LMFDB - Embedded newform 8.16.b.a.5.12

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			5.12
Root			$-70.4661 - 60.3351i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.16.b.a.5.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(134.932 + 120.670i) q^{2} -6537.39i q^{3} +(3645.36 + 32564.6i) q^{4} -116500. i q^{5} +(788869. - 882104. i) q^{6} -2.94378e6 q^{7} +(-3.43770e6 + 4.83390e6i) q^{8} -2.83885e7 q^{9} +O(q^{10})$	\(q+(134.932 + 120.670i) q^{2} -6537.39i q^{3} +(3645.36 + 32564.6i) q^{4} -116500. i q^{5} +(788869. - 882104. i) q^{6} -2.94378e6 q^{7} +(-3.43770e6 + 4.83390e6i) q^{8} -2.83885e7 q^{9} +(1.40581e7 - 1.57196e7i) q^{10} -5.06826e7i q^{11} +(2.12887e8 - 2.38311e7i) q^{12} -7.14043e7i q^{13} +(-3.97211e8 - 3.55227e8i) q^{14} -7.61605e8 q^{15} +(-1.04716e9 + 2.37419e8i) q^{16} +1.88026e9 q^{17} +(-3.83053e9 - 3.42565e9i) q^{18} -5.68095e9i q^{19} +(3.79377e9 - 4.24684e8i) q^{20} +1.92447e10i q^{21} +(6.11588e9 - 6.83871e9i) q^{22} -1.88154e10 q^{23} +(3.16011e10 + 2.24736e10i) q^{24} +1.69454e10 q^{25} +(8.61637e9 - 9.63473e9i) q^{26} +9.17826e10i q^{27} +(-1.07311e10 - 9.58631e10i) q^{28} +7.71744e10i q^{29} +(-1.02765e11 - 9.19031e10i) q^{30} +2.10456e11 q^{31} +(-1.69946e11 - 9.43262e10i) q^{32} -3.31332e11 q^{33} +(2.53707e11 + 2.26891e11i) q^{34} +3.42950e11i q^{35} +(-1.03486e11 - 9.24462e11i) q^{36} -1.49479e11i q^{37} +(6.85522e11 - 7.66543e11i) q^{38} -4.66797e11 q^{39} +(5.63148e11 + 4.00492e11i) q^{40} -5.40690e11 q^{41} +(-2.32226e12 + 2.59672e12i) q^{42} -1.85405e12i q^{43} +(1.65046e12 - 1.84756e11i) q^{44} +3.30726e12i q^{45} +(-2.53881e12 - 2.27046e12i) q^{46} +5.09285e12 q^{47} +(1.55210e12 + 6.84572e12i) q^{48} +3.91829e12 q^{49} +(2.28647e12 + 2.04480e12i) q^{50} -1.22920e13i q^{51} +(2.32525e12 - 2.60294e11i) q^{52} -1.42142e12i q^{53} +(-1.10754e13 + 1.23844e13i) q^{54} -5.90451e12 q^{55} +(1.01199e13 - 1.42299e13i) q^{56} -3.71386e13 q^{57} +(-9.31266e12 + 1.04133e13i) q^{58} -1.45000e13i q^{59} +(-2.77632e12 - 2.48014e13i) q^{60} -4.18453e12i q^{61} +(2.83973e13 + 2.53958e13i) q^{62} +8.35697e13 q^{63} +(-1.15488e13 - 3.32350e13i) q^{64} -8.31858e12 q^{65} +(-4.47073e13 - 3.99819e13i) q^{66} +5.42012e13i q^{67} +(6.85422e12 + 6.12299e13i) q^{68} +1.23004e14i q^{69} +(-4.13839e13 + 4.62750e13i) q^{70} -3.53320e12 q^{71} +(9.75914e13 - 1.37227e14i) q^{72} -6.90845e13 q^{73} +(1.80376e13 - 2.01695e13i) q^{74} -1.10778e14i q^{75} +(1.84998e14 - 2.07091e13i) q^{76} +1.49199e14i q^{77} +(-6.29860e13 - 5.63286e13i) q^{78} -2.39190e14 q^{79} +(2.76593e13 + 1.21995e14i) q^{80} +1.92674e14 q^{81} +(-7.29564e13 - 6.52452e13i) q^{82} -1.38154e14i q^{83} +(-6.26694e14 + 7.01537e13i) q^{84} -2.19050e14i q^{85} +(2.23729e14 - 2.50171e14i) q^{86} +5.04519e14 q^{87} +(2.44994e14 + 1.74232e14i) q^{88} -1.79126e14 q^{89} +(-3.99088e14 + 4.46256e14i) q^{90} +2.10199e14i q^{91} +(-6.85890e13 - 6.12717e14i) q^{92} -1.37583e15i q^{93} +(6.87188e14 + 6.14555e14i) q^{94} -6.61830e14 q^{95} +(-6.16647e14 + 1.11100e15i) q^{96} +1.74414e14 q^{97} +(5.28704e14 + 4.72822e14i) q^{98} +1.43881e15i 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 $

$2$	134.932	+	120.670i	0.745402	+	0.666616i
$2$	134.932	+	120.670i	0.745402	+	0.666616i
$3$		−	6537.39i		−	1.72582i	−0.505360	−	0.862909i	$-0.668640\pi$
$3$		−	6537.39i		−	1.72582i	0.505360	−	0.862909i	$-0.331360\pi$
$4$	3645.36	+	32564.6i	0.111248	+	0.993793i
$5$		−	116500.i		−	0.666884i	−0.942771	−	0.333442i	$-0.891790\pi$
$5$		−	116500.i		−	0.666884i	0.942771	−	0.333442i	$-0.108210\pi$
$6$	788869.	−	882104.i	1.15046	−	1.28643i
$7$	−2.94378e6			−1.35105			−0.675523	−	0.737339i	$-0.736082\pi$
$7$	−2.94378e6			−1.35105			−0.675523	+	0.737339i	$0.736082\pi$
$8$	−3.43770e6	+	4.83390e6i	−0.579554	+	0.814934i
$9$	−2.83885e7			−1.97845
$10$	1.40581e7	−	1.57196e7i	0.444555	−	0.497096i
$11$		−	5.06826e7i		−	0.784176i	−0.919928	−	0.392088i	$-0.871753\pi$
$11$		−	5.06826e7i		−	0.784176i	0.919928	−	0.392088i	$-0.128247\pi$
$12$	2.12887e8	−	2.38311e7i	1.71511	−	0.191993i
$13$		−	7.14043e7i		−	0.315609i	−0.987470	−	0.157804i	$-0.949558\pi$
$13$		−	7.14043e7i		−	0.315609i	0.987470	−	0.157804i	$-0.0504415\pi$
$14$	−3.97211e8	−	3.55227e8i	−1.00707	−	0.900629i
$15$	−7.61605e8			−1.15092
$16$	−1.04716e9	+	2.37419e8i	−0.975248	+	0.221114i
$17$	1.88026e9			1.11135			0.555675	−	0.831400i	$-0.312460\pi$
$17$	1.88026e9			1.11135			0.555675	+	0.831400i	$0.312460\pi$
$18$	−3.83053e9	−	3.42565e9i	−1.47474	−	1.31886i
$19$		−	5.68095e9i		−	1.45804i	−0.684493	−	0.729020i	$-0.739976\pi$
$19$		−	5.68095e9i		−	1.45804i	0.684493	−	0.729020i	$-0.260024\pi$
$20$	3.79377e9	−	4.24684e8i	0.662744	−	0.0741892i
$21$			1.92447e10i			2.33166i
$22$	6.11588e9	−	6.83871e9i	0.522744	−	0.584526i
$23$	−1.88154e10			−1.15227			−0.576136	−	0.817354i	$-0.695440\pi$
$23$	−1.88154e10			−1.15227			−0.576136	+	0.817354i	$0.695440\pi$
$24$	3.16011e10	+	2.24736e10i	1.40643	+	1.00020i
$25$	1.69454e10			0.555266
$26$	8.61637e9	−	9.63473e9i	0.210390	−	0.235255i
$27$			9.17826e10i			1.68862i
$28$	−1.07311e10	−	9.58631e10i	−0.150301	−	1.34266i
$29$			7.71744e10i			0.830785i	0.909642	+	0.415392i	$0.136356\pi$
$29$			7.71744e10i			0.830785i	−0.909642	+	0.415392i	$0.863644\pi$
$30$	−1.02765e11	−	9.19031e10i	−0.857898	−	0.767221i
$31$	2.10456e11			1.37388			0.686940	−	0.726714i	$-0.258954\pi$
$31$	2.10456e11			1.37388			0.686940	+	0.726714i	$0.258954\pi$
$32$	−1.69946e11	−	9.43262e10i	−0.874350	−	0.485297i
$33$	−3.31332e11			−1.35335
$34$	2.53707e11	+	2.26891e11i	0.828402	+	0.740843i
$35$			3.42950e11i			0.900992i
$36$	−1.03486e11	−	9.24462e11i	−0.220097	−	1.96617i
$37$		−	1.49479e11i		−	0.258861i	−0.991589	−	0.129430i	$-0.958685\pi$
$37$		−	1.49479e11i		−	0.258861i	0.991589	−	0.129430i	$-0.0413148\pi$
$38$	6.85522e11	−	7.66543e11i	0.971952	−	1.08683i
$39$	−4.66797e11			−0.544683
$40$	5.63148e11	+	4.00492e11i	0.543467	+	0.386495i
$41$	−5.40690e11			−0.433580			−0.216790	−	0.976218i	$-0.569559\pi$
$41$	−5.40690e11			−0.433580			−0.216790	+	0.976218i	$0.569559\pi$
$42$	−2.32226e12	+	2.59672e12i	−1.55432	+	1.73802i
$43$		−	1.85405e12i		−	1.04018i	−0.854112	−	0.520089i	$-0.825899\pi$
$43$		−	1.85405e12i		−	1.04018i	0.854112	−	0.520089i	$-0.174101\pi$
$44$	1.65046e12	−	1.84756e11i	0.779309	−	0.0872377i
$45$			3.30726e12i			1.31939i
$46$	−2.53881e12	−	2.27046e12i	−0.858906	−	0.768123i
$47$	5.09285e12			1.46631			0.733156	−	0.680060i	$-0.238046\pi$
$47$	5.09285e12			1.46631			0.733156	+	0.680060i	$0.238046\pi$
$48$	1.55210e12	+	6.84572e12i	0.381602	+	1.68310i
$49$	3.91829e12			0.825328
$50$	2.28647e12	+	2.04480e12i	0.413896	+	0.370149i
$51$		−	1.22920e13i		−	1.91799i
$52$	2.32525e12	−	2.60294e11i	0.313650	−	0.0351107i
$53$		−	1.42142e12i		−	0.166209i	−0.996541	−	0.0831045i	$-0.973516\pi$
$53$		−	1.42142e12i		−	0.166209i	0.996541	−	0.0831045i	$-0.0264835\pi$
$54$	−1.10754e13	+	1.23844e13i	−1.12566	+	1.25870i
$55$	−5.90451e12			−0.522955
$56$	1.01199e13	−	1.42299e13i	0.783004	−	1.10101i
$57$	−3.71386e13			−2.51631
$58$	−9.31266e12	+	1.04133e13i	−0.553814	+	0.619268i
$59$		−	1.45000e13i		−	0.758539i	−0.925286	−	0.379269i	$-0.876175\pi$
$59$		−	1.45000e13i		−	0.758539i	0.925286	−	0.379269i	$-0.123825\pi$
$60$	−2.77632e12	−	2.48014e13i	−0.128037	−	1.14378i
$61$		−	4.18453e12i		−	0.170480i	−0.996360	−	0.0852399i	$-0.972834\pi$
$61$		−	4.18453e12i		−	0.170480i	0.996360	−	0.0852399i	$-0.0271657\pi$
$62$	2.83973e13	+	2.53958e13i	1.02409	+	0.915849i
$63$	8.35697e13			2.67297
$64$	−1.15488e13	−	3.32350e13i	−0.328235	−	0.944596i
$65$	−8.31858e12			−0.210474
$66$	−4.47073e13	−	3.99819e13i	−1.00879	−	0.902161i
$67$			5.42012e13i			1.09257i	0.837600	+	0.546283i	$0.183958\pi$
$67$			5.42012e13i			1.09257i	−0.837600	+	0.546283i	$0.816042\pi$
$68$	6.85422e12	+	6.12299e13i	0.123635	+	1.10445i
$69$			1.23004e14i			1.98861i
$70$	−4.13839e13	+	4.62750e13i	−0.600615	+	0.671601i
$71$	−3.53320e12			−0.0461032			−0.0230516	−	0.999734i	$-0.507338\pi$
$71$	−3.53320e12			−0.0461032			−0.0230516	+	0.999734i	$0.507338\pi$
$72$	9.75914e13	−	1.37227e14i	1.14662	−	1.61230i
$73$	−6.90845e13			−0.731912			−0.365956	−	0.930632i	$-0.619258\pi$
$73$	−6.90845e13			−0.731912			−0.365956	+	0.930632i	$0.619258\pi$
$74$	1.80376e13	−	2.01695e13i	0.172560	−	0.192955i
$75$		−	1.10778e14i		−	0.958287i
$76$	1.84998e14	−	2.07091e13i	1.44899	−	0.162203i
$77$			1.49199e14i			1.05946i
$78$	−6.29860e13	−	5.63286e13i	−0.406008	−	0.363094i
$79$	−2.39190e14			−1.40133			−0.700663	−	0.713492i	$-0.747112\pi$
$79$	−2.39190e14			−1.40133			−0.700663	+	0.713492i	$0.747112\pi$
$80$	2.76593e13	+	1.21995e14i	0.147457	+	0.650377i
$81$	1.92674e14			0.935805
$82$	−7.29564e13	−	6.52452e13i	−0.323191	−	0.289031i
$83$		−	1.38154e14i		−	0.558828i	−0.960171	−	0.279414i	$-0.909860\pi$
$83$		−	1.38154e14i		−	0.558828i	0.960171	−	0.279414i	$-0.0901402\pi$
$84$	−6.26694e14	+	7.01537e13i	−2.31719	+	0.259391i
$85$		−	2.19050e14i		−	0.741141i
$86$	2.23729e14	−	2.50171e14i	0.693399	−	0.775351i
$87$	5.04519e14			1.43378
$88$	2.44994e14	+	1.74232e14i	0.639052	+	0.454472i
$89$	−1.79126e14			−0.429274			−0.214637	−	0.976694i	$-0.568857\pi$
$89$	−1.79126e14			−0.429274			−0.214637	+	0.976694i	$0.568857\pi$
$90$	−3.99088e14	+	4.46256e14i	−0.879529	+	0.983479i
$91$			2.10199e14i			0.426402i
$92$	−6.85890e13	−	6.12717e14i	−0.128188	−	1.14512i
$93$		−	1.37583e15i		−	2.37107i
$94$	6.87188e14	+	6.14555e14i	1.09299	+	0.977467i
$95$	−6.61830e14			−0.972343
$96$	−6.16647e14	+	1.11100e15i	−0.837534	+	1.50897i
$97$	1.74414e14			0.219177			0.109588	−	0.993977i	$-0.465047\pi$
$97$	1.74414e14			0.219177			0.109588	+	0.993977i	$0.465047\pi$
$98$	5.28704e14	+	4.72822e14i	0.615201	+	0.550176i
$99$			1.43881e15i			1.55145i
$100$	6.17719e13	+	5.51819e14i	0.0617719	+	0.551819i
$101$			1.54415e14i			0.143311i	0.997429	+	0.0716554i	$0.0228282\pi$
$101$			1.54415e14i			0.143311i	−0.997429	+	0.0716554i	$0.977172\pi$
$102$	1.48328e15	−	1.65858e15i	1.27856	−	1.42967i
$103$	−6.65304e14			−0.533017			−0.266509	−	0.963833i	$-0.585870\pi$
$103$	−6.65304e14			−0.533017			−0.266509	+	0.963833i	$0.585870\pi$
$104$	3.45161e14	+	2.45467e14i	0.257200	+	0.182912i
$105$	2.24200e15			1.55495
$106$	1.71524e14	−	1.91796e14i	0.110797	−	0.123892i
$107$		−	1.57638e15i		−	0.949036i	−0.880246	−	0.474518i	$-0.842622\pi$
$107$		−	1.57638e15i		−	0.949036i	0.880246	−	0.474518i	$-0.157378\pi$
$108$	−2.98886e15	+	3.34581e14i	−1.67814	+	0.187855i
$109$			8.30541e14i			0.435173i	0.976041	+	0.217587i	$0.0698185\pi$
$109$			8.30541e14i			0.435173i	−0.976041	+	0.217587i	$0.930182\pi$
$110$	−7.96709e14	−	7.12499e14i	−0.389811	−	0.348610i
$111$	−9.77199e14			−0.446746
$112$	3.08262e15	−	6.98911e14i	1.31761	−	0.298735i
$113$	−6.36937e11			−0.000254688			−0.000127344	−	1.00000i	$-0.500041\pi$
$113$	−6.36937e11			−0.000254688			−0.000127344		1.00000i	$0.500041\pi$
$114$	−5.01119e15	−	4.48153e15i	−1.87566	−	1.67741i
$115$			2.19199e15i			0.768432i
$116$	−2.51315e15	+	2.81329e14i	−0.825628	+	0.0924228i
$117$			2.02706e15i			0.624415i
$118$	1.74972e15	−	1.95652e15i	0.505654	−	0.565416i
$119$	−5.53507e15			−1.50149
$120$	2.61817e15	−	3.68152e15i	0.667020	−	0.937924i
$121$	1.60852e15			0.385068
$122$	5.04948e14	−	5.64627e14i	0.113644	−	0.127076i
$123$			3.53470e15i			0.748280i
$124$	7.67188e14	+	6.85342e15i	0.152841	+	1.36535i
$125$		−	5.52943e15i		−	1.03718i
$126$	1.12762e16	+	1.00844e16i	1.99244	+	1.78185i
$127$	1.15963e16			1.93104			0.965520	−	0.260329i	$-0.0838311\pi$
$127$	1.15963e16			1.93104			0.965520	+	0.260329i	$0.0838311\pi$
$128$	2.45218e15	−	5.87806e15i	0.385015	−	0.922910i
$129$	−1.21206e16			−1.79516
$130$	−1.12244e15	−	1.00381e15i	−0.156888	−	0.140305i
$131$		−	4.45713e15i		−	0.588193i	−0.955776	−	0.294097i	$-0.904981\pi$
$131$		−	4.45713e15i		−	0.588193i	0.955776	−	0.294097i	$-0.0950188\pi$
$132$	−1.20782e15	−	1.07897e16i	−0.150556	−	1.34494i
$133$			1.67235e16i			1.96988i
$134$	−6.54048e15	+	7.31349e15i	−0.728322	+	0.814401i
$135$	1.06927e16			1.12611
$136$	−6.46377e15	+	9.08898e15i	−0.644087	+	0.905677i
$137$	1.47282e15			0.138913			0.0694567	−	0.997585i	$-0.477873\pi$
$137$	1.47282e15			0.138913			0.0694567	+	0.997585i	$0.477873\pi$
$138$	−1.48429e16	+	1.65972e16i	−1.32564	+	1.48232i
$139$		−	7.58829e15i		−	0.641997i	−0.947080	−	0.320998i	$-0.895982\pi$
$139$		−	7.58829e15i		−	0.641997i	0.947080	−	0.320998i	$-0.104018\pi$
$140$	−1.11680e16	+	1.25018e15i	−0.895399	+	0.100233i
$141$		−	3.32939e16i		−	2.53059i
$142$	−4.76743e14	−	4.26353e14i	−0.0343654	−	0.0307331i
$143$	−3.61895e15			−0.247493
$144$	2.97275e16	−	6.73999e15i	1.92948	−	0.437462i
$145$	8.99081e15			0.554037
$146$	−9.32172e15	−	8.33645e15i	−0.545569	−	0.487904i
$147$		−	2.56154e16i		−	1.42436i
$148$	4.86771e15	−	5.44903e14i	0.257254	−	0.0287976i
$149$			3.62283e16i			1.82033i	0.414241	+	0.910167i	$0.364047\pi$
$149$			3.62283e16i			1.82033i	−0.414241	+	0.910167i	$0.635953\pi$
$150$	1.33677e16	−	1.49476e16i	0.638809	−	0.714309i
$151$	−4.46855e15			−0.203161			−0.101580	−	0.994827i	$-0.532390\pi$
$151$	−4.46855e15			−0.203161			−0.101580	+	0.994827i	$0.532390\pi$
$152$	2.74611e16	+	1.95294e16i	1.18821	+	0.845012i
$153$	−5.33778e16			−2.19875
$154$	−1.80038e16	+	2.01317e16i	−0.706252	+	0.789722i
$155$		−	2.45181e16i		−	0.916218i
$156$	−1.70164e15	−	1.52011e16i	−0.0605946	−	0.541302i
$157$			1.52635e16i			0.518092i	0.965865	+	0.259046i	$0.0834081\pi$
$157$			1.52635e16i			0.518092i	−0.965865	+	0.259046i	$0.916592\pi$
$158$	−3.22744e16	−	2.88631e16i	−1.04455	−	0.934146i
$159$	−9.29240e15			−0.286846
$160$	−1.09890e16	+	1.97986e16i	−0.323637	+	0.583090i
$161$	5.53885e16			1.55677
$162$	2.59979e16	+	2.32500e16i	0.697551	+	0.623822i
$163$			3.38759e16i			0.867928i	0.900930	+	0.433964i	$0.142886\pi$
$163$			3.38759e16i			0.867928i	−0.900930	+	0.433964i	$0.857114\pi$
$164$	−1.97101e15	−	1.76073e16i	−0.0482347	−	0.430889i
$165$			3.86001e16i			0.902524i
$166$	1.66711e16	−	1.86414e16i	0.372523	−	0.416551i
$167$	4.75659e16			1.01607			0.508033	−	0.861337i	$-0.330373\pi$
$167$	4.75659e16			1.01607			0.508033	+	0.861337i	$0.330373\pi$
$168$	−9.30267e16	−	6.61574e16i	−1.90015	−	1.35132i
$169$	4.60873e16			0.900391
$170$	2.64328e16	−	2.95569e16i	0.494056	−	0.552448i
$171$			1.61274e17i			2.88465i
$172$	6.03764e16	−	6.75868e15i	1.03372	−	0.115717i
$173$		−	1.11356e17i		−	1.82544i	−0.408581	−	0.912722i	$-0.633976\pi$
$173$		−	1.11356e17i		−	1.82544i	0.408581	−	0.912722i	$-0.366024\pi$
$174$	6.80759e16	+	6.08805e16i	1.06874	+	0.955782i
$175$	−4.98835e16			−0.750190
$176$	1.20330e16	+	5.30730e16i	0.173392	+	0.764766i
$177$	−9.47921e16			−1.30910
$178$	−2.41699e16	−	2.16152e16i	−0.319981	−	0.286160i
$179$		−	3.69235e16i		−	0.468711i	−0.972151	−	0.234356i	$-0.924702\pi$
$179$		−	3.69235e16i		−	0.468711i	0.972151	−	0.234356i	$-0.0752980\pi$
$180$	−1.07700e17	+	1.20562e16i	−1.31120	+	0.146779i
$181$			5.35211e16i			0.625080i	0.949905	+	0.312540i	$0.101180\pi$
$181$			5.35211e16i			0.625080i	−0.949905	+	0.312540i	$0.898820\pi$
$182$	−2.53647e16	+	2.83625e16i	−0.284246	+	0.317841i
$183$	−2.73559e16			−0.294217
$184$	6.46819e16	−	9.09519e16i	0.667804	−	0.939027i
$185$	−1.74142e16			−0.172630
$186$	1.66022e17	−	1.85644e17i	1.58059	−	1.76740i
$187$		−	9.52964e16i		−	0.871494i
$188$	1.85653e16	+	1.65846e17i	0.163124	+	1.45721i
$189$		−	2.70188e17i		−	2.28141i
$190$	−8.93022e16	−	7.98632e16i	−0.724786	−	0.648179i
$191$	−1.13443e17			−0.885169			−0.442584	−	0.896727i	$-0.645938\pi$
$191$	−1.13443e17			−0.885169			−0.442584	+	0.896727i	$0.645938\pi$
$192$	−2.17270e17	+	7.54987e16i	−1.63020	+	0.566474i
$193$	2.31843e17			1.67307			0.836536	−	0.547913i	$-0.184577\pi$
$193$	2.31843e17			1.67307			0.836536	+	0.547913i	$0.184577\pi$
$194$	2.35341e16	+	2.10466e16i	0.163375	+	0.146107i
$195$			5.43818e16i			0.363240i
$196$	1.42836e16	+	1.27598e17i	0.0918157	+	0.820205i
$197$			1.52888e17i			0.945972i	0.881070	+	0.472986i	$0.156824\pi$
$197$			1.52888e17i			0.945972i	−0.881070	+	0.472986i	$0.843176\pi$
$198$	−1.73621e17	+	1.94141e17i	−1.03422	+	1.15645i
$199$	−2.45169e17			−1.40627			−0.703133	−	0.711058i	$-0.748216\pi$
$199$	−2.45169e17			−1.40627			−0.703133	+	0.711058i	$0.748216\pi$
$200$	−5.82531e16	+	8.19122e16i	−0.321806	+	0.452505i
$201$	3.54334e17			1.88557
$202$	−1.86333e16	+	2.08355e16i	−0.0955333	+	0.106824i
$203$		−	2.27185e17i		−	1.12243i
$204$	4.00284e17	−	4.48087e16i	1.90608	−	0.213371i
$205$			6.29903e16i			0.289148i
$206$	−8.97709e16	−	8.02825e16i	−0.397312	−	0.355318i
$207$	5.34143e17			2.27971
$208$	1.69527e16	+	7.47720e16i	0.0697855	+	0.307797i
$209$	−2.87925e17			−1.14336
$210$	3.02518e17	+	2.70543e17i	1.15906	+	1.03655i
$211$			4.78002e16i			0.176730i	0.996088	+	0.0883652i	$0.0281643\pi$
$211$			4.78002e16i			0.176730i	−0.996088	+	0.0883652i	$0.971836\pi$
$212$	4.62881e16	−	5.18160e15i	0.165177	−	0.0184903i
$213$			2.30979e16i			0.0795657i
$214$	1.90222e17	−	2.12704e17i	0.632642	−	0.707413i
$215$	−2.15996e17			−0.693679
$216$	−4.43668e17	−	3.15521e17i	−1.37611	−	0.978646i
$217$	−6.19537e17			−1.85618
$218$	−1.00222e17	+	1.12067e17i	−0.290093	+	0.324379i
$219$			4.51632e17i			1.26315i
$220$	−2.15241e16	−	1.92278e17i	−0.0581774	−	0.519708i
$221$		−	1.34258e17i		−	0.350752i
$222$	−1.31856e17	−	1.17919e17i	−0.333005	−	0.297808i
$223$	6.52149e16			0.159243			0.0796216	−	0.996825i	$-0.474629\pi$
$223$	6.52149e16			0.159243			0.0796216	+	0.996825i	$0.474629\pi$
$224$	5.00283e17	+	2.77676e17i	1.18129	+	0.655659i
$225$	−4.81054e17			−1.09856
$226$	−8.59432e13	−	7.68593e13i	−0.000189845	−	0.000169779i
$227$		−	3.31674e16i		−	0.0708789i	−0.999372	−	0.0354395i	$-0.988717\pi$
$227$		−	3.31674e16i		−	0.0708789i	0.999372	−	0.0354395i	$-0.0112831\pi$
$228$	−1.35384e17	−	1.20940e18i	−0.279933	−	2.50069i
$229$			2.75662e16i			0.0551583i	0.999620	+	0.0275792i	$0.00877983\pi$
$229$			2.75662e16i			0.0551583i	−0.999620	+	0.0275792i	$0.991220\pi$
$230$	−2.64509e17	+	2.95770e17i	−0.512249	+	0.572791i
$231$	9.75369e17			1.82843
$232$	−3.73053e17	−	2.65303e17i	−0.677035	−	0.481484i
$233$	7.33759e17			1.28939			0.644695	−	0.764440i	$-0.276984\pi$
$233$	7.33759e17			1.28939			0.644695	+	0.764440i	$0.276984\pi$
$234$	−2.44606e17	+	2.73516e17i	−0.416245	+	0.465440i
$235$		−	5.93316e17i		−	0.977860i
$236$	4.72187e17	−	5.28577e16i	0.753830	−	0.0843856i
$237$			1.56368e18i			2.41843i
$238$	−7.46859e17	−	6.67919e17i	−1.11921	−	1.00091i
$239$	−2.31456e17			−0.336112			−0.168056	−	0.985777i	$-0.553749\pi$
$239$	−2.31456e17			−0.336112			−0.168056	+	0.985777i	$0.553749\pi$
$240$	7.97526e17	−	1.80820e17i	1.12243	−	0.254485i
$241$	−1.29566e17			−0.176751			−0.0883756	−	0.996087i	$-0.528168\pi$
$241$	−1.29566e17			−0.176751			−0.0883756	+	0.996087i	$0.528168\pi$
$242$	2.17042e17	+	1.94101e17i	0.287030	+	0.256692i
$243$			5.73955e16i			0.0735920i
$244$	1.36267e17	−	1.52541e16i	0.169422	−	0.0189655i
$245$		−	4.56481e17i		−	0.550398i
$246$	−4.26533e17	+	4.76944e17i	−0.498815	+	0.557769i
$247$	−4.05644e17			−0.460170
$248$	−7.23485e17	+	1.01732e18i	−0.796237	+	1.11962i
$249$	−9.03167e17			−0.964435
$250$	6.67237e17	−	7.46097e17i	0.691401	−	0.773117i
$251$		−	1.44426e18i		−	1.45242i	−0.687474	−	0.726209i	$-0.741281\pi$
$251$		−	1.44426e18i		−	1.45242i	0.687474	−	0.726209i	$-0.258719\pi$
$252$	3.04642e17	+	2.72141e18i	0.297362	+	2.65638i
$253$			9.53615e17i			0.903585i
$254$	1.56471e18	+	1.39933e18i	1.43940	+	1.28726i
$255$	−1.43201e18			−1.27907
$256$	1.04019e18	−	4.97234e17i	0.902217	−	0.431282i
$257$	1.40791e18			1.18598			0.592989	−	0.805210i	$-0.297948\pi$
$257$	1.40791e18			1.18598			0.592989	+	0.805210i	$0.297948\pi$
$258$	−1.63546e18	−	1.46260e18i	−1.33811	−	1.19668i
$259$			4.40032e17i			0.349733i
$260$	−3.03242e16	−	2.70891e17i	−0.0234148	−	0.209168i
$261$		−	2.19087e18i		−	1.64366i
$262$	5.37843e17	−	6.01409e17i	0.392099	−	0.438440i
$263$	2.13038e18			1.50934			0.754671	−	0.656103i	$-0.227796\pi$
$263$	2.13038e18			1.50934			0.754671	+	0.656103i	$0.227796\pi$
$264$	1.13902e18	−	1.60162e18i	0.784336	−	1.10289i
$265$	−1.65596e17			−0.110842
$266$	−2.01803e18	+	2.25654e18i	−1.31315	+	1.46835i
$267$			1.17102e18i			0.740848i
$268$	−1.76504e18	+	1.97583e17i	−1.08579	+	0.121545i
$269$		−	1.69596e18i		−	1.01455i	−0.861783	−	0.507276i	$-0.830652\pi$
$269$		−	1.69596e18i		−	1.01455i	0.861783	−	0.507276i	$-0.169348\pi$
$270$	1.44278e18	+	1.29029e18i	0.839408	+	0.750685i
$271$	1.55087e18			0.877616			0.438808	−	0.898581i	$-0.355401\pi$
$271$	1.55087e18			0.877616			0.438808	+	0.898581i	$0.355401\pi$
$272$	−1.96894e18	+	4.46410e17i	−1.08384	+	0.245735i
$273$	1.37415e18			0.735892
$274$	1.98730e17	+	1.77725e17i	0.103546	+	0.0926019i
$275$		−	8.58835e17i		−	0.435426i
$276$	−4.00557e18	+	4.48393e17i	−1.97627	+	0.221228i
$277$		−	3.49255e18i		−	1.67704i	−0.544869	−	0.838521i	$-0.683421\pi$
$277$		−	3.49255e18i		−	1.67704i	0.544869	−	0.838521i	$-0.316579\pi$
$278$	9.15681e17	−	1.02390e18i	0.427965	−	0.478545i
$279$	−5.97454e18			−2.71815
$280$	−1.65779e18	−	1.17896e18i	−0.734249	−	0.522173i
$281$	−2.11919e18			−0.913846			−0.456923	−	0.889506i	$-0.651049\pi$
$281$	−2.11919e18			−0.913846			−0.456923	+	0.889506i	$0.651049\pi$
$282$	4.01759e18	−	4.49242e18i	1.68693	−	1.88630i
$283$			4.78575e18i			1.95682i	0.206665	+	0.978412i	$0.433739\pi$
$283$			4.78575e18i			1.95682i	−0.206665	+	0.978412i	$0.566261\pi$
$284$	−1.28798e16	−	1.15057e17i	−0.00512887	−	0.0458170i
$285$			4.32664e18i			1.67809i
$286$	−4.88313e17	−	4.36700e17i	−0.184482	−	0.164983i
$287$	1.59167e18			0.585787
$288$	4.82451e18	+	2.67778e18i	1.72985	+	0.960134i
$289$	6.72950e17			0.235098
$290$	1.21315e18	+	1.08492e18i	0.412980	+	0.369330i
$291$		−	1.14022e18i		−	0.378259i
$292$	−2.51838e17	−	2.24971e18i	−0.0814235	−	0.727369i
$293$		−	1.57016e18i		−	0.494807i	−0.968913	−	0.247403i	$-0.920423\pi$
$293$		−	1.57016e18i		−	0.494807i	0.968913	−	0.247403i	$-0.0795773\pi$
$294$	3.09102e18	−	3.45634e18i	0.949504	−	1.06172i
$295$	−1.68925e18			−0.505857
$296$	7.22564e17	+	5.13863e17i	0.210954	+	0.150024i
$297$	4.65178e18			1.32418
$298$	−4.37168e18	+	4.88836e18i	−1.21346	+	1.35688i
$299$			1.34350e18i			0.363667i
$300$	3.60746e18	−	4.03827e17i	0.952339	−	0.106607i
$301$			5.45792e18i			1.40533i
$302$	−6.02952e17	−	5.39222e17i	−0.151436	−	0.135430i
$303$	1.00947e18			0.247328
$304$	1.34877e18	+	5.94889e18i	0.322393	+	1.42195i
$305$	−4.87497e17			−0.113690
$306$	−7.20238e18	−	6.44112e18i	−1.63895	−	1.46572i
$307$			5.73608e18i			1.27373i	0.770975	+	0.636865i	$0.219769\pi$
$307$			5.73608e18i			1.27373i	−0.770975	+	0.636865i	$0.780231\pi$
$308$	−4.85859e18	+	5.43882e17i	−1.05288	+	0.117862i
$309$			4.34935e18i			0.919891i
$310$	2.95861e18	−	3.30828e18i	0.610765	−	0.682951i
$311$	−3.53245e18			−0.711826			−0.355913	−	0.934519i	$-0.615830\pi$
$311$	−3.53245e18			−0.711826			−0.355913	+	0.934519i	$0.615830\pi$
$312$	1.60471e18	−	2.25645e18i	0.315673	−	0.443881i
$313$	6.76382e18			1.29900			0.649500	−	0.760361i	$-0.274978\pi$
$313$	6.76382e18			1.29900			0.649500	+	0.760361i	$0.274978\pi$
$314$	−1.84185e18	+	2.05954e18i	−0.345368	+	0.386187i
$315$		−	9.73586e18i		−	1.78256i
$316$	−8.71932e17	−	7.78912e18i	−0.155894	−	1.39263i
$317$		−	8.36431e18i		−	1.46045i	−0.683208	−	0.730223i	$-0.739416\pi$
$317$		−	8.36431e18i		−	1.46045i	0.683208	−	0.730223i	$-0.260584\pi$
$318$	−1.25384e18	−	1.12132e18i	−0.213816	−	0.191216i
$319$	3.91140e18			0.651482
$320$	−3.87187e18	+	1.34543e18i	−0.629936	+	0.218895i
$321$	−1.03054e19			−1.63786
$322$	7.47369e18	+	6.68375e18i	1.16042	+	1.03777i
$323$		−	1.06817e19i		−	1.62039i
$324$	7.02366e17	+	6.27435e18i	0.104106	+	0.929996i
$325$		−	1.20997e18i		−	0.175247i
$326$	−4.08782e18	+	4.57095e18i	−0.578574	+	0.646955i
$327$	5.42957e18			0.751030
$328$	1.85873e18	−	2.61364e18i	0.251283	−	0.353339i
$329$	−1.49922e19			−1.98106
$330$	−4.65789e18	+	5.20839e18i	−0.601637	+	0.672743i
$331$			3.43052e18i			0.433161i	0.976265	+	0.216581i	$0.0694904\pi$
$331$			3.43052e18i			0.433161i	−0.976265	+	0.216581i	$0.930510\pi$
$332$	4.49893e18	−	5.03621e17i	0.555359	−	0.0621682i
$333$			4.24348e18i			0.512142i
$334$	6.41817e18	+	5.73979e18i	0.757378	+	0.677326i
$335$	6.31443e18			0.728615
$336$	−4.56905e18	−	2.01523e19i	−0.515563	−	2.27395i
$337$	−5.29734e18			−0.584566			−0.292283	−	0.956332i	$-0.594415\pi$
$337$	−5.29734e18			−0.584566			−0.292283	+	0.956332i	$0.594415\pi$
$338$	6.21866e18	+	5.56137e18i	0.671153	+	0.600215i
$339$			4.16390e15i			0.000439544i
$340$	7.13327e18	−	7.98515e17i	0.736541	−	0.0824501i
$341$		−	1.06665e19i		−	1.07736i
$342$	−1.94610e19	+	2.17610e19i	−1.92295	+	2.15023i
$343$	2.44118e18			0.235991
$344$	8.96229e18	+	6.37367e18i	0.847677	+	0.602839i
$345$	1.43299e19			1.32617
$346$	1.34374e19	−	1.50255e19i	1.21687	−	1.36069i
$347$			1.39300e18i			0.123447i	0.998093	+	0.0617234i	$0.0196597\pi$
$347$			1.39300e18i			0.123447i	−0.998093	+	0.0617234i	$0.980340\pi$
$348$	1.83915e18	+	1.64295e19i	0.159505	+	1.42488i
$349$		−	4.87131e18i		−	0.413481i	−0.978396	−	0.206740i	$-0.933714\pi$
$349$		−	4.87131e18i		−	0.413481i	0.978396	−	0.206740i	$-0.0662855\pi$
$350$	−6.73088e18	−	6.01945e18i	−0.559193	−	0.500088i
$351$	6.55367e18			0.532943
$352$	−4.78069e18	+	8.61328e18i	−0.380558	+	0.685644i
$353$	6.38601e18			0.497645			0.248822	−	0.968549i	$-0.419956\pi$
$353$	6.38601e18			0.497645			0.248822	+	0.968549i	$0.419956\pi$
$354$	−1.27905e19	−	1.14386e19i	−0.975805	−	0.872666i
$355$			4.11618e17i			0.0307455i
$356$	−6.52980e17	−	5.83318e18i	−0.0477556	−	0.426609i
$357$			3.61849e19i			2.59129i
$358$	4.45557e18	−	4.98217e18i	0.312450	−	0.349378i
$359$	2.69213e18			0.184879			0.0924394	−	0.995718i	$-0.470534\pi$
$359$	2.69213e18			0.184879			0.0924394	+	0.995718i	$0.470534\pi$
$360$	−1.59870e19	−	1.13694e19i	−1.07522	−	0.764660i
$361$	−1.70921e19			−1.12588
$362$	−6.45840e18	+	7.22171e18i	−0.416688	+	0.465936i
$363$		−	1.05155e19i		−	0.664557i
$364$	−6.84503e18	+	7.66249e17i	−0.423755	+	0.0474362i
$365$			8.04833e18i			0.488101i
$366$	−3.69119e18	−	3.30104e18i	−0.219310	−	0.196130i
$367$	−1.25312e19			−0.729452			−0.364726	−	0.931115i	$-0.618837\pi$
$367$	−1.25312e19			−0.729452			−0.364726	+	0.931115i	$0.618837\pi$
$368$	1.97028e19	−	4.46715e18i	1.12375	−	0.254784i
$369$	1.53494e19			0.857815
$370$	−2.34974e18	−	2.10138e18i	−0.128679	−	0.115078i
$371$			4.18436e18i			0.224556i
$372$	4.48034e19	−	5.01540e18i	2.35635	−	0.263775i
$373$			2.16085e19i			1.11380i	0.830579	+	0.556901i	$0.188010\pi$
$373$			2.16085e19i			1.11380i	−0.830579	+	0.556901i	$0.811990\pi$
$374$	1.14994e19	−	1.28585e19i	0.580951	−	0.649613i
$375$	−3.61480e19			−1.78999
$376$	−1.75077e19	+	2.46183e19i	−0.849807	+	1.19495i
$377$	5.51058e18			0.262203
$378$	3.26037e19	−	3.64570e19i	1.52082	−	1.70056i
$379$		−	5.18112e18i		−	0.236935i	−0.992958	−	0.118468i	$-0.962202\pi$
$379$		−	5.18112e18i		−	0.236935i	0.992958	−	0.118468i	$-0.0377982\pi$
$380$	−2.41261e18	−	2.15522e19i	−0.108171	−	0.966308i
$381$		−	7.58095e19i		−	3.33262i
$382$	−1.53071e19	−	1.36892e19i	−0.659806	−	0.590067i
$383$	−2.12065e18			−0.0896353			−0.0448176	−	0.998995i	$-0.514271\pi$
$383$	−2.12065e18			−0.0896353			−0.0448176	+	0.998995i	$0.514271\pi$
$384$	−3.84272e19	−	1.60309e19i	−1.59277	−	0.664466i
$385$	1.73816e19			0.706536
$386$	3.12831e19	+	2.79766e19i	1.24711	+	1.11530i
$387$			5.26338e19i			2.05794i
$388$	6.35803e17	+	5.67974e18i	0.0243829	+	0.217816i
$389$			2.74314e19i			1.03187i	0.856628	+	0.515935i	$0.172556\pi$
$389$			2.74314e19i			1.03187i	−0.856628	+	0.515935i	$0.827444\pi$
$390$	−6.56227e18	+	7.33785e18i	−0.242142	+	0.270760i
$391$	−3.53779e19			−1.28058
$392$	−1.34699e19	+	1.89406e19i	−0.478322	+	0.672588i
$393$	−2.91380e19			−1.01511
$394$	−1.84491e19	+	2.06296e19i	−0.630599	+	0.705129i
$395$			2.78656e19i			0.934522i
$396$	−4.68541e19	+	5.24496e18i	−1.54182	+	0.172595i
$397$		−	4.58207e19i		−	1.47956i	−0.672848	−	0.739781i	$-0.734929\pi$
$397$		−	4.58207e19i		−	1.47956i	0.672848	−	0.739781i	$-0.265071\pi$
$398$	−3.30812e19	−	2.95846e19i	−1.04823	−	0.937439i
$399$	1.09328e20			3.39965
$400$	−1.77446e19	+	4.02316e18i	−0.541522	+	0.122777i
$401$	1.21060e19			0.362593			0.181297	−	0.983428i	$-0.441971\pi$
$401$	1.21060e19			0.362593			0.181297	+	0.983428i	$0.441971\pi$
$402$	4.78111e19	+	4.27576e19i	1.40551	+	1.25695i
$403$		−	1.50275e19i		−	0.433608i
$404$	−5.02846e18	+	5.62898e17i	−0.142421	+	0.0159430i
$405$		−	2.24465e19i		−	0.624073i
$406$	2.74145e19	−	3.06545e19i	0.748229	−	0.836661i
$407$	−7.57596e18			−0.202992
$408$	5.94182e19	+	4.22562e19i	1.56303	+	1.11158i
$409$	5.62177e19			1.45194			0.725969	−	0.687728i	$-0.241392\pi$
$409$	5.62177e19			1.45194			0.725969	+	0.687728i	$0.241392\pi$
$410$	−7.60105e18	+	8.49941e18i	−0.192750	+	0.215531i
$411$		−	9.62838e18i		−	0.239739i
$412$	−2.42527e18	−	2.16654e19i	−0.0592968	−	0.529709i
$413$			4.26848e19i			1.02482i
$414$	7.20730e19	+	6.44552e19i	1.69930	+	1.51969i
$415$	−1.60949e19			−0.372673
$416$	−6.73529e18	+	1.21348e19i	−0.153164	+	0.275952i
$417$	−4.96076e19			−1.10797
$418$	−3.88504e19	−	3.47440e19i	−0.852262	−	0.762181i
$419$		−	4.73053e19i		−	1.01931i	−0.860380	−	0.509653i	$-0.829774\pi$
$419$		−	4.73053e19i		−	1.01931i	0.860380	−	0.509653i	$-0.170226\pi$
$420$	8.17289e18	+	7.30098e19i	0.172984	+	1.54530i
$421$		−	7.20628e19i		−	1.49829i	−0.662407	−	0.749144i	$-0.730465\pi$
$421$		−	7.20628e19i		−	1.49829i	0.662407	−	0.749144i	$-0.269535\pi$
$422$	−5.76806e18	+	6.44978e18i	−0.117811	+	0.131735i
$423$	−1.44578e20			−2.90102
$424$	6.87101e18	+	4.88643e18i	0.135449	+	0.0963270i
$425$	3.18617e19			0.617094
$426$	−2.78723e18	+	3.11665e18i	−0.0530397	+	0.0593084i
$427$			1.23183e19i			0.230326i
$428$	5.13342e19	−	5.74647e18i	0.943145	−	0.105578i
$429$			2.36585e19i			0.427127i
$430$	−2.91449e19	−	2.60644e19i	−0.517069	−	0.462417i
$431$	7.24050e18			0.126238			0.0631188	−	0.998006i	$-0.479895\pi$
$431$	7.24050e18			0.126238			0.0631188	+	0.998006i	$0.479895\pi$
$432$	−2.17910e19	−	9.61115e19i	−0.373378	−	1.64682i
$433$	4.66940e19			0.786324			0.393162	−	0.919469i	$-0.371381\pi$
$433$	4.66940e19			0.786324			0.393162	+	0.919469i	$0.371381\pi$
$434$	−8.35954e19	−	7.47597e19i	−1.38360	−	1.23736i
$435$		−	5.87764e19i		−	0.956167i
$436$	−2.70462e19	+	3.02762e18i	−0.432472	+	0.0484120i
$437$			1.06890e20i			1.68006i
$438$	−5.44986e19	+	6.09397e19i	−0.842034	+	0.941552i
$439$	2.16533e19			0.328882			0.164441	−	0.986387i	$-0.447418\pi$
$439$	2.16533e19			0.328882			0.164441	+	0.986387i	$0.447418\pi$
$440$	2.02980e19	−	2.85418e19i	0.303080	−	0.426174i
$441$	−1.11235e20			−1.63287
$442$	1.62010e19	−	1.81158e19i	0.233816	−	0.261451i
$443$		−	8.18112e19i		−	1.16087i	−0.814305	−	0.580437i	$-0.802882\pi$
$443$		−	8.18112e19i		−	1.16087i	0.814305	−	0.580437i	$-0.197118\pi$
$444$	−3.56224e18	−	3.18221e19i	−0.0496994	−	0.443973i
$445$			2.08682e19i			0.286276i
$446$	8.79959e18	+	7.86951e18i	0.118700	+	0.106154i
$447$	2.36839e20			3.14157
$448$	3.39970e19	+	9.78367e19i	0.443461	+	1.27619i
$449$	−4.33067e19			−0.555529			−0.277765	−	0.960649i	$-0.589594\pi$
$449$	−4.33067e19			−0.555529			−0.277765	+	0.960649i	$0.589594\pi$
$450$	−6.49097e19	−	5.80490e19i	−0.818871	−	0.732320i
$451$			2.74036e19i			0.340003i
$452$	−2.32186e15	−	2.07416e16i	−2.83334e−5	−	0.000253107i
$453$			2.92127e19i			0.350619i
$454$	4.00232e18	−	4.47534e18i	0.0472490	−	0.0528333i
$455$	2.44881e19			0.284361
$456$	1.27672e20	−	1.79524e20i	1.45834	−	2.05063i
$457$	7.99739e19			0.898621			0.449311	−	0.893376i	$-0.351670\pi$
$457$	7.99739e19			0.898621			0.449311	+	0.893376i	$0.351670\pi$
$458$	−3.32642e18	+	3.71957e18i	−0.0367694	+	0.0411151i
$459$			1.72575e20i			1.87665i
$460$	−7.13814e19	+	7.99061e18i	−0.763662	+	0.0854862i
$461$			1.18061e20i			1.24265i	0.783551	+	0.621327i	$0.213406\pi$
$461$			1.18061e20i			1.24265i	−0.783551	+	0.621327i	$0.786594\pi$
$462$	1.31609e20	+	1.17698e20i	1.36292	+	1.21886i
$463$	−1.49744e20			−1.52578			−0.762888	−	0.646531i	$-0.776219\pi$
$463$	−1.49744e20			−1.52578			−0.762888	+	0.646531i	$0.776219\pi$
$464$	−1.83227e19	−	8.08143e19i	−0.183698	−	0.810221i
$465$	−1.60284e20			−1.58123
$466$	9.90077e19	+	8.85430e19i	0.961114	+	0.859527i
$467$			1.65316e20i			1.57920i	0.613620	+	0.789602i	$0.289713\pi$
$467$			1.65316e20i			1.57920i	−0.613620	+	0.789602i	$0.710287\pi$
$468$	−6.60105e19	+	7.38937e18i	−0.620539	+	0.0694646i
$469$		−	1.59557e20i		−	1.47611i
$470$	7.15956e19	−	8.00573e19i	0.651857	−	0.728899i
$471$	9.97835e19			0.894132
$472$	7.00915e19	+	4.98467e19i	0.618159	+	0.439614i
$473$	−9.39680e19			−0.815683
$474$	−1.88689e20	+	2.10990e20i	−1.61217	+	1.80270i
$475$		−	9.62658e19i		−	0.809599i
$476$	−2.01773e19	−	1.80247e20i	−0.167037	−	1.49217i
$477$			4.03521e19i			0.328836i
$478$	−3.12308e19	−	2.79298e19i	−0.250538	−	0.224057i
$479$	1.02704e20			0.811094			0.405547	−	0.914074i	$-0.367081\pi$
$479$	1.02704e20			0.811094			0.405547	+	0.914074i	$0.367081\pi$
$480$	1.29431e20	+	7.18393e19i	1.00631	+	0.558538i
$481$	−1.06734e19			−0.0816986
$482$	−1.74826e19	−	1.56347e19i	−0.131751	−	0.117825i
$483$		−	3.62096e20i		−	2.68671i
$484$	5.86365e18	+	5.23809e19i	0.0428378	+	0.382678i
$485$		−	2.03193e19i		−	0.146165i
$486$	−6.92593e18	+	7.74449e18i	−0.0490576	+	0.0548556i
$487$	−1.90240e20			−1.32689			−0.663443	−	0.748227i	$-0.730905\pi$
$487$	−1.90240e20			−1.32689			−0.663443	+	0.748227i	$0.730905\pi$
$488$	2.02276e19	+	1.43852e19i	0.138930	+	0.0988021i
$489$	2.21460e20			1.49789
$490$	5.50836e19	−	6.15939e19i	0.366904	−	0.410267i
$491$			8.31093e19i			0.545178i	0.962131	+	0.272589i	$0.0878799\pi$
$491$			8.31093e19i			0.545178i	−0.962131	+	0.272589i	$0.912120\pi$
$492$	−1.15106e20	+	1.28852e19i	−0.743635	+	0.0832443i
$493$			1.45108e20i			0.923292i
$494$	−5.47344e19	−	4.89492e19i	−0.343011	−	0.306756i
$495$	1.67621e20			1.03464
$496$	−2.20382e20	+	4.99663e19i	−1.33987	+	0.303784i
$497$	1.04010e19			0.0622876
$498$	−1.21866e20	−	1.08985e20i	−0.718892	−	0.642907i
$499$			7.63349e19i			0.443577i	0.975095	+	0.221789i	$0.0711895\pi$
$499$			7.63349e19i			0.443577i	−0.975095	+	0.221789i	$0.928811\pi$
$500$	1.80064e20	−	2.01567e19i	1.03074	−	0.115384i
$501$		−	3.10957e20i		−	1.75355i
$502$	1.74279e20	−	1.94877e20i	0.968204	−	1.08263i
$503$	−3.10555e20			−1.69972			−0.849862	−	0.527005i	$-0.823315\pi$
$503$	−3.10555e20			−1.69972			−0.849862	+	0.527005i	$0.823315\pi$
$504$	−2.87288e20	+	4.03967e20i	−1.54913	+	2.17830i
$505$	1.79893e19			0.0955717
$506$	−1.15073e20	+	1.28673e20i	−0.602344	+	0.673534i
$507$		−	3.01291e20i		−	1.55391i
$508$	4.22726e19	+	3.77629e20i	0.214823	+	1.91905i
$509$		−	6.83093e19i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$509$		−	6.83093e19i		−	0.342055i	0.985266	−	0.171028i	$-0.0547088\pi$
$510$	−1.93225e20	−	1.72802e20i	−0.953425	−	0.852651i
$511$	2.03370e20			0.988848
$512$	2.00356e20	+	5.84266e19i	0.960014	+	0.279954i
$513$	5.21413e20			2.46208
$514$	1.89972e20	+	1.69893e20i	0.884030	+	0.790592i
$515$			7.75079e19i			0.355461i
$516$	−4.41841e19	−	3.94704e20i	−0.199707	−	1.78402i
$517$		−	2.58119e20i		−	1.14985i
$518$	−5.30988e19	+	5.93745e19i	−0.233137	+	0.260691i
$519$	−7.27979e20			−3.15038
$520$	2.85968e19	−	4.02112e19i	0.121981	−	0.171523i
$521$	−3.80309e20			−1.59902			−0.799509	−	0.600654i	$-0.794907\pi$
$521$	−3.80309e20			−1.59902			−0.799509	+	0.600654i	$0.794907\pi$
$522$	2.64373e20	−	2.95619e20i	1.09569	−	1.22519i
$523$			3.42491e20i			1.39922i	0.714524	+	0.699611i	$0.246644\pi$
$523$			3.42491e20i			1.39922i	−0.714524	+	0.699611i	$0.753356\pi$
$524$	1.45145e20	−	1.62478e19i	0.584542	−	0.0654351i
$525$			3.26108e20i			1.29469i
$526$	2.87456e20	+	2.57073e20i	1.12507	+	1.00615i
$527$	3.95712e20			1.52686
$528$	3.46959e20	−	7.86646e19i	1.31985	−	0.299244i
$529$	8.73851e19			0.327733
$530$	−2.23442e19	−	1.99825e19i	−0.0826219	−	0.0738890i
$531$			4.11634e20i			1.50073i
$532$	−5.44594e20	+	6.09631e19i	−1.95765	+	0.219144i
$533$			3.86075e19i			0.136842i
$534$	−1.41307e20	+	1.58008e20i	−0.493861	+	0.552229i
$535$	−1.83648e20			−0.632897
$536$	−2.62003e20	−	1.86328e20i	−0.890370	−	0.633201i
$537$	−2.41383e20			−0.808910
$538$	2.04653e20	−	2.28840e20i	0.676317	−	0.756250i
$539$		−	1.98589e20i		−	0.647202i
$540$	3.89786e19	+	3.48202e20i	0.125277	+	1.11912i
$541$		−	1.80696e20i		−	0.572755i	−0.958117	−	0.286378i	$-0.907549\pi$
$541$		−	1.80696e20i		−	0.572755i	0.958117	−	0.286378i	$-0.0924512\pi$
$542$	2.09262e20	+	1.87143e20i	0.654177	+	0.585033i
$543$	3.49888e20			1.07877
$544$	−3.19542e20	−	1.77358e20i	−0.971708	−	0.539334i
$545$	9.67579e19			0.290210
$546$	1.85417e20	+	1.65819e20i	0.548535	+	0.490557i
$547$			5.97664e20i			1.74402i	0.489484	+	0.872012i	$0.337185\pi$
$547$			5.97664e20i			1.74402i	−0.489484	+	0.872012i	$0.662815\pi$
$548$	5.36895e18	+	4.79617e19i	0.0154538	+	0.138051i
$549$			1.18793e20i			0.337285i
$550$	1.03636e20	−	1.15884e20i	0.290262	−	0.324567i
$551$	4.38424e20			1.21132
$552$	−5.94588e20	−	4.22851e20i	−1.62059	−	1.15251i
$553$	7.04122e20			1.89326
$554$	4.21447e20	−	4.71257e20i	1.11794	−	1.25007i
$555$			1.13844e20i			0.297928i
$556$	2.47110e20	−	2.76620e19i	0.638012	−	0.0714206i
$557$		−	2.26558e20i		−	0.577119i	−0.957462	−	0.288559i	$-0.906824\pi$
$557$		−	2.26558e20i		−	0.577119i	0.957462	−	0.288559i	$-0.0931762\pi$
$558$	−8.06158e20	−	7.20950e20i	−2.02611	−	1.81196i
$559$	−1.32387e20			−0.328289
$560$	−8.14230e19	−	3.59125e20i	−0.199222	−	0.878690i
$561$	−6.22989e20			−1.50404
$562$	−2.85947e20	−	2.55724e20i	−0.681182	−	0.609184i
$563$		−	4.47726e20i		−	1.05245i	−0.850347	−	0.526223i	$-0.823608\pi$
$563$		−	4.47726e20i		−	1.05245i	0.850347	−	0.526223i	$-0.176392\pi$
$564$	1.08420e21	−	1.21368e20i	2.51488	−	0.281522i
$565$			7.42030e16i			0.000169847i
$566$	−5.77498e20	+	6.45751e20i	−1.30445	+	1.45862i
$567$	−5.67190e20			−1.26432
$568$	1.21461e19	−	1.70791e19i	0.0267193	−	0.0375711i
$569$	−4.70239e20			−1.02088			−0.510442	−	0.859912i	$-0.670518\pi$
$569$	−4.70239e20			−1.02088			−0.510442	+	0.859912i	$0.670518\pi$
$570$	−5.22097e20	+	5.83803e20i	−1.11864	+	1.25085i
$571$		−	1.19819e20i		−	0.253369i	−0.991943	−	0.126685i	$-0.959566\pi$
$571$		−	1.19819e20i		−	0.253369i	0.991943	−	0.126685i	$-0.0404336\pi$
$572$	−1.31924e19	−	1.17850e20i	−0.0275330	−	0.245957i
$573$			7.41619e20i			1.52764i
$574$	2.14768e20	+	1.92068e20i	0.436647	+	0.390495i
$575$	−3.18834e20			−0.639818
$576$	3.27852e20	+	9.43494e20i	0.649396	+	1.86883i
$577$	−4.06394e20			−0.794565			−0.397282	−	0.917696i	$-0.630047\pi$
$577$	−4.06394e20			−0.794565			−0.397282	+	0.917696i	$0.630047\pi$
$578$	9.08025e19	+	8.12050e19i	0.175242	+	0.156720i
$579$		−	1.51565e21i		−	2.88742i
$580$	3.27747e19	+	2.92782e20i	0.0616353	+	0.550598i
$581$			4.06696e20i			0.755003i
$582$	1.37590e20	−	1.53852e20i	0.252153	−	0.281955i
$583$	−7.20414e19			−0.130337
$584$	2.37492e20	−	3.33947e20i	0.424182	−	0.596460i
$585$	2.36153e20			0.416412
$586$	1.89471e20	−	2.11864e20i	0.329846	−	0.368830i
$587$			2.29964e20i			0.395251i	0.980278	+	0.197626i	$0.0633230\pi$
$587$			2.29964e20i			0.395251i	−0.980278	+	0.197626i	$0.936677\pi$
$588$	8.34156e20	−	9.33774e19i	1.41552	−	0.158457i
$589$		−	1.19559e21i		−	2.00317i
$590$	−2.27934e20	−	2.03842e20i	−0.377067	−	0.337212i
$591$	9.99491e20			1.63257
$592$	3.54891e19	+	1.56529e20i	0.0572377	+	0.252453i
$593$	6.05243e20			0.963873			0.481936	−	0.876206i	$-0.339934\pi$
$593$	6.05243e20			0.963873			0.481936	+	0.876206i	$0.339934\pi$
$594$	6.27675e20	+	5.61332e20i	0.987043	+	0.882716i
$595$			6.44835e20i			1.00132i
$596$	−1.17976e21	+	1.32065e20i	−1.80904	+	0.202508i
$597$			1.60277e21i			2.42696i
$598$	−1.62121e20	+	1.81282e20i	−0.242426	+	0.271078i
$599$	8.12352e20			1.19962			0.599809	−	0.800143i	$-0.295243\pi$
$599$	8.12352e20			1.19962			0.599809	+	0.800143i	$0.295243\pi$
$600$	5.35492e20	+	3.80824e20i	0.780941	+	0.555379i
$601$	1.12989e21			1.62734			0.813668	−	0.581330i	$-0.197468\pi$
$601$	1.12989e21			1.62734			0.813668	+	0.581330i	$0.197468\pi$
$602$	−6.58609e20	+	7.36449e20i	−0.936815	+	1.04754i
$603$		−	1.53869e21i		−	2.16159i
$604$	−1.62895e19	−	1.45517e20i	−0.0226011	−	0.201900i
$605$		−	1.87393e20i		−	0.256796i
$606$	1.36210e20	+	1.21813e20i	0.184359	+	0.164873i
$607$	−4.98570e19			−0.0666516			−0.0333258	−	0.999445i	$-0.510610\pi$
$607$	−4.98570e19			−0.0666516			−0.0333258	+	0.999445i	$0.510610\pi$
$608$	−5.35863e20	+	9.65453e20i	−0.707582	+	1.27484i
$609$	−1.48520e21			−1.93711
$610$	−6.57790e19	−	5.88264e19i	−0.0847449	−	0.0757877i
$611$		−	3.63651e20i		−	0.462781i
$612$	−1.94581e20	−	1.73823e21i	−0.244605	−	2.18510i
$613$		−	1.06831e20i		−	0.132662i	−0.997798	−	0.0663308i	$-0.978871\pi$
$613$		−	1.06831e20i		−	0.132662i	0.997798	−	0.0663308i	$-0.0211293\pi$
$614$	−6.92174e20	+	7.73981e20i	−0.849088	+	0.949441i
$615$	4.11792e20			0.499016
$616$	−7.21210e20	−	5.12900e20i	−0.863389	−	0.614013i
$617$	−1.55200e21			−1.83549			−0.917747	−	0.397165i	$-0.869994\pi$
$617$	−1.55200e21			−1.83549			−0.917747	+	0.397165i	$0.869994\pi$
$618$	−5.24838e20	+	5.86868e20i	−0.613213	+	0.685688i
$619$			1.56165e21i			1.80261i	0.433182	+	0.901306i	$0.357391\pi$
$619$			1.56165e21i			1.80261i	−0.433182	+	0.901306i	$0.642609\pi$
$620$	7.98422e20	−	8.93773e19i	0.910531	−	0.101927i
$621$		−	1.72693e21i		−	1.94575i
$622$	−4.76642e20	−	4.26262e20i	−0.530596	−	0.474514i
$623$	5.27309e20			0.579969
$624$	4.88814e20	−	1.10827e20i	0.531201	−	0.120437i
$625$	−1.27046e20			−0.136414
$626$	9.12656e20	+	8.16192e20i	0.968277	+	0.865934i
$627$			1.88228e21i			1.97323i
$628$	−4.97050e20	+	5.56409e19i	−0.514876	+	0.0576364i
$629$		−	2.81058e20i		−	0.287685i
$630$	1.17483e21	−	1.31368e21i	1.18828	−	1.32873i
$631$	−1.82121e21			−1.82029			−0.910143	−	0.414294i	$-0.864029\pi$
$631$	−1.82121e21			−1.82029			−0.910143	+	0.414294i	$0.864029\pi$
$632$	8.22263e20	−	1.15622e21i	0.812144	−	1.14199i
$633$	3.12488e20			0.305004
$634$	1.00932e21	−	1.12861e21i	0.973557	−	1.08862i
$635$		−	1.35097e21i		−	1.28778i
$636$	−3.38741e19	−	3.02603e20i	−0.0319109	−	0.285066i
$637$		−	2.79783e20i		−	0.260481i
$638$	5.27774e20	+	4.71990e20i	0.485615	+	0.434288i
$639$	1.00303e20			0.0912127
$640$	−6.84793e20	−	2.85679e20i	−0.615474	−	0.256760i
$641$	1.07856e21			0.958100			0.479050	−	0.877788i	$-0.340981\pi$
$641$	1.07856e21			0.958100			0.479050	+	0.877788i	$0.340981\pi$
$642$	−1.39053e21	−	1.24356e21i	−1.22087	−	1.09183i
$643$		−	1.13375e21i		−	0.983864i	−0.870634	−	0.491932i	$-0.836291\pi$
$643$		−	1.13375e21i		−	0.983864i	0.870634	−	0.491932i	$-0.163709\pi$
$644$	2.01911e20	+	1.80371e21i	0.173187	+	1.54711i
$645$			1.41205e21i			1.19716i
$646$	1.28896e21	−	1.44130e21i	1.08018	−	1.20784i
$647$	−4.52095e20			−0.374497			−0.187248	−	0.982313i	$-0.559957\pi$
$647$	−4.52095e20			−0.374497			−0.187248	+	0.982313i	$0.559957\pi$
$648$	−6.62356e20	+	9.31366e20i	−0.542349	+	0.762619i
$649$	−7.34897e20			−0.594828
$650$	1.46008e20	−	1.63264e20i	0.116822	−	0.130629i
$651$			4.05015e21i			3.20342i
$652$	−1.10316e21	+	1.23490e20i	−0.862541	+	0.0965549i
$653$			8.69838e20i			0.672341i	0.941801	+	0.336170i	$0.109132\pi$
$653$			8.69838e20i			0.672341i	−0.941801	+	0.336170i	$0.890868\pi$
$654$	7.32623e20	+	6.55188e20i	0.559819	+	0.500648i
$655$	−5.19254e20			−0.392257
$656$	5.66191e20	−	1.28370e20i	0.422848	−	0.0958706i
$657$	1.96121e21			1.44805
$658$	−2.02293e21	−	1.80912e21i	−1.47668	−	1.32060i
$659$		−	1.90480e21i		−	1.37471i	−0.726323	−	0.687353i	$-0.758773\pi$
$659$		−	1.90480e21i		−	1.37471i	0.726323	−	0.687353i	$-0.241227\pi$
$660$	−1.25700e21	+	1.40711e20i	−0.896922	+	0.100404i
$661$			1.61259e21i			1.13766i	0.822454	+	0.568832i	$0.192605\pi$
$661$			1.61259e21i			1.13766i	−0.822454	+	0.568832i	$0.807395\pi$
$662$	−4.13961e20	+	4.62887e20i	−0.288752	+	0.322879i
$663$	−8.77700e20			−0.605333
$664$	6.67823e20	+	4.74933e20i	0.455408	+	0.323871i
$665$	1.94828e21			1.31368
$666$	−5.12062e20	+	5.72582e20i	−0.341402	+	0.381751i
$667$		−	1.45207e21i		−	0.957291i
$668$	1.73395e20	+	1.54896e21i	0.113035	+	1.00976i
$669$		−	4.26335e20i		−	0.274825i
$670$	8.52020e20	+	7.61965e20i	0.543111	+	0.485706i
$671$	−2.12083e20			−0.133686
$672$	1.81527e21	−	3.27054e21i	1.13155	−	2.03869i
$673$	1.18941e21			0.733193			0.366597	−	0.930380i	$-0.380523\pi$
$673$	1.18941e21			0.733193			0.366597	+	0.930380i	$0.380523\pi$
$674$	−7.14782e20	−	6.39232e20i	−0.435737	−	0.389681i
$675$			1.55529e21i			0.937633i
$676$	1.68005e20	+	1.50082e21i	0.100166	+	0.894802i
$677$		−	1.84170e21i		−	1.08593i	−0.839754	−	0.542967i	$-0.817301\pi$
$677$		−	1.84170e21i		−	1.08593i	0.839754	−	0.542967i	$-0.182699\pi$
$678$	−5.02459e17	+	5.61844e17i	−0.000293007	+	0.000327637i
$679$	−5.13438e20			−0.296118
$680$	1.05886e21	+	7.53028e20i	0.603981	+	0.429531i
$681$	−2.16828e20			−0.122324
$682$	1.28712e21	−	1.43925e21i	0.718187	−	0.803069i
$683$			1.78677e21i			0.986084i	0.870005	+	0.493042i	$0.164115\pi$
$683$			1.78677e21i			0.986084i	−0.870005	+	0.493042i	$0.835885\pi$
$684$	−5.25182e21	+	5.87902e20i	−2.86675	+	0.320911i
$685$		−	1.71583e20i		−	0.0926392i
$686$	3.29394e20	+	2.94579e20i	0.175908	+	0.157315i
$687$	1.80211e20			0.0951932
$688$	4.40187e20	+	1.94150e21i	0.229998	+	1.01443i
$689$	−1.01496e20			−0.0524570
$690$	1.93357e21	+	1.72920e21i	0.988533	+	0.884048i
$691$			1.39911e21i			0.707565i	0.935328	+	0.353782i	$0.115105\pi$
$691$			1.39911e21i			0.707565i	−0.935328	+	0.353782i	$0.884895\pi$
$692$	3.62627e21	−	4.05933e20i	1.81411	−	0.203076i
$693$		−	4.23553e21i		−	2.09608i
$694$	−1.68094e20	+	1.87960e20i	−0.0822916	+	0.0920175i
$695$	−8.84034e20			−0.428137
$696$	−1.73439e21	+	2.43879e21i	−0.830954	+	1.16844i
$697$	−1.01664e21			−0.481859
$698$	5.87822e20	−	6.57296e20i	0.275633	−	0.308209i
$699$		−	4.79687e21i		−	2.22525i
$700$	−1.81843e20	−	1.62444e21i	−0.0834568	−	0.745533i
$701$		−	2.80815e20i		−	0.127507i	−0.997966	−	0.0637536i	$-0.979693\pi$
$701$		−	2.80815e20i		−	0.127507i	0.997966	−	0.0637536i	$-0.0203072\pi$
$702$	8.84300e20	+	7.90833e20i	0.397257	+	0.355268i
$703$	−8.49181e20			−0.377429
$704$	−1.68444e21	+	5.85321e20i	−0.740730	+	0.257394i
$705$	−3.87874e21			−1.68761
$706$	8.61678e20	+	7.70602e20i	0.370945	+	0.331738i
$707$		−	4.54564e20i		−	0.193620i
$708$	−3.45551e20	−	3.08687e21i	−0.145634	−	1.30097i
$709$		−	1.62408e21i		−	0.677268i	−0.940918	−	0.338634i	$-0.890035\pi$
$709$		−	1.62408e21i		−	0.677268i	0.940918	−	0.338634i	$-0.109965\pi$
$710$	−4.96700e19	+	5.55405e19i	−0.0204954	+	0.0229177i
$711$	6.79025e21			2.77245
$712$	6.15783e20	−	8.65878e20i	0.248787	−	0.349830i
$713$	−3.95982e21			−1.58308
$714$	−4.36645e21	+	4.88251e21i	−1.72739	+	1.93155i
$715$			4.21607e20i			0.165049i
$716$	1.20240e21	−	1.34600e20i	0.465802	−	0.0521430i
$717$			1.51312e21i			0.580068i
$718$	3.63254e20	+	3.24860e20i	0.137809	+	0.123243i
$719$	−8.37500e20			−0.314426			−0.157213	−	0.987565i	$-0.550251\pi$
$719$	−8.37500e20			−0.314426			−0.157213	+	0.987565i	$0.550251\pi$
$720$	−7.85208e20	−	3.46325e21i	−0.291737	−	1.28674i
$721$	1.95851e21			0.720131
$722$	−2.30627e21	−	2.06251e21i	−0.839232	−	0.750528i
$723$			8.47022e20i			0.305040i
$724$	−1.74289e21	+	1.95104e20i	−0.621200	+	0.0695386i
$725$			1.30775e21i			0.461306i
$726$	1.26891e21	−	1.41888e21i	0.443004	−	0.495362i
$727$	1.44613e21			0.499690			0.249845	−	0.968286i	$-0.419620\pi$
$727$	1.44613e21			0.499690			0.249845	+	0.968286i	$0.419620\pi$
$728$	−1.01608e21	−	7.22600e20i	−0.347490	−	0.247123i
$729$	3.13988e21			1.06281
$730$	−9.71195e20	+	1.08598e21i	−0.325375	+	0.363831i
$731$		−	3.48609e21i		−	1.15600i
$732$	−9.97220e19	−	8.90834e20i	−0.0327309	−	0.292391i
$733$			2.60845e21i			0.847428i	0.905796	+	0.423714i	$0.139274\pi$
$733$			2.60845e21i			0.847428i	−0.905796	+	0.423714i	$0.860726\pi$
$734$	−1.69086e21	−	1.51214e21i	−0.543735	−	0.486264i
$735$	−2.98419e21			−0.949886
$736$	3.19760e21	+	1.77479e21i	1.00749	+	0.559194i
$737$	2.74706e21			0.856765
$738$	2.07113e21	+	1.85222e21i	0.639417	+	0.571833i
$739$		−	5.00465e19i		−	0.0152947i	−0.999971	−	0.00764734i	$-0.997566\pi$
$739$		−	5.00465e19i		−	0.0152947i	0.999971	−	0.00764734i	$-0.00243425\pi$
$740$	−6.34811e19	−	5.67087e20i	−0.0192047	−	0.171558i
$741$			2.65185e21i			0.794169i
$742$	−5.04928e20	+	5.64605e20i	−0.149693	+	0.167384i
$743$	1.93952e21			0.569218			0.284609	−	0.958644i	$-0.408136\pi$
$743$	1.93952e21			0.569218			0.284609	+	0.958644i	$0.408136\pi$
$744$	6.65063e21	+	4.72971e21i	1.93226	+	1.37416i
$745$	4.22059e21			1.21395
$746$	−2.60750e21	+	2.91568e21i	−0.742477	+	0.830229i
$747$			3.92199e21i			1.10561i
$748$	3.10329e21	−	3.47389e20i	0.866084	−	0.0969515i
$749$			4.64052e21i			1.28219i
$750$	−4.87753e21	−	4.36199e21i	−1.33426	−	1.19323i
$751$	−4.65319e21			−1.26023			−0.630117	−	0.776500i	$-0.716993\pi$
$751$	−4.65319e21			−1.26023			−0.630117	+	0.776500i	$0.716993\pi$
$752$	−5.33305e21	+	1.20914e21i	−1.43002	+	0.324222i
$753$	−9.44167e21			−2.50661
$754$	7.43555e20	+	6.64964e20i	0.195446	+	0.174789i
$755$			5.20586e20i			0.135485i
$756$	8.79856e21	−	9.84932e20i	2.26724	−	0.253801i
$757$			4.33806e21i			1.10682i	0.832909	+	0.553410i	$0.186674\pi$
$757$			4.33806e21i			1.10682i	−0.832909	+	0.553410i	$0.813326\pi$
$758$	6.25208e20	−	6.99100e20i	0.157945	−	0.176612i
$759$	6.23415e21			1.55942
$760$	2.27518e21	−	3.19922e21i	0.563525	−	0.792396i
$761$	−5.63979e21			−1.38318			−0.691589	−	0.722292i	$-0.743089\pi$
$761$	−5.63979e21			−1.38318			−0.691589	+	0.722292i	$0.743089\pi$
$762$	9.14795e21	−	1.02291e22i	2.22158	−	2.48414i
$763$		−	2.44493e21i		−	0.587940i
$764$	−4.13539e20	−	3.69421e21i	−0.0984728	−	0.879674i
$765$			6.21851e21i			1.46631i
$766$	−2.86144e20	−	2.55900e20i	−0.0668143	−	0.0597523i
$767$	−1.03536e21			−0.239401
$768$	−3.25061e21	−	6.80010e21i	−0.744314	−	1.55706i
$769$	5.75883e19			0.0130583			0.00652915	−	0.999979i	$-0.497922\pi$
$769$	5.75883e19			0.0130583			0.00652915	+	0.999979i	$0.497922\pi$
$770$	2.34534e21	+	2.09744e21i	0.526653	+	0.470988i
$771$		−	9.20406e21i		−	2.04678i
$772$	8.45151e20	+	7.54988e21i	0.186125	+	1.66269i
$773$		−	9.12157e21i		−	1.98941i	−0.102790	−	0.994703i	$-0.532777\pi$
$773$		−	9.12157e21i		−	1.98941i	0.102790	−	0.994703i	$-0.467223\pi$
$774$	−6.35133e21	+	7.10199e21i	−1.37185	+	1.53399i
$775$	3.56625e21			0.762868
$776$	−5.99585e20	+	8.43102e20i	−0.127025	+	0.178615i
$777$	2.87666e21			0.603575
$778$	−3.31015e21	+	3.70137e21i	−0.687861	+	0.769158i
$779$			3.07163e21i			0.632177i
$780$	−1.77092e21	+	1.98241e20i	−0.360986	+	0.0404096i
$781$			1.79072e20i			0.0361530i
$782$	−4.77361e21	−	4.26906e21i	−0.954545	−	0.853653i
$783$	−7.08327e21			−1.40288
$784$	−4.10310e21	+	9.30279e20i	−0.804899	+	0.182491i
$785$	1.77820e21			0.345507
$786$	−3.93165e21	−	3.51609e21i	−0.756668	−	0.676691i
$787$			1.01836e22i			1.94129i	0.240516	+	0.970645i	$0.422683\pi$
$787$			1.01836e22i			1.94129i	−0.240516	+	0.970645i	$0.577317\pi$
$788$	−4.97875e21	+	5.57333e20i	−0.940100	+	0.105237i
$789$		−	1.39271e22i		−	2.60485i
$790$	−3.36255e21	+	3.75996e21i	−0.622967	+	0.696594i
$791$	1.87500e18			0.000344095
$792$	−6.95504e21	−	4.94619e21i	−1.26433	−	0.899149i
$793$	−2.98793e20			−0.0538049
$794$	5.52920e21	−	6.18269e21i	0.986299	−	1.10287i
$795$			1.08256e21i			0.191293i
$796$	−8.93729e20	−	7.98383e21i	−0.156444	−	1.39754i
$797$			5.46932e21i			0.948410i	0.880415	+	0.474205i	$0.157264\pi$
$797$			5.46932e21i			0.948410i	−0.880415	+	0.474205i	$0.842736\pi$
$798$	1.47519e22	+	1.31926e22i	2.53411	+	2.26626i
$799$	9.57587e21			1.62959
$800$	−2.87979e21	−	1.59839e21i	−0.485496	−	0.269469i
$801$	5.08513e21			0.849295
$802$	1.63350e21	+	1.46084e21i	0.270278	+	0.241710i
$803$			3.50138e21i			0.573948i
$804$	1.29168e21	+	1.15388e22i	0.209765	+	1.87387i
$805$		−	6.45275e21i		−	1.03819i
$806$	1.81337e21	−	2.02769e21i	0.289050	−	0.323212i
$807$	−1.10872e22			−1.75093
$808$	−7.46426e20	−	5.30833e20i	−0.116789	−	0.0830563i
$809$	7.55599e21			1.17132			0.585662	−	0.810555i	$-0.300834\pi$
$809$	7.55599e21			1.17132			0.585662	+	0.810555i	$0.300834\pi$
$810$	2.70862e21	−	3.02875e21i	0.416017	−	0.465185i
$811$		−	7.92931e21i		−	1.20664i	−0.797498	−	0.603321i	$-0.793844\pi$
$811$		−	7.92931e21i		−	1.20664i	0.797498	−	0.603321i	$-0.206156\pi$
$812$	7.39818e21	−	8.28170e20i	1.11546	−	0.124867i
$813$		−	1.01386e22i		−	1.51461i
$814$	−1.02224e21	−	9.14193e20i	−0.151311	−	0.135318i
$815$	3.94654e21			0.578808
$816$	2.91835e21	+	1.28717e22i	0.424094	+	1.87051i
$817$	−1.05328e22			−1.51662
$818$	7.58557e21	+	6.78380e21i	1.08228	+	0.967884i
$819$		−	5.96723e21i		−	0.843614i
$820$	−2.05125e21	+	2.29622e20i	−0.287353	+	0.0321669i
$821$			7.93968e21i			1.10212i	0.834465	+	0.551060i	$0.185777\pi$
$821$			7.93968e21i			1.10212i	−0.834465	+	0.551060i	$0.814223\pi$
$822$	1.16186e21	−	1.29918e21i	0.159814	−	0.178702i
$823$	1.04961e22			1.43064			0.715320	−	0.698797i	$-0.246281\pi$
$823$	1.04961e22			1.43064			0.715320	+	0.698797i	$0.246281\pi$
$824$	2.28712e21	−	3.21601e21i	0.308912	−	0.434374i
$825$	−5.61454e21			−0.751466
$826$	−5.15079e21	+	5.75956e21i	−0.683162	+	0.763904i
$827$			8.93568e21i			1.17445i	0.809422	+	0.587227i	$0.199781\pi$
$827$			8.93568e21i			1.17445i	−0.809422	+	0.587227i	$0.800219\pi$
$828$	1.94714e21	+	1.73941e22i	0.253612	+	2.26556i
$829$		−	7.59372e21i		−	0.980157i	−0.871678	−	0.490078i	$-0.836968\pi$
$829$		−	7.59372e21i		−	0.980157i	0.871678	−	0.490078i	$-0.163032\pi$
$830$	−2.17172e21	−	1.94218e21i	−0.277791	−	0.248430i
$831$	−2.28321e22			−2.89427
$832$	−2.37312e21	+	8.24630e20i	−0.298123	+	0.103594i
$833$	7.36741e21			0.917227
$834$	−6.69366e21	−	5.98616e21i	−0.825882	−	0.738590i
$835$		−	5.54142e21i		−	0.677599i
$836$	−1.04959e21	−	9.37618e21i	−0.127196	−	1.13626i
$837$			1.93162e22i			2.31996i
$838$	5.70834e21	−	6.38300e21i	0.679485	−	0.759792i
$839$	−8.89936e21			−1.04989			−0.524945	−	0.851136i	$-0.675914\pi$
$839$	−8.89936e21			−1.04989			−0.524945	+	0.851136i	$0.675914\pi$
$840$	−7.70733e21	+	1.08376e22i	−0.901175	+	1.26718i
$841$	2.67329e21			0.309797
$842$	8.69584e21	−	9.72359e21i	0.998782	−	1.11683i
$843$			1.38540e22i			1.57713i
$844$	−1.55659e21	+	1.74249e20i	−0.175633	+	0.0196608i
$845$		−	5.36917e21i		−	0.600456i
$846$	−1.95083e22	−	1.74463e22i	−2.16243	−	1.93387i
$847$	−4.73514e21			−0.520245
$848$	3.37473e20	+	1.48846e21i	0.0367511	+	0.162095i
$849$	3.12863e22			3.37712
$850$	4.29916e21	+	3.84476e21i	0.459983	+	0.411365i
$851$			2.81250e21i			0.298278i
$852$	−7.52175e20	+	8.42002e19i	−0.0790718	+	0.00885149i
$853$		−	4.60519e21i		−	0.479877i	−0.970788	−	0.239938i	$-0.922873\pi$
$853$		−	4.60519e21i		−	0.479877i	0.970788	−	0.239938i	$-0.0771272\pi$
$854$	−1.48646e21	+	1.66214e21i	−0.153539	+	0.171685i
$855$	1.87884e22			1.92373
$856$	7.62006e21	+	5.41913e21i	0.773402	+	0.550017i
$857$	−1.34576e21			−0.135397			−0.0676987	−	0.997706i	$-0.521566\pi$
$857$	−1.34576e21			−0.135397			−0.0676987	+	0.997706i	$0.521566\pi$
$858$	−2.85488e21	+	3.19229e21i	−0.284730	+	0.318382i
$859$		−	1.40865e22i		−	1.39269i	−0.717708	−	0.696344i	$-0.754809\pi$
$859$		−	1.40865e22i		−	1.39269i	0.717708	−	0.696344i	$-0.245191\pi$
$860$	−7.87385e20	−	7.03384e21i	−0.0771700	−	0.689373i
$861$		−	1.04054e22i		−	1.01096i
$862$	9.76976e20	+	8.73713e20i	0.0940977	+	0.0841520i
$863$	−5.91639e21			−0.564905			−0.282453	−	0.959281i	$-0.591148\pi$
$863$	−5.91639e21			−0.564905			−0.282453	+	0.959281i	$0.591148\pi$
$864$	8.65750e21	−	1.55981e22i	0.819482	−	1.47644i
$865$	−1.29730e22			−1.21736
$866$	6.30052e21	+	5.63458e21i	0.586127	+	0.524176i
$867$		−	4.39933e21i		−	0.405736i
$868$	−2.25843e21	−	2.01750e22i	−0.206495	−	1.84465i
$869$			1.21228e22i			1.09889i
$870$	7.09257e21	−	7.93083e21i	0.637396	−	0.712729i
$871$	3.87020e21			0.344824
$872$	−4.01475e21	−	2.85515e21i	−0.354638	−	0.252206i
$873$	−4.95137e21			−0.433630
$874$	−1.28984e22	+	1.44228e22i	−1.11995	+	1.25232i
$875$			1.62774e22i			1.40128i
$876$	−1.47072e22	+	1.64636e21i	−1.25531	+	0.140522i
$877$			2.20259e22i			1.86396i	0.362512	+	0.931979i	$0.381919\pi$
$877$			2.20259e22i			1.86396i	−0.362512	+	0.931979i	$0.618081\pi$
$878$	2.92172e21	+	2.61291e21i	0.245149	+	0.219238i
$879$	−1.02647e22			−0.853946
$880$	6.18300e21	−	1.40185e21i	0.510010	−	0.115633i
$881$	−1.53851e22			−1.25829			−0.629146	−	0.777287i	$-0.716595\pi$
$881$	−1.53851e22			−1.25829			−0.629146	+	0.777287i	$0.716595\pi$
$882$	−1.50091e22	−	1.34227e22i	−1.21714	−	1.08849i
$883$			8.03173e20i			0.0645809i	0.999479	+	0.0322904i	$0.0102801\pi$
$883$			8.03173e20i			0.0645809i	−0.999479	+	0.0322904i	$0.989720\pi$
$884$	4.37207e21	−	4.89420e20i	0.348574	−	0.0390202i
$885$			1.10433e22i			0.873018i
$886$	9.87218e21	−	1.10390e22i	0.773856	−	0.865317i
$887$	1.56571e22			1.21698			0.608492	−	0.793560i	$-0.291775\pi$
$887$	1.56571e22			1.21698			0.608492	+	0.793560i	$0.291775\pi$
$888$	3.35932e21	−	4.72368e21i	0.258913	−	0.364069i
$889$	−3.41370e22			−2.60893
$890$	−2.51817e21	+	2.81579e21i	−0.190836	+	0.213390i
$891$		−	9.76521e21i		−	0.733836i
$892$	2.37732e20	+	2.12370e21i	0.0177154	+	0.158255i
$893$		−	2.89322e22i		−	2.13794i
$894$	3.19571e22	+	2.85794e22i	2.34173	+	2.09422i
$895$	−4.30159e21			−0.312576
$896$	−7.21869e21	+	1.73037e22i	−0.520173	+	1.24690i
$897$	8.78299e21			0.627624
$898$	−5.84346e21	−	5.22583e21i	−0.414093	−	0.370325i
$899$			1.62418e22i			1.14140i
$900$	−1.75362e21	−	1.56653e22i	−0.122213	−	1.09174i
$901$		−	2.67264e21i		−	0.184716i
$902$	−3.30679e21	+	3.69762e21i	−0.226651	+	0.253439i
$903$	3.56805e22			2.42534
$904$	2.18960e18	−	3.07889e18i	0.000147605	−	0.000207554i
$905$	6.23520e21			0.416856
$906$	−3.52510e21	+	3.94173e21i	−0.233728	+	0.261352i
$907$		−	1.07214e22i		−	0.705011i	−0.935810	−	0.352505i	$-0.885330\pi$
$907$		−	1.07214e22i		−	0.705011i	0.935810	−	0.352505i	$-0.114670\pi$
$908$	1.08008e21	−	1.20907e20i	0.0704390	−	0.00788511i
$909$		−	4.38362e21i		−	0.283533i
$910$	3.30423e21	+	2.95499e21i	0.211963	+	0.189559i
$911$	−1.19619e22			−0.761049			−0.380524	−	0.924771i	$-0.624256\pi$
$911$	−1.19619e22			−0.761049			−0.380524	+	0.924771i	$0.624256\pi$
$912$	3.88902e22	−	8.81742e21i	2.45403	−	0.556391i
$913$	−7.00201e21			−0.438219
$914$	1.07910e22	+	9.65047e21i	0.669834	+	0.599035i
$915$			3.18696e21i			0.196209i
$916$	−8.97683e20	+	1.00489e20i	−0.0548159	+	0.00613623i
$917$			1.31208e22i			0.794677i
$918$	−2.08247e22	+	2.32859e22i	−1.25100	+	1.39886i
$919$	6.01177e21			0.358209			0.179104	−	0.983830i	$-0.442680\pi$
$919$	6.01177e21			0.358209			0.179104	+	0.983830i	$0.442680\pi$
$920$	−1.05959e22	−	7.53543e21i	−0.626222	−	0.445348i
$921$	3.74990e22			2.19823
$922$	−1.42465e22	+	1.59302e22i	−0.828372	+	0.926276i
$923$			2.52286e20i			0.0145506i
$924$	3.55557e21	+	3.17625e22i	0.203409	+	1.81708i
$925$		−	2.53297e21i		−	0.143736i
$926$	−2.02052e22	−	1.80696e22i	−1.13732	−	1.01711i
$927$	1.88870e22			1.05455
$928$	7.27957e21	−	1.31155e22i	0.403177	−	0.726396i
$929$	−2.34091e22			−1.28608			−0.643038	−	0.765834i	$-0.722326\pi$
$929$	−2.34091e22			−1.28608			−0.643038	+	0.765834i	$0.722326\pi$
$930$	−2.16275e22	−	1.93416e22i	−1.17865	−	1.05407i
$931$		−	2.22596e22i		−	1.20336i
$932$	2.67482e21	+	2.38946e22i	0.143441	+	1.28139i
$933$			2.30930e22i			1.22848i
$934$	−1.99487e22	+	2.23064e22i	−1.05272	+	1.17714i
$935$	−1.11020e22			−0.581185
$936$	−9.79862e21	−	6.96844e21i	−0.508857	−	0.361882i
$937$	1.42314e22			0.733161			0.366580	−	0.930386i	$-0.380528\pi$
$937$	1.42314e22			0.733161			0.366580	+	0.930386i	$0.380528\pi$
$938$	1.92537e22	−	2.15293e22i	0.983997	−	1.10029i
$939$		−	4.42177e22i		−	2.24184i
$940$	1.93211e22	−	2.16285e21i	0.971791	−	0.108785i
$941$			1.86876e21i			0.0932465i	0.998913	+	0.0466232i	$0.0148460\pi$
$941$			1.86876e21i			0.0932465i	−0.998913	+	0.0466232i	$0.985154\pi$
$942$	1.34640e22	+	1.20409e22i	0.666488	+	0.596042i
$943$	1.01733e22			0.499602
$944$	3.44258e21	+	1.51839e22i	0.167724	+	0.739763i
$945$	−3.14769e22			−1.52143
$946$	−1.26793e22	−	1.13391e22i	−0.608012	−	0.543747i
$947$		−	3.69289e22i		−	1.75688i	−0.477855	−	0.878439i	$-0.658586\pi$
$947$		−	3.69289e22i		−	1.75688i	0.477855	−	0.878439i	$-0.341414\pi$
$948$	−5.09205e22	+	5.70016e21i	−2.40342	+	0.269045i
$949$			4.93293e21i			0.230998i
$950$	1.16164e22	−	1.29894e22i	0.539691	−	0.603477i
$951$	−5.46808e22			−2.52047
$952$	1.90279e22	−	2.67560e22i	0.870191	−	1.22361i
$953$	3.09952e22			1.40636			0.703182	−	0.711010i	$-0.251762\pi$
$953$	3.09952e22			1.40636			0.703182	+	0.711010i	$0.251762\pi$
$954$	−4.86930e21	+	5.44480e21i	−0.219207	+	0.245115i
$955$			1.32161e22i			0.590305i
$956$	−8.43739e20	−	7.53726e21i	−0.0373916	−	0.334025i
$957$		−	2.55703e22i		−	1.12434i
$958$	1.38581e22	+	1.23933e22i	0.604591	+	0.540688i
$959$	−4.33565e21			−0.187679
$960$	8.79559e21	+	2.53119e22i	0.377773	+	1.08715i
$961$	2.08265e22			0.887545
$962$	−1.44019e21	−	1.28796e21i	−0.0608983	−	0.0544616i
$963$			4.47512e22i			1.87762i
$964$	−4.72314e20	−	4.21926e21i	−0.0196631	−	0.175654i
$965$		−	2.70097e22i		−	1.11574i
$966$	4.36943e22	−	4.88584e22i	1.79100	−	2.00268i
$967$	−1.09357e22			−0.444782			−0.222391	−	0.974958i	$-0.571386\pi$
$967$	−1.09357e22			−0.444782			−0.222391	+	0.974958i	$0.571386\pi$
$968$	−5.52963e21	+	7.77544e21i	−0.223167	+	0.313805i
$969$	−6.98302e22			−2.79650
$970$	2.45193e21	−	2.74172e21i	0.0974362	−	0.108952i
$971$		−	3.63030e21i		−	0.143152i	−0.997435	−	0.0715761i	$-0.977197\pi$
$971$		−	3.63030e21i		−	0.143152i	0.997435	−	0.0715761i	$-0.0228029\pi$
$972$	−1.86906e21	+	2.09227e20i	−0.0731352	+	0.00818693i
$973$			2.23383e22i			0.867368i
$974$	−2.56694e22	−	2.29563e22i	−0.989063	−	0.884523i
$975$	−7.91005e21			−0.302444
$976$	9.93488e20	+	4.38189e21i	0.0376955	+	0.166260i
$977$	2.72916e22			1.02759			0.513796	−	0.857913i	$-0.328239\pi$
$977$	2.72916e22			1.02759			0.513796	+	0.857913i	$0.328239\pi$
$978$	2.98821e22	+	2.67236e22i	1.11653	+	0.998514i
$979$			9.07858e21i			0.336626i
$980$	1.48651e22	−	1.66404e21i	0.546981	−	0.0612304i
$981$		−	2.35779e22i		−	0.860967i
$982$	−1.00288e22	+	1.12141e22i	−0.363424	+	0.406377i
$983$	1.33168e22			0.478903			0.239452	−	0.970908i	$-0.423032\pi$
$983$	1.33168e22			0.478903			0.239452	+	0.970908i	$0.423032\pi$
$984$	−1.70864e22	−	1.21512e22i	−0.609799	−	0.433668i
$985$	1.78115e22			0.630853
$986$	−1.75102e22	+	1.95797e22i	−0.615481	+	0.688224i
$987$			9.80100e22i			3.41894i
$988$	−1.47872e21	−	1.32096e22i	−0.0511928	−	0.457313i
$989$			3.48847e22i			1.19857i
$990$	2.26174e22	+	2.02268e22i	0.771221	+	0.689706i
$991$	5.47975e22			1.85442			0.927211	−	0.374540i	$-0.122199\pi$
$991$	5.47975e22			1.85442			0.927211	+	0.374540i	$0.122199\pi$
$992$	−3.57661e22	−	1.98515e22i	−1.20125	−	0.666739i
$993$	2.24266e22			0.747557
$994$	1.40343e21	+	1.25509e21i	0.0464293	+	0.0415219i
$995$			2.85621e22i			0.937816i
$996$	−3.29237e21	−	2.94113e22i	−0.107291	−	0.958449i
$997$			3.25018e21i			0.105122i	0.998618	+	0.0525610i	$0.0167384\pi$
$997$			3.25018e21i			0.105122i	−0.998618	+	0.0525610i	$0.983262\pi$
$998$	−9.21136e21	+	1.03000e22i	−0.295695	+	0.330643i
$999$	1.37195e22			0.437117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.16.b.a.5.12	yes	14
3.2	odd	2		72.16.d.b.37.3		14
4.3	odd	2		32.16.b.a.17.14		14
8.3	odd	2		32.16.b.a.17.1		14
8.5	even	2	inner	8.16.b.a.5.11	✓	14
24.5	odd	2		72.16.d.b.37.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.16.b.a.5.11	✓	14	8.5	even	2	inner
8.16.b.a.5.12	yes	14	1.1	even	1	trivial
32.16.b.a.17.1		14	8.3	odd	2
32.16.b.a.17.14		14	4.3	odd	2
72.16.d.b.37.3		14	3.2	odd	2
72.16.d.b.37.4		14	24.5	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)

\(f(q)\)	\(=\)	\(q+(134.932 + 120.670i) q^{2} -6537.39i q^{3} +(3645.36 + 32564.6i) q^{4} -116500. i q^{5} +(788869. - 882104. i) q^{6} -2.94378e6 q^{7} +(-3.43770e6 + 4.83390e6i) q^{8} -2.83885e7 q^{9} +O(q^{10})\)	\(q+(134.932 + 120.670i) q^{2} -6537.39i q^{3} +(3645.36 + 32564.6i) q^{4} -116500. i q^{5} +(788869. - 882104. i) q^{6} -2.94378e6 q^{7} +(-3.43770e6 + 4.83390e6i) q^{8} -2.83885e7 q^{9} +(1.40581e7 - 1.57196e7i) q^{10} -5.06826e7i q^{11} +(2.12887e8 - 2.38311e7i) q^{12} -7.14043e7i q^{13} +(-3.97211e8 - 3.55227e8i) q^{14} -7.61605e8 q^{15} +(-1.04716e9 + 2.37419e8i) q^{16} +1.88026e9 q^{17} +(-3.83053e9 - 3.42565e9i) q^{18} -5.68095e9i q^{19} +(3.79377e9 - 4.24684e8i) q^{20} +1.92447e10i q^{21} +(6.11588e9 - 6.83871e9i) q^{22} -1.88154e10 q^{23} +(3.16011e10 + 2.24736e10i) q^{24} +1.69454e10 q^{25} +(8.61637e9 - 9.63473e9i) q^{26} +9.17826e10i q^{27} +(-1.07311e10 - 9.58631e10i) q^{28} +7.71744e10i q^{29} +(-1.02765e11 - 9.19031e10i) q^{30} +2.10456e11 q^{31} +(-1.69946e11 - 9.43262e10i) q^{32} -3.31332e11 q^{33} +(2.53707e11 + 2.26891e11i) q^{34} +3.42950e11i q^{35} +(-1.03486e11 - 9.24462e11i) q^{36} -1.49479e11i q^{37} +(6.85522e11 - 7.66543e11i) q^{38} -4.66797e11 q^{39} +(5.63148e11 + 4.00492e11i) q^{40} -5.40690e11 q^{41} +(-2.32226e12 + 2.59672e12i) q^{42} -1.85405e12i q^{43} +(1.65046e12 - 1.84756e11i) q^{44} +3.30726e12i q^{45} +(-2.53881e12 - 2.27046e12i) q^{46} +5.09285e12 q^{47} +(1.55210e12 + 6.84572e12i) q^{48} +3.91829e12 q^{49} +(2.28647e12 + 2.04480e12i) q^{50} -1.22920e13i q^{51} +(2.32525e12 - 2.60294e11i) q^{52} -1.42142e12i q^{53} +(-1.10754e13 + 1.23844e13i) q^{54} -5.90451e12 q^{55} +(1.01199e13 - 1.42299e13i) q^{56} -3.71386e13 q^{57} +(-9.31266e12 + 1.04133e13i) q^{58} -1.45000e13i q^{59} +(-2.77632e12 - 2.48014e13i) q^{60} -4.18453e12i q^{61} +(2.83973e13 + 2.53958e13i) q^{62} +8.35697e13 q^{63} +(-1.15488e13 - 3.32350e13i) q^{64} -8.31858e12 q^{65} +(-4.47073e13 - 3.99819e13i) q^{66} +5.42012e13i q^{67} +(6.85422e12 + 6.12299e13i) q^{68} +1.23004e14i q^{69} +(-4.13839e13 + 4.62750e13i) q^{70} -3.53320e12 q^{71} +(9.75914e13 - 1.37227e14i) q^{72} -6.90845e13 q^{73} +(1.80376e13 - 2.01695e13i) q^{74} -1.10778e14i q^{75} +(1.84998e14 - 2.07091e13i) q^{76} +1.49199e14i q^{77} +(-6.29860e13 - 5.63286e13i) q^{78} -2.39190e14 q^{79} +(2.76593e13 + 1.21995e14i) q^{80} +1.92674e14 q^{81} +(-7.29564e13 - 6.52452e13i) q^{82} -1.38154e14i q^{83} +(-6.26694e14 + 7.01537e13i) q^{84} -2.19050e14i q^{85} +(2.23729e14 - 2.50171e14i) q^{86} +5.04519e14 q^{87} +(2.44994e14 + 1.74232e14i) q^{88} -1.79126e14 q^{89} +(-3.99088e14 + 4.46256e14i) q^{90} +2.10199e14i q^{91} +(-6.85890e13 - 6.12717e14i) q^{92} -1.37583e15i q^{93} +(6.87188e14 + 6.14555e14i) q^{94} -6.61830e14 q^{95} +(-6.16647e14 + 1.11100e15i) q^{96} +1.74414e14 q^{97} +(5.28704e14 + 4.72822e14i) q^{98} +1.43881e15i 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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