LMFDB - Embedded newform 17.10.c.a.13.1

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			13.1
Character	$\chi$	$=$	17.13
Dual form			17.10.c.a.4.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.8788i q^{2} +(-36.4169 - 36.4169i) q^{3} -1078.32 q^{4} +(454.832 + 454.832i) q^{5} +(-1452.26 + 1452.26i) q^{6} +(-6039.34 + 6039.34i) q^{7} +22584.0i q^{8} -17030.6i q^{9} +O(q^{10})$	\(q-39.8788i q^{2} +(-36.4169 - 36.4169i) q^{3} -1078.32 q^{4} +(454.832 + 454.832i) q^{5} +(-1452.26 + 1452.26i) q^{6} +(-6039.34 + 6039.34i) q^{7} +22584.0i q^{8} -17030.6i q^{9} +(18138.1 - 18138.1i) q^{10} +(-7423.20 + 7423.20i) q^{11} +(39269.0 + 39269.0i) q^{12} +48755.2 q^{13} +(240842. + 240842. i) q^{14} -33127.1i q^{15} +348526. q^{16} +(-336935. + 71150.4i) q^{17} -679160. q^{18} +157321. i q^{19} +(-490453. - 490453. i) q^{20} +439868. q^{21} +(296028. + 296028. i) q^{22} +(-1.76063e6 + 1.76063e6i) q^{23} +(822441. - 822441. i) q^{24} -1.53938e6i q^{25} -1.94430e6i q^{26} +(-1.33700e6 + 1.33700e6i) q^{27} +(6.51233e6 - 6.51233e6i) q^{28} +(-2.73196e6 - 2.73196e6i) q^{29} -1.32107e6 q^{30} +(703113. + 703113. i) q^{31} -2.33575e6i q^{32} +540660. q^{33} +(2.83739e6 + 1.34366e7i) q^{34} -5.49377e6 q^{35} +1.83644e7i q^{36} +(-5.08132e6 - 5.08132e6i) q^{37} +6.27378e6 q^{38} +(-1.77551e6 - 1.77551e6i) q^{39} +(-1.02719e7 + 1.02719e7i) q^{40} +(-1.33928e7 + 1.33928e7i) q^{41} -1.75414e7i q^{42} -1.91903e7i q^{43} +(8.00457e6 - 8.00457e6i) q^{44} +(7.74606e6 - 7.74606e6i) q^{45} +(7.02116e7 + 7.02116e7i) q^{46} +5.40395e7 q^{47} +(-1.26922e7 - 1.26922e7i) q^{48} -3.25937e7i q^{49} -6.13887e7 q^{50} +(1.48612e7 + 9.67907e6i) q^{51} -5.25735e7 q^{52} -7.91235e7i q^{53} +(5.33178e7 + 5.33178e7i) q^{54} -6.75261e6 q^{55} +(-1.36393e8 - 1.36393e8i) q^{56} +(5.72915e6 - 5.72915e6i) q^{57} +(-1.08947e8 + 1.08947e8i) q^{58} -1.82732e8i q^{59} +3.57216e7i q^{60} +(-1.24268e8 + 1.24268e8i) q^{61} +(2.80393e7 - 2.80393e7i) q^{62} +(1.02854e8 + 1.02854e8i) q^{63} +8.52982e7 q^{64} +(2.21754e7 + 2.21754e7i) q^{65} -2.15609e7i q^{66} -9.64396e7 q^{67} +(3.63323e8 - 7.67227e7i) q^{68} +1.28233e8 q^{69} +2.19085e8i q^{70} +(-1.83548e8 - 1.83548e8i) q^{71} +3.84620e8 q^{72} +(-6.90563e7 - 6.90563e7i) q^{73} +(-2.02637e8 + 2.02637e8i) q^{74} +(-5.60595e7 + 5.60595e7i) q^{75} -1.69642e8i q^{76} -8.96625e7i q^{77} +(-7.08053e7 + 7.08053e7i) q^{78} +(5.05917e7 - 5.05917e7i) q^{79} +(1.58521e8 + 1.58521e8i) q^{80} -2.37835e8 q^{81} +(5.34090e8 + 5.34090e8i) q^{82} +6.09693e8i q^{83} -4.74318e8 q^{84} +(-1.85610e8 - 1.20887e8i) q^{85} -7.65287e8 q^{86} +1.98979e8i q^{87} +(-1.67646e8 - 1.67646e8i) q^{88} -2.08272e7 q^{89} +(-3.08904e8 - 3.08904e8i) q^{90} +(-2.94449e8 + 2.94449e8i) q^{91} +(1.89851e9 - 1.89851e9i) q^{92} -5.12104e7i q^{93} -2.15503e9i q^{94} +(-7.15547e7 + 7.15547e7i) q^{95} +(-8.50609e7 + 8.50609e7i) q^{96} +(3.67131e8 + 3.67131e8i) q^{97} -1.29980e9 q^{98} +(1.26422e8 + 1.26422e8i) 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 $

$2$		−	39.8788i		−	1.76241i	−0.472734	−	0.881205i	$-0.656733\pi$
$2$		−	39.8788i		−	1.76241i	0.472734	−	0.881205i	$-0.343267\pi$
$3$	−36.4169	−	36.4169i	−0.259572	−	0.259572i	0.565308	−	0.824880i	$-0.308757\pi$
$3$	−36.4169	−	36.4169i	−0.259572	−	0.259572i	−0.824880	+	0.565308i	$0.808757\pi$
$4$	−1078.32			−2.10609
$5$	454.832	+	454.832i	0.325451	+	0.325451i	0.850854	−	0.525403i	$-0.176085\pi$
$5$	454.832	+	454.832i	0.325451	+	0.325451i	−0.525403	+	0.850854i	$0.676085\pi$
$6$	−1452.26	+	1452.26i	−0.457472	+	0.457472i
$7$	−6039.34	+	6039.34i	−0.950711	+	0.950711i	−0.998841	−	0.0481304i	$-0.984674\pi$
$7$	−6039.34	+	6039.34i	−0.950711	+	0.950711i	0.0481304	+	0.998841i	$0.484674\pi$
$8$			22584.0i			1.94938i
$9$		−	17030.6i		−	0.865245i
$10$	18138.1	−	18138.1i	0.573578	−	0.573578i
$11$	−7423.20	+	7423.20i	−0.152871	+	0.152871i	−0.779399	−	0.626528i	$-0.784475\pi$
$11$	−7423.20	+	7423.20i	−0.152871	+	0.152871i	0.626528	+	0.779399i	$0.284475\pi$
$12$	39269.0	+	39269.0i	0.546681	+	0.546681i
$13$	48755.2			0.473451			0.236726	−	0.971577i	$-0.423926\pi$
$13$	48755.2			0.473451			0.236726	+	0.971577i	$0.423926\pi$
$14$	240842.	+	240842.i	1.67554	+	1.67554i
$15$		−	33127.1i		−	0.168956i
$16$	348526.			1.32952
$17$	−336935.	+	71150.4i	−0.978423	+	0.206613i
$17$	−336935.	+	71150.4i	−0.978423	+	0.206613i
$18$	−679160.			−1.52492
$19$			157321.i			0.276947i	0.990366	+	0.138473i	$0.0442195\pi$
$19$			157321.i			0.276947i	−0.990366	+	0.138473i	$0.955780\pi$
$20$	−490453.	−	490453.i	−0.685429	−	0.685429i
$21$	439868.			0.493555
$22$	296028.	+	296028.i	0.269421	+	0.269421i
$23$	−1.76063e6	+	1.76063e6i	−1.31187	+	1.31187i	−0.391838	+	0.920034i	$0.628161\pi$
$23$	−1.76063e6	+	1.76063e6i	−1.31187	+	1.31187i	−0.920034	+	0.391838i	$0.871839\pi$
$24$	822441.	−	822441.i	0.506005	−	0.506005i
$25$		−	1.53938e6i		−	0.788163i
$26$		−	1.94430e6i		−	0.834415i
$27$	−1.33700e6	+	1.33700e6i	−0.484165	+	0.484165i
$28$	6.51233e6	−	6.51233e6i	2.00228	−	2.00228i
$29$	−2.73196e6	−	2.73196e6i	−0.717272	−	0.717272i	0.250774	−	0.968046i	$-0.419315\pi$
$29$	−2.73196e6	−	2.73196e6i	−0.717272	−	0.717272i	−0.968046	+	0.250774i	$0.919315\pi$
$30$	−1.32107e6			−0.297769
$31$	703113.	+	703113.i	0.136741	+	0.136741i	0.772164	−	0.635423i	$-0.219174\pi$
$31$	703113.	+	703113.i	0.136741	+	0.136741i	−0.635423	+	0.772164i	$0.719174\pi$
$32$		−	2.33575e6i		−	0.393778i
$33$	540660.			0.0793618
$34$	2.83739e6	+	1.34366e7i	0.364136	+	1.72438i
$35$	−5.49377e6			−0.618820
$36$			1.83644e7i			1.82228i
$37$	−5.08132e6	−	5.08132e6i	−0.445727	−	0.445727i	0.448204	−	0.893931i	$-0.352064\pi$
$37$	−5.08132e6	−	5.08132e6i	−0.445727	−	0.445727i	−0.893931	+	0.448204i	$0.852064\pi$
$38$	6.27378e6			0.488093
$39$	−1.77551e6	−	1.77551e6i	−0.122895	−	0.122895i
$40$	−1.02719e7	+	1.02719e7i	−0.634428	+	0.634428i
$41$	−1.33928e7	+	1.33928e7i	−0.740193	+	0.740193i	−0.972615	−	0.232422i	$-0.925335\pi$
$41$	−1.33928e7	+	1.33928e7i	−0.740193	+	0.740193i	0.232422	+	0.972615i	$0.425335\pi$
$42$		−	1.75414e7i		−	0.869847i
$43$		−	1.91903e7i		−	0.856002i	−0.903778	−	0.428001i	$-0.859218\pi$
$43$		−	1.91903e7i		−	0.856002i	0.903778	−	0.428001i	$-0.140782\pi$
$44$	8.00457e6	−	8.00457e6i	0.321959	−	0.321959i
$45$	7.74606e6	−	7.74606e6i	0.281595	−	0.281595i
$46$	7.02116e7	+	7.02116e7i	2.31206	+	2.31206i
$47$	5.40395e7			1.61537			0.807683	−	0.589617i	$-0.200721\pi$
$47$	5.40395e7			1.61537			0.807683	+	0.589617i	$0.200721\pi$
$48$	−1.26922e7	−	1.26922e7i	−0.345106	−	0.345106i
$49$		−	3.25937e7i		−	0.807702i
$50$	−6.13887e7			−1.38907
$51$	1.48612e7	+	9.67907e6i	0.307602	+	0.200340i
$52$	−5.25735e7			−0.997131
$53$		−	7.91235e7i		−	1.37741i	−0.725041	−	0.688706i	$-0.758179\pi$
$53$		−	7.91235e7i		−	1.37741i	0.725041	−	0.688706i	$-0.241821\pi$
$54$	5.33178e7	+	5.33178e7i	0.853297	+	0.853297i
$55$	−6.75261e6			−0.0995038
$56$	−1.36393e8	−	1.36393e8i	−1.85330	−	1.85330i
$57$	5.72915e6	−	5.72915e6i	0.0718875	−	0.0718875i
$58$	−1.08947e8	+	1.08947e8i	−1.26413	+	1.26413i
$59$		−	1.82732e8i		−	1.96327i	−0.190773	−	0.981634i	$-0.561099\pi$
$59$		−	1.82732e8i		−	1.96327i	0.190773	−	0.981634i	$-0.438901\pi$
$60$			3.57216e7i			0.355836i
$61$	−1.24268e8	+	1.24268e8i	−1.14914	+	1.14914i	−0.162422	+	0.986721i	$0.551931\pi$
$61$	−1.24268e8	+	1.24268e8i	−1.14914	+	1.14914i	−0.986721	+	0.162422i	$0.948069\pi$
$62$	2.80393e7	−	2.80393e7i	0.240993	−	0.240993i
$63$	1.02854e8	+	1.02854e8i	0.822598	+	0.822598i
$64$	8.52982e7			0.635521
$65$	2.21754e7	+	2.21754e7i	0.154085	+	0.154085i
$66$		−	2.15609e7i		−	0.139868i
$67$	−9.64396e7			−0.584681			−0.292340	−	0.956314i	$-0.594434\pi$
$67$	−9.64396e7			−0.584681			−0.292340	+	0.956314i	$0.594434\pi$
$68$	3.63323e8	−	7.67227e7i	2.06064	−	0.435145i
$69$	1.28233e8			0.681050
$70$			2.19085e8i			1.09061i
$71$	−1.83548e8	−	1.83548e8i	−0.857208	−	0.857208i	0.133801	−	0.991008i	$-0.457282\pi$
$71$	−1.83548e8	−	1.83548e8i	−0.857208	−	0.857208i	−0.991008	+	0.133801i	$0.957282\pi$
$72$	3.84620e8			1.68669
$73$	−6.90563e7	−	6.90563e7i	−0.284610	−	0.284610i	0.550334	−	0.834944i	$-0.314500\pi$
$73$	−6.90563e7	−	6.90563e7i	−0.284610	−	0.284610i	−0.834944	+	0.550334i	$0.814500\pi$
$74$	−2.02637e8	+	2.02637e8i	−0.785553	+	0.785553i
$75$	−5.60595e7	+	5.60595e7i	−0.204585	+	0.204585i
$76$		−	1.69642e8i		−	0.583274i
$77$		−	8.96625e7i		−	0.290671i
$78$	−7.08053e7	+	7.08053e7i	−0.216591	+	0.216591i
$79$	5.05917e7	−	5.05917e7i	0.146136	−	0.146136i	−0.630253	−	0.776389i	$-0.717049\pi$
$79$	5.05917e7	−	5.05917e7i	0.146136	−	0.146136i	0.776389	+	0.630253i	$0.217049\pi$
$80$	1.58521e8	+	1.58521e8i	0.432694	+	0.432694i
$81$	−2.37835e8			−0.613894
$82$	5.34090e8	+	5.34090e8i	1.30452	+	1.30452i
$83$			6.09693e8i			1.41013i	0.709141	+	0.705066i	$0.249083\pi$
$83$			6.09693e8i			1.41013i	−0.709141	+	0.705066i	$0.750917\pi$
$84$	−4.74318e8			−1.03947
$85$	−1.85610e8	−	1.20887e8i	−0.385671	−	0.251186i
$86$	−7.65287e8			−1.50863
$87$			1.98979e8i			0.372367i
$88$	−1.67646e8	−	1.67646e8i	−0.298003	−	0.298003i
$89$	−2.08272e7			−0.0351864			−0.0175932	−	0.999845i	$-0.505600\pi$
$89$	−2.08272e7			−0.0351864			−0.0175932	+	0.999845i	$0.505600\pi$
$90$	−3.08904e8	−	3.08904e8i	−0.496286	−	0.496286i
$91$	−2.94449e8	+	2.94449e8i	−0.450115	+	0.450115i
$92$	1.89851e9	−	1.89851e9i	2.76292	−	2.76292i
$93$		−	5.12104e7i		−	0.0709880i
$94$		−	2.15503e9i		−	2.84694i
$95$	−7.15547e7	+	7.15547e7i	−0.0901325	+	0.0901325i
$96$	−8.50609e7	+	8.50609e7i	−0.102214	+	0.102214i
$97$	3.67131e8	+	3.67131e8i	0.421064	+	0.421064i	0.885570	−	0.464506i	$-0.153768\pi$
$97$	3.67131e8	+	3.67131e8i	0.421064	+	0.421064i	−0.464506	+	0.885570i	$0.653768\pi$
$98$	−1.29980e9			−1.42350
$99$	1.26422e8	+	1.26422e8i	0.132271	+	0.132271i
$100$			1.65994e9i			1.65994i
$101$	1.18694e8			0.113496			0.0567481	−	0.998389i	$-0.481927\pi$
$101$	1.18694e8			0.113496			0.0567481	+	0.998389i	$0.481927\pi$
$102$	3.85990e8	−	5.92648e8i	0.353081	−	0.542121i
$103$	1.88391e9			1.64928			0.824639	−	0.565660i	$-0.191378\pi$
$103$	1.88391e9			1.64928			0.824639	+	0.565660i	$0.191378\pi$
$104$			1.10109e9i			0.922937i
$105$	2.00066e8	+	2.00066e8i	0.160628	+	0.160628i
$106$	−3.15535e9			−2.42756
$107$	3.96214e8	+	3.96214e8i	0.292215	+	0.292215i	0.837955	−	0.545739i	$-0.183751\pi$
$107$	3.96214e8	+	3.96214e8i	0.292215	+	0.292215i	−0.545739	+	0.837955i	$0.683751\pi$
$108$	1.44171e9	−	1.44171e9i	1.01969	−	1.01969i
$109$	1.55692e9	−	1.55692e9i	1.05645	−	1.05645i	0.0581386	−	0.998309i	$-0.481483\pi$
$109$	1.55692e9	−	1.55692e9i	1.05645	−	1.05645i	0.998309	−	0.0581386i	$-0.0185165\pi$
$110$			2.69286e8i			0.175367i
$111$			3.70092e8i			0.231396i
$112$	−2.10487e9	+	2.10487e9i	−1.26399	+	1.26399i
$113$	−1.28261e9	+	1.28261e9i	−0.740019	+	0.740019i	−0.972581	−	0.232562i	$-0.925289\pi$
$113$	−1.28261e9	+	1.28261e9i	−0.740019	+	0.740019i	0.232562	+	0.972581i	$0.425289\pi$
$114$	−2.28472e8	−	2.28472e8i	−0.126695	−	0.126695i
$115$	−1.60158e9			−0.853900
$116$	2.94592e9	+	2.94592e9i	1.51064	+	1.51064i
$117$		−	8.30330e8i		−	0.409651i
$118$	−7.28712e9			−3.46008
$119$	1.60517e9	−	2.46457e9i	0.733768	−	1.12663i
$120$	7.48145e8			0.329359
$121$			2.24774e9i			0.953261i
$122$	4.95565e9	+	4.95565e9i	2.02526	+	2.02526i
$123$	9.75451e8			0.384267
$124$	−7.58178e8	−	7.58178e8i	−0.287988	−	0.287988i
$125$	1.58850e9	−	1.58850e9i	0.581960	−	0.581960i
$126$	4.10168e9	−	4.10168e9i	1.44975	−	1.44975i
$127$			3.23202e9i			1.10245i	0.834358	+	0.551223i	$0.185839\pi$
$127$			3.23202e9i			1.10245i	−0.834358	+	0.551223i	$0.814161\pi$
$128$		−	4.59750e9i		−	1.51383i
$129$	−6.98853e8	+	6.98853e8i	−0.222194	+	0.222194i
$130$	8.84327e8	−	8.84327e8i	0.271561	−	0.271561i
$131$	1.53632e9	+	1.53632e9i	0.455786	+	0.455786i	0.897269	−	0.441484i	$-0.145548\pi$
$131$	1.53632e9	+	1.53632e9i	0.455786	+	0.455786i	−0.441484	+	0.897269i	$0.645548\pi$
$132$	−5.83003e8			−0.167143
$133$	−9.50116e8	−	9.50116e8i	−0.263296	−	0.263296i
$134$			3.84589e9i			1.03045i
$135$	−1.21622e9			−0.315144
$136$	−1.60686e9	−	7.60937e9i	−0.402767	−	1.90732i
$137$	−1.85915e9			−0.450891			−0.225445	−	0.974256i	$-0.572384\pi$
$137$	−1.85915e9			−0.450891			−0.225445	+	0.974256i	$0.572384\pi$
$138$		−	5.11378e9i		−	1.20029i
$139$	−3.00687e9	−	3.00687e9i	−0.683199	−	0.683199i	0.277520	−	0.960720i	$-0.410487\pi$
$139$	−3.00687e9	−	3.00687e9i	−0.683199	−	0.683199i	−0.960720	+	0.277520i	$0.910487\pi$
$140$	5.92402e9			1.30329
$141$	−1.96795e9	−	1.96795e9i	−0.419304	−	0.419304i
$142$	−7.31965e9	+	7.31965e9i	−1.51075	+	1.51075i
$143$	−3.61919e8	+	3.61919e8i	−0.0723768	+	0.0723768i
$144$		−	5.93561e9i		−	1.15036i
$145$		−	2.48517e9i		−	0.466874i
$146$	−2.75388e9	+	2.75388e9i	−0.501600	+	0.501600i
$147$	−1.18696e9	+	1.18696e9i	−0.209657	+	0.209657i
$148$	5.47928e9	+	5.47928e9i	0.938740	+	0.938740i
$149$	−7.81863e9			−1.29955			−0.649774	−	0.760127i	$-0.725137\pi$
$149$	−7.81863e9			−1.29955			−0.649774	+	0.760127i	$0.725137\pi$
$150$	2.23559e9	+	2.23559e9i	0.360563	+	0.360563i
$151$			2.92868e9i			0.458433i	0.973375	+	0.229217i	$0.0736164\pi$
$151$			2.92868e9i			0.458433i	−0.973375	+	0.229217i	$0.926384\pi$
$152$	−3.55295e9			−0.539874
$153$	1.21174e9	+	5.73822e9i	0.178771	+	0.846575i
$154$	−3.57563e9			−0.512282
$155$			6.39596e8i			0.0890047i
$156$	1.91457e9	+	1.91457e9i	0.258827	+	0.258827i
$157$	8.97773e9			1.17928			0.589642	−	0.807665i	$-0.299269\pi$
$157$	8.97773e9			1.17928			0.589642	+	0.807665i	$0.299269\pi$
$158$	−2.01753e9	−	2.01753e9i	−0.257551	−	0.257551i
$159$	−2.88143e9	+	2.88143e9i	−0.357537	+	0.357537i
$160$	1.06237e9	−	1.06237e9i	0.128156	−	0.128156i
$161$		−	2.12660e10i		−	2.49442i
$162$			9.48457e9i			1.08193i
$163$	2.68962e8	−	2.68962e8i	0.0298432	−	0.0298432i	−0.692028	−	0.721871i	$-0.743282\pi$
$163$	2.68962e8	−	2.68962e8i	0.0298432	−	0.0298432i	0.721871	+	0.692028i	$0.243282\pi$
$164$	1.44417e10	−	1.44417e10i	1.55891	−	1.55891i
$165$	2.45909e8	+	2.45909e8i	0.0258284	+	0.0258284i
$166$	2.43138e10			2.48523
$167$	−1.81729e9	−	1.81729e9i	−0.180800	−	0.180800i	0.610904	−	0.791705i	$-0.290806\pi$
$167$	−1.81729e9	−	1.81729e9i	−0.180800	−	0.180800i	−0.791705	+	0.610904i	$0.790806\pi$
$168$			9.93401e9i			0.962128i
$169$	−8.22743e9			−0.775844
$170$	−4.82084e9	+	7.40192e9i	−0.442693	+	0.679710i
$171$	2.67928e9			0.239627
$172$			2.06933e10i			1.80282i
$173$	−5.79552e9	−	5.79552e9i	−0.491910	−	0.491910i	0.416998	−	0.908907i	$-0.363082\pi$
$173$	−5.79552e9	−	5.79552e9i	−0.491910	−	0.491910i	−0.908907	+	0.416998i	$0.863082\pi$
$174$	7.93505e9			0.656263
$175$	9.29685e9	+	9.29685e9i	0.749315	+	0.749315i
$176$	−2.58718e9	+	2.58718e9i	−0.203245	+	0.203245i
$177$	−6.65452e9	+	6.65452e9i	−0.509609	+	0.509609i
$178$			8.30562e8i			0.0620129i
$179$			6.62962e9i			0.482669i	0.970442	+	0.241335i	$0.0775852\pi$
$179$			6.62962e9i			0.482669i	−0.970442	+	0.241335i	$0.922415\pi$
$180$	−8.35271e9	+	8.35271e9i	−0.593064	+	0.593064i
$181$	8.22939e9	−	8.22939e9i	0.569920	−	0.569920i	−0.362186	−	0.932106i	$-0.617969\pi$
$181$	8.22939e9	−	8.22939e9i	0.569920	−	0.569920i	0.932106	+	0.362186i	$0.117969\pi$
$182$	1.17423e10	+	1.17423e10i	0.793288	+	0.793288i
$183$	9.05090e9			0.596571
$184$	−3.97620e10	−	3.97620e10i	−2.55734	−	2.55734i
$185$		−	4.62229e9i		−	0.290125i
$186$	−2.04221e9			−0.125110
$187$	1.97298e9	−	3.02930e9i	0.117987	−	0.181157i
$188$	−5.82717e10			−3.40210
$189$		−	1.61492e10i		−	0.920602i
$190$	2.85351e9	+	2.85351e9i	0.158850	+	0.158850i
$191$	−1.79571e10			−0.976306			−0.488153	−	0.872758i	$-0.662329\pi$
$191$	−1.79571e10			−0.976306			−0.488153	+	0.872758i	$0.662329\pi$
$192$	−3.10630e9	−	3.10630e9i	−0.164963	−	0.164963i
$193$	1.35748e10	−	1.35748e10i	0.704248	−	0.704248i	−0.261072	−	0.965319i	$-0.584076\pi$
$193$	1.35748e10	−	1.35748e10i	0.704248	−	0.704248i	0.965319	+	0.261072i	$0.0840759\pi$
$194$	1.46407e10	−	1.46407e10i	0.742088	−	0.742088i
$195$		−	1.61512e9i		−	0.0799924i
$196$			3.51463e10i			1.70109i
$197$	2.67707e9	−	2.67707e9i	0.126638	−	0.126638i	−0.640947	−	0.767585i	$-0.721458\pi$
$197$	2.67707e9	−	2.67707e9i	0.126638	−	0.126638i	0.767585	+	0.640947i	$0.221458\pi$
$198$	5.04154e9	−	5.04154e9i	0.233115	−	0.233115i
$199$	2.96047e9	+	2.96047e9i	0.133820	+	0.133820i	0.770844	−	0.637024i	$-0.219835\pi$
$199$	2.96047e9	+	2.96047e9i	0.133820	+	0.133820i	−0.637024	+	0.770844i	$0.719835\pi$
$200$	3.47655e10			1.53643
$201$	3.51203e9	+	3.51203e9i	0.151767	+	0.151767i
$202$		−	4.73336e9i		−	0.200027i
$203$	3.29985e10			1.36384
$204$	−1.60251e10	−	1.04371e10i	−0.647837	−	0.421934i
$205$	−1.21830e10			−0.481793
$206$		−	7.51282e10i		−	2.90670i
$207$	2.99845e10	+	2.99845e10i	1.13509	+	1.13509i
$208$	1.69924e10			0.629463
$209$	−1.16783e9	−	1.16783e9i	−0.0423370	−	0.0423370i
$210$	7.97839e9	−	7.97839e9i	0.283093	−	0.283093i
$211$	−2.23159e10	+	2.23159e10i	−0.775074	+	0.775074i	−0.978989	−	0.203915i	$-0.934633\pi$
$211$	−2.23159e10	+	2.23159e10i	−0.775074	+	0.775074i	0.203915	+	0.978989i	$0.434633\pi$
$212$			8.53202e10i			2.90095i
$213$			1.33685e10i			0.445014i
$214$	1.58005e10	−	1.58005e10i	0.515003	−	0.515003i
$215$	8.72837e9	−	8.72837e9i	0.278587	−	0.278587i
$216$	−3.01948e10	−	3.01948e10i	−0.943822	−	0.943822i
$217$	−8.49267e9			−0.260001
$218$	−6.20882e10	−	6.20882e10i	−1.86189	−	1.86189i
$219$			5.02964e9i			0.147754i
$220$	7.28146e9			0.209564
$221$	−1.64273e10	+	3.46895e9i	−0.463236	+	0.0978211i
$222$	1.47588e10			0.407815
$223$			1.78382e10i			0.483036i	0.970396	+	0.241518i	$0.0776453\pi$
$223$			1.78382e10i			0.483036i	−0.970396	+	0.241518i	$0.922355\pi$
$224$	1.41064e10	+	1.41064e10i	0.374369	+	0.374369i
$225$	−2.62166e10			−0.681954
$226$	5.11491e10	+	5.11491e10i	1.30422	+	1.30422i
$227$	−1.00912e10	+	1.00912e10i	−0.252248	+	0.252248i	−0.821892	−	0.569644i	$-0.807081\pi$
$227$	−1.00912e10	+	1.00912e10i	−0.252248	+	0.252248i	0.569644	+	0.821892i	$0.307081\pi$
$228$	−6.17784e9	+	6.17784e9i	−0.151402	+	0.151402i
$229$			5.07272e10i			1.21894i	0.792810	+	0.609469i	$0.208617\pi$
$229$			5.07272e10i			1.21894i	−0.792810	+	0.609469i	$0.791383\pi$
$230$			6.38689e10i			1.50492i
$231$	−3.26523e9	+	3.26523e9i	−0.0754501	+	0.0754501i
$232$	6.16987e10	−	6.16987e10i	1.39824	−	1.39824i
$233$	−5.16302e10	−	5.16302e10i	−1.14763	−	1.14763i	−0.987017	−	0.160613i	$-0.948653\pi$
$233$	−5.16302e10	−	5.16302e10i	−1.14763	−	1.14763i	−0.160613	−	0.987017i	$-0.551347\pi$
$234$	−3.31126e10			−0.721974
$235$	2.45789e10	+	2.45789e10i	0.525723	+	0.525723i
$236$			1.97043e11i			4.13482i
$237$	−3.68479e9			−0.0758656
$238$	−9.82840e10	−	6.40121e10i	−1.98558	−	1.29320i
$239$	1.91354e10			0.379357			0.189678	−	0.981846i	$-0.439255\pi$
$239$	1.91354e10			0.379357			0.189678	+	0.981846i	$0.439255\pi$
$240$		−	1.15457e10i		−	0.224630i
$241$	−1.44815e10	−	1.44815e10i	−0.276527	−	0.276527i	0.555194	−	0.831721i	$-0.312644\pi$
$241$	−1.44815e10	−	1.44815e10i	−0.276527	−	0.276527i	−0.831721	+	0.555194i	$0.812644\pi$
$242$	8.96371e10			1.68004
$243$	3.49773e10	+	3.49773e10i	0.643515	+	0.643515i
$244$	1.34000e11	−	1.34000e11i	2.42020	−	2.42020i
$245$	1.48246e10	−	1.48246e10i	0.262867	−	0.262867i
$246$		−	3.88998e10i		−	0.677235i
$247$			7.67022e9i			0.131121i
$248$	−1.58791e10	+	1.58791e10i	−0.266559	+	0.266559i
$249$	2.22032e10	−	2.22032e10i	0.366031	−	0.366031i
$250$	−6.33475e10	−	6.33475e10i	−1.02565	−	1.02565i
$251$	−5.46041e10			−0.868348			−0.434174	−	0.900829i	$-0.642960\pi$
$251$	−5.46041e10			−0.868348			−0.434174	+	0.900829i	$0.642960\pi$
$252$	−1.10909e11	−	1.10909e11i	−1.73246	−	1.73246i
$253$		−	2.61389e10i		−	0.401094i
$254$	1.28889e11			1.94296
$255$	2.35701e9	+	1.11617e10i	0.0349084	+	0.165310i
$256$	−1.39670e11			−2.03246
$257$		−	4.07263e10i		−	0.582339i	−0.956672	−	0.291169i	$-0.905956\pi$
$257$		−	4.07263e10i		−	0.582339i	0.956672	−	0.291169i	$-0.0940443\pi$
$258$	2.78694e10	+	2.78694e10i	0.391597	+	0.391597i
$259$	6.13757e10			0.847515
$260$	−2.39121e10	−	2.39121e10i	−0.324517	−	0.324517i
$261$	−4.65270e10	+	4.65270e10i	−0.620616	+	0.620616i
$262$	6.12665e10	−	6.12665e10i	0.803281	−	0.803281i
$263$			1.13057e11i			1.45713i	0.684979	+	0.728563i	$0.259811\pi$
$263$			1.13057e11i			1.45713i	−0.684979	+	0.728563i	$0.740189\pi$
$264$			1.22103e10i			0.154706i
$265$	3.59879e10	−	3.59879e10i	0.448280	−	0.448280i
$266$	−3.78895e10	+	3.78895e10i	−0.464036	+	0.464036i
$267$	7.58461e8	+	7.58461e8i	0.00913340	+	0.00913340i
$268$	1.03992e11			1.23139
$269$	−4.44570e10	−	4.44570e10i	−0.517672	−	0.517672i	0.399194	−	0.916866i	$-0.369290\pi$
$269$	−4.44570e10	−	4.44570e10i	−0.517672	−	0.517672i	−0.916866	+	0.399194i	$0.869290\pi$
$270$			4.85013e10i			0.555413i
$271$	−3.81228e10			−0.429361			−0.214680	−	0.976684i	$-0.568871\pi$
$271$	−3.81228e10			−0.429361			−0.214680	+	0.976684i	$0.568871\pi$
$272$	−1.17431e11	+	2.47977e10i	−1.30083	+	0.274696i
$273$	2.14459e10			0.233675
$274$			7.41405e10i			0.794654i
$275$	1.14271e10	+	1.14271e10i	0.120487	+	0.120487i
$276$	−1.38276e11			−1.43435
$277$	7.67424e9	+	7.67424e9i	0.0783207	+	0.0783207i	0.745182	−	0.666861i	$-0.232363\pi$
$277$	7.67424e9	+	7.67424e9i	0.0783207	+	0.0783207i	−0.666861	+	0.745182i	$0.732363\pi$
$278$	−1.19910e11	+	1.19910e11i	−1.20408	+	1.20408i
$279$	1.19744e10	−	1.19744e10i	0.118314	−	0.118314i
$280$		−	1.24071e11i		−	1.20632i
$281$		−	1.39999e11i		−	1.33951i	−0.742583	−	0.669754i	$-0.766399\pi$
$281$		−	1.39999e11i		−	1.33951i	0.742583	−	0.669754i	$-0.233601\pi$
$282$	−7.84795e10	+	7.84795e10i	−0.738985	+	0.738985i
$283$	1.42229e10	−	1.42229e10i	0.131811	−	0.131811i	−0.638123	−	0.769934i	$-0.720289\pi$
$283$	1.42229e10	−	1.42229e10i	0.131811	−	0.131811i	0.769934	+	0.638123i	$0.220289\pi$
$284$	1.97923e11	+	1.97923e11i	1.80536	+	1.80536i
$285$	5.21160e9			0.0467917
$286$	1.44329e10	+	1.44329e10i	0.127558	+	0.127558i
$287$		−	1.61768e11i		−	1.40742i
$288$	−3.97793e10			−0.340715
$289$	1.08463e11	−	4.79462e10i	0.914622	−	0.404309i
$290$	−9.91054e10			−0.822823
$291$		−	2.67396e10i		−	0.218593i
$292$	7.44646e10	+	7.44646e10i	0.599414	+	0.599414i
$293$	7.89243e10			0.625614			0.312807	−	0.949817i	$-0.398731\pi$
$293$	7.89243e10			0.625614			0.312807	+	0.949817i	$0.398731\pi$
$294$	4.73346e10	+	4.73346e10i	0.369501	+	0.369501i
$295$	8.31121e10	−	8.31121e10i	0.638948	−	0.638948i
$296$	1.14757e11	−	1.14757e11i	0.868892	−	0.868892i
$297$		−	1.98496e10i		−	0.148029i
$298$			3.11797e11i			2.29034i
$299$	−8.58395e10	+	8.58395e10i	−0.621108	+	0.621108i
$300$	6.04500e10	−	6.04500e10i	0.430874	−	0.430874i
$301$	1.15897e11	+	1.15897e11i	0.813810	+	0.813810i
$302$	1.16792e11			0.807947
$303$	−4.32246e9	−	4.32246e9i	−0.0294604	−	0.0294604i
$304$			5.48305e10i			0.368206i
$305$	−1.13042e11			−0.747980
$306$	2.28833e11	−	4.83225e10i	1.49201	−	0.315067i
$307$	−1.70879e11			−1.09791			−0.548955	−	0.835852i	$-0.684974\pi$
$307$	−1.70879e11			−1.09791			−0.548955	+	0.835852i	$0.684974\pi$
$308$			9.66846e10i			0.612180i
$309$	−6.86064e10	−	6.86064e10i	−0.428106	−	0.428106i
$310$	2.55063e10			0.156863
$311$	−3.17813e10	−	3.17813e10i	−0.192642	−	0.192642i	0.604195	−	0.796837i	$-0.293495\pi$
$311$	−3.17813e10	−	3.17813e10i	−0.192642	−	0.192642i	−0.796837	+	0.604195i	$0.793495\pi$
$312$	4.00983e10	−	4.00983e10i	0.239569	−	0.239569i
$313$	−1.53809e11	+	1.53809e11i	−0.905801	+	0.905801i	−0.995930	−	0.0901289i	$-0.971272\pi$
$313$	−1.53809e11	+	1.53809e11i	−0.905801	+	0.905801i	0.0901289	+	0.995930i	$0.471272\pi$
$314$		−	3.58021e11i		−	2.07838i
$315$			9.35622e10i			0.535430i
$316$	−5.45539e10	+	5.45539e10i	−0.307775	+	0.307775i
$317$	1.95435e11	−	1.95435e11i	1.08702	−	1.08702i	0.0911809	−	0.995834i	$-0.470936\pi$
$317$	1.95435e11	−	1.95435e11i	1.08702	−	1.08702i	0.995834	−	0.0911809i	$-0.0290641\pi$
$318$	1.14908e11	+	1.14908e11i	0.630128	+	0.630128i
$319$	4.05598e10			0.219300
$320$	3.87963e10	+	3.87963e10i	0.206831	+	0.206831i
$321$		−	2.88578e10i		−	0.151702i
$322$	−8.48063e11			−4.39619
$323$	−1.11935e10	−	5.30071e10i	−0.0572207	−	0.270971i
$324$	2.56462e11			1.29291
$325$		−	7.50528e10i		−	0.373157i
$326$	−1.07259e10	−	1.07259e10i	−0.0525960	−	0.0525960i
$327$	−1.13397e11			−0.548448
$328$	−3.02464e11	−	3.02464e11i	−1.44292	−	1.44292i
$329$	−3.26363e11	+	3.26363e11i	−1.53575	+	1.53575i
$330$	9.80657e9	−	9.80657e9i	0.0455202	−	0.0455202i
$331$		−	6.29336e10i		−	0.288175i	−0.989565	−	0.144088i	$-0.953975\pi$
$331$		−	6.29336e10i		−	0.288175i	0.989565	−	0.144088i	$-0.0460247\pi$
$332$		−	6.57443e11i		−	2.96986i
$333$	−8.65380e10	+	8.65380e10i	−0.385663	+	0.385663i
$334$	−7.24712e10	+	7.24712e10i	−0.318644	+	0.318644i
$335$	−4.38638e10	−	4.38638e10i	−0.190285	−	0.190285i
$336$	1.53305e11			0.656192
$337$	2.57272e11	+	2.57272e11i	1.08657	+	1.08657i	0.995879	+	0.0906912i	$0.0289076\pi$
$337$	2.57272e11	+	2.57272e11i	1.08657	+	1.08657i	0.0906912	+	0.995879i	$0.471092\pi$
$338$			3.28100e11i			1.36735i
$339$	9.34177e10			0.384176
$340$	2.00147e11	+	1.30355e11i	0.812257	+	0.529021i
$341$	−1.04387e10			−0.0418072
$342$		−	1.06846e11i		−	0.422320i
$343$	−4.68649e10	−	4.68649e10i	−0.182820	−	0.182820i
$344$	4.33396e11			1.66867
$345$	5.83245e10	+	5.83245e10i	0.221649	+	0.221649i
$346$	−2.31118e11	+	2.31118e11i	−0.866946	+	0.866946i
$347$	1.40145e11	−	1.40145e11i	0.518915	−	0.518915i	−0.398328	−	0.917243i	$-0.630410\pi$
$347$	1.40145e11	−	1.40145e11i	0.518915	−	0.518915i	0.917243	+	0.398328i	$0.130410\pi$
$348$		−	2.14563e11i		−	0.784238i
$349$		−	4.56154e10i		−	0.164588i	−0.996608	−	0.0822939i	$-0.973775\pi$
$349$		−	4.56154e10i		−	0.164588i	0.996608	−	0.0822939i	$-0.0262246\pi$
$350$	3.70747e11	−	3.70747e11i	1.32060	−	1.32060i
$351$	−6.51855e10	+	6.51855e10i	−0.229229	+	0.229229i
$352$	1.73388e10	+	1.73388e10i	0.0601971	+	0.0601971i
$353$	−4.27533e11			−1.46549			−0.732747	−	0.680501i	$-0.761762\pi$
$353$	−4.27533e11			−1.46549			−0.732747	+	0.680501i	$0.761762\pi$
$354$	2.65374e11	+	2.65374e11i	0.898140	+	0.898140i
$355$		−	1.66966e11i		−	0.557958i
$356$	2.24583e10			0.0741057
$357$	−1.48207e11	+	3.12968e10i	−0.482906	+	0.101975i
$358$	2.64381e11			0.850661
$359$		−	1.25702e11i		−	0.399408i	−0.979856	−	0.199704i	$-0.936002\pi$
$359$		−	1.25702e11i		−	0.399408i	0.979856	−	0.199704i	$-0.0639981\pi$
$360$	1.74937e11	+	1.74937e11i	0.548936	+	0.548936i
$361$	2.97938e11			0.923301
$362$	−3.28178e11	−	3.28178e11i	−1.00443	−	1.00443i
$363$	8.18558e10	−	8.18558e10i	0.247440	−	0.247440i
$364$	3.17509e11	−	3.17509e11i	0.947983	−	0.947983i
$365$		−	6.28180e10i		−	0.185253i
$366$		−	3.60939e11i		−	1.05140i
$367$	−3.49368e11	+	3.49368e11i	−1.00528	+	1.00528i	−0.00529152	+	0.999986i	$0.501684\pi$
$367$	−3.49368e11	+	3.49368e11i	−1.00528	+	1.00528i	−0.999986	+	0.00529152i	$0.998316\pi$
$368$	−6.13623e11	+	6.13623e11i	−1.74416	+	1.74416i
$369$	2.28088e11	+	2.28088e11i	0.640448	+	0.640448i
$370$	−1.84331e11			−0.511318
$371$	4.77854e11	+	4.77854e11i	1.30952	+	1.30952i
$372$			5.52210e10i			0.149507i
$373$	2.93141e11			0.784128			0.392064	−	0.919938i	$-0.371761\pi$
$373$	2.93141e11			0.784128			0.392064	+	0.919938i	$0.371761\pi$
$374$	−1.20805e11	−	7.86799e10i	−0.319273	−	0.207942i
$375$	−1.15697e11			−0.302121
$376$			1.22043e12i			3.14896i
$377$	−1.33197e11	−	1.33197e11i	−0.339593	−	0.339593i
$378$	−6.44009e11			−1.62248
$379$	1.60491e11	+	1.60491e11i	0.399554	+	0.399554i	0.878076	−	0.478522i	$-0.158827\pi$
$379$	1.60491e11	+	1.60491e11i	0.399554	+	0.399554i	−0.478522	+	0.878076i	$0.658827\pi$
$380$	7.71586e10	−	7.71586e10i	0.189827	−	0.189827i
$381$	1.17700e11	−	1.17700e11i	0.286164	−	0.286164i
$382$			7.16107e11i			1.72065i
$383$			4.93526e10i			0.117197i	0.998282	+	0.0585984i	$0.0186631\pi$
$383$			4.93526e10i			0.117197i	−0.998282	+	0.0585984i	$0.981337\pi$
$384$	−1.67427e11	+	1.67427e11i	−0.392947	+	0.392947i
$385$	4.07813e10	−	4.07813e10i	0.0945993	−	0.0945993i
$386$	−5.41346e11	−	5.41346e11i	−1.24117	−	1.24117i
$387$	−3.26823e11			−0.740651
$388$	−3.95884e11	−	3.95884e11i	−0.886799	−	0.886799i
$389$			5.38311e11i			1.19196i	0.803001	+	0.595978i	$0.203235\pi$
$389$			5.38311e11i			1.19196i	−0.803001	+	0.595978i	$0.796765\pi$
$390$	−6.44090e10			−0.140979
$391$	4.67948e11	−	7.18486e11i	1.01252	−	1.55462i
$392$	7.36097e11			1.57452
$393$		−	1.11896e11i		−	0.236618i
$394$	−1.06758e11	−	1.06758e11i	−0.223187	−	0.223187i
$395$	4.60214e10			0.0951202
$396$	−1.36323e11	−	1.36323e11i	−0.278573	−	0.278573i
$397$	3.11125e11	−	3.11125e11i	0.628605	−	0.628605i	−0.319112	−	0.947717i	$-0.603385\pi$
$397$	3.11125e11	−	3.11125e11i	0.628605	−	0.628605i	0.947717	+	0.319112i	$0.103385\pi$
$398$	1.18060e11	−	1.18060e11i	0.235846	−	0.235846i
$399$			6.92006e10i			0.136688i
$400$		−	5.36514e11i		−	1.04788i
$401$	2.89079e11	−	2.89079e11i	0.558300	−	0.558300i	−0.370523	−	0.928823i	$-0.620822\pi$
$401$	2.89079e11	−	2.89079e11i	0.558300	−	0.558300i	0.928823	+	0.370523i	$0.120822\pi$
$402$	1.40056e11	−	1.40056e11i	0.267475	−	0.267475i
$403$	3.42804e10	+	3.42804e10i	0.0647400	+	0.0647400i
$404$	−1.27989e11			−0.239033
$405$	−1.08175e11	−	1.08175e11i	−0.199792	−	0.199792i
$406$		−	1.31594e12i		−	2.40364i
$407$	7.54393e10			0.136277
$408$	−2.18593e11	+	3.35627e11i	−0.390539	+	0.599633i
$409$	1.58089e11			0.279349			0.139674	−	0.990197i	$-0.455394\pi$
$409$	1.58089e11			0.279349			0.139674	+	0.990197i	$0.455394\pi$
$410$			4.85842e11i			0.849117i
$411$	6.77044e10	+	6.77044e10i	0.117039	+	0.117039i
$412$	−2.03146e12			−3.47352
$413$	1.10358e12	+	1.10358e12i	1.86650	+	1.86650i
$414$	1.19575e12	−	1.19575e12i	2.00050	−	2.00050i
$415$	−2.77308e11	+	2.77308e11i	−0.458929	+	0.458929i
$416$		−	1.13880e11i		−	0.186435i
$417$			2.19002e11i			0.354679i
$418$	−4.65715e10	+	4.65715e10i	−0.0746151	+	0.0746151i
$419$	−2.62019e10	+	2.62019e10i	−0.0415308	+	0.0415308i	−0.727567	−	0.686036i	$-0.759349\pi$
$419$	−2.62019e10	+	2.62019e10i	−0.0415308	+	0.0415308i	0.686036	+	0.727567i	$0.259349\pi$
$420$	−2.15735e11	−	2.15735e11i	−0.338297	−	0.338297i
$421$	−1.15949e12			−1.79887			−0.899433	−	0.437059i	$-0.856020\pi$
$421$	−1.15949e12			−1.79887			−0.899433	+	0.437059i	$0.856020\pi$
$422$	8.89931e11	+	8.89931e11i	1.36600	+	1.36600i
$423$		−	9.20326e11i		−	1.39769i
$424$	1.78693e12			2.68510
$425$	1.09528e11	+	5.18672e11i	0.162845	+	0.771157i
$426$	5.33118e11			0.784297
$427$		−	1.50099e12i		−	2.18501i
$428$	−4.27245e11	−	4.27245e11i	−0.615431	−	0.615431i
$429$	2.63600e10			0.0375740
$430$	−3.48077e11	−	3.48077e11i	−0.490984	−	0.490984i
$431$	−4.97835e11	+	4.97835e11i	−0.694924	+	0.694924i	−0.963311	−	0.268387i	$-0.913509\pi$
$431$	−4.97835e11	+	4.97835e11i	−0.694924	+	0.694924i	0.268387	+	0.963311i	$0.413509\pi$
$432$	−4.65978e11	+	4.65978e11i	−0.643707	+	0.643707i
$433$			5.00556e11i			0.684317i	0.939642	+	0.342159i	$0.111158\pi$
$433$			5.00556e11i			0.684317i	−0.939642	+	0.342159i	$0.888842\pi$
$434$			3.38677e11i			0.458229i
$435$	−9.05021e10	+	9.05021e10i	−0.121187	+	0.121187i
$436$	−1.67886e12	+	1.67886e12i	−2.22497	+	2.22497i
$437$	−2.76984e11	−	2.76984e11i	−0.363319	−	0.363319i
$438$	2.00576e11			0.260402
$439$	−6.62950e11	−	6.62950e11i	−0.851904	−	0.851904i	0.138464	−	0.990368i	$-0.455784\pi$
$439$	−6.62950e11	−	6.62950e11i	−0.851904	−	0.851904i	−0.990368	+	0.138464i	$0.955784\pi$
$440$		−	1.52501e11i		−	0.193971i
$441$	−5.55090e11			−0.698860
$442$	1.38337e11	+	6.55102e11i	0.172401	+	0.816411i
$443$	−9.51595e11			−1.17391			−0.586956	−	0.809619i	$-0.699674\pi$
$443$	−9.51595e11			−1.17391			−0.586956	+	0.809619i	$0.699674\pi$
$444$		−	3.99077e11i		−	0.487341i
$445$	−9.47285e9	−	9.47285e9i	−0.0114515	−	0.0114515i
$446$	7.11367e11			0.851308
$447$	2.84730e11	+	2.84730e11i	0.337326	+	0.337326i
$448$	−5.15145e11	+	5.15145e11i	−0.604197	+	0.604197i
$449$	−2.69198e11	+	2.69198e11i	−0.312581	+	0.312581i	−0.845909	−	0.533328i	$-0.820941\pi$
$449$	−2.69198e11	+	2.69198e11i	−0.312581	+	0.312581i	0.533328	+	0.845909i	$0.320941\pi$
$450$			1.04549e12i			1.20188i
$451$		−	1.98835e11i		−	0.226308i
$452$	1.38306e12	−	1.38306e12i	1.55855	−	1.55855i
$453$	1.06654e11	−	1.06654e11i	0.118996	−	0.118996i
$454$	4.02426e11	+	4.02426e11i	0.444565	+	0.444565i
$455$	−2.67849e11			−0.292981
$456$	1.29387e11	+	1.29387e11i	0.140136	+	0.140136i
$457$			3.50653e11i			0.376058i	0.982164	+	0.188029i	$0.0602098\pi$
$457$			3.50653e11i			0.376058i	−0.982164	+	0.188029i	$0.939790\pi$
$458$	2.02294e12			2.14827
$459$	3.55354e11	−	5.45610e11i	0.373683	−	0.573753i
$460$	1.72701e12			1.79839
$461$			3.47127e11i			0.357959i	0.983853	+	0.178980i	$0.0572796\pi$
$461$			3.47127e11i			0.357959i	−0.983853	+	0.178980i	$0.942720\pi$
$462$	1.30213e11	+	1.30213e11i	0.132974	+	0.132974i
$463$	7.28682e11			0.736926			0.368463	−	0.929642i	$-0.379884\pi$
$463$	7.28682e11			0.736926			0.368463	+	0.929642i	$0.379884\pi$
$464$	−9.52159e11	−	9.52159e11i	−0.953627	−	0.953627i
$465$	2.32921e10	−	2.32921e10i	0.0231031	−	0.0231031i
$466$	−2.05895e12	+	2.05895e12i	−2.02260	+	2.02260i
$467$			7.42744e11i			0.722625i	0.932445	+	0.361313i	$0.117671\pi$
$467$			7.42744e11i			0.722625i	−0.932445	+	0.361313i	$0.882329\pi$
$468$			8.95360e11i			0.862762i
$469$	5.82432e11	−	5.82432e11i	0.555862	−	0.555862i
$470$	9.80176e11	−	9.80176e11i	0.926539	−	0.926539i
$471$	−3.26941e11	−	3.26941e11i	−0.306109	−	0.306109i
$472$	4.12682e12			3.82716
$473$	1.42454e11	+	1.42454e11i	0.130858	+	0.130858i
$474$			1.46945e11i			0.133706i
$475$	2.42177e11			0.218279
$476$	−1.73088e12	+	2.65759e12i	−1.54538	+	2.37277i
$477$	−1.34752e12			−1.19180
$478$		−	7.63098e11i		−	0.668582i
$479$	−1.56264e12	−	1.56264e12i	−1.35628	−	1.35628i	−0.878460	−	0.477816i	$-0.841428\pi$
$479$	−1.56264e12	−	1.56264e12i	−1.35628	−	1.35628i	−0.477816	−	0.878460i	$-0.658572\pi$
$480$	−7.73768e10			−0.0665312
$481$	−2.47741e11	−	2.47741e11i	−0.211030	−	0.211030i
$482$	−5.77505e11	+	5.77505e11i	−0.487354	+	0.487354i
$483$	−7.74443e11	+	7.74443e11i	−0.647482	+	0.647482i
$484$		−	2.42378e12i		−	2.00765i
$485$			3.33966e11i			0.274072i
$486$	1.39485e12	−	1.39485e12i	1.13414	−	1.13414i
$487$	1.63344e12	−	1.63344e12i	1.31590	−	1.31590i	0.398913	−	0.916989i	$-0.369388\pi$
$487$	1.63344e12	−	1.63344e12i	1.31590	−	1.31590i	0.916989	−	0.398913i	$-0.130612\pi$
$488$	−2.80647e12	−	2.80647e12i	−2.24012	−	2.24012i
$489$	−1.95895e10			−0.0154929
$490$	−5.91188e11	−	5.91188e11i	−0.463280	−	0.463280i
$491$		−	1.20022e12i		−	0.931950i	−0.884798	−	0.465975i	$-0.845704\pi$
$491$		−	1.20022e12i		−	0.931950i	0.884798	−	0.465975i	$-0.154296\pi$
$492$	−1.05185e12			−0.809299
$493$	1.11487e12	+	7.26115e11i	0.849992	+	0.553597i
$494$	3.05879e11			0.231089
$495$			1.15001e11i			0.0860952i
$496$	2.45053e11	+	2.45053e11i	0.181799	+	0.181799i
$497$	2.21701e12			1.62991
$498$	−8.85435e11	−	8.85435e11i	−0.645096	−	0.645096i
$499$	−9.29738e11	+	9.29738e11i	−0.671287	+	0.671287i	−0.958013	−	0.286726i	$-0.907433\pi$
$499$	−9.29738e11	+	9.29738e11i	−0.671287	+	0.671287i	0.286726	+	0.958013i	$0.407433\pi$
$500$	−1.71291e12	+	1.71291e12i	−1.22566	+	1.22566i
$501$			1.32360e11i			0.0938614i
$502$			2.17755e12i			1.53038i
$503$	−7.51636e11	+	7.51636e11i	−0.523542	+	0.523542i	−0.918639	−	0.395097i	$-0.870711\pi$
$503$	−7.51636e11	+	7.51636e11i	−0.523542	+	0.523542i	0.395097	+	0.918639i	$0.370711\pi$
$504$	−2.32285e12	+	2.32285e12i	−1.60356	+	1.60356i
$505$	5.39856e10	+	5.39856e10i	0.0369374	+	0.0369374i
$506$	−1.04239e12			−0.706891
$507$	2.99618e11	+	2.99618e11i	0.201387	+	0.201387i
$508$		−	3.48515e12i		−	2.32185i
$509$	−7.45127e10			−0.0492040			−0.0246020	−	0.999697i	$-0.507832\pi$
$509$	−7.45127e10			−0.0492040			−0.0246020	+	0.999697i	$0.507832\pi$
$510$	4.45115e11	−	9.39946e10i	0.291344	−	0.0615230i
$511$	8.34109e11			0.541164
$512$			3.21594e12i			2.06821i
$513$	−2.10338e11	−	2.10338e11i	−0.134088	−	0.134088i
$514$	−1.62411e12			−1.02632
$515$	8.56864e11	+	8.56864e11i	0.536759	+	0.536759i
$516$	7.53585e11	−	7.53585e11i	0.467960	−	0.467960i
$517$	−4.01146e11	+	4.01146e11i	−0.246942	+	0.246942i
$518$		−	2.44759e12i		−	1.49367i
$519$			4.22110e11i			0.255372i
$520$	−5.00810e11	+	5.00810e11i	−0.300371	+	0.300371i
$521$	1.14066e12	−	1.14066e12i	0.678244	−	0.678244i	−0.281359	−	0.959603i	$-0.590785\pi$
$521$	1.14066e12	−	1.14066e12i	0.678244	−	0.678244i	0.959603	+	0.281359i	$0.0907850\pi$
$522$	1.85544e12	+	1.85544e12i	1.09378	+	1.09378i
$523$	2.14308e12			1.25251			0.626255	−	0.779619i	$-0.284587\pi$
$523$	2.14308e12			1.25251			0.626255	+	0.779619i	$0.284587\pi$
$524$	−1.65664e12	−	1.65664e12i	−0.959925	−	0.959925i
$525$		−	6.77125e11i		−	0.389002i
$526$	4.50858e12			2.56805
$527$	−2.86930e11	−	1.86877e11i	−0.162042	−	0.105538i
$528$	1.88434e11			0.105513
$529$		−	4.39845e12i		−	2.44202i
$530$	−1.43515e12	−	1.43515e12i	−0.790054	−	0.790054i
$531$	−3.11203e12			−1.69871
$532$	1.02453e12	+	1.02453e12i	0.554525	+	0.554525i
$533$	−6.52970e11	+	6.52970e11i	−0.350445	+	0.350445i
$534$	3.02465e10	−	3.02465e10i	0.0160968	−	0.0160968i
$535$			3.60422e11i			0.190204i
$536$		−	2.17800e12i		−	1.13977i
$537$	2.41430e11	−	2.41430e11i	0.125287	−	0.125287i
$538$	−1.77289e12	+	1.77289e12i	−0.912351	+	0.912351i
$539$	2.41949e11	+	2.41949e11i	0.123474	+	0.123474i
$540$	1.31147e12			0.663721
$541$	8.05895e11	+	8.05895e11i	0.404474	+	0.404474i	0.879806	−	0.475332i	$-0.157672\pi$
$541$	8.05895e11	+	8.05895e11i	0.404474	+	0.404474i	−0.475332	+	0.879806i	$0.657672\pi$
$542$			1.52029e12i			0.756710i
$543$	−5.99378e11			−0.295870
$544$	1.66190e11	+	7.86998e11i	0.0813596	+	0.385282i
$545$	1.41628e12			0.687644
$546$		−	8.55234e11i		−	0.411830i
$547$	2.11967e12	+	2.11967e12i	1.01234	+	1.01234i	0.999923	+	0.0124141i	$0.00395164\pi$
$547$	2.11967e12	+	2.11967e12i	1.01234	+	1.01234i	0.0124141	+	0.999923i	$0.496048\pi$
$548$	2.00475e12			0.949616
$549$	2.11636e12	+	2.11636e12i	0.994290	+	0.994290i
$550$	4.55700e11	−	4.55700e11i	0.212348	−	0.212348i
$551$	4.29795e11	−	4.29795e11i	0.198646	−	0.198646i
$552$			2.89602e12i			1.32763i
$553$			6.11081e11i			0.277866i
$554$	3.06039e11	−	3.06039e11i	0.138033	−	0.138033i
$555$	−1.68330e11	+	1.68330e11i	−0.0753082	+	0.0753082i
$556$	3.24236e12	+	3.24236e12i	1.43888	+	1.43888i
$557$	−3.34785e12			−1.47373			−0.736864	−	0.676041i	$-0.763694\pi$
$557$	−3.34785e12			−1.47373			−0.736864	+	0.676041i	$0.763694\pi$
$558$	−4.77526e11	−	4.77526e11i	−0.208518	−	0.208518i
$559$		−	9.35628e11i		−	0.405275i
$560$	−1.91472e12			−0.822733
$561$	−1.82168e11	+	3.84682e10i	−0.0776494	+	0.0163972i
$562$	−5.58298e12			−2.36076
$563$			1.26601e12i			0.531066i	0.964102	+	0.265533i	$0.0855478\pi$
$563$			1.26601e12i			0.531066i	−0.964102	+	0.265533i	$0.914452\pi$
$564$	2.12208e12	+	2.12208e12i	0.883090	+	0.883090i
$565$	−1.16675e12			−0.481680
$566$	−5.67193e11	−	5.67193e11i	−0.232304	−	0.232304i
$567$	1.43637e12	−	1.43637e12i	0.583635	−	0.583635i
$568$	4.14525e12	−	4.14525e12i	1.67102	−	1.67102i
$569$			2.28842e12i			0.915230i	0.889150	+	0.457615i	$0.151296\pi$
$569$			2.28842e12i			0.915230i	−0.889150	+	0.457615i	$0.848704\pi$
$570$		−	2.07832e11i		−	0.0824662i
$571$	−2.21334e12	+	2.21334e12i	−0.871336	+	0.871336i	−0.992618	−	0.121282i	$-0.961299\pi$
$571$	−2.21334e12	+	2.21334e12i	−0.871336	+	0.871336i	0.121282	+	0.992618i	$0.461299\pi$
$572$	3.90264e11	−	3.90264e11i	0.152432	−	0.152432i
$573$	6.53942e11	+	6.53942e11i	0.253421	+	0.253421i
$574$	−6.45110e12			−2.48045
$575$	2.71027e12	+	2.71027e12i	1.03397	+	1.03397i
$576$		−	1.45268e12i		−	0.549882i
$577$	−3.70965e12			−1.39329			−0.696646	−	0.717415i	$-0.745325\pi$
$577$	−3.70965e12			−1.39329			−0.696646	+	0.717415i	$0.745325\pi$
$578$	−1.91204e12	−	4.32538e12i	−0.712559	−	1.61194i
$579$	−9.88705e11			−0.365606
$580$			2.67980e12i			0.983277i
$581$	−3.68215e12	−	3.68215e12i	−1.34063	−	1.34063i
$582$	−1.06634e12			−0.385250
$583$	5.87349e11	+	5.87349e11i	0.210566	+	0.210566i
$584$	1.55957e12	−	1.55957e12i	0.554814	−	0.554814i
$585$	3.77660e11	−	3.77660e11i	0.133321	−	0.133321i
$586$		−	3.14740e12i		−	1.10259i
$587$		−	6.72633e11i		−	0.233833i	−0.993142	−	0.116917i	$-0.962699\pi$
$587$		−	6.72633e11i		−	0.233833i	0.993142	−	0.116917i	$-0.0373011\pi$
$588$	1.27992e12	−	1.27992e12i	0.441555	−	0.441555i
$589$	−1.10614e11	+	1.10614e11i	−0.0378698	+	0.0378698i
$590$	−3.31441e12	−	3.31441e12i	−1.12609	−	1.12609i
$591$	−1.94982e11			−0.0657431
$592$	−1.77097e12	−	1.77097e12i	−0.592603	−	0.592603i
$593$			4.60461e12i			1.52914i	0.644542	+	0.764569i	$0.277048\pi$
$593$			4.60461e12i			1.52914i	−0.644542	+	0.764569i	$0.722952\pi$
$594$	−7.91577e11			−0.260888
$595$	1.85104e12	−	3.90884e11i	0.605467	−	0.127856i
$596$	8.43096e12			2.73696
$597$		−	2.15622e11i		−	0.0694719i
$598$	3.42318e12	+	3.42318e12i	1.09465	+	1.09465i
$599$	1.27742e12			0.405429			0.202714	−	0.979238i	$-0.435024\pi$
$599$	1.27742e12			0.405429			0.202714	+	0.979238i	$0.435024\pi$
$600$	−1.26605e12	−	1.26605e12i	−0.398814	−	0.398814i
$601$	7.44744e11	−	7.44744e11i	0.232848	−	0.232848i	−0.581033	−	0.813880i	$-0.697351\pi$
$601$	7.44744e11	−	7.44744e11i	0.232848	−	0.232848i	0.813880	+	0.581033i	$0.197351\pi$
$602$	4.62183e12	−	4.62183e12i	1.43427	−	1.43427i
$603$			1.64243e12i			0.505892i
$604$		−	3.15805e12i		−	0.965501i
$605$	−1.02234e12	+	1.02234e12i	−0.310240	+	0.310240i
$606$	−1.72374e11	+	1.72374e11i	−0.0519213	+	0.0519213i
$607$	−2.98225e12	−	2.98225e12i	−0.891651	−	0.891651i	0.103027	−	0.994679i	$-0.467147\pi$
$607$	−2.98225e12	−	2.98225e12i	−0.891651	−	0.891651i	−0.994679	+	0.103027i	$0.967147\pi$
$608$	3.67463e11			0.109056
$609$	−1.20170e12	−	1.20170e12i	−0.354013	−	0.354013i
$610$			4.50797e12i			1.31825i
$611$	2.63470e12			0.764797
$612$	−1.30663e12	−	6.18762e12i	−0.376507	−	1.78296i
$613$	1.28630e12			0.367933			0.183967	−	0.982932i	$-0.441106\pi$
$613$	1.28630e12			0.367933			0.183967	+	0.982932i	$0.441106\pi$
$614$			6.81446e12i			1.93497i
$615$	4.43666e11	+	4.43666e11i	0.125060	+	0.125060i
$616$	2.02494e12			0.566630
$617$	7.33066e11	+	7.33066e11i	0.203639	+	0.203639i	0.801557	−	0.597918i	$-0.204005\pi$
$617$	7.33066e11	+	7.33066e11i	0.203639	+	0.203639i	−0.597918	+	0.801557i	$0.704005\pi$
$618$	−2.73594e12	+	2.73594e12i	−0.754498	+	0.754498i
$619$	1.42675e11	−	1.42675e11i	0.0390607	−	0.0390607i	−0.687307	−	0.726367i	$-0.741207\pi$
$619$	1.42675e11	−	1.42675e11i	0.0390607	−	0.0390607i	0.726367	+	0.687307i	$0.241207\pi$
$620$		−	6.89687e11i		−	0.187452i
$621$		−	4.70790e12i		−	1.27033i
$622$	−1.26740e12	+	1.26740e12i	−0.339513	+	0.339513i
$623$	1.25782e11	−	1.25782e11i	0.0334521	−	0.0334521i
$624$	−6.18812e11	−	6.18812e11i	−0.163391	−	0.163391i
$625$	−1.56160e12			−0.409365
$626$	6.13372e12	+	6.13372e12i	1.59639	+	1.59639i
$627$			8.50573e10i			0.0219790i
$628$	−9.68085e12			−2.48368
$629$	2.07362e12	+	1.35054e12i	0.528202	+	0.344016i
$630$	3.73115e12			0.943648
$631$		−	2.26379e12i		−	0.568466i	−0.958755	−	0.284233i	$-0.908261\pi$
$631$		−	2.26379e12i		−	0.568466i	0.958755	−	0.284233i	$-0.0917390\pi$
$632$	1.14256e12	+	1.14256e12i	0.284875	+	0.284875i
$633$	1.62535e12			0.402375
$634$	−7.79371e12	−	7.79371e12i	−1.91577	−	1.91577i
$635$	−1.47003e12	+	1.47003e12i	−0.358792	+	0.358792i
$636$	3.10710e12	−	3.10710e12i	0.753005	−	0.753005i
$637$		−	1.58911e12i		−	0.382407i
$638$		−	1.61748e12i		−	0.386496i
$639$	−3.12593e12	+	3.12593e12i	−0.741695	+	0.741695i
$640$	2.09109e12	−	2.09109e12i	0.492677	−	0.492677i
$641$	−4.10388e12	−	4.10388e12i	−0.960138	−	0.960138i	0.0390975	−	0.999235i	$-0.487552\pi$
$641$	−4.10388e12	−	4.10388e12i	−0.960138	−	0.960138i	−0.999235	+	0.0390975i	$0.987552\pi$
$642$	−1.15081e12			−0.267361
$643$	4.15703e12	+	4.15703e12i	0.959035	+	0.959035i	0.999193	−	0.0401588i	$-0.0127864\pi$
$643$	4.15703e12	+	4.15703e12i	0.959035	+	0.959035i	−0.0401588	+	0.999193i	$0.512786\pi$
$644$			2.29315e13i			5.25347i
$645$	−6.35721e11			−0.144626
$646$	−2.11386e12	+	4.46382e11i	−0.477562	+	0.100846i
$647$	−7.10089e12			−1.59310			−0.796551	−	0.604572i	$-0.793344\pi$
$647$	−7.10089e12			−1.59310			−0.796551	+	0.604572i	$0.793344\pi$
$648$		−	5.37128e12i		−	1.19671i
$649$	1.35645e12	+	1.35645e12i	0.300126	+	0.300126i
$650$	−2.99301e12			−0.657656
$651$	3.09277e11	+	3.09277e11i	0.0674890	+	0.0674890i
$652$	−2.90026e11	+	2.90026e11i	−0.0628525	+	0.0628525i
$653$	4.94436e12	−	4.94436e12i	1.06415	−	1.06415i	0.0663486	−	0.997797i	$-0.478865\pi$
$653$	4.94436e12	−	4.94436e12i	1.06415	−	1.06415i	0.997797	−	0.0663486i	$-0.0211349\pi$
$654$			4.52212e12i			0.966590i
$655$			1.39753e12i			0.296672i
$656$	−4.66775e12	+	4.66775e12i	−0.984102	+	0.984102i
$657$	−1.17607e12	+	1.17607e12i	−0.246258	+	0.246258i
$658$	1.30150e13	+	1.30150e13i	2.70661	+	2.70661i
$659$	4.88819e12			1.00963			0.504817	−	0.863226i	$-0.331560\pi$
$659$	4.88819e12			1.00963			0.504817	+	0.863226i	$0.331560\pi$
$660$	−2.65168e11	−	2.65168e11i	−0.0543969	−	0.0543969i
$661$		−	8.25354e12i		−	1.68164i	−0.541312	−	0.840822i	$-0.682072\pi$
$661$		−	8.25354e12i		−	1.68164i	0.541312	−	0.840822i	$-0.317928\pi$
$662$	−2.50971e12			−0.507883
$663$	7.24562e11	+	4.71905e11i	0.145635	+	0.0948513i
$664$	−1.37693e13			−2.74889
$665$		−	8.64286e11i		−	0.171380i
$666$	3.45103e12	+	3.45103e12i	0.679696	+	0.679696i
$667$	9.61992e12			1.88194
$668$	1.95961e12	+	1.95961e12i	0.380782	+	0.380782i
$669$	6.49613e11	−	6.49613e11i	0.125383	−	0.125383i
$670$	−1.74923e12	+	1.74923e12i	−0.335360	+	0.335360i
$671$		−	1.84493e12i		−	0.351341i
$672$		−	1.02742e12i		−	0.194351i
$673$	1.58047e12	−	1.58047e12i	0.296974	−	0.296974i	−0.542854	−	0.839827i	$-0.682656\pi$
$673$	1.58047e12	−	1.58047e12i	0.296974	−	0.296974i	0.839827	+	0.542854i	$0.182656\pi$
$674$	1.02597e13	−	1.02597e13i	1.91498	−	1.91498i
$675$	2.05815e12	+	2.05815e12i	0.381601	+	0.381601i
$676$	8.87178e12			1.63400
$677$	−6.59712e12	−	6.59712e12i	−1.20699	−	1.20699i	−0.971996	−	0.234998i	$-0.924491\pi$
$677$	−6.59712e12	−	6.59712e12i	−1.20699	−	1.20699i	−0.234998	−	0.971996i	$-0.575509\pi$
$678$		−	3.72538e12i		−	0.677076i
$679$	−4.43446e12			−0.800621
$680$	2.73013e12	−	4.19183e12i	0.489658	−	0.751820i
$681$	7.34983e11			0.130953
$682$			4.16282e11i			0.0736815i
$683$	−1.50905e11	−	1.50905e11i	−0.0265344	−	0.0265344i	0.693715	−	0.720250i	$-0.255973\pi$
$683$	−1.50905e11	−	1.50905e11i	−0.0265344	−	0.0265344i	−0.720250	+	0.693715i	$0.755973\pi$
$684$	−2.88911e12			−0.504675
$685$	−8.45599e11	−	8.45599e11i	−0.146743	−	0.146743i
$686$	−1.86891e12	+	1.86891e12i	−0.322204	+	0.322204i
$687$	1.84733e12	−	1.84733e12i	0.316402	−	0.316402i
$688$		−	6.68833e12i		−	1.13807i
$689$		−	3.85768e12i		−	0.652138i
$690$	2.32591e12	−	2.32591e12i	0.390636	−	0.390636i
$691$	−6.18683e12	+	6.18683e12i	−1.03233	+	1.03233i	−0.0328672	+	0.999460i	$0.510464\pi$
$691$	−6.18683e12	+	6.18683e12i	−1.03233	+	1.03233i	−0.999460	+	0.0328672i	$0.989536\pi$
$692$	6.24941e12	+	6.24941e12i	1.03601	+	1.03601i
$693$	−1.52701e12			−0.251502
$694$	−5.58882e12	−	5.58882e12i	−0.914540	−	0.914540i
$695$		−	2.73524e12i		−	0.444696i
$696$	−4.49376e12			−0.725885
$697$	3.55961e12	−	5.46542e12i	0.571288	−	0.877155i
$698$	−1.81909e12			−0.290071
$699$			3.76043e12i			0.595785i
$700$	−1.00250e13	−	1.00250e13i	−1.57812	−	1.57812i
$701$	−1.57028e12			−0.245610			−0.122805	−	0.992431i	$-0.539189\pi$
$701$	−1.57028e12			−0.245610			−0.122805	+	0.992431i	$0.539189\pi$
$702$	2.59952e12	+	2.59952e12i	0.403995	+	0.403995i
$703$	7.99399e11	−	7.99399e11i	0.123443	−	0.123443i
$704$	−6.33186e11	+	6.33186e11i	−0.0971526	+	0.0971526i
$705$		−	1.79017e12i		−	0.272926i
$706$			1.70495e13i			2.58280i
$707$	−7.16831e11	+	7.16831e11i	−0.107902	+	0.107902i
$708$	7.17569e12	−	7.17569e12i	1.07328	−	1.07328i
$709$	7.32896e12	+	7.32896e12i	1.08927	+	1.08927i	0.995604	+	0.0936633i	$0.0298577\pi$
$709$	7.32896e12	+	7.32896e12i	1.08927	+	1.08927i	0.0936633	+	0.995604i	$0.470142\pi$
$710$	−6.65842e12			−0.983351
$711$	−8.61607e11	−	8.61607e11i	−0.126443	−	0.126443i
$712$		−	4.70362e11i		−	0.0685917i
$713$	−2.47583e12			−0.358772
$714$	1.24808e12	+	5.91033e12i	0.179722	+	0.851078i
$715$	−3.29225e11			−0.0471102
$716$		−	7.14883e12i		−	1.01654i
$717$	−6.96854e11	−	6.96854e11i	−0.0984703	−	0.0984703i
$718$	−5.01284e12			−0.703921
$719$	−3.46074e12	−	3.46074e12i	−0.482936	−	0.482936i	0.423132	−	0.906068i	$-0.360931\pi$
$719$	−3.46074e12	−	3.46074e12i	−0.482936	−	0.482936i	−0.906068	+	0.423132i	$0.860931\pi$
$720$	2.69970e12	−	2.69970e12i	0.374386	−	0.374386i
$721$	−1.13776e13	+	1.13776e13i	−1.56799	+	1.56799i
$722$		−	1.18814e13i		−	1.62723i
$723$			1.05474e12i			0.143557i
$724$	−8.87389e12	+	8.87389e12i	−1.20030	+	1.20030i
$725$	−4.20553e12	+	4.20553e12i	−0.565327	+	0.565327i
$726$	−3.26431e12	−	3.26431e12i	−0.436090	−	0.436090i
$727$	6.39882e12			0.849562			0.424781	−	0.905296i	$-0.360351\pi$
$727$	6.39882e12			0.849562			0.424781	+	0.905296i	$0.360351\pi$
$728$	−6.64985e12	−	6.64985e12i	−0.877446	−	0.877446i
$729$			2.13377e12i			0.279817i
$730$	−2.50510e12			−0.326492
$731$	1.36540e12	+	6.46591e12i	0.176861	+	0.837532i
$732$	−9.75974e12			−1.25643
$733$			7.38435e12i			0.944809i	0.881382	+	0.472405i	$0.156614\pi$
$733$			7.38435e12i			0.944809i	−0.881382	+	0.472405i	$0.843386\pi$
$734$	1.39324e13	+	1.39324e13i	1.77171	+	1.77171i
$735$	−1.07974e12			−0.136466
$736$	4.11238e12	+	4.11238e12i	0.516587	+	0.516587i
$737$	7.15890e11	−	7.15890e11i	0.0893805	−	0.0893805i
$738$	9.09588e12	−	9.09588e12i	1.12873	−	1.12873i
$739$		−	5.40480e12i		−	0.666622i	−0.942817	−	0.333311i	$-0.891834\pi$
$739$		−	5.40480e12i		−	0.666622i	0.942817	−	0.333311i	$-0.108166\pi$
$740$			4.98430e12i			0.611028i
$741$	2.79326e11	−	2.79326e11i	0.0340353	−	0.0340353i
$742$	1.90562e13	−	1.90562e13i	2.30791	−	2.30791i
$743$	−3.78121e12	−	3.78121e12i	−0.455178	−	0.455178i	0.441891	−	0.897069i	$-0.354308\pi$
$743$	−3.78121e12	−	3.78121e12i	−0.455178	−	0.455178i	−0.897069	+	0.441891i	$0.854308\pi$
$744$	1.15654e12			0.138383
$745$	−3.55616e12	−	3.55616e12i	−0.422939	−	0.422939i
$746$		−	1.16901e13i		−	1.38196i
$747$	1.03835e13			1.22011
$748$	−2.12749e12	+	3.26655e12i	−0.248491	+	0.381533i
$749$	−4.78575e12			−0.555625
$750$			4.61385e12i			0.532460i
$751$	−6.84159e12	−	6.84159e12i	−0.784833	−	0.784833i	0.195809	−	0.980642i	$-0.437267\pi$
$751$	−6.84159e12	−	6.84159e12i	−0.784833	−	0.784833i	−0.980642	+	0.195809i	$0.937267\pi$
$752$	1.88342e13			2.14766
$753$	1.98851e12	+	1.98851e12i	0.225399	+	0.225399i
$754$	−5.31174e12	+	5.31174e12i	−0.598503	+	0.598503i
$755$	−1.33206e12	+	1.33206e12i	−0.149198	+	0.149198i
$756$			1.74139e13i			1.93887i
$757$			6.07681e11i			0.0672581i	0.999434	+	0.0336290i	$0.0107065\pi$
$757$			6.07681e11i			0.0672581i	−0.999434	+	0.0336290i	$0.989294\pi$
$758$	6.40020e12	−	6.40020e12i	0.704177	−	0.704177i
$759$	−9.51900e11	+	9.51900e11i	−0.104113	+	0.104113i
$760$	−1.61599e12	−	1.61599e12i	−0.175703	−	0.175703i
$761$	6.43550e12			0.695587			0.347794	−	0.937571i	$-0.386931\pi$
$761$	6.43550e12			0.695587			0.347794	+	0.937571i	$0.386931\pi$
$762$	−4.69375e12	−	4.69375e12i	−0.504339	−	0.504339i
$763$			1.88056e13i			2.00875i
$764$	1.93634e13			2.05619
$765$	−2.05879e12	+	3.16106e12i	−0.217338	+	0.333700i
$766$	1.96812e12			0.206549
$767$		−	8.90911e12i		−	0.929512i
$768$	5.08634e12	+	5.08634e12i	0.527570	+	0.527570i
$769$	6.57512e12			0.678008			0.339004	−	0.940785i	$-0.389910\pi$
$769$	6.57512e12			0.678008			0.339004	+	0.940785i	$0.389910\pi$
$770$	−1.62631e12	−	1.62631e12i	−0.166723	−	0.166723i
$771$	−1.48313e12	+	1.48313e12i	−0.151159	+	0.151159i
$772$	−1.46379e13	+	1.46379e13i	−1.48321	+	1.48321i
$773$			1.56803e12i			0.157959i	0.996876	+	0.0789797i	$0.0251662\pi$
$773$			1.56803e12i			0.157959i	−0.996876	+	0.0789797i	$0.974834\pi$
$774$			1.30333e13i			1.30533i
$775$	1.08236e12	−	1.08236e12i	0.107774	−	0.107774i
$776$	−8.29131e12	+	8.29131e12i	−0.820815	+	0.820815i
$777$	−2.23511e12	−	2.23511e12i	−0.219991	−	0.219991i
$778$	2.14672e13			2.10072
$779$	−2.10698e12	−	2.10698e12i	−0.204994	−	0.204994i
$780$			1.74161e12i			0.168471i
$781$	2.72502e12			0.262084
$782$	−2.86524e13	−	1.86612e13i	−2.73987	−	1.78447i
$783$	7.30525e12			0.694556
$784$		−	1.13597e13i		−	1.07386i
$785$	4.08336e12	+	4.08336e12i	0.383799	+	0.383799i
$786$	−4.46228e12			−0.417018
$787$	1.20869e13	+	1.20869e13i	1.12312	+	1.12312i	0.991269	+	0.131854i	$0.0420929\pi$
$787$	1.20869e13	+	1.20869e13i	1.12312	+	1.12312i	0.131854	+	0.991269i	$0.457907\pi$
$788$	−2.88674e12	+	2.88674e12i	−0.266710	+	0.266710i
$789$	4.11719e12	−	4.11719e12i	0.378229	−	0.378229i
$790$		−	1.83528e12i		−	0.167641i
$791$		−	1.54923e13i		−	1.40709i
$792$	−2.85511e12	+	2.85511e12i	−0.257846	+	0.257846i
$793$	−6.05869e12	+	6.05869e12i	−0.544064	+	0.544064i
$794$	−1.24073e13	−	1.24073e13i	−1.10786	−	1.10786i
$795$	−2.62113e12			−0.232722
$796$	−3.19233e12	−	3.19233e12i	−0.281837	−	0.281837i
$797$			2.49661e12i			0.219174i	0.993977	+	0.109587i	$0.0349528\pi$
$797$			2.49661e12i			0.219174i	−0.993977	+	0.109587i	$0.965047\pi$
$798$	2.75964e12			0.240901
$799$	−1.82078e13	+	3.84493e12i	−1.58051	+	0.333755i
$800$	−3.59561e12			−0.310362
$801$			3.54699e11i			0.0304449i
$802$	−1.15281e13	−	1.15281e13i	−0.983953	−	0.983953i
$803$	1.02524e12			0.0870171
$804$	−3.78709e12	−	3.78709e12i	−0.319634	−	0.319634i
$805$	9.67246e12	−	9.67246e12i	0.811812	−	0.811812i
$806$	1.36706e12	−	1.36706e12i	0.114098	−	0.114098i
$807$			3.23798e12i			0.268746i
$808$			2.68058e12i			0.221247i
$809$	−1.99317e12	+	1.99317e12i	−0.163597	+	0.163597i	−0.784158	−	0.620561i	$-0.786905\pi$
$809$	−1.99317e12	+	1.99317e12i	−0.163597	+	0.163597i	0.620561	+	0.784158i	$0.286905\pi$
$810$	−4.31388e12	+	4.31388e12i	−0.352116	+	0.352116i
$811$	−7.55423e12	−	7.55423e12i	−0.613192	−	0.613192i	0.330585	−	0.943776i	$-0.392754\pi$
$811$	−7.55423e12	−	7.55423e12i	−0.613192	−	0.613192i	−0.943776	+	0.330585i	$0.892754\pi$
$812$	−3.55829e13			−2.87236
$813$	1.38831e12	+	1.38831e12i	0.111450	+	0.111450i
$814$		−	3.00843e12i		−	0.240176i
$815$	2.44664e11			0.0194250
$816$	5.17952e12	+	3.37341e12i	0.408963	+	0.266356i
$817$	3.01905e12			0.237067
$818$		−	6.30440e12i		−	0.492327i
$819$	5.01465e12	+	5.01465e12i	0.389460	+	0.389460i
$820$	1.31371e13			1.01470
$821$	3.84892e12	+	3.84892e12i	0.295662	+	0.295662i	0.839312	−	0.543650i	$-0.182958\pi$
$821$	3.84892e12	+	3.84892e12i	0.295662	+	0.295662i	−0.543650	+	0.839312i	$0.682958\pi$
$822$	2.69997e12	−	2.69997e12i	0.206270	−	0.206270i
$823$	−5.06036e12	+	5.06036e12i	−0.384487	+	0.384487i	−0.872716	−	0.488229i	$-0.837643\pi$
$823$	−5.06036e12	+	5.06036e12i	−0.384487	+	0.384487i	0.488229	+	0.872716i	$0.337643\pi$
$824$			4.25464e13i			3.21507i
$825$		−	8.32282e11i		−	0.0625501i
$826$	4.40094e13	−	4.40094e13i	3.28954	−	3.28954i
$827$	−5.52020e12	+	5.52020e12i	−0.410374	+	0.410374i	−0.881869	−	0.471495i	$-0.843715\pi$
$827$	−5.52020e12	+	5.52020e12i	−0.410374	+	0.410374i	0.471495	+	0.881869i	$0.343715\pi$
$828$	−3.23328e13	−	3.23328e13i	−2.39060	−	2.39060i
$829$	2.40083e13			1.76549			0.882745	−	0.469853i	$-0.155693\pi$
$829$	2.40083e13			1.76549			0.882745	+	0.469853i	$0.155693\pi$
$830$	1.10587e13	+	1.10587e13i	0.808821	+	0.808821i
$831$		−	5.58945e11i		−	0.0406597i
$832$	4.15873e12			0.300889
$833$	2.31905e12	+	1.09820e13i	0.166881	+	0.790274i
$834$	8.73352e12			0.625089
$835$		−	1.65312e12i		−	0.117683i
$836$	1.25929e12	+	1.25929e12i	0.0891655	+	0.0891655i
$837$	−1.88012e12			−0.132410
$838$	1.04490e12	+	1.04490e12i	0.0731942	+	0.0731942i
$839$	1.85843e13	−	1.85843e13i	1.29485	−	1.29485i	0.363093	−	0.931753i	$-0.381721\pi$
$839$	1.85843e13	−	1.85843e13i	1.29485	−	1.29485i	0.931753	−	0.363093i	$-0.118279\pi$
$840$	−4.51830e12	+	4.51830e12i	−0.313125	+	0.313125i
$841$			4.20083e11i			0.0289570i
$842$			4.62392e13i			3.17034i
$843$	−5.09832e12	+	5.09832e12i	−0.347699	+	0.347699i
$844$	2.40636e13	−	2.40636e13i	1.63237	−	1.63237i
$845$	−3.74210e12	−	3.74210e12i	−0.252499	−	0.252499i
$846$	−3.67015e13			−2.46330
$847$	−1.35749e13	−	1.35749e13i	−0.906276	−	0.906276i
$848$		−	2.75766e13i		−	1.83130i
$849$	−1.03591e12			−0.0684286
$850$	2.06840e13	−	4.36783e12i	1.35909	−	0.286999i
$851$	1.78926e13			1.16947
$852$		−	1.44155e13i		−	0.937239i
$853$	7.65253e12	+	7.65253e12i	0.494919	+	0.494919i	0.909852	−	0.414933i	$-0.136195\pi$
$853$	7.65253e12	+	7.65253e12i	0.494919	+	0.494919i	−0.414933	+	0.909852i	$0.636195\pi$
$854$	−5.98577e13			−3.85088
$855$	1.21862e12	+	1.21862e12i	0.0779867	+	0.0779867i
$856$	−8.94812e12	+	8.94812e12i	−0.569639	+	0.569639i
$857$	1.25399e13	−	1.25399e13i	0.794107	−	0.794107i	−0.188052	−	0.982159i	$-0.560217\pi$
$857$	1.25399e13	−	1.25399e13i	0.794107	−	0.794107i	0.982159	+	0.188052i	$0.0602175\pi$
$858$		−	1.05120e12i		−	0.0662207i
$859$		−	2.50677e13i		−	1.57089i	−0.618933	−	0.785444i	$-0.712435\pi$
$859$		−	2.50677e13i		−	1.57089i	0.618933	−	0.785444i	$-0.287565\pi$
$860$	−9.41196e12	+	9.41196e12i	−0.586728	+	0.586728i
$861$	−5.89108e12	+	5.89108e12i	−0.365326	+	0.365326i
$862$	1.98530e13	+	1.98530e13i	1.22474	+	1.22474i
$863$	7.61230e12			0.467161			0.233581	−	0.972337i	$-0.424956\pi$
$863$	7.61230e12			0.467161			0.233581	+	0.972337i	$0.424956\pi$
$864$	3.12289e12	+	3.12289e12i	0.190654	+	0.190654i
$865$		−	5.27198e12i		−	0.320185i
$866$	1.99616e13			1.20605
$867$	−5.69595e12	−	2.20384e12i	−0.342358	−	0.132463i
$868$	9.15780e12			0.547586
$869$			7.51104e11i			0.0446798i
$870$	3.60911e12	+	3.60911e12i	0.213582	+	0.213582i
$871$	−4.70193e12			−0.276818
$872$	3.51616e13	+	3.51616e13i	2.05942	+	2.05942i
$873$	6.25247e12	−	6.25247e12i	0.364324	−	0.364324i
$874$	−1.10458e13	+	1.10458e13i	−0.640316	+	0.640316i
$875$			1.91870e13i			1.10655i
$876$		−	5.42354e12i		−	0.311182i
$877$	−2.12412e13	+	2.12412e13i	−1.21250	+	1.21250i	−0.242297	+	0.970202i	$0.577901\pi$
$877$	−2.12412e13	+	2.12412e13i	−1.21250	+	1.21250i	−0.970202	+	0.242297i	$0.922099\pi$
$878$	−2.64376e13	+	2.64376e13i	−1.50140	+	1.50140i
$879$	−2.87418e12	−	2.87418e12i	−0.162392	−	0.162392i
$880$	−2.35346e12			−0.132292
$881$	−1.16168e13	−	1.16168e13i	−0.649670	−	0.649670i	0.303243	−	0.952913i	$-0.401931\pi$
$881$	−1.16168e13	−	1.16168e13i	−0.649670	−	0.649670i	−0.952913	+	0.303243i	$0.901931\pi$
$882$			2.21363e13i			1.23168i
$883$	−1.94571e13			−1.07710			−0.538548	−	0.842595i	$-0.681027\pi$
$883$	−1.94571e13			−1.07710			−0.538548	+	0.842595i	$0.681027\pi$
$884$	1.77139e13	−	3.74063e12i	0.975615	−	0.206020i
$885$	−6.05338e12			−0.331706
$886$			3.79485e13i			2.06891i
$887$	−2.04643e12	−	2.04643e12i	−0.111005	−	0.111005i	0.649423	−	0.760427i	$-0.275011\pi$
$887$	−2.04643e12	−	2.04643e12i	−0.111005	−	0.111005i	−0.760427	+	0.649423i	$0.775011\pi$
$888$	−8.35818e12			−0.451080
$889$	−1.95193e13	−	1.95193e13i	−1.04811	−	1.04811i
$890$	−3.77766e11	+	3.77766e11i	−0.0201822	+	0.0201822i
$891$	1.76550e12	−	1.76550e12i	0.0938463	−	0.0938463i
$892$		−	1.92353e13i		−	1.01732i
$893$			8.50156e12i			0.447370i
$894$	1.13547e13	−	1.13547e13i	0.594507	−	0.594507i
$895$	−3.01536e12	+	3.01536e12i	−0.157085	+	0.157085i
$896$	2.77658e13	+	2.77658e13i	1.43921	+	1.43921i
$897$	6.25202e12			0.322444
$898$	1.07353e13	+	1.07353e13i	0.550896	+	0.550896i
$899$		−	3.84175e12i		−	0.196160i
$900$	2.82698e13			1.43626
$901$	5.62967e12	+	2.66595e13i	0.284591	+	1.34769i
$902$	−7.92931e12			−0.398847
$903$		−	8.44122e12i		−	0.422484i
$904$	−2.89666e13	−	2.89666e13i	−1.44258	−	1.44258i
$905$	7.48597e12			0.370962
$906$	−4.25322e12	−	4.25322e12i	−0.209720	−	0.209720i
$907$	−7.11957e12	+	7.11957e12i	−0.349318	+	0.349318i	−0.859856	−	0.510537i	$-0.829446\pi$
$907$	−7.11957e12	+	7.11957e12i	−0.349318	+	0.349318i	0.510537	+	0.859856i	$0.329446\pi$
$908$	1.08816e13	−	1.08816e13i	0.531257	−	0.531257i
$909$		−	2.02143e12i		−	0.0982020i
$910$			1.06815e13i			0.516353i
$911$	7.19464e12	−	7.19464e12i	0.346080	−	0.346080i	−0.512567	−	0.858647i	$-0.671305\pi$
$911$	7.19464e12	−	7.19464e12i	0.346080	−	0.346080i	0.858647	+	0.512567i	$0.171305\pi$
$912$	1.99676e12	−	1.99676e12i	0.0955759	−	0.0955759i
$913$	−4.52588e12	−	4.52588e12i	−0.215568	−	0.215568i
$914$	1.39836e13			0.662767
$915$	4.11663e12	+	4.11663e12i	0.194154	+	0.194154i
$916$		−	5.47000e13i		−	2.56719i
$917$	−1.85567e13			−0.866640
$918$	−2.17582e13	−	1.41711e13i	−1.01119	−	0.658583i
$919$	−2.39977e13			−1.10981			−0.554906	−	0.831913i	$-0.687246\pi$
$919$	−2.39977e13			−1.10981			−0.554906	+	0.831913i	$0.687246\pi$
$920$		−	3.61701e13i		−	1.66458i
$921$	6.22290e12	+	6.22290e12i	0.284987	+	0.284987i
$922$	1.38430e13			0.630871
$923$	−8.94889e12	−	8.94889e12i	−0.405846	−	0.405846i
$924$	3.52096e12	−	3.52096e12i	0.158905	−	0.158905i
$925$	−7.82209e12	+	7.82209e12i	−0.351306	+	0.351306i
$926$		−	2.90590e13i		−	1.29877i
$927$		−	3.20842e13i		−	1.42703i
$928$	−6.38119e12	+	6.38119e12i	−0.282446	+	0.282446i
$929$	−2.50502e13	+	2.50502e13i	−1.10342	+	1.10342i	−0.109425	+	0.993995i	$0.534901\pi$
$929$	−2.50502e13	+	2.50502e13i	−1.10342	+	1.10342i	−0.993995	+	0.109425i	$0.965099\pi$
$930$	−9.28861e11	−	9.28861e11i	−0.0407171	−	0.0407171i
$931$	5.12768e12			0.223690
$932$	5.56737e13	+	5.56737e13i	2.41701	+	2.41701i
$933$			2.31475e12i			0.100009i
$934$	2.96197e13			1.27356
$935$	2.27519e12	−	4.80451e11i	0.0973568	−	0.0205588i
$936$	1.87522e13			0.798567
$937$			2.81598e13i			1.19344i	0.802449	+	0.596721i	$0.203530\pi$
$937$			2.81598e13i			1.19344i	−0.802449	+	0.596721i	$0.796470\pi$
$938$	−2.32267e13	−	2.32267e13i	−0.979657	−	0.979657i
$939$	1.12025e13			0.470241
$940$	−2.65038e13	−	2.65038e13i	−1.10722	−	1.10722i
$941$	4.26774e12	−	4.26774e12i	0.177437	−	0.177437i	−0.612801	−	0.790238i	$-0.709957\pi$
$941$	4.26774e12	−	4.26774e12i	0.177437	−	0.177437i	0.790238	+	0.612801i	$0.209957\pi$
$942$	−1.30380e13	+	1.30380e13i	−0.539489	+	0.539489i
$943$		−	4.71595e13i		−	1.94208i
$944$		−	6.36867e13i		−	2.61021i
$945$	7.34515e12	−	7.34515e12i	0.299611	−	0.299611i
$946$	5.68088e12	−	5.68088e12i	0.230625	−	0.230625i
$947$	1.65756e13	+	1.65756e13i	0.669721	+	0.669721i	0.957651	−	0.287930i	$-0.0929672\pi$
$947$	1.65756e13	+	1.65756e13i	0.669721	+	0.669721i	−0.287930	+	0.957651i	$0.592967\pi$
$948$	3.97337e12			0.159780
$949$	−3.36685e12	−	3.36685e12i	−0.134749	−	0.134749i
$950$		−	9.65774e12i		−	0.384697i
$951$	−1.42343e13			−0.564317
$952$	5.56600e13	+	3.62512e13i	2.19622	+	1.43039i
$953$	1.13861e13			0.447154			0.223577	−	0.974686i	$-0.428227\pi$
$953$	1.13861e13			0.447154			0.223577	+	0.974686i	$0.428227\pi$
$954$			5.37375e13i			2.10044i
$955$	−8.16745e12	−	8.16745e12i	−0.317740	−	0.317740i
$956$	−2.06341e13			−0.798959
$957$	−1.47706e12	−	1.47706e12i	−0.0569240	−	0.0569240i
$958$	−6.23160e13	+	6.23160e13i	−2.39031	+	2.39031i
$959$	1.12280e13	−	1.12280e13i	0.428667	−	0.428667i
$960$		−	2.82569e12i		−	0.107375i
$961$		−	2.54509e13i		−	0.962604i
$962$	−9.87959e12	+	9.87959e12i	−0.371921	+	0.371921i
$963$	6.74777e12	−	6.74777e12i	0.252838	−	0.252838i
$964$	1.56157e13	+	1.56157e13i	0.582390	+	0.582390i
$965$	1.23485e13			0.458396
$966$	3.08839e13	+	3.08839e13i	1.14113	+	1.14113i
$967$			1.21489e13i			0.446803i	0.974726	+	0.223402i	$0.0717162\pi$
$967$			1.21489e13i			0.446803i	−0.974726	+	0.223402i	$0.928284\pi$
$968$	−5.07631e13			−1.85827
$969$	−1.52272e12	+	2.33799e12i	−0.0554835	+	0.0851893i
$970$	1.33182e13			0.483027
$971$			3.38846e13i			1.22325i	0.791148	+	0.611625i	$0.209484\pi$
$971$			3.38846e13i			1.22325i	−0.791148	+	0.611625i	$0.790516\pi$
$972$	−3.77167e13	−	3.77167e13i	−1.35530	−	1.35530i
$973$	3.63190e13			1.29905
$974$	−6.51397e13	−	6.51397e13i	−2.31916	−	2.31916i
$975$	−2.73319e12	+	2.73319e12i	−0.0968611	+	0.0968611i
$976$	−4.33105e13	+	4.33105e13i	−1.52781	+	1.52781i
$977$			2.16284e13i			0.759451i	0.925099	+	0.379725i	$0.123982\pi$
$977$			2.16284e13i			0.759451i	−0.925099	+	0.379725i	$0.876018\pi$
$978$			7.81206e11i			0.0273049i
$979$	1.54604e11	−	1.54604e11i	0.00537897	−	0.00537897i
$980$	−1.59857e13	+	1.59857e13i	−0.553622	+	0.553622i
$981$	−2.65153e13	−	2.65153e13i	−0.914085	−	0.914085i
$982$	−4.78632e13			−1.64248
$983$	−3.09895e13	−	3.09895e13i	−1.05858	−	1.05858i	−0.998174	−	0.0604054i	$-0.980761\pi$
$983$	−3.09895e13	−	3.09895e13i	−1.05858	−	1.05858i	−0.0604054	−	0.998174i	$-0.519239\pi$
$984$			2.20296e13i			0.749082i
$985$	2.43524e12			0.0824286
$986$	2.89566e13	−	4.44599e13i	0.975665	−	1.49803i
$987$	2.37703e13			0.797273
$988$		−	8.27093e12i		−	0.276152i
$989$	3.37870e13	+	3.37870e13i	1.12297	+	1.12297i
$990$	4.58611e12			0.151735
$991$	−1.64040e13	−	1.64040e13i	−0.540280	−	0.540280i	0.383331	−	0.923611i	$-0.374777\pi$
$991$	−1.64040e13	−	1.64040e13i	−0.540280	−	0.540280i	−0.923611	+	0.383331i	$0.874777\pi$
$992$	1.64230e12	−	1.64230e12i	0.0538455	−	0.0538455i
$993$	−2.29185e12	+	2.29185e12i	−0.0748022	+	0.0748022i
$994$		−	8.84118e13i		−	2.87257i
$995$			2.69303e12i			0.0871039i
$996$	−2.39420e13	+	2.39420e13i	−0.770893	+	0.770893i
$997$	2.33163e13	−	2.33163e13i	0.747362	−	0.747362i	−0.226621	−	0.973983i	$-0.572768\pi$
$997$	2.33163e13	−	2.33163e13i	0.747362	−	0.747362i	0.973983	+	0.226621i	$0.0727679\pi$
$998$	3.70768e13	+	3.70768e13i	1.18308	+	1.18308i
$999$	1.35874e13			0.431611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.c.a.13.1	yes	24
17.2	even	8		289.10.a.f.1.23		24
17.4	even	4	inner	17.10.c.a.4.12	✓	24
17.15	even	8		289.10.a.f.1.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.12	✓	24	17.4	even	4	inner
17.10.c.a.13.1	yes	24	1.1	even	1	trivial
289.10.a.f.1.23		24	17.2	even	8
289.10.a.f.1.24		24	17.15	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-39.8788i q^{2} +(-36.4169 - 36.4169i) q^{3} -1078.32 q^{4} +(454.832 + 454.832i) q^{5} +(-1452.26 + 1452.26i) q^{6} +(-6039.34 + 6039.34i) q^{7} +22584.0i q^{8} -17030.6i q^{9} +O(q^{10})\)	\(q-39.8788i q^{2} +(-36.4169 - 36.4169i) q^{3} -1078.32 q^{4} +(454.832 + 454.832i) q^{5} +(-1452.26 + 1452.26i) q^{6} +(-6039.34 + 6039.34i) q^{7} +22584.0i q^{8} -17030.6i q^{9} +(18138.1 - 18138.1i) q^{10} +(-7423.20 + 7423.20i) q^{11} +(39269.0 + 39269.0i) q^{12} +48755.2 q^{13} +(240842. + 240842. i) q^{14} -33127.1i q^{15} +348526. q^{16} +(-336935. + 71150.4i) q^{17} -679160. q^{18} +157321. i q^{19} +(-490453. - 490453. i) q^{20} +439868. q^{21} +(296028. + 296028. i) q^{22} +(-1.76063e6 + 1.76063e6i) q^{23} +(822441. - 822441. i) q^{24} -1.53938e6i q^{25} -1.94430e6i q^{26} +(-1.33700e6 + 1.33700e6i) q^{27} +(6.51233e6 - 6.51233e6i) q^{28} +(-2.73196e6 - 2.73196e6i) q^{29} -1.32107e6 q^{30} +(703113. + 703113. i) q^{31} -2.33575e6i q^{32} +540660. q^{33} +(2.83739e6 + 1.34366e7i) q^{34} -5.49377e6 q^{35} +1.83644e7i q^{36} +(-5.08132e6 - 5.08132e6i) q^{37} +6.27378e6 q^{38} +(-1.77551e6 - 1.77551e6i) q^{39} +(-1.02719e7 + 1.02719e7i) q^{40} +(-1.33928e7 + 1.33928e7i) q^{41} -1.75414e7i q^{42} -1.91903e7i q^{43} +(8.00457e6 - 8.00457e6i) q^{44} +(7.74606e6 - 7.74606e6i) q^{45} +(7.02116e7 + 7.02116e7i) q^{46} +5.40395e7 q^{47} +(-1.26922e7 - 1.26922e7i) q^{48} -3.25937e7i q^{49} -6.13887e7 q^{50} +(1.48612e7 + 9.67907e6i) q^{51} -5.25735e7 q^{52} -7.91235e7i q^{53} +(5.33178e7 + 5.33178e7i) q^{54} -6.75261e6 q^{55} +(-1.36393e8 - 1.36393e8i) q^{56} +(5.72915e6 - 5.72915e6i) q^{57} +(-1.08947e8 + 1.08947e8i) q^{58} -1.82732e8i q^{59} +3.57216e7i q^{60} +(-1.24268e8 + 1.24268e8i) q^{61} +(2.80393e7 - 2.80393e7i) q^{62} +(1.02854e8 + 1.02854e8i) q^{63} +8.52982e7 q^{64} +(2.21754e7 + 2.21754e7i) q^{65} -2.15609e7i q^{66} -9.64396e7 q^{67} +(3.63323e8 - 7.67227e7i) q^{68} +1.28233e8 q^{69} +2.19085e8i q^{70} +(-1.83548e8 - 1.83548e8i) q^{71} +3.84620e8 q^{72} +(-6.90563e7 - 6.90563e7i) q^{73} +(-2.02637e8 + 2.02637e8i) q^{74} +(-5.60595e7 + 5.60595e7i) q^{75} -1.69642e8i q^{76} -8.96625e7i q^{77} +(-7.08053e7 + 7.08053e7i) q^{78} +(5.05917e7 - 5.05917e7i) q^{79} +(1.58521e8 + 1.58521e8i) q^{80} -2.37835e8 q^{81} +(5.34090e8 + 5.34090e8i) q^{82} +6.09693e8i q^{83} -4.74318e8 q^{84} +(-1.85610e8 - 1.20887e8i) q^{85} -7.65287e8 q^{86} +1.98979e8i q^{87} +(-1.67646e8 - 1.67646e8i) q^{88} -2.08272e7 q^{89} +(-3.08904e8 - 3.08904e8i) q^{90} +(-2.94449e8 + 2.94449e8i) q^{91} +(1.89851e9 - 1.89851e9i) q^{92} -5.12104e7i q^{93} -2.15503e9i q^{94} +(-7.15547e7 + 7.15547e7i) q^{95} +(-8.50609e7 + 8.50609e7i) q^{96} +(3.67131e8 + 3.67131e8i) q^{97} -1.29980e9 q^{98} +(1.26422e8 + 1.26422e8i) 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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