LMFDB - Embedded newform 100.9.j.b.11.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.18
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.2154 - 7.34320i) q^{2} +(23.9209 + 7.77239i) q^{3} +(148.155 + 208.773i) q^{4} +(443.111 - 440.770i) q^{5} +(-282.972 - 286.144i) q^{6} -2979.31i q^{7} +(-573.020 - 4055.72i) q^{8} +(-4796.16 - 3484.61i) q^{9} +(-9535.65 + 3011.87i) q^{10} +(-1572.76 - 2164.72i) q^{11} +(1921.34 + 6145.56i) q^{12} +(-7228.32 - 5251.68i) q^{13} +(-21877.7 + 42352.1i) q^{14} +(14025.5 - 7099.60i) q^{15} +(-21636.2 + 61861.5i) q^{16} +(-5405.02 - 16634.9i) q^{17} +(42591.1 + 84754.3i) q^{18} +(-72375.6 + 23516.2i) q^{19} +(157670. + 27207.3i) q^{20} +(23156.4 - 71267.9i) q^{21} +(6461.44 + 42321.4i) q^{22} +(55583.6 + 76504.3i) q^{23} +(17815.4 - 101470. i) q^{24} +(2069.22 - 390620. i) q^{25} +(64189.3 + 127734. i) q^{26} +(-184642. - 254139. i) q^{27} +(621999. - 441400. i) q^{28} +(105628. - 325091. i) q^{29} +(-251511. - 2068.11i) q^{30} +(-1.08360e6 + 352082. i) q^{31} +(761829. - 720506. i) q^{32} +(-20796.9 - 64006.1i) q^{33} +(-45319.1 + 276162. i) q^{34} +(-1.31319e6 - 1.32016e6i) q^{35} +(16918.4 - 1.51757e6i) q^{36} +(1.80740e6 + 1.31315e6i) q^{37} +(1.20153e6 + 197175. i) q^{38} +(-132090. - 181807. i) q^{39} +(-2.04155e6 - 1.54456e6i) q^{40} +(2.33729e6 + 1.69814e6i) q^{41} +(-852511. + 843060. i) q^{42} +210225. i q^{43} +(218922. - 649063. i) q^{44} +(-3.66114e6 + 569932. i) q^{45} +(-228357. - 1.49570e6i) q^{46} +(-534618. - 173708. i) q^{47} +(-998371. + 1.31162e6i) q^{48} -3.11150e6 q^{49} +(-2.89781e6 + 5.53762e6i) q^{50} -439933. i q^{51} +(25497.8 - 2.28714e6i) q^{52} +(-2.11588e6 + 6.51200e6i) q^{53} +(758576. + 4.96855e6i) q^{54} +(-1.65105e6 - 265985. i) q^{55} +(-1.20833e7 + 1.70721e6i) q^{56} -1.91407e6 q^{57} +(-3.88876e6 + 3.84565e6i) q^{58} +(-5.55230e6 + 7.64209e6i) q^{59} +(3.56014e6 + 1.87630e6i) q^{60} +(-1.62764e6 + 1.18255e6i) q^{61} +(1.79892e7 + 2.95208e6i) q^{62} +(-1.03817e7 + 1.42893e7i) q^{63} +(-1.61205e7 + 4.64802e6i) q^{64} +(-5.51773e6 + 858948. i) q^{65} +(-174374. + 1.06259e6i) q^{66} +(1.60727e7 - 5.22233e6i) q^{67} +(2.67214e6 - 3.59297e6i) q^{68} +(734992. + 2.26207e6i) q^{69} +(8.97329e6 + 2.84097e7i) q^{70} +(-3.07619e7 - 9.99514e6i) q^{71} +(-1.13843e7 + 2.14486e7i) q^{72} +(-2.43171e7 + 1.76674e7i) q^{73} +(-1.60502e7 - 3.19391e7i) q^{74} +(3.08554e6 - 9.32791e6i) q^{75} +(-1.56324e7 - 1.16260e7i) q^{76} +(-6.44936e6 + 4.68574e6i) q^{77} +(542673. + 3.55442e6i) q^{78} +(-5.19131e7 - 1.68676e7i) q^{79} +(1.76794e7 + 3.69481e7i) q^{80} +(9.57799e6 + 2.94780e7i) q^{81} +(-2.07558e7 - 4.13030e7i) q^{82} +(-8.13518e7 + 2.64328e7i) q^{83} +(1.83095e7 - 5.72428e6i) q^{84} +(-9.72719e6 - 4.98875e6i) q^{85} +(1.54372e6 - 2.98842e6i) q^{86} +(5.05347e6 - 6.95550e6i) q^{87} +(-7.87826e6 + 7.61909e6i) q^{88} +(8.23488e7 - 5.98299e7i) q^{89} +(5.62297e7 + 1.87827e7i) q^{90} +(-1.56464e7 + 2.15354e7i) q^{91} +(-7.73704e6 + 2.29388e7i) q^{92} -2.86572e7 q^{93} +(6.32424e6 + 6.39513e6i) q^{94} +(-2.17051e7 + 4.23213e7i) q^{95} +(2.38237e7 - 1.13140e7i) q^{96} +(2.82622e7 - 8.69821e7i) q^{97} +(4.42311e7 + 2.28483e7i) q^{98} +1.58628e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−14.2154	−	7.34320i	−0.888462	−	0.458950i
$2$	−14.2154	−	7.34320i	−0.888462	−	0.458950i
$3$	23.9209	+	7.77239i	0.295320	+	0.0959554i	0.452930	−	0.891546i	$-0.350379\pi$
$3$	23.9209	+	7.77239i	0.295320	+	0.0959554i	−0.157610	+	0.987501i	$0.550379\pi$
$4$	148.155	+	208.773i	0.578730	+	0.815519i
$5$	443.111	−	440.770i	0.708977	−	0.705231i
$5$	443.111	−	440.770i	0.708977	−	0.705231i
$6$	−282.972	−	286.144i	−0.218342	−	0.220790i
$7$		−	2979.31i		−	1.24086i	−0.784261	−	0.620431i	$-0.786958\pi$
$7$		−	2979.31i		−	1.24086i	0.784261	−	0.620431i	$-0.213042\pi$
$8$	−573.020	−	4055.72i	−0.139897	−	0.990166i
$9$	−4796.16	−	3484.61i	−0.731010	−	0.531110i
$10$	−9535.65	+	3011.87i	−0.953565	+	0.301187i
$11$	−1572.76	−	2164.72i	−0.107422	−	0.147853i	0.751922	−	0.659253i	$-0.229127\pi$
$11$	−1572.76	−	2164.72i	−0.107422	−	0.147853i	−0.859343	+	0.511400i	$0.829127\pi$
$12$	1921.34	+	6145.56i	0.0926573	+	0.296372i
$13$	−7228.32	−	5251.68i	−0.253084	−	0.183876i	0.454009	−	0.890997i	$-0.349993\pi$
$13$	−7228.32	−	5251.68i	−0.253084	−	0.183876i	−0.707092	+	0.707121i	$0.749993\pi$
$14$	−21877.7	+	42352.1i	−0.569494	+	1.10246i
$15$	14025.5	−	7099.60i	0.277046	−	0.140239i
$16$	−21636.2	+	61861.5i	−0.330143	+	0.943931i
$17$	−5405.02	−	16634.9i	−0.0647144	−	0.199171i	0.913471	−	0.406904i	$-0.133391\pi$
$17$	−5405.02	−	16634.9i	−0.0647144	−	0.199171i	−0.978186	+	0.207733i	$0.933391\pi$
$18$	42591.1	+	84754.3i	0.405722	+	0.807368i
$19$	−72375.6	+	23516.2i	−0.555364	+	0.180449i	−0.573234	−	0.819392i	$-0.694311\pi$
$19$	−72375.6	+	23516.2i	−0.555364	+	0.180449i	0.0178702	+	0.999840i	$0.494311\pi$
$20$	157670.	+	27207.3i	0.985436	+	0.170046i
$21$	23156.4	−	71267.9i	0.119067	−	0.366452i
$22$	6461.44	+	42321.4i	0.0275828	+	0.180663i
$23$	55583.6	+	76504.3i	0.198626	+	0.273385i	0.896698	−	0.442642i	$-0.145959\pi$
$23$	55583.6	+	76504.3i	0.198626	+	0.273385i	−0.698073	+	0.716027i	$0.745959\pi$
$24$	17815.4	−	101470.i	0.0536972	−	0.305840i
$25$	2069.22	−	390620.i	0.00529719	−	0.999986i
$26$	64189.3	+	127734.i	0.140465	+	0.279520i
$27$	−184642.	−	254139.i	−0.347437	−	0.478206i
$28$	621999.	−	441400.i	1.01195	−	0.718125i
$29$	105628.	−	325091.i	0.149344	−	0.459635i	−0.848200	−	0.529677i	$-0.822313\pi$
$29$	105628.	−	325091.i	0.149344	−	0.459635i	0.997544	+	0.0700418i	$0.0223133\pi$
$30$	−251511.	−	2068.11i	−0.310508	−	0.00255322i
$31$	−1.08360e6	+	352082.i	−1.17333	+	0.381238i	−0.829885	−	0.557934i	$-0.811594\pi$
$31$	−1.08360e6	+	352082.i	−1.17333	+	0.381238i	−0.343446	+	0.939172i	$0.611594\pi$
$32$	761829.	−	720506.i	0.726536	−	0.687128i
$33$	−20796.9	−	64006.1i	−0.0175365	−	0.0539717i
$34$	−45319.1	+	276162.i	−0.0339130	+	0.206656i
$35$	−1.31319e6	−	1.32016e6i	−0.875095	−	0.879743i
$36$	16918.4	−	1.51757e6i	0.0100728	−	0.903522i
$37$	1.80740e6	+	1.31315e6i	0.964379	+	0.700663i	0.954164	−	0.299285i	$-0.0967482\pi$
$37$	1.80740e6	+	1.31315e6i	0.964379	+	0.700663i	0.0102157	+	0.999948i	$0.496748\pi$
$38$	1.20153e6	+	197175.i	0.576237	+	0.0945623i
$39$	−132090.	−	181807.i	−0.0570968	−	0.0785871i
$40$	−2.04155e6	−	1.54456e6i	−0.797480	−	0.603345i
$41$	2.33729e6	+	1.69814e6i	0.827138	+	0.600951i	0.918748	−	0.394844i	$-0.129201\pi$
$41$	2.33729e6	+	1.69814e6i	0.827138	+	0.600951i	−0.0916101	+	0.995795i	$0.529201\pi$
$42$	−852511.	+	843060.i	−0.273970	+	0.270933i
$43$			210225.i			0.0614907i	0.999527	+	0.0307454i	$0.00978809\pi$
$43$			210225.i			0.0614907i	−0.999527	+	0.0307454i	$0.990212\pi$
$44$	218922.	−	649063.i	0.0584089	−	0.173171i
$45$	−3.66114e6	+	569932.i	−0.892825	+	0.138987i
$46$	−228357.	−	1.49570e6i	−0.0510015	−	0.334051i
$47$	−534618.	−	173708.i	−0.109560	−	0.0355982i	0.253724	−	0.967277i	$-0.418345\pi$
$47$	−534618.	−	173708.i	−0.109560	−	0.0355982i	−0.363284	+	0.931678i	$0.618345\pi$
$48$	−998371.	+	1.31162e6i	−0.188073	+	0.247083i
$49$	−3.11150e6			−0.539740
$50$	−2.89781e6	+	5.53762e6i	−0.463650	+	0.886019i
$51$		−	439933.i		−	0.0650288i
$52$	25497.8	−	2.28714e6i	0.00348729	−	0.312809i
$53$	−2.11588e6	+	6.51200e6i	−0.268156	+	0.825299i	0.722794	+	0.691064i	$0.242858\pi$
$53$	−2.11588e6	+	6.51200e6i	−0.268156	+	0.825299i	−0.990950	+	0.134235i	$0.957142\pi$
$54$	758576.	+	4.96855e6i	0.0892122	+	0.584325i
$55$	−1.65105e6	−	265985.i	−0.180430	−	0.0290674i
$56$	−1.20833e7	+	1.70721e6i	−1.22866	+	0.173594i
$57$	−1.91407e6			−0.181325
$58$	−3.88876e6	+	3.84565e6i	−0.343636	+	0.339827i
$59$	−5.55230e6	+	7.64209e6i	−0.458211	+	0.630673i	−0.974136	−	0.225960i	$-0.927448\pi$
$59$	−5.55230e6	+	7.64209e6i	−0.458211	+	0.630673i	0.515926	+	0.856633i	$0.327448\pi$
$60$	3.56014e6	+	1.87630e6i	0.274703	+	0.144776i
$61$	−1.62764e6	+	1.18255e6i	−0.117554	+	0.0854082i	−0.645009	−	0.764175i	$-0.723146\pi$
$61$	−1.62764e6	+	1.18255e6i	−0.117554	+	0.0854082i	0.527455	+	0.849583i	$0.323146\pi$
$62$	1.79892e7	+	2.95208e6i	1.21743	+	0.199784i
$63$	−1.03817e7	+	1.42893e7i	−0.659035	+	0.907084i
$64$	−1.61205e7	+	4.64802e6i	−0.960857	+	0.277043i
$65$	−5.51773e6	+	858948.i	−0.309106	+	0.0481186i
$66$	−174374.	+	1.06259e6i	−0.00918981	+	0.0560001i
$67$	1.60727e7	−	5.22233e6i	0.797607	−	0.259158i	0.118267	−	0.992982i	$-0.462266\pi$
$67$	1.60727e7	−	5.22233e6i	0.797607	−	0.259158i	0.679340	+	0.733824i	$0.262266\pi$
$68$	2.67214e6	−	3.59297e6i	0.124975	−	0.168042i
$69$	734992.	+	2.26207e6i	0.0324255	+	0.0997953i
$70$	8.97329e6	+	2.84097e7i	0.373731	+	1.18324i
$71$	−3.07619e7	−	9.99514e6i	−1.21054	−	0.393329i	−0.366912	−	0.930256i	$-0.619585\pi$
$71$	−3.07619e7	−	9.99514e6i	−1.21054	−	0.393329i	−0.843629	+	0.536927i	$0.819585\pi$
$72$	−1.13843e7	+	2.14486e7i	−0.423621	+	0.798123i
$73$	−2.43171e7	+	1.76674e7i	−0.856288	+	0.622130i	−0.926873	−	0.375376i	$-0.877514\pi$
$73$	−2.43171e7	+	1.76674e7i	−0.856288	+	0.622130i	0.0705845	+	0.997506i	$0.477514\pi$
$74$	−1.60502e7	−	3.19391e7i	−0.535246	−	1.06511i
$75$	3.08554e6	−	9.32791e6i	0.0975184	−	0.294808i
$76$	−1.56324e7	−	1.16260e7i	−0.468565	−	0.348479i
$77$	−6.44936e6	+	4.68574e6i	−0.183465	+	0.133295i
$78$	542673.	+	3.55442e6i	0.0146609	+	0.0960262i
$79$	−5.19131e7	−	1.68676e7i	−1.33281	−	0.433057i	−0.445936	−	0.895065i	$-0.647129\pi$
$79$	−5.19131e7	−	1.68676e7i	−1.33281	−	0.433057i	−0.886876	+	0.462008i	$0.847129\pi$
$80$	1.76794e7	+	3.69481e7i	0.431626	+	0.902053i
$81$	9.57799e6	+	2.94780e7i	0.222502	+	0.684792i
$82$	−2.07558e7	−	4.13030e7i	−0.459075	−	0.913537i
$83$	−8.13518e7	+	2.64328e7i	−1.71417	+	0.556969i	−0.991020	−	0.133717i	$-0.957309\pi$
$83$	−8.13518e7	+	2.64328e7i	−1.71417	+	0.556969i	−0.723155	+	0.690686i	$0.757309\pi$
$84$	1.83095e7	−	5.72428e6i	0.367757	−	0.114975i
$85$	−9.72719e6	−	4.98875e6i	−0.186342	−	0.0955687i
$86$	1.54372e6	−	2.98842e6i	0.0282212	−	0.0546322i
$87$	5.05347e6	−	6.95550e6i	0.0882089	−	0.121409i
$88$	−7.87826e6	+	7.61909e6i	−0.131371	+	0.127049i
$89$	8.23488e7	−	5.98299e7i	1.31249	−	0.953583i	0.312501	−	0.949918i	$-0.398833\pi$
$89$	8.23488e7	−	5.98299e7i	1.31249	−	0.953583i	0.999993	−	0.00366510i	$-0.00116664\pi$
$90$	5.62297e7	+	1.87827e7i	0.857029	+	0.286278i
$91$	−1.56464e7	+	2.15354e7i	−0.228165	+	0.314042i
$92$	−7.73704e6	+	2.29388e7i	−0.108000	+	0.320199i
$93$	−2.86572e7			−0.383090
$94$	6.32424e6	+	6.39513e6i	0.0810022	+	0.0819102i
$95$	−2.17051e7	+	4.23213e7i	−0.266482	+	0.519594i
$96$	2.38237e7	−	1.13140e7i	0.280495	−	0.133208i
$97$	2.82622e7	−	8.69821e7i	0.319241	−	0.982523i	−0.654732	−	0.755861i	$-0.727219\pi$
$97$	2.82622e7	−	8.69821e7i	0.319241	−	0.982523i	0.973973	−	0.226662i	$-0.0727814\pi$
$98$	4.42311e7	+	2.28483e7i	0.479539	+	0.247714i
$99$			1.58628e7i			0.165135i
$100$	8.18573e7	−	5.74402e7i	0.818573	−	0.574402i
$101$	9.68254e7			0.930473			0.465236	−	0.885186i	$-0.345969\pi$
$101$	9.68254e7			0.930473			0.465236	+	0.885186i	$0.345969\pi$
$102$	−3.23052e6	+	6.25382e6i	−0.0298450	+	0.0577756i
$103$	3.12222e6	+	1.01447e6i	0.0277405	+	0.00901344i	0.322854	−	0.946449i	$-0.395358\pi$
$103$	3.12222e6	+	1.01447e6i	0.0277405	+	0.00901344i	−0.295114	+	0.955462i	$0.595358\pi$
$104$	−1.71574e7	+	3.23254e7i	−0.146662	+	0.276319i
$105$	−2.11519e7	−	4.17862e7i	−0.174017	−	0.343776i
$106$	7.78970e7	−	7.70334e7i	0.617017	−	0.610177i
$107$			9.48926e7i			0.723931i	0.932191	+	0.361966i	$0.117894\pi$
$107$			9.48926e7i			0.723931i	−0.932191	+	0.361966i	$0.882106\pi$
$108$	2.57015e7	−	7.62002e7i	0.188914	−	0.560094i
$109$	−1.27808e8	−	9.28580e7i	−0.905425	−	0.657830i	0.0344288	−	0.999407i	$-0.489039\pi$
$109$	−1.27808e8	−	9.28580e7i	−0.905425	−	0.657830i	−0.939854	+	0.341578i	$0.889039\pi$
$110$	2.15171e7	+	1.59050e7i	0.146965	+	0.108634i
$111$	3.30284e7	+	4.54597e7i	0.217568	+	0.299457i
$112$	1.84305e8	+	6.44611e7i	1.17129	+	0.409662i
$113$	−1.30711e8	−	9.49672e7i	−0.801676	−	0.582452i	0.109730	−	0.993961i	$-0.465002\pi$
$113$	−1.30711e8	−	9.49672e7i	−0.801676	−	0.582452i	−0.911405	+	0.411510i	$0.865002\pi$
$114$	2.72093e7	+	1.40554e7i	0.161101	+	0.0832192i
$115$	5.83505e7	+	9.40030e6i	0.333621	+	0.0537465i
$116$	8.35196e7	−	2.61115e7i	0.461271	−	0.144211i
$117$	1.63681e7	+	5.03758e7i	0.0873483	+	0.268831i
$118$	1.35046e8	−	6.78637e7i	0.696550	−	0.350033i
$119$	−4.95606e7	+	1.61032e7i	−0.247143	+	0.0803017i
$120$	−3.68309e7	−	5.28151e7i	−0.177618	−	0.254703i
$121$	6.40281e7	−	1.97058e8i	0.298696	−	0.919291i
$122$	3.18212e7	−	4.85833e6i	0.143641	−	0.0219304i
$123$	4.27117e7	+	5.87876e7i	0.186606	+	0.256841i
$124$	−2.34045e8	−	1.74063e8i	−0.989949	−	0.736240i
$125$	−1.71256e8	−	1.74000e8i	−0.701466	−	0.712703i
$126$	2.52509e8	−	1.26892e8i	1.00183	−	0.503446i
$127$	−1.09892e8	−	1.51253e8i	−0.422425	−	0.581418i	0.543769	−	0.839235i	$-0.316997\pi$
$127$	−1.09892e8	−	1.51253e8i	−0.422425	−	0.581418i	−0.966194	+	0.257817i	$0.916997\pi$
$128$	2.63291e8	+	5.23027e7i	0.980834	+	0.194843i
$129$	−1.63395e6	+	5.02877e6i	−0.00590036	+	0.0181595i
$130$	8.47441e7	+	2.83075e7i	0.296713	+	0.0991124i
$131$	−1.99289e8	+	6.47530e7i	−0.676704	+	0.219874i	−0.627152	−	0.778897i	$-0.715779\pi$
$131$	−1.99289e8	+	6.47530e7i	−0.676704	+	0.219874i	−0.0495521	+	0.998772i	$0.515779\pi$
$132$	1.02816e7	−	1.38246e7i	0.0338661	−	0.0455364i
$133$	7.00622e7	+	2.15629e8i	0.223912	+	0.689130i
$134$	−2.66828e8	−	4.37874e7i	−0.827584	−	0.135809i
$135$	−1.93834e8	−	3.12267e7i	−0.583571	−	0.0940137i
$136$	−6.43694e7	+	3.14534e7i	−0.188159	+	0.0919415i
$137$	1.45244e8	+	1.05526e8i	0.412304	+	0.299556i	0.774534	−	0.632533i	$-0.217985\pi$
$137$	1.45244e8	+	1.05526e8i	0.412304	+	0.299556i	−0.362230	+	0.932089i	$0.617985\pi$
$138$	6.16264e6	−	3.75534e7i	0.0169922	−	0.103546i
$139$	2.35524e8	+	3.24171e8i	0.630923	+	0.868392i	0.998091	−	0.0617633i	$-0.0196724\pi$
$139$	2.35524e8	+	3.24171e8i	0.630923	+	0.868392i	−0.367167	+	0.930155i	$0.619672\pi$
$140$	8.10591e7	−	4.69747e8i	0.211003	−	1.22279i
$141$	−1.14384e7	−	8.31052e6i	−0.0289395	−	0.0210258i
$142$	3.63896e8	+	3.67975e8i	0.895002	+	0.905035i
$143$			2.39069e7i			0.0571714i
$144$	3.19334e8	−	2.21303e8i	0.742669	−	0.514681i
$145$	−9.64852e7	−	1.90609e8i	−0.218267	−	0.431193i
$146$	4.75412e8	−	7.25838e7i	1.04631	−	0.159745i
$147$	−7.44299e7	−	2.41837e7i	−0.159396	−	0.0517910i
$148$	−6.37558e6	+	5.71887e8i	−0.0132884	+	1.19196i
$149$	−8.58273e8			−1.74133			−0.870663	−	0.491879i	$-0.836310\pi$
$149$	−8.58273e8			−1.74133			−0.870663	+	0.491879i	$0.836310\pi$
$150$	−1.12359e8	+	1.09942e8i	−0.221943	+	0.217170i
$151$		−	5.85568e7i		−	0.112634i	−0.998413	−	0.0563170i	$-0.982064\pi$
$151$		−	5.85568e7i		−	0.112634i	0.998413	−	0.0563170i	$-0.0179358\pi$
$152$	1.36848e8	+	2.80060e8i	0.256368	+	0.524658i
$153$	−3.20430e7	+	9.86181e7i	−0.0584746	+	0.179966i
$154$	1.26089e8	−	1.92507e7i	0.224178	−	0.0342265i
$155$	−3.24966e8	+	6.33627e8i	−0.563004	+	1.09776i
$156$	1.83865e7	−	5.45124e7i	0.0310456	−	0.0920443i
$157$	5.04632e8			0.830571			0.415285	−	0.909691i	$-0.363682\pi$
$157$	5.04632e8			0.830571			0.415285	+	0.909691i	$0.363682\pi$
$158$	6.14104e8	+	6.20988e8i	0.985402	+	0.996449i
$159$	−1.01228e8	+	1.39328e8i	−0.158384	+	0.217997i
$160$	1.99973e7	−	6.55055e8i	0.0305135	−	0.999534i
$161$	2.27930e8	−	1.65601e8i	0.339233	−	0.246467i
$162$	8.03081e7	−	4.89375e8i	0.116600	−	0.710529i
$163$	1.99928e8	−	2.75178e8i	0.283220	−	0.389819i	−0.643577	−	0.765381i	$-0.722550\pi$
$163$	1.99928e8	−	2.75178e8i	0.283220	−	0.389819i	0.926797	+	0.375563i	$0.122550\pi$
$164$	−8.24476e6	+	7.39552e8i	−0.0113973	+	1.02234i
$165$	−3.74273e7	−	1.91952e7i	−0.0504955	−	0.0258974i
$166$	1.35055e9	+	2.21630e8i	1.77860	+	0.291874i
$167$	−1.02615e9	+	3.33417e8i	−1.31931	+	0.428669i	−0.882257	−	0.470768i	$-0.843977\pi$
$167$	−1.02615e9	+	3.33417e8i	−1.31931	+	0.428669i	−0.437050	+	0.899437i	$0.643977\pi$
$168$	−3.02312e8	−	5.30777e7i	−0.379506	−	0.0666309i
$169$	−2.27406e8	−	6.99884e8i	−0.278776	−	0.857985i
$170$	1.01643e8	+	1.42346e8i	0.121697	+	0.170431i
$171$	4.29070e8	+	1.39413e8i	0.501815	+	0.163050i
$172$	−4.38892e7	+	3.11458e7i	−0.0501469	+	0.0355865i
$173$	−3.06541e8	+	2.22715e8i	−0.342219	+	0.248637i	−0.745598	−	0.666396i	$-0.767836\pi$
$173$	−3.06541e8	+	2.22715e8i	−0.342219	+	0.248637i	0.403378	+	0.915033i	$0.367836\pi$
$174$	−1.22913e8	+	6.17666e7i	−0.134091	+	0.0673840i
$175$	−1.16378e9	−	6.16484e6i	−1.24085	−	0.00657309i
$176$	1.67941e8	−	5.04568e7i	0.175028	−	0.0525859i
$177$	−1.92214e8	+	1.39651e8i	−0.195835	+	0.142283i
$178$	−1.60996e9	+	2.45802e8i	−1.60375	+	0.244853i
$179$	−2.28414e6	−	742164.i	−0.00222491	−	0.000722915i	0.307904	−	0.951417i	$-0.400372\pi$
$179$	−2.28414e6	−	742164.i	−0.00222491	−	0.000722915i	−0.310129	+	0.950694i	$0.600372\pi$
$180$	−6.61402e8	−	6.79909e8i	−0.630051	−	0.647680i
$181$	−5.59385e8	−	1.72161e9i	−0.521190	−	1.60406i	−0.771729	−	0.635952i	$-0.780608\pi$
$181$	−5.59385e8	−	1.72161e9i	−0.521190	−	1.60406i	0.250539	−	0.968107i	$-0.419392\pi$
$182$	3.80559e8	−	1.91240e8i	0.346845	−	0.174298i
$183$	−4.81259e7	+	1.56370e7i	−0.0429116	+	0.0139428i
$184$	2.78429e8	−	2.69270e8i	0.242909	−	0.234918i
$185$	1.37968e9	−	2.14775e8i	1.17785	−	0.183357i
$186$	4.07373e8	+	2.10435e8i	0.340361	+	0.175819i
$187$	−2.75091e7	+	3.78630e7i	−0.0224963	+	0.0309634i
$188$	−4.29408e7	−	1.37349e8i	−0.0343747	−	0.109950i
$189$	−7.57158e8	+	5.50107e8i	−0.593389	+	0.431122i
$190$	6.19320e8	−	4.42228e8i	0.475227	−	0.339338i
$191$	9.39990e8	−	1.29378e9i	0.706301	−	0.972139i	−0.293568	−	0.955938i	$-0.594843\pi$
$191$	9.39990e8	−	1.29378e9i	0.706301	−	0.972139i	0.999869	−	0.0162013i	$-0.00515725\pi$
$192$	−4.21744e8	−	1.41099e7i	−0.310345	−	0.0103829i
$193$	1.02147e9			0.736203			0.368102	−	0.929786i	$-0.380008\pi$
$193$	1.02147e9			0.736203			0.368102	+	0.929786i	$0.380008\pi$
$194$	−1.04048e9	+	1.02895e9i	−0.734563	+	0.726419i
$195$	−1.38665e8	−	2.23391e7i	−0.0959024	−	0.0154499i
$196$	−4.60983e8	−	6.49596e8i	−0.312364	−	0.440169i
$197$	−6.67059e8	+	2.05300e9i	−0.442894	+	1.36309i	0.441884	+	0.897072i	$0.354310\pi$
$197$	−6.67059e8	+	2.05300e9i	−0.442894	+	1.36309i	−0.884777	+	0.466014i	$0.845690\pi$
$198$	1.16484e8	−	2.25496e8i	0.0757886	−	0.146716i
$199$		−	1.17695e9i		−	0.750492i	−0.926925	−	0.375246i	$-0.877558\pi$
$199$		−	1.17695e9i		−	0.750492i	0.926925	−	0.375246i	$-0.122442\pi$
$200$	−1.58543e9	+	2.15441e8i	−0.990893	+	0.134650i
$201$	4.25064e8			0.260417
$202$	−1.37641e9	−	7.11008e8i	−0.826690	−	0.427040i
$203$	−9.68547e8	−	3.14700e8i	−0.570344	−	0.185316i
$204$	9.18461e7	−	6.51782e7i	0.0530322	−	0.0376341i
$205$	1.78417e9	−	2.77743e8i	1.01023	−	0.157263i
$206$	−3.69341e7	−	3.73482e7i	−0.0205097	−	0.0207396i
$207$		−	5.60614e8i		−	0.305339i
$208$	4.81270e8	−	3.33528e8i	0.257120	−	0.178188i
$209$	1.64735e8	+	1.19687e8i	0.0863379	+	0.0627282i
$210$	−6.16153e6	+	7.49330e8i	−0.00316819	+	0.385297i
$211$	1.32474e9	+	1.82335e9i	0.668345	+	0.919898i	0.999721	−	0.0236005i	$-0.00751297\pi$
$211$	1.32474e9	+	1.82335e9i	0.668345	+	0.919898i	−0.331376	+	0.943499i	$0.607513\pi$
$212$	−1.67301e9	+	5.23047e8i	−0.828237	+	0.258939i
$213$	−6.58167e8	−	4.78186e8i	−0.319755	−	0.232316i
$214$	6.96815e8	−	1.34894e9i	0.332248	−	0.643185i
$215$	9.26606e7	+	9.31527e7i	0.0433652	+	0.0435955i
$216$	−9.24911e8	+	8.94484e8i	−0.424898	+	0.410920i
$217$	1.04896e9	+	3.22837e9i	0.473065	+	1.45594i
$218$	1.13497e9	+	2.25853e9i	0.502525	+	1.00000i
$219$	−7.19005e8	+	2.33619e8i	−0.312576	+	0.101562i
$220$	−1.89080e8	−	3.84101e8i	−0.0807153	−	0.163966i
$221$	−4.82922e7	+	1.48628e8i	−0.0202445	+	0.0623062i
$222$	−1.35692e8	−	8.88762e8i	−0.0558655	−	0.365910i
$223$	2.06285e9	+	2.83927e9i	0.834157	+	1.14812i	0.987135	+	0.159889i	$0.0511136\pi$
$223$	2.06285e9	+	2.83927e9i	0.834157	+	1.14812i	−0.152978	+	0.988230i	$0.548886\pi$
$224$	−2.14661e9	−	2.26972e9i	−0.852631	−	0.901532i
$225$	−1.37108e9	+	1.86626e9i	−0.534975	+	0.728187i
$226$	1.16075e9	+	2.30983e9i	0.444943	+	0.885415i
$227$	−4.56586e8	−	6.28437e8i	−0.171957	−	0.236678i	0.714337	−	0.699802i	$-0.246728\pi$
$227$	−4.56586e8	−	6.28437e8i	−0.171957	−	0.236678i	−0.886294	+	0.463124i	$0.846728\pi$
$228$	−2.83579e8	−	3.99606e8i	−0.104938	−	0.147874i
$229$	4.81681e8	−	1.48246e9i	0.175153	−	0.539066i	−0.824487	−	0.565880i	$-0.808536\pi$
$229$	4.81681e8	−	1.48246e9i	0.175153	−	0.539066i	0.999640	+	0.0268148i	$0.00853643\pi$
$230$	−7.60447e8	−	5.62108e8i	−0.271742	−	0.200867i
$231$	−1.90694e8	+	6.19603e7i	−0.0669714	+	0.0217603i
$232$	−1.37901e9	−	2.42116e8i	−0.476008	−	0.0835740i
$233$	2.00742e8	+	6.17821e8i	0.0681106	+	0.209623i	0.979319	−	0.202323i	$-0.0648492\pi$
$233$	2.00742e8	+	6.17821e8i	0.0681106	+	0.209623i	−0.911208	+	0.411946i	$0.864849\pi$
$234$	1.37241e8	−	8.36306e8i	0.0457740	−	0.278934i
$235$	−3.13460e8	+	1.58672e8i	−0.102781	+	0.0520269i
$236$	−2.41806e9	−	2.69573e7i	−0.779506	−	0.00869018i
$237$	−1.11071e9	−	8.06978e8i	−0.352052	−	0.255781i
$238$	8.22773e8	+	1.35020e8i	0.256432	+	0.0420813i
$239$	−2.45716e9	−	3.38199e9i	−0.753081	−	1.03653i	−0.997758	−	0.0669226i	$-0.978682\pi$
$239$	−2.45716e9	−	3.38199e9i	−0.753081	−	1.03653i	0.244677	−	0.969605i	$-0.421318\pi$
$240$	1.35733e8	+	1.02124e9i	0.0409111	+	0.307811i
$241$	1.03476e9	+	7.51799e8i	0.306742	+	0.222861i	0.730497	−	0.682916i	$-0.239288\pi$
$241$	1.03476e9	+	7.51799e8i	0.306742	+	0.222861i	−0.423756	+	0.905777i	$0.639288\pi$
$242$	−2.35722e9	+	2.33109e9i	−0.687289	+	0.679669i
$243$			2.84061e9i			0.814679i
$244$	−4.88027e8	−	1.64606e8i	−0.137684	−	0.0464395i
$245$	−1.37874e9	+	1.37145e9i	−0.382664	+	0.380642i
$246$	−1.75475e8	−	1.14933e9i	−0.0479152	−	0.313837i
$247$	6.46654e8	+	2.10111e8i	0.173734	+	0.0564495i
$248$	2.04887e9	+	4.19301e9i	0.541635	+	1.10846i
$249$	−2.15146e9			−0.559675
$250$	1.15676e9	+	3.73104e9i	0.296131	+	0.955147i
$251$		−	5.34789e9i		−	1.34737i	−0.739018	−	0.673686i	$-0.764710\pi$
$251$		−	5.34789e9i		−	1.34737i	0.739018	−	0.673686i	$-0.235290\pi$
$252$	−4.52132e9	−	5.04050e7i	−1.12115	−	0.0124989i
$253$	7.81905e7	−	2.40646e8i	0.0190841	−	0.0587348i
$254$	4.51473e8	+	2.95707e9i	0.108467	+	0.710439i
$255$	−1.93909e8	−	1.94939e8i	−0.0458604	−	0.0461039i
$256$	−3.35871e9	−	2.67690e9i	−0.782011	−	0.623264i
$257$	1.11535e9			0.255670			0.127835	−	0.991795i	$-0.459197\pi$
$257$	1.11535e9			0.255670			0.127835	+	0.991795i	$0.459197\pi$
$258$	6.01544e7	−	5.94875e7i	0.0135765	−	0.0134260i
$259$	3.91230e9	−	5.38481e9i	0.869426	−	1.19666i
$260$	−9.96804e8	−	1.02469e9i	−0.218130	−	0.224234i
$261$	−1.63943e9	+	1.19111e9i	−0.353289	+	0.256680i
$262$	3.30847e9	+	5.42931e8i	0.702137	+	0.115223i
$263$	2.32880e9	−	3.20531e9i	0.486753	−	0.669958i	−0.493032	−	0.870011i	$-0.664111\pi$
$263$	2.32880e9	−	3.20531e9i	0.486753	−	0.669958i	0.979785	+	0.200053i	$0.0641115\pi$
$264$	−2.47674e8	+	1.21023e8i	−0.0509876	+	0.0249145i
$265$	1.93273e9	+	3.81815e9i	0.391910	+	0.774230i
$266$	5.87447e8	−	3.57974e9i	0.117339	−	0.715031i
$267$	2.43488e9	−	7.91141e8i	0.479107	−	0.155671i
$268$	3.47153e9	+	2.58183e9i	0.672948	+	0.500481i
$269$	2.62041e8	+	8.06479e8i	0.0500449	+	0.154023i	0.972956	−	0.230991i	$-0.0741968\pi$
$269$	2.62041e8	+	8.06479e8i	0.0500449	+	0.154023i	−0.922911	+	0.385013i	$0.874197\pi$
$270$	2.52612e9	+	1.86726e9i	0.475333	+	0.351358i
$271$	5.60697e9	+	1.82181e9i	1.03956	+	0.337775i	0.778565	−	0.627564i	$-0.215948\pi$
$271$	5.60697e9	+	1.82181e9i	1.03956	+	0.337775i	0.260999	+	0.965339i	$0.415948\pi$
$272$	1.14601e9	+	2.55552e7i	0.209368	+	0.00466879i
$273$	−5.41658e8	+	3.93538e8i	−0.0975157	+	0.0708493i
$274$	−1.28981e9	−	2.56665e9i	−0.228835	−	0.455371i
$275$	−8.48835e8	+	6.09871e8i	−0.148420	+	0.106637i
$276$	−3.63367e8	+	4.88583e8i	−0.0626194	+	0.0841981i
$277$	5.75953e8	−	4.18455e8i	0.0978292	−	0.0710770i	−0.537795	−	0.843075i	$-0.680743\pi$
$277$	5.75953e8	−	4.18455e8i	0.0978292	−	0.0710770i	0.635624	+	0.771998i	$0.280743\pi$
$278$	−9.67617e8	−	6.33773e9i	−0.162003	−	1.06110i
$279$	6.42397e9	+	2.08727e9i	1.06020	+	0.344479i
$280$	−4.60173e9	+	6.08241e9i	−0.748668	+	0.989564i
$281$	−2.20741e9	−	6.79372e9i	−0.354045	−	1.08964i	−0.956561	−	0.291532i	$-0.905835\pi$
$281$	−2.20741e9	−	6.79372e9i	−0.354045	−	1.08964i	0.602516	−	0.798107i	$-0.294165\pi$
$282$	1.01576e8	+	2.02132e8i	0.0160619	+	0.0319624i
$283$	−3.20196e8	+	1.04038e8i	−0.0499194	+	0.0162198i	−0.333870	−	0.942619i	$-0.608355\pi$
$283$	−3.20196e8	+	1.04038e8i	−0.0499194	+	0.0162198i	0.283951	+	0.958839i	$0.408355\pi$
$284$	−2.47081e9	−	7.90308e9i	−0.379810	−	1.21485i
$285$	−8.48145e8	+	8.43664e8i	−0.128555	+	0.127876i
$286$	1.75553e8	−	3.39846e8i	0.0262388	−	0.0507946i
$287$	5.05930e9	−	6.96353e9i	0.745698	−	1.02636i
$288$	−6.16454e9	+	8.00982e8i	−0.896046	+	0.116427i
$289$	5.39600e9	−	3.92042e9i	0.773536	−	0.562007i
$290$	−2.81060e7	+	3.41809e9i	−0.00397381	+	0.483272i
$291$	1.35212e9	−	1.86103e9i	0.188557	−	0.259526i
$292$	−7.29117e9	−	2.45924e9i	−1.00292	−	0.338274i
$293$	5.10197e9			0.692257			0.346128	−	0.938187i	$-0.387496\pi$
$293$	5.10197e9			0.692257			0.346128	+	0.938187i	$0.387496\pi$
$294$	8.80465e8	+	8.90335e8i	0.117848	+	0.119169i
$295$	9.08116e8	+	5.83358e9i	0.119909	+	0.770277i
$296$	4.29011e9	−	8.08278e9i	0.558858	−	1.05292i
$297$	−2.59740e8	+	7.99397e8i	−0.0333820	+	0.102739i
$298$	1.22007e10	+	6.30247e9i	1.54710	+	0.799182i
$299$		−	8.44905e8i		−	0.105712i
$300$	2.40455e9	−	7.37797e8i	0.296858	−	0.0910861i
$301$	6.26324e8			0.0763015
$302$	−4.29994e8	+	8.32408e8i	−0.0516934	+	0.100071i
$303$	2.31615e9	+	7.52564e8i	0.274787	+	0.0892839i
$304$	1.11186e8	−	4.98606e9i	0.0130184	−	0.583799i
$305$	−1.99993e8	+	1.24141e9i	−0.0231108	+	0.143455i
$306$	1.17968e9	−	1.16660e9i	0.134548	−	0.133056i
$307$		−	3.79168e9i		−	0.426853i	−0.976959	−	0.213426i	$-0.931538\pi$
$307$		−	3.79168e9i		−	0.426853i	0.976959	−	0.213426i	$-0.0684624\pi$
$308$	−1.93376e9	−	6.52237e8i	−0.214882	−	0.0724774i
$309$	6.68016e7	+	4.85342e7i	0.00732745	+	0.00532370i
$310$	9.27237e9	−	6.62097e9i	1.00402	−	0.716927i
$311$	9.16918e9	+	1.26203e10i	0.980142	+	1.34905i	0.936753	+	0.349992i	$0.113816\pi$
$311$	9.16918e9	+	1.26203e10i	0.980142	+	1.34905i	0.0433897	+	0.999058i	$0.486184\pi$
$312$	−6.61666e8	+	6.39899e8i	−0.0698265	+	0.0675295i
$313$	1.02960e10	+	7.48047e9i	1.07273	+	0.779384i	0.976401	−	0.215965i	$-0.0692898\pi$
$313$	1.02960e10	+	7.48047e9i	1.07273	+	0.779384i	0.0963294	+	0.995350i	$0.469290\pi$
$314$	−7.17355e9	−	3.70562e9i	−0.737931	−	0.381190i
$315$	1.69800e9	+	1.09077e10i	0.172463	+	1.10787i
$316$	−4.16969e9	−	1.33371e10i	−0.418172	−	1.33756i
$317$	−1.85012e9	−	5.69408e9i	−0.183216	−	0.563880i	0.816697	−	0.577066i	$-0.195803\pi$
$317$	−1.85012e9	−	5.69408e9i	−0.183216	−	0.563880i	−0.999913	+	0.0131863i	$0.995803\pi$
$318$	2.46210e9	−	1.23727e9i	0.240767	−	0.120991i
$319$	−8.69858e8	+	2.82634e8i	−0.0840012	+	0.0272936i
$320$	−5.09447e9	+	9.16502e9i	−0.485846	+	0.874044i
$321$	−7.37542e8	+	2.26992e9i	−0.0694651	+	0.213792i
$322$	−4.45616e9	+	6.80347e8i	−0.414512	+	0.0632859i
$323$	7.82382e8	+	1.07686e9i	0.0718801	+	0.0989345i
$324$	−4.73519e9	+	6.36694e9i	−0.429692	+	0.577764i
$325$	−2.06637e9	+	2.81266e9i	−0.185214	+	0.252106i
$326$	−4.86274e9	+	2.44365e9i	−0.430537	+	0.216355i
$327$	−2.33556e9	−	3.21463e9i	−0.204268	−	0.281151i
$328$	5.54788e9	−	1.04525e10i	0.479327	−	0.903076i
$329$	−5.17530e8	+	1.59279e9i	−0.0441725	+	0.135949i
$330$	3.91089e8	+	5.47703e8i	0.0329777	+	0.0461838i
$331$	4.78995e9	−	1.55635e9i	0.399043	−	0.129657i	−0.102619	−	0.994721i	$-0.532722\pi$
$331$	4.78995e9	−	1.55635e9i	0.399043	−	0.129657i	0.501662	+	0.865064i	$0.332722\pi$
$332$	−1.75711e10	−	1.30679e10i	−1.44626	−	1.07561i
$333$	−4.09275e9	−	1.25962e10i	−0.332842	−	1.02438i
$334$	1.70355e10	+	2.79558e9i	1.36889	+	0.224640i
$335$	4.82013e9	−	9.39842e9i	0.382719	−	0.746235i
$336$	3.90772e9	+	2.97446e9i	0.306596	+	0.233373i
$337$	−9.27479e9	−	6.73853e9i	−0.719092	−	0.522451i	0.167002	−	0.985957i	$-0.446591\pi$
$337$	−9.27479e9	−	6.73853e9i	−0.719092	−	0.522451i	−0.886094	+	0.463506i	$0.846591\pi$
$338$	−1.90672e9	+	1.16190e10i	−0.146090	+	0.890231i
$339$	−2.38861e9	−	3.28764e9i	−0.180862	−	0.248935i
$340$	−3.99616e8	−	2.76988e9i	−0.0299038	−	0.207274i
$341$	2.46639e9	+	1.79194e9i	0.182408	+	0.132527i
$342$	−5.07566e9	−	5.13256e9i	−0.371012	−	0.375171i
$343$		−	7.90502e9i		−	0.571119i
$344$	8.52612e8	−	1.20463e8i	0.0608860	−	0.00860239i
$345$	1.32274e9	+	6.78386e8i	0.0933677	+	0.0478851i
$346$	5.99304e9	−	9.14992e8i	0.418161	−	0.0638429i
$347$	−1.63695e10	−	5.31878e9i	−1.12906	−	0.366855i	−0.315843	−	0.948812i	$-0.602287\pi$
$347$	−1.63695e10	−	5.31878e9i	−1.12906	−	0.366855i	−0.813220	+	0.581957i	$0.802287\pi$
$348$	2.20082e9	+	2.45354e7i	0.150061	+	0.00167292i
$349$	9.89300e9			0.666847			0.333423	−	0.942777i	$-0.391796\pi$
$349$	9.89300e9			0.666847			0.333423	+	0.942777i	$0.391796\pi$
$350$	1.64983e10	+	8.63348e9i	1.09943	+	0.575326i
$351$			2.80668e9i			0.184912i
$352$	−2.75786e9	−	5.15961e8i	−0.179640	−	0.0336083i
$353$	4.48663e9	−	1.38084e10i	0.288949	−	0.889295i	−0.696238	−	0.717811i	$-0.745144\pi$
$353$	4.48663e9	−	1.38084e10i	0.288949	−	0.889295i	0.985187	−	0.171484i	$-0.0548560\pi$
$354$	3.75788e9	−	5.73737e8i	0.239293	−	0.0365342i
$355$	−1.80365e10	+	9.12995e9i	−1.13563	+	0.574851i
$356$	2.46912e10	+	8.32810e9i	1.53724	+	0.518497i
$357$	−1.31070e9			−0.0806918
$358$	2.70202e7	+	2.73231e7i	0.00164496	+	0.00166340i
$359$	4.99405e9	−	6.87372e9i	0.300660	−	0.413823i	−0.631780	−	0.775148i	$-0.717675\pi$
$359$	4.99405e9	−	6.87372e9i	0.300660	−	0.413823i	0.932440	+	0.361325i	$0.117675\pi$
$360$	4.40939e9	+	1.45220e10i	0.262524	+	0.864601i
$361$	−9.05478e9	+	6.57868e9i	−0.533150	+	0.387356i
$362$	−4.69024e9	+	2.85810e10i	−0.273125	+	1.66435i
$363$	3.06323e9	−	4.21617e9i	0.176422	−	0.242824i
$364$	−6.81410e9	−	7.59658e7i	−0.388153	−	0.00432725i
$365$	−2.98791e9	+	1.85468e10i	−0.168343	+	1.04496i
$366$	7.98954e8	+	1.31111e8i	0.0445244	+	0.00730659i
$367$	−1.95260e10	+	6.34438e9i	−1.07634	+	0.349724i	−0.792953	−	0.609282i	$-0.791458\pi$
$367$	−1.95260e10	+	6.34438e9i	−1.07634	+	0.349724i	−0.283386	+	0.959006i	$0.591458\pi$
$368$	−5.93529e9	+	1.78322e9i	−0.323631	+	0.0972329i
$369$	−5.29266e9	−	1.62891e10i	−0.285475	−	0.878603i
$370$	−2.11898e10	−	7.07813e9i	−1.13063	−	0.377669i
$371$	1.94013e10	+	6.30386e9i	1.02408	+	0.332745i
$372$	−4.24570e9	−	5.98284e9i	−0.221706	−	0.312418i
$373$	2.84965e10	−	2.07039e10i	1.47216	−	1.06959i	0.492183	−	0.870492i	$-0.336199\pi$
$373$	2.84965e10	−	2.07039e10i	1.47216	−	1.06959i	0.979980	−	0.199098i	$-0.0638011\pi$
$374$	6.69089e8	−	3.36233e8i	0.0341977	−	0.0171852i
$375$	−2.74422e9	−	5.49331e9i	−0.138769	−	0.277785i
$376$	−3.98164e8	+	2.26780e9i	−0.0199210	+	0.113463i
$377$	−2.47079e9	+	1.79514e9i	−0.122312	+	0.0888652i
$378$	1.48028e10	−	2.26003e9i	0.725067	−	0.110700i
$379$	−1.81242e10	−	5.88891e9i	−0.878420	−	0.285416i	−0.165119	−	0.986274i	$-0.552801\pi$
$379$	−1.81242e10	−	5.88891e9i	−0.878420	−	0.285416i	−0.713301	+	0.700858i	$0.752801\pi$
$380$	−1.20513e10	+	1.73866e9i	−0.577960	+	0.0833834i
$381$	−1.45311e9	−	4.47223e9i	−0.0689604	−	0.212238i
$382$	−2.28628e10	+	1.14891e10i	−1.07368	+	0.539553i
$383$	−3.62521e10	+	1.17790e10i	−1.68476	+	0.547412i	−0.985826	−	0.167773i	$-0.946342\pi$
$383$	−3.62521e10	+	1.17790e10i	−1.68476	+	0.547412i	−0.698935	+	0.715185i	$0.746342\pi$
$384$	5.89165e9	+	3.29753e9i	0.270964	+	0.151657i
$385$	−7.92451e8	+	4.91898e9i	−0.0360686	+	0.223889i
$386$	−1.45206e10	−	7.50088e9i	−0.654089	−	0.337880i
$387$	7.32551e8	−	1.00827e9i	0.0326583	−	0.0449503i
$388$	2.23467e10	−	6.98644e9i	0.986021	−	0.308269i
$389$	−2.69563e10	+	1.95849e10i	−1.17723	+	0.855308i	−0.991857	−	0.127360i	$-0.959350\pi$
$389$	−2.69563e10	+	1.95849e10i	−1.17723	+	0.855308i	−0.185374	+	0.982668i	$0.559350\pi$
$390$	1.80714e9	+	1.33581e9i	0.0781149	+	0.0577411i
$391$	9.72213e8	−	1.33814e9i	0.0415963	−	0.0572523i
$392$	1.78295e9	+	1.26194e10i	0.0755083	+	0.534433i
$393$	−5.27047e9			−0.220943
$394$	2.45581e10	−	2.42858e10i	1.01908	−	1.00778i
$395$	−3.04380e10	+	1.54075e10i	−1.25034	+	0.632914i
$396$	−3.31172e9	+	2.35015e9i	−0.134671	+	0.0955685i
$397$	−1.40201e10	+	4.31493e10i	−0.564401	+	1.73705i	0.105323	+	0.994438i	$0.466412\pi$
$397$	−1.40201e10	+	4.31493e10i	−0.564401	+	1.73705i	−0.669724	+	0.742610i	$0.733588\pi$
$398$	−8.64258e9	+	1.67308e10i	−0.344438	+	0.666783i
$399$			5.70261e9i			0.225000i
$400$	2.41195e10	+	8.57954e9i	0.942169	+	0.335138i
$401$	−4.35465e10			−1.68413			−0.842065	−	0.539376i	$-0.818660\pi$
$401$	−4.35465e10			−1.68413			−0.842065	+	0.539376i	$0.818660\pi$
$402$	−6.04245e9	−	3.12133e9i	−0.231371	−	0.119518i
$403$	9.68160e9	+	3.14574e9i	0.367051	+	0.119262i
$404$	1.43452e10	+	2.02145e10i	0.538493	+	0.758818i
$405$	1.72371e10	+	8.84034e9i	0.640686	+	0.328586i
$406$	1.14574e10	+	1.15858e10i	0.421678	+	0.426405i
$407$		−	5.97779e9i		−	0.217853i
$408$	−1.78425e9	+	2.52090e8i	−0.0643893	+	0.00909737i
$409$	−1.31774e10	−	9.57392e9i	−0.470908	−	0.342134i	0.326887	−	0.945063i	$-0.394000\pi$
$409$	−1.31774e10	−	9.57392e9i	−0.470908	−	0.342134i	−0.797795	+	0.602929i	$0.794000\pi$
$410$	−2.74022e10	−	9.15329e9i	−0.969729	−	0.323923i
$411$	2.65419e9	+	3.65318e9i	0.0930176	+	0.128028i
$412$	2.50778e8	+	8.02133e8i	0.00870364	+	0.0278393i
$413$	2.27682e10	+	1.65420e10i	0.782578	+	0.568577i
$414$	−4.11670e9	+	7.96935e9i	−0.140135	+	0.271282i
$415$	−2.43971e10	+	4.75701e10i	−0.822518	+	1.60377i
$416$	−9.29061e9	+	1.20717e9i	−0.310221	+	0.0403082i
$417$	3.11438e9	+	9.58507e9i	0.102998	+	0.316994i
$418$	−1.46289e9	−	2.91108e9i	−0.0479189	−	0.0953564i
$419$	−3.54437e10	+	1.15164e10i	−1.14996	+	0.373645i	−0.821129	−	0.570743i	$-0.806655\pi$
$419$	−3.54437e10	+	1.15164e10i	−1.14996	+	0.373645i	−0.328833	+	0.944388i	$0.606655\pi$
$420$	5.59007e9	−	1.06068e10i	0.179647	−	0.340868i
$421$	6.25257e8	−	1.92434e9i	0.0199035	−	0.0612568i	−0.940611	−	0.339485i	$-0.889747\pi$
$421$	6.25257e8	−	1.92434e9i	0.0199035	−	0.0612568i	0.960515	+	0.278228i	$0.0897472\pi$
$422$	−5.44250e9	−	3.56474e10i	−0.171612	−	1.12403i
$423$	1.95881e9	+	2.69607e9i	0.0611830	+	0.0842111i
$424$	2.76233e10	+	4.84990e9i	0.854697	+	0.150062i
$425$	−6.50911e9	+	2.07688e9i	−0.199511	+	0.0636585i
$426$	5.84469e9	+	1.16307e10i	0.177469	+	0.353156i
$427$	3.52318e9	+	4.84924e9i	0.105980	+	0.145869i
$428$	−1.98110e10	+	1.40588e10i	−0.590380	+	0.418961i
$429$	−1.85814e8	+	5.71875e8i	−0.00548591	+	0.0168839i
$430$	−6.33168e8	−	2.00463e9i	−0.0185202	−	0.0586354i
$431$	1.35314e10	−	4.39662e9i	0.392134	−	0.127412i	−0.106312	−	0.994333i	$-0.533904\pi$
$431$	1.35314e10	−	4.39662e9i	0.392134	−	0.127412i	0.498446	+	0.866921i	$0.333904\pi$
$432$	1.97163e10	−	5.92365e9i	0.566098	−	0.170080i
$433$	−4.55944e9	−	1.40325e10i	−0.129706	−	0.399194i	0.865023	−	0.501732i	$-0.167304\pi$
$433$	−4.55944e9	−	1.40325e10i	−0.129706	−	0.399194i	−0.994729	+	0.102538i	$0.967304\pi$
$434$	8.79516e9	−	5.35953e10i	0.247905	−	1.51066i
$435$	−8.26528e8	−	5.30947e9i	−0.0230834	−	0.148284i
$436$	4.50840e8	−	4.04402e10i	0.0124760	−	1.11910i
$437$	−5.82199e9	−	4.22992e9i	−0.159641	−	0.115986i
$438$	1.19365e10	+	1.95881e9i	0.324324	+	0.0532226i
$439$	−3.59392e10	−	4.94660e10i	−0.967632	−	1.33183i	−0.943234	−	0.332128i	$-0.892233\pi$
$439$	−3.59392e10	−	4.94660e10i	−0.967632	−	1.33183i	−0.0243973	−	0.999702i	$-0.507767\pi$
$440$	−1.32677e8	+	6.84860e9i	−0.00353984	+	0.182722i
$441$	1.49232e10	+	1.08424e10i	0.394556	+	0.286662i
$442$	1.77790e9	−	1.75819e9i	0.0465819	−	0.0460655i
$443$			4.13606e10i			1.07392i	0.843608	+	0.536960i	$0.180427\pi$
$443$			4.13606e10i			1.07392i	−0.843608	+	0.536960i	$0.819573\pi$
$444$	−4.59744e9	+	1.36305e10i	−0.118300	+	0.350736i
$445$	1.01184e10	−	6.28081e10i	0.258032	−	1.60168i
$446$	−8.47490e9	−	5.55092e10i	−0.214188	−	1.40290i
$447$	−2.05307e10	−	6.67083e9i	−0.514249	−	0.167090i
$448$	1.38479e10	+	4.80280e10i	0.343773	+	1.19229i
$449$	−3.57981e10			−0.880794			−0.440397	−	0.897803i	$-0.645162\pi$
$449$	−3.57981e10			−0.880794			−0.440397	+	0.897803i	$0.645162\pi$
$450$	3.31948e10	−	1.64615e10i	0.809506	−	0.401440i
$451$		−	7.73035e9i		−	0.186850i
$452$	4.61081e8	−	4.13588e10i	0.0110465	−	0.990864i
$453$	4.55126e8	−	1.40073e9i	0.0108078	−	0.0332631i
$454$	1.87582e9	+	1.22863e10i	0.0441537	+	0.289199i
$455$	2.55907e9	+	1.64390e10i	0.0597086	+	0.383558i
$456$	1.09680e9	+	7.76293e9i	0.0253669	+	0.179542i
$457$	2.73470e10			0.626966			0.313483	−	0.949594i	$-0.398504\pi$
$457$	2.73470e10			0.626966			0.313483	+	0.949594i	$0.398504\pi$
$458$	−1.77333e10	+	1.75367e10i	−0.403021	+	0.398553i
$459$	−3.22958e9	+	4.44514e9i	−0.0727604	+	0.100146i
$460$	6.68238e9	+	1.35747e10i	0.149245	+	0.303179i
$461$	6.71775e10	−	4.88073e10i	1.48737	−	1.08064i	0.512287	−	0.858814i	$-0.328798\pi$
$461$	6.71775e10	−	4.88073e10i	1.48737	−	1.08064i	0.975086	−	0.221826i	$-0.0712016\pi$
$462$	3.16578e9	+	5.19515e8i	0.0694885	+	0.0114033i
$463$	3.09475e10	−	4.25956e10i	0.673445	−	0.926917i	−0.326388	−	0.945236i	$-0.605831\pi$
$463$	3.09475e10	−	4.25956e10i	0.673445	−	0.926917i	0.999832	+	0.0183191i	$0.00583148\pi$
$464$	1.78252e10	+	1.35681e10i	0.384559	+	0.292716i
$465$	−1.26983e10	+	1.26312e10i	−0.271602	+	0.270167i
$466$	1.68315e9	−	1.02567e10i	0.0356927	−	0.217501i
$467$	6.65587e10	−	2.16262e10i	1.39939	−	0.454688i	0.490394	−	0.871501i	$-0.336853\pi$
$467$	6.65587e10	−	2.16262e10i	1.39939	−	0.454688i	0.908992	+	0.416813i	$0.136853\pi$
$468$	−8.09209e9	+	1.08806e10i	−0.168685	+	0.226815i
$469$	−1.55589e10	−	4.78855e10i	−0.321580	−	0.989721i
$470$	5.62112e9	+	4.62209e7i	0.115194	+	0.000947211i
$471$	1.20713e10	+	3.92220e9i	0.245284	+	0.0796977i
$472$	3.41758e10	+	1.81395e10i	0.688573	+	0.365475i
$473$	4.55076e8	−	3.30632e8i	0.00909159	−	0.00660543i
$474$	9.86338e9	+	1.96277e10i	0.195395	+	0.388826i
$475$	9.03614e9	+	2.83200e10i	0.177504	+	0.556312i
$476$	−1.07046e10	−	7.96114e9i	−0.208517	−	0.155077i
$477$	3.28399e10	−	2.38596e10i	0.634349	−	0.460882i
$478$	1.00949e10	+	6.61197e10i	0.193370	+	1.26654i
$479$	−4.06306e10	−	1.32017e10i	−0.771812	−	0.250777i	−0.103472	−	0.994632i	$-0.532995\pi$
$479$	−4.06306e10	−	1.32017e10i	−0.771812	−	0.250777i	−0.668341	+	0.743855i	$0.732995\pi$
$480$	5.56969e9	−	1.55141e10i	0.104922	−	0.292255i
$481$	−6.16821e9	−	1.89838e10i	−0.115234	−	0.354652i
$482$	−9.18895e9	−	1.82856e10i	−0.170246	−	0.338782i
$483$	6.73942e9	−	2.18977e9i	0.123832	−	0.0402355i
$484$	5.06265e10	−	1.58278e10i	0.922564	−	0.288429i
$485$	−2.58158e10	−	5.09998e10i	−0.466572	−	0.921726i
$486$	2.08592e10	−	4.03804e10i	0.373897	−	0.723811i
$487$	4.42546e10	−	6.09113e10i	0.786761	−	1.08288i	−0.207743	−	0.978183i	$-0.566612\pi$
$487$	4.42546e10	−	6.09113e10i	0.786761	−	1.08288i	0.994504	−	0.104700i	$-0.0333882\pi$
$488$	5.72876e9	+	5.92362e9i	0.101014	+	0.104450i
$489$	6.92126e9	−	5.02859e9i	0.121046	−	0.0879449i
$490$	2.96701e10	−	9.37141e9i	0.514678	−	0.162563i
$491$	−2.76936e10	+	3.81169e10i	−0.476489	+	0.655831i	−0.977825	−	0.209422i	$-0.932842\pi$
$491$	−2.76936e10	+	3.81169e10i	−0.476489	+	0.655831i	0.501336	+	0.865252i	$0.332842\pi$
$492$	−5.94531e9	+	1.76267e10i	−0.101464	+	0.300823i
$493$	−5.97879e9			−0.101210
$494$	−7.64955e9	−	7.73531e9i	−0.128448	−	0.129888i
$495$	6.99183e9	+	7.02897e9i	0.116458	+	0.117077i
$496$	1.66466e9	−	7.46506e10i	0.0275042	−	1.23341i
$497$	−2.97786e10	+	9.16492e10i	−0.488067	+	1.50212i
$498$	3.05838e10	+	1.57986e10i	0.497250	+	0.256863i
$499$			5.50740e10i			0.888268i	0.895960	+	0.444134i	$0.146489\pi$
$499$			5.50740e10i			0.888268i	−0.895960	+	0.444134i	$0.853511\pi$
$500$	1.09540e10	−	6.15326e10i	0.175263	−	0.984522i
$501$	−2.71380e10			−0.430751
$502$	−3.92706e10	+	7.60224e10i	−0.618376	+	1.19709i
$503$	−8.02755e10	−	2.60831e10i	−1.25404	−	0.407462i	−0.394672	−	0.918822i	$-0.629142\pi$
$503$	−8.02755e10	−	2.60831e10i	−1.25404	−	0.407462i	−0.859367	+	0.511360i	$0.829142\pi$
$504$	6.39022e10	+	3.39174e10i	0.990361	+	0.525655i
$505$	4.29044e10	−	4.26777e10i	0.659684	−	0.656199i
$506$	−2.87862e9	+	2.84670e9i	−0.0439118	+	0.0434250i
$507$		−	1.85094e10i		−	0.280130i
$508$	1.52965e10	−	4.53512e10i	0.229687	−	0.680979i
$509$	2.55058e10	+	1.85310e10i	0.379986	+	0.276076i	0.761340	−	0.648353i	$-0.224542\pi$
$509$	2.55058e10	+	1.85310e10i	0.379986	+	0.276076i	−0.381354	+	0.924429i	$0.624542\pi$
$510$	1.32502e9	+	4.19505e9i	0.0195858	+	0.0620092i
$511$	5.26367e10	+	7.24481e10i	0.771978	+	1.06254i
$512$	2.80884e10	+	6.27169e10i	0.408740	+	0.912651i
$513$	1.93400e10	+	1.40513e10i	0.279246	+	0.202884i
$514$	−1.58552e10	−	8.19025e9i	−0.227153	−	0.117340i
$515$	1.83064e9	−	9.26657e8i	0.0260239	−	0.0131732i
$516$	−1.29195e9	+	4.03913e8i	−0.0182241	+	0.00569756i
$517$	4.64797e8	+	1.43050e9i	0.00650580	+	0.0200228i
$518$	−9.51566e10	+	4.78185e10i	−1.32166	+	0.664166i
$519$	−9.06378e9	+	2.94500e9i	−0.124922	+	0.0405897i
$520$	6.64542e9	+	2.18862e10i	0.0908885	+	0.299334i
$521$	−1.90322e10	+	5.85750e10i	−0.258308	+	0.794989i	0.734852	+	0.678227i	$0.237251\pi$
$521$	−1.90322e10	+	5.85750e10i	−0.258308	+	0.794989i	−0.993160	+	0.116762i	$0.962749\pi$
$522$	3.20517e10	−	4.89351e9i	0.431687	−	0.0659081i
$523$	−1.51439e10	−	2.08438e10i	−0.202410	−	0.278594i	0.695730	−	0.718304i	$-0.255081\pi$
$523$	−1.51439e10	−	2.08438e10i	−0.202410	−	0.278594i	−0.898140	+	0.439710i	$0.855081\pi$
$524$	−4.30443e10	−	3.20127e10i	−0.570941	−	0.424617i
$525$	−2.77907e10	−	9.19279e9i	−0.365816	−	0.121007i
$526$	−5.66420e10	+	2.84640e10i	−0.739939	+	0.371837i
$527$	1.17137e10	+	1.61225e10i	0.151863	+	0.209021i
$528$	4.40948e9	+	9.83287e7i	0.0567351	+	0.00126516i
$529$	2.14361e10	−	6.59734e10i	0.273730	−	0.842454i
$530$	5.63001e8	−	6.84690e10i	0.00713519	−	0.867741i
$531$	5.32595e10	−	1.73050e10i	0.669913	−	0.217668i
$532$	−3.46375e10	+	4.65736e10i	−0.432414	+	0.581425i
$533$	−7.97660e9	−	2.45495e10i	−0.0988346	−	0.304182i
$534$	−4.04223e10	−	6.63344e9i	−0.497114	−	0.0815781i
$535$	4.18258e10	+	4.20479e10i	0.510539	+	0.513251i
$536$	−3.03903e10	−	6.21938e10i	−0.368193	−	0.753508i
$537$	−4.88705e7	−	3.55065e7i	−0.000587692	−	0.000426983i
$538$	2.19712e9	−	1.33886e10i	0.0262256	−	0.159811i
$539$	4.89363e9	+	6.73551e9i	0.0579797	+	0.0798023i
$540$	−2.21981e10	−	4.50936e10i	−0.261060	−	0.530322i
$541$	5.26721e10	+	3.82685e10i	0.614881	+	0.446737i	0.851130	−	0.524955i	$-0.175918\pi$
$541$	5.26721e10	+	3.82685e10i	0.614881	+	0.446737i	−0.236249	+	0.971693i	$0.575918\pi$
$542$	−6.63273e10	−	6.70709e10i	−0.768591	−	0.777207i
$543$		−	4.55303e10i		−	0.523722i
$544$	−1.61033e10	−	8.77862e9i	−0.183873	−	0.100238i
$545$	−9.75621e10	+	1.51875e10i	−1.10585	+	0.172148i
$546$	1.05897e10	−	1.61679e9i	0.119155	−	0.0181921i
$547$	9.48039e10	+	3.08036e10i	1.05895	+	0.344075i	0.786176	−	0.618003i	$-0.212058\pi$
$547$	9.48039e10	+	3.08036e10i	1.05895	+	0.344075i	0.272777	+	0.962077i	$0.412058\pi$
$548$	−5.12347e8	+	4.59573e10i	−0.00568122	+	0.509603i
$549$	1.19271e10			0.131295
$550$	1.65449e10	−	2.43639e9i	0.180806	−	0.0266254i
$551$			2.60126e10i			0.282214i
$552$	8.75317e9	−	4.27713e9i	0.0942777	−	0.0460677i
$553$	−5.02538e10	+	1.54665e11i	−0.537364	+	1.65384i
$554$	−1.12602e10	+	1.71916e9i	−0.119538	+	0.0182506i
$555$	3.46725e10	+	5.58576e9i	0.365438	+	0.0588723i
$556$	−3.27841e10	+	9.71987e10i	−0.343056	+	1.01709i
$557$	3.65008e10			0.379211			0.189606	−	0.981860i	$-0.439279\pi$
$557$	3.65008e10			0.379211			0.189606	+	0.981860i	$0.439279\pi$
$558$	−7.59920e10	−	7.68439e10i	−0.783846	−	0.792634i
$559$	1.10403e9	−	1.51957e9i	0.0113067	−	0.0155623i
$560$	1.10080e11	−	5.26724e10i	1.11932	−	0.535589i
$561$	−9.52330e8	+	6.91908e8i	−0.00961471	+	0.00698549i
$562$	−1.85084e10	+	1.12785e11i	−0.185534	+	1.13059i
$563$	1.08423e11	−	1.49232e11i	1.07917	−	1.48535i	0.218732	−	0.975785i	$-0.429808\pi$
$563$	1.08423e11	−	1.49232e11i	1.07917	−	1.48535i	0.860435	−	0.509561i	$-0.170192\pi$
$564$	4.03489e7	−	3.61928e9i	0.000398763	−	0.0357689i
$565$	−9.97781e10	+	1.55325e10i	−0.979133	+	0.152422i
$566$	5.31568e9	+	8.72320e8i	0.0517956	+	0.00849983i
$567$	8.78242e10	−	2.85358e10i	0.849732	−	0.276095i
$568$	−2.29103e10	+	1.30489e11i	−0.220109	+	1.25366i
$569$	1.13831e10	+	3.50335e10i	0.108595	+	0.334221i	0.990557	−	0.137099i	$-0.0437778\pi$
$569$	1.13831e10	+	3.50335e10i	0.108595	+	0.334221i	−0.881962	+	0.471320i	$0.843778\pi$
$570$	1.82519e10	−	5.76492e9i	0.172905	−	0.0546127i
$571$	−3.14761e10	−	1.02272e10i	−0.296099	−	0.0962084i	0.157200	−	0.987567i	$-0.449753\pi$
$571$	−3.14761e10	−	1.02272e10i	−0.296099	−	0.0962084i	−0.453299	+	0.891358i	$0.649753\pi$
$572$	−4.99111e9	+	3.54192e9i	−0.0466244	+	0.0330868i
$573$	3.25412e10	−	2.36426e10i	0.301867	−	0.219319i
$574$	−1.23055e11	+	6.18379e10i	−1.13357	+	0.569649i
$575$	2.99991e10	−	2.15537e10i	0.274433	−	0.197175i
$576$	9.35131e10	+	3.38811e10i	0.849537	+	0.307799i
$577$	1.33842e11	−	9.72418e10i	1.20750	−	0.877303i	0.212502	−	0.977161i	$-0.431839\pi$
$577$	1.33842e11	−	9.72418e10i	1.20750	−	0.877303i	0.995002	+	0.0998578i	$0.0318388\pi$
$578$	−1.05495e11	+	1.61065e10i	−0.945190	+	0.144308i
$579$	2.44346e10	+	7.93929e9i	0.217416	+	0.0706427i
$580$	2.54993e10	−	4.83832e10i	0.225328	−	0.427545i
$581$	7.87516e10	+	2.42372e11i	0.691122	+	2.12705i
$582$	−3.28868e10	+	1.65264e10i	−0.286635	+	0.144041i
$583$	1.74244e10	−	5.66153e9i	0.150829	−	0.0490072i
$584$	8.55882e10	+	8.84995e10i	0.735804	+	0.760833i
$585$	2.94570e10	+	1.51075e10i	0.251516	+	0.128994i
$586$	−7.25265e10	−	3.74647e10i	−0.615044	−	0.317711i
$587$	1.27053e11	−	1.74873e11i	1.07012	−	1.47289i	0.200158	−	0.979764i	$-0.435854\pi$
$587$	1.27053e11	−	1.74873e11i	1.07012	−	1.47289i	0.869958	−	0.493125i	$-0.164146\pi$
$588$	−5.97825e9	−	1.91219e10i	−0.0500109	−	0.159964i
$589$	7.01462e10	−	5.09642e10i	0.582832	−	0.423452i
$590$	2.99279e10	−	8.95951e10i	0.246984	−	0.739395i
$591$	−3.19134e10	+	4.39250e10i	−0.261591	+	0.360049i
$592$	−1.20339e11	+	8.33968e10i	−0.979760	+	0.678989i
$593$	−1.07772e10			−0.0871537			−0.0435768	−	0.999050i	$-0.513875\pi$
$593$	−1.07772e10			−0.0871537			−0.0435768	+	0.999050i	$0.513875\pi$
$594$	9.56243e9	−	9.45642e9i	0.0768109	−	0.0759593i
$595$	−1.48630e10	+	2.89803e10i	−0.118588	+	0.231225i
$596$	−1.27157e11	−	1.79184e11i	−1.00776	−	1.42009i
$597$	9.14771e9	−	2.81538e10i	0.0720137	−	0.221635i
$598$	−6.20430e9	+	1.20107e10i	−0.0485164	+	0.0939209i
$599$		−	5.81919e10i		−	0.452018i	−0.974125	−	0.226009i	$-0.927432\pi$
$599$		−	5.81919e10i		−	0.452018i	0.974125	−	0.226009i	$-0.0725678\pi$
$600$	−3.95994e10	−	7.16902e9i	−0.305551	−	0.0553165i
$601$	−1.58431e11			−1.21434			−0.607172	−	0.794570i	$-0.707696\pi$
$601$	−1.58431e11			−1.21434			−0.607172	+	0.794570i	$0.707696\pi$
$602$	−8.90345e9	−	4.59922e9i	−0.0677910	−	0.0350186i
$603$	−9.52849e10	−	3.09599e10i	−0.720700	−	0.234170i
$604$	1.22251e10	−	8.67548e9i	0.0918552	−	0.0651847i
$605$	−5.84858e10	−	1.15540e11i	−0.436545	−	0.862406i
$606$	−2.73988e10	−	2.77060e10i	−0.203161	−	0.205439i
$607$			1.13850e11i			0.838648i	0.907837	+	0.419324i	$0.137733\pi$
$607$			1.13850e11i			0.838648i	−0.907837	+	0.419324i	$0.862267\pi$
$608$	−3.81942e10	+	7.00624e10i	−0.279501	+	0.512708i
$609$	−2.07226e10	−	1.50558e10i	−0.150652	−	0.109455i
$610$	1.19589e10	−	1.61786e10i	0.0863719	−	0.116848i
$611$	2.95213e9	+	4.06326e9i	0.0211822	+	0.0291548i
$612$	−2.53361e10	+	7.92106e9i	−0.180607	+	0.0564648i
$613$	3.67488e10	+	2.66996e10i	0.260256	+	0.189087i	0.710260	−	0.703939i	$-0.248577\pi$
$613$	3.67488e10	+	2.66996e10i	0.260256	+	0.189087i	−0.450004	+	0.893027i	$0.648577\pi$
$614$	−2.78431e10	+	5.39002e10i	−0.195904	+	0.379243i
$615$	4.48378e10	+	7.22339e9i	0.313432	+	0.0504941i
$616$	2.26997e10	+	2.34718e10i	0.157651	+	0.163013i
$617$	4.42547e10	+	1.36202e11i	0.305364	+	0.939815i	0.979541	+	0.201245i	$0.0644986\pi$
$617$	4.42547e10	+	1.36202e11i	0.305364	+	0.939815i	−0.674177	+	0.738570i	$0.735501\pi$
$618$	−5.93215e8	−	1.18047e9i	−0.00406685	−	0.00809284i
$619$	−2.37811e11	+	7.72694e10i	−1.61983	+	0.526314i	−0.971901	−	0.235389i	$-0.924364\pi$
$619$	−2.37811e11	+	7.72694e10i	−1.61983	+	0.526314i	−0.647927	+	0.761703i	$0.724364\pi$
$620$	−1.80430e11	+	2.60309e10i	−1.22107	+	0.176166i
$621$	9.17959e9	−	2.82519e10i	0.0617244	−	0.189968i
$622$	−3.76702e10	−	2.46734e11i	−0.251673	−	1.64842i
$623$	−1.78252e11	−	2.45343e11i	−1.18327	−	1.62862i
$624$	1.41048e10	−	4.23768e9i	0.0930309	−	0.0279505i
$625$	−1.52579e11	−	1.61655e9i	−0.999944	−	0.0105942i
$626$	−9.14309e10	−	1.81943e11i	−0.595382	−	1.18478i
$627$	3.01037e9	+	4.14342e9i	0.0194782	+	0.0268095i
$628$	7.47638e10	+	1.05354e11i	0.480676	+	0.677346i
$629$	1.20752e10	−	3.71636e10i	0.0771421	−	0.237419i
$630$	5.59594e10	−	1.67526e11i	0.355231	−	1.06346i
$631$	1.70625e11	−	5.54394e10i	1.07628	−	0.349704i	0.283349	−	0.959017i	$-0.408555\pi$
$631$	1.70625e11	−	5.54394e10i	1.07628	−	0.349704i	0.792930	+	0.609313i	$0.208555\pi$
$632$	−3.86630e10	+	2.20211e11i	−0.242341	+	1.38029i
$633$	1.75173e10	+	5.39126e10i	0.109107	+	0.335796i
$634$	−1.55126e10	+	9.45294e10i	−0.0960124	+	0.585073i
$635$	−1.15362e11	−	1.85848e10i	−0.709524	−	0.114305i
$636$	−4.40853e10	−	4.91476e8i	−0.269442	−	0.00300382i
$637$	2.24909e10	+	1.63406e10i	0.136599	+	0.0992453i
$638$	1.44408e10	+	2.36978e9i	0.0871583	+	0.0143030i
$639$	1.12710e11	+	1.55132e11i	0.676017	+	0.930458i
$640$	1.39720e11	−	9.28747e10i	0.832798	−	0.553576i
$641$	1.31921e11	+	9.58461e10i	0.781415	+	0.567731i	0.905403	−	0.424553i	$-0.139569\pi$
$641$	1.31921e11	+	9.58461e10i	0.781415	+	0.567731i	−0.123989	+	0.992284i	$0.539569\pi$
$642$	2.71529e10	−	2.68519e10i	0.159837	−	0.158065i
$643$		−	3.04362e11i		−	1.78052i	−0.455454	−	0.890259i	$-0.650523\pi$
$643$		−	3.04362e11i		−	1.78052i	0.455454	−	0.890259i	$-0.349477\pi$
$644$	6.83419e10	+	2.30510e10i	0.397323	+	0.134013i
$645$	1.49251e9	+	2.94850e9i	0.00862340	+	0.0170358i
$646$	−3.21430e9	−	2.10531e10i	−0.0184568	−	0.120889i
$647$	5.08883e10	+	1.65346e10i	0.290403	+	0.0943575i	0.450596	−	0.892728i	$-0.351212\pi$
$647$	5.08883e10	+	1.65346e10i	0.290403	+	0.0943575i	−0.160193	+	0.987086i	$0.551212\pi$
$648$	1.14066e11	−	5.57372e10i	0.646930	−	0.316115i
$649$	2.52754e10			0.142469
$650$	5.00281e10	−	2.48093e10i	0.280260	−	0.138983i
$651$			8.53786e10i			0.475363i
$652$	8.70700e10	+	9.70683e8i	0.481812	+	0.00537140i
$653$	1.76184e10	−	5.42240e10i	0.0968980	−	0.298221i	−0.890846	−	0.454306i	$-0.849887\pi$
$653$	1.76184e10	−	5.42240e10i	0.0968980	−	0.298221i	0.987744	+	0.156085i	$0.0498873\pi$
$654$	9.59531e9	+	6.28477e10i	0.0524503	+	0.343541i
$655$	−5.97660e10	+	1.16533e11i	−0.324705	+	0.633119i
$656$	−1.55620e11	+	1.07847e11i	−0.840330	+	0.582362i
$657$	1.78193e11			0.956375
$658$	1.90531e10	−	1.88419e10i	0.101639	−	0.100513i
$659$	−1.83069e11	+	2.51973e11i	−0.970672	+	1.33602i	−0.0289657	+	0.999580i	$0.509221\pi$
$659$	−1.83069e11	+	2.51973e11i	−0.970672	+	1.33602i	−0.941707	+	0.336435i	$0.890779\pi$
$660$	−1.53760e9	−	1.06577e10i	−0.00810341	−	0.0561676i
$661$	−8.86777e10	+	6.44281e10i	−0.464525	+	0.337497i	−0.795304	−	0.606211i	$-0.792689\pi$
$661$	−8.86777e10	+	6.44281e10i	−0.464525	+	0.337497i	0.330779	+	0.943708i	$0.392689\pi$
$662$	−7.95197e10	−	1.30494e10i	−0.414040	−	0.0679454i
$663$	−2.31039e9	+	3.17998e9i	−0.0119572	+	0.0164577i
$664$	1.53820e11	+	3.14794e11i	0.791300	+	1.61940i
$665$	1.26088e11	+	6.46664e10i	0.644745	+	0.330668i
$666$	−3.43163e10	+	2.09114e11i	−0.174423	+	1.06288i
$667$	3.07421e10	−	9.98870e9i	0.155321	−	0.0504668i
$668$	−2.21638e11	−	1.64835e11i	−1.11311	−	0.827837i
$669$	2.72774e10	+	8.39512e10i	0.136175	+	0.419105i
$670$	−1.37534e11	+	9.82070e10i	−0.682515	+	0.487353i
$671$	5.11976e9	+	1.66351e9i	0.0252557	+	0.00820608i
$672$	−3.37078e10	−	7.09783e10i	−0.165293	−	0.348055i
$673$	−1.10494e10	+	8.02786e9i	−0.0538615	+	0.0391327i	−0.614390	−	0.789002i	$-0.710598\pi$
$673$	−1.10494e10	+	8.02786e9i	−0.0538615	+	0.0391327i	0.560529	+	0.828135i	$0.310598\pi$
$674$	8.23624e10	+	1.63897e11i	0.399107	+	0.794205i
$675$	−9.96535e10	+	7.15991e10i	−0.480040	+	0.344899i
$676$	1.12426e11	−	1.51168e11i	0.538367	−	0.723889i
$677$	−1.41619e11	+	1.02893e11i	−0.674168	+	0.489812i	−0.871418	−	0.490541i	$-0.836799\pi$
$677$	−1.41619e11	+	1.02893e11i	−0.674168	+	0.489812i	0.197250	+	0.980353i	$0.436799\pi$
$678$	9.81326e9	+	6.42752e10i	0.0464402	+	0.304176i
$679$	−2.59147e11	−	8.42019e10i	−1.21918	−	0.396135i
$680$	−1.46591e10	+	4.23094e10i	−0.0685601	+	0.197880i
$681$	−6.03752e9	−	1.85816e10i	−0.0280718	−	0.0863960i
$682$	−2.19022e10	−	4.35843e10i	−0.101239	−	0.201462i
$683$	1.16477e11	−	3.78457e10i	0.535251	−	0.173914i	−0.0289043	−	0.999582i	$-0.509202\pi$
$683$	1.16477e11	−	3.78457e10i	0.535251	−	0.173914i	0.564156	+	0.825669i	$0.309202\pi$
$684$	3.44631e10	+	1.10233e11i	0.157445	+	0.503601i
$685$	1.10872e11	−	1.72595e10i	0.503570	−	0.0783910i
$686$	−5.80481e10	+	1.12373e11i	−0.262115	+	0.507418i
$687$	2.30445e10	−	3.17181e10i	0.103452	−	0.142390i
$688$	−1.30048e10	−	4.54847e9i	−0.0580430	−	0.0203007i
$689$	4.94932e10	−	3.59589e10i	0.219619	−	0.159562i
$690$	−1.38217e10	−	1.93566e10i	−0.0609768	−	0.0853952i
$691$	1.47645e11	−	2.03216e11i	0.647601	−	0.891346i	−0.351392	−	0.936229i	$-0.614291\pi$
$691$	1.47645e11	−	2.03216e11i	0.647601	−	0.891346i	0.998992	+	0.0448828i	$0.0142914\pi$
$692$	−9.19125e10	−	3.10011e10i	−0.400821	−	0.135193i
$693$	4.72602e10			0.204910
$694$	1.93642e11	+	1.95813e11i	0.834761	+	0.844119i
$695$	2.47248e11	+	3.98319e10i	1.05973	+	0.170723i
$696$	−3.11053e10	−	1.65098e10i	−0.132555	−	0.0703566i
$697$	1.56154e10	−	4.80592e10i	0.0661640	−	0.203632i
$698$	−1.40633e11	−	7.26462e10i	−0.592468	−	0.306049i
$699$			1.63391e10i			0.0684415i
$700$	−1.71132e11	−	2.43878e11i	−0.712754	−	1.01574i
$701$	−2.98200e11			−1.23491			−0.617455	−	0.786606i	$-0.711836\pi$
$701$	−2.98200e11			−1.23491			−0.617455	+	0.786606i	$0.711836\pi$
$702$	2.06100e10	−	3.98980e10i	0.0848651	−	0.164287i
$703$	−1.61692e11	−	5.25370e10i	−0.662015	−	0.215102i
$704$	3.54153e10	+	2.75861e10i	0.144178	+	0.112305i
$705$	−8.73152e9	+	1.35924e9i	−0.0353454	+	0.00550224i
$706$	−1.65177e11	+	1.63346e11i	−0.664862	+	0.657492i
$707$		−	2.88473e11i		−	1.15459i
$708$	−5.76328e10	−	1.94390e10i	−0.229370	−	0.0773642i
$709$	−5.31939e10	−	3.86477e10i	−0.210512	−	0.152946i	0.477533	−	0.878614i	$-0.341531\pi$
$709$	−5.31939e10	−	3.86477e10i	−0.210512	−	0.152946i	−0.688045	+	0.725668i	$0.741531\pi$
$710$	3.23439e11	+	2.65955e9i	1.27280	+	0.0104658i
$711$	1.90207e11	+	2.61797e11i	0.744299	+	1.02444i
$712$	−2.89841e11	−	2.99700e11i	−1.12782	−	1.16618i
$713$	−8.71659e10	−	6.33298e10i	−0.337279	−	0.245047i
$714$	1.86321e10	+	9.62471e9i	0.0716916	+	0.0370335i
$715$	1.05374e10	+	1.05934e10i	0.0403191	+	0.0405332i
$716$	−1.83464e8	−	5.86823e8i	−0.000698068	−	0.00223283i
$717$	−3.24914e10	−	9.99984e10i	−0.122940	−	0.378370i
$718$	−1.21468e11	+	6.10404e10i	−0.457049	+	0.229678i
$719$	−2.15612e11	+	7.00564e10i	−0.806782	+	0.262139i	−0.683234	−	0.730199i	$-0.739427\pi$
$719$	−2.15612e11	+	7.00564e10i	−0.806782	+	0.262139i	−0.123548	+	0.992339i	$0.539427\pi$
$720$	4.39565e10	−	2.38815e11i	0.163566	−	0.888651i
$721$	3.02242e9	−	9.30206e9i	0.0111844	−	0.0344222i
$722$	1.77026e11	−	2.70275e10i	0.651460	−	0.0994621i
$723$	1.89092e10	+	2.60263e10i	0.0692023	+	0.0952488i
$724$	2.76550e11	−	3.71849e11i	1.00651	−	1.35336i
$725$	−1.26768e11	−	4.19332e10i	−0.458837	−	0.151777i
$726$	−7.45051e10	+	3.74406e10i	−0.268188	+	0.134771i
$727$	1.59372e11	+	2.19356e11i	0.570524	+	0.785259i	0.992617	−	0.121294i	$-0.0387043\pi$
$727$	1.59372e11	+	2.19356e11i	0.570524	+	0.785259i	−0.422093	+	0.906553i	$0.638704\pi$
$728$	9.63073e10	+	5.11172e10i	0.342873	+	0.181987i
$729$	4.07629e10	−	1.25455e11i	0.144329	−	0.444200i
$730$	1.78667e11	−	2.41710e11i	0.629149	−	0.851144i
$731$	3.49707e9	−	1.13627e9i	0.0122471	−	0.00397934i
$732$	−1.03947e10	−	7.73067e9i	−0.0362048	−	0.0269261i
$733$	−1.40103e11	−	4.31193e11i	−0.485324	−	1.49367i	−0.831511	−	0.555508i	$-0.812524\pi$
$733$	−1.40103e11	−	4.31193e11i	−0.485324	−	1.49367i	0.346187	−	0.938165i	$-0.387476\pi$
$734$	3.24158e11	+	5.31954e10i	1.11679	+	0.183269i
$735$	−4.36402e10	+	2.20904e10i	−0.149533	+	0.0756926i
$736$	9.74670e10	+	1.82348e10i	0.332159	+	0.0621428i
$737$	−3.65833e10	−	2.65793e10i	−0.123997	−	0.0900894i
$738$	−4.43771e10	+	2.70422e11i	−0.149601	+	0.911624i
$739$	−8.21413e10	−	1.13058e11i	−0.275413	−	0.379073i	0.648795	−	0.760963i	$-0.275273\pi$
$739$	−8.21413e10	−	1.13058e11i	−0.275413	−	0.379073i	−0.924208	+	0.381890i	$0.875273\pi$
$740$	2.49245e11	+	2.56219e11i	0.831190	+	0.854447i
$741$	1.38355e10	+	1.00521e10i	0.0458904	+	0.0333414i
$742$	−2.29507e11	−	2.32079e11i	−0.757146	−	0.765634i
$743$		−	3.20508e11i		−	1.05168i	−0.850584	−	0.525840i	$-0.823751\pi$
$743$		−	3.20508e11i		−	1.05168i	0.850584	−	0.525840i	$-0.176249\pi$
$744$	1.64211e10	+	1.16225e11i	0.0535934	+	0.379323i
$745$	−3.80310e11	+	3.78301e11i	−1.23456	+	1.22804i
$746$	−5.57122e11	+	8.50589e10i	−1.79885	+	0.274640i
$747$	4.82284e11	+	1.56704e11i	1.54889	+	0.503265i
$748$	−1.19804e10	−	1.33561e8i	−0.0382705	−	0.000426652i
$749$	2.82715e11			0.898299
$750$	−1.32827e9	+	9.82409e10i	−0.00419800	+	0.310490i
$751$			3.58573e11i			1.12724i	0.826033	+	0.563621i	$0.190592\pi$
$751$			3.58573e11i			1.12724i	−0.826033	+	0.563621i	$0.809408\pi$
$752$	2.23130e10	−	2.93139e10i	0.0697727	−	0.0916646i
$753$	4.15659e10	−	1.27927e11i	0.129288	−	0.397906i
$754$	4.83053e10	−	7.37504e9i	0.149455	−	0.0228181i
$755$	−2.58101e10	−	2.59472e10i	−0.0794331	−	0.0798550i
$756$	−2.27024e11	−	7.65729e10i	−0.695000	−	0.234416i
$757$	6.53419e10			0.198979			0.0994897	−	0.995039i	$-0.468279\pi$
$757$	6.53419e10			0.198979			0.0994897	+	0.995039i	$0.468279\pi$
$758$	2.14399e11	+	2.16803e11i	0.649452	+	0.656732i
$759$	3.74078e9	−	5.14874e9i	0.0112718	−	0.0155144i
$760$	1.84081e11	+	6.37790e10i	0.551764	+	0.191172i
$761$	−4.52282e11	+	3.28602e11i	−1.34856	+	0.979786i	−0.349478	+	0.936945i	$0.613641\pi$
$761$	−4.52282e11	+	3.28602e11i	−1.34856	+	0.979786i	−0.999082	+	0.0428416i	$0.986359\pi$
$762$	−1.21838e10	+	7.42450e10i	−0.0361380	+	0.220215i
$763$	−2.76653e11	+	3.80780e11i	−0.816276	+	1.12351i
$764$	4.09371e11	+	4.56380e9i	1.20156	+	0.0133953i
$765$	2.92693e10	+	5.78223e10i	0.0854607	+	0.168830i
$766$	6.01834e11	+	9.87629e10i	1.74808	+	0.286866i
$767$	8.02677e10	−	2.60805e10i	0.231931	−	0.0753590i
$768$	−5.95377e10	−	9.01392e10i	−0.171138	−	0.259101i
$769$	−7.79853e10	−	2.40014e11i	−0.223001	−	0.686328i	−0.998488	−	0.0549640i	$-0.982496\pi$
$769$	−7.79853e10	−	2.40014e11i	−0.223001	−	0.686328i	0.775487	−	0.631364i	$-0.217504\pi$
$770$	4.73861e10	−	6.41062e10i	0.134799	−	0.182363i
$771$	2.66803e10	+	8.66895e9i	0.0755045	+	0.0245329i
$772$	1.51336e11	+	2.13256e11i	0.426063	+	0.600388i
$773$	4.86746e11	−	3.53642e11i	1.36328	−	0.990479i	0.365049	−	0.930988i	$-0.381052\pi$
$773$	4.86746e11	−	3.53642e11i	1.36328	−	0.990479i	0.998229	−	0.0594910i	$-0.0189478\pi$
$774$	−1.78174e10	+	8.95369e9i	−0.0496457	+	0.0249481i
$775$	1.35288e11	+	4.24002e11i	0.375018	+	1.17533i
$776$	−3.68970e11	−	6.47811e10i	−1.01752	−	0.178649i
$777$	1.35439e11	−	9.84020e10i	0.371585	−	0.269973i
$778$	5.27010e11	−	8.04616e10i	1.43847	−	0.219619i
$779$	−2.09097e11	−	6.79397e10i	−0.567803	−	0.184491i
$780$	−1.58802e10	−	3.22592e10i	−0.0429019	−	0.0871516i
$781$	2.67444e10	+	8.23107e10i	0.0718833	+	0.221234i
$782$	−2.36466e10	+	1.18830e10i	−0.0632327	+	0.0317759i
$783$	−1.02122e11	+	3.31813e10i	−0.271688	+	0.0882768i
$784$	6.73211e10	−	1.92482e11i	0.178191	−	0.509478i
$785$	2.23608e11	−	2.22427e11i	0.588856	−	0.585744i
$786$	7.49218e10	+	3.87021e10i	0.196299	+	0.101402i
$787$	−1.28274e10	+	1.76554e10i	−0.0334380	+	0.0460234i	−0.825409	−	0.564536i	$-0.809055\pi$
$787$	−1.28274e10	+	1.76554e10i	−0.0334380	+	0.0460234i	0.791971	+	0.610559i	$0.209055\pi$
$788$	−5.27438e11	+	1.64898e11i	−1.36794	+	0.427671i
$789$	8.06200e10	−	5.85738e10i	0.208034	−	0.151146i
$790$	5.45829e11	+	4.48820e9i	1.40135	+	0.0115229i
$791$	−2.82937e11	+	3.89429e11i	−0.722742	+	0.994770i
$792$	6.43350e10	−	9.08969e9i	0.163511	−	0.0231019i
$793$	1.79755e10			0.0454556
$794$	5.16155e11	−	5.10432e11i	1.29867	−	1.28427i
$795$	1.65565e10	+	1.06356e11i	0.0414475	+	0.266252i
$796$	2.45715e11	−	1.74371e11i	0.612040	−	0.434332i
$797$	3.44524e10	−	1.06034e11i	0.0853859	−	0.262791i	−0.899243	−	0.437449i	$-0.855882\pi$
$797$	3.44524e10	−	1.06034e11i	0.0853859	−	0.262791i	0.984629	+	0.174658i	$0.0558821\pi$
$798$	4.18754e10	−	8.10648e10i	0.103264	−	0.199904i
$799$			9.83223e9i			0.0241249i
$800$	−2.79867e11	−	2.99076e11i	−0.683270	−	0.730166i
$801$	−6.03442e11			−1.46590
$802$	6.19031e11	+	3.19770e11i	1.49629	+	0.772931i
$803$	7.64898e10	+	2.48530e10i	0.183968	+	0.0597747i
$804$	6.29752e10	+	8.87417e10i	0.150711	+	0.212375i
$805$	2.80064e10	−	1.73844e11i	0.0666920	−	0.413977i
$806$	−1.14528e11	−	1.15812e11i	−0.271376	−	0.274418i
$807$			2.13284e10i			0.0502881i
$808$	−5.54829e10	−	3.92697e11i	−0.130171	−	0.921322i
$809$	2.16456e11	+	1.57264e11i	0.505330	+	0.367144i	0.811049	−	0.584978i	$-0.198897\pi$
$809$	2.16456e11	+	1.57264e11i	0.505330	+	0.367144i	−0.305719	+	0.952122i	$0.598897\pi$
$810$	−1.80116e11	−	2.52245e11i	−0.418420	−	0.585979i
$811$	−2.76061e11	−	3.79965e11i	−0.638147	−	0.878334i	0.360368	−	0.932810i	$-0.382651\pi$
$811$	−2.76061e11	−	3.79965e11i	−0.638147	−	0.878334i	−0.998515	+	0.0544760i	$0.982651\pi$
$812$	−7.77942e10	−	2.48831e11i	−0.178946	−	0.572374i
$813$	1.19964e11	+	8.71591e10i	0.274593	+	0.199503i
$814$	−4.38961e10	+	8.49766e10i	−0.0999834	+	0.193554i
$815$	−3.26996e10	−	2.10056e11i	−0.0741160	−	0.476108i
$816$	2.72149e10	+	9.51850e9i	0.0613827	+	0.0214688i
$817$	−4.94369e9	−	1.52151e10i	−0.0110959	−	0.0341497i
$818$	1.17018e11	+	2.32861e11i	0.261361	+	0.520096i
$819$	1.50085e11	−	4.87656e10i	0.333582	−	0.108387i
$820$	3.22319e11	+	3.31338e11i	0.712903	+	0.732850i
$821$	2.35145e11	−	7.23703e11i	0.517564	−	1.59290i	−0.261005	−	0.965338i	$-0.584054\pi$
$821$	2.35145e11	−	7.23703e11i	0.517564	−	1.59290i	0.778568	−	0.627560i	$-0.215946\pi$
$822$	−1.09044e10	−	7.14217e10i	−0.0238843	−	0.156438i
$823$	−4.57837e11	−	6.30158e11i	−0.997955	−	1.37357i	−0.926571	−	0.376119i	$-0.877258\pi$
$823$	−4.57837e11	−	6.30158e11i	−0.997955	−	1.37357i	−0.0713839	−	0.997449i	$-0.522742\pi$
$824$	2.32531e9	−	1.32442e10i	0.00504397	−	0.0287287i
$825$	−2.50451e10	+	7.99122e9i	−0.0540638	+	0.0172503i
$826$	−2.02187e11	−	4.02343e11i	−0.434343	−	0.864323i
$827$	−3.06625e10	−	4.22033e10i	−0.0655519	−	0.0902244i	0.774982	−	0.631983i	$-0.217759\pi$
$827$	−3.06625e10	−	4.22033e10i	−0.0655519	−	0.0902244i	−0.840534	+	0.541759i	$0.817759\pi$
$828$	1.17041e11	−	8.30577e10i	0.249010	−	0.176709i
$829$	1.78666e11	−	5.49878e11i	0.378290	−	1.16426i	−0.562943	−	0.826496i	$-0.690331\pi$
$829$	1.78666e11	−	5.49878e11i	0.378290	−	1.16426i	0.941232	−	0.337760i	$-0.109669\pi$
$830$	6.96131e11	−	4.97075e11i	1.46683	−	1.04739i
$831$	1.70297e10	−	5.53330e9i	0.0357112	−	0.0116033i
$832$	1.40934e11	+	5.10625e10i	0.294119	+	0.106563i
$833$	1.68177e10	+	5.17595e10i	0.0349290	+	0.107500i
$834$	2.61130e10	−	1.59125e11i	0.0539749	−	0.328908i
$835$	−3.07739e11	+	6.00037e11i	−0.633048	+	1.23433i
$836$	−5.81100e8	+	5.21245e10i	−0.00118967	+	0.106713i
$837$	2.89555e11	+	2.10374e11i	0.589970	+	0.428638i
$838$	5.88414e11	+	9.65606e10i	1.19318	+	0.195805i
$839$	−3.03165e11	−	4.17270e11i	−0.611830	−	0.842111i	0.384897	−	0.922960i	$-0.374237\pi$
$839$	−3.03165e11	−	4.17270e11i	−0.611830	−	0.842111i	−0.996726	+	0.0808483i	$0.974237\pi$
$840$	−1.57353e11	+	1.09731e11i	−0.316051	+	0.220399i
$841$	3.10181e11	+	2.25360e11i	0.620057	+	0.450497i
$842$	−2.30191e10	+	2.27639e10i	−0.0457973	+	0.0452896i
$843$		−	1.79669e11i		−	0.355765i
$844$	−1.84399e11	+	5.46708e11i	−0.363403	+	1.07742i
$845$	−4.09254e11	−	2.09892e11i	−0.802724	−	0.411690i
$846$	−8.04747e9	−	5.27096e10i	−0.0157101	−	0.102898i
$847$	−5.87098e11	−	1.90760e11i	−1.14071	−	0.370641i
$848$	−3.57062e11	−	2.71787e11i	−0.690495	−	0.525587i
$849$	−8.46801e9			−0.0162986
$850$	1.07781e11	+	1.82740e10i	0.206474	+	0.0350072i
$851$			2.11264e11i			0.402816i
$852$	2.32167e9	−	2.08253e11i	0.00440598	−	0.395215i
$853$	−1.11735e11	+	3.43886e11i	−0.211054	+	0.649558i	0.788356	+	0.615219i	$0.210932\pi$
$853$	−1.11735e11	+	3.43886e11i	−0.211054	+	0.649558i	−0.999410	+	0.0343386i	$0.989068\pi$
$854$	−1.44745e10	−	9.48053e10i	−0.0272127	−	0.178238i
$855$	2.51575e11	−	1.27345e11i	0.470763	−	0.238297i
$856$	3.84858e11	−	5.43754e10i	0.716812	−	0.101276i
$857$	−1.03972e12			−1.92749			−0.963746	−	0.266821i	$-0.914027\pi$
$857$	−1.03972e12			−1.92749			−0.963746	+	0.266821i	$0.914027\pi$
$858$	6.84081e9	−	6.76497e9i	0.0126229	−	0.0124829i
$859$	−2.63350e11	+	3.62471e11i	−0.483684	+	0.665733i	−0.979208	−	0.202861i	$-0.934976\pi$
$859$	−2.63350e11	+	3.62471e11i	−0.483684	+	0.665733i	0.495524	+	0.868594i	$0.334976\pi$
$860$	−5.71965e9	+	3.31461e10i	−0.0104562	+	0.0605952i
$861$	1.75146e11	−	1.27251e11i	0.318705	−	0.231553i
$862$	−2.24640e11	−	3.68641e10i	−0.406871	−	0.0667690i
$863$	−7.02512e10	+	9.66925e10i	−0.126652	+	0.174321i	−0.867634	−	0.497204i	$-0.834360\pi$
$863$	−7.02512e10	+	9.66925e10i	−0.126652	+	0.174321i	0.740982	+	0.671525i	$0.234360\pi$
$864$	−3.23774e11	−	6.05740e10i	−0.581015	−	0.108701i
$865$	−3.76656e10	+	2.33801e11i	−0.0672791	+	0.417621i
$866$	−3.82293e10	+	2.32959e11i	−0.0679711	+	0.414197i
$867$	1.59548e11	−	5.18404e10i	0.282368	−	0.0917471i
$868$	−5.18587e11	+	6.97293e11i	−0.913573	+	1.22839i
$869$	4.51333e10	+	1.38906e11i	0.0791439	+	0.243580i
$870$	−2.72391e10	+	8.15456e10i	−0.0475461	+	0.142339i
$871$	−1.43604e11	−	4.66599e10i	−0.249514	−	0.0810721i
$872$	−3.03370e11	+	5.71563e11i	−0.524694	+	0.988550i
$873$	−4.38649e11	+	3.18697e11i	−0.755197	+	0.548683i
$874$	5.17007e10	+	1.02882e11i	0.0886035	+	0.176317i
$875$	−5.18399e11	+	5.10226e11i	−0.884367	+	0.870423i
$876$	−1.55297e11	−	1.15497e11i	−0.263723	−	0.196135i
$877$	4.92028e11	−	3.57479e11i	0.831747	−	0.604299i	−0.0883061	−	0.996093i	$-0.528145\pi$
$877$	4.92028e11	−	3.57479e11i	0.831747	−	0.604299i	0.920053	+	0.391794i	$0.128145\pi$
$878$	1.47651e11	+	9.67088e11i	0.248461	+	1.62738i
$879$	1.22044e11	+	3.96545e10i	0.204437	+	0.0664257i
$880$	5.21767e10	−	9.63813e10i	0.0870053	−	0.160717i
$881$	1.81024e11	+	5.57134e11i	0.300491	+	0.924817i	0.981321	+	0.192376i	$0.0616192\pi$
$881$	1.81024e11	+	5.57134e11i	0.300491	+	0.924817i	−0.680830	+	0.732441i	$0.738381\pi$
$882$	−1.32522e11	−	2.63713e11i	−0.218985	−	0.435769i
$883$	3.78994e11	−	1.23143e11i	0.623432	−	0.202565i	0.0197686	−	0.999805i	$-0.493707\pi$
$883$	3.78994e11	−	1.23143e11i	0.623432	−	0.202565i	0.603664	+	0.797239i	$0.293707\pi$
$884$	−3.81842e10	+	1.19379e10i	−0.0625281	+	0.0195487i
$885$	−2.36178e10	+	1.46603e11i	−0.0385005	+	0.238984i
$886$	3.03719e11	−	5.87957e11i	0.492876	−	0.954138i
$887$	2.34632e11	−	3.22943e11i	0.379046	−	0.521712i	−0.576285	−	0.817249i	$-0.695498\pi$
$887$	2.34632e11	−	3.22943e11i	0.379046	−	0.521712i	0.955332	+	0.295536i	$0.0954983\pi$
$888$	1.65446e11	−	1.60003e11i	0.266075	−	0.257322i
$889$	−4.50629e11	+	3.27401e11i	−0.721460	+	0.524171i
$890$	−6.05050e11	+	8.18541e11i	−0.964342	+	1.30461i
$891$	4.87477e10	−	6.70955e10i	0.0773470	−	0.106459i
$892$	−2.87141e11	+	8.51318e11i	−0.453561	+	1.34472i
$893$	4.27782e10			0.0672693
$894$	2.42867e11	+	2.45589e11i	0.380205	+	0.384467i
$895$	−1.33925e9	+	6.77921e8i	−0.00208723	+	0.00105654i
$896$	1.55826e11	−	7.84425e11i	0.241773	−	1.21708i
$897$	6.56693e9	−	2.02109e10i	0.0101436	−	0.0312188i
$898$	5.08884e11	+	2.62872e11i	0.782552	+	0.404240i
$899$			3.89457e11i			0.596240i
$900$	−5.92758e11	−	9.74882e9i	−0.903456	−	0.0148587i
$901$	1.19763e11			0.181729
$902$	−5.67655e10	+	1.09890e11i	−0.0857548	+	0.166009i
$903$	1.49823e10	+	4.86803e9i	0.0225334	+	0.00732154i
$904$	−3.10260e11	+	5.84546e11i	−0.464571	+	0.875276i
$905$	−1.00670e12	−	5.16304e11i	−1.50074	−	0.769681i
$906$	−1.67557e10	+	1.65699e10i	−0.0248685	+	0.0245928i
$907$		−	7.43208e11i		−	1.09820i	−0.835757	−	0.549100i	$-0.814971\pi$
$907$		−	7.43208e11i		−	1.09820i	0.835757	−	0.549100i	$-0.185029\pi$
$908$	6.35551e10	−	1.88429e11i	0.0934990	−	0.277207i
$909$	−4.64390e11	−	3.37399e11i	−0.680185	−	0.494183i
$910$	8.43368e10	−	2.52479e11i	0.122985	−	0.368180i
$911$	4.99846e11	+	6.87979e11i	0.725709	+	0.998853i	0.999315	+	0.0370108i	$0.0117836\pi$
$911$	4.99846e11	+	6.87979e11i	0.725709	+	0.998853i	−0.273606	+	0.961842i	$0.588216\pi$
$912$	4.14133e10	−	1.18407e11i	0.0598632	−	0.171158i
$913$	1.85166e11	+	1.34531e11i	0.266489	+	0.193615i
$914$	−3.88748e11	−	2.00814e11i	−0.557036	−	0.287746i
$915$	−1.44328e10	+	2.81414e10i	−0.0205904	+	0.0401477i
$916$	3.80861e11	−	1.19072e11i	0.540985	−	0.169133i
$917$	1.92919e11	+	5.93745e11i	0.272834	+	0.839697i
$918$	7.85513e10	−	3.94739e10i	0.110607	−	0.0555827i
$919$	−2.54991e11	+	8.28514e10i	−0.357488	+	0.116155i	−0.482255	−	0.876031i	$-0.660182\pi$
$919$	−2.54991e11	+	8.28514e10i	−0.357488	+	0.116155i	0.124766	+	0.992186i	$0.460182\pi$
$920$	4.68899e9	−	2.42040e11i	0.00654527	−	0.337859i
$921$	2.94704e10	−	9.07006e10i	0.0409588	−	0.126058i
$922$	−1.31336e12	+	2.00518e11i	−1.81743	+	0.277478i
$923$	1.69865e11	+	2.33800e11i	0.234044	+	0.322134i
$924$	−4.11879e10	−	3.06321e10i	−0.0565044	−	0.0420231i
$925$	5.16684e11	−	7.03289e11i	0.705761	−	0.960654i
$926$	−7.52719e11	+	3.78260e11i	−1.02374	+	0.514453i
$927$	−1.14396e10	−	1.57453e10i	−0.0154915	−	0.0213222i
$928$	−1.53759e11	−	3.23770e11i	−0.207324	−	0.436560i
$929$	−2.72545e11	+	8.38809e11i	−0.365912	+	1.12616i	0.583497	+	0.812115i	$0.301684\pi$
$929$	−2.72545e11	+	8.38809e11i	−0.365912	+	1.12616i	−0.949408	+	0.314044i	$0.898316\pi$
$930$	2.73265e11	−	8.63115e10i	0.365302	−	0.115382i
$931$	2.25196e11	−	7.31707e10i	0.299752	−	0.0973954i
$932$	−9.92433e10	+	1.33443e11i	−0.131534	+	0.176861i
$933$	1.21246e11	+	3.73156e11i	0.160007	+	0.492452i
$934$	−1.10496e12	−	1.81328e11i	−1.45198	−	0.238275i
$935$	4.49930e9	+	2.89027e10i	0.00588706	+	0.0378174i
$936$	1.94931e11	−	9.52507e10i	0.253967	−	0.124098i
$937$	5.08403e11	+	3.69376e11i	0.659553	+	0.479193i	0.866512	−	0.499156i	$-0.166357\pi$
$937$	5.08403e11	+	3.69376e11i	0.659553	+	0.479193i	−0.206959	+	0.978350i	$0.566357\pi$
$938$	−1.30456e11	+	7.94964e11i	−0.168521	+	1.02692i
$939$	1.88149e11	+	2.58964e11i	0.242013	+	0.333102i
$940$	−7.95670e10	−	4.19340e10i	−0.101911	−	0.0537100i
$941$	1.52284e11	+	1.10641e11i	0.194221	+	0.141110i	0.680646	−	0.732613i	$-0.261699\pi$
$941$	1.52284e11	+	1.10641e11i	0.194221	+	0.141110i	−0.486425	+	0.873722i	$0.661699\pi$
$942$	−1.42797e11	−	1.44397e11i	−0.181349	−	0.183382i
$943$			2.73202e11i			0.345491i
$944$	−3.52620e11	−	5.08820e11i	−0.444037	−	0.640731i
$945$	−9.30341e10	+	5.77491e11i	−0.116658	+	0.724132i
$946$	−8.89699e9	+	1.35835e9i	−0.0111091	+	0.00169609i
$947$	7.07205e11	+	2.29785e11i	0.879317	+	0.285707i	0.713674	−	0.700478i	$-0.247030\pi$
$947$	7.07205e11	+	2.29785e11i	0.879317	+	0.285707i	0.165643	+	0.986186i	$0.447030\pi$
$948$	3.91801e9	−	3.51444e11i	0.00485101	−	0.435134i
$949$	2.68555e11			0.331107
$950$	7.95068e10	−	4.68934e11i	0.0976134	−	0.575728i
$951$		−	1.50588e11i		−	0.184106i
$952$	9.37094e10	+	1.91777e11i	0.114087	+	0.233479i
$953$	−3.79555e11	+	1.16815e12i	−0.460154	+	1.41621i	0.404823	+	0.914395i	$0.367333\pi$
$953$	−3.79555e11	+	1.16815e12i	−0.460154	+	1.41621i	−0.864976	+	0.501813i	$0.832667\pi$
$954$	−6.42038e11	+	9.80236e10i	−0.775117	+	0.118341i
$955$	−1.53742e11	−	9.87609e11i	−0.184832	−	1.18733i
$956$	3.42028e11	−	1.01405e12i	0.409477	−	1.21402i
$957$	−2.30046e10			−0.0274262
$958$	4.80638e11	+	4.86026e11i	0.570632	+	0.577029i
$959$	3.14395e11	−	4.32728e11i	0.371708	−	0.511612i
$960$	−1.93099e11	+	1.79640e11i	−0.227350	+	0.211503i
$961$	3.60215e11	−	2.61712e11i	0.422346	−	0.306853i
$962$	−5.17183e10	+	3.15157e11i	−0.0603870	+	0.367982i
$963$	3.30664e11	−	4.55120e11i	0.384487	−	0.529201i
$964$	−3.65010e9	+	3.27413e11i	−0.00422666	+	0.379130i
$965$	4.52626e11	−	4.50234e11i	0.521951	−	0.519194i
$966$	−1.11883e11	−	1.83604e10i	−0.128486	−	0.0210850i
$967$	−1.39747e12	+	4.54064e11i	−1.59821	+	0.519291i	−0.966665	−	0.256044i	$-0.917581\pi$
$967$	−1.39747e12	+	4.54064e11i	−1.59821	+	0.519291i	−0.631550	+	0.775335i	$0.717581\pi$
$968$	−8.35902e11	−	1.46762e11i	−0.952038	−	0.167152i
$969$	1.03456e10	+	3.18404e10i	0.0117344	+	0.0361147i
$970$	−7.52011e9	+	9.14553e11i	−0.00849449	+	1.03305i
$971$	7.12341e11	+	2.31454e11i	0.801330	+	0.260368i	0.680921	−	0.732357i	$-0.261580\pi$
$971$	7.12341e11	+	2.31454e11i	0.801330	+	0.260368i	0.120408	+	0.992724i	$0.461580\pi$
$972$	−5.93042e11	+	4.20850e11i	−0.664386	+	0.471479i
$973$	9.65808e11	−	7.01700e11i	1.07755	−	0.782889i
$974$	−1.07638e12	+	5.40907e11i	−1.19600	+	0.601017i
$975$	−7.12905e10	+	5.12208e10i	−0.0788884	+	0.0566797i
$976$	−3.79382e10	−	1.26274e11i	−0.0418097	−	0.139160i
$977$	−1.28096e12	+	9.30672e11i	−1.40591	+	1.02145i	−0.412008	+	0.911180i	$0.635173\pi$
$977$	−1.28096e12	+	9.30672e11i	−1.40591	+	1.02145i	−0.993901	+	0.110273i	$0.964827\pi$
$978$	−1.35314e11	+	2.06592e10i	−0.147907	+	0.0225818i
$979$	−2.59030e11	−	8.41638e10i	−0.281980	−	0.0916209i
$980$	−4.90589e11	−	8.46555e10i	−0.531880	−	0.0917806i
$981$	2.89414e11	+	8.90724e11i	0.312495	+	0.961760i
$982$	6.73575e11	−	3.38488e11i	0.724336	−	0.363996i
$983$	2.41989e11	−	7.86271e10i	0.259168	−	0.0842089i	−0.176551	−	0.984292i	$-0.556494\pi$
$983$	2.41989e11	−	7.86271e10i	0.259168	−	0.0842089i	0.435719	+	0.900083i	$0.356494\pi$
$984$	2.13951e11	−	2.06913e11i	0.228210	−	0.220703i
$985$	6.09318e11	+	1.20372e12i	0.647290	+	1.27874i
$986$	8.49908e10	+	4.39034e10i	0.0899217	+	0.0464505i
$987$	−2.47596e10	+	3.40787e10i	−0.0260901	+	0.0359099i
$988$	5.19395e10	+	1.66133e11i	0.0545093	+	0.174352i
$989$	−1.60831e10	+	1.16850e10i	−0.0168106	+	0.0122136i
$990$	−4.77766e10	−	1.51262e11i	−0.0497364	−	0.157467i
$991$	7.51916e11	−	1.03492e12i	0.779605	−	1.07303i	−0.215721	−	0.976455i	$-0.569210\pi$
$991$	7.51916e11	−	1.03492e12i	0.779605	−	1.07303i	0.995325	−	0.0965788i	$-0.0307900\pi$
$992$	−5.71838e11	+	1.04896e12i	−0.590508	+	1.08321i
$993$	1.26677e11			0.130287
$994$	1.09631e12	−	1.08416e12i	1.12302	−	1.11057i
$995$	−5.18764e11	−	5.21519e11i	−0.529270	−	0.532081i
$996$	−3.18749e11	−	4.49166e11i	−0.323901	−	0.456425i
$997$	3.60361e11	−	1.10908e12i	0.364718	−	1.12249i	−0.585439	−	0.810716i	$-0.699078\pi$
$997$	3.60361e11	−	1.10908e12i	0.364718	−	1.12249i	0.950157	−	0.311771i	$-0.100922\pi$
$998$	4.04419e11	−	7.82898e11i	0.407671	−	0.789193i
$999$		−	7.01795e11i		−	0.704609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.18	✓	464
4.3	odd	2	inner	100.9.j.b.11.62	yes	464
25.16	even	5	inner	100.9.j.b.91.62	yes	464
100.91	odd	10	inner	100.9.j.b.91.18	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.18	✓	464	1.1	even	1	trivial
100.9.j.b.11.62	yes	464	4.3	odd	2	inner
100.9.j.b.91.18	yes	464	100.91	odd	10	inner
100.9.j.b.91.62	yes	464	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.2154 - 7.34320i) q^{2} +(23.9209 + 7.77239i) q^{3} +(148.155 + 208.773i) q^{4} +(443.111 - 440.770i) q^{5} +(-282.972 - 286.144i) q^{6} -2979.31i q^{7} +(-573.020 - 4055.72i) q^{8} +(-4796.16 - 3484.61i) q^{9} +(-9535.65 + 3011.87i) q^{10} +(-1572.76 - 2164.72i) q^{11} +(1921.34 + 6145.56i) q^{12} +(-7228.32 - 5251.68i) q^{13} +(-21877.7 + 42352.1i) q^{14} +(14025.5 - 7099.60i) q^{15} +(-21636.2 + 61861.5i) q^{16} +(-5405.02 - 16634.9i) q^{17} +(42591.1 + 84754.3i) q^{18} +(-72375.6 + 23516.2i) q^{19} +(157670. + 27207.3i) q^{20} +(23156.4 - 71267.9i) q^{21} +(6461.44 + 42321.4i) q^{22} +(55583.6 + 76504.3i) q^{23} +(17815.4 - 101470. i) q^{24} +(2069.22 - 390620. i) q^{25} +(64189.3 + 127734. i) q^{26} +(-184642. - 254139. i) q^{27} +(621999. - 441400. i) q^{28} +(105628. - 325091. i) q^{29} +(-251511. - 2068.11i) q^{30} +(-1.08360e6 + 352082. i) q^{31} +(761829. - 720506. i) q^{32} +(-20796.9 - 64006.1i) q^{33} +(-45319.1 + 276162. i) q^{34} +(-1.31319e6 - 1.32016e6i) q^{35} +(16918.4 - 1.51757e6i) q^{36} +(1.80740e6 + 1.31315e6i) q^{37} +(1.20153e6 + 197175. i) q^{38} +(-132090. - 181807. i) q^{39} +(-2.04155e6 - 1.54456e6i) q^{40} +(2.33729e6 + 1.69814e6i) q^{41} +(-852511. + 843060. i) q^{42} +210225. i q^{43} +(218922. - 649063. i) q^{44} +(-3.66114e6 + 569932. i) q^{45} +(-228357. - 1.49570e6i) q^{46} +(-534618. - 173708. i) q^{47} +(-998371. + 1.31162e6i) q^{48} -3.11150e6 q^{49} +(-2.89781e6 + 5.53762e6i) q^{50} -439933. i q^{51} +(25497.8 - 2.28714e6i) q^{52} +(-2.11588e6 + 6.51200e6i) q^{53} +(758576. + 4.96855e6i) q^{54} +(-1.65105e6 - 265985. i) q^{55} +(-1.20833e7 + 1.70721e6i) q^{56} -1.91407e6 q^{57} +(-3.88876e6 + 3.84565e6i) q^{58} +(-5.55230e6 + 7.64209e6i) q^{59} +(3.56014e6 + 1.87630e6i) q^{60} +(-1.62764e6 + 1.18255e6i) q^{61} +(1.79892e7 + 2.95208e6i) q^{62} +(-1.03817e7 + 1.42893e7i) q^{63} +(-1.61205e7 + 4.64802e6i) q^{64} +(-5.51773e6 + 858948. i) q^{65} +(-174374. + 1.06259e6i) q^{66} +(1.60727e7 - 5.22233e6i) q^{67} +(2.67214e6 - 3.59297e6i) q^{68} +(734992. + 2.26207e6i) q^{69} +(8.97329e6 + 2.84097e7i) q^{70} +(-3.07619e7 - 9.99514e6i) q^{71} +(-1.13843e7 + 2.14486e7i) q^{72} +(-2.43171e7 + 1.76674e7i) q^{73} +(-1.60502e7 - 3.19391e7i) q^{74} +(3.08554e6 - 9.32791e6i) q^{75} +(-1.56324e7 - 1.16260e7i) q^{76} +(-6.44936e6 + 4.68574e6i) q^{77} +(542673. + 3.55442e6i) q^{78} +(-5.19131e7 - 1.68676e7i) q^{79} +(1.76794e7 + 3.69481e7i) q^{80} +(9.57799e6 + 2.94780e7i) q^{81} +(-2.07558e7 - 4.13030e7i) q^{82} +(-8.13518e7 + 2.64328e7i) q^{83} +(1.83095e7 - 5.72428e6i) q^{84} +(-9.72719e6 - 4.98875e6i) q^{85} +(1.54372e6 - 2.98842e6i) q^{86} +(5.05347e6 - 6.95550e6i) q^{87} +(-7.87826e6 + 7.61909e6i) q^{88} +(8.23488e7 - 5.98299e7i) q^{89} +(5.62297e7 + 1.87827e7i) q^{90} +(-1.56464e7 + 2.15354e7i) q^{91} +(-7.73704e6 + 2.29388e7i) q^{92} -2.86572e7 q^{93} +(6.32424e6 + 6.39513e6i) q^{94} +(-2.17051e7 + 4.23213e7i) q^{95} +(2.38237e7 - 1.13140e7i) q^{96} +(2.82622e7 - 8.69821e7i) q^{97} +(4.42311e7 + 2.28483e7i) q^{98} +1.58628e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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