LMFDB - Embedded newform 17.10.c.a.13.5

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			13.5
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.9147i q^{2} +(-71.7165 - 71.7165i) q^{3} +345.210 q^{4} +(1469.78 + 1469.78i) q^{5} +(-926.198 + 926.198i) q^{6} +(1528.49 - 1528.49i) q^{7} -11070.6i q^{8} -9396.49i q^{9} +O(q^{10})$	\(q-12.9147i q^{2} +(-71.7165 - 71.7165i) q^{3} +345.210 q^{4} +(1469.78 + 1469.78i) q^{5} +(-926.198 + 926.198i) q^{6} +(1528.49 - 1528.49i) q^{7} -11070.6i q^{8} -9396.49i q^{9} +(18981.8 - 18981.8i) q^{10} +(9296.34 - 9296.34i) q^{11} +(-24757.3 - 24757.3i) q^{12} +17852.0 q^{13} +(-19740.0 - 19740.0i) q^{14} -210815. i q^{15} +33773.6 q^{16} +(182508. - 292025. i) q^{17} -121353. q^{18} +30951.0i q^{19} +(507384. + 507384. i) q^{20} -219236. q^{21} +(-120060. - 120060. i) q^{22} +(136941. - 136941. i) q^{23} +(-793947. + 793947. i) q^{24} +2.36740e6i q^{25} -230553. i q^{26} +(-2.08548e6 + 2.08548e6i) q^{27} +(527650. - 527650. i) q^{28} +(1.29550e6 + 1.29550e6i) q^{29} -2.72262e6 q^{30} +(371750. + 371750. i) q^{31} -6.10434e6i q^{32} -1.33340e6 q^{33} +(-3.77143e6 - 2.35703e6i) q^{34} +4.49310e6 q^{35} -3.24376e6i q^{36} +(1.26009e7 + 1.26009e7i) q^{37} +399723. q^{38} +(-1.28028e6 - 1.28028e6i) q^{39} +(1.62714e7 - 1.62714e7i) q^{40} +(-1.08697e7 + 1.08697e7i) q^{41} +2.83137e6i q^{42} -4.23089e7i q^{43} +(3.20919e6 - 3.20919e6i) q^{44} +(1.38108e7 - 1.38108e7i) q^{45} +(-1.76855e6 - 1.76855e6i) q^{46} -5.91782e7 q^{47} +(-2.42212e6 - 2.42212e6i) q^{48} +3.56810e7i q^{49} +3.05743e7 q^{50} +(-3.40319e7 + 7.85424e6i) q^{51} +6.16269e6 q^{52} +8.32863e7i q^{53} +(2.69334e7 + 2.69334e7i) q^{54} +2.73272e7 q^{55} +(-1.69213e7 - 1.69213e7i) q^{56} +(2.21970e6 - 2.21970e6i) q^{57} +(1.67310e7 - 1.67310e7i) q^{58} +9.24034e7i q^{59} -7.27756e7i q^{60} +(-7.20746e7 + 7.20746e7i) q^{61} +(4.80105e6 - 4.80105e6i) q^{62} +(-1.43624e7 - 1.43624e7i) q^{63} -6.15437e7 q^{64} +(2.62385e7 + 2.62385e7i) q^{65} +1.72205e7i q^{66} +1.25363e8 q^{67} +(6.30035e7 - 1.00810e8i) q^{68} -1.96418e7 q^{69} -5.80271e7i q^{70} +(-1.51869e8 - 1.51869e8i) q^{71} -1.04025e8 q^{72} +(-7.28077e7 - 7.28077e7i) q^{73} +(1.62737e8 - 1.62737e8i) q^{74} +(1.69782e8 - 1.69782e8i) q^{75} +1.06846e7i q^{76} -2.84187e7i q^{77} +(-1.65345e7 + 1.65345e7i) q^{78} +(6.78112e6 - 6.78112e6i) q^{79} +(4.96398e7 + 4.96398e7i) q^{80} +1.14176e8 q^{81} +(1.40379e8 + 1.40379e8i) q^{82} +6.13699e8i q^{83} -7.56824e7 q^{84} +(6.97461e8 - 1.60967e8i) q^{85} -5.46408e8 q^{86} -1.85817e8i q^{87} +(-1.02916e8 - 1.02916e8i) q^{88} -5.89040e8 q^{89} +(-1.78363e8 - 1.78363e8i) q^{90} +(2.72866e7 - 2.72866e7i) q^{91} +(4.72733e7 - 4.72733e7i) q^{92} -5.33212e7i q^{93} +7.64270e8i q^{94} +(-4.54912e7 + 4.54912e7i) q^{95} +(-4.37782e8 + 4.37782e8i) q^{96} +(6.15665e8 + 6.15665e8i) q^{97} +4.60811e8 q^{98} +(-8.73530e7 - 8.73530e7i) 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 $

$2$		−	12.9147i		−	0.570755i	−0.958415	−	0.285378i	$-0.907881\pi$
$2$		−	12.9147i		−	0.570755i	0.958415	−	0.285378i	$-0.0921190\pi$
$3$	−71.7165	−	71.7165i	−0.511180	−	0.511180i	0.403708	−	0.914888i	$-0.367721\pi$
$3$	−71.7165	−	71.7165i	−0.511180	−	0.511180i	−0.914888	+	0.403708i	$0.867721\pi$
$4$	345.210			0.674238
$5$	1469.78	+	1469.78i	1.05169	+	1.05169i	0.998589	+	0.0531021i	$0.0169109\pi$
$5$	1469.78	+	1469.78i	1.05169	+	1.05169i	0.0531021	+	0.998589i	$0.483089\pi$
$6$	−926.198	+	926.198i	−0.291758	+	0.291758i
$7$	1528.49	−	1528.49i	0.240614	−	0.240614i	−0.576490	−	0.817104i	$-0.695578\pi$
$7$	1528.49	−	1528.49i	0.240614	−	0.240614i	0.817104	+	0.576490i	$0.195578\pi$
$8$		−	11070.6i		−	0.955580i
$9$		−	9396.49i		−	0.477391i
$10$	18981.8	−	18981.8i	0.600258	−	0.600258i
$11$	9296.34	−	9296.34i	0.191445	−	0.191445i	−0.604875	−	0.796320i	$-0.706777\pi$
$11$	9296.34	−	9296.34i	0.191445	−	0.191445i	0.796320	+	0.604875i	$0.206777\pi$
$12$	−24757.3	−	24757.3i	−0.344657	−	0.344657i
$13$	17852.0			0.173357			0.0866785	−	0.996236i	$-0.472375\pi$
$13$	17852.0			0.173357			0.0866785	+	0.996236i	$0.472375\pi$
$14$	−19740.0	−	19740.0i	−0.137332	−	0.137332i
$15$		−	210815.i		−	1.07521i
$16$	33773.6			0.128836
$17$	182508.	−	292025.i	0.529982	−	0.848009i
$17$	182508.	−	292025.i	0.529982	−	0.848009i
$18$	−121353.			−0.272473
$19$			30951.0i			0.0544858i	0.999629	+	0.0272429i	$0.00867276\pi$
$19$			30951.0i			0.0544858i	−0.999629	+	0.0272429i	$0.991327\pi$
$20$	507384.	+	507384.i	0.709091	+	0.709091i
$21$	−219236.			−0.245994
$22$	−120060.	−	120060.i	−0.109269	−	0.109269i
$23$	136941.	−	136941.i	0.102037	−	0.102037i	−0.654245	−	0.756282i	$-0.727014\pi$
$23$	136941.	−	136941.i	0.102037	−	0.102037i	0.756282	+	0.654245i	$0.227014\pi$
$24$	−793947.	+	793947.i	−0.488473	+	0.488473i
$25$			2.36740e6i			1.21211i
$26$		−	230553.i		−	0.0989444i
$27$	−2.08548e6	+	2.08548e6i	−0.755212	+	0.755212i
$28$	527650.	−	527650.i	0.162231	−	0.162231i
$29$	1.29550e6	+	1.29550e6i	0.340130	+	0.340130i	0.856416	−	0.516286i	$-0.172686\pi$
$29$	1.29550e6	+	1.29550e6i	0.340130	+	0.340130i	−0.516286	+	0.856416i	$0.672686\pi$
$30$	−2.72262e6			−0.613680
$31$	371750.	+	371750.i	0.0722975	+	0.0722975i	0.742331	−	0.670033i	$-0.233720\pi$
$31$	371750.	+	371750.i	0.0722975	+	0.0722975i	−0.670033	+	0.742331i	$0.733720\pi$
$32$		−	6.10434e6i		−	1.02911i
$33$	−1.33340e6			−0.195726
$34$	−3.77143e6	−	2.35703e6i	−0.484006	−	0.302490i
$35$	4.49310e6			0.506104
$36$		−	3.24376e6i		−	0.321875i
$37$	1.26009e7	+	1.26009e7i	1.10534	+	1.10534i	0.993755	+	0.111581i	$0.0355915\pi$
$37$	1.26009e7	+	1.26009e7i	1.10534	+	1.10534i	0.111581	+	0.993755i	$0.464408\pi$
$38$	399723.			0.0310981
$39$	−1.28028e6	−	1.28028e6i	−0.0886166	−	0.0886166i
$40$	1.62714e7	−	1.62714e7i	1.00498	−	1.00498i
$41$	−1.08697e7	+	1.08697e7i	−0.600745	+	0.600745i	−0.940510	−	0.339765i	$-0.889652\pi$
$41$	−1.08697e7	+	1.08697e7i	−0.600745	+	0.600745i	0.339765	+	0.940510i	$0.389652\pi$
$42$			2.83137e6i			0.140402i
$43$		−	4.23089e7i		−	1.88723i	−0.331051	−	0.943613i	$-0.607403\pi$
$43$		−	4.23089e7i		−	1.88723i	0.331051	−	0.943613i	$-0.392597\pi$
$44$	3.20919e6	−	3.20919e6i	0.129080	−	0.129080i
$45$	1.38108e7	−	1.38108e7i	0.502068	−	0.502068i
$46$	−1.76855e6	−	1.76855e6i	−0.0582381	−	0.0582381i
$47$	−5.91782e7			−1.76897			−0.884487	−	0.466565i	$-0.845491\pi$
$47$	−5.91782e7			−1.76897			−0.884487	+	0.466565i	$0.845491\pi$
$48$	−2.42212e6	−	2.42212e6i	−0.0658583	−	0.0658583i
$49$			3.56810e7i			0.884210i
$50$	3.05743e7			0.691817
$51$	−3.40319e7	+	7.85424e6i	−0.704401	+	0.162569i
$52$	6.16269e6			0.116884
$53$			8.32863e7i			1.44988i	0.688811	+	0.724941i	$0.258133\pi$
$53$			8.32863e7i			1.44988i	−0.688811	+	0.724941i	$0.741867\pi$
$54$	2.69334e7	+	2.69334e7i	0.431041	+	0.431041i
$55$	2.73272e7			0.402683
$56$	−1.69213e7	−	1.69213e7i	−0.229926	−	0.229926i
$57$	2.21970e6	−	2.21970e6i	0.0278520	−	0.0278520i
$58$	1.67310e7	−	1.67310e7i	0.194131	−	0.194131i
$59$			9.24034e7i			0.992782i	0.868099	+	0.496391i	$0.165342\pi$
$59$			9.24034e7i			0.992782i	−0.868099	+	0.496391i	$0.834658\pi$
$60$		−	7.27756e7i		−	0.724945i
$61$	−7.20746e7	+	7.20746e7i	−0.666496	+	0.666496i	−0.956903	−	0.290407i	$-0.906209\pi$
$61$	−7.20746e7	+	7.20746e7i	−0.666496	+	0.666496i	0.290407	+	0.956903i	$0.406209\pi$
$62$	4.80105e6	−	4.80105e6i	0.0412642	−	0.0412642i
$63$	−1.43624e7	−	1.43624e7i	−0.114867	−	0.114867i
$64$	−6.15437e7			−0.458536
$65$	2.62385e7	+	2.62385e7i	0.182318	+	0.182318i
$66$			1.72205e7i			0.111712i
$67$	1.25363e8			0.760031			0.380015	−	0.924980i	$-0.375919\pi$
$67$	1.25363e8			0.760031			0.380015	+	0.924980i	$0.375919\pi$
$68$	6.30035e7	−	1.00810e8i	0.357334	−	0.571760i
$69$	−1.96418e7			−0.104318
$70$		−	5.80271e7i		−	0.288861i
$71$	−1.51869e8	−	1.51869e8i	−0.709261	−	0.709261i	0.257119	−	0.966380i	$-0.417227\pi$
$71$	−1.51869e8	−	1.51869e8i	−0.709261	−	0.709261i	−0.966380	+	0.257119i	$0.917227\pi$
$72$	−1.04025e8			−0.456185
$73$	−7.28077e7	−	7.28077e7i	−0.300071	−	0.300071i	0.540970	−	0.841042i	$-0.318057\pi$
$73$	−7.28077e7	−	7.28077e7i	−0.300071	−	0.300071i	−0.841042	+	0.540970i	$0.818057\pi$
$74$	1.62737e8	−	1.62737e8i	0.630877	−	0.630877i
$75$	1.69782e8	−	1.69782e8i	0.619605	−	0.619605i
$76$			1.06846e7i			0.0367364i
$77$		−	2.84187e7i		−	0.0921290i
$78$	−1.65345e7	+	1.65345e7i	−0.0505784	+	0.0505784i
$79$	6.78112e6	−	6.78112e6i	0.0195875	−	0.0195875i	−0.697245	−	0.716833i	$-0.745591\pi$
$79$	6.78112e6	−	6.78112e6i	0.0195875	−	0.0195875i	0.716833	+	0.697245i	$0.245591\pi$
$80$	4.96398e7	+	4.96398e7i	0.135496	+	0.135496i
$81$	1.14176e8			0.294707
$82$	1.40379e8	+	1.40379e8i	0.342879	+	0.342879i
$83$			6.13699e8i			1.41940i	0.704505	+	0.709699i	$0.251169\pi$
$83$			6.13699e8i			1.41940i	−0.704505	+	0.709699i	$0.748831\pi$
$84$	−7.56824e7			−0.165859
$85$	6.97461e8	−	1.60967e8i	1.44922	−	0.334467i
$86$	−5.46408e8			−1.07714
$87$		−	1.85817e8i		−	0.347735i
$88$	−1.02916e8	−	1.02916e8i	−0.182942	−	0.182942i
$89$	−5.89040e8			−0.995153			−0.497576	−	0.867420i	$-0.665777\pi$
$89$	−5.89040e8			−0.995153			−0.497576	+	0.867420i	$0.665777\pi$
$90$	−1.78363e8	−	1.78363e8i	−0.286558	−	0.286558i
$91$	2.72866e7	−	2.72866e7i	0.0417122	−	0.0417122i
$92$	4.72733e7	−	4.72733e7i	0.0687972	−	0.0687972i
$93$		−	5.33212e7i		−	0.0739140i
$94$			7.64270e8i			1.00965i
$95$	−4.54912e7	+	4.54912e7i	−0.0573022	+	0.0573022i
$96$	−4.37782e8	+	4.37782e8i	−0.526062	+	0.526062i
$97$	6.15665e8	+	6.15665e8i	0.706109	+	0.706109i	0.965715	−	0.259605i	$-0.0835925\pi$
$97$	6.15665e8	+	6.15665e8i	0.706109	+	0.706109i	−0.259605	+	0.965715i	$0.583593\pi$
$98$	4.60811e8			0.504667
$99$	−8.73530e7	−	8.73530e7i	−0.0913943	−	0.0913943i
$100$			8.17250e8i			0.817250i
$101$	−1.76796e9			−1.69054			−0.845271	−	0.534338i	$-0.820561\pi$
$101$	−1.76796e9			−1.69054			−0.845271	+	0.534338i	$0.820561\pi$
$102$	1.01435e8	+	4.39512e8i	0.0927872	+	0.402040i
$103$	8.32197e8			0.728549			0.364275	−	0.931292i	$-0.381317\pi$
$103$	8.32197e8			0.728549			0.364275	+	0.931292i	$0.381317\pi$
$104$		−	1.97633e8i		−	0.165657i
$105$	−3.22229e8	−	3.22229e8i	−0.258710	−	0.258710i
$106$	1.07562e9			0.827527
$107$	−1.05847e9	−	1.05847e9i	−0.780638	−	0.780638i	0.199301	−	0.979938i	$-0.436133\pi$
$107$	−1.05847e9	−	1.05847e9i	−0.780638	−	0.780638i	−0.979938	+	0.199301i	$0.936133\pi$
$108$	−7.19928e8	+	7.19928e8i	−0.509193	+	0.509193i
$109$	8.84730e8	−	8.84730e8i	0.600332	−	0.600332i	−0.340068	−	0.940401i	$-0.610450\pi$
$109$	8.84730e8	−	8.84730e8i	0.600332	−	0.600332i	0.940401	+	0.340068i	$0.110450\pi$
$110$		−	3.52923e8i		−	0.229833i
$111$		−	1.80739e9i		−	1.13005i
$112$	5.16225e7	−	5.16225e7i	0.0309998	−	0.0309998i
$113$	1.85397e9	−	1.85397e9i	1.06967	−	1.06967i	0.0722833	−	0.997384i	$-0.476971\pi$
$113$	1.85397e9	−	1.85397e9i	1.06967	−	1.06967i	0.997384	−	0.0722833i	$-0.0230286\pi$
$114$	−2.86668e7	−	2.86668e7i	−0.0158967	−	0.0158967i
$115$	4.02546e8			0.214623
$116$	4.47218e8	+	4.47218e8i	0.229329	+	0.229329i
$117$		−	1.67746e8i		−	0.0827591i
$118$	1.19336e9			0.566636
$119$	−1.67397e8	−	7.25319e8i	−0.0765219	−	0.331564i
$120$	−2.33386e9			−1.02745
$121$			2.18510e9i			0.926697i
$122$	9.30823e8	+	9.30823e8i	0.380406	+	0.380406i
$123$	1.55907e9			0.614178
$124$	1.28332e8	+	1.28332e8i	0.0487458	+	0.0487458i
$125$	−6.08894e8	+	6.08894e8i	−0.223073	+	0.223073i
$126$	−1.85487e8	+	1.85487e8i	−0.0655610	+	0.0655610i
$127$		−	3.13001e9i		−	1.06765i	−0.845595	−	0.533825i	$-0.820754\pi$
$127$		−	3.13001e9i		−	1.06765i	0.845595	−	0.533825i	$-0.179246\pi$
$128$		−	2.33060e9i		−	0.767402i
$129$	−3.03425e9	+	3.03425e9i	−0.964711	+	0.964711i
$130$	3.38863e8	−	3.38863e8i	0.104059	−	0.104059i
$131$	9.29768e8	+	9.29768e8i	0.275838	+	0.275838i	0.831445	−	0.555607i	$-0.187514\pi$
$131$	9.29768e8	+	9.29768e8i	0.275838	+	0.275838i	−0.555607	+	0.831445i	$0.687514\pi$
$132$	−4.60304e8			−0.131966
$133$	4.73083e7	+	4.73083e7i	0.0131101	+	0.0131101i
$134$		−	1.61902e9i		−	0.433792i
$135$	−6.13040e9			−1.58850
$136$	−3.23290e9	−	2.02047e9i	−0.810341	−	0.506440i
$137$	5.14400e8			0.124755			0.0623775	−	0.998053i	$-0.480132\pi$
$137$	5.14400e8			0.124755			0.0623775	+	0.998053i	$0.480132\pi$
$138$			2.53668e8i			0.0595402i
$139$	5.52824e9	+	5.52824e9i	1.25609	+	1.25609i	0.952944	+	0.303145i	$0.0980366\pi$
$139$	5.52824e9	+	5.52824e9i	1.25609	+	1.25609i	0.303145	+	0.952944i	$0.401963\pi$
$140$	1.55106e9			0.341235
$141$	4.24405e9	+	4.24405e9i	0.904263	+	0.904263i
$142$	−1.96134e9	+	1.96134e9i	−0.404814	+	0.404814i
$143$	1.65958e8	−	1.65958e8i	0.0331884	−	0.0331884i
$144$		−	3.17353e8i		−	0.0615051i
$145$			3.80820e9i			0.715424i
$146$	−9.40291e8	+	9.40291e8i	−0.171267	+	0.171267i
$147$	2.55892e9	−	2.55892e9i	0.451990	−	0.451990i
$148$	4.34997e9	+	4.34997e9i	0.745260	+	0.745260i
$149$	−8.47199e9			−1.40814			−0.704072	−	0.710128i	$-0.748637\pi$
$149$	−8.47199e9			−1.40814			−0.704072	+	0.710128i	$0.748637\pi$
$150$	−2.19268e9	−	2.19268e9i	−0.353643	−	0.353643i
$151$			1.13940e9i			0.178353i	0.996016	+	0.0891766i	$0.0284236\pi$
$151$			1.13940e9i			0.178353i	−0.996016	+	0.0891766i	$0.971576\pi$
$152$	3.42647e8			0.0520656
$153$	−2.74401e9	−	1.71493e9i	−0.404832	−	0.253008i
$154$	−3.67020e8			−0.0525831
$155$			1.09278e9i			0.152069i
$156$	−4.41966e8	−	4.41966e8i	−0.0597487	−	0.0597487i
$157$	3.27009e9			0.429547			0.214774	−	0.976664i	$-0.431099\pi$
$157$	3.27009e9			0.429547			0.214774	+	0.976664i	$0.431099\pi$
$158$	−8.75762e7	−	8.75762e7i	−0.0111797	−	0.0111797i
$159$	5.97301e9	−	5.97301e9i	0.741150	−	0.741150i
$160$	8.97205e9	−	8.97205e9i	1.08231	−	1.08231i
$161$		−	4.18625e8i		−	0.0491030i
$162$		−	1.47454e9i		−	0.168206i
$163$	−1.48147e9	+	1.48147e9i	−0.164380	+	0.164380i	−0.784504	−	0.620124i	$-0.787082\pi$
$163$	−1.48147e9	+	1.48147e9i	−0.164380	+	0.164380i	0.620124	+	0.784504i	$0.287082\pi$
$164$	−3.75233e9	+	3.75233e9i	−0.405046	+	0.405046i
$165$	−1.95981e9	−	1.95981e9i	−0.205843	−	0.205843i
$166$	7.92575e9			0.810129
$167$	−9.95815e9	−	9.95815e9i	−0.990728	−	0.990728i	0.00922917	−	0.999957i	$-0.497062\pi$
$167$	−9.95815e9	−	9.95815e9i	−0.990728	−	0.990728i	−0.999957	+	0.00922917i	$0.997062\pi$
$168$			2.42708e9i			0.235067i
$169$	−1.02858e10			−0.969947
$170$	−2.07885e9	−	9.00751e9i	−0.190899	−	0.827150i
$171$	2.90831e8			0.0260110
$172$		−	1.46055e10i		−	1.27244i
$173$	2.81899e9	+	2.81899e9i	0.239268	+	0.239268i	0.816547	−	0.577279i	$-0.195885\pi$
$173$	2.81899e9	+	2.81899e9i	0.239268	+	0.239268i	−0.577279	+	0.816547i	$0.695885\pi$
$174$	−2.39977e9			−0.198472
$175$	3.61855e9	+	3.61855e9i	0.291651	+	0.291651i
$176$	3.13971e8	−	3.13971e8i	0.0246651	−	0.0246651i
$177$	6.62685e9	−	6.62685e9i	0.507490	−	0.507490i
$178$			7.60728e9i			0.567989i
$179$			1.82891e10i			1.33154i	0.746158	+	0.665769i	$0.231896\pi$
$179$			1.82891e10i			1.33154i	−0.746158	+	0.665769i	$0.768104\pi$
$180$	4.76763e9	−	4.76763e9i	0.338513	−	0.338513i
$181$	7.93111e9	−	7.93111e9i	0.549263	−	0.549263i	−0.376965	−	0.926228i	$-0.623032\pi$
$181$	7.93111e9	−	7.93111e9i	0.549263	−	0.549263i	0.926228	+	0.376965i	$0.123032\pi$
$182$	−3.52398e8	−	3.52398e8i	−0.0238074	−	0.0238074i
$183$	1.03379e10			0.681399
$184$	−1.51602e9	−	1.51602e9i	−0.0975044	−	0.0975044i
$185$			3.70412e10i			2.32495i
$186$	−6.88628e8			−0.0421868
$187$	−1.01812e9	−	4.41142e9i	−0.0608849	−	0.263810i
$188$	−2.04289e10			−1.19271
$189$			6.37527e9i			0.363430i
$190$	5.87507e8	+	5.87507e8i	0.0327056	+	0.0327056i
$191$	6.63597e9			0.360790			0.180395	−	0.983594i	$-0.442262\pi$
$191$	6.63597e9			0.360790			0.180395	+	0.983594i	$0.442262\pi$
$192$	4.41370e9	+	4.41370e9i	0.234394	+	0.234394i
$193$	−9.08302e9	+	9.08302e9i	−0.471218	+	0.471218i	−0.902309	−	0.431090i	$-0.858129\pi$
$193$	−9.08302e9	+	9.08302e9i	−0.471218	+	0.471218i	0.431090	+	0.902309i	$0.358129\pi$
$194$	7.95114e9	−	7.95114e9i	0.403016	−	0.403016i
$195$		−	3.76347e9i		−	0.186395i
$196$			1.23175e10i			0.596168i
$197$	−6.47024e9	+	6.47024e9i	−0.306071	+	0.306071i	−0.843383	−	0.537312i	$-0.819440\pi$
$197$	−6.47024e9	+	6.47024e9i	−0.306071	+	0.306071i	0.537312	+	0.843383i	$0.319440\pi$
$198$	−1.12814e9	+	1.12814e9i	−0.0521638	+	0.0521638i
$199$	−2.84352e10	−	2.84352e10i	−1.28534	−	1.28534i	−0.937588	−	0.347749i	$-0.886946\pi$
$199$	−2.84352e10	−	2.84352e10i	−1.28534	−	1.28534i	−0.347749	−	0.937588i	$-0.613054\pi$
$200$	2.62086e10			1.15827
$201$	−8.99056e9	−	8.99056e9i	−0.388512	−	0.388512i
$202$			2.28327e10i			0.964886i
$203$	3.96030e9			0.163680
$204$	−1.17481e10	+	2.71136e9i	−0.474934	+	0.109610i
$205$	−3.19522e10			−1.26360
$206$		−	1.07476e10i		−	0.415823i
$207$	−1.28676e9	−	1.28676e9i	−0.0487115	−	0.0487115i
$208$	6.02925e8			0.0223346
$209$	2.87731e8	+	2.87731e8i	0.0104311	+	0.0104311i
$210$	−4.16150e9	+	4.16150e9i	−0.147660	+	0.147660i
$211$	6.41392e9	−	6.41392e9i	0.222768	−	0.222768i	−0.586895	−	0.809663i	$-0.699650\pi$
$211$	6.41392e9	−	6.41392e9i	0.222768	−	0.222768i	0.809663	+	0.586895i	$0.199650\pi$
$212$			2.87513e10i			0.977566i
$213$			2.17830e10i			0.725119i
$214$	−1.36698e10	+	1.36698e10i	−0.445553	+	0.445553i
$215$	6.21849e10	−	6.21849e10i	1.98478	−	1.98478i
$216$	2.30876e10	+	2.30876e10i	0.721666	+	0.721666i
$217$	1.13643e9			0.0347916
$218$	−1.14260e10	−	1.14260e10i	−0.342643	−	0.342643i
$219$			1.04430e10i			0.306781i
$220$	9.43363e9			0.271504
$221$	3.25812e9	−	5.21323e9i	0.0918760	−	0.147008i
$222$	−2.33419e10			−0.644982
$223$		−	2.83923e10i		−	0.768827i	−0.923161	−	0.384414i	$-0.874404\pi$
$223$		−	2.83923e10i		−	0.768827i	0.923161	−	0.384414i	$-0.125596\pi$
$224$	−9.33041e9	−	9.33041e9i	−0.247620	−	0.247620i
$225$	2.22452e10			0.578650
$226$	−2.39434e10	−	2.39434e10i	−0.610518	−	0.610518i
$227$	5.47361e10	−	5.47361e10i	1.36822	−	1.36822i	0.505252	−	0.862972i	$-0.331400\pi$
$227$	5.47361e10	−	5.47361e10i	1.36822	−	1.36822i	0.862972	−	0.505252i	$-0.168600\pi$
$228$	7.66262e8	−	7.66262e8i	0.0187789	−	0.0187789i
$229$		−	1.04661e9i		−	0.0251492i	−0.999921	−	0.0125746i	$-0.995997\pi$
$229$		−	1.04661e9i		−	0.0251492i	0.999921	−	0.0125746i	$-0.00400272\pi$
$230$		−	5.19877e9i		−	0.122497i
$231$	−2.03809e9	+	2.03809e9i	−0.0470945	+	0.0470945i
$232$	1.43419e10	−	1.43419e10i	0.325022	−	0.325022i
$233$	4.30006e10	+	4.30006e10i	0.955814	+	0.955814i	0.999064	−	0.0432505i	$-0.0137714\pi$
$233$	4.30006e10	+	4.30006e10i	0.955814	+	0.955814i	−0.0432505	+	0.999064i	$0.513771\pi$
$234$	−2.16639e9			−0.0472352
$235$	−8.69791e10	−	8.69791e10i	−1.86041	−	1.86041i
$236$			3.18986e10i			0.669372i
$237$	−9.72636e8			−0.0200255
$238$	−9.36729e9	+	2.16188e9i	−0.189242	+	0.0436753i
$239$	−4.87053e10			−0.965574			−0.482787	−	0.875738i	$-0.660375\pi$
$239$	−4.87053e10			−0.965574			−0.482787	+	0.875738i	$0.660375\pi$
$240$		−	7.11999e9i		−	0.138525i
$241$	6.08834e10	+	6.08834e10i	1.16258	+	1.16258i	0.983909	+	0.178669i	$0.0571790\pi$
$241$	6.08834e10	+	6.08834e10i	1.16258	+	1.16258i	0.178669	+	0.983909i	$0.442821\pi$
$242$	2.82200e10			0.528917
$243$	3.28602e10	+	3.28602e10i	0.604564	+	0.604564i
$244$	−2.48809e10	+	2.48809e10i	−0.449377	+	0.449377i
$245$	−5.24434e10	+	5.24434e10i	−0.929915	+	0.929915i
$246$		−	2.01350e10i		−	0.350545i
$247$			5.52537e8i			0.00944550i
$248$	4.11550e9	−	4.11550e9i	0.0690861	−	0.0690861i
$249$	4.40124e10	−	4.40124e10i	0.725567	−	0.725567i
$250$	7.86370e9	+	7.86370e9i	0.127320	+	0.127320i
$251$	−1.62824e10			−0.258933			−0.129466	−	0.991584i	$-0.541326\pi$
$251$	−1.62824e10			−0.258933			−0.129466	+	0.991584i	$0.541326\pi$
$252$	−4.95806e9	−	4.95806e9i	−0.0774478	−	0.0774478i
$253$		−	2.54609e9i		−	0.0390690i
$254$	−4.04232e10			−0.609366
$255$	−6.15635e10	−	3.84754e10i	−0.911785	−	0.569839i
$256$	−6.16094e10			−0.896535
$257$			5.50549e10i			0.787221i	0.919277	+	0.393611i	$0.128774\pi$
$257$			5.50549e10i			0.787221i	−0.919277	+	0.393611i	$0.871226\pi$
$258$	3.91865e10	+	3.91865e10i	0.550614	+	0.550614i
$259$	3.85208e10			0.531919
$260$	9.05781e9	+	9.05781e9i	0.122926	+	0.122926i
$261$	1.21731e10	−	1.21731e10i	0.162375	−	0.162375i
$262$	1.20077e10	−	1.20077e10i	0.157436	−	0.157436i
$263$			1.36741e10i			0.176237i	0.996110	+	0.0881186i	$0.0280854\pi$
$263$			1.36741e10i			0.176237i	−0.996110	+	0.0881186i	$0.971915\pi$
$264$			1.47616e10i			0.187032i
$265$	−1.22413e11	+	1.22413e11i	−1.52483	+	1.52483i
$266$	6.10973e8	−	6.10973e8i	0.00748264	−	0.00748264i
$267$	4.22439e10	+	4.22439e10i	0.508702	+	0.508702i
$268$	4.32764e10			0.512442
$269$	−6.71813e10	−	6.71813e10i	−0.782282	−	0.782282i	0.197933	−	0.980215i	$-0.436577\pi$
$269$	−6.71813e10	−	6.71813e10i	−0.782282	−	0.782282i	−0.980215	+	0.197933i	$0.936577\pi$
$270$			7.91724e10i			0.906645i
$271$	7.91380e10			0.891299			0.445650	−	0.895208i	$-0.352973\pi$
$271$	7.91380e10			0.891299			0.445650	+	0.895208i	$0.352973\pi$
$272$	6.16393e9	−	9.86274e9i	0.0682807	−	0.109254i
$273$	−3.91380e9			−0.0426448
$274$		−	6.64333e9i		−	0.0712046i
$275$	2.20082e10	+	2.20082e10i	0.232053	+	0.232053i
$276$	−6.78055e9			−0.0703354
$277$	−1.78820e10	−	1.78820e10i	−0.182497	−	0.182497i	0.609946	−	0.792443i	$-0.291191\pi$
$277$	−1.78820e10	−	1.78820e10i	−0.182497	−	0.182497i	−0.792443	+	0.609946i	$0.791191\pi$
$278$	7.13957e10	−	7.13957e10i	0.716920	−	0.716920i
$279$	3.49314e9	−	3.49314e9i	0.0345142	−	0.0345142i
$280$		−	4.97414e10i		−	0.483623i
$281$			9.53062e8i			0.00911891i	0.999990	+	0.00455946i	$0.00145132\pi$
$281$			9.53062e8i			0.00911891i	−0.999990	+	0.00455946i	$0.998549\pi$
$282$	5.48108e10	−	5.48108e10i	0.516113	−	0.516113i
$283$	2.67839e10	−	2.67839e10i	0.248219	−	0.248219i	−0.572020	−	0.820239i	$-0.693840\pi$
$283$	2.67839e10	−	2.67839e10i	0.248219	−	0.248219i	0.820239	+	0.572020i	$0.193840\pi$
$284$	−5.24266e10	−	5.24266e10i	−0.478211	−	0.478211i
$285$	6.52495e9			0.0585835
$286$	−2.14330e9	−	2.14330e9i	−0.0189425	−	0.0189425i
$287$			3.32285e10i			0.289096i
$288$	−5.73593e10			−0.491290
$289$	−5.19698e10	−	1.06594e11i	−0.438239	−	0.898859i
$290$	4.91818e10			0.408332
$291$		−	8.83067e10i		−	0.721897i
$292$	−2.51339e10	−	2.51339e10i	−0.202320	−	0.202320i
$293$	1.17365e11			0.930325			0.465163	−	0.885225i	$-0.345996\pi$
$293$	1.17365e11			0.930325			0.465163	+	0.885225i	$0.345996\pi$
$294$	−3.30477e10	−	3.30477e10i	−0.257976	−	0.257976i
$295$	−1.35813e11	+	1.35813e11i	−1.04410	+	1.04410i
$296$	1.39500e11	−	1.39500e11i	1.05624	−	1.05624i
$297$			3.87747e10i			0.289164i
$298$			1.09413e11i			0.803706i
$299$	2.44466e9	−	2.44466e9i	0.0176888	−	0.0176888i
$300$	5.86103e10	−	5.86103e10i	0.417762	−	0.417762i
$301$	−6.46687e10	−	6.46687e10i	−0.454093	−	0.454093i
$302$	1.47151e10			0.101796
$303$	1.26792e11	+	1.26792e11i	0.864170	+	0.864170i
$304$			1.04533e9i			0.00701973i
$305$	−2.11868e11			−1.40190
$306$	−2.21478e10	+	3.54381e10i	−0.144406	+	0.231060i
$307$	−8.18712e10			−0.526028			−0.263014	−	0.964792i	$-0.584717\pi$
$307$	−8.18712e10			−0.526028			−0.263014	+	0.964792i	$0.584717\pi$
$308$		−	9.81043e9i		−	0.0621169i
$309$	−5.96823e10	−	5.96823e10i	−0.372419	−	0.372419i
$310$	1.41130e10			0.0867943
$311$	1.19969e11	+	1.19969e11i	0.727190	+	0.727190i	0.970059	−	0.242869i	$-0.0780885\pi$
$311$	1.19969e11	+	1.19969e11i	0.727190	+	0.727190i	−0.242869	+	0.970059i	$0.578088\pi$
$312$	−1.41735e10	+	1.41735e10i	−0.0846803	+	0.0846803i
$313$	2.30356e11	−	2.30356e11i	1.35660	−	1.35660i	0.478516	−	0.878079i	$-0.341175\pi$
$313$	2.30356e11	−	2.30356e11i	1.35660	−	1.35660i	0.878079	−	0.478516i	$-0.158825\pi$
$314$		−	4.22323e10i		−	0.245166i
$315$		−	4.22193e10i		−	0.241609i
$316$	2.34091e9	−	2.34091e9i	0.0132067	−	0.0132067i
$317$	−9.23129e10	+	9.23129e10i	−0.513447	+	0.513447i	−0.915581	−	0.402134i	$-0.868269\pi$
$317$	−9.23129e10	+	9.23129e10i	−0.513447	+	0.513447i	0.402134	+	0.915581i	$0.368269\pi$
$318$	−7.71397e10	−	7.71397e10i	−0.423015	−	0.423015i
$319$	2.40868e10			0.130233
$320$	−9.04559e10	−	9.04559e10i	−0.482239	−	0.482239i
$321$			1.51819e11i			0.798092i
$322$	−5.40642e9			−0.0280258
$323$	9.03848e9	+	5.64879e9i	0.0462045	+	0.0288765i
$324$	3.94145e10			0.198703
$325$			4.22628e10i			0.210128i
$326$	1.91328e10	+	1.91328e10i	0.0938207	+	0.0938207i
$327$	−1.26900e11			−0.613755
$328$	1.20334e11	+	1.20334e11i	0.574061	+	0.574061i
$329$	−9.04533e10	+	9.04533e10i	−0.425640	+	0.425640i
$330$	−2.53104e10	+	2.53104e10i	−0.117486	+	0.117486i
$331$			1.07749e11i			0.493385i	0.969094	+	0.246692i	$0.0793438\pi$
$331$			1.07749e11i			0.493385i	−0.969094	+	0.246692i	$0.920656\pi$
$332$			2.11855e11i			0.957013i
$333$	1.18404e11	−	1.18404e11i	0.527678	−	0.527678i
$334$	−1.28607e11	+	1.28607e11i	−0.565463	+	0.565463i
$335$	1.84256e11	+	1.84256e11i	0.799318	+	0.799318i
$336$	−7.40438e9			−0.0316929
$337$	1.79887e11	+	1.79887e11i	0.759741	+	0.759741i	0.976275	−	0.216534i	$-0.0694754\pi$
$337$	1.79887e11	+	1.79887e11i	0.759741	+	0.759741i	−0.216534	+	0.976275i	$0.569475\pi$
$338$			1.32838e11i			0.553603i
$339$	−2.65920e11			−1.09358
$340$	2.40770e11	−	5.55676e10i	0.977120	−	0.225510i
$341$	6.91183e9			0.0276821
$342$		−	3.75599e9i		−	0.0148459i
$343$	1.16218e11	+	1.16218e11i	0.453368	+	0.453368i
$344$	−4.68386e11			−1.80340
$345$	−2.88692e10	−	2.88692e10i	−0.109711	−	0.109711i
$346$	3.64064e10	−	3.64064e10i	0.136564	−	0.136564i
$347$	2.85257e10	−	2.85257e10i	0.105622	−	0.105622i	−0.652321	−	0.757943i	$-0.726205\pi$
$347$	2.85257e10	−	2.85257e10i	0.105622	−	0.105622i	0.757943	+	0.652321i	$0.226205\pi$
$348$		−	6.41459e10i		−	0.234456i
$349$		−	2.78080e11i		−	1.00336i	−0.865054	−	0.501679i	$-0.832716\pi$
$349$		−	2.78080e11i		−	1.00336i	0.865054	−	0.501679i	$-0.167284\pi$
$350$	4.67325e10	−	4.67325e10i	0.166461	−	0.166461i
$351$	−3.72299e10	+	3.72299e10i	−0.130921	+	0.130921i
$352$	−5.67480e10	−	5.67480e10i	−0.197019	−	0.197019i
$353$	−2.25144e11			−0.771746			−0.385873	−	0.922552i	$-0.626100\pi$
$353$	−2.25144e11			−0.771746			−0.385873	+	0.922552i	$0.626100\pi$
$354$	−8.55839e10	−	8.55839e10i	−0.289652	−	0.289652i
$355$		−	4.46428e11i		−	1.49185i
$356$	−2.03343e11			−0.670970
$357$	−4.00122e10	+	6.40224e10i	−0.130372	+	0.208605i
$358$	2.36198e11			0.759982
$359$		−	2.26898e11i		−	0.720952i	−0.932768	−	0.360476i	$-0.882614\pi$
$359$		−	2.26898e11i		−	0.720952i	0.932768	−	0.360476i	$-0.117386\pi$
$360$	−1.52894e11	−	1.52894e11i	−0.479766	−	0.479766i
$361$	3.21730e11			0.997031
$362$	−1.02428e11	−	1.02428e11i	−0.313495	−	0.313495i
$363$	1.56708e11	−	1.56708e11i	0.473709	−	0.473709i
$364$	9.41960e9	−	9.41960e9i	0.0281239	−	0.0281239i
$365$		−	2.14023e11i		−	0.631164i
$366$		−	1.33511e11i		−	0.388912i
$367$	−2.67507e11	+	2.67507e11i	−0.769730	+	0.769730i	−0.978059	−	0.208329i	$-0.933198\pi$
$367$	−2.67507e11	+	2.67507e11i	−0.769730	+	0.769730i	0.208329	+	0.978059i	$0.433198\pi$
$368$	4.62497e9	−	4.62497e9i	0.0131460	−	0.0131460i
$369$	1.02137e11	+	1.02137e11i	0.286790	+	0.286790i
$370$	4.78377e11			1.32697
$371$	1.27302e11	+	1.27302e11i	0.348862	+	0.348862i
$372$		−	1.84070e10i		−	0.0498357i
$373$	6.56421e11			1.75587			0.877935	−	0.478779i	$-0.158921\pi$
$373$	6.56421e11			1.75587			0.877935	+	0.478779i	$0.158921\pi$
$374$	−5.69723e10	+	1.31487e10i	−0.150571	+	0.0347504i
$375$	8.73355e10			0.228061
$376$			6.55140e11i			1.69040i
$377$	2.31272e10	+	2.31272e10i	0.0589639	+	0.0589639i
$378$	8.23348e10			0.207429
$379$	−3.56783e11	−	3.56783e11i	−0.888235	−	0.888235i	0.106118	−	0.994354i	$-0.466158\pi$
$379$	−3.56783e11	−	3.56783e11i	−0.888235	−	0.888235i	−0.994354	+	0.106118i	$0.966158\pi$
$380$	−1.57040e10	+	1.57040e10i	−0.0386354	+	0.0386354i
$381$	−2.24473e11	+	2.24473e11i	−0.545760	+	0.545760i
$382$		−	8.57017e10i		−	0.205923i
$383$		−	3.41936e11i		−	0.811990i	−0.913875	−	0.405995i	$-0.866925\pi$
$383$		−	3.41936e11i		−	0.811990i	0.913875	−	0.405995i	$-0.133075\pi$
$384$	−1.67143e11	+	1.67143e11i	−0.392280	+	0.392280i
$385$	4.17694e10	−	4.17694e10i	0.0968913	−	0.0968913i
$386$	1.17305e11	+	1.17305e11i	0.268950	+	0.268950i
$387$	−3.97555e11			−0.900945
$388$	2.12534e11	+	2.12534e11i	0.476086	+	0.476086i
$389$		−	7.41610e11i		−	1.64211i	−0.570849	−	0.821055i	$-0.693386\pi$
$389$		−	7.41610e11i		−	1.64211i	0.570849	−	0.821055i	$-0.306614\pi$
$390$	−4.86042e10			−0.106386
$391$	−1.49974e10	−	6.49829e10i	−0.0324505	−	0.140606i
$392$	3.95012e11			0.844933
$393$		−	1.33359e11i		−	0.282005i
$394$	8.35613e10	+	8.35613e10i	0.174692	+	0.174692i
$395$	1.99335e10			0.0412000
$396$	−3.01551e10	−	3.01551e10i	−0.0616216	−	0.0616216i
$397$	−1.72783e11	+	1.72783e11i	−0.349095	+	0.349095i	−0.859773	−	0.510677i	$-0.829395\pi$
$397$	−1.72783e11	+	1.72783e11i	−0.349095	+	0.349095i	0.510677	+	0.859773i	$0.329395\pi$
$398$	−3.67232e11	+	3.67232e11i	−0.733613	+	0.733613i
$399$		−	6.78557e9i		−	0.0134032i
$400$			7.99555e10i			0.156163i
$401$	2.96342e11	−	2.96342e11i	0.572327	−	0.572327i	−0.360451	−	0.932778i	$-0.617377\pi$
$401$	2.96342e11	−	2.96342e11i	0.572327	−	0.572327i	0.932778	+	0.360451i	$0.117377\pi$
$402$	−1.16111e11	+	1.16111e11i	−0.221745	+	0.221745i
$403$	6.63647e9	+	6.63647e9i	0.0125333	+	0.0125333i
$404$	−6.10317e11			−1.13983
$405$	1.67813e11	+	1.67813e11i	0.309941	+	0.309941i
$406$		−	5.11462e10i		−	0.0934214i
$407$	2.34285e11			0.423223
$408$	8.69513e10	+	3.76754e11i	0.155348	+	0.673112i
$409$	−5.47241e11			−0.966994			−0.483497	−	0.875346i	$-0.660634\pi$
$409$	−5.47241e11			−0.966994			−0.483497	+	0.875346i	$0.660634\pi$
$410$			4.12654e11i			0.721205i
$411$	−3.68910e10	−	3.68910e10i	−0.0637723	−	0.0637723i
$412$	2.87283e11			0.491216
$413$	1.41238e11	+	1.41238e11i	0.238877	+	0.238877i
$414$	−1.66181e10	+	1.66181e10i	−0.0278023	+	0.0278023i
$415$	−9.02005e11	+	9.02005e11i	−1.49277	+	1.49277i
$416$		−	1.08975e11i		−	0.178404i
$417$		−	7.92933e11i		−	1.28417i
$418$	3.71597e9	−	3.71597e9i	0.00595358	−	0.00595358i
$419$	−4.46264e11	+	4.46264e11i	−0.707341	+	0.707341i	−0.965975	−	0.258635i	$-0.916727\pi$
$419$	−4.46264e11	+	4.46264e11i	−0.707341	+	0.707341i	0.258635	+	0.965975i	$0.416727\pi$
$420$	−1.11237e11	−	1.11237e11i	−0.174432	−	0.174432i
$421$	−2.59316e11			−0.402309			−0.201154	−	0.979560i	$-0.564469\pi$
$421$	−2.59316e11			−0.402309			−0.201154	+	0.979560i	$0.564469\pi$
$422$	−8.28339e10	−	8.28339e10i	−0.127146	−	0.127146i
$423$			5.56067e11i			0.844492i
$424$	9.22032e11			1.38548
$425$	6.91341e11	+	4.32068e11i	1.02788	+	0.642395i
$426$	2.81321e11			0.413866
$427$			2.20330e11i			0.320737i
$428$	−3.65393e11	−	3.65393e11i	−0.526336	−	0.526336i
$429$	−2.38039e10			−0.0339305
$430$	−8.03101e11	−	8.03101e11i	−1.13282	−	1.13282i
$431$	2.26593e11	−	2.26593e11i	0.316300	−	0.316300i	−0.531044	−	0.847344i	$-0.678200\pi$
$431$	2.26593e11	−	2.26593e11i	0.316300	−	0.316300i	0.847344	+	0.531044i	$0.178200\pi$
$432$	−7.04341e10	+	7.04341e10i	−0.0972984	+	0.0972984i
$433$			6.08153e11i			0.831414i	0.909499	+	0.415707i	$0.136466\pi$
$433$			6.08153e11i			0.831414i	−0.909499	+	0.415707i	$0.863534\pi$
$434$		−	1.46767e10i		−	0.0198575i
$435$	2.73111e11	−	2.73111e11i	0.365710	−	0.365710i
$436$	3.05418e11	−	3.05418e11i	0.404767	−	0.404767i
$437$	4.23845e9	+	4.23845e9i	0.00555956	+	0.00555956i
$438$	1.34869e11			0.175097
$439$	6.84271e11	+	6.84271e11i	0.879301	+	0.879301i	0.993462	−	0.114161i	$-0.0364180\pi$
$439$	6.84271e11	+	6.84271e11i	0.879301	+	0.879301i	−0.114161	+	0.993462i	$0.536418\pi$
$440$		−	3.02529e11i		−	0.384796i
$441$	3.35276e11			0.422114
$442$	−6.73274e10	−	4.20777e10i	−0.0839058	−	0.0524387i
$443$	9.00554e11			1.11095			0.555473	−	0.831535i	$-0.312537\pi$
$443$	9.00554e11			1.11095			0.555473	+	0.831535i	$0.312537\pi$
$444$		−	6.23929e11i		−	0.761924i
$445$	−8.65761e11	−	8.65761e11i	−1.04659	−	1.04659i
$446$	−3.66679e11			−0.438812
$447$	6.07581e11	+	6.07581e11i	0.719815	+	0.719815i
$448$	−9.40689e10	+	9.40689e10i	−0.110330	+	0.110330i
$449$	−1.79017e11	+	1.79017e11i	−0.207867	+	0.207867i	−0.803360	−	0.595493i	$-0.796957\pi$
$449$	−1.79017e11	+	1.79017e11i	−0.207867	+	0.207867i	0.595493	+	0.803360i	$0.296957\pi$
$450$		−	2.87291e11i		−	0.330267i
$451$			2.02097e11i			0.230020i
$452$	6.40008e11	−	6.40008e11i	0.721211	−	0.721211i
$453$	8.17140e10	−	8.17140e10i	0.0911705	−	0.0911705i
$454$	−7.06901e11	−	7.06901e11i	−0.780921	−	0.780921i
$455$	8.02107e10			0.0877366
$456$	−2.45734e10	−	2.45734e10i	−0.0266149	−	0.0266149i
$457$		−	1.51148e12i		−	1.62099i	−0.585745	−	0.810495i	$-0.699198\pi$
$457$		−	1.51148e12i		−	1.62099i	0.585745	−	0.810495i	$-0.300802\pi$
$458$	−1.35166e10			−0.0143540
$459$	2.28397e11	+	9.89629e11i	0.240178	+	1.04068i
$460$	1.38963e11			0.144707
$461$		−	8.09197e11i		−	0.834450i	−0.908803	−	0.417225i	$-0.863003\pi$
$461$		−	8.09197e11i		−	0.834450i	0.908803	−	0.417225i	$-0.136997\pi$
$462$	2.63214e10	+	2.63214e10i	0.0268794	+	0.0268794i
$463$	−1.55999e12			−1.57764			−0.788819	−	0.614625i	$-0.789307\pi$
$463$	−1.55999e12			−1.57764			−0.788819	+	0.614625i	$0.789307\pi$
$464$	4.37535e10	+	4.37535e10i	0.0438210	+	0.0438210i
$465$	7.83706e10	−	7.83706e10i	0.0777347	−	0.0777347i
$466$	5.55341e11	−	5.55341e11i	0.545536	−	0.545536i
$467$			3.66882e11i			0.356944i	0.983945	+	0.178472i	$0.0571154\pi$
$467$			3.66882e11i			0.356944i	−0.983945	+	0.178472i	$0.942885\pi$
$468$		−	5.79076e10i		−	0.0557993i
$469$	1.91615e11	−	1.91615e11i	0.182874	−	0.182874i
$470$	−1.12331e12	+	1.12331e12i	−1.06184	+	1.06184i
$471$	−2.34519e11	−	2.34519e11i	−0.219576	−	0.219576i
$472$	1.02296e12			0.948683
$473$	−3.93318e11	−	3.93318e11i	−0.361301	−	0.361301i
$474$			1.25613e10i			0.0114296i
$475$	−7.32734e10			−0.0660427
$476$	−5.77871e10	−	2.50387e11i	−0.0515940	−	0.223553i
$477$	7.82599e11			0.692160
$478$			6.29015e11i			0.551106i
$479$	−4.05611e11	−	4.05611e11i	−0.352047	−	0.352047i	0.508824	−	0.860871i	$-0.330080\pi$
$479$	−4.05611e11	−	4.05611e11i	−0.352047	−	0.352047i	−0.860871	+	0.508824i	$0.830080\pi$
$480$	−1.28689e12			−1.10651
$481$	2.24951e11	+	2.24951e11i	0.191618	+	0.191618i
$482$	7.86292e11	−	7.86292e11i	0.663547	−	0.663547i
$483$	−3.00223e10	+	3.00223e10i	−0.0251005	+	0.0251005i
$484$			7.54320e11i			0.624815i
$485$			1.80979e12i			1.48522i
$486$	4.24380e11	−	4.24380e11i	0.345058	−	0.345058i
$487$	−1.10600e12	+	1.10600e12i	−0.890995	+	0.890995i	−0.994617	−	0.103622i	$-0.966957\pi$
$487$	−1.10600e12	+	1.10600e12i	−0.890995	+	0.890995i	0.103622	+	0.994617i	$0.466957\pi$
$488$	7.97910e11	+	7.97910e11i	0.636891	+	0.636891i
$489$	2.12492e11			0.168055
$490$	6.77292e11	+	6.77292e11i	0.530754	+	0.530754i
$491$			1.20510e11i			0.0935743i	0.998905	+	0.0467872i	$0.0148983\pi$
$491$			1.20510e11i			0.0935743i	−0.998905	+	0.0467872i	$0.985102\pi$
$492$	5.38208e11			0.414102
$493$	6.14756e11	−	1.41880e11i	0.468696	−	0.108171i
$494$	7.13585e9			0.00539107
$495$		−	2.56780e11i		−	0.192237i
$496$	1.25553e10	+	1.25553e10i	0.00931452	+	0.00931452i
$497$	−4.64260e11			−0.341316
$498$	−5.68407e11	−	5.68407e11i	−0.414121	−	0.414121i
$499$	−3.50759e11	+	3.50759e11i	−0.253254	+	0.253254i	−0.822303	−	0.569049i	$-0.807311\pi$
$499$	−3.50759e11	+	3.50759e11i	−0.253254	+	0.253254i	0.569049	+	0.822303i	$0.307311\pi$
$500$	−2.10196e11	+	2.10196e11i	−0.150404	+	0.150404i
$501$			1.42833e12i			1.01288i
$502$			2.10283e11i			0.147787i
$503$	−1.04939e11	+	1.04939e11i	−0.0730941	+	0.0730941i	−0.742709	−	0.669615i	$-0.766459\pi$
$503$	−1.04939e11	+	1.04939e11i	−0.0730941	+	0.0730941i	0.669615	+	0.742709i	$0.266459\pi$
$504$	−1.59001e11	+	1.59001e11i	−0.109765	+	0.109765i
$505$	−2.59852e12	−	2.59852e12i	−1.77793	−	1.77793i
$506$	−3.28821e10			−0.0222988
$507$	7.37662e11	+	7.37662e11i	0.495817	+	0.495817i
$508$		−	1.08051e12i		−	0.719850i
$509$	8.49687e11			0.561085			0.280543	−	0.959842i	$-0.409486\pi$
$509$	8.49687e11			0.561085			0.280543	+	0.959842i	$0.409486\pi$
$510$	−4.96899e11	+	7.95075e11i	−0.325239	+	0.520406i
$511$	−2.22572e11			−0.144403
$512$		−	3.97599e11i		−	0.255700i
$513$	−6.45476e10	−	6.45476e10i	−0.0411483	−	0.0411483i
$514$	7.11018e11			0.449311
$515$	1.22315e12	+	1.22315e12i	0.766209	+	0.766209i
$516$	−1.04745e12	+	1.04745e12i	−0.650446	+	0.650446i
$517$	−5.50141e11	+	5.50141e11i	−0.338662	+	0.338662i
$518$		−	4.97485e11i		−	0.303596i
$519$		−	4.04336e11i		−	0.244618i
$520$	2.90477e11	−	2.90477e11i	0.174220	−	0.174220i
$521$	−3.27998e11	+	3.27998e11i	−0.195030	+	0.195030i	−0.797866	−	0.602835i	$-0.794038\pi$
$521$	−3.27998e11	+	3.27998e11i	−0.195030	+	0.195030i	0.602835	+	0.797866i	$0.294038\pi$
$522$	−1.57212e11	−	1.57212e11i	−0.0926764	−	0.0926764i
$523$	3.01502e11			0.176211			0.0881054	−	0.996111i	$-0.471919\pi$
$523$	3.01502e11			0.176211			0.0881054	+	0.996111i	$0.471919\pi$
$524$	3.20965e11	+	3.20965e11i	0.185980	+	0.185980i
$525$		−	5.19019e11i		−	0.298172i
$526$	1.76597e11			0.100588
$527$	1.76408e11	−	4.07132e10i	0.0996253	−	0.0229926i
$528$	−4.50338e10			−0.0252165
$529$			1.76365e12i			0.979177i
$530$	1.58093e12	+	1.58093e12i	0.870303	+	0.870303i
$531$	8.68267e11			0.473945
$532$	1.63313e10	+	1.63313e10i	0.00883931	+	0.00883931i
$533$	−1.94046e11	+	1.94046e11i	−0.104143	+	0.104143i
$534$	5.45568e11	−	5.45568e11i	0.290344	−	0.290344i
$535$		−	3.11143e12i		−	1.64198i
$536$		−	1.38784e12i		−	0.726271i
$537$	1.31163e12	−	1.31163e12i	0.680655	−	0.680655i
$538$	−8.67628e11	+	8.67628e11i	−0.446492	+	0.446492i
$539$	3.31703e11	+	3.31703e11i	0.169278	+	0.169278i
$540$	−2.11628e12			−1.07103
$541$	−1.45414e12	−	1.45414e12i	−0.729827	−	0.729827i	0.240758	−	0.970585i	$-0.422604\pi$
$541$	−1.45414e12	−	1.45414e12i	−0.729827	−	0.729827i	−0.970585	+	0.240758i	$0.922604\pi$
$542$		−	1.02205e12i		−	0.508714i
$543$	−1.13758e12			−0.561544
$544$	−1.78262e12	−	1.11409e12i	−0.872698	−	0.545412i
$545$	2.60072e12			1.26273
$546$			5.05456e10i			0.0243398i
$547$	−2.20303e12	−	2.20303e12i	−1.05215	−	1.05215i	−0.998563	−	0.0535847i	$-0.982935\pi$
$547$	−2.20303e12	−	2.20303e12i	−1.05215	−	1.05215i	−0.0535847	−	0.998563i	$-0.517065\pi$
$548$	1.77576e11			0.0841147
$549$	6.77248e11	+	6.77248e11i	0.318179	+	0.318179i
$550$	2.84229e11	−	2.84229e11i	0.132445	−	0.132445i
$551$	−4.00969e10	+	4.00969e10i	−0.0185323	+	0.0185323i
$552$			2.17447e11i			0.0996845i
$553$		−	2.07297e10i		−	0.00942607i
$554$	−2.30941e11	+	2.30941e11i	−0.104161	+	0.104161i
$555$	2.65647e12	−	2.65647e12i	1.18846	−	1.18846i
$556$	1.90841e12	+	1.90841e12i	0.846904	+	0.846904i
$557$	−2.06457e12			−0.908828			−0.454414	−	0.890791i	$-0.650151\pi$
$557$	−2.06457e12			−0.908828			−0.454414	+	0.890791i	$0.650151\pi$
$558$	−4.51130e10	−	4.51130e10i	−0.0196991	−	0.0196991i
$559$		−	7.55298e11i		−	0.327164i
$560$	1.51748e11			0.0652043
$561$	−2.43356e11	+	3.89387e11i	−0.103731	+	0.165977i
$562$	1.23085e10			0.00520467
$563$		−	3.11121e12i		−	1.30509i	−0.757748	−	0.652547i	$-0.773700\pi$
$563$		−	3.11121e12i		−	1.30509i	0.757748	−	0.652547i	$-0.226300\pi$
$564$	1.46509e12	+	1.46509e12i	0.609689	+	0.609689i
$565$	5.44986e12			2.24992
$566$	−3.45907e11	−	3.45907e11i	−0.141672	−	0.141672i
$567$	1.74516e11	−	1.74516e11i	0.0709107	−	0.0709107i
$568$	−1.68128e12	+	1.68128e12i	−0.677756	+	0.677756i
$569$			4.33084e11i			0.173207i	0.996243	+	0.0866037i	$0.0276014\pi$
$569$			4.33084e11i			0.173207i	−0.996243	+	0.0866037i	$0.972399\pi$
$570$		−	8.42678e10i		−	0.0334368i
$571$	−2.87891e12	+	2.87891e12i	−1.13335	+	1.13335i	−0.143738	+	0.989616i	$0.545912\pi$
$571$	−2.87891e12	+	2.87891e12i	−1.13335	+	1.13335i	−0.989616	+	0.143738i	$0.954088\pi$
$572$	5.72904e10	−	5.72904e10i	0.0223769	−	0.0223769i
$573$	−4.75909e11	−	4.75909e11i	−0.184429	−	0.184429i
$574$	4.29136e11			0.165003
$575$	3.24193e11	+	3.24193e11i	0.123680	+	0.123680i
$576$			5.78295e11i			0.218901i
$577$	−2.10704e12			−0.791375			−0.395687	−	0.918385i	$-0.629494\pi$
$577$	−2.10704e12			−0.791375			−0.395687	+	0.918385i	$0.629494\pi$
$578$	−1.37663e12	+	6.71176e11i	−0.513028	+	0.250127i
$579$	1.30280e12			0.481754
$580$			1.31463e12i			0.482366i
$581$	9.38033e11	+	9.38033e11i	0.341527	+	0.341527i
$582$	−1.14046e12			−0.412027
$583$	7.74259e11	+	7.74259e11i	0.277573	+	0.277573i
$584$	−8.06027e11	+	8.06027e11i	−0.286742	+	0.286742i
$585$	2.46550e11	−	2.46550e11i	0.0870370	−	0.0870370i
$586$		−	1.51574e12i		−	0.530988i
$587$		−	1.65360e12i		−	0.574857i	−0.957802	−	0.287428i	$-0.907200\pi$
$587$		−	1.65360e12i		−	0.574857i	0.957802	−	0.287428i	$-0.0928004\pi$
$588$	8.83365e11	−	8.83365e11i	0.304749	−	0.304749i
$589$	−1.15060e10	+	1.15060e10i	−0.00393919	+	0.00393919i
$590$	1.75399e12	+	1.75399e12i	0.595926	+	0.595926i
$591$	9.28046e11			0.312915
$592$	4.25578e11	+	4.25578e11i	0.142407	+	0.142407i
$593$			1.28308e12i			0.426096i	0.977042	+	0.213048i	$0.0683391\pi$
$593$			1.28308e12i			0.426096i	−0.977042	+	0.213048i	$0.931661\pi$
$594$	5.00764e11			0.165042
$595$	8.20024e11	−	1.31210e12i	0.268226	−	0.429181i
$596$	−2.92462e12			−0.949425
$597$			4.07854e12i			1.31408i
$598$	−3.15721e10	−	3.15721e10i	−0.0100960	−	0.0100960i
$599$	−2.16567e12			−0.687341			−0.343671	−	0.939090i	$-0.611670\pi$
$599$	−2.16567e12			−0.687341			−0.343671	+	0.939090i	$0.611670\pi$
$600$	−1.87959e12	−	1.87959e12i	−0.592083	−	0.592083i
$601$	−5.43265e11	+	5.43265e11i	−0.169854	+	0.169854i	−0.786915	−	0.617061i	$-0.788323\pi$
$601$	−5.43265e11	+	5.43265e11i	−0.169854	+	0.169854i	0.617061	+	0.786915i	$0.288323\pi$
$602$	−8.35179e11	+	8.35179e11i	−0.259176	+	0.259176i
$603$		−	1.17797e12i		−	0.362832i
$604$			3.93333e11i			0.120253i
$605$	−3.21163e12	+	3.21163e12i	−0.974599	+	0.974599i
$606$	1.63748e12	−	1.63748e12i	0.493230	−	0.493230i
$607$	2.04434e12	+	2.04434e12i	0.611228	+	0.611228i	0.943266	−	0.332038i	$-0.107736\pi$
$607$	2.04434e12	+	2.04434e12i	0.611228	+	0.611228i	−0.332038	+	0.943266i	$0.607736\pi$
$608$	1.88935e11			0.0560721
$609$	−2.84019e11	−	2.84019e11i	−0.0836700	−	0.0836700i
$610$			2.73621e12i			0.800140i
$611$	−1.05645e12			−0.306664
$612$	−9.47261e11	−	5.92011e11i	−0.272953	−	0.170588i
$613$	−5.08236e12			−1.45376			−0.726881	−	0.686763i	$-0.759031\pi$
$613$	−5.08236e12			−1.45376			−0.726881	+	0.686763i	$0.759031\pi$
$614$			1.05734e12i			0.300233i
$615$	2.29150e12	+	2.29150e12i	0.645925	+	0.645925i
$616$	−3.14613e11			−0.0880367
$617$	−2.00800e12	−	2.00800e12i	−0.557802	−	0.557802i	0.370879	−	0.928681i	$-0.379056\pi$
$617$	−2.00800e12	−	2.00800e12i	−0.557802	−	0.557802i	−0.928681	+	0.370879i	$0.879056\pi$
$618$	−7.70780e11	+	7.70780e11i	−0.212560	+	0.212560i
$619$	1.94797e12	−	1.94797e12i	0.533304	−	0.533304i	−0.388250	−	0.921554i	$-0.626920\pi$
$619$	1.94797e12	−	1.94797e12i	0.533304	−	0.533304i	0.921554	+	0.388250i	$0.126920\pi$
$620$			3.77240e11i			0.102531i
$621$			5.71174e11i			0.154119i
$622$	1.54937e12	−	1.54937e12i	0.415048	−	0.415048i
$623$	−9.00341e11	+	9.00341e11i	−0.239448	+	0.239448i
$624$	−4.32397e10	−	4.32397e10i	−0.0114170	−	0.0114170i
$625$	2.83394e12			0.742901
$626$	−2.97498e12	−	2.97498e12i	−0.774284	−	0.774284i
$627$		−	4.12701e10i		−	0.0106643i
$628$	1.12887e12			0.289617
$629$	5.97955e12	−	1.38003e12i	1.52314	−	0.351527i
$630$	−5.45250e11			−0.137900
$631$		−	4.35581e12i		−	1.09380i	−0.837199	−	0.546899i	$-0.815808\pi$
$631$		−	4.35581e12i		−	1.09380i	0.837199	−	0.546899i	$-0.184192\pi$
$632$	−7.50712e10	−	7.50712e10i	−0.0187174	−	0.0187174i
$633$	−9.19968e11			−0.227749
$634$	1.19219e12	+	1.19219e12i	0.293053	+	0.293053i
$635$	4.60043e12	−	4.60043e12i	1.12284	−	1.12284i
$636$	2.06194e12	−	2.06194e12i	0.499712	−	0.499712i
$637$			6.36978e11i			0.153284i
$638$		−	3.11074e11i		−	0.0743310i
$639$	−1.42703e12	+	1.42703e12i	−0.338595	+	0.338595i
$640$	3.42548e12	−	3.42548e12i	0.807070	−	0.807070i
$641$	6.91638e11	+	6.91638e11i	0.161815	+	0.161815i	0.783370	−	0.621556i	$-0.213499\pi$
$641$	6.91638e11	+	6.91638e11i	0.161815	+	0.161815i	−0.621556	+	0.783370i	$0.713499\pi$
$642$	1.96070e12			0.455515
$643$	4.75762e11	+	4.75762e11i	0.109759	+	0.109759i	0.759853	−	0.650094i	$-0.225271\pi$
$643$	4.75762e11	+	4.75762e11i	0.109759	+	0.109759i	−0.650094	+	0.759853i	$0.725271\pi$
$644$		−	1.44513e11i		−	0.0331072i
$645$	−8.91937e12			−2.02916
$646$	7.29525e10	−	1.16729e11i	0.0164814	−	0.0263714i
$647$	−6.23882e12			−1.39969			−0.699847	−	0.714293i	$-0.746748\pi$
$647$	−6.23882e12			−1.39969			−0.699847	+	0.714293i	$0.746748\pi$
$648$		−	1.26399e12i		−	0.281616i
$649$	8.59014e11	+	8.59014e11i	0.190064	+	0.190064i
$650$	5.45812e11			0.119931
$651$	−8.15009e10	−	8.15009e10i	−0.0177848	−	0.0177848i
$652$	−5.11419e11	+	5.11419e11i	−0.110831	+	0.110831i
$653$	6.43537e12	−	6.43537e12i	1.38505	−	1.38505i	0.549652	−	0.835393i	$-0.314760\pi$
$653$	6.43537e12	−	6.43537e12i	1.38505	−	1.38505i	0.835393	−	0.549652i	$-0.185240\pi$
$654$			1.63887e12i			0.350304i
$655$			2.73311e12i			0.580192i
$656$	−3.67109e11	+	3.67109e11i	−0.0773976	+	0.0773976i
$657$	−6.84136e11	+	6.84136e11i	−0.143251	+	0.143251i
$658$	1.16818e12	+	1.16818e12i	0.242936	+	0.242936i
$659$	5.03909e12			1.04080			0.520400	−	0.853922i	$-0.325783\pi$
$659$	5.03909e12			1.04080			0.520400	+	0.853922i	$0.325783\pi$
$660$	−6.76547e11	−	6.76547e11i	−0.138788	−	0.138788i
$661$			8.54137e12i			1.74029i	0.492798	+	0.870144i	$0.335974\pi$
$661$			8.54137e12i			1.74029i	−0.492798	+	0.870144i	$0.664026\pi$
$662$	1.39154e12			0.281602
$663$	−6.07536e11	+	1.40214e11i	−0.122113	+	0.0281825i
$664$	6.79404e12			1.35635
$665$			1.39066e11i			0.0275755i
$666$	−1.52916e12	−	1.52916e12i	−0.301175	−	0.301175i
$667$	3.54812e11			0.0694116
$668$	−3.43765e12	−	3.43765e12i	−0.667987	−	0.667987i
$669$	−2.03620e12	+	2.03620e12i	−0.393009	+	0.393009i
$670$	2.37961e12	−	2.37961e12i	0.456215	−	0.456215i
$671$			1.34006e12i			0.255195i
$672$			1.33829e12i			0.253156i
$673$	−1.11708e12	+	1.11708e12i	−0.209901	+	0.209901i	−0.804226	−	0.594324i	$-0.797420\pi$
$673$	−1.11708e12	+	1.11708e12i	−0.209901	+	0.209901i	0.594324	+	0.804226i	$0.297420\pi$
$674$	2.32319e12	−	2.32319e12i	0.433626	−	0.433626i
$675$	−4.93716e12	−	4.93716e12i	−0.915399	−	0.915399i
$676$	−3.55076e12			−0.653976
$677$	−9.08386e11	−	9.08386e11i	−0.166196	−	0.166196i	0.619109	−	0.785305i	$-0.287494\pi$
$677$	−9.08386e11	−	9.08386e11i	−0.166196	−	0.166196i	−0.785305	+	0.619109i	$0.787494\pi$
$678$			3.43428e12i			0.624169i
$679$	1.88208e12			0.339800
$680$	−1.78201e12	−	7.72133e12i	−0.319610	−	1.38485i
$681$	−7.85096e12			−1.39882
$682$		−	8.92643e10i		−	0.0157997i
$683$	−5.52716e12	−	5.52716e12i	−0.971871	−	0.971871i	0.0277441	−	0.999615i	$-0.491168\pi$
$683$	−5.52716e12	−	5.52716e12i	−0.971871	−	0.971871i	−0.999615	+	0.0277441i	$0.991168\pi$
$684$	1.00398e11			0.0175376
$685$	7.56056e11	+	7.56056e11i	0.131204	+	0.131204i
$686$	1.50092e12	−	1.50092e12i	0.258762	−	0.258762i
$687$	−7.50590e10	+	7.50590e10i	−0.0128558	+	0.0128558i
$688$		−	1.42892e12i		−	0.243143i
$689$			1.48683e12i			0.251347i
$690$	−3.72838e11	+	3.72838e11i	−0.0626179	+	0.0626179i
$691$	3.74393e12	−	3.74393e12i	0.624708	−	0.624708i	−0.322024	−	0.946732i	$-0.604363\pi$
$691$	3.74393e12	−	3.74393e12i	0.624708	−	0.624708i	0.946732	+	0.322024i	$0.104363\pi$
$692$	9.73142e11	+	9.73142e11i	0.161324	+	0.161324i
$693$	−2.67036e11			−0.0439816
$694$	−3.68401e11	−	3.68401e11i	−0.0602842	−	0.0602842i
$695$			1.62506e13i			2.64204i
$696$	−2.05711e12			−0.332289
$697$	1.19043e12	+	5.15803e12i	0.191054	+	0.827822i
$698$	−3.59133e12			−0.572672
$699$		−	6.16771e12i		−	0.977185i
$700$	1.24916e12	+	1.24916e12i	0.196642	+	0.196642i
$701$	4.08705e12			0.639262			0.319631	−	0.947542i	$-0.396441\pi$
$701$	4.08705e12			0.639262			0.319631	+	0.947542i	$0.396441\pi$
$702$	4.80814e11	+	4.80814e11i	0.0747240	+	0.0747240i
$703$	−3.90011e11	+	3.90011e11i	−0.0602252	+	0.0602252i
$704$	−5.72132e11	+	5.72132e11i	−0.0877847	+	0.0877847i
$705$			1.24757e13i			1.90201i
$706$			2.90767e12i			0.440478i
$707$	−2.70231e12	+	2.70231e12i	−0.406768	+	0.406768i
$708$	2.28766e12	−	2.28766e12i	0.342169	−	0.342169i
$709$	4.96699e12	+	4.96699e12i	0.738219	+	0.738219i	0.972233	−	0.234014i	$-0.0751863\pi$
$709$	4.96699e12	+	4.96699e12i	0.738219	+	0.738219i	−0.234014	+	0.972233i	$0.575186\pi$
$710$	−5.76550e12			−0.851479
$711$	−6.37187e10	−	6.37187e10i	−0.00935090	−	0.00935090i
$712$			6.52104e12i			0.950948i
$713$	1.01815e11			0.0147540
$714$	8.26832e11	+	5.16746e11i	0.119063	+	0.0744107i
$715$	4.87845e11			0.0698079
$716$			6.31358e12i			0.897773i
$717$	3.49297e12	+	3.49297e12i	0.493581	+	0.493581i
$718$	−2.93033e12			−0.411487
$719$	7.44461e12	+	7.44461e12i	1.03887	+	1.03887i	0.999213	+	0.0396590i	$0.0126272\pi$
$719$	7.44461e12	+	7.44461e12i	1.03887	+	1.03887i	0.0396590	+	0.999213i	$0.487373\pi$
$720$	4.66440e11	−	4.66440e11i	0.0646844	−	0.0646844i
$721$	1.27201e12	−	1.27201e12i	0.175299	−	0.175299i
$722$		−	4.15505e12i		−	0.569061i
$723$		−	8.73269e12i		−	1.18857i
$724$	2.73790e12	−	2.73790e12i	0.370334	−	0.370334i
$725$	−3.06696e12	+	3.06696e12i	−0.412275	+	0.412275i
$726$	−2.02384e12	−	2.02384e12i	−0.270372	−	0.270372i
$727$	9.94519e11			0.132041			0.0660204	−	0.997818i	$-0.478970\pi$
$727$	9.94519e11			0.132041			0.0660204	+	0.997818i	$0.478970\pi$
$728$	−3.02079e11	−	3.02079e11i	−0.0398593	−	0.0398593i
$729$		−	6.96056e12i		−	0.912788i
$730$	−2.76405e12			−0.360240
$731$	−1.23553e13	−	7.72170e12i	−1.60038	−	1.00020i
$732$	3.56874e12			0.459425
$733$		−	3.00202e12i		−	0.384101i	−0.981385	−	0.192051i	$-0.938486\pi$
$733$		−	3.00202e12i		−	0.384101i	0.981385	−	0.192051i	$-0.0615137\pi$
$734$	3.45478e12	+	3.45478e12i	0.439327	+	0.439327i
$735$	7.52211e12			0.950708
$736$	−8.35932e11	−	8.35932e11i	−0.105008	−	0.105008i
$737$	1.16541e12	−	1.16541e12i	0.145504	−	0.145504i
$738$	1.31907e12	−	1.31907e12i	0.163687	−	0.163687i
$739$		−	1.31885e13i		−	1.62665i	−0.581810	−	0.813325i	$-0.697655\pi$
$739$		−	1.31885e13i		−	1.62665i	0.581810	−	0.813325i	$-0.302345\pi$
$740$			1.27870e13i			1.56757i
$741$	3.96260e10	−	3.96260e10i	0.00482835	−	0.00482835i
$742$	1.64407e12	−	1.64407e12i	0.199115	−	0.199115i
$743$	−2.98672e12	−	2.98672e12i	−0.359539	−	0.359539i	0.504104	−	0.863643i	$-0.331823\pi$
$743$	−2.98672e12	−	2.98672e12i	−0.359539	−	0.359539i	−0.863643	+	0.504104i	$0.831823\pi$
$744$	−5.90299e11			−0.0706308
$745$	−1.24520e13	−	1.24520e13i	−1.48093	−	1.48093i
$746$		−	8.47749e12i		−	1.00217i
$747$	5.76662e12			0.677608
$748$	−3.51464e11	−	1.52287e12i	−0.0410510	−	0.177871i
$749$	−3.23571e12			−0.375665
$750$		−	1.12791e12i		−	0.130167i
$751$	5.87216e12	+	5.87216e12i	0.673625	+	0.673625i	0.958550	−	0.284925i	$-0.0919687\pi$
$751$	5.87216e12	+	5.87216e12i	0.673625	+	0.673625i	−0.284925	+	0.958550i	$0.591969\pi$
$752$	−1.99866e12			−0.227907
$753$	1.16772e12	+	1.16772e12i	0.132361	+	0.132361i
$754$	2.98681e11	−	2.98681e11i	0.0336540	−	0.0336540i
$755$	−1.67468e12	+	1.67468e12i	−0.187573	+	0.187573i
$756$			2.20081e12i			0.245038i
$757$		−	9.58086e12i		−	1.06041i	−0.847870	−	0.530204i	$-0.822115\pi$
$757$		−	9.58086e12i		−	1.06041i	0.847870	−	0.530204i	$-0.177885\pi$
$758$	−4.60776e12	+	4.60776e12i	−0.506965	+	0.506965i
$759$	−1.82597e11	+	1.82597e11i	−0.0199713	+	0.0199713i
$760$	5.03617e11	+	5.03617e11i	0.0547569	+	0.0547569i
$761$	3.82260e12			0.413169			0.206585	−	0.978429i	$-0.433765\pi$
$761$	3.82260e12			0.413169			0.206585	+	0.978429i	$0.433765\pi$
$762$	2.89901e12	+	2.89901e12i	0.311496	+	0.311496i
$763$		−	2.70460e12i		−	0.288897i
$764$	2.29081e12			0.243259
$765$	−1.51253e12	−	6.55368e12i	−0.159671	−	0.691845i
$766$	−4.41601e12			−0.463448
$767$			1.64958e12i			0.172106i
$768$	4.41841e12	+	4.41841e12i	0.458290	+	0.458290i
$769$	1.25991e13			1.29919			0.649595	−	0.760281i	$-0.274939\pi$
$769$	1.25991e13			1.29919			0.649595	+	0.760281i	$0.274939\pi$
$770$	−5.39440e11	−	5.39440e11i	−0.0553012	−	0.0553012i
$771$	3.94834e12	−	3.94834e12i	0.402411	−	0.402411i
$772$	−3.13555e12	+	3.13555e12i	−0.317714	+	0.317714i
$773$			3.83859e12i			0.386691i	0.981131	+	0.193345i	$0.0619338\pi$
$773$			3.83859e12i			0.386691i	−0.981131	+	0.193345i	$0.938066\pi$
$774$			5.13431e12i			0.514219i
$775$	−8.80081e11	+	8.80081e11i	−0.0876324	+	0.0876324i
$776$	6.81580e12	−	6.81580e12i	0.674744	−	0.674744i
$777$	−2.76257e12	−	2.76257e12i	−0.271906	−	0.271906i
$778$	−9.57768e12			−0.937243
$779$	−3.36428e11	−	3.36428e11i	−0.0327321	−	0.0327321i
$780$		−	1.29919e12i		−	0.125674i
$781$	−2.82365e12			−0.271570
$782$	−8.39235e11	+	1.93688e11i	−0.0802515	+	0.0185213i
$783$	−5.40346e12			−0.513741
$784$			1.20508e12i			0.113918i
$785$	4.80632e12	+	4.80632e12i	0.451751	+	0.451751i
$786$	−1.72230e12			−0.160956
$787$	1.59940e12	+	1.59940e12i	0.148618	+	0.148618i	0.777500	−	0.628883i	$-0.216487\pi$
$787$	1.59940e12	+	1.59940e12i	0.148618	+	0.148618i	−0.628883	+	0.777500i	$0.716487\pi$
$788$	−2.23359e12	+	2.23359e12i	−0.206365	+	0.206365i
$789$	9.80658e11	−	9.80658e11i	0.0900888	−	0.0900888i
$790$		−	2.57436e11i		−	0.0235151i
$791$		−	5.66754e12i		−	0.514754i
$792$	−9.67052e11	+	9.67052e11i	−0.0873346	+	0.0873346i
$793$	−1.28667e12	+	1.28667e12i	−0.115542	+	0.115542i
$794$	2.23145e12	+	2.23145e12i	0.199248	+	0.199248i
$795$	1.75580e13			1.55892
$796$	−9.81610e12	−	9.81610e12i	−0.866623	−	0.866623i
$797$		−	1.88804e13i		−	1.65748i	−0.559632	−	0.828741i	$-0.689058\pi$
$797$		−	1.88804e13i		−	1.65748i	0.559632	−	0.828741i	$-0.310942\pi$
$798$	−8.76337e10			−0.00764994
$799$	−1.08005e13	+	1.72815e13i	−0.937524	+	1.50011i
$800$	1.44514e13			1.24740
$801$			5.53491e12i			0.475077i
$802$	−3.82718e12	−	3.82718e12i	−0.326658	−	0.326658i
$803$	−1.35369e12			−0.114895
$804$	−3.10363e12	−	3.10363e12i	−0.261950	−	0.261950i
$805$	6.15287e11	−	6.15287e11i	0.0516412	−	0.0516412i
$806$	8.57082e10	−	8.57082e10i	0.00715344	−	0.00715344i
$807$			9.63602e12i			0.799773i
$808$			1.95724e13i			1.61545i
$809$	2.54255e11	−	2.54255e11i	0.0208690	−	0.0208690i	−0.696595	−	0.717464i	$-0.745303\pi$
$809$	2.54255e11	−	2.54255e11i	0.0208690	−	0.0208690i	0.717464	+	0.696595i	$0.245303\pi$
$810$	2.16726e12	−	2.16726e12i	0.176900	−	0.176900i
$811$	1.37319e13	+	1.37319e13i	1.11465	+	1.11465i	0.992514	+	0.122133i	$0.0389733\pi$
$811$	1.37319e13	+	1.37319e13i	1.11465	+	1.11465i	0.122133	+	0.992514i	$0.461027\pi$
$812$	1.36714e12			0.110360
$813$	−5.67550e12	−	5.67550e12i	−0.455614	−	0.455614i
$814$		−	3.02572e12i		−	0.241557i
$815$	−4.35488e12			−0.345754
$816$	−1.14938e12	+	2.65266e11i	−0.0907521	+	0.0209447i
$817$	1.30950e12			0.102827
$818$			7.06746e12i			0.551917i
$819$	−2.56398e11	−	2.56398e11i	−0.0199130	−	0.0199130i
$820$	−1.10302e13			−0.851966
$821$	8.52535e12	+	8.52535e12i	0.654889	+	0.654889i	0.954166	−	0.299277i	$-0.0967455\pi$
$821$	8.52535e12	+	8.52535e12i	0.654889	+	0.654889i	−0.299277	+	0.954166i	$0.596745\pi$
$822$	−4.76436e11	+	4.76436e11i	−0.0363983	+	0.0363983i
$823$	−1.27479e13	+	1.27479e13i	−0.968591	+	0.968591i	−0.999522	−	0.0309304i	$-0.990153\pi$
$823$	−1.27479e13	+	1.27479e13i	−0.968591	+	0.968591i	0.0309304	+	0.999522i	$0.490153\pi$
$824$		−	9.21295e12i		−	0.696187i
$825$		−	3.15670e12i		−	0.237241i
$826$	1.82404e12	−	1.82404e12i	0.136341	−	0.136341i
$827$	−1.08521e13	+	1.08521e13i	−0.806750	+	0.806750i	−0.984141	−	0.177390i	$-0.943234\pi$
$827$	−1.08521e13	+	1.08521e13i	−0.806750	+	0.806750i	0.177390	+	0.984141i	$0.443234\pi$
$828$	−4.44203e11	−	4.44203e11i	−0.0328431	−	0.0328431i
$829$	−1.06941e13			−0.786412			−0.393206	−	0.919450i	$-0.628634\pi$
$829$	−1.06941e13			−0.786412			−0.393206	+	0.919450i	$0.628634\pi$
$830$	1.16491e13	+	1.16491e13i	0.852005	+	0.852005i
$831$			2.56487e12i			0.186578i
$832$	−1.09868e12			−0.0794905
$833$	1.04198e13	+	6.51206e12i	0.749818	+	0.468615i
$834$	−1.02405e13			−0.732949
$835$		−	2.92726e13i		−	2.08388i
$836$	9.93277e10	+	9.93277e10i	0.00703302	+	0.00703302i
$837$	−1.55055e12			−0.109200
$838$	5.76337e12	+	5.76337e12i	0.403718	+	0.403718i
$839$	−8.80425e12	+	8.80425e12i	−0.613428	+	0.613428i	−0.943838	−	0.330410i	$-0.892813\pi$
$839$	−8.80425e12	+	8.80425e12i	−0.613428	+	0.613428i	0.330410	+	0.943838i	$0.392813\pi$
$840$	−3.56728e12	+	3.56728e12i	−0.247218	+	0.247218i
$841$		−	1.11505e13i		−	0.768623i
$842$			3.34899e12i			0.229620i
$843$	6.83503e10	−	6.83503e10i	0.00466140	−	0.00466140i
$844$	2.21415e12	−	2.21415e12i	0.150199	−	0.150199i
$845$	−1.51179e13	−	1.51179e13i	−1.02009	−	1.02009i
$846$	7.18145e12			0.481998
$847$	3.33991e12	+	3.33991e12i	0.222977	+	0.222977i
$848$			2.81288e12i			0.186797i
$849$	−3.84170e12			−0.253769
$850$	5.58004e12	−	8.92847e12i	0.366651	−	0.586667i
$851$	3.45116e12			0.225570
$852$			7.51971e12i			0.488903i
$853$	−1.22011e13	−	1.22011e13i	−0.789095	−	0.789095i	0.192251	−	0.981346i	$-0.438421\pi$
$853$	−1.22011e13	−	1.22011e13i	−0.789095	−	0.789095i	−0.981346	+	0.192251i	$0.938421\pi$
$854$	2.84551e12			0.183062
$855$	4.27458e11	+	4.27458e11i	0.0273556	+	0.0273556i
$856$	−1.17179e13	+	1.17179e13i	−0.745962	+	0.745962i
$857$	4.00243e12	−	4.00243e12i	0.253461	−	0.253461i	−0.568927	−	0.822388i	$-0.692641\pi$
$857$	4.00243e12	−	4.00243e12i	0.253461	−	0.253461i	0.822388	+	0.568927i	$0.192641\pi$
$858$			3.07420e11i			0.0193660i
$859$		−	6.43103e12i		−	0.403006i	−0.979488	−	0.201503i	$-0.935417\pi$
$859$		−	6.43103e12i		−	0.403006i	0.979488	−	0.201503i	$-0.0645825\pi$
$860$	2.14669e13	−	2.14669e13i	1.33821	−	1.33821i
$861$	2.38303e12	−	2.38303e12i	0.147780	−	0.147780i
$862$	−2.92638e12	−	2.92638e12i	−0.180530	−	0.180530i
$863$	1.51972e13			0.932645			0.466322	−	0.884615i	$-0.345579\pi$
$863$	1.51972e13			0.932645			0.466322	+	0.884615i	$0.345579\pi$
$864$	1.27305e13	+	1.27305e13i	0.777199	+	0.777199i
$865$			8.28660e12i			0.503273i
$866$	7.85412e12			0.474534
$867$	−3.91744e12	+	1.13716e13i	−0.235459	+	0.683497i
$868$	3.92308e11			0.0234578
$869$		−	1.26079e11i		−	0.00749988i
$870$	−3.52714e12	−	3.52714e12i	−0.208731	−	0.208731i
$871$	2.23797e12			0.131757
$872$	−9.79452e12	−	9.79452e12i	−0.573666	−	0.573666i
$873$	5.78509e12	−	5.78509e12i	0.337090	−	0.337090i
$874$	5.47384e10	−	5.47384e10i	0.00317315	−	0.00317315i
$875$			1.86138e12i			0.107349i
$876$			3.60504e12i			0.206843i
$877$	1.10261e13	−	1.10261e13i	0.629398	−	0.629398i	−0.318518	−	0.947917i	$-0.603185\pi$
$877$	1.10261e13	−	1.10261e13i	0.629398	−	0.629398i	0.947917	+	0.318518i	$0.103185\pi$
$878$	8.83716e12	−	8.83716e12i	0.501866	−	0.501866i
$879$	−8.41702e12	−	8.41702e12i	−0.475563	−	0.475563i
$880$	9.22938e11			0.0518800
$881$	−4.62112e12	−	4.62112e12i	−0.258437	−	0.258437i	0.565981	−	0.824418i	$-0.308498\pi$
$881$	−4.62112e12	−	4.62112e12i	−0.258437	−	0.258437i	−0.824418	+	0.565981i	$0.808498\pi$
$882$		−	4.33000e12i		−	0.240924i
$883$	7.83304e12			0.433618			0.216809	−	0.976214i	$-0.430435\pi$
$883$	7.83304e12			0.433618			0.216809	+	0.976214i	$0.430435\pi$
$884$	1.12474e12	−	1.79966e12i	0.0619464	−	0.0991187i
$885$	1.94801e13			1.06745
$886$		−	1.16304e13i		−	0.634078i
$887$	−1.20187e13	−	1.20187e13i	−0.651929	−	0.651929i	0.301528	−	0.953457i	$-0.402503\pi$
$887$	−1.20187e13	−	1.20187e13i	−0.651929	−	0.651929i	−0.953457	+	0.301528i	$0.902503\pi$
$888$	−2.00089e13			−1.07985
$889$	−4.78418e12	−	4.78418e12i	−0.256892	−	0.256892i
$890$	−1.11811e13	+	1.11811e13i	−0.597349	+	0.597349i
$891$	1.06142e12	−	1.06142e12i	0.0564203	−	0.0564203i
$892$		−	9.80131e12i		−	0.518373i
$893$		−	1.83162e12i		−	0.0963840i
$894$	7.84674e12	−	7.84674e12i	0.410838	−	0.410838i
$895$	−2.68810e13	+	2.68810e13i	−1.40037	+	1.40037i
$896$	−3.56230e12	−	3.56230e12i	−0.184648	−	0.184648i
$897$	−3.50645e11			−0.0180843
$898$	2.31195e12	+	2.31195e12i	0.118641	+	0.118641i
$899$			9.63201e11i			0.0491811i
$900$	7.67928e12			0.390148
$901$	2.43217e13	+	1.52004e13i	1.22951	+	0.768410i
$902$	2.61003e12			0.131285
$903$			9.27563e12i			0.464247i
$904$	−2.05246e13	−	2.05246e13i	−1.02215	−	1.02215i
$905$	2.33140e13			1.15531
$906$	−1.05531e12	−	1.05531e12i	−0.0520361	−	0.0520361i
$907$	1.90952e13	−	1.90952e13i	0.936896	−	0.936896i	−0.0612276	−	0.998124i	$-0.519502\pi$
$907$	1.90952e13	−	1.90952e13i	0.936896	−	0.936896i	0.998124	+	0.0612276i	$0.0195016\pi$
$908$	1.88954e13	−	1.88954e13i	0.922509	−	0.922509i
$909$			1.66126e13i			0.807049i
$910$		−	1.03590e12i		−	0.0500761i
$911$	−2.90991e13	+	2.90991e13i	−1.39974	+	1.39974i	−0.598948	+	0.800788i	$0.704415\pi$
$911$	−2.90991e13	+	2.90991e13i	−1.39974	+	1.39974i	−0.800788	+	0.598948i	$0.795585\pi$
$912$	7.49671e10	−	7.49671e10i	0.00358834	−	0.00358834i
$913$	5.70516e12	+	5.70516e12i	0.271737	+	0.271737i
$914$	−1.95204e13			−0.925189
$915$	1.51944e13	+	1.51944e13i	0.716621	+	0.716621i
$916$		−	3.61299e11i		−	0.0169566i
$917$	2.84228e12			0.132741
$918$	1.27808e13	−	2.94968e12i	0.593971	−	0.137083i
$919$	−3.01787e12			−0.139566			−0.0697832	−	0.997562i	$-0.522231\pi$
$919$	−3.01787e12			−0.139566			−0.0697832	+	0.997562i	$0.522231\pi$
$920$		−	4.45644e12i		−	0.205089i
$921$	5.87152e12	+	5.87152e12i	0.268895	+	0.268895i
$922$	−1.04506e13			−0.476267
$923$	−2.71116e12	−	2.71116e12i	−0.122955	−	0.122955i
$924$	−7.03570e11	+	7.03570e11i	−0.0317529	+	0.0317529i
$925$	−2.98314e13	+	2.98314e13i	−1.33979	+	1.33979i
$926$			2.01468e13i			0.900445i
$927$		−	7.81973e12i		−	0.347803i
$928$	7.90814e12	−	7.90814e12i	0.350033	−	0.350033i
$929$	−2.02091e13	+	2.02091e13i	−0.890176	+	0.890176i	−0.994539	−	0.104363i	$-0.966720\pi$
$929$	−2.02091e13	+	2.02091e13i	−0.890176	+	0.890176i	0.104363	+	0.994539i	$0.466720\pi$
$930$	−1.01213e12	−	1.01213e12i	−0.0443675	−	0.0443675i
$931$	−1.10436e12			−0.0481769
$932$	1.48443e13	+	1.48443e13i	0.644446	+	0.644446i
$933$		−	1.72075e13i		−	0.743450i
$934$	4.73818e12			0.203728
$935$	4.98743e12	−	7.98024e12i	0.213415	−	0.341479i
$936$	−1.85705e12			−0.0790829
$937$			3.78192e13i			1.60282i	0.598117	+	0.801409i	$0.295916\pi$
$937$			3.78192e13i			1.60282i	−0.598117	+	0.801409i	$0.704084\pi$
$938$	−2.47466e12	−	2.47466e12i	−0.104376	−	0.104376i
$939$	−3.30407e13			−1.38693
$940$	−3.00261e13	−	3.00261e13i	−1.25436	−	1.25436i
$941$	1.53482e13	−	1.53482e13i	0.638122	−	0.638122i	−0.311970	−	0.950092i	$-0.600989\pi$
$941$	1.53482e13	−	1.53482e13i	0.638122	−	0.638122i	0.950092	+	0.311970i	$0.100989\pi$
$942$	−3.02875e12	+	3.02875e12i	−0.125324	+	0.125324i
$943$			2.97701e12i			0.122596i
$944$			3.12079e12i			0.127906i
$945$	−9.37026e12	+	9.37026e12i	−0.382216	+	0.382216i
$946$	−5.07959e12	+	5.07959e12i	−0.206214	+	0.206214i
$947$	−9.13521e12	−	9.13521e12i	−0.369100	−	0.369100i	0.498049	−	0.867149i	$-0.334050\pi$
$947$	−9.13521e12	−	9.13521e12i	−0.369100	−	0.369100i	−0.867149	+	0.498049i	$0.834050\pi$
$948$	−3.35764e11			−0.0135019
$949$	−1.29976e12	−	1.29976e12i	−0.0520194	−	0.0520194i
$950$			9.46305e11i			0.0376942i
$951$	1.32407e13			0.524927
$952$	−8.02973e12	+	1.85319e12i	−0.316836	+	0.0731229i
$953$	2.66939e13			1.04832			0.524159	−	0.851620i	$-0.324380\pi$
$953$	2.66939e13			1.04832			0.524159	+	0.851620i	$0.324380\pi$
$954$		−	1.01070e13i		−	0.395054i
$955$	9.75344e12	+	9.75344e12i	0.379440	+	0.379440i
$956$	−1.68135e13			−0.651027
$957$	−1.72742e12	−	1.72742e12i	−0.0665723	−	0.0665723i
$958$	−5.23836e12	+	5.23836e12i	−0.200933	+	0.200933i
$959$	7.86255e11	−	7.86255e11i	0.0300179	−	0.0300179i
$960$			1.29744e13i			0.493021i
$961$		−	2.61632e13i		−	0.989546i
$962$	2.90518e12	−	2.90518e12i	0.109367	−	0.109367i
$963$	−9.94585e12	+	9.94585e12i	−0.372669	+	0.372669i
$964$	2.10176e13	+	2.10176e13i	0.783855	+	0.783855i
$965$	−2.67001e13			−0.991153
$966$	3.87729e11	+	3.87729e11i	0.0143262	+	0.0143262i
$967$		−	2.52091e13i		−	0.927124i	−0.886064	−	0.463562i	$-0.846571\pi$
$967$		−	2.52091e13i		−	0.927124i	0.886064	−	0.463562i	$-0.153429\pi$
$968$	2.41905e13			0.885534
$969$	−2.43096e11	−	1.05332e12i	−0.00885771	−	0.0383798i
$970$	2.33729e13			0.847696
$971$			3.23630e13i			1.16832i	0.811638	+	0.584161i	$0.198576\pi$
$971$			3.23630e13i			1.16832i	−0.811638	+	0.584161i	$0.801424\pi$
$972$	1.13437e13	+	1.13437e13i	0.407620	+	0.407620i
$973$	1.68997e13			0.604466
$974$	1.42837e13	+	1.42837e13i	0.508540	+	0.508540i
$975$	3.03094e12	−	3.03094e12i	0.107413	−	0.107413i
$976$	−2.43421e12	+	2.43421e12i	−0.0858687	+	0.0858687i
$977$		−	3.01878e13i		−	1.06000i	−0.847997	−	0.530001i	$-0.822192\pi$
$977$		−	3.01878e13i		−	1.06000i	0.847997	−	0.530001i	$-0.177808\pi$
$978$		−	2.74427e12i		−	0.0959184i
$979$	−5.47592e12	+	5.47592e12i	−0.190517	+	0.190517i
$980$	−1.81040e13	+	1.81040e13i	−0.626985	+	0.626985i
$981$	−8.31336e12	−	8.31336e12i	−0.286593	−	0.286593i
$982$	1.55635e12			0.0534080
$983$	2.83115e13	+	2.83115e13i	0.967100	+	0.967100i	0.999476	−	0.0323756i	$-0.0103073\pi$
$983$	2.83115e13	+	2.83115e13i	0.967100	+	0.967100i	−0.0323756	+	0.999476i	$0.510307\pi$
$984$		−	1.72599e13i		−	0.586896i
$985$	−1.90197e13			−0.643785
$986$	−1.83234e12	−	7.93939e12i	−0.0617390	−	0.267511i
$987$	1.29740e13			0.435157
$988$			1.90741e11i			0.00636852i
$989$	−5.79381e12	−	5.79381e12i	−0.192567	−	0.192567i
$990$	−3.31624e12			−0.109720
$991$	1.25293e13	+	1.25293e13i	0.412662	+	0.412662i	0.882665	−	0.470003i	$-0.155747\pi$
$991$	1.25293e13	+	1.25293e13i	0.412662	+	0.412662i	−0.470003	+	0.882665i	$0.655747\pi$
$992$	2.26929e12	−	2.26929e12i	0.0744024	−	0.0744024i
$993$	7.72736e12	−	7.72736e12i	0.252208	−	0.252208i
$994$			5.99578e12i			0.194808i
$995$		−	8.35870e13i		−	2.70355i
$996$	1.51935e13	−	1.51935e13i	0.489205	−	0.489205i
$997$	1.07480e13	−	1.07480e13i	0.344510	−	0.344510i	−0.513550	−	0.858060i	$-0.671670\pi$
$997$	1.07480e13	−	1.07480e13i	0.344510	−	0.344510i	0.858060	+	0.513550i	$0.171670\pi$
$998$	4.52996e12	+	4.52996e12i	0.144546	+	0.144546i
$999$	−5.25579e13			−1.66953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.5	yes	24
17.2	even	8		289.10.a.f.1.15		24
17.4	even	4	inner	17.10.c.a.4.8	✓	24
17.15	even	8		289.10.a.f.1.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.8	✓	24	17.4	even	4	inner
17.10.c.a.13.5	yes	24	1.1	even	1	trivial
289.10.a.f.1.15		24	17.2	even	8
289.10.a.f.1.16		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)

\(f(q)\)	\(=\)	\(q-12.9147i q^{2} +(-71.7165 - 71.7165i) q^{3} +345.210 q^{4} +(1469.78 + 1469.78i) q^{5} +(-926.198 + 926.198i) q^{6} +(1528.49 - 1528.49i) q^{7} -11070.6i q^{8} -9396.49i q^{9} +O(q^{10})\)	\(q-12.9147i q^{2} +(-71.7165 - 71.7165i) q^{3} +345.210 q^{4} +(1469.78 + 1469.78i) q^{5} +(-926.198 + 926.198i) q^{6} +(1528.49 - 1528.49i) q^{7} -11070.6i q^{8} -9396.49i q^{9} +(18981.8 - 18981.8i) q^{10} +(9296.34 - 9296.34i) q^{11} +(-24757.3 - 24757.3i) q^{12} +17852.0 q^{13} +(-19740.0 - 19740.0i) q^{14} -210815. i q^{15} +33773.6 q^{16} +(182508. - 292025. i) q^{17} -121353. q^{18} +30951.0i q^{19} +(507384. + 507384. i) q^{20} -219236. q^{21} +(-120060. - 120060. i) q^{22} +(136941. - 136941. i) q^{23} +(-793947. + 793947. i) q^{24} +2.36740e6i q^{25} -230553. i q^{26} +(-2.08548e6 + 2.08548e6i) q^{27} +(527650. - 527650. i) q^{28} +(1.29550e6 + 1.29550e6i) q^{29} -2.72262e6 q^{30} +(371750. + 371750. i) q^{31} -6.10434e6i q^{32} -1.33340e6 q^{33} +(-3.77143e6 - 2.35703e6i) q^{34} +4.49310e6 q^{35} -3.24376e6i q^{36} +(1.26009e7 + 1.26009e7i) q^{37} +399723. q^{38} +(-1.28028e6 - 1.28028e6i) q^{39} +(1.62714e7 - 1.62714e7i) q^{40} +(-1.08697e7 + 1.08697e7i) q^{41} +2.83137e6i q^{42} -4.23089e7i q^{43} +(3.20919e6 - 3.20919e6i) q^{44} +(1.38108e7 - 1.38108e7i) q^{45} +(-1.76855e6 - 1.76855e6i) q^{46} -5.91782e7 q^{47} +(-2.42212e6 - 2.42212e6i) q^{48} +3.56810e7i q^{49} +3.05743e7 q^{50} +(-3.40319e7 + 7.85424e6i) q^{51} +6.16269e6 q^{52} +8.32863e7i q^{53} +(2.69334e7 + 2.69334e7i) q^{54} +2.73272e7 q^{55} +(-1.69213e7 - 1.69213e7i) q^{56} +(2.21970e6 - 2.21970e6i) q^{57} +(1.67310e7 - 1.67310e7i) q^{58} +9.24034e7i q^{59} -7.27756e7i q^{60} +(-7.20746e7 + 7.20746e7i) q^{61} +(4.80105e6 - 4.80105e6i) q^{62} +(-1.43624e7 - 1.43624e7i) q^{63} -6.15437e7 q^{64} +(2.62385e7 + 2.62385e7i) q^{65} +1.72205e7i q^{66} +1.25363e8 q^{67} +(6.30035e7 - 1.00810e8i) q^{68} -1.96418e7 q^{69} -5.80271e7i q^{70} +(-1.51869e8 - 1.51869e8i) q^{71} -1.04025e8 q^{72} +(-7.28077e7 - 7.28077e7i) q^{73} +(1.62737e8 - 1.62737e8i) q^{74} +(1.69782e8 - 1.69782e8i) q^{75} +1.06846e7i q^{76} -2.84187e7i q^{77} +(-1.65345e7 + 1.65345e7i) q^{78} +(6.78112e6 - 6.78112e6i) q^{79} +(4.96398e7 + 4.96398e7i) q^{80} +1.14176e8 q^{81} +(1.40379e8 + 1.40379e8i) q^{82} +6.13699e8i q^{83} -7.56824e7 q^{84} +(6.97461e8 - 1.60967e8i) q^{85} -5.46408e8 q^{86} -1.85817e8i q^{87} +(-1.02916e8 - 1.02916e8i) q^{88} -5.89040e8 q^{89} +(-1.78363e8 - 1.78363e8i) q^{90} +(2.72866e7 - 2.72866e7i) q^{91} +(4.72733e7 - 4.72733e7i) q^{92} -5.33212e7i q^{93} +7.64270e8i q^{94} +(-4.54912e7 + 4.54912e7i) q^{95} +(-4.37782e8 + 4.37782e8i) q^{96} +(6.15665e8 + 6.15665e8i) q^{97} +4.60811e8 q^{98} +(-8.73530e7 - 8.73530e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7 + 21946 * q^10 + 18132 * q^11 - 95142 * q^12 + 244832 * q^13 - 341100 * q^14 - 279932 * q^16 - 98022 * q^17 + 888764 * q^18 + 1364262 * q^20 - 775748 * q^21 - 4573190 * q^22 - 377526 * q^23 - 307054 * q^24 + 3996108 * q^27 - 1024780 * q^28 + 2160042 * q^29 + 39084792 * q^30 - 585086 * q^31 - 30349992 * q^33 + 4441318 * q^34 - 25532364 * q^35 + 1515390 * q^37 + 13171392 * q^38 - 25687084 * q^39 - 63240118 * q^40 - 72707928 * q^41 - 3606450 * q^44 + 156729418 * q^45 + 118549536 * q^46 + 153365328 * q^47 + 26098270 * q^48 - 236105676 * q^50 + 256903592 * q^51 - 209898380 * q^52 - 187411976 * q^54 + 255767540 * q^55 - 107638596 * q^56 - 443390988 * q^57 - 281433730 * q^58 + 52149382 * q^61 + 176928228 * q^62 + 620111642 * q^63 + 1006108924 * q^64 - 489714396 * q^65 - 26076868 * q^67 - 308011950 * q^68 - 751973532 * q^69 + 149240178 * q^71 + 1171736028 * q^72 - 175256556 * q^73 - 37609818 * q^74 - 233543476 * q^75 - 1202722924 * q^78 - 469987182 * q^79 + 481103586 * q^80 + 347156560 * q^81 - 984422080 * q^82 - 935672904 * q^84 - 725828294 * q^85 + 690159588 * q^86 + 992281114 * q^88 - 191594460 * q^89 + 914946474 * q^90 + 926854816 * q^91 + 3064830552 * q^92 + 1213246572 * q^95 + 3594247550 * q^96 - 2200567348 * q^97 - 4413444720 * q^98 - 1224966600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more