LMFDB - Embedded newform 8.10.b.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,10,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	8.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:	$4.12028668931$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 59x^{6} - 313x^{5} - 315x^{4} - 92091x^{3} + 1261649x^{2} - 16074123x + 251007534 $ x^8 - x^7 + 59x^6 - 313x^5 - 315x^4 - 92091x^3 + 1261649x^2 - 16074123x + 251007534
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.6
Root			$-2.43481 - 11.2224i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.10.b.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.86961 + 22.4447i) q^{2} -247.414i q^{3} +(-495.531 + 128.815i) q^{4} -1417.55i q^{5} +(5553.14 - 709.983i) q^{6} +5087.57 q^{7} +(-4313.20 - 10752.4i) q^{8} -41530.8 q^{9} +O(q^{10})$	\(q+(2.86961 + 22.4447i) q^{2} -247.414i q^{3} +(-495.531 + 128.815i) q^{4} -1417.55i q^{5} +(5553.14 - 709.983i) q^{6} +5087.57 q^{7} +(-4313.20 - 10752.4i) q^{8} -41530.8 q^{9} +(31816.6 - 4067.83i) q^{10} +14811.2i q^{11} +(31870.7 + 122601. i) q^{12} -64089.8i q^{13} +(14599.3 + 114189. i) q^{14} -350723. q^{15} +(228957. - 127664. i) q^{16} +251342. q^{17} +(-119177. - 932147. i) q^{18} +511568. i q^{19} +(182602. + 702441. i) q^{20} -1.25874e6i q^{21} +(-332432. + 42502.3i) q^{22} +1.96905e6 q^{23} +(-2.66030e6 + 1.06715e6i) q^{24} -56329.6 q^{25} +(1.43848e6 - 183913. i) q^{26} +5.40545e6i q^{27} +(-2.52105e6 + 655356. i) q^{28} -2.16116e6i q^{29} +(-1.00644e6 - 7.87187e6i) q^{30} -3.03997e6 q^{31} +(3.52240e6 + 4.77253e6i) q^{32} +3.66449e6 q^{33} +(721253. + 5.64129e6i) q^{34} -7.21189e6i q^{35} +(2.05798e7 - 5.34980e6i) q^{36} -8.74315e6i q^{37} +(-1.14820e7 + 1.46800e6i) q^{38} -1.58567e7 q^{39} +(-1.52421e7 + 6.11419e6i) q^{40} -1.48418e7 q^{41} +(2.82520e7 - 3.61208e6i) q^{42} -153307. i q^{43} +(-1.90790e6 - 7.33938e6i) q^{44} +5.88721e7i q^{45} +(5.65042e6 + 4.41949e7i) q^{46} +5.17595e7 q^{47} +(-3.15858e7 - 5.66473e7i) q^{48} -1.44703e7 q^{49} +(-161644. - 1.26430e6i) q^{50} -6.21855e7i q^{51} +(8.25574e6 + 3.17584e7i) q^{52} -4.26277e7i q^{53} +(-1.21324e8 + 1.55116e7i) q^{54} +2.09956e7 q^{55} +(-2.19437e7 - 5.47035e7i) q^{56} +1.26569e8 q^{57} +(4.85067e7 - 6.20170e6i) q^{58} -1.15231e7i q^{59} +(1.73794e8 - 4.51784e7i) q^{60} +1.95800e8i q^{61} +(-8.72353e6 - 6.82312e7i) q^{62} -2.11291e8 q^{63} +(-9.70103e7 + 9.27545e7i) q^{64} -9.08506e7 q^{65} +(1.05157e7 + 8.22485e7i) q^{66} +1.69718e8i q^{67} +(-1.24547e8 + 3.23766e7i) q^{68} -4.87172e8i q^{69} +(1.61869e8 - 2.06953e7i) q^{70} +2.23552e8 q^{71} +(1.79131e8 + 4.46555e8i) q^{72} -4.10130e8 q^{73} +(1.96238e8 - 2.50895e7i) q^{74} +1.39367e7i q^{75} +(-6.58977e7 - 2.53497e8i) q^{76} +7.53528e7i q^{77} +(-4.55026e7 - 3.55899e8i) q^{78} +2.51240e7 q^{79} +(-1.80970e8 - 3.24559e8i) q^{80} +5.19935e8 q^{81} +(-4.25902e7 - 3.33120e8i) q^{82} +4.73174e8i q^{83} +(1.62144e8 + 6.23742e8i) q^{84} -3.56290e8i q^{85} +(3.44094e6 - 439932. i) q^{86} -5.34702e8 q^{87} +(1.59255e8 - 6.38836e7i) q^{88} +8.45560e8 q^{89} +(-1.32137e9 + 1.68940e8i) q^{90} -3.26061e8i q^{91} +(-9.75726e8 + 2.53644e8i) q^{92} +7.52131e8i q^{93} +(1.48530e8 + 1.16173e9i) q^{94} +7.25174e8 q^{95} +(1.18079e9 - 8.71491e8i) q^{96} -7.97179e8 q^{97} +(-4.15241e7 - 3.24781e8i) q^{98} -6.15119e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9}+O(q^{10}) $ 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9	\( 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9} + 26392 q^{10} + 54760 q^{12} - 72336 q^{14} - 163136 q^{15} + 185616 q^{16} - 102000 q^{17} - 23614 q^{18} + 1245264 q^{20} - 2373124 q^{22} + 3412032 q^{23} - 3961456 q^{24} - 2423384 q^{25} + 4551240 q^{26} + 7509920 q^{28} - 15284368 q^{30} + 803584 q^{31} - 14113248 q^{32} + 58272 q^{33} + 27757244 q^{34} + 57226188 q^{36} - 63661140 q^{38} - 17590208 q^{39} - 93063648 q^{40} - 2180784 q^{41} + 127541344 q^{42} + 114013320 q^{44} - 131840944 q^{46} + 7432320 q^{47} - 217917408 q^{48} + 24436680 q^{49} + 231784902 q^{50} + 219270896 q^{52} - 362934280 q^{54} + 7056832 q^{55} - 358503360 q^{56} + 134003744 q^{57} + 375425192 q^{58} + 516952992 q^{60} - 344291904 q^{62} - 223198400 q^{63} - 316815296 q^{64} - 146501760 q^{65} + 239713176 q^{66} + 79875048 q^{68} - 56202048 q^{70} + 560234688 q^{71} + 112273016 q^{72} - 523987120 q^{73} - 65773608 q^{74} - 87532760 q^{76} + 318117968 q^{78} - 248943744 q^{79} + 890441280 q^{80} + 231960296 q^{81} - 1051981172 q^{82} - 1275608768 q^{84} + 1492810428 q^{86} + 540527424 q^{87} + 1544767952 q^{88} + 744827856 q^{89} - 3218579800 q^{90} - 2959012128 q^{92} + 3068552352 q^{94} - 1465245504 q^{95} + 4296343616 q^{96} - 9932784 q^{97} - 3062604162 q^{98}+O(q^{100}) \) 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9 + 26392 * q^10 + 54760 * q^12 - 72336 * q^14 - 163136 * q^15 + 185616 * q^16 - 102000 * q^17 - 23614 * q^18 + 1245264 * q^20 - 2373124 * q^22 + 3412032 * q^23 - 3961456 * q^24 - 2423384 * q^25 + 4551240 * q^26 + 7509920 * q^28 - 15284368 * q^30 + 803584 * q^31 - 14113248 * q^32 + 58272 * q^33 + 27757244 * q^34 + 57226188 * q^36 - 63661140 * q^38 - 17590208 * q^39 - 93063648 * q^40 - 2180784 * q^41 + 127541344 * q^42 + 114013320 * q^44 - 131840944 * q^46 + 7432320 * q^47 - 217917408 * q^48 + 24436680 * q^49 + 231784902 * q^50 + 219270896 * q^52 - 362934280 * q^54 + 7056832 * q^55 - 358503360 * q^56 + 134003744 * q^57 + 375425192 * q^58 + 516952992 * q^60 - 344291904 * q^62 - 223198400 * q^63 - 316815296 * q^64 - 146501760 * q^65 + 239713176 * q^66 + 79875048 * q^68 - 56202048 * q^70 + 560234688 * q^71 + 112273016 * q^72 - 523987120 * q^73 - 65773608 * q^74 - 87532760 * q^76 + 318117968 * q^78 - 248943744 * q^79 + 890441280 * q^80 + 231960296 * q^81 - 1051981172 * q^82 - 1275608768 * q^84 + 1492810428 * q^86 + 540527424 * q^87 + 1544767952 * q^88 + 744827856 * q^89 - 3218579800 * q^90 - 2959012128 * q^92 + 3068552352 * q^94 - 1465245504 * q^95 + 4296343616 * q^96 - 9932784 * q^97 - 3062604162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	2.86961	+	22.4447i	0.126820	+	0.991926i
$2$	2.86961	+	22.4447i	0.126820	+	0.991926i
$3$		−	247.414i		−	1.76351i	−0.471704	−	0.881757i	$-0.656361\pi$
$3$		−	247.414i		−	1.76351i	0.471704	−	0.881757i	$-0.343639\pi$
$4$	−495.531	+	128.815i	−0.967833	+	0.251592i
$5$		−	1417.55i		−	1.01432i	−0.861853	−	0.507159i	$-0.830696\pi$
$5$		−	1417.55i		−	1.01432i	0.861853	−	0.507159i	$-0.169304\pi$
$6$	5553.14	−	709.983i	1.74928	−	0.223649i
$7$	5087.57			0.800883			0.400441	−	0.916322i	$-0.368857\pi$
$7$	5087.57			0.800883			0.400441	+	0.916322i	$0.368857\pi$
$8$	−4313.20	−	10752.4i	−0.372302	−	0.928112i
$9$	−41530.8			−2.10998
$10$	31816.6	−	4067.83i	1.00613	−	0.128636i
$11$			14811.2i			0.305016i	0.988302	+	0.152508i	$0.0487349\pi$
$11$			14811.2i			0.305016i	−0.988302	+	0.152508i	$0.951265\pi$
$12$	31870.7	+	122601.i	0.443687	+	1.70679i
$13$		−	64089.8i		−	0.622363i	−0.950351	−	0.311181i	$-0.899275\pi$
$13$		−	64089.8i		−	0.622363i	0.950351	−	0.311181i	$-0.100725\pi$
$14$	14599.3	+	114189.i	0.101568	+	0.794416i
$15$	−350723.			−1.78876
$16$	228957.	−	127664.i	0.873403	−	0.486999i
$17$	251342.			0.729868			0.364934	−	0.931033i	$-0.381092\pi$
$17$	251342.			0.729868			0.364934	+	0.931033i	$0.381092\pi$
$18$	−119177.	−	932147.i	−0.267588	−	2.09295i
$19$			511568.i			0.900558i	0.892888	+	0.450279i	$0.148676\pi$
$19$			511568.i			0.900558i	−0.892888	+	0.450279i	$0.851324\pi$
$20$	182602.	+	702441.i	0.255195	+	0.981691i
$21$		−	1.25874e6i		−	1.41237i
$22$	−332432.	+	42502.3i	−0.302553	+	0.0386821i
$23$	1.96905e6			1.46718			0.733588	−	0.679594i	$-0.237844\pi$
$23$	1.96905e6			1.46718			0.733588	+	0.679594i	$0.237844\pi$
$24$	−2.66030e6	+	1.06715e6i	−1.63674	+	0.656559i
$25$	−56329.6			−0.0288408
$26$	1.43848e6	−	183913.i	0.617337	−	0.0789281i
$27$			5.40545e6i			1.95747i
$28$	−2.52105e6	+	655356.i	−0.775121	+	0.201496i
$29$		−	2.16116e6i		−	0.567409i	−0.958912	−	0.283705i	$-0.908436\pi$
$29$		−	2.16116e6i		−	0.567409i	0.958912	−	0.283705i	$-0.0915636\pi$
$30$	−1.00644e6	−	7.87187e6i	−0.226851	−	1.77432i
$31$	−3.03997e6			−0.591210			−0.295605	−	0.955310i	$-0.595521\pi$
$31$	−3.03997e6			−0.591210			−0.295605	+	0.955310i	$0.595521\pi$
$32$	3.52240e6	+	4.77253e6i	0.593832	+	0.804589i
$33$	3.66449e6			0.537899
$34$	721253.	+	5.64129e6i	0.0925620	+	0.723975i
$35$		−	7.21189e6i		−	0.812350i
$36$	2.05798e7	−	5.34980e6i	2.04211	−	0.530855i
$37$		−	8.74315e6i		−	0.766938i	−0.923554	−	0.383469i	$-0.874729\pi$
$37$		−	8.74315e6i		−	0.766938i	0.923554	−	0.383469i	$-0.125271\pi$
$38$	−1.14820e7	+	1.46800e6i	−0.893287	+	0.114209i
$39$	−1.58567e7			−1.09755
$40$	−1.52421e7	+	6.11419e6i	−0.941400	+	0.377632i
$41$	−1.48418e7			−0.820274			−0.410137	−	0.912024i	$-0.634519\pi$
$41$	−1.48418e7			−0.820274			−0.410137	+	0.912024i	$0.634519\pi$
$42$	2.82520e7	−	3.61208e6i	1.40096	−	0.179117i
$43$		−	153307.i		−	0.00683840i	−0.999994	−	0.00341920i	$-0.998912\pi$
$43$		−	153307.i		−	0.00683840i	0.999994	−	0.00341920i	$-0.00108837\pi$
$44$	−1.90790e6	−	7.33938e6i	−0.0767396	−	0.295204i
$45$			5.88721e7i			2.14019i
$46$	5.65042e6	+	4.41949e7i	0.186068	+	1.45533i
$47$	5.17595e7			1.54721			0.773605	−	0.633668i	$-0.218451\pi$
$47$	5.17595e7			1.54721			0.773605	+	0.633668i	$0.218451\pi$
$48$	−3.15858e7	−	5.66473e7i	−0.858829	−	1.54026i
$49$	−1.44703e7			−0.358587
$50$	−161644.	−	1.26430e6i	−0.00365759	−	0.0286079i
$51$		−	6.21855e7i		−	1.28713i
$52$	8.25574e6	+	3.17584e7i	0.156582	+	0.602343i
$53$		−	4.26277e7i		−	0.742080i	−0.928617	−	0.371040i	$-0.879001\pi$
$53$		−	4.26277e7i		−	0.742080i	0.928617	−	0.371040i	$-0.120999\pi$
$54$	−1.21324e8	+	1.55116e7i	−1.94166	+	0.248247i
$55$	2.09956e7			0.309383
$56$	−2.19437e7	−	5.47035e7i	−0.298170	−	0.743309i
$57$	1.26569e8			1.58815
$58$	4.85067e7	−	6.20170e6i	0.562828	−	0.0719589i
$59$		−	1.15231e7i		−	0.123804i	−0.998082	−	0.0619021i	$-0.980283\pi$
$59$		−	1.15231e7i		−	0.123804i	0.998082	−	0.0619021i	$-0.0197167\pi$
$60$	1.73794e8	−	4.51784e7i	1.73123	−	0.450039i
$61$			1.95800e8i			1.81062i	0.424748	+	0.905312i	$0.360363\pi$
$61$			1.95800e8i			1.81062i	−0.424748	+	0.905312i	$0.639637\pi$
$62$	−8.72353e6	−	6.82312e7i	−0.0749773	−	0.586436i
$63$	−2.11291e8			−1.68985
$64$	−9.70103e7	+	9.27545e7i	−0.722783	+	0.691075i
$65$	−9.08506e7			−0.631274
$66$	1.05157e7	+	8.22485e7i	0.0682165	+	0.533556i
$67$			1.69718e8i			1.02894i	0.857508	+	0.514470i	$0.172011\pi$
$67$			1.69718e8i			1.02894i	−0.857508	+	0.514470i	$0.827989\pi$
$68$	−1.24547e8	+	3.23766e7i	−0.706390	+	0.183629i
$69$		−	4.87172e8i		−	2.58739i
$70$	1.61869e8	−	2.06953e7i	0.805790	−	0.103022i
$71$	2.23552e8			1.04404			0.522018	−	0.852934i	$-0.325179\pi$
$71$	2.23552e8			1.04404			0.522018	+	0.852934i	$0.325179\pi$
$72$	1.79131e8	+	4.46555e8i	0.785550	+	1.95830i
$73$	−4.10130e8			−1.69032			−0.845159	−	0.534514i	$-0.820495\pi$
$73$	−4.10130e8			−1.69032			−0.845159	+	0.534514i	$0.820495\pi$
$74$	1.96238e8	−	2.50895e7i	0.760746	−	0.0972632i
$75$			1.39367e7i			0.0508611i
$76$	−6.58977e7	−	2.53497e8i	−0.226574	−	0.871590i
$77$			7.53528e7i			0.244282i
$78$	−4.55026e7	−	3.55899e8i	−0.139191	−	1.08868i
$79$	2.51240e7			0.0725716			0.0362858	−	0.999341i	$-0.488447\pi$
$79$	2.51240e7			0.0725716			0.0362858	+	0.999341i	$0.488447\pi$
$80$	−1.80970e8	−	3.24559e8i	−0.493972	−	0.885908i
$81$	5.19935e8			1.34204
$82$	−4.25902e7	−	3.33120e8i	−0.104027	−	0.813651i
$83$			4.73174e8i			1.09438i	0.837008	+	0.547191i	$0.184303\pi$
$83$			4.73174e8i			1.09438i	−0.837008	+	0.547191i	$0.815697\pi$
$84$	1.62144e8	+	6.23742e8i	0.355341	+	1.36694i
$85$		−	3.56290e8i		−	0.740318i
$86$	3.44094e6	−	439932.i	0.00678318	−	0.000867247i
$87$	−5.34702e8			−1.00063
$88$	1.59255e8	−	6.38836e7i	0.283089	−	0.113558i
$89$	8.45560e8			1.42853			0.714265	−	0.699875i	$-0.246761\pi$
$89$	8.45560e8			1.42853			0.714265	+	0.699875i	$0.246761\pi$
$90$	−1.32137e9	+	1.68940e8i	−2.12291	+	0.271420i
$91$		−	3.26061e8i		−	0.498439i
$92$	−9.75726e8	+	2.53644e8i	−1.41998	+	0.369130i
$93$			7.52131e8i			1.04261i
$94$	1.48530e8	+	1.16173e9i	0.196217	+	1.53472i
$95$	7.25174e8			0.913452
$96$	1.18079e9	−	8.71491e8i	1.41890	−	1.04723i
$97$	−7.97179e8			−0.914288			−0.457144	−	0.889393i	$-0.651128\pi$
$97$	−7.97179e8			−0.914288			−0.457144	+	0.889393i	$0.651128\pi$
$98$	−4.15241e7	−	3.24781e8i	−0.0454760	−	0.355692i
$99$		−	6.15119e8i		−	0.643578i
$100$	2.79130e7	−	7.25611e6i	0.0279130	−	0.00725611i
$101$			8.00801e8i			0.765735i	0.923803	+	0.382868i	$0.125063\pi$
$101$			8.00801e8i			0.765735i	−0.923803	+	0.382868i	$0.874937\pi$
$102$	1.39574e9	−	1.78448e8i	1.27674	−	0.163234i
$103$	8.20324e8			0.718155			0.359077	−	0.933308i	$-0.383091\pi$
$103$	8.20324e8			0.718155			0.359077	+	0.933308i	$0.383091\pi$
$104$	−6.89118e8	+	2.76432e8i	−0.577622	+	0.231707i
$105$	−1.78432e9			−1.43259
$106$	9.56767e8	−	1.22325e8i	0.736088	−	0.0941107i
$107$		−	5.88826e8i		−	0.434270i	−0.976142	−	0.217135i	$-0.930329\pi$
$107$		−	5.88826e8i		−	0.434270i	0.976142	−	0.217135i	$-0.0696712\pi$
$108$	−6.96305e8	−	2.67857e9i	−0.492484	−	1.89450i
$109$		−	8.89549e8i		−	0.603602i	−0.953371	−	0.301801i	$-0.902412\pi$
$109$		−	8.89549e8i		−	0.603602i	0.953371	−	0.301801i	$-0.0975878\pi$
$110$	6.02492e7	+	4.71240e8i	0.0392360	+	0.306885i
$111$	−2.16318e9			−1.35251
$112$	1.16484e9	−	6.49498e8i	0.699493	−	0.390029i
$113$	3.64198e8			0.210128			0.105064	−	0.994465i	$-0.466495\pi$
$113$	3.64198e8			0.210128			0.105064	+	0.994465i	$0.466495\pi$
$114$	3.63204e8	+	2.84081e9i	0.201409	+	1.57532i
$115$		−	2.79124e9i		−	1.48818i
$116$	2.78391e8	+	1.07092e9i	0.142756	+	0.549158i
$117$			2.66170e9i			1.31317i
$118$	2.58633e8	−	3.30669e7i	0.122805	−	0.0157009i
$119$	1.27872e9			0.584539
$120$	1.51274e9	+	3.77111e9i	0.665960	+	1.66017i
$121$	2.13858e9			0.906965
$122$	−4.39467e9	+	5.61870e8i	−1.79600	+	0.229624i
$123$			3.67207e9i			1.44656i
$124$	1.50640e9	−	3.91594e8i	0.572192	−	0.148744i
$125$		−	2.68881e9i		−	0.985064i
$126$	−6.06322e8	−	4.74236e9i	−0.214307	−	1.67620i
$127$	−3.86422e9			−1.31809			−0.659046	−	0.752103i	$-0.729040\pi$
$127$	−3.86422e9			−1.31809			−0.659046	+	0.752103i	$0.729040\pi$
$128$	−2.36023e9	−	1.91120e9i	−0.777159	−	0.629305i
$129$	−3.79304e7			−0.0120596
$130$	−2.60706e8	−	2.03912e9i	−0.0800582	−	0.626176i
$131$			3.05723e9i			0.907000i	0.891256	+	0.453500i	$0.149825\pi$
$131$			3.05723e9i			0.907000i	−0.891256	+	0.453500i	$0.850175\pi$
$132$	−1.81587e9	+	4.72043e8i	−0.520597	+	0.135331i
$133$			2.60263e9i			0.721242i
$134$	−3.80926e9	+	4.87024e8i	−1.02063	+	0.130490i
$135$	7.66251e9			1.98550
$136$	−1.08409e9	−	2.70252e9i	−0.271731	−	0.677399i
$137$	3.15497e9			0.765160			0.382580	−	0.923922i	$-0.375036\pi$
$137$	3.15497e9			0.765160			0.382580	+	0.923922i	$0.375036\pi$
$138$	1.09344e10	−	1.39799e9i	2.56649	−	0.328133i
$139$		−	1.46170e9i		−	0.332117i	−0.986116	−	0.166058i	$-0.946896\pi$
$139$		−	1.46170e9i		−	0.332117i	0.986116	−	0.166058i	$-0.0531040\pi$
$140$	9.29002e8	+	3.57371e9i	0.204381	+	0.786219i
$141$		−	1.28060e10i		−	2.72853i
$142$	6.41507e8	+	5.01756e9i	0.132405	+	1.03561i
$143$	9.49244e8			0.189830
$144$	−9.50877e9	+	5.30198e9i	−1.84286	+	1.02756i
$145$	−3.06356e9			−0.575534
$146$	−1.17691e9	−	9.20525e9i	−0.214367	−	1.67667i
$147$			3.58015e9i			0.632373i
$148$	1.12625e9	+	4.33250e9i	0.192956	+	0.742268i
$149$			2.14316e9i			0.356218i	0.984011	+	0.178109i	$0.0569980\pi$
$149$			2.14316e9i			0.356218i	−0.984011	+	0.178109i	$0.943002\pi$
$150$	−3.12806e8	+	3.99931e7i	−0.0504504	+	0.00645021i
$151$	−4.26252e9			−0.667222			−0.333611	−	0.942711i	$-0.608267\pi$
$151$	−4.26252e9			−0.667222			−0.333611	+	0.942711i	$0.608267\pi$
$152$	5.50058e9	−	2.20650e9i	0.835819	−	0.335279i
$153$	−1.04384e10			−1.54001
$154$	−1.69127e9	+	2.16233e8i	−0.242309	+	0.0309798i
$155$			4.30931e9i			0.599674i
$156$	7.85749e9	−	2.04259e9i	1.06224	−	0.276134i
$157$			1.08699e10i			1.42783i	0.700232	+	0.713915i	$0.253080\pi$
$157$			1.08699e10i			1.42783i	−0.700232	+	0.713915i	$0.746920\pi$
$158$	7.20961e7	+	5.63901e8i	0.00920354	+	0.0719856i
$159$	−1.05467e10			−1.30867
$160$	6.76532e9	−	4.99318e9i	0.816109	−	0.602334i
$161$	1.00177e10			1.17504
$162$	1.49201e9	+	1.16698e10i	0.170198	+	1.33121i
$163$		−	4.36394e9i		−	0.484211i	−0.970250	−	0.242105i	$-0.922162\pi$
$163$		−	4.36394e9i		−	0.484211i	0.970250	−	0.242105i	$-0.0778380\pi$
$164$	7.35456e9	−	1.91185e9i	0.793888	−	0.206375i
$165$		−	5.19461e9i		−	0.545601i
$166$	−1.06203e10	+	1.35783e9i	−1.08555	+	0.138790i
$167$	−7.71676e8			−0.0767734			−0.0383867	−	0.999263i	$-0.512222\pi$
$167$	−7.71676e8			−0.0767734			−0.0383867	+	0.999263i	$0.512222\pi$
$168$	−1.35344e10	+	5.42918e9i	−1.31084	+	0.525827i
$169$	6.49700e9			0.612665
$170$	7.99683e9	−	1.02241e9i	0.734341	−	0.0938872i
$171$		−	2.12458e10i		−	1.90016i
$172$	1.97483e7	+	7.59684e7i	0.00172049	+	0.00661843i
$173$			1.47368e9i			0.125082i	0.998042	+	0.0625411i	$0.0199204\pi$
$173$			1.47368e9i			0.125082i	−0.998042	+	0.0625411i	$0.980080\pi$
$174$	−1.53439e9	−	1.20012e10i	−0.126901	−	0.992555i
$175$	−2.86581e8			−0.0230981
$176$	1.89085e9	+	3.39112e9i	0.148542	+	0.266401i
$177$	−2.85098e9			−0.218331
$178$	2.42643e9	+	1.89784e10i	0.181166	+	1.41700i
$179$		−	1.18045e9i		−	0.0859429i	−0.999076	−	0.0429714i	$-0.986318\pi$
$179$		−	1.18045e9i		−	0.0859429i	0.999076	−	0.0429714i	$-0.0136825\pi$
$180$	−7.58362e9	−	2.91729e10i	−0.538456	−	2.07135i
$181$			1.33366e10i			0.923616i	0.886980	+	0.461808i	$0.152799\pi$
$181$			1.33366e10i			0.923616i	−0.886980	+	0.461808i	$0.847201\pi$
$182$	7.31834e9	−	9.35668e8i	0.494415	−	0.0632122i
$183$	4.84437e10			3.19306
$184$	−8.49293e9	−	2.11720e10i	−0.546232	−	1.36170i
$185$	−1.23939e10			−0.777919
$186$	−1.68814e10	+	2.15833e9i	−1.03419	+	0.132224i
$187$			3.72266e9i			0.222621i
$188$	−2.56484e10	+	6.66741e9i	−1.49744	+	0.389266i
$189$			2.75006e10i			1.56770i
$190$	2.08097e9	+	1.62763e10i	0.115844	+	0.906077i
$191$	−2.67293e10			−1.45324			−0.726619	−	0.687040i	$-0.758910\pi$
$191$	−2.67293e10			−1.45324			−0.726619	+	0.687040i	$0.758910\pi$
$192$	2.29488e10	+	2.40017e10i	1.21872	+	1.27464i
$193$	−1.13253e10			−0.587548			−0.293774	−	0.955875i	$-0.594911\pi$
$193$	−1.13253e10			−0.587548			−0.293774	+	0.955875i	$0.594911\pi$
$194$	−2.28759e9	−	1.78924e10i	−0.115950	−	0.906905i
$195$			2.24777e10i			1.11326i
$196$	7.17047e9	−	1.86399e9i	0.347052	−	0.0902177i
$197$		−	3.97475e10i		−	1.88024i	−0.340850	−	0.940118i	$-0.610715\pi$
$197$		−	3.97475e10i		−	1.88024i	0.340850	−	0.940118i	$-0.389285\pi$
$198$	1.38062e10	−	1.76515e9i	0.638381	−	0.0816186i
$199$	2.07651e10			0.938630			0.469315	−	0.883031i	$-0.344501\pi$
$199$	2.07651e10			0.938630			0.469315	+	0.883031i	$0.344501\pi$
$200$	2.42961e8	+	6.05678e8i	0.0107375	+	0.0267674i
$201$	4.19905e10			1.81455
$202$	−1.79738e10	+	2.29799e9i	−0.759552	+	0.0971107i
$203$		−	1.09951e10i		−	0.454428i
$204$	8.01044e9	+	3.08148e10i	0.323833	+	1.24573i
$205$			2.10390e10i			0.832018i
$206$	2.35401e9	+	1.84120e10i	0.0910765	+	0.712356i
$207$	−8.17763e10			−3.09572
$208$	−8.18194e9	−	1.46738e10i	−0.303090	−	0.543573i
$209$	−7.57691e9			−0.274684
$210$	−5.12032e9	−	4.00487e10i	−0.181681	−	1.42102i
$211$		−	5.11435e10i		−	1.77631i	−0.459541	−	0.888157i	$-0.651986\pi$
$211$		−	5.11435e10i		−	1.77631i	0.459541	−	0.888157i	$-0.348014\pi$
$212$	5.49110e9	+	2.11233e10i	0.186702	+	0.718210i
$213$		−	5.53099e10i		−	1.84117i
$214$	1.32160e10	−	1.68970e9i	0.430763	−	0.0550742i
$215$	−2.17321e8			−0.00693631
$216$	5.81216e10	−	2.33148e10i	1.81675	−	0.728769i
$217$	−1.54660e10			−0.473490
$218$	1.99657e10	−	2.55266e9i	0.598728	−	0.0765489i
$219$			1.01472e11i			2.98090i
$220$	−1.04040e10	+	2.70455e9i	−0.299431	+	0.0778383i
$221$		−	1.61084e10i		−	0.454243i
$222$	−6.20749e9	−	4.85520e10i	−0.171525	−	1.34159i
$223$	4.79011e10			1.29710			0.648550	−	0.761172i	$-0.275376\pi$
$223$	4.79011e10			1.29710			0.648550	+	0.761172i	$0.275376\pi$
$224$	1.79204e10	+	2.42806e10i	0.475590	+	0.644382i
$225$	2.33941e9			0.0608535
$226$	1.04511e9	+	8.17432e9i	0.0266485	+	0.208432i
$227$			4.51527e10i			1.12867i	0.825545	+	0.564336i	$0.190868\pi$
$227$			4.51527e10i			1.12867i	−0.825545	+	0.564336i	$0.809132\pi$
$228$	−6.27189e10	+	1.63040e10i	−1.53706	+	0.399566i
$229$			1.30792e10i			0.314282i	0.987576	+	0.157141i	$0.0502278\pi$
$229$			1.30792e10i			0.314282i	−0.987576	+	0.157141i	$0.949772\pi$
$230$	6.26485e10	−	8.00977e9i	1.47617	−	0.188732i
$231$	1.86433e10			0.430794
$232$	−2.32377e10	+	9.32154e9i	−0.526619	+	0.211247i
$233$	−7.90446e10			−1.75700			−0.878498	−	0.477746i	$-0.841454\pi$
$233$	−7.90446e10			−1.75700			−0.878498	+	0.477746i	$0.841454\pi$
$234$	−5.97410e10	+	7.63804e9i	−1.30257	+	0.166537i
$235$		−	7.33717e10i		−	1.56936i
$236$	1.48435e9	+	5.71005e9i	0.0311482	+	0.119822i
$237$		−	6.21603e9i		−	0.127981i
$238$	3.66942e9	+	2.87004e10i	0.0741313	+	0.579819i
$239$	1.26518e10			0.250819			0.125410	−	0.992105i	$-0.459975\pi$
$239$	1.26518e10			0.250819			0.125410	+	0.992105i	$0.459975\pi$
$240$	−8.03005e10	+	4.47746e10i	−1.56231	+	0.871126i
$241$	5.85645e10			1.11830			0.559149	−	0.829067i	$-0.311128\pi$
$241$	5.85645e10			1.11830			0.559149	+	0.829067i	$0.311128\pi$
$242$	6.13689e9	+	4.79998e10i	0.115021	+	0.899642i
$243$		−	2.22438e10i		−	0.409243i
$244$	−2.52220e10	−	9.70248e10i	−0.455539	−	1.75238i
$245$			2.05124e10i			0.363721i
$246$	−8.24186e10	+	1.05374e10i	−1.43488	+	0.183454i
$247$	3.27862e10			0.560474
$248$	1.31120e10	+	3.26869e10i	0.220108	+	0.548709i
$249$	1.17070e11			1.92996
$250$	6.03495e10	−	7.71583e9i	0.977111	−	0.124926i
$251$			6.88194e10i			1.09441i	0.837000	+	0.547204i	$0.184308\pi$
$251$			6.88194e10i			1.09441i	−0.837000	+	0.547204i	$0.815692\pi$
$252$	1.04701e11	−	2.72175e10i	1.63549	−	0.425153i
$253$			2.91640e10i			0.447512i
$254$	−1.10888e10	−	8.67314e10i	−0.167161	−	1.30745i
$255$	−8.81512e10			−1.30556
$256$	3.61234e10	−	5.84591e10i	0.525664	−	0.850692i
$257$	−1.19348e10			−0.170654			−0.0853271	−	0.996353i	$-0.527194\pi$
$257$	−1.19348e10			−0.170654			−0.0853271	+	0.996353i	$0.527194\pi$
$258$	−1.08845e8	−	8.51336e8i	−0.00152940	−	0.0119622i
$259$		−	4.44814e10i		−	0.614227i
$260$	4.50192e10	−	1.17029e10i	0.610968	−	0.158824i
$261$			8.97548e10i			1.19722i
$262$	−6.86187e10	+	8.77307e9i	−0.899677	+	0.115026i
$263$	3.19598e10			0.411911			0.205956	−	0.978561i	$-0.433970\pi$
$263$	3.19598e10			0.411911			0.205956	+	0.978561i	$0.433970\pi$
$264$	−1.58057e10	−	3.94021e10i	−0.200261	−	0.499231i
$265$	−6.04270e10			−0.752705
$266$	−5.84154e10	+	7.46855e9i	−0.715418	+	0.0914680i
$267$		−	2.09204e11i		−	2.51923i
$268$	−2.18622e10	−	8.41003e10i	−0.258874	−	0.995843i
$269$		−	7.08498e10i		−	0.824999i	−0.910958	−	0.412500i	$-0.864656\pi$
$269$		−	7.08498e10i		−	0.824999i	0.910958	−	0.412500i	$-0.135344\pi$
$270$	2.19884e10	+	1.71983e11i	0.251801	+	1.96947i
$271$	−8.70264e10			−0.980143			−0.490071	−	0.871682i	$-0.663029\pi$
$271$	−8.70264e10			−0.980143			−0.490071	+	0.871682i	$0.663029\pi$
$272$	5.75465e10	−	3.20872e10i	0.637469	−	0.355445i
$273$	−8.06721e10			−0.879005
$274$	9.05354e9	+	7.08124e10i	0.0970378	+	0.758982i
$275$		−	8.34307e8i		−	0.00879688i
$276$	6.27552e10	+	2.41409e11i	0.650967	+	2.50416i
$277$			1.55080e11i			1.58270i	0.611365	+	0.791349i	$0.290621\pi$
$277$			1.55080e11i			1.58270i	−0.611365	+	0.791349i	$0.709379\pi$
$278$	3.28074e10	−	4.19450e9i	0.329435	−	0.0421191i
$279$	1.26252e11			1.24744
$280$	−7.75451e10	+	3.11064e10i	−0.753951	+	0.302439i
$281$	−2.79959e10			−0.267865			−0.133933	−	0.990990i	$-0.542761\pi$
$281$	−2.79959e10			−0.267865			−0.133933	+	0.990990i	$0.542761\pi$
$282$	2.87428e11	−	3.67483e10i	2.70650	−	0.346032i
$283$			9.14271e10i			0.847298i	0.905826	+	0.423649i	$0.139251\pi$
$283$			9.14271e10i			0.847298i	−0.905826	+	0.423649i	$0.860749\pi$
$284$	−1.10777e11	+	2.87969e10i	−1.01045	+	0.262672i
$285$		−	1.79418e11i		−	1.61089i
$286$	2.72396e9	+	2.13055e10i	0.0240743	+	0.188298i
$287$	−7.55086e10			−0.656943
$288$	−1.46288e11	−	1.98207e11i	−1.25297	−	1.69767i
$289$	−5.54153e10			−0.467293
$290$	−8.79123e9	−	6.87608e10i	−0.0729892	−	0.570887i
$291$			1.97233e11i			1.61236i
$292$	2.03232e11	−	5.28310e10i	1.63595	−	0.425271i
$293$			9.37104e10i			0.742819i	0.928469	+	0.371410i	$0.121125\pi$
$293$			9.37104e10i			0.742819i	−0.928469	+	0.371410i	$0.878875\pi$
$294$	−8.03555e10	+	1.02736e10i	−0.627267	+	0.0801977i
$295$	−1.63346e10			−0.125577
$296$	−9.40098e10	+	3.77110e10i	−0.711804	+	0.285532i
$297$	−8.00610e10			−0.597059
$298$	−4.81026e10	+	6.15004e9i	−0.353342	+	0.0451757i
$299$		−	1.26196e11i		−	0.913116i
$300$	−1.79527e9	−	6.90608e9i	−0.0127963	−	0.0492251i
$301$		−	7.79960e8i		−	0.00547676i
$302$	−1.22318e10	−	9.56711e10i	−0.0846172	−	0.661835i
$303$	1.98130e11			1.35038
$304$	6.53087e10	+	1.17127e11i	0.438571	+	0.786550i
$305$	2.77557e11			1.83655
$306$	−2.99542e10	−	2.34287e11i	−0.195304	−	1.52757i
$307$		−	1.03026e11i		−	0.661951i	−0.943639	−	0.330976i	$-0.892622\pi$
$307$		−	1.03026e11i		−	0.661951i	0.943639	−	0.330976i	$-0.107378\pi$
$308$	−9.70659e9	−	3.73396e10i	−0.0614594	−	0.236424i
$309$		−	2.02960e11i		−	1.26648i
$310$	−9.67213e10	+	1.23661e10i	−0.594833	+	0.0760508i
$311$	−1.43254e11			−0.868333			−0.434167	−	0.900833i	$-0.642957\pi$
$311$	−1.43254e11			−0.868333			−0.434167	+	0.900833i	$0.642957\pi$
$312$	6.83932e10	+	1.70498e11i	0.408618	+	1.01864i
$313$	2.53850e11			1.49495			0.747477	−	0.664287i	$-0.231265\pi$
$313$	2.53850e11			1.49495			0.747477	+	0.664287i	$0.231265\pi$
$314$	−2.43972e11	+	3.11924e10i	−1.41630	+	0.181078i
$315$			2.99516e11i			1.71404i
$316$	−1.24497e10	+	3.23635e9i	−0.0702372	+	0.0182585i
$317$		−	2.17416e11i		−	1.20927i	−0.796502	−	0.604636i	$-0.793318\pi$
$317$		−	2.17416e11i		−	1.20927i	0.796502	−	0.604636i	$-0.206682\pi$
$318$	−3.02650e10	−	2.36718e11i	−0.165966	−	1.29810i
$319$	3.20093e10			0.173069
$320$	1.31484e11	+	1.37517e11i	0.700970	+	0.733132i
$321$	−1.45684e11			−0.765841
$322$	2.87469e10	+	2.24844e11i	0.149018	+	1.16555i
$323$			1.28578e11i			0.657289i
$324$	−2.57644e11	+	6.69756e10i	−1.29887	+	0.337648i
$325$			3.61015e9i			0.0179494i
$326$	9.79474e10	−	1.25228e10i	0.480301	−	0.0614077i
$327$	−2.20087e11			−1.06446
$328$	6.40157e10	+	1.59585e11i	0.305389	+	0.761306i
$329$	2.63330e11			1.23913
$330$	1.16592e11	−	1.49065e10i	0.541196	−	0.0691932i
$331$			2.98163e10i			0.136530i	0.997667	+	0.0682650i	$0.0217463\pi$
$331$			2.98163e10i			0.136530i	−0.997667	+	0.0682650i	$0.978254\pi$
$332$	−6.09520e10	−	2.34472e11i	−0.275338	−	1.05918i
$333$			3.63110e11i			1.61823i
$334$	−2.21441e9	−	1.73201e10i	−0.00973642	−	0.0761535i
$335$	2.40584e11			1.04367
$336$	−1.60695e11	−	2.88197e11i	−0.687822	−	1.23357i
$337$	−3.56448e11			−1.50543			−0.752716	−	0.658346i	$-0.771257\pi$
$337$	−3.56448e11			−1.50543			−0.752716	+	0.658346i	$0.771257\pi$
$338$	1.86439e10	+	1.45823e11i	0.0776982	+	0.607718i
$339$		−	9.01078e10i		−	0.370564i
$340$	4.58956e10	+	1.76553e11i	0.186258	+	0.716505i
$341$		−	4.50255e10i		−	0.180328i
$342$	4.76856e11	−	6.09672e10i	1.88482	−	0.240979i
$343$	−2.78920e11			−1.08807
$344$	−1.64842e9	+	6.61245e8i	−0.00634680	+	0.00254595i
$345$	−6.90592e11			−2.62443
$346$	−3.30763e10	+	4.22889e9i	−0.124072	+	0.0158629i
$347$			3.73598e10i			0.138332i	0.997605	+	0.0691659i	$0.0220338\pi$
$347$			3.73598e10i			0.138332i	−0.997605	+	0.0691659i	$0.977966\pi$
$348$	2.64961e11	−	6.88778e10i	0.968448	−	0.251752i
$349$		−	1.15752e11i		−	0.417653i	−0.977953	−	0.208827i	$-0.933036\pi$
$349$		−	1.15752e11i		−	0.417653i	0.977953	−	0.208827i	$-0.0669644\pi$
$350$	−8.22375e8	−	6.43222e9i	−0.00292930	−	0.0229116i
$351$	3.46434e11			1.21826
$352$	−7.06868e10	+	5.21708e10i	−0.245412	+	0.181128i
$353$	1.94182e11			0.665614			0.332807	−	0.942995i	$-0.392004\pi$
$353$	1.94182e11			0.665614			0.332807	+	0.942995i	$0.392004\pi$
$354$	−8.18121e9	−	6.39895e10i	−0.0276887	−	0.216568i
$355$		−	3.16897e11i		−	1.05899i
$356$	−4.19001e11	+	1.08921e11i	−1.38258	+	0.359407i
$357$		−	3.16373e11i		−	1.03084i
$358$	2.64949e10	−	3.38744e9i	0.0852490	−	0.0108993i
$359$	2.22958e11			0.708432			0.354216	−	0.935164i	$-0.384748\pi$
$359$	2.22958e11			0.708432			0.354216	+	0.935164i	$0.384748\pi$
$360$	6.33016e11	−	2.53927e11i	1.98634	−	0.796797i
$361$	6.09863e10			0.188995
$362$	−2.99336e11	+	3.82708e10i	−0.916158	+	0.117133i
$363$		−	5.29114e11i		−	1.59945i
$364$	4.20016e10	+	1.61573e11i	0.125404	+	0.482406i
$365$			5.81381e11i			1.71452i
$366$	1.39015e11	+	1.08730e12i	0.404944	+	3.16728i
$367$	−2.95151e11			−0.849272			−0.424636	−	0.905364i	$-0.639598\pi$
$367$	−2.95151e11			−0.849272			−0.424636	+	0.905364i	$0.639598\pi$
$368$	4.50829e11	−	2.51377e11i	1.28144	−	0.714513i
$369$	6.16391e11			1.73076
$370$	−3.55656e10	−	2.78177e11i	−0.0986558	−	0.771638i
$371$		−	2.16871e11i		−	0.594319i
$372$	−9.68860e10	−	3.72704e11i	−0.262312	−	1.00907i
$373$		−	1.80321e10i		−	0.0482343i	−0.999709	−	0.0241172i	$-0.992323\pi$
$373$		−	1.80321e10i		−	0.0482343i	0.999709	−	0.0241172i	$-0.00767748\pi$
$374$	−8.35541e10	+	1.06826e10i	−0.220824	+	0.0282328i
$375$	−6.65249e11			−1.73717
$376$	−2.23249e11	−	5.56538e11i	−0.576029	−	1.43598i
$377$	−1.38508e11			−0.353134
$378$	−6.17243e11	+	7.89160e10i	−1.55505	+	0.198816i
$379$			6.09778e11i			1.51808i	0.651042	+	0.759042i	$0.274332\pi$
$379$			6.09778e11i			1.51808i	−0.651042	+	0.759042i	$0.725668\pi$
$380$	−3.59346e11	+	9.34135e10i	−0.884070	+	0.229818i
$381$			9.56064e11i			2.32447i
$382$	−7.67026e10	−	5.99931e11i	−0.184300	−	1.44150i
$383$	1.33302e11			0.316549			0.158274	−	0.987395i	$-0.449407\pi$
$383$	1.33302e11			0.316549			0.158274	+	0.987395i	$0.449407\pi$
$384$	−4.72858e11	+	5.83955e11i	−1.10979	+	1.37053i
$385$	1.06816e11			0.247779
$386$	−3.24993e10	−	2.54194e11i	−0.0745129	−	0.582804i
$387$			6.36697e9i			0.0144289i
$388$	3.95026e11	−	1.02689e11i	0.884878	−	0.230028i
$389$			2.05551e10i			0.0455142i	0.999741	+	0.0227571i	$0.00724444\pi$
$389$			2.05551e10i			0.0455142i	−0.999741	+	0.0227571i	$0.992756\pi$
$390$	−5.04506e11	+	6.45023e10i	−1.10427	+	0.141184i
$391$	4.94905e11			1.07084
$392$	6.24132e10	+	1.55590e11i	0.133503	+	0.332809i
$393$	7.56402e11			1.59951
$394$	8.92122e11	−	1.14060e11i	1.86505	−	0.238452i
$395$		−	3.56146e10i		−	0.0736107i
$396$	7.92367e10	+	3.04810e11i	0.161919	+	0.622876i
$397$		−	5.93486e11i		−	1.19909i	−0.800339	−	0.599547i	$-0.795347\pi$
$397$		−	5.93486e11i		−	1.19909i	0.800339	−	0.599547i	$-0.204653\pi$
$398$	5.95877e10	+	4.66066e11i	0.119037	+	0.931051i
$399$	6.43929e11			1.27192
$400$	−1.28971e10	+	7.19125e9i	−0.0251896	+	0.0140454i
$401$	−1.00640e12			−1.94367			−0.971836	−	0.235660i	$-0.924275\pi$
$401$	−1.00640e12			−1.94367			−0.971836	+	0.235660i	$0.924275\pi$
$402$	1.20497e11	+	9.42466e11i	0.230122	+	1.79990i
$403$			1.94831e11i			0.367947i
$404$	−1.03155e11	−	3.96822e11i	−0.192653	−	0.741104i
$405$		−	7.37035e11i		−	1.36126i
$406$	2.46781e11	−	3.15516e10i	0.450759	−	0.0576307i
$407$	1.29496e11			0.233928
$408$	−6.68643e11	+	2.68219e11i	−1.19460	+	0.479202i
$409$	−3.40532e11			−0.601732			−0.300866	−	0.953666i	$-0.597276\pi$
$409$	−3.40532e11			−0.601732			−0.300866	+	0.953666i	$0.597276\pi$
$410$	−4.72215e11	+	6.03738e10i	−0.825301	+	0.105517i
$411$		−	7.80584e11i		−	1.34937i
$412$	−4.06496e11	+	1.05670e11i	−0.695054	+	0.180682i
$413$		−	5.86246e10i		−	0.0991527i
$414$	−2.34666e11	−	1.83545e12i	−0.392599	−	3.07072i
$415$	6.70749e11			1.11005
$416$	3.05871e11	−	2.25750e11i	0.500746	−	0.369579i
$417$	−3.61644e11			−0.585692
$418$	−2.17428e10	−	1.70062e11i	−0.0348355	−	0.272466i
$419$			8.47876e11i			1.34391i	0.740593	+	0.671953i	$0.234544\pi$
$419$			8.47876e11i			1.34391i	−0.740593	+	0.671953i	$0.765456\pi$
$420$	8.84187e11	−	2.29848e11i	1.38651	−	0.360429i
$421$		−	5.27094e11i		−	0.817747i	−0.912591	−	0.408873i	$-0.865922\pi$
$421$		−	5.27094e11i		−	0.817747i	0.912591	−	0.408873i	$-0.134078\pi$
$422$	1.14790e12	−	1.46762e11i	1.76197	−	0.225272i
$423$	−2.14961e12			−3.26459
$424$	−4.58350e11	+	1.83862e11i	−0.688733	+	0.276278i
$425$	−1.41580e10			−0.0210499
$426$	1.24142e12	−	1.58718e11i	1.82631	−	0.233498i
$427$			9.96145e11i			1.45010i
$428$	7.58497e10	+	2.91781e11i	0.109259	+	0.420301i
$429$		−	2.34856e11i		−	0.334768i
$430$	−6.23627e8	−	4.87771e9i	−0.000879664	−	0.00688030i
$431$	1.12919e11			0.157622			0.0788112	−	0.996890i	$-0.474888\pi$
$431$	1.12919e11			0.157622			0.0788112	+	0.996890i	$0.474888\pi$
$432$	6.90081e11	+	1.23762e12i	0.953286	+	1.70966i
$433$	9.18037e11			1.25506			0.627530	−	0.778592i	$-0.284066\pi$
$433$	9.18037e11			1.25506			0.627530	+	0.778592i	$0.284066\pi$
$434$	−4.43815e10	−	3.47131e11i	−0.0600480	−	0.469666i
$435$			7.57969e11i			1.01496i
$436$	1.14588e11	+	4.40799e11i	0.151862	+	0.584186i
$437$			1.00730e12i			1.32128i
$438$	−2.27751e12	+	2.91185e11i	−2.95683	+	0.378038i
$439$	−9.32700e11			−1.19854			−0.599269	−	0.800548i	$-0.704542\pi$
$439$	−9.32700e11			−1.19854			−0.599269	+	0.800548i	$0.704542\pi$
$440$	−9.05583e10	−	2.25753e11i	−0.115184	−	0.287142i
$441$	6.00962e11			0.756612
$442$	3.61549e11	−	4.62249e10i	0.450575	−	0.0576071i
$443$		−	1.58499e12i		−	1.95528i	−0.210283	−	0.977641i	$-0.567439\pi$
$443$		−	1.58499e12i		−	1.95528i	0.210283	−	0.977641i	$-0.432561\pi$
$444$	1.07192e12	−	2.78651e11i	1.30900	−	0.340280i
$445$		−	1.19863e12i		−	1.44898i
$446$	1.37457e11	+	1.07513e12i	0.164498	+	1.28663i
$447$	5.30248e11			0.628196
$448$	−4.93546e11	+	4.71895e11i	−0.578864	+	0.553470i
$449$	−5.33305e11			−0.619251			−0.309626	−	0.950859i	$-0.600204\pi$
$449$	−5.33305e11			−0.619251			−0.309626	+	0.950859i	$0.600204\pi$
$450$	6.71321e9	+	5.25075e10i	0.00771745	+	0.0603621i
$451$		−	2.19824e11i		−	0.250196i
$452$	−1.80471e11	+	4.69143e10i	−0.203369	+	0.0528667i
$453$			1.05461e12i			1.17666i
$454$	−1.01344e12	+	1.29571e11i	−1.11956	+	0.143138i
$455$	−4.62208e11			−0.505576
$456$	−5.45918e11	−	1.36092e12i	−0.591270	−	1.47398i
$457$	−6.95059e11			−0.745416			−0.372708	−	0.927949i	$-0.621571\pi$
$457$	−6.95059e11			−0.745416			−0.372708	+	0.927949i	$0.621571\pi$
$458$	−2.93558e11	+	3.75321e10i	−0.311745	+	0.0398573i
$459$			1.35862e12i			1.42869i
$460$	3.59554e11	+	1.38314e12i	0.374415	+	1.44031i
$461$		−	1.51250e12i		−	1.55970i	−0.625966	−	0.779851i	$-0.715295\pi$
$461$		−	1.51250e12i		−	1.55970i	0.625966	−	0.779851i	$-0.284705\pi$
$462$	5.34992e10	+	4.18445e11i	0.0546334	+	0.427316i
$463$	1.10015e12			1.11260			0.556300	−	0.830981i	$-0.312220\pi$
$463$	1.10015e12			1.11260			0.556300	+	0.830981i	$0.312220\pi$
$464$	−2.75902e11	−	4.94814e11i	−0.276328	−	0.495577i
$465$	1.06619e12			1.05753
$466$	−2.26827e11	−	1.77413e12i	−0.222823	−	1.74281i
$467$		−	7.29651e11i		−	0.709887i	−0.934888	−	0.354944i	$-0.884500\pi$
$467$		−	7.29651e11i		−	0.709887i	0.934888	−	0.354944i	$-0.115500\pi$
$468$	−3.42867e11	−	1.31895e12i	−0.330385	−	1.27093i
$469$			8.63450e11i			0.824061i
$470$	1.64681e12	−	2.10548e11i	1.55669	−	0.199027i
$471$	2.68936e12			2.51800
$472$	−1.23901e11	+	4.97015e10i	−0.114904	+	0.0460925i
$473$	2.27066e9			0.00208582
$474$	1.39517e11	−	1.78376e10i	0.126948	−	0.0162306i
$475$		−	2.88164e10i		−	0.0259728i
$476$	−6.33644e11	+	1.64718e11i	−0.565736	+	0.147065i
$477$			1.77036e12i			1.56578i
$478$	3.63057e10	+	2.83965e11i	0.0318089	+	0.248794i
$479$	−9.75429e11			−0.846614			−0.423307	−	0.905986i	$-0.639131\pi$
$479$	−9.75429e11			−0.846614			−0.423307	+	0.905986i	$0.639131\pi$
$480$	−1.23538e12	−	1.67384e12i	−1.06222	−	1.43922i
$481$	−5.60346e11			−0.477314
$482$	1.68057e11	+	1.31446e12i	0.141823	+	1.10927i
$483$		−	2.47852e12i		−	2.07219i
$484$	−1.05973e12	+	2.75481e11i	−0.877791	+	0.228186i
$485$			1.13004e12i			0.927378i
$486$	4.99256e11	−	6.38311e10i	0.405938	−	0.0519002i
$487$	7.09068e11			0.571225			0.285613	−	0.958345i	$-0.407803\pi$
$487$	7.09068e11			0.571225			0.285613	+	0.958345i	$0.407803\pi$
$488$	2.10532e12	−	8.44525e11i	1.68046	−	0.674098i
$489$	−1.07970e12			−0.853913
$490$	−4.60394e11	+	5.88626e10i	−0.360784	+	0.0461272i
$491$			8.30763e10i			0.0645075i	0.999480	+	0.0322538i	$0.0102685\pi$
$491$			8.30763e10i			0.0645075i	−0.999480	+	0.0322538i	$0.989732\pi$
$492$	−4.73019e11	−	1.81962e12i	−0.363945	−	1.40003i
$493$		−	5.43190e11i		−	0.414134i
$494$	9.40838e10	+	7.35878e11i	0.0710794	+	0.555948i
$495$	−8.71964e11			−0.652792
$496$	−6.96023e11	+	3.88094e11i	−0.516364	+	0.287918i
$497$	1.13734e12			0.836151
$498$	3.35945e11	+	2.62760e12i	0.244758	+	1.91438i
$499$			1.54674e12i			1.11677i	0.829581	+	0.558386i	$0.188579\pi$
$499$			1.54674e12i			1.11677i	−0.829581	+	0.558386i	$0.811421\pi$
$500$	3.46359e11	+	1.33239e12i	0.247835	+	0.953378i
$501$			1.90924e11i			0.135391i
$502$	−1.54463e12	+	1.97485e11i	−1.08557	+	0.138793i
$503$	−9.81095e11			−0.683369			−0.341684	−	0.939815i	$-0.610997\pi$
$503$	−9.81095e11			−0.683369			−0.341684	+	0.939815i	$0.610997\pi$
$504$	9.11339e11	+	2.27188e12i	0.629133	+	1.56837i
$505$	1.13518e12			0.776699
$506$	−6.54577e11	+	8.36893e10i	−0.443898	+	0.0567535i
$507$		−	1.60745e12i		−	1.08044i
$508$	1.91484e12	−	4.97771e11i	1.27569	−	0.331622i
$509$		−	1.02396e12i		−	0.676167i	−0.941116	−	0.338083i	$-0.890221\pi$
$509$		−	1.02396e12i		−	0.676167i	0.941116	−	0.338083i	$-0.109779\pi$
$510$	−2.52960e11	−	1.97853e12i	−0.165571	−	1.29502i
$511$	−2.08656e12			−1.35375
$512$	1.41576e12	+	6.43024e11i	0.910488	+	0.413535i
$513$	−2.76525e12			−1.76282
$514$	−3.42483e10	−	2.67874e11i	−0.0216424	−	0.169276i
$515$		−	1.16285e12i		−	0.728437i
$516$	1.87957e10	−	4.88601e9i	0.0116717	−	0.00303411i
$517$			7.66618e11i			0.471923i
$518$	9.98372e11	−	1.27644e11i	0.609268	−	0.0778964i
$519$	3.64609e11			0.220584
$520$	3.91857e11	+	9.76861e11i	0.235024	+	0.585892i
$521$	1.53658e11			0.0913664			0.0456832	−	0.998956i	$-0.485454\pi$
$521$	1.53658e11			0.0913664			0.0456832	+	0.998956i	$0.485454\pi$
$522$	−2.01452e12	+	2.57561e11i	−1.18756	+	0.151832i
$523$			2.08535e12i			1.21877i	0.792875	+	0.609385i	$0.208583\pi$
$523$			2.08535e12i			1.21877i	−0.792875	+	0.609385i	$0.791417\pi$
$524$	−3.93818e11	−	1.51495e12i	−0.228194	−	0.877825i
$525$			7.09041e10i			0.0407338i
$526$	9.17123e10	+	7.17329e11i	0.0522386	+	0.408585i
$527$	−7.64071e11			−0.431505
$528$	8.39012e11	−	4.67823e11i	0.469803	−	0.261956i
$529$	2.07602e12			1.15261
$530$	−1.73402e11	−	1.35627e12i	−0.0954582	−	0.746628i
$531$			4.78564e11i			0.261225i
$532$	−3.35259e11	−	1.28968e12i	−0.181459	−	0.698042i
$533$			9.51207e11i			0.510508i
$534$	4.69552e12	−	6.00333e11i	2.49889	−	0.319490i
$535$	−8.34691e11			−0.440488
$536$	1.82487e12	−	7.32027e11i	0.954972	−	0.383076i
$537$	−2.92061e11			−0.151562
$538$	1.59020e12	−	2.03312e11i	0.818338	−	0.104627i
$539$		−	2.14322e11i		−	0.109375i
$540$	−3.79701e12	+	9.87048e11i	−1.92163	+	0.499536i
$541$		−	4.46995e11i		−	0.224344i	−0.993689	−	0.112172i	$-0.964219\pi$
$541$		−	4.46995e11i		−	0.224344i	0.993689	−	0.112172i	$-0.0357808\pi$
$542$	−2.49732e11	−	1.95328e12i	−0.124302	−	0.972229i
$543$	3.29966e12			1.62881
$544$	8.85325e11	+	1.19954e12i	0.433419	+	0.587244i
$545$	−1.26098e12			−0.612244
$546$	−2.31498e11	−	1.81066e12i	−0.111476	−	0.871908i
$547$			3.46729e11i			0.165595i	0.996566	+	0.0827974i	$0.0263854\pi$
$547$			3.46729e11i			0.165595i	−0.996566	+	0.0827974i	$0.973615\pi$
$548$	−1.56338e12	+	4.06408e11i	−0.740548	+	0.192508i
$549$		−	8.13172e12i		−	3.82038i
$550$	1.87258e10	−	2.39414e9i	0.00872585	−	0.00111562i
$551$	1.10558e12			0.510985
$552$	−5.23826e12	+	2.10127e12i	−2.40138	+	0.963288i
$553$	1.27820e11			0.0581213
$554$	−3.48073e12	+	4.45020e11i	−1.56992	+	0.200718i
$555$			3.06642e12i			1.37187i
$556$	1.88289e11	+	7.24315e11i	0.0835580	+	0.321434i
$557$			5.59793e11i			0.246422i	0.992380	+	0.123211i	$0.0393192\pi$
$557$			5.59793e11i			0.246422i	−0.992380	+	0.123211i	$0.960681\pi$
$558$	3.62295e11	+	2.83370e12i	0.158201	+	1.23737i
$559$	−9.82542e9			−0.00425596
$560$	−9.20698e11	−	1.65121e12i	−0.395613	−	0.709508i
$561$	9.21039e11			0.392595
$562$	−8.03374e10	−	6.28360e11i	−0.0339707	−	0.265702i
$563$			2.30313e12i			0.966119i	0.875587	+	0.483060i	$0.160475\pi$
$563$			2.30313e12i			0.966119i	−0.875587	+	0.483060i	$0.839525\pi$
$564$	1.64961e12	+	6.34578e12i	0.686477	+	2.64076i
$565$		−	5.16270e11i		−	0.213137i
$566$	−2.05206e12	+	2.62360e11i	−0.840457	+	0.107454i
$567$	2.64520e12			1.07482
$568$	−9.64225e11	−	2.40372e12i	−0.388697	−	0.968983i
$569$	−8.14910e11			−0.325915			−0.162958	−	0.986633i	$-0.552103\pi$
$569$	−8.14910e11			−0.325915			−0.162958	+	0.986633i	$0.552103\pi$
$570$	4.02699e12	−	5.14861e11i	1.59788	−	0.204293i
$571$		−	3.63502e12i		−	1.43102i	−0.698605	−	0.715508i	$-0.746195\pi$
$571$		−	3.63502e12i		−	1.43102i	0.698605	−	0.715508i	$-0.253805\pi$
$572$	−4.70379e11	+	1.22277e11i	−0.183724	+	0.0477599i
$573$			6.61320e12i			2.56281i
$574$	−2.16680e11	−	1.69477e12i	−0.0833136	−	0.651639i
$575$	−1.10916e11			−0.0423145
$576$	4.02891e12	−	3.85217e12i	1.52506	−	1.45816i
$577$	2.45038e11			0.0920326			0.0460163	−	0.998941i	$-0.485347\pi$
$577$	2.45038e11			0.0920326			0.0460163	+	0.998941i	$0.485347\pi$
$578$	−1.59020e11	−	1.24378e12i	−0.0592621	−	0.463520i
$579$			2.80205e12i			1.03615i
$580$	1.51809e12	−	3.94634e11i	0.557021	−	0.144800i
$581$			2.40730e12i			0.876472i
$582$	−4.42685e12	+	5.65983e11i	−1.59934	+	0.204480i
$583$	6.31366e11			0.226346
$584$	1.76897e12	+	4.40988e12i	0.629309	+	1.56880i
$585$	3.77310e12			1.33198
$586$	−2.10330e12	+	2.68912e11i	−0.736822	+	0.0942045i
$587$			2.81390e12i			0.978223i	0.872221	+	0.489112i	$0.162679\pi$
$587$			2.81390e12i			0.978223i	−0.872221	+	0.489112i	$0.837321\pi$
$588$	−4.61178e11	−	1.77407e12i	−0.159100	−	0.612032i
$589$		−	1.55515e12i		−	0.532419i
$590$	−4.68740e10	−	3.66626e11i	−0.0159257	−	0.124563i
$591$	−9.83410e12			−3.31582
$592$	−1.11618e12	−	2.00181e12i	−0.373498	−	0.669846i
$593$	7.42491e11			0.246573			0.123286	−	0.992371i	$-0.460657\pi$
$593$	7.42491e11			0.246573			0.123286	+	0.992371i	$0.460657\pi$
$594$	−2.29744e11	−	1.79695e12i	−0.0757191	−	0.592238i
$595$		−	1.81265e12i		−	0.592908i
$596$	−2.76072e11	−	1.06200e12i	−0.0896218	−	0.344760i
$597$		−	5.13757e12i		−	1.65529i
$598$	2.83244e12	−	3.62134e11i	0.905743	−	0.115801i
$599$	8.31869e11			0.264018			0.132009	−	0.991248i	$-0.457857\pi$
$599$	8.31869e11			0.264018			0.132009	+	0.991248i	$0.457857\pi$
$600$	1.49853e11	−	6.01120e10i	0.0472048	−	0.0189357i
$601$	−1.71774e12			−0.537060			−0.268530	−	0.963271i	$-0.586538\pi$
$601$	−1.71774e12			−0.537060			−0.268530	+	0.963271i	$0.586538\pi$
$602$	1.75060e10	−	2.23818e9i	0.00543253	−	0.000694563i
$603$		−	7.04851e12i		−	2.17105i
$604$	2.11221e12	−	5.49078e11i	0.645760	−	0.167868i
$605$		−	3.03155e12i		−	0.919951i
$606$	5.68555e11	+	4.44696e12i	0.171256	+	1.33948i
$607$	−2.97709e12			−0.890107			−0.445053	−	0.895504i	$-0.646815\pi$
$607$	−2.97709e12			−0.890107			−0.445053	+	0.895504i	$0.646815\pi$
$608$	−2.44147e12	+	1.80194e12i	−0.724580	+	0.534780i
$609$	−2.72033e12			−0.801391
$610$	7.96480e11	+	6.22968e12i	0.232911	+	1.82172i
$611$		−	3.31725e12i		−	0.962926i
$612$	5.17255e12	−	1.34463e12i	1.49047	−	0.387454i
$613$			3.26103e12i			0.932788i	0.884577	+	0.466394i	$0.154447\pi$
$613$			3.26103e12i			0.932788i	−0.884577	+	0.466394i	$0.845553\pi$
$614$	2.31240e12	−	2.95646e11i	0.656607	−	0.0839488i
$615$	5.20535e12			1.46728
$616$	8.10223e11	−	3.25012e11i	0.226721	−	0.0909465i
$617$	4.07434e12			1.13181			0.565906	−	0.824470i	$-0.308527\pi$
$617$	4.07434e12			1.13181			0.565906	+	0.824470i	$0.308527\pi$
$618$	4.55538e12	−	5.82416e11i	1.25625	−	0.160615i
$619$		−	3.60019e12i		−	0.985638i	−0.870132	−	0.492819i	$-0.835966\pi$
$619$		−	3.60019e12i		−	0.985638i	0.870132	−	0.492819i	$-0.164034\pi$
$620$	−5.55106e11	−	2.13540e12i	−0.150873	−	0.580385i
$621$			1.06436e13i			2.87195i
$622$	−4.11085e11	−	3.21531e12i	−0.110122	−	0.861322i
$623$	4.30184e12			1.14409
$624$	−3.63051e12	+	2.02433e12i	−0.958599	+	0.534503i
$625$	−3.92154e12			−1.02801
$626$	7.28452e11	+	5.69760e12i	0.189590	+	1.48288i
$627$			1.87464e12i			0.484410i
$628$	−1.40021e12	−	5.38636e12i	−0.359231	−	1.38190i
$629$		−	2.19752e12i		−	0.559763i
$630$	−6.72254e12	+	8.59493e11i	−1.70020	+	0.217375i
$631$	4.14069e12			1.03978			0.519890	−	0.854233i	$-0.325973\pi$
$631$	4.14069e12			1.03978			0.519890	+	0.854233i	$0.325973\pi$
$632$	−1.08365e11	−	2.70143e11i	−0.0270185	−	0.0673546i
$633$	−1.26536e13			−3.13255
$634$	4.87984e12	−	6.23899e11i	1.19951	−	0.153360i
$635$			5.47774e12i			1.33696i
$636$	5.22622e12	−	1.35858e12i	1.26657	−	0.329251i
$637$			9.27396e11i			0.223171i
$638$	9.18544e10	+	7.18441e11i	0.0219486	+	0.171671i
$639$	−9.28429e12			−2.20290
$640$	−2.70922e12	+	3.34575e12i	−0.638315	+	0.788286i
$641$	1.23747e12			0.289516			0.144758	−	0.989467i	$-0.453760\pi$
$641$	1.23747e12			0.289516			0.144758	+	0.989467i	$0.453760\pi$
$642$	−4.18056e11	−	3.26983e12i	−0.0971241	−	0.759657i
$643$		−	2.36693e12i		−	0.546054i	−0.962006	−	0.273027i	$-0.911975\pi$
$643$		−	2.36693e12i		−	0.546054i	0.962006	−	0.273027i	$-0.0880248\pi$
$644$	−4.96407e12	+	1.29043e12i	−1.13724	+	0.295630i
$645$			5.37683e10i			0.0122323i
$646$	−2.88590e12	+	3.68970e11i	−0.651982	+	0.0833574i
$647$	5.75807e12			1.29184			0.645918	−	0.763406i	$-0.276475\pi$
$647$	5.75807e12			1.29184			0.645918	+	0.763406i	$0.276475\pi$
$648$	−2.24259e12	−	5.59055e12i	−0.499645	−	1.24557i
$649$	1.70671e11			0.0377622
$650$	−8.10288e10	+	1.03597e10i	−0.0178045	+	0.00227635i
$651$			3.82652e12i			0.835006i
$652$	5.62142e11	+	2.16247e12i	0.121824	+	0.468635i
$653$		−	1.19202e12i		−	0.256552i	−0.991739	−	0.128276i	$-0.959056\pi$
$653$		−	1.19202e12i		−	0.256552i	0.991739	−	0.128276i	$-0.0409443\pi$
$654$	−6.31565e11	−	4.93979e12i	−0.134995	−	1.05587i
$655$	4.33379e12			0.919987
$656$	−3.39814e12	+	1.89476e12i	−0.716429	+	0.399472i
$657$	1.70330e13			3.56654
$658$	7.55654e11	+	5.91036e12i	0.157147	+	1.22913i
$659$		−	6.40718e11i		−	0.132337i	−0.997808	−	0.0661687i	$-0.978922\pi$
$659$		−	6.40718e11i		−	0.132337i	0.997808	−	0.0661687i	$-0.0210776\pi$
$660$	6.69145e11	+	2.57409e12i	0.137269	+	0.528051i
$661$			6.37585e12i			1.29907i	0.760333	+	0.649533i	$0.225036\pi$
$661$			6.37585e12i			1.29907i	−0.760333	+	0.649533i	$0.774964\pi$
$662$	−6.69219e11	+	8.55613e10i	−0.135428	+	0.0173148i
$663$	−3.98545e12			−0.801063
$664$	5.08775e12	−	2.04089e12i	1.01571	−	0.407440i
$665$	3.68937e12			0.731568
$666$	−8.14990e12	+	1.04198e12i	−1.60516	+	0.205224i
$667$		−	4.25545e12i		−	0.832490i
$668$	3.82389e11	−	9.94037e10i	0.0743039	−	0.0193156i
$669$		−	1.18514e13i		−	2.28745i
$670$	6.90382e11	+	5.39983e12i	0.132359	+	1.03525i
$671$	−2.90002e12			−0.552268
$672$	6.00736e12	−	4.43377e12i	1.13638	−	0.838709i
$673$	−5.29863e12			−0.995624			−0.497812	−	0.867285i	$-0.665863\pi$
$673$	−5.29863e12			−0.995624			−0.497812	+	0.867285i	$0.665863\pi$
$674$	−1.02287e12	−	8.00036e12i	−0.190919	−	1.49328i
$675$		−	3.04487e11i		−	0.0564549i
$676$	−3.21946e12	+	8.36913e11i	−0.592957	+	0.154142i
$677$			2.91606e12i			0.533516i	0.963764	+	0.266758i	$0.0859525\pi$
$677$			2.91606e12i			0.533516i	−0.963764	+	0.266758i	$0.914048\pi$
$678$	2.02244e12	−	2.58574e11i	0.367572	−	0.0469950i
$679$	−4.05570e12			−0.732237
$680$	−3.83097e12	+	1.53675e12i	−0.687098	+	0.275622i
$681$	1.11714e13			1.99043
$682$	1.01058e12	−	1.29206e11i	0.178872	−	0.0228692i
$683$		−	1.41684e12i		−	0.249131i	−0.992211	−	0.124565i	$-0.960246\pi$
$683$		−	1.41684e12i		−	0.249131i	0.992211	−	0.124565i	$-0.0397536\pi$
$684$	2.73678e12	+	1.05279e13i	0.478066	+	1.83904i
$685$		−	4.47233e12i		−	0.776116i
$686$	−8.00393e11	−	6.26028e12i	−0.137989	−	1.07928i
$687$	3.23597e12			0.554241
$688$	−1.95718e10	−	3.51008e10i	−0.00333029	−	0.00597268i
$689$	−2.73200e12			−0.461843
$690$	−1.98173e12	−	1.55001e13i	−0.332831	−	2.60324i
$691$			1.87083e12i			0.312164i	0.987744	+	0.156082i	$0.0498865\pi$
$691$			1.87083e12i			0.312164i	−0.987744	+	0.156082i	$0.950114\pi$
$692$	−1.89832e11	−	7.30253e11i	−0.0314697	−	0.121059i
$693$		−	3.12946e12i		−	0.515430i
$694$	−8.38530e11	+	1.07208e11i	−0.137215	+	0.0175433i
$695$	−2.07203e12			−0.336872
$696$	2.30628e12	+	5.74933e12i	0.372538	+	0.928701i
$697$	−3.73036e12			−0.598692
$698$	2.59803e12	−	3.32165e11i	0.414281	−	0.0529668i
$699$			1.95568e13i			3.09849i
$700$	1.42009e11	−	3.69160e10i	0.0223551	−	0.00581130i
$701$		−	8.31406e12i		−	1.30042i	−0.759757	−	0.650208i	$-0.774682\pi$
$701$		−	8.31406e12i		−	1.30042i	0.759757	−	0.650208i	$-0.225318\pi$
$702$	9.94131e11	+	7.77561e12i	0.154499	+	1.20842i
$703$	4.47271e12			0.690672
$704$	−1.37380e12	−	1.43684e12i	−0.210789	−	0.220460i
$705$	−1.81532e13			−2.76759
$706$	5.57227e11	+	4.35836e12i	0.0844133	+	0.660240i
$707$			4.07413e12i			0.613264i
$708$	1.41275e12	−	3.67250e11i	0.211308	−	0.0549303i
$709$			1.00136e13i			1.48827i	0.668030	+	0.744134i	$0.267138\pi$
$709$			1.00136e13i			1.48827i	−0.668030	+	0.744134i	$0.732862\pi$
$710$	7.11265e12	−	9.09370e11i	1.05043	−	0.134301i
$711$	−1.04342e12			−0.153125
$712$	−3.64707e12	−	9.09180e12i	−0.531844	−	1.32584i
$713$	−5.98586e12			−0.867409
$714$	7.10090e12	−	9.07867e11i	1.02252	−	0.130732i
$715$		−	1.34560e12i		−	0.192548i
$716$	1.52060e11	+	5.84951e11i	0.0216226	+	0.0831784i
$717$		−	3.13023e12i		−	0.442323i
$718$	6.39803e11	+	5.00423e12i	0.0898435	+	0.702712i
$719$	−3.50640e12			−0.489307			−0.244654	−	0.969611i	$-0.578674\pi$
$719$	−3.50640e12			−0.489307			−0.244654	+	0.969611i	$0.578674\pi$
$720$	7.51583e12	+	1.34792e13i	1.04227	+	1.86925i
$721$	4.17346e12			0.575158
$722$	1.75007e11	+	1.36882e12i	0.0239683	+	0.187469i
$723$		−	1.44897e13i		−	1.97213i
$724$	−1.71796e12	−	6.60869e12i	−0.232375	−	0.893906i
$725$			1.21737e11i			0.0163645i
$726$	1.18758e13	−	1.51835e12i	1.58653	−	0.202842i
$727$	−2.99547e11			−0.0397703			−0.0198852	−	0.999802i	$-0.506330\pi$
$727$	−2.99547e11			−0.0397703			−0.0198852	+	0.999802i	$0.506330\pi$
$728$	−3.50594e12	+	1.40637e12i	−0.462608	+	0.185570i
$729$	4.73045e12			0.620338
$730$	−1.30489e13	+	1.66834e12i	−1.70068	+	0.217436i
$731$		−	3.85325e10i		−	0.00499113i
$732$	−2.40053e13	+	6.24028e12i	−3.09035	+	0.803349i
$733$			6.88627e10i			0.00881082i	0.999990	+	0.00440541i	$0.00140229\pi$
$733$			6.88627e10i			0.00881082i	−0.999990	+	0.00440541i	$0.998598\pi$
$734$	−8.46968e11	−	6.62457e12i	−0.107705	−	0.842414i
$735$	5.07505e12			0.641427
$736$	6.93579e12	+	9.39738e12i	0.871256	+	1.18047i
$737$	−2.51372e12			−0.313843
$738$	1.76880e12	+	1.38347e13i	0.219496	+	1.71679i
$739$			9.78319e12i			1.20665i	0.797496	+	0.603324i	$0.206157\pi$
$739$			9.78319e12i			1.20665i	−0.797496	+	0.603324i	$0.793843\pi$
$740$	6.14154e12	−	1.59652e12i	0.752896	−	0.195718i
$741$		−	8.11178e12i		−	0.988404i
$742$	4.86762e12	−	6.22337e11i	0.589520	−	0.0753716i
$743$	−1.30634e12			−0.157256			−0.0786279	−	0.996904i	$-0.525054\pi$
$743$	−1.30634e12			−0.157256			−0.0786279	+	0.996904i	$0.525054\pi$
$744$	8.08721e12	−	3.24410e12i	0.967655	−	0.388164i
$745$	3.03804e12			0.361319
$746$	4.04725e11	−	5.17451e10i	0.0478449	−	0.00611709i
$747$		−	1.96513e13i		−	2.30913i
$748$	−4.79536e11	−	1.84469e12i	−0.0560098	−	0.215460i
$749$		−	2.99569e12i		−	0.347799i
$750$	−1.90901e12	−	1.49313e13i	−0.220309	−	1.72315i
$751$	−1.05656e13			−1.21204			−0.606019	−	0.795451i	$-0.707234\pi$
$751$	−1.05656e13			−1.21204			−0.606019	+	0.795451i	$0.707234\pi$
$752$	1.18507e13	−	6.60781e12i	1.35134	−	0.753490i
$753$	1.70269e13			1.93000
$754$	−3.97465e11	−	3.10878e12i	−0.0447846	−	0.350283i
$755$			6.04235e12i			0.676775i
$756$	−3.54250e12	−	1.36274e13i	−0.394422	−	1.51728i
$757$			1.53287e13i			1.69658i	0.529535	+	0.848288i	$0.322366\pi$
$757$			1.53287e13i			1.69658i	−0.529535	+	0.848288i	$0.677634\pi$
$758$	−1.36863e13	+	1.74983e12i	−1.50583	+	0.192524i
$759$	7.21558e12			0.789193
$760$	−3.12782e12	−	7.79736e12i	−0.340080	−	0.847786i
$761$	−3.80613e12			−0.411389			−0.205695	−	0.978616i	$-0.565945\pi$
$761$	−3.80613e12			−0.411389			−0.205695	+	0.978616i	$0.565945\pi$
$762$	−2.14586e13	+	2.74353e12i	−2.30571	+	0.294790i
$763$		−	4.52564e12i		−	0.483414i
$764$	1.32452e13	−	3.44314e12i	1.40649	−	0.365624i
$765$			1.47970e13i			1.56206i
$766$	3.82524e11	+	2.99192e12i	0.0401448	+	0.313993i
$767$	−7.38513e11			−0.0770511
$768$	−1.44636e13	−	8.93743e12i	−1.50021	−	0.927016i
$769$	3.96740e12			0.409107			0.204554	−	0.978855i	$-0.434426\pi$
$769$	3.96740e12			0.409107			0.204554	+	0.978855i	$0.434426\pi$
$770$	3.06522e11	+	2.39747e12i	0.0314234	+	0.245779i
$771$			2.95285e12i			0.300951i
$772$	5.61205e12	−	1.45888e12i	0.568648	−	0.147823i
$773$			7.06875e12i			0.712090i	0.934469	+	0.356045i	$0.115875\pi$
$773$			7.06875e12i			0.712090i	−0.934469	+	0.356045i	$0.884125\pi$
$774$	−1.42905e11	+	1.82707e10i	−0.0143124	+	0.00182988i
$775$	1.71240e11			0.0170509
$776$	3.43839e12	+	8.57158e12i	0.340391	+	0.848561i
$777$	−1.10053e13			−1.08320
$778$	−4.61354e11	+	5.89853e10i	−0.0451467	+	0.00577212i
$779$		−	7.59258e12i		−	0.738704i
$780$	−2.89547e12	−	1.11384e13i	−0.280088	−	1.07745i
$781$			3.31106e12i			0.318448i
$782$	1.42019e12	+	1.11080e13i	0.135805	+	1.06220i
$783$	1.16821e13			1.11069
$784$	−3.31307e12	+	1.84733e12i	−0.313191	+	0.174631i
$785$	1.54086e13			1.44827
$786$	2.17058e12	+	1.69772e13i	0.202850	+	1.58659i
$787$		−	8.40522e12i		−	0.781021i	−0.920598	−	0.390511i	$-0.872298\pi$
$787$		−	8.40522e12i		−	0.781021i	0.920598	−	0.390511i	$-0.127702\pi$
$788$	5.12009e12	+	1.96961e13i	0.473053	+	1.81975i
$789$		−	7.90732e12i		−	0.726411i
$790$	7.99359e11	−	1.02200e11i	0.0730163	−	0.00933532i
$791$	1.85288e12			0.168288
$792$	−6.61400e12	+	2.65313e12i	−0.597312	+	0.239605i
$793$	1.25488e13			1.12686
$794$	1.33206e13	−	1.70308e12i	1.18941	−	0.152069i
$795$			1.49505e13i			1.32741i
$796$	−1.02897e13	+	2.67486e12i	−0.908438	+	0.236152i
$797$			2.76521e11i			0.0242754i	0.999926	+	0.0121377i	$0.00386364\pi$
$797$			2.76521e11i			0.0242754i	−0.999926	+	0.0121377i	$0.996136\pi$
$798$	1.84783e12	+	1.44528e13i	0.161305	+	1.26165i
$799$	1.30093e13			1.12926
$800$	−1.98415e11	−	2.68835e11i	−0.0171266	−	0.0232050i
$801$	−3.51168e13			−3.01417
$802$	−2.88799e12	−	2.25885e13i	−0.246497	−	1.92798i
$803$		−	6.07450e12i		−	0.515574i
$804$	−2.08076e13	+	5.40902e12i	−1.75618	+	0.456527i
$805$		−	1.42006e13i		−	1.19186i
$806$	−4.37292e12	+	5.59089e11i	−0.364976	+	0.0466631i
$807$	−1.75292e13			−1.45490
$808$	8.61053e12	−	3.45402e12i	0.710688	−	0.285084i
$809$	−1.10211e13			−0.904601			−0.452300	−	0.891866i	$-0.649396\pi$
$809$	−1.10211e13			−0.904601			−0.452300	+	0.891866i	$0.649396\pi$
$810$	1.65425e13	−	2.11501e12i	1.35027	−	0.172635i
$811$		−	2.02649e13i		−	1.64494i	−0.568808	−	0.822470i	$-0.692595\pi$
$811$		−	2.02649e13i		−	1.64494i	0.568808	−	0.822470i	$-0.307405\pi$
$812$	1.41633e12	+	5.44839e12i	0.114331	+	0.439811i
$813$			2.15316e13i			1.72850i
$814$	3.71604e11	+	2.90651e12i	0.0296668	+	0.232039i
$815$	−6.18611e12			−0.491144
$816$	−7.93884e12	−	1.42378e13i	−0.626832	−	1.12418i
$817$	7.84270e10			0.00615838
$818$	−9.77195e11	−	7.64314e12i	−0.0763117	−	0.596873i
$819$			1.35416e13i			1.05170i
$820$	−2.71015e12	−	1.04255e13i	−0.209329	−	0.805255i
$821$		−	4.75674e12i		−	0.365397i	−0.983169	−	0.182699i	$-0.941517\pi$
$821$		−	4.75674e12i		−	0.365397i	0.983169	−	0.182699i	$-0.0584833\pi$
$822$	1.75200e13	−	2.23997e12i	1.33848	−	0.171127i
$823$	−1.58721e13			−1.20596			−0.602981	−	0.797755i	$-0.706021\pi$
$823$	−1.58721e13			−1.20596			−0.602981	+	0.797755i	$0.706021\pi$
$824$	−3.53823e12	−	8.82045e12i	−0.267370	−	0.666528i
$825$	−2.06419e11			−0.0155134
$826$	1.31581e12	−	1.68230e11i	0.0983521	−	0.0125746i
$827$			1.83601e13i			1.36490i	0.730932	+	0.682451i	$0.239086\pi$
$827$			1.83601e13i			1.36490i	−0.730932	+	0.682451i	$0.760914\pi$
$828$	4.05227e13	−	1.05340e13i	2.99614	−	0.778858i
$829$		−	6.16980e12i		−	0.453707i	−0.973929	−	0.226854i	$-0.927156\pi$
$829$		−	6.16980e12i		−	0.453707i	0.973929	−	0.226854i	$-0.0728439\pi$
$830$	1.92479e12	+	1.50548e13i	0.140777	+	1.10109i
$831$	3.83691e13			2.79111
$832$	5.94461e12	+	6.21736e12i	0.430099	+	0.449833i
$833$	−3.63698e12			−0.261721
$834$	−1.03778e12	−	8.11701e12i	−0.0742776	−	0.580963i
$835$			1.09389e12i			0.0778727i
$836$	3.75459e12	−	9.76022e11i	0.265849	−	0.0691085i
$837$		−	1.64324e13i		−	1.15727i
$838$	−1.90303e13	+	2.43307e12i	−1.33306	+	0.170434i
$839$	−2.48397e13			−1.73068			−0.865342	−	0.501183i	$-0.832899\pi$
$839$	−2.48397e13			−1.73068			−0.865342	+	0.501183i	$0.832899\pi$
$840$	7.69615e12	+	1.91858e13i	0.533356	+	1.32960i
$841$	9.83652e12			0.678047
$842$	1.18305e13	−	1.51256e12i	0.811144	−	0.103707i
$843$			6.92659e12i			0.472384i
$844$	6.58807e12	+	2.53432e13i	0.446907	+	1.71918i
$845$		−	9.20984e12i		−	0.621437i
$846$	−6.16855e12	−	4.82474e13i	−0.414015	−	3.23823i
$847$	1.08802e13			0.726373
$848$	−5.44202e12	−	9.75993e12i	−0.361392	−	0.648135i
$849$	2.26204e13			1.49422
$850$	−4.06279e10	−	3.17772e11i	−0.00266956	−	0.0208800i
$851$		−	1.72157e13i		−	1.12523i
$852$	7.12476e12	+	2.74078e13i	0.463225	+	1.78195i
$853$		−	2.52887e13i		−	1.63552i	−0.575560	−	0.817760i	$-0.695216\pi$
$853$		−	2.52887e13i		−	1.63552i	0.575560	−	0.817760i	$-0.304784\pi$
$854$	−2.23582e13	+	2.85855e12i	−1.43839	+	0.183901i
$855$	−3.01170e13			−1.92737
$856$	−6.33129e12	+	2.53972e12i	−0.403051	+	0.161679i
$857$	−1.49919e13			−0.949387			−0.474693	−	0.880151i	$-0.657441\pi$
$857$	−1.49919e13			−0.949387			−0.474693	+	0.880151i	$0.657441\pi$
$858$	5.27128e12	−	6.73947e11i	0.332065	−	0.0424554i
$859$			1.48492e13i			0.930540i	0.885169	+	0.465270i	$0.154043\pi$
$859$			1.48492e13i			0.930540i	−0.885169	+	0.465270i	$0.845957\pi$
$860$	1.07689e11	−	2.79943e10i	0.00671319	−	0.00174512i
$861$			1.86819e13i			1.15853i
$862$	3.24033e11	+	2.53443e12i	0.0199897	+	0.156350i
$863$	−2.31037e13			−1.41786			−0.708928	−	0.705281i	$-0.750821\pi$
$863$	−2.31037e13			−1.41786			−0.708928	+	0.705281i	$0.750821\pi$
$864$	−2.57977e13	+	1.90401e13i	−1.57496	+	1.16241i
$865$	2.08902e12			0.126873
$866$	2.63441e12	+	2.06051e13i	0.159167	+	1.24493i
$867$			1.37105e13i			0.824077i
$868$	7.66390e12	−	1.99226e12i	0.458259	−	0.119126i
$869$			3.72116e11i			0.0221355i
$870$	−1.70124e13	+	2.17508e12i	−1.00677	+	0.128718i
$871$	1.08772e13			0.640374
$872$	−9.56478e12	+	3.83681e12i	−0.560210	+	0.224722i
$873$	3.31074e13			1.92913
$874$	−2.26087e13	+	2.89057e12i	−1.31061	+	0.167565i
$875$		−	1.36795e13i		−	0.788921i
$876$	−1.30711e13	−	5.02825e13i	−0.749972	−	2.88502i
$877$		−	1.71535e11i		−	0.00979164i	−0.999988	−	0.00489582i	$-0.998442\pi$
$877$		−	1.71535e11i		−	0.00979164i	0.999988	−	0.00489582i	$-0.00155839\pi$
$878$	−2.67649e12	−	2.09342e13i	−0.151999	−	1.18886i
$879$	2.31853e13			1.30997
$880$	4.80709e12	−	2.68038e12i	0.270216	−	0.150669i
$881$	1.01574e13			0.568058			0.284029	−	0.958816i	$-0.408329\pi$
$881$	1.01574e13			0.568058			0.284029	+	0.958816i	$0.408329\pi$
$882$	1.72453e12	+	1.34884e13i	0.0959537	+	0.750503i
$883$			1.93867e13i			1.07320i	0.843837	+	0.536600i	$0.180292\pi$
$883$			1.93867e13i			1.07320i	−0.843837	+	0.536600i	$0.819708\pi$
$884$	2.07501e12	+	7.98222e12i	0.114284	+	0.439631i
$885$			4.04141e12i			0.221457i
$886$	3.55746e13	−	4.54830e12i	1.93949	−	0.247969i
$887$	2.56537e13			1.39153			0.695766	−	0.718268i	$-0.255065\pi$
$887$	2.56537e13			1.39153			0.695766	+	0.718268i	$0.255065\pi$
$888$	9.33023e12	+	2.32594e13i	0.503540	+	1.25528i
$889$	−1.96595e13			−1.05564
$890$	2.69028e13	−	3.43959e12i	1.43728	−	0.183760i
$891$			7.70084e12i			0.409344i
$892$	−2.37364e13	+	6.17039e12i	−1.25538	+	0.326340i
$893$			2.64785e13i			1.39335i
$894$	1.52161e12	+	1.19013e13i	0.0796679	+	0.623124i
$895$	−1.67335e12			−0.0871734
$896$	−1.20078e13	−	9.72335e12i	−0.622413	−	0.503999i
$897$	−3.12227e13			−1.61029
$898$	−1.53038e12	−	1.19699e13i	−0.0785335	−	0.614251i
$899$			6.56987e12i			0.335458i
$900$	−1.15925e12	+	3.01352e11i	−0.0588960	+	0.0153103i
$901$		−	1.07141e13i		−	0.541621i
$902$	4.93389e12	−	6.30810e11i	0.248176	−	0.0317299i
$903$	−1.92973e11			−0.00965834
$904$	−1.57086e12	−	3.91600e12i	−0.0782312	−	0.195023i
$905$	1.89053e13			0.936840
$906$	−2.36704e13	+	3.02632e12i	−1.16715	+	0.149224i
$907$			3.07269e13i			1.50760i	0.657105	+	0.753799i	$0.271781\pi$
$907$			3.07269e13i			1.50760i	−0.657105	+	0.753799i	$0.728219\pi$
$908$	−5.81636e12	−	2.23746e13i	−0.283965	−	1.09237i
$909$		−	3.32579e13i		−	1.61569i
$910$	−1.32636e12	−	1.03741e13i	−0.0641172	−	0.501494i
$911$	2.80997e13			1.35166			0.675832	−	0.737056i	$-0.263785\pi$
$911$	2.80997e13			1.35166			0.675832	+	0.737056i	$0.263785\pi$
$912$	2.89789e13	−	1.61583e13i	1.38709	−	0.773426i
$913$	−7.00825e12			−0.333804
$914$	−1.99455e12	−	1.56004e13i	−0.0945337	−	0.739397i
$915$		−	6.86714e13i		−	3.23878i
$916$	−1.68479e12	−	6.48112e12i	−0.0790710	−	0.304173i
$917$			1.55539e13i			0.726401i
$918$	−3.04937e13	+	3.89870e12i	−1.41716	+	0.181187i
$919$	1.57307e13			0.727494			0.363747	−	0.931498i	$-0.381497\pi$
$919$	1.57307e13			0.727494			0.363747	+	0.931498i	$0.381497\pi$
$920$	−3.00125e13	+	1.20392e13i	−1.38120	+	0.554053i
$921$	−2.54902e13			−1.16736
$922$	3.39476e13	−	4.34029e12i	1.54711	−	0.197802i
$923$		−	1.43274e13i		−	0.649770i
$924$	−9.23835e12	+	2.40155e12i	−0.416937	+	0.108385i
$925$			4.92498e11i			0.0221191i
$926$	3.15702e12	+	2.46927e13i	0.141100	+	1.10362i
$927$	−3.40687e13			−1.51529
$928$	1.03142e13	−	7.61247e12i	0.456532	−	0.336946i
$929$	−6.66185e12			−0.293443			−0.146722	−	0.989178i	$-0.546872\pi$
$929$	−6.66185e12			−0.293443			−0.146722	+	0.989178i	$0.546872\pi$
$930$	3.05954e12	+	2.39302e13i	0.134117	+	1.04900i
$931$		−	7.40252e12i		−	0.322928i
$932$	3.91690e13	−	1.01822e13i	1.70048	−	0.442047i
$933$			3.54432e13i			1.53132i
$934$	1.63768e13	−	2.09382e12i	0.704155	−	0.0900280i
$935$	5.27707e12			0.225809
$936$	2.86196e13	−	1.14804e13i	1.21877	−	0.488897i
$937$	2.89231e12			0.122579			0.0612897	−	0.998120i	$-0.480479\pi$
$937$	2.89231e12			0.122579			0.0612897	+	0.998120i	$0.480479\pi$
$938$	−1.93799e13	+	2.47777e12i	−0.817407	+	0.104507i
$939$		−	6.28061e13i		−	2.63637i
$940$	9.45140e12	+	3.63579e13i	0.394840	+	1.51888i
$941$		−	7.76858e12i		−	0.322990i	−0.986874	−	0.161495i	$-0.948369\pi$
$941$		−	7.76858e12i		−	0.322990i	0.986874	−	0.161495i	$-0.0516315\pi$
$942$	7.71743e12	+	6.03620e13i	0.319333	+	2.49767i
$943$	−2.92243e13			−1.20349
$944$	−1.47108e12	−	2.63830e12i	−0.0602925	−	0.108131i
$945$	3.89835e13			1.59015
$946$	6.51591e9	+	5.09643e10i	0.000264524	+	0.00206898i
$947$			9.80623e12i			0.396212i	0.980181	+	0.198106i	$0.0634790\pi$
$947$			9.80623e12i			0.396212i	−0.980181	+	0.198106i	$0.936521\pi$
$948$	8.00720e11	+	3.08023e12i	0.0321991	+	0.123864i
$949$			2.62851e13i			1.05199i
$950$	6.46776e11	−	8.26919e10i	0.0257631	−	0.00329387i
$951$	−5.37917e13			−2.13257
$952$	−5.51537e12	−	1.37493e13i	−0.217625	−	0.542517i
$953$	2.10091e12			0.0825067			0.0412534	−	0.999149i	$-0.486865\pi$
$953$	2.10091e12			0.0825067			0.0412534	+	0.999149i	$0.486865\pi$
$954$	−3.97353e13	+	5.08026e12i	−1.55313	+	0.198572i
$955$			3.78901e13i			1.47405i
$956$	−6.26934e12	+	1.62974e12i	−0.242751	+	0.0631042i
$957$		−	7.91956e12i		−	0.305209i
$958$	−2.79910e12	−	2.18932e13i	−0.107368	−	0.839779i
$959$	1.60511e13			0.612804
$960$	3.40237e13	−	3.25311e13i	1.29289	−	1.23617i
$961$	−1.71982e13			−0.650471
$962$	−1.60798e12	−	1.25768e13i	−0.0605330	−	0.473460i
$963$			2.44544e13i			0.916302i
$964$	−2.90205e13	+	7.54400e12i	−1.08233	+	0.281355i
$965$			1.60543e13i			0.595960i
$966$	5.56297e13	−	7.11239e12i	2.05546	−	0.262796i
$967$	−3.69001e13			−1.35709			−0.678544	−	0.734560i	$-0.737389\pi$
$967$	−3.69001e13			−1.35709			−0.678544	+	0.734560i	$0.737389\pi$
$968$	−9.22412e12	−	2.29948e13i	−0.337665	−	0.841765i
$969$	3.18121e13			1.15914
$970$	−2.53635e13	+	3.24278e12i	−0.919890	+	0.117610i
$971$			1.52779e13i			0.551542i	0.961223	+	0.275771i	$0.0889331\pi$
$971$			1.52779e13i			0.551542i	−0.961223	+	0.275771i	$0.911067\pi$
$972$	2.86534e12	+	1.10225e13i	0.102962	+	0.396079i
$973$		−	7.43648e12i		−	0.265986i
$974$	2.03475e12	+	1.59148e13i	0.0724429	+	0.566613i
$975$	8.93202e11			0.0316540
$976$	2.49966e13	+	4.48298e13i	0.881771	+	1.58140i
$977$	−1.67353e13			−0.587637			−0.293818	−	0.955861i	$-0.594926\pi$
$977$	−1.67353e13			−0.587637			−0.293818	+	0.955861i	$0.594926\pi$
$978$	−3.09832e12	−	2.42336e13i	−0.108293	−	0.847018i
$979$			1.25237e13i			0.435724i
$980$	−2.64231e12	−	1.01645e13i	−0.0915095	−	0.352021i
$981$			3.69437e13i			1.27359i
$982$	−1.86462e12	+	2.38397e11i	−0.0639867	+	0.00818085i
$983$	4.18461e13			1.42943			0.714717	−	0.699414i	$-0.246556\pi$
$983$	4.18461e13			1.42943			0.714717	+	0.699414i	$0.246556\pi$
$984$	3.94835e13	−	1.58384e13i	1.34257	−	0.538558i
$985$	−5.63442e13			−1.90716
$986$	1.21918e13	−	1.55875e12i	0.410790	−	0.0525205i
$987$		−	6.51515e13i		−	2.18523i
$988$	−1.62466e13	+	4.22337e12i	−0.542445	+	0.141011i
$989$		−	3.01870e11i		−	0.0100331i
$990$	−2.50220e12	−	1.95710e13i	−0.0827872	−	0.647521i
$991$	4.79950e13			1.58075			0.790377	−	0.612620i	$-0.209885\pi$
$991$	4.79950e13			1.58075			0.790377	+	0.612620i	$0.209885\pi$
$992$	−1.07080e13	−	1.45084e13i	−0.351079	−	0.475681i
$993$	7.37698e12			0.240773
$994$	3.26371e12	+	2.55272e13i	0.106041	+	0.829400i
$995$		−	2.94356e13i		−	0.952069i
$996$	−5.80117e13	+	1.50804e13i	−1.86788	+	0.485563i
$997$		−	3.46659e13i		−	1.11115i	−0.831465	−	0.555576i	$-0.812498\pi$
$997$		−	3.46659e13i		−	1.11115i	0.831465	−	0.555576i	$-0.187502\pi$
$998$	−3.47161e13	+	4.43854e12i	−1.10776	+	0.141629i
$999$	4.72607e13			1.50126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.10.b.a.5.6	yes	8
3.2	odd	2		72.10.d.b.37.3		8
4.3	odd	2		32.10.b.a.17.8		8
8.3	odd	2		32.10.b.a.17.1		8
8.5	even	2	inner	8.10.b.a.5.5	✓	8
12.11	even	2		288.10.d.b.145.7		8
16.3	odd	4		256.10.a.s.1.1		8
16.5	even	4		256.10.a.p.1.1		8
16.11	odd	4		256.10.a.s.1.8		8
16.13	even	4		256.10.a.p.1.8		8
24.5	odd	2		72.10.d.b.37.4		8
24.11	even	2		288.10.d.b.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.10.b.a.5.5	✓	8	8.5	even	2	inner
8.10.b.a.5.6	yes	8	1.1	even	1	trivial
32.10.b.a.17.1		8	8.3	odd	2
32.10.b.a.17.8		8	4.3	odd	2
72.10.d.b.37.3		8	3.2	odd	2
72.10.d.b.37.4		8	24.5	odd	2
256.10.a.p.1.1		8	16.5	even	4
256.10.a.p.1.8		8	16.13	even	4
256.10.a.s.1.1		8	16.3	odd	4
256.10.a.s.1.8		8	16.11	odd	4
288.10.d.b.145.2		8	24.11	even	2
288.10.d.b.145.7		8	12.11	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.86961 + 22.4447i) q^{2} -247.414i q^{3} +(-495.531 + 128.815i) q^{4} -1417.55i q^{5} +(5553.14 - 709.983i) q^{6} +5087.57 q^{7} +(-4313.20 - 10752.4i) q^{8} -41530.8 q^{9} +O(q^{10})\)	\(q+(2.86961 + 22.4447i) q^{2} -247.414i q^{3} +(-495.531 + 128.815i) q^{4} -1417.55i q^{5} +(5553.14 - 709.983i) q^{6} +5087.57 q^{7} +(-4313.20 - 10752.4i) q^{8} -41530.8 q^{9} +(31816.6 - 4067.83i) q^{10} +14811.2i q^{11} +(31870.7 + 122601. i) q^{12} -64089.8i q^{13} +(14599.3 + 114189. i) q^{14} -350723. q^{15} +(228957. - 127664. i) q^{16} +251342. q^{17} +(-119177. - 932147. i) q^{18} +511568. i q^{19} +(182602. + 702441. i) q^{20} -1.25874e6i q^{21} +(-332432. + 42502.3i) q^{22} +1.96905e6 q^{23} +(-2.66030e6 + 1.06715e6i) q^{24} -56329.6 q^{25} +(1.43848e6 - 183913. i) q^{26} +5.40545e6i q^{27} +(-2.52105e6 + 655356. i) q^{28} -2.16116e6i q^{29} +(-1.00644e6 - 7.87187e6i) q^{30} -3.03997e6 q^{31} +(3.52240e6 + 4.77253e6i) q^{32} +3.66449e6 q^{33} +(721253. + 5.64129e6i) q^{34} -7.21189e6i q^{35} +(2.05798e7 - 5.34980e6i) q^{36} -8.74315e6i q^{37} +(-1.14820e7 + 1.46800e6i) q^{38} -1.58567e7 q^{39} +(-1.52421e7 + 6.11419e6i) q^{40} -1.48418e7 q^{41} +(2.82520e7 - 3.61208e6i) q^{42} -153307. i q^{43} +(-1.90790e6 - 7.33938e6i) q^{44} +5.88721e7i q^{45} +(5.65042e6 + 4.41949e7i) q^{46} +5.17595e7 q^{47} +(-3.15858e7 - 5.66473e7i) q^{48} -1.44703e7 q^{49} +(-161644. - 1.26430e6i) q^{50} -6.21855e7i q^{51} +(8.25574e6 + 3.17584e7i) q^{52} -4.26277e7i q^{53} +(-1.21324e8 + 1.55116e7i) q^{54} +2.09956e7 q^{55} +(-2.19437e7 - 5.47035e7i) q^{56} +1.26569e8 q^{57} +(4.85067e7 - 6.20170e6i) q^{58} -1.15231e7i q^{59} +(1.73794e8 - 4.51784e7i) q^{60} +1.95800e8i q^{61} +(-8.72353e6 - 6.82312e7i) q^{62} -2.11291e8 q^{63} +(-9.70103e7 + 9.27545e7i) q^{64} -9.08506e7 q^{65} +(1.05157e7 + 8.22485e7i) q^{66} +1.69718e8i q^{67} +(-1.24547e8 + 3.23766e7i) q^{68} -4.87172e8i q^{69} +(1.61869e8 - 2.06953e7i) q^{70} +2.23552e8 q^{71} +(1.79131e8 + 4.46555e8i) q^{72} -4.10130e8 q^{73} +(1.96238e8 - 2.50895e7i) q^{74} +1.39367e7i q^{75} +(-6.58977e7 - 2.53497e8i) q^{76} +7.53528e7i q^{77} +(-4.55026e7 - 3.55899e8i) q^{78} +2.51240e7 q^{79} +(-1.80970e8 - 3.24559e8i) q^{80} +5.19935e8 q^{81} +(-4.25902e7 - 3.33120e8i) q^{82} +4.73174e8i q^{83} +(1.62144e8 + 6.23742e8i) q^{84} -3.56290e8i q^{85} +(3.44094e6 - 439932. i) q^{86} -5.34702e8 q^{87} +(1.59255e8 - 6.38836e7i) q^{88} +8.45560e8 q^{89} +(-1.32137e9 + 1.68940e8i) q^{90} -3.26061e8i q^{91} +(-9.75726e8 + 2.53644e8i) q^{92} +7.52131e8i q^{93} +(1.48530e8 + 1.16173e9i) q^{94} +7.25174e8 q^{95} +(1.18079e9 - 8.71491e8i) q^{96} -7.97179e8 q^{97} +(-4.15241e7 - 3.24781e8i) q^{98} -6.15119e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9}+O(q^{10}) \) 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9	\( 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9} + 26392 q^{10} + 54760 q^{12} - 72336 q^{14} - 163136 q^{15} + 185616 q^{16} - 102000 q^{17} - 23614 q^{18} + 1245264 q^{20} - 2373124 q^{22} + 3412032 q^{23} - 3961456 q^{24} - 2423384 q^{25} + 4551240 q^{26} + 7509920 q^{28} - 15284368 q^{30} + 803584 q^{31} - 14113248 q^{32} + 58272 q^{33} + 27757244 q^{34} + 57226188 q^{36} - 63661140 q^{38} - 17590208 q^{39} - 93063648 q^{40} - 2180784 q^{41} + 127541344 q^{42} + 114013320 q^{44} - 131840944 q^{46} + 7432320 q^{47} - 217917408 q^{48} + 24436680 q^{49} + 231784902 q^{50} + 219270896 q^{52} - 362934280 q^{54} + 7056832 q^{55} - 358503360 q^{56} + 134003744 q^{57} + 375425192 q^{58} + 516952992 q^{60} - 344291904 q^{62} - 223198400 q^{63} - 316815296 q^{64} - 146501760 q^{65} + 239713176 q^{66} + 79875048 q^{68} - 56202048 q^{70} + 560234688 q^{71} + 112273016 q^{72} - 523987120 q^{73} - 65773608 q^{74} - 87532760 q^{76} + 318117968 q^{78} - 248943744 q^{79} + 890441280 q^{80} + 231960296 q^{81} - 1051981172 q^{82} - 1275608768 q^{84} + 1492810428 q^{86} + 540527424 q^{87} + 1544767952 q^{88} + 744827856 q^{89} - 3218579800 q^{90} - 2959012128 q^{92} + 3068552352 q^{94} - 1465245504 q^{95} + 4296343616 q^{96} - 9932784 q^{97} - 3062604162 q^{98}+O(q^{100}) \) 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9 + 26392 * q^10 + 54760 * q^12 - 72336 * q^14 - 163136 * q^15 + 185616 * q^16 - 102000 * q^17 - 23614 * q^18 + 1245264 * q^20 - 2373124 * q^22 + 3412032 * q^23 - 3961456 * q^24 - 2423384 * q^25 + 4551240 * q^26 + 7509920 * q^28 - 15284368 * q^30 + 803584 * q^31 - 14113248 * q^32 + 58272 * q^33 + 27757244 * q^34 + 57226188 * q^36 - 63661140 * q^38 - 17590208 * q^39 - 93063648 * q^40 - 2180784 * q^41 + 127541344 * q^42 + 114013320 * q^44 - 131840944 * q^46 + 7432320 * q^47 - 217917408 * q^48 + 24436680 * q^49 + 231784902 * q^50 + 219270896 * q^52 - 362934280 * q^54 + 7056832 * q^55 - 358503360 * q^56 + 134003744 * q^57 + 375425192 * q^58 + 516952992 * q^60 - 344291904 * q^62 - 223198400 * q^63 - 316815296 * q^64 - 146501760 * q^65 + 239713176 * q^66 + 79875048 * q^68 - 56202048 * q^70 + 560234688 * q^71 + 112273016 * q^72 - 523987120 * q^73 - 65773608 * q^74 - 87532760 * q^76 + 318117968 * q^78 - 248943744 * q^79 + 890441280 * q^80 + 231960296 * q^81 - 1051981172 * q^82 - 1275608768 * q^84 + 1492810428 * q^86 + 540527424 * q^87 + 1544767952 * q^88 + 744827856 * q^89 - 3218579800 * q^90 - 2959012128 * q^92 + 3068552352 * q^94 - 1465245504 * q^95 + 4296343616 * q^96 - 9932784 * q^97 - 3062604162 * q^98

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