LMFDB - Embedded newform 12.16.b.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,16,Mod(11,12)]

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, 1]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	12.b (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:	$17.1232206120$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	12.11
Dual form			12.16.b.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-172.746 + 54.1000i) q^{2} +(3105.31 - 2169.32i) q^{3} +(26914.4 - 18691.1i) q^{4} +192307. i q^{5} +(-419070. + 542739. i) q^{6} +366926. i q^{7} +(-3.63816e6 + 4.68489e6i) q^{8} +(4.93700e6 - 1.34728e7i) q^{9} +O(q^{10})$	\(q+(-172.746 + 54.1000i) q^{2} +(3105.31 - 2169.32i) q^{3} +(26914.4 - 18691.1i) q^{4} +192307. i q^{5} +(-419070. + 542739. i) q^{6} +366926. i q^{7} +(-3.63816e6 + 4.68489e6i) q^{8} +(4.93700e6 - 1.34728e7i) q^{9} +(-1.04038e7 - 3.32203e7i) q^{10} +5.82623e7 q^{11} +(4.30304e7 - 1.16428e8i) q^{12} -2.65726e8 q^{13} +(-1.98507e7 - 6.33850e7i) q^{14} +(4.17176e8 + 5.97173e8i) q^{15} +(3.75025e8 - 1.00612e9i) q^{16} +1.79306e9i q^{17} +(-1.23967e8 + 2.59447e9i) q^{18} +4.75795e9i q^{19} +(3.59444e9 + 5.17582e9i) q^{20} +(7.95981e8 + 1.13942e9i) q^{21} +(-1.00646e10 + 3.15199e9i) q^{22} +1.92879e10 q^{23} +(-1.13459e9 + 2.24404e10i) q^{24} -6.46444e9 q^{25} +(4.59032e10 - 1.43758e10i) q^{26} +(-1.38960e10 - 5.25473e10i) q^{27} +(6.85827e9 + 9.87559e9i) q^{28} +1.16647e11i q^{29} +(-1.04373e11 - 8.05901e10i) q^{30} +1.69225e11i q^{31} +(-1.03529e10 + 1.94092e11i) q^{32} +(1.80923e11 - 1.26390e11i) q^{33} +(-9.70044e10 - 3.09743e11i) q^{34} -7.05625e10 q^{35} +(-1.18946e11 - 4.54891e11i) q^{36} +7.59020e11 q^{37} +(-2.57405e11 - 8.21916e11i) q^{38} +(-8.25163e11 + 5.76446e11i) q^{39} +(-9.00937e11 - 6.99644e11i) q^{40} +1.15439e12i q^{41} +(-1.99145e11 - 1.53768e11i) q^{42} -1.91686e12i q^{43} +(1.56809e12 - 1.08899e12i) q^{44} +(2.59092e12 + 9.49421e11i) q^{45} +(-3.33191e12 + 1.04348e12i) q^{46} -1.35211e12 q^{47} +(-1.01803e12 - 3.93787e12i) q^{48} +4.61293e12 q^{49} +(1.11671e12 - 3.49727e11i) q^{50} +(3.88971e12 + 5.56800e12i) q^{51} +(-7.15186e12 + 4.96673e12i) q^{52} +7.61817e12i q^{53} +(5.24328e12 + 8.32556e12i) q^{54} +1.12043e13i q^{55} +(-1.71901e12 - 1.33494e12i) q^{56} +(1.03215e13 + 1.47749e13i) q^{57} +(-6.31060e12 - 2.01503e13i) q^{58} +1.15688e12 q^{59} +(2.23899e13 + 8.27506e12i) q^{60} -2.88756e13 q^{61} +(-9.15509e12 - 2.92330e13i) q^{62} +(4.94353e12 + 1.81152e12i) q^{63} +(-8.71197e12 - 3.40887e13i) q^{64} -5.11011e13i q^{65} +(-2.44160e13 + 3.16212e13i) q^{66} -7.60288e13i q^{67} +(3.35143e13 + 4.82590e13i) q^{68} +(5.98950e13 - 4.18417e13i) q^{69} +(1.21894e13 - 3.81744e12i) q^{70} -6.50083e13 q^{71} +(4.51571e13 + 7.21456e13i) q^{72} -1.24297e14 q^{73} +(-1.31118e14 + 4.10630e13i) q^{74} +(-2.00741e13 + 1.40234e13i) q^{75} +(8.89314e13 + 1.28057e14i) q^{76} +2.13780e13i q^{77} +(1.11358e14 - 1.44220e14i) q^{78} -5.22032e13i q^{79} +(1.93484e14 + 7.21199e13i) q^{80} +(-1.57143e14 - 1.33031e14i) q^{81} +(-6.24524e13 - 1.99416e14i) q^{82} +3.24461e14 q^{83} +(4.27204e13 + 1.57890e13i) q^{84} -3.44817e14 q^{85} +(1.03702e14 + 3.31130e14i) q^{86} +(2.53044e14 + 3.62225e14i) q^{87} +(-2.11968e14 + 2.72952e14i) q^{88} -1.32252e14i q^{89} +(-4.98935e14 - 2.38397e13i) q^{90} -9.75020e13i q^{91} +(5.19122e14 - 3.60513e14i) q^{92} +(3.67104e14 + 5.25497e14i) q^{93} +(2.33571e14 - 7.31490e13i) q^{94} -9.14987e14 q^{95} +(3.88899e14 + 6.25175e14i) q^{96} +8.29770e14 q^{97} +(-7.96865e14 + 2.49560e14i) q^{98} +(2.87641e14 - 7.84958e14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) $ 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

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 $

$2$	−172.746	+	54.1000i	−0.954296	+	0.298863i
$2$	−172.746	+	54.1000i	−0.954296	+	0.298863i
$3$	3105.31	−	2169.32i	0.819777	−	0.572683i
$3$	3105.31	−	2169.32i	0.819777	−	0.572683i
$4$	26914.4	−	18691.1i	0.821361	−	0.570408i
$5$			192307.i			1.10083i	0.834891	+	0.550415i	$0.185530\pi$
$5$			192307.i			1.10083i	−0.834891	+	0.550415i	$0.814470\pi$
$6$	−419070.	+	542739.i	−0.611156	+	0.791510i
$7$			366926.i			0.168401i	0.996449	+	0.0842003i	$0.0268335\pi$
$7$			366926.i			0.168401i	−0.996449	+	0.0842003i	$0.973166\pi$
$8$	−3.63816e6	+	4.68489e6i	−0.613348	+	0.789813i
$9$	4.93700e6	−	1.34728e7i	0.344068	−	0.938945i
$10$	−1.04038e7	−	3.32203e7i	−0.328998	−	1.05052i
$11$	5.82623e7			0.901452			0.450726	−	0.892662i	$-0.351165\pi$
$11$	5.82623e7			0.901452			0.450726	+	0.892662i	$0.351165\pi$
$12$	4.30304e7	−	1.16428e8i	0.346670	−	0.937987i
$13$	−2.65726e8			−1.17452			−0.587259	−	0.809399i	$-0.699793\pi$
$13$	−2.65726e8			−1.17452			−0.587259	+	0.809399i	$0.699793\pi$
$14$	−1.98507e7	−	6.33850e7i	−0.0503287	−	0.160704i
$15$	4.17176e8	+	5.97173e8i	0.630427	+	0.902435i
$16$	3.75025e8	−	1.00612e9i	0.349269	−	0.937022i
$17$			1.79306e9i			1.05981i	0.848058	+	0.529904i	$0.177772\pi$
$17$			1.79306e9i			1.05981i	−0.848058	+	0.529904i	$0.822228\pi$
$18$	−1.23967e8	+	2.59447e9i	−0.0477268	+	0.998860i
$19$			4.75795e9i			1.22115i	0.791960	+	0.610573i	$0.209061\pi$
$19$			4.75795e9i			1.22115i	−0.791960	+	0.610573i	$0.790939\pi$
$20$	3.59444e9	+	5.17582e9i	0.627922	+	0.904179i
$21$	7.95981e8	+	1.13942e9i	0.0964401	+	0.138051i
$22$	−1.00646e10	+	3.15199e9i	−0.860252	+	0.269411i
$23$	1.92879e10			1.18121			0.590604	−	0.806961i	$-0.298889\pi$
$23$	1.92879e10			1.18121			0.590604	+	0.806961i	$0.298889\pi$
$24$	−1.13459e9	+	2.24404e10i	−0.0504958	+	0.998724i
$25$	−6.46444e9			−0.211827
$26$	4.59032e10	−	1.43758e10i	1.12084	−	0.351020i
$27$	−1.38960e10	−	5.25473e10i	−0.255658	−	0.966767i
$28$	6.85827e9	+	9.87559e9i	0.0960570	+	0.138318i
$29$			1.16647e11i			1.25571i	0.778332	+	0.627853i	$0.216066\pi$
$29$			1.16647e11i			1.25571i	−0.778332	+	0.627853i	$0.783934\pi$
$30$	−1.04373e11	−	8.05901e10i	−0.871318	−	0.672779i
$31$			1.69225e11i			1.10472i	0.833606	+	0.552360i	$0.186273\pi$
$31$			1.69225e11i			1.10472i	−0.833606	+	0.552360i	$0.813727\pi$
$32$	−1.03529e10	+	1.94092e11i	−0.0532644	+	0.998580i
$33$	1.80923e11	−	1.26390e11i	0.738989	−	0.516246i
$34$	−9.70044e10	−	3.09743e11i	−0.316738	−	1.01137i
$35$	−7.05625e10			−0.185380
$36$	−1.18946e11	−	4.54891e11i	−0.252977	−	0.967472i
$37$	7.59020e11			1.31444			0.657219	−	0.753699i	$-0.271733\pi$
$37$	7.59020e11			1.31444			0.657219	+	0.753699i	$0.271733\pi$
$38$	−2.57405e11	−	8.21916e11i	−0.364956	−	1.16533i
$39$	−8.25163e11	+	5.76446e11i	−0.962842	+	0.672626i
$40$	−9.00937e11	−	6.99644e11i	−0.869450	−	0.675192i
$41$			1.15439e12i			0.925705i	0.886435	+	0.462852i	$0.153174\pi$
$41$			1.15439e12i			0.925705i	−0.886435	+	0.462852i	$0.846826\pi$
$42$	−1.99145e11	−	1.53768e11i	−0.133291	−	0.102919i
$43$		−	1.91686e12i		−	1.07542i	−0.843130	−	0.537709i	$-0.819290\pi$
$43$		−	1.91686e12i		−	1.07542i	0.843130	−	0.537709i	$-0.180710\pi$
$44$	1.56809e12	−	1.08899e12i	0.740418	−	0.514196i
$45$	2.59092e12	+	9.49421e11i	1.03362	+	0.378761i
$46$	−3.33191e12	+	1.04348e12i	−1.12722	+	0.353020i
$47$	−1.35211e12			−0.389293			−0.194647	−	0.980873i	$-0.562356\pi$
$47$	−1.35211e12			−0.389293			−0.194647	+	0.980873i	$0.562356\pi$
$48$	−1.01803e12	−	3.93787e12i	−0.250294	−	0.968170i
$49$	4.61293e12			0.971641
$50$	1.11671e12	−	3.49727e11i	0.202145	−	0.0633073i
$51$	3.88971e12	+	5.56800e12i	0.606934	+	0.868806i
$52$	−7.15186e12	+	4.96673e12i	−0.964703	+	0.669954i
$53$			7.61817e12i			0.890803i	0.895331	+	0.445402i	$0.146939\pi$
$53$			7.61817e12i			0.890803i	−0.895331	+	0.445402i	$0.853061\pi$
$54$	5.24328e12	+	8.32556e12i	0.532905	+	0.846175i
$55$			1.12043e13i			0.992345i
$56$	−1.71901e12	−	1.33494e12i	−0.133005	−	0.103288i
$57$	1.03215e13	+	1.47749e13i	0.699329	+	1.00107i
$58$	−6.31060e12	−	2.01503e13i	−0.375285	−	1.19832i
$59$	1.15688e12			0.0605200			0.0302600	−	0.999542i	$-0.490366\pi$
$59$	1.15688e12			0.0605200			0.0302600	+	0.999542i	$0.490366\pi$
$60$	2.23899e13	+	8.27506e12i	1.03256	+	0.381625i
$61$	−2.88756e13			−1.17641			−0.588204	−	0.808713i	$-0.700165\pi$
$61$	−2.88756e13			−1.17641			−0.588204	+	0.808713i	$0.700165\pi$
$62$	−9.15509e12	−	2.92330e13i	−0.330160	−	1.05423i
$63$	4.94353e12	+	1.81152e12i	0.158119	+	0.0579413i
$64$	−8.71197e12	−	3.40887e13i	−0.247609	−	0.968860i
$65$		−	5.11011e13i		−	1.29294i
$66$	−2.44160e13	+	3.16212e13i	−0.550928	+	0.713509i
$67$		−	7.60288e13i		−	1.53256i	−0.642508	−	0.766279i	$-0.722106\pi$
$67$		−	7.60288e13i		−	1.53256i	0.642508	−	0.766279i	$-0.277894\pi$
$68$	3.35143e13	+	4.82590e13i	0.604523	+	0.870485i
$69$	5.98950e13	−	4.18417e13i	0.968328	−	0.676458i
$70$	1.21894e13	−	3.81744e12i	0.176908	−	0.0554034i
$71$	−6.50083e13			−0.848264			−0.424132	−	0.905600i	$-0.639421\pi$
$71$	−6.50083e13			−0.848264			−0.424132	+	0.905600i	$0.639421\pi$
$72$	4.51571e13	+	7.21456e13i	0.530557	+	0.847649i
$73$	−1.24297e14			−1.31686			−0.658428	−	0.752644i	$-0.728778\pi$
$73$	−1.24297e14			−1.31686			−0.658428	+	0.752644i	$0.728778\pi$
$74$	−1.31118e14	+	4.10630e13i	−1.25436	+	0.392838i
$75$	−2.00741e13	+	1.40234e13i	−0.173651	+	0.121310i
$76$	8.89314e13	+	1.28057e14i	0.696551	+	1.00300i
$77$			2.13780e13i			0.151805i
$78$	1.11358e14	−	1.44220e14i	0.717813	−	0.929643i
$79$		−	5.22032e13i		−	0.305840i	−0.988239	−	0.152920i	$-0.951132\pi$
$79$		−	5.22032e13i		−	0.305840i	0.988239	−	0.152920i	$-0.0488677\pi$
$80$	1.93484e14	+	7.21199e13i	1.03150	+	0.384486i
$81$	−1.57143e14	−	1.33031e14i	−0.763234	−	0.646122i
$82$	−6.24524e13	−	1.99416e14i	−0.276659	−	0.883396i
$83$	3.24461e14			1.31243			0.656217	−	0.754572i	$-0.272156\pi$
$83$	3.24461e14			1.31243			0.656217	+	0.754572i	$0.272156\pi$
$84$	4.27204e13	+	1.57890e13i	0.157958	+	0.0583794i
$85$	−3.44817e14			−1.16667
$86$	1.03702e14	+	3.31130e14i	0.321403	+	1.02627i
$87$	2.53044e14	+	3.62225e14i	0.719122	+	1.02940i
$88$	−2.11968e14	+	2.72952e14i	−0.552904	+	0.711978i
$89$		−	1.32252e14i		−	0.316939i	−0.987364	−	0.158470i	$-0.949344\pi$
$89$		−	1.32252e14i		−	0.316939i	0.987364	−	0.158470i	$-0.0506560\pi$
$90$	−4.98935e14	−	2.38397e13i	−1.09958	−	0.0525391i
$91$		−	9.75020e13i		−	0.197789i
$92$	5.19122e14	−	3.60513e14i	0.970199	−	0.673771i
$93$	3.67104e14	+	5.25497e14i	0.632654	+	0.905624i
$94$	2.33571e14	−	7.31490e13i	0.371501	−	0.116345i
$95$	−9.14987e14			−1.34427
$96$	3.88899e14	+	6.25175e14i	0.528205	+	0.849117i
$97$	8.29770e14			1.04272			0.521362	−	0.853335i	$-0.325424\pi$
$97$	8.29770e14			1.04272			0.521362	+	0.853335i	$0.325424\pi$
$98$	−7.96865e14	+	2.49560e14i	−0.927233	+	0.290388i
$99$	2.87641e14	−	7.84958e14i	0.310161	−	0.846413i
$100$	−1.73986e14	+	1.20828e14i	−0.173986	+	0.120828i
$101$			3.17804e14i			0.294951i	0.989066	+	0.147475i	$0.0471147\pi$
$101$			3.17804e14i			0.294951i	−0.989066	+	0.147475i	$0.952885\pi$
$102$	−9.73162e14	−	7.51416e14i	−0.838849	−	0.647708i
$103$			7.00724e14i			0.561394i	0.959796	+	0.280697i	$0.0905656\pi$
$103$			7.00724e14i			0.561394i	−0.959796	+	0.280697i	$0.909434\pi$
$104$	9.66755e14	−	1.24490e15i	0.720388	−	0.927649i
$105$	−2.19119e14	+	1.53073e14i	−0.151971	+	0.106164i
$106$	−4.12144e14	−	1.31601e15i	−0.266228	−	0.850090i
$107$	−2.55131e15			−1.53598			−0.767989	−	0.640463i	$-0.778743\pi$
$107$	−2.55131e15			−1.53598			−0.767989	+	0.640463i	$0.778743\pi$
$108$	−1.35617e15	−	1.15455e15i	−0.761440	−	0.648236i
$109$	3.30599e15			1.73222			0.866110	−	0.499854i	$-0.166613\pi$
$109$	3.30599e15			1.73222			0.866110	+	0.499854i	$0.166613\pi$
$110$	−6.06151e14	−	1.93549e15i	−0.296576	−	0.946991i
$111$	2.35699e15	−	1.64656e15i	1.07755	−	0.752757i
$112$	3.69172e14	+	1.37606e14i	0.157795	+	0.0588171i
$113$		−	1.65938e15i		−	0.663524i	−0.943363	−	0.331762i	$-0.892357\pi$
$113$		−	1.65938e15i		−	0.663524i	0.943363	−	0.331762i	$-0.107643\pi$
$114$	−2.58232e15	−	1.99391e15i	−0.966549	−	0.746310i
$115$			3.70920e15i			1.30031i
$116$	2.18026e15	+	3.13948e15i	0.716265	+	1.03139i
$117$	−1.31189e15	+	3.58009e15i	−0.404114	+	1.10281i
$118$	−1.99847e14	+	6.25874e13i	−0.0577540	+	0.0180872i
$119$	−6.57919e14			−0.178472
$120$	−4.31544e15	−	2.18190e14i	−1.09943	−	0.0555873i
$121$	−7.82751e14			−0.187384
$122$	4.98815e15	−	1.56217e15i	1.12264	−	0.351585i
$123$	2.50424e15	+	3.58473e15i	0.530135	+	0.758871i
$124$	3.16301e15	+	4.55459e15i	0.630141	+	0.907374i
$125$			4.62559e15i			0.867645i
$126$	−9.51979e14	−	4.54868e13i	−0.168209	−	0.00803722i
$127$		−	6.17912e15i		−	1.02896i	−0.857502	−	0.514480i	$-0.827985\pi$
$127$		−	6.17912e15i		−	1.02896i	0.857502	−	0.514480i	$-0.172015\pi$
$128$	3.34916e15	+	5.41737e15i	0.525849	+	0.850578i
$129$	−4.15829e15	−	5.95245e15i	−0.615874	−	0.881603i
$130$	2.76457e15	+	8.82750e15i	0.386414	+	1.23385i
$131$	−3.27392e15			−0.432049			−0.216024	−	0.976388i	$-0.569309\pi$
$131$	−3.27392e15			−0.432049			−0.216024	+	0.976388i	$0.569309\pi$
$132$	2.50705e15	−	6.78335e15i	0.312506	−	0.845550i
$133$	−1.74581e15			−0.205642
$134$	4.11316e15	+	1.31337e16i	0.458026	+	1.46251i
$135$	1.01052e16	−	2.67229e15i	1.06425	−	0.281437i
$136$	−8.40027e15	−	6.52342e15i	−0.837050	−	0.650031i
$137$		−	1.42408e16i		−	1.34316i	−0.740931	−	0.671581i	$-0.765615\pi$
$137$		−	1.42408e16i		−	1.34316i	0.740931	−	0.671581i	$-0.234385\pi$
$138$	−8.08298e15	+	1.04683e16i	−0.721902	+	0.934939i
$139$		−	3.07112e15i		−	0.259828i	−0.991525	−	0.129914i	$-0.958530\pi$
$139$		−	3.07112e15i		−	0.259828i	0.991525	−	0.129914i	$-0.0414700\pi$
$140$	−1.89915e15	+	1.31889e15i	−0.152264	+	0.105742i
$141$	−4.19871e15	+	2.93315e15i	−0.319134	+	0.222942i
$142$	1.12299e16	−	3.51695e15i	0.809495	−	0.253515i
$143$	−1.54818e16			−1.05877
$144$	−1.17038e16	−	1.00199e16i	−0.759640	−	0.650344i
$145$	−2.24320e16			−1.38232
$146$	2.14718e16	−	6.72446e15i	1.25667	−	0.393560i
$147$	1.43246e16	−	1.00069e16i	0.796529	−	0.556442i
$148$	2.04285e16	−	1.41869e16i	1.07963	−	0.749767i
$149$		−	1.69736e16i		−	0.852857i	−0.904521	−	0.426428i	$-0.859772\pi$
$149$		−	1.69736e16i		−	0.852857i	0.904521	−	0.426428i	$-0.140228\pi$
$150$	2.70905e15	−	3.50850e15i	0.129459	−	0.167663i
$151$			1.41671e16i			0.644099i	0.946723	+	0.322049i	$0.104372\pi$
$151$			1.41671e16i			0.644099i	−0.946723	+	0.322049i	$0.895628\pi$
$152$	−2.22904e16	−	1.73102e16i	−0.964477	−	0.748987i
$153$	2.41575e16	+	8.85233e15i	0.995101	+	0.364646i
$154$	−1.15655e15	−	3.69296e15i	−0.0453689	−	0.144867i
$155$	−3.25432e16			−1.21611
$156$	−1.14343e16	+	3.09379e16i	−0.407170	+	1.10168i
$157$	1.51155e15			0.0513070			0.0256535	−	0.999671i	$-0.491833\pi$
$157$	1.51155e15			0.0513070			0.0256535	+	0.999671i	$0.491833\pi$
$158$	2.82420e15	+	9.01790e15i	0.0914043	+	0.291862i
$159$	1.65263e16	+	2.36568e16i	0.510148	+	0.730260i
$160$	−3.73253e16	−	1.99094e15i	−1.09927	−	0.0586351i
$161$			7.07724e15i			0.198916i
$162$	3.43428e16	+	1.44791e16i	0.921453	+	0.388489i
$163$		−	3.95773e16i		−	1.01400i	−0.861945	−	0.507001i	$-0.830754\pi$
$163$		−	3.95773e16i		−	1.01400i	0.861945	−	0.507001i	$-0.169246\pi$
$164$	2.15768e16	+	3.10696e16i	0.528029	+	0.760338i
$165$	2.43056e16	+	3.47927e16i	0.568299	+	0.813502i
$166$	−5.60494e16	+	1.75534e16i	−1.25245	+	0.392238i
$167$	−1.27693e16			−0.272767			−0.136384	−	0.990656i	$-0.543548\pi$
$167$	−1.27693e16			−0.272767			−0.136384	+	0.990656i	$0.543548\pi$
$168$	−8.23396e15	−	4.16312e14i	−0.168186	−	0.00850352i
$169$	1.94246e16			0.379491
$170$	5.95658e16	−	1.86546e16i	1.11335	−	0.348674i
$171$	6.41030e16	+	2.34900e16i	1.14659	+	0.420157i
$172$	−3.58283e16	−	5.15911e16i	−0.613427	−	0.883307i
$173$			1.88835e16i			0.309555i	0.987949	+	0.154777i	$0.0494660\pi$
$173$			1.88835e16i			0.309555i	−0.987949	+	0.154777i	$0.950534\pi$
$174$	−6.33088e16	−	4.88832e16i	−0.993905	−	0.767432i
$175$		−	2.37197e15i		−	0.0356717i
$176$	2.18498e16	−	5.86189e16i	0.314849	−	0.844681i
$177$	3.59248e15	−	2.50965e15i	0.0496129	−	0.0346588i
$178$	7.15482e15	+	2.28460e16i	0.0947216	+	0.302454i
$179$	5.46837e15			0.0694160			0.0347080	−	0.999397i	$-0.488950\pi$
$179$	5.46837e15			0.0694160			0.0347080	+	0.999397i	$0.488950\pi$
$180$	8.74787e16	−	2.28742e16i	1.06502	−	0.278485i
$181$	1.53462e16			0.179230			0.0896149	−	0.995976i	$-0.471436\pi$
$181$	1.53462e16			0.179230			0.0896149	+	0.995976i	$0.471436\pi$
$182$	5.27486e15	+	1.68431e16i	0.0591120	+	0.188750i
$183$	−8.96678e16	+	6.26405e16i	−0.964392	+	0.673709i
$184$	−7.01725e16	+	9.03617e16i	−0.724492	+	0.932934i
$185$			1.45965e17i			1.44697i
$186$	−9.18451e16	−	7.09171e16i	−0.874397	−	0.675156i
$187$			1.04468e17i			0.955366i
$188$	−3.63911e16	+	2.52724e16i	−0.319750	+	0.222056i
$189$	1.92810e16	−	5.09879e15i	0.162804	−	0.0430530i
$190$	1.58060e17	−	4.95008e16i	1.28283	−	0.401754i
$191$	5.89196e16			0.459737			0.229868	−	0.973222i	$-0.426170\pi$
$191$	5.89196e16			0.459737			0.229868	+	0.973222i	$0.426170\pi$
$192$	−1.01003e17	−	8.69571e16i	−0.757834	−	0.652448i
$193$	1.35662e17			0.978988			0.489494	−	0.872007i	$-0.337181\pi$
$193$	1.35662e17			0.978988			0.489494	+	0.872007i	$0.337181\pi$
$194$	−1.43339e17	+	4.48906e16i	−0.995068	+	0.311632i
$195$	−1.10855e17	−	1.58685e17i	−0.740447	−	1.05993i
$196$	1.24154e17	−	8.62208e16i	0.798069	−	0.554232i
$197$		−	2.97594e17i		−	1.84131i	−0.390377	−	0.920655i	$-0.627655\pi$
$197$		−	2.97594e17i		−	1.84131i	0.390377	−	0.920655i	$-0.372345\pi$
$198$	−7.22261e15	+	1.51160e17i	−0.0430234	+	0.900425i
$199$		−	7.47663e16i		−	0.428852i	−0.976740	−	0.214426i	$-0.931212\pi$
$199$		−	7.47663e16i		−	0.428852i	0.976740	−	0.214426i	$-0.0687882\pi$
$200$	2.35187e16	−	3.02852e16i	0.129923	−	0.167304i
$201$	−1.64931e17	−	2.36093e17i	−0.877670	−	1.25636i
$202$	−1.71932e16	−	5.48994e16i	−0.0881499	−	0.281470i
$203$	−4.28008e16			−0.211462
$204$	2.08761e17	+	7.71560e16i	0.994086	+	0.367404i
$205$	−2.21997e17			−1.01904
$206$	−3.79092e16	−	1.21047e17i	−0.167780	−	0.535736i
$207$	9.52245e16	−	2.59863e17i	0.406416	−	1.10909i
$208$	−9.96540e16	+	2.67353e17i	−0.410223	+	1.10055i
$209$			2.77209e17i			1.10080i
$210$	2.95706e16	−	3.82970e16i	0.113296	−	0.146730i
$211$		−	9.84802e16i		−	0.364108i	−0.983288	−	0.182054i	$-0.941725\pi$
$211$		−	9.84802e16i		−	0.364108i	0.983288	−	0.182054i	$-0.0582746\pi$
$212$	1.42392e17	+	2.05038e17i	0.508122	+	0.731672i
$213$	−2.01871e17	+	1.41024e17i	−0.695388	+	0.485787i
$214$	4.40729e17	−	1.38026e17i	1.46578	−	0.459048i
$215$	3.68626e17			1.18385
$216$	2.96734e17	+	1.26074e17i	0.920373	+	0.391042i
$217$	−6.20931e16			−0.186035
$218$	−5.71097e17	+	1.78854e17i	−1.65305	+	0.517697i
$219$	−3.85980e17	+	2.69639e17i	−1.07953	+	0.754141i
$220$	2.09420e17	+	3.01555e17i	0.566042	+	0.815074i
$221$		−	4.76462e17i		−	1.24476i
$222$	−3.18082e17	+	4.11950e17i	−0.803327	+	1.04039i
$223$			5.94036e17i			1.45053i	0.688470	+	0.725265i	$0.258283\pi$
$223$			5.94036e17i			1.45053i	−0.688470	+	0.725265i	$0.741717\pi$
$224$	−7.12175e16	−	3.79875e15i	−0.168161	−	0.00896976i
$225$	−3.19150e16	+	8.70943e16i	−0.0728829	+	0.198894i
$226$	8.97724e16	+	2.86651e17i	0.198303	+	0.633199i
$227$	5.63635e17			1.20449			0.602246	−	0.798310i	$-0.294273\pi$
$227$	5.63635e17			1.20449			0.602246	+	0.798310i	$0.294273\pi$
$228$	5.53957e17	+	2.04736e17i	1.14542	+	0.423335i
$229$	8.89600e16			0.178004			0.0890018	−	0.996031i	$-0.471632\pi$
$229$	8.89600e16			0.178004			0.0890018	+	0.996031i	$0.471632\pi$
$230$	−2.00668e17	−	6.40750e17i	−0.388615	−	1.24088i
$231$	4.63757e16	+	6.63852e16i	0.0869361	+	0.124446i
$232$	−5.46477e17	−	4.24380e17i	−0.991773	−	0.770185i
$233$			4.00191e17i			0.703231i	0.936145	+	0.351615i	$0.114367\pi$
$233$			4.00191e17i			0.703231i	−0.936145	+	0.351615i	$0.885633\pi$
$234$	3.29413e16	−	6.89419e17i	0.0560560	−	1.17318i
$235$		−	2.60020e17i		−	0.428546i
$236$	3.11368e16	−	2.16234e16i	0.0497088	−	0.0345211i
$237$	−1.13246e17	−	1.62107e17i	−0.175149	−	0.250720i
$238$	1.13653e17	−	3.55935e16i	0.170315	−	0.0533388i
$239$	1.20504e16			0.0174991			0.00874955	−	0.999962i	$-0.497215\pi$
$239$	1.20504e16			0.0174991			0.00874955	+	0.999962i	$0.497215\pi$
$240$	7.57279e17	−	1.95774e17i	1.06579	−	0.275531i
$241$	1.82776e17			0.249339			0.124670	−	0.992198i	$-0.460213\pi$
$241$	1.82776e17			0.249339			0.124670	+	0.992198i	$0.460213\pi$
$242$	1.35217e17	−	4.23469e16i	0.178820	−	0.0560023i
$243$	−7.76565e17	−	7.22082e16i	−0.995705	−	0.0925848i
$244$	−7.77170e17	+	5.39718e17i	−0.966256	+	0.671032i
$245$			8.87099e17i			1.06961i
$246$	−6.26531e17	−	4.83769e17i	−0.732705	−	0.565750i
$247$		−	1.26431e18i		−	1.43426i
$248$	−7.92801e17	−	6.15668e17i	−0.872522	−	0.677577i
$249$	1.00755e18	−	7.03861e17i	1.07590	−	0.751608i
$250$	−2.50245e17	−	7.99052e17i	−0.259307	−	0.827990i
$251$	−6.57440e17			−0.661155			−0.330577	−	0.943779i	$-0.607243\pi$
$251$	−6.57440e17			−0.661155			−0.330577	+	0.943779i	$0.607243\pi$
$252$	1.66911e17	−	4.36444e16i	0.162923	−	0.0426015i
$253$	1.12376e18			1.06480
$254$	3.34291e17	+	1.06742e18i	0.307519	+	0.981933i
$255$	−1.07077e18	+	7.48020e17i	−0.956408	+	0.668131i
$256$	−8.71634e17	−	7.54640e17i	−0.756022	−	0.654546i
$257$			2.60184e16i			0.0219171i	0.999940	+	0.0109585i	$0.00348828\pi$
$257$			2.60184e16i			0.0219171i	−0.999940	+	0.0109585i	$0.996512\pi$
$258$	1.04036e18	+	8.03299e17i	0.851205	+	0.657248i
$259$			2.78504e17i			0.221352i
$260$	−9.55137e17	−	1.37535e18i	−0.737506	−	1.06197i
$261$	1.57156e18	+	5.75886e17i	1.17904	+	0.432049i
$262$	5.65556e17	−	1.77119e17i	0.412302	−	0.129124i
$263$	1.97106e18			1.39647			0.698235	−	0.715869i	$-0.253969\pi$
$263$	1.97106e18			1.39647			0.698235	+	0.715869i	$0.253969\pi$
$264$	−6.61040e16	+	1.30743e18i	−0.0455196	+	0.900302i
$265$	−1.46503e18			−0.980623
$266$	3.01583e17	−	9.44487e16i	0.196243	−	0.0614587i
$267$	−2.86896e17	−	4.10683e17i	−0.181506	−	0.259820i
$268$	−1.42106e18	−	2.04627e18i	−0.874184	−	1.25878i
$269$			6.36304e17i			0.380647i	0.981721	+	0.190324i	$0.0609537\pi$
$269$			6.36304e17i			0.380647i	−0.981721	+	0.190324i	$0.939046\pi$
$270$	−1.60106e18	+	1.00832e18i	−0.931495	+	0.586638i
$271$			2.86005e18i			1.61847i	0.587486	+	0.809234i	$0.300118\pi$
$271$			2.86005e18i			1.61847i	−0.587486	+	0.809234i	$0.699882\pi$
$272$	1.80403e18	+	6.72441e17i	0.993064	+	0.370158i
$273$	−2.11513e17	−	3.02774e17i	−0.113271	−	0.162143i
$274$	7.70425e17	+	2.46003e18i	0.401422	+	1.28177i
$275$	−3.76633e17			−0.190952
$276$	8.29967e17	−	2.24565e18i	0.409490	−	1.10796i
$277$	−1.76482e18			−0.847425			−0.423713	−	0.905797i	$-0.639273\pi$
$277$	−1.76482e18			−0.847425			−0.423713	+	0.905797i	$0.639273\pi$
$278$	1.66147e17	+	5.30523e17i	0.0776529	+	0.247952i
$279$	2.27994e18	+	8.35465e17i	1.03727	+	0.380099i
$280$	2.56718e17	−	3.30577e17i	0.113703	−	0.146416i
$281$		−	2.48281e17i		−	0.107065i	−0.998566	−	0.0535323i	$-0.982952\pi$
$281$		−	2.48281e17i		−	0.107065i	0.998566	−	0.0535323i	$-0.0170480\pi$
$282$	5.66627e17	−	7.33840e17i	0.237919	−	0.308130i
$283$		−	2.81935e18i		−	1.15279i	−0.817171	−	0.576395i	$-0.804459\pi$
$283$		−	2.81935e18i		−	1.15279i	0.817171	−	0.576395i	$-0.195541\pi$
$284$	−1.74966e18	+	1.21508e18i	−0.696732	+	0.483857i
$285$	−2.84132e18	+	1.98490e18i	−1.10200	+	0.769843i
$286$	2.67442e18	−	8.37568e17i	1.01038	−	0.316428i
$287$	−4.23575e17			−0.155889
$288$	2.56386e18	+	1.09772e18i	0.919285	+	0.393592i
$289$	−3.52629e17			−0.123192
$290$	3.87504e18	−	1.21357e18i	1.31914	−	0.413125i
$291$	2.57669e18	−	1.80004e18i	0.854801	−	0.597151i
$292$	−3.34537e18	+	2.32325e18i	−1.08161	+	0.751145i
$293$		−	3.51723e18i		−	1.10839i	−0.832386	−	0.554196i	$-0.813026\pi$
$293$		−	3.51723e18i		−	1.10839i	0.832386	−	0.554196i	$-0.186974\pi$
$294$	−1.93314e18	+	2.50361e18i	−0.593824	+	0.769064i
$295$			2.22477e17i			0.0666223i
$296$	−2.76144e18	+	3.55592e18i	−0.806208	+	1.03816i
$297$	−8.09610e17	−	3.06153e18i	−0.230464	−	0.871494i
$298$	9.18271e17	+	2.93212e18i	0.254888	+	0.813878i
$299$	−5.12531e18			−1.38735
$300$	−2.78168e17	+	7.52640e17i	−0.0734340	+	0.198691i
$301$	7.03347e17			0.181101
$302$	−7.66438e17	−	2.44730e18i	−0.192497	−	0.614661i
$303$	6.89419e17	+	9.86881e17i	0.168913	+	0.241794i
$304$	4.78706e18	+	1.78435e18i	1.14424	+	0.426508i
$305$		−	5.55299e18i		−	1.29502i
$306$	−4.65203e18	−	2.22280e17i	−1.05860	−	0.0505812i
$307$		−	6.33924e18i		−	1.40766i	−0.710366	−	0.703832i	$-0.751471\pi$
$307$		−	6.33924e18i		−	1.40766i	0.710366	−	0.703832i	$-0.248529\pi$
$308$	3.99578e17	+	5.75375e17i	0.0865908	+	0.124687i
$309$	1.52009e18	+	2.17597e18i	0.321501	+	0.460218i
$310$	5.62171e18	−	1.76059e18i	1.16053	−	0.363450i
$311$	−1.17266e18			−0.236302			−0.118151	−	0.992996i	$-0.537697\pi$
$311$	−1.17266e18			−0.236302			−0.118151	+	0.992996i	$0.537697\pi$
$312$	3.01491e17	−	5.96300e18i	0.0593082	−	1.17302i
$313$	1.54937e18			0.297559			0.148779	−	0.988870i	$-0.452466\pi$
$313$	1.54937e18			0.297559			0.148779	+	0.988870i	$0.452466\pi$
$314$	−2.61115e17	+	8.17752e16i	−0.0489620	+	0.0153338i
$315$	−3.48367e17	+	9.50677e17i	−0.0637835	+	0.174062i
$316$	−9.75737e17	−	1.40502e18i	−0.174454	−	0.251205i
$317$			4.47609e18i			0.781545i	0.920487	+	0.390772i	$0.127792\pi$
$317$			4.47609e18i			0.781545i	−0.920487	+	0.390772i	$0.872208\pi$
$318$	−4.13468e18	−	3.19255e18i	−0.705080	−	0.544420i
$319$			6.79612e18i			1.13196i
$320$	6.55550e18	−	1.67537e18i	1.06655	−	0.272575i
$321$	−7.92262e18	+	5.53461e18i	−1.25916	+	0.879629i
$322$	−3.82879e17	−	1.22257e18i	−0.0594487	−	0.189825i
$323$	−8.53126e18			−1.29418
$324$	−6.71590e18	−	6.43257e17i	−0.995444	−	0.0953448i
$325$	1.71777e18			0.248794
$326$	2.14113e18	+	6.83682e18i	0.303048	+	0.967658i
$327$	1.02661e19	−	7.17175e18i	1.42003	−	0.992013i
$328$	−5.40817e18	−	4.19984e18i	−0.731134	−	0.567779i
$329$		−	4.96123e17i		−	0.0655572i
$330$	−6.08099e18	−	4.69536e18i	−0.785452	−	0.606478i
$331$			1.18893e19i			1.50122i	0.660743	+	0.750612i	$0.270241\pi$
$331$			1.18893e19i			1.50122i	−0.660743	+	0.750612i	$0.729759\pi$
$332$	8.73267e18	−	6.06455e18i	1.07798	−	0.748623i
$333$	3.74728e18	−	1.02261e19i	0.452257	−	1.23419i
$334$	2.20584e18	−	6.90818e17i	0.260301	−	0.0815202i
$335$	1.46209e19			1.68709
$336$	1.44491e18	−	3.73541e17i	0.163040	−	0.0421497i
$337$	9.60248e18			1.05964			0.529821	−	0.848109i	$-0.322259\pi$
$337$	9.60248e18			1.05964			0.529821	+	0.848109i	$0.322259\pi$
$338$	−3.35552e18	+	1.05087e18i	−0.362147	+	0.113416i
$339$	−3.59972e18	−	5.15288e18i	−0.379989	−	0.543942i
$340$	−9.28055e18	+	6.44503e18i	−0.958256	+	0.665477i
$341$			9.85945e18i			0.995852i
$342$	−1.23443e19	−	5.89828e17i	−1.21975	−	0.0582814i
$343$			3.43461e18i			0.332025i
$344$	8.98028e18	+	6.97385e18i	0.849379	+	0.659606i
$345$	8.04645e18	+	1.15182e19i	0.744665	+	1.06596i
$346$	−1.02160e18	−	3.26206e18i	−0.0925146	−	0.295407i
$347$	−2.02287e19			−1.79266			−0.896328	−	0.443393i	$-0.853775\pi$
$347$	−2.02287e19			−1.79266			−0.896328	+	0.443393i	$0.853775\pi$
$348$	1.35809e19	+	5.01936e18i	1.17784	+	0.435316i
$349$	3.79849e18			0.322418			0.161209	−	0.986920i	$-0.448461\pi$
$349$	3.79849e18			0.322418			0.161209	+	0.986920i	$0.448461\pi$
$350$	1.28324e17	+	4.09749e17i	0.0106610	+	0.0340414i
$351$	3.69252e18	+	1.39632e19i	0.300275	+	1.13548i
$352$	−6.03184e17	+	1.13083e19i	−0.0480153	+	0.900172i
$353$			1.33957e19i			1.04389i	0.852978	+	0.521946i	$0.174794\pi$
$353$			1.33957e19i			1.04389i	−0.852978	+	0.521946i	$0.825206\pi$
$354$	−4.84814e17	+	6.27885e17i	−0.0369872	+	0.0479022i
$355$		−	1.25016e19i		−	0.933795i
$356$	−2.47193e18	−	3.55947e18i	−0.180785	−	0.260322i
$357$	−2.04304e18	+	1.42724e18i	−0.146307	+	0.102208i
$358$	−9.44638e17	+	2.95839e17i	−0.0662434	+	0.0207459i
$359$	3.32549e18			0.228374			0.114187	−	0.993459i	$-0.463574\pi$
$359$	3.32549e18			0.228374			0.114187	+	0.993459i	$0.463574\pi$
$360$	−1.38741e19	+	8.68403e18i	−0.933118	+	0.584053i
$361$	−7.45692e18			−0.491196
$362$	−2.65099e18	+	8.30228e17i	−0.171038	+	0.0535652i
$363$	−2.43069e18	+	1.69804e18i	−0.153613	+	0.107312i
$364$	−1.82242e18	−	2.62420e18i	−0.112821	−	0.162457i
$365$		−	2.39031e19i		−	1.44963i
$366$	1.21009e19	−	1.56719e19i	0.718968	−	0.931139i
$367$		−	1.51431e19i		−	0.881496i	−0.897631	−	0.440748i	$-0.854713\pi$
$367$		−	1.51431e19i		−	0.881496i	0.897631	−	0.440748i	$-0.145287\pi$
$368$	7.23345e18	−	1.94060e19i	0.412560	−	1.10682i
$369$	1.55529e19	+	5.69921e18i	0.869185	+	0.318506i
$370$	−7.89671e18	−	2.52149e19i	−0.432447	−	1.38084i
$371$	−2.79531e18			−0.150012
$372$	1.97025e19	+	7.28183e18i	1.03621	+	0.382973i
$373$	−1.95522e19			−1.00781			−0.503906	−	0.863758i	$-0.668104\pi$
$373$	−1.95522e19			−1.00781			−0.503906	+	0.863758i	$0.668104\pi$
$374$	−5.65170e18	−	1.80464e19i	−0.285524	−	0.911702i
$375$	1.00344e19	+	1.43639e19i	0.496885	+	0.711275i
$376$	4.91918e18	−	6.33446e18i	0.238772	−	0.307469i
$377$		−	3.09961e19i		−	1.47485i
$378$	−3.05487e18	+	1.92390e18i	−0.142496	+	0.0897415i
$379$		−	1.79901e19i		−	0.822694i	−0.911479	−	0.411347i	$-0.865058\pi$
$379$		−	1.79901e19i		−	0.822694i	0.911479	−	0.411347i	$-0.134942\pi$
$380$	−2.46263e19	+	1.71021e19i	−1.10413	+	0.766785i
$381$	−1.34045e19	−	1.91881e19i	−0.589268	−	0.843518i
$382$	−1.01781e19	+	3.18755e18i	−0.438725	+	0.137398i
$383$	9.69154e18			0.409640			0.204820	−	0.978800i	$-0.434339\pi$
$383$	9.69154e18			0.409640			0.204820	+	0.978800i	$0.434339\pi$
$384$	2.21522e19	+	9.55723e18i	0.918190	+	0.396139i
$385$	−4.11114e18			−0.167111
$386$	−2.34350e19	+	7.33930e18i	−0.934244	+	0.292584i
$387$	−2.58256e19	−	9.46356e18i	−1.00976	−	0.370017i
$388$	2.23327e19	−	1.55093e19i	0.856454	−	0.594778i
$389$			1.62174e19i			0.610040i	0.952346	+	0.305020i	$0.0986631\pi$
$389$			1.62174e19i			0.610040i	−0.952346	+	0.305020i	$0.901337\pi$
$390$	2.77345e19	+	2.14149e19i	1.02338	+	0.790190i
$391$			3.45843e19i			1.25185i
$392$	−1.67826e19	+	2.16110e19i	−0.595954	+	0.767415i
$393$	−1.01665e19	+	7.10217e18i	−0.354184	+	0.247427i
$394$	1.60998e19	+	5.14081e19i	0.550300	+	1.75716i
$395$	1.00391e19			0.336678
$396$	−6.93008e18	−	2.65030e19i	−0.228047	−	0.872130i
$397$	−1.26630e19			−0.408892			−0.204446	−	0.978878i	$-0.565539\pi$
$397$	−1.26630e19			−0.408892			−0.204446	+	0.978878i	$0.565539\pi$
$398$	4.04486e18	+	1.29156e19i	0.128168	+	0.409252i
$399$	−5.42130e18	+	3.78723e18i	−0.168580	+	0.117767i
$400$	−2.42433e18	+	6.50400e18i	−0.0739846	+	0.198486i
$401$			2.88280e19i			0.863440i	0.902008	+	0.431720i	$0.142093\pi$
$401$			2.88280e19i			0.863440i	−0.902008	+	0.431720i	$0.857907\pi$
$402$	4.12638e19	+	3.18614e19i	1.21304	+	0.936632i
$403$		−	4.49676e19i		−	1.29751i
$404$	5.94012e18	+	8.55350e18i	0.168242	+	0.242261i
$405$	2.55828e19	−	3.02197e19i	0.711271	−	0.840191i
$406$	7.39367e18	−	2.31553e18i	0.201797	−	0.0631981i
$407$	4.42223e19			1.18490
$408$	−4.02368e19	−	2.03439e18i	−1.05846	−	0.0535159i
$409$	−5.66206e19			−1.46234			−0.731172	−	0.682193i	$-0.761026\pi$
$409$	−5.66206e19			−1.46234			−0.731172	+	0.682193i	$0.761026\pi$
$410$	3.83491e19	−	1.20100e19i	0.972469	−	0.304555i
$411$	−3.08928e19	−	4.42220e19i	−0.769207	−	1.10109i
$412$	1.30973e19	+	1.88595e19i	0.320224	+	0.461107i
$413$			4.24491e17i			0.0101916i
$414$	−2.39107e18	+	5.00419e19i	−0.0563753	+	1.17986i
$415$			6.23962e19i			1.44477i
$416$	2.75104e18	−	5.15754e19i	0.0625600	−	1.17285i
$417$	−6.66223e18	−	9.53677e18i	−0.148799	−	0.213001i
$418$	−1.49970e19	−	4.78867e19i	−0.328990	−	1.05049i
$419$	4.18823e19			0.902454			0.451227	−	0.892409i	$-0.350987\pi$
$419$	4.18823e19			0.902454			0.451227	+	0.892409i	$0.350987\pi$
$420$	−3.03634e18	+	8.21543e18i	−0.0642658	+	0.173884i
$421$	4.58733e19			0.953771			0.476886	−	0.878965i	$-0.341766\pi$
$421$	4.58733e19			0.953771			0.476886	+	0.878965i	$0.341766\pi$
$422$	5.32779e18	+	1.70121e19i	0.108819	+	0.347467i
$423$	−6.67535e18	+	1.82167e19i	−0.133943	+	0.365525i
$424$	−3.56903e19	−	2.77161e19i	−0.703568	−	0.546372i
$425$		−	1.15911e19i		−	0.224496i
$426$	2.72430e19	−	3.52825e19i	0.518422	−	0.671410i
$427$		−	1.05952e19i		−	0.198108i
$428$	−6.86670e19	+	4.76869e19i	−1.26159	+	0.876135i
$429$	−4.80759e19	+	3.35851e19i	−0.867956	+	0.606340i
$430$	−6.36787e19	+	1.99427e19i	−1.12975	+	0.353810i
$431$	6.45252e19			1.12499			0.562497	−	0.826800i	$-0.309841\pi$
$431$	6.45252e19			1.12499			0.562497	+	0.826800i	$0.309841\pi$
$432$	−5.80802e19	−	5.72553e18i	−0.995176	−	0.0981042i
$433$	1.06501e20			1.79348			0.896739	−	0.442561i	$-0.145930\pi$
$433$	1.06501e20			1.79348			0.896739	+	0.442561i	$0.145930\pi$
$434$	1.07263e19	−	3.35924e18i	0.177533	−	0.0555992i
$435$	−6.96584e19	+	4.86622e19i	−1.13319	+	0.791631i
$436$	8.89787e19	−	6.17927e19i	1.42278	−	0.988072i
$437$			9.17709e19i			1.44243i
$438$	5.20890e19	−	6.74607e19i	0.804804	−	1.04230i
$439$			6.60898e18i			0.100381i	0.998740	+	0.0501904i	$0.0159828\pi$
$439$			6.60898e18i			0.100381i	−0.998740	+	0.0501904i	$0.984017\pi$
$440$	−5.24907e19	−	4.07629e19i	−0.783767	−	0.608653i
$441$	2.27740e19	−	6.21492e19i	0.334311	−	0.912317i
$442$	2.57766e19	+	8.23070e19i	0.372014	+	1.18787i
$443$	−1.21405e20			−1.72270			−0.861350	−	0.508012i	$-0.830381\pi$
$443$	−1.21405e20			−1.72270			−0.861350	+	0.508012i	$0.830381\pi$
$444$	3.26610e19	−	8.83709e19i	0.455677	−	1.23293i
$445$	2.54329e19			0.348896
$446$	−3.21374e19	−	1.02617e20i	−0.433510	−	1.38423i
$447$	−3.68211e19	−	5.27082e19i	−0.488417	−	0.699152i
$448$	1.25080e19	−	3.19665e18i	0.163157	−	0.0416975i
$449$			4.05552e19i			0.520235i	0.965577	+	0.260117i	$0.0837613\pi$
$449$			4.05552e19i			0.520235i	−0.965577	+	0.260117i	$0.916239\pi$
$450$	8.01377e17	−	1.67718e19i	0.0101098	−	0.211585i
$451$			6.72572e19i			0.834478i
$452$	−3.10156e19	−	4.46611e19i	−0.378480	−	0.544993i
$453$	3.07329e19	+	4.39931e19i	0.368864	+	0.528017i
$454$	−9.73657e19	+	3.04927e19i	−1.14944	+	0.359979i
$455$	1.87503e19			0.217732
$456$	−1.06770e20	−	5.39833e18i	−1.21959	−	0.0616627i
$457$	8.35573e19			0.938887			0.469443	−	0.882963i	$-0.344455\pi$
$457$	8.35573e19			0.938887			0.469443	+	0.882963i	$0.344455\pi$
$458$	−1.53675e19	+	4.81274e18i	−0.169868	+	0.0531988i
$459$	9.42202e19	−	2.49162e19i	1.02459	−	0.270949i
$460$	6.93292e19	+	9.98309e19i	0.741707	+	1.06802i
$461$		−	1.21790e20i		−	1.28190i	−0.767583	−	0.640949i	$-0.778541\pi$
$461$		−	1.21790e20i		−	1.28190i	0.767583	−	0.640949i	$-0.221459\pi$
$462$	−1.16027e19	−	8.95886e18i	−0.120155	−	0.0927765i
$463$		−	9.75950e19i		−	0.994421i	−0.867630	−	0.497210i	$-0.834358\pi$
$463$		−	9.75950e19i		−	0.994421i	0.867630	−	0.497210i	$-0.165642\pi$
$464$	1.17361e20	+	4.37455e19i	1.17663	+	0.438580i
$465$	−1.01057e20	+	7.05966e19i	−0.996938	+	0.696445i
$466$	−2.16503e19	−	6.91314e19i	−0.210170	−	0.671090i
$467$	−8.49606e19			−0.811598			−0.405799	−	0.913962i	$-0.633007\pi$
$467$	−8.49606e19			−0.811598			−0.405799	+	0.913962i	$0.633007\pi$
$468$	3.16071e19	+	1.20877e20i	0.297126	+	1.13631i
$469$	2.78970e19			0.258084
$470$	1.40671e19	+	4.49173e19i	0.128077	+	0.408959i
$471$	4.69385e18	−	3.27905e18i	0.0420603	−	0.0293826i
$472$	−4.20892e18	+	5.41986e18i	−0.0371198	+	0.0477995i
$473$		−	1.11681e20i		−	0.969438i
$474$	2.83327e19	+	2.18768e19i	0.242075	+	0.186916i
$475$		−	3.07575e19i		−	0.258671i
$476$	−1.77075e19	+	1.22973e19i	−0.146590	+	0.101802i
$477$	1.02638e20	+	3.76110e19i	0.836415	+	0.306497i
$478$	−2.08165e18	+	6.51925e17i	−0.0166993	+	0.00522984i
$479$	1.14293e20			0.902614			0.451307	−	0.892369i	$-0.350958\pi$
$479$	1.14293e20			0.902614			0.451307	+	0.892369i	$0.350958\pi$
$480$	−1.20226e20	+	7.47880e19i	−0.934733	+	0.581464i
$481$	−2.01692e20			−1.54383
$482$	−3.15738e19	+	9.88818e18i	−0.237944	+	0.0745184i
$483$	1.53528e19	+	2.19770e19i	0.113916	+	0.163067i
$484$	−2.10673e19	+	1.46305e19i	−0.153910	+	0.106886i
$485$			1.59571e20i			1.14786i
$486$	1.38055e20	−	2.95385e19i	0.977867	−	0.209226i
$487$			1.23060e20i			0.858319i	0.903229	+	0.429159i	$0.141190\pi$
$487$			1.23060e20i			0.858319i	−0.903229	+	0.429159i	$0.858810\pi$
$488$	1.05054e20	−	1.35279e20i	0.721547	−	0.929142i
$489$	−8.58558e19	−	1.22900e20i	−0.580702	−	0.831256i
$490$	−4.79921e19	−	1.53243e20i	−0.319668	−	1.02073i
$491$	7.15084e19			0.469079			0.234539	−	0.972107i	$-0.424642\pi$
$491$	7.15084e19			0.469079			0.234539	+	0.972107i	$0.424642\pi$
$492$	1.34403e20	+	4.96738e19i	0.868299	+	0.320914i
$493$	−2.09154e20			−1.33081
$494$	6.83993e19	+	2.18405e20i	0.428647	+	1.36871i
$495$	1.50953e20	+	5.53155e19i	0.931757	+	0.341435i
$496$	1.70261e20	+	6.34636e19i	1.03515	+	0.385845i
$497$		−	2.38533e19i		−	0.142848i
$498$	−1.35972e20	+	1.76098e20i	−0.802101	+	1.03880i
$499$			2.71090e19i			0.157529i	0.996893	+	0.0787643i	$0.0250974\pi$
$499$			2.71090e19i			0.157529i	−0.996893	+	0.0787643i	$0.974903\pi$
$500$	8.64575e19	+	1.24495e20i	0.494912	+	0.712650i
$501$	−3.96525e19	+	2.77006e19i	−0.223608	+	0.156209i
$502$	1.13570e20	−	3.55675e19i	0.630937	−	0.197595i
$503$	−1.85993e20			−1.01797			−0.508987	−	0.860774i	$-0.669980\pi$
$503$	−1.85993e20			−1.01797			−0.508987	+	0.860774i	$0.669980\pi$
$504$	−2.64721e19	+	1.65693e19i	−0.142745	+	0.0893461i
$505$	−6.11160e19			−0.324690
$506$	−1.94125e20	+	6.07954e19i	−1.01614	+	0.318231i
$507$	6.03194e19	−	4.21382e19i	0.311098	−	0.217328i
$508$	−1.15495e20	−	1.66307e20i	−0.586927	−	0.845148i
$509$		−	1.57965e20i		−	0.791004i	−0.918465	−	0.395502i	$-0.870571\pi$
$509$		−	1.57965e20i		−	0.791004i	0.918465	−	0.395502i	$-0.129429\pi$
$510$	1.44503e20	−	1.87146e20i	0.713016	−	0.923430i
$511$		−	4.56077e19i		−	0.221759i
$512$	1.91397e20	+	8.32056e19i	0.917089	+	0.398683i
$513$	2.50017e20	−	6.61162e19i	1.18056	−	0.312196i
$514$	−1.40760e18	−	4.49458e18i	−0.00655021	−	0.0209154i
$515$	−1.34754e20			−0.617999
$516$	−2.23176e20	−	8.24834e19i	−1.00873	−	0.372815i
$517$	−7.87768e19			−0.350929
$518$	−1.50671e19	−	4.81105e19i	−0.0661541	−	0.211235i
$519$	4.09644e19	+	5.86392e19i	0.177277	+	0.253766i
$520$	2.39403e20	+	1.85914e20i	1.02118	+	0.793024i
$521$		−	3.72856e19i		−	0.156768i	−0.996923	−	0.0783842i	$-0.975024\pi$
$521$		−	3.72856e19i		−	0.156768i	0.996923	−	0.0783842i	$-0.0249761\pi$
$522$	−3.02637e20	−	1.44604e19i	−1.25428	−	0.0599309i
$523$		−	2.95684e20i		−	1.20800i	−0.796985	−	0.603998i	$-0.793573\pi$
$523$		−	2.95684e20i		−	1.20800i	0.796985	−	0.603998i	$-0.206427\pi$
$524$	−8.81154e19	+	6.11932e19i	−0.354868	+	0.246444i
$525$	−5.14557e18	−	7.36571e18i	−0.0204286	−	0.0292429i
$526$	−3.40493e20	+	1.06634e20i	−1.33265	+	0.417354i
$527$	−3.03430e20			−1.17079
$528$	−5.93127e19	−	2.29429e20i	−0.225628	−	0.872759i
$529$	1.05389e20			0.395254
$530$	2.53078e20	−	7.92581e19i	0.935805	−	0.293072i
$531$	5.71153e18	−	1.55865e19i	0.0208230	−	0.0568250i
$532$	−4.69875e19	+	3.26313e19i	−0.168906	+	0.117300i
$533$		−	3.06751e20i		−	1.08726i
$534$	7.17782e19	+	5.54227e19i	0.250861	+	0.193699i
$535$		−	4.90635e20i		−	1.69085i
$536$	3.56186e20	+	2.76605e20i	1.21043	+	0.939991i
$537$	1.69810e19	−	1.18626e19i	0.0569057	−	0.0397534i
$538$	−3.44241e19	−	1.09919e20i	−0.113762	−	0.363250i
$539$	2.68760e20			0.875888
$540$	2.22027e20	−	2.60801e20i	0.713597	−	0.838216i
$541$	2.62259e20			0.831287			0.415644	−	0.909528i	$-0.363556\pi$
$541$	2.62259e20			0.831287			0.415644	+	0.909528i	$0.363556\pi$
$542$	−1.54729e20	−	4.94063e20i	−0.483701	−	1.54450i
$543$	4.76546e19	−	3.32907e19i	0.146928	−	0.102642i
$544$	−3.48018e20	−	1.85633e19i	−1.05830	−	0.0564501i
$545$			6.35765e20i			1.90688i
$546$	5.29181e19	+	4.08601e19i	0.156552	+	0.120880i
$547$			5.35824e20i			1.56357i	0.623548	+	0.781785i	$0.285691\pi$
$547$			5.35824e20i			1.56357i	−0.623548	+	0.781785i	$0.714309\pi$
$548$	−2.66176e20	−	3.83281e20i	−0.766151	−	1.10322i
$549$	−1.42559e20	+	3.89037e20i	−0.404765	+	1.10458i
$550$	6.50619e19	−	2.03759e19i	0.182224	−	0.0570685i
$551$	−5.54999e20			−1.53340
$552$	−2.18839e19	+	4.32828e20i	−0.0596461	+	1.17970i
$553$	1.91547e19			0.0515036
$554$	3.04865e20	−	9.54767e19i	0.808694	−	0.253264i
$555$	3.16645e20	+	4.53267e20i	0.828657	+	1.18620i
$556$	−5.74026e19	−	8.26571e19i	−0.148208	−	0.213412i
$557$		−	3.25986e20i		−	0.830395i	−0.909731	−	0.415197i	$-0.863712\pi$
$557$		−	3.25986e20i		−	0.830395i	0.909731	−	0.415197i	$-0.136288\pi$
$558$	−4.39049e20	−	2.09783e19i	−1.10346	−	0.0527248i
$559$			5.09361e20i			1.26310i
$560$	−2.64627e19	+	7.09944e19i	−0.0647476	+	0.173706i
$561$	2.26624e20	+	3.24404e20i	0.547122	+	0.783187i
$562$	1.34320e19	+	4.28896e19i	0.0319977	+	0.102171i
$563$	2.38947e20			0.561680			0.280840	−	0.959755i	$-0.409387\pi$
$563$	2.38947e20			0.561680			0.280840	+	0.959755i	$0.409387\pi$
$564$	−5.81817e19	+	1.57423e20i	−0.134956	+	0.365152i
$565$	3.19110e20			0.730428
$566$	1.52527e20	+	4.87031e20i	0.344527	+	1.10010i
$567$	4.88125e19	−	5.76599e19i	0.108807	−	0.128529i
$568$	2.36511e20	−	3.04557e20i	0.520281	−	0.669970i
$569$			3.74243e20i			0.812478i	0.913767	+	0.406239i	$0.133160\pi$
$569$			3.74243e20i			0.812478i	−0.913767	+	0.406239i	$0.866840\pi$
$570$	3.83443e20	−	4.96599e20i	0.821561	−	1.06401i
$571$			5.52406e18i			0.0116812i	0.999983	+	0.00584060i	$0.00185913\pi$
$571$			5.52406e18i			0.0116812i	−0.999983	+	0.00584060i	$0.998141\pi$
$572$	−4.16684e20	+	2.89373e20i	−0.869634	+	0.603932i
$573$	1.82964e20	−	1.27815e20i	0.376882	−	0.263283i
$574$	7.31709e19	−	2.29154e19i	0.148764	−	0.0465896i
$575$	−1.24686e20			−0.250212
$576$	−5.02283e20	−	5.09213e19i	−0.994900	−	0.100863i
$577$	3.96346e20			0.774918			0.387459	−	0.921887i	$-0.373353\pi$
$577$	3.96346e20			0.774918			0.387459	+	0.921887i	$0.373353\pi$
$578$	6.09152e19	−	1.90772e19i	0.117562	−	0.0368177i
$579$	4.21272e20	−	2.94294e20i	0.802552	−	0.560650i
$580$	−6.03744e20	+	4.19280e20i	−1.13538	+	0.788486i
$581$			1.19053e20i			0.221014i
$582$	−3.47731e20	+	4.50348e20i	−0.637267	+	0.825327i
$583$			4.43852e20i			0.803016i
$584$	4.52211e20	−	5.82316e20i	0.807690	−	1.04007i
$585$	−6.88476e20	−	2.52286e20i	−1.21400	−	0.444861i
$586$	1.90282e20	+	6.07587e20i	0.331258	+	1.05773i
$587$	3.17027e20			0.544892			0.272446	−	0.962171i	$-0.412167\pi$
$587$	3.17027e20			0.544892			0.272446	+	0.962171i	$0.412167\pi$
$588$	1.98496e20	−	5.37072e20i	0.336839	−	0.911387i
$589$	−8.05164e20			−1.34902
$590$	−1.20360e19	−	3.84320e19i	−0.0199110	−	0.0635774i
$591$	−6.45576e20	−	9.24121e20i	−1.05449	−	1.50946i
$592$	2.84651e20	−	7.63665e20i	0.459093	−	1.23166i
$593$		−	4.19163e20i		−	0.667533i	−0.942656	−	0.333766i	$-0.891680\pi$
$593$		−	4.19163e20i		−	0.667533i	0.942656	−	0.333766i	$-0.108320\pi$
$594$	3.05486e20	+	4.85066e20i	0.480388	+	0.762786i
$595$		−	1.26523e20i		−	0.196468i
$596$	−3.17255e20	−	4.56833e20i	−0.486477	−	0.700504i
$597$	−1.62192e20	−	2.32173e20i	−0.245597	−	0.351563i
$598$	8.85377e20	−	2.77279e20i	1.32394	−	0.414628i
$599$	3.07394e20			0.453935			0.226968	−	0.973902i	$-0.427119\pi$
$599$	3.07394e20			0.453935			0.226968	+	0.973902i	$0.427119\pi$
$600$	7.33450e18	−	1.45064e20i	0.0106964	−	0.211557i
$601$	5.16084e20			0.743295			0.371648	−	0.928374i	$-0.378793\pi$
$601$	5.16084e20			0.743295			0.371648	+	0.928374i	$0.378793\pi$
$602$	−1.21500e20	+	3.80511e19i	−0.172824	+	0.0541245i
$603$	−1.02432e21	−	3.75354e20i	−1.43899	−	0.527305i
$604$	2.64798e20	+	3.81297e20i	0.367399	+	0.529038i
$605$		−	1.50529e20i		−	0.206278i
$606$	−1.72485e20	−	1.33182e20i	−0.233456	−	0.180261i
$607$		−	1.37109e21i		−	1.83295i	−0.400087	−	0.916477i	$-0.631020\pi$
$607$		−	1.37109e21i		−	1.83295i	0.400087	−	0.916477i	$-0.368980\pi$
$608$	−9.23480e20	−	4.92586e19i	−1.21941	−	0.0650436i
$609$	−1.32910e20	+	9.28487e19i	−0.173351	+	0.121100i
$610$	3.00417e20	+	9.59257e20i	0.387035	+	1.23584i
$611$	3.59290e20			0.457232
$612$	8.15645e20	−	2.13277e20i	1.02533	−	0.268107i
$613$	5.55383e20			0.689667			0.344833	−	0.938664i	$-0.387935\pi$
$613$	5.55383e20			0.689667			0.344833	+	0.938664i	$0.387935\pi$
$614$	3.42953e20	+	1.09508e21i	0.420699	+	1.34333i
$615$	−6.89369e20	+	4.81582e20i	−0.835388	+	0.583589i
$616$	−1.00153e20	−	7.77765e19i	−0.119898	−	0.0931092i
$617$		−	6.14682e20i		−	0.726962i	−0.931602	−	0.363481i	$-0.881588\pi$
$617$		−	6.14682e20i		−	0.726962i	0.931602	−	0.363481i	$-0.118412\pi$
$618$	−3.80310e20	−	2.93652e20i	−0.444349	−	0.343099i
$619$			1.57029e21i			1.81259i	0.422644	+	0.906296i	$0.361102\pi$
$619$			1.57029e21i			1.81259i	−0.422644	+	0.906296i	$0.638898\pi$
$620$	−8.75880e20	+	6.08269e20i	−0.998865	+	0.693678i
$621$	−2.68024e20	−	1.01353e21i	−0.301986	−	1.14195i
$622$	2.02572e20	−	6.34407e19i	0.225502	−	0.0706220i
$623$	4.85266e19			0.0533728
$624$	2.70517e20	+	1.04639e21i	0.293975	+	1.13713i
$625$	−1.08681e21			−1.16696
$626$	−2.67647e20	+	8.38209e19i	−0.283959	+	0.0889293i
$627$	6.01355e20	+	8.60820e20i	0.630412	+	0.902414i
$628$	4.06825e19	−	2.82527e19i	0.0421416	−	0.0292659i
$629$			1.36097e21i			1.39305i
$630$	8.74743e18	−	1.83072e20i	0.00884761	−	0.185169i
$631$		−	1.30996e21i		−	1.30930i	−0.755933	−	0.654649i	$-0.772816\pi$
$631$		−	1.30996e21i		−	1.30930i	0.755933	−	0.654649i	$-0.227184\pi$
$632$	2.44566e20	+	1.89924e20i	0.241556	+	0.187586i
$633$	−2.13635e20	−	3.05812e20i	−0.208519	−	0.298488i
$634$	−2.42156e20	−	7.73226e20i	−0.233575	−	0.745825i
$635$	1.18829e21			1.13271
$636$	8.86966e20	+	3.27813e20i	0.835562	+	0.308815i
$637$	−1.22578e21			−1.14121
$638$	−3.67670e20	−	1.17400e21i	−0.338301	−	1.08022i
$639$	−3.20946e20	+	8.75846e20i	−0.291861	+	0.796473i
$640$	−1.04180e21	+	6.44067e20i	−0.936342	+	0.578870i
$641$		−	4.21198e20i		−	0.374155i	−0.982345	−	0.187077i	$-0.940099\pi$
$641$		−	4.21198e20i		−	0.374155i	0.982345	−	0.187077i	$-0.0599015\pi$
$642$	1.06918e21	−	1.38470e21i	0.938722	−	1.21574i
$643$		−	4.03246e20i		−	0.349936i	−0.984574	−	0.174968i	$-0.944018\pi$
$643$		−	4.03246e20i		−	0.349936i	0.984574	−	0.174968i	$-0.0559821\pi$
$644$	1.32282e20	+	1.90480e20i	0.113463	+	0.163382i
$645$	1.14470e21	−	7.99668e20i	0.970495	−	0.677973i
$646$	1.47374e21	−	4.61542e20i	1.23503	−	0.386783i
$647$	4.33098e20			0.358760			0.179380	−	0.983780i	$-0.442591\pi$
$647$	4.33098e20			0.358760			0.179380	+	0.983780i	$0.442591\pi$
$648$	1.19495e21	−	2.52211e20i	0.978444	−	0.206515i
$649$	6.74027e19			0.0545559
$650$	−2.96738e20	+	9.29315e19i	−0.237423	+	0.0743555i
$651$	−1.92818e20	+	1.34700e20i	−0.152508	+	0.106539i
$652$	−7.39744e20	−	1.06520e21i	−0.578395	−	0.832862i
$653$			6.53749e20i			0.505315i	0.967556	+	0.252657i	$0.0813046\pi$
$653$			6.53749e20i			0.505315i	−0.967556	+	0.252657i	$0.918695\pi$
$654$	−1.38544e21	+	1.79429e21i	−1.05866	+	1.37107i
$655$		−	6.29597e20i		−	0.475612i
$656$	1.16145e21	+	4.32924e20i	0.867406	+	0.323320i
$657$	−6.13653e20	+	1.67463e21i	−0.453088	+	1.23645i
$658$	2.68403e19	+	8.57033e19i	0.0195926	+	0.0625609i
$659$	1.91228e21			1.38010			0.690049	−	0.723763i	$-0.257589\pi$
$659$	1.91228e21			1.38010			0.690049	+	0.723763i	$0.257589\pi$
$660$	1.30449e21	+	4.82124e20i	0.930807	+	0.344016i
$661$	−1.12374e21			−0.792787			−0.396394	−	0.918081i	$-0.629738\pi$
$661$	−1.12374e21			−0.792787			−0.396394	+	0.918081i	$0.629738\pi$
$662$	−6.43211e20	−	2.05383e21i	−0.448661	−	1.43261i
$663$	−1.03360e21	−	1.47956e21i	−0.712854	−	1.02043i
$664$	−1.18044e21	+	1.52007e21i	−0.804978	+	1.03658i
$665$		−	3.35733e20i		−	0.226376i
$666$	−9.40935e19	+	1.96925e21i	−0.0627340	+	1.31294i
$667$			2.24988e21i			1.48325i
$668$	−3.43677e20	+	2.38672e20i	−0.224041	+	0.155589i
$669$	1.28866e21	+	1.84467e21i	0.830694	+	1.18911i
$670$	−2.52570e21	+	7.90990e20i	−1.60998	+	0.504208i
$671$	−1.68236e21			−1.06047
$672$	−2.29393e20	+	1.42697e20i	−0.142992	+	0.0889500i
$673$	2.21640e21			1.36627			0.683133	−	0.730294i	$-0.260617\pi$
$673$	2.21640e21			1.36627			0.683133	+	0.730294i	$0.260617\pi$
$674$	−1.65879e21	+	5.19495e20i	−1.01121	+	0.316688i
$675$	8.98296e19	+	3.39689e20i	0.0541553	+	0.204787i
$676$	5.22801e20	−	3.63068e20i	0.311700	−	0.216465i
$677$			1.25306e21i			0.738853i	0.929260	+	0.369426i	$0.120446\pi$
$677$			1.25306e21i			0.738853i	−0.929260	+	0.369426i	$0.879554\pi$
$678$	9.00609e20	+	6.95395e20i	0.525186	+	0.405517i
$679$			3.04464e20i			0.175595i
$680$	1.25450e21	−	1.61543e21i	0.715573	−	0.921450i
$681$	1.75026e21	−	1.22270e21i	0.987415	−	0.689792i
$682$	−5.33397e20	−	1.70318e21i	−0.297624	−	0.950337i
$683$	−2.33201e21			−1.28699			−0.643494	−	0.765451i	$-0.722516\pi$
$683$	−2.33201e21			−1.28699			−0.643494	+	0.765451i	$0.722516\pi$
$684$	2.16435e21	−	5.65939e20i	1.18142	−	0.308922i
$685$	2.73860e21			1.47859
$686$	−1.85812e20	−	5.93315e20i	−0.0992302	−	0.316851i
$687$	2.76249e20	−	1.92983e20i	0.145923	−	0.101940i
$688$	−1.92859e21	−	7.18871e20i	−1.00769	−	0.375610i
$689$		−	2.02435e21i		−	1.04626i
$690$	−2.01313e21	−	1.55442e21i	−1.02921	−	0.794692i
$691$		−	2.54645e21i		−	1.28781i	−0.765107	−	0.643903i	$-0.777314\pi$
$691$		−	2.54645e21i		−	1.28781i	0.765107	−	0.643903i	$-0.222686\pi$
$692$	3.52955e20	+	5.08238e20i	0.176573	+	0.254256i
$693$	2.88022e20	+	1.05543e20i	0.142536	+	0.0522313i
$694$	3.49443e21	−	1.09437e21i	1.71072	−	0.535759i
$695$	5.90597e20			0.286026
$696$	−2.61760e21	−	1.32347e20i	−1.25410	−	0.0634079i
$697$	−2.06988e21			−0.981069
$698$	−6.56173e20	+	2.05498e20i	−0.307683	+	0.0963591i
$699$	8.68142e20	+	1.24272e21i	0.402728	+	0.576492i
$700$	−4.43349e19	−	6.38402e19i	−0.0203475	−	0.0292994i
$701$			4.23946e20i			0.192497i	0.995357	+	0.0962487i	$0.0306844\pi$
$701$			4.23946e20i			0.192497i	−0.995357	+	0.0962487i	$0.969316\pi$
$702$	−1.39328e21	−	2.21232e21i	−0.625906	−	0.993847i
$703$			3.61138e21i			1.60512i
$704$	−5.07579e20	−	1.98609e21i	−0.223208	−	0.873381i
$705$	−5.64066e20	−	8.07442e20i	−0.245421	−	0.351312i
$706$	−7.24709e20	−	2.31406e21i	−0.311981	−	0.996182i
$707$	−1.16611e20			−0.0496698
$708$	4.97811e19	−	1.34693e20i	0.0209805	−	0.0567670i
$709$	−7.76846e20			−0.323958			−0.161979	−	0.986794i	$-0.551788\pi$
$709$	−7.76846e20			−0.323958			−0.161979	+	0.986794i	$0.551788\pi$
$710$	6.76335e20	+	2.15959e21i	0.279077	+	0.891117i
$711$	−7.03325e20	−	2.57727e20i	−0.287167	−	0.105230i
$712$	6.19585e20	+	4.81153e20i	0.250323	+	0.194394i
$713$			3.26400e21i			1.30490i
$714$	2.75714e20	−	3.57079e20i	0.109074	−	0.141263i
$715$		−	2.97727e21i		−	1.16553i
$716$	1.47178e20	−	1.02210e20i	0.0570156	−	0.0395955i
$717$	3.74201e19	−	2.61411e19i	0.0143454	−	0.0100214i
$718$	−5.74465e20	+	1.79909e20i	−0.217937	+	0.0682527i
$719$	−2.11639e21			−0.794563			−0.397281	−	0.917697i	$-0.630046\pi$
$719$	−2.11639e21			−0.794563			−0.397281	+	0.917697i	$0.630046\pi$
$720$	1.92689e21	−	2.25072e21i	0.715918	−	0.836234i
$721$	−2.57114e20			−0.0945390
$722$	1.28815e21	−	4.03419e20i	0.468747	−	0.146801i
$723$	5.67576e20	−	3.96499e20i	0.204403	−	0.142792i
$724$	4.13032e20	−	2.86837e20i	0.147212	−	0.102234i
$725$		−	7.54057e20i		−	0.265992i
$726$	3.28027e20	−	4.24830e20i	0.114521	−	0.148317i
$727$		−	2.04743e21i		−	0.707457i	−0.935348	−	0.353728i	$-0.884914\pi$
$727$		−	2.04743e21i		−	0.707457i	0.935348	−	0.353728i	$-0.115086\pi$
$728$	4.56786e20	+	3.54728e20i	0.156217	+	0.121314i
$729$	−2.56812e21	+	1.46039e21i	−0.869277	+	0.494324i
$730$	1.29316e21	+	4.12917e21i	0.433242	+	1.38338i
$731$	3.43704e21			1.13974
$732$	−1.24253e21	+	3.36192e21i	−0.407825	+	1.10346i
$733$	6.60453e20			0.214567			0.107283	−	0.994228i	$-0.465785\pi$
$733$	6.60453e20			0.214567			0.107283	+	0.994228i	$0.465785\pi$
$734$	8.19244e20	+	2.61592e21i	0.263447	+	0.841208i
$735$	1.92440e21	+	2.75472e21i	0.612549	+	0.876843i
$736$	−1.99686e20	+	3.74363e21i	−0.0629164	+	1.17953i
$737$		−	4.42961e21i		−	1.38153i
$738$	−2.99502e21	−	1.43106e20i	−0.924650	−	0.0441809i
$739$			2.11800e21i			0.647281i	0.946180	+	0.323641i	$0.104907\pi$
$739$			2.11800e21i			0.647281i	−0.946180	+	0.323641i	$0.895093\pi$
$740$	2.72825e21	+	3.92855e21i	0.825366	+	1.18849i
$741$	−2.74270e21	−	3.92608e21i	−0.821375	−	1.17577i
$742$	4.82878e20	−	1.51226e20i	0.143156	−	0.0448330i
$743$	−1.48465e21			−0.435721			−0.217861	−	0.975980i	$-0.569908\pi$
$743$	−1.48465e21			−0.435721			−0.217861	+	0.975980i	$0.569908\pi$
$744$	−3.79747e21	−	1.92001e20i	−1.10331	−	0.0557837i
$745$	3.26414e21			0.938850
$746$	3.37757e21	−	1.05778e21i	0.961751	−	0.301198i
$747$	1.60187e21	−	4.37141e21i	0.451567	−	1.23230i
$748$	1.95262e21	+	2.81168e21i	0.544948	+	0.784701i
$749$		−	9.36143e20i		−	0.258660i
$750$	−2.51049e21	−	1.93844e21i	−0.686750	−	0.530266i
$751$			2.10147e21i			0.569147i	0.958654	+	0.284573i	$0.0918520\pi$
$751$			2.10147e21i			0.569147i	−0.958654	+	0.284573i	$0.908148\pi$
$752$	−5.07073e20	+	1.36038e21i	−0.135968	+	0.364776i
$753$	−2.04155e21	+	1.42620e21i	−0.541999	+	0.378632i
$754$	1.67689e21	+	5.35446e21i	0.440778	+	1.40744i
$755$	−2.72442e21			−0.709043
$756$	4.23633e20	−	4.97614e20i	0.109163	−	0.128227i
$757$	−3.55979e21			−0.908250			−0.454125	−	0.890938i	$-0.650048\pi$
$757$	−3.55979e21			−0.908250			−0.454125	+	0.890938i	$0.650048\pi$
$758$	9.73263e20	+	3.10771e21i	0.245873	+	0.785094i
$759$	3.48962e21	−	2.43779e21i	0.872901	−	0.609795i
$760$	3.32887e21	−	4.28661e21i	0.824507	−	1.06172i
$761$			2.44120e21i			0.598712i	0.954142	+	0.299356i	$0.0967718\pi$
$761$			2.44120e21i			0.598712i	−0.954142	+	0.299356i	$0.903228\pi$
$762$	3.35365e21	+	2.58948e21i	0.814433	+	0.628855i
$763$			1.21305e21i			0.291707i
$764$	1.58578e21	−	1.10127e21i	0.377610	−	0.262238i
$765$	−1.70237e21	+	4.64567e21i	−0.401413	+	1.09544i
$766$	−1.67418e21	+	5.24313e20i	−0.390918	+	0.122426i
$767$	−3.07414e20			−0.0710818
$768$	−4.34375e21	−	4.52538e20i	−0.994617	−	0.103621i
$769$	−2.11282e21			−0.479087			−0.239544	−	0.970886i	$-0.576998\pi$
$769$	−2.11282e21			−0.479087			−0.239544	+	0.970886i	$0.576998\pi$
$770$	7.10182e20	−	2.22413e20i	0.159474	−	0.0499435i
$771$	5.64423e19	+	8.07953e19i	0.0125515	+	0.0179671i
$772$	3.65125e21	−	2.53567e21i	0.804103	−	0.558423i
$773$		−	4.35995e21i		−	0.950901i	−0.879742	−	0.475451i	$-0.842285\pi$
$773$		−	4.35995e21i		−	0.950901i	0.879742	−	0.475451i	$-0.157715\pi$
$774$	4.97324e21	+	2.37628e20i	1.07419	+	0.0513263i
$775$		−	1.09395e21i		−	0.234009i
$776$	−3.01883e21	+	3.88738e21i	−0.639553	+	0.823557i
$777$	6.04165e20	+	8.64843e20i	0.126765	+	0.181459i
$778$	−8.77360e20	−	2.80148e21i	−0.182319	−	0.582159i
$779$	−5.49251e21			−1.13042
$780$	−5.94958e21	−	2.19890e21i	−1.21276	−	0.448225i
$781$	−3.78753e21			−0.764670
$782$	−1.87101e21	−	5.97431e21i	−0.374133	−	1.19464i
$783$	6.12947e21	−	1.62092e21i	1.21398	−	0.321032i
$784$	1.72996e21	−	4.64116e21i	0.339364	−	0.910450i
$785$			2.90683e20i			0.0564803i
$786$	1.37200e21	−	1.77688e21i	0.264049	−	0.341971i
$787$			2.84479e21i			0.542300i	0.962537	+	0.271150i	$0.0874040\pi$
$787$			2.84479e21i			0.542300i	−0.962537	+	0.271150i	$0.912596\pi$
$788$	−5.56236e21	−	8.00955e21i	−1.05030	−	1.51238i
$789$	6.12075e21	−	4.27586e21i	1.14479	−	0.799735i
$790$	−1.73421e21	+	5.43113e20i	−0.321290	+	0.100621i
$791$	6.08869e20			0.111738
$792$	2.63096e21	+	4.20337e21i	0.478272	+	0.764115i
$793$	7.67302e21			1.38171
$794$	2.18749e21	−	6.85071e20i	0.390204	−	0.122203i
$795$	−4.54937e21	+	3.17812e21i	−0.803892	+	0.561586i
$796$	−1.39747e21	−	2.01229e21i	−0.244621	−	0.352243i
$797$		−	6.38006e21i		−	1.10634i	−0.833069	−	0.553168i	$-0.813419\pi$
$797$		−	6.38006e21i		−	1.10634i	0.833069	−	0.553168i	$-0.186581\pi$
$798$	7.31618e20	−	9.47522e20i	0.125679	−	0.162767i
$799$		−	2.42440e21i		−	0.412576i
$800$	6.69257e19	−	1.25470e21i	0.0112828	−	0.211526i
$801$	−1.78181e21	−	6.52927e20i	−0.297589	−	0.109049i
$802$	−1.55960e21	−	4.97993e21i	−0.258051	−	0.823977i
$803$	−7.24181e21			−1.18708
$804$	−8.85185e21	−	3.27155e21i	−1.43752	−	0.531292i
$805$	−1.36100e21			−0.218973
$806$	2.43275e21	+	7.76797e21i	0.387779	+	1.23821i
$807$	1.38035e21	+	1.97592e21i	0.217990	+	0.312046i
$808$	−1.48888e21	−	1.15622e21i	−0.232956	−	0.180907i
$809$			5.52770e21i			0.856900i	0.903565	+	0.428450i	$0.140940\pi$
$809$			5.52770e21i			0.856900i	−0.903565	+	0.428450i	$0.859060\pi$
$810$	−2.78443e21	+	6.60437e21i	−0.427660	+	1.01436i
$811$		−	4.30582e21i		−	0.655238i	−0.944810	−	0.327619i	$-0.893754\pi$
$811$		−	4.30582e21i		−	0.655238i	0.944810	−	0.327619i	$-0.106246\pi$
$812$	−1.15196e21	+	7.99995e20i	−0.173686	+	0.120619i
$813$	6.20437e21	+	8.88135e21i	0.926870	+	1.32678i
$814$	−7.63922e21	+	2.39243e21i	−1.13075	+	0.354124i
$815$	7.61099e21			1.11624
$816$	7.06081e21	−	1.82538e21i	1.02607	−	0.265264i
$817$	9.12033e21			1.31324
$818$	9.78098e21	−	3.06318e21i	1.39551	−	0.437041i
$819$	−1.31363e21	−	4.81368e20i	−0.185713	−	0.0680530i
$820$	−5.97490e21	+	4.14937e21i	−0.837003	+	0.581271i
$821$			3.59883e21i			0.499560i	0.968303	+	0.249780i	$0.0803584\pi$
$821$			3.59883e21i			0.499560i	−0.968303	+	0.249780i	$0.919642\pi$
$822$	7.72901e21	+	5.96787e21i	1.06313	+	0.820882i
$823$			3.27217e21i			0.446003i	0.974818	+	0.223001i	$0.0715855\pi$
$823$			3.27217e21i			0.446003i	−0.974818	+	0.223001i	$0.928415\pi$
$824$	−3.28281e21	−	2.54934e21i	−0.443396	−	0.344330i
$825$	−1.16956e21	+	8.17038e20i	−0.156538	+	0.109355i
$826$	−2.29650e19	−	7.33290e19i	−0.00304590	−	0.00972581i
$827$	−9.00622e21			−1.18373			−0.591863	−	0.806039i	$-0.701607\pi$
$827$	−9.00622e21			−1.18373			−0.591863	+	0.806039i	$0.701607\pi$
$828$	−2.29422e21	−	8.77390e21i	−0.298819	−	1.14279i
$829$	−6.29161e20			−0.0812088			−0.0406044	−	0.999175i	$-0.512928\pi$
$829$	−6.29161e20			−0.0812088			−0.0406044	+	0.999175i	$0.512928\pi$
$830$	−3.37564e21	−	1.07787e22i	−0.431788	−	1.37873i
$831$	−5.48031e21	+	3.82845e21i	−0.694700	+	0.485306i
$832$	2.31500e21	+	9.05827e21i	0.290821	+	1.13794i
$833$			8.27124e21i			1.02975i
$834$	1.66681e21	+	1.28701e21i	0.205656	+	0.158795i
$835$		−	2.45562e21i		−	0.300270i
$836$	5.18135e21	+	7.46090e21i	0.627908	+	0.904158i
$837$	8.89232e21	−	2.35154e21i	1.06801	−	0.282431i
$838$	−7.23499e21	+	2.26583e21i	−0.861208	+	0.269710i
$839$	9.00218e21			1.06202			0.531011	−	0.847365i	$-0.321812\pi$
$839$	9.00218e21			1.06202			0.531011	+	0.847365i	$0.321812\pi$
$840$	8.00597e19	−	1.58345e21i	0.00936093	−	0.185144i
$841$	−4.97731e21			−0.576799
$842$	−7.92443e21	+	2.48175e21i	−0.910180	+	0.285047i
$843$	−5.38601e20	−	7.70990e20i	−0.0613141	−	0.0877691i
$844$	−1.84071e21	−	2.65053e21i	−0.207690	−	0.299065i
$845$			3.73549e21i			0.417755i
$846$	1.67617e20	−	3.50800e21i	0.0185797	−	0.388850i
$847$		−	2.87212e20i		−	0.0315556i
$848$	7.66480e21	+	2.85700e21i	0.834703	+	0.311130i
$849$	−6.11606e21	−	8.75494e21i	−0.660183	−	0.945030i
$850$	6.27079e20	+	2.00232e21i	0.0670935	+	0.214235i
$851$	1.46399e22			1.55263
$852$	−2.79734e21	+	7.56877e21i	−0.294068	+	0.795661i
$853$	−8.93521e21			−0.931080			−0.465540	−	0.885027i	$-0.654140\pi$
$853$	−8.93521e21			−0.931080			−0.465540	+	0.885027i	$0.654140\pi$
$854$	5.73202e20	+	1.83028e21i	0.0592071	+	0.189053i
$855$	−4.51729e21	+	1.23275e22i	−0.462522	+	1.26220i
$856$	9.28208e21	−	1.19526e22i	0.942089	−	1.21314i
$857$			4.67205e21i			0.470058i	0.971988	+	0.235029i	$0.0755185\pi$
$857$			4.67205e21i			0.470058i	−0.971988	+	0.235029i	$0.924482\pi$
$858$	6.48797e21	−	8.40259e21i	0.647074	−	0.838028i
$859$		−	1.22809e22i		−	1.21418i	−0.794634	−	0.607089i	$-0.792337\pi$
$859$		−	1.22809e22i		−	1.21418i	0.794634	−	0.607089i	$-0.207663\pi$
$860$	9.92134e21	−	6.89004e21i	0.972371	−	0.675279i
$861$	−1.31533e21	+	9.18870e20i	−0.127794	+	0.0892751i
$862$	−1.11465e22	+	3.49082e21i	−1.07358	+	0.336219i
$863$	1.44766e22			1.38224			0.691122	−	0.722739i	$-0.257117\pi$
$863$	1.44766e22			1.38224			0.691122	+	0.722739i	$0.257117\pi$
$864$	1.03429e22	−	2.15308e21i	0.979012	−	0.203801i
$865$	−3.63144e21			−0.340767
$866$	−1.83977e22	+	5.76173e21i	−1.71151	+	0.536005i
$867$	−1.09502e21	+	7.64965e20i	−0.100990	+	0.0705502i
$868$	−1.67120e21	+	1.16059e21i	−0.152802	+	0.106116i
$869$		−	3.04148e21i		−	0.275700i
$870$	9.40058e21	−	1.21747e22i	0.844812	−	1.09412i
$871$			2.02029e22i			1.80002i
$872$	−1.20277e22	+	1.54882e22i	−1.06245	+	1.36813i
$873$	4.09658e21	−	1.11793e22i	0.358768	−	0.979060i
$874$	−4.96481e21	−	1.58531e22i	−0.431089	−	1.37650i
$875$	−1.69725e21			−0.146112
$876$	−5.34854e21	+	1.44716e22i	−0.456514	+	1.23519i
$877$	−3.55529e20			−0.0300870			−0.0150435	−	0.999887i	$-0.504789\pi$
$877$	−3.55529e20			−0.0300870			−0.0150435	+	0.999887i	$0.504789\pi$
$878$	−3.57546e20	−	1.14168e21i	−0.0300002	−	0.0957930i
$879$	−7.62999e21	−	1.09221e22i	−0.634757	−	0.908634i
$880$	1.12728e22	+	4.20187e21i	0.929850	+	0.346596i
$881$		−	1.27170e22i		−	1.04008i	−0.854143	−	0.520039i	$-0.825918\pi$
$881$		−	1.27170e22i		−	1.04008i	0.854143	−	0.520039i	$-0.174082\pi$
$882$	−5.71851e20	+	1.19681e22i	−0.0463733	+	0.970534i
$883$		−	6.00264e21i		−	0.482655i	−0.970444	−	0.241327i	$-0.922417\pi$
$883$		−	6.00264e21i		−	0.482655i	0.970444	−	0.241327i	$-0.0775828\pi$
$884$	−8.90562e21	−	1.28237e22i	−0.710023	−	1.02240i
$885$	4.82623e20	+	6.90859e20i	0.0381534	+	0.0546154i
$886$	2.09723e22	−	6.56803e21i	1.64397	−	0.514852i
$887$	−7.74214e21			−0.601774			−0.300887	−	0.953660i	$-0.597283\pi$
$887$	−7.74214e21			−0.601774			−0.300887	+	0.953660i	$0.597283\pi$
$888$	−8.61178e20	+	1.70327e22i	−0.0663737	+	1.31276i
$889$	2.26728e21			0.173278
$890$	−4.39344e21	+	1.37592e21i	−0.332951	+	0.104272i
$891$	−9.15552e21	−	7.75068e21i	−0.688019	−	0.582448i
$892$	1.11032e22	+	1.59881e22i	0.827394	+	1.19141i
$893$		−	6.43325e21i		−	0.475384i
$894$	9.21222e21	+	7.11311e21i	0.675045	+	0.521228i
$895$			1.05161e21i			0.0764153i
$896$	−1.98778e21	+	1.22889e21i	−0.143238	+	0.0885533i
$897$	−1.59157e22	+	1.11184e22i	−1.13732	+	0.794512i
$898$	−2.19404e21	−	7.00576e21i	−0.155479	−	0.496458i
$899$	−1.97396e22			−1.38720
$900$	7.68920e20	+	2.94062e21i	0.0535874	+	0.204937i
$901$	−1.36598e22			−0.944080
$902$	−3.63862e21	−	1.16184e22i	−0.249395	−	0.796339i
$903$	2.18411e21	−	1.52579e21i	0.148462	−	0.103713i
$904$	7.77400e21	+	6.03708e21i	0.524060	+	0.406971i
$905$			2.95117e21i			0.197302i
$906$	−7.68901e21	−	5.93698e21i	−0.509811	−	0.393645i
$907$		−	1.12207e22i		−	0.737848i	−0.929460	−	0.368924i	$-0.879726\pi$
$907$		−	1.12207e22i		−	0.737848i	0.929460	−	0.368924i	$-0.120274\pi$
$908$	1.51699e22	−	1.05350e22i	0.989323	−	0.687052i
$909$	4.28172e21	+	1.56900e21i	0.276942	+	0.101483i
$910$	−3.23904e21	+	1.01439e21i	−0.207781	+	0.0650723i
$911$	2.80400e22			1.78398			0.891991	−	0.452054i	$-0.149308\pi$
$911$	2.80400e22			1.78398			0.891991	+	0.452054i	$0.149308\pi$
$912$	1.87361e22	−	4.84372e21i	1.18228	−	0.305646i
$913$	1.89039e22			1.18310
$914$	−1.44342e22	+	4.52046e21i	−0.895976	+	0.280599i
$915$	−1.20462e22	−	1.72438e22i	−0.741639	−	1.06163i
$916$	2.39430e21	−	1.66276e21i	0.146205	−	0.101535i
$917$		−	1.20129e21i		−	0.0727573i
$918$	−1.49282e22	+	9.40150e21i	−0.896783	+	0.564777i
$919$		−	1.01200e22i		−	0.602996i	−0.953467	−	0.301498i	$-0.902513\pi$
$919$		−	1.01200e22i		−	0.602996i	0.953467	−	0.301498i	$-0.0974866\pi$
$920$	−1.73772e22	−	1.34947e22i	−1.02700	−	0.797542i
$921$	−1.37518e22	−	1.96853e22i	−0.806146	−	1.15397i
$922$	6.58883e21	+	2.10387e22i	0.383113	+	1.22331i
$923$	1.72744e22			0.996301
$924$	2.48899e21	+	9.19903e20i	0.142391	+	0.0526262i
$925$	−4.90664e21			−0.278433
$926$	5.27989e21	+	1.68591e22i	0.297196	+	0.948972i
$927$	9.44073e21	+	3.45948e21i	0.527118	+	0.193158i
$928$	−2.26402e22	−	1.20763e21i	−1.25392	−	0.0668845i
$929$		−	3.33154e22i		−	1.83032i	−0.403091	−	0.915160i	$-0.632064\pi$
$929$		−	3.33154e22i		−	1.83032i	0.403091	−	0.915160i	$-0.367936\pi$
$930$	1.36379e22	−	1.76625e22i	0.743232	−	0.962563i
$931$			2.19481e22i			1.18652i
$932$	7.48002e21	+	1.07709e22i	0.401128	+	0.577606i
$933$	−3.64146e21	+	2.54387e21i	−0.193715	+	0.135326i
$934$	1.46766e22	−	4.59637e21i	0.774505	−	0.242557i
$935$	−2.00899e22			−1.05170
$936$	−1.19994e22	−	1.91710e22i	−0.623149	−	0.995579i
$937$	−2.02290e21			−0.104214			−0.0521072	−	0.998641i	$-0.516594\pi$
$937$	−2.02290e21			−0.104214			−0.0521072	+	0.998641i	$0.516594\pi$
$938$	−4.81909e21	+	1.50923e21i	−0.246288	+	0.0771317i
$939$	4.81127e21	−	3.36108e21i	0.243932	−	0.170407i
$940$	−4.86006e21	−	6.99826e21i	−0.244446	−	0.351991i
$941$			3.26283e22i			1.62807i	0.580817	+	0.814034i	$0.302733\pi$
$941$			3.26283e22i			1.62807i	−0.580817	+	0.814034i	$0.697267\pi$
$942$	−6.33447e20	+	8.20380e20i	−0.0313566	+	0.0406100i
$943$			2.22657e22i			1.09345i
$944$	4.33860e20	−	1.16396e21i	0.0211378	−	0.0567086i
$945$	9.80534e20	+	3.70787e21i	0.0473941	+	0.179220i
$946$	6.04194e21	+	1.92924e22i	0.289729	+	0.925131i
$947$	1.21535e22			0.578196			0.289098	−	0.957299i	$-0.406645\pi$
$947$	1.21535e22			0.578196			0.289098	+	0.957299i	$0.406645\pi$
$948$	−6.07790e21	−	2.24633e21i	−0.286874	−	0.106026i
$949$	3.30289e22			1.54667
$950$	1.66398e21	+	5.31323e21i	0.0773074	+	0.246849i
$951$	9.71007e21	+	1.38996e22i	0.447578	+	0.640692i
$952$	2.39362e21	−	3.08228e21i	0.109466	−	0.140960i
$953$			3.75589e22i			1.70418i	0.523392	+	0.852092i	$0.324666\pi$
$953$			3.75589e22i			1.70418i	−0.523392	+	0.852092i	$0.675334\pi$
$954$	−1.97651e22	−	9.44402e20i	−0.889788	−	0.0425152i
$955$			1.13306e22i			0.506092i
$956$	3.24328e20	−	2.25235e20i	0.0143731	−	0.00998163i
$957$	1.47430e22	+	2.11041e22i	0.648254	+	0.927954i
$958$	−1.97436e22	+	6.18324e21i	−0.861361	+	0.269758i
$959$	5.22531e21			0.226189
$960$	1.67225e22	−	1.94235e22i	0.718234	−	0.834246i
$961$	−5.17188e21			−0.220406
$962$	3.48414e22	−	1.09115e22i	1.47327	−	0.461395i
$963$	−1.25958e22	+	3.43734e22i	−0.528482	+	1.44220i
$964$	4.91930e21	−	3.41629e21i	0.204798	−	0.142225i
$965$			2.60887e22i			1.07770i
$966$	−3.84110e21	−	2.96586e21i	−0.157444	−	0.121569i
$967$		−	1.62164e22i		−	0.659562i	−0.944057	−	0.329781i	$-0.893025\pi$
$967$		−	1.62164e22i		−	0.659562i	0.944057	−	0.329781i	$-0.106975\pi$
$968$	2.84777e21	−	3.66710e21i	0.114932	−	0.147999i
$969$	−2.64922e22	+	1.85070e22i	−1.06094	+	0.741155i
$970$	−8.63278e21	−	2.75652e22i	−0.343054	−	1.09540i
$971$	−2.35111e22			−0.927105			−0.463552	−	0.886070i	$-0.653425\pi$
$971$	−2.35111e22			−0.927105			−0.463552	+	0.886070i	$0.653425\pi$
$972$	−2.22504e22	+	1.25714e22i	−0.870645	+	0.491913i
$973$	1.12687e21			0.0437551
$974$	−6.65753e21	−	2.12581e22i	−0.256520	−	0.819090i
$975$	5.33422e21	−	3.72640e21i	0.203956	−	0.142480i
$976$	−1.08291e22	+	2.90524e22i	−0.410883	+	1.10232i
$977$		−	2.34420e22i		−	0.882642i	−0.897349	−	0.441321i	$-0.854510\pi$
$977$		−	2.34420e22i		−	0.882642i	0.897349	−	0.441321i	$-0.145490\pi$
$978$	2.14801e22	+	1.65856e22i	0.802593	+	0.619713i
$979$		−	7.70529e21i		−	0.285706i
$980$	1.65809e22	+	2.38757e22i	0.610115	+	0.878538i
$981$	1.63217e22	−	4.45411e22i	0.596002	−	1.62646i
$982$	−1.23528e22	+	3.86861e21i	−0.447640	+	0.140190i
$983$	−7.38390e21			−0.265543			−0.132771	−	0.991147i	$-0.542388\pi$
$983$	−7.38390e21			−0.265543			−0.132771	+	0.991147i	$0.542388\pi$
$984$	−2.59049e22	−	1.30976e21i	−0.924524	−	0.0467442i
$985$	5.72294e22			2.02697
$986$	3.61306e22	−	1.13153e22i	1.26998	−	0.397730i
$987$	−1.07625e21	−	1.54062e21i	−0.0375435	−	0.0537423i
$988$	−2.36314e22	−	3.40281e22i	−0.818112	−	1.17804i
$989$		−	3.69723e22i		−	1.27029i
$990$	−2.90691e22	−	1.38896e21i	−0.991215	−	0.0473615i
$991$		−	2.65560e22i		−	0.898690i	−0.893358	−	0.449345i	$-0.851657\pi$
$991$		−	2.65560e22i		−	0.898690i	0.893358	−	0.449345i	$-0.148343\pi$
$992$	−3.28453e22	−	1.75197e21i	−1.10315	−	0.0588423i
$993$	2.57917e22	+	3.69199e22i	0.859726	+	1.23067i
$994$	1.29046e21	+	4.12055e21i	0.0426921	+	0.136319i
$995$	1.43781e22			0.472094
$996$	1.39617e22	−	3.77763e22i	0.454981	−	1.23105i
$997$	−5.38757e22			−1.74253			−0.871263	−	0.490816i	$-0.836699\pi$
$997$	−5.38757e22			−1.74253			−0.871263	+	0.490816i	$0.836699\pi$
$998$	−1.46660e21	−	4.68297e21i	−0.0470795	−	0.150329i
$999$	−1.05473e22	−	3.98844e22i	−0.336047	−	1.27076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.16.b.a.11.2	yes	28
3.2	odd	2	inner	12.16.b.a.11.27	yes	28
4.3	odd	2	inner	12.16.b.a.11.28	yes	28
12.11	even	2	inner	12.16.b.a.11.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.16.b.a.11.1	✓	28	12.11	even	2	inner
12.16.b.a.11.2	yes	28	1.1	even	1	trivial
12.16.b.a.11.27	yes	28	3.2	odd	2	inner
12.16.b.a.11.28	yes	28	4.3	odd	2	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-172.746 + 54.1000i) q^{2} +(3105.31 - 2169.32i) q^{3} +(26914.4 - 18691.1i) q^{4} +192307. i q^{5} +(-419070. + 542739. i) q^{6} +366926. i q^{7} +(-3.63816e6 + 4.68489e6i) q^{8} +(4.93700e6 - 1.34728e7i) q^{9} +O(q^{10})\)	\(q+(-172.746 + 54.1000i) q^{2} +(3105.31 - 2169.32i) q^{3} +(26914.4 - 18691.1i) q^{4} +192307. i q^{5} +(-419070. + 542739. i) q^{6} +366926. i q^{7} +(-3.63816e6 + 4.68489e6i) q^{8} +(4.93700e6 - 1.34728e7i) q^{9} +(-1.04038e7 - 3.32203e7i) q^{10} +5.82623e7 q^{11} +(4.30304e7 - 1.16428e8i) q^{12} -2.65726e8 q^{13} +(-1.98507e7 - 6.33850e7i) q^{14} +(4.17176e8 + 5.97173e8i) q^{15} +(3.75025e8 - 1.00612e9i) q^{16} +1.79306e9i q^{17} +(-1.23967e8 + 2.59447e9i) q^{18} +4.75795e9i q^{19} +(3.59444e9 + 5.17582e9i) q^{20} +(7.95981e8 + 1.13942e9i) q^{21} +(-1.00646e10 + 3.15199e9i) q^{22} +1.92879e10 q^{23} +(-1.13459e9 + 2.24404e10i) q^{24} -6.46444e9 q^{25} +(4.59032e10 - 1.43758e10i) q^{26} +(-1.38960e10 - 5.25473e10i) q^{27} +(6.85827e9 + 9.87559e9i) q^{28} +1.16647e11i q^{29} +(-1.04373e11 - 8.05901e10i) q^{30} +1.69225e11i q^{31} +(-1.03529e10 + 1.94092e11i) q^{32} +(1.80923e11 - 1.26390e11i) q^{33} +(-9.70044e10 - 3.09743e11i) q^{34} -7.05625e10 q^{35} +(-1.18946e11 - 4.54891e11i) q^{36} +7.59020e11 q^{37} +(-2.57405e11 - 8.21916e11i) q^{38} +(-8.25163e11 + 5.76446e11i) q^{39} +(-9.00937e11 - 6.99644e11i) q^{40} +1.15439e12i q^{41} +(-1.99145e11 - 1.53768e11i) q^{42} -1.91686e12i q^{43} +(1.56809e12 - 1.08899e12i) q^{44} +(2.59092e12 + 9.49421e11i) q^{45} +(-3.33191e12 + 1.04348e12i) q^{46} -1.35211e12 q^{47} +(-1.01803e12 - 3.93787e12i) q^{48} +4.61293e12 q^{49} +(1.11671e12 - 3.49727e11i) q^{50} +(3.88971e12 + 5.56800e12i) q^{51} +(-7.15186e12 + 4.96673e12i) q^{52} +7.61817e12i q^{53} +(5.24328e12 + 8.32556e12i) q^{54} +1.12043e13i q^{55} +(-1.71901e12 - 1.33494e12i) q^{56} +(1.03215e13 + 1.47749e13i) q^{57} +(-6.31060e12 - 2.01503e13i) q^{58} +1.15688e12 q^{59} +(2.23899e13 + 8.27506e12i) q^{60} -2.88756e13 q^{61} +(-9.15509e12 - 2.92330e13i) q^{62} +(4.94353e12 + 1.81152e12i) q^{63} +(-8.71197e12 - 3.40887e13i) q^{64} -5.11011e13i q^{65} +(-2.44160e13 + 3.16212e13i) q^{66} -7.60288e13i q^{67} +(3.35143e13 + 4.82590e13i) q^{68} +(5.98950e13 - 4.18417e13i) q^{69} +(1.21894e13 - 3.81744e12i) q^{70} -6.50083e13 q^{71} +(4.51571e13 + 7.21456e13i) q^{72} -1.24297e14 q^{73} +(-1.31118e14 + 4.10630e13i) q^{74} +(-2.00741e13 + 1.40234e13i) q^{75} +(8.89314e13 + 1.28057e14i) q^{76} +2.13780e13i q^{77} +(1.11358e14 - 1.44220e14i) q^{78} -5.22032e13i q^{79} +(1.93484e14 + 7.21199e13i) q^{80} +(-1.57143e14 - 1.33031e14i) q^{81} +(-6.24524e13 - 1.99416e14i) q^{82} +3.24461e14 q^{83} +(4.27204e13 + 1.57890e13i) q^{84} -3.44817e14 q^{85} +(1.03702e14 + 3.31130e14i) q^{86} +(2.53044e14 + 3.62225e14i) q^{87} +(-2.11968e14 + 2.72952e14i) q^{88} -1.32252e14i q^{89} +(-4.98935e14 - 2.38397e13i) q^{90} -9.75020e13i q^{91} +(5.19122e14 - 3.60513e14i) q^{92} +(3.67104e14 + 5.25497e14i) q^{93} +(2.33571e14 - 7.31490e13i) q^{94} -9.14987e14 q^{95} +(3.88899e14 + 6.25175e14i) q^{96} +8.29770e14 q^{97} +(-7.96865e14 + 2.49560e14i) q^{98} +(2.87641e14 - 7.84958e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9}+O(q^{10}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9	\( 28 q + 26968 q^{4} + 823656 q^{6} - 3812052 q^{9} - 43831600 q^{10} - 226414248 q^{12} + 124527272 q^{13} - 1459325408 q^{16} - 4234777584 q^{18} - 7261350648 q^{21} - 2533670160 q^{22} - 18487781856 q^{24} - 146804950740 q^{25} + 5481093840 q^{28} + 8237058960 q^{30} + 204574669728 q^{33} + 450165745472 q^{34} + 232631927160 q^{36} + 386069193224 q^{37} + 1945471012160 q^{40} + 1938106219632 q^{42} - 5007113912640 q^{45} + 2270790222432 q^{46} + 5846474725152 q^{48} - 18480860963084 q^{49} - 6113229405424 q^{52} + 1626598700568 q^{54} + 8085872464056 q^{57} - 19395437098192 q^{58} - 10924219377600 q^{60} - 16392792556696 q^{61} + 21633892829056 q^{64} + 4928819126448 q^{66} + 137029869973056 q^{69} + 91772543171040 q^{70} + 66924493142592 q^{72} + 158451626683736 q^{73} - 205265768291280 q^{76} + 58364283489648 q^{78} + 116126816635836 q^{81} - 750029796726880 q^{82} - 92605433207856 q^{84} - 30099357052160 q^{85} - 619691835246912 q^{88} - 471443548913520 q^{90} - 777661615138584 q^{93} + 13\!\cdots\!00 q^{94}+ \cdots - 824166397720648 q^{97}+O(q^{100}) \) 28 * q + 26968 * q^4 + 823656 * q^6 - 3812052 * q^9 - 43831600 * q^10 - 226414248 * q^12 + 124527272 * q^13 - 1459325408 * q^16 - 4234777584 * q^18 - 7261350648 * q^21 - 2533670160 * q^22 - 18487781856 * q^24 - 146804950740 * q^25 + 5481093840 * q^28 + 8237058960 * q^30 + 204574669728 * q^33 + 450165745472 * q^34 + 232631927160 * q^36 + 386069193224 * q^37 + 1945471012160 * q^40 + 1938106219632 * q^42 - 5007113912640 * q^45 + 2270790222432 * q^46 + 5846474725152 * q^48 - 18480860963084 * q^49 - 6113229405424 * q^52 + 1626598700568 * q^54 + 8085872464056 * q^57 - 19395437098192 * q^58 - 10924219377600 * q^60 - 16392792556696 * q^61 + 21633892829056 * q^64 + 4928819126448 * q^66 + 137029869973056 * q^69 + 91772543171040 * q^70 + 66924493142592 * q^72 + 158451626683736 * q^73 - 205265768291280 * q^76 + 58364283489648 * q^78 + 116126816635836 * q^81 - 750029796726880 * q^82 - 92605433207856 * q^84 - 30099357052160 * q^85 - 619691835246912 * q^88 - 471443548913520 * q^90 - 777661615138584 * q^93 + 1301107064491200 * q^94 + 525428335287168 * q^96 - 824166397720648 * q^97

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