−	0.191373i
$977$	2.64853e16	+	4.58739e16i	0.951885	+	1.64871i	0.741340	+	0.671129i	$0.234190\pi$
$977$	2.64853e16	+	4.58739e16i	0.951885	+	1.64871i	0.210545	+	0.977584i	$0.432476\pi$
$978$	−2.44727e16	+	4.23880e16i	−0.874618	+	1.51488i
$979$	8.57201e14			0.0304634
$980$		0			0
$981$	5.31835e15			0.186895
$982$	−8.51908e15	+	1.47555e16i	−0.297700	+	0.515632i
$983$	1.40471e16	+	2.43304e16i	0.488139	+	0.845482i	0.999907	−	0.0136420i	$-0.00434253\pi$
$983$	1.40471e16	+	2.43304e16i	0.488139	+	0.845482i	−0.511768	+	0.859124i	$0.671009\pi$
$984$	1.12068e16	+	1.94108e16i	0.387266	+	0.670764i
$985$	−2.48351e15	+	4.30156e15i	−0.0853427	+	0.147818i
$986$	5.13217e15			0.175379
$987$		0			0
$988$	−3.34375e16			−1.12998
$989$	−1.07560e16	+	1.86299e16i	−0.361468	+	0.626082i
$990$	−6.69111e14	−	1.15893e15i	−0.0223617	−	0.0387316i
$991$	−1.56466e16	−	2.71007e16i	−0.520014	−	0.900690i	−0.999729	−	0.0232660i	$-0.992594\pi$
$991$	−1.56466e16	−	2.71007e16i	−0.520014	−	0.900690i	0.479716	−	0.877424i	$-0.340740\pi$
$992$	−1.72800e15	+	2.99298e15i	−0.0571122	+	0.0989213i
$993$	2.94185e15			0.0966939
$994$		0			0
$995$	1.78211e16			0.579307
$996$	1.05144e16	−	1.82115e16i	0.339907	−	0.588736i
$997$	2.20997e16	+	3.82777e16i	0.710497	+	1.23062i	0.964671	+	0.263459i	$0.0848632\pi$
$997$	2.20997e16	+	3.82777e16i	0.710497	+	1.23062i	−0.254174	+	0.967159i	$0.581803\pi$
$998$	5.30509e15	+	9.18868e15i	0.169619	+	0.293789i
$999$	8.34798e15	−	1.44591e16i	0.265443	−	0.459760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.12.c.l.79.4		8
7.2	even	3		98.12.a.l.1.1		4
7.3	odd	6		14.12.c.a.11.1	yes	8
7.4	even	3	inner	98.12.c.l.67.4		8
7.5	odd	6		98.12.a.j.1.4		4
7.6	odd	2		14.12.c.a.9.1	✓	8
21.17	even	6		126.12.g.e.109.2		8
21.20	even	2		126.12.g.e.37.2		8
28.3	even	6		112.12.i.a.81.4		8
28.27	even	2		112.12.i.a.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.c.a.9.1	✓	8	7.6	odd	2
14.12.c.a.11.1	yes	8	7.3	odd	6
98.12.a.j.1.4		4	7.5	odd	6
98.12.a.l.1.1		4	7.2	even	3
98.12.c.l.67.4		8	7.4	even	3	inner
98.12.c.l.79.4		8	1.1	even	1	trivial
112.12.i.a.65.4		8	28.27	even	2
112.12.i.a.81.4		8	28.3	even	6
126.12.g.e.37.2		8	21.20	even	2
126.12.g.e.109.2		8	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-16.0000 + 27.7128i) q^{2} +(271.738 + 470.665i) q^{3} +(-512.000 - 886.810i) q^{4} +(-3667.11 + 6351.63i) q^{5} -17391.3 q^{6} +32768.0 q^{8} +(-59110.0 + 102381. i) q^{9} +O(q^{10})\)	\(q+(-16.0000 + 27.7128i) q^{2} +(271.738 + 470.665i) q^{3} +(-512.000 - 886.810i) q^{4} +(-3667.11 + 6351.63i) q^{5} -17391.3 q^{6} +32768.0 q^{8} +(-59110.0 + 102381. i) q^{9} +(-117348. - 203252. i) q^{10} +(-24115.9 - 41769.9i) q^{11} +(278260. - 481961. i) q^{12} +1.82289e6 q^{13} -3.98598e6 q^{15} +(-524288. + 908093. i) q^{16} +(-3.35793e6 - 5.81611e6i) q^{17} +(-1.89152e6 - 3.27621e6i) q^{18} +(8.95659e6 - 1.55133e7i) q^{19} +7.51025e6 q^{20} +1.54342e6 q^{22} +(1.04379e7 - 1.80789e7i) q^{23} +(8.90432e6 + 1.54227e7i) q^{24} +(-2.48139e6 - 4.29789e6i) q^{25} +(-2.91663e7 + 5.05174e7i) q^{26} +3.20255e7 q^{27} +2.38808e7 q^{29} +(6.37757e7 - 1.10463e8i) q^{30} +(-5.14984e7 - 8.91978e7i) q^{31} +(-1.67772e7 - 2.90590e7i) q^{32} +(1.31064e7 - 2.27010e7i) q^{33} +2.14908e8 q^{34} +1.21057e8 q^{36} +(2.60667e8 - 4.51488e8i) q^{37} +(2.86611e8 + 4.96425e8i) q^{38} +(4.95349e8 + 8.57970e8i) q^{39} +(-1.20164e8 + 2.08130e8i) q^{40} +1.25858e9 q^{41} -1.03048e9 q^{43} +(-2.46947e7 + 4.27724e7i) q^{44} +(-4.33526e8 - 7.50889e8i) q^{45} +(3.34012e8 + 5.78526e8i) q^{46} +(7.99740e8 - 1.38519e9i) q^{47} -5.69877e8 q^{48} +1.58809e8 q^{50} +(1.82496e9 - 3.16092e9i) q^{51} +(-9.33320e8 - 1.61656e9i) q^{52} +(-2.29236e9 - 3.97049e9i) q^{53} +(-5.12408e8 + 8.87516e8i) q^{54} +3.53743e8 q^{55} +9.73540e9 q^{57} +(-3.82093e8 + 6.61804e8i) q^{58} +(-2.88236e9 - 4.99240e9i) q^{59} +(2.04082e9 + 3.53481e9i) q^{60} +(-2.91537e9 + 5.04957e9i) q^{61} +3.29590e9 q^{62} +1.07374e9 q^{64} +(-6.68475e9 + 1.15783e10i) q^{65} +(4.19406e8 + 7.26432e8i) q^{66} +(-7.79178e9 - 1.34958e10i) q^{67} +(-3.43852e9 + 5.95570e9i) q^{68} +1.13455e10 q^{69} -7.49669e8 q^{71} +(-1.93692e9 + 3.35484e9i) q^{72} +(-5.51048e9 - 9.54443e9i) q^{73} +(8.34133e9 + 1.44476e10i) q^{74} +(1.34858e9 - 2.33580e9i) q^{75} -1.83431e10 q^{76} -3.17024e10 q^{78} +(-1.78570e10 + 3.09292e10i) q^{79} +(-3.84525e9 - 6.66016e9i) q^{80} +(1.91737e10 + 3.32098e10i) q^{81} +(-2.01373e10 + 3.48788e10i) q^{82} +3.77864e10 q^{83} +4.92557e10 q^{85} +(1.64876e10 - 2.85574e10i) q^{86} +(6.48933e9 + 1.12398e10i) q^{87} +(-7.90229e8 - 1.36872e9i) q^{88} +(-8.88627e9 + 1.53915e10i) q^{89} +2.77457e10 q^{90} -2.13768e10 q^{92} +(2.79882e10 - 4.84769e10i) q^{93} +(2.55917e10 + 4.43261e10i) q^{94} +(6.56897e10 + 1.13778e11i) q^{95} +(9.11803e9 - 1.57929e10i) q^{96} +8.79572e10 q^{97} +5.70196e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{2} - 266 q^{3} - 4096 q^{4} - 7504 q^{5} + 17024 q^{6} + 262144 q^{8} - 123520 q^{9}+O(q^{10}) \) 8 * q - 128 * q^2 - 266 * q^3 - 4096 * q^4 - 7504 * q^5 + 17024 * q^6 + 262144 * q^8 - 123520 * q^9	\( 8 q - 128 q^{2} - 266 q^{3} - 4096 q^{4} - 7504 q^{5} + 17024 q^{6} + 262144 q^{8} - 123520 q^{9} - 240128 q^{10} + 213026 q^{11} - 272384 q^{12} + 2609712 q^{13} + 2275500 q^{15} - 4194304 q^{16} - 8854244 q^{17} - 3952640 q^{18} - 7232806 q^{19} + 15368192 q^{20} - 13633664 q^{22} - 10649134 q^{23} - 8716288 q^{24} - 119407256 q^{25} - 41755392 q^{26} - 19012196 q^{27} - 221414576 q^{29} - 36408000 q^{30} - 486231270 q^{31} - 134217728 q^{32} - 489871116 q^{33} + 566671616 q^{34} + 252968960 q^{36} + 463131040 q^{37} - 231449792 q^{38} + 493924396 q^{39} - 245891072 q^{40} + 1617723408 q^{41} + 2926896352 q^{43} + 218138624 q^{44} - 2871035832 q^{45} - 340772288 q^{46} + 894091254 q^{47} + 557842432 q^{48} + 7642064384 q^{50} + 6950287158 q^{51} - 1336172544 q^{52} - 1448863512 q^{53} + 304195136 q^{54} + 25123348964 q^{55} + 18014730520 q^{57} + 3542633216 q^{58} - 14386900738 q^{59} - 1165056000 q^{60} - 10854402216 q^{61} + 31118801280 q^{62} + 8589934592 q^{64} + 5495584080 q^{65} - 15675875712 q^{66} + 19629545546 q^{67} - 9066745856 q^{68} + 92767078992 q^{69} + 1474804928 q^{71} - 4047503360 q^{72} - 21420158732 q^{73} + 14820193280 q^{74} - 63738659600 q^{75} + 14812786688 q^{76} - 31611161344 q^{78} - 60246238086 q^{79} - 7868514304 q^{80} + 100835656724 q^{81} - 25883574528 q^{82} + 139893582304 q^{83} + 109585554592 q^{85} - 46830341632 q^{86} + 77636109684 q^{87} + 6980435968 q^{88} - 126354105612 q^{89} + 183746293248 q^{90} + 21809426432 q^{92} - 213975312128 q^{93} + 28610920128 q^{94} + 368499346550 q^{95} - 8925478912 q^{96} + 538182884176 q^{97} + 393415805736 q^{99}+O(q^{100}) \) 8 * q - 128 * q^2 - 266 * q^3 - 4096 * q^4 - 7504 * q^5 + 17024 * q^6 + 262144 * q^8 - 123520 * q^9 - 240128 * q^10 + 213026 * q^11 - 272384 * q^12 + 2609712 * q^13 + 2275500 * q^15 - 4194304 * q^16 - 8854244 * q^17 - 3952640 * q^18 - 7232806 * q^19 + 15368192 * q^20 - 13633664 * q^22 - 10649134 * q^23 - 8716288 * q^24 - 119407256 * q^25 - 41755392 * q^26 - 19012196 * q^27 - 221414576 * q^29 - 36408000 * q^30 - 486231270 * q^31 - 134217728 * q^32 - 489871116 * q^33 + 566671616 * q^34 + 252968960 * q^36 + 463131040 * q^37 - 231449792 * q^38 + 493924396 * q^39 - 245891072 * q^40 + 1617723408 * q^41 + 2926896352 * q^43 + 218138624 * q^44 - 2871035832 * q^45 - 340772288 * q^46 + 894091254 * q^47 + 557842432 * q^48 + 7642064384 * q^50 + 6950287158 * q^51 - 1336172544 * q^52 - 1448863512 * q^53 + 304195136 * q^54 + 25123348964 * q^55 + 18014730520 * q^57 + 3542633216 * q^58 - 14386900738 * q^59 - 1165056000 * q^60 - 10854402216 * q^61 + 31118801280 * q^62 + 8589934592 * q^64 + 5495584080 * q^65 - 15675875712 * q^66 + 19629545546 * q^67 - 9066745856 * q^68 + 92767078992 * q^69 + 1474804928 * q^71 - 4047503360 * q^72 - 21420158732 * q^73 + 14820193280 * q^74 - 63738659600 * q^75 + 14812786688 * q^76 - 31611161344 * q^78 - 60246238086 * q^79 - 7868514304 * q^80 + 100835656724 * q^81 - 25883574528 * q^82 + 139893582304 * q^83 + 109585554592 * q^85 - 46830341632 * q^86 + 77636109684 * q^87 + 6980435968 * q^88 - 126354105612 * q^89 + 183746293248 * q^90 + 21809426432 * q^92 - 213975312128 * q^93 + 28610920128 * q^94 + 368499346550 * q^95 - 8925478912 * q^96 + 538182884176 * q^97 + 393415805736 * q^99

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