LMFDB - Embedded newform 51.7.f.a.38.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,7,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7327582646$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.5
Character	$\chi$	$=$	51.38
Dual form			51.7.f.a.47.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-12.6359 q^{2} +(-17.0115 + 20.9669i) q^{3} +95.6654 q^{4} +(152.781 + 152.781i) q^{5} +(214.955 - 264.935i) q^{6} +(-234.270 - 234.270i) q^{7} -400.120 q^{8} +(-150.221 - 713.355i) q^{9} +(-1930.52 - 1930.52i) q^{10} +(826.986 - 826.986i) q^{11} +(-1627.41 + 2005.81i) q^{12} +3295.33 q^{13} +(2960.21 + 2960.21i) q^{14} +(-5802.36 + 604.315i) q^{15} -1066.71 q^{16} +(4339.52 + 2303.50i) q^{17} +(1898.17 + 9013.86i) q^{18} -4749.07i q^{19} +(14615.8 + 14615.8i) q^{20} +(8897.19 - 926.640i) q^{21} +(-10449.7 + 10449.7i) q^{22} +(6365.30 - 6365.30i) q^{23} +(6806.63 - 8389.28i) q^{24} +31058.9i q^{25} -41639.4 q^{26} +(17512.3 + 8985.53i) q^{27} +(-22411.5 - 22411.5i) q^{28} +(8142.32 + 8142.32i) q^{29} +(73317.9 - 7636.05i) q^{30} +(-14072.4 + 14072.4i) q^{31} +39086.6 q^{32} +(3271.09 + 31407.5i) q^{33} +(-54833.7 - 29106.7i) q^{34} -71583.9i q^{35} +(-14371.0 - 68243.4i) q^{36} +(35074.8 - 35074.8i) q^{37} +60008.7i q^{38} +(-56058.4 + 69092.9i) q^{39} +(-61130.7 - 61130.7i) q^{40} +(-78359.7 + 78359.7i) q^{41} +(-112424. + 11708.9i) q^{42} -21553.6i q^{43} +(79113.9 - 79113.9i) q^{44} +(86036.0 - 131938. i) q^{45} +(-80431.1 + 80431.1i) q^{46} +96781.2i q^{47} +(18146.4 - 22365.7i) q^{48} -7884.09i q^{49} -392456. i q^{50} +(-122119. + 51800.4i) q^{51} +315250. q^{52} -70085.0 q^{53} +(-221283. - 113540. i) q^{54} +252695. q^{55} +(93736.2 + 93736.2i) q^{56} +(99573.3 + 80788.6i) q^{57} +(-102885. - 102885. i) q^{58} +154214. q^{59} +(-555085. + 57812.0i) q^{60} +(272130. + 272130. i) q^{61} +(177817. - 177817. i) q^{62} +(-131925. + 202310. i) q^{63} -425624. q^{64} +(503464. + 503464. i) q^{65} +(-41333.1 - 396862. i) q^{66} -204935. q^{67} +(415142. + 220365. i) q^{68} +(25177.5 + 241743. i) q^{69} +904525. i q^{70} +(-5096.66 - 5096.66i) q^{71} +(60106.5 + 285428. i) q^{72} +(350161. - 350161. i) q^{73} +(-443201. + 443201. i) q^{74} +(-651209. - 528357. i) q^{75} -454322. i q^{76} -387476. q^{77} +(708348. - 873050. i) q^{78} +(-265648. - 265648. i) q^{79} +(-162973. - 162973. i) q^{80} +(-486308. + 214322. i) q^{81} +(990143. - 990143. i) q^{82} +465170. q^{83} +(851153. - 88647.5i) q^{84} +(311065. + 1.01493e6i) q^{85} +272348. i q^{86} +(-309232. + 32206.4i) q^{87} +(-330894. + 330894. i) q^{88} +12773.7i q^{89} +(-1.08714e6 + 1.66715e6i) q^{90} +(-771998. - 771998. i) q^{91} +(608939. - 608939. i) q^{92} +(-55662.5 - 534446. i) q^{93} -1.22292e6i q^{94} +(725567. - 725567. i) q^{95} +(-664919. + 819524. i) q^{96} +(-117193. + 117193. i) q^{97} +99622.4i q^{98} +(-714165. - 465703. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) $ 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−12.6359			−1.57948			−0.789742	−	0.613439i	$-0.789786\pi$
$2$	−12.6359			−1.57948			−0.789742	+	0.613439i	$0.789786\pi$
$3$	−17.0115	+	20.9669i	−0.630054	+	0.776551i
$3$	−17.0115	+	20.9669i	−0.630054	+	0.776551i
$4$	95.6654			1.49477
$5$	152.781	+	152.781i	1.22225	+	1.22225i	0.966832	+	0.255414i	$0.0822118\pi$
$5$	152.781	+	152.781i	1.22225	+	1.22225i	0.255414	+	0.966832i	$0.417788\pi$
$6$	214.955	−	264.935i	0.995160	−	1.22655i
$7$	−234.270	−	234.270i	−0.683003	−	0.683003i	0.277673	−	0.960676i	$-0.410437\pi$
$7$	−234.270	−	234.270i	−0.683003	−	0.683003i	−0.960676	+	0.277673i	$0.910437\pi$
$8$	−400.120			−0.781485
$9$	−150.221	−	713.355i	−0.206064	−	0.978538i
$10$	−1930.52	−	1930.52i	−1.93052	−	1.93052i
$11$	826.986	−	826.986i	0.621327	−	0.621327i	−0.324544	−	0.945871i	$-0.605211\pi$
$11$	826.986	−	826.986i	0.621327	−	0.621327i	0.945871	+	0.324544i	$0.105211\pi$
$12$	−1627.41	+	2005.81i	−0.941787	+	1.16077i
$13$	3295.33			1.49992			0.749962	−	0.661480i	$-0.230072\pi$
$13$	3295.33			1.49992			0.749962	+	0.661480i	$0.230072\pi$
$14$	2960.21	+	2960.21i	1.07879	+	1.07879i
$15$	−5802.36	+	604.315i	−1.71922	+	0.179056i
$16$	−1066.71			−0.260428
$17$	4339.52	+	2303.50i	0.883274	+	0.468858i
$17$	4339.52	+	2303.50i	0.883274	+	0.468858i
$18$	1898.17	+	9013.86i	0.325476	+	1.54559i
$19$		−	4749.07i		−	0.692386i	−0.938163	−	0.346193i	$-0.887474\pi$
$19$		−	4749.07i		−	0.692386i	0.938163	−	0.346193i	$-0.112526\pi$
$20$	14615.8	+	14615.8i	1.82698	+	1.82698i
$21$	8897.19	−	926.640i	0.960716	−	0.100058i
$22$	−10449.7	+	10449.7i	−0.981376	+	0.981376i
$23$	6365.30	−	6365.30i	0.523161	−	0.523161i	−0.395364	−	0.918525i	$-0.629381\pi$
$23$	6365.30	−	6365.30i	0.523161	−	0.523161i	0.918525	+	0.395364i	$0.129381\pi$
$24$	6806.63	−	8389.28i	0.492378	−	0.606864i
$25$			31058.9i			1.98777i
$26$	−41639.4			−2.36911
$27$	17512.3	+	8985.53i	0.889717	+	0.456512i
$28$	−22411.5	−	22411.5i	−1.02093	−	1.02093i
$29$	8142.32	+	8142.32i	0.333852	+	0.333852i	0.854047	−	0.520195i	$-0.174141\pi$
$29$	8142.32	+	8142.32i	0.333852	+	0.333852i	−0.520195	+	0.854047i	$0.674141\pi$
$30$	73317.9	−	7636.05i	2.71548	−	0.282817i
$31$	−14072.4	+	14072.4i	−0.472371	+	0.472371i	−0.902681	−	0.430310i	$-0.858404\pi$
$31$	−14072.4	+	14072.4i	−0.472371	+	0.472371i	0.430310	+	0.902681i	$0.358404\pi$
$32$	39086.6			1.19283
$33$	3271.09	+	31407.5i	0.0910229	+	0.873961i
$34$	−54833.7	−	29106.7i	−1.39512	−	0.740554i
$35$		−	71583.9i		−	1.66960i
$36$	−14371.0	−	68243.4i	−0.308019	−	1.46269i
$37$	35074.8	−	35074.8i	0.692453	−	0.692453i	−0.270318	−	0.962771i	$-0.587129\pi$
$37$	35074.8	−	35074.8i	0.692453	−	0.692453i	0.962771	+	0.270318i	$0.0871288\pi$
$38$			60008.7i			1.09361i
$39$	−56058.4	+	69092.9i	−0.945033	+	1.16477i
$40$	−61130.7	−	61130.7i	−0.955167	−	0.955167i
$41$	−78359.7	+	78359.7i	−1.13695	+	1.13695i	−0.147955	+	0.988994i	$0.547269\pi$
$41$	−78359.7	+	78359.7i	−1.13695	+	1.13695i	−0.988994	+	0.147955i	$0.952731\pi$
$42$	−112424.	+	11708.9i	−1.51744	+	0.158041i
$43$		−	21553.6i		−	0.271090i	−0.990771	−	0.135545i	$-0.956721\pi$
$43$		−	21553.6i		−	0.271090i	0.990771	−	0.135545i	$-0.0432785\pi$
$44$	79113.9	−	79113.9i	0.928742	−	0.928742i
$45$	86036.0	−	131938.i	0.944153	−	1.44788i
$46$	−80431.1	+	80431.1i	−0.826325	+	0.826325i
$47$			96781.2i			0.932175i	0.884739	+	0.466088i	$0.154337\pi$
$47$			96781.2i			0.932175i	−0.884739	+	0.466088i	$0.845663\pi$
$48$	18146.4	−	22365.7i	0.164084	−	0.202236i
$49$		−	7884.09i		−	0.0670136i
$50$		−	392456.i		−	3.13965i
$51$	−122119.	+	51800.4i	−0.920602	+	0.390502i
$52$	315250.			2.24205
$53$	−70085.0			−0.470758			−0.235379	−	0.971904i	$-0.575633\pi$
$53$	−70085.0			−0.470758			−0.235379	+	0.971904i	$0.575633\pi$
$54$	−221283.	−	113540.i	−1.40529	−	0.721054i
$55$	252695.			1.51883
$56$	93736.2	+	93736.2i	0.533757	+	0.533757i
$57$	99573.3	+	80788.6i	0.537673	+	0.436240i
$58$	−102885.	−	102885.i	−0.527314	−	0.527314i
$59$	154214.			0.750875			0.375437	−	0.926848i	$-0.377493\pi$
$59$	154214.			0.750875			0.375437	+	0.926848i	$0.377493\pi$
$60$	−555085.	+	57812.0i	−2.56984	+	0.267648i
$61$	272130.	+	272130.i	1.19891	+	1.19891i	0.974494	+	0.224416i	$0.0720473\pi$
$61$	272130.	+	272130.i	1.19891	+	1.19891i	0.224416	+	0.974494i	$0.427953\pi$
$62$	177817.	−	177817.i	0.746103	−	0.746103i
$63$	−131925.	+	202310.i	−0.527602	+	0.809087i
$64$	−425624.			−1.62362
$65$	503464.	+	503464.i	1.83328	+	1.83328i
$66$	−41333.1	−	396862.i	−0.143769	−	1.38041i
$67$	−204935.			−0.681382			−0.340691	−	0.940175i	$-0.610661\pi$
$67$	−204935.			−0.681382			−0.340691	+	0.940175i	$0.610661\pi$
$68$	415142.	+	220365.i	1.32029	+	0.700836i
$69$	25177.5	+	241743.i	0.0766419	+	0.735881i
$70$			904525.i			2.63710i
$71$	−5096.66	−	5096.66i	−0.0142400	−	0.0142400i	0.699951	−	0.714191i	$-0.253205\pi$
$71$	−5096.66	−	5096.66i	−0.0142400	−	0.0142400i	−0.714191	+	0.699951i	$0.753205\pi$
$72$	60106.5	+	285428.i	0.161036	+	0.764713i
$73$	350161.	−	350161.i	0.900119	−	0.900119i	−0.0953274	−	0.995446i	$-0.530390\pi$
$73$	350161.	−	350161.i	0.900119	−	0.900119i	0.995446	+	0.0953274i	$0.0303898\pi$
$74$	−443201.	+	443201.i	−1.09372	+	1.09372i
$75$	−651209.	−	528357.i	−1.54361	−	1.25240i
$76$		−	454322.i		−	1.03496i
$77$	−387476.			−0.848736
$78$	708348.	−	873050.i	1.49267	−	1.83973i
$79$	−265648.	−	265648.i	−0.538798	−	0.538798i	0.384378	−	0.923176i	$-0.374416\pi$
$79$	−265648.	−	265648.i	−0.538798	−	0.538798i	−0.923176	+	0.384378i	$0.874416\pi$
$80$	−162973.	−	162973.i	−0.318307	−	0.318307i
$81$	−486308.	+	214322.i	−0.915075	+	0.403284i
$82$	990143.	−	990143.i	1.79579	−	1.79579i
$83$	465170.			0.813538			0.406769	−	0.913531i	$-0.366655\pi$
$83$	465170.			0.813538			0.406769	+	0.913531i	$0.366655\pi$
$84$	851153.	−	88647.5i	1.43605	−	0.149564i
$85$	311065.	+	1.01493e6i	0.506518	+	1.65264i
$86$			272348.i			0.428183i
$87$	−309232.	+	32206.4i	−0.469598	+	0.0489086i
$88$	−330894.	+	330894.i	−0.485558	+	0.485558i
$89$			12773.7i			0.0181196i	0.999959	+	0.00905979i	$0.00288386\pi$
$89$			12773.7i			0.0181196i	−0.999959	+	0.00905979i	$0.997116\pi$
$90$	−1.08714e6	+	1.66715e6i	−1.49128	+	2.28690i
$91$	−771998.	−	771998.i	−1.02445	−	1.02445i
$92$	608939.	−	608939.i	0.782006	−	0.782006i
$93$	−55662.5	−	534446.i	−0.0692012	−	0.664439i
$94$		−	1.22292e6i		−	1.47236i
$95$	725567.	−	725567.i	0.846265	−	0.846265i
$96$	−664919.	+	819524.i	−0.751546	+	0.926292i
$97$	−117193.	+	117193.i	−0.128406	+	0.128406i	−0.768389	−	0.639983i	$-0.778941\pi$
$97$	−117193.	+	117193.i	−0.128406	+	0.128406i	0.639983	+	0.768389i	$0.278941\pi$
$98$			99622.4i			0.105847i
$99$	−714165.	−	465703.i	−0.736025	−	0.479959i
$100$			2.97126e6i			2.97126i
$101$			364480.i			0.353761i	0.984232	+	0.176880i	$0.0566006\pi$
$101$			364480.i			0.353761i	−0.984232	+	0.176880i	$0.943399\pi$
$102$	1.54308e6	−	654544.i	1.45408	−	0.616791i
$103$	708196.			0.648099			0.324050	−	0.946040i	$-0.394955\pi$
$103$	708196.			0.648099			0.324050	+	0.946040i	$0.394955\pi$
$104$	−1.31853e6			−1.17217
$105$	1.50089e6	+	1.21775e6i	1.29653	+	1.05193i
$106$	885585.			0.743554
$107$	946161.	+	946161.i	0.772349	+	0.772349i	0.978517	−	0.206167i	$-0.0660991\pi$
$107$	946161.	+	946161.i	0.772349	+	0.772349i	−0.206167	+	0.978517i	$0.566099\pi$
$108$	1.67532e6	+	859605.i	1.32992	+	0.682382i
$109$	−1.75349e6	−	1.75349e6i	−1.35402	−	1.35402i	−0.881116	−	0.472900i	$-0.843207\pi$
$109$	−1.75349e6	−	1.75349e6i	−1.35402	−	1.35402i	−0.472900	−	0.881116i	$-0.656793\pi$
$110$	−3.19302e6			−2.39897
$111$	138736.	+	1.33208e6i	0.101443	+	0.974008i
$112$	249899.	+	249899.i	0.177873	+	0.177873i
$113$	777427.	−	777427.i	0.538796	−	0.538796i	−0.384380	−	0.923175i	$-0.625585\pi$
$113$	777427.	−	777427.i	0.538796	−	0.538796i	0.923175	+	0.384380i	$0.125585\pi$
$114$	−1.25820e6	−	1.02084e6i	−0.849246	−	0.689035i
$115$	1.94499e6			1.27886
$116$	778938.	+	778938.i	0.499033	+	0.499033i
$117$	−495028.	−	2.35074e6i	−0.309081	−	1.46773i
$118$	−1.94863e6			−1.18599
$119$	−476979.	−	1.55626e6i	−0.283047	−	0.923510i
$120$	2.32164e6	−	241799.i	1.34354	−	0.139930i
$121$			403750.i			0.227907i
$122$	−3.43860e6	−	3.43860e6i	−1.89366	−	1.89366i
$123$	−309947.	−	2.97597e6i	−0.166560	−	1.59924i
$124$	−1.34624e6	+	1.34624e6i	−0.706087	+	0.706087i
$125$	−2.35800e6	+	2.35800e6i	−1.20730	+	1.20730i
$126$	1.66699e6	−	2.55636e6i	0.833340	−	1.27794i
$127$			2.79704e6i			1.36549i	0.730658	+	0.682743i	$0.239213\pi$
$127$			2.79704e6i			1.36549i	−0.730658	+	0.682743i	$0.760787\pi$
$128$	2.87659e6			1.37166
$129$	451911.	+	366657.i	0.210515	+	0.170801i
$130$	−6.36171e6	−	6.36171e6i	−2.89563	−	2.89563i
$131$	−4825.44	−	4825.44i	−0.00214646	−	0.00214646i	0.706033	−	0.708179i	$-0.250483\pi$
$131$	−4825.44	−	4825.44i	−0.00214646	−	0.00214646i	−0.708179	+	0.706033i	$0.750483\pi$
$132$	312930.	+	3.00462e6i	0.136058	+	1.30637i
$133$	−1.11257e6	+	1.11257e6i	−0.472901	+	0.472901i
$134$	2.58953e6			1.07623
$135$	1.30273e6	+	4.04836e6i	0.529483	+	1.64542i
$136$	−1.73633e6	−	921677.i	−0.690265	−	0.366406i
$137$			1.94026e6i			0.754569i	0.926097	+	0.377285i	$0.123142\pi$
$137$			1.94026e6i			0.754569i	−0.926097	+	0.377285i	$0.876858\pi$
$138$	−318140.	−	3.05464e6i	−0.121055	−	1.16231i
$139$	3.23966e6	−	3.23966e6i	1.20630	−	1.20630i	0.234084	−	0.972216i	$-0.424791\pi$
$139$	3.23966e6	−	3.23966e6i	1.20630	−	1.20630i	0.972216	−	0.234084i	$-0.0752089\pi$
$140$		−	6.84810e6i		−	2.49566i
$141$	−2.02920e6	−	1.64639e6i	−0.723882	−	0.587320i
$142$	64400.8	+	64400.8i	0.0224919	+	0.0224919i
$143$	2.72519e6	−	2.72519e6i	0.931943	−	0.931943i
$144$	160243.	+	760945.i	0.0536650	+	0.254839i
$145$			2.48798e6i			0.816099i
$146$	−4.42460e6	+	4.42460e6i	−1.42172	+	1.42172i
$147$	165305.	+	134120.i	0.0520395	+	0.0422222i
$148$	3.35545e6	−	3.35545e6i	1.03506	−	1.03506i
$149$			2.50359e6i			0.756840i	0.925634	+	0.378420i	$0.123533\pi$
$149$			2.50359e6i			0.756840i	−0.925634	+	0.378420i	$0.876467\pi$
$150$	8.22859e6	+	6.67626e6i	2.43810	+	1.97815i
$151$			3.70156e6i			1.07511i	0.843228	+	0.537556i	$0.180652\pi$
$151$			3.70156e6i			1.07511i	−0.843228	+	0.537556i	$0.819348\pi$
$152$			1.90020e6i			0.541089i
$153$	991324.	−	3.44165e6i	0.276784	−	0.960932i
$154$	4.89610e6			1.34057
$155$	−4.29998e6			−1.15471
$156$	−5.36285e6	+	6.60980e6i	−1.41261	+	1.74106i
$157$	−3.28644e6			−0.849234			−0.424617	−	0.905373i	$-0.639591\pi$
$157$	−3.28644e6			−0.849234			−0.424617	+	0.905373i	$0.639591\pi$
$158$	3.35670e6	+	3.35670e6i	0.851023	+	0.851023i
$159$	1.19225e6	−	1.46946e6i	0.296603	−	0.365567i
$160$	5.97168e6	+	5.97168e6i	1.45793	+	1.45793i
$161$	−2.98240e6			−0.714641
$162$	6.14493e6	−	2.70814e6i	1.44535	−	0.636981i
$163$	2.65200e6	+	2.65200e6i	0.612365	+	0.612365i	0.943562	−	0.331197i	$-0.107452\pi$
$163$	2.65200e6	+	2.65200e6i	0.612365	+	0.612365i	−0.331197	+	0.943562i	$0.607452\pi$
$164$	−7.49631e6	+	7.49631e6i	−1.69948	+	1.69948i
$165$	−4.29871e6	+	5.29823e6i	−0.956943	+	1.17945i
$166$	−5.87784e6			−1.28497
$167$	−57067.7	−	57067.7i	−0.0122530	−	0.0122530i	0.700954	−	0.713207i	$-0.252758\pi$
$167$	−57067.7	−	57067.7i	−0.0122530	−	0.0122530i	−0.713207	+	0.700954i	$0.752758\pi$
$168$	−3.55995e6	+	370768.i	−0.750785	+	0.0781941i
$169$	6.03242e6			1.24977
$170$	−3.93058e6	−	1.28245e7i	−0.800037	−	2.61032i
$171$	−3.38777e6	+	713410.i	−0.677526	+	0.142676i
$172$		−	2.06193e6i		−	0.405218i
$173$	2.93252e6	+	2.93252e6i	0.566374	+	0.566374i	0.931111	−	0.364737i	$-0.118841\pi$
$173$	2.93252e6	+	2.93252e6i	0.566374	+	0.566374i	−0.364737	+	0.931111i	$0.618841\pi$
$174$	3.90741e6	−	406957.i	0.741723	−	0.0772503i
$175$	7.27617e6	−	7.27617e6i	1.35765	−	1.35765i
$176$	−882157.	+	882157.i	−0.161811	+	0.161811i
$177$	−2.62340e6	+	3.23339e6i	−0.473091	+	0.583093i
$178$		−	161407.i		−	0.0286196i
$179$	−4.09118e6			−0.713329			−0.356664	−	0.934233i	$-0.616086\pi$
$179$	−4.09118e6			−0.713329			−0.356664	+	0.934233i	$0.616086\pi$
$180$	8.23067e6	−	1.26219e7i	1.41129	−	2.16424i
$181$	1.43482e6	+	1.43482e6i	0.241970	+	0.241970i	0.817665	−	0.575695i	$-0.195268\pi$
$181$	1.43482e6	+	1.43482e6i	0.241970	+	0.241970i	−0.575695	+	0.817665i	$0.695268\pi$
$182$	9.75488e6	+	9.75488e6i	1.61811	+	1.61811i
$183$	−1.03350e7	+	1.07639e6i	−1.68639	+	0.175637i
$184$	−2.54689e6	+	2.54689e6i	−0.408842	+	0.408842i
$185$	1.07175e7			1.69270
$186$	703344.	+	6.75320e6i	0.109302	+	1.04947i
$187$	5.49368e6	−	1.68376e6i	0.840115	−	0.257487i
$188$			9.25861e6i			1.39339i
$189$	−1.99757e6	−	6.20765e6i	−0.295880	−	0.919479i
$190$	−9.16817e6	+	9.16817e6i	−1.33666	+	1.33666i
$191$		−	1.34216e7i		−	1.92621i	−0.269128	−	0.963104i	$-0.586735\pi$
$191$		−	1.34216e7i		−	1.92621i	0.269128	−	0.963104i	$-0.413265\pi$
$192$	7.24047e6	−	8.92400e6i	1.02297	−	1.26083i
$193$	3.35003e6	+	3.35003e6i	0.465990	+	0.465990i	0.900613	−	0.434623i	$-0.143118\pi$
$193$	3.35003e6	+	3.35003e6i	0.465990	+	0.465990i	−0.434623	+	0.900613i	$0.643118\pi$
$194$	1.48083e6	−	1.48083e6i	0.202815	−	0.202815i
$195$	−1.91207e7	+	1.99142e6i	−2.57870	+	0.268571i
$196$		−	754235.i		−	0.100170i
$197$	6.41778e6	−	6.41778e6i	0.839433	−	0.839433i	−0.149351	−	0.988784i	$-0.547718\pi$
$197$	6.41778e6	−	6.41778e6i	0.839433	−	0.839433i	0.988784	+	0.149351i	$0.0477184\pi$
$198$	9.02410e6	+	5.88457e6i	1.16254	+	0.758087i
$199$	5.33938e6	−	5.33938e6i	0.677535	−	0.677535i	−0.281907	−	0.959442i	$-0.590967\pi$
$199$	5.33938e6	−	5.33938e6i	0.677535	−	0.677535i	0.959442	+	0.281907i	$0.0909670\pi$
$200$		−	1.24273e7i		−	1.55341i
$201$	3.48623e6	−	4.29684e6i	0.429307	−	0.529128i
$202$		−	4.60553e6i		−	0.558760i
$203$		−	3.81500e6i		−	0.456044i
$204$	−1.16825e7	+	4.95551e6i	−1.37609	+	0.583711i
$205$	−2.39437e7			−2.77926
$206$	−8.94868e6			−1.02366
$207$	−5.49692e6	−	3.58451e6i	−0.619738	−	0.404128i
$208$	−3.51518e6			−0.390623
$209$	−3.92742e6	−	3.92742e6i	−0.430198	−	0.430198i
$210$	−1.89651e7	−	1.53873e7i	−2.04784	−	1.66152i
$211$	−2.41713e6	−	2.41713e6i	−0.257308	−	0.257308i	0.566651	−	0.823958i	$-0.308239\pi$
$211$	−2.41713e6	−	2.41713e6i	−0.257308	−	0.257308i	−0.823958	+	0.566651i	$0.808239\pi$
$212$	−6.70471e6			−0.703675
$213$	193563.	−	20159.5i	0.0200301	−	0.00208613i
$214$	−1.19556e7	−	1.19556e7i	−1.21991	−	1.21991i
$215$	3.29297e6	−	3.29297e6i	0.331339	−	0.331339i
$216$	−7.00703e6	−	3.59529e6i	−0.695301	−	0.356758i
$217$	6.59348e6			0.645261
$218$	2.21569e7	+	2.21569e7i	2.13865	+	2.13865i
$219$	1.38504e6	+	1.32986e7i	0.131865	+	1.26611i
$220$	2.41742e7			2.27030
$221$	1.43002e7	+	7.59080e6i	1.32484	+	0.703252i
$222$	−1.75305e6	−	1.68320e7i	−0.160227	−	1.53843i
$223$		−	2.75969e6i		−	0.248855i	−0.992229	−	0.124427i	$-0.960291\pi$
$223$		−	2.75969e6i		−	0.248855i	0.992229	−	0.124427i	$-0.0397094\pi$
$224$	−9.15681e6	−	9.15681e6i	−0.814705	−	0.814705i
$225$	2.21560e7	−	4.66570e6i	1.94511	−	0.409609i
$226$	−9.82347e6	+	9.82347e6i	−0.851019	+	0.851019i
$227$	−4.32080e6	+	4.32080e6i	−0.369391	+	0.369391i	−0.867255	−	0.497864i	$-0.834118\pi$
$227$	−4.32080e6	+	4.32080e6i	−0.369391	+	0.369391i	0.497864	+	0.867255i	$0.334118\pi$
$228$	9.52572e6	+	7.72868e6i	0.803699	+	0.652080i
$229$		−	9.35552e6i		−	0.779043i	−0.921017	−	0.389522i	$-0.872640\pi$
$229$		−	9.35552e6i		−	0.779043i	0.921017	−	0.389522i	$-0.127360\pi$
$230$	−2.45767e7			−2.01994
$231$	6.59153e6	−	8.12417e6i	0.534749	−	0.659087i
$232$	−3.25791e6	−	3.25791e6i	−0.260900	−	0.260900i
$233$	−5.39981e6	−	5.39981e6i	−0.426885	−	0.426885i	0.460681	−	0.887566i	$-0.347605\pi$
$233$	−5.39981e6	−	5.39981e6i	−0.426885	−	0.426885i	−0.887566	+	0.460681i	$0.847605\pi$
$234$	6.25512e6	+	2.97037e7i	0.488189	+	2.31826i
$235$	−1.47863e7	+	1.47863e7i	−1.13935	+	1.13935i
$236$	1.47529e7			1.12239
$237$	1.00889e7	−	1.05076e6i	0.757876	−	0.0789326i
$238$	6.02705e6	+	1.96647e7i	0.447069	+	1.45867i
$239$			1.79480e7i			1.31469i	0.753590	+	0.657345i	$0.228321\pi$
$239$			1.79480e7i			1.31469i	−0.753590	+	0.657345i	$0.771679\pi$
$240$	6.18946e6	−	644631.i	0.447733	−	0.0466313i
$241$	−8.45448e6	+	8.45448e6i	−0.603999	+	0.603999i	−0.941371	−	0.337372i	$-0.890462\pi$
$241$	−8.45448e6	+	8.45448e6i	−0.603999	+	0.603999i	0.337372	+	0.941371i	$0.390462\pi$
$242$		−	5.10174e6i		−	0.359975i
$243$	3.77915e6	−	1.38423e7i	0.263376	−	0.964693i
$244$	2.60334e7	+	2.60334e7i	1.79210	+	1.79210i
$245$	1.20454e6	−	1.20454e6i	0.0819071	−	0.0819071i
$246$	3.91645e6	+	3.76040e7i	0.263080	+	2.52597i
$247$		−	1.56498e7i		−	1.03853i
$248$	5.63065e6	−	5.63065e6i	0.369151	−	0.369151i
$249$	−7.91322e6	+	9.75318e6i	−0.512573	+	0.631754i
$250$	2.97954e7	−	2.97954e7i	1.90691	−	1.90691i
$251$			1.20287e6i			0.0760671i	0.999276	+	0.0380336i	$0.0121094\pi$
$251$			1.20287e6i			0.0760671i	−0.999276	+	0.0380336i	$0.987891\pi$
$252$	−1.26207e7	+	1.93541e7i	−0.788645	+	1.20940i
$253$		−	1.05280e7i		−	0.650107i
$254$		−	3.53430e7i		−	2.15676i
$255$	−2.65715e7	−	1.07433e7i	−1.60249	−	0.647913i
$256$	−9.10829e6			−0.542896
$257$	3.96560e6			0.233620			0.116810	−	0.993154i	$-0.462733\pi$
$257$	3.96560e6			0.233620			0.116810	+	0.993154i	$0.462733\pi$
$258$	−5.71029e6	−	4.63304e6i	−0.332506	−	0.269778i
$259$	−1.64340e7			−0.945895
$260$	4.81641e7	+	4.81641e7i	2.74033	+	2.74033i
$261$	4.58521e6	−	7.03151e6i	0.257892	−	0.395482i
$262$	60973.6	+	60973.6i	0.00339030	+	0.00339030i
$263$	−1.90075e7			−1.04486			−0.522429	−	0.852683i	$-0.674974\pi$
$263$	−1.90075e7			−1.04486			−0.522429	+	0.852683i	$0.674974\pi$
$264$	−1.30883e6	−	1.25668e7i	−0.0711330	−	0.682988i
$265$	−1.07076e7	−	1.07076e7i	−0.575381	−	0.575381i
$266$	1.40582e7	−	1.40582e7i	0.746941	−	0.746941i
$267$	−267826.	−	217300.i	−0.0140708	−	0.0114163i
$268$	−1.96052e7			−1.01851
$269$	−1.54725e7	−	1.54725e7i	−0.794886	−	0.794886i	0.187398	−	0.982284i	$-0.439994\pi$
$269$	−1.54725e7	−	1.54725e7i	−0.794886	−	0.794886i	−0.982284	+	0.187398i	$0.939994\pi$
$270$	−1.64611e7	−	5.11546e7i	−0.836310	−	2.59892i
$271$	−2.20343e7			−1.10711			−0.553555	−	0.832813i	$-0.686729\pi$
$271$	−2.20343e7			−1.10711			−0.553555	+	0.832813i	$0.686729\pi$
$272$	−4.62903e6	−	2.45717e6i	−0.230029	−	0.122104i
$273$	2.93192e7	−	3.05359e6i	1.44100	−	0.150080i
$274$		−	2.45169e7i		−	1.19183i
$275$	2.56853e7	+	2.56853e7i	1.23505	+	1.23505i
$276$	2.40862e6	+	2.31265e7i	0.114562	+	1.09997i
$277$	−7.53926e6	+	7.53926e6i	−0.354723	+	0.354723i	−0.861864	−	0.507140i	$-0.830703\pi$
$277$	−7.53926e6	+	7.53926e6i	−0.354723	+	0.354723i	0.507140	+	0.861864i	$0.330703\pi$
$278$	−4.09360e7	+	4.09360e7i	−1.90533	+	1.90533i
$279$	1.21526e7	+	7.92464e6i	0.559572	+	0.364894i
$280$			2.86422e7i			1.30476i
$281$	1.52587e7			0.687701			0.343851	−	0.939024i	$-0.388269\pi$
$281$	1.52587e7			0.687701			0.343851	+	0.939024i	$0.388269\pi$
$282$	2.56407e7	+	2.08036e7i	1.14336	+	0.927664i
$283$	−2.32705e7	−	2.32705e7i	−1.02670	−	1.02670i	−0.999634	−	0.0270714i	$-0.991382\pi$
$283$	−2.32705e7	−	2.32705e7i	−1.02670	−	1.02670i	−0.0270714	−	0.999634i	$-0.508618\pi$
$284$	−487575.	−	487575.i	−0.0212856	−	0.0212856i
$285$	2.86993e6	+	2.75558e7i	0.123976	+	1.19036i
$286$	−3.44352e7	+	3.44352e7i	−1.47199	+	1.47199i
$287$	3.67146e7			1.55308
$288$	−5.87162e6	−	2.78826e7i	−0.245799	−	1.16723i
$289$	1.35254e7	+	1.99922e7i	0.560344	+	0.828260i
$290$		−	3.14378e7i		−	1.28902i
$291$	−463548.	−	4.45078e6i	−0.0188112	−	0.180616i
$292$	3.34983e7	−	3.34983e7i	1.34547	−	1.34547i
$293$			4.49841e7i			1.78836i	0.447703	+	0.894182i	$0.352242\pi$
$293$			4.49841e7i			1.78836i	−0.447703	+	0.894182i	$0.647758\pi$
$294$	−2.08877e6	−	1.69472e6i	−0.0821957	−	0.0666893i
$295$	2.35609e7	+	2.35609e7i	0.917753	+	0.917753i
$296$	−1.40342e7	+	1.40342e7i	−0.541142	+	0.541142i
$297$	2.19133e7	−	7.05152e6i	0.836448	−	0.269162i
$298$		−	3.16351e7i		−	1.19542i
$299$	2.09758e7	−	2.09758e7i	0.784702	−	0.784702i
$300$	−6.22981e7	−	5.05455e7i	−2.30734	−	1.87206i
$301$	−5.04935e6	+	5.04935e6i	−0.185155	+	0.185155i
$302$		−	4.67724e7i		−	1.69812i
$303$	−7.64201e6	−	6.20034e6i	−0.274713	−	0.222888i
$304$			5.06590e6i			0.180317i
$305$			8.31523e7i			2.93072i
$306$	−1.25263e7	+	4.34883e7i	−0.437177	+	1.51778i
$307$	3.54378e7			1.22476			0.612381	−	0.790563i	$-0.290212\pi$
$307$	3.54378e7			1.22476			0.612381	+	0.790563i	$0.290212\pi$
$308$	−3.70680e7			−1.26867
$309$	−1.20474e7	+	1.48487e7i	−0.408338	+	0.503283i
$310$	5.43341e7			1.82384
$311$	−3.09565e7	−	3.09565e7i	−1.02913	−	1.02913i	−0.999563	−	0.0295668i	$-0.990587\pi$
$311$	−3.09565e7	−	3.09565e7i	−1.02913	−	1.02913i	−0.0295668	−	0.999563i	$-0.509413\pi$
$312$	2.24301e7	−	2.76455e7i	0.738530	−	0.910250i
$313$	3.39478e6	+	3.39478e6i	0.110708	+	0.110708i	0.760291	−	0.649583i	$-0.225056\pi$
$313$	3.39478e6	+	3.39478e6i	0.110708	+	0.110708i	−0.649583	+	0.760291i	$0.725056\pi$
$314$	4.15271e7			1.34135
$315$	−5.10647e7	+	1.07534e7i	−1.63376	+	0.344044i
$316$	−2.54134e7	−	2.54134e7i	−0.805380	−	0.805380i
$317$	2.46207e7	−	2.46207e7i	0.772899	−	0.772899i	−0.205713	−	0.978612i	$-0.565951\pi$
$317$	2.46207e7	−	2.46207e7i	0.772899	−	0.772899i	0.978612	+	0.205713i	$0.0659514\pi$
$318$	−1.50651e7	+	1.85680e7i	−0.468479	+	0.577408i
$319$	1.34672e7			0.414862
$320$	−6.50271e7	−	6.50271e7i	−1.98447	−	1.98447i
$321$	−3.59336e7	+	3.74248e6i	−1.08639	+	0.113147i
$322$	3.76852e7			1.12876
$323$	1.09395e7	−	2.06087e7i	0.324631	−	0.611566i
$324$	−4.65229e7	+	2.05032e7i	−1.36783	+	0.602818i
$325$			1.02349e8i			2.98150i
$326$	−3.35103e7	−	3.35103e7i	−0.967221	−	0.967221i
$327$	6.65946e7	−	6.93582e6i	1.90457	−	0.198360i
$328$	3.13533e7	−	3.13533e7i	0.888509	−	0.888509i
$329$	2.26729e7	−	2.26729e7i	0.636678	−	0.636678i
$330$	5.43180e7	−	6.69478e7i	1.51148	−	1.86292i
$331$			5.89968e6i			0.162684i	0.996686	+	0.0813419i	$0.0259206\pi$
$331$			5.89968e6i			0.162684i	−0.996686	+	0.0813419i	$0.974079\pi$
$332$	4.45007e7			1.21605
$333$	−3.02898e7	−	1.97518e7i	−0.820282	−	0.534902i
$334$	721101.	+	721101.i	0.0193534	+	0.0193534i
$335$	−3.13101e7	−	3.13101e7i	−0.832817	−	0.832817i
$336$	−9.49075e6	+	988460.i	−0.250197	+	0.0260580i
$337$	3.30790e7	−	3.30790e7i	0.864297	−	0.864297i	−0.127537	−	0.991834i	$-0.540707\pi$
$337$	3.30790e7	−	3.30790e7i	0.864297	−	0.864297i	0.991834	+	0.127537i	$0.0407071\pi$
$338$	−7.62249e7			−1.97400
$339$	3.07506e6	+	2.95254e7i	0.0789323	+	0.757873i
$340$	2.97582e7	+	9.70933e7i	0.757129	+	2.47032i
$341$			2.32753e7i			0.586993i
$342$	4.28075e7	−	9.01457e6i	1.07014	−	0.225355i
$343$	−2.94086e7	+	2.94086e7i	−0.728774	+	0.728774i
$344$			8.62402e6i			0.211853i
$345$	−3.30871e7	+	4.07804e7i	−0.805752	+	0.993102i
$346$	−3.70550e7	−	3.70550e7i	−0.894579	−	0.894579i
$347$	−4.73773e7	+	4.73773e7i	−1.13392	+	1.13392i	−0.144399	+	0.989520i	$0.546125\pi$
$347$	−4.73773e7	+	4.73773e7i	−1.13392	+	1.13392i	−0.989520	+	0.144399i	$0.953875\pi$
$348$	−2.95828e7	+	3.08104e6i	−0.701942	+	0.0731071i
$349$		−	6.80195e7i		−	1.60014i	−0.599909	−	0.800068i	$-0.704797\pi$
$349$		−	6.80195e7i		−	1.60014i	0.599909	−	0.800068i	$-0.295203\pi$
$350$	−9.19408e7	+	9.19408e7i	−2.14439	+	2.14439i
$351$	5.77089e7	+	2.96103e7i	1.33451	+	0.684734i
$352$	3.23240e7	−	3.23240e7i	0.741135	−	0.741135i
$353$		−	4.85060e7i		−	1.10274i	−0.834262	−	0.551368i	$-0.814106\pi$
$353$		−	4.85060e7i		−	1.10274i	0.834262	−	0.551368i	$-0.185894\pi$
$354$	3.31490e7	−	4.08567e7i	0.747241	−	0.920986i
$355$		−	1.55734e6i		−	0.0348096i
$356$			1.22201e6i			0.0270846i
$357$	4.07441e7	+	1.64735e7i	0.895488	+	0.362060i
$358$	5.16957e7			1.12669
$359$	−3.72731e7			−0.805587			−0.402794	−	0.915291i	$-0.631961\pi$
$359$	−3.72731e7			−0.805587			−0.402794	+	0.915291i	$0.631961\pi$
$360$	−3.44247e7	+	5.27910e7i	−0.737842	+	1.13149i
$361$	2.44922e7			0.520602
$362$	−1.81302e7	−	1.81302e7i	−0.382188	−	0.382188i
$363$	−8.46539e6	−	6.86838e6i	−0.176981	−	0.143593i
$364$	−7.38535e7	−	7.38535e7i	−1.53132	−	1.53132i
$365$	1.06996e8			2.20033
$366$	1.30592e8	−	1.36012e7i	2.66363	−	0.277417i
$367$	−3.08610e7	−	3.08610e7i	−0.624326	−	0.624326i	0.322309	−	0.946635i	$-0.395541\pi$
$367$	−3.08610e7	−	3.08610e7i	−0.624326	−	0.624326i	−0.946635	+	0.322309i	$0.895541\pi$
$368$	−6.78995e6	+	6.78995e6i	−0.136246	+	0.136246i
$369$	6.76695e7	+	4.41270e7i	1.34683	+	0.878264i
$370$	−1.35425e8			−2.67359
$371$	1.64188e7	+	1.64188e7i	0.321529	+	0.321529i
$372$	−5.32498e6	−	5.11280e7i	−0.103440	−	0.993185i
$373$	−6.37386e7			−1.22822			−0.614110	−	0.789220i	$-0.710485\pi$
$373$	−6.37386e7			−1.22822			−0.614110	+	0.789220i	$0.710485\pi$
$374$	−6.94175e7	+	2.12758e7i	−1.32695	+	0.406697i
$375$	−9.32693e6	−	8.95530e7i	−0.176866	−	1.69819i
$376$		−	3.87241e7i		−	0.728481i
$377$	2.68317e7	+	2.68317e7i	0.500753	+	0.500753i
$378$	2.52410e7	+	7.84391e7i	0.467338	+	1.45230i
$379$	3.82733e7	−	3.82733e7i	0.703037	−	0.703037i	−0.262025	−	0.965061i	$-0.584390\pi$
$379$	3.82733e7	−	3.82733e7i	0.703037	−	0.703037i	0.965061	+	0.262025i	$0.0843902\pi$
$380$	6.94117e7	−	6.94117e7i	1.26497	−	1.26497i
$381$	−5.86452e7	−	4.75817e7i	−1.06037	−	0.860330i
$382$			1.69593e8i			3.04242i
$383$	8.08791e6			0.143959			0.0719797	−	0.997406i	$-0.477068\pi$
$383$	8.08791e6			0.143959			0.0719797	+	0.997406i	$0.477068\pi$
$384$	−4.89349e7	+	6.03131e7i	−0.864222	+	1.06517i
$385$	−5.91989e7	−	5.91989e7i	−1.03736	−	1.03736i
$386$	−4.23305e7	−	4.23305e7i	−0.736023	−	0.736023i
$387$	−1.53753e7	+	3.23780e6i	−0.265272	+	0.0558620i
$388$	−1.12113e7	+	1.12113e7i	−0.191937	+	0.191937i
$389$	4.51648e7			0.767275			0.383638	−	0.923484i	$-0.374671\pi$
$389$	4.51648e7			0.767275			0.383638	+	0.923484i	$0.374671\pi$
$390$	2.41607e8	−	2.51633e7i	4.07301	−	0.424203i
$391$	4.22848e7	−	1.29599e7i	0.707382	−	0.216806i
$392$			3.15458e6i			0.0523702i
$393$	183262.	−	19086.7i	0.00301922	−	0.000314451i
$394$	−8.10943e7	+	8.10943e7i	−1.32587	+	1.32587i
$395$		−	8.11719e7i		−	1.31709i
$396$	−6.83209e7	−	4.45517e7i	−1.10019	−	0.717429i
$397$	−2.33934e7	−	2.33934e7i	−0.373871	−	0.373871i	0.495014	−	0.868885i	$-0.335163\pi$
$397$	−2.33934e7	−	2.33934e7i	−0.373871	−	0.373871i	−0.868885	+	0.495014i	$0.835163\pi$
$398$	−6.74677e7	+	6.74677e7i	−1.07016	+	1.07016i
$399$	−4.40068e6	−	4.22534e7i	−0.0692790	−	0.665186i
$400$		−	3.31310e7i		−	0.517671i
$401$	−8.11904e7	+	8.11904e7i	−1.25913	+	1.25913i	−0.307626	+	0.951507i	$0.599535\pi$
$401$	−8.11904e7	+	8.11904e7i	−1.25913	+	1.25913i	−0.951507	+	0.307626i	$0.900465\pi$
$402$	−4.40516e7	+	5.42944e7i	−0.678085	+	0.835750i
$403$	−4.63733e7	+	4.63733e7i	−0.708521	+	0.708521i
$404$			3.48681e7i			0.528792i
$405$	−1.07043e8	−	4.15543e7i	−1.61136	−	0.625534i
$406$			4.82059e7i			0.720315i
$407$		−	5.80128e7i		−	0.860479i
$408$	4.88622e7	−	2.07264e7i	0.719437	−	0.305171i
$409$	−2.11173e6			−0.0308652			−0.0154326	−	0.999881i	$-0.504913\pi$
$409$	−2.11173e6			−0.0308652			−0.0154326	+	0.999881i	$0.504913\pi$
$410$	3.02550e8			4.38980
$411$	−4.06813e7	−	3.30067e7i	−0.585962	−	0.475419i
$412$	6.77498e7			0.968761
$413$	−3.61277e7	−	3.61277e7i	−0.512850	−	0.512850i
$414$	6.94584e7	+	4.52935e7i	0.978866	+	0.638314i
$415$	7.10691e7	+	7.10691e7i	0.994343	+	0.994343i
$416$	1.28803e8			1.78915
$417$	1.28143e7	+	1.23037e8i	0.176720	+	1.69679i
$418$	4.96263e7	+	4.96263e7i	0.679491	+	0.679491i
$419$	−1.04751e7	+	1.04751e7i	−0.142401	+	0.142401i	−0.774714	−	0.632312i	$-0.782106\pi$
$419$	−1.04751e7	+	1.04751e7i	−0.142401	+	0.142401i	0.632312	+	0.774714i	$0.282106\pi$
$420$	1.43583e8	+	1.16496e8i	1.93801	+	1.57240i
$421$	1.10429e8			1.47991			0.739956	−	0.672656i	$-0.234846\pi$
$421$	1.10429e8			1.47991			0.739956	+	0.672656i	$0.234846\pi$
$422$	3.05426e7	+	3.05426e7i	0.406414	+	0.406414i
$423$	6.90393e7	−	1.45386e7i	0.912169	−	0.192088i
$424$	2.80424e7			0.367890
$425$	−7.15442e7	+	1.34781e8i	−0.931982	+	1.75574i
$426$	−2.44584e6	+	254733.i	−0.0316372	+	0.00329501i
$427$		−	1.27504e8i		−	1.63772i
$428$	9.05149e7	+	9.05149e7i	1.15449	+	1.15449i
$429$	1.07793e7	+	1.03498e8i	0.136527	+	1.31088i
$430$	−4.16096e7	+	4.16096e7i	−0.523344	+	0.523344i
$431$	−6.85807e7	+	6.85807e7i	−0.856584	+	0.856584i	−0.990934	−	0.134350i	$-0.957105\pi$
$431$	−6.85807e7	+	6.85807e7i	−0.856584	+	0.856584i	0.134350	+	0.990934i	$0.457105\pi$
$432$	−1.86806e7	−	9.58499e6i	−0.231707	−	0.118889i
$433$			1.57784e7i			0.194357i	0.995267	+	0.0971785i	$0.0309818\pi$
$433$			1.57784e7i			0.194357i	−0.995267	+	0.0971785i	$0.969018\pi$
$434$	−8.33144e7			−1.01918
$435$	−5.21652e7	−	4.23241e7i	−0.633743	−	0.514186i
$436$	−1.67748e8	−	1.67748e8i	−2.02395	−	2.02395i
$437$	−3.02293e7	−	3.02293e7i	−0.362229	−	0.362229i
$438$	−1.75012e7	−	1.68039e8i	−0.208279	−	1.99980i
$439$	−1.29430e7	+	1.29430e7i	−0.152983	+	0.152983i	−0.779449	−	0.626466i	$-0.784501\pi$
$439$	−1.29430e7	+	1.29430e7i	−0.152983	+	0.152983i	0.626466	+	0.779449i	$0.284501\pi$
$440$	−1.01108e8			−1.18694
$441$	−5.62415e6	+	1.18436e6i	−0.0655754	+	0.0138091i
$442$	−1.80695e8	−	9.59164e7i	−2.09257	−	1.11078i
$443$			3.13562e7i			0.360672i	0.983605	+	0.180336i	$0.0577185\pi$
$443$			3.13562e7i			0.360672i	−0.983605	+	0.180336i	$0.942282\pi$
$444$	1.32723e7	+	1.27434e8i	0.151634	+	1.45592i
$445$	−1.95158e6	+	1.95158e6i	−0.0221466	+	0.0221466i
$446$			3.48712e7i			0.393063i
$447$	−5.24925e7	−	4.25897e7i	−0.587726	−	0.476850i
$448$	9.97108e7	+	9.97108e7i	1.10894	+	1.10894i
$449$	2.42050e6	−	2.42050e6i	0.0267403	−	0.0267403i	−0.693610	−	0.720351i	$-0.743981\pi$
$449$	2.42050e6	−	2.42050e6i	0.0267403	−	0.0267403i	0.720351	+	0.693610i	$0.243981\pi$
$450$	−2.79961e8	+	5.89552e7i	−3.07227	+	0.646971i
$451$			1.29605e8i			1.41283i
$452$	7.43728e7	−	7.43728e7i	0.805377	−	0.805377i
$453$	−7.76101e7	−	6.29688e7i	−0.834879	−	0.677378i
$454$	5.45971e7	−	5.45971e7i	0.583447	−	0.583447i
$455$		−	2.35893e8i		−	2.50427i
$456$	−3.98413e7	−	3.23252e7i	−0.420184	−	0.340915i
$457$		−	6.27788e7i		−	0.657756i	−0.944372	−	0.328878i	$-0.893330\pi$
$457$		−	6.27788e7i		−	0.657756i	0.944372	−	0.328878i	$-0.106670\pi$
$458$			1.18215e8i			1.23049i
$459$	5.52969e7	+	7.93325e7i	0.571824	+	0.820376i
$460$	1.86068e8			1.91161
$461$	4.73768e7			0.483574			0.241787	−	0.970329i	$-0.422266\pi$
$461$	4.73768e7			0.483574			0.241787	+	0.970329i	$0.422266\pi$
$462$	−8.32898e7	+	1.02656e8i	−0.844628	+	1.04102i
$463$	−1.27252e8			−1.28210			−0.641048	−	0.767501i	$-0.721500\pi$
$463$	−1.27252e8			−1.28210			−0.641048	+	0.767501i	$0.721500\pi$
$464$	−8.68552e6	−	8.68552e6i	−0.0869445	−	0.0869445i
$465$	7.31490e7	−	9.01573e7i	0.727527	−	0.896689i
$466$	6.82314e7	+	6.82314e7i	0.674258	+	0.674258i
$467$	1.06113e8			1.04188			0.520939	−	0.853594i	$-0.325582\pi$
$467$	1.06113e8			1.04188			0.520939	+	0.853594i	$0.325582\pi$
$468$	−4.73571e7	−	2.24885e8i	−0.462006	−	2.19393i
$469$	4.80100e7	+	4.80100e7i	0.465386	+	0.465386i
$470$	1.86838e8	−	1.86838e8i	1.79958	−	1.79958i
$471$	5.59072e7	−	6.89065e7i	0.535063	−	0.659474i
$472$	−6.17041e7			−0.586797
$473$	−1.78245e7	−	1.78245e7i	−0.168435	−	0.168435i
$474$	−1.27482e8	+	1.32772e7i	−1.19705	+	0.124673i
$475$	1.47501e8			1.37630
$476$	−4.56304e7	−	1.48880e8i	−0.423091	−	1.38044i
$477$	1.05282e7	+	4.99954e7i	0.0970064	+	0.460654i
$478$		−	2.26789e8i		−	2.07653i
$479$	−9.27101e7	−	9.27101e7i	−0.843568	−	0.843568i	0.145753	−	0.989321i	$-0.453440\pi$
$479$	−9.27101e7	−	9.27101e7i	−0.843568	−	0.843568i	−0.989321	+	0.145753i	$0.953440\pi$
$480$	−2.26794e8	+	2.36206e7i	−2.05073	+	0.213583i
$481$	1.15583e8	−	1.15583e8i	1.03863	−	1.03863i
$482$	1.06830e8	−	1.06830e8i	0.954007	−	0.954007i
$483$	5.07349e7	−	6.25316e7i	0.450262	−	0.554955i
$484$			3.86250e7i			0.340668i
$485$	−3.58095e7			−0.313887
$486$	−4.77529e7	+	1.74910e8i	−0.415998	+	1.52372i
$487$	−4.20033e7	−	4.20033e7i	−0.363661	−	0.363661i	0.501498	−	0.865159i	$-0.332783\pi$
$487$	−4.20033e7	−	4.20033e7i	−0.363661	−	0.363661i	−0.865159	+	0.501498i	$0.832783\pi$
$488$	−1.08885e8	−	1.08885e8i	−0.936930	−	0.936930i
$489$	−1.00718e8	+	1.04898e7i	−0.861356	+	0.0897100i
$490$	−1.52204e7	+	1.52204e7i	−0.129371	+	0.129371i
$491$	−1.03571e8			−0.874971			−0.437486	−	0.899225i	$-0.644131\pi$
$491$	−1.03571e8			−0.874971			−0.437486	+	0.899225i	$0.644131\pi$
$492$	−2.96512e7	−	2.84697e8i	−0.248970	−	2.39050i
$493$	1.65780e7	+	5.40896e7i	0.138353	+	0.451412i
$494$			1.97749e8i			1.64034i
$495$	−3.79601e7	−	1.80261e8i	−0.312976	−	1.48623i
$496$	1.50112e7	−	1.50112e7i	0.123019	−	0.123019i
$497$			2.38799e6i			0.0194520i
$498$	9.99905e7	−	1.23240e8i	0.809601	−	0.997846i
$499$	5.37330e6	+	5.37330e6i	0.0432454	+	0.0432454i	0.728399	−	0.685153i	$-0.240265\pi$
$499$	5.37330e6	+	5.37330e6i	0.0432454	+	0.0432454i	−0.685153	+	0.728399i	$0.740265\pi$
$500$	−2.25579e8	+	2.25579e8i	−1.80463	+	1.80463i
$501$	2.16734e6	−	225728.i	0.0172351	−	0.00179503i
$502$		−	1.51993e7i		−	0.120147i
$503$	1.54453e8	−	1.54453e8i	1.21365	−	1.21365i	0.243832	−	0.969817i	$-0.421595\pi$
$503$	1.54453e8	−	1.54453e8i	1.21365	−	1.21365i	0.969817	−	0.243832i	$-0.0784047\pi$
$504$	5.27860e7	−	8.09483e7i	0.412313	−	0.632290i
$505$	−5.56855e7	+	5.56855e7i	−0.432383	+	0.432383i
$506$			1.33031e8i			1.02683i
$507$	−1.02620e8	+	1.26481e8i	−0.787425	+	0.970514i
$508$			2.67580e8i			2.04109i
$509$		−	936414.i		−	0.00710092i	−0.999994	−	0.00355046i	$-0.998870\pi$
$509$		−	936414.i		−	0.00710092i	0.999994	−	0.00355046i	$-0.00113015\pi$
$510$	3.35754e8	+	1.35751e8i	2.53111	+	1.02337i
$511$	−1.64065e8			−1.22957
$512$	−6.90103e7			−0.514167
$513$	4.26729e7	−	8.31672e7i	0.316083	−	0.616027i
$514$	−5.01088e7			−0.368999
$515$	1.08199e8	+	1.08199e8i	0.792137	+	0.792137i
$516$	4.32323e7	+	3.50764e7i	0.314673	+	0.255309i
$517$	8.00367e7	+	8.00367e7i	0.579185	+	0.579185i
$518$	2.07658e8			1.49403
$519$	−1.11372e8	+	1.15994e7i	−0.796665	+	0.0829725i
$520$	−2.01446e8	−	2.01446e8i	−1.43268	−	1.43268i
$521$	−1.01283e8	+	1.01283e8i	−0.716184	+	0.716184i	−0.967822	−	0.251637i	$-0.919031\pi$
$521$	−1.01283e8	+	1.01283e8i	−0.716184	+	0.716184i	0.251637	+	0.967822i	$0.419031\pi$
$522$	−5.79382e7	+	8.88493e7i	−0.407337	+	0.624658i
$523$	1.39869e8			0.977721			0.488860	−	0.872362i	$-0.337413\pi$
$523$	1.39869e8			0.977721			0.488860	+	0.872362i	$0.337413\pi$
$524$	−461627.	−	461627.i	−0.00320847	−	0.00320847i
$525$	2.87804e7	+	2.76337e8i	0.198893	+	1.90968i
$526$	2.40176e8			1.65034
$527$	−9.34833e7	+	2.86517e7i	−0.638707	+	0.195758i
$528$	−3.48932e6	−	3.35029e7i	−0.0237049	−	0.227604i
$529$			6.70018e7i			0.452605i
$530$	1.35300e8	+	1.35300e8i	0.908806	+	0.908806i
$531$	−2.31662e7	−	1.10009e8i	−0.154729	−	0.734760i
$532$	−1.06434e8	+	1.06434e8i	−0.706880	+	0.706880i
$533$	−2.58221e8	+	2.58221e8i	−1.70534	+	1.70534i
$534$	3.38421e6	+	2.74577e6i	0.0222246	+	0.0180319i
$535$			2.89110e8i			1.88800i
$536$	8.19985e7			0.532490
$537$	6.95970e7	−	8.57794e7i	0.449436	−	0.553937i
$538$	1.95509e8	+	1.95509e8i	1.25551	+	1.25551i
$539$	−6.52003e6	−	6.52003e6i	−0.0416374	−	0.0416374i
$540$	1.24626e8	+	3.87288e8i	0.791456	+	2.45953i
$541$	2.14427e8	−	2.14427e8i	1.35421	−	1.35421i	0.473329	−	0.880886i	$-0.343052\pi$
$541$	2.14427e8	−	2.14427e8i	1.35421	−	1.35421i	0.880886	−	0.473329i	$-0.156948\pi$
$542$	2.78422e8			1.74866
$543$	−5.44921e7	+	5.67534e6i	−0.340356	+	0.0354481i
$544$	1.69617e8	+	9.00359e7i	1.05359	+	0.559267i
$545$		−	5.35799e8i		−	3.30988i
$546$	−3.70474e8	+	3.85848e7i	−2.27604	+	0.237049i
$547$	−1.13361e8	+	1.13361e8i	−0.692628	+	0.692628i	−0.962809	−	0.270181i	$-0.912916\pi$
$547$	−1.13361e8	+	1.13361e8i	−0.692628	+	0.692628i	0.270181	+	0.962809i	$0.412916\pi$
$548$			1.85616e8i			1.12791i
$549$	1.53245e8	−	2.35004e8i	0.926126	−	1.42023i
$550$	−3.24556e8	−	3.24556e8i	−1.95075	−	1.95075i
$551$	3.86685e7	−	3.86685e7i	0.231154	−	0.231154i
$552$	−1.00740e7	−	9.67265e7i	−0.0598945	−	0.575080i
$553$			1.24467e8i			0.736001i
$554$	9.52652e7	−	9.52652e7i	0.560280	−	0.560280i
$555$	−1.82320e8	+	2.24713e8i	−1.06649	+	1.31447i
$556$	3.09924e8	−	3.09924e8i	1.80314	−	1.80314i
$557$			5.75406e7i			0.332973i	0.986044	+	0.166486i	$0.0532422\pi$
$557$			5.75406e7i			0.332973i	−0.986044	+	0.166486i	$0.946758\pi$
$558$	−1.53559e8	−	1.00135e8i	−0.883835	−	0.576345i
$559$		−	7.10262e7i		−	0.406615i
$560$			7.63595e7i			0.434810i
$561$	−5.81523e7	+	1.43829e8i	−0.329366	+	0.814624i
$562$	−1.92808e8			−1.08621
$563$	1.38348e8			0.775260			0.387630	−	0.921815i	$-0.373294\pi$
$563$	1.38348e8			0.775260			0.387630	+	0.921815i	$0.373294\pi$
$564$	−1.94124e8	−	1.57502e8i	−1.08204	−	0.877910i
$565$	2.37552e8			1.31708
$566$	2.94043e8	+	2.94043e8i	1.62166	+	1.62166i
$567$	1.64137e8	+	6.37183e7i	0.900443	+	0.349555i
$568$	2.03928e6	+	2.03928e6i	0.0111284	+	0.0111284i
$569$	3.01865e7			0.163861			0.0819305	−	0.996638i	$-0.473891\pi$
$569$	3.01865e7			0.163861			0.0819305	+	0.996638i	$0.473891\pi$
$570$	−3.62641e7	−	3.48192e8i	−0.195818	−	1.88016i
$571$	−8.23062e7	−	8.23062e7i	−0.442104	−	0.442104i	0.450615	−	0.892718i	$-0.351205\pi$
$571$	−8.23062e7	−	8.23062e7i	−0.442104	−	0.442104i	−0.892718	+	0.450615i	$0.851205\pi$
$572$	2.60707e8	−	2.60707e8i	1.39304	−	1.39304i
$573$	2.81409e8	+	2.28320e8i	1.49580	+	1.21362i
$574$	−4.63922e8			−2.45307
$575$	1.97699e8	+	1.97699e8i	1.03992	+	1.03992i
$576$	6.39376e7	+	3.03620e8i	0.334571	+	1.58878i
$577$	−1.34115e8			−0.698152			−0.349076	−	0.937094i	$-0.613504\pi$
$577$	−1.34115e8			−0.698152			−0.349076	+	0.937094i	$0.613504\pi$
$578$	−1.70905e8	−	2.52619e8i	−0.885055	−	1.30822i
$579$	−1.27228e8	+	1.32508e7i	−0.655463	+	0.0682664i
$580$			2.38014e8i			1.21988i
$581$	−1.08975e8	−	1.08975e8i	−0.555649	−	0.555649i
$582$	5.85733e6	+	5.62395e7i	0.0297119	+	0.285281i
$583$	−5.79593e7	+	5.79593e7i	−0.292494	+	0.292494i
$584$	−1.40107e8	+	1.40107e8i	−0.703429	+	0.703429i
$585$	2.83517e8	−	4.34779e8i	1.41616	−	2.17170i
$586$		−	5.68413e8i		−	2.82469i
$587$	−8.57122e7			−0.423768			−0.211884	−	0.977295i	$-0.567960\pi$
$587$	−8.57122e7			−0.423768			−0.211884	+	0.977295i	$0.567960\pi$
$588$	1.58140e7	+	1.28306e7i	0.0777873	+	0.0631126i
$589$	6.68308e7	+	6.68308e7i	0.327063	+	0.327063i
$590$	−2.97713e8	−	2.97713e8i	−1.44958	−	1.44958i
$591$	2.53851e7	+	2.43737e8i	0.122975	+	1.18075i
$592$	−3.74148e7	+	3.74148e7i	−0.180334	+	0.180334i
$593$	−9.68831e7			−0.464605			−0.232303	−	0.972644i	$-0.574626\pi$
$593$	−9.68831e7			−0.464605			−0.232303	+	0.972644i	$0.574626\pi$
$594$	−2.76894e8	+	8.91021e7i	−1.32116	+	0.425137i
$595$	1.64893e8	−	3.10640e8i	0.782803	−	1.47471i
$596$			2.39507e8i			1.13130i
$597$	2.11196e7	+	2.02781e8i	0.0992572	+	0.953024i
$598$	−2.65048e8	+	2.65048e8i	−1.23942	+	1.23942i
$599$			1.70806e8i			0.794738i	0.917659	+	0.397369i	$0.130077\pi$
$599$			1.70806e8i			0.794738i	−0.917659	+	0.397369i	$0.869923\pi$
$600$	2.60562e8	+	2.11406e8i	1.20630	+	0.978734i
$601$	−3.04214e7	−	3.04214e7i	−0.140138	−	0.140138i	0.633558	−	0.773696i	$-0.281594\pi$
$601$	−3.04214e7	−	3.04214e7i	−0.140138	−	0.140138i	−0.773696	+	0.633558i	$0.781594\pi$
$602$	6.38030e7	−	6.38030e7i	0.292450	−	0.292450i
$603$	3.07855e7	+	1.46191e8i	0.140409	+	0.666759i
$604$			3.54111e8i			1.60705i
$605$	−6.16853e7	+	6.16853e7i	−0.278558	+	0.278558i
$606$	9.65636e7	+	7.83467e7i	0.433906	+	0.352049i
$607$	−1.38089e8	+	1.38089e8i	−0.617436	+	0.617436i	−0.944873	−	0.327437i	$-0.893815\pi$
$607$	−1.38089e8	+	1.38089e8i	−0.617436	+	0.617436i	0.327437	+	0.944873i	$0.393815\pi$
$608$		−	1.85625e8i		−	0.825897i
$609$	7.99887e7	+	6.48987e7i	0.354142	+	0.287332i
$610$		−	1.05070e9i		−	4.62903i
$611$			3.18926e8i			1.39819i
$612$	9.48355e7	−	3.29247e8i	0.413730	−	1.43637i
$613$	−2.32245e8			−1.00824			−0.504122	−	0.863632i	$-0.668184\pi$
$613$	−2.32245e8			−1.00824			−0.504122	+	0.863632i	$0.668184\pi$
$614$	−4.47788e8			−1.93449
$615$	4.07317e8	−	5.02025e8i	1.75108	−	2.15824i
$616$	1.55037e8			0.663275
$617$	−9.12925e7	−	9.12925e7i	−0.388669	−	0.388669i	0.485544	−	0.874212i	$-0.338622\pi$
$617$	−9.12925e7	−	9.12925e7i	−0.388669	−	0.388669i	−0.874212	+	0.485544i	$0.838622\pi$
$618$	1.52230e8	−	1.87626e8i	0.644963	−	0.794927i
$619$	−1.41173e8	−	1.41173e8i	−0.595222	−	0.595222i	0.343815	−	0.939037i	$-0.388281\pi$
$619$	−1.41173e8	−	1.41173e8i	−0.595222	−	0.595222i	−0.939037	+	0.343815i	$0.888281\pi$
$620$	−4.11360e8			−1.72602
$621$	1.68667e8	−	5.42754e7i	0.704295	−	0.226636i
$622$	3.91162e8	+	3.91162e8i	1.62549	+	1.62549i
$623$	2.99250e6	−	2.99250e6i	0.0123757	−	0.0123757i
$624$	5.97983e7	−	7.37024e7i	0.246113	−	0.303339i
$625$	−2.35219e8			−0.963459
$626$	−4.28961e7	−	4.28961e7i	−0.174862	−	0.174862i
$627$	1.49157e8	−	1.55346e7i	0.605118	−	0.0630229i
$628$	−3.14399e8			−1.26941
$629$	2.33003e8	−	7.14132e7i	0.936288	−	0.286963i
$630$	6.45247e8	−	1.35879e8i	2.58050	−	0.543413i
$631$		−	1.89946e6i		−	0.00756035i	−0.999993	−	0.00378017i	$-0.998797\pi$
$631$		−	1.89946e6i		−	0.00756035i	0.999993	−	0.00378017i	$-0.00120327\pi$
$632$	1.06291e8	+	1.06291e8i	0.421063	+	0.421063i
$633$	9.17986e7	−	9.56081e6i	0.361930	−	0.0376950i
$634$	−3.11104e8	+	3.11104e8i	−1.22078	+	1.22078i
$635$	−4.27334e8	+	4.27334e8i	−1.66896	+	1.66896i
$636$	1.14057e8	−	1.40577e8i	0.443353	−	0.546440i
$637$		−	2.59807e7i		−	0.100515i
$638$	−1.70169e8			−0.655269
$639$	−2.87010e6	+	4.40135e6i	−0.0110001	+	0.0168688i
$640$	4.39487e8	+	4.39487e8i	1.67651	+	1.67651i
$641$	−3.07503e8	−	3.07503e8i	−1.16755	−	1.16755i	−0.982783	−	0.184765i	$-0.940848\pi$
$641$	−3.07503e8	−	3.07503e8i	−1.16755	−	1.16755i	−0.184765	−	0.982783i	$-0.559152\pi$
$642$	4.54053e8	−	4.72895e7i	1.71594	−	0.178715i
$643$	5.94917e7	−	5.94917e7i	0.223781	−	0.223781i	−0.586307	−	0.810089i	$-0.699419\pi$
$643$	5.94917e7	−	5.94917e7i	0.223781	−	0.223781i	0.810089	+	0.586307i	$0.199419\pi$
$644$	−2.85312e8			−1.06823
$645$	1.30251e7	+	1.25061e8i	0.0485404	+	0.466063i
$646$	−1.38230e8	+	2.60409e8i	−0.512749	+	0.965959i
$647$			1.86353e8i			0.688057i	0.938959	+	0.344028i	$0.111792\pi$
$647$			1.86353e8i			0.688057i	−0.938959	+	0.344028i	$0.888208\pi$
$648$	1.94582e8	−	8.57544e7i	0.715118	−	0.315160i
$649$	1.27533e8	−	1.27533e8i	0.466538	−	0.466538i
$650$		−	1.29328e9i		−	4.70924i
$651$	−1.12165e8	+	1.38245e8i	−0.406549	+	0.501079i
$652$	2.53704e8	+	2.53704e8i	0.915346	+	0.915346i
$653$	1.91870e8	−	1.91870e8i	0.689077	−	0.689077i	−0.272951	−	0.962028i	$-0.588000\pi$
$653$	1.91870e8	−	1.91870e8i	0.689077	−	0.689077i	0.962028	+	0.272951i	$0.0879998\pi$
$654$	−8.41482e8	+	8.76402e7i	−3.00823	+	0.313307i
$655$		−	1.47447e6i		−	0.00524700i
$656$	8.35873e7	−	8.35873e7i	0.296094	−	0.296094i
$657$	−3.02391e8	−	1.97188e8i	−1.06628	−	0.695318i
$658$	−2.86492e8	+	2.86492e8i	−1.00562	+	1.00562i
$659$		−	8.10899e7i		−	0.283342i	−0.989914	−	0.141671i	$-0.954753\pi$
$659$		−	8.10899e7i		−	0.283342i	0.989914	−	0.141671i	$-0.0452474\pi$
$660$	−4.11238e8	+	5.06857e8i	−1.43041	+	1.76301i
$661$		−	3.08070e8i		−	1.06671i	−0.845892	−	0.533354i	$-0.820931\pi$
$661$		−	3.08070e8i		−	1.06671i	0.845892	−	0.533354i	$-0.179069\pi$
$662$		−	7.45476e7i		−	0.256957i
$663$	−4.02422e8	+	1.70700e8i	−1.38083	+	0.585723i
$664$	−1.86124e8			−0.635768
$665$	−3.39957e8			−1.15600
$666$	3.82738e8	+	2.49581e8i	1.29562	+	0.844870i
$667$	1.03657e8			0.349317
$668$	−5.45941e6	−	5.45941e6i	−0.0183154	−	0.0183154i
$669$	5.78622e7	+	4.69464e7i	0.193249	+	0.156792i
$670$	3.95630e8	+	3.95630e8i	1.31542	+	1.31542i
$671$	4.50095e8			1.48983
$672$	3.47761e8	−	3.62192e7i	1.14597	−	0.119352i
$673$	−1.77474e8	−	1.77474e8i	−0.582223	−	0.582223i	0.353291	−	0.935514i	$-0.385063\pi$
$673$	−1.77474e8	−	1.77474e8i	−0.582223	−	0.582223i	−0.935514	+	0.353291i	$0.885063\pi$
$674$	−4.17982e8	+	4.17982e8i	−1.36514	+	1.36514i
$675$	−2.79081e8	+	5.43913e8i	−0.907441	+	1.76855i
$676$	5.77094e8			1.86813
$677$	2.71693e8	+	2.71693e8i	0.875614	+	0.875614i	0.993077	−	0.117463i	$-0.0374762\pi$
$677$	2.71693e8	+	2.71693e8i	0.875614	+	0.875614i	−0.117463	+	0.993077i	$0.537476\pi$
$678$	−3.88561e7	−	3.73079e8i	−0.124672	−	1.19705i
$679$	5.49094e7			0.175403
$680$	−1.24464e8	−	4.06093e8i	−0.395836	−	1.29151i
$681$	−1.70906e7	−	1.64097e8i	−0.0541149	−	0.519587i
$682$		−	2.94104e8i		−	0.927147i
$683$	−4.91626e7	−	4.91626e7i	−0.154302	−	0.154302i	0.625734	−	0.780036i	$-0.284799\pi$
$683$	−4.91626e7	−	4.91626e7i	−0.154302	−	0.154302i	−0.780036	+	0.625734i	$0.784799\pi$
$684$	−3.24093e8	+	6.82487e7i	−1.01275	+	0.213268i
$685$	−2.96435e8	+	2.96435e8i	−0.922269	+	0.922269i
$686$	3.71604e8	−	3.71604e8i	1.15109	−	1.15109i
$687$	1.96156e8	+	1.59151e8i	0.604967	+	0.490839i
$688$			2.29915e7i			0.0705995i
$689$	−2.30953e8			−0.706101
$690$	4.18085e8	−	5.15296e8i	1.27267	−	1.56859i
$691$	−1.29931e8	−	1.29931e8i	−0.393803	−	0.393803i	0.482238	−	0.876040i	$-0.339824\pi$
$691$	−1.29931e8	−	1.29931e8i	−0.393803	−	0.393803i	−0.876040	+	0.482238i	$0.839824\pi$
$692$	2.80541e8	+	2.80541e8i	0.846600	+	0.846600i
$693$	5.82070e7	+	2.76408e8i	0.174894	+	0.830521i
$694$	5.98654e8	−	5.98654e8i	1.79101	−	1.79101i
$695$	9.89916e8			2.94879
$696$	1.23730e8	−	1.28864e7i	0.366984	−	0.0382213i
$697$	−5.20545e8	+	1.59542e8i	−1.53730	+	0.471169i
$698$			8.59486e8i			2.52739i
$699$	2.05076e8	−	2.13586e7i	0.600459	−	0.0625377i
$700$	6.96078e8	−	6.96078e8i	2.02938	−	2.02938i
$701$		−	4.36637e8i		−	1.26755i	−0.773516	−	0.633776i	$-0.781504\pi$
$701$		−	4.36637e8i		−	1.26755i	0.773516	−	0.633776i	$-0.218496\pi$
$702$	−7.29203e8	−	3.74153e8i	−2.10784	−	1.08153i
$703$	−1.66573e8	−	1.66573e8i	−0.479445	−	0.479445i
$704$	−3.51985e8	+	3.51985e8i	−1.00880	+	1.00880i
$705$	−5.84863e7	−	5.61559e8i	−0.166912	−	1.60261i
$706$			6.12916e8i			1.74176i
$707$	8.53868e7	−	8.53868e7i	0.241620	−	0.241620i
$708$	−2.50969e8	+	3.09323e8i	−0.707164	+	0.871591i
$709$	2.64424e7	−	2.64424e7i	0.0741928	−	0.0741928i	−0.669037	−	0.743229i	$-0.733293\pi$
$709$	2.64424e7	−	2.64424e7i	0.0741928	−	0.0741928i	0.743229	+	0.669037i	$0.233293\pi$
$710$			1.96784e7i			0.0549813i
$711$	−1.49596e8	+	2.29407e8i	−0.416207	+	0.638262i
$712$		−	5.11103e6i		−	0.0141602i
$713$			1.79150e8i			0.494252i
$714$	−5.14837e8	−	2.08157e8i	−1.41441	−	0.571869i
$715$	8.32714e8			2.27813
$716$	−3.91385e8			−1.06626
$717$	−3.76315e8	−	3.05322e8i	−1.02092	−	0.828326i
$718$	4.70979e8			1.27241
$719$	−1.70594e8	−	1.70594e8i	−0.458963	−	0.458963i	0.439352	−	0.898315i	$-0.355208\pi$
$719$	−1.70594e8	−	1.70594e8i	−0.458963	−	0.458963i	−0.898315	+	0.439352i	$0.855208\pi$
$720$	−9.17758e7	+	1.40740e8i	−0.245884	+	0.377068i
$721$	−1.65909e8	−	1.65909e8i	−0.442654	−	0.442654i
$722$	−3.09480e8			−0.822283
$723$	−3.34412e7	−	3.21087e8i	−0.0884844	−	0.849588i
$724$	1.37263e8	+	1.37263e8i	0.361690	+	0.361690i
$725$	−2.52891e8	+	2.52891e8i	−0.663621	+	0.663621i
$726$	1.06968e8	+	8.67880e7i	0.279539	+	0.226804i
$727$	4.63757e8			1.20694			0.603472	−	0.797384i	$-0.293784\pi$
$727$	4.63757e8			1.20694			0.603472	+	0.797384i	$0.293784\pi$
$728$	3.08892e8	+	3.08892e8i	0.800595	+	0.800595i
$729$	2.25941e8	+	3.14715e8i	0.583193	+	0.812334i
$730$	−1.35199e9			−3.47539
$731$	4.96486e7	−	9.35322e7i	0.127103	−	0.239447i
$732$	−9.88705e8	+	1.02973e8i	−2.52077	+	0.262538i
$733$			2.14036e8i			0.543470i	0.962372	+	0.271735i	$0.0875975\pi$
$733$			2.14036e8i			0.543470i	−0.962372	+	0.271735i	$0.912403\pi$
$734$	3.89955e8	+	3.89955e8i	0.986113	+	0.986113i
$735$	4.76447e6	+	4.57463e7i	0.0119992	+	0.115211i
$736$	2.48798e8	−	2.48798e8i	0.624041	−	0.624041i
$737$	−1.69478e8	+	1.69478e8i	−0.423361	+	0.423361i
$738$	−8.55063e8	−	5.57583e8i	−2.12730	−	1.38720i
$739$		−	5.81069e8i		−	1.43978i	−0.694091	−	0.719888i	$-0.744193\pi$
$739$		−	5.81069e8i		−	1.43978i	0.694091	−	0.719888i	$-0.255807\pi$
$740$	1.02530e9			2.53019
$741$	3.28127e8	+	2.66226e8i	0.806469	+	0.654327i
$742$	−2.07466e8	−	2.07466e8i	−0.507850	−	0.507850i
$743$	1.18024e8	+	1.18024e8i	0.287742	+	0.287742i	0.836187	−	0.548444i	$-0.184780\pi$
$743$	1.18024e8	+	1.18024e8i	0.287742	+	0.287742i	−0.548444	+	0.836187i	$0.684780\pi$
$744$	2.22717e7	+	2.13843e8i	0.0540797	+	0.519249i
$745$	−3.82500e8	+	3.82500e8i	−0.925045	+	0.925045i
$746$	8.05394e8			1.93996
$747$	−6.98783e7	−	3.31831e8i	−0.167641	−	0.796078i
$748$	5.25556e8	−	1.61078e8i	1.25578	−	0.384885i
$749$		−	4.43314e8i		−	1.05503i
$750$	1.17854e8	+	1.13158e9i	0.279358	+	2.68227i
$751$	−1.06346e8	+	1.06346e8i	−0.251074	+	0.251074i	−0.821411	−	0.570337i	$-0.806813\pi$
$751$	−1.06346e8	+	1.06346e8i	−0.251074	+	0.251074i	0.570337	+	0.821411i	$0.306813\pi$
$752$		−	1.03238e8i		−	0.242765i
$753$	−2.52204e7	−	2.04625e7i	−0.0590701	−	0.0479264i
$754$	−3.39042e8	−	3.39042e8i	−0.790932	−	0.790932i
$755$	−5.65526e8	+	5.65526e8i	−1.31405	+	1.31405i
$756$	−1.91098e8	−	5.93857e8i	−0.442274	−	1.37441i
$757$		−	3.27324e7i		−	0.0754555i	−0.999288	−	0.0377277i	$-0.987988\pi$
$757$		−	3.27324e7i		−	0.0754555i	0.999288	−	0.0377277i	$-0.0120120\pi$
$758$	−4.83616e8	+	4.83616e8i	−1.11044	+	1.11044i
$759$	2.20740e8	+	1.79097e8i	0.504842	+	0.409603i
$760$	−2.90314e8	+	2.90314e8i	−0.661344	+	0.661344i
$761$			1.27966e7i			0.0290362i	0.999895	+	0.0145181i	$0.00462142\pi$
$761$			1.27966e7i			0.0290362i	−0.999895	+	0.0145181i	$0.995379\pi$
$762$	7.41034e8	+	6.01237e8i	1.67484	+	1.35888i
$763$			8.21580e8i			1.84959i
$764$		−	1.28398e9i		−	2.87924i
$765$	6.77273e8	−	3.74363e8i	1.51279	−	0.836197i
$766$	−1.02198e8			−0.227382
$767$	5.08186e8			1.12626
$768$	1.54945e8	−	1.90972e8i	0.342054	−	0.421587i
$769$	3.62389e8			0.796885			0.398442	−	0.917193i	$-0.369551\pi$
$769$	3.62389e8			0.796885			0.398442	+	0.917193i	$0.369551\pi$
$770$	7.48030e8	+	7.48030e8i	1.63850	+	1.63850i
$771$	−6.74606e7	+	8.31462e7i	−0.147193	+	0.181418i
$772$	3.20482e8	+	3.20482e8i	0.696548	+	0.696548i
$773$	−5.08874e8			−1.10172			−0.550861	−	0.834597i	$-0.685701\pi$
$773$	−5.08874e8			−1.10172			−0.550861	+	0.834597i	$0.685701\pi$
$774$	1.94281e8	−	4.09124e7i	0.418993	−	0.0882332i
$775$	−4.37073e8	−	4.37073e8i	−0.938964	−	0.938964i
$776$	4.68911e7	−	4.68911e7i	0.100347	−	0.100347i
$777$	2.79566e8	−	3.44569e8i	0.595965	−	0.734536i
$778$	−5.70697e8			−1.21190
$779$	3.72136e8	+	3.72136e8i	0.787207	+	0.787207i
$780$	−1.82919e9	+	1.90510e8i	−3.85456	+	0.401452i
$781$	−8.42974e6			−0.0176954
$782$	−5.34306e8	+	1.63760e8i	−1.11730	+	0.342442i
$783$	6.94277e7	+	2.15754e8i	0.144626	+	0.449441i
$784$			8.41007e6i			0.0174522i
$785$	−5.02105e8	−	5.02105e8i	−1.03797	−	1.03797i
$786$	−2.31568e6	+	241177.i	−0.00476881	+	0.000496671i
$787$	−4.43019e7	+	4.43019e7i	−0.0908862	+	0.0908862i	−0.751088	−	0.660202i	$-0.770471\pi$
$787$	−4.43019e7	+	4.43019e7i	−0.0908862	+	0.0908862i	0.660202	+	0.751088i	$0.270471\pi$
$788$	6.13960e8	−	6.13960e8i	1.25476	−	1.25476i
$789$	3.23345e8	−	3.98528e8i	0.658317	−	0.811387i
$790$			1.02568e9i			2.08032i
$791$	−3.64255e8			−0.735998
$792$	2.85752e8	+	1.86337e8i	0.575193	+	0.375081i
$793$	8.96758e8	+	8.96758e8i	1.79827	+	1.79827i
$794$	2.95596e8	+	2.95596e8i	0.590524	+	0.590524i
$795$	4.06658e8	−	4.23534e7i	0.809335	−	0.0842920i
$796$	5.10794e8	−	5.10794e8i	1.01276	−	1.01276i
$797$	6.59857e7			0.130339			0.0651696	−	0.997874i	$-0.479241\pi$
$797$	6.59857e7			0.130339			0.0651696	+	0.997874i	$0.479241\pi$
$798$	5.56065e7	+	5.33909e8i	0.109425	+	1.05065i
$799$	−2.22935e8	+	4.19984e8i	−0.437058	+	0.823366i
$800$			1.21399e9i			2.37107i
$801$	9.11220e6	−	1.91888e6i	0.0177307	−	0.00373380i
$802$	1.02591e9	−	1.02591e9i	1.98878	−	1.98878i
$803$		−	5.79157e8i		−	1.11854i
$804$	3.33512e8	−	4.11059e8i	0.641717	−	0.790926i
$805$	−4.55653e8	−	4.55653e8i	−0.873467	−	0.873467i
$806$	5.85967e8	−	5.85967e8i	1.11910	−	1.11910i
$807$	5.87621e8	−	6.12006e7i	1.11809	−	0.116449i
$808$		−	1.45836e8i		−	0.276459i
$809$	2.69334e8	−	2.69334e8i	0.508681	−	0.508681i	−0.405440	−	0.914121i	$-0.632882\pi$
$809$	2.69334e8	−	2.69334e8i	0.508681	−	0.508681i	0.914121	+	0.405440i	$0.132882\pi$
$810$	1.35258e9	+	5.25075e8i	2.54512	+	0.988022i
$811$	−1.50609e8	+	1.50609e8i	−0.282351	+	0.282351i	−0.834046	−	0.551695i	$-0.813981\pi$
$811$	−1.50609e8	+	1.50609e8i	−0.282351	+	0.282351i	0.551695	+	0.834046i	$0.313981\pi$
$812$		−	3.64964e8i		−	0.681682i
$813$	3.74835e8	−	4.61990e8i	0.697539	−	0.859728i
$814$			7.33042e8i			1.35911i
$815$			8.10348e8i			1.49692i
$816$	1.30266e8	−	5.52562e7i	0.239751	−	0.101698i
$817$	−1.02359e8			−0.187699
$818$	2.66836e7			0.0487511
$819$	−4.34738e8	+	6.66679e8i	−0.791363	+	1.21357i
$820$	−2.29058e9			−4.15436
$821$	−6.03152e8	−	6.03152e8i	−1.08993	−	1.08993i	−0.995535	−	0.0943922i	$-0.969909\pi$
$821$	−6.03152e8	−	6.03152e8i	−1.08993	−	1.08993i	−0.0943922	−	0.995535i	$-0.530091\pi$
$822$	5.14044e8	+	4.17069e8i	0.925518	+	0.750917i
$823$	1.14891e8	+	1.14891e8i	0.206104	+	0.206104i	0.802609	−	0.596505i	$-0.203445\pi$
$823$	1.14891e8	+	1.14891e8i	0.206104	+	0.206104i	−0.596505	+	0.802609i	$0.703445\pi$
$824$	−2.83364e8			−0.506480
$825$	−9.75484e8	+	1.01596e8i	−1.73723	+	0.180933i
$826$	4.56505e8	+	4.56505e8i	0.810038	+	0.810038i
$827$	6.91243e8	−	6.91243e8i	1.22212	−	1.22212i	0.255245	−	0.966876i	$-0.417844\pi$
$827$	6.91243e8	−	6.91243e8i	1.22212	−	1.22212i	0.966876	−	0.255245i	$-0.0821560\pi$
$828$	−5.25865e8	−	3.42914e8i	−0.926367	−	0.604080i
$829$	3.74500e8			0.657338			0.328669	−	0.944445i	$-0.393400\pi$
$829$	3.74500e8			0.657338			0.328669	+	0.944445i	$0.393400\pi$
$830$	−8.98020e8	−	8.98020e8i	−1.57055	−	1.57055i
$831$	−2.98211e7	−	2.86329e8i	−0.0519661	−	0.498956i
$832$	−1.40257e9			−2.43532
$833$	1.81610e7	−	3.42132e7i	0.0314199	−	0.0591914i
$834$	−1.61920e8	−	1.55468e9i	−0.279127	−	2.68005i
$835$		−	1.74377e7i		−	0.0299523i
$836$	−3.75718e8	−	3.75718e8i	−0.643047	−	0.643047i
$837$	−3.72888e8	+	1.19992e8i	−0.635919	+	0.204633i
$838$	1.32362e8	−	1.32362e8i	0.224921	−	0.224921i
$839$	−7.32182e8	+	7.32182e8i	−1.23975	+	1.23975i	−0.279642	+	0.960104i	$0.590216\pi$
$839$	−7.32182e8	+	7.32182e8i	−1.23975	+	1.23975i	−0.960104	+	0.279642i	$0.909784\pi$
$840$	−6.00537e8	−	4.87245e8i	−1.01322	−	0.822072i
$841$		−	4.62229e8i		−	0.777086i
$842$	−1.39536e9			−2.33750
$843$	−2.59573e8	+	3.19928e8i	−0.433289	+	0.534035i
$844$	−2.31236e8	−	2.31236e8i	−0.384616	−	0.384616i
$845$	9.21638e8	+	9.21638e8i	1.52753	+	1.52753i
$846$	−8.72372e8	+	1.83708e8i	−1.44076	+	0.303400i
$847$	9.45866e7	−	9.45866e7i	0.155661	−	0.155661i
$848$	7.47606e7			0.122599
$849$	8.83773e8	−	9.20448e7i	1.44417	−	0.150410i
$850$	9.04023e8	−	1.70307e9i	1.47205	−	2.77317i
$851$		−	4.46523e8i		−	0.724529i
$852$	1.85173e7	−	1.92857e6i	0.0299404	−	0.00311829i
$853$	−6.87062e8	+	6.87062e8i	−1.10700	+	1.10700i	−0.113460	+	0.993543i	$0.536193\pi$
$853$	−6.87062e8	+	6.87062e8i	−1.10700	+	1.10700i	−0.993543	+	0.113460i	$0.963807\pi$
$854$			1.61112e9i			2.58675i
$855$	−6.26582e8	−	4.08591e8i	−1.00249	−	0.653718i
$856$	−3.78578e8	−	3.78578e8i	−0.603580	−	0.603580i
$857$	3.10597e8	−	3.10597e8i	0.493463	−	0.493463i	−0.415933	−	0.909395i	$-0.636545\pi$
$857$	3.10597e8	−	3.10597e8i	0.493463	−	0.493463i	0.909395	+	0.415933i	$0.136545\pi$
$858$	−1.36206e8	−	1.30779e9i	−0.215643	−	2.07051i
$859$		−	7.55834e8i		−	1.19247i	−0.802811	−	0.596234i	$-0.796663\pi$
$859$		−	7.55834e8i		−	1.19247i	0.802811	−	0.596234i	$-0.203337\pi$
$860$	3.15023e8	−	3.15023e8i	0.495276	−	0.495276i
$861$	−6.24569e8	+	7.69792e8i	−0.978524	+	1.20605i
$862$	8.66577e8	−	8.66577e8i	1.35296	−	1.35296i
$863$		−	1.27058e9i		−	1.97684i	−0.151757	−	0.988418i	$-0.548493\pi$
$863$		−	1.27058e9i		−	1.97684i	0.151757	−	0.988418i	$-0.451507\pi$
$864$	6.84496e8	+	3.51214e8i	1.06128	+	0.544540i
$865$			8.96066e8i			1.38450i
$866$		−	1.99374e8i		−	0.306984i
$867$	−6.49260e8	−	5.65114e7i	−0.996233	−	0.0867120i
$868$	6.30768e8			0.964519
$869$	−4.39375e8			−0.669539
$870$	6.59153e8	+	5.34803e8i	1.00099	+	0.812149i
$871$	−6.75328e8			−1.02202
$872$	7.01607e8	+	7.01607e8i	1.05814	+	1.05814i
$873$	1.01205e8	+	6.59950e7i	0.152110	+	0.0991901i
$874$	3.81973e8	+	3.81973e8i	0.572135	+	0.572135i
$875$	1.10482e9			1.64918
$876$	1.32501e8	+	1.27221e9i	0.197109	+	1.89255i
$877$	−3.65180e8	−	3.65180e8i	−0.541387	−	0.541387i	0.382549	−	0.923935i	$-0.375046\pi$
$877$	−3.65180e8	−	3.65180e8i	−0.541387	−	0.541387i	−0.923935	+	0.382549i	$0.875046\pi$
$878$	1.63546e8	−	1.63546e8i	0.241634	−	0.241634i
$879$	−9.43176e8	−	7.65245e8i	−1.38876	−	1.12677i
$880$	−2.69553e8			−0.395546
$881$	−6.20869e8	−	6.20869e8i	−0.907972	−	0.907972i	0.0881367	−	0.996108i	$-0.471909\pi$
$881$	−6.20869e8	−	6.20869e8i	−0.907972	−	0.907972i	−0.996108	+	0.0881367i	$0.971909\pi$
$882$	7.10661e7	−	1.49654e7i	0.103575	−	0.0218113i
$883$	−5.30588e8			−0.770682			−0.385341	−	0.922774i	$-0.625916\pi$
$883$	−5.30588e8			−0.770682			−0.385341	+	0.922774i	$0.625916\pi$
$884$	1.36803e9	+	7.26177e8i	1.98034	+	1.05120i
$885$	−8.94804e8	+	9.31937e7i	−1.29092	+	0.134449i
$886$		−	3.96213e8i		−	0.569675i
$887$	9.21365e8	+	9.21365e8i	1.32026	+	1.32026i	0.913559	+	0.406705i	$0.133322\pi$
$887$	9.21365e8	+	9.21365e8i	1.32026	+	1.32026i	0.406705	+	0.913559i	$0.366678\pi$
$888$	−5.55112e7	−	5.32994e8i	−0.0792760	−	0.761173i
$889$	6.55262e8	−	6.55262e8i	0.932631	−	0.932631i
$890$	2.46599e7	−	2.46599e7i	0.0349802	−	0.0349802i
$891$	−2.24929e8	+	5.79411e8i	−0.317989	+	0.819131i
$892$		−	2.64007e8i		−	0.371982i
$893$	4.59621e8			0.645425
$894$	6.63289e8	+	5.38158e8i	0.928304	+	0.753178i
$895$	−6.25054e8	−	6.25054e8i	−0.871863	−	0.871863i
$896$	−6.73898e8	−	6.73898e8i	−0.936850	−	0.936850i
$897$	8.29684e7	+	7.96626e8i	0.114957	+	1.10377i
$898$	−3.05852e7	+	3.05852e7i	−0.0422359	+	0.0422359i
$899$	−2.29164e8			−0.315404
$900$	2.11956e9	−	4.46346e8i	2.90749	−	0.612272i
$901$	−3.04135e8	−	1.61441e8i	−0.415808	−	0.220718i
$902$		−	1.63767e9i		−	2.23155i
$903$	−1.99724e7	−	1.91766e8i	−0.0271248	−	0.260441i
$904$	−3.11064e8	+	3.11064e8i	−0.421061	+	0.421061i
$905$			4.38426e8i			0.591494i
$906$	9.80672e8	+	7.95666e8i	1.31868	+	1.06991i
$907$	8.63378e8	+	8.63378e8i	1.15712	+	1.15712i	0.985092	+	0.172030i	$0.0550325\pi$
$907$	8.63378e8	+	8.63378e8i	1.15712	+	1.15712i	0.172030	+	0.985092i	$0.444968\pi$
$908$	−4.13351e8	+	4.13351e8i	−0.552155	+	0.552155i
$909$	2.60003e8	−	5.47525e7i	0.346168	−	0.0728975i
$910$			2.98071e9i			3.95545i
$911$	−7.82268e8	+	7.82268e8i	−1.03467	+	1.03467i	−0.0352890	+	0.999377i	$0.511235\pi$
$911$	−7.82268e8	+	7.82268e8i	−1.03467	+	1.03467i	−0.999377	+	0.0352890i	$0.988765\pi$
$912$	−1.06216e8	−	8.61784e7i	−0.140025	−	0.113609i
$913$	3.84689e8	−	3.84689e8i	0.505473	−	0.505473i
$914$			7.93266e8i			1.03892i
$915$	−1.74345e9	−	1.41454e9i	−2.27586	−	1.84651i
$916$		−	8.95000e8i		−	1.16449i
$917$			2.26091e6i			0.00293208i
$918$	−6.98725e8	−	1.00244e9i	−0.903188	−	1.29577i
$919$	6.95135e8			0.895618			0.447809	−	0.894129i	$-0.352205\pi$
$919$	6.95135e8			0.895618			0.447809	+	0.894129i	$0.352205\pi$
$920$	−7.78230e8			−0.999412
$921$	−6.02849e8	+	7.43021e8i	−0.771666	+	0.951091i
$922$	−5.98648e8			−0.763798
$923$	−1.67952e7	−	1.67952e7i	−0.0213590	−	0.0213590i
$924$	6.30581e8	−	7.77202e8i	0.799328	−	0.985185i
$925$	1.08939e9	+	1.08939e9i	1.37644	+	1.37644i
$926$	1.60794e9			2.02505
$927$	−1.06386e8	−	5.05195e8i	−0.133550	−	0.634190i
$928$	3.18255e8	+	3.18255e8i	0.398228	+	0.398228i
$929$	2.88702e8	−	2.88702e8i	0.360083	−	0.360083i	−0.503760	−	0.863843i	$-0.668051\pi$
$929$	2.88702e8	−	2.88702e8i	0.360083	−	0.360083i	0.863843	+	0.503760i	$0.168051\pi$
$930$	−9.24301e8	+	1.13922e9i	−1.14912	+	1.41631i
$931$	−3.74421e7			−0.0463993
$932$	−5.16575e8	−	5.16575e8i	−0.638096	−	0.638096i
$933$	1.17567e9	−	1.22446e8i	1.44758	−	0.150765i
$934$	−1.34083e9			−1.64563
$935$	1.09658e9	+	5.82083e8i	1.34154	+	0.712114i
$936$	1.98071e8	+	9.40580e8i	0.241542	+	1.14701i
$937$		−	1.36203e9i		−	1.65565i	−0.560985	−	0.827826i	$-0.689577\pi$
$937$		−	1.36203e9i		−	1.65565i	0.560985	−	0.827826i	$-0.310423\pi$
$938$	−6.06649e8	−	6.06649e8i	−0.735070	−	0.735070i
$939$	−1.28928e8	+	1.34279e7i	−0.155723	+	0.0162185i
$940$	−1.41454e9	+	1.41454e9i	−1.70306	+	1.70306i
$941$	3.12542e8	−	3.12542e8i	0.375094	−	0.375094i	−0.494235	−	0.869328i	$-0.664552\pi$
$941$	3.12542e8	−	3.12542e8i	0.375094	−	0.375094i	0.869328	+	0.494235i	$0.164552\pi$
$942$	−7.06436e8	+	8.70694e8i	−0.845124	+	1.04163i
$943$			9.97565e8i			1.18961i
$944$	−1.64502e8			−0.195549
$945$	6.43219e8	−	1.25360e9i	0.762191	−	1.48547i
$946$	2.25228e8	+	2.25228e8i	0.266041	+	0.266041i
$947$	−9.83200e8	−	9.83200e8i	−1.15769	−	1.15769i	−0.984971	−	0.172718i	$-0.944745\pi$
$947$	−9.83200e8	−	9.83200e8i	−1.15769	−	1.15769i	−0.172718	−	0.984971i	$-0.555255\pi$
$948$	9.65158e8	−	1.00521e8i	1.13285	−	0.117986i
$949$	1.15390e9	−	1.15390e9i	1.35011	−	1.35011i
$950$	−1.86380e9			−2.17385
$951$	9.73857e7	+	9.35054e8i	0.113228	+	1.08716i
$952$	1.90849e8	+	6.22692e8i	0.221197	+	0.721709i
$953$			1.33127e8i			0.153810i	0.997038	+	0.0769052i	$0.0245039\pi$
$953$			1.33127e8i			0.153810i	−0.997038	+	0.0769052i	$0.975496\pi$
$954$	−1.33033e8	−	6.31736e8i	−0.153220	−	0.727596i
$955$	2.05056e9	−	2.05056e9i	2.35430	−	2.35430i
$956$			1.71701e9i			1.96516i
$957$	−2.29096e8	+	2.82364e8i	−0.261386	+	0.322162i
$958$	1.17147e9	+	1.17147e9i	1.33240	+	1.33240i
$959$	4.54546e8	−	4.54546e8i	0.515373	−	0.515373i
$960$	2.46962e9	−	2.57211e8i	2.79136	−	0.290720i
$961$			4.91439e8i			0.553732i
$962$	−1.46050e9	+	1.46050e9i	−1.64050	+	1.64050i
$963$	5.32815e8	−	8.17082e8i	0.596620	−	0.914927i
$964$	−8.08802e8	+	8.08802e8i	−0.902841	+	0.902841i
$965$			1.02364e9i			1.13911i
$966$	−6.41080e8	+	7.90142e8i	−0.711182	+	0.876544i
$967$			4.84326e8i			0.535622i	0.963471	+	0.267811i	$0.0863003\pi$
$967$			4.84326e8i			0.535622i	−0.963471	+	0.267811i	$0.913700\pi$
$968$		−	1.61549e8i		−	0.178106i
$969$	2.46004e8	+	5.79951e8i	0.270378	+	0.637412i
$970$	4.52485e8			0.495780
$971$	1.18638e9			1.29589			0.647943	−	0.761689i	$-0.275630\pi$
$971$	1.18638e9			1.29589			0.647943	+	0.761689i	$0.275630\pi$
$972$	3.61534e8	−	1.32423e9i	0.393687	−	1.44200i
$973$	−1.51791e9			−1.64781
$974$	5.30749e8	+	5.30749e8i	0.574397	+	0.574397i
$975$	−2.14595e9	−	1.74111e9i	−2.31529	−	1.87851i
$976$	−2.90284e8	−	2.90284e8i	−0.312230	−	0.312230i
$977$	−1.68632e9			−1.80824			−0.904122	−	0.427275i	$-0.859474\pi$
$977$	−1.68632e9			−1.80824			−0.904122	+	0.427275i	$0.859474\pi$
$978$	1.27267e9	−	1.32548e8i	1.36050	−	0.141696i
$979$	1.05637e7	+	1.05637e7i	0.0112582	+	0.0112582i
$980$	1.15233e8	−	1.15233e8i	0.122433	−	0.122433i
$981$	−9.87449e8	+	1.51427e9i	−1.04594	+	1.60397i
$982$	1.30871e9			1.38200
$983$	1.85531e7	+	1.85531e7i	0.0195324	+	0.0195324i	0.716806	−	0.697273i	$-0.245604\pi$
$983$	1.85531e7	+	1.85531e7i	0.0195324	+	0.0195324i	−0.697273	+	0.716806i	$0.745604\pi$
$984$	1.24016e8	+	1.19075e9i	0.130164	+	1.24978i
$985$	1.96103e9			2.05199
$986$	−2.09477e8	−	6.83470e8i	−0.218527	−	0.712998i
$987$	8.96814e7	+	8.61081e8i	0.0932719	+	0.895555i
$988$		−	1.49714e9i		−	1.55236i
$989$	−1.37195e8	−	1.37195e8i	−0.141824	−	0.141824i
$990$	4.79659e8	+	2.27776e9i	0.494341	+	2.34748i
$991$	−9.33997e8	+	9.33997e8i	−0.959675	+	0.959675i	−0.999218	−	0.0395425i	$-0.987410\pi$
$991$	−9.33997e8	+	9.33997e8i	−0.959675	+	0.959675i	0.0395425	+	0.999218i	$0.487410\pi$
$992$	−5.50042e8	+	5.50042e8i	−0.563457	+	0.563457i
$993$	−1.23698e8	−	1.00362e8i	−0.126332	−	0.102500i
$994$		−	3.01744e7i		−	0.0307241i
$995$	1.63151e9			1.65623
$996$	−7.57022e8	+	9.33042e8i	−0.766179	+	0.944328i
$997$	2.72972e8	+	2.72972e8i	0.275443	+	0.275443i	0.831287	−	0.555844i	$-0.187605\pi$
$997$	2.72972e8	+	2.72972e8i	0.275443	+	0.275443i	−0.555844	+	0.831287i	$0.687605\pi$
$998$	−6.78964e7	−	6.78964e7i	−0.0683054	−	0.0683054i
$999$	9.29407e8	−	2.99075e8i	0.932201	−	0.299974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.7.f.a.38.5	✓	68
3.2	odd	2	inner	51.7.f.a.38.30	yes	68
17.13	even	4	inner	51.7.f.a.47.30	yes	68
51.47	odd	4	inner	51.7.f.a.47.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.7.f.a.38.5	✓	68	1.1	even	1	trivial
51.7.f.a.38.30	yes	68	3.2	odd	2	inner
51.7.f.a.47.5	yes	68	51.47	odd	4	inner
51.7.f.a.47.30	yes	68	17.13	even	4	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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-12.6359 q^{2} +(-17.0115 + 20.9669i) q^{3} +95.6654 q^{4} +(152.781 + 152.781i) q^{5} +(214.955 - 264.935i) q^{6} +(-234.270 - 234.270i) q^{7} -400.120 q^{8} +(-150.221 - 713.355i) q^{9} +(-1930.52 - 1930.52i) q^{10} +(826.986 - 826.986i) q^{11} +(-1627.41 + 2005.81i) q^{12} +3295.33 q^{13} +(2960.21 + 2960.21i) q^{14} +(-5802.36 + 604.315i) q^{15} -1066.71 q^{16} +(4339.52 + 2303.50i) q^{17} +(1898.17 + 9013.86i) q^{18} -4749.07i q^{19} +(14615.8 + 14615.8i) q^{20} +(8897.19 - 926.640i) q^{21} +(-10449.7 + 10449.7i) q^{22} +(6365.30 - 6365.30i) q^{23} +(6806.63 - 8389.28i) q^{24} +31058.9i q^{25} -41639.4 q^{26} +(17512.3 + 8985.53i) q^{27} +(-22411.5 - 22411.5i) q^{28} +(8142.32 + 8142.32i) q^{29} +(73317.9 - 7636.05i) q^{30} +(-14072.4 + 14072.4i) q^{31} +39086.6 q^{32} +(3271.09 + 31407.5i) q^{33} +(-54833.7 - 29106.7i) q^{34} -71583.9i q^{35} +(-14371.0 - 68243.4i) q^{36} +(35074.8 - 35074.8i) q^{37} +60008.7i q^{38} +(-56058.4 + 69092.9i) q^{39} +(-61130.7 - 61130.7i) q^{40} +(-78359.7 + 78359.7i) q^{41} +(-112424. + 11708.9i) q^{42} -21553.6i q^{43} +(79113.9 - 79113.9i) q^{44} +(86036.0 - 131938. i) q^{45} +(-80431.1 + 80431.1i) q^{46} +96781.2i q^{47} +(18146.4 - 22365.7i) q^{48} -7884.09i q^{49} -392456. i q^{50} +(-122119. + 51800.4i) q^{51} +315250. q^{52} -70085.0 q^{53} +(-221283. - 113540. i) q^{54} +252695. q^{55} +(93736.2 + 93736.2i) q^{56} +(99573.3 + 80788.6i) q^{57} +(-102885. - 102885. i) q^{58} +154214. q^{59} +(-555085. + 57812.0i) q^{60} +(272130. + 272130. i) q^{61} +(177817. - 177817. i) q^{62} +(-131925. + 202310. i) q^{63} -425624. q^{64} +(503464. + 503464. i) q^{65} +(-41333.1 - 396862. i) q^{66} -204935. q^{67} +(415142. + 220365. i) q^{68} +(25177.5 + 241743. i) q^{69} +904525. i q^{70} +(-5096.66 - 5096.66i) q^{71} +(60106.5 + 285428. i) q^{72} +(350161. - 350161. i) q^{73} +(-443201. + 443201. i) q^{74} +(-651209. - 528357. i) q^{75} -454322. i q^{76} -387476. q^{77} +(708348. - 873050. i) q^{78} +(-265648. - 265648. i) q^{79} +(-162973. - 162973. i) q^{80} +(-486308. + 214322. i) q^{81} +(990143. - 990143. i) q^{82} +465170. q^{83} +(851153. - 88647.5i) q^{84} +(311065. + 1.01493e6i) q^{85} +272348. i q^{86} +(-309232. + 32206.4i) q^{87} +(-330894. + 330894. i) q^{88} +12773.7i q^{89} +(-1.08714e6 + 1.66715e6i) q^{90} +(-771998. - 771998. i) q^{91} +(608939. - 608939. i) q^{92} +(-55662.5 - 534446. i) q^{93} -1.22292e6i q^{94} +(725567. - 725567. i) q^{95} +(-664919. + 819524. i) q^{96} +(-117193. + 117193. i) q^{97} +99622.4i q^{98} +(-714165. - 465703. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) \) 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

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