LMFDB - Embedded newform 17.10.c.a.4.2

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			4.2
Character	$\chi$	$=$	17.4
Dual form			17.10.c.a.13.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-36.7615i q^{2} +(151.130 - 151.130i) q^{3} -839.411 q^{4} +(-1546.81 + 1546.81i) q^{5} +(-5555.78 - 5555.78i) q^{6} +(-1021.13 - 1021.13i) q^{7} +12036.1i q^{8} -25997.7i q^{9} +O(q^{10})$	\(q-36.7615i q^{2} +(151.130 - 151.130i) q^{3} -839.411 q^{4} +(-1546.81 + 1546.81i) q^{5} +(-5555.78 - 5555.78i) q^{6} +(-1021.13 - 1021.13i) q^{7} +12036.1i q^{8} -25997.7i q^{9} +(56863.1 + 56863.1i) q^{10} +(-53788.6 - 53788.6i) q^{11} +(-126860. + 126860. i) q^{12} +61852.4 q^{13} +(-37538.2 + 37538.2i) q^{14} +467539. i q^{15} +12688.8 q^{16} +(344270. - 8106.40i) q^{17} -955716. q^{18} -1.04250e6i q^{19} +(1.29841e6 - 1.29841e6i) q^{20} -308646. q^{21} +(-1.97735e6 + 1.97735e6i) q^{22} +(190153. + 190153. i) q^{23} +(1.81903e6 + 1.81903e6i) q^{24} -2.83211e6i q^{25} -2.27379e6i q^{26} +(-954344. - 954344. i) q^{27} +(857144. + 857144. i) q^{28} +(-1.22125e6 + 1.22125e6i) q^{29} +1.71875e7 q^{30} +(2.56439e6 - 2.56439e6i) q^{31} +5.69605e6i q^{32} -1.62582e7 q^{33} +(-298004. - 1.26559e7i) q^{34} +3.15897e6 q^{35} +2.18228e7i q^{36} +(-2.54786e6 + 2.54786e6i) q^{37} -3.83239e7 q^{38} +(9.34776e6 - 9.34776e6i) q^{39} +(-1.86176e7 - 1.86176e7i) q^{40} +(-1.43737e7 - 1.43737e7i) q^{41} +1.13463e7i q^{42} +7.95939e6i q^{43} +(4.51508e7 + 4.51508e7i) q^{44} +(4.02135e7 + 4.02135e7i) q^{45} +(6.99032e6 - 6.99032e6i) q^{46} +4.08106e7 q^{47} +(1.91766e6 - 1.91766e6i) q^{48} -3.82682e7i q^{49} -1.04113e8 q^{50} +(5.08046e7 - 5.32548e7i) q^{51} -5.19196e7 q^{52} +3.85473e7i q^{53} +(-3.50832e7 + 3.50832e7i) q^{54} +1.66401e8 q^{55} +(1.22904e7 - 1.22904e7i) q^{56} +(-1.57553e8 - 1.57553e8i) q^{57} +(4.48951e7 + 4.48951e7i) q^{58} +1.05644e8i q^{59} -3.92458e8i q^{60} +(1.80743e7 + 1.80743e7i) q^{61} +(-9.42710e7 - 9.42710e7i) q^{62} +(-2.65469e7 + 2.65469e7i) q^{63} +2.15892e8 q^{64} +(-9.56737e7 + 9.56737e7i) q^{65} +5.97676e8i q^{66} +2.50869e8 q^{67} +(-2.88985e8 + 6.80460e6i) q^{68} +5.74757e7 q^{69} -1.16129e8i q^{70} +(-5.97752e7 + 5.97752e7i) q^{71} +3.12912e8 q^{72} +(1.19031e8 - 1.19031e8i) q^{73} +(9.36633e7 + 9.36633e7i) q^{74} +(-4.28017e8 - 4.28017e8i) q^{75} +8.75087e8i q^{76} +1.09850e8i q^{77} +(-3.43638e8 - 3.43638e8i) q^{78} +(-3.85937e8 - 3.85937e8i) q^{79} +(-1.96272e7 + 1.96272e7i) q^{80} +2.23252e8 q^{81} +(-5.28401e8 + 5.28401e8i) q^{82} -4.07060e8i q^{83} +2.59081e8 q^{84} +(-5.19981e8 + 5.45059e8i) q^{85} +2.92599e8 q^{86} +3.69136e8i q^{87} +(6.47408e8 - 6.47408e8i) q^{88} -4.72366e8 q^{89} +(1.47831e9 - 1.47831e9i) q^{90} +(-6.31590e7 - 6.31590e7i) q^{91} +(-1.59617e8 - 1.59617e8i) q^{92} -7.75114e8i q^{93} -1.50026e9i q^{94} +(1.61255e9 + 1.61255e9i) q^{95} +(8.60845e8 + 8.60845e8i) q^{96} +(2.90656e8 - 2.90656e8i) q^{97} -1.40680e9 q^{98} +(-1.39838e9 + 1.39838e9i) 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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	36.7615i		−	1.62465i	−0.583208	−	0.812323i	$-0.698203\pi$
$2$		−	36.7615i		−	1.62465i	0.583208	−	0.812323i	$-0.301797\pi$
$3$	151.130	−	151.130i	1.07722	−	1.07722i	0.0804661	−	0.996757i	$-0.474359\pi$
$3$	151.130	−	151.130i	1.07722	−	1.07722i	0.996757	−	0.0804661i	$-0.0256409\pi$
$4$	−839.411			−1.63948
$5$	−1546.81	+	1546.81i	−1.10681	+	1.10681i	−0.113238	+	0.993568i	$0.536122\pi$
$5$	−1546.81	+	1546.81i	−1.10681	+	1.10681i	−0.993568	+	0.113238i	$0.963878\pi$
$6$	−5555.78	−	5555.78i	−1.75011	−	1.75011i
$7$	−1021.13	−	1021.13i	−0.160745	−	0.160745i	0.622152	−	0.782897i	$-0.286259\pi$
$7$	−1021.13	−	1021.13i	−0.160745	−	0.160745i	−0.782897	+	0.622152i	$0.786259\pi$
$8$			12036.1i			1.03892i
$9$		−	25997.7i		−	1.32082i
$10$	56863.1	+	56863.1i	1.79817	+	1.79817i
$11$	−53788.6	−	53788.6i	−1.10770	−	1.10770i	−0.993452	−	0.114251i	$-0.963553\pi$
$11$	−53788.6	−	53788.6i	−1.10770	−	1.10770i	−0.114251	−	0.993452i	$-0.536447\pi$
$12$	−126860.	+	126860.i	−1.76608	+	1.76608i
$13$	61852.4			0.600636			0.300318	−	0.953839i	$-0.402907\pi$
$13$	61852.4			0.600636			0.300318	+	0.953839i	$0.402907\pi$
$14$	−37538.2	+	37538.2i	−0.261154	+	0.261154i
$15$			467539.i			2.38455i
$16$	12688.8			0.0484040
$17$	344270.	−	8106.40i	0.999723	−	0.0235401i
$17$	344270.	−	8106.40i	0.999723	−	0.0235401i
$18$	−955716.			−2.14587
$19$		−	1.04250e6i		−	1.83521i	−0.397497	−	0.917604i	$-0.630121\pi$
$19$		−	1.04250e6i		−	1.83521i	0.397497	−	0.917604i	$-0.369879\pi$
$20$	1.29841e6	−	1.29841e6i	1.81458	−	1.81458i
$21$	−308646.			−0.346317
$22$	−1.97735e6	+	1.97735e6i	−1.79963	+	1.79963i
$23$	190153.	+	190153.i	0.141686	+	0.141686i	0.774392	−	0.632706i	$-0.218056\pi$
$23$	190153.	+	190153.i	0.141686	+	0.141686i	−0.632706	+	0.774392i	$0.718056\pi$
$24$	1.81903e6	+	1.81903e6i	1.11915	+	1.11915i
$25$		−	2.83211e6i		−	1.45004i
$26$		−	2.27379e6i		−	0.975821i
$27$	−954344.	−	954344.i	−0.345596	−	0.345596i
$28$	857144.	+	857144.i	0.263538	+	0.263538i
$29$	−1.22125e6	+	1.22125e6i	−0.320638	+	0.320638i	−0.849012	−	0.528374i	$-0.822802\pi$
$29$	−1.22125e6	+	1.22125e6i	−0.320638	+	0.320638i	0.528374	+	0.849012i	$0.322802\pi$
$30$	1.71875e7			3.87406
$31$	2.56439e6	−	2.56439e6i	0.498720	−	0.498720i	−0.412319	−	0.911039i	$-0.635281\pi$
$31$	2.56439e6	−	2.56439e6i	0.498720	−	0.498720i	0.911039	+	0.412319i	$0.135281\pi$
$32$			5.69605e6i			0.960282i
$33$	−1.62582e7			−2.38649
$34$	−298004.	−	1.26559e7i	−0.0382443	−	1.62420i
$35$	3.15897e6			0.355827
$36$			2.18228e7i			2.16545i
$37$	−2.54786e6	+	2.54786e6i	−0.223495	+	0.223495i	−0.809968	−	0.586473i	$-0.800516\pi$
$37$	−2.54786e6	+	2.54786e6i	−0.223495	+	0.223495i	0.586473	+	0.809968i	$0.300516\pi$
$38$	−3.83239e7			−2.98156
$39$	9.34776e6	−	9.34776e6i	0.647019	−	0.647019i
$40$	−1.86176e7	−	1.86176e7i	−1.14988	−	1.14988i
$41$	−1.43737e7	−	1.43737e7i	−0.794406	−	0.794406i	0.187801	−	0.982207i	$-0.439864\pi$
$41$	−1.43737e7	−	1.43737e7i	−0.794406	−	0.794406i	−0.982207	+	0.187801i	$0.939864\pi$
$42$			1.13463e7i			0.562642i
$43$			7.95939e6i			0.355035i	0.984118	+	0.177518i	$0.0568067\pi$
$43$			7.95939e6i			0.355035i	−0.984118	+	0.177518i	$0.943193\pi$
$44$	4.51508e7	+	4.51508e7i	1.81605	+	1.81605i
$45$	4.02135e7	+	4.02135e7i	1.46189	+	1.46189i
$46$	6.99032e6	−	6.99032e6i	0.230190	−	0.230190i
$47$	4.08106e7			1.21992			0.609962	−	0.792431i	$-0.291185\pi$
$47$	4.08106e7			1.21992			0.609962	+	0.792431i	$0.291185\pi$
$48$	1.91766e6	−	1.91766e6i	0.0521419	−	0.0521419i
$49$		−	3.82682e7i		−	0.948322i
$50$	−1.04113e8			−2.35580
$51$	5.08046e7	−	5.32548e7i	1.05157	−	1.10228i
$52$	−5.19196e7			−0.984728
$53$			3.85473e7i			0.671047i	0.942032	+	0.335523i	$0.108913\pi$
$53$			3.85473e7i			0.671047i	−0.942032	+	0.335523i	$0.891087\pi$
$54$	−3.50832e7	+	3.50832e7i	−0.561471	+	0.561471i
$55$	1.66401e8			2.45202
$56$	1.22904e7	−	1.22904e7i	0.167002	−	0.167002i
$57$	−1.57553e8	−	1.57553e8i	−1.97693	−	1.97693i
$58$	4.48951e7	+	4.48951e7i	0.520923	+	0.520923i
$59$			1.05644e8i			1.13504i	0.823360	+	0.567520i	$0.192097\pi$
$59$			1.05644e8i			1.13504i	−0.823360	+	0.567520i	$0.807903\pi$
$60$		−	3.92458e8i		−	3.90942i
$61$	1.80743e7	+	1.80743e7i	0.167139	+	0.167139i	0.785721	−	0.618582i	$-0.212292\pi$
$61$	1.80743e7	+	1.80743e7i	0.167139	+	0.167139i	−0.618582	+	0.785721i	$0.712292\pi$
$62$	−9.42710e7	−	9.42710e7i	−0.810244	−	0.810244i
$63$	−2.65469e7	+	2.65469e7i	−0.212316	+	0.212316i
$64$	2.15892e8			1.60852
$65$	−9.56737e7	+	9.56737e7i	−0.664787	+	0.664787i
$66$			5.97676e8i			3.87720i
$67$	2.50869e8			1.52094			0.760468	−	0.649376i	$-0.224970\pi$
$67$	2.50869e8			1.52094			0.760468	+	0.649376i	$0.224970\pi$
$68$	−2.88985e8	+	6.80460e6i	−1.63902	+	0.0385934i
$69$	5.74757e7			0.305256
$70$		−	1.16129e8i		−	0.578094i
$71$	−5.97752e7	+	5.97752e7i	−0.279164	+	0.279164i	−0.832775	−	0.553611i	$-0.813249\pi$
$71$	−5.97752e7	+	5.97752e7i	−0.279164	+	0.279164i	0.553611	+	0.832775i	$0.313249\pi$
$72$	3.12912e8			1.37223
$73$	1.19031e8	−	1.19031e8i	0.490577	−	0.490577i	−0.417911	−	0.908488i	$-0.637238\pi$
$73$	1.19031e8	−	1.19031e8i	0.490577	−	0.490577i	0.908488	+	0.417911i	$0.137238\pi$
$74$	9.36633e7	+	9.36633e7i	0.363100	+	0.363100i
$75$	−4.28017e8	−	4.28017e8i	−1.56201	−	1.56201i
$76$			8.75087e8i			3.00878i
$77$			1.09850e8i			0.356116i
$78$	−3.43638e8	−	3.43638e8i	−1.05118	−	1.05118i
$79$	−3.85937e8	−	3.85937e8i	−1.11479	−	1.11479i	−0.992493	−	0.122300i	$-0.960973\pi$
$79$	−3.85937e8	−	3.85937e8i	−1.11479	−	1.11479i	−0.122300	−	0.992493i	$-0.539027\pi$
$80$	−1.96272e7	+	1.96272e7i	−0.0535738	+	0.0535738i
$81$	2.23252e8			0.576253
$82$	−5.28401e8	+	5.28401e8i	−1.29063	+	1.29063i
$83$		−	4.07060e8i		−	0.941471i	−0.882274	−	0.470736i	$-0.843989\pi$
$83$		−	4.07060e8i		−	0.941471i	0.882274	−	0.470736i	$-0.156011\pi$
$84$	2.59081e8			0.567778
$85$	−5.19981e8	+	5.45059e8i	−1.08044	+	1.13255i
$86$	2.92599e8			0.576807
$87$			3.69136e8i			0.690797i
$88$	6.47408e8	−	6.47408e8i	1.15082	−	1.15082i
$89$	−4.72366e8			−0.798039			−0.399019	−	0.916943i	$-0.630649\pi$
$89$	−4.72366e8			−0.798039			−0.399019	+	0.916943i	$0.630649\pi$
$90$	1.47831e9	−	1.47831e9i	2.37506	−	2.37506i
$91$	−6.31590e7	−	6.31590e7i	−0.0965493	−	0.0965493i
$92$	−1.59617e8	−	1.59617e8i	−0.232291	−	0.232291i
$93$		−	7.75114e8i		−	1.07447i
$94$		−	1.50026e9i		−	1.98194i
$95$	1.61255e9	+	1.61255e9i	2.03122	+	2.03122i
$96$	8.60845e8	+	8.60845e8i	1.03444	+	1.03444i
$97$	2.90656e8	−	2.90656e8i	0.333355	−	0.333355i	−0.520504	−	0.853859i	$-0.674256\pi$
$97$	2.90656e8	−	2.90656e8i	0.333355	−	0.333355i	0.853859	+	0.520504i	$0.174256\pi$
$98$	−1.40680e9			−1.54069
$99$	−1.39838e9	+	1.39838e9i	−1.46308	+	1.46308i
$100$			2.37730e9i			2.37730i
$101$	−3.41004e8			−0.326072			−0.163036	−	0.986620i	$-0.552129\pi$
$101$	−3.41004e8			−0.326072			−0.163036	+	0.986620i	$0.552129\pi$
$102$	−1.95773e9	−	1.86765e9i	−1.79082	−	1.70842i
$103$	1.07921e9			0.944793			0.472396	−	0.881386i	$-0.343389\pi$
$103$	1.07921e9			0.944793			0.472396	+	0.881386i	$0.343389\pi$
$104$			7.44464e8i			0.624013i
$105$	4.77416e8	−	4.77416e8i	0.383306	−	0.383306i
$106$	1.41706e9			1.09021
$107$	5.37867e8	−	5.37867e8i	0.396687	−	0.396687i	−0.480376	−	0.877063i	$-0.659500\pi$
$107$	5.37867e8	−	5.37867e8i	0.396687	−	0.396687i	0.877063	+	0.480376i	$0.159500\pi$
$108$	8.01088e8	+	8.01088e8i	0.566595	+	0.566595i
$109$	−2.35701e8	−	2.35701e8i	−0.159935	−	0.159935i	0.622603	−	0.782538i	$-0.286075\pi$
$109$	−2.35701e8	−	2.35701e8i	−0.159935	−	0.159935i	−0.782538	+	0.622603i	$0.786075\pi$
$110$		−	6.11717e9i		−	3.98367i
$111$			7.70118e8i			0.481508i
$112$	−1.29569e7	−	1.29569e7i	−0.00778071	−	0.00778071i
$113$	8.13918e8	+	8.13918e8i	0.469600	+	0.469600i	0.901785	−	0.432185i	$-0.142257\pi$
$113$	8.13918e8	+	8.13918e8i	0.469600	+	0.469600i	−0.432185	+	0.901785i	$0.642257\pi$
$114$	−5.79191e9	+	5.79191e9i	−3.21181	+	3.21181i
$115$	−5.88260e8			−0.313638
$116$	1.02513e9	−	1.02513e9i	0.525677	−	0.525677i
$117$		−	1.60802e9i		−	0.793332i
$118$	3.88364e9			1.84404
$119$	−3.59821e8	−	3.43266e8i	−0.164485	−	0.156917i
$120$	−5.62737e9			−2.47736
$121$			3.42848e9i			1.45401i
$122$	6.64440e8	−	6.64440e8i	0.271542	−	0.271542i
$123$	−4.34461e9			−1.71150
$124$	−2.15258e9	+	2.15258e9i	−0.817639	+	0.817639i
$125$	1.35961e9	+	1.35961e9i	0.498104	+	0.498104i
$126$	9.75906e8	+	9.75906e8i	0.344938	+	0.344938i
$127$		−	4.73219e8i		−	0.161416i	−0.996738	−	0.0807078i	$-0.974282\pi$
$127$		−	4.73219e8i		−	0.161416i	0.996738	−	0.0807078i	$-0.0257181\pi$
$128$		−	5.02015e9i		−	1.65300i
$129$	1.20290e9	+	1.20290e9i	0.382452	+	0.382452i
$130$	3.51711e9	+	3.51711e9i	1.08004	+	1.08004i
$131$	−1.17907e9	+	1.17907e9i	−0.349800	+	0.349800i	−0.860035	−	0.510235i	$-0.829558\pi$
$131$	−1.17907e9	+	1.17907e9i	−0.349800	+	0.349800i	0.510235	+	0.860035i	$0.329558\pi$
$132$	1.36473e10			3.91259
$133$	−1.06452e9	+	1.06452e9i	−0.295001	+	0.295001i
$134$		−	9.22234e9i		−	2.47098i
$135$	2.95238e9			0.765014
$136$	9.75698e7	+	4.14369e9i	0.0244563	+	1.03863i
$137$	−2.29550e9			−0.556718			−0.278359	−	0.960477i	$-0.589790\pi$
$137$	−2.29550e9			−0.556718			−0.278359	+	0.960477i	$0.589790\pi$
$138$		−	2.11290e9i		−	0.495932i
$139$	−1.94461e9	+	1.94461e9i	−0.441842	+	0.441842i	−0.892631	−	0.450789i	$-0.851143\pi$
$139$	−1.94461e9	+	1.94461e9i	−0.441842	+	0.441842i	0.450789	+	0.892631i	$0.351143\pi$
$140$	−2.65168e9			−0.583370
$141$	6.16772e9	−	6.16772e9i	1.31413	−	1.31413i
$142$	2.19743e9	+	2.19743e9i	0.453542	+	0.453542i
$143$	−3.32695e9	−	3.32695e9i	−0.665326	−	0.665326i
$144$		−	3.29880e8i		−	0.0639330i
$145$		−	3.77809e9i		−	0.709767i
$146$	−4.37576e9	−	4.37576e9i	−0.797014	−	0.797014i
$147$	−5.78349e9	−	5.78349e9i	−1.02155	−	1.02155i
$148$	2.13870e9	−	2.13870e9i	0.366415	−	0.366415i
$149$	−3.61630e9			−0.601072			−0.300536	−	0.953771i	$-0.597165\pi$
$149$	−3.61630e9			−0.601072			−0.300536	+	0.953771i	$0.597165\pi$
$150$	−1.57346e10	+	1.57346e10i	−2.53772	+	2.53772i
$151$		−	5.46695e9i		−	0.855754i	−0.903837	−	0.427877i	$-0.859262\pi$
$151$		−	5.46695e9i		−	0.855754i	0.903837	−	0.427877i	$-0.140738\pi$
$152$	1.25477e10			1.90664
$153$	−2.10748e8	−	8.95025e9i	−0.0310922	−	1.32045i
$154$	4.03825e9			0.578562
$155$			7.93324e9i			1.10397i
$156$	−7.84662e9	+	7.84662e9i	−1.06077	+	1.06077i
$157$	1.17900e10			1.54869			0.774343	−	0.632766i	$-0.218080\pi$
$157$	1.17900e10			1.54869			0.774343	+	0.632766i	$0.218080\pi$
$158$	−1.41876e10	+	1.41876e10i	−1.81114	+	1.81114i
$159$	5.82567e9	+	5.82567e9i	0.722867	+	0.722867i
$160$	−8.81069e9	−	8.81069e9i	−1.06285	−	1.06285i
$161$		−	3.88340e8i		−	0.0455508i
$162$		−	8.20710e9i		−	0.936208i
$163$	1.07238e10	+	1.07238e10i	1.18988	+	1.18988i	0.977100	+	0.212779i	$0.0682514\pi$
$163$	1.07238e10	+	1.07238e10i	1.18988	+	1.18988i	0.212779	+	0.977100i	$0.431749\pi$
$164$	1.20655e10	+	1.20655e10i	1.30241	+	1.30241i
$165$	2.51483e10	−	2.51483e10i	2.64138	−	2.64138i
$166$	−1.49642e10			−1.52956
$167$	−3.14198e9	+	3.14198e9i	−0.312593	+	0.312593i	−0.845913	−	0.533320i	$-0.820944\pi$
$167$	−3.14198e9	+	3.14198e9i	−0.312593	+	0.312593i	0.533320	+	0.845913i	$0.320944\pi$
$168$		−	3.71491e9i		−	0.359796i
$169$	−6.77878e9			−0.639237
$170$	2.00372e10	+	1.91153e10i	1.84000	+	1.75534i
$171$	−2.71026e10			−2.42398
$172$		−	6.68120e9i		−	0.582072i
$173$	−1.15695e10	+	1.15695e10i	−0.981994	+	0.981994i	−0.999841	−	0.0178468i	$-0.994319\pi$
$173$	−1.15695e10	+	1.15695e10i	−0.981994	+	0.981994i	0.0178468	+	0.999841i	$0.494319\pi$
$174$	1.35700e10			1.12230
$175$	−2.89193e9	+	2.89193e9i	−0.233087	+	0.233087i
$176$	−6.82514e8	−	6.82514e8i	−0.0536172	−	0.0536172i
$177$	1.59660e10	+	1.59660e10i	1.22269	+	1.22269i
$178$			1.73649e10i			1.29653i
$179$			2.95047e9i			0.214809i	0.994215	+	0.107405i	$0.0342540\pi$
$179$			2.95047e9i			0.214809i	−0.994215	+	0.107405i	$0.965746\pi$
$180$	−3.37556e10	−	3.37556e10i	−2.39674	−	2.39674i
$181$	1.02465e9	+	1.02465e9i	0.0709613	+	0.0709613i	0.741697	−	0.670735i	$-0.234021\pi$
$181$	1.02465e9	+	1.02465e9i	0.0709613	+	0.0709613i	−0.670735	+	0.741697i	$0.734021\pi$
$182$	−2.32182e9	+	2.32182e9i	−0.156858	+	0.156858i
$183$	5.46315e9			0.360092
$184$	−2.28871e9	+	2.28871e9i	−0.147201	+	0.147201i
$185$		−	7.88210e9i		−	0.494731i
$186$	−2.84944e10			−1.74563
$187$	−1.89539e10	−	1.80818e10i	−1.13347	−	1.08132i
$188$	−3.42569e10			−2.00003
$189$			1.94901e9i			0.111106i
$190$	5.92798e10	−	5.92798e10i	3.30001	−	3.30001i
$191$	1.50851e10			0.820161			0.410081	−	0.912049i	$-0.365501\pi$
$191$	1.50851e10			0.820161			0.410081	+	0.912049i	$0.365501\pi$
$192$	3.26278e10	−	3.26278e10i	1.73274	−	1.73274i
$193$	−1.73675e10	−	1.73675e10i	−0.901008	−	0.901008i	0.0945157	−	0.995523i	$-0.469870\pi$
$193$	−1.73675e10	−	1.73675e10i	−0.901008	−	0.901008i	−0.995523	+	0.0945157i	$0.969870\pi$
$194$	−1.06850e10	−	1.06850e10i	−0.541583	−	0.541583i
$195$			2.89184e10i			1.43225i
$196$			3.21228e10i			1.55475i
$197$	−3.45372e9	−	3.45372e9i	−0.163376	−	0.163376i	0.620684	−	0.784061i	$-0.286855\pi$
$197$	−3.45372e9	−	3.45372e9i	−0.163376	−	0.163376i	−0.784061	+	0.620684i	$0.786855\pi$
$198$	5.14067e10	+	5.14067e10i	2.37698	+	2.37698i
$199$	−1.15900e10	+	1.15900e10i	−0.523897	+	0.523897i	−0.918746	−	0.394849i	$-0.870797\pi$
$199$	−1.15900e10	+	1.15900e10i	−0.523897	+	0.523897i	0.394849	+	0.918746i	$0.370797\pi$
$200$	3.40876e10			1.50647
$201$	3.79139e10	−	3.79139e10i	1.63839	−	1.63839i
$202$			1.25358e10i			0.529751i
$203$	2.49410e9			0.103082
$204$	−4.26459e10	+	4.47027e10i	−1.72402	+	1.80717i
$205$	4.44668e10			1.75851
$206$		−	3.96733e10i		−	1.53495i
$207$	4.94354e9	−	4.94354e9i	0.187142	−	0.187142i
$208$	7.84833e8			0.0290732
$209$	−5.60747e10	+	5.60747e10i	−2.03286	+	2.03286i
$210$	−1.75506e10	−	1.75506e10i	−0.622736	−	0.622736i
$211$	2.84396e10	+	2.84396e10i	0.987763	+	0.987763i	0.999926	−	0.0121627i	$-0.00387160\pi$
$211$	2.84396e10	+	2.84396e10i	0.987763	+	0.987763i	−0.0121627	+	0.999926i	$0.503872\pi$
$212$		−	3.23571e10i		−	1.10016i
$213$			1.80677e10i			0.601443i
$214$	−1.97728e10	−	1.97728e10i	−0.644476	−	0.644476i
$215$	−1.23116e10	−	1.23116e10i	−0.392955	−	0.392955i
$216$	1.14866e10	−	1.14866e10i	0.359047	−	0.359047i
$217$	−5.23713e9			−0.160334
$218$	−8.66474e9	+	8.66474e9i	−0.259837	+	0.259837i
$219$		−	3.59784e10i		−	1.05692i
$220$	−1.39679e11			−4.02003
$221$	2.12939e10	−	5.01400e8i	0.600469	−	0.0141390i
$222$	2.83107e10			0.782281
$223$			3.40332e10i			0.921575i	0.887510	+	0.460788i	$0.152433\pi$
$223$			3.40332e10i			0.921575i	−0.887510	+	0.460788i	$0.847567\pi$
$224$	5.81638e9	−	5.81638e9i	0.154361	−	0.154361i
$225$	−7.36283e10			−1.91524
$226$	2.99209e10	−	2.99209e10i	0.762933	−	0.762933i
$227$	3.70503e9	+	3.70503e9i	0.0926138	+	0.0926138i	0.751896	−	0.659282i	$-0.229140\pi$
$227$	3.70503e9	+	3.70503e9i	0.0926138	+	0.0926138i	−0.659282	+	0.751896i	$0.729140\pi$
$228$	1.32252e11	+	1.32252e11i	3.24113	+	3.24113i
$229$		−	6.10304e10i		−	1.46652i	−0.679950	−	0.733258i	$-0.737999\pi$
$229$		−	6.10304e10i		−	1.46652i	0.679950	−	0.733258i	$-0.262001\pi$
$230$			2.16254e10i			0.509551i
$231$	1.66016e10	+	1.66016e10i	0.383616	+	0.383616i
$232$	−1.46992e10	−	1.46992e10i	−0.333117	−	0.333117i
$233$	1.47280e10	−	1.47280e10i	0.327374	−	0.327374i	−0.524213	−	0.851587i	$-0.675641\pi$
$233$	1.47280e10	−	1.47280e10i	0.327374	−	0.327374i	0.851587	+	0.524213i	$0.175641\pi$
$234$	−5.91133e10			−1.28888
$235$	−6.31262e10	+	6.31262e10i	−1.35022	+	1.35022i
$236$		−	8.86788e10i		−	1.86087i
$237$	−1.16653e11			−2.40176
$238$	−1.26190e10	+	1.32276e10i	−0.254934	+	0.267229i
$239$	−2.41341e10			−0.478454			−0.239227	−	0.970964i	$-0.576894\pi$
$239$	−2.41341e10			−0.478454			−0.239227	+	0.970964i	$0.576894\pi$
$240$			5.93252e9i			0.115422i
$241$	3.54365e10	−	3.54365e10i	0.676666	−	0.676666i	−0.282578	−	0.959244i	$-0.591190\pi$
$241$	3.54365e10	−	3.54365e10i	0.676666	−	0.676666i	0.959244	+	0.282578i	$0.0911896\pi$
$242$	1.26036e11			2.36225
$243$	5.25245e10	−	5.25245e10i	0.966349	−	0.966349i
$244$	−1.51718e10	−	1.51718e10i	−0.274020	−	0.274020i
$245$	5.91936e10	+	5.91936e10i	1.04961	+	1.04961i
$246$			1.59715e11i			2.78059i
$247$		−	6.44811e10i		−	1.10229i
$248$	3.08654e10	+	3.08654e10i	0.518131	+	0.518131i
$249$	−6.15191e10	−	6.15191e10i	−1.01417	−	1.01417i
$250$	4.99815e10	−	4.99815e10i	0.809243	−	0.809243i
$251$	2.66112e10			0.423187			0.211594	−	0.977358i	$-0.432135\pi$
$251$	2.66112e10			0.423187			0.211594	+	0.977358i	$0.432135\pi$
$252$	2.22838e10	−	2.22838e10i	0.348086	−	0.348086i
$253$		−	2.04561e10i		−	0.313893i
$254$	−1.73963e10			−0.262243
$255$	3.79006e9	+	1.60960e11i	0.0561326	+	2.38389i
$256$	−7.40119e10			−1.07701
$257$		−	1.12286e9i		−	0.0160555i	−0.999968	−	0.00802777i	$-0.997445\pi$
$257$		−	1.12286e9i		−	0.0160555i	0.999968	−	0.00802777i	$-0.00255535\pi$
$258$	4.42206e10	−	4.42206e10i	0.621350	−	0.621350i
$259$	5.20337e9			0.0718515
$260$	8.03096e10	−	8.03096e10i	1.08990	−	1.08990i
$261$	3.17498e10	+	3.17498e10i	0.423505	+	0.423505i
$262$	4.33445e10	+	4.33445e10i	0.568301	+	0.568301i
$263$		−	3.28551e10i		−	0.423450i	−0.977329	−	0.211725i	$-0.932092\pi$
$263$		−	3.28551e10i		−	0.423450i	0.977329	−	0.211725i	$-0.0679081\pi$
$264$		−	1.95686e11i		−	2.47937i
$265$	−5.96253e10	−	5.96253e10i	−0.742718	−	0.742718i
$266$	3.91335e10	+	3.91335e10i	0.479272	+	0.479272i
$267$	−7.13888e10	+	7.13888e10i	−0.859666	+	0.859666i
$268$	−2.10582e11			−2.49354
$269$	7.44860e10	−	7.44860e10i	0.867340	−	0.867340i	−0.124838	−	0.992177i	$-0.539841\pi$
$269$	7.44860e10	−	7.44860e10i	0.867340	−	0.867340i	0.992177	+	0.124838i	$0.0398410\pi$
$270$		−	1.08534e11i		−	1.24288i
$271$	1.63792e11			1.84473			0.922363	−	0.386324i	$-0.126255\pi$
$271$	1.63792e11			1.84473			0.922363	+	0.386324i	$0.126255\pi$
$272$	4.36838e9	−	1.02861e8i	0.0483906	−	0.00113943i
$273$	−1.90905e10			−0.208010
$274$			8.43862e10i			0.904470i
$275$	−1.52335e11	+	1.52335e11i	−1.60621	+	1.60621i
$276$	−4.82458e10			−0.500459
$277$	−8.27358e9	+	8.27358e9i	−0.0844373	+	0.0844373i	−0.748064	−	0.663627i	$-0.769016\pi$
$277$	−8.27358e9	+	8.27358e9i	−0.0844373	+	0.0844373i	0.663627	+	0.748064i	$0.269016\pi$
$278$	7.14870e10	+	7.14870e10i	0.717836	+	0.717836i
$279$	−6.66683e10	−	6.66683e10i	−0.658720	−	0.658720i
$280$			3.80218e10i			0.369677i
$281$			6.90962e10i			0.661113i	0.943786	+	0.330556i	$0.107236\pi$
$281$			6.90962e10i			0.661113i	−0.943786	+	0.330556i	$0.892764\pi$
$282$	−2.26735e11	−	2.26735e11i	−2.13500	−	2.13500i
$283$	−5.63253e10	−	5.63253e10i	−0.521993	−	0.521993i	0.396180	−	0.918173i	$-0.370336\pi$
$283$	−5.63253e10	−	5.63253e10i	−0.521993	−	0.521993i	−0.918173	+	0.396180i	$0.870336\pi$
$284$	5.01760e10	−	5.01760e10i	0.457682	−	0.457682i
$285$	4.87410e11			4.37615
$286$	−1.22304e11	+	1.22304e11i	−1.08092	+	1.08092i
$287$			2.93548e10i			0.255394i
$288$	1.48084e11			1.26836
$289$	1.18456e11	−	5.58159e9i	0.998892	−	0.0470671i
$290$	−1.38888e11			−1.15312
$291$		−	8.78538e10i		−	0.718195i
$292$	−9.99159e10	+	9.99159e10i	−0.804289	+	0.804289i
$293$	2.06133e10			0.163396			0.0816982	−	0.996657i	$-0.473966\pi$
$293$	2.06133e10			0.163396			0.0816982	+	0.996657i	$0.473966\pi$
$294$	−2.12610e11	+	2.12610e11i	−1.65966	+	1.65966i
$295$	−1.63411e11	−	1.63411e11i	−1.25627	−	1.25627i
$296$	−3.06664e10	−	3.06664e10i	−0.232194	−	0.232194i
$297$			1.02666e11i			0.765635i
$298$			1.32941e11i			0.976529i
$299$	1.17614e10	+	1.17614e10i	0.0851019	+	0.0851019i
$300$	3.59282e11	+	3.59282e11i	2.56088	+	2.56088i
$301$	8.12753e9	−	8.12753e9i	0.0570702	−	0.0570702i
$302$	−2.00974e11			−1.39030
$303$	−5.15360e10	+	5.15360e10i	−0.351252	+	0.351252i
$304$		−	1.32281e10i		−	0.0888313i
$305$	−5.59150e10			−0.369981
$306$	−3.29025e11	+	7.74741e9i	−2.14527	+	0.0505138i
$307$	1.72164e10			0.110616			0.0553082	−	0.998469i	$-0.482386\pi$
$307$	1.72164e10			0.110616			0.0553082	+	0.998469i	$0.482386\pi$
$308$		−	9.22092e10i		−	0.583843i
$309$	1.63101e11	−	1.63101e11i	1.01775	−	1.01775i
$310$	2.91638e11			1.79356
$311$	−1.17702e11	+	1.17702e11i	−0.713448	+	0.713448i	−0.967255	−	0.253807i	$-0.918317\pi$
$311$	−1.17702e11	+	1.17702e11i	−0.713448	+	0.713448i	0.253807	+	0.967255i	$0.418317\pi$
$312$	1.12511e11	+	1.12511e11i	0.672202	+	0.672202i
$313$	5.03574e9	+	5.03574e9i	0.0296561	+	0.0296561i	0.721779	−	0.692123i	$-0.243325\pi$
$313$	5.03574e9	+	5.03574e9i	0.0296561	+	0.0296561i	−0.692123	+	0.721779i	$0.743325\pi$
$314$		−	4.33417e11i		−	2.51607i
$315$		−	8.21260e10i		−	0.469984i
$316$	3.23960e11	+	3.23960e11i	1.82768	+	1.82768i
$317$	1.02870e11	+	1.02870e11i	0.572168	+	0.572168i	0.932734	−	0.360566i	$-0.117416\pi$
$317$	1.02870e11	+	1.02870e11i	0.572168	+	0.572168i	−0.360566	+	0.932734i	$0.617416\pi$
$318$	2.14161e11	−	2.14161e11i	1.17440	−	1.17440i
$319$	1.31379e11			0.710342
$320$	−3.33944e11	+	3.33944e11i	−1.78032	+	1.78032i
$321$		−	1.62576e11i		−	0.854641i
$322$	−1.42760e10			−0.0740039
$323$	−8.45092e9	−	3.58902e11i	−0.0432009	−	1.83470i
$324$	−1.87401e11			−0.944753
$325$		−	1.75172e11i		−	0.870945i
$326$	3.94222e11	−	3.94222e11i	1.93313	−	1.93313i
$327$	−7.12432e10			−0.344571
$328$	1.73004e11	−	1.73004e11i	0.825325	−	0.825325i
$329$	−4.16727e10	−	4.16727e10i	−0.196097	−	0.196097i
$330$	−9.24490e11	−	9.24490e11i	−4.29130	−	4.29130i
$331$		−	9.98473e9i		−	0.0457204i	−0.999739	−	0.0228602i	$-0.992723\pi$
$331$		−	9.98473e9i		−	0.0457204i	0.999739	−	0.0228602i	$-0.00727726\pi$
$332$			3.41691e11i			1.54352i
$333$	6.62386e10	+	6.62386e10i	0.295197	+	0.295197i
$334$	1.15504e11	+	1.15504e11i	0.507853	+	0.507853i
$335$	−3.88046e11	+	3.88046e11i	−1.68338	+	1.68338i
$336$	−3.91635e9			−0.0167631
$337$	−2.39889e11	+	2.39889e11i	−1.01316	+	1.01316i	−0.0132442	+	0.999912i	$0.504216\pi$
$337$	−2.39889e11	+	2.39889e11i	−1.01316	+	1.01316i	−0.999912	+	0.0132442i	$0.995784\pi$
$338$			2.49199e11i			1.03853i
$339$	2.46015e11			1.01173
$340$	4.36478e11	−	4.57529e11i	1.77136	−	1.85679i
$341$	−2.75870e11			−1.10487
$342$			9.96335e11i			3.93811i
$343$	−8.02827e10	+	8.02827e10i	−0.313183	+	0.313183i
$344$	−9.58004e10			−0.368854
$345$	−8.89039e10	+	8.89039e10i	−0.337859	+	0.337859i
$346$	4.25314e11	+	4.25314e11i	1.59539	+	1.59539i
$347$	2.40711e11	+	2.40711e11i	0.891277	+	0.891277i	0.994643	−	0.103367i	$-0.0329615\pi$
$347$	2.40711e11	+	2.40711e11i	0.891277	+	0.891277i	−0.103367	+	0.994643i	$0.532961\pi$
$348$		−	3.09857e11i		−	1.13254i
$349$		−	3.97277e11i		−	1.43344i	−0.697363	−	0.716719i	$-0.745643\pi$
$349$		−	3.97277e11i		−	1.43344i	0.697363	−	0.716719i	$-0.254357\pi$
$350$	1.06312e11	+	1.06312e11i	0.378683	+	0.378683i
$351$	−5.90285e10	−	5.90285e10i	−0.207577	−	0.207577i
$352$	3.06383e11	−	3.06383e11i	1.06371	−	1.06371i
$353$	1.64439e11			0.563661			0.281831	−	0.959464i	$-0.409058\pi$
$353$	1.64439e11			0.563661			0.281831	+	0.959464i	$0.409058\pi$
$354$	5.86935e11	−	5.86935e11i	1.98644	−	1.98644i
$355$		−	1.84922e11i		−	0.617960i
$356$	3.96510e11			1.30836
$357$	−1.06258e11	+	2.50201e9i	−0.346221	+	0.00815232i
$358$	1.08464e11			0.348989
$359$		−	5.88255e11i		−	1.86914i	−0.355785	−	0.934568i	$-0.615786\pi$
$359$		−	5.88255e11i		−	1.86914i	0.355785	−	0.934568i	$-0.384214\pi$
$360$	−4.84015e11	+	4.84015e11i	−1.51879	+	1.51879i
$361$	−7.64120e11			−2.36799
$362$	3.76677e10	−	3.76677e10i	0.115287	−	0.115287i
$363$	5.18148e11	+	5.18148e11i	1.56630	+	1.56630i
$364$	5.30164e10	+	5.30164e10i	0.158290	+	0.158290i
$365$			3.68236e11i			1.08595i
$366$		−	2.00834e11i		−	0.585022i
$367$	1.59032e10	+	1.59032e10i	0.0457601	+	0.0457601i	0.729617	−	0.683856i	$-0.239699\pi$
$367$	1.59032e10	+	1.59032e10i	0.0457601	+	0.0457601i	−0.683856	+	0.729617i	$0.739699\pi$
$368$	2.41282e9	+	2.41282e9i	0.00685818	+	0.00685818i
$369$	−3.73684e11	+	3.73684e11i	−1.04927	+	1.04927i
$370$	−2.89758e11			−0.803763
$371$	3.93616e10	−	3.93616e10i	0.107868	−	0.107868i
$372$			6.50640e11i			1.76156i
$373$	−2.68589e11			−0.718452			−0.359226	−	0.933251i	$-0.616959\pi$
$373$	−2.68589e11			−0.718452			−0.359226	+	0.933251i	$0.616959\pi$
$374$	−6.64715e11	+	6.96773e11i	−1.75676	+	1.84149i
$375$	4.10957e11			1.07314
$376$			4.91203e11i			1.26740i
$377$	−7.55373e10	+	7.55373e10i	−0.192586	+	0.192586i
$378$	7.16487e10			0.180507
$379$	−8.66652e10	+	8.66652e10i	−0.215759	+	0.215759i	−0.806708	−	0.590950i	$-0.798753\pi$
$379$	−8.66652e10	+	8.66652e10i	−0.215759	+	0.215759i	0.590950	+	0.806708i	$0.298753\pi$
$380$	−1.35359e12	−	1.35359e12i	−3.33013	−	3.33013i
$381$	−7.15177e10	−	7.15177e10i	−0.173881	−	0.173881i
$382$		−	5.54553e11i		−	1.33247i
$383$		−	8.38894e11i		−	1.99211i	−0.0887531	−	0.996054i	$-0.528288\pi$
$383$		−	8.38894e11i		−	1.99211i	0.0887531	−	0.996054i	$-0.471712\pi$
$384$	−7.58697e11	−	7.58697e11i	−1.78065	−	1.78065i
$385$	−1.69917e11	−	1.69917e11i	−0.394151	−	0.394151i
$386$	−6.38455e11	+	6.38455e11i	−1.46382	+	1.46382i
$387$	2.06926e11			0.468938
$388$	−2.43980e11	+	2.43980e11i	−0.546527	+	0.546527i
$389$			4.49034e11i			0.994274i	0.867672	+	0.497137i	$0.165615\pi$
$389$			4.49034e11i			0.994274i	−0.867672	+	0.497137i	$0.834385\pi$
$390$	1.06308e12			2.32690
$391$	6.70055e10	+	6.39226e10i	0.144982	+	0.138312i
$392$	4.60602e11			0.985232
$393$			3.56387e11i			0.753625i
$394$	−1.26964e11	+	1.26964e11i	−0.265428	+	0.265428i
$395$	1.19394e12			2.46772
$396$	1.17382e12	−	1.17382e12i	2.39868	−	2.39868i
$397$	5.91499e11	+	5.91499e11i	1.19508	+	1.19508i	0.975622	+	0.219457i	$0.0704285\pi$
$397$	5.91499e11	+	5.91499e11i	1.19508	+	1.19508i	0.219457	+	0.975622i	$0.429571\pi$
$398$	4.26068e11	+	4.26068e11i	0.851148	+	0.851148i
$399$			3.21764e11i			0.635563i
$400$		−	3.59361e10i		−	0.0701876i
$401$	3.81721e11	+	3.81721e11i	0.737218	+	0.737218i	0.972039	−	0.234821i	$-0.0754503\pi$
$401$	3.81721e11	+	3.81721e11i	0.737218	+	0.737218i	−0.234821	+	0.972039i	$0.575450\pi$
$402$	−1.39377e12	−	1.39377e12i	−2.66180	−	2.66180i
$403$	1.58614e11	−	1.58614e11i	0.299549	−	0.299549i
$404$	2.86242e11			0.534586
$405$	−3.45329e11	+	3.45329e11i	−0.637801	+	0.637801i
$406$		−	9.16871e10i		−	0.167472i
$407$	2.74092e11			0.495132
$408$	6.40983e11	+	6.11491e11i	1.14518	+	1.09250i
$409$	2.38000e11			0.420554			0.210277	−	0.977642i	$-0.432563\pi$
$409$	2.38000e11			0.420554			0.210277	+	0.977642i	$0.432563\pi$
$410$		−	1.63467e12i		−	2.85695i
$411$	−3.46920e11	+	3.46920e11i	−0.599710	+	0.599710i
$412$	−9.05897e11			−1.54896
$413$	1.07876e11	−	1.07876e11i	0.182452	−	0.182452i
$414$	−1.81732e11	−	1.81732e11i	−0.304040	−	0.304040i
$415$	6.29644e11	+	6.29644e11i	1.04203	+	1.04203i
$416$			3.52314e11i			0.576780i
$417$			5.87780e11i			0.951924i
$418$	2.06139e12	+	2.06139e12i	3.30269	+	3.30269i
$419$	−8.70458e11	−	8.70458e11i	−1.37970	−	1.37970i	−0.845115	−	0.534585i	$-0.820468\pi$
$419$	−8.70458e11	−	8.70458e11i	−1.37970	−	1.37970i	−0.534585	−	0.845115i	$-0.679532\pi$
$420$	−4.00748e11	+	4.00748e11i	−0.628420	+	0.628420i
$421$	−6.84349e11			−1.06172			−0.530858	−	0.847461i	$-0.678130\pi$
$421$	−6.84349e11			−1.06172			−0.530858	+	0.847461i	$0.678130\pi$
$422$	1.04548e12	−	1.04548e12i	1.60477	−	1.60477i
$423$		−	1.06098e12i		−	1.61130i
$424$	−4.63961e11			−0.697165
$425$	−2.29582e10	−	9.75010e11i	−0.0341340	−	1.44964i
$426$	6.64196e11			0.977132
$427$		−	3.69123e10i		−	0.0537335i
$428$	−4.51492e11	+	4.51492e11i	−0.650358	+	0.650358i
$429$	−1.00561e12			−1.43341
$430$	−4.52595e11	+	4.52595e11i	−0.638413	+	0.638413i
$431$	−5.16079e11	−	5.16079e11i	−0.720392	−	0.720392i	0.248293	−	0.968685i	$-0.420130\pi$
$431$	−5.16079e11	−	5.16079e11i	−0.720392	−	0.720392i	−0.968685	+	0.248293i	$0.920130\pi$
$432$	−1.21095e10	−	1.21095e10i	−0.0167282	−	0.0167282i
$433$		−	5.77752e11i		−	0.789852i	−0.918713	−	0.394926i	$-0.870770\pi$
$433$		−	5.77752e11i		−	0.789852i	0.918713	−	0.394926i	$-0.129230\pi$
$434$			1.92525e11i			0.260485i
$435$	−5.70983e11	−	5.70983e11i	−0.764578	−	0.764578i
$436$	1.97850e11	+	1.97850e11i	0.262209	+	0.262209i
$437$	1.98235e11	−	1.98235e11i	0.260024	−	0.260024i
$438$	−1.32262e12			−1.71712
$439$	−1.68411e11	+	1.68411e11i	−0.216412	+	0.216412i	−0.806985	−	0.590573i	$-0.798902\pi$
$439$	−1.68411e11	+	1.68411e11i	−0.216412	+	0.216412i	0.590573	+	0.806985i	$0.298902\pi$
$440$			2.00283e12i			2.54746i
$441$	−9.94886e11			−1.25256
$442$	−1.84322e10	−	7.82798e11i	−0.0229709	−	0.975550i
$443$	1.23250e12			1.52044			0.760220	−	0.649665i	$-0.225091\pi$
$443$	1.23250e12			1.52044			0.760220	+	0.649665i	$0.225091\pi$
$444$		−	6.46446e11i		−	0.789421i
$445$	7.30660e11	−	7.30660e11i	0.883274	−	0.883274i
$446$	1.25111e12			1.49723
$447$	−5.46532e11	+	5.46532e11i	−0.647488	+	0.647488i
$448$	−2.20453e11	−	2.20453e11i	−0.258562	−	0.258562i
$449$	−2.37744e11	−	2.37744e11i	−0.276058	−	0.276058i	0.555475	−	0.831533i	$-0.312536\pi$
$449$	−2.37744e11	−	2.37744e11i	−0.276058	−	0.276058i	−0.831533	+	0.555475i	$0.812536\pi$
$450$			2.70669e12i			3.11159i
$451$			1.54629e12i			1.75993i
$452$	−6.83212e11	−	6.83212e11i	−0.769897	−	0.769897i
$453$	−8.26222e11	−	8.26222e11i	−0.921838	−	0.921838i
$454$	1.36203e11	−	1.36203e11i	0.150465	−	0.150465i
$455$	1.95390e11			0.213723
$456$	1.89634e12	−	1.89634e12i	2.05387	−	2.05387i
$457$		−	5.70226e11i		−	0.611539i	−0.952106	−	0.305769i	$-0.901086\pi$
$457$		−	5.70226e11i		−	0.611539i	0.952106	−	0.305769i	$-0.0989136\pi$
$458$	−2.24357e12			−2.38257
$459$	−3.36289e11	−	3.20816e11i	−0.353635	−	0.337364i
$460$	4.93792e11			0.514202
$461$			1.88591e12i			1.94476i	0.233403	+	0.972380i	$0.425014\pi$
$461$			1.88591e12i			1.94476i	−0.233403	+	0.972380i	$0.574986\pi$
$462$	6.10302e11	−	6.10302e11i	0.623241	−	0.623241i
$463$	2.34282e11			0.236932			0.118466	−	0.992958i	$-0.462202\pi$
$463$	2.34282e11			0.236932			0.118466	+	0.992958i	$0.462202\pi$
$464$	−1.54962e10	+	1.54962e10i	−0.0155201	+	0.0155201i
$465$	1.19895e12	+	1.19895e12i	1.18922	+	1.18922i
$466$	−5.41426e11	−	5.41426e11i	−0.531866	−	0.531866i
$467$			4.47116e11i			0.435005i	0.976060	+	0.217503i	$0.0697910\pi$
$467$			4.47116e11i			0.435005i	−0.976060	+	0.217503i	$0.930209\pi$
$468$			1.34979e12i			1.30065i
$469$	−2.56169e11	−	2.56169e11i	−0.244483	−	0.244483i
$470$	2.32062e12	+	2.32062e12i	2.19363	+	2.19363i
$471$	1.78182e12	−	1.78182e12i	1.66828	−	1.66828i
$472$	−1.27155e12			−1.17922
$473$	4.28124e11	−	4.28124e11i	0.393274	−	0.393274i
$474$			4.28836e12i			3.90201i
$475$	−2.95247e12			−2.66112
$476$	3.02038e11	+	2.88141e11i	0.269668	+	0.257261i
$477$	1.00214e12			0.886332
$478$			8.87207e11i			0.777319i
$479$	6.89144e11	−	6.89144e11i	0.598136	−	0.598136i	−0.341680	−	0.939816i	$-0.610996\pi$
$479$	6.89144e11	−	6.89144e11i	0.598136	−	0.598136i	0.939816	+	0.341680i	$0.110996\pi$
$480$	−2.66312e12			−2.28984
$481$	−1.57591e11	+	1.57591e11i	−0.134239	+	0.134239i
$482$	−1.30270e12	−	1.30270e12i	−1.09934	−	1.09934i
$483$	−5.86899e10	−	5.86899e10i	−0.0490684	−	0.0490684i
$484$		−	2.87791e12i		−	2.38382i
$485$			8.99178e11i			0.737918i
$486$	−1.93088e12	−	1.93088e12i	−1.56998	−	1.56998i
$487$	2.50560e11	+	2.50560e11i	0.201851	+	0.201851i	0.800793	−	0.598942i	$-0.204412\pi$
$487$	2.50560e11	+	2.50560e11i	0.201851	+	0.201851i	−0.598942	+	0.800793i	$0.704412\pi$
$488$	−2.17545e11	+	2.17545e11i	−0.173644	+	0.173644i
$489$	3.24137e12			2.56353
$490$	2.17605e12	−	2.17605e12i	1.70524	−	1.70524i
$491$		−	1.43848e12i		−	1.11696i	−0.829518	−	0.558480i	$-0.811385\pi$
$491$		−	1.43848e12i		−	1.11696i	0.829518	−	0.558480i	$-0.188615\pi$
$492$	3.64692e12			2.80597
$493$	−4.10541e11	+	4.30341e11i	−0.313001	+	0.328097i
$494$	−2.37043e12			−1.79083
$495$		−	4.32605e12i		−	3.23868i
$496$	3.25391e10	−	3.25391e10i	0.0241400	−	0.0241400i
$497$	1.22076e11			0.0897484
$498$	−2.26154e12	+	2.26154e12i	−1.64768	+	1.64768i
$499$	−6.13818e11	−	6.13818e11i	−0.443187	−	0.443187i	0.449894	−	0.893082i	$-0.351462\pi$
$499$	−6.13818e11	−	6.13818e11i	−0.443187	−	0.443187i	−0.893082	+	0.449894i	$0.851462\pi$
$500$	−1.14127e12	−	1.14127e12i	−0.816630	−	0.816630i
$501$			9.49697e11i			0.673466i
$502$		−	9.78268e11i		−	0.687529i
$503$	1.93070e12	+	1.93070e12i	1.34480	+	1.34480i	0.891209	+	0.453593i	$0.149858\pi$
$503$	1.93070e12	+	1.93070e12i	1.34480	+	1.34480i	0.453593	+	0.891209i	$0.350142\pi$
$504$	−3.19523e11	−	3.19523e11i	−0.220579	−	0.220579i
$505$	5.27467e11	−	5.27467e11i	0.360898	−	0.360898i
$506$	−7.51999e11			−0.509965
$507$	−1.02448e12	+	1.02448e12i	−0.688601	+	0.688601i
$508$			3.97226e11i			0.264637i
$509$	2.31278e12			1.52723			0.763615	−	0.645672i	$-0.223423\pi$
$509$	2.31278e12			1.52723			0.763615	+	0.645672i	$0.223423\pi$
$510$	5.91713e12	−	1.39328e11i	3.87298	−	0.0911955i
$511$	−2.43091e11			−0.157716
$512$			1.50471e11i			0.0967694i
$513$	−9.94905e11	+	9.94905e11i	−0.634240	+	0.634240i
$514$	−4.12779e10			−0.0260846
$515$	−1.66932e12	+	1.66932e12i	−1.04570	+	1.04570i
$516$	−1.00973e12	−	1.00973e12i	−0.627021	−	0.627021i
$517$	−2.19515e12	−	2.19515e12i	−1.35131	−	1.35131i
$518$		−	1.91284e11i		−	0.116733i
$519$			3.49702e12i			2.11565i
$520$	−1.15154e12	−	1.15154e12i	−0.690661	−	0.690661i
$521$	2.53529e9	+	2.53529e9i	0.00150750	+	0.00150750i	0.707860	−	0.706353i	$-0.249661\pi$
$521$	2.53529e9	+	2.53529e9i	0.00150750	+	0.00150750i	−0.706353	+	0.707860i	$0.749661\pi$
$522$	1.16717e12	−	1.16717e12i	0.688045	−	0.688045i
$523$	−7.11572e11			−0.415873			−0.207937	−	0.978142i	$-0.566675\pi$
$523$	−7.11572e11			−0.415873			−0.207937	+	0.978142i	$0.566675\pi$
$524$	9.89727e11	−	9.89727e11i	0.573488	−	0.573488i
$525$			8.74118e11i			0.502173i
$526$	−1.20781e12			−0.687957
$527$	8.62056e11	−	9.03632e11i	0.486842	−	0.510322i
$528$	−2.06297e11			−0.115515
$529$		−	1.72884e12i		−	0.959850i
$530$	−2.19192e12	+	2.19192e12i	−1.20665	+	1.20665i
$531$	2.74650e12			1.49918
$532$	8.93573e11	−	8.93573e11i	0.483646	−	0.483646i
$533$	−8.89050e11	−	8.89050e11i	−0.477148	−	0.477148i
$534$	2.62436e12	+	2.62436e12i	1.39665	+	1.39665i
$535$			1.66395e12i			0.878111i
$536$			3.01950e12i			1.58013i
$537$	4.45905e11	+	4.45905e11i	0.231397	+	0.231397i
$538$	−2.73822e12	−	2.73822e12i	−1.40912	−	1.40912i
$539$	−2.05839e12	+	2.05839e12i	−1.05046	+	1.05046i
$540$	−2.47826e12			−1.25422
$541$	−1.65425e12	+	1.65425e12i	−0.830258	+	0.830258i	−0.987552	−	0.157294i	$-0.949723\pi$
$541$	−1.65425e12	+	1.65425e12i	−0.830258	+	0.830258i	0.157294	+	0.987552i	$0.449723\pi$
$542$		−	6.02126e12i		−	2.99703i
$543$	3.09711e11			0.152882
$544$	4.61744e10	+	1.96098e12i	0.0226051	+	0.960016i
$545$	7.29169e11			0.354033
$546$			7.01796e11i			0.337943i
$547$	1.00520e12	−	1.00520e12i	0.480075	−	0.480075i	−0.425081	−	0.905155i	$-0.639754\pi$
$547$	1.00520e12	−	1.00520e12i	0.480075	−	0.480075i	0.905155	+	0.425081i	$0.139754\pi$
$548$	1.92687e12			0.912725
$549$	4.69891e11	−	4.69891e11i	0.220761	−	0.220761i
$550$	5.60007e12	+	5.60007e12i	2.60952	+	2.60952i
$551$	1.27316e12	+	1.27316e12i	0.588436	+	0.588436i
$552$			6.91787e11i			0.317137i
$553$			7.88180e11i			0.358395i
$554$	3.04149e11	+	3.04149e11i	0.137181	+	0.137181i
$555$	−1.19122e12	−	1.19122e12i	−0.532936	−	0.532936i
$556$	1.63233e12	−	1.63233e12i	0.724388	−	0.724388i
$557$	−4.32681e11			−0.190467			−0.0952334	−	0.995455i	$-0.530360\pi$
$557$	−4.32681e11			−0.190467			−0.0952334	+	0.995455i	$0.530360\pi$
$558$	−2.45083e12	+	2.45083e12i	−1.07019	+	1.07019i
$559$			4.92307e11i			0.213247i
$560$	4.00836e10			0.0172235
$561$	−5.59721e12	+	1.31795e11i	−2.38583	+	0.0561781i
$562$	2.54008e12			1.07407
$563$			9.29044e11i			0.389716i	0.980831	+	0.194858i	$0.0624246\pi$
$563$			9.29044e11i			0.389716i	−0.980831	+	0.194858i	$0.937575\pi$
$564$	−5.17725e12	+	5.17725e12i	−2.15448	+	2.15448i
$565$	−2.51795e12			−1.03951
$566$	−2.07061e12	+	2.07061e12i	−0.848054	+	0.848054i
$567$	−2.27969e11	−	2.27969e11i	−0.0926299	−	0.0926299i
$568$	−7.19464e11	−	7.19464e11i	−0.290029	−	0.290029i
$569$			7.31058e11i			0.292379i	0.989257	+	0.146190i	$0.0467010\pi$
$569$			7.31058e11i			0.292379i	−0.989257	+	0.146190i	$0.953299\pi$
$570$		−	1.79179e13i		−	7.10970i
$571$	−1.39474e12	−	1.39474e12i	−0.549076	−	0.549076i	0.377098	−	0.926173i	$-0.376922\pi$
$571$	−1.39474e12	−	1.39474e12i	−0.549076	−	0.549076i	−0.926173	+	0.377098i	$0.876922\pi$
$572$	2.79268e12	+	2.79268e12i	1.09079	+	1.09079i
$573$	2.27982e12	−	2.27982e12i	0.883497	−	0.883497i
$574$	1.07913e12			0.414924
$575$	5.38533e11	−	5.38533e11i	0.205450	−	0.205450i
$576$		−	5.61270e12i		−	2.12457i
$577$	4.96540e12			1.86493			0.932467	−	0.361256i	$-0.117652\pi$
$577$	4.96540e12			1.86493			0.932467	+	0.361256i	$0.117652\pi$
$578$	−2.05188e11	−	4.35464e12i	−0.0764674	−	1.62285i
$579$	−5.24950e12			−1.94117
$580$			3.17137e12i			1.16365i
$581$	−4.15659e11	+	4.15659e11i	−0.151337	+	0.151337i
$582$	−3.22964e12			−1.16681
$583$	2.07341e12	−	2.07341e12i	0.743320	−	0.743320i
$584$	1.43267e12	+	1.43267e12i	0.509671	+	0.509671i
$585$	2.48730e12	+	2.48730e12i	0.878065	+	0.878065i
$586$		−	7.57776e11i		−	0.265461i
$587$			3.66373e12i			1.27366i	0.771005	+	0.636829i	$0.219754\pi$
$587$			3.66373e12i			1.27366i	−0.771005	+	0.636829i	$0.780246\pi$
$588$	4.85472e12	+	4.85472e12i	1.67481	+	1.67481i
$589$	−2.67338e12	−	2.67338e12i	−0.915255	−	0.915255i
$590$	−6.00724e12	+	6.00724e12i	−2.04099	+	2.04099i
$591$	−1.04392e12			−0.351985
$592$	−3.23293e10	+	3.23293e10i	−0.0108181	+	0.0108181i
$593$		−	4.77019e12i		−	1.58413i	−0.610439	−	0.792063i	$-0.709007\pi$
$593$		−	4.77019e12i		−	1.58413i	0.610439	−	0.792063i	$-0.290993\pi$
$594$	3.77415e12			1.24389
$595$	1.08754e12	−	2.56079e10i	0.355729	−	0.00837620i
$596$	3.03556e12			0.985442
$597$			3.50321e12i			1.12871i
$598$	4.32368e11	−	4.32368e11i	0.138260	−	0.138260i
$599$	−1.72396e12			−0.547150			−0.273575	−	0.961851i	$-0.588206\pi$
$599$	−1.72396e12			−0.547150			−0.273575	+	0.961851i	$0.588206\pi$
$600$	5.15167e12	−	5.15167e12i	1.62281	−	1.62281i
$601$	3.71083e12	+	3.71083e12i	1.16021	+	1.16021i	0.984430	+	0.175778i	$0.0562440\pi$
$601$	3.71083e12	+	3.71083e12i	1.16021	+	1.16021i	0.175778	+	0.984430i	$0.443756\pi$
$602$	−2.98781e11	−	2.98781e11i	−0.0927189	−	0.0927189i
$603$		−	6.52202e12i		−	2.00888i
$604$			4.58902e12i			1.40299i
$605$	−5.30321e12	−	5.30321e12i	−1.60931	−	1.60931i
$606$	1.89454e12	+	1.89454e12i	0.570660	+	0.570660i
$607$	−4.03482e12	+	4.03482e12i	−1.20635	+	1.20635i	−0.234155	+	0.972199i	$0.575232\pi$
$607$	−4.03482e12	+	4.03482e12i	−1.20635	+	1.20635i	−0.972199	+	0.234155i	$0.924768\pi$
$608$	5.93813e12			1.76232
$609$	3.76935e11	−	3.76935e11i	0.111042	−	0.111042i
$610$			2.05552e12i			0.601088i
$611$	2.52423e12			0.732730
$612$	1.76904e11	+	7.51294e12i	0.0509749	+	2.16485i
$613$	−1.99333e12			−0.570173			−0.285086	−	0.958502i	$-0.592022\pi$
$613$	−1.99333e12			−0.570173			−0.285086	+	0.958502i	$0.592022\pi$
$614$		−	6.32901e11i		−	0.179712i
$615$	6.72028e12	−	6.72028e12i	1.89430	−	1.89430i
$616$	−1.32217e12			−0.369976
$617$	−2.21807e11	+	2.21807e11i	−0.0616159	+	0.0616159i	−0.737243	−	0.675627i	$-0.763873\pi$
$617$	−2.21807e11	+	2.21807e11i	−0.0616159	+	0.0616159i	0.675627	+	0.737243i	$0.263873\pi$
$618$	−5.99583e12	−	5.99583e12i	−1.65349	−	1.65349i
$619$	−1.62777e12	−	1.62777e12i	−0.445642	−	0.445642i	0.448261	−	0.893903i	$-0.352043\pi$
$619$	−1.62777e12	−	1.62777e12i	−0.445642	−	0.445642i	−0.893903	+	0.448261i	$0.852043\pi$
$620$		−	6.65926e12i		−	1.80994i
$621$		−	3.62943e11i		−	0.0979323i
$622$	4.32691e12	+	4.32691e12i	1.15910	+	1.15910i
$623$	4.82345e11	+	4.82345e11i	0.128281	+	0.128281i
$624$	1.18612e11	−	1.18612e11i	0.0313183	−	0.0313183i
$625$	1.32533e12			0.347428
$626$	1.85122e11	−	1.85122e11i	0.0481807	−	0.0481807i
$627$			1.69492e13i			4.37970i
$628$	−9.89662e12			−2.53903
$629$	−8.56499e11	+	8.97807e11i	−0.218172	+	0.228694i
$630$	−3.01908e12			−0.763558
$631$		−	4.58901e11i		−	0.115236i	−0.998339	−	0.0576178i	$-0.981650\pi$
$631$		−	4.58901e11i		−	0.115236i	0.998339	−	0.0576178i	$-0.0183505\pi$
$632$	4.64519e12	−	4.64519e12i	1.15818	−	1.15818i
$633$	8.59618e12			2.12808
$634$	3.78168e12	−	3.78168e12i	0.929571	−	0.929571i
$635$	7.31979e11	+	7.31979e11i	0.178656	+	0.178656i
$636$	−4.89013e12	−	4.89013e12i	−1.18512	−	1.18512i
$637$		−	2.36698e12i		−	0.569596i
$638$		−	4.82969e12i		−	1.15406i
$639$	1.55402e12	+	1.55402e12i	0.368725	+	0.368725i
$640$	7.76522e12	+	7.76522e12i	1.82955	+	1.82955i
$641$	−7.27738e11	+	7.27738e11i	−0.170260	+	0.170260i	−0.787094	−	0.616833i	$-0.788415\pi$
$641$	−7.27738e11	+	7.27738e11i	−0.170260	+	0.170260i	0.616833	+	0.787094i	$0.288415\pi$
$642$	−5.97654e12			−1.38849
$643$	−2.94204e12	+	2.94204e12i	−0.678734	+	0.678734i	−0.959714	−	0.280980i	$-0.909341\pi$
$643$	−2.94204e12	+	2.94204e12i	−0.678734	+	0.678734i	0.280980	+	0.959714i	$0.409341\pi$
$644$			3.25977e11i			0.0746794i
$645$	−3.72132e12			−0.846601
$646$	−1.31938e13	+	3.10669e11i	−2.98074	+	0.0701862i
$647$	−3.69231e12			−0.828378			−0.414189	−	0.910191i	$-0.635935\pi$
$647$	−3.69231e12			−0.828378			−0.414189	+	0.910191i	$0.635935\pi$
$648$			2.68710e12i			0.598682i
$649$	5.68245e12	−	5.68245e12i	1.25729	−	1.25729i
$650$	−6.43961e12			−1.41498
$651$	−7.91489e11	+	7.91489e11i	−0.172715	+	0.172715i
$652$	−9.00165e12	−	9.00165e12i	−1.95078	−	1.95078i
$653$	2.68005e11	+	2.68005e11i	0.0576812	+	0.0576812i	0.735359	−	0.677678i	$-0.237014\pi$
$653$	2.68005e11	+	2.68005e11i	0.0576812	+	0.0576812i	−0.677678	+	0.735359i	$0.737014\pi$
$654$			2.61901e12i			0.559805i
$655$		−	3.64760e12i		−	0.774321i
$656$	−1.82386e11	−	1.82386e11i	−0.0384524	−	0.0384524i
$657$	−3.09453e12	−	3.09453e12i	−0.647964	−	0.647964i
$658$	−1.53195e12	+	1.53195e12i	−0.318588	+	0.318588i
$659$	7.58856e12			1.56738			0.783691	−	0.621150i	$-0.213334\pi$
$659$	7.58856e12			1.56738			0.783691	+	0.621150i	$0.213334\pi$
$660$	−2.11098e13	+	2.11098e13i	−4.33047	+	4.33047i
$661$			4.30690e12i			0.877522i	0.898604	+	0.438761i	$0.144582\pi$
$661$			4.30690e12i			0.877522i	−0.898604	+	0.438761i	$0.855418\pi$
$662$	−3.67054e11			−0.0742795
$663$	3.14238e12	−	3.29394e12i	0.631609	−	0.662071i
$664$	4.89943e12			0.978114
$665$		−	3.29323e12i		−	0.653017i
$666$	2.43503e12	−	2.43503e12i	0.479591	−	0.479591i
$667$	−4.64450e11			−0.0908599
$668$	2.63742e12	−	2.63742e12i	0.512489	−	0.512489i
$669$	5.14344e12	+	5.14344e12i	0.992742	+	0.992742i
$670$	1.42652e13	+	1.42652e13i	2.73490	+	2.73490i
$671$		−	1.94438e12i		−	0.370280i
$672$		−	1.75806e12i		−	0.332562i
$673$	−5.19489e12	−	5.19489e12i	−0.976131	−	0.976131i	0.0235906	−	0.999722i	$-0.492490\pi$
$673$	−5.19489e12	−	5.19489e12i	−0.976131	−	0.976131i	−0.999722	+	0.0235906i	$0.992490\pi$
$674$	8.81871e12	+	8.81871e12i	1.64602	+	1.64602i
$675$	−2.70280e12	+	2.70280e12i	−0.501127	+	0.501127i
$676$	5.69019e12			1.04801
$677$	6.88850e12	−	6.88850e12i	1.26030	−	1.26030i	0.309360	−	0.950945i	$-0.399885\pi$
$677$	6.88850e12	−	6.88850e12i	1.26030	−	1.26030i	0.950945	−	0.309360i	$-0.100115\pi$
$678$		−	9.04391e12i		−	1.64370i
$679$	−5.93592e11			−0.107170
$680$	−6.56042e12	−	6.25857e12i	−1.17663	−	1.12250i
$681$	1.11989e12			0.199532
$682$			1.01414e13i			1.79502i
$683$	−7.20781e12	+	7.20781e12i	−1.26739	+	1.26739i	−0.319958	+	0.947432i	$0.603669\pi$
$683$	−7.20781e12	+	7.20781e12i	−1.26739	+	1.26739i	−0.947432	+	0.319958i	$0.896331\pi$
$684$	2.27503e13			3.97405
$685$	3.55070e12	−	3.55070e12i	0.616179	−	0.616179i
$686$	2.95132e12	+	2.95132e12i	0.508812	+	0.508812i
$687$	−9.22355e12	−	9.22355e12i	−1.57977	−	1.57977i
$688$			1.00995e11i			0.0171851i
$689$			2.38424e12i			0.403055i
$690$	3.26825e12	+	3.26825e12i	0.548901	+	0.548901i
$691$	6.86046e12	+	6.86046e12i	1.14473	+	1.14473i	0.987574	+	0.157153i	$0.0502315\pi$
$691$	6.86046e12	+	6.86046e12i	1.14473	+	1.14473i	0.157153	+	0.987574i	$0.449769\pi$
$692$	9.71161e12	−	9.71161e12i	1.60995	−	1.60995i
$693$	2.85585e12			0.470365
$694$	8.84889e12	−	8.84889e12i	1.44801	−	1.44801i
$695$		−	6.01589e12i		−	0.978066i
$696$	−4.44298e12			−0.717683
$697$	−5.06497e12	−	4.83193e12i	−0.812886	−	0.775485i
$698$	−1.46045e13			−2.32883
$699$		−	4.45171e12i		−	0.705309i
$700$	2.42752e12	−	2.42752e12i	0.382140	−	0.382140i
$701$	5.20929e12			0.814794			0.407397	−	0.913251i	$-0.366437\pi$
$701$	5.20929e12			0.814794			0.407397	+	0.913251i	$0.366437\pi$
$702$	−2.16998e12	+	2.16998e12i	−0.337239	+	0.337239i
$703$	2.65615e12	+	2.65615e12i	0.410160	+	0.410160i
$704$	−1.16125e13	−	1.16125e13i	−1.78176	−	1.78176i
$705$			1.90806e13i			2.90897i
$706$		−	6.04503e12i		−	0.915750i
$707$	3.48208e11	+	3.48208e11i	0.0524144	+	0.0524144i
$708$	−1.34021e13	−	1.34021e13i	−2.00457	−	2.00457i
$709$	5.48443e10	−	5.48443e10i	0.00815124	−	0.00815124i	−0.703019	−	0.711171i	$-0.748165\pi$
$709$	5.48443e10	−	5.48443e10i	0.00815124	−	0.00815124i	0.711171	+	0.703019i	$0.248165\pi$
$710$	−6.79801e12			−1.00397
$711$	−1.00335e13	+	1.00335e13i	−1.47244	+	1.47244i
$712$		−	5.68547e12i		−	0.829099i
$713$	9.75254e11			0.141324
$714$	9.19776e10	+	3.90620e12i	0.0132446	+	0.562487i
$715$	1.02923e13			1.47277
$716$		−	2.47666e12i		−	0.352174i
$717$	−3.64739e12	+	3.64739e12i	−0.515402	+	0.515402i
$718$	−2.16252e13			−3.03668
$719$	−4.05554e12	+	4.05554e12i	−0.565937	+	0.565937i	−0.930988	−	0.365051i	$-0.881052\pi$
$719$	−4.05554e12	+	4.05554e12i	−0.565937	+	0.565937i	0.365051	+	0.930988i	$0.381052\pi$
$720$	5.10261e11	+	5.10261e11i	0.0707614	+	0.0707614i
$721$	−1.10200e12	−	1.10200e12i	−0.151871	−	0.151871i
$722$			2.80902e13i			3.84714i
$723$		−	1.07111e13i		−	1.45784i
$724$	−8.60102e11	−	8.60102e11i	−0.116339	−	0.116339i
$725$	3.45872e12	+	3.45872e12i	0.464937	+	0.464937i
$726$	1.90479e13	−	1.90479e13i	2.54468	−	2.54468i
$727$	−7.17424e12			−0.952513			−0.476256	−	0.879306i	$-0.658007\pi$
$727$	−7.17424e12			−0.952513			−0.476256	+	0.879306i	$0.658007\pi$
$728$	7.60191e11	−	7.60191e11i	0.100307	−	0.100307i
$729$		−	1.14818e13i		−	1.50569i
$730$	1.35369e13			1.76428
$731$	6.45219e10	+	2.74018e12i	0.00835755	+	0.354937i
$732$	−4.58583e12			−0.590362
$733$			2.59216e12i			0.331661i	0.986154	+	0.165830i	$0.0530304\pi$
$733$			2.59216e12i			0.331661i	−0.986154	+	0.165830i	$0.946970\pi$
$734$	5.84626e11	−	5.84626e11i	0.0743440	−	0.0743440i
$735$	1.78919e13			2.26133
$736$	−1.08312e12	+	1.08312e12i	−0.136059	+	0.136059i
$737$	−1.34939e13	−	1.34939e13i	−1.68474	−	1.68474i
$738$	1.37372e13	+	1.37372e13i	1.70469	+	1.70469i
$739$		−	6.31144e12i		−	0.778446i	−0.921143	−	0.389223i	$-0.872743\pi$
$739$		−	6.31144e12i		−	0.778446i	0.921143	−	0.389223i	$-0.127257\pi$
$740$			6.61633e12i			0.811100i
$741$	−9.74505e12	−	9.74505e12i	−1.18741	−	1.18741i
$742$	−1.44700e12	−	1.44700e12i	−0.175247	−	0.175247i
$743$	−8.11408e10	+	8.11408e10i	−0.00976764	+	0.00976764i	−0.711974	−	0.702206i	$-0.752199\pi$
$743$	−8.11408e10	+	8.11408e10i	−0.00976764	+	0.00976764i	0.702206	+	0.711974i	$0.252199\pi$
$744$	9.32939e12			1.11629
$745$	5.59372e12	−	5.59372e12i	0.665269	−	0.665269i
$746$			9.87374e12i			1.16723i
$747$	−1.05826e13			−1.24351
$748$	1.59101e13	+	1.51781e13i	1.85830	+	1.77280i
$749$	−1.09846e12			−0.127531
$750$		−	1.51074e13i		−	1.74347i
$751$	3.00641e12	−	3.00641e12i	0.344881	−	0.344881i	−0.513318	−	0.858199i	$-0.671584\pi$
$751$	3.00641e12	−	3.00641e12i	0.344881	−	0.344881i	0.858199	+	0.513318i	$0.171584\pi$
$752$	5.17838e11			0.0590492
$753$	4.02175e12	−	4.02175e12i	0.455867	−	0.455867i
$754$	2.77687e12	+	2.77687e12i	0.312885	+	0.312885i
$755$	8.45632e12	+	8.45632e12i	0.947154	+	0.947154i
$756$		−	1.63602e12i		−	0.182155i
$757$			1.23621e13i			1.36824i	0.729371	+	0.684118i	$0.239813\pi$
$757$			1.23621e13i			1.36824i	−0.729371	+	0.684118i	$0.760187\pi$
$758$	3.18595e12	+	3.18595e12i	0.350531	+	0.350531i
$759$	−3.09154e12	−	3.09154e12i	−0.338133	−	0.338133i
$760$	−1.94089e13	+	1.94089e13i	−2.11028	+	2.11028i
$761$	1.78926e12			0.193393			0.0966966	−	0.995314i	$-0.469172\pi$
$761$	1.78926e12			0.193393			0.0966966	+	0.995314i	$0.469172\pi$
$762$	−2.62910e12	+	2.62910e12i	−0.282495	+	0.282495i
$763$			4.81361e11i			0.0514174i
$764$	−1.26626e13			−1.34463
$765$	1.41703e13	+	1.35183e13i	1.49590	+	1.42707i
$766$	−3.08391e13			−3.23647
$767$			6.53433e12i			0.681745i
$768$	−1.11854e13	+	1.11854e13i	−1.16018	+	1.16018i
$769$	−7.61998e12			−0.785752			−0.392876	−	0.919591i	$-0.628520\pi$
$769$	−7.61998e12			−0.785752			−0.392876	+	0.919591i	$0.628520\pi$
$770$	−6.24640e12	+	6.24640e12i	−0.640356	+	0.640356i
$771$	−1.69698e11	−	1.69698e11i	−0.0172954	−	0.0172954i
$772$	1.45784e13	+	1.45784e13i	1.47718	+	1.47718i
$773$		−	5.46599e12i		−	0.550632i	−0.961354	−	0.275316i	$-0.911218\pi$
$773$		−	5.46599e12i		−	0.550632i	0.961354	−	0.275316i	$-0.0887825\pi$
$774$		−	7.60691e12i		−	0.761858i
$775$	−7.26263e12	−	7.26263e12i	−0.723163	−	0.723163i
$776$	3.49838e12	+	3.49838e12i	0.346329	+	0.346329i
$777$	7.86387e11	−	7.86387e11i	0.0774001	−	0.0774001i
$778$	1.65072e13			1.61534
$779$	−1.49846e13	+	1.49846e13i	−1.45790	+	1.45790i
$780$		−	2.42744e13i		−	2.34814i
$781$	6.43046e12			0.618461
$782$	2.34989e12	−	2.46323e12i	0.224708	−	0.235545i
$783$	2.33099e12			0.221622
$784$		−	4.85578e11i		−	0.0459026i
$785$	−1.82368e13	+	1.82368e13i	−1.71410	+	1.71410i
$786$	1.31013e13			1.22437
$787$	9.00058e11	−	9.00058e11i	0.0836342	−	0.0836342i	−0.664052	−	0.747686i	$-0.731165\pi$
$787$	9.00058e11	−	9.00058e11i	0.0836342	−	0.0836342i	0.747686	+	0.664052i	$0.231165\pi$
$788$	2.89909e12	+	2.89909e12i	0.267851	+	0.267851i
$789$	−4.96540e12	−	4.96540e12i	−0.456150	−	0.456150i
$790$		−	4.38911e13i		−	4.00917i
$791$		−	1.66223e12i		−	0.150972i
$792$	−1.68311e13	−	1.68311e13i	−1.52002	−	1.52002i
$793$	1.11794e12	+	1.11794e12i	0.100390	+	0.100390i
$794$	2.17444e13	−	2.17444e13i	1.94158	−	1.94158i
$795$	−1.80224e13			−1.60015
$796$	9.72882e12	−	9.72882e12i	0.858917	−	0.858917i
$797$			1.54063e12i			0.135250i	0.997711	+	0.0676248i	$0.0215421\pi$
$797$			1.54063e12i			0.135250i	−0.997711	+	0.0676248i	$0.978458\pi$
$798$	1.18285e13			1.03257
$799$	1.40499e13	−	3.30827e11i	1.21959	−	0.0287171i
$800$	1.61318e13			1.39244
$801$			1.22804e13i			1.05407i
$802$	1.40326e13	−	1.40326e13i	1.19772	−	1.19772i
$803$	−1.28050e13			−1.08683
$804$	−3.18254e13	+	3.18254e13i	−2.68609	+	2.68609i
$805$	6.00688e11	+	6.00688e11i	0.0504159	+	0.0504159i
$806$	−5.83088e12	−	5.83088e12i	−0.486661	−	0.486661i
$807$		−	2.25142e13i		−	1.86864i
$808$		−	4.10437e12i		−	0.338763i
$809$	1.16614e13	+	1.16614e13i	0.957151	+	0.957151i	0.999119	−	0.0419677i	$-0.0133627\pi$
$809$	1.16614e13	+	1.16614e13i	0.957151	+	0.957151i	−0.0419677	+	0.999119i	$0.513363\pi$
$810$	1.26948e13	+	1.26948e13i	1.03620	+	1.03620i
$811$	−8.98356e12	+	8.98356e12i	−0.729214	+	0.729214i	−0.970463	−	0.241249i	$-0.922443\pi$
$811$	−8.98356e12	+	8.98356e12i	−0.729214	+	0.729214i	0.241249	+	0.970463i	$0.422443\pi$
$812$	−2.09358e12			−0.169000
$813$	2.47540e13	−	2.47540e13i	1.98718	−	1.98718i
$814$		−	1.00760e13i		−	0.804415i
$815$	−3.31752e13			−2.63393
$816$	6.44650e11	−	6.75740e11i	0.0509000	−	0.0533549i
$817$	8.29767e12			0.651563
$818$		−	8.74924e12i		−	0.683251i
$819$	−1.64199e12	+	1.64199e12i	−0.127524	+	0.127524i
$820$	−3.73260e13			−2.88303
$821$	1.58452e13	−	1.58452e13i	1.21718	−	1.21718i	0.248562	−	0.968616i	$-0.420042\pi$
$821$	1.58452e13	−	1.58452e13i	1.21718	−	1.21718i	0.968616	−	0.248562i	$-0.0799581\pi$
$822$	1.27533e13	+	1.27533e13i	0.974316	+	0.974316i
$823$	1.36970e13	+	1.36970e13i	1.04070	+	1.04070i	0.999136	+	0.0415627i	$0.0132336\pi$
$823$	1.36970e13	+	1.36970e13i	1.04070	+	1.04070i	0.0415627	+	0.999136i	$0.486766\pi$
$824$			1.29895e13i			0.981565i
$825$			4.60449e13i			3.46050i
$826$	−3.96568e12	−	3.96568e12i	−0.296420	−	0.296420i
$827$	2.39545e12	+	2.39545e12i	0.178079	+	0.178079i	0.790518	−	0.612439i	$-0.209812\pi$
$827$	2.39545e12	+	2.39545e12i	0.178079	+	0.178079i	−0.612439	+	0.790518i	$0.709812\pi$
$828$	−4.14967e12	+	4.14967e12i	−0.306815	+	0.306815i
$829$	−1.60725e13			−1.18192			−0.590960	−	0.806701i	$-0.701251\pi$
$829$	−1.60725e13			−1.18192			−0.590960	+	0.806701i	$0.701251\pi$
$830$	2.31467e13	−	2.31467e13i	1.69292	−	1.69292i
$831$			2.50078e12i			0.181916i
$832$	1.33534e13			0.966136
$833$	−3.10217e11	−	1.31746e13i	−0.0223236	−	0.948059i
$834$	2.16077e13			1.54654
$835$		−	9.72009e12i		−	0.691960i
$836$	4.70697e13	−	4.70697e13i	3.33283	−	3.33283i
$837$	−4.89463e12			−0.344711
$838$	−3.19994e13	+	3.19994e13i	−2.24152	+	2.24152i
$839$	1.34935e13	+	1.34935e13i	0.940144	+	0.940144i	0.998307	−	0.0581627i	$-0.0185242\pi$
$839$	1.34935e13	+	1.34935e13i	0.940144	+	0.940144i	−0.0581627	+	0.998307i	$0.518524\pi$
$840$	5.74625e12	+	5.74625e12i	0.398224	+	0.398224i
$841$			1.15242e13i			0.794383i
$842$			2.51577e13i			1.72491i
$843$	1.04425e13	+	1.04425e13i	0.712166	+	0.712166i
$844$	−2.38725e13	−	2.38725e13i	−1.61941	−	1.61941i
$845$	1.04855e13	−	1.04855e13i	0.707511	−	0.707511i
$846$	−3.90034e13			−2.61779
$847$	3.50091e12	−	3.50091e12i	0.233725	−	0.233725i
$848$			4.89120e11i			0.0324813i
$849$	−1.70249e13			−1.12461
$850$	−3.58429e13	+	8.43978e11i	−2.35515	+	0.0554556i
$851$	−9.68967e11			−0.0633324
$852$		−	1.51662e13i		−	0.986051i
$853$	−8.66032e12	+	8.66032e12i	−0.560097	+	0.560097i	−0.929335	−	0.369238i	$-0.879619\pi$
$853$	−8.66032e12	+	8.66032e12i	−0.560097	+	0.560097i	0.369238	+	0.929335i	$0.379619\pi$
$854$	−1.35695e12			−0.0872980
$855$	4.19226e13	−	4.19226e13i	2.68287	−	2.68287i
$856$	6.47385e12	+	6.47385e12i	0.412126	+	0.412126i
$857$	−2.00340e12	−	2.00340e12i	−0.126869	−	0.126869i	0.640821	−	0.767690i	$-0.278594\pi$
$857$	−2.00340e12	−	2.00340e12i	−0.126869	−	0.126869i	−0.767690	+	0.640821i	$0.778594\pi$
$858$			3.69677e13i			2.32878i
$859$			5.31654e12i			0.333166i	0.986027	+	0.166583i	$0.0532733\pi$
$859$			5.31654e12i			0.333166i	−0.986027	+	0.166583i	$0.946727\pi$
$860$	1.03345e13	+	1.03345e13i	0.644240	+	0.644240i
$861$	4.43640e12	+	4.43640e12i	0.275116	+	0.275116i
$862$	−1.89719e13	+	1.89719e13i	−1.17038	+	1.17038i
$863$	1.93500e13			1.18750			0.593749	−	0.804650i	$-0.297647\pi$
$863$	1.93500e13			1.18750			0.593749	+	0.804650i	$0.297647\pi$
$864$	5.43599e12	−	5.43599e12i	0.331869	−	0.331869i
$865$		−	3.57917e13i		−	2.17375i
$866$	−2.12391e13			−1.28323
$867$	1.70588e13	−	1.87459e13i	1.02533	−	1.12673i
$868$	4.39611e12			0.262863
$869$			4.15180e13i			2.46972i
$870$	−2.09902e13	+	2.09902e13i	−1.24217	+	1.24217i
$871$	1.55168e13			0.913528
$872$	2.83693e12	−	2.83693e12i	0.166159	−	0.166159i
$873$	−7.55639e12	−	7.55639e12i	−0.440302	−	0.440302i
$874$	−7.28741e12	−	7.28741e12i	−0.422447	−	0.422447i
$875$		−	2.77667e12i		−	0.160136i
$876$			3.02006e13i			1.73280i
$877$	−5.93043e12	−	5.93043e12i	−0.338523	−	0.338523i	0.517288	−	0.855811i	$-0.326941\pi$
$877$	−5.93043e12	−	5.93043e12i	−0.338523	−	0.338523i	−0.855811	+	0.517288i	$0.826941\pi$
$878$	6.19107e12	+	6.19107e12i	0.351593	+	0.351593i
$879$	3.11529e12	−	3.11529e12i	0.176015	−	0.176015i
$880$	2.11144e12			0.118688
$881$	−1.43857e13	+	1.43857e13i	−0.804527	+	0.804527i	−0.983799	−	0.179273i	$-0.942626\pi$
$881$	−1.43857e13	+	1.43857e13i	−0.804527	+	0.804527i	0.179273	+	0.983799i	$0.442626\pi$
$882$			3.65736e13i			2.03497i
$883$	5.99288e12			0.331751			0.165876	−	0.986147i	$-0.446955\pi$
$883$	5.99288e12			0.331751			0.165876	+	0.986147i	$0.446955\pi$
$884$	−1.78744e13	+	4.20881e11i	−0.984455	+	0.0231806i
$885$	−4.93927e13			−2.70656
$886$		−	4.53085e13i		−	2.47018i
$887$	6.46765e12	−	6.46765e12i	0.350825	−	0.350825i	−0.509592	−	0.860416i	$-0.670204\pi$
$887$	6.46765e12	−	6.46765e12i	0.350825	−	0.350825i	0.860416	+	0.509592i	$0.170204\pi$
$888$	−9.26925e12			−0.500249
$889$	−4.83216e11	+	4.83216e11i	−0.0259468	+	0.0259468i
$890$	−2.68602e13	−	2.68602e13i	−1.43501	−	1.43501i
$891$	−1.20084e13	−	1.20084e13i	−0.638318	−	0.638318i
$892$		−	2.85678e13i		−	1.51090i
$893$		−	4.25451e13i		−	2.23881i
$894$	2.00914e13	+	2.00914e13i	1.05194	+	1.05194i
$895$	−4.56381e12	−	4.56381e12i	−0.237752	−	0.237752i
$896$	−5.12621e12	+	5.12621e12i	−0.265711	+	0.265711i
$897$	3.55501e12			0.183347
$898$	−8.73983e12	+	8.73983e12i	−0.448497	+	0.448497i
$899$			6.26354e12i			0.319817i
$900$	6.18044e13			3.13999
$901$	3.12480e11	+	1.32707e13i	0.0157965	+	0.670861i
$902$	5.68439e13			2.85927
$903$		−	2.45663e12i		−	0.122955i
$904$	−9.79644e12	+	9.79644e12i	−0.487877	+	0.487877i
$905$	−3.16987e12			−0.157081
$906$	−3.03732e13	+	3.03732e13i	−1.49766	+	1.49766i
$907$	8.82855e12	+	8.82855e12i	0.433168	+	0.433168i	0.889705	−	0.456536i	$-0.150910\pi$
$907$	8.82855e12	+	8.82855e12i	0.433168	+	0.433168i	−0.456536	+	0.889705i	$0.650910\pi$
$908$	−3.11005e12	−	3.11005e12i	−0.151838	−	0.151838i
$909$			8.86532e12i			0.430682i
$910$		−	7.18283e12i		−	0.347224i
$911$	−2.14427e13	−	2.14427e13i	−1.03145	−	1.03145i	−0.999489	−	0.0319569i	$-0.989826\pi$
$911$	−2.14427e13	−	2.14427e13i	−1.03145	−	1.03145i	−0.0319569	−	0.999489i	$-0.510174\pi$
$912$	−1.99917e12	−	1.99917e12i	−0.0956912	−	0.0956912i
$913$	−2.18952e13	+	2.18952e13i	−1.04287	+	1.04287i
$914$	−2.09624e13			−0.993534
$915$	−8.45045e12	+	8.45045e12i	−0.398552	+	0.398552i
$916$			5.12296e13i			2.40432i
$917$	2.40796e12			0.112457
$918$	−1.17937e13	+	1.23625e13i	−0.548098	+	0.574532i
$919$	3.21656e13			1.48755			0.743776	−	0.668429i	$-0.233033\pi$
$919$	3.21656e13			1.48755			0.743776	+	0.668429i	$0.233033\pi$
$920$		−	7.08039e12i		−	0.325846i
$921$	2.60192e12	−	2.60192e12i	0.119159	−	0.119159i
$922$	6.93289e13			3.15955
$923$	−3.69724e12	+	3.69724e12i	−0.167676	+	0.167676i
$924$	−1.39356e13	−	1.39356e13i	−0.628929	−	0.628929i
$925$	7.21581e12	+	7.21581e12i	0.324076	+	0.324076i
$926$		−	8.61256e12i		−	0.384931i
$927$		−	2.80569e13i		−	1.24790i
$928$	−6.95631e12	−	6.95631e12i	−0.307902	−	0.307902i
$929$	−2.70609e13	−	2.70609e13i	−1.19199	−	1.19199i	−0.976509	−	0.215476i	$-0.930870\pi$
$929$	−2.70609e13	−	2.70609e13i	−1.19199	−	1.19199i	−0.215476	−	0.976509i	$-0.569130\pi$
$930$	4.40754e13	−	4.40754e13i	1.93207	−	1.93207i
$931$	−3.98946e13			−1.74037
$932$	−1.23629e13	+	1.23629e13i	−0.536721	+	0.536721i
$933$			3.55767e13i			1.53709i
$934$	1.64367e13			0.706729
$935$	5.72871e13	−	1.34892e12i	2.45134	−	0.0577208i
$936$	1.93544e13			0.824210
$937$			1.50633e13i			0.638399i	0.947688	+	0.319199i	$0.103414\pi$
$937$			1.50633e13i			0.638399i	−0.947688	+	0.319199i	$0.896586\pi$
$938$	−9.41716e12	+	9.41716e12i	−0.397198	+	0.397198i
$939$	1.52211e12			0.0638925
$940$	5.29888e13	−	5.29888e13i	2.21365	−	2.21365i
$941$	−2.30773e12	−	2.30773e12i	−0.0959469	−	0.0959469i	0.657504	−	0.753451i	$-0.271612\pi$
$941$	−2.30773e12	−	2.30773e12i	−0.0959469	−	0.0959469i	−0.753451	+	0.657504i	$0.771612\pi$
$942$	−6.55024e13	−	6.55024e13i	−2.71037	−	2.71037i
$943$		−	5.46642e12i		−	0.225113i
$944$			1.34050e12i			0.0549404i
$945$	−3.01475e12	−	3.01475e12i	−0.122972	−	0.122972i
$946$	−1.57385e13	−	1.57385e13i	−0.638931	−	0.638931i
$947$	8.96737e12	−	8.96737e12i	0.362318	−	0.362318i	−0.502347	−	0.864666i	$-0.667530\pi$
$947$	8.96737e12	−	8.96737e12i	0.362318	−	0.362318i	0.864666	+	0.502347i	$0.167530\pi$
$948$	9.79203e13			3.93763
$949$	7.36235e12	−	7.36235e12i	0.294658	−	0.294658i
$950$			1.08537e14i			4.32338i
$951$	3.10937e13			1.23271
$952$	4.13160e12	−	4.33086e12i	0.163024	−	0.170887i
$953$	−4.11789e13			−1.61717			−0.808587	−	0.588377i	$-0.799767\pi$
$953$	−4.11789e13			−1.61717			−0.808587	+	0.588377i	$0.799767\pi$
$954$		−	3.68403e13i		−	1.43998i
$955$	−2.33338e13	+	2.33338e13i	−0.907759	+	0.907759i
$956$	2.02584e13			0.784414
$957$	1.98553e13	−	1.98553e13i	0.765198	−	0.765198i
$958$	−2.53340e13	−	2.53340e13i	−0.971759	−	0.971759i
$959$	2.34400e12	+	2.34400e12i	0.0894897	+	0.0894897i
$960$			1.00938e14i			3.83561i
$961$			1.32874e13i			0.502557i
$962$	5.79330e12	+	5.79330e12i	0.218091	+	0.218091i
$963$	−1.39833e13	−	1.39833e13i	−0.523952	−	0.523952i
$964$	−2.97458e13	+	2.97458e13i	−1.10938	+	1.10938i
$965$	5.37283e13			1.99448
$966$	−2.15753e12	+	2.15753e12i	−0.0797187	+	0.0797187i
$967$			6.11328e12i			0.224831i	0.993661	+	0.112415i	$0.0358587\pi$
$967$			6.11328e12i			0.224831i	−0.993661	+	0.112415i	$0.964141\pi$
$968$	−4.12657e13			−1.51060
$969$	−5.55182e13	−	5.29638e13i	−2.02292	−	1.92984i
$970$	3.30552e13			1.19885
$971$			1.20763e13i			0.435960i	0.975953	+	0.217980i	$0.0699468\pi$
$971$			1.20763e13i			0.435960i	−0.975953	+	0.217980i	$0.930053\pi$
$972$	−4.40897e13	+	4.40897e13i	−1.58431	+	1.58431i
$973$	3.97139e12			0.142048
$974$	9.21096e12	−	9.21096e12i	0.327936	−	0.327936i
$975$	−2.64738e13	−	2.64738e13i	−0.938202	−	0.938202i
$976$	2.29342e11	+	2.29342e11i	0.00809019	+	0.00809019i
$977$		−	2.07066e13i		−	0.727082i	−0.931578	−	0.363541i	$-0.881568\pi$
$977$		−	2.07066e13i		−	0.727082i	0.931578	−	0.363541i	$-0.118432\pi$
$978$		−	1.19158e14i		−	4.16483i
$979$	2.54079e13	+	2.54079e13i	0.883990	+	0.883990i
$980$	−4.96878e13	−	4.96878e13i	−1.72081	−	1.72081i
$981$	−6.12769e12	+	6.12769e12i	−0.211245	+	0.211245i
$982$	−5.28808e13			−1.81466
$983$	3.64493e13	−	3.64493e13i	1.24508	−	1.24508i	0.287216	−	0.957866i	$-0.407270\pi$
$983$	3.64493e13	−	3.64493e13i	1.24508	−	1.24508i	0.957866	−	0.287216i	$-0.0927298\pi$
$984$		−	5.22924e13i		−	1.77812i
$985$	1.06845e13			0.361651
$986$	1.58200e13	+	1.50921e13i	0.533041	+	0.508516i
$987$	−1.25960e13			−0.422480
$988$			5.41262e13i			1.80718i
$989$	−1.51350e12	+	1.51350e12i	−0.0503036	+	0.0503036i
$990$	−1.59032e14			−5.26172
$991$	−3.59955e12	+	3.59955e12i	−0.118554	+	0.118554i	−0.763895	−	0.645341i	$-0.776715\pi$
$991$	−3.59955e12	+	3.59955e12i	−0.118554	+	0.118554i	0.645341	+	0.763895i	$0.276715\pi$
$992$	1.46069e13	+	1.46069e13i	0.478912	+	0.478912i
$993$	−1.50899e12	−	1.50899e12i	−0.0492511	−	0.0492511i
$994$		−	4.48770e12i		−	0.145809i
$995$		−	3.58552e13i		−	1.15971i
$996$	5.16398e13	+	5.16398e13i	1.66271	+	1.66271i
$997$	3.59897e13	+	3.59897e13i	1.15359	+	1.15359i	0.985828	+	0.167758i	$0.0536526\pi$
$997$	3.59897e13	+	3.59897e13i	1.15359	+	1.15359i	0.167758	+	0.985828i	$0.446347\pi$
$998$	−2.25649e13	+	2.25649e13i	−0.720023	+	0.720023i
$999$	4.86307e12			0.154478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.4.2	✓	24
17.8	even	8		289.10.a.f.1.3		24
17.9	even	8		289.10.a.f.1.4		24
17.13	even	4	inner	17.10.c.a.13.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.2	✓	24	1.1	even	1	trivial
17.10.c.a.13.11	yes	24	17.13	even	4	inner
289.10.a.f.1.3		24	17.8	even	8
289.10.a.f.1.4		24	17.9	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)

\(f(q)\)	\(=\)	\(q-36.7615i q^{2} +(151.130 - 151.130i) q^{3} -839.411 q^{4} +(-1546.81 + 1546.81i) q^{5} +(-5555.78 - 5555.78i) q^{6} +(-1021.13 - 1021.13i) q^{7} +12036.1i q^{8} -25997.7i q^{9} +O(q^{10})\)	\(q-36.7615i q^{2} +(151.130 - 151.130i) q^{3} -839.411 q^{4} +(-1546.81 + 1546.81i) q^{5} +(-5555.78 - 5555.78i) q^{6} +(-1021.13 - 1021.13i) q^{7} +12036.1i q^{8} -25997.7i q^{9} +(56863.1 + 56863.1i) q^{10} +(-53788.6 - 53788.6i) q^{11} +(-126860. + 126860. i) q^{12} +61852.4 q^{13} +(-37538.2 + 37538.2i) q^{14} +467539. i q^{15} +12688.8 q^{16} +(344270. - 8106.40i) q^{17} -955716. q^{18} -1.04250e6i q^{19} +(1.29841e6 - 1.29841e6i) q^{20} -308646. q^{21} +(-1.97735e6 + 1.97735e6i) q^{22} +(190153. + 190153. i) q^{23} +(1.81903e6 + 1.81903e6i) q^{24} -2.83211e6i q^{25} -2.27379e6i q^{26} +(-954344. - 954344. i) q^{27} +(857144. + 857144. i) q^{28} +(-1.22125e6 + 1.22125e6i) q^{29} +1.71875e7 q^{30} +(2.56439e6 - 2.56439e6i) q^{31} +5.69605e6i q^{32} -1.62582e7 q^{33} +(-298004. - 1.26559e7i) q^{34} +3.15897e6 q^{35} +2.18228e7i q^{36} +(-2.54786e6 + 2.54786e6i) q^{37} -3.83239e7 q^{38} +(9.34776e6 - 9.34776e6i) q^{39} +(-1.86176e7 - 1.86176e7i) q^{40} +(-1.43737e7 - 1.43737e7i) q^{41} +1.13463e7i q^{42} +7.95939e6i q^{43} +(4.51508e7 + 4.51508e7i) q^{44} +(4.02135e7 + 4.02135e7i) q^{45} +(6.99032e6 - 6.99032e6i) q^{46} +4.08106e7 q^{47} +(1.91766e6 - 1.91766e6i) q^{48} -3.82682e7i q^{49} -1.04113e8 q^{50} +(5.08046e7 - 5.32548e7i) q^{51} -5.19196e7 q^{52} +3.85473e7i q^{53} +(-3.50832e7 + 3.50832e7i) q^{54} +1.66401e8 q^{55} +(1.22904e7 - 1.22904e7i) q^{56} +(-1.57553e8 - 1.57553e8i) q^{57} +(4.48951e7 + 4.48951e7i) q^{58} +1.05644e8i q^{59} -3.92458e8i q^{60} +(1.80743e7 + 1.80743e7i) q^{61} +(-9.42710e7 - 9.42710e7i) q^{62} +(-2.65469e7 + 2.65469e7i) q^{63} +2.15892e8 q^{64} +(-9.56737e7 + 9.56737e7i) q^{65} +5.97676e8i q^{66} +2.50869e8 q^{67} +(-2.88985e8 + 6.80460e6i) q^{68} +5.74757e7 q^{69} -1.16129e8i q^{70} +(-5.97752e7 + 5.97752e7i) q^{71} +3.12912e8 q^{72} +(1.19031e8 - 1.19031e8i) q^{73} +(9.36633e7 + 9.36633e7i) q^{74} +(-4.28017e8 - 4.28017e8i) q^{75} +8.75087e8i q^{76} +1.09850e8i q^{77} +(-3.43638e8 - 3.43638e8i) q^{78} +(-3.85937e8 - 3.85937e8i) q^{79} +(-1.96272e7 + 1.96272e7i) q^{80} +2.23252e8 q^{81} +(-5.28401e8 + 5.28401e8i) q^{82} -4.07060e8i q^{83} +2.59081e8 q^{84} +(-5.19981e8 + 5.45059e8i) q^{85} +2.92599e8 q^{86} +3.69136e8i q^{87} +(6.47408e8 - 6.47408e8i) q^{88} -4.72366e8 q^{89} +(1.47831e9 - 1.47831e9i) q^{90} +(-6.31590e7 - 6.31590e7i) q^{91} +(-1.59617e8 - 1.59617e8i) q^{92} -7.75114e8i q^{93} -1.50026e9i q^{94} +(1.61255e9 + 1.61255e9i) q^{95} +(8.60845e8 + 8.60845e8i) q^{96} +(2.90656e8 - 2.90656e8i) q^{97} -1.40680e9 q^{98} +(-1.39838e9 + 1.39838e9i) 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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