LMFDB - Embedded newform 17.10.c.a.13.8

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			13.8
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+12.8587i q^{2} +(-144.765 - 144.765i) q^{3} +346.654 q^{4} +(-85.3199 - 85.3199i) q^{5} +(1861.49 - 1861.49i) q^{6} +(-3200.21 + 3200.21i) q^{7} +11041.2i q^{8} +22230.9i q^{9} +O(q^{10})$	\(q+12.8587i q^{2} +(-144.765 - 144.765i) q^{3} +346.654 q^{4} +(-85.3199 - 85.3199i) q^{5} +(1861.49 - 1861.49i) q^{6} +(-3200.21 + 3200.21i) q^{7} +11041.2i q^{8} +22230.9i q^{9} +(1097.10 - 1097.10i) q^{10} +(-40916.6 + 40916.6i) q^{11} +(-50183.5 - 50183.5i) q^{12} -50786.7 q^{13} +(-41150.5 - 41150.5i) q^{14} +24702.7i q^{15} +35512.1 q^{16} +(-51551.8 + 340485. i) q^{17} -285861. q^{18} +815845. i q^{19} +(-29576.5 - 29576.5i) q^{20} +926557. q^{21} +(-526133. - 526133. i) q^{22} +(526927. - 526927. i) q^{23} +(1.59838e6 - 1.59838e6i) q^{24} -1.93857e6i q^{25} -653050. i q^{26} +(368852. - 368852. i) q^{27} +(-1.10937e6 + 1.10937e6i) q^{28} +(-714818. - 714818. i) q^{29} -317644. q^{30} +(-924541. - 924541. i) q^{31} +6.10972e6i q^{32} +1.18466e7 q^{33} +(-4.37819e6 - 662888. i) q^{34} +546083. q^{35} +7.70645e6i q^{36} +(-1.11504e7 - 1.11504e7i) q^{37} -1.04907e7 q^{38} +(7.35215e6 + 7.35215e6i) q^{39} +(942031. - 942031. i) q^{40} +(-3.49520e6 + 3.49520e6i) q^{41} +1.19143e7i q^{42} -4.64999e6i q^{43} +(-1.41839e7 + 1.41839e7i) q^{44} +(1.89674e6 - 1.89674e6i) q^{45} +(6.77559e6 + 6.77559e6i) q^{46} -3.34810e7 q^{47} +(-5.14092e6 - 5.14092e6i) q^{48} +1.98710e7i q^{49} +2.49274e7 q^{50} +(5.67533e7 - 4.18275e7i) q^{51} -1.76054e7 q^{52} -5.09370e7i q^{53} +(4.74295e6 + 4.74295e6i) q^{54} +6.98199e6 q^{55} +(-3.53340e7 - 3.53340e7i) q^{56} +(1.18106e8 - 1.18106e8i) q^{57} +(9.19162e6 - 9.19162e6i) q^{58} +1.72235e8i q^{59} +8.56330e6i q^{60} +(3.40091e7 - 3.40091e7i) q^{61} +(1.18884e7 - 1.18884e7i) q^{62} +(-7.11436e7 - 7.11436e7i) q^{63} -6.03807e7 q^{64} +(4.33312e6 + 4.33312e6i) q^{65} +1.52332e8i q^{66} +2.00253e8 q^{67} +(-1.78706e7 + 1.18031e8i) q^{68} -1.52561e8 q^{69} +7.02191e6i q^{70} +(7.24254e7 + 7.24254e7i) q^{71} -2.45455e8 q^{72} +(-3.09947e8 - 3.09947e8i) q^{73} +(1.43379e8 - 1.43379e8i) q^{74} +(-2.80637e8 + 2.80637e8i) q^{75} +2.82816e8i q^{76} -2.61883e8i q^{77} +(-9.45390e7 + 9.45390e7i) q^{78} +(2.19857e8 - 2.19857e8i) q^{79} +(-3.02989e6 - 3.02989e6i) q^{80} +3.30778e8 q^{81} +(-4.49437e7 - 4.49437e7i) q^{82} +8.30705e8i q^{83} +3.21195e8 q^{84} +(3.34486e7 - 2.46518e7i) q^{85} +5.97928e7 q^{86} +2.06962e8i q^{87} +(-4.51766e8 - 4.51766e8i) q^{88} +6.52199e7 q^{89} +(2.43896e7 + 2.43896e7i) q^{90} +(1.62528e8 - 1.62528e8i) q^{91} +(1.82661e8 - 1.82661e8i) q^{92} +2.67683e8i q^{93} -4.30522e8i q^{94} +(6.96078e7 - 6.96078e7i) q^{95} +(8.84474e8 - 8.84474e8i) q^{96} +(-1.59423e8 - 1.59423e8i) q^{97} -2.55514e8 q^{98} +(-9.09613e8 - 9.09613e8i) 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 $

$2$			12.8587i			0.568279i	0.958783	+	0.284139i	$0.0917079\pi$
$2$			12.8587i			0.568279i	−0.958783	+	0.284139i	$0.908292\pi$
$3$	−144.765	−	144.765i	−1.03185	−	1.03185i	−0.999476	−	0.0323791i	$-0.989692\pi$
$3$	−144.765	−	144.765i	−1.03185	−	1.03185i	−0.0323791	−	0.999476i	$-0.510308\pi$
$4$	346.654			0.677059
$5$	−85.3199	−	85.3199i	−0.0610500	−	0.0610500i	0.675923	−	0.736973i	$-0.263745\pi$
$5$	−85.3199	−	85.3199i	−0.0610500	−	0.0610500i	−0.736973	+	0.675923i	$0.763745\pi$
$6$	1861.49	−	1861.49i	0.586381	−	0.586381i
$7$	−3200.21	+	3200.21i	−0.503775	+	0.503775i	−0.912609	−	0.408834i	$-0.865936\pi$
$7$	−3200.21	+	3200.21i	−0.503775	+	0.503775i	0.408834	+	0.912609i	$0.365936\pi$
$8$			11041.2i			0.953037i
$9$			22230.9i			1.12945i
$10$	1097.10	−	1097.10i	0.0346934	−	0.0346934i
$11$	−40916.6	+	40916.6i	−0.842620	+	0.842620i	−0.989199	−	0.146579i	$-0.953174\pi$
$11$	−40916.6	+	40916.6i	−0.842620	+	0.842620i	0.146579	+	0.989199i	$0.453174\pi$
$12$	−50183.5	−	50183.5i	−0.698627	−	0.698627i
$13$	−50786.7			−0.493179			−0.246590	−	0.969120i	$-0.579310\pi$
$13$	−50786.7			−0.493179			−0.246590	+	0.969120i	$0.579310\pi$
$14$	−41150.5	−	41150.5i	−0.286285	−	0.286285i
$15$			24702.7i			0.125989i
$16$	35512.1			0.135468
$17$	−51551.8	+	340485.i	−0.149701	+	0.988731i
$17$	−51551.8	+	340485.i	−0.149701	+	0.988731i
$18$	−285861.			−0.641842
$19$			815845.i			1.43621i	0.695937	+	0.718103i	$0.254989\pi$
$19$			815845.i			1.43621i	−0.695937	+	0.718103i	$0.745011\pi$
$20$	−29576.5	−	29576.5i	−0.0413344	−	0.0413344i
$21$	926557.			1.03965
$22$	−526133.	−	526133.i	−0.478843	−	0.478843i
$23$	526927.	−	526927.i	0.392622	−	0.392622i	−0.482999	−	0.875621i	$-0.660452\pi$
$23$	526927.	−	526927.i	0.392622	−	0.392622i	0.875621	+	0.482999i	$0.160452\pi$
$24$	1.59838e6	−	1.59838e6i	0.983396	−	0.983396i
$25$		−	1.93857e6i		−	0.992546i
$26$		−	653050.i		−	0.280263i
$27$	368852.	−	368852.i	0.133572	−	0.133572i
$28$	−1.10937e6	+	1.10937e6i	−0.341086	+	0.341086i
$29$	−714818.	−	714818.i	−0.187674	−	0.187674i	0.607016	−	0.794690i	$-0.292367\pi$
$29$	−714818.	−	714818.i	−0.187674	−	0.187674i	−0.794690	+	0.607016i	$0.792367\pi$
$30$	−317644.			−0.0715971
$31$	−924541.	−	924541.i	−0.179804	−	0.179804i	0.611467	−	0.791270i	$-0.290580\pi$
$31$	−924541.	−	924541.i	−0.179804	−	0.179804i	−0.791270	+	0.611467i	$0.790580\pi$
$32$			6.10972e6i			1.03002i
$33$	1.18466e7			1.73892
$34$	−4.37819e6	−	662888.i	−0.561875	−	0.0850717i
$35$	546083.			0.0615109
$36$			7.70645e6i			0.764703i
$37$	−1.11504e7	−	1.11504e7i	−0.978098	−	0.978098i	0.0216670	−	0.999765i	$-0.493103\pi$
$37$	−1.11504e7	−	1.11504e7i	−0.978098	−	0.978098i	−0.999765	+	0.0216670i	$0.993103\pi$
$38$	−1.04907e7			−0.816165
$39$	7.35215e6	+	7.35215e6i	0.508889	+	0.508889i
$40$	942031.	−	942031.i	0.0581829	−	0.0581829i
$41$	−3.49520e6	+	3.49520e6i	−0.193172	+	0.193172i	−0.797065	−	0.603893i	$-0.793615\pi$
$41$	−3.49520e6	+	3.49520e6i	−0.193172	+	0.193172i	0.603893	+	0.797065i	$0.293615\pi$
$42$			1.19143e7i			0.590809i
$43$		−	4.64999e6i		−	0.207417i	−0.994608	−	0.103708i	$-0.966929\pi$
$43$		−	4.64999e6i		−	0.207417i	0.994608	−	0.103708i	$-0.0330709\pi$
$44$	−1.41839e7	+	1.41839e7i	−0.570504	+	0.570504i
$45$	1.89674e6	−	1.89674e6i	0.0689528	−	0.0689528i
$46$	6.77559e6	+	6.77559e6i	0.223119	+	0.223119i
$47$	−3.34810e7			−1.00082			−0.500412	−	0.865787i	$-0.666818\pi$
$47$	−3.34810e7			−1.00082			−0.500412	+	0.865787i	$0.666818\pi$
$48$	−5.14092e6	−	5.14092e6i	−0.139783	−	0.139783i
$49$			1.98710e7i			0.492421i
$50$	2.49274e7			0.564043
$51$	5.67533e7	−	4.18275e7i	1.17470	−	0.865758i
$52$	−1.76054e7			−0.333912
$53$		−	5.09370e7i		−	0.886731i	−0.896341	−	0.443366i	$-0.853784\pi$
$53$		−	5.09370e7i		−	0.886731i	0.896341	−	0.443366i	$-0.146216\pi$
$54$	4.74295e6	+	4.74295e6i	0.0759061	+	0.0759061i
$55$	6.98199e6			0.102884
$56$	−3.53340e7	−	3.53340e7i	−0.480117	−	0.480117i
$57$	1.18106e8	−	1.18106e8i	1.48196	−	1.48196i
$58$	9.19162e6	−	9.19162e6i	0.106651	−	0.106651i
$59$			1.72235e8i			1.85049i	0.379371	+	0.925245i	$0.376140\pi$
$59$			1.72235e8i			1.85049i	−0.379371	+	0.925245i	$0.623860\pi$
$60$			8.56330e6i			0.0853023i
$61$	3.40091e7	−	3.40091e7i	0.314492	−	0.314492i	−0.532155	−	0.846647i	$-0.678618\pi$
$61$	3.40091e7	−	3.40091e7i	0.314492	−	0.314492i	0.846647	+	0.532155i	$0.178618\pi$
$62$	1.18884e7	−	1.18884e7i	0.102179	−	0.102179i
$63$	−7.11436e7	−	7.11436e7i	−0.568988	−	0.568988i
$64$	−6.03807e7			−0.449871
$65$	4.33312e6	+	4.33312e6i	0.0301086	+	0.0301086i
$66$			1.52332e8i			0.988194i
$67$	2.00253e8			1.21407			0.607033	−	0.794677i	$-0.292360\pi$
$67$	2.00253e8			1.21407			0.607033	+	0.794677i	$0.292360\pi$
$68$	−1.78706e7	+	1.18031e8i	−0.101356	+	0.669429i
$69$	−1.52561e8			−0.810259
$70$			7.02191e6i			0.0349554i
$71$	7.24254e7	+	7.24254e7i	0.338242	+	0.338242i	0.855706	−	0.517463i	$-0.173124\pi$
$71$	7.24254e7	+	7.24254e7i	0.338242	+	0.338242i	−0.517463	+	0.855706i	$0.673124\pi$
$72$	−2.45455e8			−1.07641
$73$	−3.09947e8	−	3.09947e8i	−1.27742	−	1.27742i	−0.942105	−	0.335319i	$-0.891156\pi$
$73$	−3.09947e8	−	3.09947e8i	−1.27742	−	1.27742i	−0.335319	−	0.942105i	$-0.608844\pi$
$74$	1.43379e8	−	1.43379e8i	0.555833	−	0.555833i
$75$	−2.80637e8	+	2.80637e8i	−1.02416	+	1.02416i
$76$			2.82816e8i			0.972396i
$77$		−	2.61883e8i		−	0.848983i
$78$	−9.45390e7	+	9.45390e7i	−0.289191	+	0.289191i
$79$	2.19857e8	−	2.19857e8i	0.635064	−	0.635064i	−0.314270	−	0.949334i	$-0.601760\pi$
$79$	2.19857e8	−	2.19857e8i	0.635064	−	0.635064i	0.949334	+	0.314270i	$0.101760\pi$
$80$	−3.02989e6	−	3.02989e6i	−0.00827031	−	0.00827031i
$81$	3.30778e8			0.853795
$82$	−4.49437e7	−	4.49437e7i	−0.109776	−	0.109776i
$83$			8.30705e8i			1.92130i	0.277761	+	0.960650i	$0.410408\pi$
$83$			8.30705e8i			1.92130i	−0.277761	+	0.960650i	$0.589592\pi$
$84$	3.21195e8			0.703902
$85$	3.34486e7	−	2.46518e7i	0.0695012	−	0.0512228i
$86$	5.97928e7			0.117871
$87$			2.06962e8i			0.387305i
$88$	−4.51766e8	−	4.51766e8i	−0.803049	−	0.803049i
$89$	6.52199e7			0.110186			0.0550928	−	0.998481i	$-0.482455\pi$
$89$	6.52199e7			0.110186			0.0550928	+	0.998481i	$0.482455\pi$
$90$	2.43896e7	+	2.43896e7i	0.0391844	+	0.0391844i
$91$	1.62528e8	−	1.62528e8i	0.248452	−	0.248452i
$92$	1.82661e8	−	1.82661e8i	0.265829	−	0.265829i
$93$			2.67683e8i			0.371063i
$94$		−	4.30522e8i		−	0.568748i
$95$	6.96078e7	−	6.96078e7i	0.0876803	−	0.0876803i
$96$	8.84474e8	−	8.84474e8i	1.06283	−	1.06283i
$97$	−1.59423e8	−	1.59423e8i	−0.182843	−	0.182843i	0.609750	−	0.792594i	$-0.291270\pi$
$97$	−1.59423e8	−	1.59423e8i	−0.182843	−	0.182843i	−0.792594	+	0.609750i	$0.791270\pi$
$98$	−2.55514e8			−0.279832
$99$	−9.09613e8	−	9.09613e8i	−0.951696	−	0.951696i
$100$		−	6.72012e8i		−	0.672012i
$101$	1.79147e9			1.71303			0.856514	−	0.516124i	$-0.172626\pi$
$101$	1.79147e9			1.71303			0.856514	+	0.516124i	$0.172626\pi$
$102$	5.37847e8	+	7.29773e8i	0.491992	+	0.667555i
$103$	−2.00302e9			−1.75355			−0.876773	−	0.480904i	$-0.840308\pi$
$103$	−2.00302e9			−1.75355			−0.876773	+	0.480904i	$0.840308\pi$
$104$		−	5.60744e8i		−	0.470018i
$105$	−7.90538e7	−	7.90538e7i	−0.0634704	−	0.0634704i
$106$	6.54983e8			0.503911
$107$	5.51678e8	+	5.51678e8i	0.406873	+	0.406873i	0.880647	−	0.473774i	$-0.157109\pi$
$107$	5.51678e8	+	5.51678e8i	0.406873	+	0.406873i	−0.473774	+	0.880647i	$0.657109\pi$
$108$	1.27864e8	−	1.27864e8i	0.0904361	−	0.0904361i
$109$	−1.52440e9	+	1.52440e9i	−1.03438	+	1.03438i	−0.0349930	+	0.999388i	$0.511141\pi$
$109$	−1.52440e9	+	1.52440e9i	−1.03438	+	1.03438i	−0.999388	+	0.0349930i	$0.988859\pi$
$110$			8.97793e7i			0.0584668i
$111$			3.22838e9i			2.01851i
$112$	−1.13646e8	+	1.13646e8i	−0.0682454	+	0.0682454i
$113$	−8.00180e8	+	8.00180e8i	−0.461673	+	0.461673i	−0.899204	−	0.437530i	$-0.855853\pi$
$113$	−8.00180e8	+	8.00180e8i	−0.461673	+	0.461673i	0.437530	+	0.899204i	$0.355853\pi$
$114$	1.51869e9	+	1.51869e9i	0.842164	+	0.842164i
$115$	−8.99147e7			−0.0479392
$116$	−2.47795e8	−	2.47795e8i	−0.127067	−	0.127067i
$117$		−	1.12904e9i		−	0.557021i
$118$	−2.21471e9			−1.05159
$119$	−9.24647e8	−	1.25460e9i	−0.422683	−	0.573514i
$120$	−2.72747e8			−0.120073
$121$		−	9.90381e8i		−	0.420018i
$122$	4.37312e8	+	4.37312e8i	0.178719	+	0.178719i
$123$	1.01197e9			0.398651
$124$	−3.20496e8	−	3.20496e8i	−0.121738	−	0.121738i
$125$	−3.32039e8	+	3.32039e8i	−0.121645	+	0.121645i
$126$	9.14813e8	−	9.14813e8i	0.323344	−	0.323344i
$127$		−	3.66984e9i		−	1.25179i	−0.779908	−	0.625894i	$-0.784734\pi$
$127$		−	3.66984e9i		−	1.25179i	0.779908	−	0.625894i	$-0.215266\pi$
$128$			2.35176e9i			0.774369i
$129$	−6.73157e8	+	6.73157e8i	−0.214024	+	0.214024i
$130$	−5.57182e7	+	5.57182e7i	−0.0171101	+	0.0171101i
$131$	−1.34806e9	−	1.34806e9i	−0.399933	−	0.399933i	0.478276	−	0.878210i	$-0.341262\pi$
$131$	−1.34806e9	−	1.34806e9i	−0.399933	−	0.399933i	−0.878210	+	0.478276i	$0.841262\pi$
$132$	4.10667e9			1.17735
$133$	−2.61087e9	−	2.61087e9i	−0.723525	−	0.723525i
$134$			2.57499e9i			0.689928i
$135$	−6.29408e7			−0.0163091
$136$	−3.75935e9	−	5.69192e8i	−0.942298	−	0.142670i
$137$	2.68382e9			0.650895			0.325448	−	0.945560i	$-0.394485\pi$
$137$	2.68382e9			0.650895			0.325448	+	0.945560i	$0.394485\pi$
$138$		−	1.96174e9i		−	0.460453i
$139$	3.06981e9	+	3.06981e9i	0.697501	+	0.697501i	0.963871	−	0.266370i	$-0.0858243\pi$
$139$	3.06981e9	+	3.06981e9i	0.697501	+	0.697501i	−0.266370	+	0.963871i	$0.585824\pi$
$140$	1.89302e8			0.0416465
$141$	4.84688e9	+	4.84688e9i	1.03271	+	1.03271i
$142$	−9.31295e8	+	9.31295e8i	−0.192216	+	0.192216i
$143$	2.07802e9	−	2.07802e9i	0.415563	−	0.415563i
$144$			7.89467e8i			0.153004i
$145$			1.21976e8i			0.0229150i
$146$	3.98551e9	−	3.98551e9i	0.725933	−	0.725933i
$147$	2.87662e9	−	2.87662e9i	0.508107	−	0.508107i
$148$	−3.86533e9	−	3.86533e9i	−0.662230	−	0.662230i
$149$	7.27303e9			1.20886			0.604432	−	0.796657i	$-0.293400\pi$
$149$	7.27303e9			1.20886			0.604432	+	0.796657i	$0.293400\pi$
$150$	−3.60862e9	−	3.60862e9i	−0.582010	−	0.582010i
$151$		−	4.35149e9i		−	0.681149i	−0.940218	−	0.340574i	$-0.889379\pi$
$151$		−	4.35149e9i		−	0.681149i	0.940218	−	0.340574i	$-0.110621\pi$
$152$	−9.00788e9			−1.36876
$153$	−7.56931e9	−	1.14604e9i	−1.11672	−	0.169079i
$154$	3.36747e9			0.482459
$155$			1.57764e8i			0.0219540i
$156$	2.54865e9	+	2.54865e9i	0.344548	+	0.344548i
$157$	8.25994e9			1.08500			0.542498	−	0.840057i	$-0.317478\pi$
$157$	8.25994e9			1.08500			0.542498	+	0.840057i	$0.317478\pi$
$158$	2.82707e9	+	2.82707e9i	0.360894	+	0.360894i
$159$	−7.37391e9	+	7.37391e9i	−0.914978	+	0.914978i
$160$	5.21280e8	−	5.21280e8i	0.0628827	−	0.0628827i
$161$			3.37255e9i			0.395587i
$162$			4.25336e9i			0.485194i
$163$	−3.57804e9	+	3.57804e9i	−0.397009	+	0.397009i	−0.877177	−	0.480168i	$-0.840576\pi$
$163$	−3.57804e9	+	3.57804e9i	−0.397009	+	0.397009i	0.480168	+	0.877177i	$0.340576\pi$
$164$	−1.21163e9	+	1.21163e9i	−0.130789	+	0.130789i
$165$	−1.01075e9	−	1.01075e9i	−0.106161	−	0.106161i
$166$	−1.06818e10			−1.09183
$167$	−1.03033e9	−	1.03033e9i	−0.102506	−	0.102506i	0.653994	−	0.756500i	$-0.273092\pi$
$167$	−1.03033e9	−	1.03033e9i	−0.102506	−	0.102506i	−0.756500	+	0.653994i	$0.773092\pi$
$168$			1.02303e10i			0.990822i
$169$	−8.02521e9			−0.756774
$170$	3.16990e8	+	4.30105e8i	0.0291088	+	0.0394961i
$171$	−1.81370e10			−1.62212
$172$		−	1.61194e9i		−	0.140433i
$173$	6.57271e9	+	6.57271e9i	0.557875	+	0.557875i	0.928702	−	0.370827i	$-0.120926\pi$
$173$	6.57271e9	+	6.57271e9i	0.557875	+	0.557875i	−0.370827	+	0.928702i	$0.620926\pi$
$174$	−2.66125e9			−0.220097
$175$	6.20381e9	+	6.20381e9i	0.500020	+	0.500020i
$176$	−1.45303e9	+	1.45303e9i	−0.114148	+	0.114148i
$177$	2.49336e10	−	2.49336e10i	1.90944	−	1.90944i
$178$			8.38642e8i			0.0626162i
$179$			5.29738e9i			0.385676i	0.981231	+	0.192838i	$0.0617692\pi$
$179$			5.29738e9i			0.385676i	−0.981231	+	0.192838i	$0.938231\pi$
$180$	6.57513e8	−	6.57513e8i	0.0466851	−	0.0466851i
$181$	1.44218e10	−	1.44218e10i	0.998771	−	0.998771i	−0.00122856	−	0.999999i	$-0.500391\pi$
$181$	1.44218e10	−	1.44218e10i	0.998771	−	0.998771i	0.999999	+	0.00122856i	$0.000391062\pi$
$182$	2.08990e9	+	2.08990e9i	0.141190	+	0.141190i
$183$	−9.84666e9			−0.649021
$184$	5.81789e9	+	5.81789e9i	0.374184	+	0.374184i
$185$			1.90270e9i			0.119426i
$186$	−3.44205e9			−0.210867
$187$	−1.18222e10	−	1.60408e10i	−0.706984	−	0.959266i
$188$	−1.16063e10			−0.677617
$189$			2.36081e9i			0.134580i
$190$	8.95065e8	+	8.95065e8i	0.0498269	+	0.0498269i
$191$	1.13020e9			0.0614478			0.0307239	−	0.999528i	$-0.490219\pi$
$191$	1.13020e9			0.0614478			0.0307239	+	0.999528i	$0.490219\pi$
$192$	8.74103e9	+	8.74103e9i	0.464202	+	0.464202i
$193$	2.52689e10	−	2.52689e10i	1.31093	−	1.31093i	0.390195	−	0.920732i	$-0.372408\pi$
$193$	2.52689e10	−	2.52689e10i	1.31093	−	1.31093i	0.920732	−	0.390195i	$-0.127592\pi$
$194$	2.04998e9	−	2.04998e9i	0.103906	−	0.103906i
$195$		−	1.25457e9i		−	0.0621354i
$196$			6.88835e9i			0.333398i
$197$	−2.51679e10	+	2.51679e10i	−1.19055	+	1.19055i	−0.213640	+	0.976912i	$0.568532\pi$
$197$	−2.51679e10	+	2.51679e10i	−1.19055	+	1.19055i	−0.976912	+	0.213640i	$0.931468\pi$
$198$	1.16964e10	−	1.16964e10i	0.540829	−	0.540829i
$199$	2.20881e10	+	2.20881e10i	0.998436	+	0.998436i	0.999999	−	0.00156230i	$-0.000497295\pi$
$199$	2.20881e10	+	2.20881e10i	0.998436	+	0.998436i	−0.00156230	+	0.999999i	$0.500497\pi$
$200$	2.14040e10			0.945933
$201$	−2.89896e10	−	2.89896e10i	−1.25274	−	1.25274i
$202$			2.30360e10i			0.973477i
$203$	4.57513e9			0.189091
$204$	1.96738e10	−	1.44997e10i	0.795339	−	0.586169i
$205$	5.96420e8			0.0235863
$206$		−	2.57562e10i		−	0.996503i
$207$	1.17141e10	+	1.17141e10i	0.443447	+	0.443447i
$208$	−1.80354e9			−0.0668100
$209$	−3.33816e10	−	3.33816e10i	−1.21018	−	1.21018i
$210$	1.01653e9	−	1.01653e9i	0.0360689	−	0.0360689i
$211$	−2.04603e10	+	2.04603e10i	−0.710627	+	0.710627i	−0.966666	−	0.256039i	$-0.917582\pi$
$211$	−2.04603e10	+	2.04603e10i	−0.710627	+	0.710627i	0.256039	+	0.966666i	$0.417582\pi$
$212$		−	1.76575e10i		−	0.600370i
$213$		−	2.09693e10i		−	0.698034i
$214$	−7.09385e9	+	7.09385e9i	−0.231217	+	0.231217i
$215$	−3.96737e8	+	3.96737e8i	−0.0126628	+	0.0126628i
$216$	4.07256e9	+	4.07256e9i	0.127299	+	0.127299i
$217$	5.91745e9			0.181161
$218$	−1.96018e10	−	1.96018e10i	−0.587817	−	0.587817i
$219$			8.97391e10i			2.63623i
$220$	2.42034e9			0.0696585
$221$	2.61815e9	−	1.72921e10i	0.0738293	−	0.487622i
$222$	−4.15127e10			−1.14708
$223$			5.45398e10i			1.47687i	0.674326	+	0.738434i	$0.264434\pi$
$223$			5.45398e10i			1.47687i	−0.674326	+	0.738434i	$0.735566\pi$
$224$	−1.95524e10	−	1.95524e10i	−0.518899	−	0.518899i
$225$	4.30961e10			1.12103
$226$	−1.02893e10	−	1.02893e10i	−0.262359	−	0.262359i
$227$	−6.48779e9	+	6.48779e9i	−0.162174	+	0.162174i	−0.783529	−	0.621355i	$-0.786582\pi$
$227$	−6.48779e9	+	6.48779e9i	−0.162174	+	0.162174i	0.621355	+	0.783529i	$0.286582\pi$
$228$	4.09419e10	−	4.09419e10i	1.00337	−	1.00337i
$229$			2.94750e10i			0.708263i	0.935196	+	0.354131i	$0.115223\pi$
$229$			2.94750e10i			0.708263i	−0.935196	+	0.354131i	$0.884777\pi$
$230$		−	1.15619e9i		−	0.0272428i
$231$	−3.79115e10	+	3.79115e10i	−0.876027	+	0.876027i
$232$	7.89243e9	−	7.89243e9i	0.178861	−	0.178861i
$233$	3.92131e10	+	3.92131e10i	0.871625	+	0.871625i	0.992649	−	0.121025i	$-0.0386181\pi$
$233$	3.92131e10	+	3.92131e10i	0.871625	+	0.871625i	−0.121025	+	0.992649i	$0.538618\pi$
$234$	1.45179e10			0.316543
$235$	2.85660e9	+	2.85660e9i	0.0611003	+	0.0611003i
$236$			5.97059e10i			1.25289i
$237$	−6.36552e10			−1.31059
$238$	1.61325e10	−	1.18897e10i	0.325916	−	0.240202i
$239$	−6.16221e10			−1.22165			−0.610823	−	0.791767i	$-0.709161\pi$
$239$	−6.16221e10			−1.22165			−0.610823	+	0.791767i	$0.709161\pi$
$240$			8.77245e8i			0.0170675i
$241$	3.17781e10	+	3.17781e10i	0.606808	+	0.606808i	0.942111	−	0.335302i	$-0.108838\pi$
$241$	3.17781e10	+	3.17781e10i	0.606808	+	0.606808i	−0.335302	+	0.942111i	$0.608838\pi$
$242$	1.27350e10			0.238687
$243$	−5.51452e10	−	5.51452e10i	−1.01456	−	1.01456i
$244$	1.17894e10	−	1.17894e10i	0.212930	−	0.212930i
$245$	1.69539e9	−	1.69539e9i	0.0300623	−	0.0300623i
$246$			1.30126e10i			0.226545i
$247$		−	4.14341e10i		−	0.708307i
$248$	1.02080e10	−	1.02080e10i	0.171360	−	0.171360i
$249$	1.20257e11	−	1.20257e11i	1.98250	−	1.98250i
$250$	−4.26958e9	−	4.26958e9i	−0.0691282	−	0.0691282i
$251$	−3.67666e10			−0.584685			−0.292343	−	0.956314i	$-0.594435\pi$
$251$	−3.67666e10			−0.584685			−0.292343	+	0.956314i	$0.594435\pi$
$252$	−2.46622e10	−	2.46622e10i	−0.385239	−	0.385239i
$253$			4.31201e10i			0.661663i
$254$	4.71893e10			0.711365
$255$	−8.41091e9	−	1.27347e9i	−0.124570	−	0.0188607i
$256$	−6.11554e10			−0.889929
$257$		−	1.06275e11i		−	1.51962i	−0.650148	−	0.759808i	$-0.725293\pi$
$257$		−	1.06275e11i		−	1.51962i	0.650148	−	0.759808i	$-0.274707\pi$
$258$	−8.65591e9	−	8.65591e9i	−0.121625	−	0.121625i
$259$	7.13671e10			0.985484
$260$	1.50209e9	+	1.50209e9i	0.0203853	+	0.0203853i
$261$	1.58911e10	−	1.58911e10i	0.211968	−	0.211968i
$262$	1.73342e10	−	1.73342e10i	0.227274	−	0.227274i
$263$		−	4.15683e10i		−	0.535749i	−0.963454	−	0.267875i	$-0.913679\pi$
$263$		−	4.15683e10i		−	0.535749i	0.963454	−	0.267875i	$-0.0863213\pi$
$264$			1.30800e11i			1.65726i
$265$	−4.34594e9	+	4.34594e9i	−0.0541349	+	0.0541349i
$266$	3.35724e10	−	3.35724e10i	0.411164	−	0.411164i
$267$	−9.44157e9	−	9.44157e9i	−0.113696	−	0.113696i
$268$	6.94185e10			0.821994
$269$	1.36436e10	+	1.36436e10i	0.158871	+	0.158871i	0.782066	−	0.623195i	$-0.214166\pi$
$269$	1.36436e10	+	1.36436e10i	0.158871	+	0.158871i	−0.623195	+	0.782066i	$0.714166\pi$
$270$		−	8.09336e8i		−	0.00926813i
$271$	−5.51694e10			−0.621350			−0.310675	−	0.950516i	$-0.600555\pi$
$271$	−5.51694e10			−0.621350			−0.310675	+	0.950516i	$0.600555\pi$
$272$	−1.83071e9	+	1.20914e10i	−0.0202796	+	0.133941i
$273$	−4.70568e10			−0.512732
$274$			3.45104e10i			0.369890i
$275$	7.93194e10	+	7.93194e10i	0.836339	+	0.836339i
$276$	−5.28860e10			−0.548593
$277$	1.05739e11	+	1.05739e11i	1.07914	+	1.07914i	0.996587	+	0.0825522i	$0.0263071\pi$
$277$	1.05739e11	+	1.05739e11i	1.07914	+	1.07914i	0.0825522	+	0.996587i	$0.473693\pi$
$278$	−3.94737e10	+	3.94737e10i	−0.396375	+	0.396375i
$279$	2.05534e10	−	2.05534e10i	0.203079	−	0.203079i
$280$			6.02939e9i			0.0586222i
$281$		−	8.27561e10i		−	0.791811i	−0.918291	−	0.395906i	$-0.870431\pi$
$281$		−	8.27561e10i		−	0.791811i	0.918291	−	0.395906i	$-0.129569\pi$
$282$	−6.23245e10	+	6.23245e10i	−0.586865	+	0.586865i
$283$	3.63906e10	−	3.63906e10i	0.337249	−	0.337249i	−0.518082	−	0.855331i	$-0.673354\pi$
$283$	3.63906e10	−	3.63906e10i	0.337249	−	0.337249i	0.855331	+	0.518082i	$0.173354\pi$
$284$	2.51066e10	+	2.51066e10i	0.229010	+	0.229010i
$285$	−2.01536e10			−0.180947
$286$	2.67206e10	+	2.67206e10i	0.236156	+	0.236156i
$287$		−	2.23707e10i		−	0.194631i
$288$	−1.35825e11			−1.16336
$289$	−1.13273e11	−	3.51053e10i	−0.955179	−	0.296027i
$290$	−1.56846e9			−0.0130221
$291$			4.61579e10i			0.377336i
$292$	−1.07445e11	−	1.07445e11i	−0.864891	−	0.864891i
$293$	−1.21927e11			−0.966484			−0.483242	−	0.875487i	$-0.660541\pi$
$293$	−1.21927e11			−0.966484			−0.483242	+	0.875487i	$0.660541\pi$
$294$	3.69896e10	+	3.69896e10i	0.288746	+	0.288746i
$295$	1.46951e10	−	1.46951e10i	0.112972	−	0.112972i
$296$	1.23113e11	−	1.23113e11i	0.932164	−	0.932164i
$297$			3.01843e10i			0.225101i
$298$			9.35216e10i			0.686972i
$299$	−2.67609e10	+	2.67609e10i	−0.193633	+	0.193633i
$300$	−9.72840e10	+	9.72840e10i	−0.693419	+	0.693419i
$301$	1.48809e10	+	1.48809e10i	0.104491	+	0.104491i
$302$	5.59545e10			0.387082
$303$	−2.59343e11	−	2.59343e11i	−1.76760	−	1.76760i
$304$			2.89724e10i			0.194560i
$305$	−5.80330e9			−0.0383995
$306$	1.47366e10	−	9.73313e10i	0.0960841	−	0.634609i
$307$	9.71611e10			0.624266			0.312133	−	0.950038i	$-0.398957\pi$
$307$	9.71611e10			0.624266			0.312133	+	0.950038i	$0.398957\pi$
$308$		−	9.07828e10i		−	0.574811i
$309$	2.89967e11	+	2.89967e11i	1.80940	+	1.80940i
$310$	−2.02863e9			−0.0124760
$311$	1.57770e11	+	1.57770e11i	0.956317	+	0.956317i	0.999085	−	0.0427677i	$-0.0136175\pi$
$311$	1.57770e11	+	1.57770e11i	0.956317	+	0.956317i	−0.0427677	+	0.999085i	$0.513618\pi$
$312$	−8.11763e10	+	8.11763e10i	−0.484991	+	0.484991i
$313$	−1.12949e10	+	1.12949e10i	−0.0665171	+	0.0665171i	−0.739583	−	0.673066i	$-0.764977\pi$
$313$	−1.12949e10	+	1.12949e10i	−0.0665171	+	0.0665171i	0.673066	+	0.739583i	$0.264977\pi$
$314$			1.06212e11i			0.616581i
$315$			1.21399e10i			0.0694734i
$316$	7.62142e10	−	7.62142e10i	0.429976	−	0.429976i
$317$	−1.42973e11	+	1.42973e11i	−0.795220	+	0.795220i	−0.982337	−	0.187118i	$-0.940085\pi$
$317$	−1.42973e11	+	1.42973e11i	−0.795220	+	0.795220i	0.187118	+	0.982337i	$0.440085\pi$
$318$	−9.48188e10	−	9.48188e10i	−0.519963	−	0.519963i
$319$	5.84958e10			0.316276
$320$	5.15168e9	+	5.15168e9i	0.0274646	+	0.0274646i
$321$		−	1.59728e11i		−	0.839667i
$322$	−4.33666e10			−0.224804
$323$	−2.77783e11	−	4.20583e10i	−1.42002	−	0.215001i
$324$	1.14665e11			0.578069
$325$			9.84534e10i			0.489503i
$326$	−4.60089e10	−	4.60089e10i	−0.225612	−	0.225612i
$327$	4.41361e11			2.13466
$328$	−3.85911e10	−	3.85911e10i	−0.184100	−	0.184100i
$329$	1.07146e11	−	1.07146e11i	0.504191	−	0.504191i
$330$	1.29969e10	−	1.29969e10i	0.0603292	−	0.0603292i
$331$		−	3.68035e11i		−	1.68524i	−0.538505	−	0.842622i	$-0.681011\pi$
$331$		−	3.68035e11i		−	1.68524i	0.538505	−	0.842622i	$-0.318989\pi$
$332$			2.87967e11i			1.30083i
$333$	2.47884e11	−	2.47884e11i	1.10471	−	1.10471i
$334$	1.32486e10	−	1.32486e10i	0.0582522	−	0.0582522i
$335$	−1.70856e10	−	1.70856e10i	−0.0741187	−	0.0741187i
$336$	3.29040e10			0.140839
$337$	−9.59112e10	−	9.59112e10i	−0.405074	−	0.405074i	0.474942	−	0.880017i	$-0.342469\pi$
$337$	−9.59112e10	−	9.59112e10i	−0.405074	−	0.405074i	−0.880017	+	0.474942i	$0.842469\pi$
$338$		−	1.03194e11i		−	0.430059i
$339$	2.31676e11			0.952759
$340$	1.15951e10	−	8.54565e9i	0.0470564	−	0.0346809i
$341$	7.56581e10			0.303013
$342$		−	2.33218e11i		−	0.921817i
$343$	−1.92731e11	−	1.92731e11i	−0.751845	−	0.751845i
$344$	5.13413e10			0.197676
$345$	1.30165e10	+	1.30165e10i	0.0494663	+	0.0494663i
$346$	−8.45164e10	+	8.45164e10i	−0.317029	+	0.317029i
$347$	−1.07632e11	+	1.07632e11i	−0.398528	+	0.398528i	−0.877713	−	0.479186i	$-0.840932\pi$
$347$	−1.07632e11	+	1.07632e11i	−0.398528	+	0.398528i	0.479186	+	0.877713i	$0.340932\pi$
$348$			7.17441e10i			0.262228i
$349$			1.78457e11i			0.643903i	0.946756	+	0.321951i	$0.104339\pi$
$349$			1.78457e11i			0.643903i	−0.946756	+	0.321951i	$0.895661\pi$
$350$	−7.97729e10	+	7.97729e10i	−0.284151	+	0.284151i
$351$	−1.87328e10	+	1.87328e10i	−0.0658749	+	0.0658749i
$352$	−2.49988e11	−	2.49988e11i	−0.867917	−	0.867917i
$353$	−2.96867e11			−1.01760			−0.508798	−	0.860886i	$-0.669910\pi$
$353$	−2.96867e11			−1.01760			−0.508798	+	0.860886i	$0.669910\pi$
$354$	3.20613e11	+	3.20613e11i	1.08509	+	1.08509i
$355$		−	1.23587e10i		−	0.0412994i
$356$	2.26088e10			0.0746022
$357$	−4.77657e10	+	3.15479e11i	−0.155636	+	1.02793i
$358$	−6.81173e10			−0.219171
$359$			1.67133e11i			0.531052i	0.964104	+	0.265526i	$0.0855457\pi$
$359$			1.67133e11i			0.531052i	−0.964104	+	0.265526i	$0.914454\pi$
$360$	2.09422e10	+	2.09422e10i	0.0657146	+	0.0657146i
$361$	−3.42916e11			−1.06269
$362$	1.85445e11	+	1.85445e11i	0.567580	+	0.567580i
$363$	−1.43373e11	+	1.43373e11i	−0.433398	+	0.433398i
$364$	5.63410e10	−	5.63410e10i	0.168216	−	0.168216i
$365$			5.28893e10i			0.155973i
$366$		−	1.26615e11i		−	0.368825i
$367$	−2.27989e11	+	2.27989e11i	−0.656020	+	0.656020i	−0.954436	−	0.298416i	$-0.903542\pi$
$367$	−2.27989e11	+	2.27989e11i	−0.656020	+	0.656020i	0.298416	+	0.954436i	$0.403542\pi$
$368$	1.87123e10	−	1.87123e10i	0.0531877	−	0.0531877i
$369$	−7.77015e10	−	7.77015e10i	−0.218178	−	0.218178i
$370$	−2.44662e10			−0.0678671
$371$	1.63009e11	+	1.63009e11i	0.446713	+	0.446713i
$372$			9.27934e10i			0.251231i
$373$	−3.84623e10			−0.102883			−0.0514417	−	0.998676i	$-0.516382\pi$
$373$	−3.84623e10			−0.102883			−0.0514417	+	0.998676i	$0.516382\pi$
$374$	2.06264e11	−	1.52018e11i	0.545131	−	0.401764i
$375$	9.61353e10			0.251040
$376$		−	3.69669e11i		−	0.953823i
$377$	3.63033e10	+	3.63033e10i	0.0925571	+	0.0925571i
$378$	−3.03569e10			−0.0764793
$379$	−6.94178e10	−	6.94178e10i	−0.172820	−	0.172820i	0.615397	−	0.788217i	$-0.288996\pi$
$379$	−6.94178e10	−	6.94178e10i	−0.172820	−	0.172820i	−0.788217	+	0.615397i	$0.788996\pi$
$380$	2.41299e10	−	2.41299e10i	0.0593647	−	0.0593647i
$381$	−5.31266e11	+	5.31266e11i	−1.29166	+	1.29166i
$382$			1.45329e10i			0.0349195i
$383$		−	3.91752e11i		−	0.930286i	−0.885236	−	0.465143i	$-0.846003\pi$
$383$		−	3.91752e11i		−	0.930286i	0.885236	−	0.465143i	$-0.153997\pi$
$384$	3.40453e11	−	3.40453e11i	0.799036	−	0.799036i
$385$	−2.23438e10	+	2.23438e10i	−0.0518304	+	0.0518304i
$386$	3.24925e11	+	3.24925e11i	0.744972	+	0.744972i
$387$	1.03374e11			0.234267
$388$	−5.52648e10	−	5.52648e10i	−0.123796	−	0.123796i
$389$		−	4.40744e11i		−	0.975917i	−0.872867	−	0.487959i	$-0.837742\pi$
$389$		−	4.40744e11i		−	0.975917i	0.872867	−	0.487959i	$-0.162258\pi$
$390$	1.61321e10			0.0353102
$391$	1.52247e11	+	2.06575e11i	0.329422	+	0.446974i
$392$	−2.19398e11			−0.469295
$393$			3.90304e11i			0.825346i
$394$	−3.23626e11	−	3.23626e11i	−0.676566	−	0.676566i
$395$	−3.75163e10			−0.0775413
$396$	−3.15321e11	−	3.15321e11i	−0.644354	−	0.644354i
$397$	2.39361e11	−	2.39361e11i	0.483612	−	0.483612i	−0.422671	−	0.906283i	$-0.638908\pi$
$397$	2.39361e11	−	2.39361e11i	0.483612	−	0.483612i	0.906283	+	0.422671i	$0.138908\pi$
$398$	−2.84025e11	+	2.84025e11i	−0.567390	+	0.567390i
$399$			7.55927e11i			1.49315i
$400$		−	6.88426e10i		−	0.134458i
$401$	−1.21560e11	+	1.21560e11i	−0.234769	+	0.234769i	−0.814680	−	0.579911i	$-0.803087\pi$
$401$	−1.21560e11	+	1.21560e11i	−0.234769	+	0.234769i	0.579911	+	0.814680i	$0.303087\pi$
$402$	3.72769e11	−	3.72769e11i	0.711905	−	0.711905i
$403$	4.69544e10	+	4.69544e10i	0.0886755	+	0.0886755i
$404$	6.21022e11			1.15982
$405$	−2.82219e10	−	2.82219e10i	−0.0521241	−	0.0521241i
$406$			5.88302e10i			0.107457i
$407$	9.12471e11			1.64833
$408$	4.61825e11	+	6.26623e11i	0.825100	+	1.11953i
$409$	1.81166e11			0.320126			0.160063	−	0.987107i	$-0.448830\pi$
$409$	1.81166e11			0.320126			0.160063	+	0.987107i	$0.448830\pi$
$410$			7.66918e9i			0.0134036i
$411$	−3.88524e11	−	3.88524e11i	−0.671629	−	0.671629i
$412$	−6.94354e11			−1.18725
$413$	−5.51187e11	−	5.51187e11i	−0.932231	−	0.932231i
$414$	−1.50628e11	+	1.50628e11i	−0.252001	+	0.252001i
$415$	7.08757e10	−	7.08757e10i	0.117295	−	0.117295i
$416$		−	3.10292e11i		−	0.507985i
$417$		−	8.88803e11i		−	1.43944i
$418$	4.29243e11	−	4.29243e11i	0.687717	−	0.687717i
$419$	−3.78081e11	+	3.78081e11i	−0.599268	+	0.599268i	−0.940118	−	0.340850i	$-0.889285\pi$
$419$	−3.78081e11	+	3.78081e11i	−0.599268	+	0.599268i	0.340850	+	0.940118i	$0.389285\pi$
$420$	−2.74043e10	−	2.74043e10i	−0.0429732	−	0.0429732i
$421$	4.75293e10			0.0737381			0.0368691	−	0.999320i	$-0.488262\pi$
$421$	4.75293e10			0.0737381			0.0368691	+	0.999320i	$0.488262\pi$
$422$	−2.63093e11	−	2.63093e11i	−0.403835	−	0.403835i
$423$		−	7.44314e11i		−	1.13038i
$424$	5.62404e11			0.845088
$425$	6.60053e11	+	9.99366e10i	0.981361	+	0.148585i
$426$	2.69638e11			0.396678
$427$			2.17672e11i			0.316867i
$428$	1.91242e11	+	1.91242e11i	0.275477	+	0.275477i
$429$	−6.01649e11			−0.857601
$430$	−5.10151e9	−	5.10151e9i	−0.00719600	−	0.00719600i
$431$	5.96831e11	−	5.96831e11i	0.833112	−	0.833112i	−0.154829	−	0.987941i	$-0.549483\pi$
$431$	5.96831e11	−	5.96831e11i	0.833112	−	0.833112i	0.987941	+	0.154829i	$0.0494827\pi$
$432$	1.30987e10	−	1.30987e10i	0.0180947	−	0.0180947i
$433$		−	2.09001e10i		−	0.0285728i	−0.999898	−	0.0142864i	$-0.995452\pi$
$433$		−	2.09001e10i		−	0.0285728i	0.999898	−	0.0142864i	$-0.00454766\pi$
$434$			7.60906e10i			0.102950i
$435$	1.76580e10	−	1.76580e10i	0.0236450	−	0.0236450i
$436$	−5.28440e11	+	5.28440e11i	−0.700337	+	0.700337i
$437$	4.29891e11	+	4.29891e11i	0.563886	+	0.563886i
$438$	−1.15393e12			−1.49811
$439$	8.39039e11	+	8.39039e11i	1.07818	+	1.07818i	0.996673	+	0.0815085i	$0.0259738\pi$
$439$	8.39039e11	+	8.39039e11i	1.07818	+	1.07818i	0.0815085	+	0.996673i	$0.474026\pi$
$440$			7.70893e10i			0.0980522i
$441$	−4.41750e11			−0.556164
$442$	2.22354e11	+	3.36659e10i	0.277105	+	0.0419556i
$443$	4.19386e11			0.517366			0.258683	−	0.965962i	$-0.416712\pi$
$443$	4.19386e11			0.517366			0.258683	+	0.965962i	$0.416712\pi$
$444$			1.11913e12i			1.36665i
$445$	−5.56456e9	−	5.56456e9i	−0.00672683	−	0.00672683i
$446$	−7.01310e11			−0.839273
$447$	−1.05288e12	−	1.05288e12i	−1.24737	−	1.24737i
$448$	1.93231e11	−	1.93231e11i	0.226634	−	0.226634i
$449$	−4.83298e11	+	4.83298e11i	−0.561185	+	0.561185i	−0.929644	−	0.368459i	$-0.879886\pi$
$449$	−4.83298e11	+	4.83298e11i	−0.561185	+	0.561185i	0.368459	+	0.929644i	$0.379886\pi$
$450$			5.54160e11i			0.637057i
$451$		−	2.86023e11i		−	0.325542i
$452$	−2.77386e11	+	2.77386e11i	−0.312580	+	0.312580i
$453$	−6.29944e11	+	6.29944e11i	−0.702846	+	0.702846i
$454$	−8.34244e10	−	8.34244e10i	−0.0921599	−	0.0921599i
$455$	−2.77337e10			−0.0303359
$456$	1.30403e12	+	1.30403e12i	1.41236	+	1.41236i
$457$			1.13726e12i			1.21966i	0.792533	+	0.609829i	$0.208762\pi$
$457$			1.13726e12i			1.21966i	−0.792533	+	0.609829i	$0.791238\pi$
$458$	−3.79010e11			−0.402491
$459$	1.06574e11	+	1.44604e11i	0.112071	+	0.152063i
$460$	−3.11693e10			−0.0324577
$461$		−	4.01702e11i		−	0.414238i	−0.978316	−	0.207119i	$-0.933591\pi$
$461$		−	4.01702e11i		−	0.414238i	0.978316	−	0.207119i	$-0.0664087\pi$
$462$	−4.87492e11	−	4.87492e11i	−0.497828	−	0.497828i
$463$	1.71828e12			1.73772			0.868859	−	0.495059i	$-0.164854\pi$
$463$	1.71828e12			1.73772			0.868859	+	0.495059i	$0.164854\pi$
$464$	−2.53847e10	−	2.53847e10i	−0.0254238	−	0.0254238i
$465$	2.28387e10	−	2.28387e10i	0.0226534	−	0.0226534i
$466$	−5.04229e11	+	5.04229e11i	−0.495326	+	0.495326i
$467$		−	1.25508e12i		−	1.22108i	−0.791984	−	0.610542i	$-0.790952\pi$
$467$		−	1.25508e12i		−	1.22108i	0.791984	−	0.610542i	$-0.209048\pi$
$468$		−	3.91385e11i		−	0.377136i
$469$	−6.40851e11	+	6.40851e11i	−0.611616	+	0.611616i
$470$	−3.67321e10	+	3.67321e10i	−0.0347220	+	0.0347220i
$471$	−1.19575e12	−	1.19575e12i	−1.11956	−	1.11956i
$472$	−1.90167e12			−1.76359
$473$	1.90262e11	+	1.90262e11i	0.174774	+	0.174774i
$474$		−	8.18522e11i		−	0.744780i
$475$	1.58157e12			1.42550
$476$	−3.20533e11	−	4.34912e11i	−0.286181	−	0.388303i
$477$	1.13238e12			1.00152
$478$		−	7.92379e11i		−	0.694236i
$479$	−7.80669e11	−	7.80669e11i	−0.677575	−	0.677575i	0.281876	−	0.959451i	$-0.409043\pi$
$479$	−7.80669e11	−	7.80669e11i	−0.677575	−	0.677575i	−0.959451	+	0.281876i	$0.909043\pi$
$480$	−1.50927e11			−0.129772
$481$	5.66292e11	+	5.66292e11i	0.482378	+	0.482378i
$482$	−4.08625e11	+	4.08625e11i	−0.344836	+	0.344836i
$483$	4.88228e11	−	4.88228e11i	0.408188	−	0.408188i
$484$		−	3.43320e11i		−	0.284377i
$485$			2.72040e10i			0.0223252i
$486$	7.09095e11	−	7.09095e11i	0.576555	−	0.576555i
$487$	−8.55242e11	+	8.55242e11i	−0.688983	+	0.688983i	−0.962007	−	0.273024i	$-0.911976\pi$
$487$	−8.55242e11	+	8.55242e11i	−0.688983	+	0.688983i	0.273024	+	0.962007i	$0.411976\pi$
$488$	3.75500e11	+	3.75500e11i	0.299723	+	0.299723i
$489$	1.03595e12			0.819312
$490$	2.18005e10	+	2.18005e10i	0.0170838	+	0.0170838i
$491$		−	8.42274e11i		−	0.654014i	−0.945022	−	0.327007i	$-0.893960\pi$
$491$		−	8.42274e11i		−	0.654014i	0.945022	−	0.327007i	$-0.106040\pi$
$492$	3.50803e11			0.269910
$493$	2.80235e11	−	2.06535e11i	0.213654	−	0.157464i
$494$	5.32788e11			0.402516
$495$			1.55216e11i			0.116202i
$496$	−3.28324e10	−	3.28324e10i	−0.0243576	−	0.0243576i
$497$	−4.63552e11			−0.340796
$498$	1.54635e12	+	1.54635e12i	1.12661	+	1.12661i
$499$	−1.20714e12	+	1.20714e12i	−0.871575	+	0.871575i	−0.992644	−	0.121069i	$-0.961368\pi$
$499$	−1.20714e12	+	1.20714e12i	−0.871575	+	0.871575i	0.121069	+	0.992644i	$0.461368\pi$
$500$	−1.15103e11	+	1.15103e11i	−0.0823607	+	0.0823607i
$501$			2.98311e11i			0.211543i
$502$		−	4.72771e11i		−	0.332264i
$503$	9.27469e11	−	9.27469e11i	0.646016	−	0.646016i	−0.306011	−	0.952028i	$-0.598995\pi$
$503$	9.27469e11	−	9.27469e11i	0.646016	−	0.646016i	0.952028	+	0.306011i	$0.0989946\pi$
$504$	7.85508e11	−	7.85508e11i	0.542267	−	0.542267i
$505$	−1.52848e11	−	1.52848e11i	−0.104580	−	0.104580i
$506$	−5.54467e11			−0.376009
$507$	1.16177e12	+	1.16177e12i	0.780881	+	0.780881i
$508$		−	1.27217e12i		−	0.847534i
$509$	−2.27732e12			−1.50382			−0.751908	−	0.659268i	$-0.770866\pi$
$509$	−2.27732e12			−1.50382			−0.751908	+	0.659268i	$0.770866\pi$
$510$	1.63751e10	−	1.08153e11i	0.0107181	−	0.0707903i
$511$	1.98379e12			1.28707
$512$			4.17721e11i			0.268641i
$513$	3.00926e11	+	3.00926e11i	0.191837	+	0.191837i
$514$	1.36656e12			0.863566
$515$	1.70897e11	+	1.70897e11i	0.107054	+	0.107054i
$516$	−2.33353e11	+	2.33353e11i	−0.144907	+	0.144907i
$517$	1.36993e12	−	1.36993e12i	0.843315	−	0.843315i
$518$			9.17688e11i			0.560030i
$519$		−	1.90300e12i		−	1.15129i
$520$	−4.78427e10	+	4.78427e10i	−0.0286946	+	0.0286946i
$521$	−2.26404e12	+	2.26404e12i	−1.34622	+	1.34622i	−0.456485	+	0.889731i	$0.650892\pi$
$521$	−2.26404e12	+	2.26404e12i	−1.34622	+	1.34622i	−0.889731	+	0.456485i	$0.849108\pi$
$522$	2.04338e11	+	2.04338e11i	0.120457	+	0.120457i
$523$	−2.74758e11			−0.160580			−0.0802902	−	0.996772i	$-0.525585\pi$
$523$	−2.74758e11			−0.160580			−0.0802902	+	0.996772i	$0.525585\pi$
$524$	−4.67310e11	−	4.67310e11i	−0.270778	−	0.270778i
$525$		−	1.79619e12i		−	1.03190i
$526$	5.34514e11			0.304455
$527$	3.62455e11	−	2.67131e11i	0.204694	−	0.150861i
$528$	4.20697e11			0.235568
$529$			1.24585e12i			0.691695i
$530$	−5.58831e10	−	5.58831e10i	−0.0307637	−	0.0307637i
$531$	−3.82894e12			−2.09003
$532$	−9.05070e11	−	9.05070e11i	−0.489869	−	0.489869i
$533$	1.77510e11	−	1.77510e11i	0.0952686	−	0.0952686i
$534$	1.21406e11	−	1.21406e11i	0.0646108	−	0.0646108i
$535$		−	9.41383e10i		−	0.0496791i
$536$			2.21102e12i			1.15705i
$537$	7.66876e11	−	7.66876e11i	0.397961	−	0.397961i
$538$	−1.75439e11	+	1.75439e11i	−0.0902831	+	0.0902831i
$539$	−8.13051e11	−	8.13051e11i	−0.414924	−	0.414924i
$540$	−2.18187e10			−0.0110422
$541$	−5.43534e11	−	5.43534e11i	−0.272797	−	0.272797i	0.557428	−	0.830225i	$-0.311788\pi$
$541$	−5.43534e11	−	5.43534e11i	−0.272797	−	0.272797i	−0.830225	+	0.557428i	$0.811788\pi$
$542$		−	7.09406e11i		−	0.353100i
$543$	−4.17555e12			−2.06117
$544$	−2.08027e12	−	3.14967e11i	−1.01841	−	0.154195i
$545$	2.60124e11			0.126298
$546$		−	6.05089e11i		−	0.291375i
$547$	2.30894e12	+	2.30894e12i	1.10273	+	1.10273i	0.994080	+	0.108653i	$0.0346537\pi$
$547$	2.30894e12	+	2.30894e12i	1.10273	+	1.10273i	0.108653	+	0.994080i	$0.465346\pi$
$548$	9.30358e11			0.440694
$549$	7.56053e11	+	7.56053e11i	0.355203	+	0.355203i
$550$	−1.01994e12	+	1.01994e12i	−0.475274	+	0.475274i
$551$	5.83181e11	−	5.83181e11i	0.269539	−	0.269539i
$552$		−	1.68446e12i		−	0.772207i
$553$			1.40717e12i			0.639859i
$554$	−1.35967e12	+	1.35967e12i	−0.613252	+	0.613252i
$555$	2.75445e11	−	2.75445e11i	0.123230	−	0.123230i
$556$	1.06416e12	+	1.06416e12i	0.472249	+	0.472249i
$557$	1.66914e12			0.734760			0.367380	−	0.930071i	$-0.380255\pi$
$557$	1.66914e12			0.734760			0.367380	+	0.930071i	$0.380255\pi$
$558$	2.64290e11	+	2.64290e11i	0.115406	+	0.115406i
$559$			2.36158e11i			0.102294i
$560$	1.93926e10			0.00833276
$561$	−6.10713e11	+	4.03359e12i	−0.260318	+	1.71933i
$562$	1.06413e12			0.449970
$563$			1.13172e12i			0.474734i	0.971420	+	0.237367i	$0.0762844\pi$
$563$			1.13172e12i			0.474734i	−0.971420	+	0.237367i	$0.923716\pi$
$564$	1.68019e12	+	1.68019e12i	0.699203	+	0.699203i
$565$	1.36543e11			0.0563703
$566$	4.67936e11	+	4.67936e11i	0.191652	+	0.191652i
$567$	−1.05856e12	+	1.05856e12i	−0.430121	+	0.430121i
$568$	−7.99660e11	+	7.99660e11i	−0.322358	+	0.322358i
$569$		−	2.09042e12i		−	0.836042i	−0.908437	−	0.418021i	$-0.862724\pi$
$569$		−	2.09042e12i		−	0.836042i	0.908437	−	0.418021i	$-0.137276\pi$
$570$		−	2.59149e11i		−	0.102828i
$571$	4.43448e11	−	4.43448e11i	0.174574	−	0.174574i	−0.614412	−	0.788986i	$-0.710607\pi$
$571$	4.43448e11	−	4.43448e11i	0.174574	−	0.174574i	0.788986	+	0.614412i	$0.210607\pi$
$572$	7.20353e11	−	7.20353e11i	0.281361	−	0.281361i
$573$	−1.63614e11	−	1.63614e11i	−0.0634052	−	0.0634052i
$574$	2.87658e11			0.110605
$575$	−1.02148e12	−	1.02148e12i	−0.389696	−	0.389696i
$576$		−	1.34232e12i		−	0.508106i
$577$	1.42436e12			0.534968			0.267484	−	0.963562i	$-0.413808\pi$
$577$	1.42436e12			0.534968			0.267484	+	0.963562i	$0.413808\pi$
$578$	4.51408e11	−	1.45654e12i	0.168226	−	0.542808i
$579$	−7.31612e12			−2.70537
$580$			4.22837e10i			0.0155148i
$581$	−2.65843e12	−	2.65843e12i	−0.967904	−	0.967904i
$582$	−5.93530e11			−0.214432
$583$	2.08417e12	+	2.08417e12i	0.747178	+	0.747178i
$584$	3.42218e12	−	3.42218e12i	1.21743	−	1.21743i
$585$	−9.63292e10	+	9.63292e10i	−0.0340061	+	0.0340061i
$586$		−	1.56782e12i		−	0.549233i
$587$			3.09625e12i			1.07638i	0.842824	+	0.538189i	$0.180891\pi$
$587$			3.09625e12i			1.07638i	−0.842824	+	0.538189i	$0.819109\pi$
$588$	9.97193e11	−	9.97193e11i	0.344018	−	0.344018i
$589$	7.54283e11	−	7.54283e11i	0.258235	−	0.258235i
$590$	1.88959e11	+	1.88959e11i	0.0641998	+	0.0641998i
$591$	7.28687e12			2.45695
$592$	−3.95974e11	−	3.95974e11i	−0.132501	−	0.132501i
$593$			1.01140e12i			0.335874i	0.985798	+	0.167937i	$0.0537106\pi$
$593$			1.01140e12i			0.335874i	−0.985798	+	0.167937i	$0.946289\pi$
$594$	−3.88130e11			−0.127920
$595$	−2.81516e10	+	1.85933e11i	−0.00920823	+	0.0608178i
$596$	2.52123e12			0.818472
$597$		−	6.39519e12i		−	2.06048i
$598$	−3.44110e11	−	3.44110e11i	−0.110038	−	0.110038i
$599$	1.80697e12			0.573495			0.286747	−	0.958006i	$-0.407426\pi$
$599$	1.80697e12			0.573495			0.286747	+	0.958006i	$0.407426\pi$
$600$	−3.09856e12	−	3.09856e12i	−0.976066	−	0.976066i
$601$	9.99867e11	−	9.99867e11i	0.312613	−	0.312613i	−0.533308	−	0.845921i	$-0.679051\pi$
$601$	9.99867e11	−	9.99867e11i	0.312613	−	0.312613i	0.845921	+	0.533308i	$0.179051\pi$
$602$	−1.91349e11	+	1.91349e11i	−0.0593803	+	0.0593803i
$603$			4.45181e12i			1.37122i
$604$		−	1.50846e12i		−	0.461178i
$605$	−8.44992e10	+	8.44992e10i	−0.0256421	+	0.0256421i
$606$	3.33481e12	−	3.33481e12i	1.00449	−	1.00449i
$607$	−8.41981e11	−	8.41981e11i	−0.251741	−	0.251741i	0.569943	−	0.821684i	$-0.306965\pi$
$607$	−8.41981e11	−	8.41981e11i	−0.251741	−	0.251741i	−0.821684	+	0.569943i	$0.806965\pi$
$608$	−4.98458e12			−1.47932
$609$	−6.62320e11	−	6.62320e11i	−0.195115	−	0.195115i
$610$		−	7.46228e10i		−	0.0218216i
$611$	1.70039e12			0.493586
$612$	−2.62393e12	−	3.97281e11i	−0.756086	−	0.114477i
$613$	−3.81378e11			−0.109090			−0.0545448	−	0.998511i	$-0.517371\pi$
$613$	−3.81378e11			−0.109090			−0.0545448	+	0.998511i	$0.517371\pi$
$614$			1.24936e12i			0.354757i
$615$	−8.63409e10	−	8.63409e10i	−0.0243376	−	0.0243376i
$616$	2.89149e12			0.809112
$617$	1.41713e12	+	1.41713e12i	0.393666	+	0.393666i	0.875992	−	0.482326i	$-0.160208\pi$
$617$	1.41713e12	+	1.41713e12i	0.393666	+	0.393666i	−0.482326	+	0.875992i	$0.660208\pi$
$618$	−3.72860e12	+	3.72860e12i	−1.02825	+	1.02825i
$619$	−8.49752e11	+	8.49752e11i	−0.232640	+	0.232640i	−0.813794	−	0.581154i	$-0.802601\pi$
$619$	−8.49752e11	+	8.49752e11i	−0.232640	+	0.232640i	0.581154	+	0.813794i	$0.302601\pi$
$620$			5.46894e10i			0.0148642i
$621$		−	3.88716e11i		−	0.104887i
$622$	−2.02871e12	+	2.02871e12i	−0.543455	+	0.543455i
$623$	−2.08717e11	+	2.08717e11i	−0.0555088	+	0.0555088i
$624$	2.61090e11	+	2.61090e11i	0.0689382	+	0.0689382i
$625$	−3.72960e12			−0.977693
$626$	−1.45238e11	−	1.45238e11i	−0.0378003	−	0.0378003i
$627$			9.66498e12i			2.49745i
$628$	2.86334e12			0.734607
$629$	4.37137e12	−	3.22172e12i	1.11350	−	0.820654i
$630$	−1.56104e11			−0.0394803
$631$		−	9.59070e11i		−	0.240834i	−0.992723	−	0.120417i	$-0.961577\pi$
$631$		−	9.59070e11i		−	0.240834i	0.992723	−	0.120417i	$-0.0384232\pi$
$632$	2.42747e12	+	2.42747e12i	0.605240	+	0.605240i
$633$	5.92389e12			1.46653
$634$	−1.83844e12	−	1.83844e12i	−0.451907	−	0.451907i
$635$	−3.13111e11	+	3.13111e11i	−0.0764216	+	0.0764216i
$636$	−2.55620e12	+	2.55620e12i	−0.619494	+	0.619494i
$637$		−	1.00918e12i		−	0.242852i
$638$			7.52179e11i			0.179733i
$639$	−1.61008e12	+	1.61008e12i	−0.382027	+	0.382027i
$640$	2.00652e11	−	2.00652e11i	0.0472752	−	0.0472752i
$641$	1.25149e12	+	1.25149e12i	0.292796	+	0.292796i	0.838184	−	0.545388i	$-0.183617\pi$
$641$	1.25149e12	+	1.25149e12i	0.292796	+	0.292796i	−0.545388	+	0.838184i	$0.683617\pi$
$642$	2.05389e12			0.477165
$643$	−5.32993e12	−	5.32993e12i	−1.22962	−	1.22962i	−0.964106	−	0.265517i	$-0.914457\pi$
$643$	−5.32993e12	−	5.32993e12i	−1.22962	−	1.22962i	−0.265517	−	0.964106i	$-0.585543\pi$
$644$			1.16911e12i			0.267836i
$645$	1.14867e11			0.0261323
$646$	5.40814e11	−	3.57193e12i	0.122180	−	0.806968i
$647$	−5.30405e12			−1.18998			−0.594989	−	0.803734i	$-0.702843\pi$
$647$	−5.30405e12			−1.18998			−0.594989	+	0.803734i	$0.702843\pi$
$648$			3.65217e12i			0.813698i
$649$	−7.04725e12	−	7.04725e12i	−1.55926	−	1.55926i
$650$	−1.26598e12			−0.278174
$651$	−8.56641e11	−	8.56641e11i	−0.186932	−	0.186932i
$652$	−1.24034e12	+	1.24034e12i	−0.268799	+	0.268799i
$653$	−2.41467e11	+	2.41467e11i	−0.0519695	+	0.0519695i	−0.732614	−	0.680644i	$-0.761700\pi$
$653$	−2.41467e11	+	2.41467e11i	−0.0519695	+	0.0519695i	0.680644	+	0.732614i	$0.261700\pi$
$654$			5.67532e12i			1.21308i
$655$			2.30032e11i			0.0488318i
$656$	−1.24122e11	+	1.24122e11i	−0.0261686	+	0.0261686i
$657$	6.89042e12	−	6.89042e12i	1.44278	−	1.44278i
$658$	1.37776e12	+	1.37776e12i	0.286521	+	0.286521i
$659$	1.73640e12			0.358646			0.179323	−	0.983790i	$-0.442609\pi$
$659$	1.73640e12			0.358646			0.179323	+	0.983790i	$0.442609\pi$
$660$	−3.50381e11	−	3.50381e11i	−0.0718774	−	0.0718774i
$661$			7.10034e12i			1.44668i	0.690492	+	0.723340i	$0.257394\pi$
$661$			7.10034e12i			1.44668i	−0.690492	+	0.723340i	$0.742606\pi$
$662$	4.73244e12			0.957689
$663$	−2.88232e12	+	2.12428e12i	−0.579336	+	0.426974i
$664$	−9.17195e12			−1.83107
$665$			4.45519e11i			0.0883423i
$666$	3.18746e12	+	3.18746e12i	0.627784	+	0.627784i
$667$	−7.53314e11			−0.147370
$668$	−3.57167e11	−	3.57167e11i	−0.0694029	−	0.0694029i
$669$	7.89546e12	−	7.89546e12i	1.52391	−	1.52391i
$670$	2.19698e11	−	2.19698e11i	0.0421201	−	0.0421201i
$671$			2.78307e12i			0.529996i
$672$			5.66100e12i			1.07086i
$673$	−6.04832e11	+	6.04832e11i	−0.113649	+	0.113649i	−0.761645	−	0.647995i	$-0.775608\pi$
$673$	−6.04832e11	+	6.04832e11i	−0.113649	+	0.113649i	0.647995	+	0.761645i	$0.275608\pi$
$674$	1.23329e12	−	1.23329e12i	0.230195	−	0.230195i
$675$	−7.15044e11	−	7.15044e11i	−0.132576	−	0.132576i
$676$	−2.78197e12			−0.512381
$677$	−7.12737e12	−	7.12737e12i	−1.30401	−	1.30401i	−0.925666	−	0.378342i	$-0.876494\pi$
$677$	−7.12737e12	−	7.12737e12i	−1.30401	−	1.30401i	−0.378342	−	0.925666i	$-0.623506\pi$
$678$			2.97905e12i			0.541433i
$679$	1.02038e12			0.184224
$680$	2.72184e11	+	3.69311e11i	0.0488172	+	0.0662373i
$681$	1.87841e12			0.334679
$682$			9.72864e11i			0.172196i
$683$	3.03863e12	+	3.03863e12i	0.534300	+	0.534300i	0.921849	−	0.387549i	$-0.126678\pi$
$683$	3.03863e12	+	3.03863e12i	0.534300	+	0.534300i	−0.387549	+	0.921849i	$0.626678\pi$
$684$	−6.28727e12			−1.09827
$685$	−2.28983e11	−	2.28983e11i	−0.0397371	−	0.0397371i
$686$	2.47827e12	−	2.47827e12i	0.427258	−	0.427258i
$687$	4.26696e12	−	4.26696e12i	0.730824	−	0.730824i
$688$		−	1.65131e11i		−	0.0280983i
$689$			2.58692e12i			0.437318i
$690$	−1.67375e11	+	1.67375e11i	−0.0281106	+	0.0281106i
$691$	−5.51319e12	+	5.51319e12i	−0.919923	+	0.919923i	−0.997023	−	0.0771005i	$-0.975434\pi$
$691$	−5.51319e12	+	5.51319e12i	−0.919923	+	0.919923i	0.0771005	+	0.997023i	$0.475434\pi$
$692$	2.27846e12	+	2.27846e12i	0.377714	+	0.377714i
$693$	5.82190e12			0.958882
$694$	−1.38400e12	−	1.38400e12i	−0.226475	−	0.226475i
$695$		−	5.23832e11i		−	0.0851648i
$696$	−2.28510e12			−0.369116
$697$	−1.00988e12	−	1.37025e12i	−0.162077	−	0.219913i
$698$	−2.29473e12			−0.365916
$699$		−	1.13534e13i		−	1.79878i
$700$	2.15058e12	+	2.15058e12i	0.338543	+	0.338543i
$701$	2.38474e12			0.373000			0.186500	−	0.982455i	$-0.440286\pi$
$701$	2.38474e12			0.373000			0.186500	+	0.982455i	$0.440286\pi$
$702$	−2.40879e11	−	2.40879e11i	−0.0374353	−	0.0374353i
$703$	9.09699e12	−	9.09699e12i	1.40475	−	1.40475i
$704$	2.47057e12	−	2.47057e12i	0.379071	−	0.379071i
$705$		−	8.27071e11i		−	0.126093i
$706$		−	3.81732e12i		−	0.578279i
$707$	−5.73309e12	+	5.73309e12i	−0.862981	+	0.862981i
$708$	8.64334e12	−	8.64334e12i	1.29280	−	1.29280i
$709$	−3.97625e12	−	3.97625e12i	−0.590971	−	0.590971i	0.346923	−	0.937894i	$-0.387227\pi$
$709$	−3.97625e12	−	3.97625e12i	−0.590971	−	0.590971i	−0.937894	+	0.346923i	$0.887227\pi$
$710$	1.58916e11			0.0234696
$711$	4.88762e12	+	4.88762e12i	0.717272	+	0.717272i
$712$			7.20104e11i			0.105011i
$713$	−9.74332e11			−0.141190
$714$	−4.05665e12	−	6.14204e11i	−0.584151	−	0.0884445i
$715$	−3.54592e11			−0.0507402
$716$			1.83636e12i			0.261125i
$717$	8.92073e12	+	8.92073e12i	1.26056	+	1.26056i
$718$	−2.14911e12			−0.301786
$719$	−1.08444e12	−	1.08444e12i	−0.151330	−	0.151330i	0.627382	−	0.778712i	$-0.284126\pi$
$719$	−1.08444e12	−	1.08444e12i	−0.151330	−	0.151330i	−0.778712	+	0.627382i	$0.784126\pi$
$720$	6.73573e10	−	6.73573e10i	0.00934089	−	0.00934089i
$721$	6.41007e12	−	6.41007e12i	0.883393	−	0.883393i
$722$		−	4.40944e12i		−	0.603902i
$723$		−	9.20073e12i		−	1.25228i
$724$	4.99938e12	−	4.99938e12i	0.676227	−	0.676227i
$725$	−1.38572e12	+	1.38572e12i	−0.186275	+	0.186275i
$726$	−1.84358e12	−	1.84358e12i	−0.246291	−	0.246291i
$727$	1.19798e12			0.159054			0.0795268	−	0.996833i	$-0.474659\pi$
$727$	1.19798e12			0.159054			0.0795268	+	0.996833i	$0.474659\pi$
$728$	1.79450e12	+	1.79450e12i	0.236784	+	0.236784i
$729$			9.45552e12i			1.23997i
$730$	−6.80087e11			−0.0886364
$731$	1.58325e12	+	2.39715e11i	0.205080	+	0.0310504i
$732$	−3.41338e12			−0.439426
$733$			8.71100e12i			1.11455i	0.830328	+	0.557276i	$0.188153\pi$
$733$			8.71100e12i			1.11455i	−0.830328	+	0.557276i	$0.811847\pi$
$734$	−2.93164e12	−	2.93164e12i	−0.372802	−	0.372802i
$735$	−4.90866e11			−0.0620398
$736$	3.21937e12	+	3.21937e12i	0.404409	+	0.404409i
$737$	−8.19366e12	+	8.19366e12i	−1.02300	+	1.02300i
$738$	9.99140e11	−	9.99140e11i	0.123986	−	0.123986i
$739$			1.05005e13i			1.29512i	0.762015	+	0.647560i	$0.224210\pi$
$739$			1.05005e13i			1.29512i	−0.762015	+	0.647560i	$0.775790\pi$
$740$			6.59580e11i			0.0808583i
$741$	−5.99821e12	+	5.99821e12i	−0.730870	+	0.730870i
$742$	−2.09608e12	+	2.09608e12i	−0.253858	+	0.253858i
$743$	9.41077e12	+	9.41077e12i	1.13286	+	1.13286i	0.989700	+	0.143158i	$0.0457256\pi$
$743$	9.41077e12	+	9.41077e12i	1.13286	+	1.13286i	0.143158	+	0.989700i	$0.454274\pi$
$744$	−2.95553e12			−0.353637
$745$	−6.20535e11	−	6.20535e11i	−0.0738011	−	0.0738011i
$746$		−	4.94575e11i		−	0.0584665i
$747$	−1.84673e13			−2.17001
$748$	−4.09820e12	−	5.56061e12i	−0.478670	−	0.649480i
$749$	−3.53097e12			−0.409945
$750$			1.23617e12i			0.142661i
$751$	−6.49504e12	−	6.49504e12i	−0.745079	−	0.745079i	0.228472	−	0.973551i	$-0.426627\pi$
$751$	−6.49504e12	−	6.49504e12i	−0.745079	−	0.745079i	−0.973551	+	0.228472i	$0.926627\pi$
$752$	−1.18898e12			−0.135580
$753$	5.32253e12	+	5.32253e12i	0.603310	+	0.603310i
$754$	−4.66812e11	+	4.66812e11i	−0.0525982	+	0.0525982i
$755$	−3.71269e11	+	3.71269e11i	−0.0415841	+	0.0415841i
$756$			8.18383e11i			0.0911189i
$757$			1.11837e13i			1.23781i	0.785467	+	0.618903i	$0.212423\pi$
$757$			1.11837e13i			1.23781i	−0.785467	+	0.618903i	$0.787577\pi$
$758$	8.92622e11	−	8.92622e11i	0.0982101	−	0.0982101i
$759$	6.24229e12	−	6.24229e12i	0.682740	−	0.682740i
$760$	7.68552e11	+	7.68552e11i	0.0835626	+	0.0835626i
$761$	−4.29799e12			−0.464553			−0.232276	−	0.972650i	$-0.574617\pi$
$761$	−4.29799e12			−0.464553			−0.232276	+	0.972650i	$0.574617\pi$
$762$	−6.83138e12	−	6.83138e12i	−0.734025	−	0.734025i
$763$		−	9.75681e12i		−	1.04219i
$764$	3.91790e11			0.0416038
$765$	5.48032e11	+	7.43593e11i	0.0578535	+	0.0784981i
$766$	5.03741e12			0.528662
$767$		−	8.74723e12i		−	0.912623i
$768$	8.85318e12	+	8.85318e12i	0.918277	+	0.918277i
$769$	9.88894e12			1.01972			0.509860	−	0.860257i	$-0.329697\pi$
$769$	9.88894e12			1.01972			0.509860	+	0.860257i	$0.329697\pi$
$770$	−2.87312e11	−	2.87312e11i	−0.0294541	−	0.0294541i
$771$	−1.53850e13	+	1.53850e13i	−1.56802	+	1.56802i
$772$	8.75957e12	−	8.75957e12i	0.887575	−	0.887575i
$773$		−	1.06695e13i		−	1.07482i	−0.843322	−	0.537409i	$-0.819403\pi$
$773$		−	1.06695e13i		−	1.07482i	0.843322	−	0.537409i	$-0.180597\pi$
$774$			1.32925e12i			0.133129i
$775$	−1.79228e12	+	1.79228e12i	−0.178463	+	0.178463i
$776$	1.76022e12	−	1.76022e12i	0.174257	−	0.174257i
$777$	−1.03315e13	−	1.03315e13i	−1.01688	−	1.01688i
$778$	5.66738e12			0.554593
$779$	−2.85154e12	−	2.85154e12i	−0.277435	−	0.277435i
$780$		−	4.34902e11i		−	0.0420693i
$781$	−5.92679e12			−0.570020
$782$	−2.65628e12	+	1.95769e12i	−0.254006	+	0.187204i
$783$	−5.27324e11			−0.0501360
$784$			7.05659e11i			0.0667072i
$785$	−7.04738e11	−	7.04738e11i	−0.0662390	−	0.0662390i
$786$	−5.01879e12			−0.469027
$787$	9.85561e12	+	9.85561e12i	0.915793	+	0.915793i	0.996720	−	0.0809272i	$-0.0257881\pi$
$787$	9.85561e12	+	9.85561e12i	0.915793	+	0.915793i	−0.0809272	+	0.996720i	$0.525788\pi$
$788$	−8.72455e12	+	8.72455e12i	−0.806074	+	0.806074i
$789$	−6.01764e12	+	6.01764e12i	−0.552815	+	0.552815i
$790$		−	4.82410e11i		−	0.0440651i
$791$		−	5.12148e12i		−	0.465159i
$792$	1.00432e13	−	1.00432e13i	0.907002	−	0.907002i
$793$	−1.72721e12	+	1.72721e12i	−0.155101	+	0.155101i
$794$	3.07787e12	+	3.07787e12i	0.274826	+	0.274826i
$795$	1.25828e12			0.111719
$796$	7.65695e12	+	7.65695e12i	0.676000	+	0.676000i
$797$		−	5.24283e11i		−	0.0460260i	−0.999735	−	0.0230130i	$-0.992674\pi$
$797$		−	5.24283e11i		−	0.0460260i	0.999735	−	0.0230130i	$-0.00732592\pi$
$798$	−9.72023e12			−0.848523
$799$	1.72601e12	−	1.13998e13i	0.149824	−	0.989547i
$800$	1.18441e13			1.02234
$801$			1.44990e12i			0.124449i
$802$	−1.56310e12	−	1.56310e12i	−0.133415	−	0.133415i
$803$	2.53639e13			2.15277
$804$	−1.00494e13	−	1.00494e13i	−0.848178	−	0.848178i
$805$	2.87746e11	−	2.87746e11i	0.0241506	−	0.0241506i
$806$	−6.03772e11	+	6.03772e11i	−0.0503924	+	0.0503924i
$807$		−	3.95025e12i		−	0.327864i
$808$			1.97800e13i			1.63258i
$809$	−4.08467e12	+	4.08467e12i	−0.335266	+	0.335266i	−0.854582	−	0.519316i	$-0.826187\pi$
$809$	−4.08467e12	+	4.08467e12i	−0.335266	+	0.335266i	0.519316	+	0.854582i	$0.326187\pi$
$810$	3.62897e11	−	3.62897e11i	0.0296211	−	0.0296211i
$811$	−2.94545e11	−	2.94545e11i	−0.0239088	−	0.0239088i	0.695051	−	0.718960i	$-0.255382\pi$
$811$	−2.94545e11	−	2.94545e11i	−0.0239088	−	0.0239088i	−0.718960	+	0.695051i	$0.755382\pi$
$812$	1.58599e12			0.128026
$813$	7.98661e12	+	7.98661e12i	0.641143	+	0.641143i
$814$			1.17332e13i			0.936712i
$815$	6.10556e11			0.0484748
$816$	2.01543e12	−	1.48538e12i	0.159134	−	0.117282i
$817$	3.79367e12			0.297893
$818$			2.32956e12i			0.181921i
$819$	3.61315e12	+	3.61315e12i	0.280613	+	0.280613i
$820$	2.06752e11			0.0159693
$821$	7.14153e12	+	7.14153e12i	0.548589	+	0.548589i	0.926032	−	0.377444i	$-0.123197\pi$
$821$	7.14153e12	+	7.14153e12i	0.548589	+	0.548589i	−0.377444	+	0.926032i	$0.623197\pi$
$822$	4.99591e12	−	4.99591e12i	0.381673	−	0.381673i
$823$	3.38757e12	−	3.38757e12i	0.257389	−	0.257389i	−0.566602	−	0.823991i	$-0.691742\pi$
$823$	3.38757e12	−	3.38757e12i	0.257389	−	0.257389i	0.823991	+	0.566602i	$0.191742\pi$
$824$		−	2.21156e13i		−	1.67120i
$825$		−	2.29654e13i		−	1.72596i
$826$	7.08754e12	−	7.08754e12i	0.529767	−	0.529767i
$827$	−1.42921e13	+	1.42921e13i	−1.06248	+	1.06248i	−0.0645681	+	0.997913i	$0.520567\pi$
$827$	−1.42921e13	+	1.42921e13i	−1.06248	+	1.06248i	−0.997913	+	0.0645681i	$0.979433\pi$
$828$	4.06073e12	+	4.06073e12i	0.300240	+	0.300240i
$829$	−9.90972e12			−0.728729			−0.364364	−	0.931256i	$-0.618714\pi$
$829$	−9.90972e12			−0.728729			−0.364364	+	0.931256i	$0.618714\pi$
$830$	9.11368e11	+	9.11368e11i	0.0666565	+	0.0666565i
$831$		−	3.06147e13i		−	2.22703i
$832$	3.06654e12			0.221867
$833$	−6.76577e12	−	1.02438e12i	−0.486872	−	0.0737157i
$834$	1.14288e13			0.818003
$835$			1.75815e11i			0.0125160i
$836$	−1.15719e13	−	1.15719e13i	−0.819360	−	0.819360i
$837$	−6.82038e11			−0.0480335
$838$	−4.86162e12	−	4.86162e12i	−0.340551	−	0.340551i
$839$	5.97618e12	−	5.97618e12i	0.416385	−	0.416385i	−0.467571	−	0.883956i	$-0.654871\pi$
$839$	5.97618e12	−	5.97618e12i	0.416385	−	0.416385i	0.883956	+	0.467571i	$0.154871\pi$
$840$	8.72846e11	−	8.72846e11i	0.0604896	−	0.0604896i
$841$		−	1.34852e13i		−	0.929557i
$842$			6.11165e11i			0.0419038i
$843$	−1.19802e13	+	1.19802e13i	−0.817034	+	0.817034i
$844$	−7.09266e12	+	7.09266e12i	−0.481137	+	0.481137i
$845$	6.84710e11	+	6.84710e11i	0.0462010	+	0.0462010i
$846$	9.57090e12			0.642371
$847$	3.16942e12	+	3.16942e12i	0.211595	+	0.211595i
$848$		−	1.80888e12i		−	0.120124i
$849$	−1.05362e13			−0.695984
$850$	−1.28505e12	+	8.48742e12i	−0.0844376	+	0.557687i
$851$	−1.17509e13			−0.768047
$852$		−	7.26911e12i		−	0.472610i
$853$	6.35933e12	+	6.35933e12i	0.411283	+	0.411283i	0.882185	−	0.470902i	$-0.156072\pi$
$853$	6.35933e12	+	6.35933e12i	0.411283	+	0.411283i	−0.470902	+	0.882185i	$0.656072\pi$
$854$	−2.79898e12			−0.180069
$855$	1.54745e12	+	1.54745e12i	0.0990304	+	0.0990304i
$856$	−6.09117e12	+	6.09117e12i	−0.387765	+	0.387765i
$857$	1.22041e12	−	1.22041e12i	0.0772848	−	0.0772848i	−0.667408	−	0.744692i	$-0.732596\pi$
$857$	1.22041e12	−	1.22041e12i	0.0772848	−	0.0772848i	0.744692	+	0.667408i	$0.232596\pi$
$858$		−	7.73642e12i		−	0.487357i
$859$		−	4.15450e12i		−	0.260345i	−0.991491	−	0.130173i	$-0.958447\pi$
$859$		−	4.15450e12i		−	0.260345i	0.991491	−	0.130173i	$-0.0415531\pi$
$860$	−1.37530e11	+	1.37530e11i	−0.00857346	+	0.00857346i
$861$	−3.23850e12	+	3.23850e12i	−0.200831	+	0.200831i
$862$	7.67446e12	+	7.67446e12i	0.473440	+	0.473440i
$863$	3.76231e11			0.0230890			0.0115445	−	0.999933i	$-0.496325\pi$
$863$	3.76231e11			0.0230890			0.0115445	+	0.999933i	$0.496325\pi$
$864$	2.25358e12	+	2.25358e12i	0.137582	+	0.137582i
$865$		−	1.12157e12i		−	0.0681165i
$866$	2.68748e11			0.0162373
$867$	1.13159e13	+	2.14800e13i	0.680149	+	1.29106i
$868$	2.05131e12			0.122657
$869$			1.79916e13i			1.07024i
$870$	2.27058e11	+	2.27058e11i	0.0134369	+	0.0134369i
$871$	−1.01702e13			−0.598752
$872$	−1.68312e13	−	1.68312e13i	−0.985803	−	0.985803i
$873$	3.54413e12	−	3.54413e12i	0.206512	−	0.206512i
$874$	−5.52783e12	+	5.52783e12i	−0.320445	+	0.320445i
$875$		−	2.12519e12i		−	0.122563i
$876$			3.11085e13i			1.78488i
$877$	−1.35734e13	+	1.35734e13i	−0.774804	+	0.774804i	−0.978942	−	0.204138i	$-0.934561\pi$
$877$	−1.35734e13	+	1.35734e13i	−0.774804	+	0.774804i	0.204138	+	0.978942i	$0.434561\pi$
$878$	−1.07889e13	+	1.07889e13i	−0.612708	+	0.612708i
$879$	1.76507e13	+	1.76507e13i	0.997271	+	0.997271i
$880$	2.47945e11			0.0139375
$881$	−8.65229e11	−	8.65229e11i	−0.0483882	−	0.0483882i	0.682499	−	0.730887i	$-0.260893\pi$
$881$	−8.65229e11	−	8.65229e11i	−0.0483882	−	0.0483882i	−0.730887	+	0.682499i	$0.760893\pi$
$882$		−	5.68032e12i		−	0.316056i
$883$	1.57603e13			0.872451			0.436225	−	0.899837i	$-0.356315\pi$
$883$	1.57603e13			0.872451			0.436225	+	0.899837i	$0.356315\pi$
$884$	9.07591e11	−	5.99439e12i	0.0499868	−	0.330149i
$885$	−4.25466e12			−0.233142
$886$			5.39276e12i			0.294008i
$887$	2.71858e12	+	2.71858e12i	0.147464	+	0.147464i	0.776984	−	0.629520i	$-0.216748\pi$
$887$	2.71858e12	+	2.71858e12i	0.147464	+	0.147464i	−0.629520	+	0.776984i	$0.716748\pi$
$888$	−3.56451e13			−1.92372
$889$	1.17443e13	+	1.17443e13i	0.630620	+	0.630620i
$890$	7.15529e10	−	7.15529e10i	0.00382272	−	0.00382272i
$891$	−1.35343e13	+	1.35343e13i	−0.719425	+	0.719425i
$892$			1.89064e13i			0.999926i
$893$		−	2.73153e13i		−	1.43739i
$894$	1.35387e13	−	1.35387e13i	0.708855	−	0.708855i
$895$	4.51972e11	−	4.51972e11i	0.0235455	−	0.0235455i
$896$	−7.52611e12	−	7.52611e12i	−0.390108	−	0.390108i
$897$	7.74809e12			0.399603
$898$	−6.21458e12	−	6.21458e12i	−0.318910	−	0.318910i
$899$			1.32176e12i			0.0674891i
$900$	1.49395e13			0.759003
$901$	1.73433e13	+	2.62590e12i	0.876739	+	0.132744i
$902$	3.67788e12			0.184998
$903$		−	4.30848e12i		−	0.215640i
$904$	−8.83492e12	−	8.83492e12i	−0.439992	−	0.439992i
$905$	−2.46093e12			−0.121950
$906$	−8.10026e12	−	8.10026e12i	−0.399413	−	0.399413i
$907$	2.12739e13	−	2.12739e13i	1.04379	−	1.04379i	0.0447958	−	0.998996i	$-0.485736\pi$
$907$	2.12739e13	−	2.12739e13i	1.04379	−	1.04379i	0.998996	−	0.0447958i	$-0.0142637\pi$
$908$	−2.24902e12	+	2.24902e12i	−0.109801	+	0.109801i
$909$			3.98261e13i			1.93478i
$910$		−	3.56620e11i		−	0.0172393i
$911$	2.30275e13	−	2.30275e13i	1.10768	−	1.10768i	0.114226	−	0.993455i	$-0.463561\pi$
$911$	2.30275e13	−	2.30275e13i	1.10768	−	1.10768i	0.993455	−	0.114226i	$-0.0364388\pi$
$912$	4.19419e12	−	4.19419e12i	0.200757	−	0.200757i
$913$	−3.39896e13	−	3.39896e13i	−1.61893	−	1.61893i
$914$	−1.46237e13			−0.693105
$915$	8.40116e11	+	8.40116e11i	0.0396227	+	0.0396227i
$916$			1.02176e13i			0.479536i
$917$	8.62813e12			0.402953
$918$	−1.85941e12	+	1.37040e12i	−0.0864139	+	0.0636876i
$919$	1.18128e13			0.546304			0.273152	−	0.961971i	$-0.411934\pi$
$919$	1.18128e13			0.546304			0.273152	+	0.961971i	$0.411934\pi$
$920$		−	9.92763e11i		−	0.0456878i
$921$	−1.40655e13	−	1.40655e13i	−0.644152	−	0.644152i
$922$	5.16535e12			0.235402
$923$	−3.67825e12	−	3.67825e12i	−0.166814	−	0.166814i
$924$	−1.31422e13	+	1.31422e13i	−0.593122	+	0.593122i
$925$	−2.16158e13	+	2.16158e13i	−0.970807	+	0.970807i
$926$			2.20948e13i			0.987509i
$927$		−	4.45289e13i		−	1.98054i
$928$	4.36734e12	−	4.36734e12i	0.193308	−	0.193308i
$929$	2.34720e13	−	2.34720e13i	1.03390	−	1.03390i	0.0344963	−	0.999405i	$-0.489017\pi$
$929$	2.34720e13	−	2.34720e13i	1.03390	−	1.03390i	0.999405	−	0.0344963i	$-0.0109827\pi$
$930$	2.93675e11	+	2.93675e11i	0.0128734	+	0.0128734i
$931$	−1.62116e13			−0.707217
$932$	1.35934e13	+	1.35934e13i	0.590141	+	0.590141i
$933$		−	4.56791e13i		−	1.97356i
$934$	1.61387e13			0.693916
$935$	−3.59934e11	+	2.37727e12i	−0.0154018	+	0.101725i
$936$	1.24659e13			0.530862
$937$			7.61249e12i			0.322625i	0.986903	+	0.161313i	$0.0515728\pi$
$937$			7.61249e12i			0.322625i	−0.986903	+	0.161313i	$0.948427\pi$
$938$	−8.24050e12	−	8.24050e12i	−0.347569	−	0.347569i
$939$	3.27022e12			0.137272
$940$	9.90251e11	+	9.90251e11i	0.0413685	+	0.0413685i
$941$	−6.36153e12	+	6.36153e12i	−0.264490	+	0.264490i	−0.826875	−	0.562386i	$-0.809884\pi$
$941$	−6.36153e12	+	6.36153e12i	−0.264490	+	0.264490i	0.562386	+	0.826875i	$0.309884\pi$
$942$	1.53758e13	−	1.53758e13i	0.636222	−	0.636222i
$943$			3.68343e12i			0.151687i
$944$			6.11642e12i			0.250682i
$945$	2.01424e11	−	2.01424e11i	0.00821613	−	0.00821613i
$946$	−2.44651e12	+	2.44651e12i	−0.0993202	+	0.0993202i
$947$	2.91860e12	+	2.91860e12i	0.117923	+	0.117923i	0.763606	−	0.645683i	$-0.223427\pi$
$947$	2.91860e12	+	2.91860e12i	0.117923	+	0.117923i	−0.645683	+	0.763606i	$0.723427\pi$
$948$	−2.20663e13			−0.887345
$949$	1.57412e13	+	1.57412e13i	0.629999	+	0.629999i
$950$			2.03369e13i			0.810081i
$951$	4.13950e13			1.64110
$952$	1.38522e13	−	1.02092e13i	0.546580	−	0.402833i
$953$	1.80381e13			0.708389			0.354195	−	0.935172i	$-0.384755\pi$
$953$	1.80381e13			0.708389			0.354195	+	0.935172i	$0.384755\pi$
$954$			1.45609e13i			0.569141i
$955$	−9.64288e10	−	9.64288e10i	−0.00375139	−	0.00375139i
$956$	−2.13615e13			−0.827127
$957$	−8.46816e12	−	8.46816e12i	−0.326351	−	0.326351i
$958$	1.00384e13	−	1.00384e13i	0.385051	−	0.385051i
$959$	−8.58878e12	+	8.58878e12i	−0.327905	+	0.327905i
$960$		−	1.49157e12i		−	0.0566790i
$961$		−	2.47301e13i		−	0.935341i
$962$	−7.28177e12	+	7.28177e12i	−0.274125	+	0.274125i
$963$	−1.22643e13	+	1.22643e13i	−0.459542	+	0.459542i
$964$	1.10160e13	+	1.10160e13i	0.410845	+	0.410845i
$965$	−4.31188e12			−0.160064
$966$	6.27797e12	+	6.27797e12i	0.231965	+	0.231965i
$967$			3.92827e12i			0.144472i	0.997388	+	0.0722358i	$0.0230134\pi$
$967$			3.92827e12i			0.144472i	−0.997388	+	0.0722358i	$0.976987\pi$
$968$	1.09350e13			0.400293
$969$	3.41248e13	+	4.63019e13i	1.24341	+	1.68711i
$970$	−3.49808e11			−0.0126869
$971$		−	3.04563e13i		−	1.09949i	−0.835333	−	0.549744i	$-0.814725\pi$
$971$		−	3.04563e13i		−	1.09949i	0.835333	−	0.549744i	$-0.185275\pi$
$972$	−1.91163e13	−	1.91163e13i	−0.686920	−	0.686920i
$973$	−1.96481e13			−0.702768
$974$	−1.09973e13	−	1.09973e13i	−0.391535	−	0.391535i
$975$	1.42526e13	−	1.42526e13i	0.505096	−	0.505096i
$976$	1.20773e12	−	1.20773e12i	0.0426036	−	0.0426036i
$977$			1.55251e13i			0.545140i	0.962136	+	0.272570i	$0.0878736\pi$
$977$			1.55251e13i			0.545140i	−0.962136	+	0.272570i	$0.912126\pi$
$978$			1.33210e13i			0.465598i
$979$	−2.66857e12	+	2.66857e12i	−0.0928447	+	0.0928447i
$980$	5.87713e11	−	5.87713e11i	0.0203539	−	0.0203539i
$981$	−3.38889e13	−	3.38889e13i	−1.16828	−	1.16828i
$982$	1.08305e13			0.371662
$983$	2.83320e13	+	2.83320e13i	0.967801	+	0.967801i	0.999498	−	0.0316963i	$-0.0100909\pi$
$983$	2.83320e13	+	2.83320e13i	0.967801	+	0.967801i	−0.0316963	+	0.999498i	$0.510091\pi$
$984$			1.11733e13i			0.379930i
$985$	4.29464e12			0.145366
$986$	2.65577e12	+	3.60346e12i	0.0894837	+	0.121415i
$987$	−3.10221e13			−1.04050
$988$		−	1.43633e13i		−	0.479566i
$989$	−2.45021e12	−	2.45021e12i	−0.0814365	−	0.0814365i
$990$	−1.99588e12			−0.0660352
$991$	−1.75792e12	−	1.75792e12i	−0.0578985	−	0.0578985i	0.677565	−	0.735463i	$-0.263035\pi$
$991$	−1.75792e12	−	1.75792e12i	−0.0578985	−	0.0578985i	−0.735463	+	0.677565i	$0.763035\pi$
$992$	5.64868e12	−	5.64868e12i	0.185202	−	0.185202i
$993$	−5.32786e13	+	5.32786e13i	−1.73893	+	1.73893i
$994$		−	5.96067e12i		−	0.193667i
$995$		−	3.76912e12i		−	0.121909i
$996$	4.16876e13	−	4.16876e13i	1.34227	−	1.34227i
$997$	−1.73945e13	+	1.73945e13i	−0.557549	+	0.557549i	−0.928609	−	0.371060i	$-0.878994\pi$
$997$	−1.73945e13	+	1.73945e13i	−0.557549	+	0.557549i	0.371060	+	0.928609i	$0.378994\pi$
$998$	−1.55222e13	−	1.55222e13i	−0.495298	−	0.495298i
$999$	−8.22569e12			−0.261293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.8	yes	24
17.2	even	8		289.10.a.f.1.9		24
17.4	even	4	inner	17.10.c.a.4.5	✓	24
17.15	even	8		289.10.a.f.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.5	✓	24	17.4	even	4	inner
17.10.c.a.13.8	yes	24	1.1	even	1	trivial
289.10.a.f.1.9		24	17.2	even	8
289.10.a.f.1.10		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)

\(f(q)\)	\(=\)	\(q+12.8587i q^{2} +(-144.765 - 144.765i) q^{3} +346.654 q^{4} +(-85.3199 - 85.3199i) q^{5} +(1861.49 - 1861.49i) q^{6} +(-3200.21 + 3200.21i) q^{7} +11041.2i q^{8} +22230.9i q^{9} +O(q^{10})\)	\(q+12.8587i q^{2} +(-144.765 - 144.765i) q^{3} +346.654 q^{4} +(-85.3199 - 85.3199i) q^{5} +(1861.49 - 1861.49i) q^{6} +(-3200.21 + 3200.21i) q^{7} +11041.2i q^{8} +22230.9i q^{9} +(1097.10 - 1097.10i) q^{10} +(-40916.6 + 40916.6i) q^{11} +(-50183.5 - 50183.5i) q^{12} -50786.7 q^{13} +(-41150.5 - 41150.5i) q^{14} +24702.7i q^{15} +35512.1 q^{16} +(-51551.8 + 340485. i) q^{17} -285861. q^{18} +815845. i q^{19} +(-29576.5 - 29576.5i) q^{20} +926557. q^{21} +(-526133. - 526133. i) q^{22} +(526927. - 526927. i) q^{23} +(1.59838e6 - 1.59838e6i) q^{24} -1.93857e6i q^{25} -653050. i q^{26} +(368852. - 368852. i) q^{27} +(-1.10937e6 + 1.10937e6i) q^{28} +(-714818. - 714818. i) q^{29} -317644. q^{30} +(-924541. - 924541. i) q^{31} +6.10972e6i q^{32} +1.18466e7 q^{33} +(-4.37819e6 - 662888. i) q^{34} +546083. q^{35} +7.70645e6i q^{36} +(-1.11504e7 - 1.11504e7i) q^{37} -1.04907e7 q^{38} +(7.35215e6 + 7.35215e6i) q^{39} +(942031. - 942031. i) q^{40} +(-3.49520e6 + 3.49520e6i) q^{41} +1.19143e7i q^{42} -4.64999e6i q^{43} +(-1.41839e7 + 1.41839e7i) q^{44} +(1.89674e6 - 1.89674e6i) q^{45} +(6.77559e6 + 6.77559e6i) q^{46} -3.34810e7 q^{47} +(-5.14092e6 - 5.14092e6i) q^{48} +1.98710e7i q^{49} +2.49274e7 q^{50} +(5.67533e7 - 4.18275e7i) q^{51} -1.76054e7 q^{52} -5.09370e7i q^{53} +(4.74295e6 + 4.74295e6i) q^{54} +6.98199e6 q^{55} +(-3.53340e7 - 3.53340e7i) q^{56} +(1.18106e8 - 1.18106e8i) q^{57} +(9.19162e6 - 9.19162e6i) q^{58} +1.72235e8i q^{59} +8.56330e6i q^{60} +(3.40091e7 - 3.40091e7i) q^{61} +(1.18884e7 - 1.18884e7i) q^{62} +(-7.11436e7 - 7.11436e7i) q^{63} -6.03807e7 q^{64} +(4.33312e6 + 4.33312e6i) q^{65} +1.52332e8i q^{66} +2.00253e8 q^{67} +(-1.78706e7 + 1.18031e8i) q^{68} -1.52561e8 q^{69} +7.02191e6i q^{70} +(7.24254e7 + 7.24254e7i) q^{71} -2.45455e8 q^{72} +(-3.09947e8 - 3.09947e8i) q^{73} +(1.43379e8 - 1.43379e8i) q^{74} +(-2.80637e8 + 2.80637e8i) q^{75} +2.82816e8i q^{76} -2.61883e8i q^{77} +(-9.45390e7 + 9.45390e7i) q^{78} +(2.19857e8 - 2.19857e8i) q^{79} +(-3.02989e6 - 3.02989e6i) q^{80} +3.30778e8 q^{81} +(-4.49437e7 - 4.49437e7i) q^{82} +8.30705e8i q^{83} +3.21195e8 q^{84} +(3.34486e7 - 2.46518e7i) q^{85} +5.97928e7 q^{86} +2.06962e8i q^{87} +(-4.51766e8 - 4.51766e8i) q^{88} +6.52199e7 q^{89} +(2.43896e7 + 2.43896e7i) q^{90} +(1.62528e8 - 1.62528e8i) q^{91} +(1.82661e8 - 1.82661e8i) q^{92} +2.67683e8i q^{93} -4.30522e8i q^{94} +(6.96078e7 - 6.96078e7i) q^{95} +(8.84474e8 - 8.84474e8i) q^{96} +(-1.59423e8 - 1.59423e8i) q^{97} -2.55514e8 q^{98} +(-9.09613e8 - 9.09613e8i) 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

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