LMFDB - Embedded newform 12.17.d.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,17,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	12.d (of order $2$, degree $1$, 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:	$19.4789452628$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 37115 x^{14} + 433616 x^{13} + 965822723 x^{12} + 11579264195 x^{11} + \cdots + 43\!\cdots\!49 $ x^16 - x^15 + 37115x^14 + 433616x^13 + 965822723x^12 + 11579264195x^11 + 12661863519850x^10 + 162120109773543x^9 + 120758933936870280x^8 + 1240343233445130327x^7 + 553297868296926315210x^6 + 3641854073469392130003x^5 + 1781463130185670341595803x^4 + 12984494303085096280528944x^3 + 125765846444242947670566147x^2 - 206760575884676576961270033x + 435779119237071236287541049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{106}\cdot 3^{51} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.3
Root			$36.4487 + 63.1310i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.17.d.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-235.541 - 100.281i) q^{2} -3788.00i q^{3} +(45423.4 + 47240.7i) q^{4} +699204. q^{5} +(-379865. + 892229. i) q^{6} +4.77594e6i q^{7} +(-5.96172e6 - 1.56822e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})$	\(q+(-235.541 - 100.281i) q^{2} -3788.00i q^{3} +(45423.4 + 47240.7i) q^{4} +699204. q^{5} +(-379865. + 892229. i) q^{6} +4.77594e6i q^{7} +(-5.96172e6 - 1.56822e7i) q^{8} -1.43489e7 q^{9} +(-1.64691e8 - 7.01170e7i) q^{10} +3.02715e8i q^{11} +(1.78948e8 - 1.72063e8i) q^{12} -7.87862e8 q^{13} +(4.78937e8 - 1.12493e9i) q^{14} -2.64858e9i q^{15} +(-1.68403e8 + 4.29166e9i) q^{16} -1.70368e9 q^{17} +(3.37976e9 + 1.43893e9i) q^{18} +1.50372e10i q^{19} +(3.17602e10 + 3.30309e10i) q^{20} +1.80913e10 q^{21} +(3.03566e10 - 7.13019e10i) q^{22} +1.14606e11i q^{23} +(-5.94043e10 + 2.25830e10i) q^{24} +3.36298e11 q^{25} +(1.85574e11 + 7.90078e10i) q^{26} +5.43536e10i q^{27} +(-2.25619e11 + 2.16939e11i) q^{28} -5.20244e11 q^{29} +(-2.65603e11 + 6.23850e11i) q^{30} -3.94051e11i q^{31} +(4.70039e11 - 9.93976e11i) q^{32} +1.14668e12 q^{33} +(4.01287e11 + 1.70847e11i) q^{34} +3.33936e12i q^{35} +(-6.51776e11 - 6.77853e11i) q^{36} +1.57195e12 q^{37} +(1.50795e12 - 3.54189e12i) q^{38} +2.98442e12i q^{39} +(-4.16846e12 - 1.09651e13i) q^{40} -4.91938e12 q^{41} +(-4.26124e12 - 1.81421e12i) q^{42} -7.30424e12i q^{43} +(-1.43005e13 + 1.37503e13i) q^{44} -1.00328e13 q^{45} +(1.14928e13 - 2.69944e13i) q^{46} +2.40861e13i q^{47} +(1.62568e13 + 6.37911e11i) q^{48} +1.04233e13 q^{49} +(-7.92120e13 - 3.37243e13i) q^{50} +6.45353e12i q^{51} +(-3.57874e13 - 3.72192e13i) q^{52} +1.16916e14 q^{53} +(5.45064e12 - 1.28025e13i) q^{54} +2.11659e14i q^{55} +(7.48975e13 - 2.84728e13i) q^{56} +5.69609e13 q^{57} +(1.22539e14 + 5.21707e13i) q^{58} +1.48155e14i q^{59} +(1.25121e14 - 1.20307e14i) q^{60} +1.03715e14 q^{61} +(-3.95159e13 + 9.28153e13i) q^{62} -6.85296e13i q^{63} +(-2.10391e14 + 1.86986e14i) q^{64} -5.50876e14 q^{65} +(-2.70091e14 - 1.14991e14i) q^{66} -3.79266e14i q^{67} +(-7.73868e13 - 8.04830e13i) q^{68} +4.34126e14 q^{69} +(3.34875e14 - 7.86556e14i) q^{70} +7.89683e14i q^{71} +(8.55442e13 + 2.25023e14i) q^{72} +1.80749e14 q^{73} +(-3.70258e14 - 1.57637e14i) q^{74} -1.27389e15i q^{75} +(-7.10369e14 + 6.83041e14i) q^{76} -1.44575e15 q^{77} +(2.99281e14 - 7.02954e14i) q^{78} -1.58248e15i q^{79} +(-1.17748e14 + 3.00075e15i) q^{80} +2.05891e14 q^{81} +(1.15872e15 + 4.93321e14i) q^{82} -3.30136e15i q^{83} +(8.21766e14 + 8.54644e14i) q^{84} -1.19122e15 q^{85} +(-7.32478e14 + 1.72045e15i) q^{86} +1.97068e15i q^{87} +(4.74725e15 - 1.80470e15i) q^{88} -1.42349e14 q^{89} +(2.36314e15 + 1.00610e15i) q^{90} -3.76279e15i q^{91} +(-5.41406e15 + 5.20578e15i) q^{92} -1.49266e15 q^{93} +(2.41538e15 - 5.67326e15i) q^{94} +1.05141e16i q^{95} +(-3.76518e15 - 1.78051e15i) q^{96} -4.90826e14 q^{97} +(-2.45511e15 - 1.04526e15i) q^{98} -4.34363e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) $ 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9 - 49800172 * q^10 + 425284020 * q^12 - 906419296 * q^13 - 806064072 * q^14 - 2108540816 * q^16 + 12240765600 * q^17 + 2668896702 * q^18 + 1002788712 * q^20 + 39806479296 * q^21 + 216706355928 * q^22 - 111931394832 * q^24 + 206381182512 * q^25 + 1054507182588 * q^26 - 1526063922288 * q^28 + 327679573728 * q^29 + 1192344308100 * q^30 - 5158730488416 * q^32 + 679591529280 * q^33 + 9473293385948 * q^34 - 1959888509316 * q^36 - 8149494749152 * q^37 + 23318999782920 * q^38 - 28671795971776 * q^40 - 25536724613472 * q^41 + 5103781482168 * q^42 - 11442227373552 * q^44 - 5081579320608 * q^45 + 9929654732736 * q^46 + 29246734238832 * q^48 - 93287012964080 * q^49 - 133601044957998 * q^50 + 302261844234872 * q^52 - 86928436629792 * q^53 - 22406076560826 * q^54 + 530930989929024 * q^56 + 48687411524544 * q^57 - 189801665049916 * q^58 + 268455359263896 * q^60 + 476028596468000 * q^61 - 419080420491096 * q^62 + 305944925720704 * q^64 - 1276571708976192 * q^65 - 64815073701480 * q^66 - 1393626893610696 * q^68 + 384812600884992 * q^69 + 1815049064679696 * q^70 - 210694758737760 * q^72 - 368686901901280 * q^73 + 875633111941836 * q^74 - 4351002030861264 * q^76 - 81504772370688 * q^77 + 1907392409236620 * q^78 - 8190389938127328 * q^80 + 3294258113514384 * q^81 + 2390391408733340 * q^82 - 510964995024720 * q^84 + 10085047677398464 * q^85 - 894939801424296 * q^86 + 669091386916800 * q^88 - 5711067674201568 * q^89 + 714578036612004 * q^90 + 7708247605922304 * q^92 + 7132614781502016 * q^93 - 9487273535547696 * q^94 + 8786531038601952 * q^96 - 13564951560560608 * q^97 - 33011660914531290 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−235.541	−	100.281i	−0.920083	−	0.391723i
$2$	−235.541	−	100.281i	−0.920083	−	0.391723i
$3$		−	3788.00i		−	0.577350i
$3$		−	3788.00i		−	0.577350i
$4$	45423.4	+	47240.7i	0.693106	+	0.720836i
$5$	699204.			1.78996			0.894981	−	0.446105i	$-0.147189\pi$
$5$	699204.			1.78996			0.894981	+	0.446105i	$0.147189\pi$
$6$	−379865.	+	892229.i	−0.226162	+	0.531210i
$7$			4.77594e6i			0.828466i	0.910171	+	0.414233i	$0.135950\pi$
$7$			4.77594e6i			0.828466i	−0.910171	+	0.414233i	$0.864050\pi$
$8$	−5.96172e6	−	1.56822e7i	−0.355346	−	0.934735i
$9$	−1.43489e7			−0.333333
$10$	−1.64691e8	−	7.01170e7i	−1.64691	−	0.701170i
$11$			3.02715e8i			1.41219i	0.708118	+	0.706094i	$0.249544\pi$
$11$			3.02715e8i			1.41219i	−0.708118	+	0.706094i	$0.750456\pi$
$12$	1.78948e8	−	1.72063e8i	0.416175	−	0.400165i
$13$	−7.87862e8			−0.965836			−0.482918	−	0.875665i	$-0.660423\pi$
$13$	−7.87862e8			−0.965836			−0.482918	+	0.875665i	$0.660423\pi$
$14$	4.78937e8	−	1.12493e9i	0.324530	−	0.762258i
$15$		−	2.64858e9i		−	1.03343i
$16$	−1.68403e8	+	4.29166e9i	−0.0392094	+	0.999231i
$17$	−1.70368e9			−0.244229			−0.122114	−	0.992516i	$-0.538967\pi$
$17$	−1.70368e9			−0.244229			−0.122114	+	0.992516i	$0.538967\pi$
$18$	3.37976e9	+	1.43893e9i	0.306694	+	0.130574i
$19$			1.50372e10i			0.885398i	0.896670	+	0.442699i	$0.145979\pi$
$19$			1.50372e10i			0.885398i	−0.896670	+	0.442699i	$0.854021\pi$
$20$	3.17602e10	+	3.30309e10i	1.24063	+	1.29027i
$21$	1.80913e10			0.478315
$22$	3.03566e10	−	7.13019e10i	0.553187	−	1.29933i
$23$			1.14606e11i			1.46347i	0.681589	+	0.731735i	$0.261289\pi$
$23$			1.14606e11i			1.46347i	−0.681589	+	0.731735i	$0.738711\pi$
$24$	−5.94043e10	+	2.25830e10i	−0.539669	+	0.205159i
$25$	3.36298e11			2.20396
$26$	1.85574e11	+	7.90078e10i	0.888650	+	0.378341i
$27$			5.43536e10i			0.192450i
$28$	−2.25619e11	+	2.16939e11i	−0.597189	+	0.574215i
$29$	−5.20244e11			−1.03998			−0.519988	−	0.854174i	$-0.674063\pi$
$29$	−5.20244e11			−1.03998			−0.519988	+	0.854174i	$0.674063\pi$
$30$	−2.65603e11	+	6.23850e11i	−0.404820	+	0.950846i
$31$		−	3.94051e11i		−	0.462018i	−0.972952	−	0.231009i	$-0.925797\pi$
$31$		−	3.94051e11i		−	0.462018i	0.972952	−	0.231009i	$-0.0742027\pi$
$32$	4.70039e11	−	9.93976e11i	0.427498	−	0.904016i
$33$	1.14668e12			0.815327
$34$	4.01287e11	+	1.70847e11i	0.224711	+	0.0956700i
$35$			3.33936e12i			1.48292i
$36$	−6.51776e11	−	6.77853e11i	−0.231035	−	0.240279i
$37$	1.57195e12			0.447532			0.223766	−	0.974643i	$-0.428165\pi$
$37$	1.57195e12			0.447532			0.223766	+	0.974643i	$0.428165\pi$
$38$	1.50795e12	−	3.54189e12i	0.346831	−	0.814640i
$39$			2.98442e12i			0.557626i
$40$	−4.16846e12	−	1.09651e13i	−0.636056	−	1.67314i
$41$	−4.91938e12			−0.616083			−0.308041	−	0.951373i	$-0.599674\pi$
$41$	−4.91938e12			−0.616083			−0.308041	+	0.951373i	$0.599674\pi$
$42$	−4.26124e12	−	1.81421e12i	−0.440090	−	0.187367i
$43$		−	7.30424e12i		−	0.624925i	−0.949930	−	0.312462i	$-0.898846\pi$
$43$		−	7.30424e12i		−	0.624925i	0.949930	−	0.312462i	$-0.101154\pi$
$44$	−1.43005e13	+	1.37503e13i	−1.01796	+	0.978795i
$45$	−1.00328e13			−0.596654
$46$	1.14928e13	−	2.69944e13i	0.573276	−	1.34651i
$47$			2.40861e13i			1.01154i	0.862669	+	0.505770i	$0.168791\pi$
$47$			2.40861e13i			1.01154i	−0.862669	+	0.505770i	$0.831209\pi$
$48$	1.62568e13	+	6.37911e11i	0.576906	+	0.0226376i
$49$	1.04233e13			0.313643
$50$	−7.92120e13	−	3.37243e13i	−2.02783	−	0.863343i
$51$			6.45353e12i			0.141005i
$52$	−3.57874e13	−	3.72192e13i	−0.669427	−	0.696210i
$53$	1.16916e14			1.87787			0.938936	−	0.344093i	$-0.111814\pi$
$53$	1.16916e14			1.87787			0.938936	+	0.344093i	$0.111814\pi$
$54$	5.45064e12	−	1.28025e13i	0.0753872	−	0.177070i
$55$			2.11659e14i			2.52776i
$56$	7.48975e13	−	2.84728e13i	0.774396	−	0.294392i
$57$	5.69609e13			0.511185
$58$	1.22539e14	+	5.21707e13i	0.956864	+	0.407383i
$59$			1.48155e14i			1.00902i	0.863406	+	0.504510i	$0.168327\pi$
$59$			1.48155e14i			1.00902i	−0.863406	+	0.504510i	$0.831673\pi$
$60$	1.25121e14	−	1.20307e14i	0.744937	−	0.716279i
$61$	1.03715e14			0.541007			0.270503	−	0.962719i	$-0.412810\pi$
$61$	1.03715e14			0.541007			0.270503	+	0.962719i	$0.412810\pi$
$62$	−3.95159e13	+	9.28153e13i	−0.180983	+	0.425095i
$63$		−	6.85296e13i		−	0.276155i
$64$	−2.10391e14	+	1.86986e14i	−0.747458	+	0.664309i
$65$	−5.50876e14			−1.72881
$66$	−2.70091e14	−	1.14991e14i	−0.750168	−	0.319383i
$67$		−	3.79266e14i		−	0.933998i	−0.884258	−	0.466999i	$-0.845335\pi$
$67$		−	3.79266e14i		−	0.933998i	0.884258	−	0.466999i	$-0.154665\pi$
$68$	−7.73868e13	−	8.04830e13i	−0.169276	−	0.176049i
$69$	4.34126e14			0.844935
$70$	3.34875e14	−	7.86556e14i	0.580896	−	1.36441i
$71$			7.89683e14i			1.22289i	0.791289	+	0.611443i	$0.209411\pi$
$71$			7.89683e14i			1.22289i	−0.791289	+	0.611443i	$0.790589\pi$
$72$	8.55442e13	+	2.25023e14i	0.118449	+	0.311578i
$73$	1.80749e14			0.224126			0.112063	−	0.993701i	$-0.464254\pi$
$73$	1.80749e14			0.224126			0.112063	+	0.993701i	$0.464254\pi$
$74$	−3.70258e14	−	1.57637e14i	−0.411767	−	0.175309i
$75$		−	1.27389e15i		−	1.27246i
$76$	−7.10369e14	+	6.83041e14i	−0.638227	+	0.613675i
$77$	−1.44575e15			−1.16995
$78$	2.99281e14	−	7.02954e14i	0.218435	−	0.513062i
$79$		−	1.58248e15i		−	1.04309i	−0.853223	−	0.521546i	$-0.825356\pi$
$79$		−	1.58248e15i		−	1.04309i	0.853223	−	0.521546i	$-0.174644\pi$
$80$	−1.17748e14	+	3.00075e15i	−0.0701834	+	1.78858i
$81$	2.05891e14			0.111111
$82$	1.15872e15	+	4.93321e14i	0.566847	+	0.241334i
$83$		−	3.30136e15i		−	1.46578i	−0.680347	−	0.732890i	$-0.738171\pi$
$83$		−	3.30136e15i		−	1.46578i	0.680347	−	0.732890i	$-0.261829\pi$
$84$	8.21766e14	+	8.54644e14i	0.331523	+	0.344787i
$85$	−1.19122e15			−0.437160
$86$	−7.32478e14	+	1.72045e15i	−0.244798	+	0.574983i
$87$			1.97068e15i			0.600430i
$88$	4.74725e15	−	1.80470e15i	1.32002	−	0.501816i
$89$	−1.42349e14			−0.0361605			−0.0180802	−	0.999837i	$-0.505755\pi$
$89$	−1.42349e14			−0.0361605			−0.0180802	+	0.999837i	$0.505755\pi$
$90$	2.36314e15	+	1.00610e15i	0.548971	+	0.233723i
$91$		−	3.76279e15i		−	0.800163i
$92$	−5.41406e15	+	5.20578e15i	−1.05492	+	1.01434i
$93$	−1.49266e15			−0.266746
$94$	2.41538e15	−	5.67326e15i	0.396244	−	0.930700i
$95$			1.05141e16i			1.58483i
$96$	−3.76518e15	−	1.78051e15i	−0.521934	−	0.246816i
$97$	−4.90826e14			−0.0626259			−0.0313129	−	0.999510i	$-0.509969\pi$
$97$	−4.90826e14			−0.0626259			−0.0313129	+	0.999510i	$0.509969\pi$
$98$	−2.45511e15	−	1.04526e15i	−0.288578	−	0.122861i
$99$		−	4.34363e15i		−	0.470729i
$100$	1.52758e16	+	1.58869e16i	1.52758	+	1.58869i
$101$	1.06609e16			0.984515			0.492258	−	0.870450i	$-0.336172\pi$
$101$	1.06609e16			0.984515			0.492258	+	0.870450i	$0.336172\pi$
$102$	6.47168e14	−	1.52007e15i	0.0552351	−	0.129737i
$103$			2.27378e15i			0.179494i	0.995965	+	0.0897470i	$0.0286059\pi$
$103$			2.27378e15i			0.179494i	−0.995965	+	0.0897470i	$0.971394\pi$
$104$	4.69702e15	+	1.23555e16i	0.343206	+	0.902801i
$105$	1.26495e16			0.856166
$106$	−2.75385e16	−	1.17244e16i	−1.72780	−	0.735606i
$107$		−	1.52107e16i		−	0.885279i	−0.896700	−	0.442640i	$-0.854042\pi$
$107$		−	1.52107e16i		−	0.885279i	0.896700	−	0.442640i	$-0.145958\pi$
$108$	−2.56770e15	+	2.46892e15i	−0.138725	+	0.133388i
$109$	−1.10349e16			−0.553805			−0.276903	−	0.960898i	$-0.589308\pi$
$109$	−1.10349e16			−0.553805			−0.276903	+	0.960898i	$0.589308\pi$
$110$	2.12255e16	−	4.98545e16i	0.990183	−	2.32575i
$111$		−	5.95453e15i		−	0.258383i
$112$	−2.04968e16	−	8.04284e14i	−0.827829	−	0.0324837i
$113$	−2.61509e16			−0.983694			−0.491847	−	0.870682i	$-0.663678\pi$
$113$	−2.61509e16			−0.983694			−0.491847	+	0.870682i	$0.663678\pi$
$114$	−1.34166e16	−	5.71211e15i	−0.470333	−	0.200243i
$115$			8.01328e16i			2.61955i
$116$	−2.36312e16	−	2.45767e16i	−0.720813	−	0.749652i
$117$	1.13050e16			0.321945
$118$	1.48571e16	−	3.48966e16i	0.395257	−	0.928382i
$119$		−	8.13668e15i		−	0.202335i
$120$	−4.15357e16	+	1.57901e16i	−0.965987	+	0.367227i
$121$	−4.56866e16			−0.994274
$122$	−2.44292e16	−	1.04007e16i	−0.497771	−	0.211925i
$123$			1.86346e16i			0.355696i
$124$	1.86153e16	−	1.78991e16i	0.333039	−	0.320227i
$125$	1.28451e17			2.15504
$126$	−6.87223e15	+	1.61415e16i	−0.108177	+	0.254086i
$127$		−	2.72321e16i		−	0.402394i	−0.979551	−	0.201197i	$-0.935517\pi$
$127$		−	2.72321e16i		−	0.402394i	0.979551	−	0.201197i	$-0.0644832\pi$
$128$	6.83069e16	−	2.29448e16i	0.947949	−	0.318423i
$129$	−2.76684e16			−0.360800
$130$	1.29754e17	+	5.52425e16i	1.59065	+	0.677215i
$131$			8.42511e15i			0.0971416i	0.998820	+	0.0485708i	$0.0154667\pi$
$131$			8.42511e15i			0.0971416i	−0.998820	+	0.0485708i	$0.984533\pi$
$132$	5.20862e16	+	5.41701e16i	0.565108	+	0.587717i
$133$	−7.18169e16			−0.733523
$134$	−3.80333e16	+	8.93328e16i	−0.365869	+	0.859355i
$135$			3.80042e16i			0.344478i
$136$	1.01569e16	+	2.67175e16i	0.0867857	+	0.228289i
$137$	2.19721e17			1.77055			0.885273	−	0.465071i	$-0.153971\pi$
$137$	2.19721e17			1.77055			0.885273	+	0.465071i	$0.153971\pi$
$138$	−1.02255e17	−	4.35347e16i	−0.777410	−	0.330981i
$139$			1.12015e17i			0.803816i	0.915680	+	0.401908i	$0.131653\pi$
$139$			1.12015e17i			0.803816i	−0.915680	+	0.401908i	$0.868347\pi$
$140$	−1.57754e17	+	1.51685e17i	−1.06894	+	1.02782i
$141$	9.12378e16			0.584012
$142$	7.91903e16	−	1.86003e17i	0.479033	−	1.12516i
$143$		−	2.38498e17i		−	1.36394i
$144$	2.41640e15	−	6.15807e16i	0.0130698	−	0.333077i
$145$	−3.63756e17			−1.86152
$146$	−4.25739e16	−	1.81257e16i	−0.206215	−	0.0877956i
$147$		−	3.94834e16i		−	0.181082i
$148$	7.14031e16	+	7.42599e16i	0.310187	+	0.322597i
$149$	−1.83406e17			−0.754959			−0.377479	−	0.926018i	$-0.623209\pi$
$149$	−1.83406e17			−0.754959			−0.377479	+	0.926018i	$0.623209\pi$
$150$	−1.27748e17	+	3.00055e17i	−0.498451	+	1.17077i
$151$		−	2.81231e17i		−	1.04051i	−0.854010	−	0.520257i	$-0.825836\pi$
$151$		−	2.81231e17i		−	1.04051i	0.854010	−	0.520257i	$-0.174164\pi$
$152$	2.35817e17	−	8.96477e16i	0.827613	−	0.314623i
$153$	2.44459e16			0.0814095
$154$	3.40534e17	+	1.44982e17i	1.07645	+	0.458297i
$155$		−	2.75522e17i		−	0.826995i
$156$	−1.40986e17	+	1.35562e17i	−0.401957	+	0.386494i
$157$	−2.50414e17			−0.678362			−0.339181	−	0.940721i	$-0.610150\pi$
$157$	−2.50414e17			−0.678362			−0.339181	+	0.940721i	$0.610150\pi$
$158$	−1.58693e17	+	3.72740e17i	−0.408603	+	0.959731i
$159$		−	4.42876e17i		−	1.08419i
$160$	3.28653e17	−	6.94992e17i	0.765205	−	1.61815i
$161$	−5.47351e17			−1.21244
$162$	−4.84959e16	−	2.06470e16i	−0.102231	−	0.0435248i
$163$			4.44858e16i			0.0892731i	0.999003	+	0.0446366i	$0.0142130\pi$
$163$			4.44858e16i			0.0892731i	−0.999003	+	0.0446366i	$0.985787\pi$
$164$	−2.23455e17	−	2.32395e17i	−0.427010	−	0.444095i
$165$	8.01765e17			1.45940
$166$	−3.31065e17	+	7.77607e17i	−0.574180	+	1.34864i
$167$			6.95649e17i			1.14990i	0.818190	+	0.574948i	$0.194978\pi$
$167$			6.95649e17i			1.14990i	−0.818190	+	0.574948i	$0.805022\pi$
$168$	−1.07855e17	−	2.83712e17i	−0.169968	−	0.447098i
$169$	−4.46893e16			−0.0671599
$170$	2.80581e17	+	1.19457e17i	0.402223	+	0.171246i
$171$		−	2.15768e17i		−	0.295133i
$172$	3.45058e17	−	3.31783e17i	0.450468	−	0.433139i
$173$	9.60819e17			1.19749			0.598746	−	0.800939i	$-0.295666\pi$
$173$	9.60819e17			1.19749			0.598746	+	0.800939i	$0.295666\pi$
$174$	1.97622e17	−	4.64177e17i	0.235203	−	0.552446i
$175$			1.60614e18i			1.82591i
$176$	−1.29915e18	−	5.09782e16i	−1.41110	−	0.0553711i
$177$	5.61210e17			0.582558
$178$	3.35290e16	+	1.42749e16i	0.0332706	+	0.0141649i
$179$			9.41384e15i			0.00893187i	0.999990	+	0.00446594i	$0.00142156\pi$
$179$			9.41384e15i			0.00893187i	−0.999990	+	0.00446594i	$0.998578\pi$
$180$	−4.55724e17	−	4.73957e17i	−0.413544	−	0.430090i
$181$	−1.72647e18			−1.49876			−0.749379	−	0.662142i	$-0.769648\pi$
$181$	−1.72647e18			−1.49876			−0.749379	+	0.662142i	$0.769648\pi$
$182$	−3.77337e17	+	8.86292e17i	−0.313443	+	0.736217i
$183$		−	3.92872e17i		−	0.312351i
$184$	1.79728e18	−	6.83248e17i	1.36796	−	0.520039i
$185$	1.09911e18			0.801065
$186$	3.51584e17	+	1.49686e17i	0.245429	+	0.104491i
$187$		−	5.15729e17i		−	0.344897i
$188$	−1.13784e18	+	1.09407e18i	−0.729154	+	0.701103i
$189$	−2.59590e17			−0.159438
$190$	1.05436e18	−	2.47650e18i	0.620814	−	1.45817i
$191$			2.51604e18i			1.42053i	0.703935	+	0.710265i	$0.251425\pi$
$191$			2.51604e18i			1.42053i	−0.703935	+	0.710265i	$0.748575\pi$
$192$	7.08303e17	+	7.96959e17i	0.383539	+	0.431545i
$193$	2.73902e18			1.42277			0.711387	−	0.702800i	$-0.248067\pi$
$193$	2.73902e18			1.42277			0.711387	+	0.702800i	$0.248067\pi$
$194$	1.15610e17	+	4.92206e16i	0.0576210	+	0.0245320i
$195$			2.08672e18i			0.998129i
$196$	4.73461e17	+	4.92403e17i	0.217388	+	0.226085i
$197$	5.88143e17			0.259271			0.129635	−	0.991562i	$-0.458619\pi$
$197$	5.88143e17			0.259271			0.129635	+	0.991562i	$0.458619\pi$
$198$	−4.35584e17	+	1.02310e18i	−0.184396	+	0.433110i
$199$			1.45408e18i			0.591241i	0.955305	+	0.295621i	$0.0955264\pi$
$199$			1.45408e18i			0.591241i	−0.955305	+	0.295621i	$0.904474\pi$
$200$	−2.00491e18	−	5.27390e18i	−0.783169	−	2.06012i
$201$	−1.43666e18			−0.539244
$202$	−2.51108e18	−	1.06909e18i	−0.905836	−	0.385658i
$203$		−	2.48466e18i		−	0.861585i
$204$	−3.04869e17	+	2.93141e17i	−0.101642	+	0.0977316i
$205$	−3.43965e18			−1.10276
$206$	2.28017e17	−	5.35568e17i	0.0703120	−	0.165149i
$207$		−	1.64447e18i		−	0.487823i
$208$	1.32679e17	−	3.38124e18i	0.0378699	−	0.965094i
$209$	−4.55199e18			−1.25035
$210$	−2.97947e18	−	1.26850e18i	−0.787744	−	0.335380i
$211$		−	3.01365e18i		−	0.767067i	−0.923527	−	0.383534i	$-0.874707\pi$
$211$		−	3.01365e18i		−	0.767067i	0.923527	−	0.383534i	$-0.125293\pi$
$212$	5.31070e18	+	5.52318e18i	1.30156	+	1.35364i
$213$	2.99131e18			0.706033
$214$	−1.52535e18	+	3.58276e18i	−0.346785	+	0.814531i
$215$		−	5.10715e18i		−	1.11859i
$216$	8.52386e17	−	3.24041e17i	0.179890	−	0.0683864i
$217$	1.88197e18			0.382767
$218$	2.59918e18	+	1.10659e18i	0.509547	+	0.216939i
$219$		−	6.84677e17i		−	0.129399i
$220$	−9.99894e18	+	9.61428e18i	−1.82210	+	1.75201i
$221$	1.34226e18			0.235885
$222$	−5.97127e17	+	1.40254e18i	−0.101215	+	0.237734i
$223$		−	9.06110e18i		−	1.48164i	−0.671705	−	0.740819i	$-0.734438\pi$
$223$		−	9.06110e18i		−	1.48164i	0.671705	−	0.740819i	$-0.265562\pi$
$224$	4.74718e18	+	2.24488e18i	0.748947	+	0.354168i
$225$	−4.82550e18			−0.734654
$226$	6.15963e18	+	2.62245e18i	0.905080	+	0.385336i
$227$			5.13157e18i			0.727852i	0.931428	+	0.363926i	$0.118564\pi$
$227$			5.13157e18i			0.727852i	−0.931428	+	0.363926i	$0.881436\pi$
$228$	2.58736e18	+	2.69087e18i	0.354305	+	0.368481i
$229$	1.30342e18			0.172345			0.0861727	−	0.996280i	$-0.472536\pi$
$229$	1.30342e18			0.172345			0.0861727	+	0.996280i	$0.472536\pi$
$230$	8.03581e18	−	1.88746e19i	1.02614	−	2.41021i
$231$			5.47649e18i			0.675471i
$232$	3.10155e18	+	8.15859e18i	0.369551	+	0.972101i
$233$	1.53404e18			0.176599			0.0882997	−	0.996094i	$-0.471857\pi$
$233$	1.53404e18			0.176599			0.0882997	+	0.996094i	$0.471857\pi$
$234$	−2.66279e18	−	1.13368e18i	−0.296217	−	0.126114i
$235$			1.68411e19i			1.81062i
$236$	−6.99894e18	+	6.72969e18i	−0.727338	+	0.699357i
$237$	−5.99444e18			−0.602229
$238$	−8.15956e17	+	1.91652e18i	−0.0792594	+	0.186165i
$239$		−	1.25572e19i		−	1.17953i	−0.807575	−	0.589765i	$-0.799220\pi$
$239$		−	1.25572e19i		−	1.17953i	0.807575	−	0.589765i	$-0.200780\pi$
$240$	1.13668e19	+	4.46029e17i	1.03264	+	0.0405204i
$241$	1.86329e19			1.63736			0.818678	−	0.574253i	$-0.194708\pi$
$241$	1.86329e19			1.63736			0.818678	+	0.574253i	$0.194708\pi$
$242$	1.07611e19	+	4.58151e18i	0.914814	+	0.389480i
$243$		−	7.79915e17i		−	0.0641500i
$244$	4.71108e18	+	4.89957e18i	0.374975	+	0.389977i
$245$	7.28800e18			0.561409
$246$	1.86870e18	−	4.38921e18i	0.139334	−	0.327270i
$247$		−	1.18473e19i		−	0.855150i
$248$	−6.17961e18	+	2.34922e18i	−0.431865	+	0.164176i
$249$	−1.25056e19			−0.846268
$250$	−3.02554e19	−	1.28812e19i	−1.98282	−	0.844181i
$251$		−	1.00236e19i		−	0.636260i	−0.948047	−	0.318130i	$-0.896945\pi$
$251$		−	1.00236e19i		−	0.636260i	0.948047	−	0.318130i	$-0.103055\pi$
$252$	3.23739e18	−	3.11284e18i	0.199063	−	0.191405i
$253$	−3.46929e19			−2.06669
$254$	−2.73087e18	+	6.41429e18i	−0.157627	+	0.370236i
$255$			4.51233e18i			0.252394i
$256$	−1.83900e19	−	1.44546e18i	−0.996925	−	0.0783586i
$257$	−1.44458e19			−0.759062			−0.379531	−	0.925179i	$-0.623915\pi$
$257$	−1.44458e19			−0.759062			−0.379531	+	0.925179i	$0.623915\pi$
$258$	6.51706e18	+	2.77462e18i	0.331966	+	0.141334i
$259$			7.50753e18i			0.370765i
$260$	−2.50227e19	−	2.60238e19i	−1.19825	−	1.24619i
$261$	7.46493e18			0.346658
$262$	8.44880e17	−	1.98446e18i	0.0380526	−	0.0893783i
$263$			2.96388e19i			1.29483i	0.762136	+	0.647417i	$0.224151\pi$
$263$			2.96388e19i			1.29483i	−0.762136	+	0.647417i	$0.775849\pi$
$264$	−6.83620e18	−	1.79826e19i	−0.289723	−	0.762114i
$265$	8.17479e19			3.36132
$266$	1.69158e19	+	7.20189e18i	0.674902	+	0.287338i
$267$			5.39217e17i			0.0208773i
$268$	1.79168e19	−	1.72275e19i	0.673259	−	0.647359i
$269$	−1.66638e19			−0.607791			−0.303896	−	0.952705i	$-0.598287\pi$
$269$	−1.66638e19			−0.607791			−0.303896	+	0.952705i	$0.598287\pi$
$270$	3.81111e18	−	8.95156e18i	0.134940	−	0.316949i
$271$		−	3.23000e19i		−	1.11032i	−0.831743	−	0.555160i	$-0.812657\pi$
$271$		−	3.23000e19i		−	1.11032i	0.831743	−	0.555160i	$-0.187343\pi$
$272$	2.86905e17	−	7.31162e18i	0.00957606	−	0.244041i
$273$	−1.42534e19			−0.461974
$274$	−5.17534e19	−	2.20339e19i	−1.62905	−	0.693564i
$275$			1.01802e20i			3.11241i
$276$	1.97195e19	+	2.05084e19i	0.585629	+	0.609060i
$277$	3.98776e19			1.15051			0.575255	−	0.817974i	$-0.304903\pi$
$277$	3.98776e19			1.15051			0.575255	+	0.817974i	$0.304903\pi$
$278$	1.12330e19	−	2.63841e19i	0.314873	−	0.739577i
$279$			5.65421e18i			0.154006i
$280$	5.23686e19	−	1.99083e19i	1.38614	−	0.526951i
$281$	−5.53485e19			−1.42382			−0.711911	−	0.702270i	$-0.752170\pi$
$281$	−5.53485e19			−1.42382			−0.711911	+	0.702270i	$0.752170\pi$
$282$	−2.14903e19	−	9.14944e18i	−0.537340	−	0.228771i
$283$		−	5.53274e19i		−	1.34477i	−0.740201	−	0.672386i	$-0.765269\pi$
$283$		−	5.53274e19i		−	1.34477i	0.740201	−	0.672386i	$-0.234731\pi$
$284$	−3.73052e19	+	3.58700e19i	−0.881500	+	0.847589i
$285$	3.98273e19			0.915001
$286$	−2.39168e19	+	5.61761e19i	−0.534288	+	1.25494i
$287$		−	2.34947e19i		−	0.510404i
$288$	−6.74455e18	+	1.42625e19i	−0.142499	+	0.301339i
$289$	−4.57587e19			−0.940352
$290$	8.56796e19	+	3.64779e19i	1.71275	+	0.729199i
$291$			1.85925e18i			0.0361571i
$292$	8.21023e18	+	8.53872e18i	0.155343	+	0.161558i
$293$	−1.23414e19			−0.227207			−0.113604	−	0.993526i	$-0.536239\pi$
$293$	−1.23414e19			−0.227207			−0.113604	+	0.993526i	$0.536239\pi$
$294$	−3.95944e18	+	9.29996e18i	−0.0709341	+	0.166611i
$295$			1.03590e20i			1.80611i
$296$	−9.37151e18	−	2.46517e19i	−0.159029	−	0.418324i
$297$	−1.64536e19			−0.271776
$298$	4.31997e19	+	1.83922e19i	0.694625	+	0.295735i
$299$		−	9.02936e19i		−	1.41347i
$300$	6.01797e19	−	5.78646e19i	0.917233	−	0.881947i
$301$	3.48847e19			0.517729
$302$	−2.82022e19	+	6.62415e19i	−0.407594	+	0.957359i
$303$		−	4.03834e19i		−	0.568410i
$304$	−6.45347e19	−	2.53232e18i	−0.884717	−	0.0347160i
$305$	7.25179e19			0.968381
$306$	−5.75803e18	−	2.45147e18i	−0.0749035	−	0.0318900i
$307$			4.11506e19i			0.521518i	0.965404	+	0.260759i	$0.0839728\pi$
$307$			4.11506e19i			0.521518i	−0.965404	+	0.260759i	$0.916027\pi$
$308$	−6.56708e19	−	6.82983e19i	−0.810899	−	0.843342i
$309$	8.61306e18			0.103631
$310$	−2.76297e19	+	6.48968e19i	−0.323953	+	0.760904i
$311$		−	5.30276e19i		−	0.605925i	−0.953002	−	0.302963i	$-0.902024\pi$
$311$		−	5.30276e19i		−	0.605925i	0.953002	−	0.302963i	$-0.0979758\pi$
$312$	4.68024e19	−	1.77923e19i	0.521232	−	0.198150i
$313$	−8.64344e19			−0.938279			−0.469139	−	0.883124i	$-0.655436\pi$
$313$	−8.64344e19			−0.938279			−0.469139	+	0.883124i	$0.655436\pi$
$314$	5.89828e19	+	2.51118e19i	0.624149	+	0.265730i
$315$		−	4.79161e19i		−	0.494308i
$316$	7.47577e19	−	7.18817e19i	0.751898	−	0.722973i
$317$	1.22687e20			1.20316			0.601582	−	0.798811i	$-0.294537\pi$
$317$	1.22687e20			1.20316			0.601582	+	0.798811i	$0.294537\pi$
$318$	−4.44121e19	+	1.04316e20i	−0.424702	+	0.997544i
$319$		−	1.57486e20i		−	1.46864i
$320$	−1.47106e20	+	1.30742e20i	−1.33792	+	1.18909i
$321$	−5.76182e19			−0.511116
$322$	1.28924e20	+	5.48890e19i	1.11554	+	0.474940i
$323$		−	2.56186e19i		−	0.216240i
$324$	9.35227e18	+	9.72644e18i	0.0770117	+	0.0800929i
$325$	−2.64956e20			−2.12867
$326$	4.46109e18	−	1.04782e19i	0.0349704	−	0.0821387i
$327$			4.18002e19i			0.319740i
$328$	2.93279e19	+	7.71469e19i	0.218923	+	0.575874i
$329$	−1.15034e20			−0.838026
$330$	−1.88849e20	−	8.04019e19i	−1.34277	−	0.571682i
$331$		−	3.07525e19i		−	0.213431i	−0.994290	−	0.106715i	$-0.965967\pi$
$331$		−	3.07525e19i		−	0.213431i	0.994290	−	0.106715i	$-0.0340334\pi$
$332$	1.55959e20	−	1.49959e20i	1.05659	−	1.01594i
$333$	−2.25557e19			−0.149177
$334$	6.97605e19	−	1.63854e20i	0.450441	−	1.05800i
$335$		−	2.65184e20i		−	1.67182i
$336$	−3.04663e18	+	7.76416e19i	−0.0187545	+	0.477948i
$337$	−4.33395e19			−0.260522			−0.130261	−	0.991480i	$-0.541582\pi$
$337$	−4.33395e19			−0.260522			−0.130261	+	0.991480i	$0.541582\pi$
$338$	1.05262e19	+	4.48150e18i	0.0617927	+	0.0263081i
$339$			9.90596e19i			0.567936i
$340$	−5.41092e19	−	5.62740e19i	−0.302998	−	0.315120i
$341$	1.19285e20			0.652457
$342$	−2.16374e19	+	5.08222e19i	−0.115610	+	0.271547i
$343$			2.08500e20i			1.08831i
$344$	−1.14547e20	+	4.35459e19i	−0.584139	+	0.222065i
$345$	3.03543e20			1.51240
$346$	−2.26312e20	−	9.63521e19i	−1.10179	−	0.469086i
$347$			4.13436e20i			1.96686i	0.181297	+	0.983428i	$0.441971\pi$
$347$			4.13436e20i			1.96686i	−0.181297	+	0.983428i	$0.558029\pi$
$348$	−9.30964e19	+	8.95150e19i	−0.432812	+	0.416161i
$349$	8.08195e19			0.367208			0.183604	−	0.983000i	$-0.441224\pi$
$349$	8.08195e19			0.367208			0.183604	+	0.983000i	$0.441224\pi$
$350$	1.61066e20	−	3.78312e20i	0.715251	−	1.67999i
$351$		−	4.28232e19i		−	0.185875i
$352$	3.00892e20	+	1.42288e20i	1.27664	+	0.603708i
$353$	1.72655e20			0.716112			0.358056	−	0.933700i	$-0.383440\pi$
$353$	1.72655e20			0.716112			0.358056	+	0.933700i	$0.383440\pi$
$354$	−1.32188e20	−	5.62788e19i	−0.536001	−	0.228201i
$355$			5.52149e20i			2.18892i
$356$	−6.46597e18	−	6.72466e18i	−0.0250630	−	0.0260658i
$357$	−3.08217e19			−0.116818
$358$	9.44031e17	−	2.21735e18i	0.00349882	−	0.00821807i
$359$		−	2.40882e20i		−	0.873068i	−0.899688	−	0.436534i	$-0.856206\pi$
$359$		−	2.40882e20i		−	0.873068i	0.899688	−	0.436534i	$-0.143794\pi$
$360$	5.98128e19	+	1.57337e20i	0.212019	+	0.557713i
$361$	6.23235e19			0.216070
$362$	4.06656e20	+	1.73133e20i	1.37898	+	0.587098i
$363$			1.73061e20i			0.574044i
$364$	1.77757e20	−	1.70918e20i	0.576786	−	0.554598i
$365$	1.26380e20			0.401178
$366$	−3.93977e19	+	9.25375e19i	−0.122355	+	0.287388i
$367$		−	5.01479e20i		−	1.52379i	−0.647702	−	0.761894i	$-0.724270\pi$
$367$		−	5.01479e20i		−	1.52379i	0.647702	−	0.761894i	$-0.275730\pi$
$368$	−4.91850e20	−	1.93000e19i	−1.46234	−	0.0573818i
$369$	7.05877e19			0.205361
$370$	−2.58886e20	−	1.10220e20i	−0.737046	−	0.313796i
$371$			5.58383e20i			1.55575i
$372$	−6.78018e19	−	7.05145e19i	−0.184883	−	0.192280i
$373$	−5.65276e19			−0.150866			−0.0754328	−	0.997151i	$-0.524034\pi$
$373$	−5.65276e19			−0.150866			−0.0754328	+	0.997151i	$0.524034\pi$
$374$	−5.17179e19	+	1.21475e20i	−0.135104	+	0.317333i
$375$		−	4.86570e20i		−	1.24421i
$376$	3.77723e20	−	1.43594e20i	0.945521	−	0.359447i
$377$	4.09881e20			1.00445
$378$	6.11441e19	+	2.60320e19i	0.146697	+	0.0624558i
$379$			4.40881e20i			1.03564i	0.855491	+	0.517818i	$0.173256\pi$
$379$			4.40881e20i			1.03564i	−0.855491	+	0.517818i	$0.826744\pi$
$380$	−4.96693e20	+	4.77585e20i	−1.14240	+	1.09845i
$381$	−1.03155e20			−0.232322
$382$	2.52311e20	−	5.92631e20i	0.556455	−	1.30700i
$383$		−	1.32406e20i		−	0.285968i	−0.989725	−	0.142984i	$-0.954330\pi$
$383$		−	1.32406e20i		−	0.285968i	0.989725	−	0.142984i	$-0.0456697\pi$
$384$	−8.69147e19	−	2.58746e20i	−0.183841	−	0.547299i
$385$	−1.01087e21			−2.09417
$386$	−6.45151e20	−	2.74672e20i	−1.30907	−	0.557334i
$387$			1.04808e20i			0.208308i
$388$	−2.22950e19	−	2.31870e19i	−0.0434063	−	0.0451430i
$389$	−8.60726e20			−1.64160			−0.820801	−	0.571214i	$-0.806473\pi$
$389$	−8.60726e20			−1.64160			−0.820801	+	0.571214i	$0.806473\pi$
$390$	2.09258e20	−	4.91508e20i	0.390990	−	0.918361i
$391$		−	1.95252e20i		−	0.357421i
$392$	−6.21407e19	−	1.63461e20i	−0.111452	−	0.293173i
$393$	3.19143e19			0.0560847
$394$	−1.38532e20	−	5.89797e19i	−0.238550	−	0.101562i
$395$		−	1.10648e21i		−	1.86709i
$396$	2.05196e20	−	1.97302e20i	0.339319	−	0.326265i
$397$	6.14295e20			0.995527			0.497763	−	0.867313i	$-0.334155\pi$
$397$	6.14295e20			0.995527			0.497763	+	0.867313i	$0.334155\pi$
$398$	1.45817e20	−	3.42497e20i	0.231603	−	0.543991i
$399$			2.72042e20i			0.423500i
$400$	−5.66336e19	+	1.44328e21i	−0.0864160	+	2.20227i
$401$	3.29737e20			0.493188			0.246594	−	0.969119i	$-0.420689\pi$
$401$	3.29737e20			0.493188			0.246594	+	0.969119i	$0.420689\pi$
$402$	3.38392e20	+	1.44070e20i	0.496149	+	0.211234i
$403$			3.10458e20i			0.446234i
$404$	4.84254e20	+	5.03628e20i	0.682373	+	0.709674i
$405$	1.43960e20			0.198885
$406$	−2.49164e20	+	5.85239e20i	−0.337503	+	0.792730i
$407$			4.75852e20i			0.631999i
$408$	1.01206e20	−	3.84741e19i	0.131803	−	0.0501057i
$409$	−5.09890e20			−0.651163			−0.325582	−	0.945514i	$-0.605560\pi$
$409$	−5.09890e20			−0.651163			−0.325582	+	0.945514i	$0.605560\pi$
$410$	8.10178e20	+	3.44932e20i	1.01463	+	0.431979i
$411$		−	8.32303e20i		−	1.02223i
$412$	−1.07415e20	+	1.03283e20i	−0.129386	+	0.124408i
$413$	−7.07579e20			−0.835939
$414$	−1.64909e20	+	3.87340e20i	−0.191092	+	0.448838i
$415$		−	2.30833e21i		−	2.62369i
$416$	−3.70326e20	+	7.83117e20i	−0.412893	+	0.873132i
$417$	4.24311e20			0.464083
$418$	1.07218e21	+	4.56479e20i	1.15042	+	0.489791i
$419$			5.60784e20i			0.590315i	0.955449	+	0.295157i	$0.0953721\pi$
$419$			5.60784e20i			0.590315i	−0.955449	+	0.295157i	$0.904628\pi$
$420$	5.74581e20	+	5.97570e20i	0.593413	+	0.617155i
$421$	1.65263e21			1.67463			0.837317	−	0.546718i	$-0.184123\pi$
$421$	1.65263e21			1.67463			0.837317	+	0.546718i	$0.184123\pi$
$422$	−3.02213e20	+	7.09839e20i	−0.300478	+	0.705765i
$423$		−	3.45609e20i		−	0.337180i
$424$	−6.97019e20	−	1.83350e21i	−0.667295	−	1.75531i
$425$	−5.72943e20			−0.538270
$426$	−7.04578e20	−	2.99973e20i	−0.649609	−	0.276570i
$427$			4.95337e20i			0.448206i
$428$	7.18567e20	−	6.90923e20i	0.638141	−	0.613592i
$429$	−9.03428e20			−0.787472
$430$	−5.12151e20	+	1.20295e21i	−0.438178	+	1.02920i
$431$			7.13973e20i			0.599603i	0.954002	+	0.299801i	$0.0969204\pi$
$431$			7.13973e20i			0.599603i	−0.954002	+	0.299801i	$0.903080\pi$
$432$	−2.33267e20	−	9.15332e18i	−0.192302	−	0.00754586i
$433$	2.38940e21			1.93368			0.966842	−	0.255376i	$-0.0821994\pi$
$433$	2.38940e21			1.93368			0.966842	+	0.255376i	$0.0821994\pi$
$434$	−4.43281e20	−	1.88726e20i	−0.352177	−	0.149939i
$435$			1.37791e21i			1.07475i
$436$	−5.01243e20	−	5.21297e20i	−0.383846	−	0.399203i
$437$	−1.72335e21			−1.29575
$438$	−6.86602e19	+	1.61270e20i	−0.0506888	+	0.119058i
$439$			2.03140e20i			0.147258i	0.997286	+	0.0736290i	$0.0234581\pi$
$439$			2.03140e20i			0.147258i	−0.997286	+	0.0736290i	$0.976542\pi$
$440$	3.31929e21	−	1.26185e21i	2.36279	−	0.898230i
$441$	−1.49563e20			−0.104548
$442$	−3.16159e20	−	1.34604e20i	−0.217034	−	0.0924016i
$443$			1.37369e21i			0.926101i	0.886332	+	0.463050i	$0.153245\pi$
$443$			1.37369e21i			0.926101i	−0.886332	+	0.463050i	$0.846755\pi$
$444$	2.81296e20	−	2.70475e20i	0.186252	−	0.179087i
$445$	−9.95309e19			−0.0647258
$446$	−9.08658e20	+	2.13426e21i	−0.580392	+	1.36323i
$447$			6.94741e20i			0.435876i
$448$	−8.93036e20	−	1.00481e21i	−0.550358	−	0.619244i
$449$	−1.70076e20			−0.102961			−0.0514803	−	0.998674i	$-0.516394\pi$
$449$	−1.70076e20			−0.102961			−0.0514803	+	0.998674i	$0.516394\pi$
$450$	1.13661e21	+	4.83907e20i	0.675942	+	0.287781i
$451$		−	1.48917e21i		−	0.870025i
$452$	−1.18786e21	−	1.23539e21i	−0.681803	−	0.709082i
$453$	−1.06530e21			−0.600741
$454$	5.14600e20	−	1.20870e21i	0.285117	−	0.669685i
$455$		−	2.63095e21i		−	1.43226i
$456$	−3.39585e20	−	8.93275e20i	−0.181648	−	0.477822i
$457$	−1.76543e21			−0.927944			−0.463972	−	0.885850i	$-0.653576\pi$
$457$	−1.76543e21			−0.927944			−0.463972	+	0.885850i	$0.653576\pi$
$458$	−3.07009e20	−	1.30708e20i	−0.158572	−	0.0675117i
$459$		−	9.26011e19i		−	0.0470018i
$460$	−3.78553e21	+	3.63990e21i	−1.88827	+	1.81563i
$461$	3.77126e21			1.84875			0.924376	−	0.381482i	$-0.124586\pi$
$461$	3.77126e21			1.84875			0.924376	+	0.381482i	$0.124586\pi$
$462$	5.49189e20	−	1.28994e21i	0.264598	−	0.621489i
$463$			9.35018e20i			0.442764i	0.975187	+	0.221382i	$0.0710567\pi$
$463$			9.35018e20i			0.442764i	−0.975187	+	0.221382i	$0.928943\pi$
$464$	8.76108e19	−	2.23271e21i	0.0407768	−	1.03918i
$465$	−1.04368e21			−0.477466
$466$	−3.61330e20	−	1.53835e20i	−0.162486	−	0.0691781i
$467$			9.41266e20i			0.416081i	0.978120	+	0.208040i	$0.0667085\pi$
$467$			9.41266e20i			0.416081i	−0.978120	+	0.208040i	$0.933291\pi$
$468$	5.13510e20	+	5.34055e20i	0.223142	+	0.232070i
$469$	1.81135e21			0.773786
$470$	1.68884e21	−	3.96676e21i	0.709261	−	1.66592i
$471$			9.48567e20i			0.391652i
$472$	2.32340e21	−	8.83257e20i	0.943166	−	0.358551i
$473$	2.21110e21			0.882511
$474$	1.41194e21	+	6.01130e20i	0.554101	+	0.235907i
$475$			5.05698e21i			1.95138i
$476$	3.84382e20	−	3.69595e20i	0.145850	−	0.140240i
$477$	−1.67761e21			−0.625957
$478$	−1.25925e21	+	2.95774e21i	−0.462050	+	1.08527i
$479$		−	3.33303e21i		−	1.20270i	−0.798988	−	0.601348i	$-0.794631\pi$
$479$		−	3.33303e21i		−	1.20270i	0.798988	−	0.601348i	$-0.205369\pi$
$480$	−2.63263e21	−	1.24494e21i	−0.934242	−	0.441791i
$481$	−1.23848e21			−0.432243
$482$	−4.38880e21	−	1.86852e21i	−1.50650	−	0.641390i
$483$			2.07336e21i			0.700000i
$484$	−2.07524e21	−	2.15827e21i	−0.689137	−	0.716708i
$485$	−3.43187e20			−0.112098
$486$	−7.82108e19	+	1.83702e20i	−0.0251291	+	0.0590234i
$487$		−	1.39475e21i		−	0.440823i	−0.975407	−	0.220412i	$-0.929260\pi$
$487$		−	1.39475e21i		−	0.440823i	0.975407	−	0.220412i	$-0.0707401\pi$
$488$	−6.18320e20	−	1.62648e21i	−0.192245	−	0.505698i
$489$	1.68512e20			0.0515419
$490$	−1.71662e21	−	7.30849e20i	−0.516543	−	0.219917i
$491$			4.93920e21i			1.46219i	0.682273	+	0.731097i	$0.260991\pi$
$491$			4.93920e21i			1.46219i	−0.682273	+	0.731097i	$0.739009\pi$
$492$	−8.80311e20	+	8.46445e20i	−0.256398	+	0.246535i
$493$	8.86329e20			0.253992
$494$	−1.18806e21	+	2.79052e21i	−0.334982	+	0.786809i
$495$		−	3.03708e21i		−	0.842587i
$496$	1.69114e21	+	6.63595e19i	0.461663	+	0.0181155i
$497$	−3.77148e21			−1.01312
$498$	2.94557e21	+	1.25407e21i	0.778637	+	0.331503i
$499$		−	1.99837e21i		−	0.519843i	−0.965630	−	0.259922i	$-0.916303\pi$
$499$		−	1.99837e21i		−	0.519843i	0.965630	−	0.259922i	$-0.0836967\pi$
$500$	5.83466e21	+	6.06810e21i	1.49367	+	1.55343i
$501$	2.63512e21			0.663893
$502$	−1.00518e21	+	2.36097e21i	−0.249238	+	0.585412i
$503$		−	3.93204e21i		−	0.959565i	−0.877387	−	0.479782i	$-0.840716\pi$
$503$		−	3.93204e21i		−	0.959565i	0.877387	−	0.479782i	$-0.159284\pi$
$504$	−1.07470e21	+	4.08554e20i	−0.258132	+	0.0981308i
$505$	7.45413e21			1.76224
$506$	8.17161e21	+	3.47904e21i	1.90153	+	0.809573i
$507$			1.69283e20i			0.0387748i
$508$	1.28647e21	−	1.23697e21i	0.290060	−	0.278902i
$509$	−1.26514e21			−0.280799			−0.140400	−	0.990095i	$-0.544839\pi$
$509$	−1.26514e21			−0.280799			−0.140400	+	0.990095i	$0.544839\pi$
$510$	4.52502e20	−	1.06284e21i	0.0988687	−	0.232224i
$511$			8.63248e20i			0.185681i
$512$	4.18666e21	+	2.18464e21i	0.886559	+	0.462615i
$513$	−8.17327e20			−0.170395
$514$	3.40259e21	+	1.44864e21i	0.698400	+	0.297342i
$515$			1.58983e21i			0.321287i
$516$	−1.25679e21	−	1.30708e21i	−0.250073	−	0.260078i
$517$	−7.29121e21			−1.42848
$518$	7.52864e20	−	1.76833e21i	0.145237	−	0.341135i
$519$		−	3.63958e21i		−	0.691373i
$520$	3.28417e21	+	8.63898e21i	0.614326	+	1.61598i
$521$	−3.21561e21			−0.592328			−0.296164	−	0.955137i	$-0.595707\pi$
$521$	−3.21561e21			−0.592328			−0.296164	+	0.955137i	$0.595707\pi$
$522$	−1.75830e21	−	7.48592e20i	−0.318955	−	0.135794i
$523$		−	1.03502e21i		−	0.184899i	−0.995717	−	0.0924493i	$-0.970530\pi$
$523$		−	1.03502e21i		−	0.184899i	0.995717	−	0.0924493i	$-0.0294696\pi$
$524$	−3.98008e20	+	3.82697e20i	−0.0700232	+	0.0673294i
$525$	6.08405e21			1.05419
$526$	2.97221e21	−	6.98115e21i	0.507217	−	1.19136i
$527$			6.71337e20i			0.112838i
$528$	−1.93105e20	+	4.92118e21i	−0.0319685	+	0.814700i
$529$	−7.00188e21			−1.14175
$530$	−1.92550e22	−	8.19777e21i	−3.09269	−	1.31671i
$531$		−	2.12586e21i		−	0.336340i
$532$	−3.26217e21	−	3.39268e21i	−0.508409	−	0.528750i
$533$	3.87579e21			0.595035
$534$	5.40733e19	−	1.27008e20i	0.00817811	−	0.0192088i
$535$		−	1.06354e22i		−	1.58462i
$536$	−5.94775e21	+	2.26108e21i	−0.873040	+	0.331893i
$537$	3.56596e19			0.00515682
$538$	3.92500e21	+	1.67106e21i	0.559219	+	0.238086i
$539$			3.15528e21i			0.442923i
$540$	−1.79535e21	+	1.72628e21i	−0.248312	+	0.238760i
$541$	−3.93823e21			−0.536689			−0.268344	−	0.963323i	$-0.586477\pi$
$541$	−3.93823e21			−0.536689			−0.268344	+	0.963323i	$0.586477\pi$
$542$	−3.23908e21	+	7.60799e21i	−0.434939	+	1.02159i
$543$			6.53987e21i			0.865308i
$544$	−8.00796e20	+	1.69342e21i	−0.104407	+	0.220787i
$545$	−7.71565e21			−0.991290
$546$	3.35727e21	+	1.42935e21i	0.425055	+	0.180966i
$547$		−	5.88632e21i		−	0.734421i	−0.930138	−	0.367211i	$-0.880313\pi$
$547$		−	5.88632e21i		−	0.734421i	0.930138	−	0.367211i	$-0.119687\pi$
$548$	9.98047e21	+	1.03798e22i	1.22718	+	1.27627i
$549$	−1.48820e21			−0.180336
$550$	1.02089e22	−	2.39787e22i	1.21920	−	2.86367i
$551$		−	7.82302e21i		−	0.920792i
$552$	−2.58814e21	−	6.80807e21i	−0.300244	−	0.789790i
$553$	7.55785e21			0.864167
$554$	−9.39281e21	−	3.99897e21i	−1.05857	−	0.450682i
$555$		−	4.16343e21i		−	0.462495i
$556$	−5.29165e21	+	5.08808e21i	−0.579420	+	0.557129i
$557$	7.08571e21			0.764790			0.382395	−	0.923999i	$-0.375099\pi$
$557$	7.08571e21			0.764790			0.382395	+	0.923999i	$0.375099\pi$
$558$	5.67010e20	−	1.33180e21i	0.0603278	−	0.141698i
$559$			5.75474e21i			0.603575i
$560$	−1.43314e22	−	5.62358e20i	−1.48178	−	0.0581446i
$561$	−1.95358e21			−0.199126
$562$	1.30369e22	+	5.55042e21i	1.31003	+	0.557744i
$563$		−	1.46094e22i		−	1.44732i	−0.690156	−	0.723661i	$-0.742458\pi$
$563$		−	1.46094e22i		−	1.44732i	0.690156	−	0.723661i	$-0.257542\pi$
$564$	4.14433e21	+	4.31014e21i	0.404782	+	0.420977i
$565$	−1.82848e22			−1.76077
$566$	−5.54830e21	+	1.30319e22i	−0.526779	+	1.23730i
$567$			9.83325e20i			0.0920518i
$568$	1.23840e22	−	4.70787e21i	1.14307	−	0.434548i
$569$	1.08451e22			0.987041			0.493520	−	0.869734i	$-0.335710\pi$
$569$	1.08451e22			0.987041			0.493520	+	0.869734i	$0.335710\pi$
$570$	−9.38097e21	−	3.99393e21i	−0.841877	−	0.358427i
$571$			1.98361e22i			1.75536i	0.479246	+	0.877681i	$0.340910\pi$
$571$			1.98361e22i			1.75536i	−0.479246	+	0.877681i	$0.659090\pi$
$572$	1.12668e22	−	1.08334e22i	0.983179	−	0.945356i
$573$	9.53074e21			0.820143
$574$	−2.35607e21	+	5.53396e21i	−0.199937	+	0.469614i
$575$			3.85417e22i			3.22543i
$576$	3.01888e21	−	2.68305e21i	0.249153	−	0.221436i
$577$	−8.29059e20			−0.0674806			−0.0337403	−	0.999431i	$-0.510742\pi$
$577$	−8.29059e20			−0.0674806			−0.0337403	+	0.999431i	$0.510742\pi$
$578$	1.07781e22	+	4.58873e21i	0.865202	+	0.368358i
$579$		−	1.03754e22i		−	0.821440i
$580$	−1.65230e22	−	1.71841e22i	−1.29023	−	1.34185i
$581$	1.57671e22			1.21435
$582$	1.86448e20	−	4.37929e20i	0.0141636	−	0.0332675i
$583$			3.53921e22i			2.65191i
$584$	−1.07758e21	−	2.83455e21i	−0.0796425	−	0.209499i
$585$	7.90447e21			0.576270
$586$	2.90690e21	+	1.23761e21i	0.209049	+	0.0890023i
$587$			8.76814e20i			0.0622017i	0.999516	+	0.0311009i	$0.00990131\pi$
$587$			8.76814e20i			0.0622017i	−0.999516	+	0.0311009i	$0.990099\pi$
$588$	1.86522e21	−	1.79347e21i	0.130530	−	0.125509i
$589$	5.92544e21			0.409070
$590$	1.03882e22	−	2.43998e22i	0.707494	−	1.66177i
$591$		−	2.22788e21i		−	0.149690i
$592$	−2.64721e20	+	6.74627e21i	−0.0175475	+	0.447188i
$593$	2.18546e21			0.142924			0.0714620	−	0.997443i	$-0.477234\pi$
$593$	2.18546e21			0.142924			0.0714620	+	0.997443i	$0.477234\pi$
$594$	3.87551e21	+	1.64999e21i	0.250056	+	0.106461i
$595$		−	5.68919e21i		−	0.362172i
$596$	−8.33092e21	−	8.66423e21i	−0.523266	−	0.544202i
$597$	5.50806e21			0.341353
$598$	−9.05475e21	+	2.12679e22i	−0.553690	+	1.30051i
$599$		−	1.50421e22i		−	0.907602i	−0.891103	−	0.453801i	$-0.850068\pi$
$599$		−	1.50421e22i		−	0.907602i	0.891103	−	0.453801i	$-0.149932\pi$
$600$	−1.99775e22	+	7.59460e21i	−1.18941	+	0.452163i
$601$	−6.60237e19			−0.00387886			−0.00193943	−	0.999998i	$-0.500617\pi$
$601$	−6.60237e19			−0.00387886			−0.00193943	+	0.999998i	$0.500617\pi$
$602$	−8.21678e21	−	3.49828e21i	−0.476354	−	0.202807i
$603$			5.44206e21i			0.311333i
$604$	1.32856e22	−	1.27745e22i	0.750040	−	0.721186i
$605$	−3.19442e22			−1.77971
$606$	−4.04970e21	+	9.51196e21i	−0.222660	+	0.522985i
$607$		−	1.41497e22i		−	0.767782i	−0.923378	−	0.383891i	$-0.874584\pi$
$607$		−	1.41497e22i		−	0.767782i	0.923378	−	0.383891i	$-0.125416\pi$
$608$	1.49466e22	+	7.06808e21i	0.800414	+	0.378506i
$609$	−9.41187e21			−0.497436
$610$	−1.70810e22	−	7.27218e21i	−0.890991	−	0.379338i
$611$		−	1.89765e22i		−	0.976982i
$612$	1.11042e21	+	1.15484e21i	0.0564254	+	0.0586829i
$613$	−2.18614e22			−1.09646			−0.548231	−	0.836327i	$-0.684698\pi$
$613$	−2.18614e22			−1.09646			−0.548231	+	0.836327i	$0.684698\pi$
$614$	4.12663e21	−	9.69267e21i	0.204291	−	0.479840i
$615$			1.30294e22i			0.636681i
$616$	8.61916e21	+	2.26726e22i	0.415737	+	1.09359i
$617$	1.97100e22			0.938438			0.469219	−	0.883082i	$-0.344535\pi$
$617$	1.97100e22			0.938438			0.469219	+	0.883082i	$0.344535\pi$
$618$	−2.02873e21	−	8.63728e20i	−0.0953491	−	0.0405947i
$619$		−	2.44385e22i		−	1.13383i	−0.823776	−	0.566916i	$-0.808137\pi$
$619$		−	2.44385e22i		−	1.13383i	0.823776	−	0.566916i	$-0.191863\pi$
$620$	1.30159e22	−	1.25151e22i	0.596128	−	0.573195i
$621$	−6.22924e21			−0.281645
$622$	−5.31768e21	+	1.24902e22i	−0.237355	+	0.557502i
$623$		−	6.79851e20i		−	0.0299577i
$624$	−1.28081e22	−	5.02586e20i	−0.557197	−	0.0218642i
$625$	3.84981e22			1.65348
$626$	2.03589e22	+	8.66774e21i	0.863294	+	0.367546i
$627$			1.72429e22i			0.721889i
$628$	−1.13746e22	−	1.18297e22i	−0.470176	−	0.488988i
$629$	−2.67809e21			−0.109300
$630$	−4.80509e21	+	1.12862e22i	−0.193632	+	0.454804i
$631$		−	1.35375e22i		−	0.538646i	−0.963050	−	0.269323i	$-0.913200\pi$
$631$		−	1.35375e22i		−	0.538646i	0.963050	−	0.269323i	$-0.0867998\pi$
$632$	−2.48169e22	+	9.43433e21i	−0.975014	+	0.370659i
$633$	−1.14157e22			−0.442866
$634$	−2.88979e22	−	1.23032e22i	−1.10701	−	0.471308i
$635$		−	1.90408e22i		−	0.720270i
$636$	2.09218e22	−	2.01169e22i	0.781523	−	0.751458i
$637$	−8.21212e21			−0.302928
$638$	−1.57928e22	+	3.70944e22i	−0.575301	+	1.35127i
$639$		−	1.13311e22i		−	0.407628i
$640$	4.77604e22	−	1.60431e22i	1.69679	−	0.569964i
$641$	−4.44404e21			−0.155924			−0.0779622	−	0.996956i	$-0.524841\pi$
$641$	−4.44404e21			−0.155924			−0.0779622	+	0.996956i	$0.524841\pi$
$642$	1.35715e22	+	5.77803e21i	0.470269	+	0.200216i
$643$			2.17900e21i			0.0745708i	0.999305	+	0.0372854i	$0.0118711\pi$
$643$			2.17900e21i			0.0745708i	−0.999305	+	0.0372854i	$0.988129\pi$
$644$	−2.48625e22	−	2.58573e22i	−0.840346	−	0.873968i
$645$	−1.93459e22			−0.645819
$646$	−2.56906e21	+	6.03424e21i	−0.0847061	+	0.198958i
$647$			6.95471e21i			0.226488i	0.993567	+	0.113244i	$0.0361242\pi$
$647$			6.95471e21i			0.226488i	−0.993567	+	0.113244i	$0.963876\pi$
$648$	−1.22747e21	−	3.22884e21i	−0.0394829	−	0.103859i
$649$	−4.48487e22			−1.42492
$650$	6.24082e22	+	2.65701e22i	1.95855	+	0.833848i
$651$		−	7.12888e21i		−	0.220990i
$652$	−2.10154e21	+	2.02070e21i	−0.0643513	+	0.0618757i
$653$	2.73568e22			0.827484			0.413742	−	0.910394i	$-0.364222\pi$
$653$	2.73568e22			0.827484			0.413742	+	0.910394i	$0.364222\pi$
$654$	4.19178e21	−	9.84568e21i	0.125250	−	0.294187i
$655$			5.89087e21i			0.173880i
$656$	8.28439e20	−	2.11123e22i	0.0241563	−	0.615609i
$657$	−2.59355e21			−0.0747088
$658$	2.70952e22	+	1.15357e22i	0.771054	+	0.328275i
$659$		−	2.23203e22i		−	0.627505i	−0.949505	−	0.313752i	$-0.898414\pi$
$659$		−	2.23203e22i		−	0.627505i	0.949505	−	0.313752i	$-0.101586\pi$
$660$	3.64188e22	+	3.78759e22i	1.01152	+	1.05199i
$661$	2.70207e22			0.741456			0.370728	−	0.928741i	$-0.379108\pi$
$661$	2.70207e22			0.741456			0.370728	+	0.928741i	$0.379108\pi$
$662$	−3.08390e21	+	7.24349e21i	−0.0836058	+	0.196374i
$663$		−	5.08449e21i		−	0.136188i
$664$	−5.17728e22	+	1.96818e22i	−1.37012	+	0.520859i
$665$	−5.02146e22			−1.31298
$666$	5.31280e21	+	2.26191e21i	0.137256	+	0.0584363i
$667$		−	5.96230e22i		−	1.52197i
$668$	−3.28630e22	+	3.15987e22i	−0.828886	+	0.796999i
$669$	−3.43234e22			−0.855424
$670$	−2.65930e22	+	6.24618e22i	−0.654891	+	1.53821i
$671$			3.13961e22i			0.764003i
$672$	8.50360e21	−	1.79823e22i	0.204479	−	0.432405i
$673$	2.96721e22			0.705063			0.352532	−	0.935800i	$-0.385321\pi$
$673$	2.96721e22			0.705063			0.352532	+	0.935800i	$0.385321\pi$
$674$	1.02082e22	+	4.34614e21i	0.239702	+	0.102053i
$675$			1.82790e22i			0.424152i
$676$	−2.02994e21	−	2.11116e21i	−0.0465489	−	0.0484113i
$677$	3.19341e22			0.723678			0.361839	−	0.932241i	$-0.382149\pi$
$677$	3.19341e22			0.723678			0.361839	+	0.932241i	$0.382149\pi$
$678$	9.93382e21	−	2.33326e22i	0.222474	−	0.522548i
$679$		−	2.34416e21i		−	0.0518834i
$680$	7.10171e21	+	1.86810e22i	0.155343	+	0.408628i
$681$	1.94384e22			0.420226
$682$	−2.80966e22	−	1.19621e22i	−0.600314	−	0.255582i
$683$			8.96899e21i			0.189399i	0.995506	+	0.0946995i	$0.0301890\pi$
$683$			8.96899e21i			0.189399i	−0.995506	+	0.0946995i	$0.969811\pi$
$684$	1.01930e22	−	9.80089e21i	0.212742	−	0.204558i
$685$	1.53630e23			3.16921
$686$	2.09086e22	−	4.91103e22i	0.426316	−	1.00134i
$687$		−	4.93734e21i		−	0.0995037i
$688$	3.13474e22	+	1.23006e21i	0.624444	+	0.0245029i
$689$	−9.21135e22			−1.81372
$690$	−7.14968e22	−	3.04396e22i	−1.39153	−	0.592443i
$691$			8.81888e22i			1.69664i	0.529485	+	0.848319i	$0.322385\pi$
$691$			8.81888e22i			1.69664i	−0.529485	+	0.848319i	$0.677615\pi$
$692$	4.36436e22	+	4.53898e22i	0.829989	+	0.863196i
$693$	2.07449e22			0.389983
$694$	4.14599e22	−	9.73813e22i	0.770464	−	1.80967i
$695$			7.83211e22i			1.43880i
$696$	3.09047e22	−	1.17487e22i	0.561243	−	0.213361i
$697$	8.38104e21			0.150465
$698$	−1.90363e22	−	8.10467e21i	−0.337862	−	0.143844i
$699$		−	5.81093e21i		−	0.101960i
$700$	−7.58752e22	+	7.29562e22i	−1.31618	+	1.26555i
$701$	−2.40363e22			−0.412215			−0.206108	−	0.978529i	$-0.566080\pi$
$701$	−2.40363e22			−0.412215			−0.206108	+	0.978529i	$0.566080\pi$
$702$	−4.29436e21	+	1.00866e22i	−0.0728117	+	0.171021i
$703$			2.36377e22i			0.396244i
$704$	−5.66036e22	−	6.36884e22i	−0.938129	−	1.05555i
$705$	6.37938e22			1.04536
$706$	−4.06673e22	−	1.73140e22i	−0.658882	−	0.280518i
$707$			5.09158e22i			0.815638i
$708$	2.54920e22	+	2.65119e22i	0.403774	+	0.419929i
$709$	−5.85854e22			−0.917529			−0.458764	−	0.888558i	$-0.651708\pi$
$709$	−5.85854e22			−0.917529			−0.458764	+	0.888558i	$0.651708\pi$
$710$	5.53701e22	−	1.30054e23i	0.857450	−	2.01399i
$711$			2.27069e22i			0.347697i
$712$	8.48645e20	+	2.23235e21i	0.0128495	+	0.0338005i
$713$	4.51606e22			0.676150
$714$	7.25978e21	+	3.09084e21i	0.107483	+	0.0457604i
$715$		−	1.66758e23i		−	2.44140i
$716$	−4.44717e20	+	4.27608e20i	−0.00643842	+	0.00619073i
$717$	−4.75666e22			−0.681002
$718$	−2.41559e22	+	5.67375e22i	−0.342001	+	0.803295i
$719$		−	3.88400e22i		−	0.543811i	−0.962324	−	0.271905i	$-0.912346\pi$
$719$		−	3.88400e22i		−	0.543811i	0.962324	−	0.271905i	$-0.0876538\pi$
$720$	1.68956e21	−	4.30574e22i	0.0233945	−	0.596195i
$721$	−1.08594e22			−0.148705
$722$	−1.46797e22	−	6.24987e21i	−0.198802	−	0.0846396i
$723$		−	7.05811e22i		−	0.945328i
$724$	−7.84223e22	−	8.15599e22i	−1.03880	−	1.08036i
$725$	−1.74957e23			−2.29206
$726$	1.73547e22	−	4.07629e22i	0.224867	−	0.528168i
$727$			1.26747e23i			1.62428i	0.583461	+	0.812141i	$0.301698\pi$
$727$			1.26747e23i			1.62428i	−0.583461	+	0.812141i	$0.698302\pi$
$728$	−5.90090e22	+	2.24327e22i	−0.747940	+	0.284335i
$729$	−2.95431e21			−0.0370370
$730$	−2.97678e22	−	1.26736e22i	−0.369117	−	0.157151i
$731$			1.24441e22i			0.152624i
$732$	1.85595e22	−	1.78456e22i	0.225154	−	0.216492i
$733$	3.58338e22			0.429993			0.214996	−	0.976615i	$-0.431026\pi$
$733$	3.58338e22			0.429993			0.214996	+	0.976615i	$0.431026\pi$
$734$	−5.02889e22	+	1.18119e23i	−0.596903	+	1.40201i
$735$		−	2.76069e22i		−	0.324130i
$736$	1.13915e23	+	5.38692e22i	1.32300	+	0.625631i
$737$	1.14810e23			1.31898
$738$	−1.66263e22	−	7.07862e21i	−0.188949	−	0.0804447i
$739$		−	7.54803e22i		−	0.848551i	−0.905533	−	0.424276i	$-0.860529\pi$
$739$		−	7.54803e22i		−	0.848551i	0.905533	−	0.424276i	$-0.139471\pi$
$740$	4.99253e22	+	5.19228e22i	0.555223	+	0.577437i
$741$	−4.48774e22			−0.493721
$742$	5.59953e22	−	1.31522e23i	0.609425	−	1.43142i
$743$			1.28868e23i			1.38751i	0.720212	+	0.693754i	$0.244044\pi$
$743$			1.28868e23i			1.38751i	−0.720212	+	0.693754i	$0.755956\pi$
$744$	8.89885e21	+	2.34083e22i	0.0947873	+	0.249337i
$745$	−1.28238e23			−1.35135
$746$	1.33146e22	+	5.66866e21i	0.138809	+	0.0590976i
$747$			4.73710e22i			0.488593i
$748$	2.43634e22	−	2.34262e22i	0.248614	−	0.239050i
$749$	7.26457e22			0.733424
$750$	−4.87938e22	+	1.14607e23i	−0.487388	+	1.14478i
$751$			1.23858e23i			1.22407i	0.790831	+	0.612035i	$0.209649\pi$
$751$			1.23858e23i			1.22407i	−0.790831	+	0.612035i	$0.790351\pi$
$752$	−1.03369e23	−	4.05617e21i	−1.01076	−	0.0396619i
$753$	−3.79694e22			−0.367345
$754$	−9.65438e22	−	4.11033e22i	−0.924174	−	0.393465i
$755$		−	1.96638e23i		−	1.86248i
$756$	−1.17914e22	−	1.22632e22i	−0.110508	−	0.114929i
$757$	1.89216e23			1.75465			0.877324	−	0.479898i	$-0.159326\pi$
$757$	1.89216e23			1.75465			0.877324	+	0.479898i	$0.159326\pi$
$758$	4.42120e22	−	1.03846e23i	0.405683	−	0.952872i
$759$			1.31416e23i			1.19321i
$760$	1.64884e23	−	6.26820e22i	1.48139	−	0.563163i
$761$	1.51919e23			1.35063			0.675313	−	0.737531i	$-0.264009\pi$
$761$	1.51919e23			1.35063			0.675313	+	0.737531i	$0.264009\pi$
$762$	2.42973e22	+	1.03445e22i	0.213756	+	0.0910061i
$763$		−	5.27022e22i		−	0.458809i
$764$	−1.18859e23	+	1.14287e23i	−1.02397	+	0.984577i
$765$	1.70927e22			0.145720
$766$	−1.32778e22	+	3.11870e22i	−0.112020	+	0.263114i
$767$		−	1.16726e23i		−	0.974548i
$768$	−5.47540e21	+	6.96613e22i	−0.0452403	+	0.575575i
$769$	−9.74177e22			−0.796576			−0.398288	−	0.917260i	$-0.630396\pi$
$769$	−9.74177e22			−0.796576			−0.398288	+	0.917260i	$0.630396\pi$
$770$	2.38102e23	+	1.01372e23i	1.92681	+	0.820334i
$771$			5.47207e22i			0.438245i
$772$	1.24415e23	+	1.29393e23i	0.986133	+	1.02559i
$773$	1.72643e23			1.35429			0.677145	−	0.735849i	$-0.263217\pi$
$773$	1.72643e23			1.35429			0.677145	+	0.735849i	$0.263217\pi$
$774$	1.05103e22	−	2.46866e22i	0.0815992	−	0.191661i
$775$		−	1.32519e23i		−	1.01827i
$776$	2.92617e21	+	7.69726e21i	0.0222539	+	0.0585386i
$777$	2.84385e22			0.214061
$778$	2.02736e23	+	8.63146e22i	1.51041	+	0.643054i
$779$		−	7.39737e22i		−	0.545479i
$780$	−9.85780e22	+	9.47857e22i	−0.719487	+	0.691809i
$781$	−2.39049e23			−1.72694
$782$	−1.95801e22	+	4.59898e22i	−0.140010	+	0.328857i
$783$		−	2.82771e22i		−	0.200143i
$784$	−1.75531e21	+	4.47332e22i	−0.0122978	+	0.313402i
$785$	−1.75090e23			−1.21424
$786$	−7.51713e21	−	3.20040e21i	−0.0516026	−	0.0219697i
$787$			1.47774e23i			1.00416i	0.864822	+	0.502078i	$0.167431\pi$
$787$			1.47774e23i			1.00416i	−0.864822	+	0.502078i	$0.832569\pi$
$788$	2.67154e22	+	2.77843e22i	0.179702	+	0.186892i
$789$	1.12272e23			0.747573
$790$	−1.10959e23	+	2.60621e23i	−0.731384	+	1.71788i
$791$		−	1.24895e23i		−	0.814957i
$792$	−6.81179e22	+	2.58955e22i	−0.440007	+	0.167272i
$793$	−8.17131e22			−0.522524
$794$	−1.44692e23	−	6.16022e22i	−0.915967	−	0.389971i
$795$		−	3.09660e23i		−	1.94066i
$796$	−6.86919e22	+	6.60494e22i	−0.426188	+	0.409793i
$797$	−4.36225e22			−0.267944			−0.133972	−	0.990985i	$-0.542773\pi$
$797$	−4.36225e22			−0.267944			−0.133972	+	0.990985i	$0.542773\pi$
$798$	2.72807e22	−	6.40771e22i	0.165895	−	0.389655i
$799$		−	4.10349e22i		−	0.247047i
$800$	1.58073e23	−	3.34272e23i	0.942189	−	1.99242i
$801$	2.04255e21			0.0120535
$802$	−7.76666e22	−	3.30664e22i	−0.453774	−	0.193193i
$803$			5.47154e22i			0.316509i
$804$	−6.52579e22	−	6.78688e22i	−0.373753	−	0.388706i
$805$	−3.82710e23			−2.17021
$806$	3.11331e22	−	7.31257e22i	0.174800	−	0.410572i
$807$			6.31222e22i			0.350909i
$808$	−6.35573e22	−	1.67187e23i	−0.349844	−	0.920261i
$809$	−1.15871e23			−0.631520			−0.315760	−	0.948839i	$-0.602259\pi$
$809$	−1.15871e23			−0.631520			−0.315760	+	0.948839i	$0.602259\pi$
$810$	−3.39085e22	−	1.44365e22i	−0.182990	−	0.0779077i
$811$			1.58216e23i			0.845442i	0.906260	+	0.422721i	$0.138925\pi$
$811$			1.58216e23i			0.845442i	−0.906260	+	0.422721i	$0.861075\pi$
$812$	1.17377e23	−	1.12861e23i	0.621061	−	0.597169i
$813$	−1.22352e23			−0.641044
$814$	4.77190e22	−	1.12083e23i	0.247569	−	0.581492i
$815$			3.11046e22i			0.159795i
$816$	−2.76964e22	−	1.08679e21i	−0.140897	−	0.00552874i
$817$	1.09836e23			0.553307
$818$	1.20100e23	+	5.11323e22i	0.599124	+	0.255076i
$819$			5.39919e22i			0.266721i
$820$	−1.56240e23	−	1.62491e23i	−0.764332	−	0.794912i
$821$	2.50054e23			1.21140			0.605701	−	0.795692i	$-0.292893\pi$
$821$	2.50054e23			1.21140			0.605701	+	0.795692i	$0.292893\pi$
$822$	−8.34643e22	+	1.96042e23i	−0.400430	+	0.940532i
$823$		−	1.30788e23i		−	0.621398i	−0.950508	−	0.310699i	$-0.899437\pi$
$823$		−	1.30788e23i		−	0.621398i	0.950508	−	0.310699i	$-0.100563\pi$
$824$	3.56579e22	−	1.35556e22i	0.167779	−	0.0637825i
$825$	3.85627e23			1.79695
$826$	1.66664e23	+	7.09569e22i	0.769133	+	0.327457i
$827$			1.00134e23i			0.457655i	0.973467	+	0.228827i	$0.0734892\pi$
$827$			1.00134e23i			0.457655i	−0.973467	+	0.228827i	$0.926511\pi$
$828$	7.76858e22	−	7.46973e22i	0.351641	−	0.338113i
$829$	2.46600e23			1.10549			0.552746	−	0.833349i	$-0.313580\pi$
$829$	2.46600e23			1.10549			0.552746	+	0.833349i	$0.313580\pi$
$830$	−2.31482e23	+	5.43706e23i	−1.02776	+	2.41401i
$831$		−	1.51056e23i		−	0.664248i
$832$	1.65759e23	−	1.47320e23i	0.721922	−	0.641614i
$833$	−1.77579e22			−0.0766006
$834$	−9.99428e22	−	4.25504e22i	−0.426995	−	0.181792i
$835$			4.86400e23i			2.05827i
$836$	−2.06767e23	−	2.15039e23i	−0.866624	−	0.901296i
$837$	2.14181e22			0.0889155
$838$	5.62361e22	−	1.32088e23i	0.231240	−	0.543139i
$839$		−	2.45920e23i		−	1.00161i	−0.865560	−	0.500805i	$-0.833037\pi$
$839$		−	2.45920e23i		−	1.00161i	0.865560	−	0.500805i	$-0.166963\pi$
$840$	−7.54126e22	−	1.98372e23i	−0.304235	−	0.800288i
$841$	2.04073e22			0.0815488
$842$	−3.89263e23	−	1.65728e23i	−1.54080	−	0.655993i
$843$			2.09660e23i			0.822044i
$844$	1.42367e23	−	1.36890e23i	0.552930	−	0.531659i
$845$	−3.12469e22			−0.120214
$846$	−3.46580e22	+	8.14051e22i	−0.132081	+	0.310233i
$847$		−	2.18197e23i		−	0.823722i
$848$	−1.96890e22	+	5.01763e23i	−0.0736303	+	1.87643i
$849$	−2.09580e23			−0.776405
$850$	1.34952e23	+	5.74555e22i	0.495253	+	0.210853i
$851$			1.80154e23i			0.654950i
$852$	1.35876e23	+	1.41312e23i	0.489356	+	0.508934i
$853$	−4.11660e23			−1.46874			−0.734372	−	0.678747i	$-0.762523\pi$
$853$	−4.11660e23			−1.46874			−0.734372	+	0.678747i	$0.762523\pi$
$854$	4.96730e22	−	1.16672e23i	0.175573	−	0.412387i
$855$		−	1.50866e23i		−	0.528276i
$856$	−2.38539e23	+	9.06822e22i	−0.827501	+	0.314581i
$857$	2.13770e22			0.0734684			0.0367342	−	0.999325i	$-0.488305\pi$
$857$	2.13770e22			0.0734684			0.0367342	+	0.999325i	$0.488305\pi$
$858$	2.12795e23	+	9.05969e22i	0.724540	+	0.308471i
$859$			1.31672e23i			0.444170i	0.975027	+	0.222085i	$0.0712862\pi$
$859$			1.31672e23i			0.444170i	−0.975027	+	0.222085i	$0.928714\pi$
$860$	2.41266e23	−	2.31984e23i	0.806321	−	0.775301i
$861$	−8.89977e22			−0.294682
$862$	7.15981e22	−	1.68170e23i	0.234878	−	0.551684i
$863$			2.26730e23i			0.736923i	0.929643	+	0.368461i	$0.120115\pi$
$863$			2.26730e23i			0.736923i	−0.929643	+	0.368461i	$0.879885\pi$
$864$	5.40262e22	+	2.55483e22i	0.173978	+	0.0822720i
$865$	6.71808e23			2.14346
$866$	−5.62802e23	−	2.39612e23i	−1.77915	−	0.757469i
$867$			1.73334e23i			0.542913i
$868$	8.54853e22	+	8.89055e22i	0.265298	+	0.275912i
$869$	4.79041e23			1.47304
$870$	1.38178e23	−	3.24554e23i	0.421003	−	0.988856i
$871$			2.98810e23i			0.902089i
$872$	6.57871e22	+	1.73052e23i	0.196793	+	0.517661i
$873$	7.04282e21			0.0208753
$874$	4.05921e23	+	1.72820e23i	1.19220	+	0.507577i
$875$			6.13473e23i			1.78538i
$876$	3.23446e22	−	3.11003e22i	0.0932758	−	0.0896875i
$877$	−2.54957e23			−0.728568			−0.364284	−	0.931288i	$-0.618686\pi$
$877$	−2.54957e23			−0.728568			−0.364284	+	0.931288i	$0.618686\pi$
$878$	2.03711e22	−	4.78478e22i	0.0576844	−	0.135490i
$879$			4.67490e22i			0.131178i
$880$	−9.08371e23	−	3.56441e22i	−2.52582	−	0.0991121i
$881$	1.40519e22			0.0387193			0.0193596	−	0.999813i	$-0.493837\pi$
$881$	1.40519e22			0.0387193			0.0193596	+	0.999813i	$0.493837\pi$
$882$	3.52282e22	+	1.49983e22i	0.0961926	+	0.0409538i
$883$		−	6.97861e23i		−	1.88835i	−0.329438	−	0.944177i	$-0.606859\pi$
$883$		−	6.97861e23i		−	1.88835i	0.329438	−	0.944177i	$-0.393141\pi$
$884$	6.09702e22	+	6.34096e22i	0.163493	+	0.170034i
$885$	3.92400e23			1.04276
$886$	1.37755e23	−	3.23560e23i	0.362775	−	0.852089i
$887$		−	2.37497e22i		−	0.0619826i	−0.999520	−	0.0309913i	$-0.990134\pi$
$887$		−	2.37497e22i		−	0.0619826i	0.999520	−	0.0309913i	$-0.00986641\pi$
$888$	−9.33804e22	+	3.54992e22i	−0.241519	+	0.0918153i
$889$	1.30059e23			0.333370
$890$	2.34436e22	+	9.98107e21i	0.0595531	+	0.0253546i
$891$			6.23263e22i			0.156910i
$892$	4.28053e23	−	4.11585e23i	1.06802	−	1.02693i
$893$	−3.62187e23			−0.895615
$894$	6.96694e22	−	1.63640e23i	0.170743	−	0.401042i
$895$			6.58219e21i			0.0159877i
$896$	1.09583e23	+	3.26230e23i	0.263802	+	0.785344i
$897$	−3.42032e23			−0.816069
$898$	4.00598e22	+	1.70554e22i	0.0947323	+	0.0403321i
$899$			2.05003e23i			0.480488i
$900$	−2.19191e23	−	2.27960e23i	−0.509192	−	0.529565i
$901$	−1.99187e23			−0.458630
$902$	−1.49336e23	+	3.50761e23i	−0.340809	+	0.800495i
$903$		−	1.32143e23i		−	0.298911i
$904$	1.55905e23	+	4.10106e23i	0.349552	+	0.919493i
$905$	−1.20716e24			−2.68272
$906$	2.50923e23	+	1.06830e23i	0.552731	+	0.235324i
$907$		−	5.71473e23i		−	1.24778i	−0.781513	−	0.623889i	$-0.785552\pi$
$907$		−	5.71473e23i		−	1.24778i	0.781513	−	0.623889i	$-0.214448\pi$
$908$	−2.42419e23	+	2.33093e23i	−0.524662	+	0.504478i
$909$	−1.52972e23			−0.328172
$910$	−2.63835e23	+	6.19698e23i	−0.561050	+	1.31780i
$911$		−	4.04153e23i		−	0.851920i	−0.904742	−	0.425960i	$-0.859936\pi$
$911$		−	4.04153e23i		−	0.851920i	0.904742	−	0.425960i	$-0.140064\pi$
$912$	−9.59240e21	+	2.44457e23i	−0.0200433	+	0.510792i
$913$	9.99372e23			2.06996
$914$	4.15832e23	+	1.77040e23i	0.853785	+	0.363497i
$915$		−	2.74697e23i		−	0.559095i
$916$	5.92056e22	+	6.15744e22i	0.119454	+	0.124233i
$917$	−4.02379e22			−0.0804786
$918$	−9.28615e21	+	2.18114e22i	−0.0184117	+	0.0432456i
$919$		−	4.15747e23i		−	0.817157i	−0.912723	−	0.408578i	$-0.866025\pi$
$919$		−	4.15747e23i		−	0.817157i	0.912723	−	0.408578i	$-0.133975\pi$
$920$	1.25666e24	−	4.77729e23i	2.44859	−	0.930849i
$921$	1.55878e23			0.301099
$922$	−8.88287e23	−	3.78186e23i	−1.70101	−	0.724200i
$923$		−	6.22161e23i		−	1.18111i
$924$	−2.58713e23	+	2.48761e23i	−0.486904	+	0.468173i
$925$	5.28642e23			0.986343
$926$	9.37647e22	−	2.20235e23i	0.173441	−	0.407379i
$927$		−	3.26262e22i		−	0.0598314i
$928$	−2.44535e23	+	5.17110e23i	−0.444588	+	0.940155i
$929$	−3.05652e23			−0.550936			−0.275468	−	0.961310i	$-0.588833\pi$
$929$	−3.05652e23			−0.550936			−0.275468	+	0.961310i	$0.588833\pi$
$930$	2.45829e23	+	1.04661e23i	0.439308	+	0.187034i
$931$			1.56737e23i			0.277699i
$932$	6.96812e22	+	7.24691e22i	0.122402	+	0.127299i
$933$	−2.00868e23			−0.349831
$934$	9.43913e22	−	2.21707e23i	0.162989	−	0.382829i
$935$		−	3.60600e23i		−	0.617351i
$936$	−6.73970e22	−	1.77287e23i	−0.114402	−	0.300934i
$937$	−7.66753e23			−1.29044			−0.645221	−	0.763996i	$-0.723235\pi$
$937$	−7.66753e23			−1.29044			−0.645221	+	0.763996i	$0.723235\pi$
$938$	−4.26649e23	−	1.81645e23i	−0.711947	−	0.303110i
$939$			3.27413e23i			0.541716i
$940$	−7.95583e23	+	7.64977e23i	−1.30516	+	1.25495i
$941$	3.70350e22			0.0602415			0.0301207	−	0.999546i	$-0.490411\pi$
$941$	3.70350e22			0.0602415			0.0301207	+	0.999546i	$0.490411\pi$
$942$	9.51234e22	−	2.23427e23i	0.153419	−	0.360353i
$943$		−	5.63789e23i		−	0.901619i
$944$	−6.35831e23	−	2.49497e22i	−1.00824	−	0.0395631i
$945$	−1.81506e23			−0.285389
$946$	−5.20806e23	−	2.21732e23i	−0.811983	−	0.345700i
$947$		−	4.42301e23i		−	0.683783i	−0.939739	−	0.341891i	$-0.888933\pi$
$947$		−	4.42301e23i		−	0.683783i	0.939739	−	0.341891i	$-0.111067\pi$
$948$	−2.72288e23	−	2.83182e23i	−0.417408	−	0.434109i
$949$	−1.42405e23			−0.216470
$950$	5.07120e23	−	1.19113e24i	0.764403	−	1.79543i
$951$		−	4.64738e23i		−	0.694647i
$952$	−1.27601e23	+	4.85086e22i	−0.189130	+	0.0718990i
$953$	4.87297e22			0.0716227			0.0358114	−	0.999359i	$-0.488598\pi$
$953$	4.87297e22			0.0716227			0.0358114	+	0.999359i	$0.488598\pi$
$954$	3.95147e23	+	1.68233e23i	0.575932	+	0.245202i
$955$			1.75922e24i			2.54269i
$956$	5.93210e23	−	5.70390e23i	0.850248	−	0.817539i
$957$	−5.96555e23			−0.847920
$958$	−3.34241e23	+	7.85067e23i	−0.471124	+	1.10658i
$959$			1.04938e24i			1.46684i
$960$	4.95248e23	+	5.57237e23i	0.686520	+	0.772449i
$961$	5.72147e23			0.786539
$962$	2.91713e23	+	1.24196e23i	0.397699	+	0.169320i
$963$			2.18258e23i			0.295093i
$964$	8.46367e23	+	8.80229e23i	1.13486	+	1.18026i
$965$	1.91513e24			2.54671
$966$	2.07919e23	−	4.88362e23i	0.274207	−	0.644058i
$967$		−	3.05837e23i		−	0.400016i	−0.979794	−	0.200008i	$-0.935903\pi$
$967$		−	3.05837e23i		−	0.400016i	0.979794	−	0.200008i	$-0.0640968\pi$
$968$	2.72371e23	+	7.16469e23i	0.353311	+	0.929382i
$969$	−9.70431e22			−0.124846
$970$	8.08348e22	+	3.44152e22i	0.103139	+	0.0439114i
$971$		−	1.95639e23i		−	0.247572i	−0.992309	−	0.123786i	$-0.960496\pi$
$971$		−	1.95639e23i		−	0.247572i	0.992309	−	0.123786i	$-0.0395036\pi$
$972$	3.68437e22	−	3.54263e22i	0.0462417	−	0.0444627i
$973$	−5.34976e23			−0.665935
$974$	−1.39867e23	+	3.28521e23i	−0.172681	+	0.405594i
$975$			1.00365e24i			1.22899i
$976$	−1.74659e22	+	4.45110e23i	−0.0212126	+	0.540591i
$977$	−7.88200e23			−0.949467			−0.474733	−	0.880130i	$-0.657455\pi$
$977$	−7.88200e23			−0.949467			−0.474733	+	0.880130i	$0.657455\pi$
$978$	−3.96915e22	−	1.68986e22i	−0.0474228	−	0.0201902i
$979$		−	4.30911e22i		−	0.0510654i
$980$	3.31045e23	+	3.44290e23i	0.389116	+	0.404684i
$981$	1.58339e23			0.184602
$982$	4.95309e23	−	1.16339e24i	0.572776	−	1.34534i
$983$		−	1.62319e24i		−	1.86184i	−0.365223	−	0.930920i	$-0.619007\pi$
$983$		−	1.62319e24i		−	1.86184i	0.365223	−	0.930920i	$-0.380993\pi$
$984$	2.92232e23	−	1.11094e23i	0.332481	−	0.126395i
$985$	4.11232e23			0.464084
$986$	−2.08767e23	−	8.88821e22i	−0.233693	−	0.0994945i
$987$			4.35747e23i			0.483835i
$988$	5.59673e23	−	5.38142e23i	0.616423	−	0.592709i
$989$	8.37109e23			0.914559
$990$	−3.04562e23	+	7.15358e23i	−0.330061	+	0.775250i
$991$			5.28881e23i			0.568550i	0.958743	+	0.284275i	$0.0917529\pi$
$991$			5.28881e23i			0.568550i	−0.958743	+	0.284275i	$0.908247\pi$
$992$	−3.91678e23	−	1.85220e23i	−0.417672	−	0.197512i
$993$	−1.16490e23			−0.123224
$994$	8.88339e23	+	3.78209e23i	0.932154	+	0.396863i
$995$			1.01670e24i			1.05830i
$996$	−5.68044e23	−	5.90771e23i	−0.586553	−	0.610021i
$997$	5.29174e23			0.542047			0.271023	−	0.962573i	$-0.412638\pi$
$997$	5.29174e23			0.542047			0.271023	+	0.962573i	$0.412638\pi$
$998$	−2.00399e23	+	4.70700e23i	−0.203635	+	0.478299i
$999$			8.54410e22i			0.0861276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.17.d.a.7.3	✓	16
3.2	odd	2		36.17.d.d.19.14		16
4.3	odd	2	inner	12.17.d.a.7.4	yes	16
12.11	even	2		36.17.d.d.19.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.17.d.a.7.3	✓	16	1.1	even	1	trivial
12.17.d.a.7.4	yes	16	4.3	odd	2	inner
36.17.d.d.19.13		16	12.11	even	2
36.17.d.d.19.14		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-235.541 - 100.281i) q^{2} -3788.00i q^{3} +(45423.4 + 47240.7i) q^{4} +699204. q^{5} +(-379865. + 892229. i) q^{6} +4.77594e6i q^{7} +(-5.96172e6 - 1.56822e7i) q^{8} -1.43489e7 q^{9} +O(q^{10})\)	\(q+(-235.541 - 100.281i) q^{2} -3788.00i q^{3} +(45423.4 + 47240.7i) q^{4} +699204. q^{5} +(-379865. + 892229. i) q^{6} +4.77594e6i q^{7} +(-5.96172e6 - 1.56822e7i) q^{8} -1.43489e7 q^{9} +(-1.64691e8 - 7.01170e7i) q^{10} +3.02715e8i q^{11} +(1.78948e8 - 1.72063e8i) q^{12} -7.87862e8 q^{13} +(4.78937e8 - 1.12493e9i) q^{14} -2.64858e9i q^{15} +(-1.68403e8 + 4.29166e9i) q^{16} -1.70368e9 q^{17} +(3.37976e9 + 1.43893e9i) q^{18} +1.50372e10i q^{19} +(3.17602e10 + 3.30309e10i) q^{20} +1.80913e10 q^{21} +(3.03566e10 - 7.13019e10i) q^{22} +1.14606e11i q^{23} +(-5.94043e10 + 2.25830e10i) q^{24} +3.36298e11 q^{25} +(1.85574e11 + 7.90078e10i) q^{26} +5.43536e10i q^{27} +(-2.25619e11 + 2.16939e11i) q^{28} -5.20244e11 q^{29} +(-2.65603e11 + 6.23850e11i) q^{30} -3.94051e11i q^{31} +(4.70039e11 - 9.93976e11i) q^{32} +1.14668e12 q^{33} +(4.01287e11 + 1.70847e11i) q^{34} +3.33936e12i q^{35} +(-6.51776e11 - 6.77853e11i) q^{36} +1.57195e12 q^{37} +(1.50795e12 - 3.54189e12i) q^{38} +2.98442e12i q^{39} +(-4.16846e12 - 1.09651e13i) q^{40} -4.91938e12 q^{41} +(-4.26124e12 - 1.81421e12i) q^{42} -7.30424e12i q^{43} +(-1.43005e13 + 1.37503e13i) q^{44} -1.00328e13 q^{45} +(1.14928e13 - 2.69944e13i) q^{46} +2.40861e13i q^{47} +(1.62568e13 + 6.37911e11i) q^{48} +1.04233e13 q^{49} +(-7.92120e13 - 3.37243e13i) q^{50} +6.45353e12i q^{51} +(-3.57874e13 - 3.72192e13i) q^{52} +1.16916e14 q^{53} +(5.45064e12 - 1.28025e13i) q^{54} +2.11659e14i q^{55} +(7.48975e13 - 2.84728e13i) q^{56} +5.69609e13 q^{57} +(1.22539e14 + 5.21707e13i) q^{58} +1.48155e14i q^{59} +(1.25121e14 - 1.20307e14i) q^{60} +1.03715e14 q^{61} +(-3.95159e13 + 9.28153e13i) q^{62} -6.85296e13i q^{63} +(-2.10391e14 + 1.86986e14i) q^{64} -5.50876e14 q^{65} +(-2.70091e14 - 1.14991e14i) q^{66} -3.79266e14i q^{67} +(-7.73868e13 - 8.04830e13i) q^{68} +4.34126e14 q^{69} +(3.34875e14 - 7.86556e14i) q^{70} +7.89683e14i q^{71} +(8.55442e13 + 2.25023e14i) q^{72} +1.80749e14 q^{73} +(-3.70258e14 - 1.57637e14i) q^{74} -1.27389e15i q^{75} +(-7.10369e14 + 6.83041e14i) q^{76} -1.44575e15 q^{77} +(2.99281e14 - 7.02954e14i) q^{78} -1.58248e15i q^{79} +(-1.17748e14 + 3.00075e15i) q^{80} +2.05891e14 q^{81} +(1.15872e15 + 4.93321e14i) q^{82} -3.30136e15i q^{83} +(8.21766e14 + 8.54644e14i) q^{84} -1.19122e15 q^{85} +(-7.32478e14 + 1.72045e15i) q^{86} +1.97068e15i q^{87} +(4.74725e15 - 1.80470e15i) q^{88} -1.42349e14 q^{89} +(2.36314e15 + 1.00610e15i) q^{90} -3.76279e15i q^{91} +(-5.41406e15 + 5.20578e15i) q^{92} -1.49266e15 q^{93} +(2.41538e15 - 5.67326e15i) q^{94} +1.05141e16i q^{95} +(-3.76518e15 - 1.78051e15i) q^{96} -4.90826e14 q^{97} +(-2.45511e15 - 1.04526e15i) q^{98} -4.34363e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9}+O(q^{10}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9	\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 12\!\cdots\!92 q^{65}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 186 * q^2 + 136588 * q^4 + 354144 * q^5 + 1561518 * q^6 + 14683680 * q^8 - 229582512 * q^9 - 49800172 * q^10 + 425284020 * q^12 - 906419296 * q^13 - 806064072 * q^14 - 2108540816 * q^16 + 12240765600 * q^17 + 2668896702 * q^18 + 1002788712 * q^20 + 39806479296 * q^21 + 216706355928 * q^22 - 111931394832 * q^24 + 206381182512 * q^25 + 1054507182588 * q^26 - 1526063922288 * q^28 + 327679573728 * q^29 + 1192344308100 * q^30 - 5158730488416 * q^32 + 679591529280 * q^33 + 9473293385948 * q^34 - 1959888509316 * q^36 - 8149494749152 * q^37 + 23318999782920 * q^38 - 28671795971776 * q^40 - 25536724613472 * q^41 + 5103781482168 * q^42 - 11442227373552 * q^44 - 5081579320608 * q^45 + 9929654732736 * q^46 + 29246734238832 * q^48 - 93287012964080 * q^49 - 133601044957998 * q^50 + 302261844234872 * q^52 - 86928436629792 * q^53 - 22406076560826 * q^54 + 530930989929024 * q^56 + 48687411524544 * q^57 - 189801665049916 * q^58 + 268455359263896 * q^60 + 476028596468000 * q^61 - 419080420491096 * q^62 + 305944925720704 * q^64 - 1276571708976192 * q^65 - 64815073701480 * q^66 - 1393626893610696 * q^68 + 384812600884992 * q^69 + 1815049064679696 * q^70 - 210694758737760 * q^72 - 368686901901280 * q^73 + 875633111941836 * q^74 - 4351002030861264 * q^76 - 81504772370688 * q^77 + 1907392409236620 * q^78 - 8190389938127328 * q^80 + 3294258113514384 * q^81 + 2390391408733340 * q^82 - 510964995024720 * q^84 + 10085047677398464 * q^85 - 894939801424296 * q^86 + 669091386916800 * q^88 - 5711067674201568 * q^89 + 714578036612004 * q^90 + 7708247605922304 * q^92 + 7132614781502016 * q^93 - 9487273535547696 * q^94 + 8786531038601952 * q^96 - 13564951560560608 * q^97 - 33011660914531290 * q^98

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