LMFDB - Embedded newform 8.16.b.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,16,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, 16, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 16 $
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:	$11.4154804080$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 6354 x^{12} + 136110 x^{11} + 41390651 x^{10} - 1368564777 x^{9} + \cdots + 24\!\cdots\!00 $ x^14 - 3x^13 - 6354x^12 + 136110x^11 + 41390651x^10 - 1368564777x^9 - 361745089708x^8 + 52039630950804x^7 - 1350212102075609x^6 - 202833046637545317x^5 + 15458794901317392766x^4 + 1792289418481984019550x^3 - 184645940533558790286339x^2 - 14754933471339430268597775*x + 2433324183085485312818967200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.5
Root			$48.9348 + 74.1268i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.16.b.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-103.870 - 148.254i) q^{2} -6357.96i q^{3} +(-11190.2 + 30798.1i) q^{4} +267219. i q^{5} +(-942590. + 660399. i) q^{6} +120583. q^{7} +(5.72825e6 - 1.53999e6i) q^{8} -2.60748e7 q^{9} +O(q^{10})$	\(q+(-103.870 - 148.254i) q^{2} -6357.96i q^{3} +(-11190.2 + 30798.1i) q^{4} +267219. i q^{5} +(-942590. + 660399. i) q^{6} +120583. q^{7} +(5.72825e6 - 1.53999e6i) q^{8} -2.60748e7 q^{9} +(3.96161e7 - 2.77559e7i) q^{10} +9.60941e7i q^{11} +(1.95813e8 + 7.11470e7i) q^{12} -1.64009e8i q^{13} +(-1.25249e7 - 1.78769e7i) q^{14} +1.69897e9 q^{15} +(-8.23300e8 - 6.89274e8i) q^{16} -1.25524e8 q^{17} +(2.70838e9 + 3.86568e9i) q^{18} +4.61207e9i q^{19} +(-8.22982e9 - 2.99024e9i) q^{20} -7.66663e8i q^{21} +(1.42463e10 - 9.98125e9i) q^{22} +6.78047e9 q^{23} +(-9.79122e9 - 3.64200e10i) q^{24} -4.08883e10 q^{25} +(-2.43149e10 + 1.70355e10i) q^{26} +7.45526e10i q^{27} +(-1.34935e9 + 3.71373e9i) q^{28} +7.66507e10i q^{29} +(-1.76471e11 - 2.51878e11i) q^{30} +2.28582e10 q^{31} +(-1.66715e10 + 1.93652e11i) q^{32} +6.10963e11 q^{33} +(1.30381e10 + 1.86094e10i) q^{34} +3.22221e10i q^{35} +(2.91782e11 - 8.03052e11i) q^{36} +8.61660e11i q^{37} +(6.83755e11 - 4.79054e11i) q^{38} -1.04276e12 q^{39} +(4.11515e11 + 1.53070e12i) q^{40} -3.52968e11 q^{41} +(-1.13660e11 + 7.96329e10i) q^{42} +1.68998e12i q^{43} +(-2.95951e12 - 1.07531e12i) q^{44} -6.96767e12i q^{45} +(-7.04285e11 - 1.00523e12i) q^{46} +3.84783e12 q^{47} +(-4.38238e12 + 5.23451e12i) q^{48} -4.73302e12 q^{49} +(4.24705e12 + 6.06184e12i) q^{50} +7.98078e11i q^{51} +(5.05115e12 + 1.83529e12i) q^{52} -9.03015e12i q^{53} +(1.10527e13 - 7.74375e12i) q^{54} -2.56782e13 q^{55} +(6.90730e11 - 1.85697e11i) q^{56} +2.93234e13 q^{57} +(1.13637e13 - 7.96167e12i) q^{58} +1.13978e13i q^{59} +(-1.90118e13 + 5.23249e13i) q^{60} -3.96597e12i q^{61} +(-2.37427e12 - 3.38881e12i) q^{62} -3.14418e12 q^{63} +(3.04412e13 - 1.76429e13i) q^{64} +4.38262e13 q^{65} +(-6.34604e13 - 9.05774e13i) q^{66} +4.34443e13i q^{67} +(1.40464e12 - 3.86590e12i) q^{68} -4.31100e13i q^{69} +(4.77704e12 - 3.34689e12i) q^{70} -3.11414e13 q^{71} +(-1.49363e14 + 4.01550e13i) q^{72} -8.34468e13 q^{73} +(1.27744e14 - 8.95003e13i) q^{74} +2.59966e14i q^{75} +(-1.42043e14 - 5.16100e13i) q^{76} +1.15873e13i q^{77} +(1.08311e14 + 1.54593e14i) q^{78} +7.31635e12 q^{79} +(1.84187e14 - 2.20001e14i) q^{80} +9.98580e13 q^{81} +(3.66626e13 + 5.23287e13i) q^{82} -3.96179e14i q^{83} +(2.36117e13 + 8.57912e12i) q^{84} -3.35424e13i q^{85} +(2.50546e14 - 1.75538e14i) q^{86} +4.87342e14 q^{87} +(1.47984e14 + 5.50451e14i) q^{88} +9.54011e13 q^{89} +(-1.03298e15 + 7.23729e14i) q^{90} -1.97767e13i q^{91} +(-7.58749e13 + 2.08825e14i) q^{92} -1.45332e14i q^{93} +(-3.99673e14 - 5.70455e14i) q^{94} -1.23243e15 q^{95} +(1.23123e15 + 1.05997e14i) q^{96} -1.16047e15 q^{97} +(4.91617e14 + 7.01687e14i) q^{98} -2.50563e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9}+O(q^{10}) $ 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17} + 526853306 q^{18} - 3449250768 q^{20} + 28367364252 q^{22} - 35548816080 q^{23} + 40155187088 q^{24} - 75899954794 q^{25} + 17666210712 q^{26} + 79863955680 q^{28} - 124878825712 q^{30} - 105758138816 q^{31} - 37651613280 q^{32} - 150458001384 q^{33} + 537472307308 q^{34} + 338679650892 q^{36} + 1649727781164 q^{38} - 2251546247120 q^{39} + 1251083710304 q^{40} - 53229185940 q^{41} - 2437011096800 q^{42} - 3416842360344 q^{44} - 3303531082064 q^{46} + 12527998446432 q^{47} - 6441543679584 q^{48} + 8427385380990 q^{49} + 1179755527374 q^{50} - 2436018627056 q^{52} + 3357642572216 q^{54} - 30557833792176 q^{55} + 7549064859072 q^{56} + 18277230892472 q^{57} - 8014960165320 q^{58} - 53574657402912 q^{60} + 77882578979904 q^{62} + 36142362113776 q^{63} + 76083381630528 q^{64} + 5437123965600 q^{65} - 134116957601160 q^{66} - 69772560247896 q^{68} + 133952399750848 q^{70} - 173249927708016 q^{71} + 163390222317848 q^{72} - 182057837882196 q^{73} + 2072780135688 q^{74} - 248503439494072 q^{76} + 636498768647600 q^{78} - 294370273271392 q^{79} + 766230078246336 q^{80} + 256903428263798 q^{81} - 10\!\cdots\!32 q^{82}+ \cdots - 51\!\cdots\!58 q^{98}+O(q^{100}) \) 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9 + 58467784 * q^10 + 399357832 * q^12 - 518960496 * q^14 + 712135312 * q^15 - 1435931120 * q^16 + 728554812 * q^17 + 526853306 * q^18 - 3449250768 * q^20 + 28367364252 * q^22 - 35548816080 * q^23 + 40155187088 * q^24 - 75899954794 * q^25 + 17666210712 * q^26 + 79863955680 * q^28 - 124878825712 * q^30 - 105758138816 * q^31 - 37651613280 * q^32 - 150458001384 * q^33 + 537472307308 * q^34 + 338679650892 * q^36 + 1649727781164 * q^38 - 2251546247120 * q^39 + 1251083710304 * q^40 - 53229185940 * q^41 - 2437011096800 * q^42 - 3416842360344 * q^44 - 3303531082064 * q^46 + 12527998446432 * q^47 - 6441543679584 * q^48 + 8427385380990 * q^49 + 1179755527374 * q^50 - 2436018627056 * q^52 + 3357642572216 * q^54 - 30557833792176 * q^55 + 7549064859072 * q^56 + 18277230892472 * q^57 - 8014960165320 * q^58 - 53574657402912 * q^60 + 77882578979904 * q^62 + 36142362113776 * q^63 + 76083381630528 * q^64 + 5437123965600 * q^65 - 134116957601160 * q^66 - 69772560247896 * q^68 + 133952399750848 * q^70 - 173249927708016 * q^71 + 163390222317848 * q^72 - 182057837882196 * q^73 + 2072780135688 * q^74 - 248503439494072 * q^76 + 636498768647600 * q^78 - 294370273271392 * q^79 + 766230078246336 * q^80 + 256903428263798 * q^81 - 1021513680215332 * q^82 - 1701668269684544 * q^84 + 1418597672590812 * q^86 + 1493385390675312 * q^87 + 1948789255860816 * q^88 + 314213951649228 * q^89 - 3574690367103304 * q^90 - 3044080509008736 * q^92 + 3407319354561120 * q^94 - 851301047679984 * q^95 + 4705878559349312 * q^96 - 672574291859236 * q^97 - 5140373067292458 * 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 $

$2$	−103.870	−	148.254i	−0.573804	−	0.818993i
$2$	−103.870	−	148.254i	−0.573804	−	0.818993i
$3$		−	6357.96i		−	1.67845i	−0.543784	−	0.839225i	$-0.683009\pi$
$3$		−	6357.96i		−	1.67845i	0.543784	−	0.839225i	$-0.316991\pi$
$4$	−11190.2	+	30798.1i	−0.341498	+	0.939882i
$5$			267219.i			1.52965i	0.644238	+	0.764825i	$0.277175\pi$
$5$			267219.i			1.52965i	−0.644238	+	0.764825i	$0.722825\pi$
$6$	−942590.	+	660399.i	−1.37464	+	0.963101i
$7$	120583.			0.0553415			0.0276708	−	0.999617i	$-0.491191\pi$
$7$	120583.			0.0553415			0.0276708	+	0.999617i	$0.491191\pi$
$8$	5.72825e6	−	1.53999e6i	0.965710	−	0.259623i
$9$	−2.60748e7			−1.81720
$10$	3.96161e7	−	2.77559e7i	1.25277	−	0.877719i
$11$			9.60941e7i			1.48680i	0.668849	+	0.743398i	$0.266787\pi$
$11$			9.60941e7i			1.48680i	−0.668849	+	0.743398i	$0.733213\pi$
$12$	1.95813e8	+	7.11470e7i	1.57755	+	0.573188i
$13$		−	1.64009e8i		−	0.724923i	−0.931999	−	0.362461i	$-0.881937\pi$
$13$		−	1.64009e8i		−	0.724923i	0.931999	−	0.362461i	$-0.118063\pi$
$14$	−1.25249e7	−	1.78769e7i	−0.0317552	−	0.0453243i
$15$	1.69897e9			2.56744
$16$	−8.23300e8	−	6.89274e8i	−0.766758	−	0.641936i
$17$	−1.25524e8			−0.0741926			−0.0370963	−	0.999312i	$-0.511811\pi$
$17$	−1.25524e8			−0.0741926			−0.0370963	+	0.999312i	$0.511811\pi$
$18$	2.70838e9	+	3.86568e9i	1.04271	+	1.48827i
$19$			4.61207e9i			1.18371i	0.806046	+	0.591853i	$0.201603\pi$
$19$			4.61207e9i			1.18371i	−0.806046	+	0.591853i	$0.798397\pi$
$20$	−8.22982e9	−	2.99024e9i	−1.43769	−	0.522373i
$21$		−	7.66663e8i		−	0.0928880i
$22$	1.42463e10	−	9.98125e9i	1.21768	−	0.853130i
$23$	6.78047e9			0.415242			0.207621	−	0.978209i	$-0.433428\pi$
$23$	6.78047e9			0.415242			0.207621	+	0.978209i	$0.433428\pi$
$24$	−9.79122e9	−	3.64200e10i	−0.435765	−	1.62090i
$25$	−4.08883e10			−1.33983
$26$	−2.43149e10	+	1.70355e10i	−0.593706	+	0.415963i
$27$			7.45526e10i			1.37162i
$28$	−1.34935e9	+	3.71373e9i	−0.0188990	+	0.0520145i
$29$			7.66507e10i			0.825146i	0.910924	+	0.412573i	$0.135370\pi$
$29$			7.66507e10i			0.825146i	−0.910924	+	0.412573i	$0.864630\pi$
$30$	−1.76471e11	−	2.51878e11i	−1.47321	−	2.10272i
$31$	2.28582e10			0.149221			0.0746104	−	0.997213i	$-0.476229\pi$
$31$	2.28582e10			0.149221			0.0746104	+	0.997213i	$0.476229\pi$
$32$	−1.66715e10	+	1.93652e11i	−0.0857728	+	0.996315i
$33$	6.10963e11			2.49551
$34$	1.30381e10	+	1.86094e10i	0.0425720	+	0.0607632i
$35$			3.22221e10i			0.0846532i
$36$	2.91782e11	−	8.03052e11i	0.620569	−	1.70795i
$37$			8.61660e11i			1.49219i	0.665841	+	0.746093i	$0.268073\pi$
$37$			8.61660e11i			1.49219i	−0.665841	+	0.746093i	$0.731927\pi$
$38$	6.83755e11	−	4.79054e11i	0.969446	−	0.679215i
$39$	−1.04276e12			−1.21675
$40$	4.11515e11	+	1.53070e12i	0.397133	+	1.47720i
$41$	−3.52968e11			−0.283045			−0.141523	−	0.989935i	$-0.545200\pi$
$41$	−3.52968e11			−0.283045			−0.141523	+	0.989935i	$0.545200\pi$
$42$	−1.13660e11	+	7.96329e10i	−0.0760746	+	0.0532995i
$43$			1.68998e12i			0.948132i	0.880489	+	0.474066i	$0.157214\pi$
$43$			1.68998e12i			0.948132i	−0.880489	+	0.474066i	$0.842786\pi$
$44$	−2.95951e12	−	1.07531e12i	−1.39741	−	0.507739i
$45$		−	6.96767e12i		−	2.77967i
$46$	−7.04285e11	−	1.00523e12i	−0.238267	−	0.340080i
$47$	3.84783e12			1.10785			0.553927	−	0.832565i	$-0.313129\pi$
$47$	3.84783e12			1.10785			0.553927	+	0.832565i	$0.313129\pi$
$48$	−4.38238e12	+	5.23451e12i	−1.07746	+	1.28696i
$49$	−4.73302e12			−0.996937
$50$	4.24705e12	+	6.06184e12i	0.768799	+	1.09731i
$51$			7.98078e11i			0.124529i
$52$	5.05115e12	+	1.83529e12i	0.681342	+	0.247560i
$53$		−	9.03015e12i		−	1.05591i	−0.849273	−	0.527954i	$-0.822959\pi$
$53$		−	9.03015e12i		−	1.05591i	0.849273	−	0.527954i	$-0.177041\pi$
$54$	1.10527e13	−	7.74375e12i	1.12335	−	0.787042i
$55$	−2.56782e13			−2.27428
$56$	6.90730e11	−	1.85697e11i	0.0534439	−	0.0143680i
$57$	2.93234e13			1.98679
$58$	1.13637e13	−	7.96167e12i	0.675789	−	0.473472i
$59$			1.13978e13i			0.596254i	0.954526	+	0.298127i	$0.0963620\pi$
$59$			1.13978e13i			0.596254i	−0.954526	+	0.298127i	$0.903638\pi$
$60$	−1.90118e13	+	5.23249e13i	−0.876777	+	2.41309i
$61$		−	3.96597e12i		−	0.161575i	−0.996731	−	0.0807877i	$-0.974256\pi$
$61$		−	3.96597e12i		−	0.161575i	0.996731	−	0.0807877i	$-0.0257436\pi$
$62$	−2.37427e12	−	3.38881e12i	−0.0856235	−	0.122211i
$63$	−3.14418e12			−0.100566
$64$	3.04412e13	−	1.76429e13i	0.865191	−	0.501442i
$65$	4.38262e13			1.10888
$66$	−6.34604e13	−	9.05774e13i	−1.43194	−	2.04381i
$67$			4.34443e13i			0.875733i	0.899040	+	0.437866i	$0.144266\pi$
$67$			4.34443e13i			0.875733i	−0.899040	+	0.437866i	$0.855734\pi$
$68$	1.40464e12	−	3.86590e12i	0.0253366	−	0.0697323i
$69$		−	4.31100e13i		−	0.696963i
$70$	4.77704e12	−	3.34689e12i	0.0693303	−	0.0485743i
$71$	−3.11414e13			−0.406350			−0.203175	−	0.979142i	$-0.565126\pi$
$71$	−3.11414e13			−0.406350			−0.203175	+	0.979142i	$0.565126\pi$
$72$	−1.49363e14	+	4.01550e13i	−1.75488	+	0.471787i
$73$	−8.34468e13			−0.884073			−0.442037	−	0.896997i	$-0.645744\pi$
$73$	−8.34468e13			−0.884073			−0.442037	+	0.896997i	$0.645744\pi$
$74$	1.27744e14	−	8.95003e13i	1.22209	−	0.856222i
$75$			2.59966e14i			2.24884i
$76$	−1.42043e14	−	5.16100e13i	−1.11254	−	0.404234i
$77$			1.15873e13i			0.0822816i
$78$	1.08311e14	+	1.54593e14i	0.698174	+	0.996507i
$79$	7.31635e12			0.0428638			0.0214319	−	0.999770i	$-0.493177\pi$
$79$	7.31635e12			0.0428638			0.0214319	+	0.999770i	$0.493177\pi$
$80$	1.84187e14	−	2.20001e14i	0.981938	−	1.17287i
$81$	9.98580e13			0.485004
$82$	3.66626e13	+	5.23287e13i	0.162413	+	0.231812i
$83$		−	3.96179e14i		−	1.60253i	−0.598312	−	0.801263i	$-0.704162\pi$
$83$		−	3.96179e14i		−	1.60253i	0.598312	−	0.801263i	$-0.295838\pi$
$84$	2.36117e13	+	8.57912e12i	0.0873038	+	0.0317211i
$85$		−	3.35424e13i		−	0.113489i
$86$	2.50546e14	−	1.75538e14i	0.776513	−	0.544042i
$87$	4.87342e14			1.38497
$88$	1.47984e14	+	5.50451e14i	0.386007	+	1.43581i
$89$	9.54011e13			0.228628			0.114314	−	0.993445i	$-0.463533\pi$
$89$	9.54011e13			0.228628			0.114314	+	0.993445i	$0.463533\pi$
$90$	−1.03298e15	+	7.23729e14i	−2.27653	+	1.59499i
$91$		−	1.97767e13i		−	0.0401183i
$92$	−7.58749e13	+	2.08825e14i	−0.141804	+	0.390278i
$93$		−	1.45332e14i		−	0.250460i
$94$	−3.99673e14	−	5.70455e14i	−0.635691	−	0.907324i
$95$	−1.23243e15			−1.81066
$96$	1.23123e15	+	1.05997e14i	1.67226	+	0.143965i
$97$	−1.16047e15			−1.45830			−0.729150	−	0.684354i	$-0.760084\pi$
$97$	−1.16047e15			−1.45830			−0.729150	+	0.684354i	$0.760084\pi$
$98$	4.91617e14	+	7.01687e14i	0.572046	+	0.816484i
$99$		−	2.50563e15i		−	2.70180i
$100$	4.57549e14	−	1.25928e15i	0.457549	−	1.25928i
$101$			2.07199e15i			1.92299i	0.274818	+	0.961496i	$0.411382\pi$
$101$			2.07199e15i			1.92299i	−0.274818	+	0.961496i	$0.588618\pi$
$102$	1.18318e14	−	8.28960e13i	0.101988	−	0.0714549i
$103$	4.51671e14			0.361862			0.180931	−	0.983496i	$-0.442089\pi$
$103$	4.51671e14			0.361862			0.180931	+	0.983496i	$0.442089\pi$
$104$	−2.52572e14	−	9.39482e14i	−0.188207	−	0.700065i
$105$	2.04867e14			0.142086
$106$	−1.33875e15	+	9.37958e14i	−0.864781	+	0.605884i
$107$			1.58456e15i			0.953962i	0.878914	+	0.476981i	$0.158269\pi$
$107$			1.58456e15i			0.953962i	−0.878914	+	0.476981i	$0.841731\pi$
$108$	−2.29608e15	−	8.34260e14i	−1.28916	−	0.468407i
$109$		−	1.34658e15i		−	0.705562i	−0.935706	−	0.352781i	$-0.885236\pi$
$109$		−	1.34658e15i		−	0.705562i	0.935706	−	0.352781i	$-0.114764\pi$
$110$	2.66718e15	+	3.80688e15i	1.30499	+	1.86262i
$111$	5.47840e15			2.50456
$112$	−9.92761e13	−	8.31148e13i	−0.0424335	−	0.0355257i
$113$	1.52322e13			0.00609081			0.00304541	−	0.999995i	$-0.499031\pi$
$113$	1.52322e13			0.00609081			0.00304541	+	0.999995i	$0.499031\pi$
$114$	−3.04581e15	−	4.34729e15i	−1.14003	−	1.62717i
$115$			1.81187e15i			0.635175i
$116$	−2.36069e15	−	8.57738e14i	−0.775541	−	0.281786i
$117$			4.27649e15i			1.31733i
$118$	1.68977e15	−	1.18389e15i	0.488328	−	0.342133i
$119$	−1.51361e13			−0.00410593
$120$	9.73210e15	−	2.61640e15i	2.47940	−	0.666568i
$121$	−5.05683e15			−1.21056
$122$	−5.87968e14	+	4.11943e14i	−0.132329	+	0.0927126i
$123$			2.24416e15i			0.475078i
$124$	−2.55788e14	+	7.03989e14i	−0.0509587	+	0.140250i
$125$		−	2.77126e15i		−	0.519819i
$126$	3.26584e14	+	4.66135e14i	0.0577054	+	0.0823631i
$127$	−7.11367e15			−1.18458			−0.592292	−	0.805724i	$-0.701777\pi$
$127$	−7.11367e15			−1.18458			−0.592292	+	0.805724i	$0.701777\pi$
$128$	−5.77754e15	−	2.68045e15i	−0.907127	−	0.420856i
$129$	1.07448e16			1.59139
$130$	−4.55221e15	−	6.49739e15i	−0.636278	−	0.908163i
$131$		−	6.33055e15i		−	0.835424i	−0.908580	−	0.417712i	$-0.862832\pi$
$131$		−	6.33055e15i		−	0.835424i	0.908580	−	0.417712i	$-0.137168\pi$
$132$	−6.83680e15	+	1.88165e16i	−0.852214	+	2.34549i
$133$			5.56138e14i			0.0655081i
$134$	6.44077e15	−	4.51254e15i	0.717219	−	0.502499i
$135$	−1.99219e16			−2.09810
$136$	−7.19033e14	+	1.93306e14i	−0.0716485	+	0.0192621i
$137$	1.26171e16			1.19002			0.595011	−	0.803718i	$-0.297148\pi$
$137$	1.26171e16			1.19002			0.595011	+	0.803718i	$0.297148\pi$
$138$	−6.39121e15	+	4.47782e15i	−0.570807	+	0.399920i
$139$		−	3.53179e15i		−	0.298802i	−0.988777	−	0.149401i	$-0.952265\pi$
$139$		−	3.53179e15i		−	0.298802i	0.988777	−	0.149401i	$-0.0477345\pi$
$140$	−9.92378e14	−	3.60572e14i	−0.0795640	−	0.0289089i
$141$		−	2.44644e16i		−	1.85948i
$142$	3.23464e15	+	4.61682e15i	0.233165	+	0.332798i
$143$	1.57603e16			1.07781
$144$	2.14674e16	+	1.79727e16i	1.39335	+	1.16652i
$145$	−2.04825e16			−1.26219
$146$	8.66758e15	+	1.23713e16i	0.507285	+	0.724049i
$147$			3.00924e16i			1.67331i
$148$	−2.65375e16	−	9.64216e15i	−1.40248	−	0.509579i
$149$		−	5.94079e15i		−	0.298502i	−0.988799	−	0.149251i	$-0.952314\pi$
$149$		−	5.94079e15i		−	0.298502i	0.988799	−	0.149251i	$-0.0476862\pi$
$150$	3.85409e16	−	2.70026e16i	1.84178	−	1.29039i
$151$	2.55527e16			1.16174			0.580871	−	0.813995i	$-0.302712\pi$
$151$	2.55527e16			1.16174			0.580871	+	0.813995i	$0.302712\pi$
$152$	7.10256e15	+	2.64191e16i	0.307318	+	1.14312i
$153$	3.27301e15			0.134822
$154$	1.71786e15	−	1.20357e15i	0.0673880	−	0.0472135i
$155$			6.10815e15i			0.228256i
$156$	1.16687e16	−	3.21150e16i	0.415517	−	1.14360i
$157$		−	5.29272e16i		−	1.79652i	−0.439466	−	0.898259i	$-0.644832\pi$
$157$		−	5.29272e16i		−	1.79652i	0.439466	−	0.898259i	$-0.355168\pi$
$158$	−7.59946e14	−	1.08467e15i	−0.0245954	−	0.0351052i
$159$	−5.74133e16			−1.77229
$160$	−5.17474e16	−	4.45493e15i	−1.52401	−	0.131202i
$161$	8.17610e14			0.0229801
$162$	−1.03722e16	−	1.48043e16i	−0.278297	−	0.397215i
$163$			2.94167e16i			0.753679i	0.926279	+	0.376840i	$0.122989\pi$
$163$			2.94167e16i			0.753679i	−0.926279	+	0.376840i	$0.877011\pi$
$164$	3.94979e15	−	1.08707e16i	0.0966595	−	0.266029i
$165$			1.63261e17i			3.81726i
$166$	−5.87349e16	+	4.11509e16i	−1.31246	+	0.919536i
$167$	4.03066e16			0.860999			0.430500	−	0.902591i	$-0.358337\pi$
$167$	4.03066e16			0.860999			0.430500	+	0.902591i	$0.358337\pi$
$168$	−1.18066e15	−	4.39163e15i	−0.0241159	−	0.0897029i
$169$	2.42871e16			0.474487
$170$	−4.97278e15	+	3.48404e15i	−0.0929464	+	0.0651202i
$171$		−	1.20259e17i		−	2.15102i
$172$	−5.20482e16	−	1.89113e16i	−0.891132	−	0.323785i
$173$		−	8.00780e16i		−	1.31271i	−0.754454	−	0.656353i	$-0.772098\pi$
$173$		−	8.00780e16i		−	1.31271i	0.754454	−	0.656353i	$-0.227902\pi$
$174$	−5.06200e16	−	7.22502e16i	−0.794699	−	1.13428i
$175$	−4.93044e15			−0.0741482
$176$	6.62352e16	−	7.91143e16i	0.954429	−	1.14001i
$177$	7.24669e16			1.00078
$178$	−9.90928e15	−	1.41436e16i	−0.131187	−	0.187244i
$179$			6.28967e16i			0.798418i	0.916860	+	0.399209i	$0.130715\pi$
$179$			6.28967e16i			0.798418i	−0.916860	+	0.399209i	$0.869285\pi$
$180$	2.14591e17	+	7.79697e16i	2.61257	+	0.949254i
$181$			1.40644e17i			1.64260i	0.570496	+	0.821300i	$0.306751\pi$
$181$			1.40644e17i			1.64260i	−0.570496	+	0.821300i	$0.693249\pi$
$182$	−2.93196e15	+	2.05419e15i	−0.0328566	+	0.0230200i
$183$	−2.52155e16			−0.271196
$184$	3.88402e16	−	1.04419e16i	0.401003	−	0.107807i
$185$	−2.30252e17			−2.28252
$186$	−2.15459e16	+	1.50955e16i	−0.205125	+	0.143715i
$187$		−	1.20621e16i		−	0.110309i
$188$	−4.30581e16	+	1.18506e17i	−0.378330	+	1.04125i
$189$			8.98978e15i			0.0759077i
$190$	1.28012e17	+	1.82712e17i	1.03896	+	1.48291i
$191$	2.42747e17			1.89411			0.947053	−	0.321076i	$-0.104045\pi$
$191$	2.42747e17			1.89411			0.947053	+	0.321076i	$0.104045\pi$
$192$	−1.12173e17	−	1.93544e17i	−0.841645	−	1.45218i
$193$	−8.44339e16			−0.609308			−0.304654	−	0.952463i	$-0.598541\pi$
$193$	−8.44339e16			−0.609308			−0.304654	+	0.952463i	$0.598541\pi$
$194$	1.20538e17	+	1.72044e17i	0.836778	+	1.19434i
$195$		−	2.78645e17i		−	1.86120i
$196$	5.29635e16	−	1.45768e17i	0.340452	−	0.937004i
$197$		−	1.91310e17i		−	1.18370i	−0.806048	−	0.591850i	$-0.798398\pi$
$197$		−	1.91310e17i		−	1.18370i	0.806048	−	0.591850i	$-0.201602\pi$
$198$	−3.71469e17	+	2.60259e17i	−2.21275	+	1.55030i
$199$	1.18533e16			0.0679895			0.0339948	−	0.999422i	$-0.489177\pi$
$199$	1.18533e16			0.0679895			0.0339948	+	0.999422i	$0.489177\pi$
$200$	−2.34218e17	+	6.29678e16i	−1.29389	+	0.347851i
$201$	2.76217e17			1.46987
$202$	3.07180e17	−	2.15217e17i	1.57492	−	1.10342i
$203$			9.24278e15i			0.0456649i
$204$	−2.45792e16	−	8.93066e15i	−0.117042	−	0.0425263i
$205$		−	9.43197e16i		−	0.432960i
$206$	−4.69149e16	−	6.69619e16i	−0.207638	−	0.296363i
$207$	−1.76799e17			−0.754576
$208$	−1.13047e17	+	1.35028e17i	−0.465354	+	0.555840i
$209$	−4.43193e17			−1.75993
$210$	−2.12794e16	−	3.03722e16i	−0.0815296	−	0.116368i
$211$			9.00677e16i			0.333005i	0.986041	+	0.166502i	$0.0532474\pi$
$211$			9.00677e16i			0.333005i	−0.986041	+	0.166502i	$0.946753\pi$
$212$	2.78111e17	+	1.01049e17i	0.992429	+	0.360591i
$213$			1.97996e17i			0.682038i
$214$	2.34917e17	−	1.64588e17i	0.781288	−	0.547387i
$215$	−4.51595e17			−1.45031
$216$	1.14810e17	+	4.27055e17i	0.356105	+	1.32459i
$217$	2.75631e15			0.00825811
$218$	−1.99636e17	+	1.39869e17i	−0.577850	+	0.404854i
$219$			5.30551e17i			1.48387i
$220$	2.87344e17	−	7.90837e17i	0.776662	−	2.13755i
$221$			2.05870e16i			0.0537839i
$222$	−5.69039e17	−	8.12192e17i	−1.43713	−	2.05122i
$223$	4.15081e17			1.01355			0.506777	−	0.862077i	$-0.330837\pi$
$223$	4.15081e17			1.01355			0.506777	+	0.862077i	$0.330837\pi$
$224$	−2.01030e15	+	2.33511e16i	−0.00474680	+	0.0551376i
$225$	1.06615e18			2.43473
$226$	−1.58217e15	−	2.25823e15i	−0.00349493	−	0.00498833i
$227$		−	3.49083e17i		−	0.745993i	−0.927833	−	0.372996i	$-0.878330\pi$
$227$		−	3.49083e17i		−	0.745993i	0.927833	−	0.372996i	$-0.121670\pi$
$228$	−3.28135e17	+	9.03103e17i	−0.678486	+	1.86735i
$229$			4.66508e15i			0.00933453i	0.999989	+	0.00466727i	$0.00148564\pi$
$229$			4.66508e15i			0.00933453i	−0.999989	+	0.00466727i	$0.998514\pi$
$230$	2.68616e17	−	1.88198e17i	0.520203	−	0.364466i
$231$	7.36718e16			0.138106
$232$	1.18042e17	+	4.39074e17i	0.214227	+	0.796852i
$233$	6.90379e17			1.21316			0.606580	−	0.795022i	$-0.292541\pi$
$233$	6.90379e17			1.21316			0.606580	+	0.795022i	$0.292541\pi$
$234$	6.34004e17	−	4.44197e17i	1.07888	−	0.755887i
$235$			1.02821e18i			1.69463i
$236$	−3.51031e17	−	1.27544e17i	−0.560409	−	0.203620i
$237$		−	4.65170e16i		−	0.0719448i
$238$	1.57218e15	+	2.24398e15i	0.00235600	+	0.00336273i
$239$	−9.82227e17			−1.42635			−0.713177	−	0.700984i	$-0.752745\pi$
$239$	−9.82227e17			−1.42635			−0.713177	+	0.700984i	$0.752745\pi$
$240$	−1.39876e18	−	1.17105e18i	−1.96861	−	1.64813i
$241$	−6.25947e16			−0.0853906			−0.0426953	−	0.999088i	$-0.513594\pi$
$241$	−6.25947e16			−0.0853906			−0.0426953	+	0.999088i	$0.513594\pi$
$242$	5.25250e17	+	7.49692e17i	0.694626	+	0.991443i
$243$			4.34855e17i			0.557567i
$244$	1.22144e17	+	4.43800e16i	0.151862	+	0.0551777i
$245$		−	1.26475e18i		−	1.52497i
$246$	3.32704e17	−	2.33100e17i	0.389085	−	0.272601i
$247$	7.56419e17			0.858095
$248$	1.30937e17	−	3.52015e16i	0.144104	−	0.0387412i
$249$	−2.51889e18			−2.68976
$250$	−4.10849e17	+	2.87850e17i	−0.425728	+	0.298274i
$251$		−	8.66947e17i		−	0.871846i	−0.899984	−	0.435923i	$-0.856422\pi$
$251$		−	8.66947e17i		−	0.871846i	0.899984	−	0.435923i	$-0.143578\pi$
$252$	3.51840e16	−	9.68346e16i	0.0343432	−	0.0945206i
$253$			6.51563e17i			0.617380i
$254$	7.38894e17	+	1.05463e18i	0.679718	+	0.970165i
$255$	−2.13261e17			−0.190485
$256$	2.02724e17	+	1.13496e18i	0.175835	+	0.984420i
$257$	−6.75670e17			−0.569162			−0.284581	−	0.958652i	$-0.591854\pi$
$257$	−6.75670e17			−0.569162			−0.284581	+	0.958652i	$0.591854\pi$
$258$	−1.11606e18	−	1.59296e18i	−0.913147	−	1.30334i
$259$			1.03902e17i			0.0825799i
$260$	−4.90425e17	+	1.34976e18i	−0.378680	+	1.04221i
$261$		−	1.99865e18i		−	1.49945i
$262$	−9.38526e17	+	6.57552e17i	−0.684206	+	0.479369i
$263$	−4.36818e16			−0.0309480			−0.0154740	−	0.999880i	$-0.504926\pi$
$263$	−4.36818e16			−0.0309480			−0.0154740	+	0.999880i	$0.504926\pi$
$264$	3.49974e18	−	9.40878e17i	2.40994	−	0.647894i
$265$	2.41303e18			1.61517
$266$	8.24494e16	−	5.77658e16i	0.0536506	−	0.0375888i
$267$		−	6.06557e17i		−	0.383740i
$268$	−1.33800e18	−	4.86151e17i	−0.823086	−	0.299061i
$269$			1.39181e18i			0.832604i	0.909226	+	0.416302i	$0.136674\pi$
$269$			1.39181e18i			0.832604i	−0.909226	+	0.416302i	$0.863326\pi$
$270$	2.06927e18	+	2.95349e18i	1.20390	+	1.71833i
$271$	1.21335e18			0.686617			0.343309	−	0.939223i	$-0.388452\pi$
$271$	1.21335e18			0.686617			0.343309	+	0.939223i	$0.388452\pi$
$272$	1.03344e17	+	8.65205e16i	0.0568877	+	0.0476269i
$273$	−1.25739e17			−0.0673366
$274$	−1.31053e18	−	1.87053e18i	−0.682839	−	0.974619i
$275$		−	3.92913e18i		−	1.99205i
$276$	1.32770e18	+	4.82410e17i	0.655063	+	0.238012i
$277$			1.97331e18i			0.947540i	0.880649	+	0.473770i	$0.157107\pi$
$277$			1.97331e18i			0.947540i	−0.880649	+	0.473770i	$0.842893\pi$
$278$	−5.23600e17	+	3.66845e17i	−0.244717	+	0.171454i
$279$	−5.96023e17			−0.271164
$280$	4.96218e16	+	1.84576e17i	0.0219779	+	0.0817504i
$281$	2.31539e18			0.998449			0.499225	−	0.866473i	$-0.333618\pi$
$281$	2.31539e18			0.998449			0.499225	+	0.866473i	$0.333618\pi$
$282$	−3.62693e18	+	2.54111e18i	−1.52290	+	1.06698i
$283$		−	2.72039e18i		−	1.11233i	−0.831073	−	0.556163i	$-0.812273\pi$
$283$		−	2.72039e18i		−	1.11233i	0.831073	−	0.556163i	$-0.187727\pi$
$284$	3.48479e17	−	9.59094e17i	0.138768	−	0.381921i
$285$			7.83575e18i			3.03910i
$286$	−1.63701e18	−	2.33651e18i	−0.618453	−	0.882721i
$287$	−4.25620e16			−0.0156642
$288$	4.34705e17	−	5.04942e18i	0.155866	−	1.81050i
$289$	−2.84667e18			−0.994495
$290$	2.12751e18	+	3.03660e18i	0.724247	+	1.03372i
$291$			7.37824e18i			2.44768i
$292$	9.33788e17	−	2.57000e18i	0.301909	−	0.830925i
$293$		−	5.75600e18i		−	1.81390i	−0.421237	−	0.906951i	$-0.638404\pi$
$293$		−	5.75600e18i		−	1.81390i	0.421237	−	0.906951i	$-0.361596\pi$
$294$	4.46130e18	−	3.12568e18i	1.37043	−	0.960152i
$295$	−3.04571e18			−0.912061
$296$	1.32695e18	+	4.93580e18i	0.387407	+	1.44102i
$297$	−7.16406e18			−2.03932
$298$	−8.80742e17	+	6.17067e17i	−0.244471	+	0.171281i
$299$		−	1.11206e18i		−	0.301018i
$300$	−8.00646e18	−	2.90908e18i	−2.11364	−	0.767974i
$301$			2.03783e17i			0.0524711i
$302$	−2.65415e18	−	3.78828e18i	−0.666612	−	0.951459i
$303$	1.31736e19			3.22765
$304$	3.17898e18	−	3.79712e18i	0.759864	−	0.907616i
$305$	1.05978e18			0.247154
$306$	−3.39966e17	−	4.85236e17i	−0.0773616	−	0.110419i
$307$			2.54727e18i			0.565636i	0.959174	+	0.282818i	$0.0912692\pi$
$307$			2.54727e18i			0.565636i	−0.959174	+	0.282818i	$0.908731\pi$
$308$	−3.56867e17	−	1.29665e17i	−0.0773350	−	0.0280990i
$309$		−	2.87171e18i		−	0.607368i
$310$	9.05554e17	−	6.34451e17i	0.186940	−	0.130974i
$311$	−5.78305e17			−0.116534			−0.0582671	−	0.998301i	$-0.518558\pi$
$311$	−5.78305e17			−0.116534			−0.0582671	+	0.998301i	$0.518558\pi$
$312$	−5.97319e18	+	1.60584e18i	−1.17502	+	0.315896i
$313$	2.11174e18			0.405562			0.202781	−	0.979224i	$-0.435002\pi$
$313$	2.11174e18			0.405562			0.202781	+	0.979224i	$0.435002\pi$
$314$	−7.84665e18	+	5.49753e18i	−1.47134	+	1.03085i
$315$		−	8.40183e17i		−	0.153831i
$316$	−8.18715e16	+	2.25329e17i	−0.0146379	+	0.0402870i
$317$			6.00631e17i			0.104873i	0.998624	+	0.0524364i	$0.0166987\pi$
$317$			6.00631e17i			0.104873i	−0.998624	+	0.0524364i	$0.983301\pi$
$318$	5.96350e18	+	8.51173e18i	1.01695	+	1.45149i
$319$	−7.36568e18			−1.22682
$320$	4.71452e18	+	8.13447e18i	0.767031	+	1.32344i
$321$	1.00746e19			1.60118
$322$	−8.49248e16	−	1.21214e17i	−0.0131861	−	0.0188205i
$323$		−	5.78926e17i		−	0.0878222i
$324$	−1.11743e18	+	3.07543e18i	−0.165628	+	0.455847i
$325$			6.70604e18i			0.971272i
$326$	4.36113e18	−	3.05550e18i	0.617258	−	0.432464i
$327$	−8.56153e18			−1.18425
$328$	−2.02189e18	+	5.43568e17i	−0.273340	+	0.0734852i
$329$	4.63984e17			0.0613103
$330$	2.42040e19	−	1.69578e19i	3.12631	−	2.19036i
$331$		−	3.00162e18i		−	0.379006i	−0.981880	−	0.189503i	$-0.939312\pi$
$331$		−	3.00162e18i		−	0.379006i	0.981880	−	0.189503i	$-0.0606877\pi$
$332$	1.22015e19	+	4.43332e18i	1.50619	+	0.547260i
$333$		−	2.24676e19i		−	2.71159i
$334$	−4.18663e18	−	5.97560e18i	−0.494045	−	0.705152i
$335$	−1.16091e19			−1.33956
$336$	−5.28441e17	+	6.31193e17i	−0.0596282	+	0.0712226i
$337$	6.11724e16			0.00675042			0.00337521	−	0.999994i	$-0.498926\pi$
$337$	6.11724e16			0.00675042			0.00337521	+	0.999994i	$0.498926\pi$
$338$	−2.52269e18	−	3.60064e18i	−0.272263	−	0.388602i
$339$		−	9.68460e16i		−	0.0102231i
$340$	1.03304e18	+	3.75347e17i	0.106666	+	0.0387562i
$341$			2.19654e18i			0.221861i
$342$	−1.78288e19	+	1.24912e19i	−1.76167	+	1.23427i
$343$	−1.14320e18			−0.110514
$344$	2.60256e18	+	9.68063e18i	0.246157	+	0.915620i
$345$	1.15198e19			1.06611
$346$	−1.18719e19	+	8.31767e18i	−1.07510	+	0.753236i
$347$			8.50746e18i			0.753926i	0.926228	+	0.376963i	$0.123032\pi$
$347$			8.50746e18i			0.753926i	−0.926228	+	0.376963i	$0.876968\pi$
$348$	−5.45346e18	+	1.50092e19i	−0.472964	+	1.30171i
$349$		−	7.39145e17i		−	0.0627392i	−0.999508	−	0.0313696i	$-0.990013\pi$
$349$		−	7.39145e17i		−	0.0627392i	0.999508	−	0.0313696i	$-0.00998689\pi$
$350$	5.12123e17	+	7.30955e17i	0.0425465	+	0.0607268i
$351$	1.22273e19			0.994320
$352$	−1.86088e19	−	1.60203e18i	−1.48132	−	0.127527i
$353$	−2.03790e19			−1.58808			−0.794042	−	0.607863i	$-0.792027\pi$
$353$	−2.03790e19			−1.58808			−0.794042	+	0.607863i	$0.792027\pi$
$354$	−7.52711e18	−	1.07435e19i	−0.574253	−	0.819634i
$355$		−	8.32156e18i		−	0.621573i
$356$	−1.06756e18	+	2.93817e18i	−0.0780759	+	0.214883i
$357$			9.62347e16i			0.00689160i
$358$	9.32466e18	−	6.53305e18i	0.653898	−	0.458135i
$359$	6.59964e18			0.453223			0.226611	−	0.973985i	$-0.427235\pi$
$359$	6.59964e18			0.453223			0.226611	+	0.973985i	$0.427235\pi$
$360$	−1.07302e19	−	3.99125e19i	−0.721668	−	2.68436i
$361$	−6.09005e18			−0.401159
$362$	2.08510e19	−	1.46086e19i	1.34528	−	0.942530i
$363$			3.21511e19i			2.03187i
$364$	6.09083e17	+	2.21305e17i	0.0377065	+	0.0137003i
$365$		−	2.22986e19i		−	1.35232i
$366$	2.61912e18	+	3.73828e18i	0.155613	+	0.222108i
$367$	7.81363e18			0.454839			0.227419	−	0.973797i	$-0.426971\pi$
$367$	7.81363e18			0.454839			0.227419	+	0.973797i	$0.426971\pi$
$368$	−5.58236e18	−	4.67360e18i	−0.318390	−	0.266559i
$369$	9.20355e18			0.514349
$370$	2.39162e19	+	3.41356e19i	1.30972	+	1.86937i
$371$		−	1.08888e18i		−	0.0584355i
$372$	4.47593e18	+	1.62629e18i	0.235403	+	0.0855316i
$373$			3.65402e19i			1.88345i	0.336382	+	0.941726i	$0.390797\pi$
$373$			3.65402e19i			1.88345i	−0.336382	+	0.941726i	$0.609203\pi$
$374$	−1.78825e18	+	1.25289e18i	−0.0903425	+	0.0632959i
$375$	−1.76196e19			−0.872491
$376$	2.20413e19	−	5.92564e18i	1.06987	−	0.287625i
$377$	1.25714e19			0.598167
$378$	1.33277e18	−	9.33765e17i	0.0621678	−	0.0435561i
$379$		−	5.85785e18i		−	0.267882i	−0.990989	−	0.133941i	$-0.957237\pi$
$379$		−	5.85785e18i		−	0.267882i	0.990989	−	0.133941i	$-0.0427633\pi$
$380$	1.37912e19	−	3.79565e19i	0.618336	−	1.70180i
$381$			4.52284e19i			1.98826i
$382$	−2.52141e19	−	3.59882e19i	−1.08685	−	1.55126i
$383$	3.82207e19			1.61550			0.807752	−	0.589522i	$-0.200684\pi$
$383$	3.82207e19			1.61550			0.807752	+	0.589522i	$0.200684\pi$
$384$	−1.70422e19	+	3.67334e19i	−0.706386	+	1.52257i
$385$	−3.09635e18			−0.125862
$386$	8.77012e18	+	1.25176e19i	0.349624	+	0.499019i
$387$		−	4.40659e19i		−	1.72294i
$388$	1.29859e19	−	3.57403e19i	0.498007	−	1.37063i
$389$			9.25088e18i			0.347985i	0.984747	+	0.173993i	$0.0556669\pi$
$389$			9.25088e18i			0.347985i	−0.984747	+	0.173993i	$0.944333\pi$
$390$	−4.13102e19	+	2.89428e19i	−1.52431	+	1.06796i
$391$	−8.51113e17			−0.0308078
$392$	−2.71119e19	+	7.28882e18i	−0.962752	+	0.258828i
$393$	−4.02494e19			−1.40222
$394$	−2.83624e19	+	1.98713e19i	−0.969442	+	0.679212i
$395$			1.95507e18i			0.0655667i
$396$	7.71686e19	+	2.80386e19i	2.53937	+	0.922660i
$397$		−	5.20456e19i		−	1.68056i	−0.542150	−	0.840282i	$-0.682389\pi$
$397$		−	5.20456e19i		−	1.68056i	0.542150	−	0.840282i	$-0.317611\pi$
$398$	−1.23120e18	−	1.75730e18i	−0.0390127	−	0.0556829i
$399$	3.53590e18			0.109952
$400$	3.36634e19	+	2.81833e19i	1.02732	+	0.860085i
$401$	3.31013e19			0.991430			0.495715	−	0.868485i	$-0.334906\pi$
$401$	3.31013e19			0.991430			0.495715	+	0.868485i	$0.334906\pi$
$402$	−2.86906e19	−	4.09502e19i	−0.843419	−	1.20382i
$403$		−	3.74894e18i		−	0.108174i
$404$	−6.38133e19	−	2.31860e19i	−1.80739	−	0.656699i
$405$			2.66839e19i			0.741886i
$406$	1.37027e18	−	9.60043e17i	0.0373992	−	0.0262027i
$407$	−8.28005e19			−2.21858
$408$	1.22903e18	+	4.57158e18i	0.0323305	+	0.120258i
$409$	−2.01464e19			−0.520323			−0.260162	−	0.965565i	$-0.583776\pi$
$409$	−2.01464e19			−0.520323			−0.260162	+	0.965565i	$0.583776\pi$
$410$	−1.39832e19	+	9.79694e18i	−0.354591	+	0.248434i
$411$		−	8.02190e19i		−	1.99739i
$412$	−5.05430e18	+	1.39106e19i	−0.123575	+	0.340108i
$413$			1.37438e18i			0.0329976i
$414$	1.83641e19	+	2.62111e19i	0.432978	+	0.617992i
$415$	1.05866e20			2.45131
$416$	3.17606e19	+	2.73427e18i	0.722251	+	0.0621786i
$417$	−2.24550e19			−0.501524
$418$	4.60342e19	+	6.57049e19i	1.00985	+	1.44137i
$419$			6.19828e18i			0.133557i	0.997768	+	0.0667784i	$0.0212720\pi$
$419$			6.19828e18i			0.133557i	−0.997768	+	0.0667784i	$0.978728\pi$
$420$	−2.29250e18	+	6.30950e18i	−0.0485222	+	0.133544i
$421$			1.87462e19i			0.389760i	0.980827	+	0.194880i	$0.0624317\pi$
$421$			1.87462e19i			0.389760i	−0.980827	+	0.194880i	$0.937568\pi$
$422$	1.33529e19	−	9.35529e18i	0.272729	−	0.191079i
$423$	−1.00331e20			−2.01319
$424$	−1.39064e19	−	5.17269e19i	−0.274138	−	1.01970i
$425$	5.13247e18			0.0994053
$426$	2.93536e19	−	2.05657e19i	0.558584	−	0.391356i
$427$		−	4.78228e17i		−	0.00894183i
$428$	−4.88014e19	−	1.77316e19i	−0.896612	−	0.325776i
$429$		−	1.00203e20i		−	1.80905i
$430$	4.69070e19	+	6.69506e19i	0.832193	+	1.18779i
$431$	4.50478e19			0.785405			0.392702	−	0.919666i	$-0.371540\pi$
$431$	4.50478e19			0.785405			0.392702	+	0.919666i	$0.371540\pi$
$432$	5.13872e19	−	6.13791e19i	0.880494	−	1.05170i
$433$	−8.20647e19			−1.38197			−0.690983	−	0.722871i	$-0.742822\pi$
$433$	−8.20647e19			−1.38197			−0.690983	+	0.722871i	$0.742822\pi$
$434$	−2.86297e17	−	4.08633e17i	−0.00473854	−	0.00676333i
$435$			1.30227e20i			2.11851i
$436$	4.14722e19	+	1.50686e19i	0.663145	+	0.240948i
$437$			3.12720e19i			0.491524i
$438$	7.86561e19	−	5.51082e19i	1.21528	−	0.851452i
$439$	8.92387e19			1.35541			0.677703	−	0.735336i	$-0.262975\pi$
$439$	8.92387e19			1.35541			0.677703	+	0.735336i	$0.262975\pi$
$440$	−1.47091e20	+	3.95442e19i	−2.19629	+	0.590456i
$441$	1.23412e20			1.81163
$442$	3.05210e18	−	2.13837e18i	0.0440486	−	0.0308614i
$443$			8.32102e19i			1.18072i	0.807138	+	0.590362i	$0.201015\pi$
$443$			8.32102e19i			1.18072i	−0.807138	+	0.590362i	$0.798985\pi$
$444$	−6.13045e19	+	1.68724e20i	−0.855303	+	2.35399i
$445$			2.54930e19i			0.349720i
$446$	−4.31143e19	−	6.15373e19i	−0.581581	−	0.830093i
$447$	−3.77713e19			−0.501020
$448$	3.67070e18	−	2.12744e18i	0.0478810	−	0.0277506i
$449$	6.70535e19			0.860150			0.430075	−	0.902793i	$-0.358487\pi$
$449$	6.70535e19			0.860150			0.430075	+	0.902793i	$0.358487\pi$
$450$	−1.10741e20	−	1.58061e20i	−1.39706	−	1.99403i
$451$		−	3.39181e19i		−	0.420831i
$452$	−1.70452e17	+	4.69123e17i	−0.00208000	+	0.00572465i
$453$		−	1.62463e20i		−	1.94993i
$454$	−5.17528e19	+	3.62591e19i	−0.610963	+	0.428054i
$455$	5.28470e18			0.0613670
$456$	1.67971e20	−	4.51578e19i	1.91866	−	0.515818i
$457$	2.49692e19			0.280565			0.140282	−	0.990112i	$-0.455199\pi$
$457$	2.49692e19			0.280565			0.140282	+	0.990112i	$0.455199\pi$
$458$	6.91614e17	−	4.84560e17i	0.00764492	−	0.00535619i
$459$		−	9.35815e18i		−	0.101764i
$460$	−5.58021e19	−	2.02752e19i	−0.596989	−	0.216911i
$461$			1.25078e20i			1.31650i	0.752797	+	0.658252i	$0.228704\pi$
$461$			1.25078e20i			1.31650i	−0.752797	+	0.658252i	$0.771296\pi$
$462$	−7.65226e18	−	1.09221e19i	−0.0792455	−	0.113107i
$463$	−2.00408e19			−0.204201			−0.102101	−	0.994774i	$-0.532556\pi$
$463$	−2.00408e19			−0.204201			−0.102101	+	0.994774i	$0.532556\pi$
$464$	5.28333e19	−	6.31065e19i	0.529692	−	0.632687i
$465$	3.88354e19			0.383116
$466$	−7.17094e19	−	1.02351e20i	−0.696116	−	0.993570i
$467$			1.69751e20i			1.62157i	0.585344	+	0.810785i	$0.300960\pi$
$467$			1.69751e20i			1.62157i	−0.585344	+	0.810785i	$0.699040\pi$
$468$	−1.31708e20	−	4.78548e19i	−1.23813	−	0.449865i
$469$			5.23865e18i			0.0484644i
$470$	1.52436e20	−	1.06800e20i	1.38789	−	0.972384i
$471$	−3.36509e20			−3.01537
$472$	1.75526e19	+	6.52895e19i	0.154802	+	0.575809i
$473$	−1.62397e20			−1.40968
$474$	−6.89632e18	+	4.83171e18i	−0.0589223	+	0.0412822i
$475$		−	1.88580e20i		−	1.58596i
$476$	1.69376e17	−	4.66162e17i	0.00140217	−	0.00385909i
$477$			2.35459e20i			1.91879i
$478$	1.02024e20	+	1.45619e20i	0.818448	+	1.16817i
$479$	−5.75801e19			−0.454733			−0.227366	−	0.973809i	$-0.573011\pi$
$479$	−5.75801e19			−0.454733			−0.227366	+	0.973809i	$0.573011\pi$
$480$	−2.83243e19	+	3.29008e20i	−0.220217	+	2.55798i
$481$	1.41320e20			1.08172
$482$	6.50169e18	+	9.27989e18i	0.0489974	+	0.0699343i
$483$		−	5.19833e18i		−	0.0385710i
$484$	5.65870e19	−	1.55740e20i	0.413406	−	1.13779i
$485$		−	3.10100e20i		−	2.23069i
$486$	6.44687e19	−	4.51682e19i	0.456643	−	0.319934i
$487$	−7.29502e19			−0.508814			−0.254407	−	0.967097i	$-0.581880\pi$
$487$	−7.29502e19			−0.508814			−0.254407	+	0.967097i	$0.581880\pi$
$488$	−6.10756e18	−	2.27180e19i	−0.0419488	−	0.156035i
$489$	1.87030e20			1.26501
$490$	−1.87504e20	+	1.31369e20i	−1.24894	+	0.875031i
$491$			1.69291e20i			1.11051i	0.831680	+	0.555256i	$0.187380\pi$
$491$			1.69291e20i			1.11051i	−0.831680	+	0.555256i	$0.812620\pi$
$492$	−6.91157e19	−	2.51126e19i	−0.446517	−	0.162238i
$493$		−	9.62151e18i		−	0.0612197i
$494$	−7.85690e19	−	1.12142e20i	−0.492378	−	0.702774i
$495$	6.69552e20			4.13281
$496$	−1.88192e19	−	1.57556e19i	−0.114416	−	0.0957903i
$497$	−3.75512e18			−0.0224880
$498$	2.61636e20	+	3.73434e20i	1.54340	+	2.20290i
$499$		−	3.02072e20i		−	1.75532i	−0.479281	−	0.877661i	$-0.659103\pi$
$499$		−	3.02072e20i		−	1.75532i	0.479281	−	0.877661i	$-0.340897\pi$
$500$	8.53495e19	+	3.10110e19i	0.488569	+	0.177517i
$501$		−	2.56268e20i		−	1.44514i
$502$	−1.28528e20	+	9.00494e19i	−0.714035	+	0.500268i
$503$	2.31647e20			1.26785			0.633925	−	0.773395i	$-0.281443\pi$
$503$	2.31647e20			1.26785			0.633925	+	0.773395i	$0.281443\pi$
$504$	−1.80106e19	+	4.84201e18i	−0.0971179	+	0.0261094i
$505$	−5.53675e20			−2.94151
$506$	9.65965e19	−	6.76776e19i	0.505630	−	0.354255i
$507$		−	1.54416e20i		−	0.796403i
$508$	7.96035e19	−	2.19087e20i	0.404533	−	1.11337i
$509$			7.79841e19i			0.390502i	0.980753	+	0.195251i	$0.0625521\pi$
$509$			7.79841e19i			0.390502i	−0.980753	+	0.195251i	$0.937448\pi$
$510$	2.21514e19	+	3.16168e19i	0.109301	+	0.156006i
$511$	−1.00623e19			−0.0489260
$512$	1.47205e20	−	1.47942e20i	0.705338	−	0.708871i
$513$	−3.43842e20			−1.62360
$514$	7.01815e19	+	1.00170e20i	0.326587	+	0.466140i
$515$			1.20695e20i			0.553523i
$516$	−1.20237e20	+	3.30920e20i	−0.543458	+	1.49572i
$517$			3.69754e20i			1.64715i
$518$	1.54038e19	−	1.07922e19i	0.0676323	−	0.0473847i
$519$	−5.09133e20			−2.20331
$520$	2.51047e20	−	6.74921e19i	1.07085	−	0.287891i
$521$	3.41951e20			1.43774			0.718871	−	0.695144i	$-0.244659\pi$
$521$	3.41951e20			1.43774			0.718871	+	0.695144i	$0.244659\pi$
$522$	−2.96307e20	+	2.07599e20i	−1.22804	+	0.860391i
$523$			2.11396e20i			0.863642i	0.901959	+	0.431821i	$0.142129\pi$
$523$			2.11396e20i			0.863642i	−0.901959	+	0.431821i	$0.857871\pi$
$524$	1.94969e20	+	7.08402e19i	0.785200	+	0.285296i
$525$			3.13476e19i			0.124454i
$526$	4.53721e18	+	6.47598e18i	0.0177581	+	0.0253462i
$527$	−2.86926e18			−0.0110711
$528$	−5.03005e20	−	4.21121e20i	−1.91345	−	1.60196i
$529$	−2.20660e20			−0.827574
$530$	−2.50640e20	−	3.57740e20i	−0.926790	−	1.32281i
$531$		−	2.97195e20i		−	1.08351i
$532$	−1.71280e19	−	6.22330e18i	−0.0615699	−	0.0223709i
$533$			5.78898e19i			0.205186i
$534$	−8.99242e19	+	6.30028e19i	−0.314280	+	0.220191i
$535$	−4.23425e20			−1.45923
$536$	6.69039e19	+	2.48860e20i	0.227361	+	0.845704i
$537$	3.99895e20			1.34010
$538$	2.06341e20	−	1.44567e20i	0.681897	−	0.477751i
$539$		−	4.54815e20i		−	1.48224i
$540$	2.22930e20	−	6.13555e20i	0.716498	−	1.97197i
$541$			5.13131e20i			1.62648i	0.581929	+	0.813240i	$0.302298\pi$
$541$			5.13131e20i			1.62648i	−0.581929	+	0.813240i	$0.697702\pi$
$542$	−1.26030e20	−	1.79883e20i	−0.393984	−	0.562334i
$543$	8.94209e20			2.75702
$544$	2.09267e18	−	2.43080e19i	0.00636370	−	0.0739191i
$545$	3.59833e20			1.07926
$546$	1.30605e19	+	1.86413e19i	0.0386380	+	0.0551482i
$547$		−	6.07670e20i		−	1.77322i	−0.462516	−	0.886611i	$-0.653053\pi$
$547$		−	6.07670e20i		−	1.77322i	0.462516	−	0.886611i	$-0.346947\pi$
$548$	−1.41188e20	+	3.88582e20i	−0.406391	+	1.11848i
$549$			1.03412e20i			0.293614i
$550$	−5.82507e20	+	4.08117e20i	−1.63148	+	1.14305i
$551$	−3.53518e20			−0.976731
$552$	−6.63891e19	−	2.46944e20i	−0.180948	−	0.673064i
$553$	8.82228e17			0.00237215
$554$	2.92550e20	−	2.04967e20i	0.776028	−	0.543702i
$555$			1.46393e21i			3.83110i
$556$	1.08772e20	+	3.95215e19i	0.280839	+	0.102040i
$557$			1.16265e20i			0.296166i	0.988975	+	0.148083i	$0.0473102\pi$
$557$			1.16265e20i			0.296166i	−0.988975	+	0.148083i	$0.952690\pi$
$558$	6.19086e19	+	8.83625e19i	0.155595	+	0.222081i
$559$	2.77172e20			0.687322
$560$	2.22098e19	−	2.65284e19i	0.0543420	−	0.0649085i
$561$	−7.66905e19			−0.185149
$562$	−2.40498e20	−	3.43264e20i	−0.572914	−	0.817723i
$563$			4.19500e20i			0.986095i	0.870002	+	0.493048i	$0.164117\pi$
$563$			4.19500e20i			0.986095i	−0.870002	+	0.493048i	$0.835883\pi$
$564$	7.53456e20	+	2.73762e20i	1.74769	+	0.635008i
$565$			4.07034e18i			0.00931681i
$566$	−4.03307e20	+	2.82565e20i	−0.910987	+	0.638257i
$567$	1.20412e19			0.0268409
$568$	−1.78385e20	+	4.79575e19i	−0.392416	+	0.105498i
$569$	−2.54681e20			−0.552910			−0.276455	−	0.961027i	$-0.589160\pi$
$569$	−2.54681e20			−0.552910			−0.276455	+	0.961027i	$0.589160\pi$
$570$	1.16168e21	−	8.13897e20i	2.48900	−	1.74384i
$571$		−	5.64239e20i		−	1.19314i	−0.802560	−	0.596571i	$-0.796529\pi$
$571$		−	5.64239e20i		−	1.19314i	0.802560	−	0.596571i	$-0.203471\pi$
$572$	−1.76361e20	+	4.85386e20i	−0.368071	+	1.01302i
$573$		−	1.54338e21i		−	3.17916i
$574$	4.42089e18	+	6.30996e18i	0.00898816	+	0.0128288i
$575$	−2.77242e20			−0.556353
$576$	−7.93748e20	+	4.60035e20i	−1.57222	+	0.911218i
$577$	2.42327e20			0.473787			0.236893	−	0.971536i	$-0.423871\pi$
$577$	2.42327e20			0.473787			0.236893	+	0.971536i	$0.423871\pi$
$578$	2.95682e20	+	4.22028e20i	0.570645	+	0.814485i
$579$			5.36828e20i			1.02269i
$580$	2.29204e20	−	6.30822e20i	0.431034	−	1.18631i
$581$		−	4.77724e19i		−	0.0886863i
$582$	1.09385e21	−	7.66375e20i	2.00464	−	1.40449i
$583$	8.67744e20			1.56992
$584$	−4.78004e20	+	1.28507e20i	−0.853758	+	0.229526i
$585$	−1.14276e21			−2.01505
$586$	−8.53347e20	+	5.97873e20i	−1.48557	+	1.04082i
$587$			2.53984e20i			0.436536i	0.975889	+	0.218268i	$0.0700407\pi$
$587$			2.53984e20i			0.436536i	−0.975889	+	0.218268i	$0.929959\pi$
$588$	−9.26787e20	−	3.36740e20i	−1.57271	−	0.571432i
$589$			1.05424e20i			0.176634i
$590$	3.16357e20	+	4.51538e20i	0.523344	+	0.746971i
$591$	−1.21634e21			−1.98678
$592$	5.93920e20	−	7.09405e20i	0.957889	−	1.14415i
$593$	4.91791e20			0.783196			0.391598	−	0.920136i	$-0.371922\pi$
$593$	4.91791e20			0.783196			0.391598	+	0.920136i	$0.371922\pi$
$594$	7.44128e20	+	1.06210e21i	1.17017	+	1.67019i
$595$		−	4.04465e18i		−	0.00628063i
$596$	1.82965e20	+	6.64787e19i	0.280557	+	0.101938i
$597$		−	7.53630e19i		−	0.114117i
$598$	−1.64866e20	+	1.15509e20i	−0.246532	+	0.172725i
$599$	−1.22676e21			−1.81159			−0.905793	−	0.423721i	$-0.860724\pi$
$599$	−1.22676e21			−1.81159			−0.905793	+	0.423721i	$0.860724\pi$
$600$	4.00347e20	+	1.48915e21i	0.583851	+	2.17172i
$601$	8.81075e20			1.26898			0.634489	−	0.772932i	$-0.281210\pi$
$601$	8.81075e20			1.26898			0.634489	+	0.772932i	$0.281210\pi$
$602$	3.02116e19	−	2.11669e19i	0.0429734	−	0.0301081i
$603$		−	1.13280e21i		−	1.59138i
$604$	−2.85940e20	+	7.86974e20i	−0.396733	+	1.09190i
$605$		−	1.35128e21i		−	1.85174i
$606$	−1.36834e21	−	1.95304e21i	−1.85204	−	2.64342i
$607$	8.63946e20			1.15497			0.577486	−	0.816401i	$-0.304034\pi$
$607$	8.63946e20			1.15497			0.577486	+	0.816401i	$0.304034\pi$
$608$	−8.93135e20	−	7.68900e19i	−1.17934	−	0.101530i
$609$	5.87652e19			0.0766462
$610$	−1.10079e20	−	1.57116e20i	−0.141818	−	0.202417i
$611$		−	6.31078e20i		−	0.803108i
$612$	−3.66257e19	+	1.00802e20i	−0.0460416	+	0.126717i
$613$			5.43647e20i			0.675092i	0.941309	+	0.337546i	$0.109597\pi$
$613$			5.43647e20i			0.675092i	−0.941309	+	0.337546i	$0.890403\pi$
$614$	3.77642e20	−	2.64584e20i	0.463252	−	0.324564i
$615$	−5.99681e20			−0.726703
$616$	1.78444e19	+	6.63750e19i	0.0213622	+	0.0794601i
$617$	9.53349e20			1.12749			0.563745	−	0.825949i	$-0.309360\pi$
$617$	9.53349e20			1.12749			0.563745	+	0.825949i	$0.309360\pi$
$618$	−4.25741e20	+	2.98283e20i	−0.497430	+	0.348510i
$619$			5.58681e20i			0.644888i	0.946589	+	0.322444i	$0.104504\pi$
$619$			5.58681e20i			0.644888i	−0.946589	+	0.322444i	$0.895496\pi$
$620$	−1.88119e20	−	6.83515e19i	−0.214534	−	0.0779489i
$621$			5.05502e20i			0.569555i
$622$	6.00683e19	+	8.57357e19i	0.0668678	+	0.0954407i
$623$	1.15038e19			0.0126526
$624$	8.58505e20	+	7.18748e20i	0.932950	+	0.781074i
$625$	−5.07280e20			−0.544687
$626$	−2.19345e20	−	3.13073e20i	−0.232713	−	0.332153i
$627$			2.81780e21i			2.95395i
$628$	1.63006e21	+	5.92267e20i	1.68852	+	0.613508i
$629$		−	1.08159e20i		−	0.110709i
$630$	−1.24560e20	+	8.72695e19i	−0.125987	+	0.0882690i
$631$	3.62782e20			0.362599			0.181299	−	0.983428i	$-0.441970\pi$
$631$	3.62782e20			0.362599			0.181299	+	0.983428i	$0.441970\pi$
$632$	4.19098e19	−	1.12671e19i	0.0413940	−	0.0111285i
$633$	5.72647e20			0.558932
$634$	8.90456e19	−	6.23872e19i	0.0858901	−	0.0601764i
$635$		−	1.90091e21i		−	1.81200i
$636$	6.42468e20	−	1.76822e21i	0.605234	−	1.66574i
$637$			7.76256e20i			0.722702i
$638$	7.65070e20	+	1.09199e21i	0.703957	+	1.00476i
$639$	8.12004e20			0.738417
$640$	7.16268e20	−	1.54387e21i	0.643762	−	1.38759i
$641$	−1.61218e21			−1.43212			−0.716059	−	0.698040i	$-0.754056\pi$
$641$	−1.61218e21			−1.43212			−0.716059	+	0.698040i	$0.754056\pi$
$642$	−1.04644e21	−	1.49359e21i	−0.918762	−	1.31135i
$643$		−	7.38606e20i		−	0.640959i	−0.947255	−	0.320480i	$-0.896156\pi$
$643$		−	7.38606e20i		−	0.640959i	0.947255	−	0.320480i	$-0.103844\pi$
$644$	−9.14923e18	+	2.51808e19i	−0.00784767	+	0.0215986i
$645$			2.87122e21i			2.43427i
$646$	−8.58278e19	+	6.01328e19i	−0.0719257	+	0.0503927i
$647$	−1.36574e20			−0.113132			−0.0565659	−	0.998399i	$-0.518015\pi$
$647$	−1.36574e20			−0.113132			−0.0565659	+	0.998399i	$0.518015\pi$
$648$	5.72011e20	−	1.53781e20i	0.468373	−	0.125918i
$649$	−1.09526e21			−0.886509
$650$	9.94194e20	−	6.96554e20i	0.795465	−	0.557320i
$651$		−	1.75245e19i		−	0.0138608i
$652$	−9.05977e20	−	3.29179e20i	−0.708370	−	0.257380i
$653$		−	1.25905e21i		−	0.973183i	−0.873630	−	0.486592i	$-0.838240\pi$
$653$		−	1.25905e21i		−	0.973183i	0.873630	−	0.486592i	$-0.161760\pi$
$654$	8.89283e20	+	1.26928e21i	0.679527	+	0.969892i
$655$	1.69164e21			1.27791
$656$	2.90598e20	+	2.43292e20i	0.217027	+	0.181697i
$657$	2.17586e21			1.60653
$658$	−4.81938e19	−	6.87872e19i	−0.0351801	−	0.0502127i
$659$			8.06495e20i			0.582051i	0.956715	+	0.291026i	$0.0939965\pi$
$659$			8.06495e20i			0.582051i	−0.956715	+	0.291026i	$0.906003\pi$
$660$	−5.02811e21	−	1.82692e21i	−3.58778	−	1.30359i
$661$			1.10006e21i			0.776081i	0.921642	+	0.388041i	$0.126848\pi$
$661$			1.10006e21i			0.776081i	−0.921642	+	0.388041i	$0.873152\pi$
$662$	−4.45001e20	+	3.11777e20i	−0.310403	+	0.217475i
$663$	1.30892e20			0.0902735
$664$	−6.10112e20	−	2.26941e21i	−0.416054	−	1.54758i
$665$	−1.48610e20			−0.100204
$666$	−3.33090e21	+	2.33370e21i	−2.22078	+	1.55592i
$667$			5.19728e20i			0.342635i
$668$	−4.51040e20	+	1.24137e21i	−0.294030	+	0.809238i
$669$		−	2.63907e21i		−	1.70120i
$670$	1.20584e21	+	1.72109e21i	0.768647	+	1.09709i
$671$	3.81106e20			0.240230
$672$	1.48466e20	+	1.27814e19i	0.0925457	+	0.00796726i
$673$	−2.15849e21			−1.33057			−0.665285	−	0.746589i	$-0.731690\pi$
$673$	−2.15849e21			−1.33057			−0.665285	+	0.746589i	$0.731690\pi$
$674$	−6.35395e18	−	9.06902e18i	−0.00387342	−	0.00552855i
$675$		−	3.04833e21i		−	1.83774i
$676$	−2.71777e20	+	7.47994e20i	−0.162037	+	0.445962i
$677$			3.56159e20i			0.210005i	0.994472	+	0.105002i	$0.0334850\pi$
$677$			3.56159e20i			0.210005i	−0.994472	+	0.105002i	$0.966515\pi$
$678$	−1.43578e19	+	1.00594e19i	−0.00837267	+	0.00586607i
$679$	−1.39933e20			−0.0807046
$680$	−5.16551e19	−	1.92139e20i	−0.0294643	−	0.109597i
$681$	−2.21946e21			−1.25211
$682$	3.25645e20	−	2.28154e20i	0.181703	−	0.127305i
$683$			1.66633e21i			0.919614i	0.888019	+	0.459807i	$0.152081\pi$
$683$			1.66633e21i			0.919614i	−0.888019	+	0.459807i	$0.847919\pi$
$684$	3.70373e21	+	1.34572e21i	2.02171	+	0.734571i
$685$			3.37152e21i			1.82032i
$686$	1.18744e20	+	1.69483e20i	0.0634131	+	0.0905098i
$687$	2.96604e19			0.0156676
$688$	1.16486e21	−	1.39136e21i	0.608640	−	0.726988i
$689$	−1.48102e21			−0.765451
$690$	−1.19656e21	−	1.70785e21i	−0.611737	−	0.873136i
$691$		−	1.01961e21i		−	0.515640i	−0.966193	−	0.257820i	$-0.916996\pi$
$691$		−	1.01961e21i		−	0.515640i	0.966193	−	0.257820i	$-0.0830042\pi$
$692$	2.46625e21	+	8.96091e20i	1.23379	+	0.448287i
$693$		−	3.02137e20i		−	0.149522i
$694$	1.26126e21	−	8.83666e20i	0.617460	−	0.432606i
$695$	9.43760e20			0.457063
$696$	2.79161e21	−	7.50504e20i	1.33748	−	0.359570i
$697$	4.43060e19			0.0209999
$698$	−1.09581e20	+	7.67747e19i	−0.0513830	+	0.0360000i
$699$		−	4.38940e21i		−	2.03623i
$700$	5.51727e19	−	1.51848e20i	0.0253215	−	0.0696906i
$701$		−	2.21860e21i		−	1.00738i	−0.863885	−	0.503690i	$-0.831976\pi$
$701$		−	2.21860e21i		−	1.00738i	0.863885	−	0.503690i	$-0.168024\pi$
$702$	−1.27004e21	−	1.81274e21i	−0.570545	−	0.814341i
$703$	−3.97404e21			−1.76631
$704$	1.69538e21	+	2.92522e21i	0.745542	+	1.28636i
$705$	6.53734e21			2.84435
$706$	2.11676e21	+	3.02127e21i	0.911249	+	1.30063i
$707$			2.49847e20i			0.106421i
$708$	−8.10920e20	+	2.23184e21i	−0.341766	+	0.940619i
$709$		−	4.74711e21i		−	1.97962i	−0.142383	−	0.989812i	$-0.545476\pi$
$709$		−	4.74711e21i		−	1.97962i	0.142383	−	0.989812i	$-0.454524\pi$
$710$	−1.23370e21	+	8.64357e20i	−0.509064	+	0.356661i
$711$	−1.90772e20			−0.0778920
$712$	5.46481e20	−	1.46917e20i	0.220788	−	0.0593571i
$713$	1.54989e20			0.0619627
$714$	1.42671e19	−	9.99586e18i	0.00564417	−	0.00395443i
$715$			4.21144e21i			1.64868i
$716$	−1.93710e21	−	7.03828e20i	−0.750419	−	0.272658i
$717$			6.24496e21i			2.39407i
$718$	−6.85502e20	−	9.78420e20i	−0.260061	−	0.371186i
$719$	−2.72163e20			−0.102179			−0.0510896	−	0.998694i	$-0.516269\pi$
$719$	−2.72163e20			−0.102179			−0.0510896	+	0.998694i	$0.516269\pi$
$720$	−4.80263e21	+	5.73648e21i	−1.78437	+	2.13134i
$721$	5.44639e19			0.0200260
$722$	6.32571e20	+	9.02872e20i	0.230187	+	0.328547i
$723$			3.97975e20i			0.143324i
$724$	−4.33156e21	−	1.57384e21i	−1.54385	−	0.560945i
$725$		−	3.13412e21i		−	1.10555i
$726$	4.76652e21	−	3.33952e21i	1.66409	−	1.16590i
$727$	3.64179e21			1.25837			0.629184	−	0.777257i	$-0.283389\pi$
$727$	3.64179e21			1.25837			0.629184	+	0.777257i	$0.283389\pi$
$728$	−3.04559e19	−	1.13286e20i	−0.0104157	−	0.0387427i
$729$	4.19764e21			1.42085
$730$	−3.30584e21	+	2.31614e21i	−1.10754	+	0.775968i
$731$		−	2.12134e20i		−	0.0703443i
$732$	2.82166e20	−	7.76587e20i	0.0926131	−	0.254893i
$733$			2.24321e21i			0.728770i	0.931248	+	0.364385i	$0.118721\pi$
$733$			2.24321e21i			0.728770i	−0.931248	+	0.364385i	$0.881279\pi$
$734$	−8.11599e20	−	1.15840e21i	−0.260988	−	0.372510i
$735$	−8.04125e21			−2.55958
$736$	−1.13041e20	+	1.31305e21i	−0.0356164	+	0.413712i
$737$	−4.17474e21			−1.30204
$738$	−9.55969e20	−	1.36446e21i	−0.295135	−	0.421248i
$739$		−	4.72145e21i		−	1.44292i	−0.692456	−	0.721460i	$-0.743471\pi$
$739$		−	4.72145e21i		−	1.44292i	0.692456	−	0.721460i	$-0.256529\pi$
$740$	2.57657e21	−	7.09131e21i	0.779478	−	2.14530i
$741$		−	4.80928e21i		−	1.44027i
$742$	−1.61431e20	+	1.13102e20i	−0.0478583	+	0.0335305i
$743$	3.14778e21			0.923822			0.461911	−	0.886926i	$-0.347164\pi$
$743$	3.14778e21			0.923822			0.461911	+	0.886926i	$0.347164\pi$
$744$	−2.23810e20	−	8.32495e20i	−0.0650253	−	0.241872i
$745$	1.58749e21			0.456603
$746$	5.41721e21	−	3.79541e21i	1.54253	−	1.08073i
$747$			1.03303e22i			2.91210i
$748$	3.71490e20	+	1.34978e20i	0.103678	+	0.0376704i
$749$			1.91071e20i			0.0527937i
$750$	1.83014e21	+	2.61216e21i	0.500639	+	0.714564i
$751$	−1.50411e20			−0.0407361			−0.0203681	−	0.999793i	$-0.506484\pi$
$751$	−1.50411e20			−0.0407361			−0.0203681	+	0.999793i	$0.506484\pi$
$752$	−3.16792e21	−	2.65221e21i	−0.849456	−	0.711172i
$753$	−5.51202e21			−1.46335
$754$	−1.30578e21	−	1.86375e21i	−0.343231	−	0.489895i
$755$			6.82817e21i			1.77706i
$756$	−2.76868e20	−	1.00598e20i	−0.0713443	−	0.0259223i
$757$		−	4.49997e21i		−	1.14813i	−0.818811	−	0.574064i	$-0.805366\pi$
$757$		−	4.49997e21i		−	1.14813i	0.818811	−	0.574064i	$-0.194634\pi$
$758$	−8.68447e20	+	6.08453e20i	−0.219394	+	0.153712i
$759$	4.14261e21			1.03624
$760$	−7.05967e21	+	1.89794e21i	−1.74857	+	0.470089i
$761$	−2.33535e21			−0.572754			−0.286377	−	0.958117i	$-0.592451\pi$
$761$	−2.33535e21			−0.572754			−0.286377	+	0.958117i	$0.592451\pi$
$762$	6.70527e21	−	4.69786e21i	1.62837	−	1.14087i
$763$		−	1.62375e20i		−	0.0390469i
$764$	−2.71640e21	+	7.47615e21i	−0.646834	+	1.78024i
$765$			8.74611e20i			0.206231i
$766$	−3.96997e21	−	5.66636e21i	−0.926983	−	1.32309i
$767$	1.86934e21			0.432238
$768$	7.21602e21	−	1.28891e21i	1.65230	−	0.295130i
$769$	1.43868e21			0.326224			0.163112	−	0.986608i	$-0.447847\pi$
$769$	1.43868e21			0.326224			0.163112	+	0.986608i	$0.447847\pi$
$770$	3.21617e20	+	4.59045e20i	0.0722201	+	0.103080i
$771$			4.29588e21i			0.955310i
$772$	9.44834e20	−	2.60040e21i	0.208078	−	0.572678i
$773$			5.51890e21i			1.20367i	0.798621	+	0.601834i	$0.205563\pi$
$773$			5.51890e21i			1.20367i	−0.798621	+	0.601834i	$0.794437\pi$
$774$	−6.53293e21	+	4.57711e21i	−1.41108	+	0.988630i
$775$	−9.34634e20			−0.199930
$776$	−6.64747e21	+	1.78712e21i	−1.40829	+	0.378609i
$777$	6.60603e20			0.138606
$778$	1.37148e21	−	9.60885e20i	0.284998	−	0.199675i
$779$		−	1.62791e21i		−	0.335043i
$780$	8.58174e21	+	3.11810e21i	1.74931	+	0.635595i
$781$		−	2.99250e21i		−	0.604160i
$782$	8.84047e19	+	1.26180e20i	0.0176777	+	0.0252314i
$783$	−5.71451e21			−1.13179
$784$	3.89670e21	+	3.26235e21i	0.764409	+	0.639970i
$785$	1.41432e22			2.74804
$786$	4.18069e21	+	5.96711e21i	0.804597	+	1.14841i
$787$		−	6.07126e21i		−	1.15736i	−0.815555	−	0.578680i	$-0.803568\pi$
$787$		−	6.07126e21i		−	1.15736i	0.815555	−	0.578680i	$-0.196432\pi$
$788$	5.89199e21	+	2.14080e21i	1.11254	+	0.404232i
$789$			2.77727e20i			0.0519447i
$790$	2.89845e20	−	2.03072e20i	0.0536986	−	0.0376224i
$791$	1.83675e18			0.000337075
$792$	−3.85866e21	−	1.43529e22i	−0.701451	−	2.60916i
$793$	−6.50453e20			−0.117130
$794$	−7.71594e21	+	5.40595e21i	−1.37637	+	0.964314i
$795$		−	1.53419e22i		−	2.71098i
$796$	−1.32641e20	+	3.65059e20i	−0.0232183	+	0.0639022i
$797$			1.11112e22i			1.92674i	0.268184	+	0.963368i	$0.413577\pi$
$797$			1.11112e22i			1.92674i	−0.268184	+	0.963368i	$0.586423\pi$
$798$	−3.67273e20	−	5.24210e20i	−0.0630909	−	0.0900499i
$799$	−4.82996e20			−0.0821945
$800$	6.81669e20	−	7.91810e21i	0.114921	−	1.33489i
$801$	−2.48756e21			−0.415461
$802$	−3.43822e21	−	4.90738e21i	−0.568886	−	0.811974i
$803$		−	8.01874e21i		−	1.31444i
$804$	−3.09093e21	+	8.50695e21i	−0.501959	+	1.38151i
$805$			2.18481e20i			0.0351515i
$806$	−5.55794e20	+	3.89401e20i	−0.0885934	+	0.0620704i
$807$	8.84909e21			1.39748
$808$	3.19085e21	+	1.18689e22i	0.499254	+	1.85705i
$809$	4.64825e21			0.720568			0.360284	−	0.932843i	$-0.382680\pi$
$809$	4.64825e21			0.720568			0.360284	+	0.932843i	$0.382680\pi$
$810$	3.95599e21	−	2.77165e21i	0.607600	−	0.425697i
$811$			6.95327e21i			1.05811i	0.848586	+	0.529057i	$0.177454\pi$
$811$			6.95327e21i			1.05811i	−0.848586	+	0.529057i	$0.822546\pi$
$812$	−2.84660e20	−	1.03429e20i	−0.0429196	−	0.0155945i
$813$		−	7.71440e21i		−	1.15245i
$814$	8.60045e21	+	1.22755e22i	1.27303	+	1.81700i
$815$	−7.86069e21			−1.15287
$816$	5.50094e20	−	6.57057e20i	0.0799394	−	0.0954832i
$817$	−7.79431e21			−1.12231
$818$	2.09260e21	+	2.98678e21i	0.298563	+	0.426141i
$819$			5.15672e20i			0.0729028i
$820$	2.90486e21	+	1.05546e21i	0.406932	+	0.147855i
$821$			1.63651e21i			0.227167i	0.993528	+	0.113584i	$0.0362330\pi$
$821$			1.63651e21i			0.227167i	−0.993528	+	0.113584i	$0.963767\pi$
$822$	−1.18927e22	+	8.33231e21i	−1.63585	+	1.14611i
$823$	−1.30316e22			−1.77623			−0.888116	−	0.459620i	$-0.847986\pi$
$823$	−1.30316e22			−1.77623			−0.888116	+	0.459620i	$0.847986\pi$
$824$	2.58728e21	−	6.95571e20i	0.349454	−	0.0939479i
$825$	−2.49812e22			−3.34356
$826$	2.03757e20	−	1.42757e20i	0.0270248	−	0.0189342i
$827$		−	5.43834e21i		−	0.714784i	−0.933954	−	0.357392i	$-0.883666\pi$
$827$		−	5.43834e21i		−	0.714784i	0.933954	−	0.357392i	$-0.116334\pi$
$828$	1.97842e21	−	5.44507e21i	0.257686	−	0.709212i
$829$		−	4.84909e21i		−	0.625894i	−0.949771	−	0.312947i	$-0.898684\pi$
$829$		−	4.84909e21i		−	0.625894i	0.949771	−	0.312947i	$-0.101316\pi$
$830$	−1.09963e22	−	1.56951e22i	−1.40657	−	2.00760i
$831$	1.25462e22			1.59040
$832$	−2.89359e21	−	4.99262e21i	−0.363507	−	0.627197i
$833$	5.94108e20			0.0739653
$834$	2.33239e21	+	3.32903e21i	0.287777	+	0.410745i
$835$			1.07707e22i			1.31703i
$836$	4.95942e21	−	1.36495e22i	0.601013	−	1.65413i
$837$			1.70414e21i			0.204675i
$838$	9.18917e20	−	6.43813e20i	0.109382	−	0.0766354i
$839$	9.02485e21			1.06470			0.532348	−	0.846526i	$-0.321310\pi$
$839$	9.02485e21			1.06470			0.532348	+	0.846526i	$0.321310\pi$
$840$	1.17353e21	−	3.15493e20i	0.137214	−	0.0368889i
$841$	2.75386e21			0.319133
$842$	2.77919e21	−	1.94716e21i	0.319210	−	0.223646i
$843$		−	1.47211e22i		−	1.67585i
$844$	−2.77391e21	−	1.00788e21i	−0.312985	−	0.113721i
$845$			6.48996e21i			0.725799i
$846$	1.04214e22	+	1.48745e22i	1.15517	+	1.64879i
$847$	−6.09768e20			−0.0669945
$848$	−6.22425e21	+	7.43452e21i	−0.677826	+	0.809625i
$849$	−1.72961e22			−1.86698
$850$	−5.33108e20	−	7.60907e20i	−0.0570392	−	0.0814122i
$851$			5.84246e21i			0.619618i
$852$	−6.09788e21	−	2.21561e21i	−0.641036	−	0.232915i
$853$			4.32653e21i			0.450840i	0.974262	+	0.225420i	$0.0723754\pi$
$853$			4.32653e21i			0.450840i	−0.974262	+	0.225420i	$0.927625\pi$
$854$	−7.08991e19	+	4.96734e19i	−0.00732329	+	0.00513086i
$855$	3.21354e22			3.29031
$856$	2.44021e21	+	9.07676e21i	0.247671	+	0.921250i
$857$	1.15996e22			1.16704			0.583521	−	0.812098i	$-0.301675\pi$
$857$	1.15996e22			1.16704			0.583521	+	0.812098i	$0.301675\pi$
$858$	−1.48555e22	+	1.04081e22i	−1.48160	+	1.03804i
$859$			2.37330e21i			0.234641i	0.993094	+	0.117321i	$0.0374305\pi$
$859$			2.37330e21i			0.234641i	−0.993094	+	0.117321i	$0.962569\pi$
$860$	5.05345e21	−	1.39083e22i	0.495278	−	1.36312i
$861$			2.70607e20i			0.0262915i
$862$	−4.67909e21	−	6.67849e21i	−0.450668	−	0.643241i
$863$	−9.83961e21			−0.939501			−0.469750	−	0.882799i	$-0.655656\pi$
$863$	−9.83961e21			−0.939501			−0.469750	+	0.882799i	$0.655656\pi$
$864$	−1.44372e22	−	1.24290e21i	−1.36657	−	0.117648i
$865$	2.13984e22			2.00798
$866$	8.52403e21	+	1.21664e22i	0.792977	+	1.13182i
$867$			1.80990e22i			1.66921i
$868$	−3.08438e19	+	8.48891e19i	−0.00282013	+	0.00776165i
$869$			7.03058e20i			0.0637298i
$870$	1.93066e22	−	1.35266e22i	1.73505	−	1.21561i
$871$	7.12524e21			0.634838
$872$	−2.07373e21	−	7.71357e21i	−0.183180	−	0.681368i
$873$	3.02591e22			2.65002
$874$	4.63618e21	−	3.24821e21i	0.402555	−	0.282038i
$875$		−	3.34167e20i		−	0.0287676i
$876$	−1.63400e22	−	5.93699e21i	−1.39467	−	0.506740i
$877$		−	1.13967e22i		−	0.964457i	−0.876046	−	0.482228i	$-0.839828\pi$
$877$		−	1.13967e22i		−	0.964457i	0.876046	−	0.482228i	$-0.160172\pi$
$878$	−9.26919e21	−	1.32300e22i	−0.777737	−	1.11007i
$879$	−3.65964e22			−3.04454
$880$	2.11408e22	+	1.76993e22i	1.74382	+	1.45994i
$881$	−1.32703e22			−1.08533			−0.542665	−	0.839949i	$-0.682585\pi$
$881$	−1.32703e22			−1.08533			−0.542665	+	0.839949i	$0.682585\pi$
$882$	−1.28188e22	−	1.82963e22i	−1.03952	−	1.48371i
$883$		−	1.60387e22i		−	1.28963i	−0.764340	−	0.644813i	$-0.776935\pi$
$883$		−	1.60387e22i		−	1.28963i	0.764340	−	0.644813i	$-0.223065\pi$
$884$	−6.34041e20	−	2.30373e20i	−0.0505505	−	0.0183671i
$885$			1.93645e22i			1.53085i
$886$	1.23362e22	−	8.64301e21i	0.967005	−	0.677504i
$887$	−1.17227e22			−0.911169			−0.455584	−	0.890193i	$-0.650570\pi$
$887$	−1.17227e22			−0.911169			−0.455584	+	0.890193i	$0.650570\pi$
$888$	3.13816e22	−	8.43670e21i	2.41868	−	0.650243i
$889$	−8.57788e20			−0.0655566
$890$	3.77942e21	−	2.64795e21i	0.286418	−	0.200671i
$891$			9.59577e21i			0.721102i
$892$	−4.64485e21	+	1.27837e22i	−0.346127	+	0.952622i
$893$			1.77465e22i			1.31137i
$894$	3.92329e21	+	5.59973e21i	0.287487	+	0.410332i
$895$	−1.68072e22			−1.22130
$896$	−6.96674e20	−	3.23217e20i	−0.0502018	−	0.0232908i
$897$	−7.07041e21			−0.505244
$898$	−6.96482e21	−	9.94092e21i	−0.493557	−	0.704456i
$899$			1.75210e21i			0.123129i
$900$	−1.19305e22	+	3.28355e22i	−0.831457	+	2.28836i
$901$			1.13350e21i			0.0783405i
$902$	−5.02848e21	+	3.52306e21i	−0.344658	+	0.241474i
$903$	1.29565e21			0.0880701
$904$	8.72540e19	−	2.34575e19i	0.00588196	−	0.00158132i
$905$	−3.75827e22			−2.51260
$906$	−2.40857e22	+	1.68750e22i	−1.59698	+	1.11888i
$907$			1.91784e22i			1.26112i	0.776139	+	0.630562i	$0.217175\pi$
$907$			1.91784e22i			1.26112i	−0.776139	+	0.630562i	$0.782825\pi$
$908$	1.07511e22	+	3.90631e21i	0.701145	+	0.254755i
$909$		−	5.40267e22i		−	3.49445i
$910$	−5.48920e20	−	7.83475e20i	−0.0352126	−	0.0502591i
$911$	2.32929e22			1.48196			0.740978	−	0.671530i	$-0.234362\pi$
$911$	2.32929e22			1.48196			0.740978	+	0.671530i	$0.234362\pi$
$912$	−2.41419e22	−	2.02118e22i	−1.52339	−	1.27539i
$913$	3.80704e22			2.38263
$914$	−2.59354e21	−	3.70177e21i	−0.160989	−	0.229781i
$915$		−	6.73805e21i		−	0.414835i
$916$	−1.43675e20	−	5.22032e19i	−0.00877336	−	0.00318773i
$917$		−	7.63357e20i		−	0.0462336i
$918$	−1.38738e21	+	9.72027e20i	−0.0833441	+	0.0583927i
$919$	2.98532e21			0.177879			0.0889394	−	0.996037i	$-0.471652\pi$
$919$	2.98532e21			0.177879			0.0889394	+	0.996037i	$0.471652\pi$
$920$	2.79027e21	+	1.03788e22i	0.164906	+	0.613394i
$921$	1.61954e22			0.949392
$922$	1.85432e22	−	1.29918e22i	1.07821	−	0.755415i
$923$			5.10746e21i			0.294572i
$924$	−8.24403e20	+	2.26895e21i	−0.0471628	+	0.129803i
$925$		−	3.52318e22i		−	1.99927i
$926$	2.08163e21	+	2.97112e21i	0.117171	+	0.167239i
$927$	−1.17772e22			−0.657574
$928$	−1.48435e22	−	1.27788e21i	−0.822105	−	0.0707751i
$929$	1.47039e21			0.0807821			0.0403910	−	0.999184i	$-0.487140\pi$
$929$	1.47039e21			0.0807821			0.0403910	+	0.999184i	$0.487140\pi$
$930$	−4.03381e21	−	5.75748e21i	−0.219833	−	0.313769i
$931$		−	2.18290e22i		−	1.18008i
$932$	−7.72549e21	+	2.12623e22i	−0.414292	+	1.14023i
$933$			3.67684e21i			0.195597i
$934$	2.51662e22	−	1.76320e22i	1.32805	−	0.930464i
$935$	3.22323e21			0.168735
$936$	6.58576e21	+	2.44968e22i	0.342009	+	1.27215i
$937$	−1.35569e22			−0.698417			−0.349208	−	0.937045i	$-0.613549\pi$
$937$	−1.35569e22			−0.698417			−0.349208	+	0.937045i	$0.613549\pi$
$938$	7.76648e20	−	5.44136e20i	0.0396920	−	0.0278091i
$939$		−	1.34264e22i		−	0.680716i
$940$	−3.16670e22	−	1.15059e22i	−1.59275	−	0.578713i
$941$		−	1.13116e22i		−	0.564418i	−0.959353	−	0.282209i	$-0.908933\pi$
$941$		−	1.13116e22i		−	0.564418i	0.959353	−	0.282209i	$-0.0910672\pi$
$942$	3.49531e22	+	4.98887e22i	1.73023	+	2.46956i
$943$	−2.39329e21			−0.117532
$944$	7.85622e21	−	9.38382e21i	0.382758	−	0.457183i
$945$	−2.40224e21			−0.116112
$946$	1.68681e22	+	2.40760e22i	0.808879	+	1.15452i
$947$			1.72242e22i			0.819433i	0.912213	+	0.409716i	$0.134372\pi$
$947$			1.72242e22i			0.819433i	−0.912213	+	0.409716i	$0.865628\pi$
$948$	1.43264e21	+	5.20536e20i	0.0676197	+	0.0245690i
$949$			1.36860e22i			0.640885i
$950$	−2.79576e22	+	1.95877e22i	−1.29889	+	0.910032i
$951$	3.81879e21			0.176024
$952$	−8.67032e19	+	2.33095e19i	−0.00396514	+	0.00106600i
$953$	−8.21718e21			−0.372843			−0.186421	−	0.982470i	$-0.559689\pi$
$953$	−8.21718e21			−0.372843			−0.186421	+	0.982470i	$0.559689\pi$
$954$	3.49076e22	−	2.44570e22i	1.57148	−	1.10101i
$955$			6.48667e22i			2.89732i
$956$	1.09913e22	−	3.02507e22i	0.487098	−	1.34061i
$957$			4.68307e22i			2.05916i
$958$	5.98082e21	+	8.53646e21i	0.260927	+	0.372423i
$959$	1.52141e21			0.0658576
$960$	5.17186e22	−	2.99747e22i	2.22133	−	1.28742i
$961$	−2.29428e22			−0.977733
$962$	−1.46788e22	−	2.09511e22i	−0.620695	−	0.885921i
$963$		−	4.13171e22i		−	1.73353i
$964$	7.00448e20	−	1.92780e21i	0.0291607	−	0.0802571i
$965$		−	2.25623e22i		−	0.932029i
$966$	−7.70671e20	+	5.39949e20i	−0.0315894	+	0.0221322i
$967$	−1.45625e22			−0.592296			−0.296148	−	0.955142i	$-0.595702\pi$
$967$	−1.45625e22			−0.592296			−0.296148	+	0.955142i	$0.595702\pi$
$968$	−2.89667e22	+	7.78748e21i	−1.16905	+	0.314291i
$969$	−3.68079e21			−0.147405
$970$	−4.59734e22	+	3.22100e22i	−1.82692	+	1.27998i
$971$		−	4.44965e22i		−	1.75462i	−0.479928	−	0.877308i	$-0.659337\pi$
$971$		−	4.44965e22i		−	1.75462i	0.479928	−	0.877308i	$-0.340663\pi$
$972$	−1.33927e22	−	4.86612e21i	−0.524047	−	0.190408i
$973$		−	4.25874e20i		−	0.0165362i
$974$	7.57730e21	+	1.08151e22i	0.291959	+	0.416715i
$975$	4.26367e22			1.63023
$976$	−2.73364e21	+	3.26518e21i	−0.103721	+	0.123889i
$977$	7.34006e21			0.276370			0.138185	−	0.990406i	$-0.455873\pi$
$977$	7.34006e21			0.276370			0.138185	+	0.990406i	$0.455873\pi$
$978$	−1.94267e22	−	2.77279e22i	−0.725869	−	1.03604i
$979$			9.16749e21i			0.339923i
$980$	3.89519e22	+	1.41529e22i	1.43329	+	0.520773i
$981$			3.51119e22i			1.28214i
$982$	2.50980e22	−	1.75842e22i	0.909501	−	0.637216i
$983$	1.35957e22			0.488934			0.244467	−	0.969658i	$-0.421387\pi$
$983$	1.35957e22			0.488934			0.244467	+	0.969658i	$0.421387\pi$
$984$	3.45599e21	+	1.28551e22i	0.123341	+	0.458787i
$985$	5.11217e22			1.81065
$986$	−1.42642e21	+	9.99382e20i	−0.0501385	+	0.0351281i
$987$		−	2.94999e21i		−	0.102906i
$988$	−8.46449e21	+	2.32962e22i	−0.293038	+	0.806508i
$989$			1.14589e22i			0.393704i
$990$	−6.95461e22	−	9.92634e22i	−2.37142	−	3.38474i
$991$	−2.67627e21			−0.0905686			−0.0452843	−	0.998974i	$-0.514419\pi$
$991$	−2.67627e21			−0.0905686			−0.0452843	+	0.998974i	$0.514419\pi$
$992$	−3.81080e20	+	4.42653e21i	−0.0127991	+	0.148671i
$993$	−1.90842e22			−0.636143
$994$	3.90043e20	+	5.56710e20i	0.0129037	+	0.0184175i
$995$			3.16743e21i			0.104000i
$996$	2.81869e22	−	7.75769e22i	0.918549	−	2.52806i
$997$		−	1.79920e22i		−	0.581924i	−0.956735	−	0.290962i	$-0.906025\pi$
$997$		−	1.79920e22i		−	0.581924i	0.956735	−	0.290962i	$-0.0939754\pi$
$998$	−4.47833e22	+	3.13761e22i	−1.43760	+	1.00721i
$999$	−6.42390e22			−2.04672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.16.b.a.5.5	✓	14
3.2	odd	2		72.16.d.b.37.10		14
4.3	odd	2		32.16.b.a.17.13		14
8.3	odd	2		32.16.b.a.17.2		14
8.5	even	2	inner	8.16.b.a.5.6	yes	14
24.5	odd	2		72.16.d.b.37.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.16.b.a.5.5	✓	14	1.1	even	1	trivial
8.16.b.a.5.6	yes	14	8.5	even	2	inner
32.16.b.a.17.2		14	8.3	odd	2
32.16.b.a.17.13		14	4.3	odd	2
72.16.d.b.37.9		14	24.5	odd	2
72.16.d.b.37.10		14	3.2	odd	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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-103.870 - 148.254i) q^{2} -6357.96i q^{3} +(-11190.2 + 30798.1i) q^{4} +267219. i q^{5} +(-942590. + 660399. i) q^{6} +120583. q^{7} +(5.72825e6 - 1.53999e6i) q^{8} -2.60748e7 q^{9} +O(q^{10})\)	\(q+(-103.870 - 148.254i) q^{2} -6357.96i q^{3} +(-11190.2 + 30798.1i) q^{4} +267219. i q^{5} +(-942590. + 660399. i) q^{6} +120583. q^{7} +(5.72825e6 - 1.53999e6i) q^{8} -2.60748e7 q^{9} +(3.96161e7 - 2.77559e7i) q^{10} +9.60941e7i q^{11} +(1.95813e8 + 7.11470e7i) q^{12} -1.64009e8i q^{13} +(-1.25249e7 - 1.78769e7i) q^{14} +1.69897e9 q^{15} +(-8.23300e8 - 6.89274e8i) q^{16} -1.25524e8 q^{17} +(2.70838e9 + 3.86568e9i) q^{18} +4.61207e9i q^{19} +(-8.22982e9 - 2.99024e9i) q^{20} -7.66663e8i q^{21} +(1.42463e10 - 9.98125e9i) q^{22} +6.78047e9 q^{23} +(-9.79122e9 - 3.64200e10i) q^{24} -4.08883e10 q^{25} +(-2.43149e10 + 1.70355e10i) q^{26} +7.45526e10i q^{27} +(-1.34935e9 + 3.71373e9i) q^{28} +7.66507e10i q^{29} +(-1.76471e11 - 2.51878e11i) q^{30} +2.28582e10 q^{31} +(-1.66715e10 + 1.93652e11i) q^{32} +6.10963e11 q^{33} +(1.30381e10 + 1.86094e10i) q^{34} +3.22221e10i q^{35} +(2.91782e11 - 8.03052e11i) q^{36} +8.61660e11i q^{37} +(6.83755e11 - 4.79054e11i) q^{38} -1.04276e12 q^{39} +(4.11515e11 + 1.53070e12i) q^{40} -3.52968e11 q^{41} +(-1.13660e11 + 7.96329e10i) q^{42} +1.68998e12i q^{43} +(-2.95951e12 - 1.07531e12i) q^{44} -6.96767e12i q^{45} +(-7.04285e11 - 1.00523e12i) q^{46} +3.84783e12 q^{47} +(-4.38238e12 + 5.23451e12i) q^{48} -4.73302e12 q^{49} +(4.24705e12 + 6.06184e12i) q^{50} +7.98078e11i q^{51} +(5.05115e12 + 1.83529e12i) q^{52} -9.03015e12i q^{53} +(1.10527e13 - 7.74375e12i) q^{54} -2.56782e13 q^{55} +(6.90730e11 - 1.85697e11i) q^{56} +2.93234e13 q^{57} +(1.13637e13 - 7.96167e12i) q^{58} +1.13978e13i q^{59} +(-1.90118e13 + 5.23249e13i) q^{60} -3.96597e12i q^{61} +(-2.37427e12 - 3.38881e12i) q^{62} -3.14418e12 q^{63} +(3.04412e13 - 1.76429e13i) q^{64} +4.38262e13 q^{65} +(-6.34604e13 - 9.05774e13i) q^{66} +4.34443e13i q^{67} +(1.40464e12 - 3.86590e12i) q^{68} -4.31100e13i q^{69} +(4.77704e12 - 3.34689e12i) q^{70} -3.11414e13 q^{71} +(-1.49363e14 + 4.01550e13i) q^{72} -8.34468e13 q^{73} +(1.27744e14 - 8.95003e13i) q^{74} +2.59966e14i q^{75} +(-1.42043e14 - 5.16100e13i) q^{76} +1.15873e13i q^{77} +(1.08311e14 + 1.54593e14i) q^{78} +7.31635e12 q^{79} +(1.84187e14 - 2.20001e14i) q^{80} +9.98580e13 q^{81} +(3.66626e13 + 5.23287e13i) q^{82} -3.96179e14i q^{83} +(2.36117e13 + 8.57912e12i) q^{84} -3.35424e13i q^{85} +(2.50546e14 - 1.75538e14i) q^{86} +4.87342e14 q^{87} +(1.47984e14 + 5.50451e14i) q^{88} +9.54011e13 q^{89} +(-1.03298e15 + 7.23729e14i) q^{90} -1.97767e13i q^{91} +(-7.58749e13 + 2.08825e14i) q^{92} -1.45332e14i q^{93} +(-3.99673e14 - 5.70455e14i) q^{94} -1.23243e15 q^{95} +(1.23123e15 + 1.05997e14i) q^{96} -1.16047e15 q^{97} +(4.91617e14 + 7.01687e14i) q^{98} -2.50563e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9}+O(q^{10}) \) 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17} + 526853306 q^{18} - 3449250768 q^{20} + 28367364252 q^{22} - 35548816080 q^{23} + 40155187088 q^{24} - 75899954794 q^{25} + 17666210712 q^{26} + 79863955680 q^{28} - 124878825712 q^{30} - 105758138816 q^{31} - 37651613280 q^{32} - 150458001384 q^{33} + 537472307308 q^{34} + 338679650892 q^{36} + 1649727781164 q^{38} - 2251546247120 q^{39} + 1251083710304 q^{40} - 53229185940 q^{41} - 2437011096800 q^{42} - 3416842360344 q^{44} - 3303531082064 q^{46} + 12527998446432 q^{47} - 6441543679584 q^{48} + 8427385380990 q^{49} + 1179755527374 q^{50} - 2436018627056 q^{52} + 3357642572216 q^{54} - 30557833792176 q^{55} + 7549064859072 q^{56} + 18277230892472 q^{57} - 8014960165320 q^{58} - 53574657402912 q^{60} + 77882578979904 q^{62} + 36142362113776 q^{63} + 76083381630528 q^{64} + 5437123965600 q^{65} - 134116957601160 q^{66} - 69772560247896 q^{68} + 133952399750848 q^{70} - 173249927708016 q^{71} + 163390222317848 q^{72} - 182057837882196 q^{73} + 2072780135688 q^{74} - 248503439494072 q^{76} + 636498768647600 q^{78} - 294370273271392 q^{79} + 766230078246336 q^{80} + 256903428263798 q^{81} - 10\!\cdots\!32 q^{82}+ \cdots - 51\!\cdots\!58 q^{98}+O(q^{100}) \) 14 * q - 90 * q^2 + 51444 * q^4 - 189428 * q^6 - 1647088 * q^7 + 1889640 * q^8 - 57395630 * q^9 + 58467784 * q^10 + 399357832 * q^12 - 518960496 * q^14 + 712135312 * q^15 - 1435931120 * q^16 + 728554812 * q^17 + 526853306 * q^18 - 3449250768 * q^20 + 28367364252 * q^22 - 35548816080 * q^23 + 40155187088 * q^24 - 75899954794 * q^25 + 17666210712 * q^26 + 79863955680 * q^28 - 124878825712 * q^30 - 105758138816 * q^31 - 37651613280 * q^32 - 150458001384 * q^33 + 537472307308 * q^34 + 338679650892 * q^36 + 1649727781164 * q^38 - 2251546247120 * q^39 + 1251083710304 * q^40 - 53229185940 * q^41 - 2437011096800 * q^42 - 3416842360344 * q^44 - 3303531082064 * q^46 + 12527998446432 * q^47 - 6441543679584 * q^48 + 8427385380990 * q^49 + 1179755527374 * q^50 - 2436018627056 * q^52 + 3357642572216 * q^54 - 30557833792176 * q^55 + 7549064859072 * q^56 + 18277230892472 * q^57 - 8014960165320 * q^58 - 53574657402912 * q^60 + 77882578979904 * q^62 + 36142362113776 * q^63 + 76083381630528 * q^64 + 5437123965600 * q^65 - 134116957601160 * q^66 - 69772560247896 * q^68 + 133952399750848 * q^70 - 173249927708016 * q^71 + 163390222317848 * q^72 - 182057837882196 * q^73 + 2072780135688 * q^74 - 248503439494072 * q^76 + 636498768647600 * q^78 - 294370273271392 * q^79 + 766230078246336 * q^80 + 256903428263798 * q^81 - 1021513680215332 * q^82 - 1701668269684544 * q^84 + 1418597672590812 * q^86 + 1493385390675312 * q^87 + 1948789255860816 * q^88 + 314213951649228 * q^89 - 3574690367103304 * q^90 - 3044080509008736 * q^92 + 3407319354561120 * q^94 - 851301047679984 * q^95 + 4705878559349312 * q^96 - 672574291859236 * q^97 - 5140373067292458 * q^98

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