LMFDB - Embedded newform 8.16.b.a.5.14

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			5.14
Root			$-93.3164 - 5.91227i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.16.b.a.5.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(180.633 + 11.8245i) q^{2} +1858.96i q^{3} +(32488.4 + 4271.80i) q^{4} -290191. i q^{5} +(-21981.3 + 335789. i) q^{6} +1.26027e6 q^{7} +(5.81795e6 + 1.15579e6i) q^{8} +1.08932e7 q^{9} +O(q^{10})$	\(q+(180.633 + 11.8245i) q^{2} +1858.96i q^{3} +(32488.4 + 4271.80i) q^{4} -290191. i q^{5} +(-21981.3 + 335789. i) q^{6} +1.26027e6 q^{7} +(5.81795e6 + 1.15579e6i) q^{8} +1.08932e7 q^{9} +(3.43137e6 - 5.24180e7i) q^{10} +9.81513e7i q^{11} +(-7.94110e6 + 6.03946e7i) q^{12} -3.04482e8i q^{13} +(2.27647e8 + 1.49022e7i) q^{14} +5.39453e8 q^{15} +(1.03725e9 + 2.77567e8i) q^{16} +6.26054e8 q^{17} +(1.96766e9 + 1.28807e8i) q^{18} -5.70219e8i q^{19} +(1.23964e9 - 9.42783e9i) q^{20} +2.34280e9i q^{21} +(-1.16059e9 + 1.77293e10i) q^{22} -2.03517e10 q^{23} +(-2.14856e9 + 1.08153e10i) q^{24} -5.36932e10 q^{25} +(3.60035e9 - 5.49993e10i) q^{26} +4.69240e10i q^{27} +(4.09442e10 + 5.38364e9i) q^{28} -3.55070e10i q^{29} +(9.74429e10 + 6.37879e9i) q^{30} -1.37553e11 q^{31} +(1.84078e11 + 6.24027e10i) q^{32} -1.82459e11 q^{33} +(1.13086e11 + 7.40280e9i) q^{34} -3.65720e11i q^{35} +(3.53901e11 + 4.65334e10i) q^{36} +6.95044e11i q^{37} +(6.74257e9 - 1.03000e11i) q^{38} +5.66019e11 q^{39} +(3.35399e11 - 1.68832e12i) q^{40} -6.94552e11 q^{41} +(-2.77025e10 + 4.23186e11i) q^{42} +1.01781e12i q^{43} +(-4.19283e11 + 3.18878e12i) q^{44} -3.16110e12i q^{45} +(-3.67619e12 - 2.40650e11i) q^{46} +2.94174e12 q^{47} +(-5.15987e11 + 1.92820e12i) q^{48} -3.15927e12 q^{49} +(-9.69874e12 - 6.34897e11i) q^{50} +1.16381e12i q^{51} +(1.30068e12 - 9.89211e12i) q^{52} +5.17445e12i q^{53} +(-5.54855e11 + 8.47601e12i) q^{54} +2.84826e13 q^{55} +(7.33221e12 + 1.45661e12i) q^{56} +1.06001e12 q^{57} +(4.19854e11 - 6.41373e12i) q^{58} -2.55439e13i q^{59} +(1.75259e13 + 2.30443e12i) q^{60} +8.74172e12i q^{61} +(-2.48465e13 - 1.62650e12i) q^{62} +1.37284e13 q^{63} +(3.25127e13 + 1.34486e13i) q^{64} -8.83578e13 q^{65} +(-3.29581e13 - 2.15750e12i) q^{66} +6.72032e13i q^{67} +(2.03395e13 + 2.67438e12i) q^{68} -3.78330e13i q^{69} +(4.32447e12 - 6.60610e13i) q^{70} -2.21325e13 q^{71} +(6.33759e13 + 1.25902e13i) q^{72} -1.27473e14 q^{73} +(-8.21858e12 + 1.25548e14i) q^{74} -9.98134e13i q^{75} +(2.43586e12 - 1.85255e13i) q^{76} +1.23698e14i q^{77} +(1.02242e14 + 6.69292e12i) q^{78} +7.24152e13 q^{79} +(8.05475e13 - 3.00999e14i) q^{80} +6.90753e13 q^{81} +(-1.25459e14 - 8.21276e12i) q^{82} +1.55075e14i q^{83} +(-1.00080e13 + 7.61137e13i) q^{84} -1.81675e14i q^{85} +(-1.20352e13 + 1.83851e14i) q^{86} +6.60061e13 q^{87} +(-1.13442e14 + 5.71040e14i) q^{88} +6.61821e14 q^{89} +(3.73786e13 - 5.70998e14i) q^{90} -3.83730e14i q^{91} +(-6.61194e14 - 8.69385e13i) q^{92} -2.55705e14i q^{93} +(5.31374e14 + 3.47847e13i) q^{94} -1.65472e14 q^{95} +(-1.16004e14 + 3.42194e14i) q^{96} +4.81808e14 q^{97} +(-5.70668e14 - 3.73569e13i) q^{98} +1.06918e15i 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 $

$2$	180.633	+	11.8245i	0.997864	+	0.0653220i
$2$	180.633	+	11.8245i	0.997864	+	0.0653220i
$3$			1858.96i			0.490750i	0.969428	+	0.245375i	$0.0789111\pi$
$3$			1858.96i			0.490750i	−0.969428	+	0.245375i	$0.921089\pi$
$4$	32488.4	+	4271.80i	0.991466	+	0.130365i
$5$		−	290191.i		−	1.66115i	−0.556907	−	0.830575i	$-0.688012\pi$
$5$		−	290191.i		−	1.66115i	0.556907	−	0.830575i	$-0.311988\pi$
$6$	−21981.3	+	335789.i	−0.0320568	+	0.489702i
$7$	1.26027e6			0.578402			0.289201	−	0.957268i	$-0.406610\pi$
$7$	1.26027e6			0.578402			0.289201	+	0.957268i	$0.406610\pi$
$8$	5.81795e6	+	1.15579e6i	0.980833	+	0.194851i
$9$	1.08932e7			0.759164
$10$	3.43137e6	−	5.24180e7i	0.108510	−	1.65760i
$11$			9.81513e7i			1.51863i	0.650725	+	0.759314i	$0.274465\pi$
$11$			9.81513e7i			1.51863i	−0.650725	+	0.759314i	$0.725535\pi$
$12$	−7.94110e6	+	6.03946e7i	−0.0639766	+	0.486562i
$13$		−	3.04482e8i		−	1.34582i	−0.739726	−	0.672908i	$-0.765045\pi$
$13$		−	3.04482e8i		−	1.34582i	0.739726	−	0.672908i	$-0.234955\pi$
$14$	2.27647e8	+	1.49022e7i	0.577166	+	0.0377824i
$15$	5.39453e8			0.815210
$16$	1.03725e9	+	2.77567e8i	0.966010	+	0.258505i
$17$	6.26054e8			0.370037			0.185018	−	0.982735i	$-0.440766\pi$
$17$	6.26054e8			0.370037			0.185018	+	0.982735i	$0.440766\pi$
$18$	1.96766e9	+	1.28807e8i	0.757543	+	0.0495901i
$19$		−	5.70219e8i		−	0.146349i	−0.997319	−	0.0731745i	$-0.976687\pi$
$19$		−	5.70219e8i		−	0.146349i	0.997319	−	0.0731745i	$-0.0233130\pi$
$20$	1.23964e9	−	9.42783e9i	0.216556	−	1.64697i
$21$			2.34280e9i			0.283851i
$22$	−1.16059e9	+	1.77293e10i	−0.0991997	+	1.51538i
$23$	−2.03517e10			−1.24636			−0.623178	−	0.782080i	$-0.714159\pi$
$23$	−2.03517e10			−1.24636			−0.623178	+	0.782080i	$0.714159\pi$
$24$	−2.14856e9	+	1.08153e10i	−0.0956232	+	0.481344i
$25$	−5.36932e10			−1.75942
$26$	3.60035e9	−	5.49993e10i	0.0879114	−	1.34294i
$27$			4.69240e10i			0.863310i
$28$	4.09442e10	+	5.38364e9i	0.573466	+	0.0754033i
$29$		−	3.55070e10i		−	0.382234i	−0.981567	−	0.191117i	$-0.938789\pi$
$29$		−	3.55070e10i		−	0.382234i	0.981567	−	0.191117i	$-0.0612110\pi$
$30$	9.74429e10	+	6.37879e9i	0.813469	+	0.0532511i
$31$	−1.37553e11			−0.897958			−0.448979	−	0.893542i	$-0.648212\pi$
$31$	−1.37553e11			−0.897958			−0.448979	+	0.893542i	$0.648212\pi$
$32$	1.84078e11	+	6.24027e10i	0.947061	+	0.321054i
$33$	−1.82459e11			−0.745267
$34$	1.13086e11	+	7.40280e9i	0.369247	+	0.0241715i
$35$		−	3.65720e11i		−	0.960812i
$36$	3.53901e11	+	4.65334e10i	0.752685	+	0.0989684i
$37$			6.95044e11i			1.20365i	0.798629	+	0.601824i	$0.205559\pi$
$37$			6.95044e11i			1.20365i	−0.798629	+	0.601824i	$0.794441\pi$
$38$	6.74257e9	−	1.03000e11i	0.00955980	−	0.146036i
$39$	5.66019e11			0.660460
$40$	3.35399e11	−	1.68832e12i	0.323677	−	1.62931i
$41$	−6.94552e11			−0.556962			−0.278481	−	0.960442i	$-0.589831\pi$
$41$	−6.94552e11			−0.556962			−0.278481	+	0.960442i	$0.589831\pi$
$42$	−2.77025e10	+	4.23186e11i	−0.0185417	+	0.283245i
$43$			1.01781e12i			0.571025i	0.958375	+	0.285513i	$0.0921639\pi$
$43$			1.01781e12i			0.571025i	−0.958375	+	0.285513i	$0.907836\pi$
$44$	−4.19283e11	+	3.18878e12i	−0.197976	+	1.50567i
$45$		−	3.16110e12i		−	1.26108i
$46$	−3.67619e12	−	2.40650e11i	−1.24370	−	0.0814145i
$47$	2.94174e12			0.846974			0.423487	−	0.905902i	$-0.360806\pi$
$47$	2.94174e12			0.846974			0.423487	+	0.905902i	$0.360806\pi$
$48$	−5.15987e11	+	1.92820e12i	−0.126861	+	0.474070i
$49$	−3.15927e12			−0.665451
$50$	−9.69874e12	−	6.34897e11i	−1.75566	−	0.114929i
$51$			1.16381e12i			0.181596i
$52$	1.30068e12	−	9.89211e12i	0.175447	−	1.33433i
$53$			5.17445e12i			0.605056i	0.953141	+	0.302528i	$0.0978305\pi$
$53$			5.17445e12i			0.605056i	−0.953141	+	0.302528i	$0.902169\pi$
$54$	−5.54855e11	+	8.47601e12i	−0.0563931	+	0.861467i
$55$	2.84826e13			2.52267
$56$	7.33221e12	+	1.45661e12i	0.567316	+	0.112702i
$57$	1.06001e12			0.0718208
$58$	4.19854e11	−	6.41373e12i	0.0249683	−	0.381417i
$59$		−	2.55439e13i		−	1.33628i	−0.744035	−	0.668140i	$-0.767091\pi$
$59$		−	2.55439e13i		−	1.33628i	0.744035	−	0.668140i	$-0.232909\pi$
$60$	1.75259e13	+	2.30443e12i	0.808253	+	0.106275i
$61$			8.74172e12i			0.356142i	0.984018	+	0.178071i	$0.0569856\pi$
$61$			8.74172e12i			0.356142i	−0.984018	+	0.178071i	$0.943014\pi$
$62$	−2.48465e13	−	1.62650e12i	−0.896040	−	0.0586564i
$63$	1.37284e13			0.439102
$64$	3.25127e13	+	1.34486e13i	0.924066	+	0.382233i
$65$	−8.83578e13			−2.23560
$66$	−3.29581e13	−	2.15750e12i	−0.743675	−	0.0486823i
$67$			6.72032e13i			1.35466i	0.735681	+	0.677328i	$0.236862\pi$
$67$			6.72032e13i			1.35466i	−0.735681	+	0.677328i	$0.763138\pi$
$68$	2.03395e13	+	2.67438e12i	0.366879	+	0.0482398i
$69$		−	3.78330e13i		−	0.611650i
$70$	4.32447e12	−	6.60610e13i	0.0627621	−	0.958760i
$71$	−2.21325e13			−0.288797			−0.144399	−	0.989520i	$-0.546125\pi$
$71$	−2.21325e13			−0.288797			−0.144399	+	0.989520i	$0.546125\pi$
$72$	6.33759e13	+	1.25902e13i	0.744613	+	0.147924i
$73$	−1.27473e14			−1.35050			−0.675252	−	0.737587i	$-0.735965\pi$
$73$	−1.27473e14			−1.35050			−0.675252	+	0.737587i	$0.735965\pi$
$74$	−8.21858e12	+	1.25548e14i	−0.0786247	+	1.20108i
$75$		−	9.98134e13i		−	0.863435i
$76$	2.43586e12	−	1.85255e13i	0.0190788	−	0.145100i
$77$			1.23698e14i			0.878377i
$78$	1.02242e14	+	6.69292e12i	0.659049	+	0.0431425i
$79$	7.24152e13			0.424255			0.212127	−	0.977242i	$-0.431961\pi$
$79$	7.24152e13			0.424255			0.212127	+	0.977242i	$0.431961\pi$
$80$	8.05475e13	−	3.00999e14i	0.429415	−	1.60469i
$81$	6.90753e13			0.335494
$82$	−1.25459e14	−	8.21276e12i	−0.555773	−	0.0363819i
$83$			1.55075e14i			0.627274i	0.949543	+	0.313637i	$0.101547\pi$
$83$			1.55075e14i			0.627274i	−0.949543	+	0.313637i	$0.898453\pi$
$84$	−1.00080e13	+	7.61137e13i	−0.0370042	+	0.281429i
$85$		−	1.81675e14i		−	0.614686i
$86$	−1.20352e13	+	1.83851e14i	−0.0373005	+	0.569806i
$87$	6.60061e13			0.187581
$88$	−1.13442e14	+	5.71040e14i	−0.295906	+	1.48952i
$89$	6.61821e14			1.58604			0.793022	−	0.609192i	$-0.208506\pi$
$89$	6.61821e14			1.58604			0.793022	+	0.609192i	$0.208506\pi$
$90$	3.73786e13	−	5.70998e14i	0.0823766	−	1.25839i
$91$		−	3.83730e14i		−	0.778423i
$92$	−6.61194e14	−	8.69385e13i	−1.23572	−	0.162481i
$93$		−	2.55705e14i		−	0.440673i
$94$	5.31374e14	+	3.47847e13i	0.845165	+	0.0553260i
$95$	−1.65472e14			−0.243107
$96$	−1.16004e14	+	3.42194e14i	−0.157558	+	0.464770i
$97$	4.81808e14			0.605460			0.302730	−	0.953076i	$-0.402102\pi$
$97$	4.81808e14			0.605460			0.302730	+	0.953076i	$0.402102\pi$
$98$	−5.70668e14	−	3.73569e13i	−0.664030	−	0.0434686i
$99$			1.06918e15i			1.15289i
$100$	−1.74440e15	−	2.29366e14i	−1.74440	−	0.229366i
$101$			1.19918e15i			1.11294i	0.830867	+	0.556471i	$0.187845\pi$
$101$			1.19918e15i			1.11294i	−0.830867	+	0.556471i	$0.812155\pi$
$102$	−1.37615e13	+	2.10222e14i	−0.0118622	+	0.181208i
$103$	−1.94385e15			−1.55734			−0.778670	−	0.627434i	$-0.784105\pi$
$103$	−1.94385e15			−1.55734			−0.778670	+	0.627434i	$0.784105\pi$
$104$	3.51916e14	−	1.77146e15i	0.262234	−	1.32002i
$105$	6.79859e14			0.471519
$106$	−6.11855e13	+	9.34676e14i	−0.0395234	+	0.603764i
$107$		−	3.00752e15i		−	1.81063i	−0.424739	−	0.905316i	$-0.639634\pi$
$107$		−	3.00752e15i		−	1.81063i	0.424739	−	0.905316i	$-0.360366\pi$
$108$	−2.00450e14	+	1.52448e15i	−0.112545	+	0.855943i
$109$		−	1.05051e15i		−	0.550427i	−0.961383	−	0.275214i	$-0.911251\pi$
$109$		−	1.05051e15i		−	0.550427i	0.961383	−	0.275214i	$-0.0887486\pi$
$110$	5.14489e15	+	3.36794e14i	2.51728	+	0.164786i
$111$	−1.29206e15			−0.590691
$112$	1.30721e15	+	3.49811e14i	0.558742	+	0.149520i
$113$	1.90217e15			0.760607			0.380303	−	0.924862i	$-0.375820\pi$
$113$	1.90217e15			0.760607			0.380303	+	0.924862i	$0.375820\pi$
$114$	1.91473e14	+	1.25342e13i	0.0716674	+	0.00469148i
$115$			5.90588e15i			2.07039i
$116$	1.51679e14	−	1.15356e15i	0.0498299	−	0.378972i
$117$		−	3.31677e15i		−	1.02170i
$118$	3.02045e14	−	4.61407e15i	0.0872885	−	1.33343i
$119$	7.89000e14			0.214030
$120$	3.13851e15	+	6.23493e14i	0.799584	+	0.158844i
$121$	−5.45644e15			−1.30623
$122$	−1.03367e14	+	1.57904e15i	−0.0232639	+	0.355381i
$123$		−	1.29114e15i		−	0.273329i
$124$	−4.46886e15	−	5.87597e14i	−0.890295	−	0.117062i
$125$			6.72534e15i			1.26151i
$126$	2.47980e15	+	1.62332e14i	0.438164	+	0.0286830i
$127$	−4.55964e15			−0.759281			−0.379640	−	0.925134i	$-0.623952\pi$
$127$	−4.55964e15			−0.759281			−0.379640	+	0.925134i	$0.623952\pi$
$128$	5.71383e15	+	2.81371e15i	0.897124	+	0.441778i
$129$	−1.89208e15			−0.280231
$130$	−1.59603e16	−	1.04479e15i	−2.23083	−	0.146034i
$131$		−	1.02016e16i		−	1.34627i	−0.739519	−	0.673136i	$-0.764947\pi$
$131$		−	1.02016e16i		−	1.34627i	0.739519	−	0.673136i	$-0.235053\pi$
$132$	−5.92781e15	−	7.79430e14i	−0.738907	−	0.0971567i
$133$		−	7.18632e14i		−	0.0846485i
$134$	−7.94647e14	+	1.21391e16i	−0.0884888	+	1.35176i
$135$	1.36169e16			1.43409
$136$	3.64235e15	+	7.23585e14i	0.362944	+	0.0721021i
$137$	1.00633e15			0.0949148			0.0474574	−	0.998873i	$-0.484888\pi$
$137$	1.00633e15			0.0949148			0.0474574	+	0.998873i	$0.484888\pi$
$138$	4.47358e14	−	6.83389e15i	0.0399542	−	0.610344i
$139$			7.02401e15i			0.594257i	0.954837	+	0.297129i	$0.0960290\pi$
$139$			7.02401e15i			0.594257i	−0.954837	+	0.297129i	$0.903971\pi$
$140$	1.56228e15	−	1.18816e16i	0.125256	−	0.952612i
$141$			5.46857e15i			0.415653i
$142$	−3.99786e15	−	2.61707e14i	−0.288181	−	0.0188648i
$143$	2.98853e16			2.04379
$144$	1.12989e16	+	3.02359e15i	0.733360	+	0.196248i
$145$	−1.03038e16			−0.634948
$146$	−2.30258e16	−	1.50731e15i	−1.34762	−	0.0882177i
$147$		−	5.87296e15i		−	0.326570i
$148$	−2.96909e15	+	2.25808e16i	−0.156913	+	1.19338i
$149$		−	2.85325e16i		−	1.43365i	−0.697255	−	0.716824i	$-0.745595\pi$
$149$		−	2.85325e16i		−	1.43365i	0.697255	−	0.716824i	$-0.254405\pi$
$150$	1.18025e15	−	1.80296e16i	0.0564013	−	0.861591i
$151$	2.85155e15			0.129644			0.0648222	−	0.997897i	$-0.479352\pi$
$151$	2.85155e15			0.129644			0.0648222	+	0.997897i	$0.479352\pi$
$152$	6.59051e14	−	3.31750e15i	0.0285162	−	0.143544i
$153$	6.81972e15			0.280919
$154$	−1.46267e15	+	2.23438e16i	−0.0573773	+	0.876501i
$155$			3.99165e16i			1.49164i
$156$	1.83890e16	+	2.41792e15i	0.654824	+	0.0861008i
$157$			9.50020e15i			0.322467i	0.986916	+	0.161233i	$0.0515472\pi$
$157$			9.50020e15i			0.322467i	−0.986916	+	0.161233i	$0.948453\pi$
$158$	1.30806e16	+	8.56277e14i	0.423349	+	0.0277132i
$159$	−9.61910e15			−0.296931
$160$	1.81087e16	−	5.34178e16i	0.533319	−	1.57321i
$161$	−2.56487e16			−0.720895
$162$	1.24773e16	+	8.16784e14i	0.334778	+	0.0219151i
$163$		−	6.08927e16i		−	1.56012i	−0.625705	−	0.780060i	$-0.715188\pi$
$163$		−	6.08927e16i		−	1.56012i	0.625705	−	0.780060i	$-0.284812\pi$
$164$	−2.25649e16	−	2.96699e15i	−0.552209	−	0.0726084i
$165$			5.29481e16i			1.23800i
$166$	−1.83370e15	+	2.80117e16i	−0.0409748	+	0.625934i
$167$	−5.75741e16			−1.22985			−0.614927	−	0.788584i	$-0.710814\pi$
$167$	−5.75741e16			−1.22985			−0.614927	+	0.788584i	$0.710814\pi$
$168$	−2.70778e15	+	1.36303e16i	−0.0553086	+	0.278410i
$169$	−4.15231e16			−0.811222
$170$	2.14823e15	−	3.28165e16i	0.0401525	−	0.613374i
$171$		−	6.21149e15i		−	0.111103i
$172$	−4.34790e15	+	3.30671e16i	−0.0744417	+	0.566152i
$173$		−	2.16370e16i		−	0.354692i	−0.984149	−	0.177346i	$-0.943249\pi$
$173$		−	2.16370e16i		−	0.354692i	0.984149	−	0.177346i	$-0.0567512\pi$
$174$	1.19229e16	+	7.80492e14i	0.187181	+	0.0122532i
$175$	−6.76681e16			−1.01765
$176$	−2.72436e16	+	1.01807e17i	−0.392572	+	1.46701i
$177$	4.74851e16			0.655780
$178$	1.19547e17	+	7.82573e15i	1.58266	+	0.103604i
$179$			6.49679e16i			0.824710i	0.911023	+	0.412355i	$0.135294\pi$
$179$			6.49679e16i			0.824710i	−0.911023	+	0.412355i	$0.864706\pi$
$180$	1.35036e16	−	1.02699e17i	0.164401	−	1.25032i
$181$		−	6.33200e16i		−	0.739523i	−0.929127	−	0.369761i	$-0.879439\pi$
$181$		−	6.33200e16i		−	0.739523i	0.929127	−	0.369761i	$-0.120561\pi$
$182$	4.53743e15	−	6.93142e16i	0.0508481	−	0.776760i
$183$	−1.62505e16			−0.174777
$184$	−1.18405e17	−	2.35222e16i	−1.22247	−	0.242854i
$185$	2.01695e17			1.99944
$186$	3.02359e15	−	4.61887e16i	0.0287857	−	0.439732i
$187$			6.14481e16i			0.561948i
$188$	9.55723e16	+	1.25665e16i	0.839746	+	0.110416i
$189$			5.91371e16i			0.499340i
$190$	−2.98897e16	−	1.95663e15i	−0.242588	−	0.0158803i
$191$	7.61809e16			0.594423			0.297212	−	0.954812i	$-0.403943\pi$
$191$	7.61809e16			0.594423			0.297212	+	0.954812i	$0.403943\pi$
$192$	−2.50004e16	+	6.04398e16i	−0.187581	+	0.453486i
$193$	1.31762e17			0.950849			0.475425	−	0.879756i	$-0.342294\pi$
$193$	1.31762e17			0.950849			0.475425	+	0.879756i	$0.342294\pi$
$194$	8.70302e16	+	5.69715e15i	0.604167	+	0.0395499i
$195$		−	1.64254e17i		−	1.09712i
$196$	−1.02640e17	−	1.34958e16i	−0.659772	−	0.0867515i
$197$		−	1.38251e17i		−	0.855406i	−0.903919	−	0.427703i	$-0.859323\pi$
$197$		−	1.38251e17i		−	0.855406i	0.903919	−	0.427703i	$-0.140677\pi$
$198$	−1.26426e16	+	1.93129e17i	−0.0753089	+	1.15042i
$199$	−1.07768e16			−0.0618150			−0.0309075	−	0.999522i	$-0.509840\pi$
$199$	−1.07768e16			−0.0618150			−0.0309075	+	0.999522i	$0.509840\pi$
$200$	−3.12384e17	−	6.20578e16i	−1.72569	−	0.342824i
$201$	−1.24928e17			−0.664798
$202$	−1.41797e16	+	2.16611e17i	−0.0726996	+	1.11057i
$203$		−	4.47486e16i		−	0.221085i
$204$	−4.97156e15	+	3.78103e16i	−0.0236737	+	0.180046i
$205$			2.01553e17i			0.925198i
$206$	−3.51123e17	−	2.29851e16i	−1.55401	−	0.101728i
$207$	−2.21695e17			−0.946189
$208$	8.45142e16	−	3.15822e17i	0.347900	−	1.30007i
$209$	5.59677e16			0.222249
$210$	1.22805e17	+	8.03902e15i	0.470512	+	0.0308005i
$211$			3.20233e17i			1.18399i	0.805942	+	0.591995i	$0.201660\pi$
$211$			3.20233e17i			1.18399i	−0.805942	+	0.591995i	$0.798340\pi$
$212$	−2.21042e16	+	1.68109e17i	−0.0788781	+	0.599892i
$213$		−	4.11435e16i		−	0.141727i
$214$	3.55625e16	−	5.43256e17i	0.118274	−	1.80676i
$215$	2.95361e17			0.948558
$216$	−5.42341e16	+	2.73002e17i	−0.168217	+	0.846763i
$217$	−1.73354e17			−0.519381
$218$	1.24218e16	−	1.89756e17i	0.0359550	−	0.549252i
$219$		−	2.36967e17i		−	0.662761i
$220$	9.25354e17	+	1.21672e17i	2.50114	+	0.328867i
$221$		−	1.90622e17i		−	0.498002i
$222$	−2.33388e17	−	1.52780e16i	−0.589429	−	0.0385851i
$223$	2.84887e17			0.695642			0.347821	−	0.937561i	$-0.386922\pi$
$223$	2.84887e17			0.695642			0.347821	+	0.937561i	$0.386922\pi$
$224$	2.31989e17	+	7.86445e16i	0.547782	+	0.185698i
$225$	−5.84889e17			−1.33569
$226$	3.43593e17	+	2.24922e16i	0.758982	+	0.0496843i
$227$			2.22335e17i			0.475132i	0.971371	+	0.237566i	$0.0763496\pi$
$227$			2.22335e17i			0.475132i	−0.971371	+	0.237566i	$0.923650\pi$
$228$	3.44381e16	+	4.52816e15i	0.0712079	+	0.00936291i
$229$			1.88161e17i			0.376499i	0.982121	+	0.188250i	$0.0602814\pi$
$229$			1.88161e17i			0.376499i	−0.982121	+	0.188250i	$0.939719\pi$
$230$	−6.98344e16	+	1.06680e18i	−0.135242	+	2.06596i
$231$	−2.29949e17			−0.431064
$232$	4.10385e16	−	2.06578e17i	0.0744787	−	0.374908i
$233$	−4.12831e17			−0.725442			−0.362721	−	0.931898i	$-0.618152\pi$
$233$	−4.12831e17			−0.725442			−0.362721	+	0.931898i	$0.618152\pi$
$234$	3.92193e16	−	5.99117e17i	0.0667392	−	1.01951i
$235$		−	8.53666e17i		−	1.40695i
$236$	1.09118e17	−	8.29880e17i	0.174204	−	1.32488i
$237$			1.34617e17i			0.208203i
$238$	1.42519e17	+	9.32956e15i	0.213573	+	0.0139809i
$239$	6.47168e17			0.939795			0.469897	−	0.882721i	$-0.344291\pi$
$239$	6.47168e17			0.939795			0.469897	+	0.882721i	$0.344291\pi$
$240$	5.59545e17	+	1.49735e17i	0.787501	+	0.210736i
$241$	−2.19632e17			−0.299618			−0.149809	−	0.988715i	$-0.547866\pi$
$241$	−2.19632e17			−0.299618			−0.149809	+	0.988715i	$0.547866\pi$
$242$	−9.85611e17	−	6.45199e16i	−1.30344	−	0.0853254i
$243$			8.01717e17i			1.02795i
$244$	−3.73429e16	+	2.84004e17i	−0.0464284	+	0.353103i
$245$			9.16792e17i			1.10541i
$246$	1.52672e16	−	2.33223e17i	0.0178544	−	0.272746i
$247$	−1.73621e17			−0.196959
$248$	−8.00274e17	−	1.58981e17i	−0.880747	−	0.174968i
$249$	−2.88279e17			−0.307835
$250$	−7.95241e16	+	1.21482e18i	−0.0824040	+	1.25881i
$251$		−	2.91655e17i		−	0.293303i	−0.989188	−	0.146652i	$-0.953150\pi$
$251$		−	2.91655e17i		−	0.293303i	0.989188	−	0.146652i	$-0.0468497\pi$
$252$	4.46013e17	+	5.86449e16i	0.435355	+	0.0572435i
$253$		−	1.99755e18i		−	1.89275i
$254$	−8.23620e17	−	5.39156e16i	−0.757659	−	0.0495977i
$255$	3.37727e17			0.301658
$256$	9.98834e17	+	5.75811e17i	0.866351	+	0.499436i
$257$	8.57227e17			0.722101			0.361050	−	0.932546i	$-0.382418\pi$
$257$	8.57227e17			0.722101			0.361050	+	0.932546i	$0.382418\pi$
$258$	−3.41771e17	−	2.23729e16i	−0.279632	−	0.0183052i
$259$			8.75946e17i			0.696192i
$260$	−2.87060e18	−	3.77447e17i	−2.21652	−	0.291444i
$261$		−	3.86784e17i		−	0.290178i
$262$	1.20629e17	−	1.84274e18i	0.0879411	−	1.34340i
$263$	3.80213e17			0.269376			0.134688	−	0.990888i	$-0.456997\pi$
$263$	3.80213e17			0.269376			0.134688	+	0.990888i	$0.456997\pi$
$264$	−1.06154e18	−	2.10884e17i	−0.730982	−	0.145216i
$265$	1.50158e18			1.00509
$266$	8.49749e15	−	1.29808e17i	0.00552941	−	0.0844677i
$267$			1.23030e18i			0.778352i
$268$	−2.87078e17	+	2.18332e18i	−0.176600	+	1.34310i
$269$			1.59898e18i			0.956536i	0.878214	+	0.478268i	$0.158735\pi$
$269$			1.59898e18i			0.956536i	−0.878214	+	0.478268i	$0.841265\pi$
$270$	2.45966e18	+	1.61014e17i	1.43102	+	0.0936774i
$271$	−4.79907e17			−0.271574			−0.135787	−	0.990738i	$-0.543356\pi$
$271$	−4.79907e17			−0.271574			−0.135787	+	0.990738i	$0.543356\pi$
$272$	6.49372e17	+	1.73772e17i	0.357459	+	0.0956563i
$273$	7.13339e17			0.382011
$274$	1.81775e17	+	1.18993e16i	0.0947121	+	0.00620002i
$275$		−	5.27006e18i		−	2.67190i
$276$	1.61615e17	−	1.22913e18i	0.0797377	−	0.606430i
$277$			6.67858e17i			0.320690i	0.987061	+	0.160345i	$0.0512607\pi$
$277$			6.67858e17i			0.320690i	−0.987061	+	0.160345i	$0.948739\pi$
$278$	−8.30557e16	+	1.26877e18i	−0.0388180	+	0.592988i
$279$	−1.49838e18			−0.681698
$280$	4.22694e17	−	2.12774e18i	0.187215	−	0.942396i
$281$	4.04339e18			1.74361			0.871803	−	0.489857i	$-0.162951\pi$
$281$	4.04339e18			1.74361			0.871803	+	0.489857i	$0.162951\pi$
$282$	−6.46634e16	+	9.87803e17i	−0.0271513	+	0.414765i
$283$			1.73833e18i			0.710777i	0.934719	+	0.355388i	$0.115651\pi$
$283$			1.73833e18i			0.710777i	−0.934719	+	0.355388i	$0.884349\pi$
$284$	−7.19049e17	−	9.45457e16i	−0.286333	−	0.0376491i
$285$		−	3.07606e17i		−	0.119305i
$286$	5.39826e18	+	3.53380e17i	2.03943	+	0.133505i
$287$	−8.75326e17			−0.322148
$288$	2.00520e18	+	6.79764e17i	0.718975	+	0.243733i
$289$	−2.47048e18			−0.863073
$290$	−1.86121e18	−	1.21838e17i	−0.633591	−	0.0414760i
$291$			8.95661e17i			0.297130i
$292$	−4.14138e18	−	5.44538e17i	−1.33898	−	0.176058i
$293$		−	8.46641e17i		−	0.266804i	−0.991062	−	0.133402i	$-0.957410\pi$
$293$		−	8.46641e17i		−	0.266804i	0.991062	−	0.133402i	$-0.0425901\pi$
$294$	6.94450e16	−	1.06085e18i	0.0213322	−	0.325873i
$295$	−7.41261e18			−2.21976
$296$	−8.03323e17	+	4.04373e18i	−0.234532	+	1.18058i
$297$	−4.60566e18			−1.31105
$298$	3.37383e17	−	5.15390e18i	0.0936487	−	1.43059i
$299$			6.19673e18i			1.67737i
$300$	4.26383e17	−	3.24277e18i	0.112562	−	0.856066i
$301$			1.28273e18i			0.330282i
$302$	5.15083e17	+	3.37183e16i	0.129368	+	0.00846863i
$303$	−2.22922e18			−0.546177
$304$	1.58274e17	−	5.91457e17i	0.0378319	−	0.141374i
$305$	2.53677e18			0.591605
$306$	1.23186e18	+	8.06400e16i	0.280319	+	0.0183502i
$307$		−	2.23744e18i		−	0.496836i	−0.968653	−	0.248418i	$-0.920089\pi$
$307$		−	2.23744e18i		−	0.496836i	0.968653	−	0.248418i	$-0.0799106\pi$
$308$	−5.28411e17	+	4.01873e18i	−0.114510	+	0.870881i
$309$		−	3.61354e18i		−	0.764265i
$310$	−4.71994e17	+	7.21023e18i	−0.0974371	+	1.48846i
$311$	8.89953e18			1.79335			0.896673	−	0.442694i	$-0.145977\pi$
$311$	8.89953e18			1.79335			0.896673	+	0.442694i	$0.145977\pi$
$312$	3.29307e18	+	6.54197e17i	0.647801	+	0.128691i
$313$	−4.42301e18			−0.849445			−0.424722	−	0.905324i	$-0.639628\pi$
$313$	−4.42301e18			−0.849445			−0.424722	+	0.905324i	$0.639628\pi$
$314$	−1.12335e17	+	1.71605e18i	−0.0210642	+	0.321778i
$315$		−	3.98385e18i		−	0.729414i
$316$	2.35265e18	+	3.09343e17i	0.420634	+	0.0553080i
$317$		−	7.11739e18i		−	1.24273i	−0.783522	−	0.621364i	$-0.786579\pi$
$317$		−	7.11739e18i		−	1.24273i	0.783522	−	0.621364i	$-0.213421\pi$
$318$	−1.73752e18	−	1.13741e17i	−0.296297	−	0.0193961i
$319$	3.48506e18			0.580471
$320$	3.90266e18	−	9.43488e18i	0.634945	−	1.53501i
$321$	5.59086e18			0.888568
$322$	−4.63300e18	−	3.03285e17i	−0.719355	−	0.0470903i
$323$		−	3.56988e17i		−	0.0541545i
$324$	2.24414e18	+	2.95076e17i	0.332631	+	0.0437367i
$325$			1.63486e19i			2.36785i
$326$	7.20028e17	−	1.09992e19i	0.101910	−	1.55679i
$327$	1.95285e18			0.270122
$328$	−4.04087e18	−	8.02754e17i	−0.546287	−	0.108525i
$329$	3.70740e18			0.489891
$330$	−6.26086e17	+	9.56415e18i	−0.0808686	+	1.23536i
$331$		−	6.49509e18i		−	0.820116i	−0.912060	−	0.410058i	$-0.865509\pi$
$331$		−	6.49509e18i		−	0.820116i	0.912060	−	0.410058i	$-0.134491\pi$
$332$	−6.62451e17	+	5.03814e18i	−0.0817745	+	0.621921i
$333$			7.57124e18i			0.913766i
$334$	−1.03998e19	−	6.80787e17i	−1.22723	−	0.0803364i
$335$	1.95018e19			2.25029
$336$	−6.50285e17	+	2.43006e18i	−0.0733768	+	0.274203i
$337$	−8.36981e18			−0.923616			−0.461808	−	0.886980i	$-0.652799\pi$
$337$	−8.36981e18			−0.923616			−0.461808	+	0.886980i	$0.652799\pi$
$338$	−7.50044e18	−	4.90992e17i	−0.809490	−	0.0529906i
$339$			3.53605e18i			0.373268i
$340$	7.76080e17	−	5.90233e18i	0.0801336	−	0.609441i
$341$		−	1.35010e19i		−	1.36366i
$342$	7.34480e16	−	1.12200e18i	0.00725746	−	0.110866i
$343$	−9.96478e18			−0.963300
$344$	−1.17638e18	+	5.92159e18i	−0.111265	+	0.560080i
$345$	−1.09788e19			−1.01604
$346$	2.55848e17	−	3.90835e18i	0.0231692	−	0.353935i
$347$			5.36645e18i			0.475572i	0.971318	+	0.237786i	$0.0764216\pi$
$347$			5.36645e18i			0.475572i	−0.971318	+	0.237786i	$0.923578\pi$
$348$	2.14443e18	+	2.81965e17i	0.185981	+	0.0244540i
$349$		−	1.57562e19i		−	1.33740i	−0.743534	−	0.668699i	$-0.766852\pi$
$349$		−	1.57562e19i		−	1.33740i	0.743534	−	0.668699i	$-0.233148\pi$
$350$	−1.22231e19	−	8.00144e17i	−1.01548	−	0.0664749i
$351$	1.42875e19			1.16186
$352$	−6.12491e18	+	1.80675e19i	−0.487562	+	1.43823i
$353$	−9.01560e18			−0.702561			−0.351281	−	0.936270i	$-0.614254\pi$
$353$	−9.01560e18			−0.702561			−0.351281	+	0.936270i	$0.614254\pi$
$354$	8.57737e18	+	5.61490e17i	0.654379	+	0.0428368i
$355$			6.42266e18i			0.479736i
$356$	2.15015e19	+	2.82717e18i	1.57251	+	0.206765i
$357$			1.46672e18i			0.105035i
$358$	−7.68216e17	+	1.17353e19i	−0.0538717	+	0.822949i
$359$	−1.68743e19			−1.15882			−0.579412	−	0.815035i	$-0.696718\pi$
$359$	−1.68743e19			−1.15882			−0.579412	+	0.815035i	$0.696718\pi$
$360$	3.65356e18	−	1.83911e19i	0.245724	−	1.23691i
$361$	1.48560e19			0.978582
$362$	7.48730e17	−	1.14377e19i	0.0483071	−	0.737943i
$363$		−	1.01433e19i		−	0.641032i
$364$	1.63922e18	−	1.24668e19i	0.101479	−	0.771780i
$365$			3.69914e19i			2.24339i
$366$	−2.93537e18	−	1.92155e17i	−0.174403	−	0.0114168i
$367$	−1.10764e19			−0.644768			−0.322384	−	0.946609i	$-0.604484\pi$
$367$	−1.10764e19			−0.644768			−0.322384	+	0.946609i	$0.604484\pi$
$368$	−2.11097e19	−	5.64898e18i	−1.20399	−	0.322189i
$369$	−7.56588e18			−0.422826
$370$	3.64328e19	+	2.38496e18i	1.99517	+	0.130607i
$371$			6.52123e18i			0.349965i
$372$	1.09232e18	−	8.30743e18i	0.0574483	−	0.436913i
$373$		−	2.00597e19i		−	1.03397i	−0.855995	−	0.516984i	$-0.827055\pi$
$373$		−	2.00597e19i		−	1.03397i	0.855995	−	0.516984i	$-0.172945\pi$
$374$	−7.26595e17	+	1.10995e19i	−0.0367076	+	0.560748i
$375$	−1.25021e19			−0.619084
$376$	1.71149e19	+	3.40002e18i	0.830740	+	0.165034i
$377$	−1.08112e19			−0.514417
$378$	−6.99269e17	+	1.06821e19i	−0.0326179	+	0.498274i
$379$		−	1.03163e19i		−	0.471770i	−0.971781	−	0.235885i	$-0.924201\pi$
$379$		−	1.03163e19i		−	0.471770i	0.971781	−	0.235885i	$-0.0757988\pi$
$380$	−5.37592e18	−	7.06864e17i	−0.241033	−	0.0316927i
$381$		−	8.47618e18i		−	0.372617i
$382$	1.37608e19	+	9.00804e17i	0.593154	+	0.0388289i
$383$	1.58453e18			0.0669744			0.0334872	−	0.999439i	$-0.489339\pi$
$383$	1.58453e18			0.0669744			0.0334872	+	0.999439i	$0.489339\pi$
$384$	−5.23057e18	+	1.06218e19i	−0.216803	+	0.440264i
$385$	3.58959e19			1.45911
$386$	2.38006e19	+	1.55803e18i	0.948818	+	0.0621113i
$387$			1.10872e19i			0.433502i
$388$	1.56531e19	+	2.05818e18i	0.600293	+	0.0789308i
$389$		−	1.37817e18i		−	0.0518420i	−0.999664	−	0.0259210i	$-0.991748\pi$
$389$		−	1.37817e18i		−	0.0518420i	0.999664	−	0.0259210i	$-0.00825183\pi$
$390$	1.94222e18	−	2.96696e19i	0.0716662	−	1.09478i
$391$	−1.27413e19			−0.461198
$392$	−1.83805e19	−	3.65144e18i	−0.652697	−	0.129664i
$393$	1.89643e19			0.660683
$394$	1.63476e18	−	2.49727e19i	0.0558768	−	0.853579i
$395$		−	2.10142e19i		−	0.704751i
$396$	−4.56732e18	+	3.47359e19i	−0.150296	+	1.14305i
$397$			2.02566e19i			0.654092i	0.945008	+	0.327046i	$0.106053\pi$
$397$			2.02566e19i			0.654092i	−0.945008	+	0.327046i	$0.893947\pi$
$398$	−1.94665e18	−	1.27431e17i	−0.0616830	−	0.00403788i
$399$	1.33591e18			0.0415413
$400$	−5.56930e19	−	1.49035e19i	−1.69961	−	0.454818i
$401$	−9.25607e17			−0.0277232			−0.0138616	−	0.999904i	$-0.504412\pi$
$401$	−9.25607e17			−0.0277232			−0.0138616	+	0.999904i	$0.504412\pi$
$402$	−2.25661e19	−	1.47722e18i	−0.663378	−	0.0434259i
$403$			4.18822e19i			1.20849i
$404$	−5.12264e18	+	3.89593e19i	−0.145089	+	1.10345i
$405$		−	2.00450e19i		−	0.557306i
$406$	5.29131e17	−	8.08305e18i	0.0144417	−	0.220613i
$407$	−6.82195e19			−1.82789
$408$	−1.34512e18	+	6.77098e18i	−0.0353841	+	0.178115i
$409$	4.94945e19			1.27830			0.639148	−	0.769083i	$-0.279287\pi$
$409$	4.94945e19			1.27830			0.639148	+	0.769083i	$0.279287\pi$
$410$	−2.38327e18	+	3.64070e19i	−0.0604357	+	0.923222i
$411$			1.87072e18i			0.0465795i
$412$	−6.31525e19	−	8.30373e18i	−1.54405	−	0.203022i
$413$		−	3.21923e19i		−	0.772907i
$414$	−4.00454e19	−	2.62144e18i	−0.944169	−	0.0618070i
$415$	4.50015e19			1.04200
$416$	1.90005e19	−	5.60485e19i	0.432080	−	1.27457i
$417$	−1.30574e19			−0.291632
$418$	1.01096e19	+	6.61793e17i	0.221775	+	0.0145178i
$419$		−	6.22046e19i		−	1.34035i	−0.742205	−	0.670173i	$-0.766220\pi$
$419$		−	6.22046e19i		−	1.34035i	0.742205	−	0.670173i	$-0.233780\pi$
$420$	2.20875e19	+	2.90422e18i	0.467495	+	0.0614695i
$421$			3.79369e19i			0.788762i	0.918947	+	0.394381i	$0.129041\pi$
$421$			3.79369e19i			0.788762i	−0.918947	+	0.394381i	$0.870959\pi$
$422$	−3.78661e18	+	5.78446e19i	−0.0773406	+	1.18146i
$423$	3.20449e19			0.642992
$424$	−5.98056e18	+	3.01047e19i	−0.117896	+	0.593459i
$425$	−3.36148e19			−0.651049
$426$	4.86503e17	−	7.43186e18i	0.00925792	−	0.141425i
$427$			1.10170e19i			0.205993i
$428$	1.28475e19	−	9.77094e19i	0.236043	−	1.79518i
$429$			5.55555e19i			1.00299i
$430$	5.33518e19	+	3.49250e18i	0.946532	+	0.0619617i
$431$	9.10237e19			1.58699			0.793497	−	0.608574i	$-0.208258\pi$
$431$	9.10237e19			1.58699			0.793497	+	0.608574i	$0.208258\pi$
$432$	−1.30246e19	+	4.86717e19i	−0.223170	+	0.833966i
$433$	7.12134e19			1.19923			0.599615	−	0.800288i	$-0.295320\pi$
$433$	7.12134e19			1.19923			0.599615	+	0.800288i	$0.295320\pi$
$434$	−3.13134e19	−	2.04983e18i	−0.518271	−	0.0339270i
$435$		−	1.91544e19i		−	0.311601i
$436$	4.48755e18	−	3.41292e19i	0.0717564	−	0.545730i
$437$			1.16049e19i			0.182403i
$438$	2.80202e18	−	4.28040e19i	0.0432928	−	0.661345i
$439$	−5.81164e19			−0.882704			−0.441352	−	0.897334i	$-0.645501\pi$
$439$	−5.81164e19			−0.882704			−0.441352	+	0.897334i	$0.645501\pi$
$440$	1.65710e20	+	3.29198e19i	2.47431	+	0.491544i
$441$	−3.44145e19			−0.505187
$442$	2.25402e18	−	3.44326e19i	0.0325305	−	0.496938i
$443$			1.24589e20i			1.76788i	0.467605	+	0.883938i	$0.345117\pi$
$443$			1.24589e20i			1.76788i	−0.467605	+	0.883938i	$0.654883\pi$
$444$	−4.19769e19	−	5.51942e18i	−0.585650	−	0.0770054i
$445$		−	1.92054e20i		−	2.63466i
$446$	5.14599e19	+	3.36866e18i	0.694156	+	0.0454407i
$447$	5.30407e19			0.703563
$448$	4.09749e19	+	1.69489e19i	0.534482	+	0.221084i
$449$	−1.49517e20			−1.91797			−0.958985	−	0.283456i	$-0.908519\pi$
$449$	−1.49517e20			−1.91797			−0.958985	+	0.283456i	$0.908519\pi$
$450$	−1.05650e20	−	6.91604e18i	−1.33283	−	0.0872497i
$451$		−	6.81712e19i		−	0.845818i
$452$	6.17983e19	+	8.12567e18i	0.754116	+	0.0991564i
$453$			5.30092e18i			0.0636230i
$454$	−2.62901e18	+	4.01610e19i	−0.0310366	+	0.474117i
$455$	−1.11355e20			−1.29308
$456$	6.16711e18	+	1.22515e18i	0.0704442	+	0.0139944i
$457$	−9.69974e19			−1.08990			−0.544952	−	0.838467i	$-0.683452\pi$
$457$	−9.69974e19			−1.08990			−0.544952	+	0.838467i	$0.683452\pi$
$458$	−2.22492e18	+	3.39881e19i	−0.0245937	+	0.375695i
$459$			2.93770e19i			0.319457i
$460$	−2.52287e19	+	1.91872e20i	−0.269906	+	2.05272i
$461$			1.55135e20i			1.63288i	0.577431	+	0.816439i	$0.304055\pi$
$461$			1.55135e20i			1.63288i	−0.577431	+	0.816439i	$0.695945\pi$
$462$	−4.15363e19	−	2.71904e18i	−0.430143	−	0.0281579i
$463$	8.54675e19			0.870850			0.435425	−	0.900225i	$-0.356598\pi$
$463$	8.54675e19			0.870850			0.435425	+	0.900225i	$0.356598\pi$
$464$	9.85559e18	−	3.68295e19i	0.0988093	−	0.369242i
$465$	−7.42032e19			−0.732024
$466$	−7.45707e19	−	4.88153e18i	−0.723892	−	0.0473873i
$467$		−	8.76389e19i		−	0.837183i	−0.908175	−	0.418591i	$-0.862524\pi$
$467$		−	8.76389e19i		−	0.837183i	0.908175	−	0.418591i	$-0.137476\pi$
$468$	1.41686e19	−	1.07756e20i	0.133193	−	1.01298i
$469$			8.46944e19i			0.783535i
$470$	1.00942e19	−	1.54200e20i	0.0919048	−	1.40395i
$471$	−1.76605e19			−0.158251
$472$	2.95233e19	−	1.48613e20i	0.260376	−	1.31067i
$473$	−9.98999e19			−0.867174
$474$	−1.59178e18	+	2.43162e19i	−0.0136002	+	0.207759i
$475$			3.06168e19i			0.257489i
$476$	2.56333e19	+	3.37045e18i	0.212203	+	0.0279020i
$477$			5.63662e19i			0.459337i
$478$	1.16900e20	+	7.65247e18i	0.937788	+	0.0613892i
$479$	1.65573e20			1.30759			0.653797	−	0.756670i	$-0.273175\pi$
$479$	1.65573e20			1.30759			0.653797	+	0.756670i	$0.273175\pi$
$480$	9.93016e19	+	3.36633e19i	0.772053	+	0.261727i
$481$	2.11628e20			1.61989
$482$	−3.96727e19	−	2.59705e18i	−0.298978	−	0.0195716i
$483$		−	4.76800e19i		−	0.353780i
$484$	−1.77271e20	−	2.33088e19i	−1.29508	−	0.170286i
$485$		−	1.39816e20i		−	1.00576i
$486$	−9.47993e18	+	1.44816e20i	−0.0671480	+	1.02576i
$487$	−2.31728e20			−1.61626			−0.808131	−	0.589003i	$-0.799521\pi$
$487$	−2.31728e20			−1.61626			−0.808131	+	0.589003i	$0.799521\pi$
$488$	−1.01036e19	+	5.08589e19i	−0.0693946	+	0.349316i
$489$	1.13197e20			0.765629
$490$	−1.08406e19	+	1.65603e20i	−0.0722078	+	1.10305i
$491$		−	4.55837e19i		−	0.299019i	−0.988760	−	0.149509i	$-0.952231\pi$
$491$		−	4.55837e19i		−	0.299019i	0.988760	−	0.149509i	$-0.0477694\pi$
$492$	5.51551e18	−	4.19472e19i	0.0356326	−	0.270997i
$493$		−	2.22293e19i		−	0.141441i
$494$	−3.13617e19	−	2.05299e18i	−0.196538	−	0.0128657i
$495$	3.10266e20			1.91512
$496$	−1.42676e20	−	3.81801e19i	−0.867437	−	0.232127i
$497$	−2.78930e19			−0.167041
$498$	−5.20726e19	−	3.40877e18i	−0.307177	−	0.0201084i
$499$			8.94164e19i			0.519593i	0.965663	+	0.259796i	$0.0836554\pi$
$499$			8.94164e19i			0.519593i	−0.965663	+	0.259796i	$0.916345\pi$
$500$	−2.87293e19	+	2.18495e20i	−0.164456	+	1.25074i
$501$		−	1.07028e20i		−	0.603551i
$502$	3.44869e18	−	5.26825e19i	0.0191592	−	0.292677i
$503$	−7.58265e19			−0.415012			−0.207506	−	0.978234i	$-0.566535\pi$
$503$	−7.58265e19			−0.415012			−0.207506	+	0.978234i	$0.566535\pi$
$504$	7.98710e19	+	1.58671e19i	0.430686	+	0.0855595i
$505$	3.47990e20			1.84876
$506$	2.36201e19	−	3.60823e20i	0.123638	−	1.88871i
$507$		−	7.71898e19i		−	0.398108i
$508$	−1.48135e20	−	1.94779e19i	−0.752801	−	0.0989836i
$509$		−	2.19542e20i		−	1.09934i	−0.835381	−	0.549672i	$-0.814753\pi$
$509$		−	2.19542e20i		−	1.09934i	0.835381	−	0.549672i	$-0.185247\pi$
$510$	6.10045e19	+	3.99347e18i	0.301013	+	0.0197049i
$511$	−1.60651e20			−0.781134
$512$	1.73613e20	+	1.15821e20i	0.831876	+	0.554962i
$513$	2.67570e19			0.126345
$514$	1.54843e20	+	1.01363e19i	0.720558	+	0.0471690i
$515$			5.64087e20i			2.58697i
$516$	−6.14705e19	−	8.08257e18i	−0.277839	−	0.0365323i
$517$			2.88736e20i			1.28624i
$518$	−1.03577e19	+	1.58225e20i	−0.0454767	+	0.694705i
$519$	4.02223e19			0.174065
$520$	−5.14061e20	−	1.02123e20i	−2.19275	−	0.435609i
$521$	−2.44441e19			−0.102776			−0.0513879	−	0.998679i	$-0.516364\pi$
$521$	−2.44441e19			−0.102776			−0.0513879	+	0.998679i	$0.516364\pi$
$522$	4.57354e18	−	6.98659e19i	0.0189550	−	0.289558i
$523$		−	2.97518e20i		−	1.21549i	−0.794133	−	0.607744i	$-0.792075\pi$
$523$		−	2.97518e20i		−	1.21549i	0.794133	−	0.607744i	$-0.207925\pi$
$524$	4.35791e19	−	3.31433e20i	0.175507	−	1.33478i
$525$		−	1.25792e20i		−	0.499412i
$526$	6.86788e19	+	4.49584e18i	0.268800	+	0.0175962i
$527$	−8.61154e19			−0.332278
$528$	−1.89255e20	−	5.06448e19i	−0.719935	−	0.192655i
$529$	1.47557e20			0.553406
$530$	2.71234e20	+	1.77555e19i	1.00294	+	0.0656543i
$531$		−	2.78254e20i		−	1.01446i
$532$	3.06985e18	−	2.33472e19i	0.0110352	−	0.0839261i
$533$			2.11478e20i			0.749569i
$534$	−1.45477e19	+	2.22232e20i	−0.0508435	+	0.776690i
$535$	−8.72755e20			−3.00773
$536$	−7.76725e19	+	3.90985e20i	−0.263956	+	1.32869i
$537$	−1.20773e20			−0.404727
$538$	−1.89072e19	+	2.88828e20i	−0.0624828	+	0.954493i
$539$		−	3.10087e20i		−	1.01057i
$540$	4.42391e20	+	5.81687e19i	1.42185	+	0.186955i
$541$			2.64565e20i			0.838596i	0.907849	+	0.419298i	$0.137724\pi$
$541$			2.64565e20i			0.838596i	−0.907849	+	0.419298i	$0.862276\pi$
$542$	−8.66870e19	−	5.67469e18i	−0.270994	−	0.0177397i
$543$	1.17709e20			0.362921
$544$	1.15243e20	+	3.90675e19i	0.350447	+	0.118802i
$545$	−3.04847e20			−0.914342
$546$	1.28852e20	+	8.43491e18i	0.381195	+	0.0249537i
$547$			2.07387e20i			0.605169i	0.953123	+	0.302584i	$0.0978494\pi$
$547$			2.07387e20i			0.605169i	−0.953123	+	0.302584i	$0.902151\pi$
$548$	3.26939e19	+	4.29882e18i	0.0941048	+	0.0123736i
$549$			9.52251e19i			0.270370i
$550$	6.23160e19	−	9.51944e20i	0.174534	−	2.66619i
$551$	−2.02468e19			−0.0559395
$552$	4.37269e19	−	2.20111e20i	0.119181	−	0.599927i
$553$	9.12630e19			0.245390
$554$	−7.89711e18	+	1.20637e20i	−0.0209481	+	0.320005i
$555$			3.74944e20i			0.981225i
$556$	−3.00052e19	+	2.28199e20i	−0.0774703	+	0.589186i
$557$		−	3.53993e20i		−	0.901738i	−0.892590	−	0.450869i	$-0.851114\pi$
$557$		−	3.53993e20i		−	0.901738i	0.892590	−	0.450869i	$-0.148886\pi$
$558$	−2.70657e20	−	1.77177e19i	−0.680242	−	0.0445298i
$559$	3.09906e20			0.768495
$560$	1.01512e20	−	3.79341e20i	0.248374	−	0.928154i
$561$	−1.14229e20			−0.275776
$562$	7.30368e20	+	4.78112e19i	1.73988	+	0.113896i
$563$		−	1.16560e20i		−	0.273992i	−0.990572	−	0.136996i	$-0.956255\pi$
$563$		−	1.16560e20i		−	0.273992i	0.990572	−	0.136996i	$-0.0437447\pi$
$564$	−2.33606e19	+	1.77665e20i	−0.0541866	+	0.412106i
$565$		−	5.51991e20i		−	1.26348i
$566$	−2.05549e19	+	3.13999e20i	−0.0464294	+	0.709259i
$567$	8.70538e19			0.194050
$568$	−1.28766e20	−	2.55805e19i	−0.283262	−	0.0562725i
$569$	1.44331e20			0.313341			0.156670	−	0.987651i	$-0.449924\pi$
$569$	1.44331e20			0.313341			0.156670	+	0.987651i	$0.449924\pi$
$570$	3.63730e18	−	5.55638e19i	0.00779324	−	0.119050i
$571$			2.46922e20i			0.522142i	0.965320	+	0.261071i	$0.0840756\pi$
$571$			2.46922e20i			0.522142i	−0.965320	+	0.261071i	$0.915924\pi$
$572$	9.70924e20	+	1.27664e20i	2.02635	+	0.266439i
$573$			1.41617e20i			0.291714i
$574$	−1.58112e20	−	1.03503e19i	−0.321460	−	0.0210433i
$575$	1.09275e21			2.19286
$576$	3.54166e20	+	1.46498e20i	0.701518	+	0.290177i
$577$	1.52447e20			0.298059			0.149029	−	0.988833i	$-0.452385\pi$
$577$	1.52447e20			0.298059			0.149029	+	0.988833i	$0.452385\pi$
$578$	−4.46249e20	−	2.92123e19i	−0.861229	−	0.0563776i
$579$			2.44941e20i			0.466630i
$580$	−3.34754e20	−	4.40158e19i	−0.629529	−	0.0827749i
$581$			1.95437e20i			0.362816i
$582$	−1.05908e19	+	1.61786e20i	−0.0194091	+	0.296495i
$583$	−5.07880e20			−0.918854
$584$	−7.41630e20	−	1.47331e20i	−1.32462	−	0.263147i
$585$	−9.62497e20			−1.69719
$586$	1.00111e19	−	1.52931e20i	0.0174281	−	0.266234i
$587$		−	7.28116e20i		−	1.25145i	−0.780042	−	0.625727i	$-0.784802\pi$
$587$		−	7.28116e20i		−	1.25145i	0.780042	−	0.625727i	$-0.215198\pi$
$588$	2.50881e19	−	1.90803e20i	0.0425733	−	0.323784i
$589$			7.84351e19i			0.131415i
$590$	−1.33896e21	−	8.76507e19i	−2.21502	−	0.144999i
$591$	2.57004e20			0.419791
$592$	−1.92922e20	+	7.20931e20i	−0.311149	+	1.16274i
$593$	6.32845e19			0.100783			0.0503915	−	0.998730i	$-0.483953\pi$
$593$	6.32845e19			0.100783			0.0503915	+	0.998730i	$0.483953\pi$
$594$	−8.31932e20	−	5.44598e19i	−1.30825	−	0.0856402i
$595$		−	2.28960e20i		−	0.355536i
$596$	1.21885e20	−	9.26973e20i	0.186897	−	1.42141i
$597$		−	2.00337e19i		−	0.0303357i
$598$	−7.32734e19	+	1.11933e21i	−0.109569	+	1.67379i
$599$	7.33623e20			1.08336			0.541679	−	0.840586i	$-0.317789\pi$
$599$	7.33623e20			1.08336			0.541679	+	0.840586i	$0.317789\pi$
$600$	1.15363e20	−	5.80709e20i	0.168241	−	0.846885i
$601$	−1.96003e20			−0.282295			−0.141148	−	0.989989i	$-0.545079\pi$
$601$	−1.96003e20			−0.282295			−0.141148	+	0.989989i	$0.545079\pi$
$602$	−1.51676e19	+	2.31702e20i	−0.0215747	+	0.329577i
$603$			7.32056e20i			1.02841i
$604$	9.26422e19	+	1.21812e19i	0.128538	+	0.0169011i
$605$			1.58341e21i			2.16984i
$606$	−4.02670e20	−	2.63595e19i	−0.545011	−	0.0356774i
$607$	2.86277e20			0.382711			0.191356	−	0.981521i	$-0.438712\pi$
$607$	2.86277e20			0.382711			0.191356	+	0.981521i	$0.438712\pi$
$608$	3.55832e19	−	1.04965e20i	0.0469860	−	0.138601i
$609$	8.31858e19			0.108497
$610$	4.58223e20	+	2.99961e19i	0.590341	+	0.0386448i
$611$		−	8.95705e20i		−	1.13987i
$612$	2.21561e20	+	2.91325e19i	0.278521	+	0.0366219i
$613$		−	1.49673e21i		−	1.85862i	−0.369303	−	0.929309i	$-0.620404\pi$
$613$		−	1.49673e21i		−	1.85862i	0.369303	−	0.929309i	$-0.379596\pi$
$614$	2.64567e19	−	4.04154e20i	0.0324543	−	0.495775i
$615$	−3.74678e20			−0.454041
$616$	−1.42968e20	+	7.19666e20i	−0.171153	+	0.861541i
$617$	2.70955e20			0.320448			0.160224	−	0.987081i	$-0.448778\pi$
$617$	2.70955e20			0.320448			0.160224	+	0.987081i	$0.448778\pi$
$618$	4.27284e19	−	6.52723e20i	0.0499233	−	0.762633i
$619$		−	9.61598e19i		−	0.110998i	−0.998459	−	0.0554988i	$-0.982325\pi$
$619$		−	9.61598e19i		−	0.110998i	0.998459	−	0.0554988i	$-0.0176749\pi$
$620$	−1.70515e20	+	1.29682e21i	−0.194458	+	1.47891i
$621$		−	9.54985e20i		−	1.07599i
$622$	1.60755e21	+	1.05233e20i	1.78952	+	0.117145i
$623$	8.34076e20			0.917371
$624$	5.87101e20	+	1.57108e20i	0.638011	+	0.170732i
$625$	3.13047e20			0.336132
$626$	−7.98940e20	−	5.23000e19i	−0.847630	−	0.0554874i
$627$			1.04042e20i			0.109069i
$628$	−4.05829e19	+	3.08646e20i	−0.0420384	+	0.319715i
$629$			4.35135e20i			0.445394i
$630$	4.71072e19	−	7.19614e20i	0.0476468	−	0.727856i
$631$	−6.38381e20			−0.638057			−0.319029	−	0.947745i	$-0.603357\pi$
$631$	−6.38381e20			−0.638057			−0.319029	+	0.947745i	$0.603357\pi$
$632$	4.21308e20	+	8.36966e19i	0.416123	+	0.0826665i
$633$	−5.95301e20			−0.581044
$634$	8.41598e19	−	1.28563e21i	0.0811775	−	1.24007i
$635$			1.32317e21i			1.26128i
$636$	−3.12509e20	−	4.10909e19i	−0.294397	−	0.0387094i
$637$			9.61940e20i			0.895575i
$638$	6.29516e20	+	4.12092e19i	0.579231	+	0.0379175i
$639$	−2.41093e20			−0.219245
$640$	8.16512e20	−	1.65810e21i	0.733859	−	1.49026i
$641$	−7.24707e20			−0.643765			−0.321882	−	0.946780i	$-0.604316\pi$
$641$	−7.24707e20			−0.643765			−0.321882	+	0.946780i	$0.604316\pi$
$642$	1.00989e21	+	6.61093e19i	0.886670	+	0.0580430i
$643$			2.26091e19i			0.0196201i	0.999952	+	0.00981006i	$0.00312269\pi$
$643$			2.26091e19i			0.0196201i	−0.999952	+	0.00981006i	$0.996877\pi$
$644$	−8.33286e20	−	1.09566e20i	−0.714743	−	0.0939794i
$645$			5.49063e20i			0.465505i
$646$	4.22122e18	−	6.44837e19i	0.00353748	−	0.0540388i
$647$	−1.14582e21			−0.949148			−0.474574	−	0.880215i	$-0.657398\pi$
$647$	−1.14582e21			−0.949148			−0.474574	+	0.880215i	$0.657398\pi$
$648$	4.01876e20	+	7.98363e19i	0.329064	+	0.0653714i
$649$	2.50717e21			2.02931
$650$	−1.93314e20	+	2.95309e21i	−0.154673	+	2.36280i
$651$		−	3.22258e20i		−	0.254886i
$652$	2.60121e20	−	1.97830e21i	0.203385	−	1.54681i
$653$		−	1.94286e21i		−	1.50173i	−0.660454	−	0.750866i	$-0.729636\pi$
$653$		−	1.94286e21i		−	1.50173i	0.660454	−	0.750866i	$-0.270364\pi$
$654$	3.52748e20	+	2.30915e19i	0.269545	+	0.0176449i
$655$	−2.96041e21			−2.23636
$656$	−7.20421e20	−	1.92785e20i	−0.538031	−	0.143977i
$657$	−1.38858e21			−1.02525
$658$	6.69677e20	+	4.38383e19i	0.488845	+	0.0320007i
$659$		−	8.62593e20i		−	0.622537i	−0.950322	−	0.311269i	$-0.899246\pi$
$659$		−	8.62593e20i		−	0.622537i	0.950322	−	0.311269i	$-0.100754\pi$
$660$	−2.26183e20	+	1.72020e21i	−0.161392	+	1.22743i
$661$			1.45427e21i			1.02597i	0.858398	+	0.512984i	$0.171460\pi$
$661$			1.45427e21i			1.02597i	−0.858398	+	0.512984i	$0.828540\pi$
$662$	7.68014e19	−	1.17323e21i	0.0535716	−	0.818364i
$663$	3.54359e20			0.244395
$664$	−1.79234e20	+	9.02221e20i	−0.122225	+	0.615251i
$665$	−2.08540e20			−0.140614
$666$	−8.95264e19	+	1.36761e21i	−0.0596890	+	0.911815i
$667$			7.22629e20i			0.476400i
$668$	−1.87049e21	−	2.45945e20i	−1.21936	−	0.160330i
$669$			5.29593e20i			0.341387i
$670$	3.52265e21	+	2.30599e20i	2.24548	+	0.146993i
$671$	−8.58011e20			−0.540847
$672$	−1.46197e20	+	4.31258e20i	−0.0911316	+	0.268824i
$673$	2.10999e21			1.30067			0.650336	−	0.759647i	$-0.274628\pi$
$673$	2.10999e21			1.30067			0.650336	+	0.759647i	$0.274628\pi$
$674$	−1.51186e21	−	9.89692e19i	−0.921643	−	0.0603324i
$675$		−	2.51950e21i		−	1.51892i
$676$	−1.34902e21	−	1.77378e20i	−0.804299	−	0.105755i
$677$		−	1.82037e21i		−	1.07336i	−0.843786	−	0.536680i	$-0.819678\pi$
$677$		−	1.82037e21i		−	1.07336i	0.843786	−	0.536680i	$-0.180322\pi$
$678$	−4.18122e19	+	6.38727e20i	−0.0243826	+	0.372471i
$679$	6.07209e20			0.350199
$680$	2.09978e20	−	1.05698e21i	0.119772	−	0.602905i
$681$	−4.13312e20			−0.233171
$682$	1.59643e20	−	2.43872e21i	0.0890772	−	1.36075i
$683$			1.88174e21i			1.03850i	0.854624	+	0.519248i	$0.173788\pi$
$683$			1.88174e21i			1.03850i	−0.854624	+	0.519248i	$0.826212\pi$
$684$	2.65342e19	−	2.01801e20i	0.0144839	−	0.110155i
$685$		−	2.92026e20i		−	0.157668i
$686$	−1.79996e21	−	1.17829e20i	−0.961243	−	0.0629247i
$687$	−3.49784e20			−0.184767
$688$	−2.82512e20	+	1.05572e21i	−0.147613	+	0.551616i
$689$	1.57553e21			0.814294
$690$	−1.98313e21	−	1.29819e20i	−1.01387	−	0.0663699i
$691$			3.50914e21i			1.77466i	0.461135	+	0.887330i	$0.347442\pi$
$691$			3.50914e21i			1.77466i	−0.461135	+	0.887330i	$0.652558\pi$
$692$	9.24290e19	−	7.02951e20i	0.0462394	−	0.351665i
$693$			1.34746e21i			0.666832i
$694$	−6.34558e19	+	9.69356e20i	−0.0310653	+	0.474556i
$695$	2.03830e21			0.987150
$696$	3.84020e20	+	7.62890e19i	0.183986	+	0.0365504i
$697$	−4.34827e20			−0.206097
$698$	1.86310e20	−	2.84608e21i	0.0873614	−	1.33454i
$699$		−	7.67436e20i		−	0.356011i
$700$	−2.19843e21	−	2.89064e20i	−1.00897	−	0.132666i
$701$		−	4.75438e20i		−	0.215878i	−0.994158	−	0.107939i	$-0.965575\pi$
$701$		−	4.75438e20i		−	0.215878i	0.994158	−	0.107939i	$-0.0344251\pi$
$702$	2.58079e21	+	1.68943e20i	1.15938	+	0.0758948i
$703$	3.96327e20			0.176153
$704$	−1.32000e21	+	3.19116e21i	−0.580469	+	1.40331i
$705$	1.58693e21			0.690461
$706$	−1.62851e21	−	1.06605e20i	−0.701061	−	0.0458927i
$707$			1.51129e21i			0.643728i
$708$	1.54271e21	+	2.02847e20i	0.650184	+	0.0854907i
$709$		−	2.02240e21i		−	0.843373i	−0.906742	−	0.421687i	$-0.861438\pi$
$709$		−	2.02240e21i		−	0.843373i	0.906742	−	0.421687i	$-0.138562\pi$
$710$	−7.59449e19	+	1.16014e21i	−0.0313373	+	0.478711i
$711$	7.88832e20			0.322079
$712$	3.85044e21	+	7.64924e20i	1.55564	+	0.309042i
$713$	2.79943e21			1.11918
$714$	−1.73433e19	+	2.64937e20i	−0.00686111	+	0.104811i
$715$		−	8.67243e21i		−	3.39505i
$716$	−2.77530e20	+	2.11070e21i	−0.107513	+	0.817672i
$717$			1.20306e21i			0.461205i
$718$	−3.04805e21	−	1.99531e20i	−1.15635	−	0.0756967i
$719$	4.23037e21			1.58822			0.794112	−	0.607772i	$-0.207936\pi$
$719$	4.23037e21			1.58822			0.794112	+	0.607772i	$0.207936\pi$
$720$	8.77418e20	−	3.27884e21i	0.325997	−	1.21822i
$721$	−2.44978e21			−0.900768
$722$	2.68348e21	+	1.75665e20i	0.976492	+	0.0639229i
$723$		−	4.08287e20i		−	0.147037i
$724$	2.70490e20	−	2.05716e21i	0.0964078	−	0.733212i
$725$			1.90648e21i			0.672509i
$726$	1.19940e20	−	1.83221e21i	0.0418735	−	0.639663i
$727$	−7.62091e20			−0.263329			−0.131664	−	0.991294i	$-0.542032\pi$
$727$	−7.62091e20			−0.263329			−0.131664	+	0.991294i	$0.542032\pi$
$728$	4.43510e20	−	2.23252e21i	0.151676	−	0.763503i
$729$	−4.99204e20			−0.168975
$730$	−4.37407e20	+	6.68187e21i	−0.146543	+	2.23860i
$731$			6.37207e20i			0.211300i
$732$	−5.27952e20	−	6.94189e19i	−0.173285	−	0.0227848i
$733$			2.81226e21i			0.913641i	0.889559	+	0.456821i	$0.151012\pi$
$733$			2.81226e21i			0.913641i	−0.889559	+	0.456821i	$0.848988\pi$
$734$	−2.00076e21	−	1.30974e20i	−0.643391	−	0.0421175i
$735$	−1.70428e21			−0.542482
$736$	−3.74631e21	−	1.27000e21i	−1.18038	−	0.400148i
$737$	−6.59608e21			−2.05722
$738$	−1.36664e21	−	8.94630e19i	−0.421923	−	0.0276198i
$739$			5.97793e21i			1.82691i	0.406939	+	0.913455i	$0.366596\pi$
$739$			5.97793e21i			1.82691i	−0.406939	+	0.913455i	$0.633404\pi$
$740$	6.55276e21	+	8.61602e20i	1.98238	+	0.260657i
$741$		−	3.22755e20i		−	0.0966576i
$742$	−7.71105e19	+	1.17795e21i	−0.0228604	+	0.349218i
$743$	2.28812e21			0.671527			0.335764	−	0.941946i	$-0.391006\pi$
$743$	2.28812e21			0.671527			0.335764	+	0.941946i	$0.391006\pi$
$744$	2.95540e20	−	1.48768e21i	0.0858656	−	0.432227i
$745$	−8.27986e21			−2.38150
$746$	2.37196e20	−	3.62343e21i	0.0675409	−	1.03176i
$747$			1.68926e21i			0.476204i
$748$	−2.62494e20	+	1.99635e21i	−0.0732583	+	0.557152i
$749$		−	3.79030e21i		−	1.04727i
$750$	−2.25830e21	−	1.47832e20i	−0.617762	−	0.0404398i
$751$	−3.94337e21			−1.06799			−0.533996	−	0.845487i	$-0.679310\pi$
$751$	−3.94337e21			−1.06799			−0.533996	+	0.845487i	$0.679310\pi$
$752$	3.05130e21	+	8.16531e20i	0.818185	+	0.218947i
$753$	5.42176e20			0.143939
$754$	−1.95286e21	−	1.27838e20i	−0.513318	−	0.0336027i
$755$		−	8.27493e20i		−	0.215359i
$756$	−2.52622e20	+	1.92127e21i	−0.0650965	+	0.495079i
$757$		−	1.52988e21i		−	0.390336i	−0.980770	−	0.195168i	$-0.937475\pi$
$757$		−	1.52988e21i		−	0.390336i	0.980770	−	0.195168i	$-0.0625253\pi$
$758$	1.21986e20	−	1.86346e21i	0.0308169	−	0.470762i
$759$	3.71336e21			0.928868
$760$	−9.62709e20	−	1.91251e20i	−0.238448	−	0.0473697i
$761$	1.44614e21			0.354671			0.177336	−	0.984150i	$-0.443252\pi$
$761$	1.44614e21			0.354671			0.177336	+	0.984150i	$0.443252\pi$
$762$	1.00227e20	−	1.53108e21i	0.0243401	−	0.371822i
$763$		−	1.32393e21i		−	0.318368i
$764$	2.47499e21	+	3.25430e20i	0.589351	+	0.0774920i
$765$		−	1.97902e21i		−	0.466648i
$766$	2.86218e20	+	1.87363e19i	0.0668314	+	0.00437490i
$767$	−7.77765e21			−1.79839
$768$	−1.07041e21	+	1.85679e21i	−0.245099	+	0.425162i
$769$	1.78954e21			0.405782			0.202891	−	0.979201i	$-0.434966\pi$
$769$	1.78954e21			0.405782			0.202891	+	0.979201i	$0.434966\pi$
$770$	6.48398e21	+	4.24453e20i	1.45600	+	0.0953123i
$771$			1.59355e21i			0.354371i
$772$	4.28074e21	+	5.62862e20i	0.942735	+	0.123957i
$773$			4.44104e21i			0.968586i	0.874906	+	0.484293i	$0.160923\pi$
$773$			4.44104e21i			0.968586i	−0.874906	+	0.484293i	$0.839077\pi$
$774$	−1.31101e20	+	2.00272e21i	−0.0283172	+	0.432576i
$775$	7.38563e21			1.57988
$776$	2.80313e21	+	5.56867e20i	0.593855	+	0.117975i
$777$	−1.62835e21			−0.341657
$778$	1.62963e19	−	2.48943e20i	0.00338642	−	0.0517313i
$779$			3.96047e20i			0.0815108i
$780$	7.01658e20	−	5.33633e21i	0.143026	−	1.08776i
$781$		−	2.17234e21i		−	0.438576i
$782$	−2.30149e21	−	1.50660e20i	−0.460213	−	0.0301264i
$783$	1.66613e21			0.329986
$784$	−3.27694e21	−	8.76911e20i	−0.642833	−	0.172022i
$785$	2.75687e21			0.535666
$786$	3.42558e21	+	2.24245e20i	0.659272	+	0.0431571i
$787$		−	3.43008e21i		−	0.653874i	−0.945046	−	0.326937i	$-0.893983\pi$
$787$		−	3.43008e21i		−	0.653874i	0.945046	−	0.326937i	$-0.106017\pi$
$788$	5.90582e20	−	4.49156e21i	0.111515	−	0.848106i
$789$			7.06800e20i			0.132196i
$790$	2.48484e20	−	3.79586e21i	0.0460357	−	0.703245i
$791$	2.39725e21			0.439936
$792$	−1.23574e21	+	6.22043e21i	−0.224641	+	1.13079i
$793$	2.66169e21			0.479302
$794$	−2.39526e20	+	3.65901e21i	−0.0427266	+	0.652695i
$795$			2.79138e21i			0.493247i
$796$	−3.50122e20	−	4.60365e19i	−0.0612875	−	0.00805851i
$797$			1.81349e21i			0.314469i	0.987561	+	0.157234i	$0.0502578\pi$
$797$			1.81349e21i			0.314469i	−0.987561	+	0.157234i	$0.949742\pi$
$798$	2.41309e20	+	1.57965e19i	0.0414525	+	0.00271356i
$799$	1.84169e21			0.313412
$800$	−9.88375e21	−	3.35060e21i	−1.66628	−	0.564869i
$801$	7.20933e21			1.20407
$802$	−1.67195e20	−	1.09449e19i	−0.0276640	−	0.00181094i
$803$		−	1.25116e22i		−	2.05091i
$804$	−4.05871e21	−	5.33667e20i	−0.659124	−	0.0866663i
$805$			7.44303e21i			1.19751i
$806$	−4.95238e20	+	7.56530e21i	−0.0789408	+	1.20591i
$807$	−2.97244e21			−0.469420
$808$	−1.38599e21	+	6.97675e21i	−0.216858	+	1.09161i
$809$	1.55831e21			0.241568			0.120784	−	0.992679i	$-0.461459\pi$
$809$	1.55831e21			0.241568			0.120784	+	0.992679i	$0.461459\pi$
$810$	2.37023e20	−	3.62079e21i	0.0364043	−	0.556116i
$811$			2.19869e21i			0.334586i	0.985907	+	0.167293i	$0.0535027\pi$
$811$			2.19869e21i			0.334586i	−0.985907	+	0.167293i	$0.946497\pi$
$812$	1.91157e20	−	1.45381e21i	0.0288217	−	0.219198i
$813$		−	8.92129e20i		−	0.133275i
$814$	−1.23227e22	−	8.06665e20i	−1.82399	−	0.119402i
$815$	−1.76705e22			−2.59159
$816$	−3.23036e20	+	1.20716e21i	−0.0469434	+	0.175423i
$817$	5.80377e20			0.0835689
$818$	8.94032e21	+	5.85249e20i	1.27557	+	0.0835009i
$819$		−	4.18004e21i		−	0.590951i
$820$	−8.60992e20	+	6.54811e21i	−0.120613	+	0.917302i
$821$		−	4.69997e21i		−	0.652411i	−0.945299	−	0.326205i	$-0.894230\pi$
$821$		−	4.69997e21i		−	0.652411i	0.945299	−	0.326205i	$-0.105770\pi$
$822$	−2.21204e19	+	3.37913e20i	−0.00304266	+	0.0464800i
$823$	5.67810e21			0.773934			0.386967	−	0.922094i	$-0.373523\pi$
$823$	5.67810e21			0.773934			0.386967	+	0.922094i	$0.373523\pi$
$824$	−1.13092e22	−	2.24667e21i	−1.52749	−	0.303449i
$825$	9.79682e21			1.31124
$826$	3.80660e20	−	5.81499e21i	0.0504878	−	0.771256i
$827$			1.14459e22i			1.50438i	0.658946	+	0.752190i	$0.271003\pi$
$827$			1.14459e22i			1.50438i	−0.658946	+	0.752190i	$0.728997\pi$
$828$	−7.20250e21	−	9.47036e20i	−0.938115	−	0.123350i
$829$		−	8.78189e21i		−	1.13352i	−0.823883	−	0.566760i	$-0.808197\pi$
$829$		−	8.78189e21i		−	1.13352i	0.823883	−	0.566760i	$-0.191803\pi$
$830$	8.12874e21	+	5.32122e20i	1.03977	+	0.0680652i
$831$	−1.24152e21			−0.157379
$832$	4.09485e21	−	9.89951e21i	0.514415	−	1.24362i
$833$	−1.97787e21			−0.246242
$834$	−2.35859e21	−	1.54397e20i	−0.291009	−	0.0190500i
$835$			1.67075e22i			2.04297i
$836$	1.81830e21	+	2.39083e20i	0.220353	+	0.0289735i
$837$		−	6.45452e21i		−	0.775217i
$838$	7.35541e20	−	1.12362e22i	0.0875541	−	1.33748i
$839$	4.73338e21			0.558414			0.279207	−	0.960231i	$-0.409928\pi$
$839$	4.73338e21			0.558414			0.279207	+	0.960231i	$0.409928\pi$
$840$	3.95538e21	+	7.85772e20i	0.462481	+	0.0918759i
$841$	7.36844e21			0.853897
$842$	−4.48586e20	+	6.85264e21i	−0.0515235	+	0.787078i
$843$			7.51650e21i			0.855675i
$844$	−1.36797e21	+	1.04039e22i	−0.154351	+	1.17389i
$845$			1.20496e22i			1.34756i
$846$	5.78835e21	+	3.78916e20i	0.641619	+	0.0420015i
$847$	−6.87661e21			−0.755525
$848$	−1.43626e21	+	5.36718e21i	−0.156410	+	0.584490i
$849$	−3.23148e21			−0.348814
$850$	−6.07194e21	−	3.97480e20i	−0.649659	−	0.0425278i
$851$		−	1.41453e22i		−	1.50018i
$852$	1.75757e20	−	1.33668e21i	0.0184763	−	0.140518i
$853$		−	6.81363e21i		−	0.710004i	−0.934865	−	0.355002i	$-0.884480\pi$
$853$		−	6.81363e21i		−	0.710004i	0.934865	−	0.355002i	$-0.115520\pi$
$854$	−1.30270e20	+	1.99002e21i	−0.0134559	+	0.205553i
$855$	−1.80252e21			−0.184558
$856$	3.47605e21	−	1.74976e22i	0.352803	−	1.77593i
$857$	−1.20231e22			−1.20965			−0.604825	−	0.796359i	$-0.706757\pi$
$857$	−1.20231e22			−1.20965			−0.604825	+	0.796359i	$0.706757\pi$
$858$	−6.56919e20	+	1.00351e22i	−0.0655174	+	1.00085i
$859$		−	1.96935e22i		−	1.94704i	−0.228606	−	0.973519i	$-0.573417\pi$
$859$		−	1.96935e22i		−	1.94704i	0.228606	−	0.973519i	$-0.426583\pi$
$860$	9.59578e21	+	1.26172e21i	0.940463	+	0.123659i
$861$		−	1.62720e21i		−	0.158094i
$862$	1.64419e22	+	1.07631e21i	1.58360	+	0.103666i
$863$	−1.75887e22			−1.67939			−0.839695	−	0.543058i	$-0.817266\pi$
$863$	−1.75887e22			−1.67939			−0.839695	+	0.543058i	$0.817266\pi$
$864$	−2.92819e21	+	8.63770e21i	−0.277170	+	0.817607i
$865$	−6.27886e21			−0.589197
$866$	1.28635e22	+	8.42066e20i	1.19667	+	0.0783361i
$867$		−	4.59252e21i		−	0.423553i
$868$	−5.63199e21	−	7.40533e20i	−0.514948	−	0.0677090i
$869$			7.10765e21i			0.644285i
$870$	2.26492e20	−	3.45991e21i	0.0203544	−	0.310935i
$871$	2.04621e22			1.82312
$872$	1.21416e21	−	6.11179e21i	0.107251	−	0.539877i
$873$	5.24841e21			0.459644
$874$	−1.37223e20	+	2.09623e21i	−0.0119149	+	0.182013i
$875$			8.47577e21i			0.729657i
$876$	1.01227e21	−	7.69867e21i	0.0864008	−	0.657105i
$877$			1.93194e22i			1.63492i	0.575983	+	0.817462i	$0.304620\pi$
$877$			1.93194e22i			1.63492i	−0.575983	+	0.817462i	$0.695380\pi$
$878$	−1.04977e22	−	6.87200e20i	−0.880819	−	0.0576600i
$879$	1.57387e21			0.130934
$880$	2.95435e22	+	7.90585e21i	2.43692	+	0.652121i
$881$	4.62940e21			0.378621			0.189311	−	0.981917i	$-0.439375\pi$
$881$	4.62940e21			0.378621			0.189311	+	0.981917i	$0.439375\pi$
$882$	−6.21638e21	−	4.06936e20i	−0.504108	−	0.0329998i
$883$			5.41532e21i			0.435431i	0.976012	+	0.217715i	$0.0698604\pi$
$883$			5.41532e21i			0.435431i	−0.976012	+	0.217715i	$0.930140\pi$
$884$	8.14298e20	−	6.19299e21i	0.0649220	−	0.493752i
$885$		−	1.37798e22i		−	1.08935i
$886$	−1.47321e21	+	2.25048e22i	−0.115481	+	1.76410i
$887$	−1.26185e22			−0.980797			−0.490399	−	0.871498i	$-0.663149\pi$
$887$	−1.26185e22			−0.980797			−0.490399	+	0.871498i	$0.663149\pi$
$888$	−7.51714e21	−	1.49334e21i	−0.579369	−	0.115097i
$889$	−5.74639e21			−0.439169
$890$	2.27095e21	−	3.46913e22i	0.172101	−	2.62903i
$891$			6.77983e21i			0.509491i
$892$	9.25550e21	+	1.21698e21i	0.689706	+	0.0906873i
$893$		−	1.67743e21i		−	0.123954i
$894$	9.58089e21	+	6.27182e20i	0.702060	+	0.0459581i
$895$	1.88531e22			1.36997
$896$	7.20099e21	+	3.54604e21i	0.518898	+	0.255525i
$897$	−1.15195e22			−0.823169
$898$	−2.70076e22	−	1.76797e21i	−1.91387	−	0.125286i
$899$			4.88408e21i			0.343230i
$900$	−1.90021e22	−	2.49853e21i	−1.32429	−	0.174127i
$901$			3.23949e21i			0.223893i
$902$	8.06093e20	−	1.23140e22i	0.0552505	−	0.844012i
$903$	−2.38454e21			−0.162086
$904$	1.10667e22	+	2.19850e21i	0.746028	+	0.148205i
$905$	−1.83749e22			−1.22846
$906$	−6.26809e19	+	9.57519e20i	−0.00415598	+	0.0634871i
$907$		−	1.94803e22i		−	1.28098i	−0.767967	−	0.640489i	$-0.778732\pi$
$907$		−	1.94803e22i		−	1.28098i	0.767967	−	0.640489i	$-0.221268\pi$
$908$	−9.49771e20	+	7.22330e21i	−0.0619405	+	0.471077i
$909$			1.30628e22i			0.844906i
$910$	−2.01144e22	−	1.31672e21i	−1.29031	−	0.0844663i
$911$	1.13836e22			0.724254			0.362127	−	0.932129i	$-0.382051\pi$
$911$	1.13836e22			0.724254			0.362127	+	0.932129i	$0.382051\pi$
$912$	1.09949e21	+	2.94225e20i	0.0693796	+	0.0185660i
$913$	−1.52209e22			−0.952595
$914$	−1.75209e22	−	1.14695e21i	−1.08758	−	0.0711947i
$915$			4.71575e21i			0.290330i
$916$	−8.03787e20	+	6.11305e21i	−0.0490823	+	0.373286i
$917$		−	1.28568e22i		−	0.778686i
$918$	−3.47369e20	+	5.30644e21i	−0.0208675	+	0.318774i
$919$	2.62399e22			1.56349			0.781746	−	0.623597i	$-0.214329\pi$
$919$	2.62399e22			1.56349			0.781746	+	0.623597i	$0.214329\pi$
$920$	−6.82594e21	+	3.43601e22i	−0.403417	+	2.03070i
$921$	4.15930e21			0.243822
$922$	−1.83440e21	+	2.80225e22i	−0.106663	+	1.62939i
$923$			6.73894e21i			0.388668i
$924$	−7.47066e21	−	9.82295e20i	−0.427385	−	0.0561956i
$925$		−	3.73191e22i		−	2.11772i
$926$	1.54382e22	+	1.01061e21i	0.868990	+	0.0568856i
$927$	−2.11747e22			−1.18228
$928$	2.21573e21	−	6.53607e21i	0.122718	−	0.361999i
$929$	2.40119e22			1.31920			0.659598	−	0.751618i	$-0.270726\pi$
$929$	2.40119e22			1.31920			0.659598	+	0.751618i	$0.270726\pi$
$930$	−1.34035e22	−	8.77419e20i	−0.730461	−	0.0478173i
$931$			1.80148e21i			0.0973881i
$932$	−1.34122e22	−	1.76353e21i	−0.719251	−	0.0945722i
$933$			1.65439e22i			0.880085i
$934$	1.03629e21	−	1.58305e22i	0.0546864	−	0.835395i
$935$	1.78317e22			0.933479
$936$	3.83348e21	−	1.92968e22i	0.199078	−	1.00211i
$937$	−1.34584e22			−0.693341			−0.346671	−	0.937987i	$-0.612688\pi$
$937$	−1.34584e22			−0.693341			−0.346671	+	0.937987i	$0.612688\pi$
$938$	−1.00147e21	+	1.52986e22i	−0.0511821	+	0.781862i
$939$		−	8.22219e21i		−	0.416865i
$940$	3.64669e21	−	2.77342e22i	0.183417	−	1.39494i
$941$			1.34511e21i			0.0671172i	0.999437	+	0.0335586i	$0.0106840\pi$
$941$			1.34511e21i			0.0671172i	−0.999437	+	0.0335586i	$0.989316\pi$
$942$	−3.19006e21	−	2.08827e20i	−0.157913	−	0.0103373i
$943$	1.41353e22			0.694174
$944$	7.09016e21	−	2.64953e22i	0.345435	−	1.29086i
$945$	1.71611e22			0.829479
$946$	−1.80452e22	−	1.18127e21i	−0.865322	−	0.0566456i
$947$			2.00072e22i			0.951835i	0.879490	+	0.475917i	$0.157884\pi$
$947$			2.00072e22i			0.951835i	−0.879490	+	0.475917i	$0.842116\pi$
$948$	−5.75057e20	+	4.37349e21i	−0.0271424	+	0.206426i
$949$			3.88131e22i			1.81753i
$950$	−3.62030e20	+	5.53040e21i	−0.0168197	+	0.256939i
$951$	1.32309e22			0.609869
$952$	4.59036e21	+	9.11915e20i	0.209928	+	0.0417040i
$953$	2.84287e22			1.28991			0.644956	−	0.764220i	$-0.276876\pi$
$953$	2.84287e22			1.28991			0.644956	+	0.764220i	$0.276876\pi$
$954$	−6.66505e20	+	1.01816e22i	−0.0300048	+	0.458356i
$955$		−	2.21070e22i		−	0.987426i
$956$	2.10254e22	+	2.76457e21i	0.931775	+	0.122516i
$957$			6.47859e21i			0.284866i
$958$	2.99079e22	+	1.95782e21i	1.30480	+	0.0854147i
$959$	1.26825e21			0.0548989
$960$	1.75391e22	+	7.25490e21i	0.753308	+	0.311600i
$961$	−4.54454e21			−0.193671
$962$	3.82270e22	+	2.50241e21i	1.61643	+	0.105814i
$963$		−	3.27614e22i		−	1.37457i
$964$	−7.13548e21	−	9.38223e20i	−0.297061	−	0.0390596i
$965$		−	3.82362e22i		−	1.57950i
$966$	5.63794e20	−	8.61257e21i	0.0231096	−	0.353024i
$967$	−1.28151e22			−0.521222			−0.260611	−	0.965444i	$-0.583924\pi$
$967$	−1.28151e22			−0.521222			−0.260611	+	0.965444i	$0.583924\pi$
$968$	−3.17453e22	−	6.30648e21i	−1.28119	−	0.254520i
$969$	6.63626e20			0.0265763
$970$	1.65326e21	−	2.52554e22i	0.0656982	−	1.00361i
$971$		−	9.93289e20i		−	0.0391680i	−0.999808	−	0.0195840i	$-0.993766\pi$
$971$		−	9.93289e20i		−	0.0391680i	0.999808	−	0.0195840i	$-0.00623418\pi$
$972$	−3.42477e21	+	2.60465e22i	−0.134009	+	1.01918i
$973$			8.85218e21i			0.343719i
$974$	−4.18577e22	−	2.74008e21i	−1.61281	−	0.105577i
$975$	−3.03913e22			−1.16202
$976$	−2.42642e21	+	9.06731e21i	−0.0920644	+	0.344037i
$977$	−5.30610e21			−0.199787			−0.0998933	−	0.994998i	$-0.531850\pi$
$977$	−5.30610e21			−0.199787			−0.0998933	+	0.994998i	$0.531850\pi$
$978$	2.04471e22	+	1.33850e21i	0.763994	+	0.0500124i
$979$			6.49586e22i			2.40861i
$980$	−3.91635e21	+	2.97851e22i	−0.144107	+	1.09598i
$981$		−	1.14433e22i		−	0.417865i
$982$	5.39007e20	−	8.23391e21i	0.0195325	−	0.298380i
$983$	−3.43620e22			−1.23574			−0.617870	−	0.786281i	$-0.712004\pi$
$983$	−3.43620e22			−1.23574			−0.617870	+	0.786281i	$0.712004\pi$
$984$	1.49229e21	−	7.51181e21i	0.0532585	−	0.268091i
$985$	−4.01193e22			−1.42096
$986$	2.62851e20	−	4.01534e21i	0.00923918	−	0.141139i
$987$			6.89190e21i			0.240414i
$988$	−5.64066e21	−	7.41674e20i	−0.195278	−	0.0256765i
$989$		−	2.07143e22i		−	0.711701i
$990$	5.60442e22	+	3.66876e21i	1.91103	+	0.125099i
$991$	−3.47863e22			−1.17722			−0.588608	−	0.808418i	$-0.700324\pi$
$991$	−3.47863e22			−1.17722			−0.588608	+	0.808418i	$0.700324\pi$
$992$	−2.53205e22	−	8.58366e21i	−0.850421	−	0.288293i
$993$	1.20741e22			0.402472
$994$	−5.03840e21	−	3.29822e20i	−0.166684	−	0.0109114i
$995$			3.12734e21i			0.102684i
$996$	−9.36571e21	−	1.23147e21i	−0.305208	−	0.0401309i
$997$			5.81285e21i			0.188008i	0.995572	+	0.0940038i	$0.0299666\pi$
$997$			5.81285e21i			0.188008i	−0.995572	+	0.0940038i	$0.970033\pi$
$998$	−1.05731e21	+	1.61515e22i	−0.0339408	+	0.518483i
$999$	−3.26143e22			−1.03912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.16.b.a.5.14	yes	14
3.2	odd	2		72.16.d.b.37.1		14
4.3	odd	2		32.16.b.a.17.6		14
8.3	odd	2		32.16.b.a.17.9		14
8.5	even	2	inner	8.16.b.a.5.13	✓	14
24.5	odd	2		72.16.d.b.37.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.16.b.a.5.13	✓	14	8.5	even	2	inner
8.16.b.a.5.14	yes	14	1.1	even	1	trivial
32.16.b.a.17.6		14	4.3	odd	2
32.16.b.a.17.9		14	8.3	odd	2
72.16.d.b.37.1		14	3.2	odd	2
72.16.d.b.37.2		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)

\(f(q)\)	\(=\)	\(q+(180.633 + 11.8245i) q^{2} +1858.96i q^{3} +(32488.4 + 4271.80i) q^{4} -290191. i q^{5} +(-21981.3 + 335789. i) q^{6} +1.26027e6 q^{7} +(5.81795e6 + 1.15579e6i) q^{8} +1.08932e7 q^{9} +O(q^{10})\)	\(q+(180.633 + 11.8245i) q^{2} +1858.96i q^{3} +(32488.4 + 4271.80i) q^{4} -290191. i q^{5} +(-21981.3 + 335789. i) q^{6} +1.26027e6 q^{7} +(5.81795e6 + 1.15579e6i) q^{8} +1.08932e7 q^{9} +(3.43137e6 - 5.24180e7i) q^{10} +9.81513e7i q^{11} +(-7.94110e6 + 6.03946e7i) q^{12} -3.04482e8i q^{13} +(2.27647e8 + 1.49022e7i) q^{14} +5.39453e8 q^{15} +(1.03725e9 + 2.77567e8i) q^{16} +6.26054e8 q^{17} +(1.96766e9 + 1.28807e8i) q^{18} -5.70219e8i q^{19} +(1.23964e9 - 9.42783e9i) q^{20} +2.34280e9i q^{21} +(-1.16059e9 + 1.77293e10i) q^{22} -2.03517e10 q^{23} +(-2.14856e9 + 1.08153e10i) q^{24} -5.36932e10 q^{25} +(3.60035e9 - 5.49993e10i) q^{26} +4.69240e10i q^{27} +(4.09442e10 + 5.38364e9i) q^{28} -3.55070e10i q^{29} +(9.74429e10 + 6.37879e9i) q^{30} -1.37553e11 q^{31} +(1.84078e11 + 6.24027e10i) q^{32} -1.82459e11 q^{33} +(1.13086e11 + 7.40280e9i) q^{34} -3.65720e11i q^{35} +(3.53901e11 + 4.65334e10i) q^{36} +6.95044e11i q^{37} +(6.74257e9 - 1.03000e11i) q^{38} +5.66019e11 q^{39} +(3.35399e11 - 1.68832e12i) q^{40} -6.94552e11 q^{41} +(-2.77025e10 + 4.23186e11i) q^{42} +1.01781e12i q^{43} +(-4.19283e11 + 3.18878e12i) q^{44} -3.16110e12i q^{45} +(-3.67619e12 - 2.40650e11i) q^{46} +2.94174e12 q^{47} +(-5.15987e11 + 1.92820e12i) q^{48} -3.15927e12 q^{49} +(-9.69874e12 - 6.34897e11i) q^{50} +1.16381e12i q^{51} +(1.30068e12 - 9.89211e12i) q^{52} +5.17445e12i q^{53} +(-5.54855e11 + 8.47601e12i) q^{54} +2.84826e13 q^{55} +(7.33221e12 + 1.45661e12i) q^{56} +1.06001e12 q^{57} +(4.19854e11 - 6.41373e12i) q^{58} -2.55439e13i q^{59} +(1.75259e13 + 2.30443e12i) q^{60} +8.74172e12i q^{61} +(-2.48465e13 - 1.62650e12i) q^{62} +1.37284e13 q^{63} +(3.25127e13 + 1.34486e13i) q^{64} -8.83578e13 q^{65} +(-3.29581e13 - 2.15750e12i) q^{66} +6.72032e13i q^{67} +(2.03395e13 + 2.67438e12i) q^{68} -3.78330e13i q^{69} +(4.32447e12 - 6.60610e13i) q^{70} -2.21325e13 q^{71} +(6.33759e13 + 1.25902e13i) q^{72} -1.27473e14 q^{73} +(-8.21858e12 + 1.25548e14i) q^{74} -9.98134e13i q^{75} +(2.43586e12 - 1.85255e13i) q^{76} +1.23698e14i q^{77} +(1.02242e14 + 6.69292e12i) q^{78} +7.24152e13 q^{79} +(8.05475e13 - 3.00999e14i) q^{80} +6.90753e13 q^{81} +(-1.25459e14 - 8.21276e12i) q^{82} +1.55075e14i q^{83} +(-1.00080e13 + 7.61137e13i) q^{84} -1.81675e14i q^{85} +(-1.20352e13 + 1.83851e14i) q^{86} +6.60061e13 q^{87} +(-1.13442e14 + 5.71040e14i) q^{88} +6.61821e14 q^{89} +(3.73786e13 - 5.70998e14i) q^{90} -3.83730e14i q^{91} +(-6.61194e14 - 8.69385e13i) q^{92} -2.55705e14i q^{93} +(5.31374e14 + 3.47847e13i) q^{94} -1.65472e14 q^{95} +(-1.16004e14 + 3.42194e14i) q^{96} +4.81808e14 q^{97} +(-5.70668e14 - 3.73569e13i) q^{98} +1.06918e15i 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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