LMFDB - Embedded newform 29.15.c.a.12.8

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			12.8
Character	$\chi$	$=$	29.12
Dual form			29.15.c.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-118.027 - 118.027i) q^{2} +(1825.31 + 1825.31i) q^{3} +11476.7i q^{4} +35591.1i q^{5} -430872. i q^{6} +1.00122e6 q^{7} +(-579197. + 579197. i) q^{8} +1.88056e6i q^{9} +O(q^{10})$	\(q+(-118.027 - 118.027i) q^{2} +(1825.31 + 1825.31i) q^{3} +11476.7i q^{4} +35591.1i q^{5} -430872. i q^{6} +1.00122e6 q^{7} +(-579197. + 579197. i) q^{8} +1.88056e6i q^{9} +(4.20070e6 - 4.20070e6i) q^{10} +(-1.18591e7 - 1.18591e7i) q^{11} +(-2.09485e7 + 2.09485e7i) q^{12} -7.46551e7i q^{13} +(-1.18171e8 - 1.18171e8i) q^{14} +(-6.49648e7 + 6.49648e7i) q^{15} +3.24755e8 q^{16} +(-2.12934e8 - 2.12934e8i) q^{17} +(2.21957e8 - 2.21957e8i) q^{18} +(9.29600e8 + 9.29600e8i) q^{19} -4.08467e8 q^{20} +(1.82754e9 + 1.82754e9i) q^{21} +2.79938e9i q^{22} -3.94562e9 q^{23} -2.11443e9 q^{24} +4.83679e9 q^{25} +(-8.81130e9 + 8.81130e9i) q^{26} +(5.29780e9 - 5.29780e9i) q^{27} +1.14906e10i q^{28} +(9.07598e9 + 1.46692e10i) q^{29} +1.53352e10 q^{30} +(1.91023e10 + 1.91023e10i) q^{31} +(-2.88403e10 - 2.88403e10i) q^{32} -4.32931e10i q^{33} +5.02640e10i q^{34} +3.56344e10i q^{35} -2.15826e10 q^{36} +(6.47258e10 - 6.47258e10i) q^{37} -2.19436e11i q^{38} +(1.36269e11 - 1.36269e11i) q^{39} +(-2.06142e10 - 2.06142e10i) q^{40} +(1.48600e11 - 1.48600e11i) q^{41} -4.31397e11i q^{42} +(-3.12432e11 - 3.12432e11i) q^{43} +(1.36103e11 - 1.36103e11i) q^{44} -6.69311e10 q^{45} +(4.65689e11 + 4.65689e11i) q^{46} +(5.20174e9 - 5.20174e9i) q^{47} +(5.92780e11 + 5.92780e11i) q^{48} +3.24215e11 q^{49} +(-5.70871e11 - 5.70871e11i) q^{50} -7.77344e11i q^{51} +8.56791e11 q^{52} +7.90931e11 q^{53} -1.25057e12 q^{54} +(4.22078e11 - 4.22078e11i) q^{55} +(-5.79903e11 + 5.79903e11i) q^{56} +3.39362e12i q^{57} +(6.60148e11 - 2.80257e12i) q^{58} +2.14334e12 q^{59} +(-7.45579e11 - 7.45579e11i) q^{60} +(2.70290e12 + 2.70290e12i) q^{61} -4.50916e12i q^{62} +1.88285e12i q^{63} +1.48706e12i q^{64} +2.65705e12 q^{65} +(-5.10975e12 + 5.10975e12i) q^{66} +4.04921e12i q^{67} +(2.44378e12 - 2.44378e12i) q^{68} +(-7.20199e12 - 7.20199e12i) q^{69} +(4.20582e12 - 4.20582e12i) q^{70} -6.43340e12i q^{71} +(-1.08922e12 - 1.08922e12i) q^{72} +(1.04802e13 - 1.04802e13i) q^{73} -1.52788e13 q^{74} +(8.82866e12 + 8.82866e12i) q^{75} +(-1.06687e13 + 1.06687e13i) q^{76} +(-1.18736e13 - 1.18736e13i) q^{77} -3.21667e13 q^{78} +(7.26896e12 + 7.26896e12i) q^{79} +1.15584e13i q^{80} +2.83349e13 q^{81} -3.50775e13 q^{82} +3.99680e13 q^{83} +(-2.09740e13 + 2.09740e13i) q^{84} +(7.57856e12 - 7.57856e12i) q^{85} +7.37506e13i q^{86} +(-1.02093e13 + 4.33423e13i) q^{87} +1.37375e13 q^{88} +(-2.45165e13 - 2.45165e13i) q^{89} +(7.89967e12 + 7.89967e12i) q^{90} -7.47460e13i q^{91} -4.52826e13i q^{92} +6.97352e13i q^{93} -1.22789e12 q^{94} +(-3.30855e13 + 3.30855e13i) q^{95} -1.05285e14i q^{96} +(-6.59737e13 + 6.59737e13i) q^{97} +(-3.82661e13 - 3.82661e13i) q^{98} +(2.23018e13 - 2.23018e13i) 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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−118.027	−	118.027i	−0.922085	−	0.922085i	0.0750920	−	0.997177i	$-0.476075\pi$
$2$	−118.027	−	118.027i	−0.922085	−	0.922085i	−0.997177	+	0.0750920i	$0.976075\pi$
$3$	1825.31	+	1825.31i	0.834619	+	0.834619i	0.988145	−	0.153525i	$-0.0490627\pi$
$3$	1825.31	+	1825.31i	0.834619	+	0.834619i	−0.153525	+	0.988145i	$0.549063\pi$
$4$			11476.7i			0.700480i
$5$			35591.1i			0.455566i	0.973712	+	0.227783i	$0.0731476\pi$
$5$			35591.1i			0.455566i	−0.973712	+	0.227783i	$0.926852\pi$
$6$		−	430872.i		−	1.53918i
$7$	1.00122e6			1.21575			0.607873	−	0.794035i	$-0.292023\pi$
$7$	1.00122e6			1.21575			0.607873	+	0.794035i	$0.292023\pi$
$8$	−579197.	+	579197.i	−0.276183	+	0.276183i
$9$			1.88056e6i			0.393178i
$10$	4.20070e6	−	4.20070e6i	0.420070	−	0.420070i
$11$	−1.18591e7	−	1.18591e7i	−0.608560	−	0.608560i	0.334010	−	0.942570i	$-0.391598\pi$
$11$	−1.18591e7	−	1.18591e7i	−0.608560	−	0.608560i	−0.942570	+	0.334010i	$0.891598\pi$
$12$	−2.09485e7	+	2.09485e7i	−0.584634	+	0.584634i
$13$		−	7.46551e7i		−	1.18975i	−0.803818	−	0.594875i	$-0.797202\pi$
$13$		−	7.46551e7i		−	1.18975i	0.803818	−	0.594875i	$-0.202798\pi$
$14$	−1.18171e8	−	1.18171e8i	−1.12102	−	1.12102i
$15$	−6.49648e7	+	6.49648e7i	−0.380224	+	0.380224i
$16$	3.24755e8			1.20981
$17$	−2.12934e8	−	2.12934e8i	−0.518924	−	0.518924i	0.398322	−	0.917246i	$-0.369593\pi$
$17$	−2.12934e8	−	2.12934e8i	−0.518924	−	0.518924i	−0.917246	+	0.398322i	$0.869593\pi$
$18$	2.21957e8	−	2.21957e8i	0.362544	−	0.362544i
$19$	9.29600e8	+	9.29600e8i	1.03997	+	1.03997i	0.999167	+	0.0408035i	$0.0129918\pi$
$19$	9.29600e8	+	9.29600e8i	1.03997	+	1.03997i	0.0408035	+	0.999167i	$0.487008\pi$
$20$	−4.08467e8			−0.319115
$21$	1.82754e9	+	1.82754e9i	1.01468	+	1.01468i
$22$			2.79938e9i			1.12229i
$23$	−3.94562e9			−1.15883			−0.579416	−	0.815032i	$-0.696719\pi$
$23$	−3.94562e9			−1.15883			−0.579416	+	0.815032i	$0.696719\pi$
$24$	−2.11443e9			−0.461015
$25$	4.83679e9			0.792460
$26$	−8.81130e9	+	8.81130e9i	−1.09705	+	1.09705i
$27$	5.29780e9	−	5.29780e9i	0.506465	−	0.506465i
$28$			1.14906e10i			0.851605i
$29$	9.07598e9	+	1.46692e10i	0.526147	+	0.850393i
$29$	9.07598e9	+	1.46692e10i	0.526147	+	0.850393i
$30$	1.53352e10			0.701197
$31$	1.91023e10	+	1.91023e10i	0.694310	+	0.694310i	0.963177	−	0.268868i	$-0.0866494\pi$
$31$	1.91023e10	+	1.91023e10i	0.694310	+	0.694310i	−0.268868	+	0.963177i	$0.586649\pi$
$32$	−2.88403e10	−	2.88403e10i	−0.839362	−	0.839362i
$33$		−	4.32931e10i		−	1.01583i
$34$			5.02640e10i			0.956983i
$35$			3.56344e10i			0.553852i
$36$	−2.15826e10			−0.275414
$37$	6.47258e10	−	6.47258e10i	0.681813	−	0.681813i	−0.278596	−	0.960408i	$-0.589869\pi$
$37$	6.47258e10	−	6.47258e10i	0.681813	−	0.681813i	0.960408	+	0.278596i	$0.0898690\pi$
$38$		−	2.19436e11i		−	1.91788i
$39$	1.36269e11	−	1.36269e11i	0.992988	−	0.992988i
$40$	−2.06142e10	−	2.06142e10i	−0.125819	−	0.125819i
$41$	1.48600e11	−	1.48600e11i	0.763012	−	0.763012i	−0.213854	−	0.976866i	$-0.568602\pi$
$41$	1.48600e11	−	1.48600e11i	0.763012	−	0.763012i	0.976866	+	0.213854i	$0.0686017\pi$
$42$		−	4.31397e11i		−	1.87125i
$43$	−3.12432e11	−	3.12432e11i	−1.14941	−	1.14941i	−0.986668	−	0.162744i	$-0.947966\pi$
$43$	−3.12432e11	−	3.12432e11i	−1.14941	−	1.14941i	−0.162744	−	0.986668i	$-0.552034\pi$
$44$	1.36103e11	−	1.36103e11i	0.426284	−	0.426284i
$45$	−6.69311e10			−0.179119
$46$	4.65689e11	+	4.65689e11i	1.06854	+	1.06854i
$47$	5.20174e9	−	5.20174e9i	0.0102675	−	0.0102675i	−0.701954	−	0.712222i	$-0.747689\pi$
$47$	5.20174e9	−	5.20174e9i	0.0102675	−	0.0102675i	0.712222	+	0.701954i	$0.247689\pi$
$48$	5.92780e11	+	5.92780e11i	1.00973	+	1.00973i
$49$	3.24215e11			0.478036
$50$	−5.70871e11	−	5.70871e11i	−0.730715	−	0.730715i
$51$		−	7.77344e11i		−	0.866207i
$52$	8.56791e11			0.833396
$53$	7.90931e11			0.673298			0.336649	−	0.941630i	$-0.390706\pi$
$53$	7.90931e11			0.673298			0.336649	+	0.941630i	$0.390706\pi$
$54$	−1.25057e12			−0.934007
$55$	4.22078e11	−	4.22078e11i	0.277239	−	0.277239i
$56$	−5.79903e11	+	5.79903e11i	−0.335768	+	0.335768i
$57$			3.39362e12i			1.73596i
$58$	6.60148e11	−	2.80257e12i	0.298982	−	1.26929i
$59$	2.14334e12			0.861246			0.430623	−	0.902532i	$-0.358294\pi$
$59$	2.14334e12			0.861246			0.430623	+	0.902532i	$0.358294\pi$
$60$	−7.45579e11	−	7.45579e11i	−0.266339	−	0.266339i
$61$	2.70290e12	+	2.70290e12i	0.860046	+	0.860046i	0.991343	−	0.131297i	$-0.0419143\pi$
$61$	2.70290e12	+	2.70290e12i	0.860046	+	0.860046i	−0.131297	+	0.991343i	$0.541914\pi$
$62$		−	4.50916e12i		−	1.28042i
$63$			1.88285e12i			0.478005i
$64$			1.48706e12i			0.338118i
$65$	2.65705e12			0.542009
$66$	−5.10975e12	+	5.10975e12i	−0.936682	+	0.936682i
$67$			4.04921e12i			0.668108i	0.942554	+	0.334054i	$0.108417\pi$
$67$			4.04921e12i			0.668108i	−0.942554	+	0.334054i	$0.891583\pi$
$68$	2.44378e12	−	2.44378e12i	0.363496	−	0.363496i
$69$	−7.20199e12	−	7.20199e12i	−0.967184	−	0.967184i
$70$	4.20582e12	−	4.20582e12i	0.510698	−	0.510698i
$71$		−	6.43340e12i		−	0.707347i	−0.935369	−	0.353673i	$-0.884932\pi$
$71$		−	6.43340e12i		−	0.707347i	0.935369	−	0.353673i	$-0.115068\pi$
$72$	−1.08922e12	−	1.08922e12i	−0.108589	−	0.108589i
$73$	1.04802e13	−	1.04802e13i	0.948657	−	0.948657i	−0.0500878	−	0.998745i	$-0.515950\pi$
$73$	1.04802e13	−	1.04802e13i	0.948657	−	0.948657i	0.998745	+	0.0500878i	$0.0159501\pi$
$74$	−1.52788e13			−1.25738
$75$	8.82866e12	+	8.82866e12i	0.661402	+	0.661402i
$76$	−1.06687e13	+	1.06687e13i	−0.728479	+	0.728479i
$77$	−1.18736e13	−	1.18736e13i	−0.739853	−	0.739853i
$78$	−3.21667e13			−1.83124
$79$	7.26896e12	+	7.26896e12i	0.378515	+	0.378515i	0.870566	−	0.492052i	$-0.163753\pi$
$79$	7.26896e12	+	7.26896e12i	0.378515	+	0.378515i	−0.492052	+	0.870566i	$0.663753\pi$
$80$			1.15584e13i			0.551147i
$81$	2.83349e13			1.23859
$82$	−3.50775e13			−1.40712
$83$	3.99680e13			1.47288			0.736438	−	0.676506i	$-0.236507\pi$
$83$	3.99680e13			1.47288			0.736438	+	0.676506i	$0.236507\pi$
$84$	−2.09740e13	+	2.09740e13i	−0.710766	+	0.710766i
$85$	7.57856e12	−	7.57856e12i	0.236404	−	0.236404i
$86$			7.37506e13i			2.11971i
$87$	−1.02093e13	+	4.33423e13i	−0.270622	+	1.14889i
$88$	1.37375e13			0.336147
$89$	−2.45165e13	−	2.45165e13i	−0.554279	−	0.554279i	0.373394	−	0.927673i	$-0.378194\pi$
$89$	−2.45165e13	−	2.45165e13i	−0.554279	−	0.554279i	−0.927673	+	0.373394i	$0.878194\pi$
$90$	7.89967e12	+	7.89967e12i	0.165162	+	0.165162i
$91$		−	7.47460e13i		−	1.44643i
$92$		−	4.52826e13i		−	0.811739i
$93$			6.97352e13i			1.15897i
$94$	−1.22789e12			−0.0189350
$95$	−3.30855e13	+	3.30855e13i	−0.473775	+	0.473775i
$96$		−	1.05285e14i		−	1.40110i
$97$	−6.59737e13	+	6.59737e13i	−0.816524	+	0.816524i	−0.985603	−	0.169078i	$-0.945921\pi$
$97$	−6.59737e13	+	6.59737e13i	−0.816524	+	0.816524i	0.169078	+	0.985603i	$0.445921\pi$
$98$	−3.82661e13	−	3.82661e13i	−0.440790	−	0.440790i
$99$	2.23018e13	−	2.23018e13i	0.239272	−	0.239272i
$100$			5.55102e13i			0.555102i
$101$	1.61484e13	+	1.61484e13i	0.150619	+	0.150619i	0.778394	−	0.627776i	$-0.216034\pi$
$101$	1.61484e13	+	1.61484e13i	0.150619	+	0.150619i	−0.627776	+	0.778394i	$0.716034\pi$
$102$	−9.17474e13	+	9.17474e13i	−0.798716	+	0.798716i
$103$	1.08718e14			0.883980			0.441990	−	0.897020i	$-0.354273\pi$
$103$	1.08718e14			0.883980			0.441990	+	0.897020i	$0.354273\pi$
$104$	4.32400e13	+	4.32400e13i	0.328589	+	0.328589i
$105$	−6.50439e13	+	6.50439e13i	−0.462255	+	0.462255i
$106$	−9.33510e13	−	9.33510e13i	−0.620838	−	0.620838i
$107$	2.02062e14			1.25834			0.629169	−	0.777269i	$-0.283395\pi$
$107$	2.02062e14			1.25834			0.629169	+	0.777269i	$0.283395\pi$
$108$	6.08011e13	+	6.08011e13i	0.354769	+	0.354769i
$109$		−	5.86041e13i		−	0.320585i	−0.987070	−	0.160292i	$-0.948756\pi$
$109$		−	5.86041e13i		−	0.320585i	0.987070	−	0.160292i	$-0.0512437\pi$
$110$	−9.96331e13			−0.511275
$111$	2.36289e14			1.13811
$112$	3.25151e14			1.47082
$113$	−1.83743e14	+	1.83743e14i	−0.781021	+	0.781021i	−0.980003	−	0.198982i	$-0.936236\pi$
$113$	−1.83743e14	+	1.83743e14i	−0.781021	+	0.781021i	0.198982	+	0.980003i	$0.436236\pi$
$114$	4.00538e14	−	4.00538e14i	1.60070	−	1.60070i
$115$		−	1.40429e14i		−	0.527924i
$116$	−1.68353e14	+	1.04162e14i	−0.595684	+	0.368556i
$117$	1.40393e14			0.467784
$118$	−2.52972e14	−	2.52972e14i	−0.794141	−	0.794141i
$119$	−2.13194e14	−	2.13194e14i	−0.630879	−	0.630879i
$120$		−	7.52549e13i		−	0.210023i
$121$		−	9.84732e13i		−	0.259311i
$122$		−	6.38030e14i		−	1.58607i
$123$	5.42482e14			1.27365
$124$	−2.19230e14	+	2.19230e14i	−0.486350	+	0.486350i
$125$			3.89377e14i			0.816583i
$126$	2.22227e14	−	2.22227e14i	0.440761	−	0.440761i
$127$	−6.23661e14	−	6.23661e14i	−1.17037	−	1.17037i	−0.982122	−	0.188247i	$-0.939719\pi$
$127$	−6.23661e14	−	6.23661e14i	−1.17037	−	1.17037i	−0.188247	−	0.982122i	$-0.560281\pi$
$128$	−2.97006e14	+	2.97006e14i	−0.527589	+	0.527589i
$129$		−	1.14057e15i		−	1.91864i
$130$	−3.13603e14	−	3.13603e14i	−0.499778	−	0.499778i
$131$	−3.69995e13	+	3.69995e13i	−0.0558852	+	0.0558852i	−0.734497	−	0.678612i	$-0.762582\pi$
$131$	−3.69995e13	+	3.69995e13i	−0.0558852	+	0.0558852i	0.678612	+	0.734497i	$0.262582\pi$
$132$	4.96861e14			0.711569
$133$	9.30733e14	+	9.30733e14i	1.26434	+	1.26434i
$134$	4.77915e14	−	4.77915e14i	0.616052	−	0.616052i
$135$	1.88554e14	+	1.88554e14i	0.230728	+	0.230728i
$136$	2.46662e14			0.286636
$137$	−6.85059e13	−	6.85059e13i	−0.0756282	−	0.0756282i	0.668281	−	0.743909i	$-0.267030\pi$
$137$	−6.85059e13	−	6.85059e13i	−0.0756282	−	0.0756282i	−0.743909	+	0.668281i	$0.767030\pi$
$138$			1.70006e15i			1.78365i
$139$	4.28499e14			0.427412			0.213706	−	0.976898i	$-0.431447\pi$
$139$	4.28499e14			0.427412			0.213706	+	0.976898i	$0.431447\pi$
$140$	−4.08964e14			−0.387962
$141$	1.89896e13			0.0171389
$142$	−7.59314e14	+	7.59314e14i	−0.652233	+	0.652233i
$143$	−8.85342e14	+	8.85342e14i	−0.724034	+	0.724034i
$144$			6.10722e14i			0.475670i
$145$	−5.22092e14	+	3.23024e14i	−0.387410	+	0.239695i
$146$	−2.47389e15			−1.74948
$147$	5.91794e14	+	5.91794e14i	0.398978	+	0.398978i
$148$	7.42836e14	+	7.42836e14i	0.477596	+	0.477596i
$149$			2.82515e15i			1.73276i	0.499386	+	0.866380i	$0.333559\pi$
$149$			2.82515e15i			1.73276i	−0.499386	+	0.866380i	$0.666441\pi$
$150$		−	2.08404e15i		−	1.21974i
$151$			6.51438e14i			0.363944i	0.983304	+	0.181972i	$0.0582480\pi$
$151$			6.51438e14i			0.363944i	−0.983304	+	0.181972i	$0.941752\pi$
$152$	−1.07684e15			−0.574444
$153$	4.00436e14	−	4.00436e14i	0.204030	−	0.204030i
$154$			2.80280e15i			1.36441i
$155$	−6.79870e14	+	6.79870e14i	−0.316304	+	0.316304i
$156$	1.56391e15	+	1.56391e15i	0.695568	+	0.695568i
$157$	6.99826e14	−	6.99826e14i	0.297641	−	0.297641i	−0.542448	−	0.840089i	$-0.682503\pi$
$157$	6.99826e14	−	6.99826e14i	0.297641	−	0.297641i	0.840089	+	0.542448i	$0.182503\pi$
$158$		−	1.71586e15i		−	0.698045i
$159$	1.44370e15	+	1.44370e15i	0.561947	+	0.561947i
$160$	1.02646e15	−	1.02646e15i	0.382385	−	0.382385i
$161$	−3.95043e15			−1.40884
$162$	−3.34428e15	−	3.34428e15i	−1.14208	−	1.14208i
$163$	4.19687e14	−	4.19687e14i	0.137282	−	0.137282i	−0.635127	−	0.772408i	$-0.719052\pi$
$163$	4.19687e14	−	4.19687e14i	0.137282	−	0.137282i	0.772408	+	0.635127i	$0.219052\pi$
$164$	1.70543e15	+	1.70543e15i	0.534474	+	0.534474i
$165$	1.54085e15			0.462778
$166$	−4.71730e15	−	4.71730e15i	−1.35812	−	1.35812i
$167$		−	4.68283e15i		−	1.29269i	−0.763047	−	0.646343i	$-0.776298\pi$
$167$		−	4.68283e15i		−	1.29269i	0.763047	−	0.646343i	$-0.223702\pi$
$168$	−2.11701e15			−0.560477
$169$	−1.63600e15			−0.415505
$170$	−1.78895e15			−0.435969
$171$	−1.74817e15	+	1.74817e15i	−0.408894	+	0.408894i
$172$	3.58567e15	−	3.58567e15i	0.805140	−	0.805140i
$173$		−	1.23842e15i		−	0.267021i	−0.991047	−	0.133510i	$-0.957375\pi$
$173$		−	1.23842e15i		−	0.267021i	0.991047	−	0.133510i	$-0.0426250\pi$
$174$	6.32053e15	−	3.91058e15i	1.30891	−	0.809835i
$175$	4.84269e15			0.963429
$176$	−3.85131e15	−	3.85131e15i	−0.736240	−	0.736240i
$177$	3.91227e15	+	3.91227e15i	0.718812	+	0.718812i
$178$			5.78721e15i			1.02219i
$179$		−	5.86153e15i		−	0.995496i	−0.867322	−	0.497748i	$-0.834160\pi$
$179$		−	5.86153e15i		−	0.995496i	0.867322	−	0.497748i	$-0.165840\pi$
$180$		−	7.68146e14i		−	0.125469i
$181$	−1.41551e15			−0.222415			−0.111207	−	0.993797i	$-0.535472\pi$
$181$	−1.41551e15			−0.222415			−0.111207	+	0.993797i	$0.535472\pi$
$182$	−8.82204e15	+	8.82204e15i	−1.33373	+	1.33373i
$183$			9.86728e15i			1.43562i
$184$	2.28529e15	−	2.28529e15i	0.320050	−	0.320050i
$185$	2.30366e15	+	2.30366e15i	0.310610	+	0.310610i
$186$	8.23063e15	−	8.23063e15i	1.06867	−	1.06867i
$187$			5.05042e15i			0.631592i
$188$	5.96986e13	+	5.96986e13i	0.00719216	+	0.00719216i
$189$	5.30426e15	−	5.30426e15i	0.615732	−	0.615732i
$190$	7.80994e15			0.873721
$191$	−4.60527e15	−	4.60527e15i	−0.496617	−	0.496617i	0.413766	−	0.910383i	$-0.364213\pi$
$191$	−4.60527e15	−	4.60527e15i	−0.496617	−	0.496617i	−0.910383	+	0.413766i	$0.864213\pi$
$192$	−2.71435e15	+	2.71435e15i	−0.282200	+	0.282200i
$193$	1.46018e14	+	1.46018e14i	0.0146388	+	0.0146388i	0.714388	−	0.699750i	$-0.246705\pi$
$193$	1.46018e14	+	1.46018e14i	0.0146388	+	0.0146388i	−0.699750	+	0.714388i	$0.746705\pi$
$194$	1.55733e16			1.50581
$195$	4.84995e15	+	4.84995e15i	0.452371	+	0.452371i
$196$			3.72091e15i			0.334855i
$197$	4.71325e14			0.0409315			0.0204657	−	0.999791i	$-0.493485\pi$
$197$	4.71325e14			0.0409315			0.0204657	+	0.999791i	$0.493485\pi$
$198$	−5.26441e15			−0.441259
$199$	−1.81861e16			−1.47152			−0.735762	−	0.677240i	$-0.763176\pi$
$199$	−1.81861e16			−1.47152			−0.735762	+	0.677240i	$0.763176\pi$
$200$	−2.80146e15	+	2.80146e15i	−0.218864	+	0.218864i
$201$	−7.39107e15	+	7.39107e15i	−0.557616	+	0.557616i
$202$		−	3.81188e15i		−	0.277766i
$203$	9.08703e15	+	1.46871e16i	0.639661	+	1.03386i
$204$	8.92131e15			0.606761
$205$	5.28882e15	+	5.28882e15i	0.347602	+	0.347602i
$206$	−1.28317e16	−	1.28317e16i	−0.815104	−	0.815104i
$207$		−	7.41998e15i		−	0.455628i
$208$		−	2.42446e16i		−	1.43937i
$209$		−	2.20485e16i		−	1.26577i
$210$	1.53539e16			0.852477
$211$	−9.53358e15	+	9.53358e15i	−0.512010	+	0.512010i	−0.915142	−	0.403132i	$-0.867922\pi$
$211$	−9.53358e15	+	9.53358e15i	−0.512010	+	0.512010i	0.403132	+	0.915142i	$0.367922\pi$
$212$			9.07724e15i			0.471632i
$213$	1.17430e16	−	1.17430e16i	0.590365	−	0.590365i
$214$	−2.38487e16	−	2.38487e16i	−1.16029	−	1.16029i
$215$	1.11198e16	−	1.11198e16i	0.523633	−	0.523633i
$216$			6.13695e15i			0.279754i
$217$	1.91255e16	+	1.91255e16i	0.844103	+	0.844103i
$218$	−6.91686e15	+	6.91686e15i	−0.295606	+	0.295606i
$219$	3.82592e16			1.58353
$220$	4.84405e15	+	4.84405e15i	0.194200	+	0.194200i
$221$	−1.58966e16	+	1.58966e16i	−0.617390	+	0.617390i
$222$	−2.78885e16	−	2.78885e16i	−1.04943	−	1.04943i
$223$	5.07331e16			1.84994			0.924970	−	0.380040i	$-0.124090\pi$
$223$	5.07331e16			1.84994			0.924970	+	0.380040i	$0.124090\pi$
$224$	−2.88754e16	−	2.88754e16i	−1.02045	−	1.02045i
$225$			9.09588e15i			0.311578i
$226$	4.33733e16			1.44034
$227$	−5.84479e16			−1.88186			−0.940931	−	0.338599i	$-0.890047\pi$
$227$	−5.84479e16			−1.88186			−0.940931	+	0.338599i	$0.890047\pi$
$228$	−3.89475e16			−1.21600
$229$	−2.01877e16	+	2.01877e16i	−0.611276	+	0.611276i	−0.943279	−	0.332002i	$-0.892276\pi$
$229$	−2.01877e16	+	2.01877e16i	−0.611276	+	0.611276i	0.332002	+	0.943279i	$0.392276\pi$
$230$	−1.65744e16	+	1.65744e16i	−0.486791	+	0.486791i
$231$		−	4.33459e16i		−	1.23499i
$232$	−1.37531e16	−	3.23957e15i	−0.380177	−	0.0895512i
$233$	4.18770e16			1.12327			0.561634	−	0.827386i	$-0.310173\pi$
$233$	4.18770e16			1.12327			0.561634	+	0.827386i	$0.310173\pi$
$234$	−1.65702e16	−	1.65702e16i	−0.431336	−	0.431336i
$235$	1.85135e14	+	1.85135e14i	0.00467751	+	0.00467751i
$236$			2.45984e16i			0.603285i
$237$			2.65362e16i			0.631831i
$238$			5.03252e16i			1.16345i
$239$	−5.92064e16			−1.32918			−0.664589	−	0.747209i	$-0.731394\pi$
$239$	−5.92064e16			−1.32918			−0.664589	+	0.747209i	$0.731394\pi$
$240$	−2.10977e16	+	2.10977e16i	−0.459998	+	0.459998i
$241$			6.64323e16i			1.40689i	0.710750	+	0.703444i	$0.248356\pi$
$241$			6.64323e16i			1.40689i	−0.710750	+	0.703444i	$0.751644\pi$
$242$	−1.16225e16	+	1.16225e16i	−0.239106	+	0.239106i
$243$	2.63809e16	+	2.63809e16i	0.527285	+	0.527285i
$244$	−3.10203e16	+	3.10203e16i	−0.602445	+	0.602445i
$245$			1.15392e16i			0.217777i
$246$	−6.40274e16	−	6.40274e16i	−1.17441	−	1.17441i
$247$	6.93994e16	−	6.93994e16i	1.23731	−	1.23731i
$248$	−2.21280e16			−0.383513
$249$	7.29541e16	+	7.29541e16i	1.22929	+	1.22929i
$250$	4.59569e16	−	4.59569e16i	0.752959	−	0.752959i
$251$	−5.90079e16	−	5.90079e16i	−0.940144	−	0.940144i	0.0581634	−	0.998307i	$-0.481476\pi$
$251$	−5.90079e16	−	5.90079e16i	−0.940144	−	0.940144i	−0.998307	+	0.0581634i	$0.981476\pi$
$252$	−2.16089e16			−0.334833
$253$	4.67915e16	+	4.67915e16i	0.705218	+	0.705218i
$254$			1.47218e17i			2.15836i
$255$	2.76665e16			0.394614
$256$	9.44733e16			1.31108
$257$	−1.41881e16			−0.191599			−0.0957995	−	0.995401i	$-0.530541\pi$
$257$	−1.41881e16			−0.191599			−0.0957995	+	0.995401i	$0.530541\pi$
$258$	−1.34618e17	+	1.34618e17i	−1.76915	+	1.76915i
$259$	6.48046e16	−	6.48046e16i	0.828910	−	0.828910i
$260$			3.04941e16i			0.379667i
$261$	−2.75863e16	+	1.70679e16i	−0.334356	+	0.206870i
$262$	8.73387e15			0.103062
$263$	2.89895e16	+	2.89895e16i	0.333081	+	0.333081i	0.853755	−	0.520674i	$-0.174319\pi$
$263$	2.89895e16	+	2.89895e16i	0.333081	+	0.333081i	−0.520674	+	0.853755i	$0.674319\pi$
$264$	2.50753e16	+	2.50753e16i	0.280555	+	0.280555i
$265$			2.81501e16i			0.306731i
$266$		−	2.19703e17i		−	2.33166i
$267$		−	8.95006e16i		−	0.925224i
$268$	−4.64714e16			−0.467996
$269$	−9.55466e16	+	9.55466e16i	−0.937452	+	0.937452i	−0.998156	−	0.0607036i	$-0.980666\pi$
$269$	−9.55466e16	+	9.55466e16i	−0.937452	+	0.937452i	0.0607036	+	0.998156i	$0.480666\pi$
$270$		−	4.45090e16i		−	0.425501i
$271$	6.47186e16	−	6.47186e16i	0.602899	−	0.602899i	−0.338182	−	0.941081i	$-0.609812\pi$
$271$	6.47186e16	−	6.47186e16i	0.602899	−	0.602899i	0.941081	+	0.338182i	$0.109812\pi$
$272$	−6.91516e16	−	6.91516e16i	−0.627798	−	0.627798i
$273$	1.36435e17	−	1.36435e17i	1.20722	−	1.20722i
$274$			1.61711e16i			0.139471i
$275$	−5.73600e16	−	5.73600e16i	−0.482259	−	0.482259i
$276$	8.26548e16	−	8.26548e16i	0.677493	−	0.677493i
$277$	−1.36574e17			−1.09147			−0.545733	−	0.837959i	$-0.683749\pi$
$277$	−1.36574e17			−1.09147			−0.545733	+	0.837959i	$0.683749\pi$
$278$	−5.05744e16	−	5.05744e16i	−0.394110	−	0.394110i
$279$	−3.59230e16	+	3.59230e16i	−0.272988	+	0.272988i
$280$	−2.06394e16	−	2.06394e16i	−0.152964	−	0.152964i
$281$	2.28330e17			1.65051			0.825256	−	0.564759i	$-0.191031\pi$
$281$	2.28330e17			1.65051			0.825256	+	0.564759i	$0.191031\pi$
$282$	−2.24128e15	−	2.24128e15i	−0.0158035	−	0.0158035i
$283$			7.69074e16i			0.529009i	0.964384	+	0.264504i	$0.0852084\pi$
$283$			7.69074e16i			0.529009i	−0.964384	+	0.264504i	$0.914792\pi$
$284$	7.38340e16			0.495482
$285$	−1.20783e17			−0.790843
$286$	2.08988e17			1.33524
$287$	1.48781e17	−	1.48781e17i	0.927628	−	0.927628i
$288$	5.42359e16	−	5.42359e16i	0.330019	−	0.330019i
$289$		−	7.76957e16i		−	0.461436i
$290$	9.97463e16	+	2.34954e16i	0.578243	+	0.136206i
$291$	−2.40845e17			−1.36297
$292$	1.20278e17	+	1.20278e17i	0.664515	+	0.664515i
$293$	8.46125e15	+	8.46125e15i	0.0456417	+	0.0456417i	0.729559	−	0.683918i	$-0.239725\pi$
$293$	8.46125e15	+	8.46125e15i	0.0456417	+	0.0456417i	−0.683918	+	0.729559i	$0.739725\pi$
$294$		−	1.39695e17i		−	0.735783i
$295$			7.62838e16i			0.392354i
$296$			7.49780e16i			0.376610i
$297$	−1.25654e17			−0.616428
$298$	3.33444e17	−	3.33444e17i	1.59775	−	1.59775i
$299$			2.94561e17i			1.37872i
$300$	−1.01324e17	+	1.01324e17i	−0.463299	+	0.463299i
$301$	−3.12812e17	−	3.12812e17i	−1.39739	−	1.39739i
$302$	7.68871e16	−	7.68871e16i	0.335587	−	0.335587i
$303$			5.89516e16i			0.251418i
$304$	3.01893e17	+	3.01893e17i	1.25816	+	1.25816i
$305$	−9.61992e16	+	9.61992e16i	−0.391807	+	0.391807i
$306$	−9.45244e16			−0.376265
$307$	−1.87543e17	−	1.87543e17i	−0.729680	−	0.729680i	0.240876	−	0.970556i	$-0.422565\pi$
$307$	−1.87543e17	−	1.87543e17i	−0.729680	−	0.729680i	−0.970556	+	0.240876i	$0.922565\pi$
$308$	1.36269e17	−	1.36269e17i	0.518252	−	0.518252i
$309$	1.98445e17	+	1.98445e17i	0.737787	+	0.737787i
$310$	1.60486e17			0.583317
$311$	−2.05198e17	−	2.05198e17i	−0.729207	−	0.729207i	0.241254	−	0.970462i	$-0.422441\pi$
$311$	−2.05198e17	−	2.05198e17i	−0.729207	−	0.729207i	−0.970462	+	0.241254i	$0.922441\pi$
$312$			1.57853e17i			0.548493i
$313$	−2.92966e17			−0.995421			−0.497711	−	0.867343i	$-0.665826\pi$
$313$	−2.92966e17			−0.995421			−0.497711	+	0.867343i	$0.665826\pi$
$314$	−1.65197e17			−0.548900
$315$	−6.70127e16			−0.217762
$316$	−8.34234e16	+	8.34234e16i	−0.265142	+	0.265142i
$317$	−2.90072e17	+	2.90072e17i	−0.901760	+	0.901760i	−0.995588	−	0.0938281i	$-0.970090\pi$
$317$	−2.90072e17	+	2.90072e17i	−0.901760	+	0.901760i	0.0938281	+	0.995588i	$0.470090\pi$
$318$		−	3.40790e17i		−	1.03633i
$319$	6.63304e16	−	2.81596e17i	0.197323	−	0.837707i
$320$	−5.29260e16			−0.154035
$321$	3.68825e17	+	3.68825e17i	1.05023	+	1.05023i
$322$	4.66257e17	+	4.66257e17i	1.29907	+	1.29907i
$323$		−	3.95888e17i		−	1.07933i
$324$			3.25191e17i			0.867607i
$325$		−	3.61091e17i		−	0.942829i
$326$	−9.90686e16			−0.253170
$327$	1.06971e17	−	1.06971e17i	0.267566	−	0.267566i
$328$			1.72137e17i			0.421461i
$329$	5.20808e15	−	5.20808e15i	0.0124826	−	0.0124826i
$330$	−1.81861e17	−	1.81861e17i	−0.426720	−	0.426720i
$331$	−2.46921e17	+	2.46921e17i	−0.567233	+	0.567233i	−0.931352	−	0.364119i	$-0.881370\pi$
$331$	−2.46921e17	+	2.46921e17i	−0.567233	+	0.567233i	0.364119	+	0.931352i	$0.381370\pi$
$332$			4.58699e17i			1.03172i
$333$	1.21721e17	+	1.21721e17i	0.268074	+	0.268074i
$334$	−5.52699e17	+	5.52699e17i	−1.19196	+	1.19196i
$335$	−1.44116e17			−0.304367
$336$	5.93502e17	+	5.93502e17i	1.22757	+	1.22757i
$337$	−6.73151e17	+	6.73151e17i	−1.36365	+	1.36365i	−0.494436	+	0.869214i	$0.664625\pi$
$337$	−6.73151e17	+	6.73151e17i	−1.36365	+	1.36365i	−0.869214	+	0.494436i	$0.835375\pi$
$338$	1.93092e17	+	1.93092e17i	0.383131	+	0.383131i
$339$	−6.70778e17			−1.30371
$340$	8.69766e16	+	8.69766e16i	0.165596	+	0.165596i
$341$		−	4.53072e17i		−	0.845057i
$342$	4.12662e17			0.754070
$343$	−3.54439e17			−0.634575
$344$	3.61919e17			0.634896
$345$	2.56327e17	−	2.56327e17i	0.440616	−	0.440616i
$346$	−1.46167e17	+	1.46167e17i	−0.246216	+	0.246216i
$347$			6.82232e16i			0.112623i	0.998413	+	0.0563113i	$0.0179339\pi$
$347$			6.82232e16i			0.112623i	−0.998413	+	0.0563113i	$0.982066\pi$
$348$	−4.97425e17	−	1.17169e17i	−0.804773	−	0.189565i
$349$	−2.34749e16			−0.0372243			−0.0186121	−	0.999827i	$-0.505925\pi$
$349$	−2.34749e16			−0.0372243			−0.0186121	+	0.999827i	$0.505925\pi$
$350$	−5.71567e17	−	5.71567e17i	−0.888363	−	0.888363i
$351$	−3.95508e17	−	3.95508e17i	−0.602567	−	0.602567i
$352$			6.84039e17i			1.02160i
$353$		−	1.00370e18i		−	1.46954i	−0.678315	−	0.734771i	$-0.737289\pi$
$353$		−	1.00370e18i		−	1.46954i	0.678315	−	0.734771i	$-0.262711\pi$
$354$		−	9.23505e17i		−	1.32561i
$355$	2.28972e17			0.322243
$356$	2.81368e17	−	2.81368e17i	0.388262	−	0.388262i
$357$		−	7.78291e17i		−	1.05309i
$358$	−6.91817e17	+	6.91817e17i	−0.917932	+	0.917932i
$359$	7.40106e17	+	7.40106e17i	0.963015	+	0.963015i	0.999340	−	0.0363253i	$-0.0115653\pi$
$359$	7.40106e17	+	7.40106e17i	0.963015	+	0.963015i	−0.0363253	+	0.999340i	$0.511565\pi$
$360$	3.87663e16	−	3.87663e16i	0.0494695	−	0.0494695i
$361$			9.29307e17i			1.16308i
$362$	1.67068e17	+	1.67068e17i	0.205085	+	0.205085i
$363$	1.79744e17	−	1.79744e17i	0.216426	−	0.216426i
$364$	8.57835e17			1.01320
$365$	3.73001e17	+	3.73001e17i	0.432175	+	0.432175i
$366$	1.16460e18	−	1.16460e18i	1.32376	−	1.32376i
$367$	−5.24805e17	−	5.24805e17i	−0.585242	−	0.585242i	0.351097	−	0.936339i	$-0.385809\pi$
$367$	−5.24805e17	−	5.24805e17i	−0.585242	−	0.585242i	−0.936339	+	0.351097i	$0.885809\pi$
$368$	−1.28136e18			−1.40196
$369$	2.79451e17	+	2.79451e17i	0.300000	+	0.300000i
$370$		−	5.43787e17i		−	0.572818i
$371$	7.91894e17			0.818559
$372$	−8.00328e17			−0.811834
$373$	3.16742e17			0.315315			0.157657	−	0.987494i	$-0.449606\pi$
$373$	3.16742e17			0.315315			0.157657	+	0.987494i	$0.449606\pi$
$374$	5.96085e17	−	5.96085e17i	0.582381	−	0.582381i
$375$	−7.10735e17	+	7.10735e17i	−0.681536	+	0.681536i
$376$			6.02567e15i			0.00567140i
$377$	1.09513e18	−	6.77567e17i	1.01176	−	0.625984i
$378$	−1.25209e18			−1.13551
$379$	1.35286e18	+	1.35286e18i	1.20442	+	1.20442i	0.972807	+	0.231616i	$0.0744011\pi$
$379$	1.35286e18	+	1.35286e18i	1.20442	+	1.20442i	0.231616	+	0.972807i	$0.425599\pi$
$380$	−3.79711e17	−	3.79711e17i	−0.331870	−	0.331870i
$381$		−	2.27675e18i		−	1.95362i
$382$			1.08709e18i			0.915845i
$383$		−	1.07969e18i		−	0.893119i	−0.894754	−	0.446559i	$-0.852649\pi$
$383$		−	1.07969e18i		−	0.893119i	0.894754	−	0.446559i	$-0.147351\pi$
$384$	−1.08426e18			−0.880671
$385$	4.22592e17	−	4.22592e17i	0.337052	−	0.337052i
$386$		−	3.44680e16i		−	0.0269963i
$387$	5.87546e17	−	5.87546e17i	0.451924	−	0.451924i
$388$	−7.57158e17	−	7.57158e17i	−0.571959	−	0.571959i
$389$	−1.20173e17	+	1.20173e17i	−0.0891575	+	0.0891575i	−0.750279	−	0.661121i	$-0.770081\pi$
$389$	−1.20173e17	+	1.20173e17i	−0.0891575	+	0.0891575i	0.661121	+	0.750279i	$0.270081\pi$
$390$		−	1.14485e18i		−	0.834249i
$391$	8.40159e17	+	8.40159e17i	0.601346	+	0.601346i
$392$	−1.87785e17	+	1.87785e17i	−0.132025	+	0.132025i
$393$	−1.35071e17			−0.0932858
$394$	−5.56290e16	−	5.56290e16i	−0.0377423	−	0.0377423i
$395$	−2.58710e17	+	2.58710e17i	−0.172438	+	0.172438i
$396$	2.55950e17	+	2.55950e17i	0.167606	+	0.167606i
$397$	−2.09297e18			−1.34657			−0.673284	−	0.739384i	$-0.735117\pi$
$397$	−2.09297e18			−1.34657			−0.673284	+	0.739384i	$0.735117\pi$
$398$	2.14644e18	+	2.14644e18i	1.35687	+	1.35687i
$399$			3.39776e18i			2.11048i
$400$	1.57077e18			0.958724
$401$	−5.75828e17			−0.345368			−0.172684	−	0.984977i	$-0.555244\pi$
$401$	−5.75828e17			−0.345368			−0.172684	+	0.984977i	$0.555244\pi$
$402$	1.74469e18			1.02834
$403$	1.42608e18	−	1.42608e18i	0.826055	−	0.826055i
$404$	−1.85329e17	+	1.85329e17i	−0.105505	+	0.105505i
$405$			1.00847e18i			0.564259i
$406$	6.60953e17	−	2.80598e18i	0.363486	−	1.54313i
$407$	−1.53518e18			−0.829847
$408$	4.50235e17	+	4.50235e17i	0.239232	+	0.239232i
$409$	2.30597e17	+	2.30597e17i	0.120445	+	0.120445i	0.764760	−	0.644315i	$-0.222857\pi$
$409$	2.30597e17	+	2.30597e17i	0.120445	+	0.120445i	−0.644315	+	0.764760i	$0.722857\pi$
$410$		−	1.24845e18i		−	0.641036i
$411$		−	2.50089e17i		−	0.126242i
$412$			1.24772e18i			0.619210i
$413$	2.14595e18			1.04706
$414$	−8.75757e17	+	8.75757e17i	−0.420127	+	0.420127i
$415$			1.42250e18i			0.670991i
$416$	−2.15307e18	+	2.15307e18i	−0.998631	+	0.998631i
$417$	7.82145e17	+	7.82145e17i	0.356726	+	0.356726i
$418$	−2.60231e18	+	2.60231e18i	−1.16715	+	1.16715i
$419$		−	2.07331e17i		−	0.0914464i	−0.998954	−	0.0457232i	$-0.985441\pi$
$419$		−	2.07331e17i		−	0.0914464i	0.998954	−	0.0457232i	$-0.0145592\pi$
$420$	−7.46487e17	−	7.46487e17i	−0.323800	−	0.323800i
$421$	3.10389e18	−	3.10389e18i	1.32413	−	1.32413i	0.413739	−	0.910396i	$-0.364223\pi$
$421$	3.10389e18	−	3.10389e18i	1.32413	−	1.32413i	0.910396	−	0.413739i	$-0.135777\pi$
$422$	2.25044e18			0.944233
$423$	9.78219e15	+	9.78219e15i	0.00403695	+	0.00403695i
$424$	−4.58105e17	+	4.58105e17i	−0.185953	+	0.185953i
$425$	−1.02992e18	−	1.02992e18i	−0.411226	−	0.411226i
$426$	−2.77197e18			−1.08873
$427$	2.70620e18	+	2.70620e18i	1.04560	+	1.04560i
$428$			2.31899e18i			0.881440i
$429$	−3.23205e18			−1.20858
$430$	−2.62486e18			−0.965667
$431$	6.71479e17			0.243048			0.121524	−	0.992589i	$-0.461222\pi$
$431$	6.71479e17			0.243048			0.121524	+	0.992589i	$0.461222\pi$
$432$	1.72049e18	−	1.72049e18i	0.612725	−	0.612725i
$433$	2.76480e18	−	2.76480e18i	0.968830	−	0.968830i	−0.0306983	−	0.999529i	$-0.509773\pi$
$433$	2.76480e18	−	2.76480e18i	0.968830	−	0.968830i	0.999529	+	0.0306983i	$0.00977311\pi$
$434$		−	4.51465e18i		−	1.55667i
$435$	−1.54260e18	−	3.63361e17i	−0.523393	−	0.123286i
$436$	6.72580e17			0.224563
$437$	−3.66785e18	−	3.66785e18i	−1.20515	−	1.20515i
$438$	−4.51562e18	−	4.51562e18i	−1.46015	−	1.46015i
$439$		−	5.14562e18i		−	1.63752i	−0.574137	−	0.818759i	$-0.694662\pi$
$439$		−	5.14562e18i		−	1.63752i	0.574137	−	0.818759i	$-0.305338\pi$
$440$			4.88933e17i			0.153137i
$441$			6.09706e17i			0.187953i
$442$	3.75246e18			1.13857
$443$	1.04241e18	−	1.04241e18i	0.311324	−	0.311324i	−0.534098	−	0.845422i	$-0.679349\pi$
$443$	1.04241e18	−	1.04241e18i	0.311324	−	0.311324i	0.845422	+	0.534098i	$0.179349\pi$
$444$			2.71181e18i			0.797222i
$445$	8.72569e17	−	8.72569e17i	0.252511	−	0.252511i
$446$	−5.98787e18	−	5.98787e18i	−1.70580	−	1.70580i
$447$	−5.15679e18	+	5.15679e18i	−1.44619	+	1.44619i
$448$			1.48887e18i			0.411066i
$449$	2.02730e18	+	2.02730e18i	0.551054	+	0.551054i	0.926745	−	0.375691i	$-0.122595\pi$
$449$	2.02730e18	+	2.02730e18i	0.551054	+	0.551054i	−0.375691	+	0.926745i	$0.622595\pi$
$450$	1.07356e18	−	1.07356e18i	0.287301	−	0.287301i
$451$	−3.52452e18			−0.928676
$452$	−2.10876e18	−	2.10876e18i	−0.547090	−	0.547090i
$453$	−1.18908e18	+	1.18908e18i	−0.303754	+	0.303754i
$454$	6.89842e18	+	6.89842e18i	1.73524	+	1.73524i
$455$	2.66029e18			0.658945
$456$	−1.96558e18	−	1.96558e18i	−0.479442	−	0.479442i
$457$			6.65165e18i			1.59778i	0.601480	+	0.798888i	$0.294578\pi$
$457$			6.65165e18i			1.59778i	−0.601480	+	0.798888i	$0.705422\pi$
$458$	4.76537e18			1.12730
$459$	−2.25617e18			−0.525633
$460$	1.61165e18			0.369800
$461$	−2.00479e18	+	2.00479e18i	−0.453067	+	0.453067i	−0.896371	−	0.443305i	$-0.853806\pi$
$461$	−2.00479e18	+	2.00479e18i	−0.453067	+	0.453067i	0.443305	+	0.896371i	$0.353806\pi$
$462$	−5.11598e18	+	5.11598e18i	−1.13877	+	1.13877i
$463$			2.49059e18i			0.546055i	0.962006	+	0.273027i	$0.0880250\pi$
$463$			2.49059e18i			0.546055i	−0.962006	+	0.273027i	$0.911975\pi$
$464$	2.94747e18	+	4.76389e18i	0.636537	+	1.02881i
$465$	−2.48195e18			−0.527986
$466$	−4.94260e18	−	4.94260e18i	−1.03575	−	1.03575i
$467$	3.54294e18	+	3.54294e18i	0.731384	+	0.731384i	0.970894	−	0.239510i	$-0.0769867\pi$
$467$	3.54294e18	+	3.54294e18i	0.731384	+	0.731384i	−0.239510	+	0.970894i	$0.576987\pi$
$468$			1.61125e18i			0.327673i
$469$			4.05414e18i			0.812249i
$470$		−	4.37019e16i		−	0.00862612i
$471$	2.55480e18			0.496834
$472$	−1.24142e18	+	1.24142e18i	−0.237861	+	0.237861i
$473$			7.41032e18i			1.39897i
$474$	3.13199e18	−	3.13199e18i	0.582602	−	0.582602i
$475$	4.49628e18	+	4.49628e18i	0.824135	+	0.824135i
$476$	2.44675e18	−	2.44675e18i	0.441918	−	0.441918i
$477$			1.48739e18i			0.264726i
$478$	6.98795e18	+	6.98795e18i	1.22562	+	1.22562i
$479$	−6.00366e18	+	6.00366e18i	−1.03769	+	1.03769i	−0.0384280	+	0.999261i	$0.512235\pi$
$479$	−6.00366e18	+	6.00366e18i	−1.03769	+	1.03769i	−0.999261	+	0.0384280i	$0.987765\pi$
$480$	3.74720e18			0.638291
$481$	−4.83211e18	−	4.83211e18i	−0.811187	−	0.811187i
$482$	7.84079e18	−	7.84079e18i	1.29727	−	1.29727i
$483$	−7.21077e18	−	7.21077e18i	−1.17585	−	1.17585i
$484$	1.13014e18			0.181642
$485$	−2.34808e18	−	2.34808e18i	−0.371980	−	0.371980i
$486$		−	6.22731e18i		−	0.972403i
$487$	5.37757e18			0.827720			0.413860	−	0.910341i	$-0.364180\pi$
$487$	5.37757e18			0.827720			0.413860	+	0.910341i	$0.364180\pi$
$488$	−3.13103e18			−0.475060
$489$	1.53212e18			0.229156
$490$	1.36193e18	−	1.36193e18i	0.200809	−	0.200809i
$491$	−5.92512e18	+	5.92512e18i	−0.861245	+	0.861245i	−0.991483	−	0.130238i	$-0.958426\pi$
$491$	−5.92512e18	+	5.92512e18i	−0.861245	+	0.861245i	0.130238	+	0.991483i	$0.458426\pi$
$492$			6.22588e18i			0.892165i
$493$	1.19099e18	−	5.05616e18i	0.168259	−	0.714320i
$494$	−1.63820e19			−2.28180
$495$	7.93743e17	+	7.93743e17i	0.109004	+	0.109004i
$496$	6.20356e18	+	6.20356e18i	0.839981	+	0.839981i
$497$		−	6.44124e18i		−	0.859953i
$498$		−	1.72211e19i		−	2.26702i
$499$		−	1.56967e18i		−	0.203754i	−0.994797	−	0.101877i	$-0.967515\pi$
$499$		−	1.56967e18i		−	0.203754i	0.994797	−	0.101877i	$-0.0324848\pi$
$500$	−4.46875e18			−0.572000
$501$	8.54762e18	−	8.54762e18i	1.07890	−	1.07890i
$502$			1.39290e19i			1.73378i
$503$	−4.89694e18	+	4.89694e18i	−0.601103	+	0.601103i	−0.940605	−	0.339502i	$-0.889741\pi$
$503$	−4.89694e18	+	4.89694e18i	−0.601103	+	0.601103i	0.339502	+	0.940605i	$0.389741\pi$
$504$	−1.09054e18	−	1.09054e18i	−0.132017	−	0.132017i
$505$	−5.74737e17	+	5.74737e17i	−0.0686166	+	0.0686166i
$506$		−	1.10453e19i		−	1.30054i
$507$	−2.98621e18	−	2.98621e18i	−0.346789	−	0.346789i
$508$	7.15755e18	−	7.15755e18i	0.819820	−	0.819820i
$509$	1.22476e19			1.38366			0.691828	−	0.722062i	$-0.256806\pi$
$509$	1.22476e19			1.38366			0.691828	+	0.722062i	$0.256806\pi$
$510$	−3.26539e18	−	3.26539e18i	−0.363868	−	0.363868i
$511$	1.04930e19	−	1.04930e19i	1.15333	−	1.15333i
$512$	−6.28424e18	−	6.28424e18i	−0.681339	−	0.681339i
$513$	9.84968e18			1.05342
$514$	1.67458e18	+	1.67458e18i	0.176671	+	0.176671i
$515$			3.86940e18i			0.402711i
$516$	1.30899e19			1.34397
$517$	−1.23376e17			−0.0124967
$518$	−1.52974e19			−1.52865
$519$	2.26050e18	−	2.26050e18i	0.222861	−	0.222861i
$520$	−1.53896e18	+	1.53896e18i	−0.149694	+	0.149694i
$521$		−	9.38887e18i		−	0.901051i	−0.892764	−	0.450526i	$-0.851237\pi$
$521$		−	9.38887e18i		−	0.901051i	0.892764	−	0.450526i	$-0.148763\pi$
$522$	5.27039e18	+	1.24145e18i	0.499056	+	0.117553i
$523$	5.54072e18			0.517672			0.258836	−	0.965921i	$-0.416661\pi$
$523$	5.54072e18			0.517672			0.258836	+	0.965921i	$0.416661\pi$
$524$	−4.24631e17	−	4.24631e17i	−0.0391465	−	0.0391465i
$525$	8.83941e18	+	8.83941e18i	0.804097	+	0.804097i
$526$		−	6.84307e18i		−	0.614258i
$527$		−	8.13506e18i		−	0.720587i
$528$		−	1.40597e19i		−	1.22896i
$529$	3.97510e18			0.342892
$530$	3.32246e18	−	3.32246e18i	0.282832	−	0.282832i
$531$			4.03068e18i			0.338623i
$532$	−1.06817e19	+	1.06817e19i	−0.885644	+	0.885644i
$533$	−1.10937e19	−	1.10937e19i	−0.907793	−	0.907793i
$534$	−1.05635e19	+	1.05635e19i	−0.853135	+	0.853135i
$535$			7.19158e18i			0.573255i
$536$	−2.34529e18	−	2.34529e18i	−0.184520	−	0.184520i
$537$	1.06991e19	−	1.06991e19i	0.830860	−	0.830860i
$538$	2.25541e19			1.72882
$539$	−3.84490e18	−	3.84490e18i	−0.290913	−	0.290913i
$540$	−2.16398e18	+	2.16398e18i	−0.161620	+	0.161620i
$541$	−9.63227e17	−	9.63227e17i	−0.0710146	−	0.0710146i	0.670707	−	0.741722i	$-0.265991\pi$
$541$	−9.63227e17	−	9.63227e17i	−0.0710146	−	0.0710146i	−0.741722	+	0.670707i	$0.765991\pi$
$542$	−1.52771e19			−1.11185
$543$	−2.58375e18	−	2.58375e18i	−0.185632	−	0.185632i
$544$			1.22822e19i			0.871130i
$545$	2.08578e18			0.146047
$546$	−3.22059e19			−2.22632
$547$	9.21813e18			0.629117			0.314558	−	0.949238i	$-0.398144\pi$
$547$	9.21813e18			0.629117			0.314558	+	0.949238i	$0.398144\pi$
$548$	7.86219e17	−	7.86219e17i	0.0529761	−	0.0529761i
$549$	−5.08297e18	+	5.08297e18i	−0.338151	+	0.338151i
$550$			1.35400e19i			0.889367i
$551$	−5.19945e18	+	2.20735e19i	−0.337207	+	1.43156i
$552$	8.34275e18			0.534239
$553$	7.27781e18	+	7.27781e18i	0.460177	+	0.460177i
$554$	1.61194e19	+	1.61194e19i	1.00642	+	1.00642i
$555$			8.40979e18i			0.518483i
$556$			4.91774e18i			0.299393i
$557$			8.26551e18i			0.496917i	0.968643	+	0.248458i	$0.0799239\pi$
$557$			8.26551e18i			0.496917i	−0.968643	+	0.248458i	$0.920076\pi$
$558$	8.47975e18			0.503435
$559$	−2.33246e19	+	2.33246e19i	−1.36751	+	1.36751i
$560$			1.15725e19i			0.670054i
$561$	−9.21860e18	+	9.21860e18i	−0.527139	+	0.527139i
$562$	−2.69491e19	−	2.69491e19i	−1.52191	−	1.52191i
$563$	1.27260e17	−	1.27260e17i	0.00709797	−	0.00709797i	−0.703549	−	0.710647i	$-0.748402\pi$
$563$	1.27260e17	−	1.27260e17i	0.00709797	−	0.00709797i	0.710647	+	0.703549i	$0.248402\pi$
$564$			2.17937e17i			0.0120054i
$565$	−6.53962e18	−	6.53962e18i	−0.355806	−	0.355806i
$566$	9.07713e18	−	9.07713e18i	0.487791	−	0.487791i
$567$	2.83695e19			1.50581
$568$	3.72621e18	+	3.72621e18i	0.195357	+	0.195357i
$569$	5.10535e18	−	5.10535e18i	0.264387	−	0.264387i	−0.562447	−	0.826833i	$-0.690140\pi$
$569$	5.10535e18	−	5.10535e18i	0.264387	−	0.264387i	0.826833	+	0.562447i	$0.190140\pi$
$570$	1.42556e19	+	1.42556e19i	0.729224	+	0.729224i
$571$	4.67272e17			0.0236111			0.0118056	−	0.999930i	$-0.496242\pi$
$571$	4.67272e17			0.0236111			0.0118056	+	0.999930i	$0.496242\pi$
$572$	−1.01608e19	−	1.01608e19i	−0.507171	−	0.507171i
$573$		−	1.68121e19i		−	0.828972i
$574$	−3.51203e19			−1.71070
$575$	−1.90842e19			−0.918328
$576$	−2.79651e18			−0.132941
$577$	−7.19214e18	+	7.19214e18i	−0.337775	+	0.337775i	−0.855529	−	0.517754i	$-0.826768\pi$
$577$	−7.19214e18	+	7.19214e18i	−0.337775	+	0.337775i	0.517754	+	0.855529i	$0.326768\pi$
$578$	−9.17017e18	+	9.17017e18i	−0.425483	+	0.425483i
$579$			5.33056e17i			0.0244356i
$580$	−3.70723e18	−	5.99187e18i	−0.167901	−	0.271373i
$581$	4.00167e19			1.79064
$582$	2.84262e19	+	2.84262e19i	1.25678	+	1.25678i
$583$	−9.37973e18	−	9.37973e18i	−0.409742	−	0.409742i
$584$			1.21402e19i			0.524006i
$585$			4.99675e18i			0.213106i
$586$		−	1.99731e18i		−	0.0841709i
$587$	−3.02626e19			−1.26020			−0.630101	−	0.776514i	$-0.716986\pi$
$587$	−3.02626e19			−1.26020			−0.630101	+	0.776514i	$0.716986\pi$
$588$	−6.79182e18	+	6.79182e18i	−0.279476	+	0.279476i
$589$			3.55150e19i			1.44412i
$590$	9.00353e18	−	9.00353e18i	0.361783	−	0.361783i
$591$	8.60316e17	+	8.60316e17i	0.0341622	+	0.0341622i
$592$	2.10200e19	−	2.10200e19i	0.824862	−	0.824862i
$593$		−	2.80716e19i		−	1.08864i	−0.838878	−	0.544319i	$-0.816788\pi$
$593$		−	2.80716e19i		−	1.08864i	0.838878	−	0.544319i	$-0.183212\pi$
$594$	1.48306e19	+	1.48306e19i	0.568399	+	0.568399i
$595$	7.58780e18	−	7.58780e18i	0.287407	−	0.287407i
$596$	−3.24233e19			−1.21376
$597$	−3.31952e19	−	3.31952e19i	−1.22816	−	1.22816i
$598$	3.47661e19	−	3.47661e19i	1.27130	−	1.27130i
$599$	−2.48893e19	−	2.48893e19i	−0.899548	−	0.899548i	0.0958484	−	0.995396i	$-0.469444\pi$
$599$	−2.48893e19	−	2.48893e19i	−0.899548	−	0.899548i	−0.995396	+	0.0958484i	$0.969444\pi$
$600$	−1.02271e19			−0.365336
$601$	−1.04019e19	−	1.04019e19i	−0.367273	−	0.367273i	0.499209	−	0.866482i	$-0.333624\pi$
$601$	−1.04019e19	−	1.04019e19i	−0.367273	−	0.367273i	−0.866482	+	0.499209i	$0.833624\pi$
$602$			7.38405e19i			2.57703i
$603$	−7.61478e18			−0.262686
$604$	−7.47633e18			−0.254935
$605$	3.50476e18			0.118133
$606$	6.95787e18	−	6.95787e18i	0.231829	−	0.231829i
$607$	5.93544e18	−	5.93544e18i	0.195494	−	0.195494i	−0.602571	−	0.798065i	$-0.705857\pi$
$607$	5.93544e18	−	5.93544e18i	0.195494	−	0.195494i	0.798065	+	0.602571i	$0.205857\pi$
$608$		−	5.36199e19i		−	1.74582i
$609$	−1.02218e19	+	4.33951e19i	−0.329007	+	1.39675i
$610$	2.27082e19			0.722559
$611$	−3.88336e17	−	3.88336e17i	−0.0122157	−	0.0122157i
$612$	4.59567e18	+	4.59567e18i	0.142919	+	0.142919i
$613$		−	4.18993e19i		−	1.28820i	−0.764941	−	0.644101i	$-0.777232\pi$
$613$		−	4.18993e19i		−	1.28820i	0.764941	−	0.644101i	$-0.222768\pi$
$614$			4.42702e19i			1.34565i
$615$			1.93075e19i			0.580230i
$616$	1.37543e19			0.408670
$617$	2.95586e19	−	2.95586e19i	0.868336	−	0.868336i	−0.123952	−	0.992288i	$-0.539557\pi$
$617$	2.95586e19	−	2.95586e19i	0.868336	−	0.868336i	0.992288	+	0.123952i	$0.0395568\pi$
$618$		−	4.68437e19i		−	1.36060i
$619$	−2.56365e19	+	2.56365e19i	−0.736247	+	0.736247i	−0.971849	−	0.235603i	$-0.924294\pi$
$619$	−2.56365e19	+	2.56365e19i	−0.736247	+	0.736247i	0.235603	+	0.971849i	$0.424294\pi$
$620$	−7.80264e18	−	7.80264e18i	−0.221564	−	0.221564i
$621$	−2.09031e19	+	2.09031e19i	−0.586908	+	0.586908i
$622$			4.84378e19i			1.34478i
$623$	−2.45464e19	−	2.45464e19i	−0.673862	−	0.673862i
$624$	4.42540e19	−	4.42540e19i	1.20133	−	1.20133i
$625$	1.56631e19			0.420453
$626$	3.45778e19	+	3.45778e19i	0.917862	+	0.917862i
$627$	4.02453e19	−	4.02453e19i	1.05643	−	1.05643i
$628$	8.03167e18	+	8.03167e18i	0.208492	+	0.208492i
$629$	−2.75647e19			−0.707618
$630$	7.90929e18	+	7.90929e18i	0.200795	+	0.200795i
$631$		−	3.83414e19i		−	0.962637i	−0.876546	−	0.481319i	$-0.840158\pi$
$631$		−	3.83414e19i		−	0.962637i	0.876546	−	0.481319i	$-0.159842\pi$
$632$	−8.42032e18			−0.209078
$633$	−3.48035e19			−0.854667
$634$	6.84726e19			1.66300
$635$	2.21968e19	−	2.21968e19i	0.533180	−	0.533180i
$636$	−1.65688e19	+	1.65688e19i	−0.393633	+	0.393633i
$637$		−	2.42043e19i		−	0.568744i
$638$	−4.10647e19	+	2.54071e19i	−0.954385	+	0.590488i
$639$	1.20984e19			0.278113
$640$	−1.05708e19	−	1.05708e19i	−0.240351	−	0.240351i
$641$	4.37186e19	+	4.37186e19i	0.983240	+	0.983240i	0.999862	−	0.0166214i	$-0.00529100\pi$
$641$	4.37186e19	+	4.37186e19i	0.983240	+	0.983240i	−0.0166214	+	0.999862i	$0.505291\pi$
$642$		−	8.70626e19i		−	1.93681i
$643$		−	7.90623e19i		−	1.73977i	−0.493252	−	0.869887i	$-0.664192\pi$
$643$		−	7.90623e19i		−	1.73977i	0.493252	−	0.869887i	$-0.335808\pi$
$644$		−	4.53377e19i		−	0.986867i
$645$	4.05941e19			0.874068
$646$	−4.67254e19	+	4.67254e19i	−0.995234	+	0.995234i
$647$			3.86248e19i			0.813834i	0.913465	+	0.406917i	$0.133396\pi$
$647$			3.86248e19i			0.813834i	−0.913465	+	0.406917i	$0.866604\pi$
$648$	−1.64115e19	+	1.64115e19i	−0.342077	+	0.342077i
$649$	−2.54181e19	−	2.54181e19i	−0.524119	−	0.524119i
$650$	−4.26184e19	+	4.26184e19i	−0.869369	+	0.869369i
$651$			6.98202e19i			1.40901i
$652$	4.81661e18	+	4.81661e18i	0.0961630	+	0.0961630i
$653$	−2.53171e17	+	2.53171e17i	−0.00500059	+	0.00500059i	−0.709603	−	0.704602i	$-0.751126\pi$
$653$	−2.53171e17	+	2.53171e17i	−0.00500059	+	0.00500059i	0.704602	+	0.709603i	$0.251126\pi$
$654$	−2.52509e19			−0.493437
$655$	−1.31685e18	−	1.31685e18i	−0.0254594	−	0.0254594i
$656$	4.82586e19	−	4.82586e19i	0.923097	−	0.923097i
$657$	1.97086e19	+	1.97086e19i	0.372991	+	0.372991i
$658$	−1.22939e18			−0.0230201
$659$	2.00340e19	+	2.00340e19i	0.371168	+	0.371168i	0.867903	−	0.496735i	$-0.165468\pi$
$659$	2.00340e19	+	2.00340e19i	0.371168	+	0.371168i	−0.496735	+	0.867903i	$0.665468\pi$
$660$			1.76838e19i			0.324166i
$661$	2.89400e19			0.524914			0.262457	−	0.964944i	$-0.415467\pi$
$661$	2.89400e19			0.524914			0.262457	+	0.964944i	$0.415467\pi$
$662$	5.82865e19			1.04607
$663$	−5.80326e19			−1.03057
$664$	−2.31494e19	+	2.31494e19i	−0.406783	+	0.406783i
$665$	−3.31258e19	+	3.31258e19i	−0.575989	+	0.575989i
$666$		−	2.87326e19i		−	0.494374i
$667$	−3.58104e19	−	5.78790e19i	−0.609717	−	0.985463i
$668$	5.37432e19			0.905500
$669$	9.26038e19	+	9.26038e19i	1.54400	+	1.54400i
$670$	1.70095e19	+	1.70095e19i	0.280652	+	0.280652i
$671$		−	6.41080e19i		−	1.04678i
$672$		−	1.05413e20i		−	1.70338i
$673$			8.66108e19i			1.38505i	0.721392	+	0.692527i	$0.243503\pi$
$673$			8.66108e19i			1.38505i	−0.721392	+	0.692527i	$0.756497\pi$
$674$	1.58900e20			2.51480
$675$	2.56244e19	−	2.56244e19i	0.401353	−	0.401353i
$676$		−	1.87758e19i		−	0.291053i
$677$	7.84231e18	−	7.84231e18i	0.120316	−	0.120316i	−0.644385	−	0.764701i	$-0.722887\pi$
$677$	7.84231e18	−	7.84231e18i	0.120316	−	0.120316i	0.764701	+	0.644385i	$0.222887\pi$
$678$	7.91698e19	+	7.91698e19i	1.20213	+	1.20213i
$679$	−6.60541e19	+	6.60541e19i	−0.992685	+	0.992685i
$680$			8.77897e18i			0.130581i
$681$	−1.06686e20	−	1.06686e20i	−1.57064	−	1.57064i
$682$	−5.34746e19	+	5.34746e19i	−0.779214	+	0.779214i
$683$	−1.03276e19			−0.148954			−0.0744772	−	0.997223i	$-0.523729\pi$
$683$	−1.03276e19			−0.148954			−0.0744772	+	0.997223i	$0.523729\pi$
$684$	−2.00632e19	−	2.00632e19i	−0.286422	−	0.286422i
$685$	2.43820e18	−	2.43820e18i	0.0344536	−	0.0344536i
$686$	4.18333e19	+	4.18333e19i	0.585132	+	0.585132i
$687$	−7.36975e19			−1.02037
$688$	−1.01464e20	−	1.01464e20i	−1.39057	−	1.39057i
$689$		−	5.90470e19i		−	0.801056i
$690$	−6.05068e19			−0.812570
$691$	−9.41777e19			−1.25199			−0.625996	−	0.779826i	$-0.715307\pi$
$691$	−9.41777e19			−1.25199			−0.625996	+	0.779826i	$0.715307\pi$
$692$	1.42129e19			0.187043
$693$	2.23289e19	−	2.23289e19i	0.290894	−	0.290894i
$694$	8.05217e18	−	8.05217e18i	0.103848	−	0.103848i
$695$			1.52507e19i			0.194714i
$696$	−1.91905e19	−	3.10170e19i	−0.242562	−	0.392044i
$697$	−6.32840e19			−0.791890
$698$	2.77067e18	+	2.77067e18i	0.0343239	+	0.0343239i
$699$	7.64385e19	+	7.64385e19i	0.937502	+	0.937502i
$700$			5.55779e19i			0.674863i
$701$			1.18080e20i			1.41954i	0.704432	+	0.709771i	$0.251202\pi$
$701$			1.18080e20i			1.41954i	−0.704432	+	0.709771i	$0.748798\pi$
$702$			9.33610e19i			1.11124i
$703$	1.20338e20			1.41813
$704$	1.76352e19	−	1.76352e19i	0.205765	−	0.205765i
$705$			6.75860e17i			0.00780788i
$706$	−1.18464e20	+	1.18464e20i	−1.35504	+	1.35504i
$707$	1.61680e19	+	1.61680e19i	0.183114	+	0.183114i
$708$	−4.48998e19	+	4.48998e19i	−0.503514	+	0.503514i
$709$		−	1.36826e20i		−	1.51931i	−0.650327	−	0.759654i	$-0.725368\pi$
$709$		−	1.36826e20i		−	1.51931i	0.650327	−	0.759654i	$-0.274632\pi$
$710$	−2.70248e19	−	2.70248e19i	−0.297135	−	0.297135i
$711$	−1.36697e19	+	1.36697e19i	−0.148824	+	0.148824i
$712$	2.83998e19			0.306165
$713$	−7.53703e19	−	7.53703e19i	−0.804588	−	0.804588i
$714$	−9.18592e19	+	9.18592e19i	−0.971036	+	0.971036i
$715$	−3.15103e19	−	3.15103e19i	−0.329845	−	0.329845i
$716$	6.72708e19			0.697325
$717$	−1.08070e20	−	1.08070e20i	−1.10936	−	1.10936i
$718$		−	1.74705e20i		−	1.77596i
$719$	4.80359e19			0.483575			0.241787	−	0.970329i	$-0.422266\pi$
$719$	4.80359e19			0.483575			0.241787	+	0.970329i	$0.422266\pi$
$720$	−2.17362e19			−0.216699
$721$	1.08851e20			1.07469
$722$	1.09683e20	−	1.09683e20i	1.07246	−	1.07246i
$723$	−1.21260e20	+	1.21260e20i	−1.17422	+	1.17422i
$724$		−	1.62454e19i		−	0.155797i
$725$	4.38986e19	+	7.09518e19i	0.416951	+	0.673903i
$726$	−4.24293e19			−0.399125
$727$	1.05588e20	+	1.05588e20i	0.983727	+	0.983727i	0.999870	−	0.0161428i	$-0.00513865\pi$
$727$	1.05588e20	+	1.05588e20i	0.983727	+	0.983727i	−0.0161428	+	0.999870i	$0.505139\pi$
$728$	4.32927e19	+	4.32927e19i	0.399480	+	0.399480i
$729$		−	3.92184e19i		−	0.358424i
$730$		−	8.80483e19i		−	0.797005i
$731$			1.33055e20i			1.19291i
$732$	−1.13243e20			−1.00562
$733$	7.07271e19	−	7.07271e19i	0.622097	−	0.622097i	−0.323970	−	0.946067i	$-0.605018\pi$
$733$	7.07271e19	−	7.07271e19i	0.622097	−	0.622097i	0.946067	+	0.323970i	$0.105018\pi$
$734$			1.23882e20i			1.07928i
$735$	−2.10626e19	+	2.10626e19i	−0.181761	+	0.181761i
$736$	1.13793e20	+	1.13793e20i	0.972680	+	0.972680i
$737$	4.80200e19	−	4.80200e19i	0.406583	−	0.406583i
$738$		−	6.59654e19i		−	0.553250i
$739$	−6.70825e19	−	6.70825e19i	−0.557312	−	0.557312i	0.371229	−	0.928541i	$-0.378936\pi$
$739$	−6.70825e19	−	6.70825e19i	−0.557312	−	0.557312i	−0.928541	+	0.371229i	$0.878936\pi$
$740$	−2.64383e19	+	2.64383e19i	−0.217576	+	0.217576i
$741$	2.53351e20			2.06536
$742$	−9.34648e19	−	9.34648e19i	−0.754780	−	0.754780i
$743$	−1.28673e20	+	1.28673e20i	−1.02936	+	1.02936i	−0.0298031	+	0.999556i	$0.509488\pi$
$743$	−1.28673e20	+	1.28673e20i	−1.02936	+	1.02936i	−0.999556	+	0.0298031i	$0.990512\pi$
$744$	−4.03905e19	−	4.03905e19i	−0.320087	−	0.320087i
$745$	−1.00550e20			−0.789386
$746$	−3.73841e19	−	3.73841e19i	−0.290747	−	0.290747i
$747$			7.51622e19i			0.579103i
$748$	−5.79620e19			−0.442417
$749$	2.02308e20			1.52982
$750$	1.67772e20			1.25687
$751$	−1.16948e20	+	1.16948e20i	−0.867985	+	0.867985i	−0.992249	−	0.124265i	$-0.960343\pi$
$751$	−1.16948e20	+	1.16948e20i	−0.867985	+	0.867985i	0.124265	+	0.992249i	$0.460343\pi$
$752$	1.68929e18	−	1.68929e18i	0.0124217	−	0.0124217i
$753$		−	2.15416e20i		−	1.56932i
$754$	−2.09226e20	−	4.92834e19i	−1.51013	−	0.355714i
$755$	−2.31854e19			−0.165800
$756$	6.08752e19	+	6.08752e19i	0.431308	+	0.431308i
$757$	−1.63672e20	−	1.63672e20i	−1.14896	−	1.14896i	−0.986758	−	0.162198i	$-0.948142\pi$
$757$	−1.63672e20	−	1.63672e20i	−1.14896	−	1.14896i	−0.162198	−	0.986758i	$-0.551858\pi$
$758$		−	3.19348e20i		−	2.22116i
$759$			1.70818e20i			1.17718i
$760$		−	3.83260e19i		−	0.261697i
$761$	2.55455e20			1.72831			0.864154	−	0.503227i	$-0.167854\pi$
$761$	2.55455e20			1.72831			0.864154	+	0.503227i	$0.167854\pi$
$762$	−2.68718e20	+	2.68718e20i	−1.80141	+	1.80141i
$763$		−	5.86755e19i		−	0.389749i
$764$	5.28531e19	−	5.28531e19i	0.347870	−	0.347870i
$765$	1.42519e19	+	1.42519e19i	0.0929489	+	0.0929489i
$766$	−1.27433e20	+	1.27433e20i	−0.823531	+	0.823531i
$767$		−	1.60011e20i		−	1.02467i
$768$	1.72443e20	+	1.72443e20i	1.09425	+	1.09425i
$769$	−1.29145e20	+	1.29145e20i	−0.812071	+	0.812071i	−0.984944	−	0.172873i	$-0.944695\pi$
$769$	−1.29145e20	+	1.29145e20i	−0.812071	+	0.812071i	0.172873	+	0.984944i	$0.444695\pi$
$770$	−9.97545e19			−0.621580
$771$	−2.58978e19	−	2.58978e19i	−0.159912	−	0.159912i
$772$	−1.67580e18	+	1.67580e18i	−0.0102542	+	0.0102542i
$773$	1.61673e20	+	1.61673e20i	0.980351	+	0.980351i	0.999811	−	0.0194597i	$-0.00619462\pi$
$773$	1.61673e20	+	1.61673e20i	0.980351	+	0.980351i	−0.0194597	+	0.999811i	$0.506195\pi$
$774$	−1.38692e20			−0.833424
$775$	9.23937e19	+	9.23937e19i	0.550213	+	0.550213i
$776$		−	7.64236e19i		−	0.451020i
$777$	2.36577e20			1.38365
$778$	2.83672e19			0.164422
$779$	2.76277e20			1.58702
$780$	−5.56612e19	+	5.56612e19i	−0.316877	+	0.316877i
$781$	−7.62944e19	+	7.62944e19i	−0.430463	+	0.430463i
$782$		−	1.98323e20i		−	1.10898i
$783$	1.25797e20	+	2.96317e19i	0.697170	+	0.164219i
$784$	1.05291e20			0.578332
$785$	2.49076e19	+	2.49076e19i	0.135595	+	0.135595i
$786$	1.59420e19	+	1.59420e19i	0.0860174	+	0.0860174i
$787$		−	2.02576e20i		−	1.08334i	−0.840591	−	0.541670i	$-0.817792\pi$
$787$		−	2.02576e20i		−	1.08334i	0.840591	−	0.541670i	$-0.182208\pi$
$788$			5.40924e18i			0.0286717i
$789$			1.05830e20i			0.555992i
$790$	6.10694e19			0.318005
$791$	−1.83967e20	+	1.83967e20i	−0.949523	+	0.949523i
$792$			2.58342e19i			0.132166i
$793$	2.01785e20	−	2.01785e20i	1.02324	−	1.02324i
$794$	2.47026e20	+	2.47026e20i	1.24165	+	1.24165i
$795$	−5.13826e19	+	5.13826e19i	−0.256004	+	0.256004i
$796$		−	2.08715e20i		−	1.03077i
$797$	1.96272e20	+	1.96272e20i	0.960836	+	0.960836i	0.999261	−	0.0384251i	$-0.0122341\pi$
$797$	1.96272e20	+	1.96272e20i	0.960836	+	0.960836i	−0.0384251	+	0.999261i	$0.512234\pi$
$798$	4.01026e20	−	4.01026e20i	1.94604	−	1.94604i
$799$	−2.21526e18			−0.0106561
$800$	−1.39494e20	−	1.39494e20i	−0.665161	−	0.665161i
$801$	4.61048e19	−	4.61048e19i	0.217931	−	0.217931i
$802$	6.79631e19	+	6.79631e19i	0.318458	+	0.318458i
$803$	−2.48571e20			−1.15463
$804$	−8.48248e19	−	8.48248e19i	−0.390599	−	0.390599i
$805$		−	1.40600e20i		−	0.641821i
$806$	−3.36632e20			−1.52339
$807$	−3.48805e20			−1.56483
$808$	−1.87062e19			−0.0831965
$809$	−1.69526e20	+	1.69526e20i	−0.747473	+	0.747473i	−0.974004	−	0.226531i	$-0.927262\pi$
$809$	−1.69526e20	+	1.69526e20i	−0.747473	+	0.747473i	0.226531	+	0.974004i	$0.427262\pi$
$810$	1.19027e20	−	1.19027e20i	0.520294	−	0.520294i
$811$			2.18905e19i			0.0948656i	0.998874	+	0.0474328i	$0.0151040\pi$
$811$			2.18905e19i			0.0948656i	−0.998874	+	0.0474328i	$0.984896\pi$
$812$	−1.68558e20	+	1.04289e20i	−0.724199	+	0.448070i
$813$	2.36263e20			1.00638
$814$	1.81192e20	+	1.81192e20i	0.765189	+	0.765189i
$815$	1.49371e19	+	1.49371e19i	0.0625408	+	0.0625408i
$816$		−	2.52447e20i		−	1.04794i
$817$		−	5.80873e20i		−	2.39071i
$818$		−	5.44332e19i		−	0.222122i
$819$	1.40564e20			0.568706
$820$	−6.06980e19	+	6.06980e19i	−0.243488	+	0.243488i
$821$		−	1.89444e20i		−	0.753492i	−0.926317	−	0.376746i	$-0.877043\pi$
$821$		−	1.89444e20i		−	0.753492i	0.926317	−	0.376746i	$-0.122957\pi$
$822$	−2.95172e19	+	2.95172e19i	−0.116405	+	0.116405i
$823$	1.82560e20	+	1.82560e20i	0.713851	+	0.713851i	0.967339	−	0.253488i	$-0.0815778\pi$
$823$	1.82560e20	+	1.82560e20i	0.713851	+	0.713851i	−0.253488	+	0.967339i	$0.581578\pi$
$824$	−6.29694e19	+	6.29694e19i	−0.244140	+	0.244140i
$825$		−	2.09400e20i		−	0.805005i
$826$	−2.53280e20	−	2.53280e20i	−0.965474	−	0.965474i
$827$	5.62285e19	−	5.62285e19i	0.212529	−	0.212529i	−0.592812	−	0.805341i	$-0.701982\pi$
$827$	5.62285e19	−	5.62285e19i	0.212529	−	0.212529i	0.805341	+	0.592812i	$0.201982\pi$
$828$	8.51566e19			0.319158
$829$	−1.13021e20	−	1.13021e20i	−0.420026	−	0.420026i	0.465187	−	0.885213i	$-0.345987\pi$
$829$	−1.13021e20	−	1.13021e20i	−0.420026	−	0.420026i	−0.885213	+	0.465187i	$0.845987\pi$
$830$	1.67894e20	−	1.67894e20i	0.618711	−	0.618711i
$831$	−2.49291e20	−	2.49291e20i	−0.910959	−	0.910959i
$832$	1.11017e20			0.402276
$833$	−6.90366e19	−	6.90366e19i	−0.248064	−	0.248064i
$834$		−	1.84628e20i		−	0.657863i
$835$	1.66667e20			0.588903
$836$	2.53043e20			0.886645
$837$	2.02400e20			0.703287
$838$	−2.44706e19	+	2.44706e19i	−0.0843213	+	0.0843213i
$839$	−3.69553e20	+	3.69553e20i	−1.26282	+	1.26282i	−0.313106	+	0.949718i	$0.601370\pi$
$839$	−3.69553e20	+	3.69553e20i	−1.26282	+	1.26282i	−0.949718	+	0.313106i	$0.898630\pi$
$840$		−	7.53466e19i		−	0.255334i
$841$	−1.32812e20	+	2.66274e20i	−0.446338	+	0.894864i
$842$	−7.32685e20			−2.44193
$843$	4.16773e20	+	4.16773e20i	1.37755	+	1.37755i
$844$	−1.09414e20	−	1.09414e20i	−0.358653	−	0.358653i
$845$		−	5.82270e19i		−	0.189290i
$846$		−	2.30912e18i		−	0.00744482i
$847$		−	9.85931e19i		−	0.315256i
$848$	2.56859e20			0.814561
$849$	−1.40380e20	+	1.40380e20i	−0.441521	+	0.441521i
$850$			2.43116e20i			0.758371i
$851$	−2.55383e20	+	2.55383e20i	−0.790107	+	0.790107i
$852$	1.34770e20	+	1.34770e20i	0.413539	+	0.413539i
$853$	1.04873e20	−	1.04873e20i	0.319168	−	0.319168i	−0.529280	−	0.848448i	$-0.677538\pi$
$853$	1.04873e20	−	1.04873e20i	0.319168	−	0.319168i	0.848448	+	0.529280i	$0.177538\pi$
$854$		−	6.38807e20i		−	1.92826i
$855$	−6.22192e19	−	6.22192e19i	−0.186278	−	0.186278i
$856$	−1.17034e20	+	1.17034e20i	−0.347531	+	0.347531i
$857$	−1.20069e20			−0.353643			−0.176822	−	0.984243i	$-0.556582\pi$
$857$	−1.20069e20			−0.353643			−0.176822	+	0.984243i	$0.556582\pi$
$858$	3.81469e20	+	3.81469e20i	1.11442	+	1.11442i
$859$	−3.39793e20	+	3.39793e20i	−0.984607	+	0.984607i	−0.999883	−	0.0152763i	$-0.995137\pi$
$859$	−3.39793e20	+	3.39793e20i	−0.984607	+	0.984607i	0.0152763	+	0.999883i	$0.495137\pi$
$860$	1.27618e20	+	1.27618e20i	0.366794	+	0.366794i
$861$	5.43143e20			1.54843
$862$	−7.92526e19	−	7.92526e19i	−0.224111	−	0.224111i
$863$			4.08380e20i			1.14548i	0.819736	+	0.572742i	$0.194120\pi$
$863$			4.08380e20i			1.14548i	−0.819736	+	0.572742i	$0.805880\pi$
$864$	−3.05580e20			−0.850215
$865$	4.40767e19			0.121645
$866$	−6.52640e20			−1.78669
$867$	1.41819e20	−	1.41819e20i	0.385124	−	0.385124i
$868$	−2.19497e20	+	2.19497e20i	−0.591278	+	0.591278i
$869$		−	1.72407e20i		−	0.460697i
$870$	1.39182e20	+	2.24954e20i	0.368933	+	0.596293i
$871$	3.02294e20			0.794882
$872$	3.39434e19	+	3.39434e19i	0.0885400	+	0.0885400i
$873$	−1.24068e20	−	1.24068e20i	−0.321040	−	0.321040i
$874$			8.65810e20i			2.22250i
$875$			3.89852e20i			0.992757i
$876$			4.39088e20i			1.10923i
$877$	6.86133e20			1.71954			0.859768	−	0.510684i	$-0.170608\pi$
$877$	6.86133e20			1.71954			0.859768	+	0.510684i	$0.170608\pi$
$878$	−6.07321e20	+	6.07321e20i	−1.50993	+	1.50993i
$879$			3.08889e19i			0.0761868i
$880$	1.37072e20	−	1.37072e20i	0.335406	−	0.335406i
$881$	−1.01291e20	−	1.01291e20i	−0.245890	−	0.245890i	0.573392	−	0.819281i	$-0.305627\pi$
$881$	−1.01291e20	−	1.01291e20i	−0.245890	−	0.245890i	−0.819281	+	0.573392i	$0.805627\pi$
$882$	7.19617e19	−	7.19617e19i	0.173309	−	0.173309i
$883$			5.79509e20i			1.38463i	0.721593	+	0.692317i	$0.243410\pi$
$883$			5.79509e20i			1.38463i	−0.721593	+	0.692317i	$0.756590\pi$
$884$	−1.82440e20	−	1.82440e20i	−0.432469	−	0.432469i
$885$	−1.39242e20	+	1.39242e20i	−0.327466	+	0.327466i
$886$	−2.46065e20			−0.574134
$887$	9.65407e19	+	9.65407e19i	0.223483	+	0.223483i	0.809964	−	0.586480i	$-0.199487\pi$
$887$	9.65407e19	+	9.65407e19i	0.223483	+	0.223483i	−0.586480	+	0.809964i	$0.699487\pi$
$888$	−1.36858e20	+	1.36858e20i	−0.314326	+	0.314326i
$889$	−6.24421e20	−	6.24421e20i	−1.42287	−	1.42287i
$890$	−2.05973e20			−0.465672
$891$	−3.36027e20	−	3.36027e20i	−0.753755	−	0.753755i
$892$			5.82247e20i			1.29585i
$893$	9.67108e18			0.0213558
$894$	1.21728e21			2.66703
$895$	2.08618e20			0.453514
$896$	−2.97368e20	+	2.97368e20i	−0.641413	+	0.641413i
$897$	−5.37665e20	+	5.37665e20i	−1.15071	+	1.15071i
$898$		−	4.78552e20i		−	1.01624i
$899$	−1.06843e20	+	4.53586e20i	−0.225127	+	0.955745i
$900$	−1.04390e20			−0.218254
$901$	−1.68416e20	−	1.68416e20i	−0.349390	−	0.349390i
$902$	4.15988e20	+	4.15988e20i	0.856318	+	0.856318i
$903$		−	1.14196e21i		−	2.33258i
$904$		−	2.12847e20i		−	0.431409i
$905$		−	5.03796e19i		−	0.101324i
$906$	2.80686e20			0.560175
$907$	9.50950e19	−	9.50950e19i	0.188324	−	0.188324i	−0.606647	−	0.794971i	$-0.707486\pi$
$907$	9.50950e19	−	9.50950e19i	0.188324	−	0.188324i	0.794971	+	0.606647i	$0.207486\pi$
$908$		−	6.70787e20i		−	1.31821i
$909$	−3.03679e19	+	3.03679e19i	−0.0592200	+	0.0592200i
$910$	−3.13986e20	−	3.13986e20i	−0.607603	−	0.607603i
$911$	5.90623e20	−	5.90623e20i	1.13418	−	1.13418i	0.144703	−	0.989475i	$-0.453777\pi$
$911$	5.90623e20	−	5.90623e20i	1.13418	−	1.13418i	0.989475	−	0.144703i	$-0.0462228\pi$
$912$			1.10210e21i			2.10018i
$913$	−4.73985e20	−	4.73985e20i	−0.896332	−	0.896332i
$914$	7.85073e20	−	7.85073e20i	1.47328	−	1.47328i
$915$	−3.51187e20			−0.654020
$916$	−2.31687e20	−	2.31687e20i	−0.428187	−	0.428187i
$917$	−3.70446e19	+	3.70446e19i	−0.0679422	+	0.0679422i
$918$	2.66289e20	+	2.66289e20i	0.484678	+	0.484678i
$919$	2.81911e20			0.509218			0.254609	−	0.967044i	$-0.418053\pi$
$919$	2.81911e20			0.509218			0.254609	+	0.967044i	$0.418053\pi$
$920$	8.13360e19	+	8.13360e19i	0.145804	+	0.145804i
$921$		−	6.84649e20i		−	1.21801i
$922$	4.73238e20			0.835531
$923$	−4.80286e20			−0.841566
$924$	4.97466e20			0.865087
$925$	3.13065e20	−	3.13065e20i	0.540309	−	0.540309i
$926$	2.93957e20	−	2.93957e20i	0.503509	−	0.503509i
$927$			2.04451e20i			0.347562i
$928$	1.61310e20	−	6.84817e20i	0.272160	−	1.15542i
$929$	−9.09066e20			−1.52225			−0.761124	−	0.648606i	$-0.775352\pi$
$929$	−9.09066e20			−1.52225			−0.761124	+	0.648606i	$0.775352\pi$
$930$	2.92937e20	+	2.92937e20i	0.486848	+	0.486848i
$931$	3.01391e20	+	3.01391e20i	0.497144	+	0.497144i
$932$			4.80608e20i			0.786827i
$933$		−	7.49102e20i		−	1.21722i
$934$		−	8.36324e20i		−	1.34880i
$935$	−1.79750e20			−0.287732
$936$	−8.13154e19	+	8.13154e19i	−0.129194	+	0.129194i
$937$			1.19648e21i			1.88681i	0.331649	+	0.943403i	$0.392395\pi$
$937$			1.19648e21i			1.88681i	−0.331649	+	0.943403i	$0.607605\pi$
$938$	4.78498e20	−	4.78498e20i	0.748962	−	0.748962i
$939$	−5.34754e20	−	5.34754e20i	−0.830798	−	0.830798i
$940$	−2.12474e18	+	2.12474e18i	−0.00327650	+	0.00327650i
$941$			5.96329e20i			0.912764i	0.889784	+	0.456382i	$0.150855\pi$
$941$			5.96329e20i			0.912764i	−0.889784	+	0.456382i	$0.849145\pi$
$942$	−3.01535e20	−	3.01535e20i	−0.458123	−	0.458123i
$943$	−5.86318e20	+	5.86318e20i	−0.884202	+	0.884202i
$944$	6.96061e20			1.04194
$945$	1.88784e20	+	1.88784e20i	0.280506	+	0.280506i
$946$	8.74616e20	−	8.74616e20i	1.28997	−	1.28997i
$947$	−8.10530e20	−	8.10530e20i	−1.18664	−	1.18664i	−0.977990	−	0.208650i	$-0.933093\pi$
$947$	−8.10530e20	−	8.10530e20i	−1.18664	−	1.18664i	−0.208650	−	0.977990i	$-0.566907\pi$
$948$	−3.04547e20			−0.442585
$949$	−7.82399e20	−	7.82399e20i	−1.12866	−	1.12866i
$950$		−	1.06136e21i		−	1.51984i
$951$	−1.05894e21			−1.50525
$952$	2.46963e20			0.348476
$953$	1.33133e20			0.186481			0.0932405	−	0.995644i	$-0.470277\pi$
$953$	1.33133e20			0.186481			0.0932405	+	0.995644i	$0.470277\pi$
$954$	1.75552e20	−	1.75552e20i	0.244100	−	0.244100i
$955$	1.63906e20	−	1.63906e20i	0.226241	−	0.226241i
$956$		−	6.79492e20i		−	0.931063i
$957$	6.35075e20	−	3.92927e20i	0.863856	−	0.534477i
$958$	1.41719e21			1.91367
$959$	−6.85894e19	−	6.85894e19i	−0.0919447	−	0.0919447i
$960$	−9.66065e19	−	9.66065e19i	−0.128561	−	0.128561i
$961$		−	2.71503e19i		−	0.0358684i
$962$			1.14064e21i			1.49597i
$963$			3.79989e20i			0.494751i
$964$	−7.62421e20			−0.985497
$965$	−5.19692e18	+	5.19692e18i	−0.00666891	+	0.00666891i
$966$			1.70213e21i			2.16846i
$967$	−3.06494e20	+	3.06494e20i	−0.387647	+	0.387647i	−0.873847	−	0.486200i	$-0.838383\pi$
$967$	−3.06494e20	+	3.06494e20i	−0.387647	+	0.387647i	0.486200	+	0.873847i	$0.338383\pi$
$968$	5.70354e19	+	5.70354e19i	0.0716171	+	0.0716171i
$969$	7.22619e20	−	7.22619e20i	0.900830	−	0.900830i
$970$			5.54272e20i			0.685995i
$971$	6.66765e20	+	6.66765e20i	0.819292	+	0.819292i	0.986005	−	0.166714i	$-0.0533156\pi$
$971$	6.66765e20	+	6.66765e20i	0.819292	+	0.819292i	−0.166714	+	0.986005i	$0.553316\pi$
$972$	−3.02765e20	+	3.02765e20i	−0.369353	+	0.369353i
$973$	4.29021e20			0.519624
$974$	−6.34698e20	−	6.34698e20i	−0.763228	−	0.763228i
$975$	6.59104e20	−	6.59104e20i	0.786904	−	0.786904i
$976$	8.77782e20	+	8.77782e20i	1.04049	+	1.04049i
$977$	5.74534e20			0.676166			0.338083	−	0.941116i	$-0.390221\pi$
$977$	5.74534e20			0.676166			0.338083	+	0.941116i	$0.390221\pi$
$978$	−1.80831e20	−	1.80831e20i	−0.211301	−	0.211301i
$979$			5.81488e20i			0.674624i
$980$	−1.32431e20			−0.152548
$981$	1.10209e20			0.126047
$982$	1.39865e21			1.58828
$983$	−1.20379e20	+	1.20379e20i	−0.135730	+	0.135730i	−0.771708	−	0.635977i	$-0.780597\pi$
$983$	−1.20379e20	+	1.20379e20i	−0.135730	+	0.135730i	0.635977	+	0.771708i	$0.280597\pi$
$984$	−3.14204e20	+	3.14204e20i	−0.351760	+	0.351760i
$985$			1.67750e19i			0.0186470i
$986$	−7.37331e20	+	4.56194e20i	−0.813812	+	0.503514i
$987$	1.90127e19			0.0208365
$988$	7.96473e20	+	7.96473e20i	0.866708	+	0.866708i
$989$	1.23274e21	+	1.23274e21i	1.33198	+	1.33198i
$990$		−	1.87366e20i		−	0.201022i
$991$			7.11837e20i			0.758342i	0.925327	+	0.379171i	$0.123791\pi$
$991$			7.11837e20i			0.758342i	−0.925327	+	0.379171i	$0.876209\pi$
$992$		−	1.10183e21i		−	1.16555i
$993$	−9.01414e20			−0.946847
$994$	−7.60239e20	+	7.60239e20i	−0.792950	+	0.792950i
$995$		−	6.47261e20i		−	0.670375i
$996$	−8.37270e20	+	8.37270e20i	−0.861093	+	0.861093i
$997$	9.24495e20	+	9.24495e20i	0.944144	+	0.944144i	0.998521	−	0.0543761i	$-0.0173170\pi$
$997$	9.24495e20	+	9.24495e20i	0.944144	+	0.944144i	−0.0543761	+	0.998521i	$0.517317\pi$
$998$	−1.85264e20	+	1.85264e20i	−0.187878	+	0.187878i
$999$		−	6.85809e20i		−	0.690628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.15.c.a.12.8	✓	68
29.17	odd	4	inner	29.15.c.a.17.8	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.15.c.a.12.8	✓	68	1.1	even	1	trivial
29.15.c.a.17.8	yes	68	29.17	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(-118.027 - 118.027i) q^{2} +(1825.31 + 1825.31i) q^{3} +11476.7i q^{4} +35591.1i q^{5} -430872. i q^{6} +1.00122e6 q^{7} +(-579197. + 579197. i) q^{8} +1.88056e6i q^{9} +O(q^{10})\)	\(q+(-118.027 - 118.027i) q^{2} +(1825.31 + 1825.31i) q^{3} +11476.7i q^{4} +35591.1i q^{5} -430872. i q^{6} +1.00122e6 q^{7} +(-579197. + 579197. i) q^{8} +1.88056e6i q^{9} +(4.20070e6 - 4.20070e6i) q^{10} +(-1.18591e7 - 1.18591e7i) q^{11} +(-2.09485e7 + 2.09485e7i) q^{12} -7.46551e7i q^{13} +(-1.18171e8 - 1.18171e8i) q^{14} +(-6.49648e7 + 6.49648e7i) q^{15} +3.24755e8 q^{16} +(-2.12934e8 - 2.12934e8i) q^{17} +(2.21957e8 - 2.21957e8i) q^{18} +(9.29600e8 + 9.29600e8i) q^{19} -4.08467e8 q^{20} +(1.82754e9 + 1.82754e9i) q^{21} +2.79938e9i q^{22} -3.94562e9 q^{23} -2.11443e9 q^{24} +4.83679e9 q^{25} +(-8.81130e9 + 8.81130e9i) q^{26} +(5.29780e9 - 5.29780e9i) q^{27} +1.14906e10i q^{28} +(9.07598e9 + 1.46692e10i) q^{29} +1.53352e10 q^{30} +(1.91023e10 + 1.91023e10i) q^{31} +(-2.88403e10 - 2.88403e10i) q^{32} -4.32931e10i q^{33} +5.02640e10i q^{34} +3.56344e10i q^{35} -2.15826e10 q^{36} +(6.47258e10 - 6.47258e10i) q^{37} -2.19436e11i q^{38} +(1.36269e11 - 1.36269e11i) q^{39} +(-2.06142e10 - 2.06142e10i) q^{40} +(1.48600e11 - 1.48600e11i) q^{41} -4.31397e11i q^{42} +(-3.12432e11 - 3.12432e11i) q^{43} +(1.36103e11 - 1.36103e11i) q^{44} -6.69311e10 q^{45} +(4.65689e11 + 4.65689e11i) q^{46} +(5.20174e9 - 5.20174e9i) q^{47} +(5.92780e11 + 5.92780e11i) q^{48} +3.24215e11 q^{49} +(-5.70871e11 - 5.70871e11i) q^{50} -7.77344e11i q^{51} +8.56791e11 q^{52} +7.90931e11 q^{53} -1.25057e12 q^{54} +(4.22078e11 - 4.22078e11i) q^{55} +(-5.79903e11 + 5.79903e11i) q^{56} +3.39362e12i q^{57} +(6.60148e11 - 2.80257e12i) q^{58} +2.14334e12 q^{59} +(-7.45579e11 - 7.45579e11i) q^{60} +(2.70290e12 + 2.70290e12i) q^{61} -4.50916e12i q^{62} +1.88285e12i q^{63} +1.48706e12i q^{64} +2.65705e12 q^{65} +(-5.10975e12 + 5.10975e12i) q^{66} +4.04921e12i q^{67} +(2.44378e12 - 2.44378e12i) q^{68} +(-7.20199e12 - 7.20199e12i) q^{69} +(4.20582e12 - 4.20582e12i) q^{70} -6.43340e12i q^{71} +(-1.08922e12 - 1.08922e12i) q^{72} +(1.04802e13 - 1.04802e13i) q^{73} -1.52788e13 q^{74} +(8.82866e12 + 8.82866e12i) q^{75} +(-1.06687e13 + 1.06687e13i) q^{76} +(-1.18736e13 - 1.18736e13i) q^{77} -3.21667e13 q^{78} +(7.26896e12 + 7.26896e12i) q^{79} +1.15584e13i q^{80} +2.83349e13 q^{81} -3.50775e13 q^{82} +3.99680e13 q^{83} +(-2.09740e13 + 2.09740e13i) q^{84} +(7.57856e12 - 7.57856e12i) q^{85} +7.37506e13i q^{86} +(-1.02093e13 + 4.33423e13i) q^{87} +1.37375e13 q^{88} +(-2.45165e13 - 2.45165e13i) q^{89} +(7.89967e12 + 7.89967e12i) q^{90} -7.47460e13i q^{91} -4.52826e13i q^{92} +6.97352e13i q^{93} -1.22789e12 q^{94} +(-3.30855e13 + 3.30855e13i) q^{95} -1.05285e14i q^{96} +(-6.59737e13 + 6.59737e13i) q^{97} +(-3.82661e13 - 3.82661e13i) q^{98} +(2.23018e13 - 2.23018e13i) 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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