LMFDB - Embedded newform 17.10.c.a.13.10

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			13.10
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.4159i q^{2} +(42.7255 + 42.7255i) q^{3} -474.957 q^{4} +(1118.79 + 1118.79i) q^{5} +(-1342.26 + 1342.26i) q^{6} +(-7416.51 + 7416.51i) q^{7} +1163.73i q^{8} -16032.1i q^{9} +O(q^{10})$	\(q+31.4159i q^{2} +(42.7255 + 42.7255i) q^{3} -474.957 q^{4} +(1118.79 + 1118.79i) q^{5} +(-1342.26 + 1342.26i) q^{6} +(-7416.51 + 7416.51i) q^{7} +1163.73i q^{8} -16032.1i q^{9} +(-35147.8 + 35147.8i) q^{10} +(55286.6 - 55286.6i) q^{11} +(-20292.8 - 20292.8i) q^{12} -111709. q^{13} +(-232996. - 232996. i) q^{14} +95601.8i q^{15} -279738. q^{16} +(245670. + 241318. i) q^{17} +503661. q^{18} +202367. i q^{19} +(-531377. - 531377. i) q^{20} -633749. q^{21} +(1.73688e6 + 1.73688e6i) q^{22} +(-536747. + 536747. i) q^{23} +(-49721.2 + 49721.2i) q^{24} +550256. i q^{25} -3.50943e6i q^{26} +(1.52595e6 - 1.52595e6i) q^{27} +(3.52252e6 - 3.52252e6i) q^{28} +(5.29614e6 + 5.29614e6i) q^{29} -3.00341e6 q^{30} +(751860. + 751860. i) q^{31} -8.19237e6i q^{32} +4.72430e6 q^{33} +(-7.58121e6 + 7.71792e6i) q^{34} -1.65950e7 q^{35} +7.61454e6i q^{36} +(7.95621e6 + 7.95621e6i) q^{37} -6.35754e6 q^{38} +(-4.77282e6 - 4.77282e6i) q^{39} +(-1.30197e6 + 1.30197e6i) q^{40} +(-928424. + 928424. i) q^{41} -1.99098e7i q^{42} +5.13056e6i q^{43} +(-2.62588e7 + 2.62588e7i) q^{44} +(1.79365e7 - 1.79365e7i) q^{45} +(-1.68624e7 - 1.68624e7i) q^{46} +2.33308e7 q^{47} +(-1.19519e7 - 1.19519e7i) q^{48} -6.96556e7i q^{49} -1.72868e7 q^{50} +(185922. + 2.08068e7i) q^{51} +5.30569e7 q^{52} +4.46435e7i q^{53} +(4.79389e7 + 4.79389e7i) q^{54} +1.23708e8 q^{55} +(-8.63084e6 - 8.63084e6i) q^{56} +(-8.64625e6 + 8.64625e6i) q^{57} +(-1.66383e8 + 1.66383e8i) q^{58} -1.89411e7i q^{59} -4.54068e7i q^{60} +(9.54433e7 - 9.54433e7i) q^{61} +(-2.36203e7 + 2.36203e7i) q^{62} +(1.18902e8 + 1.18902e8i) q^{63} +1.14145e8 q^{64} +(-1.24979e8 - 1.24979e8i) q^{65} +1.48418e8i q^{66} -3.24318e6 q^{67} +(-1.16682e8 - 1.14616e8i) q^{68} -4.58657e7 q^{69} -5.21347e8i q^{70} +(-1.71449e8 - 1.71449e8i) q^{71} +1.86570e7 q^{72} +(8.06012e7 + 8.06012e7i) q^{73} +(-2.49951e8 + 2.49951e8i) q^{74} +(-2.35100e7 + 2.35100e7i) q^{75} -9.61157e7i q^{76} +8.20068e8i q^{77} +(1.49942e8 - 1.49942e8i) q^{78} +(-3.01368e7 + 3.01368e7i) q^{79} +(-3.12968e8 - 3.12968e8i) q^{80} -1.85165e8 q^{81} +(-2.91672e7 - 2.91672e7i) q^{82} -4.37207e8i q^{83} +3.01003e8 q^{84} +(4.86847e6 + 5.44837e8i) q^{85} -1.61181e8 q^{86} +4.52561e8i q^{87} +(6.43389e7 + 6.43389e7i) q^{88} -5.60941e7 q^{89} +(5.63491e8 + 5.63491e8i) q^{90} +(8.28490e8 - 8.28490e8i) q^{91} +(2.54932e8 - 2.54932e8i) q^{92} +6.42473e7i q^{93} +7.32958e8i q^{94} +(-2.26406e8 + 2.26406e8i) q^{95} +(3.50024e8 - 3.50024e8i) q^{96} +(-1.07707e9 - 1.07707e9i) q^{97} +2.18829e9 q^{98} +(-8.86358e8 - 8.86358e8i) 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 $

$2$			31.4159i			1.38840i	0.719783	+	0.694199i	$0.244241\pi$
$2$			31.4159i			1.38840i	−0.719783	+	0.694199i	$0.755759\pi$
$3$	42.7255	+	42.7255i	0.304538	+	0.304538i	0.842786	−	0.538248i	$-0.180914\pi$
$3$	42.7255	+	42.7255i	0.304538	+	0.304538i	−0.538248	+	0.842786i	$0.680914\pi$
$4$	−474.957			−0.927651
$5$	1118.79	+	1118.79i	0.800541	+	0.800541i	0.983180	−	0.182639i	$-0.0584640\pi$
$5$	1118.79	+	1118.79i	0.800541	+	0.800541i	−0.182639	+	0.983180i	$0.558464\pi$
$6$	−1342.26	+	1342.26i	−0.422821	+	0.422821i
$7$	−7416.51	+	7416.51i	−1.16750	+	1.16750i	−0.184711	+	0.982793i	$0.559135\pi$
$7$	−7416.51	+	7416.51i	−1.16750	+	1.16750i	−0.982793	+	0.184711i	$0.940865\pi$
$8$			1163.73i			0.100450i
$9$		−	16032.1i		−	0.814513i
$10$	−35147.8	+	35147.8i	−1.11147	+	1.11147i
$11$	55286.6	−	55286.6i	1.13855	−	1.13855i	0.149843	−	0.988710i	$-0.452123\pi$
$11$	55286.6	−	55286.6i	1.13855	−	1.13855i	0.988710	−	0.149843i	$-0.0478767\pi$
$12$	−20292.8	−	20292.8i	−0.282505	−	0.282505i
$13$	−111709.			−1.08478			−0.542391	−	0.840126i	$-0.682481\pi$
$13$	−111709.			−1.08478			−0.542391	+	0.840126i	$0.682481\pi$
$14$	−232996.	−	232996.i	−1.62096	−	1.62096i
$15$			95601.8i			0.487591i
$16$	−279738.			−1.06711
$17$	245670.	+	241318.i	0.713397	+	0.700760i
$17$	245670.	+	241318.i	0.713397	+	0.700760i
$18$	503661.			1.13087
$19$			202367.i			0.356245i	0.984008	+	0.178123i	$0.0570023\pi$
$19$			202367.i			0.356245i	−0.984008	+	0.178123i	$0.942998\pi$
$20$	−531377.	−	531377.i	−0.742622	−	0.742622i
$21$	−633749.			−0.711099
$22$	1.73688e6	+	1.73688e6i	1.58076	+	1.58076i
$23$	−536747.	+	536747.i	−0.399940	+	0.399940i	−0.878212	−	0.478272i	$-0.841263\pi$
$23$	−536747.	+	536747.i	−0.399940	+	0.399940i	0.478272	+	0.878212i	$0.341263\pi$
$24$	−49721.2	+	49721.2i	−0.0305908	+	0.0305908i
$25$			550256.i			0.281731i
$26$		−	3.50943e6i		−	1.50611i
$27$	1.52595e6	−	1.52595e6i	0.552589	−	0.552589i
$28$	3.52252e6	−	3.52252e6i	1.08304	−	1.08304i
$29$	5.29614e6	+	5.29614e6i	1.39049	+	1.39049i	0.824215	+	0.566277i	$0.191617\pi$
$29$	5.29614e6	+	5.29614e6i	1.39049	+	1.39049i	0.566277	+	0.824215i	$0.308383\pi$
$30$	−3.00341e6			−0.676970
$31$	751860.	+	751860.i	0.146221	+	0.146221i	0.776427	−	0.630207i	$-0.217030\pi$
$31$	751860.	+	751860.i	0.146221	+	0.146221i	−0.630207	+	0.776427i	$0.717030\pi$
$32$		−	8.19237e6i		−	1.38113i
$33$	4.72430e6			0.693466
$34$	−7.58121e6	+	7.71792e6i	−0.972935	+	0.990479i
$35$	−1.65950e7			−1.86927
$36$			7.61454e6i			0.755583i
$37$	7.95621e6	+	7.95621e6i	0.697908	+	0.697908i	0.963959	−	0.266051i	$-0.0857189\pi$
$37$	7.95621e6	+	7.95621e6i	0.697908	+	0.697908i	−0.266051	+	0.963959i	$0.585719\pi$
$38$	−6.35754e6			−0.494610
$39$	−4.77282e6	−	4.77282e6i	−0.330358	−	0.330358i
$40$	−1.30197e6	+	1.30197e6i	−0.0804141	+	0.0804141i
$41$	−928424.	+	928424.i	−0.0513120	+	0.0513120i	−0.732297	−	0.680985i	$-0.761552\pi$
$41$	−928424.	+	928424.i	−0.0513120	+	0.0513120i	0.680985	+	0.732297i	$0.261552\pi$
$42$		−	1.99098e7i		−	0.987289i
$43$			5.13056e6i			0.228853i	0.993432	+	0.114427i	$0.0365030\pi$
$43$			5.13056e6i			0.228853i	−0.993432	+	0.114427i	$0.963497\pi$
$44$	−2.62588e7	+	2.62588e7i	−1.05618	+	1.05618i
$45$	1.79365e7	−	1.79365e7i	0.652051	−	0.652051i
$46$	−1.68624e7	−	1.68624e7i	−0.555276	−	0.555276i
$47$	2.33308e7			0.697412			0.348706	−	0.937232i	$-0.386621\pi$
$47$	2.33308e7			0.697412			0.348706	+	0.937232i	$0.386621\pi$
$48$	−1.19519e7	−	1.19519e7i	−0.324977	−	0.324977i
$49$		−	6.96556e7i		−	1.72613i
$50$	−1.72868e7			−0.391155
$51$	185922.	+	2.08068e7i	0.00384827	+	0.430665i
$52$	5.30569e7			1.00630
$53$			4.46435e7i			0.777172i	0.921413	+	0.388586i	$0.127036\pi$
$53$			4.46435e7i			0.777172i	−0.921413	+	0.388586i	$0.872964\pi$
$54$	4.79389e7	+	4.79389e7i	0.767213	+	0.767213i
$55$	1.23708e8			1.82292
$56$	−8.63084e6	−	8.63084e6i	−0.117275	−	0.117275i
$57$	−8.64625e6	+	8.64625e6i	−0.108490	+	0.108490i
$58$	−1.66383e8	+	1.66383e8i	−1.93056	+	1.93056i
$59$		−	1.89411e7i		−	0.203503i	−0.994810	−	0.101751i	$-0.967555\pi$
$59$		−	1.89411e7i		−	0.203503i	0.994810	−	0.101751i	$-0.0324446\pi$
$60$		−	4.54068e7i		−	0.452314i
$61$	9.54433e7	−	9.54433e7i	0.882595	−	0.882595i	−0.111203	−	0.993798i	$-0.535470\pi$
$61$	9.54433e7	−	9.54433e7i	0.882595	−	0.882595i	0.993798	+	0.111203i	$0.0354704\pi$
$62$	−2.36203e7	+	2.36203e7i	−0.203013	+	0.203013i
$63$	1.18902e8	+	1.18902e8i	0.950947	+	0.950947i
$64$	1.14145e8			0.850446
$65$	−1.24979e8	−	1.24979e8i	−0.868412	−	0.868412i
$66$			1.48418e8i			0.962807i
$67$	−3.24318e6			−0.0196623			−0.00983115	−	0.999952i	$-0.503129\pi$
$67$	−3.24318e6			−0.0196623			−0.00983115	+	0.999952i	$0.503129\pi$
$68$	−1.16682e8	−	1.14616e8i	−0.661783	−	0.650061i
$69$	−4.58657e7			−0.243594
$70$		−	5.21347e8i		−	2.59529i
$71$	−1.71449e8	−	1.71449e8i	−0.800705	−	0.800705i	0.182501	−	0.983206i	$-0.441581\pi$
$71$	−1.71449e8	−	1.71449e8i	−0.800705	−	0.800705i	−0.983206	+	0.182501i	$0.941581\pi$
$72$	1.86570e7			0.0818176
$73$	8.06012e7	+	8.06012e7i	0.332192	+	0.332192i	0.853418	−	0.521227i	$-0.174525\pi$
$73$	8.06012e7	+	8.06012e7i	0.332192	+	0.332192i	−0.521227	+	0.853418i	$0.674525\pi$
$74$	−2.49951e8	+	2.49951e8i	−0.968975	+	0.968975i
$75$	−2.35100e7	+	2.35100e7i	−0.0857978	+	0.0857978i
$76$		−	9.61157e7i		−	0.330471i
$77$			8.20068e8i			2.65853i
$78$	1.49942e8	−	1.49942e8i	0.458668	−	0.458668i
$79$	−3.01368e7	+	3.01368e7i	−0.0870513	+	0.0870513i	−0.749292	−	0.662240i	$-0.769606\pi$
$79$	−3.01368e7	+	3.01368e7i	−0.0870513	+	0.0870513i	0.662240	+	0.749292i	$0.269606\pi$
$80$	−3.12968e8	−	3.12968e8i	−0.854269	−	0.854269i
$81$	−1.85165e8			−0.477944
$82$	−2.91672e7	−	2.91672e7i	−0.0712415	−	0.0712415i
$83$		−	4.37207e8i		−	1.01120i	−0.862769	−	0.505598i	$-0.831272\pi$
$83$		−	4.37207e8i		−	1.01120i	0.862769	−	0.505598i	$-0.168728\pi$
$84$	3.01003e8			0.659652
$85$	4.86847e6	+	5.44837e8i	0.0101160	+	1.13209i
$86$	−1.61181e8			−0.317739
$87$			4.52561e8i			0.846916i
$88$	6.43389e7	+	6.43389e7i	0.114367	+	0.114367i
$89$	−5.60941e7			−0.0947681			−0.0473840	−	0.998877i	$-0.515088\pi$
$89$	−5.60941e7			−0.0947681			−0.0473840	+	0.998877i	$0.515088\pi$
$90$	5.63491e8	+	5.63491e8i	0.905306	+	0.905306i
$91$	8.28490e8	−	8.28490e8i	1.26649	−	1.26649i
$92$	2.54932e8	−	2.54932e8i	0.371004	−	0.371004i
$93$			6.42473e7i			0.0890598i
$94$			7.32958e8i			0.968286i
$95$	−2.26406e8	+	2.26406e8i	−0.285189	+	0.285189i
$96$	3.50024e8	−	3.50024e8i	0.420607	−	0.420607i
$97$	−1.07707e9	−	1.07707e9i	−1.23530	−	1.23530i	−0.961900	−	0.273402i	$-0.911851\pi$
$97$	−1.07707e9	−	1.07707e9i	−1.23530	−	1.23530i	−0.273402	−	0.961900i	$-0.588149\pi$
$98$	2.18829e9			2.39656
$99$	−8.86358e8	−	8.86358e8i	−0.927366	−	0.927366i
$100$		−	2.61348e8i		−	0.261348i
$101$	1.68043e9			1.60684			0.803422	−	0.595411i	$-0.203011\pi$
$101$	1.68043e9			1.60684			0.803422	+	0.595411i	$0.203011\pi$
$102$	−6.53664e8	+	5.84092e6i	−0.597935	+	0.00534294i
$103$	−1.19381e9			−1.04513			−0.522563	−	0.852600i	$-0.675024\pi$
$103$	−1.19381e9			−1.04513			−0.522563	+	0.852600i	$0.675024\pi$
$104$		−	1.29999e8i		−	0.108966i
$105$	−7.09032e8	−	7.09032e8i	−0.569264	−	0.569264i
$106$	−1.40251e9			−1.07902
$107$	1.23443e9	+	1.23443e9i	0.910415	+	0.910415i	0.996305	−	0.0858898i	$-0.0273733\pi$
$107$	1.23443e9	+	1.23443e9i	0.910415	+	0.910415i	−0.0858898	+	0.996305i	$0.527373\pi$
$108$	−7.24759e8	+	7.24759e8i	−0.512609	+	0.512609i
$109$	4.33195e8	−	4.33195e8i	0.293944	−	0.293944i	−0.544692	−	0.838636i	$-0.683353\pi$
$109$	4.33195e8	−	4.33195e8i	0.293944	−	0.293944i	0.838636	+	0.544692i	$0.183353\pi$
$110$			3.88640e9i			2.53093i
$111$			6.79866e8i			0.425080i
$112$	2.07468e9	−	2.07468e9i	1.24586	−	1.24586i
$113$	−6.23337e8	+	6.23337e8i	−0.359642	+	0.359642i	−0.863681	−	0.504039i	$-0.831847\pi$
$113$	−6.23337e8	+	6.23337e8i	−0.359642	+	0.359642i	0.504039	+	0.863681i	$0.331847\pi$
$114$	−2.71629e8	−	2.71629e8i	−0.150628	−	0.150628i
$115$	−1.20101e9			−0.640336
$116$	−2.51544e9	−	2.51544e9i	−1.28989	−	1.28989i
$117$			1.79092e9i			0.883569i
$118$	5.95050e8			0.282543
$119$	−3.61175e9	+	3.22733e7i	−1.65103	+	0.0147531i
$120$	−1.11255e8			−0.0489783
$121$		−	3.75528e9i		−	1.59260i
$122$	2.99844e9	+	2.99844e9i	1.22539	+	1.22539i
$123$	−7.93348e7			−0.0312529
$124$	−3.57101e8	−	3.57101e8i	−0.135642	−	0.135642i
$125$	1.56952e9	−	1.56952e9i	0.575004	−	0.575004i
$126$	−3.73541e9	+	3.73541e9i	−1.32029	+	1.32029i
$127$		−	8.61290e8i		−	0.293787i	−0.989152	−	0.146894i	$-0.953073\pi$
$127$		−	8.61290e8i		−	0.293787i	0.989152	−	0.146894i	$-0.0469275\pi$
$128$		−	6.08535e8i		−	0.200374i
$129$	−2.19206e8	+	2.19206e8i	−0.0696945	+	0.0696945i
$130$	3.92632e9	−	3.92632e9i	1.20570	−	1.20570i
$131$	−5.52585e8	−	5.52585e8i	−0.163938	−	0.163938i	0.620371	−	0.784309i	$-0.286982\pi$
$131$	−5.52585e8	−	5.52585e8i	−0.163938	−	0.163938i	−0.784309	+	0.620371i	$0.786982\pi$
$132$	−2.24384e9			−0.643294
$133$	−1.50086e9	−	1.50086e9i	−0.415917	−	0.415917i
$134$		−	1.01887e8i		−	0.0272991i
$135$	3.41442e9			0.884740
$136$	−2.80830e8	+	2.85894e8i	−0.0703912	+	0.0716605i
$137$	6.19075e9			1.50141			0.750707	−	0.660635i	$-0.229713\pi$
$137$	6.19075e9			1.50141			0.750707	+	0.660635i	$0.229713\pi$
$138$		−	1.44091e9i		−	0.338206i
$139$	−1.70670e8	−	1.70670e8i	−0.0387785	−	0.0387785i	0.687452	−	0.726230i	$-0.258729\pi$
$139$	−1.70670e8	−	1.70670e8i	−0.0387785	−	0.0387785i	−0.726230	+	0.687452i	$0.758729\pi$
$140$	7.88193e9			1.73403
$141$	9.96822e8	+	9.96822e8i	0.212389	+	0.212389i
$142$	5.38622e9	−	5.38622e9i	1.11170	−	1.11170i
$143$	−6.17601e9	+	6.17601e9i	−1.23508	+	1.23508i
$144$			4.48477e9i			0.869179i
$145$			1.18505e10i			2.22629i
$146$	−2.53216e9	+	2.53216e9i	−0.461215	+	0.461215i
$147$	2.97607e9	−	2.97607e9i	0.525673	−	0.525673i
$148$	−3.77886e9	−	3.77886e9i	−0.647415	−	0.647415i
$149$	1.37424e9			0.228415			0.114208	−	0.993457i	$-0.463567\pi$
$149$	1.37424e9			0.228415			0.114208	+	0.993457i	$0.463567\pi$
$150$	−7.38586e8	−	7.38586e8i	−0.119122	−	0.119122i
$151$			4.38413e9i			0.686258i	0.939288	+	0.343129i	$0.111487\pi$
$151$			4.38413e9i			0.686258i	−0.939288	+	0.343129i	$0.888513\pi$
$152$	−2.35501e8			−0.0357847
$153$	3.86882e9	−	3.93859e9i	0.570778	−	0.581071i
$154$	−2.57631e10			−3.69110
$155$			1.68235e9i			0.234112i
$156$	2.26689e9	+	2.26689e9i	0.306457	+	0.306457i
$157$	8.04346e9			1.05656			0.528280	−	0.849070i	$-0.322837\pi$
$157$	8.04346e9			1.05656			0.528280	+	0.849070i	$0.322837\pi$
$158$	−9.46775e8	−	9.46775e8i	−0.120862	−	0.120862i
$159$	−1.90742e9	+	1.90742e9i	−0.236679	+	0.236679i
$160$	9.16554e9	−	9.16554e9i	1.10565	−	1.10565i
$161$		−	7.96158e9i		−	0.933863i
$162$		−	5.81713e9i		−	0.663577i
$163$	−3.56716e9	+	3.56716e9i	−0.395802	+	0.395802i	−0.876750	−	0.480947i	$-0.840293\pi$
$163$	−3.56716e9	+	3.56716e9i	−0.395802	+	0.395802i	0.480947	+	0.876750i	$0.340293\pi$
$164$	4.40961e8	−	4.40961e8i	0.0475996	−	0.0475996i
$165$	5.28550e9	+	5.28550e9i	0.555148	+	0.555148i
$166$	1.37352e10			1.40394
$167$	−1.33521e10	−	1.33521e10i	−1.32839	−	1.32839i	−0.906777	−	0.421610i	$-0.861465\pi$
$167$	−1.33521e10	−	1.33521e10i	−1.32839	−	1.32839i	−0.421610	−	0.906777i	$-0.638535\pi$
$168$		−	7.37515e8i		−	0.0714297i
$169$	1.87437e9			0.176752
$170$	−1.71165e10	+	1.52947e8i	−1.57179	+	0.0140450i
$171$	3.24436e9			0.290166
$172$		−	2.43680e9i		−	0.212296i
$173$	−2.14639e9	−	2.14639e9i	−0.182180	−	0.182180i	0.610125	−	0.792305i	$-0.291119\pi$
$173$	−2.14639e9	−	2.14639e9i	−0.182180	−	0.182180i	−0.792305	+	0.610125i	$0.791119\pi$
$174$	−1.42176e10			−1.17586
$175$	−4.08097e9	−	4.08097e9i	−0.328922	−	0.328922i
$176$	−1.54658e10	+	1.54658e10i	−1.21497	+	1.21497i
$177$	8.09268e8	−	8.09268e8i	0.0619744	−	0.0619744i
$178$		−	1.76225e9i		−	0.131576i
$179$		−	9.45985e9i		−	0.688724i	−0.938837	−	0.344362i	$-0.888095\pi$
$179$		−	9.45985e9i		−	0.688724i	0.938837	−	0.344362i	$-0.111905\pi$
$180$	−8.51907e9	+	8.51907e9i	−0.604875	+	0.604875i
$181$	5.32625e9	−	5.32625e9i	0.368865	−	0.368865i	−0.498198	−	0.867063i	$-0.666005\pi$
$181$	5.32625e9	−	5.32625e9i	0.368865	−	0.368865i	0.867063	+	0.498198i	$0.166005\pi$
$182$	2.60277e10	+	2.60277e10i	1.75839	+	1.75839i
$183$	8.15574e9			0.537568
$184$	−6.24631e8	−	6.24631e8i	−0.0401738	−	0.0401738i
$185$			1.78026e10i			1.11741i
$186$	−2.01838e9			−0.123650
$187$	2.69239e10	−	2.40583e8i	1.61009	−	0.0143872i
$188$	−1.10811e10			−0.646955
$189$			2.26344e10i			1.29030i
$190$	−7.11275e9	−	7.11275e9i	−0.395955	−	0.395955i
$191$	−7.27813e9			−0.395703			−0.197852	−	0.980232i	$-0.563396\pi$
$191$	−7.27813e9			−0.395703			−0.197852	+	0.980232i	$0.563396\pi$
$192$	4.87690e9	+	4.87690e9i	0.258993	+	0.258993i
$193$	5.37750e9	−	5.37750e9i	0.278979	−	0.278979i	−0.553722	−	0.832702i	$-0.686793\pi$
$193$	5.37750e9	−	5.37750e9i	0.278979	−	0.278979i	0.832702	+	0.553722i	$0.186793\pi$
$194$	3.38372e10	−	3.38372e10i	1.71509	−	1.71509i
$195$		−	1.06796e10i		−	0.528930i
$196$			3.30834e10i			1.60125i
$197$	1.54200e10	−	1.54200e10i	0.729433	−	0.729433i	−0.241074	−	0.970507i	$-0.577500\pi$
$197$	1.54200e10	−	1.54200e10i	0.729433	−	0.729433i	0.970507	+	0.241074i	$0.0774997\pi$
$198$	2.78457e10	−	2.78457e10i	1.28755	−	1.28755i
$199$	−9.91231e9	−	9.91231e9i	−0.448060	−	0.448060i	0.446649	−	0.894709i	$-0.352617\pi$
$199$	−9.91231e9	−	9.91231e9i	−0.448060	−	0.448060i	−0.894709	+	0.446649i	$0.852617\pi$
$200$	−6.40351e8			−0.0282998
$201$	−1.38567e8	−	1.38567e8i	−0.00598793	−	0.00598793i
$202$			5.27921e10i			2.23094i
$203$	−7.85577e10			−3.24681
$204$	−8.83052e7	−	9.88234e9i	−0.00356985	−	0.399507i
$205$	−2.07742e9			−0.0821547
$206$		−	3.75047e10i		−	1.45105i
$207$	8.60516e9	+	8.60516e9i	0.325756	+	0.325756i
$208$	3.12492e10			1.15759
$209$	1.11882e10	+	1.11882e10i	0.405604	+	0.405604i
$210$	2.22748e10	−	2.22748e10i	0.790365	−	0.790365i
$211$	2.40766e10	−	2.40766e10i	0.836225	−	0.836225i	−0.152134	−	0.988360i	$-0.548615\pi$
$211$	2.40766e10	−	2.40766e10i	0.836225	−	0.836225i	0.988360	+	0.152134i	$0.0486146\pi$
$212$		−	2.12038e10i		−	0.720944i
$213$		−	1.46505e10i		−	0.487691i
$214$	−3.87807e10	+	3.87807e10i	−1.26402	+	1.26402i
$215$	−5.74002e9	+	5.74002e9i	−0.183206	+	0.183206i
$216$	1.77579e9	+	1.77579e9i	0.0555074	+	0.0555074i
$217$	−1.11524e10			−0.341427
$218$	1.36092e10	+	1.36092e10i	0.408111	+	0.408111i
$219$			6.88746e9i			0.202330i
$220$	−5.87561e10			−1.69103
$221$	−2.74435e10	−	2.69574e10i	−0.773880	−	0.760172i
$222$	−2.13586e10			−0.590180
$223$			1.18689e10i			0.321396i	0.987004	+	0.160698i	$0.0513744\pi$
$223$			1.18689e10i			0.321396i	−0.987004	+	0.160698i	$0.948626\pi$
$224$	6.07588e10	+	6.07588e10i	1.61248	+	1.61248i
$225$	8.82173e9			0.229473
$226$	−1.95827e10	−	1.95827e10i	−0.499326	−	0.499326i
$227$	−2.98510e10	+	2.98510e10i	−0.746179	+	0.746179i	−0.973759	−	0.227580i	$-0.926919\pi$
$227$	−2.98510e10	+	2.98510e10i	−0.746179	+	0.746179i	0.227580	+	0.973759i	$0.426919\pi$
$228$	4.10660e9	−	4.10660e9i	0.100641	−	0.100641i
$229$			3.83719e10i			0.922047i	0.887388	+	0.461024i	$0.152518\pi$
$229$			3.83719e10i			0.922047i	−0.887388	+	0.461024i	$0.847482\pi$
$230$		−	3.77309e10i		−	0.889042i
$231$	−3.50378e10	+	3.50378e10i	−0.809624	+	0.809624i
$232$	−6.16330e9	+	6.16330e9i	−0.139675	+	0.139675i
$233$	1.13342e9	+	1.13342e9i	0.0251935	+	0.0251935i	0.719591	−	0.694398i	$-0.244329\pi$
$233$	1.13342e9	+	1.13342e9i	0.0251935	+	0.0251935i	−0.694398	+	0.719591i	$0.744329\pi$
$234$	−5.62634e10			−1.22675
$235$	2.61023e10	+	2.61023e10i	0.558307	+	0.558307i
$236$			8.99620e9i			0.188780i
$237$	−2.57522e9			−0.0530209
$238$	−1.01389e9	−	1.13466e11i	−0.0204831	−	2.29229i
$239$	−5.18864e10			−1.02864			−0.514320	−	0.857598i	$-0.671956\pi$
$239$	−5.18864e10			−1.02864			−0.514320	+	0.857598i	$0.671956\pi$
$240$		−	2.67434e10i		−	0.520315i
$241$	3.02367e10	+	3.02367e10i	0.577376	+	0.577376i	0.934179	−	0.356804i	$-0.116134\pi$
$241$	3.02367e10	+	3.02367e10i	0.577376	+	0.577376i	−0.356804	+	0.934179i	$0.616134\pi$
$242$	1.17975e11			2.21117
$243$	−3.79465e10	−	3.79465e10i	−0.698141	−	0.698141i
$244$	−4.53315e10	+	4.53315e10i	−0.818740	+	0.818740i
$245$	7.79299e10	−	7.79299e10i	1.38184	−	1.38184i
$246$		−	2.49237e9i		−	0.0433915i
$247$		−	2.26062e10i		−	0.386448i
$248$	−8.74965e8	+	8.74965e8i	−0.0146878	+	0.0146878i
$249$	1.86799e10	−	1.86799e10i	0.307948	−	0.307948i
$250$	4.93077e10	+	4.93077e10i	0.798334	+	0.798334i
$251$	3.86901e10			0.615273			0.307637	−	0.951504i	$-0.400462\pi$
$251$	3.86901e10			0.615273			0.307637	+	0.951504i	$0.400462\pi$
$252$	−5.64733e10	−	5.64733e10i	−0.882146	−	0.882146i
$253$			5.93499e10i			0.910705i
$254$	2.70582e10			0.407894
$255$	−2.30704e10	+	2.34864e10i	−0.341684	+	0.347846i
$256$	7.75598e10			1.12864
$257$			3.96876e10i			0.567487i	0.958900	+	0.283743i	$0.0915764\pi$
$257$			3.96876e10i			0.567487i	−0.958900	+	0.283743i	$0.908424\pi$
$258$	−6.88655e9	−	6.88655e9i	−0.0967638	−	0.0967638i
$259$	−1.18015e11			−1.62962
$260$	5.93595e10	+	5.93595e10i	0.805583	+	0.805583i
$261$	8.49080e10	−	8.49080e10i	1.13257	−	1.13257i
$262$	1.73600e10	−	1.73600e10i	0.227611	−	0.227611i
$263$		−	4.03518e10i		−	0.520070i	−0.965599	−	0.260035i	$-0.916266\pi$
$263$		−	4.03518e10i		−	0.520070i	0.965599	−	0.260035i	$-0.0837341\pi$
$264$			5.49783e9i			0.0696584i
$265$	−4.99467e10	+	4.99467e10i	−0.622157	+	0.622157i
$266$	4.71507e10	−	4.71507e10i	0.577459	−	0.577459i
$267$	−2.39665e9	−	2.39665e9i	−0.0288605	−	0.0288605i
$268$	1.54037e9			0.0182398
$269$	−1.76079e10	−	1.76079e10i	−0.205032	−	0.205032i	0.597120	−	0.802152i	$-0.296312\pi$
$269$	−1.76079e10	−	1.76079e10i	−0.205032	−	0.205032i	−0.802152	+	0.597120i	$0.796312\pi$
$270$			1.07267e11i			1.22837i
$271$	−5.46121e10			−0.615074			−0.307537	−	0.951536i	$-0.599505\pi$
$271$	−5.46121e10			−0.615074			−0.307537	+	0.951536i	$0.599505\pi$
$272$	−6.87230e10	−	6.75057e10i	−0.761276	−	0.747792i
$273$	7.07954e10			0.771388
$274$			1.94488e11i			2.08456i
$275$	3.04218e10	+	3.04218e10i	0.320765	+	0.320765i
$276$	2.17842e10			0.225970
$277$	3.96543e10	+	3.96543e10i	0.404698	+	0.404698i	0.879885	−	0.475187i	$-0.157619\pi$
$277$	3.96543e10	+	3.96543e10i	0.404698	+	0.404698i	−0.475187	+	0.879885i	$0.657619\pi$
$278$	5.36175e9	−	5.36175e9i	0.0538400	−	0.0538400i
$279$	1.20539e10	−	1.20539e10i	0.119099	−	0.119099i
$280$		−	1.93122e10i		−	0.187767i
$281$			1.76224e10i			0.168611i	0.996440	+	0.0843057i	$0.0268672\pi$
$281$			1.76224e10i			0.168611i	−0.996440	+	0.0843057i	$0.973133\pi$
$282$	−3.13160e10	+	3.13160e10i	−0.294880	+	0.294880i
$283$	9.95863e10	−	9.95863e10i	0.922913	−	0.922913i	−0.0743218	−	0.997234i	$-0.523679\pi$
$283$	9.95863e10	−	9.95863e10i	0.922913	−	0.922913i	0.997234	+	0.0743218i	$0.0236792\pi$
$284$	8.14309e10	+	8.14309e10i	0.742774	+	0.742774i
$285$	−1.93467e10			−0.173702
$286$	−1.94025e11	−	1.94025e11i	−1.71479	−	1.71479i
$287$		−	1.37713e10i		−	0.119814i
$288$	−1.31341e11			−1.12495
$289$	2.11915e9	+	1.18569e11i	0.0178699	+	0.999840i
$290$	−3.72295e11			−3.09098
$291$		−	9.20372e10i		−	0.752393i
$292$	−3.82821e10	−	3.82821e10i	−0.308158	−	0.308158i
$293$	8.38614e10			0.664749			0.332375	−	0.943147i	$-0.392150\pi$
$293$	8.38614e10			0.664749			0.332375	+	0.943147i	$0.392150\pi$
$294$	9.34959e10	+	9.34959e10i	0.729843	+	0.729843i
$295$	2.11911e10	−	2.11911e10i	0.162912	−	0.162912i
$296$	−9.25890e9	+	9.25890e9i	−0.0701046	+	0.0701046i
$297$		−	1.68729e11i		−	1.25830i
$298$			4.31730e10i			0.317132i
$299$	5.99594e10	−	5.99594e10i	0.433848	−	0.433848i
$300$	1.11662e10	−	1.11662e10i	0.0795904	−	0.0795904i
$301$	−3.80508e10	−	3.80508e10i	−0.267187	−	0.267187i
$302$	−1.37731e11			−0.952799
$303$	7.17972e10	+	7.17972e10i	0.489345	+	0.489345i
$304$		−	5.66097e10i		−	0.380154i
$305$	2.13562e11			1.41311
$306$	1.23734e11	+	1.21542e11i	0.806758	+	0.792468i
$307$	−1.75664e11			−1.12865			−0.564325	−	0.825553i	$-0.690863\pi$
$307$	−1.75664e11			−1.12865			−0.564325	+	0.825553i	$0.690863\pi$
$308$		−	3.89497e11i		−	2.46619i
$309$	−5.10063e10	−	5.10063e10i	−0.318281	−	0.318281i
$310$	−5.28524e10			−0.325040
$311$	−1.86658e11	−	1.86658e11i	−1.13142	−	1.13142i	−0.989941	−	0.141482i	$-0.954813\pi$
$311$	−1.86658e11	−	1.86658e11i	−1.13142	−	1.13142i	−0.141482	−	0.989941i	$-0.545187\pi$
$312$	5.55429e9	−	5.55429e9i	0.0331843	−	0.0331843i
$313$	−1.80158e10	+	1.80158e10i	−0.106097	+	0.106097i	−0.758163	−	0.652066i	$-0.773903\pi$
$313$	−1.80158e10	+	1.80158e10i	−0.106097	+	0.106097i	0.652066	+	0.758163i	$0.273903\pi$
$314$			2.52692e11i			1.46693i
$315$			2.66052e11i			1.52254i
$316$	1.43137e10	−	1.43137e10i	0.0807532	−	0.0807532i
$317$	−1.76812e11	+	1.76812e11i	−0.983436	+	0.983436i	−0.999865	−	0.0164287i	$-0.994770\pi$
$317$	−1.76812e11	+	1.76812e11i	−0.983436	+	0.983436i	0.0164287	+	0.999865i	$0.494770\pi$
$318$	−5.99232e10	−	5.99232e10i	−0.328604	−	0.328604i
$319$	5.85612e11			3.16630
$320$	1.27704e11	+	1.27704e11i	0.680816	+	0.680816i
$321$			1.05483e11i			0.554512i
$322$	2.50120e11			1.29657
$323$	−4.88348e10	+	4.97154e10i	−0.249642	+	0.254144i
$324$	8.79456e10			0.443365
$325$		−	6.14684e10i		−	0.305617i
$326$	−1.12065e11	−	1.12065e11i	−0.549531	−	0.549531i
$327$	3.70170e10			0.179034
$328$	−1.08044e9	−	1.08044e9i	−0.00515427	−	0.00515427i
$329$	−1.73033e11	+	1.73033e11i	−0.814232	+	0.814232i
$330$	−1.66049e11	+	1.66049e11i	−0.770766	+	0.770766i
$331$			3.65757e11i			1.67482i	0.546579	+	0.837408i	$0.315930\pi$
$331$			3.65757e11i			1.67482i	−0.546579	+	0.837408i	$0.684070\pi$
$332$			2.07654e11i			0.938037i
$333$	1.27554e11	−	1.27554e11i	0.568455	−	0.568455i
$334$	4.19467e11	−	4.19467e11i	1.84433	−	1.84433i
$335$	−3.62844e9	−	3.62844e9i	−0.0157405	−	0.0157405i
$336$	1.77283e11			0.758825
$337$	−3.22556e11	−	3.22556e11i	−1.36229	−	1.36229i	−0.870987	−	0.491307i	$-0.836519\pi$
$337$	−3.22556e11	−	3.22556e11i	−1.36229	−	1.36229i	−0.491307	−	0.870987i	$-0.663481\pi$
$338$			5.88850e10i			0.245403i
$339$	−5.32649e10			−0.219049
$340$	−2.31232e9	−	2.58774e11i	−0.00938409	−	1.05018i
$341$	8.31356e10			0.332960
$342$			1.01924e11i			0.402866i
$343$	2.17318e11	+	2.17318e11i	0.847760	+	0.847760i
$344$	−5.97060e9			−0.0229882
$345$	−5.13140e10	−	5.13140e10i	−0.195007	−	0.195007i
$346$	6.74307e10	−	6.74307e10i	0.252939	−	0.252939i
$347$	−2.37824e11	+	2.37824e11i	−0.880590	+	0.880590i	−0.993595	−	0.113004i	$-0.963953\pi$
$347$	−2.37824e11	+	2.37824e11i	−0.880590	+	0.880590i	0.113004	+	0.993595i	$0.463953\pi$
$348$		−	2.14947e11i		−	0.785643i
$349$		−	3.19659e8i		−	0.00115338i	−1.00000		0.000576690i	$-0.999816\pi$
$349$		−	3.19659e8i		−	0.00115338i	1.00000		0.000576690i	$-0.000183566\pi$
$350$	1.28207e11	−	1.28207e11i	0.456675	−	0.456675i
$351$	−1.70462e11	+	1.70462e11i	−0.599438	+	0.599438i
$352$	−4.52929e11	−	4.52929e11i	−1.57249	−	1.57249i
$353$	5.74697e10			0.196994			0.0984970	−	0.995137i	$-0.468597\pi$
$353$	5.74697e10			0.196994			0.0984970	+	0.995137i	$0.468597\pi$
$354$	2.54239e10	+	2.54239e10i	0.0860452	+	0.0860452i
$355$		−	3.83631e11i		−	1.28199i
$356$	2.66423e10			0.0879117
$357$	−1.55693e11	−	1.52935e11i	−0.507296	−	0.498310i
$358$	2.97189e11			0.956224
$359$		−	1.28501e10i		−	0.0408302i	−0.999792	−	0.0204151i	$-0.993501\pi$
$359$		−	1.28501e10i		−	0.0408302i	0.999792	−	0.0204151i	$-0.00649879\pi$
$360$	2.08733e10	+	2.08733e10i	0.0654983	+	0.0654983i
$361$	2.81735e11			0.873089
$362$	1.67329e11	+	1.67329e11i	0.512132	+	0.512132i
$363$	1.60446e11	−	1.60446e11i	0.485009	−	0.485009i
$364$	−3.93497e11	+	3.93497e11i	−1.17486	+	1.17486i
$365$			1.80352e11i			0.531866i
$366$			2.56220e11i			0.746359i
$367$	−8.49432e10	+	8.49432e10i	−0.244417	+	0.244417i	−0.818675	−	0.574258i	$-0.805291\pi$
$367$	−8.49432e10	+	8.49432e10i	−0.244417	+	0.244417i	0.574258	+	0.818675i	$0.305291\pi$
$368$	1.50149e11	−	1.50149e11i	0.426782	−	0.426782i
$369$	1.48845e10	+	1.48845e10i	0.0417943	+	0.0417943i
$370$	−5.59285e11			−1.55141
$371$	−3.31099e11	−	3.31099e11i	−0.907351	−	0.907351i
$372$		−	3.05147e10i		−	0.0826163i
$373$	2.29521e11			0.613949			0.306975	−	0.951718i	$-0.400683\pi$
$373$	2.29521e11			0.613949			0.306975	+	0.951718i	$0.400683\pi$
$374$	7.55812e9	+	8.45838e11i	0.0199752	+	2.23545i
$375$	1.34117e11			0.350221
$376$			2.71509e10i			0.0700549i
$377$	−5.91626e11	−	5.91626e11i	−1.50838	−	1.50838i
$378$	−7.11079e11			−1.79145
$379$	−1.30965e10	−	1.30965e10i	−0.0326046	−	0.0326046i	0.690617	−	0.723221i	$-0.257339\pi$
$379$	−1.30965e10	−	1.30965e10i	−0.0326046	−	0.0326046i	−0.723221	+	0.690617i	$0.757339\pi$
$380$	1.07533e11	−	1.07533e11i	0.264555	−	0.264555i
$381$	3.67991e10	−	3.67991e10i	0.0894694	−	0.0894694i
$382$		−	2.28649e11i		−	0.549394i
$383$		−	7.04308e11i		−	1.67251i	−0.548343	−	0.836253i	$-0.684741\pi$
$383$		−	7.04308e11i		−	1.67251i	0.548343	−	0.836253i	$-0.315259\pi$
$384$	2.60000e10	−	2.60000e10i	0.0610214	−	0.0610214i
$385$	−9.17483e11	+	9.17483e11i	−2.12826	+	2.12826i
$386$	1.68939e11	+	1.68939e11i	0.387335	+	0.387335i
$387$	8.22534e10			0.186404
$388$	5.11564e11	+	5.11564e11i	1.14593	+	1.14593i
$389$			8.72755e11i			1.93250i	0.257611	+	0.966249i	$0.417065\pi$
$389$			8.72755e11i			1.93250i	−0.257611	+	0.966249i	$0.582935\pi$
$390$	3.35508e11			0.734365
$391$	−2.61389e11	+	2.33568e9i	−0.565578	+	0.00505381i
$392$	8.10605e10			0.173389
$393$		−	4.72190e10i		−	0.0998506i
$394$	4.84431e11	+	4.84431e11i	1.01274	+	1.01274i
$395$	−6.74335e10			−0.139376
$396$	4.20982e11	+	4.20982e11i	0.860271	+	0.860271i
$397$	3.22262e11	−	3.22262e11i	0.651105	−	0.651105i	−0.302154	−	0.953259i	$-0.597706\pi$
$397$	3.22262e11	−	3.22262e11i	0.651105	−	0.651105i	0.953259	+	0.302154i	$0.0977057\pi$
$398$	3.11404e11	−	3.11404e11i	0.622086	−	0.622086i
$399$		−	1.28250e11i		−	0.253326i
$400$		−	1.53927e11i		−	0.300639i
$401$	6.35462e11	−	6.35462e11i	1.22727	−	1.22727i	0.262276	−	0.964993i	$-0.415527\pi$
$401$	6.35462e11	−	6.35462e11i	1.22727	−	1.22727i	0.964993	−	0.262276i	$-0.0844730\pi$
$402$	4.35319e9	−	4.35319e9i	0.00831363	−	0.00831363i
$403$	−8.39895e10	−	8.39895e10i	−0.158618	−	0.158618i
$404$	−7.98131e11			−1.49059
$405$	−2.07161e11	−	2.07161e11i	−0.382614	−	0.382614i
$406$		−	2.46796e12i		−	4.50787i
$407$	8.79744e11			1.58921
$408$	−2.42136e10	+	2.16364e8i	−0.0432602	+	0.000386558i
$409$	−1.95210e11			−0.344943			−0.172472	−	0.985015i	$-0.555175\pi$
$409$	−1.95210e11			−0.344943			−0.172472	+	0.985015i	$0.555175\pi$
$410$		−	6.52640e10i		−	0.114063i
$411$	2.64503e11	+	2.64503e11i	0.457238	+	0.457238i
$412$	5.67010e11			0.969513
$413$	1.40477e11	+	1.40477e11i	0.237590	+	0.237590i
$414$	−2.70339e11	+	2.70339e11i	−0.452279	+	0.452279i
$415$	4.89142e11	−	4.89142e11i	0.809504	−	0.809504i
$416$			9.15161e11i			1.49823i
$417$		−	1.45839e10i		−	0.0236191i
$418$	−3.51487e11	+	3.51487e11i	−0.563140	+	0.563140i
$419$	9.76087e10	−	9.76087e10i	0.154712	−	0.154712i	−0.625506	−	0.780219i	$-0.715108\pi$
$419$	9.76087e10	−	9.76087e10i	0.154712	−	0.154712i	0.780219	+	0.625506i	$0.215108\pi$
$420$	3.36760e11	+	3.36760e11i	0.528078	+	0.528078i
$421$	−7.45047e11			−1.15588			−0.577942	−	0.816078i	$-0.696144\pi$
$421$	−7.45047e11			−1.15588			−0.577942	+	0.816078i	$0.696144\pi$
$422$	7.56386e11	+	7.56386e11i	1.16101	+	1.16101i
$423$		−	3.74041e11i		−	0.568051i
$424$	−5.19531e10			−0.0780666
$425$	−1.32787e11	+	1.35181e11i	−0.197426	+	0.200986i
$426$	4.60259e11			0.677109
$427$			1.41571e12i			2.06087i
$428$	−5.86301e11	−	5.86301e11i	−0.844547	−	0.844547i
$429$	−5.27747e11			−0.752259
$430$	−1.80328e11	−	1.80328e11i	−0.254363	−	0.254363i
$431$	−7.22197e10	+	7.22197e10i	−0.100811	+	0.100811i	−0.755713	−	0.654902i	$-0.772710\pi$
$431$	−7.22197e10	+	7.22197e10i	−0.100811	+	0.100811i	0.654902	+	0.755713i	$0.272710\pi$
$432$	−4.26865e11	+	4.26865e11i	−0.589676	+	0.589676i
$433$		−	1.06370e12i		−	1.45420i	−0.686530	−	0.727102i	$-0.740867\pi$
$433$		−	1.06370e12i		−	1.45420i	0.686530	−	0.727102i	$-0.259133\pi$
$434$		−	3.50361e11i		−	0.474037i
$435$	−5.06321e11	+	5.06321e11i	−0.677991	+	0.677991i
$436$	−2.05749e11	+	2.05749e11i	−0.272677	+	0.272677i
$437$	−1.08620e11	−	1.08620e11i	−0.142477	−	0.142477i
$438$	−2.16376e11			−0.280915
$439$	9.34636e11	+	9.34636e11i	1.20103	+	1.20103i	0.973855	+	0.227171i	$0.0729476\pi$
$439$	9.34636e11	+	9.34636e11i	1.20103	+	1.20103i	0.227171	+	0.973855i	$0.427052\pi$
$440$			1.43963e11i			0.183111i
$441$	−1.11672e12			−1.40595
$442$	8.46889e11	−	8.62160e11i	1.05542	−	1.07445i
$443$	1.29502e12			1.59757			0.798784	−	0.601618i	$-0.205477\pi$
$443$	1.29502e12			1.59757			0.798784	+	0.601618i	$0.205477\pi$
$444$		−	3.22907e11i		−	0.394325i
$445$	−6.27575e10	−	6.27575e10i	−0.0758657	−	0.0758657i
$446$	−3.72873e11			−0.446225
$447$	5.87153e10	+	5.87153e10i	0.0695612	+	0.0695612i
$448$	−8.46556e11	+	8.46556e11i	−0.992898	+	0.992898i
$449$	−3.00328e11	+	3.00328e11i	−0.348728	+	0.348728i	−0.859636	−	0.510908i	$-0.829309\pi$
$449$	−3.00328e11	+	3.00328e11i	−0.348728	+	0.348728i	0.510908	+	0.859636i	$0.329309\pi$
$450$			2.77142e11i			0.318601i
$451$			1.02659e11i			0.116843i
$452$	2.96059e11	−	2.96059e11i	0.333622	−	0.333622i
$453$	−1.87314e11	+	1.87314e11i	−0.208992	+	0.208992i
$454$	−9.37797e11	−	9.37797e11i	−1.03599	−	1.03599i
$455$	1.85381e12			2.02775
$456$	−1.00619e10	−	1.00619e10i	−0.0108978	−	0.0108978i
$457$			4.27181e11i			0.458131i	0.973411	+	0.229065i	$0.0735670\pi$
$457$			4.27181e11i			0.458131i	−0.973411	+	0.229065i	$0.926433\pi$
$458$	−1.20549e12			−1.28017
$459$	7.43116e11	−	6.64023e9i	0.781447	−	0.00698274i
$460$	5.70431e11			0.594008
$461$			1.13997e12i			1.17554i	0.809027	+	0.587771i	$0.199994\pi$
$461$			1.13997e12i			1.17554i	−0.809027	+	0.587771i	$0.800006\pi$
$462$	−1.10074e12	−	1.10074e12i	−1.12408	−	1.12408i
$463$	−1.72036e12			−1.73982			−0.869909	−	0.493213i	$-0.835822\pi$
$463$	−1.72036e12			−1.73982			−0.869909	+	0.493213i	$0.835822\pi$
$464$	−1.48153e12	−	1.48153e12i	−1.48381	−	1.48381i
$465$	−7.18792e10	+	7.18792e10i	−0.0712960	+	0.0712960i
$466$	−3.56073e10	+	3.56073e10i	−0.0349786	+	0.0349786i
$467$		−	1.58108e12i		−	1.53825i	−0.639099	−	0.769125i	$-0.720693\pi$
$467$		−	1.58108e12i		−	1.53825i	0.639099	−	0.769125i	$-0.279307\pi$
$468$		−	8.50612e11i		−	0.819643i
$469$	2.40531e10	−	2.40531e10i	0.0229558	−	0.0229558i
$470$	−8.20026e11	+	8.20026e11i	−0.775153	+	0.775153i
$471$	3.43661e11	+	3.43661e11i	0.321763	+	0.321763i
$472$	2.20424e10			0.0204418
$473$	2.83651e11	+	2.83651e11i	0.260561	+	0.260561i
$474$		−	8.09029e10i		−	0.0736142i
$475$	−1.11354e11			−0.100365
$476$	1.71542e12	−	1.53284e10i	1.53158	−	0.0136857i
$477$	7.15727e11			0.633016
$478$		−	1.63006e12i		−	1.42816i
$479$	7.69672e11	+	7.69672e11i	0.668030	+	0.668030i	0.957260	−	0.289230i	$-0.0933991\pi$
$479$	7.69672e11	+	7.69672e11i	0.668030	+	0.668030i	−0.289230	+	0.957260i	$0.593399\pi$
$480$	7.83206e11			0.673427
$481$	−8.88779e11	−	8.88779e11i	−0.757078	−	0.757078i
$482$	−9.49914e11	+	9.49914e11i	−0.801627	+	0.801627i
$483$	3.40163e11	−	3.40163e11i	0.284397	−	0.284397i
$484$			1.78360e12i			1.47738i
$485$		−	2.41004e12i		−	1.97782i
$486$	1.19212e12	−	1.19212e12i	0.969298	−	0.969298i
$487$	−1.46633e12	+	1.46633e12i	−1.18127	+	1.18127i	−0.201859	+	0.979415i	$0.564698\pi$
$487$	−1.46633e12	+	1.46633e12i	−1.18127	+	1.18127i	−0.979415	+	0.201859i	$0.935302\pi$
$488$	1.11071e11	+	1.11071e11i	0.0886564	+	0.0886564i
$489$	−3.04818e11			−0.241074
$490$	2.44824e12	+	2.44824e12i	1.91854	+	1.91854i
$491$			1.27855e11i			0.0992772i	0.998767	+	0.0496386i	$0.0158069\pi$
$491$			1.27855e11i			0.0992772i	−0.998767	+	0.0496386i	$0.984193\pi$
$492$	3.76806e10			0.0289918
$493$	2.30464e10	+	2.57915e12i	0.0175708	+	1.96637i
$494$	7.10194e11			0.536544
$495$		−	1.98330e12i		−	1.48479i
$496$	−2.10324e11	−	2.10324e11i	−0.156035	−	0.156035i
$497$	2.54311e12			1.86965
$498$	5.86845e11	+	5.86845e11i	0.427555	+	0.427555i
$499$	1.11051e12	−	1.11051e12i	0.801808	−	0.801808i	−0.181570	−	0.983378i	$-0.558118\pi$
$499$	1.11051e12	−	1.11051e12i	0.801808	−	0.801808i	0.983378	+	0.181570i	$0.0581179\pi$
$500$	−7.45453e11	+	7.45453e11i	−0.533403	+	0.533403i
$501$		−	1.14095e12i		−	0.809090i
$502$			1.21548e12i			0.854245i
$503$	−7.85410e11	+	7.85410e11i	−0.547067	+	0.547067i	−0.925591	−	0.378524i	$-0.876432\pi$
$503$	−7.85410e11	+	7.85410e11i	−0.547067	+	0.547067i	0.378524	+	0.925591i	$0.376432\pi$
$504$	−1.38370e11	+	1.38370e11i	−0.0955223	+	0.0955223i
$505$	1.88004e12	+	1.88004e12i	1.28634	+	1.28634i
$506$	−1.86453e12			−1.26442
$507$	8.00835e10	+	8.00835e10i	0.0538279	+	0.0538279i
$508$			4.09076e11i			0.272532i
$509$	−2.12203e12			−1.40127			−0.700636	−	0.713519i	$-0.747100\pi$
$509$	−2.12203e12			−1.40127			−0.700636	+	0.713519i	$0.747100\pi$
$510$	−7.37847e11	−	7.24778e11i	−0.482948	−	0.474394i
$511$	−1.19556e12			−0.775670
$512$			2.12504e12i			1.36663i
$513$	3.08801e11	+	3.08801e11i	0.196857	+	0.196857i
$514$	−1.24682e12			−0.787898
$515$	−1.33563e12	−	1.33563e12i	−0.836666	−	0.836666i
$516$	1.04113e11	−	1.04113e11i	0.0646522	−	0.0646522i
$517$	1.28988e12	−	1.28988e12i	0.794041	−	0.794041i
$518$		−	3.70753e12i		−	2.26256i
$519$		−	1.83411e11i		−	0.110962i
$520$	1.45442e11	−	1.45442e11i	0.0872317	−	0.0872317i
$521$	1.16203e12	−	1.16203e12i	0.690950	−	0.690950i	−0.271491	−	0.962441i	$-0.587517\pi$
$521$	1.16203e12	−	1.16203e12i	0.690950	−	0.690950i	0.962441	+	0.271491i	$0.0875168\pi$
$522$	2.66746e12	+	2.66746e12i	1.57246	+	1.57246i
$523$	1.94542e12			1.13699			0.568493	−	0.822688i	$-0.307527\pi$
$523$	1.94542e12			1.13699			0.568493	+	0.822688i	$0.307527\pi$
$524$	2.62454e11	+	2.62454e11i	0.152077	+	0.152077i
$525$		−	3.48724e11i		−	0.200339i
$526$	1.26769e12			0.722065
$527$	3.27176e9	+	3.66147e11i	0.00184771	+	0.206779i
$528$	−1.32157e12			−0.740008
$529$			1.22496e12i			0.680096i
$530$	−1.56912e12	−	1.56912e12i	−0.863803	−	0.863803i
$531$	−3.03664e11			−0.165756
$532$	7.12843e11	+	7.12843e11i	0.385826	+	0.385826i
$533$	1.03713e11	−	1.03713e11i	0.0556623	−	0.0556623i
$534$	7.52929e10	−	7.52929e10i	0.0400699	−	0.0400699i
$535$			2.76213e12i			1.45765i
$536$		−	3.77420e9i		−	0.00197507i
$537$	4.04177e11	−	4.04177e11i	0.209743	−	0.209743i
$538$	5.53167e11	−	5.53167e11i	0.284666	−	0.284666i
$539$	−3.85102e12	−	3.85102e12i	−1.96529	−	1.96529i
$540$	−1.62170e12			−0.820729
$541$	−1.82521e12	−	1.82521e12i	−0.916061	−	0.916061i	0.0806789	−	0.996740i	$-0.474291\pi$
$541$	−1.82521e12	−	1.82521e12i	−0.916061	−	0.916061i	−0.996740	+	0.0806789i	$0.974291\pi$
$542$		−	1.71569e12i		−	0.853967i
$543$	4.55133e11			0.224667
$544$	1.97697e12	−	2.01262e12i	0.967842	−	0.985294i
$545$	9.69309e11			0.470628
$546$			2.22410e12i			1.07099i
$547$	−5.74750e11	−	5.74750e11i	−0.274496	−	0.274496i	0.556411	−	0.830907i	$-0.312178\pi$
$547$	−5.74750e11	−	5.74750e11i	−0.274496	−	0.274496i	−0.830907	+	0.556411i	$0.812178\pi$
$548$	−2.94034e12			−1.39279
$549$	−1.53015e12	−	1.53015e12i	−0.718885	−	0.718885i
$550$	−9.55727e11	+	9.55727e11i	−0.445350	+	0.445350i
$551$	−1.07176e12	+	1.07176e12i	−0.495356	+	0.495356i
$552$		−	5.33754e10i		−	0.0244689i
$553$		−	4.47020e11i		−	0.203266i
$554$	−1.24577e12	+	1.24577e12i	−0.561883	+	0.561883i
$555$	−7.60628e11	+	7.60628e11i	−0.340293	+	0.340293i
$556$	8.10609e10	+	8.10609e10i	0.0359729	+	0.0359729i
$557$	−2.77064e12			−1.21964			−0.609819	−	0.792540i	$-0.708758\pi$
$557$	−2.77064e12			−1.21964			−0.609819	+	0.792540i	$0.708758\pi$
$558$	3.78683e11	+	3.78683e11i	0.165357	+	0.165357i
$559$		−	5.73129e11i		−	0.248256i
$560$	4.64226e12			1.99472
$561$	1.16062e12	+	1.14006e12i	0.494716	+	0.485953i
$562$	−5.53623e11			−0.234100
$563$			3.89099e12i			1.63220i	0.577914	+	0.816098i	$0.303867\pi$
$563$			3.89099e12i			1.63220i	−0.577914	+	0.816098i	$0.696133\pi$
$564$	−4.73448e11	−	4.73448e11i	−0.197023	−	0.197023i
$565$	−1.39477e12			−0.575816
$566$	3.12859e12	+	3.12859e12i	1.28137	+	1.28137i
$567$	1.37328e12	−	1.37328e12i	0.558001	−	0.558001i
$568$	1.99521e11	−	1.99521e11i	0.0804306	−	0.0804306i
$569$			1.29595e12i			0.518304i	0.965837	+	0.259152i	$0.0834430\pi$
$569$			1.29595e12i			0.518304i	−0.965837	+	0.259152i	$0.916557\pi$
$570$		−	6.07792e11i		−	0.241167i
$571$	−2.59957e12	+	2.59957e12i	−1.02338	+	1.02338i	−0.0236645	+	0.999720i	$0.507533\pi$
$571$	−2.59957e12	+	2.59957e12i	−1.02338	+	1.02338i	−0.999720	+	0.0236645i	$0.992467\pi$
$572$	2.93334e12	−	2.93334e12i	1.14572	−	1.14572i
$573$	−3.10962e11	−	3.10962e11i	−0.120507	−	0.120507i
$574$	4.32638e11			0.166349
$575$	−2.95348e11	−	2.95348e11i	−0.112675	−	0.112675i
$576$		−	1.82998e12i		−	0.692699i
$577$	−7.12314e11			−0.267535			−0.133767	−	0.991013i	$-0.542707\pi$
$577$	−7.12314e11			−0.267535			−0.133767	+	0.991013i	$0.542707\pi$
$578$	−3.72495e12	+	6.65750e10i	−1.38818	+	0.0248105i
$579$	4.59513e11			0.169920
$580$		−	5.62850e12i		−	2.06522i
$581$	3.24255e12	+	3.24255e12i	1.18058	+	1.18058i
$582$	2.89143e12			1.04462
$583$	2.46819e12	+	2.46819e12i	0.884851	+	0.884851i
$584$	−9.37984e10	+	9.37984e10i	−0.0333686	+	0.0333686i
$585$	−2.00367e12	+	2.00367e12i	−0.707333	+	0.707333i
$586$			2.63458e12i			0.922937i
$587$			2.45642e11i			0.0853948i	0.999088	+	0.0426974i	$0.0135951\pi$
$587$			2.45642e11i			0.0853948i	−0.999088	+	0.0426974i	$0.986405\pi$
$588$	−1.41351e12	+	1.41351e12i	−0.487641	+	0.487641i
$589$	−1.52152e11	+	1.52152e11i	−0.0520905	+	0.0520905i
$590$	6.65736e11	+	6.65736e11i	0.226187	+	0.226187i
$591$	1.31765e12			0.444280
$592$	−2.22565e12	−	2.22565e12i	−0.744748	−	0.744748i
$593$			7.70573e11i			0.255899i	0.991781	+	0.127949i	$0.0408395\pi$
$593$			7.70573e11i			0.255899i	−0.991781	+	0.127949i	$0.959161\pi$
$594$	5.30076e12			1.74703
$595$	−4.07689e12	−	4.00468e12i	−1.33353	−	1.30991i
$596$	−6.52706e11			−0.211890
$597$		−	8.47018e11i		−	0.272903i
$598$	1.88368e12	+	1.88368e12i	0.602353	+	0.602353i
$599$	4.21472e12			1.33767			0.668834	−	0.743412i	$-0.266794\pi$
$599$	4.21472e12			1.33767			0.668834	+	0.743412i	$0.266794\pi$
$600$	−2.73593e10	−	2.73593e10i	−0.00861837	−	0.00861837i
$601$	8.80760e11	−	8.80760e11i	0.275374	−	0.275374i	−0.555885	−	0.831259i	$-0.687621\pi$
$601$	8.80760e11	−	8.80760e11i	0.275374	−	0.275374i	0.831259	+	0.555885i	$0.187621\pi$
$602$	1.19540e12	−	1.19540e12i	0.370962	−	0.370962i
$603$			5.19948e10i			0.0160152i
$604$		−	2.08227e12i		−	0.636608i
$605$	4.20136e12	−	4.20136e12i	1.27494	−	1.27494i
$606$	−2.25557e12	+	2.25557e12i	−0.679406	+	0.679406i
$607$	−2.35251e12	−	2.35251e12i	−0.703367	−	0.703367i	0.261765	−	0.965132i	$-0.415695\pi$
$607$	−2.35251e12	−	2.35251e12i	−0.703367	−	0.703367i	−0.965132	+	0.261765i	$0.915695\pi$
$608$	1.65787e12			0.492021
$609$	−3.35642e12	−	3.35642e12i	−0.988778	−	0.988778i
$610$			6.70924e12i			1.96195i
$611$	−2.60626e12			−0.756541
$612$	−1.83753e12	+	1.87066e12i	−0.529483	+	0.539031i
$613$	2.74693e12			0.785733			0.392867	−	0.919595i	$-0.371483\pi$
$613$	2.74693e12			0.785733			0.392867	+	0.919595i	$0.371483\pi$
$614$		−	5.51863e12i		−	1.56702i
$615$	−8.87590e10	−	8.87590e10i	−0.0250193	−	0.0250193i
$616$	−9.54340e11			−0.267048
$617$	1.61431e12	+	1.61431e12i	0.448438	+	0.448438i	0.894835	−	0.446397i	$-0.147293\pi$
$617$	1.61431e12	+	1.61431e12i	0.448438	+	0.448438i	−0.446397	+	0.894835i	$0.647293\pi$
$618$	1.60241e12	−	1.60241e12i	0.441901	−	0.441901i
$619$	9.24619e9	−	9.24619e9i	0.00253137	−	0.00253137i	−0.705840	−	0.708371i	$-0.749430\pi$
$619$	9.24619e9	−	9.24619e9i	0.00253137	−	0.00253137i	0.708371	+	0.705840i	$0.249430\pi$
$620$		−	7.99043e11i		−	0.217174i
$621$			1.63809e12i			0.442005i
$622$	5.86403e12	−	5.86403e12i	1.57087	−	1.57087i
$623$	4.16022e11	−	4.16022e11i	0.110642	−	0.110642i
$624$	1.33514e12	+	1.33514e12i	0.352530	+	0.352530i
$625$	4.58663e12			1.20236
$626$	−5.65981e11	−	5.65981e11i	−0.147305	−	0.147305i
$627$			9.56044e11i			0.247044i
$628$	−3.82030e12			−0.980119
$629$	3.46218e10	+	3.87457e12i	0.00881906	+	0.986952i
$630$	−8.35827e12			−2.11390
$631$		−	1.82848e12i		−	0.459154i	−0.973291	−	0.229577i	$-0.926266\pi$
$631$		−	1.82848e12i		−	0.459154i	0.973291	−	0.229577i	$-0.0737342\pi$
$632$	−3.50712e10	−	3.50712e10i	−0.00874428	−	0.00874428i
$633$	2.05737e12			0.509325
$634$	−5.55472e12	−	5.55472e12i	−1.36540	−	1.36540i
$635$	9.63602e11	−	9.63602e11i	0.235189	−	0.235189i
$636$	9.05942e11	−	9.05942e11i	0.219555	−	0.219555i
$637$			7.78114e12i			1.87248i
$638$			1.83975e13i			4.39608i
$639$	−2.74868e12	+	2.74868e12i	−0.652184	+	0.652184i
$640$	6.80822e11	−	6.80822e11i	0.160407	−	0.160407i
$641$	−3.07033e12	−	3.07033e12i	−0.718330	−	0.718330i	0.249933	−	0.968263i	$-0.419591\pi$
$641$	−3.07033e12	−	3.07033e12i	−0.718330	−	0.718330i	−0.968263	+	0.249933i	$0.919591\pi$
$642$	−3.31385e12			−0.769884
$643$	−5.58184e11	−	5.58184e11i	−0.128774	−	0.128774i	0.639782	−	0.768556i	$-0.279025\pi$
$643$	−5.58184e11	−	5.58184e11i	−0.128774	−	0.128774i	−0.768556	+	0.639782i	$0.779025\pi$
$644$			3.78141e12i			0.866298i
$645$	−4.90491e11			−0.111587
$646$	−1.56185e12	−	1.53419e12i	−0.352853	−	0.346603i
$647$	2.49662e11			0.0560122			0.0280061	−	0.999608i	$-0.491084\pi$
$647$	2.49662e11			0.0560122			0.0280061	+	0.999608i	$0.491084\pi$
$648$		−	2.15483e11i		−	0.0480093i
$649$	−1.04719e12	−	1.04719e12i	−0.231699	−	0.231699i
$650$	1.93108e12			0.424318
$651$	−4.76490e11	−	4.76490e11i	−0.103978	−	0.103978i
$652$	1.69425e12	−	1.69425e12i	0.367166	−	0.367166i
$653$	−1.75865e12	+	1.75865e12i	−0.378503	+	0.378503i	−0.870562	−	0.492059i	$-0.836245\pi$
$653$	−1.75865e12	+	1.75865e12i	−0.378503	+	0.378503i	0.492059	+	0.870562i	$0.336245\pi$
$654$			1.16292e12i			0.248571i
$655$		−	1.23645e12i		−	0.262477i
$656$	2.59715e11	−	2.59715e11i	0.0547558	−	0.0547558i
$657$	1.29220e12	−	1.29220e12i	0.270574	−	0.270574i
$658$	−5.43599e12	−	5.43599e12i	−1.13048	−	1.13048i
$659$	1.78184e12			0.368031			0.184015	−	0.982923i	$-0.441090\pi$
$659$	1.78184e12			0.368031			0.184015	+	0.982923i	$0.441090\pi$
$660$	−2.51039e12	−	2.51039e12i	−0.514983	−	0.514983i
$661$			3.14479e11i			0.0640744i	0.999487	+	0.0320372i	$0.0101995\pi$
$661$			3.14479e11i			0.0640744i	−0.999487	+	0.0320372i	$0.989800\pi$
$662$	−1.14906e13			−2.32531
$663$	−2.07692e10	−	2.32430e12i	−0.00417454	−	0.467178i
$664$	5.08792e11			0.101574
$665$		−	3.35829e12i		−	0.665918i
$666$	4.00723e12	+	4.00723e12i	0.789242	+	0.789242i
$667$	−5.68538e12			−1.11223
$668$	6.34166e12	+	6.34166e12i	1.23228	+	1.23228i
$669$	−5.07107e11	+	5.07107e11i	−0.0978773	+	0.0978773i
$670$	1.13990e11	−	1.13990e11i	0.0218541	−	0.0218541i
$671$		−	1.05535e13i		−	2.00976i
$672$			5.19191e12i			0.982121i
$673$	4.65524e11	−	4.65524e11i	0.0874731	−	0.0874731i	−0.662016	−	0.749489i	$-0.730299\pi$
$673$	4.65524e11	−	4.65524e11i	0.0874731	−	0.0874731i	0.749489	+	0.662016i	$0.230299\pi$
$674$	1.01334e13	−	1.01334e13i	1.89141	−	1.89141i
$675$	8.39660e11	+	8.39660e11i	0.155681	+	0.155681i
$676$	−8.90246e11			−0.163965
$677$	−2.45627e12	−	2.45627e12i	−0.449394	−	0.449394i	0.445759	−	0.895153i	$-0.352934\pi$
$677$	−2.45627e12	−	2.45627e12i	−0.449394	−	0.449394i	−0.895153	+	0.445759i	$0.852934\pi$
$678$		−	1.67336e12i		−	0.304128i
$679$	1.59763e13			2.88444
$680$	−6.34045e11	+	5.66560e9i	−0.113718	+	0.00101615i
$681$	−2.55080e12			−0.454480
$682$			2.61178e12i			0.462282i
$683$	−2.70618e12	−	2.70618e12i	−0.475843	−	0.475843i	0.427956	−	0.903800i	$-0.359234\pi$
$683$	−2.70618e12	−	2.70618e12i	−0.475843	−	0.475843i	−0.903800	+	0.427956i	$0.859234\pi$
$684$	−1.54093e12			−0.269173
$685$	6.92614e12	+	6.92614e12i	1.20194	+	1.20194i
$686$	−6.82724e12	+	6.82724e12i	−1.17703	+	1.17703i
$687$	−1.63946e12	+	1.63946e12i	−0.280799	+	0.280799i
$688$		−	1.43521e12i		−	0.244212i
$689$		−	4.98708e12i		−	0.843062i
$690$	1.61207e12	−	1.61207e12i	0.270747	−	0.270747i
$691$	−4.70569e11	+	4.70569e11i	−0.0785186	+	0.0785186i	−0.745275	−	0.666757i	$-0.767682\pi$
$691$	−4.70569e11	+	4.70569e11i	−0.0785186	+	0.0785186i	0.666757	+	0.745275i	$0.267682\pi$
$692$	1.01944e12	+	1.01944e12i	0.169000	+	0.169000i
$693$	1.31474e13			2.16541
$694$	−7.47146e12	−	7.47146e12i	−1.22261	−	1.22261i
$695$		−	3.81888e11i		−	0.0620875i
$696$	−5.26660e11			−0.0850725
$697$	−4.52131e11	+	4.04008e9i	−0.0725632	+	0.000648400i
$698$	1.00424e10			0.00160135
$699$			9.68519e10i			0.0153448i
$700$	1.93829e12	+	1.93829e12i	0.305125	+	0.305125i
$701$	8.18142e12			1.27967			0.639835	−	0.768513i	$-0.279003\pi$
$701$	8.18142e12			1.27967			0.639835	+	0.768513i	$0.279003\pi$
$702$	−5.35520e12	−	5.35520e12i	−0.832259	−	0.832259i
$703$	−1.61007e12	+	1.61007e12i	−0.248626	+	0.248626i
$704$	6.31069e12	−	6.31069e12i	0.968277	−	0.968277i
$705$			2.23047e12i			0.340052i
$706$			1.80546e12i			0.273506i
$707$	−1.24629e13	+	1.24629e13i	−1.87600	+	1.87600i
$708$	−3.84368e11	+	3.84368e11i	−0.0574906	+	0.0574906i
$709$	8.88440e12	+	8.88440e12i	1.32044	+	1.32044i	0.913415	+	0.407029i	$0.133435\pi$
$709$	8.88440e12	+	8.88440e12i	1.32044	+	1.32044i	0.407029	+	0.913415i	$0.366565\pi$
$710$	1.20521e13			1.77992
$711$	4.83155e11	+	4.83155e11i	0.0709044	+	0.0709044i
$712$		−	6.52786e10i		−	0.00951943i
$713$	−8.07118e11			−0.116959
$714$	4.80459e12	−	4.89122e12i	0.691853	−	0.704329i
$715$	−1.38193e13			−1.97747
$716$			4.49302e12i			0.638896i
$717$	−2.21688e12	−	2.21688e12i	−0.313260	−	0.313260i
$718$	4.03698e11			0.0566887
$719$	2.05898e12	+	2.05898e12i	0.287324	+	0.287324i	0.836021	−	0.548697i	$-0.184876\pi$
$719$	2.05898e12	+	2.05898e12i	0.287324	+	0.287324i	−0.548697	+	0.836021i	$0.684876\pi$
$720$	−5.01752e12	+	5.01752e12i	−0.695813	+	0.695813i
$721$	8.85393e12	−	8.85393e12i	1.22019	−	1.22019i
$722$			8.85096e12i			1.21220i
$723$			2.58376e12i			0.351666i
$724$	−2.52974e12	+	2.52974e12i	−0.342178	+	0.342178i
$725$	−2.91423e12	+	2.91423e12i	−0.391745	+	0.391745i
$726$	5.04056e12	+	5.04056e12i	0.673386	+	0.673386i
$727$	−6.75451e12			−0.896786			−0.448393	−	0.893836i	$-0.648004\pi$
$727$	−6.75451e12			−0.896786			−0.448393	+	0.893836i	$0.648004\pi$
$728$	9.64141e11	+	9.64141e11i	0.127218	+	0.127218i
$729$			4.02040e11i			0.0527225i
$730$	−5.66590e12			−0.738442
$731$	−1.23810e12	+	1.26042e12i	−0.160371	+	0.163263i
$732$	−3.87363e12			−0.498675
$733$		−	7.06417e12i		−	0.903843i	−0.892058	−	0.451922i	$-0.850739\pi$
$733$		−	7.06417e12i		−	0.903843i	0.892058	−	0.451922i	$-0.149261\pi$
$734$	−2.66856e12	−	2.66856e12i	−0.339348	−	0.339348i
$735$	6.65920e12			0.841645
$736$	4.39724e12	+	4.39724e12i	0.552369	+	0.552369i
$737$	−1.79305e11	+	1.79305e11i	−0.0223866	+	0.0223866i
$738$	−4.67611e11	+	4.67611e11i	−0.0580271	+	0.0580271i
$739$		−	1.12061e13i		−	1.38215i	−0.722783	−	0.691075i	$-0.757138\pi$
$739$		−	1.12061e13i		−	1.38215i	0.722783	−	0.691075i	$-0.242862\pi$
$740$		−	8.45549e12i		−	1.03656i
$741$	9.65862e11	−	9.65862e11i	0.117688	−	0.117688i
$742$	1.04018e13	−	1.04018e13i	1.25976	−	1.25976i
$743$	5.97926e12	+	5.97926e12i	0.719777	+	0.719777i	0.968559	−	0.248783i	$-0.0800304\pi$
$743$	5.97926e12	+	5.97926e12i	0.719777	+	0.719777i	−0.248783	+	0.968559i	$0.580030\pi$
$744$	−7.47667e10			−0.00894602
$745$	1.53749e12	+	1.53749e12i	0.182856	+	0.182856i
$746$			7.21060e12i			0.852406i
$747$	−7.00932e12			−0.823632
$748$	−1.27877e13	+	1.14266e11i	−1.49360	+	0.0133463i
$749$	−1.83103e13			−2.12583
$750$			4.21340e12i			0.486247i
$751$	1.00093e12	+	1.00093e12i	0.114822	+	0.114822i	0.762183	−	0.647362i	$-0.224128\pi$
$751$	1.00093e12	+	1.00093e12i	0.114822	+	0.114822i	−0.647362	+	0.762183i	$0.724128\pi$
$752$	−6.52651e12			−0.744219
$753$	1.65306e12	+	1.65306e12i	0.187374	+	0.187374i
$754$	1.85864e13	−	1.85864e13i	2.09423	−	2.09423i
$755$	−4.90492e12	+	4.90492e12i	−0.549377	+	0.549377i
$756$		−	1.07504e13i		−	1.19695i
$757$		−	9.02103e12i		−	0.998446i	−0.866473	−	0.499223i	$-0.833619\pi$
$757$		−	9.02103e12i		−	0.998446i	0.866473	−	0.499223i	$-0.166381\pi$
$758$	4.11438e11	−	4.11438e11i	0.0452682	−	0.0452682i
$759$	−2.53576e12	+	2.53576e12i	−0.277345	+	0.277345i
$760$	−2.63477e11	−	2.63477e11i	−0.0286471	−	0.0286471i
$761$	−1.71746e13			−1.85633			−0.928165	−	0.372169i	$-0.878614\pi$
$761$	−1.71746e13			−1.85633			−0.928165	+	0.372169i	$0.878614\pi$
$762$	1.15608e12	+	1.15608e12i	0.124219	+	0.124219i
$763$			6.42559e12i			0.686361i
$764$	3.45680e12			0.367075
$765$	8.73485e12	−	7.80516e10i	0.922102	−	0.00823959i
$766$	2.21264e13			2.32211
$767$			2.11589e12i			0.220756i
$768$	3.31379e12	+	3.31379e12i	0.343715	+	0.343715i
$769$	4.58214e12			0.472498			0.236249	−	0.971693i	$-0.424082\pi$
$769$	4.58214e12			0.472498			0.236249	+	0.971693i	$0.424082\pi$
$770$	−2.88235e13	−	2.88235e13i	−2.95487	−	2.95487i
$771$	−1.69567e12	+	1.69567e12i	−0.172822	+	0.172822i
$772$	−2.55408e12	+	2.55408e12i	−0.258796	+	0.258796i
$773$			1.36741e12i			0.137750i	0.997625	+	0.0688750i	$0.0219410\pi$
$773$			1.36741e12i			0.137750i	−0.997625	+	0.0688750i	$0.978059\pi$
$774$			2.58406e12i			0.258803i
$775$	−4.13715e11	+	4.13715e11i	−0.0411949	+	0.0411949i
$776$	1.25343e12	−	1.25343e12i	0.124086	−	0.124086i
$777$	−5.04223e12	−	5.04223e12i	−0.496282	−	0.496282i
$778$	−2.74183e13			−2.68308
$779$	−1.87882e11	−	1.87882e11i	−0.0182796	−	0.0182796i
$780$			5.07234e12i			0.490662i
$781$	−1.89577e13			−1.82329
$782$	−7.33776e10	−	8.21177e12i	−0.00701670	−	0.785247i
$783$	1.61632e13			1.53674
$784$			1.94853e13i			1.84198i
$785$	8.99894e12	+	8.99894e12i	0.845820	+	0.845820i
$786$	1.48343e12			0.138632
$787$	7.91156e12	+	7.91156e12i	0.735150	+	0.735150i	0.971635	−	0.236485i	$-0.0759955\pi$
$787$	7.91156e12	+	7.91156e12i	0.735150	+	0.735150i	−0.236485	+	0.971635i	$0.575995\pi$
$788$	−7.32382e12	+	7.32382e12i	−0.676659	+	0.676659i
$789$	1.72405e12	−	1.72405e12i	0.158381	−	0.158381i
$790$		−	2.11848e12i		−	0.193510i
$791$		−	9.24597e12i		−	0.839766i
$792$	1.03148e12	−	1.03148e12i	0.0931536	−	0.0931536i
$793$	−1.06619e13	+	1.06619e13i	−0.957423	+	0.957423i
$794$	1.01241e13	+	1.01241e13i	0.903994	+	0.903994i
$795$	−4.26800e12			−0.378942
$796$	4.70792e12	+	4.70792e12i	0.415643	+	0.415643i
$797$		−	1.02469e13i		−	0.899561i	−0.893139	−	0.449781i	$-0.851502\pi$
$797$		−	1.02469e13i		−	0.899561i	0.893139	−	0.449781i	$-0.148498\pi$
$798$	4.02908e12			0.351717
$799$	5.73167e12	+	5.63015e12i	0.497532	+	0.488719i
$800$	4.50790e12			0.389107
$801$			8.99304e11i			0.0771898i
$802$	1.99636e13	+	1.99636e13i	1.70394	+	1.70394i
$803$	8.91234e12			0.756436
$804$	6.58132e10	+	6.58132e10i	0.00555470	+	0.00555470i
$805$	8.90734e12	−	8.90734e12i	0.747595	−	0.747595i
$806$	2.63860e12	−	2.63860e12i	0.220225	−	0.220225i
$807$		−	1.50461e12i		−	0.124880i
$808$			1.95557e12i			0.161407i
$809$	−5.96297e12	+	5.96297e12i	−0.489434	+	0.489434i	−0.908128	−	0.418693i	$-0.862488\pi$
$809$	−5.96297e12	+	5.96297e12i	−0.489434	+	0.489434i	0.418693	+	0.908128i	$0.362488\pi$
$810$	6.50814e12	−	6.50814e12i	0.531220	−	0.531220i
$811$	−8.76715e12	−	8.76715e12i	−0.711647	−	0.711647i	0.255233	−	0.966880i	$-0.417848\pi$
$811$	−8.76715e12	−	8.76715e12i	−0.711647	−	0.711647i	−0.966880	+	0.255233i	$0.917848\pi$
$812$	3.73116e13			3.01190
$813$	−2.33333e12	−	2.33333e12i	−0.187314	−	0.187314i
$814$			2.76379e13i			2.20646i
$815$	−7.98180e12			−0.633712
$816$	−5.20095e10	−	5.82045e12i	−0.00410655	−	0.459569i
$817$	−1.03826e12			−0.0815278
$818$		−	6.13270e12i		−	0.478918i
$819$	−1.32824e13	−	1.32824e13i	−1.03157	−	1.03157i
$820$	9.86686e11			0.0762108
$821$	−7.88979e12	−	7.88979e12i	−0.606067	−	0.606067i	0.335849	−	0.941916i	$-0.390977\pi$
$821$	−7.88979e12	−	7.88979e12i	−0.606067	−	0.606067i	−0.941916	+	0.335849i	$0.890977\pi$
$822$	−8.30959e12	+	8.30959e12i	−0.634829	+	0.634829i
$823$	1.51447e13	−	1.51447e13i	1.15070	−	1.15070i	0.164282	−	0.986413i	$-0.447469\pi$
$823$	1.51447e13	−	1.51447e13i	1.15070	−	1.15070i	0.986413	−	0.164282i	$-0.0525307\pi$
$824$		−	1.38928e12i		−	0.104983i
$825$			2.59957e12i			0.195371i
$826$	−4.41320e12	+	4.41320e12i	−0.329870	+	0.329870i
$827$	5.40215e12	−	5.40215e12i	0.401598	−	0.401598i	−0.477198	−	0.878796i	$-0.658347\pi$
$827$	5.40215e12	−	5.40215e12i	0.401598	−	0.401598i	0.878796	+	0.477198i	$0.158347\pi$
$828$	−4.08708e12	−	4.08708e12i	−0.302188	−	0.302188i
$829$	−2.44316e13			−1.79662			−0.898309	−	0.439365i	$-0.855204\pi$
$829$	−2.44316e13			−1.79662			−0.898309	+	0.439365i	$0.855204\pi$
$830$	1.53668e13	+	1.53668e13i	1.12391	+	1.12391i
$831$			3.38850e12i			0.246492i
$832$	−1.27510e13			−0.922548
$833$	1.68091e13	−	1.71123e13i	1.20960	−	1.23142i
$834$	4.58167e11			0.0327927
$835$		−	2.98763e13i		−	2.12686i
$836$	−5.31391e12	−	5.31391e12i	−0.376259	−	0.376259i
$837$	2.29460e12			0.161600
$838$	3.06646e12	+	3.06646e12i	0.214803	+	0.214803i
$839$	1.67910e12	−	1.67910e12i	0.116990	−	0.116990i	−0.646188	−	0.763178i	$-0.723638\pi$
$839$	1.67910e12	−	1.67910e12i	0.116990	−	0.116990i	0.763178	+	0.646188i	$0.223638\pi$
$840$	8.25124e11	−	8.25124e11i	0.0571824	−	0.0571824i
$841$			4.15911e13i			2.86694i
$842$		−	2.34063e13i		−	1.60483i
$843$	−7.52927e11	+	7.52927e11i	−0.0513486	+	0.0513486i
$844$	−1.14353e13	+	1.14353e13i	−0.775725	+	0.775725i
$845$	2.09703e12	+	2.09703e12i	0.141498	+	0.141498i
$846$	1.17508e13			0.788682
$847$	2.78510e13	+	2.78510e13i	1.85937	+	1.85937i
$848$		−	1.24885e13i		−	0.829331i
$849$	8.50976e12			0.562125
$850$	−4.24683e12	−	4.17161e12i	−0.279049	−	0.274106i
$851$	−8.54095e12			−0.558243
$852$			6.95836e12i			0.452407i
$853$	−5.04684e12	−	5.04684e12i	−0.326399	−	0.326399i	0.524816	−	0.851215i	$-0.324134\pi$
$853$	−5.04684e12	−	5.04684e12i	−0.326399	−	0.326399i	−0.851215	+	0.524816i	$0.824134\pi$
$854$	−4.44758e13			−2.86130
$855$	3.62976e12	+	3.62976e12i	0.232290	+	0.232290i
$856$	−1.43655e12	+	1.43655e12i	−0.0914509	+	0.0914509i
$857$	−8.55545e11	+	8.55545e11i	−0.0541788	+	0.0541788i	−0.733677	−	0.679498i	$-0.762197\pi$
$857$	−8.55545e11	+	8.55545e11i	−0.0541788	+	0.0541788i	0.679498	+	0.733677i	$0.262197\pi$
$858$		−	1.65796e13i		−	1.04444i
$859$		−	2.16132e13i		−	1.35441i	−0.735796	−	0.677203i	$-0.763192\pi$
$859$		−	2.16132e13i		−	1.35441i	0.735796	−	0.677203i	$-0.236808\pi$
$860$	2.72626e12	−	2.72626e12i	0.169951	−	0.169951i
$861$	5.88387e11	−	5.88387e11i	0.0364879	−	0.0364879i
$862$	−2.26884e12	−	2.26884e12i	−0.139966	−	0.139966i
$863$	2.21387e13			1.35864			0.679319	−	0.733843i	$-0.262275\pi$
$863$	2.21387e13			1.35864			0.679319	+	0.733843i	$0.262275\pi$
$864$	−1.25011e13	−	1.25011e13i	−0.763198	−	0.763198i
$865$		−	4.80272e12i		−	0.291685i
$866$	3.34172e13			2.01901
$867$	−4.97538e12	+	5.15646e12i	−0.299048	+	0.309932i
$868$	5.29689e12			0.316725
$869$			3.33233e12i			0.198225i
$870$	−1.59065e13	−	1.59065e13i	−0.941322	−	0.941322i
$871$	3.62292e11			0.0213293
$872$	5.04124e11	+	5.04124e11i	0.0295266	+	0.0295266i
$873$	−1.72677e13	+	1.72677e13i	−1.00617	+	1.00617i
$874$	3.41239e12	−	3.41239e12i	0.197814	−	0.197814i
$875$			2.32807e13i			1.34264i
$876$		−	3.27125e12i		−	0.187692i
$877$	5.11107e11	−	5.11107e11i	0.0291752	−	0.0291752i	−0.692369	−	0.721544i	$-0.743433\pi$
$877$	5.11107e11	−	5.11107e11i	0.0291752	−	0.0291752i	0.721544	+	0.692369i	$0.243433\pi$
$878$	−2.93624e13	+	2.93624e13i	−1.66750	+	1.66750i
$879$	3.58303e12	+	3.58303e12i	0.202442	+	0.202442i
$880$	−3.46059e13			−1.94526
$881$	2.27032e12	+	2.27032e12i	0.126968	+	0.126968i	0.767735	−	0.640767i	$-0.221384\pi$
$881$	2.27032e12	+	2.27032e12i	0.126968	+	0.126968i	−0.640767	+	0.767735i	$0.721384\pi$
$882$		−	3.50828e13i		−	1.95203i
$883$	−2.33032e13			−1.29001			−0.645004	−	0.764179i	$-0.723144\pi$
$883$	−2.33032e13			−1.29001			−0.645004	+	0.764179i	$0.723144\pi$
$884$	1.30345e13	+	1.28036e13i	0.717890	+	0.705174i
$885$	1.81080e12			0.0992261
$886$			4.06841e13i			2.21806i
$887$	−5.64791e12	−	5.64791e12i	−0.306360	−	0.306360i	0.537136	−	0.843496i	$-0.319506\pi$
$887$	−5.64791e12	−	5.64791e12i	−0.306360	−	0.306360i	−0.843496	+	0.537136i	$0.819506\pi$
$888$	−7.91183e11			−0.0426991
$889$	6.38776e12	+	6.38776e12i	0.342998	+	0.342998i
$890$	1.97158e12	−	1.97158e12i	0.105332	−	0.105332i
$891$	−1.02372e13	+	1.02372e13i	−0.544164	+	0.544164i
$892$		−	5.63724e12i		−	0.298143i
$893$			4.72139e12i			0.248450i
$894$	−1.84459e12	+	1.84459e12i	−0.0965787	+	0.0965787i
$895$	1.05836e13	−	1.05836e13i	0.551352	−	0.551352i
$896$	4.51320e12	+	4.51320e12i	0.233937	+	0.233937i
$897$	5.12360e12			0.264247
$898$	−9.43506e12	−	9.43506e12i	−0.484173	−	0.484173i
$899$			7.96392e12i			0.406638i
$900$	−4.18994e12			−0.212871
$901$	−1.07733e13	+	1.09675e13i	−0.544611	+	0.554432i
$902$	−3.22512e12			−0.162224
$903$		−	3.25149e12i		−	0.162737i
$904$	−7.25399e11	−	7.25399e11i	−0.0361259	−	0.0361259i
$905$	1.19179e13			0.590583
$906$	−5.88465e12	−	5.88465e12i	−0.290164	−	0.290164i
$907$	8.73458e12	−	8.73458e12i	0.428557	−	0.428557i	−0.459579	−	0.888137i	$-0.652000\pi$
$907$	8.73458e12	−	8.73458e12i	0.428557	−	0.428557i	0.888137	+	0.459579i	$0.152000\pi$
$908$	1.41780e13	−	1.41780e13i	0.692194	−	0.692194i
$909$		−	2.69407e13i		−	1.30879i
$910$			5.82391e13i			2.81532i
$911$	1.35297e13	−	1.35297e13i	0.650813	−	0.650813i	−0.302376	−	0.953189i	$-0.597780\pi$
$911$	1.35297e13	−	1.35297e13i	0.650813	−	0.650813i	0.953189	+	0.302376i	$0.0977798\pi$
$912$	2.41868e12	−	2.41868e12i	0.115772	−	0.115772i
$913$	−2.41717e13	−	2.41717e13i	−1.15130	−	1.15130i
$914$	−1.34203e13			−0.636068
$915$	9.12455e12	+	9.12455e12i	0.430345	+	0.430345i
$916$		−	1.82250e13i		−	0.855338i
$917$	8.19651e12			0.382796
$918$	2.08609e11	+	2.33456e13i	0.00969483	+	1.08496i
$919$	2.87258e13			1.32847			0.664236	−	0.747523i	$-0.268757\pi$
$919$	2.87258e13			1.32847			0.664236	+	0.747523i	$0.268757\pi$
$920$		−	1.39766e12i		−	0.0643216i
$921$	−7.50532e12	−	7.50532e12i	−0.343717	−	0.343717i
$922$	−3.58131e13			−1.63212
$923$	1.91524e13	+	1.91524e13i	0.868590	+	0.868590i
$924$	1.66415e13	−	1.66415e13i	0.751048	−	0.751048i
$925$	−4.37795e12	+	4.37795e12i	−0.196622	+	0.196622i
$926$		−	5.40465e13i		−	2.41556i
$927$			1.91393e13i			0.851269i
$928$	4.33880e13	−	4.33880e13i	1.92045	−	1.92045i
$929$	−7.69099e12	+	7.69099e12i	−0.338775	+	0.338775i	−0.855906	−	0.517131i	$-0.827000\pi$
$929$	−7.69099e12	+	7.69099e12i	−0.338775	+	0.338775i	0.517131	+	0.855906i	$0.327000\pi$
$930$	−2.25815e12	−	2.25815e12i	−0.0989872	−	0.0989872i
$931$	1.40960e13			0.614925
$932$	−5.38325e11	−	5.38325e11i	−0.0233708	−	0.0233708i
$933$		−	1.59501e13i		−	0.689124i
$934$	4.96709e13			2.13570
$935$	3.03913e13	+	2.98530e13i	1.30046	+	1.27743i
$936$	−2.08416e12			−0.0887542
$937$		−	2.93915e13i		−	1.24564i	−0.782363	−	0.622822i	$-0.785986\pi$
$937$		−	2.93915e13i		−	1.24564i	0.782363	−	0.622822i	$-0.214014\pi$
$938$	7.55648e11	+	7.55648e11i	0.0318718	+	0.0318718i
$939$	−1.53947e12			−0.0646213
$940$	−1.23975e13	−	1.23975e13i	−0.517914	−	0.517914i
$941$	−1.23654e10	+	1.23654e10i	−0.000514108	+	0.000514108i	−0.707364	−	0.706850i	$-0.750116\pi$
$941$	−1.23654e10	+	1.23654e10i	−0.000514108	+	0.000514108i	0.706850	+	0.707364i	$0.250116\pi$
$942$	−1.07964e13	+	1.07964e13i	−0.446735	+	0.446735i
$943$		−	9.96658e11i		−	0.0410434i
$944$			5.29853e12i			0.217161i
$945$	−2.53231e13	+	2.53231e13i	−1.03294	+	1.03294i
$946$	−8.91116e12	+	8.91116e12i	−0.361763	+	0.361763i
$947$	2.38185e13	+	2.38185e13i	0.962365	+	0.962365i	0.999317	−	0.0369525i	$-0.0117650\pi$
$947$	2.38185e13	+	2.38185e13i	0.962365	+	0.962365i	−0.0369525	+	0.999317i	$0.511765\pi$
$948$	1.22312e12			0.0491849
$949$	−9.00387e12	−	9.00387e12i	−0.360356	−	0.360356i
$950$		−	3.49827e12i		−	0.139347i
$951$	−1.51088e13			−0.598988
$952$	−3.75575e10	−	4.20311e12i	−0.00148194	−	0.165846i
$953$	−1.95197e13			−0.766577			−0.383288	−	0.923629i	$-0.625208\pi$
$953$	−1.95197e13			−0.766577			−0.383288	+	0.923629i	$0.625208\pi$
$954$			2.24852e13i			0.878879i
$955$	−8.14270e12	−	8.14270e12i	−0.316777	−	0.316777i
$956$	2.46438e13			0.954218
$957$	2.50206e13	+	2.50206e13i	0.964259	+	0.964259i
$958$	−2.41799e13	+	2.41799e13i	−0.927492	+	0.927492i
$959$	−4.59137e13	+	4.59137e13i	−1.75291	+	1.75291i
$960$			1.09125e13i			0.414669i
$961$		−	2.53090e13i		−	0.957239i
$962$	2.79218e13	−	2.79218e13i	1.05113	−	1.05113i
$963$	1.97904e13	−	1.97904e13i	0.741545	−	0.741545i
$964$	−1.43612e13	−	1.43612e13i	−0.535603	−	0.535603i
$965$	1.20326e13			0.446669
$966$	1.06865e13	+	1.06865e13i	0.394856	+	0.394856i
$967$			5.04513e12i			0.185547i	0.995687	+	0.0927733i	$0.0295732\pi$
$967$			5.04513e12i			0.185547i	−0.995687	+	0.0927733i	$0.970427\pi$
$968$	4.37014e12			0.159977
$969$	−4.21061e12	+	3.76246e10i	−0.153422	+	0.00137093i
$970$	7.57135e13			2.74600
$971$		−	2.97871e13i		−	1.07533i	−0.843158	−	0.537665i	$-0.819306\pi$
$971$		−	2.97871e13i		−	1.07533i	0.843158	−	0.537665i	$-0.180694\pi$
$972$	1.80229e13	+	1.80229e13i	0.647631	+	0.647631i
$973$	2.53155e12			0.0905480
$974$	−4.60660e13	−	4.60660e13i	−1.64008	−	1.64008i
$975$	2.62627e12	−	2.62627e12i	0.0930720	−	0.0930720i
$976$	−2.66991e13	+	2.66991e13i	−0.941830	+	0.941830i
$977$			1.68301e13i			0.590965i	0.955348	+	0.295483i	$0.0954804\pi$
$977$			1.68301e13i			0.590965i	−0.955348	+	0.295483i	$0.904520\pi$
$978$		−	9.57611e12i		−	0.334707i
$979$	−3.10125e12	+	3.10125e12i	−0.107898	+	0.107898i
$980$	−3.70134e13	+	3.70134e13i	−1.28186	+	1.28186i
$981$	−6.94501e12	−	6.94501e12i	−0.239421	−	0.239421i
$982$	−4.01666e12			−0.137836
$983$	−3.20321e13	−	3.20321e13i	−1.09419	−	1.09419i	−0.995076	−	0.0991174i	$-0.968398\pi$
$983$	−3.20321e13	−	3.20321e13i	−1.09419	−	1.09419i	−0.0991174	−	0.995076i	$-0.531602\pi$
$984$		−	9.23246e10i		−	0.00313935i
$985$	3.45034e13			1.16788
$986$	−8.10264e13	+	7.24024e11i	−2.73011	+	0.0243953i
$987$	−1.47859e13			−0.495929
$988$			1.07370e13i			0.358489i
$989$	−2.75381e12	−	2.75381e12i	−0.0915275	−	0.0915275i
$990$	6.23070e13			2.06148
$991$	3.63412e13	+	3.63412e13i	1.19693	+	1.19693i	0.975082	+	0.221846i	$0.0712083\pi$
$991$	3.63412e13	+	3.63412e13i	1.19693	+	1.19693i	0.221846	+	0.975082i	$0.428792\pi$
$992$	6.15952e12	−	6.15952e12i	0.201950	−	0.201950i
$993$	−1.56272e13	+	1.56272e13i	−0.510045	+	0.510045i
$994$			7.98939e13i			2.59582i
$995$		−	2.21796e13i		−	0.717380i
$996$	−8.87215e12	+	8.87215e12i	−0.285668	+	0.285668i
$997$	−2.32301e13	+	2.32301e13i	−0.744600	+	0.744600i	−0.973459	−	0.228859i	$-0.926500\pi$
$997$	−2.32301e13	+	2.32301e13i	−0.744600	+	0.744600i	0.228859	+	0.973459i	$0.426500\pi$
$998$	3.48877e13	+	3.48877e13i	1.11323	+	1.11323i
$999$	2.42815e13			0.771312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.10	yes	24
17.2	even	8		289.10.a.f.1.6		24
17.4	even	4	inner	17.10.c.a.4.3	✓	24
17.15	even	8		289.10.a.f.1.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.3	✓	24	17.4	even	4	inner
17.10.c.a.13.10	yes	24	1.1	even	1	trivial
289.10.a.f.1.5		24	17.15	even	8
289.10.a.f.1.6		24	17.2	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)

\(f(q)\)	\(=\)	\(q+31.4159i q^{2} +(42.7255 + 42.7255i) q^{3} -474.957 q^{4} +(1118.79 + 1118.79i) q^{5} +(-1342.26 + 1342.26i) q^{6} +(-7416.51 + 7416.51i) q^{7} +1163.73i q^{8} -16032.1i q^{9} +O(q^{10})\)	\(q+31.4159i q^{2} +(42.7255 + 42.7255i) q^{3} -474.957 q^{4} +(1118.79 + 1118.79i) q^{5} +(-1342.26 + 1342.26i) q^{6} +(-7416.51 + 7416.51i) q^{7} +1163.73i q^{8} -16032.1i q^{9} +(-35147.8 + 35147.8i) q^{10} +(55286.6 - 55286.6i) q^{11} +(-20292.8 - 20292.8i) q^{12} -111709. q^{13} +(-232996. - 232996. i) q^{14} +95601.8i q^{15} -279738. q^{16} +(245670. + 241318. i) q^{17} +503661. q^{18} +202367. i q^{19} +(-531377. - 531377. i) q^{20} -633749. q^{21} +(1.73688e6 + 1.73688e6i) q^{22} +(-536747. + 536747. i) q^{23} +(-49721.2 + 49721.2i) q^{24} +550256. i q^{25} -3.50943e6i q^{26} +(1.52595e6 - 1.52595e6i) q^{27} +(3.52252e6 - 3.52252e6i) q^{28} +(5.29614e6 + 5.29614e6i) q^{29} -3.00341e6 q^{30} +(751860. + 751860. i) q^{31} -8.19237e6i q^{32} +4.72430e6 q^{33} +(-7.58121e6 + 7.71792e6i) q^{34} -1.65950e7 q^{35} +7.61454e6i q^{36} +(7.95621e6 + 7.95621e6i) q^{37} -6.35754e6 q^{38} +(-4.77282e6 - 4.77282e6i) q^{39} +(-1.30197e6 + 1.30197e6i) q^{40} +(-928424. + 928424. i) q^{41} -1.99098e7i q^{42} +5.13056e6i q^{43} +(-2.62588e7 + 2.62588e7i) q^{44} +(1.79365e7 - 1.79365e7i) q^{45} +(-1.68624e7 - 1.68624e7i) q^{46} +2.33308e7 q^{47} +(-1.19519e7 - 1.19519e7i) q^{48} -6.96556e7i q^{49} -1.72868e7 q^{50} +(185922. + 2.08068e7i) q^{51} +5.30569e7 q^{52} +4.46435e7i q^{53} +(4.79389e7 + 4.79389e7i) q^{54} +1.23708e8 q^{55} +(-8.63084e6 - 8.63084e6i) q^{56} +(-8.64625e6 + 8.64625e6i) q^{57} +(-1.66383e8 + 1.66383e8i) q^{58} -1.89411e7i q^{59} -4.54068e7i q^{60} +(9.54433e7 - 9.54433e7i) q^{61} +(-2.36203e7 + 2.36203e7i) q^{62} +(1.18902e8 + 1.18902e8i) q^{63} +1.14145e8 q^{64} +(-1.24979e8 - 1.24979e8i) q^{65} +1.48418e8i q^{66} -3.24318e6 q^{67} +(-1.16682e8 - 1.14616e8i) q^{68} -4.58657e7 q^{69} -5.21347e8i q^{70} +(-1.71449e8 - 1.71449e8i) q^{71} +1.86570e7 q^{72} +(8.06012e7 + 8.06012e7i) q^{73} +(-2.49951e8 + 2.49951e8i) q^{74} +(-2.35100e7 + 2.35100e7i) q^{75} -9.61157e7i q^{76} +8.20068e8i q^{77} +(1.49942e8 - 1.49942e8i) q^{78} +(-3.01368e7 + 3.01368e7i) q^{79} +(-3.12968e8 - 3.12968e8i) q^{80} -1.85165e8 q^{81} +(-2.91672e7 - 2.91672e7i) q^{82} -4.37207e8i q^{83} +3.01003e8 q^{84} +(4.86847e6 + 5.44837e8i) q^{85} -1.61181e8 q^{86} +4.52561e8i q^{87} +(6.43389e7 + 6.43389e7i) q^{88} -5.60941e7 q^{89} +(5.63491e8 + 5.63491e8i) q^{90} +(8.28490e8 - 8.28490e8i) q^{91} +(2.54932e8 - 2.54932e8i) q^{92} +6.42473e7i q^{93} +7.32958e8i q^{94} +(-2.26406e8 + 2.26406e8i) q^{95} +(3.50024e8 - 3.50024e8i) q^{96} +(-1.07707e9 - 1.07707e9i) q^{97} +2.18829e9 q^{98} +(-8.86358e8 - 8.86358e8i) 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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