LMFDB - Embedded newform 17.12.c.a.13.11

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			13.11
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.2416i q^{2} +(149.760 + 149.760i) q^{3} +1008.48 q^{4} +(-6170.50 - 6170.50i) q^{5} +(-4828.50 + 4828.50i) q^{6} +(-42929.1 + 42929.1i) q^{7} +98545.8i q^{8} -132291. i q^{9} +O(q^{10})$	\(q+32.2416i q^{2} +(149.760 + 149.760i) q^{3} +1008.48 q^{4} +(-6170.50 - 6170.50i) q^{5} +(-4828.50 + 4828.50i) q^{6} +(-42929.1 + 42929.1i) q^{7} +98545.8i q^{8} -132291. i q^{9} +(198947. - 198947. i) q^{10} +(-441672. + 441672. i) q^{11} +(151030. + 151030. i) q^{12} -891124. q^{13} +(-1.38410e6 - 1.38410e6i) q^{14} -1.84819e6i q^{15} -1.11191e6 q^{16} +(-5.37096e6 - 2.32909e6i) q^{17} +4.26527e6 q^{18} -6.04031e6i q^{19} +(-6.22283e6 - 6.22283e6i) q^{20} -1.28581e7 q^{21} +(-1.42402e7 - 1.42402e7i) q^{22} +(-8.63920e6 + 8.63920e6i) q^{23} +(-1.47582e7 + 1.47582e7i) q^{24} +2.73220e7i q^{25} -2.87312e7i q^{26} +(4.63414e7 - 4.63414e7i) q^{27} +(-4.32931e7 + 4.32931e7i) q^{28} +(1.30044e8 + 1.30044e8i) q^{29} +5.95885e7 q^{30} +(-1.44941e8 - 1.44941e8i) q^{31} +1.65972e8i q^{32} -1.32289e8 q^{33} +(7.50937e7 - 1.73168e8i) q^{34} +5.29788e8 q^{35} -1.33413e8i q^{36} +(4.84369e8 + 4.84369e8i) q^{37} +1.94749e8 q^{38} +(-1.33455e8 - 1.33455e8i) q^{39} +(6.08077e8 - 6.08077e8i) q^{40} +(-9.68577e8 + 9.68577e8i) q^{41} -4.14566e8i q^{42} +1.03458e8i q^{43} +(-4.45417e8 + 4.45417e8i) q^{44} +(-8.16301e8 + 8.16301e8i) q^{45} +(-2.78542e8 - 2.78542e8i) q^{46} -8.10441e8 q^{47} +(-1.66519e8 - 1.66519e8i) q^{48} -1.70848e9i q^{49} -8.80905e8 q^{50} +(-4.55550e8 - 1.15316e9i) q^{51} -8.98680e8 q^{52} -1.65122e9i q^{53} +(1.49412e9 + 1.49412e9i) q^{54} +5.45067e9 q^{55} +(-4.23048e9 - 4.23048e9i) q^{56} +(9.04596e8 - 9.04596e8i) q^{57} +(-4.19284e9 + 4.19284e9i) q^{58} -1.05861e9i q^{59} -1.86386e9i q^{60} +(-4.61763e9 + 4.61763e9i) q^{61} +(4.67314e9 - 4.67314e9i) q^{62} +(5.67913e9 + 5.67913e9i) q^{63} -7.62839e9 q^{64} +(5.49868e9 + 5.49868e9i) q^{65} -4.26522e9i q^{66} +1.58192e10 q^{67} +(-5.41651e9 - 2.34884e9i) q^{68} -2.58761e9 q^{69} +1.70812e10i q^{70} +(3.86481e9 + 3.86481e9i) q^{71} +1.30367e10 q^{72} +(1.10836e10 + 1.10836e10i) q^{73} +(-1.56168e10 + 1.56168e10i) q^{74} +(-4.09174e9 + 4.09174e9i) q^{75} -6.09153e9i q^{76} -3.79211e10i q^{77} +(4.30279e9 - 4.30279e9i) q^{78} +(2.68062e10 - 2.68062e10i) q^{79} +(6.86101e9 + 6.86101e9i) q^{80} -9.55479e9 q^{81} +(-3.12285e10 - 3.12285e10i) q^{82} +7.65509e9i q^{83} -1.29671e10 q^{84} +(1.87698e10 + 4.75132e10i) q^{85} -3.33565e9 q^{86} +3.89509e10i q^{87} +(-4.35249e10 - 4.35249e10i) q^{88} -7.53622e10 q^{89} +(-2.63189e10 - 2.63189e10i) q^{90} +(3.82551e10 - 3.82551e10i) q^{91} +(-8.71246e9 + 8.71246e9i) q^{92} -4.34128e10i q^{93} -2.61299e10i q^{94} +(-3.72717e10 + 3.72717e10i) q^{95} +(-2.48560e10 + 2.48560e10i) q^{96} +(4.94921e10 + 4.94921e10i) q^{97} +5.50842e10 q^{98} +(5.84292e10 + 5.84292e10i) 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 $

$2$			32.2416i			0.712445i	0.934401	+	0.356223i	$0.115936\pi$
$2$			32.2416i			0.712445i	−0.934401	+	0.356223i	$0.884064\pi$
$3$	149.760	+	149.760i	0.355819	+	0.355819i	0.862269	−	0.506451i	$-0.169043\pi$
$3$	149.760	+	149.760i	0.355819	+	0.355819i	−0.506451	+	0.862269i	$0.669043\pi$
$4$	1008.48			0.492422
$5$	−6170.50	−	6170.50i	−0.883050	−	0.883050i	0.110793	−	0.993843i	$-0.464661\pi$
$5$	−6170.50	−	6170.50i	−0.883050	−	0.883050i	−0.993843	+	0.110793i	$0.964661\pi$
$6$	−4828.50	+	4828.50i	−0.253501	+	0.253501i
$7$	−42929.1	+	42929.1i	−0.965411	+	0.965411i	−0.999421	−	0.0340104i	$-0.989172\pi$
$7$	−42929.1	+	42929.1i	−0.965411	+	0.965411i	0.0340104	+	0.999421i	$0.489172\pi$
$8$			98545.8i			1.06327i
$9$		−	132291.i		−	0.746786i
$10$	198947.	−	198947.i	0.629125	−	0.629125i
$11$	−441672.	+	441672.i	−0.826875	+	0.826875i	−0.987083	−	0.160208i	$-0.948783\pi$
$11$	−441672.	+	441672.i	−0.826875	+	0.826875i	0.160208	+	0.987083i	$0.448783\pi$
$12$	151030.	+	151030.i	0.175213	+	0.175213i
$13$	−891124.			−0.665656			−0.332828	−	0.942988i	$-0.608003\pi$
$13$	−891124.			−0.665656			−0.332828	+	0.942988i	$0.608003\pi$
$14$	−1.38410e6	−	1.38410e6i	−0.687803	−	0.687803i
$15$		−	1.84819e6i		−	0.628411i
$16$	−1.11191e6			−0.265099
$17$	−5.37096e6	−	2.32909e6i	−0.917451	−	0.397849i
$17$	−5.37096e6	−	2.32909e6i	−0.917451	−	0.397849i
$18$	4.26527e6			0.532044
$19$		−	6.04031e6i		−	0.559647i	−0.960051	−	0.279824i	$-0.909724\pi$
$19$		−	6.04031e6i		−	0.559647i	0.960051	−	0.279824i	$-0.0902760\pi$
$20$	−6.22283e6	−	6.22283e6i	−0.434833	−	0.434833i
$21$	−1.28581e7			−0.687022
$22$	−1.42402e7	−	1.42402e7i	−0.589103	−	0.589103i
$23$	−8.63920e6	+	8.63920e6i	−0.279879	+	0.279879i	−0.833061	−	0.553182i	$-0.813414\pi$
$23$	−8.63920e6	+	8.63920e6i	−0.279879	+	0.279879i	0.553182	+	0.833061i	$0.313414\pi$
$24$	−1.47582e7	+	1.47582e7i	−0.378331	+	0.378331i
$25$			2.73220e7i			0.559555i
$26$		−	2.87312e7i		−	0.474243i
$27$	4.63414e7	−	4.63414e7i	0.621539	−	0.621539i
$28$	−4.32931e7	+	4.32931e7i	−0.475389	+	0.475389i
$29$	1.30044e8	+	1.30044e8i	1.17734	+	1.17734i	0.980419	+	0.196923i	$0.0630951\pi$
$29$	1.30044e8	+	1.30044e8i	1.17734	+	1.17734i	0.196923	+	0.980419i	$0.436905\pi$
$30$	5.95885e7			0.447709
$31$	−1.44941e8	−	1.44941e8i	−0.909292	−	0.909292i	0.0869232	−	0.996215i	$-0.472297\pi$
$31$	−1.44941e8	−	1.44941e8i	−0.909292	−	0.909292i	−0.996215	+	0.0869232i	$0.972297\pi$
$32$			1.65972e8i			0.874400i
$33$	−1.32289e8			−0.588435
$34$	7.50937e7	−	1.73168e8i	0.283445	−	0.653634i
$35$	5.29788e8			1.70501
$36$		−	1.33413e8i		−	0.367734i
$37$	4.84369e8	+	4.84369e8i	1.14833	+	1.14833i	0.986881	+	0.161449i	$0.0516167\pi$
$37$	4.84369e8	+	4.84369e8i	1.14833	+	1.14833i	0.161449	+	0.986881i	$0.448383\pi$
$38$	1.94749e8			0.398718
$39$	−1.33455e8	−	1.33455e8i	−0.236853	−	0.236853i
$40$	6.08077e8	−	6.08077e8i	0.938920	−	0.938920i
$41$	−9.68577e8	+	9.68577e8i	−1.30564	+	1.30564i	−0.381107	+	0.924531i	$0.624457\pi$
$41$	−9.68577e8	+	9.68577e8i	−1.30564	+	1.30564i	−0.924531	+	0.381107i	$0.875543\pi$
$42$		−	4.14566e8i		−	0.489466i
$43$			1.03458e8i			0.107322i	0.998559	+	0.0536608i	$0.0170890\pi$
$43$			1.03458e8i			0.107322i	−0.998559	+	0.0536608i	$0.982911\pi$
$44$	−4.45417e8	+	4.45417e8i	−0.407171	+	0.407171i
$45$	−8.16301e8	+	8.16301e8i	−0.659450	+	0.659450i
$46$	−2.78542e8	−	2.78542e8i	−0.199399	−	0.199399i
$47$	−8.10441e8			−0.515446			−0.257723	−	0.966219i	$-0.582972\pi$
$47$	−8.10441e8			−0.515446			−0.257723	+	0.966219i	$0.582972\pi$
$48$	−1.66519e8	−	1.66519e8i	−0.0943271	−	0.0943271i
$49$		−	1.70848e9i		−	0.864037i
$50$	−8.80905e8			−0.398652
$51$	−4.55550e8	−	1.15316e9i	−0.184884	−	0.468008i
$52$	−8.98680e8			−0.327783
$53$		−	1.65122e9i		−	0.542360i	−0.962529	−	0.271180i	$-0.912586\pi$
$53$		−	1.65122e9i		−	0.542360i	0.962529	−	0.271180i	$-0.0874139\pi$
$54$	1.49412e9	+	1.49412e9i	0.442812	+	0.442812i
$55$	5.45067e9			1.46034
$56$	−4.23048e9	−	4.23048e9i	−1.02649	−	1.02649i
$57$	9.04596e8	−	9.04596e8i	0.199133	−	0.199133i
$58$	−4.19284e9	+	4.19284e9i	−0.838792	+	0.838792i
$59$		−	1.05861e9i		−	0.192775i	−0.995344	−	0.0963875i	$-0.969271\pi$
$59$		−	1.05861e9i		−	0.192775i	0.995344	−	0.0963875i	$-0.0307288\pi$
$60$		−	1.86386e9i		−	0.309443i
$61$	−4.61763e9	+	4.61763e9i	−0.700011	+	0.700011i	−0.964413	−	0.264401i	$-0.914826\pi$
$61$	−4.61763e9	+	4.61763e9i	−0.700011	+	0.700011i	0.264401	+	0.964413i	$0.414826\pi$
$62$	4.67314e9	−	4.67314e9i	0.647821	−	0.647821i
$63$	5.67913e9	+	5.67913e9i	0.720956	+	0.720956i
$64$	−7.62839e9			−0.888061
$65$	5.49868e9	+	5.49868e9i	0.587807	+	0.587807i
$66$		−	4.26522e9i		−	0.419228i
$67$	1.58192e10			1.43144			0.715721	−	0.698386i	$-0.246098\pi$
$67$	1.58192e10			1.43144			0.715721	+	0.698386i	$0.246098\pi$
$68$	−5.41651e9	−	2.34884e9i	−0.451773	−	0.195909i
$69$	−2.58761e9			−0.199172
$70$			1.70812e10i			1.21473i
$71$	3.86481e9	+	3.86481e9i	0.254218	+	0.254218i	0.822698	−	0.568479i	$-0.192468\pi$
$71$	3.86481e9	+	3.86481e9i	0.254218	+	0.254218i	−0.568479	+	0.822698i	$0.692468\pi$
$72$	1.30367e10			0.794035
$73$	1.10836e10	+	1.10836e10i	0.625755	+	0.625755i	0.946997	−	0.321242i	$-0.104100\pi$
$73$	1.10836e10	+	1.10836e10i	0.625755	+	0.625755i	−0.321242	+	0.946997i	$0.604100\pi$
$74$	−1.56168e10	+	1.56168e10i	−0.818122	+	0.818122i
$75$	−4.09174e9	+	4.09174e9i	−0.199100	+	0.199100i
$76$		−	6.09153e9i		−	0.275582i
$77$		−	3.79211e10i		−	1.59655i
$78$	4.30279e9	−	4.30279e9i	0.168744	−	0.168744i
$79$	2.68062e10	−	2.68062e10i	0.980138	−	0.980138i	−0.0196690	−	0.999807i	$-0.506261\pi$
$79$	2.68062e10	−	2.68062e10i	0.980138	−	0.980138i	0.999807	+	0.0196690i	$0.00626123\pi$
$80$	6.86101e9	+	6.86101e9i	0.234096	+	0.234096i
$81$	−9.55479e9			−0.304476
$82$	−3.12285e10	−	3.12285e10i	−0.930196	−	0.930196i
$83$			7.65509e9i			0.213315i	0.994296	+	0.106657i	$0.0340148\pi$
$83$			7.65509e9i			0.213315i	−0.994296	+	0.106657i	$0.965985\pi$
$84$	−1.29671e10			−0.338305
$85$	1.87698e10	+	4.75132e10i	0.458835	+	1.16148i
$86$	−3.33565e9			−0.0764607
$87$			3.89509e10i			0.837840i
$88$	−4.35249e10	−	4.35249e10i	−0.879190	−	0.879190i
$89$	−7.53622e10			−1.43057			−0.715284	−	0.698834i	$-0.753703\pi$
$89$	−7.53622e10			−1.43057			−0.715284	+	0.698834i	$0.753703\pi$
$90$	−2.63189e10	−	2.63189e10i	−0.469822	−	0.469822i
$91$	3.82551e10	−	3.82551e10i	0.642631	−	0.642631i
$92$	−8.71246e9	+	8.71246e9i	−0.137819	+	0.137819i
$93$		−	4.34128e10i		−	0.647086i
$94$		−	2.61299e10i		−	0.367227i
$95$	−3.72717e10	+	3.72717e10i	−0.494197	+	0.494197i
$96$	−2.48560e10	+	2.48560e10i	−0.311128	+	0.311128i
$97$	4.94921e10	+	4.94921e10i	0.585183	+	0.585183i	0.936323	−	0.351140i	$-0.114206\pi$
$97$	4.94921e10	+	4.94921e10i	0.585183	+	0.585183i	−0.351140	+	0.936323i	$0.614206\pi$
$98$	5.50842e10			0.615579
$99$	5.84292e10	+	5.84292e10i	0.617499	+	0.617499i
$100$			2.75537e10i			0.275537i
$101$	−4.23747e10			−0.401180			−0.200590	−	0.979675i	$-0.564286\pi$
$101$	−4.23747e10			−0.401180			−0.200590	+	0.979675i	$0.564286\pi$
$102$	3.71797e10	−	1.46876e10i	0.333430	−	0.131720i
$103$	−1.13096e11			−0.961265			−0.480633	−	0.876922i	$-0.659593\pi$
$103$	−1.13096e11			−0.961265			−0.480633	+	0.876922i	$0.659593\pi$
$104$		−	8.78165e10i		−	0.707771i
$105$	7.93409e10	+	7.93409e10i	0.606675	+	0.606675i
$106$	5.32380e10			0.386402
$107$	−1.16203e11	−	1.16203e11i	−0.800953	−	0.800953i	0.182292	−	0.983244i	$-0.441648\pi$
$107$	−1.16203e11	−	1.16203e11i	−0.800953	−	0.800953i	−0.983244	+	0.182292i	$0.941648\pi$
$108$	4.67344e10	−	4.67344e10i	0.306059	−	0.306059i
$109$	1.47666e11	−	1.47666e11i	0.919252	−	0.919252i	−0.0777231	−	0.996975i	$-0.524765\pi$
$109$	1.47666e11	−	1.47666e11i	0.919252	−	0.919252i	0.996975	+	0.0777231i	$0.0247650\pi$
$110$			1.75738e11i			1.04042i
$111$			1.45078e11i			0.817194i
$112$	4.77331e10	−	4.77331e10i	0.255929	−	0.255929i
$113$	−5.32464e10	+	5.32464e10i	−0.271869	+	0.271869i	−0.829852	−	0.557983i	$-0.811575\pi$
$113$	−5.32464e10	+	5.32464e10i	−0.271869	+	0.271869i	0.557983	+	0.829852i	$0.311575\pi$
$114$	2.91656e10	+	2.91656e10i	0.141871	+	0.141871i
$115$	1.06616e11			0.494295
$116$	1.31147e11	+	1.31147e11i	0.579749	+	0.579749i
$117$			1.17888e11i			0.497103i
$118$	3.41313e10			0.137342
$119$	3.30556e11	−	1.30585e11i	1.26980	−	0.501630i
$120$	1.82131e11			0.668170
$121$		−	1.04836e11i		−	0.367445i
$122$	−1.48880e11	−	1.48880e11i	−0.498720	−	0.498720i
$123$	−2.90108e11			−0.929140
$124$	−1.46171e11	−	1.46171e11i	−0.447755	−	0.447755i
$125$	−1.32703e11	+	1.32703e11i	−0.388935	+	0.388935i
$126$	−1.83104e11	+	1.83104e11i	−0.513642	+	0.513642i
$127$		−	1.05385e11i		−	0.283048i	−0.989935	−	0.141524i	$-0.954800\pi$
$127$		−	1.05385e11i		−	0.283048i	0.989935	−	0.141524i	$-0.0452002\pi$
$128$			9.39596e10i			0.241705i
$129$	−1.54938e10	+	1.54938e10i	−0.0381870	+	0.0381870i
$130$	−1.77286e11	+	1.77286e11i	−0.418780	+	0.418780i
$131$	−3.67710e11	−	3.67710e11i	−0.832748	−	0.832748i	0.155144	−	0.987892i	$-0.450416\pi$
$131$	−3.67710e11	−	3.67710e11i	−0.832748	−	0.832748i	−0.987892	+	0.155144i	$0.950416\pi$
$132$	−1.33411e11			−0.289758
$133$	2.59305e11	+	2.59305e11i	0.540290	+	0.540290i
$134$			5.10037e11i			1.01982i
$135$	−5.71899e11			−1.09770
$136$	2.29522e11	−	5.29285e11i	0.423020	−	0.975497i
$137$	2.01732e10			0.0357118			0.0178559	−	0.999841i	$-0.494316\pi$
$137$	2.01732e10			0.0357118			0.0178559	+	0.999841i	$0.494316\pi$
$138$		−	8.34287e10i		−	0.141899i
$139$	−3.52167e11	−	3.52167e11i	−0.575662	−	0.575662i	0.358043	−	0.933705i	$-0.383444\pi$
$139$	−3.52167e11	−	3.52167e11i	−0.575662	−	0.575662i	−0.933705	+	0.358043i	$0.883444\pi$
$140$	5.34280e11			0.839585
$141$	−1.21372e11	−	1.21372e11i	−0.183405	−	0.183405i
$142$	−1.24607e11	+	1.24607e11i	−0.181117	+	0.181117i
$143$	3.93584e11	−	3.93584e11i	0.550414	−	0.550414i
$144$			1.47095e11i			0.197972i
$145$		−	1.60488e12i		−	2.07930i
$146$	−3.57352e11	+	3.57352e11i	−0.445816	+	0.445816i
$147$	2.55862e11	−	2.55862e11i	0.307440	−	0.307440i
$148$	4.88476e11	+	4.88476e11i	0.565463	+	0.565463i
$149$	−1.31024e12			−1.46159			−0.730794	−	0.682598i	$-0.760850\pi$
$149$	−1.31024e12			−1.46159			−0.730794	+	0.682598i	$0.760850\pi$
$150$	−1.31924e11	−	1.31924e11i	−0.141848	−	0.141848i
$151$			2.75143e11i			0.285224i	0.989779	+	0.142612i	$0.0455501\pi$
$151$			2.75143e11i			0.285224i	−0.989779	+	0.142612i	$0.954450\pi$
$152$	5.95247e11			0.595055
$153$	−3.08118e11	+	7.10530e11i	−0.297108	+	0.685140i
$154$	1.22264e12			1.13745
$155$			1.78872e12i			1.60590i
$156$	−1.34586e11	−	1.34586e11i	−0.116631	−	0.116631i
$157$	−1.48210e11			−0.124002			−0.0620010	−	0.998076i	$-0.519748\pi$
$157$	−1.48210e11			−0.124002			−0.0620010	+	0.998076i	$0.519748\pi$
$158$	8.64276e11	+	8.64276e11i	0.698294	+	0.698294i
$159$	2.47287e11	−	2.47287e11i	0.192982	−	0.192982i
$160$	1.02413e12	−	1.02413e12i	0.772139	−	0.772139i
$161$		−	7.41746e11i		−	0.540397i
$162$		−	3.08062e11i		−	0.216923i
$163$	1.94380e11	−	1.94380e11i	0.132318	−	0.132318i	−0.637846	−	0.770164i	$-0.720174\pi$
$163$	1.94380e11	−	1.94380e11i	0.132318	−	0.132318i	0.770164	+	0.637846i	$0.220174\pi$
$164$	−9.76790e11	+	9.76790e11i	−0.642925	+	0.642925i
$165$	8.16292e11	+	8.16292e11i	0.519617	+	0.519617i
$166$	−2.46812e11			−0.151975
$167$	2.00672e12	+	2.00672e12i	1.19549	+	1.19549i	0.975503	+	0.219987i	$0.0706015\pi$
$167$	2.00672e12	+	2.00672e12i	1.19549	+	1.19549i	0.219987	+	0.975503i	$0.429399\pi$
$168$		−	1.26711e12i		−	0.730489i
$169$	−9.98059e11			−0.556903
$170$	−1.53190e12	+	6.05169e11i	−0.827488	+	0.326895i
$171$	−7.99078e11			−0.417937
$172$			1.04335e11i			0.0528475i
$173$	2.61843e12	+	2.61843e12i	1.28466	+	1.28466i	0.937988	+	0.346667i	$0.112687\pi$
$173$	2.61843e12	+	2.61843e12i	1.28466	+	1.28466i	0.346667	+	0.937988i	$0.387313\pi$
$174$	−1.25584e12			−0.596915
$175$	−1.17291e12	−	1.17291e12i	−0.540201	−	0.540201i
$176$	4.91097e11	−	4.91097e11i	0.219204	−	0.219204i
$177$	1.58538e11	−	1.58538e11i	0.0685929	−	0.0685929i
$178$		−	2.42980e12i		−	1.01920i
$179$		−	1.89957e12i		−	0.772617i	−0.922370	−	0.386308i	$-0.873750\pi$
$179$		−	1.89957e12i		−	0.772617i	0.922370	−	0.386308i	$-0.126250\pi$
$180$	−8.23224e11	+	8.23224e11i	−0.324727	+	0.324727i
$181$	1.53076e11	−	1.53076e11i	0.0585699	−	0.0585699i	−0.677215	−	0.735785i	$-0.736813\pi$
$181$	1.53076e11	−	1.53076e11i	0.0585699	−	0.0585699i	0.735785	+	0.677215i	$0.236813\pi$
$182$	1.23341e12	+	1.23341e12i	0.457840	+	0.457840i
$183$	−1.38307e12			−0.498154
$184$	−8.51357e11	−	8.51357e11i	−0.297587	−	0.297587i
$185$		−	5.97760e12i		−	2.02807i
$186$	1.39970e12			0.461013
$187$	3.40090e12	−	1.34351e12i	1.08759	−	0.429646i
$188$	−8.17314e11			−0.253817
$189$			3.97879e12i			1.20008i
$190$	−1.20170e12	−	1.20170e12i	−0.352088	−	0.352088i
$191$	−9.78355e11			−0.278492			−0.139246	−	0.990258i	$-0.544468\pi$
$191$	−9.78355e11			−0.278492			−0.139246	+	0.990258i	$0.544468\pi$
$192$	−1.14243e12	−	1.14243e12i	−0.315989	−	0.315989i
$193$	−1.69671e12	+	1.69671e12i	−0.456081	+	0.456081i	−0.897367	−	0.441285i	$-0.854523\pi$
$193$	−1.69671e12	+	1.69671e12i	−0.456081	+	0.456081i	0.441285	+	0.897367i	$0.354523\pi$
$194$	−1.59570e12	+	1.59570e12i	−0.416911	+	0.416911i
$195$			1.64696e12i			0.418305i
$196$		−	1.72297e12i		−	0.425471i
$197$	−1.47780e12	+	1.47780e12i	−0.354855	+	0.354855i	−0.861912	−	0.507058i	$-0.830733\pi$
$197$	−1.47780e12	+	1.47780e12i	−0.354855	+	0.354855i	0.507058	+	0.861912i	$0.330733\pi$
$198$	−1.88385e12	+	1.88385e12i	−0.439934	+	0.439934i
$199$	−2.95779e12	−	2.95779e12i	−0.671855	−	0.671855i	0.286289	−	0.958143i	$-0.407578\pi$
$199$	−2.95779e12	−	2.95779e12i	−0.671855	−	0.671855i	−0.958143	+	0.286289i	$0.907578\pi$
$200$	−2.69247e12			−0.594957
$201$	2.36909e12	+	2.36909e12i	0.509334	+	0.509334i
$202$		−	1.36623e12i		−	0.285819i
$203$	−1.11654e13			−2.27324
$204$	−4.59413e11	−	1.16294e12i	−0.0910410	−	0.230457i
$205$	1.19532e13			2.30589
$206$		−	3.64640e12i		−	0.684849i
$207$	1.14289e12	+	1.14289e12i	0.209010	+	0.209010i
$208$	9.90846e11			0.176465
$209$	2.66783e12	+	2.66783e12i	0.462758	+	0.462758i
$210$	−2.55808e12	+	2.55808e12i	−0.432223	+	0.432223i
$211$	−2.83402e12	+	2.83402e12i	−0.466497	+	0.466497i	−0.900778	−	0.434280i	$-0.857003\pi$
$211$	−2.83402e12	+	2.83402e12i	−0.466497	+	0.466497i	0.434280	+	0.900778i	$0.357003\pi$
$212$		−	1.66522e12i		−	0.267070i
$213$			1.15759e12i			0.180911i
$214$	3.74657e12	−	3.74657e12i	0.570635	−	0.570635i
$215$	6.38387e11	−	6.38387e11i	0.0947703	−	0.0947703i
$216$	4.56675e12	+	4.56675e12i	0.660863	+	0.660863i
$217$	1.24444e13			1.75568
$218$	4.76098e12	+	4.76098e12i	0.654917	+	0.654917i
$219$			3.31975e12i			0.445310i
$220$	5.49689e12			0.719105
$221$	4.78619e12	+	2.07551e12i	0.610706	+	0.264830i
$222$	−4.67755e12			−0.582206
$223$		−	1.06133e13i		−	1.28877i	−0.764702	−	0.644384i	$-0.777114\pi$
$223$		−	1.06133e13i		−	1.28877i	0.764702	−	0.644384i	$-0.222886\pi$
$224$	−7.12503e12	−	7.12503e12i	−0.844156	−	0.844156i
$225$	3.61446e12			0.417868
$226$	−1.71675e12	−	1.71675e12i	−0.193692	−	0.193692i
$227$	−3.78866e12	+	3.78866e12i	−0.417199	+	0.417199i	−0.884237	−	0.467038i	$-0.845321\pi$
$227$	−3.78866e12	+	3.78866e12i	−0.417199	+	0.417199i	0.467038	+	0.884237i	$0.345321\pi$
$228$	9.12267e11	−	9.12267e11i	0.0980573	−	0.0980573i
$229$			1.36885e12i			0.143635i	0.997418	+	0.0718174i	$0.0228799\pi$
$229$			1.36885e12i			0.143635i	−0.997418	+	0.0718174i	$0.977120\pi$
$230$			3.43748e12i			0.352158i
$231$	5.67906e12	−	5.67906e12i	0.568082	−	0.568082i
$232$	−1.28153e13	+	1.28153e13i	−1.25183	+	1.25183i
$233$	−7.59250e12	−	7.59250e12i	−0.724315	−	0.724315i	0.245166	−	0.969481i	$-0.421157\pi$
$233$	−7.59250e12	−	7.59250e12i	−0.724315	−	0.724315i	−0.969481	+	0.245166i	$0.921157\pi$
$234$	−3.80088e12			−0.354158
$235$	5.00083e12	+	5.00083e12i	0.455165	+	0.455165i
$236$		−	1.06759e12i		−	0.0949267i
$237$	8.02900e12			0.697502
$238$	4.21025e12	+	1.06577e13i	0.357384	+	0.904666i
$239$	1.60888e13			1.33455			0.667276	−	0.744810i	$-0.267460\pi$
$239$	1.60888e13			1.33455			0.667276	+	0.744810i	$0.267460\pi$
$240$			2.05501e12i			0.166591i
$241$	−1.19742e13	−	1.19742e13i	−0.948756	−	0.948756i	0.0499939	−	0.998750i	$-0.484080\pi$
$241$	−1.19742e13	−	1.19742e13i	−0.948756	−	0.948756i	−0.998750	+	0.0499939i	$0.984080\pi$
$242$	3.38009e12			0.261784
$243$	−9.64016e12	−	9.64016e12i	−0.729877	−	0.729877i
$244$	−4.65679e12	+	4.65679e12i	−0.344701	+	0.344701i
$245$	−1.05422e13	+	1.05422e13i	−0.762988	+	0.762988i
$246$		−	9.35354e12i		−	0.661962i
$247$			5.38266e12i			0.372532i
$248$	1.42834e13	−	1.42834e13i	0.966822	−	0.966822i
$249$	−1.14643e12	+	1.14643e12i	−0.0759013	+	0.0759013i
$250$	−4.27857e12	−	4.27857e12i	−0.277095	−	0.277095i
$251$	−1.47480e13			−0.934390			−0.467195	−	0.884154i	$-0.654735\pi$
$251$	−1.47480e13			−0.934390			−0.467195	+	0.884154i	$0.654735\pi$
$252$	5.72729e12	+	5.72729e12i	0.355014	+	0.355014i
$253$		−	7.63138e12i		−	0.462850i
$254$	3.39779e12			0.201656
$255$	−4.30460e12	+	9.92654e12i	−0.250013	+	0.576536i
$256$	−1.86523e13			−1.06026
$257$			2.42714e13i			1.35040i	0.737635	+	0.675200i	$0.235943\pi$
$257$			2.42714e13i			1.35040i	−0.737635	+	0.675200i	$0.764057\pi$
$258$	−4.99546e11	−	4.99546e11i	−0.0272061	−	0.0272061i
$259$	−4.15870e13			−2.21722
$260$	5.54531e12	+	5.54531e12i	0.289449	+	0.289449i
$261$	1.72037e13	−	1.72037e13i	0.879223	−	0.879223i
$262$	1.18556e13	−	1.18556e13i	0.593287	−	0.593287i
$263$		−	1.16714e13i		−	0.571961i	−0.958235	−	0.285980i	$-0.907681\pi$
$263$		−	1.16714e13i		−	0.571961i	0.958235	−	0.285980i	$-0.0923192\pi$
$264$		−	1.30366e13i		−	0.625664i
$265$	−1.01889e13	+	1.01889e13i	−0.478931	+	0.478931i
$266$	−8.36040e12	+	8.36040e12i	−0.384927	+	0.384927i
$267$	−1.12862e13	−	1.12862e13i	−0.509023	−	0.509023i
$268$	1.59534e13			0.704874
$269$	−8.63394e12	−	8.63394e12i	−0.373742	−	0.373742i	0.495096	−	0.868838i	$-0.335133\pi$
$269$	−8.63394e12	−	8.63394e12i	−0.373742	−	0.373742i	−0.868838	+	0.495096i	$0.835133\pi$
$270$		−	1.84389e13i		−	0.782051i
$271$	4.65213e13			1.93339			0.966697	−	0.255923i	$-0.0823794\pi$
$271$	4.65213e13			1.93339			0.966697	+	0.255923i	$0.0823794\pi$
$272$	5.97200e12	+	2.58973e12i	0.243215	+	0.105469i
$273$	1.14582e13			0.457320
$274$			6.50416e11i			0.0254427i
$275$	−1.20674e13	−	1.20674e13i	−0.462682	−	0.462682i
$276$	−2.60955e12			−0.0980768
$277$	5.30649e12	+	5.30649e12i	0.195510	+	0.195510i	0.798072	−	0.602562i	$-0.205853\pi$
$277$	5.30649e12	+	5.30649e12i	0.195510	+	0.195510i	−0.602562	+	0.798072i	$0.705853\pi$
$278$	1.13544e13	−	1.13544e13i	0.410128	−	0.410128i
$279$	−1.91744e13	+	1.91744e13i	−0.679047	+	0.679047i
$280$			5.22083e13i			1.81289i
$281$			1.18057e13i			0.401981i	0.979593	+	0.200991i	$0.0644160\pi$
$281$			1.18057e13i			0.401981i	−0.979593	+	0.200991i	$0.935584\pi$
$282$	3.91321e12	−	3.91321e12i	0.130666	−	0.130666i
$283$	−1.32199e13	+	1.32199e13i	−0.432914	+	0.432914i	−0.889619	−	0.456704i	$-0.849030\pi$
$283$	−1.32199e13	+	1.32199e13i	−0.432914	+	0.432914i	0.456704	+	0.889619i	$0.349030\pi$
$284$	3.89758e12	+	3.89758e12i	0.125183	+	0.125183i
$285$	−1.11636e13			−0.351689
$286$	1.26898e13	+	1.26898e13i	0.392140	+	0.392140i
$287$		−	8.31602e13i		−	2.52095i
$288$	2.19566e13			0.652990
$289$	2.34225e13	+	2.50189e13i	0.683433	+	0.730013i
$290$	5.17438e13			1.48139
$291$			1.48239e13i			0.416438i
$292$	1.11776e13	+	1.11776e13i	0.308135	+	0.308135i
$293$	1.66730e11			0.00451067			0.00225534	−	0.999997i	$-0.499282\pi$
$293$	1.66730e11			0.00451067			0.00225534	+	0.999997i	$0.499282\pi$
$294$	8.24941e12	+	8.24941e12i	0.219034	+	0.219034i
$295$	−6.53217e12	+	6.53217e12i	−0.170230	+	0.170230i
$296$	−4.77325e13	+	4.77325e13i	−1.22098	+	1.22098i
$297$			4.09354e13i			1.02787i
$298$		−	4.22441e13i		−	1.04130i
$299$	7.69860e12	−	7.69860e12i	0.186303	−	0.186303i
$300$	−4.12644e12	+	4.12644e12i	−0.0980412	+	0.0980412i
$301$	−4.44135e12	−	4.44135e12i	−0.103609	−	0.103609i
$302$	−8.87106e12			−0.203206
$303$	−6.34603e12	−	6.34603e12i	−0.142747	−	0.142747i
$304$			6.71625e12i			0.148362i
$305$	5.69862e13			1.23629
$306$	−2.29086e13	−	9.93422e12i	−0.488125	−	0.211673i
$307$	2.80223e13			0.586465			0.293233	−	0.956041i	$-0.405269\pi$
$307$	2.80223e13			0.586465			0.293233	+	0.956041i	$0.405269\pi$
$308$		−	3.82427e13i		−	0.786175i
$309$	−1.69373e13	−	1.69373e13i	−0.342036	−	0.342036i
$310$	−5.76713e13			−1.14412
$311$	1.79203e13	+	1.79203e13i	0.349271	+	0.349271i	0.859838	−	0.510567i	$-0.170564\pi$
$311$	1.79203e13	+	1.79203e13i	0.349271	+	0.349271i	−0.510567	+	0.859838i	$0.670564\pi$
$312$	1.31514e13	−	1.31514e13i	0.251838	−	0.251838i
$313$	−6.64045e13	+	6.64045e13i	−1.24941	+	1.24941i	−0.293424	+	0.955982i	$0.594795\pi$
$313$	−6.64045e13	+	6.64045e13i	−1.24941	+	1.24941i	−0.955982	+	0.293424i	$0.905205\pi$
$314$		−	4.77851e12i		−	0.0883446i
$315$		−	7.00861e13i		−	1.27328i
$316$	2.70336e13	−	2.70336e13i	0.482641	−	0.482641i
$317$	−6.36193e12	+	6.36193e12i	−0.111625	+	0.111625i	−0.760713	−	0.649088i	$-0.775151\pi$
$317$	−6.36193e12	+	6.36193e12i	−0.111625	+	0.111625i	0.649088	+	0.760713i	$0.275151\pi$
$318$	7.97291e12	+	7.97291e12i	0.137489	+	0.137489i
$319$	−1.14874e14			−1.94703
$320$	4.70710e13	+	4.70710e13i	0.784203	+	0.784203i
$321$		−	3.48051e13i		−	0.569988i
$322$	2.39151e13			0.385003
$323$	−1.40684e13	+	3.24423e13i	−0.222655	+	0.513449i
$324$	−9.63581e12			−0.149931
$325$		−	2.43473e13i		−	0.372471i
$326$	6.26712e12	+	6.26712e12i	0.0942695	+	0.0942695i
$327$	4.42289e13			0.654174
$328$	−9.54491e13	−	9.54491e13i	−1.38824	−	1.38824i
$329$	3.47915e13	−	3.47915e13i	0.497617	−	0.497617i
$330$	−2.63185e13	+	2.63185e13i	−0.370199	+	0.370199i
$331$		−	3.61458e13i		−	0.500040i	−0.968241	−	0.250020i	$-0.919563\pi$
$331$		−	3.61458e13i		−	0.500040i	0.968241	−	0.250020i	$-0.0804371\pi$
$332$			7.72001e12i			0.105041i
$333$	6.40776e13	−	6.40776e13i	0.857557	−	0.857557i
$334$	−6.46998e13	+	6.46998e13i	−0.851721	+	0.851721i
$335$	−9.76126e13	−	9.76126e13i	−1.26404	−	1.26404i
$336$	1.42970e13			0.182129
$337$	6.12996e13	+	6.12996e13i	0.768233	+	0.768233i	0.977795	−	0.209562i	$-0.0672039\pi$
$337$	6.12996e13	+	6.12996e13i	0.768233	+	0.768233i	−0.209562	+	0.977795i	$0.567204\pi$
$338$		−	3.21790e13i		−	0.396763i
$339$	−1.59484e13			−0.193472
$340$	1.89290e13	+	4.79161e13i	0.225940	+	0.571936i
$341$	1.28033e14			1.50374
$342$		−	2.57636e13i		−	0.297757i
$343$	−1.15412e13	−	1.15412e13i	−0.131260	−	0.131260i
$344$	−1.01953e13			−0.114112
$345$	1.59669e13	+	1.59669e13i	0.175879	+	0.175879i
$346$	−8.44222e13	+	8.44222e13i	−0.915247	+	0.915247i
$347$	−3.63370e13	+	3.63370e13i	−0.387737	+	0.387737i	−0.873879	−	0.486143i	$-0.838404\pi$
$347$	−3.63370e13	+	3.63370e13i	−0.387737	+	0.387737i	0.486143	+	0.873879i	$0.338404\pi$
$348$			3.92812e13i			0.412571i
$349$			1.46037e14i			1.50981i	0.655833	+	0.754906i	$0.272317\pi$
$349$			1.46037e14i			1.50981i	−0.655833	+	0.754906i	$0.727683\pi$
$350$	3.78164e13	−	3.78164e13i	0.384863	−	0.384863i
$351$	−4.12959e13	+	4.12959e13i	−0.413731	+	0.413731i
$352$	−7.33052e13	−	7.33052e13i	−0.723020	−	0.723020i
$353$	2.89699e13			0.281311			0.140655	−	0.990059i	$-0.455079\pi$
$353$	2.89699e13			0.281311			0.140655	+	0.990059i	$0.455079\pi$
$354$	5.11151e12	+	5.11151e12i	0.0488687	+	0.0488687i
$355$		−	4.76956e13i		−	0.448975i
$356$	−7.60013e13			−0.704443
$357$	6.90604e13	+	2.99477e13i	0.630309	+	0.273331i
$358$	6.12452e13			0.550447
$359$			2.12508e14i			1.88086i	0.339991	+	0.940429i	$0.389576\pi$
$359$			2.12508e14i			1.88086i	−0.339991	+	0.940429i	$0.610424\pi$
$360$	−8.04431e13	−	8.04431e13i	−0.701172	−	0.701172i
$361$	8.00049e13			0.686795
$362$	4.93541e12	+	4.93541e12i	0.0417278	+	0.0417278i
$363$	1.57003e13	−	1.57003e13i	0.130744	−	0.130744i
$364$	3.85795e13	−	3.85795e13i	0.316446	−	0.316446i
$365$		−	1.36782e14i		−	1.10515i
$366$		−	4.45924e13i		−	0.354907i
$367$	−1.09504e13	+	1.09504e13i	−0.0858551	+	0.0858551i	−0.748730	−	0.662875i	$-0.769336\pi$
$367$	−1.09504e13	+	1.09504e13i	−0.0858551	+	0.0858551i	0.662875	+	0.748730i	$0.269336\pi$
$368$	9.60598e12	−	9.60598e12i	0.0741957	−	0.0741957i
$369$	1.28134e14	+	1.28134e14i	0.975033	+	0.975033i
$370$	1.92727e14			1.44489
$371$	7.08854e13	+	7.08854e13i	0.523601	+	0.523601i
$372$		−	4.37810e13i		−	0.318639i
$373$	2.73382e14			1.96052			0.980260	−	0.197711i	$-0.0633507\pi$
$373$	2.73382e14			1.96052			0.980260	+	0.197711i	$0.0633507\pi$
$374$	4.33168e13	+	1.09650e14i	0.306099	+	0.774847i
$375$	−3.97473e13			−0.276781
$376$		−	7.98656e13i		−	0.548058i
$377$	−1.15886e14	−	1.15886e14i	−0.783704	−	0.783704i
$378$	−1.28282e14			−0.854992
$379$	−5.44651e11	−	5.44651e11i	−0.00357769	−	0.00357769i	0.705316	−	0.708893i	$-0.250805\pi$
$379$	−5.44651e11	−	5.44651e11i	−0.00357769	−	0.00357769i	−0.708893	+	0.705316i	$0.750805\pi$
$380$	−3.75878e13	+	3.75878e13i	−0.243353	+	0.243353i
$381$	1.57825e13	−	1.57825e13i	0.100714	−	0.100714i
$382$		−	3.15437e13i		−	0.198410i
$383$		−	1.29862e14i		−	0.805170i	−0.915383	−	0.402585i	$-0.868112\pi$
$383$		−	1.29862e14i		−	0.805170i	0.915383	−	0.402585i	$-0.131888\pi$
$384$	−1.40714e13	+	1.40714e13i	−0.0860032	+	0.0860032i
$385$	−2.33992e14	+	2.33992e14i	−1.40983	+	1.40983i
$386$	−5.47046e13	−	5.47046e13i	−0.324933	−	0.324933i
$387$	1.36865e13			0.0801463
$388$	4.99118e13	+	4.99118e13i	0.288157	+	0.288157i
$389$		−	1.75101e14i		−	0.996702i	−0.866975	−	0.498351i	$-0.833939\pi$
$389$		−	1.75101e14i		−	0.996702i	0.866975	−	0.498351i	$-0.166061\pi$
$390$	−5.31007e13			−0.298020
$391$	6.65223e13	−	2.62793e13i	0.368125	−	0.145426i
$392$	1.68364e14			0.918704
$393$		−	1.10136e14i		−	0.592614i
$394$	−4.76465e13	−	4.76465e13i	−0.252814	−	0.252814i
$395$	−3.30816e14			−1.73102
$396$	5.89247e13	+	5.89247e13i	0.304070	+	0.304070i
$397$	−1.50933e14	+	1.50933e14i	−0.768134	+	0.768134i	−0.977778	−	0.209644i	$-0.932770\pi$
$397$	−1.50933e14	+	1.50933e14i	−0.768134	+	0.768134i	0.209644	+	0.977778i	$0.432770\pi$
$398$	9.53638e13	−	9.53638e13i	0.478660	−	0.478660i
$399$			7.76669e13i			0.384490i
$400$		−	3.03795e13i		−	0.148337i
$401$	2.89211e13	−	2.89211e13i	0.139290	−	0.139290i	−0.634023	−	0.773314i	$-0.718598\pi$
$401$	2.89211e13	−	2.89211e13i	0.139290	−	0.139290i	0.773314	+	0.634023i	$0.218598\pi$
$402$	−7.63831e13	+	7.63831e13i	−0.362873	+	0.362873i
$403$	1.29161e14	+	1.29161e14i	0.605275	+	0.605275i
$404$	−4.27340e13			−0.197550
$405$	5.89578e13	+	5.89578e13i	0.268868	+	0.268868i
$406$		−	3.59989e14i		−	1.61956i
$407$	−4.27864e14			−1.89905
$408$	1.13639e14	−	4.48925e13i	0.497618	−	0.196582i
$409$	−1.33990e14			−0.578888			−0.289444	−	0.957195i	$-0.593470\pi$
$409$	−1.33990e14			−0.578888			−0.289444	+	0.957195i	$0.593470\pi$
$410$			3.85390e14i			1.64282i
$411$	3.02114e12	+	3.02114e12i	0.0127069	+	0.0127069i
$412$	−1.14055e14			−0.473348
$413$	4.54452e13	+	4.54452e13i	0.186107	+	0.186107i
$414$	−3.68485e13	+	3.68485e13i	−0.148908	+	0.148908i
$415$	4.72357e13	−	4.72357e13i	0.188368	−	0.188368i
$416$		−	1.47902e14i		−	0.582049i
$417$		−	1.05481e14i		−	0.409662i
$418$	−8.60152e13	+	8.60152e13i	−0.329690	+	0.329690i
$419$	6.28025e13	−	6.28025e13i	0.237575	−	0.237575i	−0.578270	−	0.815845i	$-0.696272\pi$
$419$	6.28025e13	−	6.28025e13i	0.237575	−	0.237575i	0.815845	+	0.578270i	$0.196272\pi$
$420$	8.00137e13	+	8.00137e13i	0.298740	+	0.298740i
$421$	−2.80733e14			−1.03453			−0.517264	−	0.855826i	$-0.673050\pi$
$421$	−2.80733e14			−1.03453			−0.517264	+	0.855826i	$0.673050\pi$
$422$	−9.13732e13	−	9.13732e13i	−0.332354	−	0.332354i
$423$			1.07214e14i			0.384928i
$424$	1.62721e14			0.576675
$425$	6.36355e13	−	1.46745e14i	0.222618	−	0.513364i
$426$	−3.73224e13			−0.128889
$427$		−	3.96461e14i		−	1.35160i
$428$	−1.17188e14	−	1.17188e14i	−0.394407	−	0.394407i
$429$	1.17886e14			0.391695
$430$	2.05826e13	+	2.05826e13i	0.0675187	+	0.0675187i
$431$	6.29432e13	−	6.29432e13i	0.203856	−	0.203856i	−0.597794	−	0.801650i	$-0.703956\pi$
$431$	6.29432e13	−	6.29432e13i	0.203856	−	0.203856i	0.801650	+	0.597794i	$0.203956\pi$
$432$	−5.15273e13	+	5.15273e13i	−0.164769	+	0.164769i
$433$		−	2.91077e14i		−	0.919018i	−0.888173	−	0.459509i	$-0.848025\pi$
$433$		−	2.91077e14i		−	0.919018i	0.888173	−	0.459509i	$-0.151975\pi$
$434$			4.01227e14i			1.25083i
$435$	2.40346e14	−	2.40346e14i	0.739855	−	0.739855i
$436$	1.48918e14	−	1.48918e14i	0.452660	−	0.452660i
$437$	5.21834e13	+	5.21834e13i	0.156634	+	0.156634i
$438$	−1.07034e14			−0.317259
$439$	4.31926e14	+	4.31926e14i	1.26431	+	1.26431i	0.948983	+	0.315329i	$0.102115\pi$
$439$	4.31926e14	+	4.31926e14i	1.26431	+	1.26431i	0.315329	+	0.948983i	$0.397885\pi$
$440$			5.37141e14i			1.55274i
$441$	−2.26017e14			−0.645251
$442$	−6.69178e13	+	1.54314e14i	−0.188677	+	0.435095i
$443$	5.56704e14			1.55026			0.775129	−	0.631802i	$-0.217685\pi$
$443$	5.56704e14			1.55026			0.775129	+	0.631802i	$0.217685\pi$
$444$			1.46308e14i			0.402404i
$445$	4.65023e14	+	4.65023e14i	1.26326	+	1.26326i
$446$	3.42191e14			0.918177
$447$	−1.96221e14	−	1.96221e14i	−0.520060	−	0.520060i
$448$	3.27480e14	−	3.27480e14i	0.857344	−	0.857344i
$449$	−2.75388e14	+	2.75388e14i	−0.712179	+	0.712179i	−0.966991	−	0.254811i	$-0.917987\pi$
$449$	−2.75388e14	+	2.75388e14i	−0.712179	+	0.712179i	0.254811	+	0.966991i	$0.417987\pi$
$450$			1.16536e14i			0.297708i
$451$		−	8.55586e14i		−	2.15920i
$452$	−5.36980e13	+	5.36980e13i	−0.133874	+	0.133874i
$453$	−4.12054e13	+	4.12054e13i	−0.101488	+	0.101488i
$454$	−1.22152e14	−	1.22152e14i	−0.297232	−	0.297232i
$455$	−4.72106e14			−1.13495
$456$	8.91441e13	+	8.91441e13i	0.211732	+	0.211732i
$457$		−	5.87210e14i		−	1.37802i	−0.724754	−	0.689008i	$-0.758047\pi$
$457$		−	5.87210e14i		−	1.37802i	0.724754	−	0.689008i	$-0.241953\pi$
$458$	−4.41338e13			−0.102332
$459$	−3.56831e14	+	1.40964e14i	−0.817510	+	0.322953i
$460$	1.07520e14			0.243401
$461$			2.22562e14i			0.497847i	0.968523	+	0.248924i	$0.0800768\pi$
$461$			2.22562e14i			0.497847i	−0.968523	+	0.248924i	$0.919923\pi$
$462$	1.83102e14	+	1.83102e14i	0.404727	+	0.404727i
$463$	4.50120e14			0.983181			0.491590	−	0.870827i	$-0.336416\pi$
$463$	4.50120e14			0.983181			0.491590	+	0.870827i	$0.336416\pi$
$464$	−1.44597e14	−	1.44597e14i	−0.312112	−	0.312112i
$465$	−2.67879e14	+	2.67879e14i	−0.571409	+	0.571409i
$466$	2.44794e14	−	2.44794e14i	0.516035	−	0.516035i
$467$			5.07202e14i			1.05667i	0.849037	+	0.528333i	$0.177183\pi$
$467$			5.07202e14i			1.05667i	−0.849037	+	0.528333i	$0.822817\pi$
$468$			1.18887e14i			0.244784i
$469$	−6.79105e14	+	6.79105e14i	−1.38193	+	1.38193i
$470$	−1.61235e14	+	1.61235e14i	−0.324280	+	0.324280i
$471$	−2.21959e13	−	2.21959e13i	−0.0441222	−	0.0441222i
$472$	1.04322e14			0.204972
$473$	−4.56944e13	−	4.56944e13i	−0.0887415	−	0.0887415i
$474$			2.58868e14i			0.496932i
$475$	1.65033e14			0.313153
$476$	3.33359e14	−	1.31692e14i	0.625280	−	0.247013i
$477$	−2.18442e14			−0.405027
$478$			5.18729e14i			0.950795i
$479$	−1.55322e13	−	1.55322e13i	−0.0281442	−	0.0281442i	0.692895	−	0.721039i	$-0.256335\pi$
$479$	−1.55322e13	−	1.55322e13i	−0.0281442	−	0.0281442i	−0.721039	+	0.692895i	$0.756335\pi$
$480$	3.06747e14			0.549483
$481$	−4.31633e14	−	4.31633e14i	−0.764392	−	0.764392i
$482$	3.86069e14	−	3.86069e14i	0.675936	−	0.675936i
$483$	1.11084e14	−	1.11084e14i	0.192283	−	0.192283i
$484$		−	1.05725e14i		−	0.180938i
$485$		−	6.10782e14i		−	1.03349i
$486$	3.10814e14	−	3.10814e14i	0.519998	−	0.519998i
$487$	4.96508e14	−	4.96508e14i	0.821328	−	0.821328i	−0.164971	−	0.986298i	$-0.552753\pi$
$487$	4.96508e14	−	4.96508e14i	0.821328	−	0.821328i	0.986298	+	0.164971i	$0.0527529\pi$
$488$	−4.55048e14	−	4.55048e14i	−0.744300	−	0.744300i
$489$	5.82206e13			0.0941625
$490$	−3.39897e14	−	3.39897e14i	−0.543587	−	0.543587i
$491$			1.24054e15i			1.96183i	0.194440	+	0.980914i	$0.437711\pi$
$491$			1.24054e15i			1.96183i	−0.194440	+	0.980914i	$0.562289\pi$
$492$	−2.92568e14			−0.457529
$493$	−3.95578e14	−	1.00135e15i	−0.611750	−	1.54856i
$494$	−1.73546e14			−0.265409
$495$		−	7.21075e14i		−	1.09057i
$496$	1.61161e14	+	1.61161e14i	0.241052	+	0.241052i
$497$	−3.31825e14			−0.490850
$498$	−3.69626e13	−	3.69626e13i	−0.0540755	−	0.0540755i
$499$	−5.70651e14	+	5.70651e14i	−0.825690	+	0.825690i	−0.986917	−	0.161227i	$-0.948455\pi$
$499$	−5.70651e14	+	5.70651e14i	−0.825690	+	0.825690i	0.161227	+	0.986917i	$0.448455\pi$
$500$	−1.33829e14	+	1.33829e14i	−0.191520	+	0.191520i
$501$			6.01052e14i			0.850755i
$502$		−	4.75500e14i		−	0.665702i
$503$	−9.00928e12	+	9.00928e12i	−0.0124757	+	0.0124757i	−0.713317	−	0.700841i	$-0.752808\pi$
$503$	−9.00928e12	+	9.00928e12i	−0.0124757	+	0.0124757i	0.700841	+	0.713317i	$0.252808\pi$
$504$	−5.59654e14	+	5.59654e14i	−0.766570	+	0.766570i
$505$	2.61473e14	+	2.61473e14i	0.354262	+	0.354262i
$506$	2.46048e14			0.329755
$507$	−1.49469e14	−	1.49469e14i	−0.198156	−	0.198156i
$508$		−	1.06279e14i		−	0.139379i
$509$	3.28238e14			0.425835			0.212917	−	0.977070i	$-0.431703\pi$
$509$	3.28238e14			0.425835			0.212917	+	0.977070i	$0.431703\pi$
$510$	−3.20047e14	−	1.38787e14i	−0.410751	−	0.178120i
$511$	−9.51615e14			−1.20822
$512$		−	4.08952e14i		−	0.513674i
$513$	−2.79916e14	−	2.79916e14i	−0.347843	−	0.347843i
$514$	−7.82548e14			−0.962086
$515$	6.97860e14	+	6.97860e14i	0.848845	+	0.848845i
$516$	−1.56252e13	+	1.56252e13i	−0.0188041	+	0.0188041i
$517$	3.57949e14	−	3.57949e14i	0.426210	−	0.426210i
$518$		−	1.34083e15i		−	1.57965i
$519$			7.84270e14i			0.914208i
$520$	−5.41872e14	+	5.41872e14i	−0.624997	+	0.624997i
$521$	1.02391e15	−	1.02391e15i	1.16857	−	1.16857i	0.186026	−	0.982545i	$-0.440439\pi$
$521$	1.02391e15	−	1.02391e15i	1.16857	−	1.16857i	0.982545	−	0.186026i	$-0.0595608\pi$
$522$	5.54675e14	+	5.54675e14i	0.626398	+	0.626398i
$523$	1.10321e15			1.23282			0.616410	−	0.787425i	$-0.288586\pi$
$523$	1.10321e15			1.23282			0.616410	+	0.787425i	$0.288586\pi$
$524$	−3.70828e14	−	3.70828e14i	−0.410063	−	0.410063i
$525$		−	3.51309e14i		−	0.384427i
$526$	3.76304e14			0.407491
$527$	4.40893e14	+	1.11606e15i	0.472470	+	1.19599i
$528$	1.47093e14			0.155993
$529$			8.03538e14i			0.843335i
$530$	−3.28505e14	−	3.28505e14i	−0.341212	−	0.341212i
$531$	−1.40045e14			−0.143962
$532$	2.61504e14	+	2.61504e14i	0.266050	+	0.266050i
$533$	8.63122e14	−	8.63122e14i	0.869105	−	0.869105i
$534$	3.63886e14	−	3.63886e14i	0.362651	−	0.362651i
$535$			1.43406e15i			1.41456i
$536$			1.55892e15i			1.52201i
$537$	2.84480e14	−	2.84480e14i	0.274911	−	0.274911i
$538$	2.78372e14	−	2.78372e14i	0.266271	−	0.266271i
$539$	7.54589e14	+	7.54589e14i	0.714451	+	0.714451i
$540$	−5.76749e14			−0.540531
$541$	−8.95532e14	−	8.95532e14i	−0.830800	−	0.830800i	0.156826	−	0.987626i	$-0.449874\pi$
$541$	−8.95532e14	−	8.95532e14i	−0.830800	−	0.830800i	−0.987626	+	0.156826i	$0.949874\pi$
$542$			1.49992e15i			1.37744i
$543$	4.58492e13			0.0416805
$544$	3.86565e14	−	8.91430e14i	0.347879	−	0.802219i
$545$	−1.82235e15			−1.62349
$546$			3.69429e14i			0.325816i
$547$	2.99400e14	+	2.99400e14i	0.261410	+	0.261410i	0.825627	−	0.564217i	$-0.190822\pi$
$547$	2.99400e14	+	2.99400e14i	0.261410	+	0.261410i	−0.564217	+	0.825627i	$0.690822\pi$
$548$	2.03443e13			0.0175853
$549$	6.10871e14	+	6.10871e14i	0.522759	+	0.522759i
$550$	3.89071e14	−	3.89071e14i	0.329636	−	0.329636i
$551$	7.85508e14	−	7.85508e14i	0.658896	−	0.658896i
$552$		−	2.54998e14i		−	0.211774i
$553$			2.30153e15i			1.89247i
$554$	−1.71090e14	+	1.71090e14i	−0.139290	+	0.139290i
$555$	8.95204e14	−	8.95204e14i	0.721623	−	0.721623i
$556$	−3.55154e14	−	3.55154e14i	−0.283469	−	0.283469i
$557$	−5.32702e14			−0.420999			−0.210500	−	0.977594i	$-0.567509\pi$
$557$	−5.32702e14			−0.420999			−0.210500	+	0.977594i	$0.567509\pi$
$558$	−6.18215e14	−	6.18215e14i	−0.483784	−	0.483784i
$559$		−	9.21938e13i		−	0.0714392i
$560$	−5.89074e14			−0.451997
$561$	7.10521e14	+	3.08114e14i	0.539860	+	0.234108i
$562$	−3.80633e14			−0.286389
$563$		−	1.89667e15i		−	1.41318i	−0.707625	−	0.706588i	$-0.750233\pi$
$563$		−	1.89667e15i		−	1.41318i	0.707625	−	0.706588i	$-0.249767\pi$
$564$	−1.22401e14	−	1.22401e14i	−0.0903128	−	0.0903128i
$565$	6.57114e14			0.480147
$566$	−4.26230e14	−	4.26230e14i	−0.308428	−	0.308428i
$567$	4.10178e14	−	4.10178e14i	0.293945	−	0.293945i
$568$	−3.80860e14	+	3.80860e14i	−0.270302	+	0.270302i
$569$		−	1.02798e14i		−	0.0722546i	−0.999347	−	0.0361273i	$-0.988498\pi$
$569$		−	1.02798e14i		−	0.0722546i	0.999347	−	0.0361273i	$-0.0115022\pi$
$570$		−	3.59933e14i		−	0.250559i
$571$	1.43771e14	−	1.43771e14i	0.0991229	−	0.0991229i	−0.655806	−	0.754929i	$-0.727671\pi$
$571$	1.43771e14	−	1.43771e14i	0.0991229	−	0.0991229i	0.754929	+	0.655806i	$0.227671\pi$
$572$	3.96922e14	−	3.96922e14i	0.271036	−	0.271036i
$573$	−1.46518e14	−	1.46518e14i	−0.0990927	−	0.0990927i
$574$	2.68122e15			1.79604
$575$	−2.36040e14	−	2.36040e14i	−0.156608	−	0.156608i
$576$			1.00917e15i			0.663192i
$577$	−4.34791e14			−0.283018			−0.141509	−	0.989937i	$-0.545195\pi$
$577$	−4.34791e14			−0.283018			−0.141509	+	0.989937i	$0.545195\pi$
$578$	−8.06651e14	+	7.55180e14i	−0.520095	+	0.486908i
$579$	−5.08198e14			−0.324564
$580$		−	1.61849e15i		−	1.02389i
$581$	−3.28626e14	−	3.28626e14i	−0.205936	−	0.205936i
$582$	−4.77945e14			−0.296689
$583$	7.29297e14	+	7.29297e14i	0.448464	+	0.448464i
$584$	−1.09224e15	+	1.09224e15i	−0.665346	+	0.665346i
$585$	7.27426e14	−	7.27426e14i	0.438966	−	0.438966i
$586$			5.37564e12i			0.00321361i
$587$			8.26697e14i			0.489595i	0.969574	+	0.244797i	$0.0787214\pi$
$587$			8.26697e14i			0.489595i	−0.969574	+	0.244797i	$0.921279\pi$
$588$	2.58032e14	−	2.58032e14i	0.151390	−	0.151390i
$589$	−8.75491e14	+	8.75491e14i	−0.508883	+	0.508883i
$590$	−2.10607e14	−	2.10607e14i	−0.121280	−	0.121280i
$591$	−4.42629e14			−0.252528
$592$	−5.38572e14	−	5.38572e14i	−0.304421	−	0.304421i
$593$			3.86889e14i			0.216663i	0.994115	+	0.108332i	$0.0345508\pi$
$593$			3.86889e14i			0.216663i	−0.994115	+	0.108332i	$0.965449\pi$
$594$	−1.31982e15			−0.732301
$595$	−2.84547e15	−	1.23393e15i	−1.56427	−	0.678337i
$596$	−1.32135e15			−0.719718
$597$		−	8.85916e14i		−	0.478117i
$598$	2.48215e14	+	2.48215e14i	0.132731	+	0.132731i
$599$	2.73585e15			1.44959			0.724793	−	0.688966i	$-0.241935\pi$
$599$	2.73585e15			1.44959			0.724793	+	0.688966i	$0.241935\pi$
$600$	−4.03224e14	−	4.03224e14i	−0.211697	−	0.211697i
$601$	−1.15442e15	+	1.15442e15i	−0.600558	+	0.600558i	−0.940461	−	0.339902i	$-0.889606\pi$
$601$	−1.15442e15	+	1.15442e15i	−0.600558	+	0.600558i	0.339902	+	0.940461i	$0.389606\pi$
$602$	1.43196e14	−	1.43196e14i	0.0738160	−	0.0738160i
$603$		−	2.09274e15i		−	1.06898i
$604$			2.77477e14i			0.140450i
$605$	−6.46892e14	+	6.46892e14i	−0.324472	+	0.324472i
$606$	2.04606e14	−	2.04606e14i	0.101700	−	0.101700i
$607$	−1.17975e15	−	1.17975e15i	−0.581102	−	0.581102i	0.354104	−	0.935206i	$-0.384786\pi$
$607$	−1.17975e15	−	1.17975e15i	−0.581102	−	0.581102i	−0.935206	+	0.354104i	$0.884786\pi$
$608$	1.00252e15			0.489356
$609$	−1.67212e15	−	1.67212e15i	−0.808860	−	0.808860i
$610$			1.83732e15i			0.880789i
$611$	7.22203e14			0.343110
$612$	−3.10731e14	+	7.16555e14i	−0.146302	+	0.337378i
$613$	−2.46467e15			−1.15008			−0.575038	−	0.818127i	$-0.695013\pi$
$613$	−2.46467e15			−1.15008			−0.575038	+	0.818127i	$0.695013\pi$
$614$			9.03482e14i			0.417824i
$615$	1.79011e15	+	1.79011e15i	0.820477	+	0.820477i
$616$	3.73697e15			1.69756
$617$	−5.39173e14	−	5.39173e14i	−0.242750	−	0.242750i	0.575237	−	0.817987i	$-0.304910\pi$
$617$	−5.39173e14	−	5.39173e14i	−0.242750	−	0.242750i	−0.817987	+	0.575237i	$0.804910\pi$
$618$	5.46084e14	−	5.46084e14i	0.243682	−	0.243682i
$619$	−2.59657e15	+	2.59657e15i	−1.14842	+	1.14842i	−0.161559	+	0.986863i	$0.551652\pi$
$619$	−2.59657e15	+	2.59657e15i	−1.14842	+	1.14842i	−0.986863	+	0.161559i	$0.948348\pi$
$620$			1.80389e15i			0.790780i
$621$			8.00705e14i			0.347912i
$622$	−5.77779e14	+	5.77779e14i	−0.248837	+	0.248837i
$623$	3.23523e15	−	3.23523e15i	1.38109	−	1.38109i
$624$	1.48389e14	+	1.48389e14i	0.0627894	+	0.0627894i
$625$	2.97178e15			1.24645
$626$	−2.14099e15	−	2.14099e15i	−0.890134	−	0.890134i
$627$			7.99069e14i			0.329316i
$628$	−1.49466e14			−0.0610612
$629$	−1.47339e15	−	3.72967e15i	−0.596675	−	1.51040i
$630$	2.25969e15			0.907142
$631$			2.58955e15i			1.03054i	0.857029	+	0.515268i	$0.172308\pi$
$631$			2.58955e15i			1.03054i	−0.857029	+	0.515268i	$0.827692\pi$
$632$	2.64164e15	+	2.64164e15i	1.04215	+	1.04215i
$633$	−8.48844e14			−0.331977
$634$	−2.05119e14	−	2.05119e14i	−0.0795270	−	0.0795270i
$635$	−6.50280e14	+	6.50280e14i	−0.249945	+	0.249945i
$636$	2.49384e14	−	2.49384e14i	0.0950284	−	0.0950284i
$637$			1.52247e15i			0.575151i
$638$		−	3.70372e15i		−	1.38715i
$639$	5.11279e14	−	5.11279e14i	0.189847	−	0.189847i
$640$	5.79777e14	−	5.79777e14i	0.213438	−	0.213438i
$641$	−7.74872e14	−	7.74872e14i	−0.282821	−	0.282821i	0.551412	−	0.834233i	$-0.314089\pi$
$641$	−7.74872e14	−	7.74872e14i	−0.282821	−	0.282821i	−0.834233	+	0.551412i	$0.814089\pi$
$642$	1.12217e15			0.406085
$643$	9.80629e14	+	9.80629e14i	0.351839	+	0.351839i	0.860794	−	0.508954i	$-0.169968\pi$
$643$	9.80629e14	+	9.80629e14i	0.351839	+	0.351839i	−0.508954	+	0.860794i	$0.669968\pi$
$644$		−	7.48036e14i		−	0.266103i
$645$	1.91209e14			0.0674421
$646$	−1.04599e15	−	4.53589e14i	−0.365804	−	0.158629i
$647$	3.19227e15			1.10695			0.553473	−	0.832867i	$-0.313302\pi$
$647$	3.19227e15			1.10695			0.553473	+	0.832867i	$0.313302\pi$
$648$		−	9.41584e14i		−	0.323740i
$649$	4.67559e14	+	4.67559e14i	0.159401	+	0.159401i
$650$	7.84996e14			0.265365
$651$	1.86367e15	+	1.86367e15i	0.624704	+	0.624704i
$652$	1.96028e14	−	1.96028e14i	0.0651564	−	0.0651564i
$653$	−3.01175e14	+	3.01175e14i	−0.0992652	+	0.0992652i	−0.754995	−	0.655730i	$-0.772361\pi$
$653$	−3.01175e14	+	3.01175e14i	−0.0992652	+	0.0992652i	0.655730	+	0.754995i	$0.272361\pi$
$654$			1.42601e15i			0.466063i
$655$			4.53791e15i			1.47072i
$656$	1.07697e15	−	1.07697e15i	0.346123	−	0.346123i
$657$	1.46626e15	−	1.46626e15i	0.467305	−	0.467305i
$658$	1.12173e15	+	1.12173e15i	0.354525	+	0.354525i
$659$	−5.87001e15			−1.83979			−0.919896	−	0.392161i	$-0.871727\pi$
$659$	−5.87001e15			−1.83979			−0.919896	+	0.392161i	$0.871727\pi$
$660$	8.23214e14	+	8.23214e14i	0.255871	+	0.255871i
$661$		−	1.15457e15i		−	0.355886i	−0.984041	−	0.177943i	$-0.943056\pi$
$661$		−	1.15457e15i		−	0.355886i	0.984041	−	0.177943i	$-0.0569442\pi$
$662$	1.16540e15			0.356251
$663$	4.05951e14	+	1.02761e15i	0.123069	+	0.311532i
$664$	−7.54377e14			−0.226811
$665$		−	3.20008e15i		−	0.954206i
$666$	2.06596e15	+	2.06596e15i	0.610963	+	0.610963i
$667$	−2.24696e15			−0.659027
$668$	2.02374e15	+	2.02374e15i	0.588685	+	0.588685i
$669$	1.58945e15	−	1.58945e15i	0.458568	−	0.458568i
$670$	3.14719e15	−	3.14719e15i	0.900556	−	0.900556i
$671$		−	4.07895e15i		−	1.15764i
$672$		−	2.13409e15i		−	0.600732i
$673$	−4.28537e15	+	4.28537e15i	−1.19648	+	1.19648i	−0.221265	+	0.975214i	$0.571019\pi$
$673$	−4.28537e15	+	4.28537e15i	−1.19648	+	1.19648i	−0.975214	+	0.221265i	$0.928981\pi$
$674$	−1.97640e15	+	1.97640e15i	−0.547324	+	0.547324i
$675$	1.26614e15	+	1.26614e15i	0.347785	+	0.347785i
$676$	−1.00652e15			−0.274231
$677$	−7.41339e14	−	7.41339e14i	−0.200345	−	0.200345i	0.599803	−	0.800148i	$-0.295246\pi$
$677$	−7.41339e14	−	7.41339e14i	−0.200345	−	0.200345i	−0.800148	+	0.599803i	$0.795246\pi$
$678$		−	5.14201e14i		−	0.137838i
$679$	−4.24930e15			−1.12988
$680$	−4.68222e15	+	1.84969e15i	−1.23496	+	0.487865i
$681$	−1.13478e15			−0.296894
$682$			4.12799e15i			1.07133i
$683$	−2.88082e15	−	2.88082e15i	−0.741655	−	0.741655i	0.231241	−	0.972896i	$-0.425721\pi$
$683$	−2.88082e15	−	2.88082e15i	−0.741655	−	0.741655i	−0.972896	+	0.231241i	$0.925721\pi$
$684$	−8.05854e14			−0.205801
$685$	−1.24479e14	−	1.24479e14i	−0.0315353	−	0.0315353i
$686$	3.72106e14	−	3.72106e14i	0.0935156	−	0.0935156i
$687$	−2.04998e14	+	2.04998e14i	−0.0511080	+	0.0511080i
$688$		−	1.15035e14i		−	0.0284508i
$689$			1.47144e15i			0.361025i
$690$	−5.14797e14	+	5.14797e14i	−0.125304	+	0.125304i
$691$	1.10023e15	−	1.10023e15i	0.265677	−	0.265677i	−0.561679	−	0.827355i	$-0.689844\pi$
$691$	1.10023e15	−	1.10023e15i	0.265677	−	0.265677i	0.827355	+	0.561679i	$0.189844\pi$
$692$	2.64063e15	+	2.64063e15i	0.632592	+	0.632592i
$693$	−5.01662e15			−1.19228
$694$	−1.17156e15	−	1.17156e15i	−0.276241	−	0.276241i
$695$			4.34610e15i			1.01668i
$696$	−3.83844e15			−0.890850
$697$	7.45809e15	−	2.94628e15i	1.71731	−	0.678413i
$698$	−4.70846e15			−1.07566
$699$		−	2.27410e15i		−	0.515449i
$700$	−1.18285e15	−	1.18285e15i	−0.266007	−	0.266007i
$701$	3.24342e15			0.723692			0.361846	−	0.932238i	$-0.382147\pi$
$701$	3.24342e15			0.723692			0.361846	+	0.932238i	$0.382147\pi$
$702$	−1.33145e15	−	1.33145e15i	−0.294761	−	0.294761i
$703$	2.92574e15	−	2.92574e15i	0.642660	−	0.642660i
$704$	3.36924e15	−	3.36924e15i	0.734316	−	0.734316i
$705$			1.49785e15i			0.323912i
$706$			9.34036e14i			0.200418i
$707$	1.81911e15	−	1.81911e15i	0.387303	−	0.387303i
$708$	1.59882e14	−	1.59882e14i	0.0337767	−	0.0337767i
$709$	−1.78579e15	−	1.78579e15i	−0.374349	−	0.374349i	0.494710	−	0.869058i	$-0.335274\pi$
$709$	−1.78579e15	−	1.78579e15i	−0.374349	−	0.374349i	−0.869058	+	0.494710i	$0.835274\pi$
$710$	1.53778e15			0.319870
$711$	−3.54622e15	−	3.54622e15i	−0.731953	−	0.731953i
$712$		−	7.42663e15i		−	1.52108i
$713$	2.50436e15			0.508984
$714$	−9.65563e14	+	2.22662e15i	−0.194733	+	0.449061i
$715$	−4.85722e15			−0.972086
$716$		−	1.91568e15i		−	0.380453i
$717$	2.40946e15	+	2.40946e15i	0.474858	+	0.474858i
$718$	−6.85160e15			−1.34001
$719$	3.74270e15	+	3.74270e15i	0.726400	+	0.726400i	0.969901	−	0.243501i	$-0.0782958\pi$
$719$	3.74270e15	+	3.74270e15i	0.726400	+	0.726400i	−0.243501	+	0.969901i	$0.578296\pi$
$720$	9.07650e14	−	9.07650e14i	0.174819	−	0.174819i
$721$	4.85511e15	−	4.85511e15i	0.928016	−	0.928016i
$722$			2.57949e15i			0.489304i
$723$		−	3.58652e15i		−	0.675170i
$724$	1.54374e14	−	1.54374e14i	0.0288411	−	0.0288411i
$725$	−3.55308e15	+	3.55308e15i	−0.658788	+	0.658788i
$726$	5.06201e14	+	5.06201e14i	0.0931477	+	0.0931477i
$727$	3.55995e14			0.0650137			0.0325069	−	0.999472i	$-0.489651\pi$
$727$	3.55995e14			0.0650137			0.0325069	+	0.999472i	$0.489651\pi$
$728$	3.76988e15	+	3.76988e15i	0.683290	+	0.683290i
$729$		−	1.19482e15i		−	0.214931i
$730$	4.41008e15			0.787356
$731$	2.40963e14	−	5.55668e14i	0.0426977	−	0.0984623i
$732$	−1.39480e15			−0.245302
$733$			6.09680e15i			1.06422i	0.846676	+	0.532108i	$0.178600\pi$
$733$			6.09680e15i			1.06422i	−0.846676	+	0.532108i	$0.821400\pi$
$734$	−3.53058e14	−	3.53058e14i	−0.0611671	−	0.0611671i
$735$	−3.15760e15			−0.542971
$736$	−1.43387e15	−	1.43387e15i	−0.244726	−	0.244726i
$737$	−6.98691e15	+	6.98691e15i	−1.18362	+	1.18362i
$738$	−4.13124e15	+	4.13124e15i	−0.694657	+	0.694657i
$739$		−	7.07171e15i		−	1.18027i	−0.807306	−	0.590133i	$-0.799075\pi$
$739$		−	7.07171e15i		−	1.18027i	0.807306	−	0.590133i	$-0.200925\pi$
$740$		−	6.02829e15i		−	0.998664i
$741$	−8.06107e14	+	8.06107e14i	−0.132554	+	0.132554i
$742$	−2.28546e15	+	2.28546e15i	−0.373037	+	0.373037i
$743$	4.72007e15	+	4.72007e15i	0.764734	+	0.764734i	0.977174	−	0.212440i	$-0.0681411\pi$
$743$	4.72007e15	+	4.72007e15i	0.764734	+	0.764734i	−0.212440	+	0.977174i	$0.568141\pi$
$744$	4.27815e15			0.688026
$745$	8.08481e15	+	8.08481e15i	1.29066	+	1.29066i
$746$			8.81427e15i			1.39676i
$747$	1.01270e15			0.159301
$748$	3.42974e15	−	1.35490e15i	0.535552	−	0.211567i
$749$	9.97698e15			1.54650
$750$		−	1.28152e15i		−	0.197191i
$751$	−8.16305e15	−	8.16305e15i	−1.24690	−	1.24690i	−0.957080	−	0.289823i	$-0.906403\pi$
$751$	−8.16305e15	−	8.16305e15i	−1.24690	−	1.24690i	−0.289823	−	0.957080i	$-0.593597\pi$
$752$	9.01134e14			0.136644
$753$	−2.20866e15	−	2.20866e15i	−0.332473	−	0.332473i
$754$	3.73634e15	−	3.73634e15i	0.558347	−	0.558347i
$755$	1.69777e15	−	1.69777e15i	0.251867	−	0.251867i
$756$			4.01253e15i			0.590946i
$757$			4.60891e15i			0.673862i	0.941529	+	0.336931i	$0.109389\pi$
$757$			4.60891e15i			0.673862i	−0.941529	+	0.336931i	$0.890611\pi$
$758$	1.75604e13	−	1.75604e13i	0.00254891	−	0.00254891i
$759$	1.14287e15	−	1.14287e15i	0.164691	−	0.164691i
$760$	−3.67297e15	−	3.67297e15i	−0.525464	−	0.525464i
$761$	4.33565e15			0.615798			0.307899	−	0.951419i	$-0.400374\pi$
$761$	4.33565e15			0.615798			0.307899	+	0.951419i	$0.400374\pi$
$762$	5.08853e14	+	5.08853e14i	0.0717529	+	0.0717529i
$763$			1.26783e16i			1.77491i
$764$	−9.86651e14			−0.137136
$765$	6.28557e15	−	2.48308e15i	0.867374	−	0.342652i
$766$	4.18694e15			0.573639
$767$			9.43355e14i			0.128322i
$768$	−2.79337e15	−	2.79337e15i	−0.377261	−	0.377261i
$769$	2.76083e15			0.370208			0.185104	−	0.982719i	$-0.440738\pi$
$769$	2.76083e15			0.370208			0.185104	+	0.982719i	$0.440738\pi$
$770$	−7.54428e15	−	7.54428e15i	−1.00443	−	1.00443i
$771$	−3.63488e15	+	3.63488e15i	−0.480497	+	0.480497i
$772$	−1.71110e15	+	1.71110e15i	−0.224584	+	0.224584i
$773$			7.18686e15i			0.936596i	0.883571	+	0.468298i	$0.155133\pi$
$773$			7.18686e15i			0.936596i	−0.883571	+	0.468298i	$0.844867\pi$
$774$			4.41276e14i			0.0570998i
$775$	3.96009e15	−	3.96009e15i	0.508799	−	0.508799i
$776$	−4.87724e15	+	4.87724e15i	−0.622206	+	0.622206i
$777$	−6.22807e15	−	6.22807e15i	−0.788928	−	0.788928i
$778$	5.64553e15			0.710096
$779$	5.85050e15	+	5.85050e15i	0.730697	+	0.730697i
$780$			1.66093e15i			0.205983i
$781$	−3.41395e15			−0.420414
$782$	8.47286e14	+	2.14479e15i	0.103608	+	0.262269i
$783$	1.20529e16			1.46353
$784$			1.89967e15i			0.229055i
$785$	9.14528e14	+	9.14528e14i	0.109500	+	0.109500i
$786$	3.55097e15			0.422205
$787$	−9.13331e15	−	9.13331e15i	−1.07837	−	1.07837i	−0.996656	−	0.0817119i	$-0.973961\pi$
$787$	−9.13331e15	−	9.13331e15i	−1.07837	−	1.07837i	−0.0817119	−	0.996656i	$-0.526039\pi$
$788$	−1.49033e15	+	1.49033e15i	−0.174738	+	0.174738i
$789$	1.74791e15	−	1.74791e15i	0.203514	−	0.203514i
$790$		−	1.06660e16i		−	1.23326i
$791$		−	4.57164e15i		−	0.524930i
$792$	−5.75795e15	+	5.75795e15i	−0.656567	+	0.656567i
$793$	4.11488e15	−	4.11488e15i	0.465966	−	0.465966i
$794$	−4.86633e15	−	4.86633e15i	−0.547253	−	0.547253i
$795$	−3.05176e15			−0.340825
$796$	−2.98287e15	−	2.98287e15i	−0.330836	−	0.330836i
$797$		−	1.43942e16i		−	1.58551i	−0.609542	−	0.792753i	$-0.708647\pi$
$797$		−	1.43942e16i		−	1.58551i	0.609542	−	0.792753i	$-0.291353\pi$
$798$	−2.50410e15			−0.273928
$799$	4.35285e15	+	1.88759e15i	0.472897	+	0.205070i
$800$	−4.53469e15			−0.489275
$801$			9.96974e15i			1.06833i
$802$	9.32464e14	+	9.32464e14i	0.0992368	+	0.0992368i
$803$	−9.79061e15			−1.03484
$804$	2.38918e15	+	2.38918e15i	0.250807	+	0.250807i
$805$	−4.57694e15	+	4.57694e15i	−0.477197	+	0.477197i
$806$	−4.16435e15	+	4.16435e15i	−0.431225	+	0.431225i
$807$		−	2.58604e15i		−	0.265968i
$808$		−	4.17585e15i		−	0.426562i
$809$	8.38491e15	−	8.38491e15i	0.850710	−	0.850710i	−0.139510	−	0.990221i	$-0.544553\pi$
$809$	8.38491e15	−	8.38491e15i	0.850710	−	0.850710i	0.990221	+	0.139510i	$0.0445528\pi$
$810$	−1.90089e15	+	1.90089e15i	−0.191554	+	0.191554i
$811$	7.45777e15	+	7.45777e15i	0.746439	+	0.746439i	0.973809	−	0.227370i	$-0.0730126\pi$
$811$	7.45777e15	+	7.45777e15i	0.746439	+	0.746439i	−0.227370	+	0.973809i	$0.573013\pi$
$812$	−1.12601e16			−1.11939
$813$	6.96702e15	+	6.96702e15i	0.687937	+	0.687937i
$814$		−	1.37950e16i		−	1.35297i
$815$	−2.39884e15			−0.233687
$816$	5.06528e14	+	1.28220e15i	0.0490126	+	0.124068i
$817$	6.24917e14			0.0600622
$818$		−	4.32006e15i		−	0.412426i
$819$	−5.06081e15	−	5.06081e15i	−0.479908	−	0.479908i
$820$	1.20546e16			1.13547
$821$	−5.83529e15	−	5.83529e15i	−0.545978	−	0.545978i	0.379297	−	0.925275i	$-0.376166\pi$
$821$	−5.83529e15	−	5.83529e15i	−0.545978	−	0.545978i	−0.925275	+	0.379297i	$0.876166\pi$
$822$	−9.74062e13	+	9.74062e13i	−0.00905298	+	0.00905298i
$823$	−1.25882e16	+	1.25882e16i	−1.16216	+	1.16216i	−0.178155	+	0.984002i	$0.557013\pi$
$823$	−1.25882e16	+	1.25882e16i	−1.16216	+	1.16216i	−0.984002	+	0.178155i	$0.942987\pi$
$824$		−	1.11451e16i		−	1.02208i
$825$		−	3.61441e15i		−	0.329262i
$826$	−1.46523e15	+	1.46523e15i	−0.132591	+	0.132591i
$827$	−9.83358e15	+	9.83358e15i	−0.883957	+	0.883957i	−0.993934	−	0.109977i	$-0.964922\pi$
$827$	−9.83358e15	+	9.83358e15i	−0.883957	+	0.883957i	0.109977	+	0.993934i	$0.464922\pi$
$828$	1.15258e15	+	1.15258e15i	0.102921	+	0.102921i
$829$	−5.29290e15			−0.469509			−0.234754	−	0.972055i	$-0.575429\pi$
$829$	−5.29290e15			−0.469509			−0.234754	+	0.972055i	$0.575429\pi$
$830$	1.52296e15	+	1.52296e15i	0.134202	+	0.134202i
$831$			1.58940e15i			0.139132i
$832$	6.79784e15			0.591143
$833$	−3.97922e15	+	9.17620e15i	−0.343756	+	0.792712i
$834$	3.40088e15			0.291862
$835$		−	2.47649e16i		−	2.11135i
$836$	2.69046e15	+	2.69046e15i	0.227872	+	0.227872i
$837$	−1.34336e16			−1.13032
$838$	2.02485e15	+	2.02485e15i	0.169259	+	0.169259i
$839$	5.16167e15	−	5.16167e15i	0.428647	−	0.428647i	−0.459521	−	0.888167i	$-0.651979\pi$
$839$	5.16167e15	−	5.16167e15i	0.428647	−	0.428647i	0.888167	+	0.459521i	$0.151979\pi$
$840$	−7.81871e15	+	7.81871e15i	−0.645059	+	0.645059i
$841$			2.16226e16i			1.77227i
$842$		−	9.05129e15i		−	0.737045i
$843$	−1.76801e15	+	1.76801e15i	−0.143032	+	0.143032i
$844$	−2.85805e15	+	2.85805e15i	−0.229713	+	0.229713i
$845$	6.15852e15	+	6.15852e15i	0.491773	+	0.491773i
$846$	−3.45675e15			−0.274240
$847$	4.50052e15	+	4.50052e15i	0.354735	+	0.354735i
$848$			1.83600e15i			0.143779i
$849$	−3.95961e15			−0.308078
$850$	4.73131e15	+	2.05171e15i	0.365744	+	0.158603i
$851$	−8.36912e15			−0.642787
$852$			1.16740e15i			0.0890846i
$853$	4.96870e15	+	4.96870e15i	0.376724	+	0.376724i	0.869919	−	0.493195i	$-0.164171\pi$
$853$	4.96870e15	+	4.96870e15i	0.376724	+	0.376724i	−0.493195	+	0.869919i	$0.664171\pi$
$854$	1.27825e16			0.962939
$855$	4.93071e15	+	4.93071e15i	0.369059	+	0.369059i
$856$	1.14513e16	−	1.14513e16i	0.851628	−	0.851628i
$857$	5.51771e14	−	5.51771e14i	0.0407723	−	0.0407723i	−0.686427	−	0.727199i	$-0.740822\pi$
$857$	5.51771e14	−	5.51771e14i	0.0407723	−	0.0407723i	0.727199	+	0.686427i	$0.240822\pi$
$858$			3.80084e15i			0.279061i
$859$		−	5.65870e15i		−	0.412814i	−0.978466	−	0.206407i	$-0.933823\pi$
$859$		−	5.65870e15i		−	0.412814i	0.978466	−	0.206407i	$-0.0661771\pi$
$860$	6.43800e14	−	6.43800e14i	0.0466670	−	0.0466670i
$861$	1.24541e16	−	1.24541e16i	0.897002	−	0.897002i
$862$	2.02939e15	+	2.02939e15i	0.145236	+	0.145236i
$863$	−1.00774e16			−0.716619			−0.358309	−	0.933603i	$-0.616647\pi$
$863$	−1.00774e16			−0.716619			−0.358309	+	0.933603i	$0.616647\pi$
$864$	7.69138e15	+	7.69138e15i	0.543474	+	0.543474i
$865$		−	3.23140e16i		−	2.26883i
$866$	9.38478e15			0.654750
$867$	−2.39078e14	+	7.25459e15i	−0.0165742	+	0.502930i
$868$	1.25499e16			0.864536
$869$			2.36791e16i			1.62090i
$870$	7.74915e15	+	7.74915e15i	0.527106	+	0.527106i
$871$	−1.40969e16			−0.952848
$872$	1.45519e16	+	1.45519e16i	0.977412	+	0.977412i
$873$	6.54736e15	−	6.54736e15i	0.437006	−	0.437006i
$874$	−1.68248e15	+	1.68248e15i	−0.111593	+	0.111593i
$875$		−	1.13937e16i		−	0.750964i
$876$			3.34790e15i			0.219281i
$877$	1.25522e16	−	1.25522e16i	0.816999	−	0.816999i	−0.168673	−	0.985672i	$-0.553948\pi$
$877$	1.25522e16	−	1.25522e16i	0.816999	−	0.816999i	0.985672	+	0.168673i	$0.0539481\pi$
$878$	−1.39260e16	+	1.39260e16i	−0.900752	+	0.900752i
$879$	2.49694e13	+	2.49694e13i	0.00160498	+	0.00160498i
$880$	−6.06063e15			−0.387136
$881$	−1.71985e15	−	1.71985e15i	−0.109175	−	0.109175i	0.650409	−	0.759584i	$-0.274597\pi$
$881$	−1.71985e15	−	1.71985e15i	−0.109175	−	0.109175i	−0.759584	+	0.650409i	$0.774597\pi$
$882$		−	7.28715e15i		−	0.459706i
$883$	1.51644e16			0.950698			0.475349	−	0.879797i	$-0.342322\pi$
$883$	1.51644e16			0.950698			0.475349	+	0.879797i	$0.342322\pi$
$884$	4.82678e15	+	2.09311e15i	0.300725	+	0.130408i
$885$	−1.95651e15			−0.121142
$886$			1.79490e16i			1.10447i
$887$	−1.24065e16	−	1.24065e16i	−0.758698	−	0.758698i	0.217387	−	0.976085i	$-0.430247\pi$
$887$	−1.24065e16	−	1.24065e16i	−0.758698	−	0.758698i	−0.976085	+	0.217387i	$0.930247\pi$
$888$	−1.42968e16			−0.868897
$889$	4.52409e15	+	4.52409e15i	0.273257	+	0.273257i
$890$	−1.49931e16	+	1.49931e16i	−0.900006	+	0.900006i
$891$	4.22008e15	−	4.22008e15i	0.251764	−	0.251764i
$892$		−	1.07033e16i		−	0.634618i
$893$			4.89532e15i			0.288468i
$894$	6.32647e15	−	6.32647e15i	0.370514	−	0.370514i
$895$	−1.17213e16	+	1.17213e16i	−0.682259	+	0.682259i
$896$	−4.03360e15	−	4.03360e15i	−0.233345	−	0.233345i
$897$	2.30588e15			0.132580
$898$	−8.87893e15	−	8.87893e15i	−0.507389	−	0.507389i
$899$		−	3.76977e16i		−	2.14110i
$900$	3.64511e15			0.205767
$901$	−3.84585e15	+	8.86864e15i	−0.215777	+	0.497589i
$902$	2.75855e16			1.53831
$903$		−	1.33027e15i		−	0.0737323i
$904$	−5.24721e15	−	5.24721e15i	−0.289069	−	0.289069i
$905$	−1.88911e15			−0.103440
$906$	−1.32853e15	−	1.32853e15i	−0.0723046	−	0.0723046i
$907$	−1.21244e16	+	1.21244e16i	−0.655875	+	0.655875i	−0.954401	−	0.298526i	$-0.903505\pi$
$907$	−1.21244e16	+	1.21244e16i	−0.655875	+	0.655875i	0.298526	+	0.954401i	$0.403505\pi$
$908$	−3.82079e15	+	3.82079e15i	−0.205438	+	0.205438i
$909$			5.60579e15i			0.299596i
$910$		−	1.52215e16i		−	0.808591i
$911$	−7.81015e15	+	7.81015e15i	−0.412390	+	0.412390i	−0.882570	−	0.470180i	$-0.844189\pi$
$911$	−7.81015e15	+	7.81015e15i	−0.412390	+	0.412390i	0.470180	+	0.882570i	$0.344189\pi$
$912$	−1.00583e15	+	1.00583e15i	−0.0527899	+	0.0527899i
$913$	−3.38104e15	−	3.38104e15i	−0.176385	−	0.176385i
$914$	1.89326e16			0.981761
$915$	8.53424e15	+	8.53424e15i	0.439895	+	0.439895i
$916$			1.38046e15i			0.0707290i
$917$	3.15709e16			1.60789
$918$	−4.54491e15	−	1.15048e16i	−0.230086	−	0.582431i
$919$	2.52195e16			1.26911			0.634557	−	0.772876i	$-0.281183\pi$
$919$	2.52195e16			1.26911			0.634557	+	0.772876i	$0.281183\pi$
$920$			1.05066e16i			0.525568i
$921$	4.19661e15	+	4.19661e15i	0.208675	+	0.208675i
$922$	−7.17576e15			−0.354689
$923$	−3.44402e15	−	3.44402e15i	−0.169222	−	0.169222i
$924$	5.72722e15	−	5.72722e15i	0.279736	−	0.279736i
$925$	−1.32339e16	+	1.32339e16i	−0.642554	+	0.642554i
$926$			1.45126e16i			0.700462i
$927$			1.49616e16i			0.717860i
$928$	−2.15838e16	+	2.15838e16i	−1.02947	+	1.02947i
$929$	2.03987e15	−	2.03987e15i	0.0967201	−	0.0967201i	−0.657091	−	0.753811i	$-0.728213\pi$
$929$	2.03987e15	−	2.03987e15i	0.0967201	−	0.0967201i	0.753811	+	0.657091i	$0.228213\pi$
$930$	−8.63684e15	−	8.63684e15i	−0.407098	−	0.407098i
$931$	−1.03198e16			−0.483556
$932$	−7.65689e15	−	7.65689e15i	−0.356668	−	0.356668i
$933$			5.36748e15i			0.248555i
$934$	−1.63530e16			−0.752817
$935$	−2.92753e16	−	1.26951e16i	−1.33979	−	0.580996i
$936$	−1.16173e16			−0.528554
$937$		−	1.24450e16i		−	0.562894i	−0.959577	−	0.281447i	$-0.909186\pi$
$937$		−	1.24450e16i		−	0.562894i	0.959577	−	0.281447i	$-0.0908143\pi$
$938$	−2.18954e16	−	2.18954e16i	−0.984550	−	0.984550i
$939$	−1.98895e16			−0.889124
$940$	5.04323e15	+	5.04323e15i	0.224133	+	0.224133i
$941$	−4.21159e15	+	4.21159e15i	−0.186081	+	0.186081i	−0.794000	−	0.607918i	$-0.792005\pi$
$941$	−4.21159e15	+	4.21159e15i	−0.186081	+	0.186081i	0.607918	+	0.794000i	$0.292005\pi$
$942$	7.15630e14	−	7.15630e14i	0.0314346	−	0.0314346i
$943$		−	1.67355e16i		−	0.730842i
$944$			1.17708e15i			0.0511045i
$945$	2.45511e16	−	2.45511e16i	1.05973	−	1.05973i
$946$	1.47326e15	−	1.47326e15i	0.0632235	−	0.0632235i
$947$	−2.52329e16	−	2.52329e16i	−1.07657	−	1.07657i	−0.996815	−	0.0797548i	$-0.974586\pi$
$947$	−2.52329e16	−	2.52329e16i	−1.07657	−	1.07657i	−0.0797548	−	0.996815i	$-0.525414\pi$
$948$	8.09709e15			0.343465
$949$	−9.87684e15	−	9.87684e15i	−0.416537	−	0.416537i
$950$			5.32094e15i			0.223105i
$951$	−1.90552e15			−0.0794368
$952$	1.28686e16	+	3.25749e16i	0.533367	+	1.35014i
$953$	−1.71151e16			−0.705291			−0.352646	−	0.935757i	$-0.614718\pi$
$953$	−1.71151e16			−0.705291			−0.352646	+	0.935757i	$0.614718\pi$
$954$		−	7.04290e15i		−	0.288560i
$955$	6.03694e15	+	6.03694e15i	0.245923	+	0.245923i
$956$	1.62252e16			0.657163
$957$	−1.72035e16	−	1.72035e16i	−0.692789	−	0.692789i
$958$	5.00784e14	−	5.00784e14i	0.0200512	−	0.0200512i
$959$	−8.66017e14	+	8.66017e14i	−0.0344766	+	0.0344766i
$960$			1.40987e16i			0.558068i
$961$			1.66076e16i			0.653623i
$962$	1.39165e16	−	1.39165e16i	0.544588	−	0.544588i
$963$	−1.53726e16	+	1.53726e16i	−0.598141	+	0.598141i
$964$	−1.20758e16	−	1.20758e16i	−0.467188	−	0.467188i
$965$	2.09391e16			0.805485
$966$	3.58152e15	+	3.58152e15i	0.136991	+	0.136991i
$967$			3.66270e16i			1.39302i	0.717549	+	0.696508i	$0.245264\pi$
$967$			3.66270e16i			1.39302i	−0.717549	+	0.696508i	$0.754736\pi$
$968$	1.03312e16			0.390692
$969$	−6.96544e15	+	2.75166e15i	−0.261919	+	0.103470i
$970$	1.96926e16			0.736306
$971$		−	2.55635e16i		−	0.950417i	−0.879873	−	0.475208i	$-0.842373\pi$
$971$		−	2.55635e16i		−	0.950417i	0.879873	−	0.475208i	$-0.157627\pi$
$972$	−9.72191e15	−	9.72191e15i	−0.359407	−	0.359407i
$973$	3.02364e16			1.11150
$974$	1.60082e16	+	1.60082e16i	0.585151	+	0.585151i
$975$	3.64625e15	−	3.64625e15i	0.132532	−	0.132532i
$976$	5.13437e15	−	5.13437e15i	0.185572	−	0.185572i
$977$			1.36507e16i			0.490610i	0.969446	+	0.245305i	$0.0788880\pi$
$977$			1.36507e16i			0.490610i	−0.969446	+	0.245305i	$0.921112\pi$
$978$			1.87713e15i			0.0670856i
$979$	3.32854e16	−	3.32854e16i	1.18290	−	1.18290i
$980$	−1.06316e16	+	1.06316e16i	−0.375712	+	0.375712i
$981$	−1.95349e16	−	1.95349e16i	−0.686485	−	0.686485i
$982$	−3.99968e16			−1.39770
$983$	3.71752e16	+	3.71752e16i	1.29184	+	1.29184i	0.933648	+	0.358192i	$0.116607\pi$
$983$	3.71752e16	+	3.71752e16i	1.29184	+	1.29184i	0.358192	+	0.933648i	$0.383393\pi$
$984$		−	2.85889e16i		−	0.987926i
$985$	1.82375e16			0.626709
$986$	3.22851e16	−	1.27541e16i	1.10326	−	0.435838i
$987$	1.04207e16			0.354123
$988$			5.42831e15i			0.183443i
$989$	−8.93793e14	−	8.93793e14i	−0.0300371	−	0.0300371i
$990$	2.32486e16			0.776968
$991$	7.40249e15	+	7.40249e15i	0.246021	+	0.246021i	0.819336	−	0.573314i	$-0.194343\pi$
$991$	7.40249e15	+	7.40249e15i	0.246021	+	0.246021i	−0.573314	+	0.819336i	$0.694343\pi$
$992$	2.40562e16	−	2.40562e16i	0.795085	−	0.795085i
$993$	5.41320e15	−	5.41320e15i	0.177923	−	0.177923i
$994$		−	1.06986e16i		−	0.349704i
$995$			3.65021e16i			1.18656i
$996$	−1.15615e15	+	1.15615e15i	−0.0373755	+	0.0373755i
$997$	−3.49304e16	+	3.49304e16i	−1.12300	+	1.12300i	−0.131714	+	0.991288i	$0.542048\pi$
$997$	−3.49304e16	+	3.49304e16i	−1.12300	+	1.12300i	−0.991288	+	0.131714i	$0.957952\pi$
$998$	−1.83987e16	−	1.83987e16i	−0.588259	−	0.588259i
$999$	4.48927e16			1.42746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.11	yes	32
17.4	even	4	inner	17.12.c.a.4.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.6	✓	32	17.4	even	4	inner
17.12.c.a.13.11	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)

\(f(q)\)	\(=\)	\(q+32.2416i q^{2} +(149.760 + 149.760i) q^{3} +1008.48 q^{4} +(-6170.50 - 6170.50i) q^{5} +(-4828.50 + 4828.50i) q^{6} +(-42929.1 + 42929.1i) q^{7} +98545.8i q^{8} -132291. i q^{9} +O(q^{10})\)	\(q+32.2416i q^{2} +(149.760 + 149.760i) q^{3} +1008.48 q^{4} +(-6170.50 - 6170.50i) q^{5} +(-4828.50 + 4828.50i) q^{6} +(-42929.1 + 42929.1i) q^{7} +98545.8i q^{8} -132291. i q^{9} +(198947. - 198947. i) q^{10} +(-441672. + 441672. i) q^{11} +(151030. + 151030. i) q^{12} -891124. q^{13} +(-1.38410e6 - 1.38410e6i) q^{14} -1.84819e6i q^{15} -1.11191e6 q^{16} +(-5.37096e6 - 2.32909e6i) q^{17} +4.26527e6 q^{18} -6.04031e6i q^{19} +(-6.22283e6 - 6.22283e6i) q^{20} -1.28581e7 q^{21} +(-1.42402e7 - 1.42402e7i) q^{22} +(-8.63920e6 + 8.63920e6i) q^{23} +(-1.47582e7 + 1.47582e7i) q^{24} +2.73220e7i q^{25} -2.87312e7i q^{26} +(4.63414e7 - 4.63414e7i) q^{27} +(-4.32931e7 + 4.32931e7i) q^{28} +(1.30044e8 + 1.30044e8i) q^{29} +5.95885e7 q^{30} +(-1.44941e8 - 1.44941e8i) q^{31} +1.65972e8i q^{32} -1.32289e8 q^{33} +(7.50937e7 - 1.73168e8i) q^{34} +5.29788e8 q^{35} -1.33413e8i q^{36} +(4.84369e8 + 4.84369e8i) q^{37} +1.94749e8 q^{38} +(-1.33455e8 - 1.33455e8i) q^{39} +(6.08077e8 - 6.08077e8i) q^{40} +(-9.68577e8 + 9.68577e8i) q^{41} -4.14566e8i q^{42} +1.03458e8i q^{43} +(-4.45417e8 + 4.45417e8i) q^{44} +(-8.16301e8 + 8.16301e8i) q^{45} +(-2.78542e8 - 2.78542e8i) q^{46} -8.10441e8 q^{47} +(-1.66519e8 - 1.66519e8i) q^{48} -1.70848e9i q^{49} -8.80905e8 q^{50} +(-4.55550e8 - 1.15316e9i) q^{51} -8.98680e8 q^{52} -1.65122e9i q^{53} +(1.49412e9 + 1.49412e9i) q^{54} +5.45067e9 q^{55} +(-4.23048e9 - 4.23048e9i) q^{56} +(9.04596e8 - 9.04596e8i) q^{57} +(-4.19284e9 + 4.19284e9i) q^{58} -1.05861e9i q^{59} -1.86386e9i q^{60} +(-4.61763e9 + 4.61763e9i) q^{61} +(4.67314e9 - 4.67314e9i) q^{62} +(5.67913e9 + 5.67913e9i) q^{63} -7.62839e9 q^{64} +(5.49868e9 + 5.49868e9i) q^{65} -4.26522e9i q^{66} +1.58192e10 q^{67} +(-5.41651e9 - 2.34884e9i) q^{68} -2.58761e9 q^{69} +1.70812e10i q^{70} +(3.86481e9 + 3.86481e9i) q^{71} +1.30367e10 q^{72} +(1.10836e10 + 1.10836e10i) q^{73} +(-1.56168e10 + 1.56168e10i) q^{74} +(-4.09174e9 + 4.09174e9i) q^{75} -6.09153e9i q^{76} -3.79211e10i q^{77} +(4.30279e9 - 4.30279e9i) q^{78} +(2.68062e10 - 2.68062e10i) q^{79} +(6.86101e9 + 6.86101e9i) q^{80} -9.55479e9 q^{81} +(-3.12285e10 - 3.12285e10i) q^{82} +7.65509e9i q^{83} -1.29671e10 q^{84} +(1.87698e10 + 4.75132e10i) q^{85} -3.33565e9 q^{86} +3.89509e10i q^{87} +(-4.35249e10 - 4.35249e10i) q^{88} -7.53622e10 q^{89} +(-2.63189e10 - 2.63189e10i) q^{90} +(3.82551e10 - 3.82551e10i) q^{91} +(-8.71246e9 + 8.71246e9i) q^{92} -4.34128e10i q^{93} -2.61299e10i q^{94} +(-3.72717e10 + 3.72717e10i) q^{95} +(-2.48560e10 + 2.48560e10i) q^{96} +(4.94921e10 + 4.94921e10i) q^{97} +5.50842e10 q^{98} +(5.84292e10 + 5.84292e10i) 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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