LMFDB - Embedded newform 17.12.c.a.13.1

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			13.1
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-88.6653i q^{2} +(-145.298 - 145.298i) q^{3} -5813.53 q^{4} +(-6386.08 - 6386.08i) q^{5} +(-12882.9 + 12882.9i) q^{6} +(27657.5 - 27657.5i) q^{7} +333872. i q^{8} -134924. i q^{9} +O(q^{10})$	\(q-88.6653i q^{2} +(-145.298 - 145.298i) q^{3} -5813.53 q^{4} +(-6386.08 - 6386.08i) q^{5} +(-12882.9 + 12882.9i) q^{6} +(27657.5 - 27657.5i) q^{7} +333872. i q^{8} -134924. i q^{9} +(-566224. + 566224. i) q^{10} +(326010. - 326010. i) q^{11} +(844692. + 844692. i) q^{12} -942273. q^{13} +(-2.45226e6 - 2.45226e6i) q^{14} +1.85577e6i q^{15} +1.76967e7 q^{16} +(5.69555e6 + 1.35373e6i) q^{17} -1.19631e7 q^{18} -1.34809e7i q^{19} +(3.71257e7 + 3.71257e7i) q^{20} -8.03715e6 q^{21} +(-2.89058e7 - 2.89058e7i) q^{22} +(-1.73146e7 + 1.73146e7i) q^{23} +(4.85108e7 - 4.85108e7i) q^{24} +3.27360e7i q^{25} +8.35469e7i q^{26} +(-4.53432e7 + 4.53432e7i) q^{27} +(-1.60788e8 + 1.60788e8i) q^{28} +(5.58148e7 + 5.58148e7i) q^{29} +1.64542e8 q^{30} +(-5.79594e7 - 5.79594e7i) q^{31} -8.85314e8i q^{32} -9.47371e7 q^{33} +(1.20028e8 - 5.04998e8i) q^{34} -3.53246e8 q^{35} +7.84386e8i q^{36} +(2.77393e8 + 2.77393e8i) q^{37} -1.19529e9 q^{38} +(1.36910e8 + 1.36910e8i) q^{39} +(2.13213e9 - 2.13213e9i) q^{40} +(-2.25930e8 + 2.25930e8i) q^{41} +7.12616e8i q^{42} +5.89362e8i q^{43} +(-1.89527e9 + 1.89527e9i) q^{44} +(-8.61637e8 + 8.61637e8i) q^{45} +(1.53520e9 + 1.53520e9i) q^{46} -1.28340e9 q^{47} +(-2.57129e9 - 2.57129e9i) q^{48} +4.47450e8i q^{49} +2.90254e9 q^{50} +(-6.30857e8 - 1.02424e9i) q^{51} +5.47793e9 q^{52} -4.86248e9i q^{53} +(4.02037e9 + 4.02037e9i) q^{54} -4.16386e9 q^{55} +(9.23406e9 + 9.23406e9i) q^{56} +(-1.95875e9 + 1.95875e9i) q^{57} +(4.94883e9 - 4.94883e9i) q^{58} -1.51765e9i q^{59} -1.07885e10i q^{60} +(6.58302e9 - 6.58302e9i) q^{61} +(-5.13898e9 + 5.13898e9i) q^{62} +(-3.73167e9 - 3.73167e9i) q^{63} -4.22537e10 q^{64} +(6.01744e9 + 6.01744e9i) q^{65} +8.39989e9i q^{66} +1.16438e10 q^{67} +(-3.31113e10 - 7.86992e9i) q^{68} +5.03153e9 q^{69} +3.13207e10i q^{70} +(-1.63879e10 - 1.63879e10i) q^{71} +4.50473e10 q^{72} +(-3.10339e9 - 3.10339e9i) q^{73} +(2.45951e10 - 2.45951e10i) q^{74} +(4.75646e9 - 4.75646e9i) q^{75} +7.83719e10i q^{76} -1.80333e10i q^{77} +(1.21392e10 - 1.21392e10i) q^{78} +(1.85319e10 - 1.85319e10i) q^{79} +(-1.13013e11 - 1.13013e11i) q^{80} -1.07249e10 q^{81} +(2.00321e10 + 2.00321e10i) q^{82} +4.03852e10i q^{83} +4.67242e10 q^{84} +(-2.77273e10 - 4.50173e10i) q^{85} +5.22559e10 q^{86} -1.62195e10i q^{87} +(1.08846e11 + 1.08846e11i) q^{88} -6.44743e10 q^{89} +(7.63973e10 + 7.63973e10i) q^{90} +(-2.60609e10 + 2.60609e10i) q^{91} +(1.00659e11 - 1.00659e11i) q^{92} +1.68427e10i q^{93} +1.13793e11i q^{94} +(-8.60904e10 + 8.60904e10i) q^{95} +(-1.28634e11 + 1.28634e11i) q^{96} +(-3.87960e10 - 3.87960e10i) q^{97} +3.96733e10 q^{98} +(-4.39867e10 - 4.39867e10i) 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 $

$2$		−	88.6653i		−	1.95924i	−0.200850	−	0.979622i	$-0.564370\pi$
$2$		−	88.6653i		−	1.95924i	0.200850	−	0.979622i	$-0.435630\pi$
$3$	−145.298	−	145.298i	−0.345217	−	0.345217i	0.513108	−	0.858324i	$-0.328494\pi$
$3$	−145.298	−	145.298i	−0.345217	−	0.345217i	−0.858324	+	0.513108i	$0.828494\pi$
$4$	−5813.53			−2.83864
$5$	−6386.08	−	6386.08i	−0.913902	−	0.913902i	0.0826748	−	0.996577i	$-0.473654\pi$
$5$	−6386.08	−	6386.08i	−0.913902	−	0.913902i	−0.996577	+	0.0826748i	$0.973654\pi$
$6$	−12882.9	+	12882.9i	−0.676364	+	0.676364i
$7$	27657.5	−	27657.5i	0.621977	−	0.621977i	−0.324060	−	0.946037i	$-0.605048\pi$
$7$	27657.5	−	27657.5i	0.621977	−	0.621977i	0.946037	+	0.324060i	$0.105048\pi$
$8$			333872.i			3.60234i
$9$		−	134924.i		−	0.761651i
$10$	−566224.	+	566224.i	−1.79056	+	1.79056i
$11$	326010.	−	326010.i	0.610340	−	0.610340i	−0.332695	−	0.943035i	$-0.607958\pi$
$11$	326010.	−	326010.i	0.610340	−	0.610340i	0.943035	+	0.332695i	$0.107958\pi$
$12$	844692.	+	844692.i	0.979945	+	0.979945i
$13$	−942273.			−0.703864			−0.351932	−	0.936026i	$-0.614475\pi$
$13$	−942273.			−0.703864			−0.351932	+	0.936026i	$0.614475\pi$
$14$	−2.45226e6	−	2.45226e6i	−1.21860	−	1.21860i
$15$			1.85577e6i			0.630988i
$16$	1.76967e7			4.21922
$17$	5.69555e6	+	1.35373e6i	0.972897	+	0.231239i
$17$	5.69555e6	+	1.35373e6i	0.972897	+	0.231239i
$18$	−1.19631e7			−1.49226
$19$		−	1.34809e7i		−	1.24904i	−0.781010	−	0.624519i	$-0.785295\pi$
$19$		−	1.34809e7i		−	1.24904i	0.781010	−	0.624519i	$-0.214705\pi$
$20$	3.71257e7	+	3.71257e7i	2.59424	+	2.59424i
$21$	−8.03715e6			−0.429433
$22$	−2.89058e7	−	2.89058e7i	−1.19580	−	1.19580i
$23$	−1.73146e7	+	1.73146e7i	−0.560930	+	0.560930i	−0.929572	−	0.368642i	$-0.879823\pi$
$23$	−1.73146e7	+	1.73146e7i	−0.560930	+	0.560930i	0.368642	+	0.929572i	$0.379823\pi$
$24$	4.85108e7	−	4.85108e7i	1.24359	−	1.24359i
$25$			3.27360e7i			0.670433i
$26$			8.35469e7i			1.37904i
$27$	−4.53432e7	+	4.53432e7i	−0.608151	+	0.608151i
$28$	−1.60788e8	+	1.60788e8i	−1.76557	+	1.76557i
$29$	5.58148e7	+	5.58148e7i	0.505313	+	0.505313i	0.913084	−	0.407771i	$-0.133694\pi$
$29$	5.58148e7	+	5.58148e7i	0.505313	+	0.505313i	−0.407771	+	0.913084i	$0.633694\pi$
$30$	1.64542e8			1.23626
$31$	−5.79594e7	−	5.79594e7i	−0.363609	−	0.363609i	0.501531	−	0.865140i	$-0.332770\pi$
$31$	−5.79594e7	−	5.79594e7i	−0.363609	−	0.363609i	−0.865140	+	0.501531i	$0.832770\pi$
$32$		−	8.85314e8i		−	4.66415i
$33$	−9.47371e7			−0.421399
$34$	1.20028e8	−	5.04998e8i	0.453054	−	1.90614i
$35$	−3.53246e8			−1.13685
$36$			7.84386e8i			2.16205i
$37$	2.77393e8	+	2.77393e8i	0.657637	+	0.657637i	0.954820	−	0.297184i	$-0.0960473\pi$
$37$	2.77393e8	+	2.77393e8i	0.657637	+	0.657637i	−0.297184	+	0.954820i	$0.596047\pi$
$38$	−1.19529e9			−2.44717
$39$	1.36910e8	+	1.36910e8i	0.242985	+	0.242985i
$40$	2.13213e9	−	2.13213e9i	3.29218	−	3.29218i
$41$	−2.25930e8	+	2.25930e8i	−0.304553	+	0.304553i	−0.842792	−	0.538239i	$-0.819090\pi$
$41$	−2.25930e8	+	2.25930e8i	−0.304553	+	0.304553i	0.538239	+	0.842792i	$0.319090\pi$
$42$			7.12616e8i			0.841365i
$43$			5.89362e8i			0.611372i	0.952132	+	0.305686i	$0.0988858\pi$
$43$			5.89362e8i			0.611372i	−0.952132	+	0.305686i	$0.901114\pi$
$44$	−1.89527e9	+	1.89527e9i	−1.73253	+	1.73253i
$45$	−8.61637e8	+	8.61637e8i	−0.696074	+	0.696074i
$46$	1.53520e9	+	1.53520e9i	1.09900	+	1.09900i
$47$	−1.28340e9			−0.816252			−0.408126	−	0.912925i	$-0.633818\pi$
$47$	−1.28340e9			−0.816252			−0.408126	+	0.912925i	$0.633818\pi$
$48$	−2.57129e9	−	2.57129e9i	−1.45655	−	1.45655i
$49$			4.47450e8i			0.226290i
$50$	2.90254e9			1.31354
$51$	−6.30857e8	−	1.02424e9i	−0.256033	−	0.415688i
$52$	5.47793e9			1.99801
$53$		−	4.86248e9i		−	1.59713i	−0.601908	−	0.798565i	$-0.705593\pi$
$53$		−	4.86248e9i		−	1.59713i	0.601908	−	0.798565i	$-0.294407\pi$
$54$	4.02037e9	+	4.02037e9i	1.19152	+	1.19152i
$55$	−4.16386e9			−1.11558
$56$	9.23406e9	+	9.23406e9i	2.24057	+	2.24057i
$57$	−1.95875e9	+	1.95875e9i	−0.431189	+	0.431189i
$58$	4.94883e9	−	4.94883e9i	0.990031	−	0.990031i
$59$		−	1.51765e9i		−	0.276367i	−0.990407	−	0.138183i	$-0.955874\pi$
$59$		−	1.51765e9i		−	0.276367i	0.990407	−	0.138183i	$-0.0441263\pi$
$60$		−	1.07885e10i		−	1.79115i
$61$	6.58302e9	−	6.58302e9i	0.997955	−	0.997955i	−0.00204338	−	0.999998i	$-0.500650\pi$
$61$	6.58302e9	−	6.58302e9i	0.997955	−	0.997955i	0.999998	+	0.00204338i	$0.000650428\pi$
$62$	−5.13898e9	+	5.13898e9i	−0.712398	+	0.712398i
$63$	−3.73167e9	−	3.73167e9i	−0.473729	−	0.473729i
$64$	−4.22537e10			−4.91898
$65$	6.01744e9	+	6.01744e9i	0.643262	+	0.643262i
$66$			8.39989e9i			0.825623i
$67$	1.16438e10			1.05362			0.526810	−	0.849983i	$-0.323388\pi$
$67$	1.16438e10			1.05362			0.526810	+	0.849983i	$0.323388\pi$
$68$	−3.31113e10	−	7.86992e9i	−2.76170	−	0.656405i
$69$	5.03153e9			0.387285
$70$			3.13207e10i			2.22737i
$71$	−1.63879e10	−	1.63879e10i	−1.07796	−	1.07796i	−0.996692	−	0.0812664i	$-0.974104\pi$
$71$	−1.63879e10	−	1.63879e10i	−1.07796	−	1.07796i	−0.0812664	−	0.996692i	$-0.525896\pi$
$72$	4.50473e10			2.74372
$73$	−3.10339e9	−	3.10339e9i	−0.175211	−	0.175211i	0.614054	−	0.789264i	$-0.289538\pi$
$73$	−3.10339e9	−	3.10339e9i	−0.175211	−	0.175211i	−0.789264	+	0.614054i	$0.789538\pi$
$74$	2.45951e10	−	2.45951e10i	1.28847	−	1.28847i
$75$	4.75646e9	−	4.75646e9i	0.231445	−	0.231445i
$76$			7.83719e10i			3.54556i
$77$		−	1.80333e10i		−	0.759234i
$78$	1.21392e10	−	1.21392e10i	0.476068	−	0.476068i
$79$	1.85319e10	−	1.85319e10i	0.677595	−	0.677595i	−0.281860	−	0.959455i	$-0.590951\pi$
$79$	1.85319e10	−	1.85319e10i	0.677595	−	0.677595i	0.959455	+	0.281860i	$0.0909514\pi$
$80$	−1.13013e11	−	1.13013e11i	−3.85596	−	3.85596i
$81$	−1.07249e10			−0.341763
$82$	2.00321e10	+	2.00321e10i	0.596693	+	0.596693i
$83$			4.03852e10i			1.12536i	0.826673	+	0.562682i	$0.190230\pi$
$83$			4.03852e10i			1.12536i	−0.826673	+	0.562682i	$0.809770\pi$
$84$	4.67242e10			1.21901
$85$	−2.77273e10	−	4.50173e10i	−0.677802	−	1.10046i
$86$	5.22559e10			1.19783
$87$		−	1.62195e10i		−	0.348885i
$88$	1.08846e11	+	1.08846e11i	2.19865	+	2.19865i
$89$	−6.44743e10			−1.22389			−0.611944	−	0.790901i	$-0.709612\pi$
$89$	−6.44743e10			−1.22389			−0.611944	+	0.790901i	$0.709612\pi$
$90$	7.63973e10	+	7.63973e10i	1.36378	+	1.36378i
$91$	−2.60609e10	+	2.60609e10i	−0.437787	+	0.437787i
$92$	1.00659e11	−	1.00659e11i	1.59228	−	1.59228i
$93$			1.68427e10i			0.251048i
$94$			1.13793e11i			1.59924i
$95$	−8.60904e10	+	8.60904e10i	−1.14150	+	1.14150i
$96$	−1.28634e11	+	1.28634e11i	−1.61014	+	1.61014i
$97$	−3.87960e10	−	3.87960e10i	−0.458715	−	0.458715i	0.439519	−	0.898233i	$-0.355149\pi$
$97$	−3.87960e10	−	3.87960e10i	−0.458715	−	0.458715i	−0.898233	+	0.439519i	$0.855149\pi$
$98$	3.96733e10			0.443358
$99$	−4.39867e10	−	4.39867e10i	−0.464866	−	0.464866i
$100$		−	1.90312e11i		−	1.90312i
$101$	−2.58769e9			−0.0244988			−0.0122494	−	0.999925i	$-0.503899\pi$
$101$	−2.58769e9			−0.0244988			−0.0122494	+	0.999925i	$0.503899\pi$
$102$	−9.08148e10	+	5.59351e10i	−0.814434	+	0.501630i
$103$	1.46824e11			1.24794			0.623968	−	0.781450i	$-0.285520\pi$
$103$	1.46824e11			1.24794			0.623968	+	0.781450i	$0.285520\pi$
$104$		−	3.14598e11i		−	2.53555i
$105$	5.13259e10	+	5.13259e10i	0.392460	+	0.392460i
$106$	−4.31133e11			−3.12917
$107$	5.03837e10	+	5.03837e10i	0.347280	+	0.347280i	0.859095	−	0.511816i	$-0.171027\pi$
$107$	5.03837e10	+	5.03837e10i	0.347280	+	0.347280i	−0.511816	+	0.859095i	$0.671027\pi$
$108$	2.63604e11	−	2.63604e11i	1.72632	−	1.72632i
$109$	−1.64295e11	+	1.64295e11i	−1.02277	+	1.02277i	−0.0230338	+	0.999735i	$0.507333\pi$
$109$	−1.64295e11	+	1.64295e11i	−1.02277	+	1.02277i	−0.999735	+	0.0230338i	$0.992667\pi$
$110$			3.69190e11i			2.18570i
$111$		−	8.06091e10i		−	0.454054i
$112$	4.89447e11	−	4.89447e11i	2.62426	−	2.62426i
$113$	−5.95118e10	+	5.95118e10i	−0.303859	+	0.303859i	−0.842521	−	0.538663i	$-0.818930\pi$
$113$	−5.95118e10	+	5.95118e10i	−0.303859	+	0.303859i	0.538663	+	0.842521i	$0.318930\pi$
$114$	1.73673e11	+	1.73673e11i	0.844804	+	0.844804i
$115$	2.21145e11			1.02527
$116$	−3.24481e11	−	3.24481e11i	−1.43440	−	1.43440i
$117$			1.27135e11i			0.536098i
$118$	−1.34563e11			−0.541470
$119$	1.94966e11	−	1.20084e11i	0.748945	−	0.461294i
$120$	−6.19587e11			−2.27303
$121$			7.27461e10i			0.254971i
$122$	−5.83685e11	−	5.83685e11i	−1.95524	−	1.95524i
$123$	6.56542e10			0.210273
$124$	3.36948e11	+	3.36948e11i	1.03215	+	1.03215i
$125$	−1.02766e11	+	1.02766e11i	−0.301192	+	0.301192i
$126$	−3.30869e11	+	3.30869e11i	−0.928151	+	0.928151i
$127$		−	2.19856e11i		−	0.590498i	−0.955420	−	0.295249i	$-0.904597\pi$
$127$		−	2.19856e11i		−	0.590498i	0.955420	−	0.295249i	$-0.0954026\pi$
$128$			1.93332e12i			4.97334i
$129$	8.56329e10	−	8.56329e10i	0.211056	−	0.211056i
$130$	5.33538e11	−	5.33538e11i	1.26031	−	1.26031i
$131$	−3.08010e10	−	3.08010e10i	−0.0697546	−	0.0697546i	0.671369	−	0.741123i	$-0.265707\pi$
$131$	−3.08010e10	−	3.08010e10i	−0.0697546	−	0.0697546i	−0.741123	+	0.671369i	$0.765707\pi$
$132$	5.50757e11			1.19620
$133$	−3.72849e11	−	3.72849e11i	−0.776872	−	0.776872i
$134$		−	1.03240e12i		−	2.06430i
$135$	5.79131e11			1.11158
$136$	−4.51971e11	+	1.90158e12i	−0.833002	+	3.50470i
$137$	3.73466e11			0.661131			0.330565	−	0.943783i	$-0.392761\pi$
$137$	3.73466e11			0.661131			0.330565	+	0.943783i	$0.392761\pi$
$138$		−	4.46122e11i		−	0.758785i
$139$	6.75028e10	+	6.75028e10i	0.110342	+	0.110342i	0.760122	−	0.649780i	$-0.225139\pi$
$139$	6.75028e10	+	6.75028e10i	0.110342	+	0.110342i	−0.649780	+	0.760122i	$0.725139\pi$
$140$	2.05361e12			3.22711
$141$	1.86475e11	+	1.86475e11i	0.281784	+	0.281784i
$142$	−1.45304e12	+	1.45304e12i	−2.11198	+	2.11198i
$143$	−3.07191e11	+	3.07191e11i	−0.429596	+	0.429596i
$144$		−	2.38771e12i		−	3.21357i
$145$		−	7.12876e11i		−	0.923612i
$146$	−2.75163e11	+	2.75163e11i	−0.343281	+	0.343281i
$147$	6.50134e10	−	6.50134e10i	0.0781192	−	0.0781192i
$148$	−1.61263e12	−	1.61263e12i	−1.86679	−	1.86679i
$149$	1.12199e12			1.25160			0.625799	−	0.779984i	$-0.284773\pi$
$149$	1.12199e12			1.25160			0.625799	+	0.779984i	$0.284773\pi$
$150$	−4.21733e11	−	4.21733e11i	−0.453456	−	0.453456i
$151$			4.38906e11i			0.454986i	0.973780	+	0.227493i	$0.0730529\pi$
$151$			4.38906e11i			0.454986i	−0.973780	+	0.227493i	$0.926947\pi$
$152$	4.50090e12			4.49946
$153$	1.82650e11	−	7.68468e11i	0.176124	−	0.741008i
$154$	−1.59893e12			−1.48752
$155$			7.40267e11i			0.664605i
$156$	−7.95931e11	−	7.95931e11i	−0.689747	−	0.689747i
$157$	9.19144e11			0.769016			0.384508	−	0.923122i	$-0.374371\pi$
$157$	9.19144e11			0.769016			0.384508	+	0.923122i	$0.374371\pi$
$158$	−1.64313e12	−	1.64313e12i	−1.32757	−	1.32757i
$159$	−7.06507e11	+	7.06507e11i	−0.551356	+	0.551356i
$160$	−5.65369e12	+	5.65369e12i	−4.26257	+	4.26257i
$161$			9.57756e11i			0.697770i
$162$			9.50925e11i			0.669597i
$163$	3.00455e11	−	3.00455e11i	0.204525	−	0.204525i	−0.597410	−	0.801936i	$-0.703804\pi$
$163$	3.00455e11	−	3.00455e11i	0.204525	−	0.204525i	0.801936	+	0.597410i	$0.203804\pi$
$164$	1.31345e12	−	1.31345e12i	0.864514	−	0.864514i
$165$	6.04999e11	+	6.04999e11i	0.385117	+	0.385117i
$166$	3.58077e12			2.20486
$167$	−5.96799e11	−	5.96799e11i	−0.355539	−	0.355539i	0.506626	−	0.862166i	$-0.330892\pi$
$167$	−5.96799e11	−	5.96799e11i	−0.355539	−	0.355539i	−0.862166	+	0.506626i	$0.830892\pi$
$168$		−	2.68337e12i		−	1.54696i
$169$	−9.04281e11			−0.504576
$170$	−3.99147e12	+	2.45845e12i	−2.15607	+	1.32798i
$171$	−1.81891e12			−0.951331
$172$		−	3.42627e12i		−	1.73546i
$173$	−1.44123e12	−	1.44123e12i	−0.707097	−	0.707097i	0.258827	−	0.965924i	$-0.416664\pi$
$173$	−1.44123e12	−	1.44123e12i	−0.707097	−	0.707097i	−0.965924	+	0.258827i	$0.916664\pi$
$174$	−1.43811e12			−0.683550
$175$	9.05396e11	+	9.05396e11i	0.416994	+	0.416994i
$176$	5.76931e12	−	5.76931e12i	2.57516	−	2.57516i
$177$	−2.20511e11	+	2.20511e11i	−0.0954064	+	0.0954064i
$178$			5.71663e12i			2.39790i
$179$			4.02921e12i			1.63881i	0.573217	+	0.819403i	$0.305695\pi$
$179$			4.02921e12i			1.63881i	−0.573217	+	0.819403i	$0.694305\pi$
$180$	5.00915e12	−	5.00915e12i	1.97590	−	1.97590i
$181$	−5.89688e11	+	5.89688e11i	−0.225627	+	0.225627i	−0.810863	−	0.585236i	$-0.801002\pi$
$181$	−5.89688e11	+	5.89688e11i	−0.225627	+	0.225627i	0.585236	+	0.810863i	$0.301002\pi$
$182$	2.31070e12	+	2.31070e12i	0.857731	+	0.857731i
$183$	−1.91299e12			−0.689021
$184$	−5.78084e12	−	5.78084e12i	−2.02066	−	2.02066i
$185$		−	3.54291e12i		−	1.20203i
$186$	1.49336e12			0.491863
$187$	2.29814e12	−	1.41548e12i	0.734932	−	0.452663i
$188$	7.46109e12			2.31704
$189$			2.50816e12i			0.756512i
$190$	7.63323e12	+	7.63323e12i	2.23647	+	2.23647i
$191$	−2.78808e12			−0.793635			−0.396818	−	0.917897i	$-0.629885\pi$
$191$	−2.78808e12			−0.793635			−0.396818	+	0.917897i	$0.629885\pi$
$192$	6.13937e12	+	6.13937e12i	1.69811	+	1.69811i
$193$	2.58640e11	−	2.58640e11i	0.0695233	−	0.0695233i	−0.671490	−	0.741013i	$-0.734345\pi$
$193$	2.58640e11	−	2.58640e11i	0.0695233	−	0.0695233i	0.741013	+	0.671490i	$0.234345\pi$
$194$	−3.43986e12	+	3.43986e12i	−0.898734	+	0.898734i
$195$		−	1.74864e12i		−	0.444130i
$196$		−	2.60126e12i		−	0.642356i
$197$	−2.92476e12	+	2.92476e12i	−0.702305	+	0.702305i	−0.964905	−	0.262600i	$-0.915420\pi$
$197$	−2.92476e12	+	2.92476e12i	−0.702305	+	0.702305i	0.262600	+	0.964905i	$0.415420\pi$
$198$	−3.90009e12	+	3.90009e12i	−0.910786	+	0.910786i
$199$	−3.88728e12	−	3.88728e12i	−0.882986	−	0.882986i	0.110851	−	0.993837i	$-0.464642\pi$
$199$	−3.88728e12	−	3.88728e12i	−0.882986	−	0.882986i	−0.993837	+	0.110851i	$0.964642\pi$
$200$	−1.09296e13			−2.41513
$201$	−1.69182e12	−	1.69182e12i	−0.363727	−	0.363727i
$202$			2.29438e11i			0.0479991i
$203$	3.08740e12			0.628585
$204$	3.66751e12	+	5.95447e12i	0.726783	+	1.17999i
$205$	2.88561e12			0.556662
$206$		−	1.30182e13i		−	2.44501i
$207$	2.33615e12	+	2.33615e12i	0.427233	+	0.427233i
$208$	−1.66751e13			−2.96976
$209$	−4.39493e12	−	4.39493e12i	−0.762337	−	0.762337i
$210$	4.55082e12	−	4.55082e12i	0.768925	−	0.768925i
$211$	5.47586e12	−	5.47586e12i	0.901361	−	0.901361i	−0.0941930	−	0.995554i	$-0.530027\pi$
$211$	5.47586e12	−	5.47586e12i	0.901361	−	0.901361i	0.995554	+	0.0941930i	$0.0300271\pi$
$212$			2.82682e13i			4.53367i
$213$			4.76224e12i			0.744259i
$214$	4.46729e12	−	4.46729e12i	0.680406	−	0.680406i
$215$	3.76371e12	−	3.76371e12i	0.558734	−	0.558734i
$216$	−1.51388e13	−	1.51388e13i	−2.19077	−	2.19077i
$217$	−3.20602e12			−0.452312
$218$	1.45672e13	+	1.45672e13i	2.00385	+	2.00385i
$219$			9.01831e11i			0.120971i
$220$	2.42067e13			3.16673
$221$	−5.36677e12	−	1.27558e12i	−0.684787	−	0.162761i
$222$	−7.14723e12			−0.889603
$223$			7.37190e12i			0.895164i	0.894243	+	0.447582i	$0.147715\pi$
$223$			7.37190e12i			0.895164i	−0.894243	+	0.447582i	$0.852285\pi$
$224$	−2.44856e13	−	2.44856e13i	−2.90099	−	2.90099i
$225$	4.41688e12			0.510636
$226$	5.27663e12	+	5.27663e12i	0.595333	+	0.595333i
$227$	1.01600e13	−	1.01600e13i	1.11880	−	1.11880i	0.126885	−	0.991917i	$-0.459502\pi$
$227$	1.01600e13	−	1.01600e13i	1.11880	−	1.11880i	0.991917	−	0.126885i	$-0.0404979\pi$
$228$	1.13872e13	−	1.13872e13i	1.22399	−	1.22399i
$229$		−	1.44542e13i		−	1.51669i	−0.651851	−	0.758347i	$-0.726007\pi$
$229$		−	1.44542e13i		−	1.51669i	0.651851	−	0.758347i	$-0.273993\pi$
$230$		−	1.96078e13i		−	2.00875i
$231$	−2.62019e12	+	2.62019e12i	−0.262100	+	0.262100i
$232$	−1.86350e13	+	1.86350e13i	−1.82031	+	1.82031i
$233$	−1.29986e13	−	1.29986e13i	−1.24005	−	1.24005i	−0.959980	−	0.280068i	$-0.909643\pi$
$233$	−1.29986e13	−	1.29986e13i	−1.24005	−	1.24005i	−0.280068	−	0.959980i	$-0.590357\pi$
$234$	1.12725e13			1.05035
$235$	8.19591e12	+	8.19591e12i	0.745975	+	0.745975i
$236$			8.82290e12i			0.784505i
$237$	−5.38528e12			−0.467834
$238$	−1.06473e13	−	1.72867e13i	−0.903787	−	1.46737i
$239$	−1.14668e13			−0.951160			−0.475580	−	0.879672i	$-0.657762\pi$
$239$	−1.14668e13			−0.951160			−0.475580	+	0.879672i	$0.657762\pi$
$240$			3.28409e13i			2.66228i
$241$	6.31013e11	+	6.31013e11i	0.0499971	+	0.0499971i	0.731663	−	0.681666i	$-0.238744\pi$
$241$	6.31013e11	+	6.31013e11i	0.0499971	+	0.0499971i	−0.681666	+	0.731663i	$0.738744\pi$
$242$	6.45005e12			0.499550
$243$	9.59072e12	+	9.59072e12i	0.726134	+	0.726134i
$244$	−3.82705e13	+	3.82705e13i	−2.83283	+	2.83283i
$245$	2.85745e12	−	2.85745e12i	0.206807	−	0.206807i
$246$		−	5.82124e12i		−	0.411977i
$247$			1.27027e13i			0.879152i
$248$	1.93510e13	−	1.93510e13i	1.30984	−	1.30984i
$249$	5.86788e12	−	5.86788e12i	0.388494	−	0.388494i
$250$	9.11175e12	+	9.11175e12i	0.590108	+	0.590108i
$251$	5.86425e12			0.371541			0.185770	−	0.982593i	$-0.440522\pi$
$251$	5.86425e12			0.371541			0.185770	+	0.982593i	$0.440522\pi$
$252$	2.16942e13	+	2.16942e13i	1.34474	+	1.34474i
$253$			1.12895e13i			0.684716i
$254$	−1.94936e13			−1.15693
$255$	−2.51220e12	+	1.05696e13i	−0.145909	+	0.613886i
$256$	8.48823e13			4.82500
$257$		−	2.45129e12i		−	0.136384i	−0.997672	−	0.0681919i	$-0.978277\pi$
$257$		−	2.45129e12i		−	0.136384i	0.997672	−	0.0681919i	$-0.0217230\pi$
$258$	−7.59266e12	−	7.59266e12i	−0.413510	−	0.413510i
$259$	1.53440e13			0.818069
$260$	−3.49825e13	−	3.49825e13i	−1.82599	−	1.82599i
$261$	7.53076e12	−	7.53076e12i	0.384872	−	0.384872i
$262$	−2.73098e12	+	2.73098e12i	−0.136666	+	0.136666i
$263$		−	1.15133e12i		−	0.0564214i	−0.999602	−	0.0282107i	$-0.991019\pi$
$263$		−	1.15133e12i		−	0.0564214i	0.999602	−	0.0282107i	$-0.00898094\pi$
$264$		−	3.16300e13i		−	1.51802i
$265$	−3.10522e13	+	3.10522e13i	−1.45962	+	1.45962i
$266$	−3.30588e13	+	3.30588e13i	−1.52208	+	1.52208i
$267$	9.36797e12	+	9.36797e12i	0.422506	+	0.422506i
$268$	−6.76917e13			−2.99084
$269$	−1.22376e13	−	1.22376e13i	−0.529735	−	0.529735i	0.390758	−	0.920493i	$-0.372213\pi$
$269$	−1.22376e13	−	1.22376e13i	−0.529735	−	0.529735i	−0.920493	+	0.390758i	$0.872213\pi$
$270$		−	5.13488e13i		−	2.17786i
$271$	1.08031e13			0.448970			0.224485	−	0.974478i	$-0.427930\pi$
$271$	1.08031e13			0.448970			0.224485	+	0.974478i	$0.427930\pi$
$272$	1.00793e14	+	2.39565e13i	4.10487	+	0.975650i
$273$	7.57319e12			0.302262
$274$		−	3.31134e13i		−	1.29532i
$275$	1.06723e13	+	1.06723e13i	0.409192	+	0.409192i
$276$	−2.92510e13			−1.09936
$277$	−2.14303e13	−	2.14303e13i	−0.789567	−	0.789567i	0.191856	−	0.981423i	$-0.438549\pi$
$277$	−2.14303e13	−	2.14303e13i	−0.789567	−	0.789567i	−0.981423	+	0.191856i	$0.938549\pi$
$278$	5.98516e12	−	5.98516e12i	0.216187	−	0.216187i
$279$	−7.82012e12	+	7.82012e12i	−0.276943	+	0.276943i
$280$		−	1.17939e14i		−	4.09532i
$281$			1.95067e12i			0.0664200i	0.999448	+	0.0332100i	$0.0105730\pi$
$281$			1.95067e12i			0.0664200i	−0.999448	+	0.0332100i	$0.989427\pi$
$282$	1.65339e13	−	1.65339e13i	0.552083	−	0.552083i
$283$	−9.18899e12	+	9.18899e12i	−0.300914	+	0.300914i	−0.841371	−	0.540457i	$-0.818251\pi$
$283$	−9.18899e12	+	9.18899e12i	−0.300914	+	0.300914i	0.540457	+	0.841371i	$0.318251\pi$
$284$	9.52715e13	+	9.52715e13i	3.05993	+	3.05993i
$285$	2.50175e13			0.788128
$286$	2.72372e13	+	2.72372e13i	0.841683	+	0.841683i
$287$			1.24973e13i			0.378849i
$288$	−1.19450e14			−3.55245
$289$	3.06067e13	+	1.54204e13i	0.893057	+	0.449944i
$290$	−6.32073e13			−1.80958
$291$			1.12739e13i			0.316712i
$292$	1.80416e13	+	1.80416e13i	0.497360	+	0.497360i
$293$	−4.19374e13			−1.13457			−0.567283	−	0.823523i	$-0.692005\pi$
$293$	−4.19374e13			−1.13457			−0.567283	+	0.823523i	$0.692005\pi$
$294$	−5.76443e12	−	5.76443e12i	−0.153055	−	0.153055i
$295$	−9.69184e12	+	9.69184e12i	−0.252572	+	0.252572i
$296$	−9.26137e13	+	9.26137e13i	−2.36903	+	2.36903i
$297$			2.95647e13i			0.742358i
$298$		−	9.94817e13i		−	2.45219i
$299$	1.63151e13	−	1.63151e13i	0.394818	−	0.394818i
$300$	−2.76518e13	+	2.76518e13i	−0.656987	+	0.656987i
$301$	1.63003e13	+	1.63003e13i	0.380259	+	0.380259i
$302$	3.89157e13			0.891429
$303$	3.75985e11	+	3.75985e11i	0.00845738	+	0.00845738i
$304$		−	2.38568e14i		−	5.26997i
$305$	−8.40794e13			−1.82406
$306$	−6.81364e13	−	1.61947e13i	−1.45182	−	0.345069i
$307$	5.48477e13			1.14788			0.573941	−	0.818896i	$-0.305414\pi$
$307$	5.48477e13			1.14788			0.573941	+	0.818896i	$0.305414\pi$
$308$			1.04837e14i			2.15519i
$309$	−2.13332e13	−	2.13332e13i	−0.430808	−	0.430808i
$310$	6.56359e13			1.30212
$311$	5.93077e11	+	5.93077e11i	0.0115592	+	0.0115592i	0.712863	−	0.701304i	$-0.247398\pi$
$311$	5.93077e11	+	5.93077e11i	0.0115592	+	0.0115592i	−0.701304	+	0.712863i	$0.747398\pi$
$312$	−4.57104e13	+	4.57104e13i	−0.875316	+	0.875316i
$313$	3.91771e13	−	3.91771e13i	0.737121	−	0.737121i	−0.234899	−	0.972020i	$-0.575476\pi$
$313$	3.91771e13	−	3.91771e13i	0.737121	−	0.737121i	0.972020	+	0.234899i	$0.0754759\pi$
$314$		−	8.14961e13i		−	1.50669i
$315$			4.76615e13i			0.865884i
$316$	−1.07736e14	+	1.07736e14i	−1.92345	+	1.92345i
$317$	5.77285e13	−	5.77285e13i	1.01290	−	1.01290i	0.0129798	−	0.999916i	$-0.495868\pi$
$317$	5.77285e13	−	5.77285e13i	1.01290	−	1.01290i	0.999916	−	0.0129798i	$-0.00413173\pi$
$318$	6.26426e13	+	6.26426e13i	1.08024	+	1.08024i
$319$	3.63924e13			0.616825
$320$	2.69836e14	+	2.69836e14i	4.49547	+	4.49547i
$321$		−	1.46413e13i		−	0.239774i
$322$	8.49197e13			1.36710
$323$	1.82495e13	−	7.67814e13i	0.288827	−	1.21518i
$324$	6.23495e13			0.970142
$325$		−	3.08462e13i		−	0.471893i
$326$	−2.66399e13	−	2.66399e13i	−0.400715	−	0.400715i
$327$	4.77432e13			0.706153
$328$	−7.54316e13	−	7.54316e13i	−1.09710	−	1.09710i
$329$	−3.54957e13	+	3.54957e13i	−0.507690	+	0.507690i
$330$	5.36424e13	−	5.36424e13i	0.754539	−	0.754539i
$331$		−	2.25644e13i		−	0.312155i	−0.987745	−	0.156077i	$-0.950115\pi$
$331$		−	2.25644e13i		−	0.312155i	0.987745	−	0.156077i	$-0.0498849\pi$
$332$		−	2.34781e14i		−	3.19450i
$333$	3.74270e13	−	3.74270e13i	0.500890	−	0.500890i
$334$	−5.29153e13	+	5.29153e13i	−0.696588	+	0.696588i
$335$	−7.43584e13	−	7.43584e13i	−0.962905	−	0.962905i
$336$	−1.42231e14			−1.81187
$337$	−7.24529e13	−	7.24529e13i	−0.908012	−	0.908012i	0.0881000	−	0.996112i	$-0.471920\pi$
$337$	−7.24529e13	−	7.24529e13i	−0.908012	−	0.908012i	−0.996112	+	0.0881000i	$0.971920\pi$
$338$			8.01783e13i			0.988588i
$339$	1.72938e13			0.209794
$340$	1.61193e14	+	2.61709e14i	1.92403	+	3.12381i
$341$	−3.77907e13			−0.443850
$342$			1.61274e14i			1.86389i
$343$	6.70633e13	+	6.70633e13i	0.762724	+	0.762724i
$344$	−1.96771e14			−2.20237
$345$	−3.21318e13	−	3.21318e13i	−0.353940	−	0.353940i
$346$	−1.27787e14	+	1.27787e14i	−1.38538	+	1.38538i
$347$	−3.04425e13	+	3.04425e13i	−0.324839	+	0.324839i	−0.850620	−	0.525781i	$-0.823773\pi$
$347$	−3.04425e13	+	3.04425e13i	−0.324839	+	0.324839i	0.525781	+	0.850620i	$0.323773\pi$
$348$			9.42926e13i			0.990357i
$349$		−	6.74356e13i		−	0.697187i	−0.937274	−	0.348593i	$-0.886659\pi$
$349$		−	6.74356e13i		−	0.697187i	0.937274	−	0.348593i	$-0.113341\pi$
$350$	8.02772e13	−	8.02772e13i	0.816992	−	0.816992i
$351$	4.27257e13	−	4.27257e13i	0.428055	−	0.428055i
$352$	−2.88622e14	−	2.88622e14i	−2.84672	−	2.84672i
$353$	−1.14013e13			−0.110712			−0.0553558	−	0.998467i	$-0.517629\pi$
$353$	−1.14013e13			−0.110712			−0.0553558	+	0.998467i	$0.517629\pi$
$354$	1.95517e13	+	1.95517e13i	0.186924	+	0.186924i
$355$			2.09309e14i			1.97030i
$356$	3.74823e14			3.47417
$357$	−4.57760e13	−	1.08801e13i	−0.417794	−	0.0993019i
$358$	3.57251e14			3.21082
$359$			1.50607e14i			1.33299i	0.745510	+	0.666494i	$0.232206\pi$
$359$			1.50607e14i			1.33299i	−0.745510	+	0.666494i	$0.767794\pi$
$360$	−2.87676e14	−	2.87676e14i	−2.50749	−	2.50749i
$361$	−6.52456e13			−0.560095
$362$	5.22848e13	+	5.22848e13i	0.442057	+	0.442057i
$363$	1.05698e13	−	1.05698e13i	0.0880201	−	0.0880201i
$364$	1.51506e14	−	1.51506e14i	1.24272	−	1.24272i
$365$			3.96370e13i			0.320251i
$366$			1.69616e14i			1.34996i
$367$	4.32710e13	−	4.32710e13i	0.339261	−	0.339261i	−0.516828	−	0.856089i	$-0.672887\pi$
$367$	4.32710e13	−	4.32710e13i	0.339261	−	0.339261i	0.856089	+	0.516828i	$0.172887\pi$
$368$	−3.06411e14	+	3.06411e14i	−2.36669	+	2.36669i
$369$	3.04834e13	+	3.04834e13i	0.231963	+	0.231963i
$370$	−3.14133e14			−2.35507
$371$	−1.34484e14	−	1.34484e14i	−0.993378	−	0.993378i
$372$		−	9.79156e13i		−	0.712633i
$373$	−1.85347e14			−1.32919			−0.664594	−	0.747204i	$-0.731396\pi$
$373$	−1.85347e14			−1.32919			−0.664594	+	0.747204i	$0.731396\pi$
$374$	−1.25504e14	−	2.03765e14i	−0.886877	−	1.43991i
$375$	2.98632e13			0.207953
$376$		−	4.28491e14i		−	2.94042i
$377$	−5.25928e13	−	5.25928e13i	−0.355671	−	0.355671i
$378$	2.22387e14			1.48219
$379$	9.80718e13	+	9.80718e13i	0.644211	+	0.644211i	0.951588	−	0.307377i	$-0.0994511\pi$
$379$	9.80718e13	+	9.80718e13i	0.644211	+	0.644211i	−0.307377	+	0.951588i	$0.599451\pi$
$380$	5.00489e14	−	5.00489e14i	3.24030	−	3.24030i
$381$	−3.19446e13	+	3.19446e13i	−0.203850	+	0.203850i
$382$			2.47205e14i			1.55493i
$383$		−	1.24696e14i		−	0.773140i	−0.922260	−	0.386570i	$-0.873660\pi$
$383$		−	1.24696e14i		−	0.773140i	0.922260	−	0.386570i	$-0.126340\pi$
$384$	2.80906e14	−	2.80906e14i	1.71688	−	1.71688i
$385$	−1.15162e14	+	1.15162e14i	−0.693865	+	0.693865i
$386$	−2.29324e13	−	2.29324e13i	−0.136213	−	0.136213i
$387$	7.95192e13			0.465652
$388$	2.25542e14	+	2.25542e14i	1.30212	+	1.30212i
$389$			1.69918e13i			0.0967199i	0.998830	+	0.0483600i	$0.0153995\pi$
$389$			1.69918e13i			0.0967199i	−0.998830	+	0.0483600i	$0.984601\pi$
$390$	−1.55043e14			−0.870158
$391$	−1.22055e14	+	7.51769e13i	−0.675436	+	0.416018i
$392$	−1.49391e14			−0.815174
$393$			8.95063e12i			0.0481609i
$394$	2.59324e14	+	2.59324e14i	1.37599	+	1.37599i
$395$	−2.36692e14			−1.23851
$396$	2.55718e14	+	2.55718e14i	1.31959	+	1.31959i
$397$	6.76478e13	−	6.76478e13i	0.344275	−	0.344275i	−0.513697	−	0.857972i	$-0.671724\pi$
$397$	6.76478e13	−	6.76478e13i	0.344275	−	0.344275i	0.857972	+	0.513697i	$0.171724\pi$
$398$	−3.44666e14	+	3.44666e14i	−1.72998	+	1.72998i
$399$			1.08348e14i			0.536378i
$400$			5.79319e14i			2.82871i
$401$	1.06453e14	−	1.06453e14i	0.512702	−	0.512702i	−0.402651	−	0.915354i	$-0.631911\pi$
$401$	1.06453e14	−	1.06453e14i	0.512702	−	0.512702i	0.915354	+	0.402651i	$0.131911\pi$
$402$	−1.50006e14	+	1.50006e14i	−0.712630	+	0.712630i
$403$	5.46136e13	+	5.46136e13i	0.255931	+	0.255931i
$404$	1.50436e13			0.0695431
$405$	6.84900e13	+	6.84900e13i	0.312338	+	0.312338i
$406$		−	2.73745e14i		−	1.23155i
$407$	1.80866e14			0.802764
$408$	3.41966e14	−	2.10625e14i	1.49745	−	0.922316i
$409$	−6.88792e13			−0.297584			−0.148792	−	0.988868i	$-0.547539\pi$
$409$	−6.88792e13			−0.297584			−0.148792	+	0.988868i	$0.547539\pi$
$410$		−	2.55854e14i		−	1.09064i
$411$	−5.42637e13	−	5.42637e13i	−0.228233	−	0.228233i
$412$	−8.53565e14			−3.54244
$413$	−4.19745e13	−	4.19745e13i	−0.171894	−	0.171894i
$414$	2.07136e14	−	2.07136e14i	0.837053	−	0.837053i
$415$	2.57903e14	−	2.57903e14i	1.02847	−	1.02847i
$416$			8.34208e14i			3.28292i
$417$		−	1.96160e13i		−	0.0761837i
$418$	−3.89677e14	+	3.89677e14i	−1.49360	+	1.49360i
$419$	−2.95264e14	+	2.95264e14i	−1.11695	+	1.11695i	−0.124761	+	0.992187i	$0.539816\pi$
$419$	−2.95264e14	+	2.95264e14i	−1.11695	+	1.11695i	−0.992187	+	0.124761i	$0.960184\pi$
$420$	−2.98384e14	−	2.98384e14i	−1.11405	−	1.11405i
$421$	2.98117e14			1.09859			0.549294	−	0.835629i	$-0.314897\pi$
$421$	2.98117e14			1.09859			0.549294	+	0.835629i	$0.314897\pi$
$422$	−4.85518e14	−	4.85518e14i	−1.76599	−	1.76599i
$423$			1.73162e14i			0.621699i
$424$	1.62344e15			5.75341
$425$	−4.43156e13	+	1.86450e14i	−0.155030	+	0.652262i
$426$	4.22246e14			1.45818
$427$		−	3.64140e14i		−	1.24141i
$428$	−2.92907e14	−	2.92907e14i	−0.985801	−	0.985801i
$429$	8.92682e13			0.296607
$430$	−3.33711e14	−	3.33711e14i	−1.09470	−	1.09470i
$431$	6.98849e13	−	6.98849e13i	0.226338	−	0.226338i	−0.584823	−	0.811161i	$-0.698836\pi$
$431$	6.98849e13	−	6.98849e13i	0.226338	−	0.226338i	0.811161	+	0.584823i	$0.198836\pi$
$432$	−8.02425e14	+	8.02425e14i	−2.56593	+	2.56593i
$433$		−	5.26388e14i		−	1.66197i	−0.556296	−	0.830984i	$-0.687778\pi$
$433$		−	5.26388e14i		−	1.66197i	0.556296	−	0.830984i	$-0.312222\pi$
$434$			2.84263e14i			0.886190i
$435$	−1.03579e14	+	1.03579e14i	−0.318846	+	0.318846i
$436$	9.55131e14	−	9.55131e14i	2.90327	−	2.90327i
$437$	2.33417e14	+	2.33417e14i	0.700622	+	0.700622i
$438$	7.99611e13			0.237012
$439$	7.09127e12	+	7.09127e12i	0.0207572	+	0.0207572i	0.717409	−	0.696652i	$-0.245328\pi$
$439$	7.09127e12	+	7.09127e12i	0.0207572	+	0.0207572i	−0.696652	+	0.717409i	$0.745328\pi$
$440$		−	1.39019e15i		−	4.01870i
$441$	6.03718e13			0.172354
$442$	−1.13100e14	+	4.75846e14i	−0.318888	+	1.34166i
$443$	6.42328e13			0.178869			0.0894347	−	0.995993i	$-0.471494\pi$
$443$	6.42328e13			0.178869			0.0894347	+	0.995993i	$0.471494\pi$
$444$			4.68623e14i			1.28890i
$445$	4.11738e14	+	4.11738e14i	1.11851	+	1.11851i
$446$	6.53632e14			1.75385
$447$	−1.63023e14	−	1.63023e14i	−0.432073	−	0.432073i
$448$	−1.16863e15	+	1.16863e15i	−3.05949	+	3.05949i
$449$	1.40321e14	−	1.40321e14i	0.362885	−	0.362885i	−0.501989	−	0.864874i	$-0.667398\pi$
$449$	1.40321e14	−	1.40321e14i	0.362885	−	0.362885i	0.864874	+	0.501989i	$0.167398\pi$
$450$		−	3.91623e14i		−	1.00046i
$451$			1.47311e14i			0.371761i
$452$	3.45973e14	−	3.45973e14i	0.862544	−	0.862544i
$453$	6.37720e13	−	6.37720e13i	0.157069	−	0.157069i
$454$	−9.00843e14	−	9.00843e14i	−2.19201	−	2.19201i
$455$	3.32855e14			0.800188
$456$	−6.53971e14	−	6.53971e14i	−1.55329	−	1.55329i
$457$			2.61097e14i			0.612721i	0.951916	+	0.306360i	$0.0991113\pi$
$457$			2.61097e14i			0.612721i	−0.951916	+	0.306360i	$0.900889\pi$
$458$	−1.28158e15			−2.97157
$459$	−3.19637e14	+	1.96872e14i	−0.732297	+	0.451040i
$460$	−1.28563e15			−2.91037
$461$			2.10925e12i			0.00471817i	0.999997	+	0.00235908i	$0.000750920\pi$
$461$			2.10925e12i			0.00471817i	−0.999997	+	0.00235908i	$0.999249\pi$
$462$	2.32320e14	+	2.32320e14i	0.513518	+	0.513518i
$463$	6.58012e14			1.43727			0.718635	−	0.695388i	$-0.244767\pi$
$463$	6.58012e14			1.43727			0.718635	+	0.695388i	$0.244767\pi$
$464$	9.87738e14	+	9.87738e14i	2.13203	+	2.13203i
$465$	1.07559e14	−	1.07559e14i	0.229433	−	0.229433i
$466$	−1.15252e15	+	1.15252e15i	−2.42956	+	2.42956i
$467$		−	2.62373e14i		−	0.546609i	−0.961928	−	0.273305i	$-0.911883\pi$
$467$		−	2.62373e14i		−	0.546609i	0.961928	−	0.273305i	$-0.0881167\pi$
$468$		−	7.39106e14i		−	1.52179i
$469$	3.22039e14	−	3.22039e14i	0.655327	−	0.655327i
$470$	7.26693e14	−	7.26693e14i	1.46155	−	1.46155i
$471$	−1.33549e14	−	1.33549e14i	−0.265477	−	0.265477i
$472$	5.06700e14			0.995566
$473$	1.92138e14	+	1.92138e14i	0.373145	+	0.373145i
$474$			4.77487e14i			0.916602i
$475$	4.41312e14			0.837396
$476$	−1.13344e15	+	6.98113e14i	−2.12598	+	1.30945i
$477$	−6.56066e14			−1.21646
$478$			1.01671e15i			1.86355i
$479$	−5.92587e14	−	5.92587e14i	−1.07376	−	1.07376i	−0.997054	−	0.0767058i	$-0.975560\pi$
$479$	−5.92587e14	−	5.92587e14i	−1.07376	−	1.07376i	−0.0767058	−	0.997054i	$-0.524440\pi$
$480$	1.64293e15			2.94302
$481$	−2.61380e14	−	2.61380e14i	−0.462887	−	0.462887i
$482$	5.59490e13	−	5.59490e13i	0.0979565	−	0.0979565i
$483$	1.39160e14	−	1.39160e14i	0.240882	−	0.240882i
$484$		−	4.22912e14i		−	0.723769i
$485$			4.95509e14i			0.838441i
$486$	8.50363e14	−	8.50363e14i	1.42267	−	1.42267i
$487$	−4.45736e14	+	4.45736e14i	−0.737342	+	0.737342i	−0.972063	−	0.234721i	$-0.924582\pi$
$487$	−4.45736e14	+	4.45736e14i	−0.737342	+	0.737342i	0.234721	+	0.972063i	$0.424582\pi$
$488$	2.19788e15	+	2.19788e15i	3.59497	+	3.59497i
$489$	−8.73107e13			−0.141211
$490$	−2.53357e14	−	2.53357e14i	−0.405186	−	0.405186i
$491$		−	6.72641e13i		−	0.106374i	−0.998585	−	0.0531870i	$-0.983062\pi$
$491$		−	6.72641e13i		−	0.106374i	0.998585	−	0.0531870i	$-0.0169379\pi$
$492$	−3.81682e14			−0.596890
$493$	2.42338e14	+	3.93454e14i	0.374769	+	0.608465i
$494$	1.12629e15			1.72247
$495$			5.61805e14i			0.849684i
$496$	−1.02569e15	−	1.02569e15i	−1.53415	−	1.53415i
$497$	−9.06497e14			−1.34093
$498$	−5.20277e14	−	5.20277e14i	−0.761155	−	0.761155i
$499$	2.27156e14	−	2.27156e14i	0.328678	−	0.328678i	−0.523406	−	0.852084i	$-0.675339\pi$
$499$	2.27156e14	−	2.27156e14i	0.328678	−	0.328678i	0.852084	+	0.523406i	$0.175339\pi$
$500$	5.97432e14	−	5.97432e14i	0.854974	−	0.854974i
$501$			1.73427e14i			0.245476i
$502$		−	5.19955e14i		−	0.727939i
$503$	−3.02533e14	+	3.02533e14i	−0.418938	+	0.418938i	−0.884837	−	0.465900i	$-0.845731\pi$
$503$	−3.02533e14	+	3.02533e14i	−0.418938	+	0.418938i	0.465900	+	0.884837i	$0.345731\pi$
$504$	1.24590e15	−	1.24590e15i	1.70653	−	1.70653i
$505$	1.65252e13	+	1.65252e13i	0.0223895	+	0.0223895i
$506$	1.00098e15			1.34152
$507$	1.31390e14	+	1.31390e14i	0.174188	+	0.174188i
$508$			1.27814e15i			1.67621i
$509$	−3.60923e13			−0.0468238			−0.0234119	−	0.999726i	$-0.507453\pi$
$509$	−3.60923e13			−0.0468238			−0.0234119	+	0.999726i	$0.507453\pi$
$510$	9.37157e14	+	2.22745e14i	1.20275	+	0.285872i
$511$	−1.71664e14			−0.217954
$512$		−	3.56668e15i		−	4.48001i
$513$	6.11269e14	+	6.11269e14i	0.759604	+	0.759604i
$514$	−2.17344e14			−0.267209
$515$	−9.37630e14	−	9.37630e14i	−1.14049	−	1.14049i
$516$	−4.97829e14	+	4.97829e14i	−0.599111	+	0.599111i
$517$	−4.18402e14	+	4.18402e14i	−0.498191	+	0.498191i
$518$		−	1.36048e15i		−	1.60280i
$519$			4.18814e14i			0.488203i
$520$	−2.00905e15	+	2.00905e15i	−2.31725	+	2.31725i
$521$	−1.11978e15	+	1.11978e15i	−1.27799	+	1.27799i	−0.336196	+	0.941792i	$0.609140\pi$
$521$	−1.11978e15	+	1.11978e15i	−1.27799	+	1.27799i	−0.941792	+	0.336196i	$0.890860\pi$
$522$	−6.67717e14	−	6.67717e14i	−0.754058	−	0.754058i
$523$	8.04516e13			0.0899033			0.0449516	−	0.998989i	$-0.485687\pi$
$523$	8.04516e13			0.0899033			0.0449516	+	0.998989i	$0.485687\pi$
$524$	1.79063e14	+	1.79063e14i	0.198008	+	0.198008i
$525$		−	2.63104e14i		−	0.287906i
$526$	−1.02083e14			−0.110543
$527$	−2.51649e14	−	4.08572e14i	−0.269673	−	0.437834i
$528$	−1.67653e15			−1.77798
$529$			3.53221e14i			0.370715i
$530$	2.75325e15	+	2.75325e15i	2.85975	+	2.85975i
$531$	−2.04768e14			−0.210495
$532$	2.16757e15	+	2.16757e15i	2.20526	+	2.20526i
$533$	2.12888e14	−	2.12888e14i	0.214364	−	0.214364i
$534$	8.30613e14	−	8.30613e14i	0.827793	−	0.827793i
$535$		−	6.43509e14i		−	0.634759i
$536$			3.88754e15i			3.79550i
$537$	5.85434e14	−	5.85434e14i	0.565743	−	0.565743i
$538$	−1.08505e15	+	1.08505e15i	−1.03788	+	1.03788i
$539$	1.45873e14	+	1.45873e14i	0.138114	+	0.138114i
$540$	−3.36679e15			−3.15537
$541$	−1.29483e15	−	1.29483e15i	−1.20123	−	1.20123i	−0.973792	−	0.227440i	$-0.926964\pi$
$541$	−1.29483e15	−	1.29483e15i	−1.20123	−	1.20123i	−0.227440	−	0.973792i	$-0.573036\pi$
$542$		−	9.57860e14i		−	0.879642i
$543$	1.71361e14			0.155780
$544$	1.19847e15	−	5.04235e15i	1.07853	−	4.53774i
$545$	2.09840e15			1.86942
$546$		−	6.71479e14i		−	0.592206i
$547$	−4.80173e14	−	4.80173e14i	−0.419245	−	0.419245i	0.465699	−	0.884943i	$-0.345803\pi$
$547$	−4.80173e14	−	4.80173e14i	−0.419245	−	0.419245i	−0.884943	+	0.465699i	$0.845803\pi$
$548$	−2.17115e15			−1.87671
$549$	−8.88208e14	−	8.88208e14i	−0.760093	−	0.760093i
$550$	9.46260e14	−	9.46260e14i	0.801707	−	0.801707i
$551$	7.52436e14	−	7.52436e14i	0.631155	−	0.631155i
$552$			1.67989e15i			1.39513i
$553$		−	1.02509e15i		−	0.842897i
$554$	−1.90012e15	+	1.90012e15i	−1.54695	+	1.54695i
$555$	−5.14777e14	+	5.14777e14i	−0.414961	+	0.414961i
$556$	−3.92430e14	−	3.92430e14i	−0.313221	−	0.313221i
$557$	2.09997e15			1.65962			0.829810	−	0.558045i	$-0.188448\pi$
$557$	2.09997e15			1.65962			0.829810	+	0.558045i	$0.188448\pi$
$558$	6.93373e14	+	6.93373e14i	0.542599	+	0.542599i
$559$		−	5.55340e14i		−	0.430322i
$560$	−6.25130e15			−4.79663
$561$	−5.39580e14	−	1.28248e14i	−0.409978	−	0.0974440i
$562$	1.72957e14			0.130133
$563$			1.42361e15i			1.06071i	0.847776	+	0.530354i	$0.177941\pi$
$563$			1.42361e15i			1.06071i	−0.847776	+	0.530354i	$0.822059\pi$
$564$	−1.08408e15	−	1.08408e15i	−0.799882	−	0.799882i
$565$	7.60094e14			0.555394
$566$	8.14744e14	+	8.14744e14i	0.589564	+	0.589564i
$567$	−2.96624e14	+	2.96624e14i	−0.212569	+	0.212569i
$568$	5.47145e15	−	5.47145e15i	3.88317	−	3.88317i
$569$			1.82302e15i			1.28137i	0.767806	+	0.640683i	$0.221349\pi$
$569$			1.82302e15i			1.28137i	−0.767806	+	0.640683i	$0.778651\pi$
$570$		−	2.21818e15i		−	1.54413i
$571$	3.81891e14	−	3.81891e14i	0.263294	−	0.263294i	−0.563097	−	0.826391i	$-0.690390\pi$
$571$	3.81891e14	−	3.81891e14i	0.263294	−	0.263294i	0.826391	+	0.563097i	$0.190390\pi$
$572$	1.78586e15	−	1.78586e15i	1.21947	−	1.21947i
$573$	4.05101e14	+	4.05101e14i	0.273976	+	0.273976i
$574$	1.10808e15			0.742258
$575$	−5.66809e14	−	5.66809e14i	−0.376066	−	0.376066i
$576$			5.70105e15i			3.74655i
$577$	−2.21145e13			−0.0143949			−0.00719747	−	0.999974i	$-0.502291\pi$
$577$	−2.21145e13			−0.0143949			−0.00719747	+	0.999974i	$0.502291\pi$
$578$	1.36726e15	−	2.71376e15i	0.881550	−	1.74972i
$579$	−7.51596e13			−0.0480012
$580$			4.14432e15i			2.62180i
$581$	1.11696e15	+	1.11696e15i	0.699950	+	0.699950i
$582$	9.99607e14			0.620516
$583$	−1.58522e15	−	1.58522e15i	−0.974792	−	0.974792i
$584$	1.03613e15	−	1.03613e15i	0.631168	−	0.631168i
$585$	8.11898e14	−	8.11898e14i	0.489941	−	0.489941i
$586$			3.71839e15i			2.22289i
$587$		−	2.46123e15i		−	1.45761i	−0.684719	−	0.728807i	$-0.740075\pi$
$587$		−	2.46123e15i		−	1.45761i	0.684719	−	0.728807i	$-0.259925\pi$
$588$	−3.77957e14	+	3.77957e14i	−0.221752	+	0.221752i
$589$	−7.81347e14	+	7.81347e14i	−0.454161	+	0.454161i
$590$	8.59330e14	+	8.59330e14i	0.494850	+	0.494850i
$591$	8.49921e14			0.484894
$592$	4.90894e15	+	4.90894e15i	2.77472	+	2.77472i
$593$			1.52981e15i			0.856716i	0.903609	+	0.428358i	$0.140908\pi$
$593$			1.52981e15i			0.856716i	−0.903609	+	0.428358i	$0.859092\pi$
$594$	2.62136e15			1.45446
$595$	−2.01193e15	−	4.78199e14i	−1.10604	−	0.262885i
$596$	−6.52273e15			−3.55283
$597$			1.12962e15i			0.609643i
$598$	−1.44658e15	−	1.44658e15i	−0.773545	−	0.773545i
$599$	−1.26935e15			−0.672562			−0.336281	−	0.941762i	$-0.609169\pi$
$599$	−1.26935e15			−0.672562			−0.336281	+	0.941762i	$0.609169\pi$
$600$	1.58805e15	+	1.58805e15i	0.833742	+	0.833742i
$601$	8.01275e14	−	8.01275e14i	0.416843	−	0.416843i	−0.467271	−	0.884114i	$-0.654763\pi$
$601$	8.01275e14	−	8.01275e14i	0.416843	−	0.416843i	0.884114	+	0.467271i	$0.154763\pi$
$602$	1.44527e15	−	1.44527e15i	0.745020	−	0.745020i
$603$		−	1.57103e15i		−	0.802491i
$604$		−	2.55159e15i		−	1.29154i
$605$	4.64563e14	−	4.64563e14i	0.233018	−	0.233018i
$606$	3.33368e13	−	3.33368e13i	0.0165701	−	0.0165701i
$607$	−2.66815e15	−	2.66815e15i	−1.31423	−	1.31423i	−0.918265	−	0.395967i	$-0.870410\pi$
$607$	−2.66815e15	−	2.66815e15i	−1.31423	−	1.31423i	−0.395967	−	0.918265i	$-0.629590\pi$
$608$	−1.19349e16			−5.82570
$609$	−4.48592e14	−	4.48592e14i	−0.216998	−	0.216998i
$610$			7.45492e15i			3.57379i
$611$	1.20932e15			0.574530
$612$	−1.06184e15	+	4.46751e15i	−0.499951	+	2.10345i
$613$	3.43739e15			1.60397			0.801986	−	0.597343i	$-0.203777\pi$
$613$	3.43739e15			1.60397			0.801986	+	0.597343i	$0.203777\pi$
$614$		−	4.86309e15i		−	2.24898i
$615$	−4.19273e14	−	4.19273e14i	−0.192169	−	0.192169i
$616$	6.02080e15			2.73502
$617$	6.65046e14	+	6.65046e14i	0.299422	+	0.299422i	0.840787	−	0.541366i	$-0.182093\pi$
$617$	6.65046e14	+	6.65046e14i	0.299422	+	0.299422i	−0.541366	+	0.840787i	$0.682093\pi$
$618$	−1.89151e15	+	1.89151e15i	−0.844058	+	0.844058i
$619$	−7.51214e14	+	7.51214e14i	−0.332250	+	0.332250i	−0.853440	−	0.521190i	$-0.825488\pi$
$619$	−7.51214e14	+	7.51214e14i	−0.332250	+	0.332250i	0.521190	+	0.853440i	$0.325488\pi$
$620$		−	4.30356e15i		−	1.88657i
$621$		−	1.57020e15i		−	0.682260i
$622$	5.25853e13	−	5.25853e13i	0.0226473	−	0.0226473i
$623$	−1.78320e15	+	1.78320e15i	−0.761230	+	0.761230i
$624$	2.42286e15	+	2.42286e15i	1.02521	+	1.02521i
$625$	2.91098e15			1.22095
$626$	−3.47365e15	−	3.47365e15i	−1.44420	−	1.44420i
$627$			1.27715e15i			0.526343i
$628$	−5.34347e15			−2.18296
$629$	1.20439e15	+	1.95542e15i	0.487741	+	0.791884i
$630$	4.22592e15			1.69648
$631$			2.91335e15i			1.15939i	0.814832	+	0.579697i	$0.196829\pi$
$631$			2.91335e15i			1.15939i	−0.814832	+	0.579697i	$0.803171\pi$
$632$	6.18727e15	+	6.18727e15i	2.44093	+	2.44093i
$633$	−1.59126e15			−0.622330
$634$	−5.11852e15	−	5.11852e15i	−1.98451	−	1.98451i
$635$	−1.40402e15	+	1.40402e15i	−0.539657	+	0.539657i
$636$	4.10730e15	−	4.10730e15i	1.56510	−	1.56510i
$637$		−	4.21620e14i		−	0.159278i
$638$		−	3.22674e15i		−	1.20851i
$639$	−2.21112e15	+	2.21112e15i	−0.821028	+	0.821028i
$640$	1.23463e16	−	1.23463e16i	4.54514	−	4.54514i
$641$	7.31157e14	+	7.31157e14i	0.266865	+	0.266865i	0.827836	−	0.560971i	$-0.189572\pi$
$641$	7.31157e14	+	7.31157e14i	0.266865	+	0.266865i	−0.560971	+	0.827836i	$0.689572\pi$
$642$	−1.29817e15			−0.469775
$643$	2.59745e15	+	2.59745e15i	0.931937	+	0.931937i	0.997827	−	0.0658897i	$-0.0209886\pi$
$643$	2.59745e15	+	2.59745e15i	0.931937	+	0.931937i	−0.0658897	+	0.997827i	$0.520989\pi$
$644$		−	5.56794e15i		−	1.98072i
$645$	−1.09372e15			−0.385768
$646$	−6.80785e15	−	1.61810e15i	−2.38084	−	0.565882i
$647$	2.85882e15			0.991319			0.495659	−	0.868517i	$-0.334926\pi$
$647$	2.85882e15			0.991319			0.495659	+	0.868517i	$0.334926\pi$
$648$		−	3.58074e15i		−	1.23115i
$649$	−4.94770e14	−	4.94770e14i	−0.168678	−	0.168678i
$650$	−2.73499e15			−0.924554
$651$	4.65828e14	+	4.65828e14i	0.156146	+	0.156146i
$652$	−1.74670e15	+	1.74670e15i	−0.580573	+	0.580573i
$653$	−1.24929e15	+	1.24929e15i	−0.411755	+	0.411755i	−0.882350	−	0.470594i	$-0.844040\pi$
$653$	−1.24929e15	+	1.24929e15i	−0.411755	+	0.411755i	0.470594	+	0.882350i	$0.344040\pi$
$654$		−	4.23316e15i		−	1.38353i
$655$			3.93396e14i			0.127498i
$656$	−3.99821e15	+	3.99821e15i	−1.28498	+	1.28498i
$657$	−4.18722e14	+	4.18722e14i	−0.133449	+	0.133449i
$658$	3.14724e15	+	3.14724e15i	0.994688	+	0.994688i
$659$	6.22954e15			1.95248			0.976239	−	0.216696i	$-0.0695279\pi$
$659$	6.22954e15			1.95248			0.976239	+	0.216696i	$0.0695279\pi$
$660$	−3.51718e15	−	3.51718e15i	−1.09321	−	1.09321i
$661$			5.63014e14i			0.173545i	0.996228	+	0.0867723i	$0.0276553\pi$
$661$			5.63014e14i			0.173545i	−0.996228	+	0.0867723i	$0.972345\pi$
$662$	−2.00068e15			−0.611587
$663$	5.94440e14	+	9.65118e14i	0.180212	+	0.292588i
$664$	−1.34835e16			−4.05394
$665$			4.76210e15i			1.41997i
$666$	−3.31848e15	−	3.31848e15i	−0.981365	−	0.981365i
$667$	−1.93282e15			−0.566890
$668$	3.46951e15	+	3.46951e15i	1.00925	+	1.00925i
$669$	1.07112e15	−	1.07112e15i	0.309026	−	0.309026i
$670$	−6.59301e15	+	6.59301e15i	−1.88657	+	1.88657i
$671$		−	4.29226e15i		−	1.21818i
$672$			7.11540e15i			2.00294i
$673$	2.97135e15	−	2.97135e15i	0.829604	−	0.829604i	−0.157858	−	0.987462i	$-0.550459\pi$
$673$	2.97135e15	−	2.97135e15i	0.829604	−	0.829604i	0.987462	+	0.157858i	$0.0504589\pi$
$674$	−6.42406e15	+	6.42406e15i	−1.77902	+	1.77902i
$675$	−1.48435e15	−	1.48435e15i	−0.407725	−	0.407725i
$676$	5.25707e15			1.43231
$677$	−2.62492e15	−	2.62492e15i	−0.709379	−	0.709379i	0.257026	−	0.966405i	$-0.417258\pi$
$677$	−2.62492e15	−	2.62492e15i	−0.709379	−	0.709379i	−0.966405	+	0.257026i	$0.917258\pi$
$678$		−	1.53336e15i		−	0.411038i
$679$	−2.14600e15			−0.570620
$680$	1.50300e16	−	9.25735e15i	3.96424	−	2.44167i
$681$	−2.95246e15			−0.772458
$682$			3.35072e15i			0.869610i
$683$	5.12734e15	+	5.12734e15i	1.32001	+	1.32001i	0.913762	+	0.406251i	$0.133164\pi$
$683$	5.12734e15	+	5.12734e15i	1.32001	+	1.32001i	0.406251	+	0.913762i	$0.366836\pi$
$684$	1.05743e16			2.70048
$685$	−2.38498e15	−	2.38498e15i	−0.604209	−	0.604209i
$686$	5.94619e15	−	5.94619e15i	1.49436	−	1.49436i
$687$	−2.10016e15	+	2.10016e15i	−0.523588	+	0.523588i
$688$			1.04298e16i			2.57951i
$689$			4.58178e15i			1.12416i
$690$	−2.84897e15	+	2.84897e15i	−0.693455	+	0.693455i
$691$	4.00976e15	−	4.00976e15i	0.968253	−	0.968253i	−0.0312587	−	0.999511i	$-0.509952\pi$
$691$	4.00976e15	−	4.00976e15i	0.968253	−	0.968253i	0.999511	+	0.0312587i	$0.00995158\pi$
$692$	8.37862e15	+	8.37862e15i	2.00719	+	2.00719i
$693$	−2.43313e15			−0.578271
$694$	2.69919e15	+	2.69919e15i	0.636439	+	0.636439i
$695$		−	8.62157e14i		−	0.201683i
$696$	5.41523e15			1.25680
$697$	−1.59264e15	+	9.80948e14i	−0.366723	+	0.225874i
$698$	−5.97919e15			−1.36596
$699$			3.77733e15i			0.856170i
$700$	−5.26355e15	−	5.26355e15i	−1.18369	−	1.18369i
$701$	−6.98186e15			−1.55784			−0.778918	−	0.627126i	$-0.784231\pi$
$701$	−6.98186e15			−1.55784			−0.778918	+	0.627126i	$0.784231\pi$
$702$	−3.78829e15	−	3.78829e15i	−0.838665	−	0.838665i
$703$	3.73952e15	−	3.73952e15i	0.821413	−	0.821413i
$704$	−1.37752e16	+	1.37752e16i	−3.00225	+	3.00225i
$705$		−	2.38169e15i		−	0.515046i
$706$			1.01090e15i			0.216911i
$707$	−7.15690e13	+	7.15690e13i	−0.0152377	+	0.0152377i
$708$	1.28195e15	−	1.28195e15i	0.270824	−	0.270824i
$709$	8.63464e14	+	8.63464e14i	0.181005	+	0.181005i	0.791794	−	0.610789i	$-0.209148\pi$
$709$	8.63464e14	+	8.63464e14i	0.181005	+	0.181005i	−0.610789	+	0.791794i	$0.709148\pi$
$710$	1.85584e16			3.86029
$711$	−2.50040e15	−	2.50040e15i	−0.516091	−	0.516091i
$712$		−	2.15261e16i		−	4.40886i
$713$	2.00708e15			0.407918
$714$	−9.64686e14	+	4.05874e15i	−0.194557	+	0.818561i
$715$	3.92349e15			0.785217
$716$		−	2.34239e16i		−	4.65198i
$717$	1.66610e15	+	1.66610e15i	0.328356	+	0.328356i
$718$	1.33536e16			2.61165
$719$	−5.65758e15	−	5.65758e15i	−1.09805	−	1.09805i	−0.994639	−	0.103410i	$-0.967025\pi$
$719$	−5.65758e15	−	5.65758e15i	−1.09805	−	1.09805i	−0.103410	−	0.994639i	$-0.532975\pi$
$720$	−1.52481e16	+	1.52481e16i	−2.93689	+	2.93689i
$721$	4.06079e15	−	4.06079e15i	0.776187	−	0.776187i
$722$			5.78502e15i			1.09736i
$723$		−	1.83369e14i		−	0.0345197i
$724$	3.42817e15	−	3.42817e15i	0.640472	−	0.640472i
$725$	−1.82715e15	+	1.82715e15i	−0.338778	+	0.338778i
$726$	−9.37178e14	−	9.37178e14i	−0.172453	−	0.172453i
$727$	1.81727e14			0.0331879			0.0165939	−	0.999862i	$-0.494718\pi$
$727$	1.81727e14			0.0331879			0.0165939	+	0.999862i	$0.494718\pi$
$728$	−8.70101e15	−	8.70101e15i	−1.57706	−	1.57706i
$729$		−	8.87135e14i		−	0.159584i
$730$	3.51443e15			0.627449
$731$	−7.97834e14	+	3.35674e15i	−0.141373	+	0.594802i
$732$	1.11212e16			1.95588
$733$		−	8.37095e14i		−	0.146118i	−0.997328	−	0.0730589i	$-0.976724\pi$
$733$		−	8.37095e14i		−	0.146118i	0.997328	−	0.0730589i	$-0.0232761\pi$
$734$	−3.83664e15	−	3.83664e15i	−0.664695	−	0.664695i
$735$	−8.30362e14			−0.142787
$736$	1.53288e16	+	1.53288e16i	2.61626	+	2.61626i
$737$	3.79601e15	−	3.79601e15i	0.643066	−	0.643066i
$738$	2.70282e15	−	2.70282e15i	0.454472	−	0.454472i
$739$		−	8.65692e15i		−	1.44484i	−0.691456	−	0.722418i	$-0.743030\pi$
$739$		−	8.65692e15i		−	1.44484i	0.691456	−	0.722418i	$-0.256970\pi$
$740$			2.05968e16i			3.41213i
$741$	1.84568e15	−	1.84568e15i	0.303498	−	0.303498i
$742$	−1.19241e16	+	1.19241e16i	−1.94627	+	1.94627i
$743$	2.01197e15	+	2.01197e15i	0.325974	+	0.325974i	0.851053	−	0.525079i	$-0.175964\pi$
$743$	2.01197e15	+	2.01197e15i	0.325974	+	0.325974i	−0.525079	+	0.851053i	$0.675964\pi$
$744$	−5.62330e15			−0.904358
$745$	−7.16513e15	−	7.16513e15i	−1.14384	−	1.14384i
$746$			1.64338e16i			2.60421i
$747$	5.44894e15			0.857135
$748$	−1.33603e16	+	8.22894e15i	−2.08621	+	1.28495i
$749$	2.78698e15			0.432000
$750$		−	2.64783e15i		−	0.407430i
$751$	5.87904e15	+	5.87904e15i	0.898021	+	0.898021i	0.995261	−	0.0972397i	$-0.0310013\pi$
$751$	5.87904e15	+	5.87904e15i	0.898021	+	0.898021i	−0.0972397	+	0.995261i	$0.531001\pi$
$752$	−2.27120e16			−3.44395
$753$	−8.52061e14	−	8.52061e14i	−0.128262	−	0.128262i
$754$	−4.66315e15	+	4.66315e15i	−0.696847	+	0.696847i
$755$	2.80289e15	−	2.80289e15i	0.415813	−	0.415813i
$756$		−	1.45813e16i		−	2.14746i
$757$		−	1.31015e15i		−	0.191555i	−0.995403	−	0.0957777i	$-0.969466\pi$
$757$		−	1.31015e15i		−	0.191555i	0.995403	−	0.0957777i	$-0.0305338\pi$
$758$	8.69556e15	−	8.69556e15i	1.26217	−	1.26217i
$759$	1.64033e15	−	1.64033e15i	0.236375	−	0.236375i
$760$	−2.87431e16	−	2.87431e16i	−4.11206	−	4.11206i
$761$	−1.17591e16			−1.67017			−0.835084	−	0.550123i	$-0.814581\pi$
$761$	−1.17591e16			−1.67017			−0.835084	+	0.550123i	$0.814581\pi$
$762$	2.83238e15	+	2.83238e15i	0.399391	+	0.399391i
$763$			9.08796e15i			1.27228i
$764$	1.62086e16			2.25284
$765$	−6.07392e15	+	3.74108e15i	−0.838168	+	0.516249i
$766$	−1.10562e16			−1.51477
$767$			1.43004e15i			0.194524i
$768$	−1.23332e16	−	1.23332e16i	−1.66567	−	1.66567i
$769$	1.20242e16			1.61236			0.806180	−	0.591671i	$-0.201531\pi$
$769$	1.20242e16			1.61236			0.806180	+	0.591671i	$0.201531\pi$
$770$	1.02109e16	+	1.02109e16i	1.35945	+	1.35945i
$771$	−3.56167e14	+	3.56167e14i	−0.0470820	+	0.0470820i
$772$	−1.50361e15	+	1.50361e15i	−0.197351	+	0.197351i
$773$			4.67654e15i			0.609449i	0.952441	+	0.304724i	$0.0985644\pi$
$773$			4.67654e15i			0.609449i	−0.952441	+	0.304724i	$0.901436\pi$
$774$		−	7.05059e15i		−	0.912326i
$775$	1.89736e15	−	1.89736e15i	0.243775	−	0.243775i
$776$	1.29529e16	−	1.29529e16i	1.65245	−	1.65245i
$777$	−2.22945e15	−	2.22945e15i	−0.282411	−	0.282411i
$778$	1.50658e15			0.189498
$779$	3.04575e15	+	3.04575e15i	0.380398	+	0.380398i
$780$			1.01658e16i			1.26072i
$781$	−1.06852e16			−1.31584
$782$	6.66558e15	+	1.08221e16i	0.815080	+	1.32334i
$783$	−5.06164e15			−0.614613
$784$			7.91839e15i			0.954769i
$785$	−5.86973e15	−	5.86973e15i	−0.702805	−	0.702805i
$786$	7.93610e14			0.0943589
$787$	−6.41491e15	−	6.41491e15i	−0.757407	−	0.757407i	0.218443	−	0.975850i	$-0.429902\pi$
$787$	−6.41491e15	−	6.41491e15i	−0.757407	−	0.757407i	−0.975850	+	0.218443i	$0.929902\pi$
$788$	1.70032e16	−	1.70032e16i	1.99359	−	1.99359i
$789$	−1.67286e14	+	1.67286e14i	−0.0194776	+	0.0194776i
$790$			2.09864e16i			2.42655i
$791$			3.29190e15i			0.377986i
$792$	1.46859e16	−	1.46859e16i	1.67460	−	1.67460i
$793$	−6.20300e15	+	6.20300e15i	−0.702424	+	0.702424i
$794$	−5.99801e15	−	5.99801e15i	−0.674519	−	0.674519i
$795$	9.02362e15			1.00777
$796$	2.25988e16	+	2.25988e16i	2.50648	+	2.50648i
$797$		−	5.25262e15i		−	0.578569i	−0.957243	−	0.289284i	$-0.906583\pi$
$797$		−	5.25262e15i		−	0.578569i	0.957243	−	0.289284i	$-0.0934173\pi$
$798$	9.60673e15			1.05090
$799$	−7.30968e15	−	1.73737e15i	−0.794130	−	0.188750i
$800$	2.89816e16			3.12700
$801$			8.69914e15i			0.932175i
$802$	−9.43871e15	−	9.43871e15i	−1.00451	−	1.00451i
$803$	−2.02348e15			−0.213876
$804$	9.83544e15	+	9.83544e15i	1.03249	+	1.03249i
$805$	6.11631e15	−	6.11631e15i	0.637694	−	0.637694i
$806$	4.84233e15	−	4.84233e15i	0.501431	−	0.501431i
$807$			3.55619e15i			0.365747i
$808$		−	8.63955e14i		−	0.0882528i
$809$	2.67772e15	−	2.67772e15i	0.271674	−	0.271674i	−0.558100	−	0.829774i	$-0.688469\pi$
$809$	2.67772e15	−	2.67772e15i	0.271674	−	0.271674i	0.829774	+	0.558100i	$0.188469\pi$
$810$	6.07269e15	−	6.07269e15i	0.611946	−	0.611946i
$811$	−7.12679e14	−	7.12679e14i	−0.0713311	−	0.0713311i	0.670541	−	0.741872i	$-0.266062\pi$
$811$	−7.12679e14	−	7.12679e14i	−0.0713311	−	0.0713311i	−0.741872	+	0.670541i	$0.766062\pi$
$812$	−1.79487e16			−1.78433
$813$	−1.56967e15	−	1.56967e15i	−0.154992	−	0.154992i
$814$		−	1.60365e16i		−	1.57281i
$815$	−3.83746e15			−0.373832
$816$	−1.11641e16	−	1.81257e16i	−1.08026	−	1.75388i
$817$	7.94515e15			0.763627
$818$			6.10719e15i			0.583040i
$819$	3.51625e15	+	3.51625e15i	0.333441	+	0.333441i
$820$	−1.67756e16			−1.58016
$821$	−9.82196e15	−	9.82196e15i	−0.918990	−	0.918990i	0.0779664	−	0.996956i	$-0.475157\pi$
$821$	−9.82196e15	−	9.82196e15i	−0.918990	−	0.918990i	−0.996956	+	0.0779664i	$0.975157\pi$
$822$	−4.81130e15	+	4.81130e15i	−0.447165	+	0.447165i
$823$	−5.17411e15	+	5.17411e15i	−0.477679	+	0.477679i	−0.904389	−	0.426709i	$-0.859673\pi$
$823$	−5.17411e15	+	5.17411e15i	−0.477679	+	0.477679i	0.426709	+	0.904389i	$0.359673\pi$
$824$			4.90204e16i			4.49549i
$825$		−	3.10131e15i		−	0.282520i
$826$	−3.72168e15	+	3.72168e15i	−0.336782	+	0.336782i
$827$	−1.18886e16	+	1.18886e16i	−1.06869	+	1.06869i	−0.0712267	+	0.997460i	$0.522691\pi$
$827$	−1.18886e16	+	1.18886e16i	−1.06869	+	1.06869i	−0.997460	+	0.0712267i	$0.977309\pi$
$828$	−1.35813e16	−	1.35813e16i	−1.21276	−	1.21276i
$829$	−1.28467e16			−1.13958			−0.569788	−	0.821792i	$-0.692975\pi$
$829$	−1.28467e16			−1.13958			−0.569788	+	0.821792i	$0.692975\pi$
$830$	−2.28671e16	−	2.28671e16i	−2.01503	−	2.01503i
$831$			6.22754e15i			0.545143i
$832$	3.98146e16			3.46229
$833$	−6.05725e14	+	2.54847e15i	−0.0523272	+	0.220157i
$834$	−1.73926e15			−0.149263
$835$			7.62242e15i			0.649856i
$836$	2.55500e16	+	2.55500e16i	2.16400	+	2.16400i
$837$	5.25613e15			0.442258
$838$	2.61796e16	+	2.61796e16i	2.18837	+	2.18837i
$839$	4.42885e15	−	4.42885e15i	0.367790	−	0.367790i	−0.498881	−	0.866671i	$-0.666255\pi$
$839$	4.42885e15	−	4.42885e15i	0.367790	−	0.367790i	0.866671	+	0.498881i	$0.166255\pi$
$840$	−1.71363e16	+	1.71363e16i	−1.41377	+	1.41377i
$841$		−	5.96993e15i		−	0.489318i
$842$		−	2.64326e16i		−	2.15240i
$843$	2.83428e14	−	2.83428e14i	0.0229293	−	0.0229293i
$844$	−3.18341e16	+	3.18341e16i	−2.55864	+	2.55864i
$845$	5.77482e15	+	5.77482e15i	0.461133	+	0.461133i
$846$	1.53535e16			1.21806
$847$	2.01198e15	+	2.01198e15i	0.158586	+	0.158586i
$848$		−	8.60498e16i		−	6.73865i
$849$	2.67028e15			0.207761
$850$	1.65316e16	+	3.92925e15i	1.27794	+	0.303743i
$851$	−9.60588e15			−0.737776
$852$		−	2.76854e16i		−	2.11268i
$853$	1.38217e16	+	1.38217e16i	1.04795	+	1.04795i	0.998791	+	0.0491631i	$0.0156554\pi$
$853$	1.38217e16	+	1.38217e16i	1.04795	+	1.04795i	0.0491631	+	0.998791i	$0.484345\pi$
$854$	−3.22865e16			−2.43222
$855$	1.16157e16	+	1.16157e16i	0.869423	+	0.869423i
$856$	−1.68217e16	+	1.68217e16i	−1.25102	+	1.25102i
$857$	1.10602e16	−	1.10602e16i	0.817275	−	0.817275i	−0.168437	−	0.985712i	$-0.553872\pi$
$857$	1.10602e16	−	1.10602e16i	0.817275	−	0.817275i	0.985712	+	0.168437i	$0.0538721\pi$
$858$		−	7.91499e15i		−	0.581126i
$859$			4.75797e15i			0.347104i	0.984825	+	0.173552i	$0.0555244\pi$
$859$			4.75797e15i			0.347104i	−0.984825	+	0.173552i	$0.944476\pi$
$860$	−2.18805e16	+	2.18805e16i	−1.58604	+	1.58604i
$861$	1.81583e15	−	1.81583e15i	0.130785	−	0.130785i
$862$	−6.19636e15	−	6.19636e15i	−0.443452	−	0.443452i
$863$	2.50924e16			1.78436			0.892182	−	0.451677i	$-0.149174\pi$
$863$	2.50924e16			1.78436			0.892182	+	0.451677i	$0.149174\pi$
$864$	4.01430e16	+	4.01430e16i	2.83651	+	2.83651i
$865$			1.84076e16i			1.29243i
$866$	−4.66723e16			−3.25620
$867$	−2.20654e15	−	6.68764e15i	−0.152970	−	0.463626i
$868$	1.86383e16			1.28395
$869$		−	1.20832e16i		−	0.827127i
$870$	9.18387e15	+	9.18387e15i	0.624698	+	0.624698i
$871$	−1.09717e16			−0.741605
$872$	−5.48533e16	−	5.48533e16i	−3.68436	−	3.68436i
$873$	−5.23452e15	+	5.23452e15i	−0.349381	+	0.349381i
$874$	2.06960e16	−	2.06960e16i	1.37269	−	1.37269i
$875$			5.68449e15i			0.374669i
$876$		−	5.24282e15i		−	0.343394i
$877$	5.45749e15	−	5.45749e15i	0.355218	−	0.355218i	−0.506829	−	0.862047i	$-0.669182\pi$
$877$	5.45749e15	−	5.45749e15i	0.355218	−	0.355218i	0.862047	+	0.506829i	$0.169182\pi$
$878$	6.28750e14	−	6.28750e14i	0.0406685	−	0.0406685i
$879$	6.09341e15	+	6.09341e15i	0.391671	+	0.391671i
$880$	−7.36866e16			−4.70689
$881$	−1.83421e16	−	1.83421e16i	−1.16435	−	1.16435i	−0.983514	−	0.180832i	$-0.942121\pi$
$881$	−1.83421e16	−	1.83421e16i	−1.16435	−	1.16435i	−0.180832	−	0.983514i	$-0.557879\pi$
$882$		−	5.35288e15i		−	0.337684i
$883$	2.65840e16			1.66662			0.833310	−	0.552806i	$-0.186443\pi$
$883$	2.65840e16			1.66662			0.833310	+	0.552806i	$0.186443\pi$
$884$	3.11999e16	+	7.41562e15i	1.94386	+	0.462019i
$885$	2.81640e15			0.174384
$886$		−	5.69521e15i		−	0.350449i
$887$	−1.86547e16	−	1.86547e16i	−1.14080	−	1.14080i	−0.988304	−	0.152496i	$-0.951269\pi$
$887$	−1.86547e16	−	1.86547e16i	−1.14080	−	1.14080i	−0.152496	−	0.988304i	$-0.548731\pi$
$888$	2.69131e16			1.63566
$889$	−6.08068e15	−	6.08068e15i	−0.367276	−	0.367276i
$890$	3.65069e16	−	3.65069e16i	2.19144	−	2.19144i
$891$	−3.49643e15	+	3.49643e15i	−0.208592	+	0.208592i
$892$		−	4.28568e16i		−	2.54105i
$893$			1.73015e16i			1.01953i
$894$	−1.44545e16	+	1.44545e16i	−0.846536	+	0.846536i
$895$	2.57308e16	−	2.57308e16i	1.49771	−	1.49771i
$896$	5.34707e16	+	5.34707e16i	3.09330	+	3.09330i
$897$	−4.74108e15			−0.272596
$898$	−1.24416e16	−	1.24416e16i	−0.710980	−	0.710980i
$899$		−	6.46998e15i		−	0.367472i
$900$	−2.56776e16			−1.44951
$901$	6.58246e15	−	2.76945e16i	0.369319	−	1.55384i
$902$	1.30614e16			0.728371
$903$		−	4.73679e15i		−	0.262543i
$904$	−1.98693e16	−	1.98693e16i	−1.09460	−	1.09460i
$905$	7.53159e15			0.412401
$906$	−5.65436e15	−	5.65436e15i	−0.307736	−	0.307736i
$907$	−8.22396e15	+	8.22396e15i	−0.444878	+	0.444878i	−0.893647	−	0.448770i	$-0.851862\pi$
$907$	−8.22396e15	+	8.22396e15i	−0.444878	+	0.444878i	0.448770	+	0.893647i	$0.351862\pi$
$908$	−5.90657e16	+	5.90657e16i	−3.17587	+	3.17587i
$909$			3.49142e14i			0.0186595i
$910$		−	2.95126e16i		−	1.56776i
$911$	−1.39336e16	+	1.39336e16i	−0.735719	+	0.735719i	−0.971746	−	0.236027i	$-0.924155\pi$
$911$	−1.39336e16	+	1.39336e16i	−0.735719	+	0.735719i	0.236027	+	0.971746i	$0.424155\pi$
$912$	−3.46634e16	+	3.46634e16i	−1.81928	+	1.81928i
$913$	1.31660e16	+	1.31660e16i	0.686854	+	0.686854i
$914$	2.31502e16			1.20047
$915$	1.22165e16	+	1.22165e16i	0.629698	+	0.629698i
$916$			8.40297e16i			4.30534i
$917$	−1.70376e15			−0.0867714
$918$	1.74557e16	+	2.83407e16i	0.883697	+	1.43475i
$919$	3.35251e16			1.68708			0.843539	−	0.537069i	$-0.180468\pi$
$919$	3.35251e16			1.68708			0.843539	+	0.537069i	$0.180468\pi$
$920$			7.38339e16i			3.69337i
$921$	−7.96925e15	−	7.96925e15i	−0.396268	−	0.396268i
$922$	1.87017e14			0.00924404
$923$	1.54419e16	+	1.54419e16i	0.758736	+	0.758736i
$924$	1.52326e16	−	1.52326e16i	0.744007	−	0.744007i
$925$	−9.08074e15	+	9.08074e15i	−0.440901	+	0.440901i
$926$		−	5.83428e16i		−	2.81596i
$927$		−	1.98101e16i		−	0.950492i
$928$	4.94136e16	−	4.94136e16i	2.35685	−	2.35685i
$929$	5.90284e15	−	5.90284e15i	0.279882	−	0.279882i	−0.553180	−	0.833062i	$-0.686586\pi$
$929$	5.90284e15	−	5.90284e15i	0.279882	−	0.279882i	0.833062	+	0.553180i	$0.186586\pi$
$930$	−9.53675e15	−	9.53675e15i	−0.449515	−	0.449515i
$931$	6.03205e15			0.282645
$932$	7.55677e16	+	7.55677e16i	3.52005	+	3.52005i
$933$		−	1.72345e14i		−	0.00798088i
$934$	−2.32634e16			−1.07094
$935$	−2.37155e16	−	5.63672e15i	−1.08535	−	0.257966i
$936$	−4.24469e16			−1.93121
$937$			1.55616e16i			0.703860i	0.936026	+	0.351930i	$0.114475\pi$
$937$			1.55616e16i			0.703860i	−0.936026	+	0.351930i	$0.885525\pi$
$938$	−2.85537e16	−	2.85537e16i	−1.28395	−	1.28395i
$939$	−1.13847e16			−0.508933
$940$	−4.76472e16	−	4.76472e16i	−2.11755	−	2.11755i
$941$	−3.04735e16	+	3.04735e16i	−1.34642	+	1.34642i	−0.456895	+	0.889521i	$0.651038\pi$
$941$	−3.04735e16	+	3.04735e16i	−1.34642	+	1.34642i	−0.889521	+	0.456895i	$0.848962\pi$
$942$	−1.18412e16	+	1.18412e16i	−0.520134	+	0.520134i
$943$		−	7.82375e15i		−	0.341665i
$944$		−	2.68574e16i		−	1.16605i
$945$	1.60173e16	−	1.60173e16i	0.691377	−	0.691377i
$946$	1.70360e16	−	1.70360e16i	0.731081	−	0.731081i
$947$	9.73308e15	+	9.73308e15i	0.415265	+	0.415265i	0.883568	−	0.468303i	$-0.155134\pi$
$947$	9.73308e15	+	9.73308e15i	0.415265	+	0.415265i	−0.468303	+	0.883568i	$0.655134\pi$
$948$	3.13075e16			1.32801
$949$	2.92424e15	+	2.92424e15i	0.123324	+	0.123324i
$950$		−	3.91290e16i		−	1.64066i
$951$	−1.67756e16			−0.699337
$952$	4.00927e16	+	6.50935e16i	1.66174	+	2.69795i
$953$	−2.77314e16			−1.14277			−0.571387	−	0.820681i	$-0.693594\pi$
$953$	−2.77314e16			−1.14277			−0.571387	+	0.820681i	$0.693594\pi$
$954$			5.81703e16i			2.38333i
$955$	1.78049e16	+	1.78049e16i	0.725305	+	0.725305i
$956$	6.66625e16			2.70000
$957$	−5.28773e15	−	5.28773e15i	−0.212938	−	0.212938i
$958$	−5.25419e16	+	5.25419e16i	−2.10376	+	2.10376i
$959$	1.03291e16	−	1.03291e16i	0.411208	−	0.411208i
$960$		−	7.84130e16i		−	3.10382i
$961$		−	1.86899e16i		−	0.735577i
$962$	−2.31753e16	+	2.31753e16i	−0.906908	+	0.906908i
$963$	6.79798e15	−	6.79798e15i	0.264506	−	0.264506i
$964$	−3.66841e15	−	3.66841e15i	−0.141924	−	0.141924i
$965$	−3.30339e15			−0.127075
$966$	−1.23386e16	−	1.23386e16i	−0.471947	−	0.471947i
$967$		−	1.87420e16i		−	0.712805i	−0.934333	−	0.356403i	$-0.884003\pi$
$967$		−	1.87420e16i		−	0.712805i	0.934333	−	0.356403i	$-0.115997\pi$
$968$	−2.42879e16			−0.918491
$969$	−1.38078e16	+	8.50455e15i	−0.519210	+	0.319794i
$970$	4.39345e16			1.64271
$971$		−	3.32727e16i		−	1.23704i	−0.785771	−	0.618518i	$-0.787734\pi$
$971$		−	3.32727e16i		−	1.23704i	0.785771	−	0.618518i	$-0.212266\pi$
$972$	−5.57559e16	−	5.57559e16i	−2.06123	−	2.06123i
$973$	3.73392e15			0.137260
$974$	3.95213e16	+	3.95213e16i	1.44463	+	1.44463i
$975$	−4.48189e15	+	4.48189e15i	−0.162905	+	0.162905i
$976$	1.16498e17	−	1.16498e17i	4.21059	−	4.21059i
$977$		−	1.49080e16i		−	0.535794i	−0.963448	−	0.267897i	$-0.913671\pi$
$977$		−	1.49080e16i		−	0.535794i	0.963448	−	0.267897i	$-0.0863287\pi$
$978$			7.74142e15i			0.276667i
$979$	−2.10193e16	+	2.10193e16i	−0.746988	+	0.746988i
$980$	−1.66119e16	+	1.66119e16i	−0.587050	+	0.587050i
$981$	2.21673e16	+	2.21673e16i	0.778993	+	0.778993i
$982$	−5.96399e15			−0.208412
$983$	1.46695e16	+	1.46695e16i	0.509765	+	0.509765i	0.914454	−	0.404689i	$-0.132620\pi$
$983$	1.46695e16	+	1.46695e16i	0.509765	+	0.509765i	−0.404689	+	0.914454i	$0.632620\pi$
$984$			2.19201e16i			0.757475i
$985$	3.73555e16			1.28367
$986$	3.48857e16	−	2.14870e16i	1.19213	−	0.734264i
$987$	1.03149e16			0.350526
$988$		−	7.38477e16i		−	2.49559i
$989$	−1.02045e16	−	1.02045e16i	−0.342937	−	0.342937i
$990$	4.98126e16			1.66474
$991$	−2.61866e16	−	2.61866e16i	−0.870310	−	0.870310i	0.122196	−	0.992506i	$-0.461006\pi$
$991$	−2.61866e16	−	2.61866e16i	−0.870310	−	0.870310i	−0.992506	+	0.122196i	$0.961006\pi$
$992$	−5.13122e16	+	5.13122e16i	−1.69592	+	1.69592i
$993$	−3.27855e15	+	3.27855e15i	−0.107761	+	0.107761i
$994$			8.03748e16i			2.62721i
$995$			4.96490e16i			1.61392i
$996$	−3.41131e16	+	3.41131e16i	−1.10279	+	1.10279i
$997$	−2.27402e16	+	2.27402e16i	−0.731089	+	0.731089i	−0.970835	−	0.239747i	$-0.922936\pi$
$997$	−2.27402e16	+	2.27402e16i	−0.731089	+	0.731089i	0.239747	+	0.970835i	$0.422936\pi$
$998$	−2.01408e16	−	2.01408e16i	−0.643961	−	0.643961i
$999$	−2.51558e16			−0.799885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.1	yes	32
17.4	even	4	inner	17.12.c.a.4.16	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.16	✓	32	17.4	even	4	inner
17.12.c.a.13.1	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)

\(f(q)\)	\(=\)	\(q-88.6653i q^{2} +(-145.298 - 145.298i) q^{3} -5813.53 q^{4} +(-6386.08 - 6386.08i) q^{5} +(-12882.9 + 12882.9i) q^{6} +(27657.5 - 27657.5i) q^{7} +333872. i q^{8} -134924. i q^{9} +O(q^{10})\)	\(q-88.6653i q^{2} +(-145.298 - 145.298i) q^{3} -5813.53 q^{4} +(-6386.08 - 6386.08i) q^{5} +(-12882.9 + 12882.9i) q^{6} +(27657.5 - 27657.5i) q^{7} +333872. i q^{8} -134924. i q^{9} +(-566224. + 566224. i) q^{10} +(326010. - 326010. i) q^{11} +(844692. + 844692. i) q^{12} -942273. q^{13} +(-2.45226e6 - 2.45226e6i) q^{14} +1.85577e6i q^{15} +1.76967e7 q^{16} +(5.69555e6 + 1.35373e6i) q^{17} -1.19631e7 q^{18} -1.34809e7i q^{19} +(3.71257e7 + 3.71257e7i) q^{20} -8.03715e6 q^{21} +(-2.89058e7 - 2.89058e7i) q^{22} +(-1.73146e7 + 1.73146e7i) q^{23} +(4.85108e7 - 4.85108e7i) q^{24} +3.27360e7i q^{25} +8.35469e7i q^{26} +(-4.53432e7 + 4.53432e7i) q^{27} +(-1.60788e8 + 1.60788e8i) q^{28} +(5.58148e7 + 5.58148e7i) q^{29} +1.64542e8 q^{30} +(-5.79594e7 - 5.79594e7i) q^{31} -8.85314e8i q^{32} -9.47371e7 q^{33} +(1.20028e8 - 5.04998e8i) q^{34} -3.53246e8 q^{35} +7.84386e8i q^{36} +(2.77393e8 + 2.77393e8i) q^{37} -1.19529e9 q^{38} +(1.36910e8 + 1.36910e8i) q^{39} +(2.13213e9 - 2.13213e9i) q^{40} +(-2.25930e8 + 2.25930e8i) q^{41} +7.12616e8i q^{42} +5.89362e8i q^{43} +(-1.89527e9 + 1.89527e9i) q^{44} +(-8.61637e8 + 8.61637e8i) q^{45} +(1.53520e9 + 1.53520e9i) q^{46} -1.28340e9 q^{47} +(-2.57129e9 - 2.57129e9i) q^{48} +4.47450e8i q^{49} +2.90254e9 q^{50} +(-6.30857e8 - 1.02424e9i) q^{51} +5.47793e9 q^{52} -4.86248e9i q^{53} +(4.02037e9 + 4.02037e9i) q^{54} -4.16386e9 q^{55} +(9.23406e9 + 9.23406e9i) q^{56} +(-1.95875e9 + 1.95875e9i) q^{57} +(4.94883e9 - 4.94883e9i) q^{58} -1.51765e9i q^{59} -1.07885e10i q^{60} +(6.58302e9 - 6.58302e9i) q^{61} +(-5.13898e9 + 5.13898e9i) q^{62} +(-3.73167e9 - 3.73167e9i) q^{63} -4.22537e10 q^{64} +(6.01744e9 + 6.01744e9i) q^{65} +8.39989e9i q^{66} +1.16438e10 q^{67} +(-3.31113e10 - 7.86992e9i) q^{68} +5.03153e9 q^{69} +3.13207e10i q^{70} +(-1.63879e10 - 1.63879e10i) q^{71} +4.50473e10 q^{72} +(-3.10339e9 - 3.10339e9i) q^{73} +(2.45951e10 - 2.45951e10i) q^{74} +(4.75646e9 - 4.75646e9i) q^{75} +7.83719e10i q^{76} -1.80333e10i q^{77} +(1.21392e10 - 1.21392e10i) q^{78} +(1.85319e10 - 1.85319e10i) q^{79} +(-1.13013e11 - 1.13013e11i) q^{80} -1.07249e10 q^{81} +(2.00321e10 + 2.00321e10i) q^{82} +4.03852e10i q^{83} +4.67242e10 q^{84} +(-2.77273e10 - 4.50173e10i) q^{85} +5.22559e10 q^{86} -1.62195e10i q^{87} +(1.08846e11 + 1.08846e11i) q^{88} -6.44743e10 q^{89} +(7.63973e10 + 7.63973e10i) q^{90} +(-2.60609e10 + 2.60609e10i) q^{91} +(1.00659e11 - 1.00659e11i) q^{92} +1.68427e10i q^{93} +1.13793e11i q^{94} +(-8.60904e10 + 8.60904e10i) q^{95} +(-1.28634e11 + 1.28634e11i) q^{96} +(-3.87960e10 - 3.87960e10i) q^{97} +3.96733e10 q^{98} +(-4.39867e10 - 4.39867e10i) 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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