LMFDB - Embedded newform 8.10.b.a.5.2

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			5.2
Root			$9.73909 - 3.55976i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.10.b.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.4782 + 7.11952i) q^{2} -100.481i q^{3} +(410.625 - 305.829i) q^{4} +2583.09i q^{5} +(715.380 + 2158.16i) q^{6} +6967.65 q^{7} +(-6642.12 + 9492.10i) q^{8} +9586.48 q^{9} +O(q^{10})$	\(q+(-21.4782 + 7.11952i) q^{2} -100.481i q^{3} +(410.625 - 305.829i) q^{4} +2583.09i q^{5} +(715.380 + 2158.16i) q^{6} +6967.65 q^{7} +(-6642.12 + 9492.10i) q^{8} +9586.48 q^{9} +(-18390.4 - 55480.1i) q^{10} +25054.5i q^{11} +(-30730.1 - 41260.2i) q^{12} +29701.4i q^{13} +(-149652. + 49606.3i) q^{14} +259553. q^{15} +(75081.4 - 251162. i) q^{16} -138527. q^{17} +(-205900. + 68251.2i) q^{18} +489569. i q^{19} +(789984. + 1.06068e6i) q^{20} -700119. i q^{21} +(-178376. - 538124. i) q^{22} +847079. q^{23} +(953780. + 667409. i) q^{24} -4.71924e6 q^{25} +(-211460. - 637933. i) q^{26} -2.94104e6i q^{27} +(2.86109e6 - 2.13091e6i) q^{28} -1.13646e6i q^{29} +(-5.57472e6 + 1.84789e6i) q^{30} +4.35747e6 q^{31} +(175542. + 5.92904e6i) q^{32} +2.51751e6 q^{33} +(2.97532e6 - 986249. i) q^{34} +1.79981e7i q^{35} +(3.93645e6 - 2.93182e6i) q^{36} +535315. i q^{37} +(-3.48550e6 - 1.05151e7i) q^{38} +2.98444e6 q^{39} +(-2.45190e7 - 1.71572e7i) q^{40} +1.45816e7 q^{41} +(4.98451e6 + 1.50373e7i) q^{42} -3.96441e7i q^{43} +(7.66238e6 + 1.02880e7i) q^{44} +2.47628e7i q^{45} +(-1.81937e7 + 6.03080e6i) q^{46} -4.48997e7 q^{47} +(-2.52371e7 - 7.54428e6i) q^{48} +8.19448e6 q^{49} +(1.01361e8 - 3.35988e7i) q^{50} +1.39194e7i q^{51} +(9.08355e6 + 1.21961e7i) q^{52} -4.85666e7i q^{53} +(2.09388e7 + 6.31682e7i) q^{54} -6.47180e7 q^{55} +(-4.62799e7 + 6.61376e7i) q^{56} +4.91926e7 q^{57} +(8.09108e6 + 2.44092e7i) q^{58} -4.19685e6i q^{59} +(1.06579e8 - 7.93787e7i) q^{60} +6.38659e7i q^{61} +(-9.35906e7 + 3.10231e7i) q^{62} +6.67952e7 q^{63} +(-4.59823e7 - 1.26095e8i) q^{64} -7.67215e7 q^{65} +(-5.40715e7 + 1.79235e7i) q^{66} -5.79621e7i q^{67} +(-5.68828e7 + 4.23657e7i) q^{68} -8.51157e7i q^{69} +(-1.28138e8 - 3.86566e8i) q^{70} +2.74912e8 q^{71} +(-6.36745e7 + 9.09959e7i) q^{72} -9.16969e7 q^{73} +(-3.81119e6 - 1.14976e7i) q^{74} +4.74196e8i q^{75} +(1.49724e8 + 2.01029e8i) q^{76} +1.74571e8i q^{77} +(-6.41004e7 + 2.12478e7i) q^{78} +2.02396e8 q^{79} +(6.48774e8 + 1.93942e8i) q^{80} -1.06829e8 q^{81} +(-3.13186e8 + 1.03814e8i) q^{82} -6.11053e8i q^{83} +(-2.14117e8 - 2.87486e8i) q^{84} -3.57829e8i q^{85} +(2.82247e8 + 8.51483e8i) q^{86} -1.14193e8 q^{87} +(-2.37819e8 - 1.66415e8i) q^{88} -7.71588e8 q^{89} +(-1.76299e8 - 5.31859e8i) q^{90} +2.06949e8i q^{91} +(3.47831e8 - 2.59061e8i) q^{92} -4.37845e8i q^{93} +(9.64363e8 - 3.19664e8i) q^{94} -1.26460e9 q^{95} +(5.95759e8 - 1.76387e7i) q^{96} +1.08292e9 q^{97} +(-1.76003e8 + 5.83408e7i) q^{98} +2.40184e8i 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 $

$2$	−21.4782	+	7.11952i	−0.949211	+	0.314642i
$2$	−21.4782	+	7.11952i	−0.949211	+	0.314642i
$3$		−	100.481i		−	0.716210i	−0.933681	−	0.358105i	$-0.883423\pi$
$3$		−	100.481i		−	0.716210i	0.933681	−	0.358105i	$-0.116577\pi$
$4$	410.625	−	305.829i	0.802001	−	0.597322i
$5$			2583.09i			1.84831i	0.382017	+	0.924155i	$0.375230\pi$
$5$			2583.09i			1.84831i	−0.382017	+	0.924155i	$0.624770\pi$
$6$	715.380	+	2158.16i	0.225349	+	0.679834i
$7$	6967.65			1.09684			0.548422	−	0.836202i	$-0.315229\pi$
$7$	6967.65			1.09684			0.548422	+	0.836202i	$0.315229\pi$
$8$	−6642.12	+	9492.10i	−0.573326	+	0.819327i
$9$	9586.48			0.487044
$10$	−18390.4	−	55480.1i	−0.581555	−	1.75444i
$11$			25054.5i			0.515962i	0.966150	+	0.257981i	$0.0830572\pi$
$11$			25054.5i			0.515962i	−0.966150	+	0.257981i	$0.916943\pi$
$12$	−30730.1	−	41260.2i	−0.427808	−	0.574401i
$13$			29701.4i			0.288425i	0.989547	+	0.144212i	$0.0460648\pi$
$13$			29701.4i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$14$	−149652.	+	49606.3i	−1.04114	+	0.345113i
$15$	259553.			1.32378
$16$	75081.4	−	251162.i	0.286413	−	0.958106i
$17$	−138527.			−0.402268			−0.201134	−	0.979564i	$-0.564463\pi$
$17$	−138527.			−0.402268			−0.201134	+	0.979564i	$0.564463\pi$
$18$	−205900.	+	68251.2i	−0.462307	+	0.153244i
$19$			489569.i			0.861832i	0.902392	+	0.430916i	$0.141809\pi$
$19$			489569.i			0.861832i	−0.902392	+	0.430916i	$0.858191\pi$
$20$	789984.	+	1.06068e6i	1.10404	+	1.48235i
$21$		−	700119.i		−	0.785570i
$22$	−178376.	−	538124.i	−0.162343	−	0.489757i
$23$	847079.			0.631173			0.315587	−	0.948897i	$-0.397799\pi$
$23$	847079.			0.631173			0.315587	+	0.948897i	$0.397799\pi$
$24$	953780.	+	667409.i	0.586810	+	0.410622i
$25$	−4.71924e6			−2.41625
$26$	−211460.	−	637933.i	−0.0907503	−	0.273776i
$27$		−	2.94104e6i		−	1.06504i
$28$	2.86109e6	−	2.13091e6i	0.879671	−	0.655169i
$29$		−	1.13646e6i		−	0.298376i	−0.988809	−	0.149188i	$-0.952334\pi$
$29$		−	1.13646e6i		−	0.298376i	0.988809	−	0.149188i	$-0.0476660\pi$
$30$	−5.57472e6	+	1.84789e6i	−1.25654	+	0.416515i
$31$	4.35747e6			0.847436			0.423718	−	0.905794i	$-0.360725\pi$
$31$	4.35747e6			0.847436			0.423718	+	0.905794i	$0.360725\pi$
$32$	175542.	+	5.92904e6i	0.0295941	+	0.999562i
$33$	2.51751e6			0.369537
$34$	2.97532e6	−	986249.i	0.381837	−	0.126570i
$35$			1.79981e7i			2.02731i
$36$	3.93645e6	−	2.93182e6i	0.390610	−	0.290922i
$37$			535315.i			0.0469571i	0.999724	+	0.0234786i	$0.00747415\pi$
$37$			535315.i			0.0469571i	−0.999724	+	0.0234786i	$0.992526\pi$
$38$	−3.48550e6	−	1.05151e7i	−0.271168	−	0.818060i
$39$	2.98444e6			0.206572
$40$	−2.45190e7	−	1.71572e7i	−1.51437	−	1.05968i
$41$	1.45816e7			0.805894			0.402947	−	0.915223i	$-0.367986\pi$
$41$	1.45816e7			0.805894			0.402947	+	0.915223i	$0.367986\pi$
$42$	4.98451e6	+	1.50373e7i	0.247173	+	0.745672i
$43$		−	3.96441e7i		−	1.76836i	−0.467148	−	0.884179i	$-0.654719\pi$
$43$		−	3.96441e7i		−	1.76836i	0.467148	−	0.884179i	$-0.345281\pi$
$44$	7.66238e6	+	1.02880e7i	0.308196	+	0.413802i
$45$			2.47628e7i			0.900208i
$46$	−1.81937e7	+	6.03080e6i	−0.599116	+	0.198593i
$47$	−4.48997e7			−1.34216			−0.671078	−	0.741387i	$-0.734168\pi$
$47$	−4.48997e7			−1.34216			−0.671078	+	0.741387i	$0.734168\pi$
$48$	−2.52371e7	−	7.54428e6i	−0.686205	−	0.205131i
$49$	8.19448e6			0.203067
$50$	1.01361e8	−	3.35988e7i	2.29353	−	0.760253i
$51$			1.39194e7i			0.288108i
$52$	9.08355e6	+	1.21961e7i	0.172282	+	0.231317i
$53$		−	4.85666e7i		−	0.845466i	−0.906254	−	0.422733i	$-0.861071\pi$
$53$		−	4.85666e7i		−	0.845466i	0.906254	−	0.422733i	$-0.138929\pi$
$54$	2.09388e7	+	6.31682e7i	0.335104	+	1.01094i
$55$	−6.47180e7			−0.953658
$56$	−4.62799e7	+	6.61376e7i	−0.628849	+	0.898674i
$57$	4.91926e7			0.617252
$58$	8.09108e6	+	2.44092e7i	0.0938816	+	0.283222i
$59$		−	4.19685e6i		−	0.0450910i	−0.999746	−	0.0225455i	$-0.992823\pi$
$59$		−	4.19685e6i		−	0.0450910i	0.999746	−	0.0225455i	$-0.00717706\pi$
$60$	1.06579e8	−	7.93787e7i	1.06167	−	0.790722i
$61$			6.38659e7i			0.590588i	0.955406	+	0.295294i	$0.0954176\pi$
$61$			6.38659e7i			0.590588i	−0.955406	+	0.295294i	$0.904582\pi$
$62$	−9.35906e7	+	3.10231e7i	−0.804395	+	0.266638i
$63$	6.67952e7			0.534211
$64$	−4.59823e7	−	1.26095e8i	−0.342595	−	0.939483i
$65$	−7.67215e7			−0.533098
$66$	−5.40715e7	+	1.79235e7i	−0.350768	+	0.116272i
$67$		−	5.79621e7i		−	0.351404i	−0.984443	−	0.175702i	$-0.943780\pi$
$67$		−	5.79621e7i		−	0.351404i	0.984443	−	0.175702i	$-0.0562196\pi$
$68$	−5.68828e7	+	4.23657e7i	−0.322619	+	0.240284i
$69$		−	8.51157e7i		−	0.452052i
$70$	−1.28138e8	−	3.86566e8i	−0.637875	−	1.92434i
$71$	2.74912e8			1.28390			0.641950	−	0.766746i	$-0.278125\pi$
$71$	2.74912e8			1.28390			0.641950	+	0.766746i	$0.278125\pi$
$72$	−6.36745e7	+	9.09959e7i	−0.279235	+	0.399048i
$73$	−9.16969e7			−0.377921			−0.188961	−	0.981985i	$-0.560512\pi$
$73$	−9.16969e7			−0.377921			−0.188961	+	0.981985i	$0.560512\pi$
$74$	−3.81119e6	−	1.14976e7i	−0.0147747	−	0.0445722i
$75$			4.74196e8i			1.73054i
$76$	1.49724e8	+	2.01029e8i	0.514791	+	0.691191i
$77$			1.74571e8i			0.565930i
$78$	−6.41004e7	+	2.12478e7i	−0.196081	+	0.0649962i
$79$	2.02396e8			0.584627			0.292314	−	0.956322i	$-0.405575\pi$
$79$	2.02396e8			0.584627			0.292314	+	0.956322i	$0.405575\pi$
$80$	6.48774e8	+	1.93942e8i	1.77088	+	0.529379i
$81$	−1.06829e8			−0.275744
$82$	−3.13186e8	+	1.03814e8i	−0.764963	+	0.253568i
$83$		−	6.11053e8i		−	1.41328i	−0.707574	−	0.706639i	$-0.750210\pi$
$83$		−	6.11053e8i		−	1.41328i	0.707574	−	0.706639i	$-0.249790\pi$
$84$	−2.14117e8	−	2.87486e8i	−0.469238	−	0.630028i
$85$		−	3.57829e8i		−	0.743516i
$86$	2.82247e8	+	8.51483e8i	0.556399	+	1.67854i
$87$	−1.14193e8			−0.213700
$88$	−2.37819e8	−	1.66415e8i	−0.422742	−	0.295814i
$89$	−7.71588e8			−1.30356			−0.651779	−	0.758409i	$-0.725977\pi$
$89$	−7.71588e8			−1.30356			−0.651779	+	0.758409i	$0.725977\pi$
$90$	−1.76299e8	−	5.31859e8i	−0.283243	−	0.854487i
$91$			2.06949e8i			0.316357i
$92$	3.47831e8	−	2.59061e8i	0.506202	−	0.377014i
$93$		−	4.37845e8i		−	0.606942i
$94$	9.64363e8	−	3.19664e8i	1.27399	−	0.422298i
$95$	−1.26460e9			−1.59293
$96$	5.95759e8	−	1.76387e7i	0.715896	−	0.0211956i
$97$	1.08292e9			1.24200			0.621001	−	0.783810i	$-0.286726\pi$
$97$	1.08292e9			1.24200			0.621001	+	0.783810i	$0.286726\pi$
$98$	−1.76003e8	+	5.83408e7i	−0.192753	+	0.0638933i
$99$			2.40184e8i			0.251296i
$100$	−1.93784e9	+	1.44328e9i	−1.93784	+	1.44328i
$101$			6.22244e8i			0.594996i	0.954722	+	0.297498i	$0.0961522\pi$
$101$			6.22244e8i			0.594996i	−0.954722	+	0.297498i	$0.903848\pi$
$102$	−9.90997e7	−	2.98964e8i	−0.0906508	−	0.273475i
$103$	6.34170e8			0.555186			0.277593	−	0.960699i	$-0.410463\pi$
$103$	6.34170e8			0.555186			0.277593	+	0.960699i	$0.410463\pi$
$104$	−2.81929e8	−	1.97280e8i	−0.236314	−	0.165361i
$105$	1.80847e9			1.45198
$106$	3.45771e8	+	1.04312e9i	0.266019	+	0.802526i
$107$		−	1.54145e9i		−	1.13685i	−0.822735	−	0.568425i	$-0.807553\pi$
$107$		−	1.54145e9i		−	1.13685i	0.822735	−	0.568425i	$-0.192447\pi$
$108$	−8.99455e8	−	1.20766e9i	−0.636169	−	0.854160i
$109$			2.19786e9i			1.49135i	0.666309	+	0.745676i	$0.267873\pi$
$109$			2.19786e9i			1.49135i	−0.666309	+	0.745676i	$0.732127\pi$
$110$	1.39002e9	−	4.60761e8i	0.905222	−	0.300060i
$111$	5.37892e7			0.0336311
$112$	5.23140e8	−	1.75001e9i	0.314150	−	1.05089i
$113$	−5.43476e8			−0.313565			−0.156782	−	0.987633i	$-0.550112\pi$
$113$	−5.43476e8			−0.313565			−0.156782	+	0.987633i	$0.550112\pi$
$114$	−1.05657e9	+	3.50228e8i	−0.585902	+	0.194213i
$115$			2.18808e9i			1.16660i
$116$	−3.47563e8	−	4.66660e8i	−0.178227	−	0.239298i
$117$			2.84732e8i			0.140475i
$118$	2.98796e7	+	9.01407e7i	0.0141875	+	0.0428008i
$119$	−9.65210e8			−0.441225
$120$	−1.72398e9	+	2.46370e9i	−0.758956	+	1.08461i
$121$	1.73022e9			0.733783
$122$	−4.54695e8	−	1.37172e9i	−0.185823	−	0.560592i
$123$		−	1.46518e9i		−	0.577189i
$124$	1.78929e9	−	1.33264e9i	0.679645	−	0.506192i
$125$		−	7.14513e9i		−	2.61767i
$126$	−1.43464e9	+	4.75550e8i	−0.507079	+	0.168085i
$127$	−2.41305e9			−0.823093			−0.411547	−	0.911389i	$-0.635011\pi$
$127$	−2.41305e9			−0.823093			−0.411547	+	0.911389i	$0.635011\pi$
$128$	1.88535e9	+	2.38093e9i	0.620795	+	0.783973i
$129$	−3.98349e9			−1.26652
$130$	1.64784e9	−	5.46221e8i	0.506022	−	0.167735i
$131$			1.57746e9i			0.467990i	0.972238	+	0.233995i	$0.0751799\pi$
$131$			1.57746e9i			0.467990i	−0.972238	+	0.233995i	$0.924820\pi$
$132$	1.03375e9	−	7.69926e8i	0.296369	−	0.220733i
$133$			3.41114e9i			0.945295i
$134$	4.12662e8	+	1.24492e9i	0.110566	+	0.333557i
$135$	7.59698e9			1.96852
$136$	9.20115e8	−	1.31492e9i	0.230631	−	0.329589i
$137$	−6.39076e9			−1.54992			−0.774961	−	0.632009i	$-0.782231\pi$
$137$	−6.39076e9			−1.54992			−0.774961	+	0.632009i	$0.782231\pi$
$138$	6.05983e8	+	1.82813e9i	0.142234	+	0.429093i
$139$		−	2.45897e9i		−	0.558710i	−0.960188	−	0.279355i	$-0.909879\pi$
$139$		−	2.45897e9i		−	0.558710i	0.960188	−	0.279355i	$-0.0901206\pi$
$140$	5.50433e9	+	7.39045e9i	1.21096	+	1.62590i
$141$			4.51158e9i			0.961265i
$142$	−5.90462e9	+	1.95724e9i	−1.21869	+	0.403969i
$143$	−7.44153e8			−0.148816
$144$	7.19766e8	−	2.40776e9i	0.139496	−	0.466640i
$145$	2.93559e9			0.551492
$146$	1.96948e9	−	6.52838e8i	0.358727	−	0.118910i
$147$		−	8.23393e8i		−	0.145438i
$148$	1.63715e8	+	2.19814e8i	0.0280485	+	0.0376597i
$149$		−	3.84540e9i		−	0.639150i	−0.947561	−	0.319575i	$-0.896460\pi$
$149$		−	3.84540e9i		−	0.639150i	0.947561	−	0.319575i	$-0.103540\pi$
$150$	−3.37605e9	−	1.01849e10i	−0.544501	−	1.64265i
$151$	4.07627e9			0.638067			0.319034	−	0.947743i	$-0.396642\pi$
$151$	4.07627e9			0.638067			0.319034	+	0.947743i	$0.396642\pi$
$152$	−4.64704e9	−	3.25177e9i	−0.706123	−	0.494111i
$153$	−1.32799e9			−0.195922
$154$	−1.24286e9	−	3.74946e9i	−0.178065	−	0.537187i
$155$			1.12557e10i			1.56632i
$156$	1.22549e9	−	9.12728e8i	0.165671	−	0.123390i
$157$		−	7.59409e9i		−	0.997533i	−0.866736	−	0.498767i	$-0.833786\pi$
$157$		−	7.59409e9i		−	0.997533i	0.866736	−	0.498767i	$-0.166214\pi$
$158$	−4.34709e9	+	1.44096e9i	−0.554935	+	0.183948i
$159$	−4.88004e9			−0.605531
$160$	−1.53153e10	+	4.53441e8i	−1.84750	+	0.0546991i
$161$	5.90214e9			0.692298
$162$	2.29449e9	−	7.60572e8i	0.261740	−	0.0867606i
$163$		−	7.71277e9i		−	0.855788i	−0.903829	−	0.427894i	$-0.859256\pi$
$163$		−	7.71277e9i		−	0.855788i	0.903829	−	0.427894i	$-0.140744\pi$
$164$	5.98757e9	−	4.45948e9i	0.646328	−	0.481378i
$165$			6.50295e9i			0.683019i
$166$	4.35041e9	+	1.31243e10i	0.444676	+	1.34150i
$167$	1.01170e10			1.00653			0.503265	−	0.864132i	$-0.332132\pi$
$167$	1.01170e10			1.00653			0.503265	+	0.864132i	$0.332132\pi$
$168$	6.64560e9	+	4.65027e9i	0.643639	+	0.450388i
$169$	9.72232e9			0.916811
$170$	2.54757e9	+	7.68552e9i	0.233941	+	0.705753i
$171$			4.69324e9i			0.419750i
$172$	−1.21243e10	−	1.62788e10i	−1.05628	−	1.41823i
$173$			1.89724e10i			1.61033i	0.593053	+	0.805164i	$0.297922\pi$
$173$			1.89724e10i			1.61033i	−0.593053	+	0.805164i	$0.702078\pi$
$174$	2.45267e9	−	8.13003e8i	0.202846	−	0.0672389i
$175$	−3.28820e10			−2.65025
$176$	6.29272e9	+	1.88112e9i	0.494347	+	0.147778i
$177$	−4.21706e8			−0.0322946
$178$	1.65723e10	−	5.49334e9i	1.23735	−	0.410153i
$179$		−	1.72674e10i		−	1.25716i	−0.777746	−	0.628578i	$-0.783637\pi$
$179$		−	1.72674e10i		−	1.25716i	0.777746	−	0.628578i	$-0.216363\pi$
$180$	7.57317e9	+	1.01682e10i	0.537714	+	0.721968i
$181$		−	1.03363e10i		−	0.715830i	−0.933754	−	0.357915i	$-0.883488\pi$
$181$		−	1.03363e10i		−	0.715830i	0.933754	−	0.357915i	$-0.116512\pi$
$182$	−1.47338e9	−	4.44489e9i	−0.0995390	−	0.300289i
$183$	6.41733e9			0.422985
$184$	−5.62640e9	+	8.04056e9i	−0.361868	+	0.517137i
$185$	−1.38277e9			−0.0867913
$186$	3.11725e9	+	9.40411e9i	0.190969	+	0.576115i
$187$		−	3.47073e9i		−	0.207555i
$188$	−1.84369e10	+	1.37316e10i	−1.07641	+	0.801699i
$189$		−	2.04921e10i		−	1.16818i
$190$	2.71613e10	−	9.00336e9i	1.51203	−	0.501203i
$191$	−9.14299e9			−0.497094			−0.248547	−	0.968620i	$-0.579953\pi$
$191$	−9.14299e9			−0.497094			−0.248547	+	0.968620i	$0.579953\pi$
$192$	−1.26702e10	+	4.62037e9i	−0.672867	+	0.245370i
$193$	8.45502e8			0.0438639			0.0219319	−	0.999759i	$-0.493018\pi$
$193$	8.45502e8			0.0438639			0.0219319	+	0.999759i	$0.493018\pi$
$194$	−2.32591e10	+	7.70985e9i	−1.17892	+	0.390785i
$195$			7.70909e9i			0.381810i
$196$	3.36486e9	−	2.50611e9i	0.162860	−	0.121296i
$197$			2.12407e9i			0.100478i	0.998737	+	0.0502390i	$0.0159983\pi$
$197$			2.12407e9i			0.100478i	−0.998737	+	0.0502390i	$0.984002\pi$
$198$	−1.71000e9	−	5.15872e9i	−0.0790682	−	0.238533i
$199$	−2.92879e9			−0.132388			−0.0661941	−	0.997807i	$-0.521086\pi$
$199$	−2.92879e9			−0.132388			−0.0661941	+	0.997807i	$0.521086\pi$
$200$	3.13458e10	−	4.47955e10i	1.38530	−	1.97970i
$201$	−5.82411e9			−0.251679
$202$	−4.43008e9	−	1.33647e10i	−0.187211	−	0.564777i
$203$		−	7.91848e9i		−	0.327272i
$204$	4.25696e9	+	5.71566e9i	0.172093	+	0.231063i
$205$			3.76656e10i			1.48954i
$206$	−1.36208e10	+	4.51499e9i	−0.526988	+	0.174684i
$207$	8.12051e9			0.307409
$208$	7.45986e9	+	2.23002e9i	0.276341	+	0.0826084i
$209$	−1.22659e10			−0.444673
$210$	−3.88427e10	+	1.28755e10i	−1.37823	+	0.456852i
$211$			3.16571e10i			1.09951i	0.835325	+	0.549757i	$0.185280\pi$
$211$			3.16571e10i			1.09951i	−0.835325	+	0.549757i	$0.814720\pi$
$212$	−1.48531e10	−	1.99427e10i	−0.505016	−	0.678065i
$213$		−	2.76236e10i		−	0.919542i
$214$	1.09744e10	+	3.31076e10i	0.357700	+	1.07911i
$215$	1.02404e11			3.26847
$216$	2.79166e10	+	1.95347e10i	0.872612	+	0.610612i
$217$	3.03613e10			0.929505
$218$	−1.56477e10	−	4.72059e10i	−0.469241	−	1.41561i
$219$			9.21383e9i			0.270671i
$220$	−2.65748e10	+	1.97926e10i	−0.764835	+	0.569641i
$221$		−	4.11446e9i		−	0.116024i
$222$	−1.15529e9	+	3.82953e8i	−0.0319230	+	0.0105818i
$223$	−4.92453e10			−1.33350			−0.666750	−	0.745282i	$-0.732315\pi$
$223$	−4.92453e10			−1.33350			−0.666750	+	0.745282i	$0.732315\pi$
$224$	1.22311e9	+	4.13115e10i	0.0324601	+	1.09636i
$225$	−4.52409e10			−1.17682
$226$	1.16729e10	−	3.86929e9i	0.297639	−	0.0986605i
$227$			5.67209e10i			1.41784i	0.705290	+	0.708919i	$0.250817\pi$
$227$			5.67209e10i			1.41784i	−0.705290	+	0.708919i	$0.749183\pi$
$228$	2.01997e10	−	1.50445e10i	0.495037	−	0.368698i
$229$		−	3.33645e9i		−	0.0801723i	−0.999196	−	0.0400862i	$-0.987237\pi$
$229$		−	3.33645e9i		−	0.0801723i	0.999196	−	0.0400862i	$-0.0127632\pi$
$230$	−1.55781e10	−	4.69960e10i	−0.367062	−	1.10735i
$231$	1.75411e10			0.405324
$232$	1.07874e10	+	7.54852e9i	0.244468	+	0.171067i
$233$	−4.60006e10			−1.02250			−0.511249	−	0.859433i	$-0.670817\pi$
$233$	−4.60006e10			−1.02250			−0.511249	+	0.859433i	$0.670817\pi$
$234$	−2.02716e9	−	6.11553e9i	−0.0441994	−	0.133341i
$235$		−	1.15980e11i		−	2.48072i
$236$	−1.28352e9	−	1.72333e9i	−0.0269338	−	0.0361630i
$237$		−	2.03370e10i		−	0.418716i
$238$	2.07310e10	−	6.87183e9i	0.418816	−	0.138828i
$239$	−4.05955e10			−0.804798			−0.402399	−	0.915464i	$-0.631824\pi$
$239$	−4.05955e10			−0.804798			−0.402399	+	0.915464i	$0.631824\pi$
$240$	1.94876e10	−	6.51898e10i	0.379147	−	1.26832i
$241$	3.45208e10			0.659181			0.329590	−	0.944124i	$-0.393089\pi$
$241$	3.45208e10			0.659181			0.329590	+	0.944124i	$0.393089\pi$
$242$	−3.71620e10	+	1.23184e10i	−0.696515	+	0.230879i
$243$		−	4.71541e10i		−	0.867544i
$244$	1.95320e10	+	2.62249e10i	0.352771	+	0.473652i
$245$			2.11671e10i			0.375331i
$246$	1.04314e10	+	3.14694e10i	0.181608	+	0.547874i
$247$	−1.45409e10			−0.248573
$248$	−2.89428e10	+	4.13616e10i	−0.485857	+	0.694327i
$249$	−6.13995e10			−1.01220
$250$	5.08700e10	+	1.53465e11i	0.823629	+	2.48472i
$251$			7.83857e10i			1.24654i	0.782008	+	0.623268i	$0.214196\pi$
$251$			7.83857e10i			1.24654i	−0.782008	+	0.623268i	$0.785804\pi$
$252$	2.74278e10	−	2.04279e10i	0.428438	−	0.319096i
$253$			2.12231e10i			0.325661i
$254$	5.18279e10	−	1.71797e10i	0.781289	−	0.258979i
$255$	−3.59552e10			−0.532513
$256$	−5.74451e10	−	3.77151e10i	−0.835936	−	0.548828i
$257$	1.06489e11			1.52267			0.761337	−	0.648356i	$-0.224543\pi$
$257$	1.06489e11			1.52267			0.761337	+	0.648356i	$0.224543\pi$
$258$	8.55582e10	−	2.83606e10i	1.20219	−	0.398498i
$259$			3.72988e9i			0.0515046i
$260$	−3.15038e10	+	2.34637e10i	−0.427545	+	0.318431i
$261$		−	1.08947e10i		−	0.145322i
$262$	−1.12307e10	−	3.38809e10i	−0.147249	−	0.444221i
$263$	−6.39865e8			−0.00824684			−0.00412342	−	0.999991i	$-0.501313\pi$
$263$	−6.39865e8			−0.00824684			−0.00412342	+	0.999991i	$0.501313\pi$
$264$	−1.67216e10	+	2.38964e10i	−0.211865	+	0.302772i
$265$	1.25452e11			1.56268
$266$	−2.42857e10	−	7.32652e10i	−0.297429	−	0.897284i
$267$			7.75302e10i			0.933620i
$268$	−1.77265e10	−	2.38007e10i	−0.209902	−	0.281827i
$269$		−	9.60820e10i		−	1.11881i	−0.828894	−	0.559406i	$-0.811029\pi$
$269$		−	9.60820e10i		−	1.11881i	0.828894	−	0.559406i	$-0.188971\pi$
$270$	−1.63169e11	+	5.40869e10i	−1.86854	+	0.619377i
$271$	−9.78435e10			−1.10197			−0.550986	−	0.834515i	$-0.685748\pi$
$271$	−9.78435e10			−1.10197			−0.550986	+	0.834515i	$0.685748\pi$
$272$	−1.04008e10	+	3.47928e10i	−0.115215	+	0.385416i
$273$	2.07945e10			0.226578
$274$	1.37262e11	−	4.54992e10i	1.47120	−	0.487670i
$275$		−	1.18238e11i		−	1.24669i
$276$	−2.60308e10	−	3.49506e10i	−0.270021	−	0.362547i
$277$			1.61396e11i			1.64716i	0.567202	+	0.823579i	$0.308026\pi$
$277$			1.61396e11i			1.64716i	−0.567202	+	0.823579i	$0.691974\pi$
$278$	1.75067e10	+	5.28142e10i	0.175793	+	0.530333i
$279$	4.17728e10			0.412738
$280$	−1.70840e11	−	1.19545e11i	−1.66103	−	1.16231i
$281$	−2.71451e10			−0.259724			−0.129862	−	0.991532i	$-0.541453\pi$
$281$	−2.71451e10			−0.259724			−0.129862	+	0.991532i	$0.541453\pi$
$282$	−3.21203e10	−	9.69006e10i	−0.302454	−	0.912443i
$283$			2.80153e10i			0.259631i	0.991538	+	0.129815i	$0.0414385\pi$
$283$			2.80153e10i			0.259631i	−0.991538	+	0.129815i	$0.958562\pi$
$284$	1.12886e11	−	8.40761e10i	1.02969	−	0.766902i
$285$			1.27069e11i			1.14087i
$286$	1.59831e10	−	5.29801e9i	0.141258	−	0.0468237i
$287$	1.01599e11			0.883940
$288$	1.68283e9	+	5.68387e10i	0.0144136	+	0.486831i
$289$	−9.93980e10			−0.838180
$290$	−6.30511e10	+	2.09000e10i	−0.523482	+	0.173522i
$291$		−	1.08813e11i		−	0.889534i
$292$	−3.76530e10	+	2.80435e10i	−0.303094	+	0.225741i
$293$		−	2.49001e10i		−	0.197377i	−0.995118	−	0.0986884i	$-0.968535\pi$
$293$		−	2.49001e10i		−	0.197377i	0.995118	−	0.0986884i	$-0.0314647\pi$
$294$	5.86217e9	+	1.76850e10i	0.0457610	+	0.138052i
$295$	1.08409e10			0.0833421
$296$	−5.08126e9	−	3.55562e9i	−0.0384733	−	0.0269217i
$297$	7.36861e10			0.549518
$298$	2.73774e10	+	8.25921e10i	0.201103	+	0.606688i
$299$			2.51594e10i			0.182046i
$300$	1.45023e11	+	1.94717e11i	1.03369	+	1.38790i
$301$		−	2.76226e11i		−	1.93961i
$302$	−8.75508e10	+	2.90211e10i	−0.605660	+	0.200762i
$303$	6.25239e10			0.426142
$304$	1.22961e11	+	3.67575e10i	0.825727	+	0.246840i
$305$	−1.64971e11			−1.09159
$306$	2.85228e10	−	9.45466e9i	0.185971	−	0.0616452i
$307$			1.71738e11i			1.10343i	0.834034	+	0.551713i	$0.186026\pi$
$307$			1.71738e11i			1.10343i	−0.834034	+	0.551713i	$0.813974\pi$
$308$	5.33887e10	+	7.16830e10i	0.338042	+	0.453877i
$309$		−	6.37223e10i		−	0.397629i
$310$	−8.01356e10	−	2.41753e11i	−0.492831	−	1.48677i
$311$	−1.24783e11			−0.756371			−0.378185	−	0.925730i	$-0.623452\pi$
$311$	−1.24783e11			−0.756371			−0.378185	+	0.925730i	$0.623452\pi$
$312$	−1.98230e10	+	2.83286e10i	−0.118433	+	0.169250i
$313$	−2.95278e10			−0.173893			−0.0869463	−	0.996213i	$-0.527711\pi$
$313$	−2.95278e10			−0.173893			−0.0869463	+	0.996213i	$0.527711\pi$
$314$	5.40663e10	+	1.63107e11i	0.313865	+	0.946869i
$315$			1.72538e11i			0.987388i
$316$	8.31087e10	−	6.18984e10i	0.468872	−	0.349211i
$317$			1.20582e11i			0.670678i	0.942098	+	0.335339i	$0.108851\pi$
$317$			1.20582e11i			0.670678i	−0.942098	+	0.335339i	$0.891149\pi$
$318$	1.04814e11	−	3.47436e10i	0.574777	−	0.190525i
$319$	2.84735e10			0.153951
$320$	3.25716e11	−	1.18777e11i	1.73646	−	0.633221i
$321$	−1.54887e11			−0.814223
$322$	−1.26767e11	+	4.20205e10i	−0.657137	+	0.217826i
$323$		−	6.78187e10i		−	0.346687i
$324$	−4.38666e10	+	3.26714e10i	−0.221147	+	0.164708i
$325$		−	1.40168e11i		−	0.696906i
$326$	5.49112e10	+	1.65656e11i	0.269266	+	0.812323i
$327$	2.20844e11			1.06812
$328$	−9.68527e10	+	1.38410e11i	−0.462040	+	0.660291i
$329$	−3.12845e11			−1.47214
$330$	−4.62979e10	−	1.39672e11i	−0.214906	−	0.648329i
$331$		−	4.18670e11i		−	1.91711i	−0.284913	−	0.958553i	$-0.591965\pi$
$331$		−	4.18670e11i		−	1.91711i	0.284913	−	0.958553i	$-0.408035\pi$
$332$	−1.86878e11	−	2.50914e11i	−0.844182	−	1.13345i
$333$			5.13179e9i			0.0228702i
$334$	−2.17294e11	+	7.20281e10i	−0.955409	+	0.316696i
$335$	1.49721e11			0.649504
$336$	−1.75843e11	−	5.25659e10i	−0.752660	−	0.224997i
$337$	2.95362e11			1.24744			0.623721	−	0.781647i	$-0.285620\pi$
$337$	2.95362e11			1.24744			0.623721	+	0.781647i	$0.285620\pi$
$338$	−2.08818e11	+	6.92183e10i	−0.870247	+	0.288467i
$339$			5.46092e10i			0.224578i
$340$	−1.09434e11	−	1.46933e11i	−0.444119	−	0.596301i
$341$			1.09174e11i			0.437245i
$342$	−3.34137e10	−	1.00802e11i	−0.132071	−	0.398431i
$343$	−2.24073e11			−0.874111
$344$	3.76306e11	+	2.63321e11i	1.44886	+	1.01385i
$345$	2.19862e11			0.835533
$346$	−1.35074e11	−	4.07492e11i	−0.506676	−	1.52854i
$347$			1.55047e10i			0.0574093i	0.999588	+	0.0287046i	$0.00913822\pi$
$347$			1.55047e10i			0.0574093i	−0.999588	+	0.0287046i	$0.990862\pi$
$348$	−4.68907e10	+	3.49237e10i	−0.171388	+	0.127648i
$349$			3.06969e11i			1.10759i	0.832652	+	0.553797i	$0.186822\pi$
$349$			3.06969e11i			1.10759i	−0.832652	+	0.553797i	$0.813178\pi$
$350$	7.06246e11	−	2.34104e11i	2.51565	−	0.833879i
$351$	8.73531e10			0.307182
$352$	−1.48549e11	+	4.39810e9i	−0.515736	+	0.0152694i
$353$	2.99671e11			1.02721			0.513604	−	0.858028i	$-0.328310\pi$
$353$	2.99671e11			1.02721			0.513604	+	0.858028i	$0.328310\pi$
$354$	9.05747e9	−	3.00234e9i	0.0306544	−	0.0101612i
$355$			7.10124e11i			2.37305i
$356$	−3.16833e11	+	2.35974e11i	−1.04546	+	0.778644i
$357$			9.69856e10i			0.316010i
$358$	1.22936e11	+	3.70873e11i	0.395554	+	1.19331i
$359$	−4.04368e11			−1.28485			−0.642424	−	0.766349i	$-0.722071\pi$
$359$	−4.04368e11			−1.28485			−0.642424	+	0.766349i	$0.722071\pi$
$360$	−2.35051e11	−	1.64477e11i	−0.737565	−	0.516113i
$361$	8.30100e10			0.257246
$362$	7.35893e10	+	2.22004e11i	0.225230	+	0.679474i
$363$		−	1.73855e11i		−	0.525542i
$364$	6.32910e10	+	8.49784e10i	0.188967	+	0.253719i
$365$		−	2.36861e11i		−	0.698516i
$366$	−1.37833e11	+	4.56884e10i	−0.401502	+	0.133089i
$367$	5.07965e11			1.46163			0.730813	−	0.682578i	$-0.239141\pi$
$367$	5.07965e11			1.46163			0.730813	+	0.682578i	$0.239141\pi$
$368$	6.35998e10	−	2.12754e11i	0.180776	−	0.604731i
$369$	1.39786e11			0.392506
$370$	2.96993e10	−	9.84465e9i	0.0823833	−	0.0273082i
$371$		−	3.38395e11i		−	0.927345i
$372$	−1.33906e11	−	1.79790e11i	−0.362540	−	0.486768i
$373$		−	6.94617e10i		−	0.185804i	−0.995675	−	0.0929022i	$-0.970386\pi$
$373$		−	6.94617e10i		−	0.185804i	0.995675	−	0.0929022i	$-0.0296144\pi$
$374$	2.47099e10	+	7.45449e10i	0.0653054	+	0.197013i
$375$	−7.17953e11			−1.87480
$376$	2.98229e11	−	4.26192e11i	0.769493	−	1.09966i
$377$	3.37546e10			0.0860591
$378$	1.45894e11	+	4.40134e11i	0.367557	+	1.10885i
$379$		−	4.45070e11i		−	1.10803i	−0.832507	−	0.554015i	$-0.813095\pi$
$379$		−	4.45070e11i		−	1.10803i	0.832507	−	0.554015i	$-0.186905\pi$
$380$	−5.19277e11	+	3.86752e11i	−1.27753	+	0.951494i
$381$			2.42466e11i			0.589507i
$382$	1.96375e11	−	6.50938e10i	0.471847	−	0.156406i
$383$	−4.50375e11			−1.06950			−0.534749	−	0.845011i	$-0.679594\pi$
$383$	−4.50375e11			−1.06950			−0.534749	+	0.845011i	$0.679594\pi$
$384$	2.39239e11	−	1.89443e11i	0.561489	−	0.444619i
$385$	−4.50932e11			−1.04601
$386$	−1.81598e10	+	6.01957e9i	−0.0416360	+	0.0138014i
$387$		−	3.80047e11i		−	0.861268i
$388$	4.44672e11	−	3.31187e11i	0.996087	−	0.741875i
$389$		−	5.76192e11i		−	1.27583i	−0.770106	−	0.637916i	$-0.779797\pi$
$389$		−	5.76192e11i		−	1.27583i	0.770106	−	0.637916i	$-0.220203\pi$
$390$	−5.48850e10	−	1.65577e11i	−0.120133	−	0.362418i
$391$	−1.17344e11			−0.253901
$392$	−5.44287e10	+	7.77829e10i	−0.116424	+	0.166378i
$393$	1.58505e11			0.335179
$394$	−1.51224e10	−	4.56212e10i	−0.0316145	−	0.0953748i
$395$			5.22807e11i			1.08057i
$396$	7.34552e10	+	9.86255e10i	0.150105	+	0.201540i
$397$			3.22788e11i			0.652169i	0.945341	+	0.326084i	$0.105729\pi$
$397$			3.22788e11i			0.652169i	−0.945341	+	0.326084i	$0.894271\pi$
$398$	6.29051e10	−	2.08516e10i	0.125664	−	0.0416548i
$399$	3.42756e11			0.677030
$400$	−3.54327e11	+	1.18529e12i	−0.692045	+	2.31503i
$401$	1.47838e11			0.285520			0.142760	−	0.989757i	$-0.454402\pi$
$401$	1.47838e11			0.285520			0.142760	+	0.989757i	$0.454402\pi$
$402$	1.25091e11	−	4.14649e10i	0.238897	−	0.0791887i
$403$			1.29423e11i			0.244421i
$404$	1.90300e11	+	2.55509e11i	0.355404	+	0.477188i
$405$		−	2.75949e11i		−	0.509661i
$406$	5.63758e10	+	1.70074e11i	0.102973	+	0.310650i
$407$	−1.34120e10			−0.0242281
$408$	−1.32125e11	−	9.24545e10i	−0.236055	−	0.165180i
$409$	−7.24078e11			−1.27947			−0.639735	−	0.768595i	$-0.720956\pi$
$409$	−7.24078e11			−1.27947			−0.639735	+	0.768595i	$0.720956\pi$
$410$	−2.68161e11	−	8.08990e11i	−0.468672	−	1.41389i
$411$			6.42153e11i			1.11007i
$412$	2.60406e11	−	1.93948e11i	0.445260	−	0.331625i
$413$		−	2.92422e10i		−	0.0494578i
$414$	−1.74414e11	+	5.78141e10i	−0.291796	+	0.0967236i
$415$	1.57841e12			2.61218
$416$	−1.76101e11	+	5.21384e9i	−0.288298	+	0.00853567i
$417$	−2.47081e11			−0.400153
$418$	2.63449e11	−	8.73272e10i	0.422088	−	0.139912i
$419$		−	6.10316e11i		−	0.967368i	−0.875243	−	0.483684i	$-0.839298\pi$
$419$		−	6.10316e11i		−	0.967368i	0.875243	−	0.483684i	$-0.160702\pi$
$420$	7.42603e11	−	5.53083e11i	1.16449	−	0.867298i
$421$			7.16040e11i			1.11088i	0.831556	+	0.555441i	$0.187450\pi$
$421$			7.16040e11i			1.11088i	−0.831556	+	0.555441i	$0.812550\pi$
$422$	−2.25384e11	−	6.79938e11i	−0.345953	−	1.04367i
$423$	−4.30430e11			−0.653689
$424$	4.60999e11	+	3.22585e11i	0.692714	+	0.484728i
$425$	6.53744e11			0.971981
$426$	1.96667e11	+	5.93304e11i	0.289326	+	0.872839i
$427$			4.44995e11i			0.647783i
$428$	−4.71421e11	−	6.32959e11i	−0.679066	−	0.911756i
$429$			7.47735e10i			0.106584i
$430$	−2.19946e12	+	7.29070e11i	−3.10247	+	1.02840i
$431$	4.78823e11			0.668385			0.334193	−	0.942505i	$-0.391536\pi$
$431$	4.78823e11			0.668385			0.334193	+	0.942505i	$0.391536\pi$
$432$	−7.38677e11	−	2.20817e11i	−1.02042	−	0.305039i
$433$	−3.13312e11			−0.428334			−0.214167	−	0.976797i	$-0.568704\pi$
$433$	−3.13312e11			−0.428334			−0.214167	+	0.976797i	$0.568704\pi$
$434$	−6.52106e11	+	2.16158e11i	−0.882296	+	0.292461i
$435$		−	2.94972e11i		−	0.394984i
$436$	6.72168e11	+	9.02494e11i	0.890817	+	1.19607i
$437$			4.14703e11i			0.543965i
$438$	−6.55981e10	−	1.97896e11i	−0.0851643	−	0.256924i
$439$	6.95985e11			0.894354			0.447177	−	0.894445i	$-0.352429\pi$
$439$	6.95985e11			0.894354			0.447177	+	0.894445i	$0.352429\pi$
$440$	4.29864e11	−	6.14310e11i	0.546757	−	0.781358i
$441$	7.85563e10			0.0989025
$442$	2.92930e10	+	8.83711e10i	0.0365059	+	0.110131i
$443$			3.55482e11i			0.438531i	0.975665	+	0.219266i	$0.0703661\pi$
$443$			3.55482e11i			0.438531i	−0.975665	+	0.219266i	$0.929634\pi$
$444$	2.20872e10	−	1.64503e10i	0.0269722	−	0.0200886i
$445$		−	1.99308e12i		−	2.40938i
$446$	1.05770e12	−	3.50603e11i	1.26577	−	0.419574i
$447$	−3.86391e11			−0.457765
$448$	−3.20388e11	−	8.78587e11i	−0.375773	−	1.03047i
$449$	−8.15188e11			−0.946562			−0.473281	−	0.880911i	$-0.656931\pi$
$449$	−8.15188e11			−0.946562			−0.473281	+	0.880911i	$0.656931\pi$
$450$	9.71693e11	−	3.22094e11i	1.11705	−	0.370277i
$451$			3.65334e11i			0.415811i
$452$	−2.23165e11	+	1.66211e11i	−0.251479	+	0.187299i
$453$		−	4.09589e11i		−	0.456990i
$454$	−4.03826e11	−	1.21826e12i	−0.446111	−	1.34583i
$455$	−5.34568e11			−0.584725
$456$	−3.26743e11	+	4.66941e11i	−0.353887	+	0.505732i
$457$	−5.94548e11			−0.637623			−0.318811	−	0.947818i	$-0.603284\pi$
$457$	−5.94548e11			−0.637623			−0.318811	+	0.947818i	$0.603284\pi$
$458$	2.37539e10	+	7.16608e10i	0.0252255	+	0.0761004i
$459$			4.07414e11i			0.428429i
$460$	6.69179e11	+	8.98481e11i	0.696838	+	0.935618i
$461$			1.42516e12i			1.46964i	0.678265	+	0.734818i	$0.262732\pi$
$461$			1.42516e12i			1.46964i	−0.678265	+	0.734818i	$0.737268\pi$
$462$	−3.76751e11	+	1.24884e11i	−0.384738	+	0.127532i
$463$	−1.04996e12			−1.06183			−0.530917	−	0.847424i	$-0.678153\pi$
$463$	−1.04996e12			−1.06183			−0.530917	+	0.847424i	$0.678153\pi$
$464$	−2.85436e11	−	8.53272e10i	−0.285876	−	0.0854588i
$465$	1.13099e12			1.12182
$466$	9.88010e11	−	3.27503e11i	0.970565	−	0.321720i
$467$		−	1.15656e11i		−	0.112523i	−0.998416	−	0.0562616i	$-0.982082\pi$
$467$		−	1.15656e11i		−	0.112523i	0.998416	−	0.0562616i	$-0.0179181\pi$
$468$	8.70793e10	+	1.16918e11i	0.0839090	+	0.112661i
$469$		−	4.03859e11i		−	0.385436i
$470$	8.25722e11	+	2.49104e12i	0.780537	+	2.35473i
$471$	−7.63065e11			−0.714443
$472$	3.98369e10	+	2.78760e10i	0.0369443	+	0.0258518i
$473$	9.93261e11			0.912406
$474$	1.44790e11	+	4.36802e11i	0.131745	+	0.397449i
$475$		−	2.31039e12i		−	2.08240i
$476$	−3.96339e11	+	2.95189e11i	−0.353863	+	0.263554i
$477$		−	4.65583e11i		−	0.411779i
$478$	8.71917e11	−	2.89020e11i	0.763923	−	0.253223i
$479$	1.37302e12			1.19170			0.595849	−	0.803096i	$-0.296816\pi$
$479$	1.37302e12			1.19170			0.595849	+	0.803096i	$0.296816\pi$
$480$	4.55623e10	+	1.53890e12i	0.0391760	+	1.32320i
$481$	−1.58996e10			−0.0135436
$482$	−7.41444e11	+	2.45772e11i	−0.625701	+	0.207406i
$483$		−	5.93056e11i		−	0.495831i
$484$	7.10472e11	−	5.29152e11i	0.588495	−	0.438305i
$485$			2.79727e12i			2.29561i
$486$	3.35715e11	+	1.01279e12i	0.272965	+	0.823482i
$487$	−1.53458e12			−1.23626			−0.618131	−	0.786075i	$-0.712110\pi$
$487$	−1.53458e12			−1.23626			−0.618131	+	0.786075i	$0.712110\pi$
$488$	−6.06221e11	−	4.24205e11i	−0.483885	−	0.338599i
$489$	−7.74990e11			−0.612923
$490$	−1.50700e11	−	4.54631e11i	−0.118095	−	0.356268i
$491$		−	5.12475e11i		−	0.397929i	−0.980007	−	0.198965i	$-0.936242\pi$
$491$		−	5.12475e11i		−	0.397929i	0.980007	−	0.198965i	$-0.0637579\pi$
$492$	−4.48095e11	−	6.01639e11i	−0.344768	−	0.462907i
$493$			1.57431e11i			0.120027i
$494$	3.12312e11	−	1.03524e11i	0.235949	−	0.0782115i
$495$	−6.20418e11			−0.464473
$496$	3.27165e11	−	1.09443e12i	0.242716	−	0.811934i
$497$	1.91549e12			1.40824
$498$	1.31875e12	−	4.37135e11i	0.960794	−	0.318481i
$499$			2.45745e12i			1.77432i	0.461463	+	0.887159i	$0.347325\pi$
$499$			2.45745e12i			1.77432i	−0.461463	+	0.887159i	$0.652675\pi$
$500$	−2.18519e12	−	2.93397e12i	−1.56359	−	2.09938i
$501$		−	1.01657e12i		−	0.720887i
$502$	−5.58069e11	−	1.68358e12i	−0.392212	−	1.18323i
$503$	−2.11765e11			−0.147502			−0.0737512	−	0.997277i	$-0.523497\pi$
$503$	−2.11765e11			−0.147502			−0.0737512	+	0.997277i	$0.523497\pi$
$504$	−4.43662e11	+	6.34027e11i	−0.306277	+	0.437694i
$505$	−1.60731e12			−1.09974
$506$	−1.51098e11	−	4.55833e11i	−0.102467	−	0.309121i
$507$		−	9.76913e11i		−	0.656629i
$508$	−9.90857e11	+	7.37979e11i	−0.660122	+	0.491652i
$509$		−	2.27707e12i		−	1.50365i	−0.659363	−	0.751824i	$-0.729174\pi$
$509$		−	2.27707e12i		−	1.50365i	0.659363	−	0.751824i	$-0.270826\pi$
$510$	7.72252e11	−	2.55984e11i	0.505467	−	0.167551i
$511$	−6.38911e11			−0.414521
$512$	1.50233e12	+	4.01071e11i	0.966163	+	0.257933i
$513$	1.43984e12			0.917881
$514$	−2.28720e12	+	7.58153e11i	−1.44534	+	0.479097i
$515$			1.63812e12i			1.02616i
$516$	−1.63572e12	+	1.21827e12i	−1.01575	+	0.756517i
$517$		−	1.12494e12i		−	0.692501i
$518$	−2.65550e10	−	8.01111e10i	−0.0162055	−	0.0488888i
$519$	1.90637e12			1.15333
$520$	5.09593e11	−	7.28249e11i	0.305639	−	0.436782i
$521$	3.15742e12			1.87742			0.938712	−	0.344703i	$-0.112020\pi$
$521$	3.15742e12			1.87742			0.938712	+	0.344703i	$0.112020\pi$
$522$	7.75650e10	+	2.33998e11i	0.0457245	+	0.137942i
$523$			6.70464e11i			0.391848i	0.980619	+	0.195924i	$0.0627706\pi$
$523$			6.70464e11i			0.391848i	−0.980619	+	0.195924i	$0.937229\pi$
$524$	4.82431e11	+	6.47742e11i	0.279541	+	0.375328i
$525$			3.30403e12i			1.89814i
$526$	1.37431e10	−	4.55553e9i	0.00782799	−	0.00259480i
$527$	−6.03629e11			−0.340896
$528$	1.89018e11	−	6.32302e11i	0.105840	−	0.354056i
$529$	−1.08361e12			−0.601621
$530$	−2.69448e12	+	8.93159e11i	−1.48332	+	0.491685i
$531$		−	4.02330e10i		−	0.0219613i
$532$	1.04323e12	+	1.40070e12i	0.564646	+	0.758128i
$533$			4.33094e11i			0.232440i
$534$	−5.51978e11	−	1.66521e12i	−0.293756	−	0.886202i
$535$	3.98172e12			2.10125
$536$	5.50182e11	+	3.84991e11i	0.287915	+	0.201469i
$537$	−1.73506e12			−0.900387
$538$	6.84058e11	+	2.06367e12i	0.352025	+	1.06199i
$539$			2.05308e11i			0.104775i
$540$	3.11951e12	−	2.32338e12i	1.57875	−	1.17584i
$541$			6.87645e11i			0.345125i	0.984999	+	0.172562i	$0.0552047\pi$
$541$			6.87645e11i			0.345125i	−0.984999	+	0.172562i	$0.944795\pi$
$542$	2.10150e12	−	6.96599e11i	1.04600	−	0.346726i
$543$	−1.03860e12			−0.512685
$544$	−2.43173e10	−	8.21335e11i	−0.0119048	−	0.402092i
$545$	−5.67726e12			−2.75648
$546$	−4.46629e11	+	1.48047e11i	−0.215070	+	0.0712908i
$547$		−	2.73174e12i		−	1.30466i	−0.757936	−	0.652328i	$-0.773792\pi$
$547$		−	2.73174e12i		−	1.30466i	0.757936	−	0.652328i	$-0.226208\pi$
$548$	−2.62420e12	+	1.95448e12i	−1.24304	+	0.925803i
$549$			6.12249e11i			0.287642i
$550$	8.41798e11	+	2.53954e12i	0.392262	+	1.18338i
$551$	5.56377e11			0.257150
$552$	8.07927e11	+	5.65348e11i	0.370379	+	0.259173i
$553$	1.41022e12			0.641245
$554$	−1.14907e12	−	3.46650e12i	−0.518264	−	1.56350i
$555$			1.38942e11i			0.0621608i
$556$	−7.52024e11	−	1.00971e12i	−0.333730	−	0.448086i
$557$		−	3.59464e12i		−	1.58236i	−0.611580	−	0.791182i	$-0.709466\pi$
$557$		−	3.59464e12i		−	1.58236i	0.611580	−	0.791182i	$-0.290534\pi$
$558$	−8.97204e11	+	2.97403e11i	−0.391776	+	0.129865i
$559$	1.17749e12			0.510038
$560$	4.52043e12	+	1.35132e12i	1.94238	+	0.580647i
$561$	−3.48744e11			−0.148653
$562$	5.83027e11	−	1.93260e11i	0.246533	−	0.0817200i
$563$		−	4.60263e11i		−	0.193072i	−0.995330	−	0.0965358i	$-0.969224\pi$
$563$		−	4.60263e11i		−	0.193072i	0.995330	−	0.0965358i	$-0.0307762\pi$
$564$	1.37977e12	+	1.85257e12i	0.574185	+	0.770936i
$565$		−	1.40385e12i		−	0.579565i
$566$	−1.99455e11	−	6.01717e11i	−0.0816906	−	0.246444i
$567$	−7.44347e11			−0.302449
$568$	−1.82600e12	+	2.60950e12i	−0.736094	+	1.05194i
$569$	−1.91911e12			−0.767527			−0.383764	−	0.923431i	$-0.625372\pi$
$569$	−1.91911e12			−0.767527			−0.383764	+	0.923431i	$0.625372\pi$
$570$	−9.04671e11	−	2.72921e12i	−0.358966	−	1.08293i
$571$			2.01838e12i			0.794586i	0.917692	+	0.397293i	$0.130050\pi$
$571$			2.01838e12i			0.794586i	−0.917692	+	0.397293i	$0.869950\pi$
$572$	−3.05568e11	+	2.27583e11i	−0.119351	+	0.0888912i
$573$			9.18701e11i			0.356023i
$574$	−2.18217e12	+	7.23340e11i	−0.839046	+	0.278124i
$575$	−3.99757e12			−1.52507
$576$	−4.40808e11	−	1.20881e12i	−0.166859	−	0.457570i
$577$	−6.91957e11			−0.259889			−0.129945	−	0.991521i	$-0.541480\pi$
$577$	−6.91957e11			−0.259889			−0.129945	+	0.991521i	$0.541480\pi$
$578$	2.13489e12	−	7.07667e11i	0.795610	−	0.263726i
$579$		−	8.49572e10i		−	0.0314157i
$580$	1.20543e12	−	8.97788e11i	0.442298	−	0.329419i
$581$		−	4.25760e12i		−	1.55015i
$582$	7.74697e11	+	2.33711e12i	0.279884	+	0.844355i
$583$	1.21681e12			0.436229
$584$	6.09061e11	−	8.70396e11i	0.216672	−	0.309641i
$585$	−7.35490e11			−0.259642
$586$	1.77277e11	+	5.34808e11i	0.0621029	+	0.187352i
$587$			1.99542e12i			0.693686i	0.937923	+	0.346843i	$0.112746\pi$
$587$			1.99542e12i			0.693686i	−0.937923	+	0.346843i	$0.887254\pi$
$588$	−2.51817e11	−	3.38106e11i	−0.0868736	−	0.116642i
$589$			2.13328e12i			0.730347i
$590$	−2.32842e11	+	7.71817e10i	−0.0791092	+	0.0262229i
$591$	2.13430e11			0.0719633
$592$	1.34451e11	+	4.01922e10i	0.0449899	+	0.0134491i
$593$	5.19417e12			1.72492			0.862462	−	0.506121i	$-0.168921\pi$
$593$	5.19417e12			1.72492			0.862462	+	0.506121i	$0.168921\pi$
$594$	−1.58264e12	+	5.24610e11i	−0.521608	+	0.172901i
$595$		−	2.49323e12i		−	0.815521i
$596$	−1.17603e12	−	1.57901e12i	−0.381778	−	0.512599i
$597$			2.94289e11i			0.0948177i
$598$	−1.79123e11	−	5.40379e11i	−0.0572792	−	0.172800i
$599$	4.47443e12			1.42010			0.710048	−	0.704154i	$-0.248673\pi$
$599$	4.47443e12			1.42010			0.710048	+	0.704154i	$0.248673\pi$
$600$	−4.50112e12	−	3.14967e12i	−1.41788	−	0.992165i
$601$	3.10552e12			0.970955			0.485477	−	0.874249i	$-0.338646\pi$
$601$	3.10552e12			0.970955			0.485477	+	0.874249i	$0.338646\pi$
$602$	1.96660e12	+	5.93283e12i	0.610283	+	1.84110i
$603$		−	5.55652e11i		−	0.171149i
$604$	1.67382e12	−	1.24664e12i	0.511731	−	0.381132i
$605$			4.46932e12i			1.35626i
$606$	−1.34290e12	+	4.45141e11i	−0.404499	+	0.134082i
$607$	−3.79043e12			−1.13329			−0.566643	−	0.823964i	$-0.691758\pi$
$607$	−3.79043e12			−1.13329			−0.566643	+	0.823964i	$0.691758\pi$
$608$	−2.90268e12	+	8.59398e10i	−0.861455	+	0.0255052i
$609$	−7.95660e11			−0.234396
$610$	3.54329e12	−	1.17452e12i	1.03615	−	0.343459i
$611$		−	1.33358e12i		−	0.387111i
$612$	−5.45306e11	+	4.06138e11i	−0.157130	+	0.117029i
$613$			6.09780e12i			1.74422i	0.489310	+	0.872110i	$0.337249\pi$
$613$			6.09780e12i			1.74422i	−0.489310	+	0.872110i	$0.662751\pi$
$614$	−1.22269e12	−	3.68862e12i	−0.347184	−	1.04738i
$615$	3.78470e12			1.06682
$616$	−1.65704e12	−	1.15952e12i	−0.463682	−	0.324462i
$617$	−2.07665e12			−0.576872			−0.288436	−	0.957499i	$-0.593135\pi$
$617$	−2.07665e12			−0.576872			−0.288436	+	0.957499i	$0.593135\pi$
$618$	4.53673e11	+	1.36864e12i	0.125111	+	0.377434i
$619$			6.03694e12i			1.65276i	0.563115	+	0.826379i	$0.309603\pi$
$619$			6.03694e12i			1.65276i	−0.563115	+	0.826379i	$0.690397\pi$
$620$	3.44233e12	+	4.62189e12i	0.935600	+	1.25619i
$621$		−	2.49129e12i		−	0.672221i
$622$	2.68012e12	−	8.88398e11i	0.717955	−	0.237986i
$623$	−5.37615e12			−1.42980
$624$	2.24076e11	−	7.49578e11i	0.0591649	−	0.197918i
$625$	9.23927e12			2.42202
$626$	6.34202e11	−	2.10224e11i	0.165061	−	0.0547138i
$627$			1.23249e12i			0.318479i
$628$	−2.32249e12	−	3.11832e12i	−0.595849	−	0.800023i
$629$		−	7.41558e10i		−	0.0188893i
$630$	−1.22839e12	−	3.70581e12i	−0.310673	−	0.937239i
$631$	−7.01879e12			−1.76250			−0.881252	−	0.472648i	$-0.843298\pi$
$631$	−7.01879e12			−1.76250			−0.881252	+	0.472648i	$0.843298\pi$
$632$	−1.34434e12	+	1.92116e12i	−0.335182	+	0.479001i
$633$	3.18095e12			0.787482
$634$	−8.58483e11	−	2.58987e12i	−0.211023	−	0.636615i
$635$		−	6.23312e12i		−	1.52133i
$636$	−2.00387e12	+	1.49246e12i	−0.485637	+	0.361697i
$637$			2.43388e11i			0.0585695i
$638$	−6.11558e11	+	2.02718e11i	−0.146132	+	0.0484394i
$639$	2.63544e12			0.625316
$640$	−6.15015e12	+	4.87005e12i	−1.44903	+	1.14742i
$641$	−6.65994e12			−1.55815			−0.779075	−	0.626931i	$-0.784311\pi$
$641$	−6.65994e12			−1.55815			−0.779075	+	0.626931i	$0.784311\pi$
$642$	3.32670e12	−	1.10272e12i	0.772869	−	0.256188i
$643$		−	3.60863e12i		−	0.832516i	−0.909247	−	0.416258i	$-0.863341\pi$
$643$		−	3.60863e12i		−	0.832516i	0.909247	−	0.416258i	$-0.136659\pi$
$644$	2.42357e12	−	1.80505e12i	0.555224	−	0.413525i
$645$		−	1.02897e13i		−	2.34091i
$646$	4.82837e11	+	1.45662e12i	0.109082	+	0.329079i
$647$	3.26245e12			0.731938			0.365969	−	0.930627i	$-0.380738\pi$
$647$	3.26245e12			0.731938			0.365969	+	0.930627i	$0.380738\pi$
$648$	7.09571e11	−	1.01403e12i	0.158091	−	0.225925i
$649$	1.05150e11			0.0232652
$650$	9.97931e11	+	3.01056e12i	0.219276	+	0.661511i
$651$		−	3.05075e12i		−	0.665720i
$652$	−2.35879e12	−	3.16705e12i	−0.511181	−	0.686343i
$653$		−	4.35965e11i		−	0.0938302i	−0.998899	−	0.0469151i	$-0.985061\pi$
$653$		−	4.35965e11i		−	0.0938302i	0.998899	−	0.0469151i	$-0.0149390\pi$
$654$	−4.74332e12	+	1.57230e12i	−1.01387	+	0.336075i
$655$	−4.07471e12			−0.864990
$656$	1.09481e12	−	3.66234e12i	0.230818	−	0.772132i
$657$	−8.79050e11			−0.184064
$658$	6.71934e12	−	2.22731e12i	1.39737	−	0.463195i
$659$			2.27883e12i			0.470683i	0.971913	+	0.235341i	$0.0756208\pi$
$659$			2.27883e12i			0.470683i	−0.971913	+	0.235341i	$0.924379\pi$
$660$	1.98879e12	+	2.67027e12i	0.407982	+	0.547782i
$661$			6.28607e12i			1.28077i	0.768052	+	0.640387i	$0.221226\pi$
$661$			6.28607e12i			1.28077i	−0.768052	+	0.640387i	$0.778774\pi$
$662$	2.98073e12	+	8.99228e12i	0.603201	+	1.81974i
$663$	−4.13427e11			−0.0830975
$664$	5.80018e12	+	4.05869e12i	1.15794	+	0.810269i
$665$	−8.81130e12			−1.74720
$666$	−3.65359e10	−	1.10221e11i	−0.00719591	−	0.0217086i
$667$		−	9.62674e11i		−	0.188327i
$668$	4.15428e12	−	3.09407e12i	0.807239	−	0.601223i
$669$			4.94824e12i			0.955065i
$670$	−3.21574e12	+	1.06594e12i	−0.616516	+	0.204361i
$671$	−1.60012e12			−0.304721
$672$	4.15104e12	−	1.22900e11i	0.785226	−	0.0232483i
$673$	−1.30391e12			−0.245007			−0.122504	−	0.992468i	$-0.539092\pi$
$673$	−1.30391e12			−0.245007			−0.122504	+	0.992468i	$0.539092\pi$
$674$	−6.34385e12	+	2.10284e12i	−1.18409	+	0.392497i
$675$			1.38795e13i			2.57339i
$676$	3.99223e12	−	2.97337e12i	0.735284	−	0.547632i
$677$			3.77662e12i			0.690962i	0.938426	+	0.345481i	$0.112284\pi$
$677$			3.77662e12i			0.690962i	−0.938426	+	0.345481i	$0.887716\pi$
$678$	−3.88792e11	−	1.17291e12i	−0.0706616	−	0.213172i
$679$	7.54538e12			1.36228
$680$	3.39655e12	+	2.37674e12i	0.609183	+	0.426277i
$681$	5.69939e12			1.01547
$682$	−7.77267e11	−	2.34486e12i	−0.137575	−	0.415037i
$683$		−	8.09351e12i		−	1.42313i	−0.702622	−	0.711563i	$-0.747987\pi$
$683$		−	8.09351e12i		−	1.42313i	0.702622	−	0.711563i	$-0.252013\pi$
$684$	1.43533e12	+	1.92716e12i	0.250726	+	0.336640i
$685$		−	1.65079e13i		−	2.86474i
$686$	4.81269e12	−	1.59530e12i	0.829716	−	0.275032i
$687$	−3.35251e11			−0.0574202
$688$	−9.95708e12	−	2.97653e12i	−1.69428	−	0.506480i
$689$	1.44250e12			0.243853
$690$	−4.72223e12	+	1.56531e12i	−0.793097	+	0.262893i
$691$		−	1.04215e12i		−	0.173891i	−0.996213	−	0.0869455i	$-0.972289\pi$
$691$		−	1.04215e12i		−	0.173891i	0.996213	−	0.0869455i	$-0.0277106\pi$
$692$	5.80230e12	+	7.79052e12i	0.961884	+	1.29148i
$693$			1.67352e12i			0.275633i
$694$	−1.10386e11	−	3.33014e11i	−0.0180633	−	0.0544935i
$695$	6.35174e12			1.03267
$696$	7.58486e11	−	1.08394e12i	0.122520	−	0.175090i
$697$	−2.01995e12			−0.324185
$698$	−2.18548e12	−	6.59315e12i	−0.348495	−	1.05134i
$699$			4.62221e12i			0.732322i
$700$	−1.35022e13	+	1.00563e13i	−2.12551	+	1.58305i
$701$		−	2.19669e12i		−	0.343587i	−0.985133	−	0.171794i	$-0.945044\pi$
$701$		−	2.19669e12i		−	0.343587i	0.985133	−	0.171794i	$-0.0549562\pi$
$702$	−1.87618e12	+	6.21912e11i	−0.291581	+	0.0966523i
$703$	−2.62073e11			−0.0404692
$704$	3.15925e12	−	1.15206e12i	0.484738	−	0.176766i
$705$	−1.16538e13			−1.77672
$706$	−6.43638e12	+	2.13351e12i	−0.975036	+	0.323202i
$707$			4.33557e12i			0.652618i
$708$	−1.73163e11	+	1.28970e11i	−0.0259003	+	0.0192903i
$709$		−	7.02990e11i		−	0.104482i	−0.998635	−	0.0522410i	$-0.983364\pi$
$709$		−	7.02990e11i		−	0.104482i	0.998635	−	0.0522410i	$-0.0166364\pi$
$710$	−5.05574e12	−	1.52522e13i	−0.746659	−	2.25252i
$711$	1.94026e12			0.284739
$712$	5.12498e12	−	7.32399e12i	0.747363	−	1.06804i
$713$	3.69112e12			0.534879
$714$	−6.90492e11	−	2.08308e12i	−0.0994298	−	0.299960i
$715$		−	1.92222e12i		−	0.275058i
$716$	−5.28088e12	−	7.09044e12i	−0.750927	−	1.00824i
$717$			4.07909e12i			0.576404i
$718$	8.68510e12	−	2.87891e12i	1.21959	−	0.404267i
$719$	1.18349e13			1.65152			0.825759	−	0.564022i	$-0.190747\pi$
$719$	1.18349e13			1.65152			0.825759	+	0.564022i	$0.190747\pi$
$720$	6.21946e12	+	1.85922e12i	0.862495	+	0.257831i
$721$	4.41867e12			0.608952
$722$	−1.78290e12	+	5.90992e11i	−0.244180	+	0.0809401i
$723$		−	3.46870e12i		−	0.472111i
$724$	−3.16113e12	−	4.24433e12i	−0.427581	−	0.574097i
$725$			5.36325e12i			0.720953i
$726$	1.23777e12	+	3.73409e12i	0.165357	+	0.498850i
$727$	−4.66170e12			−0.618927			−0.309464	−	0.950911i	$-0.600150\pi$
$727$	−4.66170e12			−0.618927			−0.309464	+	0.950911i	$0.600150\pi$
$728$	−1.96438e12	−	1.37458e12i	−0.259200	−	0.181376i
$729$	−6.84083e12			−0.897088
$730$	1.68634e12	+	5.08735e12i	0.219782	+	0.663039i
$731$			5.49179e12i			0.711354i
$732$	2.63512e12	−	1.96261e12i	0.339234	−	0.252658i
$733$			1.16839e13i			1.49493i	0.664300	+	0.747466i	$0.268730\pi$
$733$			1.16839e13i			1.49493i	−0.664300	+	0.747466i	$0.731270\pi$
$734$	−1.09102e13	+	3.61647e12i	−1.38739	+	0.459888i
$735$	2.12690e12			0.268815
$736$	1.48698e11	+	5.02237e12i	0.0186790	+	0.630897i
$737$	1.45221e12			0.181311
$738$	−3.00236e12	+	9.95212e11i	−0.372571	+	0.123499i
$739$		−	1.25228e13i		−	1.54455i	−0.635290	−	0.772274i	$-0.719119\pi$
$739$		−	1.25228e13i		−	1.54455i	0.635290	−	0.772274i	$-0.280881\pi$
$740$	−5.67799e11	+	4.22890e11i	−0.0696068	+	0.0518424i
$741$			1.46109e12i			0.178031i
$742$	2.40921e12	+	7.26811e12i	0.291781	+	0.880246i
$743$	−1.10289e13			−1.32765			−0.663823	−	0.747890i	$-0.731067\pi$
$743$	−1.10289e13			−1.32765			−0.663823	+	0.747890i	$0.731067\pi$
$744$	4.15607e12	+	2.90822e12i	0.497284	+	0.347975i
$745$	9.93301e12			1.18135
$746$	4.94534e11	+	1.49191e12i	0.0584617	+	0.176367i
$747$		−	5.85785e12i		−	0.688328i
$748$	−1.06145e12	−	1.42517e12i	−0.123977	−	0.166459i
$749$		−	1.07403e13i		−	1.24695i
$750$	1.54203e13	−	5.11149e12i	1.77958	−	0.589891i
$751$	−6.45522e12			−0.740511			−0.370255	−	0.928930i	$-0.620730\pi$
$751$	−6.45522e12			−0.740511			−0.370255	+	0.928930i	$0.620730\pi$
$752$	−3.37113e12	+	1.12771e13i	−0.384410	+	1.28593i
$753$	7.87631e12			0.892781
$754$	−7.24987e11	+	2.40317e11i	−0.0816882	+	0.0270778i
$755$			1.05294e13i			1.17935i
$756$	−6.26708e12	−	8.41457e12i	−0.697778	−	0.936880i
$757$		−	6.48010e12i		−	0.717217i	−0.933488	−	0.358608i	$-0.883251\pi$
$757$		−	6.48010e12i		−	0.717217i	0.933488	−	0.358608i	$-0.116749\pi$
$758$	3.16868e12	+	9.55929e12i	0.348632	+	1.05175i
$759$	2.13253e12			0.233242
$760$	8.39963e12	−	1.20037e13i	0.913270	−	1.30513i
$761$	2.62886e12			0.284142			0.142071	−	0.989856i	$-0.454624\pi$
$761$	2.62886e12			0.284142			0.142071	+	0.989856i	$0.454624\pi$
$762$	−1.72625e12	−	5.20774e12i	−0.185483	−	0.559566i
$763$			1.53139e13i			1.63578i
$764$	−3.75434e12	+	2.79619e12i	−0.398670	+	0.296925i
$765$		−	3.43032e12i		−	0.362125i
$766$	9.67325e12	−	3.20646e12i	1.01518	−	0.336509i
$767$	1.24652e11			0.0130053
$768$	−3.78967e12	+	5.77216e12i	−0.393076	+	0.598705i
$769$	−1.43517e13			−1.47991			−0.739955	−	0.672656i	$-0.765153\pi$
$769$	−1.43517e13			−1.47991			−0.739955	+	0.672656i	$0.765153\pi$
$770$	9.68520e12	−	3.21042e12i	0.992888	−	0.329120i
$771$		−	1.07002e13i		−	1.09055i
$772$	3.47184e11	−	2.58579e11i	0.0351789	−	0.0262008i
$773$		−	6.56407e12i		−	0.661250i	−0.943762	−	0.330625i	$-0.892740\pi$
$773$		−	6.56407e12i		−	0.661250i	0.943762	−	0.330625i	$-0.107260\pi$
$774$	2.70576e12	+	8.16273e12i	0.270991	+	0.817525i
$775$	−2.05640e13			−2.04762
$776$	−7.19286e12	+	1.02792e13i	−0.712072	+	1.01761i
$777$	3.74784e11			0.0368881
$778$	4.10221e12	+	1.23756e13i	0.401430	+	1.21103i
$779$			7.13870e12i			0.694545i
$780$	2.35766e12	+	3.16554e12i	0.228064	+	0.306212i
$781$			6.88778e12i			0.662444i
$782$	2.52033e12	−	8.35431e11i	0.241005	−	0.0798877i
$783$	−3.34238e12			−0.317781
$784$	6.15253e11	−	2.05814e12i	0.0581609	−	0.194560i
$785$	1.96162e13			1.84375
$786$	−3.40440e12	+	1.12848e12i	−0.318155	+	0.105461i
$787$		−	1.96637e13i		−	1.82717i	−0.406649	−	0.913584i	$-0.633303\pi$
$787$		−	1.96637e13i		−	1.82717i	0.406649	−	0.913584i	$-0.366697\pi$
$788$	6.49602e11	+	8.72196e11i	0.0600177	+	0.0805835i
$789$			6.42945e10i			0.00590646i
$790$	−3.72213e12	−	1.12289e13i	−0.339993	−	1.02569i
$791$	−3.78675e12			−0.343932
$792$	−2.27985e12	−	1.59533e12i	−0.205894	−	0.144075i
$793$	−1.89691e12			−0.170340
$794$	−2.29810e12	−	6.93290e12i	−0.205199	−	0.619046i
$795$		−	1.26056e13i		−	1.11921i
$796$	−1.20263e12	+	8.95708e11i	−0.106175	+	0.0790784i
$797$			2.05859e12i			0.180721i	0.995909	+	0.0903603i	$0.0288019\pi$
$797$			2.05859e12i			0.180721i	−0.995909	+	0.0903603i	$0.971198\pi$
$798$	−7.36179e12	+	2.44026e12i	−0.642644	+	0.213022i
$799$	6.21983e12			0.539906
$800$	−8.28424e11	−	2.79806e13i	−0.0715069	−	2.41519i
$801$	−7.39681e12			−0.634890
$802$	−3.17530e12	+	1.05254e12i	−0.271019	+	0.0898365i
$803$		−	2.29741e12i		−	0.194993i
$804$	−2.39152e12	+	1.78118e12i	−0.201847	+	0.150334i
$805$			1.52458e13i			1.27958i
$806$	−9.21431e11	−	2.77977e12i	−0.0769051	−	0.232007i
$807$	−9.65446e12			−0.801304
$808$	−5.90640e12	−	4.13302e12i	−0.487497	−	0.341127i
$809$	−9.44339e12			−0.775103			−0.387552	−	0.921848i	$-0.626679\pi$
$809$	−9.44339e12			−0.775103			−0.387552	+	0.921848i	$0.626679\pi$
$810$	1.96463e12	+	5.92689e12i	0.160361	+	0.483776i
$811$			3.40891e12i			0.276708i	0.990383	+	0.138354i	$0.0441812\pi$
$811$			3.40891e12i			0.276708i	−0.990383	+	0.138354i	$0.955819\pi$
$812$	−2.42170e12	−	3.25152e12i	−0.195487	−	0.262473i
$813$			9.83146e12i			0.789242i
$814$	2.88066e11	−	9.54872e10i	0.0229976	−	0.00762317i
$815$	1.99228e13			1.58176
$816$	3.49603e12	+	1.04509e12i	0.276038	+	0.0825178i
$817$	1.94085e13			1.52403
$818$	1.55519e13	−	5.15509e12i	1.21449	−	0.402575i
$819$			1.98391e12i			0.154080i
$820$	1.15192e13	+	1.54664e13i	0.889737	+	1.19462i
$821$			1.44900e12i			0.111307i	0.998450	+	0.0556535i	$0.0177242\pi$
$821$			1.44900e12i			0.111307i	−0.998450	+	0.0556535i	$0.982276\pi$
$822$	−4.57182e12	−	1.37923e13i	−0.349274	−	1.05369i
$823$	9.50599e12			0.722267			0.361134	−	0.932514i	$-0.382390\pi$
$823$	9.50599e12			0.722267			0.361134	+	0.932514i	$0.382390\pi$
$824$	−4.21223e12	+	6.01961e12i	−0.318302	+	0.454879i
$825$	−1.18807e13			−0.892894
$826$	2.08190e11	+	6.28069e11i	0.0155615	+	0.0469458i
$827$			1.32590e13i			0.985683i	0.870119	+	0.492842i	$0.164042\pi$
$827$			1.32590e13i			0.985683i	−0.870119	+	0.492842i	$0.835958\pi$
$828$	3.33448e12	−	2.48349e12i	0.246542	−	0.183622i
$829$		−	1.63326e13i		−	1.20104i	−0.799608	−	0.600522i	$-0.794960\pi$
$829$		−	1.63326e13i		−	1.20104i	0.799608	−	0.600522i	$-0.205040\pi$
$830$	−3.39013e13	+	1.12375e13i	−2.47951	+	0.821899i
$831$	1.62173e13			1.17971
$832$	3.74521e12	−	1.36574e12i	0.270970	−	0.0988127i
$833$	−1.13516e12			−0.0816873
$834$	5.30684e12	−	1.75910e12i	0.379830	−	0.125905i
$835$			2.61331e13i			1.86038i
$836$	−5.03667e12	+	3.75126e12i	−0.356628	+	0.265613i
$837$		−	1.28155e13i		−	0.902549i
$838$	4.34516e12	+	1.31085e13i	0.304374	+	0.918236i
$839$	2.23005e12			0.155377			0.0776884	−	0.996978i	$-0.475246\pi$
$839$	2.23005e12			0.155377			0.0776884	+	0.996978i	$0.475246\pi$
$840$	−1.20121e13	+	1.71662e13i	−0.832456	+	1.18965i
$841$	1.32156e13			0.910972
$842$	−5.09786e12	−	1.53792e13i	−0.349529	−	1.05446i
$843$			2.72758e12i			0.186017i
$844$	9.68167e12	+	1.29992e13i	0.656764	+	0.881812i
$845$			2.51137e13i			1.69455i
$846$	9.24485e12	−	3.06446e12i	0.620488	−	0.205678i
$847$	1.20556e13			0.804846
$848$	−1.21981e13	−	3.64645e12i	−0.810047	−	0.242152i
$849$	2.81501e12			0.185950
$850$	−1.40412e13	+	4.65435e12i	−0.922614	+	0.305825i
$851$			4.53454e11i			0.0296381i
$852$	−8.44809e12	−	1.13429e13i	−0.549263	−	0.737474i
$853$		−	2.83205e13i		−	1.83160i	−0.401633	−	0.915801i	$-0.631557\pi$
$853$		−	2.83205e13i		−	1.83160i	0.401633	−	0.915801i	$-0.368443\pi$
$854$	−3.16815e12	−	9.55768e12i	−0.203819	−	0.614882i
$855$	−1.21231e13			−0.775828
$856$	1.46316e13	+	1.02385e13i	0.931453	+	0.651786i
$857$	−6.76700e12			−0.428531			−0.214266	−	0.976775i	$-0.568736\pi$
$857$	−6.76700e12			−0.428531			−0.214266	+	0.976775i	$0.568736\pi$
$858$	−5.32352e11	−	1.60600e12i	−0.0335356	−	0.101170i
$859$		−	2.30991e12i		−	0.144753i	−0.997377	−	0.0723763i	$-0.976942\pi$
$859$		−	2.30991e12i		−	0.144753i	0.997377	−	0.0723763i	$-0.0230582\pi$
$860$	4.20497e13	−	3.13182e13i	2.62132	−	1.95233i
$861$		−	1.02089e13i		−	0.633087i
$862$	−1.02842e13	+	3.40899e12i	−0.634438	+	0.210302i
$863$	−1.05303e13			−0.646237			−0.323119	−	0.946358i	$-0.604731\pi$
$863$	−1.05303e13			−0.646237			−0.323119	+	0.946358i	$0.604731\pi$
$864$	1.74376e13	−	5.16275e11i	1.06457	−	0.0315188i
$865$	−4.90074e13			−2.97638
$866$	6.72938e12	−	2.23064e12i	0.406579	−	0.134772i
$867$			9.98766e12i			0.600313i
$868$	1.24671e13	−	9.28537e12i	0.745464	−	0.555214i
$869$			5.07091e12i			0.301646i
$870$	2.10006e12	+	6.33547e12i	0.124278	+	0.374923i
$871$	1.72156e12			0.101354
$872$	−2.08623e13	−	1.45984e13i	−1.22190	−	0.855030i
$873$	1.03814e13			0.604909
$874$	−2.95249e12	−	8.90708e12i	−0.171154	−	0.516338i
$875$		−	4.97848e13i		−	2.87118i
$876$	2.81786e12	+	3.78343e12i	0.161678	+	0.217079i
$877$			1.37761e13i			0.786373i	0.919459	+	0.393186i	$0.128627\pi$
$877$			1.37761e13i			0.786373i	−0.919459	+	0.393186i	$0.871373\pi$
$878$	−1.49485e13	+	4.95508e12i	−0.848931	+	0.281401i
$879$	−2.50199e12			−0.141363
$880$	−4.85911e12	+	1.62547e13i	−0.273140	+	0.913706i
$881$	−1.13133e13			−0.632698			−0.316349	−	0.948643i	$-0.602457\pi$
$881$	−1.13133e13			−0.632698			−0.316349	+	0.948643i	$0.602457\pi$
$882$	−1.68725e12	+	5.59283e11i	−0.0938793	+	0.0311188i
$883$			3.91577e12i			0.216768i	0.994109	+	0.108384i	$0.0345675\pi$
$883$			3.91577e12i			0.216768i	−0.994109	+	0.108384i	$0.965432\pi$
$884$	−1.25832e12	−	1.68950e12i	−0.0693037	−	0.0930514i
$885$		−	1.08930e12i		−	0.0596904i
$886$	−2.53086e12	−	7.63510e12i	−0.137980	−	0.416259i
$887$	−1.62707e12			−0.0882573			−0.0441287	−	0.999026i	$-0.514051\pi$
$887$	−1.62707e12			−0.0882573			−0.0441287	+	0.999026i	$0.514051\pi$
$888$	−3.57274e11	+	5.10573e11i	−0.0192816	+	0.0275549i
$889$	−1.68133e13			−0.902805
$890$	1.41898e13	+	4.28078e13i	0.758091	+	2.28701i
$891$		−	2.67654e12i		−	0.142274i
$892$	−2.02213e13	+	1.50606e13i	−1.06947	+	0.796528i
$893$		−	2.19815e13i		−	1.15671i
$894$	8.29897e12	−	2.75092e12i	0.434516	−	0.144032i
$895$	4.46034e13			2.32362
$896$	1.31365e13	+	1.65895e13i	0.680915	+	0.859896i
$897$	2.52806e12			0.130383
$898$	1.75088e13	−	5.80375e12i	0.898487	−	0.297828i
$899$		−	4.95211e12i		−	0.252855i
$900$	−1.85770e13	+	1.38360e13i	−0.943812	+	0.702941i
$901$			6.72780e12i			0.340104i
$902$	−2.60101e12	−	7.84671e12i	−0.130831	−	0.394692i
$903$	−2.77556e13			−1.38917
$904$	3.60983e12	−	5.15873e12i	0.179775	−	0.256912i
$905$	2.66995e13			1.32308
$906$	2.91608e12	+	8.79723e12i	0.143788	+	0.433780i
$907$			7.72659e12i			0.379101i	0.981871	+	0.189551i	$0.0607031\pi$
$907$			7.72659e12i			0.379101i	−0.981871	+	0.189551i	$0.939297\pi$
$908$	1.73469e13	+	2.32910e13i	0.846906	+	1.13711i
$909$			5.96513e12i			0.289789i
$910$	1.14816e13	−	3.80587e12i	0.555028	−	0.183979i
$911$	−1.47051e13			−0.707350			−0.353675	−	0.935368i	$-0.615068\pi$
$911$	−1.47051e13			−0.707350			−0.353675	+	0.935368i	$0.615068\pi$
$912$	3.69345e12	−	1.23553e13i	0.176789	−	0.591393i
$913$	1.53096e13			0.729198
$914$	1.27698e13	−	4.23290e12i	0.605238	−	0.200623i
$915$			1.65766e13i			0.781807i
$916$	−1.02038e12	−	1.37003e12i	−0.0478887	−	0.0642983i
$917$			1.09911e13i			0.513312i
$918$	−2.90060e12	−	8.75052e12i	−0.134802	−	0.406670i
$919$	−3.87199e13			−1.79066			−0.895332	−	0.445399i	$-0.853062\pi$
$919$	−3.87199e13			−1.79066			−0.895332	+	0.445399i	$0.853062\pi$
$920$	−2.07695e13	−	1.45335e13i	−0.955831	−	0.668844i
$921$	1.72565e13			0.790285
$922$	−1.01465e13	−	3.06099e13i	−0.462408	−	1.39499i
$923$			8.16529e12i			0.370309i
$924$	7.20281e12	−	5.36457e12i	0.325071	−	0.242109i
$925$		−	2.52628e12i		−	0.113460i
$926$	2.25512e13	−	7.47519e12i	1.00790	−	0.334097i
$927$	6.07946e12			0.270400
$928$	6.73814e12	−	1.99497e11i	0.298246	−	0.00883019i
$929$	7.75866e12			0.341756			0.170878	−	0.985292i	$-0.445340\pi$
$929$	7.75866e12			0.341756			0.170878	+	0.985292i	$0.445340\pi$
$930$	−2.42917e13	+	8.05214e12i	−1.06484	+	0.352970i
$931$			4.01176e12i			0.175010i
$932$	−1.88890e13	+	1.40683e13i	−0.820044	+	0.610760i
$933$			1.25384e13i			0.541720i
$934$	8.23415e11	+	2.48408e12i	0.0354045	+	0.106808i
$935$	8.96521e12			0.383626
$936$	−2.70271e12	−	1.89122e12i	−0.115095	−	0.0805382i
$937$	−1.60112e13			−0.678573			−0.339286	−	0.940683i	$-0.610186\pi$
$937$	−1.60112e13			−0.678573			−0.339286	+	0.940683i	$0.610186\pi$
$938$	2.87528e12	+	8.67416e12i	0.121274	+	0.365860i
$939$			2.96699e12i			0.124543i
$940$	−3.54700e13	−	4.76243e13i	−1.48179	−	1.98954i
$941$			1.55404e13i			0.646115i	0.946379	+	0.323057i	$0.104711\pi$
$941$			1.55404e13i			0.646115i	−0.946379	+	0.323057i	$0.895289\pi$
$942$	1.63893e13	−	5.43266e12i	0.678157	−	0.224793i
$943$	1.23518e13			0.508659
$944$	−1.05409e12	−	3.15105e11i	−0.0432019	−	0.0129146i
$945$	5.29330e13			2.15915
$946$	−2.13334e13	+	7.07154e12i	−0.866065	+	0.287081i
$947$		−	1.38291e13i		−	0.558750i	−0.960182	−	0.279375i	$-0.909873\pi$
$947$		−	1.38291e13i		−	0.558750i	0.960182	−	0.279375i	$-0.0901273\pi$
$948$	−6.21964e12	−	8.35088e12i	−0.250108	−	0.335811i
$949$		−	2.72353e12i		−	0.109002i
$950$	1.64489e13	+	4.96231e13i	0.655210	+	1.97664i
$951$	1.21162e13			0.480346
$952$	6.41104e12	−	9.16187e12i	0.252966	−	0.361508i
$953$	−1.62441e12			−0.0637935			−0.0318967	−	0.999491i	$-0.510155\pi$
$953$	−1.62441e12			−0.0637935			−0.0318967	+	0.999491i	$0.510155\pi$
$954$	3.31473e12	+	9.99988e12i	0.129563	+	0.390865i
$955$		−	2.36172e13i		−	0.918784i
$956$	−1.66695e13	+	1.24153e13i	−0.645449	+	0.480724i
$957$		−	2.86105e12i		−	0.110261i
$958$	−2.94899e13	+	9.77523e12i	−1.13117	+	0.374958i
$959$	−4.45285e13			−1.70002
$960$	−1.19348e13	−	3.27284e13i	−0.453519	−	1.24367i
$961$	−7.45207e12			−0.281852
$962$	3.41495e11	−	1.13198e11i	0.0128557	−	0.00426137i
$963$		−	1.47771e13i		−	0.553696i
$964$	1.41751e13	−	1.05575e13i	0.528664	−	0.393743i
$965$			2.18401e12i			0.0810740i
$966$	4.22228e12	+	1.27378e13i	0.156009	+	0.470648i
$967$	2.99781e13			1.10252			0.551259	−	0.834334i	$-0.314148\pi$
$967$	2.99781e13			1.10252			0.551259	+	0.834334i	$0.314148\pi$
$968$	−1.14923e13	+	1.64234e13i	−0.420697	+	0.601209i
$969$	−6.81452e12			−0.248301
$970$	−1.99153e13	−	6.00804e13i	−0.722293	−	2.17901i
$971$			3.61921e13i			1.30655i	0.757119	+	0.653277i	$0.226606\pi$
$971$			3.61921e13i			1.30655i	−0.757119	+	0.653277i	$0.773394\pi$
$972$	−1.44211e13	−	1.93627e13i	−0.518203	−	0.695772i
$973$		−	1.71332e13i		−	0.612818i
$974$	3.29601e13	−	1.09255e13i	1.17347	−	0.388979i
$975$	−1.40843e13			−0.499131
$976$	1.60407e13	+	4.79514e12i	0.565846	+	0.169152i
$977$	2.29688e13			0.806515			0.403258	−	0.915087i	$-0.367878\pi$
$977$	2.29688e13			0.806515			0.403258	+	0.915087i	$0.367878\pi$
$978$	1.66454e13	−	5.51756e12i	0.581793	−	0.192851i
$979$		−	1.93317e13i		−	0.672586i
$980$	6.47351e12	+	8.69174e12i	0.224193	+	0.301016i
$981$			2.10697e13i			0.726353i
$982$	3.64858e12	+	1.10070e13i	0.125205	+	0.377719i
$983$	−2.02509e13			−0.691758			−0.345879	−	0.938279i	$-0.612419\pi$
$983$	−2.02509e13			−0.691758			−0.345879	+	0.938279i	$0.612419\pi$
$984$	1.39076e13	+	9.73190e12i	0.472907	+	0.330918i
$985$	−5.48667e12			−0.185715
$986$	−1.12084e12	−	3.38134e12i	−0.0377656	−	0.113931i
$987$			3.14351e13i			1.05436i
$988$	−5.97085e12	+	4.44703e12i	−0.199356	+	0.148478i
$989$		−	3.35817e13i		−	1.11614i
$990$	1.33254e13	−	4.41708e12i	0.440883	−	0.146143i
$991$	−1.63486e12			−0.0538456			−0.0269228	−	0.999638i	$-0.508571\pi$
$991$	−1.63486e12			−0.0538456			−0.0269228	+	0.999638i	$0.508571\pi$
$992$	7.64918e11	+	2.58356e13i	0.0250791	+	0.847065i
$993$	−4.20686e13			−1.37305
$994$	−4.11413e13	+	1.36374e13i	−1.33672	+	0.443091i
$995$		−	7.56533e12i		−	0.244694i
$996$	−2.52122e13	+	1.87777e13i	−0.811789	+	0.604611i
$997$			9.91675e12i			0.317864i	0.987290	+	0.158932i	$0.0508050\pi$
$997$			9.91675e12i			0.317864i	−0.987290	+	0.158932i	$0.949195\pi$
$998$	−1.74959e13	−	5.27815e13i	−0.558274	−	1.68420i
$999$	1.57438e12			0.0500110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.10.b.a.5.2	yes	8
3.2	odd	2		72.10.d.b.37.7		8
4.3	odd	2		32.10.b.a.17.6		8
8.3	odd	2		32.10.b.a.17.3		8
8.5	even	2	inner	8.10.b.a.5.1	✓	8
12.11	even	2		288.10.d.b.145.1		8
16.3	odd	4		256.10.a.s.1.3		8
16.5	even	4		256.10.a.p.1.3		8
16.11	odd	4		256.10.a.s.1.6		8
16.13	even	4		256.10.a.p.1.6		8
24.5	odd	2		72.10.d.b.37.8		8
24.11	even	2		288.10.d.b.145.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.10.b.a.5.1	✓	8	8.5	even	2	inner
8.10.b.a.5.2	yes	8	1.1	even	1	trivial
32.10.b.a.17.3		8	8.3	odd	2
32.10.b.a.17.6		8	4.3	odd	2
72.10.d.b.37.7		8	3.2	odd	2
72.10.d.b.37.8		8	24.5	odd	2
256.10.a.p.1.3		8	16.5	even	4
256.10.a.p.1.6		8	16.13	even	4
256.10.a.s.1.3		8	16.3	odd	4
256.10.a.s.1.6		8	16.11	odd	4
288.10.d.b.145.1		8	12.11	even	2
288.10.d.b.145.8		8	24.11	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)

\(f(q)\)	\(=\)	\(q+(-21.4782 + 7.11952i) q^{2} -100.481i q^{3} +(410.625 - 305.829i) q^{4} +2583.09i q^{5} +(715.380 + 2158.16i) q^{6} +6967.65 q^{7} +(-6642.12 + 9492.10i) q^{8} +9586.48 q^{9} +O(q^{10})\)	\(q+(-21.4782 + 7.11952i) q^{2} -100.481i q^{3} +(410.625 - 305.829i) q^{4} +2583.09i q^{5} +(715.380 + 2158.16i) q^{6} +6967.65 q^{7} +(-6642.12 + 9492.10i) q^{8} +9586.48 q^{9} +(-18390.4 - 55480.1i) q^{10} +25054.5i q^{11} +(-30730.1 - 41260.2i) q^{12} +29701.4i q^{13} +(-149652. + 49606.3i) q^{14} +259553. q^{15} +(75081.4 - 251162. i) q^{16} -138527. q^{17} +(-205900. + 68251.2i) q^{18} +489569. i q^{19} +(789984. + 1.06068e6i) q^{20} -700119. i q^{21} +(-178376. - 538124. i) q^{22} +847079. q^{23} +(953780. + 667409. i) q^{24} -4.71924e6 q^{25} +(-211460. - 637933. i) q^{26} -2.94104e6i q^{27} +(2.86109e6 - 2.13091e6i) q^{28} -1.13646e6i q^{29} +(-5.57472e6 + 1.84789e6i) q^{30} +4.35747e6 q^{31} +(175542. + 5.92904e6i) q^{32} +2.51751e6 q^{33} +(2.97532e6 - 986249. i) q^{34} +1.79981e7i q^{35} +(3.93645e6 - 2.93182e6i) q^{36} +535315. i q^{37} +(-3.48550e6 - 1.05151e7i) q^{38} +2.98444e6 q^{39} +(-2.45190e7 - 1.71572e7i) q^{40} +1.45816e7 q^{41} +(4.98451e6 + 1.50373e7i) q^{42} -3.96441e7i q^{43} +(7.66238e6 + 1.02880e7i) q^{44} +2.47628e7i q^{45} +(-1.81937e7 + 6.03080e6i) q^{46} -4.48997e7 q^{47} +(-2.52371e7 - 7.54428e6i) q^{48} +8.19448e6 q^{49} +(1.01361e8 - 3.35988e7i) q^{50} +1.39194e7i q^{51} +(9.08355e6 + 1.21961e7i) q^{52} -4.85666e7i q^{53} +(2.09388e7 + 6.31682e7i) q^{54} -6.47180e7 q^{55} +(-4.62799e7 + 6.61376e7i) q^{56} +4.91926e7 q^{57} +(8.09108e6 + 2.44092e7i) q^{58} -4.19685e6i q^{59} +(1.06579e8 - 7.93787e7i) q^{60} +6.38659e7i q^{61} +(-9.35906e7 + 3.10231e7i) q^{62} +6.67952e7 q^{63} +(-4.59823e7 - 1.26095e8i) q^{64} -7.67215e7 q^{65} +(-5.40715e7 + 1.79235e7i) q^{66} -5.79621e7i q^{67} +(-5.68828e7 + 4.23657e7i) q^{68} -8.51157e7i q^{69} +(-1.28138e8 - 3.86566e8i) q^{70} +2.74912e8 q^{71} +(-6.36745e7 + 9.09959e7i) q^{72} -9.16969e7 q^{73} +(-3.81119e6 - 1.14976e7i) q^{74} +4.74196e8i q^{75} +(1.49724e8 + 2.01029e8i) q^{76} +1.74571e8i q^{77} +(-6.41004e7 + 2.12478e7i) q^{78} +2.02396e8 q^{79} +(6.48774e8 + 1.93942e8i) q^{80} -1.06829e8 q^{81} +(-3.13186e8 + 1.03814e8i) q^{82} -6.11053e8i q^{83} +(-2.14117e8 - 2.87486e8i) q^{84} -3.57829e8i q^{85} +(2.82247e8 + 8.51483e8i) q^{86} -1.14193e8 q^{87} +(-2.37819e8 - 1.66415e8i) q^{88} -7.71588e8 q^{89} +(-1.76299e8 - 5.31859e8i) q^{90} +2.06949e8i q^{91} +(3.47831e8 - 2.59061e8i) q^{92} -4.37845e8i q^{93} +(9.64363e8 - 3.19664e8i) q^{94} -1.26460e9 q^{95} +(5.95759e8 - 1.76387e7i) q^{96} +1.08292e9 q^{97} +(-1.76003e8 + 5.83408e7i) q^{98} +2.40184e8i 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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