LMFDB - Embedded newform 25.8.d.a.6.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,8,Mod(6,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, 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:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			6.17
Character	$\chi$	$=$	25.6
Dual form			25.8.d.a.21.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.59046 + 20.2833i) q^{2} +(-51.4446 + 37.3767i) q^{3} +(-264.426 + 192.117i) q^{4} +(176.749 + 216.529i) q^{5} +(-1097.17 - 797.139i) q^{6} +1543.62 q^{7} +(-3430.94 - 2492.72i) q^{8} +(573.708 - 1765.69i) q^{9} +O(q^{10})$	\(q+(6.59046 + 20.2833i) q^{2} +(-51.4446 + 37.3767i) q^{3} +(-264.426 + 192.117i) q^{4} +(176.749 + 216.529i) q^{5} +(-1097.17 - 797.139i) q^{6} +1543.62 q^{7} +(-3430.94 - 2492.72i) q^{8} +(573.708 - 1765.69i) q^{9} +(-3227.08 + 5012.09i) q^{10} +(712.104 + 2191.63i) q^{11} +(6422.60 - 19766.7i) q^{12} +(664.159 - 2044.07i) q^{13} +(10173.1 + 31309.7i) q^{14} +(-17185.9 - 4532.95i) q^{15} +(15021.1 - 46230.2i) q^{16} +(4202.55 + 3053.33i) q^{17} +39595.2 q^{18} +(-14406.8 - 10467.1i) q^{19} +(-88335.8 - 23299.4i) q^{20} +(-79410.7 + 57695.3i) q^{21} +(-39760.5 + 28887.7i) q^{22} +(-2236.04 - 6881.81i) q^{23} +269673. q^{24} +(-15644.6 + 76542.6i) q^{25} +45837.7 q^{26} +(-6493.18 - 19984.0i) q^{27} +(-408172. + 296555. i) q^{28} +(127644. - 92738.5i) q^{29} +(-21319.6 - 378462. i) q^{30} +(129225. + 93887.3i) q^{31} +493867. q^{32} +(-118550. - 86131.4i) q^{33} +(-34235.0 + 105365. i) q^{34} +(272833. + 334238. i) q^{35} +(187516. + 577114. i) q^{36} +(-62818.0 + 193334. i) q^{37} +(117361. - 361200. i) q^{38} +(42233.2 + 129980. i) q^{39} +(-66668.2 - 1.18348e6i) q^{40} +(-61887.0 + 190468. i) q^{41} +(-1.69361e6 - 1.23048e6i) q^{42} -888992. q^{43} +(-609347. - 442717. i) q^{44} +(483726. - 187860. i) q^{45} +(124850. - 90708.6i) q^{46} +(301678. - 219182. i) q^{47} +(955176. + 2.93973e6i) q^{48} +1.55921e6 q^{49} +(-1.65564e6 + 187126. i) q^{50} -330321. q^{51} +(217079. + 668101. i) q^{52} +(1.34009e6 - 973631. i) q^{53} +(362549. - 263407. i) q^{54} +(-348688. + 541559. i) q^{55} +(-5.29606e6 - 3.84781e6i) q^{56} +1.13238e6 q^{57} +(2.72228e6 + 1.97785e6i) q^{58} +(-95844.0 + 294977. i) q^{59} +(5.41525e6 - 2.10307e6i) q^{60} +(107241. + 330055. i) q^{61} +(-1.05270e6 + 3.23987e6i) q^{62} +(885586. - 2.72555e6i) q^{63} +(1.33211e6 + 4.09981e6i) q^{64} +(559990. - 217478. i) q^{65} +(965736. - 2.97223e6i) q^{66} +(-963858. - 700284. i) q^{67} -1.69786e6 q^{68} +(372251. + 270456. i) q^{69} +(-4.98137e6 + 7.73674e6i) q^{70} +(546613. - 397138. i) q^{71} +(-6.36974e6 + 4.62789e6i) q^{72} +(136373. + 419714. i) q^{73} -4.33546e6 q^{74} +(-2.05608e6 - 4.52244e6i) q^{75} +5.82043e6 q^{76} +(1.09922e6 + 3.38304e6i) q^{77} +(-2.35810e6 + 1.71326e6i) q^{78} +(-5.77304e6 + 4.19436e6i) q^{79} +(1.26651e7 - 4.91863e6i) q^{80} +(4.36582e6 + 3.17195e6i) q^{81} -4.27120e6 q^{82} +(-2.04209e6 - 1.48367e6i) q^{83} +(9.91403e6 - 3.05123e7i) q^{84} +(81661.7 + 1.44965e6i) q^{85} +(-5.85886e6 - 1.80317e7i) q^{86} +(-3.10031e6 + 9.54178e6i) q^{87} +(3.01994e6 - 9.29442e6i) q^{88} +(3.43771e6 + 1.05802e7i) q^{89} +(6.99841e6 + 8.57350e6i) q^{90} +(1.02521e6 - 3.15526e6i) q^{91} +(1.91338e6 + 1.39015e6i) q^{92} -1.01571e7 q^{93} +(6.43394e6 + 4.67453e6i) q^{94} +(-279944. - 4.96953e6i) q^{95} +(-2.54068e7 + 1.84591e7i) q^{96} +(1.06841e7 - 7.76246e6i) q^{97} +(1.02759e7 + 3.16260e7i) q^{98} +4.27828e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9}+O(q^{10}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16} + 71504 q^{17} + 116208 q^{18} - 48685 q^{19} - 138265 q^{20} - 2274 q^{21} - 271952 q^{22} - 63227 q^{23} + 553980 q^{24} + 276615 q^{25} + 675246 q^{26} - 270235 q^{27} - 782613 q^{28} - 99655 q^{29} - 1011285 q^{30} + 39051 q^{31} + 1045974 q^{32} + 1766456 q^{33} + 605893 q^{34} - 476935 q^{35} - 2928227 q^{36} + 83909 q^{37} + 1937525 q^{38} + 1316257 q^{39} + 2903410 q^{40} - 1964944 q^{41} - 3462547 q^{42} - 3439822 q^{43} - 3557652 q^{44} - 2121790 q^{45} + 2982521 q^{46} + 1663474 q^{47} + 1678378 q^{48} + 6584354 q^{49} + 408485 q^{50} + 3922076 q^{51} - 5301176 q^{52} + 788553 q^{53} - 6946145 q^{54} - 2630560 q^{55} - 415350 q^{56} - 14598410 q^{57} + 4727030 q^{58} - 3625740 q^{59} + 29158890 q^{60} - 4161559 q^{61} + 19658928 q^{62} + 2426738 q^{63} - 4408596 q^{64} - 2030220 q^{65} - 6985528 q^{66} + 8470434 q^{67} - 29099218 q^{68} - 360673 q^{69} - 22417320 q^{70} - 4808044 q^{71} + 25676065 q^{72} + 5517633 q^{73} + 14050068 q^{74} + 257240 q^{75} + 22502000 q^{76} - 9936772 q^{77} + 14948561 q^{78} - 5343505 q^{79} - 3987180 q^{80} - 5865817 q^{81} - 76614542 q^{82} - 645927 q^{83} + 5992628 q^{84} + 48268560 q^{85} - 27540609 q^{86} + 65370380 q^{87} - 3612320 q^{88} + 11153500 q^{89} + 7267975 q^{90} - 9123484 q^{91} - 33863736 q^{92} - 118704764 q^{93} - 30761227 q^{94} - 26382485 q^{95} + 1256206 q^{96} + 55538244 q^{97} + 102201752 q^{98} + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	6.59046	+	20.2833i	0.582520	+	1.79281i	0.609010	+	0.793163i	$0.291567\pi$
$2$	6.59046	+	20.2833i	0.582520	+	1.79281i	−0.0264901	+	0.999649i	$0.508433\pi$
$3$	−51.4446	+	37.3767i	−1.10006	+	0.799238i	−0.981069	−	0.193658i	$-0.937965\pi$
$3$	−51.4446	+	37.3767i	−1.10006	+	0.799238i	−0.118988	+	0.992896i	$0.537965\pi$
$4$	−264.426	+	192.117i	−2.06583	+	1.50091i
$5$	176.749	+	216.529i	0.632356	+	0.774678i
$5$	176.749	+	216.529i	0.632356	+	0.774678i
$6$	−1097.17	−	797.139i	−2.07369	−	1.50662i
$7$	1543.62			1.70097			0.850485	−	0.526000i	$-0.176309\pi$
$7$	1543.62			1.70097			0.850485	+	0.526000i	$0.176309\pi$
$8$	−3430.94	−	2492.72i	−2.36918	−	1.72131i
$9$	573.708	−	1765.69i	0.262327	−	0.807358i
$10$	−3227.08	+	5012.09i	−1.02049	+	1.58496i
$11$	712.104	+	2191.63i	0.161313	+	0.496470i	0.998746	−	0.0500705i	$-0.0159446\pi$
$11$	712.104	+	2191.63i	0.161313	+	0.496470i	−0.837433	+	0.546540i	$0.815945\pi$
$12$	6422.60	−	19766.7i	1.07294	−	3.30218i
$13$	664.159	−	2044.07i	0.0838437	−	0.258044i	−0.900342	−	0.435182i	$-0.856684\pi$
$13$	664.159	−	2044.07i	0.0838437	−	0.258044i	0.984186	+	0.177138i	$0.0566839\pi$
$14$	10173.1	+	31309.7i	0.990848	+	3.04952i
$15$	−17185.9	−	4532.95i	−1.31478	−	0.346786i
$16$	15021.1	−	46230.2i	0.916815	−	2.82167i
$17$	4202.55	+	3053.33i	0.207463	+	0.150731i	0.686665	−	0.726974i	$-0.259074\pi$
$17$	4202.55	+	3053.33i	0.207463	+	0.150731i	−0.479202	+	0.877705i	$0.659074\pi$
$18$	39595.2			1.60025
$19$	−14406.8	−	10467.1i	−0.481869	−	0.350098i	0.320180	−	0.947357i	$-0.396257\pi$
$19$	−14406.8	−	10467.1i	−0.481869	−	0.350098i	−0.802049	+	0.597259i	$0.796257\pi$
$20$	−88335.8	−	23299.4i	−2.46906	−	0.651239i
$21$	−79410.7	+	57695.3i	−1.87116	+	1.35948i
$22$	−39760.5	+	28887.7i	−0.796109	+	0.578407i
$23$	−2236.04	−	6881.81i	−0.0383205	−	0.117938i	0.930066	−	0.367392i	$-0.119749\pi$
$23$	−2236.04	−	6881.81i	−0.0383205	−	0.117938i	−0.968387	+	0.249453i	$0.919749\pi$
$24$	269673.			3.98197
$25$	−15644.6	+	76542.6i	−0.200251	+	0.979745i
$26$	45837.7			0.511466
$27$	−6493.18	−	19984.0i	−0.0634869	−	0.195393i
$28$	−408172.	+	296555.i	−3.51391	+	2.55300i
$29$	127644.	−	92738.5i	0.971865	−	0.706101i	0.0159889	−	0.999872i	$-0.494910\pi$
$29$	127644.	−	92738.5i	0.971865	−	0.706101i	0.955876	+	0.293771i	$0.0949103\pi$
$30$	−21319.6	−	378462.i	−0.144163	−	2.55916i
$31$	129225.	+	93887.3i	0.779076	+	0.566032i	0.904702	−	0.426046i	$-0.140094\pi$
$31$	129225.	+	93887.3i	0.779076	+	0.566032i	−0.125625	+	0.992078i	$0.540094\pi$
$32$	493867.			2.66431
$33$	−118550.	−	86131.4i	−0.574251	−	0.417218i
$34$	−34235.0	+	105365.i	−0.149381	+	0.459746i
$35$	272833.	+	334238.i	1.07562	+	1.31770i
$36$	187516.	+	577114.i	0.669852	+	2.06159i
$37$	−62818.0	+	193334.i	−0.203882	+	0.627483i	0.795876	+	0.605460i	$0.207011\pi$
$37$	−62818.0	+	193334.i	−0.203882	+	0.627483i	−0.999757	+	0.0220230i	$0.992989\pi$
$38$	117361.	−	361200.i	0.346962	−	1.06784i
$39$	42233.2	+	129980.i	0.114006	+	0.350875i
$40$	−66668.2	−	1.18348e6i	−0.164706	−	2.92383i
$41$	−61887.0	+	190468.i	−0.140235	+	0.431598i	−0.996367	−	0.0851578i	$-0.972861\pi$
$41$	−61887.0	+	190468.i	−0.140235	+	0.431598i	0.856133	+	0.516756i	$0.172861\pi$
$42$	−1.69361e6	−	1.23048e6i	−3.52728	−	2.56272i
$43$	−888992.			−1.70513			−0.852566	−	0.522619i	$-0.824955\pi$
$43$	−888992.			−1.70513			−0.852566	+	0.522619i	$0.824955\pi$
$44$	−609347.	−	442717.i	−1.07840	−	0.783504i
$45$	483726.	−	187860.i	0.791326	−	0.307320i
$46$	124850.	−	90708.6i	0.189119	−	0.137403i
$47$	301678.	−	219182.i	0.423840	−	0.307937i	−0.355341	−	0.934737i	$-0.615635\pi$
$47$	301678.	−	219182.i	0.423840	−	0.307937i	0.779181	+	0.626799i	$0.215635\pi$
$48$	955176.	+	2.93973e6i	1.24663	+	3.83675i
$49$	1.55921e6			1.89330
$50$	−1.65564e6	+	187126.i	−1.87315	+	0.211709i
$51$	−330321.			−0.348691
$52$	217079.	+	668101.i	0.214095	+	0.658917i
$53$	1.34009e6	−	973631.i	1.23642	−	0.898315i	0.239070	−	0.971002i	$-0.423157\pi$
$53$	1.34009e6	−	973631.i	1.23642	−	0.898315i	0.997355	+	0.0726872i	$0.0231575\pi$
$54$	362549.	−	263407.i	0.313320	−	0.227640i
$55$	−348688.	+	541559.i	−0.282597	+	0.438911i
$56$	−5.29606e6	−	3.84781e6i	−4.02990	−	2.92790i
$57$	1.13238e6			0.809895
$58$	2.72228e6	+	1.97785e6i	1.83204	+	1.33105i
$59$	−95844.0	+	294977.i	−0.0607551	+	0.186985i	−0.976828	−	0.214028i	$-0.931342\pi$
$59$	−95844.0	+	294977.i	−0.0607551	+	0.186985i	0.916072	+	0.401013i	$0.131342\pi$
$60$	5.41525e6	−	2.10307e6i	3.23660	−	1.25697i
$61$	107241.	+	330055.i	0.0604934	+	0.186180i	0.976736	−	0.214443i	$-0.0687937\pi$
$61$	107241.	+	330055.i	0.0604934	+	0.186180i	−0.916243	+	0.400623i	$0.868794\pi$
$62$	−1.05270e6	+	3.23987e6i	−0.560962	+	1.72646i
$63$	885586.	−	2.72555e6i	0.446210	−	1.37329i
$64$	1.33211e6	+	4.09981e6i	0.635199	+	1.95494i
$65$	559990.	−	217478.i	0.252920	−	0.0982242i
$66$	965736.	−	2.97223e6i	0.413480	−	1.27256i
$67$	−963858.	−	700284.i	−0.391517	−	0.284454i	0.374560	−	0.927203i	$-0.377794\pi$
$67$	−963858.	−	700284.i	−0.391517	−	0.284454i	−0.766077	+	0.642749i	$0.777794\pi$
$68$	−1.69786e6			−0.654817
$69$	372251.	+	270456.i	0.136416	+	0.0991118i
$70$	−4.98137e6	+	7.73674e6i	−1.73582	+	2.69597i
$71$	546613.	−	397138.i	0.181249	−	0.131685i	−0.493461	−	0.869768i	$-0.664269\pi$
$71$	546613.	−	397138.i	0.181249	−	0.131685i	0.674710	+	0.738083i	$0.264269\pi$
$72$	−6.36974e6	+	4.62789e6i	−2.01121	+	1.46123i
$73$	136373.	+	419714.i	0.0410298	+	0.126277i	0.969473	−	0.245197i	$-0.0788526\pi$
$73$	136373.	+	419714.i	0.0410298	+	0.126277i	−0.928444	+	0.371474i	$0.878853\pi$
$74$	−4.33546e6			−1.24372
$75$	−2.05608e6	−	4.52244e6i	−0.562762	−	1.23782i
$76$	5.82043e6			1.52092
$77$	1.09922e6	+	3.38304e6i	0.274388	+	0.844480i
$78$	−2.35810e6	+	1.71326e6i	−0.562641	+	0.408783i
$79$	−5.77304e6	+	4.19436e6i	−1.31738	+	0.957129i	−0.317414	+	0.948287i	$0.602815\pi$
$79$	−5.77304e6	+	4.19436e6i	−1.31738	+	0.957129i	−0.999961	+	0.00884210i	$0.997185\pi$
$80$	1.26651e7	−	4.91863e6i	2.76563	−	1.07406i
$81$	4.36582e6	+	3.17195e6i	0.912785	+	0.663177i
$82$	−4.27120e6			−0.855464
$83$	−2.04209e6	−	1.48367e6i	−0.392014	−	0.284815i	0.374266	−	0.927321i	$-0.377895\pi$
$83$	−2.04209e6	−	1.48367e6i	−0.392014	−	0.284815i	−0.766280	+	0.642506i	$0.777895\pi$
$84$	9.91403e6	−	3.05123e7i	1.82504	−	5.61690i
$85$	81661.7	+	1.44965e6i	0.0144229	+	0.256033i
$86$	−5.85886e6	−	1.80317e7i	−0.993274	−	3.05698i
$87$	−3.10031e6	+	9.54178e6i	−0.504764	+	1.55350i
$88$	3.01994e6	−	9.29442e6i	0.472399	−	1.45390i
$89$	3.43771e6	+	1.05802e7i	0.516897	+	1.59085i	0.779803	+	0.626025i	$0.215319\pi$
$89$	3.43771e6	+	1.05802e7i	0.516897	+	1.59085i	−0.262905	+	0.964822i	$0.584681\pi$
$90$	6.99841e6	+	8.57350e6i	1.01193	+	1.23968i
$91$	1.02521e6	−	3.15526e6i	0.142616	−	0.438926i
$92$	1.91338e6	+	1.39015e6i	0.256179	+	0.186125i
$93$	−1.01571e7			−1.30942
$94$	6.43394e6	+	4.67453e6i	0.798969	+	0.580485i
$95$	−279944.	−	4.96953e6i	−0.0334996	−	0.594679i
$96$	−2.54068e7	+	1.84591e7i	−2.93089	+	2.12942i
$97$	1.06841e7	−	7.76246e6i	1.18860	−	0.863571i	0.195488	−	0.980706i	$-0.437371\pi$
$97$	1.06841e7	−	7.76246e6i	1.18860	−	0.863571i	0.993116	+	0.117135i	$0.0373710\pi$
$98$	1.02759e7	+	3.16260e7i	1.10288	+	3.39432i
$99$	4.27828e6			0.443146
$100$	−1.05683e7	−	2.32454e7i	−1.05683	−	2.32454i
$101$	−5.28994e6			−0.510888			−0.255444	−	0.966824i	$-0.582222\pi$
$101$	−5.28994e6			−0.510888			−0.255444	+	0.966824i	$0.582222\pi$
$102$	−2.17697e6	−	6.70003e6i	−0.203120	−	0.625138i
$103$	170405.	−	123806.i	0.0153657	−	0.0111638i	−0.580076	−	0.814562i	$-0.696977\pi$
$103$	170405.	−	123806.i	0.0153657	−	0.0111638i	0.595442	+	0.803399i	$0.296977\pi$
$104$	−7.37399e6	+	5.35752e6i	−0.642815	+	0.467033i
$105$	−2.65285e7	−	6.99714e6i	−2.23640	−	0.589873i
$106$	2.85803e7	+	2.07648e7i	2.33075	+	1.69339i
$107$	−4.57510e6			−0.361041			−0.180521	−	0.983571i	$-0.557778\pi$
$107$	−4.57510e6			−0.361041			−0.180521	+	0.983571i	$0.557778\pi$
$108$	5.55622e6	+	4.03683e6i	0.424420	+	0.308359i
$109$	−5.18305e6	+	1.59518e7i	−0.383348	+	1.17982i	0.554324	+	0.832301i	$0.312977\pi$
$109$	−5.18305e6	+	1.59518e7i	−0.383348	+	1.17982i	−0.937672	+	0.347522i	$0.887023\pi$
$110$	−1.32826e7	−	3.50343e6i	−0.951503	−	0.250968i
$111$	−3.99453e6	−	1.22939e7i	−0.277227	−	0.853217i
$112$	2.31868e7	−	7.13617e7i	1.55947	−	4.79957i
$113$	7.01087e6	−	2.15772e7i	0.457085	−	1.40676i	−0.411584	−	0.911372i	$-0.635024\pi$
$113$	7.01087e6	−	2.15772e7i	0.457085	−	1.40676i	0.868670	−	0.495392i	$-0.164976\pi$
$114$	7.46287e6	+	2.29684e7i	0.471780	+	1.45199i
$115$	1.09489e6	−	1.70052e6i	0.0671321	−	0.104265i
$116$	−1.59357e7	+	4.90449e7i	−0.947910	+	2.91737i
$117$	−3.22817e6	−	2.34540e6i	−0.186340	−	0.135384i
$118$	−6.61478e6			−0.370620
$119$	6.48712e6	+	4.71317e6i	0.352889	+	0.256389i
$120$	4.76644e7	+	5.83920e7i	2.51802	+	3.08474i
$121$	1.14693e7	−	8.33294e6i	0.588557	−	0.427611i
$122$	−5.98785e6	+	4.35043e6i	−0.298546	+	0.216907i
$123$	−3.93533e6	−	1.21117e7i	−0.190684	−	0.586864i
$124$	−5.22077e7			−2.45900
$125$	−1.93388e7	+	1.01413e7i	−0.885616	+	0.464418i
$126$	6.11198e7			2.72198
$127$	9.45796e6	+	2.91086e7i	0.409717	+	1.26098i	0.916891	+	0.399137i	$0.130690\pi$
$127$	9.45796e6	+	2.91086e7i	0.409717	+	1.26098i	−0.507174	+	0.861844i	$0.669310\pi$
$128$	−2.32367e7	+	1.68824e7i	−0.979352	+	0.711541i
$129$	4.57338e7	−	3.32276e7i	1.87574	−	1.36281i
$130$	8.10177e6	+	9.92520e6i	0.323428	+	0.396221i
$131$	−1.06158e7	−	7.71286e6i	−0.412577	−	0.299755i	0.362067	−	0.932152i	$-0.382071\pi$
$131$	−1.06158e7	−	7.71286e6i	−0.412577	−	0.299755i	−0.774644	+	0.632397i	$0.782071\pi$
$132$	4.78949e7			1.81251
$133$	−2.22385e7	−	1.61572e7i	−0.819644	−	0.595506i
$134$	7.85183e6	−	2.41655e7i	0.281906	−	0.867617i
$135$	3.17944e6	−	4.93811e6i	0.111220	−	0.172740i
$136$	−6.80758e6	−	2.09516e7i	−0.232063	−	0.714217i
$137$	7.30888e6	−	2.24944e7i	0.242845	−	0.747399i	−0.753139	−	0.657862i	$-0.771461\pi$
$137$	7.30888e6	−	2.24944e7i	0.242845	−	0.747399i	0.995983	−	0.0895374i	$-0.0285389\pi$
$138$	−3.03245e6	+	9.33293e6i	−0.0982240	+	0.302302i
$139$	−8.62037e6	−	2.65308e7i	−0.272254	−	0.837911i	−0.989933	−	0.141537i	$-0.954795\pi$
$139$	−8.62037e6	−	2.65308e7i	−0.272254	−	0.837911i	0.717679	−	0.696374i	$-0.245205\pi$
$140$	−1.36357e8	−	3.59654e7i	−4.19980	−	1.10774i
$141$	−7.32741e6	+	2.25515e7i	−0.220132	+	0.677497i
$142$	1.16577e7	+	8.46982e6i	0.341668	+	0.248236i
$143$	4.95280e6			0.141636
$144$	−7.30106e7	−	5.30453e7i	−2.03759	−	1.48040i
$145$	4.26414e7	+	1.12471e7i	1.16157	+	0.306374i
$146$	−7.61444e6	+	5.53221e6i	−0.202490	+	0.147117i
$147$	−8.02130e7	+	5.82781e7i	−2.08273	+	1.51320i
$148$	−2.05320e7	−	6.31908e7i	−0.520612	−	1.60228i
$149$	7.42764e7			1.83950			0.919748	−	0.392510i	$-0.128393\pi$
$149$	7.42764e7			1.83950			0.919748	+	0.392510i	$0.128393\pi$
$150$	7.81798e7	−	7.15091e7i	1.89136	−	1.72998i
$151$	5.35271e7			1.26519			0.632593	−	0.774484i	$-0.281990\pi$
$151$	5.35271e7			1.26519			0.632593	+	0.774484i	$0.281990\pi$
$152$	2.33371e7	+	7.18241e7i	0.539006	+	1.65889i
$153$	7.80228e6	−	5.66869e6i	0.176117	−	0.127957i
$154$	−6.13750e7	+	4.45915e7i	−1.35416	+	0.983852i
$155$	2.51103e6	+	4.45754e7i	0.0541615	+	0.961467i
$156$	−3.61390e7	−	2.62565e7i	−0.762148	−	0.553733i
$157$	−4.29684e7			−0.886136			−0.443068	−	0.896488i	$-0.646110\pi$
$157$	−4.29684e7			−0.886136			−0.443068	+	0.896488i	$0.646110\pi$
$158$	−1.23123e8	−	8.94538e7i	−2.48335	−	1.80426i
$159$	−3.25492e7	+	1.00176e8i	−0.642170	+	1.97640i
$160$	8.72904e7	+	1.06936e8i	1.68479	+	2.06398i
$161$	−3.45159e6	−	1.06229e7i	−0.0651821	−	0.200610i
$162$	−3.55651e7	+	1.09458e8i	−0.657236	+	2.02276i
$163$	2.64782e7	−	8.14916e7i	0.478886	−	1.47386i	−0.361758	−	0.932272i	$-0.617823\pi$
$163$	2.64782e7	−	8.14916e7i	0.478886	−	1.47386i	0.840644	−	0.541588i	$-0.182177\pi$
$164$	−2.02277e7	−	6.22543e7i	−0.358090	−	1.10209i
$165$	−2.30359e6	−	4.08931e7i	−0.0399220	−	0.708689i
$166$	1.66354e7	−	5.11985e7i	0.282263	−	0.868718i
$167$	−4.71370e7	−	3.42470e7i	−0.783167	−	0.569004i	0.122761	−	0.992436i	$-0.460825\pi$
$167$	−4.71370e7	−	3.42470e7i	−0.783167	−	0.569004i	−0.905928	+	0.423432i	$0.860825\pi$
$168$	4.16272e8			6.77321
$169$	4.70275e7	+	3.41675e7i	0.749460	+	0.544514i
$170$	−2.88655e7	+	1.12102e7i	−0.450617	+	0.175002i
$171$	−2.67470e7	+	1.94328e7i	−0.409062	+	0.297201i
$172$	2.35072e8	−	1.70790e8i	3.52251	−	2.55925i
$173$	1.80831e7	+	5.56539e7i	0.265528	+	0.817211i	0.991571	+	0.129562i	$0.0413572\pi$
$173$	1.80831e7	+	5.56539e7i	0.265528	+	0.817211i	−0.726043	+	0.687649i	$0.758643\pi$
$174$	−2.13972e8			−3.07917
$175$	−2.41493e7	+	1.18152e8i	−0.340621	+	1.66652i
$176$	1.12016e8			1.54877
$177$	−6.09462e6	−	1.87573e7i	−0.0826114	−	0.254252i
$178$	−1.91946e8	+	1.39457e8i	−2.55099	+	1.85340i
$179$	5.47211e7	−	3.97572e7i	0.713131	−	0.518120i	−0.171051	−	0.985262i	$-0.554716\pi$
$179$	5.47211e7	−	3.97572e7i	0.713131	−	0.518120i	0.884182	+	0.467142i	$0.154716\pi$
$180$	−9.18187e7	+	1.42607e8i	−1.17348	+	1.82258i
$181$	1.04369e7	+	7.58283e6i	0.130826	+	0.0950509i	0.651274	−	0.758843i	$-0.274235\pi$
$181$	1.04369e7	+	7.58283e6i	0.130826	+	0.0950509i	−0.520448	+	0.853894i	$0.674235\pi$
$182$	7.07559e7			0.869987
$183$	−1.78534e7	−	1.29712e7i	−0.215348	−	0.156460i
$184$	−9.48275e6	+	2.91849e7i	−0.112220	+	0.345379i
$185$	−5.29654e7	+	2.05696e7i	−0.615023	+	0.238850i
$186$	−6.69400e7	−	2.06020e8i	−0.762765	−	2.34755i
$187$	−3.69912e6	+	1.13847e7i	−0.0413668	+	0.127314i
$188$	−3.76630e7	+	1.15915e8i	−0.413392	+	1.27229i
$189$	−1.00230e7	−	3.08476e7i	−0.107989	−	0.332357i
$190$	9.89538e7	−	3.84297e7i	1.04663	−	0.406471i
$191$	2.38586e7	−	7.34292e7i	0.247758	−	0.762522i	−0.747412	−	0.664361i	$-0.768704\pi$
$191$	2.38586e7	−	7.34292e7i	0.247758	−	0.762522i	0.995171	−	0.0981610i	$-0.0312960\pi$
$192$	−2.21767e8	−	1.61123e8i	−2.26122	−	1.64287i
$193$	3.51888e7			0.352334			0.176167	−	0.984360i	$-0.443630\pi$
$193$	3.51888e7			0.352334			0.176167	+	0.984360i	$0.443630\pi$
$194$	2.27862e8	+	1.65551e8i	2.24061	+	1.62790i
$195$	−2.06799e7	+	3.21186e7i	−0.199722	+	0.310196i
$196$	−4.12296e8	+	2.99550e8i	−3.91122	+	2.84167i
$197$	−2.64634e7	+	1.92268e7i	−0.246612	+	0.179174i	−0.704224	−	0.709978i	$-0.748705\pi$
$197$	−2.64634e7	+	1.92268e7i	−0.246612	+	0.179174i	0.457612	+	0.889152i	$0.348705\pi$
$198$	2.81959e7	+	8.67779e7i	0.258141	+	0.794477i
$199$	−1.44003e8			−1.29535			−0.647673	−	0.761919i	$-0.724258\pi$
$199$	−1.44003e8			−1.29535			−0.647673	+	0.761919i	$0.724258\pi$
$200$	2.44475e8	−	2.23615e8i	2.16087	−	1.97650i
$201$	7.57595e7			0.658038
$202$	−3.48631e7	−	1.07298e8i	−0.297602	−	0.915926i
$203$	1.97033e8	−	1.43153e8i	1.65311	−	1.20106i
$204$	8.73456e7	−	6.34603e7i	0.720336	−	0.523355i
$205$	−5.21804e7	+	2.02648e7i	−0.423028	+	0.164287i
$206$	3.63425e6	+	2.64044e6i	0.0289654	+	0.0210446i
$207$	−1.34340e7			−0.105271
$208$	−8.45214e7	−	6.14084e7i	−0.651246	−	0.473158i
$209$	1.26809e7	−	3.90279e7i	0.0960815	−	0.295708i
$210$	−3.29093e7	−	5.84200e8i	−0.245217	−	4.35306i
$211$	5.89552e7	+	1.81446e8i	0.432050	+	1.32971i	0.896080	+	0.443893i	$0.146403\pi$
$211$	5.89552e7	+	1.81446e8i	0.432050	+	1.32971i	−0.464030	+	0.885820i	$0.653597\pi$
$212$	−1.67303e8	+	5.14906e8i	−1.20595	+	3.71153i
$213$	−1.32766e7	+	4.08612e7i	−0.0941365	+	0.289722i
$214$	−3.01520e7	−	9.27983e7i	−0.210314	−	0.647279i
$215$	−1.57128e8	−	1.92492e8i	−1.07825	−	1.32093i
$216$	−2.75368e7	+	8.47495e7i	−0.185919	+	0.572201i
$217$	1.99474e8	+	1.44926e8i	1.32519	+	0.962803i
$218$	−3.57715e8			−2.33851
$219$	−2.27032e7	−	1.64948e7i	−0.146060	−	0.106119i
$220$	−1.18405e7	−	2.10191e8i	−0.0749706	−	1.33087i
$221$	9.03238e6	−	6.56241e6i	0.0562898	−	0.0408969i
$222$	2.23036e8	−	1.62045e8i	1.36817	−	0.994031i
$223$	9.12273e7	+	2.80769e8i	0.550881	+	1.69544i	0.706580	+	0.707634i	$0.250237\pi$
$223$	9.12273e7	+	2.80769e8i	0.550881	+	1.69544i	−0.155698	+	0.987805i	$0.549763\pi$
$224$	7.62341e8			4.53191
$225$	1.26175e8	+	7.15367e7i	0.738474	+	0.418687i
$226$	4.83863e8			2.78832
$227$	−7.77792e7	−	2.39380e8i	−0.441340	−	1.35830i	−0.886448	−	0.462827i	$-0.846835\pi$
$227$	−7.77792e7	−	2.39380e8i	−0.441340	−	1.35830i	0.445109	−	0.895477i	$-0.353165\pi$
$228$	−2.99429e8	+	2.17548e8i	−1.67310	+	1.21558i
$229$	1.15848e8	−	8.41686e7i	0.637477	−	0.463154i	−0.221505	−	0.975159i	$-0.571097\pi$
$229$	1.15848e8	−	8.41686e7i	0.637477	−	0.463154i	0.858983	+	0.512005i	$0.171097\pi$
$230$	4.17081e7	+	1.10009e7i	0.226034	+	0.0596186i
$231$	−1.82995e8	−	1.32954e8i	−0.976783	−	0.709674i
$232$	−6.69109e8			−3.51794
$233$	−6.47957e7	−	4.70768e7i	−0.335583	−	0.243816i	0.407213	−	0.913333i	$-0.366501\pi$
$233$	−6.47957e7	−	4.70768e7i	−0.335583	−	0.243816i	−0.742796	+	0.669518i	$0.766501\pi$
$234$	2.62975e7	−	8.09354e7i	0.134171	−	0.412936i
$235$	1.00781e8	+	2.65819e7i	0.506570	+	0.133613i
$236$	−3.13264e7	−	9.64129e7i	−0.155138	−	0.477467i
$237$	1.40220e8	−	4.31554e8i	0.684214	−	2.10579i
$238$	−5.28458e7	+	1.62643e8i	−0.254092	+	0.782015i
$239$	−1.46974e7	−	4.52340e7i	−0.0696384	−	0.214325i	0.910181	−	0.414212i	$-0.135943\pi$
$239$	−1.46974e7	−	4.52340e7i	−0.0696384	−	0.214325i	−0.979819	+	0.199887i	$0.935943\pi$
$240$	−4.67710e8	+	7.26418e8i	−2.18392	+	3.39193i
$241$	−3.44153e7	+	1.05919e8i	−0.158377	+	0.487434i	−0.998487	−	0.0549815i	$-0.982490\pi$
$241$	−3.44153e7	+	1.05919e8i	−0.158377	+	0.487434i	0.840111	+	0.542415i	$0.182490\pi$
$242$	2.44608e8	+	1.77718e8i	1.10947	+	0.806079i
$243$	−2.97201e8			−1.32870
$244$	−9.17665e7	−	6.66723e7i	−0.404408	−	0.293820i
$245$	2.75589e8	+	3.37614e8i	1.19724	+	1.46669i
$246$	2.19730e8	−	1.59643e8i	0.941059	−	0.683719i
$247$	−3.09639e7	+	2.24966e7i	−0.130742	+	0.0949899i
$248$	−2.09327e8	−	6.44244e8i	−0.871456	−	2.68206i
$249$	1.60509e8			0.658873
$250$	−3.33152e8	−	3.25421e8i	−1.34850	−	1.31721i
$251$	−3.74845e8			−1.49621			−0.748106	−	0.663579i	$-0.769037\pi$
$251$	−3.74845e8			−1.49621			−0.748106	+	0.663579i	$0.769037\pi$
$252$	2.89452e8	+	8.90843e8i	1.13940	+	3.50671i
$253$	1.34901e7	−	9.80113e6i	0.0523713	−	0.0380500i
$254$	−5.28088e8	+	3.83678e8i	−2.02203	+	1.46909i
$255$	−5.83840e7	−	7.15242e7i	−0.220497	−	0.270123i
$256$	−4.91718e7	−	3.57254e7i	−0.183179	−	0.133087i
$257$	1.84331e8			0.677381			0.338691	−	0.940898i	$-0.390016\pi$
$257$	1.84331e8			0.677381			0.338691	+	0.940898i	$0.390016\pi$
$258$	9.75373e8	+	7.08650e8i	3.53591	+	2.56899i
$259$	−9.69669e7	+	2.98433e8i	−0.346796	+	1.06733i
$260$	−1.06295e8	+	1.65090e8i	−0.375064	+	0.582525i
$261$	−9.05175e7	−	2.78584e8i	−0.315131	−	0.969872i
$262$	8.64793e7	−	2.66156e8i	0.297069	−	0.914285i
$263$	7.85695e7	−	2.41812e8i	0.266323	−	0.819659i	−0.725062	−	0.688683i	$-0.758189\pi$
$263$	7.85695e7	−	2.41812e8i	0.266323	−	0.819659i	0.991386	−	0.130975i	$-0.0418109\pi$
$264$	1.92035e8	+	5.91023e8i	0.642343	+	1.97693i
$265$	4.47678e8	+	1.18080e8i	1.47777	+	0.389775i
$266$	1.81161e8	−	5.57555e8i	0.590171	−	1.81636i
$267$	−5.72304e8	−	4.15803e8i	−1.84008	−	1.33690i
$268$	3.89405e8			1.23575
$269$	−2.07858e8	−	1.51018e8i	−0.651079	−	0.473036i	0.212560	−	0.977148i	$-0.431820\pi$
$269$	−2.07858e8	−	1.51018e8i	−0.651079	−	0.473036i	−0.863638	+	0.504112i	$0.831820\pi$
$270$	1.21115e8	+	3.19454e7i	0.374478	+	0.0987722i
$271$	−2.91298e8	+	2.11640e8i	−0.889088	+	0.645960i	−0.935640	−	0.352956i	$-0.885177\pi$
$271$	−2.91298e8	+	2.11640e8i	−0.889088	+	0.645960i	0.0465524	+	0.998916i	$0.485177\pi$
$272$	2.04283e8	−	1.48420e8i	0.615518	−	0.447200i
$273$	6.51919e7	+	2.00640e8i	0.193921	+	0.596827i
$274$	5.04431e8			1.48141
$275$	−1.78893e8	+	2.02191e7i	−0.518717	+	0.0586269i
$276$	−1.50392e8			−0.430569
$277$	7.56075e6	+	2.32696e7i	0.0213740	+	0.0657823i	0.961175	−	0.275941i	$-0.0889894\pi$
$277$	7.56075e6	+	2.32696e7i	0.0213740	+	0.0657823i	−0.939801	+	0.341723i	$0.888989\pi$
$278$	4.81321e8	−	3.49700e8i	1.34362	−	0.976200i
$279$	2.39914e8	−	1.74307e8i	0.661363	−	0.480509i
$280$	−1.02910e8	−	1.82685e9i	−0.280159	−	4.97335i
$281$	−2.43234e7	−	1.76720e7i	−0.0653962	−	0.0475131i	0.554607	−	0.832113i	$-0.312869\pi$
$281$	−2.43234e7	−	1.76720e7i	−0.0653962	−	0.0475131i	−0.620003	+	0.784599i	$0.712869\pi$
$282$	−5.05710e8			−1.34286
$283$	−1.29147e8	−	9.38307e7i	−0.338713	−	0.246089i	0.405406	−	0.914137i	$-0.367130\pi$
$283$	−1.29147e8	−	9.38307e7i	−0.338713	−	0.246089i	−0.744118	+	0.668048i	$0.767130\pi$
$284$	−6.82419e7	+	2.10027e8i	−0.176782	+	0.544078i
$285$	2.00146e8	+	2.45192e8i	0.512142	+	0.627407i
$286$	3.26412e7	+	1.00459e8i	0.0825059	+	0.253927i
$287$	−9.55298e7	+	2.94010e8i	−0.238535	+	0.734135i
$288$	2.83335e8	−	8.72017e8i	0.698920	−	2.15105i
$289$	−1.18463e8	−	3.64592e8i	−0.288696	−	0.888514i
$290$	5.28978e7	+	9.39034e8i	0.127363	+	2.26094i
$291$	−2.59504e8	+	7.98673e8i	−0.617333	+	1.89996i
$292$	−1.16695e8	−	8.47836e7i	−0.274291	−	0.199284i
$293$	−2.85302e8			−0.662625			−0.331313	−	0.943521i	$-0.607491\pi$
$293$	−2.85302e8			−0.662625			−0.331313	+	0.943521i	$0.607491\pi$
$294$	−1.71072e9	−	1.24291e9i	−3.92611	−	2.85248i
$295$	−8.08115e7	+	3.13840e7i	−0.183272	+	0.0711755i
$296$	6.97452e8	−	5.06729e8i	1.56312	−	1.13568i
$297$	3.91736e7	−	2.84613e7i	0.0867653	−	0.0630387i
$298$	4.89515e8	+	1.50657e9i	1.07154	+	3.29787i
$299$	−1.55520e7			−0.0336463
$300$	1.41252e9	+	8.00844e8i	3.02043	+	1.71247i
$301$	−1.37226e9			−2.90038
$302$	3.52768e8	+	1.08571e9i	0.736996	+	2.26824i
$303$	2.72139e8	−	1.97720e8i	0.562006	−	0.408321i
$304$	−7.00302e8	+	5.08799e8i	−1.42964	+	1.03870i
$305$	−5.25117e7	+	8.15578e7i	−0.105976	+	0.164595i
$306$	1.66401e8	+	1.20897e8i	0.331994	+	0.241208i
$307$	4.51854e6			0.00891280			0.00445640	−	0.999990i	$-0.498581\pi$
$307$	4.51854e6			0.00891280			0.00445640	+	0.999990i	$0.498581\pi$
$308$	−9.40599e8	−	6.83385e8i	−1.83433	−	1.33272i
$309$	−4.13893e6	+	1.27383e7i	−0.00798056	+	0.0245616i
$310$	−8.87590e8	+	3.44705e8i	−1.69218	+	0.657175i
$311$	2.63389e8	+	8.10628e8i	0.496519	+	1.52813i	0.814575	+	0.580058i	$0.196970\pi$
$311$	2.63389e8	+	8.10628e8i	0.496519	+	1.52813i	−0.318056	+	0.948072i	$0.603030\pi$
$312$	1.79106e8	−	5.51231e8i	0.333863	−	1.02752i
$313$	2.38445e8	−	7.33858e8i	0.439524	−	1.35272i	−0.448854	−	0.893605i	$-0.648168\pi$
$313$	2.38445e8	−	7.33858e8i	0.439524	−	1.35272i	0.888378	−	0.459112i	$-0.151832\pi$
$314$	−2.83182e8	−	8.71543e8i	−0.516192	−	1.58868i
$315$	7.46688e8	−	2.89984e8i	1.34602	−	0.522741i
$316$	7.20735e8	−	2.21819e9i	1.28490	−	3.95453i
$317$	2.16473e8	+	1.57277e8i	0.381678	+	0.277305i	0.762037	−	0.647534i	$-0.224200\pi$
$317$	2.16473e8	+	1.57277e8i	0.381678	+	0.277305i	−0.380359	+	0.924839i	$0.624200\pi$
$318$	−2.24642e9			−3.91738
$319$	2.94144e8	+	2.13708e8i	0.507332	+	0.368598i
$320$	−6.52278e8	+	1.01308e9i	−1.11278	+	1.72829i
$321$	2.35364e8	−	1.71002e8i	0.397166	−	0.288558i
$322$	1.92720e8	−	1.40019e8i	0.321686	−	0.233718i
$323$	−2.85855e7	−	8.79771e7i	−0.0471995	−	0.145265i
$324$	−1.76382e9			−2.88103
$325$	1.46068e8	+	8.28151e7i	0.236028	+	0.133819i
$326$	1.82743e9			2.92131
$327$	−3.29585e8	−	1.01436e9i	−0.521255	−	1.60426i
$328$	6.87116e8	−	4.99219e8i	1.07516	−	0.781146i
$329$	4.65676e8	−	3.38333e8i	0.720938	−	0.523792i
$330$	8.14267e8	−	3.16229e8i	1.24729	−	0.484398i
$331$	3.93112e8	+	2.85613e8i	0.595825	+	0.432892i	0.844395	−	0.535722i	$-0.179960\pi$
$331$	3.93112e8	+	2.85613e8i	0.595825	+	0.432892i	−0.248569	+	0.968614i	$0.579960\pi$
$332$	8.25018e8			1.23732
$333$	3.05329e8	+	2.21834e8i	0.453120	+	0.329211i
$334$	3.83990e8	−	1.18180e9i	0.563907	−	1.73553i
$335$	−1.87292e7	−	3.32478e8i	−0.0272183	−	0.483176i
$336$	1.47443e9	+	4.53782e9i	2.12049	+	6.52619i
$337$	−1.24708e8	+	3.83813e8i	−0.177497	+	0.546280i	−0.999739	−	0.0228588i	$-0.992723\pi$
$337$	−1.24708e8	+	3.83813e8i	−0.177497	+	0.546280i	0.822242	+	0.569139i	$0.192723\pi$
$338$	−3.83098e8	+	1.17905e9i	−0.539637	+	1.66083i
$339$	4.45814e8	+	1.37207e9i	0.621519	+	1.91284i
$340$	−3.00095e8	−	3.67635e8i	−0.414078	−	0.507272i
$341$	−1.13745e8	+	3.50070e8i	−0.155343	+	0.478096i
$342$	−5.70438e8	−	4.14447e8i	−0.771111	−	0.560245i
$343$	1.13559e9			1.51947
$344$	3.05008e9	+	2.21601e9i	4.03977	+	2.93506i
$345$	7.23339e6	+	1.28406e8i	0.00948364	+	0.168352i
$346$	−1.00967e9	+	7.33570e8i	−1.31043	+	0.952084i
$347$	1.09787e9	−	7.97648e8i	1.41058	−	1.02484i	0.417339	−	0.908751i	$-0.362963\pi$
$347$	1.09787e9	−	7.97648e8i	1.41058	−	1.02484i	0.993238	−	0.116094i	$-0.0370373\pi$
$348$	−1.01333e9	−	3.11872e9i	−1.28892	−	3.96687i
$349$	−5.47696e8			−0.689685			−0.344843	−	0.938661i	$-0.612068\pi$
$349$	−5.47696e8			−0.689685			−0.344843	+	0.938661i	$0.612068\pi$
$350$	−2.55568e9	+	2.88851e8i	−3.18617	+	0.360110i
$351$	−4.51611e7			−0.0557430
$352$	3.51684e8	+	1.08237e9i	0.429787	+	1.32275i
$353$	−9.26071e8	+	6.72830e8i	−1.12055	+	0.814131i	−0.984293	−	0.176542i	$-0.943509\pi$
$353$	−9.26071e8	+	6.72830e8i	−1.12055	+	0.814131i	−0.136262	+	0.990673i	$0.543509\pi$
$354$	3.40295e8	−	2.47239e8i	0.407703	−	0.296214i
$355$	1.82605e8	+	4.81639e7i	0.216628	+	0.0571376i
$356$	−2.94165e9	−	2.13723e9i	−3.45554	−	2.51060i
$357$	−5.09890e8			−0.593113
$358$	1.16705e9	+	8.47909e8i	1.34430	+	0.976694i
$359$	1.21983e8	−	3.75426e8i	0.139146	−	0.428246i	−0.857066	−	0.515206i	$-0.827715\pi$
$359$	1.21983e8	−	3.75426e8i	0.139146	−	0.428246i	0.996212	+	0.0869602i	$0.0277153\pi$
$360$	−2.12792e9	−	5.61259e8i	−2.40379	−	0.634023i
$361$	−1.78228e8	−	5.48528e8i	−0.199388	−	0.613654i
$362$	−8.50214e7	+	2.61669e8i	−0.0941994	+	0.289916i
$363$	−2.78576e8	+	8.57369e8i	−0.305682	+	0.940794i
$364$	3.35087e8	+	1.03129e9i	0.364169	+	1.12080i
$365$	−6.67764e7	+	1.03713e8i	−0.0718783	+	0.111637i
$366$	1.45438e8	−	4.47612e8i	0.155058	−	0.477219i
$367$	2.23030e8	+	1.62040e8i	0.235522	+	0.171117i	0.699286	−	0.714842i	$-0.253501\pi$
$367$	2.23030e8	+	1.62040e8i	0.235522	+	0.171117i	−0.463764	+	0.885959i	$0.653501\pi$
$368$	−3.51735e8			−0.367916
$369$	3.00804e8	+	2.18547e8i	0.311667	+	0.226439i
$370$	−7.66288e8	−	9.38752e8i	−0.786476	−	0.963485i
$371$	2.06858e9	−	1.50291e9i	2.10312	−	1.52801i
$372$	2.68580e9	−	1.95135e9i	2.70504	−	1.96533i
$373$	−6.78238e7	−	2.08740e8i	−0.0676707	−	0.208269i	0.911503	−	0.411294i	$-0.134923\pi$
$373$	−6.78238e7	−	2.08740e8i	−0.0676707	−	0.208269i	−0.979174	+	0.203024i	$0.934923\pi$
$374$	−2.55299e8			−0.252347
$375$	6.15830e8	−	1.24454e9i	0.603048	−	1.21870i
$376$	−1.58140e9			−1.53421
$377$	−1.04788e8	−	3.22506e8i	−0.100721	−	0.309986i
$378$	5.59636e8	−	4.06600e8i	0.532948	−	0.387209i
$379$	−7.07257e8	+	5.13853e8i	−0.667329	+	0.484843i	−0.869130	−	0.494583i	$-0.835321\pi$
$379$	−7.07257e8	+	5.13853e8i	−0.667329	+	0.484843i	0.201801	+	0.979427i	$0.435321\pi$
$380$	1.02875e9	+	1.26029e9i	0.961766	+	1.17823i
$381$	−1.57454e9	−	1.14397e9i	−1.45854	−	1.05969i
$382$	1.64663e9			1.51138
$383$	−1.86445e8	−	1.35460e8i	−0.169572	−	0.123202i	0.499762	−	0.866163i	$-0.333421\pi$
$383$	−1.86445e8	−	1.35460e8i	−0.169572	−	0.123202i	−0.669335	+	0.742961i	$0.733421\pi$
$384$	5.64391e8	−	1.73702e9i	0.508652	−	1.56547i
$385$	−5.38240e8	+	8.35960e8i	−0.480688	+	0.746574i
$386$	2.31911e8	+	7.13747e8i	0.205241	+	0.631668i
$387$	−5.10022e8	+	1.56969e9i	−0.447302	+	1.37665i
$388$	−1.33386e9	+	4.10519e9i	−1.15931	+	3.56798i
$389$	−1.64376e8	−	5.05896e8i	−0.141584	−	0.435750i	0.854972	−	0.518674i	$-0.173574\pi$
$389$	−1.64376e8	−	5.05896e8i	−0.141584	−	0.435750i	−0.996556	+	0.0829238i	$0.973574\pi$
$390$	−7.87763e8	−	2.07780e8i	−0.672465	−	0.177369i
$391$	1.16154e7	−	3.57485e7i	0.00982687	−	0.0302440i
$392$	−5.34956e9	−	3.88668e9i	−4.48556	−	3.25895i
$393$	8.34408e8			0.693433
$394$	−5.64390e8	−	4.10054e8i	−0.464882	−	0.337757i
$395$	−1.92858e9	−	5.08681e8i	−1.57452	−	0.415294i
$396$	−1.13129e9	+	8.21930e8i	−0.915462	+	0.665122i
$397$	5.87700e8	−	4.26989e8i	0.471399	−	0.342492i	−0.326587	−	0.945167i	$-0.605899\pi$
$397$	5.87700e8	−	4.26989e8i	0.471399	−	0.342492i	0.797986	+	0.602675i	$0.205899\pi$
$398$	−9.49046e8	−	2.92086e9i	−0.754565	−	2.32231i
$399$	1.74795e9			1.37761
$400$	3.30358e9	+	1.87300e9i	2.58092	+	1.46329i
$401$	1.22448e9			0.948299			0.474149	−	0.880444i	$-0.342756\pi$
$401$	1.22448e9			0.948299			0.474149	+	0.880444i	$0.342756\pi$
$402$	4.99290e8	+	1.53666e9i	0.383320	+	1.17974i
$403$	2.77738e8	−	2.01789e8i	0.211382	−	0.153578i
$404$	1.39880e9	−	1.01629e9i	1.05541	−	0.766798i
$405$	8.48343e7	+	1.50597e9i	0.0634569	+	1.12648i
$406$	4.20215e9	+	3.05304e9i	3.11624	+	2.26408i
$407$	−4.68449e8			−0.344415
$408$	1.13331e9	+	8.23400e8i	0.826113	+	0.600206i
$409$	−1.54573e6	+	4.75726e6i	−0.00111712	+	0.00343815i	−0.951614	−	0.307297i	$-0.900575\pi$
$409$	−1.54573e6	+	4.75726e6i	−0.00111712	+	0.00343815i	0.950496	+	0.310736i	$0.100575\pi$
$410$	−7.54931e8	−	9.24839e8i	−0.540958	−	0.662709i
$411$	4.64764e8	+	1.43040e9i	0.330207	+	1.01627i
$412$	−2.12742e7	+	6.54751e7i	−0.0149869	+	0.0461250i
$413$	−1.47946e8	+	4.55332e8i	−0.103343	+	0.318056i
$414$	−8.85363e7	−	2.72487e8i	−0.0613225	−	0.188731i
$415$	−3.96808e7	−	7.04408e8i	−0.0272529	−	0.483789i
$416$	3.28006e8	−	1.00950e9i	0.223386	−	0.687510i
$417$	1.43510e9	+	1.04266e9i	0.969186	+	0.704155i
$418$	8.75191e8			0.586119
$419$	−1.76723e9	−	1.28397e9i	−1.17366	−	0.852715i	−0.182219	−	0.983258i	$-0.558328\pi$
$419$	−1.76723e9	−	1.28397e9i	−1.17366	−	0.852715i	−0.991443	+	0.130542i	$0.958328\pi$
$420$	8.35908e9	−	3.24633e9i	5.50536	−	2.13806i
$421$	−2.31932e8	+	1.68508e8i	−0.151486	+	0.110061i	−0.660947	−	0.750433i	$-0.729845\pi$
$421$	−2.31932e8	+	1.68508e8i	−0.151486	+	0.110061i	0.509460	+	0.860494i	$0.329845\pi$
$422$	−3.29178e9	+	2.39162e9i	−2.13225	+	1.54917i
$423$	−2.13933e8	−	6.58418e8i	−0.137431	−	0.422971i
$424$	−7.02475e9			−4.47559
$425$	−2.99457e8	+	2.73906e8i	−0.189223	+	0.173077i
$426$	−9.16300e8			−0.574254
$427$	1.65540e8	+	5.09479e8i	0.102897	+	0.316686i
$428$	1.20977e9	−	8.78952e8i	0.745849	−	0.541891i
$429$	−2.54795e8	+	1.85119e8i	−0.155808	+	0.113201i
$430$	2.86884e9	−	4.45570e9i	1.74007	−	2.70257i
$431$	1.48329e8	+	1.07767e8i	0.0892393	+	0.0648361i	0.631510	−	0.775368i	$-0.282435\pi$
$431$	1.48329e8	+	1.07767e8i	0.0892393	+	0.0648361i	−0.542271	+	0.840204i	$0.682435\pi$
$432$	−1.02140e9			−0.609539
$433$	−2.24891e9	−	1.63393e9i	−1.33127	−	0.967221i	−0.999717	−	0.0237826i	$-0.992429\pi$
$433$	−2.24891e9	−	1.63393e9i	−1.33127	−	0.967221i	−0.331548	−	0.943438i	$-0.607571\pi$
$434$	−1.62496e9	+	5.00112e9i	−0.954179	+	2.93666i
$435$	−2.61405e9	+	1.01519e9i	−1.52265	+	0.591338i
$436$	−1.69407e9	−	5.21382e9i	−0.978880	−	3.01268i
$437$	−3.98187e7	+	1.22549e8i	−0.0228246	+	0.0702468i
$438$	1.84946e8	−	5.69205e8i	0.105168	−	0.323675i
$439$	5.22318e7	+	1.60753e8i	0.0294652	+	0.0906845i	0.964708	−	0.263323i	$-0.0848186\pi$
$439$	5.22318e7	+	1.60753e8i	0.0294652	+	0.0906845i	−0.935242	+	0.354008i	$0.884819\pi$
$440$	2.54628e9	−	9.88875e8i	1.42502	−	0.553423i
$441$	8.94533e8	−	2.75309e9i	0.496662	−	1.52857i
$442$	1.92635e8	+	1.39958e8i	0.106110	+	0.0770937i
$443$	2.40351e9			1.31351			0.656754	−	0.754105i	$-0.271929\pi$
$443$	2.40351e9			1.31351			0.656754	+	0.754105i	$0.271929\pi$
$444$	3.41812e9	+	2.48341e9i	1.85331	+	1.34651i
$445$	−1.68331e9	+	2.61440e9i	−0.905530	+	1.40641i
$446$	−5.09370e9	+	3.70079e9i	−2.71870	+	1.97525i
$447$	−3.82112e9	+	2.77620e9i	−2.02355	+	1.47019i
$448$	2.05626e9	+	6.32853e9i	1.08045	+	3.32529i
$449$	8.12090e8			0.423391			0.211696	−	0.977336i	$-0.432101\pi$
$449$	8.12090e8			0.423391			0.211696	+	0.977336i	$0.432101\pi$
$450$	−6.19450e8	+	3.03072e9i	−0.320452	+	1.56784i
$451$	−4.61506e8			−0.236897
$452$	2.29149e9	+	7.05248e9i	1.16717	+	3.59217i
$453$	−2.75368e9	+	2.00067e9i	−1.39178	+	1.01119i
$454$	4.34282e9	−	3.15525e9i	2.17809	−	1.58248i
$455$	8.64410e8	−	3.35703e8i	0.430210	−	0.167076i
$456$	−3.88511e9	−	2.82270e9i	−1.91879	−	1.39408i
$457$	−2.50747e9			−1.22894			−0.614468	−	0.788942i	$-0.710629\pi$
$457$	−2.50747e9			−1.22894			−0.614468	+	0.788942i	$0.710629\pi$
$458$	2.47071e9	+	1.79508e9i	1.20169	+	0.873080i
$459$	3.37297e7	−	1.03809e8i	0.0162805	−	0.0501063i
$460$	3.71797e7	+	6.60009e8i	0.0178096	+	0.316153i
$461$	5.23822e8	+	1.61216e9i	0.249018	+	0.766398i	0.994950	+	0.100376i	$0.0320044\pi$
$461$	5.23822e8	+	1.61216e9i	0.249018	+	0.766398i	−0.745932	+	0.666022i	$0.767996\pi$
$462$	1.49073e9	−	4.58799e9i	0.703317	−	2.16459i
$463$	5.14227e8	−	1.58263e9i	0.240780	−	0.741046i	−0.755522	−	0.655124i	$-0.772616\pi$
$463$	5.14227e8	−	1.58263e9i	0.240780	−	0.741046i	0.996302	−	0.0859219i	$-0.0273836\pi$
$464$	−2.36997e9	−	7.29401e9i	−1.10136	−	3.38964i
$465$	−1.79526e9	−	2.19931e9i	−0.828022	−	1.01438i
$466$	5.27842e8	−	1.62453e9i	0.241631	−	0.743665i
$467$	2.18293e9	+	1.58599e9i	0.991814	+	0.720595i	0.960318	−	0.278909i	$-0.0899727\pi$
$467$	2.18293e9	+	1.58599e9i	0.991814	+	0.720595i	0.0314964	+	0.999504i	$0.489973\pi$
$468$	1.30420e9			0.588145
$469$	−1.48783e9	−	1.08097e9i	−0.665959	−	0.483848i
$470$	1.25021e8	+	2.21935e9i	0.0555444	+	0.986016i
$471$	2.21049e9	−	1.60602e9i	0.974801	−	0.708234i
$472$	1.06413e9	−	7.73137e8i	0.465799	−	0.338423i
$473$	−6.33054e8	−	1.94834e9i	−0.275060	−	0.846547i
$474$	9.67747e9			4.17386
$475$	1.02657e9	−	9.38976e8i	0.439501	−	0.402001i
$476$	−2.62084e9			−1.11382
$477$	−9.50313e8	−	2.92476e9i	−0.400915	−	1.23389i
$478$	8.20635e8	−	5.96226e8i	0.343678	−	0.249697i
$479$	1.28012e9	−	9.30064e8i	0.532203	−	0.386668i	−0.288978	−	0.957336i	$-0.593315\pi$
$479$	1.28012e9	−	9.30064e8i	0.532203	−	0.386668i	0.821181	+	0.570668i	$0.193315\pi$
$480$	−8.48755e9	−	2.23867e9i	−3.50298	−	0.923946i
$481$	3.53467e8	+	2.56809e8i	0.144824	+	0.105221i
$482$	−2.37521e9			−0.966134
$483$	5.74614e8	+	4.17481e8i	0.232039	+	0.168586i
$484$	−1.43189e9	+	4.40689e9i	−0.574050	+	1.76674i
$485$	3.56920e9	+	9.41412e8i	1.42061	+	0.374700i
$486$	−1.95869e9	−	6.02823e9i	−0.773996	−	2.38211i
$487$	4.63917e8	−	1.42779e9i	0.182007	−	0.560161i	−0.817877	−	0.575394i	$-0.804849\pi$
$487$	4.63917e8	−	1.42779e9i	0.182007	−	0.560161i	0.999884	+	0.0152324i	$0.00484883\pi$
$488$	4.54797e8	−	1.39972e9i	0.177153	−	0.545221i
$489$	1.68372e9	+	5.18197e9i	0.651163	+	2.00407i
$490$	−5.03169e9	+	7.81490e9i	−1.93209	+	3.00080i
$491$	3.78250e8	−	1.16413e9i	0.144209	−	0.443830i	−0.852699	−	0.522402i	$-0.825036\pi$
$491$	3.78250e8	−	1.16413e9i	0.144209	−	0.443830i	0.996908	+	0.0785717i	$0.0250360\pi$
$492$	3.36746e9	+	2.44660e9i	1.27475	+	0.926160i
$493$	8.19589e8			0.308058
$494$	−6.60373e8	−	4.79789e8i	−0.246459	−	0.179063i
$495$	7.56182e8	+	9.26373e8i	0.280226	+	0.343295i
$496$	6.28153e9	−	4.56380e9i	2.31142	−	1.67935i
$497$	8.43761e8	−	6.13029e8i	0.308299	−	0.223992i
$498$	1.05783e9	+	3.25566e9i	0.383806	+	1.18123i
$499$	−9.14240e8			−0.329388			−0.164694	−	0.986345i	$-0.552664\pi$
$499$	−9.14240e8			−0.329388			−0.164694	+	0.986345i	$0.552664\pi$
$500$	3.16538e9	−	6.39694e9i	1.13248	−	2.28864i
$501$	3.70498e9			1.31630
$502$	−2.47040e9	−	7.60311e9i	−0.871574	−	2.68243i
$503$	3.22245e9	−	2.34125e9i	1.12901	−	0.820276i	0.143462	−	0.989656i	$-0.454177\pi$
$503$	3.22245e9	−	2.34125e9i	1.12901	−	0.820276i	0.985551	+	0.169380i	$0.0541765\pi$
$504$	−9.83245e9	+	7.14369e9i	−3.42101	+	2.48551i
$505$	−9.34991e8	−	1.14542e9i	−0.323063	−	0.395774i
$506$	2.87706e8	+	2.09030e8i	0.0987237	+	0.0717270i
$507$	−3.69638e9			−1.25965
$508$	−8.09318e9	−	5.88004e9i	−2.73903	−	1.99002i
$509$	1.55904e8	−	4.79822e8i	0.0524016	−	0.161275i	−0.921431	−	0.388542i	$-0.872979\pi$
$509$	1.55904e8	−	4.79822e8i	0.0524016	−	0.161275i	0.973833	+	0.227267i	$0.0729789\pi$
$510$	1.06597e9	−	1.65560e9i	0.355836	−	0.552662i
$511$	2.10508e8	+	6.47878e8i	0.0697904	+	0.214793i
$512$	−7.35513e8	+	2.26368e9i	−0.242184	+	0.745365i
$513$	−1.15629e8	+	3.55869e8i	−0.0378142	+	0.116380i
$514$	1.21483e9	+	3.73886e9i	0.394588	+	1.21442i
$515$	5.69265e7	+	1.50149e7i	0.0183649	+	0.00484393i
$516$	−5.70964e9	+	1.75725e10i	−1.82951	+	5.63065i
$517$	6.95192e8	+	5.05086e8i	0.221252	+	0.160749i
$518$	−6.69229e9			−2.11554
$519$	−3.01043e9	−	2.18721e9i	−0.945242	−	0.686759i
$520$	−2.46340e9	−	6.49747e8i	−0.768288	−	0.202644i
$521$	−3.04115e8	+	2.20952e8i	−0.0942118	+	0.0684489i	−0.633894	−	0.773420i	$-0.718544\pi$
$521$	−3.04115e8	+	2.20952e8i	−0.0942118	+	0.0684489i	0.539682	+	0.841869i	$0.318544\pi$
$522$	5.05407e9	−	3.67199e9i	1.55523	−	1.12994i
$523$	−1.08434e9	−	3.33725e9i	−0.331443	−	1.02008i	−0.968448	−	0.249217i	$-0.919827\pi$
$523$	−1.08434e9	−	3.33725e9i	−0.331443	−	1.02008i	0.637004	−	0.770860i	$-0.280173\pi$
$524$	4.28887e9			1.30222
$525$	−3.17379e9	−	6.98092e9i	−0.957241	−	2.10550i
$526$	5.42257e9			1.62463
$527$	2.56405e8	+	7.89132e8i	0.0763112	+	0.234862i
$528$	−5.76261e9	+	4.18678e9i	−1.70373	+	1.23783i
$529$	2.71220e9	−	1.97053e9i	0.796576	−	0.578746i
$530$	5.55357e8	+	9.85862e9i	0.162034	+	2.87641i
$531$	4.65853e8	+	3.38462e8i	0.135026	+	0.0981023i
$532$	8.98451e9			2.58704
$533$	3.48228e8	+	2.53003e8i	0.0996137	+	0.0723736i
$534$	4.66213e9	−	1.43486e10i	1.32492	−	4.07769i
$535$	−8.08644e8	−	9.90641e8i	−0.228307	−	0.279691i
$536$	1.56132e9	+	4.80526e9i	0.437942	+	1.34785i
$537$	−1.32911e9	+	4.09059e9i	−0.370383	+	1.13992i
$538$	1.69326e9	−	5.21133e9i	0.468799	−	1.44281i
$539$	1.11032e9	+	3.41721e9i	0.305413	+	0.939964i
$540$	1.07965e8	+	1.91659e9i	0.0295058	+	0.523782i
$541$	−9.67380e8	+	2.97729e9i	−0.262668	+	0.808408i	0.729554	+	0.683923i	$0.239728\pi$
$541$	−9.67380e8	+	2.97729e9i	−0.262668	+	0.808408i	−0.992222	+	0.124485i	$0.960272\pi$
$542$	−6.21256e9	−	4.51369e9i	−1.67600	−	1.21768i
$543$	−8.20341e8			−0.219885
$544$	2.07550e9	+	1.50794e9i	0.552747	+	0.401594i
$545$	−4.37013e9	+	1.69718e9i	−1.15640	+	0.449098i
$546$	−3.64001e9	+	2.64462e9i	−0.957035	+	0.695327i
$547$	2.78680e9	−	2.02473e9i	0.728032	−	0.528946i	−0.160908	−	0.986969i	$-0.551442\pi$
$547$	2.78680e9	−	2.02473e9i	0.728032	−	0.528946i	0.888940	+	0.458023i	$0.151442\pi$
$548$	2.38889e9	+	7.35226e9i	0.620105	+	1.90849i
$549$	6.44301e8			0.166183
$550$	−1.58910e9	−	3.49531e9i	−0.407270	−	0.895810i
$551$	−2.80963e9			−0.715516
$552$	−6.02999e8	−	1.85584e9i	−0.152591	−	0.469627i
$553$	−8.91136e9	+	6.47448e9i	−2.24081	+	1.62805i
$554$	−4.22156e8	+	3.06714e8i	−0.105485	+	0.0766390i
$555$	1.95596e9	−	3.03787e9i	0.485662	−	0.754298i
$556$	7.37645e9	+	5.35931e9i	1.82006	+	1.32235i
$557$	4.32793e9			1.06117			0.530587	−	0.847630i	$-0.321971\pi$
$557$	4.32793e9			1.06117			0.530587	+	0.847630i	$0.321971\pi$
$558$	5.11668e9	+	3.71749e9i	1.24672	+	0.905794i
$559$	−5.90432e8	+	1.81716e9i	−0.142965	+	0.440000i
$560$	1.95501e10	−	7.59249e9i	4.70426	−	1.82695i
$561$	−2.35223e8	−	7.23942e8i	−0.0562484	−	0.173115i
$562$	1.98145e8	−	6.09827e8i	0.0470875	−	0.144920i
$563$	−1.09718e9	+	3.37678e9i	−0.259119	+	0.797487i	0.733871	+	0.679289i	$0.237712\pi$
$563$	−1.09718e9	+	3.37678e9i	−0.259119	+	0.797487i	−0.992990	+	0.118198i	$0.962288\pi$
$564$	−2.39495e9	−	7.37091e9i	−0.562108	−	1.72999i
$565$	5.91126e9	−	2.29570e9i	1.37883	−	0.535482i
$566$	1.05206e9	−	3.23792e9i	0.243885	−	0.750600i
$567$	6.73916e9	+	4.89628e9i	1.55262	+	1.12804i
$568$	−2.86535e9			−0.656083
$569$	−3.69407e9	−	2.68390e9i	−0.840645	−	0.610764i	0.0819057	−	0.996640i	$-0.473899\pi$
$569$	−3.69407e9	−	2.68390e9i	−0.840645	−	0.610764i	−0.922551	+	0.385876i	$0.873899\pi$
$570$	−3.65426e9	+	5.67556e9i	−0.826490	+	1.28365i
$571$	1.33957e9	−	9.73255e8i	0.301120	−	0.218776i	−0.426957	−	0.904272i	$-0.640414\pi$
$571$	1.33957e9	−	9.73255e8i	0.301120	−	0.218776i	0.728077	+	0.685496i	$0.240414\pi$
$572$	−1.30965e9	+	9.51515e8i	−0.292596	+	0.212583i
$573$	1.51714e9	+	4.66929e9i	0.336888	+	1.03683i
$574$	−6.59310e9			−1.45512
$575$	5.61734e8	−	6.34888e7i	0.123223	−	0.0139271i
$576$	8.00324e9			1.74497
$577$	1.57881e9	+	4.85907e9i	0.342148	+	1.05302i	0.963093	+	0.269169i	$0.0867489\pi$
$577$	1.57881e9	+	4.85907e9i	0.342148	+	1.05302i	−0.620945	+	0.783854i	$0.713251\pi$
$578$	6.61442e9	−	4.80565e9i	1.42477	−	1.03515i
$579$	−1.81027e9	+	1.31524e9i	−0.387587	+	0.281599i
$580$	−1.34363e10	+	5.21811e9i	−2.85943	+	1.11049i
$581$	−3.15221e9	−	2.29021e9i	−0.666804	−	0.484461i
$582$	−1.79100e10			−3.76587
$583$	3.08812e9	+	2.24365e9i	0.645437	+	0.468938i
$584$	5.78342e8	−	1.77995e9i	0.120154	−	0.369797i
$585$	−6.27281e7	−	1.11354e9i	−0.0129544	−	0.229964i
$586$	−1.88027e9	−	5.78688e9i	−0.385992	−	1.18796i
$587$	−7.49782e8	+	2.30759e9i	−0.153004	+	0.470897i	−0.997953	−	0.0639494i	$-0.979630\pi$
$587$	−7.49782e8	+	2.30759e9i	−0.153004	+	0.470897i	0.844950	+	0.534846i	$0.179630\pi$
$588$	1.00142e10	−	3.08205e10i	2.03140	−	6.25200i
$589$	−8.78981e8	−	2.70522e9i	−0.177246	−	0.545506i
$590$	−1.16916e9	−	1.43229e9i	−0.234364	−	0.287111i
$591$	6.42766e8	−	1.97823e9i	0.128085	−	0.394204i
$592$	7.99426e9	+	5.80817e9i	1.58362	+	1.15057i
$593$	3.56163e9			0.701387			0.350694	−	0.936490i	$-0.385946\pi$
$593$	3.56163e9			0.701387			0.350694	+	0.936490i	$0.385946\pi$
$594$	8.35462e8	+	6.06999e8i	0.163559	+	0.118833i
$595$	1.26054e8	+	2.23770e9i	0.0245329	+	0.435504i
$596$	−1.96406e10	+	1.42697e10i	−3.80008	+	2.76092i
$597$	7.40817e9	−	5.38235e9i	1.42495	−	1.03529i
$598$	−1.02495e8	−	3.15447e8i	−0.0195996	−	0.0603215i
$599$	1.10839e9			0.210717			0.105358	−	0.994434i	$-0.466401\pi$
$599$	1.10839e9			0.210717			0.105358	+	0.994434i	$0.466401\pi$
$600$	−4.21892e9	+	2.06415e10i	−0.797393	+	3.90131i
$601$	5.74736e9			1.07996			0.539980	−	0.841678i	$-0.318432\pi$
$601$	5.74736e9			1.07996			0.539980	+	0.841678i	$0.318432\pi$
$602$	−9.04385e9	−	2.78341e10i	−1.68953	−	5.19983i
$603$	−1.78946e9	+	1.30012e9i	−0.332362	+	0.241475i
$604$	−1.41540e10	+	1.02835e10i	−2.61366	+	1.89893i
$605$	3.83151e9	+	1.01060e9i	0.703439	+	0.185539i
$606$	5.80395e9	+	4.21681e9i	1.05942	+	0.769716i
$607$	4.84040e9			0.878457			0.439229	−	0.898375i	$-0.355252\pi$
$607$	4.84040e9			0.878457			0.439229	+	0.898375i	$0.355252\pi$
$608$	−7.11502e9	−	5.16936e9i	−1.28385	−	0.932770i
$609$	−4.78570e9	+	1.47289e10i	−0.858588	+	2.64246i
$610$	−2.00034e9	−	5.27610e8i	−0.356820	−	0.0941149i
$611$	−2.47661e8	−	7.62224e8i	−0.0439252	−	0.135188i
$612$	−9.74075e8	+	2.99790e9i	−0.171776	+	0.528672i
$613$	−6.37027e8	+	1.96057e9i	−0.111698	+	0.343772i	−0.991244	−	0.132042i	$-0.957847\pi$
$613$	−6.37027e8	+	1.96057e9i	−0.111698	+	0.343772i	0.879546	+	0.475814i	$0.157847\pi$
$614$	2.97793e7	+	9.16511e7i	0.00519188	+	0.0159790i
$615$	1.92697e9	−	2.99284e9i	0.334050	−	0.518825i
$616$	4.66163e9	−	1.43470e10i	0.803537	−	2.47303i
$617$	−9.11307e9	−	6.62103e9i	−1.56195	−	1.13482i	−0.934390	−	0.356253i	$-0.884054\pi$
$617$	−9.11307e9	−	6.62103e9i	−1.56195	−	1.13482i	−0.627559	−	0.778569i	$-0.715946\pi$
$618$	−2.85653e8			−0.0486832
$619$	−6.04604e9	−	4.39271e9i	−1.02460	−	0.744415i	−0.0573786	−	0.998352i	$-0.518274\pi$
$619$	−6.04604e9	−	4.39271e9i	−1.02460	−	0.744415i	−0.967221	+	0.253938i	$0.918274\pi$
$620$	−9.22766e9	−	1.13045e10i	−1.55497	−	1.90493i
$621$	−1.23007e8	+	8.93697e7i	−0.0206115	+	0.0149751i
$622$	−1.47064e10	+	1.06848e10i	−2.45042	+	1.78033i
$623$	5.30651e9	+	1.63318e10i	0.879227	+	2.70598i
$624$	6.64341e9			1.09457
$625$	−5.61401e9	−	2.39495e9i	−0.919799	−	0.392389i
$626$	1.64566e10			2.68120
$627$	8.06369e8	+	2.48175e9i	0.130646	+	0.402088i
$628$	1.13620e10	−	8.25495e9i	1.83060	−	1.33001i
$629$	−8.54307e8	+	6.20691e8i	−0.136879	+	0.0994484i
$630$	1.08029e10	+	1.32342e10i	1.72126	+	2.10866i
$631$	−6.01013e9	−	4.36662e9i	−0.952316	−	0.691898i	−0.000962767	−	1.00000i	$-0.500306\pi$
$631$	−6.01013e9	−	4.36662e9i	−0.952316	−	0.691898i	−0.951354	+	0.308101i	$0.900306\pi$
$632$	3.02623e10			4.76862
$633$	−9.81476e9	−	7.13084e9i	−1.53804	−	1.11745i
$634$	−1.76345e9	+	5.42733e9i	−0.274821	+	0.845812i
$635$	−4.63117e9	+	7.19284e9i	−0.717766	+	1.11479i
$636$	−1.06386e10	−	3.27424e10i	−1.63978	−	5.04673i
$637$	1.03556e9	−	3.18714e9i	0.158741	−	0.488555i
$638$	−2.39617e9	+	7.37465e9i	−0.365296	+	1.12427i
$639$	−3.87627e8	−	1.19299e9i	−0.0587707	−	0.180878i
$640$	−7.76259e9	−	2.04746e9i	−1.17051	−	0.308735i
$641$	−6.61185e8	+	2.03492e9i	−0.0991561	+	0.305171i	−0.988315	−	0.152428i	$-0.951291\pi$
$641$	−6.61185e8	+	2.03492e9i	−0.0991561	+	0.305171i	0.889158	+	0.457600i	$0.151291\pi$
$642$	5.01965e9	+	3.64699e9i	0.748688	+	0.543953i
$643$	−3.73927e9			−0.554687			−0.277344	−	0.960771i	$-0.589454\pi$
$643$	−3.73927e9			−0.554687			−0.277344	+	0.960771i	$0.589454\pi$
$644$	2.95352e9	+	2.14586e9i	0.435752	+	0.316593i
$645$	1.52781e10	+	4.02976e9i	2.24187	+	0.591316i
$646$	1.59608e9	−	1.15962e9i	0.232938	−	0.169239i
$647$	8.88840e9	−	6.45780e9i	1.29020	−	0.937388i	0.290395	−	0.956907i	$-0.406213\pi$
$647$	8.88840e9	−	6.45780e9i	1.29020	−	0.937388i	0.999809	+	0.0195189i	$0.00621344\pi$
$648$	−7.07206e9	−	2.17656e10i	−1.02102	−	3.14237i
$649$	−7.14732e8			−0.102633
$650$	−7.17113e8	+	3.50854e9i	−0.102421	+	0.501106i
$651$	−1.56787e10			−2.22729
$652$	8.65436e9	+	2.66354e10i	1.22284	+	3.76350i
$653$	6.58231e9	−	4.78233e9i	0.925086	−	0.672114i	−0.0196988	−	0.999806i	$-0.506271\pi$
$653$	6.58231e9	−	4.78233e9i	0.925086	−	0.672114i	0.944785	+	0.327692i	$0.106271\pi$
$654$	1.84025e10	−	1.33702e10i	2.57249	−	1.86903i
$655$	−2.06281e8	−	3.66188e9i	−0.0286824	−	0.509166i
$656$	7.87578e9	+	5.72209e9i	1.08926	+	0.791391i
$657$	8.19324e8			0.112714
$658$	9.93155e9	+	7.21569e9i	1.35902	+	0.987387i
$659$	1.93825e9	−	5.96531e9i	0.263821	−	0.811959i	−0.728141	−	0.685427i	$-0.759615\pi$
$659$	1.93825e9	−	5.96531e9i	0.263821	−	0.811959i	0.991963	−	0.126532i	$-0.0403846\pi$
$660$	8.46537e9	+	1.03706e10i	1.14615	+	1.40411i
$661$	−1.80536e9	−	5.55632e9i	−0.243141	−	0.748311i	−0.995937	−	0.0900564i	$-0.971295\pi$
$661$	−1.80536e9	−	5.55632e9i	−0.243141	−	0.748311i	0.752796	−	0.658254i	$-0.228705\pi$
$662$	−3.20239e9	+	9.85596e9i	−0.429014	+	1.32037i
$663$	−2.19386e8	+	6.75201e8i	−0.0292356	+	0.0899778i
$664$	3.30792e9	+	1.01807e10i	0.438497	+	1.34956i
$665$	−4.32127e8	−	7.67106e9i	−0.0569817	−	1.01153i
$666$	−2.48729e9	+	7.65509e9i	−0.326262	+	1.00413i
$667$	−9.23624e8	−	6.71052e8i	−0.120519	−	0.0875621i
$668$	1.90437e10			2.47191
$669$	−1.51874e10	−	1.10343e10i	−1.96106	−	1.42479i
$670$	6.62032e9	−	2.57107e9i	0.850389	−	0.330257i
$671$	−6.46992e8	+	4.70067e8i	−0.0826742	+	0.0600663i
$672$	−3.92183e10	+	2.84938e10i	−4.98536	+	3.62207i
$673$	−1.27581e9	−	3.92654e9i	−0.161337	−	0.496544i	0.837411	−	0.546574i	$-0.184068\pi$
$673$	−1.27581e9	−	3.92654e9i	−0.161337	−	0.496544i	−0.998748	+	0.0500301i	$0.984068\pi$
$674$	−8.60690e9			−1.08277
$675$	1.63121e9	−	1.84364e8i	0.204148	−	0.0230734i
$676$	−1.89994e10			−2.36552
$677$	−1.87779e9	−	5.77925e9i	−0.232588	−	0.715832i	−0.997432	−	0.0716171i	$-0.977184\pi$
$677$	−1.87779e9	−	5.77925e9i	−0.232588	−	0.715832i	0.764844	−	0.644215i	$-0.222816\pi$
$678$	−2.48921e10	+	1.80852e10i	−3.06731	+	2.22853i
$679$	1.64922e10	−	1.19823e10i	2.02178	−	1.46891i
$680$	3.33339e9	−	5.17721e9i	0.406542	−	0.631414i
$681$	1.29485e10	+	9.40766e9i	1.57111	+	1.14148i
$682$	−7.85023e9			−0.947626
$683$	−2.92171e9	−	2.12275e9i	−0.350885	−	0.254933i	0.398355	−	0.917231i	$-0.369581\pi$
$683$	−2.92171e9	−	2.12275e9i	−0.350885	−	0.254933i	−0.749240	+	0.662298i	$0.769581\pi$
$684$	3.33923e9	−	1.02771e10i	0.398979	−	1.22793i
$685$	6.16253e9	−	2.39328e9i	0.732558	−	0.284496i
$686$	7.48406e9	+	2.30336e10i	0.885122	+	2.72412i
$687$	−2.81381e9	+	8.66003e9i	−0.331091	+	1.01899i
$688$	−1.33536e10	+	4.10982e10i	−1.56329	+	4.81131i
$689$	−1.10014e9	−	3.38588e9i	−0.128139	−	0.394370i
$690$	−2.55683e9	+	9.92972e8i	−0.296299	+	0.115071i
$691$	−4.55325e9	+	1.40135e10i	−0.524987	+	1.61574i	0.239354	+	0.970932i	$0.423064\pi$
$691$	−4.55325e9	+	1.40135e10i	−0.524987	+	1.61574i	−0.764341	+	0.644812i	$0.776936\pi$
$692$	−1.54737e10	−	1.12423e10i	−1.77510	−	1.28968i
$693$	6.60403e9			0.753777
$694$	2.34144e10	+	1.70116e10i	2.65904	+	1.93191i
$695$	4.22104e9	−	6.55585e9i	0.476950	−	0.740768i
$696$	3.44220e10	−	2.50090e10i	3.86994	−	2.81167i
$697$	−8.41646e8	+	6.11491e8i	−0.0941488	+	0.0684031i
$698$	−3.60957e9	−	1.11091e10i	−0.401755	−	1.23648i
$699$	5.09296e9			0.564027
$700$	−1.63134e10	−	3.58820e10i	−1.79763	−	3.95397i
$701$	1.07796e10			1.18192			0.590961	−	0.806700i	$-0.298749\pi$
$701$	1.07796e10			1.18192			0.590961	+	0.806700i	$0.298749\pi$
$702$	−2.97633e8	−	9.16019e8i	−0.0324714	−	0.0999366i
$703$	2.92865e9	−	2.12779e9i	0.317925	−	0.230986i
$704$	−8.03666e9	+	5.83897e9i	−0.868103	+	0.630714i
$705$	−6.17816e9	+	2.39935e9i	−0.664044	+	0.257888i
$706$	−1.97505e10	−	1.43496e10i	−2.11233	−	1.53470i
$707$	−8.16564e9			−0.869005
$708$	5.21517e9	+	3.78904e9i	0.552271	+	0.401248i
$709$	−5.46765e9	+	1.68277e10i	−0.576154	+	1.77322i	0.0560611	+	0.998427i	$0.482146\pi$
$709$	−5.46765e9	+	1.68277e10i	−0.576154	+	1.77322i	−0.632215	+	0.774793i	$0.717854\pi$
$710$	2.26527e8	+	4.02127e9i	0.0237528	+	0.421656i
$711$	4.09391e9	+	1.25997e10i	0.427164	+	1.31467i
$712$	1.45789e10	−	4.48692e10i	1.51372	−	4.65874i
$713$	3.57164e8	−	1.09924e9i	0.0369023	−	0.113574i
$714$	−3.36041e9	−	1.03423e10i	−0.345500	−	1.06334i
$715$	8.75402e8	+	1.07242e9i	0.0895646	+	0.109722i
$716$	−6.83165e9	+	2.10257e10i	−0.695553	+	2.14069i
$717$	2.44680e9	+	1.77770e9i	0.247903	+	0.180112i
$718$	8.41882e9			0.848820
$719$	−1.00263e10	−	7.28457e9i	−1.00599	−	0.730891i	−0.0426220	−	0.999091i	$-0.513571\pi$
$719$	−1.00263e10	−	7.28457e9i	−1.00599	−	0.730891i	−0.963363	+	0.268200i	$0.913571\pi$
$720$	−1.41870e9	−	2.51846e10i	−0.141654	−	2.51461i
$721$	2.63040e8	−	1.91109e8i	0.0261365	−	0.0189893i
$722$	9.95138e9	−	7.23010e9i	0.984019	−	0.714931i
$723$	−2.18843e9	−	6.73530e9i	−0.215352	−	0.662785i
$724$	−4.21657e9			−0.412928
$725$	5.10151e9	+	1.12210e10i	0.497182	+	1.09358i
$726$	−1.92263e10			−1.86473
$727$	−3.77728e9	−	1.16253e10i	−0.364594	−	1.12210i	−0.950235	−	0.311534i	$-0.899157\pi$
$727$	−3.77728e9	−	1.16253e10i	−0.364594	−	1.12210i	0.585641	−	0.810570i	$-0.300843\pi$
$728$	−1.13826e10	+	8.26996e9i	−1.09341	+	0.794408i
$729$	5.74132e9	−	4.17131e9i	0.548865	−	0.398774i
$730$	−2.54373e9	−	6.70934e8i	−0.242014	−	0.0638336i
$731$	−3.73603e9	−	2.71438e9i	−0.353753	−	0.257016i
$732$	7.21288e9			0.679704
$733$	5.41226e9	+	3.93224e9i	0.507592	+	0.368787i	0.811909	−	0.583783i	$-0.198428\pi$
$733$	5.41226e9	+	3.93224e9i	0.507592	+	0.368787i	−0.304317	+	0.952571i	$0.598428\pi$
$734$	−1.81686e9	+	5.59171e9i	−0.169584	+	0.521925i
$735$	−2.67965e10	−	7.06783e9i	−2.48927	−	0.656569i
$736$	−1.10430e9	−	3.39870e9i	−0.102098	−	0.314225i
$737$	8.48396e8	−	2.61109e9i	0.0780661	−	0.240263i
$738$	−2.45042e9	+	7.54163e9i	−0.224411	+	0.690666i
$739$	−1.80176e9	−	5.54525e9i	−0.164226	−	0.505436i	0.834752	−	0.550625i	$-0.185611\pi$
$739$	−1.80176e9	−	5.54525e9i	−0.164226	−	0.505436i	−0.998978	+	0.0451898i	$0.985611\pi$
$740$	1.00536e10	−	1.56147e10i	0.912037	−	1.41652i
$741$	7.52077e8	−	2.31466e9i	0.0679045	−	0.208989i
$742$	4.41170e10	+	3.20529e10i	3.96454	+	2.88041i
$743$	−1.63841e10			−1.46542			−0.732708	−	0.680543i	$-0.761744\pi$
$743$	−1.63841e10			−1.46542			−0.732708	+	0.680543i	$0.761744\pi$
$744$	3.48484e10	+	2.53189e10i	3.10226	+	2.25392i
$745$	1.31283e10	+	1.60830e10i	1.16322	+	1.42502i
$746$	3.78696e9	−	2.75139e9i	0.333968	−	0.242642i
$747$	−3.79126e9	+	2.75451e9i	−0.332783	+	0.241781i
$748$	−1.20905e9	−	3.72107e9i	−0.105630	−	0.325097i
$749$	−7.06220e9			−0.614121
$750$	2.93020e10	+	4.28903e9i	2.53619	+	0.371231i
$751$	−1.17098e10			−1.00881			−0.504404	−	0.863467i	$-0.668288\pi$
$751$	−1.17098e10			−1.00881			−0.504404	+	0.863467i	$0.668288\pi$
$752$	−5.60129e9	−	1.72390e10i	−0.480314	−	1.47825i
$753$	1.92837e10	−	1.40104e10i	1.64592	−	1.19583i
$754$	5.85089e9	−	4.25092e9i	0.497075	−	0.361146i
$755$	9.46087e9	+	1.15902e10i	0.800049	+	0.980112i
$756$	8.57667e9	+	6.23132e9i	0.721926	+	0.524510i
$757$	−2.17696e10			−1.82396			−0.911979	−	0.410238i	$-0.865446\pi$
$757$	−2.17696e10			−1.82396			−0.911979	+	0.410238i	$0.865446\pi$
$758$	−1.50838e10	−	1.09590e10i	−1.25797	−	0.913965i
$759$	−3.27659e8	+	1.00843e9i	−0.0272004	+	0.0837143i
$760$	−1.14272e10	+	1.77480e10i	−0.944261	+	1.46657i
$761$	−3.32562e9	−	1.02352e10i	−0.273543	−	0.841880i	−0.989601	−	0.143839i	$-0.954055\pi$
$761$	−3.32562e9	−	1.02352e10i	−0.273543	−	0.841880i	0.716058	−	0.698041i	$-0.245945\pi$
$762$	1.28266e10	−	3.94763e10i	1.05020	−	3.23217i
$763$	−8.00065e9	+	2.46235e10i	−0.652063	+	2.00684i
$764$	7.79814e9	+	2.40002e10i	0.632651	+	1.94710i
$765$	2.60648e9	+	6.87485e8i	0.210494	+	0.0555198i
$766$	1.51883e9	−	4.67448e9i	0.122098	−	0.375779i
$767$	5.39299e8	+	3.91824e8i	0.0431565	+	0.0313550i
$768$	3.86492e9			0.307876
$769$	1.63420e10	+	1.18731e10i	1.29587	+	0.941505i	0.999906	−	0.0136936i	$-0.00435895\pi$
$769$	1.63420e10	+	1.18731e10i	1.29587	+	0.941505i	0.295965	+	0.955199i	$0.404359\pi$
$770$	−2.05033e10	−	5.40795e9i	−1.61848	−	0.426889i
$771$	−9.48285e9	+	6.88969e9i	−0.745158	+	0.541389i
$772$	−9.30484e9	+	6.76036e9i	−0.727861	+	0.528822i
$773$	5.38180e9	+	1.65635e10i	0.419082	+	1.28980i	0.908548	+	0.417781i	$0.137192\pi$
$773$	5.38180e9	+	1.65635e10i	0.419082	+	1.28980i	−0.489465	+	0.872023i	$0.662808\pi$
$774$	−3.51998e10			−2.72864
$775$	−9.20805e9	+	8.42237e9i	−0.710578	+	0.649948i
$776$	−5.60062e10			−4.30249
$777$	−6.16603e9	−	1.89771e10i	−0.471554	−	1.45130i
$778$	9.17796e9	−	6.66817e9i	0.698743	−	0.507666i
$779$	2.88525e9	−	2.09625e9i	0.218676	−	0.158878i
$780$	−7.02233e8	−	1.24659e10i	−0.0529847	−	0.940576i
$781$	1.25962e9	+	9.15170e8i	0.0946155	+	0.0687422i
$782$	8.01650e8			0.0599461
$783$	−2.68209e9	−	1.94866e9i	−0.199668	−	0.145067i
$784$	2.34211e10	−	7.20826e10i	1.73580	−	5.34225i
$785$	−7.59462e9	−	9.30391e9i	−0.560354	−	0.686470i
$786$	5.49913e9	+	1.69246e10i	0.403939	+	1.24320i
$787$	−1.87664e9	+	5.77571e9i	−0.137237	+	0.422371i	−0.995931	−	0.0901168i	$-0.971276\pi$
$787$	−1.87664e9	+	5.77571e9i	−0.137237	+	0.422371i	0.858695	+	0.512488i	$0.171276\pi$
$788$	3.30383e9	−	1.01681e10i	0.240534	−	0.740286i
$789$	4.99616e9	+	1.53766e10i	0.362132	+	1.11453i
$790$	−2.39245e9	−	4.24705e10i	−0.172643	−	3.06473i
$791$	1.08221e10	−	3.33070e10i	0.777488	−	2.39286i
$792$	−1.46785e10	−	1.06646e10i	−1.04989	−	0.762791i
$793$	7.45882e8			0.0531146
$794$	1.25340e10	+	9.10647e9i	0.888622	+	0.645622i
$795$	−2.74440e10	+	1.06582e10i	−1.93715	+	0.752312i
$796$	3.80781e10	−	2.76654e10i	2.67596	−	1.94420i
$797$	−1.13286e10	+	8.23072e9i	−0.792634	+	0.575882i	−0.908744	−	0.417354i	$-0.862957\pi$
$797$	−1.13286e10	+	8.23072e9i	−0.792634	+	0.575882i	0.116110	+	0.993236i	$0.462957\pi$
$798$	1.15198e10	+	3.54544e10i	0.802483	+	2.46979i
$799$	1.93705e9			0.134347
$800$	−7.72634e9	+	3.78018e10i	−0.533530	+	2.61034i
$801$	2.06536e10			1.41998
$802$	8.06986e9	+	2.48365e10i	0.552403	+	1.70012i
$803$	−8.22745e8	+	5.97759e8i	−0.0560739	+	0.0407401i
$804$	−2.00328e10	+	1.45547e10i	−1.35939	+	0.987657i
$805$	1.69010e9	−	2.62495e9i	0.114190	−	0.177352i
$806$	5.92337e9	+	4.30358e9i	0.398471	+	0.289506i
$807$	1.63377e10			1.09429
$808$	1.81495e10	+	1.31864e10i	1.21039	+	0.879397i
$809$	−2.93164e9	+	9.02265e9i	−0.194666	+	0.599121i	0.805314	+	0.592848i	$0.201997\pi$
$809$	−2.93164e9	+	9.02265e9i	−0.194666	+	0.599121i	−0.999980	+	0.00627256i	$0.998003\pi$
$810$	−2.99869e10	+	1.16457e10i	−1.98260	+	0.769962i
$811$	3.15193e9	+	9.70064e9i	0.207493	+	0.638598i	0.999602	+	0.0282179i	$0.00898323\pi$
$811$	3.15193e9	+	9.70064e9i	0.207493	+	0.638598i	−0.792109	+	0.610380i	$0.791017\pi$
$812$	−2.45986e10	+	7.57066e10i	−1.61237	+	4.96235i
$813$	7.07528e9	−	2.17755e10i	0.461771	−	1.42119i
$814$	−3.08729e9	−	9.50171e9i	−0.200628	−	0.617471i
$815$	2.23253e10	−	8.67025e9i	1.44459	−	0.561022i
$816$	−4.96179e9	+	1.52708e10i	−0.319685	+	0.983890i
$817$	1.28075e10	+	9.30518e9i	0.821650	+	0.596964i
$818$	−1.06680e8			−0.00681471
$819$	−4.98306e9	−	3.62040e9i	−0.316958	−	0.230284i
$820$	9.90465e9	−	1.53833e10i	0.627322	−	0.974316i
$821$	−2.96729e9	+	2.15586e9i	−0.187136	+	0.135963i	−0.677409	−	0.735607i	$-0.736897\pi$
$821$	−2.96729e9	+	2.15586e9i	−0.187136	+	0.135963i	0.490273	+	0.871569i	$0.336897\pi$
$822$	−2.59502e10	+	1.88539e10i	−1.62963	+	1.18400i
$823$	−3.78860e9	−	1.16601e10i	−0.236908	−	0.729126i	−0.996863	−	0.0791509i	$-0.974779\pi$
$823$	−3.78860e9	−	1.16601e10i	−0.236908	−	0.729126i	0.759955	−	0.649976i	$-0.225221\pi$
$824$	−8.93263e8			−0.0556204
$825$	8.44738e9	−	7.72660e9i	0.523761	−	0.479071i
$826$	−1.02107e10			−0.630413
$827$	4.19828e9	+	1.29210e10i	0.258109	+	0.794376i	0.993201	+	0.116410i	$0.0371386\pi$
$827$	4.19828e9	+	1.29210e10i	0.258109	+	0.794376i	−0.735093	+	0.677967i	$0.762861\pi$
$828$	3.55230e9	−	2.58090e9i	0.217472	−	0.158003i
$829$	2.63766e9	−	1.91637e9i	0.160797	−	0.116826i	−0.504477	−	0.863425i	$-0.668315\pi$
$829$	2.63766e9	−	1.91637e9i	0.160797	−	0.116826i	0.665274	+	0.746599i	$0.268315\pi$
$830$	1.40262e10	−	5.44723e9i	0.851467	−	0.330676i
$831$	−1.25870e9	−	9.14498e8i	−0.0760884	−	0.0552814i
$832$	9.26503e9			0.557719
$833$	6.55266e9	+	4.76079e9i	0.392790	+	0.285378i
$834$	−1.16907e10	+	3.59803e10i	−0.697847	+	2.14775i
$835$	−9.15942e8	−	1.62597e10i	−0.0544459	−	0.966515i
$836$	4.14475e9	+	1.27562e10i	0.245344	+	0.755092i
$837$	1.03716e9	−	3.19205e9i	0.0611374	−	0.188162i
$838$	1.43963e10	−	4.43072e10i	0.845077	−	2.60088i
$839$	−4.88383e9	−	1.50309e10i	−0.285492	−	0.878654i	−0.986251	−	0.165256i	$-0.947155\pi$
$839$	−4.88383e9	−	1.50309e10i	−0.285492	−	0.878654i	0.700759	−	0.713398i	$-0.252845\pi$
$840$	7.35756e10	+	9.01349e10i	4.28308	+	5.24705i
$841$	2.36195e9	−	7.26932e9i	0.136925	−	0.421413i
$842$	−4.94645e9	−	3.59380e9i	−0.285562	−	0.207473i
$843$	1.91183e9			0.109914
$844$	−5.04480e10	−	3.66526e10i	−2.88832	−	2.09849i
$845$	9.13813e8	+	1.62219e10i	0.0521026	+	0.924917i
$846$	1.19450e10	−	8.67855e9i	0.678250	−	0.492778i
$847$	1.77042e10	−	1.28629e10i	1.00112	−	0.727354i
$848$	−2.48815e10	−	7.65775e10i	−1.40117	−	4.31237i
$849$	1.01510e10			0.569287
$850$	−7.52928e9	−	4.26882e9i	−0.420521	−	0.238420i
$851$	1.47095e9			0.0818172
$852$	−4.33943e9	−	1.33554e10i	−0.240378	−	0.739807i
$853$	−1.58266e10	+	1.14987e10i	−0.873103	+	0.634347i	−0.931418	−	0.363952i	$-0.881427\pi$
$853$	−1.58266e10	+	1.14987e10i	−0.873103	+	0.634347i	0.0583146	+	0.998298i	$0.481427\pi$
$854$	−9.24295e9	+	6.71540e9i	−0.507818	+	0.368951i
$855$	−8.93528e9	−	2.35677e9i	−0.488907	−	0.128954i
$856$	1.56969e10	+	1.14045e10i	0.855372	+	0.621464i
$857$	−1.41468e10			−0.767757			−0.383879	−	0.923384i	$-0.625412\pi$
$857$	−1.41468e10			−0.767757			−0.383879	+	0.923384i	$0.625412\pi$
$858$	−5.43405e9	−	3.94807e9i	−0.293709	−	0.213392i
$859$	4.83756e9	−	1.48885e10i	0.260406	−	0.801446i	−0.732311	−	0.680971i	$-0.761558\pi$
$859$	4.83756e9	−	1.48885e10i	0.260406	−	0.801446i	0.992716	−	0.120475i	$-0.0384419\pi$
$860$	7.85298e10	+	2.07130e10i	4.21008	+	1.11045i
$861$	−6.07464e9	−	1.86958e10i	−0.324347	−	0.998237i
$862$	−1.20833e9	+	3.71885e9i	−0.0642553	+	0.197758i
$863$	−5.44454e8	+	1.67566e9i	−0.0288352	+	0.0887457i	−0.964438	−	0.264308i	$-0.914857\pi$
$863$	−5.44454e8	+	1.67566e9i	−0.0288352	+	0.0887457i	0.935603	+	0.353053i	$0.114857\pi$
$864$	−3.20677e9	−	9.86941e9i	−0.169149	−	0.520587i
$865$	−8.85452e9	+	1.37523e10i	−0.465167	+	0.722467i
$866$	1.83202e10	−	5.63838e10i	0.958556	−	2.95013i
$867$	1.97215e10	+	1.43285e10i	1.02772	+	0.746680i
$868$	−8.05887e10			−4.18269
$869$	−1.33035e10	−	9.66554e9i	−0.687695	−	0.499640i
$870$	−3.78193e10	−	4.63311e10i	−1.94713	−	2.38537i
$871$	−2.07158e9	+	1.50509e9i	−0.106228	+	0.0771792i
$872$	5.75462e10	−	4.18097e10i	2.93906	−	2.13535i
$873$	−7.57656e9	−	2.33182e10i	−0.385409	−	1.18617i
$874$	−2.74814e9			−0.139235
$875$	−2.98518e10	+	1.56543e10i	−1.50641	+	0.789961i
$876$	9.17224e9			0.461011
$877$	2.25360e9	+	6.93586e9i	0.112818	+	0.347217i	0.991486	−	0.130216i	$-0.0415671\pi$
$877$	2.25360e9	+	6.93586e9i	0.112818	+	0.347217i	−0.878668	+	0.477434i	$0.841567\pi$
$878$	−2.91638e9	+	2.11887e9i	−0.145416	+	0.105651i
$879$	1.46772e10	−	1.06636e10i	0.728925	−	0.529595i
$880$	1.97987e10	+	2.42547e10i	0.979372	+	1.19979i
$881$	1.17868e10	+	8.56358e9i	0.580736	+	0.421929i	0.838989	−	0.544148i	$-0.183147\pi$
$881$	1.17868e10	+	8.56358e9i	0.580736	+	0.421929i	−0.258254	+	0.966077i	$0.583147\pi$
$882$	6.17372e10			3.02975
$883$	1.68579e10	+	1.22480e10i	0.824027	+	0.598690i	0.917863	−	0.396897i	$-0.129913\pi$
$883$	1.68579e10	+	1.22480e10i	0.824027	+	0.598690i	−0.0938364	+	0.995588i	$0.529913\pi$
$884$	−1.12765e9	+	3.47054e9i	−0.0549023	+	0.168972i
$885$	2.98428e9	−	4.63500e9i	0.144723	−	0.224775i
$886$	1.58402e10	+	4.87512e10i	0.765144	+	2.35487i
$887$	−1.07072e10	+	3.29533e10i	−0.515160	+	1.58550i	0.267830	+	0.963466i	$0.413693\pi$
$887$	−1.07072e10	+	3.29533e10i	−0.515160	+	1.58550i	−0.782990	+	0.622034i	$0.786307\pi$
$888$	−1.69403e10	+	5.21369e10i	−0.811850	+	2.49862i
$889$	1.45995e10	+	4.49325e10i	0.696917	+	2.14489i
$890$	−6.41226e10	−	1.69130e10i	−3.04892	−	0.804183i
$891$	−3.84283e9	+	1.18270e10i	−0.182003	+	0.560149i
$892$	−7.80633e10	−	5.67163e10i	−3.68273	−	2.67566i
$893$	−6.64041e9			−0.312043
$894$	−8.14936e10	−	5.92086e10i	−3.81454	−	2.77143i
$895$	1.82805e10	+	4.82166e9i	0.852329	+	0.224810i
$896$	−3.58685e10	+	2.60600e10i	−1.66585	+	1.21031i
$897$	8.00066e8	−	5.81282e8i	0.0370128	−	0.0268914i
$898$	5.35204e9	+	1.64719e10i	0.246634	+	0.759061i
$899$	2.52017e10			1.15683
$900$	−4.71074e10	+	5.32421e9i	−2.15397	+	0.243448i
$901$	8.60460e9			0.391917
$902$	−3.04154e9	−	9.36089e9i	−0.137997	−	0.424712i
$903$	7.05955e10	−	5.12906e10i	3.19058	−	2.31809i
$904$	−7.78399e10	+	5.65540e10i	−3.50439	+	2.54609i
$905$	2.02804e8	+	3.60014e9i	0.00909507	+	0.161454i
$906$	−5.87282e10	−	4.26686e10i	−2.62360	−	1.90616i
$907$	−1.79375e10			−0.798247			−0.399124	−	0.916897i	$-0.630686\pi$
$907$	−1.79375e10			−0.798247			−0.399124	+	0.916897i	$0.630686\pi$
$908$	6.65557e10	+	4.83555e10i	2.95043	+	2.14361i
$909$	−3.03488e9	+	9.34041e9i	−0.134020	+	0.412470i
$910$	1.25060e10	+	1.53207e10i	0.550142	+	0.673960i
$911$	3.29455e9	+	1.01396e10i	0.144372	+	0.444330i	0.996930	−	0.0783022i	$-0.0249499\pi$
$911$	3.29455e9	+	1.01396e10i	0.144372	+	0.444330i	−0.852558	+	0.522633i	$0.824950\pi$
$912$	1.70095e10	−	5.23499e10i	0.742523	−	2.28525i
$913$	1.79747e9	−	5.53203e9i	0.0781651	−	0.240567i
$914$	−1.65254e10	−	5.08599e10i	−0.715879	−	2.20325i
$915$	−3.46917e8	−	6.15842e9i	−0.0149710	−	0.265763i
$916$	−1.44631e10	+	4.45127e10i	−0.621764	+	1.91359i
$917$	−1.63868e10	−	1.19057e10i	−0.701780	−	0.509873i
$918$	2.32790e9			0.0993148
$919$	3.52672e10	+	2.56231e10i	1.49888	+	1.08900i	0.970824	+	0.239792i	$0.0770791\pi$
$919$	3.52672e10	+	2.56231e10i	1.49888	+	1.08900i	0.528057	+	0.849209i	$0.322921\pi$
$920$	−7.99545e9	+	3.10511e9i	−0.338521	+	0.131468i
$921$	−2.32454e8	+	1.68888e8i	−0.00980458	+	0.00712345i
$922$	−2.92477e10	+	2.12497e10i	−1.22895	+	0.892884i
$923$	−4.48740e8	−	1.38108e9i	−0.0187840	−	0.0578113i
$924$	7.39314e10			3.08302
$925$	−1.38155e10	−	7.83288e9i	−0.573945	−	0.325406i
$926$	3.54900e10			1.46881
$927$	−1.20841e8	−	3.71911e8i	−0.00498237	−	0.0153342i
$928$	6.30389e10	−	4.58004e10i	2.58935	−	1.88127i
$929$	1.31974e9	−	9.58846e8i	0.0540048	−	0.0392368i	−0.560455	−	0.828185i	$-0.689374\pi$
$929$	1.31974e9	−	9.58846e8i	0.0540048	−	0.0392368i	0.614460	+	0.788948i	$0.289374\pi$
$930$	3.27778e10	−	5.09083e10i	1.33625	−	2.07538i
$931$	−2.24632e10	−	1.63205e10i	−0.912320	−	0.662839i
$932$	2.61779e10			1.05920
$933$	−4.38485e10	−	3.18578e10i	−1.76754	−	1.28419i
$934$	−1.77827e10	+	5.47295e10i	−0.714140	+	2.19790i
$935$	−3.11894e9	+	1.21127e9i	−0.124786	+	0.0484619i
$936$	5.22921e9	+	1.60939e10i	0.208435	+	0.641497i
$937$	1.09730e10	−	3.37714e10i	0.435750	−	1.34110i	−0.456567	−	0.889689i	$-0.650921\pi$
$937$	1.09730e10	−	3.37714e10i	0.435750	−	1.34110i	0.892316	−	0.451411i	$-0.149079\pi$
$938$	1.21202e10	−	3.73022e10i	0.479513	−	1.47579i
$939$	1.51625e10	+	4.66653e10i	0.597641	+	1.83935i
$940$	−3.17558e10	+	1.23327e10i	−1.24703	+	0.484296i
$941$	−7.37681e6	+	2.27035e7i	−0.000288606	+	0.000888238i	−0.951201	−	0.308573i	$-0.900149\pi$
$941$	−7.37681e6	+	2.27035e7i	−0.000288606	+	0.000888238i	0.950912	+	0.309461i	$0.100149\pi$
$942$	4.71435e10	+	3.42518e10i	1.83757	+	1.33507i
$943$	1.44915e9			0.0562759
$944$	1.21972e10	+	8.86176e9i	0.471908	+	0.342861i
$945$	4.90784e9	−	7.62255e9i	0.189182	−	0.293825i
$946$	3.53468e10	−	2.56809e10i	1.35747	−	0.986260i
$947$	−1.42974e10	+	1.03876e10i	−0.547055	+	0.397459i	−0.826699	−	0.562645i	$-0.809784\pi$
$947$	−1.42974e10	+	1.03876e10i	−0.547055	+	0.397459i	0.279643	+	0.960104i	$0.409784\pi$
$948$	4.58308e10	+	1.41053e11i	1.74714	+	5.37715i
$949$	9.48499e8			0.0360251
$950$	2.58111e10	+	1.46340e10i	0.976730	+	0.553770i
$951$	−1.70149e10			−0.641500
$952$	−1.05083e10	−	3.23412e10i	−0.394733	−	1.21486i
$953$	−2.83273e10	+	2.05810e10i	−1.06018	+	0.770265i	−0.974122	−	0.226025i	$-0.927427\pi$
$953$	−2.83273e10	+	2.05810e10i	−1.06018	+	0.770265i	−0.0860577	+	0.996290i	$0.527427\pi$
$954$	5.30610e10	−	3.85511e10i	1.97859	−	1.43753i
$955$	2.01165e10	−	7.81246e9i	0.747380	−	0.290253i
$956$	1.25766e10	+	9.13743e9i	0.465544	+	0.338237i
$957$	−2.31198e10			−0.852692
$958$	2.73014e10	+	1.98356e10i	1.00324	+	0.728898i
$959$	1.12821e10	−	3.47228e10i	0.413071	−	1.27130i
$960$	−4.30926e9	−	7.64973e10i	−0.157200	−	2.79059i
$961$	−6.17638e8	−	1.90089e9i	−0.0224493	−	0.0690917i
$962$	−2.87943e9	+	8.86198e9i	−0.104278	+	0.320936i
$963$	−2.62477e9	+	8.07822e9i	−0.0947108	+	0.291490i
$964$	−1.12486e10	−	3.46196e10i	−0.404416	−	1.24466i
$965$	6.21959e9	+	7.61940e9i	0.222801	+	0.272945i
$966$	−4.68095e9	+	1.44065e10i	−0.167076	+	0.514207i
$967$	−5.38151e9	−	3.90990e9i	−0.191387	−	0.139051i	0.487966	−	0.872863i	$-0.337739\pi$
$967$	−5.38151e9	−	3.90990e9i	−0.191387	−	0.139051i	−0.679352	+	0.733812i	$0.737739\pi$
$968$	−6.01222e10			−2.13045
$969$	4.75886e9	+	3.45751e9i	0.168023	+	0.122076i
$970$	4.42769e9	+	7.85997e10i	0.155767	+	2.76516i
$971$	−3.36599e10	+	2.44554e10i	−1.17990	+	0.857249i	−0.992161	−	0.124969i	$-0.960117\pi$
$971$	−3.36599e10	+	2.44554e10i	−1.17990	+	0.857249i	−0.187742	+	0.982218i	$0.560117\pi$
$972$	7.85876e10	−	5.70972e10i	2.74487	−	1.99427i
$973$	−1.33066e10	−	4.09534e10i	−0.463096	−	1.42526i
$974$	3.20178e10			1.11029
$975$	−1.06098e10	+	1.19915e9i	−0.366597	+	0.0414339i
$976$	1.68694e10			0.580798
$977$	−1.26257e10	−	3.88578e10i	−0.433135	−	1.33305i	−0.894985	−	0.446096i	$-0.852814\pi$
$977$	−1.26257e10	−	3.88578e10i	−0.433135	−	1.33305i	0.461850	−	0.886958i	$-0.347186\pi$
$978$	−9.40111e10	+	6.83031e10i	−3.21361	+	2.33482i
$979$	−2.07398e10	+	1.50684e10i	−0.706425	+	0.513248i
$980$	−1.37734e11	−	3.63288e10i	−4.67467	−	1.23299i
$981$	2.51924e10	+	1.83034e10i	0.851978	+	0.618998i
$982$	2.61053e10			0.879709
$983$	−1.27538e10	−	9.26621e9i	−0.428257	−	0.311147i	0.352695	−	0.935738i	$-0.385265\pi$
$983$	−1.27538e10	−	9.26621e9i	−0.428257	−	0.311147i	−0.780951	+	0.624592i	$0.785265\pi$
$984$	−1.66892e10	+	5.13642e10i	−0.558411	+	1.71861i
$985$	−8.84055e9	−	2.33178e9i	−0.294749	−	0.0777430i
$986$	5.40147e9	+	1.66240e10i	0.179450	+	0.552289i
$987$	−1.13107e10	+	3.48108e10i	−0.374438	+	1.15240i
$988$	3.86569e9	−	1.18974e10i	0.127520	−	0.392466i
$989$	1.98782e9	+	6.11788e9i	0.0653416	+	0.201101i
$990$	−1.38063e10	+	2.14431e10i	−0.452226	+	0.702369i
$991$	−7.33851e9	+	2.25856e10i	−0.239525	+	0.737181i	0.756964	+	0.653456i	$0.226682\pi$
$991$	−7.33851e9	+	2.25856e10i	−0.239525	+	0.737181i	−0.996489	+	0.0837249i	$0.973318\pi$
$992$	6.38198e10	+	4.63678e10i	2.07570	+	1.50809i
$993$	−3.08988e10			−1.00143
$994$	1.79950e10	+	1.30742e10i	0.581167	+	0.422242i
$995$	−2.54524e10	−	3.11808e10i	−0.819120	−	1.00348i
$996$	−4.24427e10	+	3.08364e10i	−1.36112	+	0.988910i
$997$	8.52859e8	−	6.19638e8i	0.0272549	−	0.0198018i	−0.574074	−	0.818803i	$-0.694638\pi$
$997$	8.52859e8	−	6.19638e8i	0.0272549	−	0.0198018i	0.601329	+	0.799001i	$0.294638\pi$
$998$	−6.02526e9	−	1.85438e10i	−0.191875	−	0.590531i
$999$	4.27146e9			0.135549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.6.17	✓	68
25.11	even	5		625.8.a.d.1.34		34
25.14	even	10		625.8.a.c.1.1		34
25.21	even	5	inner	25.8.d.a.21.17	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.6.17	✓	68	1.1	even	1	trivial
25.8.d.a.21.17	yes	68	25.21	even	5	inner
625.8.a.c.1.1		34	25.14	even	10
625.8.a.d.1.34		34	25.11	even	5

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(6.59046 + 20.2833i) q^{2} +(-51.4446 + 37.3767i) q^{3} +(-264.426 + 192.117i) q^{4} +(176.749 + 216.529i) q^{5} +(-1097.17 - 797.139i) q^{6} +1543.62 q^{7} +(-3430.94 - 2492.72i) q^{8} +(573.708 - 1765.69i) q^{9} +O(q^{10})\)	\(q+(6.59046 + 20.2833i) q^{2} +(-51.4446 + 37.3767i) q^{3} +(-264.426 + 192.117i) q^{4} +(176.749 + 216.529i) q^{5} +(-1097.17 - 797.139i) q^{6} +1543.62 q^{7} +(-3430.94 - 2492.72i) q^{8} +(573.708 - 1765.69i) q^{9} +(-3227.08 + 5012.09i) q^{10} +(712.104 + 2191.63i) q^{11} +(6422.60 - 19766.7i) q^{12} +(664.159 - 2044.07i) q^{13} +(10173.1 + 31309.7i) q^{14} +(-17185.9 - 4532.95i) q^{15} +(15021.1 - 46230.2i) q^{16} +(4202.55 + 3053.33i) q^{17} +39595.2 q^{18} +(-14406.8 - 10467.1i) q^{19} +(-88335.8 - 23299.4i) q^{20} +(-79410.7 + 57695.3i) q^{21} +(-39760.5 + 28887.7i) q^{22} +(-2236.04 - 6881.81i) q^{23} +269673. q^{24} +(-15644.6 + 76542.6i) q^{25} +45837.7 q^{26} +(-6493.18 - 19984.0i) q^{27} +(-408172. + 296555. i) q^{28} +(127644. - 92738.5i) q^{29} +(-21319.6 - 378462. i) q^{30} +(129225. + 93887.3i) q^{31} +493867. q^{32} +(-118550. - 86131.4i) q^{33} +(-34235.0 + 105365. i) q^{34} +(272833. + 334238. i) q^{35} +(187516. + 577114. i) q^{36} +(-62818.0 + 193334. i) q^{37} +(117361. - 361200. i) q^{38} +(42233.2 + 129980. i) q^{39} +(-66668.2 - 1.18348e6i) q^{40} +(-61887.0 + 190468. i) q^{41} +(-1.69361e6 - 1.23048e6i) q^{42} -888992. q^{43} +(-609347. - 442717. i) q^{44} +(483726. - 187860. i) q^{45} +(124850. - 90708.6i) q^{46} +(301678. - 219182. i) q^{47} +(955176. + 2.93973e6i) q^{48} +1.55921e6 q^{49} +(-1.65564e6 + 187126. i) q^{50} -330321. q^{51} +(217079. + 668101. i) q^{52} +(1.34009e6 - 973631. i) q^{53} +(362549. - 263407. i) q^{54} +(-348688. + 541559. i) q^{55} +(-5.29606e6 - 3.84781e6i) q^{56} +1.13238e6 q^{57} +(2.72228e6 + 1.97785e6i) q^{58} +(-95844.0 + 294977. i) q^{59} +(5.41525e6 - 2.10307e6i) q^{60} +(107241. + 330055. i) q^{61} +(-1.05270e6 + 3.23987e6i) q^{62} +(885586. - 2.72555e6i) q^{63} +(1.33211e6 + 4.09981e6i) q^{64} +(559990. - 217478. i) q^{65} +(965736. - 2.97223e6i) q^{66} +(-963858. - 700284. i) q^{67} -1.69786e6 q^{68} +(372251. + 270456. i) q^{69} +(-4.98137e6 + 7.73674e6i) q^{70} +(546613. - 397138. i) q^{71} +(-6.36974e6 + 4.62789e6i) q^{72} +(136373. + 419714. i) q^{73} -4.33546e6 q^{74} +(-2.05608e6 - 4.52244e6i) q^{75} +5.82043e6 q^{76} +(1.09922e6 + 3.38304e6i) q^{77} +(-2.35810e6 + 1.71326e6i) q^{78} +(-5.77304e6 + 4.19436e6i) q^{79} +(1.26651e7 - 4.91863e6i) q^{80} +(4.36582e6 + 3.17195e6i) q^{81} -4.27120e6 q^{82} +(-2.04209e6 - 1.48367e6i) q^{83} +(9.91403e6 - 3.05123e7i) q^{84} +(81661.7 + 1.44965e6i) q^{85} +(-5.85886e6 - 1.80317e7i) q^{86} +(-3.10031e6 + 9.54178e6i) q^{87} +(3.01994e6 - 9.29442e6i) q^{88} +(3.43771e6 + 1.05802e7i) q^{89} +(6.99841e6 + 8.57350e6i) q^{90} +(1.02521e6 - 3.15526e6i) q^{91} +(1.91338e6 + 1.39015e6i) q^{92} -1.01571e7 q^{93} +(6.43394e6 + 4.67453e6i) q^{94} +(-279944. - 4.96953e6i) q^{95} +(-2.54068e7 + 1.84591e7i) q^{96} +(1.06841e7 - 7.76246e6i) q^{97} +(1.02759e7 + 3.16260e7i) q^{98} +4.27828e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9}+O(q^{10}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16} + 71504 q^{17} + 116208 q^{18} - 48685 q^{19} - 138265 q^{20} - 2274 q^{21} - 271952 q^{22} - 63227 q^{23} + 553980 q^{24} + 276615 q^{25} + 675246 q^{26} - 270235 q^{27} - 782613 q^{28} - 99655 q^{29} - 1011285 q^{30} + 39051 q^{31} + 1045974 q^{32} + 1766456 q^{33} + 605893 q^{34} - 476935 q^{35} - 2928227 q^{36} + 83909 q^{37} + 1937525 q^{38} + 1316257 q^{39} + 2903410 q^{40} - 1964944 q^{41} - 3462547 q^{42} - 3439822 q^{43} - 3557652 q^{44} - 2121790 q^{45} + 2982521 q^{46} + 1663474 q^{47} + 1678378 q^{48} + 6584354 q^{49} + 408485 q^{50} + 3922076 q^{51} - 5301176 q^{52} + 788553 q^{53} - 6946145 q^{54} - 2630560 q^{55} - 415350 q^{56} - 14598410 q^{57} + 4727030 q^{58} - 3625740 q^{59} + 29158890 q^{60} - 4161559 q^{61} + 19658928 q^{62} + 2426738 q^{63} - 4408596 q^{64} - 2030220 q^{65} - 6985528 q^{66} + 8470434 q^{67} - 29099218 q^{68} - 360673 q^{69} - 22417320 q^{70} - 4808044 q^{71} + 25676065 q^{72} + 5517633 q^{73} + 14050068 q^{74} + 257240 q^{75} + 22502000 q^{76} - 9936772 q^{77} + 14948561 q^{78} - 5343505 q^{79} - 3987180 q^{80} - 5865817 q^{81} - 76614542 q^{82} - 645927 q^{83} + 5992628 q^{84} + 48268560 q^{85} - 27540609 q^{86} + 65370380 q^{87} - 3612320 q^{88} + 11153500 q^{89} + 7267975 q^{90} - 9123484 q^{91} - 33863736 q^{92} - 118704764 q^{93} - 30761227 q^{94} - 26382485 q^{95} + 1256206 q^{96} + 55538244 q^{97} + 102201752 q^{98} + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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