LMFDB - Embedded newform 29.15.c.a.12.4

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			12.4
Character	$\chi$	$=$	29.12
Dual form			29.15.c.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-157.774 - 157.774i) q^{2} +(3020.51 + 3020.51i) q^{3} +33401.0i q^{4} +76455.0i q^{5} -953113. i q^{6} -1.19070e6 q^{7} +(2.68483e6 - 2.68483e6i) q^{8} +1.34640e7i q^{9} +O(q^{10})$	\(q+(-157.774 - 157.774i) q^{2} +(3020.51 + 3020.51i) q^{3} +33401.0i q^{4} +76455.0i q^{5} -953113. i q^{6} -1.19070e6 q^{7} +(2.68483e6 - 2.68483e6i) q^{8} +1.34640e7i q^{9} +(1.20626e7 - 1.20626e7i) q^{10} +(-2.59610e6 - 2.59610e6i) q^{11} +(-1.00888e8 + 1.00888e8i) q^{12} +1.02359e8i q^{13} +(1.87861e8 + 1.87861e8i) q^{14} +(-2.30933e8 + 2.30933e8i) q^{15} -2.99948e8 q^{16} +(-1.87660e8 - 1.87660e8i) q^{17} +(2.12426e9 - 2.12426e9i) q^{18} +(2.50209e8 + 2.50209e8i) q^{19} -2.55367e9 q^{20} +(-3.59653e9 - 3.59653e9i) q^{21} +8.19192e8i q^{22} +2.66588e9 q^{23} +1.62191e10 q^{24} +2.58146e8 q^{25} +(1.61495e10 - 1.61495e10i) q^{26} +(-2.62211e10 + 2.62211e10i) q^{27} -3.97706e10i q^{28} +(-1.66443e10 - 4.53063e9i) q^{29} +7.28702e10 q^{30} +(9.77578e9 + 9.77578e9i) q^{31} +(3.33559e9 + 3.33559e9i) q^{32} -1.56831e10i q^{33} +5.92155e10i q^{34} -9.10352e10i q^{35} -4.49710e11 q^{36} +(7.28244e10 - 7.28244e10i) q^{37} -7.89528e10i q^{38} +(-3.09175e11 + 3.09175e11i) q^{39} +(2.05268e11 + 2.05268e11i) q^{40} +(7.53651e10 - 7.53651e10i) q^{41} +1.13487e12i q^{42} +(-9.89034e10 - 9.89034e10i) q^{43} +(8.67123e10 - 8.67123e10i) q^{44} -1.02939e12 q^{45} +(-4.20606e11 - 4.20606e11i) q^{46} +(1.42970e11 - 1.42970e11i) q^{47} +(-9.05994e11 - 9.05994e11i) q^{48} +7.39551e11 q^{49} +(-4.07287e10 - 4.07287e10i) q^{50} -1.13366e12i q^{51} -3.41888e12 q^{52} -2.36240e11 q^{53} +8.27398e12 q^{54} +(1.98485e11 - 1.98485e11i) q^{55} +(-3.19683e12 + 3.19683e12i) q^{56} +1.51152e12i q^{57} +(1.91121e12 + 3.34084e12i) q^{58} +2.90722e12 q^{59} +(-7.71339e12 - 7.71339e12i) q^{60} +(-1.31209e12 - 1.31209e12i) q^{61} -3.08472e12i q^{62} -1.60316e13i q^{63} +3.86181e12i q^{64} -7.82583e12 q^{65} +(-2.47438e12 + 2.47438e12i) q^{66} +7.85098e12i q^{67} +(6.26802e12 - 6.26802e12i) q^{68} +(8.05232e12 + 8.05232e12i) q^{69} +(-1.43629e13 + 1.43629e13i) q^{70} -1.37095e13i q^{71} +(3.61485e13 + 3.61485e13i) q^{72} +(-9.07256e12 + 9.07256e12i) q^{73} -2.29795e13 q^{74} +(7.79734e11 + 7.79734e11i) q^{75} +(-8.35723e12 + 8.35723e12i) q^{76} +(3.09119e12 + 3.09119e12i) q^{77} +9.75593e13 q^{78} +(-1.07914e13 - 1.07914e13i) q^{79} -2.29325e13i q^{80} -9.40042e13 q^{81} -2.37812e13 q^{82} -3.82913e13 q^{83} +(1.20128e14 - 1.20128e14i) q^{84} +(1.43475e13 - 1.43475e13i) q^{85} +3.12087e13i q^{86} +(-3.65894e13 - 6.39590e13i) q^{87} -1.39402e13 q^{88} +(3.65871e13 + 3.65871e13i) q^{89} +(1.62410e14 + 1.62410e14i) q^{90} -1.21879e14i q^{91} +8.90430e13i q^{92} +5.90557e13i q^{93} -4.51138e13 q^{94} +(-1.91298e13 + 1.91298e13i) q^{95} +2.01503e13i q^{96} +(2.66553e13 - 2.66553e13i) q^{97} +(-1.16682e14 - 1.16682e14i) q^{98} +(3.49538e13 - 3.49538e13i) 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 $

$2$	−157.774	−	157.774i	−1.23261	−	1.23261i	−0.962959	−	0.269646i	$-0.913093\pi$
$2$	−157.774	−	157.774i	−1.23261	−	1.23261i	−0.269646	−	0.962959i	$-0.586907\pi$
$3$	3020.51	+	3020.51i	1.38112	+	1.38112i	0.842635	+	0.538484i	$0.181003\pi$
$3$	3020.51	+	3020.51i	1.38112	+	1.38112i	0.538484	+	0.842635i	$0.318997\pi$
$4$			33401.0i			2.03863i
$5$			76455.0i			0.978624i	0.872109	+	0.489312i	$0.162752\pi$
$5$			76455.0i			0.978624i	−0.872109	+	0.489312i	$0.837248\pi$
$6$		−	953113.i		−	3.40475i
$7$	−1.19070e6			−1.44583			−0.722915	−	0.690937i	$-0.757198\pi$
$7$	−1.19070e6			−1.44583			−0.722915	+	0.690937i	$0.757198\pi$
$8$	2.68483e6	−	2.68483e6i	1.28022	−	1.28022i
$9$			1.34640e7i			2.81498i
$10$	1.20626e7	−	1.20626e7i	1.20626	−	1.20626i
$11$	−2.59610e6	−	2.59610e6i	−0.133221	−	0.133221i	0.637352	−	0.770573i	$-0.280030\pi$
$11$	−2.59610e6	−	2.59610e6i	−0.133221	−	0.133221i	−0.770573	+	0.637352i	$0.780030\pi$
$12$	−1.00888e8	+	1.00888e8i	−2.81560	+	2.81560i
$13$			1.02359e8i			1.63125i	0.578579	+	0.815626i	$0.303607\pi$
$13$			1.02359e8i			1.63125i	−0.578579	+	0.815626i	$0.696393\pi$
$14$	1.87861e8	+	1.87861e8i	1.78214	+	1.78214i
$15$	−2.30933e8	+	2.30933e8i	−1.35160	+	1.35160i
$16$	−2.99948e8			−1.11739
$17$	−1.87660e8	−	1.87660e8i	−0.457329	−	0.457329i	0.440449	−	0.897778i	$-0.354819\pi$
$17$	−1.87660e8	−	1.87660e8i	−0.457329	−	0.457329i	−0.897778	+	0.440449i	$0.854819\pi$
$18$	2.12426e9	−	2.12426e9i	3.46977	−	3.46977i
$19$	2.50209e8	+	2.50209e8i	0.279916	+	0.279916i	0.833076	−	0.553159i	$-0.186578\pi$
$19$	2.50209e8	+	2.50209e8i	0.279916	+	0.279916i	−0.553159	+	0.833076i	$0.686578\pi$
$20$	−2.55367e9			−1.99506
$21$	−3.59653e9	−	3.59653e9i	−1.99686	−	1.99686i
$22$			8.19192e8i			0.328418i
$23$	2.66588e9			0.782972			0.391486	−	0.920184i	$-0.371961\pi$
$23$	2.66588e9			0.782972			0.391486	+	0.920184i	$0.371961\pi$
$24$	1.62191e10			3.53629
$25$	2.58146e8			0.0422947
$26$	1.61495e10	−	1.61495e10i	2.01069	−	2.01069i
$27$	−2.62211e10	+	2.62211e10i	−2.50671	+	2.50671i
$28$		−	3.97706e10i		−	2.94752i
$29$	−1.66443e10	−	4.53063e9i	−0.964892	−	0.262647i
$29$	−1.66443e10	−	4.53063e9i	−0.964892	−	0.262647i
$30$	7.28702e10			3.33197
$31$	9.77578e9	+	9.77578e9i	0.355320	+	0.355320i	0.862085	−	0.506764i	$-0.169159\pi$
$31$	9.77578e9	+	9.77578e9i	0.355320	+	0.355320i	−0.506764	+	0.862085i	$0.669159\pi$
$32$	3.33559e9	+	3.33559e9i	0.0970784	+	0.0970784i
$33$		−	1.56831e10i		−	0.367988i
$34$			5.92155e10i			1.12741i
$35$		−	9.10352e10i		−	1.41492i
$36$	−4.49710e11			−5.73872
$37$	7.28244e10	−	7.28244e10i	0.767123	−	0.767123i	−0.210476	−	0.977599i	$-0.567501\pi$
$37$	7.28244e10	−	7.28244e10i	0.767123	−	0.767123i	0.977599	+	0.210476i	$0.0675014\pi$
$38$		−	7.89528e10i		−	0.690053i
$39$	−3.09175e11	+	3.09175e11i	−2.25295	+	2.25295i
$40$	2.05268e11	+	2.05268e11i	1.25286	+	1.25286i
$41$	7.53651e10	−	7.53651e10i	0.386975	−	0.386975i	−0.486632	−	0.873607i	$-0.661775\pi$
$41$	7.53651e10	−	7.53651e10i	0.386975	−	0.386975i	0.873607	+	0.486632i	$0.161775\pi$
$42$			1.13487e12i			4.92269i
$43$	−9.89034e10	−	9.89034e10i	−0.363858	−	0.363858i	0.501373	−	0.865231i	$-0.332828\pi$
$43$	−9.89034e10	−	9.89034e10i	−0.363858	−	0.363858i	−0.865231	+	0.501373i	$0.832828\pi$
$44$	8.67123e10	−	8.67123e10i	0.271589	−	0.271589i
$45$	−1.02939e12			−2.75481
$46$	−4.20606e11	−	4.20606e11i	−0.965096	−	0.965096i
$47$	1.42970e11	−	1.42970e11i	0.282202	−	0.282202i	−0.551785	−	0.833987i	$-0.686053\pi$
$47$	1.42970e11	−	1.42970e11i	0.282202	−	0.282202i	0.833987	+	0.551785i	$0.186053\pi$
$48$	−9.05994e11	−	9.05994e11i	−1.54325	−	1.54325i
$49$	7.39551e11			1.09042
$50$	−4.07287e10	−	4.07287e10i	−0.0521327	−	0.0521327i
$51$		−	1.13366e12i		−	1.26325i
$52$	−3.41888e12			−3.32552
$53$	−2.36240e11			−0.201105			−0.100552	−	0.994932i	$-0.532061\pi$
$53$	−2.36240e11			−0.201105			−0.100552	+	0.994932i	$0.532061\pi$
$54$	8.27398e12			6.17957
$55$	1.98485e11	−	1.98485e11i	0.130373	−	0.130373i
$56$	−3.19683e12	+	3.19683e12i	−1.85099	+	1.85099i
$57$			1.51152e12i			0.773196i
$58$	1.91121e12	+	3.34084e12i	0.865591	+	1.51307i
$59$	2.90722e12			1.16819			0.584096	−	0.811684i	$-0.301449\pi$
$59$	2.90722e12			1.16819			0.584096	+	0.811684i	$0.301449\pi$
$60$	−7.71339e12	−	7.71339e12i	−2.75541	−	2.75541i
$61$	−1.31209e12	−	1.31209e12i	−0.417498	−	0.417498i	0.466842	−	0.884340i	$-0.345392\pi$
$61$	−1.31209e12	−	1.31209e12i	−0.417498	−	0.417498i	−0.884340	+	0.466842i	$0.845392\pi$
$62$		−	3.08472e12i		−	0.875939i
$63$		−	1.60316e13i		−	4.06999i
$64$			3.86181e12i			0.878073i
$65$	−7.82583e12			−1.59638
$66$	−2.47438e12	+	2.47438e12i	−0.453584	+	0.453584i
$67$			7.85098e12i			1.29539i	0.761900	+	0.647695i	$0.224267\pi$
$67$			7.85098e12i			1.29539i	−0.761900	+	0.647695i	$0.775733\pi$
$68$	6.26802e12	−	6.26802e12i	0.932326	−	0.932326i
$69$	8.05232e12	+	8.05232e12i	1.08138	+	1.08138i
$70$	−1.43629e13	+	1.43629e13i	−1.74404	+	1.74404i
$71$		−	1.37095e13i		−	1.50735i	−0.657248	−	0.753674i	$-0.728280\pi$
$71$		−	1.37095e13i		−	1.50735i	0.657248	−	0.753674i	$-0.271720\pi$
$72$	3.61485e13	+	3.61485e13i	3.60381	+	3.60381i
$73$	−9.07256e12	+	9.07256e12i	−0.821239	+	0.821239i	−0.986286	−	0.165047i	$-0.947223\pi$
$73$	−9.07256e12	+	9.07256e12i	−0.821239	+	0.821239i	0.165047	+	0.986286i	$0.447223\pi$
$74$	−2.29795e13			−1.89112
$75$	7.79734e11	+	7.79734e11i	0.0584141	+	0.0584141i
$76$	−8.35723e12	+	8.35723e12i	−0.570647	+	0.570647i
$77$	3.09119e12	+	3.09119e12i	0.192615	+	0.192615i
$78$	9.75593e13			5.55401
$79$	−1.07914e13	−	1.07914e13i	−0.561937	−	0.561937i	0.367920	−	0.929857i	$-0.380070\pi$
$79$	−1.07914e13	−	1.07914e13i	−0.561937	−	0.561937i	−0.929857	+	0.367920i	$0.880070\pi$
$80$		−	2.29325e13i		−	1.09351i
$81$	−9.40042e13			−4.10915
$82$	−2.37812e13			−0.953976
$83$	−3.82913e13			−1.41108			−0.705542	−	0.708668i	$-0.749297\pi$
$83$	−3.82913e13			−1.41108			−0.705542	+	0.708668i	$0.749297\pi$
$84$	1.20128e14	−	1.20128e14i	4.07087	−	4.07087i
$85$	1.43475e13	−	1.43475e13i	0.447553	−	0.447553i
$86$			3.12087e13i			0.896987i
$87$	−3.65894e13	−	6.39590e13i	−0.969885	−	1.69538i
$88$	−1.39402e13			−0.341106
$89$	3.65871e13	+	3.65871e13i	0.827177	+	0.827177i	0.987125	−	0.159948i	$-0.0511328\pi$
$89$	3.65871e13	+	3.65871e13i	0.827177	+	0.827177i	−0.159948	+	0.987125i	$0.551133\pi$
$90$	1.62410e14	+	1.62410e14i	3.39560	+	3.39560i
$91$		−	1.21879e14i		−	2.35851i
$92$			8.90430e13i			1.59619i
$93$			5.90557e13i			0.981479i
$94$	−4.51138e13			−0.695688
$95$	−1.91298e13	+	1.91298e13i	−0.273933	+	0.273933i
$96$			2.01503e13i			0.268154i
$97$	2.66553e13	−	2.66553e13i	0.329899	−	0.329899i	−0.522649	−	0.852548i	$-0.675056\pi$
$97$	2.66553e13	−	2.66553e13i	0.329899	−	0.329899i	0.852548	+	0.522649i	$0.175056\pi$
$98$	−1.16682e14	−	1.16682e14i	−1.34406	−	1.34406i
$99$	3.49538e13	−	3.49538e13i	0.375015	−	0.375015i
$100$			8.62234e12i			0.0862234i
$101$	6.93835e13	+	6.93835e13i	0.647153	+	0.647153i	0.952304	−	0.305151i	$-0.0987070\pi$
$101$	6.93835e13	+	6.93835e13i	0.647153	+	0.647153i	−0.305151	+	0.952304i	$0.598707\pi$
$102$	−1.78861e14	+	1.78861e14i	−1.55709	+	1.55709i
$103$	−1.35496e14			−1.10171			−0.550853	−	0.834602i	$-0.685698\pi$
$103$	−1.35496e14			−1.10171			−0.550853	+	0.834602i	$0.685698\pi$
$104$	2.74815e14	+	2.74815e14i	2.08837	+	2.08837i
$105$	2.74973e14	−	2.74973e14i	1.95418	−	1.95418i
$106$	3.72724e13	+	3.72724e13i	0.247883	+	0.247883i
$107$	1.78328e14			1.11053			0.555267	−	0.831672i	$-0.312616\pi$
$107$	1.78328e14			1.11053			0.555267	+	0.831672i	$0.312616\pi$
$108$	−8.75809e14	−	8.75809e14i	−5.11026	−	5.11026i
$109$			1.16221e14i			0.635771i	0.948129	+	0.317886i	$0.102973\pi$
$109$			1.16221e14i			0.635771i	−0.948129	+	0.317886i	$0.897027\pi$
$110$	−6.26313e13			−0.321398
$111$	4.39934e14			2.11898
$112$	3.57149e14			1.61556
$113$	−2.24452e14	+	2.24452e14i	−0.954057	+	0.954057i	−0.998990	−	0.0449331i	$-0.985693\pi$
$113$	−2.24452e14	+	2.24452e14i	−0.954057	+	0.954057i	0.0449331	+	0.998990i	$0.485693\pi$
$114$	2.38478e14	−	2.38478e14i	0.953046	−	0.953046i
$115$			2.03820e14i			0.766235i
$116$	1.51327e14	−	5.55935e14i	0.535441	−	1.96706i
$117$	−1.37816e15			−4.59195
$118$	−4.58683e14	−	4.58683e14i	−1.43992	−	1.43992i
$119$	2.23447e14	+	2.23447e14i	0.661220	+	0.661220i
$120$			1.24003e15i			3.46070i
$121$		−	3.66270e14i		−	0.964504i
$122$			4.14026e14i			1.02922i
$123$	4.55282e14			1.06892
$124$	−3.26521e14	+	3.26521e14i	−0.724367	+	0.724367i
$125$			4.86381e14i			1.02001i
$126$	−2.52936e15	+	2.52936e15i	−5.01669	+	5.01669i
$127$	−2.56286e13	−	2.56286e13i	−0.0480948	−	0.0480948i	0.682650	−	0.730745i	$-0.260827\pi$
$127$	−2.56286e13	−	2.56286e13i	−0.0480948	−	0.0480948i	−0.730745	+	0.682650i	$0.760827\pi$
$128$	6.63941e14	−	6.63941e14i	1.17940	−	1.17940i
$129$		−	5.97477e14i		−	1.00506i
$130$	1.23471e15	+	1.23471e15i	1.96771	+	1.96771i
$131$	1.82754e14	−	1.82754e14i	0.276038	−	0.276038i	−0.555487	−	0.831525i	$-0.687468\pi$
$131$	1.82754e14	−	1.82754e14i	0.276038	−	0.276038i	0.831525	+	0.555487i	$0.187468\pi$
$132$	5.23830e14			0.750193
$133$	−2.97925e14	−	2.97925e14i	−0.404711	−	0.404711i
$134$	1.23868e15	−	1.23868e15i	1.59670	−	1.59670i
$135$	−2.00473e15	−	2.00473e15i	−2.45313	−	2.45313i
$136$	−1.00767e15			−1.17097
$137$	5.99325e14	+	5.99325e14i	0.661635	+	0.661635i	0.955765	−	0.294131i	$-0.0950300\pi$
$137$	5.99325e14	+	5.99325e14i	0.661635	+	0.661635i	−0.294131	+	0.955765i	$0.595030\pi$
$138$		−	2.54089e15i		−	2.66583i
$139$	−9.68743e14			−0.966284			−0.483142	−	0.875542i	$-0.660505\pi$
$139$	−9.68743e14			−0.966284			−0.483142	+	0.875542i	$0.660505\pi$
$140$	3.04066e15			2.88451
$141$	8.63685e14			0.779510
$142$	−2.16300e15	+	2.16300e15i	−1.85797	+	1.85797i
$143$	2.65733e14	−	2.65733e14i	0.217317	−	0.217317i
$144$		−	4.03849e15i		−	3.14544i
$145$	3.46389e14	−	1.27254e15i	0.257033	−	0.944267i
$146$	2.86282e15			2.02453
$147$	2.23382e15	+	2.23382e15i	1.50601	+	1.50601i
$148$	2.43241e15	+	2.43241e15i	1.56388	+	1.56388i
$149$			1.37374e15i			0.842560i	0.906931	+	0.421280i	$0.138419\pi$
$149$			1.37374e15i			0.842560i	−0.906931	+	0.421280i	$0.861581\pi$
$150$		−	2.46043e14i		−	0.144003i
$151$			4.50562e14i			0.251719i	0.992048	+	0.125860i	$0.0401689\pi$
$151$			4.50562e14i			0.251719i	−0.992048	+	0.125860i	$0.959831\pi$
$152$	1.34354e15			0.716712
$153$	2.52665e15	−	2.52665e15i	1.28737	−	1.28737i
$154$		−	9.75414e14i		−	0.474836i
$155$	−7.47408e14	+	7.47408e14i	−0.347725	+	0.347725i
$156$	−1.03268e16	−	1.03268e16i	−4.59295	−	4.59295i
$157$	2.25540e15	−	2.25540e15i	0.959239	−	0.959239i	−0.0399622	−	0.999201i	$-0.512724\pi$
$157$	2.25540e15	−	2.25540e15i	0.959239	−	0.959239i	0.999201	+	0.0399622i	$0.0127237\pi$
$158$			3.40519e15i			1.38529i
$159$	−7.13565e14	−	7.13565e14i	−0.277750	−	0.277750i
$160$	−2.55022e14	+	2.55022e14i	−0.0950032	+	0.0950032i
$161$	−3.17428e15			−1.13204
$162$	1.48314e16	+	1.48314e16i	5.06496	+	5.06496i
$163$	7.95427e14	−	7.95427e14i	0.260188	−	0.260188i	−0.564942	−	0.825130i	$-0.691102\pi$
$163$	7.95427e14	−	7.95427e14i	0.260188	−	0.260188i	0.825130	+	0.564942i	$0.191102\pi$
$164$	2.51727e15	+	2.51727e15i	0.788901	+	0.788901i
$165$	1.19905e15			0.360122
$166$	6.04135e15	+	6.04135e15i	1.73931	+	1.73931i
$167$		−	6.62312e14i		−	0.182830i	−0.995813	−	0.0914150i	$-0.970861\pi$
$167$		−	6.62312e14i		−	0.182830i	0.995813	−	0.0914150i	$-0.0291390\pi$
$168$	−1.93121e16			−5.11287
$169$	−6.53992e15			−1.66098
$170$	−4.52732e15			−1.10331
$171$	−3.36881e15	+	3.36881e15i	−0.787960	+	0.787960i
$172$	3.30347e15	−	3.30347e15i	0.741773	−	0.741773i
$173$		−	8.93103e14i		−	0.192566i	−0.995354	−	0.0962828i	$-0.969305\pi$
$173$		−	8.93103e14i		−	0.192566i	0.995354	−	0.0962828i	$-0.0306953\pi$
$174$	−4.31820e15	+	1.58639e16i	−0.894248	+	3.28522i
$175$	−3.07376e14			−0.0611510
$176$	7.78694e14	+	7.78694e14i	0.148860	+	0.148860i
$177$	8.78130e15	+	8.78130e15i	1.61341	+	1.61341i
$178$		−	1.15450e16i		−	2.03917i
$179$			9.02464e14i			0.153270i	0.997059	+	0.0766352i	$0.0244177\pi$
$179$			9.02464e14i			0.153270i	−0.997059	+	0.0766352i	$0.975582\pi$
$180$		−	3.43826e16i		−	5.61605i
$181$	−7.48276e15			−1.17574			−0.587871	−	0.808955i	$-0.700034\pi$
$181$	−7.48276e15			−1.17574			−0.587871	+	0.808955i	$0.700034\pi$
$182$	−1.92292e16	+	1.92292e16i	−2.90712	+	2.90712i
$183$		−	7.92635e15i		−	1.15323i
$184$	7.15743e15	−	7.15743e15i	1.00238	−	1.00238i
$185$	5.56779e15	+	5.56779e15i	0.750725	+	0.750725i
$186$	9.31742e15	−	9.31742e15i	1.20978	−	1.20978i
$187$			9.74367e14i			0.121852i
$188$	4.77534e15	+	4.77534e15i	0.575306	+	0.575306i
$189$	3.12215e16	−	3.12215e16i	3.62428	−	3.62428i
$190$	6.03634e15			0.675302
$191$	6.32586e14	+	6.32586e14i	0.0682159	+	0.0682159i	0.740392	−	0.672176i	$-0.234640\pi$
$191$	6.32586e14	+	6.32586e14i	0.0682159	+	0.0682159i	−0.672176	+	0.740392i	$0.734640\pi$
$192$	−1.16646e16	+	1.16646e16i	−1.21272	+	1.21272i
$193$	3.96922e15	+	3.96922e15i	0.397928	+	0.397928i	0.877501	−	0.479574i	$-0.159209\pi$
$193$	3.96922e15	+	3.96922e15i	0.397928	+	0.397928i	−0.479574	+	0.877501i	$0.659209\pi$
$194$	−8.41100e15			−0.813271
$195$	−2.36380e16	−	2.36380e16i	−2.20480	−	2.20480i
$196$			2.47017e16i			2.22298i
$197$	−3.84537e15			−0.333945			−0.166972	−	0.985962i	$-0.553399\pi$
$197$	−3.84537e15			−0.333945			−0.166972	+	0.985962i	$0.553399\pi$
$198$	−1.10296e16			−0.924491
$199$	−5.61125e15			−0.454034			−0.227017	−	0.973891i	$-0.572897\pi$
$199$	−5.61125e15			−0.454034			−0.227017	+	0.973891i	$0.572897\pi$
$200$	6.93078e14	−	6.93078e14i	0.0541467	−	0.0541467i
$201$	−2.37140e16	+	2.37140e16i	−1.78909	+	1.78909i
$202$		−	2.18938e16i		−	1.59537i
$203$	1.98184e16	+	5.39463e15i	1.39507	+	0.379743i
$204$	3.78652e16			2.57531
$205$	5.76204e15	+	5.76204e15i	0.378704	+	0.378704i
$206$	2.13777e16	+	2.13777e16i	1.35797	+	1.35797i
$207$			3.58934e16i			2.20405i
$208$		−	3.07022e16i		−	1.82275i
$209$		−	1.29914e15i		−	0.0745815i
$210$	−8.67668e16			−4.81747
$211$	3.97702e15	−	3.97702e15i	0.213590	−	0.213590i	−0.592201	−	0.805791i	$-0.701741\pi$
$211$	3.97702e15	−	3.97702e15i	0.213590	−	0.213590i	0.805791	+	0.592201i	$0.201741\pi$
$212$		−	7.89064e15i		−	0.409979i
$213$	4.14097e16	−	4.14097e16i	2.08183	−	2.08183i
$214$	−2.81354e16	−	2.81354e16i	−1.36885	−	1.36885i
$215$	7.56166e15	−	7.56166e15i	0.356080	−	0.356080i
$216$			1.40798e17i			6.41831i
$217$	−1.16401e16	−	1.16401e16i	−0.513733	−	0.513733i
$218$	1.83367e16	−	1.83367e16i	0.783655	−	0.783655i
$219$	−5.48075e16			−2.26846
$220$	6.62959e15	+	6.62959e15i	0.265783	+	0.265783i
$221$	1.92086e16	−	1.92086e16i	0.746019	−	0.746019i
$222$	−6.94099e16	−	6.94099e16i	−2.61186	−	2.61186i
$223$	−2.83263e16			−1.03289			−0.516447	−	0.856319i	$-0.672746\pi$
$223$	−2.83263e16			−1.03289			−0.516447	+	0.856319i	$0.672746\pi$
$224$	−3.97169e15	−	3.97169e15i	−0.140359	−	0.140359i
$225$			3.47568e15i			0.119059i
$226$	7.08251e16			2.35195
$227$	4.23581e16			1.36382			0.681908	−	0.731438i	$-0.261150\pi$
$227$	4.23581e16			1.36382			0.681908	+	0.731438i	$0.261150\pi$
$228$	−5.04862e16			−1.57626
$229$	−9.34763e15	+	9.34763e15i	−0.283043	+	0.283043i	−0.834322	−	0.551278i	$-0.814140\pi$
$229$	−9.34763e15	+	9.34763e15i	−0.283043	+	0.283043i	0.551278	+	0.834322i	$0.314140\pi$
$230$	3.21574e16	−	3.21574e16i	0.944466	−	0.944466i
$231$			1.86739e16i			0.532049i
$232$	−5.68509e16	+	3.25230e16i	−1.57153	+	0.899032i
$233$	1.74563e16			0.468231			0.234116	−	0.972209i	$-0.424781\pi$
$233$	1.74563e16			0.468231			0.234116	+	0.972209i	$0.424781\pi$
$234$	2.17436e17	+	2.17436e17i	5.66006	+	5.66006i
$235$	1.09308e16	+	1.09308e16i	0.276170	+	0.276170i
$236$			9.71041e16i			2.38152i
$237$		−	6.51910e16i		−	1.55220i
$238$		−	7.05081e16i		−	1.63005i
$239$	2.03817e16			0.457566			0.228783	−	0.973477i	$-0.426525\pi$
$239$	2.03817e16			0.457566			0.228783	+	0.973477i	$0.426525\pi$
$240$	6.92678e16	−	6.92678e16i	1.51026	−	1.51026i
$241$			3.28579e16i			0.695858i	0.937521	+	0.347929i	$0.113115\pi$
$241$			3.28579e16i			0.695858i	−0.937521	+	0.347929i	$0.886885\pi$
$242$	−5.77878e16	+	5.77878e16i	−1.18885	+	1.18885i
$243$	−1.58526e17	−	1.58526e17i	−3.16852	−	3.16852i
$244$	4.38250e16	−	4.38250e16i	0.851125	−	0.851125i
$245$			5.65424e16i			1.06712i
$246$	−7.18315e16	−	7.18315e16i	−1.31756	−	1.31756i
$247$	−2.56111e16	+	2.56111e16i	−0.456614	+	0.456614i
$248$	5.24926e16			0.909779
$249$	−1.15659e17	−	1.15659e17i	−1.94888	−	1.94888i
$250$	7.67380e16	−	7.67380e16i	1.25728	−	1.25728i
$251$	2.60934e16	+	2.60934e16i	0.415734	+	0.415734i	0.883730	−	0.467997i	$-0.155024\pi$
$251$	2.60934e16	+	2.60934e16i	0.415734	+	0.415734i	−0.467997	+	0.883730i	$0.655024\pi$
$252$	5.35471e17			8.29721
$253$	−6.92090e15	−	6.92090e15i	−0.104308	−	0.104308i
$254$			8.08702e15i			0.118564i
$255$	8.66737e16			1.23625
$256$	−1.46233e17			−2.02939
$257$	−4.48820e16			−0.606094			−0.303047	−	0.952976i	$-0.598004\pi$
$257$	−4.48820e16			−0.606094			−0.303047	+	0.952976i	$0.598004\pi$
$258$	−9.42661e16	+	9.42661e16i	−1.23885	+	1.23885i
$259$	−8.67123e16	+	8.67123e16i	−1.10913	+	1.10913i
$260$		−	2.61390e17i		−	3.25444i
$261$	6.10003e16	−	2.24098e17i	0.739347	−	2.71616i
$262$	−5.76675e16			−0.680491
$263$	−5.90976e16	−	5.90976e16i	−0.679016	−	0.679016i	0.280762	−	0.959778i	$-0.409413\pi$
$263$	−5.90976e16	−	5.90976e16i	−0.679016	−	0.679016i	−0.959778	+	0.280762i	$0.909413\pi$
$264$	−4.21064e16	−	4.21064e16i	−0.471108	−	0.471108i
$265$		−	1.80617e16i		−	0.196806i
$266$			9.40094e16i			0.997699i
$267$			2.21024e17i			2.28486i
$268$	−2.62230e17			−2.64082
$269$	−1.15034e17	+	1.15034e17i	−1.12865	+	1.12865i	−0.138257	+	0.990396i	$0.544150\pi$
$269$	−1.15034e17	+	1.15034e17i	−1.12865	+	1.12865i	−0.990396	+	0.138257i	$0.955850\pi$
$270$			6.32588e17i			6.04748i
$271$	3.35281e16	−	3.35281e16i	0.312337	−	0.312337i	−0.533477	−	0.845814i	$-0.679115\pi$
$271$	3.35281e16	−	3.35281e16i	0.312337	−	0.312337i	0.845814	+	0.533477i	$0.179115\pi$
$272$	5.62881e16	+	5.62881e16i	0.511016	+	0.511016i
$273$	3.68136e17	−	3.68136e17i	3.25739	−	3.25739i
$274$		−	1.89115e17i		−	1.63107i
$275$	−6.70174e14	−	6.70174e14i	−0.00563454	−	0.00563454i
$276$	−2.68955e17	+	2.68955e17i	−2.20453	+	2.20453i
$277$	−8.16117e16			−0.652220			−0.326110	−	0.945332i	$-0.605738\pi$
$277$	−8.16117e16			−0.652220			−0.326110	+	0.945332i	$0.605738\pi$
$278$	1.52842e17	+	1.52842e17i	1.19105	+	1.19105i
$279$	−1.31621e17	+	1.31621e17i	−1.00022	+	1.00022i
$280$	−2.44414e17	−	2.44414e17i	−1.81142	−	1.81142i
$281$	8.43870e16			0.610002			0.305001	−	0.952352i	$-0.401343\pi$
$281$	8.43870e16			0.610002			0.305001	+	0.952352i	$0.401343\pi$
$282$	−1.36267e17	−	1.36267e17i	−0.960828	−	0.960828i
$283$			2.68326e17i			1.84568i	0.385178	+	0.922842i	$0.374140\pi$
$283$			2.68326e17i			1.84568i	−0.385178	+	0.922842i	$0.625860\pi$
$284$	4.57911e17			3.07293
$285$	−1.15563e17			−0.756668
$286$	−8.38514e16			−0.535732
$287$	−8.97375e16	+	8.97375e16i	−0.559501	+	0.559501i
$288$	−4.49103e16	+	4.49103e16i	−0.273274	+	0.273274i
$289$		−	9.79454e16i		−	0.581700i
$290$	−2.55424e17	+	1.46122e17i	−1.48073	+	0.847089i
$291$	1.61025e17			0.911261
$292$	−3.03032e17	−	3.03032e17i	−1.67421	−	1.67421i
$293$	5.07728e16	+	5.07728e16i	0.273878	+	0.273878i	0.830659	−	0.556781i	$-0.187964\pi$
$293$	5.07728e16	+	5.07728e16i	0.273878	+	0.273878i	−0.556781	+	0.830659i	$0.687964\pi$
$294$		−	7.04876e17i		−	3.71263i
$295$			2.22272e17i			1.14322i
$296$		−	3.91042e17i		−	1.96418i
$297$	1.36145e17			0.667893
$298$	2.16740e17	−	2.16740e17i	1.03854	−	1.03854i
$299$			2.72876e17i			1.27722i
$300$	−2.60439e16	+	2.60439e16i	−0.119085	+	0.119085i
$301$	1.17765e17	+	1.17765e17i	0.526077	+	0.526077i
$302$	7.10868e16	−	7.10868e16i	0.310270	−	0.310270i
$303$			4.19147e17i			1.78759i
$304$	−7.50497e16	−	7.50497e16i	−0.312776	−	0.312776i
$305$	1.00316e17	−	1.00316e17i	0.408574	−	0.408574i
$306$	−7.97276e17			−3.17365
$307$	3.06851e16	+	3.06851e16i	0.119387	+	0.119387i	0.764276	−	0.644889i	$-0.223096\pi$
$307$	3.06851e16	+	3.06851e16i	0.119387	+	0.119387i	−0.644889	+	0.764276i	$0.723096\pi$
$308$	−1.03249e17	+	1.03249e17i	−0.392671	+	0.392671i
$309$	−4.09267e17	−	4.09267e17i	−1.52159	−	1.52159i
$310$	2.35842e17			0.857215
$311$	9.13630e16	+	9.13630e16i	0.324674	+	0.324674i	0.850557	−	0.525883i	$-0.176265\pi$
$311$	9.13630e16	+	9.13630e16i	0.324674	+	0.324674i	−0.525883	+	0.850557i	$0.676265\pi$
$312$			1.66016e18i			5.76858i
$313$	−2.30790e17			−0.784164			−0.392082	−	0.919930i	$-0.628245\pi$
$313$	−2.30790e17			−0.784164			−0.392082	+	0.919930i	$0.628245\pi$
$314$	−7.11686e17			−2.36473
$315$	1.22570e18			3.98299
$316$	3.60443e17	−	3.60443e17i	1.14558	−	1.14558i
$317$	4.37388e17	−	4.37388e17i	1.35973	−	1.35973i	0.485481	−	0.874247i	$-0.338645\pi$
$317$	4.37388e17	−	4.37388e17i	1.35973	−	1.35973i	0.874247	−	0.485481i	$-0.161355\pi$
$318$			2.25163e17i			0.684712i
$319$	3.14482e16	+	5.49721e16i	0.0935538	+	0.163534i
$320$	−2.95254e17			−0.859304
$321$	5.38640e17	+	5.38640e17i	1.53378	+	1.53378i
$322$	5.00817e17	+	5.00817e17i	1.39536	+	1.39536i
$323$		−	9.39085e16i		−	0.256028i
$324$		−	3.13983e18i		−	8.37705i
$325$			2.64235e16i			0.0689933i
$326$	−2.50995e17			−0.641418
$327$	−3.51048e17	+	3.51048e17i	−0.878076	+	0.878076i
$328$		−	4.04684e17i		−	0.990831i
$329$	−1.70235e17	+	1.70235e17i	−0.408016	+	0.408016i
$330$	−1.89178e17	−	1.89178e17i	−0.443889	−	0.443889i
$331$	3.33418e17	−	3.33418e17i	0.765938	−	0.765938i	−0.211451	−	0.977389i	$-0.567819\pi$
$331$	3.33418e17	−	3.33418e17i	0.765938	−	0.765938i	0.977389	+	0.211451i	$0.0678188\pi$
$332$		−	1.27897e18i		−	2.87668i
$333$	9.80507e17	+	9.80507e17i	2.15944	+	2.15944i
$334$	−1.04495e17	+	1.04495e17i	−0.225357	+	0.225357i
$335$	−6.00247e17			−1.26770
$336$	1.07877e18	+	1.07877e18i	2.23128	+	2.23128i
$337$	−4.16676e17	+	4.16676e17i	−0.844091	+	0.844091i	−0.989388	−	0.145297i	$-0.953586\pi$
$337$	−4.16676e17	+	4.16676e17i	−0.844091	+	0.844091i	0.145297	+	0.989388i	$0.453586\pi$
$338$	1.03183e18	+	1.03183e18i	2.04734	+	2.04734i
$339$	−1.35592e18			−2.63533
$340$	4.79221e17	+	4.79221e17i	0.912397	+	0.912397i
$341$		−	5.07578e16i		−	0.0946722i
$342$	1.06302e18			1.94249
$343$	−7.30237e16			−0.130739
$344$	−5.31077e17			−0.931641
$345$	−6.15640e17	+	6.15640e17i	−1.05826	+	1.05826i
$346$	−1.40908e17	+	1.40908e17i	−0.237357	+	0.237357i
$347$		−	4.00712e15i		−	0.00661494i	−0.999995	−	0.00330747i	$-0.998947\pi$
$347$		−	4.00712e15i		−	0.00661494i	0.999995	−	0.00330747i	$-0.00105280\pi$
$348$	2.13629e18	−	1.22212e18i	3.45625	−	1.97724i
$349$	8.89525e17			1.41052			0.705262	−	0.708947i	$-0.250830\pi$
$349$	8.89525e17			1.41052			0.705262	+	0.708947i	$0.250830\pi$
$350$	4.84958e16	+	4.84958e16i	0.0753750	+	0.0753750i
$351$	−2.68395e18	−	2.68395e18i	−4.08908	−	4.08908i
$352$		−	1.73190e16i		−	0.0258658i
$353$			1.33257e18i			1.95104i	0.219911	+	0.975520i	$0.429423\pi$
$353$			1.33257e18i			1.95104i	−0.219911	+	0.975520i	$0.570577\pi$
$354$		−	2.77091e18i		−	3.97741i
$355$	1.04816e18			1.47513
$356$	−1.22205e18	+	1.22205e18i	−1.68631	+	1.68631i
$357$			1.34985e18i			1.82645i
$358$	1.42385e17	−	1.42385e17i	0.188922	−	0.188922i
$359$	−5.38417e17	−	5.38417e17i	−0.700580	−	0.700580i	0.263955	−	0.964535i	$-0.414973\pi$
$359$	−5.38417e17	−	5.38417e17i	−0.700580	−	0.700580i	−0.964535	+	0.263955i	$0.914973\pi$
$360$	−2.76373e18	+	2.76373e18i	−3.52678	+	3.52678i
$361$		−	6.73797e17i		−	0.843294i
$362$	1.18058e18	+	1.18058e18i	1.44923	+	1.44923i
$363$	1.10632e18	−	1.10632e18i	1.33210	−	1.33210i
$364$	4.07087e18			4.80814
$365$	−6.93642e17	−	6.93642e17i	−0.803685	−	0.803685i
$366$	−1.25057e18	+	1.25057e18i	−1.42148	+	1.42148i
$367$	6.89628e17	+	6.89628e17i	0.769046	+	0.769046i	0.977939	−	0.208892i	$-0.0669859\pi$
$367$	6.89628e17	+	6.89628e17i	0.769046	+	0.769046i	−0.208892	+	0.977939i	$0.566986\pi$
$368$	−7.99625e17			−0.874886
$369$	1.01471e18	+	1.01471e18i	1.08933	+	1.08933i
$370$		−	1.75690e18i		−	1.85070i
$371$	2.81292e17			0.290763
$372$	−1.97252e18			−2.00088
$373$	−3.83446e17			−0.381718			−0.190859	−	0.981617i	$-0.561127\pi$
$373$	−3.83446e17			−0.381718			−0.190859	+	0.981617i	$0.561127\pi$
$374$	1.53729e17	−	1.53729e17i	0.150195	−	0.150195i
$375$	−1.46912e18	+	1.46912e18i	−1.40876	+	1.40876i
$376$		−	7.67700e17i		−	0.722564i
$377$	4.63749e17	−	1.70368e18i	0.428443	−	1.57398i
$378$	−9.85186e18			−8.93461
$379$	1.15981e18	+	1.15981e18i	1.03255	+	1.03255i	0.999452	+	0.0331025i	$0.0105388\pi$
$379$	1.15981e18	+	1.15981e18i	1.03255	+	1.03255i	0.0331025	+	0.999452i	$0.489461\pi$
$380$	−6.38952e17	−	6.38952e17i	−0.558449	−	0.558449i
$381$		−	1.54823e17i		−	0.132849i
$382$		−	1.99611e17i		−	0.168167i
$383$			2.39487e17i			0.198103i	0.995082	+	0.0990513i	$0.0315808\pi$
$383$			2.39487e17i			0.198103i	−0.995082	+	0.0990513i	$0.968419\pi$
$384$	4.01088e18			3.25777
$385$	−2.36337e17	+	2.36337e17i	−0.188498	+	0.188498i
$386$		−	1.25248e18i		−	0.980976i
$387$	1.33163e18	−	1.33163e18i	1.02426	−	1.02426i
$388$	8.90313e17	+	8.90313e17i	0.672544	+	0.672544i
$389$	−6.83814e17	+	6.83814e17i	−0.507330	+	0.507330i	−0.913706	−	0.406376i	$-0.866792\pi$
$389$	−6.83814e17	+	6.83814e17i	−0.507330	+	0.507330i	0.406376	+	0.913706i	$0.366792\pi$
$390$			7.45890e18i			5.43529i
$391$	−5.00279e17	−	5.00279e17i	−0.358076	−	0.358076i
$392$	1.98557e18	−	1.98557e18i	1.39599	−	1.39599i
$393$	1.10402e18			0.762482
$394$	6.06698e17	+	6.06698e17i	0.411622	+	0.411622i
$395$	8.25056e17	−	8.25056e17i	0.549925	−	0.549925i
$396$	1.16749e18	+	1.16749e18i	0.764518	+	0.764518i
$397$	−2.67127e18			−1.71864			−0.859320	−	0.511438i	$-0.829113\pi$
$397$	−2.67127e18			−1.71864			−0.859320	+	0.511438i	$0.829113\pi$
$398$	8.85307e17	+	8.85307e17i	0.559644	+	0.559644i
$399$		−	1.79977e18i		−	1.11791i
$400$	−7.74304e16			−0.0472598
$401$	−1.01642e18			−0.609624			−0.304812	−	0.952413i	$-0.598594\pi$
$401$	−1.01642e18			−0.609624			−0.304812	+	0.952413i	$0.598594\pi$
$402$	7.48287e18			4.41048
$403$	−1.00064e18	+	1.00064e18i	−0.579617	+	0.579617i
$404$	−2.31748e18	+	2.31748e18i	−1.31931	+	1.31931i
$405$		−	7.18710e18i		−	4.02132i
$406$	−2.27569e18	−	3.97795e18i	−1.25150	−	2.18764i
$407$	−3.78119e17			−0.204394
$408$	−3.04367e18	−	3.04367e18i	−1.61725	−	1.61725i
$409$	1.00876e18	+	1.00876e18i	0.526895	+	0.526895i	0.919645	−	0.392750i	$-0.128476\pi$
$409$	1.00876e18	+	1.00876e18i	0.526895	+	0.526895i	−0.392750	+	0.919645i	$0.628476\pi$
$410$		−	1.81819e18i		−	0.933584i
$411$			3.62053e18i			1.82759i
$412$		−	4.52570e18i		−	2.24598i
$413$	−3.46164e18			−1.68901
$414$	5.66303e18	−	5.66303e18i	2.71673	−	2.71673i
$415$		−	2.92756e18i		−	1.38092i
$416$	−3.41426e17	+	3.41426e17i	−0.158359	+	0.158359i
$417$	−2.92610e18	−	2.92610e18i	−1.33455	−	1.33455i
$418$	−2.04969e17	+	2.04969e17i	−0.0919295	+	0.0919295i
$419$		−	2.27186e18i		−	1.00203i	−0.865437	−	0.501017i	$-0.832959\pi$
$419$		−	2.27186e18i		−	1.00203i	0.865437	−	0.501017i	$-0.167041\pi$
$420$	9.18436e18	+	9.18436e18i	3.98386	+	3.98386i
$421$	−2.59765e18	+	2.59765e18i	−1.10817	+	1.10817i	−0.114776	+	0.993391i	$0.536615\pi$
$421$	−2.59765e18	+	2.59765e18i	−1.10817	+	1.10817i	−0.993391	+	0.114776i	$0.963385\pi$
$422$	−1.25494e18			−0.526544
$423$	1.92495e18	+	1.92495e18i	0.794394	+	0.794394i
$424$	−6.34263e17	+	6.34263e17i	−0.257459	+	0.257459i
$425$	−4.84437e16	−	4.84437e16i	−0.0193426	−	0.0193426i
$426$	−1.30667e19			−5.13215
$427$	1.56231e18	+	1.56231e18i	0.603631	+	0.603631i
$428$			5.95631e18i			2.26397i
$429$	1.60530e18			0.600282
$430$	−2.38606e18			−0.877813
$431$	−1.99207e18			−0.721047			−0.360524	−	0.932750i	$-0.617402\pi$
$431$	−1.99207e18			−0.721047			−0.360524	+	0.932750i	$0.617402\pi$
$432$	7.86495e18	−	7.86495e18i	2.80098	−	2.80098i
$433$	−2.84555e18	+	2.84555e18i	−0.997129	+	0.997129i	−0.999996	−	0.00286699i	$-0.999087\pi$
$433$	−2.84555e18	+	2.84555e18i	−0.997129	+	0.997129i	0.00286699	+	0.999996i	$0.499087\pi$
$434$			3.67299e18i			1.26646i
$435$	4.88998e18	−	2.79744e18i	1.65914	−	0.949153i
$436$	−3.88191e18			−1.29610
$437$	6.67029e17	+	6.67029e17i	0.219167	+	0.219167i
$438$	8.64717e18	+	8.64717e18i	2.79612	+	2.79612i
$439$		−	2.46952e18i		−	0.785888i	−0.919562	−	0.392944i	$-0.871457\pi$
$439$		−	2.46952e18i		−	0.785888i	0.919562	−	0.392944i	$-0.128543\pi$
$440$		−	1.06579e18i		−	0.333814i
$441$			9.95731e18i			3.06953i
$442$	−6.06122e18			−1.83909
$443$	1.19038e18	−	1.19038e18i	0.355515	−	0.355515i	−0.506642	−	0.862157i	$-0.669113\pi$
$443$	1.19038e18	−	1.19038e18i	0.355515	−	0.355515i	0.862157	+	0.506642i	$0.169113\pi$
$444$			1.46942e19i			4.31982i
$445$	−2.79727e18	+	2.79727e18i	−0.809495	+	0.809495i
$446$	4.46914e18	+	4.46914e18i	1.27315	+	1.27315i
$447$	−4.14939e18	+	4.14939e18i	−1.16368	+	1.16368i
$448$		−	4.59827e18i		−	1.26954i
$449$	1.23674e18	+	1.23674e18i	0.336165	+	0.336165i	0.854922	−	0.518757i	$-0.173605\pi$
$449$	1.23674e18	+	1.23674e18i	0.336165	+	0.336165i	−0.518757	+	0.854922i	$0.673605\pi$
$450$	5.48370e17	−	5.48370e17i	0.146753	−	0.146753i
$451$	−3.91311e17			−0.103106
$452$	−7.49691e18	−	7.49691e18i	−1.94497	−	1.94497i
$453$	−1.36093e18	+	1.36093e18i	−0.347654	+	0.347654i
$454$	−6.68299e18	−	6.68299e18i	−1.68105	−	1.68105i
$455$	9.31824e18			2.30810
$456$	4.05817e18	+	4.05817e18i	0.989865	+	0.989865i
$457$		−	5.25704e18i		−	1.26278i	−0.775466	−	0.631390i	$-0.782485\pi$
$457$		−	5.25704e18i		−	1.26278i	0.775466	−	0.631390i	$-0.217515\pi$
$458$	2.94962e18			0.697762
$459$	9.84129e18			2.29278
$460$	−6.80779e18			−1.56207
$461$	4.36847e18	−	4.36847e18i	0.987239	−	0.987239i	−0.0126804	−	0.999920i	$-0.504036\pi$
$461$	4.36847e18	−	4.36847e18i	0.987239	−	0.987239i	0.999920	+	0.0126804i	$0.00403639\pi$
$462$	2.94625e18	−	2.94625e18i	0.655806	−	0.655806i
$463$			2.07256e18i			0.454402i	0.973848	+	0.227201i	$0.0729574\pi$
$463$			2.07256e18i			0.454402i	−0.973848	+	0.227201i	$0.927043\pi$
$464$	4.99241e18	+	1.35895e18i	1.07816	+	0.293479i
$465$	−4.51510e18			−0.960499
$466$	−2.75414e18	−	2.75414e18i	−0.577144	−	0.577144i
$467$	−1.33374e18	−	1.33374e18i	−0.275330	−	0.275330i	0.555912	−	0.831241i	$-0.312369\pi$
$467$	−1.33374e18	−	1.33374e18i	−0.275330	−	0.275330i	−0.831241	+	0.555912i	$0.812369\pi$
$468$		−	4.60317e19i		−	9.36130i
$469$		−	9.34819e18i		−	1.87291i
$470$		−	3.44918e18i		−	0.680817i
$471$	1.36249e19			2.64965
$472$	7.80539e18	−	7.80539e18i	1.49555	−	1.49555i
$473$			5.13526e17i			0.0969471i
$474$	−1.02854e19	+	1.02854e19i	−1.91326	+	1.91326i
$475$	6.45906e16	+	6.45906e16i	0.0118390	+	0.0118390i
$476$	−7.46335e18	+	7.46335e18i	−1.34799	+	1.34799i
$477$		−	3.18073e18i		−	0.566106i
$478$	−3.21569e18	−	3.21569e18i	−0.563999	−	0.563999i
$479$	1.57289e18	−	1.57289e18i	0.271862	−	0.271862i	−0.557987	−	0.829849i	$-0.688426\pi$
$479$	1.57289e18	−	1.57289e18i	0.271862	−	0.271862i	0.829849	+	0.557987i	$0.188426\pi$
$480$	−1.54059e18			−0.262422
$481$	7.45421e18	+	7.45421e18i	1.25137	+	1.25137i
$482$	5.18411e18	−	5.18411e18i	0.857718	−	0.857718i
$483$	−9.58793e18	−	9.58793e18i	−1.56349	−	1.56349i
$484$	1.22338e19			1.96627
$485$	2.03793e18	+	2.03793e18i	0.322847	+	0.322847i
$486$			5.00224e19i			7.81107i
$487$	7.72652e18			1.18927			0.594636	−	0.803995i	$-0.297296\pi$
$487$	7.72652e18			1.18927			0.594636	+	0.803995i	$0.297296\pi$
$488$	−7.04546e18			−1.06898
$489$	4.80519e18			0.718702
$490$	8.92089e18	−	8.92089e18i	1.31533	−	1.31533i
$491$	−2.22793e18	+	2.22793e18i	−0.323840	+	0.323840i	−0.850238	−	0.526398i	$-0.823542\pi$
$491$	−2.22793e18	+	2.22793e18i	−0.323840	+	0.323840i	0.526398	+	0.850238i	$0.323542\pi$
$492$			1.52069e19i			2.17913i
$493$	2.27324e18	+	3.97368e18i	0.321157	+	0.561389i
$494$	8.08150e18			1.12565
$495$	2.67240e18	+	2.67240e18i	0.366999	+	0.366999i
$496$	−2.93222e18	−	2.93222e18i	−0.397032	−	0.397032i
$497$			1.63240e19i			2.17937i
$498$			3.64959e19i			4.80439i
$499$		−	1.31173e19i		−	1.70271i	−0.524589	−	0.851356i	$-0.675781\pi$
$499$		−	1.31173e19i		−	1.70271i	0.524589	−	0.851356i	$-0.324219\pi$
$500$	−1.62456e19			−2.07944
$501$	2.00052e18	−	2.00052e18i	0.252510	−	0.252510i
$502$		−	8.23370e18i		−	1.02487i
$503$	−9.43172e18	+	9.43172e18i	−1.15775	+	1.15775i	−0.172793	+	0.984958i	$0.555279\pi$
$503$	−9.43172e18	+	9.43172e18i	−1.15775	+	1.15775i	−0.984958	+	0.172793i	$0.944721\pi$
$504$	−4.30421e19	−	4.30421e19i	−5.21050	−	5.21050i
$505$	−5.30472e18	+	5.30472e18i	−0.633319	+	0.633319i
$506$			2.18387e18i			0.257142i
$507$	−1.97539e19	−	1.97539e19i	−2.29402	−	2.29402i
$508$	8.56019e17	−	8.56019e17i	0.0980477	−	0.0980477i
$509$	−1.54176e19			−1.74178			−0.870890	−	0.491479i	$-0.836457\pi$
$509$	−1.54176e19			−1.74178			−0.870890	+	0.491479i	$0.836457\pi$
$510$	−1.36748e19	−	1.36748e19i	−1.52381	−	1.52381i
$511$	1.08027e19	−	1.08027e19i	1.18737	−	1.18737i
$512$	1.21937e19	+	1.21937e19i	1.32204	+	1.32204i
$513$	−1.31215e19			−1.40334
$514$	7.08119e18	+	7.08119e18i	0.747075	+	0.747075i
$515$		−	1.03594e19i		−	1.07816i
$516$	1.99563e19			2.04896
$517$	−7.42329e17			−0.0751905
$518$	2.73618e19			2.73424
$519$	2.69762e18	−	2.69762e18i	0.265956	−	0.265956i
$520$	−2.10110e19	+	2.10110e19i	−2.04373	+	2.04373i
$521$		−	1.22855e19i		−	1.17904i	−0.807752	−	0.589522i	$-0.799316\pi$
$521$		−	1.22855e19i		−	1.17904i	0.807752	−	0.589522i	$-0.200684\pi$
$522$	−4.49810e19	+	2.57325e19i	−4.25927	+	2.43663i
$523$	−9.28206e18			−0.867227			−0.433613	−	0.901099i	$-0.642762\pi$
$523$	−9.28206e18			−0.867227			−0.433613	+	0.901099i	$0.642762\pi$
$524$	6.10416e18	+	6.10416e18i	0.562739	+	0.562739i
$525$	−9.28431e17	−	9.28431e17i	−0.0844568	−	0.0844568i
$526$			1.86481e19i			1.67392i
$527$		−	3.66904e18i		−	0.324996i
$528$			4.70410e18i			0.411187i
$529$	−4.48591e18			−0.386955
$530$	−2.84966e18	+	2.84966e18i	−0.242584	+	0.242584i
$531$			3.91428e19i			3.28844i
$532$	9.95098e18	−	9.95098e18i	0.825058	−	0.825058i
$533$	7.71427e18	+	7.71427e18i	0.631254	+	0.631254i
$534$	3.48717e19	−	3.48717e19i	2.81633	−	2.81633i
$535$			1.36340e19i			1.08680i
$536$	2.10785e19	+	2.10785e19i	1.65839	+	1.65839i
$537$	−2.72590e18	+	2.72590e18i	−0.211685	+	0.211685i
$538$	3.62987e19			2.78237
$539$	−1.91995e18	−	1.91995e18i	−0.145267	−	0.145267i
$540$	6.69600e19	−	6.69600e19i	5.00103	−	5.00103i
$541$	−1.69732e19	−	1.69732e19i	−1.25136	−	1.25136i	−0.955111	−	0.296248i	$-0.904265\pi$
$541$	−1.69732e19	−	1.69732e19i	−1.25136	−	1.25136i	−0.296248	−	0.955111i	$-0.595735\pi$
$542$	−1.05797e19			−0.769977
$543$	−2.26017e19	−	2.26017e19i	−1.62384	−	1.62384i
$544$		−	1.25191e18i		−	0.0887935i
$545$	−8.88571e18			−0.622181
$546$	−1.16164e20			−8.03015
$547$	−9.74601e18			−0.665144			−0.332572	−	0.943078i	$-0.607916\pi$
$547$	−9.74601e18			−0.665144			−0.332572	+	0.943078i	$0.607916\pi$
$548$	−2.00180e19	+	2.00180e19i	−1.34883	+	1.34883i
$549$	1.76659e19	−	1.76659e19i	1.17525	−	1.17525i
$550$			2.11471e17i			0.0138903i
$551$	−3.03095e18	−	5.29816e18i	−0.196570	−	0.343608i
$552$	4.32382e19			2.76881
$553$	1.28493e19	+	1.28493e19i	0.812466	+	0.812466i
$554$	1.28762e19	+	1.28762e19i	0.803930	+	0.803930i
$555$			3.36351e19i			2.07368i
$556$		−	3.23569e19i		−	1.96990i
$557$		−	1.41432e19i		−	0.850277i	−0.905128	−	0.425138i	$-0.860225\pi$
$557$		−	1.41432e19i		−	0.850277i	0.905128	−	0.425138i	$-0.139775\pi$
$558$	4.15326e19			2.46575
$559$	1.01236e19	−	1.01236e19i	0.593544	−	0.593544i
$560$			2.73058e19i			1.58102i
$561$	−2.94309e18	+	2.94309e18i	−0.168292	+	0.168292i
$562$	−1.33140e19	−	1.33140e19i	−0.751892	−	0.751892i
$563$	−8.50764e18	+	8.50764e18i	−0.474515	+	0.474515i	−0.903372	−	0.428857i	$-0.858916\pi$
$563$	−8.50764e18	+	8.50764e18i	−0.474515	+	0.474515i	0.428857	+	0.903372i	$0.358916\pi$
$564$			2.88479e19i			1.58913i
$565$	−1.71605e19	−	1.71605e19i	−0.933663	−	0.933663i
$566$	4.23347e19	−	4.23347e19i	2.27500	−	2.27500i
$567$	1.11931e20			5.94114
$568$	−3.68077e19	−	3.68077e19i	−1.92975	−	1.92975i
$569$	−7.43352e18	+	7.43352e18i	−0.384954	+	0.384954i	−0.872883	−	0.487929i	$-0.837752\pi$
$569$	−7.43352e18	+	7.43352e18i	−0.384954	+	0.384954i	0.487929	+	0.872883i	$0.337752\pi$
$570$	1.82328e19	+	1.82328e19i	0.932674	+	0.932674i
$571$	6.64755e18			0.335899			0.167950	−	0.985796i	$-0.446285\pi$
$571$	6.64755e18			0.335899			0.167950	+	0.985796i	$0.446285\pi$
$572$	8.87575e18	+	8.87575e18i	0.443030	+	0.443030i
$573$			3.82146e18i			0.188429i
$574$	2.83164e19			1.37929
$575$	6.88188e17			0.0331156
$576$	−5.19953e19			−2.47176
$577$	−1.62688e19	+	1.62688e19i	−0.764057	+	0.764057i	−0.977053	−	0.212996i	$-0.931678\pi$
$577$	−1.62688e19	+	1.62688e19i	−0.764057	+	0.764057i	0.212996	+	0.977053i	$0.431678\pi$
$578$	−1.54532e19	+	1.54532e19i	−0.717007	+	0.717007i
$579$			2.39781e19i			1.09917i
$580$	4.25040e19	+	1.15697e19i	1.92501	+	0.523995i
$581$	4.55935e19			2.04019
$582$	−2.54055e19	−	2.54055e19i	−1.12323	−	1.12323i
$583$	6.13302e17	+	6.13302e17i	0.0267914	+	0.0267914i
$584$			4.87165e19i			2.10274i
$585$		−	1.05367e20i		−	4.49379i
$586$		−	1.60212e19i		−	0.675168i
$587$	−1.38598e19			−0.577152			−0.288576	−	0.957457i	$-0.593182\pi$
$587$	−1.38598e19			−0.577152			−0.288576	+	0.957457i	$0.593182\pi$
$588$	−7.46118e19	+	7.46118e19i	−3.07020	+	3.07020i
$589$			4.89198e18i			0.198920i
$590$	3.50686e19	−	3.50686e19i	1.40914	−	1.40914i
$591$	−1.16150e19	−	1.16150e19i	−0.461218	−	0.461218i
$592$	−2.18435e19	+	2.18435e19i	−0.857177	+	0.857177i
$593$			1.38884e19i			0.538604i	0.963056	+	0.269302i	$0.0867929\pi$
$593$			1.38884e19i			0.538604i	−0.963056	+	0.269302i	$0.913207\pi$
$594$	−2.14801e19	−	2.14801e19i	−0.823249	−	0.823249i
$595$	−1.70837e19	+	1.70837e19i	−0.647086	+	0.647086i
$596$	−4.58842e19			−1.71767
$597$	−1.69488e19	−	1.69488e19i	−0.627075	−	0.627075i
$598$	4.30526e19	−	4.30526e19i	1.57431	−	1.57431i
$599$	1.86538e19	+	1.86538e19i	0.674184	+	0.674184i	0.958678	−	0.284494i	$-0.0918255\pi$
$599$	1.86538e19	+	1.86538e19i	0.674184	+	0.674184i	−0.284494	+	0.958678i	$0.591825\pi$
$600$	4.18690e18			0.149566
$601$	2.41617e19	+	2.41617e19i	0.853111	+	0.853111i	0.990515	−	0.137404i	$-0.0438760\pi$
$601$	2.41617e19	+	2.41617e19i	0.853111	+	0.853111i	−0.137404	+	0.990515i	$0.543876\pi$
$602$		−	3.71603e19i		−	1.29689i
$603$	−1.05705e20			−3.64650
$604$	−1.50492e19			−0.513163
$605$	2.80032e19			0.943887
$606$	6.61303e19	−	6.61303e19i	2.20339	−	2.20339i
$607$	−3.46077e19	+	3.46077e19i	−1.13986	+	1.13986i	−0.151387	+	0.988475i	$0.548374\pi$
$607$	−3.46077e19	+	3.46077e19i	−1.13986	+	1.13986i	−0.988475	+	0.151387i	$0.951626\pi$
$608$			1.66919e18i			0.0543476i
$609$	4.35671e19	+	7.61562e19i	1.40229	+	2.45123i
$610$	−3.16543e19			−1.00722
$611$	1.46342e19	+	1.46342e19i	0.460343	+	0.460343i
$612$	8.43925e19	+	8.43925e19i	2.62448	+	2.62448i
$613$		−	5.20342e19i		−	1.59980i	−0.600134	−	0.799899i	$-0.704886\pi$
$613$		−	5.20342e19i		−	1.59980i	0.600134	−	0.799899i	$-0.295114\pi$
$614$		−	9.68258e18i		−	0.294315i
$615$			3.48086e19i			1.04607i
$616$	1.65986e19			0.493181
$617$	2.12039e19	−	2.12039e19i	0.622903	−	0.622903i	−0.323370	−	0.946273i	$-0.604816\pi$
$617$	2.12039e19	−	2.12039e19i	0.622903	−	0.622903i	0.946273	+	0.323370i	$0.104816\pi$
$618$			1.29143e20i			3.75104i
$619$	−6.16135e18	+	6.16135e18i	−0.176946	+	0.176946i	−0.790023	−	0.613077i	$-0.789932\pi$
$619$	−6.16135e18	+	6.16135e18i	−0.176946	+	0.176946i	0.613077	+	0.790023i	$0.289932\pi$
$620$	−2.49641e19	−	2.49641e19i	−0.708883	−	0.708883i
$621$	−6.99023e19	+	6.99023e19i	−1.96268	+	1.96268i
$622$		−	2.88293e19i		−	0.800390i
$623$	−4.35644e19	−	4.35644e19i	−1.19596	−	1.19596i
$624$	9.27364e19	−	9.27364e19i	2.51743	−	2.51743i
$625$	−3.56107e19			−0.955916
$626$	3.64126e19	+	3.64126e19i	0.966564	+	0.966564i
$627$	3.92405e18	−	3.92405e18i	0.103006	−	0.103006i
$628$	7.53327e19	+	7.53327e19i	1.95554	+	1.95554i
$629$	−2.73324e19			−0.701655
$630$	−1.93383e20	−	1.93383e20i	−4.90946	−	4.90946i
$631$		−	1.91579e19i		−	0.480998i	−0.970649	−	0.240499i	$-0.922689\pi$
$631$		−	1.91579e19i		−	0.480998i	0.970649	−	0.240499i	$-0.0773111\pi$
$632$	−5.79460e19			−1.43881
$633$	2.40253e19			0.589987
$634$	−1.38016e20			−3.35202
$635$	1.95943e18	−	1.95943e18i	0.0470667	−	0.0470667i
$636$	2.38338e19	−	2.38338e19i	0.566230	−	0.566230i
$637$			7.56995e19i			1.77876i
$638$	3.71145e18	−	1.36348e19i	0.0862579	−	0.316888i
$639$	1.84585e20			4.24316
$640$	5.07616e19	+	5.07616e19i	1.15419	+	1.15419i
$641$	4.71022e19	+	4.71022e19i	1.05934	+	1.05934i	0.998125	+	0.0612149i	$0.0194975\pi$
$641$	4.71022e19	+	4.71022e19i	1.05934	+	1.05934i	0.0612149	+	0.998125i	$0.480503\pi$
$642$		−	1.69966e20i		−	3.78109i
$643$			5.44255e19i			1.19764i	0.800884	+	0.598819i	$0.204363\pi$
$643$			5.44255e19i			1.19764i	−0.800884	+	0.598819i	$0.795637\pi$
$644$		−	1.06024e20i		−	2.30782i
$645$	4.56801e19			0.983580
$646$	−1.48163e19	+	1.48163e19i	−0.315581	+	0.315581i
$647$			3.86217e19i			0.813770i	0.913479	+	0.406885i	$0.133385\pi$
$647$			3.86217e19i			0.813770i	−0.913479	+	0.406885i	$0.866615\pi$
$648$	−2.52385e20	+	2.52385e20i	−5.26064	+	5.26064i
$649$	−7.54744e18	−	7.54744e18i	−0.155628	−	0.155628i
$650$	4.16893e18	−	4.16893e18i	0.0850416	−	0.0850416i
$651$		−	7.03178e19i		−	1.41905i
$652$	2.65680e19	+	2.65680e19i	0.530428	+	0.530428i
$653$	−4.74041e18	+	4.74041e18i	−0.0936318	+	0.0936318i	−0.752371	−	0.658739i	$-0.771090\pi$
$653$	−4.74041e18	+	4.74041e18i	−0.0936318	+	0.0936318i	0.658739	+	0.752371i	$0.271090\pi$
$654$	1.10772e20			2.16464
$655$	1.39725e19	+	1.39725e19i	0.270137	+	0.270137i
$656$	−2.26056e19	+	2.26056e19i	−0.432403	+	0.432403i
$657$	−1.22153e20	−	1.22153e20i	−2.31178	−	2.31178i
$658$	5.37171e19			1.00585
$659$	2.43433e18	+	2.43433e18i	0.0451005	+	0.0451005i	0.729297	−	0.684197i	$-0.239847\pi$
$659$	2.43433e18	+	2.43433e18i	0.0451005	+	0.0451005i	−0.684197	+	0.729297i	$0.739847\pi$
$660$			4.00495e19i			0.734157i
$661$	−8.37299e19			−1.51869			−0.759347	−	0.650686i	$-0.774481\pi$
$661$	−8.37299e19			−1.51869			−0.759347	+	0.650686i	$0.774481\pi$
$662$	−1.05209e20			−1.88820
$663$	1.16040e20			2.06068
$664$	−1.02805e20	+	1.02805e20i	−1.80651	+	1.80651i
$665$	2.27779e19	−	2.27779e19i	0.396060	−	0.396060i
$666$		−	3.09396e20i		−	5.32347i
$667$	−4.43717e19	−	1.20781e19i	−0.755483	−	0.205645i
$668$	2.21219e19			0.372723
$669$	−8.55599e19	−	8.55599e19i	−1.42655	−	1.42655i
$670$	9.47031e19	+	9.47031e19i	1.56257	+	1.56257i
$671$			6.81263e18i			0.111239i
$672$		−	2.39931e19i		−	0.387705i
$673$		−	1.97363e19i		−	0.315617i	−0.987470	−	0.157808i	$-0.949557\pi$
$673$		−	1.97363e19i		−	0.315617i	0.987470	−	0.157808i	$-0.0504428\pi$
$674$	1.31481e20			2.08086
$675$	−6.76888e18	+	6.76888e18i	−0.106021	+	0.106021i
$676$		−	2.18439e20i		−	3.38613i
$677$	−3.19634e19	+	3.19634e19i	−0.490380	+	0.490380i	−0.908426	−	0.418046i	$-0.862715\pi$
$677$	−3.19634e19	+	3.19634e19i	−0.490380	+	0.490380i	0.418046	+	0.908426i	$0.362715\pi$
$678$	2.13928e20	+	2.13928e20i	3.24833	+	3.24833i
$679$	−3.17385e19	+	3.17385e19i	−0.476978	+	0.476978i
$680$		−	7.70413e19i		−	1.14594i
$681$	1.27943e20	+	1.27943e20i	1.88359	+	1.88359i
$682$	−8.00824e18	+	8.00824e18i	−0.116693	+	0.116693i
$683$	1.67871e19			0.242120			0.121060	−	0.992645i	$-0.461371\pi$
$683$	1.67871e19			0.242120			0.121060	+	0.992645i	$0.461371\pi$
$684$	−1.12522e20	−	1.12522e20i	−1.60636	−	1.60636i
$685$	−4.58214e19	+	4.58214e19i	−0.647492	+	0.647492i
$686$	1.15212e19	+	1.15212e19i	0.161150	+	0.161150i
$687$	−5.64692e19			−0.781834
$688$	2.96658e19	+	2.96658e19i	0.406572	+	0.406572i
$689$		−	2.41812e19i		−	0.328052i
$690$	1.94264e20			2.60884
$691$	1.03822e20			1.38021			0.690105	−	0.723710i	$-0.257564\pi$
$691$	1.03822e20			1.38021			0.690105	+	0.723710i	$0.257564\pi$
$692$	2.98305e19			0.392571
$693$	−4.16197e19	+	4.16197e19i	−0.542208	+	0.542208i
$694$	−6.32217e17	+	6.32217e17i	−0.00815361	+	0.00815361i
$695$		−	7.40652e19i		−	0.945629i
$696$	−2.69955e20	−	7.34826e19i	−3.41214	−	0.928795i
$697$	−2.82860e19			−0.353950
$698$	−1.40344e20	−	1.40344e20i	−1.73862	−	1.73862i
$699$	5.27269e19	+	5.27269e19i	0.646683	+	0.646683i
$700$		−	1.02666e19i		−	0.124664i
$701$		−	5.68503e18i		−	0.0683450i	−0.999416	−	0.0341725i	$-0.989120\pi$
$701$		−	5.68503e18i		−	0.0683450i	0.999416	−	0.0341725i	$-0.0108796\pi$
$702$			8.46914e20i			10.0804i
$703$	3.64427e19			0.429460
$704$	1.00256e19	−	1.00256e19i	0.116978	−	0.116978i
$705$			6.60330e19i			0.762847i
$706$	2.10244e20	−	2.10244e20i	2.40486	−	2.40486i
$707$	−8.26152e19	−	8.26152e19i	−0.935673	−	0.935673i
$708$	−2.93304e20	+	2.93304e20i	−3.28916	+	3.28916i
$709$		−	1.02470e19i		−	0.113782i	−0.998380	−	0.0568909i	$-0.981881\pi$
$709$		−	1.02470e19i		−	0.113782i	0.998380	−	0.0568909i	$-0.0181187\pi$
$710$	−1.65372e20	−	1.65372e20i	−1.81825	−	1.81825i
$711$	1.45295e20	−	1.45295e20i	1.58184	−	1.58184i
$712$	1.96460e20			2.11795
$713$	2.60611e19	+	2.60611e19i	0.278206	+	0.278206i
$714$	2.12970e20	−	2.12970e20i	2.25129	−	2.25129i
$715$	2.03166e19	+	2.03166e19i	0.212672	+	0.212672i
$716$	−3.01432e19			−0.312462
$717$	6.15630e19	+	6.15630e19i	0.631954	+	0.631954i
$718$			1.69896e20i			1.72708i
$719$	1.77767e20			1.78957			0.894784	−	0.446499i	$-0.147330\pi$
$719$	1.77767e20			1.78957			0.894784	+	0.446499i	$0.147330\pi$
$720$	3.08763e20			3.07820
$721$	1.61336e20			1.59288
$722$	−1.06307e20	+	1.06307e20i	−1.03945	+	1.03945i
$723$	−9.92476e19	+	9.92476e19i	−0.961063	+	0.961063i
$724$		−	2.49931e20i		−	2.39691i
$725$	−4.29666e18	−	1.16956e18i	−0.0408098	−	0.0111086i
$726$	−3.49097e20			−3.28390
$727$	1.93395e19	+	1.93395e19i	0.180179	+	0.180179i	0.791434	−	0.611255i	$-0.209335\pi$
$727$	1.93395e19	+	1.93395e19i	0.180179	+	0.180179i	−0.611255	+	0.791434i	$0.709335\pi$
$728$	−3.27223e20	−	3.27223e20i	−3.01943	−	3.01943i
$729$		−	5.08039e20i		−	4.64306i
$730$			2.18877e20i			1.98125i
$731$			3.71204e19i			0.332806i
$732$	2.64748e20			2.35101
$733$	−8.62359e18	+	8.62359e18i	−0.0758508	+	0.0758508i	−0.744014	−	0.668164i	$-0.767081\pi$
$733$	−8.62359e18	+	8.62359e18i	−0.0758508	+	0.0758508i	0.668164	+	0.744014i	$0.267081\pi$
$734$		−	2.17610e20i		−	1.89586i
$735$	−1.70787e20	+	1.70787e20i	−1.47382	+	1.47382i
$736$	8.89228e18	+	8.89228e18i	0.0760096	+	0.0760096i
$737$	2.03819e19	−	2.03819e19i	0.172573	−	0.172573i
$738$		−	3.20190e20i		−	2.68543i
$739$	1.07904e20	+	1.07904e20i	0.896453	+	0.896453i	0.995120	−	0.0986674i	$-0.0314580\pi$
$739$	1.07904e20	+	1.07904e20i	0.896453	+	0.896453i	−0.0986674	+	0.995120i	$0.531458\pi$
$740$	−1.85970e20	+	1.85970e20i	−1.53045	+	1.53045i
$741$	−1.54717e20			−1.26128
$742$	−4.43804e19	−	4.43804e19i	−0.358396	−	0.358396i
$743$	−8.86207e19	+	8.86207e19i	−0.708947	+	0.708947i	−0.966314	−	0.257367i	$-0.917145\pi$
$743$	−8.86207e19	+	8.86207e19i	−0.708947	+	0.708947i	0.257367	+	0.966314i	$0.417145\pi$
$744$	1.58554e20	+	1.58554e20i	1.25651	+	1.25651i
$745$	−1.05029e20			−0.824549
$746$	6.04977e19	+	6.04977e19i	0.470508	+	0.470508i
$747$		−	5.15553e20i		−	3.97218i
$748$	−3.25448e19			−0.248411
$749$	−2.12335e20			−1.60564
$750$	4.63576e20			3.47290
$751$	−1.62288e20	+	1.62288e20i	−1.20450	+	1.20450i	−0.231716	+	0.972783i	$0.574434\pi$
$751$	−1.62288e20	+	1.62288e20i	−1.20450	+	1.20450i	−0.972783	+	0.231716i	$0.925566\pi$
$752$	−4.28835e19	+	4.28835e19i	−0.315330	+	0.315330i
$753$			1.57631e20i			1.14836i
$754$	−3.41964e20	+	1.95629e20i	−2.46820	+	1.41200i
$755$	−3.44477e19			−0.246338
$756$	1.04283e21	+	1.04283e21i	7.38857	+	7.38857i
$757$	8.05193e19	+	8.05193e19i	0.565235	+	0.565235i	0.930790	−	0.365555i	$-0.119121\pi$
$757$	8.05193e19	+	8.05193e19i	0.565235	+	0.565235i	−0.365555	+	0.930790i	$0.619121\pi$
$758$		−	3.65975e20i		−	2.54546i
$759$		−	4.18093e19i		−	0.288125i
$760$			1.02720e20i			0.701391i
$761$	−8.87783e19			−0.600640			−0.300320	−	0.953839i	$-0.597093\pi$
$761$	−8.87783e19			−0.600640			−0.300320	+	0.953839i	$0.597093\pi$
$762$	−2.44269e19	+	2.44269e19i	−0.163751	+	0.163751i
$763$		−	1.38385e20i		−	0.919217i
$764$	−2.11290e19	+	2.11290e19i	−0.139067	+	0.139067i
$765$	1.93175e20	+	1.93175e20i	1.25986	+	1.25986i
$766$	3.77847e19	−	3.77847e19i	0.244182	−	0.244182i
$767$			2.97579e20i			1.90562i
$768$	−4.41697e20	−	4.41697e20i	−2.80283	−	2.80283i
$769$	3.28745e19	−	3.28745e19i	0.206716	−	0.206716i	−0.596154	−	0.802870i	$-0.703305\pi$
$769$	3.28745e19	−	3.28745e19i	0.206716	−	0.206716i	0.802870	+	0.596154i	$0.203305\pi$
$770$	7.45753e19			0.464686
$771$	−1.35566e20	−	1.35566e20i	−0.837089	−	0.837089i
$772$	−1.32576e20	+	1.32576e20i	−0.811228	+	0.811228i
$773$	−1.19644e20	−	1.19644e20i	−0.725493	−	0.725493i	0.244226	−	0.969718i	$-0.421466\pi$
$773$	−1.19644e20	−	1.19644e20i	−0.725493	−	0.725493i	−0.969718	+	0.244226i	$0.921466\pi$
$774$	−4.20193e20			−2.52501
$775$	2.52358e18	+	2.52358e18i	0.0150282	+	0.0150282i
$776$		−	1.43130e20i		−	0.844691i
$777$	−5.23830e20			−3.06368
$778$	2.15775e20			1.25068
$779$	3.77141e19			0.216641
$780$	7.89532e20	−	7.89532e20i	4.49477	−	4.49477i
$781$	−3.55913e19	+	3.55913e19i	−0.200810	+	0.200810i
$782$			1.57862e20i			0.882732i
$783$	5.55229e20	−	3.17633e20i	3.07709	−	1.76033i
$784$	−2.21827e20			−1.21843
$785$	1.72437e20	+	1.72437e20i	0.938734	+	0.938734i
$786$	−1.74185e20	−	1.74185e20i	−0.939840	−	0.939840i
$787$			6.88760e19i			0.368336i	0.982895	+	0.184168i	$0.0589591\pi$
$787$			6.88760e19i			0.368336i	−0.982895	+	0.184168i	$0.941041\pi$
$788$		−	1.28439e20i		−	0.680791i
$789$		−	3.57010e20i		−	1.87560i
$790$	−2.60344e20			−1.35568
$791$	2.67256e20	−	2.67256e20i	1.37940	−	1.37940i
$792$		−	1.87690e20i		−	0.960207i
$793$	1.34304e20	−	1.34304e20i	0.681044	−	0.681044i
$794$	4.21456e20	+	4.21456e20i	2.11841	+	2.11841i
$795$	5.45556e19	−	5.45556e19i	0.271813	−	0.271813i
$796$		−	1.87421e20i		−	0.925608i
$797$	−1.75093e20	−	1.75093e20i	−0.857159	−	0.857159i	0.133843	−	0.991003i	$-0.457268\pi$
$797$	−1.75093e20	−	1.75093e20i	−0.857159	−	0.857159i	−0.991003	+	0.133843i	$0.957268\pi$
$798$	−2.83956e20	+	2.83956e20i	−1.37794	+	1.37794i
$799$	−5.36595e19			−0.258118
$800$	8.61070e17	+	8.61070e17i	0.00410590	+	0.00410590i
$801$	−4.92609e20	+	4.92609e20i	−2.32849	+	2.32849i
$802$	1.60364e20	+	1.60364e20i	0.751426	+	0.751426i
$803$	4.71065e19			0.218813
$804$	−7.92069e20	−	7.92069e20i	−3.64729	−	3.64729i
$805$		−	2.42689e20i		−	1.10785i
$806$	3.15748e20			1.42888
$807$	−6.94923e20			−3.11761
$808$	3.72565e20			1.65700
$809$	1.16998e20	−	1.16998e20i	0.515866	−	0.515866i	−0.400452	−	0.916318i	$-0.631147\pi$
$809$	1.16998e20	−	1.16998e20i	0.515866	−	0.515866i	0.916318	+	0.400452i	$0.131147\pi$
$810$	−1.13393e21	+	1.13393e21i	−4.95670	+	4.95670i
$811$			3.14845e20i			1.36443i	0.731152	+	0.682215i	$0.238983\pi$
$811$			3.14845e20i			1.36443i	−0.731152	+	0.682215i	$0.761017\pi$
$812$	−1.80186e20	+	6.61953e20i	−0.774156	+	2.84404i
$813$	2.02544e20			0.862750
$814$	5.96572e19	+	5.96572e19i	0.251937	+	0.251937i
$815$	6.08144e19	+	6.08144e19i	0.254626	+	0.254626i
$816$			3.40037e20i			1.41155i
$817$		−	4.94931e19i		−	0.203700i
$818$		−	3.18311e20i		−	1.29891i
$819$	1.64097e21			6.63918
$820$	−1.92458e20	+	1.92458e20i	−0.772037	+	0.772037i
$821$			2.34347e20i			0.932087i	0.884762	+	0.466044i	$0.154321\pi$
$821$			2.34347e20i			0.932087i	−0.884762	+	0.466044i	$0.845679\pi$
$822$	5.71224e20	−	5.71224e20i	2.25270	−	2.25270i
$823$	−2.09677e20	−	2.09677e20i	−0.819884	−	0.819884i	0.166207	−	0.986091i	$-0.446848\pi$
$823$	−2.09677e20	−	2.09677e20i	−0.819884	−	0.819884i	−0.986091	+	0.166207i	$0.946848\pi$
$824$	−3.63783e20	+	3.63783e20i	−1.41043	+	1.41043i
$825$		−	4.04853e18i		−	0.0155640i
$826$	5.46155e20	+	5.46155e20i	2.08188	+	2.08188i
$827$	−1.23026e20	+	1.23026e20i	−0.465005	+	0.465005i	−0.900292	−	0.435287i	$-0.856647\pi$
$827$	−1.23026e20	+	1.23026e20i	−0.465005	+	0.465005i	0.435287	+	0.900292i	$0.356647\pi$
$828$	−1.19887e21			−4.49326
$829$	−1.77462e20	−	1.77462e20i	−0.659513	−	0.659513i	0.295752	−	0.955265i	$-0.404430\pi$
$829$	−1.77462e20	−	1.77462e20i	−0.659513	−	0.659513i	−0.955265	+	0.295752i	$0.904430\pi$
$830$	−4.61891e20	+	4.61891e20i	−1.70213	+	1.70213i
$831$	−2.46509e20	−	2.46509e20i	−0.900794	−	0.900794i
$832$	−3.95289e20			−1.43236
$833$	−1.38784e20	−	1.38784e20i	−0.498683	−	0.498683i
$834$			9.23321e20i			3.28996i
$835$	5.06371e19			0.178922
$836$	4.33924e19			0.152044
$837$	−5.12663e20			−1.78137
$838$	−3.58439e20	+	3.58439e20i	−1.23511	+	1.23511i
$839$	4.05696e20	−	4.05696e20i	1.38633	−	1.38633i	0.553449	−	0.832883i	$-0.313311\pi$
$839$	4.05696e20	−	4.05696e20i	1.38633	−	1.38633i	0.832883	−	0.553449i	$-0.186689\pi$
$840$		−	1.47651e21i		−	5.00358i
$841$	2.56505e20	+	1.50818e20i	0.862033	+	0.506852i
$842$	8.19680e20			2.73187
$843$	2.54892e20	+	2.54892e20i	0.842486	+	0.842486i
$844$	1.32836e20	+	1.32836e20i	0.435432	+	0.435432i
$845$		−	5.00009e20i		−	1.62548i
$846$		−	6.07411e20i		−	1.95835i
$847$			4.36119e20i			1.39451i
$848$	7.08596e19			0.224713
$849$	−8.10481e20	+	8.10481e20i	−2.54911	+	2.54911i
$850$			1.52863e19i			0.0476836i
$851$	1.94141e20	−	1.94141e20i	0.600636	−	0.600636i
$852$	1.38312e21	+	1.38312e21i	4.24409	+	4.24409i
$853$	2.63227e20	−	2.63227e20i	0.801099	−	0.801099i	−0.182168	−	0.983267i	$-0.558311\pi$
$853$	2.63227e20	−	2.63227e20i	0.801099	−	0.801099i	0.983267	+	0.182168i	$0.0583115\pi$
$854$		−	4.92982e20i		−	1.48808i
$855$	−2.57563e20	−	2.57563e20i	−0.771117	−	0.771117i
$856$	4.78779e20	−	4.78779e20i	1.42173	−	1.42173i
$857$	4.60408e20			1.35606			0.678028	−	0.735036i	$-0.262835\pi$
$857$	4.60408e20			1.35606			0.678028	+	0.735036i	$0.262835\pi$
$858$	−2.53274e20	−	2.53274e20i	−0.739911	−	0.739911i
$859$	1.93894e20	−	1.93894e20i	0.561838	−	0.561838i	−0.367991	−	0.929829i	$-0.619954\pi$
$859$	1.93894e20	−	1.93894e20i	0.561838	−	0.561838i	0.929829	+	0.367991i	$0.119954\pi$
$860$	2.52567e20	+	2.52567e20i	0.725917	+	0.725917i
$861$	−5.42106e20			−1.54548
$862$	3.14296e20	+	3.14296e20i	0.888767	+	0.888767i
$863$		−	3.85219e20i		−	1.08052i	−0.841499	−	0.540259i	$-0.818326\pi$
$863$		−	3.85219e20i		−	1.08052i	0.841499	−	0.540259i	$-0.181674\pi$
$864$	−1.74925e20			−0.486695
$865$	6.82822e19			0.188449
$866$	8.97906e20			2.45813
$867$	2.95845e20	−	2.95845e20i	0.803398	−	0.803398i
$868$	3.88789e20	−	3.88789e20i	1.04731	−	1.04731i
$869$			5.60311e19i			0.149724i
$870$	−1.21287e21	−	3.30148e20i	−3.21499	−	0.875132i
$871$	−8.03616e20			−2.11311
$872$	3.12034e20	+	3.12034e20i	0.813930	+	0.813930i
$873$	3.58886e20	+	3.58886e20i	0.928661	+	0.928661i
$874$		−	2.10479e20i		−	0.540292i
$875$		−	5.79135e20i		−	1.47477i
$876$		−	1.83062e21i		−	4.62456i
$877$	−1.55216e20			−0.388992			−0.194496	−	0.980903i	$-0.562307\pi$
$877$	−1.55216e20			−0.388992			−0.194496	+	0.980903i	$0.562307\pi$
$878$	−3.89625e20	+	3.89625e20i	−0.968690	+	0.968690i
$879$			3.06719e20i			0.756517i
$880$	−5.95351e19	+	5.95351e19i	−0.145678	+	0.145678i
$881$	−3.53503e20	−	3.53503e20i	−0.858147	−	0.858147i	0.132973	−	0.991120i	$-0.457548\pi$
$881$	−3.53503e20	−	3.53503e20i	−0.858147	−	0.858147i	−0.991120	+	0.132973i	$0.957548\pi$
$882$	1.57100e21	−	1.57100e21i	3.78352	−	3.78352i
$883$			7.88527e20i			1.88405i	0.335547	+	0.942023i	$0.391079\pi$
$883$			7.88527e20i			1.88405i	−0.335547	+	0.942023i	$0.608921\pi$
$884$	6.41586e20	+	6.41586e20i	1.52086	+	1.52086i
$885$	−6.71374e20	+	6.71374e20i	−1.57893	+	1.57893i
$886$	−3.75619e20			−0.876419
$887$	3.16198e20	+	3.16198e20i	0.731970	+	0.731970i	0.971010	−	0.239039i	$-0.0768325\pi$
$887$	3.16198e20	+	3.16198e20i	0.731970	+	0.731970i	−0.239039	+	0.971010i	$0.576833\pi$
$888$	1.18115e21	−	1.18115e21i	2.71277	−	2.71277i
$889$	3.05160e19	+	3.05160e19i	0.0695369	+	0.0695369i
$890$	8.82670e20			1.99558
$891$	2.44044e20	+	2.44044e20i	0.547425	+	0.547425i
$892$		−	9.46126e20i		−	2.10569i
$893$	7.15449e19			0.157986
$894$	1.30933e21			2.86871
$895$	−6.89979e19			−0.149994
$896$	−7.90557e20	+	7.90557e20i	−1.70521	+	1.70521i
$897$	−8.24225e20	+	8.24225e20i	−1.76400	+	1.76400i
$898$		−	3.90248e20i		−	0.828718i
$899$	−1.18420e20	−	2.07001e20i	−0.249522	−	0.436169i
$900$	−1.16091e20			−0.242717
$901$	4.43327e19	+	4.43327e19i	0.0919710	+	0.0919710i
$902$	6.17385e19	+	6.17385e19i	0.127090	+	0.127090i
$903$			7.11418e20i			1.45315i
$904$			1.20523e21i			2.44281i
$905$		−	5.72095e20i		−	1.15061i
$906$	4.29437e20			0.857041
$907$	1.05727e20	−	1.05727e20i	0.209380	−	0.209380i	−0.594624	−	0.804004i	$-0.702699\pi$
$907$	1.05727e20	−	1.05727e20i	0.209380	−	0.209380i	0.804004	+	0.594624i	$0.202699\pi$
$908$			1.41480e21i			2.78032i
$909$	−9.34178e20	+	9.34178e20i	−1.82172	+	1.82172i
$910$	−1.47017e21	−	1.47017e21i	−2.84497	−	2.84497i
$911$	3.51751e20	−	3.51751e20i	0.675470	−	0.675470i	−0.283501	−	0.958972i	$-0.591496\pi$
$911$	3.51751e20	−	3.51751e20i	0.675470	−	0.675470i	0.958972	+	0.283501i	$0.0914961\pi$
$912$		−	4.53376e20i		−	0.863963i
$913$	9.94080e19	+	9.94080e19i	0.187986	+	0.187986i
$914$	−8.29421e20	+	8.29421e20i	−1.55651	+	1.55651i
$915$	6.06009e20			1.12858
$916$	−3.12220e20	−	3.12220e20i	−0.577022	−	0.577022i
$917$	−2.17606e20	+	2.17606e20i	−0.399103	+	0.399103i
$918$	−1.55269e21	−	1.55269e21i	−2.82610	−	2.82610i
$919$	−1.32924e19			−0.0240101			−0.0120050	−	0.999928i	$-0.503821\pi$
$919$	−1.32924e19			−0.0240101			−0.0120050	+	0.999928i	$0.503821\pi$
$920$	5.47222e20	+	5.47222e20i	0.980953	+	0.980953i
$921$			1.85369e20i			0.329777i
$922$	−1.37846e21			−2.43375
$923$	1.40329e21			2.45887
$924$	−6.23726e20			−1.08465
$925$	1.87994e19	−	1.87994e19i	0.0324452	−	0.0324452i
$926$	3.26995e20	−	3.26995e20i	0.560098	−	0.560098i
$927$		−	1.82432e21i		−	3.10129i
$928$	−4.04061e19	−	7.06307e19i	−0.0681728	−	0.119167i
$929$	1.09234e21			1.82915			0.914575	−	0.404417i	$-0.132525\pi$
$929$	1.09234e21			1.82915			0.914575	+	0.404417i	$0.132525\pi$
$930$	7.12364e20	+	7.12364e20i	1.18392	+	1.18392i
$931$	1.85043e20	+	1.85043e20i	0.305228	+	0.305228i
$932$			5.83057e20i			0.954551i
$933$			5.51925e20i			0.896827i
$934$			4.20858e20i			0.678746i
$935$	−7.44953e19			−0.119247
$936$	−3.70011e21	+	3.70011e21i	−5.87873	+	5.87873i
$937$			6.08601e20i			0.959745i	0.877338	+	0.479872i	$0.159317\pi$
$937$			6.08601e20i			0.959745i	−0.877338	+	0.479872i	$0.840683\pi$
$938$	−1.47490e21	+	1.47490e21i	−2.30856	+	2.30856i
$939$	−6.97103e20	−	6.97103e20i	−1.08302	−	1.08302i
$940$	−3.65099e20	+	3.65099e20i	−0.563009	+	0.563009i
$941$		−	2.91262e20i		−	0.445817i	−0.974839	−	0.222908i	$-0.928445\pi$
$941$		−	2.91262e20i		−	0.445817i	0.974839	−	0.222908i	$-0.0715551\pi$
$942$	−2.14965e21	−	2.14965e21i	−3.26597	−	3.26597i
$943$	2.00915e20	−	2.00915e20i	0.302991	−	0.302991i
$944$	−8.72015e20			−1.30533
$945$	2.38704e21	+	2.38704e21i	3.54681	+	3.54681i
$946$	8.10209e19	−	8.10209e19i	0.119498	−	0.119498i
$947$	−4.45783e20	−	4.45783e20i	−0.652640	−	0.652640i	0.300988	−	0.953628i	$-0.402684\pi$
$947$	−4.45783e20	−	4.45783e20i	−0.652640	−	0.652640i	−0.953628	+	0.300988i	$0.902684\pi$
$948$	2.17744e21			3.16438
$949$	−9.28655e20	−	9.28655e20i	−1.33965	−	1.33965i
$950$		−	2.03814e19i		−	0.0291856i
$951$	2.64227e21			3.75590
$952$	1.19983e21			1.69302
$953$	3.90772e20			0.547359			0.273680	−	0.961821i	$-0.411759\pi$
$953$	3.90772e20			0.547359			0.273680	+	0.961821i	$0.411759\pi$
$954$	−5.01835e20	+	5.01835e20i	−0.697786	+	0.697786i
$955$	−4.83643e19	+	4.83643e19i	−0.0667578	+	0.0667578i
$956$			6.80767e20i			0.932810i
$957$	−7.10542e19	+	2.61034e20i	−0.0966510	+	0.355069i
$958$	−4.96319e20			−0.670197
$959$	−7.13618e20	−	7.13618e20i	−0.956611	−	0.956611i
$960$	−8.91819e20	−	8.91819e20i	−1.18680	−	1.18680i
$961$		−	5.65812e20i		−	0.747495i
$962$		−	2.35215e21i		−	3.08489i
$963$			2.40100e21i			3.12614i
$964$	−1.09749e21			−1.41860
$965$	−3.03467e20	+	3.03467e20i	−0.389422	+	0.389422i
$966$			3.02544e21i			3.85433i
$967$	−4.08574e20	+	4.08574e20i	−0.516756	+	0.516756i	−0.916588	−	0.399832i	$-0.869068\pi$
$967$	−4.08574e20	+	4.08574e20i	−0.516756	+	0.516756i	0.399832	+	0.916588i	$0.369068\pi$
$968$	−9.83372e20	−	9.83372e20i	−1.23478	−	1.23478i
$969$	2.83651e20	−	2.83651e20i	0.353605	−	0.353605i
$970$		−	6.43063e20i		−	0.795887i
$971$	−1.57578e20	−	1.57578e20i	−0.193625	−	0.193625i	0.603636	−	0.797260i	$-0.293718\pi$
$971$	−1.57578e20	−	1.57578e20i	−0.193625	−	0.193625i	−0.797260	+	0.603636i	$0.793718\pi$
$972$	5.29492e21	−	5.29492e21i	6.45945	−	6.45945i
$973$	1.15349e21			1.39708
$974$	−1.21904e21	−	1.21904e21i	−1.46590	−	1.46590i
$975$	−7.98125e19	+	7.98125e19i	−0.0952881	+	0.0952881i
$976$	3.93558e20	+	3.93558e20i	0.466509	+	0.466509i
$977$	7.88439e20			0.927910			0.463955	−	0.885859i	$-0.346430\pi$
$977$	7.88439e20			0.927910			0.463955	+	0.885859i	$0.346430\pi$
$978$	−7.58132e20	−	7.58132e20i	−0.885876	−	0.885876i
$979$		−	1.89968e20i		−	0.220395i
$980$	−1.88857e21			−2.17546
$981$	−1.56480e21			−1.78969
$982$	7.03016e20			0.798335
$983$	−9.82330e20	+	9.82330e20i	−1.10760	+	1.10760i	−0.114134	+	0.993465i	$0.536409\pi$
$983$	−9.82330e20	+	9.82330e20i	−1.10760	+	1.10760i	−0.993465	+	0.114134i	$0.963591\pi$
$984$	1.22235e21	−	1.22235e21i	1.36846	−	1.36846i
$985$		−	2.93998e20i		−	0.326807i
$986$	2.68283e20	−	9.85599e20i	0.296111	−	1.08783i
$987$	−1.02839e21			−1.12704
$988$	−8.55435e20	−	8.55435e20i	−0.930869	−	0.930869i
$989$	−2.63665e20	−	2.63665e20i	−0.284891	−	0.284891i
$990$		−	8.43267e20i		−	0.904729i
$991$		−	6.01434e20i		−	0.640727i	−0.947295	−	0.320363i	$-0.896195\pi$
$991$		−	6.01434e20i		−	0.640727i	0.947295	−	0.320363i	$-0.103805\pi$
$992$			6.52160e19i			0.0689878i
$993$	2.01419e21			2.11570
$994$	2.57549e21	−	2.57549e21i	2.68630	−	2.68630i
$995$		−	4.29008e20i		−	0.444328i
$996$	3.86313e21	−	3.86313e21i	3.97305	−	3.97305i
$997$	−1.53152e20	−	1.53152e20i	−0.156407	−	0.156407i	0.624565	−	0.780972i	$-0.285276\pi$
$997$	−1.53152e20	−	1.53152e20i	−0.156407	−	0.156407i	−0.780972	+	0.624565i	$0.785276\pi$
$998$	−2.06956e21	+	2.06956e21i	−2.09877	+	2.09877i
$999$			3.81907e21i			3.84591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.15.c.a.12.4	✓	68
29.17	odd	4	inner	29.15.c.a.17.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.15.c.a.12.4	✓	68	1.1	even	1	trivial
29.15.c.a.17.4	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)

\(f(q)\)	\(=\)	\(q+(-157.774 - 157.774i) q^{2} +(3020.51 + 3020.51i) q^{3} +33401.0i q^{4} +76455.0i q^{5} -953113. i q^{6} -1.19070e6 q^{7} +(2.68483e6 - 2.68483e6i) q^{8} +1.34640e7i q^{9} +O(q^{10})\)	\(q+(-157.774 - 157.774i) q^{2} +(3020.51 + 3020.51i) q^{3} +33401.0i q^{4} +76455.0i q^{5} -953113. i q^{6} -1.19070e6 q^{7} +(2.68483e6 - 2.68483e6i) q^{8} +1.34640e7i q^{9} +(1.20626e7 - 1.20626e7i) q^{10} +(-2.59610e6 - 2.59610e6i) q^{11} +(-1.00888e8 + 1.00888e8i) q^{12} +1.02359e8i q^{13} +(1.87861e8 + 1.87861e8i) q^{14} +(-2.30933e8 + 2.30933e8i) q^{15} -2.99948e8 q^{16} +(-1.87660e8 - 1.87660e8i) q^{17} +(2.12426e9 - 2.12426e9i) q^{18} +(2.50209e8 + 2.50209e8i) q^{19} -2.55367e9 q^{20} +(-3.59653e9 - 3.59653e9i) q^{21} +8.19192e8i q^{22} +2.66588e9 q^{23} +1.62191e10 q^{24} +2.58146e8 q^{25} +(1.61495e10 - 1.61495e10i) q^{26} +(-2.62211e10 + 2.62211e10i) q^{27} -3.97706e10i q^{28} +(-1.66443e10 - 4.53063e9i) q^{29} +7.28702e10 q^{30} +(9.77578e9 + 9.77578e9i) q^{31} +(3.33559e9 + 3.33559e9i) q^{32} -1.56831e10i q^{33} +5.92155e10i q^{34} -9.10352e10i q^{35} -4.49710e11 q^{36} +(7.28244e10 - 7.28244e10i) q^{37} -7.89528e10i q^{38} +(-3.09175e11 + 3.09175e11i) q^{39} +(2.05268e11 + 2.05268e11i) q^{40} +(7.53651e10 - 7.53651e10i) q^{41} +1.13487e12i q^{42} +(-9.89034e10 - 9.89034e10i) q^{43} +(8.67123e10 - 8.67123e10i) q^{44} -1.02939e12 q^{45} +(-4.20606e11 - 4.20606e11i) q^{46} +(1.42970e11 - 1.42970e11i) q^{47} +(-9.05994e11 - 9.05994e11i) q^{48} +7.39551e11 q^{49} +(-4.07287e10 - 4.07287e10i) q^{50} -1.13366e12i q^{51} -3.41888e12 q^{52} -2.36240e11 q^{53} +8.27398e12 q^{54} +(1.98485e11 - 1.98485e11i) q^{55} +(-3.19683e12 + 3.19683e12i) q^{56} +1.51152e12i q^{57} +(1.91121e12 + 3.34084e12i) q^{58} +2.90722e12 q^{59} +(-7.71339e12 - 7.71339e12i) q^{60} +(-1.31209e12 - 1.31209e12i) q^{61} -3.08472e12i q^{62} -1.60316e13i q^{63} +3.86181e12i q^{64} -7.82583e12 q^{65} +(-2.47438e12 + 2.47438e12i) q^{66} +7.85098e12i q^{67} +(6.26802e12 - 6.26802e12i) q^{68} +(8.05232e12 + 8.05232e12i) q^{69} +(-1.43629e13 + 1.43629e13i) q^{70} -1.37095e13i q^{71} +(3.61485e13 + 3.61485e13i) q^{72} +(-9.07256e12 + 9.07256e12i) q^{73} -2.29795e13 q^{74} +(7.79734e11 + 7.79734e11i) q^{75} +(-8.35723e12 + 8.35723e12i) q^{76} +(3.09119e12 + 3.09119e12i) q^{77} +9.75593e13 q^{78} +(-1.07914e13 - 1.07914e13i) q^{79} -2.29325e13i q^{80} -9.40042e13 q^{81} -2.37812e13 q^{82} -3.82913e13 q^{83} +(1.20128e14 - 1.20128e14i) q^{84} +(1.43475e13 - 1.43475e13i) q^{85} +3.12087e13i q^{86} +(-3.65894e13 - 6.39590e13i) q^{87} -1.39402e13 q^{88} +(3.65871e13 + 3.65871e13i) q^{89} +(1.62410e14 + 1.62410e14i) q^{90} -1.21879e14i q^{91} +8.90430e13i q^{92} +5.90557e13i q^{93} -4.51138e13 q^{94} +(-1.91298e13 + 1.91298e13i) q^{95} +2.01503e13i q^{96} +(2.66553e13 - 2.66553e13i) q^{97} +(-1.16682e14 - 1.16682e14i) q^{98} +(3.49538e13 - 3.49538e13i) 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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