LMFDB - Embedded newform 98.10.c.d.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(67,98)] 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("98.67"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-16,170] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.10.c.d.79.1

$q$-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 - 13.8564i) q^{2} +(85.0000 - 147.224i) q^{3} +(-128.000 + 221.703i) q^{4} +(272.000 + 471.118i) q^{5} -2720.00 q^{6} +4096.00 q^{8} +(-4608.50 - 7982.16i) q^{9} +(4352.00 - 7537.89i) q^{10} +(-24412.0 + 42282.8i) q^{11} +(21760.0 + 37689.4i) q^{12} +15876.0 q^{13} +92480.0 q^{15} +(-32768.0 - 56755.8i) q^{16} +(-10709.0 + 18548.5i) q^{17} +(-73736.0 + 127714. i) q^{18} +(-358205. - 620429. i) q^{19} -139264. q^{20} +781184. q^{22} +(1.23500e6 + 2.13908e6i) q^{23} +(348160. - 603031. i) q^{24} +(828594. - 1.43517e6i) q^{25} +(-127008. - 219984. i) q^{26} +1.77922e6 q^{27} +5.55683e6 q^{29} +(-739840. - 1.28144e6i) q^{30} +(2.89967e6 - 5.02238e6i) q^{31} +(-524288. + 908093. i) q^{32} +(4.15004e6 + 7.18808e6i) q^{33} +342688. q^{34} +2.35955e6 q^{36} +(1.94721e6 + 3.37268e6i) q^{37} +(-5.73128e6 + 9.92687e6i) q^{38} +(1.34946e6 - 2.33733e6i) q^{39} +(1.11411e6 + 1.92970e6i) q^{40} +6.36086e6 q^{41} -1.87013e7 q^{43} +(-6.24947e6 - 1.08244e7i) q^{44} +(2.50702e6 - 4.34229e6i) q^{45} +(1.97600e7 - 3.42253e7i) q^{46} +(2.82695e7 + 4.89643e7i) q^{47} -1.11411e7 q^{48} -2.65150e7 q^{50} +(1.82053e6 + 3.15325e6i) q^{51} +(-2.03213e6 + 3.51975e6i) q^{52} +(2.99473e7 - 5.18703e7i) q^{53} +(-1.42338e7 - 2.46536e7i) q^{54} -2.65603e7 q^{55} -1.21790e8 q^{57} +(-4.44546e7 - 7.69976e7i) q^{58} +(8.28148e7 - 1.43439e8i) q^{59} +(-1.18374e7 + 2.05030e7i) q^{60} +(2.57095e7 + 4.45302e7i) q^{61} -9.27896e7 q^{62} +1.67772e7 q^{64} +(4.31827e6 + 7.47947e6i) q^{65} +(6.64006e7 - 1.15009e8i) q^{66} +(-4.67733e7 + 8.10137e7i) q^{67} +(-2.74150e6 - 4.74842e6i) q^{68} +4.19900e8 q^{69} -9.56335e7 q^{71} +(-1.88764e7 - 3.26949e7i) q^{72} +(1.53248e8 - 2.65434e8i) q^{73} +(3.11554e7 - 5.39628e7i) q^{74} +(-1.40861e8 - 2.43979e8i) q^{75} +1.83401e8 q^{76} -4.31827e7 q^{78} +(-2.48237e8 - 4.29959e8i) q^{79} +(1.78258e7 - 3.08752e7i) q^{80} +(2.41943e8 - 4.19057e8i) q^{81} +(-5.08869e7 - 8.81386e7i) q^{82} +3.71487e8 q^{83} -1.16514e7 q^{85} +(1.49610e8 + 2.59133e8i) q^{86} +(4.72330e8 - 8.18100e8i) q^{87} +(-9.99916e7 + 1.73190e8i) q^{88} +(-8.27413e7 - 1.43312e8i) q^{89} -8.02248e7 q^{90} -6.32320e8 q^{92} +(-4.92945e8 - 8.53805e8i) q^{93} +(4.52313e8 - 7.83428e8i) q^{94} +(1.94864e8 - 3.37514e8i) q^{95} +(8.91290e7 + 1.54376e8i) q^{96} -7.58017e8 q^{97} +4.50011e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{2} + 170 q^{3} - 256 q^{4} + 544 q^{5} - 5440 q^{6} + 8192 q^{8} - 9217 q^{9} + 8704 q^{10} - 48824 q^{11} + 43520 q^{12} + 31752 q^{13} + 184960 q^{15} - 65536 q^{16} - 21418 q^{17} - 147472 q^{18}+ \cdots + 900021616 q^{99}+O(q^{100}) $ 2 * q - 16 * q^2 + 170 * q^3 - 256 * q^4 + 544 * q^5 - 5440 * q^6 + 8192 * q^8 - 9217 * q^9 + 8704 * q^10 - 48824 * q^11 + 43520 * q^12 + 31752 * q^13 + 184960 * q^15 - 65536 * q^16 - 21418 * q^17 - 147472 * q^18 - 716410 * q^19 - 278528 * q^20 + 1562368 * q^22 + 2470000 * q^23 + 696320 * q^24 + 1657189 * q^25 - 254016 * q^26 + 3558440 * q^27 + 11113652 * q^29 - 1479680 * q^30 + 5799348 * q^31 - 1048576 * q^32 + 8300080 * q^33 + 685376 * q^34 + 4719104 * q^36 + 3894430 * q^37 - 11462560 * q^38 + 2698920 * q^39 + 2228224 * q^40 + 12721716 * q^41 - 37402592 * q^43 - 12498944 * q^44 + 5014048 * q^45 + 39520000 * q^46 + 56539068 * q^47 - 22282240 * q^48 - 53030048 * q^50 + 3641060 * q^51 - 4064256 * q^52 + 59894682 * q^53 - 28467520 * q^54 - 53120512 * q^55 - 243579400 * q^57 - 88909216 * q^58 + 165629662 * q^59 - 23674880 * q^60 + 51419016 * q^61 - 185579136 * q^62 + 33554432 * q^64 + 8636544 * q^65 + 132801280 * q^66 - 93546508 * q^67 - 5483008 * q^68 + 839800000 * q^69 - 191267072 * q^71 - 37752832 * q^72 + 306496402 * q^73 + 62310880 * q^74 - 281722130 * q^75 + 366801920 * q^76 - 86365440 * q^78 - 496474152 * q^79 + 35651584 * q^80 + 483885611 * q^81 - 101773728 * q^82 + 742973924 * q^83 - 23302784 * q^85 + 299220736 * q^86 + 944660420 * q^87 - 199983104 * q^88 - 165482550 * q^89 - 160449536 * q^90 - 1264640000 * q^92 - 985889160 * q^93 + 904625088 * q^94 + 389727040 * q^95 + 178257920 * q^96 - 1516033484 * q^97 + 900021616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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	−	13.8564i	−0.353553	−	0.612372i
$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$3$	85.0000	−	147.224i	0.605861	−	1.04938i	−0.386053	−	0.922476i	$-0.626162\pi$
$3$	85.0000	−	147.224i	0.605861	−	1.04938i	0.991915	−	0.126906i	$-0.0405047\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	272.000	+	471.118i	0.194627	+	0.337104i	0.946778	−	0.321886i	$-0.104317\pi$
$5$	272.000	+	471.118i	0.194627	+	0.337104i	−0.752151	+	0.658991i	$0.770984\pi$
$6$	−2720.00			−0.856817
$7$		0			0
$7$		0			0
$8$	4096.00			0.353553
$9$	−4608.50	−	7982.16i	−0.234136	−	0.405536i
$10$	4352.00	−	7537.89i	0.137622	−	0.238369i
$11$	−24412.0	+	42282.8i	−0.502732	+	0.870757i	0.497263	+	0.867600i	$0.334338\pi$
$11$	−24412.0	+	42282.8i	−0.502732	+	0.870757i	−0.999995	+	0.00315718i	$0.998995\pi$
$12$	21760.0	+	37689.4i	0.302931	+	0.524691i
$13$	15876.0			0.154169			0.0770843	−	0.997025i	$-0.475439\pi$
$13$	15876.0			0.154169			0.0770843	+	0.997025i	$0.475439\pi$
$14$		0			0
$15$	92480.0			0.471669
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−10709.0	+	18548.5i	−0.0310977	+	0.0538629i	−0.881155	−	0.472827i	$-0.843234\pi$
$17$	−10709.0	+	18548.5i	−0.0310977	+	0.0538629i	0.850058	+	0.526690i	$0.176567\pi$
$18$	−73736.0	+	127714.i	−0.165559	+	0.286757i
$19$	−358205.	−	620429.i	−0.630580	−	1.09220i	−0.987433	−	0.158037i	$-0.949484\pi$
$19$	−358205.	−	620429.i	−0.630580	−	1.09220i	0.356853	−	0.934161i	$-0.383850\pi$
$20$	−139264.			−0.194627
$21$		0			0
$22$	781184.			0.710970
$23$	1.23500e6	+	2.13908e6i	0.920220	+	1.59387i	0.799074	+	0.601233i	$0.205324\pi$
$23$	1.23500e6	+	2.13908e6i	0.920220	+	1.59387i	0.121146	+	0.992635i	$0.461343\pi$
$24$	348160.	−	603031.i	0.214204	−	0.371013i
$25$	828594.	−	1.43517e6i	0.424240	−	0.734806i
$26$	−127008.	−	219984.i	−0.0545068	−	0.0944086i
$27$	1.77922e6			0.644307
$28$		0			0
$29$	5.55683e6			1.45893			0.729467	−	0.684016i	$-0.239768\pi$
$29$	5.55683e6			1.45893			0.729467	+	0.684016i	$0.239768\pi$
$30$	−739840.	−	1.28144e6i	−0.166760	−	0.288837i
$31$	2.89967e6	−	5.02238e6i	0.563925	−	0.976747i	−0.433224	−	0.901287i	$-0.642624\pi$
$31$	2.89967e6	−	5.02238e6i	0.563925	−	0.976747i	0.997149	−	0.0754607i	$-0.0240427\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$	4.15004e6	+	7.18808e6i	0.609171	+	1.05512i
$34$	342688.			0.0439788
$35$		0			0
$36$	2.35955e6			0.234136
$37$	1.94721e6	+	3.37268e6i	0.170807	+	0.295847i	0.938702	−	0.344729i	$-0.112029\pi$
$37$	1.94721e6	+	3.37268e6i	0.170807	+	0.295847i	−0.767895	+	0.640576i	$0.778696\pi$
$38$	−5.73128e6	+	9.92687e6i	−0.445888	+	0.772300i
$39$	1.34946e6	−	2.33733e6i	0.0934048	−	0.161782i
$40$	1.11411e6	+	1.92970e6i	0.0688112	+	0.119184i
$41$	6.36086e6			0.351551			0.175776	−	0.984430i	$-0.443757\pi$
$41$	6.36086e6			0.351551			0.175776	+	0.984430i	$0.443757\pi$
$42$		0			0
$43$	−1.87013e7			−0.834187			−0.417094	−	0.908863i	$-0.636951\pi$
$43$	−1.87013e7			−0.834187			−0.417094	+	0.908863i	$0.636951\pi$
$44$	−6.24947e6	−	1.08244e7i	−0.251366	−	0.435378i
$45$	2.50702e6	−	4.34229e6i	0.0911386	−	0.157857i
$46$	1.97600e7	−	3.42253e7i	0.650694	−	1.12703i
$47$	2.82695e7	+	4.89643e7i	0.845042	+	1.46366i	0.885585	+	0.464478i	$0.153758\pi$
$47$	2.82695e7	+	4.89643e7i	0.845042	+	1.46366i	−0.0405427	+	0.999178i	$0.512909\pi$
$48$	−1.11411e7			−0.302931
$49$		0			0
$50$	−2.65150e7			−0.599967
$51$	1.82053e6	+	3.15325e6i	0.0376818	+	0.0652669i
$52$	−2.03213e6	+	3.51975e6i	−0.0385422	+	0.0667570i
$53$	2.99473e7	−	5.18703e7i	0.521335	−	0.902979i	−0.478357	−	0.878165i	$-0.658768\pi$
$53$	2.99473e7	−	5.18703e7i	0.521335	−	0.902979i	0.999692	−	0.0248133i	$-0.00789912\pi$
$54$	−1.42338e7	−	2.46536e7i	−0.227797	−	0.394556i
$55$	−2.65603e7			−0.391381
$56$		0			0
$57$	−1.21790e8			−1.52818
$58$	−4.44546e7	−	7.69976e7i	−0.515811	−	0.893411i
$59$	8.28148e7	−	1.43439e8i	0.889762	−	1.54111i	0.0496065	−	0.998769i	$-0.484203\pi$
$59$	8.28148e7	−	1.43439e8i	0.889762	−	1.54111i	0.840156	−	0.542345i	$-0.182463\pi$
$60$	−1.18374e7	+	2.05030e7i	−0.117917	+	0.204239i
$61$	2.57095e7	+	4.45302e7i	0.237744	+	0.411785i	0.960067	−	0.279772i	$-0.0902587\pi$
$61$	2.57095e7	+	4.45302e7i	0.237744	+	0.411785i	−0.722323	+	0.691556i	$0.756925\pi$
$62$	−9.27896e7			−0.797511
$63$		0			0
$64$	1.67772e7			0.125000
$65$	4.31827e6	+	7.47947e6i	0.0300054	+	0.0519709i
$66$	6.64006e7	−	1.15009e8i	0.430749	−	0.746080i
$67$	−4.67733e7	+	8.10137e7i	−0.283570	+	0.491158i	−0.972262	−	0.233896i	$-0.924852\pi$
$67$	−4.67733e7	+	8.10137e7i	−0.283570	+	0.491158i	0.688691	+	0.725055i	$0.258186\pi$
$68$	−2.74150e6	−	4.74842e6i	−0.0155489	−	0.0269314i
$69$	4.19900e8			2.23010
$70$		0			0
$71$	−9.56335e7			−0.446630			−0.223315	−	0.974746i	$-0.571688\pi$
$71$	−9.56335e7			−0.446630			−0.223315	+	0.974746i	$0.571688\pi$
$72$	−1.88764e7	−	3.26949e7i	−0.0827796	−	0.143378i
$73$	1.53248e8	−	2.65434e8i	0.631601	−	1.09396i	−0.355624	−	0.934629i	$-0.615732\pi$
$73$	1.53248e8	−	2.65434e8i	0.631601	−	1.09396i	0.987225	−	0.159335i	$-0.0509350\pi$
$74$	3.11554e7	−	5.39628e7i	0.120779	−	0.209195i
$75$	−1.40861e8	−	2.43979e8i	−0.514062	−	0.890381i
$76$	1.83401e8			0.630580
$77$		0			0
$78$	−4.31827e7			−0.132094
$79$	−2.48237e8	−	4.29959e8i	−0.717042	−	1.24195i	−0.962167	−	0.272462i	$-0.912162\pi$
$79$	−2.48237e8	−	4.29959e8i	−0.717042	−	1.24195i	0.245124	−	0.969492i	$-0.421171\pi$
$80$	1.78258e7	−	3.08752e7i	0.0486568	−	0.0842761i
$81$	2.41943e8	−	4.19057e8i	0.624497	−	1.08166i
$82$	−5.08869e7	−	8.81386e7i	−0.124292	−	0.215280i
$83$	3.71487e8			0.859196			0.429598	−	0.903020i	$-0.358655\pi$
$83$	3.71487e8			0.859196			0.429598	+	0.903020i	$0.358655\pi$
$84$		0			0
$85$	−1.16514e7			−0.0242099
$86$	1.49610e8	+	2.59133e8i	0.294930	+	0.510833i
$87$	4.72330e8	−	8.18100e8i	0.883912	−	1.53098i
$88$	−9.99916e7	+	1.73190e8i	−0.177743	+	0.307859i
$89$	−8.27413e7	−	1.43312e8i	−0.139787	−	0.242118i	0.787629	−	0.616150i	$-0.211308\pi$
$89$	−8.27413e7	−	1.43312e8i	−0.139787	−	0.242118i	−0.927416	+	0.374032i	$0.877975\pi$
$90$	−8.02248e7			−0.128889
$91$		0			0
$92$	−6.32320e8			−0.920220
$93$	−4.92945e8	−	8.53805e8i	−0.683321	−	1.18355i
$94$	4.52313e8	−	7.83428e8i	0.597535	−	1.03496i
$95$	1.94864e8	−	3.37514e8i	0.245456	−	0.425143i
$96$	8.91290e7	+	1.54376e8i	0.107102	+	0.185506i
$97$	−7.58017e8			−0.869373			−0.434686	−	0.900582i	$-0.643141\pi$
$97$	−7.58017e8			−0.869373			−0.434686	+	0.900582i	$0.643141\pi$
$98$		0			0
$99$	4.50011e8			0.470830
$100$	2.12120e8	+	3.67403e8i	0.212120	+	0.367403i
$101$	−4.52106e8	+	7.83071e8i	−0.432309	+	0.748781i	−0.997072	−	0.0764724i	$-0.975634\pi$
$101$	−4.52106e8	+	7.83071e8i	−0.432309	+	0.748781i	0.564763	+	0.825253i	$0.308968\pi$
$102$	2.91285e7	−	5.04520e7i	0.0266451	−	0.0461506i
$103$	9.90784e8	+	1.71609e9i	0.867384	+	1.50235i	0.864660	+	0.502357i	$0.167534\pi$
$103$	9.90784e8	+	1.71609e9i	0.867384	+	1.50235i	0.00272370	+	0.999996i	$0.499133\pi$
$104$	6.50281e7			0.0545068
$105$		0			0
$106$	−9.58315e8			−0.737279
$107$	−2.08189e8	−	3.60595e8i	−0.153544	−	0.265945i	0.778984	−	0.627044i	$-0.215735\pi$
$107$	−2.08189e8	−	3.60595e8i	−0.153544	−	0.265945i	−0.932528	+	0.361098i	$0.882402\pi$
$108$	−2.27740e8	+	3.94458e8i	−0.161077	+	0.278993i
$109$	6.34605e8	−	1.09917e9i	0.430610	−	0.745838i	−0.566316	−	0.824188i	$-0.691632\pi$
$109$	6.34605e8	−	1.09917e9i	0.430610	−	0.745838i	0.996926	+	0.0783501i	$0.0249652\pi$
$110$	2.12482e8	+	3.68030e8i	0.138374	+	0.239671i
$111$	6.62053e8			0.413942
$112$		0			0
$113$	−2.83528e9			−1.63585			−0.817923	−	0.575328i	$-0.804874\pi$
$113$	−2.83528e9			−1.63585			−0.817923	+	0.575328i	$0.804874\pi$
$114$	9.74318e8	+	1.68757e9i	0.540292	+	0.935814i
$115$	−6.71840e8	+	1.16366e9i	−0.358200	+	0.620421i
$116$	−7.11274e8	+	1.23196e9i	−0.364734	+	0.631737i
$117$	−7.31645e7	−	1.26725e8i	−0.0360964	−	0.0625209i
$118$	−2.65007e9			−1.25831
$119$		0			0
$120$	3.78798e8			0.166760
$121$	−1.29176e7	−	2.23740e7i	−0.00547834	−	0.00948877i
$122$	4.11352e8	−	7.12483e8i	0.168110	−	0.291176i
$123$	5.40673e8	−	9.36473e8i	0.212991	−	0.368912i
$124$	7.42317e8	+	1.28573e9i	0.281963	+	0.488374i
$125$	1.96401e9			0.719530
$126$		0			0
$127$	5.44282e9			1.85655			0.928277	−	0.371889i	$-0.121290\pi$
$127$	5.44282e9			1.85655			0.928277	+	0.371889i	$0.121290\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$	−1.58961e9	+	2.75329e9i	−0.505402	+	0.875382i
$130$	6.90924e7	−	1.19671e8i	0.0212170	−	0.0367490i
$131$	−3.22029e8	−	5.57770e8i	−0.0955374	−	0.165476i	0.814295	−	0.580451i	$-0.197124\pi$
$131$	−3.22029e8	−	5.57770e8i	−0.0955374	−	0.165476i	−0.909833	+	0.414975i	$0.863790\pi$
$132$	−2.12482e9			−0.609171
$133$		0			0
$134$	1.49674e9			0.401029
$135$	4.83948e8	+	8.38222e8i	0.125400	+	0.217199i
$136$	−4.38641e7	+	7.59748e7i	−0.0109947	+	0.0190434i
$137$	−8.36878e8	+	1.44951e9i	−0.202964	+	0.351544i	−0.949482	−	0.313821i	$-0.898391\pi$
$137$	−8.36878e8	+	1.44951e9i	−0.202964	+	0.351544i	0.746518	+	0.665365i	$0.231724\pi$
$138$	−3.35920e9	−	5.81831e9i	−0.788461	−	1.36565i
$139$	4.17330e9			0.948229			0.474115	−	0.880463i	$-0.342768\pi$
$139$	4.17330e9			0.948229			0.474115	+	0.880463i	$0.342768\pi$
$140$		0			0
$141$	9.61164e9			2.04791
$142$	7.65068e8	+	1.32514e9i	0.157907	+	0.273504i
$143$	−3.87565e8	+	6.71282e8i	−0.0775055	+	0.134243i
$144$	−3.02023e8	+	5.23119e8i	−0.0585340	+	0.101384i
$145$	1.51146e9	+	2.61792e9i	0.283949	+	0.491813i
$146$	−4.90394e9			−0.893218
$147$		0			0
$148$	−9.96974e8			−0.170807
$149$	2.32048e8	+	4.01919e8i	0.0385691	+	0.0668036i	0.884666	−	0.466226i	$-0.154387\pi$
$149$	2.32048e8	+	4.01919e8i	0.0385691	+	0.0668036i	−0.846096	+	0.533030i	$0.821053\pi$
$150$	−2.25378e9	+	3.90366e9i	−0.363497	+	0.629594i
$151$	−3.65965e9	+	6.33869e9i	−0.572853	+	0.992210i	0.423419	+	0.905934i	$0.360830\pi$
$151$	−3.65965e9	+	6.33869e9i	−0.572853	+	0.992210i	−0.996271	+	0.0862757i	$0.972503\pi$
$152$	−1.46721e9	−	2.54128e9i	−0.222944	−	0.386150i
$153$	1.97410e8			0.0291244
$154$		0			0
$155$	3.15485e9			0.439021
$156$	3.45462e8	+	5.98357e8i	0.0467024	+	0.0808909i
$157$	−2.21525e9	+	3.83692e9i	−0.290987	+	0.504005i	−0.974043	−	0.226361i	$-0.927317\pi$
$157$	−2.21525e9	+	3.83692e9i	−0.290987	+	0.504005i	0.683056	+	0.730366i	$0.260650\pi$
$158$	−3.97179e9	+	6.87935e9i	−0.507025	+	0.878194i
$159$	−5.09105e9	−	8.81795e9i	−0.631713	−	1.09416i
$160$	−5.70425e8			−0.0688112
$161$		0			0
$162$	−7.74217e9			−0.883172
$163$	6.68226e9	+	1.15740e10i	0.741446	+	1.28422i	0.951837	+	0.306605i	$0.0991929\pi$
$163$	6.68226e9	+	1.15740e10i	0.741446	+	1.28422i	−0.210391	+	0.977617i	$0.567474\pi$
$164$	−8.14190e8	+	1.41022e9i	−0.0878878	+	0.152226i
$165$	−2.25762e9	+	3.91032e9i	−0.237123	+	0.410709i
$166$	−2.97190e9	−	5.14747e9i	−0.303772	−	0.526148i
$167$	1.24456e10			1.23821			0.619103	−	0.785310i	$-0.287496\pi$
$167$	1.24456e10			1.23821			0.619103	+	0.785310i	$0.287496\pi$
$168$		0			0
$169$	−1.03525e10			−0.976232
$170$	9.32111e7	+	1.61446e8i	0.00855949	+	0.0148255i
$171$	−3.30158e9	+	5.71850e9i	−0.295283	+	0.511445i
$172$	2.39377e9	−	4.14612e9i	0.208547	−	0.361214i
$173$	5.22721e9	+	9.05379e9i	0.443672	+	0.768463i	0.997959	−	0.0638629i	$-0.0203420\pi$
$173$	5.22721e9	+	9.05379e9i	0.443672	+	0.768463i	−0.554286	+	0.832326i	$0.687009\pi$
$174$	−1.51146e10			−1.25004
$175$		0			0
$176$	3.19973e9			0.251366
$177$	−1.40785e10	−	2.43847e10i	−1.07815	−	1.86740i
$178$	−1.32386e9	+	2.29299e9i	−0.0988444	+	0.171204i
$179$	2.02195e9	−	3.50213e9i	0.147208	−	0.254972i	−0.782986	−	0.622039i	$-0.786305\pi$
$179$	2.02195e9	−	3.50213e9i	0.147208	−	0.254972i	0.930195	+	0.367067i	$0.119638\pi$
$180$	6.41798e8	+	1.11163e9i	0.0455693	+	0.0789283i
$181$	−1.24735e10			−0.863843			−0.431922	−	0.901911i	$-0.642164\pi$
$181$	−1.24735e10			−0.863843			−0.431922	+	0.901911i	$0.642164\pi$
$182$		0			0
$183$	8.74123e9			0.576160
$184$	5.05856e9	+	8.76168e9i	0.325347	+	0.563517i
$185$	−1.05928e9	+	1.83474e9i	−0.0664875	+	0.115160i
$186$	−7.88711e9	+	1.36609e10i	−0.483181	+	0.836894i
$187$	−5.22856e8	−	9.05614e8i	−0.0312676	−	0.0541571i
$188$	−1.44740e10			−0.845042
$189$		0			0
$190$	−6.23563e9			−0.347128
$191$	1.90974e9	+	3.30776e9i	0.103830	+	0.179839i	0.913260	−	0.407378i	$-0.133557\pi$
$191$	1.90974e9	+	3.30776e9i	0.103830	+	0.179839i	−0.809430	+	0.587217i	$0.800224\pi$
$192$	1.42606e9	−	2.47001e9i	0.0757327	−	0.131173i
$193$	1.20597e10	−	2.08879e10i	0.625644	−	1.08365i	−0.362772	−	0.931878i	$-0.618170\pi$
$193$	1.20597e10	−	2.08879e10i	0.625644	−	1.08365i	0.988416	−	0.151769i	$-0.0484969\pi$
$194$	6.06413e9	+	1.05034e10i	0.307370	+	0.532380i
$195$	1.46821e9			0.0727165
$196$		0			0
$197$	−1.24798e10			−0.590351			−0.295176	−	0.955443i	$-0.595378\pi$
$197$	−1.24798e10			−0.590351			−0.295176	+	0.955443i	$0.595378\pi$
$198$	−3.60009e9	−	6.23553e9i	−0.166464	−	0.288324i
$199$	−1.46564e9	+	2.53856e9i	−0.0662502	+	0.114749i	−0.897248	−	0.441527i	$-0.854437\pi$
$199$	−1.46564e9	+	2.53856e9i	−0.0662502	+	0.114749i	0.830998	+	0.556276i	$0.187770\pi$
$200$	3.39392e9	−	5.87845e9i	0.149992	−	0.259793i
$201$	7.95145e9	+	1.37723e10i	0.343609	+	0.595148i
$202$	1.44674e10			0.611377
$203$		0			0
$204$	−9.32111e8			−0.0376818
$205$	1.73015e9	+	2.99671e9i	0.0684214	+	0.118509i
$206$	1.58525e10	−	2.74574e10i	0.613333	−	1.06232i
$207$	1.13830e10	−	1.97159e10i	0.430913	−	0.746364i
$208$	−5.20225e8	−	9.01056e8i	−0.0192711	−	0.0333785i
$209$	3.49780e10			1.26805
$210$		0			0
$211$	3.36978e10			1.17039			0.585195	−	0.810892i	$-0.301018\pi$
$211$	3.36978e10			1.17039			0.585195	+	0.810892i	$0.301018\pi$
$212$	7.66652e9	+	1.32788e10i	0.260667	+	0.451489i
$213$	−8.12885e9	+	1.40796e10i	−0.270596	+	0.468686i
$214$	−3.33103e9	+	5.76952e9i	−0.108572	+	0.188052i
$215$	−5.08675e9	−	8.81051e9i	−0.162356	−	0.281208i
$216$	7.28769e9			0.227797
$217$		0			0
$218$	−2.03073e10			−0.608974
$219$	−2.60522e10	−	4.51237e10i	−0.765325	−	1.32558i
$220$	3.39971e9	−	5.88848e9i	0.0978453	−	0.169473i
$221$	−1.70016e8	+	2.94476e8i	−0.00479430	+	0.00830396i
$222$	−5.29642e9	−	9.17368e9i	−0.146351	−	0.253487i
$223$	3.87208e10			1.04851			0.524255	−	0.851561i	$-0.324344\pi$
$223$	3.87208e10			1.04851			0.524255	+	0.851561i	$0.324344\pi$
$224$		0			0
$225$	−1.52743e10			−0.397320
$226$	2.26822e10	+	3.92867e10i	0.578359	+	1.00175i
$227$	3.84506e10	−	6.65983e10i	0.961139	−	1.66474i	0.241492	−	0.970403i	$-0.422363\pi$
$227$	3.84506e10	−	6.65983e10i	0.961139	−	1.66474i	0.719648	−	0.694340i	$-0.244303\pi$
$228$	1.55891e10	−	2.70011e10i	0.382044	−	0.661720i
$229$	2.17557e10	+	3.76820e10i	0.522773	+	0.905470i	0.999649	+	0.0264992i	$0.00843595\pi$
$229$	2.17557e10	+	3.76820e10i	0.522773	+	0.905470i	−0.476875	+	0.878971i	$0.658231\pi$
$230$	2.14989e10			0.506571
$231$		0			0
$232$	2.27608e10			0.515811
$233$	1.03522e10	+	1.79305e10i	0.230107	+	0.398556i	0.957839	−	0.287305i	$-0.0927592\pi$
$233$	1.03522e10	+	1.79305e10i	0.230107	+	0.398556i	−0.727733	+	0.685861i	$0.759426\pi$
$234$	−1.17063e9	+	2.02760e9i	−0.0255240	+	0.0442089i
$235$	−1.53786e10	+	2.66366e10i	−0.328937	+	0.569735i
$236$	2.12006e10	+	3.67205e10i	0.444881	+	0.770557i
$237$	−8.44006e10			−1.73771
$238$		0			0
$239$	2.16220e10			0.428653			0.214326	−	0.976762i	$-0.431244\pi$
$239$	2.16220e10			0.428653			0.214326	+	0.976762i	$0.431244\pi$
$240$	−3.03038e9	−	5.24878e9i	−0.0589586	−	0.102119i
$241$	3.38894e10	−	5.86982e10i	0.647124	−	1.12085i	−0.336682	−	0.941618i	$-0.609305\pi$
$241$	3.38894e10	−	5.86982e10i	0.647124	−	1.12085i	0.983807	−	0.179234i	$-0.0573618\pi$
$242$	−2.06682e8	+	3.57984e8i	−0.00387377	+	0.00670957i
$243$	−2.36201e10	−	4.09112e10i	−0.434563	−	0.752686i
$244$	−1.31633e10			−0.237744
$245$		0			0
$246$	−1.73015e10			−0.301215
$247$	−5.68686e9	−	9.84993e9i	−0.0972157	−	0.168383i
$248$	1.18771e10	−	2.05717e10i	0.199378	−	0.345332i
$249$	3.15764e10	−	5.46919e10i	0.520554	−	0.901625i
$250$	−1.57121e10	−	2.72141e10i	−0.254392	−	0.440620i
$251$	−4.87895e9			−0.0775881			−0.0387940	−	0.999247i	$-0.512352\pi$
$251$	−4.87895e9			−0.0775881			−0.0387940	+	0.999247i	$0.512352\pi$
$252$		0			0
$253$	−1.20595e11			−1.85050
$254$	−4.35426e10	−	7.54180e10i	−0.656391	−	1.13690i
$255$	−9.90368e8	+	1.71537e9i	−0.0146678	+	0.0254054i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−1.37514e10	−	2.38182e10i	−0.196630	−	0.340573i	0.750804	−	0.660525i	$-0.229666\pi$
$257$	−1.37514e10	−	2.38182e10i	−0.196630	−	0.340573i	−0.947434	+	0.319953i	$0.896333\pi$
$258$	5.08675e10			0.714746
$259$		0			0
$260$	−2.21096e9			−0.0300054
$261$	−2.56086e10	−	4.43555e10i	−0.341589	−	0.591650i
$262$	−5.15246e9	+	8.92432e9i	−0.0675552	+	0.117009i
$263$	1.11297e10	−	1.92773e10i	0.143445	−	0.248453i	−0.785347	−	0.619056i	$-0.787515\pi$
$263$	1.11297e10	−	1.92773e10i	0.143445	−	0.248453i	0.928792	+	0.370602i	$0.120849\pi$
$264$	1.69986e10	+	2.94424e10i	0.215375	+	0.373040i
$265$	3.25827e10			0.405864
$266$		0			0
$267$	−2.81320e10			−0.338766
$268$	−1.19740e10	−	2.07395e10i	−0.141785	−	0.245579i
$269$	8.65083e9	−	1.49837e10i	0.100733	−	0.174475i	−0.811254	−	0.584694i	$-0.801215\pi$
$269$	8.65083e9	−	1.49837e10i	0.100733	−	0.174475i	0.911987	+	0.410219i	$0.134548\pi$
$270$	7.74317e9	−	1.34116e10i	0.0886710	−	0.153583i
$271$	2.40950e10	+	4.17338e10i	0.271372	+	0.470031i	0.969213	−	0.246222i	$-0.0791892\pi$
$271$	2.40950e10	+	4.17338e10i	0.271372	+	0.470031i	−0.697841	+	0.716253i	$0.745856\pi$
$272$	1.40365e9			0.0155489
$273$		0			0
$274$	2.67801e10			0.287035
$275$	4.04553e10	+	7.00706e10i	0.426558	+	0.738820i
$276$	−5.37472e10	+	9.30929e10i	−0.557526	+	0.965663i
$277$	−4.01917e10	+	6.96140e10i	−0.410183	+	0.710457i	−0.994909	−	0.100773i	$-0.967868\pi$
$277$	−4.01917e10	+	6.96140e10i	−0.410183	+	0.710457i	0.584727	+	0.811230i	$0.301202\pi$
$278$	−3.33864e10	−	5.78270e10i	−0.335250	−	0.580669i
$279$	−5.34526e10			−0.528141
$280$		0			0
$281$	−1.95595e11			−1.87146			−0.935729	−	0.352719i	$-0.885257\pi$
$281$	−1.95595e11			−1.87146			−0.935729	+	0.352719i	$0.885257\pi$
$282$	−7.68931e10	−	1.33183e11i	−0.724047	−	1.25409i
$283$	−3.01401e10	+	5.22042e10i	−0.279322	+	0.483801i	−0.971217	−	0.238198i	$-0.923443\pi$
$283$	−3.01401e10	+	5.22042e10i	−0.279322	+	0.483801i	0.691894	+	0.721999i	$0.256776\pi$
$284$	1.22411e10	−	2.12022e10i	0.111657	−	0.193396i
$285$	−3.31268e10	−	5.73773e10i	−0.297425	−	0.515155i
$286$	1.24021e10			0.109609
$287$		0			0
$288$	9.66472e9			0.0827796
$289$	5.90646e10	+	1.02303e11i	0.498066	+	0.862675i
$290$	2.41833e10	−	4.18867e10i	0.200782	−	0.347765i
$291$	−6.44314e10	+	1.11598e11i	−0.526719	+	0.912305i
$292$	3.92315e10	+	6.79510e10i	0.315800	+	0.546982i
$293$	4.86743e10			0.385830			0.192915	−	0.981216i	$-0.438206\pi$
$293$	4.86743e10			0.385830			0.192915	+	0.981216i	$0.438206\pi$
$294$		0			0
$295$	9.01025e10			0.692688
$296$	7.97579e9	+	1.38145e10i	0.0603895	+	0.104598i
$297$	−4.34343e10	+	7.52304e10i	−0.323913	+	0.561035i
$298$	3.71277e9	−	6.43070e9i	0.0272725	−	0.0472373i
$299$	1.96069e10	+	3.39601e10i	0.141869	+	0.245724i
$300$	7.21209e10			0.514062
$301$		0			0
$302$	1.17109e11			0.810136
$303$	7.68580e10	+	1.33122e11i	0.523838	+	0.907315i
$304$	−2.34753e10	+	4.06605e10i	−0.157645	+	0.273049i
$305$	−1.39860e10	+	2.42244e10i	−0.0925430	+	0.160289i
$306$	−1.57928e9	−	2.73539e9i	−0.0102970	−	0.0178350i
$307$	−2.75178e11			−1.76804			−0.884018	−	0.467453i	$-0.845172\pi$
$307$	−2.75178e11			−1.76804			−0.884018	+	0.467453i	$0.845172\pi$
$308$		0			0
$309$	3.36867e11			2.10206
$310$	−2.52388e10	−	4.37148e10i	−0.155217	−	0.268844i
$311$	5.61609e10	−	9.72735e10i	0.340418	−	0.589621i	−0.644093	−	0.764948i	$-0.722765\pi$
$311$	5.61609e10	−	9.72735e10i	0.340418	−	0.589621i	0.984510	+	0.175327i	$0.0560982\pi$
$312$	5.52739e9	−	9.57372e9i	0.0330236	−	0.0571985i
$313$	−5.30698e10	−	9.19196e10i	−0.312535	−	0.541326i	0.666376	−	0.745616i	$-0.267845\pi$
$313$	−5.30698e10	−	9.19196e10i	−0.312535	−	0.541326i	−0.978910	+	0.204290i	$0.934511\pi$
$314$	7.08880e10			0.411518
$315$		0			0
$316$	1.27097e11			0.717042
$317$	−1.15679e9	−	2.00362e9i	−0.00643409	−	0.0111442i	0.862790	−	0.505562i	$-0.168715\pi$
$317$	−1.15679e9	−	2.00362e9i	−0.00643409	−	0.0111442i	−0.869225	+	0.494418i	$0.835381\pi$
$318$	−8.14568e10	+	1.41087e11i	−0.446689	+	0.773688i
$319$	−1.35653e11	+	2.34958e11i	−0.733453	+	1.27038i
$320$	4.56340e9	+	7.90405e9i	0.0243284	+	0.0421381i
$321$	−7.07844e10			−0.372105
$322$		0			0
$323$	1.53441e10			0.0784385
$324$	6.19374e10	+	1.07279e11i	0.312248	+	0.540830i
$325$	1.31548e10	−	2.27847e10i	0.0654046	−	0.113284i
$326$	1.06916e11	−	1.85184e11i	0.524281	−	0.908082i
$327$	−1.07883e11	−	1.86858e11i	−0.521780	−	0.903749i
$328$	2.60541e10			0.124292
$329$		0			0
$330$	7.22439e10			0.335342
$331$	1.08093e11	+	1.87222e11i	0.494960	+	0.857297i	0.999983	−	0.00580952i	$-0.00184924\pi$
$331$	1.08093e11	+	1.87222e11i	0.494960	+	0.857297i	−0.505023	+	0.863106i	$0.668516\pi$
$332$	−4.75503e10	+	8.23596e10i	−0.214799	+	0.372043i
$333$	1.79475e10	−	3.10859e10i	0.0799842	−	0.138537i
$334$	−9.95651e10	−	1.72452e11i	−0.437772	−	0.758243i
$335$	−5.08893e10			−0.220762
$336$		0			0
$337$	5.00291e10			0.211294			0.105647	−	0.994404i	$-0.466309\pi$
$337$	5.00291e10			0.211294			0.105647	+	0.994404i	$0.466309\pi$
$338$	8.28196e10	+	1.43448e11i	0.345150	+	0.597818i
$339$	−2.40998e11	+	4.17422e11i	−0.991096	+	1.71663i
$340$	1.49138e9	−	2.58314e9i	0.00605247	−	0.0104832i
$341$	1.41574e11	+	2.45213e11i	0.567006	+	0.982084i
$342$	1.05650e11			0.417594
$343$		0			0
$344$	−7.66005e10			−0.294930
$345$	1.14213e11	+	1.97822e11i	0.434039	+	0.751778i
$346$	8.36354e10	−	1.44861e11i	0.313724	−	0.543386i
$347$	9.23032e10	−	1.59874e11i	0.341770	−	0.591964i	−0.642991	−	0.765874i	$-0.722307\pi$
$347$	9.23032e10	−	1.59874e11i	0.341770	−	0.591964i	0.984762	+	0.173910i	$0.0556402\pi$
$348$	1.20917e11	+	2.09434e11i	0.441956	+	0.765490i
$349$	−2.74666e11			−0.991039			−0.495520	−	0.868597i	$-0.665022\pi$
$349$	−2.74666e11			−0.991039			−0.495520	+	0.868597i	$0.665022\pi$
$350$		0			0
$351$	2.82469e10			0.0993319
$352$	−2.55978e10	−	4.43368e10i	−0.0888713	−	0.153930i
$353$	−7.90267e10	+	1.36878e11i	−0.270887	+	0.469190i	−0.969089	−	0.246711i	$-0.920650\pi$
$353$	−7.90267e10	+	1.36878e11i	−0.270887	+	0.469190i	0.698202	+	0.715900i	$0.253984\pi$
$354$	−2.25256e11	+	3.90155e11i	−0.762364	+	1.32045i
$355$	−2.60123e10	−	4.50547e10i	−0.0869264	−	0.150561i
$356$	4.23635e10			0.139787
$357$		0			0
$358$	−6.47025e10			−0.208184
$359$	−1.70380e11	−	2.95106e11i	−0.541368	−	0.937677i	−0.998826	−	0.0484457i	$-0.984573\pi$
$359$	−1.70380e11	−	2.95106e11i	−0.541368	−	0.937677i	0.457458	−	0.889231i	$-0.348760\pi$
$360$	1.02688e10	−	1.77860e10i	0.0322223	−	0.0558107i
$361$	−9.52778e10	+	1.65026e11i	−0.295263	+	0.511411i
$362$	9.97881e10	+	1.72838e11i	0.305415	+	0.528994i
$363$	−4.39200e9			−0.0132765
$364$		0			0
$365$	1.66734e11			0.491707
$366$	−6.99299e10	−	1.21122e11i	−0.203703	−	0.352824i
$367$	−3.05108e11	+	5.28462e11i	−0.877922	+	1.52061i	−0.0243052	+	0.999705i	$0.507737\pi$
$367$	−3.05108e11	+	5.28462e11i	−0.877922	+	1.52061i	−0.853617	+	0.520901i	$0.825596\pi$
$368$	8.09370e10	−	1.40187e11i	0.230055	−	0.398467i
$369$	−2.93140e10	−	5.07734e10i	−0.0823108	−	0.142566i
$370$	3.38971e10			0.0940275
$371$		0			0
$372$	2.52388e11			0.683321
$373$	−2.17465e11	−	3.76661e11i	−0.581701	−	1.00754i	−0.995278	−	0.0970670i	$-0.969054\pi$
$373$	−2.17465e11	−	3.76661e11i	−0.581701	−	1.00754i	0.413576	−	0.910469i	$-0.364279\pi$
$374$	−8.36570e9	+	1.44898e10i	−0.0221096	+	0.0382949i
$375$	1.66941e11	−	2.89150e11i	0.435935	−	0.755062i
$376$	1.15792e11	+	2.00558e11i	0.298767	+	0.517480i
$377$	8.82202e10			0.224922
$378$		0			0
$379$	−7.30677e11			−1.81907			−0.909534	−	0.415630i	$-0.863561\pi$
$379$	−7.30677e11			−1.81907			−0.909534	+	0.415630i	$0.863561\pi$
$380$	4.98851e10	+	8.64035e10i	0.122728	+	0.212571i
$381$	4.62640e11	−	8.01316e11i	1.12481	−	1.94824i
$382$	3.05558e10	−	5.29241e10i	0.0734189	−	0.127165i
$383$	1.05537e11	+	1.82795e11i	0.250617	+	0.434081i	0.963696	−	0.267003i	$-0.0860333\pi$
$383$	1.05537e11	+	1.82795e11i	0.250617	+	0.434081i	−0.713079	+	0.701084i	$0.752700\pi$
$384$	−4.56340e10			−0.107102
$385$		0			0
$386$	−3.85909e11			−0.884794
$387$	8.61849e10	+	1.49277e11i	0.195313	+	0.338293i
$388$	9.70261e10	−	1.68054e11i	0.217343	−	0.376449i
$389$	−3.60929e9	+	6.25147e9i	−0.00799186	+	0.0138423i	−0.869994	−	0.493063i	$-0.835877\pi$
$389$	−3.60929e9	+	6.25147e9i	−0.00799186	+	0.0138423i	0.862002	+	0.506905i	$0.169211\pi$
$390$	−1.17457e10	−	2.03441e10i	−0.0257092	−	0.0445296i
$391$	−5.29025e10			−0.114467
$392$		0			0
$393$	−1.09490e11			−0.231530
$394$	9.98386e10	+	1.72926e11i	0.208721	+	0.361515i
$395$	1.35041e11	−	2.33898e11i	0.279112	−	0.483436i
$396$	−5.76014e10	+	9.97685e10i	−0.117708	+	0.203876i
$397$	−3.49693e11	−	6.05687e11i	−0.706529	−	1.22374i	−0.966137	−	0.258030i	$-0.916927\pi$
$397$	−3.49693e11	−	6.05687e11i	−0.706529	−	1.22374i	0.259608	−	0.965714i	$-0.416407\pi$
$398$	4.69004e10			0.0936920
$399$		0			0
$400$	−1.08606e11			−0.212120
$401$	−3.20322e11	−	5.54814e11i	−0.618638	−	1.07151i	−0.989734	−	0.142919i	$-0.954351\pi$
$401$	−3.20322e11	−	5.54814e11i	−0.618638	−	1.07151i	0.371096	−	0.928594i	$-0.378982\pi$
$402$	1.27223e11	−	2.20357e11i	0.242968	−	0.420833i
$403$	4.60352e10	−	7.97353e10i	0.0869396	−	0.150584i
$404$	−1.15739e11	−	2.00466e11i	−0.216154	−	0.374390i
$405$	2.63234e11			0.486177
$406$		0			0
$407$	−1.90142e11			−0.343481
$408$	7.45689e9	+	1.29157e10i	0.0133225	+	0.0230753i
$409$	−6.57499e9	+	1.13882e10i	−0.0116182	+	0.0201234i	−0.871776	−	0.489905i	$-0.837032\pi$
$409$	−6.57499e9	+	1.13882e10i	−0.0116182	+	0.0201234i	0.860158	+	0.510028i	$0.170365\pi$
$410$	2.76825e10	−	4.79474e10i	0.0483813	−	0.0837988i
$411$	1.42269e11	+	2.46418e11i	0.245936	+	0.425974i
$412$	−5.07281e11			−0.867384
$413$		0			0
$414$	−3.64256e11			−0.609404
$415$	1.01044e11	+	1.75014e11i	0.167223	+	0.289639i
$416$	−8.32360e9	+	1.44169e10i	−0.0136267	+	0.0236022i
$417$	3.54731e11	−	6.14412e11i	0.574495	−	0.995055i
$418$	−2.79824e11	−	4.84669e11i	−0.448324	−	0.776519i
$419$	5.79915e11			0.919182			0.459591	−	0.888131i	$-0.347996\pi$
$419$	5.79915e11			0.919182			0.459591	+	0.888131i	$0.347996\pi$
$420$		0			0
$421$	1.66175e11			0.257808			0.128904	−	0.991657i	$-0.458854\pi$
$421$	1.66175e11			0.257808			0.128904	+	0.991657i	$0.458854\pi$
$422$	−2.69583e11	−	4.66931e11i	−0.413795	−	0.716715i
$423$	2.60560e11	−	4.51304e11i	0.395710	−	0.685389i
$424$	1.22664e11	−	2.12461e11i	0.184320	−	0.319251i
$425$	1.77468e10	+	3.07384e10i	0.0263858	+	0.0457016i
$426$	2.60123e11			0.382680
$427$		0			0
$428$	1.06593e11			0.153544
$429$	6.58860e10	+	1.14118e11i	0.0939151	+	0.162666i
$430$	−8.13880e10	+	1.40968e11i	−0.114803	+	0.198844i
$431$	−3.78862e11	+	6.56208e11i	−0.528850	+	0.915996i	0.470584	+	0.882355i	$0.344043\pi$
$431$	−3.78862e11	+	6.56208e11i	−0.528850	+	0.915996i	−0.999434	+	0.0336404i	$0.989290\pi$
$432$	−5.83015e10	−	1.00981e11i	−0.0805383	−	0.139497i
$433$	1.07485e12			1.46944			0.734719	−	0.678371i	$-0.237314\pi$
$433$	1.07485e12			1.46944			0.734719	+	0.678371i	$0.237314\pi$
$434$		0			0
$435$	5.13895e11			0.688134
$436$	1.62459e11	+	2.81387e11i	0.215305	+	0.372919i
$437$	8.84766e11	−	1.53246e12i	1.16055	−	2.01012i
$438$	−4.16835e11	+	7.21980e11i	−0.541166	+	0.937328i
$439$	8.52092e10	+	1.47587e11i	0.109496	+	0.189652i	0.915566	−	0.402168i	$-0.131743\pi$
$439$	8.52092e10	+	1.47587e11i	0.109496	+	0.189652i	−0.806070	+	0.591820i	$0.798410\pi$
$440$	−1.08791e11			−0.138374
$441$		0			0
$442$	5.44051e9			0.00678016
$443$	−6.14684e11	−	1.06466e12i	−0.758290	−	1.31340i	−0.943722	−	0.330739i	$-0.892702\pi$
$443$	−6.14684e11	−	1.06466e12i	−0.758290	−	1.31340i	0.185432	−	0.982657i	$-0.440631\pi$
$444$	−8.47428e10	+	1.46779e11i	−0.103485	+	0.179242i
$445$	4.50113e10	−	7.79618e10i	0.0544128	−	0.0942457i
$446$	−3.09767e11	−	5.36532e11i	−0.370705	−	0.642079i
$447$	7.88963e10			0.0934701
$448$		0			0
$449$	−7.25792e10			−0.0842759			−0.0421380	−	0.999112i	$-0.513417\pi$
$449$	−7.25792e10			−0.0842759			−0.0421380	+	0.999112i	$0.513417\pi$
$450$	1.22194e11	+	2.11647e11i	0.140474	+	0.243308i
$451$	−1.55281e11	+	2.68955e11i	−0.176736	+	0.306115i
$452$	3.62915e11	−	6.28588e11i	0.408961	−	0.708342i
$453$	6.22140e11	+	1.07758e12i	0.694139	+	1.20228i
$454$	−1.23042e12			−1.35926
$455$		0			0
$456$	−4.98851e11			−0.540292
$457$	3.32086e11	+	5.75190e11i	0.356146	+	0.616862i	0.987313	−	0.158784i	$-0.0507574\pi$
$457$	3.32086e11	+	5.75190e11i	0.356146	+	0.616862i	−0.631168	+	0.775646i	$0.717424\pi$
$458$	3.48091e11	−	6.02912e11i	0.369657	−	0.640264i
$459$	−1.90537e10	+	3.30019e10i	−0.0200365	+	0.0347042i
$460$	−1.71991e11	−	2.97897e11i	−0.179100	−	0.310210i
$461$	1.21501e12			1.25293			0.626463	−	0.779451i	$-0.284502\pi$
$461$	1.21501e12			1.25293			0.626463	+	0.779451i	$0.284502\pi$
$462$		0			0
$463$	2.93878e11			0.297202			0.148601	−	0.988897i	$-0.452523\pi$
$463$	2.93878e11			0.297202			0.148601	+	0.988897i	$0.452523\pi$
$464$	−1.82086e11	−	3.15382e11i	−0.182367	−	0.315869i
$465$	2.68162e11	−	4.64470e11i	0.265986	−	0.460701i
$466$	1.65634e11	−	2.86887e11i	0.162710	−	0.281822i
$467$	2.36556e11	+	4.09727e11i	0.230149	+	0.398629i	0.957852	−	0.287263i	$-0.0927454\pi$
$467$	2.36556e11	+	4.09727e11i	0.230149	+	0.398629i	−0.727703	+	0.685892i	$0.759412\pi$
$468$	3.74602e10			0.0360964
$469$		0			0
$470$	4.92116e11			0.465187
$471$	3.76592e11	+	6.52277e11i	0.352596	+	0.610714i
$472$	3.39210e11	−	5.87528e11i	0.314579	−	0.544866i
$473$	4.56536e11	−	7.90744e11i	0.419372	−	0.726374i
$474$	6.75205e11	+	1.16949e12i	0.614374	+	1.06413i
$475$	−1.18723e12			−1.07007
$476$		0			0
$477$	−5.52049e11			−0.488253
$478$	−1.72976e11	−	2.99603e11i	−0.151552	−	0.262495i
$479$	−1.02973e12	+	1.78354e12i	−0.893742	+	1.54801i	−0.0583877	+	0.998294i	$0.518596\pi$
$479$	−1.02973e12	+	1.78354e12i	−0.893742	+	1.54801i	−0.835354	+	0.549712i	$0.814737\pi$
$480$	−4.84862e10	+	8.39805e10i	−0.0416900	+	0.0722092i
$481$	3.09140e10	+	5.35446e10i	0.0263331	+	0.0456103i
$482$	−1.08446e12			−0.915172
$483$		0			0
$484$	6.61383e9			0.00547834
$485$	−2.06181e11	−	3.57115e11i	−0.169204	−	0.293069i
$486$	−3.77921e11	+	6.54579e11i	−0.307283	+	0.532229i
$487$	6.11234e11	−	1.05869e12i	0.492411	−	0.852880i	−0.507551	−	0.861622i	$-0.669449\pi$
$487$	6.11234e11	−	1.05869e12i	0.492411	−	0.852880i	0.999962	+	0.00874154i	$0.00278255\pi$
$488$	1.05306e11	+	1.82396e11i	0.0840552	+	0.145588i
$489$	2.27197e12			1.79685
$490$		0			0
$491$	1.98225e11			0.153918			0.0769592	−	0.997034i	$-0.475479\pi$
$491$	1.98225e11			0.153918			0.0769592	+	0.997034i	$0.475479\pi$
$492$	1.38412e11	+	2.39737e11i	0.106496	+	0.184456i
$493$	−5.95080e10	+	1.03071e11i	−0.0453696	+	0.0785824i
$494$	−9.09898e10	+	1.57599e11i	−0.0687419	+	0.119064i
$495$	1.22403e11	+	2.12008e11i	0.0916365	+	0.158719i
$496$	−3.80066e11			−0.281963
$497$		0			0
$498$	−1.01044e12			−0.736174
$499$	1.50372e11	+	2.60453e11i	0.108571	+	0.188051i	0.915192	−	0.403019i	$-0.132039\pi$
$499$	1.50372e11	+	2.60453e11i	0.108571	+	0.188051i	−0.806620	+	0.591070i	$0.798706\pi$
$500$	−2.51393e11	+	4.35426e11i	−0.179882	+	0.311566i
$501$	1.05788e12	−	1.83230e12i	0.750181	−	1.29935i
$502$	3.90316e10	+	6.76048e10i	0.0274315	+	0.0475128i
$503$	−3.30194e11			−0.229993			−0.114996	−	0.993366i	$-0.536686\pi$
$503$	−3.30194e11			−0.229993			−0.114996	+	0.993366i	$0.536686\pi$
$504$		0			0
$505$	−4.91891e11			−0.336556
$506$	9.64762e11	+	1.67102e12i	0.654249	+	1.13319i
$507$	−8.79958e11	+	1.52413e12i	−0.591461	+	1.02444i
$508$	−6.96682e11	+	1.20669e12i	−0.464139	+	0.803911i
$509$	−3.16199e10	−	5.47673e10i	−0.0208800	−	0.0361653i	0.855397	−	0.517974i	$-0.173313\pi$
$509$	−3.16199e10	−	5.47673e10i	−0.0208800	−	0.0361653i	−0.876277	+	0.481808i	$0.839980\pi$
$510$	3.16918e10			0.0207434
$511$		0			0
$512$	6.87195e10			0.0441942
$513$	−6.37326e11	−	1.10388e12i	−0.406287	−	0.703710i
$514$	−2.20023e11	+	3.81091e11i	−0.139038	+	0.240821i
$515$	−5.38986e11	+	9.33552e11i	−0.337633	+	0.584798i
$516$	−4.06940e11	−	7.04841e11i	−0.252701	−	0.437691i
$517$	−2.76046e12			−1.69932
$518$		0			0
$519$	1.77725e12			1.07522
$520$	1.76876e10	+	3.06359e10i	0.0106085	+	0.0183745i
$521$	−9.44970e11	+	1.63674e12i	−0.561886	+	0.973215i	0.435446	+	0.900215i	$0.356591\pi$
$521$	−9.44970e11	+	1.63674e12i	−0.561886	+	0.973215i	−0.997332	+	0.0730001i	$0.976743\pi$
$522$	−4.09738e11	+	7.09687e11i	−0.241540	+	0.418360i
$523$	4.47932e11	+	7.75840e11i	0.261791	+	0.453435i	0.966718	−	0.255845i	$-0.0823537\pi$
$523$	4.47932e11	+	7.75840e11i	0.261791	+	0.453435i	−0.704927	+	0.709280i	$0.749020\pi$
$524$	1.64879e11			0.0955374
$525$		0			0
$526$	−3.56152e11			−0.202861
$527$	6.21052e10	+	1.07569e11i	0.0350736	+	0.0607493i
$528$	2.71977e11	−	4.71078e11i	0.152293	−	0.263779i
$529$	−2.14987e12	+	3.72369e12i	−1.19361	+	2.06739i
$530$	−2.60662e11	−	4.51479e11i	−0.143495	−	0.248540i
$531$	−1.52661e12			−0.833302
$532$		0			0
$533$	1.00985e11			0.0541981
$534$	2.25056e11	+	3.89809e11i	0.119772	+	0.207451i
$535$	1.13255e11	−	1.96164e11i	0.0597676	−	0.103520i
$536$	−1.91583e11	+	3.31832e11i	−0.100257	+	0.173651i
$537$	−3.43732e11	−	5.95362e11i	−0.178376	−	0.308956i
$538$	−2.76826e11			−0.142458
$539$		0			0
$540$	−2.47781e11			−0.125400
$541$	−5.01106e11	−	8.67941e11i	−0.251502	−	0.435615i	0.712437	−	0.701736i	$-0.247591\pi$
$541$	−5.01106e11	−	8.67941e11i	−0.251502	−	0.435615i	−0.963940	+	0.266121i	$0.914258\pi$
$542$	3.85520e11	−	6.67741e11i	0.191889	−	0.332362i
$543$	−1.06025e12	+	1.83640e12i	−0.523369	+	0.906502i
$544$	−1.12292e10	−	1.94495e10i	−0.00549736	−	0.00952170i
$545$	6.90450e11			0.335234
$546$		0			0
$547$	2.73436e12			1.30591			0.652955	−	0.757396i	$-0.273529\pi$
$547$	2.73436e12			1.30591			0.652955	+	0.757396i	$0.273529\pi$
$548$	−2.14241e11	−	3.71076e11i	−0.101482	−	0.175772i
$549$	2.36965e11	−	4.10435e11i	0.111329	−	0.192827i
$550$	6.47285e11	−	1.12113e12i	0.301622	−	0.522425i
$551$	−1.99048e12	−	3.44762e12i	−0.919975	−	1.59344i
$552$	1.71991e12			0.788461
$553$		0			0
$554$	1.28613e12			0.580086
$555$	1.80078e11	+	3.11905e11i	0.0805644	+	0.139542i
$556$	−5.34183e11	+	9.25232e11i	−0.237057	+	0.410595i
$557$	2.11179e12	−	3.65773e12i	0.929614	−	1.61014i	0.145648	−	0.989336i	$-0.453473\pi$
$557$	2.11179e12	−	3.65773e12i	0.929614	−	1.61014i	0.783967	−	0.620803i	$-0.213193\pi$
$558$	4.27621e11	+	7.40661e11i	0.186726	+	0.323419i
$559$	−2.96902e11			−0.128606
$560$		0			0
$561$	−1.77771e11			−0.0757754
$562$	1.56476e12	+	2.71025e12i	0.661661	+	1.14603i
$563$	−1.54155e12	+	2.67005e12i	−0.646652	+	1.12003i	0.337265	+	0.941410i	$0.390498\pi$
$563$	−1.54155e12	+	2.67005e12i	−0.646652	+	1.12003i	−0.983917	+	0.178624i	$0.942835\pi$
$564$	−1.23029e12	+	2.13092e12i	−0.511978	+	0.886772i
$565$	−7.71195e11	−	1.33575e12i	−0.318380	−	0.551451i
$566$	9.64483e11			0.395021
$567$		0			0
$568$	−3.91715e11			−0.157907
$569$	1.37335e11	+	2.37871e11i	0.0549256	+	0.0951340i	0.892181	−	0.451678i	$-0.149174\pi$
$569$	1.37335e11	+	2.37871e11i	0.0549256	+	0.0951340i	−0.837255	+	0.546812i	$0.815841\pi$
$570$	−5.30029e11	+	9.18037e11i	−0.210311	+	0.364270i
$571$	−1.41250e12	+	2.44651e12i	−0.556064	+	0.963130i	0.441756	+	0.897135i	$0.354356\pi$
$571$	−1.41250e12	+	2.44651e12i	−0.556064	+	0.963130i	−0.997820	+	0.0659953i	$0.978978\pi$
$572$	−9.92166e10	−	1.71848e11i	−0.0387527	−	0.0671217i
$573$	6.49310e11			0.251626
$574$		0			0
$575$	4.09326e12			1.56158
$576$	−7.73178e10	−	1.33918e11i	−0.0292670	−	0.0506919i
$577$	1.88293e12	−	3.26132e12i	0.707199	−	1.22491i	−0.258693	−	0.965960i	$-0.583292\pi$
$577$	1.88293e12	−	3.26132e12i	0.707199	−	1.22491i	0.965892	−	0.258946i	$-0.0833750\pi$
$578$	9.45033e11	−	1.63685e12i	0.352186	−	0.610004i
$579$	−2.05014e12	−	3.55095e12i	−0.758107	−	1.31308i
$580$	−7.73866e11			−0.283949
$581$		0			0
$582$	2.06181e12			0.744894
$583$	1.46215e12	+	2.53252e12i	0.524183	+	0.907912i
$584$	6.27705e11	−	1.08722e12i	0.223305	−	0.386775i
$585$	3.98015e10	−	6.89382e10i	0.0140507	−	0.0243365i
$586$	−3.89395e11	−	6.74451e11i	−0.136411	−	0.236271i
$587$	3.00831e12			1.04580			0.522902	−	0.852393i	$-0.324849\pi$
$587$	3.00831e12			1.04580			0.522902	+	0.852393i	$0.324849\pi$
$588$		0			0
$589$	−4.15471e12			−1.42240
$590$	−7.20820e11	−	1.24850e12i	−0.244902	−	0.424183i
$591$	−1.06079e12	+	1.83733e12i	−0.357671	+	0.619504i
$592$	1.27613e11	−	2.21032e11i	0.0427018	−	0.0739617i
$593$	1.82387e12	+	3.15904e12i	0.605688	+	1.04908i	0.991942	+	0.126690i	$0.0404352\pi$
$593$	1.82387e12	+	3.15904e12i	0.605688	+	1.04908i	−0.386255	+	0.922392i	$0.626231\pi$
$594$	1.38990e12			0.458083
$595$		0			0
$596$	−1.18809e11			−0.0385691
$597$	2.49158e11	+	4.31555e11i	0.0802769	+	0.139044i
$598$	3.13710e11	−	5.43361e11i	0.100317	−	0.173753i
$599$	−2.08889e12	+	3.61807e12i	−0.662972	+	1.14830i	0.316859	+	0.948473i	$0.397372\pi$
$599$	−2.08889e12	+	3.61807e12i	−0.662972	+	1.14830i	−0.979831	+	0.199829i	$0.935961\pi$
$600$	−5.76967e11	−	9.99336e11i	−0.181748	−	0.314797i
$601$	−4.84445e12			−1.51464			−0.757321	−	0.653043i	$-0.773492\pi$
$601$	−4.84445e12			−1.51464			−0.757321	+	0.653043i	$0.773492\pi$
$602$		0			0
$603$	8.62218e11			0.265576
$604$	−9.36870e11	−	1.62271e12i	−0.286426	−	0.496105i
$605$	7.02720e9	−	1.21715e10i	0.00213247	−	0.00369355i
$606$	1.22973e12	−	2.12995e12i	0.370410	−	0.641568i
$607$	−7.92222e11	−	1.37217e12i	−0.236863	−	0.410259i	0.722949	−	0.690901i	$-0.242786\pi$
$607$	−7.92222e11	−	1.37217e12i	−0.236863	−	0.410259i	−0.959813	+	0.280642i	$0.909453\pi$
$608$	7.51210e11			0.222944
$609$		0			0
$610$	4.47551e11			0.130876
$611$	4.48807e11	+	7.77357e11i	0.130279	+	0.225650i
$612$	−2.52684e10	+	4.37662e10i	−0.00728110	+	0.0126112i
$613$	1.39602e11	−	2.41797e11i	0.0399318	−	0.0691638i	−0.845369	−	0.534183i	$-0.820619\pi$
$613$	1.39602e11	−	2.41797e11i	0.0399318	−	0.0691638i	0.885301	+	0.465019i	$0.153953\pi$
$614$	2.20142e12	+	3.81298e12i	0.625095	+	1.08270i
$615$	5.88252e11			0.165816
$616$		0			0
$617$	−5.55576e12			−1.54333			−0.771667	−	0.636027i	$-0.780577\pi$
$617$	−5.55576e12			−1.54333			−0.771667	+	0.636027i	$0.780577\pi$
$618$	−2.69493e12	−	4.66776e12i	−0.743190	−	1.28724i
$619$	−1.35218e12	+	2.34205e12i	−0.370192	+	0.641192i	−0.989595	−	0.143881i	$-0.954042\pi$
$619$	−1.35218e12	+	2.34205e12i	−0.370192	+	0.641192i	0.619402	+	0.785074i	$0.287375\pi$
$620$	−4.03820e11	+	6.99437e11i	−0.109755	+	0.190102i
$621$	2.19734e12	+	3.80590e12i	0.592904	+	1.02694i
$622$	−1.79715e12			−0.481423
$623$		0			0
$624$	−1.76876e11			−0.0467024
$625$	−1.08414e12	−	1.87778e12i	−0.284200	−	0.492249i
$626$	−8.49117e11	+	1.47071e12i	−0.220995	+	0.382775i
$627$	2.97313e12	−	5.14961e12i	0.768263	−	1.33067i
$628$	−5.67104e11	−	9.82253e11i	−0.145494	−	0.252002i
$629$	−8.34109e10			−0.0212469
$630$		0			0
$631$	−4.73158e12			−1.18816			−0.594078	−	0.804407i	$-0.702483\pi$
$631$	−4.73158e12			−1.18816			−0.594078	+	0.804407i	$0.702483\pi$
$632$	−1.01678e12	−	1.76111e12i	−0.253513	−	0.439097i
$633$	2.86431e12	−	4.96114e12i	0.709094	−	1.22819i
$634$	−1.85086e10	+	3.20579e10i	−0.00454959	+	0.00788012i
$635$	1.48045e12	+	2.56421e12i	0.361336	+	0.625853i
$636$	2.60662e12			0.631713
$637$		0			0
$638$	4.34090e12			1.03726
$639$	4.40727e11	+	7.63362e11i	0.104572	+	0.181124i
$640$	7.30144e10	−	1.26465e11i	0.0172028	−	0.0297961i
$641$	−6.94327e11	+	1.20261e12i	−0.162444	+	0.281361i	−0.935745	−	0.352679i	$-0.885271\pi$
$641$	−6.94327e11	+	1.20261e12i	−0.162444	+	0.281361i	0.773301	+	0.634039i	$0.218604\pi$
$642$	5.66275e11	+	9.80818e11i	0.131559	+	0.227867i
$643$	−3.09398e12			−0.713786			−0.356893	−	0.934145i	$-0.616164\pi$
$643$	−3.09398e12			−0.713786			−0.356893	+	0.934145i	$0.616164\pi$
$644$		0			0
$645$	−1.72950e12			−0.393460
$646$	−1.22753e11	−	2.12614e11i	−0.0277322	−	0.0480336i
$647$	1.15726e12	−	2.00444e12i	0.259635	−	0.449701i	−0.706509	−	0.707704i	$-0.749731\pi$
$647$	1.15726e12	−	2.00444e12i	0.259635	−	0.449701i	0.966144	+	0.258003i	$0.0830645\pi$
$648$	9.90998e11	−	1.71646e12i	0.220793	−	0.382425i
$649$	4.04335e12	+	7.00329e12i	0.894624	+	1.54953i
$650$	−4.20953e11			−0.0924960
$651$		0			0
$652$	−3.42132e12			−0.741446
$653$	4.05287e11	+	7.01978e11i	0.0872276	+	0.151083i	0.906338	−	0.422553i	$-0.138866\pi$
$653$	4.05287e11	+	7.01978e11i	0.0872276	+	0.151083i	−0.819111	+	0.573635i	$0.805533\pi$
$654$	−1.72612e12	+	2.98974e12i	−0.368954	+	0.639047i
$655$	1.75184e11	−	3.03427e11i	0.0371884	−	0.0644122i
$656$	−2.08433e11	−	3.61016e11i	−0.0439439	−	0.0761130i
$657$	−2.82498e12			−0.591522
$658$		0			0
$659$	4.57355e11			0.0944645			0.0472323	−	0.998884i	$-0.484960\pi$
$659$	4.57355e11			0.0944645			0.0472323	+	0.998884i	$0.484960\pi$
$660$	−5.77951e11	−	1.00104e12i	−0.118561	−	0.205354i
$661$	3.97279e12	−	6.88107e12i	0.809447	−	1.40200i	−0.103800	−	0.994598i	$-0.533100\pi$
$661$	3.97279e12	−	6.88107e12i	0.809447	−	1.40200i	0.913247	−	0.407406i	$-0.133566\pi$
$662$	1.72948e12	−	2.99555e12i	0.349990	−	0.606200i
$663$	2.89027e10	+	5.00610e10i	0.00580936	+	0.0100621i
$664$	1.52161e12			0.303772
$665$		0			0
$666$	−5.74319e11			−0.113115
$667$	6.86268e12	+	1.18865e13i	1.34254	+	2.32535i
$668$	−1.59304e12	+	2.75923e12i	−0.309552	+	0.536159i
$669$	3.29127e12	−	5.70065e12i	0.635252	−	1.10029i
$670$	4.07114e11	+	7.05143e11i	0.0780512	+	0.135189i
$671$	−2.51048e12			−0.478086
$672$		0			0
$673$	−8.92805e12			−1.67760			−0.838801	−	0.544439i	$-0.816743\pi$
$673$	−8.92805e12			−1.67760			−0.838801	+	0.544439i	$0.816743\pi$
$674$	−4.00232e11	−	6.93223e11i	−0.0747038	−	0.129391i
$675$	1.47425e12	−	2.55348e12i	0.273341	−	0.473440i
$676$	1.32511e12	−	2.29516e12i	0.244058	−	0.422721i
$677$	−4.00865e12	−	6.94319e12i	−0.733414	−	1.27031i	−0.955416	−	0.295264i	$-0.904592\pi$
$677$	−4.00865e12	−	6.94319e12i	−0.733414	−	1.27031i	0.222001	−	0.975046i	$-0.428741\pi$
$678$	7.71195e12			1.40162
$679$		0			0
$680$	−4.77241e10			−0.00855949
$681$	−6.53660e12	−	1.13217e13i	−1.16463	−	2.01721i
$682$	2.26518e12	−	3.92341e12i	0.400934	−	0.694438i
$683$	−2.07362e12	+	3.59162e12i	−0.364617	+	0.631534i	−0.988715	−	0.149812i	$-0.952133\pi$
$683$	−2.07362e12	+	3.59162e12i	−0.364617	+	0.631534i	0.624098	+	0.781346i	$0.285467\pi$
$684$	−8.45203e11	−	1.46394e12i	−0.147642	−	0.255723i
$685$	−9.10523e11			−0.158010
$686$		0			0
$687$	7.39694e12			1.26691
$688$	6.12804e11	+	1.06141e12i	0.104273	+	0.180607i
$689$	4.75444e11	−	8.23493e11i	0.0803735	−	0.139211i
$690$	1.82740e12	−	3.16516e12i	0.306912	−	0.531587i
$691$	−3.02790e12	−	5.24447e12i	−0.505231	−	0.875086i	−0.999982	−	0.00605086i	$-0.998074\pi$
$691$	−3.02790e12	−	5.24447e12i	−0.505231	−	0.875086i	0.494751	−	0.869035i	$-0.335259\pi$
$692$	−2.67633e12			−0.443672
$693$		0			0
$694$	−2.95370e12			−0.483336
$695$	1.13514e12	+	1.96612e12i	0.184551	+	0.319652i
$696$	1.93466e12	−	3.35094e12i	0.312510	−	0.541283i
$697$	−6.81184e10	+	1.17985e11i	−0.0109324	+	0.0189355i
$698$	2.19733e12	+	3.80589e12i	0.350385	+	0.606885i
$699$	3.51973e12			0.557651
$700$		0			0
$701$	1.88599e12			0.294990			0.147495	−	0.989063i	$-0.452879\pi$
$701$	1.88599e12			0.294990			0.147495	+	0.989063i	$0.452879\pi$
$702$	−2.25975e11	−	3.91400e11i	−0.0351191	−	0.0608281i
$703$	1.39500e12	−	2.41622e12i	0.215415	−	0.373110i
$704$	−4.09565e11	+	7.09388e11i	−0.0628415	+	0.108845i
$705$	2.61437e12	+	4.52822e12i	0.398580	+	0.690361i
$706$	2.52886e12			0.383092
$707$		0			0
$708$	7.20820e12			1.07815
$709$	2.38105e12	+	4.12410e12i	0.353884	+	0.612944i	0.986926	−	0.161173i	$-0.0515276\pi$
$709$	2.38105e12	+	4.12410e12i	0.353884	+	0.612944i	−0.633043	+	0.774117i	$0.718194\pi$
$710$	−4.16197e11	+	7.20875e11i	−0.0614662	+	0.106463i
$711$	−2.28800e12	+	3.96293e12i	−0.335771	+	0.581572i
$712$	−3.38908e11	−	5.87006e11i	−0.0494222	−	0.0856018i
$713$	1.43244e13			2.07574
$714$		0			0
$715$	−4.21671e11			−0.0603387
$716$	5.17620e11	+	8.96544e11i	0.0736042	+	0.127486i
$717$	1.83787e12	−	3.18329e12i	0.259704	−	0.449821i
$718$	−2.72607e12	+	4.72170e12i	−0.382805	+	0.663038i
$719$	2.67447e12	+	4.63231e12i	0.373213	+	0.646424i	0.990058	−	0.140661i	$-0.0449226\pi$
$719$	2.67447e12	+	4.63231e12i	0.373213	+	0.646424i	−0.616845	+	0.787085i	$0.711589\pi$
$720$	−3.28601e11			−0.0455693
$721$		0			0
$722$	3.04889e12			0.417565
$723$	−5.76120e12	−	9.97870e12i	−0.784135	−	1.35816i
$724$	1.59661e12	−	2.76541e12i	0.215961	−	0.374055i
$725$	4.60436e12	−	7.97498e12i	0.618939	−	1.07203i
$726$	3.51360e10	+	6.08573e10i	0.00469394	+	0.00813014i
$727$	−9.08222e12			−1.20583			−0.602917	−	0.797804i	$-0.705995\pi$
$727$	−9.08222e12			−1.20583			−0.602917	+	0.797804i	$0.705995\pi$
$728$		0			0
$729$	1.49349e12			0.195852
$730$	−1.33387e12	−	2.31033e12i	−0.173845	−	0.301108i
$731$	2.00272e11	−	3.46882e11i	0.0259413	−	0.0449317i
$732$	−1.11888e12	+	1.93795e12i	−0.144040	+	0.249484i
$733$	−6.02735e12	−	1.04397e13i	−0.771185	−	1.33573i	−0.936914	−	0.349560i	$-0.886331\pi$
$733$	−6.02735e12	−	1.04397e13i	−0.771185	−	1.33573i	0.165729	−	0.986171i	$-0.447002\pi$
$734$	9.76345e12			1.24157
$735$		0			0
$736$	−2.58998e12			−0.325347
$737$	−2.28366e12	−	3.95541e12i	−0.285120	−	0.493842i
$738$	−4.69024e11	+	8.12374e11i	−0.0582025	+	0.100810i
$739$	−5.40642e12	+	9.36419e12i	−0.666822	+	1.15497i	0.311966	+	0.950093i	$0.399012\pi$
$739$	−5.40642e12	+	9.36419e12i	−0.666822	+	1.15497i	−0.978788	+	0.204876i	$0.934321\pi$
$740$	−2.71177e11	−	4.69692e11i	−0.0332438	−	0.0575799i
$741$	−1.93353e12			−0.235597
$742$		0			0
$743$	6.39433e12			0.769742			0.384871	−	0.922970i	$-0.374246\pi$
$743$	6.39433e12			0.769742			0.384871	+	0.922970i	$0.374246\pi$
$744$	−2.01910e12	−	3.49719e12i	−0.241590	−	0.418447i
$745$	−1.26234e11	+	2.18644e11i	−0.0150132	+	0.0260036i
$746$	−3.47944e12	+	6.02657e12i	−0.411325	+	0.712436i
$747$	−1.71200e12	−	2.96527e12i	−0.201169	−	0.348434i
$748$	2.67702e11			0.0312676
$749$		0			0
$750$	−5.34211e12			−0.616506
$751$	1.15290e12	+	1.99688e12i	0.132255	+	0.229072i	0.924545	−	0.381072i	$-0.124445\pi$
$751$	1.15290e12	+	1.99688e12i	0.132255	+	0.229072i	−0.792291	+	0.610144i	$0.791112\pi$
$752$	1.85267e12	−	3.20892e12i	0.211260	−	0.365914i
$753$	−4.14711e11	+	7.18301e11i	−0.0470076	+	0.0814196i
$754$	−7.05761e11	−	1.22241e12i	−0.0795219	−	0.137736i
$755$	−3.98170e12			−0.445971
$756$		0			0
$757$	−6.85316e12			−0.758507			−0.379253	−	0.925293i	$-0.623819\pi$
$757$	−6.85316e12			−0.758507			−0.379253	+	0.925293i	$0.623819\pi$
$758$	5.84541e12	+	1.01246e13i	0.643138	+	1.11395i
$759$	−1.02506e13	+	1.77546e13i	−1.12114	+	1.94188i
$760$	7.98161e11	−	1.38246e12i	0.0867819	−	0.150311i
$761$	−7.77599e11	−	1.34684e12i	−0.0840474	−	0.145574i	0.820937	−	0.571018i	$-0.193451\pi$
$761$	−7.77599e11	−	1.34684e12i	−0.0840474	−	0.145574i	−0.904985	+	0.425444i	$0.860118\pi$
$762$	−1.48045e13			−1.59073
$763$		0			0
$764$	−9.77784e11			−0.103830
$765$	5.36954e10	+	9.30032e10i	0.00566841	+	0.00981797i
$766$	1.68859e12	−	2.92472e12i	0.177213	−	0.306941i
$767$	1.31477e12	−	2.27725e12i	0.137173	−	0.237591i
$768$	3.65072e11	+	6.32324e11i	0.0378663	+	0.0655864i
$769$	1.31148e12			0.135236			0.0676179	−	0.997711i	$-0.478460\pi$
$769$	1.31148e12			0.135236			0.0676179	+	0.997711i	$0.478460\pi$
$770$		0			0
$771$	−4.67549e12			−0.476521
$772$	3.08727e12	+	5.34731e12i	0.312822	+	0.541823i
$773$	−4.91005e12	+	8.50446e12i	−0.494627	+	0.856720i	−0.999981	−	0.00619265i	$-0.998029\pi$
$773$	−4.91005e12	+	8.50446e12i	−0.494627	+	0.856720i	0.505353	+	0.862912i	$0.331362\pi$
$774$	1.37896e12	−	2.38843e12i	0.138107	−	0.239209i
$775$	−4.80531e12	−	8.32304e12i	−0.478480	−	0.828751i
$776$	−3.10484e12			−0.307370
$777$		0			0
$778$	1.15497e11			0.0113022
$779$	−2.27849e12	−	3.94646e12i	−0.221681	−	0.383963i
$780$	−1.87931e11	+	3.25506e11i	−0.0181791	+	0.0314872i
$781$	2.33461e12	−	4.04366e12i	0.224535	−	0.388906i
$782$	4.23220e11	+	7.33038e11i	0.0404702	+	0.0700965i
$783$	9.88682e12			0.940001
$784$		0			0
$785$	−2.41019e12			−0.226536
$786$	8.75918e11	+	1.51713e12i	0.0818581	+	0.141782i
$787$	−2.40829e12	+	4.17128e12i	−0.223781	+	0.387600i	−0.955953	−	0.293520i	$-0.905173\pi$
$787$	−2.40829e12	+	4.17128e12i	−0.223781	+	0.387600i	0.732172	+	0.681120i	$0.238507\pi$
$788$	1.59742e12	−	2.76681e12i	0.147588	−	0.255630i
$789$	−1.89206e12	−	3.27714e12i	−0.173815	−	0.301057i
$790$	−4.32131e12			−0.394724
$791$		0			0
$792$	1.84324e12			0.166464
$793$	4.08164e11	+	7.06961e11i	0.0366527	+	0.0634843i
$794$	−5.59509e12	+	9.69099e12i	−0.499592	+	0.865318i
$795$	2.76953e12	−	4.79697e12i	0.245897	−	0.425907i
$796$	−3.75203e11	−	6.49870e11i	−0.0331251	−	0.0573744i
$797$	−7.71344e12			−0.677151			−0.338575	−	0.940939i	$-0.609945\pi$
$797$	−7.71344e12			−0.677151			−0.338575	+	0.940939i	$0.609945\pi$
$798$		0			0
$799$	−1.21095e12			−0.105116
$800$	8.68844e11	+	1.50488e12i	0.0749958	+	0.129897i
$801$	−7.62626e11	+	1.32091e12i	−0.0654584	+	0.113377i
$802$	−5.12515e12	+	8.87702e12i	−0.437443	+	0.757674i
$803$	7.48219e12	+	1.29595e13i	0.635051	+	1.09994i
$804$	−4.07114e12			−0.343609
$805$		0			0
$806$	−1.47313e12			−0.122951
$807$	−1.47064e12	−	2.54722e12i	−0.122061	−	0.211415i
$808$	−1.85183e12	+	3.20746e12i	−0.152844	+	0.264734i
$809$	−1.06435e13	+	1.84350e13i	−0.873604	+	1.51313i	−0.0153618	+	0.999882i	$0.504890\pi$
$809$	−1.06435e13	+	1.84350e13i	−0.873604	+	1.51313i	−0.858242	+	0.513245i	$0.828443\pi$
$810$	−2.10587e12	−	3.64747e12i	−0.171889	−	0.297721i
$811$	−2.45053e13			−1.98914			−0.994570	−	0.104067i	$-0.966814\pi$
$811$	−2.45053e13			−1.98914			−0.994570	+	0.104067i	$0.966814\pi$
$812$		0			0
$813$	8.19231e12			0.657656
$814$	1.52113e12	+	2.63468e12i	0.121439	+	0.210338i
$815$	−3.63515e12	+	6.29627e12i	−0.288611	+	0.499889i
$816$	1.19310e11	−	2.06651e11i	0.00942046	−	0.0163167i
$817$	6.69890e12	+	1.16028e13i	0.526022	+	0.911097i
$818$	2.10400e11			0.0164307
$819$		0			0
$820$	−8.85839e11			−0.0684214
$821$	4.86413e12	+	8.42492e12i	0.373646	+	0.647175i	0.990123	−	0.140198i	$-0.0447740\pi$
$821$	4.86413e12	+	8.42492e12i	0.373646	+	0.647175i	−0.616477	+	0.787373i	$0.711441\pi$
$822$	2.27631e12	−	3.94268e12i	0.173903	−	0.301209i
$823$	4.14372e11	−	7.17714e11i	0.0314841	−	0.0545321i	−0.849854	−	0.527018i	$-0.823310\pi$
$823$	4.14372e11	−	7.17714e11i	0.0314841	−	0.0545321i	0.881338	+	0.472486i	$0.156643\pi$
$824$	4.05825e12	+	7.02910e12i	0.306667	+	0.531162i
$825$	1.37548e13			1.03374
$826$		0			0
$827$	2.42842e13			1.80530			0.902649	−	0.430376i	$-0.141619\pi$
$827$	2.42842e13			1.80530			0.902649	+	0.430376i	$0.141619\pi$
$828$	2.91405e12	+	5.04728e12i	0.215457	+	0.373182i
$829$	9.77849e12	−	1.69368e13i	0.719078	−	1.24548i	−0.242287	−	0.970205i	$-0.577898\pi$
$829$	9.77849e12	−	1.69368e13i	0.719078	−	1.24548i	0.961365	−	0.275276i	$-0.0887692\pi$
$830$	1.61671e12	−	2.80023e12i	0.118245	−	0.204806i
$831$	6.83259e12	+	1.18344e13i	0.497028	+	0.860877i
$832$	2.66355e11			0.0192711
$833$		0			0
$834$	−1.13514e13			−0.812459
$835$	3.38521e12	+	5.86336e12i	0.240989	+	0.417405i
$836$	−4.47718e12	+	7.75471e12i	−0.317013	+	0.549082i
$837$	5.15916e12	−	8.93592e12i	0.363341	−	0.629325i
$838$	−4.63932e12	−	8.03554e12i	−0.324980	−	0.562882i
$839$	7.69577e12			0.536196			0.268098	−	0.963392i	$-0.413605\pi$
$839$	7.69577e12			0.536196			0.268098	+	0.963392i	$0.413605\pi$
$840$		0			0
$841$	1.63712e13			1.12849
$842$	−1.32940e12	−	2.30259e12i	−0.0911489	−	0.157875i
$843$	−1.66256e13	+	2.87964e13i	−1.13384	+	1.96388i
$844$	−4.31332e12	+	7.47089e12i	−0.292598	+	0.506794i
$845$	−2.81587e12	−	4.87722e12i	−0.190001	−	0.329092i
$846$	−8.33793e12			−0.559618
$847$		0			0
$848$	−3.92526e12			−0.260667
$849$	5.12382e12	+	8.87471e12i	0.338461	+	0.586232i
$850$	2.83949e11	−	4.91815e11i	0.0186576	−	0.0323159i
$851$	−4.80962e12	+	8.33051e12i	−0.314360	+	0.544488i
$852$	−2.08099e12	−	3.60437e12i	−0.135298	−	0.234343i
$853$	2.79895e12			0.181019			0.0905097	−	0.995896i	$-0.471150\pi$
$853$	2.79895e12			0.181019			0.0905097	+	0.995896i	$0.471150\pi$
$854$		0			0
$855$	−3.59211e12			−0.229881
$856$	−8.52744e11	−	1.47700e12i	−0.0542859	−	0.0940259i
$857$	−2.78071e12	+	4.81632e12i	−0.176093	+	0.305002i	−0.940539	−	0.339686i	$-0.889679\pi$
$857$	−2.78071e12	+	4.81632e12i	−0.176093	+	0.305002i	0.764446	+	0.644688i	$0.223013\pi$
$858$	1.05418e12	−	1.82589e12i	0.0664080	−	0.115022i
$859$	1.75526e12	+	3.04020e12i	0.109995	+	0.190516i	0.915768	−	0.401708i	$-0.131583\pi$
$859$	1.75526e12	+	3.04020e12i	0.109995	+	0.190516i	−0.805773	+	0.592224i	$0.798250\pi$
$860$	2.60442e12			0.162356
$861$		0			0
$862$	1.21236e13			0.747908
$863$	−7.19188e12	−	1.24567e13i	−0.441361	−	0.764459i	0.556430	−	0.830894i	$-0.312171\pi$
$863$	−7.19188e12	−	1.24567e13i	−0.441361	−	0.764459i	−0.997791	+	0.0664354i	$0.978837\pi$
$864$	−9.32824e11	+	1.61570e12i	−0.0569492	+	0.0986389i
$865$	−2.84360e12	+	4.92526e12i	−0.172702	+	0.299128i
$866$	−8.59878e12	−	1.48935e13i	−0.519525	−	0.899844i
$867$	2.00820e13			1.20704
$868$		0			0
$869$	2.42399e13			1.44192
$870$	−4.11116e12	−	7.12074e12i	−0.243292	−	0.421394i
$871$	−7.42572e11	+	1.28617e12i	−0.0437177	+	0.0757212i
$872$	2.59934e12	−	4.50219e12i	0.152244	−	0.263694i
$873$	3.49332e12	+	6.05061e12i	0.203551	+	0.352562i
$874$	−2.83125e13			−1.64126
$875$		0			0
$876$	1.33387e13			0.765325
$877$	3.17139e12	+	5.49301e12i	0.181030	+	0.313554i	0.942232	−	0.334962i	$-0.108723\pi$
$877$	3.17139e12	+	5.49301e12i	0.181030	+	0.313554i	−0.761201	+	0.648516i	$0.775390\pi$
$878$	1.36335e12	−	2.36139e12i	0.0774250	−	0.134104i
$879$	4.13732e12	−	7.16604e12i	0.233759	−	0.404883i
$880$	8.70326e11	+	1.50745e12i	0.0489227	+	0.0847366i
$881$	2.89282e13			1.61782			0.808910	−	0.587933i	$-0.200058\pi$
$881$	2.89282e13			1.61782			0.808910	+	0.587933i	$0.200058\pi$
$882$		0			0
$883$	−7.17154e12			−0.396999			−0.198500	−	0.980101i	$-0.563607\pi$
$883$	−7.17154e12			−0.396999			−0.198500	+	0.980101i	$0.563607\pi$
$884$	−4.35241e10	−	7.53860e10i	−0.00239715	−	0.00415198i
$885$	7.65872e12	−	1.32653e13i	0.419673	−	0.726895i
$886$	−9.83495e12	+	1.70346e13i	−0.536192	+	0.928712i
$887$	−8.40098e12	−	1.45509e13i	−0.455695	−	0.789286i	0.543033	−	0.839711i	$-0.317276\pi$
$887$	−8.40098e12	−	1.45509e13i	−0.455695	−	0.789286i	−0.998728	+	0.0504251i	$0.983942\pi$
$888$	2.71177e12			0.146351
$889$		0			0
$890$	−1.44036e12			−0.0769513
$891$	1.18126e13	+	2.04601e13i	0.627909	+	1.08757i
$892$	−4.95627e12	+	8.58451e12i	−0.262128	+	0.454018i
$893$	2.02526e13	−	3.50785e13i	1.06573	−	1.84591i
$894$	−6.31170e11	−	1.09322e12i	−0.0330467	−	0.0572385i
$895$	2.19989e12			0.114603
$896$		0			0
$897$	6.66633e12			0.343812
$898$	5.80634e11	+	1.00569e12i	0.0297960	+	0.0516083i
$899$	1.61130e13	−	2.79085e13i	0.822730	−	1.42501i
$900$	1.95511e12	−	3.38635e12i	0.0993300	−	0.172045i
$901$	6.41412e11	+	1.11096e12i	0.0324247	+	0.0561612i
$902$	4.96900e12			0.249942
$903$		0			0
$904$	−1.16133e13			−0.578359
$905$	−3.39279e12	−	5.87649e12i	−0.168128	−	0.291205i
$906$	9.95424e12	−	1.72412e13i	0.490830	−	0.850143i
$907$	9.39618e12	−	1.62747e13i	0.461019	−	0.798508i	−0.537993	−	0.842949i	$-0.680817\pi$
$907$	9.39618e12	−	1.62747e13i	0.461019	−	0.798508i	0.999012	+	0.0444412i	$0.0141507\pi$
$908$	9.84335e12	+	1.70492e13i	0.480570	+	0.832371i
$909$	8.33412e12			0.404876
$910$		0			0
$911$	−3.39496e13			−1.63306			−0.816529	−	0.577304i	$-0.804105\pi$
$911$	−3.39496e13			−1.63306			−0.816529	+	0.577304i	$0.804105\pi$
$912$	3.99080e12	+	6.91228e12i	0.191022	+	0.330860i
$913$	−9.06874e12	+	1.57075e13i	−0.431945	+	0.748151i
$914$	5.31337e12	−	9.20303e12i	0.251833	−	0.436187i
$915$	2.37762e12	+	4.11815e12i	0.112136	+	0.194226i
$916$	−1.11389e13			−0.522773
$917$		0			0
$918$	6.09717e11			0.0283359
$919$	−5.16434e12	−	8.94490e12i	−0.238833	−	0.413672i	0.721546	−	0.692366i	$-0.243432\pi$
$919$	−5.16434e12	−	8.94490e12i	−0.238833	−	0.413672i	−0.960380	+	0.278694i	$0.910098\pi$
$920$	−2.75186e12	+	4.76636e12i	−0.126643	+	0.219352i
$921$	−2.33901e13	+	4.05129e13i	−1.07118	+	1.85535i
$922$	−9.72007e12	−	1.68357e13i	−0.442976	−	0.767257i
$923$	−1.51828e12			−0.0688563
$924$		0			0
$925$	6.45381e12			0.289853
$926$	−2.35102e12	−	4.07209e12i	−0.105077	−	0.181999i
$927$	9.13206e12	−	1.58172e13i	0.406172	−	0.703510i
$928$	−2.91338e12	+	5.04612e12i	−0.128953	+	0.223353i
$929$	−1.39883e13	−	2.42285e13i	−0.616163	−	1.06723i	−0.990179	−	0.139803i	$-0.955353\pi$
$929$	−1.39883e13	−	2.42285e13i	−0.616163	−	1.06723i	0.374017	−	0.927422i	$-0.377980\pi$
$930$	−8.58118e12			−0.376161
$931$		0			0
$932$	−5.30030e12			−0.230107
$933$	−9.54735e12	−	1.65365e13i	−0.412492	−	0.714457i
$934$	3.78490e12	−	6.55564e12i	0.162740	−	0.281873i
$935$	2.84434e11	−	4.92654e11i	0.0121711	−	0.0210809i
$936$	−2.99682e11	−	5.19064e11i	−0.0127620	−	0.0221045i
$937$	−3.31649e13			−1.40556			−0.702782	−	0.711406i	$-0.748059\pi$
$937$	−3.31649e13			−1.40556			−0.702782	+	0.711406i	$0.748059\pi$
$938$		0			0
$939$	−1.80437e13			−0.757411
$940$	−3.93693e12	−	6.81896e12i	−0.164468	−	0.284867i
$941$	1.59655e13	−	2.76530e13i	0.663786	−	1.14971i	−0.315827	−	0.948817i	$-0.602282\pi$
$941$	1.59655e13	−	2.76530e13i	0.663786	−	1.14971i	0.979613	−	0.200894i	$-0.0643847\pi$
$942$	6.02548e12	−	1.04364e13i	0.249323	−	0.431840i
$943$	7.85566e12	+	1.36064e13i	0.323504	+	0.560326i
$944$	−1.08547e13			−0.444881
$945$		0			0
$946$	−1.46092e13			−0.593082
$947$	−1.78460e13	−	3.09102e13i	−0.721052	−	1.24890i	−0.960578	−	0.278009i	$-0.910325\pi$
$947$	−1.78460e13	−	3.09102e13i	−0.721052	−	1.24890i	0.239526	−	0.970890i	$-0.423008\pi$
$948$	1.08033e13	−	1.87118e13i	0.434428	−	0.752452i
$949$	2.43297e12	−	4.21402e12i	0.0973730	−	0.168655i
$950$	9.49781e12	+	1.64507e13i	0.378327	+	0.655282i
$951$	−3.93308e11			−0.0155927
$952$		0			0
$953$	−3.04923e13			−1.19749			−0.598745	−	0.800940i	$-0.704334\pi$
$953$	−3.04923e13			−1.19749			−0.598745	+	0.800940i	$0.704334\pi$
$954$	4.41639e12	+	7.64942e12i	0.172624	+	0.298993i
$955$	−1.03890e12	+	1.79942e12i	−0.0404163	+	0.0700031i
$956$	−2.76762e12	+	4.79366e12i	−0.107163	+	0.185612i
$957$	2.30611e13	+	3.99429e13i	0.888741	+	1.53935i
$958$	3.29512e13			1.26394
$959$		0			0
$960$	1.55156e12			0.0589586
$961$	−3.59641e12	−	6.22916e12i	−0.136023	−	0.235599i
$962$	4.94624e11	−	8.56713e11i	0.0186203	−	0.0322513i
$963$	−1.91888e12	+	3.32360e12i	−0.0719002	+	0.124535i
$964$	8.67570e12	+	1.50267e13i	0.323562	+	0.560426i
$965$	1.31209e13			0.487069
$966$		0			0
$967$	−3.45533e13			−1.27078			−0.635389	−	0.772192i	$-0.719160\pi$
$967$	−3.45533e13			−1.27078			−0.635389	+	0.772192i	$0.719160\pi$
$968$	−5.29107e10	−	9.16440e10i	−0.00193689	−	0.00335479i
$969$	1.30425e12	−	2.25902e12i	0.0475229	−	0.0823120i
$970$	−3.29889e12	+	5.71384e12i	−0.119645	+	0.207231i
$971$	−1.03354e13	−	1.79014e13i	−0.373112	−	0.646250i	0.616930	−	0.787018i	$-0.288376\pi$
$971$	−1.03354e13	−	1.79014e13i	−0.373112	−	0.646250i	−0.990043	+	0.140768i	$0.955043\pi$
$972$	1.20935e13			0.434563
$973$		0			0
$974$	−1.95595e13			−0.696374
$975$	−2.23631e12	−	3.87340e12i	−0.0792522	−	0.137269i
$976$	1.68490e12	−	2.91833e12i	0.0594360	−	0.102946i
$977$	−8.93945e10	+	1.54836e11i	−0.00313896	+	0.00543683i	−0.867591	−	0.497279i	$-0.834332\pi$
$977$	−8.93945e10	+	1.54836e11i	−0.00313896	+	0.00543683i	0.864452	+	0.502716i	$0.167666\pi$
$978$	−1.81758e13	−	3.14813e13i	−0.635284	−	1.10034i
$979$	8.07952e12			0.281102
$980$		0			0
$981$	−1.16983e13			−0.403285
$982$	−1.58580e12	−	2.74668e12i	−0.0544184	−	0.0942554i
$983$	−7.13283e12	+	1.23544e13i	−0.243652	+	0.422018i	−0.961752	−	0.273922i	$-0.911679\pi$
$983$	−7.13283e12	+	1.23544e13i	−0.243652	+	0.422018i	0.718099	+	0.695940i	$0.245012\pi$
$984$	2.21460e12	−	3.83579e12i	0.0753038	−	0.130430i
$985$	−3.39451e12	−	5.87947e12i	−0.114898	−	0.199010i
$986$	1.90426e12			0.0641622
$987$		0			0
$988$	2.91167e12			0.0972157
$989$	−2.30961e13	−	4.00036e13i	−0.767636	−	1.32958i
$990$	1.95845e12	−	3.39213e12i	0.0647968	−	0.112231i
$991$	1.35648e13	−	2.34950e13i	0.446768	−	0.773826i	−0.551405	−	0.834238i	$-0.685908\pi$
$991$	1.35648e13	−	2.34950e13i	0.446768	−	0.773826i	0.998174	+	0.0604120i	$0.0192415\pi$
$992$	3.04053e12	+	5.26635e12i	0.0996888	+	0.172666i
$993$	3.67515e13			1.19951
$994$		0			0
$995$	−1.59461e12			−0.0515764
$996$	8.08356e12	+	1.40011e13i	0.260277	+	0.450813i
$997$	−1.93362e12	+	3.34912e12i	−0.0619787	+	0.107350i	−0.895350	−	0.445364i	$-0.853074\pi$
$997$	−1.93362e12	+	3.34912e12i	−0.0619787	+	0.107350i	0.833371	+	0.552714i	$0.186408\pi$
$998$	2.40596e12	−	4.16724e12i	0.0767716	−	0.132972i
$999$	3.46452e12	+	6.00073e12i	0.110052	+	0.190616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.d.67.1		2
7.2	even	3	inner	98.10.c.d.79.1		2
7.3	odd	6		14.10.a.b.1.1	✓	1
7.4	even	3		98.10.a.b.1.1		1
7.5	odd	6		98.10.c.a.79.1		2
7.6	odd	2		98.10.c.a.67.1		2
21.17	even	6		126.10.a.a.1.1		1
28.3	even	6		112.10.a.a.1.1		1
35.3	even	12		350.10.c.d.99.1		2
35.17	even	12		350.10.c.d.99.2		2
35.24	odd	6		350.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.b.1.1	✓	1	7.3	odd	6
98.10.a.b.1.1		1	7.4	even	3
98.10.c.a.67.1		2	7.6	odd	2
98.10.c.a.79.1		2	7.5	odd	6
98.10.c.d.67.1		2	1.1	even	1	trivial
98.10.c.d.79.1		2	7.2	even	3	inner
112.10.a.a.1.1		1	28.3	even	6
126.10.a.a.1.1		1	21.17	even	6
350.10.a.a.1.1		1	35.24	odd	6
350.10.c.d.99.1		2	35.3	even	12
350.10.c.d.99.2		2	35.17	even	12

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(85.0000 - 147.224i) q^{3} +(-128.000 + 221.703i) q^{4} +(272.000 + 471.118i) q^{5} -2720.00 q^{6} +4096.00 q^{8} +(-4608.50 - 7982.16i) q^{9} +(4352.00 - 7537.89i) q^{10} +(-24412.0 + 42282.8i) q^{11} +(21760.0 + 37689.4i) q^{12} +15876.0 q^{13} +92480.0 q^{15} +(-32768.0 - 56755.8i) q^{16} +(-10709.0 + 18548.5i) q^{17} +(-73736.0 + 127714. i) q^{18} +(-358205. - 620429. i) q^{19} -139264. q^{20} +781184. q^{22} +(1.23500e6 + 2.13908e6i) q^{23} +(348160. - 603031. i) q^{24} +(828594. - 1.43517e6i) q^{25} +(-127008. - 219984. i) q^{26} +1.77922e6 q^{27} +5.55683e6 q^{29} +(-739840. - 1.28144e6i) q^{30} +(2.89967e6 - 5.02238e6i) q^{31} +(-524288. + 908093. i) q^{32} +(4.15004e6 + 7.18808e6i) q^{33} +342688. q^{34} +2.35955e6 q^{36} +(1.94721e6 + 3.37268e6i) q^{37} +(-5.73128e6 + 9.92687e6i) q^{38} +(1.34946e6 - 2.33733e6i) q^{39} +(1.11411e6 + 1.92970e6i) q^{40} +6.36086e6 q^{41} -1.87013e7 q^{43} +(-6.24947e6 - 1.08244e7i) q^{44} +(2.50702e6 - 4.34229e6i) q^{45} +(1.97600e7 - 3.42253e7i) q^{46} +(2.82695e7 + 4.89643e7i) q^{47} -1.11411e7 q^{48} -2.65150e7 q^{50} +(1.82053e6 + 3.15325e6i) q^{51} +(-2.03213e6 + 3.51975e6i) q^{52} +(2.99473e7 - 5.18703e7i) q^{53} +(-1.42338e7 - 2.46536e7i) q^{54} -2.65603e7 q^{55} -1.21790e8 q^{57} +(-4.44546e7 - 7.69976e7i) q^{58} +(8.28148e7 - 1.43439e8i) q^{59} +(-1.18374e7 + 2.05030e7i) q^{60} +(2.57095e7 + 4.45302e7i) q^{61} -9.27896e7 q^{62} +1.67772e7 q^{64} +(4.31827e6 + 7.47947e6i) q^{65} +(6.64006e7 - 1.15009e8i) q^{66} +(-4.67733e7 + 8.10137e7i) q^{67} +(-2.74150e6 - 4.74842e6i) q^{68} +4.19900e8 q^{69} -9.56335e7 q^{71} +(-1.88764e7 - 3.26949e7i) q^{72} +(1.53248e8 - 2.65434e8i) q^{73} +(3.11554e7 - 5.39628e7i) q^{74} +(-1.40861e8 - 2.43979e8i) q^{75} +1.83401e8 q^{76} -4.31827e7 q^{78} +(-2.48237e8 - 4.29959e8i) q^{79} +(1.78258e7 - 3.08752e7i) q^{80} +(2.41943e8 - 4.19057e8i) q^{81} +(-5.08869e7 - 8.81386e7i) q^{82} +3.71487e8 q^{83} -1.16514e7 q^{85} +(1.49610e8 + 2.59133e8i) q^{86} +(4.72330e8 - 8.18100e8i) q^{87} +(-9.99916e7 + 1.73190e8i) q^{88} +(-8.27413e7 - 1.43312e8i) q^{89} -8.02248e7 q^{90} -6.32320e8 q^{92} +(-4.92945e8 - 8.53805e8i) q^{93} +(4.52313e8 - 7.83428e8i) q^{94} +(1.94864e8 - 3.37514e8i) q^{95} +(8.91290e7 + 1.54376e8i) q^{96} -7.58017e8 q^{97} +4.50011e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{2} + 170 q^{3} - 256 q^{4} + 544 q^{5} - 5440 q^{6} + 8192 q^{8} - 9217 q^{9} + 8704 q^{10} - 48824 q^{11} + 43520 q^{12} + 31752 q^{13} + 184960 q^{15} - 65536 q^{16} - 21418 q^{17} - 147472 q^{18}+ \cdots + 900021616 q^{99}+O(q^{100}) \) 2 * q - 16 * q^2 + 170 * q^3 - 256 * q^4 + 544 * q^5 - 5440 * q^6 + 8192 * q^8 - 9217 * q^9 + 8704 * q^10 - 48824 * q^11 + 43520 * q^12 + 31752 * q^13 + 184960 * q^15 - 65536 * q^16 - 21418 * q^17 - 147472 * q^18 - 716410 * q^19 - 278528 * q^20 + 1562368 * q^22 + 2470000 * q^23 + 696320 * q^24 + 1657189 * q^25 - 254016 * q^26 + 3558440 * q^27 + 11113652 * q^29 - 1479680 * q^30 + 5799348 * q^31 - 1048576 * q^32 + 8300080 * q^33 + 685376 * q^34 + 4719104 * q^36 + 3894430 * q^37 - 11462560 * q^38 + 2698920 * q^39 + 2228224 * q^40 + 12721716 * q^41 - 37402592 * q^43 - 12498944 * q^44 + 5014048 * q^45 + 39520000 * q^46 + 56539068 * q^47 - 22282240 * q^48 - 53030048 * q^50 + 3641060 * q^51 - 4064256 * q^52 + 59894682 * q^53 - 28467520 * q^54 - 53120512 * q^55 - 243579400 * q^57 - 88909216 * q^58 + 165629662 * q^59 - 23674880 * q^60 + 51419016 * q^61 - 185579136 * q^62 + 33554432 * q^64 + 8636544 * q^65 + 132801280 * q^66 - 93546508 * q^67 - 5483008 * q^68 + 839800000 * q^69 - 191267072 * q^71 - 37752832 * q^72 + 306496402 * q^73 + 62310880 * q^74 - 281722130 * q^75 + 366801920 * q^76 - 86365440 * q^78 - 496474152 * q^79 + 35651584 * q^80 + 483885611 * q^81 - 101773728 * q^82 + 742973924 * q^83 - 23302784 * q^85 + 299220736 * q^86 + 944660420 * q^87 - 199983104 * q^88 - 165482550 * q^89 - 160449536 * q^90 - 1264640000 * q^92 - 985889160 * q^93 + 904625088 * q^94 + 389727040 * q^95 + 178257920 * q^96 - 1516033484 * q^97 + 900021616 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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