LMFDB - Embedded newform 38.5.d.a.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, 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:	$3.92805859719$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.7
Root			$0.500000 - 6.55779i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.5.d.a.31.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 + 1.41421i) q^{2} +(3.70447 + 2.13878i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-17.7629 + 30.7663i) q^{5} +(6.04937 + 10.4778i) q^{6} +57.6374 q^{7} +22.6274i q^{8} +(-31.3513 - 54.3020i) q^{9} +O(q^{10})$	\(q+(2.44949 + 1.41421i) q^{2} +(3.70447 + 2.13878i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-17.7629 + 30.7663i) q^{5} +(6.04937 + 10.4778i) q^{6} +57.6374 q^{7} +22.6274i q^{8} +(-31.3513 - 54.3020i) q^{9} +(-87.0203 + 50.2412i) q^{10} +144.450 q^{11} +34.2204i q^{12} +(-165.547 + 95.5784i) q^{13} +(141.182 + 81.5117i) q^{14} +(-131.605 + 75.9819i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(273.834 - 474.294i) q^{17} -177.350i q^{18} +(-208.119 - 294.971i) q^{19} -284.207 q^{20} +(213.516 + 123.274i) q^{21} +(353.828 + 204.283i) q^{22} +(97.8608 + 169.500i) q^{23} +(-48.3950 + 83.8225i) q^{24} +(-318.544 - 551.735i) q^{25} -540.673 q^{26} -614.695i q^{27} +(230.550 + 399.324i) q^{28} +(-16.6699 + 9.62437i) q^{29} -429.818 q^{30} -933.563i q^{31} +(-156.767 + 90.5097i) q^{32} +(535.110 + 308.946i) q^{33} +(1341.51 - 774.519i) q^{34} +(-1023.81 + 1773.29i) q^{35} +(250.810 - 434.416i) q^{36} +1973.80i q^{37} +(-92.6330 - 1016.85i) q^{38} -817.683 q^{39} +(-696.162 - 401.929i) q^{40} +(1409.98 + 814.052i) q^{41} +(348.670 + 603.915i) q^{42} +(-1101.61 + 1908.04i) q^{43} +(577.799 + 1000.78i) q^{44} +2227.56 q^{45} +553.584i q^{46} +(-281.608 - 487.759i) q^{47} +(-237.086 + 136.882i) q^{48} +921.075 q^{49} -1801.96i q^{50} +(2028.82 - 1171.34i) q^{51} +(-1324.37 - 764.627i) q^{52} +(-922.687 + 532.713i) q^{53} +(869.310 - 1505.69i) q^{54} +(-2565.85 + 4444.19i) q^{55} +1304.19i q^{56} +(-140.093 - 1537.83i) q^{57} -54.4436 q^{58} +(1314.02 + 758.649i) q^{59} +(-1052.84 - 607.855i) q^{60} +(-2676.67 - 4636.13i) q^{61} +(1320.26 - 2286.75i) q^{62} +(-1807.01 - 3129.83i) q^{63} -512.000 q^{64} -6791.02i q^{65} +(873.831 + 1513.52i) q^{66} +(-4365.12 + 2520.20i) q^{67} +4381.34 q^{68} +837.209i q^{69} +(-5015.63 + 2895.77i) q^{70} +(-1231.70 - 711.125i) q^{71} +(1228.71 - 709.398i) q^{72} +(2820.02 - 4884.42i) q^{73} +(-2791.37 + 4834.80i) q^{74} -2725.18i q^{75} +(1211.14 - 2621.77i) q^{76} +8325.72 q^{77} +(-2002.91 - 1156.38i) q^{78} +(532.235 + 307.286i) q^{79} +(-1136.83 - 1969.04i) q^{80} +(-1224.76 + 2121.34i) q^{81} +(2302.49 + 3988.02i) q^{82} -2748.68 q^{83} +1972.38i q^{84} +(9728.19 + 16849.7i) q^{85} +(-5396.74 + 3115.81i) q^{86} -82.3375 q^{87} +3268.53i q^{88} +(4647.00 - 2682.95i) q^{89} +(5456.39 + 3150.25i) q^{90} +(-9541.69 + 5508.90i) q^{91} +(-782.886 + 1356.00i) q^{92} +(1996.68 - 3458.36i) q^{93} -1593.02i q^{94} +(12772.0 - 1163.50i) q^{95} -774.320 q^{96} +(-8504.30 - 4909.96i) q^{97} +(2256.16 + 1302.60i) q^{98} +(-4528.69 - 7843.92i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$2$	2.44949	+	1.41421i	0.612372	+	0.353553i
$3$	3.70447	+	2.13878i	0.411608	+	0.237642i	0.691480	−	0.722395i	$-0.256959\pi$
$3$	3.70447	+	2.13878i	0.411608	+	0.237642i	−0.279873	+	0.960037i	$0.590292\pi$
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	−17.7629	+	30.7663i	−0.710518	+	1.23065i	0.254145	+	0.967166i	$0.418206\pi$
$5$	−17.7629	+	30.7663i	−0.710518	+	1.23065i	−0.964663	+	0.263487i	$0.915128\pi$
$6$	6.04937	+	10.4778i	0.168038	+	0.291051i
$7$	57.6374			1.17627			0.588137	−	0.808761i	$-0.299861\pi$
$7$	57.6374			1.17627			0.588137	+	0.808761i	$0.299861\pi$
$8$			22.6274i			0.353553i
$9$	−31.3513	−	54.3020i	−0.387053	−	0.670395i
$10$	−87.0203	+	50.2412i	−0.870203	+	0.502412i
$11$	144.450			1.19380			0.596900	−	0.802316i	$-0.296399\pi$
$11$	144.450			1.19380			0.596900	+	0.802316i	$0.296399\pi$
$12$			34.2204i			0.237642i
$13$	−165.547	+	95.5784i	−0.979566	+	0.565553i	−0.902139	−	0.431445i	$-0.858004\pi$
$13$	−165.547	+	95.5784i	−0.979566	+	0.565553i	−0.0774271	+	0.996998i	$0.524670\pi$
$14$	141.182	+	81.5117i	0.720318	+	0.415876i
$15$	−131.605	+	75.9819i	−0.584909	+	0.337697i
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	273.834	−	474.294i	0.947522	−	1.64116i	0.196902	−	0.980423i	$-0.436912\pi$
$17$	273.834	−	474.294i	0.947522	−	1.64116i	0.750621	−	0.660733i	$-0.229755\pi$
$18$		−	177.350i		−	0.547375i
$19$	−208.119	−	294.971i	−0.576506	−	0.817093i
$19$	−208.119	−	294.971i	−0.576506	−	0.817093i
$20$	−284.207			−0.710518
$21$	213.516	+	123.274i	0.484163	+	0.279532i
$22$	353.828	+	204.283i	0.731050	+	0.422072i
$23$	97.8608	+	169.500i	0.184992	+	0.320416i	0.943574	−	0.331162i	$-0.107441\pi$
$23$	97.8608	+	169.500i	0.184992	+	0.320416i	−0.758582	+	0.651578i	$0.774107\pi$
$24$	−48.3950	+	83.8225i	−0.0840190	+	0.145525i
$25$	−318.544	−	551.735i	−0.509671	−	0.882775i
$26$	−540.673			−0.799812
$27$		−	614.695i		−	0.843203i
$28$	230.550	+	399.324i	0.294069	+	0.509342i
$29$	−16.6699	+	9.62437i	−0.0198215	+	0.0114440i	−0.509878	−	0.860247i	$-0.670309\pi$
$29$	−16.6699	+	9.62437i	−0.0198215	+	0.0114440i	0.490057	+	0.871691i	$0.336976\pi$
$30$	−429.818			−0.477576
$31$		−	933.563i		−	0.971450i	−0.874112	−	0.485725i	$-0.838556\pi$
$31$		−	933.563i		−	0.971450i	0.874112	−	0.485725i	$-0.161444\pi$
$32$	−156.767	+	90.5097i	−0.153093	+	0.0883883i
$33$	535.110	+	308.946i	0.491377	+	0.283697i
$34$	1341.51	−	774.519i	1.16047	−	0.669999i
$35$	−1023.81	+	1773.29i	−0.835764	+	1.44759i
$36$	250.810	−	434.416i	0.193526	−	0.335198i
$37$			1973.80i			1.44178i	0.693049	+	0.720891i	$0.256267\pi$
$37$			1973.80i			1.44178i	−0.693049	+	0.720891i	$0.743733\pi$
$38$	−92.6330	−	1016.85i	−0.0641503	−	0.704191i
$39$	−817.683			−0.537596
$40$	−696.162	−	401.929i	−0.435101	−	0.251206i
$41$	1409.98	+	814.052i	0.838774	+	0.484267i	0.856847	−	0.515570i	$-0.172420\pi$
$41$	1409.98	+	814.052i	0.838774	+	0.484267i	−0.0180730	+	0.999837i	$0.505753\pi$
$42$	348.670	+	603.915i	0.197659	+	0.342355i
$43$	−1101.61	+	1908.04i	−0.595785	+	1.03193i	0.397651	+	0.917537i	$0.369826\pi$
$43$	−1101.61	+	1908.04i	−0.595785	+	1.03193i	−0.993436	+	0.114393i	$0.963508\pi$
$44$	577.799	+	1000.78i	0.298450	+	0.516931i
$45$	2227.56			1.10003
$46$			553.584i			0.261618i
$47$	−281.608	−	487.759i	−0.127482	−	0.220805i	0.795218	−	0.606323i	$-0.207356\pi$
$47$	−281.608	−	487.759i	−0.127482	−	0.220805i	−0.922700	+	0.385518i	$0.874023\pi$
$48$	−237.086	+	136.882i	−0.102902	+	0.0594104i
$49$	921.075			0.383622
$50$		−	1801.96i		−	0.720783i
$51$	2028.82	−	1171.34i	0.780015	−	0.450342i
$52$	−1324.37	−	764.627i	−0.489783	−	0.282776i
$53$	−922.687	+	532.713i	−0.328475	+	0.189645i	−0.655164	−	0.755487i	$-0.727400\pi$
$53$	−922.687	+	532.713i	−0.328475	+	0.189645i	0.326689	+	0.945132i	$0.394067\pi$
$54$	869.310	−	1505.69i	0.298117	−	0.516354i
$55$	−2565.85	+	4444.19i	−0.848216	+	1.46915i
$56$			1304.19i			0.415876i
$57$	−140.093	−	1537.83i	−0.0431188	−	0.473324i
$58$	−54.4436			−0.0161842
$59$	1314.02	+	758.649i	0.377483	+	0.217940i	0.676723	−	0.736238i	$-0.263400\pi$
$59$	1314.02	+	758.649i	0.377483	+	0.217940i	−0.299240	+	0.954178i	$0.596733\pi$
$60$	−1052.84	−	607.855i	−0.292454	−	0.168849i
$61$	−2676.67	−	4636.13i	−0.719341	−	1.24594i	−0.961261	−	0.275639i	$-0.911111\pi$
$61$	−2676.67	−	4636.13i	−0.719341	−	1.24594i	0.241920	−	0.970296i	$-0.422223\pi$
$62$	1320.26	−	2286.75i	0.343459	−	0.594889i
$63$	−1807.01	−	3129.83i	−0.455280	−	0.788569i
$64$	−512.000			−0.125000
$65$		−	6791.02i		−	1.60734i
$66$	873.831	+	1513.52i	0.200604	+	0.347456i
$67$	−4365.12	+	2520.20i	−0.972403	+	0.561417i	−0.899968	−	0.435956i	$-0.856410\pi$
$67$	−4365.12	+	2520.20i	−0.972403	+	0.561417i	−0.0724351	+	0.997373i	$0.523077\pi$
$68$	4381.34			0.947522
$69$			837.209i			0.175847i
$70$	−5015.63	+	2895.77i	−1.02360	+	0.590974i
$71$	−1231.70	−	711.125i	−0.244337	−	0.141068i	0.372831	−	0.927899i	$-0.378387\pi$
$71$	−1231.70	−	711.125i	−0.244337	−	0.141068i	−0.617169	+	0.786831i	$0.711720\pi$
$72$	1228.71	−	709.398i	0.237020	−	0.136844i
$73$	2820.02	−	4884.42i	0.529184	−	0.916574i	−0.470237	−	0.882540i	$-0.655831\pi$
$73$	2820.02	−	4884.42i	0.529184	−	0.916574i	0.999421	−	0.0340332i	$-0.0108352\pi$
$74$	−2791.37	+	4834.80i	−0.509747	+	0.882907i
$75$		−	2725.18i		−	0.484476i
$76$	1211.14	−	2621.77i	0.209685	−	0.453908i
$77$	8325.72			1.40424
$78$	−2002.91	−	1156.38i	−0.329209	−	0.190069i
$79$	532.235	+	307.286i	0.0852804	+	0.0492367i	0.542034	−	0.840357i	$-0.317654\pi$
$79$	532.235	+	307.286i	0.0852804	+	0.0492367i	−0.456753	+	0.889593i	$0.650988\pi$
$80$	−1136.83	−	1969.04i	−0.177629	−	0.307663i
$81$	−1224.76	+	2121.34i	−0.186673	+	0.323326i
$82$	2302.49	+	3988.02i	0.342428	+	0.593103i
$83$	−2748.68			−0.398995			−0.199498	−	0.979898i	$-0.563931\pi$
$83$	−2748.68			−0.398995			−0.199498	+	0.979898i	$0.563931\pi$
$84$			1972.38i			0.279532i
$85$	9728.19	+	16849.7i	1.34646	+	2.33214i
$86$	−5396.74	+	3115.81i	−0.729684	+	0.421283i
$87$	−82.3375			−0.0108782
$88$			3268.53i			0.422072i
$89$	4647.00	−	2682.95i	0.586668	−	0.338713i	−0.177111	−	0.984191i	$-0.556675\pi$
$89$	4647.00	−	2682.95i	0.586668	−	0.338713i	0.763779	+	0.645478i	$0.223342\pi$
$90$	5456.39	+	3150.25i	0.673629	+	0.388920i
$91$	−9541.69	+	5508.90i	−1.15224	+	0.665245i
$92$	−782.886	+	1356.00i	−0.0924960	+	0.160208i
$93$	1996.68	−	3458.36i	0.230857	−	0.399856i
$94$		−	1593.02i		−	0.180287i
$95$	12772.0	−	1163.50i	1.41518	−	0.128919i
$96$	−774.320			−0.0840190
$97$	−8504.30	−	4909.96i	−0.903847	−	0.521836i	−0.0254007	−	0.999677i	$-0.508086\pi$
$97$	−8504.30	−	4909.96i	−0.903847	−	0.521836i	−0.878446	+	0.477841i	$0.841419\pi$
$98$	2256.16	+	1302.60i	0.234919	+	0.135631i
$99$	−4528.69	−	7843.92i	−0.462064	−	0.800318i
$100$	2548.35	−	4413.88i	0.254835	−	0.441388i
$101$	−3770.42	−	6530.55i	−0.369612	−	0.640187i	0.619893	−	0.784687i	$-0.287176\pi$
$101$	−3770.42	−	6530.55i	−0.369612	−	0.640187i	−0.989505	+	0.144499i	$0.953843\pi$
$102$	6626.09			0.636879
$103$			17918.4i			1.68899i	0.535567	+	0.844493i	$0.320098\pi$
$103$			17918.4i			1.68899i	−0.535567	+	0.844493i	$0.679902\pi$
$104$	−2162.69	−	3745.89i	−0.199953	−	0.346329i
$105$	−7585.35	+	4379.40i	−0.688013	+	0.397225i
$106$	−3013.48			−0.268199
$107$		−	18844.0i		−	1.64591i	−0.568110	−	0.822953i	$-0.692325\pi$
$107$		−	18844.0i		−	1.64591i	0.568110	−	0.822953i	$-0.307675\pi$
$108$	4258.73	−	2458.78i	0.365118	−	0.210801i
$109$	−2953.45	−	1705.17i	−0.248586	−	0.143521i	0.370531	−	0.928820i	$-0.379176\pi$
$109$	−2953.45	−	1705.17i	−0.248586	−	0.143521i	−0.619116	+	0.785299i	$0.712509\pi$
$110$	−12570.1	+	7257.33i	−1.03885	+	0.599779i
$111$	−4221.51	+	7311.88i	−0.342628	+	0.593448i
$112$	−1844.40	+	3194.59i	−0.147034	+	0.254671i
$113$			14671.8i			1.14902i	0.818498	+	0.574509i	$0.194807\pi$
$113$			14671.8i			1.14902i	−0.818498	+	0.574509i	$0.805193\pi$
$114$	1831.66	−	3965.02i	0.140940	−	0.305095i
$115$	−6953.18			−0.525760
$116$	−133.359	−	76.9949i	−0.00991076	−	0.00572198i
$117$	10380.2	+	5993.01i	0.758288	+	0.437798i
$118$	2145.78	+	3716.61i	0.154107	+	0.266921i
$119$	15783.1	−	27337.1i	1.11455	−	1.93045i
$120$	−1719.27	−	2977.87i	−0.119394	−	0.206797i
$121$	6224.75			0.425159
$122$		−	15141.5i		−	1.01730i
$123$	3482.15	+	6031.26i	0.230164	+	0.398656i
$124$	6467.92	−	3734.25i	0.420650	−	0.242862i
$125$	429.447			0.0274846
$126$		−	10222.0i		−	0.643864i
$127$	−4058.49	+	2343.17i	−0.251627	+	0.145277i	−0.620509	−	0.784199i	$-0.713074\pi$
$127$	−4058.49	+	2343.17i	−0.251627	+	0.145277i	0.368882	+	0.929476i	$0.379741\pi$
$128$	−1254.14	−	724.077i	−0.0765466	−	0.0441942i
$129$	−8161.73	+	4712.18i	−0.490459	+	0.283167i
$130$	9603.95	−	16634.5i	0.568281	−	0.984291i
$131$	−5035.57	+	8721.86i	−0.293431	+	0.508237i	−0.974619	−	0.223872i	$-0.928130\pi$
$131$	−5035.57	+	8721.86i	−0.293431	+	0.508237i	0.681188	+	0.732109i	$0.261464\pi$
$132$			4943.13i			0.283697i
$133$	−11995.4	−	17001.4i	−0.678129	−	0.961126i
$134$	−14256.4			−0.793964
$135$	18911.9	+	10918.8i	1.03769	+	0.599111i
$136$	10732.1	+	6196.15i	0.580237	+	0.335000i
$137$	152.554	+	264.231i	0.00812798	+	0.0140781i	0.870061	−	0.492944i	$-0.164079\pi$
$137$	152.554	+	264.231i	0.00812798	+	0.0140781i	−0.861933	+	0.507023i	$0.830746\pi$
$138$	−1183.99	+	2050.74i	−0.0621714	+	0.107684i
$139$	−5384.92	−	9326.95i	−0.278708	−	0.482737i	0.692356	−	0.721556i	$-0.256573\pi$
$139$	−5384.92	−	9326.95i	−0.278708	−	0.482737i	−0.971064	+	0.238820i	$0.923240\pi$
$140$	−16381.0			−0.835764
$141$		−	2409.19i		−	0.121180i
$142$	−2011.36	−	3483.79i	−0.0997503	−	0.172773i
$143$	−23913.2	+	13806.3i	−1.16941	+	0.675157i
$144$	4012.96			0.193526
$145$		−	683.828i		−	0.0325245i
$146$	13815.2	−	7976.23i	0.648115	−	0.374190i
$147$	3412.09	+	1969.97i	0.157902	+	0.0911645i
$148$	−13674.9	+	7895.20i	−0.624310	+	0.360445i
$149$	−6839.66	+	11846.6i	−0.308079	+	0.533608i	−0.977942	−	0.208876i	$-0.933019\pi$
$149$	−6839.66	+	11846.6i	−0.308079	+	0.533608i	0.669863	+	0.742485i	$0.266353\pi$
$150$	3853.98	−	6675.30i	0.171288	−	0.296680i
$151$			3932.97i			0.172491i	0.996274	+	0.0862455i	$0.0274870\pi$
$151$			3932.97i			0.172491i	−0.996274	+	0.0862455i	$0.972513\pi$
$152$	6674.42	−	4709.19i	0.288886	−	0.203826i
$153$	−34340.2			−1.46696
$154$	20393.8	+	11774.3i	0.859916	+	0.496473i
$155$	28722.3	+	16582.8i	1.19552	+	0.690232i
$156$	−3270.73	−	5665.08i	−0.134399	−	0.232786i
$157$	12478.1	−	21612.7i	0.506230	−	0.876817i	−0.493744	−	0.869607i	$-0.664372\pi$
$157$	12478.1	−	21612.7i	0.506230	−	0.876817i	0.999974	−	0.00720913i	$-0.00229476\pi$
$158$	869.136	+	1505.39i	0.0348156	+	0.0603024i
$159$	−4557.42			−0.180270
$160$		−	6430.87i		−	0.251206i
$161$	5640.45	+	9769.54i	0.217601	+	0.376897i
$162$	−6000.07	+	3464.14i	−0.228626	+	0.131997i
$163$	30994.7			1.16657			0.583287	−	0.812266i	$-0.301766\pi$
$163$	30994.7			1.16657			0.583287	+	0.812266i	$0.301766\pi$
$164$			13024.8i			0.484267i
$165$	−19010.2	+	10975.6i	−0.698264	+	0.403143i
$166$	−6732.86	−	3887.22i	−0.244334	−	0.141066i
$167$	40226.3	−	23224.7i	1.44237	−	0.832753i	0.444363	−	0.895847i	$-0.353430\pi$
$167$	40226.3	−	23224.7i	1.44237	−	0.832753i	0.998008	+	0.0630935i	$0.0200966\pi$
$168$	−2789.36	+	4831.32i	−0.0988295	+	0.171178i
$169$	3989.97	−	6910.83i	0.139700	−	0.241967i
$170$			55031.0i			1.90419i
$171$	−9492.71	+	20549.0i	−0.324637	+	0.702745i
$172$	−17625.7			−0.595785
$173$	44065.9	+	25441.5i	1.47235	+	0.850061i	0.999517	−	0.0310913i	$-0.00989826\pi$
$173$	44065.9	+	25441.5i	1.47235	+	0.850061i	0.472832	+	0.881152i	$0.343232\pi$
$174$	−201.685	−	116.443i	−0.00666154	−	0.00384604i
$175$	−18360.1	−	31800.6i	−0.599513	−	1.03839i
$176$	−4622.39	+	8006.22i	−0.149225	+	0.258465i
$177$	3245.16	+	5620.78i	0.103583	+	0.179412i
$178$	15177.0			0.479013
$179$			43766.3i			1.36595i	0.730444	+	0.682973i	$0.239313\pi$
$179$			43766.3i			1.36595i	−0.730444	+	0.682973i	$0.760687\pi$
$180$	8910.25	+	15433.0i	0.275008	+	0.476328i
$181$	−35313.4	+	20388.2i	−1.07791	+	0.622332i	−0.930332	−	0.366718i	$-0.880481\pi$
$181$	−35313.4	+	20388.2i	−1.07791	+	0.622332i	−0.147579	+	0.989050i	$0.547148\pi$
$182$	−31163.0			−0.940799
$183$		−	22899.2i		−	0.683782i
$184$	−3835.34	+	2214.34i	−0.113284	+	0.0654046i
$185$	−60726.5	−	35060.5i	−1.77433	−	1.02441i
$186$	9781.71	−	5647.47i	0.282741	−	0.163241i
$187$	39555.3	−	68511.7i	1.13115	−	1.95921i
$188$	2252.86	−	3902.07i	0.0637411	−	0.110403i
$189$		−	35429.5i		−	0.991838i
$190$	32930.2	+	15212.3i	0.912194	+	0.421393i
$191$	−49984.5			−1.37015			−0.685076	−	0.728472i	$-0.740231\pi$
$191$	−49984.5			−1.37015			−0.685076	+	0.728472i	$0.740231\pi$
$192$	−1896.69	−	1095.05i	−0.0514509	−	0.0297052i
$193$	15307.8	+	8837.94i	0.410958	+	0.237267i	0.691201	−	0.722662i	$-0.257082\pi$
$193$	15307.8	+	8837.94i	0.410958	+	0.237267i	−0.280243	+	0.959929i	$0.590415\pi$
$194$	−13887.5	−	24053.8i	−0.368994	−	0.639116i
$195$	14524.5	−	25157.1i	0.381971	−	0.661594i
$196$	3684.30	+	6381.40i	0.0959054	+	0.166113i
$197$	71077.4			1.83147			0.915734	−	0.401786i	$-0.131610\pi$
$197$	71077.4			1.83147			0.915734	+	0.401786i	$0.131610\pi$
$198$		−	25618.1i		−	0.653457i
$199$	26220.6	+	45415.3i	0.662119	+	1.14682i	0.980058	+	0.198712i	$0.0636758\pi$
$199$	26220.6	+	45415.3i	0.662119	+	1.14682i	−0.317939	+	0.948111i	$0.602991\pi$
$200$	12484.3	−	7207.83i	0.312108	−	0.180196i
$201$	−21560.6			−0.533665
$202$		−	21328.7i		−	0.522711i
$203$	−960.810	+	554.724i	−0.0233155	+	0.0134612i
$204$	16230.5	+	9370.71i	0.390007	+	0.225171i
$205$	−50090.8	+	28919.9i	−1.19193	+	0.688160i
$206$	−25340.5	+	43891.1i	−0.597147	+	1.03429i
$207$	6136.12	−	10628.1i	0.143203	−	0.248036i
$208$		−	12234.0i		−	0.282776i
$209$	−30062.7	−	42608.5i	−0.688233	−	0.975446i
$210$	−24773.6			−0.561761
$211$	−12929.6	−	7464.89i	−0.290415	−	0.167671i	0.347714	−	0.937601i	$-0.386958\pi$
$211$	−12929.6	−	7464.89i	−0.290415	−	0.167671i	−0.638129	+	0.769929i	$0.720291\pi$
$212$	−7381.49	−	4261.71i	−0.164238	−	0.0948226i
$213$	−3041.87	−	5268.68i	−0.0670474	−	0.116129i
$214$	26649.4	−	46158.1i	0.581915	−	1.00791i
$215$	−39135.5	−	67784.7i	−0.846631	−	1.46641i
$216$	13909.0			0.298117
$217$		−	53808.2i		−	1.14269i
$218$	−4822.96	−	8353.61i	−0.101485	−	0.175777i
$219$	20893.4	−	12062.8i	0.435632	−	0.251512i
$220$	−41053.7			−0.848216
$221$			104690.i			2.14350i
$222$	−20681.1	+	11940.2i	−0.419631	+	0.242274i
$223$	−14187.1	−	8190.92i	−0.285288	−	0.164711i	0.350527	−	0.936553i	$-0.386003\pi$
$223$	−14187.1	−	8190.92i	−0.285288	−	0.164711i	−0.635815	+	0.771841i	$0.719336\pi$
$224$	−9035.67	+	5216.75i	−0.180080	+	0.103969i
$225$	−19973.5	+	34595.2i	−0.394539	+	0.683361i
$226$	−20749.1	+	35938.4i	−0.406239	+	0.703627i
$227$			17808.1i			0.345594i	0.984957	+	0.172797i	$0.0552805\pi$
$227$			17808.1i			0.345594i	−0.984957	+	0.172797i	$0.944720\pi$
$228$	10094.0	−	7121.90i	0.194175	−	0.137002i
$229$	93393.3			1.78092			0.890461	−	0.455060i	$-0.150382\pi$
$229$	93393.3			1.78092			0.890461	+	0.455060i	$0.150382\pi$
$230$	−17031.7	−	9833.28i	−0.321961	−	0.185884i
$231$	30842.4	+	17806.8i	0.577994	+	0.333705i
$232$	−217.775	−	377.197i	−0.00404605	−	0.00700796i
$233$	18715.1	−	32415.5i	0.344731	−	0.597092i	−0.640574	−	0.767897i	$-0.721303\pi$
$233$	18715.1	−	32415.5i	0.344731	−	0.597092i	0.985305	+	0.170804i	$0.0546367\pi$
$234$	16950.8	+	29359.6i	0.309570	+	0.536190i
$235$	20008.7			0.362313
$236$			12138.4i			0.217940i
$237$	1314.43	+	2276.66i	0.0234014	+	0.0405324i
$238$	77321.0	−	44641.3i	1.36503	−	0.788103i
$239$	−26610.8			−0.465867			−0.232934	−	0.972493i	$-0.574833\pi$
$239$	−26610.8			−0.465867			−0.232934	+	0.972493i	$0.574833\pi$
$240$		−	9725.68i		−	0.168849i
$241$	−19387.5	+	11193.4i	−0.333801	+	0.192720i	−0.657527	−	0.753431i	$-0.728398\pi$
$241$	−19387.5	+	11193.4i	−0.333801	+	0.192720i	0.323727	+	0.946151i	$0.395064\pi$
$242$	15247.5	+	8803.13i	0.260356	+	0.150316i
$243$	−52193.8	+	30134.1i	−0.883907	+	0.510324i
$244$	21413.3	−	37089.0i	0.359671	−	0.622968i
$245$	−16361.0	+	28338.1i	−0.272570	+	0.472105i
$246$			19698.0i			0.325501i
$247$	62646.2	+	28939.8i	1.02683	+	0.474352i
$248$	21124.1			0.343459
$249$	−10182.4	−	5878.80i	−0.164229	−	0.0948179i
$250$	1051.93	+	607.330i	0.0168308	+	0.00971729i
$251$	20002.6	+	34645.6i	0.317497	+	0.549921i	0.979965	−	0.199169i	$-0.0638243\pi$
$251$	20002.6	+	34645.6i	0.317497	+	0.549921i	−0.662468	+	0.749090i	$0.730491\pi$
$252$	14456.1	−	25038.6i	0.227640	−	0.394284i
$253$	14136.0	+	24484.2i	0.220844	+	0.382512i
$254$	−13255.0			−0.205452
$255$			83225.7i			1.27990i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−92099.6	+	53173.7i	−1.39441	+	0.805065i	−0.993800	−	0.111182i	$-0.964536\pi$
$257$	−92099.6	+	53173.7i	−1.39441	+	0.805065i	−0.400614	+	0.916247i	$0.631203\pi$
$258$	−26656.1			−0.400458
$259$			113765.i			1.69593i
$260$	47049.5	−	27164.1i	0.695999	−	0.401835i
$261$	1045.24	+	603.472i	0.0153439	+	0.00885883i
$262$	−24669.1	+	14242.7i	−0.359378	+	0.207487i
$263$	34717.4	−	60132.4i	0.501922	−	0.869354i	−0.498076	−	0.867134i	$-0.665960\pi$
$263$	34717.4	−	60132.4i	0.501922	−	0.869354i	0.999998	−	0.00222053i	$-0.000706816\pi$
$264$	−6990.65	+	12108.2i	−0.100302	+	0.173728i
$265$		−	37850.2i		−	0.538985i
$266$	−5339.13	−	58608.7i	−0.0754583	−	0.828322i
$267$	22952.9			0.321970
$268$	−34920.9	−	20161.6i	−0.486202	−	0.280709i
$269$	48824.7	+	28188.9i	0.674738	+	0.389560i	0.797869	−	0.602830i	$-0.205960\pi$
$269$	48824.7	+	28188.9i	0.674738	+	0.389560i	−0.123132	+	0.992390i	$0.539294\pi$
$270$	30883.0	+	53490.9i	0.423635	+	0.733758i
$271$	−20152.5	+	34905.2i	−0.274405	+	0.475283i	−0.969985	−	0.243166i	$-0.921814\pi$
$271$	−20152.5	+	34905.2i	−0.274405	+	0.475283i	0.695580	+	0.718448i	$0.255147\pi$
$272$	17525.4	+	30354.8i	0.236881	+	0.410289i
$273$	−47129.2			−0.632360
$274$			862.976i			0.0114947i
$275$	−46013.6	−	79698.0i	−0.608445	−	1.05386i
$276$	−5800.35	+	3348.84i	−0.0761441	+	0.0439618i
$277$	1727.77			0.0225178			0.0112589	−	0.999937i	$-0.496416\pi$
$277$	1727.77			0.0225178			0.0112589	+	0.999937i	$0.496416\pi$
$278$		−	30461.7i		−	0.394153i
$279$	−50694.4	+	29268.4i	−0.651255	+	0.376002i
$280$	−40125.0	−	23166.2i	−0.511799	−	0.295487i
$281$	71949.9	−	41540.3i	0.911208	−	0.526086i	0.0303881	−	0.999538i	$-0.490326\pi$
$281$	71949.9	−	41540.3i	0.911208	−	0.526086i	0.880819	+	0.473452i	$0.156992\pi$
$282$	3407.10	−	5901.27i	0.0428437	−	0.0742075i
$283$	56498.8	−	97858.9i	0.705451	−	1.22188i	−0.261078	−	0.965318i	$-0.584078\pi$
$283$	56498.8	−	97858.9i	0.705451	−	1.22188i	0.966529	−	0.256559i	$-0.0825887\pi$
$284$		−	11378.0i		−	0.141068i
$285$	49801.8	+	23006.2i	0.613133	+	0.283241i
$286$	−78100.2			−0.954816
$287$	81267.6	+	46919.9i	0.986629	+	0.569630i
$288$	9829.71	+	5675.19i	0.118510	+	0.0684219i
$289$	−108210.	−	187424.i	−1.29560	−	2.24404i
$290$	967.079	−	1675.03i	0.0114992	−	0.0199171i
$291$	−21002.6	−	36377.6i	−0.248020	−	0.429584i
$292$	45120.3			0.529184
$293$		−	14942.5i		−	0.174056i	−0.996206	−	0.0870280i	$-0.972263\pi$
$293$		−	14942.5i		−	0.174056i	0.996206	−	0.0870280i	$-0.0277370\pi$
$294$	5571.93	+	9650.86i	0.0644630	+	0.111653i
$295$	−46681.7	+	26951.7i	−0.536417	+	0.309700i
$296$	−44662.0			−0.509747
$297$		−	88792.6i		−	1.00662i
$298$	−33507.3	+	19345.5i	−0.377318	+	0.217845i
$299$	−32401.1	−	18706.8i	−0.362424	−	0.209246i
$300$	18880.6	−	10900.7i	0.209784	−	0.121119i
$301$	−63493.8	+	109974.i	−0.700806	+	1.21383i
$302$	−5562.06	+	9633.77i	−0.0609848	+	0.105629i
$303$		−	32256.3i		−	0.351341i
$304$	23008.7	−	2096.05i	0.248969	−	0.0226805i
$305$	190182.			2.04442
$306$	−84115.9	−	48564.3i	−0.898329	−	0.518650i
$307$	−132089.	−	76261.9i	−1.40149	−	0.809153i	−0.406949	−	0.913451i	$-0.633407\pi$
$307$	−132089.	−	76261.9i	−1.40149	−	0.809153i	−0.994546	+	0.104298i	$0.966741\pi$
$308$	33302.9	+	57682.3i	0.351059	+	0.608052i
$309$	−38323.5	+	66378.3i	−0.401374	+	0.695199i
$310$	46903.3	+	81239.0i	0.488068	+	0.845359i
$311$	−89623.6			−0.926620			−0.463310	−	0.886196i	$-0.653338\pi$
$311$	−89623.6			−0.926620			−0.463310	+	0.886196i	$0.653338\pi$
$312$		−	18502.1i		−	0.190069i
$313$	9663.23	+	16737.2i	0.0986356	+	0.170842i	0.911120	−	0.412141i	$-0.135219\pi$
$313$	9663.23	+	16737.2i	0.0986356	+	0.170842i	−0.812485	+	0.582983i	$0.801886\pi$
$314$	61129.8	−	35293.3i	0.620003	−	0.357959i
$315$	128391.			1.29394
$316$			4916.58i			0.0492367i
$317$	57395.2	−	33137.1i	0.571159	−	0.329759i	−0.186453	−	0.982464i	$-0.559699\pi$
$317$	57395.2	−	33137.1i	0.571159	−	0.329759i	0.757612	+	0.652705i	$0.226366\pi$
$318$	−11163.3	−	6445.16i	−0.110393	−	0.0637352i
$319$	−2407.96	+	1390.24i	−0.0236629	+	0.0136618i
$320$	9094.63	−	15752.4i	0.0888147	−	0.153832i
$321$	40303.0	−	69806.9i	0.391136	−	0.677467i
$322$			31907.2i			0.307735i
$323$	−196893.	+	17936.5i	−1.88723	+	0.171923i
$324$	−19596.1			−0.186673
$325$	105468.	+	60891.9i	0.998512	+	0.576491i
$326$	75921.3	+	43833.2i	0.714378	+	0.412446i
$327$	−7293.97	−	12633.5i	−0.0682132	−	0.118149i
$328$	−18419.9	+	31904.2i	−0.171214	+	0.296552i
$329$	−16231.2	−	28113.2i	−0.149954	−	0.259728i
$330$	−62087.2			−0.570130
$331$		−	927.898i		−	0.00846924i	−0.999991	−	0.00423462i	$-0.998652\pi$
$331$		−	927.898i		−	0.00846924i	0.999991	−	0.00423462i	$-0.00134793\pi$
$332$	−10994.7	−	19043.4i	−0.0997488	−	0.172770i
$333$	107181.	−	61881.1i	0.966563	−	0.558046i
$334$	131378.			1.17769
$335$		−	179065.i		−	1.59559i
$336$	−13665.0	+	7889.51i	−0.121041	+	0.0698830i
$337$	87765.9	+	50671.7i	0.772798	+	0.446175i	0.833872	−	0.551958i	$-0.186119\pi$
$337$	87765.9	+	50671.7i	0.772798	+	0.446175i	−0.0610737	+	0.998133i	$0.519452\pi$
$338$	19546.8	−	11285.3i	0.171097	−	0.0987828i
$339$	−31379.7	+	54351.3i	−0.273055	+	0.472944i
$340$	−77825.5	+	134798.i	−0.673231	+	1.16607i
$341$		−	134853.i		−	1.15972i
$342$	−52312.9	+	36909.8i	−0.447257	+	0.315565i
$343$	−85299.1			−0.725030
$344$	−43174.0	−	24926.5i	−0.364842	−	0.210642i
$345$	−25757.8	−	14871.3i	−0.216407	−	0.124943i
$346$	71959.4	+	124637.i	0.601084	+	1.04111i
$347$	−77248.6	+	133799.i	−0.641552	+	1.11120i	0.343535	+	0.939140i	$0.388376\pi$
$347$	−77248.6	+	133799.i	−0.641552	+	1.11120i	−0.985086	+	0.172060i	$0.944958\pi$
$348$	−329.350	−	570.451i	−0.00271956	−	0.00471042i
$349$	−39100.9			−0.321023			−0.160511	−	0.987034i	$-0.551314\pi$
$349$	−39100.9			−0.321023			−0.160511	+	0.987034i	$0.551314\pi$
$350$		−	103860.i		−	0.847839i
$351$	58751.6	+	101761.i	0.476876	+	0.825973i
$352$	−22645.0	+	13074.1i	−0.182763	+	0.105518i
$353$	35513.5			0.285000			0.142500	−	0.989795i	$-0.454486\pi$
$353$	35513.5			0.285000			0.142500	+	0.989795i	$0.454486\pi$
$354$			18357.4i			0.146489i
$355$	43757.4	−	25263.3i	0.347212	−	0.200463i
$356$	37176.0	+	21463.6i	0.293334	+	0.169357i
$357$	116936.	−	67513.0i	0.917511	−	0.529725i
$358$	−61894.8	+	107205.i	−0.482935	+	0.836467i
$359$	−47311.0	+	81945.1i	−0.367091	+	0.635820i	−0.989109	−	0.147183i	$-0.952980\pi$
$359$	−47311.0	+	81945.1i	−0.367091	+	0.635820i	0.622019	+	0.783003i	$0.286313\pi$
$360$			50404.0i			0.388920i
$361$	−43694.3	+	122778.i	−0.335282	+	0.942118i
$362$	−115333.			−0.880110
$363$	23059.4	+	13313.4i	0.174999	+	0.101036i
$364$	−76333.5	−	44071.2i	−0.576119	−	0.332623i
$365$	100184.	+	173523.i	0.751989	+	1.30248i
$366$	32384.3	−	56091.3i	0.241753	−	0.418729i
$367$	18897.2	+	32730.9i	0.140302	+	0.243011i	0.927610	−	0.373549i	$-0.121859\pi$
$367$	18897.2	+	32730.9i	0.140302	+	0.243011i	−0.787308	+	0.616560i	$0.788526\pi$
$368$	−12526.2			−0.0924960
$369$		−	102086.i		−	0.749747i
$370$	−99166.0	−	171761.i	−0.724368	−	1.25464i
$371$	−53181.3	+	30704.2i	−0.386377	+	0.223075i
$372$	31946.9			0.230857
$373$		−	18426.9i		−	0.132445i	−0.997805	−	0.0662225i	$-0.978905\pi$
$373$		−	18426.9i		−	0.132445i	0.997805	−	0.0662225i	$-0.0210947\pi$
$374$	193780.	−	111879.i	1.38537	−	0.799845i
$375$	1590.87	+	918.492i	0.0113129	+	0.00653150i
$376$	11036.7	−	6372.06i	0.0780665	−	0.0450717i
$377$	1839.76	−	3186.56i	0.0129443	−	0.0224202i
$378$	50104.8	−	86784.1i	0.350668	−	0.607374i
$379$			53187.4i			0.370280i	0.982712	+	0.185140i	$0.0592739\pi$
$379$			53187.4i			0.370280i	−0.982712	+	0.185140i	$0.940726\pi$
$380$	59148.8	+	83832.7i	0.409618	+	0.580559i
$381$	−20046.0			−0.138095
$382$	−122437.	−	70688.8i	−0.839043	−	0.484422i
$383$	−125485.	−	72448.9i	−0.855450	−	0.493894i	0.00703582	−	0.999975i	$-0.497760\pi$
$383$	−125485.	−	72448.9i	−0.855450	−	0.493894i	−0.862486	+	0.506081i	$0.831094\pi$
$384$	−3097.28	−	5364.64i	−0.0210048	−	0.0363813i
$385$	−147889.	+	256152.i	−0.997735	+	1.72813i
$386$	24997.5	+	43296.9i	0.167773	+	0.290591i
$387$	138147.			0.922401
$388$		−	78559.3i		−	0.521836i
$389$	−22790.0	−	39473.4i	−0.150607	−	0.260858i	0.780844	−	0.624726i	$-0.214789\pi$
$389$	−22790.0	−	39473.4i	−0.150607	−	0.260858i	−0.931451	+	0.363868i	$0.881456\pi$
$390$	71155.0	−	41081.4i	0.467817	−	0.270095i
$391$	107190.			0.701136
$392$			20841.6i			0.135631i
$393$	−37308.2	+	21539.9i	−0.241557	+	0.139463i
$394$	174103.	+	100519.i	1.12154	+	0.647521i
$395$	−18908.1	+	10916.6i	−0.121187	+	0.0699671i
$396$	36229.5	−	62751.3i	0.231032	−	0.400159i
$397$	89476.0	−	154977.i	0.567709	−	0.983301i	−0.429083	−	0.903265i	$-0.641163\pi$
$397$	89476.0	−	154977.i	0.567709	−	0.983301i	0.996792	−	0.0800358i	$-0.0255035\pi$
$398$			148326.i			0.936377i
$399$	−8074.59	−	88636.5i	−0.0507195	−	0.556758i
$400$	40773.7			0.254835
$401$	−117639.	−	67918.8i	−0.731580	−	0.422378i	0.0874200	−	0.996172i	$-0.472138\pi$
$401$	−117639.	−	67918.8i	−0.731580	−	0.422378i	−0.819000	+	0.573794i	$0.805471\pi$
$402$	−52812.4	−	30491.3i	−0.326802	−	0.188679i
$403$	89228.5	+	154548.i	0.549406	+	0.951600i
$404$	30163.3	−	52244.4i	0.184806	−	0.320094i
$405$	−43510.6	−	75362.6i	−0.265268	−	0.459458i
$406$	−3137.99			−0.0190371
$407$			285115.i			1.72120i
$408$	26504.4	+	45906.9i	0.159220	+	0.275777i
$409$	−49984.2	+	28858.4i	−0.298804	+	0.172514i	−0.641905	−	0.766784i	$-0.721856\pi$
$409$	−49984.2	+	28858.4i	−0.298804	+	0.172514i	0.343102	+	0.939298i	$0.388522\pi$
$410$	−163596.			−0.973205
$411$			1305.12i			0.00772619i
$412$	−124143.	+	71673.8i	−0.731352	+	0.422246i
$413$	75736.7	+	43726.6i	0.444024	+	0.256357i
$414$	30060.7	−	17355.6i	0.175388	−	0.101260i
$415$	48824.6	−	84566.7i	0.283493	−	0.491024i
$416$	17301.5	−	29967.2i	0.0999766	−	0.173164i
$417$		−	46068.5i		−	0.264931i
$418$	−13380.8	−	146884.i	−0.0765826	−	0.840663i
$419$	213159.			1.21416			0.607079	−	0.794642i	$-0.292341\pi$
$419$	213159.			1.21416			0.607079	+	0.794642i	$0.292341\pi$
$420$	−60682.8	−	35035.2i	−0.344007	−	0.198612i
$421$	−77550.3	−	44773.7i	−0.437541	−	0.252615i	0.265013	−	0.964245i	$-0.414624\pi$
$421$	−77550.3	−	44773.7i	−0.437541	−	0.252615i	−0.702554	+	0.711630i	$0.747957\pi$
$422$	−21113.9	−	36570.3i	−0.118561	−	0.205354i
$423$	−17657.5	+	30583.8i	−0.0986846	+	0.170927i
$424$	−12053.9	−	20878.0i	−0.0670497	−	0.116134i
$425$	−348913.			−1.93170
$426$		−	17207.4i		−	0.0948193i
$427$	−154276.	−	267214.i	−0.846142	−	1.46556i
$428$	130555.	−	75375.9i	0.712698	−	0.411476i
$429$	−118114.			−0.641782
$430$		−	221384.i		−	1.19732i
$431$	166815.	−	96311.0i	0.898011	−	0.518467i	0.0214568	−	0.999770i	$-0.493170\pi$
$431$	166815.	−	96311.0i	0.898011	−	0.518467i	0.876554	+	0.481303i	$0.159836\pi$
$432$	34069.9	+	19670.2i	0.182559	+	0.105400i
$433$	198315.	−	114497.i	1.05774	−	0.610686i	0.132933	−	0.991125i	$-0.457560\pi$
$433$	198315.	−	114497.i	1.05774	−	0.610686i	0.924806	+	0.380439i	$0.124227\pi$
$434$	76096.3	−	131803.i	0.404003	−	0.699753i
$435$	1462.56	−	2533.22i	0.00772919	−	0.0133873i
$436$		−	27282.8i		−	0.143521i
$437$	29630.8	−	64142.1i	0.155160	−	0.335877i
$438$	68237.4			0.355692
$439$	−223947.	−	129296.i	−1.16203	−	0.670897i	−0.210238	−	0.977650i	$-0.567424\pi$
$439$	−223947.	−	129296.i	−1.16203	−	0.670897i	−0.951789	+	0.306753i	$0.900757\pi$
$440$	−100561.	−	58058.6i	−0.519424	−	0.299890i
$441$	−28876.9	−	50016.2i	−0.148482	−	0.257178i
$442$	−148055.	+	256438.i	−0.757840	+	1.31262i
$443$	−12720.2	−	22032.0i	−0.0648166	−	0.112266i	0.831796	−	0.555081i	$-0.187313\pi$
$443$	−12720.2	−	22032.0i	−0.0648166	−	0.112266i	−0.896613	+	0.442816i	$0.853980\pi$
$444$	−67544.2			−0.342628
$445$			190628.i			0.962647i
$446$	−23167.4	−	40127.2i	−0.116468	−	0.201729i
$447$	−50674.6	+	29257.0i	−0.253615	+	0.146425i
$448$	−29510.4			−0.147034
$449$			286827.i			1.42275i	0.702814	+	0.711374i	$0.251927\pi$
$449$			286827.i			1.42275i	−0.702814	+	0.711374i	$0.748073\pi$
$450$	−97849.9	+	56493.7i	−0.483209	+	0.278981i
$451$	203671.	+	117590.i	1.00133	+	0.578118i
$452$	−101649.	+	58687.2i	−0.497539	+	0.287254i
$453$	−8411.74	+	14569.6i	−0.0409911	+	0.0709986i
$454$	−25184.5	+	43620.8i	−0.122186	+	0.211632i
$455$		−	391417.i		−	1.89067i
$456$	34797.1	−	3169.94i	0.167345	−	0.0152448i
$457$	189481.			0.907261			0.453631	−	0.891190i	$-0.350129\pi$
$457$	189481.			0.907261			0.453631	+	0.891190i	$0.350129\pi$
$458$	228766.	+	132078.i	1.09059	+	0.629651i
$459$	−291546.	−	168324.i	−1.38383	−	0.798954i
$460$	−27812.7	−	48173.1i	−0.131440	−	0.227661i
$461$	−9247.43	+	16017.0i	−0.0435130	+	0.0753668i	−0.886962	−	0.461843i	$-0.847188\pi$
$461$	−9247.43	+	16017.0i	−0.0435130	+	0.0753668i	0.843449	+	0.537210i	$0.180522\pi$
$462$	50365.4	+	87235.4i	0.235965	+	0.408704i
$463$	36606.3			0.170763			0.0853815	−	0.996348i	$-0.472789\pi$
$463$	36606.3			0.170763			0.0853815	+	0.996348i	$0.472789\pi$
$464$		−	1231.92i		−	0.00572198i
$465$	70933.9	+	122861.i	0.328056	+	0.568210i
$466$	91685.0	−	52934.4i	0.422208	−	0.243762i
$467$	209051.			0.958558			0.479279	−	0.877663i	$-0.340898\pi$
$467$	209051.			0.958558			0.479279	+	0.877663i	$0.340898\pi$
$468$			95888.2i			0.437798i
$469$	−251594.	+	145258.i	−1.14381	+	0.660381i
$470$	49011.2	+	28296.6i	0.221871	+	0.128097i
$471$	92449.2	−	53375.6i	0.416736	−	0.240603i
$472$	−17166.3	+	29732.9i	−0.0770534	+	0.133460i
$473$	−159127.	+	275616.i	−0.711248	+	1.23192i
$474$			7435.55i			0.0330946i
$475$	−96450.5	+	208787.i	−0.427482	+	0.925374i
$476$	252529.			1.11455
$477$	57854.8	+	33402.5i	0.254274	+	0.146805i
$478$	−65182.9	−	37633.4i	−0.285284	−	0.164709i
$479$	142395.	+	246635.i	0.620615	+	1.07494i	0.989371	+	0.145411i	$0.0464505\pi$
$479$	142395.	+	246635.i	0.620615	+	1.07494i	−0.368756	+	0.929526i	$0.620216\pi$
$480$	13754.2	−	23823.0i	0.0596970	−	0.103398i
$481$	−188653.	−	326756.i	−0.815404	−	1.41232i
$482$	−63319.2			−0.272547
$483$			48254.6i			0.206845i
$484$	24899.0	+	43126.4i	0.106290	+	0.184099i
$485$	302123.	−	174431.i	1.28440	−	0.741548i
$486$	−170464.			−0.721707
$487$			318832.i			1.34432i	0.740404	+	0.672162i	$0.234634\pi$
$487$			318832.i			1.34432i	−0.740404	+	0.672162i	$0.765366\pi$
$488$	104904.	−	60566.1i	0.440505	−	0.254325i
$489$	114819.	+	66290.8i	0.480171	+	0.277227i
$490$	−80152.2	+	46275.9i	−0.333829	+	0.192736i
$491$	−37286.0	+	64581.2i	−0.154662	+	0.267882i	−0.932936	−	0.360043i	$-0.882762\pi$
$491$	−37286.0	+	64581.2i	−0.154662	+	0.267882i	0.778274	+	0.627925i	$0.216095\pi$
$492$	−27857.2	+	48250.1i	−0.115082	+	0.199328i
$493$			10541.9i			0.0433736i
$494$	112524.	+	159483.i	0.461097	+	0.653521i
$495$	321771.			1.31322
$496$	51743.3	+	29874.0i	0.210325	+	0.121431i
$497$	−70992.3	−	40987.4i	−0.287408	−	0.165935i
$498$	−16627.8	−	28800.1i	−0.0670464	−	0.116128i
$499$	98295.9	−	170254.i	0.394761	−	0.683746i	−0.598310	−	0.801265i	$-0.704161\pi$
$499$	98295.9	−	170254.i	0.394761	−	0.683746i	0.993071	+	0.117519i	$0.0374940\pi$
$500$	1717.79	+	2975.30i	0.00687116	+	0.0119012i
$501$	198689.			0.791588
$502$			113152.i			0.449008i
$503$	26214.9	+	45405.5i	0.103613	+	0.179462i	0.913170	−	0.407578i	$-0.133626\pi$
$503$	26214.9	+	45405.5i	0.103613	+	0.179462i	−0.809558	+	0.587040i	$0.800293\pi$
$504$	70819.9	−	40887.9i	0.278801	−	0.160966i
$505$	267895.			1.05046
$506$			79965.1i			0.312320i
$507$	29561.4	−	17067.3i	0.115003	−	0.0663971i
$508$	−32467.9	−	18745.3i	−0.125813	−	0.0726384i
$509$	−179843.	+	103832.i	−0.694157	+	0.400772i	−0.805167	−	0.593048i	$-0.797925\pi$
$509$	−179843.	+	103832.i	−0.694157	+	0.400772i	0.111011	+	0.993819i	$0.464591\pi$
$510$	−117699.	+	203860.i	−0.452514	+	0.783777i
$511$	162539.	−	281526.i	0.622466	−	1.07814i
$512$		−	11585.2i		−	0.0441942i
$513$	−181317.	+	127929.i	−0.688975	+	0.486112i
$514$	−300796.			−1.13853
$515$	−551285.	−	318284.i	−2.07855	−	1.20005i
$516$	−65293.8	−	37697.4i	−0.245230	−	0.141583i
$517$	−40678.2	−	70456.8i	−0.152188	−	0.263598i
$518$	−160888.	+	278666.i	−0.599602	+	1.03854i
$519$	108827.	+	188494.i	0.404020	+	0.699783i
$520$	153663.			0.568281
$521$		−	125122.i		−	0.460956i	−0.973078	−	0.230478i	$-0.925971\pi$
$521$		−	125122.i		−	0.460956i	0.973078	−	0.230478i	$-0.0740290\pi$
$522$	1706.88	+	2956.40i	0.00626414	+	0.0108498i
$523$	−62316.2	+	35978.3i	−0.227823	+	0.131534i	−0.609567	−	0.792734i	$-0.708657\pi$
$523$	−62316.2	+	35978.3i	−0.227823	+	0.131534i	0.381744	+	0.924268i	$0.375323\pi$
$524$	−80569.1			−0.293431
$525$		−	157072.i		−	0.569877i
$526$	170080.	−	98195.7i	0.614726	−	0.354912i
$527$	−442784.	−	255641.i	−1.59430	−	0.920470i
$528$	−34247.0	+	19772.5i	−0.122844	+	0.0709242i
$529$	120767.	−	209175.i	0.431556	−	0.747477i
$530$	53528.3	−	92713.7i	0.190560	−	0.330060i
$531$		−	95138.5i		−	0.337417i
$532$	69807.1	−	151112.i	0.246647	−	0.533920i
$533$	−311223.			−1.09551
$534$	56222.9	+	32460.3i	0.197165	+	0.113833i
$535$	579760.	+	334724.i	2.02554	+	1.16944i
$536$	−57025.7	−	98771.3i	−0.198491	−	0.343796i
$537$	−93606.2	+	162131.i	−0.324606	+	0.562234i
$538$	79730.4	+	138097.i	0.275460	+	0.477112i
$539$	133049.			0.457968
$540$			174701.i			0.599111i
$541$	−171283.	−	296672.i	−0.585222	−	1.01363i	−0.994848	−	0.101381i	$-0.967674\pi$
$541$	−171283.	−	296672.i	−0.585222	−	1.01363i	0.409626	−	0.912254i	$-0.365659\pi$
$542$	−98726.9	+	57000.0i	−0.336076	+	0.194033i
$543$	−174423.			−0.591568
$544$			99138.5i			0.335000i
$545$	104924.	−	60577.8i	0.353249	−	0.203948i
$546$	−115442.	−	66650.7i	−0.387240	−	0.223573i
$547$	383525.	−	221428.i	1.28180	−	0.740045i	0.304619	−	0.952474i	$-0.401471\pi$
$547$	383525.	−	221428.i	1.28180	−	0.740045i	0.977176	+	0.212429i	$0.0681375\pi$
$548$	−1220.43	+	2113.85i	−0.00406399	+	0.00703904i
$549$	−167834.	+	290697.i	−0.556846	+	0.964485i
$550$		−	260293.i		−	0.860471i
$551$	6308.22	+	2914.12i	0.0207780	+	0.00959851i
$552$	−18943.9			−0.0621714
$553$	30676.7	+	17711.2i	0.100313	+	0.0579159i
$554$	4232.15	+	2443.43i	0.0137893	+	0.00796124i
$555$	−149973.	−	259761.i	−0.486886	−	0.843311i
$556$	43079.4	−	74615.6i	0.139354	−	0.241368i
$557$	27527.9	+	47679.7i	0.0887283	+	0.153682i	0.906974	−	0.421187i	$-0.138386\pi$
$557$	27527.9	+	47679.7i	0.0887283	+	0.153682i	−0.818246	+	0.574869i	$0.805053\pi$
$558$	−165567.			−0.531748
$559$		−	421159.i		−	1.34779i
$560$	−65523.9	−	113491.i	−0.208941	−	0.361896i
$561$	293062.	−	169200.i	0.931182	−	0.537618i
$562$	234987.			0.743998
$563$			151431.i			0.477747i	0.971051	+	0.238873i	$0.0767781\pi$
$563$			151431.i			0.477747i	−0.971051	+	0.238873i	$0.923222\pi$
$564$	16691.3	−	9636.74i	0.0524726	−	0.0302951i
$565$	−451398.	−	260614.i	−1.41404	−	0.816398i
$566$	276787.	−	159803.i	0.863997	−	0.498829i
$567$	−70592.0	+	122269.i	−0.219578	+	0.380321i
$568$	16090.9	−	27870.3i	0.0498751	−	0.0863863i
$569$			234376.i			0.723917i	0.932194	+	0.361958i	$0.117892\pi$
$569$			234376.i			0.723917i	−0.932194	+	0.361958i	$0.882108\pi$
$570$	89453.2	+	126784.i	0.275325	+	0.390224i
$571$	41578.6			0.127526			0.0637628	−	0.997965i	$-0.479690\pi$
$571$	41578.6			0.127526			0.0637628	+	0.997965i	$0.479690\pi$
$572$	−191306.	−	110450.i	−0.584703	−	0.337579i
$573$	−185166.	−	106906.i	−0.563965	−	0.325605i
$574$	132709.	+	229860.i	0.402790	+	0.697652i
$575$	62346.0	−	107986.i	0.188570	−	0.326613i
$576$	16051.9	+	27802.6i	0.0483816	+	0.0837994i
$577$	−71928.1			−0.216046			−0.108023	−	0.994148i	$-0.534452\pi$
$577$	−71928.1			−0.216046			−0.108023	+	0.994148i	$0.534452\pi$
$578$		−	612126.i		−	1.83225i
$579$	37804.8	+	65479.8i	0.112769	+	0.195321i
$580$	4737.70	−	2735.31i	0.0140835	−	0.00813113i
$581$	−158427.			−0.469328
$582$		−	118809.i		−	0.350753i
$583$	−133282.	+	76950.4i	−0.392134	+	0.226399i
$584$	110522.	+	63809.8i	0.324058	+	0.187095i
$585$	−368766.	+	212907.i	−1.07755	+	0.622126i
$586$	21131.9	−	36601.6i	0.0615381	−	0.106587i
$587$	177751.	−	307875.i	0.515866	−	0.893506i	−0.483964	−	0.875088i	$-0.660804\pi$
$587$	177751.	−	307875.i	0.515866	−	0.893506i	0.999830	−	0.0184185i	$-0.00586313\pi$
$588$			31519.6i			0.0911645i
$589$	−275374.	+	194292.i	−0.793765	+	0.560047i
$590$	−152462.			−0.437983
$591$	263304.	+	152019.i	0.753846	+	0.435233i
$592$	−109399.	−	63161.6i	−0.312155	−	0.180223i
$593$	141638.	+	245325.i	0.402784	+	0.697642i	0.994061	−	0.108827i	$-0.0347094\pi$
$593$	141638.	+	245325.i	0.402784	+	0.697642i	−0.591277	+	0.806468i	$0.701376\pi$
$594$	125572.	−	217497.i	0.355893	−	0.616424i
$595$	560708.	+	971175.i	1.58381	+	2.74324i
$596$	−109435.			−0.308079
$597$			224320.i			0.629388i
$598$	−52910.7	−	91644.0i	−0.147959	−	0.256272i
$599$	−48978.7	+	28277.9i	−0.136507	+	0.0788121i	−0.566698	−	0.823926i	$-0.691779\pi$
$599$	−48978.7	+	28277.9i	−0.136507	+	0.0788121i	0.430191	+	0.902738i	$0.358446\pi$
$600$	61663.7			0.171288
$601$		−	680157.i		−	1.88304i	−0.336954	−	0.941521i	$-0.609397\pi$
$601$		−	680157.i		−	1.88304i	0.336954	−	0.941521i	$-0.390603\pi$
$602$	−311055.	+	179587.i	−0.858309	+	0.495545i
$603$	273704.	+	158023.i	0.752743	+	0.434596i
$604$	−27248.4	+	15731.9i	−0.0746908	+	0.0431228i
$605$	−110570.	+	191513.i	−0.302083	+	0.523223i
$606$	45617.3	−	79011.5i	0.124218	−	0.215152i
$607$			444821.i			1.20728i	0.797257	+	0.603640i	$0.206284\pi$
$607$			444821.i			1.20728i	−0.797257	+	0.603640i	$0.793716\pi$
$608$	59323.9	+	27405.0i	0.160481	+	0.0741349i
$609$	−4745.72			−0.0127958
$610$	465849.	+	268958.i	1.25195	+	0.722811i
$611$	93238.5	+	53831.3i	0.249754	+	0.144196i
$612$	−137361.	−	237916.i	−0.366741	−	0.635214i
$613$	70542.1	−	122182.i	0.187727	−	0.325153i	−0.756765	−	0.653687i	$-0.773221\pi$
$613$	70542.1	−	122182.i	0.187727	−	0.325153i	0.944492	+	0.328534i	$0.106555\pi$
$614$	−215701.	−	373605.i	−0.572158	−	0.991006i
$615$	−247413.			−0.654142
$616$			188390.i			0.496473i
$617$	129342.	+	224026.i	0.339757	+	0.588476i	0.984387	−	0.176019i	$-0.0563220\pi$
$617$	129342.	+	224026.i	0.339757	+	0.588476i	−0.644630	+	0.764495i	$0.722989\pi$
$618$	−187746.	+	108395.i	−0.491580	+	0.283814i
$619$	−597838.			−1.56028			−0.780139	−	0.625606i	$-0.784852\pi$
$619$	−597838.			−1.56028			−0.780139	+	0.625606i	$0.784852\pi$
$620$			265325.i			0.690232i
$621$	104191.	−	60154.5i	0.270175	−	0.155986i
$622$	−219532.	−	126747.i	−0.567437	−	0.327610i
$623$	267841.	−	154638.i	0.690083	−	0.398420i
$624$	26165.9	−	45320.6i	0.0671995	−	0.116393i
$625$	191462.	−	331622.i	0.490142	−	0.848951i
$626$			54663.5i			0.139492i
$627$	−20236.4	−	222139.i	−0.0514752	−	0.565054i
$628$	199649.			0.506230
$629$	936162.	+	540493.i	2.36619	+	1.36612i
$630$	314493.	+	181572.i	0.792372	+	0.457476i
$631$	74146.6	+	128426.i	0.186223	+	0.322547i	0.943988	−	0.329980i	$-0.107042\pi$
$631$	74146.6	+	128426.i	0.186223	+	0.322547i	−0.757765	+	0.652527i	$0.773709\pi$
$632$	−6953.09	+	12043.1i	−0.0174078	+	0.0301512i
$633$	−31931.5	−	55306.9i	−0.0796914	−	0.138029i
$634$	187452.			0.466349
$635$		−	166486.i		−	0.412887i
$636$	−18229.7	−	31574.7i	−0.0450676	−	0.0780594i
$637$	−152481.	+	88034.9i	−0.375783	+	0.216958i
$638$	−7864.38			−0.0193207
$639$			89178.7i			0.218403i
$640$	44554.4	−	25723.5i	0.108775	−	0.0628015i
$641$	387126.	+	223507.i	0.942185	+	0.543971i	0.890645	−	0.454700i	$-0.150254\pi$
$641$	387126.	+	223507.i	0.942185	+	0.543971i	0.0515404	+	0.998671i	$0.483587\pi$
$642$	197444.	−	113994.i	0.479042	−	0.276575i
$643$	−205874.	+	356584.i	−0.497942	+	0.862461i	−0.999997	−	0.00237459i	$-0.999244\pi$
$643$	−205874.	+	356584.i	−0.497942	+	0.862461i	0.502055	+	0.864836i	$0.332577\pi$
$644$	−45123.6	+	78156.3i	−0.108801	+	0.188448i
$645$		−	334808.i		−	0.804780i
$646$	−507653.	−	234513.i	−1.21647	−	0.561956i
$647$	−782873.			−1.87018			−0.935089	−	0.354413i	$-0.884681\pi$
$647$	−782873.			−1.87018			−0.935089	+	0.354413i	$0.884681\pi$
$648$	−48000.5	−	27713.1i	−0.114313	−	0.0659987i
$649$	189810.	+	109587.i	0.450639	+	0.260177i
$650$	172228.	+	298308.i	0.407641	+	0.706055i
$651$	115084.	−	199331.i	0.271551	−	0.470341i
$652$	123979.	+	214738.i	0.291644	+	0.505142i
$653$	111555.			0.261614			0.130807	−	0.991408i	$-0.458243\pi$
$653$	111555.			0.261614			0.130807	+	0.991408i	$0.458243\pi$
$654$		−	41260.9i		−	0.0964680i
$655$	−178893.	−	309852.i	−0.416976	−	0.722223i
$656$	−90238.7	+	52099.3i	−0.209694	+	0.121067i
$657$	−353645.			−0.819289
$658$		−	91817.3i		−	0.212067i
$659$	−531309.	+	306751.i	−1.22342	+	0.706343i	−0.965646	−	0.259861i	$-0.916323\pi$
$659$	−531309.	+	306751.i	−1.22342	+	0.706343i	−0.257776	+	0.966205i	$0.582990\pi$
$660$	−152082.	−	87804.6i	−0.349132	−	0.201572i
$661$	−431091.	+	248890.i	−0.986656	+	0.569646i	−0.904273	−	0.426955i	$-0.859586\pi$
$661$	−431091.	+	248890.i	−0.986656	+	0.569646i	−0.0823828	+	0.996601i	$0.526253\pi$
$662$	1312.25	−	2272.88i	0.00299433	−	0.00518633i
$663$	−223909.	+	387822.i	−0.509384	+	0.882279i
$664$		−	62195.5i		−	0.141066i
$665$	736143.	−	67061.0i	1.66463	−	0.151645i
$666$	350052.			0.789196
$667$	−3262.66	−	1883.70i	−0.00733364	−	0.00423408i
$668$	321810.	+	185797.i	0.721185	+	0.416377i
$669$	−35037.1	−	60686.0i	−0.0782845	−	0.135593i
$670$	253236.	−	438617.i	0.564125	−	0.977094i
$671$	−386644.	−	669687.i	−0.858750	−	1.48740i
$672$	−44629.8			−0.0988295
$673$			233726.i			0.516032i	0.966141	+	0.258016i	$0.0830687\pi$
$673$			233726.i			0.516032i	−0.966141	+	0.258016i	$0.916931\pi$
$674$	143321.	+	248240.i	0.315494	+	0.546451i
$675$	−339149.	+	195808.i	−0.744359	+	0.429756i
$676$	63839.5			0.139700
$677$			634144.i			1.38360i	0.722089	+	0.691800i	$0.243182\pi$
$677$			634144.i			1.38360i	−0.722089	+	0.691800i	$0.756818\pi$
$678$	−153729.	+	88755.2i	−0.334422	+	0.193079i
$679$	−490166.	−	282997.i	−1.06317	−	0.613823i
$680$	−381266.	+	220124.i	−0.824537	+	0.476046i
$681$	−38087.6	+	65969.6i	−0.0821275	+	0.142249i
$682$	190711.	−	330321.i	0.410022	−	0.710179i
$683$		−	438197.i		−	0.939350i	−0.882839	−	0.469675i	$-0.844371\pi$
$683$		−	438197.i		−	0.939350i	0.882839	−	0.469675i	$-0.155629\pi$
$684$	−180338.	+	16428.4i	−0.385457	+	0.0351143i
$685$	−10839.2			−0.0231003
$686$	−208939.	−	120631.i	−0.443989	−	0.256337i
$687$	345972.	+	199747.i	0.733041	+	0.423221i
$688$	−70502.8	−	122114.i	−0.148946	−	0.257982i
$689$	101832.	−	176378.i	0.214509	−	0.371540i
$690$	−42062.4	−	72854.2i	−0.0883478	−	0.153023i
$691$	687997.			1.44089			0.720444	−	0.693513i	$-0.243938\pi$
$691$	687997.			1.44089			0.720444	+	0.693513i	$0.243938\pi$
$692$			407064.i			0.850061i
$693$	−261022.	−	452103.i	−0.543514	−	0.941393i
$694$	−378439.	+	218492.i	−0.785737	+	0.453646i
$695$	382608.			0.792108
$696$		−	1863.08i		−	0.00384604i
$697$	772201.	−	445830.i	1.58951	−	0.917707i
$698$	−95777.2	−	55297.0i	−0.196585	−	0.113499i
$699$	138659.	−	80054.9i	0.283788	−	0.163845i
$700$	146881.	−	254405.i	0.299756	−	0.519193i
$701$	266610.	−	461781.i	0.542550	−	0.939724i	−0.456207	−	0.889874i	$-0.650792\pi$
$701$	266610.	−	461781.i	0.542550	−	0.939724i	0.998757	−	0.0498501i	$-0.0158744\pi$
$702$			332349.i			0.674404i
$703$	582213.	−	410784.i	1.17807	−	0.831196i
$704$	−73958.3			−0.149225
$705$	74121.8	+	42794.2i	0.149131	+	0.0861007i
$706$	86990.0	+	50223.7i	0.174526	+	0.100763i
$707$	−217317.	−	376404.i	−0.434766	−	0.753036i
$708$	−25961.3	+	44966.3i	−0.0517916	+	0.0897058i
$709$	−439347.	−	760972.i	−0.874008	−	1.51383i	−0.857815	−	0.513958i	$-0.828179\pi$
$709$	−439347.	−	760972.i	−0.874008	−	1.51383i	−0.0161930	−	0.999869i	$-0.505155\pi$
$710$	142911.			0.283497
$711$		−	38535.3i		−	0.0762288i
$712$	60708.2	+	105150.i	0.119753	+	0.207419i
$713$	158239.	−	91359.3i	0.311268	−	0.179711i
$714$	381911.			0.749145
$715$		−	980961.i		−	1.91884i
$716$	−303222.	+	175065.i	−0.591472	+	0.341486i
$717$	−98578.9	−	56914.6i	−0.191755	−	0.110710i
$718$	−231776.	+	133816.i	−0.449593	+	0.259572i
$719$	107023.	−	185369.i	0.207024	−	0.358575i	−0.743752	−	0.668456i	$-0.766956\pi$
$719$	107023.	−	185369.i	0.207024	−	0.358575i	0.950776	+	0.309880i	$0.100289\pi$
$720$	−71282.0	+	123464.i	−0.137504	+	0.238164i
$721$			1.03277e6i			1.98671i
$722$	−280663.	+	238950.i	−0.538406	+	0.458387i
$723$	−95760.4			−0.183193
$724$	−282507.	−	163106.i	−0.538955	−	0.311166i
$725$	10620.2	+	6131.57i	0.0202049	+	0.0116653i
$726$	37655.8	+	65221.8i	0.0714429	+	0.123743i
$727$	−195439.	+	338510.i	−0.369778	+	0.640475i	−0.989531	−	0.144322i	$-0.953900\pi$
$727$	−195439.	+	338510.i	−0.369778	+	0.640475i	0.619752	+	0.784798i	$0.287233\pi$
$728$	−124652.	−	215904.i	−0.235200	−	0.407378i
$729$	−59389.6			−0.111752
$730$			566725.i			1.06347i
$731$	603314.	+	1.04497e6i	1.12904	+	1.95555i
$732$	158650.	−	91596.7i	0.296086	−	0.170945i
$733$	−437702.			−0.814648			−0.407324	−	0.913284i	$-0.633538\pi$
$733$	−437702.			−0.814648			−0.407324	+	0.913284i	$0.633538\pi$
$734$			106899.i			0.198417i
$735$	−121218.	+	69985.1i	−0.224384	+	0.129548i
$736$	−30682.8	−	17714.7i	−0.0566420	−	0.0327023i
$737$	−630541.	+	364043.i	−1.16086	+	0.670220i
$738$	144372.	−	250059.i	0.265076	−	0.459124i
$739$	−260845.	+	451796.i	−0.477632	+	0.827282i	−0.999671	−	0.0256391i	$-0.991838\pi$
$739$	−260845.	+	451796.i	−0.477632	+	0.827282i	0.522040	+	0.852921i	$0.325171\pi$
$740$		−	560968.i		−	1.02441i
$741$	170175.	+	241193.i	0.309927	+	0.439266i
$742$	−173689.			−0.315475
$743$	−561882.	−	324403.i	−1.01781	−	0.587634i	−0.104343	−	0.994541i	$-0.533274\pi$
$743$	−561882.	−	324403.i	−1.01781	−	0.587634i	−0.913470	+	0.406907i	$0.866607\pi$
$744$	78253.7	+	45179.8i	0.141371	+	0.0816203i
$745$	−242985.	−	420862.i	−0.437791	−	0.758276i
$746$	26059.6	−	45136.6i	0.0468264	−	0.0811056i
$747$	86174.5	+	149259.i	0.154432	+	0.267484i
$748$	632884.			1.13115
$749$		−	1.08612e6i		−	1.93604i
$750$	2597.89	+	4499.67i	0.00461847	+	0.00799942i
$751$	297330.	−	171664.i	0.527180	−	0.304367i	−0.212687	−	0.977120i	$-0.568222\pi$
$751$	297330.	−	171664.i	0.527180	−	0.304367i	0.739867	+	0.672753i	$0.234888\pi$
$752$	36045.8			0.0637411
$753$			171125.i			0.301802i
$754$	9012.97	−	5203.64i	0.0158535	−	0.00915302i
$755$	−121003.	−	69861.1i	−0.212277	−	0.122558i
$756$	245462.	−	141718.i	0.429479	−	0.247960i
$757$	389018.	−	673798.i	0.678856	−	1.17581i	−0.296470	−	0.955042i	$-0.595809\pi$
$757$	389018.	−	673798.i	0.678856	−	1.17581i	0.975326	−	0.220771i	$-0.0708572\pi$
$758$	−75218.3	+	130282.i	−0.130914	+	0.226749i
$759$			120935.i			0.209927i
$760$	26326.9	+	288996.i	0.0455799	+	0.500340i
$761$	−427214.			−0.737694			−0.368847	−	0.929490i	$-0.620247\pi$
$761$	−427214.			−0.737694			−0.368847	+	0.929490i	$0.620247\pi$
$762$	−49102.6	−	28349.4i	−0.0845657	−	0.0488241i
$763$	−170229.	−	98281.8i	−0.292405	−	0.168820i
$764$	−199938.	−	346303.i	−0.342538	−	0.593293i
$765$	609982.	−	1.05652e6i	1.04230	−	1.80532i
$766$	−204916.	−	354926.i	−0.349236	−	0.604895i
$767$	−290042.			−0.493026
$768$		−	17520.9i		−	0.0297052i
$769$	399183.	+	691405.i	0.675024	+	1.16918i	0.976462	+	0.215690i	$0.0692002\pi$
$769$	399183.	+	691405.i	0.675024	+	1.16918i	−0.301438	+	0.953486i	$0.597467\pi$
$770$	−724506.	+	418294.i	−1.22197	+	0.705505i
$771$	−454907.			−0.765268
$772$			141407.i			0.237267i
$773$	460472.	−	265854.i	0.770627	−	0.444922i	−0.0624714	−	0.998047i	$-0.519898\pi$
$773$	460472.	−	265854.i	0.770627	−	0.444922i	0.833098	+	0.553125i	$0.186565\pi$
$774$	338390.	+	195369.i	0.564853	+	0.326118i
$775$	−515079.	+	297381.i	−0.857572	+	0.495120i
$776$	111100.	−	192430.i	0.184497	−	0.319558i
$777$	−243317.	+	421438.i	−0.403024	+	0.698058i
$778$		−	128919.i		−	0.212990i
$779$	−53321.6	−	585322.i	−0.0878674	−	0.964539i
$780$	232391.			0.381971
$781$	−177919.	−	102722.i	−0.291690	−	0.168407i
$782$	262562.	+	151590.i	0.429357	+	0.247889i
$783$	5916.05	+	10246.9i	0.00964958	+	0.0167136i
$784$	−29474.4	+	51051.2i	−0.0479527	+	0.0830565i
$785$	443294.	+	767809.i	0.719371	+	1.24599i
$786$	−121848.			−0.197230
$787$			929506.i			1.50073i	0.661024	+	0.750365i	$0.270122\pi$
$787$			929506.i			1.50073i	−0.661024	+	0.750365i	$0.729878\pi$
$788$	284310.	+	492439.i	0.457867	+	0.793049i
$789$	257219.	−	148506.i	0.413190	−	0.238555i
$790$	−61753.7			−0.0989484
$791$			845646.i			1.35156i
$792$	177488.	−	102472.i	0.282955	−	0.163364i
$793$	886227.	+	511663.i	1.40928	+	0.813651i
$794$	438341.	−	253076.i	0.695299	−	0.401431i
$795$	80953.1	−	140215.i	0.128085	−	0.221850i
$796$	−209764.	+	363323.i	−0.331059	+	0.573412i
$797$			349224.i			0.549779i	0.961476	+	0.274889i	$0.0886412\pi$
$797$			349224.i			0.549779i	−0.961476	+	0.274889i	$0.911359\pi$
$798$	105572.	−	228533.i	0.165785	−	0.358876i
$799$	−308455.			−0.483169
$800$	99874.6	+	57662.7i	0.156054	+	0.0900979i
$801$	−291379.	−	168228.i	−0.454143	−	0.262200i
$802$	−192103.	−	332733.i	−0.298666	−	0.517305i
$803$	407352.	−	705554.i	0.631740	−	1.09421i
$804$	−86242.3	−	149376.i	−0.133416	−	0.231084i
$805$	−400764.			−0.618439
$806$			504753.i			0.776978i
$807$	120580.	+	208850.i	0.185151	+	0.320692i
$808$	147770.	−	85314.8i	0.226340	−	0.130678i
$809$	840086.			1.28359			0.641796	−	0.766876i	$-0.278190\pi$
$809$	840086.			1.28359			0.641796	+	0.766876i	$0.278190\pi$
$810$		−	246133.i		−	0.375146i
$811$	−982257.	+	567106.i	−1.49342	+	0.862229i	−0.999972	−	0.00754325i	$-0.997599\pi$
$811$	−982257.	+	567106.i	−1.49342	+	0.862229i	−0.493453	+	0.869772i	$0.664266\pi$
$812$	−7686.48	−	4437.79i	−0.0116578	−	0.00673062i
$813$	−149309.	+	86203.5i	−0.225894	+	0.130420i
$814$	−403213.	+	698386.i	−0.608536	+	1.05401i
$815$	−550557.	+	953593.i	−0.828872	+	1.43565i
$816$			149931.i			0.225171i
$817$	792080.	−	72156.7i	1.18666	−	0.108102i
$818$	−163248.			−0.243972
$819$	598288.	+	345422.i	0.891954	+	0.514970i
$820$	−400726.	−	231359.i	−0.595964	−	0.344080i
$821$	−416970.	−	722214.i	−0.618613	−	1.07147i	−0.989739	−	0.142886i	$-0.954362\pi$
$821$	−416970.	−	722214.i	−0.618613	−	1.07147i	0.371126	−	0.928582i	$-0.378972\pi$
$822$	−1845.71	+	3196.87i	−0.00273162	+	0.00473131i
$823$	160435.	+	277881.i	0.236864	+	0.410260i	0.959813	−	0.280642i	$-0.0905472\pi$
$823$	160435.	+	277881.i	0.236864	+	0.410260i	−0.722949	+	0.690901i	$0.757214\pi$
$824$	−405448.			−0.597147
$825$		−	393651.i		−	0.578368i
$826$	123678.	+	214216.i	0.181272	+	0.313972i
$827$	454612.	−	262470.i	0.664706	−	0.383768i	−0.129361	−	0.991598i	$-0.541293\pi$
$827$	454612.	−	262470.i	0.664706	−	0.383768i	0.794068	+	0.607829i	$0.207959\pi$
$828$	98177.9			0.143203
$829$		−	168815.i		−	0.245641i	−0.992429	−	0.122821i	$-0.960806\pi$
$829$		−	168815.i		−	0.245641i	0.992429	−	0.122821i	$-0.0391940\pi$
$830$	239191.	−	138097.i	0.347207	−	0.200460i
$831$	6400.46	+	3695.31i	0.00926850	+	0.00535117i
$832$	84759.9	−	48936.2i	0.122446	−	0.0706941i
$833$	252222.	−	436861.i	0.363490	−	0.629583i
$834$	65150.7	−	112844.i	0.0936671	−	0.162236i
$835$			1.65015e6i			2.36674i
$836$	174949.	−	378714.i	0.250322	−	0.541875i
$837$	−573857.			−0.819130
$838$	522130.	+	301452.i	0.743517	+	0.429270i
$839$	442064.	+	255226.i	0.628002	+	0.362577i	0.779978	−	0.625807i	$-0.215230\pi$
$839$	442064.	+	255226.i	0.628002	+	0.362577i	−0.151976	+	0.988384i	$0.548564\pi$
$840$	−99094.6	−	171637.i	−0.140440	−	0.243249i
$841$	−353455.	+	612202.i	−0.499738	+	0.865572i
$842$	−126639.	−	219345.i	−0.178626	−	0.309389i
$843$	355381.			0.500080
$844$		−	119438.i		−	0.167671i
$845$	141747.	+	245513.i	0.198519	+	0.343844i
$846$	−86503.9	+	49943.1i	−0.120863	+	0.0697806i
$847$	358779.			0.500104
$848$		−	68187.3i		−	0.0948226i
$849$	418596.	−	241677.i	0.580738	−	0.335289i
$850$	−854658.	−	493437.i	−1.18292	−	0.682958i
$851$	−334559.	+	193158.i	−0.461969	+	0.266718i
$852$	24335.0	−	42149.4i	0.0335237	−	0.0580647i
$853$	−181309.	+	314036.i	−0.249184	+	0.431600i	−0.963300	−	0.268428i	$-0.913496\pi$
$853$	−181309.	+	314036.i	−0.249184	+	0.431600i	0.714116	+	0.700028i	$0.246829\pi$
$854$		−	872719.i		−	1.19663i
$855$	−463597.	−	657066.i	−0.634174	−	0.898828i
$856$	426390.			0.581915
$857$	230212.	+	132913.i	0.313449	+	0.180970i	0.648469	−	0.761241i	$-0.275410\pi$
$857$	230212.	+	132913.i	0.313449	+	0.180970i	−0.335020	+	0.942211i	$0.608743\pi$
$858$	−289320.	−	167039.i	−0.393010	−	0.226904i
$859$	−134235.	−	232502.i	−0.181920	−	0.315095i	0.760614	−	0.649204i	$-0.224898\pi$
$859$	−134235.	−	232502.i	−0.181920	−	0.315095i	−0.942534	+	0.334109i	$0.891565\pi$
$860$	313084.	−	542278.i	0.423316	−	0.733204i
$861$	200702.	+	347626.i	0.270736	+	0.468928i
$862$	544817.			0.733223
$863$		−	832860.i		−	1.11828i	−0.829073	−	0.559140i	$-0.811131\pi$
$863$		−	832860.i		−	1.11828i	0.829073	−	0.559140i	$-0.188869\pi$
$864$	55635.8	+	96364.1i	0.0745293	+	0.129089i
$865$	−1.56548e6	+	903831.i	−2.09226	+	1.20797i
$866$	647693.			0.863641
$867$		−	925744.i		−	1.23155i
$868$	372794.	−	215233.i	0.494800	−	0.285673i
$869$	76881.3	+	44387.4i	0.101808	+	0.0587788i
$870$	7165.03	−	4136.73i	0.00946628	−	0.00546536i
$871$	481754.	−	834422.i	0.635022	−	1.09989i
$872$	38583.7	−	66828.9i	0.0507423	−	0.0878883i
$873$			615734.i			0.807913i
$874$	163291.	−	115211.i	0.213766	−	0.150824i
$875$	24752.3			0.0323295
$876$	167147.	+	96502.3i	0.217816	+	0.125756i
$877$	−254777.	−	147095.i	−0.331254	−	0.191249i	0.325144	−	0.945665i	$-0.394587\pi$
$877$	−254777.	−	147095.i	−0.331254	−	0.191249i	−0.656398	+	0.754415i	$0.727921\pi$
$878$	−365704.	−	633418.i	−0.474396	−	0.821678i
$879$	31958.7	−	55354.2i	0.0413630	−	0.0716428i
$880$	−164215.	−	284428.i	−0.212054	−	0.367288i
$881$	269270.			0.346925			0.173462	−	0.984840i	$-0.444504\pi$
$881$	269270.			0.346925			0.173462	+	0.984840i	$0.444504\pi$
$882$		−	163352.i		−	0.209985i
$883$	−557021.	−	964788.i	−0.714414	−	1.23740i	−0.963185	−	0.268839i	$-0.913360\pi$
$883$	−557021.	−	964788.i	−0.714414	−	1.23740i	0.248771	−	0.968562i	$-0.419973\pi$
$884$	−725317.	+	418762.i	−0.928161	+	0.535874i
$885$	−230574.			−0.294391
$886$		−	71956.3i		−	0.0916646i
$887$	293723.	−	169581.i	0.373329	−	0.215541i	−0.301583	−	0.953440i	$-0.597515\pi$
$887$	293723.	−	169581.i	0.373329	−	0.215541i	0.674912	+	0.737899i	$0.264182\pi$
$888$	−165449.	−	95521.9i	−0.209816	−	0.121137i
$889$	−233921.	+	135054.i	−0.295982	+	0.170885i
$890$	−269589.	+	466942.i	−0.340347	+	0.589498i
$891$	−176916.	+	306428.i	−0.222850	+	0.385987i
$892$		−	131055.i		−	0.164711i
$893$	−85266.8	+	184578.i	−0.106924	+	0.231460i
$894$	−165503.			−0.207076
$895$	−1.34653e6	−	777418.i	−1.68100	−	0.970528i
$896$	−72285.4	−	41734.0i	−0.0900398	−	0.0519845i
$897$	−80019.1	−	138597.i	−0.0994509	−	0.172254i
$898$	−405635.	+	702581.i	−0.503017	+	0.871252i
$899$	8984.96	+	15562.4i	0.0111172	+	0.0192556i
$900$	−319577.			−0.394539
$901$			583500.i			0.718772i
$902$	332594.	+	576070.i	0.408791	+	0.708047i
$903$	−470421.	+	271598.i	−0.576914	+	0.333082i
$904$	−331985.			−0.406239
$905$		−	1.44862e6i		−	1.76871i
$906$	−41208.9	+	23792.0i	−0.0502036	+	0.0289851i
$907$	−430360.	−	248469.i	−0.523139	−	0.302035i	0.215079	−	0.976597i	$-0.430999\pi$
$907$	−430360.	−	248469.i	−0.523139	−	0.302035i	−0.738218	+	0.674562i	$0.764333\pi$
$908$	−123378.	+	71232.4i	−0.149647	+	0.0863985i
$909$	−236415.	+	409482.i	−0.286119	+	0.495573i
$910$	553547.	−	958771.i	0.668454	−	1.15780i
$911$		−	1.41006e6i		−	1.69903i	−0.527564	−	0.849515i	$-0.676895\pi$
$911$		−	1.41006e6i		−	1.69903i	0.527564	−	0.849515i	$-0.323105\pi$
$912$	89718.1	+	41445.8i	0.107867	+	0.0498300i
$913$	−397046.			−0.476320
$914$	464131.	+	267966.i	0.555582	+	0.320765i
$915$	704523.	+	406757.i	0.841498	+	0.485839i
$916$	373573.	+	647048.i	0.445230	+	0.771161i
$917$	−290237.	+	502706.i	−0.345155	+	0.597826i
$918$	−476093.	−	824618.i	−0.564946	−	0.978514i
$919$	376060.			0.445273			0.222637	−	0.974902i	$-0.428534\pi$
$919$	376060.			0.445273			0.222637	+	0.974902i	$0.428534\pi$
$920$		−	157333.i		−	0.185884i
$921$	−326214.	−	565020.i	−0.384577	−	0.666107i
$922$	−45303.0	+	26155.7i	−0.0532924	+	0.0307684i
$923$	271873.			0.319126
$924$			284910.i			0.333705i
$925$	1.08901e6	−	628742.i	1.27277	−	0.734834i
$926$	89666.7	+	51769.1i	0.104571	+	0.0603738i
$927$	973008.	−	561766.i	1.13229	−	0.653727i
$928$	1742.20	−	3017.57i	0.00202302	−	0.00350398i
$929$	485919.	−	841637.i	0.563032	−	0.975199i	−0.434198	−	0.900817i	$-0.642968\pi$
$929$	485919.	−	841637.i	0.563032	−	0.975199i	0.997230	−	0.0743819i	$-0.0236984\pi$
$930$			401263.i			0.463941i
$931$	−191693.	−	271690.i	−0.221160	−	0.313455i
$932$	299442.			0.344731
$933$	−332008.	−	191685.i	−0.381404	−	0.220204i
$934$	512068.	+	295643.i	0.586994	+	0.338901i
$935$	1.40524e6	+	2.43394e6i	1.60741	+	2.78411i
$936$	−135606.	+	234877.i	−0.154785	+	0.268095i
$937$	−301442.	−	522113.i	−0.343340	−	0.594683i	0.641710	−	0.766947i	$-0.278225\pi$
$937$	−301442.	−	522113.i	−0.343340	−	0.594683i	−0.985051	+	0.172264i	$0.944892\pi$
$938$	−821703.			−0.933919
$939$			82669.9i			0.0937598i
$940$	80035.0	+	138625.i	0.0905783	+	0.156886i
$941$	−501844.	+	289740.i	−0.566747	+	0.327211i	−0.755849	−	0.654746i	$-0.772776\pi$
$941$	−501844.	+	289740.i	−0.566747	+	0.327211i	0.189102	+	0.981957i	$0.439442\pi$
$942$	301938.			0.340264
$943$			318655.i			0.358342i
$944$	−84097.2	+	48553.5i	−0.0943708	+	0.0544850i
$945$	1.09003e6	+	629331.i	1.22061	+	0.704719i
$946$	−779559.	+	450079.i	−0.871097	+	0.502928i
$947$	22184.3	−	38424.3i	0.0247369	−	0.0428456i	−0.853392	−	0.521270i	$-0.825459\pi$
$947$	22184.3	−	38424.3i	0.0247369	−	0.0428456i	0.878129	+	0.478424i	$0.158792\pi$
$948$	−10515.5	+	18213.3i	−0.0117007	+	0.0202662i
$949$			1.07813e6i			1.19713i
$950$	−531525.	+	375021.i	−0.588947	+	0.415536i
$951$	283491.			0.313458
$952$	618568.	+	357131.i	0.682517	+	0.394052i
$953$	969638.	+	559821.i	1.06764	+	0.616401i	0.927535	−	0.373736i	$-0.121923\pi$
$953$	969638.	+	559821.i	1.06764	+	0.616401i	0.140102	+	0.990137i	$0.455257\pi$
$954$	94476.5	+	163638.i	0.103807	+	0.179799i
$955$	887872.	−	1.53784e6i	0.973517	−	1.68618i
$956$	−106443.	−	184365.i	−0.116467	−	0.201726i
$957$	−11893.6			−0.0129865
$958$			805506.i			0.877683i
$959$	8792.83	+	15229.6i	0.00956074	+	0.0165597i
$960$	67381.5	−	38902.7i	0.0731136	−	0.0422122i
$961$	51980.3			0.0562849
$962$		−	1.06718e6i		−	1.15315i
$963$	−1.02327e6	+	590783.i	−1.10341	+	0.637052i
$964$	−155100.	−	89546.9i	−0.166900	−	0.0963600i
$965$	−543822.	+	313976.i	−0.583986	+	0.337164i
$966$	−68242.3	+	118199.i	−0.0731306	+	0.126666i
$967$	−123868.	+	214546.i	−0.132467	+	0.229439i	−0.924627	−	0.380874i	$-0.875623\pi$
$967$	−123868.	+	214546.i	−0.132467	+	0.229439i	0.792160	+	0.610313i	$0.208956\pi$
$968$			140850.i			0.150316i
$969$	−767745.	−	354664.i	−0.817654	−	0.377720i
$970$	986728.			1.04871
$971$	209743.	+	121095.i	0.222459	+	0.128437i	0.607088	−	0.794634i	$-0.292337\pi$
$971$	209743.	+	121095.i	0.222459	+	0.128437i	−0.384629	+	0.923071i	$0.625671\pi$
$972$	−417551.	−	241073.i	−0.441953	−	0.255162i
$973$	−310373.	−	537582.i	−0.327837	−	0.567831i
$974$	−450896.	+	780975.i	−0.475290	+	0.823227i
$975$	260468.	+	451144.i	0.273997	+	0.474576i
$976$	342614.			0.359671
$977$		−	1.57807e6i		−	1.65324i	−0.562761	−	0.826620i	$-0.690261\pi$
$977$		−	1.57807e6i		−	1.65324i	0.562761	−	0.826620i	$-0.309739\pi$
$978$	187499.	+	324757.i	0.196029	+	0.339532i
$979$	671258.	−	387551.i	0.700365	−	0.404356i
$980$	−261776.			−0.272570
$981$			213837.i			0.222201i
$982$	−182663.	+	105461.i	−0.189421	+	0.109362i
$983$	276804.	+	159813.i	0.286461	+	0.165388i	0.636345	−	0.771405i	$-0.280446\pi$
$983$	276804.	+	159813.i	0.286461	+	0.165388i	−0.349884	+	0.936793i	$0.613779\pi$
$984$	−136472.	+	78792.1i	−0.140946	+	0.0813752i
$985$	−1.26254e6	+	2.18679e6i	−1.30129	+	2.25390i
$986$	−14908.5	+	25822.3i	−0.0153349	+	0.0265608i
$987$		−	138859.i		−	0.142541i
$988$	50084.2	+	549784.i	0.0513082	+	0.563221i
$989$	−431216.			−0.440862
$990$	788175.	+	455053.i	0.804178	+	0.464293i
$991$	1.00216e6	+	578595.i	1.02044	+	0.589152i	0.914231	−	0.405192i	$-0.132795\pi$
$991$	1.00216e6	+	578595.i	1.02044	+	0.589152i	0.106209	+	0.994344i	$0.466129\pi$
$992$	84496.5	+	146352.i	0.0858649	+	0.148722i
$993$	1984.57	−	3437.37i	0.00201264	−	0.00348600i
$994$	−115930.	−	200797.i	−0.117334	−	0.203228i
$995$	−1.86302e6			−1.88179
$996$		−	94060.8i		−	0.0948179i
$997$	118329.	+	204951.i	0.119042	+	0.206186i	0.919388	−	0.393351i	$-0.128684\pi$
$997$	118329.	+	204951.i	0.119042	+	0.206186i	−0.800346	+	0.599538i	$0.795351\pi$
$998$	481550.	−	278023.i	0.483482	−	0.279138i
$999$	1.21328e6			1.21571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.d.a.27.7	✓	16
3.2	odd	2		342.5.m.c.217.4		16
4.3	odd	2		304.5.r.c.65.3		16
19.12	odd	6	inner	38.5.d.a.31.7	yes	16
57.50	even	6		342.5.m.c.145.4		16
76.31	even	6		304.5.r.c.145.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.7	✓	16	1.1	even	1	trivial
38.5.d.a.31.7	yes	16	19.12	odd	6	inner
304.5.r.c.65.3		16	4.3	odd	2
304.5.r.c.145.3		16	76.31	even	6
342.5.m.c.145.4		16	57.50	even	6
342.5.m.c.217.4		16	3.2	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 + 1.41421i) q^{2} +(3.70447 + 2.13878i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-17.7629 + 30.7663i) q^{5} +(6.04937 + 10.4778i) q^{6} +57.6374 q^{7} +22.6274i q^{8} +(-31.3513 - 54.3020i) q^{9} +O(q^{10})\)	\(q+(2.44949 + 1.41421i) q^{2} +(3.70447 + 2.13878i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-17.7629 + 30.7663i) q^{5} +(6.04937 + 10.4778i) q^{6} +57.6374 q^{7} +22.6274i q^{8} +(-31.3513 - 54.3020i) q^{9} +(-87.0203 + 50.2412i) q^{10} +144.450 q^{11} +34.2204i q^{12} +(-165.547 + 95.5784i) q^{13} +(141.182 + 81.5117i) q^{14} +(-131.605 + 75.9819i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(273.834 - 474.294i) q^{17} -177.350i q^{18} +(-208.119 - 294.971i) q^{19} -284.207 q^{20} +(213.516 + 123.274i) q^{21} +(353.828 + 204.283i) q^{22} +(97.8608 + 169.500i) q^{23} +(-48.3950 + 83.8225i) q^{24} +(-318.544 - 551.735i) q^{25} -540.673 q^{26} -614.695i q^{27} +(230.550 + 399.324i) q^{28} +(-16.6699 + 9.62437i) q^{29} -429.818 q^{30} -933.563i q^{31} +(-156.767 + 90.5097i) q^{32} +(535.110 + 308.946i) q^{33} +(1341.51 - 774.519i) q^{34} +(-1023.81 + 1773.29i) q^{35} +(250.810 - 434.416i) q^{36} +1973.80i q^{37} +(-92.6330 - 1016.85i) q^{38} -817.683 q^{39} +(-696.162 - 401.929i) q^{40} +(1409.98 + 814.052i) q^{41} +(348.670 + 603.915i) q^{42} +(-1101.61 + 1908.04i) q^{43} +(577.799 + 1000.78i) q^{44} +2227.56 q^{45} +553.584i q^{46} +(-281.608 - 487.759i) q^{47} +(-237.086 + 136.882i) q^{48} +921.075 q^{49} -1801.96i q^{50} +(2028.82 - 1171.34i) q^{51} +(-1324.37 - 764.627i) q^{52} +(-922.687 + 532.713i) q^{53} +(869.310 - 1505.69i) q^{54} +(-2565.85 + 4444.19i) q^{55} +1304.19i q^{56} +(-140.093 - 1537.83i) q^{57} -54.4436 q^{58} +(1314.02 + 758.649i) q^{59} +(-1052.84 - 607.855i) q^{60} +(-2676.67 - 4636.13i) q^{61} +(1320.26 - 2286.75i) q^{62} +(-1807.01 - 3129.83i) q^{63} -512.000 q^{64} -6791.02i q^{65} +(873.831 + 1513.52i) q^{66} +(-4365.12 + 2520.20i) q^{67} +4381.34 q^{68} +837.209i q^{69} +(-5015.63 + 2895.77i) q^{70} +(-1231.70 - 711.125i) q^{71} +(1228.71 - 709.398i) q^{72} +(2820.02 - 4884.42i) q^{73} +(-2791.37 + 4834.80i) q^{74} -2725.18i q^{75} +(1211.14 - 2621.77i) q^{76} +8325.72 q^{77} +(-2002.91 - 1156.38i) q^{78} +(532.235 + 307.286i) q^{79} +(-1136.83 - 1969.04i) q^{80} +(-1224.76 + 2121.34i) q^{81} +(2302.49 + 3988.02i) q^{82} -2748.68 q^{83} +1972.38i q^{84} +(9728.19 + 16849.7i) q^{85} +(-5396.74 + 3115.81i) q^{86} -82.3375 q^{87} +3268.53i q^{88} +(4647.00 - 2682.95i) q^{89} +(5456.39 + 3150.25i) q^{90} +(-9541.69 + 5508.90i) q^{91} +(-782.886 + 1356.00i) q^{92} +(1996.68 - 3458.36i) q^{93} -1593.02i q^{94} +(12772.0 - 1163.50i) q^{95} -774.320 q^{96} +(-8504.30 - 4909.96i) q^{97} +(2256.16 + 1302.60i) q^{98} +(-4528.69 - 7843.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9	\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99}+O(q^{100}) \) 16 * q - 12 * q^3 + 64 * q^4 - 18 * q^5 - 16 * q^6 + 72 * q^7 + 352 * q^9 - 84 * q^11 + 450 * q^13 + 288 * q^14 - 390 * q^15 - 512 * q^16 + 606 * q^17 - 306 * q^19 - 288 * q^20 - 2160 * q^21 - 1680 * q^22 - 54 * q^23 + 128 * q^24 - 434 * q^25 + 1344 * q^26 + 288 * q^28 - 4914 * q^29 + 2752 * q^30 + 7890 * q^33 - 1536 * q^34 + 2328 * q^35 - 2816 * q^36 + 1344 * q^38 + 7620 * q^39 - 1692 * q^41 + 2080 * q^42 - 7402 * q^43 - 336 * q^44 - 16720 * q^45 + 3198 * q^47 + 768 * q^48 + 24816 * q^49 + 10710 * q^51 + 3600 * q^52 + 3870 * q^53 - 16 * q^54 - 13588 * q^55 + 3702 * q^57 - 1728 * q^58 - 18288 * q^59 - 3120 * q^60 - 6522 * q^61 - 6144 * q^62 - 15676 * q^63 - 8192 * q^64 + 4960 * q^66 - 30168 * q^67 + 9696 * q^68 + 15360 * q^70 + 35874 * q^71 + 5376 * q^72 - 8080 * q^73 - 9120 * q^74 + 480 * q^76 + 34560 * q^77 - 46560 * q^78 - 30738 * q^79 - 1152 * q^80 - 30920 * q^81 + 6720 * q^82 - 1476 * q^83 + 33626 * q^85 + 288 * q^86 + 113100 * q^87 + 19782 * q^89 + 44256 * q^90 - 34260 * q^91 + 432 * q^92 - 4272 * q^93 - 23706 * q^95 + 2048 * q^96 - 9936 * q^97 + 12672 * q^98 + 3848 * q^99

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