LMFDB - Embedded newform 10.9.c.a.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)

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);

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")

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:	$\Q(i, \sqrt{249})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 125x^{2} + 3844 $ x^4 + 125*x^2 + 3844
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			$-7.38987i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.9.c.a.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} +(52.9493 - 52.9493i) q^{3} +128.000i q^{4} +(-490.341 - 387.544i) q^{5} -847.189 q^{6} +(-2624.01 - 2624.01i) q^{7} +(1024.00 - 1024.00i) q^{8} +953.736i q^{9} +(822.379 + 7023.08i) q^{10} +5372.73 q^{11} +(6777.51 + 6777.51i) q^{12} +(27972.7 - 27972.7i) q^{13} +41984.2i q^{14} +(-46483.4 + 5443.05i) q^{15} -16384.0 q^{16} +(53444.2 + 53444.2i) q^{17} +(7629.89 - 7629.89i) q^{18} -144788. i q^{19} +(49605.6 - 62763.7i) q^{20} -277879. q^{21} +(-42981.8 - 42981.8i) q^{22} +(52148.7 - 52148.7i) q^{23} -108440. i q^{24} +(90244.3 + 380058. i) q^{25} -447564. q^{26} +(397900. + 397900. i) q^{27} +(335873. - 335873. i) q^{28} -41723.4i q^{29} +(415412. + 328323. i) q^{30} +244148. q^{31} +(131072. + 131072. i) q^{32} +(284482. - 284482. i) q^{33} -855108. i q^{34} +(269741. + 2.30358e6i) q^{35} -122078. q^{36} +(-2.00653e6 - 2.00653e6i) q^{37} +(-1.15830e6 + 1.15830e6i) q^{38} -2.96228e6i q^{39} +(-898955. + 105264. i) q^{40} -4.17322e6 q^{41} +(2.22303e6 + 2.22303e6i) q^{42} +(4.01446e6 - 4.01446e6i) q^{43} +687709. i q^{44} +(369615. - 467656. i) q^{45} -834380. q^{46} +(2.26940e6 + 2.26940e6i) q^{47} +(-867522. + 867522. i) q^{48} +8.00606e6i q^{49} +(2.31851e6 - 3.76242e6i) q^{50} +5.65967e6 q^{51} +(3.58051e6 + 3.58051e6i) q^{52} +(-3.72734e6 + 3.72734e6i) q^{53} -6.36640e6i q^{54} +(-2.63447e6 - 2.08217e6i) q^{55} -5.37397e6 q^{56} +(-7.66643e6 - 7.66643e6i) q^{57} +(-333787. + 333787. i) q^{58} +1.12165e7i q^{59} +(-696710. - 5.94988e6i) q^{60} +2.02002e7 q^{61} +(-1.95319e6 - 1.95319e6i) q^{62} +(2.50261e6 - 2.50261e6i) q^{63} -2.09715e6i q^{64} +(-2.45569e7 + 2.87552e6i) q^{65} -4.55172e6 q^{66} +(-1.30857e7 - 1.30857e7i) q^{67} +(-6.84086e6 + 6.84086e6i) q^{68} -5.52248e6i q^{69} +(1.62707e7 - 2.05866e7i) q^{70} +2.61041e7 q^{71} +(976626. + 976626. i) q^{72} +(-1.85930e7 + 1.85930e7i) q^{73} +3.21044e7i q^{74} +(2.49022e7 + 1.53454e7i) q^{75} +1.85329e7 q^{76} +(-1.40981e7 - 1.40981e7i) q^{77} +(-2.36982e7 + 2.36982e7i) q^{78} -3.07594e6i q^{79} +(8.03375e6 + 6.34952e6i) q^{80} +3.58796e7 q^{81} +(3.33858e7 + 3.33858e7i) q^{82} +(2.41522e7 - 2.41522e7i) q^{83} -3.55685e7i q^{84} +(-5.49393e6 - 4.69179e7i) q^{85} -6.42313e7 q^{86} +(-2.20923e6 - 2.20923e6i) q^{87} +(5.50167e6 - 5.50167e6i) q^{88} +5.76618e6i q^{89} +(-6.69817e6 + 784332. i) q^{90} -1.46802e8 q^{91} +(6.67504e6 + 6.67504e6i) q^{92} +(1.29275e7 - 1.29275e7i) q^{93} -3.63104e7i q^{94} +(-5.61117e7 + 7.09955e7i) q^{95} +1.38804e7 q^{96} +(2.86891e7 + 2.86891e7i) q^{97} +(6.40485e7 - 6.40485e7i) q^{98} +5.12416e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} + 54 q^{3} + 90 q^{5} - 864 q^{6} - 1186 q^{7} + 4096 q^{8} - 1760 q^{10} - 19852 q^{11} + 6912 q^{12} + 73704 q^{13} - 137490 q^{15} - 65536 q^{16} + 198944 q^{17} + 98688 q^{18} + 16640 q^{20}+ \cdots + 167860352 q^{98}+O(q^{100}) $ 4 * q - 32 * q^2 + 54 * q^3 + 90 * q^5 - 864 * q^6 - 1186 * q^7 + 4096 * q^8 - 1760 * q^10 - 19852 * q^11 + 6912 * q^12 + 73704 * q^13 - 137490 * q^15 - 65536 * q^16 + 198944 * q^17 + 98688 * q^18 + 16640 * q^20 - 766572 * q^21 + 158816 * q^22 + 631334 * q^23 + 545600 * q^25 - 1179264 * q^26 + 184680 * q^27 + 151808 * q^28 + 1275360 * q^30 - 2329892 * q^31 + 524288 * q^32 + 1362948 * q^33 + 1403870 * q^35 - 1579008 * q^36 - 976356 * q^37 - 1144000 * q^38 - 40960 * q^40 - 4284652 * q^41 + 6132576 * q^42 + 7146534 * q^43 - 2624430 * q^45 - 10101344 * q^46 - 3300186 * q^47 - 884736 * q^48 + 7241600 * q^50 + 6541788 * q^51 + 9434112 * q^52 + 9989164 * q^53 - 21649020 * q^55 - 2428928 * q^56 - 19136400 * q^57 - 19957760 * q^58 - 2807040 * q^60 + 85377108 * q^61 + 18639136 * q^62 - 16175226 * q^63 - 33878940 * q^65 - 21807168 * q^66 - 57195466 * q^67 - 25464832 * q^68 + 53504320 * q^70 + 113004028 * q^71 + 12632064 * q^72 - 60875756 * q^73 + 22407150 * q^75 + 18304000 * q^76 - 90339932 * q^77 - 40023264 * q^78 - 1474560 * q^80 + 35054064 * q^81 + 34277216 * q^82 + 71051214 * q^83 + 8601320 * q^85 - 114344544 * q^86 + 58152480 * q^87 - 20328448 * q^88 + 58175520 * q^90 - 221467572 * q^91 + 80810752 * q^92 + 98985108 * q^93 - 159500600 * q^95 + 14155776 * q^96 + 139631604 * q^97 + 167860352 * 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
$3$	52.9493	−	52.9493i	0.653695	−	0.653695i	−0.300185	−	0.953881i	$-0.597049\pi$
$3$	52.9493	−	52.9493i	0.653695	−	0.653695i	0.953881	+	0.300185i	$0.0970485\pi$
$4$			128.000i			0.500000i
$5$	−490.341	−	387.544i	−0.784546	−	0.620070i
$5$	−490.341	−	387.544i	−0.784546	−	0.620070i
$6$	−847.189			−0.653695
$7$	−2624.01	−	2624.01i	−1.09288	−	1.09288i	−0.995220	−	0.0976629i	$-0.968863\pi$
$7$	−2624.01	−	2624.01i	−1.09288	−	1.09288i	−0.0976629	−	0.995220i	$-0.531137\pi$
$8$	1024.00	−	1024.00i	0.250000	−	0.250000i
$9$			953.736i			0.145364i
$10$	822.379	+	7023.08i	0.0822379	+	0.702308i
$11$	5372.73			0.366964			0.183482	−	0.983023i	$-0.441263\pi$
$11$	5372.73			0.366964			0.183482	+	0.983023i	$0.441263\pi$
$12$	6777.51	+	6777.51i	0.326848	+	0.326848i
$13$	27972.7	−	27972.7i	0.979403	−	0.979403i	−0.0203888	−	0.999792i	$-0.506490\pi$
$13$	27972.7	−	27972.7i	0.979403	−	0.979403i	0.999792	+	0.0203888i	$0.00649040\pi$
$14$			41984.2i			1.09288i
$15$	−46483.4	+	5443.05i	−0.918192	+	0.107517i
$16$	−16384.0			−0.250000
$17$	53444.2	+	53444.2i	0.639890	+	0.639890i	0.950528	−	0.310638i	$-0.100543\pi$
$17$	53444.2	+	53444.2i	0.639890	+	0.639890i	−0.310638	+	0.950528i	$0.600543\pi$
$18$	7629.89	−	7629.89i	0.0726822	−	0.0726822i
$19$		−	144788.i		−	1.11101i	−0.831513	−	0.555505i	$-0.812525\pi$
$19$		−	144788.i		−	1.11101i	0.831513	−	0.555505i	$-0.187475\pi$
$20$	49605.6	−	62763.7i	0.310035	−	0.392273i
$21$	−277879.			−1.42882
$22$	−42981.8	−	42981.8i	−0.183482	−	0.183482i
$23$	52148.7	−	52148.7i	0.186351	−	0.186351i	−0.607765	−	0.794117i	$-0.707934\pi$
$23$	52148.7	−	52148.7i	0.186351	−	0.186351i	0.794117	+	0.607765i	$0.207934\pi$
$24$		−	108440.i		−	0.326848i
$25$	90244.3	+	380058.i	0.231025	+	0.972948i
$26$	−447564.			−0.979403
$27$	397900.	+	397900.i	0.748720	+	0.748720i
$28$	335873.	−	335873.i	0.546441	−	0.546441i
$29$		−	41723.4i		−	0.0589913i	−0.999565	−	0.0294956i	$-0.990610\pi$
$29$		−	41723.4i		−	0.0589913i	0.999565	−	0.0294956i	$-0.00939012\pi$
$30$	415412.	+	328323.i	0.512854	+	0.405337i
$31$	244148.			0.264367			0.132183	−	0.991225i	$-0.457801\pi$
$31$	244148.			0.264367			0.132183	+	0.991225i	$0.457801\pi$
$32$	131072.	+	131072.i	0.125000	+	0.125000i
$33$	284482.	−	284482.i	0.239883	−	0.239883i
$34$		−	855108.i		−	0.639890i
$35$	269741.	+	2.30358e6i	0.179753	+	1.53508i
$36$	−122078.			−0.0726822
$37$	−2.00653e6	−	2.00653e6i	−1.07063	−	1.07063i	−0.997309	−	0.0733185i	$-0.976641\pi$
$37$	−2.00653e6	−	2.00653e6i	−1.07063	−	1.07063i	−0.0733185	−	0.997309i	$-0.523359\pi$
$38$	−1.15830e6	+	1.15830e6i	−0.555505	+	0.555505i
$39$		−	2.96228e6i		−	1.28046i
$40$	−898955.	+	105264.i	−0.351154	+	0.0411189i
$41$	−4.17322e6			−1.47685			−0.738424	−	0.674336i	$-0.764430\pi$
$41$	−4.17322e6			−1.47685			−0.738424	+	0.674336i	$0.764430\pi$
$42$	2.22303e6	+	2.22303e6i	0.714412	+	0.714412i
$43$	4.01446e6	−	4.01446e6i	1.17423	−	1.17423i	0.193038	−	0.981191i	$-0.438166\pi$
$43$	4.01446e6	−	4.01446e6i	1.17423	−	1.17423i	0.981191	−	0.193038i	$-0.0618340\pi$
$44$			687709.i			0.183482i
$45$	369615.	−	467656.i	0.0901362	−	0.114045i
$46$	−834380.			−0.186351
$47$	2.26940e6	+	2.26940e6i	0.465071	+	0.465071i	0.900313	−	0.435242i	$-0.143337\pi$
$47$	2.26940e6	+	2.26940e6i	0.465071	+	0.465071i	−0.435242	+	0.900313i	$0.643337\pi$
$48$	−867522.	+	867522.i	−0.163424	+	0.163424i
$49$			8.00606e6i			1.38878i
$50$	2.31851e6	−	3.76242e6i	0.370961	−	0.601987i
$51$	5.65967e6			0.836586
$52$	3.58051e6	+	3.58051e6i	0.489702	+	0.489702i
$53$	−3.72734e6	+	3.72734e6i	−0.472384	+	0.472384i	−0.902685	−	0.430301i	$-0.858407\pi$
$53$	−3.72734e6	+	3.72734e6i	−0.472384	+	0.472384i	0.430301	+	0.902685i	$0.358407\pi$
$54$		−	6.36640e6i		−	0.748720i
$55$	−2.63447e6	−	2.08217e6i	−0.287901	−	0.227544i
$56$	−5.37397e6			−0.546441
$57$	−7.66643e6	−	7.66643e6i	−0.726262	−	0.726262i
$58$	−333787.	+	333787.i	−0.0294956	+	0.0294956i
$59$			1.12165e7i			0.925653i	0.886449	+	0.462826i	$0.153165\pi$
$59$			1.12165e7i			0.925653i	−0.886449	+	0.462826i	$0.846835\pi$
$60$	−696710.	−	5.94988e6i	−0.0537585	−	0.459096i
$61$	2.02002e7			1.45893			0.729467	−	0.684016i	$-0.239768\pi$
$61$	2.02002e7			1.45893			0.729467	+	0.684016i	$0.239768\pi$
$62$	−1.95319e6	−	1.95319e6i	−0.132183	−	0.132183i
$63$	2.50261e6	−	2.50261e6i	0.158866	−	0.158866i
$64$		−	2.09715e6i		−	0.125000i
$65$	−2.45569e7	+	2.87552e6i	−1.37569	+	0.161088i
$66$	−4.55172e6			−0.239883
$67$	−1.30857e7	−	1.30857e7i	−0.649377	−	0.649377i	0.303465	−	0.952843i	$-0.401856\pi$
$67$	−1.30857e7	−	1.30857e7i	−0.649377	−	0.649377i	−0.952843	+	0.303465i	$0.901856\pi$
$68$	−6.84086e6	+	6.84086e6i	−0.319945	+	0.319945i
$69$		−	5.52248e6i		−	0.243634i
$70$	1.62707e7	−	2.05866e7i	0.677664	−	0.857417i
$71$	2.61041e7			1.02725			0.513624	−	0.858015i	$-0.328303\pi$
$71$	2.61041e7			1.02725			0.513624	+	0.858015i	$0.328303\pi$
$72$	976626.	+	976626.i	0.0363411	+	0.0363411i
$73$	−1.85930e7	+	1.85930e7i	−0.654722	+	0.654722i	−0.954126	−	0.299404i	$-0.903212\pi$
$73$	−1.85930e7	+	1.85930e7i	−0.654722	+	0.654722i	0.299404	+	0.954126i	$0.403212\pi$
$74$			3.21044e7i			1.07063i
$75$	2.49022e7	+	1.53454e7i	0.787032	+	0.484991i
$76$	1.85329e7			0.555505
$77$	−1.40981e7	−	1.40981e7i	−0.401049	−	0.401049i
$78$	−2.36982e7	+	2.36982e7i	−0.640232	+	0.640232i
$79$		−	3.07594e6i		−	0.0789714i	−0.999220	−	0.0394857i	$-0.987428\pi$
$79$		−	3.07594e6i		−	0.0789714i	0.999220	−	0.0394857i	$-0.0125720\pi$
$80$	8.03375e6	+	6.34952e6i	0.196137	+	0.155018i
$81$	3.58796e7			0.833505
$82$	3.33858e7	+	3.33858e7i	0.738424	+	0.738424i
$83$	2.41522e7	−	2.41522e7i	0.508914	−	0.508914i	−0.405279	−	0.914193i	$-0.632826\pi$
$83$	2.41522e7	−	2.41522e7i	0.508914	−	0.508914i	0.914193	+	0.405279i	$0.132826\pi$
$84$		−	3.55685e7i		−	0.714412i
$85$	−5.49393e6	−	4.69179e7i	−0.105246	−	0.898800i
$86$	−6.42313e7			−1.17423
$87$	−2.20923e6	−	2.20923e6i	−0.0385623	−	0.0385623i
$88$	5.50167e6	−	5.50167e6i	0.0917411	−	0.0917411i
$89$			5.76618e6i			0.0919027i	0.998944	+	0.0459513i	$0.0146319\pi$
$89$			5.76618e6i			0.0919027i	−0.998944	+	0.0459513i	$0.985368\pi$
$90$	−6.69817e6	+	784332.i	−0.102091	+	0.0119545i
$91$	−1.46802e8			−2.14075
$92$	6.67504e6	+	6.67504e6i	0.0931756	+	0.0931756i
$93$	1.29275e7	−	1.29275e7i	0.172815	−	0.172815i
$94$		−	3.63104e7i		−	0.465071i
$95$	−5.61117e7	+	7.09955e7i	−0.688905	+	0.871639i
$96$	1.38804e7			0.163424
$97$	2.86891e7	+	2.86891e7i	0.324063	+	0.324063i	0.850324	−	0.526260i	$-0.176406\pi$
$97$	2.86891e7	+	2.86891e7i	0.324063	+	0.324063i	−0.526260	+	0.850324i	$0.676406\pi$
$98$	6.40485e7	−	6.40485e7i	0.694392	−	0.694392i
$99$			5.12416e6i			0.0533436i
$100$	−4.86474e7	+	1.15513e7i	−0.486474	+	0.115513i
$101$	7.95260e7			0.764229			0.382115	−	0.924115i	$-0.375196\pi$
$101$	7.95260e7			0.764229			0.382115	+	0.924115i	$0.375196\pi$
$102$	−4.52774e7	−	4.52774e7i	−0.418293	−	0.418293i
$103$	4.96462e7	−	4.96462e7i	0.441100	−	0.441100i	−0.451282	−	0.892382i	$-0.649033\pi$
$103$	4.96462e7	−	4.96462e7i	0.441100	−	0.441100i	0.892382	+	0.451282i	$0.149033\pi$
$104$		−	5.72882e7i		−	0.489702i
$105$	1.36256e8	+	1.07690e8i	1.12098	+	0.885972i
$106$	5.96374e7			0.472384
$107$	6.12534e7	+	6.12534e7i	0.467300	+	0.467300i	0.901039	−	0.433739i	$-0.142806\pi$
$107$	6.12534e7	+	6.12534e7i	0.467300	+	0.467300i	−0.433739	+	0.901039i	$0.642806\pi$
$108$	−5.09312e7	+	5.09312e7i	−0.374360	+	0.374360i
$109$			9.33557e7i			0.661355i	0.943744	+	0.330678i	$0.107277\pi$
$109$			9.33557e7i			0.661355i	−0.943744	+	0.330678i	$0.892723\pi$
$110$	4.41842e6	+	3.77331e7i	0.0301784	+	0.257722i
$111$	−2.12489e8			−1.39973
$112$	4.29918e7	+	4.29918e7i	0.273221	+	0.273221i
$113$	1.17246e8	−	1.17246e8i	0.719093	−	0.719093i	−0.249327	−	0.968419i	$-0.580209\pi$
$113$	1.17246e8	−	1.17246e8i	0.719093	−	0.719093i	0.968419	+	0.249327i	$0.0802093\pi$
$114$			1.22663e8i			0.726262i
$115$	−4.57806e7	+	5.36075e6i	−0.261752	+	0.0306503i
$116$	5.34060e6			0.0294956
$117$	2.66786e7	+	2.66786e7i	0.142370	+	0.142370i
$118$	8.97318e7	−	8.97318e7i	0.462826	−	0.462826i
$119$		−	2.80477e8i		−	1.39865i
$120$	−4.20254e7	+	5.31727e7i	−0.202669	+	0.256427i
$121$	−1.85493e8			−0.865337
$122$	−1.61601e8	−	1.61601e8i	−0.729467	−	0.729467i
$123$	−2.20969e8	+	2.20969e8i	−0.965409	+	0.965409i
$124$			3.12510e7i			0.132183i
$125$	1.03039e8	−	2.21332e8i	0.422046	−	0.906574i
$126$	−4.00418e7			−0.158866
$127$	1.16482e7	+	1.16482e7i	0.0447759	+	0.0447759i	0.729140	−	0.684364i	$-0.239920\pi$
$127$	1.16482e7	+	1.16482e7i	0.0447759	+	0.0447759i	−0.684364	+	0.729140i	$0.739920\pi$
$128$	−1.67772e7	+	1.67772e7i	−0.0625000	+	0.0625000i
$129$		−	4.25126e8i		−	1.53518i
$130$	2.19459e8	+	1.73451e8i	0.768387	+	0.607299i
$131$	3.83537e8			1.30233			0.651167	−	0.758934i	$-0.274280\pi$
$131$	3.83537e8			1.30233			0.651167	+	0.758934i	$0.274280\pi$
$132$	3.64137e7	+	3.64137e7i	0.119941	+	0.119941i
$133$	−3.79925e8	+	3.79925e8i	−1.21420	+	1.21420i
$134$			2.09371e8i			0.649377i
$135$	−4.09031e7	−	3.49311e8i	−0.123146	−	1.05166i
$136$	1.09454e8			0.319945
$137$	−1.46786e7	−	1.46786e7i	−0.0416681	−	0.0416681i	0.685966	−	0.727634i	$-0.259380\pi$
$137$	−1.46786e7	−	1.46786e7i	−0.0416681	−	0.0416681i	−0.727634	+	0.685966i	$0.759380\pi$
$138$	−4.41799e7	+	4.41799e7i	−0.121817	+	0.121817i
$139$			4.00314e8i			1.07236i	0.844103	+	0.536181i	$0.180134\pi$
$139$			4.00314e8i			1.07236i	−0.844103	+	0.536181i	$0.819866\pi$
$140$	−2.94858e8	+	3.45269e7i	−0.767540	+	0.0898763i
$141$	2.40326e8			0.608030
$142$	−2.08833e8	−	2.08833e8i	−0.513624	−	0.513624i
$143$	1.50290e8	−	1.50290e8i	0.359406	−	0.359406i
$144$		−	1.56260e7i		−	0.0363411i
$145$	−1.61697e7	+	2.04587e7i	−0.0365788	+	0.0462814i
$146$	2.97487e8			0.654722
$147$	4.23916e8	+	4.23916e8i	0.907842	+	0.907842i
$148$	2.56836e8	−	2.56836e8i	0.535314	−	0.535314i
$149$			5.62457e8i			1.14115i	0.821244	+	0.570577i	$0.193281\pi$
$149$			5.62457e8i			1.14115i	−0.821244	+	0.570577i	$0.806719\pi$
$150$	−7.64540e7	−	3.21981e8i	−0.151020	−	0.636012i
$151$	−2.75254e7			−0.0529452			−0.0264726	−	0.999650i	$-0.508427\pi$
$151$	−2.75254e7			−0.0529452			−0.0264726	+	0.999650i	$0.508427\pi$
$152$	−1.48263e8	−	1.48263e8i	−0.277753	−	0.277753i
$153$	−5.09717e7	+	5.09717e7i	−0.0930172	+	0.0930172i
$154$			2.25569e8i			0.401049i
$155$	−1.19716e8	−	9.46182e7i	−0.207408	−	0.163926i
$156$	3.79171e8			0.640232
$157$	−3.22628e8	−	3.22628e8i	−0.531010	−	0.531010i	0.389863	−	0.920873i	$-0.372522\pi$
$157$	−3.22628e8	−	3.22628e8i	−0.531010	−	0.531010i	−0.920873	+	0.389863i	$0.872522\pi$
$158$	−2.46075e7	+	2.46075e7i	−0.0394857	+	0.0394857i
$159$			3.94720e8i			0.617591i
$160$	−1.34739e7	−	1.15066e8i	−0.0205595	−	0.175577i
$161$	−2.73678e8			−0.407320
$162$	−2.87037e8	−	2.87037e8i	−0.416752	−	0.416752i
$163$	2.36679e8	−	2.36679e8i	0.335281	−	0.335281i	−0.519307	−	0.854588i	$-0.673810\pi$
$163$	2.36679e8	−	2.36679e8i	0.335281	−	0.335281i	0.854588	+	0.519307i	$0.173810\pi$
$164$		−	5.34172e8i		−	0.738424i
$165$	−2.49743e8	+	2.92440e7i	−0.336944	+	0.0394549i
$166$	−3.86435e8			−0.508914
$167$	−5.45436e8	−	5.45436e8i	−0.701258	−	0.701258i	0.263422	−	0.964681i	$-0.415149\pi$
$167$	−5.45436e8	−	5.45436e8i	−0.701258	−	0.701258i	−0.964681	+	0.263422i	$0.915149\pi$
$168$	−2.84548e8	+	2.84548e8i	−0.357206	+	0.357206i
$169$		−	7.49218e8i		−	0.918462i
$170$	−3.31392e8	+	4.19295e8i	−0.396777	+	0.502023i
$171$	1.38089e8			0.161501
$172$	5.13850e8	+	5.13850e8i	0.587115	+	0.587115i
$173$	−6.41655e8	+	6.41655e8i	−0.716337	+	0.716337i	−0.967853	−	0.251516i	$-0.919071\pi$
$173$	−6.41655e8	+	6.41655e8i	−0.716337	+	0.716337i	0.251516	+	0.967853i	$0.419071\pi$
$174$			3.53476e7i			0.0385623i
$175$	7.60474e8	−	1.23408e9i	0.810834	−	1.31580i
$176$	−8.80267e7			−0.0917411
$177$	5.93905e8	+	5.93905e8i	0.605095	+	0.605095i
$178$	4.61294e7	−	4.61294e7i	0.0459513	−	0.0459513i
$179$			9.41081e8i			0.916673i	0.888779	+	0.458337i	$0.151555\pi$
$179$			9.41081e8i			0.916673i	−0.888779	+	0.458337i	$0.848445\pi$
$180$	5.98600e7	+	4.73107e7i	0.0570225	+	0.0450681i
$181$	−4.09543e8			−0.381580			−0.190790	−	0.981631i	$-0.561105\pi$
$181$	−4.09543e8			−0.381580			−0.190790	+	0.981631i	$0.561105\pi$
$182$	1.17441e9	+	1.17441e9i	1.07037	+	1.07037i
$183$	1.06959e9	−	1.06959e9i	0.953699	−	0.953699i
$184$		−	1.06801e8i		−	0.0931756i
$185$	2.06266e8	+	1.76150e9i	0.176092	+	1.50382i
$186$	−2.06840e8			−0.172815
$187$	2.87141e8	+	2.87141e8i	0.234817	+	0.234817i
$188$	−2.90483e8	+	2.90483e8i	−0.232536	+	0.232536i
$189$		−	2.08819e9i		−	1.63652i
$190$	1.01686e9	−	1.19071e8i	0.780272	−	0.0913671i
$191$	5.56054e8			0.417814			0.208907	−	0.977935i	$-0.433009\pi$
$191$	5.56054e8			0.417814			0.208907	+	0.977935i	$0.433009\pi$
$192$	−1.11043e8	−	1.11043e8i	−0.0817119	−	0.0817119i
$193$	1.72776e8	−	1.72776e8i	0.124524	−	0.124524i	−0.642098	−	0.766622i	$-0.721936\pi$
$193$	1.72776e8	−	1.72776e8i	0.124524	−	0.124524i	0.766622	+	0.642098i	$0.221936\pi$
$194$		−	4.59026e8i		−	0.324063i
$195$	−1.14801e9	+	1.45253e9i	−0.793977	+	1.00458i
$196$	−1.02478e9			−0.694392
$197$	−1.39026e9	−	1.39026e9i	−0.923060	−	0.923060i	0.0741846	−	0.997245i	$-0.476365\pi$
$197$	−1.39026e9	−	1.39026e9i	−0.923060	−	0.923060i	−0.997245	+	0.0741846i	$0.976365\pi$
$198$	4.09933e7	−	4.09933e7i	0.0266718	−	0.0266718i
$199$		−	1.80023e8i		−	0.114793i	−0.998351	−	0.0573964i	$-0.981720\pi$
$199$		−	1.80023e8i		−	0.114793i	0.998351	−	0.0573964i	$-0.0182799\pi$
$200$	4.81589e8	+	2.96769e8i	0.300993	+	0.185481i
$201$	−1.38576e9			−0.848990
$202$	−6.36208e8	−	6.36208e8i	−0.382115	−	0.382115i
$203$	−1.09483e8	+	1.09483e8i	−0.0644705	+	0.0644705i
$204$			7.24438e8i			0.418293i
$205$	2.04630e9	+	1.61731e9i	1.15866	+	0.915750i
$206$	−7.94339e8			−0.441100
$207$	4.97361e7	+	4.97361e7i	0.0270888	+	0.0270888i
$208$	−4.58305e8	+	4.58305e8i	−0.244851	+	0.244851i
$209$		−	7.77906e8i		−	0.407701i
$210$	−2.28522e8	−	1.95157e9i	−0.117503	−	1.00348i
$211$	−4.17651e8			−0.210709			−0.105355	−	0.994435i	$-0.533598\pi$
$211$	−4.17651e8			−0.210709			−0.105355	+	0.994435i	$0.533598\pi$
$212$	−4.77100e8	−	4.77100e8i	−0.236192	−	0.236192i
$213$	1.38219e9	−	1.38219e9i	0.671507	−	0.671507i
$214$		−	9.80055e8i		−	0.467300i
$215$	−3.52423e9	+	4.12675e8i	−1.64934	+	0.193132i
$216$	8.14900e8			0.374360
$217$	−6.40648e8	−	6.40648e8i	−0.288922	−	0.288922i
$218$	7.46845e8	−	7.46845e8i	0.330678	−	0.330678i
$219$			1.96897e9i			0.855978i
$220$	2.66517e8	−	3.37212e8i	0.113772	−	0.143950i
$221$	2.98996e9			1.25342
$222$	1.69991e9	+	1.69991e9i	0.699864	+	0.699864i
$223$	1.19002e9	−	1.19002e9i	0.481210	−	0.481210i	−0.424308	−	0.905518i	$-0.639483\pi$
$223$	1.19002e9	−	1.19002e9i	0.481210	−	0.481210i	0.905518	+	0.424308i	$0.139483\pi$
$224$		−	6.87869e8i		−	0.273221i
$225$	−3.62475e8	+	8.60692e7i	−0.141432	+	0.0335829i
$226$	−1.87594e9			−0.719093
$227$	2.69749e9	+	2.69749e9i	1.01591	+	1.01591i	0.999871	+	0.0160418i	$0.00510648\pi$
$227$	2.69749e9	+	2.69749e9i	1.01591	+	1.01591i	0.0160418	+	0.999871i	$0.494894\pi$
$228$	9.81303e8	−	9.81303e8i	0.363131	−	0.363131i
$229$			4.90322e9i			1.78295i	0.453069	+	0.891475i	$0.350329\pi$
$229$			4.90322e9i			1.78295i	−0.453069	+	0.891475i	$0.649671\pi$
$230$	4.09131e8	+	3.23359e8i	0.146201	+	0.115551i
$231$	−1.49297e9			−0.524328
$232$	−4.27248e7	−	4.27248e7i	−0.0147478	−	0.0147478i
$233$	−2.60187e9	+	2.60187e9i	−0.882798	+	0.882798i	−0.993818	−	0.111020i	$-0.964588\pi$
$233$	−2.60187e9	+	2.60187e9i	−0.882798	+	0.882798i	0.111020	+	0.993818i	$0.464588\pi$
$234$		−	4.26858e8i		−	0.142370i
$235$	−2.33288e8	−	1.99227e9i	−0.0764929	−	0.653247i
$236$	−1.43571e9			−0.462826
$237$	−1.62869e8	−	1.62869e8i	−0.0516232	−	0.0516232i
$238$	−2.24381e9	+	2.24381e9i	−0.699324	+	0.699324i
$239$		−	4.57968e9i		−	1.40360i	−0.712374	−	0.701800i	$-0.752380\pi$
$239$		−	4.57968e9i		−	1.40360i	0.712374	−	0.701800i	$-0.247620\pi$
$240$	7.61585e8	−	8.91789e7i	0.229548	−	0.0268793i
$241$	5.82501e9			1.72675			0.863373	−	0.504566i	$-0.168348\pi$
$241$	5.82501e9			1.72675			0.863373	+	0.504566i	$0.168348\pi$
$242$	1.48394e9	+	1.48394e9i	0.432669	+	0.432669i
$243$	−7.10820e8	+	7.10820e8i	−0.203861	+	0.203861i
$244$			2.58562e9i			0.729467i
$245$	3.10270e9	−	3.92570e9i	0.861144	−	1.08957i
$246$	3.53551e9			0.965409
$247$	−4.05012e9	−	4.05012e9i	−1.08813	−	1.08813i
$248$	2.50008e8	−	2.50008e8i	0.0660917	−	0.0660917i
$249$		−	2.55769e9i		−	0.665350i
$250$	−2.59496e9	+	9.46344e8i	−0.664310	+	0.242264i
$251$	−4.01845e9			−1.01243			−0.506214	−	0.862408i	$-0.668955\pi$
$251$	−4.01845e9			−1.01243			−0.506214	+	0.862408i	$0.668955\pi$
$252$	3.20335e8	+	3.20335e8i	0.0794331	+	0.0794331i
$253$	2.80181e8	−	2.80181e8i	0.0683843	−	0.0683843i
$254$		−	1.86372e8i		−	0.0447759i
$255$	−2.77517e9	−	2.19337e9i	−0.656340	−	0.518742i
$256$	2.68435e8			0.0625000
$257$	−1.77795e9	−	1.77795e9i	−0.407556	−	0.407556i	0.473330	−	0.880885i	$-0.343052\pi$
$257$	−1.77795e9	−	1.77795e9i	−0.407556	−	0.407556i	−0.880885	+	0.473330i	$0.843052\pi$
$258$	−3.40100e9	+	3.40100e9i	−0.767588	+	0.767588i
$259$			1.05303e10i			2.34014i
$260$	−3.68067e8	−	3.14328e9i	−0.0805440	−	0.687843i
$261$	3.97931e7			0.00857523
$262$	−3.06830e9	−	3.06830e9i	−0.651167	−	0.651167i
$263$	1.87568e9	−	1.87568e9i	0.392046	−	0.392046i	−0.483370	−	0.875416i	$-0.660588\pi$
$263$	1.87568e9	−	1.87568e9i	0.392046	−	0.392046i	0.875416	+	0.483370i	$0.160588\pi$
$264$		−	5.82620e8i		−	0.119941i
$265$	3.27218e9	−	3.83161e8i	0.663519	−	0.0776958i
$266$	6.07880e9			1.21420
$267$	3.05315e8	+	3.05315e8i	0.0600764	+	0.0600764i
$268$	1.67497e9	−	1.67497e9i	0.324689	−	0.324689i
$269$		−	5.91528e9i		−	1.12971i	−0.825191	−	0.564854i	$-0.808932\pi$
$269$		−	5.91528e9i		−	1.12971i	0.825191	−	0.564854i	$-0.191068\pi$
$270$	−2.46726e9	+	3.12171e9i	−0.464259	+	0.587405i
$271$	−1.60432e9			−0.297449			−0.148725	−	0.988879i	$-0.547517\pi$
$271$	−1.60432e9			−0.297449			−0.148725	+	0.988879i	$0.547517\pi$
$272$	−8.75630e8	−	8.75630e8i	−0.159972	−	0.159972i
$273$	−7.77304e9	+	7.77304e9i	−1.39940	+	1.39940i
$274$			2.34858e8i			0.0416681i
$275$	4.84858e8	+	2.04195e9i	0.0847781	+	0.357037i
$276$	7.06878e8			0.121817
$277$	−1.67266e9	−	1.67266e9i	−0.284111	−	0.284111i	0.550635	−	0.834746i	$-0.314386\pi$
$277$	−1.67266e9	−	1.67266e9i	−0.284111	−	0.284111i	−0.834746	+	0.550635i	$0.814386\pi$
$278$	3.20251e9	−	3.20251e9i	0.536181	−	0.536181i
$279$			2.32853e8i			0.0384295i
$280$	2.63508e9	+	2.08265e9i	0.428708	+	0.338832i
$281$	9.29346e9			1.49057			0.745285	−	0.666747i	$-0.232314\pi$
$281$	9.29346e9			1.49057			0.745285	+	0.666747i	$0.232314\pi$
$282$	−1.92261e9	−	1.92261e9i	−0.304015	−	0.304015i
$283$	4.61061e9	−	4.61061e9i	0.718808	−	0.718808i	−0.249553	−	0.968361i	$-0.580284\pi$
$283$	4.61061e9	−	4.61061e9i	0.718808	−	0.718808i	0.968361	+	0.249553i	$0.0802836\pi$
$284$			3.34132e9i			0.513624i
$285$	7.88088e8	+	6.73024e9i	0.119453	+	1.02012i
$286$	−2.40464e9			−0.359406
$287$	1.09506e10	+	1.09506e10i	1.61402	+	1.61402i
$288$	−1.25008e8	+	1.25008e8i	−0.0181706	+	0.0181706i
$289$		−	1.26318e9i		−	0.181082i
$290$	2.93027e8	−	3.43124e7i	0.0414301	−	0.00485132i
$291$	3.03814e9			0.423678
$292$	−2.37990e9	−	2.37990e9i	−0.327361	−	0.327361i
$293$	−6.99292e9	+	6.99292e9i	−0.948829	+	0.948829i	−0.998753	−	0.0499241i	$-0.984102\pi$
$293$	−6.99292e9	+	6.99292e9i	−0.948829	+	0.948829i	0.0499241	+	0.998753i	$0.484102\pi$
$294$		−	6.78265e9i		−	0.907842i
$295$	4.34688e9	−	5.49990e9i	0.573970	−	0.726217i
$296$	−4.10937e9			−0.535314
$297$	2.13781e9	+	2.13781e9i	0.274753	+	0.274753i
$298$	4.49966e9	−	4.49966e9i	0.570577	−	0.570577i
$299$		−	2.91749e9i		−	0.365026i
$300$	−1.96421e9	+	3.18748e9i	−0.242496	+	0.393516i
$301$	−2.10680e10			−2.56659
$302$	2.20204e8	+	2.20204e8i	0.0264726	+	0.0264726i
$303$	4.21085e9	−	4.21085e9i	0.499573	−	0.499573i
$304$			2.37221e9i			0.277753i
$305$	−9.90498e9	−	7.82845e9i	−1.14460	−	0.904642i
$306$	8.15547e8			0.0930172
$307$	2.31844e9	+	2.31844e9i	0.261001	+	0.261001i	0.825461	−	0.564459i	$-0.190915\pi$
$307$	2.31844e9	+	2.31844e9i	0.261001	+	0.261001i	−0.564459	+	0.825461i	$0.690915\pi$
$308$	1.80456e9	−	1.80456e9i	0.200524	−	0.200524i
$309$		−	5.25746e9i		−	0.576690i
$310$	2.00782e8	+	1.71467e9i	0.0217410	+	0.185667i
$311$	−1.45111e10			−1.55117			−0.775584	−	0.631245i	$-0.782544\pi$
$311$	−1.45111e10			−1.55117			−0.775584	+	0.631245i	$0.782544\pi$
$312$	−3.03337e9	−	3.03337e9i	−0.320116	−	0.320116i
$313$	2.03082e9	−	2.03082e9i	0.211590	−	0.211590i	−0.593353	−	0.804943i	$-0.702196\pi$
$313$	2.03082e9	−	2.03082e9i	0.211590	−	0.211590i	0.804943	+	0.593353i	$0.202196\pi$
$314$			5.16204e9i			0.531010i
$315$	−2.19701e9	+	2.57262e8i	−0.223146	+	0.0261296i
$316$	3.93720e8			0.0394857
$317$	9.69018e8	+	9.69018e8i	0.0959611	+	0.0959611i	0.753458	−	0.657497i	$-0.228385\pi$
$317$	9.69018e8	+	9.69018e8i	0.0959611	+	0.0959611i	−0.657497	+	0.753458i	$0.728385\pi$
$318$	3.15776e9	−	3.15776e9i	0.308796	−	0.308796i
$319$		−	2.24168e8i		−	0.0216477i
$320$	−8.12739e8	+	1.02832e9i	−0.0775088	+	0.0980683i
$321$	6.48666e9			0.610943
$322$	2.18942e9	+	2.18942e9i	0.203660	+	0.203660i
$323$	7.73808e9	−	7.73808e9i	0.710924	−	0.710924i
$324$			4.59259e9i			0.416752i
$325$	1.31556e10	+	8.10688e9i	1.17918	+	0.726641i
$326$	−3.78686e9			−0.335281
$327$	4.94312e9	+	4.94312e9i	0.432325	+	0.432325i
$328$	−4.27338e9	+	4.27338e9i	−0.369212	+	0.369212i
$329$		−	1.19099e10i		−	1.01654i
$330$	2.23189e9	+	1.76399e9i	0.188199	+	0.148744i
$331$	−7.63072e9			−0.635702			−0.317851	−	0.948141i	$-0.602961\pi$
$331$	−7.63072e9			−0.635702			−0.317851	+	0.948141i	$0.602961\pi$
$332$	3.09148e9	+	3.09148e9i	0.254457	+	0.254457i
$333$	1.91370e9	−	1.91370e9i	0.155631	−	0.155631i
$334$			8.72698e9i			0.701258i
$335$	1.34517e9	+	1.14877e10i	0.106807	+	0.912126i
$336$	4.55277e9			0.357206
$337$	−2.47412e9	−	2.47412e9i	−0.191824	−	0.191824i	0.604660	−	0.796484i	$-0.293309\pi$
$337$	−2.47412e9	−	2.47412e9i	−0.191824	−	0.191824i	−0.796484	+	0.604660i	$0.793309\pi$
$338$	−5.99374e9	+	5.99374e9i	−0.459231	+	0.459231i
$339$		−	1.24162e10i		−	0.940135i
$340$	6.00549e9	−	7.03222e8i	0.449400	−	0.0526232i
$341$	1.31174e9			0.0970132
$342$	−1.10472e9	−	1.10472e9i	−0.0807507	−	0.0807507i
$343$	5.88110e9	−	5.88110e9i	0.424895	−	0.424895i
$344$		−	8.22161e9i		−	0.587115i
$345$	−2.14020e9	+	2.70790e9i	−0.151070	+	0.191142i
$346$	1.02665e10			0.716337
$347$	−2.63557e9	−	2.63557e9i	−0.181785	−	0.181785i	0.610348	−	0.792133i	$-0.291029\pi$
$347$	−2.63557e9	−	2.63557e9i	−0.181785	−	0.181785i	−0.792133	+	0.610348i	$0.791029\pi$
$348$	2.82781e8	−	2.82781e8i	0.0192812	−	0.0192812i
$349$			2.46965e10i			1.66469i	0.554257	+	0.832346i	$0.313002\pi$
$349$			2.46965e10i			1.66469i	−0.554257	+	0.832346i	$0.686998\pi$
$350$	−1.59564e10	+	3.78883e9i	−1.06332	+	0.252484i
$351$	2.22607e10			1.46660
$352$	7.04214e8	+	7.04214e8i	0.0458705	+	0.0458705i
$353$	−1.25084e10	+	1.25084e10i	−0.805566	+	0.805566i	−0.983959	−	0.178393i	$-0.942910\pi$
$353$	−1.25084e10	+	1.25084e10i	−0.805566	+	0.805566i	0.178393	+	0.983959i	$0.442910\pi$
$354$		−	9.50247e9i		−	0.605095i
$355$	−1.27999e10	−	1.01165e10i	−0.805923	−	0.636966i
$356$	−7.38071e8			−0.0459513
$357$	−1.48510e10	−	1.48510e10i	−0.914290	−	0.914290i
$358$	7.52864e9	−	7.52864e9i	0.458337	−	0.458337i
$359$			2.30279e10i			1.38636i	0.720763	+	0.693181i	$0.243792\pi$
$359$			2.30279e10i			1.38636i	−0.720763	+	0.693181i	$0.756208\pi$
$360$	−1.00395e8	−	8.57365e8i	−0.00597723	−	0.0510453i
$361$	−3.97999e9			−0.234344
$362$	3.27635e9	+	3.27635e9i	0.190790	+	0.190790i
$363$	−9.82172e9	+	9.82172e9i	−0.565667	+	0.565667i
$364$		−	1.87906e10i		−	1.07037i
$365$	1.63225e10	−	1.91131e9i	0.919634	−	0.107686i
$366$	−1.71134e10			−0.953699
$367$	−9.47400e9	−	9.47400e9i	−0.522239	−	0.522239i	0.396008	−	0.918247i	$-0.370395\pi$
$367$	−9.47400e9	−	9.47400e9i	−0.522239	−	0.522239i	−0.918247	+	0.396008i	$0.870395\pi$
$368$	−8.54405e8	+	8.54405e8i	−0.0465878	+	0.0465878i
$369$		−	3.98015e9i		−	0.214681i
$370$	1.24419e10	−	1.57421e10i	0.663864	−	0.839956i
$371$	1.95612e10			1.03252
$372$	1.65472e9	+	1.65472e9i	0.0864077	+	0.0864077i
$373$	6.05089e9	−	6.05089e9i	0.312597	−	0.312597i	−0.533318	−	0.845915i	$-0.679055\pi$
$373$	6.05089e9	−	6.05089e9i	0.312597	−	0.312597i	0.845915	+	0.533318i	$0.179055\pi$
$374$		−	4.59426e9i		−	0.234817i
$375$	−6.26354e9	−	1.71752e10i	−0.316734	−	0.868513i
$376$	4.64773e9			0.232536
$377$	−1.16712e9	−	1.16712e9i	−0.0577763	−	0.0577763i
$378$	−1.67055e10	+	1.67055e10i	−0.818262	+	0.818262i
$379$		−	4.27189e9i		−	0.207044i	−0.994627	−	0.103522i	$-0.966989\pi$
$379$		−	4.27189e9i		−	0.207044i	0.994627	−	0.103522i	$-0.0330113\pi$
$380$	−9.08743e9	−	7.18230e9i	−0.435819	−	0.344452i
$381$	1.23353e9			0.0585397
$382$	−4.44843e9	−	4.44843e9i	−0.208907	−	0.208907i
$383$	−2.68406e10	+	2.68406e10i	−1.24738	+	1.24738i	−0.290502	+	0.956874i	$0.593822\pi$
$383$	−2.68406e10	+	2.68406e10i	−1.24738	+	1.24738i	−0.956874	+	0.290502i	$0.906178\pi$
$384$			1.77668e9i			0.0817119i
$385$	1.44925e9	+	1.23765e10i	0.0659628	+	0.563320i
$386$	−2.76441e9			−0.124524
$387$	3.82873e9	+	3.82873e9i	0.170691	+	0.170691i
$388$	−3.67221e9	+	3.67221e9i	−0.162032	+	0.162032i
$389$		−	9.16592e8i		−	0.0400293i	−0.999800	−	0.0200146i	$-0.993629\pi$
$389$		−	9.16592e8i		−	0.0400293i	0.999800	−	0.0200146i	$-0.00637128\pi$
$390$	2.08043e10	−	2.43611e9i	0.899280	−	0.105303i
$391$	5.57410e9			0.238489
$392$	8.19821e9	+	8.19821e9i	0.347196	+	0.347196i
$393$	2.03080e10	−	2.03080e10i	0.851330	−	0.851330i
$394$			2.22441e10i			0.923060i
$395$	−1.19206e9	+	1.50826e9i	−0.0489678	+	0.0619567i
$396$	−6.55893e8			−0.0266718
$397$	5.24090e9	+	5.24090e9i	0.210981	+	0.210981i	0.804684	−	0.593703i	$-0.202335\pi$
$397$	5.24090e9	+	5.24090e9i	0.210981	+	0.210981i	−0.593703	+	0.804684i	$0.702335\pi$
$398$	−1.44018e9	+	1.44018e9i	−0.0573964	+	0.0573964i
$399$			4.02336e10i			1.58744i
$400$	−1.47856e9	−	6.22687e9i	−0.0577563	−	0.243237i
$401$	1.76862e10			0.684000			0.342000	−	0.939700i	$-0.388896\pi$
$401$	1.76862e10			0.684000			0.342000	+	0.939700i	$0.388896\pi$
$402$	1.10860e10	+	1.10860e10i	0.424495	+	0.424495i
$403$	6.82950e9	−	6.82950e9i	0.258922	−	0.258922i
$404$			1.01793e10i			0.382115i
$405$	−1.75933e10	−	1.39049e10i	−0.653923	−	0.516832i
$406$	1.75172e9			0.0644705
$407$	−1.07805e10	−	1.07805e10i	−0.392882	−	0.392882i
$408$	5.79551e9	−	5.79551e9i	0.209147	−	0.209147i
$409$		−	2.18253e9i		−	0.0779950i	−0.999239	−	0.0389975i	$-0.987584\pi$
$409$		−	2.18253e9i		−	0.0779950i	0.999239	−	0.0389975i	$-0.0124164\pi$
$410$	−3.43197e9	−	2.93089e10i	−0.121453	−	1.03720i
$411$	−1.55445e9			−0.0544765
$412$	6.35471e9	+	6.35471e9i	0.220550	+	0.220550i
$413$	2.94321e10	−	2.94321e10i	1.01163	−	1.01163i
$414$		−	7.95778e8i		−	0.0270888i
$415$	−2.12029e10	+	2.48278e9i	−0.714829	+	0.0837040i
$416$	7.33289e9			0.244851
$417$	2.11964e10	+	2.11964e10i	0.700998	+	0.700998i
$418$	−6.22325e9	+	6.22325e9i	−0.203851	+	0.203851i
$419$		−	3.02443e10i		−	0.981268i	−0.871366	−	0.490634i	$-0.836765\pi$
$419$		−	3.02443e10i		−	0.981268i	0.871366	−	0.490634i	$-0.163235\pi$
$420$	−1.37844e10	+	1.74407e10i	−0.442986	+	0.560489i
$421$	1.77840e10			0.566109			0.283055	−	0.959104i	$-0.408652\pi$
$421$	1.77840e10			0.566109			0.283055	+	0.959104i	$0.408652\pi$
$422$	3.34121e9	+	3.34121e9i	0.105355	+	0.105355i
$423$	−2.16441e9	+	2.16441e9i	−0.0676048	+	0.0676048i
$424$			7.63359e9i			0.236192i
$425$	−1.54889e10	+	2.51349e10i	−0.474749	+	0.770410i
$426$	−2.21151e10			−0.671507
$427$	−5.30055e10	−	5.30055e10i	−1.59444	−	1.59444i
$428$	−7.84044e9	+	7.84044e9i	−0.233650	+	0.233650i
$429$		−	1.59155e10i		−	0.469884i
$430$	3.14953e10	+	2.48925e10i	0.921237	+	0.728105i
$431$	−2.12717e10			−0.616443			−0.308221	−	0.951315i	$-0.599734\pi$
$431$	−2.12717e10			−0.616443			−0.308221	+	0.951315i	$0.599734\pi$
$432$	−6.51920e9	−	6.51920e9i	−0.187180	−	0.187180i
$433$	−2.24808e10	+	2.24808e10i	−0.639529	+	0.639529i	−0.950439	−	0.310910i	$-0.899366\pi$
$433$	−2.24808e10	+	2.24808e10i	−0.639529	+	0.639529i	0.310910	+	0.950439i	$0.399366\pi$
$434$			1.02504e10i			0.288922i
$435$	2.27103e8	+	1.93945e9i	0.00634257	+	0.0541653i
$436$	−1.19495e10			−0.330678
$437$	−7.55051e9	−	7.55051e9i	−0.207038	−	0.207038i
$438$	1.57518e10	−	1.57518e10i	0.427989	−	0.427989i
$439$		−	1.46904e10i		−	0.395526i	−0.980250	−	0.197763i	$-0.936632\pi$
$439$		−	1.46904e10i		−	0.395526i	0.980250	−	0.197763i	$-0.0633676\pi$
$440$	−4.82984e9	+	5.65557e8i	−0.128861	+	0.0150892i
$441$	−7.63567e9			−0.201880
$442$	−2.39197e10	−	2.39197e10i	−0.626710	−	0.626710i
$443$	1.79953e10	−	1.79953e10i	0.467245	−	0.467245i	−0.433776	−	0.901021i	$-0.642819\pi$
$443$	1.79953e10	−	1.79953e10i	0.467245	−	0.467245i	0.901021	+	0.433776i	$0.142819\pi$
$444$		−	2.71985e10i		−	0.699864i
$445$	2.23465e9	−	2.82740e9i	0.0569861	−	0.0721019i
$446$	−1.90403e10			−0.481210
$447$	2.97817e10	+	2.97817e10i	0.745968	+	0.745968i
$448$	−5.50295e9	+	5.50295e9i	−0.136610	+	0.136610i
$449$		−	2.81226e10i		−	0.691943i	−0.938245	−	0.345972i	$-0.887549\pi$
$449$		−	2.81226e10i		−	0.691943i	0.938245	−	0.345972i	$-0.112451\pi$
$450$	3.58835e9	+	2.21124e9i	0.0875074	+	0.0539246i
$451$	−2.24216e10			−0.541951
$452$	1.50075e10	+	1.50075e10i	0.359546	+	0.359546i
$453$	−1.45745e9	+	1.45745e9i	−0.0346100	+	0.0346100i
$454$		−	4.31599e10i		−	1.01591i
$455$	7.19829e10	+	5.68921e10i	1.67951	+	1.32741i
$456$	−1.57008e10			−0.363131
$457$	5.32217e10	+	5.32217e10i	1.22018	+	1.22018i	0.967567	+	0.252614i	$0.0812901\pi$
$457$	5.32217e10	+	5.32217e10i	1.22018	+	1.22018i	0.252614	+	0.967567i	$0.418710\pi$
$458$	3.92258e10	−	3.92258e10i	0.891475	−	0.891475i
$459$			4.25310e10i			0.958196i
$460$	−6.86176e8	−	5.85992e9i	−0.0153251	−	0.130876i
$461$	2.80695e9			0.0621485			0.0310743	−	0.999517i	$-0.490107\pi$
$461$	2.80695e9			0.0621485			0.0310743	+	0.999517i	$0.490107\pi$
$462$	1.19438e10	+	1.19438e10i	0.262164	+	0.262164i
$463$	−1.84228e10	+	1.84228e10i	−0.400896	+	0.400896i	−0.878549	−	0.477653i	$-0.841488\pi$
$463$	−1.84228e10	+	1.84228e10i	−0.400896	+	0.400896i	0.477653	+	0.878549i	$0.341488\pi$
$464$			6.83596e8i			0.0147478i
$465$	−1.13489e10	+	1.32891e9i	−0.242739	+	0.0284239i
$466$	4.16299e10			0.882798
$467$	−1.19286e10	−	1.19286e10i	−0.250796	−	0.250796i	0.570501	−	0.821297i	$-0.306749\pi$
$467$	−1.19286e10	−	1.19286e10i	−0.250796	−	0.250796i	−0.821297	+	0.570501i	$0.806749\pi$
$468$	−3.41486e9	+	3.41486e9i	−0.0711852	+	0.0711852i
$469$			6.86739e10i			1.41939i
$470$	−1.40719e10	+	1.78045e10i	−0.288377	+	0.364870i
$471$	−3.41658e10			−0.694238
$472$	1.14857e10	+	1.14857e10i	0.231413	+	0.231413i
$473$	2.15686e10	−	2.15686e10i	0.430900	−	0.430900i
$474$			2.60590e9i			0.0516232i
$475$	5.50278e10	−	1.30663e10i	1.08095	−	0.256672i
$476$	3.59010e10			0.699324
$477$	−3.55490e9	−	3.55490e9i	−0.0686679	−	0.0686679i
$478$	−3.66374e10	+	3.66374e10i	−0.701800	+	0.701800i
$479$		−	8.08280e10i		−	1.53539i	−0.640813	−	0.767697i	$-0.721403\pi$
$479$		−	8.08280e10i		−	1.53539i	0.640813	−	0.767697i	$-0.278597\pi$
$480$	−6.80611e9	−	5.37925e9i	−0.128214	−	0.101334i
$481$	−1.12256e11			−2.09715
$482$	−4.66001e10	−	4.66001e10i	−0.863373	−	0.863373i
$483$	−1.44911e10	+	1.44911e10i	−0.266263	+	0.266263i
$484$		−	2.37431e10i		−	0.432669i
$485$	−2.94916e9	−	2.51857e10i	−0.0533006	−	0.455185i
$486$	1.13731e10			0.203861
$487$	7.93140e10	+	7.93140e10i	1.41005	+	1.41005i	0.759252	+	0.650797i	$0.225565\pi$
$487$	7.93140e10	+	7.93140e10i	1.41005	+	1.41005i	0.650797	+	0.759252i	$0.274435\pi$
$488$	2.06850e10	−	2.06850e10i	0.364733	−	0.364733i
$489$		−	2.50640e10i		−	0.438343i
$490$	−5.62272e10	+	6.58402e9i	−0.975355	+	0.114211i
$491$	6.00911e10			1.03391			0.516957	−	0.856011i	$-0.327065\pi$
$491$	6.00911e10			1.03391			0.516957	+	0.856011i	$0.327065\pi$
$492$	−2.82841e10	−	2.82841e10i	−0.482705	−	0.482705i
$493$	2.22988e9	−	2.22988e9i	0.0377479	−	0.0377479i
$494$			6.48019e10i			1.08813i
$495$	1.98584e9	−	2.51259e9i	0.0330768	−	0.0418505i
$496$	−4.00013e9			−0.0660917
$497$	−6.84974e10	−	6.84974e10i	−1.12266	−	1.12266i
$498$	−2.04615e10	+	2.04615e10i	−0.332675	+	0.332675i
$499$		−	1.08749e11i		−	1.75397i	−0.480516	−	0.876986i	$-0.659551\pi$
$499$		−	1.08749e11i		−	1.75397i	0.480516	−	0.876986i	$-0.340449\pi$
$500$	2.83304e10	+	1.31889e10i	0.453287	+	0.211023i
$501$	−5.77610e10			−0.916819
$502$	3.21476e10	+	3.21476e10i	0.506214	+	0.506214i
$503$	−4.36650e10	+	4.36650e10i	−0.682122	+	0.682122i	−0.960478	−	0.278356i	$-0.910210\pi$
$503$	−4.36650e10	+	4.36650e10i	−0.682122	+	0.682122i	0.278356	+	0.960478i	$0.410210\pi$
$504$		−	5.12535e9i		−	0.0794331i
$505$	−3.89949e10	−	3.08198e10i	−0.599573	−	0.473876i
$506$	−4.48289e9			−0.0683843
$507$	−3.96706e10	−	3.96706e10i	−0.600394	−	0.600394i
$508$	−1.49097e9	+	1.49097e9i	−0.0223880	+	0.0223880i
$509$			6.95461e10i			1.03610i	0.855350	+	0.518050i	$0.173342\pi$
$509$			6.95461e10i			1.03610i	−0.855350	+	0.518050i	$0.826658\pi$
$510$	4.65440e9	+	3.97484e10i	0.0687991	+	0.587541i
$511$	9.75763e10			1.43107
$512$	−2.14748e9	−	2.14748e9i	−0.0312500	−	0.0312500i
$513$	5.76112e10	−	5.76112e10i	0.831835	−	0.831835i
$514$			2.84472e10i			0.407556i
$515$	−4.35836e10	+	5.10349e9i	−0.619576	+	0.0725502i
$516$	5.44161e10			0.767588
$517$	1.21929e10	+	1.21929e10i	0.170665	+	0.170665i
$518$	8.42424e10	−	8.42424e10i	1.17007	−	1.17007i
$519$			6.79504e10i			0.936533i
$520$	−2.22017e10	+	2.80908e10i	−0.303650	+	0.384194i
$521$	1.18226e10			0.160459			0.0802294	−	0.996776i	$-0.474435\pi$
$521$	1.18226e10			0.160459			0.0802294	+	0.996776i	$0.474435\pi$
$522$	−3.18345e8	−	3.18345e8i	−0.00428762	−	0.00428762i
$523$	5.44052e10	−	5.44052e10i	0.727166	−	0.727166i	−0.242888	−	0.970054i	$-0.578095\pi$
$523$	5.44052e10	−	5.44052e10i	0.727166	−	0.727166i	0.970054	+	0.242888i	$0.0780948\pi$
$524$			4.90928e10i			0.651167i
$525$	−2.50770e10	−	1.05610e11i	−0.330095	−	1.39017i
$526$	−3.00109e10			−0.392046
$527$	1.30483e10	+	1.30483e10i	0.169166	+	0.169166i
$528$	−4.66096e9	+	4.66096e9i	−0.0599707	+	0.0599707i
$529$			7.28720e10i			0.930546i
$530$	−2.92427e10	−	2.31121e10i	−0.370607	−	0.292912i
$531$	−1.06975e10			−0.134557
$532$	−4.86304e10	−	4.86304e10i	−0.607102	−	0.607102i
$533$	−1.16736e11	+	1.16736e11i	−1.44643	+	1.44643i
$534$		−	4.88505e9i		−	0.0600764i
$535$	−6.29669e9	−	5.37735e10i	−0.0768595	−	0.656377i
$536$	−2.67995e10			−0.324689
$537$	4.98296e10	+	4.98296e10i	0.599225	+	0.599225i
$538$	−4.73223e10	+	4.73223e10i	−0.564854	+	0.564854i
$539$			4.30144e10i			0.509634i
$540$	4.47118e10	−	5.23560e9i	0.525832	−	0.0615731i
$541$	1.29671e11			1.51375			0.756873	−	0.653562i	$-0.226726\pi$
$541$	1.29671e11			1.51375			0.756873	+	0.653562i	$0.226726\pi$
$542$	1.28345e10	+	1.28345e10i	0.148725	+	0.148725i
$543$	−2.16850e10	+	2.16850e10i	−0.249437	+	0.249437i
$544$			1.40101e10i			0.159972i
$545$	3.61794e10	−	4.57761e10i	0.410087	−	0.518864i
$546$	1.24369e11			1.39940
$547$	2.70067e10	+	2.70067e10i	0.301664	+	0.301664i	0.841664	−	0.540001i	$-0.181576\pi$
$547$	2.70067e10	+	2.70067e10i	0.301664	+	0.301664i	−0.540001	+	0.841664i	$0.681576\pi$
$548$	1.87887e9	−	1.87887e9i	0.0208340	−	0.0208340i
$549$			1.92656e10i			0.212077i
$550$	1.24567e10	−	2.02144e10i	0.136130	−	0.220908i
$551$	−6.04105e9			−0.0655399
$552$	−5.65502e9	−	5.65502e9i	−0.0609085	−	0.0609085i
$553$	−8.07130e9	+	8.07130e9i	−0.0863064	+	0.0863064i
$554$			2.67625e10i			0.284111i
$555$	1.04192e11	+	8.23487e10i	1.09815	+	0.867930i
$556$	−5.12402e10			−0.536181
$557$	1.51528e9	+	1.51528e9i	0.0157425	+	0.0157425i	0.714934	−	0.699192i	$-0.246457\pi$
$557$	1.51528e9	+	1.51528e9i	0.0157425	+	0.0157425i	−0.699192	+	0.714934i	$0.746457\pi$
$558$	1.86282e9	−	1.86282e9i	0.0192148	−	0.0192148i
$559$		−	2.24591e11i		−	2.30009i
$560$	−4.41944e9	−	3.77419e10i	−0.0449382	−	0.383770i
$561$	3.04079e10			0.306997
$562$	−7.43477e10	−	7.43477e10i	−0.745285	−	0.745285i
$563$	−1.16988e11	+	1.16988e11i	−1.16441	+	1.16441i	−0.180911	+	0.983500i	$0.557905\pi$
$563$	−1.16988e11	+	1.16988e11i	−1.16441	+	1.16441i	−0.983500	+	0.180911i	$0.942095\pi$
$564$			3.07618e10i			0.304015i
$565$	−1.02929e11	+	1.20526e10i	−1.01005	+	0.118273i
$566$	−7.37698e10			−0.718808
$567$	−9.41486e10	−	9.41486e10i	−0.910923	−	0.910923i
$568$	2.67306e10	−	2.67306e10i	0.256812	−	0.256812i
$569$			6.87794e10i			0.656159i	0.944650	+	0.328080i	$0.106401\pi$
$569$			6.87794e10i			0.656159i	−0.944650	+	0.328080i	$0.893599\pi$
$570$	4.75372e10	−	6.01467e10i	0.450334	−	0.569786i
$571$	−1.03730e10			−0.0975795			−0.0487897	−	0.998809i	$-0.515536\pi$
$571$	−1.03730e10			−0.0975795			−0.0487897	+	0.998809i	$0.515536\pi$
$572$	1.92371e10	+	1.92371e10i	0.179703	+	0.179703i
$573$	2.94427e10	−	2.94427e10i	0.273123	−	0.273123i
$574$		−	1.75209e11i		−	1.61402i
$575$	2.45257e10	+	1.51134e10i	0.224362	+	0.138258i
$576$	2.00013e9			0.0181706
$577$	5.84784e10	+	5.84784e10i	0.527584	+	0.527584i	0.919851	−	0.392267i	$-0.128309\pi$
$577$	5.84784e10	+	5.84784e10i	0.527584	+	0.527584i	−0.392267	+	0.919851i	$0.628309\pi$
$578$	−1.01055e10	+	1.01055e10i	−0.0905410	+	0.0905410i
$579$		−	1.82967e10i		−	0.162802i
$580$	−2.61872e9	−	2.06972e9i	−0.0231407	−	0.0182894i
$581$	−1.26751e11			−1.11237
$582$	−2.43051e10	−	2.43051e10i	−0.211839	−	0.211839i
$583$	−2.00260e10	+	2.00260e10i	−0.173348	+	0.173348i
$584$			3.80784e10i			0.327361i
$585$	−2.74249e9	−	2.34208e10i	−0.0234165	−	0.199976i
$586$	1.11887e11			0.948829
$587$	2.36584e10	+	2.36584e10i	0.199266	+	0.199266i	0.799685	−	0.600420i	$-0.205000\pi$
$587$	2.36584e10	+	2.36584e10i	0.199266	+	0.199266i	−0.600420	+	0.799685i	$0.705000\pi$
$588$	−5.42612e10	+	5.42612e10i	−0.453921	+	0.453921i
$589$		−	3.53497e10i		−	0.293714i
$590$	−7.87742e10	+	9.22419e9i	−0.650094	+	0.0761237i
$591$	−1.47226e11			−1.20680
$592$	3.28749e10	+	3.28749e10i	0.267657	+	0.267657i
$593$	1.22246e11	−	1.22246e11i	0.988589	−	0.988589i	−0.0113464	−	0.999936i	$-0.503612\pi$
$593$	1.22246e11	−	1.22246e11i	0.988589	−	0.988589i	0.999936	+	0.0113464i	$0.00361175\pi$
$594$		−	3.42049e10i		−	0.274753i
$595$	−1.08697e11	+	1.37529e11i	−0.867261	+	1.09730i
$596$	−7.19945e10			−0.570577
$597$	−9.53208e9	−	9.53208e9i	−0.0750396	−	0.0750396i
$598$	−2.33399e10	+	2.33399e10i	−0.182513	+	0.182513i
$599$			9.59446e10i			0.745269i	0.927978	+	0.372635i	$0.121546\pi$
$599$			9.59446e10i			0.745269i	−0.927978	+	0.372635i	$0.878454\pi$
$600$	4.12135e10	−	9.78611e9i	0.318006	−	0.0755101i
$601$	1.94971e11			1.49442			0.747210	−	0.664588i	$-0.231393\pi$
$601$	1.94971e11			1.49442			0.747210	+	0.664588i	$0.231393\pi$
$602$	1.68544e11	+	1.68544e11i	1.28329	+	1.28329i
$603$	1.24803e10	−	1.24803e10i	0.0943964	−	0.0943964i
$604$		−	3.52326e9i		−	0.0264726i
$605$	9.09547e10	+	7.18866e10i	0.678897	+	0.536570i
$606$	−6.73736e10			−0.499573
$607$	−1.26277e11	−	1.26277e11i	−0.930188	−	0.930188i	0.0675290	−	0.997717i	$-0.478488\pi$
$607$	−1.26277e11	−	1.26277e11i	−0.930188	−	0.930188i	−0.997717	+	0.0675290i	$0.978488\pi$
$608$	1.89776e10	−	1.89776e10i	0.138876	−	0.138876i
$609$			1.15941e10i			0.0842882i
$610$	1.66122e10	+	1.41867e11i	0.119980	+	1.02462i
$611$	1.26963e11			0.910984
$612$	−6.52438e9	−	6.52438e9i	−0.0465086	−	0.0465086i
$613$	1.84169e11	−	1.84169e11i	1.30429	−	1.30429i	0.378826	−	0.925468i	$-0.376328\pi$
$613$	1.84169e11	−	1.84169e11i	1.30429	−	1.30429i	0.925468	−	0.378826i	$-0.123672\pi$
$614$		−	3.70951e10i		−	0.261001i
$615$	1.93986e11	−	2.27151e10i	1.35603	−	0.158786i
$616$	−2.88729e10			−0.200524
$617$	−1.20679e11	−	1.20679e11i	−0.832707	−	0.832707i	0.155180	−	0.987886i	$-0.450404\pi$
$617$	−1.20679e11	−	1.20679e11i	−0.832707	−	0.832707i	−0.987886	+	0.155180i	$0.950404\pi$
$618$	−4.20597e10	+	4.20597e10i	−0.288345	+	0.288345i
$619$			1.43750e11i			0.979143i	0.871963	+	0.489572i	$0.162847\pi$
$619$			1.43750e11i			0.979143i	−0.871963	+	0.489572i	$0.837153\pi$
$620$	1.21111e10	−	1.53237e10i	0.0819630	−	0.103704i
$621$	4.15000e10			0.279050
$622$	1.16089e11	+	1.16089e11i	0.775584	+	0.775584i
$623$	1.51305e10	−	1.51305e10i	0.100439	−	0.100439i
$624$			4.85339e10i			0.320116i
$625$	−1.36300e11	+	6.85961e10i	−0.893255	+	0.449551i
$626$	−3.24932e10			−0.211590
$627$	−4.11896e10	−	4.11896e10i	−0.266512	−	0.266512i
$628$	4.12963e10	−	4.12963e10i	0.265505	−	0.265505i
$629$		−	2.14475e11i		−	1.37017i
$630$	1.96342e10	+	1.55180e10i	0.124638	+	0.0985082i
$631$	−1.08715e11			−0.685760			−0.342880	−	0.939379i	$-0.611402\pi$
$631$	−1.08715e11			−0.685760			−0.342880	+	0.939379i	$0.611402\pi$
$632$	−3.14976e9	−	3.14976e9i	−0.0197428	−	0.0197428i
$633$	−2.21144e10	+	2.21144e10i	−0.137740	+	0.137740i
$634$		−	1.55043e10i		−	0.0959611i
$635$	−1.19741e9	−	1.02258e10i	−0.00736456	−	0.0628930i
$636$	−5.05242e10			−0.308796
$637$	2.23952e11	+	2.23952e11i	1.36018	+	1.36018i
$638$	−1.79335e9	+	1.79335e9i	−0.0108239	+	0.0108239i
$639$			2.48964e10i			0.149325i
$640$	1.47285e10	−	1.72465e9i	0.0877885	−	0.0102797i
$641$	−3.25454e11			−1.92778			−0.963890	−	0.266299i	$-0.914199\pi$
$641$	−3.25454e11			−1.92778			−0.963890	+	0.266299i	$0.914199\pi$
$642$	−5.18933e10	−	5.18933e10i	−0.305472	−	0.305472i
$643$	4.11926e10	−	4.11926e10i	0.240977	−	0.240977i	−0.576278	−	0.817254i	$-0.695495\pi$
$643$	4.11926e10	−	4.11926e10i	0.240977	−	0.240977i	0.817254	+	0.576278i	$0.195495\pi$
$644$		−	3.50307e10i		−	0.203660i
$645$	−1.64755e11	+	2.08457e11i	−0.951918	+	1.20442i
$646$	−1.23809e11			−0.710924
$647$	−8.13749e10	−	8.13749e10i	−0.464380	−	0.464380i	0.435708	−	0.900088i	$-0.356498\pi$
$647$	−8.13749e10	−	8.13749e10i	−0.464380	−	0.464380i	−0.900088	+	0.435708i	$0.856498\pi$
$648$	3.67408e10	−	3.67408e10i	0.208376	−	0.208376i
$649$			6.02630e10i			0.339682i
$650$	−4.03901e10	−	1.70100e11i	−0.226267	−	0.952908i
$651$	−6.78438e10			−0.377734
$652$	3.02949e10	+	3.02949e10i	0.167640	+	0.167640i
$653$	1.29147e11	−	1.29147e11i	0.710285	−	0.710285i	−0.256310	−	0.966595i	$-0.582507\pi$
$653$	1.29147e11	−	1.29147e11i	0.710285	−	0.710285i	0.966595	+	0.256310i	$0.0825067\pi$
$654$		−	7.90899e10i		−	0.432325i
$655$	−1.88064e11	−	1.48638e11i	−1.02174	−	0.807539i
$656$	6.83741e10			0.369212
$657$	−1.77328e10	−	1.77328e10i	−0.0951733	−	0.0951733i
$658$	−9.52788e10	+	9.52788e10i	−0.508268	+	0.508268i
$659$			2.74018e10i			0.145291i	0.997358	+	0.0726453i	$0.0231441\pi$
$659$			2.74018e10i			0.145291i	−0.997358	+	0.0726453i	$0.976856\pi$
$660$	−3.74323e9	−	3.19671e10i	−0.0197275	−	0.168472i
$661$	−1.19547e11			−0.626228			−0.313114	−	0.949716i	$-0.601372\pi$
$661$	−1.19547e11			−0.626228			−0.313114	+	0.949716i	$0.601372\pi$
$662$	6.10457e10	+	6.10457e10i	0.317851	+	0.317851i
$663$	1.58317e11	−	1.58317e11i	0.819355	−	0.819355i
$664$		−	4.94637e10i		−	0.254457i
$665$	3.33531e11	−	3.90553e10i	1.70549	−	0.199707i
$666$	−3.06192e10			−0.155631
$667$	−2.17582e9	−	2.17582e9i	−0.0109931	−	0.0109931i
$668$	6.98158e10	−	6.98158e10i	0.350629	−	0.350629i
$669$		−	1.26021e11i		−	0.629129i
$670$	8.11404e10	−	1.02663e11i	0.402660	−	0.509466i
$671$	1.08530e11			0.535377
$672$	−3.64222e10	−	3.64222e10i	−0.178603	−	0.178603i
$673$	−2.17592e11	+	2.17592e11i	−1.06068	+	1.06068i	−0.0626416	+	0.998036i	$0.519953\pi$
$673$	−2.17592e11	+	2.17592e11i	−1.06068	+	1.06068i	−0.998036	+	0.0626416i	$0.980047\pi$
$674$			3.95860e10i			0.191824i
$675$	−1.15317e11	+	1.87133e11i	−0.555492	+	0.901438i
$676$	9.58998e10			0.459231
$677$	1.34337e11	+	1.34337e11i	0.639503	+	0.639503i	0.950433	−	0.310930i	$-0.100640\pi$
$677$	1.34337e11	+	1.34337e11i	0.639503	+	0.639503i	−0.310930	+	0.950433i	$0.600640\pi$
$678$	−9.93297e10	+	9.93297e10i	−0.470068	+	0.470068i
$679$		−	1.50561e11i		−	0.708327i
$680$	−5.36697e10	−	4.24182e10i	−0.251012	−	0.198388i
$681$	2.85661e11			1.32820
$682$	−1.04939e10	−	1.04939e10i	−0.0485066	−	0.0485066i
$683$	−2.62510e11	+	2.62510e11i	−1.20632	+	1.20632i	−0.234110	+	0.972210i	$0.575218\pi$
$683$	−2.62510e11	+	2.62510e11i	−1.20632	+	1.20632i	−0.972210	+	0.234110i	$0.924782\pi$
$684$			1.76755e10i			0.0807507i
$685$	1.50893e9	+	1.28862e10i	0.00685339	+	0.0585277i
$686$	−9.40976e10			−0.424895
$687$	2.59622e11	+	2.59622e11i	1.16551	+	1.16551i
$688$	−6.57728e10	+	6.57728e10i	−0.293557	+	0.293557i
$689$			2.08528e11i			0.925310i
$690$	3.87848e10	−	4.54157e9i	0.171106	−	0.0200359i
$691$	3.13746e11			1.37615			0.688075	−	0.725639i	$-0.258456\pi$
$691$	3.13746e11			1.37615			0.688075	+	0.725639i	$0.258456\pi$
$692$	−8.21319e10	−	8.21319e10i	−0.358169	−	0.358169i
$693$	1.34459e10	−	1.34459e10i	0.0582982	−	0.0582982i
$694$			4.21692e10i			0.181785i
$695$	1.55139e11	−	1.96290e11i	0.664940	−	0.841318i
$696$	−4.52450e9			−0.0192812
$697$	−2.23035e11	−	2.23035e11i	−0.945021	−	0.945021i
$698$	1.97572e11	−	1.97572e11i	0.832346	−	0.832346i
$699$			2.75534e11i			1.15416i
$700$	1.57962e11	+	9.73406e10i	0.657901	+	0.405417i
$701$	2.56197e11			1.06097			0.530483	−	0.847696i	$-0.322011\pi$
$701$	2.56197e11			1.06097			0.530483	+	0.847696i	$0.322011\pi$
$702$	−1.78086e11	−	1.78086e11i	−0.733298	−	0.733298i
$703$	−2.90521e11	+	2.90521e11i	−1.18948	+	1.18948i
$704$		−	1.12674e10i		−	0.0458705i
$705$	−1.17842e11	−	9.31370e10i	−0.477027	−	0.377021i
$706$	2.00134e11			0.805566
$707$	−2.08677e11	−	2.08677e11i	−0.835213	−	0.835213i
$708$	−7.60198e10	+	7.60198e10i	−0.302548	+	0.302548i
$709$		−	1.51234e10i		−	0.0598499i	−0.999552	−	0.0299250i	$-0.990473\pi$
$709$		−	1.51234e10i		−	0.0598499i	0.999552	−	0.0299250i	$-0.00952683\pi$
$710$	2.14675e10	+	1.83331e11i	0.0844787	+	0.721445i
$711$	2.93364e9			0.0114796
$712$	5.90457e9	+	5.90457e9i	0.0229757	+	0.0229757i
$713$	1.27320e10	−	1.27320e10i	0.0492651	−	0.0492651i
$714$			2.37617e11i			0.914290i
$715$	−1.31937e11	+	1.54494e10i	−0.504828	+	0.0591136i
$716$	−1.20458e11			−0.458337
$717$	−2.42491e11	−	2.42491e11i	−0.917527	−	0.917527i
$718$	1.84223e11	−	1.84223e11i	0.693181	−	0.693181i
$719$		−	4.20879e11i		−	1.57486i	−0.616404	−	0.787430i	$-0.711411\pi$
$719$		−	4.20879e11i		−	1.57486i	0.616404	−	0.787430i	$-0.288589\pi$
$720$	−6.05577e9	+	7.66208e9i	−0.0225340	+	0.0285113i
$721$	−2.60544e11			−0.964140
$722$	3.18399e10	+	3.18399e10i	0.117172	+	0.117172i
$723$	3.08430e11	−	3.08430e11i	1.12877	−	1.12877i
$724$		−	5.24215e10i		−	0.190790i
$725$	1.58573e10	−	3.76530e9i	0.0573954	−	0.0136285i
$726$	1.57147e11			0.565667
$727$	2.08188e11	+	2.08188e11i	0.745277	+	0.745277i	0.973588	−	0.228312i	$-0.0733205\pi$
$727$	2.08188e11	+	2.08188e11i	0.745277	+	0.745277i	−0.228312	+	0.973588i	$0.573320\pi$
$728$	−1.50325e11	+	1.50325e11i	−0.535186	+	0.535186i
$729$			3.10681e11i			1.10003i
$730$	−1.45870e11	−	1.15289e11i	−0.513660	−	0.405974i
$731$	4.29099e11			1.50275
$732$	1.36907e11	+	1.36907e11i	0.476849	+	0.476849i
$733$	−2.48791e11	+	2.48791e11i	−0.861826	+	0.861826i	−0.991550	−	0.129725i	$-0.958591\pi$
$733$	−2.48791e11	+	2.48791e11i	−0.861826	+	0.861826i	0.129725	+	0.991550i	$0.458591\pi$
$734$			1.51584e11i			0.522239i
$735$	−4.35774e10	−	3.72149e11i	−0.149318	−	1.27517i
$736$	1.36705e10			0.0465878
$737$	−7.03058e10	−	7.03058e10i	−0.238298	−	0.238298i
$738$	−3.18412e10	+	3.18412e10i	−0.107341	+	0.107341i
$739$			1.15406e11i			0.386946i	0.981106	+	0.193473i	$0.0619752\pi$
$739$			1.15406e11i			0.386946i	−0.981106	+	0.193473i	$0.938025\pi$
$740$	−2.25472e11	+	2.64020e10i	−0.751910	+	0.0880461i
$741$	−4.28902e11			−1.42261
$742$	−1.56489e11	−	1.56489e11i	−0.516261	−	0.516261i
$743$	1.60556e11	−	1.60556e11i	0.526833	−	0.526833i	−0.392794	−	0.919627i	$-0.628491\pi$
$743$	1.60556e11	−	1.60556e11i	0.526833	−	0.526833i	0.919627	+	0.392794i	$0.128491\pi$
$744$		−	2.64755e10i		−	0.0864077i
$745$	2.17977e11	−	2.75796e11i	0.707596	−	0.895289i
$746$	−9.68143e10			−0.312597
$747$	2.30348e10	+	2.30348e10i	0.0739780	+	0.0739780i
$748$	−3.67541e10	+	3.67541e10i	−0.117408	+	0.117408i
$749$		−	3.21459e11i		−	1.02141i
$750$	−8.72932e10	+	1.87510e11i	−0.275890	+	0.592624i
$751$	−5.98277e10			−0.188080			−0.0940400	−	0.995568i	$-0.529978\pi$
$751$	−5.98277e10			−0.188080			−0.0940400	+	0.995568i	$0.529978\pi$
$752$	−3.71818e10	−	3.71818e10i	−0.116268	−	0.116268i
$753$	−2.12774e11	+	2.12774e11i	−0.661819	+	0.661819i
$754$			1.86739e10i			0.0577763i
$755$	1.34969e10	+	1.06673e10i	0.0415379	+	0.0328297i
$756$	2.67288e11			0.818262
$757$	−2.88999e11	−	2.88999e11i	−0.880060	−	0.880060i	0.113480	−	0.993540i	$-0.463800\pi$
$757$	−2.88999e11	−	2.88999e11i	−0.880060	−	0.880060i	−0.993540	+	0.113480i	$0.963800\pi$
$758$	−3.41752e10	+	3.41752e10i	−0.103522	+	0.103522i
$759$		−	2.96708e10i		−	0.0894050i
$760$	1.52410e10	+	1.30158e11i	0.0456836	+	0.390136i
$761$	−1.15311e11			−0.343819			−0.171910	−	0.985113i	$-0.554994\pi$
$761$	−1.15311e11			−0.343819			−0.171910	+	0.985113i	$0.554994\pi$
$762$	−9.86825e9	−	9.86825e9i	−0.0292698	−	0.0292698i
$763$	2.44966e11	−	2.44966e11i	0.722783	−	0.722783i
$764$			7.11748e10i			0.208907i
$765$	4.47473e10	−	5.23975e9i	0.130654	−	0.0152991i
$766$	4.29450e11			1.24738
$767$	3.13755e11	+	3.13755e11i	0.906587	+	0.906587i
$768$	1.42135e10	−	1.42135e10i	0.0408560	−	0.0408560i
$769$		−	1.71633e11i		−	0.490791i	−0.969423	−	0.245395i	$-0.921082\pi$
$769$		−	1.71633e11i		−	0.490791i	0.969423	−	0.245395i	$-0.0789178\pi$
$770$	8.74181e10	−	1.10606e11i	0.248679	−	0.314641i
$771$	−1.88283e11			−0.532835
$772$	2.21153e10	+	2.21153e10i	0.0622621	+	0.0622621i
$773$	−3.60143e11	+	3.60143e11i	−1.00869	+	1.00869i	−0.00872501	+	0.999962i	$0.502777\pi$
$773$	−3.60143e11	+	3.60143e11i	−1.00869	+	1.00869i	−0.999962	+	0.00872501i	$0.997223\pi$
$774$		−	6.12597e10i		−	0.170691i
$775$	2.20330e10	+	9.27905e10i	0.0610754	+	0.257215i
$776$	5.87553e10			0.162032
$777$	5.57572e11	+	5.57572e11i	1.52974	+	1.52974i
$778$	−7.33273e9	+	7.33273e9i	−0.0200146	+	0.0200146i
$779$			6.04232e11i			1.64079i
$780$	−1.85923e11	−	1.46946e11i	−0.502291	−	0.396989i
$781$	1.40250e11			0.376963
$782$	−4.45928e10	−	4.45928e10i	−0.119244	−	0.119244i
$783$	1.66018e10	−	1.66018e10i	0.0441679	−	0.0441679i
$784$		−	1.31171e11i		−	0.347196i
$785$	3.31653e10	+	2.83230e11i	0.0873383	+	0.745866i
$786$	−3.24929e11			−0.851330
$787$	3.81822e11	+	3.81822e11i	0.995318	+	0.995318i	0.999989	−	0.00467136i	$-0.00148694\pi$
$787$	3.81822e11	+	3.81822e11i	0.995318	+	0.995318i	−0.00467136	+	0.999989i	$0.501487\pi$
$788$	1.77953e11	−	1.77953e11i	0.461530	−	0.461530i
$789$		−	1.98632e11i		−	0.512557i
$790$	2.16026e10	−	2.52959e9i	0.0554622	−	0.00649444i
$791$	−6.15310e11			−1.57177
$792$	5.24714e9	+	5.24714e9i	0.0133359	+	0.0133359i
$793$	5.65054e11	−	5.65054e11i	1.42888	−	1.42888i
$794$		−	8.38543e10i		−	0.210981i
$795$	1.52972e11	−	1.93548e11i	0.382950	−	0.484529i
$796$	2.30429e10			0.0573964
$797$	4.32433e11	+	4.32433e11i	1.07173	+	1.07173i	0.997220	+	0.0745090i	$0.0237389\pi$
$797$	4.32433e11	+	4.32433e11i	1.07173	+	1.07173i	0.0745090	+	0.997220i	$0.476261\pi$
$798$	3.21869e11	−	3.21869e11i	0.793719	−	0.793719i
$799$			2.42573e11i			0.595189i
$800$	−3.79864e10	+	6.16434e10i	−0.0927403	+	0.150497i
$801$	−5.49941e9			−0.0133594
$802$	−1.41489e11	−	1.41489e11i	−0.342000	−	0.342000i
$803$	−9.98949e10	+	9.98949e10i	−0.240260	+	0.240260i
$804$		−	1.77377e11i		−	0.424495i
$805$	1.34195e11	+	1.06062e11i	0.319561	+	0.252567i
$806$	−1.09272e11			−0.258922
$807$	−3.13210e11	−	3.13210e11i	−0.738485	−	0.738485i
$808$	8.14346e10	−	8.14346e10i	0.191057	−	0.191057i
$809$		−	4.04427e11i		−	0.944160i	−0.881556	−	0.472080i	$-0.843503\pi$
$809$		−	4.04427e11i		−	0.944160i	0.881556	−	0.472080i	$-0.156497\pi$
$810$	2.95067e10	+	2.51986e11i	0.0685457	+	0.585377i
$811$	−6.23463e11			−1.44121			−0.720605	−	0.693346i	$-0.756136\pi$
$811$	−6.23463e11			−1.44121			−0.720605	+	0.693346i	$0.756136\pi$
$812$	−1.40138e10	−	1.40138e10i	−0.0322353	−	0.0322353i
$813$	−8.49475e10	+	8.49475e10i	−0.194441	+	0.194441i
$814$			1.72488e11i			0.392882i
$815$	−2.07777e11	+	2.43299e10i	−0.470941	+	0.0551456i
$816$	−9.27281e10			−0.209147
$817$	−5.81245e11	−	5.81245e11i	−1.30458	−	1.30458i
$818$	−1.74602e10	+	1.74602e10i	−0.0389975	+	0.0389975i
$819$		−	1.40010e11i		−	0.311188i
$820$	−2.07015e11	+	2.61927e11i	−0.457875	+	0.579328i
$821$	3.67266e11			0.808366			0.404183	−	0.914678i	$-0.367556\pi$
$821$	3.67266e11			0.808366			0.404183	+	0.914678i	$0.367556\pi$
$822$	1.24356e10	+	1.24356e10i	0.0272382	+	0.0272382i
$823$	1.17460e11	−	1.17460e11i	0.256030	−	0.256030i	−0.567407	−	0.823437i	$-0.692053\pi$
$823$	1.17460e11	−	1.17460e11i	0.256030	−	0.256030i	0.823437	+	0.567407i	$0.192053\pi$
$824$		−	1.01675e11i		−	0.220550i
$825$	1.33793e11	+	8.24468e10i	0.288813	+	0.177975i
$826$	−4.70914e11			−1.01163
$827$	−5.29740e11	−	5.29740e11i	−1.13251	−	1.13251i	−0.989759	−	0.142748i	$-0.954406\pi$
$827$	−5.29740e11	−	5.29740e11i	−1.13251	−	1.13251i	−0.142748	−	0.989759i	$-0.545594\pi$
$828$	−6.36622e9	+	6.36622e9i	−0.0135444	+	0.0135444i
$829$			2.39704e11i			0.507525i	0.967267	+	0.253762i	$0.0816681\pi$
$829$			2.39704e11i			0.507525i	−0.967267	+	0.253762i	$0.918332\pi$
$830$	1.89485e11	+	1.49761e11i	0.399267	+	0.315563i
$831$	−1.77132e11			−0.371444
$832$	−5.86631e10	−	5.86631e10i	−0.122425	−	0.122425i
$833$	−4.27878e11	+	4.27878e11i	−0.888669	+	0.888669i
$834$		−	3.39142e11i		−	0.700998i
$835$	5.60694e10	+	4.78831e11i	0.115340	+	0.984999i
$836$	9.95720e10			0.203851
$837$	9.71467e10	+	9.71467e10i	0.197937	+	0.197937i
$838$	−2.41954e11	+	2.41954e11i	−0.490634	+	0.490634i
$839$		−	5.22857e11i		−	1.05520i	−0.849493	−	0.527601i	$-0.823092\pi$
$839$		−	5.22857e11i		−	1.05520i	0.849493	−	0.527601i	$-0.176908\pi$
$840$	2.49801e11	−	2.92508e10i	0.501738	−	0.0587517i
$841$	4.98506e11			0.996520
$842$	−1.42272e11	−	1.42272e11i	−0.283055	−	0.283055i
$843$	4.92082e11	−	4.92082e11i	0.974378	−	0.974378i
$844$		−	5.34594e10i		−	0.105355i
$845$	−2.90355e11	+	3.67372e11i	−0.569511	+	0.720576i
$846$	3.46305e10			0.0676048
$847$	4.86735e11	+	4.86735e11i	0.945712	+	0.945712i
$848$	6.10687e10	−	6.10687e10i	0.118096	−	0.118096i
$849$		−	4.88258e11i		−	0.939764i
$850$	3.24990e11	−	7.71686e10i	0.622579	−	0.147831i
$851$	−2.09276e11			−0.399025
$852$	1.76921e11	+	1.76921e11i	0.335754	+	0.335754i
$853$	−2.94110e11	+	2.94110e11i	−0.555537	+	0.555537i	−0.928034	−	0.372496i	$-0.878502\pi$
$853$	−2.94110e11	+	2.94110e11i	−0.555537	+	0.555537i	0.372496	+	0.928034i	$0.378502\pi$
$854$			8.48087e11i			1.59444i
$855$	−6.77110e10	−	5.35158e10i	−0.126705	−	0.100142i
$856$	1.25447e11			0.233650
$857$	−1.69558e11	−	1.69558e11i	−0.314336	−	0.314336i	0.532251	−	0.846587i	$-0.321346\pi$
$857$	−1.69558e11	−	1.69558e11i	−0.314336	−	0.314336i	−0.846587	+	0.532251i	$0.821346\pi$
$858$	−1.27324e11	+	1.27324e11i	−0.234942	+	0.234942i
$859$		−	3.81187e11i		−	0.700109i	−0.936729	−	0.350055i	$-0.886163\pi$
$859$		−	3.81187e11i		−	0.700109i	0.936729	−	0.350055i	$-0.113837\pi$
$860$	−5.28224e10	−	4.51102e11i	−0.0965661	−	0.824671i
$861$	1.15965e12			2.11016
$862$	1.70174e11	+	1.70174e11i	0.308221	+	0.308221i
$863$	8.42734e10	−	8.42734e10i	0.151931	−	0.151931i	−0.627049	−	0.778980i	$-0.715737\pi$
$863$	8.42734e10	−	8.42734e10i	0.151931	−	0.151931i	0.778980	+	0.627049i	$0.215737\pi$
$864$			1.04307e11i			0.187180i
$865$	5.63300e11	−	6.59605e10i	1.00618	−	0.117820i
$866$	3.59693e11			0.639529
$867$	−6.68848e10	−	6.68848e10i	−0.118373	−	0.118373i
$868$	8.20029e10	−	8.20029e10i	0.144461	−	0.144461i
$869$		−	1.65262e10i		−	0.0289797i
$870$	1.36988e10	−	1.73324e10i	0.0239114	−	0.0302539i
$871$	−7.32085e11			−1.27200
$872$	9.55962e10	+	9.55962e10i	0.165339	+	0.165339i
$873$	−2.73618e10	+	2.73618e10i	−0.0471073	+	0.0471073i
$874$			1.20808e11i			0.207038i
$875$	−8.51151e11	+	3.10402e11i	−1.45203	+	0.529533i
$876$	−2.52028e11			−0.427989
$877$	3.72176e10	+	3.72176e10i	0.0629144	+	0.0629144i	0.737864	−	0.674950i	$-0.235835\pi$
$877$	3.72176e10	+	3.72176e10i	0.0629144	+	0.0629144i	−0.674950	+	0.737864i	$0.735835\pi$
$878$	−1.17523e11	+	1.17523e11i	−0.197763	+	0.197763i
$879$			7.40541e11i			1.24049i
$880$	4.31631e10	+	3.41142e10i	0.0719751	+	0.0568859i
$881$	−4.91908e10			−0.0816545			−0.0408273	−	0.999166i	$-0.512999\pi$
$881$	−4.91908e10			−0.0816545			−0.0408273	+	0.999166i	$0.512999\pi$
$882$	6.10854e10	+	6.10854e10i	0.100940	+	0.100940i
$883$	4.82360e11	−	4.82360e11i	0.793467	−	0.793467i	−0.188589	−	0.982056i	$-0.560391\pi$
$883$	4.82360e11	−	4.82360e11i	0.793467	−	0.793467i	0.982056	+	0.188589i	$0.0603914\pi$
$884$			3.82715e11i			0.626710i
$885$	−6.10518e10	−	5.21380e11i	−0.0995235	−	0.849927i
$886$	−2.87925e11			−0.467245
$887$	7.58872e11	+	7.58872e11i	1.22595	+	1.22595i	0.965481	+	0.260472i	$0.0838782\pi$
$887$	7.58872e11	+	7.58872e11i	1.22595	+	1.22595i	0.260472	+	0.965481i	$0.416122\pi$
$888$	−2.17588e11	+	2.17588e11i	−0.349932	+	0.349932i
$889$		−	6.11301e10i		−	0.0978697i
$890$	−4.04964e10	+	4.74198e9i	−0.0645440	+	0.00755788i
$891$	1.92772e11			0.305867
$892$	1.52322e11	+	1.52322e11i	0.240605	+	0.240605i
$893$	3.28582e11	−	3.28582e11i	0.516699	−	0.516699i
$894$		−	4.76508e11i		−	0.745968i
$895$	3.64710e11	−	4.61451e11i	0.568402	−	0.719173i
$896$	8.80472e10			0.136610
$897$	−1.54479e11	−	1.54479e11i	−0.238616	−	0.238616i
$898$	−2.24981e11	+	2.24981e11i	−0.345972	+	0.345972i
$899$		−	1.01867e10i		−	0.0155953i
$900$	−1.10169e10	−	4.63968e10i	−0.0167914	−	0.0707160i
$901$	−3.98410e11			−0.604548
$902$	1.79373e11	+	1.79373e11i	0.270975	+	0.270975i
$903$	−1.11553e12	+	1.11553e12i	−1.67777	+	1.67777i
$904$		−	2.40120e11i		−	0.359546i
$905$	2.00816e11	+	1.58716e11i	0.299367	+	0.236606i
$906$	2.33193e10			0.0346100
$907$	−8.25250e11	−	8.25250e11i	−1.21943	−	1.21943i	−0.967832	−	0.251597i	$-0.919044\pi$
$907$	−8.25250e11	−	8.25250e11i	−1.21943	−	1.21943i	−0.251597	−	0.967832i	$-0.580956\pi$
$908$	−3.45279e11	+	3.45279e11i	−0.507957	+	0.507957i
$909$			7.58468e10i			0.111092i
$910$	−1.20726e11	−	1.03100e12i	−0.176050	−	1.50346i
$911$	5.86650e11			0.851737			0.425869	−	0.904785i	$-0.359969\pi$
$911$	5.86650e11			0.851737			0.425869	+	0.904785i	$0.359969\pi$
$912$	1.25607e11	+	1.25607e11i	0.181566	+	0.181566i
$913$	1.29763e11	−	1.29763e11i	0.186753	−	0.186753i
$914$		−	8.51548e11i		−	1.22018i
$915$	−9.38973e11	+	1.09951e11i	−1.33958	+	0.156860i
$916$	−6.27612e11			−0.891475
$917$	−1.00641e12	−	1.00641e12i	−1.42330	−	1.42330i
$918$	3.40248e11	−	3.40248e11i	0.479098	−	0.479098i
$919$			1.27566e12i			1.78843i	0.447640	+	0.894214i	$0.352265\pi$
$919$			1.27566e12i			1.78843i	−0.447640	+	0.894214i	$0.647735\pi$
$920$	−4.13899e10	+	5.23688e10i	−0.0577755	+	0.0731006i
$921$	2.45520e11			0.341231
$922$	−2.24556e10	−	2.24556e10i	−0.0310743	−	0.0310743i
$923$	7.30203e11	−	7.30203e11i	1.00609	−	1.00609i
$924$		−	1.91100e11i		−	0.262164i
$925$	5.81519e11	−	9.43674e11i	0.794322	−	1.28901i
$926$	2.94765e11			0.400896
$927$	4.73493e10	+	4.73493e10i	0.0641202	+	0.0641202i
$928$	5.46877e9	−	5.46877e9i	0.00737391	−	0.00737391i
$929$			1.11916e12i			1.50255i	0.659991	+	0.751274i	$0.270560\pi$
$929$			1.11916e12i			1.50255i	−0.659991	+	0.751274i	$0.729440\pi$
$930$	1.01422e11	+	8.01596e10i	0.135582	+	0.107158i
$931$	1.15918e12			1.54295
$932$	−3.33039e11	−	3.33039e11i	−0.441399	−	0.441399i
$933$	−7.68353e11	+	7.68353e11i	−1.01399	+	1.01399i
$934$			1.90857e11i			0.250796i
$935$	−2.95174e10	−	2.52077e11i	−0.0386217	−	0.329828i
$936$	5.46378e10			0.0711852
$937$	3.48571e11	+	3.48571e11i	0.452202	+	0.452202i	0.896085	−	0.443883i	$-0.146399\pi$
$937$	3.48571e11	+	3.48571e11i	0.452202	+	0.452202i	−0.443883	+	0.896085i	$0.646399\pi$
$938$	5.49391e11	−	5.49391e11i	0.709693	−	0.709693i
$939$		−	2.15061e11i		−	0.276631i
$940$	2.55011e11	−	2.98609e10i	0.326623	−	0.0382465i
$941$	3.10729e11			0.396299			0.198150	−	0.980172i	$-0.436507\pi$
$941$	3.10729e11			0.396299			0.198150	+	0.980172i	$0.436507\pi$
$942$	2.73327e11	+	2.73327e11i	0.347119	+	0.347119i
$943$	−2.17628e11	+	2.17628e11i	−0.275213	+	0.275213i
$944$		−	1.83771e11i		−	0.231413i
$945$	−8.09265e11	+	1.02393e12i	−1.01476	+	1.28393i
$946$	−3.45097e11			−0.430900
$947$	−4.81109e11	−	4.81109e11i	−0.598197	−	0.598197i	0.341636	−	0.939832i	$-0.389019\pi$
$947$	−4.81109e11	−	4.81109e11i	−0.598197	−	0.598197i	−0.939832	+	0.341636i	$0.889019\pi$
$948$	2.08472e10	−	2.08472e10i	0.0258116	−	0.0258116i
$949$			1.04019e12i			1.28247i
$950$	−5.44753e11	−	3.35692e11i	−0.668813	−	0.412142i
$951$	1.02618e11			0.125459
$952$	−2.87208e11	−	2.87208e11i	−0.349662	−	0.349662i
$953$	2.19961e11	−	2.19961e11i	0.266670	−	0.266670i	−0.561087	−	0.827757i	$-0.689617\pi$
$953$	2.19961e11	−	2.19961e11i	0.266670	−	0.266670i	0.827757	+	0.561087i	$0.189617\pi$
$954$			5.68784e10i			0.0686679i
$955$	−2.72656e11	−	2.15495e11i	−0.327794	−	0.259074i
$956$	5.86199e11			0.701800
$957$	−1.18696e10	−	1.18696e10i	−0.0141510	−	0.0141510i
$958$	−6.46624e11	+	6.46624e11i	−0.767697	+	0.767697i
$959$			7.70338e10i			0.0910767i
$960$	1.14149e10	+	9.74829e10i	0.0134396	+	0.114774i
$961$	−7.93283e11			−0.930110
$962$	8.98049e11	+	8.98049e11i	1.04858	+	1.04858i
$963$	−5.84196e10	+	5.84196e10i	−0.0679287	+	0.0679287i
$964$			7.45601e11i			0.863373i
$965$	−1.51677e11	+	1.77609e10i	−0.174909	+	0.0204812i
$966$	2.31857e11			0.266263
$967$	6.94014e11	+	6.94014e11i	0.793711	+	0.793711i	0.982095	−	0.188384i	$-0.0603251\pi$
$967$	6.94014e11	+	6.94014e11i	0.793711	+	0.793711i	−0.188384	+	0.982095i	$0.560325\pi$
$968$	−1.89945e11	+	1.89945e11i	−0.216334	+	0.216334i
$969$		−	8.19453e11i		−	0.929456i
$970$	−1.77893e11	+	2.25079e11i	−0.200942	+	0.254243i
$971$	1.29419e12			1.45587			0.727935	−	0.685646i	$-0.240480\pi$
$971$	1.29419e12			1.45587			0.727935	+	0.685646i	$0.240480\pi$
$972$	−9.09850e10	−	9.09850e10i	−0.101931	−	0.101931i
$973$	1.05043e12	−	1.05043e12i	1.17197	−	1.17197i
$974$		−	1.26902e12i		−	1.41005i
$975$	1.12584e12	−	2.67328e11i	1.24582	−	0.295819i
$976$	−3.30960e11			−0.364733
$977$	2.00533e11	+	2.00533e11i	0.220093	+	0.220093i	0.808538	−	0.588444i	$-0.200259\pi$
$977$	2.00533e11	+	2.00533e11i	0.220093	+	0.220093i	−0.588444	+	0.808538i	$0.700259\pi$
$978$	−2.00512e11	+	2.00512e11i	−0.219172	+	0.219172i
$979$			3.09801e10i			0.0337250i
$980$	5.02490e11	+	3.97146e11i	0.544783	+	0.430572i
$981$	−8.90367e10			−0.0961375
$982$	−4.80729e11	−	4.80729e11i	−0.516957	−	0.516957i
$983$	4.14637e11	−	4.14637e11i	0.444072	−	0.444072i	−0.449306	−	0.893378i	$-0.648329\pi$
$983$	4.14637e11	−	4.14637e11i	0.444072	−	0.444072i	0.893378	+	0.449306i	$0.148329\pi$
$984$			4.52545e11i			0.482705i
$985$	1.42915e11	+	1.22049e12i	0.151821	+	1.29655i
$986$	−3.56780e10			−0.0377479
$987$	−6.30619e11	−	6.30619e11i	−0.664505	−	0.664505i
$988$	5.18415e11	−	5.18415e11i	0.544064	−	0.544064i
$989$		−	4.18698e11i		−	0.437638i
$990$	−3.59874e10	+	4.21400e9i	−0.0374636	+	0.00438686i
$991$	−6.51779e11			−0.675780			−0.337890	−	0.941186i	$-0.609713\pi$
$991$	−6.51779e11			−0.675780			−0.337890	+	0.941186i	$0.609713\pi$
$992$	3.20010e10	+	3.20010e10i	0.0330459	+	0.0330459i
$993$	−4.04041e11	+	4.04041e11i	−0.415555	+	0.415555i
$994$			1.09596e12i			1.12266i
$995$	−6.97667e10	+	8.82725e10i	−0.0711796	+	0.0900603i
$996$	3.27384e11			0.332675
$997$	−6.71342e11	−	6.71342e11i	−0.679459	−	0.679459i	0.280419	−	0.959878i	$-0.409527\pi$
$997$	−6.71342e11	−	6.71342e11i	−0.679459	−	0.679459i	−0.959878	+	0.280419i	$0.909527\pi$
$998$	−8.69991e11	+	8.69991e11i	−0.876986	+	0.876986i
$999$		−	1.59680e12i		−	1.60320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.9.c.a.7.2	yes	4
3.2	odd	2		90.9.g.b.37.2		4
4.3	odd	2		80.9.p.b.17.1		4
5.2	odd	4		50.9.c.e.43.1		4
5.3	odd	4	inner	10.9.c.a.3.2	✓	4
5.4	even	2		50.9.c.e.7.1		4
15.8	even	4		90.9.g.b.73.2		4
20.3	even	4		80.9.p.b.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.9.c.a.3.2	✓	4	5.3	odd	4	inner
10.9.c.a.7.2	yes	4	1.1	even	1	trivial
50.9.c.e.7.1		4	5.4	even	2
50.9.c.e.43.1		4	5.2	odd	4
80.9.p.b.17.1		4	4.3	odd	2
80.9.p.b.33.1		4	20.3	even	4
90.9.g.b.37.2		4	3.2	odd	2
90.9.g.b.73.2		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

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

\(f(q)\)	\(=\)	\(q+(-8.00000 - 8.00000i) q^{2} +(52.9493 - 52.9493i) q^{3} +128.000i q^{4} +(-490.341 - 387.544i) q^{5} -847.189 q^{6} +(-2624.01 - 2624.01i) q^{7} +(1024.00 - 1024.00i) q^{8} +953.736i q^{9} +(822.379 + 7023.08i) q^{10} +5372.73 q^{11} +(6777.51 + 6777.51i) q^{12} +(27972.7 - 27972.7i) q^{13} +41984.2i q^{14} +(-46483.4 + 5443.05i) q^{15} -16384.0 q^{16} +(53444.2 + 53444.2i) q^{17} +(7629.89 - 7629.89i) q^{18} -144788. i q^{19} +(49605.6 - 62763.7i) q^{20} -277879. q^{21} +(-42981.8 - 42981.8i) q^{22} +(52148.7 - 52148.7i) q^{23} -108440. i q^{24} +(90244.3 + 380058. i) q^{25} -447564. q^{26} +(397900. + 397900. i) q^{27} +(335873. - 335873. i) q^{28} -41723.4i q^{29} +(415412. + 328323. i) q^{30} +244148. q^{31} +(131072. + 131072. i) q^{32} +(284482. - 284482. i) q^{33} -855108. i q^{34} +(269741. + 2.30358e6i) q^{35} -122078. q^{36} +(-2.00653e6 - 2.00653e6i) q^{37} +(-1.15830e6 + 1.15830e6i) q^{38} -2.96228e6i q^{39} +(-898955. + 105264. i) q^{40} -4.17322e6 q^{41} +(2.22303e6 + 2.22303e6i) q^{42} +(4.01446e6 - 4.01446e6i) q^{43} +687709. i q^{44} +(369615. - 467656. i) q^{45} -834380. q^{46} +(2.26940e6 + 2.26940e6i) q^{47} +(-867522. + 867522. i) q^{48} +8.00606e6i q^{49} +(2.31851e6 - 3.76242e6i) q^{50} +5.65967e6 q^{51} +(3.58051e6 + 3.58051e6i) q^{52} +(-3.72734e6 + 3.72734e6i) q^{53} -6.36640e6i q^{54} +(-2.63447e6 - 2.08217e6i) q^{55} -5.37397e6 q^{56} +(-7.66643e6 - 7.66643e6i) q^{57} +(-333787. + 333787. i) q^{58} +1.12165e7i q^{59} +(-696710. - 5.94988e6i) q^{60} +2.02002e7 q^{61} +(-1.95319e6 - 1.95319e6i) q^{62} +(2.50261e6 - 2.50261e6i) q^{63} -2.09715e6i q^{64} +(-2.45569e7 + 2.87552e6i) q^{65} -4.55172e6 q^{66} +(-1.30857e7 - 1.30857e7i) q^{67} +(-6.84086e6 + 6.84086e6i) q^{68} -5.52248e6i q^{69} +(1.62707e7 - 2.05866e7i) q^{70} +2.61041e7 q^{71} +(976626. + 976626. i) q^{72} +(-1.85930e7 + 1.85930e7i) q^{73} +3.21044e7i q^{74} +(2.49022e7 + 1.53454e7i) q^{75} +1.85329e7 q^{76} +(-1.40981e7 - 1.40981e7i) q^{77} +(-2.36982e7 + 2.36982e7i) q^{78} -3.07594e6i q^{79} +(8.03375e6 + 6.34952e6i) q^{80} +3.58796e7 q^{81} +(3.33858e7 + 3.33858e7i) q^{82} +(2.41522e7 - 2.41522e7i) q^{83} -3.55685e7i q^{84} +(-5.49393e6 - 4.69179e7i) q^{85} -6.42313e7 q^{86} +(-2.20923e6 - 2.20923e6i) q^{87} +(5.50167e6 - 5.50167e6i) q^{88} +5.76618e6i q^{89} +(-6.69817e6 + 784332. i) q^{90} -1.46802e8 q^{91} +(6.67504e6 + 6.67504e6i) q^{92} +(1.29275e7 - 1.29275e7i) q^{93} -3.63104e7i q^{94} +(-5.61117e7 + 7.09955e7i) q^{95} +1.38804e7 q^{96} +(2.86891e7 + 2.86891e7i) q^{97} +(6.40485e7 - 6.40485e7i) q^{98} +5.12416e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} + 54 q^{3} + 90 q^{5} - 864 q^{6} - 1186 q^{7} + 4096 q^{8} - 1760 q^{10} - 19852 q^{11} + 6912 q^{12} + 73704 q^{13} - 137490 q^{15} - 65536 q^{16} + 198944 q^{17} + 98688 q^{18} + 16640 q^{20}+ \cdots + 167860352 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 + 54 * q^3 + 90 * q^5 - 864 * q^6 - 1186 * q^7 + 4096 * q^8 - 1760 * q^10 - 19852 * q^11 + 6912 * q^12 + 73704 * q^13 - 137490 * q^15 - 65536 * q^16 + 198944 * q^17 + 98688 * q^18 + 16640 * q^20 - 766572 * q^21 + 158816 * q^22 + 631334 * q^23 + 545600 * q^25 - 1179264 * q^26 + 184680 * q^27 + 151808 * q^28 + 1275360 * q^30 - 2329892 * q^31 + 524288 * q^32 + 1362948 * q^33 + 1403870 * q^35 - 1579008 * q^36 - 976356 * q^37 - 1144000 * q^38 - 40960 * q^40 - 4284652 * q^41 + 6132576 * q^42 + 7146534 * q^43 - 2624430 * q^45 - 10101344 * q^46 - 3300186 * q^47 - 884736 * q^48 + 7241600 * q^50 + 6541788 * q^51 + 9434112 * q^52 + 9989164 * q^53 - 21649020 * q^55 - 2428928 * q^56 - 19136400 * q^57 - 19957760 * q^58 - 2807040 * q^60 + 85377108 * q^61 + 18639136 * q^62 - 16175226 * q^63 - 33878940 * q^65 - 21807168 * q^66 - 57195466 * q^67 - 25464832 * q^68 + 53504320 * q^70 + 113004028 * q^71 + 12632064 * q^72 - 60875756 * q^73 + 22407150 * q^75 + 18304000 * q^76 - 90339932 * q^77 - 40023264 * q^78 - 1474560 * q^80 + 35054064 * q^81 + 34277216 * q^82 + 71051214 * q^83 + 8601320 * q^85 - 114344544 * q^86 + 58152480 * q^87 - 20328448 * q^88 + 58175520 * q^90 - 221467572 * q^91 + 80810752 * q^92 + 98985108 * q^93 - 159500600 * q^95 + 14155776 * q^96 + 139631604 * q^97 + 167860352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more