LMFDB - Embedded newform 17.10.c.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(4,17)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, 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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.57683i q^{2} +(-2.66069 - 2.66069i) q^{3} +420.284 q^{4} +(-1324.59 - 1324.59i) q^{5} +(25.4810 - 25.4810i) q^{6} +(1098.57 - 1098.57i) q^{7} +8928.33i q^{8} -19668.8i q^{9} +O(q^{10})$	\(q+9.57683i q^{2} +(-2.66069 - 2.66069i) q^{3} +420.284 q^{4} +(-1324.59 - 1324.59i) q^{5} +(25.4810 - 25.4810i) q^{6} +(1098.57 - 1098.57i) q^{7} +8928.33i q^{8} -19668.8i q^{9} +(12685.3 - 12685.3i) q^{10} +(48672.6 - 48672.6i) q^{11} +(-1118.25 - 1118.25i) q^{12} +53127.1 q^{13} +(10520.8 + 10520.8i) q^{14} +7048.63i q^{15} +129681. q^{16} +(61443.7 - 338840. i) q^{17} +188365. q^{18} -64384.8i q^{19} +(-556703. - 556703. i) q^{20} -5845.89 q^{21} +(466129. + 466129. i) q^{22} +(-1.71797e6 + 1.71797e6i) q^{23} +(23755.5 - 23755.5i) q^{24} +1.55593e6i q^{25} +508789. i q^{26} +(-104703. + 104703. i) q^{27} +(461710. - 461710. i) q^{28} +(-3.30460e6 - 3.30460e6i) q^{29} -67503.5 q^{30} +(2.93923e6 + 2.93923e6i) q^{31} +5.81323e6i q^{32} -259006. q^{33} +(3.24501e6 + 588436. i) q^{34} -2.91029e6 q^{35} -8.26651e6i q^{36} +(-6.90284e6 - 6.90284e6i) q^{37} +616602. q^{38} +(-141355. - 141355. i) q^{39} +(1.18263e7 - 1.18263e7i) q^{40} +(2.18642e7 - 2.18642e7i) q^{41} -55985.1i q^{42} +2.81845e7i q^{43} +(2.04563e7 - 2.04563e7i) q^{44} +(-2.60531e7 + 2.60531e7i) q^{45} +(-1.64527e7 - 1.64527e7i) q^{46} +1.87813e7 q^{47} +(-345040. - 345040. i) q^{48} +3.79399e7i q^{49} -1.49009e7 q^{50} +(-1.06503e6 + 738066. i) q^{51} +2.23285e7 q^{52} -4.47911e6i q^{53} +(-1.00272e6 - 1.00272e6i) q^{54} -1.28942e8 q^{55} +(9.80835e6 + 9.80835e6i) q^{56} +(-171308. + 171308. i) q^{57} +(3.16476e7 - 3.16476e7i) q^{58} +1.26323e8i q^{59} +2.96243e6i q^{60} +(-2.41668e7 + 2.41668e7i) q^{61} +(-2.81485e7 + 2.81485e7i) q^{62} +(-2.16075e7 - 2.16075e7i) q^{63} +1.07241e7 q^{64} +(-7.03714e7 - 7.03714e7i) q^{65} -2.48045e6i q^{66} +1.37527e8 q^{67} +(2.58238e7 - 1.42409e8i) q^{68} +9.14198e6 q^{69} -2.78713e7i q^{70} +(-2.87544e7 - 2.87544e7i) q^{71} +1.75610e8 q^{72} +(1.73725e8 + 1.73725e8i) q^{73} +(6.61073e7 - 6.61073e7i) q^{74} +(4.13985e6 - 4.13985e6i) q^{75} -2.70599e7i q^{76} -1.06940e8i q^{77} +(1.35373e6 - 1.35373e6i) q^{78} +(2.79088e8 - 2.79088e8i) q^{79} +(-1.71773e8 - 1.71773e8i) q^{80} -3.86585e8 q^{81} +(2.09390e8 + 2.09390e8i) q^{82} -3.15697e8i q^{83} -2.45693e6 q^{84} +(-5.30210e8 + 3.67435e8i) q^{85} -2.69918e8 q^{86} +1.75850e7i q^{87} +(4.34565e8 + 4.34565e8i) q^{88} +4.99389e8 q^{89} +(-2.49506e8 - 2.49506e8i) q^{90} +(5.83636e7 - 5.83636e7i) q^{91} +(-7.22036e8 + 7.22036e8i) q^{92} -1.56407e7i q^{93} +1.79865e8i q^{94} +(-8.52832e7 + 8.52832e7i) q^{95} +(1.54672e7 - 1.54672e7i) q^{96} +(5.54444e8 + 5.54444e8i) q^{97} -3.63344e8 q^{98} +(-9.57334e8 - 9.57334e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) $ 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7 + 21946 * q^10 + 18132 * q^11 - 95142 * q^12 + 244832 * q^13 - 341100 * q^14 - 279932 * q^16 - 98022 * q^17 + 888764 * q^18 + 1364262 * q^20 - 775748 * q^21 - 4573190 * q^22 - 377526 * q^23 - 307054 * q^24 + 3996108 * q^27 - 1024780 * q^28 + 2160042 * q^29 + 39084792 * q^30 - 585086 * q^31 - 30349992 * q^33 + 4441318 * q^34 - 25532364 * q^35 + 1515390 * q^37 + 13171392 * q^38 - 25687084 * q^39 - 63240118 * q^40 - 72707928 * q^41 - 3606450 * q^44 + 156729418 * q^45 + 118549536 * q^46 + 153365328 * q^47 + 26098270 * q^48 - 236105676 * q^50 + 256903592 * q^51 - 209898380 * q^52 - 187411976 * q^54 + 255767540 * q^55 - 107638596 * q^56 - 443390988 * q^57 - 281433730 * q^58 + 52149382 * q^61 + 176928228 * q^62 + 620111642 * q^63 + 1006108924 * q^64 - 489714396 * q^65 - 26076868 * q^67 - 308011950 * q^68 - 751973532 * q^69 + 149240178 * q^71 + 1171736028 * q^72 - 175256556 * q^73 - 37609818 * q^74 - 233543476 * q^75 - 1202722924 * q^78 - 469987182 * q^79 + 481103586 * q^80 + 347156560 * q^81 - 984422080 * q^82 - 935672904 * q^84 - 725828294 * q^85 + 690159588 * q^86 + 992281114 * q^88 - 191594460 * q^89 + 914946474 * q^90 + 926854816 * q^91 + 3064830552 * q^92 + 1213246572 * q^95 + 3594247550 * q^96 - 2200567348 * q^97 - 4413444720 * q^98 - 1224966600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			9.57683i			0.423240i	0.977352	+	0.211620i	$0.0678739\pi$
$2$			9.57683i			0.423240i	−0.977352	+	0.211620i	$0.932126\pi$
$3$	−2.66069	−	2.66069i	−0.0189648	−	0.0189648i	0.697561	−	0.716526i	$-0.254269\pi$
$3$	−2.66069	−	2.66069i	−0.0189648	−	0.0189648i	−0.716526	+	0.697561i	$0.754269\pi$
$4$	420.284			0.820868
$5$	−1324.59	−	1324.59i	−0.947796	−	0.947796i	0.0509069	−	0.998703i	$-0.483789\pi$
$5$	−1324.59	−	1324.59i	−0.947796	−	0.947796i	−0.998703	+	0.0509069i	$0.983789\pi$
$6$	25.4810	−	25.4810i	0.00802667	−	0.00802667i
$7$	1098.57	−	1098.57i	0.172936	−	0.172936i	−0.615332	−	0.788268i	$-0.710978\pi$
$7$	1098.57	−	1098.57i	0.172936	−	0.172936i	0.788268	+	0.615332i	$0.210978\pi$
$8$			8928.33i			0.770664i
$9$		−	19668.8i		−	0.999281i
$10$	12685.3	−	12685.3i	0.401145	−	0.401145i
$11$	48672.6	−	48672.6i	1.00235	−	1.00235i	0.00234888	−	0.999997i	$-0.499252\pi$
$11$	48672.6	−	48672.6i	1.00235	−	1.00235i	0.999997	−	0.00234888i	$-0.000747673\pi$
$12$	−1118.25	−	1118.25i	−0.0155676	−	0.0155676i
$13$	53127.1			0.515906			0.257953	−	0.966157i	$-0.416952\pi$
$13$	53127.1			0.515906			0.257953	+	0.966157i	$0.416952\pi$
$14$	10520.8	+	10520.8i	0.0731933	+	0.0731933i
$15$			7048.63i			0.0359496i
$16$	129681.			0.494692
$17$	61443.7	−	338840.i	0.178426	−	0.983953i
$17$	61443.7	−	338840.i	0.178426	−	0.983953i
$18$	188365.			0.422936
$19$		−	64384.8i		−	0.113342i	−0.998393	−	0.0566712i	$-0.981951\pi$
$19$		−	64384.8i		−	0.113342i	0.998393	−	0.0566712i	$-0.0180487\pi$
$20$	−556703.	−	556703.i	−0.778016	−	0.778016i
$21$	−5845.89			−0.00655939
$22$	466129.	+	466129.i	0.424233	+	0.424233i
$23$	−1.71797e6	+	1.71797e6i	−1.28009	+	1.28009i	−0.339475	+	0.940615i	$0.610250\pi$
$23$	−1.71797e6	+	1.71797e6i	−1.28009	+	1.28009i	−0.940615	+	0.339475i	$0.889750\pi$
$24$	23755.5	−	23755.5i	0.0146155	−	0.0146155i
$25$			1.55593e6i			0.796636i
$26$			508789.i			0.218352i
$27$	−104703.	+	104703.i	−0.0379160	+	0.0379160i
$28$	461710.	−	461710.i	0.141957	−	0.141957i
$29$	−3.30460e6	−	3.30460e6i	−0.867617	−	0.867617i	0.124591	−	0.992208i	$-0.460238\pi$
$29$	−3.30460e6	−	3.30460e6i	−0.867617	−	0.867617i	−0.992208	+	0.124591i	$0.960238\pi$
$30$	−67503.5			−0.0152153
$31$	2.93923e6	+	2.93923e6i	0.571617	+	0.571617i	0.932580	−	0.360963i	$-0.117552\pi$
$31$	2.93923e6	+	2.93923e6i	0.571617	+	0.571617i	−0.360963	+	0.932580i	$0.617552\pi$
$32$			5.81323e6i			0.980038i
$33$	−259006.			−0.0380186
$34$	3.24501e6	+	588436.i	0.416448	+	0.0755169i
$35$	−2.91029e6			−0.327816
$36$		−	8.26651e6i		−	0.820277i
$37$	−6.90284e6	−	6.90284e6i	−0.605508	−	0.605508i	0.336261	−	0.941769i	$-0.390838\pi$
$37$	−6.90284e6	−	6.90284e6i	−0.605508	−	0.605508i	−0.941769	+	0.336261i	$0.890838\pi$
$38$	616602.			0.0479710
$39$	−141355.	−	141355.i	−0.00978407	−	0.00978407i
$40$	1.18263e7	−	1.18263e7i	0.730433	−	0.730433i
$41$	2.18642e7	−	2.18642e7i	1.20839	−	1.20839i	0.236839	−	0.971549i	$-0.423889\pi$
$41$	2.18642e7	−	2.18642e7i	1.20839	−	1.20839i	0.971549	−	0.236839i	$-0.0761114\pi$
$42$		−	55985.1i		−	0.00277620i
$43$			2.81845e7i			1.25719i	0.777731	+	0.628597i	$0.216370\pi$
$43$			2.81845e7i			1.25719i	−0.777731	+	0.628597i	$0.783630\pi$
$44$	2.04563e7	−	2.04563e7i	0.822794	−	0.822794i
$45$	−2.60531e7	+	2.60531e7i	−0.947115	+	0.947115i
$46$	−1.64527e7	−	1.64527e7i	−0.541785	−	0.541785i
$47$	1.87813e7			0.561417			0.280708	−	0.959793i	$-0.409431\pi$
$47$	1.87813e7			0.561417			0.280708	+	0.959793i	$0.409431\pi$
$48$	−345040.	−	345040.i	−0.00938175	−	0.00938175i
$49$			3.79399e7i			0.940186i
$50$	−1.49009e7			−0.337168
$51$	−1.06503e6	+	738066.i	−0.0220443	+	0.0152767i
$52$	2.23285e7			0.423491
$53$		−	4.47911e6i		−	0.0779741i	−0.999240	−	0.0389871i	$-0.987587\pi$
$53$		−	4.47911e6i		−	0.0779741i	0.999240	−	0.0389871i	$-0.0124131\pi$
$54$	−1.00272e6	−	1.00272e6i	−0.0160476	−	0.0160476i
$55$	−1.28942e8			−1.90004
$56$	9.80835e6	+	9.80835e6i	0.133275	+	0.133275i
$57$	−171308.	+	171308.i	−0.00214952	+	0.00214952i
$58$	3.16476e7	−	3.16476e7i	0.367210	−	0.367210i
$59$			1.26323e8i			1.35722i	0.734499	+	0.678609i	$0.237417\pi$
$59$			1.26323e8i			1.35722i	−0.734499	+	0.678609i	$0.762583\pi$
$60$			2.96243e6i			0.0295099i
$61$	−2.41668e7	+	2.41668e7i	−0.223478	+	0.223478i	−0.809961	−	0.586484i	$-0.800512\pi$
$61$	−2.41668e7	+	2.41668e7i	−0.223478	+	0.223478i	0.586484	+	0.809961i	$0.300512\pi$
$62$	−2.81485e7	+	2.81485e7i	−0.241931	+	0.241931i
$63$	−2.16075e7	−	2.16075e7i	−0.172811	−	0.172811i
$64$	1.07241e7			0.0799009
$65$	−7.03714e7	−	7.03714e7i	−0.488974	−	0.488974i
$66$		−	2.48045e6i		−	0.0160910i
$67$	1.37527e8			0.833781			0.416890	−	0.908957i	$-0.363120\pi$
$67$	1.37527e8			0.833781			0.416890	+	0.908957i	$0.363120\pi$
$68$	2.58238e7	−	1.42409e8i	0.146464	−	0.807696i
$69$	9.14198e6			0.0485534
$70$		−	2.78713e7i		−	0.138745i
$71$	−2.87544e7	−	2.87544e7i	−0.134290	−	0.134290i	0.636767	−	0.771056i	$-0.280271\pi$
$71$	−2.87544e7	−	2.87544e7i	−0.134290	−	0.134290i	−0.771056	+	0.636767i	$0.780271\pi$
$72$	1.75610e8			0.770110
$73$	1.73725e8	+	1.73725e8i	0.715995	+	0.715995i	0.967782	−	0.251788i	$-0.0810185\pi$
$73$	1.73725e8	+	1.73725e8i	0.715995	+	0.715995i	−0.251788	+	0.967782i	$0.581018\pi$
$74$	6.61073e7	−	6.61073e7i	0.256275	−	0.256275i
$75$	4.13985e6	−	4.13985e6i	0.0151081	−	0.0151081i
$76$		−	2.70599e7i		−	0.0930391i
$77$		−	1.06940e8i		−	0.346683i
$78$	1.35373e6	−	1.35373e6i	0.00414101	−	0.00414101i
$79$	2.79088e8	−	2.79088e8i	0.806157	−	0.806157i	−0.177893	−	0.984050i	$-0.556928\pi$
$79$	2.79088e8	−	2.79088e8i	0.806157	−	0.806157i	0.984050	+	0.177893i	$0.0569281\pi$
$80$	−1.71773e8	−	1.71773e8i	−0.468867	−	0.468867i
$81$	−3.86585e8			−0.997843
$82$	2.09390e8	+	2.09390e8i	0.511438	+	0.511438i
$83$		−	3.15697e8i		−	0.730162i	−0.930976	−	0.365081i	$-0.881041\pi$
$83$		−	3.15697e8i		−	0.730162i	0.930976	−	0.365081i	$-0.118959\pi$
$84$	−2.45693e6			−0.00538439
$85$	−5.30210e8	+	3.67435e8i	−1.10170	+	0.763476i
$86$	−2.69918e8			−0.532095
$87$			1.75850e7i			0.0329084i
$88$	4.34565e8	+	4.34565e8i	0.772472	+	0.772472i
$89$	4.99389e8			0.843693			0.421846	−	0.906667i	$-0.361382\pi$
$89$	4.99389e8			0.843693			0.421846	+	0.906667i	$0.361382\pi$
$90$	−2.49506e8	−	2.49506e8i	−0.400857	−	0.400857i
$91$	5.83636e7	−	5.83636e7i	0.0892186	−	0.0892186i
$92$	−7.22036e8	+	7.22036e8i	−1.05079	+	1.05079i
$93$		−	1.56407e7i		−	0.0216812i
$94$			1.79865e8i			0.237614i
$95$	−8.52832e7	+	8.52832e7i	−0.107425	+	0.107425i
$96$	1.54672e7	−	1.54672e7i	0.0185862	−	0.0185862i
$97$	5.54444e8	+	5.54444e8i	0.635894	+	0.635894i	0.949540	−	0.313646i	$-0.101550\pi$
$97$	5.54444e8	+	5.54444e8i	0.635894	+	0.635894i	−0.313646	+	0.949540i	$0.601550\pi$
$98$	−3.63344e8			−0.397925
$99$	−9.57334e8	−	9.57334e8i	−1.00163	−	1.00163i
$100$			6.53933e8i			0.653933i
$101$	6.53522e8			0.624905			0.312452	−	0.949933i	$-0.398850\pi$
$101$	6.53522e8			0.624905			0.312452	+	0.949933i	$0.398850\pi$
$102$	−7.06833e6	−	1.01996e7i	−0.00646571	−	0.00933004i
$103$	1.02870e7			0.00900581			0.00450291	−	0.999990i	$-0.498567\pi$
$103$	1.02870e7			0.00900581			0.00450291	+	0.999990i	$0.498567\pi$
$104$			4.74336e8i			0.397590i
$105$	7.74338e6	+	7.74338e6i	0.00621697	+	0.00621697i
$106$	4.28957e7			0.0330018
$107$	−1.98220e8	−	1.98220e8i	−0.146191	−	0.146191i	0.630223	−	0.776414i	$-0.282963\pi$
$107$	−1.98220e8	−	1.98220e8i	−0.146191	−	0.146191i	−0.776414	+	0.630223i	$0.782963\pi$
$108$	−4.40051e7	+	4.40051e7i	−0.0311240	+	0.0311240i
$109$	−2.40534e8	+	2.40534e8i	−0.163214	+	0.163214i	−0.783989	−	0.620775i	$-0.786818\pi$
$109$	−2.40534e8	+	2.40534e8i	−0.163214	+	0.163214i	0.620775	+	0.783989i	$0.286818\pi$
$110$		−	1.23486e9i		−	0.804173i
$111$			3.67326e7i			0.0229667i
$112$	1.42463e8	−	1.42463e8i	0.0855499	−	0.0855499i
$113$	7.10246e8	−	7.10246e8i	0.409785	−	0.409785i	−0.471879	−	0.881663i	$-0.656424\pi$
$113$	7.10246e8	−	7.10246e8i	0.409785	−	0.409785i	0.881663	+	0.471879i	$0.156424\pi$
$114$	−1.64059e6	−	1.64059e6i	−0.000909762	−	0.000909762i
$115$	4.55120e9			2.42653
$116$	−1.38887e9	−	1.38887e9i	−0.712199	−	0.712199i
$117$		−	1.04495e9i		−	0.515535i
$118$	−1.20978e9			−0.574429
$119$	−3.04738e8	−	4.39738e8i	−0.139305	−	0.201017i
$120$	−6.29325e7			−0.0277051
$121$		−	2.38010e9i		−	1.00940i
$122$	−2.31441e8	−	2.31441e8i	−0.0945847	−	0.0945847i
$123$	−1.16348e8			−0.0458337
$124$	1.23531e9	+	1.23531e9i	0.469222	+	0.469222i
$125$	−5.26118e8	+	5.26118e8i	−0.192747	+	0.192747i
$126$	2.06931e8	−	2.06931e8i	0.0731407	−	0.0731407i
$127$			2.89317e9i			0.986865i	0.869784	+	0.493432i	$0.164258\pi$
$127$			2.89317e9i			0.986865i	−0.869784	+	0.493432i	$0.835742\pi$
$128$			3.07908e9i			1.01385i
$129$	7.49902e7	−	7.49902e7i	0.0238425	−	0.0238425i
$130$	6.73934e8	−	6.73934e8i	0.206953	−	0.206953i
$131$	1.91531e8	+	1.91531e8i	0.0568222	+	0.0568222i	0.734947	−	0.678125i	$-0.237207\pi$
$131$	1.91531e8	+	1.91531e8i	0.0568222	+	0.0568222i	−0.678125	+	0.734947i	$0.737207\pi$
$132$	−1.08856e8			−0.0312083
$133$	−7.07309e7	−	7.07309e7i	−0.0196009	−	0.0196009i
$134$			1.31707e9i			0.352889i
$135$	2.77376e8			0.0718733
$136$	3.02527e9	+	5.48589e8i	0.758298	+	0.137506i
$137$	−7.83519e9			−1.90023			−0.950117	−	0.311894i	$-0.899036\pi$
$137$	−7.83519e9			−1.90023			−0.950117	+	0.311894i	$0.899036\pi$
$138$			8.75512e7i			0.0205497i
$139$	−1.71799e9	−	1.71799e9i	−0.390350	−	0.390350i	0.484462	−	0.874812i	$-0.339015\pi$
$139$	−1.71799e9	−	1.71799e9i	−0.390350	−	0.390350i	−0.874812	+	0.484462i	$0.839015\pi$
$140$	−1.22315e9			−0.269093
$141$	−4.99713e7	−	4.99713e7i	−0.0106472	−	0.0106472i
$142$	2.75376e8	−	2.75376e8i	0.0568367	−	0.0568367i
$143$	2.58583e9	−	2.58583e9i	0.517117	−	0.517117i
$144$		−	2.55067e9i		−	0.494336i
$145$			8.75445e9i			1.64465i
$146$	−1.66374e9	+	1.66374e9i	−0.303038	+	0.303038i
$147$	1.00946e8	−	1.00946e8i	0.0178305	−	0.0178305i
$148$	−2.90115e9	−	2.90115e9i	−0.497042	−	0.497042i
$149$	−2.56491e9			−0.426319			−0.213159	−	0.977017i	$-0.568375\pi$
$149$	−2.56491e9			−0.426319			−0.213159	+	0.977017i	$0.568375\pi$
$150$	3.96466e7	+	3.96466e7i	0.00639434	+	0.00639434i
$151$			1.16618e10i			1.82544i	0.408581	+	0.912722i	$0.366024\pi$
$151$			1.16618e10i			1.82544i	−0.408581	+	0.912722i	$0.633976\pi$
$152$	5.74849e8			0.0873489
$153$	−6.66459e9	−	1.20853e9i	−0.983246	−	0.178297i
$154$	1.02415e9			0.146730
$155$		−	7.78651e9i		−	1.08355i
$156$	−5.94092e7	−	5.94092e7i	−0.00803143	−	0.00803143i
$157$	6.12170e9			0.804125			0.402063	−	0.915612i	$-0.368293\pi$
$157$	6.12170e9			0.804125			0.402063	+	0.915612i	$0.368293\pi$
$158$	2.67278e9	+	2.67278e9i	0.341198	+	0.341198i
$159$	−1.19175e7	+	1.19175e7i	−0.00147877	+	0.00147877i
$160$	7.70012e9	−	7.70012e9i	0.928876	−	0.928876i
$161$			3.77461e9i			0.442747i
$162$		−	3.70225e9i		−	0.422327i
$163$	5.27273e9	−	5.27273e9i	0.585048	−	0.585048i	−0.351238	−	0.936286i	$-0.614239\pi$
$163$	5.27273e9	−	5.27273e9i	0.585048	−	0.585048i	0.936286	+	0.351238i	$0.114239\pi$
$164$	9.18918e9	−	9.18918e9i	0.991927	−	0.991927i
$165$	3.43075e8	+	3.43075e8i	0.0360339	+	0.0360339i
$166$	3.02338e9			0.309034
$167$	−6.42570e9	−	6.42570e9i	−0.639287	−	0.639287i	0.311092	−	0.950380i	$-0.399305\pi$
$167$	−6.42570e9	−	6.42570e9i	−0.639287	−	0.639287i	−0.950380	+	0.311092i	$0.899305\pi$
$168$		−	5.21940e7i		−	0.00505509i
$169$	−7.78201e9			−0.733841
$170$	−3.51886e9	−	5.07773e9i	−0.323134	−	0.466283i
$171$	−1.26637e9			−0.113261
$172$			1.18455e10i			1.03199i
$173$	1.48153e10	+	1.48153e10i	1.25748	+	1.25748i	0.952290	+	0.305194i	$0.0987212\pi$
$173$	1.48153e10	+	1.48153e10i	1.25748	+	1.25748i	0.305194	+	0.952290i	$0.401279\pi$
$174$	−1.68409e8			−0.0139282
$175$	1.70929e9	+	1.70929e9i	0.137767	+	0.137767i
$176$	6.31189e9	−	6.31189e9i	0.495853	−	0.495853i
$177$	3.36108e8	−	3.36108e8i	0.0257394	−	0.0257394i
$178$			4.78257e9i			0.357084i
$179$		−	1.81997e10i		−	1.32503i	−0.749048	−	0.662516i	$-0.769489\pi$
$179$		−	1.81997e10i		−	1.32503i	0.749048	−	0.662516i	$-0.230511\pi$
$180$	−1.09497e10	+	1.09497e10i	−0.777456	+	0.777456i
$181$	−3.00879e9	+	3.00879e9i	−0.208371	+	0.208371i	−0.803575	−	0.595204i	$-0.797071\pi$
$181$	−3.00879e9	+	3.00879e9i	−0.208371	+	0.208371i	0.595204	+	0.803575i	$0.297071\pi$
$182$	5.58938e8	+	5.58938e8i	0.0377609	+	0.0377609i
$183$	1.28601e8			0.00847643
$184$	−1.53386e10	−	1.53386e10i	−0.986520	−	0.986520i
$185$			1.82868e10i			1.14780i
$186$	1.49789e8			0.00917637
$187$	−1.35016e10	−	1.94829e10i	−0.807418	−	1.16511i
$188$	7.89349e9			0.460849
$189$			2.30046e8i			0.0131141i
$190$	−8.16743e8	−	8.16743e8i	−0.0454668	−	0.0454668i
$191$	1.04248e10			0.566784			0.283392	−	0.959004i	$-0.408540\pi$
$191$	1.04248e10			0.566784			0.283392	+	0.959004i	$0.408540\pi$
$192$	−2.85336e7	−	2.85336e7i	−0.00151531	−	0.00151531i
$193$	1.87029e9	−	1.87029e9i	0.0970291	−	0.0970291i	−0.656926	−	0.753955i	$-0.728144\pi$
$193$	1.87029e9	−	1.87029e9i	0.0970291	−	0.0970291i	0.753955	+	0.656926i	$0.228144\pi$
$194$	−5.30982e9	+	5.30982e9i	−0.269136	+	0.269136i
$195$			3.74473e8i			0.0185466i
$196$			1.59456e10i			0.771769i
$197$	−2.52600e10	+	2.52600e10i	−1.19491	+	1.19491i	−0.219241	+	0.975671i	$0.570358\pi$
$197$	−2.52600e10	+	2.52600e10i	−1.19491	+	1.19491i	−0.975671	+	0.219241i	$0.929642\pi$
$198$	9.16823e9	−	9.16823e9i	0.423928	−	0.423928i
$199$	1.94049e10	+	1.94049e10i	0.877148	+	0.877148i	0.993239	−	0.116091i	$-0.0370364\pi$
$199$	1.94049e10	+	1.94049e10i	0.877148	+	0.877148i	−0.116091	+	0.993239i	$0.537036\pi$
$200$	−1.38919e10			−0.613939
$201$	−3.65917e8	−	3.65917e8i	−0.0158125	−	0.0158125i
$202$			6.25866e9i			0.264485i
$203$	−7.26064e9			−0.300084
$204$	−4.47616e8	+	3.10198e8i	−0.0180955	+	0.0125401i
$205$	−5.79220e10			−2.29061
$206$			9.85172e7i			0.00381162i
$207$	3.37905e10	+	3.37905e10i	1.27917	+	1.27917i
$208$	6.88955e9			0.255215
$209$	−3.13378e9	−	3.13378e9i	−0.113608	−	0.113608i
$210$	−7.41570e7	+	7.41570e7i	−0.00263127	+	0.00263127i
$211$	3.48876e10	−	3.48876e10i	1.21171	−	1.21171i	0.241251	−	0.970463i	$-0.422442\pi$
$211$	3.48876e10	−	3.48876e10i	1.21171	−	1.21171i	0.970463	−	0.241251i	$-0.0775577\pi$
$212$		−	1.88250e9i		−	0.0640064i
$213$			1.53013e8i			0.00509355i
$214$	1.89832e9	−	1.89832e9i	0.0618738	−	0.0618738i
$215$	3.73328e10	−	3.73328e10i	1.19156	−	1.19156i
$216$	−9.34823e8	−	9.34823e8i	−0.0292205	−	0.0292205i
$217$	6.45786e9			0.197706
$218$	−2.30355e9	−	2.30355e9i	−0.0690786	−	0.0690786i
$219$		−	9.24458e8i		−	0.0271574i
$220$	−5.41924e10			−1.55968
$221$	3.26432e9	−	1.80016e10i	0.0920509	−	0.507628i
$222$	−3.51782e8			−0.00972043
$223$		−	3.12685e10i		−	0.846710i	−0.905964	−	0.423355i	$-0.860852\pi$
$223$		−	3.12685e10i		−	0.846710i	0.905964	−	0.423355i	$-0.139148\pi$
$224$	6.38622e9	+	6.38622e9i	0.169484	+	0.169484i
$225$	3.06033e10			0.796063
$226$	6.80190e9	+	6.80190e9i	0.173437	+	0.173437i
$227$	−2.65065e9	+	2.65065e9i	−0.0662576	+	0.0662576i	−0.739459	−	0.673202i	$-0.764919\pi$
$227$	−2.65065e9	+	2.65065e9i	−0.0662576	+	0.0662576i	0.673202	+	0.739459i	$0.264919\pi$
$228$	−7.19981e7	+	7.19981e7i	−0.00176447	+	0.00176447i
$229$		−	4.94370e10i		−	1.18793i	−0.804489	−	0.593967i	$-0.797561\pi$
$229$		−	4.94370e10i		−	1.18793i	0.804489	−	0.593967i	$-0.202439\pi$
$230$			4.35861e10i			1.02700i
$231$	−2.84535e8	+	2.84535e8i	−0.00657478	+	0.00657478i
$232$	2.95046e10	−	2.95046e10i	0.668641	−	0.668641i
$233$	3.64572e10	+	3.64572e10i	0.810366	+	0.810366i	0.984689	−	0.174323i	$-0.0557736\pi$
$233$	3.64572e10	+	3.64572e10i	0.810366	+	0.810366i	−0.174323	+	0.984689i	$0.555774\pi$
$234$	1.00073e10			0.218195
$235$	−2.48775e10	−	2.48775e10i	−0.532109	−	0.532109i
$236$			5.30918e10i			1.11410i
$237$	−1.48513e9			−0.0305772
$238$	4.21129e9	−	2.91842e9i	0.0850784	−	0.0589593i
$239$	−6.14267e10			−1.21777			−0.608887	−	0.793257i	$-0.708384\pi$
$239$	−6.14267e10			−1.21777			−0.608887	+	0.793257i	$0.708384\pi$
$240$			9.14070e8i			0.0177840i
$241$	−5.83662e10	−	5.83662e10i	−1.11451	−	1.11451i	−0.992533	−	0.121978i	$-0.961076\pi$
$241$	−5.83662e10	−	5.83662e10i	−1.11451	−	1.11451i	−0.121978	−	0.992533i	$-0.538924\pi$
$242$	2.27938e10			0.427217
$243$	3.08945e9	+	3.08945e9i	0.0568399	+	0.0568399i
$244$	−1.01569e10	+	1.01569e10i	−0.183446	+	0.183446i
$245$	5.02547e10	−	5.02547e10i	0.891105	−	0.891105i
$246$		−	1.11424e9i		−	0.0193987i
$247$		−	3.42058e9i		−	0.0584740i
$248$	−2.62424e10	+	2.62424e10i	−0.440525	+	0.440525i
$249$	−8.39972e8	+	8.39972e8i	−0.0138474	+	0.0138474i
$250$	−5.03855e9	−	5.03855e9i	−0.0815784	−	0.0815784i
$251$	9.98436e10			1.58777			0.793887	−	0.608066i	$-0.208054\pi$
$251$	9.98436e10			1.58777			0.793887	+	0.608066i	$0.208054\pi$
$252$	−9.08130e9	−	9.08130e9i	−0.141855	−	0.141855i
$253$			1.67236e11i			2.56619i
$254$	−2.77074e10			−0.417681
$255$	2.38836e9	+	4.33094e8i	0.0353727	+	0.00641433i
$256$	−2.39970e10			−0.349203
$257$			4.07145e10i			0.582171i	0.956697	+	0.291085i	$0.0940164\pi$
$257$			4.07145e10i			0.582171i	−0.956697	+	0.291085i	$0.905984\pi$
$258$	7.18169e8	+	7.18169e8i	0.0100911	+	0.0100911i
$259$	−1.51664e10			−0.209428
$260$	−2.95760e10	−	2.95760e10i	−0.401383	−	0.401383i
$261$	−6.49977e10	+	6.49977e10i	−0.866993	+	0.866993i
$262$	−1.83426e9	+	1.83426e9i	−0.0240494	+	0.0240494i
$263$			3.57313e10i			0.460520i	0.973129	+	0.230260i	$0.0739576\pi$
$263$			3.57313e10i			0.460520i	−0.973129	+	0.230260i	$0.926042\pi$
$264$		−	2.31249e9i		−	0.0292996i
$265$	−5.93297e9	+	5.93297e9i	−0.0739036	+	0.0739036i
$266$	6.77378e8	−	6.77378e8i	0.00829590	−	0.00829590i
$267$	−1.32872e9	−	1.32872e9i	−0.0160005	−	0.0160005i
$268$	5.78005e10			0.684424
$269$	−9.38848e10	−	9.38848e10i	−1.09323	−	1.09323i	−0.995182	−	0.0980446i	$-0.968741\pi$
$269$	−9.38848e10	−	9.38848e10i	−1.09323	−	1.09323i	−0.0980446	−	0.995182i	$-0.531259\pi$
$270$			2.65639e9i			0.0304197i
$271$	−1.31223e11			−1.47791			−0.738956	−	0.673754i	$-0.764681\pi$
$271$	−1.31223e11			−1.47791			−0.738956	+	0.673754i	$0.764681\pi$
$272$	7.96805e9	−	4.39410e10i	0.0882657	−	0.486754i
$273$	−3.10575e8			−0.00338403
$274$		−	7.50363e10i		−	0.804255i
$275$	7.57312e10	+	7.57312e10i	0.798505	+	0.798505i
$276$	3.84223e9			0.0398559
$277$	2.62026e10	+	2.62026e10i	0.267415	+	0.267415i	0.828058	−	0.560643i	$-0.189446\pi$
$277$	2.62026e10	+	2.62026e10i	0.267415	+	0.267415i	−0.560643	+	0.828058i	$0.689446\pi$
$278$	1.64529e10	−	1.64529e10i	0.165212	−	0.165212i
$279$	5.78112e10	−	5.78112e10i	0.571206	−	0.571206i
$280$		−	2.59840e10i		−	0.252636i
$281$			1.01765e11i			0.973685i	0.873490	+	0.486843i	$0.161851\pi$
$281$			1.01765e11i			0.973685i	−0.873490	+	0.486843i	$0.838149\pi$
$282$	4.78566e8	−	4.78566e8i	0.00450631	−	0.00450631i
$283$	6.60369e10	−	6.60369e10i	0.611995	−	0.611995i	−0.331471	−	0.943466i	$-0.607545\pi$
$283$	6.60369e10	−	6.60369e10i	0.611995	−	0.611995i	0.943466	+	0.331471i	$0.107545\pi$
$284$	−1.20850e10	−	1.20850e10i	−0.110234	−	0.110234i
$285$	4.53825e8			0.00407461
$286$	2.47641e10	+	2.47641e10i	0.218864	+	0.218864i
$287$		−	4.80385e10i		−	0.417947i
$288$	1.14340e11			0.979333
$289$	−1.11037e11	−	4.16392e10i	−0.936329	−	0.351125i
$290$	−8.38399e10			−0.696081
$291$		−	2.95041e9i		−	0.0241192i
$292$	7.30140e10	+	7.30140e10i	0.587737	+	0.587737i
$293$	3.94765e10			0.312921			0.156460	−	0.987684i	$-0.449992\pi$
$293$	3.94765e10			0.312921			0.156460	+	0.987684i	$0.449992\pi$
$294$	9.66746e8	+	9.66746e8i	0.00754657	+	0.00754657i
$295$	1.67326e11	−	1.67326e11i	1.28637	−	1.28637i
$296$	6.16308e10	−	6.16308e10i	0.466643	−	0.466643i
$297$			1.01923e10i			0.0760099i
$298$		−	2.45637e10i		−	0.180435i
$299$	−9.12708e10	+	9.12708e10i	−0.660406	+	0.660406i
$300$	1.73991e9	−	1.73991e9i	0.0124017	−	0.0124017i
$301$	3.09625e10	+	3.09625e10i	0.217414	+	0.217414i
$302$	−1.11683e11			−0.772601
$303$	−1.73882e9	−	1.73882e9i	−0.0118512	−	0.0118512i
$304$		−	8.34946e9i		−	0.0560696i
$305$	6.40219e10			0.423623
$306$	1.15738e10	−	6.38256e10i	0.0754625	−	0.416149i
$307$	3.10911e10			0.199762			0.0998812	−	0.994999i	$-0.468154\pi$
$307$	3.10911e10			0.199762			0.0998812	+	0.994999i	$0.468154\pi$
$308$		−	4.49453e10i		−	0.284581i
$309$	−2.73706e7	−	2.73706e7i	−0.000170794	−	0.000170794i
$310$	7.45701e10			0.458603
$311$	9.41466e9	+	9.41466e9i	0.0570667	+	0.0570667i	0.735064	−	0.677997i	$-0.237152\pi$
$311$	9.41466e9	+	9.41466e9i	0.0570667	+	0.0570667i	−0.677997	+	0.735064i	$0.737152\pi$
$312$	1.26206e9	−	1.26206e9i	0.00754023	−	0.00754023i
$313$	−1.42325e11	+	1.42325e11i	−0.838168	+	0.838168i	−0.988618	−	0.150450i	$-0.951928\pi$
$313$	−1.42325e11	+	1.42325e11i	−0.838168	+	0.838168i	0.150450	+	0.988618i	$0.451928\pi$
$314$			5.86265e10i			0.340338i
$315$			5.72420e10i			0.327580i
$316$	1.17296e11	−	1.17296e11i	0.661748	−	0.661748i
$317$	2.55851e10	−	2.55851e10i	0.142305	−	0.142305i	−0.632365	−	0.774670i	$-0.717916\pi$
$317$	2.55851e10	−	2.55851e10i	0.142305	−	0.142305i	0.774670	+	0.632365i	$0.217916\pi$
$318$	−1.14132e8	−	1.14132e8i	−0.000625873	−	0.000625873i
$319$	−3.21687e11			−1.73930
$320$	−1.42050e10	−	1.42050e10i	−0.0757298	−	0.0757298i
$321$			1.05480e9i			0.00554497i
$322$	−3.61488e10			−0.187388
$323$	−2.18161e10	−	3.95604e9i	−0.111524	−	0.0202232i
$324$	−1.62475e11			−0.819097
$325$			8.26620e10i			0.410990i
$326$	5.04960e10	+	5.04960e10i	0.247616	+	0.247616i
$327$	1.27997e9			0.00619064
$328$	1.95211e11	+	1.95211e11i	0.931261	+	0.931261i
$329$	2.06325e10	−	2.06325e10i	0.0970890	−	0.0970890i
$330$	−3.28557e9	+	3.28557e9i	−0.0152510	+	0.0152510i
$331$			2.52419e11i			1.15583i	0.816096	+	0.577917i	$0.196134\pi$
$331$			2.52419e11i			1.15583i	−0.816096	+	0.577917i	$0.803866\pi$
$332$		−	1.32682e11i		−	0.599366i
$333$	−1.35771e11	+	1.35771e11i	−0.605072	+	0.605072i
$334$	6.15378e10	−	6.15378e10i	0.270572	−	0.270572i
$335$	−1.82167e11	−	1.82167e11i	−0.790255	−	0.790255i
$336$	−7.58098e8			−0.00324488
$337$	−1.24418e11	−	1.24418e11i	−0.525471	−	0.525471i	0.393747	−	0.919219i	$-0.371179\pi$
$337$	−1.24418e11	−	1.24418e11i	−0.525471	−	0.525471i	−0.919219	+	0.393747i	$0.871179\pi$
$338$		−	7.45270e10i		−	0.310591i
$339$	−3.77949e9			−0.0155430
$340$	−2.22839e11	+	1.54427e11i	−0.904349	+	0.626713i
$341$	2.86120e11			1.14592
$342$		−	1.21279e10i		−	0.0479365i
$343$	8.60106e10	+	8.60106e10i	0.335528	+	0.335528i
$344$	−2.51640e11			−0.968874
$345$	−1.21093e10	−	1.21093e10i	−0.0460187	−	0.0460187i
$346$	−1.41883e11	+	1.41883e11i	−0.532218	+	0.532218i
$347$	−8.87289e10	+	8.87289e10i	−0.328536	+	0.328536i	−0.852030	−	0.523494i	$-0.824628\pi$
$347$	−8.87289e10	+	8.87289e10i	−0.328536	+	0.328536i	0.523494	+	0.852030i	$0.324628\pi$
$348$			7.39072e9i			0.0270135i
$349$		−	2.12956e11i		−	0.768380i	−0.923254	−	0.384190i	$-0.874481\pi$
$349$		−	2.12956e11i		−	0.768380i	0.923254	−	0.384190i	$-0.125519\pi$
$350$	−1.63696e10	+	1.63696e10i	−0.0583085	+	0.0583085i
$351$	−5.56257e9	+	5.56257e9i	−0.0195611	+	0.0195611i
$352$	2.82945e11	+	2.82945e11i	0.982337	+	0.982337i
$353$	4.20619e11			1.44179			0.720896	−	0.693043i	$-0.243730\pi$
$353$	4.20619e11			1.44179			0.720896	+	0.693043i	$0.243730\pi$
$354$	3.21884e9	+	3.21884e9i	0.0108939	+	0.0108939i
$355$			7.61754e10i			0.254558i
$356$	2.09886e11			0.692560
$357$	−3.59193e8	+	1.98082e9i	−0.00117036	+	0.00645414i
$358$	1.74296e11			0.560807
$359$		−	6.56670e9i		−	0.0208652i	−0.999946	−	0.0104326i	$-0.996679\pi$
$359$		−	6.56670e9i		−	0.0208652i	0.999946	−	0.0104326i	$-0.00332086\pi$
$360$	−2.32610e11	−	2.32610e11i	−0.729907	−	0.729907i
$361$	3.18542e11			0.987154
$362$	−2.88146e10	−	2.88146e10i	−0.0881911	−	0.0881911i
$363$	−6.33272e9	+	6.33272e9i	−0.0191430	+	0.0191430i
$364$	2.45293e10	−	2.45293e10i	0.0732367	−	0.0732367i
$365$		−	4.60228e11i		−	1.35723i
$366$			1.23159e9i			0.00358756i
$367$	3.97894e11	−	3.97894e11i	1.14491	−	1.14491i	0.157368	−	0.987540i	$-0.449699\pi$
$367$	3.97894e11	−	3.97894e11i	1.14491	−	1.14491i	0.987540	−	0.157368i	$-0.0503007\pi$
$368$	−2.22787e11	+	2.22787e11i	−0.633250	+	0.633250i
$369$	−4.30044e11	−	4.30044e11i	−1.20752	−	1.20752i
$370$	−1.75130e11			−0.485793
$371$	−4.92060e9	−	4.92060e9i	−0.0134845	−	0.0134845i
$372$		−	6.57356e9i		−	0.0177974i
$373$	3.47635e11			0.929896			0.464948	−	0.885338i	$-0.346073\pi$
$373$	3.47635e11			0.929896			0.464948	+	0.885338i	$0.346073\pi$
$374$	1.86584e11	−	1.29303e11i	0.493120	−	0.341731i
$375$	2.79968e9			0.00731084
$376$			1.67686e11i			0.432664i
$377$	−1.75564e11	−	1.75564e11i	−0.447609	−	0.447609i
$378$	−2.20312e9			−0.00555040
$379$	−1.97117e11	−	1.97117e11i	−0.490736	−	0.490736i	0.417802	−	0.908538i	$-0.362801\pi$
$379$	−1.97117e11	−	1.97117e11i	−0.490736	−	0.490736i	−0.908538	+	0.417802i	$0.862801\pi$
$380$	−3.58432e10	+	3.58432e10i	−0.0881821	+	0.0881821i
$381$	7.69784e9	−	7.69784e9i	0.0187157	−	0.0187157i
$382$			9.98365e10i			0.239886i
$383$			5.20359e11i			1.23569i	0.786301	+	0.617844i	$0.211994\pi$
$383$			5.20359e11i			1.23569i	−0.786301	+	0.617844i	$0.788006\pi$
$384$	8.19247e9	−	8.19247e9i	0.0192276	−	0.0192276i
$385$	−1.41651e11	+	1.41651e11i	−0.328585	+	0.328585i
$386$	1.79115e10	+	1.79115e10i	0.0410666	+	0.0410666i
$387$	5.54356e11			1.25629
$388$	2.33024e11	+	2.33024e11i	0.521985	+	0.521985i
$389$		−	5.11901e11i		−	1.13348i	−0.823898	−	0.566738i	$-0.808205\pi$
$389$		−	5.11901e11i		−	1.13348i	0.823898	−	0.566738i	$-0.191795\pi$
$390$	−3.58626e9			−0.00784967
$391$	4.76559e11	+	6.87676e11i	1.03115	+	1.48795i
$392$	−3.38740e11			−0.724568
$393$		−	1.01921e9i		−	0.00215525i
$394$	−2.41911e11	−	2.41911e11i	−0.505735	−	0.505735i
$395$	−7.39352e11			−1.52815
$396$	−4.02353e11	−	4.02353e11i	−0.822202	−	0.822202i
$397$	1.91247e11	−	1.91247e11i	0.386400	−	0.386400i	−0.487001	−	0.873401i	$-0.661909\pi$
$397$	1.91247e11	−	1.91247e11i	0.386400	−	0.386400i	0.873401	+	0.487001i	$0.161909\pi$
$398$	−1.85837e11	+	1.85837e11i	−0.371244	+	0.371244i
$399$			3.76386e8i			0.000743457i
$400$			2.01774e11i			0.394090i
$401$	7.12157e10	−	7.12157e10i	0.137539	−	0.137539i	−0.634985	−	0.772524i	$-0.718994\pi$
$401$	7.12157e10	−	7.12157e10i	0.137539	−	0.137539i	0.772524	+	0.634985i	$0.218994\pi$
$402$	3.50433e9	−	3.50433e9i	0.00669249	−	0.00669249i
$403$	1.56152e11	+	1.56152e11i	0.294901	+	0.294901i
$404$	2.74665e11			0.512964
$405$	5.12065e11	+	5.12065e11i	0.945752	+	0.945752i
$406$		−	6.95339e10i		−	0.127008i
$407$	−6.71958e11			−1.21386
$408$	−6.58969e9	−	9.50895e9i	−0.0117732	−	0.0169888i
$409$	4.06059e11			0.717521			0.358760	−	0.933430i	$-0.383199\pi$
$409$	4.06059e11			0.717521			0.358760	+	0.933430i	$0.383199\pi$
$410$		−	5.54709e11i		−	0.969479i
$411$	2.08470e10	+	2.08470e10i	0.0360376	+	0.0360376i
$412$	4.32348e9			0.00739258
$413$	1.38775e11	+	1.38775e11i	0.234712	+	0.234712i
$414$	−3.23606e11	+	3.23606e11i	−0.541396	+	0.541396i
$415$	−4.18168e11	+	4.18168e11i	−0.692045	+	0.692045i
$416$			3.08840e11i			0.505607i
$417$			9.14208e9i			0.0148058i
$418$	3.00117e10	−	3.00117e10i	0.0480836	−	0.0480836i
$419$	−6.51835e11	+	6.51835e11i	−1.03318	+	1.03318i	−0.0337466	+	0.999430i	$0.510744\pi$
$419$	−6.51835e11	+	6.51835e11i	−1.03318	+	1.03318i	−0.999430	+	0.0337466i	$0.989256\pi$
$420$	3.25442e9	+	3.25442e9i	0.00510331	+	0.00510331i
$421$	−9.29663e11			−1.44230			−0.721150	−	0.692778i	$-0.756386\pi$
$421$	−9.29663e11			−1.44230			−0.721150	+	0.692778i	$0.756386\pi$
$422$	3.34113e11	+	3.34113e11i	0.512846	+	0.512846i
$423$		−	3.69407e11i		−	0.561013i
$424$	3.99910e10			0.0600918
$425$	5.27211e11	+	9.56021e10i	0.783853	+	0.142140i
$426$	−1.46538e9			−0.00215580
$427$			5.30975e10i			0.0772946i
$428$	−8.33087e10	−	8.33087e10i	−0.120003	−	0.120003i
$429$	−1.37602e10			−0.0196140
$430$	3.57530e11	+	3.57530e11i	0.504318	+	0.504318i
$431$	−1.68863e11	+	1.68863e11i	−0.235715	+	0.235715i	−0.815073	−	0.579358i	$-0.803303\pi$
$431$	−1.68863e11	+	1.68863e11i	−0.235715	+	0.235715i	0.579358	+	0.815073i	$0.303303\pi$
$432$	−1.35780e10	+	1.35780e10i	−0.0187567	+	0.0187567i
$433$		−	9.66720e11i		−	1.32162i	−0.750555	−	0.660808i	$-0.770214\pi$
$433$		−	9.66720e11i		−	1.32162i	0.750555	−	0.660808i	$-0.229786\pi$
$434$			6.18459e10i			0.0836771i
$435$	2.32929e10	−	2.32929e10i	0.0311905	−	0.0311905i
$436$	−1.01093e11	+	1.01093e11i	−0.133977	+	0.133977i
$437$	1.10611e11	+	1.10611e11i	0.145088	+	0.145088i
$438$	8.85337e9			0.0114941
$439$	−2.47317e11	−	2.47317e11i	−0.317807	−	0.317807i	0.530117	−	0.847924i	$-0.322148\pi$
$439$	−2.47317e11	−	2.47317e11i	−0.317807	−	0.317807i	−0.847924	+	0.530117i	$0.822148\pi$
$440$		−	1.15124e12i		−	1.46429i
$441$	7.46234e11			0.939510
$442$	1.72398e11	+	3.12619e10i	0.214848	+	0.0389596i
$443$	6.21165e11			0.766285			0.383142	−	0.923689i	$-0.374842\pi$
$443$	6.21165e11			0.766285			0.383142	+	0.923689i	$0.374842\pi$
$444$			1.54382e10i			0.0188526i
$445$	−6.61484e11	−	6.61484e11i	−0.799649	−	0.799649i
$446$	2.99453e11			0.358362
$447$	6.82444e9	+	6.82444e9i	0.00808506	+	0.00808506i
$448$	1.17811e10	−	1.17811e10i	0.0138177	−	0.0138177i
$449$	−1.52717e11	+	1.52717e11i	−0.177329	+	0.177329i	−0.790190	−	0.612862i	$-0.790018\pi$
$449$	−1.52717e11	+	1.52717e11i	−0.177329	+	0.177329i	0.612862	+	0.790190i	$0.290018\pi$
$450$			2.93083e11i			0.336926i
$451$		−	2.12838e12i		−	2.42245i
$452$	2.98505e11	−	2.98505e11i	0.336379	−	0.336379i
$453$	3.10284e10	−	3.10284e10i	0.0346192	−	0.0346192i
$454$	−2.53848e10	−	2.53848e10i	−0.0280429	−	0.0280429i
$455$	−1.54615e11			−0.169122
$456$	−1.52949e9	−	1.52949e9i	−0.00165656	−	0.00165656i
$457$			4.26877e11i			0.457804i	0.973449	+	0.228902i	$0.0735135\pi$
$457$			4.26877e11i			0.457804i	−0.973449	+	0.228902i	$0.926486\pi$
$458$	4.73450e11			0.502781
$459$	2.90443e10	+	4.19109e10i	0.0305424	+	0.0440728i
$460$	1.91280e12			1.99186
$461$			1.33434e12i			1.37598i	0.725718	+	0.687992i	$0.241508\pi$
$461$			1.33434e12i			1.37598i	−0.725718	+	0.687992i	$0.758492\pi$
$462$	−2.72494e9	−	2.72494e9i	−0.00278271	−	0.00278271i
$463$	−9.52978e11			−0.963759			−0.481880	−	0.876237i	$-0.660046\pi$
$463$	−9.52978e11			−0.963759			−0.481880	+	0.876237i	$0.660046\pi$
$464$	−4.28542e11	−	4.28542e11i	−0.429203	−	0.429203i
$465$	−2.07175e10	+	2.07175e10i	−0.0205494	+	0.0205494i
$466$	−3.49144e11	+	3.49144e11i	−0.342979	+	0.342979i
$467$			1.15911e12i			1.12772i	0.825871	+	0.563859i	$0.190684\pi$
$467$			1.15911e12i			1.12772i	−0.825871	+	0.563859i	$0.809316\pi$
$468$		−	4.39175e11i		−	0.423186i
$469$	1.51083e11	−	1.51083e11i	0.144191	−	0.144191i
$470$	2.38247e11	−	2.38247e11i	0.225210	−	0.225210i
$471$	−1.62880e10	−	1.62880e10i	−0.0152501	−	0.0152501i
$472$	−1.12786e12			−1.04596
$473$	1.37181e12	+	1.37181e12i	1.26014	+	1.26014i
$474$		−	1.42229e10i		−	0.0129415i
$475$	1.00178e11			0.0902926
$476$	−1.28077e11	−	1.84815e11i	−0.114351	−	0.165008i
$477$	−8.80989e10			−0.0779180
$478$		−	5.88273e11i		−	0.515411i
$479$	6.62402e11	+	6.62402e11i	0.574926	+	0.574926i	0.933501	−	0.358575i	$-0.116737\pi$
$479$	6.62402e11	+	6.62402e11i	0.574926	+	0.574926i	−0.358575	+	0.933501i	$0.616737\pi$
$480$	−4.09753e10			−0.0352319
$481$	−3.66727e11	−	3.66727e11i	−0.312385	−	0.312385i
$482$	5.58963e11	−	5.58963e11i	0.471706	−	0.471706i
$483$	1.00431e10	−	1.00431e10i	0.00839661	−	0.00839661i
$484$		−	1.00032e12i		−	0.828580i
$485$		−	1.46882e12i		−	1.20540i
$486$	−2.95872e10	+	2.95872e10i	−0.0240569	+	0.0240569i
$487$	−1.49252e12	+	1.49252e12i	−1.20237	+	1.20237i	−0.228932	+	0.973442i	$0.573523\pi$
$487$	−1.49252e12	+	1.49252e12i	−1.20237	+	1.20237i	−0.973442	+	0.228932i	$0.926477\pi$
$488$	−2.15769e11	−	2.15769e11i	−0.172226	−	0.172226i
$489$	−2.80582e10			−0.0221907
$490$	4.81280e11	+	4.81280e11i	0.377151	+	0.377151i
$491$		−	2.40038e12i		−	1.86386i	−0.362641	−	0.931929i	$-0.618125\pi$
$491$		−	2.40038e12i		−	1.86386i	0.362641	−	0.931929i	$-0.381875\pi$
$492$	−4.88992e10			−0.0376234
$493$	−1.32278e12	+	9.16684e11i	−1.00850	+	0.698889i
$494$	3.27583e10			0.0247485
$495$			2.53614e12i			1.89867i
$496$	3.81160e11	+	3.81160e11i	0.282775	+	0.282775i
$497$	−6.31772e10			−0.0464469
$498$	−8.04427e9	−	8.04427e9i	−0.00586077	−	0.00586077i
$499$	−3.18033e11	+	3.18033e11i	−0.229625	+	0.229625i	−0.812536	−	0.582911i	$-0.801914\pi$
$499$	−3.18033e11	+	3.18033e11i	−0.229625	+	0.229625i	0.582911	+	0.812536i	$0.301914\pi$
$500$	−2.21119e11	+	2.21119e11i	−0.158220	+	0.158220i
$501$			3.41936e10i			0.0242479i
$502$			9.56185e11i			0.672009i
$503$	−7.17670e11	+	7.17670e11i	−0.499884	+	0.499884i	−0.911402	−	0.411518i	$-0.864999\pi$
$503$	−7.17670e11	+	7.17670e11i	−0.499884	+	0.499884i	0.411518	+	0.911402i	$0.364999\pi$
$504$	1.92919e11	−	1.92919e11i	0.133180	−	0.133180i
$505$	−8.65645e11	−	8.65645e11i	−0.592282	−	0.592282i
$506$	−1.60159e12			−1.08611
$507$	2.07055e10	+	2.07055e10i	0.0139172	+	0.0139172i
$508$			1.21596e12i			0.810085i
$509$	5.53282e11			0.365356			0.182678	−	0.983173i	$-0.441523\pi$
$509$	5.53282e11			0.365356			0.182678	+	0.983173i	$0.441523\pi$
$510$	−4.14766e9	+	2.28729e10i	−0.00271480	+	0.0149711i
$511$	3.81697e11			0.247642
$512$			1.34667e12i			0.866058i
$513$	6.74129e9	+	6.74129e9i	0.00429749	+	0.00429749i
$514$	−3.89916e11			−0.246398
$515$	−1.36261e10	−	1.36261e10i	−0.00853568	−	0.00853568i
$516$	3.15172e10	−	3.15172e10i	0.0195715	−	0.0195715i
$517$	9.14136e11	−	9.14136e11i	0.562734	−	0.562734i
$518$		−	1.45246e11i		−	0.0886383i
$519$		−	7.88378e10i		−	0.0476959i
$520$	6.28299e11	−	6.28299e11i	0.376835	−	0.376835i
$521$	−1.51383e12	+	1.51383e12i	−0.900137	+	0.900137i	−0.995448	−	0.0953104i	$-0.969616\pi$
$521$	−1.51383e12	+	1.51383e12i	−0.900137	+	0.900137i	0.0953104	+	0.995448i	$0.469616\pi$
$522$	−6.22471e11	−	6.22471e11i	−0.366946	−	0.366946i
$523$	−3.97935e11			−0.232570			−0.116285	−	0.993216i	$-0.537099\pi$
$523$	−3.97935e11			−0.232570			−0.116285	+	0.993216i	$0.537099\pi$
$524$	8.04975e10	+	8.04975e10i	0.0466435	+	0.0466435i
$525$		−	9.09579e9i		−	0.00522545i
$526$	−3.42193e11			−0.194910
$527$	1.17652e12	−	8.15330e11i	0.664436	−	0.460454i
$528$	−3.35880e10			−0.0188075
$529$		−	4.10170e12i		−	2.27726i
$530$	−5.68190e10	−	5.68190e10i	−0.0312790	−	0.0312790i
$531$	2.48463e12			1.35624
$532$	−2.97271e10	−	2.97271e10i	−0.0160898	−	0.0160898i
$533$	1.16158e12	−	1.16158e12i	0.623415	−	0.623415i
$534$	1.27249e10	−	1.27249e10i	0.00677204	−	0.00677204i
$535$			5.25119e11i			0.277118i
$536$			1.22789e12i			0.642565i
$537$	−4.84239e10	+	4.84239e10i	−0.0251290	+	0.0251290i
$538$	8.99119e11	−	8.99119e11i	0.462697	−	0.462697i
$539$	1.84664e12	+	1.84664e12i	0.942392	+	0.942392i
$540$	1.16577e11			0.0589985
$541$	6.21067e11	+	6.21067e11i	0.311710	+	0.311710i	0.845572	−	0.533862i	$-0.179260\pi$
$541$	6.21067e11	+	6.21067e11i	0.311710	+	0.311710i	−0.533862	+	0.845572i	$0.679260\pi$
$542$		−	1.25670e12i		−	0.625511i
$543$	1.60109e10			0.00790345
$544$	1.96976e12	+	3.57186e11i	0.964311	+	0.174864i
$545$	6.37216e11			0.309387
$546$		−	2.97432e9i		−	0.00143226i
$547$	−1.77660e12	−	1.77660e12i	−0.848489	−	0.848489i	0.141455	−	0.989945i	$-0.454822\pi$
$547$	−1.77660e12	−	1.77660e12i	−0.848489	−	0.848489i	−0.989945	+	0.141455i	$0.954822\pi$
$548$	−3.29301e12			−1.55984
$549$	4.75332e11	+	4.75332e11i	0.223317	+	0.223317i
$550$	−7.25265e11	+	7.25265e11i	−0.337959	+	0.337959i
$551$	−2.12766e11	+	2.12766e11i	−0.0983377	+	0.0983377i
$552$			8.16226e10i			0.0374183i
$553$		−	6.13193e11i		−	0.278827i
$554$	−2.50938e11	+	2.50938e11i	−0.113181	+	0.113181i
$555$	4.86555e10	−	4.86555e10i	0.0217678	−	0.0217678i
$556$	−7.22044e11	−	7.22044e11i	−0.320426	−	0.320426i
$557$	3.99416e12			1.75823			0.879117	−	0.476606i	$-0.158133\pi$
$557$	3.99416e12			1.75823			0.879117	+	0.476606i	$0.158133\pi$
$558$	5.53648e11	+	5.53648e11i	0.241757	+	0.241757i
$559$			1.49736e12i			0.648594i
$560$	−3.77408e11			−0.162168
$561$	−1.59143e10	+	8.77615e10i	−0.00678350	+	0.0374086i
$562$	−9.74583e11			−0.412103
$563$		−	3.88071e12i		−	1.62789i	−0.580945	−	0.813943i	$-0.697317\pi$
$563$		−	3.88071e12i		−	1.62789i	0.580945	−	0.813943i	$-0.302683\pi$
$564$	−2.10021e10	−	2.10021e10i	−0.00873992	−	0.00873992i
$565$	−1.88156e12			−0.776785
$566$	6.32424e11	+	6.32424e11i	0.259021	+	0.259021i
$567$	−4.24689e11	+	4.24689e11i	−0.172563	+	0.172563i
$568$	2.56729e11	−	2.56729e11i	0.103492	−	0.103492i
$569$			1.04083e12i			0.416270i	0.978100	+	0.208135i	$0.0667394\pi$
$569$			1.04083e12i			0.416270i	−0.978100	+	0.208135i	$0.933261\pi$
$570$			4.34620e9i			0.00172454i
$571$	2.42489e12	−	2.42489e12i	0.954618	−	0.954618i	−0.0443956	−	0.999014i	$-0.514136\pi$
$571$	2.42489e12	−	2.42489e12i	0.954618	−	0.954618i	0.999014	+	0.0443956i	$0.0141362\pi$
$572$	1.08679e12	−	1.08679e12i	0.424484	−	0.424484i
$573$	−2.77372e10	−	2.77372e10i	−0.0107490	−	0.0107490i
$574$	4.60057e11			0.176892
$575$	−2.67304e12	−	2.67304e12i	−1.01977	−	1.01977i
$576$		−	2.10931e11i		−	0.0798434i
$577$	−2.26487e12			−0.850652			−0.425326	−	0.905040i	$-0.639841\pi$
$577$	−2.26487e12			−0.850652			−0.425326	+	0.905040i	$0.639841\pi$
$578$	3.98771e11	−	1.06338e12i	0.148610	−	0.396292i
$579$	−9.95255e9			−0.00368028
$580$			3.67936e12i			1.35004i
$581$	−3.46814e11	−	3.46814e11i	−0.126271	−	0.126271i
$582$	2.82556e10			0.0102082
$583$	−2.18010e11	−	2.18010e11i	−0.0781570	−	0.0781570i
$584$	−1.55107e12	+	1.55107e12i	−0.551791	+	0.551791i
$585$	−1.38412e12	+	1.38412e12i	−0.488622	+	0.488622i
$586$			3.78060e11i			0.132441i
$587$			2.23470e12i			0.776870i	0.921476	+	0.388435i	$0.126984\pi$
$587$			2.23470e12i			0.776870i	−0.921476	+	0.388435i	$0.873016\pi$
$588$	4.24262e10	−	4.24262e10i	0.0146365	−	0.0146365i
$589$	1.89241e11	−	1.89241e11i	0.0647884	−	0.0647884i
$590$	1.60245e12	+	1.60245e12i	0.544442	+	0.544442i
$591$	1.34418e11			0.0453226
$592$	−8.95164e11	−	8.95164e11i	−0.299540	−	0.299540i
$593$			3.12521e12i			1.03785i	0.854821	+	0.518923i	$0.173667\pi$
$593$			3.12521e12i			1.03785i	−0.854821	+	0.518923i	$0.826333\pi$
$594$	−9.76104e10			−0.0321704
$595$	−1.78819e11	+	9.86122e11i	−0.0584907	+	0.322555i
$596$	−1.07799e12			−0.349951
$597$		−	1.03261e11i		−	0.0332699i
$598$	−8.74084e11	−	8.74084e11i	−0.279510	−	0.279510i
$599$	4.98049e12			1.58071			0.790353	−	0.612652i	$-0.209897\pi$
$599$	4.98049e12			1.58071			0.790353	+	0.612652i	$0.209897\pi$
$600$	3.69619e10	+	3.69619e10i	0.0116432	+	0.0116432i
$601$	−1.35901e12	+	1.35901e12i	−0.424902	+	0.424902i	−0.886887	−	0.461986i	$-0.847137\pi$
$601$	−1.35901e12	+	1.35901e12i	−0.424902	+	0.424902i	0.461986	+	0.886887i	$0.347137\pi$
$602$	−2.96523e11	+	2.96523e11i	−0.0920182	+	0.0920182i
$603$		−	2.70500e12i		−	0.833181i
$604$			4.90126e12i			1.49845i
$605$	−3.15265e12	+	3.15265e12i	−0.956702	+	0.956702i
$606$	1.66524e10	−	1.66524e10i	0.00501590	−	0.00501590i
$607$	−7.82022e11	−	7.82022e11i	−0.233814	−	0.233814i	0.580469	−	0.814282i	$-0.302869\pi$
$607$	−7.82022e11	−	7.82022e11i	−0.233814	−	0.233814i	−0.814282	+	0.580469i	$0.802869\pi$
$608$	3.74284e11			0.111080
$609$	1.93183e10	+	1.93183e10i	0.00569104	+	0.00569104i
$610$			6.13127e11i			0.179294i
$611$	9.97796e11			0.289638
$612$	−2.80102e12	−	5.07925e11i	−0.807115	−	0.146359i
$613$	−3.38242e12			−0.967511			−0.483755	−	0.875203i	$-0.660728\pi$
$613$	−3.38242e12			−0.967511			−0.483755	+	0.875203i	$0.660728\pi$
$614$			2.97754e11i			0.0845474i
$615$	1.54113e11	+	1.54113e11i	0.0434410	+	0.0434410i
$616$	9.54797e11			0.267176
$617$	−1.22665e12	−	1.22665e12i	−0.340750	−	0.340750i	0.515899	−	0.856649i	$-0.327458\pi$
$617$	−1.22665e12	−	1.22665e12i	−0.340750	−	0.340750i	−0.856649	+	0.515899i	$0.827458\pi$
$618$	2.62124e8	−	2.62124e8i	7.22867e−5	−	7.22867e-5i
$619$	2.92180e12	−	2.92180e12i	0.799913	−	0.799913i	−0.183168	−	0.983082i	$-0.558635\pi$
$619$	2.92180e12	−	2.92180e12i	0.799913	−	0.799913i	0.983082	+	0.183168i	$0.0586353\pi$
$620$		−	3.27255e12i		−	0.889454i
$621$		−	3.59754e11i		−	0.0970718i
$622$	−9.01626e10	+	9.01626e10i	−0.0241529	+	0.0241529i
$623$	5.48612e11	−	5.48612e11i	0.145905	−	0.145905i
$624$	−1.83310e10	−	1.83310e10i	−0.00484010	−	0.00484010i
$625$	4.43270e12			1.16201
$626$	−1.36302e12	−	1.36302e12i	−0.354746	−	0.354746i
$627$			1.66760e10i			0.00430912i
$628$	2.57286e12			0.660081
$629$	−2.76309e12	+	1.91482e12i	−0.703830	+	0.487753i
$630$	−5.48197e11			−0.138645
$631$			1.18926e12i			0.298637i	0.988789	+	0.149318i	$0.0477079\pi$
$631$			1.18926e12i			0.298637i	−0.988789	+	0.149318i	$0.952292\pi$
$632$	2.49179e12	+	2.49179e12i	0.621276	+	0.621276i
$633$	−1.85650e11			−0.0459599
$634$	2.45024e11	+	2.45024e11i	0.0602291	+	0.0602291i
$635$	3.83226e12	−	3.83226e12i	0.935347	−	0.935347i
$636$	−5.00875e9	+	5.00875e9i	−0.00121387	+	0.00121387i
$637$			2.01564e12i			0.485048i
$638$		−	3.08074e12i		−	0.736143i
$639$	−5.65566e11	+	5.65566e11i	−0.134193	+	0.134193i
$640$	4.07850e12	−	4.07850e12i	0.960928	−	0.960928i
$641$	−9.68506e11	−	9.68506e11i	−0.226590	−	0.226590i	0.584676	−	0.811267i	$-0.301221\pi$
$641$	−9.68506e11	−	9.68506e11i	−0.226590	−	0.226590i	−0.811267	+	0.584676i	$0.801221\pi$
$642$	−1.01017e10			−0.00234685
$643$	−2.99579e12	−	2.99579e12i	−0.691133	−	0.691133i	0.271349	−	0.962481i	$-0.412530\pi$
$643$	−2.99579e12	−	2.99579e12i	−0.691133	−	0.691133i	−0.962481	+	0.271349i	$0.912530\pi$
$644$			1.58641e12i			0.363437i
$645$	−1.98662e11			−0.0451956
$646$	3.78863e10	−	2.08929e11i	0.00855926	−	0.0472012i
$647$	−7.27863e12			−1.63298			−0.816489	−	0.577361i	$-0.804082\pi$
$647$	−7.27863e12			−1.63298			−0.816489	+	0.577361i	$0.804082\pi$
$648$		−	3.45155e12i		−	0.769001i
$649$	6.14849e12	+	6.14849e12i	1.36040	+	1.36040i
$650$	−7.91640e11			−0.173947
$651$	−1.71824e10	−	1.71824e10i	−0.00374946	−	0.00374946i
$652$	2.21605e12	−	2.21605e12i	0.480247	−	0.480247i
$653$	−1.82979e12	+	1.82979e12i	−0.393814	+	0.393814i	−0.876044	−	0.482231i	$-0.839827\pi$
$653$	−1.82979e12	+	1.82979e12i	−0.393814	+	0.393814i	0.482231	+	0.876044i	$0.339827\pi$
$654$			1.22581e10i			0.00262013i
$655$		−	5.07398e11i		−	0.107712i
$656$	2.83536e12	−	2.83536e12i	0.597780	−	0.597780i
$657$	3.41697e12	−	3.41697e12i	0.715480	−	0.715480i
$658$	1.97594e11	+	1.97594e11i	0.0410920	+	0.0410920i
$659$	−3.62332e12			−0.748381			−0.374190	−	0.927352i	$-0.622079\pi$
$659$	−3.62332e12			−0.748381			−0.374190	+	0.927352i	$0.622079\pi$
$660$	1.44189e11	+	1.44189e11i	0.0295791	+	0.0295791i
$661$		−	1.90260e11i		−	0.0387651i	−0.999812	−	0.0193826i	$-0.993830\pi$
$661$		−	1.90260e11i		−	0.0387651i	0.999812	−	0.0193826i	$-0.00617005\pi$
$662$	−2.41737e12			−0.489195
$663$	−5.65820e10	+	3.92113e10i	−0.0113728	+	0.00788134i
$664$	2.81865e12			0.562709
$665$			1.87378e11i			0.0371554i
$666$	−1.30025e12	−	1.30025e12i	−0.256091	−	0.256091i
$667$	1.13544e13			2.22126
$668$	−2.70062e12	−	2.70062e12i	−0.524770	−	0.524770i
$669$	−8.31958e10	+	8.31958e10i	−0.0160577	+	0.0160577i
$670$	1.74458e12	−	1.74458e12i	0.334467	−	0.334467i
$671$			2.35252e12i			0.448004i
$672$		−	3.39835e10i		−	0.00642845i
$673$	−7.34819e12	+	7.34819e12i	−1.38074	+	1.38074i	−0.537439	+	0.843303i	$0.680608\pi$
$673$	−7.34819e12	+	7.34819e12i	−1.38074	+	1.38074i	−0.843303	+	0.537439i	$0.819392\pi$
$674$	1.19153e12	−	1.19153e12i	0.222401	−	0.222401i
$675$	−1.62911e11	−	1.62911e11i	−0.0302053	−	0.0302053i
$676$	−3.27066e12			−0.602386
$677$	−3.89320e12	−	3.89320e12i	−0.712291	−	0.712291i	0.254723	−	0.967014i	$-0.418016\pi$
$677$	−3.89320e12	−	3.89320e12i	−0.712291	−	0.712291i	−0.967014	+	0.254723i	$0.918016\pi$
$678$		−	3.61955e10i		−	0.00657841i
$679$	1.21819e12			0.219938
$680$	−3.28058e12	−	4.73389e12i	−0.588384	−	0.849040i
$681$	1.41051e10			0.00251313
$682$			2.74012e12i			0.484998i
$683$	1.36273e12	+	1.36273e12i	0.239617	+	0.239617i	0.816691	−	0.577075i	$-0.195806\pi$
$683$	1.36273e12	+	1.36273e12i	0.239617	+	0.239617i	−0.577075	+	0.816691i	$0.695806\pi$
$684$	−5.32237e11			−0.0929722
$685$	1.03784e13	+	1.03784e13i	1.80103	+	1.80103i
$686$	−8.23708e11	+	8.23708e11i	−0.142009	+	0.142009i
$687$	−1.31537e11	+	1.31537e11i	−0.0225290	+	0.0225290i
$688$			3.65498e12i			0.621924i
$689$		−	2.37962e11i		−	0.0402273i
$690$	1.15969e11	−	1.15969e11i	0.0194770	−	0.0194770i
$691$	−8.81405e11	+	8.81405e11i	−0.147070	+	0.147070i	−0.776808	−	0.629738i	$-0.783162\pi$
$691$	−8.81405e11	+	8.81405e11i	−0.147070	+	0.147070i	0.629738	+	0.776808i	$0.283162\pi$
$692$	6.22663e12	+	6.22663e12i	1.03223	+	1.03223i
$693$	−2.10339e12			−0.346434
$694$	−8.49742e11	−	8.49742e11i	−0.139049	−	0.139049i
$695$			4.55125e12i			0.739944i
$696$	−1.57005e11			−0.0253613
$697$	−6.06505e12	−	8.75189e12i	−0.973390	−	1.40460i
$698$	2.03944e12			0.325209
$699$		−	1.94002e11i		−	0.0307369i
$700$	7.18388e11	+	7.18388e11i	0.113088	+	0.113088i
$701$	−9.42697e12			−1.47449			−0.737244	−	0.675627i	$-0.763873\pi$
$701$	−9.42697e12			−1.47449			−0.737244	+	0.675627i	$0.763873\pi$
$702$	−5.32718e10	−	5.32718e10i	−0.00827904	−	0.00827904i
$703$	−4.44438e11	+	4.44438e11i	−0.0686297	+	0.0686297i
$704$	5.21971e11	−	5.21971e11i	0.0800884	−	0.0800884i
$705$			1.32382e11i			0.0201827i
$706$			4.02820e12i			0.610224i
$707$	7.17936e11	−	7.17936e11i	0.108068	−	0.108068i
$708$	1.41261e11	−	1.41261e11i	0.0211287	−	0.0211287i
$709$	−1.02338e12	−	1.02338e12i	−0.152101	−	0.152101i	0.626955	−	0.779056i	$-0.284301\pi$
$709$	−1.02338e12	−	1.02338e12i	−0.152101	−	0.152101i	−0.779056	+	0.626955i	$0.784301\pi$
$710$	−7.29519e11			−0.107739
$711$	−5.48934e12	−	5.48934e12i	−0.805577	−	0.805577i
$712$			4.45871e12i			0.650204i
$713$	−1.00990e13			−1.46344
$714$	−1.89700e10	−	3.43993e9i	−0.00273165	−	0.000495345i
$715$	−6.85032e12			−0.980243
$716$		−	7.64907e12i		−	1.08768i
$717$	1.63438e11	+	1.63438e11i	0.0230949	+	0.0230949i
$718$	6.28882e10			0.00883098
$719$	5.13310e12	+	5.13310e12i	0.716307	+	0.716307i	0.967847	−	0.251540i	$-0.0809369\pi$
$719$	5.13310e12	+	5.13310e12i	0.716307	+	0.716307i	−0.251540	+	0.967847i	$0.580937\pi$
$720$	−3.37858e12	+	3.37858e12i	−0.468530	+	0.468530i
$721$	1.13010e10	−	1.13010e10i	0.00155743	−	0.00155743i
$722$			3.05062e12i			0.417803i
$723$			3.10589e11i			0.0422730i
$724$	−1.26455e12	+	1.26455e12i	−0.171045	+	0.171045i
$725$	5.14173e12	−	5.14173e12i	0.691175	−	0.691175i
$726$	−6.06473e10	−	6.06473e10i	−0.00810209	−	0.00810209i
$727$	3.08455e12			0.409531			0.204765	−	0.978811i	$-0.434357\pi$
$727$	3.08455e12			0.409531			0.204765	+	0.978811i	$0.434357\pi$
$728$	5.21089e11	+	5.21089e11i	0.0687576	+	0.0687576i
$729$			7.59271e12i			0.995687i
$730$	4.40752e12			0.574436
$731$	9.55004e12	+	1.73176e12i	1.23702	+	0.224316i
$732$	5.40488e10			0.00695803
$733$		−	3.11662e12i		−	0.398764i	−0.979922	−	0.199382i	$-0.936106\pi$
$733$		−	3.11662e12i		−	0.398764i	0.979922	−	0.199382i	$-0.0638935\pi$
$734$	3.81057e12	+	3.81057e12i	0.484571	+	0.484571i
$735$	−2.67424e11			−0.0337993
$736$	−9.98696e12	−	9.98696e12i	−1.25454	−	1.25454i
$737$	6.69381e12	−	6.69381e12i	0.835737	−	0.835737i
$738$	4.11845e12	−	4.11845e12i	0.511070	−	0.511070i
$739$			4.75055e12i			0.585927i	0.956124	+	0.292964i	$0.0946415\pi$
$739$			4.75055e12i			0.585927i	−0.956124	+	0.292964i	$0.905359\pi$
$740$			7.68566e12i			0.942189i
$741$	−9.10110e9	+	9.10110e9i	−0.00110895	+	0.00110895i
$742$	4.71237e10	−	4.71237e10i	0.00570718	−	0.00570718i
$743$	−5.16182e12	−	5.16182e12i	−0.621374	−	0.621374i	0.324509	−	0.945883i	$-0.394801\pi$
$743$	−5.16182e12	−	5.16182e12i	−0.621374	−	0.621374i	−0.945883	+	0.324509i	$0.894801\pi$
$744$	1.39646e11			0.0167090
$745$	3.39745e12	+	3.39745e12i	0.404063	+	0.404063i
$746$			3.32925e12i			0.393569i
$747$	−6.20939e12			−0.729636
$748$	−5.67451e12	−	8.18834e12i	−0.662783	−	0.956398i
$749$	−4.35515e11			−0.0505633
$750$			2.68120e10i			0.00309424i
$751$	−1.44020e12	−	1.44020e12i	−0.165212	−	0.165212i	0.619659	−	0.784871i	$-0.287271\pi$
$751$	−1.44020e12	−	1.44020e12i	−0.165212	−	0.165212i	−0.784871	+	0.619659i	$0.787271\pi$
$752$	2.43557e12			0.277728
$753$	−2.65653e11	−	2.65653e11i	−0.0301118	−	0.0301118i
$754$	1.68134e12	−	1.68134e12i	0.189446	−	0.189446i
$755$	1.54470e13	−	1.54470e13i	1.73015	−	1.73015i
$756$			9.66849e10i			0.0107649i
$757$		−	6.50159e12i		−	0.719595i	−0.933030	−	0.359798i	$-0.882846\pi$
$757$		−	6.50159e12i		−	0.719595i	0.933030	−	0.359798i	$-0.117154\pi$
$758$	1.88776e12	−	1.88776e12i	0.207699	−	0.207699i
$759$	4.44964e11	−	4.44964e11i	0.0486673	−	0.0486673i
$760$	−7.61436e11	−	7.61436e11i	−0.0827890	−	0.0827890i
$761$	9.68338e12			1.04664			0.523318	−	0.852137i	$-0.324694\pi$
$761$	9.68338e12			1.04664			0.523318	+	0.852137i	$0.324694\pi$
$762$	7.37209e10	+	7.37209e10i	0.00792124	+	0.00792124i
$763$			5.28485e11i			0.0564510i
$764$	4.38138e12			0.465255
$765$	7.22703e12	+	1.04286e13i	0.762927	+	1.10091i
$766$	−4.98339e12			−0.522992
$767$			6.71119e12i			0.700197i
$768$	6.38487e10	+	6.38487e10i	0.00662257	+	0.00662257i
$769$	3.78295e12			0.390088			0.195044	−	0.980795i	$-0.437515\pi$
$769$	3.78295e12			0.390088			0.195044	+	0.980795i	$0.437515\pi$
$770$	−1.35657e12	−	1.35657e12i	−0.139070	−	0.139070i
$771$	1.08329e11	−	1.08329e11i	0.0110408	−	0.0110408i
$772$	7.86055e11	−	7.86055e11i	0.0796481	−	0.0796481i
$773$		−	1.52760e13i		−	1.53887i	−0.638726	−	0.769435i	$-0.720538\pi$
$773$		−	1.52760e13i		−	1.53887i	0.638726	−	0.769435i	$-0.279462\pi$
$774$			5.30898e12i			0.531712i
$775$	−4.57323e12	+	4.57323e12i	−0.455371	+	0.455371i
$776$	−4.95026e12	+	4.95026e12i	−0.490061	+	0.490061i
$777$	4.03532e10	+	4.03532e10i	0.00397176	+	0.00397176i
$778$	4.90238e12			0.479732
$779$	−1.40772e12	−	1.40772e12i	−0.136962	−	0.136962i
$780$			1.57385e11i			0.0152243i
$781$	−2.79911e12			−0.269209
$782$	−6.58575e12	+	4.56392e12i	−0.629760	+	0.436423i
$783$	6.92004e11			0.0657931
$784$			4.92007e12i			0.465103i
$785$	−8.10872e12	−	8.10872e12i	−0.762147	−	0.762147i
$786$	9.76079e9			0.000912186
$787$	−1.05851e12	−	1.05851e12i	−0.0983581	−	0.0983581i	0.656215	−	0.754574i	$-0.272156\pi$
$787$	−1.05851e12	−	1.05851e12i	−0.0983581	−	0.0983581i	−0.754574	+	0.656215i	$0.772156\pi$
$788$	−1.06164e13	+	1.06164e13i	−0.980865	+	0.980865i
$789$	9.50700e10	−	9.50700e10i	0.00873367	−	0.00873367i
$790$		−	7.08065e12i		−	0.646772i
$791$		−	1.56050e12i		−	0.141733i
$792$	8.54739e12	−	8.54739e12i	0.771917	−	0.771917i
$793$	−1.28391e12	+	1.28391e12i	−0.115294	+	0.115294i
$794$	1.83154e12	+	1.83154e12i	0.163540	+	0.163540i
$795$	3.15716e10			0.00280314
$796$	8.15558e12	+	8.15558e12i	0.720022	+	0.720022i
$797$			9.20364e12i			0.807974i	0.914765	+	0.403987i	$0.132376\pi$
$797$			9.20364e12i			0.807974i	−0.914765	+	0.403987i	$0.867624\pi$
$798$	−3.60459e9			−0.000314661
$799$	1.15399e12	−	6.36386e12i	0.100171	−	0.552408i
$800$	−9.04498e12			−0.780734
$801$		−	9.82241e12i		−	0.843086i
$802$	6.82020e11	+	6.82020e11i	0.0582120	+	0.0582120i
$803$	1.69113e13			1.43535
$804$	−1.53789e11	−	1.53789e11i	−0.0129800	−	0.0129800i
$805$	4.99979e12	−	4.99979e12i	0.419634	−	0.419634i
$806$	−1.49545e12	+	1.49545e12i	−0.124814	+	0.124814i
$807$			4.99597e11i			0.0414657i
$808$			5.83485e12i			0.481592i
$809$	−9.79518e12	+	9.79518e12i	−0.803978	+	0.803978i	−0.983715	−	0.179737i	$-0.942475\pi$
$809$	−9.79518e12	+	9.79518e12i	−0.803978	+	0.803978i	0.179737	+	0.983715i	$0.442475\pi$
$810$	−4.90395e12	+	4.90395e12i	−0.400280	+	0.400280i
$811$	−5.52144e12	−	5.52144e12i	−0.448186	−	0.448186i	0.446565	−	0.894751i	$-0.352647\pi$
$811$	−5.52144e12	−	5.52144e12i	−0.448186	−	0.448186i	−0.894751	+	0.446565i	$0.852647\pi$
$812$	−3.05153e12			−0.246329
$813$	3.49144e11	+	3.49144e11i	0.0280283	+	0.0280283i
$814$		−	6.43523e12i		−	0.513753i
$815$	−1.39684e13			−1.10901
$816$	−1.38114e11	+	9.57128e10i	−0.0109051	+	0.00755726i
$817$	1.81465e12			0.142493
$818$			3.88876e12i			0.303684i
$819$	−1.14794e12	−	1.14794e12i	−0.0891544	−	0.0891544i
$820$	−2.43437e13			−1.88029
$821$	3.47656e12	+	3.47656e12i	0.267058	+	0.267058i	0.827914	−	0.560856i	$-0.189528\pi$
$821$	3.47656e12	+	3.47656e12i	0.267058	+	0.267058i	−0.560856	+	0.827914i	$0.689528\pi$
$822$	−1.99648e11	+	1.99648e11i	−0.0152526	+	0.0152526i
$823$	−7.74632e12	+	7.74632e12i	−0.588567	+	0.588567i	−0.937243	−	0.348676i	$-0.886631\pi$
$823$	−7.74632e12	+	7.74632e12i	−0.588567	+	0.588567i	0.348676	+	0.937243i	$0.386631\pi$
$824$			9.18461e10i			0.00694046i
$825$		−	4.02995e11i		−	0.0302870i
$826$	−1.32902e12	+	1.32902e12i	−0.0993393	+	0.0993393i
$827$	2.00048e12	−	2.00048e12i	0.148717	−	0.148717i	−0.628828	−	0.777545i	$-0.716465\pi$
$827$	2.00048e12	−	2.00048e12i	0.148717	−	0.148717i	0.777545	+	0.628828i	$0.216465\pi$
$828$	1.42016e13	+	1.42016e13i	1.05003	+	1.05003i
$829$	2.90839e12			0.213873			0.106937	−	0.994266i	$-0.465896\pi$
$829$	2.90839e12			0.213873			0.106937	+	0.994266i	$0.465896\pi$
$830$	−4.00472e12	−	4.00472e12i	−0.292901	−	0.292901i
$831$		−	1.39434e11i		−	0.0101430i
$832$	5.69741e11			0.0412214
$833$	1.28556e13	+	2.33117e12i	0.925100	+	0.167753i
$834$	−8.75521e10			−0.00626642
$835$			1.70228e13i			1.21183i
$836$	−1.31708e12	−	1.31708e12i	−0.0932574	−	0.0932574i
$837$	−6.15492e11			−0.0433469
$838$	−6.24251e12	−	6.24251e12i	−0.437282	−	0.437282i
$839$	−1.84462e13	+	1.84462e13i	−1.28522	+	1.28522i	−0.347563	+	0.937657i	$0.612991\pi$
$839$	−1.84462e13	+	1.84462e13i	−1.28522	+	1.28522i	−0.937657	+	0.347563i	$0.887009\pi$
$840$	−6.91354e10	+	6.91354e10i	−0.00479119	+	0.00479119i
$841$			7.33362e12i			0.505518i
$842$		−	8.90322e12i		−	0.610439i
$843$	2.70764e11	−	2.70764e11i	0.0184658	−	0.0184658i
$844$	1.46627e13	−	1.46627e13i	0.994657	−	0.994657i
$845$	1.03079e13	+	1.03079e13i	0.695532	+	0.695532i
$846$	3.53774e12			0.237443
$847$	−2.61470e12	−	2.61470e12i	−0.174561	−	0.174561i
$848$		−	5.80854e11i		−	0.0385732i
$849$	−3.51408e11			−0.0232127
$850$	−9.15565e11	+	5.04901e12i	−0.0601595	+	0.331758i
$851$	2.37177e13			1.55021
$852$			6.43091e10i			0.00418114i
$853$	3.42782e12	+	3.42782e12i	0.221691	+	0.221691i	0.809210	−	0.587519i	$-0.199895\pi$
$853$	3.42782e12	+	3.42782e12i	0.221691	+	0.221691i	−0.587519	+	0.809210i	$0.699895\pi$
$854$	−5.08506e11			−0.0327141
$855$	1.67742e12	+	1.67742e12i	0.107348	+	0.107348i
$856$	1.76977e12	−	1.76977e12i	0.112664	−	0.112664i
$857$	−1.46298e13	+	1.46298e13i	−0.926453	+	0.926453i	−0.997475	−	0.0710216i	$-0.977374\pi$
$857$	−1.46298e13	+	1.46298e13i	−0.926453	+	0.926453i	0.0710216	+	0.997475i	$0.477374\pi$
$858$		−	1.31779e11i		−	0.00830145i
$859$		−	2.50372e13i		−	1.56898i	−0.620144	−	0.784488i	$-0.712926\pi$
$859$		−	2.50372e13i		−	1.56898i	0.620144	−	0.784488i	$-0.287074\pi$
$860$	1.56904e13	−	1.56904e13i	0.978117	−	0.978117i
$861$	−1.27816e11	+	1.27816e11i	−0.00792629	+	0.00792629i
$862$	−1.61717e12	−	1.61717e12i	−0.0997639	−	0.0997639i
$863$	−1.89430e13			−1.16252			−0.581260	−	0.813718i	$-0.697440\pi$
$863$	−1.89430e13			−1.16252			−0.581260	+	0.813718i	$0.697440\pi$
$864$	−6.08663e11	−	6.08663e11i	−0.0371591	−	0.0371591i
$865$		−	3.92482e13i		−	2.38368i
$866$	9.25811e12			0.559361
$867$	1.84647e11	+	4.06225e11i	0.0110983	+	0.0244163i
$868$	2.71414e12			0.162291
$869$		−	2.71679e13i		−	1.61610i
$870$	2.23072e11	+	2.23072e11i	0.0132011	+	0.0132011i
$871$	7.30642e12			0.430153
$872$	−2.14757e12	−	2.14757e12i	−0.125783	−	0.125783i
$873$	1.09053e13	−	1.09053e13i	0.635437	−	0.635437i
$874$	−1.05930e12	+	1.05930e12i	−0.0614072	+	0.0614072i
$875$			1.15595e12i			0.0666658i
$876$		−	3.88535e11i		−	0.0222927i
$877$	−1.20480e13	+	1.20480e13i	−0.687726	+	0.687726i	−0.961729	−	0.274003i	$-0.911652\pi$
$877$	−1.20480e13	+	1.20480e13i	−0.687726	+	0.687726i	0.274003	+	0.961729i	$0.411652\pi$
$878$	2.36851e12	−	2.36851e12i	0.134509	−	0.134509i
$879$	−1.05035e11	−	1.05035e11i	−0.00593448	−	0.00593448i
$880$	−1.67213e13			−0.939935
$881$	1.88127e13	+	1.88127e13i	1.05210	+	1.05210i	0.998566	+	0.0535389i	$0.0170501\pi$
$881$	1.88127e13	+	1.88127e13i	1.05210	+	1.05210i	0.0535389	+	0.998566i	$0.482950\pi$
$882$			7.14656e12i			0.397638i
$883$	1.28352e13			0.710525			0.355263	−	0.934767i	$-0.384391\pi$
$883$	1.28352e13			0.710525			0.355263	+	0.934767i	$0.384391\pi$
$884$	1.37194e12	−	7.56578e12i	0.0755616	−	0.416695i
$885$	−8.90407e11			−0.0487914
$886$			5.94879e12i			0.324322i
$887$	−8.37571e11	−	8.37571e11i	−0.0454324	−	0.0454324i	0.684026	−	0.729458i	$-0.260228\pi$
$887$	−8.37571e11	−	8.37571e11i	−0.0454324	−	0.0454324i	−0.729458	+	0.684026i	$0.760228\pi$
$888$	−3.27961e11			−0.0176996
$889$	3.17834e12	+	3.17834e12i	0.170664	+	0.170664i
$890$	6.33492e12	−	6.33492e12i	0.338443	−	0.338443i
$891$	−1.88161e13	+	1.88161e13i	−1.00018	+	1.00018i
$892$		−	1.31417e13i		−	0.695037i
$893$		−	1.20923e12i		−	0.0636323i
$894$	−6.53565e10	+	6.53565e10i	−0.00342192	+	0.00342192i
$895$	−2.41071e13	+	2.41071e13i	−1.25586	+	1.25586i
$896$	3.38257e12	+	3.38257e12i	0.175332	+	0.175332i
$897$	4.85687e11			0.0250490
$898$	−1.46255e12	−	1.46255e12i	−0.0750526	−	0.0750526i
$899$		−	1.94259e13i		−	0.991890i
$900$	1.28621e13			0.653463
$901$	−1.51770e12	−	2.75213e11i	−0.0767229	−	0.0139126i
$902$	2.03831e13			1.02528
$903$		−	1.64763e11i		−	0.00824643i
$904$	6.34131e12	+	6.34131e12i	0.315806	+	0.315806i
$905$	7.97079e12			0.394987
$906$	2.97154e11	+	2.97154e11i	0.0146522	+	0.0146522i
$907$	2.93748e12	−	2.93748e12i	0.144126	−	0.144126i	−0.631362	−	0.775488i	$-0.717504\pi$
$907$	2.93748e12	−	2.93748e12i	0.144126	−	0.144126i	0.775488	+	0.631362i	$0.217504\pi$
$908$	−1.11403e12	+	1.11403e12i	−0.0543887	+	0.0543887i
$909$		−	1.28540e13i		−	0.624455i
$910$		−	1.48072e12i		−	0.0715793i
$911$	−5.62595e12	+	5.62595e12i	−0.270622	+	0.270622i	−0.829351	−	0.558729i	$-0.811289\pi$
$911$	−5.62595e12	+	5.62595e12i	−0.270622	+	0.270622i	0.558729	+	0.829351i	$0.311289\pi$
$912$	−2.22153e10	+	2.22153e10i	−0.00106335	+	0.00106335i
$913$	−1.53658e13	−	1.53658e13i	−0.731875	−	0.731875i
$914$	−4.08812e12			−0.193761
$915$	−1.70342e11	−	1.70342e11i	−0.00803393	−	0.00803393i
$916$		−	2.07776e13i		−	0.975137i
$917$	4.20819e11			0.0196532
$918$	−4.01374e11	+	2.78152e11i	−0.0186534	+	0.0129268i
$919$	−1.01245e13			−0.468225			−0.234112	−	0.972210i	$-0.575218\pi$
$919$	−1.01245e13			−0.468225			−0.234112	+	0.972210i	$0.575218\pi$
$920$			4.06346e13i			1.87004i
$921$	−8.27239e10	−	8.27239e10i	−0.00378846	−	0.00378846i
$922$	−1.27788e13			−0.582372
$923$	−1.52764e12	−	1.52764e12i	−0.0692808	−	0.0692808i
$924$	−1.19585e11	+	1.19585e11i	−0.00539703	+	0.00539703i
$925$	1.07403e13	−	1.07403e13i	0.482370	−	0.482370i
$926$		−	9.12651e12i		−	0.407901i
$927$		−	2.02334e11i		−	0.00899934i
$928$	1.92104e13	−	1.92104e13i	0.850297	−	0.850297i
$929$	−2.24557e13	+	2.24557e13i	−0.989134	+	0.989134i	−0.999942	−	0.0108074i	$-0.996560\pi$
$929$	−2.24557e13	+	2.24557e13i	−0.989134	+	0.989134i	0.0108074	+	0.999942i	$0.496560\pi$
$930$	−1.98408e11	−	1.98408e11i	−0.00869733	−	0.00869733i
$931$	2.44275e12			0.106563
$932$	1.53224e13	+	1.53224e13i	0.665203	+	0.665203i
$933$		−	5.00990e10i		−	0.00216452i
$934$	−1.11006e13			−0.477295
$935$	−7.92268e12	+	4.36908e13i	−0.339016	+	1.86955i
$936$	9.32964e12			0.397304
$937$		−	1.04267e13i		−	0.441897i	−0.975286	−	0.220948i	$-0.929085\pi$
$937$		−	1.04267e13i		−	0.441897i	0.975286	−	0.220948i	$-0.0709152\pi$
$938$	1.44689e12	+	1.44689e12i	0.0610272	+	0.0610272i
$939$	7.57364e11			0.0317914
$940$	−1.04556e13	−	1.04556e13i	−0.436791	−	0.436791i
$941$	9.87041e12	−	9.87041e12i	0.410376	−	0.410376i	−0.471493	−	0.881870i	$-0.656285\pi$
$941$	9.87041e12	−	9.87041e12i	0.410376	−	0.410376i	0.881870	+	0.471493i	$0.156285\pi$
$942$	1.55987e11	−	1.55987e11i	0.00645445	−	0.00645445i
$943$			7.51242e13i			3.09369i
$944$			1.63817e13i			0.671405i
$945$	3.04716e11	−	3.04716e11i	0.0124295	−	0.0124295i
$946$	−1.31376e13	+	1.31376e13i	−0.533343	+	0.533343i
$947$	−2.38979e13	−	2.38979e13i	−0.965574	−	0.965574i	0.0338530	−	0.999427i	$-0.489222\pi$
$947$	−2.38979e13	−	2.38979e13i	−0.965574	−	0.965574i	−0.999427	+	0.0338530i	$0.989222\pi$
$948$	−6.24179e11			−0.0250999
$949$	9.22951e12	+	9.22951e12i	0.369386	+	0.369386i
$950$			9.59390e11i			0.0382155i
$951$	−1.36148e11			−0.00539757
$952$	3.92612e12	−	2.72080e12i	0.154917	−	0.107357i
$953$	3.89333e12			0.152898			0.0764492	−	0.997073i	$-0.475642\pi$
$953$	3.89333e12			0.152898			0.0764492	+	0.997073i	$0.475642\pi$
$954$		−	8.43708e11i		−	0.0329780i
$955$	−1.38085e13	−	1.38085e13i	−0.537196	−	0.537196i
$956$	−2.58167e13			−0.999632
$957$	8.55910e11	+	8.55910e11i	0.0329856	+	0.0329856i
$958$	−6.34371e12	+	6.34371e12i	−0.243332	+	0.243332i
$959$	−8.60747e12	+	8.60747e12i	−0.328618	+	0.328618i
$960$			7.55903e10i			0.00287240i
$961$		−	9.16152e12i		−	0.346507i
$962$	3.51209e12	−	3.51209e12i	0.132214	−	0.132214i
$963$	−3.89876e12	+	3.89876e12i	−0.146086	+	0.146086i
$964$	−2.45304e13	−	2.45304e13i	−0.914866	−	0.914866i
$965$	−4.95473e12			−0.183928
$966$	9.61807e10	+	9.61807e10i	0.00355378	+	0.00355378i
$967$			2.13333e13i			0.784584i	0.919841	+	0.392292i	$0.128318\pi$
$967$			2.13333e13i			0.784584i	−0.919841	+	0.392292i	$0.871682\pi$
$968$	2.12503e13			0.777905
$969$	4.75202e10	+	6.85718e10i	0.00173150	+	0.00249855i
$970$	1.40666e13			0.510172
$971$		−	6.06046e12i		−	0.218786i	−0.993999	−	0.109393i	$-0.965109\pi$
$971$		−	6.06046e12i		−	0.218786i	0.993999	−	0.109393i	$-0.0348906\pi$
$972$	1.29845e12	+	1.29845e12i	0.0466581	+	0.0466581i
$973$	−3.77465e12			−0.135011
$974$	−1.42936e13	−	1.42936e13i	−0.508893	−	0.508893i
$975$	2.19938e11	−	2.19938e11i	0.00779435	−	0.00779435i
$976$	−3.13396e12	+	3.13396e12i	−0.110553	+	0.110553i
$977$		−	3.07781e13i		−	1.08073i	−0.841432	−	0.540363i	$-0.818287\pi$
$977$		−	3.07781e13i		−	1.08073i	0.841432	−	0.540363i	$-0.181713\pi$
$978$		−	2.68709e11i		−	0.00939197i
$979$	2.43066e13	−	2.43066e13i	0.845672	−	0.845672i
$980$	2.11213e13	−	2.11213e13i	0.731480	−	0.731480i
$981$	4.73102e12	+	4.73102e12i	0.163096	+	0.163096i
$982$	2.29880e13			0.788859
$983$	1.16026e13	+	1.16026e13i	0.396336	+	0.396336i	0.876939	−	0.480603i	$-0.159582\pi$
$983$	1.16026e13	+	1.16026e13i	0.396336	+	0.396336i	−0.480603	+	0.876939i	$0.659582\pi$
$984$		−	1.03879e12i		−	0.0353224i
$985$	6.69182e13			2.26507
$986$	−8.77893e12	−	1.26680e13i	−0.295798	−	0.426837i
$987$	−1.09793e11			−0.00368255
$988$		−	1.43761e12i		−	0.0479994i
$989$	−4.84202e13	−	4.84202e13i	−1.60932	−	1.60932i
$990$	−2.42882e13			−0.803595
$991$	2.83363e13	+	2.83363e13i	0.933279	+	0.933279i	0.997909	−	0.0646300i	$-0.0205867\pi$
$991$	2.83363e13	+	2.83363e13i	0.933279	+	0.933279i	−0.0646300	+	0.997909i	$0.520587\pi$
$992$	−1.70864e13	+	1.70864e13i	−0.560206	+	0.560206i
$993$	6.71608e11	−	6.71608e11i	0.0219202	−	0.0219202i
$994$		−	6.05038e11i		−	0.0196582i
$995$		−	5.14069e13i		−	1.66271i
$996$	−3.53027e11	+	3.53027e11i	−0.0113669	+	0.0113669i
$997$	−3.64860e13	+	3.64860e13i	−1.16949	+	1.16949i	−0.187165	+	0.982329i	$0.559930\pi$
$997$	−3.64860e13	+	3.64860e13i	−1.16949	+	1.16949i	−0.982329	+	0.187165i	$0.940070\pi$
$998$	−3.04575e12	−	3.04575e12i	−0.0971866	−	0.0971866i
$999$	1.44550e12			0.0459169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.7	yes	24
17.2	even	8		289.10.a.f.1.11		24
17.4	even	4	inner	17.10.c.a.4.6	✓	24
17.15	even	8		289.10.a.f.1.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.6	✓	24	17.4	even	4	inner
17.10.c.a.13.7	yes	24	1.1	even	1	trivial
289.10.a.f.1.11		24	17.2	even	8
289.10.a.f.1.12		24	17.15	even	8

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+9.57683i q^{2} +(-2.66069 - 2.66069i) q^{3} +420.284 q^{4} +(-1324.59 - 1324.59i) q^{5} +(25.4810 - 25.4810i) q^{6} +(1098.57 - 1098.57i) q^{7} +8928.33i q^{8} -19668.8i q^{9} +O(q^{10})\)	\(q+9.57683i q^{2} +(-2.66069 - 2.66069i) q^{3} +420.284 q^{4} +(-1324.59 - 1324.59i) q^{5} +(25.4810 - 25.4810i) q^{6} +(1098.57 - 1098.57i) q^{7} +8928.33i q^{8} -19668.8i q^{9} +(12685.3 - 12685.3i) q^{10} +(48672.6 - 48672.6i) q^{11} +(-1118.25 - 1118.25i) q^{12} +53127.1 q^{13} +(10520.8 + 10520.8i) q^{14} +7048.63i q^{15} +129681. q^{16} +(61443.7 - 338840. i) q^{17} +188365. q^{18} -64384.8i q^{19} +(-556703. - 556703. i) q^{20} -5845.89 q^{21} +(466129. + 466129. i) q^{22} +(-1.71797e6 + 1.71797e6i) q^{23} +(23755.5 - 23755.5i) q^{24} +1.55593e6i q^{25} +508789. i q^{26} +(-104703. + 104703. i) q^{27} +(461710. - 461710. i) q^{28} +(-3.30460e6 - 3.30460e6i) q^{29} -67503.5 q^{30} +(2.93923e6 + 2.93923e6i) q^{31} +5.81323e6i q^{32} -259006. q^{33} +(3.24501e6 + 588436. i) q^{34} -2.91029e6 q^{35} -8.26651e6i q^{36} +(-6.90284e6 - 6.90284e6i) q^{37} +616602. q^{38} +(-141355. - 141355. i) q^{39} +(1.18263e7 - 1.18263e7i) q^{40} +(2.18642e7 - 2.18642e7i) q^{41} -55985.1i q^{42} +2.81845e7i q^{43} +(2.04563e7 - 2.04563e7i) q^{44} +(-2.60531e7 + 2.60531e7i) q^{45} +(-1.64527e7 - 1.64527e7i) q^{46} +1.87813e7 q^{47} +(-345040. - 345040. i) q^{48} +3.79399e7i q^{49} -1.49009e7 q^{50} +(-1.06503e6 + 738066. i) q^{51} +2.23285e7 q^{52} -4.47911e6i q^{53} +(-1.00272e6 - 1.00272e6i) q^{54} -1.28942e8 q^{55} +(9.80835e6 + 9.80835e6i) q^{56} +(-171308. + 171308. i) q^{57} +(3.16476e7 - 3.16476e7i) q^{58} +1.26323e8i q^{59} +2.96243e6i q^{60} +(-2.41668e7 + 2.41668e7i) q^{61} +(-2.81485e7 + 2.81485e7i) q^{62} +(-2.16075e7 - 2.16075e7i) q^{63} +1.07241e7 q^{64} +(-7.03714e7 - 7.03714e7i) q^{65} -2.48045e6i q^{66} +1.37527e8 q^{67} +(2.58238e7 - 1.42409e8i) q^{68} +9.14198e6 q^{69} -2.78713e7i q^{70} +(-2.87544e7 - 2.87544e7i) q^{71} +1.75610e8 q^{72} +(1.73725e8 + 1.73725e8i) q^{73} +(6.61073e7 - 6.61073e7i) q^{74} +(4.13985e6 - 4.13985e6i) q^{75} -2.70599e7i q^{76} -1.06940e8i q^{77} +(1.35373e6 - 1.35373e6i) q^{78} +(2.79088e8 - 2.79088e8i) q^{79} +(-1.71773e8 - 1.71773e8i) q^{80} -3.86585e8 q^{81} +(2.09390e8 + 2.09390e8i) q^{82} -3.15697e8i q^{83} -2.45693e6 q^{84} +(-5.30210e8 + 3.67435e8i) q^{85} -2.69918e8 q^{86} +1.75850e7i q^{87} +(4.34565e8 + 4.34565e8i) q^{88} +4.99389e8 q^{89} +(-2.49506e8 - 2.49506e8i) q^{90} +(5.83636e7 - 5.83636e7i) q^{91} +(-7.22036e8 + 7.22036e8i) q^{92} -1.56407e7i q^{93} +1.79865e8i q^{94} +(-8.52832e7 + 8.52832e7i) q^{95} +(1.54672e7 - 1.54672e7i) q^{96} +(5.54444e8 + 5.54444e8i) q^{97} -3.63344e8 q^{98} +(-9.57334e8 - 9.57334e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7 + 21946 * q^10 + 18132 * q^11 - 95142 * q^12 + 244832 * q^13 - 341100 * q^14 - 279932 * q^16 - 98022 * q^17 + 888764 * q^18 + 1364262 * q^20 - 775748 * q^21 - 4573190 * q^22 - 377526 * q^23 - 307054 * q^24 + 3996108 * q^27 - 1024780 * q^28 + 2160042 * q^29 + 39084792 * q^30 - 585086 * q^31 - 30349992 * q^33 + 4441318 * q^34 - 25532364 * q^35 + 1515390 * q^37 + 13171392 * q^38 - 25687084 * q^39 - 63240118 * q^40 - 72707928 * q^41 - 3606450 * q^44 + 156729418 * q^45 + 118549536 * q^46 + 153365328 * q^47 + 26098270 * q^48 - 236105676 * q^50 + 256903592 * q^51 - 209898380 * q^52 - 187411976 * q^54 + 255767540 * q^55 - 107638596 * q^56 - 443390988 * q^57 - 281433730 * q^58 + 52149382 * q^61 + 176928228 * q^62 + 620111642 * q^63 + 1006108924 * q^64 - 489714396 * q^65 - 26076868 * q^67 - 308011950 * q^68 - 751973532 * q^69 + 149240178 * q^71 + 1171736028 * q^72 - 175256556 * q^73 - 37609818 * q^74 - 233543476 * q^75 - 1202722924 * q^78 - 469987182 * q^79 + 481103586 * q^80 + 347156560 * q^81 - 984422080 * q^82 - 935672904 * q^84 - 725828294 * q^85 + 690159588 * q^86 + 992281114 * q^88 - 191594460 * q^89 + 914946474 * q^90 + 926854816 * q^91 + 3064830552 * q^92 + 1213246572 * q^95 + 3594247550 * q^96 - 2200567348 * q^97 - 4413444720 * q^98 - 1224966600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more