LMFDB - Embedded newform 8.16.b.a.5.4

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			5.4
Root			$73.6274 - 48.1688i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.16.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-153.255 + 96.3377i) q^{2} -27.2769i q^{3} +(14206.1 - 29528.4i) q^{4} +212327. i q^{5} +(2627.80 + 4180.32i) q^{6} -3.74922e6 q^{7} +(667546. + 5.89396e6i) q^{8} +1.43482e7 q^{9} +(-2.04551e7 - 3.25401e7i) q^{10} -5.02415e6i q^{11} +(-805445. - 387499. i) q^{12} -3.90933e8i q^{13} +(5.74586e8 - 3.61191e8i) q^{14} +5.79162e6 q^{15} +(-6.70115e8 - 8.38968e8i) q^{16} -2.61842e8 q^{17} +(-2.19893e9 + 1.38227e9i) q^{18} -4.51083e9i q^{19} +(6.26968e9 + 3.01634e9i) q^{20} +1.02267e8i q^{21} +(4.84015e8 + 7.69975e8i) q^{22} -4.94368e9 q^{23} +(1.60769e8 - 1.82086e7i) q^{24} -1.45651e10 q^{25} +(3.76616e10 + 5.99124e10i) q^{26} -7.82768e8i q^{27} +(-5.32618e10 + 1.10708e11i) q^{28} -1.04763e11i q^{29} +(-8.87594e8 + 5.57951e8i) q^{30} -1.41930e11 q^{31} +(1.83523e11 + 6.40186e10i) q^{32} -1.37043e8 q^{33} +(4.01286e10 - 2.52253e10i) q^{34} -7.96059e11i q^{35} +(2.03832e11 - 4.23679e11i) q^{36} -2.56429e11i q^{37} +(4.34563e11 + 6.91306e11i) q^{38} -1.06634e10 q^{39} +(-1.25145e12 + 1.41738e11i) q^{40} +9.25121e10 q^{41} +(-9.85218e9 - 1.56729e10i) q^{42} +1.59233e12i q^{43} +(-1.48355e11 - 7.13736e10i) q^{44} +3.04650e12i q^{45} +(7.57643e11 - 4.76263e11i) q^{46} -3.94340e12 q^{47} +(-2.28845e10 + 1.82787e10i) q^{48} +9.30906e12 q^{49} +(2.23217e12 - 1.40316e12i) q^{50} +7.14225e9i q^{51} +(-1.15436e13 - 5.55363e12i) q^{52} +1.04692e13i q^{53} +(7.54101e10 + 1.19963e11i) q^{54} +1.06676e12 q^{55} +(-2.50277e12 - 2.20977e13i) q^{56} -1.23042e11 q^{57} +(1.00926e13 + 1.60554e13i) q^{58} -1.98199e13i q^{59} +(8.22764e10 - 1.71018e11i) q^{60} +5.15720e12i q^{61} +(2.17515e13 - 1.36732e13i) q^{62} -5.37944e13 q^{63} +(-3.42931e13 + 7.86898e12i) q^{64} +8.30055e13 q^{65} +(2.10026e10 - 1.32024e10i) q^{66} -3.73869e13i q^{67} +(-3.71976e12 + 7.73179e12i) q^{68} +1.34848e11i q^{69} +(7.66905e13 + 1.22000e14i) q^{70} -6.81556e13 q^{71} +(9.57806e12 + 8.45675e13i) q^{72} -1.10782e14 q^{73} +(2.47037e13 + 3.92990e13i) q^{74} +3.97290e11i q^{75} +(-1.33198e14 - 6.40813e13i) q^{76} +1.88366e13i q^{77} +(1.63423e12 - 1.02729e12i) q^{78} +4.34133e13 q^{79} +(1.78135e14 - 1.42283e14i) q^{80} +2.05859e14 q^{81} +(-1.41779e13 + 8.91240e12i) q^{82} -3.97545e14i q^{83} +(3.01979e12 + 1.45282e12i) q^{84} -5.55961e13i q^{85} +(-1.53402e14 - 2.44033e14i) q^{86} -2.85761e12 q^{87} +(2.96121e13 - 3.35385e12i) q^{88} -1.70072e14 q^{89} +(-2.93493e14 - 4.66891e14i) q^{90} +1.46569e15i q^{91} +(-7.02304e13 + 1.45979e14i) q^{92} +3.87142e12i q^{93} +(6.04345e14 - 3.79898e14i) q^{94} +9.57769e14 q^{95} +(1.74623e12 - 5.00593e12i) q^{96} -7.46636e14 q^{97} +(-1.42666e15 + 8.96813e14i) q^{98} -7.20873e13i 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} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17}+ \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

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 $

$2$	−153.255	+	96.3377i	−0.846621	+	0.532195i
$2$	−153.255	+	96.3377i	−0.846621	+	0.532195i
$3$		−	27.2769i		−	0.00720089i	−0.999994	−	0.00360044i	$-0.998854\pi$
$3$		−	27.2769i		−	0.00720089i	0.999994	−	0.00360044i	$-0.00114606\pi$
$4$	14206.1	−	29528.4i	0.433536	−	0.901136i
$5$			212327.i			1.21543i	0.794156	+	0.607715i	$0.207914\pi$
$5$			212327.i			1.21543i	−0.794156	+	0.607715i	$0.792086\pi$
$6$	2627.80	+	4180.32i	0.00383228	+	0.00609643i
$7$	−3.74922e6			−1.72070			−0.860350	−	0.509704i	$-0.829755\pi$
$7$	−3.74922e6			−1.72070			−0.860350	+	0.509704i	$0.829755\pi$
$8$	667546.	+	5.89396e6i	0.112540	+	0.993647i
$9$	1.43482e7			0.999948
$10$	−2.04551e7	−	3.25401e7i	−0.646846	−	1.02901i
$11$		−	5.02415e6i		−	0.0777352i	−0.999244	−	0.0388676i	$-0.987625\pi$
$11$		−	5.02415e6i		−	0.0777352i	0.999244	−	0.0388676i	$-0.0123751\pi$
$12$	−805445.	−	387499.i	−0.00648898	−	0.00312184i
$13$		−	3.90933e8i		−	1.72793i	−0.503549	−	0.863967i	$-0.667973\pi$
$13$		−	3.90933e8i		−	1.72793i	0.503549	−	0.863967i	$-0.332027\pi$
$14$	5.74586e8	−	3.61191e8i	1.45678	−	0.915749i
$15$	5.79162e6			0.00875217
$16$	−6.70115e8	−	8.38968e8i	−0.624093	−	0.781350i
$17$	−2.61842e8			−0.154765			−0.0773825	−	0.997001i	$-0.524656\pi$
$17$	−2.61842e8			−0.154765			−0.0773825	+	0.997001i	$0.524656\pi$
$18$	−2.19893e9	+	1.38227e9i	−0.846578	+	0.532168i
$19$		−	4.51083e9i		−	1.15772i	−0.815426	−	0.578861i	$-0.803497\pi$
$19$		−	4.51083e9i		−	1.15772i	0.815426	−	0.578861i	$-0.196503\pi$
$20$	6.26968e9	+	3.01634e9i	1.09527	+	0.526932i
$21$			1.02267e8i			0.0123906i
$22$	4.84015e8	+	7.69975e8i	0.0413703	+	0.0658123i
$23$	−4.94368e9			−0.302755			−0.151378	−	0.988476i	$-0.548371\pi$
$23$	−4.94368e9			−0.302755			−0.151378	+	0.988476i	$0.548371\pi$
$24$	1.60769e8	−	1.82086e7i	0.00715514	−	0.000810387i
$25$	−1.45651e10			−0.477268
$26$	3.76616e10	+	5.99124e10i	0.919598	+	1.46291i
$27$		−	7.82768e8i		−	0.0144014i
$28$	−5.32618e10	+	1.10708e11i	−0.745985	+	1.55059i
$29$		−	1.04763e11i		−	1.12778i	−0.825851	−	0.563888i	$-0.809305\pi$
$29$		−	1.04763e11i		−	1.12778i	0.825851	−	0.563888i	$-0.190695\pi$
$30$	−8.87594e8	+	5.57951e8i	−0.00740978	+	0.00465787i
$31$	−1.41930e11			−0.926535			−0.463267	−	0.886219i	$-0.653323\pi$
$31$	−1.41930e11			−0.926535			−0.463267	+	0.886219i	$0.653323\pi$
$32$	1.83523e11	+	6.40186e10i	0.944202	+	0.329368i
$33$	−1.37043e8			−0.000559762
$34$	4.01286e10	−	2.52253e10i	0.131027	−	0.0823652i
$35$		−	7.96059e11i		−	2.09139i
$36$	2.03832e11	−	4.23679e11i	0.433513	−	0.901090i
$37$		−	2.56429e11i		−	0.444072i	−0.975038	−	0.222036i	$-0.928730\pi$
$37$		−	2.56429e11i		−	0.444072i	0.975038	−	0.222036i	$-0.0712703\pi$
$38$	4.34563e11	+	6.91306e11i	0.616134	+	0.980152i
$39$	−1.06634e10			−0.0124427
$40$	−1.25145e12	+	1.41738e11i	−1.20771	+	0.136784i
$41$	9.25121e10			0.0741856			0.0370928	−	0.999312i	$-0.488190\pi$
$41$	9.25121e10			0.0741856			0.0370928	+	0.999312i	$0.488190\pi$
$42$	−9.85218e9	−	1.56729e10i	−0.00659421	−	0.0104901i
$43$			1.59233e12i			0.893348i	0.894697	+	0.446674i	$0.147392\pi$
$43$			1.59233e12i			0.893348i	−0.894697	+	0.446674i	$0.852608\pi$
$44$	−1.48355e11	−	7.13736e10i	−0.0700500	−	0.0337010i
$45$			3.04650e12i			1.21537i
$46$	7.57643e11	−	4.76263e11i	0.256319	−	0.161125i
$47$	−3.94340e12			−1.13537			−0.567684	−	0.823246i	$-0.692161\pi$
$47$	−3.94340e12			−1.13537			−0.567684	+	0.823246i	$0.692161\pi$
$48$	−2.28845e10	+	1.82787e10i	−0.00562641	+	0.00449403i
$49$	9.30906e12			1.96081
$50$	2.23217e12	−	1.40316e12i	0.404065	−	0.254000i
$51$			7.14225e9i			0.00111445i
$52$	−1.15436e13	−	5.55363e12i	−1.55710	−	0.749121i
$53$			1.04692e13i			1.22418i	0.790789	+	0.612089i	$0.209671\pi$
$53$			1.04692e13i			1.22418i	−0.790789	+	0.612089i	$0.790329\pi$
$54$	7.54101e10	+	1.19963e11i	0.00766436	+	0.0121925i
$55$	1.06676e12			0.0944816
$56$	−2.50277e12	−	2.20977e13i	−0.193647	−	1.70977i
$57$	−1.23042e11			−0.00833663
$58$	1.00926e13	+	1.60554e13i	0.600197	+	0.954799i
$59$		−	1.98199e13i		−	1.03684i	−0.855127	−	0.518419i	$-0.826521\pi$
$59$		−	1.98199e13i		−	1.03684i	0.855127	−	0.518419i	$-0.173479\pi$
$60$	8.22764e10	−	1.71018e11i	0.00379438	−	0.00788690i
$61$			5.15720e12i			0.210107i	0.994467	+	0.105053i	$0.0335013\pi$
$61$			5.15720e12i			0.210107i	−0.994467	+	0.105053i	$0.966499\pi$
$62$	2.17515e13	−	1.36732e13i	0.784424	−	0.493098i
$63$	−5.37944e13			−1.72061
$64$	−3.42931e13	+	7.86898e12i	−0.974670	+	0.223650i
$65$	8.30055e13			2.10018
$66$	2.10026e10	−	1.32024e10i	0.000473907	−	0.000297903i
$67$		−	3.73869e13i		−	0.753630i	−0.926289	−	0.376815i	$-0.877019\pi$
$67$		−	3.73869e13i		−	0.753630i	0.926289	−	0.376815i	$-0.122981\pi$
$68$	−3.71976e12	+	7.73179e12i	−0.0670962	+	0.139464i
$69$			1.34848e11i			0.00218011i
$70$	7.66905e13	+	1.22000e14i	1.11303	+	1.77062i
$71$	−6.81556e13			−0.889332			−0.444666	−	0.895696i	$-0.646678\pi$
$71$	−6.81556e13			−0.889332			−0.444666	+	0.895696i	$0.646678\pi$
$72$	9.57806e12	+	8.45675e13i	0.112534	+	0.993596i
$73$	−1.10782e14			−1.17368			−0.586840	−	0.809703i	$-0.699628\pi$
$73$	−1.10782e14			−1.17368			−0.586840	+	0.809703i	$0.699628\pi$
$74$	2.47037e13	+	3.92990e13i	0.236333	+	0.375961i
$75$			3.97290e11i			0.00343675i
$76$	−1.33198e14	−	6.40813e13i	−1.04327	−	0.501914i
$77$			1.88366e13i			0.133759i
$78$	1.63423e12	−	1.02729e12i	0.0105342	−	0.00662193i
$79$	4.34133e13			0.254343			0.127172	−	0.991881i	$-0.459410\pi$
$79$	4.34133e13			0.254343			0.127172	+	0.991881i	$0.459410\pi$
$80$	1.78135e14	−	1.42283e14i	0.949675	−	0.758541i
$81$	2.05859e14			0.999844
$82$	−1.41779e13	+	8.91240e12i	−0.0628071	+	0.0394812i
$83$		−	3.97545e14i		−	1.60805i	−0.594594	−	0.804026i	$-0.702687\pi$
$83$		−	3.97545e14i		−	1.60805i	0.594594	−	0.804026i	$-0.297313\pi$
$84$	3.01979e12	+	1.45282e12i	0.0111656	+	0.00537176i
$85$		−	5.55961e13i		−	0.188106i
$86$	−1.53402e14	−	2.44033e14i	−0.475436	−	0.756328i
$87$	−2.85761e12			−0.00812099
$88$	2.96121e13	−	3.35385e12i	0.0772413	−	0.00874830i
$89$	−1.70072e14			−0.407576			−0.203788	−	0.979015i	$-0.565325\pi$
$89$	−1.70072e14			−0.407576			−0.203788	+	0.979015i	$0.565325\pi$
$90$	−2.93493e14	−	4.66891e14i	−0.646812	−	1.02896i
$91$			1.46569e15i			2.97326i
$92$	−7.02304e13	+	1.45979e14i	−0.131255	+	0.272824i
$93$			3.87142e12i			0.00667187i
$94$	6.04345e14	−	3.79898e14i	0.961227	−	0.604238i
$95$	9.57769e14			1.40713
$96$	1.74623e12	−	5.00593e12i	0.00237174	−	0.00679909i
$97$	−7.46636e14			−0.938255			−0.469127	−	0.883131i	$-0.655431\pi$
$97$	−7.46636e14			−0.938255			−0.469127	+	0.883131i	$0.655431\pi$
$98$	−1.42666e15	+	8.96813e14i	−1.66006	+	1.04353i
$99$		−	7.20873e13i		−	0.0777311i
$100$	−2.06913e14	+	4.30084e14i	−0.206913	+	0.430084i
$101$			4.52479e14i			0.419940i	0.977708	+	0.209970i	$0.0673367\pi$
$101$			4.52479e14i			0.419940i	−0.977708	+	0.209970i	$0.932663\pi$
$102$	−6.88068e11	−	1.09458e12i	−0.000593103	−	0.000943513i
$103$	6.77763e14			0.542999			0.271499	−	0.962439i	$-0.412481\pi$
$103$	6.77763e14			0.542999			0.271499	+	0.962439i	$0.412481\pi$
$104$	2.30414e15	−	2.60966e14i	1.71696	−	0.194461i
$105$	−2.17140e13			−0.0150599
$106$	−1.00858e15	−	1.60446e15i	−0.651502	−	1.03642i
$107$		−	2.55767e14i		−	0.153981i	−0.997032	−	0.0769905i	$-0.975469\pi$
$107$		−	2.55767e14i		−	0.153981i	0.997032	−	0.0769905i	$-0.0245311\pi$
$108$	−2.31139e13	−	1.11201e13i	−0.0129776	−	0.00624353i
$109$		−	1.67441e15i		−	0.877332i	−0.898650	−	0.438666i	$-0.855451\pi$
$109$		−	1.67441e15i		−	0.877332i	0.898650	−	0.438666i	$-0.144549\pi$
$110$	−1.63486e14	+	1.02769e14i	−0.0799901	+	0.0502827i
$111$	−6.99459e12			−0.00319772
$112$	2.51241e15	+	3.14547e15i	1.07388	+	1.34447i
$113$	−4.08558e15			−1.63367			−0.816837	−	0.576869i	$-0.804274\pi$
$113$	−4.08558e15			−1.63367			−0.816837	+	0.576869i	$0.804274\pi$
$114$	1.88567e13	−	1.18535e13i	0.00705797	−	0.00443672i
$115$		−	1.04968e15i		−	0.367977i
$116$	−3.09348e15	−	1.48827e15i	−1.01628	−	0.488931i
$117$		−	5.60917e15i		−	1.72784i
$118$	1.90940e15	+	3.03749e15i	0.551800	+	0.877809i
$119$	9.81703e14			0.266304
$120$	3.86617e12	+	3.41356e13i	0.000984968	+	0.00869657i
$121$	4.15201e15			0.993957
$122$	−4.96832e14	−	7.90366e14i	−0.111818	−	0.177881i
$123$		−	2.52345e12i		−	0.000534202i
$124$	−2.01627e15	+	4.19097e15i	−0.401686	+	0.834934i
$125$			3.38714e15i			0.635344i
$126$	8.24425e15	−	5.18242e15i	1.45671	−	0.915701i
$127$	−5.88844e15			−0.980556			−0.490278	−	0.871566i	$-0.663105\pi$
$127$	−5.88844e15			−0.980556			−0.490278	+	0.871566i	$0.663105\pi$
$128$	4.49751e15	−	4.50968e15i	0.706151	−	0.708061i
$129$	4.34340e13			0.00643290
$130$	−1.27210e16	+	7.99656e15i	−1.77806	+	1.11771i
$131$		−	2.42278e15i		−	0.319727i	−0.987139	−	0.159864i	$-0.948895\pi$
$131$		−	2.42278e15i		−	0.319727i	0.987139	−	0.159864i	$-0.0511055\pi$
$132$	−1.94685e12	+	4.04668e12i	−0.000242677	+	0.000504422i
$133$			1.69121e16i			1.99209i
$134$	3.60176e15	+	5.72972e15i	0.401078	+	0.638039i
$135$	1.66203e14			0.0175039
$136$	−1.74792e14	−	1.54329e15i	−0.0174172	−	0.153782i
$137$	6.48716e15			0.611858			0.305929	−	0.952054i	$-0.401033\pi$
$137$	6.48716e15			0.611858			0.305929	+	0.952054i	$0.401033\pi$
$138$	−1.29910e13	−	2.06662e13i	−0.00116024	−	0.00184573i
$139$			4.44611e15i			0.376157i	0.982154	+	0.188078i	$0.0602259\pi$
$139$			4.44611e15i			0.376157i	−0.982154	+	0.188078i	$0.939774\pi$
$140$	−2.35064e16	−	1.13089e16i	−1.88463	−	0.906692i
$141$			1.07564e14i			0.00817566i
$142$	1.04452e16	−	6.56595e15i	0.752928	−	0.473299i
$143$	−1.96411e15			−0.134321
$144$	−9.61492e15	−	1.20377e16i	−0.624061	−	0.781309i
$145$	2.22440e16			1.37073
$146$	1.69779e16	−	1.06725e16i	0.993662	−	0.624627i
$147$		−	2.53923e14i		−	0.0141196i
$148$	−7.57194e15	−	3.64285e15i	−0.400170	−	0.192521i
$149$		−	8.94476e15i		−	0.449440i	−0.974423	−	0.224720i	$-0.927853\pi$
$149$		−	8.94476e15i		−	0.449440i	0.974423	−	0.224720i	$-0.0721467\pi$
$150$	−3.82740e13	−	6.08867e13i	−0.00182903	−	0.00290963i
$151$	−2.17692e16			−0.989727			−0.494863	−	0.868971i	$-0.664782\pi$
$151$	−2.17692e16			−0.989727			−0.494863	+	0.868971i	$0.664782\pi$
$152$	2.65866e16	−	3.01118e15i	1.15037	−	0.130290i
$153$	−3.75695e15			−0.154757
$154$	−1.81468e15	−	2.88680e15i	−0.0711859	−	0.113243i
$155$		−	3.01355e16i		−	1.12614i
$156$	−1.51486e14	+	3.14875e14i	−0.00539434	+	0.0112125i
$157$			1.71071e16i			0.580670i	0.956925	+	0.290335i	$0.0937667\pi$
$157$			1.71071e16i			0.580670i	−0.956925	+	0.290335i	$0.906233\pi$
$158$	−6.65330e15	+	4.18234e15i	−0.215332	+	0.135360i
$159$	2.85568e14			0.00881517
$160$	−1.35929e16	+	3.89668e16i	−0.400324	+	1.14761i
$161$	1.85349e16			0.520951
$162$	−3.15489e16	+	1.98320e16i	−0.846490	+	0.532113i
$163$			3.11034e16i			0.796895i	0.917191	+	0.398448i	$0.130451\pi$
$163$			3.11034e16i			0.796895i	−0.917191	+	0.398448i	$0.869549\pi$
$164$	1.31424e15	−	2.73174e15i	0.0321621	−	0.0668513i
$165$		−	2.90980e13i		−	0.000680351i
$166$	3.82985e16	+	6.09256e16i	0.855798	+	1.36141i
$167$	5.67939e15			0.121319			0.0606594	−	0.998159i	$-0.480680\pi$
$167$	5.67939e15			0.121319			0.0606594	+	0.998159i	$0.480680\pi$
$168$	−6.02758e14	+	6.82680e13i	−0.0123119	+	0.00139443i
$169$	−1.01643e17			−1.98575
$170$	5.35600e15	+	8.52037e15i	0.100109	+	0.159254i
$171$		−	6.47221e16i		−	1.15766i
$172$	4.70191e16	+	2.26209e16i	0.805028	+	0.387298i
$173$		−	5.52689e16i		−	0.906015i	−0.891507	−	0.453007i	$-0.850351\pi$
$173$		−	5.52689e16i		−	0.906015i	0.891507	−	0.453007i	$-0.149649\pi$
$174$	4.37943e14	−	2.75296e14i	0.00687540	−	0.00432195i
$175$	5.46076e16			0.821235
$176$	−4.21510e15	+	3.36676e15i	−0.0607384	+	0.0485140i
$177$	−5.40625e14			−0.00746615
$178$	2.60644e16	−	1.63844e16i	0.345063	−	0.216910i
$179$			1.06545e17i			1.35249i	0.736677	+	0.676245i	$0.236394\pi$
$179$			1.06545e17i			1.35249i	−0.736677	+	0.676245i	$0.763606\pi$
$180$	8.99583e16	+	4.32789e16i	1.09521	+	0.526905i
$181$		−	8.62843e16i		−	1.00773i	−0.863784	−	0.503863i	$-0.831912\pi$
$181$		−	8.62843e16i		−	1.00773i	0.863784	−	0.503863i	$-0.168088\pi$
$182$	−1.41201e17	−	2.24624e17i	−1.58235	−	2.51722i
$183$	1.40673e14			0.00151296
$184$	−3.30013e15	−	2.91378e16i	−0.0340720	−	0.300832i
$185$	5.44467e16			0.539739
$186$	−3.72963e14	−	5.93313e14i	−0.00355074	−	0.00564855i
$187$			1.31553e15i			0.0120307i
$188$	−5.60204e16	+	1.16442e17i	−0.492223	+	1.02312i
$189$			2.93477e15i			0.0247805i
$190$	−1.46783e17	+	9.22693e16i	−1.19131	+	0.748868i
$191$	4.78390e16			0.373277			0.186639	−	0.982429i	$-0.440241\pi$
$191$	4.78390e16			0.373277			0.186639	+	0.982429i	$0.440241\pi$
$192$	2.14642e14	+	9.35412e14i	0.00161048	+	0.00701849i
$193$	−1.61203e17			−1.16331			−0.581653	−	0.813437i	$-0.697594\pi$
$193$	−1.61203e17			−1.16331			−0.581653	+	0.813437i	$0.697594\pi$
$194$	1.14426e17	−	7.19291e16i	0.794346	−	0.499335i
$195$		−	2.26414e15i		−	0.0151232i
$196$	1.32246e17	−	2.74882e17i	0.850081	−	1.76696i
$197$			1.71471e17i			1.06095i	0.847700	+	0.530475i	$0.177987\pi$
$197$			1.71471e17i			1.06095i	−0.847700	+	0.530475i	$0.822013\pi$
$198$	6.94473e15	+	1.10477e16i	0.0413682	+	0.0658088i
$199$	2.69360e17			1.54502			0.772512	−	0.635000i	$-0.219000\pi$
$199$	2.69360e17			1.54502			0.772512	+	0.635000i	$0.219000\pi$
$200$	−9.72285e15	−	8.58459e16i	−0.0537117	−	0.474236i
$201$	−1.01980e15			−0.00542680
$202$	−4.35907e16	−	6.93445e16i	−0.223490	−	0.355531i
$203$			3.92779e17i			1.94056i
$204$	2.10900e14	+	1.01464e14i	0.00100427	+	0.000483152i
$205$			1.96428e16i			0.0901673i
$206$	−1.03870e17	+	6.52941e16i	−0.459714	+	0.288981i
$207$	−7.09327e16			−0.302739
$208$	−3.27980e17	+	2.61970e17i	−1.35012	+	1.07839i
$209$	−2.26631e16			−0.0899957
$210$	3.32778e15	−	2.09188e15i	0.0127500	−	0.00801479i
$211$		−	3.75710e17i		−	1.38910i	−0.719444	−	0.694550i	$-0.755603\pi$
$211$		−	3.75710e17i		−	1.38910i	0.719444	−	0.694550i	$-0.244397\pi$
$212$	3.09139e17	+	1.48727e17i	1.10315	+	0.530725i
$213$			1.85908e15i			0.00640398i
$214$	2.46400e16	+	3.91976e16i	0.0819480	+	0.130364i
$215$	−3.38095e17			−1.08580
$216$	4.61360e15	−	5.22534e14i	0.0143099	−	0.00162073i
$217$	5.32127e17			1.59429
$218$	1.61309e17	+	2.56612e17i	0.466912	+	0.742768i
$219$			3.02180e15i			0.00845153i
$220$	1.51545e16	−	3.14998e16i	0.0409612	−	0.0851408i
$221$			1.02363e17i			0.267424i
$222$	1.07195e15	−	6.73842e14i	0.00270726	−	0.00170181i
$223$	−4.95089e17			−1.20892			−0.604458	−	0.796637i	$-0.706610\pi$
$223$	−4.95089e17			−1.20892			−0.604458	+	0.796637i	$0.706610\pi$
$224$	−6.88066e17	−	2.40020e17i	−1.62469	−	0.566744i
$225$	−2.08982e17			−0.477243
$226$	6.26135e17	−	3.93595e17i	1.38310	−	0.869434i
$227$		−	4.36793e17i		−	0.933430i	−0.884408	−	0.466715i	$-0.845437\pi$
$227$		−	4.36793e17i		−	0.933430i	0.884408	−	0.466715i	$-0.154563\pi$
$228$	−1.74794e15	+	3.63322e15i	−0.00361423	+	0.00751244i
$229$		−	7.16308e17i		−	1.43329i	−0.697439	−	0.716644i	$-0.745677\pi$
$229$		−	7.16308e17i		−	1.43329i	0.697439	−	0.716644i	$-0.254323\pi$
$230$	1.01123e17	+	1.60868e17i	0.195836	+	0.311538i
$231$	5.13805e14			0.000963183
$232$	6.17468e17	−	6.99341e16i	1.12061	−	0.126920i
$233$	−2.39588e16			−0.0421013			−0.0210506	−	0.999778i	$-0.506701\pi$
$233$	−2.39588e16			−0.0421013			−0.0210506	+	0.999778i	$0.506701\pi$
$234$	5.40374e17	+	8.59632e17i	0.919551	+	1.46283i
$235$		−	8.37289e17i		−	1.37996i
$236$	−5.85250e17	−	2.81563e17i	−0.934332	−	0.449506i
$237$		−	1.18418e15i		−	0.00183150i
$238$	−1.50451e17	+	9.45750e16i	−0.225459	+	0.141726i
$239$	6.30961e17			0.916259			0.458130	−	0.888885i	$-0.348520\pi$
$239$	6.30961e17			0.916259			0.458130	+	0.888885i	$0.348520\pi$
$240$	−3.88105e15	−	4.85899e15i	−0.00546217	−	0.00683851i
$241$	5.36424e17			0.731779			0.365890	−	0.930658i	$-0.380765\pi$
$241$	5.36424e17			0.731779			0.365890	+	0.930658i	$0.380765\pi$
$242$	−6.36315e17	+	3.99995e17i	−0.841506	+	0.528980i
$243$		−	1.68471e16i		−	0.0216012i
$244$	1.52284e17	+	7.32637e16i	0.189335	+	0.0910888i
$245$			1.97656e18i			2.38322i
$246$	2.43103e14	+	3.86730e14i	0.000284300	+	0.000452267i
$247$	−1.76343e18			−2.00047
$248$	−9.47448e16	−	8.36530e17i	−0.104272	−	0.920649i
$249$	−1.08438e16			−0.0115794
$250$	−3.26310e17	−	5.19096e17i	−0.338127	−	0.537896i
$251$			1.36031e18i			1.36800i	0.729483	+	0.683999i	$0.239761\pi$
$251$			1.36031e18i			1.36800i	−0.729483	+	0.683999i	$0.760239\pi$
$252$	−7.64208e17	+	1.58846e18i	−0.745947	+	1.55051i
$253$			2.48378e16i			0.0235347i
$254$	9.02432e17	−	5.67279e17i	0.830160	−	0.521848i
$255$	−1.51649e15			−0.00135453
$256$	−2.54813e17	+	1.12441e18i	−0.221015	+	0.975270i
$257$	1.26472e18			1.06536			0.532678	−	0.846318i	$-0.321186\pi$
$257$	1.26472e18			1.06536			0.532678	+	0.846318i	$0.321186\pi$
$258$	−6.65647e15	+	4.18433e15i	−0.00544623	+	0.00342356i
$259$			9.61407e17i			0.764116i
$260$	1.17918e18	−	2.45102e18i	0.910504	−	1.89255i
$261$		−	1.50316e18i		−	1.12772i
$262$	2.33405e17	+	3.71303e17i	0.170158	+	0.270688i
$263$	2.46207e18			1.74434			0.872171	−	0.489202i	$-0.162712\pi$
$263$	2.46207e18			1.74434			0.872171	+	0.489202i	$0.162712\pi$
$264$	−9.14828e13	−	8.07728e14i	−6.29955e−5	−	0.000556206i
$265$	−2.22289e18			−1.48790
$266$	−1.62927e18	−	2.59186e18i	−1.06018	−	1.68655i
$267$			4.63905e15i			0.00293491i
$268$	−1.10398e18	−	5.31122e17i	−0.679123	−	0.326726i
$269$			2.40780e17i			0.144038i	0.997403	+	0.0720192i	$0.0229443\pi$
$269$			2.40780e17i			0.144038i	−0.997403	+	0.0720192i	$0.977056\pi$
$270$	−2.54714e16	+	1.60116e16i	−0.0148192	+	0.00931549i
$271$	2.14747e18			1.21523			0.607613	−	0.794233i	$-0.292127\pi$
$271$	2.14747e18			1.21523			0.607613	+	0.794233i	$0.292127\pi$
$272$	1.75464e17	+	2.19677e17i	0.0965878	+	0.120926i
$273$	3.99796e16			0.0214101
$274$	−9.94189e17	+	6.24958e17i	−0.518012	+	0.325628i
$275$			7.31771e16i			0.0371005i
$276$	3.98186e15	+	1.91567e15i	0.00196457	+	0.000945154i
$277$		−	6.79346e17i		−	0.326206i	−0.986609	−	0.163103i	$-0.947850\pi$
$277$		−	6.79346e17i		−	0.326206i	0.986609	−	0.163103i	$-0.0521504\pi$
$278$	−4.28327e17	−	6.81387e17i	−0.200189	−	0.318462i
$279$	−2.03644e18			−0.926487
$280$	4.69194e18	−	5.31406e17i	2.07810	−	0.235365i
$281$	−1.02323e18			−0.441242			−0.220621	−	0.975360i	$-0.570808\pi$
$281$	−1.02323e18			−0.441242			−0.220621	+	0.975360i	$0.570808\pi$
$282$	−1.03625e16	−	1.64847e16i	−0.00435105	−	0.00692169i
$283$		−	1.34711e18i		−	0.550814i	−0.961328	−	0.275407i	$-0.911187\pi$
$283$		−	1.34711e18i		−	0.550814i	0.961328	−	0.275407i	$-0.0888126\pi$
$284$	−9.68226e17	+	2.01253e18i	−0.385557	+	0.801410i
$285$		−	2.61250e16i		−	0.0101326i
$286$	3.01009e17	−	1.89217e17i	0.113719	−	0.0714851i
$287$	−3.46848e17			−0.127651
$288$	2.63321e18	+	9.18550e17i	0.944153	+	0.329351i
$289$	−2.79386e18			−0.976048
$290$	−3.40900e18	+	2.14293e18i	−1.16049	+	0.729497i
$291$			2.03659e16i			0.00675627i
$292$	−1.57379e18	+	3.27123e18i	−0.508832	+	1.05764i
$293$		−	8.75390e17i		−	0.275864i	−0.990442	−	0.137932i	$-0.955954\pi$
$293$		−	8.75390e17i		−	0.275864i	0.990442	−	0.137932i	$-0.0440455\pi$
$294$	2.44623e16	+	3.89149e16i	0.00751437	+	0.0119539i
$295$	4.20829e18			1.26020
$296$	1.51138e18	−	1.71178e17i	0.441251	−	0.0499758i
$297$	−3.93274e15			−0.00111950
$298$	8.61717e17	+	1.37083e18i	0.239190	+	0.380505i
$299$			1.93265e18i			0.523141i
$300$	1.17314e16	+	5.64395e15i	0.00309698	+	0.00148996i
$301$		−	5.97000e18i		−	1.53718i
$302$	3.33624e18	−	2.09719e18i	0.837924	−	0.526728i
$303$	1.23422e16			0.00302394
$304$	−3.78444e18	+	3.02277e18i	−0.904586	+	0.722526i
$305$	−1.09501e18			−0.255370
$306$	5.75772e17	−	3.61936e17i	0.131021	−	0.0823610i
$307$			4.98617e18i			1.10721i	0.832780	+	0.553604i	$0.186748\pi$
$307$			4.98617e18i			1.10721i	−0.832780	+	0.553604i	$0.813252\pi$
$308$	5.56216e17	+	2.67595e17i	0.120535	+	0.0579893i
$309$		−	1.84873e16i		−	0.00391007i
$310$	2.90319e18	+	4.61842e18i	0.599325	+	0.953412i
$311$	−6.66934e18			−1.34394			−0.671970	−	0.740578i	$-0.734552\pi$
$311$	−6.66934e18			−1.34394			−0.671970	+	0.740578i	$0.734552\pi$
$312$	−7.11834e15	−	6.28499e16i	−0.00140029	−	0.0123636i
$313$	2.62080e18			0.503328			0.251664	−	0.967815i	$-0.419022\pi$
$313$	2.62080e18			0.503328			0.251664	+	0.967815i	$0.419022\pi$
$314$	−1.64806e18	−	2.62175e18i	−0.309030	−	0.491608i
$315$		−	1.14220e19i		−	2.09128i
$316$	6.16734e17	−	1.28193e18i	0.110267	−	0.229198i
$317$			8.89255e18i			1.55268i	0.630314	+	0.776340i	$0.282926\pi$
$317$			8.89255e18i			1.55268i	−0.630314	+	0.776340i	$0.717074\pi$
$318$	−4.37646e16	+	2.75109e16i	−0.00746311	+	0.00469139i
$319$	−5.26345e17			−0.0876678
$320$	−1.67079e18	−	7.28135e18i	−0.271830	−	1.18464i
$321$	−6.97655e15			−0.00110880
$322$	−2.84057e18	+	1.78561e18i	−0.441048	+	0.277248i
$323$			1.18113e18i			0.179175i
$324$	2.92446e18	−	6.07870e18i	0.433468	−	0.900996i
$325$			5.69396e18i			0.824688i
$326$	−2.99643e18	−	4.76675e18i	−0.424104	−	0.674669i
$327$	−4.56729e16			−0.00631757
$328$	6.17561e16	+	5.45262e17i	0.00834883	+	0.0737143i
$329$	1.47847e19			1.95363
$330$	2.80323e15	+	4.45941e15i	0.000362080	+	0.000576000i
$331$		−	1.84641e18i		−	0.233141i	−0.993182	−	0.116570i	$-0.962810\pi$
$331$		−	1.84641e18i		−	0.233141i	0.993182	−	0.116570i	$-0.0371901\pi$
$332$	−1.17389e19	−	5.64756e18i	−1.44907	−	0.697148i
$333$		−	3.67928e18i		−	0.444049i
$334$	−8.70394e17	+	5.47139e17i	−0.102711	+	0.0645653i
$335$	7.93823e18			0.915983
$336$	8.57989e16	−	6.85307e16i	0.00968137	−	0.00773287i
$337$	−3.67858e18			−0.405934			−0.202967	−	0.979186i	$-0.565058\pi$
$337$	−3.67858e18			−0.405934			−0.202967	+	0.979186i	$0.565058\pi$
$338$	1.55772e19	−	9.79201e18i	1.68118	−	1.05681i
$339$			1.11442e17i			0.0117639i
$340$	−1.64167e18	−	7.89804e17i	−0.169509	−	0.0815507i
$341$			7.13078e17i			0.0720243i
$342$	6.23518e18	+	9.91898e18i	0.616102	+	0.980101i
$343$	−1.71021e19			−1.65326
$344$	−9.38515e18	+	1.06296e18i	−0.887673	+	0.100537i
$345$	−2.86319e16			−0.00264977
$346$	5.32448e18	+	8.47023e18i	0.482177	+	0.767052i
$347$			2.01918e19i			1.78938i	0.446686	+	0.894691i	$0.352604\pi$
$347$			2.01918e19i			1.78938i	−0.446686	+	0.894691i	$0.647396\pi$
$348$	−4.05955e16	+	8.43808e16i	−0.00352074	+	0.00731811i
$349$			1.75889e19i			1.49296i	0.665409	+	0.746479i	$0.268257\pi$
$349$			1.75889e19i			1.49296i	−0.665409	+	0.746479i	$0.731743\pi$
$350$	−8.36888e18	+	5.26077e18i	−0.695275	+	0.437058i
$351$	−3.06010e17			−0.0248847
$352$	3.21639e17	−	9.22045e17i	0.0256035	−	0.0733977i
$353$	1.19045e19			0.927687			0.463844	−	0.885917i	$-0.346470\pi$
$353$	1.19045e19			0.927687			0.463844	+	0.885917i	$0.346470\pi$
$354$	8.28535e16	−	5.20826e16i	0.00632101	−	0.00397345i
$355$		−	1.44713e19i		−	1.08092i
$356$	−2.41607e18	+	5.02197e18i	−0.176699	+	0.367282i
$357$		−	2.67778e16i		−	0.00191763i
$358$	−1.02643e19	−	1.63285e19i	−0.719789	−	1.14505i
$359$	−1.45405e19			−0.998549			−0.499275	−	0.866444i	$-0.666400\pi$
$359$	−1.45405e19			−0.998549			−0.499275	+	0.866444i	$0.666400\pi$
$360$	−1.79559e19	+	2.03368e18i	−1.20765	+	0.136777i
$361$	−5.16644e18			−0.340320
$362$	8.31243e18	+	1.32235e19i	0.536307	+	0.853162i
$363$		−	1.13254e17i		−	0.00715738i
$364$	4.32796e19	+	2.08218e19i	2.67931	+	1.28901i
$365$		−	2.35221e19i		−	1.42652i
$366$	−2.15587e16	+	1.35521e16i	−0.00128090	+	0.000805188i
$367$	2.06189e19			1.20024			0.600122	−	0.799909i	$-0.295119\pi$
$367$	2.06189e19			1.20024			0.600122	+	0.799909i	$0.295119\pi$
$368$	3.31283e18	+	4.14759e18i	0.188947	+	0.236558i
$369$	1.32738e18			0.0741817
$370$	−8.34422e18	+	5.24527e18i	−0.456954	+	0.287246i
$371$		−	3.92513e19i		−	2.10644i
$372$	1.14317e17	+	5.49977e16i	0.00601227	+	0.00289250i
$373$		−	1.38141e19i		−	0.712041i	−0.934478	−	0.356020i	$-0.884133\pi$
$373$		−	1.38141e19i		−	0.712041i	0.934478	−	0.356020i	$-0.115867\pi$
$374$	−1.26736e17	−	2.01612e17i	−0.00640267	−	0.0101854i
$375$	9.23909e16			0.00457504
$376$	−2.63240e18	−	2.32422e19i	−0.127774	−	1.12816i
$377$	−4.09553e19			−1.94872
$378$	−2.82729e17	−	4.49767e17i	−0.0131881	−	0.0209797i
$379$			1.23226e19i			0.563520i	0.959485	+	0.281760i	$0.0909182\pi$
$379$			1.23226e19i			0.563520i	−0.959485	+	0.281760i	$0.909082\pi$
$380$	1.36062e19	−	2.82814e19i	0.610041	−	1.26801i
$381$			1.60619e17i			0.00706088i
$382$	−7.33155e18	+	4.60869e18i	−0.316025	+	0.198656i
$383$	2.08014e19			0.879231			0.439615	−	0.898186i	$-0.355115\pi$
$383$	2.08014e19			0.879231			0.439615	+	0.898186i	$0.355115\pi$
$384$	−1.23010e17	−	1.22678e17i	−0.00509867	−	0.00508491i
$385$	−3.99952e18			−0.162574
$386$	2.47052e19	−	1.55300e19i	0.984881	−	0.619107i
$387$			2.28471e19i			0.893302i
$388$	−1.06068e19	+	2.20470e19i	−0.406767	+	0.845495i
$389$		−	6.39681e18i		−	0.240625i	−0.992736	−	0.120313i	$-0.961610\pi$
$389$		−	6.39681e18i		−	0.240625i	0.992736	−	0.120313i	$-0.0383897\pi$
$390$	2.18122e17	+	3.46990e17i	0.00804848	+	0.0128036i
$391$	1.29446e18			0.0468559
$392$	6.21423e18	+	5.48672e19i	0.220669	+	1.94835i
$393$	−6.60861e16			−0.00230232
$394$	−1.65192e19	−	2.62788e19i	−0.564633	−	0.898224i
$395$			9.21781e18i			0.309136i
$396$	−2.12863e18	−	1.02408e18i	−0.0700463	−	0.0336992i
$397$		−	3.74951e19i		−	1.21073i	−0.795950	−	0.605363i	$-0.793028\pi$
$397$		−	3.74951e19i		−	1.21073i	0.795950	−	0.605363i	$-0.206972\pi$
$398$	−4.12807e19	+	2.59495e19i	−1.30805	+	0.822255i
$399$	4.61309e17			0.0143448
$400$	9.76027e18	+	1.22196e19i	0.297860	+	0.372913i
$401$	1.38597e19			0.415118			0.207559	−	0.978222i	$-0.433448\pi$
$401$	1.38597e19			0.415118			0.207559	+	0.978222i	$0.433448\pi$
$402$	1.56289e17	−	9.82450e16i	0.00459445	−	0.00288812i
$403$			5.54851e19i			1.60099i
$404$	1.33610e19	+	6.42796e18i	0.378424	+	0.182059i
$405$			4.37094e19i			1.21524i
$406$	−3.78394e19	−	6.01953e19i	−1.03276	−	1.64292i
$407$	−1.28834e18			−0.0345200
$408$	−4.20961e16	+	4.76778e15i	−0.00110737	+	0.000125419i
$409$	−1.43770e19			−0.371316			−0.185658	−	0.982614i	$-0.559442\pi$
$409$	−1.43770e19			−0.371316			−0.185658	+	0.982614i	$0.559442\pi$
$410$	−1.89234e18	−	3.01035e18i	−0.0479866	−	0.0763376i
$411$		−	1.76950e17i		−	0.00440592i
$412$	9.62837e18	−	2.00133e19i	0.235409	−	0.489316i
$413$			7.43090e19i			1.78409i
$414$	1.08708e19	−	6.83349e18i	0.256306	−	0.161117i
$415$	8.44094e19			1.95447
$416$	2.50270e19	−	7.17450e19i	0.569126	−	1.63152i
$417$	1.21276e17			0.00270866
$418$	3.47323e18	−	2.18331e18i	0.0761923	−	0.0478953i
$419$		−	4.61890e18i		−	0.0995254i	−0.998761	−	0.0497627i	$-0.984154\pi$
$419$		−	4.61890e18i		−	0.0995254i	0.998761	−	0.0497627i	$-0.0158465\pi$
$420$	−3.08472e17	+	6.41182e17i	−0.00652899	+	0.0135710i
$421$		−	6.03532e19i		−	1.25483i	−0.778685	−	0.627415i	$-0.784113\pi$
$421$		−	6.03532e19i		−	1.25483i	0.778685	−	0.627415i	$-0.215887\pi$
$422$	3.61950e19	+	5.75793e19i	0.739273	+	1.17604i
$423$	−5.65805e19			−1.13531
$424$	−6.17050e19	+	6.98867e18i	−1.21640	+	0.137769i
$425$	3.81375e18			0.0738644
$426$	−1.79099e17	−	2.84912e17i	−0.00340817	−	0.00542175i
$427$		−	1.93354e19i		−	0.361531i
$428$	−7.55241e18	−	3.63346e18i	−0.138758	−	0.0667563i
$429$			5.35748e16i			0.000967232i
$430$	5.18147e19	−	3.25713e19i	0.919263	−	0.577858i
$431$	−1.77001e18			−0.0308601			−0.0154300	−	0.999881i	$-0.504912\pi$
$431$	−1.77001e18			−0.0308601			−0.0154300	+	0.999881i	$0.504912\pi$
$432$	−6.56717e17	+	5.24545e17i	−0.0112525	+	0.00898782i
$433$	−5.45138e19			−0.918009			−0.459005	−	0.888434i	$-0.651794\pi$
$433$	−5.45138e19			−0.918009			−0.459005	+	0.888434i	$0.651794\pi$
$434$	−8.15510e19	+	5.12638e19i	−1.34976	+	0.848473i
$435$		−	6.06747e17i		−	0.00987048i
$436$	−4.94428e19	−	2.37869e19i	−0.790596	−	0.380355i
$437$			2.23001e19i			0.350506i
$438$	−2.91114e17	−	4.63106e17i	−0.00449787	−	0.00715525i
$439$	−9.48687e18			−0.144092			−0.0720459	−	0.997401i	$-0.522953\pi$
$439$	−9.48687e18			−0.144092			−0.0720459	+	0.997401i	$0.522953\pi$
$440$	7.12112e17	+	6.28745e18i	0.0106329	+	0.0938814i
$441$	1.33568e20			1.96071
$442$	−9.86139e18	−	1.56876e19i	−0.142322	−	0.226407i
$443$		−	1.06809e20i		−	1.51559i	−0.652495	−	0.757793i	$-0.726278\pi$
$443$		−	1.06809e20i		−	1.51559i	0.652495	−	0.757793i	$-0.273722\pi$
$444$	−9.93659e16	+	2.06539e17i	−0.00138632	+	0.00288158i
$445$		−	3.61109e19i		−	0.495380i
$446$	7.58747e19	−	4.76957e19i	1.02349	−	0.643380i
$447$	−2.43986e17			−0.00323637
$448$	1.28572e20	−	2.95025e19i	1.67711	−	0.384834i
$449$	1.33518e19			0.171274			0.0856370	−	0.996326i	$-0.472707\pi$
$449$	1.33518e19			0.171274			0.0856370	+	0.996326i	$0.472707\pi$
$450$	3.20275e19	−	2.01328e19i	0.404044	−	0.253987i
$451$		−	4.64795e17i		−	0.00576683i
$452$	−5.80402e19	+	1.20641e20i	−0.708256	+	1.47216i
$453$			5.93797e17i			0.00712691i
$454$	4.20796e19	+	6.69406e19i	0.496767	+	0.790262i
$455$	−3.11206e20			−3.61378
$456$	−8.21359e16	−	7.25202e17i	−0.000938203	−	0.00828367i
$457$	2.16636e19			0.243422			0.121711	−	0.992566i	$-0.461162\pi$
$457$	2.16636e19			0.243422			0.121711	+	0.992566i	$0.461162\pi$
$458$	6.90074e19	+	1.09778e20i	0.762790	+	1.21345i
$459$			2.04962e17i			0.00222883i
$460$	−3.09953e19	−	1.49118e19i	−0.331598	−	0.159531i
$461$		−	6.99387e19i		−	0.736141i	−0.929798	−	0.368070i	$-0.880019\pi$
$461$		−	6.99387e19i		−	0.736141i	0.929798	−	0.368070i	$-0.119981\pi$
$462$	−7.87432e16	+	4.94988e16i	−0.000815451	+	0.000512602i
$463$	1.36023e20			1.38597			0.692987	−	0.720950i	$-0.256294\pi$
$463$	1.36023e20			1.38597			0.692987	+	0.720950i	$0.256294\pi$
$464$	−8.78927e19	+	7.02032e19i	−0.881187	+	0.703837i
$465$	−8.22005e17			−0.00810919
$466$	3.67180e18	−	2.30813e18i	0.0356438	−	0.0224061i
$467$		−	6.61666e19i		−	0.632066i	−0.948748	−	0.316033i	$-0.897649\pi$
$467$		−	6.61666e19i		−	0.632066i	0.948748	−	0.316033i	$-0.102351\pi$
$468$	−1.65630e20	−	7.96844e19i	−1.55702	−	0.749082i
$469$			1.40171e20i			1.29677i
$470$	8.06625e19	+	1.28319e20i	0.734409	+	1.16830i
$471$	4.66630e17			0.00418134
$472$	1.16818e20	−	1.32307e19i	1.03025	−	0.116686i
$473$	8.00012e18			0.0694445
$474$	1.14081e17	+	1.81482e17i	0.000974714	+	0.00155058i
$475$			6.57005e19i			0.552544i
$476$	1.39462e19	−	2.89882e19i	0.115452	−	0.239976i
$477$			1.50214e20i			1.22411i
$478$	−9.66978e19	+	6.07853e19i	−0.775725	+	0.487629i
$479$	1.64521e20			1.29929			0.649645	−	0.760238i	$-0.274918\pi$
$479$	1.64521e20			1.29929			0.649645	+	0.760238i	$0.274918\pi$
$480$	1.06289e18	+	3.70772e17i	0.00826381	+	0.00288269i
$481$	−1.00246e20			−0.767328
$482$	−8.22095e19	+	5.16778e19i	−0.619540	+	0.389450i
$483$		−	5.05576e17i		−	0.00375131i
$484$	5.89838e19	−	1.22602e20i	0.430916	−	0.895691i
$485$		−	1.58531e20i		−	1.14038i
$486$	1.62301e18	+	2.58190e18i	0.0114960	+	0.0182880i
$487$	−1.58744e20			−1.10721			−0.553606	−	0.832779i	$-0.686749\pi$
$487$	−1.58744e20			−1.10721			−0.553606	+	0.832779i	$0.686749\pi$
$488$	−3.03963e19	+	3.44267e18i	−0.208772	+	0.0236454i
$489$	8.48406e17			0.00573835
$490$	−1.90417e20	−	3.02918e20i	−1.26834	−	2.01769i
$491$		−	1.10313e20i		−	0.723627i	−0.932251	−	0.361813i	$-0.882158\pi$
$491$		−	1.10313e20i		−	0.723627i	0.932251	−	0.361813i	$-0.117842\pi$
$492$	−7.45134e16	−	3.58483e16i	−0.000481389	−	0.000231596i
$493$			2.74314e19i			0.174540i
$494$	2.70254e20	−	1.69885e20i	1.69364	−	1.06464i
$495$	1.53061e19			0.0944767
$496$	9.51095e19	+	1.19075e20i	0.578244	+	0.723948i
$497$	2.55530e20			1.53027
$498$	1.66186e18	−	1.04467e18i	0.00980337	−	0.00616251i
$499$			2.19619e20i			1.27619i	0.769957	+	0.638096i	$0.220278\pi$
$499$			2.19619e20i			1.27619i	−0.769957	+	0.638096i	$0.779722\pi$
$500$	1.00017e20	+	4.81181e19i	0.572531	+	0.275444i
$501$		−	1.54916e17i		−	0.000873603i
$502$	−1.31049e20	−	2.08474e20i	−0.728042	−	1.15818i
$503$	−8.93960e18			−0.0489281			−0.0244641	−	0.999701i	$-0.507788\pi$
$503$	−8.93960e18			−0.0489281			−0.0244641	+	0.999701i	$0.507788\pi$
$504$	−3.59102e19	−	3.17062e20i	−0.193637	−	1.70968i
$505$	−9.60733e19			−0.510408
$506$	−2.39282e18	−	3.80651e18i	−0.0125251	−	0.0199250i
$507$			2.77250e18i			0.0142992i
$508$	−8.36518e19	+	1.73876e20i	−0.425106	+	0.883615i
$509$		−	1.30775e20i		−	0.654849i	−0.944877	−	0.327425i	$-0.893819\pi$
$509$		−	1.30775e20i		−	0.654849i	0.944877	−	0.327425i	$-0.106181\pi$
$510$	2.32410e17	−	1.46095e17i	0.00114677	−	0.000720875i
$511$	4.15347e20			2.01955
$512$	−6.92717e19	−	1.96869e20i	−0.331918	−	0.943308i
$513$	−3.53093e18			−0.0166728
$514$	−1.93824e20	+	1.21840e20i	−0.901953	+	0.566977i
$515$			1.43907e20i			0.659976i
$516$	6.17028e17	−	1.28254e18i	0.00278889	−	0.00579692i
$517$			1.98122e19i			0.0882581i
$518$	−9.26197e19	−	1.47340e20i	−0.406659	−	0.646917i
$519$	−1.50757e18			−0.00652411
$520$	5.54100e19	+	4.89231e20i	0.236354	+	2.08684i
$521$	−4.43914e20			−1.86645			−0.933225	−	0.359292i	$-0.883018\pi$
$521$	−4.43914e20			−1.86645			−0.933225	+	0.359292i	$0.883018\pi$
$522$	1.44810e20	+	2.30366e20i	0.600166	+	0.954749i
$523$			4.16672e20i			1.70228i	0.524936	+	0.851142i	$0.324089\pi$
$523$			4.16672e20i			1.70228i	−0.524936	+	0.851142i	$0.675911\pi$
$524$	−7.15410e19	−	3.44183e19i	−0.288118	−	0.138613i
$525$		−	1.48953e18i		−	0.00591362i
$526$	−3.77324e20	+	2.37190e20i	−1.47680	+	0.928331i
$527$	3.71633e19			0.143395
$528$	9.18348e16	+	1.14975e17i	0.000349344	+	0.000437370i
$529$	−2.42195e20			−0.908339
$530$	3.40669e20	−	2.14148e20i	1.25969	−	0.791854i
$531$		−	2.84379e20i		−	1.03678i
$532$	4.99387e20	+	2.40255e20i	1.79515	+	0.863644i
$533$		−	3.61660e19i		−	0.128188i
$534$	−4.46916e17	−	7.10958e17i	−0.00156195	−	0.00248476i
$535$	5.43063e19			0.187153
$536$	2.20357e20	−	2.49574e19i	0.748842	−	0.0848133i
$537$	2.90621e18			0.00973913
$538$	−2.31962e19	−	3.69007e19i	−0.0766566	−	0.121946i
$539$		−	4.67701e19i		−	0.152424i
$540$	2.36109e18	−	4.90770e18i	0.00758856	−	0.0157734i
$541$		−	5.91314e19i		−	0.187430i	−0.995599	−	0.0937149i	$-0.970126\pi$
$541$		−	5.91314e19i		−	0.187430i	0.995599	−	0.0937149i	$-0.0298742\pi$
$542$	−3.29110e20	+	2.06882e20i	−1.02884	+	0.646738i
$543$	−2.35357e18			−0.00725652
$544$	−4.80540e19	−	1.67628e19i	−0.146129	−	0.0509746i
$545$	3.55523e20			1.06633
$546$	−6.12707e18	+	3.85154e18i	−0.0181262	+	0.0113944i
$547$		−	5.51855e20i		−	1.61035i	−0.593038	−	0.805174i	$-0.702072\pi$
$547$		−	5.51855e20i		−	1.61035i	0.593038	−	0.805174i	$-0.297928\pi$
$548$	9.21573e19	−	1.91556e20i	0.265262	−	0.551367i
$549$			7.39963e19i			0.210096i
$550$	−7.04971e18	−	1.12147e19i	−0.0197447	−	0.0314101i
$551$	−4.72567e20			−1.30565
$552$	−7.94791e17	+	9.00175e16i	−0.00216626	+	0.000245349i
$553$	−1.62766e20			−0.437648
$554$	6.54466e19	+	1.04113e20i	0.173606	+	0.276173i
$555$		−	1.48514e18i		−	0.00388660i
$556$	1.31287e20	+	6.31618e19i	0.338968	+	0.163077i
$557$		−	2.20142e20i		−	0.560776i	−0.959887	−	0.280388i	$-0.909537\pi$
$557$		−	2.20142e20i		−	0.560776i	0.959887	−	0.280388i	$-0.0904631\pi$
$558$	3.12094e20	−	1.96185e20i	0.784383	−	0.493072i
$559$	6.22496e20			1.54365
$560$	−6.67868e20	+	5.33451e20i	−1.63411	+	1.30522i
$561$	3.58837e16			8.66316e−5
$562$	1.56815e20	−	9.85758e19i	0.373565	−	0.234827i
$563$		−	1.49041e20i		−	0.350343i	−0.984538	−	0.175171i	$-0.943952\pi$
$563$		−	1.49041e20i		−	0.350343i	0.984538	−	0.175171i	$-0.0560479\pi$
$564$	3.17619e18	+	1.52806e18i	0.00736739	+	0.00354444i
$565$		−	8.67478e20i		−	1.98561i
$566$	1.29778e20	+	2.06451e20i	0.293141	+	0.466331i
$567$	−7.71810e20			−1.72043
$568$	−4.54970e19	−	4.01706e20i	−0.100085	−	0.883682i
$569$	3.42545e20			0.743662			0.371831	−	0.928301i	$-0.378730\pi$
$569$	3.42545e20			0.743662			0.371831	+	0.928301i	$0.378730\pi$
$570$	2.51682e18	+	4.00378e18i	0.00539251	+	0.00857846i
$571$			7.46234e20i			1.57799i	0.614400	+	0.788995i	$0.289398\pi$
$571$			7.46234e20i			1.57799i	−0.614400	+	0.788995i	$0.710602\pi$
$572$	−2.79023e19	+	5.79970e19i	−0.0582331	+	0.121042i
$573$		−	1.30490e18i		−	0.00268793i
$574$	5.31561e19	−	3.34145e19i	0.108072	−	0.0679354i
$575$	7.20050e19			0.144495
$576$	−4.92044e20	+	1.12905e20i	−0.974619	+	0.223638i
$577$	−7.38201e20			−1.44330			−0.721649	−	0.692259i	$-0.756616\pi$
$577$	−7.38201e20			−1.44330			−0.721649	+	0.692259i	$0.756616\pi$
$578$	4.28173e20	−	2.69154e20i	0.826343	−	0.519448i
$579$			4.39713e18i			0.00837684i
$580$	3.16000e20	−	6.56830e20i	0.594261	−	1.23522i
$581$			1.49048e21i			2.76698i
$582$	−1.96201e18	−	3.12118e18i	−0.00359565	−	0.00572000i
$583$	5.25988e19			0.0951617
$584$	−7.39523e19	−	6.52947e20i	−0.132086	−	1.16622i
$585$	1.19098e21			2.10007
$586$	8.43331e19	+	1.34158e20i	0.146813	+	0.233552i
$587$		−	8.44752e20i		−	1.45192i	−0.687736	−	0.725961i	$-0.741395\pi$
$587$		−	8.44752e20i		−	1.45192i	0.687736	−	0.725961i	$-0.258605\pi$
$588$	−7.49794e18	−	3.60725e18i	−0.0127237	−	0.00612134i
$589$			6.40222e20i			1.07267i
$590$	−6.44941e20	+	4.05417e20i	−1.06691	+	0.670674i
$591$	4.67722e18			0.00763979
$592$	−2.15136e20	+	1.71837e20i	−0.346976	+	0.277143i
$593$	6.54220e20			1.04187			0.520935	−	0.853597i	$-0.325583\pi$
$593$	6.54220e20			1.04187			0.520935	+	0.853597i	$0.325583\pi$
$594$	6.02712e17	−	3.78871e17i	0.000947789	−	0.000595790i
$595$			2.08442e20i			0.323674i
$596$	−2.64125e20	−	1.27070e20i	−0.405007	−	0.194848i
$597$		−	7.34732e18i		−	0.0111255i
$598$	−1.86187e20	−	2.96188e20i	−0.278413	−	0.442902i
$599$	−9.15786e20			−1.35236			−0.676181	−	0.736736i	$-0.736366\pi$
$599$	−9.15786e20			−1.35236			−0.676181	+	0.736736i	$0.736366\pi$
$600$	−2.34161e18	+	2.65210e17i	−0.00341492	+	0.000386772i
$601$	2.04972e20			0.295213			0.147607	−	0.989046i	$-0.452843\pi$
$601$	2.04972e20			0.295213			0.147607	+	0.989046i	$0.452843\pi$
$602$	5.75136e20	+	9.14932e20i	0.818082	+	1.30141i
$603$		−	5.36433e20i		−	0.753591i
$604$	−3.09256e20	+	6.42810e20i	−0.429082	+	0.891879i
$605$			8.81582e20i			1.20808i
$606$	−1.89151e18	+	1.18902e18i	−0.00256014	+	0.00160933i
$607$	3.47857e20			0.465035			0.232517	−	0.972592i	$-0.425304\pi$
$607$	3.47857e20			0.465035			0.232517	+	0.972592i	$0.425304\pi$
$608$	2.88777e20	−	8.27839e20i	0.381317	−	1.09312i
$609$	1.07138e19			0.0139738
$610$	1.67816e20	−	1.05491e20i	0.216202	−	0.135907i
$611$			1.54160e21i			1.96184i
$612$	−5.33717e19	+	1.10937e20i	−0.0670927	+	0.139457i
$613$		−	6.41448e20i		−	0.796540i	−0.917268	−	0.398270i	$-0.869611\pi$
$613$		−	6.41448e20i		−	0.796540i	0.917268	−	0.398270i	$-0.130389\pi$
$614$	−4.80356e20	−	7.64155e20i	−0.589251	−	0.937387i
$615$	5.35795e17			0.000649285
$616$	−1.11022e20	+	1.25743e19i	−0.132909	+	0.0150532i
$617$	−2.44187e20			−0.288791			−0.144396	−	0.989520i	$-0.546124\pi$
$617$	−2.44187e20			−0.288791			−0.144396	+	0.989520i	$0.546124\pi$
$618$	1.78102e18	+	2.83327e18i	0.00208092	+	0.00331035i
$619$		−	1.43486e20i		−	0.165626i	−0.996565	−	0.0828132i	$-0.973610\pi$
$619$		−	1.43486e20i		−	0.165626i	0.996565	−	0.0828132i	$-0.0263905\pi$
$620$	−8.89855e20	−	4.28109e20i	−1.01480	−	0.488221i
$621$			3.86975e18i			0.00436010i
$622$	1.02211e21	−	6.42509e20i	1.13781	−	0.715239i
$623$	6.37638e20			0.701317
$624$	7.14574e18	+	8.94629e18i	0.00776538	+	0.00972207i
$625$	−1.16367e21			−1.24948
$626$	−4.01650e20	+	2.52482e20i	−0.426128	+	0.267869i
$627$			6.18179e17i			0.000648049i
$628$	5.05146e20	+	2.43025e20i	0.523263	+	0.251741i
$629$			6.71439e19i			0.0687269i
$630$	1.10037e21	+	1.75047e21i	1.11297	+	1.77052i
$631$	−5.40726e20			−0.540452			−0.270226	−	0.962797i	$-0.587098\pi$
$631$	−5.40726e20			−0.540452			−0.270226	+	0.962797i	$0.587098\pi$
$632$	2.89804e19	+	2.55876e20i	0.0286237	+	0.252727i
$633$	−1.02482e19			−0.0100028
$634$	−8.56688e20	−	1.36283e21i	−0.826329	−	1.31453i
$635$		−	1.25027e21i		−	1.19180i
$636$	4.05680e18	−	8.43237e18i	0.00382169	−	0.00794367i
$637$		−	3.63922e21i		−	3.38815i
$638$	8.06649e19	−	5.07068e19i	0.0742214	−	0.0466564i
$639$	−9.77908e20			−0.889286
$640$	9.57526e20	+	9.54942e20i	0.860599	+	0.858276i
$641$	1.45635e21			1.29369			0.646847	−	0.762619i	$-0.276087\pi$
$641$	1.45635e21			1.29369			0.646847	+	0.762619i	$0.276087\pi$
$642$	1.06919e18	−	6.72105e17i	0.000938734	−	0.000590098i
$643$		−	1.03136e21i		−	0.895009i	−0.894282	−	0.447505i	$-0.852313\pi$
$643$		−	1.03136e21i		−	0.895009i	0.894282	−	0.447505i	$-0.147687\pi$
$644$	2.63309e20	−	5.47307e20i	0.225851	−	0.469448i
$645$			9.22219e18i			0.00781873i
$646$	−1.13787e20	−	1.81013e20i	−0.0953560	−	0.151693i
$647$	1.51175e21			1.25227			0.626133	−	0.779716i	$-0.284637\pi$
$647$	1.51175e21			1.25227			0.626133	+	0.779716i	$0.284637\pi$
$648$	1.37420e20	+	1.21333e21i	0.112522	+	0.993493i
$649$	−9.95780e19			−0.0805987
$650$	−5.48543e20	−	8.72628e20i	−0.438895	−	0.698198i
$651$		−	1.45148e19i		−	0.0114803i
$652$	9.18436e20	+	4.41859e20i	0.718111	+	0.345483i
$653$			2.00833e21i			1.55233i	0.630527	+	0.776167i	$0.282839\pi$
$653$			2.00833e21i			1.55233i	−0.630527	+	0.776167i	$0.717161\pi$
$654$	6.99959e18	−	4.40002e18i	0.00534859	−	0.00336218i
$655$	5.14422e20			0.388606
$656$	−6.19937e19	−	7.76147e19i	−0.0462987	−	0.0579649i
$657$	−1.58952e21			−1.17362
$658$	−2.26582e21	+	1.42432e21i	−1.65398	+	1.03971i
$659$			1.37233e21i			0.990414i	0.868775	+	0.495207i	$0.164908\pi$
$659$			1.37233e21i			0.990414i	−0.868775	+	0.495207i	$0.835092\pi$
$660$	−8.59218e17	−	4.13369e17i	−0.000613089	−	0.000294957i
$661$			3.50454e20i			0.247241i	0.992330	+	0.123620i	$0.0394505\pi$
$661$			3.50454e20i			0.247241i	−0.992330	+	0.123620i	$0.960550\pi$
$662$	1.77879e20	+	2.82971e20i	0.124077	+	0.197382i
$663$	2.79214e18			0.00192569
$664$	2.34311e21	−	2.65379e20i	1.59784	−	0.180970i
$665$	−3.59088e21			−2.42125
$666$	3.54453e20	+	5.63868e20i	0.236321	+	0.375942i
$667$			5.17914e20i			0.341440i
$668$	8.06820e19	−	1.67703e20i	0.0525960	−	0.109325i
$669$			1.35045e19i			0.00870528i
$670$	−1.21657e21	+	7.64751e20i	−0.775491	+	0.487482i
$671$	2.59105e19			0.0163327
$672$	−6.54700e18	+	1.87683e19i	−0.00408106	+	0.0116992i
$673$	−1.62140e20			−0.0999489			−0.0499745	−	0.998750i	$-0.515914\pi$
$673$	−1.62140e20			−0.0999489			−0.0499745	+	0.998750i	$0.515914\pi$
$674$	5.63760e20	−	3.54385e20i	0.343672	−	0.216036i
$675$			1.14011e19i			0.00687333i
$676$	−1.44395e21	+	3.00135e21i	−0.860896	+	1.78944i
$677$		−	2.57858e21i		−	1.52043i	−0.649672	−	0.760215i	$-0.725094\pi$
$677$		−	2.57858e21i		−	1.52043i	0.649672	−	0.760215i	$-0.274906\pi$
$678$	−1.07361e19	−	1.70790e19i	−0.00626070	−	0.00995957i
$679$	2.79930e21			1.61445
$680$	3.27681e20	−	3.71129e19i	0.186911	−	0.0211694i
$681$	−1.19144e19			−0.00672152
$682$	−6.86963e19	−	1.09283e20i	−0.0383310	−	0.0609773i
$683$			3.54971e21i			1.95902i	0.201405	+	0.979508i	$0.435449\pi$
$683$			3.54971e21i			1.95902i	−0.201405	+	0.979508i	$0.564551\pi$
$684$	−1.91114e21	−	9.19449e20i	−1.04321	−	0.501888i
$685$			1.37740e21i			0.743670i
$686$	2.62097e21	−	1.64757e21i	1.39969	−	0.879860i
$687$	−1.95387e19			−0.0103210
$688$	1.33592e21	−	1.06705e21i	0.698017	−	0.557532i
$689$	4.09275e21			2.11530
$690$	4.38798e18	−	2.75833e18i	0.00224335	−	0.00141019i
$691$		−	8.86712e20i		−	0.448433i	−0.974539	−	0.224216i	$-0.928018\pi$
$691$		−	8.86712e20i		−	0.448433i	0.974539	−	0.224216i	$-0.0719822\pi$
$692$	−1.63201e21	−	7.85156e20i	−0.816443	−	0.392790i
$693$			2.70271e20i			0.133752i
$694$	−1.94523e21	−	3.09448e21i	−0.952301	−	1.51493i
$695$	−9.44027e20			−0.457192
$696$	−1.90759e18	−	1.68426e19i	−0.000913934	−	0.00806939i
$697$	−2.42236e19			−0.0114813
$698$	−1.69447e21	−	2.69558e21i	−0.794545	−	1.26397i
$699$			6.53522e17i			0.000303167i
$700$	7.75761e20	−	1.61248e21i	0.356035	−	0.740045i
$701$		−	1.28250e21i		−	0.582332i	−0.956673	−	0.291166i	$-0.905957\pi$
$701$		−	1.28250e21i		−	0.582332i	0.956673	−	0.291166i	$-0.0940432\pi$
$702$	4.68975e19	−	2.94803e19i	0.0210679	−	0.0132435i
$703$	−1.15671e21			−0.514112
$704$	3.95349e19	+	1.72294e20i	0.0173855	+	0.0757661i
$705$	−2.28387e19			−0.00993694
$706$	−1.82443e21	+	1.14685e21i	−0.785400	+	0.493711i
$707$		−	1.69644e21i		−	0.722592i
$708$	−7.68018e18	+	1.59638e19i	−0.00323685	+	0.00672802i
$709$			2.70973e21i			1.13000i	0.825090	+	0.565001i	$0.191124\pi$
$709$			2.70973e21i			1.13000i	−0.825090	+	0.565001i	$0.808876\pi$
$710$	1.39413e21	+	2.21779e21i	0.575261	+	0.915130i
$711$	6.22901e20			0.254330
$712$	−1.13531e20	−	1.00240e21i	−0.0458686	−	0.404987i
$713$	7.01657e20			0.280513
$714$	2.57972e18	+	4.10384e18i	0.00102055	+	0.00162350i
$715$		−	4.17032e20i		−	0.163258i
$716$	3.14610e21	+	1.51359e21i	1.21878	+	0.586353i
$717$		−	1.72107e19i		−	0.00659788i
$718$	2.22840e21	−	1.40079e21i	0.845393	−	0.531423i
$719$	−1.12808e21			−0.423520			−0.211760	−	0.977322i	$-0.567919\pi$
$719$	−1.12808e21			−0.423520			−0.211760	+	0.977322i	$0.567919\pi$
$720$	2.55592e21	−	2.04150e21i	0.949626	−	0.758502i
$721$	−2.54108e21			−0.934338
$722$	7.91782e20	−	4.97723e20i	0.288122	−	0.181117i
$723$		−	1.46320e19i		−	0.00526946i
$724$	−2.54784e21	−	1.22576e21i	−0.908098	−	0.436885i
$725$			1.52588e21i			0.538251i
$726$	1.09106e19	+	1.73567e19i	0.00380912	+	0.00605959i
$727$	−1.31253e20			−0.0453524			−0.0226762	−	0.999743i	$-0.507219\pi$
$727$	−1.31253e20			−0.0453524			−0.0226762	+	0.999743i	$0.507219\pi$
$728$	−8.63873e21	+	9.78417e20i	−2.95437	+	0.334610i
$729$	2.95339e21			0.999689
$730$	2.26606e21	+	3.60487e21i	0.759190	+	1.20773i
$731$		−	4.16940e20i		−	0.138259i
$732$	1.99841e18	−	4.15384e18i	0.000655920	−	0.00136338i
$733$			4.64602e20i			0.150939i	0.997148	+	0.0754695i	$0.0240455\pi$
$733$			4.64602e20i			0.150939i	−0.997148	+	0.0754695i	$0.975954\pi$
$734$	−3.15994e21	+	1.98637e21i	−1.01615	+	0.638764i
$735$	5.39146e19			0.0171613
$736$	−9.07277e20	−	3.16488e20i	−0.285862	−	0.0997179i
$737$	−1.87837e20			−0.0585835
$738$	−2.03427e20	+	1.27877e20i	−0.0628038	+	0.0394792i
$739$			1.37763e21i			0.421016i	0.977592	+	0.210508i	$0.0675118\pi$
$739$			1.37763e21i			0.421016i	−0.977592	+	0.210508i	$0.932488\pi$
$740$	7.73475e20	−	1.60773e21i	0.233996	−	0.486378i
$741$			4.81010e19i			0.0144051i
$742$	3.78138e21	+	6.01545e21i	1.12104	+	1.78336i
$743$	−1.35074e21			−0.396420			−0.198210	−	0.980160i	$-0.563513\pi$
$743$	−1.35074e21			−0.396420			−0.198210	+	0.980160i	$0.563513\pi$
$744$	−2.28180e19	+	2.58435e18i	−0.00662949	+	0.000750851i
$745$	1.89921e21			0.546262
$746$	1.33081e21	+	2.11707e21i	0.378945	+	0.602829i
$747$		−	5.70404e21i		−	1.60797i
$748$	3.88457e19	+	1.86886e19i	0.0108413	+	0.00521573i
$749$			9.58927e20i			0.264955i
$750$	−1.41594e19	+	8.90073e18i	−0.00387333	+	0.00243481i
$751$	−4.22334e21			−1.14382			−0.571908	−	0.820318i	$-0.693797\pi$
$751$	−4.22334e21			−1.14382			−0.571908	+	0.820318i	$0.693797\pi$
$752$	2.64253e21	+	3.30839e21i	0.708576	+	0.887120i
$753$	3.71051e19			0.00985080
$754$	6.27659e21	−	3.94554e21i	1.64983	−	1.03710i
$755$		−	4.62218e21i		−	1.20294i
$756$	8.66591e19	+	4.16916e19i	0.0223306	+	0.0107432i
$757$		−	2.74463e21i		−	0.700268i	−0.936700	−	0.350134i	$-0.886136\pi$
$757$		−	2.74463e21i		−	0.700268i	0.936700	−	0.350134i	$-0.113864\pi$
$758$	−1.18713e21	−	1.88850e21i	−0.299903	−	0.477088i
$759$	6.77499e17			0.000169471
$760$	6.39355e20	+	5.64505e21i	0.158358	+	1.39819i
$761$	3.12861e21			0.767303			0.383651	−	0.923478i	$-0.374666\pi$
$761$	3.12861e21			0.767303			0.383651	+	0.923478i	$0.374666\pi$
$762$	−1.54736e19	−	2.46156e19i	−0.00375777	−	0.00597789i
$763$			6.27774e21i			1.50963i
$764$	6.79605e20	−	1.41261e21i	0.161829	−	0.336374i
$765$		−	7.97702e20i		−	0.188096i
$766$	−3.18792e21	+	2.00396e21i	−0.744375	+	0.467923i
$767$	−7.74824e21			−1.79159
$768$	3.06705e19	+	6.95053e18i	0.00702281	+	0.00159151i
$769$	−7.41182e20			−0.168065			−0.0840325	−	0.996463i	$-0.526780\pi$
$769$	−7.41182e20			−0.168065			−0.0840325	+	0.996463i	$0.526780\pi$
$770$	6.12946e20	−	3.85304e20i	0.137639	−	0.0865214i
$771$		−	3.44976e19i		−	0.00767151i
$772$	−2.29007e21	+	4.76008e21i	−0.504335	+	1.04830i
$773$		−	1.10113e21i		−	0.240156i	−0.992764	−	0.120078i	$-0.961686\pi$
$773$		−	1.10113e21i		−	0.240156i	0.992764	−	0.120078i	$-0.0383145\pi$
$774$	−2.20103e21	−	3.50142e21i	−0.475411	−	0.756288i
$775$	2.06722e21			0.442205
$776$	−4.98414e20	−	4.40064e21i	−0.105591	−	0.932294i
$777$	2.62242e19			0.00550231
$778$	6.16254e20	+	9.80342e20i	0.128060	+	0.203719i
$779$		−	4.17306e20i		−	0.0858863i
$780$	−6.68564e19	−	3.21645e19i	−0.0136280	−	0.00655644i
$781$			3.42424e20i			0.0691324i
$782$	−1.98383e20	+	1.24706e20i	−0.0396692	+	0.0249365i
$783$	−8.20051e19			−0.0162415
$784$	−6.23814e21	−	7.81001e21i	−1.22373	−	1.53208i
$785$	−3.63230e21			−0.705763
$786$	1.01280e19	−	6.36658e18i	0.00194920	−	0.00122529i
$787$		−	4.86494e21i		−	0.927400i	−0.885992	−	0.463700i	$-0.846522\pi$
$787$		−	4.86494e21i		−	0.927400i	0.885992	−	0.463700i	$-0.153478\pi$
$788$	5.06328e21	+	2.43594e21i	0.956061	+	0.459960i
$789$		−	6.71576e19i		−	0.0125608i
$790$	−8.88022e20	−	1.41267e21i	−0.164521	−	0.261721i
$791$	1.53177e22			2.81106
$792$	4.24880e20	−	4.81216e19i	0.0772373	−	0.00874785i
$793$	2.01612e21			0.363050
$794$	3.61219e21	+	5.74631e21i	0.644343	+	1.02503i
$795$			6.06337e19i			0.0107142i
$796$	3.82656e21	−	7.95378e21i	0.669823	−	1.39228i
$797$		−	7.27501e20i		−	0.126153i	−0.998009	−	0.0630763i	$-0.979909\pi$
$797$		−	7.27501e20i		−	0.126153i	0.998009	−	0.0630763i	$-0.0200912\pi$
$798$	−7.06979e19	+	4.44415e19i	−0.0121446	+	0.00763426i
$799$	1.03255e21			0.175715
$800$	−2.67302e21	−	9.32435e20i	−0.450637	−	0.157197i
$801$	−2.44023e21			−0.407555
$802$	−2.12407e21	+	1.33521e21i	−0.351448	+	0.220924i
$803$			5.56587e20i			0.0912361i
$804$	−1.44874e19	+	3.01131e19i	−0.00235271	+	0.00489029i
$805$			3.93546e21i			0.633179i
$806$	−5.34531e21	−	8.50337e21i	−0.852040	−	1.35543i
$807$	6.56774e18			0.00103720
$808$	−2.66689e21	+	3.02050e20i	−0.417273	+	0.0472600i
$809$	−9.25113e21			−1.43410			−0.717052	−	0.697019i	$-0.754509\pi$
$809$	−9.25113e21			−1.43410			−0.717052	+	0.697019i	$0.754509\pi$
$810$	−4.21086e21	−	6.69868e21i	−0.646745	−	1.02885i
$811$			6.24913e21i			0.950962i	0.879726	+	0.475481i	$0.157726\pi$
$811$			6.24913e21i			0.950962i	−0.879726	+	0.475481i	$0.842274\pi$
$812$	1.15981e22	+	5.57986e21i	1.74871	+	0.841304i
$813$		−	5.85763e19i		−	0.00875071i
$814$	1.97444e20	−	1.24115e20i	0.0292254	−	0.0183714i
$815$	−6.60409e21			−0.968570
$816$	5.99212e18	−	4.78613e18i	0.000870772	−	0.000695518i
$817$	7.18274e21			1.03425
$818$	2.20334e21	−	1.38505e21i	0.314364	−	0.197612i
$819$			2.10300e22i			2.97310i
$820$	5.80021e20	+	2.79048e20i	0.0812530	+	0.0390908i
$821$		−	2.54183e21i		−	0.352836i	−0.984315	−	0.176418i	$-0.943549\pi$
$821$		−	2.54183e21i		−	0.352836i	0.984315	−	0.176418i	$-0.0564511\pi$
$822$	1.70469e19	+	2.71184e19i	0.00234481	+	0.00373015i
$823$	9.89186e21			1.34828			0.674139	−	0.738605i	$-0.264515\pi$
$823$	9.89186e21			1.34828			0.674139	+	0.738605i	$0.264515\pi$
$824$	4.52438e20	+	3.99471e21i	0.0611090	+	0.539549i
$825$	1.99605e18			0.000267157
$826$	−7.15876e21	−	1.13882e22i	−0.949483	−	1.51045i
$827$		−	6.74649e21i		−	0.886720i	−0.896344	−	0.443360i	$-0.853786\pi$
$827$		−	6.74649e21i		−	0.886720i	0.896344	−	0.443360i	$-0.146214\pi$
$828$	−1.00768e21	+	2.09453e21i	−0.131248	+	0.272810i
$829$			1.10282e22i			1.42347i	0.702450	+	0.711733i	$0.252089\pi$
$829$			1.10282e22i			1.42347i	−0.702450	+	0.711733i	$0.747911\pi$
$830$	−1.29361e22	+	8.13180e21i	−1.65470	+	1.04016i
$831$	−1.85305e19			−0.00234898
$832$	3.07624e21	+	1.34063e22i	0.386452	+	1.68416i
$833$	−2.43751e21			−0.303465
$834$	−1.85862e19	+	1.16835e19i	−0.00229321	+	0.00144154i
$835$			1.20589e21i			0.147454i
$836$	−3.21954e20	+	6.69205e20i	−0.0390164	+	0.0810984i
$837$			1.11098e20i			0.0133434i
$838$	4.44974e20	+	7.07869e20i	0.0529669	+	0.0842603i
$839$	6.10035e21			0.719681			0.359840	−	0.933014i	$-0.382831\pi$
$839$	6.10035e21			0.719681			0.359840	+	0.933014i	$0.382831\pi$
$840$	−1.44951e19	−	1.27982e20i	−0.00169483	−	0.0149642i
$841$	−2.34608e21			−0.271877
$842$	5.81429e21	+	9.24943e21i	0.667815	+	1.06237i
$843$			2.79106e19i			0.00317733i
$844$	−1.10941e22	−	5.33737e21i	−1.25177	−	0.602225i
$845$		−	2.15814e22i		−	2.41354i
$846$	8.67124e21	−	5.45084e21i	0.961178	−	0.604207i
$847$	−1.55668e22			−1.71030
$848$	8.78332e21	−	7.01557e21i	0.956511	−	0.764001i
$849$	−3.67450e19			−0.00396635
$850$	−5.84476e20	+	3.67408e20i	−0.0625352	+	0.0393103i
$851$			1.26770e21i			0.134445i
$852$	5.48956e19	+	2.64102e19i	0.00577086	+	0.00277636i
$853$		−	3.12392e21i		−	0.325524i	−0.986665	−	0.162762i	$-0.947960\pi$
$853$		−	3.12392e21i		−	0.325524i	0.986665	−	0.162762i	$-0.0520402\pi$
$854$	1.86273e21	+	2.96325e21i	0.192405	+	0.306080i
$855$	1.37422e22			1.40706
$856$	1.50748e21	−	1.70737e20i	0.153003	−	0.0173290i
$857$	−1.48479e22			−1.49386			−0.746930	−	0.664903i	$-0.768473\pi$
$857$	−1.48479e22			−1.49386			−0.746930	+	0.664903i	$0.768473\pi$
$858$	−5.16127e18	−	8.21059e18i	−0.000514757	−	0.000818879i
$859$		−	1.28300e22i		−	1.26846i	−0.773145	−	0.634230i	$-0.781317\pi$
$859$		−	1.28300e22i		−	1.26846i	0.773145	−	0.634230i	$-0.218683\pi$
$860$	−4.80301e21	+	9.98342e21i	−0.470734	+	0.978455i
$861$			9.46094e18i			0.000919202i
$862$	2.71263e20	−	1.70519e20i	0.0261268	−	0.0164236i
$863$	8.93741e21			0.853357			0.426678	−	0.904403i	$-0.359684\pi$
$863$	8.93741e21			0.853357			0.426678	+	0.904403i	$0.359684\pi$
$864$	5.01117e19	−	1.43656e20i	0.00474336	−	0.0135978i
$865$	1.17351e22			1.10120
$866$	8.35450e21	−	5.25173e21i	0.777206	−	0.488560i
$867$			7.62080e19i			0.00702841i
$868$	7.55945e21	−	1.57129e22i	0.691181	−	1.43667i
$869$		−	2.18115e20i		−	0.0197714i
$870$	5.84526e19	+	9.29870e19i	0.00525303	+	0.00835656i
$871$	−1.46158e22			−1.30222
$872$	9.86892e21	−	1.11775e21i	0.871759	−	0.0987348i
$873$	−1.07128e22			−0.938206
$874$	−2.14834e21	−	3.41760e21i	−0.186538	−	0.296746i
$875$		−	1.26991e22i		−	1.09324i
$876$	8.92291e19	+	4.29281e19i	0.00761598	+	0.00366404i
$877$		−	1.22013e21i		−	0.103254i	−0.998666	−	0.0516271i	$-0.983559\pi$
$877$		−	1.22013e21i		−	0.103254i	0.998666	−	0.0516271i	$-0.0164407\pi$
$878$	1.45391e21	−	9.13943e20i	0.121991	−	0.0766850i
$879$	−2.38780e19			−0.00198646
$880$	−7.14853e20	−	8.94979e20i	−0.0589653	−	0.0738232i
$881$	−1.09637e20			−0.00896679			−0.00448340	−	0.999990i	$-0.501427\pi$
$881$	−1.09637e20			−0.00896679			−0.00448340	+	0.999990i	$0.501427\pi$
$882$	−2.04699e22	+	1.28676e22i	−1.65998	+	1.04348i
$883$		−	1.75829e22i		−	1.41379i	−0.707318	−	0.706896i	$-0.750095\pi$
$883$		−	1.75829e22i		−	1.41379i	0.707318	−	0.706896i	$-0.249905\pi$
$884$	3.02261e21	+	1.45418e21i	0.240985	+	0.115938i
$885$		−	1.14789e20i		−	0.00907458i
$886$	1.02897e22	+	1.63690e22i	0.806588	+	1.28313i
$887$	−4.74859e21			−0.369094			−0.184547	−	0.982824i	$-0.559082\pi$
$887$	−4.74859e21			−0.369094			−0.184547	+	0.982824i	$0.559082\pi$
$888$	−4.66921e18	−	4.12258e19i	−0.000359870	−	0.00317740i
$889$	2.20770e22			1.68724
$890$	3.47884e21	+	5.53418e21i	0.263639	+	0.419399i
$891$		−	1.03427e21i		−	0.0777231i
$892$	−7.03328e21	+	1.46192e22i	−0.524109	+	1.08940i
$893$			1.77880e22i			1.31444i
$894$	3.73920e19	−	2.35050e19i	0.00273998	−	0.00172238i
$895$	−2.26223e22			−1.64386
$896$	−1.68621e22	+	1.69078e22i	−1.21507	+	1.21836i
$897$	5.27167e19			0.00376708
$898$	−2.04622e21	+	1.28628e21i	−0.145004	+	0.0911513i
$899$			1.48690e22i			1.04492i
$900$	−2.96882e21	+	6.17091e21i	−0.206902	+	0.430061i
$901$		−	2.74128e21i		−	0.189460i
$902$	4.47772e19	+	7.12320e19i	0.00306908	+	0.00488232i
$903$	−1.62843e20			−0.0110691
$904$	−2.72731e21	−	2.40802e22i	−0.183853	−	1.62330i
$905$	1.83205e22			1.22482
$906$	−5.72050e19	−	9.10023e19i	−0.00379291	−	0.00603380i
$907$			1.80146e22i			1.18459i	0.805720	+	0.592297i	$0.201779\pi$
$907$			1.80146e22i			1.18459i	−0.805720	+	0.592297i	$0.798221\pi$
$908$	−1.28978e22	−	6.20512e21i	−0.841147	−	0.404675i
$909$			6.49224e21i			0.419919i
$910$	4.76938e22	−	2.99808e22i	3.05951	−	1.92324i
$911$	−6.99654e21			−0.445139			−0.222570	−	0.974917i	$-0.571444\pi$
$911$	−6.99654e21			−0.445139			−0.222570	+	0.974917i	$0.571444\pi$
$912$	8.24520e19	+	1.03228e20i	0.00520283	+	0.00651382i
$913$	−1.99732e21			−0.125002
$914$	−3.32005e21	+	2.08702e21i	−0.206086	+	0.129548i
$915$			2.98685e19i			0.00183889i
$916$	−2.11515e22	−	1.01759e22i	−1.29159	−	0.621382i
$917$			9.08354e21i			0.550155i
$918$	−1.97455e19	−	3.14114e19i	−0.00118617	−	0.00188698i
$919$	8.50410e21			0.506713			0.253356	−	0.967373i	$-0.418465\pi$
$919$	8.50410e21			0.506713			0.253356	+	0.967373i	$0.418465\pi$
$920$	6.18674e21	−	7.00707e20i	0.365640	−	0.0414121i
$921$	1.36007e20			0.00797289
$922$	6.73773e21	+	1.07184e22i	0.391771	+	0.623232i
$923$			2.66443e22i			1.53671i
$924$	7.29917e18	−	1.51719e19i	0.000417574	−	0.000867959i
$925$			3.73490e21i			0.211942i
$926$	−2.08462e22	+	1.31041e22i	−1.17340	+	0.737609i
$927$	9.72465e21			0.542970
$928$	6.70678e21	−	1.92264e22i	0.371453	−	1.06485i
$929$	−4.08200e21			−0.224262			−0.112131	−	0.993693i	$-0.535768\pi$
$929$	−4.08200e21			−0.224262			−0.112131	+	0.993693i	$0.535768\pi$
$930$	1.25976e20	−	7.91901e19i	0.00686541	−	0.00431567i
$931$		−	4.19916e22i		−	2.27007i
$932$	−3.40361e20	+	7.07465e20i	−0.0182524	+	0.0379390i
$933$			1.81919e20i			0.00967756i
$934$	6.37433e21	+	1.01404e22i	0.336382	+	0.535120i
$935$	−2.79323e20			−0.0146224
$936$	3.30602e22	−	3.74438e21i	1.71687	−	0.194451i
$937$	1.01718e22			0.524023			0.262012	−	0.965065i	$-0.415614\pi$
$937$	1.01718e22			0.524023			0.262012	+	0.965065i	$0.415614\pi$
$938$	−1.35038e22	−	2.14820e22i	−0.690135	−	1.09787i
$939$		−	7.14873e19i		−	0.00362441i
$940$	−2.47238e22	−	1.18946e22i	−1.24353	−	0.598262i
$941$		−	8.93477e21i		−	0.445822i	−0.974839	−	0.222911i	$-0.928444\pi$
$941$		−	8.93477e21i		−	0.445822i	0.974839	−	0.222911i	$-0.0715559\pi$
$942$	−7.15132e19	+	4.49540e19i	−0.00354001	+	0.00222529i
$943$	−4.57350e20			−0.0224601
$944$	−1.66282e22	+	1.32816e22i	−0.810133	+	0.647083i
$945$	−6.23129e20			−0.0301189
$946$	−1.22606e21	+	7.70713e20i	−0.0587932	+	0.0369581i
$947$		−	6.04477e21i		−	0.287577i	−0.989608	−	0.143789i	$-0.954071\pi$
$947$		−	6.04477e21i		−	0.287577i	0.989608	−	0.143789i	$-0.0459286\pi$
$948$	−3.49670e19	−	1.68226e19i	−0.00165043	−	0.000794019i
$949$			4.33085e22i			2.02804i
$950$	−6.32943e21	−	1.00689e22i	−0.294061	−	0.467795i
$951$	2.42562e20			0.0111807
$952$	6.55332e20	+	5.78612e21i	0.0299698	+	0.264612i
$953$	1.77699e22			0.806284			0.403142	−	0.915137i	$-0.367918\pi$
$953$	1.77699e22			0.806284			0.403142	+	0.915137i	$0.367918\pi$
$954$	−1.44712e22	−	2.30210e22i	−0.651468	−	1.03636i
$955$			1.01575e22i			0.453692i
$956$	8.96350e21	−	1.86313e22i	0.397231	−	0.825674i
$957$			1.43571e19i			0.000631286i
$958$	−2.52137e22	+	1.58496e22i	−1.10001	+	0.691476i
$959$	−2.43218e22			−1.05282
$960$	−1.98613e20	+	4.55741e19i	−0.00853047	+	0.00195742i
$961$	−3.32112e21			−0.141534
$962$	1.53633e22	−	9.65751e21i	0.649636	−	0.408368i
$963$		−	3.66979e21i		−	0.153973i
$964$	7.62049e21	−	1.58398e22i	0.317253	−	0.659433i
$965$		−	3.42278e22i		−	1.41392i
$966$	4.87060e19	+	7.74820e19i	0.00199643	+	0.00317594i
$967$	2.36393e22			0.961471			0.480736	−	0.876866i	$-0.340370\pi$
$967$	2.36393e22			0.961471			0.480736	+	0.876866i	$0.340370\pi$
$968$	2.77165e21	+	2.44718e22i	0.111860	+	0.987643i
$969$	3.22175e19			0.00129022
$970$	1.52725e22	+	2.42956e22i	0.606906	+	0.965472i
$971$		−	5.46111e21i		−	0.215346i	−0.994186	−	0.107673i	$-0.965660\pi$
$971$		−	5.46111e21i		−	0.215346i	0.994186	−	0.107673i	$-0.0343399\pi$
$972$	−4.97468e20	−	2.39331e20i	−0.0194656	−	0.00936488i
$973$		−	1.66694e22i		−	0.647253i
$974$	2.43283e22	−	1.52930e22i	0.937389	−	0.589253i
$975$	1.55314e20			0.00593848
$976$	4.32672e21	−	3.45591e21i	0.164167	−	0.131126i
$977$	−4.80810e22			−1.81036			−0.905179	−	0.425030i	$-0.860264\pi$
$977$	−4.80810e22			−1.81036			−0.905179	+	0.425030i	$0.860264\pi$
$978$	−1.30022e20	+	8.17335e19i	−0.00485821	+	0.00305393i
$979$			8.54470e20i			0.0316830i
$980$	5.83648e22	+	2.80793e22i	2.14761	+	1.03321i
$981$		−	2.40248e22i		−	0.877287i
$982$	1.06273e22	+	1.69060e22i	0.385111	+	0.612638i
$983$	1.61464e22			0.580664			0.290332	−	0.956926i	$-0.406234\pi$
$983$	1.61464e22			0.580664			0.290332	+	0.956926i	$0.406234\pi$
$984$	1.48731e19	−	1.68452e18i	0.000530808	−	6.01190e-5i
$985$	−3.64080e22			−1.28951
$986$	−2.64267e21	−	4.20399e21i	−0.0928895	−	0.147769i
$987$		−	4.03280e20i		−	0.0140679i
$988$	−2.50515e22	+	5.20714e22i	−0.867274	+	1.80269i
$989$		−	7.87199e21i		−	0.270466i
$990$	−2.34573e21	+	1.47455e21i	−0.0799860	+	0.0502801i
$991$	1.67991e22			0.568503			0.284251	−	0.958750i	$-0.408255\pi$
$991$	1.67991e22			0.568503			0.284251	+	0.958750i	$0.408255\pi$
$992$	−2.60474e22	−	9.08617e21i	−0.874836	−	0.305171i
$993$	−5.03644e19			−0.00167882
$994$	−3.91612e22	+	2.46172e22i	−1.29556	+	0.814405i
$995$			5.71923e22i			1.87787i
$996$	−1.54048e20	+	3.20200e20i	−0.00502009	+	0.0104346i
$997$		−	3.39053e22i		−	1.09661i	−0.836277	−	0.548307i	$-0.815273\pi$
$997$		−	3.39053e22i		−	1.09661i	0.836277	−	0.548307i	$-0.184727\pi$
$998$	−2.11576e22	−	3.36577e22i	−0.679183	−	1.08045i
$999$	−2.00724e20			−0.00639527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.16.b.a.5.4	yes	14
3.2	odd	2		72.16.d.b.37.11		14
4.3	odd	2		32.16.b.a.17.8		14
8.3	odd	2		32.16.b.a.17.7		14
8.5	even	2	inner	8.16.b.a.5.3	✓	14
24.5	odd	2		72.16.d.b.37.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.16.b.a.5.3	✓	14	8.5	even	2	inner
8.16.b.a.5.4	yes	14	1.1	even	1	trivial
32.16.b.a.17.7		14	8.3	odd	2
32.16.b.a.17.8		14	4.3	odd	2
72.16.d.b.37.11		14	3.2	odd	2
72.16.d.b.37.12		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+(-153.255 + 96.3377i) q^{2} -27.2769i q^{3} +(14206.1 - 29528.4i) q^{4} +212327. i q^{5} +(2627.80 + 4180.32i) q^{6} -3.74922e6 q^{7} +(667546. + 5.89396e6i) q^{8} +1.43482e7 q^{9} +(-2.04551e7 - 3.25401e7i) q^{10} -5.02415e6i q^{11} +(-805445. - 387499. i) q^{12} -3.90933e8i q^{13} +(5.74586e8 - 3.61191e8i) q^{14} +5.79162e6 q^{15} +(-6.70115e8 - 8.38968e8i) q^{16} -2.61842e8 q^{17} +(-2.19893e9 + 1.38227e9i) q^{18} -4.51083e9i q^{19} +(6.26968e9 + 3.01634e9i) q^{20} +1.02267e8i q^{21} +(4.84015e8 + 7.69975e8i) q^{22} -4.94368e9 q^{23} +(1.60769e8 - 1.82086e7i) q^{24} -1.45651e10 q^{25} +(3.76616e10 + 5.99124e10i) q^{26} -7.82768e8i q^{27} +(-5.32618e10 + 1.10708e11i) q^{28} -1.04763e11i q^{29} +(-8.87594e8 + 5.57951e8i) q^{30} -1.41930e11 q^{31} +(1.83523e11 + 6.40186e10i) q^{32} -1.37043e8 q^{33} +(4.01286e10 - 2.52253e10i) q^{34} -7.96059e11i q^{35} +(2.03832e11 - 4.23679e11i) q^{36} -2.56429e11i q^{37} +(4.34563e11 + 6.91306e11i) q^{38} -1.06634e10 q^{39} +(-1.25145e12 + 1.41738e11i) q^{40} +9.25121e10 q^{41} +(-9.85218e9 - 1.56729e10i) q^{42} +1.59233e12i q^{43} +(-1.48355e11 - 7.13736e10i) q^{44} +3.04650e12i q^{45} +(7.57643e11 - 4.76263e11i) q^{46} -3.94340e12 q^{47} +(-2.28845e10 + 1.82787e10i) q^{48} +9.30906e12 q^{49} +(2.23217e12 - 1.40316e12i) q^{50} +7.14225e9i q^{51} +(-1.15436e13 - 5.55363e12i) q^{52} +1.04692e13i q^{53} +(7.54101e10 + 1.19963e11i) q^{54} +1.06676e12 q^{55} +(-2.50277e12 - 2.20977e13i) q^{56} -1.23042e11 q^{57} +(1.00926e13 + 1.60554e13i) q^{58} -1.98199e13i q^{59} +(8.22764e10 - 1.71018e11i) q^{60} +5.15720e12i q^{61} +(2.17515e13 - 1.36732e13i) q^{62} -5.37944e13 q^{63} +(-3.42931e13 + 7.86898e12i) q^{64} +8.30055e13 q^{65} +(2.10026e10 - 1.32024e10i) q^{66} -3.73869e13i q^{67} +(-3.71976e12 + 7.73179e12i) q^{68} +1.34848e11i q^{69} +(7.66905e13 + 1.22000e14i) q^{70} -6.81556e13 q^{71} +(9.57806e12 + 8.45675e13i) q^{72} -1.10782e14 q^{73} +(2.47037e13 + 3.92990e13i) q^{74} +3.97290e11i q^{75} +(-1.33198e14 - 6.40813e13i) q^{76} +1.88366e13i q^{77} +(1.63423e12 - 1.02729e12i) q^{78} +4.34133e13 q^{79} +(1.78135e14 - 1.42283e14i) q^{80} +2.05859e14 q^{81} +(-1.41779e13 + 8.91240e12i) q^{82} -3.97545e14i q^{83} +(3.01979e12 + 1.45282e12i) q^{84} -5.55961e13i q^{85} +(-1.53402e14 - 2.44033e14i) q^{86} -2.85761e12 q^{87} +(2.96121e13 - 3.35385e12i) q^{88} -1.70072e14 q^{89} +(-2.93493e14 - 4.66891e14i) q^{90} +1.46569e15i q^{91} +(-7.02304e13 + 1.45979e14i) q^{92} +3.87142e12i q^{93} +(6.04345e14 - 3.79898e14i) q^{94} +9.57769e14 q^{95} +(1.74623e12 - 5.00593e12i) q^{96} -7.46636e14 q^{97} +(-1.42666e15 + 8.96813e14i) q^{98} -7.20873e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 90 q^{2} + 51444 q^{4} - 189428 q^{6} - 1647088 q^{7} + 1889640 q^{8} - 57395630 q^{9} + 58467784 q^{10} + 399357832 q^{12} - 518960496 q^{14} + 712135312 q^{15} - 1435931120 q^{16} + 728554812 q^{17}+ \cdots - 51\!\cdots\!58 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more