LMFDB - Embedded newform 20.11.b.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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, 0]))

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.b (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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + \cdots + 11\!\cdots\!25 $ x^20 - x^19 + 84x^18 - 86x^17 - 51565x^16 + 188134x^15 - 12946328x^14 + 95990512x^13 + 5401091173x^12 - 59241975423x^11 + 1752287752812x^10 - 13855072435862x^9 + 53025624411849x^8 + 4768661862568058x^7 - 71663288570646432x^6 + 1087383280946073208x^5 - 9530913414031332129x^4 - 22591082233500222765x^3 + 1758197001700115583660x^2 - 51913151006968686718150x + 1126337396992659918451525
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{94}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.20
Root			$16.0838 + 4.09984i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.11.b.a.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 + 507.259i) q^{4} +1397.54 q^{5} +(1692.62 - 6385.07i) q^{6} -1527.38i q^{7} +(23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +O(q^{10})$	\(q+(30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 + 507.259i) q^{4} +1397.54 q^{5} +(1692.62 - 6385.07i) q^{6} -1527.38i q^{7} +(23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +(43228.3 + 11459.4i) q^{10} -294294. i q^{11} +(104711. - 183622. i) q^{12} +198131. q^{13} +(12524.1 - 47244.5i) q^{14} -288488. i q^{15} +(533953. + 902445. i) q^{16} +367959. q^{17} +(508442. + 134783. i) q^{18} +919311. i q^{19} +(1.24316e6 + 708916. i) q^{20} -315291. q^{21} +(2.41311e6 - 9.10298e6i) q^{22} +2.57690e6i q^{23} +(4.74452e6 - 4.82111e6i) q^{24} +1.95312e6 q^{25} +(6.12851e6 + 1.62461e6i) q^{26} -1.55823e7i q^{27} +(774779. - 1.35865e6i) q^{28} -1.40898e7 q^{29} +(2.36551e6 - 8.92340e6i) q^{30} +4.90356e7i q^{31} +(9.11626e6 + 3.22923e7i) q^{32} -6.07497e7 q^{33} +(1.13816e7 + 3.01715e6i) q^{34} -2.13458e6i q^{35} +(1.46218e7 + 8.33812e6i) q^{36} -1.21502e8 q^{37} +(-7.53806e6 + 2.84358e7i) q^{38} -4.08993e7i q^{39} +(3.26400e7 + 3.21214e7i) q^{40} -1.48908e8 q^{41} +(-9.75245e6 - 2.58528e6i) q^{42} +1.41368e8i q^{43} +(1.49283e8 - 2.61783e8i) q^{44} +2.29723e7 q^{45} +(-2.11297e7 + 7.97076e7i) q^{46} +3.99006e7i q^{47} +(1.86287e8 - 1.10221e8i) q^{48} +2.80142e8 q^{49} +(6.04133e7 + 1.60150e7i) q^{50} -7.59561e7i q^{51} +(1.76244e8 + 1.00504e8i) q^{52} +1.03715e8 q^{53} +(1.27770e8 - 4.81987e8i) q^{54} -4.11288e8i q^{55} +(3.51057e7 - 3.56724e7i) q^{56} +1.89769e8 q^{57} +(-4.35820e8 - 1.15532e8i) q^{58} +4.38769e8i q^{59} +(1.46338e8 - 2.56619e8i) q^{60} -2.83067e8 q^{61} +(-4.02077e8 + 1.51675e9i) q^{62} -2.51065e7i q^{63} +(1.71940e7 + 1.07360e9i) q^{64} +2.76897e8 q^{65} +(-1.87909e9 - 4.98128e8i) q^{66} -2.00990e9i q^{67} +(3.27311e8 + 1.86651e8i) q^{68} +5.31936e8 q^{69} +(1.75029e7 - 6.60261e7i) q^{70} +1.54881e9i q^{71} +(3.83905e8 + 3.77805e8i) q^{72} +3.44009e9 q^{73} +(-3.75824e9 - 9.96274e8i) q^{74} -4.03174e8i q^{75} +(-4.66329e8 + 8.17756e8i) q^{76} -4.49499e8 q^{77} +(3.35361e8 - 1.26508e9i) q^{78} +2.88212e9i q^{79} +(7.46222e8 + 1.26120e9i) q^{80} -2.24597e9 q^{81} +(-4.60595e9 - 1.22100e9i) q^{82} -3.41069e9i q^{83} +(-2.80461e8 - 1.59934e8i) q^{84} +5.14239e8 q^{85} +(-1.15917e9 + 4.37273e9i) q^{86} +2.90849e9i q^{87} +(6.76411e9 - 6.87330e9i) q^{88} -2.47857e9 q^{89} +(7.10569e8 + 1.88365e8i) q^{90} -3.02622e8i q^{91} +(-1.30715e9 + 2.29223e9i) q^{92} +1.01222e10 q^{93} +(-3.27173e8 + 1.23419e9i) q^{94} +1.28478e9i q^{95} +(6.66595e9 - 1.88183e9i) q^{96} -2.70022e9 q^{97} +(8.66526e9 + 2.29708e9i) q^{98} -4.83748e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * q^98

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 $

$2$	30.9316	+	8.19968i	0.966613	+	0.256240i
$2$	30.9316	+	8.19968i	0.966613	+	0.256240i
$3$		−	206.425i		−	0.849487i	−0.905314	−	0.424743i	$-0.860364\pi$
$3$		−	206.425i		−	0.849487i	0.905314	−	0.424743i	$-0.139636\pi$
$4$	889.530	+	507.259i	0.868682	+	0.495370i
$5$	1397.54			0.447214
$5$	1397.54			0.447214
$6$	1692.62	−	6385.07i	0.217673	−	0.821125i
$7$		−	1527.38i		−	0.0908778i	−0.998967	−	0.0454389i	$-0.985531\pi$
$7$		−	1527.38i		−	0.0908778i	0.998967	−	0.0454389i	$-0.0144686\pi$
$8$	23355.3	+	22984.2i	0.712746	+	0.701422i
$9$	16437.6			0.278372
$10$	43228.3	+	11459.4i	0.432283	+	0.114594i
$11$		−	294294.i		−	1.82733i	−0.406465	−	0.913666i	$-0.633239\pi$
$11$		−	294294.i		−	1.82733i	0.406465	−	0.913666i	$-0.366761\pi$
$12$	104711.	−	183622.i	0.420810	−	0.737934i
$13$	198131.			0.533625			0.266812	−	0.963749i	$-0.414030\pi$
$13$	198131.			0.533625			0.266812	+	0.963749i	$0.414030\pi$
$14$	12524.1	−	47244.5i	0.0232865	−	0.0878437i
$15$		−	288488.i		−	0.379902i
$16$	533953.	+	902445.i	0.509217	+	0.860638i
$17$	367959.			0.259152			0.129576	−	0.991569i	$-0.458638\pi$
$17$	367959.			0.259152			0.129576	+	0.991569i	$0.458638\pi$
$18$	508442.	+	134783.i	0.269078	+	0.0713302i
$19$			919311.i			0.371274i	0.982618	+	0.185637i	$0.0594349\pi$
$19$			919311.i			0.371274i	−0.982618	+	0.185637i	$0.940565\pi$
$20$	1.24316e6	+	708916.i	0.388486	+	0.221536i
$21$	−315291.			−0.0771995
$22$	2.41311e6	−	9.10298e6i	0.468236	−	1.76632i
$23$			2.57690e6i			0.400366i	0.979758	+	0.200183i	$0.0641537\pi$
$23$			2.57690e6i			0.400366i	−0.979758	+	0.200183i	$0.935846\pi$
$24$	4.74452e6	−	4.82111e6i	0.595849	−	0.605468i
$25$	1.95312e6			0.200000
$26$	6.12851e6	+	1.62461e6i	0.515808	+	0.136736i
$27$		−	1.55823e7i		−	1.08596i
$28$	774779.	−	1.35865e6i	0.0450182	−	0.0789440i
$29$	−1.40898e7			−0.686934			−0.343467	−	0.939165i	$-0.611601\pi$
$29$	−1.40898e7			−0.686934			−0.343467	+	0.939165i	$0.611601\pi$
$30$	2.36551e6	−	8.92340e6i	0.0973461	−	0.367218i
$31$			4.90356e7i			1.71279i	0.516324	+	0.856393i	$0.327300\pi$
$31$			4.90356e7i			1.71279i	−0.516324	+	0.856393i	$0.672700\pi$
$32$	9.11626e6	+	3.22923e7i	0.271686	+	0.962386i
$33$	−6.07497e7			−1.55229
$34$	1.13816e7	+	3.01715e6i	0.250500	+	0.0664052i
$35$		−	2.13458e6i		−	0.0406418i
$36$	1.46218e7	+	8.33812e6i	0.241817	+	0.137897i
$37$	−1.21502e8			−1.75216			−0.876079	−	0.482168i	$-0.839850\pi$
$37$	−1.21502e8			−1.75216			−0.876079	+	0.482168i	$0.839850\pi$
$38$	−7.53806e6	+	2.84358e7i	−0.0951353	+	0.358878i
$39$		−	4.08993e7i		−	0.453307i
$40$	3.26400e7	+	3.21214e7i	0.318750	+	0.313686i
$41$	−1.48908e8			−1.28528			−0.642640	−	0.766168i	$-0.722161\pi$
$41$	−1.48908e8			−1.28528			−0.642640	+	0.766168i	$0.722161\pi$
$42$	−9.75245e6	−	2.58528e6i	−0.0746221	−	0.0197816i
$43$			1.41368e8i			0.961630i	0.876822	+	0.480815i	$0.159659\pi$
$43$			1.41368e8i			0.961630i	−0.876822	+	0.480815i	$0.840341\pi$
$44$	1.49283e8	−	2.61783e8i	0.905206	−	1.58737i
$45$	2.29723e7			0.124492
$46$	−2.11297e7	+	7.97076e7i	−0.102590	+	0.386999i
$47$			3.99006e7i			0.173976i	0.996209	+	0.0869882i	$0.0277243\pi$
$47$			3.99006e7i			0.173976i	−0.996209	+	0.0869882i	$0.972276\pi$
$48$	1.86287e8	−	1.10221e8i	0.731101	−	0.432573i
$49$	2.80142e8			0.991741
$50$	6.04133e7	+	1.60150e7i	0.193323	+	0.0512480i
$51$		−	7.59561e7i		−	0.220146i
$52$	1.76244e8	+	1.00504e8i	0.463550	+	0.264342i
$53$	1.03715e8			0.248005			0.124003	−	0.992282i	$-0.460427\pi$
$53$	1.03715e8			0.248005			0.124003	+	0.992282i	$0.460427\pi$
$54$	1.27770e8	−	4.81987e8i	0.278267	−	1.04970i
$55$		−	4.11288e8i		−	0.817208i
$56$	3.51057e7	−	3.56724e7i	0.0637438	−	0.0647728i
$57$	1.89769e8			0.315392
$58$	−4.35820e8	−	1.15532e8i	−0.663999	−	0.176020i
$59$			4.38769e8i			0.613728i	0.951753	+	0.306864i	$0.0992797\pi$
$59$			4.38769e8i			0.613728i	−0.951753	+	0.306864i	$0.900720\pi$
$60$	1.46338e8	−	2.56619e8i	0.188192	−	0.330014i
$61$	−2.83067e8			−0.335151			−0.167575	−	0.985859i	$-0.553594\pi$
$61$	−2.83067e8			−0.335151			−0.167575	+	0.985859i	$0.553594\pi$
$62$	−4.02077e8	+	1.51675e9i	−0.438885	+	1.65560i
$63$		−	2.51065e7i		−	0.0252979i
$64$	1.71940e7	+	1.07360e9i	0.0160132	+	0.999872i
$65$	2.76897e8			0.238644
$66$	−1.87909e9	−	4.98128e8i	−1.50047	−	0.397760i
$67$		−	2.00990e9i		−	1.48868i	−0.667801	−	0.744340i	$-0.732764\pi$
$67$		−	2.00990e9i		−	1.48868i	0.667801	−	0.744340i	$-0.267236\pi$
$68$	3.27311e8	+	1.86651e8i	0.225121	+	0.128376i
$69$	5.31936e8			0.340106
$70$	1.75029e7	−	6.60261e7i	0.0104141	−	0.0392849i
$71$			1.54881e9i			0.858434i	0.903201	+	0.429217i	$0.141210\pi$
$71$			1.54881e9i			0.858434i	−0.903201	+	0.429217i	$0.858790\pi$
$72$	3.83905e8	+	3.77805e8i	0.198409	+	0.195257i
$73$	3.44009e9			1.65942			0.829709	−	0.558196i	$-0.188506\pi$
$73$	3.44009e9			1.65942			0.829709	+	0.558196i	$0.188506\pi$
$74$	−3.75824e9	−	9.96274e8i	−1.69366	−	0.448973i
$75$		−	4.03174e8i		−	0.169897i
$76$	−4.66329e8	+	8.17756e8i	−0.183918	+	0.322519i
$77$	−4.49499e8			−0.166064
$78$	3.35361e8	−	1.26508e9i	0.116155	−	0.438172i
$79$			2.88212e9i			0.936649i	0.883556	+	0.468325i	$0.155142\pi$
$79$			2.88212e9i			0.936649i	−0.883556	+	0.468325i	$0.844858\pi$
$80$	7.46222e8	+	1.26120e9i	0.227729	+	0.384889i
$81$	−2.24597e9			−0.644137
$82$	−4.60595e9	−	1.22100e9i	−1.24237	−	0.329340i
$83$		−	3.41069e9i		−	0.865868i	−0.901426	−	0.432934i	$-0.857478\pi$
$83$		−	3.41069e9i		−	0.865868i	0.901426	−	0.432934i	$-0.142522\pi$
$84$	−2.80461e8	−	1.59934e8i	−0.0670618	−	0.0382423i
$85$	5.14239e8			0.115896
$86$	−1.15917e9	+	4.37273e9i	−0.246408	+	0.929525i
$87$			2.90849e9i			0.583541i
$88$	6.76411e9	−	6.87330e9i	1.28173	−	1.30242i
$89$	−2.47857e9			−0.443865			−0.221932	−	0.975062i	$-0.571236\pi$
$89$	−2.47857e9			−0.443865			−0.221932	+	0.975062i	$0.571236\pi$
$90$	7.10569e8	+	1.88365e8i	0.120335	+	0.0318998i
$91$		−	3.02622e8i		−	0.0484946i
$92$	−1.30715e9	+	2.29223e9i	−0.198330	+	0.347791i
$93$	1.01222e10			1.45499
$94$	−3.27173e8	+	1.23419e9i	−0.0445798	+	0.168168i
$95$			1.28478e9i			0.166039i
$96$	6.66595e9	−	1.88183e9i	0.817534	−	0.230793i
$97$	−2.70022e9			−0.314442			−0.157221	−	0.987563i	$-0.550254\pi$
$97$	−2.70022e9			−0.314442			−0.157221	+	0.987563i	$0.550254\pi$
$98$	8.66526e9	+	2.29708e9i	0.958630	+	0.254124i
$99$		−	4.83748e9i		−	0.508679i
$100$	1.73736e9	+	9.90740e8i	0.173736	+	0.0990740i
$101$	−1.16539e10			−1.10883			−0.554413	−	0.832242i	$-0.687057\pi$
$101$	−1.16539e10			−1.10883			−0.554413	+	0.832242i	$0.687057\pi$
$102$	6.22816e8	−	2.34944e9i	0.0564103	−	0.212796i
$103$		−	1.62063e10i		−	1.39797i	−0.715136	−	0.698986i	$-0.753635\pi$
$103$		−	1.62063e10i		−	1.39797i	0.715136	−	0.698986i	$-0.246365\pi$
$104$	4.62740e9	+	4.55389e9i	0.380339	+	0.374296i
$105$	−4.40632e8			−0.0345247
$106$	3.20806e9	+	8.50427e8i	0.239725	+	0.0635488i
$107$			1.62492e9i			0.115854i	0.998321	+	0.0579271i	$0.0184491\pi$
$107$			1.62492e9i			0.115854i	−0.998321	+	0.0579271i	$0.981551\pi$
$108$	7.90428e9	−	1.38610e10i	0.537952	−	0.943354i
$109$	−1.11266e10			−0.723152			−0.361576	−	0.932343i	$-0.617761\pi$
$109$	−1.11266e10			−0.723152			−0.361576	+	0.932343i	$0.617761\pi$
$110$	3.37243e9	−	1.27218e10i	0.209401	−	0.789924i
$111$			2.50810e10i			1.48843i
$112$	1.37838e9	−	8.15551e8i	0.0782129	−	0.0462765i
$113$	−3.01321e9			−0.163545			−0.0817724	−	0.996651i	$-0.526058\pi$
$113$	−3.01321e9			−0.163545			−0.0817724	+	0.996651i	$0.526058\pi$
$114$	5.86987e9	+	1.55605e9i	0.304862	+	0.0808162i
$115$			3.60132e9i			0.179049i
$116$	−1.25333e10	−	7.14718e9i	−0.596727	−	0.340286i
$117$	3.25680e9			0.148546
$118$	−3.59777e9	+	1.35718e10i	−0.157262	+	0.593238i
$119$		−	5.62015e8i		−	0.0235512i
$120$	6.63067e9	−	6.73771e9i	0.266472	−	0.270774i
$121$	−6.06714e10			−2.33914
$122$	−8.75572e9	−	2.32106e9i	−0.323961	−	0.0858790i
$123$			3.07383e10i			1.09183i
$124$	−2.48738e10	+	4.36187e10i	−0.848463	+	1.48787i
$125$	2.72958e9			0.0894427
$126$	2.05866e8	−	7.76586e8i	0.00648233	−	0.0244533i
$127$			4.21591e10i			1.27607i	0.770009	+	0.638033i	$0.220252\pi$
$127$			4.21591e10i			1.27607i	−0.770009	+	0.638033i	$0.779748\pi$
$128$	−8.27137e9	+	3.33493e10i	−0.240729	+	0.970592i
$129$	2.91819e10			0.816892
$130$	8.56486e9	+	2.27046e9i	0.230677	+	0.0611502i
$131$		−	4.76933e10i		−	1.23623i	−0.786086	−	0.618117i	$-0.787896\pi$
$131$		−	4.76933e10i		−	1.23623i	0.786086	−	0.618117i	$-0.212104\pi$
$132$	−5.40387e10	−	3.08158e10i	−1.34845	−	0.768960i
$133$	1.40414e9			0.0337406
$134$	1.64806e10	−	6.21696e10i	0.381459	−	1.43898i
$135$		−	2.17770e10i		−	0.485656i
$136$	8.59378e9	+	8.45725e9i	0.184710	+	0.181775i
$137$	8.32695e10			1.72537			0.862687	−	0.505738i	$-0.168780\pi$
$137$	8.32695e10			1.72537			0.862687	+	0.505738i	$0.168780\pi$
$138$	1.64537e10	+	4.36171e9i	0.328751	+	0.0871488i
$139$		−	6.32987e10i		−	1.21989i	−0.792444	−	0.609945i	$-0.791191\pi$
$139$		−	6.32987e10i		−	1.21989i	0.792444	−	0.609945i	$-0.208809\pi$
$140$	1.08279e9	−	1.89878e9i	0.0201327	−	0.0353048i
$141$	8.23650e9			0.147791
$142$	−1.26998e10	+	4.79073e10i	−0.219965	+	0.829774i
$143$		−	5.83087e10i		−	0.975109i
$144$	8.77690e9	+	1.48340e10i	0.141752	+	0.239578i
$145$	−1.96911e10			−0.307206
$146$	1.06408e11	+	2.82077e10i	1.60401	+	0.425209i
$147$		−	5.78285e10i		−	0.842471i
$148$	−1.08079e11	−	6.16328e10i	−1.52207	−	0.867967i
$149$	1.38919e11			1.89161			0.945805	−	0.324735i	$-0.105275\pi$
$149$	1.38919e11			1.89161			0.945805	+	0.324735i	$0.105275\pi$
$150$	3.30590e9	−	1.24708e10i	0.0435345	−	0.164225i
$151$			1.00714e11i			1.28294i	0.767149	+	0.641469i	$0.221675\pi$
$151$			1.00714e11i			1.28294i	−0.767149	+	0.641469i	$0.778325\pi$
$152$	−2.11296e10	+	2.14708e10i	−0.260420	+	0.264624i
$153$	6.04837e9			0.0721408
$154$	−1.39037e10	−	3.68575e9i	−0.160520	−	0.0425523i
$155$			6.85294e10i			0.765981i
$156$	2.07465e10	−	3.63811e10i	0.224555	−	0.393780i
$157$	8.15950e10			0.855393			0.427696	−	0.903922i	$-0.359325\pi$
$157$	8.15950e10			0.855393			0.427696	+	0.903922i	$0.359325\pi$
$158$	−2.36325e10	+	8.91487e10i	−0.240007	+	0.905378i
$159$		−	2.14093e10i		−	0.210677i
$160$	1.27404e10	+	4.51299e10i	0.121502	+	0.430392i
$161$	3.93591e9			0.0363844
$162$	−6.94713e10	−	1.84162e10i	−0.622631	−	0.165054i
$163$			1.23455e11i			1.07293i	0.843924	+	0.536463i	$0.180240\pi$
$163$			1.23455e11i			1.07293i	−0.843924	+	0.536463i	$0.819760\pi$
$164$	−1.32458e11	−	7.55347e10i	−1.11650	−	0.636689i
$165$	−8.49002e10			−0.694207
$166$	2.79666e10	−	1.05498e11i	0.221870	−	0.836959i
$167$		−	1.93005e11i		−	1.48589i	−0.669354	−	0.742943i	$-0.733429\pi$
$167$		−	1.93005e11i		−	1.48589i	0.669354	−	0.742943i	$-0.266571\pi$
$168$	−7.36369e9	−	7.24671e9i	−0.0550236	−	0.0541495i
$169$	−9.86026e10			−0.715245
$170$	1.59062e10	+	4.21659e9i	0.112027	+	0.0296973i
$171$			1.51113e10i			0.103352i
$172$	−7.17101e10	+	1.25751e11i	−0.476363	+	0.835351i
$173$	−5.57217e10			−0.359579			−0.179789	−	0.983705i	$-0.557542\pi$
$173$	−5.57217e10			−0.359579			−0.179789	+	0.983705i	$0.557542\pi$
$174$	−2.38487e10	+	8.99643e10i	−0.149527	+	0.564058i
$175$		−	2.98317e9i		−	0.0181756i
$176$	2.65584e11	−	1.57139e11i	1.57267	−	0.930509i
$177$	9.05731e10			0.521354
$178$	−7.66661e10	−	2.03235e10i	−0.429046	−	0.113736i
$179$			2.93214e11i			1.59558i	0.602933	+	0.797792i	$0.293999\pi$
$179$			2.93214e11i			1.59558i	−0.602933	+	0.797792i	$0.706001\pi$
$180$	2.04345e10	+	1.16529e10i	0.108144	+	0.0616696i
$181$	−2.72240e11			−1.40139			−0.700695	−	0.713461i	$-0.747127\pi$
$181$	−2.72240e11			−1.40139			−0.700695	+	0.713461i	$0.747127\pi$
$182$	2.48141e9	−	9.36059e9i	0.0124263	−	0.0468756i
$183$			5.84322e10i			0.284706i
$184$	−5.92279e10	+	6.01840e10i	−0.280826	+	0.285359i
$185$	−1.69804e11			−0.783589
$186$	3.13096e11	+	8.29988e10i	1.40641	+	0.372827i
$187$		−	1.08288e11i		−	0.473557i
$188$	−2.02400e10	+	3.54928e10i	−0.0861827	+	0.151130i
$189$	−2.38002e10			−0.0986897
$190$	−1.05348e10	+	3.97402e10i	−0.0425458	+	0.160495i
$191$		−	2.99399e11i		−	1.17783i	−0.808195	−	0.588916i	$-0.799555\pi$
$191$		−	2.99399e11i		−	1.17783i	0.808195	−	0.588916i	$-0.200445\pi$
$192$	2.21619e11	−	3.54928e9i	0.849378	−	0.0136030i
$193$	−3.18585e11			−1.18970			−0.594852	−	0.803835i	$-0.702789\pi$
$193$	−3.18585e11			−1.18970			−0.594852	+	0.803835i	$0.702789\pi$
$194$	−8.35223e10	−	2.21410e10i	−0.303944	−	0.0805727i
$195$		−	5.71584e10i		−	0.202725i
$196$	2.49195e11	+	1.42105e11i	0.861508	+	0.491279i
$197$	4.95289e11			1.66927			0.834637	−	0.550801i	$-0.185678\pi$
$197$	4.95289e11			1.66927			0.834637	+	0.550801i	$0.185678\pi$
$198$	3.96658e10	−	1.49631e11i	0.130344	−	0.491696i
$199$			1.49165e11i			0.477972i	0.971023	+	0.238986i	$0.0768150\pi$
$199$			1.49165e11i			0.477972i	−0.971023	+	0.238986i	$0.923185\pi$
$200$	4.56157e10	+	4.48910e10i	0.142549	+	0.140284i
$201$	−4.14895e11			−1.26461
$202$	−3.60473e11	−	9.55581e10i	−1.07181	−	0.284126i
$203$			2.15205e10i			0.0624270i
$204$	3.85294e10	−	6.75652e10i	0.109054	−	0.191237i
$205$	−2.08105e11			−0.574795
$206$	1.32887e11	−	5.01288e11i	0.358216	−	1.35130i
$207$			4.23580e10i			0.111451i
$208$	1.05793e11	+	1.78802e11i	0.271731	+	0.459258i
$209$	2.70548e11			0.678441
$210$	−1.36295e10	−	3.61304e9i	−0.0333720	−	0.00884661i
$211$			4.40130e11i			1.05237i	0.850370	+	0.526186i	$0.176378\pi$
$211$			4.40130e11i			1.05237i	−0.850370	+	0.526186i	$0.823622\pi$
$212$	9.22573e10	+	5.26102e10i	0.215438	+	0.122854i
$213$	3.19714e11			0.729228
$214$	−1.33238e10	+	5.02613e10i	−0.0296865	+	0.111986i
$215$			1.97567e11i			0.430054i
$216$	3.58148e11	−	3.63930e11i	0.761717	−	0.774014i
$217$	7.48962e10			0.155654
$218$	−3.44164e11	−	9.12346e10i	−0.699009	−	0.185301i
$219$		−	7.10122e11i		−	1.40965i
$220$	2.08629e11	−	3.65853e11i	0.404820	−	0.709894i
$221$	7.29041e10			0.138290
$222$	−2.05656e11	+	7.75796e11i	−0.381397	+	1.43874i
$223$		−	9.51115e10i		−	0.172468i	−0.996275	−	0.0862340i	$-0.972517\pi$
$223$		−	9.51115e10i		−	0.172468i	0.996275	−	0.0862340i	$-0.0274833\pi$
$224$	4.93228e10	−	1.39240e10i	0.0874596	−	0.0246902i
$225$	3.21047e10			0.0556745
$226$	−9.32034e10	−	2.47073e10i	−0.158085	−	0.0419067i
$227$			1.42996e11i			0.237244i	0.992940	+	0.118622i	$0.0378476\pi$
$227$			1.42996e11i			0.237244i	−0.992940	+	0.118622i	$0.962152\pi$
$228$	1.68805e11	+	9.62621e10i	0.273976	+	0.156236i
$229$	8.22920e11			1.30671			0.653356	−	0.757050i	$-0.273360\pi$
$229$	8.22920e11			1.30671			0.653356	+	0.757050i	$0.273360\pi$
$230$	−2.95297e10	+	1.11395e11i	−0.0458796	+	0.173071i
$231$			9.27880e10i			0.141069i
$232$	−3.29071e11	−	3.23843e11i	−0.489609	−	0.481831i
$233$	1.15258e11			0.167838			0.0839192	−	0.996473i	$-0.473256\pi$
$233$	1.15258e11			0.167838			0.0839192	+	0.996473i	$0.473256\pi$
$234$	1.00738e11	+	2.67047e10i	0.143587	+	0.0380635i
$235$			5.57628e10i			0.0778046i
$236$	−2.22570e11	+	3.90299e11i	−0.304023	+	0.533135i
$237$	5.94943e11			0.795671
$238$	4.60834e9	−	1.73840e10i	0.00603476	−	0.0227649i
$239$		−	7.84274e11i		−	1.00572i	−0.864367	−	0.502862i	$-0.832281\pi$
$239$		−	7.84274e11i		−	1.00572i	0.864367	−	0.502862i	$-0.167719\pi$
$240$	2.60345e11	−	1.54039e11i	0.326958	−	0.193453i
$241$	−1.28221e12			−1.57715			−0.788576	−	0.614938i	$-0.789181\pi$
$241$	−1.28221e12			−1.57715			−0.788576	+	0.614938i	$0.789181\pi$
$242$	−1.87666e12	−	4.97486e11i	−2.26105	−	0.599382i
$243$		−	4.56498e11i		−	0.538775i
$244$	−2.51797e11	−	1.43588e11i	−0.291139	−	0.166024i
$245$	3.91511e11			0.443520
$246$	−2.52044e11	+	9.50785e11i	−0.279770	+	1.05538i
$247$			1.82144e11i			0.198121i
$248$	−1.12704e12	+	1.14524e12i	−1.20139	+	1.22078i
$249$	−7.04052e11			−0.735543
$250$	8.44302e10	+	2.23817e10i	0.0864565	+	0.0229188i
$251$			6.60746e11i			0.663233i	0.943414	+	0.331616i	$0.107594\pi$
$251$			6.60746e11i			0.663233i	−0.943414	+	0.331616i	$0.892406\pi$
$252$	1.27355e10	−	2.23330e10i	0.0125318	−	0.0219758i
$253$	7.58364e11			0.731602
$254$	−3.45692e11	+	1.30405e12i	−0.326979	+	1.23346i
$255$		−	1.06152e11i		−	0.0984525i
$256$	−5.29301e11	+	9.63725e11i	−0.481396	+	0.876503i
$257$	−1.79592e10			−0.0160185			−0.00800924	−	0.999968i	$-0.502549\pi$
$257$	−1.79592e10			−0.0160185			−0.00800924	+	0.999968i	$0.502549\pi$
$258$	9.02643e11	+	2.39282e11i	0.789619	+	0.209321i
$259$			1.85580e11i			0.159232i
$260$	2.46308e11	+	1.40458e11i	0.207306	+	0.118217i
$261$	−2.31603e11			−0.191223
$262$	3.91070e11	−	1.47523e12i	0.316773	−	1.19496i
$263$			6.81244e11i			0.541407i	0.962663	+	0.270703i	$0.0872563\pi$
$263$			6.81244e11i			0.541407i	−0.962663	+	0.270703i	$0.912744\pi$
$264$	−1.41882e12	−	1.39628e12i	−1.10639	−	1.08881i
$265$	1.44946e11			0.110911
$266$	4.34324e10	+	1.15135e10i	0.0326141	+	0.00864569i
$267$			5.11639e11i			0.377057i
$268$	1.01954e12	−	1.78787e12i	0.737447	−	1.29319i
$269$	9.92471e11			0.704622			0.352311	−	0.935883i	$-0.385396\pi$
$269$	9.92471e11			0.704622			0.352311	+	0.935883i	$0.385396\pi$
$270$	1.78564e11	−	6.73598e11i	0.124445	−	0.469442i
$271$		−	7.25450e10i		−	0.0496319i	−0.999692	−	0.0248160i	$-0.992100\pi$
$271$		−	7.25450e10i		−	0.0496319i	0.999692	−	0.0248160i	$-0.00789998\pi$
$272$	1.96473e11	+	3.32063e11i	0.131965	+	0.223036i
$273$	−6.24689e10			−0.0411956
$274$	2.57566e12	+	6.82784e11i	1.66777	+	0.442110i
$275$		−	5.74792e11i		−	0.365466i
$276$	4.73174e11	+	2.69829e11i	0.295444	+	0.168478i
$277$	3.65227e11			0.223957			0.111978	−	0.993711i	$-0.464281\pi$
$277$	3.65227e11			0.223957			0.111978	+	0.993711i	$0.464281\pi$
$278$	5.19029e11	−	1.95793e12i	0.312585	−	1.17916i
$279$			8.06028e11i			0.476792i
$280$	4.90617e10	−	4.98538e10i	0.0285071	−	0.0289673i
$281$	−2.08767e11			−0.119160			−0.0595799	−	0.998224i	$-0.518976\pi$
$281$	−2.08767e11			−0.119160			−0.0595799	+	0.998224i	$0.518976\pi$
$282$	2.54768e11	+	6.75367e10i	0.142856	+	0.0378699i
$283$		−	3.26659e12i		−	1.79954i	−0.436363	−	0.899771i	$-0.643734\pi$
$283$		−	3.26659e12i		−	1.79954i	0.436363	−	0.899771i	$-0.356266\pi$
$284$	−7.85649e11	+	1.37772e12i	−0.425243	+	0.745706i
$285$	2.65210e11			0.141048
$286$	4.78113e11	−	1.80358e12i	0.249862	−	0.942553i
$287$			2.27439e11i			0.116803i
$288$	1.49850e11	+	5.30808e11i	0.0756298	+	0.267902i
$289$	−1.88060e12			−0.932840
$290$	−6.09077e11	−	1.61461e11i	−0.296949	−	0.0787185i
$291$			5.57394e11i			0.267115i
$292$	3.06007e12	+	1.74502e12i	1.44151	+	0.822026i
$293$	2.68734e12			1.24447			0.622235	−	0.782830i	$-0.286225\pi$
$293$	2.68734e12			1.24447			0.622235	+	0.782830i	$0.286225\pi$
$294$	4.74175e11	−	1.78873e12i	0.215875	−	0.814344i
$295$			6.13199e11i			0.274468i
$296$	−2.83770e12	−	2.79262e12i	−1.24884	−	1.22900i
$297$	−4.58579e12			−1.98441
$298$	4.29700e12	+	1.13909e12i	1.82845	+	0.484706i
$299$			5.10563e11i			0.213645i
$300$	2.04514e11	−	3.58636e11i	0.0841621	−	0.147587i
$301$	2.15923e11			0.0873909
$302$	−8.25824e11	+	3.11525e12i	−0.328740	+	1.24011i
$303$			2.40565e12i			0.941933i
$304$	−8.29628e11	+	4.90869e11i	−0.319533	+	0.189059i
$305$	−3.95598e11			−0.149884
$306$	1.87086e11	+	4.95947e10i	0.0697323	+	0.0184854i
$307$		−	1.34058e12i		−	0.491588i	−0.969322	−	0.245794i	$-0.920951\pi$
$307$		−	1.34058e12i		−	0.491588i	0.969322	−	0.245794i	$-0.0790487\pi$
$308$	−3.99843e11	−	2.28013e11i	−0.144257	−	0.0822631i
$309$	−3.34539e12			−1.18756
$310$	−5.61919e11	+	2.11972e12i	−0.196275	+	0.740408i
$311$		−	2.65376e12i		−	0.912138i	−0.889945	−	0.456069i	$-0.849257\pi$
$311$		−	2.65376e12i		−	0.912138i	0.889945	−	0.456069i	$-0.150743\pi$
$312$	9.40037e11	−	9.55213e11i	0.317960	−	0.323093i
$313$	−2.02340e12			−0.673536			−0.336768	−	0.941588i	$-0.609334\pi$
$313$	−2.02340e12			−0.673536			−0.336768	+	0.941588i	$0.609334\pi$
$314$	2.52387e12	+	6.69053e11i	0.826834	+	0.219186i
$315$		−	3.50875e10i		−	0.0113136i
$316$	−1.46198e12	+	2.56374e12i	−0.463988	+	0.813650i
$317$	−9.05864e11			−0.282987			−0.141494	−	0.989939i	$-0.545190\pi$
$317$	−9.05864e11			−0.282987			−0.141494	+	0.989939i	$0.545190\pi$
$318$	1.75550e11	−	6.62225e11i	0.0539839	−	0.203643i
$319$			4.14654e12i			1.25526i
$320$	2.40294e10	+	1.50041e12i	0.00716132	+	0.447156i
$321$	3.35424e11			0.0984167
$322$	1.21744e11	+	3.22732e10i	0.0351697	+	0.00932315i
$323$			3.38269e11i			0.0962165i
$324$	−1.99785e12	−	1.13929e12i	−0.559550	−	0.319086i
$325$	3.86975e11			0.106725
$326$	−1.01229e12	+	3.81866e12i	−0.274927	+	1.03710i
$327$			2.29681e12i			0.614308i
$328$	−3.47778e12	−	3.42252e12i	−0.916078	−	0.901524i
$329$	6.09436e10			0.0158106
$330$	−2.62610e12	−	6.96155e11i	−0.671030	−	0.177884i
$331$			5.36141e11i			0.134940i	0.997721	+	0.0674698i	$0.0214926\pi$
$331$			5.36141e11i			0.134940i	−0.997721	+	0.0674698i	$0.978507\pi$
$332$	1.73010e12	−	3.03391e12i	0.428925	−	0.752164i
$333$	−1.99720e12			−0.487752
$334$	1.58258e12	−	5.96995e12i	0.380744	−	1.43628i
$335$		−	2.80893e12i		−	0.665758i
$336$	−1.68350e11	−	2.84532e11i	−0.0393113	−	0.0664409i
$337$	−1.54118e12			−0.354572			−0.177286	−	0.984159i	$-0.556732\pi$
$337$	−1.54118e12			−0.354572			−0.177286	+	0.984159i	$0.556732\pi$
$338$	−3.04994e12	−	8.08510e11i	−0.691365	−	0.183274i
$339$			6.22002e11i			0.138929i
$340$	4.57431e11	+	2.60852e11i	0.100677	+	0.0574116i
$341$	1.44309e13			3.12983
$342$	−1.23908e11	+	4.67416e11i	−0.0264830	+	0.0999018i
$343$		−	8.59333e11i		−	0.181005i
$344$	−3.24923e12	+	3.30168e12i	−0.674509	+	0.685398i
$345$	7.43404e11			0.152100
$346$	−1.72356e12	−	4.56900e11i	−0.347573	−	0.0921384i
$347$		−	4.01330e12i		−	0.797728i	−0.917010	−	0.398864i	$-0.869405\pi$
$347$		−	4.01330e12i		−	0.797728i	0.917010	−	0.398864i	$-0.130595\pi$
$348$	−1.47536e12	+	2.58719e12i	−0.289069	+	0.506912i
$349$	5.09569e12			0.984183			0.492091	−	0.870544i	$-0.336233\pi$
$349$	5.09569e12			0.984183			0.492091	+	0.870544i	$0.336233\pi$
$350$	2.44611e10	−	9.22743e10i	0.00465731	−	0.0175687i
$351$		−	3.08735e12i		−	0.579495i
$352$	9.50342e12	−	2.68286e12i	1.75860	−	0.496460i
$353$	−1.98418e12			−0.362000			−0.181000	−	0.983483i	$-0.557933\pi$
$353$	−1.98418e12			−0.362000			−0.181000	+	0.983483i	$0.557933\pi$
$354$	2.80157e12	+	7.42670e11i	0.503948	+	0.133592i
$355$			2.16453e12i			0.383903i
$356$	−2.20476e12	−	1.25728e12i	−0.385577	−	0.219877i
$357$	−1.16014e11			−0.0200064
$358$	−2.40426e12	+	9.06958e12i	−0.408852	+	1.54231i
$359$		−	3.86028e12i		−	0.647362i	−0.946166	−	0.323681i	$-0.895080\pi$
$359$		−	3.86028e12i		−	0.647362i	0.946166	−	0.323681i	$-0.104920\pi$
$360$	5.36523e11	+	5.27999e11i	0.0887311	+	0.0873214i
$361$	5.28593e12			0.862156
$362$	−8.42083e12	−	2.23228e12i	−1.35460	−	0.359092i
$363$			1.25241e13i			1.98707i
$364$	1.53508e11	−	2.69192e11i	0.0240228	−	0.0421264i
$365$	4.80767e12			0.742114
$366$	−4.79125e11	+	1.80740e12i	−0.0729531	+	0.275201i
$367$		−	5.05920e12i		−	0.759892i	−0.925009	−	0.379946i	$-0.875943\pi$
$367$		−	5.05920e12i		−	0.759892i	0.925009	−	0.379946i	$-0.124057\pi$
$368$	−2.32551e12	+	1.37594e12i	−0.344571	+	0.203873i
$369$	−2.44769e12			−0.357786
$370$	−5.25230e12	−	1.39234e12i	−0.757427	−	0.200787i
$371$		−	1.58412e11i		−	0.0225382i
$372$	9.00400e12	+	5.13457e12i	1.26392	+	0.720758i
$373$	−4.20322e12			−0.582154			−0.291077	−	0.956700i	$-0.594014\pi$
$373$	−4.20322e12			−0.582154			−0.291077	+	0.956700i	$0.594014\pi$
$374$	8.87928e11	−	3.34952e12i	0.121344	−	0.457747i
$375$		−	5.63453e11i		−	0.0759804i
$376$	−9.17085e11	+	9.31890e11i	−0.122031	+	0.124001i
$377$	−2.79163e12			−0.366565
$378$	−7.36179e11	−	1.95154e11i	−0.0953948	−	0.0252883i
$379$		−	1.01261e13i		−	1.29493i	−0.762094	−	0.647466i	$-0.775829\pi$
$379$		−	1.01261e13i		−	1.29493i	0.762094	−	0.647466i	$-0.224171\pi$
$380$	−6.51715e11	+	1.14285e12i	−0.0822507	+	0.144235i
$381$	8.70271e12			1.08400
$382$	2.45497e12	−	9.26089e12i	0.301808	−	1.13851i
$383$		−	1.15938e13i		−	1.40680i	−0.710796	−	0.703399i	$-0.751665\pi$
$383$		−	1.15938e13i		−	1.40680i	0.710796	−	0.703399i	$-0.248335\pi$
$384$	6.88414e12	+	1.70742e12i	0.824505	+	0.204496i
$385$	−6.28195e11			−0.0742661
$386$	−9.85436e12	−	2.61230e12i	−1.14998	−	0.304850i
$387$			2.32375e12i			0.267691i
$388$	−2.40193e12	−	1.36971e12i	−0.273150	−	0.155765i
$389$	3.83589e12			0.430643			0.215322	−	0.976543i	$-0.430920\pi$
$389$	3.83589e12			0.430643			0.215322	+	0.976543i	$0.430920\pi$
$390$	4.68681e11	−	1.76800e12i	0.0519463	−	0.195957i
$391$			9.48192e11i			0.103756i
$392$	6.54280e12	+	6.43885e12i	0.706859	+	0.695630i
$393$	−9.84510e12			−1.05016
$394$	1.53201e13	+	4.06121e12i	1.61354	+	0.427735i
$395$			4.02789e12i			0.418882i
$396$	2.45386e12	−	4.30309e12i	0.251984	−	0.441880i
$397$	−4.57753e11			−0.0464171			−0.0232086	−	0.999731i	$-0.507388\pi$
$397$	−4.57753e11			−0.0464171			−0.0232086	+	0.999731i	$0.507388\pi$
$398$	−1.22311e12	+	4.61393e12i	−0.122476	+	0.462014i
$399$		−	2.89850e11i		−	0.0286622i
$400$	1.04288e12	+	1.76259e12i	0.101843	+	0.172128i
$401$	2.67792e12			0.258271			0.129136	−	0.991627i	$-0.458780\pi$
$401$	2.67792e12			0.258271			0.129136	+	0.991627i	$0.458780\pi$
$402$	−1.28334e13	−	3.40201e12i	−1.22239	−	0.324045i
$403$			9.71548e12i			0.913985i
$404$	−1.03665e13	−	5.91153e12i	−0.963218	−	0.549279i
$405$	−3.13883e12			−0.288067
$406$	−1.76462e11	+	6.65665e11i	−0.0159963	+	0.0603428i
$407$			3.57571e13i			3.20177i
$408$	1.74579e12	−	1.77397e12i	0.154416	−	0.156908i
$409$	−1.32601e13			−1.15859			−0.579297	−	0.815117i	$-0.696673\pi$
$409$	−1.32601e13			−1.15859			−0.579297	+	0.815117i	$0.696673\pi$
$410$	−6.43702e12	−	1.70639e12i	−0.555604	−	0.147285i
$411$		−	1.71889e13i		−	1.46568i
$412$	8.22080e12	−	1.44160e13i	0.692513	−	1.21439i
$413$	6.70169e11			0.0557743
$414$	−3.47322e11	+	1.31020e12i	−0.0285582	+	0.107730i
$415$		−	4.76658e12i		−	0.387228i
$416$	1.80621e12	+	6.39811e12i	0.144978	+	0.513553i
$417$	−1.30665e13			−1.03628
$418$	8.36847e12	+	2.21840e12i	0.655790	+	0.173844i
$419$			1.44719e13i			1.12061i	0.828286	+	0.560306i	$0.189316\pi$
$419$			1.44719e13i			1.12061i	−0.828286	+	0.560306i	$0.810684\pi$
$420$	−3.91956e11	−	2.23515e11i	−0.0299910	−	0.0171025i
$421$	−1.64597e13			−1.24455			−0.622274	−	0.782800i	$-0.713791\pi$
$421$	−1.64597e13			−1.24455			−0.622274	+	0.782800i	$0.713791\pi$
$422$	−3.60893e12	+	1.36139e13i	−0.269660	+	1.01724i
$423$			6.55871e11i			0.0484302i
$424$	2.42228e12	+	2.38380e12i	0.176765	+	0.173956i
$425$	7.18670e11			0.0518304
$426$	9.88927e12	+	2.62155e12i	0.704882	+	0.186858i
$427$			4.32352e11i			0.0304578i
$428$	−8.24253e11	+	1.44541e12i	−0.0573907	+	0.100641i
$429$	−1.20364e13			−0.828342
$430$	−1.61999e12	+	6.11108e12i	−0.110197	+	0.415696i
$431$		−	5.96650e12i		−	0.401174i	−0.979676	−	0.200587i	$-0.935715\pi$
$431$		−	5.96650e12i		−	0.401174i	0.979676	−	0.200587i	$-0.0642850\pi$
$432$	1.40622e13	−	8.32023e12i	0.934619	−	0.552989i
$433$	−2.04949e12			−0.134650			−0.0673250	−	0.997731i	$-0.521446\pi$
$433$	−2.04949e12			−0.134650			−0.0673250	+	0.997731i	$0.521446\pi$
$434$	2.31666e12	+	6.14125e11i	0.150458	+	0.0398849i
$435$			4.06474e12i			0.260967i
$436$	−9.89745e12	−	5.64407e12i	−0.628190	−	0.358228i
$437$	−2.36897e12			−0.148646
$438$	5.82277e12	−	2.19652e13i	0.361210	−	1.36259i
$439$		−	1.83908e12i		−	0.112792i	−0.998408	−	0.0563958i	$-0.982039\pi$
$439$		−	1.83908e12i		−	0.112792i	0.998408	−	0.0563958i	$-0.0179609\pi$
$440$	9.45313e12	−	9.60573e12i	0.573208	−	0.582461i
$441$	4.60487e12			0.276073
$442$	2.25504e12	+	5.97791e11i	0.133673	+	0.0354354i
$443$		−	2.87837e13i		−	1.68705i	−0.537091	−	0.843524i	$-0.680477\pi$
$443$		−	2.87837e13i		−	1.68705i	0.537091	−	0.843524i	$-0.319523\pi$
$444$	−1.27226e13	+	2.23103e13i	−0.737326	+	1.29298i
$445$	−3.46390e12			−0.198502
$446$	7.79884e11	−	2.94195e12i	0.0441932	−	0.166710i
$447$		−	2.86765e13i		−	1.60690i
$448$	1.63981e12	−	2.62619e10i	0.0908662	−	0.00145524i
$449$	6.38160e12			0.349702			0.174851	−	0.984595i	$-0.444056\pi$
$449$	6.38160e12			0.349702			0.174851	+	0.984595i	$0.444056\pi$
$450$	9.93050e11	+	2.63248e11i	0.0538157	+	0.0142660i
$451$			4.38226e13i			2.34863i
$452$	−2.68034e12	−	1.52848e12i	−0.142068	−	0.0810152i
$453$	2.07900e13			1.08984
$454$	−1.17252e12	+	4.42310e12i	−0.0607913	+	0.229323i
$455$		−	4.22927e11i		−	0.0216875i
$456$	4.43211e12	+	4.36169e12i	0.224795	+	0.221223i
$457$	2.02709e13			1.01693			0.508465	−	0.861082i	$-0.330213\pi$
$457$	2.02709e13			1.01693			0.508465	+	0.861082i	$0.330213\pi$
$458$	2.54542e13	+	6.74768e12i	1.26309	+	0.334832i
$459$		−	5.73367e12i		−	0.281429i
$460$	−1.82680e12	+	3.20348e12i	−0.0886957	+	0.155537i
$461$	3.93541e11			0.0189010			0.00945052	−	0.999955i	$-0.496992\pi$
$461$	3.93541e11			0.0189010			0.00945052	+	0.999955i	$0.496992\pi$
$462$	−7.60833e11	+	2.87008e12i	−0.0361476	+	0.136359i
$463$			7.03622e12i			0.330700i	0.986235	+	0.165350i	$0.0528754\pi$
$463$			7.03622e12i			0.330700i	−0.986235	+	0.165350i	$0.947125\pi$
$464$	−7.52329e12	−	1.27153e13i	−0.349798	−	0.591201i
$465$	1.41462e13			0.650691
$466$	3.56511e12	+	9.45078e11i	0.162235	+	0.0430069i
$467$		−	3.74030e13i		−	1.68392i	−0.539538	−	0.841961i	$-0.681401\pi$
$467$		−	3.74030e13i		−	1.68392i	0.539538	−	0.841961i	$-0.318599\pi$
$468$	2.89702e12	+	1.65204e12i	0.129039	+	0.0735854i
$469$	−3.06990e12			−0.135288
$470$	−4.57238e11	+	1.72483e12i	−0.0199367	+	0.0752070i
$471$		−	1.68433e13i		−	0.726645i
$472$	−1.00848e13	+	1.02476e13i	−0.430483	+	0.437432i
$473$	4.16036e13			1.75722
$474$	1.84026e13	+	4.87834e12i	0.769106	+	0.203883i
$475$			1.79553e12i			0.0742548i
$476$	2.85087e11	−	4.99929e11i	0.0116666	−	0.0204585i
$477$	1.70482e12			0.0690377
$478$	6.43080e12	−	2.42589e13i	0.257707	−	0.972145i
$479$			2.13984e13i			0.848600i	0.905522	+	0.424300i	$0.139480\pi$
$479$			2.13984e13i			0.848600i	−0.905522	+	0.424300i	$0.860520\pi$
$480$	9.31595e12	−	2.62993e12i	0.365612	−	0.103214i
$481$	−2.40732e13			−0.934994
$482$	−3.96608e13	−	1.05137e13i	−1.52450	−	0.404129i
$483$		−	8.12471e11i		−	0.0309081i
$484$	−5.39690e13	−	3.07761e13i	−2.03197	−	1.15874i
$485$	−3.77368e12			−0.140623
$486$	3.74314e12	−	1.41202e13i	0.138056	−	0.520787i
$487$			1.54715e13i			0.564790i	0.959298	+	0.282395i	$0.0911289\pi$
$487$			1.54715e13i			0.564790i	−0.959298	+	0.282395i	$0.908871\pi$
$488$	−6.61110e12	−	6.50607e12i	−0.238877	−	0.235082i
$489$	2.54842e13			0.911436
$490$	1.21101e13	+	3.21026e12i	0.428712	+	0.113648i
$491$			2.70952e13i			0.949477i	0.880127	+	0.474739i	$0.157457\pi$
$491$			2.70952e13i			0.949477i	−0.880127	+	0.474739i	$0.842543\pi$
$492$	−1.55923e13	+	2.73427e13i	−0.540859	+	0.948451i
$493$	−5.18447e12			−0.178020
$494$	−1.49352e12	+	5.63401e12i	−0.0507665	+	0.191506i
$495$		−	6.76059e12i		−	0.227488i
$496$	−4.42519e13	+	2.61827e13i	−1.47409	+	0.872180i
$497$	2.36563e12			0.0780127
$498$	−2.17775e13	−	5.77301e12i	−0.710986	−	0.188476i
$499$		−	4.37577e12i		−	0.141433i	−0.997496	−	0.0707167i	$-0.977471\pi$
$499$		−	4.37577e12i		−	0.141433i	0.997496	−	0.0707167i	$-0.0225286\pi$
$500$	2.42804e12	+	1.38460e12i	0.0776973	+	0.0443072i
$501$	−3.98411e13			−1.26224
$502$	−5.41791e12	+	2.04380e13i	−0.169947	+	0.641090i
$503$			1.22895e13i			0.381676i	0.981622	+	0.190838i	$0.0611205\pi$
$503$			1.22895e13i			0.381676i	−0.981622	+	0.190838i	$0.938879\pi$
$504$	5.77054e11	−	5.86370e11i	0.0177445	−	0.0180310i
$505$	−1.62868e13			−0.495882
$506$	2.34574e13	+	6.21834e12i	0.707177	+	0.187466i
$507$			2.03541e13i			0.607591i
$508$	−2.13856e13	+	3.75018e13i	−0.632125	+	1.10850i
$509$	2.55728e13			0.748497			0.374249	−	0.927328i	$-0.377901\pi$
$509$	2.55728e13			0.748497			0.374249	+	0.927328i	$0.377901\pi$
$510$	8.70411e11	−	3.28345e12i	0.0252275	−	0.0951654i
$511$		−	5.25434e12i		−	0.150804i
$512$	−2.42744e13	+	2.54695e13i	−0.689919	+	0.723886i
$513$	1.43250e13			0.403189
$514$	−5.55507e11	−	1.47260e11i	−0.0154837	−	0.00410458i
$515$		−	2.26490e13i		−	0.625192i
$516$	2.59582e13	+	1.48028e13i	0.709620	+	0.404664i
$517$	1.17425e13			0.317913
$518$	−1.52169e12	+	5.74028e12i	−0.0408017	+	0.153916i
$519$			1.15024e13i			0.305457i
$520$	6.46699e12	+	6.36425e12i	0.170093	+	0.167390i
$521$	−2.48387e13			−0.647055			−0.323527	−	0.946219i	$-0.604869\pi$
$521$	−2.48387e13			−0.647055			−0.323527	+	0.946219i	$0.604869\pi$
$522$	−7.16384e12	−	1.89907e12i	−0.184839	−	0.0489991i
$523$		−	4.31081e13i		−	1.10167i	−0.834615	−	0.550834i	$-0.814310\pi$
$523$		−	4.31081e13i		−	1.10167i	0.834615	−	0.550834i	$-0.185690\pi$
$524$	2.41928e13	−	4.24246e13i	0.612393	−	1.07389i
$525$	−6.15802e11			−0.0154399
$526$	−5.58598e12	+	2.10720e13i	−0.138730	+	0.523331i
$527$			1.80431e13i			0.443872i
$528$	−3.24374e13	−	5.48232e13i	−0.790455	−	1.33596i
$529$	3.47861e13			0.839707
$530$	4.48340e12	+	1.18851e12i	0.107208	+	0.0284199i
$531$			7.21232e12i			0.170845i
$532$	1.24903e12	+	7.12263e11i	0.0293098	+	0.0167141i
$533$	−2.95032e13			−0.685857
$534$	−4.19528e12	+	1.58258e13i	−0.0966172	+	0.364469i
$535$			2.27089e12i			0.0518116i
$536$	4.61961e13	−	4.69418e13i	1.04419	−	1.06105i
$537$	6.05268e13			1.35543
$538$	3.06987e13	+	8.13795e12i	0.681097	+	0.180553i
$539$		−	8.24441e13i		−	1.81224i
$540$	1.10466e13	−	1.93713e13i	0.240580	−	0.421881i
$541$	−6.39742e13			−1.38044			−0.690221	−	0.723598i	$-0.742487\pi$
$541$	−6.39742e13			−1.38044			−0.690221	+	0.723598i	$0.742487\pi$
$542$	5.94846e11	−	2.24394e12i	0.0127177	−	0.0479749i
$543$			5.61972e13i			1.19046i
$544$	3.35441e12	+	1.18823e13i	0.0704080	+	0.249404i
$545$	−1.55499e13			−0.323404
$546$	−1.93226e12	−	5.12225e11i	−0.0398202	−	0.0105560i
$547$		−	7.77019e13i		−	1.58670i	−0.608765	−	0.793350i	$-0.708335\pi$
$547$		−	7.77019e13i		−	1.58670i	0.608765	−	0.793350i	$-0.291665\pi$
$548$	7.40708e13	+	4.22392e13i	1.49880	+	0.854699i
$549$	−4.65295e12			−0.0932967
$550$	4.71312e12	−	1.77793e13i	0.0936472	−	0.353265i
$551$		−	1.29529e13i		−	0.255041i
$552$	1.24235e13	+	1.22261e13i	0.242409	+	0.238558i
$553$	4.40211e12			0.0851207
$554$	1.12971e13	+	2.99474e12i	0.216479	+	0.0573867i
$555$			3.50518e13i			0.665648i
$556$	3.21088e13	−	5.63061e13i	0.604297	−	1.05970i
$557$	−2.51347e13			−0.468810			−0.234405	−	0.972139i	$-0.575314\pi$
$557$	−2.51347e13			−0.468810			−0.234405	+	0.972139i	$0.575314\pi$
$558$	−6.60918e12	+	2.49318e13i	−0.122173	+	0.460874i
$559$			2.80093e13i			0.513150i
$560$	1.92634e12	−	1.13977e12i	0.0349779	−	0.0206955i
$561$	−2.23534e13			−0.402281
$562$	−6.45749e12	−	1.71182e12i	−0.115181	−	0.0305335i
$563$			3.40287e13i			0.601593i	0.953688	+	0.300797i	$0.0972525\pi$
$563$			3.40287e13i			0.601593i	−0.953688	+	0.300797i	$0.902747\pi$
$564$	7.32662e12	+	4.17804e12i	0.128383	+	0.0732111i
$565$	−4.21109e12			−0.0731395
$566$	2.67850e13	−	1.01041e14i	0.461115	−	1.73946i
$567$			3.43045e12i			0.0585377i
$568$	−3.55982e13	+	3.61729e13i	−0.602125	+	0.611845i
$569$	−1.44547e13			−0.242352			−0.121176	−	0.992631i	$-0.538667\pi$
$569$	−1.44547e13			−0.242352			−0.121176	+	0.992631i	$0.538667\pi$
$570$	8.20339e12	+	2.17464e12i	0.136339	+	0.0361421i
$571$			7.83937e13i			1.29152i	0.763541	+	0.645759i	$0.223459\pi$
$571$			7.83937e13i			1.29152i	−0.763541	+	0.645759i	$0.776541\pi$
$572$	2.95776e13	−	5.18674e13i	0.483040	−	0.847060i
$573$	−6.18035e13			−1.00055
$574$	−1.86493e12	+	7.03506e12i	−0.0299297	+	0.112904i
$575$			5.03300e12i			0.0800733i
$576$	2.82629e11	+	1.76475e13i	0.00445763	+	0.278337i
$577$	8.39202e13			1.31216			0.656081	−	0.754691i	$-0.272213\pi$
$577$	8.39202e13			1.31216			0.656081	+	0.754691i	$0.272213\pi$
$578$	−5.81700e13	−	1.54203e13i	−0.901696	−	0.239031i
$579$			6.57640e13i			1.01064i
$580$	−1.75158e13	−	9.98848e12i	−0.266864	−	0.152181i
$581$	−5.20943e12			−0.0786882
$582$	−4.57046e12	+	1.72411e13i	−0.0684455	+	0.258196i
$583$		−	3.05225e13i		−	0.453188i
$584$	8.03442e13	+	7.90678e13i	1.18274	+	1.16395i
$585$	4.55152e12			0.0664319
$586$	8.31238e13	+	2.20353e13i	1.20292	+	0.318883i
$587$			6.78604e13i			0.973702i	0.873485	+	0.486851i	$0.161855\pi$
$587$			6.78604e13i			0.973702i	−0.873485	+	0.486851i	$0.838145\pi$
$588$	2.93340e13	−	5.14402e13i	0.417335	−	0.731839i
$589$	−4.50790e13			−0.635913
$590$	−5.02803e12	+	1.89672e13i	−0.0703296	+	0.265304i
$591$		−	1.02240e14i		−	1.41803i
$592$	−6.48761e13	−	1.09648e14i	−0.892229	−	1.50797i
$593$	−4.32732e13			−0.590127			−0.295064	−	0.955478i	$-0.595341\pi$
$593$	−4.32732e13			−0.590127			−0.295064	+	0.955478i	$0.595341\pi$
$594$	−1.41846e14	−	3.76020e13i	−1.91816	−	0.508485i
$595$		−	7.85440e11i		−	0.0105324i
$596$	1.23573e14	+	7.04681e13i	1.64321	+	0.937047i
$597$	3.07915e13			0.406031
$598$	−4.18645e12	+	1.57925e13i	−0.0547445	+	0.206512i
$599$		−	9.37963e13i		−	1.21633i	−0.793811	−	0.608165i	$-0.791906\pi$
$599$		−	9.37963e13i		−	1.21633i	0.793811	−	0.608165i	$-0.208094\pi$
$600$	9.26664e12	−	9.41624e12i	0.119170	−	0.121094i
$601$	6.78423e13			0.865224			0.432612	−	0.901580i	$-0.357592\pi$
$601$	6.78423e13			0.865224			0.432612	+	0.901580i	$0.357592\pi$
$602$	6.67884e12	+	1.77050e12i	0.0844732	+	0.0223931i
$603$		−	3.30380e13i		−	0.414407i
$604$	−5.10882e13	+	8.95883e13i	−0.635530	+	1.11447i
$605$	−8.47908e13			−1.04610
$606$	−1.97256e13	+	7.44108e13i	−0.241361	+	0.910485i
$607$			1.53821e13i			0.186668i	0.995635	+	0.0933342i	$0.0297525\pi$
$607$			1.53821e13i			0.186668i	−0.995635	+	0.0933342i	$0.970247\pi$
$608$	−2.96867e13	+	8.38068e12i	−0.357309	+	0.100870i
$609$	4.44238e12			0.0530309
$610$	−1.22365e13	−	3.24378e12i	−0.144880	−	0.0384063i
$611$			7.90556e12i			0.0928381i
$612$	5.38021e12	+	3.06809e12i	0.0626674	+	0.0357364i
$613$	−1.01243e13			−0.116966			−0.0584831	−	0.998288i	$-0.518626\pi$
$613$	−1.01243e13			−0.116966			−0.0584831	+	0.998288i	$0.518626\pi$
$614$	1.09923e13	−	4.14664e13i	0.125965	−	0.475176i
$615$			4.29581e13i			0.488280i
$616$	−1.04982e13	−	1.03314e13i	−0.118361	−	0.116481i
$617$	−5.97536e13			−0.668249			−0.334125	−	0.942529i	$-0.608441\pi$
$617$	−5.97536e13			−0.668249			−0.334125	+	0.942529i	$0.608441\pi$
$618$	−1.03478e14	−	2.74312e13i	−1.14791	−	0.304300i
$619$		−	1.02486e13i		−	0.112775i	−0.998409	−	0.0563875i	$-0.982042\pi$
$619$		−	1.02486e13i		−	0.112775i	0.998409	−	0.0563875i	$-0.0179582\pi$
$620$	−3.47621e13	+	6.09590e13i	−0.379444	+	0.665394i
$621$	4.01541e13			0.434782
$622$	2.17600e13	−	8.20852e13i	0.233726	−	0.881684i
$623$			3.78572e12i			0.0403375i
$624$	3.69093e13	−	2.18383e13i	0.390133	−	0.230832i
$625$	3.81470e12			0.0400000
$626$	−6.25872e13	−	1.65913e13i	−0.651049	−	0.172587i
$627$		−	5.58479e13i		−	0.576327i
$628$	7.25813e13	+	4.13898e13i	0.743064	+	0.423736i
$629$	−4.47076e13			−0.454076
$630$	2.87706e11	−	1.08531e12i	0.00289899	−	0.0109358i
$631$		−	4.39320e13i		−	0.439172i	−0.975593	−	0.219586i	$-0.929529\pi$
$631$		−	4.39320e13i		−	0.439172i	0.975593	−	0.219586i	$-0.0704706\pi$
$632$	−6.62433e13	+	6.73127e13i	−0.656987	+	0.667593i
$633$	9.08540e13			0.893975
$634$	−2.80198e13	−	7.42780e12i	−0.273539	−	0.0725126i
$635$			5.89192e13i			0.570674i
$636$	1.08601e13	−	1.90442e13i	0.104363	−	0.183011i
$637$	5.55049e13			0.529217
$638$	−3.40003e13	+	1.28259e14i	−0.321647	+	1.21335i
$639$			2.54588e13i			0.238964i
$640$	−1.15596e13	+	4.66071e13i	−0.107657	+	0.434062i
$641$	4.97085e13			0.459347			0.229673	−	0.973268i	$-0.426234\pi$
$641$	4.97085e13			0.459347			0.229673	+	0.973268i	$0.426234\pi$
$642$	1.03752e13	+	2.75037e12i	0.0951308	+	0.0252183i
$643$		−	6.71533e12i		−	0.0610960i	−0.999533	−	0.0305480i	$-0.990275\pi$
$643$		−	6.71533e12i		−	0.0610960i	0.999533	−	0.0305480i	$-0.00972524\pi$
$644$	3.50111e12	+	1.99652e12i	0.0316065	+	0.0180238i
$645$	4.07829e13			0.365325
$646$	−2.77370e12	+	1.04632e13i	−0.0246545	+	0.0930042i
$647$			6.66499e13i			0.587866i	0.955826	+	0.293933i	$0.0949642\pi$
$647$			6.66499e13i			0.587866i	−0.955826	+	0.293933i	$0.905036\pi$
$648$	−5.24551e13	−	5.16217e13i	−0.459106	−	0.451812i
$649$	1.29127e14			1.12149
$650$	1.19698e13	+	3.17307e12i	0.103162	+	0.0273472i
$651$		−	1.54605e13i		−	0.132226i
$652$	−6.26235e13	+	1.09817e14i	−0.531495	+	0.932032i
$653$	−7.03440e13			−0.592463			−0.296231	−	0.955116i	$-0.595730\pi$
$653$	−7.03440e13			−0.592463			−0.296231	+	0.955116i	$0.595730\pi$
$654$	−1.88331e13	+	7.10441e13i	−0.157410	+	0.593799i
$655$		−	6.66534e13i		−	0.552861i
$656$	−7.95096e13	−	1.34381e14i	−0.654486	−	1.10616i
$657$	5.65469e13			0.461936
$658$	1.88508e12	+	4.99718e11i	0.0152827	+	0.00405131i
$659$			2.63637e13i			0.212119i	0.994360	+	0.106060i	$0.0338234\pi$
$659$			2.63637e13i			0.212119i	−0.994360	+	0.106060i	$0.966177\pi$
$660$	−7.55213e13	−	4.30664e13i	−0.603045	−	0.343889i
$661$	1.68700e14			1.33693			0.668463	−	0.743745i	$-0.266952\pi$
$661$	1.68700e14			1.33693			0.668463	+	0.743745i	$0.266952\pi$
$662$	−4.39619e12	+	1.65837e13i	−0.0345769	+	0.130434i
$663$		−	1.50493e13i		−	0.117476i
$664$	7.83920e13	−	7.96575e13i	0.607339	−	0.617144i
$665$	1.96235e12			0.0150893
$666$	−6.17765e13	−	1.63764e13i	−0.471468	−	0.124982i
$667$		−	3.63079e13i		−	0.275025i
$668$	9.79034e13	−	1.71684e14i	0.736064	−	1.29076i
$669$	−1.96334e13			−0.146509
$670$	2.30323e13	−	8.68846e13i	0.170594	−	0.643530i
$671$			8.33048e13i			0.612432i
$672$	−2.87427e12	−	1.01815e13i	−0.0209740	−	0.0742957i
$673$	1.04637e14			0.757900			0.378950	−	0.925417i	$-0.376285\pi$
$673$	1.04637e14			0.757900			0.378950	+	0.925417i	$0.376285\pi$
$674$	−4.76713e13	−	1.26372e13i	−0.342734	−	0.0908556i
$675$		−	3.04343e13i		−	0.217192i
$676$	−8.77100e13	−	5.00170e13i	−0.621320	−	0.354311i
$677$	−1.48361e14			−1.04322			−0.521612	−	0.853183i	$-0.674669\pi$
$677$	−1.48361e14			−1.04322			−0.521612	+	0.853183i	$0.674669\pi$
$678$	−5.10022e12	+	1.92395e13i	−0.0355992	+	0.134291i
$679$			4.12428e12i			0.0285758i
$680$	1.20102e13	+	1.18194e13i	0.0826047	+	0.0812923i
$681$	2.95180e13			0.201535
$682$	4.46370e14	+	1.18329e14i	3.02533	+	0.801988i
$683$			1.62332e14i			1.09220i	0.837722	+	0.546098i	$0.183887\pi$
$683$			1.62332e14i			1.09220i	−0.837722	+	0.546098i	$0.816113\pi$
$684$	−7.66533e12	+	1.34419e13i	−0.0511977	+	0.0897804i
$685$	1.16373e14			0.771611
$686$	7.04626e12	−	2.65806e13i	0.0463808	−	0.174962i
$687$		−	1.69871e14i		−	1.11004i
$688$	−1.27577e14	+	7.54837e13i	−0.827616	+	0.489678i
$689$	2.05491e13			0.132342
$690$	2.29947e13	+	6.09567e12i	0.147022	+	0.0389741i
$691$		−	1.49548e14i		−	0.949269i	−0.880183	−	0.474635i	$-0.842580\pi$
$691$		−	1.49548e14i		−	0.949269i	0.880183	−	0.474635i	$-0.157420\pi$
$692$	−4.95661e13	−	2.82653e13i	−0.312359	−	0.178124i
$693$	−7.38870e12			−0.0462276
$694$	3.29078e13	−	1.24138e14i	0.204410	−	0.771094i
$695$		−	8.84626e13i		−	0.545552i
$696$	−6.68494e13	+	6.79285e13i	−0.409309	+	0.415916i
$697$	−5.47919e13			−0.333083
$698$	1.57618e14	+	4.17830e13i	0.951324	+	0.252187i
$699$		−	2.37921e13i		−	0.142576i
$700$	1.51324e12	−	2.65362e12i	0.00900363	−	0.0157888i
$701$	−1.48453e14			−0.876997			−0.438498	−	0.898732i	$-0.644489\pi$
$701$	−1.48453e14			−0.876997			−0.438498	+	0.898732i	$0.644489\pi$
$702$	2.53153e13	−	9.54966e13i	0.148490	−	0.560148i
$703$		−	1.11698e14i		−	0.650531i
$704$	3.15955e14	−	5.06010e12i	1.82710	−	0.0292614i
$705$	1.15109e13			0.0660940
$706$	−6.13740e13	−	1.62697e13i	−0.349914	−	0.0927589i
$707$			1.77999e13i			0.100768i
$708$	8.05675e13	+	4.59440e13i	0.452891	+	0.258263i
$709$	−2.32221e13			−0.129619			−0.0648097	−	0.997898i	$-0.520644\pi$
$709$	−2.32221e13			−0.129619			−0.0648097	+	0.997898i	$0.520644\pi$
$710$	−1.77485e13	+	6.69525e13i	−0.0983715	+	0.371086i
$711$			4.73752e13i			0.260737i
$712$	−5.78876e13	−	5.69679e13i	−0.316363	−	0.311337i
$713$	−1.26360e14			−0.685742
$714$	−3.58850e12	−	9.51279e11i	−0.0193385	−	0.00512645i
$715$		−	8.14889e13i		−	0.436082i
$716$	−1.48735e14	+	2.60823e14i	−0.790404	+	1.38605i
$717$	−1.61894e14			−0.854348
$718$	3.16531e13	−	1.19405e14i	0.165880	−	0.625748i
$719$			2.66908e14i			1.38905i	0.719470	+	0.694523i	$0.244385\pi$
$719$			2.66908e14i			1.38905i	−0.719470	+	0.694523i	$0.755615\pi$
$720$	1.22661e13	+	2.07312e13i	0.0633934	+	0.107142i
$721$	−2.47533e13			−0.127045
$722$	1.63502e14	+	4.33430e13i	0.833371	+	0.220919i
$723$			2.64680e14i			1.33977i
$724$	−2.42166e14	−	1.38096e14i	−1.21736	−	0.694207i
$725$	−2.75191e13			−0.137387
$726$	−1.02694e14	+	3.87391e14i	−0.509167	+	1.92073i
$727$			2.88697e14i			1.42157i	0.703407	+	0.710787i	$0.251661\pi$
$727$			2.88697e14i			1.42157i	−0.703407	+	0.710787i	$0.748339\pi$
$728$	6.95553e12	−	7.06782e12i	0.0340152	−	0.0345644i
$729$	−2.26855e14			−1.10182
$730$	1.48709e14	+	3.94214e13i	0.717337	+	0.190159i
$731$			5.20176e13i			0.249209i
$732$	−2.96403e13	+	5.19772e13i	−0.141035	+	0.247319i
$733$	−1.34165e14			−0.634043			−0.317022	−	0.948418i	$-0.602683\pi$
$733$	−1.34165e14			−0.634043			−0.317022	+	0.948418i	$0.602683\pi$
$734$	4.14839e13	−	1.56489e14i	0.194715	−	0.734522i
$735$		−	8.08177e13i		−	0.376764i
$736$	−8.32139e13	+	2.34917e13i	−0.385307	+	0.108774i
$737$	−5.91502e14			−2.72031
$738$	−7.57109e13	−	2.00702e13i	−0.345841	−	0.0916792i
$739$			4.06753e10i			0.000184548i	1.00000		9.22738e-5i	$2.93717e-5\pi$
$739$			4.06753e10i			0.000184548i	−1.00000		9.22738e-5i	$0.999971\pi$
$740$	−1.51045e14	−	8.61344e13i	−0.680690	−	0.388166i
$741$	3.75992e13			0.168301
$742$	1.29893e12	−	4.89994e12i	0.00577518	−	0.0217857i
$743$		−	3.43972e14i		−	1.51907i	−0.650465	−	0.759536i	$-0.725426\pi$
$743$		−	3.43972e14i		−	1.51907i	0.650465	−	0.759536i	$-0.274574\pi$
$744$	2.36406e14	+	2.32651e14i	1.03704	+	1.02056i
$745$	1.94146e14			0.845954
$746$	−1.30012e14	−	3.44651e13i	−0.562718	−	0.149171i
$747$		−	5.60636e13i		−	0.241034i
$748$	5.49301e13	−	9.63255e13i	0.234586	−	0.411371i
$749$	2.48187e12			0.0105286
$750$	4.62014e12	−	1.74285e13i	0.0194692	−	0.0734437i
$751$			1.75584e14i			0.734996i	0.930024	+	0.367498i	$0.119786\pi$
$751$			1.75584e14i			0.734996i	−0.930024	+	0.367498i	$0.880214\pi$
$752$	−3.60081e13	+	2.13051e13i	−0.149731	+	0.0885918i
$753$	1.36395e14			0.563408
$754$	−8.63495e13	−	2.28905e13i	−0.354326	−	0.0939286i
$755$			1.40752e14i			0.573748i
$756$	−2.11710e13	−	1.20729e13i	−0.0857300	−	0.0488879i
$757$	−1.35481e13			−0.0545005			−0.0272502	−	0.999629i	$-0.508675\pi$
$757$	−1.35481e13			−0.0545005			−0.0272502	+	0.999629i	$0.508675\pi$
$758$	8.30310e13	−	3.13217e14i	0.331814	−	1.25170i
$759$		−	1.56546e14i		−	0.621487i
$760$	−2.95296e13	+	3.00063e13i	−0.116463	+	0.118343i
$761$	7.63675e13			0.299216			0.149608	−	0.988745i	$-0.452199\pi$
$761$	7.63675e13			0.299216			0.149608	+	0.988745i	$0.452199\pi$
$762$	2.69189e14	+	7.13595e13i	1.04781	+	0.277765i
$763$			1.69946e13i			0.0657185i
$764$	1.51873e14	−	2.66324e14i	0.583462	−	1.02316i
$765$	8.45285e12			0.0322624
$766$	9.50654e13	−	3.58615e14i	0.360478	−	1.35983i
$767$			8.69338e13i			0.327500i
$768$	1.98937e14	+	1.09261e14i	0.744578	+	0.408940i
$769$	−3.71137e14			−1.38008			−0.690038	−	0.723773i	$-0.742406\pi$
$769$	−3.71137e14			−1.38008			−0.690038	+	0.723773i	$0.742406\pi$
$770$	−1.94311e13	−	5.15100e12i	−0.0717866	−	0.0190299i
$771$			3.70723e12i			0.0136075i
$772$	−2.83391e14	−	1.61605e14i	−1.03347	−	0.589344i
$773$	5.41146e14			1.96072			0.980362	−	0.197205i	$-0.0631864\pi$
$773$	5.41146e14			1.96072			0.980362	+	0.197205i	$0.0631864\pi$
$774$	−1.90540e13	+	7.18773e13i	−0.0685932	+	0.258754i
$775$			9.57727e13i			0.342557i
$776$	−6.30644e13	−	6.20625e13i	−0.224117	−	0.220557i
$777$	3.83083e13			0.135266
$778$	1.18650e14	+	3.14531e13i	0.416266	+	0.110348i
$779$		−	1.36892e14i		−	0.477191i
$780$	2.89941e13	−	5.08442e13i	0.100424	−	0.176104i
$781$	4.55806e14			1.56864
$782$	−7.77487e12	+	2.93291e13i	−0.0265864	+	0.100292i
$783$			2.19552e14i			0.745983i
$784$	1.49583e14	+	2.52813e14i	0.505011	+	0.853530i
$785$	1.14033e14			0.382543
$786$	−3.04525e14	−	8.07267e13i	−1.01510	−	0.269094i
$787$		−	4.82190e13i		−	0.159714i	−0.996806	−	0.0798572i	$-0.974554\pi$
$787$		−	4.82190e13i		−	0.159714i	0.996806	−	0.0798572i	$-0.0254464\pi$
$788$	4.40575e14	+	2.51240e14i	1.45007	+	0.826908i
$789$	1.40626e14			0.459918
$790$	−3.30274e13	+	1.24589e14i	−0.107334	+	0.404897i
$791$			4.60232e12i			0.0148626i
$792$	1.11186e14	−	1.12981e14i	0.356799	−	0.362559i
$793$	−5.60844e13			−0.178845
$794$	−1.41590e13	−	3.75343e12i	−0.0448674	−	0.0118939i
$795$		−	2.99204e13i		−	0.0942176i
$796$	−7.56655e13	+	1.32687e14i	−0.236773	+	0.415206i
$797$	1.02585e14			0.319001			0.159501	−	0.987198i	$-0.449012\pi$
$797$	1.02585e14			0.319001			0.159501	+	0.987198i	$0.449012\pi$
$798$	2.37668e12	−	8.96554e12i	0.00734440	−	0.0277052i
$799$			1.46818e13i			0.0450864i
$800$	1.78052e13	+	6.30709e13i	0.0543372	+	0.192477i
$801$	−4.07417e13			−0.123560
$802$	8.28324e13	+	2.19581e13i	0.249648	+	0.0661794i
$803$		−	1.01240e15i		−	3.03231i
$804$	−3.69062e14	−	2.10459e14i	−1.09855	−	0.626452i
$805$	5.50060e12			0.0162716
$806$	−7.96638e13	+	3.00516e14i	−0.234200	+	0.883470i
$807$		−	2.04871e14i		−	0.598567i
$808$	−2.72179e14	−	2.67855e14i	−0.790311	−	0.777756i
$809$	3.39598e14			0.979991			0.489995	−	0.871725i	$-0.336998\pi$
$809$	3.39598e14			0.979991			0.489995	+	0.871725i	$0.336998\pi$
$810$	−9.70892e13	−	2.57374e13i	−0.278449	−	0.0738142i
$811$		−	3.34618e14i		−	0.953773i	−0.878965	−	0.476886i	$-0.841765\pi$
$811$		−	3.34618e14i		−	0.953773i	0.878965	−	0.476886i	$-0.158235\pi$
$812$	−1.09165e13	+	1.91432e13i	−0.0309245	+	0.0542293i
$813$	−1.49751e13			−0.0421617
$814$	−2.93197e14	+	1.10603e15i	−0.820423	+	3.09488i
$815$			1.72533e14i			0.479827i
$816$	6.85461e13	−	4.05569e13i	0.189466	−	0.112102i
$817$	−1.29961e14			−0.357028
$818$	−4.10157e14	−	1.08729e14i	−1.11991	−	0.296878i
$819$		−	4.97438e12i		−	0.0134996i
$820$	−1.85115e14	−	1.05563e14i	−0.499314	−	0.284736i
$821$	3.85146e14			1.03255			0.516274	−	0.856424i	$-0.327319\pi$
$821$	3.85146e14			1.03255			0.516274	+	0.856424i	$0.327319\pi$
$822$	1.40944e14	−	5.31682e14i	0.375567	−	1.41675i
$823$			4.10368e14i			1.08686i	0.839454	+	0.543430i	$0.182875\pi$
$823$			4.10368e14i			1.08686i	−0.839454	+	0.543430i	$0.817125\pi$
$824$	3.72489e14	−	3.78503e14i	0.980569	−	0.996398i
$825$	−1.18652e14			−0.310459
$826$	2.07294e13	+	5.49517e12i	0.0539122	+	0.0142916i
$827$			5.90609e14i			1.52677i	0.645946	+	0.763383i	$0.276463\pi$
$827$			5.90609e14i			1.52677i	−0.645946	+	0.763383i	$0.723537\pi$
$828$	−2.14865e13	+	3.76787e13i	−0.0552095	+	0.0968154i
$829$	−1.46339e14			−0.373754			−0.186877	−	0.982383i	$-0.559837\pi$
$829$	−1.46339e14			−0.373754			−0.186877	+	0.982383i	$0.559837\pi$
$830$	3.90845e13	−	1.47438e14i	0.0992233	−	0.374300i
$831$		−	7.53921e13i		−	0.190248i
$832$	3.40667e12	+	2.12714e14i	0.00854503	+	0.533556i
$833$	1.03081e14			0.257012
$834$	−4.04167e14	−	1.07141e14i	−1.00168	−	0.265537i
$835$		−	2.69732e14i		−	0.664509i
$836$	2.40660e14	+	1.37238e14i	0.589350	+	0.336079i
$837$	7.64090e14			1.86002
$838$	−1.18665e14	+	4.47639e14i	−0.287146	+	1.08320i
$839$		−	4.02177e13i		−	0.0967402i	−0.998829	−	0.0483701i	$-0.984597\pi$
$839$		−	4.02177e13i		−	0.0967402i	0.998829	−	0.0483701i	$-0.0154027\pi$
$840$	−1.02911e13	−	1.01276e13i	−0.0246073	−	0.0242164i
$841$	−2.22185e14			−0.528122
$842$	−5.09125e14	−	1.34964e14i	−1.20300	−	0.318903i
$843$			4.30947e13i			0.101225i
$844$	−2.23260e14	+	3.91509e14i	−0.521313	+	0.914176i
$845$	−1.37801e14			−0.319867
$846$	−5.37793e12	+	2.02872e13i	−0.0124098	+	0.0468133i
$847$			9.26684e13i			0.212576i
$848$	5.53787e13	+	9.35967e13i	0.126288	+	0.213443i
$849$	−6.74306e14			−1.52869
$850$	2.22296e13	+	5.89287e12i	0.0501000	+	0.0132810i
$851$		−	3.13097e14i		−	0.701505i
$852$	2.84395e14	+	1.62178e14i	0.633468	+	0.361238i
$853$	−6.42197e14			−1.42208			−0.711038	−	0.703153i	$-0.751775\pi$
$853$	−6.42197e14			−1.42208			−0.711038	+	0.703153i	$0.751775\pi$
$854$	−3.54515e12	+	1.33734e13i	−0.00780450	+	0.0294409i
$855$			2.11187e13i			0.0462206i
$856$	−3.73474e13	+	3.79503e13i	−0.0812628	+	0.0825746i
$857$	2.32290e14			0.502489			0.251245	−	0.967924i	$-0.419160\pi$
$857$	2.32290e14			0.502489			0.251245	+	0.967924i	$0.419160\pi$
$858$	−3.72305e14	−	9.86946e13i	−0.800687	−	0.212255i
$859$			7.69555e14i			1.64541i	0.568469	+	0.822704i	$0.307536\pi$
$859$			7.69555e14i			1.64541i	−0.568469	+	0.822704i	$0.692464\pi$
$860$	−1.00218e14	+	1.75742e14i	−0.213036	+	0.373580i
$861$	4.69492e13			0.0992230
$862$	4.89234e13	−	1.84554e14i	0.102797	−	0.387781i
$863$			4.29835e14i			0.897942i	0.893546	+	0.448971i	$0.148209\pi$
$863$			4.29835e14i			0.897942i	−0.893546	+	0.448971i	$0.851791\pi$
$864$	5.03190e14	−	1.42053e14i	1.04511	−	0.295040i
$865$	−7.78734e13			−0.160808
$866$	−6.33941e13	−	1.68052e13i	−0.130155	−	0.0345027i
$867$			3.88203e14i			0.792435i
$868$	6.66225e13	+	3.79918e13i	0.135214	+	0.0771065i
$869$	8.48191e14			1.71157
$870$	−3.33296e13	+	1.25729e14i	−0.0668703	+	0.252255i
$871$		−	3.98224e14i		−	0.794396i
$872$	−2.59864e14	−	2.55736e14i	−0.515424	−	0.507235i
$873$	−4.43852e13			−0.0875320
$874$	−7.32761e13	−	1.94248e13i	−0.143683	−	0.0380890i
$875$		−	4.16911e12i		−	0.00812836i
$876$	3.60216e14	−	6.31675e14i	0.698300	−	1.22454i
$877$	−2.99857e14			−0.577985			−0.288993	−	0.957331i	$-0.593320\pi$
$877$	−2.99857e14			−0.577985			−0.288993	+	0.957331i	$0.593320\pi$
$878$	1.50798e13	−	5.68856e13i	0.0289017	−	0.109026i
$879$		−	5.54735e14i		−	1.05716i
$880$	3.71165e14	−	2.19608e14i	0.703320	−	0.416136i
$881$	−6.00394e14			−1.13125			−0.565623	−	0.824664i	$-0.691364\pi$
$881$	−6.00394e14			−1.13125			−0.565623	+	0.824664i	$0.691364\pi$
$882$	1.42436e14	+	3.77585e13i	0.266856	+	0.0707410i
$883$			4.85577e14i			0.904596i	0.891867	+	0.452298i	$0.149396\pi$
$883$			4.85577e14i			0.904596i	−0.891867	+	0.452298i	$0.850604\pi$
$884$	6.48504e13	+	3.69813e13i	0.120130	+	0.0685047i
$885$	1.26580e14			0.233157
$886$	2.36017e14	−	8.90325e14i	0.432289	−	1.63072i
$887$		−	8.89232e14i		−	1.61956i	−0.586734	−	0.809780i	$-0.699587\pi$
$887$		−	8.89232e14i		−	1.61956i	0.586734	−	0.809780i	$-0.300413\pi$
$888$	−5.76467e14	+	5.85773e14i	−1.04402	+	1.06088i
$889$	6.43932e13			0.115966
$890$	−1.07144e14	−	2.84029e13i	−0.191875	−	0.0508643i
$891$			6.60973e14i			1.17705i
$892$	4.82462e13	−	8.46046e13i	0.0854355	−	0.149820i
$893$	−3.66811e13			−0.0645930
$894$	2.35138e14	−	8.87010e14i	0.411752	−	1.55325i
$895$			4.09779e14i			0.713567i
$896$	5.09372e13	+	1.26336e13i	0.0882054	+	0.0218769i
$897$	1.05393e14			0.181489
$898$	1.97393e14	+	5.23271e13i	0.338026	+	0.0896076i
$899$		−	6.90902e14i		−	1.17657i
$900$	2.85581e13	+	1.62854e13i	0.0483634	+	0.0275795i
$901$	3.81627e13			0.0642711
$902$	−3.59331e14	+	1.35550e15i	−0.601814	+	2.27022i
$903$		−	4.45719e13i		−	0.0742374i
$904$	−7.03742e13	−	6.92562e13i	−0.116566	−	0.114714i
$905$	−3.80467e14			−0.626721
$906$	6.43067e14	+	1.70471e14i	1.05345	+	0.279261i
$907$		−	6.65566e14i		−	1.08431i	−0.840277	−	0.542157i	$-0.817608\pi$
$907$		−	6.65566e14i		−	1.08431i	0.840277	−	0.542157i	$-0.182392\pi$
$908$	−7.25360e13	+	1.27199e14i	−0.117523	+	0.206089i
$909$	−1.91562e14			−0.308667
$910$	3.46787e12	−	1.30818e13i	0.00555720	−	0.0209634i
$911$			6.58300e14i			1.04914i	0.851368	+	0.524568i	$0.175773\pi$
$911$			6.58300e14i			1.04914i	−0.851368	+	0.524568i	$0.824227\pi$
$912$	1.01328e14	+	1.71256e14i	0.160603	+	0.271439i
$913$	−1.00374e15			−1.58223
$914$	6.27011e14	+	1.66215e14i	0.982979	+	0.260578i
$915$			8.16615e13i			0.127324i
$916$	7.32012e14	+	4.17434e14i	1.13512	+	0.647307i
$917$	−7.28460e13			−0.112346
$918$	4.70142e13	−	1.77352e14i	0.0721134	−	0.272033i
$919$		−	2.48932e14i		−	0.379755i	−0.981808	−	0.189878i	$-0.939191\pi$
$919$		−	2.48932e14i		−	0.379755i	0.981808	−	0.189878i	$-0.0608091\pi$
$920$	−8.27735e13	+	8.41098e13i	−0.125589	+	0.127617i
$921$	−2.76730e14			−0.417598
$922$	1.21729e13	+	3.22691e12i	0.0182700	+	0.00484321i
$923$			3.06868e14i			0.458082i
$924$	−4.70676e13	+	8.25378e13i	−0.0698815	+	0.122544i
$925$	−2.37308e14			−0.350432
$926$	−5.76948e13	+	2.17642e14i	−0.0847387	+	0.319659i
$927$		−	2.66393e14i		−	0.389157i
$928$	−1.28446e14	−	4.54992e14i	−0.186630	−	0.661095i
$929$	6.78834e14			0.981036			0.490518	−	0.871431i	$-0.336808\pi$
$929$	6.78834e14			0.981036			0.490518	+	0.871431i	$0.336808\pi$
$930$	4.37565e14	+	1.15994e14i	0.628966	+	0.166733i
$931$			2.57538e14i			0.368208i
$932$	1.02525e14	+	5.84656e13i	0.145798	+	0.0831421i
$933$	−5.47804e14			−0.774849
$934$	3.06693e14	−	1.15694e15i	0.431488	−	1.62770i
$935$		−	1.51337e14i		−	0.211781i
$936$	7.60634e13	+	7.48550e13i	0.105876	+	0.104194i
$937$	1.72850e14			0.239315			0.119658	−	0.992815i	$-0.461820\pi$
$937$	1.72850e14			0.239315			0.119658	+	0.992815i	$0.461820\pi$
$938$	−9.49568e13	−	2.51722e13i	−0.130771	−	0.0346662i
$939$			4.17682e14i			0.572160i
$940$	−2.82862e13	+	4.96027e13i	−0.0385421	+	0.0675875i
$941$	2.67517e14			0.362580			0.181290	−	0.983430i	$-0.441973\pi$
$941$	2.67517e14			0.362580			0.181290	+	0.983430i	$0.441973\pi$
$942$	1.38110e14	−	5.20990e14i	0.186195	−	0.702384i
$943$		−	3.83719e14i		−	0.514583i
$944$	−3.95965e14	+	2.34282e14i	−0.528198	+	0.312521i
$945$	−3.32618e13			−0.0441354
$946$	1.28687e15	+	3.41137e14i	1.69855	+	0.450270i
$947$			2.68497e14i			0.352525i	0.984343	+	0.176263i	$0.0564008\pi$
$947$			2.68497e14i			0.352525i	−0.984343	+	0.176263i	$0.943599\pi$
$948$	5.29220e14	+	3.01790e14i	0.691185	+	0.394152i
$949$	6.81589e14			0.885506
$950$	−1.47228e13	+	5.55387e13i	−0.0190271	+	0.0717757i
$951$			1.86993e14i			0.240394i
$952$	1.29175e13	−	1.31260e13i	0.0165193	−	0.0167860i
$953$	1.13349e15			1.44196			0.720979	−	0.692957i	$-0.243693\pi$
$953$	1.13349e15			1.44196			0.720979	+	0.692957i	$0.243693\pi$
$954$	5.27328e13	+	1.39790e13i	0.0667328	+	0.0176902i
$955$		−	4.18422e14i		−	0.526742i
$956$	3.97830e14	−	6.97636e14i	0.498205	−	0.873654i
$957$	8.55950e14			1.06632
$958$	−1.75460e14	+	6.61886e14i	−0.217445	+	0.820268i
$959$		−	1.27185e14i		−	0.156798i
$960$	3.09722e14	−	4.96027e12i	0.379853	−	0.00608344i
$961$	−1.58486e15			−1.93364
$962$	−7.44624e14	−	1.97393e14i	−0.903778	−	0.239583i
$963$			2.67097e13i			0.0322506i
$964$	−1.14056e15	−	6.50412e14i	−1.37004	−	0.781274i
$965$	−4.45236e14			−0.532052
$966$	6.66200e12	−	2.51310e13i	0.00791989	−	0.0298762i
$967$		−	5.51099e14i		−	0.651775i	−0.945409	−	0.325887i	$-0.894337\pi$
$967$		−	5.51099e14i		−	0.651775i	0.945409	−	0.325887i	$-0.105663\pi$
$968$	−1.41699e15	−	1.39448e15i	−1.66721	−	1.64073i
$969$	6.98273e13			0.0817347
$970$	−1.16726e14	−	3.09430e13i	−0.135928	−	0.0360332i
$971$		−	1.03297e15i		−	1.19672i	−0.801228	−	0.598359i	$-0.795820\pi$
$971$		−	1.03297e15i		−	1.19672i	0.801228	−	0.598359i	$-0.204180\pi$
$972$	2.31563e14	−	4.06069e14i	0.266893	−	0.468024i
$973$	−9.66814e13			−0.110861
$974$	−1.26861e14	+	4.78558e14i	−0.144722	+	0.545934i
$975$		−	7.98814e13i		−	0.0906614i
$976$	−1.51144e14	−	2.55452e14i	−0.170664	−	0.288444i
$977$	−1.28577e14			−0.144441			−0.0722205	−	0.997389i	$-0.523009\pi$
$977$	−1.28577e14			−0.144441			−0.0722205	+	0.997389i	$0.523009\pi$
$978$	7.88267e14	+	2.08962e14i	0.881006	+	0.233547i
$979$			7.29427e14i			0.811089i
$980$	3.48261e14	+	1.98597e14i	0.385278	+	0.219707i
$981$	−1.82895e14			−0.201306
$982$	−2.22172e14	+	8.38098e14i	−0.243294	+	0.917777i
$983$			8.69065e14i			0.946858i	0.880832	+	0.473429i	$0.156984\pi$
$983$			8.69065e14i			0.946858i	−0.880832	+	0.473429i	$0.843016\pi$
$984$	−7.06495e14	+	7.17901e14i	−0.765833	+	0.778196i
$985$	6.92187e14			0.746522
$986$	−1.60364e14	−	4.25110e13i	−0.172077	−	0.0456160i
$987$		−	1.25803e13i		−	0.0134309i
$988$	−9.23943e13	+	1.62023e14i	−0.0981432	+	0.172104i
$989$	−3.64290e14			−0.385004
$990$	5.54347e13	−	2.09116e14i	0.0582916	−	0.219893i
$991$			2.07745e14i			0.217352i	0.994077	+	0.108676i	$0.0346611\pi$
$991$			2.07745e14i			0.217352i	−0.994077	+	0.108676i	$0.965339\pi$
$992$	−1.58347e15	+	4.47022e14i	−1.64836	+	0.465340i
$993$	1.10673e14			0.114629
$994$	7.31728e13	+	1.93974e13i	0.0754081	+	0.0199900i
$995$			2.08465e14i			0.213756i
$996$	−6.26276e14	−	3.57137e14i	−0.638953	−	0.364366i
$997$	1.72913e15			1.75530			0.877650	−	0.479303i	$-0.159110\pi$
$997$	1.72913e15			1.75530			0.877650	+	0.479303i	$0.159110\pi$
$998$	3.58800e13	−	1.35350e14i	0.0362409	−	0.136711i
$999$			1.89328e15i			1.90277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.b.a.11.20	yes	20
3.2	odd	2		180.11.c.a.91.1		20
4.3	odd	2	inner	20.11.b.a.11.19	✓	20
5.2	odd	4		100.11.d.c.99.18		40
5.3	odd	4		100.11.d.c.99.23		40
5.4	even	2		100.11.b.e.51.1		20
8.3	odd	2		320.11.b.d.191.7		20
8.5	even	2		320.11.b.d.191.14		20
12.11	even	2		180.11.c.a.91.2		20
20.3	even	4		100.11.d.c.99.17		40
20.7	even	4		100.11.d.c.99.24		40
20.19	odd	2		100.11.b.e.51.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.19	✓	20	4.3	odd	2	inner
20.11.b.a.11.20	yes	20	1.1	even	1	trivial
100.11.b.e.51.1		20	5.4	even	2
100.11.b.e.51.2		20	20.19	odd	2
100.11.d.c.99.17		40	20.3	even	4
100.11.d.c.99.18		40	5.2	odd	4
100.11.d.c.99.23		40	5.3	odd	4
100.11.d.c.99.24		40	20.7	even	4
180.11.c.a.91.1		20	3.2	odd	2
180.11.c.a.91.2		20	12.11	even	2
320.11.b.d.191.7		20	8.3	odd	2
320.11.b.d.191.14		20	8.5	even	2

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 + 507.259i) q^{4} +1397.54 q^{5} +(1692.62 - 6385.07i) q^{6} -1527.38i q^{7} +(23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +O(q^{10})\)	\(q+(30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 + 507.259i) q^{4} +1397.54 q^{5} +(1692.62 - 6385.07i) q^{6} -1527.38i q^{7} +(23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +(43228.3 + 11459.4i) q^{10} -294294. i q^{11} +(104711. - 183622. i) q^{12} +198131. q^{13} +(12524.1 - 47244.5i) q^{14} -288488. i q^{15} +(533953. + 902445. i) q^{16} +367959. q^{17} +(508442. + 134783. i) q^{18} +919311. i q^{19} +(1.24316e6 + 708916. i) q^{20} -315291. q^{21} +(2.41311e6 - 9.10298e6i) q^{22} +2.57690e6i q^{23} +(4.74452e6 - 4.82111e6i) q^{24} +1.95312e6 q^{25} +(6.12851e6 + 1.62461e6i) q^{26} -1.55823e7i q^{27} +(774779. - 1.35865e6i) q^{28} -1.40898e7 q^{29} +(2.36551e6 - 8.92340e6i) q^{30} +4.90356e7i q^{31} +(9.11626e6 + 3.22923e7i) q^{32} -6.07497e7 q^{33} +(1.13816e7 + 3.01715e6i) q^{34} -2.13458e6i q^{35} +(1.46218e7 + 8.33812e6i) q^{36} -1.21502e8 q^{37} +(-7.53806e6 + 2.84358e7i) q^{38} -4.08993e7i q^{39} +(3.26400e7 + 3.21214e7i) q^{40} -1.48908e8 q^{41} +(-9.75245e6 - 2.58528e6i) q^{42} +1.41368e8i q^{43} +(1.49283e8 - 2.61783e8i) q^{44} +2.29723e7 q^{45} +(-2.11297e7 + 7.97076e7i) q^{46} +3.99006e7i q^{47} +(1.86287e8 - 1.10221e8i) q^{48} +2.80142e8 q^{49} +(6.04133e7 + 1.60150e7i) q^{50} -7.59561e7i q^{51} +(1.76244e8 + 1.00504e8i) q^{52} +1.03715e8 q^{53} +(1.27770e8 - 4.81987e8i) q^{54} -4.11288e8i q^{55} +(3.51057e7 - 3.56724e7i) q^{56} +1.89769e8 q^{57} +(-4.35820e8 - 1.15532e8i) q^{58} +4.38769e8i q^{59} +(1.46338e8 - 2.56619e8i) q^{60} -2.83067e8 q^{61} +(-4.02077e8 + 1.51675e9i) q^{62} -2.51065e7i q^{63} +(1.71940e7 + 1.07360e9i) q^{64} +2.76897e8 q^{65} +(-1.87909e9 - 4.98128e8i) q^{66} -2.00990e9i q^{67} +(3.27311e8 + 1.86651e8i) q^{68} +5.31936e8 q^{69} +(1.75029e7 - 6.60261e7i) q^{70} +1.54881e9i q^{71} +(3.83905e8 + 3.77805e8i) q^{72} +3.44009e9 q^{73} +(-3.75824e9 - 9.96274e8i) q^{74} -4.03174e8i q^{75} +(-4.66329e8 + 8.17756e8i) q^{76} -4.49499e8 q^{77} +(3.35361e8 - 1.26508e9i) q^{78} +2.88212e9i q^{79} +(7.46222e8 + 1.26120e9i) q^{80} -2.24597e9 q^{81} +(-4.60595e9 - 1.22100e9i) q^{82} -3.41069e9i q^{83} +(-2.80461e8 - 1.59934e8i) q^{84} +5.14239e8 q^{85} +(-1.15917e9 + 4.37273e9i) q^{86} +2.90849e9i q^{87} +(6.76411e9 - 6.87330e9i) q^{88} -2.47857e9 q^{89} +(7.10569e8 + 1.88365e8i) q^{90} -3.02622e8i q^{91} +(-1.30715e9 + 2.29223e9i) q^{92} +1.01222e10 q^{93} +(-3.27173e8 + 1.23419e9i) q^{94} +1.28478e9i q^{95} +(6.66595e9 - 1.88183e9i) q^{96} -2.70022e9 q^{97} +(8.66526e9 + 2.29708e9i) q^{98} -4.83748e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * q^98

Introduction

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