LMFDB - Embedded newform 10.9.c.b.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10,9,Mod(3,10)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10.3"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$N$	$=$	$10 = 2 \cdot 5$
Weight:	$k$	$=$	$9$
Character orbit:	$[\chi]$	$=$	10.c (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [4,32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07378610061$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{601})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} + 301x^{2} + 22500$ x^4 + 301*x^2 + 22500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2\cdot 5^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$-12.7577i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.9.c.b.3.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 8.00000i) q^{2} +(82.7883 - 82.7883i) q^{3} +128.000i q^{4} +(-33.6352 - 624.094i) q^{5} +1324.61 q^{6} +(2718.55 + 2718.55i) q^{7} +(-1024.00 + 1024.00i) q^{8} -7146.79i q^{9} +(4723.67 - 5261.84i) q^{10} -20966.3 q^{11} +(10596.9 + 10596.9i) q^{12} +(-8095.66 + 8095.66i) q^{13} +43496.9i q^{14} +(-54452.3 - 48883.1i) q^{15} -16384.0 q^{16} +(-3141.02 - 3141.02i) q^{17} +(57174.3 - 57174.3i) q^{18} +69201.5i q^{19} +(79884.1 - 4305.31i) q^{20} +450129. q^{21} +(-167730. - 167730. i) q^{22} +(1084.70 - 1084.70i) q^{23} +169550. i q^{24} +(-388362. + 41983.1i) q^{25} -129531. q^{26} +(-48496.5 - 48496.5i) q^{27} +(-347975. + 347975. i) q^{28} +120633. i q^{29} +(-44553.6 - 826683. i) q^{30} +826466. q^{31} +(-131072. - 131072. i) q^{32} +(-1.73576e6 + 1.73576e6i) q^{33} -50256.4i q^{34} +(1.60519e6 - 1.78807e6i) q^{35} +914789. q^{36} +(-1.17029e6 - 1.17029e6i) q^{37} +(-553612. + 553612. i) q^{38} +1.34045e6i q^{39} +(673515. + 604630. i) q^{40} +1.74660e6 q^{41} +(3.60103e6 + 3.60103e6i) q^{42} +(3.03222e6 - 3.03222e6i) q^{43} -2.68368e6i q^{44} +(-4.46027e6 + 240384. i) q^{45} +17355.3 q^{46} +(-5.83610e6 - 5.83610e6i) q^{47} +(-1.35640e6 + 1.35640e6i) q^{48} +9.01626e6i q^{49} +(-3.44276e6 - 2.77103e6i) q^{50} -520080. q^{51} +(-1.03625e6 - 1.03625e6i) q^{52} +(1.97703e6 - 1.97703e6i) q^{53} -775944. i q^{54} +(705206. + 1.30849e7i) q^{55} -5.56760e6 q^{56} +(5.72907e6 + 5.72907e6i) q^{57} +(-965061. + 965061. i) q^{58} -1.58356e7i q^{59} +(6.25703e6 - 6.96989e6i) q^{60} -2.51723e6 q^{61} +(6.61173e6 + 6.61173e6i) q^{62} +(1.94289e7 - 1.94289e7i) q^{63} -2.09715e6i q^{64} +(5.32476e6 + 4.78016e6i) q^{65} -2.77722e7 q^{66} +(1.47668e7 + 1.47668e7i) q^{67} +(402051. - 402051. i) q^{68} -179602. i q^{69} +(2.71461e7 - 1.46303e6i) q^{70} -8.22222e6 q^{71} +(7.31831e6 + 7.31831e6i) q^{72} +(-3.03744e7 + 3.03744e7i) q^{73} -1.87246e7i q^{74} +(-2.86761e7 + 3.56275e7i) q^{75} -8.85779e6 q^{76} +(-5.69980e7 - 5.69980e7i) q^{77} +(-1.07236e7 + 1.07236e7i) q^{78} -4.69738e7i q^{79} +(551080. + 1.02252e7i) q^{80} +3.88602e7 q^{81} +(1.39728e7 + 1.39728e7i) q^{82} +(2.81305e7 - 2.81305e7i) q^{83} +5.76165e7i q^{84} +(-1.85465e6 + 2.06594e6i) q^{85} +4.85155e7 q^{86} +(9.98697e6 + 9.98697e6i) q^{87} +(2.14695e7 - 2.14695e7i) q^{88} +7.91918e7i q^{89} +(-3.76052e7 - 3.37591e7i) q^{90} -4.40170e7 q^{91} +(138842. + 138842. i) q^{92} +(6.84217e7 - 6.84217e7i) q^{93} -9.33776e7i q^{94} +(4.31883e7 - 2.32761e6i) q^{95} -2.17024e7 q^{96} +(1.47530e6 + 1.47530e6i) q^{97} +(-7.21301e7 + 7.21301e7i) q^{98} +1.49842e8i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 32 q^{2} + 86 q^{3} - 870 q^{5} + 1376 q^{6} + 5726 q^{7} - 4096 q^{8} - 4640 q^{10} - 14732 q^{11} + 11008 q^{12} + 45576 q^{13} - 115090 q^{15} - 65536 q^{16} + 3616 q^{17} + 60032 q^{18} + 37120 q^{20}+ \cdots - 52691072 q^{98}+O(q^{100})$ 4 * q + 32 * q^2 + 86 * q^3 - 870 * q^5 + 1376 * q^6 + 5726 * q^7 - 4096 * q^8 - 4640 * q^10 - 14732 * q^11 + 11008 * q^12 + 45576 * q^13 - 115090 * q^15 - 65536 * q^16 + 3616 * q^17 + 60032 * q^18 + 37120 * q^20 + 877268 * q^21 - 117856 * q^22 - 456794 * q^23 - 913600 * q^25 + 729216 * q^26 - 889240 * q^27 - 732928 * q^28 + 421920 * q^30 + 4672348 * q^31 - 524288 * q^32 - 4553788 * q^33 + 2956030 * q^35 + 960512 * q^36 - 5554884 * q^37 - 3932480 * q^38 + 1187840 * q^40 + 10738708 * q^41 + 7018144 * q^42 + 4913286 * q^43 - 12173390 * q^45 - 7308704 * q^46 - 5448474 * q^47 - 1409024 * q^48 - 1827200 * q^50 - 1827812 * q^51 + 5833728 * q^52 + 20290316 * q^53 - 9506940 * q^55 - 11726848 * q^56 - 2593360 * q^57 - 4236800 * q^58 + 21482240 * q^60 - 43572012 * q^61 + 37378784 * q^62 + 37877126 * q^63 + 15450660 * q^65 - 72860608 * q^66 + 9518486 * q^67 - 462848 * q^68 + 52077760 * q^70 + 20406908 * q^71 + 7684096 * q^72 - 11608364 * q^73 - 21302450 * q^75 - 62919680 * q^76 - 110066908 * q^77 - 60769056 * q^78 + 14254080 * q^80 + 96218224 * q^81 + 85909664 * q^82 + 64264686 * q^83 - 12424120 * q^85 + 78612576 * q^86 + 8501600 * q^87 + 15085568 * q^88 - 79432480 * q^90 - 70189812 * q^91 - 58469632 * q^92 + 16706132 * q^93 - 82819000 * q^95 - 22544384 * q^96 + 34113396 * q^97 - 52691072 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$ .

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	8.00000	+	8.00000i	0.500000	+	0.500000i
$2$	8.00000	+	8.00000i	0.500000	+	0.500000i
$3$	82.7883	−	82.7883i	1.02208	−	1.02208i	0.0223265	−	0.999751i	$-0.492893\pi$
$3$	82.7883	−	82.7883i	1.02208	−	1.02208i	0.999751	−	0.0223265i	$-0.00710733\pi$
$4$			128.000i			0.500000i
$5$	−33.6352	−	624.094i	−0.0538164	−	0.998551i
$5$	−33.6352	−	624.094i	−0.0538164	−	0.998551i
$6$	1324.61			1.02208
$7$	2718.55	+	2718.55i	1.13226	+	1.13226i	0.989801	+	0.142458i	$0.0455006\pi$
$7$	2718.55	+	2718.55i	1.13226	+	1.13226i	0.142458	+	0.989801i	$0.454499\pi$
$8$	−1024.00	+	1024.00i	−0.250000	+	0.250000i
$9$		−	7146.79i		−	1.08928i
$10$	4723.67	−	5261.84i	0.472367	−	0.526184i
$11$	−20966.3			−1.43203			−0.716013	−	0.698087i	$-0.754035\pi$
$11$	−20966.3			−1.43203			−0.716013	+	0.698087i	$0.754035\pi$
$12$	10596.9	+	10596.9i	0.511039	+	0.511039i
$13$	−8095.66	+	8095.66i	−0.283452	+	0.283452i	−0.834484	−	0.551032i	$-0.814234\pi$
$13$	−8095.66	+	8095.66i	−0.283452	+	0.283452i	0.551032	+	0.834484i	$0.314234\pi$
$14$			43496.9i			1.13226i
$15$	−54452.3	−	48883.1i	−1.07560	−	0.965592i
$16$	−16384.0			−0.250000
$17$	−3141.02	−	3141.02i	−0.0376076	−	0.0376076i	0.688053	−	0.725661i	$-0.258466\pi$
$17$	−3141.02	−	3141.02i	−0.0376076	−	0.0376076i	−0.725661	+	0.688053i	$0.758466\pi$
$18$	57174.3	−	57174.3i	0.544642	−	0.544642i
$19$			69201.5i			0.531008i	0.964110	+	0.265504i	$0.0855383\pi$
$19$			69201.5i			0.531008i	−0.964110	+	0.265504i	$0.914462\pi$
$20$	79884.1	−	4305.31i	0.499275	−	0.0269082i
$21$	450129.			2.31451
$22$	−167730.	−	167730.i	−0.716013	−	0.716013i
$23$	1084.70	−	1084.70i	0.00387615	−	0.00387615i	−0.705166	−	0.709042i	$-0.749128\pi$
$23$	1084.70	−	1084.70i	0.00387615	−	0.00387615i	0.709042	+	0.705166i	$0.249128\pi$
$24$			169550.i			0.511039i
$25$	−388362.	+	41983.1i	−0.994208	+	0.107477i
$26$	−129531.			−0.283452
$27$	−48496.5	−	48496.5i	−0.0912547	−	0.0912547i
$28$	−347975.	+	347975.i	−0.566129	+	0.566129i
$29$			120633.i			0.170558i	0.996357	+	0.0852792i	$0.0271782\pi$
$29$			120633.i			0.170558i	−0.996357	+	0.0852792i	$0.972822\pi$
$30$	−44553.6	−	826683.i	−0.0550045	−	1.02060i
$31$	826466.			0.894908			0.447454	−	0.894307i	$-0.352331\pi$
$31$	826466.			0.894908			0.447454	+	0.894307i	$0.352331\pi$
$32$	−131072.	−	131072.i	−0.125000	−	0.125000i
$33$	−1.73576e6	+	1.73576e6i	−1.46364	+	1.46364i
$34$		−	50256.4i		−	0.0376076i
$35$	1.60519e6	−	1.78807e6i	1.06968	−	1.19155i
$36$	914789.			0.544642
$37$	−1.17029e6	−	1.17029e6i	−0.624434	−	0.624434i	0.322228	−	0.946662i	$-0.395568\pi$
$37$	−1.17029e6	−	1.17029e6i	−0.624434	−	0.624434i	−0.946662	+	0.322228i	$0.895568\pi$
$38$	−553612.	+	553612.i	−0.265504	+	0.265504i
$39$			1.34045e6i			0.579419i
$40$	673515.	+	604630.i	0.263092	+	0.236184i
$41$	1.74660e6			0.618099			0.309049	−	0.951046i	$-0.399989\pi$
$41$	1.74660e6			0.618099			0.309049	+	0.951046i	$0.399989\pi$
$42$	3.60103e6	+	3.60103e6i	1.15726	+	1.15726i
$43$	3.03222e6	−	3.03222e6i	0.886925	−	0.886925i	−0.107302	−	0.994226i	$-0.534221\pi$
$43$	3.03222e6	−	3.03222e6i	0.886925	−	0.886925i	0.994226	+	0.107302i	$0.0342211\pi$
$44$		−	2.68368e6i		−	0.716013i
$45$	−4.46027e6	+	240384.i	−1.08771	+	0.0586213i
$46$	17355.3			0.00387615
$47$	−5.83610e6	−	5.83610e6i	−1.19600	−	1.19600i	−0.975354	−	0.220646i	$-0.929183\pi$
$47$	−5.83610e6	−	5.83610e6i	−1.19600	−	1.19600i	−0.220646	−	0.975354i	$-0.570817\pi$
$48$	−1.35640e6	+	1.35640e6i	−0.255519	+	0.255519i
$49$			9.01626e6i			1.56402i
$50$	−3.44276e6	−	2.77103e6i	−0.550842	−	0.443365i
$51$	−520080.			−0.0768758
$52$	−1.03625e6	−	1.03625e6i	−0.141726	−	0.141726i
$53$	1.97703e6	−	1.97703e6i	0.250559	−	0.250559i	−0.570641	−	0.821200i	$-0.693305\pi$
$53$	1.97703e6	−	1.97703e6i	0.250559	−	0.250559i	0.821200	+	0.570641i	$0.193305\pi$
$54$		−	775944.i		−	0.0912547i
$55$	705206.	+	1.30849e7i	0.0770664	+	1.42995i
$56$	−5.56760e6			−0.566129
$57$	5.72907e6	+	5.72907e6i	0.542731	+	0.542731i
$58$	−965061.	+	965061.i	−0.0852792	+	0.0852792i
$59$		−	1.58356e7i		−	1.30685i	−0.756990	−	0.653427i	$-0.773331\pi$
$59$		−	1.58356e7i		−	1.30685i	0.756990	−	0.653427i	$-0.226669\pi$
$60$	6.25703e6	−	6.96989e6i	0.482796	−	0.537800i
$61$	−2.51723e6			−0.181804			−0.0909019	−	0.995860i	$-0.528975\pi$
$61$	−2.51723e6			−0.181804			−0.0909019	+	0.995860i	$0.528975\pi$
$62$	6.61173e6	+	6.61173e6i	0.447454	+	0.447454i
$63$	1.94289e7	−	1.94289e7i	1.23335	−	1.23335i
$64$		−	2.09715e6i		−	0.125000i
$65$	5.32476e6	+	4.78016e6i	0.298295	+	0.267787i
$66$	−2.77722e7			−1.46364
$67$	1.47668e7	+	1.47668e7i	0.732802	+	0.732802i	0.971174	−	0.238372i	$-0.0766138\pi$
$67$	1.47668e7	+	1.47668e7i	0.732802	+	0.732802i	−0.238372	+	0.971174i	$0.576614\pi$
$68$	402051.	−	402051.i	0.0188038	−	0.0188038i
$69$		−	179602.i		−	0.00792344i
$70$	2.71461e7	−	1.46303e6i	1.13062	−	0.0609341i
$71$	−8.22222e6			−0.323561			−0.161780	−	0.986827i	$-0.551724\pi$
$71$	−8.22222e6			−0.323561			−0.161780	+	0.986827i	$0.551724\pi$
$72$	7.31831e6	+	7.31831e6i	0.272321	+	0.272321i
$73$	−3.03744e7	+	3.03744e7i	−1.06959	+	1.06959i	−0.0721980	+	0.997390i	$0.523001\pi$
$73$	−3.03744e7	+	3.03744e7i	−1.06959	+	1.06959i	−0.997390	+	0.0721980i	$0.976999\pi$
$74$		−	1.87246e7i		−	0.624434i
$75$	−2.86761e7	+	3.56275e7i	−0.906307	+	1.12601i
$76$	−8.85779e6			−0.265504
$77$	−5.69980e7	−	5.69980e7i	−1.62142	−	1.62142i
$78$	−1.07236e7	+	1.07236e7i	−0.289710	+	0.289710i
$79$		−	4.69738e7i		−	1.20600i	−0.797741	−	0.603000i	$-0.793972\pi$
$79$		−	4.69738e7i		−	1.20600i	0.797741	−	0.603000i	$-0.206028\pi$
$80$	551080.	+	1.02252e7i	0.0134541	+	0.249638i
$81$	3.88602e7			0.902745
$82$	1.39728e7	+	1.39728e7i	0.309049	+	0.309049i
$83$	2.81305e7	−	2.81305e7i	0.592740	−	0.592740i	−0.345630	−	0.938371i	$-0.612335\pi$
$83$	2.81305e7	−	2.81305e7i	0.592740	−	0.592740i	0.938371	+	0.345630i	$0.112335\pi$
$84$			5.76165e7i			1.15726i
$85$	−1.85465e6	+	2.06594e6i	−0.0355292	+	0.0395770i
$86$	4.85155e7			0.886925
$87$	9.98697e6	+	9.98697e6i	0.174324	+	0.174324i
$88$	2.14695e7	−	2.14695e7i	0.358006	−	0.358006i
$89$			7.91918e7i			1.26218i	0.775711	+	0.631088i	$0.217391\pi$
$89$			7.91918e7i			1.26218i	−0.775711	+	0.631088i	$0.782609\pi$
$90$	−3.76052e7	−	3.37591e7i	−0.573163	−	0.514542i
$91$	−4.40170e7			−0.641881
$92$	138842.	+	138842.i	0.00193807	+	0.00193807i
$93$	6.84217e7	−	6.84217e7i	0.914665	−	0.914665i
$94$		−	9.33776e7i		−	1.19600i
$95$	4.31883e7	−	2.32761e6i	0.530238	−	0.0285769i
$96$	−2.17024e7			−0.255519
$97$	1.47530e6	+	1.47530e6i	0.0166645	+	0.0166645i	0.715390	−	0.698725i	$-0.246249\pi$
$97$	1.47530e6	+	1.47530e6i	0.0166645	+	0.0166645i	−0.698725	+	0.715390i	$0.746249\pi$
$98$	−7.21301e7	+	7.21301e7i	−0.782010	+	0.782010i
$99$			1.49842e8i			1.55988i
$100$	−5.37384e6	−	4.97104e7i	−0.0537384	−	0.497104i
$101$	1.61256e8			1.54964			0.774818	−	0.632185i	$-0.217842\pi$
$101$	1.61256e8			1.54964			0.774818	+	0.632185i	$0.217842\pi$
$102$	−4.16064e6	−	4.16064e6i	−0.0384379	−	0.0384379i
$103$	−1.34152e8	+	1.34152e8i	−1.19192	+	1.19192i	−0.215397	+	0.976526i	$0.569105\pi$
$103$	−1.34152e8	+	1.34152e8i	−1.19192	+	1.19192i	−0.976526	+	0.215397i	$0.930895\pi$
$104$		−	1.65799e7i		−	0.141726i
$105$	−1.51402e7	−	2.80923e8i	−0.124559	−	2.31116i
$106$	3.16325e7			0.250559
$107$	2.02907e7	+	2.02907e7i	0.154796	+	0.154796i	0.780256	−	0.625460i	$-0.215089\pi$
$107$	2.02907e7	+	2.02907e7i	0.154796	+	0.154796i	−0.625460	+	0.780256i	$0.715089\pi$
$108$	6.20755e6	−	6.20755e6i	0.0456274	−	0.0456274i
$109$		−	5.27998e7i		−	0.374047i	−0.982355	−	0.187023i	$-0.940116\pi$
$109$		−	5.27998e7i		−	0.374047i	0.982355	−	0.187023i	$-0.0598840\pi$
$110$	−9.90379e7	+	1.10321e8i	−0.676442	+	0.753508i
$111$	−1.93772e8			−1.27644
$112$	−4.45408e7	−	4.45408e7i	−0.283065	−	0.283065i
$113$	−1.25553e8	+	1.25553e8i	−0.770041	+	0.770041i	−0.978113	−	0.208073i	$-0.933281\pi$
$113$	−1.25553e8	+	1.25553e8i	−0.770041	+	0.770041i	0.208073	+	0.978113i	$0.433281\pi$
$114$			9.16651e7i			0.542731i
$115$	−713442.	−	640474.i	−0.00407913	−	0.00366193i
$116$	−1.54410e7			−0.0852792
$117$	5.78580e7	+	5.78580e7i	0.308759	+	0.308759i
$118$	1.26685e8	−	1.26685e8i	0.653427	−	0.653427i
$119$		−	1.70781e7i		−	0.0851631i
$120$	1.05815e8	−	5.70287e6i	0.510298	−	0.0275022i
$121$	2.25226e8			1.05070
$122$	−2.01378e7	−	2.01378e7i	−0.0909019	−	0.0909019i
$123$	1.44598e8	−	1.44598e8i	0.631745	−	0.631745i
$124$			1.05788e8i			0.447454i
$125$	3.92641e7	+	2.40963e8i	0.160826	+	0.986983i
$126$	3.10863e8			1.23335
$127$	−9.69572e7	−	9.69572e7i	−0.372705	−	0.372705i	0.495757	−	0.868462i	$-0.334891\pi$
$127$	−9.69572e7	−	9.69572e7i	−0.372705	−	0.372705i	−0.868462	+	0.495757i	$0.834891\pi$
$128$	1.67772e7	−	1.67772e7i	0.0625000	−	0.0625000i
$129$		−	5.02064e8i		−	1.81301i
$130$	4.35679e6	+	8.08393e7i	0.0152543	+	0.283041i
$131$	6.19413e7			0.210327			0.105164	−	0.994455i	$-0.466463\pi$
$131$	6.19413e7			0.210327			0.105164	+	0.994455i	$0.466463\pi$
$132$	−2.22178e8	−	2.22178e8i	−0.731820	−	0.731820i
$133$	−1.88128e8	+	1.88128e8i	−0.601238	+	0.601238i
$134$			2.36268e8i			0.732802i
$135$	−2.86352e7	+	3.18976e7i	−0.0862115	+	0.0960335i
$136$	6.43282e6			0.0188038
$137$	8.79898e6	+	8.79898e6i	0.0249776	+	0.0249776i	0.719485	−	0.694508i	$-0.244378\pi$
$137$	8.79898e6	+	8.79898e6i	0.0249776	+	0.0249776i	−0.694508	+	0.719485i	$0.744378\pi$
$138$	1.43681e6	−	1.43681e6i	0.00396172	−	0.00396172i
$139$			2.71570e7i			0.0727482i	0.999338	+	0.0363741i	$0.0115808\pi$
$139$			2.71570e7i			0.0727482i	−0.999338	+	0.0363741i	$0.988419\pi$
$140$	2.28873e8	+	2.05465e8i	0.595776	+	0.534842i
$141$	−9.66321e8			−2.44481
$142$	−6.57777e7	−	6.57777e7i	−0.161780	−	0.161780i
$143$	1.69736e8	−	1.69736e8i	0.405910	−	0.405910i
$144$			1.17093e8i			0.272321i
$145$	7.52862e7	−	4.05751e6i	0.170311	−	0.00917883i
$146$	−4.85991e8			−1.06959
$147$	7.46441e8	+	7.46441e8i	1.59855	+	1.59855i
$148$	1.49797e8	−	1.49797e8i	0.312217	−	0.312217i
$149$			553367.i			0.00112271i	1.00000		0.000561355i	$0.000178685\pi$
$149$			553367.i			0.00112271i	−1.00000		0.000561355i	$0.999821\pi$
$150$	−5.14429e8	+	5.56113e7i	−1.01616	+	0.109850i
$151$	−1.27298e8			−0.244858			−0.122429	−	0.992477i	$-0.539068\pi$
$151$	−1.27298e8			−0.244858			−0.122429	+	0.992477i	$0.539068\pi$
$152$	−7.08623e7	−	7.08623e7i	−0.132752	−	0.132752i
$153$	−2.24482e7	+	2.24482e7i	−0.0409653	+	0.0409653i
$154$		−	9.11968e8i		−	1.62142i
$155$	−2.77984e7	−	5.15793e8i	−0.0481607	−	0.893611i
$156$	−1.71578e8			−0.289710
$157$	5.28456e8	+	5.28456e8i	0.869782	+	0.869782i	0.992448	−	0.122666i	$-0.0391443\pi$
$157$	5.28456e8	+	5.28456e8i	0.869782	+	0.869782i	−0.122666	+	0.992448i	$0.539144\pi$
$158$	3.75791e8	−	3.75791e8i	0.603000	−	0.603000i
$159$		−	3.27350e8i		−	0.512182i
$160$	−7.73926e7	+	8.62099e7i	−0.118092	+	0.131546i
$161$	5.89765e6			0.00877760
$162$	3.10882e8	+	3.10882e8i	0.451372	+	0.451372i
$163$	2.09644e8	−	2.09644e8i	0.296983	−	0.296983i	−0.542848	−	0.839831i	$-0.682654\pi$
$163$	2.09644e8	−	2.09644e8i	0.296983	−	0.296983i	0.839831	+	0.542848i	$0.182654\pi$
$164$			2.23565e8i			0.309049i
$165$	1.14166e9	+	1.02490e9i	1.54029	+	1.38275i
$166$	4.50087e8			0.592740
$167$	−7.26269e8	−	7.26269e8i	−0.933753	−	0.933753i	0.0641853	−	0.997938i	$-0.479555\pi$
$167$	−7.26269e8	−	7.26269e8i	−0.933753	−	0.933753i	−0.997938	+	0.0641853i	$0.979555\pi$
$168$	−4.60932e8	+	4.60932e8i	−0.578628	+	0.578628i
$169$			6.84651e8i			0.839310i
$170$	−3.13647e7	+	1.69039e6i	−0.0375531	+	0.00202391i
$171$	4.94569e8			0.578418
$172$	3.88124e8	+	3.88124e8i	0.443462	+	0.443462i
$173$	6.00999e8	−	6.00999e8i	0.670949	−	0.670949i	−0.286986	−	0.957935i	$-0.592653\pi$
$173$	6.00999e8	−	6.00999e8i	0.670949	−	0.670949i	0.957935	+	0.286986i	$0.0926533\pi$
$174$			1.59791e8i			0.174324i
$175$	−1.16992e9	−	9.41650e8i	−1.24739	−	1.00401i
$176$	3.43512e8			0.358006
$177$	−1.31100e9	−	1.31100e9i	−1.33571	−	1.33571i
$178$	−6.33534e8	+	6.33534e8i	−0.631088	+	0.631088i
$179$			9.25251e8i			0.901255i	0.892712	+	0.450627i	$0.148800\pi$
$179$			9.25251e8i			0.901255i	−0.892712	+	0.450627i	$0.851200\pi$
$180$	−3.07692e7	−	5.70915e8i	−0.0293107	−	0.543853i
$181$	−8.31703e8			−0.774914			−0.387457	−	0.921888i	$-0.626647\pi$
$181$	−8.31703e8			−0.774914			−0.387457	+	0.921888i	$0.626647\pi$
$182$	−3.52136e8	−	3.52136e8i	−0.320941	−	0.320941i
$183$	−2.08397e8	+	2.08397e8i	−0.185818	+	0.185818i
$184$			2.22147e6i			0.00193807i
$185$	−6.91008e8	+	7.69734e8i	−0.589924	+	0.657134i
$186$	1.09475e9			0.914665
$187$	6.58556e7	+	6.58556e7i	0.0538551	+	0.0538551i
$188$	7.47021e8	−	7.47021e8i	0.598000	−	0.598000i
$189$		−	2.63681e8i		−	0.206648i
$190$	3.64127e8	+	3.26885e8i	0.279408	+	0.250831i
$191$	1.17089e9			0.879799			0.439900	−	0.898047i	$-0.355014\pi$
$191$	1.17089e9			0.879799			0.439900	+	0.898047i	$0.355014\pi$
$192$	−1.73620e8	−	1.73620e8i	−0.127760	−	0.127760i
$193$	−1.41003e9	+	1.41003e9i	−1.01624	+	1.01624i	−0.0163773	+	0.999866i	$0.505213\pi$
$193$	−1.41003e9	+	1.41003e9i	−1.01624	+	1.01624i	−0.999866	+	0.0163773i	$0.994787\pi$
$194$			2.36047e7i			0.0166645i
$195$	8.36568e8	−	4.50864e7i	0.578579	−	0.0311822i
$196$	−1.15408e9			−0.782010
$197$	−7.98017e8	−	7.98017e8i	−0.529843	−	0.529843i	0.390683	−	0.920525i	$-0.372239\pi$
$197$	−7.98017e8	−	7.98017e8i	−0.529843	−	0.529843i	−0.920525	+	0.390683i	$0.872239\pi$
$198$	−1.19873e9	+	1.19873e9i	−0.779941	+	0.779941i
$199$		−	3.89588e8i		−	0.248424i	−0.992256	−	0.124212i	$-0.960360\pi$
$199$		−	3.89588e8i		−	0.248424i	0.992256	−	0.124212i	$-0.0396402\pi$
$200$	3.54692e8	−	4.40674e8i	0.221683	−	0.275421i
$201$	2.44503e9			1.49796
$202$	1.29005e9	+	1.29005e9i	0.774818	+	0.774818i
$203$	−3.27946e8	+	3.27946e8i	−0.193116	+	0.193116i
$204$		−	6.65702e7i		−	0.0384379i
$205$	−5.87473e7	−	1.09004e9i	−0.0332638	−	0.617203i
$206$	−2.14643e9			−1.19192
$207$	−7.75216e6	−	7.75216e6i	−0.00422222	−	0.00422222i
$208$	1.32639e8	−	1.32639e8i	0.0708629	−	0.0708629i
$209$		−	1.45090e9i		−	0.760417i
$210$	2.12626e9	−	2.36850e9i	1.09330	−	1.21786i
$211$	3.73042e9			1.88204			0.941019	−	0.338354i	$-0.109870\pi$
$211$	3.73042e9			1.88204			0.941019	+	0.338354i	$0.109870\pi$
$212$	2.53060e8	+	2.53060e8i	0.125280	+	0.125280i
$213$	−6.80703e8	+	6.80703e8i	−0.330704	+	0.330704i
$214$			3.24651e8i			0.154796i
$215$	−1.99438e9	−	1.79040e9i	−0.933370	−	0.837908i
$216$	9.93209e7			0.0456274
$217$	2.24679e9	+	2.24679e9i	1.01327	+	1.01327i
$218$	4.22398e8	−	4.22398e8i	0.187023	−	0.187023i
$219$			5.02929e9i			2.18640i
$220$	−1.67487e9	+	9.02664e7i	−0.714975	+	0.0385332i
$221$	5.08574e7			0.0213199
$222$	−1.55018e9	−	1.55018e9i	−0.638220	−	0.638220i
$223$	2.58624e9	−	2.58624e9i	1.04580	−	1.04580i	0.0469003	−	0.998900i	$-0.485066\pi$
$223$	2.58624e9	−	2.58624e9i	1.04580	−	1.04580i	0.998900	−	0.0469003i	$-0.0149343\pi$
$224$		−	7.12652e8i		−	0.283065i
$225$	3.00045e8	+	2.77554e9i	0.117073	+	1.08297i
$226$	−2.00885e9			−0.770041
$227$	2.28574e8	+	2.28574e8i	0.0860844	+	0.0860844i	0.748838	−	0.662753i	$-0.230612\pi$
$227$	2.28574e8	+	2.28574e8i	0.0860844	+	0.0860844i	−0.662753	+	0.748838i	$0.730612\pi$
$228$	−7.33321e8	+	7.33321e8i	−0.271366	+	0.271366i
$229$		−	4.29778e9i		−	1.56280i	−0.624033	−	0.781398i	$-0.714507\pi$
$229$		−	4.29778e9i		−	1.56280i	0.624033	−	0.781398i	$-0.285493\pi$
$230$	−583749.	−	1.08313e7i	−0.000208600	−	0.00387053i
$231$	−9.43752e9			−3.31444
$232$	−1.23528e8	−	1.23528e8i	−0.0426396	−	0.0426396i
$233$	2.83013e8	−	2.83013e8i	0.0960247	−	0.0960247i	−0.657463	−	0.753487i	$-0.728370\pi$
$233$	2.83013e8	−	2.83013e8i	0.0960247	−	0.0960247i	0.753487	+	0.657463i	$0.228370\pi$
$234$			9.25728e8i			0.308759i
$235$	−3.44598e9	+	3.83858e9i	−1.12990	+	1.25863i
$236$	2.02696e9			0.653427
$237$	−3.88888e9	−	3.88888e9i	−1.23263	−	1.23263i
$238$	1.36625e8	−	1.36625e8i	0.0425815	−	0.0425815i
$239$			5.19198e9i			1.59126i	0.605782	+	0.795630i	$0.292860\pi$
$239$			5.19198e9i			1.59126i	−0.605782	+	0.795630i	$0.707140\pi$
$240$	8.92146e8	+	8.00900e8i	0.268900	+	0.241398i
$241$	4.53061e9			1.34304			0.671519	−	0.740987i	$-0.265642\pi$
$241$	4.53061e9			1.34304			0.671519	+	0.740987i	$0.265642\pi$
$242$	1.80181e9	+	1.80181e9i	0.525349	+	0.525349i
$243$	3.53535e9	−	3.53535e9i	1.01393	−	1.01393i
$244$		−	3.22205e8i		−	0.0909019i
$245$	5.62700e9	−	3.03264e8i	1.56175	−	0.0841699i
$246$	2.31357e9			0.631745
$247$	−5.60232e8	−	5.60232e8i	−0.150515	−	0.150515i
$248$	−8.46301e8	+	8.46301e8i	−0.223727	+	0.223727i
$249$		−	4.65774e9i		−	1.21165i
$250$	−1.61359e9	+	2.24181e9i	−0.413079	+	0.573904i
$251$	−3.40464e9			−0.857780			−0.428890	−	0.903357i	$-0.641095\pi$
$251$	−3.40464e9			−0.857780			−0.428890	+	0.903357i	$0.641095\pi$
$252$	2.48690e9	+	2.48690e9i	0.616675	+	0.616675i
$253$	−2.27422e7	+	2.27422e7i	−0.00555074	+	0.00555074i
$254$		−	1.55132e9i		−	0.372705i
$255$	1.74930e7	+	3.24579e8i	0.00413717	+	0.0767643i
$256$	2.68435e8			0.0625000
$257$	3.01159e7	+	3.01159e7i	0.00690341	+	0.00690341i	0.710550	−	0.703647i	$-0.248446\pi$
$257$	3.01159e7	+	3.01159e7i	0.00690341	+	0.00690341i	−0.703647	+	0.710550i	$0.748446\pi$
$258$	4.01651e9	−	4.01651e9i	0.906505	−	0.906505i
$259$		−	6.36299e9i		−	1.41404i
$260$	−6.11860e8	+	6.81569e8i	−0.133893	+	0.149148i
$261$	8.62136e8			0.185786
$262$	4.95531e8	+	4.95531e8i	0.105164	+	0.105164i
$263$	−2.01502e9	+	2.01502e9i	−0.421169	+	0.421169i	−0.885606	−	0.464437i	$-0.846257\pi$
$263$	−2.01502e9	+	2.01502e9i	−0.421169	+	0.421169i	0.464437	+	0.885606i	$0.346257\pi$
$264$		−	3.55484e9i		−	0.731820i
$265$	−1.30035e9	−	1.16736e9i	−0.263680	−	0.236712i
$266$	−3.01005e9			−0.601238
$267$	6.55615e9	+	6.55615e9i	1.29004	+	1.29004i
$268$	−1.89015e9	+	1.89015e9i	−0.366401	+	0.366401i
$269$			9.53840e9i			1.82166i	0.412785	+	0.910828i	$0.364556\pi$
$269$			9.53840e9i			1.82166i	−0.412785	+	0.910828i	$0.635444\pi$
$270$	−4.84262e8	+	2.60991e7i	−0.0911225	+	0.00491100i
$271$	−3.84233e9			−0.712390			−0.356195	−	0.934412i	$-0.615926\pi$
$271$	−3.84233e9			−0.712390			−0.356195	+	0.934412i	$0.615926\pi$
$272$	5.14625e7	+	5.14625e7i	0.00940190	+	0.00940190i
$273$	−3.64409e9	+	3.64409e9i	−0.656052	+	0.656052i
$274$			1.40784e8i			0.0249776i
$275$	8.14252e9	−	8.80230e8i	1.42373	−	0.153910i
$276$	2.29890e7			0.00396172
$277$	−2.80174e9	−	2.80174e9i	−0.475892	−	0.475892i	0.427923	−	0.903815i	$-0.359245\pi$
$277$	−2.80174e9	−	2.80174e9i	−0.475892	−	0.475892i	−0.903815	+	0.427923i	$0.859245\pi$
$278$	−2.17256e8	+	2.17256e8i	−0.0363741	+	0.0363741i
$279$		−	5.90658e9i		−	0.974809i
$280$	1.87267e8	+	3.47471e9i	0.0304670	+	0.565309i
$281$	−8.28718e9			−1.32917			−0.664586	−	0.747212i	$-0.731392\pi$
$281$	−8.28718e9			−1.32917			−0.664586	+	0.747212i	$0.731392\pi$
$282$	−7.73057e9	−	7.73057e9i	−1.22240	−	1.22240i
$283$	−7.40766e7	+	7.40766e7i	−0.0115488	+	0.0115488i	−0.712858	−	0.701309i	$-0.752599\pi$
$283$	−7.40766e7	+	7.40766e7i	−0.0115488	+	0.0115488i	0.701309	+	0.712858i	$0.252599\pi$
$284$		−	1.05244e9i		−	0.161780i
$285$	3.38278e9	−	3.76818e9i	0.512737	−	0.571152i
$286$	2.71578e9			0.405910
$287$	4.74822e9	+	4.74822e9i	0.699848	+	0.699848i
$288$	−9.36744e8	+	9.36744e8i	−0.136160	+	0.136160i
$289$		−	6.95603e9i		−	0.997171i
$290$	6.34749e8	+	5.69829e8i	0.0897450	+	0.0805662i
$291$	2.44274e8			0.0340648
$292$	−3.88793e9	−	3.88793e9i	−0.534794	−	0.534794i
$293$	−6.33070e9	+	6.33070e9i	−0.858977	+	0.858977i	−0.991218	−	0.132241i	$-0.957783\pi$
$293$	−6.33070e9	+	6.33070e9i	−0.858977	+	0.858977i	0.132241	+	0.991218i	$0.457783\pi$
$294$			1.19431e10i			1.59855i
$295$	−9.88292e9	+	5.32635e8i	−1.30496	+	0.0703302i
$296$	2.39675e9			0.312217
$297$	1.01679e9	+	1.01679e9i	0.130679	+	0.130679i
$298$	−4.42693e6	+	4.42693e6i	−0.000561355	+	0.000561355i
$299$			1.75628e7i			0.00219740i
$300$	−4.56033e9	−	3.67054e9i	−0.563003	−	0.453154i
$301$	1.64865e10			2.00846
$302$	−1.01838e9	−	1.01838e9i	−0.122429	−	0.122429i
$303$	1.33501e10	−	1.33501e10i	1.58385	−	1.58385i
$304$		−	1.13380e9i		−	0.132752i
$305$	8.46676e7	+	1.57099e9i	0.00978403	+	0.181540i
$306$	−3.59172e8			−0.0409653
$307$	4.80692e9	+	4.80692e9i	0.541144	+	0.541144i	0.923864	−	0.382720i	$-0.125013\pi$
$307$	4.80692e9	+	4.80692e9i	0.541144	+	0.541144i	−0.382720	+	0.923864i	$0.625013\pi$
$308$	7.29574e9	−	7.29574e9i	0.810712	−	0.810712i
$309$			2.22124e10i			2.43648i
$310$	3.90396e9	−	4.34873e9i	0.422725	−	0.470886i
$311$	1.06468e10			1.13809			0.569047	−	0.822305i	$-0.307312\pi$
$311$	1.06468e10			1.13809			0.569047	+	0.822305i	$0.307312\pi$
$312$	−1.37262e9	−	1.37262e9i	−0.144855	−	0.144855i
$313$	−1.05889e10	+	1.05889e10i	−1.10325	+	1.10325i	−0.109236	+	0.994016i	$0.534840\pi$
$313$	−1.05889e10	+	1.05889e10i	−1.10325	+	1.10325i	−0.994016	+	0.109236i	$0.965160\pi$
$314$			8.45530e9i			0.869782i
$315$	−1.27790e10	−	1.14720e10i	−1.29794	−	1.16519i
$316$	6.01265e9			0.603000
$317$	−9.51101e9	−	9.51101e9i	−0.941867	−	0.941867i	0.0565338	−	0.998401i	$-0.481995\pi$
$317$	−9.51101e9	−	9.51101e9i	−0.941867	−	0.941867i	−0.998401	+	0.0565338i	$0.981995\pi$
$318$	2.61880e9	−	2.61880e9i	0.256091	−	0.256091i
$319$		−	2.52922e9i		−	0.244244i
$320$	−1.30882e9	+	7.05382e7i	−0.124819	+	0.00672705i
$321$	3.35966e9			0.316428
$322$	4.71812e7	+	4.71812e7i	0.00438880	+	0.00438880i
$323$	2.17364e8	−	2.17364e8i	0.0199699	−	0.0199699i
$324$			4.97411e9i			0.451372i
$325$	2.80417e9	−	3.48393e9i	0.251345	−	0.312274i
$326$	3.35430e9			0.296983
$327$	−4.37120e9	−	4.37120e9i	−0.382305	−	0.382305i
$328$	−1.78852e9	+	1.78852e9i	−0.154525	+	0.154525i
$329$		−	3.17315e10i		−	2.70836i
$330$	9.34125e8	+	1.73325e10i	0.0787679	+	1.46152i
$331$	−1.31018e10			−1.09149			−0.545744	−	0.837952i	$-0.683753\pi$
$331$	−1.31018e10			−1.09149			−0.545744	+	0.837952i	$0.683753\pi$
$332$	3.60070e9	+	3.60070e9i	0.296370	+	0.296370i
$333$	−8.36381e9	+	8.36381e9i	−0.680186	+	0.680186i
$334$		−	1.16203e10i		−	0.933753i
$335$	8.71918e9	−	9.71254e9i	0.692303	−	0.771176i
$336$	−7.37491e9			−0.578628
$337$	1.33341e10	+	1.33341e10i	1.03382	+	1.03382i	0.999408	+	0.0344141i	$0.0109565\pi$
$337$	1.33341e10	+	1.33341e10i	1.03382	+	1.03382i	0.0344141	+	0.999408i	$0.489043\pi$
$338$	−5.47721e9	+	5.47721e9i	−0.419655	+	0.419655i
$339$			2.07886e10i			1.57408i
$340$	−2.64441e8	−	2.37395e8i	−0.0197885	−	0.0177646i
$341$	−1.73279e10			−1.28153
$342$	3.95655e9	+	3.95655e9i	0.289209	+	0.289209i
$343$	−8.83927e9	+	8.83927e9i	−0.638616	+	0.638616i
$344$			6.20998e9i			0.443462i
$345$	−1.12088e8	+	6.04094e6i	−0.00791196	+	0.000426411i
$346$	9.61599e9			0.670949
$347$	−1.09024e10	−	1.09024e10i	−0.751973	−	0.751973i	0.222874	−	0.974847i	$-0.428456\pi$
$347$	−1.09024e10	−	1.09024e10i	−0.751973	−	0.751973i	−0.974847	+	0.222874i	$0.928456\pi$
$348$	−1.27833e9	+	1.27833e9i	−0.0871619	+	0.0871619i
$349$			9.67778e9i			0.652340i	0.945311	+	0.326170i	$0.105758\pi$
$349$			9.67778e9i			0.652340i	−0.945311	+	0.326170i	$0.894242\pi$
$350$	−1.82613e9	−	1.68925e10i	−0.121692	−	1.12570i
$351$	7.85223e8			0.0517326
$352$	2.74809e9	+	2.74809e9i	0.179003	+	0.179003i
$353$	6.27335e9	−	6.27335e9i	0.404018	−	0.404018i	−0.475628	−	0.879646i	$-0.657779\pi$
$353$	6.27335e9	−	6.27335e9i	0.404018	−	0.404018i	0.879646	+	0.475628i	$0.157779\pi$
$354$		−	2.09761e10i		−	1.33571i
$355$	2.76556e8	+	5.13144e9i	0.0174129	+	0.323092i
$356$	−1.01365e10			−0.631088
$357$	−1.41386e9	−	1.41386e9i	−0.0870432	−	0.0870432i
$358$	−7.40201e9	+	7.40201e9i	−0.450627	+	0.450627i
$359$			7.91205e9i			0.476334i	0.971224	+	0.238167i	$0.0765465\pi$
$359$			7.91205e9i			0.476334i	−0.971224	+	0.238167i	$0.923454\pi$
$360$	4.32116e9	−	4.81347e9i	0.257271	−	0.286582i
$361$	1.21947e10			0.718031
$362$	−6.65362e9	−	6.65362e9i	−0.387457	−	0.387457i
$363$	1.86461e10	−	1.86461e10i	1.07389	−	1.07389i
$364$		−	5.63417e9i		−	0.320941i
$365$	1.99782e10	+	1.79349e10i	1.12560	+	1.01048i
$366$	−3.33435e9			−0.185818
$367$	6.65934e9	+	6.65934e9i	0.367085	+	0.367085i	0.866413	−	0.499328i	$-0.166420\pi$
$367$	6.65934e9	+	6.65934e9i	0.367085	+	0.367085i	−0.499328	+	0.866413i	$0.666420\pi$
$368$	−1.77718e7	+	1.77718e7i	−0.000969036	+	0.000969036i
$369$		−	1.24826e10i		−	0.673285i
$370$	−1.16859e10	+	6.29808e8i	−0.623529	+	0.0336048i
$371$	1.07493e10			0.567396
$372$	8.75798e9	+	8.75798e9i	0.457333	+	0.457333i
$373$	1.63417e10	−	1.63417e10i	0.844230	−	0.844230i	−0.145176	−	0.989406i	$-0.546375\pi$
$373$	1.63417e10	−	1.63417e10i	0.844230	−	0.844230i	0.989406	+	0.145176i	$0.0463748\pi$
$374$			1.05369e9i			0.0538551i
$375$	2.31995e10	+	1.66983e10i	1.17315	+	0.844396i
$376$	1.19523e10			0.598000
$377$	−9.76602e8	−	9.76602e8i	−0.0483450	−	0.0483450i
$378$	2.10945e9	−	2.10945e9i	0.103324	−	0.103324i
$379$		−	9.14573e9i		−	0.443263i	−0.975130	−	0.221632i	$-0.928862\pi$
$379$		−	9.14573e9i		−	0.443263i	0.975130	−	0.221632i	$-0.0711382\pi$
$380$	2.97934e8	+	5.52810e9i	0.0142885	+	0.265119i
$381$	−1.60538e10			−0.761867
$382$	9.36714e9	+	9.36714e9i	0.439900	+	0.439900i
$383$	−6.52966e9	+	6.52966e9i	−0.303456	+	0.303456i	−0.842364	−	0.538909i	$-0.818837\pi$
$383$	−6.52966e9	+	6.52966e9i	−0.303456	+	0.303456i	0.538909	+	0.842364i	$0.318837\pi$
$384$		−	2.77791e9i		−	0.127760i
$385$	−3.36550e10	+	3.74892e10i	−1.53181	+	1.70633i
$386$	−2.25604e10			−1.01624
$387$	−2.16706e10	−	2.16706e10i	−0.966112	−	0.966112i
$388$	−1.88838e8	+	1.88838e8i	−0.00833225	+	0.00833225i
$389$		−	2.04596e10i		−	0.893507i	−0.894657	−	0.446754i	$-0.852580\pi$
$389$		−	2.04596e10i		−	0.893507i	0.894657	−	0.446754i	$-0.147420\pi$
$390$	7.05324e9	+	6.33186e9i	0.304881	+	0.273699i
$391$	−6.81417e6			−0.000291545
$392$	−9.23265e9	−	9.23265e9i	−0.391005	−	0.391005i
$393$	5.12801e9	−	5.12801e9i	0.214971	−	0.214971i
$394$		−	1.27683e10i		−	0.529843i
$395$	−2.93161e10	+	1.57998e9i	−1.20425	+	0.0649026i
$396$	−1.91797e10			−0.779941
$397$	−7.68996e9	−	7.68996e9i	−0.309572	−	0.309572i	0.535171	−	0.844744i	$-0.320247\pi$
$397$	−7.68996e9	−	7.68996e9i	−0.309572	−	0.309572i	−0.844744	+	0.535171i	$0.820247\pi$
$398$	3.11670e9	−	3.11670e9i	0.124212	−	0.124212i
$399$			3.11496e10i			1.22902i
$400$	6.36293e9	−	6.87851e8i	0.248552	−	0.0268692i
$401$	−5.85624e9			−0.226486			−0.113243	−	0.993567i	$-0.536124\pi$
$401$	−5.85624e9			−0.226486			−0.113243	+	0.993567i	$0.536124\pi$
$402$	1.95602e10	+	1.95602e10i	0.748980	+	0.748980i
$403$	−6.69079e9	+	6.69079e9i	−0.253663	+	0.253663i
$404$			2.06407e10i			0.774818i
$405$	−1.30707e9	−	2.42524e10i	−0.0485825	−	0.901437i
$406$	−5.24714e9			−0.193116
$407$	2.45366e10	+	2.45366e10i	0.894205	+	0.894205i
$408$	5.32562e8	−	5.32562e8i	0.0192189	−	0.0192189i
$409$			1.32972e10i			0.475191i	0.971364	+	0.237596i	$0.0763593\pi$
$409$			1.32972e10i			0.475191i	−0.971364	+	0.237596i	$0.923641\pi$
$410$	8.25036e9	−	9.19032e9i	0.291970	−	0.325233i
$411$	1.45690e9			0.0510580
$412$	−1.71715e10	−	1.71715e10i	−0.595962	−	0.595962i
$413$	4.30500e10	−	4.30500e10i	1.47970	−	1.47970i
$414$		−	1.24034e8i		−	0.00422222i
$415$	−1.85022e10	−	1.66099e10i	−0.623780	−	0.559982i
$416$	2.12223e9			0.0708629
$417$	2.24828e9	+	2.24828e9i	0.0743542	+	0.0743542i
$418$	1.16072e10	−	1.16072e10i	0.380209	−	0.380209i
$419$		−	6.98994e9i		−	0.226786i	−0.993550	−	0.113393i	$-0.963828\pi$
$419$		−	6.98994e9i		−	0.226786i	0.993550	−	0.113393i	$-0.0361720\pi$
$420$	3.59581e10	−	1.93794e9i	1.15558	−	0.0622793i
$421$	−2.54099e10			−0.808864			−0.404432	−	0.914568i	$-0.632531\pi$
$421$	−2.54099e10			−0.808864			−0.404432	+	0.914568i	$0.632531\pi$
$422$	2.98434e10	+	2.98434e10i	0.941019	+	0.941019i
$423$	−4.17094e10	+	4.17094e10i	−1.30278	+	1.30278i
$424$			4.04896e9i			0.125280i
$425$	1.35173e9	+	1.08799e9i	0.0414317	+	0.0333478i
$426$	−1.08912e10			−0.330704
$427$	−6.84322e9	−	6.84322e9i	−0.205849	−	0.205849i
$428$	−2.59720e9	+	2.59720e9i	−0.0773982	+	0.0773982i
$429$		−	2.81043e10i		−	0.829743i
$430$	−1.63183e9	−	3.02782e10i	−0.0477311	−	0.885639i
$431$	3.72373e10			1.07912			0.539559	−	0.841948i	$-0.318591\pi$
$431$	3.72373e10			1.07912			0.539559	+	0.841948i	$0.318591\pi$
$432$	7.94567e8	+	7.94567e8i	0.0228137	+	0.0228137i
$433$	1.34378e10	−	1.34378e10i	0.382277	−	0.382277i	−0.489645	−	0.871922i	$-0.662874\pi$
$433$	1.34378e10	−	1.34378e10i	0.382277	−	0.382277i	0.871922	+	0.489645i	$0.162874\pi$
$434$			3.59487e10i			1.01327i
$435$	5.89689e9	−	6.56872e9i	0.164690	−	0.183453i
$436$	6.75837e9			0.187023
$437$	7.50632e7	+	7.50632e7i	0.00205826	+	0.00205826i
$438$	−4.02343e10	+	4.02343e10i	−1.09320	+	1.09320i
$439$		−	4.19540e10i		−	1.12957i	−0.825237	−	0.564787i	$-0.808958\pi$
$439$		−	4.19540e10i		−	1.12957i	0.825237	−	0.564787i	$-0.191042\pi$
$440$	−1.41211e10	−	1.26768e10i	−0.376754	−	0.338221i
$441$	6.44373e10			1.70366
$442$	4.06859e8	+	4.06859e8i	0.0106599	+	0.0106599i
$443$	−3.76709e10	+	3.76709e10i	−0.978119	+	0.978119i	−0.999766	−	0.0216469i	$-0.993109\pi$
$443$	−3.76709e10	+	3.76709e10i	−0.978119	+	0.978119i	0.0216469	+	0.999766i	$0.493109\pi$
$444$		−	2.48029e10i		−	0.638220i
$445$	4.94231e10	−	2.66363e9i	1.26035	−	0.0679258i
$446$	4.13798e10			1.04580
$447$	4.58122e7	+	4.58122e7i	0.00114750	+	0.00114750i
$448$	5.70122e9	−	5.70122e9i	0.141532	−	0.141532i
$449$			5.05667e10i			1.24417i	0.782950	+	0.622085i	$0.213714\pi$
$449$			5.05667e10i			1.24417i	−0.782950	+	0.622085i	$0.786286\pi$
$450$	−1.98040e10	+	2.46047e10i	−0.482951	+	0.600023i
$451$	−3.66197e10			−0.885133
$452$	−1.60708e10	−	1.60708e10i	−0.385020	−	0.385020i
$453$	−1.05388e10	+	1.05388e10i	−0.250264	+	0.250264i
$454$			3.65719e9i			0.0860844i
$455$	1.48052e9	+	2.74708e10i	0.0345437	+	0.640951i
$456$	−1.17331e10			−0.271366
$457$	1.52066e10	+	1.52066e10i	0.348631	+	0.348631i	0.859599	−	0.510968i	$-0.170713\pi$
$457$	1.52066e10	+	1.52066e10i	0.348631	+	0.348631i	−0.510968	+	0.859599i	$0.670713\pi$
$458$	3.43822e10	−	3.43822e10i	0.781398	−	0.781398i
$459$			3.04657e8i			0.00686374i
$460$	8.19806e7	−	9.13206e7i	0.00183096	−	0.00203956i
$461$	−2.73791e10			−0.606199			−0.303100	−	0.952959i	$-0.598021\pi$
$461$	−2.73791e10			−0.606199			−0.303100	+	0.952959i	$0.598021\pi$
$462$	−7.55002e10	−	7.55002e10i	−1.65722	−	1.65722i
$463$	3.53408e10	−	3.53408e10i	0.769046	−	0.769046i	−0.208893	−	0.977939i	$-0.566986\pi$
$463$	3.53408e10	−	3.53408e10i	0.769046	−	0.769046i	0.977939	+	0.208893i	$0.0669859\pi$
$464$		−	1.97645e9i		−	0.0426396i
$465$	−4.50030e10	−	4.04002e10i	−0.962563	−	0.864116i
$466$	4.52821e9			0.0960247
$467$	−4.85998e10	−	4.85998e10i	−1.02180	−	1.02180i	−0.999757	−	0.0220454i	$-0.992982\pi$
$467$	−4.85998e10	−	4.85998e10i	−1.02180	−	1.02180i	−0.0220454	−	0.999757i	$-0.507018\pi$
$468$	−7.40583e9	+	7.40583e9i	−0.154380	+	0.154380i
$469$			8.02885e10i			1.65944i
$470$	−5.82764e10	+	3.14078e9i	−1.19427	+	0.0643644i
$471$	8.75000e10			1.77797
$472$	1.62157e10	+	1.62157e10i	0.326713	+	0.326713i
$473$	−6.35744e10	+	6.35744e10i	−1.27010	+	1.27010i
$474$		−	6.22221e10i		−	1.23263i
$475$	−2.90529e9	−	2.68753e10i	−0.0570710	−	0.527932i
$476$	2.18600e9			0.0425815
$477$	−1.41294e10	−	1.41294e10i	−0.272930	−	0.272930i
$478$	−4.15358e10	+	4.15358e10i	−0.795630	+	0.795630i
$479$			5.06476e10i			0.962093i	0.876695	+	0.481047i	$0.159743\pi$
$479$			5.06476e10i			0.962093i	−0.876695	+	0.481047i	$0.840257\pi$
$480$	7.29967e8	+	1.35444e10i	0.0137511	+	0.255149i
$481$	1.89485e10			0.353994
$482$	3.62449e10	+	3.62449e10i	0.671519	+	0.671519i
$483$	4.88257e8	−	4.88257e8i	0.00897139	−	0.00897139i
$484$			2.88290e10i			0.525349i
$485$	8.71102e8	−	9.70346e8i	0.0157435	−	0.0175372i
$486$	5.65657e10			1.01393
$487$	3.99713e9	+	3.99713e9i	0.0710612	+	0.0710612i	0.741744	−	0.670683i	$-0.233999\pi$
$487$	3.99713e9	+	3.99713e9i	0.0710612	+	0.0710612i	−0.670683	+	0.741744i	$0.733999\pi$
$488$	2.57764e9	−	2.57764e9i	0.0454510	−	0.0454510i
$489$		−	3.47121e10i		−	0.607079i
$490$	4.74421e10	+	4.25899e10i	0.822962	+	0.738792i
$491$	4.99004e10			0.858575			0.429288	−	0.903168i	$-0.358765\pi$
$491$	4.99004e10			0.858575			0.429288	+	0.903168i	$0.358765\pi$
$492$	1.85085e10	+	1.85085e10i	0.315872	+	0.315872i
$493$	3.78910e8	−	3.78910e8i	0.00641429	−	0.00641429i
$494$		−	8.96371e9i		−	0.150515i
$495$	9.35153e10	−	5.03996e9i	1.55762	−	0.0839472i
$496$	−1.35408e10			−0.223727
$497$	−2.23525e10	−	2.23525e10i	−0.366354	−	0.366354i
$498$	3.72619e10	−	3.72619e10i	0.605826	−	0.605826i
$499$		−	7.43519e10i		−	1.19920i	−0.800302	−	0.599598i	$-0.795327\pi$
$499$		−	7.43519e10i		−	1.19920i	0.800302	−	0.599598i	$-0.204673\pi$
$500$	−3.08432e10	+	5.02580e9i	−0.493491	+	0.0804128i
$501$	−1.20253e11			−1.90873
$502$	−2.72371e10	−	2.72371e10i	−0.428890	−	0.428890i
$503$	5.52095e10	−	5.52095e10i	0.862465	−	0.862465i	−0.129158	−	0.991624i	$-0.541228\pi$
$503$	5.52095e10	−	5.52095e10i	0.862465	−	0.862465i	0.991624	+	0.129158i	$0.0412276\pi$
$504$			3.97904e10i			0.616675i
$505$	−5.42387e9	−	1.00639e11i	−0.0833958	−	1.54739i
$506$	−3.63876e8			−0.00555074
$507$	5.66811e10	+	5.66811e10i	0.857840	+	0.857840i
$508$	1.24105e10	−	1.24105e10i	0.186352	−	0.186352i
$509$			1.27030e10i			0.189249i	0.995513	+	0.0946245i	$0.0301650\pi$
$509$			1.27030e10i			0.189249i	−0.995513	+	0.0946245i	$0.969835\pi$
$510$	−2.45669e9	+	2.73658e9i	−0.0363136	+	0.0404508i
$511$	−1.65149e11			−2.42210
$512$	2.14748e9	+	2.14748e9i	0.0312500	+	0.0312500i
$513$	3.35603e9	−	3.35603e9i	0.0484570	−	0.0484570i
$514$			4.81855e8i			0.00690341i
$515$	8.82358e10	+	7.92113e10i	1.25434	+	1.12605i
$516$	6.42642e10			0.906505
$517$	1.22361e11	+	1.22361e11i	1.71270	+	1.71270i
$518$	5.09039e10	−	5.09039e10i	0.707021	−	0.707021i
$519$		−	9.95114e10i		−	1.37152i
$520$	−1.03474e10	+	5.57670e8i	−0.141520	+	0.00762717i
$521$	−3.13323e10			−0.425247			−0.212623	−	0.977134i	$-0.568201\pi$
$521$	−3.13323e10			−0.425247			−0.212623	+	0.977134i	$0.568201\pi$
$522$	6.89709e9	+	6.89709e9i	0.0928932	+	0.0928932i
$523$	−1.15624e10	+	1.15624e10i	−0.154539	+	0.154539i	−0.780142	−	0.625603i	$-0.784853\pi$
$523$	−1.15624e10	+	1.15624e10i	−0.154539	+	0.154539i	0.625603	+	0.780142i	$0.284853\pi$
$524$			7.92849e9i			0.105164i
$525$	−1.74813e11	+	1.88978e10i	−2.30111	+	0.248756i
$526$	−3.22403e10			−0.421169
$527$	−2.59595e9	−	2.59595e9i	−0.0336553	−	0.0336553i
$528$	2.84387e10	−	2.84387e10i	0.365910	−	0.365910i
$529$			7.83086e10i			0.999970i
$530$	−1.06397e9	−	1.97417e10i	−0.0134842	−	0.250196i
$531$	−1.13174e11			−1.42353
$532$	−2.40804e10	−	2.40804e10i	−0.300619	−	0.300619i
$533$	−1.41399e10	+	1.41399e10i	−0.175201	+	0.175201i
$534$			1.04898e11i			1.29004i
$535$	1.19808e10	−	1.33458e10i	0.146242	−	0.162903i
$536$	−3.02424e10			−0.366401
$537$	7.65999e10	+	7.65999e10i	0.921152	+	0.921152i
$538$	−7.63072e10	+	7.63072e10i	−0.910828	+	0.910828i
$539$		−	1.89038e11i		−	2.23972i
$540$	−4.08289e9	−	3.66531e9i	−0.0480168	−	0.0431058i
$541$	1.21976e11			1.42392			0.711961	−	0.702219i	$-0.247807\pi$
$541$	1.21976e11			1.42392			0.711961	+	0.702219i	$0.247807\pi$
$542$	−3.07387e10	−	3.07387e10i	−0.356195	−	0.356195i
$543$	−6.88552e10	+	6.88552e10i	−0.792022	+	0.792022i
$544$			8.23401e8i			0.00940190i
$545$	−3.29520e10	+	1.77593e9i	−0.373505	+	0.0201298i
$546$	−5.83054e10			−0.656052
$547$	−1.11157e11	−	1.11157e11i	−1.24161	−	1.24161i	−0.959331	−	0.282283i	$-0.908908\pi$
$547$	−1.11157e11	−	1.11157e11i	−1.24161	−	1.24161i	−0.282283	−	0.959331i	$-0.591092\pi$
$548$	−1.12627e9	+	1.12627e9i	−0.0124888	+	0.0124888i
$549$			1.79901e10i			0.198036i
$550$	7.21820e10	+	5.80983e10i	0.788820	+	0.634911i
$551$	−8.34796e9			−0.0905678
$552$	1.83912e8	+	1.83912e8i	0.00198086	+	0.00198086i
$553$	1.27701e11	−	1.27701e11i	1.36550	−	1.36550i
$554$		−	4.48278e10i		−	0.475892i
$555$	6.51758e9	+	1.20932e11i	0.0686933	+	1.27459i
$556$	−3.47609e9			−0.0363741
$557$	−2.14972e10	−	2.14972e10i	−0.223337	−	0.223337i	0.586565	−	0.809902i	$-0.300480\pi$
$557$	−2.14972e10	−	2.14972e10i	−0.223337	−	0.223337i	−0.809902	+	0.586565i	$0.800480\pi$
$558$	4.72526e10	−	4.72526e10i	0.487404	−	0.487404i
$559$			4.90957e10i			0.502801i
$560$	−2.62995e10	+	2.92958e10i	−0.267421	+	0.297888i
$561$	1.09041e10			0.110088
$562$	−6.62974e10	−	6.62974e10i	−0.664586	−	0.664586i
$563$	−2.68020e10	+	2.68020e10i	−0.266768	+	0.266768i	−0.827796	−	0.561029i	$-0.810406\pi$
$563$	−2.68020e10	+	2.68020e10i	−0.266768	+	0.266768i	0.561029	+	0.827796i	$0.310406\pi$
$564$		−	1.23689e11i		−	1.22240i
$565$	8.25800e10	+	7.41340e10i	0.810366	+	0.727484i
$566$	−1.18523e9			−0.0115488
$567$	1.05644e11	+	1.05644e11i	1.02214	+	1.02214i
$568$	8.41955e9	−	8.41955e9i	0.0808901	−	0.0808901i
$569$		−	9.52278e10i		−	0.908479i	−0.890880	−	0.454240i	$-0.849911\pi$
$569$		−	9.52278e10i		−	0.908479i	0.890880	−	0.454240i	$-0.150089\pi$
$570$	5.72077e10	−	3.08318e9i	0.541945	−	0.0292078i
$571$	1.93929e11			1.82431			0.912154	−	0.409848i	$-0.134418\pi$
$571$	1.93929e11			1.82431			0.912154	+	0.409848i	$0.134418\pi$
$572$	2.17262e10	+	2.17262e10i	0.202955	+	0.202955i
$573$	9.69361e10	−	9.69361e10i	0.899223	−	0.899223i
$574$			7.59716e10i			0.699848i
$575$	−3.75719e8	+	4.66798e8i	−0.00343710	+	0.00427029i
$576$	−1.49879e10			−0.136160
$577$	−1.25849e11	−	1.25849e11i	−1.13540	−	1.13540i	−0.989265	−	0.146131i	$-0.953318\pi$
$577$	−1.25849e11	−	1.25849e11i	−1.13540	−	1.13540i	−0.146131	−	0.989265i	$-0.546682\pi$
$578$	5.56482e10	−	5.56482e10i	0.498586	−	0.498586i
$579$			2.33467e11i			2.07736i
$580$	5.19361e8	+	9.63663e9i	0.00458942	+	0.0851556i
$581$	1.52948e11			1.34227
$582$	1.95420e9	+	1.95420e9i	0.0170324	+	0.0170324i
$583$	−4.14510e10	+	4.14510e10i	−0.358807	+	0.358807i
$584$		−	6.22068e10i		−	0.534794i
$585$	3.41628e10	−	3.80549e10i	0.291696	−	0.324928i
$586$	−1.01291e11			−0.858977
$587$	3.41535e10	+	3.41535e10i	0.287662	+	0.287662i	0.836155	−	0.548493i	$-0.184798\pi$
$587$	3.41535e10	+	3.41535e10i	0.287662	+	0.287662i	−0.548493	+	0.836155i	$0.684798\pi$
$588$	−9.55444e10	+	9.55444e10i	−0.799275	+	0.799275i
$589$			5.71927e10i			0.475203i
$590$	−8.33244e10	−	7.48023e10i	−0.687645	−	0.617315i
$591$	−1.32133e11			−1.08308
$592$	1.91740e10	+	1.91740e10i	0.156108	+	0.156108i
$593$	−1.67663e11	+	1.67663e11i	−1.35588	+	1.35588i	−0.476939	+	0.878937i	$0.658254\pi$
$593$	−1.67663e11	+	1.67663e11i	−1.35588	+	1.35588i	−0.878937	+	0.476939i	$0.841746\pi$
$594$			1.62687e10i			0.130679i
$595$	−1.06583e10	+	5.74426e8i	−0.0850397	+	0.00458317i
$596$	−7.08309e7			−0.000561355
$597$	−3.22533e10	−	3.22533e10i	−0.253908	−	0.253908i
$598$	−1.40502e8	+	1.40502e8i	−0.00109870	+	0.00109870i
$599$		−	2.21439e11i		−	1.72007i	−0.510231	−	0.860037i	$-0.670440\pi$
$599$		−	2.21439e11i		−	1.72007i	0.510231	−	0.860037i	$-0.329560\pi$
$600$	−7.11825e9	−	6.58470e10i	−0.0549248	−	0.508078i
$601$	−2.25242e11			−1.72644			−0.863220	−	0.504828i	$-0.831556\pi$
$601$	−2.25242e11			−1.72644			−0.863220	+	0.504828i	$0.831556\pi$
$602$	1.31892e11	+	1.31892e11i	1.00423	+	1.00423i
$603$	1.05535e11	−	1.05535e11i	0.798229	−	0.798229i
$604$		−	1.62942e10i		−	0.122429i
$605$	−7.57554e9	−	1.40562e11i	−0.0565447	−	1.04917i
$606$	2.13601e11			1.58385
$607$	−8.03075e10	−	8.03075e10i	−0.591563	−	0.591563i	0.346490	−	0.938054i	$-0.387373\pi$
$607$	−8.03075e10	−	8.03075e10i	−0.591563	−	0.591563i	−0.938054	+	0.346490i	$0.887373\pi$
$608$	9.07038e9	−	9.07038e9i	0.0663760	−	0.0663760i
$609$			5.43002e10i			0.394759i
$610$	−1.18906e10	+	1.32452e10i	−0.0858782	+	0.0956622i
$611$	9.44942e10			0.678017
$612$	−2.87338e9	−	2.87338e9i	−0.0204827	−	0.0204827i
$613$	−5.38969e10	+	5.38969e10i	−0.381700	+	0.381700i	−0.871714	−	0.490014i	$-0.836992\pi$
$613$	−5.38969e10	+	5.38969e10i	−0.381700	+	0.381700i	0.490014	+	0.871714i	$0.336992\pi$
$614$			7.69107e10i			0.541144i
$615$	−9.51063e10	−	8.53791e10i	−0.664827	−	0.596831i
$616$	1.16732e11			0.810712
$617$	−1.37064e10	−	1.37064e10i	−0.0945766	−	0.0945766i	0.658235	−	0.752812i	$-0.271303\pi$
$617$	−1.37064e10	−	1.37064e10i	−0.0945766	−	0.0945766i	−0.752812	+	0.658235i	$0.771303\pi$
$618$	−1.77699e11	+	1.77699e11i	−1.21824	+	1.21824i
$619$			1.67460e11i			1.14064i	0.821423	+	0.570320i	$0.193181\pi$
$619$			1.67460e11i			1.14064i	−0.821423	+	0.570320i	$0.806819\pi$
$620$	6.60215e10	−	3.55819e9i	0.446806	−	0.0240804i
$621$	−1.05209e8			−0.000707433
$622$	8.51746e10	+	8.51746e10i	0.569047	+	0.569047i
$623$	−2.15287e11	+	2.15287e11i	−1.42911	+	1.42911i
$624$		−	2.19620e10i		−	0.144855i
$625$	1.49063e11	−	3.26093e10i	0.976897	−	0.213708i
$626$	−1.69423e11			−1.10325
$627$	−1.20117e11	−	1.20117e11i	−0.777205	−	0.777205i
$628$	−6.76424e10	+	6.76424e10i	−0.434891	+	0.434891i
$629$			7.35182e9i			0.0469669i
$630$	−1.04559e10	−	1.94008e11i	−0.0663745	−	1.23156i
$631$	9.05920e10			0.571442			0.285721	−	0.958313i	$-0.407767\pi$
$631$	9.05920e10			0.571442			0.285721	+	0.958313i	$0.407767\pi$
$632$	4.81012e10	+	4.81012e10i	0.301500	+	0.301500i
$633$	3.08835e11	−	3.08835e11i	1.92359	−	1.92359i
$634$		−	1.52176e11i		−	0.941867i
$635$	−5.72493e10	+	6.37716e10i	−0.352107	+	0.392223i
$636$	4.19008e10			0.256091
$637$	−7.29926e10	−	7.29926e10i	−0.443324	−	0.443324i
$638$	2.02338e10	−	2.02338e10i	0.122122	−	0.122122i
$639$			5.87625e10i			0.352449i
$640$	−1.10349e10	−	9.90626e9i	−0.0657730	−	0.0590459i
$641$	−2.71517e10			−0.160829			−0.0804147	−	0.996761i	$-0.525624\pi$
$641$	−2.71517e10			−0.160829			−0.0804147	+	0.996761i	$0.525624\pi$
$642$	2.68773e10	+	2.68773e10i	0.158214	+	0.158214i
$643$	−2.63399e10	+	2.63399e10i	−0.154089	+	0.154089i	−0.779941	−	0.625853i	$-0.784751\pi$
$643$	−2.63399e10	+	2.63399e10i	−0.154089	+	0.154089i	0.625853	+	0.779941i	$0.284751\pi$
$644$			7.54900e8i			0.00438880i
$645$	−3.13335e11	+	1.68870e10i	−1.81038	+	0.0975697i
$646$	3.47782e9			0.0199699
$647$	−2.14034e9	−	2.14034e9i	−0.0122142	−	0.0122142i	0.700973	−	0.713188i	$-0.252749\pi$
$647$	−2.14034e9	−	2.14034e9i	−0.0122142	−	0.0122142i	−0.713188	+	0.700973i	$0.752749\pi$
$648$	−3.97928e10	+	3.97928e10i	−0.225686	+	0.225686i
$649$			3.32014e11i			1.87145i
$650$	5.03048e10	−	5.43810e9i	0.281810	−	0.0304645i
$651$	3.72016e11			2.07127
$652$	2.68344e10	+	2.68344e10i	0.148491	+	0.148491i
$653$	1.29525e11	−	1.29525e11i	0.712364	−	0.712364i	−0.254665	−	0.967029i	$-0.581965\pi$
$653$	1.29525e11	−	1.29525e11i	0.712364	−	0.712364i	0.967029	+	0.254665i	$0.0819653\pi$
$654$		−	6.99392e10i		−	0.382305i
$655$	−2.08341e9	−	3.86572e10i	−0.0113190	−	0.210022i
$656$	−2.86163e10			−0.154525
$657$	2.17080e11	+	2.17080e11i	1.16509	+	1.16509i
$658$	2.53852e11	−	2.53852e11i	1.35418	−	1.35418i
$659$			1.29660e11i			0.687485i	0.939064	+	0.343742i	$0.111695\pi$
$659$			1.29660e11i			0.687485i	−0.939064	+	0.343742i	$0.888305\pi$
$660$	−1.31187e11	+	1.46133e11i	−0.691376	+	0.770144i
$661$	4.35428e10			0.228092			0.114046	−	0.993475i	$-0.463619\pi$
$661$	4.35428e10			0.228092			0.114046	+	0.993475i	$0.463619\pi$
$662$	−1.04814e11	−	1.04814e11i	−0.545744	−	0.545744i
$663$	4.21039e9	−	4.21039e9i	0.0217906	−	0.0217906i
$664$			5.76112e10i			0.296370i
$665$	1.23737e11	+	1.11082e11i	0.632724	+	0.568011i
$666$	−1.33821e11			−0.680186
$667$	1.30851e8	+	1.30851e8i	0.000661109	+	0.000661109i
$668$	9.29625e10	−	9.29625e10i	0.466876	−	0.466876i
$669$		−	4.28220e11i		−	2.13778i
$670$	1.47454e11	−	7.94694e9i	0.731740	−	0.0394367i
$671$	5.27769e10			0.260348
$672$	−5.89993e10	−	5.89993e10i	−0.289314	−	0.289314i
$673$	1.08117e11	−	1.08117e11i	0.527028	−	0.527028i	−0.392657	−	0.919685i	$-0.628444\pi$
$673$	1.08117e11	−	1.08117e11i	0.527028	−	0.527028i	0.919685	+	0.392657i	$0.128444\pi$
$674$			2.13346e11i			1.03382i
$675$	2.08703e10	+	1.67982e10i	0.100534	+	0.0809184i
$676$	−8.76353e10			−0.419655
$677$	−7.02840e10	−	7.02840e10i	−0.334581	−	0.334581i	0.519742	−	0.854323i	$-0.326028\pi$
$677$	−7.02840e10	−	7.02840e10i	−0.334581	−	0.334581i	−0.854323	+	0.519742i	$0.826028\pi$
$678$	−1.66309e11	+	1.66309e11i	−0.787041	+	0.787041i
$679$			8.02135e9i			0.0377371i
$680$	−2.16369e8	−	4.01469e9i	−0.00101195	−	0.0187766i
$681$	3.78466e10			0.175970
$682$	−1.38623e11	−	1.38623e11i	−0.640766	−	0.640766i
$683$	−1.25091e11	+	1.25091e11i	−0.574834	+	0.574834i	−0.933475	−	0.358642i	$-0.883240\pi$
$683$	−1.25091e11	+	1.25091e11i	−0.574834	+	0.574834i	0.358642	+	0.933475i	$0.383240\pi$
$684$			6.33048e10i			0.289209i
$685$	5.19544e9	−	5.78735e9i	0.0235972	−	0.0262856i
$686$	−1.41428e11			−0.638616
$687$	−3.55806e11	−	3.55806e11i	−1.59730	−	1.59730i
$688$	−4.96799e10	+	4.96799e10i	−0.221731	+	0.221731i
$689$			3.20108e10i			0.142043i
$690$	−9.45034e8	−	8.48379e8i	−0.00416918	−	0.00374277i
$691$	−1.67070e11			−0.732800			−0.366400	−	0.930457i	$-0.619410\pi$
$691$	−1.67070e11			−0.732800			−0.366400	+	0.930457i	$0.619410\pi$
$692$	7.69279e10	+	7.69279e10i	0.335475	+	0.335475i
$693$	−4.07353e11	+	4.07353e11i	−1.76619	+	1.76619i
$694$		−	1.74438e11i		−	0.751973i
$695$	1.69485e10	−	9.13431e8i	0.0726427	−	0.00391504i
$696$	−2.04533e10			−0.0871619
$697$	−5.48611e9	−	5.48611e9i	−0.0232452	−	0.0232452i
$698$	−7.74223e10	+	7.74223e10i	−0.326170	+	0.326170i
$699$		−	4.68603e10i		−	0.196289i
$700$	1.20531e11	−	1.49749e11i	0.502004	−	0.623696i
$701$	1.66014e11			0.687498			0.343749	−	0.939062i	$-0.388303\pi$
$701$	1.66014e11			0.687498			0.343749	+	0.939062i	$0.388303\pi$
$702$	6.28178e9	+	6.28178e9i	0.0258663	+	0.0258663i
$703$	8.09858e10	−	8.09858e10i	0.331579	−	0.331579i
$704$			4.39695e10i			0.179003i
$705$	3.25024e10	+	6.03075e11i	0.131571	+	2.44127i
$706$	1.00374e11			0.404018
$707$	4.38382e11	+	4.38382e11i	1.75459	+	1.75459i
$708$	1.67808e11	−	1.67808e11i	0.667853	−	0.667853i
$709$		−	3.71810e11i		−	1.47142i	−0.677297	−	0.735710i	$-0.736849\pi$
$709$		−	3.71810e11i		−	1.47142i	0.677297	−	0.735710i	$-0.263151\pi$
$710$	−3.88391e10	+	4.32640e10i	−0.152839	+	0.170252i
$711$	−3.35712e11			−1.31368
$712$	−8.10924e10	−	8.10924e10i	−0.315544	−	0.315544i
$713$	8.96472e8	−	8.96472e8i	0.00346879	−	0.00346879i
$714$		−	2.26218e10i		−	0.0870432i
$715$	−1.11640e11	−	1.00222e11i	−0.427167	−	0.383477i
$716$	−1.18432e11			−0.450627
$717$	4.29835e11	+	4.29835e11i	1.62639	+	1.62639i
$718$	−6.32964e10	+	6.32964e10i	−0.238167	+	0.238167i
$719$		−	3.16803e11i		−	1.18543i	−0.805414	−	0.592713i	$-0.798057\pi$
$719$		−	3.16803e11i		−	1.18543i	0.805414	−	0.592713i	$-0.201943\pi$
$720$	7.30771e10	−	3.93845e9i	0.271926	−	0.0146553i
$721$	−7.29399e11			−2.69913
$722$	9.75577e10	+	9.75577e10i	0.359015	+	0.359015i
$723$	3.75081e11	−	3.75081e11i	1.37269	−	1.37269i
$724$		−	1.06458e11i		−	0.387457i
$725$	−5.06454e9	−	4.68492e10i	−0.0183311	−	0.169570i
$726$	2.98338e11			1.07389
$727$	1.86694e11	+	1.86694e11i	0.668333	+	0.668333i	0.957330	−	0.288997i	$-0.0933218\pi$
$727$	1.86694e11	+	1.86694e11i	0.668333	+	0.668333i	−0.288997	+	0.957330i	$0.593322\pi$
$728$	4.50734e10	−	4.50734e10i	0.160470	−	0.160470i
$729$		−	3.30410e11i		−	1.16988i
$730$	1.63464e10	+	3.03304e11i	0.0575614	+	1.06804i
$731$	−1.90485e10			−0.0667102
$732$	−2.66748e10	−	2.66748e10i	−0.0929088	−	0.0929088i
$733$	8.03537e10	−	8.03537e10i	0.278349	−	0.278349i	−0.554101	−	0.832450i	$-0.686938\pi$
$733$	8.03537e10	−	8.03537e10i	0.278349	−	0.278349i	0.832450	+	0.554101i	$0.186938\pi$
$734$			1.06549e11i			0.367085i
$735$	4.40743e11	−	4.90956e11i	1.51020	−	1.68226i
$736$	−2.84349e8			−0.000969036
$737$	−3.09604e11	−	3.09604e11i	−1.04939	−	1.04939i
$738$	9.98606e10	−	9.98606e10i	0.336642	−	0.336642i
$739$			2.44359e11i			0.819315i	0.912239	+	0.409658i	$0.134352\pi$
$739$			2.44359e11i			0.819315i	−0.912239	+	0.409658i	$0.865648\pi$
$740$	−9.85260e10	−	8.84490e10i	−0.328567	−	0.294962i
$741$	−9.27613e10			−0.307676
$742$	8.59947e10	+	8.59947e10i	0.283698	+	0.283698i
$743$	1.76095e10	−	1.76095e10i	0.0577818	−	0.0577818i	−0.677625	−	0.735407i	$-0.736991\pi$
$743$	1.76095e10	−	1.76095e10i	0.0577818	−	0.0577818i	0.735407	+	0.677625i	$0.236991\pi$
$744$			1.40128e11i			0.457333i
$745$	3.45353e8	−	1.86126e7i	0.00112108	−	6.04202e-5i
$746$	2.61466e11			0.844230
$747$	−2.01042e11	−	2.01042e11i	−0.645662	−	0.645662i
$748$	−8.42952e9	+	8.42952e9i	−0.0269275	+	0.0269275i
$749$			1.10322e11i			0.350539i
$750$	5.20097e10	+	3.19182e11i	0.164376	+	1.00877i
$751$	9.35354e10			0.294047			0.147023	−	0.989133i	$-0.453031\pi$
$751$	9.35354e10			0.294047			0.147023	+	0.989133i	$0.453031\pi$
$752$	9.56187e10	+	9.56187e10i	0.299000	+	0.299000i
$753$	−2.81864e11	+	2.81864e11i	−0.876717	+	0.876717i
$754$		−	1.56256e10i		−	0.0483450i
$755$	4.28170e9	+	7.94460e10i	0.0131774	+	0.244503i
$756$	3.37511e10			0.103324
$757$	6.80194e10	+	6.80194e10i	0.207133	+	0.207133i	0.803048	−	0.595915i	$-0.203210\pi$
$757$	6.80194e10	+	6.80194e10i	0.207133	+	0.207133i	−0.595915	+	0.803048i	$0.703210\pi$
$758$	7.31659e10	−	7.31659e10i	0.221632	−	0.221632i
$759$			3.76558e9i			0.0113466i
$760$	−4.18413e10	+	4.66082e10i	−0.125415	+	0.139704i
$761$	1.73217e11			0.516478			0.258239	−	0.966081i	$-0.416858\pi$
$761$	1.73217e11			0.516478			0.258239	+	0.966081i	$0.416858\pi$
$762$	−1.28431e11	−	1.28431e11i	−0.380933	−	0.380933i
$763$	1.43539e11	−	1.43539e11i	0.423518	−	0.423518i
$764$			1.49874e11i			0.439900i
$765$	1.47649e10	+	1.32548e10i	0.0431106	+	0.0387014i
$766$	−1.04475e11			−0.303456
$767$	1.28200e11	+	1.28200e11i	0.370430	+	0.370430i
$768$	2.22233e10	−	2.22233e10i	0.0638798	−	0.0638798i
$769$			6.23925e11i			1.78413i	0.451905	+	0.892066i	$0.350745\pi$
$769$			6.23925e11i			1.78413i	−0.451905	+	0.892066i	$0.649255\pi$
$770$	−5.69154e11	+	3.06742e10i	−1.61907	+	0.0872592i
$771$	4.98649e9			0.0141116
$772$	−1.80483e11	−	1.80483e11i	−0.508122	−	0.508122i
$773$	−2.80444e11	+	2.80444e11i	−0.785466	+	0.785466i	−0.980747	−	0.195281i	$-0.937438\pi$
$773$	−2.80444e11	+	2.80444e11i	−0.785466	+	0.785466i	0.195281	+	0.980747i	$0.437438\pi$
$774$		−	3.46730e11i		−	0.966112i
$775$	−3.20968e11	+	3.46976e10i	−0.889724	+	0.0961818i
$776$	−3.02141e9			−0.00833225
$777$	−5.26781e11	−	5.26781e11i	−1.44526	−	1.44526i
$778$	1.63677e11	−	1.63677e11i	0.446754	−	0.446754i
$779$			1.20867e11i			0.328215i
$780$	5.77106e9	+	1.07081e11i	0.0155911	+	0.289290i
$781$	1.72389e11			0.463347
$782$	−5.45133e7	−	5.45133e7i	−0.000145773	−	0.000145773i
$783$	5.85026e9	−	5.85026e9i	0.0155643	−	0.0155643i
$784$		−	1.47722e11i		−	0.391005i
$785$	3.12032e11	−	3.47581e11i	0.821713	−	0.915330i
$786$	8.20482e10			0.214971
$787$	−2.18147e10	−	2.18147e10i	−0.0568656	−	0.0568656i	0.678102	−	0.734968i	$-0.262803\pi$
$787$	−2.18147e10	−	2.18147e10i	−0.0568656	−	0.0568656i	−0.734968	+	0.678102i	$0.762803\pi$
$788$	1.02146e11	−	1.02146e11i	0.264921	−	0.264921i
$789$			3.33640e11i			0.860934i
$790$	−2.47169e11	−	2.21889e11i	−0.634578	−	0.569675i
$791$	−6.82646e11			−1.74377
$792$	−1.53438e11	−	1.53438e11i	−0.389971	−	0.389971i
$793$	2.03786e10	−	2.03786e10i	0.0515326	−	0.0515326i
$794$		−	1.23039e11i		−	0.309572i
$795$	−2.04297e11	+	1.10105e10i	−0.511439	+	0.0275638i
$796$	4.98672e10			0.124212
$797$	1.10772e11	+	1.10772e11i	0.274534	+	0.274534i	0.830922	−	0.556389i	$-0.187813\pi$
$797$	1.10772e11	+	1.10772e11i	0.274534	+	0.274534i	−0.556389	+	0.830922i	$0.687813\pi$
$798$	−2.49197e11	+	2.49197e11i	−0.614512	+	0.614512i
$799$			3.66627e10i			0.0899574i
$800$	5.64062e10	+	4.54006e10i	0.137711	+	0.110841i
$801$	5.65967e11			1.37487
$802$	−4.68499e10	−	4.68499e10i	−0.113243	−	0.113243i
$803$	6.36839e11	−	6.36839e11i	1.53168	−	1.53168i
$804$			3.12964e11i			0.748980i
$805$	−1.98369e8	−	3.68069e9i	−0.000472379	−	0.00876488i
$806$	−1.07053e11			−0.253663
$807$	7.89668e11	+	7.89668e11i	1.86187	+	1.86187i
$808$	−1.65126e11	+	1.65126e11i	−0.387409	+	0.387409i
$809$		−	2.98150e11i		−	0.696051i	−0.937485	−	0.348025i	$-0.886852\pi$
$809$		−	2.98150e11i		−	0.696051i	0.937485	−	0.348025i	$-0.113148\pi$
$810$	1.83563e11	−	2.04476e11i	0.426427	−	0.475010i
$811$	6.76978e11			1.56492			0.782458	−	0.622704i	$-0.213966\pi$
$811$	6.76978e11			1.56492			0.782458	+	0.622704i	$0.213966\pi$
$812$	−4.19771e10	−	4.19771e10i	−0.0965581	−	0.0965581i
$813$	−3.18100e11	+	3.18100e11i	−0.728118	+	0.728118i
$814$			3.92586e11i			0.894205i
$815$	−1.37889e11	−	1.23786e11i	−0.312535	−	0.280570i
$816$	8.52099e9			0.0192189
$817$	2.09834e11	+	2.09834e11i	0.470964	+	0.470964i
$818$	−1.06378e11	+	1.06378e11i	−0.237596	+	0.237596i
$819$			3.14580e11i			0.699191i
$820$	1.39525e11	−	7.51965e9i	0.308601	−	0.0166319i
$821$	−4.64293e10			−0.102193			−0.0510963	−	0.998694i	$-0.516272\pi$
$821$	−4.64293e10			−0.102193			−0.0510963	+	0.998694i	$0.516272\pi$
$822$	1.16552e10	+	1.16552e10i	0.0255290	+	0.0255290i
$823$	−5.00668e11	+	5.00668e11i	−1.09132	+	1.09132i	−0.0959282	+	0.995388i	$0.530582\pi$
$823$	−5.00668e11	+	5.00668e11i	−1.09132	+	1.09132i	−0.995388	+	0.0959282i	$0.969418\pi$
$824$		−	2.74743e11i		−	0.595962i
$825$	6.01232e11	−	7.46977e11i	1.29786	−	1.61247i
$826$	6.88800e11			1.47970
$827$	−6.00312e11	−	6.00312e11i	−1.28338	−	1.28338i	−0.938732	−	0.344648i	$-0.887998\pi$
$827$	−6.00312e11	−	6.00312e11i	−1.28338	−	1.28338i	−0.344648	−	0.938732i	$-0.612002\pi$
$828$	9.92276e8	−	9.92276e8i	0.00211111	−	0.00211111i
$829$		−	8.51434e11i		−	1.80274i	−0.433051	−	0.901370i	$-0.642563\pi$
$829$		−	8.51434e11i		−	1.80274i	0.433051	−	0.901370i	$-0.357437\pi$
$830$	−1.51388e10	−	2.80897e11i	−0.0318991	−	0.591881i
$831$	−4.63902e11			−0.972797
$832$	1.69778e10	+	1.69778e10i	0.0354315	+	0.0354315i
$833$	2.83203e10	−	2.83203e10i	0.0588190	−	0.0588190i
$834$			3.59724e10i			0.0743542i
$835$	−4.28832e11	+	4.77689e11i	−0.882148	+	0.982651i
$836$	1.85715e11			0.380209
$837$	−4.00807e10	−	4.00807e10i	−0.0816646	−	0.0816646i
$838$	5.59195e10	−	5.59195e10i	0.113393	−	0.113393i
$839$		−	2.72456e11i		−	0.549856i	−0.961465	−	0.274928i	$-0.911346\pi$
$839$		−	2.72456e11i		−	0.549856i	0.961465	−	0.274928i	$-0.0886540\pi$
$840$	3.03168e11	+	2.72161e11i	0.608929	+	0.546650i
$841$	4.85694e11			0.970910
$842$	−2.03280e11	−	2.03280e11i	−0.404432	−	0.404432i
$843$	−6.86081e11	+	6.86081e11i	−1.35852	+	1.35852i
$844$			4.77494e11i			0.941019i
$845$	4.27287e11	−	2.30284e10i	0.838094	−	0.0451686i
$846$	−6.67350e11			−1.30278
$847$	6.12290e11	+	6.12290e11i	1.18966	+	1.18966i
$848$	−3.23917e10	+	3.23917e10i	−0.0626398	+	0.0626398i
$849$			1.22653e10i			0.0236075i
$850$	2.10992e9	+	1.95177e10i	0.00404194	+	0.0373898i
$851$	−2.53884e9			−0.00484079
$852$	−8.71300e10	−	8.71300e10i	−0.165352	−	0.165352i
$853$	−1.59406e11	+	1.59406e11i	−0.301099	+	0.301099i	−0.841444	−	0.540345i	$-0.818294\pi$
$853$	−1.59406e11	+	1.59406e11i	−0.301099	+	0.301099i	0.540345	+	0.841444i	$0.318294\pi$
$854$		−	1.09491e11i		−	0.205849i
$855$	−1.66349e10	−	3.08657e11i	−0.0311284	−	0.577580i
$856$	−4.15553e10			−0.0773982
$857$	−3.08378e11	−	3.08378e11i	−0.571690	−	0.571690i	0.360910	−	0.932601i	$-0.382466\pi$
$857$	−3.08378e11	−	3.08378e11i	−0.571690	−	0.571690i	−0.932601	+	0.360910i	$0.882466\pi$
$858$	2.24834e11	−	2.24834e11i	0.414871	−	0.414871i
$859$		−	7.24487e11i		−	1.33063i	−0.746562	−	0.665316i	$-0.768297\pi$
$859$		−	7.24487e11i		−	1.33063i	0.746562	−	0.665316i	$-0.231703\pi$
$860$	2.29171e11	−	2.55281e11i	0.418954	−	0.466685i
$861$	7.86194e11			1.43060
$862$	2.97898e11	+	2.97898e11i	0.539559	+	0.539559i
$863$	−4.20245e10	+	4.20245e10i	−0.0757634	+	0.0757634i	−0.743973	−	0.668210i	$-0.767061\pi$
$863$	−4.20245e10	+	4.20245e10i	−0.0757634	+	0.0757634i	0.668210	+	0.743973i	$0.267061\pi$
$864$			1.27131e10i			0.0228137i
$865$	−3.95295e11	−	3.54865e11i	−0.706085	−	0.633869i
$866$	2.15006e11			0.382277
$867$	−5.75877e11	−	5.75877e11i	−1.01919	−	1.01919i
$868$	−2.87589e11	+	2.87589e11i	−0.506634	+	0.506634i
$869$			9.84867e11i			1.72702i
$870$	9.97249e10	−	5.37462e9i	0.174071	−	0.00938147i
$871$	−2.39094e11			−0.415428
$872$	5.40670e10	+	5.40670e10i	0.0935117	+	0.0935117i
$873$	1.05436e10	−	1.05436e10i	0.0181524	−	0.0181524i
$874$			1.20101e9i			0.00205826i
$875$	−5.48328e11	+	7.61811e11i	−0.935424	+	1.29962i
$876$	−6.43749e11			−1.09320
$877$	−6.58815e11	−	6.58815e11i	−1.11369	−	1.11369i	−0.992647	−	0.121045i	$-0.961376\pi$
$877$	−6.58815e11	−	6.58815e11i	−1.11369	−	1.11369i	−0.121045	−	0.992647i	$-0.538624\pi$
$878$	3.35632e11	−	3.35632e11i	0.564787	−	0.564787i
$879$			1.04822e12i			1.75588i
$880$	−1.15541e10	−	2.14384e11i	−0.0192666	−	0.357488i
$881$	−4.01192e11			−0.665961			−0.332981	−	0.942934i	$-0.608054\pi$
$881$	−4.01192e11			−0.665961			−0.332981	+	0.942934i	$0.608054\pi$
$882$	5.15499e11	+	5.15499e11i	0.851831	+	0.851831i
$883$	5.60683e11	−	5.60683e11i	0.922306	−	0.922306i	−0.0748864	−	0.997192i	$-0.523859\pi$
$883$	5.60683e11	−	5.60683e11i	0.922306	−	0.922306i	0.997192	+	0.0748864i	$0.0238594\pi$
$884$			6.50974e9i			0.0106599i
$885$	−7.74094e11	+	8.62286e11i	−1.26189	+	1.40565i
$886$	−6.02735e11			−0.978119
$887$	−2.69741e11	−	2.69741e11i	−0.435765	−	0.435765i	0.454819	−	0.890584i	$-0.349704\pi$
$887$	−2.69741e11	−	2.69741e11i	−0.435765	−	0.435765i	−0.890584	+	0.454819i	$0.849704\pi$
$888$	1.98423e11	−	1.98423e11i	0.319110	−	0.319110i
$889$		−	5.27167e11i		−	0.843997i
$890$	4.16694e11	+	3.74076e11i	0.664136	+	0.596211i
$891$	−8.14754e11			−1.29275
$892$	3.31038e11	+	3.31038e11i	0.522900	+	0.522900i
$893$	4.03867e11	−	4.03867e11i	0.635086	−	0.635086i
$894$			7.32996e8i			0.00114750i
$895$	5.77444e11	−	3.11210e10i	0.899949	−	0.0485023i
$896$	9.12195e10			0.141532
$897$	1.45399e9	+	1.45399e9i	0.00224591	+	0.00224591i
$898$	−4.04534e11	+	4.04534e11i	−0.622085	+	0.622085i
$899$			9.96988e10i			0.152634i
$900$	−3.55270e11	+	3.84057e10i	−0.541487	+	0.0585364i
$901$	−1.24198e10			−0.0188459
$902$	−2.92958e11	−	2.92958e11i	−0.442567	−	0.442567i
$903$	1.36489e12	−	1.36489e12i	2.05280	−	2.05280i
$904$		−	2.57133e11i		−	0.385020i
$905$	2.79745e10	+	5.19061e11i	0.0417031	+	0.773791i
$906$	−1.68621e11			−0.250264
$907$	6.28908e11	+	6.28908e11i	0.929305	+	0.929305i	0.997661	−	0.0683564i	$-0.0217755\pi$
$907$	6.28908e11	+	6.28908e11i	0.929305	+	0.929305i	−0.0683564	+	0.997661i	$0.521775\pi$
$908$	−2.92575e10	+	2.92575e10i	−0.0430422	+	0.0430422i
$909$		−	1.15246e12i		−	1.68799i
$910$	−2.07922e11	+	2.31610e11i	−0.303204	+	0.337747i
$911$	1.00441e12			1.45827			0.729134	−	0.684371i	$-0.239923\pi$
$911$	1.00441e12			1.45827			0.729134	+	0.684371i	$0.239923\pi$
$912$	−9.38651e10	−	9.38651e10i	−0.135683	−	0.135683i
$913$	−5.89791e11	+	5.89791e11i	−0.848819	+	0.848819i
$914$			2.43305e11i			0.348631i
$915$	1.37069e11	+	1.23050e11i	0.195548	+	0.175548i
$916$	5.50116e11			0.781398
$917$	1.68391e11	+	1.68391e11i	0.238145	+	0.238145i
$918$	−2.43726e9	+	2.43726e9i	−0.00343187	+	0.00343187i
$919$		−	1.58868e11i		−	0.222727i	−0.993780	−	0.111364i	$-0.964478\pi$
$919$		−	1.58868e11i		−	0.222727i	0.993780	−	0.111364i	$-0.0355218\pi$
$920$	1.38641e9	−	7.47198e7i	0.00193526	−	0.000104300i
$921$	7.95912e11			1.10618
$922$	−2.19033e11	−	2.19033e11i	−0.303100	−	0.303100i
$923$	6.65643e10	−	6.65643e10i	0.0917138	−	0.0917138i
$924$		−	1.20800e12i		−	1.65722i
$925$	5.03629e11	+	4.05364e11i	0.687929	+	0.553705i
$926$	5.65453e11			0.769046
$927$	9.58757e11	+	9.58757e11i	1.29834	+	1.29834i
$928$	1.58116e10	−	1.58116e10i	0.0213198	−	0.0213198i
$929$			5.94996e11i			0.798824i	0.916772	+	0.399412i	$0.130786\pi$
$929$			5.94996e11i			0.798824i	−0.916772	+	0.399412i	$0.869214\pi$
$930$	−3.68221e10	−	6.83225e11i	−0.0492240	−	0.913340i
$931$	−6.23939e11			−0.830507
$932$	3.62257e10	+	3.62257e10i	0.0480124	+	0.0480124i
$933$	8.81432e11	−	8.81432e11i	1.16322	−	1.16322i
$934$		−	7.77597e11i		−	1.02180i
$935$	3.88851e10	−	4.33152e10i	0.0508787	−	0.0566753i
$936$	−1.18493e11			−0.154380
$937$	−2.52202e11	−	2.52202e11i	−0.327182	−	0.327182i	0.524332	−	0.851514i	$-0.324315\pi$
$937$	−2.52202e11	−	2.52202e11i	−0.327182	−	0.327182i	−0.851514	+	0.524332i	$0.824315\pi$
$938$	−6.42308e11	+	6.42308e11i	−0.829721	+	0.829721i
$939$			1.75328e12i			2.25522i
$940$	−4.91338e11	−	4.41085e11i	−0.629316	−	0.564951i
$941$	−9.55354e11			−1.21845			−0.609223	−	0.792999i	$-0.708518\pi$
$941$	−9.55354e11			−1.21845			−0.609223	+	0.792999i	$0.708518\pi$
$942$	7.00000e11	+	7.00000e11i	0.888985	+	0.888985i
$943$	1.89454e9	−	1.89454e9i	0.00239584	−	0.00239584i
$944$			2.59451e11i			0.326713i
$945$	−1.64562e11	+	8.86896e9i	−0.206349	+	0.0111210i
$946$	−1.01719e12			−1.27010
$947$	−5.84413e11	−	5.84413e11i	−0.726641	−	0.726641i	0.243308	−	0.969949i	$-0.421767\pi$
$947$	−5.84413e11	−	5.84413e11i	−0.726641	−	0.726641i	−0.969949	+	0.243308i	$0.921767\pi$
$948$	4.97777e11	−	4.97777e11i	0.616313	−	0.616313i
$949$		−	4.91802e11i		−	0.606353i
$950$	1.91760e11	−	2.38244e11i	0.235431	−	0.292502i
$951$	−1.57480e12			−1.92532
$952$	1.74880e10	+	1.74880e10i	0.0212908	+	0.0212908i
$953$	−4.48597e11	+	4.48597e11i	−0.543857	+	0.543857i	−0.924657	−	0.380801i	$-0.875648\pi$
$953$	−4.48597e11	+	4.48597e11i	−0.543857	+	0.543857i	0.380801	+	0.924657i	$0.375648\pi$
$954$		−	2.26071e11i		−	0.272930i
$955$	−3.93832e10	−	7.30747e11i	−0.0473476	−	0.878524i
$956$	−6.64573e11			−0.795630
$957$	−2.09390e11	−	2.09390e11i	−0.249636	−	0.249636i
$958$	−4.05181e11	+	4.05181e11i	−0.481047	+	0.481047i
$959$			4.78410e10i			0.0565621i
$960$	−1.02515e11	+	1.14195e11i	−0.120699	+	0.134450i
$961$	−1.69845e11			−0.199140
$962$	1.51588e11	+	1.51588e11i	0.176997	+	0.176997i
$963$	1.45013e11	−	1.45013e11i	0.168617	−	0.168617i
$964$			5.79918e11i			0.671519i
$965$	9.27415e11	+	8.32562e11i	1.06946	+	0.960080i
$966$	7.81210e9			0.00897139
$967$	3.45450e11	+	3.45450e11i	0.395075	+	0.395075i	0.876492	−	0.481417i	$-0.159878\pi$
$967$	3.45450e11	+	3.45450e11i	0.395075	+	0.395075i	−0.481417	+	0.876492i	$0.659878\pi$
$968$	−2.30632e11	+	2.30632e11i	−0.262674	+	0.262674i
$969$		−	3.59903e10i		−	0.0408216i
$970$	1.47316e10	−	7.93951e8i	0.0166404	−	0.000896823i
$971$	−4.22522e10			−0.0475306			−0.0237653	−	0.999718i	$-0.507565\pi$
$971$	−4.22522e10			−0.0475306			−0.0237653	+	0.999718i	$0.507565\pi$
$972$	4.52525e11	+	4.52525e11i	0.506965	+	0.506965i
$973$	−7.38277e10	+	7.38277e10i	−0.0823697	+	0.0823697i
$974$			6.39541e10i			0.0710612i
$975$	−5.62764e10	−	5.20581e11i	−0.0622741	−	0.576063i
$976$	4.12423e10			0.0454510
$977$	1.20249e12	+	1.20249e12i	1.31978	+	1.31978i	0.913944	+	0.405840i	$0.133021\pi$
$977$	1.20249e12	+	1.20249e12i	1.31978	+	1.31978i	0.405840	+	0.913944i	$0.366979\pi$
$978$	2.77697e11	−	2.77697e11i	0.303540	−	0.303540i
$979$		−	1.66036e12i		−	1.80747i
$980$	3.88178e10	+	7.20256e11i	0.0420849	+	0.780877i
$981$	−3.77349e11			−0.407443
$982$	3.99204e11	+	3.99204e11i	0.429288	+	0.429288i
$983$	−3.99506e11	+	3.99506e11i	−0.427867	+	0.427867i	−0.887901	−	0.460034i	$-0.847837\pi$
$983$	−3.99506e11	+	3.99506e11i	−0.427867	+	0.427867i	0.460034	+	0.887901i	$0.347837\pi$
$984$			2.96136e11i			0.315872i
$985$	−4.71196e11	+	5.24879e11i	−0.500561	+	0.557589i
$986$	6.06256e9			0.00641429
$987$	−2.62700e12	−	2.62700e12i	−2.76816	−	2.76816i
$988$	7.17097e10	−	7.17097e10i	0.0752576	−	0.0752576i
$989$		−	6.57812e9i		−	0.00687570i
$990$	7.88442e11	+	7.07803e11i	0.820784	+	0.736837i
$991$	1.64837e12			1.70907			0.854533	−	0.519396i	$-0.173843\pi$
$991$	1.64837e12			1.70907			0.854533	+	0.519396i	$0.173843\pi$
$992$	−1.08327e11	−	1.08327e11i	−0.111863	−	0.111863i
$993$	−1.08467e12	+	1.08467e12i	−1.11558	+	1.11558i
$994$		−	3.57641e11i		−	0.366354i
$995$	−2.43139e11	+	1.31039e10i	−0.248064	+	0.0133693i
$996$	5.96191e11			0.605826
$997$	−6.07220e11	−	6.07220e11i	−0.614562	−	0.614562i	0.329570	−	0.944131i	$-0.393096\pi$
$997$	−6.07220e11	−	6.07220e11i	−0.614562	−	0.614562i	−0.944131	+	0.329570i	$0.893096\pi$
$998$	5.94815e11	−	5.94815e11i	0.599598	−	0.599598i
$999$			1.13510e11i			0.113965i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.9.c.b.7.2	yes	4
3.2	odd	2		90.9.g.a.37.1		4
4.3	odd	2		80.9.p.a.17.1		4
5.2	odd	4		50.9.c.b.43.1		4
5.3	odd	4	inner	10.9.c.b.3.2	✓	4
5.4	even	2		50.9.c.b.7.1		4
15.8	even	4		90.9.g.a.73.1		4
20.3	even	4		80.9.p.a.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.9.c.b.3.2	✓	4	5.3	odd	4	inner
10.9.c.b.7.2	yes	4	1.1	even	1	trivial
50.9.c.b.7.1		4	5.4	even	2
50.9.c.b.43.1		4	5.2	odd	4
80.9.p.a.17.1		4	4.3	odd	2
80.9.p.a.33.1		4	20.3	even	4
90.9.g.a.37.1		4	3.2	odd	2
90.9.g.a.73.1		4	15.8	even	4

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	10.9.c.b.7.2

Level	$10$
Weight	$9$
Character	10.7
Analytic conductor	$4.074$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$