LMFDB - Embedded newform 38.6.e.b.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$38 = 2 \cdot 19$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	38.e (of order $9$ , degree $6$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	38.5
Dual form			38.6.e.b.23.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75877 + 1.36808i) q^{2} +(-5.14875 + 29.2000i) q^{3} +(12.2567 - 10.2846i) q^{4} +(68.5412 + 57.5129i) q^{5} +(-20.5950 - 116.800i) q^{6} +(68.7063 + 119.003i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-597.784 - 217.576i) q^{9} +(-336.313 - 122.408i) q^{10} +(152.529 - 264.188i) q^{11} +(237.204 + 410.849i) q^{12} +(15.9575 + 90.4993i) q^{13} +(-421.056 - 353.308i) q^{14} +(-2032.28 + 1705.28i) q^{15} +(44.4539 - 252.111i) q^{16} +(54.3140 - 19.7687i) q^{17} +2544.60 q^{18} +(920.562 - 1276.19i) q^{19} +1431.59 q^{20} +(-3828.63 + 1393.51i) q^{21} +(-211.891 + 1201.70i) q^{22} +(2223.62 - 1865.84i) q^{23} +(-1453.67 - 1219.77i) q^{24} +(847.513 + 4806.48i) q^{25} +(-183.791 - 318.335i) q^{26} +(5828.52 - 10095.3i) q^{27} +(2066.01 + 751.966i) q^{28} +(-5079.71 - 1848.86i) q^{29} +(5305.90 - 9190.09i) q^{30} +(2969.66 + 5143.60i) q^{31} +(177.816 + 1008.44i) q^{32} +(6928.96 + 5814.09i) q^{33} +(-177.109 + 148.612i) q^{34} +(-2134.98 + 12108.1i) q^{35} +(-9564.55 + 3481.21i) q^{36} -287.050 q^{37} +(-1714.25 + 6056.31i) q^{38} -2724.74 q^{39} +(-5381.01 + 1958.53i) q^{40} +(-240.363 + 1363.17i) q^{41} +(12484.5 - 10475.8i) q^{42} +(6184.72 + 5189.60i) q^{43} +(-847.565 - 4806.78i) q^{44} +(-28459.5 - 49293.2i) q^{45} +(-5805.47 + 10055.4i) q^{46} +(-1477.74 - 537.854i) q^{47} +(7132.75 + 2596.11i) q^{48} +(-1037.61 + 1797.18i) q^{49} +(-9761.26 - 16907.0i) q^{50} +(297.596 + 1687.75i) q^{51} +(1126.34 + 945.107i) q^{52} +(-29674.8 + 24900.1i) q^{53} +(-8096.90 + 45919.8i) q^{54} +(25648.8 - 9335.39i) q^{55} -8794.40 q^{56} +(32525.0 + 33451.2i) q^{57} +21622.8 q^{58} +(-1902.67 + 692.517i) q^{59} +(-7370.88 + 41802.3i) q^{60} +(16685.4 - 14000.7i) q^{61} +(-18199.1 - 15270.9i) q^{62} +(-15179.4 - 86086.8i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-4111.13 + 7120.69i) q^{65} +(-33998.5 - 12374.5i) q^{66} +(59312.6 + 21588.0i) q^{67} +(462.398 - 800.897i) q^{68} +(43033.7 + 74536.5i) q^{69} +(-8539.93 - 48432.4i) q^{70} +(-19296.9 - 16192.0i) q^{71} +(31188.4 - 26170.2i) q^{72} +(5900.50 - 33463.4i) q^{73} +(1078.96 - 392.708i) q^{74} -144713. q^{75} +(-1842.06 - 25109.5i) q^{76} +41918.9 q^{77} +(10241.7 - 3727.66i) q^{78} +(-2420.67 + 13728.3i) q^{79} +(17546.5 - 14723.3i) q^{80} +(146355. + 122806. i) q^{81} +(-961.451 - 5452.66i) q^{82} +(-40109.9 - 69472.5i) q^{83} +(-32594.7 + 56455.8i) q^{84} +(4859.70 + 1768.79i) q^{85} +(-30346.7 - 11045.3i) q^{86} +(80140.9 - 138808. i) q^{87} +(9761.87 + 16908.1i) q^{88} +(-8648.18 - 49046.2i) q^{89} +(174410. + 146347. i) q^{90} +(-9673.29 + 8116.85i) q^{91} +(8064.87 - 45738.1i) q^{92} +(-165483. + 60231.0i) q^{93} +6290.32 q^{94} +(136494. - 34527.5i) q^{95} -30362.1 q^{96} +(-38298.0 + 13939.3i) q^{97} +(1441.43 - 8174.73i) q^{98} +(-148661. + 124741. i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23}+ \cdots - 1068531 q^{99}+O(q^{100})$ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$ .

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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

)

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

$2$	−3.75877	+	1.36808i	−0.664463	+	0.241845i
$2$	−3.75877	+	1.36808i	−0.664463	+	0.241845i
$3$	−5.14875	+	29.2000i	−0.330292	+	1.87318i	0.139231	+	0.990260i	$0.455537\pi$
$3$	−5.14875	+	29.2000i	−0.330292	+	1.87318i	−0.469523	+	0.882920i	$0.655574\pi$
$4$	12.2567	−	10.2846i	0.383022	−	0.321394i
$5$	68.5412	+	57.5129i	1.22610	+	1.02882i	0.998482	+	0.0550720i	$0.0175388\pi$
$5$	68.5412	+	57.5129i	1.22610	+	1.02882i	0.227620	+	0.973750i	$0.426906\pi$
$6$	−20.5950	−	116.800i	−0.233552	−	1.32454i
$7$	68.7063	+	119.003i	0.529970	+	0.917935i	0.999389	+	0.0349593i	$0.0111302\pi$
$7$	68.7063	+	119.003i	0.529970	+	0.917935i	−0.469419	+	0.882976i	$0.655536\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	−597.784	−	217.576i	−2.46002	−	0.895373i
$10$	−336.313	−	122.408i	−1.06351	−	0.387088i
$11$	152.529	−	264.188i	0.380077	−	0.658312i	−0.610996	−	0.791634i	$-0.709231\pi$
$11$	152.529	−	264.188i	0.380077	−	0.658312i	0.991073	+	0.133321i	$0.0425642\pi$
$12$	237.204	+	410.849i	0.475519	+	0.823623i
$13$	15.9575	+	90.4993i	0.0261882	+	0.148521i	0.995098	−	0.0988935i	$-0.0315303\pi$
$13$	15.9575	+	90.4993i	0.0261882	+	0.148521i	−0.968910	+	0.247414i	$0.920419\pi$
$14$	−421.056	−	353.308i	−0.574143	−	0.481763i
$15$	−2032.28	+	1705.28i	−2.33214	+	1.95690i
$16$	44.4539	−	252.111i	0.0434120	−	0.246202i
$17$	54.3140	−	19.7687i	0.0455816	−	0.0165903i	−0.319129	−	0.947711i	$-0.603390\pi$
$17$	54.3140	−	19.7687i	0.0455816	−	0.0165903i	0.364710	+	0.931121i	$0.381168\pi$
$18$	2544.60			1.85113
$19$	920.562	−	1276.19i	0.585018	−	0.811021i
$19$	920.562	−	1276.19i	0.585018	−	0.811021i
$20$	1431.59			0.800281
$21$	−3828.63	+	1393.51i	−1.89450	+	0.689543i
$22$	−211.891	+	1201.70i	−0.0933376	+	0.529344i
$23$	2223.62	−	1865.84i	0.876479	−	0.735453i	−0.0889731	−	0.996034i	$-0.528359\pi$
$23$	2223.62	−	1865.84i	0.876479	−	0.735453i	0.965452	+	0.260581i	$0.0839141\pi$
$24$	−1453.67	−	1219.77i	−0.515154	−	0.432266i
$25$	847.513	+	4806.48i	0.271204	+	1.53807i
$26$	−183.791	−	318.335i	−0.0533200	−	0.0923530i
$27$	5828.52	−	10095.3i	1.53868	−	2.66508i
$28$	2066.01	+	751.966i	0.498009	+	0.181260i
$29$	−5079.71	−	1848.86i	−1.12161	−	0.408234i	−0.286374	−	0.958118i	$-0.592450\pi$
$29$	−5079.71	−	1848.86i	−1.12161	−	0.408234i	−0.835241	+	0.549884i	$0.814672\pi$
$30$	5305.90	−	9190.09i	1.07636	−	1.86430i
$31$	2969.66	+	5143.60i	0.555012	+	0.961310i	0.997903	+	0.0647339i	$0.0206199\pi$
$31$	2969.66	+	5143.60i	0.555012	+	0.961310i	−0.442890	+	0.896576i	$0.646047\pi$
$32$	177.816	+	1008.44i	0.0306970	+	0.174091i
$33$	6928.96	+	5814.09i	1.10760	+	0.929388i
$34$	−177.109	+	148.612i	−0.0262750	+	0.0220473i
$35$	−2134.98	+	12108.1i	−0.294594	+	1.67073i
$36$	−9564.55	+	3481.21i	−1.23001	+	0.447687i
$37$	−287.050			−0.0344710			−0.0172355	−	0.999851i	$-0.505486\pi$
$37$	−287.050			−0.0344710			−0.0172355	+	0.999851i	$0.505486\pi$
$38$	−1714.25	+	6056.31i	−0.192581	+	0.680377i
$39$	−2724.74			−0.286856
$40$	−5381.01	+	1958.53i	−0.531757	+	0.193544i
$41$	−240.363	+	1363.17i	−0.0223310	+	0.126645i	−0.993935	−	0.109966i	$-0.964926\pi$
$41$	−240.363	+	1363.17i	−0.0223310	+	0.126645i	0.971604	+	0.236611i	$0.0760368\pi$
$42$	12484.5	−	10475.8i	1.09206	−	0.916351i
$43$	6184.72	+	5189.60i	0.510093	+	0.428018i	0.861162	−	0.508331i	$-0.169737\pi$
$43$	6184.72	+	5189.60i	0.510093	+	0.428018i	−0.351069	+	0.936350i	$0.614182\pi$
$44$	−847.565	−	4806.78i	−0.0659996	−	0.374303i
$45$	−28459.5	−	49293.2i	−2.09505	−	3.62874i
$46$	−5805.47	+	10055.4i	−0.404522	+	0.700653i
$47$	−1477.74	−	537.854i	−0.0975784	−	0.0355156i	0.292770	−	0.956183i	$-0.405423\pi$
$47$	−1477.74	−	537.854i	−0.0975784	−	0.0355156i	−0.390348	+	0.920667i	$0.627645\pi$
$48$	7132.75	+	2596.11i	0.446842	+	0.162637i
$49$	−1037.61	+	1797.18i	−0.0617365	+	0.106931i
$50$	−9761.26	−	16907.0i	−0.552180	−	0.956404i
$51$	297.596	+	1687.75i	0.0160214	+	0.0908622i
$52$	1126.34	+	945.107i	0.0577643	+	0.0484700i
$53$	−29674.8	+	24900.1i	−1.45110	+	1.21762i	−0.519330	+	0.854574i	$0.673818\pi$
$53$	−29674.8	+	24900.1i	−1.45110	+	1.21762i	−0.931772	+	0.363045i	$0.881737\pi$
$54$	−8096.90	+	45919.8i	−0.377863	+	2.14297i
$55$	25648.8	−	9335.39i	1.14330	−	0.416127i
$56$	−8794.40			−0.374745
$57$	32525.0	+	33451.2i	1.32596	+	1.36372i
$58$	21622.8			0.844001
$59$	−1902.67	+	692.517i	−0.0711597	+	0.0259000i	−0.377355	−	0.926069i	$-0.623166\pi$
$59$	−1902.67	+	692.517i	−0.0711597	+	0.0259000i	0.306195	+	0.951969i	$0.400944\pi$
$60$	−7370.88	+	41802.3i	−0.264327	+	1.49907i
$61$	16685.4	−	14000.7i	0.574131	−	0.481753i	−0.308883	−	0.951100i	$-0.599955\pi$
$61$	16685.4	−	14000.7i	0.574131	−	0.481753i	0.883014	+	0.469347i	$0.155511\pi$
$62$	−18199.1	−	15270.9i	−0.601273	−	0.504528i
$63$	−15179.4	−	86086.8i	−0.481841	−	2.73266i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−4111.13	+	7120.69i	−0.120692	+	0.209044i
$66$	−33998.5	−	12374.5i	−0.960728	−	0.349676i
$67$	59312.6	+	21588.0i	1.61421	+	0.587525i	0.982267	−	0.187490i	$-0.0600351\pi$
$67$	59312.6	+	21588.0i	1.61421	+	0.587525i	0.631944	+	0.775014i	$0.282257\pi$
$68$	462.398	−	800.897i	0.0121267	−	0.0210041i
$69$	43033.7	+	74536.5i	1.08814	+	1.88472i
$70$	−8539.93	−	48432.4i	−0.208310	−	1.18138i
$71$	−19296.9	−	16192.0i	−0.454299	−	0.381202i	0.386730	−	0.922193i	$-0.373605\pi$
$71$	−19296.9	−	16192.0i	−0.454299	−	0.381202i	−0.841028	+	0.540991i	$0.818049\pi$
$72$	31188.4	−	26170.2i	0.709025	−	0.594943i
$73$	5900.50	−	33463.4i	0.129593	−	0.734958i	−0.848880	−	0.528585i	$-0.822723\pi$
$73$	5900.50	−	33463.4i	0.129593	−	0.734958i	0.978473	−	0.206373i	$-0.0661661\pi$
$74$	1078.96	−	392.708i	0.0229047	−	0.00833663i
$75$	−144713.			−2.97067
$76$	−1842.06	−	25109.5i	−0.0365823	−	0.498660i
$77$	41918.9			0.805717
$78$	10241.7	−	3727.66i	0.190605	−	0.0693745i
$79$	−2420.67	+	13728.3i	−0.0436382	+	0.247485i	−0.998822	−	0.0485295i	$-0.984547\pi$
$79$	−2420.67	+	13728.3i	−0.0436382	+	0.247485i	0.955184	+	0.296014i	$0.0956576\pi$
$80$	17546.5	−	14723.3i	0.306526	−	0.257206i
$81$	146355.	+	122806.i	2.47853	+	2.07973i
$82$	−961.451	−	5452.66i	−0.0157904	−	0.0895517i
$83$	−40109.9	−	69472.5i	−0.639082	−	1.10692i	−0.985634	−	0.168892i	$-0.945981\pi$
$83$	−40109.9	−	69472.5i	−0.639082	−	1.10692i	0.346552	−	0.938031i	$-0.387352\pi$
$84$	−32594.7	+	56455.8i	−0.504022	+	0.872992i
$85$	4859.70	+	1768.79i	0.0729562	+	0.0265539i
$86$	−30346.7	−	11045.3i	−0.442452	−	0.161039i
$87$	80140.9	−	138808.i	1.13516	−	1.96615i
$88$	9761.87	+	16908.1i	0.134377	+	0.232749i
$89$	−8648.18	−	49046.2i	−0.115731	−	0.656343i	−0.986386	−	0.164448i	$-0.947416\pi$
$89$	−8648.18	−	49046.2i	−0.115731	−	0.656343i	0.870655	−	0.491895i	$-0.163695\pi$
$90$	174410.	+	146347.i	2.26968	+	1.90449i
$91$	−9673.29	+	8116.85i	−0.122453	+	0.102751i
$92$	8064.87	−	45738.1i	0.0993408	−	0.563390i
$93$	−165483.	+	60231.0i	−1.98402	+	0.722125i
$94$	6290.32			0.0734265
$95$	136494.	−	34527.5i	1.55169	−	0.392515i
$96$	−30362.1			−0.336243
$97$	−38298.0	+	13939.3i	−0.413282	+	0.150423i	−0.540289	−	0.841479i	$-0.681685\pi$
$97$	−38298.0	+	13939.3i	−0.413282	+	0.150423i	0.127007	+	0.991902i	$0.459463\pi$
$98$	1441.43	−	8174.73i	0.0151610	−	0.0859822i
$99$	−148661.	+	124741.i	−1.52443	+	1.27915i
$100$	59820.5	+	50195.3i	0.598205	+	0.501953i
$101$	22627.5	+	128327.i	0.220716	+	1.25174i	0.870708	+	0.491800i	$0.163661\pi$
$101$	22627.5	+	128327.i	0.220716	+	1.25174i	−0.649992	+	0.759941i	$0.725228\pi$
$102$	−3427.58	−	5936.73i	−0.0326202	−	0.0564998i
$103$	−85564.0	+	148201.i	−0.794691	+	1.37644i	0.128345	+	0.991730i	$0.459034\pi$
$103$	−85564.0	+	148201.i	−0.794691	+	1.37644i	−0.923035	+	0.384715i	$0.874300\pi$
$104$	−5526.62	−	2011.52i	−0.0501044	−	0.0182365i
$105$	−342564.	−	124683.i	−3.03227	−	1.10366i
$106$	77475.3	−	134191.i	0.669729	−	1.16000i
$107$	−74229.7	−	128570.i	−0.626784	−	1.08562i	−0.988193	−	0.153215i	$-0.951037\pi$
$107$	−74229.7	−	128570.i	−0.626784	−	1.08562i	0.361409	−	0.932408i	$-0.382296\pi$
$108$	−32387.6	−	183679.i	−0.267189	−	1.51531i
$109$	−16788.0	−	14086.8i	−0.135342	−	0.113566i	0.572603	−	0.819832i	$-0.305933\pi$
$109$	−16788.0	−	14086.8i	−0.135342	−	0.113566i	−0.707946	+	0.706267i	$0.750378\pi$
$110$	−83636.3	+	70179.2i	−0.659042	+	0.553002i
$111$	1477.95	−	8381.87i	0.0113855	−	0.0645704i
$112$	33056.1	−	12031.5i	0.249004	−	0.0906302i
$113$	96750.2			0.712780			0.356390	−	0.934337i	$-0.384007\pi$
$113$	96750.2			0.712780			0.356390	+	0.934337i	$0.384007\pi$
$114$	−168018.	−	81238.4i	−1.21086	−	0.585463i
$115$	259720.			1.83130
$116$	−81275.3	+	29581.8i	−0.560807	+	0.204117i
$117$	10151.3	−	57571.0i	0.0685580	−	0.388812i
$118$	6204.29	−	5206.02i	0.0410192	−	0.0344192i
$119$	6084.24	+	5105.28i	0.0393857	+	0.0330485i
$120$	−29483.5	−	167209.i	−0.186907	−	1.06000i
$121$	33995.2	+	58881.4i	0.211083	+	0.365607i
$122$	−43562.4	+	75452.3i	−0.264980	+	0.458958i
$123$	−38566.8	−	14037.2i	−0.229854	−	0.0836599i
$124$	89298.2	+	32501.9i	0.521541	+	0.189825i
$125$	−78541.8	+	136038.i	−0.449600	+	0.778729i
$126$	174830.	+	302814.i	0.981045	+	1.69922i
$127$	28613.4	+	162275.i	0.157420	+	0.892774i	0.956540	+	0.291602i	$0.0941883\pi$
$127$	28613.4	+	162275.i	0.157420	+	0.892774i	−0.799120	+	0.601172i	$0.794701\pi$
$128$	12550.9	+	10531.4i	0.0677094	+	0.0568149i
$129$	−183380.	+	153874.i	−0.970235	+	0.814124i
$130$	5711.13	−	32389.4i	0.0296390	−	0.168091i
$131$	−120080.	+	43705.6i	−0.611354	+	0.222515i	−0.629096	−	0.777328i	$-0.716575\pi$
$131$	−120080.	+	43705.6i	−0.611354	+	0.222515i	0.0177417	+	0.999843i	$0.494352\pi$
$132$	144722.			0.722935
$133$	215119.	+	21867.0i	1.05451	+	0.107191i
$134$	−252477.			−1.21467
$135$	980103.	−	356728.i	4.62847	−	1.68463i
$136$	−642.356	+	3642.98i	−0.00297803	+	0.0168892i
$137$	−10307.4	+	8648.94i	−0.0469189	+	0.0393696i	−0.665946	−	0.746000i	$-0.731972\pi$
$137$	−10307.4	+	8648.94i	−0.0469189	+	0.0393696i	0.619027	+	0.785370i	$0.287527\pi$
$138$	−263726.	−	221292.i	−1.17884	−	0.989163i
$139$	−19213.9	−	108968.i	−0.0843488	−	0.478366i	−0.997495	−	0.0707342i	$-0.977466\pi$
$139$	−19213.9	−	108968.i	−0.0843488	−	0.478366i	0.913146	−	0.407632i	$-0.133645\pi$
$140$	98359.0	+	170363.i	0.424125	+	0.734606i
$141$	23313.8	−	40380.8i	0.0987566	−	0.171051i
$142$	94684.5	+	34462.3i	0.394056	+	0.143425i
$143$	26342.8	+	9588.01i	0.107726	+	0.0392092i
$144$	−81427.1	+	141036.i	−0.327237	+	0.566791i
$145$	−241836.	−	418872.i	−0.955214	−	1.65448i
$146$	23602.0	+	133854.i	0.0916361	+	0.519694i
$147$	−47135.4	−	39551.3i	−0.179909	−	0.150962i
$148$	−3518.29	+	2952.20i	−0.0132032	+	0.0110788i
$149$	44149.2	−	250383.i	0.162914	−	0.923930i	−0.788276	−	0.615322i	$-0.789026\pi$
$149$	44149.2	−	250383.i	0.162914	−	0.923930i	0.951189	−	0.308607i	$-0.0998629\pi$
$150$	543942.	−	197979.i	1.97390	−	0.718440i
$151$	312599.			1.11569			0.557847	−	0.829944i	$-0.311627\pi$
$151$	312599.			1.11569			0.557847	+	0.829944i	$0.311627\pi$
$152$	41275.7	+	91860.8i	0.144906	+	0.322494i
$153$	−36769.2			−0.126986
$154$	−157563.	+	57348.4i	−0.535369	+	0.194858i
$155$	−92279.4	+	523343.i	−0.308515	+	1.74967i
$156$	−33396.3	+	28022.9i	−0.109872	+	0.0921936i
$157$	−189761.	−	159228.i	−0.614409	−	0.515550i	0.281632	−	0.959523i	$-0.409124\pi$
$157$	−189761.	−	159228.i	−0.614409	−	0.515550i	−0.896041	+	0.443972i	$0.853569\pi$
$158$	−9682.67	−	54913.1i	−0.0308569	−	0.174998i
$159$	−574295.	−	994708.i	−1.80153	−	3.12034i
$160$	−45810.8	+	79346.6i	−0.141471	+	0.245035i
$161$	374817.	+	136422.i	1.13961	+	0.414783i
$162$	−718122.	−	261375.i	−2.14986	−	0.782486i
$163$	−187055.	+	323988.i	−0.551441	+	0.955124i	0.446730	+	0.894669i	$0.352589\pi$
$163$	−187055.	+	323988.i	−0.551441	+	0.955124i	−0.998171	+	0.0604553i	$0.980745\pi$
$164$	11073.6	+	19180.0i	0.0321497	+	0.0556850i
$165$	140534.	+	797009.i	0.401858	+	2.27905i
$166$	245808.	+	206257.i	0.692350	+	0.580951i
$167$	475581.	−	399060.i	1.31957	−	1.10725i	0.333179	−	0.942864i	$-0.391879\pi$
$167$	475581.	−	399060.i	1.31957	−	1.10725i	0.986395	−	0.164390i	$-0.0525656\pi$
$168$	45280.1	−	256796.i	0.123775	−	0.701966i
$169$	340966.	−	124101.i	0.918320	−	0.334241i
$170$	−20686.3			−0.0548986
$171$	−827966.	+	562596.i	−2.16532	+	1.47132i
$172$	129177.			0.332939
$173$	−209477.	+	76243.5i	−0.532135	+	0.193681i	−0.594091	−	0.804398i	$-0.702488\pi$
$173$	−209477.	+	76243.5i	−0.532135	+	0.193681i	0.0619566	+	0.998079i	$0.480266\pi$
$174$	−111331.	+	631387.i	−0.278767	+	1.58097i
$175$	−513755.	+	431092.i	−1.26812	+	1.06408i
$176$	−59824.2	−	50198.5i	−0.145578	−	0.122154i
$177$	−10425.1	−	59123.6i	−0.0250119	−	0.141850i
$178$	99605.7	+	172522.i	0.235632	+	0.408127i
$179$	214754.	−	371965.i	0.500967	−	0.867700i	−0.499033	−	0.866583i	$-0.666311\pi$
$179$	214754.	−	371965.i	0.500967	−	0.867700i	0.999999	−	0.00111653i	$-0.000355401\pi$
$180$	−855780.	−	311479.i	−1.96871	−	0.716551i
$181$	−421285.	−	153335.i	−0.955828	−	0.347893i	−0.183431	−	0.983033i	$-0.558720\pi$
$181$	−421285.	−	153335.i	−0.955828	−	0.347893i	−0.772397	+	0.635140i	$0.780943\pi$
$182$	25255.2	−	43743.2i	0.0565160	−	0.0978886i
$183$	322911.	+	559299.i	0.712780	+	1.23457i
$184$	32259.5	+	182953.i	0.0702446	+	0.398377i
$185$	−19674.8	−	16509.1i	−0.0422650	−	0.0354645i
$186$	539613.	−	452789.i	1.14367	−	0.959651i
$187$	3061.82	−	17364.4i	0.00640288	−	0.0363125i
$188$	−23643.9	+	8605.66i	−0.0487892	+	0.0177578i
$189$	1.60182e6			3.26182
$190$	−465813.	+	316516.i	−0.936111	+	0.636079i
$191$	−154108.			−0.305663			−0.152832	−	0.988252i	$-0.548839\pi$
$191$	−154108.			−0.305663			−0.152832	+	0.988252i	$0.548839\pi$
$192$	114124.	−	41537.7i	0.223421	−	0.0813186i
$193$	162839.	−	923503.i	0.314676	−	1.78462i	−0.259353	−	0.965783i	$-0.583509\pi$
$193$	162839.	−	923503.i	0.314676	−	1.78462i	0.574029	−	0.818835i	$-0.305380\pi$
$194$	124883.	−	104790.i	0.238232	−	0.199900i
$195$	−186757.	−	156708.i	−0.351714	−	0.295123i
$196$	5765.70	+	32698.9i	0.0107204	+	0.0607986i
$197$	−3836.98	−	6645.84i	−0.00704407	−	0.0122007i	0.862482	−	0.506088i	$-0.168909\pi$
$197$	−3836.98	−	6645.84i	−0.00704407	−	0.0122007i	−0.869526	+	0.493887i	$0.835576\pi$
$198$	388125.	−	672253.i	0.703573	−	1.21862i
$199$	−211297.	−	76906.0i	−0.378235	−	0.137666i	0.145905	−	0.989299i	$-0.453391\pi$
$199$	−211297.	−	76906.0i	−0.378235	−	0.137666i	−0.524139	+	0.851632i	$0.675613\pi$
$200$	−293523.	−	106834.i	−0.518880	−	0.188857i
$201$	−935756.	+	1.62078e6i	−1.63370	+	2.82965i
$202$	−260613.	−	451395.i	−0.449385	−	0.778357i
$203$	−128988.	−	731528.i	−0.219690	−	1.24592i
$204$	21005.4	+	17625.6i	0.0353391	+	0.0296530i
$205$	−94874.4	+	79609.0i	−0.157675	+	0.132305i
$206$	118864.	−	674113.i	0.195157	−	1.10679i
$207$	−1.73521e6	+	631564.i	−2.81466	+	1.02445i
$208$	23525.2			0.0377029
$209$	−196742.	−	437858.i	−0.311553	−	0.693374i
$210$	1.45819e6			2.28175
$211$	113006.	−	41130.8i	0.174741	−	0.0636005i	−0.253168	−	0.967422i	$-0.581473\pi$
$211$	113006.	−	41130.8i	0.174741	−	0.0636005i	0.427909	+	0.903822i	$0.359250\pi$
$212$	−107628.	+	610387.i	−0.164469	+	0.932750i
$213$	572161.	−	480100.i	0.864111	−	0.725075i
$214$	454906.	+	381711.i	0.679027	+	0.569771i
$215$	125439.	+	711403.i	0.185071	+	1.04959i
$216$	373025.	+	646099.i	0.544006	+	0.942247i
$217$	−408069.	+	706796.i	−0.588280	+	1.01893i
$218$	82374.3	+	29981.8i	0.117395	+	0.0427284i
$219$	946750.	+	344589.i	1.33391	+	0.485502i
$220$	218359.	−	378209.i	0.304168	−	0.526835i
$221$	2655.76	+	4599.92i	0.00365771	+	0.00633533i
$222$	5911.80	+	33527.5i	0.00805076	+	0.0456581i
$223$	16886.0	+	14169.0i	0.0227386	+	0.0190800i	0.654086	−	0.756420i	$-0.273053\pi$
$223$	16886.0	+	14169.0i	0.0227386	+	0.0190800i	−0.631347	+	0.775500i	$0.717498\pi$
$224$	−107790.	+	90446.9i	−0.143536	+	0.120441i
$225$	539144.	−	3.05764e6i	0.709984	−	4.02652i
$226$	−363662.	+	132362.i	−0.473616	+	0.172382i
$227$	1.27626e6			1.64390			0.821949	−	0.569561i	$-0.192887\pi$
$227$	1.27626e6			1.64390			0.821949	+	0.569561i	$0.192887\pi$
$228$	742682.	+	75494.3i	0.946163	+	0.0961783i
$229$	77951.9			0.0982286			0.0491143	−	0.998793i	$-0.484360\pi$
$229$	77951.9			0.0982286			0.0491143	+	0.998793i	$0.484360\pi$
$230$	−976227.	+	355317.i	−1.21683	+	0.442891i
$231$	−215830.	+	1.22403e6i	−0.266122	+	1.50925i
$232$	265025.	−	222382.i	0.323271	−	0.271257i
$233$	186016.	+	156086.i	0.224472	+	0.188354i	0.748087	−	0.663601i	$-0.230973\pi$
$233$	186016.	+	156086.i	0.224472	+	0.188354i	−0.523615	+	0.851955i	$0.675417\pi$
$234$	40605.3	+	230284.i	0.0484778	+	0.274931i
$235$	−70352.6	−	121854.i	−0.0831018	−	0.143937i
$236$	−16198.3	+	28056.2i	−0.0189316	+	0.0327906i
$237$	−388402.	−	141367.i	−0.449170	−	0.163485i
$238$	−29853.7	−	10865.9i	−0.0341630	−	0.0124343i
$239$	69523.4	−	120418.i	0.0787293	−	0.136363i	−0.823973	−	0.566630i	$-0.808247\pi$
$239$	69523.4	−	120418.i	0.0787293	−	0.136363i	0.902702	+	0.430266i	$0.141580\pi$
$240$	339578.	+	588166.i	0.380549	+	0.659131i
$241$	−107689.	−	610732.i	−0.119434	−	0.677342i	−0.984459	−	0.175614i	$-0.943809\pi$
$241$	−107689.	−	610732.i	−0.119434	−	0.677342i	0.865025	−	0.501728i	$-0.167302\pi$
$242$	−208335.	−	174813.i	−0.228677	−	0.191883i
$243$	−2.16953e6	+	1.82045e6i	−2.35695	+	1.97772i
$244$	60516.3	−	343205.i	0.0650725	−	0.369045i
$245$	−174480.	+	63505.5i	−0.185708	+	0.0675922i
$246$	164168.			0.172962
$247$	130184.	+	62945.4i	0.135774	+	0.0656480i
$248$	−380117.			−0.392453
$249$	2.23511e6	−	813514.i	2.28455	−	0.831508i
$250$	109109.	−	618789.i	0.110411	−	0.626170i
$251$	676721.	−	567837.i	0.677993	−	0.568904i	−0.237426	−	0.971406i	$-0.576304\pi$
$251$	676721.	−	567837.i	0.677993	−	0.568904i	0.915419	+	0.402502i	$0.131859\pi$
$252$	−1.07142e6	−	899027.i	−1.06282	−	0.891808i
$253$	−153766.	−	872050.i	−0.151029	−	0.856525i
$254$	−329556.	−	570808.i	−0.320513	−	0.555144i
$255$	−76669.9	+	132796.i	−0.0738371	+	0.127890i
$256$	−61583.7	−	22414.6i	−0.0587308	−	0.0213763i
$257$	−1.52060e6	−	553453.i	−1.43609	−	0.522695i	−0.497421	−	0.867509i	$-0.665720\pi$
$257$	−1.52060e6	−	553453.i	−1.43609	−	0.522695i	−0.938671	+	0.344815i	$0.887942\pi$
$258$	478771.	−	829255.i	0.447794	−	0.775602i
$259$	−19722.2	−	34159.8i	−0.0182686	−	0.0316421i
$260$	22844.5	+	129558.i	0.0209579	+	0.118858i
$261$	2.63430e6	+	2.21044e6i	2.39367	+	2.00853i
$262$	391561.	−	328558.i	0.352408	−	0.295705i
$263$	−89497.2	+	507564.i	−0.0797848	+	0.452482i	0.918576	+	0.395245i	$0.129340\pi$
$263$	−89497.2	+	507564.i	−0.0797848	+	0.452482i	−0.998361	+	0.0572373i	$0.981771\pi$
$264$	−543976.	+	197991.i	−0.480364	+	0.174838i
$265$	−3.46602e6			−3.03191
$266$	−838498.	+	212107.i	−0.726604	+	0.183802i
$267$	1.47668e6			1.26767
$268$	949002.	−	345409.i	0.807105	−	0.293762i
$269$	107698.	−	610787.i	0.0907461	−	0.514647i	−0.905222	−	0.424939i	$-0.860296\pi$
$269$	107698.	−	610787.i	0.0907461	−	0.514647i	0.995968	−	0.0897078i	$-0.0285933\pi$
$270$	−3.19595e6	+	2.68172e6i	−2.66803	+	2.23874i
$271$	860317.	+	721892.i	0.711599	+	0.597103i	0.925047	−	0.379852i	$-0.124025\pi$
$271$	860317.	+	721892.i	0.711599	+	0.597103i	−0.213448	+	0.976954i	$0.568469\pi$
$272$	−2569.43	−	14571.9i	−0.00210578	−	0.0119425i
$273$	−187207.	−	324251.i	−0.152025	−	0.263315i
$274$	26910.7	−	46610.7i	0.0216545	−	0.0375067i
$275$	1.39909e6	+	509226.i	1.11561	+	0.406049i
$276$	1.29403e6	+	470988.i	1.02252	+	0.372166i
$277$	−966368.	+	1.67380e6i	−0.756734	+	1.31070i	0.187774	+	0.982212i	$0.439873\pi$
$277$	−966368.	+	1.67380e6i	−0.756734	+	1.31070i	−0.944508	+	0.328489i	$0.893460\pi$
$278$	221297.	+	383298.i	0.171737	+	0.297457i
$279$	−656094.	−	3.72089e6i	−0.504610	−	2.86178i
$280$	−602779.	−	505792.i	−0.459476	−	0.385546i
$281$	718458.	−	602858.i	0.542795	−	0.455459i	−0.329698	−	0.944087i	$-0.606947\pi$
$281$	718458.	−	602858.i	0.542795	−	0.455459i	0.872492	+	0.488628i	$0.162502\pi$
$282$	−32387.2	+	183677.i	−0.0242522	+	0.137541i
$283$	442657.	−	161114.i	0.328550	−	0.119582i	−0.172478	−	0.985013i	$-0.555178\pi$
$283$	442657.	−	161114.i	0.328550	−	0.119582i	0.501028	+	0.865431i	$0.332955\pi$
$284$	−403045.			−0.296522
$285$	305431.	+	4.16339e6i	0.222742	+	3.03623i
$286$	−112134.			−0.0810628
$287$	−178735.	+	65054.2i	−0.128087	+	0.0466198i
$288$	113117.	−	641520.i	0.0803615	−	0.455752i
$289$	−1.08511e6	+	910519.i	−0.764242	+	0.641275i
$290$	1.48206e6	+	1.24359e6i	1.03483	+	0.868327i
$291$	−209842.	−	1.19007e6i	−0.145265	−	0.823836i
$292$	−271837.	−	470835.i	−0.186574	−	0.323156i
$293$	225114.	−	389910.i	0.153191	−	0.265335i	−0.779208	−	0.626766i	$-0.784378\pi$
$293$	225114.	−	389910.i	0.153191	−	0.265335i	0.932399	+	0.361431i	$0.117712\pi$
$294$	231281.	+	84179.2i	0.156053	+	0.0567985i
$295$	−170240.	−	61962.4i	−0.113896	−	0.0414546i
$296$	9185.61	−	15909.9i	0.00609367	−	0.0105545i
$297$	−1.77804e6	−	3.07965e6i	−1.16963	−	2.02587i
$298$	176597.	+	1.00153e6i	0.115197	+	0.653317i
$299$	204341.	+	171462.i	0.132183	+	0.110915i
$300$	−1.77370e6	+	1.48831e6i	−1.13783	+	0.954754i
$301$	−192647.	+	1.09256e6i	−0.122559	+	0.695069i
$302$	−1.17499e6	+	427661.i	−0.741338	+	0.269825i
$303$	−3.86365e6			−2.41764
$304$	−280819.	−	288815.i	−0.174278	−	0.179241i
$305$	1.94886e6			1.19958
$306$	138207.	−	50303.3i	0.0843775	−	0.0307109i
$307$	−35345.3	+	200453.i	−0.0214035	+	0.121385i	−0.993638	−	0.112625i	$-0.964074\pi$
$307$	−35345.3	+	200453.i	−0.0214035	+	0.121385i	0.972234	+	0.234011i	$0.0751851\pi$
$308$	513787.	−	431119.i	0.308608	−	0.258953i
$309$	−3.88693e6	−	3.26152e6i	−2.31585	−	1.94323i
$310$	−369118.	−	2.09337e6i	−0.218153	−	1.23721i
$311$	1.17180e6	+	2.02961e6i	0.686991	+	1.18990i	0.972807	+	0.231618i	$0.0744020\pi$
$311$	1.17180e6	+	2.02961e6i	0.686991	+	1.18990i	−0.285816	+	0.958284i	$0.592265\pi$
$312$	87191.6	−	151020.i	0.0507094	−	0.0878312i
$313$	2.00887e6	+	731169.i	1.15902	+	0.421849i	0.848748	−	0.528798i	$-0.177357\pi$
$313$	2.00887e6	+	731169.i	1.15902	+	0.421849i	0.310274	+	0.950647i	$0.399579\pi$
$314$	931105.	+	338894.i	0.532935	+	0.193973i
$315$	3.91069e6	−	6.77351e6i	2.22063	−	3.84625i
$316$	111521.	+	193159.i	0.0628257	+	0.108817i
$317$	−120470.	−	683220.i	−0.0673335	−	0.381867i	−0.999788	−	0.0205802i	$-0.993449\pi$
$317$	−120470.	−	683220.i	−0.0673335	−	0.381867i	0.932455	−	0.361287i	$-0.117662\pi$
$318$	3.51948e6	+	2.95320e6i	1.95169	+	1.63766i
$319$	−1.26325e6	+	1.05999e6i	−0.695045	+	0.583212i
$320$	63639.7	−	360919.i	0.0347419	−	0.197031i
$321$	4.13642e6	−	1.50553e6i	2.24059	−	0.815507i
$322$	−1.59549e6			−0.857539
$323$	24770.8	−	87513.3i	0.0132109	−	0.0466732i
$324$	3.05684e6			1.61774
$325$	−421459.	+	153399.i	−0.221333	+	0.0805588i
$326$	259853.	−	1.47370e6i	0.135421	−	0.768008i
$327$	497773.	−	417681.i	0.257432	−	0.216011i
$328$	−67862.7	−	56943.6i	−0.0348294	−	0.0292254i
$329$	−37524.0	−	212809.i	−0.0191126	−	0.108393i
$330$	−1.61861e6	−	2.80351e6i	−0.818196	−	1.41716i
$331$	−724122.	+	1.25422e6i	−0.363280	+	0.629219i	−0.988499	−	0.151230i	$-0.951677\pi$
$331$	−724122.	+	1.25422e6i	−0.363280	+	0.629219i	0.625219	+	0.780450i	$0.285010\pi$
$332$	−1.20611e6	−	438989.i	−0.600541	−	0.218579i
$333$	171594.	+	62455.2i	0.0847993	+	0.0308644i
$334$	−1.24166e6	+	2.15061e6i	−0.609025	+	1.05486i
$335$	2.82377e6	+	4.89091e6i	1.37473	+	2.38110i
$336$	181121.	+	1.02719e6i	0.0875225	+	0.496365i
$337$	−1.02994e6	−	864226.i	−0.494014	−	0.414527i	0.361448	−	0.932392i	$-0.382282\pi$
$337$	−1.02994e6	−	864226.i	−0.494014	−	0.414527i	−0.855462	+	0.517865i	$0.826727\pi$
$338$	−1.11183e6	+	932937.i	−0.529355	+	0.444182i
$339$	−498142.	+	2.82510e6i	−0.235426	+	1.33517i
$340$	77755.2	−	28300.6i	0.0364781	−	0.0132769i
$341$	1.81184e6			0.843789
$342$	2.34246e6	−	3.24739e6i	1.08295	−	1.50131i
$343$	2.02433e6			0.929066
$344$	−485548.	+	176725.i	−0.221226	+	0.0805196i
$345$	−1.33723e6	+	7.58381e6i	−0.604865	+	3.43036i
$346$	683070.	−	573163.i	0.306743	−	0.257388i
$347$	2.33731e6	+	1.96124e6i	1.04206	+	0.874394i	0.992237	−	0.124364i	$-0.0396892\pi$
$347$	2.33731e6	+	1.96124e6i	1.04206	+	0.874394i	0.0498251	+	0.998758i	$0.484134\pi$
$348$	−445322.	−	2.52555e6i	−0.197118	−	1.11791i
$349$	60414.7	+	104641.i	0.0265509	+	0.0459875i	0.878996	−	0.476830i	$-0.158214\pi$
$349$	60414.7	+	104641.i	0.0265509	+	0.0459875i	−0.852445	+	0.522817i	$0.824881\pi$
$350$	1.34132e6	−	2.32323e6i	0.585278	−	1.01373i
$351$	1.00663e6	+	366382.i	0.436114	+	0.158733i
$352$	293541.	+	106840.i	0.126273	+	0.0459598i
$353$	−827804.	+	1.43380e6i	−0.353582	+	0.612423i	−0.986874	−	0.161490i	$-0.948370\pi$
$353$	−827804.	+	1.43380e6i	−0.353582	+	0.612423i	0.633292	+	0.773913i	$0.281703\pi$
$354$	120071.	+	207970.i	0.0509251	+	0.0882048i
$355$	−391382.	−	2.21964e6i	−0.164828	−	0.934785i
$356$	−610419.	−	512203.i	−0.255272	−	0.214199i
$357$	−180400.	+	151374.i	−0.0749147	+	0.0628609i
$358$	−298333.	+	1.69193e6i	−0.123025	+	0.697710i
$359$	−4.38925e6	+	1.59756e6i	−1.79744	+	0.654214i	−0.798826	+	0.601562i	$0.794545\pi$
$359$	−4.38925e6	+	1.59756e6i	−1.79744	+	0.654214i	−0.998613	+	0.0526518i	$0.983233\pi$
$360$	3.64281e6			1.48143
$361$	−781231.	−	2.34963e6i	−0.315509	−	0.948923i
$362$	1.79329e6			0.719249
$363$	−1.89437e6	+	689494.i	−0.754567	+	0.274640i
$364$	−35084.1	+	198972.i	−0.0138790	+	0.0787115i
$365$	2.32900e6	−	1.95427e6i	0.915036	−	0.767806i
$366$	−1.97891e6	−	1.66051e6i	−0.772190	−	0.647945i
$367$	−696706.	−	3.95122e6i	−0.270013	−	1.53132i	−0.754371	−	0.656449i	$-0.772058\pi$
$367$	−696706.	−	3.95122e6i	−0.270013	−	1.53132i	0.484358	−	0.874870i	$-0.339053\pi$
$368$	−371550.	−	643543.i	−0.143020	−	0.247718i
$369$	440277.	−	762582.i	0.168329	−	0.291555i
$370$	96538.7	+	35137.2i	0.0366604	+	0.0133433i
$371$	−5.00202e6	−	1.82059e6i	−1.88674	−	0.686716i
$372$	−1.40883e6	+	2.44016e6i	−0.527838	+	0.914243i
$373$	586251.	+	1.01542e6i	0.218178	+	0.377896i	0.954251	−	0.299006i	$-0.0966552\pi$
$373$	586251.	+	1.01542e6i	0.218178	+	0.377896i	−0.736073	+	0.676902i	$0.763322\pi$
$374$	12247.3	+	69457.7i	0.00452752	+	0.0256768i
$375$	−3.56793e6	−	2.99385e6i	−1.31020	−	1.09939i
$376$	77098.6	−	64693.4i	0.0281240	−	0.0235988i
$377$	86261.5	−	489213.i	0.0312582	−	0.177274i
$378$	−6.02089e6	+	2.19142e6i	−2.16736	+	0.788855i
$379$	1.22032e6			0.436391			0.218196	−	0.975905i	$-0.429983\pi$
$379$	1.22032e6			0.436391			0.218196	+	0.975905i	$0.429983\pi$
$380$	1.31786e6	−	1.82698e6i	0.468179	−	0.649045i
$381$	−4.88574e6			−1.72432
$382$	579258.	−	210833.i	0.203102	−	0.0739230i
$383$	436551.	−	2.47580e6i	0.152068	−	0.862421i	−0.809349	−	0.587328i	$-0.800180\pi$
$383$	436551.	−	2.47580e6i	0.152068	−	0.862421i	0.961417	−	0.275094i	$-0.0887089\pi$
$384$	−372139.	+	312262.i	−0.128788	+	0.108066i
$385$	2.87317e6	+	2.41088e6i	0.987892	+	0.828940i
$386$	651354.	+	3.69401e6i	0.222510	+	1.26192i
$387$	−2.56800e6	−	4.44791e6i	−0.871601	−	1.50966i
$388$	−326047.	+	564730.i	−0.109952	+	0.190442i
$389$	−2.82772e6	−	1.02921e6i	−0.947464	−	0.344849i	−0.178355	−	0.983966i	$-0.557078\pi$
$389$	−2.82772e6	−	1.02921e6i	−0.947464	−	0.344849i	−0.769109	+	0.639117i	$0.779300\pi$
$390$	916365.	+	333530.i	0.305075	+	0.111038i
$391$	83888.6	−	145299.i	0.0277499	−	0.0480642i
$392$	−66406.7	−	115020.i	−0.0218271	−	0.0378057i
$393$	−657940.	−	3.73137e6i	−0.214885	−	1.21867i
$394$	23514.4	+	19730.9i	0.00763120	+	0.00640334i
$395$	−955469.	+	801734.i	−0.308123	+	0.258546i
$396$	−539178.	+	3.05783e6i	−0.172780	+	0.979885i
$397$	3.11142e6	−	1.13246e6i	0.990791	−	0.360618i	0.204764	−	0.978811i	$-0.434357\pi$
$397$	3.11142e6	−	1.13246e6i	0.990791	−	0.360618i	0.786026	+	0.618193i	$0.212135\pi$
$398$	899432.			0.284617
$399$	−1.74611e6	+	6.16888e6i	−0.549084	+	1.93988i
$400$	1.24944e6			0.390450
$401$	−4.45114e6	+	1.62008e6i	−1.38232	+	0.503125i	−0.922882	−	0.385083i	$-0.874173\pi$
$401$	−4.45114e6	+	1.62008e6i	−1.38232	+	0.503125i	−0.459442	+	0.888208i	$0.651951\pi$
$402$	1.29994e6	−	7.37232e6i	0.401197	−	2.27530i
$403$	−418104.	+	350831.i	−0.128240	+	0.107606i
$404$	1.59713e6	+	1.34015e6i	0.486841	+	0.408508i
$405$	2.96839e6	+	1.68345e7i	0.899255	+	5.09993i
$406$	1.48563e6	+	2.57318e6i	0.447295	+	0.774738i
$407$	−43783.6	+	75835.3i	−0.0131016	+	0.0226927i
$408$	−103068.	−	37513.6i	−0.0306530	−	0.0111568i
$409$	1.70521e6	+	620644.i	0.504044	+	0.183457i	0.581512	−	0.813538i	$-0.302461\pi$
$409$	1.70521e6	+	620644.i	0.504044	+	0.183457i	−0.0774680	+	0.996995i	$0.524684\pi$
$410$	247699.	−	429028.i	0.0727722	−	0.126045i
$411$	−199479.	−	345507.i	−0.0582494	−	0.100891i
$412$	475457.	+	2.69645e6i	0.137997	+	0.782618i
$413$	−213137.	−	178843.i	−0.0614871	−	0.0515938i
$414$	5.65822e6	−	4.74781e6i	1.62248	−	1.36142i
$415$	1.24638e6	−	7.06857e6i	0.355247	−	2.01470i
$416$	−88425.9	+	32184.4i	−0.0250522	+	0.00911826i
$417$	3.28078e6			0.923925
$418$	1.33853e6	+	1.37665e6i	0.374705	+	0.385374i
$419$	−4.58004e6			−1.27448			−0.637242	−	0.770664i	$-0.719925\pi$
$419$	−4.58004e6			−1.27448			−0.637242	+	0.770664i	$0.719925\pi$
$420$	−5.48102e6	+	1.99493e6i	−1.51614	+	0.551828i
$421$	−568605.	+	3.22472e6i	−0.156353	+	0.886720i	0.801186	+	0.598415i	$0.204203\pi$
$421$	−568605.	+	3.22472e6i	−0.156353	+	0.886720i	−0.957539	+	0.288305i	$0.906908\pi$
$422$	−368493.	+	309202.i	−0.100727	+	0.0845204i
$423$	766347.	+	643041.i	0.208245	+	0.174738i
$424$	−430511.	−	2.44155e6i	−0.116297	−	0.659554i
$425$	141050.	+	244305.i	0.0378791	+	0.0656085i
$426$	−1.49381e6	+	2.58735e6i	−0.398814	+	0.690766i
$427$	2.81251e6	+	1.02367e6i	0.746491	+	0.271700i
$428$	−2.23210e6	−	812417.i	−0.588985	−	0.214373i
$429$	−415602.	+	719844.i	−0.109027	+	0.188841i
$430$	−1.44475e6	−	2.50239e6i	−0.376810	−	0.652655i
$431$	−582299.	−	3.30238e6i	−0.150992	−	0.856315i	−0.962359	−	0.271780i	$-0.912388\pi$
$431$	−582299.	−	3.30238e6i	−0.150992	−	0.856315i	0.811368	−	0.584536i	$-0.198723\pi$
$432$	−2.28603e6	−	1.91821e6i	−0.589349	−	0.494523i
$433$	5.11023e6	−	4.28799e6i	1.30985	−	1.09909i	0.321494	−	0.946912i	$-0.395815\pi$
$433$	5.11023e6	−	4.28799e6i	1.30985	−	1.09909i	0.988353	−	0.152180i	$-0.0486295\pi$
$434$	566883.	−	3.21495e6i	0.144467	−	0.819314i
$435$	1.34762e7	−	4.90494e6i	3.41464	−	1.24283i
$436$	−350644.			−0.0883384
$437$	−334189.	−	4.55539e6i	−0.0837121	−	1.14110i
$438$	−4.03004e6			−1.00375
$439$	2.94187e6	−	1.07075e6i	0.728555	−	0.265172i	0.0490017	−	0.998799i	$-0.484396\pi$
$439$	2.94187e6	−	1.07075e6i	0.728555	−	0.265172i	0.679553	+	0.733627i	$0.262174\pi$
$440$	−303341.	+	1.72033e6i	−0.0746963	+	0.423624i
$441$	1.01129e6	−	848571.i	0.247616	−	0.207774i
$442$	−16275.5	−	13656.7i	−0.00396258	−	0.00332500i
$443$	−291485.	−	1.65310e6i	−0.0705679	−	0.400211i	−0.999548	−	0.0300797i	$-0.990424\pi$
$443$	−291485.	−	1.65310e6i	−0.0705679	−	0.400211i	0.928980	−	0.370131i	$-0.120687\pi$
$444$	−68089.4	−	117934.i	−0.0163916	−	0.0283911i
$445$	2.22804e6	−	3.85907e6i	0.533362	−	0.923810i
$446$	−82855.0	−	30156.7i	−0.0197234	−	0.00717872i
$447$	7.08386e6	+	2.57832e6i	1.67688	+	0.610333i
$448$	281421.	−	487435.i	0.0662463	−	0.114742i
$449$	−1.31514e6	−	2.27789e6i	−0.307862	−	0.533233i	0.670032	−	0.742332i	$-0.266280\pi$
$449$	−1.31514e6	−	2.27789e6i	−0.307862	−	0.533233i	−0.977895	+	0.209099i	$0.932947\pi$
$450$	2.15658e6	+	1.22306e7i	0.502035	+	2.84718i
$451$	323470.	+	271424.i	0.0748846	+	0.0628357i
$452$	1.18584e6	−	995037.i	0.273011	−	0.229083i
$453$	−1.60949e6	+	9.12789e6i	−0.368505	+	2.08990i
$454$	−4.79717e6	+	1.74603e6i	−1.09231	+	0.397568i
$455$	−1.12984e6			−0.255852
$456$	−2.89485e6	+	732283.i	−0.651950	+	0.164918i
$457$	−8.76096e6			−1.96228			−0.981141	−	0.193296i	$-0.938082\pi$
$457$	−8.76096e6			−1.96228			−0.981141	+	0.193296i	$0.938082\pi$
$458$	−293003.	+	106644.i	−0.0652693	+	0.0237561i
$459$	117000.	−	663538.i	0.0259211	−	0.147006i
$460$	3.18331e6	−	2.67111e6i	0.701430	−	0.588569i
$461$	−2.37088e6	−	1.98941e6i	−0.519587	−	0.435985i	0.344901	−	0.938639i	$-0.387912\pi$
$461$	−2.37088e6	−	1.98941e6i	−0.519587	−	0.435985i	−0.864488	+	0.502654i	$0.832357\pi$
$462$	−863318.	−	4.89612e6i	−0.188177	−	1.06720i
$463$	652858.	+	1.13078e6i	0.141536	+	0.245147i	0.928075	−	0.372393i	$-0.121463\pi$
$463$	652858.	+	1.13078e6i	0.141536	+	0.245147i	−0.786539	+	0.617540i	$0.788129\pi$
$464$	−691931.	+	1.19846e6i	−0.149200	+	0.258421i
$465$	−1.48065e7	−	5.38912e6i	−3.17555	−	1.15581i
$466$	−912732.	−	332207.i	−0.194706	−	0.0708670i
$467$	−2.08329e6	+	3.60836e6i	−0.442036	+	0.765629i	−0.997840	−	0.0656843i	$-0.979077\pi$
$467$	−2.08329e6	+	3.60836e6i	−0.442036	+	0.765629i	0.555805	+	0.831313i	$0.312410\pi$
$468$	−467673.	−	810034.i	−0.0987024	−	0.170958i
$469$	1.50611e6	+	8.54160e6i	0.316174	+	1.79311i
$470$	431146.	+	361774.i	0.0900284	+	0.0755428i
$471$	5.62650e6	−	4.72119e6i	1.16865	−	0.980617i
$472$	22502.4	−	127617.i	0.00464915	−	0.0263666i
$473$	2.31438e6	−	842366.i	0.475644	−	0.173120i
$474$	1.65332e6			0.337995
$475$	6.91418e6	+	3.34308e6i	1.40607	+	0.679849i
$476$	127079.			0.0257072
$477$	2.31568e7	−	8.42838e6i	4.65996	−	1.69609i
$478$	−96580.9	+	547738.i	−0.0193340	+	0.109649i
$479$	3.87663e6	−	3.25288e6i	0.771997	−	0.647783i	−0.169222	−	0.985578i	$-0.554126\pi$
$479$	3.87663e6	−	3.25288e6i	0.771997	−	0.647783i	0.941220	+	0.337795i	$0.109681\pi$
$480$	−2.08105e6	−	1.74621e6i	−0.412268	−	0.345934i
$481$	−4580.60	−	25977.8i	−0.000902733	−	0.00511965i
$482$	1.24031e6	+	2.14828e6i	0.243171	+	0.421184i
$483$	−5.91337e6	+	1.02422e7i	−1.15337	+	1.99769i
$484$	1.02224e6	+	372065.i	0.198353	+	0.0721947i
$485$	−3.42668e6	−	1.24721e6i	−0.661485	−	0.240761i
$486$	5.66425e6	−	9.81077e6i	1.08781	−	1.88414i
$487$	1.44573e6	+	2.50408e6i	0.276226	+	0.478438i	0.970444	−	0.241328i	$-0.0775828\pi$
$487$	1.44573e6	+	2.50408e6i	0.276226	+	0.478438i	−0.694218	+	0.719765i	$0.744249\pi$
$488$	242065.	+	1.37282e6i	0.0460132	+	0.260954i
$489$	−8.49735e6	−	7.13012e6i	−1.60698	−	1.34842i
$490$	568950.	−	477405.i	0.107049	−	0.0898250i
$491$	759487.	−	4.30726e6i	0.142173	−	0.806302i	−0.827421	−	0.561582i	$-0.810193\pi$
$491$	759487.	−	4.30726e6i	0.142173	−	0.806302i	0.969594	−	0.244720i	$-0.0786960\pi$
$492$	−617070.	+	224595.i	−0.114927	+	0.0418299i
$493$	−312449.			−0.0578977
$494$	−575447.	−	58494.7i	−0.106093	−	0.0107845i
$495$	−1.73636e7			−3.18513
$496$	1.42877e6	−	520030.i	0.260771	−	0.0949127i
$497$	601077.	−	3.40888e6i	0.109154	−	0.619042i
$498$	−7.28832e6	+	6.11562e6i	−1.31690	+	1.10501i
$499$	−6.77754e6	−	5.68703e6i	−1.21849	−	1.02243i	−0.998903	−	0.0468372i	$-0.985086\pi$
$499$	−6.77754e6	−	5.68703e6i	−1.21849	−	1.02243i	−0.219583	−	0.975594i	$-0.570470\pi$
$500$	436437.	+	2.47516e6i	0.0780722	+	0.442769i
$501$	9.20391e6	+	1.59416e7i	1.63824	+	2.83752i
$502$	−1.76679e6	+	3.06018e6i	−0.312915	+	0.541985i
$503$	9.49612e6	+	3.45631e6i	1.67350	+	0.609105i	0.992397	−	0.123081i	$-0.0392773\pi$
$503$	9.49612e6	+	3.45631e6i	1.67350	+	0.609105i	0.681105	+	0.732185i	$0.261500\pi$
$504$	5.25716e6	+	1.91345e6i	0.921881	+	0.335537i
$505$	−5.82954e6	+	1.00971e7i	−1.01720	+	1.76184i
$506$	1.77101e6	+	3.06747e6i	0.307499	+	0.532604i
$507$	1.86821e6	+	1.05952e7i	0.322780	+	1.83058i
$508$	2.01964e6	+	1.69468e6i	0.347227	+	0.291358i
$509$	−4.66555e6	+	3.91486e6i	−0.798194	+	0.669765i	−0.947759	−	0.318987i	$-0.896657\pi$
$509$	−4.66555e6	+	3.91486e6i	−0.798194	+	0.669765i	0.149565	+	0.988752i	$0.452213\pi$
$510$	106509.	−	604041.i	0.0181326	−	0.102835i
$511$	4.38764e6	−	1.59697e6i	0.743325	−	0.270548i
$512$	262144.			0.0441942
$513$	−7.51802e6	−	1.67317e7i	−1.26128	−	2.80702i
$514$	6.47276e6			1.08064
$515$	−1.43881e7	+	5.23686e6i	−2.39049	+	0.870067i
$516$	−665101.	+	3.77198e6i	−0.109967	+	0.623655i
$517$	−367493.	+	308364.i	−0.0604677	+	0.0507384i
$518$	120864.	+	101417.i	0.0197913	+	0.0166069i
$519$	−1.14776e6	−	6.50929e6i	−0.187040	−	1.06076i
$520$	−263112.	−	455724.i	−0.0426710	−	0.0739084i
$521$	−2.16135e6	+	3.74356e6i	−0.348843	+	0.604214i	−0.986044	−	0.166484i	$-0.946759\pi$
$521$	−2.16135e6	+	3.74356e6i	−0.348843	+	0.604214i	0.637201	+	0.770698i	$0.280092\pi$
$522$	−1.29258e7	−	4.70461e6i	−2.07626	−	0.755696i
$523$	5.13671e6	+	1.86961e6i	0.821166	+	0.298880i	0.718228	−	0.695808i	$-0.244954\pi$
$523$	5.13671e6	+	1.86961e6i	0.821166	+	0.298880i	0.102938	+	0.994688i	$0.467176\pi$
$524$	−1.02229e6	+	1.77066e6i	−0.162647	+	0.281713i
$525$	−9.94268e6	−	1.72212e7i	−1.57436	−	2.72688i
$526$	−357989.	−	2.03026e6i	−0.0564164	−	0.319953i
$527$	262976.	+	220663.i	0.0412468	+	0.0346102i
$528$	1.77381e6	−	1.48841e6i	0.276900	−	0.232347i
$529$	345476.	−	1.95929e6i	0.0536758	−	0.304410i
$530$	1.30280e7	−	4.74180e6i	2.01459	−	0.733252i
$531$	1.28806e6			0.198244
$532$	2.86154e6	−	1.94439e6i	0.438350	−	0.297855i
$533$	−127201.			−0.0193942
$534$	−5.55049e6	+	2.02021e6i	−0.842322	+	0.306580i
$535$	2.30662e6	−	1.30815e7i	0.348410	−	1.97593i
$536$	−3.09453e6	+	2.59662e6i	−0.465247	+	0.390388i
$537$	9.75566e6	+	8.18597e6i	1.45989	+	1.22500i
$538$	430793.	+	2.44315e6i	0.0641672	+	0.363910i
$539$	316530.	+	548246.i	0.0469292	+	0.0812838i
$540$	8.34403e6	−	1.44523e7i	1.23138	−	2.13281i
$541$	5.55355e6	+	2.02133e6i	0.815789	+	0.296923i	0.716013	−	0.698087i	$-0.245965\pi$
$541$	5.55355e6	+	2.02133e6i	0.815789	+	0.296923i	0.0997758	+	0.995010i	$0.468187\pi$
$542$	−4.22134e6	−	1.53644e6i	−0.617237	−	0.224656i
$543$	6.64648e6	−	1.15120e7i	0.967369	−	1.67553i
$544$	29593.5	+	51257.4i	0.00428744	+	0.00742607i
$545$	−340497.	−	1.93106e6i	−0.0491047	−	0.278486i
$546$	1.14727e6	+	962673.i	0.164696	+	0.138197i
$547$	−7.89559e6	+	6.62518e6i	−1.12828	+	0.946738i	−0.998993	−	0.0448700i	$-0.985713\pi$
$547$	−7.89559e6	+	6.62518e6i	−1.12828	+	0.946738i	−0.129285	+	0.991607i	$0.541268\pi$
$548$	−37384.0	+	212015.i	−0.00531782	+	0.0301589i
$549$	−1.30205e7	+	4.73906e6i	−1.84372	+	0.671060i
$550$	−5.95551e6			−0.839484
$551$	−7.03569e6	+	4.78069e6i	−0.987251	+	0.670828i
$552$	−5.50831e6			−0.769433
$553$	−1.80002e6	+	655153.i	−0.250302	+	0.0911025i
$554$	1.34246e6	−	7.61350e6i	0.185835	−	1.05393i
$555$	583366.	−	489502.i	0.0803912	−	0.0674562i
$556$	−1.35619e6	−	1.13798e6i	−0.186051	−	0.156116i
$557$	1.94188e6	+	1.10129e7i	0.265206	+	1.50406i	0.768447	+	0.639914i	$0.221030\pi$
$557$	1.94188e6	+	1.10129e7i	0.265206	+	1.50406i	−0.503240	+	0.864146i	$0.667859\pi$
$558$	7.55659e6	+	1.30884e7i	1.02740	+	1.77951i
$559$	−370962.	+	642526.i	−0.0502112	+	0.0869683i
$560$	2.95767e6	+	1.07650e6i	0.398547	+	0.145059i
$561$	491276.	+	178810.i	0.0659051	+	0.0239875i
$562$	−1.87576e6	+	3.24891e6i	−0.250517	+	0.433908i
$563$	−2.12649e6	−	3.68319e6i	−0.282744	−	0.489726i	0.689316	−	0.724461i	$-0.257911\pi$
$563$	−2.12649e6	−	3.68319e6i	−0.282744	−	0.489726i	−0.972060	+	0.234735i	$0.924578\pi$
$564$	−129549.	−	734709.i	−0.0171489	−	0.0972562i
$565$	6.63137e6	+	5.56438e6i	0.873941	+	0.733324i
$566$	−1.44343e6	+	1.21118e6i	−0.189389	+	0.158916i
$567$	−4.55878e6	+	2.58541e7i	−0.595513	+	3.37732i
$568$	1.51495e6	−	551398.i	0.197028	−	0.0717124i
$569$	2.55215e6			0.330465			0.165233	−	0.986255i	$-0.447163\pi$
$569$	2.55215e6			0.330465			0.165233	+	0.986255i	$0.447163\pi$
$570$	−6.84390e6	−	1.52314e7i	−0.882301	−	1.96360i
$571$	−5.71384e6			−0.733395			−0.366698	−	0.930340i	$-0.619512\pi$
$571$	−5.71384e6			−0.733395			−0.366698	+	0.930340i	$0.619512\pi$
$572$	421485.	−	153408.i	0.0538632	−	0.0196046i
$573$	793465.	−	4.49996e6i	0.100958	−	0.572562i
$574$	582824.	−	489047.i	0.0738342	−	0.0619543i
$575$	1.08527e7	+	9.10648e6i	1.36889	+	1.14863i
$576$	452469.	+	2.56608e6i	0.0568241	+	0.322266i
$577$	−7.76723e6	−	1.34532e7i	−0.971240	−	1.68224i	−0.691824	−	0.722066i	$-0.743193\pi$
$577$	−7.76723e6	−	1.34532e7i	−0.971240	−	1.68224i	−0.279415	−	0.960170i	$-0.590141\pi$
$578$	2.83303e6	−	4.90696e6i	0.352722	−	0.610932i
$579$	2.61279e7	+	9.50977e6i	3.23898	+	1.17889i
$580$	−7.27204e6	−	2.64681e6i	−0.897608	−	0.326702i
$581$	5.51161e6	−	9.54639e6i	0.677389	−	1.17327i
$582$	2.41686e6	+	4.18613e6i	0.295763	+	0.512277i
$583$	2.05204e6	+	1.16377e7i	0.250043	+	1.41807i
$584$	1.66591e6	+	1.39787e6i	0.202125	+	0.169603i
$585$	4.00686e6	−	3.36216e6i	0.484077	−	0.406189i
$586$	−312726.	+	1.77356e6i	−0.0376201	+	0.213354i
$587$	−1.51226e7	+	5.50419e6i	−1.81147	+	0.659322i	−0.814625	+	0.579987i	$0.803057\pi$
$587$	−1.51226e7	+	5.50419e6i	−1.81147	+	0.659322i	−0.996848	+	0.0793349i	$0.974720\pi$
$588$	−984495.			−0.117428
$589$	9.29798e6	+	945148.i	1.10433	+	0.112257i
$590$	724663.			0.0857050
$591$	213814.	−	77822.0i	0.0251807	−	0.00916502i
$592$	−12760.5	+	72368.5i	−0.00149646	+	0.00848682i
$593$	8.40984e6	−	7.05669e6i	0.982089	−	0.824071i	−0.00231383	−	0.999997i	$-0.500737\pi$
$593$	8.40984e6	−	7.05669e6i	0.982089	−	0.824071i	0.984403	+	0.175926i	$0.0562921\pi$
$594$	1.08965e7	+	9.14321e6i	1.26712	+	1.06324i
$595$	123401.	+	699844.i	0.0142899	+	0.0810418i
$596$	−2.03396e6	−	3.52293e6i	−0.234546	−	0.406245i
$597$	3.33357e6	−	5.77391e6i	0.382802	−	0.663032i
$598$	−1.00264e6	−	364932.i	−0.114655	−	0.0417311i
$599$	−1.35227e7	−	4.92188e6i	−1.53992	−	0.560485i	−0.573893	−	0.818930i	$-0.694568\pi$
$599$	−1.35227e7	−	4.92188e6i	−1.53992	−	0.560485i	−0.966026	+	0.258445i	$0.916790\pi$
$600$	4.63081e6	−	8.02080e6i	0.525145	−	0.909577i
$601$	−830649.	−	1.43873e6i	−0.0938062	−	0.162477i	0.815304	−	0.579034i	$-0.196570\pi$
$601$	−830649.	−	1.43873e6i	−0.0938062	−	0.162477i	−0.909110	+	0.416557i	$0.863237\pi$
$602$	−770589.	−	4.37023e6i	−0.0866626	−	0.491488i
$603$	−3.07591e7	−	2.58100e7i	−3.44493	−	2.89064i
$604$	3.83144e6	−	3.21496e6i	0.427336	−	0.358577i
$605$	−1.05637e6	+	5.99096e6i	−0.117335	+	0.665439i
$606$	1.45226e7	−	5.28578e6i	1.60643	−	0.584693i
$607$	−2.67042e6			−0.294177			−0.147088	−	0.989123i	$-0.546990\pi$
$607$	−2.67042e6			−0.294177			−0.147088	+	0.989123i	$0.546990\pi$
$608$	1.45066e6	+	701407.i	0.159150	+	0.0769505i
$609$	2.20247e7			2.40640
$610$	−7.32530e6	+	2.66619e6i	−0.797078	+	0.290113i
$611$	25094.4	−	142317.i	0.00271940	−	0.0154225i
$612$	−450670.	+	378157.i	−0.0486385	+	0.0408125i
$613$	672954.	+	564676.i	0.0723326	+	0.0606943i	0.678237	−	0.734843i	$-0.262744\pi$
$613$	672954.	+	564676.i	0.0723326	+	0.0606943i	−0.605905	+	0.795537i	$0.707189\pi$
$614$	−141381.	−	801812.i	−0.0151346	−	0.0858325i
$615$	−1.83610e6	−	3.18022e6i	−0.195753	−	0.339054i
$616$	−1.34140e6	+	2.32338e6i	−0.142432	+	0.246700i
$617$	1.29954e7	+	4.72996e6i	1.37429	+	0.500201i	0.920442	−	0.390879i	$-0.127829\pi$
$617$	1.29954e7	+	4.72996e6i	1.37429	+	0.500201i	0.453848	+	0.891079i	$0.350051\pi$
$618$	1.90721e7	+	6.94167e6i	2.00876	+	0.731127i
$619$	−3.33999e6	+	5.78502e6i	−0.350363	+	0.606846i	−0.986313	−	0.164884i	$-0.947275\pi$
$619$	−3.33999e6	+	5.78502e6i	−0.350363	+	0.606846i	0.635950	+	0.771730i	$0.280608\pi$
$620$	4.25133e6	+	7.36352e6i	0.444166	+	0.769318i
$621$	−5.87578e6	−	3.33232e7i	−0.611416	−	3.46751i
$622$	−7.18118e6	−	6.02572e6i	−0.744251	−	0.624501i
$623$	5.24246e6	−	4.39894e6i	0.541146	−	0.454076i
$624$	−121125.	+	686936.i	−0.0124530	+	0.0706244i
$625$	1.12485e6	−	409412.i	0.115185	−	0.0419237i
$626$	−8.55119e6			−0.872149
$627$	1.37984e7	−	3.49046e6i	1.40172	−	0.354579i
$628$	−3.96344e6			−0.401027
$629$	−15590.8	+	5674.60i	−0.00157124	+	0.000571885i
$630$	−5.43267e6	+	3.08102e7i	−0.545333	+	3.09274i
$631$	8.82660e6	−	7.40640e6i	0.882511	−	0.740515i	−0.0841830	−	0.996450i	$-0.526828\pi$
$631$	8.82660e6	−	7.40640e6i	0.882511	−	0.740515i	0.966694	+	0.255936i	$0.0823836\pi$
$632$	−683437.	−	573472.i	−0.0680622	−	0.0571110i
$633$	619179.	+	3.51154e6i	0.0614196	+	0.348328i
$634$	1.38752e6	+	2.40325e6i	0.137093	+	0.237452i
$635$	−7.37169e6	+	1.27681e7i	−0.725492	+	1.25659i
$636$	−1.72691e7	−	6.28545e6i	−1.69289	−	0.616160i
$637$	−179201.	−	65224.0i	−0.0174982	−	0.00636882i
$638$	3.29812e6	−	5.71250e6i	0.320785	−	0.555616i
$639$	8.01239e6	+	1.38779e7i	0.776265	+	1.34453i
$640$	254559.	+	1.44367e6i	0.0245662	+	0.139322i
$641$	1.18820e7	+	9.97017e6i	1.14220	+	0.958423i	0.999509	−	0.0313431i	$-0.00997845\pi$
$641$	1.18820e7	+	9.97017e6i	1.14220	+	0.958423i	0.142696	+	0.989767i	$0.454423\pi$
$642$	−1.34882e7	+	1.13179e7i	−1.29156	+	1.08375i
$643$	1.90688e6	−	1.08145e7i	0.181885	−	1.03152i	−0.748008	−	0.663690i	$-0.768989\pi$
$643$	1.90688e6	−	1.08145e7i	0.181885	−	1.03152i	0.929893	−	0.367831i	$-0.119899\pi$
$644$	5.99707e6	−	2.18276e6i	0.569803	−	0.207391i
$645$	−2.14188e7			−2.02720
$646$	26617.7	+	362831.i	0.00250951	+	0.0342076i
$647$	670576.			0.0629778			0.0314889	−	0.999504i	$-0.489975\pi$
$647$	670576.			0.0629778			0.0314889	+	0.999504i	$0.489975\pi$
$648$	−1.14899e7	+	4.18200e6i	−1.07493	+	0.391243i
$649$	−107259.	+	608293.i	−0.00999586	+	0.0566893i
$650$	1.37431e6	−	1.15318e6i	0.127585	−	0.107057i
$651$	−1.85374e7	−	1.55547e7i	−1.71434	−	1.43850i
$652$	1.03941e6	+	5.89481e6i	0.0957568	+	0.543064i
$653$	972476.	+	1.68438e6i	0.0892475	+	0.154581i	0.907193	−	0.420714i	$-0.138220\pi$
$653$	972476.	+	1.68438e6i	0.0892475	+	0.154581i	−0.817946	+	0.575295i	$0.804887\pi$
$654$	−1.29959e6	+	2.25096e6i	−0.118813	+	0.205790i
$655$	−1.07441e7	−	3.91052e6i	−0.978510	−	0.356149i
$656$	332984.	+	121196.i	0.0302109	+	0.0109959i
$657$	−1.08080e7	+	1.87201e7i	−0.976863	+	1.69198i
$658$	432184.	+	748565.i	0.0389139	+	0.0674008i
$659$	−498145.	−	2.82512e6i	−0.0446830	−	0.253410i	0.954281	−	0.298910i	$-0.0966230\pi$
$659$	−498145.	−	2.82512e6i	−0.0446830	−	0.253410i	−0.998964	+	0.0455001i	$0.985512\pi$
$660$	9.91941e6	+	8.32338e6i	0.886393	+	0.743772i
$661$	−4.39101e6	+	3.68450e6i	−0.390896	+	0.328001i	−0.816962	−	0.576691i	$-0.804344\pi$
$661$	−4.39101e6	+	3.68450e6i	−0.390896	+	0.328001i	0.426066	+	0.904692i	$0.359899\pi$
$662$	1.00594e6	−	5.70496e6i	0.0892127	−	0.505950i
$663$	−147991.	+	53864.5i	−0.0130753	+	0.00475903i
$664$	5.13407e6			0.451899
$665$	1.34869e7	+	1.38709e7i	1.18265	+	1.21633i
$666$	−730427.			−0.0638104
$667$	−1.47450e7	+	5.36675e6i	−1.28331	+	0.467086i
$668$	1.72489e6	−	9.78233e6i	0.149562	−	0.848206i
$669$	−500677.	+	420118.i	−0.0432506	+	0.0362916i
$670$	−1.73051e7	−	1.45207e7i	−1.48931	−	1.24968i
$671$	−1.15381e6	−	6.54359e6i	−0.0989302	−	0.561061i
$672$	−2.08606e6	−	3.61317e6i	−0.178199	−	0.308649i
$673$	7.14930e6	−	1.23830e7i	0.608452	−	1.05387i	−0.383044	−	0.923730i	$-0.625124\pi$
$673$	7.14930e6	−	1.23830e7i	0.608452	−	1.05387i	0.991496	−	0.130139i	$-0.0415423\pi$
$674$	5.05366e6	+	1.83938e6i	0.428505	+	0.155963i
$675$	5.34626e7	+	1.94588e7i	4.51638	+	1.64383i
$676$	2.90279e6	−	5.02777e6i	0.244314	−	0.423164i
$677$	−8.02151e6	−	1.38937e7i	−0.672643	−	1.16505i	−0.977152	−	0.212542i	$-0.931826\pi$
$677$	−8.02151e6	−	1.38937e7i	−0.672643	−	1.16505i	0.304509	−	0.952509i	$-0.401508\pi$
$678$	−1.99257e6	−	1.13004e7i	−0.166471	−	0.944105i
$679$	−4.29013e6	−	3.59985e6i	−0.357105	−	0.299647i
$680$	−253546.	+	212751.i	−0.0210274	+	0.0176441i
$681$	−6.57114e6	+	3.72668e7i	−0.542967	+	3.07932i
$682$	−6.81029e6	+	2.47874e6i	−0.560667	+	0.204066i
$683$	−2.01746e6			−0.165483			−0.0827416	−	0.996571i	$-0.526368\pi$
$683$	−2.01746e6			−0.165483			−0.0827416	+	0.996571i	$0.526368\pi$
$684$	−4.36207e6	+	1.54109e7i	−0.356494	+	1.25947i
$685$	−1.20391e6			−0.0980317
$686$	−7.60900e6	+	2.76945e6i	−0.617330	+	0.224690i
$687$	−401354.	+	2.27619e6i	−0.0324441	+	0.184000i
$688$	1.58329e6	−	1.32854e6i	0.127523	−	0.107005i
$689$	−2.72698e6	−	2.28820e6i	−0.218843	−	0.183631i
$690$	−5.34892e6	−	3.03352e7i	−0.427704	−	2.42563i
$691$	−1.72264e6	−	2.98370e6i	−0.137246	−	0.237717i	0.789207	−	0.614127i	$-0.210492\pi$
$691$	−1.72264e6	−	2.98370e6i	−0.137246	−	0.237717i	−0.926453	+	0.376410i	$0.877158\pi$
$692$	−1.78337e6	+	3.08888e6i	−0.141571	+	0.245209i
$693$	−2.50584e7	−	9.12053e6i	−1.98208	−	0.721418i
$694$	−1.14686e7	−	4.17422e6i	−0.903879	−	0.328985i
$695$	4.95010e6	−	8.57382e6i	0.388733	−	0.673306i
$696$	5.12902e6	+	8.88372e6i	0.401339	+	0.695139i
$697$	13892.9	+	78790.6i	0.00108321	+	0.00614317i
$698$	−370243.	−	310670.i	−0.0287639	−	0.0241358i
$699$	−5.51547e6	+	4.62803e6i	−0.426962	+	0.358264i
$700$	−1.86334e6	+	1.05675e7i	−0.143730	+	0.815133i
$701$	9.34576e6	−	3.40158e6i	0.718323	−	0.261448i	0.0431092	−	0.999070i	$-0.486274\pi$
$701$	9.34576e6	−	3.40158e6i	0.718323	−	0.261448i	0.675214	+	0.737622i	$0.264051\pi$
$702$	−4.28491e6			−0.328170
$703$	−264248.	+	366331.i	−0.0201661	+	0.0279567i
$704$	−1.24952e6			−0.0950192
$705$	3.92037e6	−	1.42690e6i	0.297067	−	0.108124i
$706$	1.14997e6	−	6.52182e6i	0.0868312	−	0.492444i
$707$	−1.37166e7	+	1.15096e7i	−1.03204	+	0.865988i
$708$	−735840.	−	617443.i	−0.0551697	−	0.0462929i
$709$	−3.57390e6	−	2.02686e7i	−0.267010	−	1.51429i	−0.763250	−	0.646103i	$-0.776398\pi$
$709$	−3.57390e6	−	2.02686e7i	−0.267010	−	1.51429i	0.496240	−	0.868185i	$-0.334714\pi$
$710$	4.50776e6	+	7.80767e6i	0.335595	+	0.581267i
$711$	4.43398e6	−	7.67988e6i	0.328942	−	0.569745i
$712$	2.99516e6	+	1.09015e6i	0.221422	+	0.0805909i
$713$	1.62006e7	+	5.89652e6i	1.19345	+	0.434382i
$714$	470992.	−	815782.i	0.0345755	−	0.0598864i
$715$	1.25414e6	+	2.17223e6i	0.0917444	+	0.158906i
$716$	−1.19333e6	−	6.76773e6i	−0.0869919	−	0.493356i
$717$	3.15825e6	+	2.65008e6i	0.229429	+	0.192514i
$718$	1.43126e7	−	1.20097e7i	1.03611	−	0.869402i
$719$	608105.	−	3.44874e6i	0.0438689	−	0.248793i	−0.954985	−	0.296654i	$-0.904129\pi$
$719$	608105.	−	3.44874e6i	0.0438689	−	0.248793i	0.998854	+	0.0478609i	$0.0152404\pi$
$720$	−1.36925e7	+	4.98366e6i	−0.984354	+	0.358275i
$721$	−2.35151e7			−1.68465
$722$	6.15095e6	+	7.76292e6i	0.439136	+	0.554220i
$723$	1.83878e7			1.30823
$724$	−6.74056e6	+	2.45336e6i	−0.477914	+	0.173946i
$725$	4.58141e6	−	2.59825e7i	0.323708	−	1.83584i
$726$	6.17721e6	−	5.18330e6i	0.434962	−	0.364976i
$727$	1.62731e7	+	1.36548e7i	1.14192	+	0.958183i	0.999500	−	0.0316233i	$-0.0100677\pi$
$727$	1.62731e7	+	1.36548e7i	1.14192	+	0.958183i	0.142418	+	0.989807i	$0.454512\pi$
$728$	−140336.	−	795887.i	−0.00981390	−	0.0556574i
$729$	−1.87740e7	−	3.25176e7i	−1.30839	−	2.26620i
$730$	−6.08060e6	+	1.05319e7i	−0.422318	+	0.731475i
$731$	438508.	+	159604.i	0.0303518	+	0.0110471i
$732$	9.70999e6	+	3.53415e6i	0.669794	+	0.243785i
$733$	−1.23297e7	+	2.13557e7i	−0.847603	+	1.46809i	0.0357389	+	0.999361i	$0.488622\pi$
$733$	−1.23297e7	+	2.13557e7i	−0.847603	+	1.46809i	−0.883342	+	0.468730i	$0.844712\pi$
$734$	8.02434e6	+	1.38986e7i	0.549755	+	0.952204i
$735$	−956008.	−	5.42179e6i	−0.0652744	−	0.370190i
$736$	2.27699e6	+	1.91062e6i	0.154941	+	0.130011i
$737$	1.47502e7	−	1.23769e7i	1.00030	−	0.839350i
$738$	−611626.	+	3.46871e6i	−0.0413376	+	0.234437i
$739$	−9.29858e6	+	3.38441e6i	−0.626333	+	0.227967i	−0.635635	−	0.771990i	$-0.719261\pi$
$739$	−9.29858e6	+	3.38441e6i	−0.626333	+	0.227967i	0.00930138	+	0.999957i	$0.497039\pi$
$740$	−410937.			−0.0275865
$741$	−2.50829e6	+	3.47729e6i	−0.167816	+	0.232646i
$742$	2.12922e7			1.41974
$743$	1.24700e7	−	4.53872e6i	0.828696	−	0.301621i	0.107372	−	0.994219i	$-0.465756\pi$
$743$	1.24700e7	−	4.53872e6i	0.828696	−	0.301621i	0.721324	+	0.692598i	$0.243534\pi$
$744$	1.95712e6	−	1.10994e7i	0.129624	−	0.735135i
$745$	1.74263e7	−	1.46224e7i	1.15031	−	0.965223i
$746$	−3.59276e6	−	3.01468e6i	−0.236364	−	0.198333i
$747$	8.86158e6	+	5.02565e7i	0.581045	+	3.29527i
$748$	−141058.	−	244320.i	−0.00921817	−	0.0159663i
$749$	1.02001e7	−	1.76671e7i	0.664354	−	1.15069i
$750$	1.75068e7	+	6.37197e6i	1.13646	+	0.413638i
$751$	−1.82592e7	−	6.64582e6i	−1.18136	−	0.429981i	−0.324679	−	0.945824i	$-0.605256\pi$
$751$	−1.82592e7	−	6.64582e6i	−1.18136	−	0.429981i	−0.856683	+	0.515844i	$0.827479\pi$
$752$	−201290.	+	348645.i	−0.0129801	+	0.0224822i
$753$	1.30966e7	+	2.26839e7i	0.841724	+	1.45791i
$754$	345046.	+	1.95685e6i	0.0221029	+	0.125352i
$755$	2.14259e7	+	1.79785e7i	1.36796	+	1.14785i
$756$	1.96331e7	−	1.64741e7i	1.24935	−	1.04833i
$757$	−3.11786e6	+	1.76823e7i	−0.197750	+	1.12150i	0.710697	+	0.703498i	$0.248380\pi$
$757$	−3.11786e6	+	1.76823e7i	−0.197750	+	1.12150i	−0.908447	+	0.417999i	$0.862732\pi$
$758$	−4.58691e6	+	1.66950e6i	−0.289966	+	0.105539i
$759$	2.62556e7			1.65431
$760$	−2.45409e6	+	8.67014e6i	−0.154119	+	0.544493i
$761$	−3.11076e7			−1.94717			−0.973587	−	0.228315i	$-0.926678\pi$
$761$	−3.11076e7			−1.94717			−0.973587	+	0.228315i	$0.926678\pi$
$762$	1.83644e7	−	6.68409e6i	1.14575	−	0.417018i
$763$	522929.	−	2.96568e6i	0.0325186	−	0.184422i
$764$	−1.88886e6	+	1.58494e6i	−0.117076	+	0.0982382i
$765$	−2.52021e6	−	2.11471e6i	−0.155698	−	0.130646i
$766$	1.74620e6	+	9.90322e6i	0.107528	+	0.609824i
$767$	−93034.1	−	161140.i	−0.00571023	−	0.00989041i
$768$	971586.	−	1.68284e6i	0.0594399	−	0.102953i
$769$	−1.91615e7	−	6.97421e6i	−1.16846	−	0.425284i	−0.316347	−	0.948644i	$-0.602456\pi$
$769$	−1.91615e7	−	6.97421e6i	−1.16846	−	0.425284i	−0.852112	+	0.523360i	$0.824678\pi$
$770$	−1.40979e7	−	5.13120e6i	−0.856892	−	0.311883i
$771$	2.39900e7	−	4.15519e7i	1.45343	−	2.51742i
$772$	−7.50200e6	−	1.29938e7i	−0.453037	−	0.784683i
$773$	3.24962e6	+	1.84295e7i	0.195607	+	1.10934i	0.911552	+	0.411185i	$0.134885\pi$
$773$	3.24962e6	+	1.84295e7i	0.195607	+	1.10934i	−0.715945	+	0.698157i	$0.754004\pi$
$774$	1.57376e7	+	1.32054e7i	0.944249	+	0.792319i
$775$	−2.22058e7	+	1.86329e7i	−1.32804	+	1.11436i
$776$	452940.	−	2.56875e6i	0.0270014	−	0.153133i
$777$	1.09901e6	−	400007.i	0.0653054	−	0.0237692i
$778$	1.20368e7			0.712955
$779$	1.51839e6	+	1.56163e6i	0.0896479	+	0.0922006i
$780$	−3.90070e6			−0.229565
$781$	−7.22108e6	+	2.62826e6i	−0.423618	+	0.154184i
$782$	−116537.	+	660913.i	−0.00681469	+	0.0386480i
$783$	−4.82720e7	+	4.05050e7i	−2.81378	+	2.36105i
$784$	406964.	+	341483.i	0.0236464	+	0.0198417i
$785$	−3.84876e6	−	2.18274e7i	−0.222919	−	1.26424i
$786$	7.57785e6	+	1.31252e7i	0.437512	+	0.757793i
$787$	1.09395e7	−	1.89477e7i	0.629591	−	1.09048i	−0.358042	−	0.933705i	$-0.616556\pi$
$787$	1.09395e7	−	1.89477e7i	0.629591	−	1.09048i	0.987634	−	0.156779i	$-0.0501110\pi$
$788$	−115379.	−	41994.4i	−0.00661926	−	0.00240921i
$789$	−1.43601e7	−	5.22664e6i	−0.821228	−	0.298903i
$790$	2.49455e6	−	4.32069e6i	0.142208	−	0.246312i
$791$	6.64734e6	+	1.15135e7i	0.377752	+	0.654286i
$792$	−2.15671e6	−	1.22313e7i	−0.122174	−	0.692884i
$793$	1.53331e6	+	1.28660e6i	0.0865858	+	0.0726541i
$794$	−1.01458e7	+	8.51334e6i	−0.571130	+	0.479235i
$795$	1.78457e7	−	1.01208e8i	1.00142	−	5.67932i
$796$	−3.38076e6	+	1.23050e6i	−0.189117	+	0.0688331i
$797$	−2.57470e7			−1.43576			−0.717879	−	0.696168i	$-0.754887\pi$
$797$	−2.57470e7			−1.43576			−0.717879	+	0.696168i	$0.754887\pi$
$798$	−1.87630e6	−	2.55762e7i	−0.104303	−	1.42177i
$799$	−90894.7			−0.00503699
$800$	−4.69636e6	+	1.70934e6i	−0.259440	+	0.0944284i
$801$	−5.50153e6	+	3.12007e7i	−0.302972	+	1.71824i
$802$	1.45144e7	−	1.21790e7i	0.796825	−	0.668616i
$803$	−7.94064e6	−	6.66299e6i	−0.434577	−	0.364653i
$804$	5.19975e6	+	2.94893e7i	0.283689	+	1.60888i
$805$	1.78444e7	+	3.09074e7i	0.970536	+	1.68102i
$806$	1.09159e6	−	1.89069e6i	0.0591866	−	0.102514i
$807$	1.72805e7	+	6.28958e6i	0.934053	+	0.339968i
$808$	−7.83668e6	−	2.85232e6i	−0.422283	−	0.153699i
$809$	−7.77456e6	+	1.34659e7i	−0.417642	+	0.723378i	−0.995702	−	0.0926168i	$-0.970477\pi$
$809$	−7.77456e6	+	1.34659e7i	−0.417642	+	0.723378i	0.578059	+	0.815995i	$0.303810\pi$
$810$	−3.41885e7	−	5.92162e7i	−1.83091	−	3.17123i
$811$	−4.01246e6	−	2.27558e7i	−0.214219	−	1.21490i	−0.882256	−	0.470770i	$-0.843976\pi$
$811$	−4.01246e6	−	2.27558e7i	−0.214219	−	1.21490i	0.668037	−	0.744128i	$-0.267135\pi$
$812$	−9.10444e6	−	7.63953e6i	−0.484577	−	0.406609i
$813$	−2.55088e7	+	2.14044e7i	−1.35352	+	1.13573i
$814$	60823.5	−	344947.i	0.00321744	−	0.0182470i
$815$	−3.14544e7	+	1.14485e7i	−1.65878	+	0.603745i
$816$	438730.			0.0230660
$817$	1.23163e7	−	3.11555e6i	0.645545	−	0.163297i
$818$	−7.25857e6			−0.379287
$819$	7.54857e6	−	2.74745e6i	0.393238	−	0.143127i
$820$	−344100.	+	1.95149e6i	−0.0178711	+	0.101352i
$821$	4.75734e6	−	3.99189e6i	0.246324	−	0.206690i	−0.511263	−	0.859424i	$-0.670822\pi$
$821$	4.75734e6	−	3.99189e6i	0.246324	−	0.206690i	0.757587	+	0.652734i	$0.226378\pi$
$822$	1.22248e6	+	1.02578e6i	0.0631046	+	0.0529510i
$823$	−127380.	−	722407.i	−0.00655543	−	0.0371777i	0.981355	−	0.192206i	$-0.0615642\pi$
$823$	−127380.	−	722407.i	−0.00655543	−	0.0371777i	−0.987910	+	0.155028i	$0.950453\pi$
$824$	−5.47610e6	−	9.48488e6i	−0.280966	−	0.486647i
$825$	−2.20729e7	+	3.82315e7i	−1.12908	+	1.95563i
$826$	1.04580e6	+	380642.i	0.0533336	+	0.0194118i
$827$	−1.75108e7	−	6.37342e6i	−0.890313	−	0.324048i	−0.143949	−	0.989585i	$-0.545980\pi$
$827$	−1.75108e7	−	6.37342e6i	−0.890313	−	0.324048i	−0.746364	+	0.665538i	$0.768202\pi$
$828$	−1.47726e7	+	2.55868e7i	−0.748824	+	1.29700i
$829$	8.76747e6	+	1.51857e7i	0.443086	+	0.767447i	0.997917	−	0.0645159i	$-0.0205503\pi$
$829$	8.76747e6	+	1.51857e7i	0.443086	+	0.767447i	−0.554831	+	0.831963i	$0.687217\pi$
$830$	4.98552e6	+	2.82743e7i	0.251197	+	1.42461i
$831$	−4.38993e7	−	3.68359e7i	−2.20524	−	1.85041i
$832$	288342.	−	241947.i	0.0144411	−	0.0121175i
$833$	−20828.5	+	118124.i	−0.00104003	+	0.00589830i
$834$	−1.23317e7	+	4.48837e6i	−0.613914	+	0.223447i
$835$	5.55480e7			2.75710
$836$	−6.91461e6	−	3.34328e6i	−0.342178	−	0.165446i
$837$	6.92349e7			3.41595
$838$	1.72153e7	−	6.26587e6i	0.846847	−	0.308227i
$839$	−3.91080e6	+	2.21793e7i	−0.191805	+	1.08778i	0.725090	+	0.688654i	$0.241798\pi$
$839$	−3.91080e6	+	2.21793e7i	−0.191805	+	1.08778i	−0.916895	+	0.399128i	$0.869313\pi$
$840$	1.78727e7	−	1.49969e7i	0.873959	−	0.733339i
$841$	6.67269e6	+	5.59905e6i	0.325320	+	0.272976i
$842$	−2.27442e6	−	1.28989e7i	−0.110558	−	0.627006i
$843$	1.39043e7	+	2.40829e7i	0.673876	+	1.16719i
$844$	962066.	−	1.66635e6i	0.0464889	−	0.0805211i
$845$	3.05076e7	+	1.11039e7i	1.46983	+	0.534974i
$846$	−3.76025e6	−	1.36862e6i	−0.180631	−	0.0657441i
$847$	−4.67136e6	+	8.09104e6i	−0.223736	+	0.387522i
$848$	4.95842e6	+	8.58824e6i	0.236785	+	0.410123i
$849$	2.42540e6	+	1.37551e7i	0.115482	+	0.654930i
$850$	−864402.	−	725319.i	−0.0410363	−	0.0344336i
$851$	−638291.	+	535590.i	−0.0302131	+	0.0253518i
$852$	2.07517e6	−	1.17689e7i	0.0979390	−	0.555440i
$853$	1.87373e7	−	6.81983e6i	0.881729	−	0.320923i	0.138822	−	0.990317i	$-0.455669\pi$
$853$	1.87373e7	−	6.81983e6i	0.881729	−	0.320923i	0.742907	+	0.669394i	$0.233446\pi$
$854$	−1.19720e7			−0.561725
$855$	−8.91063e7	−	9.05773e6i	−4.16863	−	0.423745i
$856$	9.50140e6			0.443203
$857$	1.10961e7	−	4.03865e6i	0.516082	−	0.187839i	−0.0708312	−	0.997488i	$-0.522565\pi$
$857$	1.10961e7	−	4.03865e6i	0.516082	−	0.187839i	0.586913	+	0.809650i	$0.300343\pi$
$858$	577349.	−	3.27431e6i	0.0267744	−	0.151845i
$859$	−7.02070e6	+	5.89107e6i	−0.324637	+	0.272403i	−0.790510	−	0.612449i	$-0.790185\pi$
$859$	−7.02070e6	+	5.89107e6i	−0.324637	+	0.272403i	0.465874	+	0.884851i	$0.345740\pi$
$860$	8.85397e6	+	7.42936e6i	0.408218	+	0.342535i
$861$	−979321.	−	5.55400e6i	−0.0450212	−	0.255328i
$862$	6.70665e6	+	1.16163e7i	0.307424	+	0.532473i
$863$	1.85760e7	−	3.21745e7i	0.849033	−	1.47057i	−0.0330392	−	0.999454i	$-0.510519\pi$
$863$	1.85760e7	−	3.21745e7i	0.849033	−	1.47057i	0.882072	−	0.471114i	$-0.156148\pi$
$864$	1.12169e7	+	4.08263e6i	0.511199	+	0.186061i
$865$	−1.87428e7	−	6.82182e6i	−0.851715	−	0.309999i
$866$	−1.33419e7	+	2.31088e7i	−0.604535	+	1.04709i
$867$	−2.10002e7	−	3.63734e7i	−0.948801	−	1.64337i
$868$	2.26753e6	+	1.28598e7i	0.102154	+	0.579343i
$869$	3.25763e6	+	2.73348e6i	0.146336	+	0.122791i
$870$	−4.39436e7	+	3.68731e7i	−1.96833	+	1.65162i
$871$	−1.00722e6	+	5.71224e6i	−0.0449863	+	0.255130i
$872$	1.31799e6	−	479709.i	0.0586976	−	0.0213642i
$873$	2.59268e7			1.15137
$874$	7.48828e6	+	1.66655e7i	0.331592	+	0.737970i
$875$	−2.15853e7			−0.953097
$876$	1.51480e7	−	5.51342e6i	0.666953	−	0.242751i
$877$	804137.	−	4.56049e6i	0.0353046	−	0.200222i	−0.962054	−	0.272860i	$-0.912030\pi$
$877$	804137.	−	4.56049e6i	0.0353046	−	0.200222i	0.997358	+	0.0726375i	$0.0231416\pi$
$878$	−9.59294e6	+	8.04943e6i	−0.419967	+	0.352394i
$879$	1.02263e7	+	8.58088e6i	0.446423	+	0.374593i
$880$	−1.21336e6	−	6.88133e6i	−0.0528183	−	0.299547i
$881$	1.39972e7	+	2.42438e7i	0.607575	+	1.05235i	0.991639	+	0.129045i	$0.0411911\pi$
$881$	1.39972e7	+	2.42438e7i	0.607575	+	1.05235i	−0.384063	+	0.923307i	$0.625476\pi$
$882$	−2.64029e6	+	4.57311e6i	−0.114282	+	0.197943i
$883$	−2.34654e7	−	8.54069e6i	−1.01280	−	0.368631i	−0.218295	−	0.975883i	$-0.570050\pi$
$883$	−2.34654e7	−	8.54069e6i	−1.01280	−	0.368631i	−0.794509	+	0.607252i	$0.792272\pi$
$884$	79859.3	+	29066.4i	0.00343712	+	0.00125101i
$885$	2.68582e6	−	4.65198e6i	0.115271	−	0.199655i
$886$	3.35719e6	+	5.81483e6i	0.143679	+	0.248859i
$887$	4.41712e6	+	2.50507e7i	0.188508	+	1.06908i	0.921365	+	0.388699i	$0.127075\pi$
$887$	4.41712e6	+	2.50507e7i	0.188508	+	1.06908i	−0.732857	+	0.680383i	$0.761813\pi$
$888$	417276.	+	350136.i	0.0177579	+	0.0149006i
$889$	−1.73452e7	+	1.45544e7i	−0.736081	+	0.617645i
$890$	−3.09515e6	+	1.75535e7i	−0.130981	+	0.742828i
$891$	5.47673e7	−	1.99337e7i	2.31114	−	0.841187i
$892$	352690.			0.0148416
$893$	−2.04676e6	+	1.39075e6i	−0.0858890	+	0.0583608i
$894$	−3.01540e7			−1.26183
$895$	3.61123e7	−	1.31438e7i	1.50694	−	0.548483i
$896$	−390946.	+	2.21716e6i	−0.0162685	+	0.0922630i
$897$	−6.05879e6	+	5.08393e6i	−0.251423	+	0.210969i
$898$	8.05965e6	+	6.76285e6i	0.333523	+	0.279859i
$899$	−5.57520e6	−	3.16185e7i	−0.230070	−	1.30479i
$900$	−2.48385e7	−	4.30215e7i	−1.02216	−	1.77043i
$901$	−1.11951e6	+	1.93905e6i	−0.0459428	+	0.0795752i
$902$	−1.58718e6	−	577686.i	−0.0649546	−	0.0236415i
$903$	−3.09108e7	−	1.12506e7i	−1.26151	−	0.459152i
$904$	−3.09601e6	+	5.36244e6i	−0.126003	+	0.218243i
$905$	−2.00566e7	−	3.47391e7i	−0.814023	−	1.40993i
$906$	−6.43797e6	−	3.65116e7i	−0.260573	−	1.47778i
$907$	7.27454e6	+	6.10407e6i	0.293621	+	0.246377i	0.777683	−	0.628656i	$-0.216395\pi$
$907$	7.27454e6	+	6.10407e6i	0.293621	+	0.246377i	−0.484062	+	0.875034i	$0.660839\pi$
$908$	1.56428e7	−	1.31258e7i	0.629649	−	0.528338i
$909$	1.43945e7	−	8.16351e7i	0.577811	−	3.27693i
$910$	4.24682e6	−	1.54572e6i	0.170004	−	0.0618765i
$911$	−6.43324e6			−0.256823			−0.128412	−	0.991721i	$-0.540988\pi$
$911$	−6.43324e6			−0.256823			−0.128412	+	0.991721i	$0.540988\pi$
$912$	9.87927e6	−	6.71288e6i	0.393312	−	0.267252i
$913$	−2.44718e7			−0.971601
$914$	3.29304e7	−	1.19857e7i	1.30386	−	0.474567i
$915$	−1.00342e7	+	5.69066e7i	−0.396213	+	2.24703i
$916$	955434.	−	801704.i	0.0376237	−	0.0315701i
$917$	−1.34513e7	−	1.12870e7i	−0.528253	−	0.443257i
$918$	467998.	+	2.65415e6i	0.0183290	+	0.103949i
$919$	3.88425e6	+	6.72772e6i	0.151712	+	0.262772i	0.931857	−	0.362826i	$-0.118188\pi$
$919$	3.88425e6	+	6.72772e6i	0.151712	+	0.262772i	−0.780145	+	0.625598i	$0.784855\pi$
$920$	−8.31103e6	+	1.43951e7i	−0.323732	+	0.560720i
$921$	−5.67124e6	−	2.06416e6i	−0.220307	−	0.0801854i
$922$	1.16333e7	+	4.23417e6i	0.450687	+	0.164037i
$923$	1.15744e6	−	2.00474e6i	0.0447191	−	0.0774557i
$924$	9.94330e6	+	1.72223e7i	0.383134	+	0.663608i
$925$	−243279.	−	1.37970e6i	−0.00934867	−	0.0530189i
$926$	−4.00094e6	−	3.35719e6i	−0.153333	−	0.128661i
$927$	8.33938e7	−	6.99757e7i	3.18739	−	2.67453i
$928$	961221.	−	5.45135e6i	0.0366398	−	0.207795i
$929$	3.25628e7	−	1.18519e7i	1.23789	−	0.450556i	0.361599	−	0.932334i	$-0.382231\pi$
$929$	3.25628e7	−	1.18519e7i	1.23789	−	0.450556i	0.876294	+	0.481778i	$0.160009\pi$
$930$	6.30269e7			2.38956
$931$	1.33837e6	+	2.97860e6i	0.0506061	+	0.112626i
$932$	3.88523e6			0.146513
$933$	−6.52978e7	+	2.37665e7i	−2.45581	+	0.893841i
$934$	2.89408e6	−	1.64131e7i	0.108553	−	0.615636i
$935$	1.20854e6	−	1.01408e6i	0.0452097	−	0.0379354i
$936$	2.86607e6	+	2.40492e6i	0.106929	+	0.0897244i
$937$	316830.	+	1.79683e6i	0.0117890	+	0.0668589i	0.990135	−	0.140119i	$-0.0447484\pi$
$937$	316830.	+	1.79683e6i	0.0117890	+	0.0668589i	−0.978346	+	0.206978i	$0.933637\pi$
$938$	−1.73467e7	−	3.00454e7i	−0.643740	−	1.11499i
$939$	−3.16933e7	+	5.48944e7i	−1.17302	+	2.03172i
$940$	−2.11551e6	−	769984.i	−0.0780902	−	0.0284225i
$941$	−1.87840e7	−	6.83683e6i	−0.691537	−	0.251699i	−0.0277436	−	0.999615i	$-0.508832\pi$
$941$	−1.87840e7	−	6.83683e6i	−0.691537	−	0.251699i	−0.663793	+	0.747916i	$0.731054\pi$
$942$	−1.46897e7	+	2.54434e7i	−0.539370	+	0.934216i
$943$	2.00897e6	+	3.47964e6i	0.0735690	+	0.127425i
$944$	90009.6	+	510470.i	0.00328745	+	0.0186440i
$945$	1.09791e8	+	9.21255e7i	3.99933	+	3.35583i
$946$	−7.54681e6	+	6.33252e6i	−0.274180	+	0.230064i
$947$	−2.50765e6	+	1.42216e7i	−0.0908640	+	0.515315i	0.905073	+	0.425257i	$0.139816\pi$
$947$	−2.50765e6	+	1.42216e7i	−0.0908640	+	0.515315i	−0.995937	+	0.0900580i	$0.971295\pi$
$948$	−6.21444e6	+	2.26187e6i	−0.224585	+	0.0817423i
$949$	3.12257e6			0.112550
$950$	−3.05624e7	−	3.10670e6i	−1.09870	−	0.111684i
$951$	2.05703e7			0.737545
$952$	−477659.	+	173854.i	−0.0170815	+	0.00621715i
$953$	4.96892e6	−	2.81801e7i	0.177227	−	1.00510i	−0.758315	−	0.651888i	$-0.773977\pi$
$953$	4.96892e6	−	2.81801e7i	0.177227	−	1.00510i	0.935542	−	0.353215i	$-0.114912\pi$
$954$	−7.55103e7	+	6.33607e7i	−2.68618	+	2.25397i
$955$	−1.05628e7	−	8.86322e6i	−0.374774	−	0.314473i
$956$	−386324.	−	2.19095e6i	−0.0136712	−	0.0775332i
$957$	−2.44477e7	−	4.23446e7i	−0.862894	−	1.49458i
$958$	−1.01212e7	+	1.75304e7i	−0.356301	+	0.617131i
$959$	−1.73743e6	−	632373.i	−0.0610044	−	0.0222038i
$960$	1.02112e7	+	3.71656e6i	0.357599	+	0.130156i
$961$	−3.32321e6	+	5.75596e6i	−0.116078	+	0.201052i
$962$	52757.2	+	91378.1i	0.00183799	+	0.00318350i
$963$	1.63997e7	+	9.30075e7i	0.569864	+	3.23186i
$964$	−7.60104e6	−	6.37803e6i	−0.263439	−	0.221052i
$965$	6.42745e7	−	5.39327e7i	2.22188	−	1.86438i
$966$	8.21476e6	−	4.65882e7i	0.283238	−	1.60632i
$967$	2.40128e7	−	8.73996e6i	0.825805	−	0.300568i	0.105669	−	0.994401i	$-0.466302\pi$
$967$	2.40128e7	−	8.73996e6i	0.825805	−	0.300568i	0.720136	+	0.693833i	$0.244079\pi$
$968$	−4.35138e6			−0.149258
$969$	2.42785e6	+	1.17389e6i	0.0830639	+	0.0401622i
$970$	1.45864e7			0.497759
$971$	5.57543e6	−	2.02929e6i	0.189771	−	0.0690711i	−0.245386	−	0.969425i	$-0.578915\pi$
$971$	5.57543e6	−	2.02929e6i	0.189771	−	0.0690711i	0.435158	+	0.900354i	$0.356693\pi$
$972$	−7.86869e6	+	4.46256e7i	−0.267139	+	1.51502i
$973$	1.16473e7	−	9.77327e6i	0.394407	−	0.330946i
$974$	−8.85995e6	−	7.43438e6i	−0.299250	−	0.251100i
$975$	−2.30925e6	−	1.30964e7i	−0.0777964	−	0.441205i
$976$	−2.78799e6	−	4.82895e6i	−0.0936844	−	0.162266i
$977$	−1.28785e7	+	2.23063e7i	−0.431648	+	0.747637i	−0.997015	−	0.0772024i	$-0.975401\pi$
$977$	−1.28785e7	+	2.23063e7i	−0.431648	+	0.747637i	0.565367	+	0.824839i	$0.308735\pi$
$978$	4.16942e7	+	1.51754e7i	1.39389	+	0.507334i
$979$	−1.42765e7	−	5.19624e6i	−0.476065	−	0.173274i
$980$	−1.48542e6	+	2.57283e6i	−0.0494066	+	0.0855747i
$981$	6.97067e6	+	1.20736e7i	0.231261	+	0.400556i
$982$	3.03795e6	+	1.72291e7i	0.100531	+	0.570142i
$983$	1.96767e7	+	1.65108e7i	0.649486	+	0.544983i	0.906915	−	0.421314i	$-0.138431\pi$
$983$	1.96767e7	+	1.65108e7i	0.649486	+	0.544983i	−0.257429	+	0.966297i	$0.582875\pi$
$984$	2.01216e6	−	1.68840e6i	0.0662483	−	0.0555889i
$985$	119231.	−	676190.i	0.00391559	−	0.0222064i
$986$	1.17442e6	−	427455.i	0.0384709	−	0.0140023i
$987$	6.40723e6			0.209352
$988$	2.24300e6	−	567390.i	0.0731033	−	0.0184922i
$989$	2.34354e7			0.761873
$990$	6.52658e7	−	2.37548e7i	2.11640	−	0.770306i
$991$	1.81416e6	−	1.02886e7i	0.0586803	−	0.332792i	−0.941308	−	0.337548i	$-0.890403\pi$
$991$	1.81416e6	−	1.02886e7i	0.0586803	−	0.332792i	0.999989	+	0.00475534i	$0.00151368\pi$
$992$	−4.65898e6	+	3.90935e6i	−0.150318	+	0.126132i
$993$	−3.28948e7	−	2.76020e7i	−1.05865	−	0.888315i
$994$	2.40431e6	+	1.36355e7i	0.0771834	+	0.437729i
$995$	−1.00595e7	−	1.74236e7i	−0.322121	−	0.557929i
$996$	1.90284e7	−	3.29582e7i	0.607792	−	1.05273i
$997$	−1.86719e7	−	6.79602e6i	−0.594909	−	0.216529i	0.0269780	−	0.999636i	$-0.491412\pi$
$997$	−1.86719e7	−	6.79602e6i	−0.594909	−	0.216529i	−0.621887	+	0.783107i	$0.713634\pi$
$998$	3.32555e7	+	1.21040e7i	1.05691	+	0.384683i
$999$	−1.67308e6	+	2.89786e6i	−0.0530399	+	0.0918678i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.5.1	✓	30
19.2	odd	18		722.6.a.q.1.15		15
19.4	even	9	inner	38.6.e.b.23.1	yes	30
19.17	even	9		722.6.a.r.1.1		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.5.1	✓	30	1.1	even	1	trivial
38.6.e.b.23.1	yes	30	19.4	even	9	inner
722.6.a.q.1.15		15	19.2	odd	18
722.6.a.r.1.1		15	19.17	even	9

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	38.6.e.b.5.1

Level	$38$
Weight	$6$
Character	38.5
Analytic conductor	$6.095$
Analytic rank	$0$
Dimension	$30$
Inner twists	$2$