LMFDB - Embedded newform 15.11.d.c.14.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(14,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, 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("15.14");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.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:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17880 x^{14} + 140656106 x^{12} + 568287997200 x^{10} + \cdots + 16\!\cdots\!76 $ x^16 + 17880x^14 + 140656106x^12 + 568287997200x^10 + 2185320263599761x^8 + 14044998488243281560x^6 + 65358313992126025248056x^4 + 158088257382003622736619360*x^2 + 166976847233168897062137442576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{32}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.15
Root			$19.4690 + 50.0826i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.11.d.c.14.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+50.9058 q^{2} +(190.983 - 150.248i) q^{3} +1567.41 q^{4} +(-553.573 - 3075.58i) q^{5} +(9722.16 - 7648.49i) q^{6} +8178.10i q^{7} +27662.5 q^{8} +(13900.2 - 57389.6i) q^{9} +O(q^{10})$	\(q+50.9058 q^{2} +(190.983 - 150.248i) q^{3} +1567.41 q^{4} +(-553.573 - 3075.58i) q^{5} +(9722.16 - 7648.49i) q^{6} +8178.10i q^{7} +27662.5 q^{8} +(13900.2 - 57389.6i) q^{9} +(-28180.1 - 156565. i) q^{10} +197407. i q^{11} +(299348. - 235499. i) q^{12} +212605. i q^{13} +416313. i q^{14} +(-567822. - 504211. i) q^{15} -196840. q^{16} +2.05581e6 q^{17} +(707599. - 2.92147e6i) q^{18} +1.39222e6 q^{19} +(-867673. - 4.82068e6i) q^{20} +(1.22874e6 + 1.56188e6i) q^{21} +1.00492e7i q^{22} -6.13773e6 q^{23} +(5.28307e6 - 4.15623e6i) q^{24} +(-9.15274e6 + 3.40511e6i) q^{25} +1.08228e7i q^{26} +(-5.96797e6 - 1.30489e7i) q^{27} +1.28184e7i q^{28} +3.53508e7i q^{29} +(-2.89055e7 - 2.56673e7i) q^{30} -3.56226e7 q^{31} -3.83467e7 q^{32} +(2.96600e7 + 3.77015e7i) q^{33} +1.04653e8 q^{34} +(2.51524e7 - 4.52718e6i) q^{35} +(2.17872e7 - 8.99528e7i) q^{36} -1.06122e8i q^{37} +7.08720e7 q^{38} +(3.19434e7 + 4.06039e7i) q^{39} +(-1.53132e7 - 8.50782e7i) q^{40} -1.33173e7i q^{41} +(6.25502e7 + 7.95088e7i) q^{42} -1.18665e8i q^{43} +3.09417e8i q^{44} +(-1.84201e8 - 1.09817e7i) q^{45} -3.12446e8 q^{46} +2.04173e7 q^{47} +(-3.75932e7 + 2.95748e7i) q^{48} +2.15594e8 q^{49} +(-4.65928e8 + 1.73340e8i) q^{50} +(3.92625e8 - 3.08881e8i) q^{51} +3.33238e8i q^{52} +3.25193e8 q^{53} +(-3.03805e8 - 6.64267e8i) q^{54} +(6.07142e8 - 1.09279e8i) q^{55} +2.26227e8i q^{56} +(2.65890e8 - 2.09178e8i) q^{57} +1.79956e9i q^{58} -3.81698e8i q^{59} +(-8.90007e8 - 7.90302e8i) q^{60} -4.24233e8 q^{61} -1.81340e9 q^{62} +(4.69338e8 + 1.13677e8i) q^{63} -1.75051e9 q^{64} +(6.53883e8 - 1.17692e8i) q^{65} +(1.50987e9 + 1.91923e9i) q^{66} -1.63786e9i q^{67} +3.22229e9 q^{68} +(-1.17220e9 + 9.22180e8i) q^{69} +(1.28040e9 - 2.30460e8i) q^{70} +1.20624e9i q^{71} +(3.84513e8 - 1.58754e9i) q^{72} -1.19205e9i q^{73} -5.40223e9i q^{74} +(-1.23641e9 + 2.02550e9i) q^{75} +2.18217e9 q^{76} -1.61442e9 q^{77} +(1.62611e9 + 2.06698e9i) q^{78} +3.77862e8 q^{79} +(1.08965e8 + 6.05397e8i) q^{80} +(-3.10036e9 - 1.59545e9i) q^{81} -6.77930e8i q^{82} +1.59624e9 q^{83} +(1.92594e9 + 2.44810e9i) q^{84} +(-1.13804e9 - 6.32281e9i) q^{85} -6.04075e9i q^{86} +(5.31139e9 + 6.75141e9i) q^{87} +5.46078e9i q^{88} +8.82698e9i q^{89} +(-9.37691e9 - 5.59031e8i) q^{90} -1.73870e9 q^{91} -9.62031e9 q^{92} +(-6.80332e9 + 5.35222e9i) q^{93} +1.03936e9 q^{94} +(-7.70694e8 - 4.28187e9i) q^{95} +(-7.32358e9 + 5.76151e9i) q^{96} +4.83465e9i q^{97} +1.09750e10 q^{98} +(1.13291e10 + 2.74399e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9}+O(q^{10}) $ 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9	$ 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9} - 221680 q^{10} + 731640 q^{15} - 4218352 q^{16} + 1487600 q^{19} + 2444616 q^{21} + 28021368 q^{24} - 9324800 q^{25} - 35678700 q^{30} - 77667568 q^{31} + 251882368 q^{34} - 22344768 q^{36} - 70953984 q^{39} - 179966240 q^{40} - 484245000 q^{45} - 72018968 q^{46} + 89098816 q^{49} + 686556816 q^{51} + 441096084 q^{54} + 1424671200 q^{55} + 610091280 q^{60} - 1671368368 q^{61} - 4172730848 q^{64} + 2368350000 q^{66} - 2906594616 q^{69} + 2838634200 q^{70} - 1285884000 q^{75} + 4079367264 q^{76} - 3904999600 q^{79} - 11376681984 q^{81} + 13119851016 q^{84} + 8097594320 q^{85} - 15222287520 q^{90} + 19275224832 q^{91} - 9366481832 q^{94} - 5999937552 q^{96} + 42957756000 q^{99}+O(q^{100}) $ 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9 - 221680 * q^10 + 731640 * q^15 - 4218352 * q^16 + 1487600 * q^19 + 2444616 * q^21 + 28021368 * q^24 - 9324800 * q^25 - 35678700 * q^30 - 77667568 * q^31 + 251882368 * q^34 - 22344768 * q^36 - 70953984 * q^39 - 179966240 * q^40 - 484245000 * q^45 - 72018968 * q^46 + 89098816 * q^49 + 686556816 * q^51 + 441096084 * q^54 + 1424671200 * q^55 + 610091280 * q^60 - 1671368368 * q^61 - 4172730848 * q^64 + 2368350000 * q^66 - 2906594616 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 4079367264 * q^76 - 3904999600 * q^79 - 11376681984 * q^81 + 13119851016 * q^84 + 8097594320 * q^85 - 15222287520 * q^90 + 19275224832 * q^91 - 9366481832 * q^94 - 5999937552 * q^96 + 42957756000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	50.9058			1.59081			0.795404	−	0.606080i	$-0.207259\pi$
$2$	50.9058			1.59081			0.795404	+	0.606080i	$0.207259\pi$
$3$	190.983	−	150.248i	0.785939	−	0.618304i
$3$	190.983	−	150.248i	0.785939	−	0.618304i
$4$	1567.41			1.53067
$5$	−553.573	−	3075.58i	−0.177143	−	0.984185i
$5$	−553.573	−	3075.58i	−0.177143	−	0.984185i
$6$	9722.16	−	7648.49i	1.25028	−	0.983603i
$7$			8178.10i			0.486589i	0.969952	+	0.243294i	$0.0782281\pi$
$7$			8178.10i			0.486589i	−0.969952	+	0.243294i	$0.921772\pi$
$8$	27662.5			0.844192
$9$	13900.2	−	57389.6i	0.235400	−	0.971898i
$10$	−28180.1	−	156565.i	−0.281801	−	1.56565i
$11$			197407.i			1.22574i	0.790182	+	0.612872i	$0.209986\pi$
$11$			197407.i			1.22574i	−0.790182	+	0.612872i	$0.790014\pi$
$12$	299348.	−	235499.i	1.20301	−	0.946419i
$13$			212605.i			0.572606i	0.958139	+	0.286303i	$0.0924265\pi$
$13$			212605.i			0.572606i	−0.958139	+	0.286303i	$0.907574\pi$
$14$			416313.i			0.774069i
$15$	−567822.	−	504211.i	−0.747749	−	0.663981i
$16$	−196840.			−0.187721
$17$	2.05581e6			1.44790			0.723950	−	0.689852i	$-0.242324\pi$
$17$	2.05581e6			1.44790			0.723950	+	0.689852i	$0.242324\pi$
$18$	707599.	−	2.92147e6i	0.374477	−	1.54610i
$19$	1.39222e6			0.562262			0.281131	−	0.959669i	$-0.409290\pi$
$19$	1.39222e6			0.562262			0.281131	+	0.959669i	$0.409290\pi$
$20$	−867673.	−	4.82068e6i	−0.271148	−	1.50646i
$21$	1.22874e6	+	1.56188e6i	0.300860	+	0.382429i
$22$			1.00492e7i			1.94992i
$23$	−6.13773e6			−0.953605			−0.476802	−	0.879011i	$-0.658204\pi$
$23$	−6.13773e6			−0.953605			−0.476802	+	0.879011i	$0.658204\pi$
$24$	5.28307e6	−	4.15623e6i	0.663484	−	0.521967i
$25$	−9.15274e6	+	3.40511e6i	−0.937240	+	0.348684i
$26$			1.08228e7i			0.910907i
$27$	−5.96797e6	−	1.30489e7i	−0.415918	−	0.909402i
$28$			1.28184e7i			0.744807i
$29$			3.53508e7i			1.72349i	0.507339	+	0.861747i	$0.330629\pi$
$29$			3.53508e7i			1.72349i	−0.507339	+	0.861747i	$0.669371\pi$
$30$	−2.89055e7	−	2.56673e7i	−1.18953	−	1.05627i
$31$	−3.56226e7			−1.24428			−0.622139	−	0.782907i	$-0.713736\pi$
$31$	−3.56226e7			−1.24428			−0.622139	+	0.782907i	$0.713736\pi$
$32$	−3.83467e7			−1.14282
$33$	2.96600e7	+	3.77015e7i	0.757883	+	0.963361i
$34$	1.04653e8			2.30333
$35$	2.51524e7	−	4.52718e6i	0.478894	−	0.0861960i
$36$	2.17872e7	−	8.99528e7i	0.360320	−	1.48765i
$37$		−	1.06122e8i		−	1.53037i	−0.643810	−	0.765185i	$-0.722647\pi$
$37$		−	1.06122e8i		−	1.53037i	0.643810	−	0.765185i	$-0.277353\pi$
$38$	7.08720e7			0.894451
$39$	3.19434e7	+	4.06039e7i	0.354045	+	0.450034i
$40$	−1.53132e7	−	8.50782e7i	−0.149543	−	0.830841i
$41$		−	1.33173e7i		−	0.114947i	−0.998347	−	0.0574736i	$-0.981696\pi$
$41$		−	1.33173e7i		−	0.114947i	0.998347	−	0.0574736i	$-0.0183045\pi$
$42$	6.25502e7	+	7.95088e7i	0.478610	+	0.608371i
$43$		−	1.18665e8i		−	0.807200i	−0.914936	−	0.403600i	$-0.867759\pi$
$43$		−	1.18665e8i		−	0.807200i	0.914936	−	0.403600i	$-0.132241\pi$
$44$			3.09417e8i			1.87621i
$45$	−1.84201e8	−	1.09817e7i	−0.998228	−	0.0595122i
$46$	−3.12446e8			−1.51700
$47$	2.04173e7			0.0890245			0.0445122	−	0.999009i	$-0.485827\pi$
$47$	2.04173e7			0.0890245			0.0445122	+	0.999009i	$0.485827\pi$
$48$	−3.75932e7	+	2.95748e7i	−0.147538	+	0.116069i
$49$	2.15594e8			0.763231
$50$	−4.65928e8	+	1.73340e8i	−1.49097	+	0.554689i
$51$	3.92625e8	−	3.08881e8i	1.13796	−	0.895243i
$52$			3.33238e8i			0.876471i
$53$	3.25193e8			0.777610			0.388805	−	0.921320i	$-0.372888\pi$
$53$	3.25193e8			0.777610			0.388805	+	0.921320i	$0.372888\pi$
$54$	−3.03805e8	−	6.64267e8i	−0.661646	−	1.44668i
$55$	6.07142e8	−	1.09279e8i	1.20636	−	0.217133i
$56$			2.26227e8i			0.410775i
$57$	2.65890e8	−	2.09178e8i	0.441904	−	0.347649i
$58$			1.79956e9i			2.74175i
$59$		−	3.81698e8i		−	0.533900i	−0.963710	−	0.266950i	$-0.913984\pi$
$59$		−	3.81698e8i		−	0.533900i	0.963710	−	0.266950i	$-0.0860158\pi$
$60$	−8.90007e8	−	7.90302e8i	−1.14456	−	1.01634i
$61$	−4.24233e8			−0.502291			−0.251146	−	0.967949i	$-0.580807\pi$
$61$	−4.24233e8			−0.502291			−0.251146	+	0.967949i	$0.580807\pi$
$62$	−1.81340e9			−1.97941
$63$	4.69338e8	+	1.13677e8i	0.472915	+	0.114543i
$64$	−1.75051e9			−1.63029
$65$	6.53883e8	−	1.17692e8i	0.563551	−	0.101433i
$66$	1.50987e9	+	1.91923e9i	1.20565	+	1.53252i
$67$		−	1.63786e9i		−	1.21312i	−0.795039	−	0.606558i	$-0.792550\pi$
$67$		−	1.63786e9i		−	1.21312i	0.795039	−	0.606558i	$-0.207450\pi$
$68$	3.22229e9			2.21626
$69$	−1.17220e9	+	9.22180e8i	−0.749475	+	0.589618i
$70$	1.28040e9	−	2.30460e8i	0.761828	−	0.137121i
$71$			1.20624e9i			0.668564i	0.942473	+	0.334282i	$0.108494\pi$
$71$			1.20624e9i			0.668564i	−0.942473	+	0.334282i	$0.891506\pi$
$72$	3.84513e8	−	1.58754e9i	0.198723	−	0.820469i
$73$		−	1.19205e9i		−	0.575017i	−0.957778	−	0.287508i	$-0.907173\pi$
$73$		−	1.19205e9i		−	0.575017i	0.957778	−	0.287508i	$-0.0928270\pi$
$74$		−	5.40223e9i		−	2.43452i
$75$	−1.23641e9	+	2.02550e9i	−0.521021	+	0.853544i
$76$	2.18217e9			0.860638
$77$	−1.61442e9			−0.596434
$78$	1.62611e9	+	2.06698e9i	0.563217	+	0.715917i
$79$	3.77862e8			0.122800			0.0614000	−	0.998113i	$-0.480443\pi$
$79$	3.77862e8			0.122800			0.0614000	+	0.998113i	$0.480443\pi$
$80$	1.08965e8	+	6.05397e8i	0.0332536	+	0.184753i
$81$	−3.10036e9	−	1.59545e9i	−0.889173	−	0.457571i
$82$		−	6.77930e8i		−	0.182859i
$83$	1.59624e9			0.405236			0.202618	−	0.979258i	$-0.435055\pi$
$83$	1.59624e9			0.405236			0.202618	+	0.979258i	$0.435055\pi$
$84$	1.92594e9	+	2.44810e9i	0.460517	+	0.585373i
$85$	−1.13804e9	−	6.32281e9i	−0.256486	−	1.42500i
$86$		−	6.04075e9i		−	1.28410i
$87$	5.31139e9	+	6.75141e9i	1.06564	+	1.35456i
$88$			5.46078e9i			1.03476i
$89$			8.82698e9i			1.58075i	0.612626	+	0.790373i	$0.290113\pi$
$89$			8.82698e9i			1.58075i	−0.612626	+	0.790373i	$0.709887\pi$
$90$	−9.37691e9	−	5.59031e8i	−1.58799	−	0.0946725i
$91$	−1.73870e9			−0.278624
$92$	−9.62031e9			−1.45965
$93$	−6.80332e9	+	5.35222e9i	−0.977926	+	0.769342i
$94$	1.03936e9			0.141621
$95$	−7.70694e8	−	4.28187e9i	−0.0996011	−	0.553370i
$96$	−7.32358e9	+	5.76151e9i	−0.898188	+	0.706611i
$97$			4.83465e9i			0.562997i	0.959562	+	0.281499i	$0.0908315\pi$
$97$			4.83465e9i			0.562997i	−0.959562	+	0.281499i	$0.909169\pi$
$98$	1.09750e10			1.21415
$99$	1.13291e10	+	2.74399e9i	1.19130	+	0.288541i
$100$	−1.43460e10	+	5.33719e9i	−1.43460	+	0.533719i
$101$		−	1.31030e10i		−	1.24671i	−0.781940	−	0.623353i	$-0.785770\pi$
$101$		−	1.31030e10i		−	1.24671i	0.781940	−	0.623353i	$-0.214230\pi$
$102$	1.99869e10	−	1.57239e10i	1.81028	−	1.42416i
$103$		−	6.50730e8i		−	0.0561325i	−0.999606	−	0.0280663i	$-0.991065\pi$
$103$		−	6.50730e8i		−	0.0561325i	0.999606	−	0.0280663i	$-0.00893494\pi$
$104$			5.88118e9i			0.483390i
$105$	4.12348e9	−	4.64371e9i	0.323086	−	0.363847i
$106$	1.65542e10			1.23703
$107$	−1.97051e10			−1.40495			−0.702473	−	0.711710i	$-0.747921\pi$
$107$	−1.97051e10			−1.40495			−0.702473	+	0.711710i	$0.747921\pi$
$108$	−9.35423e9	−	2.04530e10i	−0.636633	−	1.39199i
$109$	1.12463e10			0.730932			0.365466	−	0.930825i	$-0.380910\pi$
$109$	1.12463e10			0.730932			0.365466	+	0.930825i	$0.380910\pi$
$110$	3.09071e10	−	5.56296e9i	1.91909	−	0.345416i
$111$	−1.59446e10	−	2.02675e10i	−0.946234	−	1.20278i
$112$		−	1.60978e9i		−	0.0913432i
$113$	2.43658e9			0.132248			0.0661240	−	0.997811i	$-0.478937\pi$
$113$	2.43658e9			0.132248			0.0661240	+	0.997811i	$0.478937\pi$
$114$	1.35354e10	−	1.06484e10i	0.702984	−	0.553043i
$115$	3.39768e9	+	1.88771e10i	0.168925	+	0.938524i
$116$			5.54091e10i			2.63810i
$117$	1.22013e10	+	2.95524e9i	0.556515	+	0.134792i
$118$		−	1.94307e10i		−	0.849332i
$119$			1.68126e10i			0.704532i
$120$	−1.57074e10	−	1.39477e10i	−0.631244	−	0.560528i
$121$	−1.30323e10			−0.502450
$122$	−2.15960e10			−0.799049
$123$	−2.00090e9	−	2.54339e9i	−0.0710723	−	0.0903415i
$124$	−5.58351e10			−1.90458
$125$	1.55394e10	+	2.62650e10i	0.509195	+	0.860651i
$126$	2.38921e10	+	5.78682e9i	0.752317	+	0.182216i
$127$		−	1.58080e10i		−	0.478474i	−0.970961	−	0.239237i	$-0.923103\pi$
$127$		−	1.58080e10i		−	0.478474i	0.970961	−	0.239237i	$-0.0768973\pi$
$128$	−4.98440e10			−1.45065
$129$	−1.78292e10	−	2.26631e10i	−0.499095	−	0.634410i
$130$	3.32864e10	−	5.99122e9i	0.896501	−	0.161361i
$131$		−	1.02430e9i		−	0.0265503i	−0.999912	−	0.0132752i	$-0.995774\pi$
$131$		−	1.02430e9i		−	0.0265503i	0.999912	−	0.0132752i	$-0.00422574\pi$
$132$	4.64893e10	+	5.90935e10i	1.16007	+	1.47459i
$133$			1.13857e10i			0.273591i
$134$		−	8.33765e10i		−	1.92983i
$135$	−3.68293e10	+	2.55785e10i	−0.821343	+	0.570435i
$136$	5.68689e10			1.22231
$137$	1.11459e10			0.230948			0.115474	−	0.993311i	$-0.463161\pi$
$137$	1.11459e10			0.230948			0.115474	+	0.993311i	$0.463161\pi$
$138$	−5.96720e10	+	4.69444e10i	−1.19227	+	0.937968i
$139$	−2.36968e10			−0.456684			−0.228342	−	0.973581i	$-0.573330\pi$
$139$	−2.36968e10			−0.456684			−0.228342	+	0.973581i	$0.573330\pi$
$140$	3.94240e10	−	7.09592e9i	0.733028	−	0.131938i
$141$	3.89936e9	−	3.06766e9i	0.0699678	−	0.0550442i
$142$			6.14048e10i			1.06356i
$143$	−4.19698e10			−0.701869
$144$	−2.73611e9	+	1.12966e10i	−0.0441897	+	0.182446i
$145$	1.08724e11	−	1.95693e10i	1.69624	−	0.305305i
$146$		−	6.06824e10i		−	0.914741i
$147$	4.11748e10	−	3.23925e10i	0.599853	−	0.471909i
$148$		−	1.66336e11i		−	2.34249i
$149$			6.95286e10i			0.946744i	0.880863	+	0.473372i	$0.156963\pi$
$149$			6.95286e10i			0.946744i	−0.880863	+	0.473372i	$0.843037\pi$
$150$	−6.29404e10	+	1.03110e11i	−0.828845	+	1.35782i
$151$	−1.41697e11			−1.80499			−0.902497	−	0.430695i	$-0.858268\pi$
$151$	−1.41697e11			−1.80499			−0.902497	+	0.430695i	$0.858268\pi$
$152$	3.85122e10			0.474658
$153$	2.85761e10	−	1.17982e11i	0.340836	−	1.40721i
$154$	−8.21833e10			−0.948812
$155$	1.97197e10	+	1.09560e11i	0.220416	+	1.22460i
$156$	5.00683e10	+	6.36428e10i	0.541925	+	0.688853i
$157$			1.68085e10i			0.176210i	0.996111	+	0.0881049i	$0.0280811\pi$
$157$			1.68085e10i			0.176210i	−0.996111	+	0.0881049i	$0.971919\pi$
$158$	1.92354e10			0.195351
$159$	6.21064e10	−	4.88596e10i	0.611154	−	0.480800i
$160$	2.12277e10	+	1.17938e11i	0.202443	+	1.12475i
$161$		−	5.01950e10i		−	0.464014i
$162$	−1.57826e11	−	8.12177e10i	−1.41450	−	0.727907i
$163$			9.31622e10i			0.809658i	0.914392	+	0.404829i	$0.132669\pi$
$163$			9.31622e10i			0.809658i	−0.914392	+	0.404829i	$0.867331\pi$
$164$		−	2.08737e10i		−	0.175946i
$165$	9.95349e10	−	1.12092e11i	0.813871	−	0.916550i
$166$	8.12579e10			0.644652
$167$	4.49511e10			0.346065			0.173033	−	0.984916i	$-0.444643\pi$
$167$	4.49511e10			0.346065			0.173033	+	0.984916i	$0.444643\pi$
$168$	3.39901e10	+	4.32055e10i	0.253984	+	0.322844i
$169$	9.26577e10			0.672122
$170$	−5.79330e10	−	3.21868e11i	−0.408020	−	2.26690i
$171$	1.93520e10	−	7.98988e10i	0.132357	−	0.546462i
$172$		−	1.85996e11i		−	1.23556i
$173$	1.20661e11			0.778638			0.389319	−	0.921103i	$-0.372710\pi$
$173$	1.20661e11			0.778638			0.389319	+	0.921103i	$0.372710\pi$
$174$	2.70381e11	+	3.43686e11i	1.69523	+	2.15485i
$175$	−2.78474e10	−	7.48520e10i	−0.169666	−	0.456051i
$176$		−	3.88577e10i		−	0.230099i
$177$	−5.73493e10	−	7.28979e10i	−0.330112	−	0.419613i
$178$			4.49345e11i			2.51466i
$179$		−	1.25285e11i		−	0.681762i	−0.940106	−	0.340881i	$-0.889275\pi$
$179$		−	1.25285e11i		−	0.681762i	0.940106	−	0.340881i	$-0.110725\pi$
$180$	−2.88718e11	−	1.72127e10i	−1.52796	−	0.0910935i
$181$	−4.85936e10			−0.250142			−0.125071	−	0.992148i	$-0.539916\pi$
$181$	−4.85936e10			−0.250142			−0.125071	+	0.992148i	$0.539916\pi$
$182$	−8.85101e10			−0.443237
$183$	−8.10215e10	+	6.37402e10i	−0.394770	+	0.310569i
$184$	−1.69785e11			−0.805026
$185$	−3.26386e11	+	5.87463e10i	−1.50617	+	0.271095i
$186$	−3.46329e11	+	2.72459e11i	−1.55569	+	1.22387i
$187$			4.05832e11i			1.77476i
$188$	3.20022e10			0.136267
$189$	1.06715e11	−	4.88067e10i	0.442505	−	0.202381i
$190$	−3.92328e10	−	2.17972e11i	−0.158446	−	0.880306i
$191$			1.54637e11i			0.608342i	0.952618	+	0.304171i	$0.0983794\pi$
$191$			1.54637e11i			0.608342i	−0.952618	+	0.304171i	$0.901621\pi$
$192$	−3.34317e11	+	2.63010e11i	−1.28131	+	1.00801i
$193$		−	4.23429e11i		−	1.58123i	−0.612315	−	0.790614i	$-0.709762\pi$
$193$		−	4.23429e11i		−	1.58123i	0.612315	−	0.790614i	$-0.290238\pi$
$194$			2.46112e11i			0.895620i
$195$	1.07198e11	−	1.20722e11i	0.380200	−	0.428166i
$196$	3.37923e11			1.16825
$197$	5.51250e11			1.85788			0.928939	−	0.370232i	$-0.120722\pi$
$197$	5.51250e11			1.85788			0.928939	+	0.370232i	$0.120722\pi$
$198$	5.76719e11	+	1.39685e11i	1.89513	+	0.459013i
$199$	−8.03909e10			−0.257598			−0.128799	−	0.991671i	$-0.541112\pi$
$199$	−8.03909e10			−0.257598			−0.128799	+	0.991671i	$0.541112\pi$
$200$	−2.53188e11	+	9.41940e10i	−0.791211	+	0.294356i
$201$	−2.46085e11	−	3.12803e11i	−0.750074	−	0.953435i
$202$		−	6.67020e11i		−	1.98327i
$203$	−2.89103e11			−0.838633
$204$	6.15403e11	−	4.84142e11i	1.74184	−	1.37032i
$205$	−4.09585e10	+	7.37212e9i	−0.113129	+	0.0203621i
$206$		−	3.31260e10i		−	0.0892961i
$207$	−8.53154e10	+	3.52242e11i	−0.224479	+	0.926807i
$208$		−	4.18492e10i		−	0.107490i
$209$			2.74834e11i			0.689190i
$210$	2.09909e11	−	2.36392e11i	0.513967	−	0.578810i
$211$	5.98657e11			1.43142			0.715708	−	0.698399i	$-0.246104\pi$
$211$	5.98657e11			1.43142			0.715708	+	0.698399i	$0.246104\pi$
$212$	5.09709e11			1.19026
$213$	1.81235e11	+	2.30372e11i	0.413376	+	0.525450i
$214$	−1.00311e12			−2.23500
$215$	−3.64964e11	+	6.56899e10i	−0.794434	+	0.142990i
$216$	−1.65089e11	−	3.60966e11i	−0.351115	−	0.767710i
$217$		−	2.91325e11i		−	0.605452i
$218$	5.72502e11			1.16277
$219$	−1.79103e11	−	2.27662e11i	−0.355535	−	0.451928i
$220$	9.51637e11	−	1.71285e11i	1.84654	−	0.332358i
$221$			4.37075e11i			0.829077i
$222$	−8.11673e11	−	1.03173e12i	−1.50528	−	1.91339i
$223$			6.50824e11i			1.18016i	0.807346	+	0.590078i	$0.200903\pi$
$223$			6.50824e11i			1.18016i	−0.807346	+	0.590078i	$0.799097\pi$
$224$		−	3.13603e11i		−	0.556084i
$225$	6.81938e10	+	5.72604e11i	0.118258	+	0.992983i
$226$	1.24036e11			0.210381
$227$	−6.29028e11			−1.04362			−0.521808	−	0.853063i	$-0.674742\pi$
$227$	−6.29028e11			−1.04362			−0.521808	+	0.853063i	$0.674742\pi$
$228$	4.16757e11	−	3.27866e11i	0.676409	−	0.532136i
$229$	−9.59819e11			−1.52410			−0.762048	−	0.647521i	$-0.775806\pi$
$229$	−9.59819e11			−1.52410			−0.762048	+	0.647521i	$0.775806\pi$
$230$	1.72962e11	+	9.60953e11i	0.268727	+	1.49301i
$231$	−3.08327e11	+	2.42563e11i	−0.468761	+	0.368777i
$232$			9.77892e11i			1.45496i
$233$	−4.34864e10			−0.0633248			−0.0316624	−	0.999499i	$-0.510080\pi$
$233$	−4.34864e10			−0.0633248			−0.0316624	+	0.999499i	$0.510080\pi$
$234$	6.21118e11	+	1.50439e11i	0.885309	+	0.214428i
$235$	−1.13025e10	−	6.27951e10i	−0.0157701	−	0.0876166i
$236$		−	5.98275e11i		−	0.817224i
$237$	7.21653e10	−	5.67730e10i	0.0965132	−	0.0759277i
$238$			8.55861e11i			1.12078i
$239$		−	2.77725e11i		−	0.356144i	−0.984017	−	0.178072i	$-0.943014\pi$
$239$		−	2.77725e11i		−	0.356144i	0.984017	−	0.178072i	$-0.0569860\pi$
$240$	1.11770e11	+	9.92489e10i	0.140369	+	0.124643i
$241$	1.81041e11			0.222686			0.111343	−	0.993782i	$-0.464485\pi$
$241$	1.81041e11			0.222686			0.111343	+	0.993782i	$0.464485\pi$
$242$	−6.63418e11			−0.799301
$243$	−8.31829e11	+	1.61118e11i	−0.981754	+	0.190157i
$244$	−6.64946e11			−0.768842
$245$	−1.19347e11	−	6.63076e11i	−0.135201	−	0.751161i
$246$	−1.01858e11	−	1.29473e11i	−0.113062	−	0.143716i
$247$			2.95992e11i			0.321955i
$248$	−9.85410e11			−1.05041
$249$	3.04855e11	−	2.39832e11i	0.318490	−	0.250559i
$250$	7.91047e11	+	1.33704e12i	0.810032	+	1.36913i
$251$			5.59687e11i			0.561793i	0.959738	+	0.280896i	$0.0906318\pi$
$251$			5.59687e11i			0.561793i	−0.959738	+	0.280896i	$0.909368\pi$
$252$	7.35643e11	+	1.78178e11i	0.723876	+	0.175328i
$253$		−	1.21163e12i		−	1.16888i
$254$		−	8.04720e11i		−	0.761160i
$255$	−1.16734e12	−	1.03656e12i	−1.08267	−	0.961378i
$256$	−7.44833e11			−0.677421
$257$	1.73313e12			1.54584			0.772920	−	0.634504i	$-0.218796\pi$
$257$	1.73313e12			1.54584			0.772920	+	0.634504i	$0.218796\pi$
$258$	−9.07610e11	−	1.15368e12i	−0.793964	−	1.00922i
$259$	8.67876e11			0.744661
$260$	1.02490e12	−	1.84471e11i	0.862609	−	0.155261i
$261$	2.02877e12	+	4.91382e11i	1.67506	+	0.405711i
$262$		−	5.21427e10i		−	0.0422365i
$263$	3.22541e11			0.256334			0.128167	−	0.991753i	$-0.459091\pi$
$263$	3.22541e11			0.256334			0.128167	+	0.991753i	$0.459091\pi$
$264$	8.20471e11	+	1.04292e12i	0.639799	+	0.813262i
$265$	−1.80018e11	−	1.00016e12i	−0.137749	−	0.765313i
$266$			5.79598e11i			0.435230i
$267$	1.32623e12	+	1.68580e12i	0.977381	+	1.24237i
$268$		−	2.56719e12i		−	1.85688i
$269$			5.70627e11i			0.405127i	0.979269	+	0.202564i	$0.0649273\pi$
$269$			5.70627e11i			0.405127i	−0.979269	+	0.202564i	$0.935073\pi$
$270$	−1.87483e12	+	1.30210e12i	−1.30660	+	0.907453i
$271$	−1.77796e11			−0.121640			−0.0608199	−	0.998149i	$-0.519372\pi$
$271$	−1.77796e11			−0.121640			−0.0608199	+	0.998149i	$0.519372\pi$
$272$	−4.04666e11			−0.271802
$273$	−3.32063e11	+	2.61236e11i	−0.218981	+	0.172274i
$274$	5.67393e11			0.367393
$275$	−6.72195e11	−	1.80682e12i	−0.427397	−	1.14882i
$276$	−1.83732e12	+	1.44543e12i	−1.14720	+	0.902509i
$277$		−	5.44853e11i		−	0.334103i	−0.985948	−	0.167052i	$-0.946575\pi$
$277$		−	5.44853e11i		−	0.334103i	0.985948	−	0.167052i	$-0.0534247\pi$
$278$	−1.20631e12			−0.726496
$279$	−4.95160e11	+	2.04437e12i	−0.292903	+	1.20931i
$280$	6.95778e11	−	1.25233e11i	0.404278	−	0.0727660i
$281$		−	2.40808e12i		−	1.37448i	−0.726430	−	0.687240i	$-0.758822\pi$
$281$		−	2.40808e12i		−	1.37448i	0.726430	−	0.687240i	$-0.241178\pi$
$282$	1.98500e11	−	1.56162e11i	0.111305	−	0.0875647i
$283$		−	1.25441e12i		−	0.691045i	−0.938410	−	0.345523i	$-0.887702\pi$
$283$		−	1.25441e12i		−	0.691045i	0.938410	−	0.345523i	$-0.112298\pi$
$284$			1.89067e12i			1.02335i
$285$	−7.90532e11	−	7.01971e11i	−0.420431	−	0.373332i
$286$	−2.13651e12			−1.11654
$287$	1.08911e11			0.0559320
$288$	−5.33025e11	+	2.20070e12i	−0.269021	+	1.11071i
$289$	2.21037e12			1.09642
$290$	5.53470e12	−	9.96190e11i	2.69839	−	0.485682i
$291$	7.26396e11	+	9.23337e11i	0.348103	+	0.442482i
$292$		−	1.86843e12i		−	0.880161i
$293$	1.00015e12			0.463156			0.231578	−	0.972816i	$-0.425611\pi$
$293$	1.00015e12			0.463156			0.231578	+	0.972816i	$0.425611\pi$
$294$	2.09604e12	−	1.64897e12i	0.954251	−	0.750716i
$295$	−1.17394e12	+	2.11298e11i	−0.525456	+	0.0945768i
$296$		−	2.93560e12i		−	1.29193i
$297$	2.57595e12	−	1.17812e12i	1.11469	−	0.509810i
$298$			3.53941e12i			1.50609i
$299$		−	1.30491e12i		−	0.546040i
$300$	−1.93795e12	+	3.17478e12i	−0.797511	+	1.30649i
$301$	9.70456e11			0.392775
$302$	−7.21321e12			−2.87140
$303$	−1.96870e12	−	2.50246e12i	−0.770844	−	0.979835i
$304$	−2.74044e11			−0.105549
$305$	2.34844e11	+	1.30476e12i	0.0889776	+	0.494348i
$306$	1.45469e12	−	6.00599e12i	0.542205	−	2.23860i
$307$			3.95601e12i			1.45066i	0.688402	+	0.725329i	$0.258312\pi$
$307$			3.95601e12i			1.45066i	−0.688402	+	0.725329i	$0.741688\pi$
$308$	−2.53045e12			−0.912943
$309$	−9.77708e10	−	1.24278e11i	−0.0347070	−	0.0441168i
$310$	1.00385e12	+	5.57725e12i	0.350639	+	1.94810i
$311$			3.90857e12i			1.34343i	0.740808	+	0.671717i	$0.234443\pi$
$311$			3.90857e12i			1.34343i	−0.740808	+	0.671717i	$0.765557\pi$
$312$	8.83634e11	+	1.12321e12i	0.298882	+	0.379915i
$313$		−	1.23218e11i		−	0.0410158i	−0.999790	−	0.0205079i	$-0.993472\pi$
$313$		−	1.23218e11i		−	0.0410158i	0.999790	−	0.0205079i	$-0.00652833\pi$
$314$			8.55650e11i			0.280316i
$315$	8.98092e10	−	1.50641e12i	0.0289580	−	0.485727i
$316$	5.92263e11			0.187966
$317$	−1.24152e12			−0.387845			−0.193923	−	0.981017i	$-0.562121\pi$
$317$	−1.24152e12			−0.387845			−0.193923	+	0.981017i	$0.562121\pi$
$318$	3.16158e12	−	2.48724e12i	0.972229	−	0.764860i
$319$	−6.97852e12			−2.11256
$320$	9.69034e11	+	5.38382e12i	0.288795	+	1.60450i
$321$	−3.76334e12	+	2.96065e12i	−1.10420	+	0.868684i
$322$		−	2.55522e12i		−	0.738156i
$323$	2.86214e12			0.814100
$324$	−4.85951e12	−	2.50072e12i	−1.36103	−	0.700389i
$325$	−7.23944e11	−	1.94592e12i	−0.199659	−	0.536670i
$326$			4.74250e12i			1.28801i
$327$	2.14785e12	−	1.68973e12i	0.574468	−	0.451938i
$328$		−	3.68391e11i		−	0.0970375i
$329$			1.66975e11i			0.0433183i
$330$	5.06691e12	−	5.70615e12i	1.29471	−	1.45805i
$331$	3.06363e12			0.771075			0.385537	−	0.922692i	$-0.374016\pi$
$331$	3.06363e12			0.771075			0.385537	+	0.922692i	$0.374016\pi$
$332$	2.50195e12			0.620282
$333$	−6.09030e12	−	1.47511e12i	−1.48736	−	0.360250i
$334$	2.28827e12			0.550523
$335$	−5.03736e12	+	9.06674e11i	−1.19393	+	0.214895i
$336$	−2.41866e11	−	3.07441e11i	−0.0564778	−	0.0717902i
$337$			7.32668e12i			1.68561i	0.538218	+	0.842806i	$0.319098\pi$
$337$			7.32668e12i			1.68561i	−0.538218	+	0.842806i	$0.680902\pi$
$338$	4.71682e12			1.06922
$339$	4.65347e11	−	3.66092e11i	0.103939	−	0.0817695i
$340$	−1.78377e12	−	9.91040e12i	−0.392595	−	2.18121i
$341$		−	7.03217e12i		−	1.52517i
$342$	9.85132e11	−	4.06732e12i	0.210554	−	0.869316i
$343$			4.07326e12i			0.857969i
$344$		−	3.28257e12i		−	0.681432i
$345$	3.48514e12	+	3.09471e12i	0.713057	+	0.633175i
$346$	6.14234e12			1.23866
$347$	1.63438e12			0.324868			0.162434	−	0.986719i	$-0.448066\pi$
$347$	1.63438e12			0.324868			0.162434	+	0.986719i	$0.448066\pi$
$348$	8.32509e12	+	1.05822e13i	1.63115	+	2.07338i
$349$	1.29926e12			0.250940			0.125470	−	0.992097i	$-0.459956\pi$
$349$	1.29926e12			0.250940			0.125470	+	0.992097i	$0.459956\pi$
$350$	−1.41759e12	−	3.81041e12i	−0.269905	−	0.725489i
$351$	2.77426e12	−	1.26882e12i	0.520729	−	0.238157i
$352$		−	7.56992e12i		−	1.40081i
$353$	4.44094e12			0.810217			0.405109	−	0.914269i	$-0.367234\pi$
$353$	4.44094e12			0.810217			0.405109	+	0.914269i	$0.367234\pi$
$354$	−2.91941e12	−	3.71093e12i	−0.525145	−	0.667523i
$355$	3.70989e12	−	6.67743e11i	0.657990	−	0.118432i
$356$			1.38355e13i			2.41960i
$357$	2.52606e12	+	3.21093e12i	0.435615	+	0.553720i
$358$		−	6.37772e12i		−	1.08455i
$359$		−	9.25546e12i		−	1.55212i	−0.630658	−	0.776061i	$-0.717215\pi$
$359$		−	9.25546e12i		−	1.55212i	0.630658	−	0.776061i	$-0.282785\pi$
$360$	−5.09546e12	−	3.03780e11i	−0.842696	−	0.0502397i
$361$	−4.19280e12			−0.683861
$362$	−2.47370e12			−0.397927
$363$	−2.48894e12	+	1.95807e12i	−0.394895	+	0.310667i
$364$	−2.72525e12			−0.426481
$365$	−3.66625e12	+	6.59888e11i	−0.565923	+	0.101860i
$366$	−4.12447e12	+	3.24475e12i	−0.628004	+	0.494055i
$367$		−	1.09566e13i		−	1.64568i	−0.568272	−	0.822841i	$-0.692388\pi$
$367$		−	1.09566e13i		−	1.64568i	0.568272	−	0.822841i	$-0.307612\pi$
$368$	1.20815e12			0.179012
$369$	−7.64277e11	−	1.85113e11i	−0.111717	−	0.0270586i
$370$	−1.66150e13	+	2.99053e12i	−2.39602	+	0.431260i
$371$			2.65946e12i			0.378377i
$372$	−1.06636e13	+	8.38910e12i	−1.49688	+	1.17761i
$373$			8.00491e12i			1.10869i	0.832285	+	0.554347i	$0.187032\pi$
$373$			8.00491e12i			1.10869i	−0.832285	+	0.554347i	$0.812968\pi$
$374$			2.06592e13i			2.82330i
$375$	6.91402e12	+	2.68141e12i	0.932340	+	0.361582i
$376$	5.64794e11			0.0751538
$377$	−7.51575e12			−0.986883
$378$	5.43244e12	−	2.48455e12i	0.703940	−	0.321950i
$379$	1.30200e13			1.66501			0.832504	−	0.554018i	$-0.186906\pi$
$379$	1.30200e13			1.66501			0.832504	+	0.554018i	$0.186906\pi$
$380$	−1.20799e12	−	6.71143e12i	−0.152456	−	0.847027i
$381$	−2.37512e12	−	3.01906e12i	−0.295842	−	0.376052i
$382$			7.87194e12i			0.967755i
$383$	−2.49577e12			−0.302838			−0.151419	−	0.988470i	$-0.548384\pi$
$383$	−2.49577e12			−0.302838			−0.151419	+	0.988470i	$0.548384\pi$
$384$	−9.51937e12	+	7.48896e12i	−1.14012	+	0.896944i
$385$	8.93698e11	+	4.96527e12i	0.105654	+	0.587001i
$386$		−	2.15550e13i		−	2.51543i
$387$	−6.81015e12	−	1.64947e12i	−0.784516	−	0.190015i
$388$			7.57785e12i			0.861763i
$389$			3.35910e12i			0.377116i	0.982062	+	0.188558i	$0.0603814\pi$
$389$			3.35910e12i			0.377116i	−0.982062	+	0.188558i	$0.939619\pi$
$390$	5.45698e12	−	6.14544e12i	0.604825	−	0.681130i
$391$	−1.26180e13			−1.38072
$392$	5.96387e12			0.644314
$393$	−1.53899e11	−	1.95624e11i	−0.0164162	−	0.0208669i
$394$	2.80618e13			2.95553
$395$	−2.09174e11	−	1.16214e12i	−0.0217532	−	0.120858i
$396$	1.77573e13	+	4.30095e12i	1.82349	+	0.441661i
$397$			3.31190e12i			0.335834i	0.985801	+	0.167917i	$0.0537040\pi$
$397$			3.31190e12i			0.335834i	−0.985801	+	0.167917i	$0.946296\pi$
$398$	−4.09237e12			−0.409788
$399$	1.71068e12	+	2.17448e12i	0.169162	+	0.215026i
$400$	1.80163e12	−	6.70263e11i	0.175940	−	0.0654554i
$401$		−	1.07686e13i		−	1.03857i	−0.854600	−	0.519287i	$-0.826197\pi$
$401$		−	1.07686e13i		−	1.03857i	0.854600	−	0.519287i	$-0.173803\pi$
$402$	−1.25271e13	−	1.59235e13i	−1.19322	−	1.51673i
$403$		−	7.57354e12i		−	0.712481i
$404$		−	2.05377e13i		−	1.90830i
$405$	−3.19066e12	+	1.04186e13i	−0.292823	+	0.956167i
$406$	−1.47170e13			−1.33410
$407$	2.09493e13			1.87584
$408$	1.08610e13	−	8.54443e12i	0.960658	−	0.755757i
$409$	−4.75031e12			−0.415055			−0.207527	−	0.978229i	$-0.566542\pi$
$409$	−4.75031e12			−0.415055			−0.207527	+	0.978229i	$0.566542\pi$
$410$	−2.08503e12	+	3.75284e11i	−0.179967	+	0.0323922i
$411$	2.12868e12	−	1.67465e12i	0.181511	−	0.142796i
$412$		−	1.01996e12i		−	0.0859203i
$413$	3.12156e12			0.259790
$414$	−4.34305e12	+	1.79312e13i	−0.357103	+	1.47437i
$415$	−8.83635e11	−	4.90936e12i	−0.0717848	−	0.398827i
$416$		−	8.15269e12i		−	0.654387i
$417$	−4.52569e12	+	3.56039e12i	−0.358926	+	0.282369i
$418$			1.39907e13i			1.09637i
$419$			1.48450e13i			1.14950i	0.818328	+	0.574751i	$0.194901\pi$
$419$			1.48450e13i			1.14950i	−0.818328	+	0.574751i	$0.805099\pi$
$420$	6.46317e12	−	7.27857e12i	0.494537	−	0.556929i
$421$	−1.53608e13			−1.16146			−0.580728	−	0.814098i	$-0.697232\pi$
$421$	−1.53608e13			−1.16146			−0.580728	+	0.814098i	$0.697232\pi$
$422$	3.04752e13			2.27711
$423$	2.83804e11	−	1.17174e12i	0.0209564	−	0.0865227i
$424$	8.99565e12			0.656453
$425$	−1.88163e13	+	7.00028e12i	−1.35703	+	0.504859i
$426$	9.22594e12	+	1.17273e13i	0.657601	+	0.835891i
$427$		−	3.46942e12i		−	0.244409i
$428$	−3.08859e13			−2.15051
$429$	−8.01552e12	+	6.30587e12i	−0.551626	+	0.433969i
$430$	−1.85788e13	+	3.34400e12i	−1.26379	+	0.227470i
$431$			1.84497e13i			1.24052i	0.784396	+	0.620260i	$0.212973\pi$
$431$			1.84497e13i			1.24052i	−0.784396	+	0.620260i	$0.787027\pi$
$432$	1.17474e12	+	2.56855e12i	0.0780768	+	0.170714i
$433$		−	2.31045e13i		−	1.51795i	−0.651121	−	0.758974i	$-0.725701\pi$
$433$		−	2.31045e13i		−	1.51795i	0.651121	−	0.758974i	$-0.274299\pi$
$434$		−	1.48302e13i		−	0.963157i
$435$	1.78243e13	−	2.00730e13i	1.14437	−	1.28874i
$436$	1.76275e13			1.11881
$437$	−8.54505e12			−0.536176
$438$	−9.11740e12	−	1.15893e13i	−0.565588	−	0.718931i
$439$	9.38712e12			0.575718			0.287859	−	0.957673i	$-0.407057\pi$
$439$	9.38712e12			0.575718			0.287859	+	0.957673i	$0.407057\pi$
$440$	1.67951e13	−	3.02294e12i	1.01840	−	0.183302i
$441$	2.99679e12	−	1.23729e13i	0.179665	−	0.741783i
$442$			2.22497e13i			1.31890i
$443$	2.03386e13			1.19207			0.596037	−	0.802957i	$-0.296741\pi$
$443$	2.03386e13			1.19207			0.596037	+	0.802957i	$0.296741\pi$
$444$	−2.49916e13	−	3.17674e13i	−1.44837	−	1.84105i
$445$	2.71481e13	−	4.88638e12i	1.55575	−	0.280019i
$446$			3.31308e13i			1.87740i
$447$	1.04465e13	+	1.32788e13i	0.585375	+	0.744083i
$448$		−	1.43158e13i		−	0.793280i
$449$		−	4.51767e11i		−	0.0247561i	−0.999923	−	0.0123781i	$-0.996060\pi$
$449$		−	4.51767e11i		−	0.0247561i	0.999923	−	0.0123781i	$-0.00394016\pi$
$450$	3.47146e12	+	2.91489e13i	0.188126	+	1.57964i
$451$	2.62894e12			0.140896
$452$	3.81911e12			0.202428
$453$	−2.70617e13	+	2.12897e13i	−1.41862	+	1.11604i
$454$	−3.20212e13			−1.66019
$455$	9.62499e11	+	5.34752e12i	0.0493564	+	0.274218i
$456$	7.35518e12	−	5.78638e12i	0.373052	−	0.293483i
$457$		−	2.05500e11i		−	0.0103093i	−0.999987	−	0.00515466i	$-0.998359\pi$
$457$		−	2.05500e11i		−	0.0103093i	0.999987	−	0.00515466i	$-0.00164079\pi$
$458$	−4.88604e13			−2.42454
$459$	−1.22690e13	−	2.68261e13i	−0.602208	−	1.31672i
$460$	5.32554e12	+	2.95880e13i	0.258568	+	1.43657i
$461$		−	1.85609e13i		−	0.891445i	−0.895171	−	0.445722i	$-0.852947\pi$
$461$		−	1.85609e13i		−	0.891445i	0.895171	−	0.445722i	$-0.147053\pi$
$462$	−1.56956e13	+	1.23479e13i	−0.745708	+	0.586654i
$463$		−	2.09809e13i		−	0.986095i	−0.870002	−	0.493048i	$-0.835883\pi$
$463$		−	2.09809e13i		−	0.986095i	0.870002	−	0.493048i	$-0.164117\pi$
$464$		−	6.95846e12i		−	0.323537i
$465$	2.02273e13	+	1.79613e13i	0.930408	+	0.826177i
$466$	−2.21371e12			−0.100738
$467$	−2.47202e13			−1.11293			−0.556464	−	0.830872i	$-0.687842\pi$
$467$	−2.47202e13			−1.11293			−0.556464	+	0.830872i	$0.687842\pi$
$468$	1.91244e13	+	4.63206e12i	0.851841	+	0.206322i
$469$	1.33946e13			0.590289
$470$	−5.75362e11	−	3.19664e12i	−0.0250872	−	0.139381i
$471$	2.52544e12	+	3.21014e12i	0.108951	+	0.138490i
$472$		−	1.05587e13i		−	0.450714i
$473$	2.34254e13			0.989421
$474$	3.67364e12	−	2.89008e12i	0.153534	−	0.120786i
$475$	−1.27426e13	+	4.74066e12i	−0.526975	+	0.196052i
$476$			2.63522e13i			1.07841i
$477$	4.52024e12	−	1.86627e13i	0.183050	−	0.755758i
$478$		−	1.41378e13i		−	0.566556i
$479$			1.00024e13i			0.396666i	0.980135	+	0.198333i	$0.0635527\pi$
$479$			1.00024e13i			0.396666i	−0.980135	+	0.198333i	$0.936447\pi$
$480$	2.17741e13	+	1.93348e13i	0.854544	+	0.758811i
$481$	2.25620e13			0.876300
$482$	9.21606e12			0.354250
$483$	−7.54168e12	−	9.58639e12i	−0.286901	−	0.364686i
$484$	−2.04268e13			−0.769085
$485$	1.48693e13	−	2.67633e12i	0.554094	−	0.0997313i
$486$	−4.23449e13	+	8.20183e12i	−1.56178	+	0.302503i
$487$		−	3.35486e13i		−	1.22470i	−0.790587	−	0.612350i	$-0.790224\pi$
$487$		−	3.35486e13i		−	1.22470i	0.790587	−	0.612350i	$-0.209776\pi$
$488$	−1.17354e13			−0.424031
$489$	1.39974e13	+	1.77924e13i	0.500615	+	0.636342i
$490$	−6.07546e12	−	3.37544e13i	−0.215079	−	1.19495i
$491$			9.86200e12i			0.345587i	0.984958	+	0.172793i	$0.0552793\pi$
$491$			9.86200e12i			0.345587i	−0.984958	+	0.172793i	$0.944721\pi$
$492$	−3.13622e12	−	3.98652e12i	−0.108788	−	0.138283i
$493$			7.26746e13i			2.49545i
$494$			1.50677e13i			0.512168i
$495$	2.16786e12	−	3.63627e13i	0.0729468	−	1.22357i
$496$	7.01196e12			0.233578
$497$	−9.86477e12			−0.325316
$498$	1.55189e13	−	1.22088e13i	0.506657	−	0.398591i
$499$	−3.23855e13			−1.04676			−0.523381	−	0.852099i	$-0.675330\pi$
$499$	−3.23855e13			−1.04676			−0.523381	+	0.852099i	$0.675330\pi$
$500$	2.43565e13	+	4.11679e13i	0.779409	+	1.31737i
$501$	8.58491e12	−	6.75381e12i	0.271986	−	0.213974i
$502$			2.84913e13i			0.893705i
$503$	6.38005e12			0.198145			0.0990727	−	0.995080i	$-0.468412\pi$
$503$	6.38005e12			0.198145			0.0990727	+	0.995080i	$0.468412\pi$
$504$	1.29831e13	+	3.14459e12i	0.399231	+	0.0966965i
$505$	−4.02993e13	+	7.25348e12i	−1.22699	+	0.220846i
$506$		−	6.16792e13i		−	1.85946i
$507$	1.76961e13	−	1.39216e13i	0.528247	−	0.415576i
$508$		−	2.47775e13i		−	0.732386i
$509$			6.47112e12i			0.189404i	0.995506	+	0.0947022i	$0.0301899\pi$
$509$			6.47112e12i			0.189404i	−0.995506	+	0.0947022i	$0.969810\pi$
$510$	−5.94242e13	−	5.27671e13i	−1.72231	−	1.52937i
$511$	9.74872e12			0.279797
$512$	1.31239e13			0.373005
$513$	−8.30871e12	−	1.81669e13i	−0.233855	−	0.511323i
$514$	8.82262e13			2.45913
$515$	−2.00137e12	+	3.60227e11i	−0.0552448	+	0.00994351i
$516$	−2.79456e13	−	3.55222e13i	−0.763949	−	0.971072i
$517$			4.03053e12i			0.109121i
$518$	4.41800e13			1.18461
$519$	2.30442e13	−	1.81290e13i	0.611962	−	0.481435i
$520$	1.80880e13	−	3.25566e12i	0.475745	−	0.0856293i
$521$			1.32724e13i			0.345748i	0.984944	+	0.172874i	$0.0553054\pi$
$521$			1.32724e13i			0.345748i	−0.984944	+	0.172874i	$0.944695\pi$
$522$	1.03276e14	+	2.50142e13i	2.66470	+	0.645408i
$523$		−	5.67492e12i		−	0.145028i	−0.997367	−	0.0725139i	$-0.976898\pi$
$523$		−	5.67492e12i		−	0.145028i	0.997367	−	0.0725139i	$-0.0231022\pi$
$524$		−	1.60549e12i		−	0.0406398i
$525$	−1.65647e13	−	1.01115e13i	−0.415325	−	0.253523i
$526$	1.64192e13			0.407778
$527$	−7.32334e13			−1.80159
$528$	−5.83829e12	−	7.42117e12i	−0.142271	−	0.180843i
$529$	−3.75481e12			−0.0906379
$530$	−9.16398e12	−	5.09138e13i	−0.219131	−	1.21746i
$531$	−2.19055e13	−	5.30566e12i	−0.518896	−	0.125680i
$532$			1.78460e13i			0.418777i
$533$	2.83133e12			0.0658195
$534$	6.75131e13	+	8.58173e13i	1.55483	+	1.97637i
$535$	1.09082e13	+	6.06046e13i	0.248877	+	1.38273i
$536$		−	4.53072e13i		−	1.02410i
$537$	−1.88238e13	−	2.39273e13i	−0.421536	−	0.535823i
$538$			2.90483e13i			0.644479i
$539$			4.25598e13i			0.935527i
$540$	−5.77264e13	+	4.00919e13i	−1.25720	+	0.873147i
$541$	−4.08953e13			−0.882444			−0.441222	−	0.897398i	$-0.645455\pi$
$541$	−4.08953e13			−0.882444			−0.441222	+	0.897398i	$0.645455\pi$
$542$	−9.05086e12			−0.193506
$543$	−9.28056e12	+	7.30109e12i	−0.196596	+	0.154664i
$544$	−7.88336e13			−1.65469
$545$	−6.22565e12	−	3.45889e13i	−0.129480	−	0.719372i
$546$	−1.69039e13	+	1.32985e13i	−0.348357	+	0.274055i
$547$			6.40347e13i			1.30761i	0.756663	+	0.653806i	$0.226829\pi$
$547$			6.40347e13i			1.30761i	−0.756663	+	0.653806i	$0.773171\pi$
$548$	1.74702e13			0.353504
$549$	−5.89691e12	+	2.43466e13i	−0.118240	+	0.488176i
$550$	−3.42187e13	−	9.19776e13i	−0.679907	−	1.82755i
$551$			4.92160e13i			0.969055i
$552$	−3.24261e13	+	2.55098e13i	−0.632701	+	0.497751i
$553$			3.09020e12i			0.0597531i
$554$		−	2.77362e13i		−	0.531494i
$555$	−5.35078e13	+	6.02584e13i	−1.01614	+	1.14433i
$556$	−3.71425e13			−0.699032
$557$	−4.26311e13			−0.795152			−0.397576	−	0.917569i	$-0.630149\pi$
$557$	−4.26311e13			−0.795152			−0.397576	+	0.917569i	$0.630149\pi$
$558$	−2.52065e13	+	1.04070e14i	−0.465953	+	1.92378i
$559$	2.52288e13			0.462208
$560$	−4.95100e12	+	8.91130e11i	−0.0898986	+	0.0161808i
$561$	6.09755e13	+	7.75072e13i	1.09734	+	1.39485i
$562$		−	1.22585e14i		−	2.18653i
$563$	4.95070e13			0.875235			0.437617	−	0.899161i	$-0.355822\pi$
$563$	4.95070e13			0.875235			0.437617	+	0.899161i	$0.355822\pi$
$564$	6.11188e12	−	4.80826e12i	0.107098	−	0.0842544i
$565$	−1.34883e12	−	7.49391e12i	−0.0234269	−	0.130157i
$566$		−	6.38567e13i		−	1.09932i
$567$	1.30478e13	−	2.53550e13i	0.222649	−	0.432662i
$568$			3.33677e13i			0.564396i
$569$		−	8.12271e13i		−	1.36188i	−0.732338	−	0.680941i	$-0.761571\pi$
$569$		−	8.12271e13i		−	1.36188i	0.732338	−	0.680941i	$-0.238429\pi$
$570$	−4.02427e13	−	3.57344e13i	−0.668825	−	0.593899i
$571$	5.43146e13			0.894821			0.447411	−	0.894329i	$-0.352346\pi$
$571$	5.43146e13			0.894821			0.447411	+	0.894329i	$0.352346\pi$
$572$	−6.57836e13			−1.07433
$573$	2.32339e13	+	2.95331e13i	0.376140	+	0.478119i
$574$	5.54418e12			0.0889771
$575$	5.61770e13	−	2.08997e13i	0.893757	−	0.332507i
$576$	−2.43323e13	+	1.00461e14i	−0.383770	+	1.58447i
$577$		−	9.61550e13i		−	1.50346i	−0.659469	−	0.751731i	$-0.729219\pi$
$577$		−	9.61550e13i		−	1.50346i	0.659469	−	0.751731i	$-0.270781\pi$
$578$	1.12521e14			1.74419
$579$	−6.36193e13	−	8.08679e13i	−0.977679	−	1.24275i
$580$	1.70415e14	−	3.06730e13i	2.59638	−	0.467322i
$581$			1.30542e13i			0.197183i
$582$	3.69778e13	+	4.70032e13i	0.553766	+	0.703903i
$583$			6.41955e13i			0.953152i
$584$		−	3.29751e13i		−	0.485425i
$585$	2.33476e12	−	3.91620e13i	0.0340771	−	0.571591i
$586$	5.09135e13			0.736792
$587$	−6.14398e13			−0.881575			−0.440787	−	0.897612i	$-0.645301\pi$
$587$	−6.14398e13			−0.881575			−0.440787	+	0.897612i	$0.645301\pi$
$588$	6.45376e13	−	5.07722e13i	0.918177	−	0.722336i
$589$	−4.95944e13			−0.699610
$590$	−5.97605e13	+	1.07563e13i	−0.835900	+	0.150454i
$591$	1.05279e14	−	8.28241e13i	1.46018	−	1.14873i
$592$			2.08891e13i			0.287283i
$593$	4.15267e13			0.566310			0.283155	−	0.959074i	$-0.408619\pi$
$593$	4.15267e13			0.566310			0.283155	+	0.959074i	$0.408619\pi$
$594$	1.31131e14	−	5.99733e13i	1.77326	−	0.811009i
$595$	5.17086e13	−	9.30702e12i	0.693390	−	0.124803i
$596$			1.08980e14i			1.44915i
$597$	−1.53533e13	+	1.20786e13i	−0.202456	+	0.159274i
$598$		−	6.64275e13i		−	0.868645i
$599$			3.38848e12i			0.0439410i	0.999759	+	0.0219705i	$0.00699399\pi$
$599$			3.38848e12i			0.0439410i	−0.999759	+	0.0219705i	$0.993006\pi$
$600$	−3.42021e13	+	5.60304e13i	−0.439842	+	0.720555i
$601$	−2.41599e13			−0.308123			−0.154061	−	0.988061i	$-0.549235\pi$
$601$	−2.41599e13			−0.308123			−0.154061	+	0.988061i	$0.549235\pi$
$602$	4.94019e13			0.624829
$603$	−9.39961e13	−	2.27665e13i	−1.17903	−	0.285568i
$604$	−2.22097e14			−2.76285
$605$	7.21431e12	+	4.00817e13i	0.0890057	+	0.494504i
$606$	−1.00218e14	−	1.27390e14i	−1.22626	−	1.55873i
$607$			7.14259e12i			0.0866787i	0.999060	+	0.0433394i	$0.0137997\pi$
$607$			7.14259e12i			0.0866787i	−0.999060	+	0.0433394i	$0.986200\pi$
$608$	−5.33869e13			−0.642565
$609$	−5.52137e13	+	4.34370e13i	−0.659114	+	0.518530i
$610$	1.19549e13	+	6.64201e13i	0.141546	+	0.786412i
$611$			4.34082e12i			0.0509760i
$612$	4.47903e13	−	1.84926e14i	0.521708	−	2.15398i
$613$		−	8.67406e13i		−	1.00212i	−0.865412	−	0.501060i	$-0.832944\pi$
$613$		−	8.67406e13i		−	1.00212i	0.865412	−	0.501060i	$-0.167056\pi$
$614$			2.01384e14i			2.30772i
$615$	−6.71474e12	+	7.56188e12i	−0.0763227	+	0.0859517i
$616$	−4.46588e13			−0.503505
$617$	1.30072e14			1.45465			0.727325	−	0.686293i	$-0.240763\pi$
$617$	1.30072e14			1.45465			0.727325	+	0.686293i	$0.240763\pi$
$618$	−4.97710e12	−	6.32650e12i	−0.0552121	−	0.0701813i
$619$	−1.19936e12			−0.0131977			−0.00659885	−	0.999978i	$-0.502100\pi$
$619$	−1.19936e12			−0.0131977			−0.00659885	+	0.999978i	$0.502100\pi$
$620$	3.09088e13	+	1.71725e14i	0.337383	+	1.87446i
$621$	3.66298e13	+	8.00907e13i	0.396622	+	0.867210i
$622$			1.98969e14i			2.13714i
$623$	−7.21879e13			−0.769173
$624$	−6.28775e12	−	7.99248e12i	−0.0664618	−	0.0844810i
$625$	7.21778e13	−	6.23323e13i	0.756839	−	0.653601i
$626$		−	6.27250e12i		−	0.0652483i
$627$	4.12932e13	+	5.24887e13i	0.426129	+	0.541661i
$628$			2.63457e13i			0.269719i
$629$		−	2.18167e14i		−	2.21582i
$630$	4.57181e12	−	7.66853e13i	0.0460666	−	0.772697i
$631$	−8.90644e13			−0.890343			−0.445172	−	0.895445i	$-0.646857\pi$
$631$	−8.90644e13			−0.890343			−0.445172	+	0.895445i	$0.646857\pi$
$632$	1.04526e13			0.103667
$633$	1.14334e14	−	8.99470e13i	1.12501	−	0.885051i
$634$	−6.32007e13			−0.616987
$635$	−4.86188e13	+	8.75089e12i	−0.470907	+	0.0847585i
$636$	9.73459e13	−	7.65827e13i	0.935475	−	0.735945i
$637$			4.58363e13i			0.437031i
$638$	−3.55247e14			−3.36068
$639$	6.92258e13	+	1.67670e13i	0.649776	+	0.157380i
$640$	2.75923e13	+	1.53299e14i	0.256973	+	1.42771i
$641$		−	3.65233e13i		−	0.337505i	−0.985658	−	0.168752i	$-0.946026\pi$
$641$		−	3.65233e13i		−	0.337505i	0.985658	−	0.168752i	$-0.0539738\pi$
$642$	−1.91576e14	+	1.50714e14i	−1.75657	+	1.38191i
$643$			5.65540e13i			0.514527i	0.966341	+	0.257263i	$0.0828208\pi$
$643$			5.65540e13i			0.514527i	−0.966341	+	0.257263i	$0.917179\pi$
$644$		−	7.86758e13i		−	0.710251i
$645$	−5.98322e13	+	6.73807e13i	−0.535965	+	0.603583i
$646$	1.45699e14			1.29508
$647$	1.04260e14			0.919594			0.459797	−	0.888024i	$-0.347922\pi$
$647$	1.04260e14			0.919594			0.459797	+	0.888024i	$0.347922\pi$
$648$	−8.57636e13	−	4.41341e13i	−0.750633	−	0.386278i
$649$	7.53500e13			0.654425
$650$	−3.68530e13	−	9.90585e13i	−0.317618	−	0.853738i
$651$	−4.37710e13	−	5.56382e13i	−0.374353	−	0.475848i
$652$			1.46023e14i			1.23932i
$653$	7.77253e13			0.654631			0.327315	−	0.944915i	$-0.393856\pi$
$653$	7.77253e13			0.654631			0.327315	+	0.944915i	$0.393856\pi$
$654$	1.09338e14	−	8.60172e13i	0.913868	−	0.718947i
$655$	−3.15031e12	+	5.67024e11i	−0.0261304	+	0.00470321i
$656$			2.62139e12i			0.0215780i
$657$	−6.84114e13	−	1.65697e13i	−0.558858	−	0.135359i
$658$			8.50000e12i			0.0689111i
$659$			1.33902e14i			1.07736i	0.842510	+	0.538680i	$0.181077\pi$
$659$			1.33902e14i			1.07736i	−0.842510	+	0.538680i	$0.818923\pi$
$660$	1.56012e14	−	1.75694e14i	1.24577	−	1.40293i
$661$	6.42011e13			0.508786			0.254393	−	0.967101i	$-0.418124\pi$
$661$	6.42011e13			0.508786			0.254393	+	0.967101i	$0.418124\pi$
$662$	1.55957e14			1.22663
$663$	6.56696e13	+	8.34740e13i	0.512622	+	0.651604i
$664$	4.41560e13			0.342097
$665$	3.50176e13	−	6.30281e12i	0.269264	−	0.0484648i
$666$	−3.10032e14	−	7.50918e13i	−2.36611	−	0.573088i
$667$		−	2.16974e14i		−	1.64353i
$668$	7.04566e13			0.529711
$669$	9.77850e13	+	1.24297e14i	0.729695	+	0.927531i
$670$	−2.56431e14	+	4.61550e13i	−1.89931	+	0.341857i
$671$		−	8.37468e13i		−	0.615681i
$672$	−4.71182e13	−	5.98929e13i	−0.343829	−	0.437048i
$673$		−	1.45739e14i		−	1.05560i	−0.849368	−	0.527802i	$-0.823016\pi$
$673$		−	1.45739e14i		−	1.05560i	0.849368	−	0.527802i	$-0.176984\pi$
$674$			3.72971e14i			2.68148i
$675$	9.90564e13	+	9.91118e13i	0.706909	+	0.707304i
$676$	1.45232e14			1.02880
$677$	−8.91145e13			−0.626621			−0.313311	−	0.949651i	$-0.601438\pi$
$677$	−8.91145e13			−0.626621			−0.313311	+	0.949651i	$0.601438\pi$
$678$	2.36889e13	−	1.86362e13i	0.165347	−	0.130080i
$679$	−3.95382e13			−0.273948
$680$	−3.14811e13	−	1.74905e14i	−0.216524	−	1.20298i
$681$	−1.20134e14	+	9.45101e13i	−0.820218	+	0.645272i
$682$		−	3.57978e14i		−	2.42625i
$683$	−2.86475e14			−1.92745			−0.963726	−	0.266894i	$-0.914003\pi$
$683$	−2.86475e14			−1.92745			−0.963726	+	0.266894i	$0.914003\pi$
$684$	3.03325e13	−	1.25234e14i	0.202594	−	0.836452i
$685$	−6.17009e12	−	3.42802e13i	−0.0409108	−	0.227295i
$686$			2.07353e14i			1.36486i
$687$	−1.83309e14	+	1.44211e14i	−1.19785	+	0.942354i
$688$			2.33581e13i			0.151529i
$689$			6.91376e13i			0.445265i
$690$	1.77414e14	+	1.57539e14i	1.13434	+	1.00726i
$691$	−2.46521e14			−1.56482			−0.782408	−	0.622767i	$-0.786009\pi$
$691$	−2.46521e14			−1.56482			−0.782408	+	0.622767i	$0.786009\pi$
$692$	1.89124e14			1.19184
$693$	−2.24407e13	+	9.26508e13i	−0.140401	+	0.579673i
$694$	8.31997e13			0.516802
$695$	1.31179e13	+	7.28813e13i	0.0808985	+	0.449461i
$696$	1.46926e14	+	1.86761e14i	0.899607	+	1.14351i
$697$		−	2.73779e13i		−	0.166432i
$698$	6.61400e13			0.399197
$699$	−8.30517e12	+	6.53374e12i	−0.0497694	+	0.0391540i
$700$	−4.36481e13	−	1.17323e14i	−0.259702	−	0.698063i
$701$		−	3.94207e13i		−	0.232881i	−0.993198	−	0.116441i	$-0.962852\pi$
$701$		−	3.94207e13i		−	0.232881i	0.993198	−	0.116441i	$-0.0371485\pi$
$702$	1.41226e14	−	6.45903e13i	0.828380	−	0.378863i
$703$		−	1.47745e14i		−	0.860470i
$704$		−	3.45563e14i		−	1.99832i
$705$	−1.15934e13	−	1.02946e13i	−0.0665680	−	0.0591106i
$706$	2.26070e14			1.28890
$707$	1.07158e14			0.606634
$708$	−8.98896e13	−	1.14260e14i	−0.505293	−	0.642288i
$709$	9.14117e13			0.510236			0.255118	−	0.966910i	$-0.417886\pi$
$709$	9.14117e13			0.510236			0.255118	+	0.966910i	$0.417886\pi$
$710$	1.88855e14	−	3.39920e13i	1.04674	−	0.188402i
$711$	5.25235e12	−	2.16854e13i	0.0289072	−	0.119349i
$712$			2.44176e14i			1.33445i
$713$	2.18642e14			1.18655
$714$	1.28591e14	+	1.63455e14i	0.692980	+	0.880861i
$715$	2.32333e13	+	1.29081e14i	0.124332	+	0.690769i
$716$		−	1.96372e14i		−	1.04355i
$717$	−4.17276e13	−	5.30408e13i	−0.220205	−	0.279907i
$718$		−	4.71157e14i		−	2.46913i
$719$			1.72327e14i			0.896829i	0.893826	+	0.448415i	$0.148011\pi$
$719$			1.72327e14i			0.896829i	−0.893826	+	0.448415i	$0.851989\pi$
$720$	3.62582e13	+	2.16163e12i	0.187389	+	0.0111717i
$721$	5.32174e12			0.0273135
$722$	−2.13438e14			−1.08789
$723$	3.45759e13	−	2.72011e13i	0.175018	−	0.137688i
$724$	−7.61659e13			−0.382884
$725$	−1.20374e14	−	3.23557e14i	−0.600954	−	1.61533i
$726$	−1.26702e14	+	9.96772e13i	−0.628202	+	0.494211i
$727$			2.82412e14i			1.39063i	0.718705	+	0.695315i	$0.244735\pi$
$727$			2.82412e14i			1.39063i	−0.718705	+	0.695315i	$0.755265\pi$
$728$	−4.80969e13			−0.235212
$729$	−1.34658e14	+	1.55751e14i	−0.654024	+	0.756474i
$730$	−1.86633e14	+	3.35921e13i	−0.900275	+	0.162040i
$731$		−	2.43953e14i		−	1.16875i
$732$	−1.26993e14	+	9.99067e13i	−0.604263	+	0.475378i
$733$			3.17769e14i			1.50173i	0.660455	+	0.750866i	$0.270364\pi$
$733$			3.17769e14i			1.50173i	−0.660455	+	0.750866i	$0.729636\pi$
$734$		−	5.57755e14i		−	2.61796i
$735$	−1.22419e14	−	1.08705e14i	−0.570706	−	0.506771i
$736$	2.35362e14			1.08980
$737$	3.23325e14			1.48697
$738$	−3.89062e13	−	9.42334e12i	−0.177720	−	0.0430450i
$739$	1.19381e14			0.541643			0.270822	−	0.962630i	$-0.412705\pi$
$739$	1.19381e14			0.541643			0.270822	+	0.962630i	$0.412705\pi$
$740$	−5.11580e14	+	9.20792e13i	−2.30544	+	0.414957i
$741$	4.44722e13	+	5.65295e13i	0.199066	+	0.253037i
$742$			1.35382e14i			0.601924i
$743$	−4.04198e14			−1.78505			−0.892525	−	0.450997i	$-0.851068\pi$
$743$	−4.04198e14			−1.78505			−0.892525	+	0.450997i	$0.851068\pi$
$744$	−1.88197e14	+	1.48056e14i	−0.825558	+	0.649472i
$745$	2.13841e14	−	3.84892e13i	0.931771	−	0.167709i
$746$			4.07496e14i			1.76372i
$747$	2.21880e13	−	9.16076e13i	0.0953926	−	0.393848i
$748$			6.36104e14i			2.71656i
$749$		−	1.61150e14i		−	0.683632i
$750$	3.51964e14	+	1.36499e14i	1.48317	+	0.575207i
$751$	−3.96757e14			−1.66083			−0.830415	−	0.557145i	$-0.811897\pi$
$751$	−3.96757e14			−1.66083			−0.830415	+	0.557145i	$0.811897\pi$
$752$	−4.01895e12			−0.0167118
$753$	8.40917e13	+	1.06891e14i	0.347359	+	0.441535i
$754$	−3.82596e14			−1.56994
$755$	7.84397e13	+	4.35800e14i	0.319743	+	1.77645i
$756$	1.67266e14	−	7.64998e13i	0.677329	−	0.309779i
$757$			1.22108e14i			0.491208i	0.969370	+	0.245604i	$0.0789863\pi$
$757$			1.22108e14i			0.491208i	−0.969370	+	0.245604i	$0.921014\pi$
$758$	6.62797e14			2.64871
$759$	−1.82045e14	−	2.31402e14i	−0.722721	−	0.918665i
$760$	−2.13193e13	−	1.18447e14i	−0.0840825	−	0.467151i
$761$		−	2.36730e14i		−	0.927536i	−0.885957	−	0.463768i	$-0.846497\pi$
$761$		−	2.36730e14i		−	0.927536i	0.885957	−	0.463768i	$-0.153503\pi$
$762$	−1.20907e14	−	1.53688e14i	−0.470628	−	0.598226i
$763$			9.19733e13i			0.355663i
$764$			2.42379e14i			0.931170i
$765$	−3.78683e14	−	2.25763e13i	−1.44533	−	0.0861677i
$766$	−1.27049e14			−0.481758
$767$	8.11508e13			0.305714
$768$	−1.42251e14	+	1.11910e14i	−0.532412	+	0.418852i
$769$	2.25082e14			0.836968			0.418484	−	0.908224i	$-0.362562\pi$
$769$	2.25082e14			0.836968			0.418484	+	0.908224i	$0.362562\pi$
$770$	4.54945e13	+	2.52761e14i	0.168076	+	0.933806i
$771$	3.30998e14	−	2.60398e14i	1.21494	−	0.955799i
$772$		−	6.63685e14i		−	2.42034i
$773$	−5.14382e14			−1.86375			−0.931877	−	0.362776i	$-0.881829\pi$
$773$	−5.14382e14			−1.86375			−0.931877	+	0.362776i	$0.881829\pi$
$774$	−3.46677e14	−	8.39674e13i	−1.24801	−	0.302278i
$775$	3.26044e14	−	1.21299e14i	1.16619	−	0.433859i
$776$			1.33738e14i			0.475278i
$777$	1.65750e14	−	1.30396e14i	0.585258	−	0.460427i
$778$			1.70998e14i			0.599919i
$779$		−	1.85406e13i		−	0.0646305i
$780$	1.68022e14	−	1.89220e14i	0.581960	−	0.655381i
$781$	−2.38121e14			−0.819489
$782$	−6.42331e14			−2.19647
$783$	4.61290e14	−	2.10973e14i	1.56735	−	0.716832i
$784$	−4.24375e13			−0.143275
$785$	5.16958e13	−	9.30472e12i	0.173423	−	0.0312144i
$786$	−7.83434e12	−	9.95839e12i	−0.0261150	−	0.0331953i
$787$			4.58515e14i			1.51873i	0.650666	+	0.759364i	$0.274490\pi$
$787$			4.58515e14i			1.51873i	−0.650666	+	0.759364i	$0.725510\pi$
$788$	8.64032e14			2.84380
$789$	6.15999e13	−	4.84611e13i	0.201463	−	0.158492i
$790$	−1.06482e13	−	5.91600e13i	−0.0346051	−	0.192262i
$791$			1.99266e13i			0.0643504i
$792$	3.13392e14	+	7.59057e13i	1.00569	+	0.243584i
$793$		−	9.01940e13i		−	0.287615i
$794$			1.68595e14i			0.534247i
$795$	−1.84652e14	−	1.63966e14i	−0.581458	−	0.516319i
$796$	−1.26005e14			−0.394297
$797$	−3.36528e14			−1.04648			−0.523238	−	0.852186i	$-0.675276\pi$
$797$	−3.36528e14			−1.04648			−0.523238	+	0.852186i	$0.675276\pi$
$798$	8.70834e13	+	1.10694e14i	0.269104	+	0.342064i
$799$	4.19742e13			0.128899
$800$	3.50977e14	−	1.30575e14i	1.07110	−	0.398483i
$801$	5.06577e14	+	1.22696e14i	1.53632	+	0.372108i
$802$		−	5.48185e14i		−	1.65217i
$803$	2.35320e14			0.704824
$804$	−3.85714e14	−	4.90290e14i	−1.14812	−	1.45939i
$805$	−1.54379e14	+	2.77866e13i	−0.456675	+	0.0821969i
$806$		−	3.85537e14i		−	1.13342i
$807$	8.57356e13	+	1.08980e14i	0.250492	+	0.318405i
$808$		−	3.62462e14i		−	1.05246i
$809$			1.05361e14i			0.304044i	0.988377	+	0.152022i	$0.0485784\pi$
$809$			1.05361e14i			0.304044i	−0.988377	+	0.152022i	$0.951422\pi$
$810$	−1.62423e14	+	5.30367e14i	−0.465825	+	1.52108i
$811$	2.34283e14			0.667786			0.333893	−	0.942611i	$-0.391638\pi$
$811$	2.34283e14			0.667786			0.333893	+	0.942611i	$0.391638\pi$
$812$	−4.53141e14			−1.28367
$813$	−3.39561e13	+	2.67135e13i	−0.0956015	+	0.0752104i
$814$	1.06644e15			2.98411
$815$	2.86528e14	−	5.15721e13i	0.796853	−	0.143426i
$816$	−7.72845e13	+	6.08002e13i	−0.213620	+	0.168056i
$817$		−	1.65208e14i		−	0.453858i
$818$	−2.41819e14			−0.660272
$819$	−2.41682e13	+	9.97835e13i	−0.0655882	+	0.270794i
$820$	−6.41986e13	+	1.15551e13i	−0.173163	+	0.0311677i
$821$			5.17294e14i			1.38682i	0.720541	+	0.693412i	$0.243894\pi$
$821$			5.17294e14i			1.38682i	−0.720541	+	0.693412i	$0.756106\pi$
$822$	1.08363e14	−	8.52496e13i	0.288749	−	0.227161i
$823$		−	5.83446e14i		−	1.54526i	−0.634857	−	0.772630i	$-0.718941\pi$
$823$		−	5.83446e14i		−	1.54526i	0.634857	−	0.772630i	$-0.281059\pi$
$824$		−	1.80008e13i		−	0.0473867i
$825$	−3.99849e14	−	2.44076e14i	−1.04623	−	0.638639i
$826$	1.58906e14			0.413275
$827$	4.13226e14			1.06822			0.534109	−	0.845415i	$-0.320647\pi$
$827$	4.13226e14			1.06822			0.534109	+	0.845415i	$0.320647\pi$
$828$	−1.33724e14	+	5.52106e14i	−0.343603	+	1.41863i
$829$	−5.47753e14			−1.39898			−0.699491	−	0.714641i	$-0.746590\pi$
$829$	−5.47753e14			−1.39898			−0.699491	+	0.714641i	$0.746590\pi$
$830$	−4.49822e13	−	2.49915e14i	−0.114196	−	0.634457i
$831$	−8.18630e13	−	1.04058e14i	−0.206577	−	0.262585i
$832$		−	3.72166e14i		−	0.933513i
$833$	4.43221e14			1.10508
$834$	−2.30384e14	+	1.81245e14i	−0.570982	+	0.449195i
$835$	−2.48837e13	−	1.38251e14i	−0.0613032	−	0.340592i
$836$			4.30776e14i			1.05492i
$837$	2.12595e14	+	4.64837e14i	0.517518	+	1.13155i
$838$			7.55697e14i			1.82864i
$839$			5.67198e14i			1.36435i	0.731191	+	0.682173i	$0.238965\pi$
$839$			5.67198e14i			1.36435i	−0.731191	+	0.682173i	$0.761035\pi$
$840$	1.14066e14	−	1.28457e14i	0.272747	−	0.307157i
$841$	−8.28974e14			−1.97043
$842$	−7.81953e14			−1.84765
$843$	−3.61808e14	−	4.59902e14i	−0.849847	−	1.08026i
$844$	9.38339e14			2.19103
$845$	−5.12928e13	−	2.84976e14i	−0.119062	−	0.661492i
$846$	1.44473e13	−	5.96485e13i	0.0333376	−	0.137641i
$847$		−	1.06579e14i		−	0.244487i
$848$	−6.40111e13			−0.145974
$849$	−1.88472e14	−	2.39571e14i	−0.427276	−	0.543119i
$850$	−9.57860e14	+	3.56355e14i	−2.15878	+	0.803134i
$851$			6.51348e14i			1.45937i
$852$	2.84069e14	+	3.61086e14i	0.632741	+	0.804291i
$853$			7.64152e14i			1.69213i	0.533077	+	0.846067i	$0.321036\pi$
$853$			7.64152e14i			1.69213i	−0.533077	+	0.846067i	$0.678964\pi$
$854$		−	1.76614e14i		−	0.388808i
$855$	−2.56448e14	−	1.52889e13i	−0.561266	−	0.0334615i
$856$	−5.45092e14			−1.18605
$857$	−1.15205e14			−0.249211			−0.124606	−	0.992206i	$-0.539767\pi$
$857$	−1.15205e14			−0.249211			−0.124606	+	0.992206i	$0.539767\pi$
$858$	−4.08037e14	+	3.21005e14i	−0.877532	+	0.690360i
$859$	6.54322e14			1.39903			0.699513	−	0.714620i	$-0.253400\pi$
$859$	6.54322e14			1.39903			0.699513	+	0.714620i	$0.253400\pi$
$860$	−5.72047e14	+	1.02963e14i	−1.21602	+	0.218871i
$861$	2.08001e13	−	1.63636e13i	0.0439592	−	0.0345830i
$862$			9.39199e14i			1.97343i
$863$	−6.58785e14			−1.37623			−0.688113	−	0.725604i	$-0.741561\pi$
$863$	−6.58785e14			−1.37623			−0.688113	+	0.725604i	$0.741561\pi$
$864$	2.28852e14	+	5.00383e14i	0.475320	+	1.03928i
$865$	−6.67946e13	−	3.71102e14i	−0.137931	−	0.766324i
$866$		−	1.17615e15i		−	2.41476i
$867$	4.22143e14	−	3.32103e14i	0.861716	−	0.677918i
$868$		−	4.56625e14i		−	0.926746i
$869$			7.45928e13i			0.150521i
$870$	9.07359e14	−	1.02183e15i	1.82047	−	2.05014i
$871$	3.48216e14			0.694638
$872$	3.11101e14			0.617047
$873$	2.77459e14	+	6.72024e13i	0.547176	+	0.132530i
$874$	−4.34993e14			−0.852953
$875$	−2.14798e14	+	1.27083e14i	−0.418783	+	0.247769i
$876$	−2.80727e14	−	3.56838e14i	−0.544207	−	0.691753i
$877$			3.46323e14i			0.667550i	0.942653	+	0.333775i	$0.108323\pi$
$877$			3.46323e14i			0.667550i	−0.942653	+	0.333775i	$0.891677\pi$
$878$	4.77859e14			0.915857
$879$	1.91012e14	−	1.50270e14i	0.364012	−	0.286371i
$880$	−1.19510e14	+	2.15106e13i	−0.226460	+	0.0407604i
$881$		−	6.56655e13i		−	0.123725i	−0.998085	−	0.0618625i	$-0.980296\pi$
$881$		−	6.56655e13i		−	0.123725i	0.998085	−	0.0618625i	$-0.0197040\pi$
$882$	1.52554e14	−	6.29851e14i	0.285812	−	1.18003i
$883$		−	7.17599e14i		−	1.33684i	−0.743785	−	0.668418i	$-0.766972\pi$
$883$		−	7.17599e14i		−	1.33684i	0.743785	−	0.668418i	$-0.233028\pi$
$884$			6.85074e14i			1.26904i
$885$	−1.92456e14	+	2.16737e14i	−0.354499	+	0.399223i
$886$	1.03536e15			1.89636
$887$	2.72208e14			0.495773			0.247887	−	0.968789i	$-0.420264\pi$
$887$	2.72208e14			0.495773			0.247887	+	0.968789i	$0.420264\pi$
$888$	−4.41067e14	−	5.60650e14i	−0.798804	−	1.01538i
$889$	1.29279e14			0.232820
$890$	1.38200e15	−	2.48745e14i	2.47489	−	0.445456i
$891$	3.14954e14	−	6.12033e14i	0.560865	−	1.08990i
$892$			1.02011e15i			1.80643i
$893$	2.84253e13			0.0500551
$894$	5.31789e14	+	6.75969e14i	0.931219	+	1.18369i
$895$	−3.85323e14	+	6.93542e13i	−0.670980	+	0.120770i
$896$		−	4.07629e14i		−	0.705871i
$897$	−1.96060e14	−	2.49216e14i	−0.337619	−	0.429154i
$898$		−	2.29976e13i		−	0.0393822i
$899$		−	1.25929e15i		−	2.14450i
$900$	1.06887e14	+	8.97502e14i	0.181014	+	1.51993i
$901$	6.68536e14			1.12590
$902$	1.33828e14			0.224138
$903$	1.85341e14	−	1.45809e14i	0.308697	−	0.242854i
$904$	6.74020e13			0.111643
$905$	2.69001e13	+	1.49453e14i	0.0443110	+	0.246186i
$906$	−1.37760e15	+	1.08377e15i	−2.25674	+	1.77540i
$907$		−	2.16615e14i		−	0.352900i	−0.984310	−	0.176450i	$-0.943539\pi$
$907$		−	2.16615e14i		−	0.352900i	0.984310	−	0.176450i	$-0.0564613\pi$
$908$	−9.85941e14			−1.59743
$909$	−7.51977e14	−	1.82134e14i	−1.21167	−	0.293475i
$910$	4.89968e13	+	2.72220e14i	0.0785165	+	0.436227i
$911$			8.10639e14i			1.29192i	0.763371	+	0.645960i	$0.223543\pi$
$911$			8.10639e14i			1.29192i	−0.763371	+	0.645960i	$0.776457\pi$
$912$	−5.23378e13	+	4.11746e13i	−0.0829548	+	0.0652612i
$913$			3.15109e14i			0.496715i
$914$		−	1.04611e13i		−	0.0164001i
$915$	2.40889e14	+	2.13903e14i	0.375588	+	0.333512i
$916$	−1.50443e15			−2.33289
$917$	8.37681e12			0.0129191
$918$	−6.24565e14	−	1.36561e15i	−0.957998	−	2.09465i
$919$	−2.39232e14			−0.364957			−0.182478	−	0.983210i	$-0.558412\pi$
$919$	−2.39232e14			−0.364957			−0.182478	+	0.983210i	$0.558412\pi$
$920$	9.39883e13	+	5.22187e14i	0.142605	+	0.792294i
$921$	5.94382e14	+	7.55531e14i	0.896948	+	1.14013i
$922$		−	9.44858e14i		−	1.41812i
$923$	−2.56453e14			−0.382824
$924$	−4.83273e14	+	3.80194e14i	−0.717517	+	0.564476i
$925$	3.61357e14	+	9.71306e14i	0.533615	+	1.43432i
$926$		−	1.06805e15i		−	1.56869i
$927$	−3.73452e13	−	9.04525e12i	−0.0545551	−	0.0132136i
$928$		−	1.35559e15i		−	1.96964i
$929$		−	3.85573e14i		−	0.557222i	−0.960404	−	0.278611i	$-0.910126\pi$
$929$		−	3.85573e14i		−	0.557222i	0.960404	−	0.278611i	$-0.0898740\pi$
$930$	1.02969e15	+	9.14335e14i	1.48010	+	1.31429i
$931$	3.00154e14			0.429136
$932$	−6.81608e13			−0.0969293
$933$	5.87255e14	+	7.46472e14i	0.830650	+	1.05586i
$934$	−1.25840e15			−1.77045
$935$	1.24817e15	−	2.24658e14i	1.74669	−	0.314386i
$936$	3.37519e14	+	8.17493e13i	0.469806	+	0.113790i
$937$		−	1.09450e15i		−	1.51537i	−0.652619	−	0.757686i	$-0.726330\pi$
$937$		−	1.09450e15i		−	1.51537i	0.652619	−	0.757686i	$-0.273670\pi$
$938$	6.81862e14			0.939036
$939$	−1.85132e13	−	2.35325e13i	−0.0253602	−	0.0322359i
$940$	−1.77156e13	−	9.84253e13i	−0.0241388	−	0.134112i
$941$		−	8.03737e14i		−	1.08935i	−0.838649	−	0.544673i	$-0.816654\pi$
$941$		−	8.03737e14i		−	1.08935i	0.838649	−	0.544673i	$-0.183346\pi$
$942$	1.28560e14	+	1.63415e14i	0.173320	+	0.220311i
$943$			8.17382e13i			0.109614i
$944$			7.51335e13i			0.100224i
$945$	−2.09184e14	−	3.01194e14i	−0.277567	−	0.399656i
$946$	1.19249e15			1.57398
$947$	1.74430e14			0.229019			0.114510	−	0.993422i	$-0.463470\pi$
$947$	1.74430e14			0.229019			0.114510	+	0.993422i	$0.463470\pi$
$948$	1.13112e14	−	8.89863e13i	0.147730	−	0.116220i
$949$	2.53436e14			0.329258
$950$	−6.48673e14	+	2.41327e14i	−0.838316	+	0.311881i
$951$	−2.37110e14	+	1.86536e14i	−0.304823	+	0.239806i
$952$			4.65079e14i			0.594761i
$953$	−9.73346e14			−1.23823			−0.619117	−	0.785299i	$-0.712509\pi$
$953$	−9.73346e14			−1.23823			−0.619117	+	0.785299i	$0.712509\pi$
$954$	2.30106e14	−	9.50041e14i	0.291197	−	1.20227i
$955$	4.75599e14	−	8.56031e13i	0.598721	−	0.107764i
$956$		−	4.35308e14i		−	0.545138i
$957$	−1.33278e15	+	1.04851e15i	−1.66035	+	1.30621i
$958$			5.09178e14i			0.631019i
$959$			9.11525e13i			0.112377i
$960$	9.93977e14	+	8.82624e14i	1.21905	+	1.08248i
$961$	4.49342e14			0.548227
$962$	1.14854e15			1.39402
$963$	−2.73904e14	+	1.13087e15i	−0.330725	+	1.36547i
$964$	2.83765e14			0.340858
$965$	−1.30229e15	+	2.34399e14i	−1.55622	+	0.280104i
$966$	−3.83916e14	−	4.88003e14i	−0.456405	−	0.580146i
$967$		−	2.54476e13i		−	0.0300964i	−0.999887	−	0.0150482i	$-0.995210\pi$
$967$		−	2.54476e13i		−	0.0300964i	0.999887	−	0.0150482i	$-0.00479018\pi$
$968$	−3.60505e14			−0.424165
$969$	5.46620e14	−	4.30030e14i	0.639833	−	0.503361i
$970$	7.56936e14	−	1.36241e14i	0.881456	−	0.158653i
$971$			7.60628e14i			0.881204i	0.897703	+	0.440602i	$0.145235\pi$
$971$			7.60628e14i			0.881204i	−0.897703	+	0.440602i	$0.854765\pi$
$972$	−1.30381e15	+	2.52537e14i	−1.50274	+	0.291067i
$973$		−	1.93795e14i		−	0.222217i
$974$		−	1.70782e15i		−	1.94826i
$975$	−4.30631e14	−	2.62866e14i	−0.488745	−	0.298340i
$976$	8.35062e13			0.0942908
$977$	−8.51350e13			−0.0956391			−0.0478195	−	0.998856i	$-0.515227\pi$
$977$	−8.51350e13			−0.0956391			−0.0478195	+	0.998856i	$0.515227\pi$
$978$	7.12551e14	+	9.05738e14i	0.796382	+	1.01230i
$979$	−1.74251e15			−1.93759
$980$	−1.87065e14	−	1.03931e15i	−0.206949	−	1.14978i
$981$	1.56325e14	−	6.45421e14i	0.172062	−	0.710392i
$982$			5.02033e14i			0.549762i
$983$	−4.91406e14			−0.535393			−0.267696	−	0.963503i	$-0.586262\pi$
$983$	−4.91406e14			−0.535393			−0.267696	+	0.963503i	$0.586262\pi$
$984$	−5.53499e13	−	7.03565e13i	−0.0599987	−	0.0762656i
$985$	−3.05157e14	−	1.69541e15i	−0.329111	−	1.82850i
$986$			3.69956e15i			3.96978i
$987$	2.50876e13	+	3.18894e13i	0.0267839	+	0.0340456i
$988$			4.63939e14i			0.492807i
$989$			7.28335e14i			0.769750i
$990$	1.10357e14	−	1.85107e15i	0.116044	−	1.94647i
$991$	−1.07070e15			−1.12021			−0.560104	−	0.828422i	$-0.689239\pi$
$991$	−1.07070e15			−1.12021			−0.560104	+	0.828422i	$0.689239\pi$
$992$	1.36601e15			1.42199
$993$	5.85102e14	−	4.60304e14i	0.606018	−	0.476759i
$994$	−5.02175e14			−0.517515
$995$	4.45023e13	+	2.47249e14i	0.0456317	+	0.253524i
$996$	4.77831e14	−	3.75913e14i	0.487503	−	0.383523i
$997$			1.60992e15i			1.63428i	0.576436	+	0.817142i	$0.304443\pi$
$997$			1.60992e15i			1.63428i	−0.576436	+	0.817142i	$0.695557\pi$
$998$	−1.64861e15			−1.66520
$999$	−1.38478e15	+	6.33333e14i	−1.39172	+	0.636509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.d.c.14.15	yes	16
3.2	odd	2	inner	15.11.d.c.14.1	✓	16
5.2	odd	4		75.11.c.h.26.15		16
5.3	odd	4		75.11.c.h.26.2		16
5.4	even	2	inner	15.11.d.c.14.2	yes	16
15.2	even	4		75.11.c.h.26.1		16
15.8	even	4		75.11.c.h.26.16		16
15.14	odd	2	inner	15.11.d.c.14.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.d.c.14.1	✓	16	3.2	odd	2	inner
15.11.d.c.14.2	yes	16	5.4	even	2	inner
15.11.d.c.14.15	yes	16	1.1	even	1	trivial
15.11.d.c.14.16	yes	16	15.14	odd	2	inner
75.11.c.h.26.1		16	15.2	even	4
75.11.c.h.26.2		16	5.3	odd	4
75.11.c.h.26.15		16	5.2	odd	4
75.11.c.h.26.16		16	15.8	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+50.9058 q^{2} +(190.983 - 150.248i) q^{3} +1567.41 q^{4} +(-553.573 - 3075.58i) q^{5} +(9722.16 - 7648.49i) q^{6} +8178.10i q^{7} +27662.5 q^{8} +(13900.2 - 57389.6i) q^{9} +O(q^{10})\)	\(q+50.9058 q^{2} +(190.983 - 150.248i) q^{3} +1567.41 q^{4} +(-553.573 - 3075.58i) q^{5} +(9722.16 - 7648.49i) q^{6} +8178.10i q^{7} +27662.5 q^{8} +(13900.2 - 57389.6i) q^{9} +(-28180.1 - 156565. i) q^{10} +197407. i q^{11} +(299348. - 235499. i) q^{12} +212605. i q^{13} +416313. i q^{14} +(-567822. - 504211. i) q^{15} -196840. q^{16} +2.05581e6 q^{17} +(707599. - 2.92147e6i) q^{18} +1.39222e6 q^{19} +(-867673. - 4.82068e6i) q^{20} +(1.22874e6 + 1.56188e6i) q^{21} +1.00492e7i q^{22} -6.13773e6 q^{23} +(5.28307e6 - 4.15623e6i) q^{24} +(-9.15274e6 + 3.40511e6i) q^{25} +1.08228e7i q^{26} +(-5.96797e6 - 1.30489e7i) q^{27} +1.28184e7i q^{28} +3.53508e7i q^{29} +(-2.89055e7 - 2.56673e7i) q^{30} -3.56226e7 q^{31} -3.83467e7 q^{32} +(2.96600e7 + 3.77015e7i) q^{33} +1.04653e8 q^{34} +(2.51524e7 - 4.52718e6i) q^{35} +(2.17872e7 - 8.99528e7i) q^{36} -1.06122e8i q^{37} +7.08720e7 q^{38} +(3.19434e7 + 4.06039e7i) q^{39} +(-1.53132e7 - 8.50782e7i) q^{40} -1.33173e7i q^{41} +(6.25502e7 + 7.95088e7i) q^{42} -1.18665e8i q^{43} +3.09417e8i q^{44} +(-1.84201e8 - 1.09817e7i) q^{45} -3.12446e8 q^{46} +2.04173e7 q^{47} +(-3.75932e7 + 2.95748e7i) q^{48} +2.15594e8 q^{49} +(-4.65928e8 + 1.73340e8i) q^{50} +(3.92625e8 - 3.08881e8i) q^{51} +3.33238e8i q^{52} +3.25193e8 q^{53} +(-3.03805e8 - 6.64267e8i) q^{54} +(6.07142e8 - 1.09279e8i) q^{55} +2.26227e8i q^{56} +(2.65890e8 - 2.09178e8i) q^{57} +1.79956e9i q^{58} -3.81698e8i q^{59} +(-8.90007e8 - 7.90302e8i) q^{60} -4.24233e8 q^{61} -1.81340e9 q^{62} +(4.69338e8 + 1.13677e8i) q^{63} -1.75051e9 q^{64} +(6.53883e8 - 1.17692e8i) q^{65} +(1.50987e9 + 1.91923e9i) q^{66} -1.63786e9i q^{67} +3.22229e9 q^{68} +(-1.17220e9 + 9.22180e8i) q^{69} +(1.28040e9 - 2.30460e8i) q^{70} +1.20624e9i q^{71} +(3.84513e8 - 1.58754e9i) q^{72} -1.19205e9i q^{73} -5.40223e9i q^{74} +(-1.23641e9 + 2.02550e9i) q^{75} +2.18217e9 q^{76} -1.61442e9 q^{77} +(1.62611e9 + 2.06698e9i) q^{78} +3.77862e8 q^{79} +(1.08965e8 + 6.05397e8i) q^{80} +(-3.10036e9 - 1.59545e9i) q^{81} -6.77930e8i q^{82} +1.59624e9 q^{83} +(1.92594e9 + 2.44810e9i) q^{84} +(-1.13804e9 - 6.32281e9i) q^{85} -6.04075e9i q^{86} +(5.31139e9 + 6.75141e9i) q^{87} +5.46078e9i q^{88} +8.82698e9i q^{89} +(-9.37691e9 - 5.59031e8i) q^{90} -1.73870e9 q^{91} -9.62031e9 q^{92} +(-6.80332e9 + 5.35222e9i) q^{93} +1.03936e9 q^{94} +(-7.70694e8 - 4.28187e9i) q^{95} +(-7.32358e9 + 5.76151e9i) q^{96} +4.83465e9i q^{97} +1.09750e10 q^{98} +(1.13291e10 + 2.74399e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9}+O(q^{10}) \) 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9	\( 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9} - 221680 q^{10} + 731640 q^{15} - 4218352 q^{16} + 1487600 q^{19} + 2444616 q^{21} + 28021368 q^{24} - 9324800 q^{25} - 35678700 q^{30} - 77667568 q^{31} + 251882368 q^{34} - 22344768 q^{36} - 70953984 q^{39} - 179966240 q^{40} - 484245000 q^{45} - 72018968 q^{46} + 89098816 q^{49} + 686556816 q^{51} + 441096084 q^{54} + 1424671200 q^{55} + 610091280 q^{60} - 1671368368 q^{61} - 4172730848 q^{64} + 2368350000 q^{66} - 2906594616 q^{69} + 2838634200 q^{70} - 1285884000 q^{75} + 4079367264 q^{76} - 3904999600 q^{79} - 11376681984 q^{81} + 13119851016 q^{84} + 8097594320 q^{85} - 15222287520 q^{90} + 19275224832 q^{91} - 9366481832 q^{94} - 5999937552 q^{96} + 42957756000 q^{99}+O(q^{100}) \) 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9 - 221680 * q^10 + 731640 * q^15 - 4218352 * q^16 + 1487600 * q^19 + 2444616 * q^21 + 28021368 * q^24 - 9324800 * q^25 - 35678700 * q^30 - 77667568 * q^31 + 251882368 * q^34 - 22344768 * q^36 - 70953984 * q^39 - 179966240 * q^40 - 484245000 * q^45 - 72018968 * q^46 + 89098816 * q^49 + 686556816 * q^51 + 441096084 * q^54 + 1424671200 * q^55 + 610091280 * q^60 - 1671368368 * q^61 - 4172730848 * q^64 + 2368350000 * q^66 - 2906594616 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 4079367264 * q^76 - 3904999600 * q^79 - 11376681984 * q^81 + 13119851016 * q^84 + 8097594320 * q^85 - 15222287520 * q^90 + 19275224832 * q^91 - 9366481832 * q^94 - 5999937552 * q^96 + 42957756000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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