LMFDB - Embedded newform 98.8.c.f.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,8,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, 8); 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, 8, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,8,82,-64,-448,1312,0,-1024,-4537] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$30.6137324974$
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			98.8.c.f.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+(4.00000 + 6.92820i) q^{2} +(41.0000 - 71.0141i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-224.000 - 387.979i) q^{5} +656.000 q^{6} -512.000 q^{8} +(-2268.50 - 3929.16i) q^{9} +(1792.00 - 3103.84i) q^{10} +(-1204.00 + 2085.39i) q^{11} +(2624.00 + 4544.90i) q^{12} +7116.00 q^{13} -36736.0 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-1243.00 + 2152.94i) q^{17} +(18148.0 - 31433.3i) q^{18} +(-18241.0 - 31594.3i) q^{19} +28672.0 q^{20} -19264.0 q^{22} +(6440.00 + 11154.4i) q^{23} +(-20992.0 + 36359.2i) q^{24} +(-61289.5 + 106157. i) q^{25} +(28464.0 + 49301.1i) q^{26} -192700. q^{27} -88094.0 q^{29} +(-146944. - 254514. i) q^{30} +(-141318. + 244770. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(98728.0 + 171002. i) q^{33} -19888.0 q^{34} +290368. q^{36} +(107267. + 185792. i) q^{37} +(145928. - 252755. i) q^{38} +(291756. - 505336. i) q^{39} +(114688. + 198645. i) q^{40} -140874. q^{41} +36464.0 q^{43} +(-77056.0 - 133465. i) q^{44} +(-1.01629e6 + 1.76026e6i) q^{45} +(-51520.0 + 89235.3i) q^{46} +(-358434. - 620826. i) q^{47} -335872. q^{48} -980632. q^{50} +(101926. + 176541. i) q^{51} +(-227712. + 394409. i) q^{52} +(28473.0 - 49316.7i) q^{53} +(-770800. - 1.33506e6i) q^{54} +1.07878e6 q^{55} -2.99152e6 q^{57} +(-352376. - 610333. i) q^{58} +(1.07493e6 - 1.86184e6i) q^{59} +(1.17555e6 - 2.03612e6i) q^{60} +(-1.54218e6 - 2.67113e6i) q^{61} -2.26109e6 q^{62} +262144. q^{64} +(-1.59398e6 - 2.76086e6i) q^{65} +(-789824. + 1.36802e6i) q^{66} +(1.51718e6 - 2.62784e6i) q^{67} +(-79552.0 - 137788. i) q^{68} +1.05616e6 q^{69} -106624. q^{71} +(1.16147e6 + 2.01173e6i) q^{72} +(-494465. + 856439. i) q^{73} +(-858136. + 1.48634e6i) q^{74} +(5.02574e6 + 8.70484e6i) q^{75} +2.33485e6 q^{76} +4.66810e6 q^{78} +(-1.70795e6 - 2.95825e6i) q^{79} +(-917504. + 1.58916e6i) q^{80} +(-2.93949e6 + 5.09135e6i) q^{81} +(-563496. - 976004. i) q^{82} -15142.0 q^{83} +1.11373e6 q^{85} +(145856. + 252630. i) q^{86} +(-3.61185e6 + 6.25591e6i) q^{87} +(616448. - 1.06772e6i) q^{88} +(-87405.0 - 151390. i) q^{89} -1.62606e7 q^{90} -824320. q^{92} +(1.15881e7 + 2.00711e7i) q^{93} +(2.86747e6 - 4.96661e6i) q^{94} +(-8.17197e6 + 1.41543e7i) q^{95} +(-1.34349e6 - 2.32699e6i) q^{96} +1.35068e7 q^{97} +1.09251e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 82 q^{3} - 64 q^{4} - 448 q^{5} + 1312 q^{6} - 1024 q^{8} - 4537 q^{9} + 3584 q^{10} - 2408 q^{11} + 5248 q^{12} + 14232 q^{13} - 73472 q^{15} - 4096 q^{16} - 2486 q^{17} + 36296 q^{18}+ \cdots + 21850192 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 82 * q^3 - 64 * q^4 - 448 * q^5 + 1312 * q^6 - 1024 * q^8 - 4537 * q^9 + 3584 * q^10 - 2408 * q^11 + 5248 * q^12 + 14232 * q^13 - 73472 * q^15 - 4096 * q^16 - 2486 * q^17 + 36296 * q^18 - 36482 * q^19 + 57344 * q^20 - 38528 * q^22 + 12880 * q^23 - 41984 * q^24 - 122579 * q^25 + 56928 * q^26 - 385400 * q^27 - 176188 * q^29 - 293888 * q^30 - 282636 * q^31 + 32768 * q^32 + 197456 * q^33 - 39776 * q^34 + 580736 * q^36 + 214534 * q^37 + 291856 * q^38 + 583512 * q^39 + 229376 * q^40 - 281748 * q^41 + 72928 * q^43 - 154112 * q^44 - 2032576 * q^45 - 103040 * q^46 - 716868 * q^47 - 671744 * q^48 - 1961264 * q^50 + 203852 * q^51 - 455424 * q^52 + 56946 * q^53 - 1541600 * q^54 + 2157568 * q^55 - 5983048 * q^57 - 704752 * q^58 + 2149862 * q^59 + 2351104 * q^60 - 3084360 * q^61 - 4522176 * q^62 + 524288 * q^64 - 3187968 * q^65 - 1579648 * q^66 + 3034364 * q^67 - 159104 * q^68 + 2112320 * q^69 - 213248 * q^71 + 2322944 * q^72 - 988930 * q^73 - 1716272 * q^74 + 10051478 * q^75 + 4669696 * q^76 + 9336192 * q^78 - 3415896 * q^79 - 1835008 * q^80 - 5878981 * q^81 - 1126992 * q^82 - 30284 * q^83 + 2227456 * q^85 + 291712 * q^86 - 7223708 * q^87 + 1232896 * q^88 - 174810 * q^89 - 32521216 * q^90 - 1648640 * q^92 + 23176152 * q^93 + 5734944 * q^94 - 16343936 * q^95 - 2686976 * q^96 + 27013580 * q^97 + 21850192 * 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 $

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	41.0000	−	71.0141i	0.876717	−	1.51852i	0.0217948	−	0.999762i	$-0.493062\pi$
$3$	41.0000	−	71.0141i	0.876717	−	1.51852i	0.854922	−	0.518756i	$-0.173605\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−224.000	−	387.979i	−0.801407	−	1.38808i	−0.918690	−	0.394979i	$-0.870752\pi$
$5$	−224.000	−	387.979i	−0.801407	−	1.38808i	0.117283	−	0.993098i	$-0.462581\pi$
$6$	656.000			1.23987
$7$		0			0
$7$		0			0
$8$	−512.000			−0.353553
$9$	−2268.50	−	3929.16i	−1.03727	−	1.79660i
$10$	1792.00	−	3103.84i	0.566680	−	0.981519i
$11$	−1204.00	+	2085.39i	−0.272742	+	0.472403i	−0.969563	−	0.244842i	$-0.921264\pi$
$11$	−1204.00	+	2085.39i	−0.272742	+	0.472403i	0.696821	+	0.717245i	$0.254597\pi$
$12$	2624.00	+	4544.90i	0.438359	+	0.759259i
$13$	7116.00			0.898326			0.449163	−	0.893450i	$-0.351722\pi$
$13$	7116.00			0.898326			0.449163	+	0.893450i	$0.351722\pi$
$14$		0			0
$15$	−36736.0			−2.81043
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−1243.00	+	2152.94i	−0.0613621	+	0.106282i	−0.895074	−	0.445917i	$-0.852878\pi$
$17$	−1243.00	+	2152.94i	−0.0613621	+	0.106282i	0.833712	+	0.552199i	$0.186211\pi$
$18$	18148.0	−	31433.3i	0.733458	−	1.27039i
$19$	−18241.0	−	31594.3i	−0.610114	−	1.05675i	−0.991221	−	0.132217i	$-0.957790\pi$
$19$	−18241.0	−	31594.3i	−0.610114	−	1.05675i	0.381107	−	0.924531i	$-0.375543\pi$
$20$	28672.0			0.801407
$21$		0			0
$22$	−19264.0			−0.385715
$23$	6440.00	+	11154.4i	0.110367	+	0.191161i	0.915918	−	0.401365i	$-0.131464\pi$
$23$	6440.00	+	11154.4i	0.110367	+	0.191161i	−0.805551	+	0.592526i	$0.798131\pi$
$24$	−20992.0	+	36359.2i	−0.309966	+	0.536877i
$25$	−61289.5	+	106157.i	−0.784506	+	1.35880i
$26$	28464.0	+	49301.1i	0.317606	+	0.550110i
$27$	−192700.			−1.88412
$28$		0			0
$29$	−88094.0			−0.670739			−0.335369	−	0.942087i	$-0.608861\pi$
$29$	−88094.0			−0.670739			−0.335369	+	0.942087i	$0.608861\pi$
$30$	−146944.	−	254514.i	−0.993636	−	1.72103i
$31$	−141318.	+	244770.i	−0.851984	+	1.47568i	0.0274306	+	0.999624i	$0.491267\pi$
$31$	−141318.	+	244770.i	−0.851984	+	1.47568i	−0.879415	+	0.476056i	$0.842066\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	98728.0	+	171002.i	0.478235	+	0.828328i
$34$	−19888.0			−0.0867791
$35$		0			0
$36$	290368.			1.03727
$37$	107267.	+	185792.i	0.348145	+	0.603005i	0.985920	−	0.167218i	$-0.0534784\pi$
$37$	107267.	+	185792.i	0.348145	+	0.603005i	−0.637775	+	0.770223i	$0.720145\pi$
$38$	145928.	−	252755.i	0.431416	−	0.747234i
$39$	291756.	−	505336.i	0.787578	−	1.36413i
$40$	114688.	+	198645.i	0.283340	+	0.490759i
$41$	−140874.			−0.319218			−0.159609	−	0.987180i	$-0.551023\pi$
$41$	−140874.			−0.319218			−0.159609	+	0.987180i	$0.551023\pi$
$42$		0			0
$43$	36464.0			0.0699399			0.0349699	−	0.999388i	$-0.488866\pi$
$43$	36464.0			0.0699399			0.0349699	+	0.999388i	$0.488866\pi$
$44$	−77056.0	−	133465.i	−0.136371	−	0.236202i
$45$	−1.01629e6	+	1.76026e6i	−1.66254	+	2.87961i
$46$	−51520.0	+	89235.3i	−0.0780411	+	0.135171i
$47$	−358434.	−	620826.i	−0.503578	−	0.872223i	−0.999991	−	0.00413639i	$-0.998683\pi$
$47$	−358434.	−	620826.i	−0.503578	−	0.872223i	0.496414	−	0.868086i	$-0.334650\pi$
$48$	−335872.			−0.438359
$49$		0			0
$50$	−980632.			−1.10946
$51$	101926.	+	176541.i	0.107594	+	0.186359i
$52$	−227712.	+	394409.i	−0.224582	+	0.388987i
$53$	28473.0	−	49316.7i	0.0262705	−	0.0455018i	−0.852591	−	0.522578i	$-0.824970\pi$
$53$	28473.0	−	49316.7i	0.0262705	−	0.0455018i	0.878862	+	0.477077i	$0.158304\pi$
$54$	−770800.	−	1.33506e6i	−0.666137	−	1.15378i
$55$	1.07878e6			0.874309
$56$		0			0
$57$	−2.99152e6			−2.13959
$58$	−352376.	−	610333.i	−0.237142	−	0.410742i
$59$	1.07493e6	−	1.86184e6i	0.681394	−	1.18021i	−0.293161	−	0.956063i	$-0.594707\pi$
$59$	1.07493e6	−	1.86184e6i	0.681394	−	1.18021i	0.974555	−	0.224147i	$-0.0719595\pi$
$60$	1.17555e6	−	2.03612e6i	0.702607	−	1.21695i
$61$	−1.54218e6	−	2.67113e6i	−0.869923	−	1.50675i	−0.862075	−	0.506781i	$-0.830835\pi$
$61$	−1.54218e6	−	2.67113e6i	−0.869923	−	1.50675i	−0.00784785	−	0.999969i	$-0.502498\pi$
$62$	−2.26109e6			−1.20489
$63$		0			0
$64$	262144.			0.125000
$65$	−1.59398e6	−	2.76086e6i	−0.719925	−	1.24695i
$66$	−789824.	+	1.36802e6i	−0.338163	+	0.585716i
$67$	1.51718e6	−	2.62784e6i	0.616277	−	1.06742i	−0.373882	−	0.927476i	$-0.621974\pi$
$67$	1.51718e6	−	2.62784e6i	0.616277	−	1.06742i	0.990159	−	0.139947i	$-0.0446931\pi$
$68$	−79552.0	−	137788.i	−0.0306810	−	0.0531411i
$69$	1.05616e6			0.387042
$70$		0			0
$71$	−106624.			−0.0353550			−0.0176775	−	0.999844i	$-0.505627\pi$
$71$	−106624.			−0.0353550			−0.0176775	+	0.999844i	$0.505627\pi$
$72$	1.16147e6	+	2.01173e6i	0.366729	+	0.635193i
$73$	−494465.	+	856439.i	−0.148767	+	0.257671i	−0.930772	−	0.365600i	$-0.880864\pi$
$73$	−494465.	+	856439.i	−0.148767	+	0.257671i	0.782005	+	0.623272i	$0.214197\pi$
$74$	−858136.	+	1.48634e6i	−0.246176	+	0.426389i
$75$	5.02574e6	+	8.70484e6i	1.37558	+	2.38257i
$76$	2.33485e6			0.610114
$77$		0			0
$78$	4.66810e6			1.11380
$79$	−1.70795e6	−	2.95825e6i	−0.389744	−	0.675057i	0.602671	−	0.797990i	$-0.294103\pi$
$79$	−1.70795e6	−	2.95825e6i	−0.389744	−	0.675057i	−0.992415	+	0.122933i	$0.960770\pi$
$80$	−917504.	+	1.58916e6i	−0.200352	+	0.347019i
$81$	−2.93949e6	+	5.09135e6i	−0.614574	+	1.06447i
$82$	−563496.	−	976004.i	−0.112861	−	0.195480i
$83$	−15142.0			−0.00290676			−0.00145338	−	0.999999i	$-0.500463\pi$
$83$	−15142.0			−0.00290676			−0.00145338	+	0.999999i	$0.500463\pi$
$84$		0			0
$85$	1.11373e6			0.196704
$86$	145856.	+	252630.i	0.0247275	+	0.0428292i
$87$	−3.61185e6	+	6.25591e6i	−0.588048	+	1.01853i
$88$	616448.	−	1.06772e6i	0.0964289	−	0.167020i
$89$	−87405.0	−	151390.i	−0.0131423	−	0.0227631i	0.859379	−	0.511338i	$-0.170850\pi$
$89$	−87405.0	−	151390.i	−0.0131423	−	0.0227631i	−0.872522	+	0.488575i	$0.837517\pi$
$90$	−1.62606e7			−2.35119
$91$		0			0
$92$	−824320.			−0.110367
$93$	1.15881e7	+	2.00711e7i	1.49390	+	2.58751i
$94$	2.86747e6	−	4.96661e6i	0.356083	−	0.616754i
$95$	−8.17197e6	+	1.41543e7i	−0.977899	+	1.69377i
$96$	−1.34349e6	−	2.32699e6i	−0.154983	−	0.268439i
$97$	1.35068e7			1.50263			0.751313	−	0.659946i	$-0.229421\pi$
$97$	1.35068e7			1.50263			0.751313	+	0.659946i	$0.229421\pi$
$98$		0			0
$99$	1.09251e7			1.13162
$100$	−3.92253e6	−	6.79402e6i	−0.392253	−	0.679402i
$101$	9.38224e6	−	1.62505e7i	0.906112	−	1.56943i	0.0866937	−	0.996235i	$-0.472370\pi$
$101$	9.38224e6	−	1.62505e7i	0.906112	−	1.56943i	0.819418	−	0.573196i	$-0.194297\pi$
$102$	−815408.	+	1.41233e6i	−0.0760807	+	0.131776i
$103$	8.10401e6	+	1.40366e7i	0.730751	+	1.26570i	0.956562	+	0.291527i	$0.0941635\pi$
$103$	8.10401e6	+	1.40366e7i	0.730751	+	1.26570i	−0.225811	+	0.974171i	$0.572503\pi$
$104$	−3.64339e6			−0.317606
$105$		0			0
$106$	455568.			0.0371520
$107$	−3.48290e6	−	6.03256e6i	−0.274851	−	0.476056i	0.695246	−	0.718771i	$-0.255295\pi$
$107$	−3.48290e6	−	6.03256e6i	−0.274851	−	0.476056i	−0.970098	+	0.242715i	$0.921962\pi$
$108$	6.16640e6	−	1.06805e7i	0.471030	−	0.815848i
$109$	7.45195e6	−	1.29072e7i	0.551159	−	0.954636i	−0.447032	−	0.894518i	$-0.647519\pi$
$109$	7.45195e6	−	1.29072e7i	0.551159	−	0.954636i	0.998191	−	0.0601177i	$-0.0191476\pi$
$110$	4.31514e6	+	7.47403e6i	0.309115	+	0.535403i
$111$	1.75918e7			1.22090
$112$		0			0
$113$	−2.60684e7			−1.69958			−0.849788	−	0.527125i	$-0.823270\pi$
$113$	−2.60684e7			−1.69958			−0.849788	+	0.527125i	$0.823270\pi$
$114$	−1.19661e7	−	2.07259e7i	−0.756459	−	1.31023i
$115$	2.88512e6	−	4.99717e6i	0.176897	−	0.306395i
$116$	2.81901e6	−	4.88267e6i	0.167685	−	0.290438i
$117$	−1.61426e7	−	2.79599e7i	−0.931803	−	1.61393i
$118$	1.71989e7			0.963637
$119$		0			0
$120$	1.88088e7			0.993636
$121$	6.84435e6	+	1.18548e7i	0.351224	+	0.608337i
$122$	1.23374e7	−	2.13691e7i	0.615128	−	1.06543i
$123$	−5.77583e6	+	1.00040e7i	−0.279864	+	0.484738i
$124$	−9.04435e6	−	1.56653e7i	−0.425992	−	0.737840i
$125$	1.99154e7			0.912019
$126$		0			0
$127$	2.13136e7			0.923301			0.461651	−	0.887062i	$-0.347257\pi$
$127$	2.13136e7			0.923301			0.461651	+	0.887062i	$0.347257\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	1.49502e6	−	2.58946e6i	0.0613175	−	0.106205i
$130$	1.27519e7	−	2.20869e7i	0.509064	−	0.881724i
$131$	−5.23866e6	−	9.07363e6i	−0.203597	−	0.352640i	0.746088	−	0.665847i	$-0.231930\pi$
$131$	−5.23866e6	−	9.07363e6i	−0.203597	−	0.352640i	−0.949685	+	0.313207i	$0.898597\pi$
$132$	−1.26372e7			−0.478235
$133$		0			0
$134$	2.42749e7			0.871547
$135$	4.31648e7	+	7.47636e7i	1.50995	+	2.61530i
$136$	636416.	−	1.10230e6i	0.0216948	−	0.0375764i
$137$	−1.80990e7	+	3.13485e7i	−0.601359	+	1.04158i	0.391257	+	0.920281i	$0.372040\pi$
$137$	−1.80990e7	+	3.13485e7i	−0.601359	+	1.04158i	−0.992616	+	0.121302i	$0.961293\pi$
$138$	4.22464e6	+	7.31729e6i	0.136840	+	0.237014i
$139$	−5.27655e7			−1.66647			−0.833237	−	0.552916i	$-0.813515\pi$
$139$	−5.27655e7			−1.66647			−0.833237	+	0.552916i	$0.813515\pi$
$140$		0			0
$141$	−5.87832e7			−1.76598
$142$	−426496.	−	738713.i	−0.0124999	−	0.0216504i
$143$	−8.56766e6	+	1.48396e7i	−0.245011	+	0.424372i
$144$	−9.29178e6	+	1.60938e7i	−0.259316	+	0.449149i
$145$	1.97331e7	+	3.41787e7i	0.537534	+	0.931037i
$146$	−7.91144e6			−0.210388
$147$		0			0
$148$	−1.37302e7			−0.348145
$149$	−3.68001e7	−	6.37397e7i	−0.911376	−	1.57855i	−0.812122	−	0.583487i	$-0.801688\pi$
$149$	−3.68001e7	−	6.37397e7i	−0.911376	−	1.57855i	−0.0992535	−	0.995062i	$-0.531645\pi$
$150$	−4.02059e7	+	6.96387e7i	−0.972681	+	1.68473i
$151$	−8.71444e6	+	1.50939e7i	−0.205978	+	0.356764i	−0.950444	−	0.310896i	$-0.899371\pi$
$151$	−8.71444e6	+	1.50939e7i	−0.205978	+	0.356764i	0.744466	+	0.667660i	$0.232704\pi$
$152$	9.33939e6	+	1.61763e7i	0.215708	+	0.373617i
$153$	1.12790e7			0.254595
$154$		0			0
$155$	1.26621e8			2.73114
$156$	1.86724e7	+	3.23415e7i	0.393789	+	0.682063i
$157$	1.11078e7	−	1.92394e7i	0.229077	−	0.396773i	−0.728458	−	0.685091i	$-0.759763\pi$
$157$	1.11078e7	−	1.92394e7i	0.229077	−	0.396773i	0.957535	+	0.288318i	$0.0930960\pi$
$158$	1.36636e7	−	2.36660e7i	0.275591	−	0.477337i
$159$	−2.33479e6	−	4.04397e6i	−0.0460635	−	0.0797844i
$160$	−1.46801e7			−0.283340
$161$		0			0
$162$	−4.70318e7			−0.869140
$163$	−3.11898e7	−	5.40223e7i	−0.564099	−	0.977049i	−0.997133	−	0.0756711i	$-0.975890\pi$
$163$	−3.11898e7	−	5.40223e7i	−0.564099	−	0.977049i	0.433033	−	0.901378i	$-0.357443\pi$
$164$	4.50797e6	−	7.80803e6i	0.0798045	−	0.138225i
$165$	4.42301e7	−	7.66089e7i	0.766522	−	1.32765i
$166$	−60568.0	−	104907.i	−0.00102770	−	0.00178002i
$167$	3.31238e7			0.550343			0.275171	−	0.961395i	$-0.411265\pi$
$167$	3.31238e7			0.550343			0.275171	+	0.961395i	$0.411265\pi$
$168$		0			0
$169$	−1.21111e7			−0.193010
$170$	4.45491e6	+	7.71613e6i	0.0695453	+	0.120456i
$171$	−8.27594e7	+	1.43344e8i	−1.26570	+	2.19226i
$172$	−1.16685e6	+	2.02104e6i	−0.0174850	+	0.0302848i
$173$	3.52899e7	+	6.11240e7i	0.518191	+	0.897532i	0.999777	+	0.0211336i	$0.00672753\pi$
$173$	3.52899e7	+	6.11240e7i	0.518191	+	0.897532i	−0.481586	+	0.876399i	$0.659939\pi$
$174$	−5.77897e7			−0.831626
$175$		0			0
$176$	9.86317e6			0.136371
$177$	−8.81443e7	−	1.52670e8i	−1.19478	−	2.06942i
$178$	699240.	−	1.21112e6i	0.00929301	−	0.0160960i
$179$	6.05881e7	−	1.04942e8i	0.789590	−	1.36761i	−0.136628	−	0.990622i	$-0.543626\pi$
$179$	6.05881e7	−	1.04942e8i	0.789590	−	1.36761i	0.926218	−	0.376988i	$-0.123040\pi$
$180$	−6.50424e7	−	1.12657e8i	−0.831272	−	1.43980i
$181$	2.30550e7			0.288995			0.144498	−	0.989505i	$-0.453843\pi$
$181$	2.30550e7			0.288995			0.144498	+	0.989505i	$0.453843\pi$
$182$		0			0
$183$	−2.52918e8			−3.05070
$184$	−3.29728e6	−	5.71106e6i	−0.0390206	−	0.0675856i
$185$	4.80556e7	−	8.32348e7i	0.558011	−	0.966504i
$186$	−9.27046e7	+	1.60569e8i	−1.05635	+	1.82964i
$187$	−2.99314e6	−	5.18428e6i	−0.0334720	−	0.0579752i
$188$	4.58796e7			0.503578
$189$		0			0
$190$	−1.30751e8			−1.38296
$191$	1.01463e7	+	1.75740e7i	0.105364	+	0.182496i	0.913887	−	0.405969i	$-0.133066\pi$
$191$	1.01463e7	+	1.75740e7i	0.105364	+	0.182496i	−0.808523	+	0.588465i	$0.799733\pi$
$192$	1.07479e7	−	1.86159e7i	0.109590	−	0.189815i
$193$	−1.13041e7	+	1.95792e7i	−0.113184	+	0.196040i	−0.917052	−	0.398767i	$-0.869438\pi$
$193$	−1.13041e7	+	1.95792e7i	−0.113184	+	0.196040i	0.803869	+	0.594807i	$0.202772\pi$
$194$	5.40272e7	+	9.35778e7i	0.531259	+	0.920167i
$195$	−2.61413e8			−2.52468
$196$		0			0
$197$	−3.27180e7			−0.304898			−0.152449	−	0.988311i	$-0.548716\pi$
$197$	−3.27180e7			−0.304898			−0.152449	+	0.988311i	$0.548716\pi$
$198$	4.37004e7	+	7.56913e7i	0.400089	+	0.692975i
$199$	−3.62236e7	+	6.27411e7i	−0.325841	+	0.564374i	−0.981682	−	0.190525i	$-0.938981\pi$
$199$	−3.62236e7	+	6.27411e7i	−0.325841	+	0.564374i	0.655841	+	0.754899i	$0.272314\pi$
$200$	3.13802e7	−	5.43521e7i	0.277365	−	0.480410i
$201$	−1.24409e8	−	2.15483e8i	−1.08060	−	1.87166i
$202$	1.50116e8			1.28144
$203$		0			0
$204$	−1.30465e7			−0.107594
$205$	3.15558e7	+	5.46562e7i	0.255823	+	0.443099i
$206$	−6.48321e7	+	1.12292e8i	−0.516719	+	0.894984i
$207$	2.92183e7	−	5.06075e7i	0.228959	−	0.396569i
$208$	−1.45736e7	−	2.52422e7i	−0.112291	−	0.194493i
$209$	8.78487e7			0.665615
$210$		0			0
$211$	9.38006e7			0.687412			0.343706	−	0.939077i	$-0.388318\pi$
$211$	9.38006e7			0.687412			0.343706	+	0.939077i	$0.388318\pi$
$212$	1.82227e6	+	3.15627e6i	0.0131352	+	0.0227509i
$213$	−4.37158e6	+	7.57181e6i	−0.0309963	+	0.0536872i
$214$	2.78632e7	−	4.82605e7i	0.194349	−	0.336623i
$215$	−8.16794e6	−	1.41473e7i	−0.0560503	−	0.0970819i
$216$	9.86624e7			0.666137
$217$		0			0
$218$	1.19231e8			0.779457
$219$	4.05461e7	+	7.02280e7i	0.260853	+	0.451810i
$220$	−3.45211e7	+	5.97923e7i	−0.218577	+	0.378587i
$221$	−8.84519e6	+	1.53203e7i	−0.0551232	+	0.0954761i
$222$	7.03672e7	+	1.21879e8i	0.431653	+	0.747645i
$223$	1.62567e6			0.00981671			0.00490835	−	0.999988i	$-0.498438\pi$
$223$	1.62567e6			0.00981671			0.00490835	+	0.999988i	$0.498438\pi$
$224$		0			0
$225$	5.56141e8			3.25496
$226$	−1.04274e8	−	1.80607e8i	−0.600891	−	1.04077i
$227$	1.23076e8	−	2.13174e8i	0.698367	−	1.20961i	−0.270665	−	0.962674i	$-0.587244\pi$
$227$	1.23076e8	−	2.13174e8i	0.698367	−	1.20961i	0.969032	−	0.246934i	$-0.0794230\pi$
$228$	9.57288e7	−	1.65807e8i	0.534897	−	0.926470i
$229$	5.30204e7	+	9.18340e7i	0.291755	+	0.505335i	0.974225	−	0.225579i	$-0.0724274\pi$
$229$	5.30204e7	+	9.18340e7i	0.291755	+	0.505335i	−0.682470	+	0.730914i	$0.739094\pi$
$230$	4.61619e7			0.250171
$231$		0			0
$232$	4.51041e7			0.237142
$233$	1.01103e8	+	1.75116e8i	0.523623	+	0.906942i	0.999622	+	0.0274960i	$0.00875336\pi$
$233$	1.01103e8	+	1.75116e8i	0.523623	+	0.906942i	−0.475999	+	0.879446i	$0.657913\pi$
$234$	1.29141e8	−	2.23679e8i	0.658884	−	1.14122i
$235$	−1.60578e8	+	2.78130e8i	−0.807142	+	1.39801i
$236$	6.87956e7	+	1.19157e8i	0.340697	+	0.590105i
$237$	−2.80103e8			−1.36678
$238$		0			0
$239$	−3.67523e7			−0.174137			−0.0870687	−	0.996202i	$-0.527750\pi$
$239$	−3.67523e7			−0.174137			−0.0870687	+	0.996202i	$0.527750\pi$
$240$	7.52353e7	+	1.30311e8i	0.351303	+	0.608476i
$241$	−2.88208e7	+	4.99190e7i	−0.132631	+	0.229724i	−0.924690	−	0.380721i	$-0.875676\pi$
$241$	−2.88208e7	+	4.99190e7i	−0.132631	+	0.229724i	0.792059	+	0.610445i	$0.209009\pi$
$242$	−5.47548e7	+	9.48381e7i	−0.248353	+	0.430159i
$243$	3.03208e7	+	5.25171e7i	0.135556	+	0.234790i
$244$	1.97399e8			0.869923
$245$		0			0
$246$	−9.24133e7			−0.395787
$247$	−1.29803e8	−	2.24825e8i	−0.548082	−	0.949305i
$248$	7.23548e7	−	1.25322e8i	0.301222	−	0.521732i
$249$	−620822.	+	1.07530e6i	−0.00254841	+	0.00441398i
$250$	7.96616e7	+	1.37978e8i	0.322447	+	0.558495i
$251$	−2.61332e8			−1.04312			−0.521561	−	0.853214i	$-0.674650\pi$
$251$	−2.61332e8			−1.04312			−0.521561	+	0.853214i	$0.674650\pi$
$252$		0			0
$253$	−3.10150e7			−0.120407
$254$	8.52543e7	+	1.47665e8i	0.326436	+	0.565404i
$255$	4.56628e7	−	7.90904e7i	0.172454	−	0.298698i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.73813e8	−	3.01052e8i	−0.638727	−	1.10631i	−0.985712	−	0.168437i	$-0.946128\pi$
$257$	−1.73813e8	−	3.01052e8i	−0.638727	−	1.10631i	0.346985	−	0.937871i	$-0.387205\pi$
$258$	2.39204e7			0.0867160
$259$		0			0
$260$	2.04030e8			0.719925
$261$	1.99841e8	+	3.46135e8i	0.695734	+	1.20505i
$262$	4.19093e7	−	7.25891e7i	0.143965	−	0.249354i
$263$	8.82507e7	−	1.52855e8i	0.299139	−	0.518124i	−0.676800	−	0.736167i	$-0.736634\pi$
$263$	8.82507e7	−	1.52855e8i	0.299139	−	0.518124i	0.975939	+	0.218043i	$0.0699672\pi$
$264$	−5.05487e7	−	8.75530e7i	−0.169082	−	0.292858i
$265$	−2.55118e7			−0.0842133
$266$		0			0
$267$	−1.43344e7			−0.0460883
$268$	9.70996e7	+	1.68182e8i	0.308138	+	0.533711i
$269$	2.03944e8	−	3.53242e8i	0.638821	−	1.10647i	−0.346871	−	0.937913i	$-0.612756\pi$
$269$	2.03944e8	−	3.53242e8i	0.638821	−	1.10647i	0.985692	−	0.168557i	$-0.0539107\pi$
$270$	−3.45318e8	+	5.98109e8i	−1.06769	+	1.84930i
$271$	−1.58809e8	−	2.75066e8i	−0.484711	−	0.839544i	0.515135	−	0.857109i	$-0.327742\pi$
$271$	−1.58809e8	−	2.75066e8i	−0.484711	−	0.839544i	−0.999846	+	0.0175649i	$0.994409\pi$
$272$	1.01827e7			0.0306810
$273$		0			0
$274$	−2.89585e8			−0.850450
$275$	−1.47585e8	−	2.55625e8i	−0.427935	−	0.741206i
$276$	−3.37971e7	+	5.85383e7i	−0.0967605	+	0.167594i
$277$	−1.46863e8	+	2.54375e8i	−0.415178	+	0.719109i	−0.995447	−	0.0953156i	$-0.969614\pi$
$277$	−1.46863e8	+	2.54375e8i	−0.415178	+	0.719109i	0.580269	+	0.814425i	$0.302947\pi$
$278$	−2.11062e8	−	3.65570e8i	−0.589188	−	1.02050i
$279$	1.28232e9			3.53494
$280$		0			0
$281$	−5.45027e7			−0.146536			−0.0732682	−	0.997312i	$-0.523343\pi$
$281$	−5.45027e7			−0.146536			−0.0732682	+	0.997312i	$0.523343\pi$
$282$	−2.35133e8	−	4.07262e8i	−0.624369	−	1.08144i
$283$	−1.02705e8	+	1.77889e8i	−0.269362	+	0.466549i	−0.968697	−	0.248245i	$-0.920146\pi$
$283$	−1.02705e8	+	1.77889e8i	−0.269362	+	0.466549i	0.699335	+	0.714794i	$0.253480\pi$
$284$	3.41197e6	−	5.90970e6i	0.00883875	−	0.0153092i
$285$	6.70101e8	+	1.16065e9i	1.71468	+	2.96992i
$286$	−1.37083e8			−0.346498
$287$		0			0
$288$	−1.48668e8			−0.366729
$289$	2.02079e8	+	3.50012e8i	0.492469	+	0.852982i
$290$	−1.57864e8	+	2.73429e8i	−0.380094	+	0.658343i
$291$	5.53778e8	−	9.59172e8i	1.31738	−	2.28177i
$292$	−3.16458e7	−	5.48121e7i	−0.0743833	−	0.128836i
$293$	−1.18887e8			−0.276119			−0.138059	−	0.990424i	$-0.544087\pi$
$293$	−1.18887e8			−0.276119			−0.138059	+	0.990424i	$0.544087\pi$
$294$		0			0
$295$	−9.63138e8			−2.18430
$296$	−5.49207e7	−	9.51254e7i	−0.123088	−	0.213194i
$297$	2.32011e8	−	4.01854e8i	0.513879	−	0.890064i
$298$	2.94401e8	−	5.09918e8i	0.644440	−	1.11620i
$299$	4.58270e7	+	7.93748e7i	0.0991454	+	0.171725i
$300$	−6.43295e8			−1.37558
$301$		0			0
$302$	−1.39431e8			−0.291297
$303$	−7.69344e8	−	1.33254e9i	−1.58881	−	2.75189i
$304$	−7.47151e7	+	1.29410e8i	−0.152529	+	0.264187i
$305$	−6.90897e8	+	1.19667e9i	−1.39432	+	2.41504i
$306$	4.51159e7	+	7.81431e7i	0.0900129	+	0.155907i
$307$	1.63581e8			0.322663			0.161332	−	0.986900i	$-0.448421\pi$
$307$	1.63581e8			0.322663			0.161332	+	0.986900i	$0.448421\pi$
$308$		0			0
$309$	1.32906e9			2.56265
$310$	5.06484e8	+	8.77256e8i	0.965605	+	1.67248i
$311$	2.16240e8	−	3.74539e8i	0.407638	−	0.706050i	−0.586986	−	0.809597i	$-0.699686\pi$
$311$	2.16240e8	−	3.74539e8i	0.407638	−	0.706050i	0.994625	+	0.103547i	$0.0330191\pi$
$312$	−1.49379e8	+	2.58732e8i	−0.278451	+	0.482291i
$313$	2.13516e8	+	3.69821e8i	0.393574	+	0.681690i	0.992918	−	0.118802i	$-0.0379053\pi$
$313$	2.13516e8	+	3.69821e8i	0.393574	+	0.681690i	−0.599344	+	0.800491i	$0.704572\pi$
$314$	1.77726e8			0.323964
$315$		0			0
$316$	2.18617e8			0.389744
$317$	1.73751e8	+	3.00946e8i	0.306352	+	0.530616i	0.977561	−	0.210651i	$-0.0675584\pi$
$317$	1.73751e8	+	3.00946e8i	0.306352	+	0.530616i	−0.671210	+	0.741267i	$0.734225\pi$
$318$	1.86783e7	−	3.23517e7i	0.0325718	−	0.0564161i
$319$	1.06065e8	−	1.83710e8i	0.182939	−	0.316859i
$320$	−5.87203e7	−	1.01706e8i	−0.100176	−	0.173510i
$321$	−5.71195e8			−0.963867
$322$		0			0
$323$	9.06943e7			0.149751
$324$	−1.88127e8	−	3.25846e8i	−0.307287	−	0.532237i
$325$	−4.36136e8	+	7.55410e8i	−0.704742	+	1.22065i
$326$	2.49518e8	−	4.32178e8i	0.398879	−	0.690878i
$327$	−6.11060e8	−	1.05839e9i	−0.966421	−	1.67389i
$328$	7.21275e7			0.112861
$329$		0			0
$330$	7.07682e8			1.08403
$331$	4.07707e8	+	7.06169e8i	0.617945	+	1.07031i	0.989860	+	0.142045i	$0.0453679\pi$
$331$	4.07707e8	+	7.06169e8i	0.617945	+	1.07031i	−0.371915	+	0.928267i	$0.621299\pi$
$332$	484544.	−	839255.i	0.000726691	−	0.00125867i
$333$	4.86670e8	−	8.42938e8i	0.722238	−	1.25095i
$334$	1.32495e8	+	2.29489e8i	0.194575	+	0.337015i
$335$	−1.35940e9			−1.97555
$336$		0			0
$337$	−5.55790e8			−0.791054			−0.395527	−	0.918454i	$-0.629438\pi$
$337$	−5.55790e8			−0.791054			−0.395527	+	0.918454i	$0.629438\pi$
$338$	−4.84442e7	−	8.39079e7i	−0.0682392	−	0.118194i
$339$	−1.06881e9	+	1.85123e9i	−1.49005	+	2.58084i
$340$	−3.56393e7	+	6.17291e7i	−0.0491760	+	0.0851753i
$341$	−3.40294e8	−	5.89406e8i	−0.464744	−	0.804960i
$342$	−1.32415e9			−1.78997
$343$		0			0
$344$	−1.86696e7			−0.0247275
$345$	−2.36580e8	−	4.09768e8i	−0.310178	−	0.537244i
$346$	−2.82319e8	+	4.88992e8i	−0.366416	+	0.634651i
$347$	−5.38540e8	+	9.32778e8i	−0.691934	+	1.19846i	0.279269	+	0.960213i	$0.409908\pi$
$347$	−5.38540e8	+	9.32778e8i	−0.691934	+	1.19846i	−0.971203	+	0.238252i	$0.923426\pi$
$348$	−2.31159e8	−	4.00379e8i	−0.294024	−	0.509265i
$349$	1.44167e9			1.81541			0.907707	−	0.419605i	$-0.137831\pi$
$349$	1.44167e9			1.81541			0.907707	+	0.419605i	$0.137831\pi$
$350$		0			0
$351$	−1.37125e9			−1.69255
$352$	3.94527e7	+	6.83340e7i	0.0482144	+	0.0835099i
$353$	−2.86633e8	+	4.96463e8i	−0.346829	+	0.600725i	−0.985684	−	0.168602i	$-0.946075\pi$
$353$	−2.86633e8	+	4.96463e8i	−0.346829	+	0.600725i	0.638856	+	0.769327i	$0.279408\pi$
$354$	7.05155e8	−	1.22136e9i	0.844837	−	1.46330i
$355$	2.38838e7	+	4.13679e7i	0.0283337	+	0.0490755i
$356$	1.11878e7			0.0131423
$357$		0			0
$358$	9.69410e8			1.11665
$359$	4.74667e8	+	8.22148e8i	0.541451	+	0.937820i	0.998821	+	0.0485438i	$0.0154581\pi$
$359$	4.74667e8	+	8.22148e8i	0.541451	+	0.937820i	−0.457370	+	0.889276i	$0.651209\pi$
$360$	5.20339e8	−	9.01254e8i	0.587798	−	1.01810i
$361$	−2.18532e8	+	3.78509e8i	−0.244478	+	0.423449i
$362$	9.22200e7	+	1.59730e8i	0.102175	+	0.176973i
$363$	1.12247e9			1.23169
$364$		0			0
$365$	4.43041e8			0.476890
$366$	−1.01167e9	−	1.75226e9i	−1.07859	−	1.86817i
$367$	1.50885e8	−	2.61341e8i	0.159337	−	0.275979i	−0.775293	−	0.631602i	$-0.782398\pi$
$367$	1.50885e8	−	2.61341e8i	0.159337	−	0.275979i	0.934630	+	0.355622i	$0.115731\pi$
$368$	2.63782e7	−	4.56885e7i	0.0275917	−	0.0477902i
$369$	3.19573e8	+	5.53516e8i	0.331114	+	0.573506i
$370$	7.68890e8			0.789147
$371$		0			0
$372$	−1.48327e9			−1.49390
$373$	6.80910e8	+	1.17937e9i	0.679374	+	1.17671i	0.975170	+	0.221459i	$0.0710819\pi$
$373$	6.80910e8	+	1.17937e9i	0.679374	+	1.17671i	−0.295796	+	0.955251i	$0.595585\pi$
$374$	2.39452e7	−	4.14742e7i	0.0236683	−	0.0409947i
$375$	8.16531e8	−	1.41427e9i	0.799582	−	1.38492i
$376$	1.83518e8	+	3.17863e8i	0.178042	+	0.308377i
$377$	−6.26877e8			−0.602542
$378$		0			0
$379$	−1.51839e9			−1.43267			−0.716333	−	0.697758i	$-0.754181\pi$
$379$	−1.51839e9			−1.43267			−0.716333	+	0.697758i	$0.754181\pi$
$380$	−5.23006e8	−	9.05873e8i	−0.488950	−	0.846885i
$381$	8.73857e8	−	1.51356e9i	0.809474	−	1.40205i
$382$	−8.11708e7	+	1.40592e8i	−0.0745037	+	0.129044i
$383$	−2.27057e8	−	3.93274e8i	−0.206509	−	0.357684i	0.744103	−	0.668064i	$-0.232877\pi$
$383$	−2.27057e8	−	3.93274e8i	−0.206509	−	0.357684i	−0.950613	+	0.310380i	$0.899544\pi$
$384$	1.71966e8			0.154983
$385$		0			0
$386$	−1.80865e8			−0.160066
$387$	−8.27186e7	−	1.43273e8i	−0.0725462	−	0.125654i
$388$	−4.32217e8	+	7.48622e8i	−0.375657	+	0.650656i
$389$	9.18499e8	−	1.59089e9i	0.791143	−	1.37030i	−0.134117	−	0.990965i	$-0.542820\pi$
$389$	9.18499e8	−	1.59089e9i	0.791143	−	1.37030i	0.925260	−	0.379334i	$-0.123847\pi$
$390$	−1.04565e9	−	1.81112e9i	−0.892610	−	1.54605i
$391$	−3.20197e7			−0.0270893
$392$		0			0
$393$	−8.59141e8			−0.713987
$394$	−1.30872e8	−	2.26677e8i	−0.107798	−	0.186711i
$395$	−7.65161e8	+	1.32530e9i	−0.624688	+	1.08199i
$396$	−3.49603e8	+	6.05530e8i	−0.282906	+	0.490007i
$397$	−6.18339e8	−	1.07099e9i	−0.495975	−	0.859054i	0.504014	−	0.863695i	$-0.331856\pi$
$397$	−6.18339e8	−	1.07099e9i	−0.495975	−	0.859054i	−0.999989	+	0.00464153i	$0.998523\pi$
$398$	−5.79578e8			−0.460809
$399$		0			0
$400$	5.02084e8			0.392253
$401$	−7.89739e8	−	1.36787e9i	−0.611615	−	1.05935i	−0.990968	−	0.134096i	$-0.957187\pi$
$401$	−7.89739e8	−	1.36787e9i	−0.611615	−	1.05935i	0.379353	−	0.925252i	$-0.376147\pi$
$402$	9.95271e8	−	1.72386e9i	0.764100	−	1.32346i
$403$	−1.00562e9	+	1.74178e9i	−0.765360	+	1.32564i
$404$	6.00463e8	+	1.04003e9i	0.453056	+	0.784716i
$405$	2.63378e9			1.97010
$406$		0			0
$407$	−5.16598e8			−0.379815
$408$	−5.21861e7	−	9.03890e7i	−0.0380403	−	0.0658878i
$409$	9.62788e8	−	1.66760e9i	0.695823	−	1.20520i	−0.274079	−	0.961707i	$-0.588373\pi$
$409$	9.62788e8	−	1.66760e9i	0.695823	−	1.20520i	0.969902	−	0.243494i	$-0.0782936\pi$
$410$	−2.52446e8	+	4.37250e8i	−0.180894	+	0.313318i
$411$	1.48412e9	+	2.57057e9i	1.05444	+	1.82635i
$412$	−1.03731e9			−0.730751
$413$		0			0
$414$	4.67492e8			0.323797
$415$	3.39181e6	+	5.87478e6i	0.00232950	+	0.00403481i
$416$	1.16589e8	−	2.01937e8i	0.0794016	−	0.137528i
$417$	−2.16339e9	+	3.74710e9i	−1.46103	+	2.53057i
$418$	3.51395e8	+	6.08633e8i	0.235330	+	0.407604i
$419$	−2.39996e9			−1.59388			−0.796938	−	0.604062i	$-0.793548\pi$
$419$	−2.39996e9			−1.59388			−0.796938	+	0.604062i	$0.793548\pi$
$420$		0			0
$421$	1.20940e9			0.789919			0.394960	−	0.918698i	$-0.370759\pi$
$421$	1.20940e9			0.789919			0.394960	+	0.918698i	$0.370759\pi$
$422$	3.75202e8	+	6.49870e8i	0.243037	+	0.420952i
$423$	−1.62622e9	+	2.81669e9i	−1.04469	+	1.80945i
$424$	−1.45782e7	+	2.52501e7i	−0.00928801	+	0.0160873i
$425$	−1.52366e8	−	2.63905e8i	−0.0962778	−	0.166758i
$426$	−6.99453e7			−0.0438354
$427$		0			0
$428$	4.45811e8			0.274851
$429$	7.02548e8	+	1.21685e9i	0.429611	+	0.744109i
$430$	6.53435e7	−	1.13178e8i	0.0396335	−	0.0686473i
$431$	1.08143e9	−	1.87308e9i	0.650618	−	1.12690i	−0.332355	−	0.943155i	$-0.607843\pi$
$431$	1.08143e9	−	1.87308e9i	0.650618	−	1.12690i	0.982973	−	0.183750i	$-0.0588236\pi$
$432$	3.94650e8	+	6.83553e8i	0.235515	+	0.407924i
$433$	2.25750e9			1.33635			0.668174	−	0.744005i	$-0.267076\pi$
$433$	2.25750e9			1.33635			0.668174	+	0.744005i	$0.267076\pi$
$434$		0			0
$435$	3.23622e9			1.88506
$436$	4.76925e8	+	8.26058e8i	0.275580	+	0.477318i
$437$	2.34944e8	−	4.06935e8i	0.134673	−	0.233260i
$438$	−3.24369e8	+	5.61824e8i	−0.184451	+	0.319478i
$439$	3.72862e8	+	6.45816e8i	0.210340	+	0.364320i	0.951821	−	0.306654i	$-0.0992095\pi$
$439$	3.72862e8	+	6.45816e8i	0.210340	+	0.364320i	−0.741481	+	0.670974i	$0.765876\pi$
$440$	−5.52337e8			−0.309115
$441$		0			0
$442$	−1.41523e8			−0.0779559
$443$	5.51076e8	+	9.54492e8i	0.301161	+	0.521626i	0.976399	−	0.215974i	$-0.0692925\pi$
$443$	5.51076e8	+	9.54492e8i	0.301161	+	0.521626i	−0.675238	+	0.737600i	$0.735959\pi$
$444$	−5.62937e8	+	9.75036e8i	−0.305225	+	0.528665i
$445$	−3.91574e7	+	6.78227e7i	−0.0210647	+	0.0364850i
$446$	6.50269e6	+	1.12630e7i	0.00347073	+	0.00601148i
$447$	−6.03522e9			−3.19608
$448$		0			0
$449$	3.41600e9			1.78097			0.890483	−	0.455017i	$-0.150367\pi$
$449$	3.41600e9			1.78097			0.890483	+	0.455017i	$0.150367\pi$
$450$	2.22456e9	+	3.85306e9i	1.15080	+	1.99325i
$451$	1.69612e8	−	2.93777e8i	0.0870642	−	0.150800i
$452$	8.34190e8	−	1.44486e9i	0.424894	−	0.735938i
$453$	7.14584e8	+	1.23770e9i	0.361168	+	0.625562i
$454$	1.96922e9			0.987640
$455$		0			0
$456$	1.53166e9			0.756459
$457$	−2.13655e8	−	3.70061e8i	−0.104714	−	0.181371i	0.808907	−	0.587936i	$-0.200060\pi$
$457$	−2.13655e8	−	3.70061e8i	−0.104714	−	0.181371i	−0.913621	+	0.406566i	$0.866726\pi$
$458$	−4.24163e8	+	7.34672e8i	−0.206302	+	0.357326i
$459$	2.39526e8	−	4.14871e8i	0.115613	−	0.200248i
$460$	1.84648e8	+	3.19819e8i	0.0884487	+	0.153198i
$461$	2.18116e9			1.03690			0.518448	−	0.855109i	$-0.326510\pi$
$461$	2.18116e9			1.03690			0.518448	+	0.855109i	$0.326510\pi$
$462$		0			0
$463$	1.88134e8			0.0880916			0.0440458	−	0.999030i	$-0.485975\pi$
$463$	1.88134e8			0.0880916			0.0440458	+	0.999030i	$0.485975\pi$
$464$	1.80417e8	+	3.12491e8i	0.0838423	+	0.145219i
$465$	5.19146e9	−	8.99187e9i	2.39444	−	4.14729i
$466$	−8.08825e8	+	1.40093e9i	−0.370258	+	0.641305i
$467$	−4.27267e8	−	7.40048e8i	−0.194129	−	0.336241i	0.752486	−	0.658609i	$-0.228855\pi$
$467$	−4.27267e8	−	7.40048e8i	−0.194129	−	0.336241i	−0.946615	+	0.322367i	$0.895521\pi$
$468$	2.06626e9			0.931803
$469$		0			0
$470$	−2.56925e9			−1.14147
$471$	−9.10844e8	−	1.57763e9i	−0.401671	−	0.695715i
$472$	−5.50365e8	+	9.53260e8i	−0.240909	+	0.417267i
$473$	−4.39027e7	+	7.60416e7i	−0.0190755	+	0.0330398i
$474$	−1.12041e9	−	1.94061e9i	−0.483230	−	0.836980i
$475$	4.47193e9			1.91455
$476$		0			0
$477$	−2.58364e8			−0.108998
$478$	−1.47009e8	−	2.54628e8i	−0.0615669	−	0.106637i
$479$	3.41407e8	−	5.91334e8i	0.141938	−	0.245844i	−0.786288	−	0.617860i	$-0.788000\pi$
$479$	3.41407e8	−	5.91334e8i	0.141938	−	0.245844i	0.928226	+	0.372016i	$0.121333\pi$
$480$	−6.01883e8	+	1.04249e9i	−0.248409	+	0.430257i
$481$	7.63312e8	+	1.32210e9i	0.312748	+	0.541695i
$482$	−4.61132e8			−0.187569
$483$		0			0
$484$	−8.76077e8			−0.351224
$485$	−3.02552e9	−	5.24036e9i	−1.20422	−	2.08576i
$486$	−2.42566e8	+	4.20137e8i	−0.0958525	+	0.166021i
$487$	−2.07560e9	+	3.59504e9i	−0.814313	+	1.41043i	0.0955063	+	0.995429i	$0.469553\pi$
$487$	−2.07560e9	+	3.59504e9i	−0.814313	+	1.41043i	−0.909820	+	0.415004i	$0.863780\pi$
$488$	7.89596e8	+	1.36762e9i	0.307564	+	0.532717i
$489$	−5.11512e9			−1.97822
$490$		0			0
$491$	8.99538e8			0.342953			0.171476	−	0.985188i	$-0.445146\pi$
$491$	8.99538e8			0.342953			0.171476	+	0.985188i	$0.445146\pi$
$492$	−3.69653e8	−	6.40258e8i	−0.139932	−	0.242369i
$493$	1.09501e8	−	1.89661e8i	0.0411579	−	0.0712876i
$494$	1.03842e9	−	1.79860e9i	0.387552	−	0.671260i
$495$	−2.44722e9	−	4.23871e9i	−0.906891	−	1.57078i
$496$	1.15768e9			0.425992
$497$		0			0
$498$	−9.93315e6			−0.00360400
$499$	3.05555e8	+	5.29237e8i	0.110087	+	0.190677i	0.915805	−	0.401623i	$-0.131554\pi$
$499$	3.05555e8	+	5.29237e8i	0.110087	+	0.190677i	−0.805718	+	0.592299i	$0.798220\pi$
$500$	−6.37293e8	+	1.10382e9i	−0.228005	+	0.394916i
$501$	1.35808e9	−	2.35226e9i	0.482495	−	0.835705i
$502$	−1.04533e9	−	1.81056e9i	−0.368799	−	0.638779i
$503$	5.23241e9			1.83322			0.916608	−	0.399787i	$-0.130916\pi$
$503$	5.23241e9			1.83322			0.916608	+	0.399787i	$0.130916\pi$
$504$		0			0
$505$	−8.40649e9			−2.90466
$506$	−1.24060e8	−	2.14879e8i	−0.0425702	−	0.0737337i
$507$	−4.96554e8	+	8.60056e8i	−0.169215	+	0.293089i
$508$	−6.82035e8	+	1.18132e9i	−0.230825	+	0.399801i
$509$	−1.16765e8	−	2.02243e8i	−0.0392465	−	0.0679770i	0.845735	−	0.533603i	$-0.179162\pi$
$509$	−1.16765e8	−	2.02243e8i	−0.0392465	−	0.0679770i	−0.884981	+	0.465626i	$0.845829\pi$
$510$	7.30606e8			0.243886
$511$		0			0
$512$	−1.34218e8			−0.0441942
$513$	3.51504e9	+	6.08823e9i	1.14953	+	1.99104i
$514$	1.39050e9	−	2.40842e9i	0.451648	−	0.782278i
$515$	3.63060e9	−	6.28838e9i	1.17126	−	2.02868i
$516$	9.56815e7	+	1.65725e8i	0.0306587	+	0.0531025i
$517$	1.72622e9			0.549388
$518$		0			0
$519$	5.78755e9			1.81723
$520$	8.16120e8	+	1.41356e9i	0.254532	+	0.440862i
$521$	−1.11514e9	+	1.93149e9i	−0.345461	+	0.598356i	−0.985437	−	0.170039i	$-0.945611\pi$
$521$	−1.11514e9	+	1.93149e9i	−0.345461	+	0.598356i	0.639977	+	0.768394i	$0.278944\pi$
$522$	−1.59873e9	+	2.76908e9i	−0.491958	+	0.852097i
$523$	−2.37398e8	−	4.11185e8i	−0.0725638	−	0.125684i	0.827460	−	0.561524i	$-0.189785\pi$
$523$	−2.37398e8	−	4.11185e8i	−0.0725638	−	0.125684i	−0.900024	+	0.435840i	$0.856451\pi$
$524$	6.70549e8			0.203597
$525$		0			0
$526$	1.41201e9			0.423047
$527$	−3.51317e8	−	6.08498e8i	−0.104559	−	0.181102i
$528$	4.04390e8	−	7.00424e8i	0.119559	−	0.207082i
$529$	1.61947e9	−	2.80500e9i	0.475638	−	0.823830i
$530$	−1.02047e8	−	1.76751e8i	−0.0297739	−	0.0515699i
$531$	−9.75392e9			−2.82715
$532$		0			0
$533$	−1.00246e9			−0.286762
$534$	−5.73377e7	−	9.93118e7i	−0.0162947	−	0.0282232i
$535$	−1.56034e9	+	2.70259e9i	−0.440535	+	0.763029i
$536$	−7.76797e8	+	1.34545e9i	−0.217887	+	0.377391i
$537$	−4.96823e9	−	8.60522e9i	−1.38449	−	2.39802i
$538$	3.26311e9			0.903429
$539$		0			0
$540$	−5.52509e9			−1.50995
$541$	4.23985e8	+	7.34363e8i	0.115122	+	0.199398i	0.917829	−	0.396977i	$-0.129941\pi$
$541$	4.23985e8	+	7.34363e8i	0.115122	+	0.199398i	−0.802706	+	0.596375i	$0.796607\pi$
$542$	1.27047e9	−	2.20052e9i	0.342743	−	0.593648i
$543$	9.45255e8	−	1.63723e9i	0.253367	−	0.438844i
$544$	4.07306e7	+	7.05475e7i	0.0108474	+	0.0187882i
$545$	−6.67694e9			−1.76681
$546$		0			0
$547$	−6.55694e7			−0.0171295			−0.00856477	−	0.999963i	$-0.502726\pi$
$547$	−6.55694e7			−0.0171295			−0.00856477	+	0.999963i	$0.502726\pi$
$548$	−1.15834e9	−	2.00630e9i	−0.300679	−	0.520792i
$549$	−6.99687e9	+	1.21189e10i	−1.80468	+	3.12580i
$550$	1.18068e9	−	2.04500e9i	0.302596	−	0.524112i
$551$	1.60692e9	+	2.78327e9i	0.409227	+	0.708802i
$552$	−5.40754e8			−0.136840
$553$		0			0
$554$	−2.34981e9			−0.587150
$555$	−3.94056e9	−	6.82525e9i	−0.978436	−	1.69470i
$556$	1.68850e9	−	2.92456e9i	0.416619	−	0.721604i
$557$	−3.06262e8	+	5.30461e8i	−0.0750930	+	0.130065i	−0.901127	−	0.433556i	$-0.857259\pi$
$557$	−3.06262e8	+	5.30461e8i	−0.0750930	+	0.130065i	0.826034	+	0.563621i	$0.190592\pi$
$558$	5.12928e9	+	8.88417e9i	1.24979	+	2.16470i
$559$	2.59478e8			0.0628288
$560$		0			0
$561$	−4.90876e8			−0.117382
$562$	−2.18011e8	−	3.77606e8i	−0.0518085	−	0.0897349i
$563$	−3.51051e8	+	6.08037e8i	−0.0829068	+	0.143599i	−0.904497	−	0.426479i	$-0.859754\pi$
$563$	−3.51051e8	+	6.08037e8i	−0.0829068	+	0.143599i	0.821591	+	0.570078i	$0.193087\pi$
$564$	1.88106e9	−	3.25809e9i	0.441495	−	0.764692i
$565$	5.83933e9	+	1.01140e10i	1.36205	+	2.35914i
$566$	−1.64327e9			−0.380936
$567$		0			0
$568$	5.45915e7			0.0124999
$569$	−1.21788e8	−	2.10944e8i	−0.0277149	−	0.0480036i	0.851835	−	0.523810i	$-0.175490\pi$
$569$	−1.21788e8	−	2.10944e8i	−0.0277149	−	0.0480036i	−0.879550	+	0.475806i	$0.842156\pi$
$570$	−5.36081e9	+	9.28520e9i	−1.21246	+	2.10005i
$571$	−2.64459e9	+	4.58057e9i	−0.594474	+	1.02966i	0.399147	+	0.916887i	$0.369306\pi$
$571$	−2.64459e9	+	4.58057e9i	−0.594474	+	1.02966i	−0.993621	+	0.112772i	$0.964027\pi$
$572$	−5.48330e8	−	9.49736e8i	−0.122506	−	0.212186i
$573$	1.66400e9			0.369498
$574$		0			0
$575$	−1.57882e9			−0.346333
$576$	−5.94674e8	−	1.03000e9i	−0.129658	−	0.224575i
$577$	1.84228e9	−	3.19092e9i	0.399245	−	0.691513i	−0.594388	−	0.804178i	$-0.702606\pi$
$577$	1.84228e9	−	3.19092e9i	0.399245	−	0.691513i	0.993633	+	0.112666i	$0.0359390\pi$
$578$	−1.61663e9	+	2.80009e9i	−0.348228	+	0.603149i
$579$	9.26933e8	+	1.60549e9i	0.198460	+	0.343743i
$580$	−2.52583e9			−0.537534
$581$		0			0
$582$	8.86045e9			1.86305
$583$	6.85630e7	+	1.18755e8i	0.0143301	+	0.0248205i
$584$	2.53166e8	−	4.38497e8i	0.0525969	−	0.0911006i
$585$	−7.23191e9	+	1.25260e10i	−1.49351	+	2.58683i
$586$	−4.75546e8	−	8.23670e8i	−0.0976228	−	0.169088i
$587$	−4.23510e9			−0.864232			−0.432116	−	0.901818i	$-0.642233\pi$
$587$	−4.23510e9			−0.864232			−0.432116	+	0.901818i	$0.642233\pi$
$588$		0			0
$589$	1.03111e10			2.07923
$590$	−3.85255e9	−	6.67282e9i	−0.772265	−	1.33760i
$591$	−1.34144e9	+	2.32344e9i	−0.267309	+	0.462993i
$592$	4.39366e8	−	7.61004e8i	0.0870362	−	0.150751i
$593$	−4.85477e9	−	8.40872e9i	−0.956043	−	1.65592i	−0.731962	−	0.681345i	$-0.761395\pi$
$593$	−4.85477e9	−	8.40872e9i	−0.956043	−	1.65592i	−0.224081	−	0.974571i	$-0.571938\pi$
$594$	3.71217e9			0.726734
$595$		0			0
$596$	4.71042e9			0.911376
$597$	2.97034e9	+	5.14477e9i	0.571341	+	0.989592i
$598$	−3.66616e8	+	6.34998e8i	−0.0701064	+	0.121428i
$599$	2.02088e9	−	3.50027e9i	0.384191	−	0.665438i	−0.607466	−	0.794346i	$-0.707814\pi$
$599$	2.02088e9	−	3.50027e9i	0.384191	−	0.665438i	0.991657	+	0.128908i	$0.0411471\pi$
$600$	−2.57318e9	−	4.45688e9i	−0.486341	−	0.842367i
$601$	−2.62572e7			−0.00493387			−0.00246694	−	0.999997i	$-0.500785\pi$
$601$	−2.62572e7			−0.00493387			−0.00246694	+	0.999997i	$0.500785\pi$
$602$		0			0
$603$	−1.37669e10			−2.55697
$604$	−5.57724e8	−	9.66007e8i	−0.102989	−	0.178382i
$605$	3.06627e9	−	5.31094e9i	0.562946	−	0.975051i
$606$	6.15475e9	−	1.06603e10i	1.12346	−	1.94588i
$607$	3.63244e9	+	6.29158e9i	0.659232	+	1.14182i	0.980815	+	0.194942i	$0.0624519\pi$
$607$	3.63244e9	+	6.29158e9i	0.659232	+	1.14182i	−0.321583	+	0.946882i	$0.604215\pi$
$608$	−1.19544e9			−0.215708
$609$		0			0
$610$	−1.10543e10			−1.97187
$611$	−2.55062e9	−	4.41780e9i	−0.452377	−	0.783541i
$612$	−3.60927e8	+	6.25145e8i	−0.0636488	+	0.110243i
$613$	5.50186e9	−	9.52949e9i	0.964712	−	1.67093i	0.254324	−	0.967119i	$-0.418147\pi$
$613$	5.50186e9	−	9.52949e9i	0.964712	−	1.67093i	0.710387	−	0.703811i	$-0.248520\pi$
$614$	6.54325e8	+	1.13332e9i	0.114079	+	0.197590i
$615$	5.17515e9			0.897139
$616$		0			0
$617$	8.50181e8			0.145718			0.0728590	−	0.997342i	$-0.476788\pi$
$617$	8.50181e8			0.145718			0.0728590	+	0.997342i	$0.476788\pi$
$618$	5.31623e9	+	9.20798e9i	0.906033	+	1.56930i
$619$	−2.89636e9	+	5.01663e9i	−0.490834	+	0.850149i	−0.999944	−	0.0105519i	$-0.996641\pi$
$619$	−2.89636e9	+	5.01663e9i	−0.490834	+	0.850149i	0.509110	+	0.860701i	$0.329974\pi$
$620$	−4.05187e9	+	7.01804e9i	−0.682786	+	1.18262i
$621$	−1.24099e9	−	2.14945e9i	−0.207944	−	0.360170i
$622$	3.45984e9			0.576488
$623$		0			0
$624$	−2.39007e9			−0.393789
$625$	3.27194e8	+	5.66717e8i	0.0536075	+	0.0928510i
$626$	−1.70813e9	+	2.95857e9i	−0.278299	+	0.482027i
$627$	3.60179e9	−	6.23849e9i	0.583556	−	1.01075i
$628$	7.10902e8	+	1.23132e9i	0.114538	+	0.198386i
$629$	−5.33332e8			−0.0854516
$630$		0			0
$631$	−6.69052e9			−1.06012			−0.530062	−	0.847959i	$-0.677831\pi$
$631$	−6.69052e9			−1.06012			−0.530062	+	0.847959i	$0.677831\pi$
$632$	8.74469e8	+	1.51463e9i	0.137795	+	0.238669i
$633$	3.84583e9	−	6.66116e9i	0.602666	−	1.04385i
$634$	−1.39001e9	+	2.40757e9i	−0.216623	+	0.375202i
$635$	−4.77424e9	−	8.26923e9i	−0.739940	−	1.28161i
$636$	2.98853e8			0.0460635
$637$		0			0
$638$	1.69704e9			0.258714
$639$	2.41877e8	+	4.18942e8i	0.0366725	+	0.0635187i
$640$	4.69762e8	−	8.13652e8i	0.0708350	−	0.122690i
$641$	−2.38597e9	+	4.13262e9i	−0.357818	+	0.619759i	−0.987596	−	0.157016i	$-0.949813\pi$
$641$	−2.38597e9	+	4.13262e9i	−0.357818	+	0.619759i	0.629778	+	0.776775i	$0.283146\pi$
$642$	−2.28478e9	−	3.95736e9i	−0.340778	−	0.590245i
$643$	4.09295e9			0.607153			0.303576	−	0.952807i	$-0.401819\pi$
$643$	4.09295e9			0.607153			0.303576	+	0.952807i	$0.401819\pi$
$644$		0			0
$645$	−1.33954e9			−0.196561
$646$	3.62777e8	+	6.28348e8i	0.0529451	+	0.0917036i
$647$	2.69951e9	−	4.67569e9i	0.391850	−	0.678705i	−0.600843	−	0.799367i	$-0.705168\pi$
$647$	2.69951e9	−	4.67569e9i	0.391850	−	0.678705i	0.992694	+	0.120662i	$0.0385018\pi$
$648$	1.50502e9	−	2.60677e9i	0.217285	−	0.376348i
$649$	2.58843e9	+	4.48330e9i	0.371690	+	0.643786i
$650$	−6.97818e9			−0.996656
$651$		0			0
$652$	3.99229e9			0.564099
$653$	2.04893e9	+	3.54886e9i	0.287960	+	0.498761i	0.973323	−	0.229441i	$-0.0736898\pi$
$653$	2.04893e9	+	3.54886e9i	0.287960	+	0.498761i	−0.685363	+	0.728202i	$0.740356\pi$
$654$	4.88848e9	−	8.46709e9i	0.683363	−	1.18362i
$655$	−2.34692e9	+	4.06499e9i	−0.326328	+	0.565216i
$656$	2.88510e8	+	4.99714e8i	0.0399022	+	0.0691127i
$657$	4.48678e9			0.617242
$658$		0			0
$659$	−3.77455e9			−0.513766			−0.256883	−	0.966442i	$-0.582696\pi$
$659$	−3.77455e9			−0.513766			−0.256883	+	0.966442i	$0.582696\pi$
$660$	2.83073e9	+	4.90297e9i	0.383261	+	0.663827i
$661$	−4.90953e9	+	8.50355e9i	−0.661203	+	1.14524i	0.319097	+	0.947722i	$0.396620\pi$
$661$	−4.90953e9	+	8.50355e9i	−0.661203	+	1.14524i	−0.980300	+	0.197515i	$0.936713\pi$
$662$	−3.26165e9	+	5.64935e9i	−0.436953	+	0.756825i
$663$	7.25305e8	+	1.25627e9i	0.0966548	+	0.167411i
$664$	7.75270e6			0.00102770
$665$		0			0
$666$	7.78673e9			1.02140
$667$	−5.67325e8	−	9.82636e8i	−0.0740273	−	0.128219i
$668$	−1.05996e9	+	1.83591e9i	−0.137586	+	0.238305i
$669$	6.66526e7	−	1.15446e8i	0.00860648	−	0.0149069i
$670$	−5.43758e9	−	9.41817e9i	−0.698464	−	1.20977i
$671$	7.42714e9			0.949058
$672$		0			0
$673$	9.98739e9			1.26299			0.631494	−	0.775381i	$-0.282442\pi$
$673$	9.98739e9			1.26299			0.631494	+	0.775381i	$0.282442\pi$
$674$	−2.22316e9	−	3.85063e9i	−0.279680	−	0.484420i
$675$	1.18105e10	−	2.04564e10i	1.47810	−	2.56015i
$676$	3.87554e8	−	6.71263e8i	0.0482524	−	0.0835756i
$677$	−2.37780e8	−	4.11847e8i	−0.0294520	−	0.0510123i	0.850924	−	0.525289i	$-0.176043\pi$
$677$	−2.37780e8	−	4.11847e8i	−0.0294520	−	0.0510123i	−0.880376	+	0.474277i	$0.842710\pi$
$678$	−1.71009e10			−2.10724
$679$		0			0
$680$	−5.70229e8			−0.0695453
$681$	−1.00923e10	−	1.74803e10i	−1.22454	−	2.12097i
$682$	2.72235e9	−	4.71525e9i	0.328624	−	0.569193i
$683$	−1.38182e8	+	2.39339e8i	−0.0165951	+	0.0287436i	−0.874204	−	0.485559i	$-0.838616\pi$
$683$	−1.38182e8	+	2.39339e8i	−0.0165951	+	0.0287436i	0.857609	+	0.514303i	$0.171949\pi$
$684$	−5.29660e9	−	9.17398e9i	−0.632850	−	1.09613i
$685$	1.62167e10			1.92773
$686$		0			0
$687$	8.69534e9			1.02315
$688$	−7.46783e7	−	1.29347e8i	−0.00874248	−	0.0151424i
$689$	2.02614e8	−	3.50938e8i	0.0235995	−	0.0408754i
$690$	1.89264e9	−	3.27815e9i	0.219329	−	0.379889i
$691$	−4.41241e9	−	7.64252e9i	−0.508748	−	0.881178i	−0.999949	−	0.0101311i	$-0.996775\pi$
$691$	−4.41241e9	−	7.64252e9i	−0.508748	−	0.881178i	0.491201	−	0.871047i	$-0.336558\pi$
$692$	−4.51711e9			−0.518191
$693$		0			0
$694$	−8.61664e9			−0.978542
$695$	1.18195e10	+	2.04719e10i	1.33552	+	2.31319i
$696$	1.84927e9	−	3.20303e9i	0.207906	−	0.360104i
$697$	1.75106e8	−	3.03293e8i	0.0195879	−	0.0339272i
$698$	5.76666e9	+	9.98815e9i	0.641846	+	1.11171i
$699$	1.65809e10			1.83628
$700$		0			0
$701$	1.61615e10			1.77202			0.886012	−	0.463662i	$-0.153465\pi$
$701$	1.61615e10			1.77202			0.886012	+	0.463662i	$0.153465\pi$
$702$	−5.48501e9	−	9.50032e9i	−0.598408	−	1.03647i
$703$	3.91331e9	−	6.77806e9i	0.424816	−	0.735803i
$704$	−3.15621e8	+	5.46672e8i	−0.0340928	+	0.0590504i
$705$	1.31674e10	+	2.28067e10i	1.41527	+	2.45132i
$706$	−4.58613e9			−0.490490
$707$		0			0
$708$	1.12825e10			1.19478
$709$	4.18051e9	+	7.24085e9i	0.440522	+	0.763006i	0.997728	−	0.0673680i	$-0.0214602\pi$
$709$	4.18051e9	+	7.24085e9i	0.440522	+	0.763006i	−0.557207	+	0.830374i	$0.688127\pi$
$710$	−1.91070e8	+	3.30943e8i	−0.0200350	+	0.0347016i
$711$	−7.74896e9	+	1.34216e10i	−0.808537	+	1.40043i
$712$	4.47514e7	+	7.75116e7i	0.00464650	+	0.00804798i
$713$	−3.64035e9			−0.376123
$714$		0			0
$715$	7.67663e9			0.785415
$716$	3.87764e9	+	6.71627e9i	0.394795	+	0.683805i
$717$	−1.50685e9	+	2.60993e9i	−0.152669	+	0.264431i
$718$	−3.79734e9	+	6.57719e9i	−0.382863	+	0.663139i
$719$	4.09445e9	+	7.09180e9i	0.410814	+	0.711550i	0.994979	−	0.100085i	$-0.0319114\pi$
$719$	4.09445e9	+	7.09180e9i	0.410814	+	0.711550i	−0.584165	+	0.811635i	$0.698578\pi$
$720$	8.32543e9			0.831272
$721$		0			0
$722$	−3.49652e9			−0.345745
$723$	2.36330e9	+	4.09336e9i	0.232560	+	0.402806i
$724$	−7.37760e8	+	1.27784e9i	−0.0722488	+	0.125139i
$725$	5.39924e9	−	9.35175e9i	0.526198	−	0.911402i
$726$	4.48990e9	+	7.77673e9i	0.435470	+	0.754256i
$727$	−1.40657e10			−1.35766			−0.678832	−	0.734294i	$-0.737514\pi$
$727$	−1.40657e10			−1.35766			−0.678832	+	0.734294i	$0.737514\pi$
$728$		0			0
$729$	−7.88473e9			−0.753772
$730$	1.77216e9	+	3.06948e9i	0.168606	+	0.292035i
$731$	−4.53248e7	+	7.85048e7i	−0.00429165	+	0.00743336i
$732$	8.09336e9	−	1.40181e10i	0.762676	−	1.32099i
$733$	4.76816e9	+	8.25870e9i	0.447185	+	0.774547i	0.998202	−	0.0599473i	$-0.0190933\pi$
$733$	4.76816e9	+	8.25870e9i	0.447185	+	0.774547i	−0.551017	+	0.834494i	$0.685760\pi$
$734$	2.41417e9			0.225336
$735$		0			0
$736$	4.22052e8			0.0390206
$737$	3.65337e9	+	6.32783e9i	0.336169	+	0.582262i
$738$	−2.55658e9	+	4.42813e9i	−0.234133	+	0.405530i
$739$	−7.25665e9	+	1.25689e10i	−0.661425	+	1.14562i	0.318816	+	0.947817i	$0.396715\pi$
$739$	−7.25665e9	+	1.25689e10i	−0.661425	+	1.14562i	−0.980241	+	0.197805i	$0.936619\pi$
$740$	3.07556e9	+	5.32703e9i	0.279006	+	0.483252i
$741$	−2.12877e10			−1.92205
$742$		0			0
$743$	−1.88434e9			−0.168538			−0.0842692	−	0.996443i	$-0.526856\pi$
$743$	−1.88434e9			−0.168538			−0.0842692	+	0.996443i	$0.526856\pi$
$744$	−5.93309e9	−	1.02764e10i	−0.528173	−	0.914822i
$745$	−1.64865e10	+	2.85554e10i	−1.46077	+	2.53012i
$746$	−5.44728e9	+	9.43497e9i	−0.480390	+	0.832060i
$747$	3.43496e7	+	5.94953e7i	0.00301509	+	0.00522228i
$748$	3.83122e8			0.0334720
$749$		0			0
$750$	1.30645e10			1.13078
$751$	8.59707e9	+	1.48906e10i	0.740646	+	1.28284i	0.952202	+	0.305470i	$0.0988137\pi$
$751$	8.59707e9	+	1.48906e10i	0.740646	+	1.28284i	−0.211556	+	0.977366i	$0.567853\pi$
$752$	−1.46815e9	+	2.54290e9i	−0.125894	+	0.218056i
$753$	−1.07146e10	+	1.85583e10i	−0.914522	+	1.58400i
$754$	−2.50751e9	−	4.34313e9i	−0.213031	−	0.368980i
$755$	7.80814e9			0.660288
$756$		0			0
$757$	−1.02275e10			−0.856909			−0.428454	−	0.903563i	$-0.640942\pi$
$757$	−1.02275e10			−0.856909			−0.428454	+	0.903563i	$0.640942\pi$
$758$	−6.07355e9	−	1.05197e10i	−0.506524	−	0.877325i
$759$	−1.27162e9	+	2.20250e9i	−0.105563	+	0.182840i
$760$	4.18405e9	−	7.24698e9i	0.345740	−	0.598838i
$761$	−1.46903e9	−	2.54444e9i	−0.120833	−	0.209289i	0.799264	−	0.600981i	$-0.205223\pi$
$761$	−1.46903e9	−	2.54444e9i	−0.120833	−	0.209289i	−0.920096	+	0.391692i	$0.871890\pi$
$762$	1.39817e10			1.14477
$763$		0			0
$764$	−1.29873e9			−0.105364
$765$	−2.52649e9	−	4.37601e9i	−0.204034	−	0.353398i
$766$	1.81646e9	−	3.14619e9i	0.146024	−	0.252921i
$767$	7.64921e9	−	1.32488e10i	0.612115	−	1.06021i
$768$	6.87866e8	+	1.19142e9i	0.0547948	+	0.0949074i
$769$	−1.49710e10			−1.18716			−0.593579	−	0.804776i	$-0.702286\pi$
$769$	−1.49710e10			−1.18716			−0.593579	+	0.804776i	$0.702286\pi$
$770$		0			0
$771$	−2.85053e10			−2.23993
$772$	−7.23460e8	−	1.25307e9i	−0.0565918	−	0.0980199i
$773$	7.66354e9	−	1.32736e10i	0.596762	−	1.03362i	−0.396534	−	0.918020i	$-0.629787\pi$
$773$	7.66354e9	−	1.32736e10i	0.596762	−	1.03362i	0.993296	−	0.115602i	$-0.0368796\pi$
$774$	6.61749e8	−	1.14618e9i	0.0512979	−	0.0888506i
$775$	−1.73226e10	−	3.00037e10i	−1.33677	−	2.31536i
$776$	−6.91548e9			−0.531259
$777$		0			0
$778$	1.46960e10			1.11884
$779$	2.56968e9	+	4.45082e9i	0.194759	+	0.337333i
$780$	8.36523e9	−	1.44890e10i	0.631170	−	1.09322i
$781$	1.28375e8	−	2.22353e8i	0.00964279	−	0.0167018i
$782$	−1.28079e8	−	2.21839e8i	−0.00957753	−	0.0165888i
$783$	1.69757e10			1.26375
$784$		0			0
$785$	−9.95263e9			−0.734335
$786$	−3.43656e9	−	5.95230e9i	−0.252433	−	0.437226i
$787$	2.82231e8	−	4.88839e8i	0.0206392	−	0.0357482i	−0.855521	−	0.517768i	$-0.826763\pi$
$787$	2.82231e8	−	4.88839e8i	0.0206392	−	0.0357482i	0.876161	+	0.482019i	$0.160097\pi$
$788$	1.04697e9	−	1.81341e9i	0.0762245	−	0.132025i
$789$	−7.23656e9	−	1.25341e10i	−0.524521	−	0.908497i
$790$	−1.22426e10			−0.883442
$791$		0			0
$792$	−5.59365e9			−0.400089
$793$	−1.09742e10	−	1.90078e10i	−0.781475	−	1.35355i
$794$	4.94671e9	−	8.56795e9i	0.350707	−	0.607443i
$795$	−1.04598e9	+	1.81170e9i	−0.0738312	+	0.127879i
$796$	−2.31831e9	−	4.01543e9i	−0.162921	−	0.282187i
$797$	2.02786e10			1.41884			0.709421	−	0.704785i	$-0.248956\pi$
$797$	2.02786e10			1.41884			0.709421	+	0.704785i	$0.248956\pi$
$798$		0			0
$799$	1.78213e9			0.123602
$800$	2.00833e9	+	3.47854e9i	0.138682	+	0.240205i
$801$	−3.96556e8	+	6.86856e8i	−0.0272641	+	0.0472228i
$802$	6.31791e9	−	1.09429e10i	0.432477	−	0.749072i
$803$	−1.19067e9	−	2.06230e9i	−0.0811498	−	0.140556i
$804$	1.59243e10			1.08060
$805$		0			0
$806$	−1.60899e10			−1.08238
$807$	−1.67234e10	−	2.89659e10i	−1.12013	−	1.94012i
$808$	−4.80371e9	+	8.32026e9i	−0.320359	+	0.554878i
$809$	−1.60069e9	+	2.77249e9i	−0.106289	+	0.184098i	−0.914264	−	0.405119i	$-0.867230\pi$
$809$	−1.60069e9	+	2.77249e9i	−0.106289	+	0.184098i	0.807975	+	0.589217i	$0.200564\pi$
$810$	1.05351e10	+	1.82474e10i	0.696534	+	1.20643i
$811$	−2.22219e10			−1.46288			−0.731439	−	0.681907i	$-0.761151\pi$
$811$	−2.22219e10			−1.46288			−0.731439	+	0.681907i	$0.761151\pi$
$812$		0			0
$813$	−2.60447e10			−1.69982
$814$	−2.06639e9	−	3.57910e9i	−0.134285	−	0.232588i
$815$	−1.39730e10	+	2.42020e10i	−0.904146	+	1.56603i
$816$	4.17489e8	−	7.23112e8i	0.0268986	−	0.0465897i
$817$	−6.65140e8	−	1.15206e9i	−0.0426713	−	0.0739088i
$818$	1.54046e10			0.984043
$819$		0			0
$820$	−4.03914e9			−0.255823
$821$	−1.28655e9	−	2.22836e9i	−0.0811381	−	0.140535i	0.822601	−	0.568619i	$-0.192522\pi$
$821$	−1.28655e9	−	2.22836e9i	−0.0811381	−	0.140535i	−0.903739	+	0.428084i	$0.859189\pi$
$822$	−1.18730e10	+	2.05646e10i	−0.745604	+	1.29142i
$823$	2.57745e9	−	4.46427e9i	0.161172	−	0.279159i	−0.774117	−	0.633043i	$-0.781806\pi$
$823$	2.57745e9	−	4.46427e9i	0.161172	−	0.279159i	0.935289	+	0.353884i	$0.115139\pi$
$824$	−4.14925e9	−	7.18672e9i	−0.258360	−	0.447492i
$825$	−2.42040e10			−1.50071
$826$		0			0
$827$	2.02079e10			1.24237			0.621185	−	0.783664i	$-0.286651\pi$
$827$	2.02079e10			1.24237			0.621185	+	0.783664i	$0.286651\pi$
$828$	1.86997e9	+	3.23888e9i	0.114480	+	0.198285i
$829$	1.13460e10	−	1.96519e10i	0.691676	−	1.19802i	−0.279613	−	0.960113i	$-0.590206\pi$
$829$	1.13460e10	−	1.96519e10i	0.691676	−	1.19802i	0.971289	−	0.237904i	$-0.0764605\pi$
$830$	−2.71345e7	+	4.69983e7i	−0.00164721	+	0.00285304i
$831$	1.20428e10	+	2.08587e10i	0.727987	+	1.26091i
$832$	1.86542e9			0.112291
$833$		0			0
$834$	−3.46142e10			−2.06620
$835$	−7.41974e9	−	1.28514e10i	−0.441048	−	0.763918i
$836$	−2.81116e9	+	4.86907e9i	−0.166404	+	0.288220i
$837$	2.72320e10	−	4.71672e10i	1.60524	−	2.78036i
$838$	−9.59983e9	−	1.66274e10i	−0.563520	−	0.976045i
$839$	−1.18283e10			−0.691444			−0.345722	−	0.938337i	$-0.612366\pi$
$839$	−1.18283e10			−0.691444			−0.345722	+	0.938337i	$0.612366\pi$
$840$		0			0
$841$	−9.48932e9			−0.550110
$842$	4.83760e9	+	8.37897e9i	0.279279	+	0.483725i
$843$	−2.23461e9	+	3.87046e9i	−0.128471	+	0.222518i
$844$	−3.00162e9	+	5.19896e9i	−0.171853	+	0.297658i
$845$	2.71288e9	+	4.69884e9i	0.154679	+	0.267912i
$846$	−2.60194e10			−1.47741
$847$		0			0
$848$	−2.33251e8			−0.0131352
$849$	8.42177e9	+	1.45869e10i	0.472309	+	0.818064i
$850$	1.21893e9	−	2.11124e9i	0.0680787	−	0.117916i
$851$	−1.38160e9	+	2.39300e9i	−0.0768473	+	0.133103i
$852$	−2.79781e8	−	4.84596e8i	−0.0154982	−	0.0268436i
$853$	1.17141e10			0.646230			0.323115	−	0.946360i	$-0.395270\pi$
$853$	1.17141e10			0.646230			0.323115	+	0.946360i	$0.395270\pi$
$854$		0			0
$855$	7.41524e10			4.05736
$856$	1.78324e9	+	3.08867e9i	0.0971746	+	0.168311i
$857$	−8.39774e9	+	1.45453e10i	−0.455753	+	0.789387i	−0.998731	−	0.0503595i	$-0.983963\pi$
$857$	−8.39774e9	+	1.45453e10i	−0.455753	+	0.789387i	0.542978	+	0.839747i	$0.317297\pi$
$858$	−5.62039e9	+	9.73480e9i	−0.303781	+	0.526164i
$859$	9.31163e9	+	1.61282e10i	0.501244	+	0.868181i	0.999999	+	0.00143758i	$0.000457596\pi$
$859$	9.31163e9	+	1.61282e10i	0.501244	+	0.868181i	−0.498755	+	0.866743i	$0.666209\pi$
$860$	1.04550e9			0.0560503
$861$		0			0
$862$	1.73028e10			0.920113
$863$	9.78413e9	+	1.69466e10i	0.518184	+	0.897522i	0.999777	+	0.0211264i	$0.00672523\pi$
$863$	9.78413e9	+	1.69466e10i	0.518184	+	0.897522i	−0.481592	+	0.876395i	$0.659941\pi$
$864$	−3.15720e9	+	5.46843e9i	−0.166534	+	0.288446i
$865$	1.58099e10	−	2.73835e10i	0.830563	−	1.43858i
$866$	9.02999e9	+	1.56404e10i	0.472470	+	0.818343i
$867$	3.31410e10			1.72703
$868$		0			0
$869$	8.22548e9			0.425199
$870$	1.29449e10	+	2.24212e10i	0.666470	+	1.15436i
$871$	1.07963e10	−	1.86997e10i	0.553618	−	0.958894i
$872$	−3.81540e9	+	6.60846e9i	−0.194864	+	0.337515i
$873$	−3.06402e10	−	5.30703e10i	−1.55862	−	2.69961i
$874$	3.75911e9			0.190456
$875$		0			0
$876$	−5.18990e9			−0.260853
$877$	4.38040e9	+	7.58707e9i	0.219288	+	0.379818i	0.954591	−	0.297921i	$-0.0962932\pi$
$877$	4.38040e9	+	7.58707e9i	0.219288	+	0.379818i	−0.735302	+	0.677739i	$0.762960\pi$
$878$	−2.98290e9	+	5.16653e9i	−0.148733	+	0.257613i
$879$	−4.87435e9	+	8.44262e9i	−0.242078	+	0.419292i
$880$	−2.20935e9	−	3.82671e9i	−0.109289	−	0.189294i
$881$	3.59103e10			1.76931			0.884653	−	0.466250i	$-0.154395\pi$
$881$	3.59103e10			1.76931			0.884653	+	0.466250i	$0.154395\pi$
$882$		0			0
$883$	−3.42420e10			−1.67377			−0.836887	−	0.547375i	$-0.815627\pi$
$883$	−3.42420e10			−1.67377			−0.836887	+	0.547375i	$0.815627\pi$
$884$	−5.66092e8	−	9.80500e8i	−0.0275616	−	0.0477381i
$885$	−3.94887e10	+	6.83964e10i	−1.91501	+	3.31689i
$886$	−4.40861e9	+	7.63594e9i	−0.212953	+	0.368845i
$887$	−6.66497e9	−	1.15441e10i	−0.320675	−	0.555426i	0.659952	−	0.751307i	$-0.270576\pi$
$887$	−6.66497e9	−	1.15441e10i	−0.320675	−	0.555426i	−0.980628	+	0.195882i	$0.937243\pi$
$888$	−9.00700e9			−0.431653
$889$		0			0
$890$	−6.26519e8			−0.0297899
$891$	−7.07829e9	−	1.22600e10i	−0.335241	−	0.580654i
$892$	−5.20215e7	+	9.01039e7i	−0.00245418	+	0.00425076i
$893$	−1.30764e10	+	2.26490e10i	−0.614480	+	1.06431i
$894$	−2.41409e10	−	4.18133e10i	−1.12998	−	1.95719i
$895$	−5.42870e10			−2.53113
$896$		0			0
$897$	7.51563e9			0.347690
$898$	1.36640e10	+	2.36667e10i	0.629667	+	1.09061i
$899$	1.24493e10	−	2.15628e10i	0.571459	−	0.989796i
$900$	−1.77965e10	+	3.08245e10i	−0.813741	+	1.40944i
$901$	7.07839e7	+	1.22601e8i	0.00322402	+	0.00558416i
$902$	2.71380e9			0.123127
$903$		0			0
$904$	1.33470e10			0.600891
$905$	−5.16432e9	−	8.94487e9i	−0.231603	−	0.401147i
$906$	−5.71668e9	+	9.90157e9i	−0.255385	+	0.442339i
$907$	1.97816e9	−	3.42627e9i	0.0880310	−	0.152474i	−0.818648	−	0.574296i	$-0.805276\pi$
$907$	1.97816e9	−	3.42627e9i	0.0880310	−	0.152474i	0.906679	+	0.421822i	$0.138609\pi$
$908$	7.87688e9	+	1.36432e10i	0.349184	+	0.604804i
$909$	−8.51344e10			−3.75951
$910$		0			0
$911$	1.77864e10			0.779426			0.389713	−	0.920936i	$-0.372574\pi$
$911$	1.77864e10			0.779426			0.389713	+	0.920936i	$0.372574\pi$
$912$	6.12664e9	+	1.06117e10i	0.267449	+	0.463235i
$913$	1.82310e7	−	3.15770e7i	0.000792797	−	0.00137316i
$914$	1.70924e9	−	2.96049e9i	0.0740442	−	0.128248i
$915$	5.66535e10	+	9.81268e10i	2.44485	+	4.23461i
$916$	−6.78661e9			−0.291755
$917$		0			0
$918$	3.83242e9			0.163502
$919$	−1.89653e10	−	3.28489e10i	−0.806040	−	1.39610i	−0.915587	−	0.402120i	$-0.868274\pi$
$919$	−1.89653e10	−	3.28489e10i	−0.806040	−	1.39610i	0.109548	−	0.993982i	$-0.465060\pi$
$920$	−1.47718e9	+	2.55855e9i	−0.0625427	+	0.108327i
$921$	6.70684e9	−	1.16166e10i	0.282884	−	0.489970i
$922$	8.72465e9	+	1.51115e10i	0.366598	+	0.634966i
$923$	−7.58736e8			−0.0317603
$924$		0			0
$925$	−2.62974e10			−1.09249
$926$	7.52538e8	+	1.30343e9i	0.0311451	+	0.0539449i
$927$	3.67679e10	−	6.36839e10i	1.51597	−	2.62573i
$928$	−1.44333e9	+	2.49992e9i	−0.0592855	+	0.102685i
$929$	−2.11707e10	−	3.66687e10i	−0.866323	−	1.50052i	−0.865728	−	0.500515i	$-0.833144\pi$
$929$	−2.11707e10	−	3.66687e10i	−0.866323	−	1.50052i	−0.000595086	−	1.00000i	$-0.500189\pi$
$930$	8.30633e10			3.38625
$931$		0			0
$932$	−1.29412e10			−0.523623
$933$	−1.77317e10	−	3.07122e10i	−0.714767	−	1.23801i
$934$	3.41814e9	−	5.92038e9i	0.137270	−	0.237758i
$935$	−1.34093e9	+	2.32256e9i	−0.0536494	+	0.0929235i
$936$	8.26503e9	+	1.43155e10i	0.329442	+	0.570611i
$937$	1.65147e10			0.655817			0.327909	−	0.944709i	$-0.393656\pi$
$937$	1.65147e10			0.655817			0.327909	+	0.944709i	$0.393656\pi$
$938$		0			0
$939$	3.50167e10			1.38021
$940$	−1.02770e10	−	1.78003e10i	−0.403571	−	0.699005i
$941$	1.57165e10	−	2.72217e10i	0.614881	−	1.06501i	−0.375524	−	0.926813i	$-0.622537\pi$
$941$	1.57165e10	−	2.72217e10i	0.614881	−	1.06501i	0.990405	−	0.138193i	$-0.0441295\pi$
$942$	7.28675e9	−	1.26210e10i	0.284024	−	0.491945i
$943$	−9.07229e8	−	1.57137e9i	−0.0352311	−	0.0610220i
$944$	−8.80583e9			−0.340697
$945$		0			0
$946$	−7.02442e8			−0.0269769
$947$	1.63557e10	+	2.83289e10i	0.625813	+	1.08394i	0.988383	+	0.151983i	$0.0485659\pi$
$947$	1.63557e10	+	2.83289e10i	0.625813	+	1.08394i	−0.362571	+	0.931956i	$0.618101\pi$
$948$	8.96331e9	−	1.55249e10i	0.341696	−	0.591834i
$949$	−3.51861e9	+	6.09442e9i	−0.133641	+	0.231473i
$950$	1.78877e10	+	3.09824e10i	0.676896	+	1.17242i
$951$	2.84952e10			1.07433
$952$		0			0
$953$	−2.62655e10			−0.983017			−0.491509	−	0.870873i	$-0.663554\pi$
$953$	−2.62655e10			−0.983017			−0.491509	+	0.870873i	$0.663554\pi$
$954$	−1.03346e9	−	1.79000e9i	−0.0385365	−	0.0667472i
$955$	4.54556e9	−	7.87315e9i	0.168879	−	0.292507i
$956$	1.17607e9	−	2.03702e9i	0.0435344	−	0.0754037i
$957$	−8.69734e9	−	1.50642e10i	−0.320771	−	0.555591i
$958$	5.46251e9			0.200730
$959$		0			0
$960$	−9.63012e9			−0.351303
$961$	−2.61852e10	−	4.53542e10i	−0.951754	−	1.64849i
$962$	−6.10650e9	+	1.05768e10i	−0.221146	+	0.383036i
$963$	−1.58019e10	+	2.73697e10i	−0.570187	+	0.987593i
$964$	−1.84453e9	−	3.19482e9i	−0.0663156	−	0.114862i
$965$	1.01284e10			0.362825
$966$		0			0
$967$	2.58253e10			0.918443			0.459222	−	0.888322i	$-0.348128\pi$
$967$	2.58253e10			0.918443			0.459222	+	0.888322i	$0.348128\pi$
$968$	−3.50431e9	−	6.06964e9i	−0.124176	−	0.215080i
$969$	3.71846e9	−	6.44057e9i	0.131290	−	0.227400i
$970$	2.42042e10	−	4.19228e10i	0.851509	−	1.47486i
$971$	−1.12051e10	−	1.94078e10i	−0.392780	−	0.680315i	0.600035	−	0.799974i	$-0.295153\pi$
$971$	−1.12051e10	−	1.94078e10i	−0.392780	−	0.680315i	−0.992815	+	0.119659i	$0.961820\pi$
$972$	−3.88106e9			−0.135556
$973$		0			0
$974$	−3.32095e10			−1.15161
$975$	3.57632e10	+	6.19436e10i	1.23572	+	2.14033i
$976$	−6.31677e9	+	1.09410e10i	−0.217481	+	0.376688i
$977$	1.77291e10	−	3.07077e10i	0.608214	−	1.05346i	−0.383321	−	0.923615i	$-0.625220\pi$
$977$	1.77291e10	−	3.07077e10i	0.608214	−	1.05346i	0.991535	−	0.129842i	$-0.0414470\pi$
$978$	−2.04605e10	−	3.54386e10i	−0.699407	−	1.21141i
$979$	4.20942e8			0.0143378
$980$		0			0
$981$	−6.76190e10			−2.28679
$982$	3.59815e9	+	6.23218e9i	0.121252	+	0.210015i
$983$	7.28837e9	−	1.26238e10i	0.244733	−	0.423890i	−0.717323	−	0.696740i	$-0.754633\pi$
$983$	7.28837e9	−	1.26238e10i	0.244733	−	0.423890i	0.962057	+	0.272850i	$0.0879663\pi$
$984$	2.95723e9	−	5.12207e9i	0.0989468	−	0.171381i
$985$	7.32882e9	+	1.26939e10i	0.244347	+	0.423222i
$986$	1.75201e9			0.0582061
$987$		0			0
$988$	1.66148e10			0.548082
$989$	2.34828e8	+	4.06734e8i	0.00771904	+	0.0133698i
$990$	1.95778e10	−	3.39097e10i	0.641269	−	1.11071i
$991$	−6.28564e9	+	1.08871e10i	−0.205160	+	0.355347i	−0.950184	−	0.311691i	$-0.899105\pi$
$991$	−6.28564e9	+	1.08871e10i	−0.205160	+	0.355347i	0.745024	+	0.667038i	$0.232438\pi$
$992$	4.63071e9	+	8.02062e9i	0.150611	+	0.260866i
$993$	6.68639e10			2.16705
$994$		0			0
$995$	3.24564e10			1.04453
$996$	−3.97326e7	−	6.88189e7i	−0.00127421	−	0.00220699i
$997$	5.20184e9	−	9.00986e9i	0.166236	−	0.287929i	−0.770858	−	0.637007i	$-0.780172\pi$
$997$	5.20184e9	−	9.00986e9i	0.166236	−	0.287929i	0.937093	+	0.349079i	$0.113505\pi$
$998$	−2.44444e9	+	4.23389e9i	−0.0778435	+	0.134829i
$999$	−2.06704e10	−	3.58021e10i	−0.655947	−	1.13613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.c.f.67.1		2
7.2	even	3	inner	98.8.c.f.79.1		2
7.3	odd	6		98.8.a.b.1.1		1
7.4	even	3		14.8.a.a.1.1	✓	1
7.5	odd	6		98.8.c.c.79.1		2
7.6	odd	2		98.8.c.c.67.1		2
21.11	odd	6		126.8.a.d.1.1		1
28.11	odd	6		112.8.a.e.1.1		1
35.4	even	6		350.8.a.h.1.1		1
35.18	odd	12		350.8.c.d.99.2		2
35.32	odd	12		350.8.c.d.99.1		2
56.11	odd	6		448.8.a.a.1.1		1
56.53	even	6		448.8.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.a.a.1.1	✓	1	7.4	even	3
98.8.a.b.1.1		1	7.3	odd	6
98.8.c.c.67.1		2	7.6	odd	2
98.8.c.c.79.1		2	7.5	odd	6
98.8.c.f.67.1		2	1.1	even	1	trivial
98.8.c.f.79.1		2	7.2	even	3	inner
112.8.a.e.1.1		1	28.11	odd	6
126.8.a.d.1.1		1	21.11	odd	6
350.8.a.h.1.1		1	35.4	even	6
350.8.c.d.99.1		2	35.32	odd	12
350.8.c.d.99.2		2	35.18	odd	12
448.8.a.a.1.1		1	56.11	odd	6
448.8.a.j.1.1		1	56.53	even	6

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(41.0000 - 71.0141i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-224.000 - 387.979i) q^{5} +656.000 q^{6} -512.000 q^{8} +(-2268.50 - 3929.16i) q^{9} +(1792.00 - 3103.84i) q^{10} +(-1204.00 + 2085.39i) q^{11} +(2624.00 + 4544.90i) q^{12} +7116.00 q^{13} -36736.0 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-1243.00 + 2152.94i) q^{17} +(18148.0 - 31433.3i) q^{18} +(-18241.0 - 31594.3i) q^{19} +28672.0 q^{20} -19264.0 q^{22} +(6440.00 + 11154.4i) q^{23} +(-20992.0 + 36359.2i) q^{24} +(-61289.5 + 106157. i) q^{25} +(28464.0 + 49301.1i) q^{26} -192700. q^{27} -88094.0 q^{29} +(-146944. - 254514. i) q^{30} +(-141318. + 244770. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(98728.0 + 171002. i) q^{33} -19888.0 q^{34} +290368. q^{36} +(107267. + 185792. i) q^{37} +(145928. - 252755. i) q^{38} +(291756. - 505336. i) q^{39} +(114688. + 198645. i) q^{40} -140874. q^{41} +36464.0 q^{43} +(-77056.0 - 133465. i) q^{44} +(-1.01629e6 + 1.76026e6i) q^{45} +(-51520.0 + 89235.3i) q^{46} +(-358434. - 620826. i) q^{47} -335872. q^{48} -980632. q^{50} +(101926. + 176541. i) q^{51} +(-227712. + 394409. i) q^{52} +(28473.0 - 49316.7i) q^{53} +(-770800. - 1.33506e6i) q^{54} +1.07878e6 q^{55} -2.99152e6 q^{57} +(-352376. - 610333. i) q^{58} +(1.07493e6 - 1.86184e6i) q^{59} +(1.17555e6 - 2.03612e6i) q^{60} +(-1.54218e6 - 2.67113e6i) q^{61} -2.26109e6 q^{62} +262144. q^{64} +(-1.59398e6 - 2.76086e6i) q^{65} +(-789824. + 1.36802e6i) q^{66} +(1.51718e6 - 2.62784e6i) q^{67} +(-79552.0 - 137788. i) q^{68} +1.05616e6 q^{69} -106624. q^{71} +(1.16147e6 + 2.01173e6i) q^{72} +(-494465. + 856439. i) q^{73} +(-858136. + 1.48634e6i) q^{74} +(5.02574e6 + 8.70484e6i) q^{75} +2.33485e6 q^{76} +4.66810e6 q^{78} +(-1.70795e6 - 2.95825e6i) q^{79} +(-917504. + 1.58916e6i) q^{80} +(-2.93949e6 + 5.09135e6i) q^{81} +(-563496. - 976004. i) q^{82} -15142.0 q^{83} +1.11373e6 q^{85} +(145856. + 252630. i) q^{86} +(-3.61185e6 + 6.25591e6i) q^{87} +(616448. - 1.06772e6i) q^{88} +(-87405.0 - 151390. i) q^{89} -1.62606e7 q^{90} -824320. q^{92} +(1.15881e7 + 2.00711e7i) q^{93} +(2.86747e6 - 4.96661e6i) q^{94} +(-8.17197e6 + 1.41543e7i) q^{95} +(-1.34349e6 - 2.32699e6i) q^{96} +1.35068e7 q^{97} +1.09251e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 82 q^{3} - 64 q^{4} - 448 q^{5} + 1312 q^{6} - 1024 q^{8} - 4537 q^{9} + 3584 q^{10} - 2408 q^{11} + 5248 q^{12} + 14232 q^{13} - 73472 q^{15} - 4096 q^{16} - 2486 q^{17} + 36296 q^{18}+ \cdots + 21850192 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 82 * q^3 - 64 * q^4 - 448 * q^5 + 1312 * q^6 - 1024 * q^8 - 4537 * q^9 + 3584 * q^10 - 2408 * q^11 + 5248 * q^12 + 14232 * q^13 - 73472 * q^15 - 4096 * q^16 - 2486 * q^17 + 36296 * q^18 - 36482 * q^19 + 57344 * q^20 - 38528 * q^22 + 12880 * q^23 - 41984 * q^24 - 122579 * q^25 + 56928 * q^26 - 385400 * q^27 - 176188 * q^29 - 293888 * q^30 - 282636 * q^31 + 32768 * q^32 + 197456 * q^33 - 39776 * q^34 + 580736 * q^36 + 214534 * q^37 + 291856 * q^38 + 583512 * q^39 + 229376 * q^40 - 281748 * q^41 + 72928 * q^43 - 154112 * q^44 - 2032576 * q^45 - 103040 * q^46 - 716868 * q^47 - 671744 * q^48 - 1961264 * q^50 + 203852 * q^51 - 455424 * q^52 + 56946 * q^53 - 1541600 * q^54 + 2157568 * q^55 - 5983048 * q^57 - 704752 * q^58 + 2149862 * q^59 + 2351104 * q^60 - 3084360 * q^61 - 4522176 * q^62 + 524288 * q^64 - 3187968 * q^65 - 1579648 * q^66 + 3034364 * q^67 - 159104 * q^68 + 2112320 * q^69 - 213248 * q^71 + 2322944 * q^72 - 988930 * q^73 - 1716272 * q^74 + 10051478 * q^75 + 4669696 * q^76 + 9336192 * q^78 - 3415896 * q^79 - 1835008 * q^80 - 5878981 * q^81 - 1126992 * q^82 - 30284 * q^83 + 2227456 * q^85 + 291712 * q^86 - 7223708 * q^87 + 1232896 * q^88 - 174810 * q^89 - 32521216 * q^90 - 1648640 * q^92 + 23176152 * q^93 + 5734944 * q^94 - 16343936 * q^95 - 2686976 * q^96 + 27013580 * q^97 + 21850192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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