LMFDB - Embedded newform 17.10.c.a.4.10

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			4.10
Character	$\chi$	$=$	17.4
Dual form			17.10.c.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+28.8329i q^{2} +(-179.389 + 179.389i) q^{3} -319.336 q^{4} +(-1133.17 + 1133.17i) q^{5} +(-5172.29 - 5172.29i) q^{6} +(4922.20 + 4922.20i) q^{7} +5555.06i q^{8} -44677.5i q^{9} +O(q^{10})$	\(q+28.8329i q^{2} +(-179.389 + 179.389i) q^{3} -319.336 q^{4} +(-1133.17 + 1133.17i) q^{5} +(-5172.29 - 5172.29i) q^{6} +(4922.20 + 4922.20i) q^{7} +5555.06i q^{8} -44677.5i q^{9} +(-32672.5 - 32672.5i) q^{10} +(44802.3 + 44802.3i) q^{11} +(57285.2 - 57285.2i) q^{12} +114552. q^{13} +(-141921. + 141921. i) q^{14} -406554. i q^{15} -323669. q^{16} +(-274067. - 208507. i) q^{17} +1.28818e6 q^{18} +50488.5i q^{19} +(361861. - 361861. i) q^{20} -1.76597e6 q^{21} +(-1.29178e6 + 1.29178e6i) q^{22} +(805268. + 805268. i) q^{23} +(-996514. - 996514. i) q^{24} -615007. i q^{25} +3.30287e6i q^{26} +(4.48373e6 + 4.48373e6i) q^{27} +(-1.57184e6 - 1.57184e6i) q^{28} +(-1.44158e6 + 1.44158e6i) q^{29} +1.17221e7 q^{30} +(734754. - 734754. i) q^{31} -6.48811e6i q^{32} -1.60741e7 q^{33} +(6.01186e6 - 7.90215e6i) q^{34} -1.11554e7 q^{35} +1.42671e7i q^{36} +(1.30400e7 - 1.30400e7i) q^{37} -1.45573e6 q^{38} +(-2.05493e7 + 2.05493e7i) q^{39} +(-6.29480e6 - 6.29480e6i) q^{40} +(5.63189e6 + 5.63189e6i) q^{41} -5.09182e7i q^{42} -2.09816e7i q^{43} +(-1.43070e7 - 1.43070e7i) q^{44} +(5.06270e7 + 5.06270e7i) q^{45} +(-2.32182e7 + 2.32182e7i) q^{46} +6.43503e6 q^{47} +(5.80624e7 - 5.80624e7i) q^{48} +8.10258e6i q^{49} +1.77324e7 q^{50} +(8.65682e7 - 1.17607e7i) q^{51} -3.65807e7 q^{52} +1.61556e7i q^{53} +(-1.29279e8 + 1.29279e8i) q^{54} -1.01537e8 q^{55} +(-2.73431e7 + 2.73431e7i) q^{56} +(-9.05706e6 - 9.05706e6i) q^{57} +(-4.15651e7 - 4.15651e7i) q^{58} +1.17489e8i q^{59} +1.29827e8i q^{60} +(2.49073e7 + 2.49073e7i) q^{61} +(2.11851e7 + 2.11851e7i) q^{62} +(2.19912e8 - 2.19912e8i) q^{63} +2.13528e7 q^{64} +(-1.29807e8 + 1.29807e8i) q^{65} -4.63462e8i q^{66} +2.32033e8 q^{67} +(8.75195e7 + 6.65838e7i) q^{68} -2.88912e8 q^{69} -3.21641e8i q^{70} +(-5.09689e6 + 5.09689e6i) q^{71} +2.48186e8 q^{72} +(-2.23490e8 + 2.23490e8i) q^{73} +(3.75980e8 + 3.75980e8i) q^{74} +(1.10325e8 + 1.10325e8i) q^{75} -1.61228e7i q^{76} +4.41053e8i q^{77} +(-5.92497e8 - 5.92497e8i) q^{78} +(-4.12622e8 - 4.12622e8i) q^{79} +(3.66770e8 - 3.66770e8i) q^{80} -7.29271e8 q^{81} +(-1.62384e8 + 1.62384e8i) q^{82} -2.61757e8i q^{83} +5.63939e8 q^{84} +(5.46837e8 - 7.42904e7i) q^{85} +6.04960e8 q^{86} -5.17208e8i q^{87} +(-2.48880e8 + 2.48880e8i) q^{88} +8.28097e7 q^{89} +(-1.45972e9 + 1.45972e9i) q^{90} +(5.63849e8 + 5.63849e8i) q^{91} +(-2.57151e8 - 2.57151e8i) q^{92} +2.63613e8i q^{93} +1.85541e8i q^{94} +(-5.72119e7 - 5.72119e7i) q^{95} +(1.16389e9 + 1.16389e9i) q^{96} +(-1.17934e8 + 1.17934e8i) q^{97} -2.33621e8 q^{98} +(2.00166e9 - 2.00166e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) $ 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7	\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) 24 * q + 144 * q^3 - 5124 * q^4 - 1710 * q^5 - 8174 * q^6 + 3810 * q^7 + 21946 * q^10 + 18132 * q^11 - 95142 * q^12 + 244832 * q^13 - 341100 * q^14 - 279932 * q^16 - 98022 * q^17 + 888764 * q^18 + 1364262 * q^20 - 775748 * q^21 - 4573190 * q^22 - 377526 * q^23 - 307054 * q^24 + 3996108 * q^27 - 1024780 * q^28 + 2160042 * q^29 + 39084792 * q^30 - 585086 * q^31 - 30349992 * q^33 + 4441318 * q^34 - 25532364 * q^35 + 1515390 * q^37 + 13171392 * q^38 - 25687084 * q^39 - 63240118 * q^40 - 72707928 * q^41 - 3606450 * q^44 + 156729418 * q^45 + 118549536 * q^46 + 153365328 * q^47 + 26098270 * q^48 - 236105676 * q^50 + 256903592 * q^51 - 209898380 * q^52 - 187411976 * q^54 + 255767540 * q^55 - 107638596 * q^56 - 443390988 * q^57 - 281433730 * q^58 + 52149382 * q^61 + 176928228 * q^62 + 620111642 * q^63 + 1006108924 * q^64 - 489714396 * q^65 - 26076868 * q^67 - 308011950 * q^68 - 751973532 * q^69 + 149240178 * q^71 + 1171736028 * q^72 - 175256556 * q^73 - 37609818 * q^74 - 233543476 * q^75 - 1202722924 * q^78 - 469987182 * q^79 + 481103586 * q^80 + 347156560 * q^81 - 984422080 * q^82 - 935672904 * q^84 - 725828294 * q^85 + 690159588 * q^86 + 992281114 * q^88 - 191594460 * q^89 + 914946474 * q^90 + 926854816 * q^91 + 3064830552 * q^92 + 1213246572 * q^95 + 3594247550 * q^96 - 2200567348 * q^97 - 4413444720 * q^98 - 1224966600 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			28.8329i			1.27425i	0.770762	+	0.637123i	$0.219876\pi$
$2$			28.8329i			1.27425i	−0.770762	+	0.637123i	$0.780124\pi$
$3$	−179.389	+	179.389i	−1.27864	+	1.27864i	−0.337214	+	0.941428i	$0.609485\pi$
$3$	−179.389	+	179.389i	−1.27864	+	1.27864i	−0.941428	+	0.337214i	$0.890515\pi$
$4$	−319.336			−0.623703
$5$	−1133.17	+	1133.17i	−0.810828	+	0.810828i	−0.984758	−	0.173930i	$-0.944353\pi$
$5$	−1133.17	+	1133.17i	−0.810828	+	0.810828i	0.173930	+	0.984758i	$0.444353\pi$
$6$	−5172.29	−	5172.29i	−1.62931	−	1.62931i
$7$	4922.20	+	4922.20i	0.774851	+	0.774851i	0.978950	−	0.204099i	$-0.0654264\pi$
$7$	4922.20	+	4922.20i	0.774851	+	0.774851i	−0.204099	+	0.978950i	$0.565426\pi$
$8$			5555.06i			0.479494i
$9$		−	44677.5i		−	2.26985i
$10$	−32672.5	−	32672.5i	−1.03319	−	1.03319i
$11$	44802.3	+	44802.3i	0.922643	+	0.922643i	0.997216	−	0.0745727i	$-0.0237593\pi$
$11$	44802.3	+	44802.3i	0.922643	+	0.922643i	−0.0745727	+	0.997216i	$0.523759\pi$
$12$	57285.2	−	57285.2i	0.797494	−	0.797494i
$13$	114552.			1.11239			0.556197	−	0.831051i	$-0.312260\pi$
$13$	114552.			1.11239			0.556197	+	0.831051i	$0.312260\pi$
$14$	−141921.	+	141921.i	−0.987352	+	0.987352i
$15$		−	406554.i		−	2.07352i
$16$	−323669.			−1.23470
$17$	−274067.	−	208507.i	−0.795860	−	0.605481i
$17$	−274067.	−	208507.i	−0.795860	−	0.605481i
$18$	1.28818e6			2.89235
$19$			50488.5i			0.0888794i	0.999012	+	0.0444397i	$0.0141503\pi$
$19$			50488.5i			0.0888794i	−0.999012	+	0.0444397i	$0.985850\pi$
$20$	361861.	−	361861.i	0.505716	−	0.505716i
$21$	−1.76597e6			−1.98152
$22$	−1.29178e6	+	1.29178e6i	−1.17567	+	1.17567i
$23$	805268.	+	805268.i	0.600019	+	0.600019i	0.940317	−	0.340298i	$-0.110528\pi$
$23$	805268.	+	805268.i	0.600019	+	0.600019i	−0.340298	+	0.940317i	$0.610528\pi$
$24$	−996514.	−	996514.i	−0.613102	−	0.613102i
$25$		−	615007.i		−	0.314884i
$26$			3.30287e6i			1.41746i
$27$	4.48373e6	+	4.48373e6i	1.62369	+	1.62369i
$28$	−1.57184e6	−	1.57184e6i	−0.483278	−	0.483278i
$29$	−1.44158e6	+	1.44158e6i	−0.378486	+	0.378486i	−0.870556	−	0.492070i	$-0.836240\pi$
$29$	−1.44158e6	+	1.44158e6i	−0.378486	+	0.378486i	0.492070	+	0.870556i	$0.336240\pi$
$30$	1.17221e7			2.64217
$31$	734754.	−	734754.i	0.142894	−	0.142894i	−0.632041	−	0.774935i	$-0.717783\pi$
$31$	734754.	−	734754.i	0.142894	−	0.142894i	0.774935	+	0.632041i	$0.217783\pi$
$32$		−	6.48811e6i		−	1.09381i
$33$	−1.60741e7			−2.35946
$34$	6.01186e6	−	7.90215e6i	0.771532	−	1.01412i
$35$	−1.11554e7			−1.25654
$36$			1.42671e7i			1.41571i
$37$	1.30400e7	−	1.30400e7i	1.14385	−	1.14385i	0.156108	−	0.987740i	$-0.450105\pi$
$37$	1.30400e7	−	1.30400e7i	1.14385	−	1.14385i	0.987740	−	0.156108i	$-0.0498949\pi$
$38$	−1.45573e6			−0.113254
$39$	−2.05493e7	+	2.05493e7i	−1.42235	+	1.42235i
$40$	−6.29480e6	−	6.29480e6i	−0.388787	−	0.388787i
$41$	5.63189e6	+	5.63189e6i	0.311263	+	0.311263i	0.845399	−	0.534136i	$-0.179363\pi$
$41$	5.63189e6	+	5.63189e6i	0.311263	+	0.311263i	−0.534136	+	0.845399i	$0.679363\pi$
$42$		−	5.09182e7i		−	2.52494i
$43$		−	2.09816e7i		−	0.935902i	−0.883755	−	0.467951i	$-0.844992\pi$
$43$		−	2.09816e7i		−	0.935902i	0.883755	−	0.467951i	$-0.155008\pi$
$44$	−1.43070e7	−	1.43070e7i	−0.575456	−	0.575456i
$45$	5.06270e7	+	5.06270e7i	1.84046	+	1.84046i
$46$	−2.32182e7	+	2.32182e7i	−0.764572	+	0.764572i
$47$	6.43503e6			0.192358			0.0961790	−	0.995364i	$-0.469338\pi$
$47$	6.43503e6			0.192358			0.0961790	+	0.995364i	$0.469338\pi$
$48$	5.80624e7	−	5.80624e7i	1.57874	−	1.57874i
$49$			8.10258e6i			0.200789i
$50$	1.77324e7			0.401239
$51$	8.65682e7	−	1.17607e7i	1.79181	−	0.243427i
$52$	−3.65807e7			−0.693803
$53$			1.61556e7i			0.281242i	0.990063	+	0.140621i	$0.0449099\pi$
$53$			1.61556e7i			0.281242i	−0.990063	+	0.140621i	$0.955090\pi$
$54$	−1.29279e8	+	1.29279e8i	−2.06898	+	2.06898i
$55$	−1.01537e8			−1.49621
$56$	−2.73431e7	+	2.73431e7i	−0.371537	+	0.371537i
$57$	−9.05706e6	−	9.05706e6i	−0.113645	−	0.113645i
$58$	−4.15651e7	−	4.15651e7i	−0.482284	−	0.482284i
$59$			1.17489e8i			1.26230i	0.775659	+	0.631152i	$0.217417\pi$
$59$			1.17489e8i			1.26230i	−0.775659	+	0.631152i	$0.782583\pi$
$60$			1.29827e8i			1.29326i
$61$	2.49073e7	+	2.49073e7i	0.230326	+	0.230326i	0.812829	−	0.582503i	$-0.197927\pi$
$61$	2.49073e7	+	2.49073e7i	0.230326	+	0.230326i	−0.582503	+	0.812829i	$0.697927\pi$
$62$	2.11851e7	+	2.11851e7i	0.182082	+	0.182082i
$63$	2.19912e8	−	2.19912e8i	1.75880	−	1.75880i
$64$	2.13528e7			0.159091
$65$	−1.29807e8	+	1.29807e8i	−0.901959	+	0.901959i
$66$		−	4.63462e8i		−	3.00653i
$67$	2.32033e8			1.40674			0.703368	−	0.710826i	$-0.251679\pi$
$67$	2.32033e8			1.40674			0.703368	+	0.710826i	$0.251679\pi$
$68$	8.75195e7	+	6.65838e7i	0.496381	+	0.377640i
$69$	−2.88912e8			−1.53442
$70$		−	3.21641e8i		−	1.60114i
$71$	−5.09689e6	+	5.09689e6i	−0.0238036	+	0.0238036i	−0.718908	−	0.695105i	$-0.755358\pi$
$71$	−5.09689e6	+	5.09689e6i	−0.0238036	+	0.0238036i	0.695105	+	0.718908i	$0.255358\pi$
$72$	2.48186e8			1.08838
$73$	−2.23490e8	+	2.23490e8i	−0.921097	+	0.921097i	−0.997107	−	0.0760099i	$-0.975782\pi$
$73$	−2.23490e8	+	2.23490e8i	−0.921097	+	0.921097i	0.0760099	+	0.997107i	$0.475782\pi$
$74$	3.75980e8	+	3.75980e8i	1.45754	+	1.45754i
$75$	1.10325e8	+	1.10325e8i	0.402624	+	0.402624i
$76$		−	1.61228e7i		−	0.0554344i
$77$			4.41053e8i			1.42982i
$78$	−5.92497e8	−	5.92497e8i	−1.81243	−	1.81243i
$79$	−4.12622e8	−	4.12622e8i	−1.19187	−	1.19187i	−0.976541	−	0.215333i	$-0.930916\pi$
$79$	−4.12622e8	−	4.12622e8i	−1.19187	−	1.19187i	−0.215333	−	0.976541i	$-0.569084\pi$
$80$	3.66770e8	−	3.66770e8i	1.00113	−	1.00113i
$81$	−7.29271e8			−1.88238
$82$	−1.62384e8	+	1.62384e8i	−0.396625	+	0.396625i
$83$		−	2.61757e8i		−	0.605407i	−0.953085	−	0.302704i	$-0.902111\pi$
$83$		−	2.61757e8i		−	0.605407i	0.953085	−	0.302704i	$-0.0978892\pi$
$84$	5.63939e8			1.23588
$85$	5.46837e8	−	7.42904e7i	1.13625	−	0.154365i
$86$	6.04960e8			1.19257
$87$		−	5.17208e8i		−	0.967895i
$88$	−2.48880e8	+	2.48880e8i	−0.442402	+	0.442402i
$89$	8.28097e7			0.139903			0.0699513	−	0.997550i	$-0.477716\pi$
$89$	8.28097e7			0.139903			0.0699513	+	0.997550i	$0.477716\pi$
$90$	−1.45972e9	+	1.45972e9i	−2.34520	+	2.34520i
$91$	5.63849e8	+	5.63849e8i	0.861939	+	0.861939i
$92$	−2.57151e8	−	2.57151e8i	−0.374234	−	0.374234i
$93$			2.63613e8i			0.365421i
$94$			1.85541e8i			0.245111i
$95$	−5.72119e7	−	5.72119e7i	−0.0720659	−	0.0720659i
$96$	1.16389e9	+	1.16389e9i	1.39860	+	1.39860i
$97$	−1.17934e8	+	1.17934e8i	−0.135258	+	0.135258i	−0.771494	−	0.636236i	$-0.780490\pi$
$97$	−1.17934e8	+	1.17934e8i	−0.135258	+	0.135258i	0.636236	+	0.771494i	$0.280490\pi$
$98$	−2.33621e8			−0.255855
$99$	2.00166e9	−	2.00166e9i	2.09426	−	2.09426i
$100$			1.96394e8i			0.196394i
$101$	−1.93499e9			−1.85026			−0.925130	−	0.379651i	$-0.876044\pi$
$101$	−1.93499e9			−1.85026			−0.925130	+	0.379651i	$0.876044\pi$
$102$	3.39096e8	+	2.49601e9i	0.310185	+	2.28321i
$103$	−1.87339e9			−1.64006			−0.820031	−	0.572319i	$-0.806044\pi$
$103$	−1.87339e9			−1.64006			−0.820031	+	0.572319i	$0.806044\pi$
$104$			6.36344e8i			0.533386i
$105$	2.00114e9	−	2.00114e9i	1.60667	−	1.60667i
$106$	−4.65812e8			−0.358372
$107$	1.48763e9	−	1.48763e9i	1.09715	−	1.09715i	0.102412	−	0.994742i	$-0.467344\pi$
$107$	1.48763e9	−	1.48763e9i	1.09715	−	1.09715i	0.994742	−	0.102412i	$-0.0326561\pi$
$108$	−1.43182e9	−	1.43182e9i	−1.01270	−	1.01270i
$109$	7.08084e8	+	7.08084e8i	0.480469	+	0.480469i	0.905281	−	0.424812i	$-0.139660\pi$
$109$	7.08084e8	+	7.08084e8i	0.480469	+	0.480469i	−0.424812	+	0.905281i	$0.639660\pi$
$110$		−	2.92761e9i		−	1.90654i
$111$			4.67844e9i			2.92515i
$112$	−1.59316e9	−	1.59316e9i	−0.956707	−	0.956707i
$113$	1.57070e9	+	1.57070e9i	0.906237	+	0.906237i	0.995966	−	0.0897295i	$-0.0286003\pi$
$113$	1.57070e9	+	1.57070e9i	0.906237	+	0.906237i	−0.0897295	+	0.995966i	$0.528600\pi$
$114$	2.61141e8	−	2.61141e8i	0.144812	−	0.144812i
$115$	−1.82500e9			−0.973024
$116$	4.60350e8	−	4.60350e8i	0.236063	−	0.236063i
$117$		−	5.11790e9i		−	2.52497i
$118$	−3.38755e9			−1.60849
$119$	−3.22700e8	−	2.37533e9i	−0.147515	−	1.08583i
$120$	2.25843e9			0.994240
$121$			1.65655e9i			0.702540i
$122$	−7.18149e8	+	7.18149e8i	−0.293491	+	0.293491i
$123$	−2.02059e9			−0.795987
$124$	−2.34633e8	+	2.34633e8i	−0.0891235	+	0.0891235i
$125$	−1.51631e9	−	1.51631e9i	−0.555511	−	0.555511i
$126$	6.34069e9	+	6.34069e9i	2.24114	+	2.24114i
$127$			1.88159e9i			0.641814i	0.947111	+	0.320907i	$0.103988\pi$
$127$			1.88159e9i			0.641814i	−0.947111	+	0.320907i	$0.896012\pi$
$128$		−	2.70625e9i		−	0.891093i
$129$	3.76386e9	+	3.76386e9i	1.19668	+	1.19668i
$130$	−3.74270e9	−	3.74270e9i	−1.14932	−	1.14932i
$131$	2.20233e9	−	2.20233e9i	0.653373	−	0.653373i	−0.300430	−	0.953804i	$-0.597130\pi$
$131$	2.20233e9	−	2.20233e9i	0.653373	−	0.653373i	0.953804	+	0.300430i	$0.0971303\pi$
$132$	5.13303e9			1.47160
$133$	−2.48515e8	+	2.48515e8i	−0.0688684	+	0.0688684i
$134$			6.69017e9i			1.79253i
$135$	−1.01616e10			−2.63306
$136$	1.15827e9	−	1.52246e9i	0.290325	−	0.381610i
$137$	4.16041e9			1.00901			0.504503	−	0.863410i	$-0.331676\pi$
$137$	4.16041e9			1.00901			0.504503	+	0.863410i	$0.331676\pi$
$138$		−	8.33016e9i		−	1.95523i
$139$	−5.73290e8	+	5.73290e8i	−0.130259	+	0.130259i	−0.769230	−	0.638971i	$-0.779360\pi$
$139$	−5.73290e8	+	5.73290e8i	−0.130259	+	0.130259i	0.638971	+	0.769230i	$0.279360\pi$
$140$	3.56231e9			0.783710
$141$	−1.15437e9	+	1.15437e9i	−0.245957	+	0.245957i
$142$	−1.46958e8	−	1.46958e8i	−0.0303316	−	0.0303316i
$143$	5.13221e9	+	5.13221e9i	1.02634	+	1.02634i
$144$			1.44607e10i			2.80258i
$145$		−	3.26711e9i		−	0.613773i
$146$	−6.44387e9	−	6.44387e9i	−1.17370	−	1.17370i
$147$	−1.45351e9	−	1.45351e9i	−0.256738	−	0.256738i
$148$	−4.16413e9	+	4.16413e9i	−0.713422	+	0.713422i
$149$	−1.33926e9			−0.222601			−0.111301	−	0.993787i	$-0.535502\pi$
$149$	−1.33926e9			−0.222601			−0.111301	+	0.993787i	$0.535502\pi$
$150$	−3.18100e9	+	3.18100e9i	−0.513042	+	0.513042i
$151$		−	3.62654e9i		−	0.567671i	−0.958873	−	0.283835i	$-0.908393\pi$
$151$		−	3.62654e9i		−	0.567671i	0.958873	−	0.283835i	$-0.0916069\pi$
$152$	−2.80467e8			−0.0426172
$153$	−9.31557e9	+	1.22446e10i	−1.37435	+	1.80648i
$154$	−1.27168e10			−1.82195
$155$			1.66520e9i			0.231725i
$156$	6.56215e9	−	6.56215e9i	0.887126	−	0.887126i
$157$	4.56689e9			0.599891			0.299945	−	0.953956i	$-0.403032\pi$
$157$	4.56689e9			0.599891			0.299945	+	0.953956i	$0.403032\pi$
$158$	1.18971e10	−	1.18971e10i	1.51874	−	1.51874i
$159$	−2.89812e9	−	2.89812e9i	−0.359608	−	0.359608i
$160$	7.35211e9	+	7.35211e9i	0.886895	+	0.886895i
$161$			7.92738e9i			0.929851i
$162$		−	2.10270e10i		−	2.39861i
$163$	1.12494e9	+	1.12494e9i	0.124821	+	0.124821i	0.766758	−	0.641937i	$-0.221869\pi$
$163$	1.12494e9	+	1.12494e9i	0.124821	+	0.124821i	−0.641937	+	0.766758i	$0.721869\pi$
$164$	−1.79847e9	−	1.79847e9i	−0.194136	−	0.194136i
$165$	1.82146e10	−	1.82146e10i	1.91312	−	1.91312i
$166$	7.54723e9			0.771438
$167$	−3.16480e9	+	3.16480e9i	−0.314864	+	0.314864i	−0.846790	−	0.531927i	$-0.821468\pi$
$167$	−3.16480e9	+	3.16480e9i	−0.314864	+	0.314864i	0.531927	+	0.846790i	$0.321468\pi$
$168$		−	9.81009e9i		−	0.950126i
$169$	2.51770e9			0.237418
$170$	2.14201e9	+	1.57669e10i	0.196699	+	1.44786i
$171$	2.25570e9			0.201743
$172$			6.70018e9i			0.583725i
$173$	−3.39767e9	+	3.39767e9i	−0.288386	+	0.288386i	−0.836442	−	0.548056i	$-0.815368\pi$
$173$	−3.39767e9	+	3.39767e9i	−0.288386	+	0.288386i	0.548056	+	0.836442i	$0.315368\pi$
$174$	1.49126e10			1.23334
$175$	3.02719e9	−	3.02719e9i	0.243988	−	0.243988i
$176$	−1.45011e10	−	1.45011e10i	−1.13918	−	1.13918i
$177$	−2.10762e10	−	2.10762e10i	−1.61403	−	1.61403i
$178$			2.38764e9i			0.178270i
$179$			1.33451e10i			0.971592i	0.874072	+	0.485796i	$0.161470\pi$
$179$			1.33451e10i			0.971592i	−0.874072	+	0.485796i	$0.838530\pi$
$180$	−1.61670e10	−	1.61670e10i	−1.14790	−	1.14790i
$181$	5.01159e9	+	5.01159e9i	0.347074	+	0.347074i	0.859018	−	0.511945i	$-0.171075\pi$
$181$	5.01159e9	+	5.01159e9i	0.347074	+	0.347074i	−0.511945	+	0.859018i	$0.671075\pi$
$182$	−1.62574e10	+	1.62574e10i	−1.09832	+	1.09832i
$183$	−8.93616e9			−0.589008
$184$	−4.47331e9	+	4.47331e9i	−0.287706	+	0.287706i
$185$			2.95529e10i			1.85493i
$186$	−7.60072e9			−0.465636
$187$	−2.93724e9	−	2.16204e10i	−0.175652	−	1.29294i
$188$	−2.05494e9			−0.119974
$189$			4.41396e10i			2.51623i
$190$	1.64958e9	−	1.64958e9i	0.0918297	−	0.0918297i
$191$	3.04732e10			1.65679			0.828396	−	0.560143i	$-0.189254\pi$
$191$	3.04732e10			1.65679			0.828396	+	0.560143i	$0.189254\pi$
$192$	−3.83045e9	+	3.83045e9i	−0.203420	+	0.203420i
$193$	7.47611e9	+	7.47611e9i	0.387854	+	0.387854i	0.873921	−	0.486068i	$-0.161569\pi$
$193$	7.47611e9	+	7.47611e9i	0.387854	+	0.387854i	−0.486068	+	0.873921i	$0.661569\pi$
$194$	−3.40037e9	−	3.40037e9i	−0.172353	−	0.172353i
$195$		−	4.65717e10i		−	2.30657i
$196$		−	2.58745e9i		−	0.125233i
$197$	9.14937e9	+	9.14937e9i	0.432806	+	0.432806i	0.889582	−	0.456776i	$-0.150996\pi$
$197$	9.14937e9	+	9.14937e9i	0.432806	+	0.432806i	−0.456776	+	0.889582i	$0.650996\pi$
$198$	5.77136e10	+	5.77136e10i	2.66861	+	2.66861i
$199$	1.26061e10	−	1.26061e10i	0.569825	−	0.569825i	−0.362254	−	0.932079i	$-0.617993\pi$
$199$	1.26061e10	−	1.26061e10i	0.569825	−	0.569825i	0.932079	+	0.362254i	$0.117993\pi$
$200$	3.41640e9			0.150985
$201$	−4.16240e10	+	4.16240e10i	−1.79871	+	1.79871i
$202$		−	5.57914e10i		−	2.35769i
$203$	−1.41916e10			−0.586540
$204$	−2.76444e10	+	3.75562e9i	−1.11756	+	0.151826i
$205$	−1.27637e10			−0.504761
$206$		−	5.40152e10i		−	2.08984i
$207$	3.59773e10	−	3.59773e10i	1.36195	−	1.36195i
$208$	−3.70769e10			−1.37347
$209$	−2.26200e9	+	2.26200e9i	−0.0820040	+	0.0820040i
$210$	5.76987e10	+	5.76987e10i	2.04729	+	2.04729i
$211$	1.19467e10	+	1.19467e10i	0.414931	+	0.414931i	0.883452	−	0.468521i	$-0.155213\pi$
$211$	1.19467e10	+	1.19467e10i	0.414931	+	0.414931i	−0.468521	+	0.883452i	$0.655213\pi$
$212$		−	5.15905e9i		−	0.175412i
$213$		−	1.82865e9i		−	0.0608725i
$214$	4.28927e10	+	4.28927e10i	1.39804	+	1.39804i
$215$	2.37756e10	+	2.37756e10i	0.758855	+	0.758855i
$216$	−2.49074e10	+	2.49074e10i	−0.778549	+	0.778549i
$217$	7.23322e9			0.221443
$218$	−2.04161e10	+	2.04161e10i	−0.612236	+	0.612236i
$219$		−	8.01831e10i		−	2.35551i
$220$	3.24244e10			0.933191
$221$	−3.13950e10	−	2.38849e10i	−0.885309	−	0.673533i
$222$	−1.34893e11			−3.72736
$223$		−	1.23092e10i		−	0.333319i	−0.986015	−	0.166659i	$-0.946702\pi$
$223$		−	1.23092e10i		−	0.333319i	0.986015	−	0.166659i	$-0.0532980\pi$
$224$	3.19358e10	−	3.19358e10i	0.847543	−	0.847543i
$225$	−2.74770e10			−0.714739
$226$	−4.52880e10	+	4.52880e10i	−1.15477	+	1.15477i
$227$	7.91954e9	+	7.91954e9i	0.197963	+	0.197963i	0.799126	−	0.601163i	$-0.205296\pi$
$227$	7.91954e9	+	7.91954e9i	0.197963	+	0.197963i	−0.601163	+	0.799126i	$0.705296\pi$
$228$	2.89225e9	+	2.89225e9i	0.0708808	+	0.0708808i
$229$		−	5.37234e10i		−	1.29093i	−0.763788	−	0.645467i	$-0.776663\pi$
$229$		−	5.37234e10i		−	1.29093i	0.763788	−	0.645467i	$-0.223337\pi$
$230$		−	5.26202e10i		−	1.23987i
$231$	−7.91198e10	−	7.91198e10i	−1.82823	−	1.82823i
$232$	−8.00809e9	−	8.00809e9i	−0.181482	−	0.181482i
$233$	−2.25957e10	+	2.25957e10i	−0.502254	+	0.502254i	−0.912138	−	0.409884i	$-0.865569\pi$
$233$	−2.25957e10	+	2.25957e10i	−0.502254	+	0.502254i	0.409884	+	0.912138i	$0.365569\pi$
$234$	1.47564e11			3.21743
$235$	−7.29196e9	+	7.29196e9i	−0.155969	+	0.155969i
$236$		−	3.75185e10i		−	0.787303i
$237$	1.48039e11			3.04796
$238$	6.84876e10	−	9.30437e9i	1.38362	−	0.187971i
$239$	−2.64220e10			−0.523813			−0.261906	−	0.965093i	$-0.584351\pi$
$239$	−2.64220e10			−0.523813			−0.261906	+	0.965093i	$0.584351\pi$
$240$			1.31589e11i			2.56017i
$241$	−4.33826e10	+	4.33826e10i	−0.828398	+	0.828398i	−0.987295	−	0.158897i	$-0.949206\pi$
$241$	−4.33826e10	+	4.33826e10i	−0.828398	+	0.828398i	0.158897	+	0.987295i	$0.449206\pi$
$242$	−4.77632e10			−0.895209
$243$	4.25697e10	−	4.25697e10i	0.783199	−	0.783199i
$244$	−7.95380e9	−	7.95380e9i	−0.143655	−	0.143655i
$245$	−9.18157e9	−	9.18157e9i	−0.162806	−	0.162806i
$246$		−	5.82596e10i		−	1.01428i
$247$			5.78357e9i			0.0988689i
$248$	4.08160e9	+	4.08160e9i	0.0685169	+	0.0685169i
$249$	4.69563e10	+	4.69563e10i	0.774099	+	0.774099i
$250$	4.37196e10	−	4.37196e10i	0.707858	−	0.707858i
$251$	−1.01008e11			−1.60629			−0.803145	−	0.595783i	$-0.796842\pi$
$251$	−1.01008e11			−1.60629			−0.803145	+	0.595783i	$0.796842\pi$
$252$	−7.02258e10	+	7.02258e10i	−1.09697	+	1.09697i
$253$			7.21558e10i			1.10721i
$254$	−5.42518e10			−0.817829
$255$	−8.47694e10	+	1.11423e11i	−1.25548	+	1.65023i
$256$	8.89617e10			1.29456
$257$		−	6.24220e10i		−	0.892563i	−0.894893	−	0.446282i	$-0.852748\pi$
$257$		−	6.24220e10i		−	0.892563i	0.894893	−	0.446282i	$-0.147252\pi$
$258$	−1.08523e11	+	1.08523e11i	−1.52487	+	1.52487i
$259$	1.28371e11			1.77262
$260$	4.14520e10	−	4.14520e10i	0.562555	−	0.562555i
$261$	6.44064e10	+	6.44064e10i	0.859106	+	0.859106i
$262$	6.34995e10	+	6.34995e10i	0.832558	+	0.832558i
$263$			4.12563e10i			0.531728i	0.964010	+	0.265864i	$0.0856573\pi$
$263$			4.12563e10i			0.531728i	−0.964010	+	0.265864i	$0.914343\pi$
$264$		−	8.92923e10i		−	1.13135i
$265$	−1.83069e10	−	1.83069e10i	−0.228039	−	0.228039i
$266$	−7.16540e9	−	7.16540e9i	−0.0877552	−	0.0877552i
$267$	−1.48551e10	+	1.48551e10i	−0.178885	+	0.178885i
$268$	−7.40964e10			−0.877386
$269$	−5.21630e10	+	5.21630e10i	−0.607403	+	0.607403i	−0.942267	−	0.334864i	$-0.891310\pi$
$269$	−5.21630e10	+	5.21630e10i	−0.607403	+	0.607403i	0.334864	+	0.942267i	$0.391310\pi$
$270$		−	2.92989e11i		−	3.35517i
$271$	6.04771e10			0.681128			0.340564	−	0.940221i	$-0.389382\pi$
$271$	6.04771e10			0.681128			0.340564	+	0.940221i	$0.389382\pi$
$272$	8.87069e10	+	6.74871e10i	0.982646	+	0.747586i
$273$	−2.02296e11			−2.20422
$274$			1.19957e11i			1.28572i
$275$	2.75538e10	−	2.75538e10i	0.290525	−	0.290525i
$276$	9.22599e10			0.957023
$277$	4.70878e10	−	4.70878e10i	0.480562	−	0.480562i	−0.424749	−	0.905311i	$-0.639638\pi$
$277$	4.70878e10	−	4.70878e10i	0.480562	−	0.480562i	0.905311	+	0.424749i	$0.139638\pi$
$278$	−1.65296e10	−	1.65296e10i	−0.165982	−	0.165982i
$279$	−3.28270e10	−	3.28270e10i	−0.324348	−	0.324348i
$280$		−	6.19686e10i		−	0.602505i
$281$		−	1.81317e11i		−	1.73484i	−0.497578	−	0.867419i	$-0.665777\pi$
$281$		−	1.81317e11i		−	1.73484i	0.497578	−	0.867419i	$-0.334223\pi$
$282$	−3.32838e10	−	3.32838e10i	−0.313410	−	0.313410i
$283$	2.20637e10	+	2.20637e10i	0.204474	+	0.204474i	0.801914	−	0.597440i	$-0.203815\pi$
$283$	2.20637e10	+	2.20637e10i	0.204474	+	0.204474i	−0.597440	+	0.801914i	$0.703815\pi$
$284$	1.62762e9	−	1.62762e9i	0.0148464	−	0.0148464i
$285$	2.05263e10			0.184293
$286$	−1.47976e11	+	1.47976e11i	−1.30781	+	1.30781i
$287$			5.54427e10i			0.482365i
$288$	−2.89873e11			−2.48280
$289$	3.16376e10	+	1.14290e11i	0.266786	+	0.963756i
$290$	9.42003e10			0.782098
$291$		−	4.23118e10i		−	0.345894i
$292$	7.13685e10	−	7.13685e10i	0.574491	−	0.574491i
$293$	1.41584e11			1.12230			0.561151	−	0.827713i	$-0.310359\pi$
$293$	1.41584e11			1.12230			0.561151	+	0.827713i	$0.310359\pi$
$294$	4.19089e10	−	4.19089e10i	0.327147	−	0.327147i
$295$	−1.33135e11	−	1.33135e11i	−1.02351	−	1.02351i
$296$	7.24377e10	+	7.24377e10i	0.548469	+	0.548469i
$297$			4.01763e11i			2.99617i
$298$		−	3.86149e10i		−	0.283649i
$299$	9.22452e10	+	9.22452e10i	0.667457	+	0.667457i
$300$	−3.52308e10	−	3.52308e10i	−0.251118	−	0.251118i
$301$	1.03276e11	−	1.03276e11i	0.725185	−	0.725185i
$302$	1.04564e11			0.723352
$303$	3.47115e11	−	3.47115e11i	2.36582	−	2.36582i
$304$		−	1.63415e10i		−	0.109739i
$305$	−5.64482e10			−0.373509
$306$	−3.53048e11	−	2.68595e11i	−2.30191	−	1.75126i
$307$	1.60774e10			0.103299			0.0516493	−	0.998665i	$-0.483552\pi$
$307$	1.60774e10			0.103299			0.0516493	+	0.998665i	$0.483552\pi$
$308$		−	1.40844e11i		−	0.891785i
$309$	3.36064e11	−	3.36064e11i	2.09705	−	2.09705i
$310$	−4.80125e10			−0.295275
$311$	−1.76843e11	+	1.76843e11i	−1.07193	+	1.07193i	−0.0747254	+	0.997204i	$0.523808\pi$
$311$	−1.76843e11	+	1.76843e11i	−1.07193	+	1.07193i	−0.997204	+	0.0747254i	$0.976192\pi$
$312$	−1.14153e11	−	1.14153e11i	−0.682010	−	0.682010i
$313$	−1.29944e11	−	1.29944e11i	−0.765258	−	0.765258i	0.212009	−	0.977268i	$-0.431999\pi$
$313$	−1.29944e11	−	1.29944e11i	−0.765258	−	0.765258i	−0.977268	+	0.212009i	$0.931999\pi$
$314$			1.31677e11i			0.764408i
$315$			4.98393e11i			2.85217i
$316$	1.31765e11	+	1.31765e11i	0.743376	+	0.743376i
$317$	−2.92557e8	−	2.92557e8i	−0.00162721	−	0.00162721i	0.706293	−	0.707920i	$-0.250366\pi$
$317$	−2.92557e8	−	2.92557e8i	−0.00162721	−	0.00162721i	−0.707920	+	0.706293i	$0.750366\pi$
$318$	8.35613e10	−	8.35613e10i	0.458229	−	0.458229i
$319$	−1.29173e11			−0.698414
$320$	−2.41963e10	+	2.41963e10i	−0.128995	+	0.128995i
$321$			5.33727e11i			2.80574i
$322$	−2.28569e11			−1.18486
$323$	1.05272e10	−	1.38372e10i	0.0538148	−	0.0707356i
$324$	2.32883e11			1.17404
$325$		−	7.04504e10i		−	0.350274i
$326$	−3.24354e10	+	3.24354e10i	−0.159052	+	0.159052i
$327$	−2.54044e11			−1.22870
$328$	−3.12855e10	+	3.12855e10i	−0.149249	+	0.149249i
$329$	3.16745e10	+	3.16745e10i	0.149049	+	0.149049i
$330$	5.25179e11	+	5.25179e11i	2.43778	+	2.43778i
$331$		−	2.02135e11i		−	0.925586i	−0.886466	−	0.462793i	$-0.846847\pi$
$331$		−	2.02135e11i		−	0.925586i	0.886466	−	0.462793i	$-0.153153\pi$
$332$			8.35886e10i			0.377595i
$333$	−5.82593e11	−	5.82593e11i	−2.59637	−	2.59637i
$334$	−9.12504e10	−	9.12504e10i	−0.401214	−	0.401214i
$335$	−2.62932e11	+	2.62932e11i	−1.14062	+	1.14062i
$336$	5.71590e11			2.44657
$337$	−2.27894e11	+	2.27894e11i	−0.962493	+	0.962493i	−0.999322	−	0.0368290i	$-0.988274\pi$
$337$	−2.27894e11	+	2.27894e11i	−0.962493	+	0.962493i	0.0368290	+	0.999322i	$0.488274\pi$
$338$			7.25926e10i			0.302529i
$339$	−5.63533e11			−2.31750
$340$	−1.74625e11	+	2.37236e10i	−0.708681	+	0.0962777i
$341$	6.58374e10			0.263680
$342$			6.50384e10i			0.257070i
$343$	1.58746e11	−	1.58746e11i	0.619269	−	0.619269i
$344$	1.16554e11			0.448760
$345$	3.27385e11	−	3.27385e11i	1.24415	−	1.24415i
$346$	−9.79647e10	−	9.79647e10i	−0.367475	−	0.367475i
$347$	3.92735e10	+	3.92735e10i	0.145418	+	0.145418i	0.776067	−	0.630650i	$-0.217212\pi$
$347$	3.92735e10	+	3.92735e10i	0.145418	+	0.145418i	−0.630650	+	0.776067i	$0.717212\pi$
$348$			1.65163e11i			0.603680i
$349$			1.80693e11i			0.651968i	0.945375	+	0.325984i	$0.105696\pi$
$349$			1.80693e11i			0.651968i	−0.945375	+	0.325984i	$0.894304\pi$
$350$	8.72827e10	+	8.72827e10i	0.310901	+	0.310901i
$351$	5.13621e11	+	5.13621e11i	1.80618	+	1.80618i
$352$	2.90683e11	−	2.90683e11i	1.00920	−	1.00920i
$353$	−1.18291e11			−0.405475			−0.202738	−	0.979233i	$-0.564984\pi$
$353$	−1.18291e11			−0.405475			−0.202738	+	0.979233i	$0.564984\pi$
$354$	6.07688e11	−	6.07688e11i	2.05668	−	2.05668i
$355$		−	1.15512e10i		−	0.0386012i
$356$	−2.64441e10			−0.0872578
$357$	4.83995e11	+	3.68218e11i	1.57701	+	1.19977i
$358$	−3.84779e11			−1.23805
$359$		−	4.33360e11i		−	1.37697i	−0.725251	−	0.688484i	$-0.758276\pi$
$359$		−	4.33360e11i		−	1.37697i	0.725251	−	0.688484i	$-0.241724\pi$
$360$	−2.81236e11	+	2.81236e11i	−0.882490	+	0.882490i
$361$	3.20139e11			0.992100
$362$	−1.44499e11	+	1.44499e11i	−0.442257	+	0.442257i
$363$	−2.97166e11	−	2.97166e11i	−0.898297	−	0.898297i
$364$	−1.80057e11	−	1.80057e11i	−0.537595	−	0.537595i
$365$		−	5.06503e11i		−	1.49370i
$366$		−	2.57655e11i		−	0.750541i
$367$	2.94968e11	+	2.94968e11i	0.848747	+	0.848747i	0.989977	−	0.141230i	$-0.0451057\pi$
$367$	2.94968e11	+	2.94968e11i	0.848747	+	0.848747i	−0.141230	+	0.989977i	$0.545106\pi$
$368$	−2.60640e11	−	2.60640e11i	−0.740842	−	0.740842i
$369$	2.51619e11	−	2.51619e11i	0.706520	−	0.706520i
$370$	−8.52095e11			−2.36364
$371$	−7.95210e10	+	7.95210e10i	−0.217921	+	0.217921i
$372$		−	8.41811e10i		−	0.227914i
$373$	−3.22658e11			−0.863083			−0.431542	−	0.902093i	$-0.642030\pi$
$373$	−3.22658e11			−0.863083			−0.431542	+	0.902093i	$0.642030\pi$
$374$	6.23380e11	−	8.46892e10i	1.64752	−	0.223824i
$375$	5.44017e11			1.42060
$376$			3.57469e10i			0.0922346i
$377$	−1.65137e11	+	1.65137e11i	−0.421025	+	0.421025i
$378$	−1.27267e12			−3.20630
$379$	3.04808e11	−	3.04808e11i	0.758839	−	0.758839i	−0.217272	−	0.976111i	$-0.569716\pi$
$379$	3.04808e11	−	3.04808e11i	0.758839	−	0.758839i	0.976111	+	0.217272i	$0.0697160\pi$
$380$	1.82698e10	+	1.82698e10i	0.0449478	+	0.0449478i
$381$	−3.37536e11	−	3.37536e11i	−0.820651	−	0.820651i
$382$			8.78631e11i			2.11116i
$383$			7.20550e10i			0.171108i	0.996334	+	0.0855539i	$0.0272660\pi$
$383$			7.20550e10i			0.171108i	−0.996334	+	0.0855539i	$0.972734\pi$
$384$	4.85470e11	+	4.85470e11i	1.13939	+	1.13939i
$385$	−4.99786e11	−	4.99786e11i	−1.15934	−	1.15934i
$386$	−2.15558e11	+	2.15558e11i	−0.494221	+	0.494221i
$387$	−9.37405e11			−2.12436
$388$	3.76604e10	−	3.76604e10i	0.0843612	−	0.0843612i
$389$		−	2.81453e11i		−	0.623206i	−0.950212	−	0.311603i	$-0.899134\pi$
$389$		−	2.81453e11i		−	0.623206i	0.950212	−	0.311603i	$-0.100866\pi$
$390$	1.34280e12			2.93913
$391$	−5.27934e10	−	3.88601e11i	−0.114231	−	0.840831i
$392$	−4.50103e10			−0.0962775
$393$			7.90145e11i			1.67086i
$394$	−2.63803e11	+	2.63803e11i	−0.551501	+	0.551501i
$395$	9.35139e11			1.93281
$396$	−6.39201e11	+	6.39201e11i	−1.30620	+	1.30620i
$397$	4.33717e11	+	4.33717e11i	0.876292	+	0.876292i	0.993149	−	0.116857i	$-0.0372819\pi$
$397$	4.33717e11	+	4.33717e11i	0.876292	+	0.876292i	−0.116857	+	0.993149i	$0.537282\pi$
$398$	3.63470e11	+	3.63470e11i	0.726097	+	0.726097i
$399$		−	8.91614e10i		−	0.176116i
$400$			1.99059e11i			0.388786i
$401$	−6.40682e11	−	6.40682e11i	−1.23735	−	1.23735i	−0.961080	−	0.276271i	$-0.910901\pi$
$401$	−6.40682e11	−	6.40682e11i	−1.23735	−	1.23735i	−0.276271	−	0.961080i	$-0.589099\pi$
$402$	−1.20014e12	−	1.20014e12i	−2.29200	−	2.29200i
$403$	8.41677e10	−	8.41677e10i	0.158954	−	0.158954i
$404$	6.17913e11			1.15401
$405$	8.26385e11	−	8.26385e11i	1.52628	−	1.52628i
$406$		−	4.09184e11i		−	0.747396i
$407$	1.16844e12			2.11073
$408$	6.53315e10	+	4.80892e11i	0.116722	+	0.859165i
$409$	5.05301e11			0.892884			0.446442	−	0.894813i	$-0.352691\pi$
$409$	5.05301e11			0.892884			0.446442	+	0.894813i	$0.352691\pi$
$410$		−	3.68016e11i		−	0.643190i
$411$	−7.46330e11	+	7.46330e11i	−1.29016	+	1.29016i
$412$	5.98241e11			1.02291
$413$	−5.78306e11	+	5.78306e11i	−0.978098	+	0.978098i
$414$	1.03733e12	+	1.03733e12i	1.73547	+	1.73547i
$415$	2.96615e11	+	2.96615e11i	0.490881	+	0.490881i
$416$		−	7.43227e11i		−	1.21675i
$417$		−	2.05683e11i		−	0.333109i
$418$	−6.52201e10	−	6.52201e10i	−0.104493	−	0.104493i
$419$	6.04730e11	+	6.04730e11i	0.958514	+	0.958514i	0.999173	−	0.0406590i	$-0.0129457\pi$
$419$	6.04730e11	+	6.04730e11i	0.958514	+	0.958514i	−0.0406590	+	0.999173i	$0.512946\pi$
$420$	−6.39037e11	+	6.39037e11i	−1.00208	+	1.00208i
$421$	−1.94096e11			−0.301125			−0.150563	−	0.988600i	$-0.548109\pi$
$421$	−1.94096e11			−0.301125			−0.150563	+	0.988600i	$0.548109\pi$
$422$	−3.44457e11	+	3.44457e11i	−0.528725	+	0.528725i
$423$		−	2.87501e11i		−	0.436624i
$424$	−8.97451e10			−0.134854
$425$	−1.28233e11	+	1.68553e11i	−0.190656	+	0.250603i
$426$	5.27252e10			0.0775666
$427$			2.45197e11i			0.356936i
$428$	−4.75054e11	+	4.75054e11i	−0.684299	+	0.684299i
$429$	−1.84132e12			−2.62465
$430$	−6.85520e11	+	6.85520e11i	−0.966968	+	0.966968i
$431$	−1.33430e11	−	1.33430e11i	−0.186253	−	0.186253i	0.607821	−	0.794074i	$-0.292044\pi$
$431$	−1.33430e11	−	1.33430e11i	−0.186253	−	0.186253i	−0.794074	+	0.607821i	$0.792044\pi$
$432$	−1.45124e12	−	1.45124e12i	−2.00476	−	2.00476i
$433$		−	2.24845e11i		−	0.307389i	−0.988118	−	0.153694i	$-0.950883\pi$
$433$		−	2.24845e11i		−	0.307389i	0.988118	−	0.153694i	$-0.0491171\pi$
$434$			2.08555e11i			0.282173i
$435$	5.86082e11	+	5.86082e11i	0.784796	+	0.784796i
$436$	−2.26117e11	−	2.26117e11i	−0.299670	−	0.299670i
$437$	−4.06568e10	+	4.06568e10i	−0.0533294	+	0.0533294i
$438$	2.31191e12			3.00150
$439$	−6.48165e11	+	6.48165e11i	−0.832905	+	0.832905i	−0.987913	−	0.155008i	$-0.950460\pi$
$439$	−6.48165e11	+	6.48165e11i	−0.832905	+	0.832905i	0.155008	+	0.987913i	$0.450460\pi$
$440$		−	5.64044e11i		−	0.717424i
$441$	3.62003e11			0.455762
$442$	6.88672e11	−	9.05208e11i	0.858246	−	1.12810i
$443$	−4.92953e11			−0.608119			−0.304060	−	0.952653i	$-0.598342\pi$
$443$	−4.92953e11			−0.608119			−0.304060	+	0.952653i	$0.598342\pi$
$444$		−	1.49399e12i		−	1.82442i
$445$	−9.38371e10	+	9.38371e10i	−0.113437	+	0.113437i
$446$	3.54911e11			0.424730
$447$	2.40249e11	−	2.40249e11i	0.284628	−	0.284628i
$448$	1.05103e11	+	1.05103e11i	0.123272	+	0.123272i
$449$	−6.56424e11	−	6.56424e11i	−0.762212	−	0.762212i	0.214510	−	0.976722i	$-0.431185\pi$
$449$	−6.56424e11	−	6.56424e11i	−0.762212	−	0.762212i	−0.976722	+	0.214510i	$0.931185\pi$
$450$		−	7.92241e11i		−	0.910754i
$451$			5.04644e11i			0.574369i
$452$	−5.01583e11	−	5.01583e11i	−0.565223	−	0.565223i
$453$	6.50560e11	+	6.50560e11i	0.725847	+	0.725847i
$454$	−2.28343e11	+	2.28343e11i	−0.252253	+	0.252253i
$455$	−1.27787e12			−1.39777
$456$	5.03125e10	−	5.03125e10i	0.0544922	−	0.0544922i
$457$			1.66023e12i			1.78052i	0.455456	+	0.890258i	$0.349476\pi$
$457$			1.66023e12i			1.78052i	−0.455456	+	0.890258i	$0.650524\pi$
$458$	1.54900e12			1.64497
$459$	−2.93953e11	−	2.16373e12i	−0.309116	−	2.27534i
$460$	5.82790e11			0.606879
$461$		−	1.62302e11i		−	0.167367i	−0.996492	−	0.0836837i	$-0.973331\pi$
$461$		−	1.62302e11i		−	0.167367i	0.996492	−	0.0836837i	$-0.0266685\pi$
$462$	2.28125e12	−	2.28125e12i	2.32962	−	2.32962i
$463$	−7.72644e10			−0.0781385			−0.0390692	−	0.999237i	$-0.512439\pi$
$463$	−7.72644e10			−0.0781385			−0.0390692	+	0.999237i	$0.512439\pi$
$464$	4.66596e11	−	4.66596e11i	0.467315	−	0.467315i
$465$	−2.98717e11	−	2.98717e11i	−0.296293	−	0.296293i
$466$	−6.51499e11	−	6.51499e11i	−0.639996	−	0.639996i
$467$		−	6.91956e11i		−	0.673213i	−0.941645	−	0.336607i	$-0.890721\pi$
$467$		−	6.91956e11i		−	0.673213i	0.941645	−	0.336607i	$-0.109279\pi$
$468$			1.63433e12i			1.57483i
$469$	1.14211e12	+	1.14211e12i	1.09001	+	1.09001i
$470$	−2.10248e11	−	2.10248e11i	−0.198743	−	0.198743i
$471$	−8.19248e11	+	8.19248e11i	−0.767045	+	0.767045i
$472$	−6.52659e11			−0.605268
$473$	9.40024e11	−	9.40024e11i	0.863503	−	0.863503i
$474$			4.26840e12i			3.88385i
$475$	3.10508e10			0.0279867
$476$	1.03050e11	+	7.58528e11i	0.0920059	+	0.677236i
$477$	7.21790e11			0.638378
$478$		−	7.61824e11i		−	0.667466i
$479$	−1.27262e12	+	1.27262e12i	−1.10456	+	1.10456i	−0.110708	+	0.993853i	$0.535312\pi$
$479$	−1.27262e12	+	1.27262e12i	−1.10456	+	1.10456i	−0.993853	+	0.110708i	$0.964688\pi$
$480$	−2.63777e12			−2.26804
$481$	1.49376e12	−	1.49376e12i	1.27241	−	1.27241i
$482$	−1.25085e12	−	1.25085e12i	−1.05558	−	1.05558i
$483$	−1.42208e12	−	1.42208e12i	−1.18895	−	1.18895i
$484$		−	5.28997e11i		−	0.438176i
$485$		−	2.67277e11i		−	0.219343i
$486$	1.22741e12	+	1.22741e12i	0.997989	+	0.997989i
$487$	6.08524e11	+	6.08524e11i	0.490227	+	0.490227i	0.908378	−	0.418151i	$-0.137322\pi$
$487$	6.08524e11	+	6.08524e11i	0.490227	+	0.490227i	−0.418151	+	0.908378i	$0.637322\pi$
$488$	−1.38361e11	+	1.38361e11i	−0.110440	+	0.110440i
$489$	−4.03604e11			−0.319202
$490$	2.64731e11	−	2.64731e11i	0.207455	−	0.207455i
$491$			5.49516e11i			0.426692i	0.976977	+	0.213346i	$0.0684361\pi$
$491$			5.49516e11i			0.426692i	−0.976977	+	0.213346i	$0.931564\pi$
$492$	6.45249e11			0.496460
$493$	6.95671e11	−	9.45104e10i	0.530387	−	0.0720557i
$494$	−1.66757e11			−0.125983
$495$			4.53642e12i			3.39617i
$496$	−2.37817e11	+	2.37817e11i	−0.176431	+	0.176431i
$497$	−5.01758e10			−0.0368885
$498$	−1.35389e12	+	1.35389e12i	−0.986393	+	0.986393i
$499$	9.20735e11	+	9.20735e11i	0.664786	+	0.664786i	0.956504	−	0.291718i	$-0.0942269\pi$
$499$	9.20735e11	+	9.20735e11i	0.664786	+	0.664786i	−0.291718	+	0.956504i	$0.594227\pi$
$500$	4.84213e11	+	4.84213e11i	0.346474	+	0.346474i
$501$		−	1.13546e12i		−	0.805196i
$502$		−	2.91235e12i		−	2.04681i
$503$	1.09584e12	+	1.09584e12i	0.763294	+	0.763294i	0.976916	−	0.213622i	$-0.0685262\pi$
$503$	1.09584e12	+	1.09584e12i	0.763294	+	0.763294i	−0.213622	+	0.976916i	$0.568526\pi$
$504$	1.22162e12	+	1.22162e12i	0.843334	+	0.843334i
$505$	2.19267e12	−	2.19267e12i	1.50024	−	1.50024i
$506$	−2.08046e12			−1.41085
$507$	−4.51647e11	+	4.51647e11i	−0.303573	+	0.303573i
$508$		−	6.00861e11i		−	0.400302i
$509$	−1.50541e12			−0.994091			−0.497045	−	0.867725i	$-0.665582\pi$
$509$	−1.50541e12			−0.994091			−0.497045	+	0.867725i	$0.665582\pi$
$510$	−3.21265e12	−	2.44415e12i	−2.10280	−	1.59978i
$511$	−2.20013e12			−1.42743
$512$			1.17942e12i			0.758499i
$513$	−2.26377e11	+	2.26377e11i	−0.144312	+	0.144312i
$514$	1.79981e12			1.13735
$515$	2.12286e12	−	2.12286e12i	1.32981	−	1.32981i
$516$	−1.20194e12	−	1.20194e12i	−0.746376	−	0.746376i
$517$	2.88304e11	+	2.88304e11i	0.177478	+	0.177478i
$518$			3.70130e12i			2.25876i
$519$		−	1.21901e12i		−	0.737485i
$520$	−7.21084e11	−	7.21084e11i	−0.432484	−	0.432484i
$521$	−1.53182e12	−	1.53182e12i	−0.910833	−	0.910833i	0.0855048	−	0.996338i	$-0.472750\pi$
$521$	−1.53182e12	−	1.53182e12i	−0.910833	−	0.910833i	−0.996338	+	0.0855048i	$0.972750\pi$
$522$	−1.85702e12	+	1.85702e12i	−1.09471	+	1.09471i
$523$	2.82309e12			1.64994			0.824969	−	0.565178i	$-0.191192\pi$
$523$	2.82309e12			1.64994			0.824969	+	0.565178i	$0.191192\pi$
$524$	−7.03283e11	+	7.03283e11i	−0.407511	+	0.407511i
$525$			1.08609e12i			0.623947i
$526$	−1.18954e12			−0.677553
$527$	−3.54573e11	+	4.81705e10i	−0.200243	+	0.0272040i
$528$	5.20267e12			2.91322
$529$		−	5.04240e11i		−	0.279954i
$530$	5.27842e11	−	5.27842e11i	0.290578	−	0.290578i
$531$	5.24912e12			2.86524
$532$	7.93597e10	−	7.93597e10i	0.0429534	−	0.0429534i
$533$	6.45146e11	+	6.45146e11i	0.346246	+	0.346246i
$534$	−4.28316e11	−	4.28316e11i	−0.227944	−	0.227944i
$535$			3.37146e12i			1.77921i
$536$			1.28895e12i			0.674522i
$537$	−2.39396e12	−	2.39396e12i	−1.24232	−	1.24232i
$538$	−1.50401e12	−	1.50401e12i	−0.773981	−	0.773981i
$539$	−3.63015e11	+	3.63015e11i	−0.185257	+	0.185257i
$540$	3.24497e12			1.64225
$541$	−1.68440e11	+	1.68440e11i	−0.0845391	+	0.0845391i	−0.748112	−	0.663573i	$-0.769039\pi$
$541$	−1.68440e11	+	1.68440e11i	−0.0845391	+	0.0845391i	0.663573	+	0.748112i	$0.269039\pi$
$542$			1.74373e12i			0.867925i
$543$	−1.79804e12			−0.887566
$544$	−1.35282e12	+	1.77818e12i	−0.662283	+	0.870523i
$545$	−1.60475e12			−0.779156
$546$		−	5.83279e12i		−	2.80872i
$547$	−1.38372e12	+	1.38372e12i	−0.660852	+	0.660852i	−0.955581	−	0.294729i	$-0.904771\pi$
$547$	−1.38372e12	+	1.38372e12i	−0.660852	+	0.660852i	0.294729	+	0.955581i	$0.404771\pi$
$548$	−1.32857e12			−0.629320
$549$	1.11279e12	−	1.11279e12i	0.522805	−	0.522805i
$550$	7.94455e11	+	7.94455e11i	0.370201	+	0.370201i
$551$	−7.27835e10	−	7.27835e10i	−0.0336396	−	0.0336396i
$552$		−	1.60492e12i		−	0.735746i
$553$		−	4.06202e12i		−	1.84705i
$554$	1.35768e12	+	1.35768e12i	0.612355	+	0.612355i
$555$	−5.30145e12	−	5.30145e12i	−2.37179	−	2.37179i
$556$	1.83072e11	−	1.83072e11i	0.0812429	−	0.0812429i
$557$	5.54013e11			0.243877			0.121939	−	0.992538i	$-0.461089\pi$
$557$	5.54013e11			0.243877			0.121939	+	0.992538i	$0.461089\pi$
$558$	9.46497e11	−	9.46497e11i	0.413300	−	0.413300i
$559$		−	2.40349e12i		−	1.04109i
$560$	3.61064e12			1.55145
$561$	4.40537e12	+	3.35155e12i	1.87780	+	1.42861i
$562$	5.22788e12			2.21061
$563$		−	6.79128e11i		−	0.284881i	−0.989803	−	0.142441i	$-0.954505\pi$
$563$		−	6.79128e11i		−	0.284881i	0.989803	−	0.142441i	$-0.0454950\pi$
$564$	3.68632e11	−	3.68632e11i	0.153404	−	0.153404i
$565$	−3.55974e12			−1.46960
$566$	−6.36159e11	+	6.36159e11i	−0.260551	+	0.260551i
$567$	−3.58962e12	−	3.58962e12i	−1.45856	−	1.45856i
$568$	−2.83135e10	−	2.83135e10i	−0.0114137	−	0.0114137i
$569$			2.62380e12i			1.04936i	0.851299	+	0.524681i	$0.175815\pi$
$569$			2.62380e12i			1.04936i	−0.851299	+	0.524681i	$0.824185\pi$
$570$			5.91833e11i			0.234835i
$571$	1.63294e12	+	1.63294e12i	0.642847	+	0.642847i	0.951254	−	0.308408i	$-0.0997961\pi$
$571$	1.63294e12	+	1.63294e12i	0.642847	+	0.642847i	−0.308408	+	0.951254i	$0.599796\pi$
$572$	−1.63890e12	−	1.63890e12i	−0.640133	−	0.640133i
$573$	−5.46654e12	+	5.46654e12i	−2.11844	+	2.11844i
$574$	−1.59857e12			−0.614651
$575$	4.95246e11	−	4.95246e11i	0.188936	−	0.188936i
$576$		−	9.53991e11i		−	0.361113i
$577$	4.55996e12			1.71266			0.856328	−	0.516432i	$-0.172740\pi$
$577$	4.55996e12			1.71266			0.856328	+	0.516432i	$0.172740\pi$
$578$	−3.29531e12	+	9.12203e11i	−1.22806	+	0.339951i
$579$	−2.68226e12			−0.991852
$580$			1.04331e12i			0.382812i
$581$	1.28842e12	−	1.28842e12i	0.469101	−	0.469101i
$582$	1.21997e12			0.440755
$583$	−7.23807e11	+	7.23807e11i	−0.259486	+	0.259486i
$584$	−1.24150e12	−	1.24150e12i	−0.441661	−	0.441661i
$585$	5.79944e12	+	5.79944e12i	2.04731	+	2.04731i
$586$			4.08228e12i			1.43009i
$587$			6.94817e11i			0.241546i	0.992680	+	0.120773i	$0.0385372\pi$
$587$			6.94817e11i			0.241546i	−0.992680	+	0.120773i	$0.961463\pi$
$588$	4.64158e11	+	4.64158e11i	0.160128	+	0.160128i
$589$	3.70966e10	+	3.70966e10i	0.0127003	+	0.0127003i
$590$	3.83866e12	−	3.83866e12i	1.30420	−	1.30420i
$591$	−3.28258e12			−1.10681
$592$	−4.22062e12	+	4.22062e12i	−1.41231	+	1.41231i
$593$		−	3.17510e12i		−	1.05441i	−0.849737	−	0.527207i	$-0.823239\pi$
$593$		−	3.17510e12i		−	1.05441i	0.849737	−	0.527207i	$-0.176761\pi$
$594$	−1.15840e13			−3.81785
$595$	3.05731e12	+	2.32597e12i	1.00003	+	0.760812i
$596$	4.27675e11			0.138837
$597$			4.52277e12i			1.45720i
$598$	−2.65970e12	+	2.65970e12i	−0.850505	+	0.850505i
$599$	2.43909e12			0.774119			0.387060	−	0.922055i	$-0.373491\pi$
$599$	2.43909e12			0.774119			0.387060	+	0.922055i	$0.373491\pi$
$600$	−6.12863e11	+	6.12863e11i	−0.193056	+	0.193056i
$601$	−1.67326e12	−	1.67326e12i	−0.523153	−	0.523153i	0.395369	−	0.918522i	$-0.370617\pi$
$601$	−1.67326e12	−	1.67326e12i	−0.523153	−	0.523153i	−0.918522	+	0.395369i	$0.870617\pi$
$602$	2.97774e12	+	2.97774e12i	0.924064	+	0.924064i
$603$		−	1.03666e13i		−	3.19308i
$604$			1.15809e12i			0.354058i
$605$	−1.87715e12	−	1.87715e12i	−0.569639	−	0.569639i
$606$	1.00083e13	+	1.00083e13i	3.01464	+	3.01464i
$607$	4.25015e12	−	4.25015e12i	1.27074	−	1.27074i	0.325032	−	0.945703i	$-0.394625\pi$
$607$	4.25015e12	−	4.25015e12i	1.27074	−	1.27074i	0.945703	−	0.325032i	$-0.105375\pi$
$608$	3.27575e11			0.0972176
$609$	2.54580e12	−	2.54580e12i	0.749975	−	0.749975i
$610$		−	1.62757e12i		−	0.475942i
$611$	7.37146e11			0.213978
$612$	2.97480e12	−	3.91015e12i	0.857188	−	1.12671i
$613$	−3.01272e12			−0.861761			−0.430880	−	0.902409i	$-0.641797\pi$
$613$	−3.01272e12			−0.861761			−0.430880	+	0.902409i	$0.641797\pi$
$614$			4.63559e11i			0.131628i
$615$	2.28967e12	−	2.28967e12i	0.645409	−	0.645409i
$616$	−2.45007e12			−0.685592
$617$	−7.14533e11	+	7.14533e11i	−0.198490	+	0.198490i	−0.799352	−	0.600862i	$-0.794824\pi$
$617$	−7.14533e11	+	7.14533e11i	−0.198490	+	0.198490i	0.600862	+	0.799352i	$0.294824\pi$
$618$	9.68971e12	+	9.68971e12i	2.67216	+	2.67216i
$619$	−1.29214e11	−	1.29214e11i	−0.0353755	−	0.0353755i	0.689198	−	0.724573i	$-0.257963\pi$
$619$	−1.29214e11	−	1.29214e11i	−0.0353755	−	0.0353755i	−0.724573	+	0.689198i	$0.757963\pi$
$620$		−	5.31758e11i		−	0.144528i
$621$			7.22120e12i			1.94849i
$622$	−5.09890e12	−	5.09890e12i	−1.36590	−	1.36590i
$623$	4.07606e11	+	4.07606e11i	0.108404	+	0.108404i
$624$	6.65118e12	−	6.65118e12i	1.75618	−	1.75618i
$625$	4.63765e12			1.21573
$626$	3.74667e12	−	3.74667e12i	0.975128	−	0.975128i
$627$		−	8.11555e11i		−	0.209708i
$628$	−1.45837e12			−0.374154
$629$	−6.29274e12	+	8.54900e11i	−1.60292	+	0.217765i
$630$	−1.43701e13			−3.63436
$631$		−	6.42710e11i		−	0.161392i	−0.996739	−	0.0806962i	$-0.974286\pi$
$631$		−	6.42710e11i		−	0.161392i	0.996739	−	0.0806962i	$-0.0257143\pi$
$632$	2.29214e12	−	2.29214e12i	0.571497	−	0.571497i
$633$	−4.28620e12			−1.06110
$634$	8.43527e9	−	8.43527e9i	0.00207347	−	0.00207347i
$635$	−2.13216e12	−	2.13216e12i	−0.520401	−	0.520401i
$636$	9.25475e11	+	9.25475e11i	0.224289	+	0.224289i
$637$			9.28168e11i			0.223357i
$638$		−	3.72443e12i		−	0.889951i
$639$	2.27716e11	+	2.27716e11i	0.0540306	+	0.0540306i
$640$	3.06663e12	+	3.06663e12i	0.722523	+	0.722523i
$641$	−4.54040e12	+	4.54040e12i	−1.06226	+	1.06226i	−0.0643359	+	0.997928i	$0.520493\pi$
$641$	−4.54040e12	+	4.54040e12i	−1.06226	+	1.06226i	−0.997928	+	0.0643359i	$0.979507\pi$
$642$	−1.53889e13			−3.57520
$643$	4.97107e12	−	4.97107e12i	1.14683	−	1.14683i	0.159663	−	0.987172i	$-0.448959\pi$
$643$	4.97107e12	−	4.97107e12i	1.14683	−	1.14683i	0.987172	−	0.159663i	$-0.0510409\pi$
$644$		−	2.53150e12i		−	0.579951i
$645$	−8.53015e12			−1.94061
$646$	3.98968e11	+	3.03530e11i	0.0901345	+	0.0685733i
$647$	6.41347e12			1.43888			0.719439	−	0.694556i	$-0.244399\pi$
$647$	6.41347e12			1.43888			0.719439	+	0.694556i	$0.244399\pi$
$648$		−	4.05114e12i		−	0.902589i
$649$	−5.26379e12	+	5.26379e12i	−1.16466	+	1.16466i
$650$	2.03129e12			0.446336
$651$	−1.29756e12	+	1.29756e12i	−0.283147	+	0.283147i
$652$	−3.59236e11	−	3.59236e11i	−0.0778512	−	0.0778512i
$653$	−3.08063e11	−	3.08063e11i	−0.0663025	−	0.0663025i	0.673178	−	0.739480i	$-0.264929\pi$
$653$	−3.08063e11	−	3.08063e11i	−0.0663025	−	0.0663025i	−0.739480	+	0.673178i	$0.764929\pi$
$654$		−	7.32484e12i		−	1.56566i
$655$			4.99121e12i			1.05955i
$656$	−1.82287e12	−	1.82287e12i	−0.384315	−	0.384315i
$657$	9.98498e12	+	9.98498e12i	2.09075	+	2.09075i
$658$	−9.13268e11	+	9.13268e11i	−0.189925	+	0.189925i
$659$	1.79536e12			0.370823			0.185412	−	0.982661i	$-0.440638\pi$
$659$	1.79536e12			0.370823			0.185412	+	0.982661i	$0.440638\pi$
$660$	−5.81657e12	+	5.81657e12i	−1.19322	+	1.19322i
$661$		−	1.53076e12i		−	0.311889i	−0.987766	−	0.155945i	$-0.950158\pi$
$661$		−	1.53076e12i		−	0.311889i	0.987766	−	0.155945i	$-0.0498422\pi$
$662$	5.82815e12			1.17942
$663$	9.91658e12	−	1.34722e12i	1.99320	−	0.270786i
$664$	1.45408e12			0.290289
$665$		−	5.63217e11i		−	0.111681i
$666$	1.67978e13	−	1.67978e13i	3.30841	−	3.30841i
$667$	−2.32172e12			−0.454197
$668$	1.01064e12	−	1.01064e12i	0.196381	−	0.196381i
$669$	2.20814e12	+	2.20814e12i	0.426195	+	0.426195i
$670$	−7.58108e12	−	7.58108e12i	−1.45343	−	1.45343i
$671$			2.23181e12i			0.425016i
$672$			1.14578e13i			2.16741i
$673$	−7.08953e12	−	7.08953e12i	−1.33214	−	1.33214i	−0.903453	−	0.428687i	$-0.858976\pi$
$673$	−7.08953e12	−	7.08953e12i	−1.33214	−	1.33214i	−0.428687	−	0.903453i	$-0.641024\pi$
$674$	−6.57083e12	−	6.57083e12i	−1.22645	−	1.22645i
$675$	2.75752e12	−	2.75752e12i	0.511272	−	0.511272i
$676$	−8.03993e11			−0.148079
$677$	1.19396e12	−	1.19396e12i	0.218444	−	0.218444i	−0.589398	−	0.807842i	$-0.700635\pi$
$677$	1.19396e12	−	1.19396e12i	0.218444	−	0.218444i	0.807842	+	0.589398i	$0.200635\pi$
$678$		−	1.62483e13i		−	2.95307i
$679$	−1.16099e12			−0.209610
$680$	4.12688e11	+	3.03771e12i	0.0740170	+	0.544824i
$681$	−2.84135e12			−0.506247
$682$			1.89828e12i			0.335994i
$683$	−6.90549e12	+	6.90549e12i	−1.21423	+	1.21423i	−0.244610	+	0.969621i	$0.578660\pi$
$683$	−6.90549e12	+	6.90549e12i	−1.21423	+	1.21423i	−0.969621	+	0.244610i	$0.921340\pi$
$684$	−7.20327e11			−0.125828
$685$	−4.71444e12	+	4.71444e12i	−0.818130	+	0.818130i
$686$	4.57711e12	+	4.57711e12i	0.789102	+	0.789102i
$687$	9.63737e12	+	9.63737e12i	1.65064	+	1.65064i
$688$			6.79108e12i			1.15556i
$689$			1.85065e12i			0.312852i
$690$	9.43946e12	+	9.43946e12i	1.58535	+	1.58535i
$691$	−1.66059e12	−	1.66059e12i	−0.277084	−	0.277084i	0.554860	−	0.831944i	$-0.312772\pi$
$691$	−1.66059e12	−	1.66059e12i	−0.277084	−	0.277084i	−0.831944	+	0.554860i	$0.812772\pi$
$692$	1.08500e12	−	1.08500e12i	0.179867	−	0.179867i
$693$	1.97051e13			3.24549
$694$	−1.13237e12	+	1.13237e12i	−0.185298	+	0.185298i
$695$		−	1.29927e12i		−	0.211235i
$696$	2.87312e12			0.464100
$697$	−3.69227e11	−	2.71781e12i	−0.0592579	−	0.436185i
$698$	−5.20989e12			−0.830767
$699$		−	8.10681e12i		−	1.28441i
$700$	−9.66692e11	+	9.66692e11i	−0.152176	+	0.152176i
$701$	9.78498e12			1.53048			0.765242	−	0.643742i	$-0.222619\pi$
$701$	9.78498e12			1.53048			0.765242	+	0.643742i	$0.222619\pi$
$702$	−1.48092e13	+	1.48092e13i	−2.30151	+	2.30151i
$703$	6.58368e11	+	6.58368e11i	0.101665	+	0.101665i
$704$	9.56657e11	+	9.56657e11i	0.146784	+	0.146784i
$705$		−	2.61619e12i		−	0.398857i
$706$		−	3.41066e12i		−	0.516675i
$707$	−9.52442e12	−	9.52442e12i	−1.43368	−	1.43368i
$708$	6.73040e12	+	6.73040e12i	1.00668	+	1.00668i
$709$	−3.82775e12	+	3.82775e12i	−0.568899	+	0.568899i	−0.931820	−	0.362921i	$-0.881780\pi$
$709$	−3.82775e12	+	3.82775e12i	−0.568899	+	0.568899i	0.362921	+	0.931820i	$0.381780\pi$
$710$	3.33056e11			0.0491875
$711$	−1.84349e13	+	1.84349e13i	−2.70538	+	2.70538i
$712$			4.60012e11i			0.0670826i
$713$	1.18335e12			0.171478
$714$	−1.06168e13	+	1.39550e13i	−1.52880	+	2.00950i
$715$	−1.16313e13			−1.66437
$716$		−	4.26158e12i		−	0.605985i
$717$	4.73981e12	−	4.73981e12i	0.669769	−	0.669769i
$718$	1.24950e13			1.75460
$719$	−3.47724e11	+	3.47724e11i	−0.0485237	+	0.0485237i	−0.730952	−	0.682429i	$-0.760924\pi$
$719$	−3.47724e11	+	3.47724e11i	−0.0485237	+	0.0485237i	0.682429	+	0.730952i	$0.260924\pi$
$720$	−1.63864e13	−	1.63864e13i	−2.27241	−	2.27241i
$721$	−9.22120e12	−	9.22120e12i	−1.27080	−	1.27080i
$722$			9.23052e12i			1.26418i
$723$		−	1.55647e13i		−	2.11845i
$724$	−1.60038e12	−	1.60038e12i	−0.216471	−	0.216471i
$725$	8.86585e11	+	8.86585e11i	0.119179	+	0.119179i
$726$	8.56817e12	−	8.56817e12i	1.14465	−	1.14465i
$727$	−4.85245e11			−0.0644253			−0.0322127	−	0.999481i	$-0.510255\pi$
$727$	−4.85245e11			−0.0644253			−0.0322127	+	0.999481i	$0.510255\pi$
$728$	−3.13221e12	+	3.13221e12i	−0.413295	+	0.413295i
$729$			9.18785e11i			0.120487i
$730$	1.46040e13			1.90334
$731$	−4.37481e12	+	5.75036e12i	−0.566671	+	0.744847i
$732$	2.85364e12			0.367366
$733$			4.53070e12i			0.579693i	0.957073	+	0.289846i	$0.0936042\pi$
$733$			4.53070e12i			0.579693i	−0.957073	+	0.289846i	$0.906396\pi$
$734$	−8.50480e12	+	8.50480e12i	−1.08151	+	1.08151i
$735$	3.29414e12			0.416341
$736$	5.22467e12	−	5.22467e12i	0.656309	−	0.656309i
$737$	1.03956e13	+	1.03956e13i	1.29791	+	1.29791i
$738$	7.25490e12	+	7.25490e12i	0.900281	+	0.900281i
$739$			3.39131e12i			0.418281i	0.977886	+	0.209140i	$0.0670665\pi$
$739$			3.39131e12i			0.418281i	−0.977886	+	0.209140i	$0.932933\pi$
$740$		−	9.43730e12i		−	1.15692i
$741$	−1.03751e12	−	1.03751e12i	−0.126418	−	0.126418i
$742$	−2.29282e12	−	2.29282e12i	−0.277685	−	0.277685i
$743$	7.73209e12	−	7.73209e12i	0.930780	−	0.930780i	−0.0669745	−	0.997755i	$-0.521335\pi$
$743$	7.73209e12	−	7.73209e12i	0.930780	−	0.930780i	0.997755	+	0.0669745i	$0.0213346\pi$
$744$	−1.46438e12			−0.175217
$745$	1.51761e12	−	1.51761e12i	0.180491	−	0.180491i
$746$		−	9.30316e12i		−	1.09978i
$747$	−1.16947e13			−1.37418
$748$	9.37968e11	+	6.90419e12i	0.109555	+	0.806409i
$749$	1.46448e13			1.70026
$750$			1.56856e13i			1.81019i
$751$	3.63333e12	−	3.63333e12i	0.416798	−	0.416798i	−0.467301	−	0.884098i	$-0.654773\pi$
$751$	3.63333e12	−	3.63333e12i	0.416798	−	0.416798i	0.884098	+	0.467301i	$0.154773\pi$
$752$	−2.08282e12			−0.237504
$753$	1.81197e13	−	1.81197e13i	2.05387	−	2.05387i
$754$	−4.76137e12	−	4.76137e12i	−0.536489	−	0.536489i
$755$	4.10947e12	+	4.10947e12i	0.460283	+	0.460283i
$756$		−	1.40954e13i		−	1.56938i
$757$		−	8.25749e12i		−	0.913938i	−0.889483	−	0.456969i	$-0.848935\pi$
$757$		−	8.25749e12i		−	0.913938i	0.889483	−	0.456969i	$-0.151065\pi$
$758$	8.78849e12	+	8.78849e12i	0.966947	+	0.966947i
$759$	−1.29439e13	−	1.29439e13i	−1.41572	−	1.41572i
$760$	3.17815e11	−	3.17815e11i	0.0345552	−	0.0345552i
$761$	−1.37466e13			−1.48581			−0.742906	−	0.669396i	$-0.766553\pi$
$761$	−1.37466e13			−1.48581			−0.742906	+	0.669396i	$0.766553\pi$
$762$	9.73215e12	−	9.73215e12i	1.04571	−	1.04571i
$763$			6.97067e12i			0.744585i
$764$	−9.73119e12			−1.03335
$765$	−3.31911e12	−	2.44313e13i	−0.350385	−	2.57911i
$766$	−2.07756e12			−0.218033
$767$			1.34586e13i			1.40418i
$768$	−1.59587e13	+	1.59587e13i	−1.65528	+	1.65528i
$769$	1.41070e13			1.45468			0.727338	−	0.686280i	$-0.240757\pi$
$769$	1.41070e13			1.45468			0.727338	+	0.686280i	$0.240757\pi$
$770$	1.44103e13	−	1.44103e13i	1.47728	−	1.47728i
$771$	1.11978e13	+	1.11978e13i	1.14127	+	1.14127i
$772$	−2.38739e12	−	2.38739e12i	−0.241906	−	0.241906i
$773$			3.76516e12i			0.379294i	0.981852	+	0.189647i	$0.0607343\pi$
$773$			3.76516e12i			0.379294i	−0.981852	+	0.189647i	$0.939266\pi$
$774$		−	2.70281e13i		−	2.70696i
$775$	−4.51879e11	−	4.51879e11i	−0.0449950	−	0.0449950i
$776$	−6.55128e11	−	6.55128e11i	−0.0648557	−	0.0648557i
$777$	−2.30282e13	+	2.30282e13i	−2.26655	+	2.26655i
$778$	8.11509e12			0.794118
$779$	−2.84346e11	+	2.84346e11i	−0.0276649	+	0.0276649i
$780$			1.48720e13i			1.43861i
$781$	−4.56705e11			−0.0439244
$782$	1.12045e13	−	1.52219e12i	1.07143	−	0.145558i
$783$	−1.29273e13			−1.22908
$784$		−	2.62255e12i		−	0.247914i
$785$	−5.17505e12	+	5.17505e12i	−0.486408	+	0.486408i
$786$	−2.27822e13			−2.12909
$787$	4.19600e12	−	4.19600e12i	0.389897	−	0.389897i	−0.484754	−	0.874651i	$-0.661091\pi$
$787$	4.19600e12	−	4.19600e12i	0.389897	−	0.389897i	0.874651	+	0.484754i	$0.161091\pi$
$788$	−2.92172e12	−	2.92172e12i	−0.269942	−	0.269942i
$789$	−7.40092e12	−	7.40092e12i	−0.679890	−	0.679890i
$790$			2.69628e13i			2.46287i
$791$			1.54627e13i			1.40440i
$792$	1.11193e13	+	1.11193e13i	1.00419	+	1.00419i
$793$	2.85318e12	+	2.85318e12i	0.256213	+	0.256213i
$794$	−1.25053e13	+	1.25053e13i	−1.11661	+	1.11661i
$795$	6.56811e12			0.583161
$796$	−4.02558e12	+	4.02558e12i	−0.355402	+	0.355402i
$797$		−	1.41517e13i		−	1.24235i	−0.783670	−	0.621177i	$-0.786655\pi$
$797$		−	1.41517e13i		−	1.24235i	0.783670	−	0.621177i	$-0.213345\pi$
$798$	2.57078e12			0.224415
$799$	−1.76363e12	−	1.34175e12i	−0.153090	−	0.116469i
$800$	−3.99024e12			−0.344424
$801$		−	3.69973e12i		−	0.317558i
$802$	1.84727e13	−	1.84727e13i	1.57669	−	1.57669i
$803$	−2.00258e13			−1.69969
$804$	1.32920e13	−	1.32920e13i	1.12186	−	1.12186i
$805$	−8.98305e12	−	8.98305e12i	−0.753949	−	0.753949i
$806$	2.42680e12	+	2.42680e12i	0.202547	+	0.202547i
$807$		−	1.87149e13i		−	1.55330i
$808$		−	1.07490e13i		−	0.887189i
$809$	4.23447e12	+	4.23447e12i	0.347561	+	0.347561i	0.859200	−	0.511639i	$-0.170962\pi$
$809$	4.23447e12	+	4.23447e12i	0.347561	+	0.347561i	−0.511639	+	0.859200i	$0.670962\pi$
$810$	2.38271e13	+	2.38271e13i	1.94486	+	1.94486i
$811$	1.38391e13	−	1.38391e13i	1.12335	−	1.12335i	0.132113	−	0.991235i	$-0.457824\pi$
$811$	1.38391e13	−	1.38391e13i	1.12335	−	1.12335i	0.991235	−	0.132113i	$-0.0421763\pi$
$812$	4.53188e12			0.365827
$813$	−1.08489e13	+	1.08489e13i	−0.870919	+	0.870919i
$814$			3.36895e13i			2.68959i
$815$	−2.54950e12			−0.202416
$816$	−2.80194e13	+	3.80657e12i	−2.21235	+	0.300558i
$817$	1.05933e12			0.0831824
$818$			1.45693e13i			1.13775i
$819$	2.51914e13	−	2.51914e13i	1.95647	−	1.95647i
$820$	4.07593e12			0.314821
$821$	2.49777e12	−	2.49777e12i	0.191870	−	0.191870i	−0.604633	−	0.796504i	$-0.706680\pi$
$821$	2.49777e12	−	2.49777e12i	0.191870	−	0.191870i	0.796504	+	0.604633i	$0.206680\pi$
$822$	−2.15189e13	−	2.15189e13i	−1.64398	−	1.64398i
$823$	1.00995e13	+	1.00995e13i	0.767365	+	0.767365i	0.977642	−	0.210277i	$-0.0674367\pi$
$823$	1.00995e13	+	1.00995e13i	0.767365	+	0.767365i	−0.210277	+	0.977642i	$0.567437\pi$
$824$		−	1.04068e13i		−	0.786401i
$825$			9.88566e12i			0.742956i
$826$	−1.66742e13	−	1.66742e13i	−1.24634	−	1.24634i
$827$	−1.39869e12	−	1.39869e12i	−0.103979	−	0.103979i	0.653203	−	0.757182i	$-0.273425\pi$
$827$	−1.39869e12	−	1.39869e12i	−0.103979	−	0.103979i	−0.757182	+	0.653203i	$0.773425\pi$
$828$	−1.14889e13	+	1.14889e13i	−0.849456	+	0.849456i
$829$	1.38516e13			1.01860			0.509301	−	0.860588i	$-0.329904\pi$
$829$	1.38516e13			1.01860			0.509301	+	0.860588i	$0.329904\pi$
$830$	−8.55226e12	+	8.55226e12i	−0.625503	+	0.625503i
$831$			1.68940e13i			1.22893i
$832$	2.44601e12			0.176972
$833$	1.68944e12	−	2.22065e12i	0.121574	−	0.159800i
$834$	5.93044e12			0.424463
$835$		−	7.17249e12i		−	0.510600i
$836$	7.22339e11	−	7.22339e11i	0.0511462	−	0.0511462i
$837$	6.58887e12			0.464030
$838$	−1.74361e13	+	1.74361e13i	−1.22138	+	1.22138i
$839$	1.04101e13	+	1.04101e13i	0.725316	+	0.725316i	0.969683	−	0.244367i	$-0.0785801\pi$
$839$	1.04101e13	+	1.04101e13i	0.725316	+	0.725316i	−0.244367	+	0.969683i	$0.578580\pi$
$840$	1.11165e13	+	1.11165e13i	0.770388	+	0.770388i
$841$			1.03508e13i			0.713497i
$842$		−	5.59635e12i		−	0.383708i
$843$	3.25261e13	+	3.25261e13i	2.21824	+	2.21824i
$844$	−3.81501e12	−	3.81501e12i	−0.258794	−	0.258794i
$845$	−2.85297e12	+	2.85297e12i	−0.192505	+	0.192505i
$846$	8.28949e12			0.556366
$847$	−8.15389e12	+	8.15389e12i	−0.544364	+	0.544364i
$848$		−	5.22905e12i		−	0.347249i
$849$	−7.91594e12			−0.522899
$850$	−4.85988e12	−	3.69734e12i	−0.319330	−	0.242943i
$851$	2.10013e13			1.37266
$852$			5.83953e11i			0.0379664i
$853$	−8.42766e12	+	8.42766e12i	−0.545050	+	0.545050i	−0.925005	−	0.379955i	$-0.875939\pi$
$853$	−8.42766e12	+	8.42766e12i	−0.545050	+	0.545050i	0.379955	+	0.925005i	$0.375939\pi$
$854$	−7.06975e12			−0.454825
$855$	−2.55608e12	+	2.55608e12i	−0.163579	+	0.163579i
$856$	8.26387e12	+	8.26387e12i	0.526079	+	0.526079i
$857$	−1.89301e13	−	1.89301e13i	−1.19878	−	1.19878i	−0.974532	−	0.224249i	$-0.928007\pi$
$857$	−1.89301e13	−	1.89301e13i	−1.19878	−	1.19878i	−0.224249	−	0.974532i	$-0.571993\pi$
$858$		−	5.30905e13i		−	3.34445i
$859$			1.36188e13i			0.853431i	0.904386	+	0.426716i	$0.140329\pi$
$859$			1.36188e13i			0.853431i	−0.904386	+	0.426716i	$0.859671\pi$
$860$	−7.59242e12	−	7.59242e12i	−0.473301	−	0.473301i
$861$	−9.94578e12	−	9.94578e12i	−0.616772	−	0.616772i
$862$	3.84716e12	−	3.84716e12i	0.237333	−	0.237333i
$863$	−1.57643e13			−0.967446			−0.483723	−	0.875221i	$-0.660716\pi$
$863$	−1.57643e13			−0.967446			−0.483723	+	0.875221i	$0.660716\pi$
$864$	2.90909e13	−	2.90909e13i	1.77601	−	1.77601i
$865$		−	7.70026e12i		−	0.467663i
$866$	6.48293e12			0.391689
$867$	−2.61777e13	−	1.48269e13i	−1.57342	−	0.891175i
$868$	−2.30983e12			−0.138115
$869$		−	3.69729e13i		−	2.19935i
$870$	−1.68985e13	+	1.68985e13i	−1.00002	+	1.00002i
$871$	2.65798e13			1.56484
$872$	−3.93345e12	+	3.93345e12i	−0.230382	+	0.230382i
$873$	5.26898e12	+	5.26898e12i	0.307017	+	0.307017i
$874$	−1.17225e12	−	1.17225e12i	−0.0679547	−	0.0679547i
$875$		−	1.49272e13i		−	0.860878i
$876$			2.56054e13i			1.46914i
$877$	−1.83130e11	−	1.83130e11i	−0.0104535	−	0.0104535i	0.701861	−	0.712314i	$-0.252353\pi$
$877$	−1.83130e11	−	1.83130e11i	−0.0104535	−	0.0104535i	−0.712314	+	0.701861i	$0.752353\pi$
$878$	−1.86885e13	−	1.86885e13i	−1.06133	−	1.06133i
$879$	−2.53986e13	+	2.53986e13i	−1.43502	+	1.43502i
$880$	3.28643e13			1.84737
$881$	−5.24443e12	+	5.24443e12i	−0.293296	+	0.293296i	−0.838381	−	0.545085i	$-0.816497\pi$
$881$	−5.24443e12	+	5.24443e12i	−0.293296	+	0.293296i	0.545085	+	0.838381i	$0.316497\pi$
$882$			1.04376e13i			0.580754i
$883$	1.94425e13			1.07629			0.538146	−	0.842852i	$-0.319125\pi$
$883$	1.94425e13			1.07629			0.538146	+	0.842852i	$0.319125\pi$
$884$	1.00255e13	+	7.62732e12i	0.552170	+	0.420085i
$885$	4.77657e13			2.61741
$886$		−	1.42133e13i		−	0.774893i
$887$	2.08155e13	−	2.08155e13i	1.12910	−	1.12910i	0.138771	−	0.990325i	$-0.455685\pi$
$887$	2.08155e13	−	2.08155e13i	1.12910	−	1.12910i	0.990325	−	0.138771i	$-0.0443152\pi$
$888$	−2.59890e13			−1.40259
$889$	−9.26159e12	+	9.26159e12i	−0.497311	+	0.497311i
$890$	−2.70560e12	−	2.70560e12i	−0.144547	−	0.144547i
$891$	−3.26731e13	−	3.26731e13i	−1.73676	−	1.73676i
$892$			3.93079e12i			0.207892i
$893$			3.24895e11i			0.0170967i
$894$	6.92706e12	+	6.92706e12i	0.362686	+	0.362686i
$895$	−1.51222e13	−	1.51222e13i	−0.787794	−	0.787794i
$896$	1.33207e13	−	1.33207e13i	0.690465	−	0.690465i
$897$	−3.30955e13			−1.70688
$898$	1.89266e13	−	1.89266e13i	0.971246	−	0.971246i
$899$			2.11842e12i			0.108167i
$900$	8.77440e12			0.445785
$901$	3.36855e12	−	4.42771e12i	0.170287	−	0.223829i
$902$	−1.45504e13			−0.731887
$903$			3.70529e13i			1.85450i
$904$	−8.72536e12	+	8.72536e12i	−0.434535	+	0.434535i
$905$	−1.13579e13			−0.562834
$906$	−1.87575e13	+	1.87575e13i	−0.924908	+	0.924908i
$907$	−2.19209e12	−	2.19209e12i	−0.107554	−	0.107554i	0.651282	−	0.758836i	$-0.274231\pi$
$907$	−2.19209e12	−	2.19209e12i	−0.107554	−	0.107554i	−0.758836	+	0.651282i	$0.774231\pi$
$908$	−2.52899e12	−	2.52899e12i	−0.123470	−	0.123470i
$909$			8.64505e13i			4.19982i
$910$		−	3.68447e13i		−	1.78110i
$911$	−2.24498e13	−	2.24498e13i	−1.07989	−	1.07989i	−0.996519	−	0.0833713i	$-0.973431\pi$
$911$	−2.24498e13	−	2.24498e13i	−1.07989	−	1.07989i	−0.0833713	−	0.996519i	$-0.526569\pi$
$912$	2.93149e12	+	2.93149e12i	0.140317	+	0.140317i
$913$	1.17273e13	−	1.17273e13i	0.558575	−	0.558575i
$914$	−4.78693e13			−2.26882
$915$	1.01262e13	−	1.01262e13i	0.477584	−	0.477584i
$916$			1.71558e13i			0.805160i
$917$	2.16806e13			1.01253
$918$	6.23866e13	−	8.47553e12i	2.89934	−	0.393890i
$919$	−3.86061e13			−1.78540			−0.892702	−	0.450648i	$-0.851193\pi$
$919$	−3.86061e13			−1.78540			−0.892702	+	0.450648i	$0.851193\pi$
$920$		−	1.01380e13i		−	0.466560i
$921$	−2.88411e12	+	2.88411e12i	−0.132082	+	0.132082i
$922$	4.67965e12			0.213267
$923$	−5.83859e11	+	5.83859e11i	−0.0264789	+	0.0264789i
$924$	2.52658e13	+	2.52658e13i	1.14027	+	1.14027i
$925$	−8.01967e12	−	8.01967e12i	−0.360179	−	0.360179i
$926$		−	2.22776e12i		−	0.0995677i
$927$			8.36983e13i			3.72270i
$928$	9.35317e12	+	9.35317e12i	0.413993	+	0.413993i
$929$	1.80998e13	+	1.80998e13i	0.797265	+	0.797265i	0.982663	−	0.185398i	$-0.0593576\pi$
$929$	1.80998e13	+	1.80998e13i	0.797265	+	0.797265i	−0.185398	+	0.982663i	$0.559358\pi$
$930$	8.61288e12	−	8.61288e12i	0.377551	−	0.377551i
$931$	−4.09087e11			−0.0178461
$932$	7.21562e12	−	7.21562e12i	0.313258	−	0.313258i
$933$		−	6.34472e13i		−	2.74123i
$934$	1.99511e13			0.857840
$935$	2.78279e13	+	2.11712e13i	1.19077	+	0.905926i
$936$	2.84303e13			1.21071
$937$			2.65934e12i			0.112706i	0.998411	+	0.0563529i	$0.0179472\pi$
$937$			2.65934e12i			0.112706i	−0.998411	+	0.0563529i	$0.982053\pi$
$938$	−3.29304e13	+	3.29304e13i	−1.38894	+	1.38894i
$939$	4.66211e13			1.95698
$940$	2.32859e12	−	2.32859e12i	0.0972785	−	0.0972785i
$941$	2.92273e13	+	2.92273e13i	1.21516	+	1.21516i	0.969306	+	0.245859i	$0.0790699\pi$
$941$	2.92273e13	+	2.92273e13i	1.21516	+	1.21516i	0.245859	+	0.969306i	$0.420930\pi$
$942$	−2.36213e13	−	2.36213e13i	−0.977405	−	0.977405i
$943$			9.07036e12i			0.373527i
$944$		−	3.80275e13i		−	1.55856i
$945$	−5.00175e13	−	5.00175e13i	−2.04023	−	2.04023i
$946$	2.71036e13	+	2.71036e13i	1.10032	+	1.10032i
$947$	1.46511e13	−	1.46511e13i	0.591966	−	0.591966i	−0.346196	−	0.938162i	$-0.612527\pi$
$947$	1.46511e13	−	1.46511e13i	0.591966	−	0.591966i	0.938162	+	0.346196i	$0.112527\pi$
$948$	−4.72743e13			−1.90102
$949$	−2.56013e13	+	2.56013e13i	−1.02462	+	1.02462i
$950$			8.95285e11i			0.0356619i
$951$	1.04963e11			0.00416124
$952$	1.31951e13	−	1.79262e12i	0.520650	−	0.0707328i
$953$	−2.21831e13			−0.871174			−0.435587	−	0.900147i	$-0.643459\pi$
$953$	−2.21831e13			−0.871174			−0.435587	+	0.900147i	$0.643459\pi$
$954$			2.08113e13i			0.813451i
$955$	−3.45312e13	+	3.45312e13i	−1.34337	+	1.34337i
$956$	8.43751e12			0.326704
$957$	2.31721e13	−	2.31721e13i	0.893022	−	0.893022i
$958$	−3.66934e13	−	3.66934e13i	−1.40748	−	1.40748i
$959$	2.04784e13	+	2.04784e13i	0.781829	+	0.781829i
$960$		−	8.68108e12i		−	0.329878i
$961$			2.53599e13i			0.959163i
$962$	4.30693e13	+	4.30693e13i	1.62136	+	1.62136i
$963$	−6.64636e13	−	6.64636e13i	−2.49038	−	2.49038i
$964$	1.38536e13	−	1.38536e13i	0.516675	−	0.516675i
$965$	−1.69434e13			−0.628965
$966$	4.10027e13	−	4.10027e13i	1.51501	−	1.51501i
$967$			2.63617e13i			0.969514i	0.874649	+	0.484757i	$0.161092\pi$
$967$			2.63617e13i			0.969514i	−0.874649	+	0.484757i	$0.838908\pi$
$968$	−9.20224e12			−0.336864
$969$	5.93781e11	+	4.37070e12i	0.0216356	+	0.159255i
$970$	7.70636e12			0.279497
$971$		−	3.49050e12i		−	0.126009i	−0.998013	−	0.0630045i	$-0.979932\pi$
$971$		−	3.49050e12i		−	0.126009i	0.998013	−	0.0630045i	$-0.0200682\pi$
$972$	−1.35940e13	+	1.35940e13i	−0.488484	+	0.488484i
$973$	−5.64370e12			−0.201863
$974$	−1.75455e13	+	1.75455e13i	−0.624670	+	0.624670i
$975$	1.26380e13	+	1.26380e13i	0.447876	+	0.447876i
$976$	−8.06170e12	−	8.06170e12i	−0.284382	−	0.284382i
$977$		−	1.46631e13i		−	0.514875i	−0.966295	−	0.257437i	$-0.917122\pi$
$977$		−	1.46631e13i		−	0.514875i	0.966295	−	0.257437i	$-0.0828781\pi$
$978$		−	1.16371e13i		−	0.406742i
$979$	3.71007e12	+	3.71007e12i	0.129080	+	0.129080i
$980$	2.93201e12	+	2.93201e12i	0.101542	+	0.101542i
$981$	3.16354e13	−	3.16354e13i	1.09059	−	1.09059i
$982$	−1.58442e13			−0.543710
$983$	7.00196e12	−	7.00196e12i	0.239182	−	0.239182i	−0.577329	−	0.816511i	$-0.695905\pi$
$983$	7.00196e12	−	7.00196e12i	0.239182	−	0.239182i	0.816511	+	0.577329i	$0.195905\pi$
$984$		−	1.12245e13i		−	0.381671i
$985$	−2.07355e13			−0.701862
$986$	2.72501e12	+	2.00582e13i	0.0918167	+	0.675844i
$987$	−1.13641e13			−0.381160
$988$		−	1.84690e12i		−	0.0616649i
$989$	1.68958e13	−	1.68958e13i	0.561559	−	0.561559i
$990$	−1.30798e14			−4.32756
$991$	−3.62679e13	+	3.62679e13i	−1.19451	+	1.19451i	−0.218728	+	0.975786i	$0.570191\pi$
$991$	−3.62679e13	+	3.62679e13i	−1.19451	+	1.19451i	−0.975786	+	0.218728i	$0.929809\pi$
$992$	−4.76717e12	−	4.76717e12i	−0.156300	−	0.156300i
$993$	3.62608e13	+	3.62608e13i	1.18349	+	1.18349i
$994$		−	1.44671e12i		−	0.0470050i
$995$			2.85696e13i			0.924060i
$996$	−1.49948e13	−	1.49948e13i	−0.482808	−	0.482808i
$997$	−4.99220e12	−	4.99220e12i	−0.160016	−	0.160016i	0.622558	−	0.782574i	$-0.286094\pi$
$997$	−4.99220e12	−	4.99220e12i	−0.160016	−	0.160016i	−0.782574	+	0.622558i	$0.786094\pi$
$998$	−2.65475e13	+	2.65475e13i	−0.847102	+	0.847102i
$999$	1.16935e14			3.71450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.4.10	✓	24
17.8	even	8		289.10.a.f.1.20		24
17.9	even	8		289.10.a.f.1.19		24
17.13	even	4	inner	17.10.c.a.13.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.10	✓	24	1.1	even	1	trivial
17.10.c.a.13.3	yes	24	17.13	even	4	inner
289.10.a.f.1.19		24	17.9	even	8
289.10.a.f.1.20		24	17.8	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)

\(f(q)\)	\(=\)	\(q+28.8329i q^{2} +(-179.389 + 179.389i) q^{3} -319.336 q^{4} +(-1133.17 + 1133.17i) q^{5} +(-5172.29 - 5172.29i) q^{6} +(4922.20 + 4922.20i) q^{7} +5555.06i q^{8} -44677.5i q^{9} +O(q^{10})\)	\(q+28.8329i q^{2} +(-179.389 + 179.389i) q^{3} -319.336 q^{4} +(-1133.17 + 1133.17i) q^{5} +(-5172.29 - 5172.29i) q^{6} +(4922.20 + 4922.20i) q^{7} +5555.06i q^{8} -44677.5i q^{9} +(-32672.5 - 32672.5i) q^{10} +(44802.3 + 44802.3i) q^{11} +(57285.2 - 57285.2i) q^{12} +114552. q^{13} +(-141921. + 141921. i) q^{14} -406554. i q^{15} -323669. q^{16} +(-274067. - 208507. i) q^{17} +1.28818e6 q^{18} +50488.5i q^{19} +(361861. - 361861. i) q^{20} -1.76597e6 q^{21} +(-1.29178e6 + 1.29178e6i) q^{22} +(805268. + 805268. i) q^{23} +(-996514. - 996514. i) q^{24} -615007. i q^{25} +3.30287e6i q^{26} +(4.48373e6 + 4.48373e6i) q^{27} +(-1.57184e6 - 1.57184e6i) q^{28} +(-1.44158e6 + 1.44158e6i) q^{29} +1.17221e7 q^{30} +(734754. - 734754. i) q^{31} -6.48811e6i q^{32} -1.60741e7 q^{33} +(6.01186e6 - 7.90215e6i) q^{34} -1.11554e7 q^{35} +1.42671e7i q^{36} +(1.30400e7 - 1.30400e7i) q^{37} -1.45573e6 q^{38} +(-2.05493e7 + 2.05493e7i) q^{39} +(-6.29480e6 - 6.29480e6i) q^{40} +(5.63189e6 + 5.63189e6i) q^{41} -5.09182e7i q^{42} -2.09816e7i q^{43} +(-1.43070e7 - 1.43070e7i) q^{44} +(5.06270e7 + 5.06270e7i) q^{45} +(-2.32182e7 + 2.32182e7i) q^{46} +6.43503e6 q^{47} +(5.80624e7 - 5.80624e7i) q^{48} +8.10258e6i q^{49} +1.77324e7 q^{50} +(8.65682e7 - 1.17607e7i) q^{51} -3.65807e7 q^{52} +1.61556e7i q^{53} +(-1.29279e8 + 1.29279e8i) q^{54} -1.01537e8 q^{55} +(-2.73431e7 + 2.73431e7i) q^{56} +(-9.05706e6 - 9.05706e6i) q^{57} +(-4.15651e7 - 4.15651e7i) q^{58} +1.17489e8i q^{59} +1.29827e8i q^{60} +(2.49073e7 + 2.49073e7i) q^{61} +(2.11851e7 + 2.11851e7i) q^{62} +(2.19912e8 - 2.19912e8i) q^{63} +2.13528e7 q^{64} +(-1.29807e8 + 1.29807e8i) q^{65} -4.63462e8i q^{66} +2.32033e8 q^{67} +(8.75195e7 + 6.65838e7i) q^{68} -2.88912e8 q^{69} -3.21641e8i q^{70} +(-5.09689e6 + 5.09689e6i) q^{71} +2.48186e8 q^{72} +(-2.23490e8 + 2.23490e8i) q^{73} +(3.75980e8 + 3.75980e8i) q^{74} +(1.10325e8 + 1.10325e8i) q^{75} -1.61228e7i q^{76} +4.41053e8i q^{77} +(-5.92497e8 - 5.92497e8i) q^{78} +(-4.12622e8 - 4.12622e8i) q^{79} +(3.66770e8 - 3.66770e8i) q^{80} -7.29271e8 q^{81} +(-1.62384e8 + 1.62384e8i) q^{82} -2.61757e8i q^{83} +5.63939e8 q^{84} +(5.46837e8 - 7.42904e7i) q^{85} +6.04960e8 q^{86} -5.17208e8i q^{87} +(-2.48880e8 + 2.48880e8i) q^{88} +8.28097e7 q^{89} +(-1.45972e9 + 1.45972e9i) q^{90} +(5.63849e8 + 5.63849e8i) q^{91} +(-2.57151e8 - 2.57151e8i) q^{92} +2.63613e8i q^{93} +1.85541e8i q^{94} +(-5.72119e7 - 5.72119e7i) q^{95} +(1.16389e9 + 1.16389e9i) q^{96} +(-1.17934e8 + 1.17934e8i) q^{97} -2.33621e8 q^{98} +(2.00166e9 - 2.00166e9i) 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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