LMFDB - Embedded newform 29.15.c.a.17.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,15,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	29.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:	$36.0554007641$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.14
Character	$\chi$	$=$	29.17
Dual form			29.15.c.a.12.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-50.6787 + 50.6787i) q^{2} +(910.227 - 910.227i) q^{3} +11247.3i q^{4} -127648. i q^{5} +92258.2i q^{6} -1.54934e6 q^{7} +(-1.40032e6 - 1.40032e6i) q^{8} +3.12594e6i q^{9} +O(q^{10})$	\(q+(-50.6787 + 50.6787i) q^{2} +(910.227 - 910.227i) q^{3} +11247.3i q^{4} -127648. i q^{5} +92258.2i q^{6} -1.54934e6 q^{7} +(-1.40032e6 - 1.40032e6i) q^{8} +3.12594e6i q^{9} +(6.46904e6 + 6.46904e6i) q^{10} +(1.89478e6 - 1.89478e6i) q^{11} +(1.02376e7 + 1.02376e7i) q^{12} +7.31778e7i q^{13} +(7.85187e7 - 7.85187e7i) q^{14} +(-1.16189e8 - 1.16189e8i) q^{15} -4.23438e7 q^{16} +(1.23124e8 - 1.23124e8i) q^{17} +(-1.58419e8 - 1.58419e8i) q^{18} +(1.31336e7 - 1.31336e7i) q^{19} +1.43570e9 q^{20} +(-1.41025e9 + 1.41025e9i) q^{21} +1.92050e8i q^{22} +3.45143e9 q^{23} -2.54922e9 q^{24} -1.01905e10 q^{25} +(-3.70855e9 - 3.70855e9i) q^{26} +(7.19891e9 + 7.19891e9i) q^{27} -1.74260e10i q^{28} +(1.05990e10 - 1.36096e10i) q^{29} +1.17766e10 q^{30} +(2.10814e10 - 2.10814e10i) q^{31} +(2.50888e10 - 2.50888e10i) q^{32} -3.44936e9i q^{33} +1.24795e10i q^{34} +1.97771e11i q^{35} -3.51585e10 q^{36} +(-3.02037e9 - 3.02037e9i) q^{37} +1.33119e9i q^{38} +(6.66084e10 + 6.66084e10i) q^{39} +(-1.78748e11 + 1.78748e11i) q^{40} +(2.27317e11 + 2.27317e11i) q^{41} -1.42940e11i q^{42} +(-2.66277e10 + 2.66277e10i) q^{43} +(2.13112e10 + 2.13112e10i) q^{44} +3.99020e11 q^{45} +(-1.74914e11 + 1.74914e11i) q^{46} +(3.95665e11 + 3.95665e11i) q^{47} +(-3.85425e10 + 3.85425e10i) q^{48} +1.72224e12 q^{49} +(5.16442e11 - 5.16442e11i) q^{50} -2.24142e11i q^{51} -8.23056e11 q^{52} -4.44734e11 q^{53} -7.29662e11 q^{54} +(-2.41865e11 - 2.41865e11i) q^{55} +(2.16958e12 + 2.16958e12i) q^{56} -2.39092e10i q^{57} +(1.52574e11 + 1.22686e12i) q^{58} -2.41238e12 q^{59} +(1.30682e12 - 1.30682e12i) q^{60} +(-1.51318e12 + 1.51318e12i) q^{61} +2.13676e12i q^{62} -4.84316e12i q^{63} +1.84917e12i q^{64} +9.34100e12 q^{65} +(1.74809e11 + 1.74809e11i) q^{66} +8.36251e12i q^{67} +(1.38482e12 + 1.38482e12i) q^{68} +(3.14158e12 - 3.14158e12i) q^{69} +(-1.00228e13 - 1.00228e13i) q^{70} -7.18905e12i q^{71} +(4.37732e12 - 4.37732e12i) q^{72} +(-6.97575e12 - 6.97575e12i) q^{73} +3.06137e11 q^{74} +(-9.27569e12 + 9.27569e12i) q^{75} +(1.47719e11 + 1.47719e11i) q^{76} +(-2.93566e12 + 2.93566e12i) q^{77} -6.75125e12 q^{78} +(-1.62138e13 + 1.62138e13i) q^{79} +5.40511e12i q^{80} -1.84599e12 q^{81} -2.30403e13 q^{82} +4.05979e13 q^{83} +(-1.58616e13 - 1.58616e13i) q^{84} +(-1.57166e13 - 1.57166e13i) q^{85} -2.69891e12i q^{86} +(-2.74034e12 - 2.20353e13i) q^{87} -5.30659e12 q^{88} +(1.71467e13 - 1.71467e13i) q^{89} +(-2.02218e13 + 2.02218e13i) q^{90} -1.13377e14i q^{91} +3.88194e13i q^{92} -3.83778e13i q^{93} -4.01036e13 q^{94} +(-1.67649e12 - 1.67649e12i) q^{95} -4.56730e13i q^{96} +(9.87187e13 + 9.87187e13i) q^{97} +(-8.72809e13 + 8.72809e13i) q^{98} +(5.92296e12 + 5.92296e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8}+O(q^{10}) $ 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8	\( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8} + 23502846 q^{10} - 2993734 q^{11} - 76269906 q^{12} - 3845224 q^{14} + 277690070 q^{15} - 5490752792 q^{16} + 285786056 q^{17} + 5809842386 q^{18} - 1195066336 q^{19} + 1866268668 q^{20} - 8197524756 q^{21} + 2117392192 q^{23} + 8629372824 q^{24} - 73846917196 q^{25} - 16368356994 q^{26} + 33411191086 q^{27} + 48687460392 q^{29} + 128044102700 q^{30} + 73968522614 q^{31} - 2657032122 q^{32} - 259972090824 q^{36} + 95888936640 q^{37} - 571710579738 q^{39} + 977850700426 q^{40} - 57594847104 q^{41} + 48472463810 q^{43} + 1173476843650 q^{44} - 299491373708 q^{45} + 656204001636 q^{46} + 29961288922 q^{47} + 1808198535114 q^{48} + 9857850529980 q^{49} + 1443642384290 q^{50} - 11263919114280 q^{52} - 1993070689076 q^{53} + 2064324525592 q^{54} + 3054165001846 q^{55} + 8002123380864 q^{56} - 9170547007720 q^{58} - 8402401993912 q^{59} + 4455428077662 q^{60} - 4381209993964 q^{61} - 14884429709724 q^{65} - 5756218265814 q^{66} + 4595908790532 q^{68} + 51089269002600 q^{69} - 65383337180236 q^{70} + 101900024607216 q^{72} + 39493186331224 q^{73} - 152862151734316 q^{74} - 46335428712972 q^{75} + 46232026918072 q^{76} + 63231072283300 q^{77} + 111617680995888 q^{78} - 29034273461086 q^{79} - 345331621902328 q^{81} + 104609665443600 q^{82} - 2994621113016 q^{83} + 269240332456580 q^{84} + 11907997971872 q^{85} - 148747542169982 q^{87} + 186485775340436 q^{88} - 89923791148548 q^{89} + 103388070190448 q^{90} - 920451476162284 q^{94} - 393920660173420 q^{95} - 116095608365672 q^{97} + 24492650399928 q^{98} - 402079041111864 q^{99}+O(q^{100}) \) 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8 + 23502846 * q^10 - 2993734 * q^11 - 76269906 * q^12 - 3845224 * q^14 + 277690070 * q^15 - 5490752792 * q^16 + 285786056 * q^17 + 5809842386 * q^18 - 1195066336 * q^19 + 1866268668 * q^20 - 8197524756 * q^21 + 2117392192 * q^23 + 8629372824 * q^24 - 73846917196 * q^25 - 16368356994 * q^26 + 33411191086 * q^27 + 48687460392 * q^29 + 128044102700 * q^30 + 73968522614 * q^31 - 2657032122 * q^32 - 259972090824 * q^36 + 95888936640 * q^37 - 571710579738 * q^39 + 977850700426 * q^40 - 57594847104 * q^41 + 48472463810 * q^43 + 1173476843650 * q^44 - 299491373708 * q^45 + 656204001636 * q^46 + 29961288922 * q^47 + 1808198535114 * q^48 + 9857850529980 * q^49 + 1443642384290 * q^50 - 11263919114280 * q^52 - 1993070689076 * q^53 + 2064324525592 * q^54 + 3054165001846 * q^55 + 8002123380864 * q^56 - 9170547007720 * q^58 - 8402401993912 * q^59 + 4455428077662 * q^60 - 4381209993964 * q^61 - 14884429709724 * q^65 - 5756218265814 * q^66 + 4595908790532 * q^68 + 51089269002600 * q^69 - 65383337180236 * q^70 + 101900024607216 * q^72 + 39493186331224 * q^73 - 152862151734316 * q^74 - 46335428712972 * q^75 + 46232026918072 * q^76 + 63231072283300 * q^77 + 111617680995888 * q^78 - 29034273461086 * q^79 - 345331621902328 * q^81 + 104609665443600 * q^82 - 2994621113016 * q^83 + 269240332456580 * q^84 + 11907997971872 * q^85 - 148747542169982 * q^87 + 186485775340436 * q^88 - 89923791148548 * q^89 + 103388070190448 * q^90 - 920451476162284 * q^94 - 393920660173420 * q^95 - 116095608365672 * q^97 + 24492650399928 * q^98 - 402079041111864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−50.6787	+	50.6787i	−0.395927	+	0.395927i	−0.876794	−	0.480867i	$-0.840322\pi$
$2$	−50.6787	+	50.6787i	−0.395927	+	0.395927i	0.480867	+	0.876794i	$0.340322\pi$
$3$	910.227	−	910.227i	0.416199	−	0.416199i	−0.467692	−	0.883891i	$-0.654914\pi$
$3$	910.227	−	910.227i	0.416199	−	0.416199i	0.883891	+	0.467692i	$0.154914\pi$
$4$			11247.3i			0.686483i
$5$		−	127648.i		−	1.63390i	−0.576712	−	0.816948i	$-0.695664\pi$
$5$		−	127648.i		−	1.63390i	0.576712	−	0.816948i	$-0.304336\pi$
$6$			92258.2i			0.329569i
$7$	−1.54934e6			−1.88131			−0.940657	−	0.339358i	$-0.889790\pi$
$7$	−1.54934e6			−1.88131			−0.940657	+	0.339358i	$0.889790\pi$
$8$	−1.40032e6	−	1.40032e6i	−0.667724	−	0.667724i
$9$			3.12594e6i			0.653557i
$10$	6.46904e6	+	6.46904e6i	0.646904	+	0.646904i
$11$	1.89478e6	−	1.89478e6i	0.0972321	−	0.0972321i	−0.656818	−	0.754050i	$-0.728098\pi$
$11$	1.89478e6	−	1.89478e6i	0.0972321	−	0.0972321i	0.754050	+	0.656818i	$0.228098\pi$
$12$	1.02376e7	+	1.02376e7i	0.285714	+	0.285714i
$13$			7.31778e7i			1.16621i	0.812398	+	0.583104i	$0.198162\pi$
$13$			7.31778e7i			1.16621i	−0.812398	+	0.583104i	$0.801838\pi$
$14$	7.85187e7	−	7.85187e7i	0.744863	−	0.744863i
$15$	−1.16189e8	−	1.16189e8i	−0.680026	−	0.680026i
$16$	−4.23438e7			−0.157743
$17$	1.23124e8	−	1.23124e8i	0.300055	−	0.300055i	−0.540980	−	0.841035i	$-0.681947\pi$
$17$	1.23124e8	−	1.23124e8i	0.300055	−	0.300055i	0.841035	+	0.540980i	$0.181947\pi$
$18$	−1.58419e8	−	1.58419e8i	−0.258761	−	0.258761i
$19$	1.31336e7	−	1.31336e7i	0.0146930	−	0.0146930i	−0.699722	−	0.714415i	$-0.746693\pi$
$19$	1.31336e7	−	1.31336e7i	0.0146930	−	0.0146930i	0.714415	+	0.699722i	$0.246693\pi$
$20$	1.43570e9			1.12164
$21$	−1.41025e9	+	1.41025e9i	−0.783001	+	0.783001i
$22$			1.92050e8i			0.0769936i
$23$	3.45143e9			1.01369			0.506843	−	0.862038i	$-0.330812\pi$
$23$	3.45143e9			1.01369			0.506843	+	0.862038i	$0.330812\pi$
$24$	−2.54922e9			−0.555813
$25$	−1.01905e10			−1.66962
$26$	−3.70855e9	−	3.70855e9i	−0.461733	−	0.461733i
$27$	7.19891e9	+	7.19891e9i	0.688209	+	0.688209i
$28$		−	1.74260e10i		−	1.29149i
$29$	1.05990e10	−	1.36096e10i	0.614437	−	0.788966i
$29$	1.05990e10	−	1.36096e10i	0.614437	−	0.788966i
$30$	1.17766e10			0.538481
$31$	2.10814e10	−	2.10814e10i	0.766245	−	0.766245i	−0.211198	−	0.977443i	$-0.567736\pi$
$31$	2.10814e10	−	2.10814e10i	0.766245	−	0.766245i	0.977443	+	0.211198i	$0.0677364\pi$
$32$	2.50888e10	−	2.50888e10i	0.730179	−	0.730179i
$33$		−	3.44936e9i		−	0.0809358i
$34$			1.24795e10i			0.237600i
$35$			1.97771e11i			3.07387i
$36$	−3.51585e10			−0.448656
$37$	−3.02037e9	−	3.02037e9i	−0.0318162	−	0.0318162i	0.691020	−	0.722836i	$-0.257162\pi$
$37$	−3.02037e9	−	3.02037e9i	−0.0318162	−	0.0318162i	−0.722836	+	0.691020i	$0.757162\pi$
$38$			1.33119e9i			0.0116347i
$39$	6.66084e10	+	6.66084e10i	0.485374	+	0.485374i
$40$	−1.78748e11	+	1.78748e11i	−1.09099	+	1.09099i
$41$	2.27317e11	+	2.27317e11i	1.16720	+	1.16720i	0.982863	+	0.184338i	$0.0590141\pi$
$41$	2.27317e11	+	2.27317e11i	1.16720	+	1.16720i	0.184338	+	0.982863i	$0.440986\pi$
$42$		−	1.42940e11i		−	0.620023i
$43$	−2.66277e10	+	2.66277e10i	−0.0979613	+	0.0979613i	−0.754389	−	0.656428i	$-0.772067\pi$
$43$	−2.66277e10	+	2.66277e10i	−0.0979613	+	0.0979613i	0.656428	+	0.754389i	$0.272067\pi$
$44$	2.13112e10	+	2.13112e10i	0.0667482	+	0.0667482i
$45$	3.99020e11			1.06784
$46$	−1.74914e11	+	1.74914e11i	−0.401346	+	0.401346i
$47$	3.95665e11	+	3.95665e11i	0.780986	+	0.780986i	0.979997	−	0.199011i	$-0.0637731\pi$
$47$	3.95665e11	+	3.95665e11i	0.780986	+	0.780986i	−0.199011	+	0.979997i	$0.563773\pi$
$48$	−3.85425e10	+	3.85425e10i	−0.0656525	+	0.0656525i
$49$	1.72224e12			2.53934
$50$	5.16442e11	−	5.16442e11i	0.661046	−	0.661046i
$51$		−	2.24142e11i		−	0.249765i
$52$	−8.23056e11			−0.800582
$53$	−4.44734e11			−0.378590			−0.189295	−	0.981920i	$-0.560620\pi$
$53$	−4.44734e11			−0.378590			−0.189295	+	0.981920i	$0.560620\pi$
$54$	−7.29662e11			−0.544961
$55$	−2.41865e11	−	2.41865e11i	−0.158867	−	0.158867i
$56$	2.16958e12	+	2.16958e12i	1.25620	+	1.25620i
$57$		−	2.39092e10i		−	0.0122304i
$58$	1.52574e11	+	1.22686e12i	0.0691009	+	0.555645i
$59$	−2.41238e12			−0.969354			−0.484677	−	0.874693i	$-0.661063\pi$
$59$	−2.41238e12			−0.969354			−0.484677	+	0.874693i	$0.661063\pi$
$60$	1.30682e12	−	1.30682e12i	0.466827	−	0.466827i
$61$	−1.51318e12	+	1.51318e12i	−0.481483	+	0.481483i	−0.905605	−	0.424122i	$-0.860583\pi$
$61$	−1.51318e12	+	1.51318e12i	−0.481483	+	0.481483i	0.424122	+	0.905605i	$0.360583\pi$
$62$			2.13676e12i			0.606755i
$63$		−	4.84316e12i		−	1.22955i
$64$			1.84917e12i			0.420452i
$65$	9.34100e12			1.90546
$66$	1.74809e11	+	1.74809e11i	0.0320447	+	0.0320447i
$67$			8.36251e12i			1.37979i	0.723909	+	0.689895i	$0.242343\pi$
$67$			8.36251e12i			1.37979i	−0.723909	+	0.689895i	$0.757657\pi$
$68$	1.38482e12	+	1.38482e12i	0.205983	+	0.205983i
$69$	3.14158e12	−	3.14158e12i	0.421896	−	0.421896i
$70$	−1.00228e13	−	1.00228e13i	−1.21703	−	1.21703i
$71$		−	7.18905e12i		−	0.790429i	−0.918589	−	0.395215i	$-0.870670\pi$
$71$		−	7.18905e12i		−	0.790429i	0.918589	−	0.395215i	$-0.129330\pi$
$72$	4.37732e12	−	4.37732e12i	0.436396	−	0.436396i
$73$	−6.97575e12	−	6.97575e12i	−0.631438	−	0.631438i	0.316991	−	0.948429i	$-0.397328\pi$
$73$	−6.97575e12	−	6.97575e12i	−0.631438	−	0.631438i	−0.948429	+	0.316991i	$0.897328\pi$
$74$	3.06137e11			0.0251938
$75$	−9.27569e12	+	9.27569e12i	−0.694892	+	0.694892i
$76$	1.47719e11	+	1.47719e11i	0.0100865	+	0.0100865i
$77$	−2.93566e12	+	2.93566e12i	−0.182924	+	0.182924i
$78$	−6.75125e12			−0.384346
$79$	−1.62138e13	+	1.62138e13i	−0.844299	+	0.844299i	−0.989415	−	0.145115i	$-0.953645\pi$
$79$	−1.62138e13	+	1.62138e13i	−0.844299	+	0.844299i	0.145115	+	0.989415i	$0.453645\pi$
$80$			5.40511e12i			0.257736i
$81$	−1.84599e12			−0.0806928
$82$	−2.30403e13			−0.924253
$83$	4.05979e13			1.49609			0.748044	−	0.663650i	$-0.230993\pi$
$83$	4.05979e13			1.49609			0.748044	+	0.663650i	$0.230993\pi$
$84$	−1.58616e13	−	1.58616e13i	−0.537518	−	0.537518i
$85$	−1.57166e13	−	1.57166e13i	−0.490259	−	0.490259i
$86$		−	2.69891e12i		−	0.0775710i
$87$	−2.74034e12	−	2.20353e13i	−0.0726390	−	0.584095i
$88$	−5.30659e12			−0.129848
$89$	1.71467e13	−	1.71467e13i	0.387660	−	0.387660i	−0.486192	−	0.873852i	$-0.661615\pi$
$89$	1.71467e13	−	1.71467e13i	0.387660	−	0.387660i	0.873852	+	0.486192i	$0.161615\pi$
$90$	−2.02218e13	+	2.02218e13i	−0.422788	+	0.422788i
$91$		−	1.13377e14i		−	2.19400i
$92$			3.88194e13i			0.695879i
$93$		−	3.83778e13i		−	0.637821i
$94$	−4.01036e13			−0.618427
$95$	−1.67649e12	−	1.67649e12i	−0.0240068	−	0.0240068i
$96$		−	4.56730e13i		−	0.607800i
$97$	9.87187e13	+	9.87187e13i	1.22179	+	1.22179i	0.966994	+	0.254797i	$0.0820088\pi$
$97$	9.87187e13	+	9.87187e13i	1.22179	+	1.22179i	0.254797	+	0.966994i	$0.417991\pi$
$98$	−8.72809e13	+	8.72809e13i	−1.00540	+	1.00540i
$99$	5.92296e12	+	5.92296e12i	0.0635467	+	0.0635467i
$100$		−	1.14616e14i		−	1.14616i
$101$	−6.86082e13	+	6.86082e13i	−0.639921	+	0.639921i	−0.950536	−	0.310615i	$-0.899465\pi$
$101$	−6.86082e13	+	6.86082e13i	−0.639921	+	0.639921i	0.310615	+	0.950536i	$0.399465\pi$
$102$	1.13592e13	+	1.13592e13i	0.0988888	+	0.0988888i
$103$	−9.82041e13			−0.798489			−0.399245	−	0.916844i	$-0.630728\pi$
$103$	−9.82041e13			−0.798489			−0.399245	+	0.916844i	$0.630728\pi$
$104$	1.02472e14	−	1.02472e14i	0.778705	−	0.778705i
$105$	1.80016e14	+	1.80016e14i	1.27934	+	1.27934i
$106$	2.25385e13	−	2.25385e13i	0.149894	−	0.149894i
$107$	7.70763e12			0.0479993			0.0239996	−	0.999712i	$-0.492360\pi$
$107$	7.70763e12			0.0479993			0.0239996	+	0.999712i	$0.492360\pi$
$108$	−8.09686e13	+	8.09686e13i	−0.472444	+	0.472444i
$109$		−	9.06346e13i		−	0.495802i	−0.968785	−	0.247901i	$-0.920259\pi$
$109$		−	9.06346e13i		−	0.495802i	0.968785	−	0.247901i	$-0.0797409\pi$
$110$	2.45148e13			0.125800
$111$	−5.49845e12			−0.0264837
$112$	6.56051e13			0.296764
$113$	2.19996e14	+	2.19996e14i	0.935119	+	0.935119i	0.998020	−	0.0629012i	$-0.0200353\pi$
$113$	2.19996e14	+	2.19996e14i	0.935119	+	0.935119i	−0.0629012	+	0.998020i	$0.520035\pi$
$114$	1.21169e12	+	1.21169e12i	0.00484235	+	0.00484235i
$115$		−	4.40568e14i		−	1.65626i
$116$	1.53072e14	+	1.19210e14i	0.541612	+	0.421801i
$117$	−2.28749e14			−0.762182
$118$	1.22256e14	−	1.22256e14i	0.383793	−	0.383793i
$119$	−1.90762e14	+	1.90762e14i	−0.564498	+	0.564498i
$120$			3.25403e14i			0.908140i
$121$			3.72569e14i			0.981092i
$122$		−	1.53372e14i		−	0.381264i
$123$	4.13821e14			0.971576
$124$	2.37110e14	+	2.37110e14i	0.526015	+	0.526015i
$125$			5.21699e14i			1.09408i
$126$	2.45445e14	+	2.45445e14i	0.486810	+	0.486810i
$127$	2.60386e14	−	2.60386e14i	0.488642	−	0.488642i	−0.419235	−	0.907878i	$-0.637702\pi$
$127$	2.60386e14	−	2.60386e14i	0.488642	−	0.488642i	0.907878	+	0.419235i	$0.137702\pi$
$128$	3.17341e14	+	3.17341e14i	0.563711	+	0.563711i
$129$			4.84745e13i			0.0815428i
$130$	−4.73390e14	+	4.73390e14i	−0.754424	+	0.754424i
$131$	−3.47808e14	−	3.47808e14i	−0.525341	−	0.525341i	0.393839	−	0.919179i	$-0.371147\pi$
$131$	−3.47808e14	−	3.47808e14i	−0.525341	−	0.525341i	−0.919179	+	0.393839i	$0.871147\pi$
$132$	3.87961e13			0.0555611
$133$	−2.03485e13	+	2.03485e13i	−0.0276421	+	0.0276421i
$134$	−4.23801e14	−	4.23801e14i	−0.546296	−	0.546296i
$135$	9.18927e14	−	9.18927e14i	1.12446	−	1.12446i
$136$	−3.44826e14			−0.400708
$137$	5.99309e14	−	5.99309e14i	0.661617	−	0.661617i	−0.294144	−	0.955761i	$-0.595034\pi$
$137$	5.99309e14	−	5.99309e14i	0.661617	−	0.661617i	0.955761	+	0.294144i	$0.0950345\pi$
$138$			3.18423e14i			0.334080i
$139$	−1.03801e15			−1.03538			−0.517688	−	0.855569i	$-0.673207\pi$
$139$	−1.03801e15			−1.03538			−0.517688	+	0.855569i	$0.673207\pi$
$140$	−2.22440e15			−2.11016
$141$	7.20291e14			0.650091
$142$	3.64331e14	+	3.64331e14i	0.312952	+	0.312952i
$143$	1.38656e14	+	1.38656e14i	0.113393	+	0.113393i
$144$		−	1.32364e14i		−	0.103094i
$145$	−1.73724e15	−	1.35294e15i	−1.28909	−	1.00393i
$146$	7.07043e14			0.500007
$147$	1.56763e15	−	1.56763e15i	1.05687	−	1.05687i
$148$	3.39712e13	−	3.39712e13i	0.0218413	−	0.0218413i
$149$		−	1.13462e15i		−	0.695902i	−0.937513	−	0.347951i	$-0.886878\pi$
$149$		−	1.13462e15i		−	0.695902i	0.937513	−	0.347951i	$-0.113122\pi$
$150$		−	9.40159e14i		−	0.550253i
$151$			2.06213e15i			1.15206i	0.817427	+	0.576032i	$0.195400\pi$
$151$			2.06213e15i			1.15206i	−0.817427	+	0.576032i	$0.804600\pi$
$152$	−3.67826e13			−0.0196217
$153$	3.84879e14	+	3.84879e14i	0.196103	+	0.196103i
$154$		−	2.97551e14i		−	0.144849i
$155$	−2.69100e15	−	2.69100e15i	−1.25197	−	1.25197i
$156$	−7.49168e14	+	7.49168e14i	−0.333202	+	0.333202i
$157$	2.48226e15	+	2.48226e15i	1.05572	+	1.05572i	0.998353	+	0.0573697i	$0.0182714\pi$
$157$	2.48226e15	+	2.48226e15i	1.05572	+	1.05572i	0.0573697	+	0.998353i	$0.481729\pi$
$158$		−	1.64339e15i		−	0.668562i
$159$	−4.04809e14	+	4.04809e14i	−0.157569	+	0.157569i
$160$	−3.20253e15	−	3.20253e15i	−1.19304	−	1.19304i
$161$	−5.34744e15			−1.90706
$162$	9.35524e13	−	9.35524e13i	0.0319484	−	0.0319484i
$163$	3.10038e15	+	3.10038e15i	1.01415	+	1.01415i	0.999898	+	0.0142515i	$0.00453654\pi$
$163$	3.10038e15	+	3.10038e15i	1.01415	+	1.01415i	0.0142515	+	0.999898i	$0.495463\pi$
$164$	−2.55672e15	+	2.55672e15i	−0.801264	+	0.801264i
$165$	−4.40304e14			−0.132241
$166$	−2.05745e15	+	2.05745e15i	−0.592341	+	0.592341i
$167$		−	6.63789e15i		−	1.83238i	−0.400749	−	0.916188i	$-0.631250\pi$
$167$		−	6.63789e15i		−	1.83238i	0.400749	−	0.916188i	$-0.368750\pi$
$168$	3.94962e15			1.04566
$169$	−1.41761e15			−0.360039
$170$	1.59299e15			0.388213
$171$	4.10550e13	+	4.10550e13i	0.00960270	+	0.00960270i
$172$	−2.99491e14	−	2.99491e14i	−0.0672488	−	0.0672488i
$173$			3.53787e15i			0.762814i	0.924407	+	0.381407i	$0.124560\pi$
$173$			3.53787e15i			0.762814i	−0.924407	+	0.381407i	$0.875440\pi$
$174$	1.25559e15	+	9.77841e14i	0.260019	+	0.202499i
$175$	1.57886e16			3.14107
$176$	−8.02322e13	+	8.02322e13i	−0.0153377	+	0.0153377i
$177$	−2.19582e15	+	2.19582e15i	−0.403444	+	0.403444i
$178$			1.73794e15i			0.306970i
$179$		−	2.95252e15i		−	0.501443i	−0.968059	−	0.250721i	$-0.919332\pi$
$179$		−	2.95252e15i		−	0.501443i	0.968059	−	0.250721i	$-0.0806678\pi$
$180$			4.48792e15i			0.733057i
$181$	−9.05569e15			−1.42289			−0.711445	−	0.702742i	$-0.751959\pi$
$181$	−9.05569e15			−1.42289			−0.711445	+	0.702742i	$0.751959\pi$
$182$	5.74582e15	+	5.74582e15i	0.868665	+	0.868665i
$183$			2.75467e15i			0.400786i
$184$	−4.83310e15	−	4.83310e15i	−0.676863	−	0.676863i
$185$	−3.85545e14	+	3.85545e14i	−0.0519843	+	0.0519843i
$186$	1.94493e15	+	1.94493e15i	0.252531	+	0.252531i
$187$		−	4.66586e14i		−	0.0583499i
$188$	−4.45019e15	+	4.45019e15i	−0.536134	+	0.536134i
$189$	−1.11536e16	−	1.11536e16i	−1.29474	−	1.29474i
$190$	1.69924e14			0.0190099
$191$	5.81319e15	−	5.81319e15i	0.626875	−	0.626875i	−0.320405	−	0.947281i	$-0.603819\pi$
$191$	5.81319e15	−	5.81319e15i	0.626875	−	0.626875i	0.947281	+	0.320405i	$0.103819\pi$
$192$	1.68316e15	+	1.68316e15i	0.174992	+	0.174992i
$193$	1.23009e16	−	1.23009e16i	1.23321	−	1.23321i	0.270484	−	0.962724i	$-0.412816\pi$
$193$	1.23009e16	−	1.23009e16i	1.23321	−	1.23321i	0.962724	−	0.270484i	$-0.0871837\pi$
$194$	−1.00059e16			−0.967481
$195$	8.50244e15	−	8.50244e15i	0.793051	−	0.793051i
$196$			1.93706e16i			1.74322i
$197$	1.05160e15			0.0913241			0.0456621	−	0.998957i	$-0.485460\pi$
$197$	1.05160e15			0.0913241			0.0456621	+	0.998957i	$0.485460\pi$
$198$	−6.00336e14			−0.0503197
$199$	6.92169e15			0.560068			0.280034	−	0.959990i	$-0.409654\pi$
$199$	6.92169e15			0.560068			0.280034	+	0.959990i	$0.409654\pi$
$200$	1.42700e16	+	1.42700e16i	1.11484	+	1.11484i
$201$	7.61179e15	+	7.61179e15i	0.574267	+	0.574267i
$202$		−	6.95395e15i		−	0.506724i
$203$	−1.64214e16	+	2.10859e16i	−1.15595	+	1.48429i
$204$	2.52100e15			0.171460
$205$	2.90166e16	−	2.90166e16i	1.90708	−	1.90708i
$206$	4.97685e15	−	4.97685e15i	0.316144	−	0.316144i
$207$			1.07890e16i			0.662502i
$208$		−	3.09863e15i		−	0.183961i
$209$		−	4.97707e13i		−	0.00285726i
$210$	−1.82460e16			−1.01305
$211$	9.41752e15	+	9.41752e15i	0.505777	+	0.505777i	0.913227	−	0.407450i	$-0.133582\pi$
$211$	9.41752e15	+	9.41752e15i	0.505777	+	0.505777i	−0.407450	+	0.913227i	$0.633582\pi$
$212$		−	5.00207e15i		−	0.259896i
$213$	−6.54367e15	−	6.54367e15i	−0.328976	−	0.328976i
$214$	−3.90612e14	+	3.90612e14i	−0.0190042	+	0.0190042i
$215$	3.39897e15	+	3.39897e15i	0.160058	+	0.160058i
$216$		−	2.01615e16i		−	0.919068i
$217$	−3.26624e16	+	3.26624e16i	−1.44155	+	1.44155i
$218$	4.59324e15	+	4.59324e15i	0.196302	+	0.196302i
$219$	−1.26990e16			−0.525608
$220$	2.72034e15	−	2.72034e15i	0.109060	−	0.109060i
$221$	9.00995e15	+	9.00995e15i	0.349926	+	0.349926i
$222$	2.78654e14	−	2.78654e14i	0.0104856	−	0.0104856i
$223$	2.07196e16			0.755522			0.377761	−	0.925903i	$-0.376694\pi$
$223$	2.07196e16			0.755522			0.377761	+	0.925903i	$0.376694\pi$
$224$	−3.88711e16	+	3.88711e16i	−1.37370	+	1.37370i
$225$		−	3.18550e16i		−	1.09119i
$226$	−2.22983e16			−0.740477
$227$	−3.48359e16			−1.12162			−0.560810	−	0.827945i	$-0.689510\pi$
$227$	−3.48359e16			−1.12162			−0.560810	+	0.827945i	$0.689510\pi$
$228$	2.68915e14			0.00839598
$229$	−1.09156e16	−	1.09156e16i	−0.330520	−	0.330520i	0.522264	−	0.852784i	$-0.325088\pi$
$229$	−1.09156e16	−	1.09156e16i	−0.330520	−	0.330520i	−0.852784	+	0.522264i	$0.825088\pi$
$230$	2.23274e16	+	2.23274e16i	0.655758	+	0.655758i
$231$			5.34424e15i			0.152266i
$232$	−3.38997e16	+	4.21582e15i	−0.937086	+	0.116538i
$233$	5.04344e16			1.35281			0.676403	−	0.736532i	$-0.263538\pi$
$233$	5.04344e16			1.35281			0.676403	+	0.736532i	$0.263538\pi$
$234$	1.15927e16	−	1.15927e16i	0.301769	−	0.301769i
$235$	5.05059e16	−	5.05059e16i	1.27605	−	1.27605i
$236$		−	2.71329e16i		−	0.665445i
$237$			2.95166e16i			0.702793i
$238$		−	1.93351e16i		−	0.447000i
$239$	−2.68038e16			−0.601744			−0.300872	−	0.953665i	$-0.597278\pi$
$239$	−2.68038e16			−0.601744			−0.300872	+	0.953665i	$0.597278\pi$
$240$	4.91988e15	+	4.91988e15i	0.107269	+	0.107269i
$241$			2.93237e16i			0.621011i	0.950572	+	0.310505i	$0.100498\pi$
$241$			2.93237e16i			0.621011i	−0.950572	+	0.310505i	$0.899502\pi$
$242$	−1.88813e16	−	1.88813e16i	−0.388441	−	0.388441i
$243$	−3.61124e16	+	3.61124e16i	−0.721793	+	0.721793i
$244$	−1.70192e16	−	1.70192e16i	−0.330530	−	0.330530i
$245$		−	2.19841e17i		−	4.14902i
$246$	−2.09719e16	+	2.09719e16i	−0.384673	+	0.384673i
$247$	9.61091e14	+	9.61091e14i	0.0171351	+	0.0171351i
$248$	−5.90414e16			−1.02328
$249$	3.69533e16	−	3.69533e16i	0.622670	−	0.622670i
$250$	−2.64390e16	−	2.64390e16i	−0.433176	−	0.433176i
$251$	6.51793e15	−	6.51793e15i	0.103847	−	0.103847i	−0.653274	−	0.757121i	$-0.726605\pi$
$251$	6.51793e15	−	6.51793e15i	0.103847	−	0.103847i	0.757121	+	0.653274i	$0.226605\pi$
$252$	5.44726e16			0.844063
$253$	6.53969e15	−	6.53969e15i	0.0985629	−	0.0985629i
$254$			2.63920e16i			0.386933i
$255$	−2.86113e16			−0.408090
$256$	−6.24616e16			−0.866829
$257$	3.72639e16			0.503218			0.251609	−	0.967829i	$-0.419040\pi$
$257$	3.72639e16			0.503218			0.251609	+	0.967829i	$0.419040\pi$
$258$	−2.45662e15	−	2.45662e15i	−0.0322850	−	0.0322850i
$259$	4.67959e15	+	4.67959e15i	0.0598563	+	0.0598563i
$260$			1.05061e17i			1.30807i
$261$	4.25427e16	+	3.31317e16i	0.515634	+	0.401569i
$262$	3.52529e16			0.415993
$263$	−6.09866e16	+	6.09866e16i	−0.700719	+	0.700719i	−0.964565	−	0.263846i	$-0.915009\pi$
$263$	−6.09866e16	+	6.09866e16i	−0.700719	+	0.700719i	0.263846	+	0.964565i	$0.415009\pi$
$264$	−4.83020e15	+	4.83020e15i	−0.0540428	+	0.0540428i
$265$			5.67694e16i			0.618576i
$266$		−	2.06247e15i		−	0.0218885i
$267$		−	3.12148e16i		−	0.322687i
$268$	−9.40560e16			−0.947203
$269$	1.03576e17	+	1.03576e17i	1.01624	+	1.01624i	0.999866	+	0.0163698i	$0.00521091\pi$
$269$	1.03576e17	+	1.03576e17i	1.01624	+	1.01624i	0.0163698	+	0.999866i	$0.494789\pi$
$270$			9.31400e16i			0.890409i
$271$	2.94413e16	+	2.94413e16i	0.274266	+	0.274266i	0.830815	−	0.556549i	$-0.187875\pi$
$271$	2.94413e16	+	2.94413e16i	0.274266	+	0.274266i	−0.556549	+	0.830815i	$0.687875\pi$
$272$	−5.21355e15	+	5.21355e15i	−0.0473316	+	0.0473316i
$273$	−1.03199e17	−	1.03199e17i	−0.913142	−	0.913142i
$274$			6.07444e16i			0.523904i
$275$	−1.93088e16	+	1.93088e16i	−0.162340	+	0.162340i
$276$	3.53345e16	+	3.53345e16i	0.289624	+	0.289624i
$277$	1.48833e17			1.18944			0.594718	−	0.803934i	$-0.297264\pi$
$277$	1.48833e17			1.18944			0.594718	+	0.803934i	$0.297264\pi$
$278$	5.26050e16	−	5.26050e16i	0.409934	−	0.409934i
$279$	6.58993e16	+	6.58993e16i	0.500785	+	0.500785i
$280$	2.76942e17	−	2.76942e17i	2.05250	−	2.05250i
$281$	−9.02326e16			−0.652258			−0.326129	−	0.945325i	$-0.605744\pi$
$281$	−9.02326e16			−0.652258			−0.326129	+	0.945325i	$0.605744\pi$
$282$	−3.65034e16	+	3.65034e16i	−0.257389	+	0.257389i
$283$			3.25620e16i			0.223978i	0.993709	+	0.111989i	$0.0357222\pi$
$283$			3.25620e16i			0.223978i	−0.993709	+	0.111989i	$0.964278\pi$
$284$	8.08577e16			0.542617
$285$	−3.05197e15			−0.0199832
$286$	−1.40538e16			−0.0897905
$287$	−3.52193e17	−	3.52193e17i	−2.19587	−	2.19587i
$288$	7.84260e16	+	7.84260e16i	0.477213	+	0.477213i
$289$			1.38059e17i			0.819934i
$290$	1.56606e17	−	1.94757e16i	0.907866	−	0.112904i
$291$	1.79713e17			1.01702
$292$	7.84586e16	−	7.84586e16i	0.433472	−	0.433472i
$293$	−5.05255e16	+	5.05255e16i	−0.272544	+	0.272544i	−0.830124	−	0.557579i	$-0.811730\pi$
$293$	−5.05255e16	+	5.05255e16i	−0.272544	+	0.272544i	0.557579	+	0.830124i	$0.311730\pi$
$294$			1.58891e17i			0.836889i
$295$			3.07936e17i			1.58382i
$296$			8.45897e15i			0.0424889i
$297$	2.72807e16			0.133832
$298$	5.75012e16	+	5.75012e16i	0.275526	+	0.275526i
$299$			2.52568e17i			1.18217i
$300$	−1.04327e17	−	1.04327e17i	−0.477032	−	0.477032i
$301$	4.12554e16	−	4.12554e16i	0.184296	−	0.184296i
$302$	−1.04506e17	−	1.04506e17i	−0.456134	−	0.456134i
$303$			1.24898e17i			0.532669i
$304$	−5.56129e14	+	5.56129e14i	−0.00231772	+	0.00231772i
$305$	1.93154e17	+	1.93154e17i	0.786693	+	0.786693i
$306$	−3.90103e16			−0.155285
$307$	1.92600e17	−	1.92600e17i	0.749356	−	0.749356i	−0.225002	−	0.974358i	$-0.572239\pi$
$307$	1.92600e17	−	1.92600e17i	0.749356	−	0.749356i	0.974358	+	0.225002i	$0.0722389\pi$
$308$	−3.30184e16	−	3.30184e16i	−0.125574	−	0.125574i
$309$	−8.93881e16	+	8.93881e16i	−0.332331	+	0.332331i
$310$	2.72753e17			0.991374
$311$	−2.54972e17	+	2.54972e17i	−0.906086	+	0.906086i	−0.995954	−	0.0898681i	$-0.971355\pi$
$311$	−2.54972e17	+	2.54972e17i	−0.906086	+	0.906086i	0.0898681	+	0.995954i	$0.471355\pi$
$312$		−	1.86546e17i		−	0.648193i
$313$	−2.30770e17			−0.784097			−0.392048	−	0.919945i	$-0.628233\pi$
$313$	−2.30770e17			−0.784097			−0.392048	+	0.919945i	$0.628233\pi$
$314$	−2.51595e17			−0.835978
$315$	−6.18220e17			−2.00895
$316$	−1.82363e17	−	1.82363e17i	−0.579597	−	0.579597i
$317$	1.99259e17	+	1.99259e17i	0.619444	+	0.619444i	0.945389	−	0.325945i	$-0.105682\pi$
$317$	1.99259e17	+	1.99259e17i	0.619444	+	0.619444i	−0.325945	+	0.945389i	$0.605682\pi$
$318$		−	4.10303e16i		−	0.124771i
$319$	−5.70444e15	−	4.58698e16i	−0.0169699	−	0.136456i
$320$	2.36043e17			0.686975
$321$	7.01570e15	−	7.01570e15i	0.0199772	−	0.0199772i
$322$	2.71001e17	−	2.71001e17i	0.755058	−	0.755058i
$323$		−	3.23414e15i		−	0.00881741i
$324$		−	2.07625e16i		−	0.0553942i
$325$		−	7.45720e17i		−	1.94712i
$326$	−3.14247e17			−0.803059
$327$	−8.24981e16	−	8.24981e16i	−0.206353	−	0.206353i
$328$		−	6.36634e17i		−	1.55874i
$329$	−6.13022e17	−	6.13022e17i	−1.46928	−	1.46928i
$330$	2.23140e16	−	2.23140e16i	0.0523577	−	0.0523577i
$331$	3.81816e17	+	3.81816e17i	0.877119	+	0.877119i	0.993236	−	0.116117i	$-0.0370447\pi$
$331$	3.81816e17	+	3.81816e17i	0.877119	+	0.877119i	−0.116117	+	0.993236i	$0.537045\pi$
$332$			4.56619e17i			1.02704i
$333$	9.44150e15	−	9.44150e15i	0.0207937	−	0.0207937i
$334$	3.36399e17	+	3.36399e17i	0.725487	+	0.725487i
$335$	1.06746e18			2.25443
$336$	5.97156e16	−	5.97156e16i	0.123513	−	0.123513i
$337$	−8.53481e16	−	8.53481e16i	−0.172896	−	0.172896i	0.615355	−	0.788250i	$-0.289013\pi$
$337$	−8.53481e16	−	8.53481e16i	−0.172896	−	0.172896i	−0.788250	+	0.615355i	$0.789013\pi$
$338$	7.18426e16	−	7.18426e16i	0.142549	−	0.142549i
$339$	4.00494e17			0.778391
$340$	1.76770e17	−	1.76770e17i	0.336554	−	0.336554i
$341$		−	7.98892e16i		−	0.149007i
$342$	−4.16123e15			−0.00760394
$343$	−1.61754e18			−2.89599
$344$	7.45746e16			0.130822
$345$	−4.01017e17	−	4.01017e17i	−0.689333	−	0.689333i
$346$	−1.79294e17	−	1.79294e17i	−0.302019	−	0.302019i
$347$			2.47326e16i			0.0408284i	0.999792	+	0.0204142i	$0.00649850\pi$
$347$			2.47326e16i			0.0408284i	−0.999792	+	0.0204142i	$0.993502\pi$
$348$	2.47838e17	−	3.08215e16i	0.400972	−	0.0498655i
$349$	−9.03583e17			−1.43282			−0.716408	−	0.697682i	$-0.754215\pi$
$349$	−9.03583e17			−1.43282			−0.716408	+	0.697682i	$0.754215\pi$
$350$	−8.00146e17	+	8.00146e17i	−1.24364	+	1.24364i
$351$	−5.26800e17	+	5.26800e17i	−0.802594	+	0.802594i
$352$		−	9.50753e16i		−	0.141994i
$353$			4.27954e17i			0.626577i	0.949658	+	0.313288i	$0.101431\pi$
$353$			4.27954e17i			0.626577i	−0.949658	+	0.313288i	$0.898569\pi$
$354$		−	2.22562e17i		−	0.319469i
$355$	−9.17668e17			−1.29148
$356$	1.92855e17	+	1.92855e17i	0.266122	+	0.266122i
$357$			3.47273e17i			0.469887i
$358$	1.49630e17	+	1.49630e17i	0.198535	+	0.198535i
$359$	1.06381e18	−	1.06381e18i	1.38421	−	1.38421i	0.547219	−	0.836989i	$-0.315686\pi$
$359$	1.06381e18	−	1.06381e18i	1.38421	−	1.38421i	0.836989	−	0.547219i	$-0.184314\pi$
$360$	−5.58756e17	−	5.58756e17i	−0.713025	−	0.713025i
$361$			7.98662e17i			0.999568i
$362$	4.58930e17	−	4.58930e17i	0.563361	−	0.563361i
$363$	3.39123e17	+	3.39123e17i	0.408330	+	0.408330i
$364$	1.27520e18			1.50615
$365$	−8.90441e17	+	8.90441e17i	−1.03170	+	1.03170i
$366$	−1.39603e17	−	1.39603e17i	−0.158682	−	0.158682i
$367$	9.47267e17	−	9.47267e17i	1.05636	−	1.05636i	0.0580412	−	0.998314i	$-0.481515\pi$
$367$	9.47267e17	−	9.47267e17i	1.05636	−	1.05636i	0.998314	−	0.0580412i	$-0.0184855\pi$
$368$	−1.46147e17			−0.159902
$369$	−7.10581e17	+	7.10581e17i	−0.762832	+	0.762832i
$370$		−	3.90778e16i		−	0.0411640i
$371$	6.89045e17			0.712246
$372$	4.31648e17			0.437854
$373$	1.23394e18			1.22837			0.614187	−	0.789160i	$-0.289484\pi$
$373$	1.23394e18			1.22837			0.614187	+	0.789160i	$0.289484\pi$
$374$	2.36460e16	+	2.36460e16i	0.0231023	+	0.0231023i
$375$	4.74864e17	+	4.74864e17i	0.455356	+	0.455356i
$376$		−	1.10812e18i		−	1.04297i
$377$	9.95918e17	+	7.75608e17i	0.920098	+	0.716561i
$378$	1.13050e18			1.02524
$379$	−7.58083e17	+	7.58083e17i	−0.674904	+	0.674904i	−0.958843	−	0.283938i	$-0.908359\pi$
$379$	−7.58083e17	+	7.58083e17i	−0.674904	+	0.674904i	0.283938	+	0.958843i	$0.408359\pi$
$380$	1.88560e16	−	1.88560e16i	0.0164803	−	0.0164803i
$381$		−	4.74020e17i		−	0.406745i
$382$			5.89210e17i			0.496394i
$383$		−	6.42828e17i		−	0.531745i	−0.964008	−	0.265872i	$-0.914340\pi$
$383$		−	6.42828e17i		−	0.531745i	0.964008	−	0.265872i	$-0.0856600\pi$
$384$	5.77705e17			0.469232
$385$	3.74732e17	+	3.74732e17i	0.298879	+	0.298879i
$386$			1.24679e18i			0.976521i
$387$	−8.32366e16	−	8.32366e16i	−0.0640232	−	0.0640232i
$388$	−1.11032e18	+	1.11032e18i	−0.838740	+	0.838740i
$389$	−1.41465e18	−	1.41465e18i	−1.04954	−	1.04954i	−0.998707	−	0.0508364i	$-0.983811\pi$
$389$	−1.41465e18	−	1.41465e18i	−1.04954	−	1.04954i	−0.0508364	−	0.998707i	$-0.516189\pi$
$390$			8.61784e17i			0.627981i
$391$	4.24954e17	−	4.24954e17i	0.304162	−	0.304162i
$392$	−2.41169e18	−	2.41169e18i	−1.69558	−	1.69558i
$393$	−6.33169e17			−0.437293
$394$	−5.32935e16	+	5.32935e16i	−0.0361577	+	0.0361577i
$395$	2.06967e18	+	2.06967e18i	1.37950	+	1.37950i
$396$	−6.66176e16	+	6.66176e16i	−0.0436237	+	0.0436237i
$397$	1.75929e18			1.13189			0.565946	−	0.824443i	$-0.308511\pi$
$397$	1.75929e18			1.13189			0.565946	+	0.824443i	$0.308511\pi$
$398$	−3.50782e17	+	3.50782e17i	−0.221746	+	0.221746i
$399$			3.70436e16i			0.0230093i
$400$	4.31506e17			0.263370
$401$	−3.34717e17			−0.200755			−0.100378	−	0.994949i	$-0.532005\pi$
$401$	−3.34717e17			−0.200755			−0.100378	+	0.994949i	$0.532005\pi$
$402$	−7.71510e17			−0.454736
$403$	1.54269e18	+	1.54269e18i	0.893601	+	0.893601i
$404$	−7.71660e17	−	7.71660e17i	−0.439295	−	0.439295i
$405$			2.35637e17i			0.131844i
$406$	−2.36389e17	−	1.90082e18i	−0.130001	−	1.04534i
$407$	−1.14459e16			−0.00618711
$408$	−3.13871e17	+	3.13871e17i	−0.166774	+	0.166774i
$409$	−3.29146e17	+	3.29146e17i	−0.171920	+	0.171920i	−0.787822	−	0.615903i	$-0.788791\pi$
$409$	−3.29146e17	+	3.29146e17i	−0.171920	+	0.171920i	0.615903	+	0.787822i	$0.288791\pi$
$410$			2.94105e18i			1.51013i
$411$		−	1.09102e18i		−	0.550729i
$412$		−	1.10454e18i		−	0.548150i
$413$	3.73761e18			1.82366
$414$	−5.46770e17	−	5.46770e17i	−0.262302	−	0.262302i
$415$		−	5.18224e18i		−	2.44445i
$416$	1.83594e18	+	1.83594e18i	0.851540	+	0.851540i
$417$	−9.44826e17	+	9.44826e17i	−0.430923	+	0.430923i
$418$	2.52231e15	+	2.52231e15i	0.00113127	+	0.00113127i
$419$		−	2.97088e18i		−	1.31035i	−0.755477	−	0.655175i	$-0.772595\pi$
$419$		−	2.97088e18i		−	1.31035i	0.755477	−	0.655175i	$-0.227405\pi$
$420$	−2.02471e18	+	2.02471e18i	−0.878248	+	0.878248i
$421$	2.00354e18	+	2.00354e18i	0.854718	+	0.854718i	0.990710	−	0.135992i	$-0.0434222\pi$
$421$	2.00354e18	+	2.00354e18i	0.854718	+	0.854718i	−0.135992	+	0.990710i	$0.543422\pi$
$422$	−9.54535e17			−0.400502
$423$	−1.23683e18	+	1.23683e18i	−0.510418	+	0.510418i
$424$	6.22769e17	+	6.22769e17i	0.252794	+	0.252794i
$425$	−1.25470e18	+	1.25470e18i	−0.500976	+	0.500976i
$426$	6.63249e17			0.260501
$427$	2.34443e18	−	2.34443e18i	0.905821	−	0.905821i
$428$			8.66904e16i			0.0329507i
$429$	2.52416e17			0.0943879
$430$	−3.44511e17			−0.126743
$431$	−3.84467e18			−1.39161			−0.695806	−	0.718230i	$-0.744953\pi$
$431$	−3.84467e18			−1.39161			−0.695806	+	0.718230i	$0.744953\pi$
$432$	−3.04829e17	−	3.04829e17i	−0.108560	−	0.108560i
$433$	−7.50207e16	−	7.50207e16i	−0.0262885	−	0.0262885i	0.693840	−	0.720129i	$-0.255917\pi$
$433$	−7.50207e16	−	7.50207e16i	−0.0262885	−	0.0262885i	−0.720129	+	0.693840i	$0.755917\pi$
$434$		−	3.31057e18i		−	1.14150i
$435$	−2.81276e18	+	3.49799e17i	−0.954350	+	0.118684i
$436$	1.01940e18			0.340360
$437$	4.53298e16	−	4.53298e16i	0.0148941	−	0.0148941i
$438$	6.43570e17	−	6.43570e17i	0.208102	−	0.208102i
$439$		−	3.07042e18i		−	0.977116i	−0.872532	−	0.488558i	$-0.837523\pi$
$439$		−	3.07042e18i		−	0.977116i	0.872532	−	0.488558i	$-0.162477\pi$
$440$			6.77376e17i			0.212159i
$441$			5.38363e18i			1.65961i
$442$	−9.13225e17			−0.277091
$443$	1.24585e18	+	1.24585e18i	0.372082	+	0.372082i	0.868235	−	0.496153i	$-0.165254\pi$
$443$	1.24585e18	+	1.24585e18i	0.372082	+	0.372082i	−0.496153	+	0.868235i	$0.665254\pi$
$444$		−	6.18430e16i		−	0.0181807i
$445$	−2.18874e18	−	2.18874e18i	−0.633396	−	0.633396i
$446$	−1.05004e18	+	1.05004e18i	−0.299132	+	0.299132i
$447$	−1.03277e18	−	1.03277e18i	−0.289634	−	0.289634i
$448$		−	2.86500e18i		−	0.791003i
$449$	−1.94044e18	+	1.94044e18i	−0.527444	+	0.527444i	−0.919809	−	0.392366i	$-0.871657\pi$
$449$	−1.94044e18	+	1.94044e18i	−0.527444	+	0.527444i	0.392366	+	0.919809i	$0.371657\pi$
$450$	1.61437e18	+	1.61437e18i	0.432031	+	0.432031i
$451$	8.61432e17			0.226979
$452$	−2.47438e18	+	2.47438e18i	−0.641943	+	0.641943i
$453$	1.87701e18	+	1.87701e18i	0.479488	+	0.479488i
$454$	1.76544e18	−	1.76544e18i	0.444080	−	0.444080i
$455$	−1.44724e19			−3.58477
$456$	−3.34805e16	+	3.34805e16i	−0.00816655	+	0.00816655i
$457$		−	3.62949e18i		−	0.871831i	−0.899987	−	0.435916i	$-0.856425\pi$
$457$		−	3.62949e18i		−	0.871831i	0.899987	−	0.435916i	$-0.143575\pi$
$458$	1.10637e18			0.261723
$459$	1.77272e18			0.413001
$460$	4.95522e18			1.13699
$461$	4.94910e18	+	4.94910e18i	1.11846	+	1.11846i	0.991968	+	0.126490i	$0.0403712\pi$
$461$	4.94910e18	+	4.94910e18i	1.11846	+	1.11846i	0.126490	+	0.991968i	$0.459629\pi$
$462$	−2.70839e17	−	2.70839e17i	−0.0602861	−	0.0602861i
$463$		−	4.68821e18i		−	1.02787i	−0.857828	−	0.513937i	$-0.828186\pi$
$463$		−	4.68821e18i		−	1.02787i	0.857828	−	0.513937i	$-0.171814\pi$
$464$	−4.48801e17	+	5.76281e17i	−0.0969231	+	0.124454i
$465$	−4.89885e18			−1.04213
$466$	−2.55595e18	+	2.55595e18i	−0.535613	+	0.535613i
$467$	3.10142e18	−	3.10142e18i	0.640239	−	0.640239i	−0.310375	−	0.950614i	$-0.600455\pi$
$467$	3.10142e18	−	3.10142e18i	0.640239	−	0.640239i	0.950614	+	0.310375i	$0.100455\pi$
$468$		−	2.57282e18i		−	0.523226i
$469$		−	1.29564e19i		−	2.59582i
$470$			5.11915e18i			1.01045i
$471$	4.51884e18			0.878782
$472$	3.37811e18	+	3.37811e18i	0.647261	+	0.647261i
$473$			1.00907e17i			0.0190500i
$474$	−1.49586e18	−	1.49586e18i	−0.278255	−	0.278255i
$475$	−1.33839e17	+	1.33839e17i	−0.0245316	+	0.0245316i
$476$	−2.14556e18	−	2.14556e18i	−0.387518	−	0.387518i
$477$		−	1.39021e18i		−	0.247430i
$478$	1.35838e18	−	1.35838e18i	0.238247	−	0.238247i
$479$	−2.23154e18	−	2.23154e18i	−0.385706	−	0.385706i	0.487447	−	0.873153i	$-0.337928\pi$
$479$	−2.23154e18	−	2.23154e18i	−0.385706	−	0.385706i	−0.873153	+	0.487447i	$0.837928\pi$
$480$	−5.83007e18			−0.993082
$481$	2.21024e17	−	2.21024e17i	0.0371043	−	0.0371043i
$482$	−1.48609e18	−	1.48609e18i	−0.245875	−	0.245875i
$483$	−4.86739e18	+	4.86739e18i	−0.793718	+	0.793718i
$484$	−4.19042e18			−0.673503
$485$	1.26013e19	−	1.26013e19i	1.99628	−	1.99628i
$486$		−	3.66026e18i		−	0.571555i
$487$	−4.96126e18			−0.763640			−0.381820	−	0.924237i	$-0.624703\pi$
$487$	−4.96126e18			−0.763640			−0.381820	+	0.924237i	$0.624703\pi$
$488$	4.23786e18			0.642996
$489$	5.64411e18			0.844177
$490$	1.11412e19	+	1.11412e19i	1.64271	+	1.64271i
$491$	−2.54320e17	−	2.54320e17i	−0.0369666	−	0.0369666i	0.688382	−	0.725348i	$-0.258321\pi$
$491$	−2.54320e17	−	2.54320e17i	−0.0369666	−	0.0369666i	−0.725348	+	0.688382i	$0.758321\pi$
$492$			4.65439e18i			0.666971i
$493$	−3.70679e17	−	2.98065e18i	−0.0523684	−	0.421098i
$494$	−9.74136e16			−0.0135685
$495$	7.56055e17	−	7.56055e17i	0.103829	−	0.103829i
$496$	−8.92668e17	+	8.92668e17i	−0.120870	+	0.120870i
$497$			1.11383e19i			1.48705i
$498$			3.74549e18i			0.493064i
$499$			4.29483e18i			0.557497i	0.960364	+	0.278749i	$0.0899196\pi$
$499$			4.29483e18i			0.557497i	−0.960364	+	0.278749i	$0.910080\pi$
$500$	−5.86772e18			−0.751069
$501$	−6.04199e18	−	6.04199e18i	−0.762633	−	0.762633i
$502$			6.60640e17i			0.0822316i
$503$	−1.18264e18	−	1.18264e18i	−0.145170	−	0.145170i	0.630787	−	0.775956i	$-0.282732\pi$
$503$	−1.18264e18	−	1.18264e18i	−0.145170	−	0.145170i	−0.775956	+	0.630787i	$0.782732\pi$
$504$	−6.78197e18	+	6.78197e18i	−0.820998	+	0.820998i
$505$	8.75771e18	+	8.75771e18i	1.04556	+	1.04556i
$506$			6.62845e17i			0.0780474i
$507$	−1.29035e18	+	1.29035e18i	−0.149848	+	0.149848i
$508$	2.92865e18	+	2.92865e18i	0.335445	+	0.335445i
$509$	1.46422e19			1.65417			0.827086	−	0.562076i	$-0.189997\pi$
$509$	1.46422e19			1.65417			0.827086	+	0.562076i	$0.189997\pi$
$510$	1.44998e18	−	1.44998e18i	0.161574	−	0.161574i
$511$	1.08078e19	+	1.08078e19i	1.18793	+	1.18793i
$512$	−2.03384e18	+	2.03384e18i	−0.220510	+	0.220510i
$513$	1.89096e17			0.0202237
$514$	−1.88848e18	+	1.88848e18i	−0.199238	+	0.199238i
$515$			1.25356e19i			1.30465i
$516$	−5.45210e17			−0.0559778
$517$	1.49940e18			0.151874
$518$	−4.74311e17			−0.0473974
$519$	3.22026e18	+	3.22026e18i	0.317482	+	0.317482i
$520$	−1.30804e19	−	1.30804e19i	−1.27232	−	1.27232i
$521$			8.79802e18i			0.844347i	0.906515	+	0.422174i	$0.138733\pi$
$521$			8.79802e18i			0.844347i	−0.906515	+	0.422174i	$0.861267\pi$
$522$	−3.83508e18	+	4.76936e17i	−0.363146	+	0.0451613i
$523$	1.34686e19			1.25838			0.629188	−	0.777253i	$-0.283388\pi$
$523$	1.34686e19			1.25838			0.629188	+	0.777253i	$0.283388\pi$
$524$	3.91192e18	−	3.91192e18i	0.360638	−	0.360638i
$525$	1.43712e19	−	1.43712e19i	1.30731	−	1.30731i
$526$		−	6.18144e18i		−	0.554867i
$527$		−	5.19126e18i		−	0.459832i
$528$			1.46059e17i			0.0127671i
$529$	3.19509e17			0.0275609
$530$	−2.87700e18	−	2.87700e18i	−0.244911	−	0.244911i
$531$		−	7.54097e18i		−	0.633528i
$532$	−2.28867e17	−	2.28867e17i	−0.0189759	−	0.0189759i
$533$	−1.66346e19	+	1.66346e19i	−1.36120	+	1.36120i
$534$	1.58192e18	+	1.58192e18i	0.127761	+	0.127761i
$535$		−	9.83865e17i		−	0.0784258i
$536$	1.17102e19	−	1.17102e19i	0.921319	−	0.921319i
$537$	−2.68746e18	−	2.68746e18i	−0.208700	−	0.208700i
$538$	−1.04982e19			−0.804711
$539$	3.26327e18	−	3.26327e18i	0.246906	−	0.246906i
$540$	1.03355e19	+	1.03355e19i	0.771924	+	0.771924i
$541$	−1.47156e19	+	1.47156e19i	−1.08492	+	1.08492i	−0.0888737	+	0.996043i	$0.528327\pi$
$541$	−1.47156e19	+	1.47156e19i	−1.08492	+	1.08492i	−0.996043	+	0.0888737i	$0.971673\pi$
$542$	−2.98409e18			−0.217179
$543$	−8.24273e18	+	8.24273e18i	−0.592206	+	0.592206i
$544$		−	6.17807e18i		−	0.438188i
$545$	−1.15693e19			−0.810090
$546$	1.04600e19			0.723075
$547$	−6.68236e18			−0.456056			−0.228028	−	0.973655i	$-0.573228\pi$
$547$	−6.68236e18			−0.456056			−0.228028	+	0.973655i	$0.573228\pi$
$548$	6.74064e18	+	6.74064e18i	0.454189	+	0.454189i
$549$	−4.73010e18	−	4.73010e18i	−0.314676	−	0.314676i
$550$		−	1.95709e18i		−	0.128550i
$551$	−3.95403e16	−	3.17946e17i	−0.00256436	−	0.0206202i
$552$	−8.79844e18			−0.563420
$553$	2.51208e19	−	2.51208e19i	1.58839	−	1.58839i
$554$	−7.54267e18	+	7.54267e18i	−0.470930	+	0.470930i
$555$			7.01867e17i			0.0432717i
$556$		−	1.16749e19i		−	0.710769i
$557$			2.32795e19i			1.39955i	0.714364	+	0.699774i	$0.246716\pi$
$557$			2.32795e19i			1.39955i	−0.714364	+	0.699774i	$0.753284\pi$
$558$	−6.67937e18			−0.396548
$559$	−1.94856e18	−	1.94856e18i	−0.114243	−	0.114243i
$560$		−	8.37437e18i		−	0.484882i
$561$	−4.24699e17	−	4.24699e17i	−0.0242852	−	0.0242852i
$562$	4.57287e18	−	4.57287e18i	0.258246	−	0.258246i
$563$	−1.83350e19	−	1.83350e19i	−1.02264	−	1.02264i	−0.999738	−	0.0229000i	$-0.992710\pi$
$563$	−1.83350e19	−	1.83350e19i	−1.02264	−	1.02264i	−0.0229000	−	0.999738i	$-0.507290\pi$
$564$			8.10136e18i			0.446277i
$565$	2.80821e19	−	2.80821e19i	1.52789	−	1.52789i
$566$	−1.65020e18	−	1.65020e18i	−0.0886790	−	0.0886790i
$567$	2.86007e18			0.151808
$568$	−1.00670e19	+	1.00670e19i	−0.527789	+	0.527789i
$569$	−7.77395e18	−	7.77395e18i	−0.402583	−	0.402583i	0.476559	−	0.879142i	$-0.341884\pi$
$569$	−7.77395e18	−	7.77395e18i	−0.402583	−	0.402583i	−0.879142	+	0.476559i	$0.841884\pi$
$570$	1.54670e17	−	1.54670e17i	0.00791190	−	0.00791190i
$571$	8.59674e17			0.0434391			0.0217195	−	0.999764i	$-0.493086\pi$
$571$	8.59674e17			0.0434391			0.0217195	+	0.999764i	$0.493086\pi$
$572$	−1.55951e18	+	1.55951e18i	−0.0778423	+	0.0778423i
$573$		−	1.05827e19i		−	0.521810i
$574$	3.56973e19			1.73881
$575$	−3.51718e19			−1.69247
$576$	−5.78039e18			−0.274789
$577$	−1.95893e19	−	1.95893e19i	−0.920002	−	0.920002i	0.0770267	−	0.997029i	$-0.475457\pi$
$577$	−1.95893e19	−	1.95893e19i	−0.920002	−	0.920002i	−0.997029	+	0.0770267i	$0.975457\pi$
$578$	−6.99663e18	−	6.99663e18i	−0.324634	−	0.324634i
$579$		−	2.23933e19i		−	1.02652i
$580$	1.52169e19	−	1.95393e19i	0.689178	−	0.884938i
$581$	−6.29001e19			−2.81461
$582$	−9.10761e18	+	9.10761e18i	−0.402665	+	0.402665i
$583$	−8.42672e17	+	8.42672e17i	−0.0368111	+	0.0368111i
$584$			1.95366e19i			0.843253i
$585$			2.91994e19i			1.24533i
$586$		−	5.12113e18i		−	0.215815i
$587$	2.91015e19			1.21185			0.605924	−	0.795522i	$-0.292803\pi$
$587$	2.91015e19			1.21185			0.605924	+	0.795522i	$0.292803\pi$
$588$	1.76317e19	+	1.76317e19i	0.725526	+	0.725526i
$589$		−	5.53752e17i		−	0.0225169i
$590$	−1.56058e19	−	1.56058e19i	−0.627078	−	0.627078i
$591$	9.57192e17	−	9.57192e17i	0.0380090	−	0.0380090i
$592$	1.27894e17	+	1.27894e17i	0.00501879	+	0.00501879i
$593$			5.04546e18i			0.195667i	0.995203	+	0.0978335i	$0.0311913\pi$
$593$			5.04546e18i			0.195667i	−0.995203	+	0.0978335i	$0.968809\pi$
$594$	−1.38255e18	+	1.38255e18i	−0.0529877	+	0.0529877i
$595$	2.43504e19	+	2.43504e19i	0.922331	+	0.922331i
$596$	1.27615e19			0.477725
$597$	6.30031e18	−	6.30031e18i	0.233100	−	0.233100i
$598$	−1.27998e19	−	1.27998e19i	−0.468053	−	0.468053i
$599$	2.08967e19	−	2.08967e19i	0.755250	−	0.755250i	−0.220204	−	0.975454i	$-0.570672\pi$
$599$	2.08967e19	−	2.08967e19i	0.755250	−	0.755250i	0.975454	+	0.220204i	$0.0706723\pi$
$600$	2.59779e19			0.927993
$601$	−3.49596e19	+	3.49596e19i	−1.23437	+	1.23437i	−0.272102	+	0.962269i	$0.587719\pi$
$601$	−3.49596e19	+	3.49596e19i	−1.23437	+	1.23437i	−0.962269	+	0.272102i	$0.912281\pi$
$602$			4.18154e18i			0.145936i
$603$	−2.61407e19			−0.901771
$604$	−2.31935e19			−0.790874
$605$	4.75578e19			1.60300
$606$	−6.32967e18	−	6.32967e18i	−0.210898	−	0.210898i
$607$	9.04753e17	+	9.04753e17i	0.0297995	+	0.0297995i	0.721850	−	0.692050i	$-0.243292\pi$
$607$	9.04753e17	+	9.04753e17i	0.0297995	+	0.0297995i	−0.692050	+	0.721850i	$0.743292\pi$
$608$		−	6.59014e17i		−	0.0214570i
$609$	4.24573e18	+	3.41402e19i	0.136657	+	1.09887i
$610$	−1.95776e19			−0.622946
$611$	−2.89539e19	+	2.89539e19i	−0.910791	+	0.910791i
$612$	−4.32887e18	+	4.32887e18i	−0.134621	+	0.134621i
$613$			2.72706e19i			0.838438i	0.907885	+	0.419219i	$0.137696\pi$
$613$			2.72706e19i			0.838438i	−0.907885	+	0.419219i	$0.862304\pi$
$614$			1.95214e19i			0.593381i
$615$		−	5.28235e19i		−	1.58745i
$616$	8.22173e18			0.244286
$617$	−1.27945e19	−	1.27945e19i	−0.375861	−	0.375861i	0.493746	−	0.869606i	$-0.335627\pi$
$617$	−1.27945e19	−	1.27945e19i	−0.375861	−	0.375861i	−0.869606	+	0.493746i	$0.835627\pi$
$618$		−	9.06014e18i		−	0.263157i
$619$	2.37106e19	+	2.37106e19i	0.680939	+	0.680939i	0.960212	−	0.279273i	$-0.0900933\pi$
$619$	2.37106e19	+	2.37106e19i	0.680939	+	0.680939i	−0.279273	+	0.960212i	$0.590093\pi$
$620$	3.02666e19	−	3.02666e19i	0.859453	−	0.859453i
$621$	2.48465e19	+	2.48465e19i	0.697628	+	0.697628i
$622$		−	2.58432e19i		−	0.717488i
$623$	−2.65661e19	+	2.65661e19i	−0.729310	+	0.729310i
$624$	−2.82046e18	−	2.82046e18i	−0.0765645	−	0.0765645i
$625$	4.39582e18			0.117999
$626$	1.16951e19	−	1.16951e19i	0.310445	−	0.310445i
$627$	−4.53027e16	−	4.53027e16i	−0.00118919	−	0.00118919i
$628$	−2.79188e19	+	2.79188e19i	−0.724736	+	0.724736i
$629$	−7.43761e17			−0.0190932
$630$	3.13305e19	−	3.13305e19i	0.795397	−	0.795397i
$631$		−	6.68559e19i		−	1.67855i	−0.543707	−	0.839275i	$-0.682980\pi$
$631$		−	6.68559e19i		−	1.67855i	0.543707	−	0.839275i	$-0.317020\pi$
$632$	4.54091e19			1.12752
$633$	1.71442e19			0.421008
$634$	−2.01963e19			−0.490509
$635$	−3.32377e19	−	3.32377e19i	−0.798390	−	0.798390i
$636$	−4.55302e18	−	4.55302e18i	−0.108168	−	0.108168i
$637$			1.26030e20i			2.96140i
$638$	2.61371e18	+	2.03553e18i	0.0607454	+	0.0473077i
$639$	2.24725e19			0.516590
$640$	4.05080e19	−	4.05080e19i	0.921045	−	0.921045i
$641$	1.97345e19	−	1.97345e19i	0.443834	−	0.443834i	−0.449464	−	0.893298i	$-0.648385\pi$
$641$	1.97345e19	−	1.97345e19i	0.443834	−	0.443834i	0.893298	+	0.449464i	$0.148385\pi$
$642$			7.11092e17i			0.0158191i
$643$			8.08294e19i			1.77866i	0.457267	+	0.889330i	$0.348829\pi$
$643$			8.08294e19i			1.77866i	−0.457267	+	0.889330i	$0.651171\pi$
$644$		−	6.01446e19i		−	1.30917i
$645$	6.18768e18			0.133232
$646$	1.63902e17	+	1.63902e17i	0.00349105	+	0.00349105i
$647$		−	4.58508e19i		−	0.966089i	−0.875596	−	0.483044i	$-0.839531\pi$
$647$		−	4.58508e19i		−	0.966089i	0.875596	−	0.483044i	$-0.160469\pi$
$648$	2.58498e18	+	2.58498e18i	0.0538805	+	0.0538805i
$649$	−4.57093e18	+	4.57093e18i	−0.0942523	+	0.0942523i
$650$	3.77921e19	+	3.77921e19i	0.770916	+	0.770916i
$651$			5.94603e19i			1.19994i
$652$	−3.48711e19	+	3.48711e19i	−0.696197	+	0.696197i
$653$	3.31802e19	+	3.31802e19i	0.655371	+	0.655371i	0.954281	−	0.298910i	$-0.0966231\pi$
$653$	3.31802e19	+	3.31802e19i	0.655371	+	0.655371i	−0.298910	+	0.954281i	$0.596623\pi$
$654$	8.36179e18			0.163401
$655$	−4.43971e19	+	4.43971e19i	−0.858352	+	0.858352i
$656$	−9.62549e18	−	9.62549e18i	−0.184118	−	0.184118i
$657$	2.18058e19	−	2.18058e19i	0.412680	−	0.412680i
$658$	6.21342e19			1.16346
$659$	−1.60928e19	+	1.60928e19i	−0.298149	+	0.298149i	−0.840289	−	0.542139i	$-0.817614\pi$
$659$	−1.60928e19	+	1.60928e19i	−0.298149	+	0.298149i	0.542139	+	0.840289i	$0.317614\pi$
$660$		−	4.95225e18i		−	0.0907810i
$661$	3.97483e19			0.720955			0.360477	−	0.932768i	$-0.382614\pi$
$661$	3.97483e19			0.720955			0.360477	+	0.932768i	$0.382614\pi$
$662$	−3.86999e19			−0.694550
$663$	1.64022e19			0.291278
$664$	−5.68500e19	−	5.68500e19i	−0.998974	−	0.998974i
$665$	2.59745e18	+	2.59745e18i	0.0451644	+	0.0451644i
$666$			9.56965e17i			0.0164656i
$667$	3.65815e19	−	4.69724e19i	0.622846	−	0.799765i
$668$	7.46586e19			1.25790
$669$	1.88595e19	−	1.88595e19i	0.314448	−	0.314448i
$670$	−5.40974e19	+	5.40974e19i	−0.892591	+	0.892591i
$671$			5.73427e18i			0.0936312i
$672$			7.07631e19i			1.14346i
$673$			7.37017e19i			1.17862i	0.807909	+	0.589308i	$0.200599\pi$
$673$			7.37017e19i			1.17862i	−0.807909	+	0.589308i	$0.799401\pi$
$674$	8.65066e18			0.136908
$675$	−7.33606e19	−	7.33606e19i	−1.14904	−	1.14904i
$676$		−	1.59444e19i		−	0.247161i
$677$	3.24437e19	+	3.24437e19i	0.497748	+	0.497748i	0.910736	−	0.412988i	$-0.135515\pi$
$677$	3.24437e19	+	3.24437e19i	0.497748	+	0.497748i	−0.412988	+	0.910736i	$0.635515\pi$
$678$	−2.02965e19	+	2.02965e19i	−0.308186	+	0.308186i
$679$	−1.52949e20	−	1.52949e20i	−2.29857	−	2.29857i
$680$			4.40164e19i			0.654715i
$681$	−3.17086e19	+	3.17086e19i	−0.466817	+	0.466817i
$682$	4.04868e18	+	4.04868e18i	0.0589960	+	0.0589960i
$683$	6.15172e19			0.887261			0.443630	−	0.896210i	$-0.353690\pi$
$683$	6.15172e19			0.887261			0.443630	+	0.896210i	$0.353690\pi$
$684$	−4.61760e17	+	4.61760e17i	−0.00659209	+	0.00659209i
$685$	−7.65007e19	−	7.65007e19i	−1.08101	−	1.08101i
$686$	8.19749e19	−	8.19749e19i	1.14660	−	1.14660i
$687$	−1.98713e19			−0.275124
$688$	1.12752e18	−	1.12752e18i	0.0154527	−	0.0154527i
$689$		−	3.25446e19i		−	0.441514i
$690$	4.06460e19			0.545851
$691$	−1.06913e20			−1.42130			−0.710651	−	0.703545i	$-0.751599\pi$
$691$	−1.06913e20			−1.42130			−0.710651	+	0.703545i	$0.751599\pi$
$692$	−3.97916e19			−0.523659
$693$	−9.17671e18	−	9.17671e18i	−0.119551	−	0.119551i
$694$	−1.25341e18	−	1.25341e18i	−0.0161651	−	0.0161651i
$695$			1.32500e20i			1.69170i
$696$	−2.70191e19	+	3.46938e19i	−0.341512	+	0.438517i
$697$	5.59765e19			0.700449
$698$	4.57924e19	−	4.57924e19i	0.567290	−	0.567290i
$699$	4.59068e19	−	4.59068e19i	0.563037	−	0.563037i
$700$			1.77580e20i			2.15629i
$701$			4.54817e18i			0.0546777i	0.999626	+	0.0273389i	$0.00870332\pi$
$701$			4.54817e18i			0.0546777i	−0.999626	+	0.0273389i	$0.991297\pi$
$702$		−	5.33950e19i		−	0.635537i
$703$	−7.93370e16			−0.000934950
$704$	3.50377e18	+	3.50377e18i	0.0408815	+	0.0408815i
$705$		−	9.19438e19i		−	1.06218i
$706$	−2.16881e19	−	2.16881e19i	−0.248079	−	0.248079i
$707$	1.06298e20	−	1.06298e20i	1.20389	−	1.20389i
$708$	−2.46971e19	−	2.46971e19i	−0.276958	−	0.276958i
$709$		−	3.87889e19i		−	0.430709i	−0.976536	−	0.215355i	$-0.930909\pi$
$709$		−	3.87889e19i		−	0.430709i	0.976536	−	0.215355i	$-0.0690908\pi$
$710$	4.65062e19	−	4.65062e19i	0.511331	−	0.511331i
$711$	−5.06835e19	−	5.06835e19i	−0.551797	−	0.551797i
$712$	−4.80217e19			−0.517700
$713$	7.27610e19	−	7.27610e19i	0.776733	−	0.776733i
$714$	−1.75993e19	−	1.75993e19i	−0.186041	−	0.186041i
$715$	1.76991e19	−	1.76991e19i	0.185272	−	0.185272i
$716$	3.32080e19			0.344232
$717$	−2.43976e19	+	2.43976e19i	−0.250445	+	0.250445i
$718$			1.07825e20i			1.09609i
$719$	−7.63956e19			−0.769071			−0.384535	−	0.923110i	$-0.625638\pi$
$719$	−7.63956e19			−0.769071			−0.384535	+	0.923110i	$0.625638\pi$
$720$	−1.68961e19			−0.168445
$721$	1.52152e20			1.50221
$722$	−4.04751e19	−	4.04751e19i	−0.395756	−	0.395756i
$723$	2.66912e19	+	2.66912e19i	0.258464	+	0.258464i
$724$		−	1.01852e20i		−	0.976790i
$725$	−1.08009e20	+	1.38689e20i	−1.02587	+	1.31727i
$726$	−3.43726e19			−0.323337
$727$	−9.48122e19	+	9.48122e19i	−0.883330	+	0.883330i	−0.993872	−	0.110541i	$-0.964742\pi$
$727$	−9.48122e19	+	9.48122e19i	−0.883330	+	0.883330i	0.110541	+	0.993872i	$0.464742\pi$
$728$	−1.58765e20	+	1.58765e20i	−1.46499	+	1.46499i
$729$			5.69117e19i			0.520127i
$730$		−	9.02527e19i		−	0.816959i
$731$			6.55703e18i			0.0587875i
$732$	−3.09827e19			−0.275133
$733$	2.83631e19	+	2.83631e19i	0.249474	+	0.249474i	0.820755	−	0.571281i	$-0.193553\pi$
$733$	2.83631e19	+	2.83631e19i	0.249474	+	0.249474i	−0.571281	+	0.820755i	$0.693553\pi$
$734$			9.60125e19i			0.836479i
$735$	−2.00105e20	−	2.00105e20i	−1.72682	−	1.72682i
$736$	8.65920e19	−	8.65920e19i	0.740173	−	0.740173i
$737$	1.58451e19	+	1.58451e19i	0.134160	+	0.134160i
$738$		−	7.20226e19i		−	0.604051i
$739$	−1.60798e19	+	1.60798e19i	−0.133589	+	0.133589i	−0.770739	−	0.637151i	$-0.780113\pi$
$739$	−1.60798e19	+	1.60798e19i	−0.133589	+	0.133589i	0.637151	+	0.770739i	$0.280113\pi$
$740$	−4.33635e18	−	4.33635e18i	−0.0356864	−	0.0356864i
$741$	1.74962e18			0.0142632
$742$	−3.49199e19	+	3.49199e19i	−0.281998	+	0.281998i
$743$	1.97729e19	+	1.97729e19i	0.158179	+	0.158179i	0.781759	−	0.623580i	$-0.214322\pi$
$743$	1.97729e19	+	1.97729e19i	0.158179	+	0.158179i	−0.623580	+	0.781759i	$0.714322\pi$
$744$	−5.37411e19	+	5.37411e19i	−0.425889	+	0.425889i
$745$	−1.44833e20			−1.13703
$746$	−6.25342e19	+	6.25342e19i	−0.486347	+	0.486347i
$747$			1.26907e20i			0.977778i
$748$	5.24785e18			0.0400563
$749$	−1.19418e19			−0.0903017
$750$	−4.81310e19			−0.360575
$751$	5.76514e19	+	5.76514e19i	0.427888	+	0.427888i	0.887908	−	0.460020i	$-0.152158\pi$
$751$	5.76514e19	+	5.76514e19i	0.427888	+	0.427888i	−0.460020	+	0.887908i	$0.652158\pi$
$752$	−1.67540e19	−	1.67540e19i	−0.123195	−	0.123195i
$753$		−	1.18656e19i		−	0.0864420i
$754$	−8.97786e19	+	1.11650e19i	−0.647997	+	0.0805860i
$755$	2.63227e20			1.88235
$756$	1.25448e20	−	1.25448e20i	0.888816	−	0.888816i
$757$	1.90179e20	−	1.90179e20i	1.33503	−	1.33503i	0.434227	−	0.900804i	$-0.357022\pi$
$757$	1.90179e20	−	1.90179e20i	1.33503	−	1.33503i	0.900804	−	0.434227i	$-0.142978\pi$
$758$		−	7.68372e19i		−	0.534426i
$759$		−	1.19052e19i		−	0.0820436i
$760$			4.69523e18i			0.0320599i
$761$	1.64408e20			1.11232			0.556162	−	0.831074i	$-0.312273\pi$
$761$	1.64408e20			1.11232			0.556162	+	0.831074i	$0.312273\pi$
$762$	2.40227e19	+	2.40227e19i	0.161041	+	0.161041i
$763$			1.40424e20i			0.932760i
$764$	6.53830e19	+	6.53830e19i	0.430339	+	0.430339i
$765$	4.91291e19	−	4.91291e19i	0.320412	−	0.320412i
$766$	3.25776e19	+	3.25776e19i	0.210532	+	0.210532i
$767$		−	1.76533e20i		−	1.13047i
$768$	−5.68543e19	+	5.68543e19i	−0.360774	+	0.360774i
$769$	3.21513e19	+	3.21513e19i	0.202169	+	0.202169i	0.800929	−	0.598760i	$-0.204340\pi$
$769$	3.21513e19	+	3.21513e19i	0.202169	+	0.202169i	−0.598760	+	0.800929i	$0.704340\pi$
$770$	−3.79818e19			−0.236669
$771$	3.39186e19	−	3.39186e19i	0.209439	−	0.209439i
$772$	1.38353e20	+	1.38353e20i	0.846577	+	0.846577i
$773$	4.26417e19	−	4.26417e19i	0.258570	−	0.258570i	−0.565902	−	0.824472i	$-0.691472\pi$
$773$	4.26417e19	−	4.26417e19i	0.258570	−	0.258570i	0.824472	+	0.565902i	$0.191472\pi$
$774$	8.43664e18			0.0506971
$775$	−2.14831e20	+	2.14831e20i	−1.27933	+	1.27933i
$776$		−	2.76475e20i		−	1.63164i
$777$	8.51899e18			0.0498243
$778$	1.43385e20			0.831085
$779$	5.97101e18			0.0342993
$780$	9.56299e19	+	9.56299e19i	0.544417	+	0.544417i
$781$	−1.36217e19	−	1.36217e19i	−0.0768551	−	0.0768551i
$782$			4.30722e19i			0.240852i
$783$	1.74275e20	−	2.16731e19i	0.965834	−	0.120113i
$784$	−7.29263e19			−0.400564
$785$	3.16856e20	−	3.16856e20i	1.72494	−	1.72494i
$786$	3.20882e19	−	3.20882e19i	0.173136	−	0.173136i
$787$		−	4.01025e19i		−	0.214461i	−0.994234	−	0.107231i	$-0.965802\pi$
$787$		−	4.01025e19i		−	0.214461i	0.994234	−	0.107231i	$-0.0341983\pi$
$788$			1.18277e19i			0.0626925i
$789$			1.11023e20i			0.583278i
$790$	−2.09776e20			−1.09236
$791$	−3.40850e20	−	3.40850e20i	−1.75925	−	1.75925i
$792$		−	1.65881e19i		−	0.0848633i
$793$	−1.10731e20	−	1.10731e20i	−0.561509	−	0.561509i
$794$	−8.91586e19	+	8.91586e19i	−0.448146	+	0.448146i
$795$	5.16731e19	+	5.16731e19i	0.257451	+	0.257451i
$796$			7.78506e19i			0.384477i
$797$	−1.10064e20	+	1.10064e20i	−0.538813	+	0.538813i	−0.923180	−	0.384367i	$-0.874420\pi$
$797$	−1.10064e20	+	1.10064e20i	−0.538813	+	0.538813i	0.384367	+	0.923180i	$0.374420\pi$
$798$	−1.87732e18	−	1.87732e18i	−0.00910999	−	0.00910999i
$799$	9.74320e19			0.468677
$800$	−2.55668e20	+	2.55668e20i	−1.21912	+	1.21912i
$801$	5.35996e19	+	5.35996e19i	0.253358	+	0.253358i
$802$	1.69630e19	−	1.69630e19i	0.0794845	−	0.0794845i
$803$	−2.64350e19			−0.122792
$804$	−8.56124e19	+	8.56124e19i	−0.394225	+	0.394225i
$805$			6.82591e20i			3.11594i
$806$	−1.56363e20			−0.707602
$807$	1.88556e20			0.845913
$808$	1.92147e20			0.854582
$809$	1.04064e20	+	1.04064e20i	0.458840	+	0.458840i	0.898274	−	0.439435i	$-0.144821\pi$
$809$	1.04064e20	+	1.04064e20i	0.458840	+	0.458840i	−0.439435	+	0.898274i	$0.644821\pi$
$810$	−1.19418e19	−	1.19418e19i	−0.0522004	−	0.0522004i
$811$			3.24340e20i			1.40558i	0.711398	+	0.702789i	$0.248062\pi$
$811$			3.24340e20i			1.40558i	−0.711398	+	0.702789i	$0.751938\pi$
$812$	−2.37160e20	−	1.84697e20i	−1.01894	−	0.793540i
$813$	5.35966e19			0.228299
$814$	5.80061e17	−	5.80061e17i	0.00244964	−	0.00244964i
$815$	3.95758e20	−	3.95758e20i	1.65702	−	1.65702i
$816$			9.49103e18i			0.0393987i
$817$			6.99438e17i			0.00287869i
$818$		−	3.33614e19i		−	0.136135i
$819$	3.54411e20			1.43390
$820$	3.26360e20	+	3.26360e20i	1.30918	+	1.30918i
$821$			2.82495e20i			1.12359i	0.827276	+	0.561796i	$0.189889\pi$
$821$			2.82495e20i			1.12359i	−0.827276	+	0.561796i	$0.810111\pi$
$822$	5.52912e19	+	5.52912e19i	0.218049	+	0.218049i
$823$	−2.41904e20	+	2.41904e20i	−0.945896	+	0.945896i	−0.998610	−	0.0527135i	$-0.983213\pi$
$823$	−2.41904e20	+	2.41904e20i	−0.945896	+	0.945896i	0.0527135	+	0.998610i	$0.483213\pi$
$824$	1.37517e20	+	1.37517e20i	0.533171	+	0.533171i
$825$			3.51508e19i			0.135132i
$826$	−1.89417e20	+	1.89417e20i	−0.722036	+	0.722036i
$827$	−2.47711e20	−	2.47711e20i	−0.936284	−	0.936284i	0.0618044	−	0.998088i	$-0.480314\pi$
$827$	−2.47711e20	−	2.47711e20i	−0.936284	−	0.936284i	−0.998088	+	0.0618044i	$0.980314\pi$
$828$	−1.21347e20			−0.454796
$829$	2.93644e20	−	2.93644e20i	1.09129	−	1.09129i	0.0958980	−	0.995391i	$-0.469428\pi$
$829$	2.93644e20	−	2.93644e20i	1.09129	−	1.09129i	0.995391	−	0.0958980i	$-0.0305722\pi$
$830$	2.62629e20	+	2.62629e20i	0.967824	+	0.967824i
$831$	1.35472e20	−	1.35472e20i	0.495043	−	0.495043i
$832$	−1.35318e20			−0.490335
$833$	2.12050e20	−	2.12050e20i	0.761943	−	0.761943i
$834$		−	9.57650e19i		−	0.341228i
$835$	−8.47314e20			−2.99391
$836$	5.59788e17			0.00196146
$837$	3.03526e20			1.05467
$838$	1.50560e20	+	1.50560e20i	0.518803	+	0.518803i
$839$	−2.74646e20	−	2.74646e20i	−0.938511	−	0.938511i	0.0597050	−	0.998216i	$-0.480984\pi$
$839$	−2.74646e20	−	2.74646e20i	−0.938511	−	0.938511i	−0.998216	+	0.0597050i	$0.980984\pi$
$840$		−	5.04161e20i		−	1.70850i
$841$	−7.28824e19	−	2.88494e20i	−0.244935	−	0.969540i
$842$	−2.03073e20			−0.676812
$843$	−8.21322e19	+	8.21322e19i	−0.271469	+	0.271469i
$844$	−1.05922e20	+	1.05922e20i	−0.347208	+	0.347208i
$845$			1.80955e20i			0.588267i
$846$		−	1.25361e20i		−	0.404177i
$847$		−	5.77238e20i		−	1.84574i
$848$	1.88317e19			0.0597199
$849$	2.96388e19	+	2.96388e19i	0.0932195	+	0.0932195i
$850$		−	1.27173e20i		−	0.396700i
$851$	−1.04246e19	−	1.04246e19i	−0.0322517	−	0.0322517i
$852$	7.35989e19	−	7.35989e19i	0.225837	−	0.225837i
$853$	−5.42825e19	−	5.42825e19i	−0.165203	−	0.165203i	0.619664	−	0.784867i	$-0.287269\pi$
$853$	−5.42825e19	−	5.42825e19i	−0.165203	−	0.165203i	−0.784867	+	0.619664i	$0.787269\pi$
$854$			2.37625e20i			0.717278i
$855$	5.24059e18	−	5.24059e18i	0.0156898	−	0.0156898i
$856$	−1.07931e19	−	1.07931e19i	−0.0320503	−	0.0320503i
$857$	−8.74425e19			−0.257547			−0.128774	−	0.991674i	$-0.541104\pi$
$857$	−8.74425e19			−0.257547			−0.128774	+	0.991674i	$0.541104\pi$
$858$	−1.27921e19	+	1.27921e19i	−0.0373707	+	0.0373707i
$859$	1.61190e19	+	1.61190e19i	0.0467075	+	0.0467075i	0.730075	−	0.683367i	$-0.239485\pi$
$859$	1.61190e19	+	1.61190e19i	0.0467075	+	0.0467075i	−0.683367	+	0.730075i	$0.739485\pi$
$860$	−3.82294e19	+	3.82294e19i	−0.109878	+	0.109878i
$861$	−6.41151e20			−1.82784
$862$	1.94843e20	−	1.94843e20i	0.550977	−	0.550977i
$863$		−	1.39081e20i		−	0.390114i	−0.980792	−	0.195057i	$-0.937511\pi$
$863$		−	1.39081e20i		−	0.390114i	0.980792	−	0.195057i	$-0.0624892\pi$
$864$	3.61223e20			1.00503
$865$	4.51602e20			1.24636
$866$	7.60390e18			0.0208167
$867$	1.25665e20	+	1.25665e20i	0.341256	+	0.341256i
$868$	−3.67365e20	−	3.67365e20i	−0.989599	−	0.989599i
$869$			6.14433e19i			0.164186i
$870$	1.24820e20	−	1.60274e20i	0.330863	−	0.424844i
$871$	−6.11950e20			−1.60912
$872$	−1.26917e20	+	1.26917e20i	−0.331059	+	0.331059i
$873$	−3.08589e20	+	3.08589e20i	−0.798510	+	0.798510i
$874$			4.59451e18i			0.0117939i
$875$		−	8.08290e20i		−	2.05831i
$876$		−	1.42830e20i		−	0.360821i
$877$	4.08889e20			1.02473			0.512364	−	0.858768i	$-0.328770\pi$
$877$	4.08889e20			1.02473			0.512364	+	0.858768i	$0.328770\pi$
$878$	1.55605e20	+	1.55605e20i	0.386866	+	0.386866i
$879$			9.19794e19i			0.226865i
$880$	1.02415e19	+	1.02415e19i	0.0250602	+	0.0250602i
$881$	−2.33349e20	+	2.33349e20i	−0.566467	+	0.566467i	−0.931137	−	0.364670i	$-0.881182\pi$
$881$	−2.33349e20	+	2.33349e20i	−0.566467	+	0.566467i	0.364670	+	0.931137i	$0.381182\pi$
$882$	−2.72835e20	−	2.72835e20i	−0.657083	−	0.657083i
$883$		−	2.07902e19i		−	0.0496745i	−0.999692	−	0.0248372i	$-0.992093\pi$
$883$		−	2.07902e19i		−	0.0496745i	0.999692	−	0.0248372i	$-0.00790675\pi$
$884$	−1.01338e20	+	1.01338e20i	−0.240219	+	0.240219i
$885$	2.80292e20	+	2.80292e20i	0.659186	+	0.659186i
$886$	−1.26276e20			−0.294635
$887$	−2.71401e20	+	2.71401e20i	−0.628269	+	0.628269i	−0.947632	−	0.319364i	$-0.896531\pi$
$887$	−2.71401e20	+	2.71401e20i	−0.628269	+	0.628269i	0.319364	+	0.947632i	$0.396531\pi$
$888$	7.69959e18	+	7.69959e18i	0.0176838	+	0.0176838i
$889$	−4.03427e20	+	4.03427e20i	−0.919290	+	0.919290i
$890$	2.21845e20			0.501557
$891$	−3.49774e18	+	3.49774e18i	−0.00784592	+	0.00784592i
$892$			2.33040e20i			0.518654i
$893$	1.03931e19			0.0229500
$894$	1.04678e20			0.229348
$895$	−3.76883e20			−0.819305
$896$	−4.91670e20	−	4.91670e20i	−1.06052	−	1.06052i
$897$	2.29894e20	+	2.29894e20i	0.492018	+	0.492018i
$898$		−	1.96678e20i		−	0.417658i
$899$	−6.34679e19	−	5.10350e20i	−0.133732	−	1.07535i
$900$	3.58284e20			0.749082
$901$	−5.47575e19	+	5.47575e19i	−0.113598	+	0.113598i
$902$	−4.36562e19	+	4.36562e19i	−0.0898670	+	0.0898670i
$903$		−	7.51037e19i		−	0.153408i
$904$		−	6.16131e20i		−	1.24880i
$905$			1.15594e21i			2.32485i
$906$	−1.90248e20			−0.379685
$907$	−6.72713e20	−	6.72713e20i	−1.33223	−	1.33223i	−0.903372	−	0.428857i	$-0.858916\pi$
$907$	−6.72713e20	−	6.72713e20i	−1.33223	−	1.33223i	−0.428857	−	0.903372i	$-0.641084\pi$
$908$		−	3.91811e20i		−	0.769974i
$909$	−2.14465e20	−	2.14465e20i	−0.418225	−	0.418225i
$910$	7.33443e20	−	7.33443e20i	1.41931	−	1.41931i
$911$	7.57407e19	+	7.57407e19i	0.145446	+	0.145446i	0.776080	−	0.630634i	$-0.217205\pi$
$911$	7.57407e19	+	7.57407e19i	0.145446	+	0.145446i	−0.630634	+	0.776080i	$0.717205\pi$
$912$			1.01241e18i			0.00192926i
$913$	7.69240e19	−	7.69240e19i	0.145468	−	0.145468i
$914$	1.83938e20	+	1.83938e20i	0.345182	+	0.345182i
$915$	3.51629e20			0.654842
$916$	1.22771e20	−	1.22771e20i	0.226896	−	0.226896i
$917$	5.38875e20	+	5.38875e20i	0.988331	+	0.988331i
$918$	−8.98390e19	+	8.98390e19i	−0.163518	+	0.163518i
$919$	9.57161e20			1.72893			0.864463	−	0.502696i	$-0.167659\pi$
$919$	9.57161e20			1.72893			0.864463	+	0.502696i	$0.167659\pi$
$920$	−6.16936e20	+	6.16936e20i	−1.10592	+	1.10592i
$921$		−	3.50620e20i		−	0.623763i
$922$	−5.01628e20			−0.885656
$923$	5.26078e20			0.921804
$924$	−6.01085e19			−0.104528
$925$	3.07792e19	+	3.07792e19i	0.0531208	+	0.0531208i
$926$	2.37592e20	+	2.37592e20i	0.406964	+	0.406964i
$927$		−	3.06980e20i		−	0.521858i
$928$	−7.55325e19	−	6.07362e20i	−0.127438	−	1.02474i
$929$	4.36676e20			0.731222			0.365611	−	0.930768i	$-0.380860\pi$
$929$	4.36676e20			0.731222			0.365611	+	0.930768i	$0.380860\pi$
$930$	2.48267e20	−	2.48267e20i	0.412609	−	0.412609i
$931$	2.26193e19	−	2.26193e19i	0.0373106	−	0.0373106i
$932$			5.67253e20i			0.928679i
$933$			4.64164e20i			0.754224i
$934$			3.14352e20i			0.506976i
$935$	−5.95588e19			−0.0953377
$936$	3.20322e20	+	3.20322e20i	0.508928	+	0.508928i
$937$			4.94475e20i			0.779771i	0.920863	+	0.389885i	$0.127485\pi$
$937$			4.94475e20i			0.779771i	−0.920863	+	0.389885i	$0.872515\pi$
$938$	6.56613e20	+	6.56613e20i	1.02775	+	1.02775i
$939$	−2.10054e20	+	2.10054e20i	−0.326340	+	0.326340i
$940$	5.68058e20	+	5.68058e20i	0.875987	+	0.875987i
$941$		−	1.43520e20i		−	0.219677i	−0.993949	−	0.109838i	$-0.964967\pi$
$941$		−	1.43520e20i		−	0.219677i	0.993949	−	0.109838i	$-0.0350334\pi$
$942$	−2.29009e20	+	2.29009e20i	−0.347933	+	0.347933i
$943$	7.84569e20	+	7.84569e20i	1.18318	+	1.18318i
$944$	1.02150e20			0.152909
$945$	−1.42373e21	+	1.42373e21i	−2.11547	+	2.11547i
$946$	−5.11384e18	−	5.11384e18i	−0.00754239	−	0.00754239i
$947$	−4.49306e20	+	4.49306e20i	−0.657798	+	0.657798i	−0.954859	−	0.297061i	$-0.903994\pi$
$947$	−4.49306e20	+	4.49306e20i	−0.657798	+	0.657798i	0.297061	+	0.954859i	$0.403994\pi$
$948$	−3.31983e20			−0.482456
$949$	5.10470e20	−	5.10470e20i	0.736388	−	0.736388i
$950$		−	1.35655e19i		−	0.0194255i
$951$	3.62741e20			0.515624
$952$	5.34255e20			0.753858
$953$	1.67187e19			0.0234181			0.0117091	−	0.999931i	$-0.496273\pi$
$953$	1.67187e19			0.0234181			0.0117091	+	0.999931i	$0.496273\pi$
$954$	7.04540e19	+	7.04540e19i	0.0979642	+	0.0979642i
$955$	−7.42043e20	−	7.42043e20i	−1.02425	−	1.02425i
$956$		−	3.01472e20i		−	0.413087i
$957$	−4.69443e19	−	3.65596e19i	−0.0638556	−	0.0497299i
$958$	2.26183e20			0.305423
$959$	−9.28536e20	+	9.28536e20i	−1.24471	+	1.24471i
$960$	2.14853e20	−	2.14853e20i	0.285919	−	0.285919i
$961$		−	1.31908e20i		−	0.174264i
$962$			2.24024e19i			0.0293812i
$963$			2.40936e19i			0.0313702i
$964$	−3.29814e20			−0.426314
$965$	−1.57019e21	−	1.57019e21i	−2.01493	−	2.01493i
$966$		−	4.93346e20i		−	0.628509i
$967$	2.04905e20	+	2.04905e20i	0.259160	+	0.259160i	0.824712	−	0.565552i	$-0.191337\pi$
$967$	2.04905e20	+	2.04905e20i	0.259160	+	0.259160i	−0.565552	+	0.824712i	$0.691337\pi$
$968$	5.21716e20	−	5.21716e20i	0.655099	−	0.655099i
$969$	−2.94380e18	−	2.94380e18i	−0.00366980	−	0.00366980i
$970$			1.27723e21i			1.58076i
$971$	−1.56543e20	+	1.56543e20i	−0.192353	+	0.192353i	−0.796712	−	0.604359i	$-0.793429\pi$
$971$	−1.56543e20	+	1.56543e20i	−0.192353	+	0.192353i	0.604359	+	0.796712i	$0.293429\pi$
$972$	−4.06169e20	−	4.06169e20i	−0.495499	−	0.495499i
$973$	1.60823e21			1.94787
$974$	2.51430e20	−	2.51430e20i	0.302346	−	0.302346i
$975$	−6.78775e20	−	6.78775e20i	−0.810388	−	0.810388i
$976$	6.40737e19	−	6.40737e19i	0.0759506	−	0.0759506i
$977$	4.87350e20			0.573560			0.286780	−	0.957996i	$-0.407415\pi$
$977$	4.87350e20			0.573560			0.286780	+	0.957996i	$0.407415\pi$
$978$	−2.86036e20	+	2.86036e20i	−0.334232	+	0.334232i
$979$		−	6.49784e19i		−	0.0753859i
$980$	2.47263e21			2.84824
$981$	2.83318e20			0.324035
$982$	2.57772e19			0.0292722
$983$	8.01735e19	+	8.01735e19i	0.0903974	+	0.0903974i	0.750859	−	0.660462i	$-0.229640\pi$
$983$	8.01735e19	+	8.01735e19i	0.0903974	+	0.0903974i	−0.660462	+	0.750859i	$0.729640\pi$
$984$	−5.79482e20	−	5.79482e20i	−0.648745	−	0.648745i
$985$		−	1.34234e20i		−	0.149214i
$986$	1.69841e20	+	1.32270e20i	0.187458	+	0.145990i
$987$	−1.11598e21			−1.22303
$988$	−1.08097e19	+	1.08097e19i	−0.0117629	+	0.0117629i
$989$	−9.19035e19	+	9.19035e19i	−0.0993020	+	0.0993020i
$990$			7.66317e19i			0.0822171i
$991$			9.53010e20i			1.01527i	0.861572	+	0.507635i	$0.169480\pi$
$991$			9.53010e20i			1.01527i	−0.861572	+	0.507635i	$0.830520\pi$
$992$		−	1.05781e21i		−	1.11899i
$993$	6.95079e20			0.730112
$994$	−5.64474e20	−	5.64474e20i	−0.588762	−	0.588762i
$995$		−	8.83541e20i		−	0.915092i
$996$	4.15627e20	+	4.15627e20i	0.427453	+	0.427453i
$997$	−2.28483e20	+	2.28483e20i	−0.233340	+	0.233340i	−0.814085	−	0.580745i	$-0.802761\pi$
$997$	−2.28483e20	+	2.28483e20i	−0.233340	+	0.233340i	0.580745	+	0.814085i	$0.302761\pi$
$998$	−2.17656e20	−	2.17656e20i	−0.220728	−	0.220728i
$999$		−	4.34867e19i		−	0.0437924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.15.c.a.17.14	yes	68
29.12	odd	4	inner	29.15.c.a.12.14	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.15.c.a.12.14	✓	68	29.12	odd	4	inner
29.15.c.a.17.14	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-50.6787 + 50.6787i) q^{2} +(910.227 - 910.227i) q^{3} +11247.3i q^{4} -127648. i q^{5} +92258.2i q^{6} -1.54934e6 q^{7} +(-1.40032e6 - 1.40032e6i) q^{8} +3.12594e6i q^{9} +O(q^{10})\)	\(q+(-50.6787 + 50.6787i) q^{2} +(910.227 - 910.227i) q^{3} +11247.3i q^{4} -127648. i q^{5} +92258.2i q^{6} -1.54934e6 q^{7} +(-1.40032e6 - 1.40032e6i) q^{8} +3.12594e6i q^{9} +(6.46904e6 + 6.46904e6i) q^{10} +(1.89478e6 - 1.89478e6i) q^{11} +(1.02376e7 + 1.02376e7i) q^{12} +7.31778e7i q^{13} +(7.85187e7 - 7.85187e7i) q^{14} +(-1.16189e8 - 1.16189e8i) q^{15} -4.23438e7 q^{16} +(1.23124e8 - 1.23124e8i) q^{17} +(-1.58419e8 - 1.58419e8i) q^{18} +(1.31336e7 - 1.31336e7i) q^{19} +1.43570e9 q^{20} +(-1.41025e9 + 1.41025e9i) q^{21} +1.92050e8i q^{22} +3.45143e9 q^{23} -2.54922e9 q^{24} -1.01905e10 q^{25} +(-3.70855e9 - 3.70855e9i) q^{26} +(7.19891e9 + 7.19891e9i) q^{27} -1.74260e10i q^{28} +(1.05990e10 - 1.36096e10i) q^{29} +1.17766e10 q^{30} +(2.10814e10 - 2.10814e10i) q^{31} +(2.50888e10 - 2.50888e10i) q^{32} -3.44936e9i q^{33} +1.24795e10i q^{34} +1.97771e11i q^{35} -3.51585e10 q^{36} +(-3.02037e9 - 3.02037e9i) q^{37} +1.33119e9i q^{38} +(6.66084e10 + 6.66084e10i) q^{39} +(-1.78748e11 + 1.78748e11i) q^{40} +(2.27317e11 + 2.27317e11i) q^{41} -1.42940e11i q^{42} +(-2.66277e10 + 2.66277e10i) q^{43} +(2.13112e10 + 2.13112e10i) q^{44} +3.99020e11 q^{45} +(-1.74914e11 + 1.74914e11i) q^{46} +(3.95665e11 + 3.95665e11i) q^{47} +(-3.85425e10 + 3.85425e10i) q^{48} +1.72224e12 q^{49} +(5.16442e11 - 5.16442e11i) q^{50} -2.24142e11i q^{51} -8.23056e11 q^{52} -4.44734e11 q^{53} -7.29662e11 q^{54} +(-2.41865e11 - 2.41865e11i) q^{55} +(2.16958e12 + 2.16958e12i) q^{56} -2.39092e10i q^{57} +(1.52574e11 + 1.22686e12i) q^{58} -2.41238e12 q^{59} +(1.30682e12 - 1.30682e12i) q^{60} +(-1.51318e12 + 1.51318e12i) q^{61} +2.13676e12i q^{62} -4.84316e12i q^{63} +1.84917e12i q^{64} +9.34100e12 q^{65} +(1.74809e11 + 1.74809e11i) q^{66} +8.36251e12i q^{67} +(1.38482e12 + 1.38482e12i) q^{68} +(3.14158e12 - 3.14158e12i) q^{69} +(-1.00228e13 - 1.00228e13i) q^{70} -7.18905e12i q^{71} +(4.37732e12 - 4.37732e12i) q^{72} +(-6.97575e12 - 6.97575e12i) q^{73} +3.06137e11 q^{74} +(-9.27569e12 + 9.27569e12i) q^{75} +(1.47719e11 + 1.47719e11i) q^{76} +(-2.93566e12 + 2.93566e12i) q^{77} -6.75125e12 q^{78} +(-1.62138e13 + 1.62138e13i) q^{79} +5.40511e12i q^{80} -1.84599e12 q^{81} -2.30403e13 q^{82} +4.05979e13 q^{83} +(-1.58616e13 - 1.58616e13i) q^{84} +(-1.57166e13 - 1.57166e13i) q^{85} -2.69891e12i q^{86} +(-2.74034e12 - 2.20353e13i) q^{87} -5.30659e12 q^{88} +(1.71467e13 - 1.71467e13i) q^{89} +(-2.02218e13 + 2.02218e13i) q^{90} -1.13377e14i q^{91} +3.88194e13i q^{92} -3.83778e13i q^{93} -4.01036e13 q^{94} +(-1.67649e12 - 1.67649e12i) q^{95} -4.56730e13i q^{96} +(9.87187e13 + 9.87187e13i) q^{97} +(-8.72809e13 + 8.72809e13i) q^{98} +(5.92296e12 + 5.92296e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8}+O(q^{10}) \) 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8	\( 68 q - 312 q^{2} - 2 q^{3} - 4 q^{7} - 689310 q^{8} + 23502846 q^{10} - 2993734 q^{11} - 76269906 q^{12} - 3845224 q^{14} + 277690070 q^{15} - 5490752792 q^{16} + 285786056 q^{17} + 5809842386 q^{18} - 1195066336 q^{19} + 1866268668 q^{20} - 8197524756 q^{21} + 2117392192 q^{23} + 8629372824 q^{24} - 73846917196 q^{25} - 16368356994 q^{26} + 33411191086 q^{27} + 48687460392 q^{29} + 128044102700 q^{30} + 73968522614 q^{31} - 2657032122 q^{32} - 259972090824 q^{36} + 95888936640 q^{37} - 571710579738 q^{39} + 977850700426 q^{40} - 57594847104 q^{41} + 48472463810 q^{43} + 1173476843650 q^{44} - 299491373708 q^{45} + 656204001636 q^{46} + 29961288922 q^{47} + 1808198535114 q^{48} + 9857850529980 q^{49} + 1443642384290 q^{50} - 11263919114280 q^{52} - 1993070689076 q^{53} + 2064324525592 q^{54} + 3054165001846 q^{55} + 8002123380864 q^{56} - 9170547007720 q^{58} - 8402401993912 q^{59} + 4455428077662 q^{60} - 4381209993964 q^{61} - 14884429709724 q^{65} - 5756218265814 q^{66} + 4595908790532 q^{68} + 51089269002600 q^{69} - 65383337180236 q^{70} + 101900024607216 q^{72} + 39493186331224 q^{73} - 152862151734316 q^{74} - 46335428712972 q^{75} + 46232026918072 q^{76} + 63231072283300 q^{77} + 111617680995888 q^{78} - 29034273461086 q^{79} - 345331621902328 q^{81} + 104609665443600 q^{82} - 2994621113016 q^{83} + 269240332456580 q^{84} + 11907997971872 q^{85} - 148747542169982 q^{87} + 186485775340436 q^{88} - 89923791148548 q^{89} + 103388070190448 q^{90} - 920451476162284 q^{94} - 393920660173420 q^{95} - 116095608365672 q^{97} + 24492650399928 q^{98} - 402079041111864 q^{99}+O(q^{100}) \) 68 * q - 312 * q^2 - 2 * q^3 - 4 * q^7 - 689310 * q^8 + 23502846 * q^10 - 2993734 * q^11 - 76269906 * q^12 - 3845224 * q^14 + 277690070 * q^15 - 5490752792 * q^16 + 285786056 * q^17 + 5809842386 * q^18 - 1195066336 * q^19 + 1866268668 * q^20 - 8197524756 * q^21 + 2117392192 * q^23 + 8629372824 * q^24 - 73846917196 * q^25 - 16368356994 * q^26 + 33411191086 * q^27 + 48687460392 * q^29 + 128044102700 * q^30 + 73968522614 * q^31 - 2657032122 * q^32 - 259972090824 * q^36 + 95888936640 * q^37 - 571710579738 * q^39 + 977850700426 * q^40 - 57594847104 * q^41 + 48472463810 * q^43 + 1173476843650 * q^44 - 299491373708 * q^45 + 656204001636 * q^46 + 29961288922 * q^47 + 1808198535114 * q^48 + 9857850529980 * q^49 + 1443642384290 * q^50 - 11263919114280 * q^52 - 1993070689076 * q^53 + 2064324525592 * q^54 + 3054165001846 * q^55 + 8002123380864 * q^56 - 9170547007720 * q^58 - 8402401993912 * q^59 + 4455428077662 * q^60 - 4381209993964 * q^61 - 14884429709724 * q^65 - 5756218265814 * q^66 + 4595908790532 * q^68 + 51089269002600 * q^69 - 65383337180236 * q^70 + 101900024607216 * q^72 + 39493186331224 * q^73 - 152862151734316 * q^74 - 46335428712972 * q^75 + 46232026918072 * q^76 + 63231072283300 * q^77 + 111617680995888 * q^78 - 29034273461086 * q^79 - 345331621902328 * q^81 + 104609665443600 * q^82 - 2994621113016 * q^83 + 269240332456580 * q^84 + 11907997971872 * q^85 - 148747542169982 * q^87 + 186485775340436 * q^88 - 89923791148548 * q^89 + 103388070190448 * q^90 - 920451476162284 * q^94 - 393920660173420 * q^95 - 116095608365672 * q^97 + 24492650399928 * q^98 - 402079041111864 * q^99

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