LMFDB - Embedded newform 17.12.c.a.13.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.13
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+58.2592i q^{2} +(-297.283 - 297.283i) q^{3} -1346.14 q^{4} +(8591.36 + 8591.36i) q^{5} +(17319.5 - 17319.5i) q^{6} +(-6474.40 + 6474.40i) q^{7} +40889.9i q^{8} -393.067i q^{9} +O(q^{10})$	\(q+58.2592i q^{2} +(-297.283 - 297.283i) q^{3} -1346.14 q^{4} +(8591.36 + 8591.36i) q^{5} +(17319.5 - 17319.5i) q^{6} +(-6474.40 + 6474.40i) q^{7} +40889.9i q^{8} -393.067i q^{9} +(-500526. + 500526. i) q^{10} +(-338079. + 338079. i) q^{11} +(400184. + 400184. i) q^{12} +89079.5 q^{13} +(-377194. - 377194. i) q^{14} -5.10813e6i q^{15} -5.13911e6 q^{16} +(-3.96894e6 - 4.30342e6i) q^{17} +22899.8 q^{18} +9.31254e6i q^{19} +(-1.15652e7 - 1.15652e7i) q^{20} +3.84945e6 q^{21} +(-1.96962e7 - 1.96962e7i) q^{22} +(-2.02749e7 + 2.02749e7i) q^{23} +(1.21558e7 - 1.21558e7i) q^{24} +9.87949e7i q^{25} +5.18970e6i q^{26} +(-5.27796e7 + 5.27796e7i) q^{27} +(8.71545e6 - 8.71545e6i) q^{28} +(-8.86253e7 - 8.86253e7i) q^{29} +2.97596e8 q^{30} +(1.59001e7 + 1.59001e7i) q^{31} -2.15658e8i q^{32} +2.01010e8 q^{33} +(2.50714e8 - 2.31227e8i) q^{34} -1.11248e8 q^{35} +529123. i q^{36} +(4.54105e8 + 4.54105e8i) q^{37} -5.42541e8 q^{38} +(-2.64818e7 - 2.64818e7i) q^{39} +(-3.51300e8 + 3.51300e8i) q^{40} +(3.12434e8 - 3.12434e8i) q^{41} +2.24266e8i q^{42} +3.68446e8i q^{43} +(4.55101e8 - 4.55101e8i) q^{44} +(3.37698e6 - 3.37698e6i) q^{45} +(-1.18120e9 - 1.18120e9i) q^{46} +1.29364e9 q^{47} +(1.52777e9 + 1.52777e9i) q^{48} +1.89349e9i q^{49} -5.75572e9 q^{50} +(-9.94369e7 + 2.45923e9i) q^{51} -1.19913e8 q^{52} -5.26505e9i q^{53} +(-3.07490e9 - 3.07490e9i) q^{54} -5.80912e9 q^{55} +(-2.64737e8 - 2.64737e8i) q^{56} +(2.76846e9 - 2.76846e9i) q^{57} +(5.16324e9 - 5.16324e9i) q^{58} +7.45256e9i q^{59} +6.87625e9i q^{60} +(9.07407e9 - 9.07407e9i) q^{61} +(-9.26328e8 + 9.26328e8i) q^{62} +(2.54487e6 + 2.54487e6i) q^{63} +2.03918e9 q^{64} +(7.65314e8 + 7.65314e8i) q^{65} +1.17107e10i q^{66} -7.43714e9 q^{67} +(5.34274e9 + 5.79301e9i) q^{68} +1.20547e10 q^{69} -6.48122e9i q^{70} +(6.64487e8 + 6.64487e8i) q^{71} +1.60725e7 q^{72} +(1.61191e10 + 1.61191e10i) q^{73} +(-2.64558e10 + 2.64558e10i) q^{74} +(2.93700e10 - 2.93700e10i) q^{75} -1.25360e10i q^{76} -4.37772e9i q^{77} +(1.54281e9 - 1.54281e9i) q^{78} +(-2.22991e10 + 2.22991e10i) q^{79} +(-4.41519e10 - 4.41519e10i) q^{80} +3.13113e10 q^{81} +(1.82022e10 + 1.82022e10i) q^{82} -1.70274e10i q^{83} -5.18190e9 q^{84} +(2.87369e9 - 7.10708e10i) q^{85} -2.14654e10 q^{86} +5.26935e10i q^{87} +(-1.38240e10 - 1.38240e10i) q^{88} -4.19525e10 q^{89} +(1.96740e8 + 1.96740e8i) q^{90} +(-5.76736e8 + 5.76736e8i) q^{91} +(2.72928e10 - 2.72928e10i) q^{92} -9.45365e9i q^{93} +7.53665e10i q^{94} +(-8.00074e10 + 8.00074e10i) q^{95} +(-6.41114e10 + 6.41114e10i) q^{96} +(7.05559e10 + 7.05559e10i) q^{97} -1.10313e11 q^{98} +(1.32888e8 + 1.32888e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) $ 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7} + 178138 q^{10} - 24816 q^{11} + 1322202 q^{12} - 1533752 q^{13} - 757692 q^{14} + 22082308 q^{16} + 17346416 q^{17} + 16775420 q^{18} + 11716134 q^{20} + 16504072 q^{21} + 55362010 q^{22} - 70945120 q^{23} - 7042078 q^{24} - 27445824 q^{27} + 339432756 q^{28} + 185239264 q^{29} - 1261021320 q^{30} + 415468304 q^{31} - 1075445880 q^{33} + 969384454 q^{34} - 1094449168 q^{35} - 49028824 q^{37} - 1340995872 q^{38} + 3217138400 q^{39} + 1182717098 q^{40} - 1419194816 q^{41} - 509236610 q^{44} + 1839923056 q^{45} - 3796371488 q^{46} - 8774740352 q^{47} + 4059548014 q^{48} + 4114666548 q^{50} - 9057963232 q^{51} + 18756164724 q^{52} + 25648728424 q^{54} - 17548144256 q^{55} + 966113388 q^{56} + 23148052104 q^{57} + 32800009486 q^{58} + 1217387240 q^{61} - 42857202380 q^{62} - 58090649872 q^{63} - 43481694148 q^{64} - 12772720712 q^{65} + 17181896368 q^{67} - 120669329406 q^{68} + 84389704104 q^{69} + 36350065824 q^{71} - 62012005860 q^{72} + 41295758480 q^{73} + 108372466886 q^{74} + 143581200752 q^{75} + 103160490932 q^{78} - 86305741264 q^{79} - 278909687742 q^{80} - 398139885080 q^{81} + 84221472400 q^{82} + 278009687832 q^{84} - 131899000528 q^{85} + 214354160644 q^{86} + 95628137594 q^{88} - 158760835496 q^{89} + 629605313178 q^{90} + 149211106624 q^{91} + 288480507416 q^{92} - 267919909216 q^{95} - 242746850002 q^{96} - 126853433800 q^{97} - 829249376752 q^{98} + 229465269792 q^{99}+O(q^{100}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7 + 178138 * q^10 - 24816 * q^11 + 1322202 * q^12 - 1533752 * q^13 - 757692 * q^14 + 22082308 * q^16 + 17346416 * q^17 + 16775420 * q^18 + 11716134 * q^20 + 16504072 * q^21 + 55362010 * q^22 - 70945120 * q^23 - 7042078 * q^24 - 27445824 * q^27 + 339432756 * q^28 + 185239264 * q^29 - 1261021320 * q^30 + 415468304 * q^31 - 1075445880 * q^33 + 969384454 * q^34 - 1094449168 * q^35 - 49028824 * q^37 - 1340995872 * q^38 + 3217138400 * q^39 + 1182717098 * q^40 - 1419194816 * q^41 - 509236610 * q^44 + 1839923056 * q^45 - 3796371488 * q^46 - 8774740352 * q^47 + 4059548014 * q^48 + 4114666548 * q^50 - 9057963232 * q^51 + 18756164724 * q^52 + 25648728424 * q^54 - 17548144256 * q^55 + 966113388 * q^56 + 23148052104 * q^57 + 32800009486 * q^58 + 1217387240 * q^61 - 42857202380 * q^62 - 58090649872 * q^63 - 43481694148 * q^64 - 12772720712 * q^65 + 17181896368 * q^67 - 120669329406 * q^68 + 84389704104 * q^69 + 36350065824 * q^71 - 62012005860 * q^72 + 41295758480 * q^73 + 108372466886 * q^74 + 143581200752 * q^75 + 103160490932 * q^78 - 86305741264 * q^79 - 278909687742 * q^80 - 398139885080 * q^81 + 84221472400 * q^82 + 278009687832 * q^84 - 131899000528 * q^85 + 214354160644 * q^86 + 95628137594 * q^88 - 158760835496 * q^89 + 629605313178 * q^90 + 149211106624 * q^91 + 288480507416 * q^92 - 267919909216 * q^95 - 242746850002 * q^96 - 126853433800 * q^97 - 829249376752 * q^98 + 229465269792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			58.2592i			1.28736i	0.765295	+	0.643680i	$0.222593\pi$
$2$			58.2592i			1.28736i	−0.765295	+	0.643680i	$0.777407\pi$
$3$	−297.283	−	297.283i	−0.706322	−	0.706322i	0.259438	−	0.965760i	$-0.416463\pi$
$3$	−297.283	−	297.283i	−0.706322	−	0.706322i	−0.965760	+	0.259438i	$0.916463\pi$
$4$	−1346.14			−0.657295
$5$	8591.36	+	8591.36i	1.22950	+	1.22950i	0.964155	+	0.265341i	$0.0854847\pi$
$5$	8591.36	+	8591.36i	1.22950	+	1.22950i	0.265341	+	0.964155i	$0.414515\pi$
$6$	17319.5	−	17319.5i	0.909290	−	0.909290i
$7$	−6474.40	+	6474.40i	−0.145600	+	0.145600i	−0.776149	−	0.630549i	$-0.782830\pi$
$7$	−6474.40	+	6474.40i	−0.145600	+	0.145600i	0.630549	+	0.776149i	$0.282830\pi$
$8$			40889.9i			0.441185i
$9$		−	393.067i		−	0.00221888i
$10$	−500526.	+	500526.i	−1.58280	+	1.58280i
$11$	−338079.	+	338079.i	−0.632934	+	0.632934i	−0.948803	−	0.315869i	$-0.897704\pi$
$11$	−338079.	+	338079.i	−0.632934	+	0.632934i	0.315869	+	0.948803i	$0.397704\pi$
$12$	400184.	+	400184.i	0.464262	+	0.464262i
$13$	89079.5			0.0665410			0.0332705	−	0.999446i	$-0.489408\pi$
$13$	89079.5			0.0665410			0.0332705	+	0.999446i	$0.489408\pi$
$14$	−377194.	−	377194.i	−0.187439	−	0.187439i
$15$		−	5.10813e6i		−	1.73684i
$16$	−5.13911e6			−1.22526
$17$	−3.96894e6	−	4.30342e6i	−0.677962	−	0.735097i
$17$	−3.96894e6	−	4.30342e6i	−0.677962	−	0.735097i
$18$	22899.8			0.00285649
$19$			9.31254e6i			0.862826i	0.902155	+	0.431413i	$0.141985\pi$
$19$			9.31254e6i			0.862826i	−0.902155	+	0.431413i	$0.858015\pi$
$20$	−1.15652e7	−	1.15652e7i	−0.808141	−	0.808141i
$21$	3.84945e6			0.205680
$22$	−1.96962e7	−	1.96962e7i	−0.814813	−	0.814813i
$23$	−2.02749e7	+	2.02749e7i	−0.656833	+	0.656833i	−0.954629	−	0.297796i	$-0.903748\pi$
$23$	−2.02749e7	+	2.02749e7i	−0.656833	+	0.656833i	0.297796	+	0.954629i	$0.403748\pi$
$24$	1.21558e7	−	1.21558e7i	0.311619	−	0.311619i
$25$			9.87949e7i			2.02332i
$26$			5.18970e6i			0.0856622i
$27$	−5.27796e7	+	5.27796e7i	−0.707889	+	0.707889i
$28$	8.71545e6	−	8.71545e6i	0.0957019	−	0.0957019i
$29$	−8.86253e7	−	8.86253e7i	−0.802359	−	0.802359i	0.181105	−	0.983464i	$-0.442033\pi$
$29$	−8.86253e7	−	8.86253e7i	−0.802359	−	0.802359i	−0.983464	+	0.181105i	$0.942033\pi$
$30$	2.97596e8			2.23594
$31$	1.59001e7	+	1.59001e7i	0.0997495	+	0.0997495i	0.755220	−	0.655471i	$-0.227530\pi$
$31$	1.59001e7	+	1.59001e7i	0.0997495	+	0.0997495i	−0.655471	+	0.755220i	$0.727530\pi$
$32$		−	2.15658e8i		−	1.13616i
$33$	2.01010e8			0.894110
$34$	2.50714e8	−	2.31227e8i	0.946335	−	0.872780i
$35$	−1.11248e8			−0.358028
$36$			529123.i			0.00145846i
$37$	4.54105e8	+	4.54105e8i	1.07658	+	1.07658i	0.996814	+	0.0797671i	$0.0254177\pi$
$37$	4.54105e8	+	4.54105e8i	1.07658	+	1.07658i	0.0797671	+	0.996814i	$0.474582\pi$
$38$	−5.42541e8			−1.11077
$39$	−2.64818e7	−	2.64818e7i	−0.0469994	−	0.0469994i
$40$	−3.51300e8	+	3.51300e8i	−0.542435	+	0.542435i
$41$	3.12434e8	−	3.12434e8i	0.421160	−	0.421160i	−0.464443	−	0.885603i	$-0.653745\pi$
$41$	3.12434e8	−	3.12434e8i	0.421160	−	0.421160i	0.885603	+	0.464443i	$0.153745\pi$
$42$			2.24266e8i			0.264785i
$43$			3.68446e8i			0.382206i	0.981570	+	0.191103i	$0.0612064\pi$
$43$			3.68446e8i			0.382206i	−0.981570	+	0.191103i	$0.938794\pi$
$44$	4.55101e8	−	4.55101e8i	0.416024	−	0.416024i
$45$	3.37698e6	−	3.37698e6i	0.00272810	−	0.00272810i
$46$	−1.18120e9	−	1.18120e9i	−0.845580	−	0.845580i
$47$	1.29364e9			0.822764			0.411382	−	0.911463i	$-0.365046\pi$
$47$	1.29364e9			0.822764			0.411382	+	0.911463i	$0.365046\pi$
$48$	1.52777e9	+	1.52777e9i	0.865427	+	0.865427i
$49$			1.89349e9i			0.957601i
$50$	−5.75572e9			−2.60474
$51$	−9.94369e7	+	2.45923e9i	−0.0403563	+	0.998074i
$52$	−1.19913e8			−0.0437370
$53$		−	5.26505e9i		−	1.72936i	−0.502323	−	0.864680i	$-0.667521\pi$
$53$		−	5.26505e9i		−	1.72936i	0.502323	−	0.864680i	$-0.332479\pi$
$54$	−3.07490e9	−	3.07490e9i	−0.911308	−	0.911308i
$55$	−5.80912e9			−1.55638
$56$	−2.64737e8	−	2.64737e8i	−0.0642364	−	0.0642364i
$57$	2.76846e9	−	2.76846e9i	0.609433	−	0.609433i
$58$	5.16324e9	−	5.16324e9i	1.03292	−	1.03292i
$59$			7.45256e9i			1.35712i	0.734543	+	0.678562i	$0.237397\pi$
$59$			7.45256e9i			1.35712i	−0.734543	+	0.678562i	$0.762603\pi$
$60$			6.87625e9i			1.14162i
$61$	9.07407e9	−	9.07407e9i	1.37559	−	1.37559i	0.523658	−	0.851929i	$-0.324567\pi$
$61$	9.07407e9	−	9.07407e9i	1.37559	−	1.37559i	0.851929	−	0.523658i	$-0.175433\pi$
$62$	−9.26328e8	+	9.26328e8i	−0.128413	+	0.128413i
$63$	2.54487e6	+	2.54487e6i	0.000323068	+	0.000323068i
$64$	2.03918e9			0.237392
$65$	7.65314e8	+	7.65314e8i	0.0818119	+	0.0818119i
$66$			1.17107e10i			1.15104i
$67$	−7.43714e9			−0.672968			−0.336484	−	0.941689i	$-0.609238\pi$
$67$	−7.43714e9			−0.672968			−0.336484	+	0.941689i	$0.609238\pi$
$68$	5.34274e9	+	5.79301e9i	0.445621	+	0.483176i
$69$	1.20547e10			0.927871
$70$		−	6.48122e9i		−	0.460911i
$71$	6.64487e8	+	6.64487e8i	0.0437084	+	0.0437084i	0.728623	−	0.684915i	$-0.240161\pi$
$71$	6.64487e8	+	6.64487e8i	0.0437084	+	0.0437084i	−0.684915	+	0.728623i	$0.740161\pi$
$72$	1.60725e7			0.000978934
$73$	1.61191e10	+	1.61191e10i	0.910050	+	0.910050i	0.996276	−	0.0862259i	$-0.0274807\pi$
$73$	1.61191e10	+	1.61191e10i	0.910050	+	0.910050i	−0.0862259	+	0.996276i	$0.527481\pi$
$74$	−2.64558e10	+	2.64558e10i	−1.38595	+	1.38595i
$75$	2.93700e10	−	2.93700e10i	1.42912	−	1.42912i
$76$		−	1.25360e10i		−	0.567131i
$77$		−	4.37772e9i		−	0.184310i
$78$	1.54281e9	−	1.54281e9i	0.0605051	−	0.0605051i
$79$	−2.22991e10	+	2.22991e10i	−0.815339	+	0.815339i	−0.985429	−	0.170089i	$-0.945594\pi$
$79$	−2.22991e10	+	2.22991e10i	−0.815339	+	0.815339i	0.170089	+	0.985429i	$0.445594\pi$
$80$	−4.41519e10	−	4.41519e10i	−1.50645	−	1.50645i
$81$	3.13113e10			0.997776
$82$	1.82022e10	+	1.82022e10i	0.542184	+	0.542184i
$83$		−	1.70274e10i		−	0.474482i	−0.971451	−	0.237241i	$-0.923757\pi$
$83$		−	1.70274e10i		−	0.474482i	0.971451	−	0.237241i	$-0.0762431\pi$
$84$	−5.18190e9			−0.135193
$85$	2.87369e9	−	7.10708e10i	0.0702483	−	1.73735i
$86$	−2.14654e10			−0.492036
$87$			5.26935e10i			1.13345i
$88$	−1.38240e10	−	1.38240e10i	−0.279241	−	0.279241i
$89$	−4.19525e10			−0.796366			−0.398183	−	0.917306i	$-0.630359\pi$
$89$	−4.19525e10			−0.796366			−0.398183	+	0.917306i	$0.630359\pi$
$90$	1.96740e8	+	1.96740e8i	0.00351204	+	0.00351204i
$91$	−5.76736e8	+	5.76736e8i	−0.00968835	+	0.00968835i
$92$	2.72928e10	−	2.72928e10i	0.431733	−	0.431733i
$93$		−	9.45365e9i		−	0.140911i
$94$			7.53665e10i			1.05919i
$95$	−8.00074e10	+	8.00074e10i	−1.06084	+	1.06084i
$96$	−6.41114e10	+	6.41114e10i	−0.802497	+	0.802497i
$97$	7.05559e10	+	7.05559e10i	0.834235	+	0.834235i	0.988093	−	0.153858i	$-0.0491697\pi$
$97$	7.05559e10	+	7.05559e10i	0.834235	+	0.834235i	−0.153858	+	0.988093i	$0.549170\pi$
$98$	−1.10313e11			−1.23278
$99$	1.32888e8	+	1.32888e8i	0.00140440	+	0.00140440i
$100$		−	1.32992e11i		−	1.32992i
$101$	−2.41188e10			−0.228343			−0.114172	−	0.993461i	$-0.536421\pi$
$101$	−2.41188e10			−0.228343			−0.114172	+	0.993461i	$0.536421\pi$
$102$	−1.43273e11	−	5.79312e9i	−1.28488	−	0.0519531i
$103$	1.87089e11			1.59017			0.795083	−	0.606500i	$-0.207427\pi$
$103$	1.87089e11			1.59017			0.795083	+	0.606500i	$0.207427\pi$
$104$			3.64245e9i			0.0293569i
$105$	3.30721e10	+	3.30721e10i	0.252883	+	0.252883i
$106$	3.06738e11			2.22631
$107$	1.22405e11	+	1.22405e11i	0.843700	+	0.843700i	0.989338	−	0.145638i	$-0.0465234\pi$
$107$	1.22405e11	+	1.22405e11i	0.843700	+	0.843700i	−0.145638	+	0.989338i	$0.546523\pi$
$108$	7.10487e10	−	7.10487e10i	0.465292	−	0.465292i
$109$	4.23826e10	−	4.23826e10i	0.263841	−	0.263841i	−0.562772	−	0.826612i	$-0.690265\pi$
$109$	4.23826e10	−	4.23826e10i	0.263841	−	0.263841i	0.826612	+	0.562772i	$0.190265\pi$
$110$		−	3.38435e11i		−	2.00362i
$111$		−	2.69995e11i		−	1.52082i
$112$	3.32726e10	−	3.32726e10i	0.178397	−	0.178397i
$113$	−2.63530e10	+	2.63530e10i	−0.134554	+	0.134554i	−0.771176	−	0.636622i	$-0.780331\pi$
$113$	−2.63530e10	+	2.63530e10i	−0.134554	+	0.134554i	0.636622	+	0.771176i	$0.280331\pi$
$114$	1.61288e11	+	1.61288e11i	0.784559	+	0.784559i
$115$	−3.48378e11			−1.61515
$116$	1.19302e11	+	1.19302e11i	0.527387	+	0.527387i
$117$		−	3.50142e7i		−	0.000147646i
$118$	−4.34181e11			−1.74711
$119$	5.35586e10	+	2.16560e9i	0.205741	+	0.00831896i
$120$	2.08871e11			0.766267
$121$			5.67171e10i			0.198790i
$122$	5.28648e11	+	5.28648e11i	1.77087	+	1.77087i
$123$	−1.85762e11			−0.594949
$124$	−2.14038e10	−	2.14038e10i	−0.0655648	−	0.0655648i
$125$	−4.29283e11	+	4.29283e11i	−1.25817	+	1.25817i
$126$	−1.48262e8	+	1.48262e8i	−0.000415904	+	0.000415904i
$127$		−	2.04514e11i		−	0.549291i	−0.961546	−	0.274645i	$-0.911440\pi$
$127$		−	2.04514e11i		−	0.549291i	0.961546	−	0.274645i	$-0.0885604\pi$
$128$		−	3.22866e11i		−	0.830554i
$129$	1.09533e11	−	1.09533e11i	0.269960	−	0.269960i
$130$	−4.45866e10	+	4.45866e10i	−0.105321	+	0.105321i
$131$	3.44627e11	+	3.44627e11i	0.780471	+	0.780471i	0.979910	−	0.199439i	$-0.0639120\pi$
$131$	3.44627e11	+	3.44627e11i	0.780471	+	0.780471i	−0.199439	+	0.979910i	$0.563912\pi$
$132$	−2.70587e11			−0.587694
$133$	−6.02931e10	−	6.02931e10i	−0.125627	−	0.125627i
$134$		−	4.33282e11i		−	0.866352i
$135$	−9.06897e11			−1.74069
$136$	1.75966e11	−	1.62289e11i	0.324314	−	0.299106i
$137$	−6.65632e10			−0.117834			−0.0589171	−	0.998263i	$-0.518765\pi$
$137$	−6.65632e10			−0.117834			−0.0589171	+	0.998263i	$0.518765\pi$
$138$			7.02300e11i			1.19450i
$139$	−4.10154e11	−	4.10154e11i	−0.670449	−	0.670449i	0.287371	−	0.957819i	$-0.407219\pi$
$139$	−4.10154e11	−	4.10154e11i	−0.670449	−	0.670449i	−0.957819	+	0.287371i	$0.907219\pi$
$140$	1.49755e11			0.235330
$141$	−3.84577e11	−	3.84577e11i	−0.581136	−	0.581136i
$142$	−3.87125e10	+	3.87125e10i	−0.0562685	+	0.0562685i
$143$	−3.01159e10	+	3.01159e10i	−0.0421160	+	0.0421160i
$144$			2.02001e9i			0.00271870i
$145$		−	1.52282e12i		−	1.97300i
$146$	−9.39087e11	+	9.39087e11i	−1.17156	+	1.17156i
$147$	5.62902e11	−	5.62902e11i	0.676375	−	0.676375i
$148$	−6.11288e11	−	6.11288e11i	−0.707631	−	0.707631i
$149$	1.47499e12			1.64538			0.822688	−	0.568493i	$-0.192473\pi$
$149$	1.47499e12			1.64538			0.822688	+	0.568493i	$0.192473\pi$
$150$	1.71108e12	+	1.71108e12i	1.83979	+	1.83979i
$151$		−	6.22234e10i		−	0.0645031i	−0.999480	−	0.0322516i	$-0.989732\pi$
$151$		−	6.22234e10i		−	0.0645031i	0.999480	−	0.0322516i	$-0.0102678\pi$
$152$	−3.80788e11			−0.380666
$153$	−1.69153e9	+	1.56006e9i	−0.00163109	+	0.00150431i
$154$	2.55042e11			0.237273
$155$			2.73207e11i			0.245283i
$156$	3.56482e10	+	3.56482e10i	0.0308924	+	0.0308924i
$157$	−9.88976e8			−0.000827442			−0.000413721	−	1.00000i	$-0.500132\pi$
$157$	−9.88976e8			−0.000827442			−0.000413721		1.00000i	$0.500132\pi$
$158$	−1.29913e12	−	1.29913e12i	−1.04963	−	1.04963i
$159$	−1.56521e12	+	1.56521e12i	−1.22148	+	1.22148i
$160$	1.85280e12	−	1.85280e12i	1.39691	−	1.39691i
$161$		−	2.62535e11i		−	0.191269i
$162$			1.82417e12i			1.28450i
$163$	3.76686e10	−	3.76686e10i	0.0256418	−	0.0256418i	−0.694170	−	0.719811i	$-0.744228\pi$
$163$	3.76686e10	−	3.76686e10i	0.0256418	−	0.0256418i	0.719811	+	0.694170i	$0.244228\pi$
$164$	−4.20580e11	+	4.20580e11i	−0.276826	+	0.276826i
$165$	1.72695e12	+	1.72695e12i	1.09930	+	1.09930i
$166$	9.92006e11			0.610829
$167$	1.81854e12	+	1.81854e12i	1.08338	+	1.08338i	0.996192	+	0.0871888i	$0.0277884\pi$
$167$	1.81854e12	+	1.81854e12i	1.08338	+	1.08338i	0.0871888	+	0.996192i	$0.472212\pi$
$168$			1.57404e11i			0.0907431i
$169$	−1.78423e12			−0.995572
$170$	4.14053e12	+	1.67419e11i	2.23659	+	0.0904349i
$171$	3.66045e9			0.00191450
$172$		−	4.95980e11i		−	0.251222i
$173$	−8.95569e11	−	8.95569e11i	−0.439385	−	0.439385i	0.452420	−	0.891805i	$-0.350561\pi$
$173$	−8.95569e11	−	8.95569e11i	−0.439385	−	0.439385i	−0.891805	+	0.452420i	$0.850561\pi$
$174$	−3.06989e12			−1.45915
$175$	−6.39638e11	−	6.39638e11i	−0.294595	−	0.294595i
$176$	1.73742e12	−	1.73742e12i	0.775507	−	0.775507i
$177$	2.21552e12	−	2.21552e12i	0.958567	−	0.958567i
$178$		−	2.44412e12i		−	1.02521i
$179$		−	3.25422e12i		−	1.32360i	−0.749683	−	0.661798i	$-0.769794\pi$
$179$		−	3.25422e12i		−	1.32360i	0.749683	−	0.661798i	$-0.230206\pi$
$180$	−4.54589e9	+	4.54589e9i	−0.00179316	+	0.00179316i
$181$	−3.56680e12	+	3.56680e12i	−1.36473	+	1.36473i	−0.496954	+	0.867777i	$0.665548\pi$
$181$	−3.56680e12	+	3.56680e12i	−1.36473	+	1.36473i	−0.867777	+	0.496954i	$0.834452\pi$
$182$	−3.36002e10	−	3.36002e10i	−0.0124724	−	0.0124724i
$183$	−5.39513e12			−1.94321
$184$	−8.29037e11	−	8.29037e11i	−0.289785	−	0.289785i
$185$			7.80276e12i			2.64730i
$186$	5.50763e11			0.181403
$187$	2.79671e12	+	1.13083e11i	0.894373	+	0.0361632i
$188$	−1.74142e12			−0.540799
$189$		−	6.83432e11i		−	0.206137i
$190$	−4.66117e12	−	4.66117e12i	−1.36568	−	1.36568i
$191$	3.45514e11			0.0983519			0.0491759	−	0.998790i	$-0.484341\pi$
$191$	3.45514e11			0.0983519			0.0491759	+	0.998790i	$0.484341\pi$
$192$	−6.06214e11	−	6.06214e11i	−0.167675	−	0.167675i
$193$	2.13086e12	−	2.13086e12i	0.572784	−	0.572784i	−0.360122	−	0.932905i	$-0.617265\pi$
$193$	2.13086e12	−	2.13086e12i	0.572784	−	0.572784i	0.932905	+	0.360122i	$0.117265\pi$
$194$	−4.11053e12	+	4.11053e12i	−1.07396	+	1.07396i
$195$		−	4.55029e11i		−	0.115571i
$196$		−	2.54890e12i		−	0.629426i
$197$	2.85169e12	−	2.85169e12i	0.684760	−	0.684760i	−0.276309	−	0.961069i	$-0.589111\pi$
$197$	2.85169e12	−	2.85169e12i	0.684760	−	0.684760i	0.961069	+	0.276309i	$0.0891114\pi$
$198$	−7.74194e9	+	7.74194e9i	−0.00180797	+	0.00180797i
$199$	3.67967e12	+	3.67967e12i	0.835827	+	0.835827i	0.988307	−	0.152479i	$-0.0487258\pi$
$199$	3.67967e12	+	3.67967e12i	0.835827	+	0.835827i	−0.152479	+	0.988307i	$0.548726\pi$
$200$	−4.03971e12			−0.892659
$201$	2.21093e12	+	2.21093e12i	0.475332	+	0.475332i
$202$		−	1.40514e12i		−	0.293960i
$203$	1.14759e12			0.233646
$204$	1.33856e11	−	3.31046e12i	0.0265260	−	0.656029i
$205$	5.36847e12			1.03563
$206$			1.08996e13i			2.04712i
$207$	7.96939e9	+	7.96939e9i	0.00145743	+	0.00145743i
$208$	−4.57789e11			−0.0815299
$209$	−3.14837e12	−	3.14837e12i	−0.546112	−	0.546112i
$210$	−1.92675e12	+	1.92675e12i	−0.325552	+	0.325552i
$211$	3.32748e12	−	3.32748e12i	0.547724	−	0.547724i	−0.378058	−	0.925782i	$-0.623408\pi$
$211$	3.32748e12	−	3.32748e12i	0.547724	−	0.547724i	0.925782	+	0.378058i	$0.123408\pi$
$212$			7.08749e12i			1.13670i
$213$		−	3.95081e11i		−	0.0617445i
$214$	−7.13122e12	+	7.13122e12i	−1.08615	+	1.08615i
$215$	−3.16545e12	+	3.16545e12i	−0.469921	+	0.469921i
$216$	−2.15815e12	−	2.15815e12i	−0.312310	−	0.312310i
$217$	−2.05887e11			−0.0290470
$218$	2.46918e12	+	2.46918e12i	0.339658	+	0.339658i
$219$		−	9.58386e12i		−	1.28558i
$220$	7.81988e12			1.02300
$221$	−3.53551e11	−	3.83347e11i	−0.0451122	−	0.0489141i
$222$	1.57297e13			1.95785
$223$		−	1.28002e13i		−	1.55432i	−0.629303	−	0.777160i	$-0.716660\pi$
$223$		−	1.28002e13i		−	1.55432i	0.629303	−	0.777160i	$-0.283340\pi$
$224$	1.39626e12	+	1.39626e12i	0.165425	+	0.165425i
$225$	3.88331e10			0.00448950
$226$	−1.53530e12	−	1.53530e12i	−0.173220	−	0.173220i
$227$	8.98650e12	−	8.98650e12i	0.989574	−	0.989574i	−0.0103722	−	0.999946i	$-0.503302\pi$
$227$	8.98650e12	−	8.98650e12i	0.989574	−	0.989574i	0.999946	+	0.0103722i	$0.00330163\pi$
$228$	−3.72673e12	+	3.72673e12i	−0.400577	+	0.400577i
$229$			4.45702e12i			0.467680i	0.972275	+	0.233840i	$0.0751292\pi$
$229$			4.45702e12i			0.467680i	−0.972275	+	0.233840i	$0.924871\pi$
$230$		−	2.02962e13i		−	2.07928i
$231$	−1.30142e12	+	1.30142e12i	−0.130182	+	0.130182i
$232$	3.62388e12	−	3.62388e12i	0.353989	−	0.353989i
$233$	−1.97296e12	−	1.97296e12i	−0.188218	−	0.188218i	0.606707	−	0.794925i	$-0.292490\pi$
$233$	−1.97296e12	−	1.97296e12i	−0.188218	−	0.188218i	−0.794925	+	0.606707i	$0.792490\pi$
$234$	2.03990e9			0.000190074
$235$	1.11141e13	+	1.11141e13i	1.01159	+	1.01159i
$236$		−	1.00322e13i		−	0.892031i
$237$	1.32583e13			1.15178
$238$	−1.26166e11	+	3.12028e12i	−0.0107095	+	0.264863i
$239$	−2.08510e13			−1.72957			−0.864786	−	0.502140i	$-0.832546\pi$
$239$	−2.08510e13			−1.72957			−0.864786	+	0.502140i	$0.832546\pi$
$240$			2.62512e13i			2.12808i
$241$	1.16582e13	+	1.16582e13i	0.923714	+	0.923714i	0.997290	−	0.0735753i	$-0.0234409\pi$
$241$	1.16582e13	+	1.16582e13i	0.923714	+	0.923714i	−0.0735753	+	0.997290i	$0.523441\pi$
$242$	−3.30429e12			−0.255914
$243$	4.14459e10	+	4.14459e10i	0.00313796	+	0.00313796i
$244$	−1.22150e13	+	1.22150e13i	−0.904166	+	0.904166i
$245$	−1.62677e13	+	1.62677e13i	−1.17737	+	1.17737i
$246$		−	1.08224e13i		−	0.765913i
$247$			8.29556e11i			0.0574133i
$248$	−6.50153e11	+	6.50153e11i	−0.0440080	+	0.0440080i
$249$	−5.06196e12	+	5.06196e12i	−0.335137	+	0.335137i
$250$	−2.50097e13	−	2.50097e13i	−1.61972	−	1.61972i
$251$	−2.11300e13			−1.33873			−0.669366	−	0.742933i	$-0.733434\pi$
$251$	−2.11300e13			−1.33873			−0.669366	+	0.742933i	$0.733434\pi$
$252$	−3.42576e9	−	3.42576e9i	−0.000212351	−	0.000212351i
$253$		−	1.37090e13i		−	0.831464i
$254$	1.19148e13			0.707134
$255$	−2.19824e13	+	2.02738e13i	−1.27675	+	1.17751i
$256$	2.29862e13			1.30661
$257$		−	1.94360e13i		−	1.08137i	−0.841225	−	0.540685i	$-0.818165\pi$
$257$		−	1.94360e13i		−	1.08137i	0.841225	−	0.540685i	$-0.181835\pi$
$258$	6.38129e12	+	6.38129e12i	0.347536	+	0.347536i
$259$	−5.88011e12			−0.313500
$260$	−1.03022e12	−	1.03022e12i	−0.0537745	−	0.0537745i
$261$	−3.48357e10	+	3.48357e10i	−0.00178034	+	0.00178034i
$262$	−2.00777e13	+	2.00777e13i	−1.00475	+	1.00475i
$263$			2.24378e13i			1.09957i	0.835305	+	0.549787i	$0.185291\pi$
$263$			2.24378e13i			1.09957i	−0.835305	+	0.549787i	$0.814709\pi$
$264$			8.21927e12i			0.394468i
$265$	4.52340e13	−	4.52340e13i	2.12624	−	2.12624i
$266$	3.51263e12	−	3.51263e12i	0.161727	−	0.161727i
$267$	1.24717e13	+	1.24717e13i	0.562491	+	0.562491i
$268$	1.00114e13			0.442338
$269$	−1.02039e13	−	1.02039e13i	−0.441702	−	0.441702i	0.450881	−	0.892584i	$-0.351110\pi$
$269$	−1.02039e13	−	1.02039e13i	−0.441702	−	0.441702i	−0.892584	+	0.450881i	$0.851110\pi$
$270$		−	5.28351e13i		−	2.24090i
$271$	−3.76201e13			−1.56347			−0.781734	−	0.623612i	$-0.785664\pi$
$271$	−3.76201e13			−1.56347			−0.781734	+	0.623612i	$0.785664\pi$
$272$	2.03968e13	+	2.21157e13i	0.830678	+	0.900684i
$273$	3.42907e11			0.0136862
$274$		−	3.87792e12i		−	0.151695i
$275$	−3.34005e13	−	3.34005e13i	−1.28063	−	1.28063i
$276$	−1.62274e13			−0.609885
$277$	2.93061e13	+	2.93061e13i	1.07974	+	1.07974i	0.996532	+	0.0832089i	$0.0265169\pi$
$277$	2.93061e13	+	2.93061e13i	1.07974	+	1.07974i	0.0832089	+	0.996532i	$0.473483\pi$
$278$	2.38953e13	−	2.38953e13i	0.863109	−	0.863109i
$279$	6.24981e9	−	6.24981e9i	0.000221332	−	0.000221332i
$280$		−	4.54891e12i		−	0.157957i
$281$			1.87917e13i			0.639854i	0.947442	+	0.319927i	$0.103658\pi$
$281$			1.87917e13i			0.639854i	−0.947442	+	0.319927i	$0.896342\pi$
$282$	2.24052e13	−	2.24052e13i	0.748132	−	0.748132i
$283$	−3.25149e13	+	3.25149e13i	−1.06477	+	1.06477i	−0.0670209	+	0.997752i	$0.521349\pi$
$283$	−3.25149e13	+	3.25149e13i	−1.06477	+	1.06477i	−0.997752	+	0.0670209i	$0.978651\pi$
$284$	−8.94492e11	−	8.94492e11i	−0.0287293	−	0.0287293i
$285$	4.75696e13			1.49859
$286$	−1.75453e12	−	1.75453e12i	−0.0542185	−	0.0542185i
$287$			4.04565e12i			0.122641i
$288$	−8.47681e10			−0.00252100
$289$	−2.76699e12	+	3.41600e13i	−0.0807364	+	0.996735i
$290$	8.87186e13			2.53995
$291$		−	4.19501e13i		−	1.17848i
$292$	−2.16986e13	−	2.16986e13i	−0.598171	−	0.598171i
$293$	−4.20637e12			−0.113798			−0.0568992	−	0.998380i	$-0.518121\pi$
$293$	−4.20637e12			−0.113798			−0.0568992	+	0.998380i	$0.518121\pi$
$294$	3.27942e13	+	3.27942e13i	0.870738	+	0.870738i
$295$	−6.40277e13	+	6.40277e13i	−1.66858	+	1.66858i
$296$	−1.85683e13	+	1.85683e13i	−0.474971	+	0.474971i
$297$		−	3.56873e13i		−	0.896094i
$298$			8.59319e13i			2.11819i
$299$	−1.80608e12	+	1.80608e12i	−0.0437063	+	0.0437063i
$300$	−3.95362e13	+	3.95362e13i	−0.939350	+	0.939350i
$301$	−2.38547e12	−	2.38547e12i	−0.0556490	−	0.0556490i
$302$	3.62509e12			0.0830387
$303$	7.17010e12	+	7.17010e12i	0.161284	+	0.161284i
$304$		−	4.78581e13i		−	1.05718i
$305$	1.55917e14			3.38256
$306$	−9.08878e10	−	9.85475e10i	−0.00193659	−	0.00209980i
$307$	−6.95102e12			−0.145475			−0.0727374	−	0.997351i	$-0.523173\pi$
$307$	−6.95102e12			−0.145475			−0.0727374	+	0.997351i	$0.523173\pi$
$308$			5.89302e12i			0.121146i
$309$	−5.56182e13	−	5.56182e13i	−1.12317	−	1.12317i
$310$	−1.59168e13			−0.315768
$311$	−5.21823e13	−	5.21823e13i	−1.01705	−	1.01705i	−0.999852	−	0.0171941i	$-0.994527\pi$
$311$	−5.21823e13	−	5.21823e13i	−1.01705	−	1.01705i	−0.0171941	−	0.999852i	$-0.505473\pi$
$312$	1.08284e12	−	1.08284e12i	0.0207354	−	0.0207354i
$313$	−1.46429e13	+	1.46429e13i	−0.275507	+	0.275507i	−0.831312	−	0.555806i	$-0.812410\pi$
$313$	−1.46429e13	+	1.46429e13i	−0.275507	+	0.275507i	0.555806	+	0.831312i	$0.312410\pi$
$314$		−	5.76170e10i		−	0.00106522i
$315$			4.37279e10i			0.000794421i
$316$	3.00177e13	−	3.00177e13i	0.535918	−	0.535918i
$317$	−1.90235e13	+	1.90235e13i	−0.333783	+	0.333783i	−0.854021	−	0.520238i	$-0.825843\pi$
$317$	−1.90235e13	+	1.90235e13i	−0.333783	+	0.333783i	0.520238	+	0.854021i	$0.325843\pi$
$318$	−9.11879e13	−	9.11879e13i	−1.57249	−	1.57249i
$319$	5.99247e13			1.01568
$320$	1.75194e13	+	1.75194e13i	0.291873	+	0.291873i
$321$		−	7.27777e13i		−	1.19185i
$322$	1.52951e13			0.246232
$323$	4.00758e13	−	3.69609e13i	0.634261	−	0.584963i
$324$	−4.21493e13			−0.655833
$325$			8.80060e12i			0.134634i
$326$	2.19455e12	+	2.19455e12i	0.0330102	+	0.0330102i
$327$	−2.51992e13			−0.372713
$328$	1.27754e13	+	1.27754e13i	0.185809	+	0.185809i
$329$	−8.37555e12	+	8.37555e12i	−0.119794	+	0.119794i
$330$	−1.00611e14	+	1.00611e14i	−1.41520	+	1.41520i
$331$		−	8.42717e10i		−	0.00116581i	−1.00000		0.000582905i	$-0.999814\pi$
$331$		−	8.42717e10i		−	0.00116581i	1.00000		0.000582905i	$-0.000185545\pi$
$332$			2.29213e13i			0.311875i
$333$	1.78494e11	−	1.78494e11i	0.00238880	−	0.00238880i
$334$	−1.05946e14	+	1.05946e14i	−1.39470	+	1.39470i
$335$	−6.38952e13	−	6.38952e13i	−0.827412	−	0.827412i
$336$	−1.97828e13			−0.252012
$337$	1.91757e12	+	1.91757e12i	0.0240318	+	0.0240318i	0.719021	−	0.694989i	$-0.244591\pi$
$337$	1.91757e12	+	1.91757e12i	0.0240318	+	0.0240318i	−0.694989	+	0.719021i	$0.744591\pi$
$338$		−	1.03948e14i		−	1.28166i
$339$	1.56685e13			0.190077
$340$	−3.86839e12	+	9.56713e13i	−0.0461739	+	1.14195i
$341$	−1.07510e13			−0.126270
$342$			2.13255e11i			0.00246465i
$343$	−2.50612e13	−	2.50612e13i	−0.285026	−	0.285026i
$344$	−1.50657e13			−0.168623
$345$	1.03567e14	+	1.03567e14i	1.14081	+	1.14081i
$346$	5.21752e13	−	5.21752e13i	0.565647	−	0.565647i
$347$	9.18512e12	−	9.18512e12i	0.0980105	−	0.0980105i	−0.656401	−	0.754412i	$-0.727922\pi$
$347$	9.18512e12	−	9.18512e12i	0.0980105	−	0.0980105i	0.754412	+	0.656401i	$0.227922\pi$
$348$		−	7.09329e13i		−	0.745009i
$349$			3.84752e13i			0.397778i	0.980022	+	0.198889i	$0.0637333\pi$
$349$			3.84752e13i			0.397778i	−0.980022	+	0.198889i	$0.936267\pi$
$350$	3.72648e13	−	3.72648e13i	0.379249	−	0.379249i
$351$	−4.70158e12	+	4.70158e12i	−0.0471036	+	0.0471036i
$352$	7.29094e13	+	7.29094e13i	0.719116	+	0.719116i
$353$	−3.63602e12			−0.0353073			−0.0176537	−	0.999844i	$-0.505620\pi$
$353$	−3.63602e12			−0.0353073			−0.0176537	+	0.999844i	$0.505620\pi$
$354$	1.29074e14	+	1.29074e14i	1.23402	+	1.23402i
$355$			1.14177e13i			0.107479i
$356$	5.64739e13			0.523447
$357$	−1.52782e13	−	1.65658e13i	−0.139443	−	0.151195i
$358$	1.89588e14			1.70394
$359$			1.17555e14i			1.04045i	0.854028	+	0.520226i	$0.174152\pi$
$359$			1.17555e14i			1.04045i	−0.854028	+	0.520226i	$0.825848\pi$
$360$	1.38084e11	+	1.38084e11i	0.00120360	+	0.00120360i
$361$	2.97669e13			0.255531
$362$	−2.07799e14	−	2.07799e14i	−1.75690	−	1.75690i
$363$	1.68610e13	−	1.68610e13i	0.140410	−	0.140410i
$364$	7.76368e11	−	7.76368e11i	0.00636810	−	0.00636810i
$365$			2.76970e14i			2.23780i
$366$		−	3.14316e14i		−	2.50161i
$367$	9.25998e13	−	9.25998e13i	0.726017	−	0.726017i	−0.243807	−	0.969824i	$-0.578396\pi$
$367$	9.25998e13	−	9.25998e13i	0.726017	−	0.726017i	0.969824	+	0.243807i	$0.0783963\pi$
$368$	1.04195e14	−	1.04195e14i	0.804790	−	0.804790i
$369$	−1.22808e11	−	1.22808e11i	−0.000934502	−	0.000934502i
$370$	−4.54583e14			−3.40803
$371$	3.40881e13	+	3.40881e13i	0.251794	+	0.251794i
$372$			1.27259e13i			0.0926197i
$373$	5.72603e13			0.410634			0.205317	−	0.978696i	$-0.434177\pi$
$373$	5.72603e13			0.410634			0.205317	+	0.978696i	$0.434177\pi$
$374$	−6.58811e12	+	1.62934e14i	−0.0465551	+	1.15138i
$375$	2.55237e14			1.77734
$376$			5.28968e13i			0.362991i
$377$	−7.89470e12	−	7.89470e12i	−0.0533898	−	0.0533898i
$378$	3.98163e13			0.265372
$379$	−1.55035e13	−	1.55035e13i	−0.101839	−	0.101839i	0.654352	−	0.756190i	$-0.272942\pi$
$379$	−1.55035e13	−	1.55035e13i	−0.101839	−	0.101839i	−0.756190	+	0.654352i	$0.772942\pi$
$380$	1.07701e14	−	1.07701e14i	0.697285	−	0.697285i
$381$	−6.07984e13	+	6.07984e13i	−0.387976	+	0.387976i
$382$			2.01294e13i			0.126614i
$383$		−	2.20280e14i		−	1.36578i	−0.730519	−	0.682892i	$-0.760722\pi$
$383$		−	2.20280e14i		−	1.36578i	0.730519	−	0.682892i	$-0.239278\pi$
$384$	−9.59825e13	+	9.59825e13i	−0.586638	+	0.586638i
$385$	3.76106e13	−	3.76106e13i	0.226608	−	0.226608i
$386$	1.24143e14	+	1.24143e14i	0.737378	+	0.737378i
$387$	1.44824e11			0.000848067
$388$	−9.49781e13	−	9.49781e13i	−0.548339	−	0.548339i
$389$		−	8.10664e13i		−	0.461443i	−0.973020	−	0.230721i	$-0.925891\pi$
$389$		−	8.10664e13i		−	0.461443i	0.973020	−	0.230721i	$-0.0741086\pi$
$390$	2.65097e13			0.148782
$391$	1.67721e14	+	6.78166e12i	0.928144	+	0.0375287i
$392$	−7.74246e13			−0.422479
$393$		−	2.04903e14i		−	1.10253i
$394$	1.66137e14	+	1.66137e14i	0.881532	+	0.881532i
$395$	−3.83159e14			−2.00491
$396$	−1.78885e11	−	1.78885e11i	−0.000923105	−	0.000923105i
$397$	−1.05388e13	+	1.05388e13i	−0.0536346	+	0.0536346i	−0.733415	−	0.679781i	$-0.762075\pi$
$397$	−1.05388e13	+	1.05388e13i	−0.0536346	+	0.0536346i	0.679781	+	0.733415i	$0.262075\pi$
$398$	−2.14375e14	+	2.14375e14i	−1.07601	+	1.07601i
$399$			3.58482e13i			0.177466i
$400$		−	5.07718e14i		−	2.47909i
$401$	−1.12451e14	+	1.12451e14i	−0.541590	+	0.541590i	−0.923995	−	0.382405i	$-0.875096\pi$
$401$	−1.12451e14	+	1.12451e14i	−0.541590	+	0.541590i	0.382405	+	0.923995i	$0.375096\pi$
$402$	−1.28807e14	+	1.28807e14i	−0.611923	+	0.611923i
$403$	1.41637e12	+	1.41637e12i	0.00663743	+	0.00663743i
$404$	3.24673e13			0.150089
$405$	2.69007e14	+	2.69007e14i	1.22676	+	1.22676i
$406$			6.68578e13i			0.300787i
$407$	−3.07046e14			−1.36281
$408$	−1.00558e14	−	4.06596e12i	−0.440335	−	0.0178046i
$409$	−8.83085e13			−0.381526			−0.190763	−	0.981636i	$-0.561096\pi$
$409$	−8.83085e13			−0.381526			−0.190763	+	0.981636i	$0.561096\pi$
$410$			3.12763e14i			1.33323i
$411$	1.97881e13	+	1.97881e13i	0.0832289	+	0.0832289i
$412$	−2.51847e14			−1.04521
$413$	−4.82509e13	−	4.82509e13i	−0.197597	−	0.197597i
$414$	−4.64290e11	+	4.64290e11i	−0.00187624	+	0.00187624i
$415$	1.46289e14	−	1.46289e14i	0.583374	−	0.583374i
$416$		−	1.92107e13i		−	0.0756014i
$417$			2.43863e14i			0.947105i
$418$	1.83422e14	−	1.83422e14i	0.703042	−	0.703042i
$419$	−8.77290e13	+	8.77290e13i	−0.331868	+	0.331868i	−0.853296	−	0.521427i	$-0.825400\pi$
$419$	−8.77290e13	+	8.77290e13i	−0.331868	+	0.331868i	0.521427	+	0.853296i	$0.325400\pi$
$420$	−4.45196e13	−	4.45196e13i	−0.166219	−	0.166219i
$421$	−2.12874e14			−0.784461			−0.392230	−	0.919867i	$-0.628296\pi$
$421$	−2.12874e14			−0.784461			−0.392230	+	0.919867i	$0.628296\pi$
$422$	1.93856e14	+	1.93856e14i	0.705118	+	0.705118i
$423$		−	5.08488e11i		−	0.00182561i
$424$	2.15287e14			0.762967
$425$	4.25156e14	−	3.92111e14i	1.48734	−	1.37173i
$426$	2.30171e13			0.0794873
$427$			1.17498e14i			0.400570i
$428$	−1.64774e14	−	1.64774e14i	−0.554560	−	0.554560i
$429$	1.79059e13			0.0594950
$430$	−1.84417e14	−	1.84417e14i	−0.604957	−	0.604957i
$431$	−1.45889e14	+	1.45889e14i	−0.472496	+	0.472496i	−0.902721	−	0.430226i	$-0.858434\pi$
$431$	−1.45889e14	+	1.45889e14i	−0.472496	+	0.472496i	0.430226	+	0.902721i	$0.358434\pi$
$432$	2.71240e14	−	2.71240e14i	0.867347	−	0.867347i
$433$		−	3.90476e14i		−	1.23285i	−0.787412	−	0.616427i	$-0.788580\pi$
$433$		−	3.90476e14i		−	1.23285i	0.787412	−	0.616427i	$-0.211420\pi$
$434$		−	1.19948e13i		−	0.0373939i
$435$	−4.52709e14	+	4.52709e14i	−1.39357	+	1.39357i
$436$	−5.70529e13	+	5.70529e13i	−0.173421	+	0.173421i
$437$	−1.88811e14	−	1.88811e14i	−0.566733	−	0.566733i
$438$	5.58348e14			1.65500
$439$	2.83283e14	+	2.83283e14i	0.829212	+	0.829212i	0.987408	−	0.158195i	$-0.0505676\pi$
$439$	2.83283e14	+	2.83283e14i	0.829212	+	0.829212i	−0.158195	+	0.987408i	$0.550568\pi$
$440$		−	2.37534e14i		−	0.686651i
$441$	7.44269e11			0.00212480
$442$	2.23335e13	−	2.05976e13i	0.0629701	−	0.0580757i
$443$	−2.58307e14			−0.719308			−0.359654	−	0.933086i	$-0.617105\pi$
$443$	−2.58307e14			−0.719308			−0.359654	+	0.933086i	$0.617105\pi$
$444$			3.63451e14i			0.999630i
$445$	−3.60429e14	−	3.60429e14i	−0.979129	−	0.979129i
$446$	7.45731e14			2.00097
$447$	−4.38490e14	−	4.38490e14i	−1.16217	−	1.16217i
$448$	−1.32025e13	+	1.32025e13i	−0.0345642	+	0.0345642i
$449$	3.80996e14	−	3.80996e14i	0.985294	−	0.985294i	−0.0145997	−	0.999893i	$-0.504647\pi$
$449$	3.80996e14	−	3.80996e14i	0.985294	−	0.985294i	0.999893	+	0.0145997i	$0.00464740\pi$
$450$			2.26238e12i			0.00577960i
$451$			2.11255e14i			0.533133i
$452$	3.54748e13	−	3.54748e13i	0.0884419	−	0.0884419i
$453$	−1.84979e13	+	1.84979e13i	−0.0455600	+	0.0455600i
$454$	5.23547e14	+	5.23547e14i	1.27394	+	1.27394i
$455$	−9.90991e12			−0.0238236
$456$	1.13202e14	+	1.13202e14i	0.268873	+	0.268873i
$457$			3.01030e14i			0.706433i	0.935542	+	0.353217i	$0.114912\pi$
$457$			3.01030e14i			0.706433i	−0.935542	+	0.353217i	$0.885088\pi$
$458$	−2.59662e14			−0.602073
$459$	4.36612e14	+	1.76540e13i	1.00029	+	0.0404459i
$460$	4.68965e14			1.06163
$461$			3.92047e13i			0.0876966i	0.999038	+	0.0438483i	$0.0139618\pi$
$461$			3.92047e13i			0.0876966i	−0.999038	+	0.0438483i	$0.986038\pi$
$462$	−7.58197e13	−	7.58197e13i	−0.167591	−	0.167591i
$463$	4.90563e14			1.07152			0.535758	−	0.844371i	$-0.320026\pi$
$463$	4.90563e14			1.07152			0.535758	+	0.844371i	$0.320026\pi$
$464$	4.55455e14	+	4.55455e14i	0.983097	+	0.983097i
$465$	8.12198e13	−	8.12198e13i	0.173249	−	0.173249i
$466$	1.14943e14	−	1.14943e14i	0.242304	−	0.242304i
$467$		−	4.10608e14i		−	0.855431i	−0.903913	−	0.427715i	$-0.859319\pi$
$467$		−	4.10608e14i		−	0.855431i	0.903913	−	0.427715i	$-0.140681\pi$
$468$			4.71340e10i			9.70471e-5i
$469$	4.81510e13	−	4.81510e13i	0.0979839	−	0.0979839i
$470$	−6.47501e14	+	6.47501e14i	−1.30227	+	1.30227i
$471$	2.94005e11	+	2.94005e11i	0.000584441	+	0.000584441i
$472$	−3.04734e14			−0.598743
$473$	−1.24564e14	−	1.24564e14i	−0.241911	−	0.241911i
$474$			7.72417e14i			1.48276i
$475$	−9.20032e14			−1.74577
$476$	−7.20973e13	−	2.91520e12i	−0.135232	−	0.00546801i
$477$	−2.06952e12			−0.00383723
$478$		−	1.21476e15i		−	2.22658i
$479$	2.82015e13	+	2.82015e13i	0.0511007	+	0.0511007i	0.732195	−	0.681095i	$-0.238496\pi$
$479$	2.82015e13	+	2.82015e13i	0.0511007	+	0.0511007i	−0.681095	+	0.732195i	$0.738496\pi$
$480$	−1.10161e15			−1.97333
$481$	4.04514e13	+	4.04514e13i	0.0716368	+	0.0716368i
$482$	−6.79198e14	+	6.79198e14i	−1.18915	+	1.18915i
$483$	−7.80472e13	+	7.80472e13i	−0.135098	+	0.135098i
$484$		−	7.63491e13i		−	0.130664i
$485$			1.21234e15i			2.05138i
$486$	−2.41461e12	+	2.41461e12i	−0.00403968	+	0.00403968i
$487$	5.56351e14	−	5.56351e14i	0.920322	−	0.920322i	−0.0767300	−	0.997052i	$-0.524448\pi$
$487$	5.56351e14	−	5.56351e14i	0.920322	−	0.920322i	0.997052	+	0.0767300i	$0.0244480\pi$
$488$	3.71037e14	+	3.71037e14i	0.606888	+	0.606888i
$489$	−2.23965e13			−0.0362227
$490$	−9.47742e14	−	9.47742e14i	−1.51569	−	1.51569i
$491$		−	2.52108e14i		−	0.398693i	−0.979929	−	0.199347i	$-0.936118\pi$
$491$		−	2.52108e14i		−	0.398693i	0.979929	−	0.199347i	$-0.0638820\pi$
$492$	2.50062e14			0.391057
$493$	−2.96439e13	+	7.33141e14i	−0.0458435	+	1.13378i
$494$	−4.83293e13			−0.0739116
$495$			2.28337e12i			0.00345341i
$496$	−8.17123e13	−	8.17123e13i	−0.122219	−	0.122219i
$497$	−8.60431e12			−0.0127279
$498$	−2.94906e14	−	2.94906e14i	−0.431442	−	0.431442i
$499$	−1.82938e14	+	1.82938e14i	−0.264699	+	0.264699i	−0.826960	−	0.562261i	$-0.809932\pi$
$499$	−1.82938e14	+	1.82938e14i	−0.264699	+	0.264699i	0.562261	+	0.826960i	$0.309932\pi$
$500$	5.77875e14	−	5.77875e14i	0.826988	−	0.826988i
$501$		−	1.08124e15i		−	1.53043i
$502$		−	1.23102e15i		−	1.72343i
$503$	7.90137e14	−	7.90137e14i	1.09415	−	1.09415i	0.0990746	−	0.995080i	$-0.468412\pi$
$503$	7.90137e14	−	7.90137e14i	1.09415	−	1.09415i	0.995080	−	0.0990746i	$-0.0315882\pi$
$504$	−1.04060e11	+	1.04060e11i	−0.000142533	+	0.000142533i
$505$	−2.07213e14	−	2.07213e14i	−0.280747	−	0.280747i
$506$	7.98677e14			1.07039
$507$	5.30419e14	+	5.30419e14i	0.703194	+	0.703194i
$508$			2.75304e14i			0.361046i
$509$	−1.00232e15			−1.30034			−0.650172	−	0.759787i	$-0.725303\pi$
$509$	−1.00232e15			−1.30034			−0.650172	+	0.759787i	$0.725303\pi$
$510$	−1.18114e15	−	1.28068e15i	−1.51588	−	1.64363i
$511$	−2.08723e14			−0.265006
$512$			6.77928e14i			0.851528i
$513$	−4.91512e14	−	4.91512e14i	−0.610785	−	0.610785i
$514$	1.13233e15			1.39211
$515$	1.60735e15	+	1.60735e15i	1.95510	+	1.95510i
$516$	−1.47446e14	+	1.47446e14i	−0.177444	+	0.177444i
$517$	−4.37353e14	+	4.37353e14i	−0.520755	+	0.520755i
$518$		−	3.42571e14i		−	0.403587i
$519$			5.32474e14i			0.620695i
$520$	−3.12936e13	+	3.12936e13i	−0.0360942	+	0.0360942i
$521$	2.70693e14	−	2.70693e14i	0.308937	−	0.308937i	−0.535560	−	0.844497i	$-0.679900\pi$
$521$	2.70693e14	−	2.70693e14i	0.308937	−	0.308937i	0.844497	+	0.535560i	$0.179900\pi$
$522$	−2.02950e12	−	2.02950e12i	−0.00229193	−	0.00229193i
$523$	−5.83231e14			−0.651750			−0.325875	−	0.945413i	$-0.605659\pi$
$523$	−5.83231e14			−0.651750			−0.325875	+	0.945413i	$0.605659\pi$
$524$	−4.63916e14	−	4.63916e14i	−0.513000	−	0.513000i
$525$			3.80307e14i			0.416157i
$526$	−1.30721e15			−1.41555
$527$	5.31836e12	−	1.31531e14i	0.00569928	−	0.140952i
$528$	−1.03301e15			−1.09552
$529$			1.30669e14i			0.137141i
$530$	2.63530e15	+	2.63530e15i	2.73724	+	2.73724i
$531$	2.92936e12			0.00301129
$532$	8.11629e13	+	8.11629e13i	0.0825741	+	0.0825741i
$533$	2.78315e13	−	2.78315e13i	0.0280244	−	0.0280244i
$534$	−7.26594e14	+	7.26594e14i	−0.724128	+	0.724128i
$535$			2.10325e15i			2.07465i
$536$		−	3.04104e14i		−	0.296903i
$537$	−9.67423e14	+	9.67423e14i	−0.934884	+	0.934884i
$538$	5.94473e14	−	5.94473e14i	0.568630	−	0.568630i
$539$	−6.40149e14	−	6.40149e14i	−0.606098	−	0.606098i
$540$	1.22081e15			1.14415
$541$	−4.49478e14	−	4.49478e14i	−0.416988	−	0.416988i	0.467176	−	0.884164i	$-0.345271\pi$
$541$	−4.49478e14	−	4.49478e14i	−0.416988	−	0.416988i	−0.884164	+	0.467176i	$0.845271\pi$
$542$		−	2.19172e15i		−	2.01275i
$543$	2.12070e15			1.92788
$544$	−9.28067e14	+	8.55933e14i	−0.835191	+	0.770275i
$545$	7.28248e14			0.648782
$546$			1.99775e13i			0.0176190i
$547$	6.63326e14	+	6.63326e14i	0.579158	+	0.579158i	0.934671	−	0.355513i	$-0.115694\pi$
$547$	6.63326e14	+	6.63326e14i	0.579158	+	0.579158i	−0.355513	+	0.934671i	$0.615694\pi$
$548$	8.96034e13			0.0774518
$549$	−3.56672e12	−	3.56672e12i	−0.00305226	−	0.00305226i
$550$	1.94589e15	−	1.94589e15i	1.64863	−	1.64863i
$551$	8.25327e14	−	8.25327e14i	0.692297	−	0.692297i
$552$			4.92916e14i			0.409363i
$553$		−	2.88747e14i		−	0.237426i
$554$	−1.70735e15	+	1.70735e15i	−1.39001	+	1.39001i
$555$	2.31962e15	−	2.31962e15i	1.86985	−	1.86985i
$556$	5.52125e14	+	5.52125e14i	0.440682	+	0.440682i
$557$	1.09460e14			0.0865073			0.0432537	−	0.999064i	$-0.486228\pi$
$557$	1.09460e14			0.0865073			0.0432537	+	0.999064i	$0.486228\pi$
$558$	3.64109e11	+	3.64109e11i	0.000284934	+	0.000284934i
$559$			3.28210e13i			0.0254324i
$560$	5.71715e14			0.438677
$561$	−7.97796e14	−	8.65031e14i	−0.606172	−	0.657258i
$562$	−1.09479e15			−0.823722
$563$		−	1.96436e15i		−	1.46361i	−0.681514	−	0.731805i	$-0.738678\pi$
$563$		−	1.96436e15i		−	1.46361i	0.681514	−	0.731805i	$-0.261322\pi$
$564$	5.17694e14	+	5.17694e14i	0.381978	+	0.381978i
$565$	−4.52816e14			−0.330868
$566$	−1.89429e15	−	1.89429e15i	−1.37075	−	1.37075i
$567$	−2.02722e14	+	2.02722e14i	−0.145276	+	0.145276i
$568$	−2.71708e13	+	2.71708e13i	−0.0192835	+	0.0192835i
$569$			1.84809e15i			1.29899i	0.760365	+	0.649496i	$0.225020\pi$
$569$			1.84809e15i			1.29899i	−0.760365	+	0.649496i	$0.774980\pi$
$570$			2.77137e15i			1.92923i
$571$	1.73544e15	−	1.73544e15i	1.19650	−	1.19650i	0.221291	−	0.975208i	$-0.428973\pi$
$571$	1.73544e15	−	1.73544e15i	1.19650	−	1.19650i	0.975208	−	0.221291i	$-0.0710269\pi$
$572$	4.05402e13	−	4.05402e13i	0.0276827	−	0.0276827i
$573$	−1.02715e14	−	1.02715e14i	−0.0694681	−	0.0694681i
$574$	−2.35696e14			−0.157884
$575$	−2.00305e15	−	2.00305e15i	−1.32898	−	1.32898i
$576$		−	8.01536e11i		−	0.000526744i
$577$	2.56313e13			0.0166842			0.00834208	−	0.999965i	$-0.497345\pi$
$577$	2.56313e13			0.0166842			0.00834208	+	0.999965i	$0.497345\pi$
$578$	−1.99014e15	−	1.61203e14i	−1.28316	−	0.103937i
$579$	−1.26694e15			−0.809139
$580$			2.04994e15i			1.29684i
$581$	1.10242e14	+	1.10242e14i	0.0690844	+	0.0690844i
$582$	2.44398e15			1.51712
$583$	1.78000e15	+	1.78000e15i	1.09457	+	1.09457i
$584$	−6.59108e14	+	6.59108e14i	−0.401500	+	0.401500i
$585$	3.00820e11	−	3.00820e11i	0.000181530	−	0.000181530i
$586$		−	2.45060e14i		−	0.146499i
$587$			1.12967e15i			0.669024i	0.942392	+	0.334512i	$0.108571\pi$
$587$			1.12967e15i			0.669024i	−0.942392	+	0.334512i	$0.891429\pi$
$588$	−7.57745e14	+	7.57745e14i	−0.444578	+	0.444578i
$589$	−1.48070e14	+	1.48070e14i	−0.0860665	+	0.0860665i
$590$	−3.73020e15	−	3.73020e15i	−2.14806	−	2.14806i
$591$	−1.69552e15			−0.967321
$592$	−2.33369e15	−	2.33369e15i	−1.31909	−	1.31909i
$593$			2.52938e14i			0.141649i	0.997489	+	0.0708243i	$0.0225630\pi$
$593$			2.52938e14i			0.141649i	−0.997489	+	0.0708243i	$0.977437\pi$
$594$	2.07912e15			1.15359
$595$	4.41536e14	+	4.78747e14i	0.242729	+	0.263186i
$596$	−1.98555e15			−1.08150
$597$		−	2.18780e15i		−	1.18073i
$598$	−1.05221e14	−	1.05221e14i	−0.0562658	−	0.0562658i
$599$	8.01621e13			0.0424738			0.0212369	−	0.999774i	$-0.493240\pi$
$599$	8.01621e13			0.0424738			0.0212369	+	0.999774i	$0.493240\pi$
$600$	1.20094e15	+	1.20094e15i	0.630504	+	0.630504i
$601$	−6.08822e14	+	6.08822e14i	−0.316724	+	0.316724i	−0.847507	−	0.530784i	$-0.821898\pi$
$601$	−6.08822e14	+	6.08822e14i	−0.316724	+	0.316724i	0.530784	+	0.847507i	$0.321898\pi$
$602$	1.38976e14	−	1.38976e14i	0.0716403	−	0.0716403i
$603$			2.92329e12i			0.00149323i
$604$			8.37614e13i			0.0423976i
$605$	−4.87277e14	+	4.87277e14i	−0.244411	+	0.244411i
$606$	−4.17724e14	+	4.17724e14i	−0.207630	+	0.207630i
$607$	2.57592e15	+	2.57592e15i	1.26880	+	1.26880i	0.946707	+	0.322097i	$0.104388\pi$
$607$	2.57592e15	+	2.57592e15i	1.26880	+	1.26880i	0.322097	+	0.946707i	$0.395612\pi$
$608$	2.00832e15			0.980311
$609$	−3.41159e14	−	3.41159e14i	−0.165030	−	0.165030i
$610$			9.08362e15i			4.35457i
$611$	1.15237e14			0.0547476
$612$	2.27704e12	−	2.10006e12i	0.00107211	−	0.000988777i
$613$	−7.32905e14			−0.341991			−0.170996	−	0.985272i	$-0.554698\pi$
$613$	−7.32905e14			−0.341991			−0.170996	+	0.985272i	$0.554698\pi$
$614$		−	4.04961e14i		−	0.187278i
$615$	−1.59595e15	−	1.59595e15i	−0.731487	−	0.731487i
$616$	1.79004e14			0.0813147
$617$	1.08922e15	+	1.08922e15i	0.490398	+	0.490398i	0.908432	−	0.418033i	$-0.137281\pi$
$617$	1.08922e15	+	1.08922e15i	0.490398	+	0.490398i	−0.418033	+	0.908432i	$0.637281\pi$
$618$	3.24027e15	−	3.24027e15i	1.44592	−	1.44592i
$619$	−2.66420e15	+	2.66420e15i	−1.17833	+	1.17833i	−0.198165	+	0.980169i	$0.563498\pi$
$619$	−2.66420e15	+	2.66420e15i	−1.17833	+	1.17833i	−0.980169	+	0.198165i	$0.936502\pi$
$620$		−	3.67775e14i		−	0.161223i
$621$		−	2.14020e15i		−	0.929930i
$622$	3.04010e15	−	3.04010e15i	1.30930	−	1.30930i
$623$	2.71617e14	−	2.71617e14i	0.115951	−	0.115951i
$624$	1.36093e14	+	1.36093e14i	0.0575864	+	0.0575864i
$625$	−2.55228e15			−1.07051
$626$	−8.53082e14	−	8.53082e14i	−0.354676	−	0.354676i
$627$			1.87191e15i			0.771461i
$628$	1.33130e12			0.000543874
$629$	1.51892e14	−	3.75652e15i	0.0615114	−	1.52127i
$630$	−2.54755e12			−0.00102270
$631$		−	2.72882e15i		−	1.08596i	−0.839746	−	0.542979i	$-0.817296\pi$
$631$		−	2.72882e15i		−	1.08596i	0.839746	−	0.542979i	$-0.182704\pi$
$632$	−9.11807e14	−	9.11807e14i	−0.359715	−	0.359715i
$633$	−1.97840e15			−0.773739
$634$	−1.10829e15	−	1.10829e15i	−0.429699	−	0.429699i
$635$	1.75705e15	−	1.75705e15i	0.675350	−	0.675350i
$636$	2.10699e15	−	2.10699e15i	0.802875	−	0.802875i
$637$			1.68671e14i			0.0637198i
$638$			3.49117e15i			1.30755i
$639$	2.61188e11	−	2.61188e11i	9.69836e−5	−	9.69836e-5i
$640$	2.77386e15	−	2.77386e15i	1.02116	−	1.02116i
$641$	3.37408e15	+	3.37408e15i	1.23150	+	1.23150i	0.963386	+	0.268118i	$0.0864018\pi$
$641$	3.37408e15	+	3.37408e15i	1.23150	+	1.23150i	0.268118	+	0.963386i	$0.413598\pi$
$642$	4.23998e15			1.53434
$643$	−1.00741e15	−	1.00741e15i	−0.361449	−	0.361449i	0.502897	−	0.864346i	$-0.332268\pi$
$643$	−1.00741e15	−	1.00741e15i	−0.361449	−	0.361449i	−0.864346	+	0.502897i	$0.832268\pi$
$644$			3.53409e14i			0.125720i
$645$	1.88207e15			0.663830
$646$	2.15331e15	+	2.33478e15i	0.753058	+	0.816522i
$647$	−1.50577e15			−0.522138			−0.261069	−	0.965320i	$-0.584075\pi$
$647$	−1.50577e15			−0.522138			−0.261069	+	0.965320i	$0.584075\pi$
$648$			1.28031e15i			0.440204i
$649$	−2.51955e15	−	2.51955e15i	−0.858970	−	0.858970i
$650$	−5.12717e14			−0.173322
$651$	6.12067e13	+	6.12067e13i	0.0205165	+	0.0205165i
$652$	−5.07072e13	+	5.07072e13i	−0.0168542	+	0.0168542i
$653$	−4.71717e14	+	4.71717e14i	−0.155474	+	0.155474i	−0.780558	−	0.625084i	$-0.785065\pi$
$653$	−4.71717e14	+	4.71717e14i	−0.155474	+	0.155474i	0.625084	+	0.780558i	$0.285065\pi$
$654$		−	1.46809e15i		−	0.479815i
$655$			5.92163e15i			1.91917i
$656$	−1.60563e15	+	1.60563e15i	−0.516030	+	0.516030i
$657$	6.33589e12	−	6.33589e12i	0.00201929	−	0.00201929i
$658$	−4.87953e14	−	4.87953e14i	−0.154218	−	0.154218i
$659$	3.44738e15			1.08049			0.540243	−	0.841509i	$-0.318332\pi$
$659$	3.44738e15			1.08049			0.540243	+	0.841509i	$0.318332\pi$
$660$	−2.32472e15	−	2.32472e15i	−0.722567	−	0.722567i
$661$			2.10685e15i			0.649420i	0.945814	+	0.324710i	$0.105267\pi$
$661$			2.10685e15i			0.649420i	−0.945814	+	0.324710i	$0.894733\pi$
$662$	4.90961e12			0.00150082
$663$	−8.85779e12	+	2.19067e14i	−0.00268535	+	0.0664129i
$664$	6.96250e14			0.209334
$665$		−	1.03600e15i		−	0.308916i
$666$	1.03989e13	+	1.03989e13i	0.00307524	+	0.00307524i
$667$	3.59373e15			1.05403
$668$	−2.44800e15	−	2.44800e15i	−0.712100	−	0.712100i
$669$	−3.80528e15	+	3.80528e15i	−1.09785	+	1.09785i
$670$	3.72248e15	−	3.72248e15i	1.06518	−	1.06518i
$671$			6.13550e15i			1.74131i
$672$		−	8.30166e14i		−	0.233687i
$673$	−7.94604e14	+	7.94604e14i	−0.221854	+	0.221854i	−0.809279	−	0.587425i	$-0.800142\pi$
$673$	−7.94604e14	+	7.94604e14i	−0.221854	+	0.221854i	0.587425	+	0.809279i	$0.300142\pi$
$674$	−1.11716e14	+	1.11716e14i	−0.0309376	+	0.0309376i
$675$	−5.21436e15	−	5.21436e15i	−1.43229	−	1.43229i
$676$	2.40182e15			0.654384
$677$	3.52722e15	+	3.52722e15i	0.953224	+	0.953224i	0.998954	−	0.0457302i	$-0.0145614\pi$
$677$	3.52722e15	+	3.52722e15i	0.953224	+	0.953224i	−0.0457302	+	0.998954i	$0.514561\pi$
$678$			9.12838e14i			0.244698i
$679$	−9.13614e14			−0.242929
$680$	2.90608e15	+	1.17505e14i	0.766493	+	0.0309925i
$681$	−5.34306e15			−1.39792
$682$		−	6.26344e14i		−	0.162554i
$683$	4.16443e14	+	4.16443e14i	0.107212	+	0.107212i	0.758678	−	0.651466i	$-0.225846\pi$
$683$	4.16443e14	+	4.16443e14i	0.107212	+	0.107212i	−0.651466	+	0.758678i	$0.725846\pi$
$684$	−4.92748e12			−0.00125839
$685$	−5.71869e14	−	5.71869e14i	−0.144877	−	0.144877i
$686$	1.46005e15	−	1.46005e15i	0.366931	−	0.366931i
$687$	1.32499e15	−	1.32499e15i	0.330333	−	0.330333i
$688$		−	1.89348e15i		−	0.468301i
$689$		−	4.69008e14i		−	0.115073i
$690$	−6.03371e15	+	6.03371e15i	−1.46864	+	1.46864i
$691$	−1.16320e14	+	1.16320e14i	−0.0280882	+	0.0280882i	−0.721011	−	0.692923i	$-0.756322\pi$
$691$	−1.16320e14	+	1.16320e14i	−0.0280882	+	0.0280882i	0.692923	+	0.721011i	$0.256322\pi$
$692$	1.20556e15	+	1.20556e15i	0.288806	+	0.288806i
$693$	−1.72074e12			−0.000408961
$694$	5.35118e14	+	5.35118e14i	0.126175	+	0.126175i
$695$		−	7.04756e15i		−	1.64863i
$696$	−2.15463e15			−0.500060
$697$	−2.58457e15	−	1.04505e14i	−0.595124	−	0.0240633i
$698$	−2.24153e15			−0.512083
$699$			1.17305e15i			0.265885i
$700$	8.61042e14	+	8.61042e14i	0.193636	+	0.193636i
$701$	−9.50071e14			−0.211986			−0.105993	−	0.994367i	$-0.533802\pi$
$701$	−9.50071e14			−0.211986			−0.105993	+	0.994367i	$0.533802\pi$
$702$	−2.73910e14	−	2.73910e14i	−0.0606393	−	0.0606393i
$703$	−4.22887e15	+	4.22887e15i	−0.928902	+	0.928902i
$704$	−6.89405e14	+	6.89405e14i	−0.150254	+	0.150254i
$705$		−	6.60808e15i		−	1.42901i
$706$		−	2.11832e14i		−	0.0454533i
$707$	1.56155e14	−	1.56155e14i	0.0332467	−	0.0332467i
$708$	−2.98240e15	+	2.98240e15i	−0.630061	+	0.630061i
$709$	2.65999e15	+	2.65999e15i	0.557603	+	0.557603i	0.928624	−	0.371021i	$-0.120992\pi$
$709$	2.65999e15	+	2.65999e15i	0.557603	+	0.557603i	−0.371021	+	0.928624i	$0.620992\pi$
$710$	−6.65186e14			−0.138364
$711$	8.76505e12	+	8.76505e12i	0.00180914	+	0.00180914i
$712$		−	1.71543e15i		−	0.351345i
$713$	−6.44745e14			−0.131038
$714$	9.65113e14	−	8.90099e14i	0.194643	−	0.179514i
$715$	−5.17473e14			−0.103563
$716$			4.38063e15i			0.869992i
$717$	6.19864e15	+	6.19864e15i	1.22163	+	1.22163i
$718$	−6.84868e15			−1.33944
$719$	−6.62016e15	−	6.62016e15i	−1.28487	−	1.28487i	−0.937862	−	0.347009i	$-0.887197\pi$
$719$	−6.62016e15	−	6.62016e15i	−1.28487	−	1.28487i	−0.347009	−	0.937862i	$-0.612803\pi$
$720$	−1.73547e13	+	1.73547e13i	−0.00334263	+	0.00334263i
$721$	−1.21129e15	+	1.21129e15i	−0.231528	+	0.231528i
$722$			1.73420e15i			0.328960i
$723$		−	6.93156e15i		−	1.30488i
$724$	4.80142e15	−	4.80142e15i	0.897030	−	0.897030i
$725$	8.75574e15	−	8.75574e15i	1.62343	−	1.62343i
$726$	9.82309e14	+	9.82309e14i	0.180758	+	0.180758i
$727$	−7.19985e15			−1.31487			−0.657437	−	0.753509i	$-0.728360\pi$
$727$	−7.19985e15			−1.31487			−0.657437	+	0.753509i	$0.728360\pi$
$728$	−2.35827e13	−	2.35827e13i	−0.00427435	−	0.00427435i
$729$		−	5.57134e15i		−	1.00221i
$730$	−1.61361e16			−2.88086
$731$	1.58558e15	−	1.46234e15i	0.280959	−	0.259121i
$732$	7.26259e15			1.27726
$733$		−	4.11182e15i		−	0.717731i	−0.933389	−	0.358866i	$-0.883164\pi$
$733$		−	4.11182e15i		−	0.717731i	0.933389	−	0.358866i	$-0.116836\pi$
$734$	5.39479e15	+	5.39479e15i	0.934645	+	0.934645i
$735$	9.67219e15			1.66320
$736$	4.37244e15	+	4.37244e15i	0.746270	+	0.746270i
$737$	2.51434e15	−	2.51434e15i	0.425944	−	0.425944i
$738$	7.15467e12	−	7.15467e12i	0.00120304	−	0.00120304i
$739$		−	2.67883e15i		−	0.447096i	−0.974693	−	0.223548i	$-0.928236\pi$
$739$		−	2.67883e15i		−	0.447096i	0.974693	−	0.223548i	$-0.0717639\pi$
$740$		−	1.05036e16i		−	1.74006i
$741$	2.46613e14	−	2.46613e14i	0.0405523	−	0.0405523i
$742$	−1.98594e15	+	1.98594e15i	−0.324150	+	0.324150i
$743$	8.24712e15	+	8.24712e15i	1.33618	+	1.33618i	0.899730	+	0.436447i	$0.143763\pi$
$743$	8.24712e15	+	8.24712e15i	1.33618	+	1.33618i	0.436447	+	0.899730i	$0.356237\pi$
$744$	3.86558e14			0.0621676
$745$	1.26722e16	+	1.26722e16i	2.02298	+	2.02298i
$746$			3.33594e15i			0.528634i
$747$	−6.69293e12			−0.00105282
$748$	−3.76476e15	−	1.52225e14i	−0.587866	−	0.0237699i
$749$	−1.58500e15			−0.245685
$750$			1.48699e16i			2.28808i
$751$	1.69871e15	+	1.69871e15i	0.259477	+	0.259477i	0.824841	−	0.565364i	$-0.191264\pi$
$751$	1.69871e15	+	1.69871e15i	0.259477	+	0.259477i	−0.565364	+	0.824841i	$0.691264\pi$
$752$	−6.64816e15			−1.00810
$753$	6.28158e15	+	6.28158e15i	0.945576	+	0.945576i
$754$	4.59939e14	−	4.59939e14i	0.0687319	−	0.0687319i
$755$	5.34584e14	−	5.34584e14i	0.0793063	−	0.0793063i
$756$			9.19995e14i			0.135493i
$757$		−	9.91715e15i		−	1.44997i	−0.688763	−	0.724986i	$-0.741846\pi$
$757$		−	9.91715e15i		−	1.44997i	0.688763	−	0.724986i	$-0.258154\pi$
$758$	9.03222e14	−	9.03222e14i	0.131103	−	0.131103i
$759$	−4.07545e15	+	4.07545e15i	−0.587281	+	0.587281i
$760$	−3.27149e15	−	3.27149e15i	−0.468027	−	0.468027i
$761$	−6.76906e15			−0.961419			−0.480709	−	0.876880i	$-0.659621\pi$
$761$	−6.76906e15			−0.961419			−0.480709	+	0.876880i	$0.659621\pi$
$762$	−3.54207e15	−	3.54207e15i	−0.499465	−	0.499465i
$763$			5.48804e14i			0.0768302i
$764$	−4.65111e14			−0.0646462
$765$	−2.79356e13	−	1.12955e12i	−0.00385496	−	0.000155872i
$766$	1.28334e16			1.75825
$767$			6.63871e14i			0.0903044i
$768$	−6.83340e15	−	6.83340e15i	−0.922890	−	0.922890i
$769$	4.46116e15			0.598210			0.299105	−	0.954220i	$-0.403312\pi$
$769$	4.46116e15			0.598210			0.299105	+	0.954220i	$0.403312\pi$
$770$	2.19116e15	+	2.19116e15i	0.291726	+	0.291726i
$771$	−5.77798e15	+	5.77798e15i	−0.763795	+	0.763795i
$772$	−2.86844e15	+	2.86844e15i	−0.376488	+	0.376488i
$773$		−	6.90956e14i		−	0.0900458i	−0.998986	−	0.0450229i	$-0.985664\pi$
$773$		−	6.90956e14i		−	0.0900458i	0.998986	−	0.0450229i	$-0.0143361\pi$
$774$			8.43734e12i			0.00109177i
$775$	−1.57085e15	+	1.57085e15i	−0.201825	+	0.201825i
$776$	−2.88502e15	+	2.88502e15i	−0.368052	+	0.368052i
$777$	1.74806e15	+	1.74806e15i	0.221432	+	0.221432i
$778$	4.72286e15			0.594043
$779$	2.90955e15	+	2.90955e15i	0.363388	+	0.363388i
$780$			6.12533e14i			0.0759642i
$781$	−4.49298e14			−0.0553291
$782$	−3.95094e14	+	9.77130e15i	−0.0483130	+	1.19485i
$783$	9.35522e15			1.13596
$784$		−	9.73085e15i		−	1.17331i
$785$	−8.49666e12	−	8.49666e12i	−0.00101734	−	0.00101734i
$786$	1.19375e16			1.41935
$787$	−1.82208e15	−	1.82208e15i	−0.215133	−	0.215133i	0.591311	−	0.806444i	$-0.298611\pi$
$787$	−1.82208e15	−	1.82208e15i	−0.215133	−	0.215133i	−0.806444	+	0.591311i	$0.798611\pi$
$788$	−3.83877e15	+	3.83877e15i	−0.450089	+	0.450089i
$789$	6.67038e15	−	6.67038e15i	0.776653	−	0.776653i
$790$		−	2.23226e16i		−	2.58104i
$791$		−	3.41239e14i		−	0.0391821i
$792$	−5.43376e12	+	5.43376e12i	−0.000619601	+	0.000619601i
$793$	8.08313e14	−	8.08313e14i	0.0915329	−	0.0915329i
$794$	−6.13985e14	−	6.13985e14i	−0.0690470	−	0.0690470i
$795$	−2.68945e16			−3.00362
$796$	−4.95334e15	−	4.95334e15i	−0.549385	−	0.549385i
$797$		−	2.48377e15i		−	0.273583i	−0.990600	−	0.136792i	$-0.956321\pi$
$797$		−	2.48377e15i		−	0.273583i	0.990600	−	0.136792i	$-0.0436791\pi$
$798$	−2.08849e15			−0.228463
$799$	−5.13438e15	−	5.56708e15i	−0.557803	−	0.604812i
$800$	2.13059e16			2.29882
$801$			1.64901e13i			0.00176704i
$802$	−6.55133e15	−	6.55133e15i	−0.697221	−	0.697221i
$803$	−1.08991e16			−1.15200
$804$	−2.97622e15	−	2.97622e15i	−0.312433	−	0.312433i
$805$	2.25554e15	−	2.25554e15i	0.235165	−	0.235165i
$806$	−8.25169e13	+	8.25169e13i	−0.00854476	+	0.00854476i
$807$			6.06690e15i			0.623968i
$808$		−	9.86214e14i		−	0.100742i
$809$	−7.69775e15	+	7.69775e15i	−0.780993	+	0.780993i	−0.979998	−	0.199006i	$-0.936229\pi$
$809$	−7.69775e15	+	7.69775e15i	−0.780993	+	0.780993i	0.199006	+	0.979998i	$0.436229\pi$
$810$	−1.56721e16	+	1.56721e16i	−1.57928	+	1.57928i
$811$	8.38035e11	+	8.38035e11i	8.38779e−5	+	8.38779e-5i	0.707149	−	0.707065i	$-0.249981\pi$
$811$	8.38035e11	+	8.38035e11i	8.38779e−5	+	8.38779e-5i	−0.707065	+	0.707149i	$0.749981\pi$
$812$	−1.54482e15			−0.153575
$813$	1.11838e16	+	1.11838e16i	1.10431	+	1.10431i
$814$		−	1.78883e16i		−	1.75442i
$815$	6.47250e14			0.0630529
$816$	5.11017e14	−	1.26382e16i	0.0494469	−	1.22290i
$817$	−3.43117e15			−0.329777
$818$		−	5.14478e15i		−	0.491161i
$819$	2.26696e11	+	2.26696e11i	2.14972e−5	+	2.14972e-5i
$820$	−7.22671e15			−0.680713
$821$	−1.12823e15	−	1.12823e15i	−0.105563	−	0.105563i	0.652353	−	0.757916i	$-0.273782\pi$
$821$	−1.12823e15	−	1.12823e15i	−0.105563	−	0.105563i	−0.757916	+	0.652353i	$0.773782\pi$
$822$	−1.15284e15	+	1.15284e15i	−0.107145	+	0.107145i
$823$	6.44515e15	−	6.44515e15i	0.595023	−	0.595023i	−0.343961	−	0.938984i	$-0.611769\pi$
$823$	6.44515e15	−	6.44515e15i	0.595023	−	0.595023i	0.938984	+	0.343961i	$0.111769\pi$
$824$			7.65003e15i			0.701558i
$825$			1.98588e16i			1.80907i
$826$	2.81106e15	−	2.81106e15i	0.254378	−	0.254378i
$827$	−1.17189e16	+	1.17189e16i	−1.05343	+	1.05343i	−0.0549419	+	0.998490i	$0.517497\pi$
$827$	−1.17189e16	+	1.17189e16i	−1.05343	+	1.05343i	−0.998490	+	0.0549419i	$0.982503\pi$
$828$	−1.07279e13	−	1.07279e13i	−0.000957962	−	0.000957962i
$829$	1.25893e16			1.11674			0.558370	−	0.829592i	$-0.311427\pi$
$829$	1.25893e16			1.11674			0.558370	+	0.829592i	$0.311427\pi$
$830$	8.52268e15	+	8.52268e15i	0.751012	+	0.751012i
$831$		−	1.74244e16i		−	1.52529i
$832$	1.81649e14			0.0157963
$833$	8.14849e15	−	7.51514e15i	0.703930	−	0.649217i
$834$	−1.42073e16			−1.21926
$835$			3.12474e16i			2.66402i
$836$	4.23815e15	+	4.23815e15i	0.358956	+	0.358956i
$837$	−1.67840e15			−0.141223
$838$	−5.11102e15	−	5.11102e15i	−0.427234	−	0.427234i
$839$	3.91071e15	−	3.91071e15i	0.324762	−	0.324762i	−0.525828	−	0.850591i	$-0.676245\pi$
$839$	3.91071e15	−	3.91071e15i	0.324762	−	0.324762i	0.850591	+	0.525828i	$0.176245\pi$
$840$	−1.35231e15	+	1.35231e15i	−0.111568	+	0.111568i
$841$			3.50839e15i			0.287561i
$842$		−	1.24019e16i		−	1.00988i
$843$	5.58644e15	−	5.58644e15i	0.451943	−	0.451943i
$844$	−4.47925e15	+	4.47925e15i	−0.360016	+	0.360016i
$845$	−1.53289e16	−	1.53289e16i	−1.22405	−	1.22405i
$846$	2.96241e13			0.00235022
$847$	−3.67209e14	−	3.67209e14i	−0.0289437	−	0.0289437i
$848$			2.70577e16i			2.11891i
$849$	1.93322e16			1.50414
$850$	2.28441e16	+	2.47693e16i	1.76591	+	1.91474i
$851$	−1.84138e16			−1.41427
$852$			5.31834e14i			0.0405843i
$853$	−1.25283e15	−	1.25283e15i	−0.0949889	−	0.0949889i	0.658015	−	0.753004i	$-0.271396\pi$
$853$	−1.25283e15	−	1.25283e15i	−0.0949889	−	0.0949889i	−0.753004	+	0.658015i	$0.771396\pi$
$854$	−6.84536e15			−0.515677
$855$	3.14483e13	+	3.14483e13i	0.00235387	+	0.00235387i
$856$	−5.00512e15	+	5.00512e15i	−0.372228	+	0.372228i
$857$	−1.01632e16	+	1.01632e16i	−0.750995	+	0.750995i	−0.974665	−	0.223670i	$-0.928196\pi$
$857$	−1.01632e16	+	1.01632e16i	−0.750995	+	0.750995i	0.223670	+	0.974665i	$0.428196\pi$
$858$			1.04318e15i			0.0765914i
$859$		−	5.27643e15i		−	0.384926i	−0.981304	−	0.192463i	$-0.938352\pi$
$859$		−	5.27643e15i		−	0.384926i	0.981304	−	0.192463i	$-0.0616476\pi$
$860$	4.26114e15	−	4.26114e15i	0.308876	−	0.308876i
$861$	1.20270e15	−	1.20270e15i	0.0866244	−	0.0866244i
$862$	−8.49939e15	−	8.49939e15i	−0.608272	−	0.608272i
$863$	7.22901e15			0.514067			0.257033	−	0.966402i	$-0.417255\pi$
$863$	7.22901e15			0.514067			0.257033	+	0.966402i	$0.417255\pi$
$864$	1.13823e16	+	1.13823e16i	0.804278	+	0.804278i
$865$		−	1.53883e16i		−	1.08044i
$866$	2.27489e16			1.58713
$867$	1.09778e16	−	9.33260e15i	0.761042	−	0.646990i
$868$	2.77153e14			0.0190924
$869$		−	1.50777e16i		−	1.03211i
$870$	−2.63745e16	−	2.63745e16i	−1.79403	−	1.79403i
$871$	−6.62497e14			−0.0447800
$872$	1.73302e15	+	1.73302e15i	0.116402	+	0.116402i
$873$	2.77332e13	−	2.77332e13i	0.00185106	−	0.00185106i
$874$	1.10000e16	−	1.10000e16i	0.729589	−	0.729589i
$875$		−	5.55870e15i		−	0.366378i
$876$			1.29012e16i			0.845002i
$877$	1.22983e15	−	1.22983e15i	0.0800473	−	0.0800473i	−0.665950	−	0.745997i	$-0.731973\pi$
$877$	1.22983e15	−	1.22983e15i	0.0800473	−	0.0800473i	0.745997	+	0.665950i	$0.231973\pi$
$878$	−1.65039e16	+	1.65039e16i	−1.06749	+	1.06749i
$879$	1.25048e15	+	1.25048e15i	0.0803782	+	0.0803782i
$880$	2.98537e16			1.90697
$881$	−3.87754e15	−	3.87754e15i	−0.246144	−	0.246144i	0.573242	−	0.819386i	$-0.305685\pi$
$881$	−3.87754e15	−	3.87754e15i	−0.246144	−	0.246144i	−0.819386	+	0.573242i	$0.805685\pi$
$882$			4.33606e13i			0.00273538i
$883$	−3.94652e15			−0.247418			−0.123709	−	0.992319i	$-0.539479\pi$
$883$	−3.94652e15			−0.247418			−0.123709	+	0.992319i	$0.539479\pi$
$884$	4.75929e14	+	5.16038e14i	0.0296520	+	0.0321510i
$885$	3.80686e16			2.35711
$886$		−	1.50487e16i		−	0.926008i
$887$	−8.20691e15	−	8.20691e15i	−0.501880	−	0.501880i	0.410142	−	0.912022i	$-0.365479\pi$
$887$	−8.20691e15	−	8.20691e15i	−0.501880	−	0.501880i	−0.912022	+	0.410142i	$0.865479\pi$
$888$	1.10401e16			0.670965
$889$	1.32410e15	+	1.32410e15i	0.0799765	+	0.0799765i
$890$	2.09983e16	−	2.09983e16i	1.26049	−	1.26049i
$891$	−1.05857e16	+	1.05857e16i	−0.631526	+	0.631526i
$892$			1.72309e16i			1.02165i
$893$			1.20471e16i			0.709903i
$894$	2.55461e16	−	2.55461e16i	1.49612	−	1.49612i
$895$	2.79582e16	−	2.79582e16i	1.62735	−	1.62735i
$896$	2.09037e15	+	2.09037e15i	0.120928	+	0.120928i
$897$	1.07383e15			0.0617415
$898$	2.21965e16	+	2.21965e16i	1.26843	+	1.26843i
$899$		−	2.81830e15i		−	0.160070i
$900$	−5.22747e13			−0.00295092
$901$	−2.26577e16	+	2.08967e16i	−1.27125	+	1.17244i
$902$	−1.23075e16			−0.686333
$903$			1.41832e15i			0.0786123i
$904$	−1.07757e15	−	1.07757e15i	−0.0593634	−	0.0593634i
$905$	−6.12874e16			−3.35586
$906$	−1.07768e15	−	1.07768e15i	−0.0586520	−	0.0586520i
$907$	−1.48506e16	+	1.48506e16i	−0.803347	+	0.803347i	−0.983617	−	0.180270i	$-0.942303\pi$
$907$	−1.48506e16	+	1.48506e16i	−0.803347	+	0.803347i	0.180270	+	0.983617i	$0.442303\pi$
$908$	−1.20971e16	+	1.20971e16i	−0.650442	+	0.650442i
$909$			9.48030e12i			0.000506665i
$910$		−	5.77344e14i		−	0.0306695i
$911$	1.04637e16	−	1.04637e16i	0.552503	−	0.552503i	−0.374659	−	0.927163i	$-0.622240\pi$
$911$	1.04637e16	−	1.04637e16i	0.552503	−	0.552503i	0.927163	+	0.374659i	$0.122240\pi$
$912$	−1.42274e16	+	1.42274e16i	−0.746713	+	0.746713i
$913$	5.75662e15	+	5.75662e15i	0.300316	+	0.300316i
$914$	−1.75378e16			−0.909433
$915$	−4.63515e16	−	4.63515e16i	−2.38917	−	2.38917i
$916$		−	5.99977e15i		−	0.307404i
$917$	−4.46250e15			−0.227273
$918$	−1.02851e15	+	2.54367e16i	−0.0520684	+	1.28773i
$919$	2.12732e16			1.07053			0.535264	−	0.844685i	$-0.320212\pi$
$919$	2.12732e16			1.07053			0.535264	+	0.844685i	$0.320212\pi$
$920$		−	1.42451e16i		−	0.712579i
$921$	2.06642e15	+	2.06642e15i	0.102752	+	0.102752i
$922$	−2.28403e15			−0.112897
$923$	5.91921e13	+	5.91921e13i	0.00290840	+	0.00290840i
$924$	1.75189e15	−	1.75189e15i	0.0855680	−	0.0855680i
$925$	−4.48633e16	+	4.48633e16i	−2.17827	+	2.17827i
$926$			2.85798e16i			1.37943i
$927$		−	7.35384e13i		−	0.00352838i
$928$	−1.91128e16	+	1.91128e16i	−0.911611	+	0.911611i
$929$	1.48671e16	−	1.48671e16i	0.704918	−	0.704918i	−0.260544	−	0.965462i	$-0.583902\pi$
$929$	1.48671e16	−	1.48671e16i	0.704918	−	0.704918i	0.965462	+	0.260544i	$0.0839018\pi$
$930$	4.73180e15	+	4.73180e15i	0.223034	+	0.223034i
$931$	−1.76332e16			−0.826244
$932$	2.65588e15	+	2.65588e15i	0.123715	+	0.123715i
$933$			3.10258e16i			1.43672i
$934$	2.39217e16			1.10125
$935$	2.30560e16	+	2.49991e16i	1.05516	+	1.14409i
$936$	1.43173e12			6.51393e−5
$937$		−	1.22780e16i		−	0.555341i	−0.960676	−	0.277671i	$-0.910438\pi$
$937$		−	1.22780e16i		−	0.555341i	0.960676	−	0.277671i	$-0.0895624\pi$
$938$	2.80524e15	+	2.80524e15i	0.126141	+	0.126141i
$939$	8.70613e15			0.389193
$940$	−1.49612e16	−	1.49612e16i	−0.664910	−	0.664910i
$941$	1.02235e16	−	1.02235e16i	0.451708	−	0.451708i	−0.444213	−	0.895921i	$-0.646517\pi$
$941$	1.02235e16	−	1.02235e16i	0.451708	−	0.451708i	0.895921	+	0.444213i	$0.146517\pi$
$942$	−1.71285e13	+	1.71285e13i	−0.000752385	+	0.000752385i
$943$			1.26691e16i			0.553264i
$944$		−	3.82995e16i		−	1.66283i
$945$	5.87162e15	−	5.87162e15i	0.253444	−	0.253444i
$946$	7.25699e15	−	7.25699e15i	0.311426	−	0.311426i
$947$	−8.32759e15	−	8.32759e15i	−0.355299	−	0.355299i	0.506777	−	0.862077i	$-0.330837\pi$
$947$	−8.32759e15	−	8.32759e15i	−0.355299	−	0.355299i	−0.862077	+	0.506777i	$0.830837\pi$
$948$	−1.78475e16			−0.757062
$949$	1.43588e15	+	1.43588e15i	0.0605556	+	0.0605556i
$950$		−	5.36004e16i		−	2.24744i
$951$	1.13107e16			0.471517
$952$	−8.85509e13	+	2.19000e15i	−0.00367020	+	0.0907698i
$953$	1.57840e16			0.650440			0.325220	−	0.945638i	$-0.394562\pi$
$953$	1.57840e16			0.650440			0.325220	+	0.945638i	$0.394562\pi$
$954$		−	1.20569e14i		−	0.00493990i
$955$	2.96844e15	+	2.96844e15i	0.120923	+	0.120923i
$956$	2.80684e16			1.13684
$957$	−1.78146e16	−	1.78146e16i	−0.717397	−	0.717397i
$958$	−1.64300e15	+	1.64300e15i	−0.0657850	+	0.0657850i
$959$	4.30957e14	−	4.30957e14i	0.0171566	−	0.0171566i
$960$		−	1.04164e16i		−	0.412312i
$961$		−	2.49029e16i		−	0.980100i
$962$	−2.35667e15	+	2.35667e15i	−0.0922223	+	0.0922223i
$963$	4.81134e13	−	4.81134e13i	0.00187207	−	0.00187207i
$964$	−1.56936e16	−	1.56936e16i	−0.607153	−	0.607153i
$965$	3.66141e16			1.40847
$966$	−4.54697e15	−	4.54697e15i	−0.173919	−	0.173919i
$967$			1.40289e15i			0.0533555i	0.999644	+	0.0266777i	$0.00849280\pi$
$967$			1.40289e15i			0.0533555i	−0.999644	+	0.0266777i	$0.991507\pi$
$968$	−2.31915e15			−0.0877031
$969$	−2.29017e16	−	9.26010e14i	−0.861165	−	0.0348205i
$970$	−7.06302e16			−2.64086
$971$			3.05777e16i			1.13684i	0.822739	+	0.568419i	$0.192445\pi$
$971$			3.05777e16i			1.13684i	−0.822739	+	0.568419i	$0.807555\pi$
$972$	−5.57920e13	−	5.57920e13i	−0.00206256	−	0.00206256i
$973$	5.31100e15			0.195234
$974$	3.24126e16	+	3.24126e16i	1.18479	+	1.18479i
$975$	2.61627e15	−	2.61627e15i	0.0950948	−	0.0950948i
$976$	−4.66326e16	+	4.66326e16i	−1.68545	+	1.68545i
$977$		−	1.55095e16i		−	0.557412i	−0.960376	−	0.278706i	$-0.910094\pi$
$977$		−	1.55095e16i		−	0.557412i	0.960376	−	0.278706i	$-0.0899055\pi$
$978$		−	1.30480e15i		−	0.0466316i
$979$	1.41832e16	−	1.41832e16i	0.504047	−	0.504047i
$980$	2.18986e16	−	2.18986e16i	0.773877	−	0.773877i
$981$	−1.66592e13	−	1.66592e13i	−0.000585429	−	0.000585429i
$982$	1.46876e16			0.513262
$983$	2.35298e16	+	2.35298e16i	0.817661	+	0.817661i	0.985769	−	0.168108i	$-0.0537656\pi$
$983$	2.35298e16	+	2.35298e16i	0.817661	+	0.817661i	−0.168108	+	0.985769i	$0.553766\pi$
$984$		−	7.59580e15i		−	0.262483i
$985$	4.89998e16			1.68382
$986$	−4.27122e16	−	1.72703e15i	−1.45958	−	0.0590171i
$987$	4.97981e15			0.169227
$988$		−	1.11670e15i		−	0.0377375i
$989$	−7.47019e15	−	7.47019e15i	−0.251045	−	0.251045i
$990$	−1.33028e14			−0.00444578
$991$	−1.69049e16	−	1.69049e16i	−0.561833	−	0.561833i	0.367995	−	0.929828i	$-0.380044\pi$
$991$	−1.69049e16	−	1.69049e16i	−0.561833	−	0.561833i	−0.929828	+	0.367995i	$0.880044\pi$
$992$	3.42899e15	−	3.42899e15i	0.113332	−	0.113332i
$993$	−2.50525e13	+	2.50525e13i	−0.000823438	+	0.000823438i
$994$		−	5.01280e14i		−	0.0163853i
$995$			6.32267e16i			2.05529i
$996$	6.81411e15	−	6.81411e15i	0.220284	−	0.220284i
$997$	−4.33726e15	+	4.33726e15i	−0.139442	+	0.139442i	−0.773382	−	0.633940i	$-0.781436\pi$
$997$	−4.33726e15	+	4.33726e15i	−0.139442	+	0.139442i	0.633940	+	0.773382i	$0.281436\pi$
$998$	−1.06578e16	−	1.06578e16i	−0.340762	−	0.340762i
$999$	−4.79349e16			−1.52420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.13	yes	32
17.4	even	4	inner	17.12.c.a.4.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.4	✓	32	17.4	even	4	inner
17.12.c.a.13.13	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+58.2592i q^{2} +(-297.283 - 297.283i) q^{3} -1346.14 q^{4} +(8591.36 + 8591.36i) q^{5} +(17319.5 - 17319.5i) q^{6} +(-6474.40 + 6474.40i) q^{7} +40889.9i q^{8} -393.067i q^{9} +O(q^{10})\)	\(q+58.2592i q^{2} +(-297.283 - 297.283i) q^{3} -1346.14 q^{4} +(8591.36 + 8591.36i) q^{5} +(17319.5 - 17319.5i) q^{6} +(-6474.40 + 6474.40i) q^{7} +40889.9i q^{8} -393.067i q^{9} +(-500526. + 500526. i) q^{10} +(-338079. + 338079. i) q^{11} +(400184. + 400184. i) q^{12} +89079.5 q^{13} +(-377194. - 377194. i) q^{14} -5.10813e6i q^{15} -5.13911e6 q^{16} +(-3.96894e6 - 4.30342e6i) q^{17} +22899.8 q^{18} +9.31254e6i q^{19} +(-1.15652e7 - 1.15652e7i) q^{20} +3.84945e6 q^{21} +(-1.96962e7 - 1.96962e7i) q^{22} +(-2.02749e7 + 2.02749e7i) q^{23} +(1.21558e7 - 1.21558e7i) q^{24} +9.87949e7i q^{25} +5.18970e6i q^{26} +(-5.27796e7 + 5.27796e7i) q^{27} +(8.71545e6 - 8.71545e6i) q^{28} +(-8.86253e7 - 8.86253e7i) q^{29} +2.97596e8 q^{30} +(1.59001e7 + 1.59001e7i) q^{31} -2.15658e8i q^{32} +2.01010e8 q^{33} +(2.50714e8 - 2.31227e8i) q^{34} -1.11248e8 q^{35} +529123. i q^{36} +(4.54105e8 + 4.54105e8i) q^{37} -5.42541e8 q^{38} +(-2.64818e7 - 2.64818e7i) q^{39} +(-3.51300e8 + 3.51300e8i) q^{40} +(3.12434e8 - 3.12434e8i) q^{41} +2.24266e8i q^{42} +3.68446e8i q^{43} +(4.55101e8 - 4.55101e8i) q^{44} +(3.37698e6 - 3.37698e6i) q^{45} +(-1.18120e9 - 1.18120e9i) q^{46} +1.29364e9 q^{47} +(1.52777e9 + 1.52777e9i) q^{48} +1.89349e9i q^{49} -5.75572e9 q^{50} +(-9.94369e7 + 2.45923e9i) q^{51} -1.19913e8 q^{52} -5.26505e9i q^{53} +(-3.07490e9 - 3.07490e9i) q^{54} -5.80912e9 q^{55} +(-2.64737e8 - 2.64737e8i) q^{56} +(2.76846e9 - 2.76846e9i) q^{57} +(5.16324e9 - 5.16324e9i) q^{58} +7.45256e9i q^{59} +6.87625e9i q^{60} +(9.07407e9 - 9.07407e9i) q^{61} +(-9.26328e8 + 9.26328e8i) q^{62} +(2.54487e6 + 2.54487e6i) q^{63} +2.03918e9 q^{64} +(7.65314e8 + 7.65314e8i) q^{65} +1.17107e10i q^{66} -7.43714e9 q^{67} +(5.34274e9 + 5.79301e9i) q^{68} +1.20547e10 q^{69} -6.48122e9i q^{70} +(6.64487e8 + 6.64487e8i) q^{71} +1.60725e7 q^{72} +(1.61191e10 + 1.61191e10i) q^{73} +(-2.64558e10 + 2.64558e10i) q^{74} +(2.93700e10 - 2.93700e10i) q^{75} -1.25360e10i q^{76} -4.37772e9i q^{77} +(1.54281e9 - 1.54281e9i) q^{78} +(-2.22991e10 + 2.22991e10i) q^{79} +(-4.41519e10 - 4.41519e10i) q^{80} +3.13113e10 q^{81} +(1.82022e10 + 1.82022e10i) q^{82} -1.70274e10i q^{83} -5.18190e9 q^{84} +(2.87369e9 - 7.10708e10i) q^{85} -2.14654e10 q^{86} +5.26935e10i q^{87} +(-1.38240e10 - 1.38240e10i) q^{88} -4.19525e10 q^{89} +(1.96740e8 + 1.96740e8i) q^{90} +(-5.76736e8 + 5.76736e8i) q^{91} +(2.72928e10 - 2.72928e10i) q^{92} -9.45365e9i q^{93} +7.53665e10i q^{94} +(-8.00074e10 + 8.00074e10i) q^{95} +(-6.41114e10 + 6.41114e10i) q^{96} +(7.05559e10 + 7.05559e10i) q^{97} -1.10313e11 q^{98} +(1.32888e8 + 1.32888e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7} + 178138 q^{10} - 24816 q^{11} + 1322202 q^{12} - 1533752 q^{13} - 757692 q^{14} + 22082308 q^{16} + 17346416 q^{17} + 16775420 q^{18} + 11716134 q^{20} + 16504072 q^{21} + 55362010 q^{22} - 70945120 q^{23} - 7042078 q^{24} - 27445824 q^{27} + 339432756 q^{28} + 185239264 q^{29} - 1261021320 q^{30} + 415468304 q^{31} - 1075445880 q^{33} + 969384454 q^{34} - 1094449168 q^{35} - 49028824 q^{37} - 1340995872 q^{38} + 3217138400 q^{39} + 1182717098 q^{40} - 1419194816 q^{41} - 509236610 q^{44} + 1839923056 q^{45} - 3796371488 q^{46} - 8774740352 q^{47} + 4059548014 q^{48} + 4114666548 q^{50} - 9057963232 q^{51} + 18756164724 q^{52} + 25648728424 q^{54} - 17548144256 q^{55} + 966113388 q^{56} + 23148052104 q^{57} + 32800009486 q^{58} + 1217387240 q^{61} - 42857202380 q^{62} - 58090649872 q^{63} - 43481694148 q^{64} - 12772720712 q^{65} + 17181896368 q^{67} - 120669329406 q^{68} + 84389704104 q^{69} + 36350065824 q^{71} - 62012005860 q^{72} + 41295758480 q^{73} + 108372466886 q^{74} + 143581200752 q^{75} + 103160490932 q^{78} - 86305741264 q^{79} - 278909687742 q^{80} - 398139885080 q^{81} + 84221472400 q^{82} + 278009687832 q^{84} - 131899000528 q^{85} + 214354160644 q^{86} + 95628137594 q^{88} - 158760835496 q^{89} + 629605313178 q^{90} + 149211106624 q^{91} + 288480507416 q^{92} - 267919909216 q^{95} - 242746850002 q^{96} - 126853433800 q^{97} - 829249376752 q^{98} + 229465269792 q^{99}+O(q^{100}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7 + 178138 * q^10 - 24816 * q^11 + 1322202 * q^12 - 1533752 * q^13 - 757692 * q^14 + 22082308 * q^16 + 17346416 * q^17 + 16775420 * q^18 + 11716134 * q^20 + 16504072 * q^21 + 55362010 * q^22 - 70945120 * q^23 - 7042078 * q^24 - 27445824 * q^27 + 339432756 * q^28 + 185239264 * q^29 - 1261021320 * q^30 + 415468304 * q^31 - 1075445880 * q^33 + 969384454 * q^34 - 1094449168 * q^35 - 49028824 * q^37 - 1340995872 * q^38 + 3217138400 * q^39 + 1182717098 * q^40 - 1419194816 * q^41 - 509236610 * q^44 + 1839923056 * q^45 - 3796371488 * q^46 - 8774740352 * q^47 + 4059548014 * q^48 + 4114666548 * q^50 - 9057963232 * q^51 + 18756164724 * q^52 + 25648728424 * q^54 - 17548144256 * q^55 + 966113388 * q^56 + 23148052104 * q^57 + 32800009486 * q^58 + 1217387240 * q^61 - 42857202380 * q^62 - 58090649872 * q^63 - 43481694148 * q^64 - 12772720712 * q^65 + 17181896368 * q^67 - 120669329406 * q^68 + 84389704104 * q^69 + 36350065824 * q^71 - 62012005860 * q^72 + 41295758480 * q^73 + 108372466886 * q^74 + 143581200752 * q^75 + 103160490932 * q^78 - 86305741264 * q^79 - 278909687742 * q^80 - 398139885080 * q^81 + 84221472400 * q^82 + 278009687832 * q^84 - 131899000528 * q^85 + 214354160644 * q^86 + 95628137594 * q^88 - 158760835496 * q^89 + 629605313178 * q^90 + 149211106624 * q^91 + 288480507416 * q^92 - 267919909216 * q^95 - 242746850002 * q^96 - 126853433800 * q^97 - 829249376752 * q^98 + 229465269792 * q^99

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