LMFDB - Embedded newform 20.11.d.d.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.d (of order $2$, degree $1$, 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:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	20.19
Dual form			20.11.d.d.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.8278 - 23.3997i) q^{2} +416.738 q^{3} +(-71.0958 + 1021.53i) q^{4} +(-2532.23 - 1831.23i) q^{5} +(-9096.47 - 9751.56i) q^{6} -9550.48 q^{7} +(25455.4 - 20634.1i) q^{8} +114622. q^{9} +O(q^{10})$	\(q+(-21.8278 - 23.3997i) q^{2} +416.738 q^{3} +(-71.0958 + 1021.53i) q^{4} +(-2532.23 - 1831.23i) q^{5} +(-9096.47 - 9751.56i) q^{6} -9550.48 q^{7} +(25455.4 - 20634.1i) q^{8} +114622. q^{9} +(12422.7 + 99225.4i) q^{10} -304718. i q^{11} +(-29628.3 + 425710. i) q^{12} -29399.0i q^{13} +(208466. + 223479. i) q^{14} +(-1.05528e6 - 763145. i) q^{15} +(-1.03847e6 - 145253. i) q^{16} -1.45461e6i q^{17} +(-2.50193e6 - 2.68211e6i) q^{18} -637402. i q^{19} +(2.05069e6 - 2.45656e6i) q^{20} -3.98005e6 q^{21} +(-7.13032e6 + 6.65132e6i) q^{22} -342491. q^{23} +(1.06082e7 - 8.59901e6i) q^{24} +(3.05879e6 + 9.27422e6i) q^{25} +(-687930. + 641716. i) q^{26} +2.31592e7 q^{27} +(678998. - 9.75609e6i) q^{28} -2.17387e7 q^{29} +(5.17699e6 + 4.13510e7i) q^{30} -2.54411e7i q^{31} +(1.92686e7 + 2.74704e7i) q^{32} -1.26988e8i q^{33} +(-3.40376e7 + 3.17510e7i) q^{34} +(2.41840e7 + 1.74892e7i) q^{35} +(-8.14910e6 + 1.17089e8i) q^{36} +6.66155e7i q^{37} +(-1.49150e7 + 1.39131e7i) q^{38} -1.22517e7i q^{39} +(-1.02245e8 + 5.63560e6i) q^{40} +9.83932e7 q^{41} +(8.68756e7 + 9.31321e7i) q^{42} +9.92286e7 q^{43} +(3.11278e8 + 2.16642e7i) q^{44} +(-2.90249e8 - 2.09899e8i) q^{45} +(7.47582e6 + 8.01421e6i) q^{46} +2.47915e8 q^{47} +(-4.32769e8 - 6.05323e7i) q^{48} -1.91264e8 q^{49} +(1.50248e8 - 2.74011e8i) q^{50} -6.06193e8i q^{51} +(3.00320e7 + 2.09015e6i) q^{52} +4.80828e8i q^{53} +(-5.05514e8 - 5.41919e8i) q^{54} +(-5.58010e8 + 7.71617e8i) q^{55} +(-2.43111e8 + 1.97065e8i) q^{56} -2.65630e8i q^{57} +(4.74508e8 + 5.08680e8i) q^{58} -4.28595e8i q^{59} +(8.54600e8 - 1.02374e9i) q^{60} +1.43573e9 q^{61} +(-5.95315e8 + 5.55323e8i) q^{62} -1.09469e9 q^{63} +(2.22210e8 - 1.05050e9i) q^{64} +(-5.38365e7 + 7.44452e7i) q^{65} +(-2.97148e9 + 2.77186e9i) q^{66} -1.31808e8 q^{67} +(1.48593e9 + 1.03417e8i) q^{68} -1.42729e8 q^{69} +(-1.18642e8 - 9.47650e8i) q^{70} -1.02003e8i q^{71} +(2.91773e9 - 2.36511e9i) q^{72} +8.16380e8i q^{73} +(1.55879e9 - 1.45407e9i) q^{74} +(1.27471e9 + 3.86492e9i) q^{75} +(6.51125e8 + 4.53166e7i) q^{76} +2.91020e9i q^{77} +(-2.86686e8 + 2.67427e8i) q^{78} +1.66028e9i q^{79} +(2.36365e9 + 2.26949e9i) q^{80} +2.88303e9 q^{81} +(-2.14771e9 - 2.30238e9i) q^{82} +4.49918e9 q^{83} +(2.82964e8 - 4.06573e9i) q^{84} +(-2.66374e9 + 3.68342e9i) q^{85} +(-2.16594e9 - 2.32192e9i) q^{86} -9.05934e9 q^{87} +(-6.28758e9 - 7.75671e9i) q^{88} -1.63227e9 q^{89} +(1.42390e9 + 1.13734e10i) q^{90} +2.80775e8i q^{91} +(2.43497e7 - 3.49865e8i) q^{92} -1.06023e10i q^{93} +(-5.41144e9 - 5.80115e9i) q^{94} +(-1.16723e9 + 1.61405e9i) q^{95} +(8.02994e9 + 1.14480e10i) q^{96} -8.94698e9i q^{97} +(4.17486e9 + 4.47552e9i) q^{98} -3.49273e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−21.8278	−	23.3997i	−0.682118	−	0.731242i
$2$	−21.8278	−	23.3997i	−0.682118	−	0.731242i
$3$	416.738			1.71497			0.857486	−	0.514508i	$-0.172025\pi$
$3$	416.738			1.71497			0.857486	+	0.514508i	$0.172025\pi$
$4$	−71.0958	+	1021.53i	−0.0694294	+	0.997587i
$5$	−2532.23	−	1831.23i	−0.810315	−	0.585995i
$5$	−2532.23	−	1831.23i	−0.810315	−	0.585995i
$6$	−9096.47	−	9751.56i	−1.16981	−	1.25406i
$7$	−9550.48			−0.568244			−0.284122	−	0.958788i	$-0.591702\pi$
$7$	−9550.48			−0.568244			−0.284122	+	0.958788i	$0.591702\pi$
$8$	25455.4	−	20634.1i	0.776836	−	0.629702i
$9$	114622.			1.94113
$10$	12422.7	+	99225.4i	0.124227	+	0.992254i
$11$		−	304718.i		−	1.89206i	−0.324080	−	0.946030i	$-0.605055\pi$
$11$		−	304718.i		−	1.89206i	0.324080	−	0.946030i	$-0.394945\pi$
$12$	−29628.3	+	425710.i	−0.119069	+	1.71083i
$13$		−	29399.0i		−	0.0791801i	−0.999216	−	0.0395901i	$-0.987395\pi$
$13$		−	29399.0i		−	0.0791801i	0.999216	−	0.0395901i	$-0.0126052\pi$
$14$	208466.	+	223479.i	0.387610	+	0.415524i
$15$	−1.05528e6	−	763145.i	−1.38967	−	1.00496i
$16$	−1.03847e6	−	145253.i	−0.990359	−	0.138524i
$17$		−	1.45461e6i		−	1.02448i	−0.858843	−	0.512239i	$-0.828816\pi$
$17$		−	1.45461e6i		−	1.02448i	0.858843	−	0.512239i	$-0.171184\pi$
$18$	−2.50193e6	−	2.68211e6i	−1.32408	−	1.41943i
$19$		−	637402.i		−	0.257422i	−0.991682	−	0.128711i	$-0.958916\pi$
$19$		−	637402.i		−	0.257422i	0.991682	−	0.128711i	$-0.0410839\pi$
$20$	2.05069e6	−	2.45656e6i	0.640840	−	0.767674i
$21$	−3.98005e6			−0.974522
$22$	−7.13032e6	+	6.65132e6i	−1.38355	+	1.29061i
$23$	−342491.			−0.0532121			−0.0266060	−	0.999646i	$-0.508470\pi$
$23$	−342491.			−0.0532121			−0.0266060	+	0.999646i	$0.508470\pi$
$24$	1.06082e7	−	8.59901e6i	1.33225	−	1.07992i
$25$	3.05879e6	+	9.27422e6i	0.313220	+	0.949681i
$26$	−687930.	+	641716.i	−0.0578998	+	0.0540102i
$27$	2.31592e7			1.61400
$28$	678998.	−	9.75609e6i	0.0394529	−	0.566873i
$29$	−2.17387e7			−1.05985			−0.529924	−	0.848045i	$-0.677780\pi$
$29$	−2.17387e7			−1.05985			−0.529924	+	0.848045i	$0.677780\pi$
$30$	5.17699e6	+	4.13510e7i	0.213045	+	1.70169i
$31$		−	2.54411e7i		−	0.888644i	−0.895867	−	0.444322i	$-0.853445\pi$
$31$		−	2.54411e7i		−	0.888644i	0.895867	−	0.444322i	$-0.146555\pi$
$32$	1.92686e7	+	2.74704e7i	0.574248	+	0.818682i
$33$		−	1.26988e8i		−	3.24483i
$34$	−3.40376e7	+	3.17510e7i	−0.749142	+	0.698816i
$35$	2.41840e7	+	1.74892e7i	0.460457	+	0.332988i
$36$	−8.14910e6	+	1.17089e8i	−0.134771	+	1.93644i
$37$			6.66155e7i			0.960654i	0.877090	+	0.480327i	$0.159482\pi$
$37$			6.66155e7i			0.960654i	−0.877090	+	0.480327i	$0.840518\pi$
$38$	−1.49150e7	+	1.39131e7i	−0.188238	+	0.175592i
$39$		−	1.22517e7i		−	0.135792i
$40$	−1.02245e8	+	5.63560e6i	−0.998484	+	0.0550352i
$41$	9.83932e7			0.849270			0.424635	−	0.905365i	$-0.360402\pi$
$41$	9.83932e7			0.849270			0.424635	+	0.905365i	$0.360402\pi$
$42$	8.68756e7	+	9.31321e7i	0.664739	+	0.712611i
$43$	9.92286e7			0.674986			0.337493	−	0.941328i	$-0.390421\pi$
$43$	9.92286e7			0.674986			0.337493	+	0.941328i	$0.390421\pi$
$44$	3.11278e8	+	2.16642e7i	1.88749	+	0.131365i
$45$	−2.90249e8	−	2.09899e8i	−1.57292	−	1.13749i
$46$	7.47582e6	+	8.01421e6i	0.0362969	+	0.0389109i
$47$	2.47915e8			1.08097			0.540486	−	0.841353i	$-0.318241\pi$
$47$	2.47915e8			1.08097			0.540486	+	0.841353i	$0.318241\pi$
$48$	−4.32769e8	−	6.05323e7i	−1.69844	−	0.237564i
$49$	−1.91264e8			−0.677099
$50$	1.50248e8	−	2.74011e8i	0.480793	−	0.876834i
$51$		−	6.06193e8i		−	1.75695i
$52$	3.00320e7	+	2.09015e6i	0.0789891	+	0.00549743i
$53$			4.80828e8i			1.14977i	0.818234	+	0.574885i	$0.194953\pi$
$53$			4.80828e8i			1.14977i	−0.818234	+	0.574885i	$0.805047\pi$
$54$	−5.05514e8	−	5.41919e8i	−1.10094	−	1.18023i
$55$	−5.58010e8	+	7.71617e8i	−1.10874	+	1.53316i
$56$	−2.43111e8	+	1.97065e8i	−0.441433	+	0.357825i
$57$		−	2.65630e8i		−	0.441471i
$58$	4.74508e8	+	5.08680e8i	0.722942	+	0.775005i
$59$		−	4.28595e8i		−	0.599497i	−0.954018	−	0.299749i	$-0.903097\pi$
$59$		−	4.28595e8i		−	0.599497i	0.954018	−	0.299749i	$-0.0969029\pi$
$60$	8.54600e8	−	1.02374e9i	1.09902	−	1.31654i
$61$	1.43573e9			1.69990			0.849950	−	0.526863i	$-0.176632\pi$
$61$	1.43573e9			1.69990			0.849950	+	0.526863i	$0.176632\pi$
$62$	−5.95315e8	+	5.55323e8i	−0.649813	+	0.606160i
$63$	−1.09469e9			−1.10303
$64$	2.22210e8	−	1.05050e9i	0.206950	−	0.978352i
$65$	−5.38365e7	+	7.44452e7i	−0.0463991	+	0.0641608i
$66$	−2.97148e9	+	2.77186e9i	−2.37275	+	2.21336i
$67$	−1.31808e8			−0.0976268			−0.0488134	−	0.998808i	$-0.515544\pi$
$67$	−1.31808e8			−0.0976268			−0.0488134	+	0.998808i	$0.515544\pi$
$68$	1.48593e9	+	1.03417e8i	1.02201	+	0.0711290i
$69$	−1.42729e8			−0.0912572
$70$	−1.18642e8	−	9.47650e8i	−0.0705910	−	0.563842i
$71$		−	1.02003e8i		−	0.0565354i	−0.999600	−	0.0282677i	$-0.991001\pi$
$71$		−	1.02003e8i		−	0.0565354i	0.999600	−	0.0282677i	$-0.00899909\pi$
$72$	2.91773e9	−	2.36511e9i	1.50794	−	1.22233i
$73$			8.16380e8i			0.393802i	0.980423	+	0.196901i	$0.0630878\pi$
$73$			8.16380e8i			0.393802i	−0.980423	+	0.196901i	$0.936912\pi$
$74$	1.55879e9	−	1.45407e9i	0.702470	−	0.655279i
$75$	1.27471e9	+	3.86492e9i	0.537164	+	1.62867i
$76$	6.51125e8	+	4.53166e7i	0.256801	+	0.0178727i
$77$			2.91020e9i			1.07515i
$78$	−2.86686e8	+	2.67427e8i	−0.0992966	+	0.0926260i
$79$			1.66028e9i			0.539568i	0.962921	+	0.269784i	$0.0869523\pi$
$79$			1.66028e9i			0.539568i	−0.962921	+	0.269784i	$0.913048\pi$
$80$	2.36365e9	+	2.26949e9i	0.721328	+	0.692593i
$81$	2.88303e9			0.826844
$82$	−2.14771e9	−	2.30238e9i	−0.579303	−	0.621022i
$83$	4.49918e9			1.14220			0.571101	−	0.820880i	$-0.306517\pi$
$83$	4.49918e9			1.14220			0.571101	+	0.820880i	$0.306517\pi$
$84$	2.82964e8	−	4.06573e9i	0.0676605	−	0.972171i
$85$	−2.66374e9	+	3.68342e9i	−0.600339	+	0.830150i
$86$	−2.16594e9	−	2.32192e9i	−0.460420	−	0.493578i
$87$	−9.05934e9			−1.81761
$88$	−6.28758e9	−	7.75671e9i	−1.19143	−	1.46982i
$89$	−1.63227e9			−0.292308			−0.146154	−	0.989262i	$-0.546690\pi$
$89$	−1.63227e9			−0.292308			−0.146154	+	0.989262i	$0.546690\pi$
$90$	1.42390e9	+	1.13734e10i	0.241139	+	1.92609i
$91$			2.80775e8i			0.0449936i
$92$	2.43497e7	−	3.49865e8i	0.00369449	−	0.0530837i
$93$		−	1.06023e10i		−	1.52400i
$94$	−5.41144e9	−	5.80115e9i	−0.737350	−	0.790451i
$95$	−1.16723e9	+	1.61405e9i	−0.150848	+	0.208593i
$96$	8.02994e9	+	1.14480e10i	0.984818	+	1.40402i
$97$		−	8.94698e9i		−	1.04188i	−0.853593	−	0.520940i	$-0.825581\pi$
$97$		−	8.94698e9i		−	1.04188i	0.853593	−	0.520940i	$-0.174419\pi$
$98$	4.17486e9	+	4.47552e9i	0.461861	+	0.495123i
$99$		−	3.49273e10i		−	3.67273i
$100$	−9.69136e9	+	2.46529e9i	−0.969136	+	0.246529i
$101$	−5.86404e9			−0.557943			−0.278971	−	0.960299i	$-0.589993\pi$
$101$	−5.86404e9			−0.557943			−0.278971	+	0.960299i	$0.589993\pi$
$102$	−1.41848e10	+	1.32318e10i	−1.28476	+	1.19845i
$103$	−9.55593e8			−0.0824303			−0.0412152	−	0.999150i	$-0.513123\pi$
$103$	−9.55593e8			−0.0824303			−0.0412152	+	0.999150i	$0.513123\pi$
$104$	−6.06622e8	−	7.48363e8i	−0.0498599	−	0.0615100i
$105$	1.00784e10	+	7.28840e9i	0.789670	+	0.571065i
$106$	1.12513e10	−	1.04954e10i	0.840760	−	0.784279i
$107$	2.15073e10			1.53344			0.766722	−	0.641980i	$-0.221887\pi$
$107$	2.15073e10			1.53344			0.766722	+	0.641980i	$0.221887\pi$
$108$	−1.64652e9	+	2.36578e10i	−0.112059	+	1.61011i
$109$	−1.62936e9			−0.105897			−0.0529487	−	0.998597i	$-0.516862\pi$
$109$	−1.62936e9			−0.105897			−0.0529487	+	0.998597i	$0.516862\pi$
$110$	3.02358e10	−	3.78541e9i	1.87740	−	0.235044i
$111$			2.77612e10i			1.64749i
$112$	9.91785e9	+	1.38723e9i	0.562766	+	0.0787153i
$113$		−	2.14606e9i		−	0.116480i	−0.998303	−	0.0582398i	$-0.981451\pi$
$113$		−	2.14606e9i		−	0.116480i	0.998303	−	0.0582398i	$-0.0185488\pi$
$114$	−6.21567e9	+	5.79811e9i	−0.322822	+	0.301136i
$115$	8.67268e8	+	6.27182e8i	0.0431185	+	0.0311820i
$116$	1.54553e9	−	2.22067e10i	0.0735847	−	1.05729i
$117$		−	3.36976e9i		−	0.153699i
$118$	−1.00290e10	+	9.35529e9i	−0.438378	+	0.408928i
$119$			1.38923e10i			0.582154i
$120$	−4.26093e10	+	2.34857e9i	−1.71237	+	0.0943838i
$121$	−6.69157e10			−2.57989
$122$	−3.13388e10	−	3.35957e10i	−1.15953	−	1.24304i
$123$	4.10042e10			1.45647
$124$	2.59888e10	+	1.80876e9i	0.886499	+	0.0616980i
$125$	9.23769e9	−	2.90859e10i	0.302701	−	0.953086i
$126$	2.38947e10	+	2.56155e10i	0.752399	+	0.806584i
$127$	−1.37096e10			−0.414959			−0.207480	−	0.978239i	$-0.566526\pi$
$127$	−1.37096e10			−0.414959			−0.207480	+	0.978239i	$0.566526\pi$
$128$	−2.94317e10	+	1.77304e10i	−0.856576	+	0.516021i
$129$	4.13523e10			1.15758
$130$	2.91713e9	−	3.65214e8i	0.0785668	−	0.00983628i
$131$			4.21233e10i			1.09186i	0.837832	+	0.545928i	$0.183823\pi$
$131$			4.21233e10i			1.09186i	−0.837832	+	0.545928i	$0.816177\pi$
$132$	1.29721e11	+	9.02828e9i	3.23700	+	0.225287i
$133$			6.08750e9i			0.146278i
$134$	2.87708e9	+	3.08428e9i	0.0665930	+	0.0713888i
$135$	−5.86445e10	−	4.24099e10i	−1.30785	−	0.945798i
$136$	−3.00146e10	−	3.70277e10i	−0.645117	−	0.795852i
$137$			7.92811e10i			1.64273i	0.570402	+	0.821366i	$0.306788\pi$
$137$			7.92811e10i			1.64273i	−0.570402	+	0.821366i	$0.693212\pi$
$138$	3.11546e9	+	3.33982e9i	0.0622482	+	0.0667311i
$139$		−	4.26508e10i		−	0.821965i	−0.911643	−	0.410983i	$-0.865186\pi$
$139$		−	4.26508e10i		−	0.821965i	0.911643	−	0.410983i	$-0.134814\pi$
$140$	−1.95851e10	+	2.34613e10i	−0.364154	+	0.436226i
$141$	1.03316e11			1.85383
$142$	−2.38684e9	+	2.22650e9i	−0.0413411	+	0.0385639i
$143$	−8.95842e9			−0.149814
$144$	−1.19031e11	−	1.66491e10i	−1.92241	−	0.268892i
$145$	5.50475e10	+	3.98086e10i	0.858811	+	0.621065i
$146$	1.91031e10	−	1.78198e10i	0.287965	−	0.268620i
$147$	−7.97068e10			−1.16120
$148$	−6.80497e10	−	4.73608e9i	−0.958336	−	0.0666977i
$149$	−8.38535e10			−1.14180			−0.570899	−	0.821020i	$-0.693405\pi$
$149$	−8.38535e10			−1.14180			−0.570899	+	0.821020i	$0.693405\pi$
$150$	6.26140e10	−	1.14191e11i	0.824546	−	1.50375i
$151$		−	9.39184e10i		−	1.19637i	−0.801358	−	0.598185i	$-0.795889\pi$
$151$		−	9.39184e10i		−	1.19637i	0.801358	−	0.598185i	$-0.204111\pi$
$152$	−1.31522e10	−	1.62253e10i	−0.162099	−	0.199975i
$153$		−	1.66730e11i		−	1.98864i
$154$	6.80980e10	−	6.35233e10i	0.786196	−	0.733380i
$155$	−4.65886e10	+	6.44228e10i	−0.520741	+	0.720081i
$156$	1.25155e10	+	8.71043e8i	0.135464	+	0.00942794i
$157$			7.57143e10i			0.793742i	0.917874	+	0.396871i	$0.129904\pi$
$157$			7.57143e10i			0.793742i	−0.917874	+	0.396871i	$0.870096\pi$
$158$	3.88501e10	−	3.62402e10i	0.394555	−	0.368049i
$159$			2.00379e11i			1.97182i
$160$	1.51224e9	−	1.04847e11i	0.0144218	−	0.999896i
$161$	3.27096e9			0.0302375
$162$	−6.29301e10	−	6.74621e10i	−0.564005	−	0.604623i
$163$	9.08791e9			0.0789816			0.0394908	−	0.999220i	$-0.487426\pi$
$163$	9.08791e9			0.0789816			0.0394908	+	0.999220i	$0.487426\pi$
$164$	−6.99534e9	+	1.00512e11i	−0.0589644	+	0.847221i
$165$	−2.32544e11	+	3.21562e11i	−1.90145	+	2.62933i
$166$	−9.82071e10	−	1.05280e11i	−0.779116	−	0.835226i
$167$	1.36718e11			1.05255			0.526277	−	0.850313i	$-0.323587\pi$
$167$	1.36718e11			1.05255			0.526277	+	0.850313i	$0.323587\pi$
$168$	−1.01314e11	+	8.21247e10i	−0.757044	+	0.613659i
$169$	1.36994e11			0.993731
$170$	1.44335e11	−	1.80702e10i	1.01654	−	0.127268i
$171$		−	7.30600e10i		−	0.499688i
$172$	−7.05474e9	+	1.01365e11i	−0.0468639	+	0.673357i
$173$		−	1.77462e11i		−	1.14518i	−0.819842	−	0.572590i	$-0.805939\pi$
$173$		−	1.77462e11i		−	1.14518i	0.819842	−	0.572590i	$-0.194061\pi$
$174$	1.97745e11	+	2.11986e11i	1.23982	+	1.32911i
$175$	−2.92129e10	−	8.85733e10i	−0.177986	−	0.539650i
$176$	−4.42611e10	+	3.16440e11i	−0.262095	+	1.87382i
$177$		−	1.78612e11i		−	1.02812i
$178$	3.56287e10	+	3.81946e10i	0.199389	+	0.213748i
$179$			2.19519e11i			1.19456i	0.802034	+	0.597278i	$0.203751\pi$
$179$			2.19519e11i			1.19456i	−0.802034	+	0.597278i	$0.796249\pi$
$180$	2.35053e11	−	2.81574e11i	1.24395	−	1.49015i
$181$	1.22633e11			0.631271			0.315635	−	0.948881i	$-0.397782\pi$
$181$	1.22633e11			0.631271			0.315635	+	0.948881i	$0.397782\pi$
$182$	6.57006e9	−	6.12869e9i	0.0329012	−	0.0306910i
$183$	5.98323e11			2.91528
$184$	−8.71824e9	+	7.06700e9i	−0.0413371	+	0.0335078i
$185$	1.21989e11	−	1.68686e11i	0.562938	−	0.778432i
$186$	−2.48091e11	+	2.31424e11i	−1.11441	+	1.03955i
$187$	−4.43247e11			−1.93837
$188$	−1.76257e10	+	2.53253e11i	−0.0750512	+	1.07836i
$189$	−2.21181e11			−0.917148
$190$	6.32465e10	−	7.91823e9i	0.255428	−	0.0319787i
$191$		−	4.84046e11i		−	1.90423i	−0.305740	−	0.952115i	$-0.598904\pi$
$191$		−	4.84046e11i		−	1.90423i	0.305740	−	0.952115i	$-0.401096\pi$
$192$	9.26035e10	−	4.37782e11i	0.354913	−	1.67784i
$193$		−	1.06363e11i		−	0.397195i	−0.980081	−	0.198598i	$-0.936361\pi$
$193$		−	1.06363e11i		−	0.397195i	0.980081	−	0.198598i	$-0.0636387\pi$
$194$	−2.09357e11	+	1.95293e11i	−0.761867	+	0.710686i
$195$	−2.24357e10	+	3.10242e10i	−0.0795732	+	0.110034i
$196$	1.35980e10	−	1.95381e11i	0.0470106	−	0.675465i
$197$			4.15793e10i			0.140135i	0.997542	+	0.0700675i	$0.0223215\pi$
$197$			4.15793e10i			0.140135i	−0.997542	+	0.0700675i	$0.977679\pi$
$198$	−8.17289e11	+	7.62384e11i	−2.68565	+	2.50523i
$199$		−	1.12622e11i		−	0.360875i	−0.983586	−	0.180437i	$-0.942249\pi$
$199$		−	1.12622e11i		−	0.360875i	0.983586	−	0.180437i	$-0.0577513\pi$
$200$	2.69228e11	+	1.72963e11i	0.841337	+	0.540511i
$201$	−5.49295e10			−0.167427
$202$	1.27999e11	+	1.37217e11i	0.380583	+	0.407991i
$203$	2.07615e11			0.602252
$204$	6.19243e11	+	4.30977e10i	1.75271	+	0.121984i
$205$	−2.49155e11	−	1.80181e11i	−0.688176	−	0.497668i
$206$	2.08585e10	+	2.23606e10i	0.0562272	+	0.0602765i
$207$	−3.92569e10			−0.103291
$208$	−4.27029e9	+	3.05299e10i	−0.0109683	+	0.0784168i
$209$	−1.94228e11			−0.487058
$210$	−4.94428e10	−	3.94922e11i	−0.121062	−	0.966973i
$211$			2.42315e10i			0.0579387i	0.999580	+	0.0289693i	$0.00922252\pi$
$211$			2.42315e10i			0.0579387i	−0.999580	+	0.0289693i	$0.990777\pi$
$212$	−4.91180e11	−	3.41849e10i	−1.14700	−	0.0798279i
$213$		−	4.25085e10i		−	0.0969566i
$214$	−4.69458e11	−	5.03266e11i	−1.04599	−	1.12132i
$215$	−2.51270e11	−	1.81711e11i	−0.546951	−	0.395538i
$216$	5.89526e11	−	4.77869e11i	1.25382	−	1.01634i
$217$			2.42975e11i			0.504967i
$218$	3.55654e10	+	3.81266e10i	0.0722345	+	0.0774366i
$219$			3.40217e11i			0.675359i
$220$	−7.48557e11	−	6.24882e11i	−1.45248	−	1.21251i
$221$	−4.27642e10			−0.0811184
$222$	6.49605e11	−	6.05966e11i	1.20472	−	1.12379i
$223$	−1.02257e11			−0.185425			−0.0927127	−	0.995693i	$-0.529554\pi$
$223$	−1.02257e11			−0.185425			−0.0927127	+	0.995693i	$0.529554\pi$
$224$	−1.84024e11	−	2.62355e11i	−0.326313	−	0.465211i
$225$	3.50603e11	+	1.06303e12i	0.608000	+	1.84345i
$226$	−5.02173e10	+	4.68438e10i	−0.0851748	+	0.0794529i
$227$	4.18186e11			0.693809			0.346905	−	0.937900i	$-0.387233\pi$
$227$	4.18186e11			0.693809			0.346905	+	0.937900i	$0.387233\pi$
$228$	2.71348e11	+	1.88851e10i	0.440406	+	0.0306511i
$229$	2.68061e11			0.425653			0.212826	−	0.977090i	$-0.431733\pi$
$229$	2.68061e11			0.425653			0.212826	+	0.977090i	$0.431733\pi$
$230$	−4.25465e9	−	3.39838e10i	−0.00661036	−	0.0527999i
$231$			1.21279e12i			1.84385i
$232$	−5.53367e11	+	4.48558e11i	−0.823328	+	0.667389i
$233$		−	1.21171e12i		−	1.76449i	−0.470789	−	0.882246i	$-0.656031\pi$
$233$		−	1.21171e12i		−	1.76449i	0.470789	−	0.882246i	$-0.343969\pi$
$234$	−7.88516e10	+	7.35544e10i	−0.112391	+	0.104841i
$235$	−6.27780e11	−	4.53991e11i	−0.875927	−	0.633443i
$236$	4.37823e11	+	3.04713e10i	0.598051	+	0.0416228i
$237$			6.91902e11i			0.925343i
$238$	3.25075e11	−	3.03237e11i	0.425695	−	0.397098i
$239$		−	9.58986e11i		−	1.22977i	−0.788618	−	0.614883i	$-0.789203\pi$
$239$		−	9.58986e11i		−	1.22977i	0.788618	−	0.614883i	$-0.210797\pi$
$240$	9.85022e11	+	9.45782e11i	1.23706	+	1.18778i
$241$	−2.60656e10			−0.0320614			−0.0160307	−	0.999872i	$-0.505103\pi$
$241$	−2.60656e10			−0.0320614			−0.0160307	+	0.999872i	$0.505103\pi$
$242$	1.46062e12	+	1.56581e12i	1.75979	+	1.88652i
$243$	−1.66060e11			−0.195990
$244$	−1.02074e11	+	1.46664e12i	−0.118023	+	1.69580i
$245$	4.84324e11	+	3.50248e11i	0.548663	+	0.396776i
$246$	−8.95031e11	−	9.59487e11i	−0.993487	−	1.06503i
$247$	−1.87390e10			−0.0203827
$248$	−5.24954e11	−	6.47613e11i	−0.559581	−	0.690331i
$249$	1.87498e12			1.95884
$250$	−8.82240e11	+	4.18720e11i	−0.903414	+	0.428770i
$251$			8.20788e11i			0.823877i	0.911212	+	0.411938i	$0.135148\pi$
$251$			8.20788e11i			0.823877i	−0.911212	+	0.411938i	$0.864852\pi$
$252$	7.78278e10	−	1.11826e12i	0.0765830	−	1.10037i
$253$			1.04363e11i			0.100680i
$254$	2.99250e11	+	3.20800e11i	0.283051	+	0.303435i
$255$	−1.11008e12	+	1.53502e12i	−1.02956	+	1.42368i
$256$	1.05731e12	+	3.01680e11i	0.961622	+	0.274377i
$257$			2.87608e11i			0.256529i	0.991740	+	0.128264i	$0.0409406\pi$
$257$			2.87608e11i			0.256529i	−0.991740	+	0.128264i	$0.959059\pi$
$258$	−9.02630e11	−	9.67634e11i	−0.789607	−	0.846472i
$259$		−	6.36210e11i		−	0.545886i
$260$	−7.22204e10	−	6.02883e10i	−0.0607845	−	0.0507418i
$261$	−2.49172e12			−2.05730
$262$	9.85673e11	−	9.19457e11i	0.798411	−	0.744775i
$263$	7.38343e11			0.586786			0.293393	−	0.955992i	$-0.405216\pi$
$263$	7.38343e11			0.586786			0.293393	+	0.955992i	$0.405216\pi$
$264$	−2.62027e12	−	3.23252e12i	−2.04328	−	2.52070i
$265$	8.80509e11	−	1.21757e12i	0.673759	−	0.931675i
$266$	1.42446e11	−	1.32877e11i	0.106965	−	0.0997792i
$267$	−6.80227e11			−0.501300
$268$	9.37101e9	−	1.34646e11i	0.00677817	−	0.0973912i
$269$	−2.24925e12			−1.59690			−0.798448	−	0.602064i	$-0.794345\pi$
$269$	−2.24925e12			−1.59690			−0.798448	+	0.602064i	$0.794345\pi$
$270$	2.87699e11	+	2.29798e12i	0.200502	+	1.60150i
$271$			2.00787e12i			1.37369i	0.726803	+	0.686846i	$0.241005\pi$
$271$			2.00787e12i			1.37369i	−0.726803	+	0.686846i	$0.758995\pi$
$272$	−2.11287e11	+	1.51057e12i	−0.141915	+	1.01460i
$273$			1.17010e11i			0.0771628i
$274$	1.85516e12	−	1.73053e12i	1.20123	−	1.12054i
$275$	2.82602e12	−	9.32069e11i	1.79685	−	0.592631i
$276$	1.01474e10	−	1.45802e11i	0.00633594	−	0.0910370i
$277$			1.76307e12i			1.08111i	0.841308	+	0.540556i	$0.181786\pi$
$277$			1.76307e12i			1.08111i	−0.841308	+	0.540556i	$0.818214\pi$
$278$	−9.98018e11	+	9.30973e11i	−0.601055	+	0.560677i
$279$		−	2.91610e12i		−	1.72497i
$280$	9.76487e11	−	5.38227e10i	0.567383	−	0.0312734i
$281$	2.28145e12			1.30220			0.651102	−	0.758990i	$-0.274307\pi$
$281$	2.28145e12			1.30220			0.651102	+	0.758990i	$0.274307\pi$
$282$	−2.25515e12	−	2.41756e12i	−1.26453	−	1.35560i
$283$	3.76141e11			0.207214			0.103607	−	0.994618i	$-0.466962\pi$
$283$	3.76141e11			0.207214			0.103607	+	0.994618i	$0.466962\pi$
$284$	1.04199e11	+	7.25197e9i	0.0563990	+	0.00392522i
$285$	−4.86430e11	+	6.72637e11i	−0.258700	+	0.357731i
$286$	1.95542e11	+	2.09625e11i	0.102191	+	0.109550i
$287$	−9.39702e11			−0.482593
$288$	2.20859e12	+	3.14870e12i	1.11469	+	1.58916i
$289$	−9.99061e10			−0.0495568
$290$	−2.70052e11	−	2.15703e12i	−0.131661	−	1.05164i
$291$		−	3.72855e12i		−	1.78679i
$292$	−8.33956e11	−	5.80412e10i	−0.392852	−	0.0273415i
$293$			9.68854e11i			0.448663i	0.974513	+	0.224332i	$0.0720199\pi$
$293$			9.68854e11i			0.448663i	−0.974513	+	0.224332i	$0.927980\pi$
$294$	1.73982e12	+	1.86512e12i	0.792079	+	0.849121i
$295$	−7.84858e11	+	1.08530e12i	−0.351302	+	0.485782i
$296$	1.37455e12	+	1.69572e12i	0.604926	+	0.746271i
$297$		−	7.05702e12i		−	3.05379i
$298$	1.83034e12	+	1.96215e12i	0.778842	+	0.834931i
$299$			1.00689e10i			0.00421334i
$300$	−4.03876e12	+	1.02738e12i	−1.66204	+	0.422790i
$301$	−9.47681e11			−0.383557
$302$	−2.19767e12	+	2.05003e12i	−0.874836	+	0.816066i
$303$	−2.44377e12			−0.956856
$304$	−9.25844e10	+	6.61921e11i	−0.0356591	+	0.254940i
$305$	−3.63560e12	−	2.62916e12i	−1.37745	−	0.996133i
$306$	−3.90144e12	+	3.63935e12i	−1.45418	+	1.35649i
$307$	3.35153e12			1.22900			0.614498	−	0.788918i	$-0.289358\pi$
$307$	3.35153e12			1.22900			0.614498	+	0.788918i	$0.289358\pi$
$308$	−2.97286e12	−	2.06903e11i	−1.07256	−	0.0746472i
$309$	−3.98232e11			−0.141366
$310$	2.52440e12	−	3.16046e11i	0.881760	−	0.110393i
$311$		−	4.18197e12i		−	1.43741i	−0.695318	−	0.718703i	$-0.744736\pi$
$311$		−	4.18197e12i		−	1.43741i	0.695318	−	0.718703i	$-0.255264\pi$
$312$	−2.52803e11	−	3.11871e11i	−0.0855083	−	0.105488i
$313$			2.98987e12i			0.995246i	0.867393	+	0.497623i	$0.165794\pi$
$313$			2.98987e12i			0.995246i	−0.867393	+	0.497623i	$0.834206\pi$
$314$	1.77169e12	−	1.65267e12i	0.580418	−	0.541426i
$315$	2.77201e12	+	2.00463e12i	0.893804	+	0.646372i
$316$	−1.69602e12	−	1.18039e11i	−0.538266	−	0.0374619i
$317$		−	2.67540e12i		−	0.835780i	−0.908498	−	0.417890i	$-0.862770\pi$
$317$		−	2.67540e12i		−	0.835780i	0.908498	−	0.417890i	$-0.137230\pi$
$318$	4.68883e12	−	4.37384e12i	1.44188	−	1.34502i
$319$			6.62417e12i			2.00530i
$320$	−2.48639e12	+	2.25318e12i	−0.741003	+	0.671501i
$321$	8.96292e12			2.62981
$322$	−7.13977e10	−	7.65395e10i	−0.0206255	−	0.0221109i
$323$	−9.27174e11			−0.263723
$324$	−2.04971e11	+	2.94509e12i	−0.0574073	+	0.824849i
$325$	2.72653e11	−	8.99255e10i	0.0751958	−	0.0248008i
$326$	−1.98369e11	−	2.12655e11i	−0.0538748	−	0.0577546i
$327$	−6.79017e11			−0.181611
$328$	2.50464e12	−	2.03025e12i	0.659744	−	0.534788i
$329$	−2.36771e12			−0.614255
$330$	1.26004e13	−	1.57752e12i	3.21969	−	0.403094i
$331$			2.58043e12i			0.649460i	0.945807	+	0.324730i	$0.105273\pi$
$331$			2.58043e12i			0.649460i	−0.945807	+	0.324730i	$0.894727\pi$
$332$	−3.19872e11	+	4.59604e12i	−0.0793024	+	1.13945i
$333$			7.63558e12i			1.86475i
$334$	−2.98426e12	−	3.19917e12i	−0.717967	−	0.769672i
$335$	3.33770e11	+	2.41372e11i	0.0791084	+	0.0572088i
$336$	4.13315e12	+	5.78113e11i	0.965127	+	0.134995i
$337$			5.83826e12i			1.34318i	0.740924	+	0.671589i	$0.234388\pi$
$337$			5.83826e12i			1.34318i	−0.740924	+	0.671589i	$0.765612\pi$
$338$	−2.99028e12	−	3.20563e12i	−0.677842	−	0.726657i
$339$		−	8.94346e11i		−	0.199759i
$340$	−3.57334e12	−	2.98296e12i	−0.786466	−	0.656527i
$341$	−7.75237e12			−1.68137
$342$	−1.70959e12	+	1.59474e12i	−0.365393	+	0.340847i
$343$	4.52443e12			0.953001
$344$	2.52590e12	−	2.04749e12i	0.524354	−	0.425040i
$345$	3.61423e11	+	2.61370e11i	0.0739471	+	0.0534762i
$346$	−4.15256e12	+	3.87360e12i	−0.837404	+	0.781149i
$347$	1.67841e12			0.333619			0.166810	−	0.985989i	$-0.446653\pi$
$347$	1.67841e12			0.333619			0.166810	+	0.985989i	$0.446653\pi$
$348$	6.44081e11	−	9.25438e12i	0.126196	−	1.81322i
$349$	3.42380e11			0.0661274			0.0330637	−	0.999453i	$-0.489474\pi$
$349$	3.42380e11			0.0661274			0.0330637	+	0.999453i	$0.489474\pi$
$350$	−1.43494e12	+	2.61693e12i	−0.273208	+	0.498256i
$351$		−	6.80858e11i		−	0.127797i
$352$	8.37073e12	−	5.87148e12i	1.54899	−	1.08651i
$353$		−	1.01215e13i		−	1.84660i	−0.384080	−	0.923300i	$-0.625481\pi$
$353$		−	1.01215e13i		−	1.84660i	0.384080	−	0.923300i	$-0.374519\pi$
$354$	−4.17947e12	+	3.89870e12i	−0.751805	+	0.701300i
$355$	−1.86791e11	+	2.58295e11i	−0.0331295	+	0.0458115i
$356$	1.16047e11	−	1.66741e12i	0.0202948	−	0.291603i
$357$			5.78943e12i			0.998377i
$358$	5.13668e12	−	4.79161e12i	0.873509	−	0.814829i
$359$			2.75104e12i			0.461344i	0.973032	+	0.230672i	$0.0740924\pi$
$359$			2.75104e12i			0.461344i	−0.973032	+	0.230672i	$0.925908\pi$
$360$	−1.17195e13	+	6.45962e11i	−1.93818	+	0.106830i
$361$	5.72478e12			0.933734
$362$	−2.67681e12	−	2.86959e12i	−0.430601	−	0.461611i
$363$	−2.78863e13			−4.42443
$364$	−2.86820e11	−	1.99619e10i	−0.0448851	−	0.00312388i
$365$	1.49498e12	−	2.06727e12i	0.230766	−	0.319104i
$366$	−1.30601e13	−	1.40006e13i	−1.98857	−	2.13177i
$367$	−6.50707e12			−0.977361			−0.488681	−	0.872463i	$-0.662522\pi$
$367$	−6.50707e12			−0.977361			−0.488681	+	0.872463i	$0.662522\pi$
$368$	3.55666e11	+	4.97478e10i	0.0526991	+	0.00737114i
$369$	1.12780e13			1.64854
$370$	−6.60995e12	+	8.27542e11i	−0.953212	+	0.119339i
$371$		−	4.59214e12i		−	0.653350i
$372$	1.08305e13	+	7.53777e11i	1.52032	+	0.105810i
$373$			5.74229e12i			0.795319i	0.917533	+	0.397659i	$0.130177\pi$
$373$			5.74229e12i			0.795319i	−0.917533	+	0.397659i	$0.869823\pi$
$374$	9.67510e12	+	1.03719e13i	1.32220	+	1.41742i
$375$	3.84970e12	−	1.21212e13i	0.519123	−	1.63451i
$376$	6.31078e12	−	5.11551e12i	0.839738	−	0.680690i
$377$			6.39097e11i			0.0839189i
$378$	4.82790e12	+	5.17559e12i	0.625603	+	0.670657i
$379$			7.38772e12i			0.944744i	0.881399	+	0.472372i	$0.156602\pi$
$379$			7.38772e12i			0.944744i	−0.881399	+	0.472372i	$0.843398\pi$
$380$	−1.56582e12	−	1.30711e12i	−0.197616	−	0.164966i
$381$	−5.71330e12			−0.711643
$382$	−1.13265e13	+	1.05656e13i	−1.39245	+	1.29891i
$383$	6.66386e12			0.808596			0.404298	−	0.914627i	$-0.367516\pi$
$383$	6.66386e12			0.808596			0.404298	+	0.914627i	$0.367516\pi$
$384$	−1.22653e13	+	7.38891e12i	−1.46900	+	0.884962i
$385$	5.32926e12	−	7.36931e12i	0.630033	−	0.871211i
$386$	−2.48887e12	+	2.32167e12i	−0.290446	+	0.270934i
$387$	1.13737e13			1.31023
$388$	9.13960e12	+	6.36092e11i	1.03937	+	0.0723372i
$389$	−6.05803e11			−0.0680116			−0.0340058	−	0.999422i	$-0.510826\pi$
$389$	−6.05803e11			−0.0680116			−0.0340058	+	0.999422i	$0.510826\pi$
$390$	1.21568e12	−	1.52199e11i	0.134740	−	0.0168689i
$391$			4.98192e11i			0.0545147i
$392$	−4.86869e12	+	3.94655e12i	−0.525995	+	0.426371i
$393$			1.75544e13i			1.87250i
$394$	9.72946e11	−	9.07585e11i	0.102473	−	0.0955886i
$395$	3.04036e12	−	4.20422e12i	0.316184	−	0.437220i
$396$	3.56792e13	+	2.48318e12i	3.66386	+	0.254995i
$397$		−	1.14630e13i		−	1.16237i	−0.813772	−	0.581185i	$-0.802589\pi$
$397$		−	1.14630e13i		−	1.16237i	0.813772	−	0.581185i	$-0.197411\pi$
$398$	−2.63532e12	+	2.45828e12i	−0.263887	+	0.246159i
$399$			2.53689e12i			0.250863i
$400$	−1.82935e12	−	1.00753e13i	−0.178647	−	0.983913i
$401$	−1.34427e13			−1.29648			−0.648238	−	0.761438i	$-0.724494\pi$
$401$	−1.34427e13			−1.29648			−0.648238	+	0.761438i	$0.724494\pi$
$402$	1.19899e12	+	1.28534e12i	0.114205	+	0.122430i
$403$	−7.47944e11			−0.0703629
$404$	4.16908e11	−	5.99028e12i	0.0387377	−	0.556597i
$405$	−7.30050e12	−	5.27949e12i	−0.670004	−	0.484526i
$406$	−4.53177e12	−	4.85814e12i	−0.410807	−	0.440392i
$407$	2.02990e13			1.81761
$408$	−1.25082e13	−	1.54309e13i	−1.10636	−	1.36486i
$409$	−1.31509e13			−1.14905			−0.574524	−	0.818487i	$-0.694813\pi$
$409$	−1.31509e13			−1.14905			−0.574524	+	0.818487i	$0.694813\pi$
$410$	1.22231e12	+	9.76311e12i	0.105502	+	0.842692i
$411$			3.30394e13i			2.81724i
$412$	6.79386e10	−	9.76166e11i	0.00572309	−	0.0822314i
$413$			4.09329e12i			0.340661i
$414$	8.56891e11	+	9.18601e11i	0.0704569	+	0.0755310i
$415$	−1.13930e13	−	8.23905e12i	−0.925543	−	0.669324i
$416$	8.07603e11	−	5.66477e11i	0.0648233	−	0.0454690i
$417$		−	1.77742e13i		−	1.40965i
$418$	4.23957e12	+	4.54488e12i	0.332231	+	0.356157i
$419$		−	7.49560e12i		−	0.580412i	−0.956964	−	0.290206i	$-0.906276\pi$
$419$		−	7.49560e12i		−	0.580412i	0.956964	−	0.290206i	$-0.0937238\pi$
$420$	−8.16184e12	+	9.77721e12i	−0.624513	+	0.748116i
$421$	7.33758e12			0.554807			0.277404	−	0.960753i	$-0.410526\pi$
$421$	7.33758e12			0.554807			0.277404	+	0.960753i	$0.410526\pi$
$422$	5.67012e11	−	5.28921e11i	0.0423672	−	0.0395210i
$423$	2.84164e13			2.09830
$424$	9.92146e12	+	1.22397e13i	0.724013	+	0.893183i
$425$	1.34904e13	−	4.44936e12i	0.972928	−	0.320888i
$426$	−9.94688e11	+	9.27866e11i	−0.0708988	+	0.0661359i
$427$	−1.37119e13			−0.965958
$428$	−1.52908e12	+	2.19704e13i	−0.106466	+	1.52974i
$429$	−3.73331e12			−0.256926
$430$	1.23268e12	+	9.84600e12i	0.0838512	+	0.669758i
$431$		−	1.48486e13i		−	0.998389i	−0.866490	−	0.499194i	$-0.833629\pi$
$431$		−	1.48486e13i		−	0.998389i	0.866490	−	0.499194i	$-0.166371\pi$
$432$	−2.40500e13	−	3.36394e12i	−1.59844	−	0.223578i
$433$			8.12536e12i			0.533830i	0.963720	+	0.266915i	$0.0860043\pi$
$433$			8.12536e12i			0.533830i	−0.963720	+	0.266915i	$0.913996\pi$
$434$	5.68555e12	−	5.30360e12i	0.369253	−	0.344447i
$435$	2.29404e13	+	1.65898e13i	1.47284	+	1.06511i
$436$	1.15841e11	−	1.66444e12i	0.00735239	−	0.105642i
$437$			2.18305e11i			0.0136980i
$438$	7.96098e12	−	7.42617e12i	0.493851	−	0.460675i
$439$		−	1.41396e13i		−	0.867191i	−0.901108	−	0.433596i	$-0.857245\pi$
$439$		−	1.41396e13i		−	0.867191i	0.901108	−	0.433596i	$-0.142755\pi$
$440$	1.71727e12	+	3.11558e13i	0.104130	+	1.88919i
$441$	−2.19229e13			−1.31433
$442$	9.33448e11	+	1.00067e12i	0.0553323	+	0.0593172i
$443$	−3.08342e13			−1.80723			−0.903615	−	0.428345i	$-0.859097\pi$
$443$	−3.08342e13			−1.80723			−0.903615	+	0.428345i	$0.859097\pi$
$444$	−2.83589e13	−	1.97371e12i	−1.64352	−	0.114385i
$445$	4.13328e12	+	2.98906e12i	0.236862	+	0.171291i
$446$	2.23205e12	+	2.39279e12i	0.126482	+	0.135591i
$447$	−3.49449e13			−1.95815
$448$	−2.12222e12	+	1.00327e13i	−0.117598	+	0.555943i
$449$	1.92091e13			1.05263			0.526315	−	0.850289i	$-0.323573\pi$
$449$	1.92091e13			1.05263			0.526315	+	0.850289i	$0.323573\pi$
$450$	1.72216e13	−	3.14075e13i	0.933280	−	1.70205i
$451$		−	2.99822e13i		−	1.60687i
$452$	2.19226e12	+	1.52576e11i	0.116199	+	0.00808712i
$453$		−	3.91393e13i		−	2.05174i
$454$	−9.12807e12	−	9.78544e12i	−0.473260	−	0.507342i
$455$	5.14164e11	−	7.10988e11i	0.0263660	−	0.0364590i
$456$	−5.48103e12	−	6.76170e12i	−0.277995	−	0.342951i
$457$			4.70963e12i			0.236268i	0.992998	+	0.118134i	$0.0376913\pi$
$457$			4.70963e12i			0.236268i	−0.992998	+	0.118134i	$0.962309\pi$
$458$	−5.85117e12	−	6.27255e12i	−0.290346	−	0.311255i
$459$		−	3.36877e13i		−	1.65351i
$460$	−7.02343e11	+	8.41349e11i	−0.0341005	+	0.0408495i
$461$	2.27175e13			1.09108			0.545539	−	0.838085i	$-0.316325\pi$
$461$	2.27175e13			1.09108			0.545539	+	0.838085i	$0.316325\pi$
$462$	2.83790e13	−	2.64726e13i	1.34830	−	1.25773i
$463$	1.18956e13			0.559088			0.279544	−	0.960133i	$-0.409817\pi$
$463$	1.18956e13			0.559088			0.279544	+	0.960133i	$0.409817\pi$
$464$	2.25749e13	+	3.15761e12i	1.04963	+	0.146814i
$465$	−1.94152e13	+	2.68474e13i	−0.893055	+	1.23492i
$466$	−2.83537e13	+	2.64490e13i	−1.29027	+	1.20359i
$467$	1.58065e13			0.711626			0.355813	−	0.934557i	$-0.384204\pi$
$467$	1.58065e13			0.711626			0.355813	+	0.934557i	$0.384204\pi$
$468$	3.44231e12	+	2.39576e11i	0.153328	+	0.0106712i
$469$	1.25883e12			0.0554758
$470$	3.07977e12	+	2.45995e13i	0.134285	+	1.07260i
$471$			3.15530e13i			1.36124i
$472$	−8.84367e12	−	1.09101e13i	−0.377505	−	0.465711i
$473$		−	3.02368e13i		−	1.27711i
$474$	1.61903e13	−	1.51027e13i	0.676650	−	0.631193i
$475$	5.91141e12	−	1.94968e12i	0.244469	−	0.0806298i
$476$	−1.41913e13	−	9.87680e11i	−0.580749	−	0.0404186i
$477$			5.51133e13i			2.23185i
$478$	−2.24400e13	+	2.09325e13i	−0.899257	+	0.838846i
$479$			2.95581e13i			1.17219i	0.810242	+	0.586096i	$0.199336\pi$
$479$			2.95581e13i			1.17219i	−0.810242	+	0.586096i	$0.800664\pi$
$480$	6.30208e11	−	4.36936e13i	0.0247330	−	1.71479i
$481$	1.95843e12			0.0760647
$482$	5.68954e11	+	6.09928e11i	0.0218696	+	0.0234446i
$483$	1.36313e12			0.0518564
$484$	4.75742e12	−	6.83563e13i	0.179120	−	2.57366i
$485$	−1.63840e13	+	2.26558e13i	−0.610536	+	0.844251i
$486$	3.62473e12	+	3.88577e12i	0.133689	+	0.143316i
$487$	−3.11474e13			−1.13704			−0.568521	−	0.822668i	$-0.692484\pi$
$487$	−3.11474e13			−1.13704			−0.568521	+	0.822668i	$0.692484\pi$
$488$	3.65470e13	−	2.96250e13i	1.32054	−	1.07043i
$489$	3.78728e12			0.135451
$490$	−2.37600e12	−	1.89782e13i	−0.0841137	−	0.671854i
$491$		−	5.82733e12i		−	0.204203i	−0.994774	−	0.102102i	$-0.967443\pi$
$491$		−	5.82733e12i		−	0.204203i	0.994774	−	0.102102i	$-0.0325567\pi$
$492$	−2.91522e12	+	4.18870e13i	−0.101122	+	1.45296i
$493$			3.16214e13i			1.08579i
$494$	4.09031e11	+	4.38488e11i	0.0139034	+	0.0149047i
$495$	−6.39600e13	+	8.84440e13i	−2.15220	+	2.97606i
$496$	−3.69539e12	+	2.64198e13i	−0.123098	+	0.880076i
$497$			9.74177e11i			0.0321259i
$498$	−4.09266e13	−	4.38740e13i	−1.33616	−	1.43239i
$499$			2.52918e13i			0.817481i	0.912651	+	0.408741i	$0.134032\pi$
$499$			2.52918e13i			0.817481i	−0.912651	+	0.408741i	$0.865968\pi$
$500$	2.90553e13	+	1.15045e13i	0.929769	+	0.368143i
$501$	5.69757e13			1.80510
$502$	1.92062e13	−	1.79160e13i	0.602453	−	0.561981i
$503$	4.06385e13			1.26211			0.631055	−	0.775738i	$-0.282622\pi$
$503$	4.06385e13			1.26211			0.631055	+	0.775738i	$0.282622\pi$
$504$	−2.78658e13	+	2.25879e13i	−0.856876	+	0.694583i
$505$	1.48491e13	+	1.07384e13i	0.452109	+	0.326952i
$506$	2.44207e12	−	2.27802e12i	0.0736217	−	0.0686760i
$507$	5.70907e13			1.70422
$508$	9.74692e11	−	1.40047e13i	0.0288104	−	0.413958i
$509$	−5.38766e13			−1.57693			−0.788463	−	0.615082i	$-0.789123\pi$
$509$	−5.38766e13			−1.57693			−0.788463	+	0.615082i	$0.789123\pi$
$510$	6.01497e13	−	7.53052e12i	1.74334	−	0.218260i
$511$		−	7.79682e12i		−	0.223776i
$512$	−1.60196e13	−	3.13259e13i	−0.455304	−	0.890336i
$513$		−	1.47617e13i		−	0.415480i
$514$	6.72996e12	−	6.27785e12i	0.187585	−	0.174983i
$515$	2.41979e12	+	1.74991e12i	0.0667945	+	0.0483037i
$516$	−2.93998e12	+	4.22426e13i	−0.0803702	+	1.15479i
$517$		−	7.55443e13i		−	2.04526i
$518$	−1.48872e13	+	1.38871e13i	−0.399175	+	0.372359i
$519$		−	7.39550e13i		−	1.96395i
$520$	1.65681e11	+	3.00590e12i	0.00435769	+	0.0790601i
$521$	3.40381e13			0.886700			0.443350	−	0.896349i	$-0.353790\pi$
$521$	3.40381e13			0.886700			0.443350	+	0.896349i	$0.353790\pi$
$522$	5.43888e13	+	5.83057e13i	1.40332	+	1.50438i
$523$	−8.76448e12			−0.223984			−0.111992	−	0.993709i	$-0.535723\pi$
$523$	−8.76448e12			−0.223984			−0.111992	+	0.993709i	$0.535723\pi$
$524$	−4.30301e13	−	2.99478e12i	−1.08922	−	0.0758070i
$525$	−1.21741e13	−	3.69118e13i	−0.305240	−	0.925485i
$526$	−1.61164e13	−	1.72770e13i	−0.400257	−	0.429082i
$527$	−3.70070e13			−0.910397
$528$	−1.84453e13	+	1.31872e14i	−0.449486	+	3.21354i
$529$	−4.13092e13			−0.997168
$530$	−4.77104e13	+	5.97317e12i	−1.14086	+	0.142832i
$531$		−	4.91263e13i		−	1.16370i
$532$	−6.21855e12	−	4.32795e11i	−0.145926	−	0.0101560i
$533$		−	2.89267e12i		−	0.0672453i
$534$	1.48478e13	+	1.59171e13i	0.341946	+	0.366571i
$535$	−5.44616e13	−	3.93850e13i	−1.24257	−	0.898590i
$536$	−3.35523e12	+	2.71975e12i	−0.0758400	+	0.0614758i
$537$			9.14818e13i			2.04863i
$538$	4.90962e13	+	5.26319e13i	1.08927	+	1.16772i
$539$			5.82815e13i			1.28111i
$540$	4.74923e13	−	5.68919e13i	1.03432	−	1.23903i
$541$	8.58042e12			0.185149			0.0925747	−	0.995706i	$-0.470490\pi$
$541$	8.58042e12			0.185149			0.0925747	+	0.995706i	$0.470490\pi$
$542$	4.69837e13	−	4.38274e13i	1.00450	−	0.937021i
$543$	5.11059e13			1.08261
$544$	3.99588e13	−	2.80283e13i	0.838722	−	0.588304i
$545$	4.12592e12	+	2.98374e12i	0.0858102	+	0.0620553i
$546$	2.73799e12	−	2.55406e12i	0.0564247	−	0.0526342i
$547$	3.27597e13			0.668965			0.334482	−	0.942402i	$-0.391439\pi$
$547$	3.27597e13			0.668965			0.334482	+	0.942402i	$0.391439\pi$
$548$	−8.09879e13	−	5.63655e12i	−1.63877	−	0.114054i
$549$	1.64566e14			3.29972
$550$	−8.34960e13	−	4.57832e13i	−1.65902	−	0.909689i
$551$			1.38563e13i			0.272828i
$552$	−3.63322e12	+	2.94509e12i	−0.0708919	+	0.0574649i
$553$		−	1.58565e13i		−	0.306606i
$554$	4.12554e13	−	3.84839e13i	0.790555	−	0.737447i
$555$	5.08373e13	−	7.02979e13i	0.965423	−	1.33499i
$556$	4.35691e13	+	3.03229e12i	0.819982	+	0.0570686i
$557$		−	7.72359e12i		−	0.144060i	−0.997402	−	0.0720300i	$-0.977052\pi$
$557$		−	7.72359e12i		−	0.144060i	0.997402	−	0.0720300i	$-0.0229477\pi$
$558$	−6.82360e13	+	6.36520e13i	−1.26137	+	1.17663i
$559$		−	2.91723e12i		−	0.0534455i
$560$	−2.25740e13	−	2.16747e13i	−0.409891	−	0.393562i
$561$	−1.84718e14			−3.32426
$562$	−4.97989e13	−	5.33853e13i	−0.888257	−	0.952226i
$563$	−3.60219e13			−0.636832			−0.318416	−	0.947951i	$-0.603151\pi$
$563$	−3.60219e13			−0.636832			−0.318416	+	0.947951i	$0.603151\pi$
$564$	−7.34531e12	+	1.05540e14i	−0.128711	+	1.84936i
$565$	−3.92994e12	+	5.43433e12i	−0.0682565	+	0.0943852i
$566$	−8.21032e12	−	8.80159e12i	−0.141344	−	0.151523i
$567$	−2.75343e13			−0.469849
$568$	−2.10474e12	−	2.59652e12i	−0.0356005	−	0.0439188i
$569$	−1.08481e14			−1.81884			−0.909419	−	0.415880i	$-0.863474\pi$
$569$	−1.08481e14			−1.81884			−0.909419	+	0.415880i	$0.863474\pi$
$570$	2.63572e13	−	3.29983e12i	0.438051	−	0.0548425i
$571$			5.26590e13i			0.867545i	0.901023	+	0.433772i	$0.142818\pi$
$571$			5.26590e13i			0.867545i	−0.901023	+	0.433772i	$0.857182\pi$
$572$	6.36905e11	−	9.15128e12i	0.0104015	−	0.149452i
$573$		−	2.01720e14i		−	3.26570i
$574$	2.05116e13	+	2.19888e13i	0.329185	+	0.352892i
$575$	−1.04761e12	−	3.17634e12i	−0.0166671	−	0.0505345i
$576$	2.54701e13	−	1.20410e14i	0.401715	−	1.89910i
$577$			3.84056e13i			0.600503i	0.953860	+	0.300252i	$0.0970706\pi$
$577$			3.84056e13i			0.600503i	−0.953860	+	0.300252i	$0.902929\pi$
$578$	2.18073e12	+	2.33778e12i	0.0338036	+	0.0362380i
$579$		−	4.43255e13i		−	0.681178i
$580$	−4.45793e13	+	5.34024e13i	−0.679193	+	0.813618i
$581$	−4.29693e13			−0.649049
$582$	−8.72470e13	+	8.13859e13i	−1.30658	+	1.21881i
$583$	1.46517e14			2.17543
$584$	1.68453e13	+	2.07813e13i	0.247978	+	0.305920i
$585$	−6.17082e12	+	8.53303e12i	−0.0900666	+	0.124544i
$586$	2.26709e13	−	2.11479e13i	0.328081	−	0.306041i
$587$	−8.97615e13			−1.28795			−0.643976	−	0.765046i	$-0.722716\pi$
$587$	−8.97615e13			−1.28795			−0.643976	+	0.765046i	$0.722716\pi$
$588$	5.66682e12	−	8.14228e13i	0.0806218	−	1.15840i
$589$	−1.62162e13			−0.228756
$590$	4.25275e13	−	5.32429e12i	0.594854	−	0.0744735i
$591$			1.73277e13i			0.240327i
$592$	9.67609e12	−	6.91780e13i	0.133073	−	0.951392i
$593$			1.00456e14i			1.36994i	0.728570	+	0.684971i	$0.240185\pi$
$593$			1.00456e14i			1.36994i	−0.728570	+	0.684971i	$0.759815\pi$
$594$	−1.65132e14	+	1.54039e14i	−2.23306	+	2.08305i
$595$	2.54400e13	−	3.51784e13i	0.341139	−	0.471728i
$596$	5.96162e12	−	8.56587e13i	0.0792745	−	1.13904i
$597$		−	4.69337e13i		−	0.618890i
$598$	2.35610e11	−	2.19782e11i	0.00308097	−	0.00287400i
$599$			6.48107e13i			0.840451i	0.907420	+	0.420226i	$0.138049\pi$
$599$			6.48107e13i			0.840451i	−0.907420	+	0.420226i	$0.861951\pi$
$600$	1.12197e14	+	7.20804e13i	1.44287	+	0.926960i
$601$	4.74003e13			0.604517			0.302258	−	0.953226i	$-0.402259\pi$
$601$	4.74003e13			0.604517			0.302258	+	0.953226i	$0.402259\pi$
$602$	2.06858e13	+	2.21755e13i	0.261631	+	0.280473i
$603$	−1.51081e13			−0.189506
$604$	9.59403e13	+	6.67720e12i	1.19348	+	0.0830633i
$605$	1.69446e14	+	1.22538e14i	2.09052	+	1.51180i
$606$	5.33420e13	+	5.71835e13i	0.652689	+	0.699693i
$607$	1.17381e14			1.42448			0.712239	−	0.701937i	$-0.247681\pi$
$607$	1.17381e14			1.42448			0.712239	+	0.701937i	$0.247681\pi$
$608$	1.75097e13	−	1.22818e13i	0.210747	−	0.147824i
$609$	8.65211e13			1.03285
$610$	1.78356e13	+	1.42461e14i	0.211173	+	1.68673i
$611$		−	7.28847e12i		−	0.0855914i
$612$	1.70320e14	+	1.18538e13i	1.98384	+	0.138070i
$613$		−	2.07653e13i		−	0.239903i	−0.992780	−	0.119951i	$-0.961726\pi$
$613$		−	2.07653e13i		−	0.239903i	0.992780	−	0.119951i	$-0.0382738\pi$
$614$	−7.31564e13	−	7.84249e13i	−0.838321	−	0.898694i
$615$	−1.03832e14	−	7.50883e13i	−1.18020	−	0.853486i
$616$	6.00494e13	+	7.40803e13i	0.677026	+	0.835217i
$617$		−	9.43318e13i		−	1.05495i	−0.849570	−	0.527476i	$-0.823139\pi$
$617$		−	9.43318e13i		−	1.05495i	0.849570	−	0.527476i	$-0.176861\pi$
$618$	8.69252e12	+	9.31853e12i	0.0964281	+	0.103372i
$619$			7.17966e13i			0.790042i	0.918672	+	0.395021i	$0.129263\pi$
$619$			7.17966e13i			0.790042i	−0.918672	+	0.395021i	$0.870737\pi$
$620$	−6.24976e13	−	5.21718e13i	−0.682189	−	0.569479i
$621$	−7.93182e12			−0.0858845
$622$	−9.78571e13	+	9.12832e13i	−1.05109	+	0.980480i
$623$	1.55889e13			0.166102
$624$	−1.77959e12	+	1.27230e13i	−0.0188104	+	0.134483i
$625$	−7.66550e13	+	5.67358e13i	−0.803786	+	0.594918i
$626$	6.99621e13	−	6.52622e13i	0.727765	−	0.678875i
$627$	−8.09422e13			−0.835290
$628$	−7.73443e13	−	5.38296e12i	−0.791827	−	0.0551091i
$629$	9.68998e13			0.984169
$630$	−1.35990e13	−	1.08621e14i	−0.137026	−	1.09449i
$631$			8.38051e13i			0.837768i	0.908040	+	0.418884i	$0.137579\pi$
$631$			8.38051e13i			0.837768i	−0.908040	+	0.418884i	$0.862421\pi$
$632$	3.42584e13	+	4.22631e13i	0.339767	+	0.419156i
$633$			1.00982e13i			0.0993632i
$634$	−6.26036e13	+	5.83980e13i	−0.611157	+	0.570100i
$635$	3.47158e13	+	2.51054e13i	0.336247	+	0.243164i
$636$	−2.04693e14	−	1.42461e13i	−1.96706	−	0.136902i
$637$			5.62297e12i			0.0536128i
$638$	1.55004e14	−	1.44591e14i	1.46636	−	1.36785i
$639$		−	1.16917e13i		−	0.109742i
$640$	1.06996e14	+	8.99895e12i	0.996482	+	0.0838093i
$641$	1.43838e14			1.32918			0.664589	−	0.747209i	$-0.268607\pi$
$641$	1.43838e14			1.32918			0.664589	+	0.747209i	$0.268607\pi$
$642$	−1.95641e14	−	2.09730e14i	−1.79384	−	1.92303i
$643$	−1.78879e14			−1.62744			−0.813718	−	0.581261i	$-0.802560\pi$
$643$	−1.78879e14			−1.62744			−0.813718	+	0.581261i	$0.802560\pi$
$644$	−2.32551e11	+	3.34138e12i	−0.00209937	+	0.0301645i
$645$	−1.04714e14	−	7.57258e13i	−0.938006	−	0.678337i
$646$	2.02381e13	+	2.16956e13i	0.179890	+	0.192846i
$647$	−7.28610e13			−0.642649			−0.321324	−	0.946969i	$-0.604128\pi$
$647$	−7.28610e13			−0.642649			−0.321324	+	0.946969i	$0.604128\pi$
$648$	7.33885e13	−	5.94886e13i	0.642322	−	0.520666i
$649$	−1.30601e14			−1.13428
$650$	−8.05565e12	−	4.41714e12i	−0.0694279	−	0.0380693i
$651$			1.01257e14i			0.866003i
$652$	−6.46112e11	+	9.28356e12i	−0.00548365	+	0.0787910i
$653$			1.66164e14i			1.39949i	0.714391	+	0.699746i	$0.246704\pi$
$653$			1.66164e14i			1.39949i	−0.714391	+	0.699746i	$0.753296\pi$
$654$	1.48214e13	+	1.58888e13i	0.123880	+	0.132801i
$655$	7.71375e13	−	1.06666e14i	0.639822	−	0.884747i
$656$	−1.02178e14	−	1.42919e13i	−0.841083	−	0.117644i
$657$			9.35747e13i			0.764420i
$658$	5.16819e13	+	5.54038e13i	0.418995	+	0.449169i
$659$			1.90459e14i			1.53241i	0.642598	+	0.766203i	$0.277856\pi$
$659$			1.90459e14i			1.53241i	−0.642598	+	0.766203i	$0.722144\pi$
$660$	−3.11952e14	−	2.60412e14i	−2.49097	−	2.07942i
$661$	−1.33724e14			−1.05974			−0.529872	−	0.848077i	$-0.677760\pi$
$661$	−1.33724e14			−1.05974			−0.529872	+	0.848077i	$0.677760\pi$
$662$	6.03814e13	−	5.63251e13i	0.474912	−	0.443008i
$663$	−1.78215e13			−0.139116
$664$	1.14528e14	−	9.28364e13i	0.887304	−	0.719247i
$665$	1.11476e13	−	1.54150e13i	0.0857184	−	0.118532i
$666$	1.78670e14	−	1.66668e14i	1.36358	−	1.27198i
$667$	7.44531e12			0.0563967
$668$	−9.72010e12	+	1.39662e14i	−0.0730783	+	1.05001i
$669$	−4.26144e13			−0.317999
$670$	−1.63741e12	−	1.30787e13i	−0.0121278	−	0.0968705i
$671$		−	4.37493e14i		−	3.21631i
$672$	−7.66897e13	−	1.09333e14i	−0.559617	−	0.797823i
$673$		−	5.74113e13i		−	0.415836i	−0.978146	−	0.207918i	$-0.933331\pi$
$673$		−	5.74113e13i		−	0.415836i	0.978146	−	0.207918i	$-0.0666687\pi$
$674$	1.36614e14	−	1.27436e14i	0.982189	−	0.916207i
$675$	7.08391e13	+	2.14783e14i	0.505539	+	1.53279i
$676$	−9.73970e12	+	1.39944e14i	−0.0689942	+	0.991332i
$677$			2.05698e14i			1.44639i	0.690643	+	0.723196i	$0.257327\pi$
$677$			2.05698e14i			1.44639i	−0.690643	+	0.723196i	$0.742673\pi$
$678$	−2.09275e13	+	1.95216e13i	−0.146072	+	0.136259i
$679$			8.54479e13i			0.592042i
$680$	8.19762e12	+	1.48727e14i	0.0563824	+	1.02293i
$681$	1.74274e14			1.18986
$682$	1.69217e14	+	1.81403e14i	1.14689	+	1.22949i
$683$	−1.32682e14			−0.892707			−0.446354	−	0.894857i	$-0.647278\pi$
$683$	−1.32682e14			−0.892707			−0.446354	+	0.894857i	$0.647278\pi$
$684$	7.46329e13	+	5.19426e12i	0.498483	+	0.0346931i
$685$	1.45182e14	−	2.00758e14i	0.962632	−	1.33113i
$686$	−9.87583e13	−	1.05871e14i	−0.650060	−	0.696875i
$687$	1.11711e14			0.729982
$688$	−1.03046e14	−	1.44132e13i	−0.668479	−	0.0935016i
$689$	1.41359e13			0.0910389
$690$	−1.77308e12	−	1.41624e13i	−0.0113366	−	0.0905503i
$691$		−	2.33711e13i		−	0.148351i	−0.997245	−	0.0741753i	$-0.976368\pi$
$691$		−	2.33711e13i		−	0.148351i	0.997245	−	0.0741753i	$-0.0236324\pi$
$692$	1.81282e14	+	1.26168e13i	1.14242	+	0.0795093i
$693$			3.33572e14i			2.08700i
$694$	−3.66360e13	−	3.92744e13i	−0.227568	−	0.243956i
$695$	−7.81036e13	+	1.08002e14i	−0.481667	+	0.666051i
$696$	−2.30609e14	+	1.86931e14i	−1.41198	+	1.14455i
$697$		−	1.43124e14i		−	0.870059i
$698$	−7.47340e12	−	8.01161e12i	−0.0451067	−	0.0483551i
$699$		−	5.04966e14i		−	3.02605i
$700$	9.25571e13	−	2.35447e13i	0.550706	−	0.140088i
$701$	5.83512e13			0.344714			0.172357	−	0.985035i	$-0.444862\pi$
$701$	5.83512e13			0.344714			0.172357	+	0.985035i	$0.444862\pi$
$702$	−1.59319e13	+	1.48616e13i	−0.0934506	+	0.0871727i
$703$	4.24609e13			0.247293
$704$	−3.20105e14	−	6.77115e13i	−1.85110	−	0.391561i
$705$	−2.61620e14	−	1.89195e14i	−1.50219	−	1.08634i
$706$	−2.36841e14	+	2.20931e14i	−1.35031	+	1.25960i
$707$	5.60044e13			0.317048
$708$	1.82457e14	+	1.26986e13i	1.02564	+	0.0713819i
$709$	1.09508e14			0.611244			0.305622	−	0.952153i	$-0.401136\pi$
$709$	1.09508e14			0.611244			0.305622	+	0.952153i	$0.401136\pi$
$710$	1.01213e13	−	1.26715e12i	0.0560975	−	0.00702321i
$711$			1.90304e14i			1.04737i
$712$	−4.15499e13	+	3.36803e13i	−0.227076	+	0.184067i
$713$			8.71336e12i			0.0472866i
$714$	1.35471e14	−	1.26370e14i	0.730055	−	0.681011i
$715$	2.26848e13	+	1.64050e13i	0.121396	+	0.0877899i
$716$	−2.24245e14	−	1.56069e13i	−1.19167	−	0.0829374i
$717$		−	3.99646e14i		−	2.10901i
$718$	6.43736e13	−	6.00491e13i	0.337354	−	0.314691i
$719$			1.77812e13i			0.0925372i	0.998929	+	0.0462686i	$0.0147330\pi$
$719$			1.77812e13i			0.0925372i	−0.998929	+	0.0462686i	$0.985267\pi$
$720$	2.70925e14	+	2.60132e14i	1.40019	+	1.34441i
$721$	9.12637e12			0.0468405
$722$	−1.24959e14	−	1.33958e14i	−0.636917	−	0.682785i
$723$	−1.08625e13			−0.0549843
$724$	−8.71871e12	+	1.25273e14i	−0.0438288	+	0.629747i
$725$	−6.64942e13	−	2.01610e14i	−0.331966	−	1.00652i
$726$	6.08696e14	+	6.52532e14i	3.01799	+	3.23533i
$727$	9.64984e13			0.475169			0.237585	−	0.971367i	$-0.423644\pi$
$727$	9.64984e13			0.475169			0.237585	+	0.971367i	$0.423644\pi$
$728$	5.79353e12	+	7.14723e12i	0.0283326	+	0.0349527i
$729$	−2.39444e14			−1.16296
$730$	−8.10056e13	+	1.01416e13i	−0.390752	+	0.0489207i
$731$		−	1.44339e14i		−	0.691509i
$732$	−4.25382e13	+	6.11204e14i	−0.202406	+	2.90824i
$733$		−	1.87541e14i		−	0.886292i	−0.896449	−	0.443146i	$-0.853862\pi$
$733$		−	1.87541e14i		−	0.886292i	0.896449	−	0.443146i	$-0.146138\pi$
$734$	1.42035e14	+	1.52264e14i	0.666676	+	0.714687i
$735$	2.01836e14	+	1.45962e14i	0.940941	+	0.680460i
$736$	−6.59931e12	−	9.40837e12i	−0.0305569	−	0.0435638i
$737$			4.01644e13i			0.184716i
$738$	−2.46173e14	−	2.63902e14i	−1.12450	−	1.20548i
$739$		−	9.38025e13i		−	0.425591i	−0.977097	−	0.212795i	$-0.931743\pi$
$739$		−	9.38025e13i		−	0.425591i	0.977097	−	0.212795i	$-0.0682568\pi$
$740$	1.63645e14	+	1.36608e14i	0.737469	+	0.615626i
$741$	−7.80926e12			−0.0349558
$742$	−1.07455e14	+	1.00236e14i	−0.477757	+	0.445662i
$743$	−1.41345e14			−0.624217			−0.312108	−	0.950047i	$-0.601035\pi$
$743$	−1.41345e14			−0.624217			−0.312108	+	0.950047i	$0.601035\pi$
$744$	−2.18768e14	−	2.69885e14i	−0.959665	−	1.18390i
$745$	2.12337e14	+	1.53555e14i	0.925217	+	0.669088i
$746$	1.34368e14	−	1.25342e14i	0.581570	−	0.542501i
$747$	5.15703e14			2.21716
$748$	3.15130e13	−	4.52790e14i	0.134580	−	1.93370i
$749$	−2.05405e14			−0.871370
$750$	−3.67663e14	+	1.74497e14i	−1.54933	+	0.735327i
$751$			8.16971e13i			0.341985i	0.985272	+	0.170993i	$0.0546974\pi$
$751$			8.16971e13i			0.341985i	−0.985272	+	0.170993i	$0.945303\pi$
$752$	−2.57452e14	−	3.60104e13i	−1.07055	−	0.149740i
$753$			3.42053e14i			1.41292i
$754$	1.49547e13	−	1.39501e13i	0.0613650	−	0.0572426i
$755$	−1.71986e14	+	2.37823e14i	−0.701067	+	0.969437i
$756$	1.57251e13	−	2.25943e14i	0.0636771	−	0.914935i
$757$			1.78329e14i			0.717370i	0.933459	+	0.358685i	$0.116775\pi$
$757$			1.78329e14i			0.717370i	−0.933459	+	0.358685i	$0.883225\pi$
$758$	1.72871e14	−	1.61257e14i	0.690837	−	0.644427i
$759$			4.34921e13i			0.172664i
$760$	3.59215e12	+	6.51711e13i	0.0141673	+	0.257032i
$761$	−1.75974e13			−0.0689487			−0.0344743	−	0.999406i	$-0.510976\pi$
$761$	−1.75974e13			−0.0689487			−0.0344743	+	0.999406i	$0.510976\pi$
$762$	1.24709e14	+	1.33690e14i	0.485425	+	0.520383i
$763$	1.55612e13			0.0601755
$764$	4.94467e14	+	3.44136e13i	1.89963	+	0.132210i
$765$	−3.05322e14	+	4.22199e14i	−1.16533	+	1.61143i
$766$	−1.45457e14	−	1.55933e14i	−0.551558	−	0.591280i
$767$	−1.26003e13			−0.0474683
$768$	4.40623e14	+	1.25722e14i	1.64915	+	0.470548i
$769$	1.26337e14			0.469786			0.234893	−	0.972021i	$-0.424526\pi$
$769$	1.26337e14			0.469786			0.234893	+	0.972021i	$0.424526\pi$
$770$	−2.88766e14	+	3.61525e13i	−1.06682	+	0.133562i
$771$			1.19857e14i			0.439939i
$772$	1.08653e14	+	7.56196e12i	0.396237	+	0.0275770i
$773$		−	4.56574e14i		−	1.65430i	−0.561982	−	0.827150i	$-0.689961\pi$
$773$		−	4.56574e14i		−	1.65430i	0.561982	−	0.827150i	$-0.310039\pi$
$774$	−2.48264e14	−	2.66143e14i	−0.893734	−	0.958097i
$775$	2.35947e14	−	7.78191e13i	0.843928	−	0.278341i
$776$	−1.84613e14	−	2.27749e14i	−0.656075	−	0.809371i
$777$		−	2.65133e14i		−	0.936178i
$778$	1.32233e13	+	1.41756e13i	0.0463920	+	0.0497329i
$779$		−	6.27161e13i		−	0.218621i
$780$	−3.00970e13	−	2.51244e13i	−0.104244	−	0.0870208i
$781$	−3.10821e13			−0.106968
$782$	1.16576e13	−	1.08744e13i	0.0398634	−	0.0371854i
$783$	−5.03451e14			−1.71060
$784$	1.98621e14	+	2.77816e13i	0.670571	+	0.0937943i
$785$	1.38651e14	−	1.91726e14i	0.465129	−	0.643181i
$786$	4.10767e14	−	3.83173e14i	1.36925	−	1.27727i
$787$	−2.89814e14			−0.959943			−0.479972	−	0.877284i	$-0.659353\pi$
$787$	−2.89814e14			−0.959943			−0.479972	+	0.877284i	$0.659353\pi$
$788$	−4.24745e13	−	2.95611e12i	−0.139797	−	0.00972949i
$789$	3.07696e14			1.00632
$790$	−1.64742e14	+	2.06251e13i	−0.535388	+	0.0670287i
$791$			2.04959e13i			0.0661889i
$792$	−7.20692e14	−	8.89086e14i	−2.31272	−	2.85311i
$793$		−	4.22091e13i		−	0.134598i
$794$	−2.68230e14	+	2.50211e14i	−0.849973	+	0.792874i
$795$	3.66942e14	−	5.07408e14i	1.15548	−	1.59780i
$796$	1.15046e14	+	8.00692e12i	0.360004	+	0.0250553i
$797$			3.96700e14i			1.23359i	0.787124	+	0.616795i	$0.211569\pi$
$797$			3.96700e14i			1.23359i	−0.787124	+	0.616795i	$0.788431\pi$
$798$	5.93626e13	−	5.53747e13i	0.183442	−	0.171118i
$799$		−	3.60621e14i		−	1.10743i
$800$	−1.95828e14	+	2.62727e14i	−0.597620	+	0.801779i
$801$	−1.87093e14			−0.567407
$802$	2.93424e14	+	3.14556e14i	0.884350	+	0.948038i
$803$	2.48766e14			0.745097
$804$	3.90526e12	−	5.61121e13i	0.0116244	−	0.167023i
$805$	−8.28282e12	−	5.98988e12i	−0.0245019	−	0.0177190i
$806$	1.63260e13	+	1.75017e13i	0.0479958	+	0.0514523i
$807$	−9.37348e14			−2.73863
$808$	−1.49271e14	+	1.20999e14i	−0.433430	+	0.351338i
$809$	3.38576e14			0.977043			0.488522	−	0.872552i	$-0.337536\pi$
$809$	3.38576e14			0.977043			0.488522	+	0.872552i	$0.337536\pi$
$810$	3.58149e13	+	2.86069e14i	0.102716	+	0.820439i
$811$			1.76436e14i			0.502903i	0.967870	+	0.251451i	$0.0809078\pi$
$811$			1.76436e14i			0.502903i	−0.967870	+	0.251451i	$0.919092\pi$
$812$	−1.47605e13	+	2.12085e14i	−0.0418140	+	0.600799i
$813$			8.36756e14i			2.35584i
$814$	−4.43081e14	−	4.74990e14i	−1.23983	−	1.32912i
$815$	−2.30127e13	−	1.66421e13i	−0.0640000	−	0.0462828i
$816$	−8.80511e13	+	6.29511e14i	−0.243380	+	1.74001i
$817$		−	6.32486e13i		−	0.173756i
$818$	2.87055e14	+	3.07727e14i	0.783787	+	0.840233i
$819$			3.21828e13i			0.0873383i
$820$	2.01774e14	−	2.41709e14i	0.544247	−	0.651963i
$821$	−1.72172e14			−0.461579			−0.230790	−	0.973004i	$-0.574131\pi$
$821$	−1.72172e14			−0.461579			−0.230790	+	0.973004i	$0.574131\pi$
$822$	7.73114e14	−	7.21178e14i	2.06008	−	1.92169i
$823$	−7.17888e14			−1.90133			−0.950665	−	0.310220i	$-0.899597\pi$
$823$	−7.17888e14			−1.90133			−0.950665	+	0.310220i	$0.899597\pi$
$824$	−2.43250e13	+	1.97178e13i	−0.0640349	+	0.0519066i
$825$	1.17771e15	−	3.88429e14i	3.08155	−	1.01635i
$826$	9.57819e13	−	8.93475e13i	0.249106	−	0.232371i
$827$	−1.28185e14			−0.331367			−0.165684	−	0.986179i	$-0.552983\pi$
$827$	−1.28185e14			−0.331367			−0.165684	+	0.986179i	$0.552983\pi$
$828$	2.79100e12	−	4.01020e13i	0.00717146	−	0.103042i
$829$	−5.18132e14			−1.32333			−0.661665	−	0.749800i	$-0.730150\pi$
$829$	−5.18132e14			−1.32333			−0.661665	+	0.749800i	$0.730150\pi$
$830$	5.58918e13	+	4.46433e14i	0.141892	+	1.13335i
$831$			7.34739e14i			1.85408i
$832$	−3.08836e13	−	6.53277e12i	−0.0774660	−	0.0163863i
$833$			2.78215e14i			0.693673i
$834$	−4.15912e14	+	3.87972e14i	−1.03079	+	0.961546i
$835$	−3.46203e14	−	2.50363e14i	−0.852900	−	0.616791i
$836$	1.38088e13	−	1.98409e14i	0.0338161	−	0.485882i
$837$		−	5.89196e14i		−	1.43427i
$838$	−1.75395e14	+	1.63612e14i	−0.424421	+	0.395909i
$839$			2.97140e14i			0.714744i	0.933962	+	0.357372i	$0.116327\pi$
$839$			2.97140e14i			0.714744i	−0.933962	+	0.357372i	$0.883673\pi$
$840$	4.06939e14	−	2.24300e13i	0.973045	−	0.0536330i
$841$	5.18638e13			0.123278
$842$	−1.60163e14	−	1.71697e14i	−0.378444	−	0.405698i
$843$	9.50766e14			2.23324
$844$	−2.47532e13	−	1.72276e12i	−0.0577989	−	0.00402265i
$845$	−3.46901e14	−	2.50868e14i	−0.805235	−	0.582321i
$846$	−6.20268e14	−	6.64937e14i	−1.43129	−	1.53437i
$847$	6.39077e14			1.46601
$848$	6.98417e13	−	4.99324e14i	0.159270	−	1.13868i
$849$	1.56752e14			0.355365
$850$	−3.98580e14	−	2.18552e14i	−0.898298	−	0.492562i
$851$		−	2.28152e13i		−	0.0511184i
$852$	4.34236e13	+	3.02217e12i	0.0967227	+	0.00673165i
$853$			6.60408e14i			1.46240i	0.682161	+	0.731202i	$0.261040\pi$
$853$			6.60408e14i			1.46240i	−0.682161	+	0.731202i	$0.738960\pi$
$854$	2.99300e14	+	3.20855e14i	0.658898	+	0.706349i
$855$	−1.33790e14	+	1.85005e14i	−0.292815	+	0.404905i
$856$	5.47477e14	−	4.43784e14i	1.19123	−	0.965613i
$857$			2.10749e14i			0.455891i	0.973674	+	0.227946i	$0.0732008\pi$
$857$			2.10749e14i			0.455891i	−0.973674	+	0.227946i	$0.926799\pi$
$858$	8.14899e13	+	8.73585e13i	0.175254	+	0.187875i
$859$			4.34528e14i			0.929079i	0.885553	+	0.464539i	$0.153780\pi$
$859$			4.34528e14i			0.929079i	−0.885553	+	0.464539i	$0.846220\pi$
$860$	2.03487e14	−	2.43761e14i	0.432558	−	0.518169i
$861$	−3.91610e14			−0.827633
$862$	−3.47454e14	+	3.24112e14i	−0.730064	+	0.681019i
$863$	5.11819e14			1.06921			0.534605	−	0.845102i	$-0.320461\pi$
$863$	5.11819e14			1.06921			0.534605	+	0.845102i	$0.320461\pi$
$864$	4.46244e14	+	6.36192e14i	0.926838	+	1.32136i
$865$	−3.24974e14	+	4.49374e14i	−0.671070	+	0.927957i
$866$	1.90131e14	−	1.77359e14i	0.390359	−	0.364135i
$867$	−4.16347e13			−0.0849884
$868$	−2.48206e14	−	1.72745e13i	−0.503748	−	0.0350595i
$869$	5.05917e14			1.02089
$870$	−1.12541e14	−	8.98917e14i	−0.225795	−	1.80353i
$871$			3.87504e12i			0.00773010i
$872$	−4.14760e13	+	3.36204e13i	−0.0822649	+	0.0666838i
$873$		−	1.02552e15i		−	2.02242i
$874$	5.10827e12	−	4.76511e12i	0.0100165	−	0.00934363i
$875$	−8.82244e13	+	2.77784e14i	−0.172008	+	0.541585i
$876$	−3.47541e14	−	2.41880e13i	−0.673730	−	0.0468898i
$877$			3.75389e14i			0.723575i	0.932261	+	0.361787i	$0.117833\pi$
$877$			3.75389e14i			0.723575i	−0.932261	+	0.361787i	$0.882167\pi$
$878$	−3.30863e14	+	3.08636e14i	−0.634126	+	0.591527i
$879$			4.03758e14i			0.769444i
$880$	6.91554e14	−	7.20247e14i	1.31043	−	1.36480i
$881$	−5.23418e14			−0.986210			−0.493105	−	0.869970i	$-0.664138\pi$
$881$	−5.23418e14			−0.986210			−0.493105	+	0.869970i	$0.664138\pi$
$882$	4.78529e14	+	5.12991e14i	0.896531	+	0.961096i
$883$	−1.65257e14			−0.307862			−0.153931	−	0.988082i	$-0.549193\pi$
$883$	−1.65257e14			−0.307862			−0.153931	+	0.988082i	$0.549193\pi$
$884$	3.04035e12	−	4.36849e13i	0.00563200	−	0.0809226i
$885$	−3.27080e14	+	4.52287e14i	−0.602473	+	0.833102i
$886$	6.73041e14	+	7.21511e14i	1.23274	+	1.32152i
$887$	9.07021e14			1.65196			0.825980	−	0.563700i	$-0.190622\pi$
$887$	9.07021e14			1.65196			0.825980	+	0.563700i	$0.190622\pi$
$888$	5.72828e14	+	7.06672e14i	1.03743	+	1.27983i
$889$	1.30933e14			0.235798
$890$	−2.02771e13	−	1.61962e14i	−0.0363124	−	0.290044i
$891$		−	8.78510e14i		−	1.56444i
$892$	7.27004e12	−	1.04459e14i	0.0128740	−	0.184978i
$893$		−	1.58022e14i		−	0.278266i
$894$	7.62770e14	+	8.17702e14i	1.33569	+	1.43188i
$895$	4.01990e14	−	5.55873e14i	0.700004	−	0.967967i
$896$	2.81087e14	−	1.69333e14i	0.486744	−	0.293226i
$897$			4.19610e12i			0.00722576i
$898$	−4.19293e14	−	4.49489e14i	−0.718019	−	0.769728i
$899$			5.53057e14i			0.941827i
$900$	−1.11084e15	+	2.82575e14i	−1.88121	+	0.478543i
$901$	6.99420e14			1.17791
$902$	−7.01575e14	+	6.54445e14i	−1.17501	+	1.09608i
$903$	−3.94935e14			−0.657789
$904$	−4.42820e13	−	5.46288e13i	−0.0733475	−	0.0904856i
$905$	−3.10536e14	−	2.24570e14i	−0.511528	−	0.369921i
$906$	−9.15851e14	+	8.54325e14i	−1.50032	+	1.39953i
$907$	−8.39001e13			−0.136687			−0.0683433	−	0.997662i	$-0.521771\pi$
$907$	−8.39001e13			−0.136687			−0.0683433	+	0.997662i	$0.521771\pi$
$908$	−2.97312e13	+	4.27189e14i	−0.0481708	+	0.692135i
$909$	−6.72145e14			−1.08304
$910$	−2.78600e13	+	3.48797e12i	−0.0446451	+	0.00558941i
$911$		−	1.07489e15i		−	1.71305i	−0.516105	−	0.856526i	$-0.672618\pi$
$911$		−	1.07489e15i		−	1.71305i	0.516105	−	0.856526i	$-0.327382\pi$
$912$	−3.85834e13	+	2.75848e14i	−0.0611543	+	0.437215i
$913$		−	1.37098e15i		−	2.16111i
$914$	1.10204e14	−	1.02801e14i	0.172769	−	0.161163i
$915$	−1.51509e15	−	1.09567e15i	−2.36229	−	1.70834i
$916$	−1.90580e13	+	2.73832e14i	−0.0295528	+	0.424626i
$917$		−	4.02297e14i		−	0.620441i
$918$	−7.88283e14	+	7.35327e14i	−1.20912	+	1.12789i
$919$		−	1.10438e15i		−	1.68478i	−0.538869	−	0.842389i	$-0.681148\pi$
$919$		−	1.10438e15i		−	1.68478i	0.538869	−	0.842389i	$-0.318852\pi$
$920$	3.50180e13	−	1.93014e12i	0.0531314	−	0.00292854i
$921$	1.39671e15			2.10769
$922$	−4.95873e14	−	5.31584e14i	−0.744244	−	0.797842i
$923$	−2.99879e12			−0.00447648
$924$	−1.23890e15	−	8.62244e13i	−1.83940	−	0.128018i
$925$	−6.17807e14	+	2.03763e14i	−0.912314	+	0.300896i
$926$	−2.59654e14	−	2.78353e14i	−0.381364	−	0.408829i
$927$	−1.09532e14			−0.160008
$928$	−4.18873e14	−	5.97171e14i	−0.608615	−	0.867678i
$929$	−6.55366e14			−0.947120			−0.473560	−	0.880761i	$-0.657031\pi$
$929$	−6.55366e14			−0.947120			−0.473560	+	0.880761i	$0.657031\pi$
$930$	1.05202e15	−	1.31708e14i	1.51219	−	0.189321i
$931$			1.21912e14i			0.174300i
$932$	1.23780e15	+	8.61475e13i	1.76023	+	0.122508i
$933$		−	1.74279e15i		−	2.46511i
$934$	−3.45021e14	−	3.69868e14i	−0.485413	−	0.520371i
$935$	1.12240e15	+	8.11689e14i	1.57069	+	1.13588i
$936$	−6.95320e13	−	8.57786e13i	−0.0967844	−	0.119399i
$937$			4.27785e13i			0.0592280i	0.999561	+	0.0296140i	$0.00942781\pi$
$937$			4.27785e13i			0.0592280i	−0.999561	+	0.0296140i	$0.990572\pi$
$938$	−2.74775e13	−	2.94564e13i	−0.0378411	−	0.0405663i
$939$			1.24599e15i			1.70682i
$940$	5.08397e14	−	6.09018e14i	0.692730	−	0.829834i
$941$	−1.83872e14			−0.249211			−0.124606	−	0.992206i	$-0.539767\pi$
$941$	−1.83872e14			−0.249211			−0.124606	+	0.992206i	$0.539767\pi$
$942$	7.38332e14	−	6.88732e14i	0.995399	−	0.928530i
$943$	−3.36988e13			−0.0451914
$944$	−6.22546e13	+	4.45082e14i	−0.0830447	+	0.593718i
$945$	5.60083e14	+	4.05035e14i	0.743179	+	0.537444i
$946$	−7.07532e14	+	6.60001e14i	−0.933879	+	0.871142i
$947$	−6.38008e14			−0.837676			−0.418838	−	0.908061i	$-0.637563\pi$
$947$	−6.38008e14			−0.837676			−0.418838	+	0.908061i	$0.637563\pi$
$948$	−7.06798e14	−	4.91913e13i	−0.923110	−	0.0642461i
$949$	2.40008e13			0.0311813
$950$	−1.74655e14	−	9.57683e13i	−0.225716	−	0.123767i
$951$		−	1.11494e15i		−	1.43334i
$952$	2.86654e14	+	3.53633e14i	0.366584	+	0.452238i
$953$			7.66894e13i			0.0975598i	0.998810	+	0.0487799i	$0.0155333\pi$
$953$			7.66894e13i			0.0975598i	−0.998810	+	0.0487799i	$0.984467\pi$
$954$	1.28964e15	−	1.20300e15i	1.63202	−	1.52238i
$955$	−8.86401e14	+	1.22572e15i	−1.11587	+	1.54303i
$956$	9.79632e14	+	6.81798e13i	1.22680	+	0.0853820i
$957$			2.76054e15i			3.43902i
$958$	6.91652e14	−	6.45188e14i	0.857156	−	0.799574i
$959$		−	7.57172e14i		−	0.933473i
$960$	−1.03617e15	+	9.38988e14i	−1.27080	+	1.15161i
$961$	1.72378e14			0.210312
$962$	−4.27482e13	−	4.58268e13i	−0.0518851	−	0.0556217i
$963$	2.46520e15			2.97661
$964$	1.85315e12	−	2.66267e13i	0.00222600	−	0.0319840i
$965$	−1.94775e14	+	2.69336e14i	−0.232754	+	0.321853i
$966$	−2.97541e13	−	3.18969e13i	−0.0353722	−	0.0379195i
$967$	−2.25580e14			−0.266789			−0.133395	−	0.991063i	$-0.542588\pi$
$967$	−2.25580e14			−0.266789			−0.133395	+	0.991063i	$0.542588\pi$
$968$	−1.70336e15	+	1.38074e15i	−2.00415	+	1.62456i
$969$	−3.86389e14			−0.452278
$970$	8.87768e14	−	1.11145e14i	1.03381	−	0.129429i
$971$		−	5.77792e14i		−	0.669384i	−0.942328	−	0.334692i	$-0.891368\pi$
$971$		−	5.77792e14i		−	0.669384i	0.942328	−	0.334692i	$-0.108632\pi$
$972$	1.18062e13	−	1.69636e14i	0.0136075	−	0.195518i
$973$			4.07336e14i			0.467077i
$974$	6.79878e14	+	7.28841e14i	0.775598	+	0.831453i
$975$	1.13625e14	−	3.74754e13i	0.128959	−	0.0425327i
$976$	−1.49096e15	−	2.08544e14i	−1.68351	−	0.235477i
$977$		−	8.28261e14i		−	0.930453i	−0.885192	−	0.465226i	$-0.845973\pi$
$977$		−	8.28261e14i		−	0.930453i	0.885192	−	0.465226i	$-0.154027\pi$
$978$	−8.26678e13	−	8.86213e13i	−0.0923937	−	0.0990475i
$979$			4.97381e14i			0.553064i
$980$	−3.92222e14	+	4.69850e14i	−0.433912	+	0.519791i
$981$	−1.86760e14			−0.205560
$982$	−1.36358e14	+	1.27198e14i	−0.149322	+	0.139291i
$983$	1.37976e15			1.50327			0.751633	−	0.659582i	$-0.229267\pi$
$983$	1.37976e15			1.50327			0.751633	+	0.659582i	$0.229267\pi$
$984$	1.04378e15	−	8.46084e14i	1.13144	−	0.917145i
$985$	7.61415e13	−	1.05289e14i	0.0821183	−	0.113553i
$986$	7.39933e14	−	6.90225e14i	0.793976	−	0.740638i
$987$	−9.86715e14			−1.05343
$988$	1.33226e12	−	1.91424e13i	0.00141516	−	0.0203335i
$989$	−3.39849e13			−0.0359174
$990$	3.46567e15	−	4.33889e14i	3.64428	−	0.456250i
$991$			1.62380e15i			1.69889i	0.527679	+	0.849444i	$0.323062\pi$
$991$			1.62380e15i			1.69889i	−0.527679	+	0.849444i	$0.676938\pi$
$992$	6.98878e14	−	4.90213e14i	0.727516	−	0.510301i
$993$			1.07536e15i			1.11380i
$994$	2.27955e13	−	2.12641e13i	0.0234918	−	0.0219137i
$995$	−2.06237e14	+	2.85184e14i	−0.211471	+	0.292422i
$996$	−1.33303e14	+	1.91534e15i	−0.136001	+	1.95412i
$997$		−	6.99475e14i		−	0.710062i	−0.934854	−	0.355031i	$-0.884470\pi$
$997$		−	6.99475e14i		−	0.710062i	0.934854	−	0.355031i	$-0.115530\pi$
$998$	5.91823e14	−	5.52065e14i	0.597776	−	0.557619i
$999$			1.54276e15i			1.55050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.d.d.19.7	✓	24
4.3	odd	2	inner	20.11.d.d.19.17	yes	24
5.2	odd	4		100.11.b.h.51.19		24
5.3	odd	4		100.11.b.h.51.6		24
5.4	even	2	inner	20.11.d.d.19.18	yes	24
20.3	even	4		100.11.b.h.51.5		24
20.7	even	4		100.11.b.h.51.20		24
20.19	odd	2	inner	20.11.d.d.19.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.7	✓	24	1.1	even	1	trivial
20.11.d.d.19.8	yes	24	20.19	odd	2	inner
20.11.d.d.19.17	yes	24	4.3	odd	2	inner
20.11.d.d.19.18	yes	24	5.4	even	2	inner
100.11.b.h.51.5		24	20.3	even	4
100.11.b.h.51.6		24	5.3	odd	4
100.11.b.h.51.19		24	5.2	odd	4
100.11.b.h.51.20		24	20.7	even	4

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.8278 - 23.3997i) q^{2} +416.738 q^{3} +(-71.0958 + 1021.53i) q^{4} +(-2532.23 - 1831.23i) q^{5} +(-9096.47 - 9751.56i) q^{6} -9550.48 q^{7} +(25455.4 - 20634.1i) q^{8} +114622. q^{9} +O(q^{10})\)	\(q+(-21.8278 - 23.3997i) q^{2} +416.738 q^{3} +(-71.0958 + 1021.53i) q^{4} +(-2532.23 - 1831.23i) q^{5} +(-9096.47 - 9751.56i) q^{6} -9550.48 q^{7} +(25455.4 - 20634.1i) q^{8} +114622. q^{9} +(12422.7 + 99225.4i) q^{10} -304718. i q^{11} +(-29628.3 + 425710. i) q^{12} -29399.0i q^{13} +(208466. + 223479. i) q^{14} +(-1.05528e6 - 763145. i) q^{15} +(-1.03847e6 - 145253. i) q^{16} -1.45461e6i q^{17} +(-2.50193e6 - 2.68211e6i) q^{18} -637402. i q^{19} +(2.05069e6 - 2.45656e6i) q^{20} -3.98005e6 q^{21} +(-7.13032e6 + 6.65132e6i) q^{22} -342491. q^{23} +(1.06082e7 - 8.59901e6i) q^{24} +(3.05879e6 + 9.27422e6i) q^{25} +(-687930. + 641716. i) q^{26} +2.31592e7 q^{27} +(678998. - 9.75609e6i) q^{28} -2.17387e7 q^{29} +(5.17699e6 + 4.13510e7i) q^{30} -2.54411e7i q^{31} +(1.92686e7 + 2.74704e7i) q^{32} -1.26988e8i q^{33} +(-3.40376e7 + 3.17510e7i) q^{34} +(2.41840e7 + 1.74892e7i) q^{35} +(-8.14910e6 + 1.17089e8i) q^{36} +6.66155e7i q^{37} +(-1.49150e7 + 1.39131e7i) q^{38} -1.22517e7i q^{39} +(-1.02245e8 + 5.63560e6i) q^{40} +9.83932e7 q^{41} +(8.68756e7 + 9.31321e7i) q^{42} +9.92286e7 q^{43} +(3.11278e8 + 2.16642e7i) q^{44} +(-2.90249e8 - 2.09899e8i) q^{45} +(7.47582e6 + 8.01421e6i) q^{46} +2.47915e8 q^{47} +(-4.32769e8 - 6.05323e7i) q^{48} -1.91264e8 q^{49} +(1.50248e8 - 2.74011e8i) q^{50} -6.06193e8i q^{51} +(3.00320e7 + 2.09015e6i) q^{52} +4.80828e8i q^{53} +(-5.05514e8 - 5.41919e8i) q^{54} +(-5.58010e8 + 7.71617e8i) q^{55} +(-2.43111e8 + 1.97065e8i) q^{56} -2.65630e8i q^{57} +(4.74508e8 + 5.08680e8i) q^{58} -4.28595e8i q^{59} +(8.54600e8 - 1.02374e9i) q^{60} +1.43573e9 q^{61} +(-5.95315e8 + 5.55323e8i) q^{62} -1.09469e9 q^{63} +(2.22210e8 - 1.05050e9i) q^{64} +(-5.38365e7 + 7.44452e7i) q^{65} +(-2.97148e9 + 2.77186e9i) q^{66} -1.31808e8 q^{67} +(1.48593e9 + 1.03417e8i) q^{68} -1.42729e8 q^{69} +(-1.18642e8 - 9.47650e8i) q^{70} -1.02003e8i q^{71} +(2.91773e9 - 2.36511e9i) q^{72} +8.16380e8i q^{73} +(1.55879e9 - 1.45407e9i) q^{74} +(1.27471e9 + 3.86492e9i) q^{75} +(6.51125e8 + 4.53166e7i) q^{76} +2.91020e9i q^{77} +(-2.86686e8 + 2.67427e8i) q^{78} +1.66028e9i q^{79} +(2.36365e9 + 2.26949e9i) q^{80} +2.88303e9 q^{81} +(-2.14771e9 - 2.30238e9i) q^{82} +4.49918e9 q^{83} +(2.82964e8 - 4.06573e9i) q^{84} +(-2.66374e9 + 3.68342e9i) q^{85} +(-2.16594e9 - 2.32192e9i) q^{86} -9.05934e9 q^{87} +(-6.28758e9 - 7.75671e9i) q^{88} -1.63227e9 q^{89} +(1.42390e9 + 1.13734e10i) q^{90} +2.80775e8i q^{91} +(2.43497e7 - 3.49865e8i) q^{92} -1.06023e10i q^{93} +(-5.41144e9 - 5.80115e9i) q^{94} +(-1.16723e9 + 1.61405e9i) q^{95} +(8.02994e9 + 1.14480e10i) q^{96} -8.94698e9i q^{97} +(4.17486e9 + 4.47552e9i) q^{98} -3.49273e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

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