LMFDB - Embedded newform 18.5.d.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,5,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	18.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:	$1.86065933551$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.221456830464.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 38x^{6} - 100x^{5} + 449x^{4} - 736x^{3} + 1900x^{2} - 1548x + 2307 $ x^8 - 4x^7 + 38x^6 - 100x^5 + 449x^4 - 736x^3 + 1900x^2 - 1548*x + 2307
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.4
Root			$0.500000 + 3.61825i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.5.d.a.5.4

$q$-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} +(5.62909 - 7.02235i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-1.91371 + 1.10488i) q^{5} +(23.7195 - 9.24044i) q^{6} +(-21.9913 + 38.0900i) q^{7} +22.6274i q^{8} +(-17.6268 - 79.0588i) q^{9} -6.25016 q^{10} +(-183.766 - 106.097i) q^{11} +(71.1686 + 10.9101i) q^{12} +(88.7063 + 153.644i) q^{13} +(-107.735 + 62.2008i) q^{14} +(-3.01358 + 19.6582i) q^{15} +(-32.0000 + 55.4256i) q^{16} -43.3642i q^{17} +(68.6294 - 218.582i) q^{18} +528.015 q^{19} +(-15.3097 - 8.83905i) q^{20} +(143.691 + 368.843i) q^{21} +(-300.089 - 519.769i) q^{22} +(517.028 - 298.506i) q^{23} +(158.898 + 127.372i) q^{24} +(-310.058 + 537.037i) q^{25} +501.799i q^{26} +(-654.401 - 321.247i) q^{27} -351.861 q^{28} +(380.563 + 219.718i) q^{29} +(-35.1827 + 43.8908i) q^{30} +(-756.471 - 1310.25i) q^{31} +(-156.767 + 90.5097i) q^{32} +(-1779.49 + 693.238i) q^{33} +(61.3263 - 106.220i) q^{34} -97.1911i q^{35} +(477.228 - 438.357i) q^{36} +702.206 q^{37} +(1293.37 + 746.726i) q^{38} +(1578.28 + 241.948i) q^{39} +(-25.0006 - 43.3023i) q^{40} +(517.534 - 298.798i) q^{41} +(-169.653 + 1106.69i) q^{42} +(46.1125 - 79.8692i) q^{43} -1697.56i q^{44} +(121.083 + 131.820i) q^{45} +1688.61 q^{46} +(-1490.34 - 860.449i) q^{47} +(209.087 + 536.711i) q^{48} +(233.266 + 404.029i) q^{49} +(-1518.97 + 876.978i) q^{50} +(-304.519 - 244.101i) q^{51} +(-709.650 + 1229.15i) q^{52} +1311.69i q^{53} +(-1148.64 - 1712.36i) q^{54} +468.900 q^{55} +(-861.879 - 497.606i) q^{56} +(2972.24 - 3707.91i) q^{57} +(621.457 + 1076.40i) q^{58} +(-3418.31 + 1973.56i) q^{59} +(-148.250 + 57.7542i) q^{60} +(-2112.34 + 3658.68i) q^{61} -4279.24i q^{62} +(3398.99 + 1067.20i) q^{63} -512.000 q^{64} +(-339.516 - 196.020i) q^{65} +(-5339.23 - 818.496i) q^{66} +(-322.592 - 558.746i) q^{67} +(300.436 - 173.457i) q^{68} +(814.180 - 5311.07i) q^{69} +(137.449 - 238.069i) q^{70} +6397.63i q^{71} +(1788.90 - 398.849i) q^{72} -3196.15 q^{73} +(1720.05 + 993.069i) q^{74} +(2025.92 + 5200.37i) q^{75} +(2112.06 + 3658.20i) q^{76} +(8082.51 - 4666.44i) q^{77} +(3523.80 + 2824.67i) q^{78} +(4782.69 - 8283.86i) q^{79} -141.425i q^{80} +(-5939.59 + 2787.10i) q^{81} +1690.26 q^{82} +(-3074.70 - 1775.18i) q^{83} +(-1980.65 + 2470.89i) q^{84} +(47.9123 + 82.9866i) q^{85} +(225.904 - 130.426i) q^{86} +(3685.16 - 1435.64i) q^{87} +(2400.71 - 4158.15i) q^{88} -502.000i q^{89} +(110.170 + 494.130i) q^{90} -7803.06 q^{91} +(4136.22 + 2388.05i) q^{92} +(-13459.2 - 2063.28i) q^{93} +(-2433.72 - 4215.32i) q^{94} +(-1010.47 + 583.394i) q^{95} +(-246.866 + 1610.36i) q^{96} +(3714.42 - 6433.56i) q^{97} +1319.55i q^{98} +(-5148.73 + 16398.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22}+ \cdots - 22338 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	5.62909	−	7.02235i	0.625454	−	0.780261i
$3$	5.62909	−	7.02235i	0.625454	−	0.780261i
$4$	4.00000	+	6.92820i	0.250000	+	0.433013i
$5$	−1.91371	+	1.10488i	−0.0765485	+	0.0441953i	−0.537786	−	0.843082i	$-0.680739\pi$
$5$	−1.91371	+	1.10488i	−0.0765485	+	0.0441953i	0.461237	+	0.887277i	$0.347406\pi$
$6$	23.7195	−	9.24044i	0.658875	−	0.256679i
$7$	−21.9913	+	38.0900i	−0.448802	+	0.777348i	−0.998308	−	0.0581419i	$-0.981482\pi$
$7$	−21.9913	+	38.0900i	−0.448802	+	0.777348i	0.549507	+	0.835489i	$0.314816\pi$
$8$			22.6274i			0.353553i
$9$	−17.6268	−	79.0588i	−0.217615	−	0.976035i
$10$	−6.25016			−0.0625016
$11$	−183.766	−	106.097i	−1.51873	−	0.876838i	−0.999757	−	0.0220466i	$-0.992982\pi$
$11$	−183.766	−	106.097i	−1.51873	−	0.876838i	−0.518971	−	0.854792i	$-0.673685\pi$
$12$	71.1686	+	10.9101i	0.494226	+	0.0757643i
$13$	88.7063	+	153.644i	0.524889	+	0.909135i	0.999580	+	0.0289822i	$0.00922662\pi$
$13$	88.7063	+	153.644i	0.524889	+	0.909135i	−0.474691	+	0.880153i	$0.657440\pi$
$14$	−107.735	+	62.2008i	−0.549668	+	0.317351i
$15$	−3.01358	+	19.6582i	−0.0133937	+	0.0873699i
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$		−	43.3642i		−	0.150049i	−0.997182	−	0.0750246i	$-0.976096\pi$
$17$		−	43.3642i		−	0.150049i	0.997182	−	0.0750246i	$-0.0239035\pi$
$18$	68.6294	−	218.582i	0.211819	−	0.674635i
$19$	528.015			1.46265			0.731323	−	0.682031i	$-0.238903\pi$
$19$	528.015			1.46265			0.731323	+	0.682031i	$0.238903\pi$
$20$	−15.3097	−	8.83905i	−0.0382742	−	0.0220976i
$21$	143.691	+	368.843i	0.325829	+	0.836378i
$22$	−300.089	−	519.769i	−0.620018	−	1.07390i
$23$	517.028	−	298.506i	0.977369	−	0.564284i	0.0758941	−	0.997116i	$-0.475819\pi$
$23$	517.028	−	298.506i	0.977369	−	0.564284i	0.901475	+	0.432832i	$0.142486\pi$
$24$	158.898	+	127.372i	0.275864	+	0.221131i
$25$	−310.058	+	537.037i	−0.496094	+	0.859259i
$26$			501.799i			0.742306i
$27$	−654.401	−	321.247i	−0.897670	−	0.440669i
$28$	−351.861			−0.448802
$29$	380.563	+	219.718i	0.452513	+	0.261258i	0.708891	−	0.705318i	$-0.249196\pi$
$29$	380.563	+	219.718i	0.452513	+	0.261258i	−0.256378	+	0.966577i	$0.582529\pi$
$30$	−35.1827	+	43.8908i	−0.0390918	+	0.0487675i
$31$	−756.471	−	1310.25i	−0.787170	−	1.36342i	−0.927694	−	0.373342i	$-0.878212\pi$
$31$	−756.471	−	1310.25i	−0.787170	−	1.36342i	0.140523	−	0.990077i	$-0.455121\pi$
$32$	−156.767	+	90.5097i	−0.153093	+	0.0883883i
$33$	−1779.49	+	693.238i	−1.63406	+	0.636583i
$34$	61.3263	−	106.220i	0.0530504	−	0.0918860i
$35$		−	97.1911i		−	0.0793397i
$36$	477.228	−	438.357i	0.368232	−	0.338239i
$37$	702.206			0.512933			0.256467	−	0.966553i	$-0.417442\pi$
$37$	702.206			0.512933			0.256467	+	0.966553i	$0.417442\pi$
$38$	1293.37	+	746.726i	0.895684	+	0.517123i
$39$	1578.28	+	241.948i	1.03766	+	0.159071i
$40$	−25.0006	−	43.3023i	−0.0156254	−	0.0270640i
$41$	517.534	−	298.798i	0.307873	−	0.177750i	−0.338101	−	0.941110i	$-0.609785\pi$
$41$	517.534	−	298.798i	0.307873	−	0.177750i	0.645974	+	0.763359i	$0.276451\pi$
$42$	−169.653	+	1106.69i	−0.0961754	+	0.627373i
$43$	46.1125	−	79.8692i	0.0249392	−	0.0431959i	−0.853286	−	0.521442i	$-0.825394\pi$
$43$	46.1125	−	79.8692i	0.0249392	−	0.0431959i	0.878226	+	0.478247i	$0.158727\pi$
$44$		−	1697.56i		−	0.876838i
$45$	121.083	+	131.820i	0.0597942	+	0.0650964i
$46$	1688.61			0.798018
$47$	−1490.34	−	860.449i	−0.674668	−	0.389520i	0.123175	−	0.992385i	$-0.460692\pi$
$47$	−1490.34	−	860.449i	−0.674668	−	0.389520i	−0.797843	+	0.602865i	$0.794026\pi$
$48$	209.087	+	536.711i	0.0907497	+	0.232947i
$49$	233.266	+	404.029i	0.0971538	+	0.168275i
$50$	−1518.97	+	876.978i	−0.607588	+	0.350791i
$51$	−304.519	−	244.101i	−0.117078	−	0.0938489i
$52$	−709.650	+	1229.15i	−0.262445	+	0.454567i
$53$			1311.69i			0.466958i	0.972362	+	0.233479i	$0.0750111\pi$
$53$			1311.69i			0.466958i	−0.972362	+	0.233479i	$0.924989\pi$
$54$	−1148.64	−	1712.36i	−0.393908	−	0.587228i
$55$	468.900			0.155008
$56$	−861.879	−	497.606i	−0.274834	−	0.158675i
$57$	2972.24	−	3707.91i	0.914818	−	1.14125i
$58$	621.457	+	1076.40i	0.184738	+	0.319975i
$59$	−3418.31	+	1973.56i	−0.981990	+	0.566952i	−0.902870	−	0.429913i	$-0.858544\pi$
$59$	−3418.31	+	1973.56i	−0.981990	+	0.566952i	−0.0791193	+	0.996865i	$0.525211\pi$
$60$	−148.250	+	57.7542i	−0.0411807	+	0.0160428i
$61$	−2112.34	+	3658.68i	−0.567681	+	0.983253i	0.429114	+	0.903251i	$0.358826\pi$
$61$	−2112.34	+	3658.68i	−0.567681	+	0.983253i	−0.996795	+	0.0800020i	$0.974507\pi$
$62$		−	4279.24i		−	1.11323i
$63$	3398.99	+	1067.20i	0.856384	+	0.268884i
$64$	−512.000			−0.125000
$65$	−339.516	−	196.020i	−0.0803589	−	0.0463953i
$66$	−5339.23	−	818.496i	−1.22572	−	0.187901i
$67$	−322.592	−	558.746i	−0.0718628	−	0.124470i	0.827855	−	0.560942i	$-0.189561\pi$
$67$	−322.592	−	558.746i	−0.0718628	−	0.124470i	−0.899718	+	0.436472i	$0.856228\pi$
$68$	300.436	−	173.457i	0.0649732	−	0.0375123i
$69$	814.180	−	5311.07i	0.171010	−	1.11554i
$70$	137.449	−	238.069i	0.0280508	−	0.0485854i
$71$			6397.63i			1.26912i	0.772874	+	0.634560i	$0.218819\pi$
$71$			6397.63i			1.26912i	−0.772874	+	0.634560i	$0.781181\pi$
$72$	1788.90	−	398.849i	0.345080	−	0.0769384i
$73$	−3196.15			−0.599766			−0.299883	−	0.953976i	$-0.596948\pi$
$73$	−3196.15			−0.599766			−0.299883	+	0.953976i	$0.596948\pi$
$74$	1720.05	+	993.069i	0.314106	+	0.181349i
$75$	2025.92	+	5200.37i	0.360163	+	0.924510i
$76$	2112.06	+	3658.20i	0.365662	+	0.633344i
$77$	8082.51	−	4666.44i	1.36322	−	0.787053i
$78$	3523.80	+	2824.67i	0.579192	+	0.464278i
$79$	4782.69	−	8283.86i	0.766334	−	1.32733i	−0.173204	−	0.984886i	$-0.555412\pi$
$79$	4782.69	−	8283.86i	0.766334	−	1.32733i	0.939538	−	0.342444i	$-0.111255\pi$
$80$		−	141.425i		−	0.0220976i
$81$	−5939.59	+	2787.10i	−0.905288	+	0.424799i
$82$	1690.26			0.251377
$83$	−3074.70	−	1775.18i	−0.446321	−	0.257683i	0.259954	−	0.965621i	$-0.416292\pi$
$83$	−3074.70	−	1775.18i	−0.446321	−	0.257683i	−0.706275	+	0.707938i	$0.749626\pi$
$84$	−1980.65	+	2470.89i	−0.280705	+	0.350183i
$85$	47.9123	+	82.9866i	0.00663146	+	0.0114860i
$86$	225.904	−	130.426i	0.0305441	−	0.0176346i
$87$	3685.16	−	1435.64i	0.486876	−	0.189673i
$88$	2400.71	−	4158.15i	0.310009	−	0.536952i
$89$		−	502.000i		−	0.0633759i	−0.999498	−	0.0316879i	$-0.989912\pi$
$89$		−	502.000i		−	0.0633759i	0.999498	−	0.0316879i	$-0.0100883\pi$
$90$	110.170	+	494.130i	0.0136012	+	0.0610037i
$91$	−7803.06			−0.942285
$92$	4136.22	+	2388.05i	0.488684	+	0.282142i
$93$	−13459.2	−	2063.28i	−1.55616	−	0.238558i
$94$	−2433.72	−	4215.32i	−0.275432	−	0.477062i
$95$	−1010.47	+	583.394i	−0.111963	+	0.0646420i
$96$	−246.866	+	1610.36i	−0.0267867	+	0.174735i
$97$	3714.42	−	6433.56i	0.394773	−	0.683767i	−0.598299	−	0.801273i	$-0.704157\pi$
$97$	3714.42	−	6433.56i	0.394773	−	0.683767i	0.993072	+	0.117506i	$0.0374899\pi$
$98$			1319.55i			0.137396i
$99$	−5148.73	+	16398.5i	−0.525327	+	1.67314i
$100$	−4960.94			−0.496094
$101$	−793.864	−	458.338i	−0.0778222	−	0.0449307i	0.460584	−	0.887616i	$-0.347640\pi$
$101$	−793.864	−	458.338i	−0.0778222	−	0.0449307i	−0.538406	+	0.842685i	$0.680973\pi$
$102$	−400.705	−	1028.58i	−0.0385145	−	0.0988636i
$103$	1777.12	+	3078.07i	0.167511	+	0.290137i	0.937544	−	0.347866i	$-0.113094\pi$
$103$	1777.12	+	3078.07i	0.167511	+	0.290137i	−0.770033	+	0.638004i	$0.779760\pi$
$104$	−3476.56	+	2007.19i	−0.321428	+	0.185576i
$105$	−682.510	−	547.097i	−0.0619057	−	0.0496233i
$106$	−1855.00	+	3212.96i	−0.165095	+	0.285952i
$107$			550.477i			0.0480808i	0.999711	+	0.0240404i	$0.00765304\pi$
$107$			550.477i			0.0480808i	−0.999711	+	0.0240404i	$0.992347\pi$
$108$	−391.937	−	5818.82i	−0.0336023	−	0.498870i
$109$	−2561.93			−0.215633			−0.107816	−	0.994171i	$-0.534386\pi$
$109$	−2561.93			−0.215633			−0.107816	+	0.994171i	$0.534386\pi$
$110$	1148.57	+	663.125i	0.0949229	+	0.0548037i
$111$	3952.78	−	4931.14i	0.320816	−	0.400222i
$112$	−1407.44	−	2437.76i	−0.112200	−	0.194337i
$113$	17598.8	−	10160.7i	1.37825	−	0.795731i	0.386299	−	0.922374i	$-0.373753\pi$
$113$	17598.8	−	10160.7i	1.37825	−	0.795731i	0.991948	+	0.126642i	$0.0404200\pi$
$114$	12524.3	−	4879.09i	0.963701	−	0.375430i
$115$	−659.628	+	1142.51i	−0.0498774	+	0.0863902i
$116$			3515.49i			0.261258i
$117$	10583.3	−	9721.26i	0.773124	−	0.710151i
$118$	−11164.1			−0.801791
$119$	1651.74	+	953.635i	0.116640	+	0.0673424i
$120$	−444.815	−	68.1895i	−0.0308899	−	0.00473538i
$121$	15192.8	+	26314.7i	1.03769	+	1.79733i
$122$	−10348.3	+	5974.60i	−0.695265	+	0.401411i
$123$	814.977	−	5316.27i	0.0538685	−	0.351396i
$124$	6051.77	−	10482.0i	0.393585	−	0.681710i
$125$		−	2751.41i		−	0.176090i
$126$	6816.54	+	7420.99i	0.429361	+	0.467435i
$127$	21354.6			1.32399			0.661995	−	0.749508i	$-0.269710\pi$
$127$	21354.6			1.32399			0.661995	+	0.749508i	$0.269710\pi$
$128$	−1254.14	−	724.077i	−0.0765466	−	0.0441942i
$129$	−301.298	−	773.409i	−0.0181058	−	0.0464761i
$130$	−554.428	−	960.298i	−0.0328064	−	0.0568223i
$131$	−26706.4	+	15419.0i	−1.55623	+	0.898489i	−0.558616	+	0.829426i	$0.688667\pi$
$131$	−26706.4	+	15419.0i	−1.55623	+	0.898489i	−0.997612	+	0.0690626i	$0.977999\pi$
$132$	−11920.9	−	9555.70i	−0.684163	−	0.548422i
$133$	−11611.7	+	20112.1i	−0.656438	+	1.13698i
$134$		−	1824.86i		−	0.101629i
$135$	1607.28	−	108.261i	0.0881907	−	0.00594025i
$136$	981.220			0.0530504
$137$	−9523.95	−	5498.66i	−0.507430	−	0.292965i	0.224347	−	0.974509i	$-0.427975\pi$
$137$	−9523.95	−	5498.66i	−0.507430	−	0.292965i	−0.731777	+	0.681545i	$0.761309\pi$
$138$	9505.31	−	11858.0i	0.499124	−	0.622663i
$139$	−8472.63	−	14675.0i	−0.438519	−	0.759537i	0.559056	−	0.829130i	$-0.311163\pi$
$139$	−8472.63	−	14675.0i	−0.438519	−	0.759537i	−0.997576	+	0.0695923i	$0.977830\pi$
$140$	673.360	−	388.764i	0.0343551	−	0.0198349i
$141$	−14431.6	+	5622.16i	−0.725901	+	0.282790i
$142$	−9047.62	+	15670.9i	−0.448701	+	0.777174i
$143$		−	37646.0i		−	1.84097i
$144$	4945.94	+	1552.91i	0.238520	+	0.0748894i
$145$	−971.051			−0.0461856
$146$	−7828.95	−	4520.04i	−0.367280	−	0.212049i
$147$	4150.31	+	636.237i	0.192064	+	0.0294432i
$148$	2808.82	+	4865.03i	0.128233	+	0.222107i
$149$	−14383.7	+	8304.42i	−0.647885	+	0.374056i	−0.787645	−	0.616129i	$-0.788700\pi$
$149$	−14383.7	+	8304.42i	−0.647885	+	0.374056i	0.139761	+	0.990185i	$0.455367\pi$
$150$	−2391.97	+	15603.3i	−0.106310	+	0.693481i
$151$	5515.31	−	9552.80i	0.241889	−	0.418964i	−0.719363	−	0.694634i	$-0.755566\pi$
$151$	5515.31	−	9552.80i	0.241889	−	0.418964i	0.961252	+	0.275670i	$0.0888996\pi$
$152$			11947.6i			0.517123i
$153$	−3428.32	+	764.371i	−0.146453	+	0.0326529i
$154$	26397.4			1.11306
$155$	2895.33	+	1671.62i	0.120513	+	0.0695784i
$156$	4636.84	+	11902.4i	0.190534	+	0.489086i
$157$	−9967.29	−	17263.9i	−0.404369	−	0.700388i	0.589879	−	0.807492i	$-0.299176\pi$
$157$	−9967.29	−	17263.9i	−0.404369	−	0.700388i	−0.994248	+	0.107104i	$0.965842\pi$
$158$	23430.3	−	13527.5i	0.938564	−	0.541880i
$159$	9211.12	+	7383.59i	0.364349	+	0.292061i
$160$	200.005	−	346.419i	0.00781269	−	0.0135320i
$161$			26258.2i			1.01301i
$162$	−18490.5	−	1572.87i	−0.704562	−	0.0599325i
$163$	−7936.22			−0.298702			−0.149351	−	0.988784i	$-0.547718\pi$
$163$	−7936.22			−0.298702			−0.149351	+	0.988784i	$0.547718\pi$
$164$	4140.27	+	2390.39i	0.153936	+	0.0888752i
$165$	2639.48	−	3292.78i	0.0969506	−	0.120947i
$166$	−5020.97	−	8696.57i	−0.182210	−	0.315596i
$167$	16616.5	−	9593.52i	0.595807	−	0.343989i	−0.171583	−	0.985170i	$-0.554888\pi$
$167$	16616.5	−	9593.52i	0.595807	−	0.343989i	0.767390	+	0.641180i	$0.221555\pi$
$168$	−8345.95	+	3251.35i	−0.295704	+	0.115198i
$169$	−1457.11	+	2523.79i	−0.0510176	+	0.0883650i
$170$			271.033i			0.00937831i
$171$	−9307.21	−	41744.3i	−0.318293	−	1.42759i
$172$	737.800			0.0249392
$173$	45196.2	+	26094.1i	1.51011	+	0.871865i	0.999930	+	0.0118002i	$0.00375621\pi$
$173$	45196.2	+	26094.1i	1.51011	+	0.871865i	0.510184	+	0.860065i	$0.329577\pi$
$174$	11057.1	+	1695.03i	0.365209	+	0.0559861i
$175$	−13637.2	−	23620.3i	−0.445295	−	0.771274i
$176$	11761.0	−	6790.24i	0.379682	−	0.219210i
$177$	−5382.91	+	35113.9i	−0.171819	+	1.12081i
$178$	709.936	−	1229.64i	0.0224068	−	0.0388096i
$179$			12197.1i			0.380672i	0.981719	+	0.190336i	$0.0609578\pi$
$179$			12197.1i			0.380672i	−0.981719	+	0.190336i	$0.939042\pi$
$180$	−428.945	+	1366.17i	−0.0132390	+	0.0421657i
$181$	6870.48			0.209715			0.104858	−	0.994487i	$-0.466561\pi$
$181$	6870.48			0.209715			0.104858	+	0.994487i	$0.466561\pi$
$182$	−19113.5	−	11035.2i	−0.577029	−	0.333148i
$183$	13802.0	+	35428.6i	0.412135	+	1.05792i
$184$	6754.43	+	11699.0i	0.199505	+	0.345552i
$185$	−1343.82	+	775.855i	−0.0392643	+	0.0226692i
$186$	−30050.4	−	24088.2i	−0.868608	−	0.696272i
$187$	−4600.83	+	7968.87i	−0.131569	+	0.227884i
$188$		−	13767.2i		−	0.389520i
$189$	26627.5	−	17861.5i	0.745429	−	0.500029i
$190$	−3300.18			−0.0914176
$191$	35951.4	+	20756.5i	0.985482	+	0.568968i	0.903921	−	0.427700i	$-0.140676\pi$
$191$	35951.4	+	20756.5i	0.985482	+	0.568968i	0.0815609	+	0.996668i	$0.474009\pi$
$192$	−2882.09	+	3595.44i	−0.0781818	+	0.0975326i
$193$	−29868.0	−	51732.9i	−0.801847	−	1.38884i	−0.918399	−	0.395654i	$-0.870518\pi$
$193$	−29868.0	−	51732.9i	−0.801847	−	1.38884i	0.116553	−	0.993184i	$-0.462816\pi$
$194$	18196.9	−	10506.0i	0.483496	−	0.279147i
$195$	−3287.69	+	1280.79i	−0.0864612	+	0.0336828i
$196$	−1866.13	+	3232.23i	−0.0485769	+	0.0841377i
$197$			12371.6i			0.318783i	0.987215	+	0.159391i	$0.0509532\pi$
$197$			12371.6i			0.318783i	−0.987215	+	0.159391i	$0.949047\pi$
$198$	−35802.7	+	32886.5i	−0.913242	+	0.838856i
$199$	−16836.3			−0.425149			−0.212575	−	0.977145i	$-0.568185\pi$
$199$	−16836.3			−0.425149			−0.212575	+	0.977145i	$0.568185\pi$
$200$	−12151.8	−	7015.82i	−0.303794	−	0.175396i
$201$	−5739.61	−	879.875i	−0.142066	−	0.0217785i
$202$	−1296.37	−	2245.39i	−0.0317708	−	0.0550286i
$203$	−16738.2	+	9663.78i	−0.406177	+	0.234507i
$204$	473.106	−	3086.17i	0.0113684	−	0.0741583i
$205$	−660.274	+	1143.63i	−0.0157114	+	0.0272130i
$206$			10052.9i			0.236896i
$207$	−32713.1	−	35613.9i	−0.763451	−	0.831150i
$208$	−11354.4			−0.262445
$209$	−97031.3	−	56021.1i	−2.22136	−	1.28250i
$210$	−898.089	−	2305.32i	−0.0203648	−	0.0522749i
$211$	22606.7	+	39155.9i	0.507776	+	0.879493i	0.999959	+	0.00900203i	$0.00286547\pi$
$211$	22606.7	+	39155.9i	0.507776	+	0.879493i	−0.492184	+	0.870491i	$0.663801\pi$
$212$	−9087.63	+	5246.74i	−0.202199	+	0.116740i
$213$	44926.4	+	36012.8i	0.990244	+	0.793776i
$214$	−778.493	+	1348.39i	−0.0169991	+	0.0294434i
$215$			203.795i			0.00440877i
$216$	7269.00	−	14807.4i	0.155800	−	0.317374i
$217$	66543.1			1.41313
$218$	−6275.43	−	3623.12i	−0.132048	−	0.0762377i
$219$	−17991.4	+	22444.5i	−0.375126	+	0.467974i
$220$	1875.60	+	3248.64i	0.0387521	+	0.0671206i
$221$	6662.64	−	3846.68i	0.136415	−	0.0787592i
$222$	16656.0	−	6488.69i	0.337959	−	0.131659i
$223$	−25333.0	+	43878.0i	−0.509420	+	0.882341i	0.490520	+	0.871430i	$0.336807\pi$
$223$	−25333.0	+	43878.0i	−0.509420	+	0.882341i	−0.999940	+	0.0109118i	$0.996527\pi$
$224$		−	7961.70i		−	0.158675i
$225$	47922.8	+	15046.6i	0.946624	+	0.297217i
$226$	57477.6			1.12533
$227$	34671.8	+	20017.8i	0.672860	+	0.388476i	0.797159	−	0.603769i	$-0.206335\pi$
$227$	34671.8	+	20017.8i	0.672860	+	0.388476i	−0.124299	+	0.992245i	$0.539668\pi$
$228$	37578.1	+	5760.68i	0.722878	+	0.110816i
$229$	13383.7	+	23181.3i	0.255215	+	0.442045i	0.964954	−	0.262419i	$-0.0845204\pi$
$229$	13383.7	+	23181.3i	0.255215	+	0.442045i	−0.709739	+	0.704465i	$0.751187\pi$
$230$	−3231.51	+	1865.71i	−0.0610871	+	0.0352686i
$231$	12727.8	−	83026.0i	0.238522	−	1.55593i
$232$	−4971.66	+	8611.17i	−0.0923688	+	0.159987i
$233$		−	39898.5i		−	0.734927i	−0.930038	−	0.367464i	$-0.880226\pi$
$233$		−	39898.5i		−	0.734927i	0.930038	−	0.367464i	$-0.119774\pi$
$234$	39671.6	−	8845.09i	0.724516	−	0.161537i
$235$	3802.78			0.0688597
$236$	−27346.4	−	15788.5i	−0.490995	−	0.283476i
$237$	−31250.0	−	80216.3i	−0.556357	−	1.42812i
$238$	2697.29	+	4671.84i	0.0476182	+	0.0824772i
$239$	−43509.3	+	25120.1i	−0.761704	+	0.439770i	−0.829907	−	0.557902i	$-0.811607\pi$
$239$	−43509.3	+	25120.1i	−0.761704	+	0.439770i	0.0682035	+	0.997671i	$0.478273\pi$
$240$	−993.135	−	796.093i	−0.0172419	−	0.0138211i
$241$	34630.4	−	59981.6i	0.596243	−	1.03272i	−0.397127	−	0.917764i	$-0.629993\pi$
$241$	34630.4	−	59981.6i	0.596243	−	1.03272i	0.993370	−	0.114960i	$-0.0366740\pi$
$242$			85943.6i			1.46752i
$243$	−13862.5	+	57398.8i	−0.234762	+	0.972053i
$244$	−33797.5			−0.567681
$245$	−892.809	−	515.464i	−0.0148740	−	0.00858748i
$246$	9514.61	−	11869.6i	0.157225	−	0.196140i
$247$	46838.3	+	81126.3i	0.767727	+	1.32974i
$248$	29647.5	−	17117.0i	0.482041	−	0.278307i
$249$	−29773.7	+	11599.0i	−0.480213	+	0.187077i
$250$	3891.09	−	6739.56i	0.0622574	−	0.107833i
$251$		−	117510.i		−	1.86521i	−0.360904	−	0.932603i	$-0.617532\pi$
$251$		−	117510.i		−	1.86521i	0.360904	−	0.932603i	$-0.382468\pi$
$252$	6202.17	+	27817.7i	0.0976658	+	0.438046i
$253$	−126683.			−1.97914
$254$	52308.0	+	30200.0i	0.810775	+	0.468101i
$255$	852.463	+	130.682i	0.0131098	+	0.00200971i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−53336.3	+	30793.7i	−0.807526	+	0.466225i	−0.846096	−	0.533030i	$-0.821053\pi$
$257$	−53336.3	+	30793.7i	−0.807526	+	0.466225i	0.0385699	+	0.999256i	$0.487720\pi$
$258$	355.738	−	2320.56i	0.00534430	−	0.0348620i
$259$	−15442.4	+	26747.0i	−0.230205	+	0.398728i
$260$		−	3136.32i		−	0.0463953i
$261$	10662.6	−	33959.8i	0.156524	−	0.498522i
$262$	−87222.9			−1.27066
$263$	22201.4	+	12818.0i	0.320974	+	0.185314i	0.651827	−	0.758368i	$-0.274003\pi$
$263$	22201.4	+	12818.0i	0.320974	+	0.185314i	−0.330853	+	0.943682i	$0.607336\pi$
$264$	−15686.2	−	40265.2i	−0.225066	−	0.577727i
$265$	−1449.26	−	2510.19i	−0.0206374	−	0.0357449i
$266$	−56885.7	+	32842.9i	−0.803969	+	0.464172i
$267$	−3525.22	−	2825.80i	−0.0494497	−	0.0396387i
$268$	2580.74	−	4469.97i	0.0359314	−	0.0622350i
$269$			70454.4i			0.973652i	0.873499	+	0.486826i	$0.161845\pi$
$269$			70454.4i			0.973652i	−0.873499	+	0.486826i	$0.838155\pi$
$270$	4090.11	+	2007.85i	0.0561058	+	0.0275425i
$271$	−677.821			−0.00922946			−0.00461473	−	0.999989i	$-0.501469\pi$
$271$	−677.821			−0.00922946			−0.00461473	+	0.999989i	$0.501469\pi$
$272$	2403.49	+	1387.65i	0.0324866	+	0.0187561i
$273$	−43924.1	+	54795.8i	−0.589356	+	0.735228i
$274$	−15552.6	−	26937.8i	−0.207157	−	0.358807i
$275$	113956.	−	65792.8i	1.50686	−	0.869988i
$276$	40052.9	−	15603.5i	0.525794	−	0.204835i
$277$	52964.2	−	91736.6i	0.690276	−	1.19559i	−0.281472	−	0.959570i	$-0.590823\pi$
$277$	52964.2	−	91736.6i	0.690276	−	1.19559i	0.971747	−	0.236023i	$-0.0758441\pi$
$278$		−	47928.4i		−	0.620160i
$279$	−90252.3	+	82901.1i	−1.15944	+	1.06501i
$280$	2199.18			0.0280508
$281$	−626.791	−	361.878i	−0.00793798	−	0.00458300i	0.496026	−	0.868308i	$-0.334792\pi$
$281$	−626.791	−	361.878i	−0.00793798	−	0.00458300i	−0.503964	+	0.863725i	$0.668125\pi$
$282$	−43301.1	−	6638.00i	−0.544503	−	0.0834716i
$283$	10787.6	+	18684.6i	0.134695	+	0.233299i	0.925481	−	0.378794i	$-0.123661\pi$
$283$	10787.6	+	18684.6i	0.134695	+	0.233299i	−0.790786	+	0.612093i	$0.790328\pi$
$284$	−44324.1	+	25590.5i	−0.549545	+	0.317280i
$285$	−1591.22	+	10379.8i	−0.0195902	+	0.127791i
$286$	53239.5	−	92213.6i	0.650882	−	1.12736i
$287$			26283.8i			0.319099i
$288$	9918.89	+	10798.4i	0.119585	+	0.130190i
$289$	81640.5			0.977485
$290$	−2378.58	−	1373.27i	−0.0282828	−	0.0163291i
$291$	−24269.9	−	62299.0i	−0.286604	−	0.735691i
$292$	−12784.6	−	22143.6i	−0.149942	−	0.259706i
$293$	90289.5	−	52128.7i	1.05172	−	0.607213i	0.128593	−	0.991697i	$-0.458954\pi$
$293$	90289.5	−	52128.7i	1.05172	−	0.607213i	0.923132	+	0.384484i	$0.125621\pi$
$294$	9266.37	+	7427.88i	0.107205	+	0.0859351i
$295$	4361.10	−	7553.65i	0.0501132	−	0.0867986i
$296$			15889.1i			0.181349i
$297$	86173.3	+	128465.i	0.976921	+	1.45637i
$298$	−46976.9			−0.528996
$299$	91727.3	+	52958.8i	1.02602	+	0.592373i
$300$	−27925.5	+	34837.4i	−0.310284	+	0.387082i
$301$	2028.15	+	3512.85i	0.0223855	+	0.0387728i
$302$	27019.4	−	15599.7i	0.296252	−	0.171041i
$303$	−7687.34	+	2994.77i	−0.0837319	+	0.0326196i
$304$	−16896.5	+	29265.6i	−0.182831	+	0.316672i
$305$		−	9335.55i		−	0.100355i
$306$	−9478.63	−	2976.06i	−0.101228	−	0.0317833i
$307$	3762.72			0.0399232			0.0199616	−	0.999801i	$-0.493646\pi$
$307$	3762.72			0.0399232			0.0199616	+	0.999801i	$0.493646\pi$
$308$	64660.1	+	37331.5i	0.681608	+	0.393527i
$309$	31618.8	+	4847.13i	0.331153	+	0.0507654i
$310$	4728.06	+	8189.24i	0.0491994	+	0.0852158i
$311$	−72658.7	+	41949.5i	−0.751220	+	0.433717i	−0.826135	−	0.563473i	$-0.809465\pi$
$311$	−72658.7	+	41949.5i	−0.751220	+	0.433717i	0.0749146	+	0.997190i	$0.476132\pi$
$312$	−5474.65	+	35712.3i	−0.0562402	+	0.366867i
$313$	17717.5	−	30687.5i	0.180848	−	0.313237i	−0.761322	−	0.648374i	$-0.775449\pi$
$313$	17717.5	−	30687.5i	0.180848	−	0.313237i	0.942169	+	0.335137i	$0.108783\pi$
$314$		−	56383.5i		−	0.571864i
$315$	−7683.81	+	1713.17i	−0.0774383	+	0.0172655i
$316$	76523.1			0.766334
$317$	−132069.	−	76250.1i	−1.31426	−	0.758791i	−0.331465	−	0.943468i	$-0.607543\pi$
$317$	−132069.	−	76250.1i	−1.31426	−	0.758791i	−0.982799	+	0.184677i	$0.940876\pi$
$318$	12120.6	+	31112.5i	0.119858	+	0.307667i
$319$	−46623.1	−	80753.6i	−0.458163	−	0.793561i
$320$	979.820	−	565.699i	0.00956856	−	0.00552441i
$321$	3865.64	+	3098.68i	0.0375156	+	0.0300723i
$322$	−37134.6	+	64319.1i	−0.358152	+	0.620338i
$323$		−	22897.0i		−	0.219469i
$324$	−43068.0	−	30002.3i	−0.410265	−	0.285801i
$325$	−110017.			−1.04158
$326$	−19439.7	−	11223.5i	−0.182917	−	0.105607i
$327$	−14421.3	+	17990.8i	−0.134868	+	0.168250i
$328$	6761.03	+	11710.5i	0.0628442	+	0.108849i
$329$	65549.1	−	37844.8i	0.605584	−	0.349634i
$330$	11122.1	−	4332.85i	0.102131	−	0.0397874i
$331$	18573.5	−	32170.2i	0.169526	−	0.293628i	−0.768727	−	0.639577i	$-0.779110\pi$
$331$	18573.5	−	32170.2i	0.169526	−	0.293628i	0.938253	+	0.345949i	$0.112443\pi$
$332$		−	28402.9i		−	0.257683i
$333$	−12377.6	−	55515.6i	−0.111622	−	0.500641i
$334$	54269.1			0.486474
$335$	1234.70	+	712.853i	0.0110020	+	0.00635199i
$336$	−25041.4	−	3838.82i	−0.221810	−	0.0340031i
$337$	21032.6	+	36429.5i	0.185197	+	0.320770i	0.943643	−	0.330966i	$-0.107374\pi$
$337$	21032.6	+	36429.5i	0.185197	+	0.320770i	−0.758446	+	0.651736i	$0.774041\pi$
$338$	−7138.36	+	4121.34i	−0.0624835	+	0.0360749i
$339$	27713.4	−	180781.i	0.241152	−	1.57309i
$340$	−383.299	+	663.893i	−0.00331573	+	0.00574302i
$341$			321038.i			2.76088i
$342$	36237.4	−	115415.i	0.309817	−	0.986752i
$343$	−126121.			−1.07201
$344$	1807.23	+	1043.41i	0.0152721	+	0.00881732i
$345$	4310.00	+	11063.4i	0.0362109	+	0.0929504i
$346$	73805.1	+	127834.i	0.616502	+	1.06781i
$347$	−92575.6	+	53448.5i	−0.768843	+	0.443892i	−0.832462	−	0.554083i	$-0.813069\pi$
$347$	−92575.6	+	53448.5i	−0.768843	+	0.443892i	0.0636189	+	0.997974i	$0.479736\pi$
$348$	24687.0	+	19789.0i	0.203850	+	0.163405i
$349$	−94844.8	+	164276.i	−0.778686	+	1.34872i	0.154013	+	0.988069i	$0.450780\pi$
$349$	−94844.8	+	164276.i	−0.778686	+	1.34872i	−0.932699	+	0.360655i	$0.882553\pi$
$350$		−	77143.5i		−	0.629743i
$351$	−8691.83	−	129041.i	−0.0705500	−	1.04741i
$352$	38411.4			0.310009
$353$	−186532.	−	107694.i	−1.49694	−	0.864257i	−0.496944	−	0.867783i	$-0.665545\pi$
$353$	−186532.	−	107694.i	−1.49694	−	0.864257i	−0.999994	+	0.00352519i	$0.998878\pi$
$354$	−62843.9	+	78398.5i	−0.501483	+	0.625606i
$355$	−7068.63	−	12243.2i	−0.0560891	−	0.0971491i
$356$	3477.96	−	2008.00i	0.0274426	−	0.0158440i
$357$	15994.6	−	6231.03i	0.125498	−	0.0488904i
$358$	−17249.3	+	29876.7i	−0.134588	+	0.233113i
$359$		−	116777.i		−	0.906085i	−0.891489	−	0.453043i	$-0.850339\pi$
$359$		−	116777.i		−	0.906085i	0.891489	−	0.453043i	$-0.149661\pi$
$360$	−2982.75	+	2739.80i	−0.0230151	+	0.0211404i
$361$	148479.			1.13933
$362$	16829.2	+	9716.33i	0.128424	+	0.0741455i
$363$	270313.	+	41438.6i	2.05142	+	0.314479i
$364$	−31212.3	−	54061.2i	−0.235571	−	0.408021i
$365$	6116.52	−	3531.37i	0.0459112	−	0.0265068i
$366$	−16295.8	+	106301.i	−0.121650	+	0.793552i
$367$	−63101.8	+	109295.i	−0.468500	+	0.811465i	−0.999352	−	0.0359992i	$-0.988539\pi$
$367$	−63101.8	+	109295.i	−0.468500	+	0.811465i	0.530852	+	0.847464i	$0.321872\pi$
$368$			38208.8i			0.282142i
$369$	−32745.1	−	35648.8i	−0.240488	−	0.261813i
$370$	−4388.90			−0.0320591
$371$	−49962.2	−	28845.7i	−0.362989	−	0.209572i
$372$	−39542.1	−	101502.i	−0.285742	−	0.733477i
$373$	−55732.4	−	96531.3i	−0.400581	−	0.693826i	0.593215	−	0.805044i	$-0.297858\pi$
$373$	−55732.4	−	96531.3i	−0.400581	−	0.693826i	−0.993796	+	0.111218i	$0.964525\pi$
$374$	−22539.4	+	13013.1i	−0.161138	+	0.0930332i
$375$	−19321.4	−	15487.9i	−0.137397	−	0.110137i
$376$	19469.7	−	33722.6i	0.137716	−	0.238531i
$377$			77961.6i			0.548527i
$378$	90483.7	−	6094.70i	0.633267	−	0.0426549i
$379$	200558.			1.39624			0.698121	−	0.715980i	$-0.254020\pi$
$379$	200558.			1.39624			0.698121	+	0.715980i	$0.254020\pi$
$380$	−8083.75	−	4667.16i	−0.0559816	−	0.0323210i
$381$	120207.	−	149960.i	0.828095	−	1.03306i
$382$	58708.3	+	101686.i	0.402321	+	0.696841i
$383$	65495.5	−	37813.8i	0.446492	−	0.257782i	−0.259856	−	0.965648i	$-0.583675\pi$
$383$	65495.5	−	37813.8i	0.446492	−	0.257782i	0.706347	+	0.707865i	$0.250342\pi$
$384$	−12144.4	+	4731.11i	−0.0823593	+	0.0320849i
$385$	−10311.7	+	17860.4i	−0.0695681	+	0.120495i
$386$		−	168959.i		−	1.13398i
$387$	−7127.18	−	2237.76i	−0.0475878	−	0.0149414i
$388$	59430.7			0.394773
$389$	237715.	+	137245.i	1.57093	+	0.906977i	0.996055	+	0.0887346i	$0.0282823\pi$
$389$	237715.	+	137245.i	1.57093	+	0.906977i	0.574874	+	0.818242i	$0.305051\pi$
$390$	−9864.47	−	1512.21i	−0.0648552	−	0.00994221i
$391$	−12944.5	−	22420.5i	−0.0846704	−	0.146653i
$392$	−9142.14	+	5278.22i	−0.0594943	+	0.0343491i
$393$	−42055.4	+	274337.i	−0.272293	+	1.77623i
$394$	−17496.1	+	30304.2i	−0.112707	+	0.195214i
$395$			21137.2i			0.135473i
$396$	−134207.	+	29922.5i	−0.855825	+	0.190813i
$397$	3509.10			0.0222646			0.0111323	−	0.999938i	$-0.496456\pi$
$397$	3509.10			0.0222646			0.0111323	+	0.999938i	$0.496456\pi$
$398$	−41240.4	−	23810.2i	−0.260350	−	0.150313i
$399$	75870.8	+	194754.i	0.476573	+	1.22332i
$400$	−19843.7	−	34370.4i	−0.124023	−	0.214815i
$401$	−14126.3	+	8155.82i	−0.0878496	+	0.0507200i	−0.543281	−	0.839551i	$-0.682818\pi$
$401$	−14126.3	+	8155.82i	−0.0878496	+	0.0507200i	0.455432	+	0.890271i	$0.349485\pi$
$402$	−12814.8	−	10272.3i	−0.0792975	−	0.0635645i
$403$	134207.	−	232454.i	0.826355	−	1.43129i
$404$		−	7333.40i		−	0.0449307i
$405$	8287.25	−	11896.3i	0.0505243	−	0.0725271i
$406$	−54666.6			−0.331642
$407$	−129042.	−	74502.2i	−0.779007	−	0.449760i
$408$	5523.37	−	6890.47i	0.0331806	−	0.0413932i
$409$	3742.95	+	6482.97i	0.0223752	+	0.0387550i	0.876996	−	0.480497i	$-0.159544\pi$
$409$	3742.95	+	6482.97i	0.0223752	+	0.0387550i	−0.854621	+	0.519252i	$0.826210\pi$
$410$	−3234.67	+	1867.54i	−0.0192425	+	0.0111097i
$411$	−92224.6	+	35928.1i	−0.545963	+	0.212692i
$412$	−14217.0	+	24624.5i	−0.0837554	+	0.145069i
$413$		−	173604.i		−	1.01780i
$414$	−29764.7	−	133499.i	−0.173660	−	0.778894i
$415$	7845.46			0.0455535
$416$	−27812.5	−	16057.6i	−0.160714	−	0.0927882i
$417$	−150746.	−	23109.2i	−0.866911	−	0.132896i
$418$	−158451.	−	274446.i	−0.906867	−	1.57074i
$419$	−94399.3	+	54501.5i	−0.537701	+	0.310442i	−0.744147	−	0.668016i	$-0.767144\pi$
$419$	−94399.3	+	54501.5i	−0.537701	+	0.310442i	0.206446	+	0.978458i	$0.433810\pi$
$420$	1060.36	−	6916.96i	0.00601111	−	0.0392118i
$421$	−165636.	+	286890.i	−0.934525	+	1.61865i	−0.159047	+	0.987271i	$0.550842\pi$
$421$	−165636.	+	286890.i	−0.934525	+	1.61865i	−0.775478	+	0.631374i	$0.782491\pi$
$422$			127883.i			0.718103i
$423$	−41756.2	+	132992.i	−0.233367	+	0.743264i
$424$	−29680.1			−0.165095
$425$	23288.2	+	13445.4i	0.128931	+	0.0744384i
$426$	59116.9	+	151749.i	0.325756	+	0.836191i
$427$	−92906.2	−	160918.i	−0.509553	−	0.882571i
$428$	−3813.82	+	2201.91i	−0.0208196	+	0.0120202i
$429$	−264364.	−	211913.i	−1.43644	−	1.15144i
$430$	−288.210	+	499.195i	−0.00155874	+	0.00269981i
$431$			270347.i			1.45535i	0.685922	+	0.727675i	$0.259399\pi$
$431$			270347.i			1.45535i	−0.685922	+	0.727675i	$0.740601\pi$
$432$	38746.2	−	25990.7i	0.207616	−	0.139268i
$433$	−7609.14			−0.0405845			−0.0202922	−	0.999794i	$-0.506460\pi$
$433$	−7609.14			−0.0405845			−0.0202922	+	0.999794i	$0.506460\pi$
$434$	162997.	+	94106.1i	0.865364	+	0.499618i
$435$	−5466.13	+	6819.06i	−0.0288869	+	0.0360368i
$436$	−10247.7	−	17749.6i	−0.0539082	−	0.0933717i
$437$	272999.	−	157616.i	1.42954	−	0.825348i
$438$	−75811.1	+	29533.9i	−0.395171	+	0.153947i
$439$	49775.5	−	86213.8i	0.258278	−	0.447350i	−0.707503	−	0.706710i	$-0.750178\pi$
$439$	49775.5	−	86213.8i	0.258278	−	0.447350i	0.965781	+	0.259360i	$0.0835117\pi$
$440$			10610.0i			0.0548037i
$441$	27830.3	−	25563.5i	0.143101	−	0.131445i
$442$	21760.1			0.111382
$443$	192291.	+	111019.i	0.979830	+	0.565705i	0.902219	−	0.431279i	$-0.141937\pi$
$443$	192291.	+	111019.i	0.979830	+	0.565705i	0.0776111	+	0.996984i	$0.475271\pi$
$444$	49975.0	+	7661.11i	0.253505	+	0.0388620i
$445$	554.651	+	960.684i	0.00280091	+	0.00485133i
$446$	−124106.	+	71652.4i	−0.623910	+	0.360214i
$447$	−22650.4	+	147754.i	−0.113360	+	0.739474i
$448$	11259.5	−	19502.1i	0.0561002	−	0.0971684i
$449$		−	353910.i		−	1.75550i	−0.479122	−	0.877749i	$-0.659045\pi$
$449$		−	353910.i		−	1.75550i	0.479122	−	0.877749i	$-0.340955\pi$
$450$	96107.4	+	104630.i	0.474604	+	0.516690i
$451$	−126807.			−0.623433
$452$	140791.	+	81285.6i	0.689124	+	0.397866i
$453$	−36036.9	−	92504.0i	−0.175611	−	0.450780i
$454$	56618.8	+	98066.7i	0.274694	+	0.475784i
$455$	14932.8	−	8621.46i	0.0721305	−	0.0416445i
$456$	83900.4	+	67254.2i	0.403491	+	0.323437i
$457$	128991.	−	223419.i	0.617629	−	1.06976i	−0.372288	−	0.928117i	$-0.621427\pi$
$457$	128991.	−	223419.i	0.617629	−	1.06976i	0.989917	−	0.141647i	$-0.0452399\pi$
$458$			75709.8i			0.360929i
$459$	−13930.6	+	28377.6i	−0.0661220	+	0.134695i
$460$	−10554.1			−0.0498774
$461$	183775.	+	106103.i	0.864738	+	0.499257i	0.865596	−	0.500743i	$-0.166940\pi$
$461$	183775.	+	106103.i	0.864738	+	0.499257i	−0.000858089		1.00000i	$0.500273\pi$
$462$	148593.	−	185371.i	0.696169	−	0.868478i
$463$	34545.2	+	59834.0i	0.161148	+	0.279117i	0.935281	−	0.353907i	$-0.115147\pi$
$463$	34545.2	+	59834.0i	0.161148	+	0.279117i	−0.774133	+	0.633024i	$0.781814\pi$
$464$	−24356.1	+	14062.0i	−0.113128	+	0.0653146i
$465$	28036.8	−	10922.3i	0.129665	−	0.0505138i
$466$	56425.0	−	97730.9i	0.259836	−	0.450049i
$467$		−	126113.i		−	0.578264i	−0.957289	−	0.289132i	$-0.906633\pi$
$467$		−	126113.i		−	0.578264i	0.957289	−	0.289132i	$-0.0933667\pi$
$468$	109684.	+	34438.2i	0.500785	+	0.157235i
$469$	28376.9			0.129009
$470$	9314.86	+	5377.94i	0.0421678	+	0.0243456i
$471$	−177340.	−	27185.9i	−0.799400	−	0.122547i
$472$	−44656.6	−	77347.4i	−0.200448	−	0.347186i
$473$	−16947.8	+	9784.84i	−0.0757516	+	0.0437352i
$474$	36896.4	−	240683.i	0.164221	−	1.07125i
$475$	−163716.	+	283564.i	−0.725609	+	1.25679i
$476$			15258.2i			0.0673424i
$477$	103700.	−	23120.8i	0.455768	−	0.101617i
$478$	−142101.			−0.621928
$479$	−248690.	−	143582.i	−1.08390	−	0.625788i	−0.151952	−	0.988388i	$-0.548556\pi$
$479$	−248690.	−	143582.i	−1.08390	−	0.625788i	−0.931945	+	0.362599i	$0.881889\pi$
$480$	−1306.83	−	3354.53i	−0.00567200	−	0.0145596i
$481$	62290.1	+	107890.i	0.269233	+	0.466326i
$482$	169654.	−	97949.6i	0.730246	−	0.421608i
$483$	184394.	+	147809.i	0.790410	+	0.633589i
$484$	−121543.	+	210518.i	−0.518845	+	0.898666i
$485$			16416.0i			0.0697884i
$486$	−115130.	+	120993.i	−0.487434	+	0.512258i
$487$	274661.			1.15808			0.579040	−	0.815299i	$-0.303427\pi$
$487$	274661.			1.15808			0.579040	+	0.815299i	$0.303427\pi$
$488$	−82786.5	−	47796.8i	−0.347632	−	0.200706i
$489$	−44673.7	+	55730.9i	−0.186825	+	0.233066i
$490$	−1457.95	−	2525.25i	−0.00607227	−	0.0105175i
$491$	−274978.	+	158759.i	−1.14060	+	0.658528i	−0.946580	−	0.322469i	$-0.895487\pi$
$491$	−274978.	+	158759.i	−1.14060	+	0.658528i	−0.194024	+	0.980997i	$0.562154\pi$
$492$	40092.1	−	15618.7i	0.165626	−	0.0645232i
$493$	9527.92	−	16502.8i	0.0392016	−	0.0678992i
$494$			264957.i			1.08573i
$495$	−8265.20	−	37070.7i	−0.0337321	−	0.151294i
$496$	96828.3			0.393585
$497$	−243686.	−	140692.i	−0.986547	−	0.569583i
$498$	−89333.8	−	13694.8i	−0.360211	−	0.0552199i
$499$	97561.4	+	168981.i	0.391811	+	0.678637i	0.992688	−	0.120704i	$-0.0385153\pi$
$499$	97561.4	+	168981.i	0.391811	+	0.678637i	−0.600877	+	0.799341i	$0.705182\pi$
$500$	19062.4	−	11005.7i	0.0762494	−	0.0440226i
$501$	26166.5	−	170689.i	0.104248	−	0.680034i
$502$	166184.	−	287839.i	0.659450	−	1.14220i
$503$		−	21373.6i		−	0.0844777i	−0.999108	−	0.0422388i	$-0.986551\pi$
$503$		−	21373.6i		−	0.0844777i	0.999108	−	0.0422388i	$-0.0134490\pi$
$504$	−24148.0	+	76910.3i	−0.0950649	+	0.302777i
$505$	2025.64			0.00794289
$506$	−310309.	−	179157.i	−1.21197	−	0.699733i
$507$	9520.74	+	24439.0i	0.0370386	+	0.0950752i
$508$	85418.6	+	147949.i	0.330998	+	0.573305i
$509$	−69165.6	+	39932.8i	−0.266965	+	0.154132i	−0.627508	−	0.778610i	$-0.715925\pi$
$509$	−69165.6	+	39932.8i	−0.266965	+	0.154132i	0.360543	+	0.932743i	$0.382592\pi$
$510$	1903.29	+	1525.67i	0.00731753	+	0.00586570i
$511$	70287.5	−	121742.i	0.269176	−	0.466227i
$512$		−	11585.2i		−	0.0441942i
$513$	−345534.	−	169624.i	−1.31297	−	0.644542i
$514$	−174196.			−0.659342
$515$	−6801.80	−	3927.02i	−0.0256454	−	0.0148064i
$516$	4153.14	−	5181.09i	0.0155983	−	0.0194591i
$517$	182583.	+	316243.i	0.683091	+	1.18315i
$518$	−75652.1	+	43677.7i	−0.281943	+	0.162780i
$519$	437655.	−	170498.i	1.62479	−	0.632972i
$520$	4435.42	−	7682.38i	0.0164032	−	0.0284112i
$521$		−	142732.i		−	0.525830i	−0.964819	−	0.262915i	$-0.915316\pi$
$521$		−	142732.i		−	0.525830i	0.964819	−	0.262915i	$-0.0846839\pi$
$522$	74144.3	−	68105.1i	0.272105	−	0.249942i
$523$	−232027.			−0.848271			−0.424136	−	0.905599i	$-0.639422\pi$
$523$	−232027.			−0.848271			−0.424136	+	0.905599i	$0.639422\pi$
$524$	−213651.	−	123352.i	−0.778114	−	0.449244i
$525$	−242635.	−	37195.6i	−0.880307	−	0.134950i
$526$	36254.8	+	62795.1i	0.131037	+	0.226963i
$527$	−56817.8	+	32803.8i	−0.204580	+	0.118114i
$528$	18520.5	−	120813.i	0.0664330	−	0.433357i
$529$	38291.5	−	66322.9i	0.136833	−	0.237002i
$530$		−	8198.24i		−	0.0291856i
$531$	216281.	+	235460.i	0.767060	+	0.835079i
$532$	−185788.			−0.656438
$533$	91817.0	+	53010.6i	0.323198	+	0.186599i
$534$	−4638.71	−	11907.2i	−0.0162673	−	0.0417568i
$535$	−608.213	−	1053.45i	−0.00212495	−	0.00368051i
$536$	12643.0	−	7299.43i	0.0440068	−	0.0254073i
$537$	85652.4	+	68658.6i	0.297024	+	0.238093i
$538$	−99637.6	+	172577.i	−0.344238	+	0.596238i
$539$		−	98995.8i		−	0.340753i
$540$	7179.16	+	10702.5i	0.0246199	+	0.0367026i
$541$	−376322.			−1.28577			−0.642887	−	0.765961i	$-0.722264\pi$
$541$	−376322.			−1.28577			−0.642887	+	0.765961i	$0.722264\pi$
$542$	−1660.32	−	958.583i	−0.00565187	−	0.00326311i
$543$	38674.5	−	48246.9i	0.131167	−	0.163633i
$544$	3924.88	+	6798.09i	0.0132626	+	0.0229715i
$545$	4902.80	−	2830.63i	0.0165064	−	0.00952995i
$546$	−185085.	+	72103.8i	−0.620848	+	0.241865i
$547$	137517.	−	238187.i	0.459602	−	0.796054i	−0.539338	−	0.842090i	$-0.681325\pi$
$547$	137517.	−	238187.i	0.459602	−	0.796054i	0.998940	+	0.0460355i	$0.0146587\pi$
$548$		−	87978.5i		−	0.292965i
$549$	326485.	+	102508.i	1.08322	+	0.340106i
$550$	372180.			1.23035
$551$	200943.	+	116015.i	0.661866	+	0.382129i
$552$	120176.	+	18422.8i	0.394402	+	0.0604613i
$553$	210355.	+	364346.i	0.687864	+	1.19142i
$554$	259470.	−	149805.i	0.845412	−	0.488099i
$555$	−2116.15	+	13804.1i	−0.00687007	+	0.0448149i
$556$	67781.0	−	117400.i	0.219260	−	0.379769i
$557$			318602.i			1.02692i	0.858112	+	0.513462i	$0.171637\pi$
$557$			318602.i			1.02692i	−0.858112	+	0.513462i	$0.828363\pi$
$558$	−338312.	+	75429.3i	−1.08655	+	0.242254i
$559$	16361.9			0.0523612
$560$	5386.88	+	3110.12i	0.0171775	+	0.00991746i
$561$	30061.7	+	77166.1i	0.0955187	+	0.245189i
$562$	−1023.55	−	1772.83i	−0.00324067	−	0.00561300i
$563$	−41192.5	+	23782.5i	−0.129958	+	0.0750311i	−0.563569	−	0.826069i	$-0.690572\pi$
$563$	−41192.5	+	23782.5i	−0.129958	+	0.0750311i	0.433612	+	0.901100i	$0.357239\pi$
$564$	−96678.0	−	77496.7i	−0.303927	−	0.243627i
$565$	−22452.7	+	38889.3i	−0.0703351	+	0.121824i
$566$			61023.8i			0.190487i
$567$	24458.4	−	287531.i	0.0760785	−	0.894374i
$568$	−144762.			−0.448701
$569$	271738.	+	156888.i	0.839318	+	0.484580i	0.857032	−	0.515263i	$-0.172306\pi$
$569$	271738.	+	156888.i	0.839318	+	0.484580i	−0.0177144	+	0.999843i	$0.505639\pi$
$570$	−18577.0	+	23175.0i	−0.0571775	+	0.0713296i
$571$	−162047.	−	280674.i	−0.497015	−	0.860856i	0.502979	−	0.864299i	$-0.332237\pi$
$571$	−162047.	−	280674.i	−0.497015	−	0.860856i	−0.999994	+	0.00344295i	$0.998904\pi$
$572$	260819.	−	150584.i	0.797164	−	0.460243i
$573$	348133.	−	135623.i	1.06032	−	0.413070i
$574$	−37171.0	+	64382.0i	−0.112818	+	0.195407i
$575$			370218.i			1.11975i
$576$	9024.91	+	40478.1i	0.0272018	+	0.122004i
$577$	−292524.			−0.878636			−0.439318	−	0.898332i	$-0.644780\pi$
$577$	−292524.			−0.878636			−0.439318	+	0.898332i	$0.644780\pi$
$578$	199978.	+	115457.i	0.598585	+	0.345593i
$579$	−531416.	−	81465.3i	−1.58518	−	0.243005i
$580$	−3884.21	−	6727.64i	−0.0115464	−	0.0199989i
$581$	135233.	−	78077.0i	0.400619	−	0.231297i
$582$	28655.2	−	186924.i	0.0845974	−	0.551847i
$583$	139167.	−	241043.i	0.409447	−	0.709183i
$584$		−	72320.7i		−	0.212049i
$585$	−9512.52	+	30297.0i	−0.0277961	+	0.0885294i
$586$	294884.			0.858729
$587$	−32013.0	−	18482.7i	−0.0929073	−	0.0536400i	0.452827	−	0.891599i	$-0.350416\pi$
$587$	−32013.0	−	18482.7i	−0.0929073	−	0.0536400i	−0.545734	+	0.837959i	$0.683749\pi$
$588$	12193.3	+	31299.1i	0.0352667	+	0.0905269i
$589$	−399428.	−	691830.i	−1.15135	−	1.99420i
$590$	21364.9	−	12335.1i	0.0613759	−	0.0354354i
$591$	86877.9	+	69641.0i	0.248734	+	0.199384i
$592$	−22470.6	+	38920.2i	−0.0641167	+	0.111053i
$593$			5939.58i			0.0168906i	0.999964	+	0.00844532i	$0.00268826\pi$
$593$			5939.58i			0.0168906i	−0.999964	+	0.00844532i	$0.997312\pi$
$594$	29404.0	+	436540.i	0.0833362	+	1.23723i
$595$	−4214.62			−0.0119049
$596$	−115069.	−	66435.4i	−0.323942	−	0.187028i
$597$	−94773.1	+	118231.i	−0.265911	+	0.331727i
$598$	149790.	+	259444.i	0.418871	+	0.725506i
$599$	135382.	−	78162.8i	0.377318	−	0.217845i	−0.299333	−	0.954149i	$-0.596764\pi$
$599$	135382.	−	78162.8i	0.377318	−	0.217845i	0.676651	+	0.736304i	$0.263431\pi$
$600$	−117671.	+	45841.2i	−0.326864	+	0.127337i
$601$	−70819.1	+	122662.i	−0.196066	+	0.339596i	−0.947249	−	0.320498i	$-0.896150\pi$
$601$	−70819.1	+	122662.i	−0.196066	+	0.339596i	0.751184	+	0.660093i	$0.229483\pi$
$602$			11472.9i			0.0316578i
$603$	−38487.5	+	35352.7i	−0.105849	+	0.0972271i
$604$	88245.0			0.241889
$605$	−58149.4	−	33572.6i	−0.158867	−	0.0917220i
$606$	−23065.3	−	3535.88i	−0.0628078	−	0.00962836i
$607$	−133819.	−	231782.i	−0.363196	−	0.629074i	0.625289	−	0.780393i	$-0.284981\pi$
$607$	−133819.	−	231782.i	−0.363196	−	0.629074i	−0.988485	+	0.151320i	$0.951648\pi$
$608$	−82775.5	+	47790.5i	−0.223921	+	0.129281i
$609$	−26358.1	+	171939.i	−0.0710689	+	0.463597i
$610$	13202.5	−	22867.3i	0.0354809	−	0.0614548i
$611$		−	305309.i		−	0.817819i
$612$	−19009.0	−	20694.6i	−0.0507524	−	0.0552529i
$613$	191952.			0.510825			0.255413	−	0.966832i	$-0.417789\pi$
$613$	191952.			0.510825			0.255413	+	0.966832i	$0.417789\pi$
$614$	9216.74	+	5321.29i	0.0244479	+	0.0141150i
$615$	4314.21	+	11074.3i	0.0114065	+	0.0292795i
$616$	105589.	+	182886.i	0.278265	+	0.481970i
$617$	−332409.	+	191917.i	−0.873178	+	0.504130i	−0.868403	−	0.495859i	$-0.834853\pi$
$617$	−332409.	+	191917.i	−0.873178	+	0.504130i	−0.00477496	+	0.999989i	$0.501520\pi$
$618$	70595.2	+	56588.8i	0.184841	+	0.148168i
$619$	−60619.2	+	104996.i	−0.158208	+	0.274025i	−0.934223	−	0.356691i	$-0.883905\pi$
$619$	−60619.2	+	104996.i	−0.158208	+	0.274025i	0.776014	+	0.630715i	$0.217238\pi$
$620$			26745.9i			0.0695784i
$621$	−434238.	+	29248.9i	−1.12602	+	0.0758450i
$622$	−237302.			−0.613368
$623$	19121.2	+	11039.6i	0.0492651	+	0.0284432i
$624$	−63914.9	+	79734.6i	−0.164147	+	0.204775i
$625$	−190747.	−	330383.i	−0.488311	−	0.845780i
$626$	86797.5	−	50112.5i	0.221492	−	0.127879i
$627$	−939597.	+	366040.i	−2.39005	+	0.931095i
$628$	79738.4	−	138111.i	0.202185	−	0.350194i
$629$		−	30450.6i		−	0.0769653i
$630$	−21244.2	−	6670.17i	−0.0535253	−	0.0168057i
$631$	−455676.			−1.14445			−0.572226	−	0.820096i	$-0.693920\pi$
$631$	−455676.			−1.14445			−0.572226	+	0.820096i	$0.693920\pi$
$632$	187442.	+	108220.i	0.469282	+	0.270940i
$633$	402222.	+	61660.0i	1.00382	+	0.153885i
$634$	−215668.	−	373548.i	−0.536546	−	0.929325i
$635$	−40866.6	+	23594.4i	−0.101349	+	0.0585141i
$636$	−14310.6	+	93350.9i	−0.0353788	+	0.230783i
$637$	−41384.4	+	71679.9i	−0.101990	+	0.176652i
$638$		−	263740.i		−	0.647940i
$639$	505789.	−	112770.i	1.23870	−	0.276179i
$640$	3200.08			0.00781269
$641$	496152.	+	286453.i	1.20753	+	0.697168i	0.962219	−	0.272276i	$-0.0877763\pi$
$641$	496152.	+	286453.i	1.20753	+	0.697168i	0.245312	+	0.969444i	$0.421110\pi$
$642$	5086.66	+	13057.0i	0.0123413	+	0.0316792i
$643$	224632.	+	389074.i	0.543313	+	0.941046i	0.998711	+	0.0507578i	$0.0161637\pi$
$643$	224632.	+	389074.i	0.543313	+	0.941046i	−0.455398	+	0.890288i	$0.650503\pi$
$644$	−181922.	+	105033.i	−0.438645	+	0.253252i
$645$	1431.12	+	1147.18i	0.00343999	+	0.00275748i
$646$	32381.2	−	56085.9i	0.0775940	−	0.134397i
$647$		−	502638.i		−	1.20073i	−0.799725	−	0.600366i	$-0.795021\pi$
$647$		−	502638.i		−	1.20073i	0.799725	−	0.600366i	$-0.204979\pi$
$648$	−63065.0	−	134398.i	−0.150189	−	0.320068i
$649$	837558.			1.98850
$650$	−269484.	−	155587.i	−0.637833	−	0.368253i
$651$	374577.	−	467289.i	0.883850	−	1.10261i
$652$	−31744.9	−	54983.8i	−0.0746756	−	0.129342i
$653$	−595663.	+	343906.i	−1.39693	+	0.806517i	−0.994070	−	0.108745i	$-0.965317\pi$
$653$	−595663.	+	343906.i	−1.39693	+	0.806517i	−0.402859	+	0.915262i	$0.631983\pi$
$654$	−60767.7	+	23673.4i	−0.142075	+	0.0553484i
$655$	34072.3	−	59014.9i	0.0794179	−	0.137556i
$656$			38246.2i			0.0888752i
$657$	56337.9	+	252684.i	0.130518	+	0.585393i
$658$	214082.			0.494458
$659$	−233033.	−	134542.i	−0.536595	−	0.309803i	0.207103	−	0.978319i	$-0.433597\pi$
$659$	−233033.	−	134542.i	−0.536595	−	0.309803i	−0.743698	+	0.668516i	$0.766930\pi$
$660$	33371.0	+	5115.73i	0.0766093	+	0.0117441i
$661$	200626.	+	347494.i	0.459181	+	0.795324i	0.998918	−	0.0465092i	$-0.0148097\pi$
$661$	200626.	+	347494.i	0.459181	+	0.795324i	−0.539737	+	0.841834i	$0.681476\pi$
$662$	90991.0	−	52533.7i	0.207626	−	0.119873i
$663$	10491.9	−	68440.7i	0.0238685	−	0.155700i
$664$	40167.7	−	69572.6i	0.0911048	−	0.157798i
$665$		−	51318.4i		−	0.116046i
$666$	48192.0	−	153489.i	0.108649	−	0.346043i
$667$	262349.			0.589696
$668$	132932.	+	76748.1i	0.297903	+	0.171995i
$669$	165525.	+	424890.i	0.369838	+	0.949345i
$670$	2016.25	+	3492.25i	0.00449154	+	0.00777957i
$671$	776354.	−	448228.i	1.72431	−	0.995529i
$672$	−55909.8	−	44817.1i	−0.123808	−	0.0992442i
$673$	54368.5	−	94169.0i	0.120038	−	0.207911i	−0.799745	−	0.600340i	$-0.795032\pi$
$673$	54368.5	−	94169.0i	0.120038	−	0.207911i	0.919782	+	0.392429i	$0.128365\pi$
$674$			118978.i			0.261907i
$675$	375424.	−	251832.i	0.823977	−	0.552718i
$676$	−23313.8			−0.0510176
$677$	−82318.9	−	47526.9i	−0.179607	−	0.103696i	0.407501	−	0.913205i	$-0.366400\pi$
$677$	−82318.9	−	47526.9i	−0.179607	−	0.103696i	−0.587108	+	0.809509i	$0.699734\pi$
$678$	323546.	−	403628.i	0.703845	−	0.878054i
$679$	163370.	+	282965.i	0.354350	+	0.613752i
$680$	−1877.77	+	1084.13i	−0.00406093	+	0.00234458i
$681$	335742.	−	130796.i	0.723956	−	0.282033i
$682$	−454017.	+	786380.i	−0.976120	+	1.69069i
$683$			704385.i			1.50997i	0.655741	+	0.754986i	$0.272356\pi$
$683$			704385.i			1.50997i	−0.655741	+	0.754986i	$0.727644\pi$
$684$	251984.	−	231459.i	0.538593	−	0.494723i
$685$	24301.5			0.0517906
$686$	−308933.	−	178363.i	−0.656472	−	0.379015i
$687$	238125.	+	36504.3i	0.504536	+	0.0773447i
$688$	2951.20	+	5111.63i	0.00623479	+	0.0107990i
$689$	−201532.	+	116355.i	−0.424528	+	0.245101i
$690$	−5088.75	+	33195.0i	−0.0106884	+	0.0697228i
$691$	−441540.	+	764770.i	−0.924729	+	1.60168i	−0.132731	+	0.991152i	$0.542375\pi$
$691$	−441540.	+	764770.i	−0.924729	+	1.60168i	−0.791997	+	0.610525i	$0.790959\pi$
$692$			417505.i			0.871865i
$693$	−511392.	−	556739.i	−1.06485	−	1.15927i
$694$	−302351.			−0.627757
$695$	32428.3	+	18722.5i	0.0671359	+	0.0387609i
$696$	32484.7	+	83385.7i	0.0670596	+	0.172137i
$697$	−12957.2	−	22442.5i	−0.0266713	−	0.0461960i
$698$	−464643.	+	268262.i	−0.953692	+	0.550614i
$699$	−280181.	−	224592.i	−0.573435	−	0.459663i
$700$	109097.	−	188962.i	0.222648	−	0.385637i
$701$		−	713342.i		−	1.45165i	−0.687879	−	0.725825i	$-0.741458\pi$
$701$		−	713342.i		−	1.45165i	0.687879	−	0.725825i	$-0.258542\pi$
$702$	161202.	−	328378.i	0.327111	−	0.666345i
$703$	370775.			0.750240
$704$	94088.3	+	54321.9i	0.189841	+	0.109605i
$705$	21406.2	−	26704.4i	0.0430686	−	0.0537286i
$706$	−304605.	−	527592.i	−0.611122	−	1.05849i
$707$	34916.2	−	20158.9i	0.0698535	−	0.0403299i
$708$	−264808.	+	103162.i	−0.528280	+	0.205803i
$709$	−39245.0	+	67974.3i	−0.0780713	+	0.135223i	−0.902418	−	0.430862i	$-0.858210\pi$
$709$	−39245.0	+	67974.3i	−0.0780713	+	0.135223i	0.824346	+	0.566086i	$0.191543\pi$
$710$		−	39986.2i		−	0.0793219i
$711$	−739216.	−	232096.i	−1.46229	−	0.459122i
$712$	11359.0			0.0224068
$713$	−782233.	−	451623.i	−1.53871	−	0.888376i
$714$	47990.5	+	7356.89i	0.0941368	+	0.0144310i
$715$	41594.4	+	72043.6i	0.0813623	+	0.140924i
$716$	−84504.1	+	48788.5i	−0.164836	+	0.0951681i
$717$	−68515.4	+	446940.i	−0.133275	+	0.869383i
$718$	165148.	−	286044.i	0.320349	−	0.554862i
$719$			146207.i			0.282820i	0.989951	+	0.141410i	$0.0451636\pi$
$719$			146207.i			0.282820i	−0.989951	+	0.141410i	$0.954836\pi$
$720$	−11180.9	+	2492.87i	−0.0215681	+	0.00480877i
$721$	−156325.			−0.300717
$722$	363698.	+	209981.i	0.697696	+	0.402815i
$723$	−226274.	−	580829.i	−0.432871	−	1.11115i
$724$	27481.9	+	47600.1i	0.0524288	+	0.0908094i
$725$	−235994.	+	136251.i	−0.448978	+	0.259217i
$726$	603526.	+	483784.i	1.14505	+	0.917864i
$727$	−352617.	+	610750.i	−0.667166	+	1.15557i	0.311527	+	0.950237i	$0.399159\pi$
$727$	−352617.	+	610750.i	−0.667166	+	1.15557i	−0.978693	+	0.205328i	$0.934174\pi$
$728$		−	176563.i		−	0.333148i
$729$	325041.	+	420450.i	0.611622	+	0.791150i
$730$	19976.5			0.0374863
$731$	−3463.47	−	1999.63i	−0.00648151	−	0.00374210i
$732$	−190249.	+	237338.i	−0.355058	+	0.442939i
$733$	−65548.2	−	113533.i	−0.121998	−	0.211307i	0.798558	−	0.601919i	$-0.205597\pi$
$733$	−65548.2	−	113533.i	−0.121998	−	0.211307i	−0.920555	+	0.390612i	$0.872263\pi$
$734$	−309134.	+	178479.i	−0.573793	+	0.331279i
$735$	−8645.46	+	3368.03i	−0.0160035	+	0.00623449i
$736$	−54035.4	+	93592.1i	−0.0997523	+	0.172776i
$737$			136905.i			0.252048i
$738$	−29793.8	−	133630.i	−0.0547033	−	0.245353i
$739$	82938.7			0.151869			0.0759344	−	0.997113i	$-0.475806\pi$
$739$	82938.7			0.151869			0.0759344	+	0.997113i	$0.475806\pi$
$740$	−10750.6	−	6206.84i	−0.0196321	−	0.0113346i
$741$	833354.	+	127752.i	1.51772	+	0.232665i
$742$	−81587.9	−	141314.i	−0.148190	−	0.256672i
$743$	726053.	−	419187.i	1.31520	−	0.759329i	0.332244	−	0.943193i	$-0.392194\pi$
$743$	726053.	−	419187.i	1.31520	−	0.759329i	0.982952	+	0.183865i	$0.0588608\pi$
$744$	46686.8	−	304548.i	0.0843428	−	0.550186i
$745$	18350.8	−	31784.5i	0.0330630	−	0.0572669i
$746$		−	315270.i		−	0.566507i
$747$	−86146.5	+	274373.i	−0.154382	+	0.491700i
$748$	−73613.3			−0.131569
$749$	−20967.7	−	12105.7i	−0.0373755	−	0.0215788i
$750$	−25424.3	−	65262.1i	−0.0451987	−	0.116022i
$751$	−154122.	−	266948.i	−0.273266	−	0.473311i	0.696430	−	0.717625i	$-0.254771\pi$
$751$	−154122.	−	266948.i	−0.273266	−	0.473311i	−0.969696	+	0.244314i	$0.921437\pi$
$752$	95381.8	−	55068.7i	0.168667	−	0.0973799i
$753$	−825195.	−	661473.i	−1.45535	−	1.16660i
$754$	−110254.	+	190966.i	−0.193934	+	0.335903i
$755$			24375.1i			0.0427614i
$756$	230258.	+	113034.i	0.402876	+	0.197773i
$757$	298072.			0.520151			0.260075	−	0.965588i	$-0.416253\pi$
$757$	298072.			0.520151			0.260075	+	0.965588i	$0.416253\pi$
$758$	491264.	+	283631.i	0.855020	+	0.493646i
$759$	−713110.	+	889612.i	−1.23786	+	1.54425i
$760$	−13200.7	−	22864.3i	−0.0228544	−	0.0395850i
$761$	205714.	−	118769.i	0.355218	−	0.205085i	−0.311763	−	0.950160i	$-0.600920\pi$
$761$	205714.	−	118769.i	0.355218	−	0.205085i	0.666981	+	0.745075i	$0.267586\pi$
$762$	506521.	−	197326.i	0.872344	−	0.339840i
$763$	56340.2	−	97584.1i	0.0967764	−	0.167622i
$764$			332104.i			0.568968i
$765$	5716.28	−	5250.68i	0.00976767	−	0.00897207i
$766$	213907.			0.364559
$767$	−606450.	−	350134.i	−1.03087	−	0.595174i
$768$	−36438.3	−	5585.95i	−0.0617783	−	0.00947053i
$769$	−346986.	−	600997.i	−0.586758	−	1.01629i	−0.994654	−	0.103266i	$-0.967071\pi$
$769$	−346986.	−	600997.i	−0.586758	−	1.01629i	0.407896	−	0.913029i	$-0.366263\pi$
$770$	−50516.9	+	29166.0i	−0.0852031	+	0.0491920i
$771$	−83990.3	+	547887.i	−0.141293	+	0.921684i
$772$	238944.	−	413863.i	0.400923	−	0.694419i
$773$		−	106414.i		−	0.178091i	−0.996028	−	0.0890454i	$-0.971618\pi$
$773$		−	106414.i		−	0.178091i	0.996028	−	0.0890454i	$-0.0283816\pi$
$774$	−14293.3	−	15560.7i	−0.0238589	−	0.0259746i
$775$	938201.			1.56204
$776$	145575.	+	84047.7i	0.241748	+	0.139573i
$777$	100900.	+	259003.i	0.167129	+	0.429006i
$778$	388186.	+	672358.i	0.641329	+	1.11081i
$779$	273266.	−	157770.i	0.450309	−	0.259986i
$780$	−22024.3	−	17654.6i	−0.0362004	−	0.0290181i
$781$	678772.	−	1.17567e6i	1.11281	−	1.92745i
$782$		−	73225.1i		−	0.119742i
$783$	−178457.	−	266039.i	−0.291079	−	0.433932i
$784$	−29858.1			−0.0485769
$785$	38149.1	+	22025.4i	0.0619077	+	0.0357424i
$786$	−490985.	+	612509.i	−0.794736	+	0.991443i
$787$	−48361.5	−	83764.7i	−0.0780820	−	0.135242i	0.824340	−	0.566094i	$-0.191546\pi$
$787$	−48361.5	−	83764.7i	−0.0780820	−	0.135242i	−0.902422	+	0.430853i	$0.858213\pi$
$788$	−85713.2	+	49486.5i	−0.138037	+	0.0796957i
$789$	214986.	−	83752.6i	0.345348	−	0.134538i
$790$	−29892.6	+	51775.4i	−0.0478971	+	0.0829602i
$791$			893787.i			1.42850i
$792$	−371055.	−	116502.i	−0.591546	−	0.185731i
$793$	−749512.			−1.19188
$794$	8595.51	+	4962.62i	0.0136342	+	0.00787173i
$795$	−25785.4	−	3952.87i	−0.0407981	−	0.00625430i
$796$	−67345.3	−	116646.i	−0.106287	−	0.184095i
$797$	473218.	−	273213.i	0.744980	−	0.430115i	−0.0788969	−	0.996883i	$-0.525140\pi$
$797$	473218.	−	273213.i	0.744980	−	0.430115i	0.823877	+	0.566768i	$0.191806\pi$
$798$	−89579.6	+	584347.i	−0.140671	+	0.917624i
$799$	−37312.7	+	64627.5i	−0.0584471	+	0.101233i
$800$		−	112253.i		−	0.175396i
$801$	−39687.6	+	8848.65i	−0.0618571	+	0.0137915i
$802$	−46136.3			−0.0717289
$803$	587345.	+	339104.i	0.910882	+	0.525898i
$804$	−16862.5	−	43284.7i	−0.0260861	−	0.0669610i
$805$	−29012.2	−	50250.5i	−0.0447701	−	0.0775441i
$806$	657479.	−	379596.i	1.01207	−	0.584321i
$807$	494756.	+	396594.i	0.759703	+	0.608974i
$808$	10371.0	−	17963.1i	0.0158854	−	0.0275143i
$809$			467941.i			0.714981i	0.933917	+	0.357490i	$0.116367\pi$
$809$			467941.i			0.714981i	−0.933917	+	0.357490i	$0.883633\pi$
$810$	37123.4	−	17419.8i	0.0565819	−	0.0265506i
$811$	−1.15071e6			−1.74954			−0.874771	−	0.484537i	$-0.838988\pi$
$811$	−1.15071e6			−1.74954			−0.874771	+	0.484537i	$0.838988\pi$
$812$	−133905.	−	77310.2i	−0.203089	−	0.117253i
$813$	−3815.51	+	4759.89i	−0.00577260	+	0.00720139i
$814$	−210724.	−	364985.i	−0.318028	−	0.550841i
$815$	15187.6	−	8768.59i	0.0228652	−	0.0132012i
$816$	23274.0	−	9066.91i	0.0349536	−	0.0136169i
$817$	24348.1	−	42172.2i	0.0364772	−	0.0631803i
$818$			21173.3i			0.0316433i
$819$	137543.	+	616901.i	0.205055	+	0.919703i
$820$	−10564.4			−0.0157114
$821$	411132.	+	237367.i	0.609952	+	0.352156i	0.772947	−	0.634471i	$-0.218782\pi$
$821$	411132.	+	237367.i	0.609952	+	0.352156i	−0.162995	+	0.986627i	$0.552115\pi$
$822$	−276713.	−	42419.8i	−0.409531	−	0.0627805i
$823$	599334.	+	1.03808e6i	0.884849	+	1.53260i	0.845886	+	0.533363i	$0.179072\pi$
$823$	599334.	+	1.03808e6i	0.884849	+	1.53260i	0.0389627	+	0.999241i	$0.487595\pi$
$824$	−69648.7	+	40211.7i	−0.102579	+	0.0592240i
$825$	179451.	−	1.17060e6i	0.263656	−	1.71988i
$826$	245514.	−	425242.i	0.359845	−	0.623270i
$827$		−	227743.i		−	0.332993i	−0.986042	−	0.166496i	$-0.946755\pi$
$827$		−	227743.i		−	0.332993i	0.986042	−	0.166496i	$-0.0532454\pi$
$828$	115888.	−	369099.i	0.169036	−	0.538371i
$829$	17171.5			0.0249862			0.0124931	−	0.999922i	$-0.496023\pi$
$829$	17171.5			0.0249862			0.0124931	+	0.999922i	$0.496023\pi$
$830$	19217.4	+	11095.2i	0.0278957	+	0.0161056i
$831$	−346067.	−	888326.i	−0.501139	−	1.28638i
$832$	−45417.6	−	78665.6i	−0.0656112	−	0.113642i
$833$	17520.4	−	10115.4i	0.0252496	−	0.0145779i
$834$	−336570.	−	269793.i	−0.483886	−	0.387881i
$835$	−21199.4	+	36718.4i	−0.0304054	+	0.0526637i
$836$		−	896337.i		−	1.28250i
$837$	74122.3	+	1.10044e6i	0.105803	+	1.57078i
$838$	−308307.			−0.439031
$839$	−655294.	−	378334.i	−0.930920	−	0.537467i	−0.0438177	−	0.999040i	$-0.513952\pi$
$839$	−655294.	−	378334.i	−0.930920	−	0.537467i	−0.887102	+	0.461573i	$0.847285\pi$
$840$	12379.4	−	15443.4i	0.0175445	−	0.0218870i
$841$	−257088.	−	445290.i	−0.363488	−	0.629580i
$842$	−811448.	+	468490.i	−1.14456	+	0.660809i
$843$	−6069.49	+	2364.50i	−0.00854078	+	0.00332725i
$844$	−180853.	+	313247.i	−0.253888	+	0.439747i
$845$		−	6439.75i		−	0.00901894i
$846$	−290360.	+	266709.i	−0.405691	+	0.372647i
$847$	−1.33644e6			−1.86287
$848$	−72701.0	−	41974.0i	−0.101099	−	0.0583698i
$849$	191934.	+	29423.3i	0.266279	+	0.0408203i
$850$	38029.5	+	65868.9i	0.0526359	+	0.0911681i
$851$	363060.	−	209613.i	0.501325	−	0.289440i
$852$	−69798.5	+	455311.i	−0.0961539	+	0.627232i
$853$	281438.	−	487465.i	0.386798	−	0.669954i	−0.605219	−	0.796059i	$-0.706914\pi$
$853$	281438.	−	487465.i	0.386798	−	0.669954i	0.992017	+	0.126105i	$0.0402477\pi$
$854$		−	525557.i		−	0.720616i
$855$	63933.8	+	69603.1i	0.0874577	+	0.0952130i
$856$	−12455.9			−0.0169991
$857$	753246.	+	434887.i	1.02559	+	0.592127i	0.915719	−	0.401819i	$-0.131622\pi$
$857$	753246.	+	434887.i	1.02559	+	0.592127i	0.109874	+	0.993945i	$0.464955\pi$
$858$	−347866.	−	892945.i	−0.472539	−	1.21297i
$859$	−211385.	−	366130.i	−0.286476	−	0.496191i	0.686490	−	0.727139i	$-0.259151\pi$
$859$	−211385.	−	366130.i	−0.286476	−	0.496191i	−0.972966	+	0.230948i	$0.925817\pi$
$860$	−1411.94	+	815.182i	−0.00190905	+	0.00110219i
$861$	184574.	+	147954.i	0.248980	+	0.199582i
$862$	−382329.	+	662213.i	−0.514544	+	0.891217i
$863$			1.33087e6i			1.78696i	0.449100	+	0.893482i	$0.351745\pi$
$863$			1.33087e6i			1.78696i	−0.449100	+	0.893482i	$0.648255\pi$
$864$	131665.	−	8868.53i	0.176377	−	0.0118802i
$865$	−115323.			−0.154129
$866$	−18638.5	−	10761.0i	−0.0248528	−	0.0143488i
$867$	459562.	−	573308.i	0.611372	−	0.762694i
$868$	266172.	+	461024.i	0.353284	+	0.611905i
$869$	−1.75779e6	+	1.01486e6i	−2.32771	+	1.34390i
$870$	−23032.8	+	8972.94i	−0.0304305	+	0.0118549i
$871$	57231.9	−	99128.6i	0.0754401	−	0.130666i
$872$		−	57969.9i		−	0.0762377i
$873$	−574103.	−	180255.i	−0.753289	−	0.236515i
$874$	891610.			1.16722
$875$	104801.	+	60507.1i	0.136884	+	0.0790297i
$876$	−227466.	−	34870.2i	−0.296420	−	0.0454408i
$877$	638412.	+	1.10576e6i	0.830045	+	1.43768i	0.898001	+	0.439992i	$0.145019\pi$
$877$	638412.	+	1.10576e6i	0.830045	+	1.43768i	−0.0679561	+	0.997688i	$0.521648\pi$
$878$	243849.	−	140787.i	0.316324	−	0.182630i
$879$	142182.	−	927481.i	0.184020	−	1.20040i
$880$	−15004.8	+	25989.1i	−0.0193761	+	0.0335603i
$881$		−	404060.i		−	0.520588i	−0.965529	−	0.260294i	$-0.916181\pi$
$881$		−	404060.i		−	0.520588i	0.965529	−	0.260294i	$-0.0838194\pi$
$882$	104322.	−	23259.5i	0.134104	−	0.0298994i
$883$	728109.			0.933845			0.466923	−	0.884298i	$-0.345363\pi$
$883$	728109.			0.933845			0.466923	+	0.884298i	$0.345363\pi$
$884$	53301.1	+	30773.4i	0.0682075	+	0.0393796i
$885$	−28495.3	−	73145.3i	−0.0363821	−	0.0933899i
$886$	314009.	+	543880.i	0.400014	+	0.692844i
$887$	94847.0	−	54759.9i	0.120552	−	0.0696010i	−0.438511	−	0.898726i	$-0.644494\pi$
$887$	94847.0	−	54759.9i	0.120552	−	0.0696010i	0.559064	+	0.829125i	$0.311161\pi$
$888$	111579.	+	89441.1i	0.141500	+	0.113426i
$889$	−469616.	+	813399.i	−0.594209	+	1.02920i
$890$			3137.58i			0.00396109i
$891$	1.38720e6	+	118000.i	1.74737	+	0.148637i
$892$	−405327.			−0.509420
$893$	−786923.	−	454330.i	−0.986800	−	0.569729i
$894$	−264437.	+	329888.i	−0.330862	+	0.412755i
$895$	−13476.4	−	23341.8i	−0.0168239	−	0.0291399i
$896$	55160.3	−	31846.8i	0.0687085	−	0.0396689i
$897$	888236.	−	346032.i	1.10393	−	0.430062i
$898$	500504.	−	866899.i	0.620662	−	1.07502i
$899$		−	664842.i		−	0.822620i
$900$	87445.3	+	392206.i	0.107957	+	0.484205i
$901$	56880.2			0.0700667
$902$	−310612.	−	179332.i	−0.381773	−	0.220417i
$903$	36085.1	+	5531.80i	0.0442540	+	0.00678408i
$904$	229910.	+	398216.i	0.281334	+	0.487284i
$905$	−13148.1	+	7591.07i	−0.0160534	+	0.00926842i
$906$	42548.3	−	277552.i	0.0518353	−	0.338133i
$907$	714661.	−	1.23783e6i	0.868731	−	1.50469i	0.00543754	−	0.999985i	$-0.498269\pi$
$907$	714661.	−	1.23783e6i	0.868731	−	1.50469i	0.863294	−	0.504702i	$-0.168397\pi$
$908$			320284.i			0.388476i
$909$	−22242.4	+	70841.0i	−0.0269186	+	0.0857347i
$910$	48770.4			0.0588943
$911$	−487451.	−	281430.i	−0.587347	−	0.339105i	0.176701	−	0.984265i	$-0.443457\pi$
$911$	−487451.	−	281430.i	−0.587347	−	0.339105i	−0.764048	+	0.645160i	$0.776791\pi$
$912$	110401.	+	283391.i	0.132735	+	0.340720i
$913$	376684.	+	652436.i	0.451893	+	0.782702i
$914$	631925.	−	364842.i	0.756438	−	0.436730i
$915$	−65557.5	−	52550.6i	−0.0783033	−	0.0627676i
$916$	−107070.	+	185450.i	−0.127608	+	0.221023i
$917$		−	1.35633e6i		−	1.61297i
$918$	−74255.0	+	49809.7i	−0.0881130	+	0.0591056i
$919$	290385.			0.343829			0.171915	−	0.985112i	$-0.445005\pi$
$919$	290385.			0.343829			0.171915	+	0.985112i	$0.445005\pi$
$920$	−25852.0	−	14925.7i	−0.0305435	−	0.0176343i
$921$	21180.7	−	26423.1i	0.0249701	−	0.0311505i
$922$	300103.	+	519794.i	0.353028	+	0.611462i
$923$	−982956.	+	567510.i	−1.15380	+	0.666147i
$924$	626132.	−	243923.i	0.733368	−	0.285699i
$925$	−217725.	+	377111.i	−0.254463	+	0.440743i
$926$			195417.i			0.227898i
$927$	212023.	−	194754.i	0.246731	−	0.226635i
$928$	−79546.6			−0.0923688
$929$	280640.	+	162027.i	0.325176	+	0.187740i	0.653697	−	0.756756i	$-0.273217\pi$
$929$	280640.	+	162027.i	0.325176	+	0.187740i	−0.328522	+	0.944496i	$0.606550\pi$
$930$	84122.4	+	12895.8i	0.0972625	+	0.0149102i
$931$	123168.	+	213334.i	0.142102	+	0.246127i
$932$	276425.	−	159594.i	0.318233	−	0.183732i
$933$	−114418.	+	746373.i	−0.131441	+	0.857418i
$934$	178351.	−	308913.i	0.204447	−	0.354113i
$935$		−	20333.5i		−	0.0232589i
$936$	219967.	+	239473.i	0.251076	+	0.273341i
$937$	−672276.			−0.765717			−0.382859	−	0.923807i	$-0.625060\pi$
$937$	−672276.			−0.765717			−0.382859	+	0.923807i	$0.625060\pi$
$938$	69508.9	+	40131.0i	0.0790014	+	0.0456115i
$939$	−115765.	−	297161.i	−0.131295	−	0.337024i
$940$	15211.1	+	26346.4i	0.0172149	+	0.0298171i
$941$	47102.5	−	27194.6i	0.0531942	−	0.0307117i	−0.473167	−	0.880973i	$-0.656889\pi$
$941$	47102.5	−	27194.6i	0.0531942	−	0.0307117i	0.526361	+	0.850261i	$0.323556\pi$
$942$	−395945.	−	317388.i	−0.446203	−	0.357675i
$943$	178386.	−	308974.i	0.200603	−	0.347455i
$944$		−	252616.i		−	0.283476i
$945$	−31222.4	+	63602.0i	−0.0349625	+	0.0712208i
$946$	−55351.4			−0.0618509
$947$	290380.	+	167651.i	0.323793	+	0.186942i	0.653082	−	0.757287i	$-0.273476\pi$
$947$	290380.	+	167651.i	0.323793	+	0.186942i	−0.329289	+	0.944229i	$0.606809\pi$
$948$	430755.	−	537372.i	0.479307	−	0.597941i
$949$	−283519.	−	491069.i	−0.314811	−	0.545268i
$950$	−802039.	+	463058.i	−0.888686	+	0.513083i
$951$	−1.27888e6	+	498217.i	−1.41407	+	0.550880i
$952$	−21578.3	+	37374.7i	−0.0238091	+	0.0412386i
$953$			1.29405e6i			1.42484i	0.701753	+	0.712421i	$0.252401\pi$
$953$			1.29405e6i			1.42484i	−0.701753	+	0.712421i	$0.747599\pi$
$954$	286711.	+	90020.3i	0.315027	+	0.0989108i
$955$	−91734.0			−0.100583
$956$	−348074.	−	200961.i	−0.380852	−	0.219885i
$957$	−829525.	−	127165.i	−0.905745	−	0.138849i
$958$	−406110.	−	703403.i	−0.442499	−	0.766431i
$959$	418888.	−	241845.i	0.455471	−	0.262966i
$960$	1542.95	−	10065.0i	0.00167421	−	0.0109212i
$961$	−682735.	+	1.18253e6i	−0.739274	+	1.28046i
$962$			352366.i			0.380753i
$963$	43520.1	−	9703.14i	0.0469286	−	0.0104631i
$964$	554087.			0.596243
$965$	114317.	+	66001.2i	0.122760	+	0.0708757i
$966$	242637.	+	622830.i	0.260018	+	0.667445i
$967$	−495246.	−	857790.i	−0.529624	−	0.917336i	−0.999403	−	0.0345516i	$-0.989000\pi$
$967$	−495246.	−	857790.i	−0.529624	−	0.917336i	0.469779	−	0.882784i	$-0.344334\pi$
$968$	−595435.	+	343774.i	−0.635453	+	0.366879i
$969$	−160790.	−	128889.i	−0.171243	−	0.137268i
$970$	−23215.7	+	40210.8i	−0.0246739	+	0.0427365i
$971$		−	1.17055e6i		−	1.24152i	−0.784002	−	0.620758i	$-0.786825\pi$
$971$		−	1.17055e6i		−	1.24152i	0.784002	−	0.620758i	$-0.213175\pi$
$972$	−453120.	+	133553.i	−0.479602	+	0.141358i
$973$	745296.			0.787233
$974$	672779.	+	388429.i	0.709176	+	0.409443i
$975$	−619293.	+	772575.i	−0.651458	+	0.812702i
$976$	−135190.	−	234156.i	−0.141920	−	0.245813i
$977$	454795.	−	262576.i	0.476460	−	0.275084i	−0.242480	−	0.970156i	$-0.577961\pi$
$977$	454795.	−	262576.i	0.476460	−	0.275084i	0.718940	+	0.695072i	$0.244628\pi$
$978$	−188243.	+	73334.2i	−0.196807	+	0.0766706i
$979$	−53260.9	+	92250.7i	−0.0555704	+	0.0962507i
$980$		−	8247.42i		−	0.00858748i
$981$	45158.6	+	202543.i	0.0469248	+	0.210465i
$982$	−898075.			−0.931300
$983$	−1.31637e6	−	760008.i	−1.36230	−	0.786522i	−0.372367	−	0.928086i	$-0.621454\pi$
$983$	−1.31637e6	−	760008.i	−1.36230	−	0.786522i	−0.989929	+	0.141563i	$0.954787\pi$
$984$	120293.	+	18440.8i	0.124237	+	0.0190454i
$985$	−13669.2	−	23675.7i	−0.0140887	−	0.0244023i
$986$	46677.1	−	26949.0i	0.0480120	−	0.0277197i
$987$	103222.	−	673340.i	0.105959	−	0.691194i
$988$	−374706.	+	649010.i	−0.383864	+	0.664871i
$989$		−	55059.5i		−	0.0562911i
$990$	32180.4	−	102493.i	0.0328338	−	0.104574i
$991$	−1.13839e6			−1.15916			−0.579580	−	0.814915i	$-0.696783\pi$
$991$	−1.13839e6			−1.15916			−0.579580	+	0.814915i	$0.696783\pi$
$992$	237180.	+	136936.i	0.241021	+	0.139153i
$993$	−121359.	−	311518.i	−0.123076	−	0.315925i
$994$	−397938.	−	689248.i	−0.402756	−	0.697594i
$995$	32219.9	−	18602.2i	0.0325445	−	0.0187896i
$996$	−199455.	−	159882.i	−0.201060	−	0.161169i
$997$	396715.	−	687130.i	0.399106	−	0.691272i	−0.594510	−	0.804088i	$-0.702654\pi$
$997$	396715.	−	687130.i	0.399106	−	0.691272i	0.993616	+	0.112817i	$0.0359872\pi$
$998$			551890.i			0.554105i
$999$	−459524.	−	225582.i	−0.460445	−	0.226034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.5.d.a.11.4	yes	8
3.2	odd	2		54.5.d.a.35.2		8
4.3	odd	2		144.5.q.b.65.2		8
9.2	odd	6		162.5.b.c.161.7		8
9.4	even	3		54.5.d.a.17.2		8
9.5	odd	6	inner	18.5.d.a.5.4	✓	8
9.7	even	3		162.5.b.c.161.2		8
12.11	even	2		432.5.q.b.305.3		8
36.7	odd	6		1296.5.e.e.161.4		8
36.11	even	6		1296.5.e.e.161.5		8
36.23	even	6		144.5.q.b.113.2		8
36.31	odd	6		432.5.q.b.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.5.d.a.5.4	✓	8	9.5	odd	6	inner
18.5.d.a.11.4	yes	8	1.1	even	1	trivial
54.5.d.a.17.2		8	9.4	even	3
54.5.d.a.35.2		8	3.2	odd	2
144.5.q.b.65.2		8	4.3	odd	2
144.5.q.b.113.2		8	36.23	even	6
162.5.b.c.161.2		8	9.7	even	3
162.5.b.c.161.7		8	9.2	odd	6
432.5.q.b.17.3		8	36.31	odd	6
432.5.q.b.305.3		8	12.11	even	2
1296.5.e.e.161.4		8	36.7	odd	6
1296.5.e.e.161.5		8	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44949 + 1.41421i) q^{2} +(5.62909 - 7.02235i) q^{3} +(4.00000 + 6.92820i) q^{4} +(-1.91371 + 1.10488i) q^{5} +(23.7195 - 9.24044i) q^{6} +(-21.9913 + 38.0900i) q^{7} +22.6274i q^{8} +(-17.6268 - 79.0588i) q^{9} -6.25016 q^{10} +(-183.766 - 106.097i) q^{11} +(71.1686 + 10.9101i) q^{12} +(88.7063 + 153.644i) q^{13} +(-107.735 + 62.2008i) q^{14} +(-3.01358 + 19.6582i) q^{15} +(-32.0000 + 55.4256i) q^{16} -43.3642i q^{17} +(68.6294 - 218.582i) q^{18} +528.015 q^{19} +(-15.3097 - 8.83905i) q^{20} +(143.691 + 368.843i) q^{21} +(-300.089 - 519.769i) q^{22} +(517.028 - 298.506i) q^{23} +(158.898 + 127.372i) q^{24} +(-310.058 + 537.037i) q^{25} +501.799i q^{26} +(-654.401 - 321.247i) q^{27} -351.861 q^{28} +(380.563 + 219.718i) q^{29} +(-35.1827 + 43.8908i) q^{30} +(-756.471 - 1310.25i) q^{31} +(-156.767 + 90.5097i) q^{32} +(-1779.49 + 693.238i) q^{33} +(61.3263 - 106.220i) q^{34} -97.1911i q^{35} +(477.228 - 438.357i) q^{36} +702.206 q^{37} +(1293.37 + 746.726i) q^{38} +(1578.28 + 241.948i) q^{39} +(-25.0006 - 43.3023i) q^{40} +(517.534 - 298.798i) q^{41} +(-169.653 + 1106.69i) q^{42} +(46.1125 - 79.8692i) q^{43} -1697.56i q^{44} +(121.083 + 131.820i) q^{45} +1688.61 q^{46} +(-1490.34 - 860.449i) q^{47} +(209.087 + 536.711i) q^{48} +(233.266 + 404.029i) q^{49} +(-1518.97 + 876.978i) q^{50} +(-304.519 - 244.101i) q^{51} +(-709.650 + 1229.15i) q^{52} +1311.69i q^{53} +(-1148.64 - 1712.36i) q^{54} +468.900 q^{55} +(-861.879 - 497.606i) q^{56} +(2972.24 - 3707.91i) q^{57} +(621.457 + 1076.40i) q^{58} +(-3418.31 + 1973.56i) q^{59} +(-148.250 + 57.7542i) q^{60} +(-2112.34 + 3658.68i) q^{61} -4279.24i q^{62} +(3398.99 + 1067.20i) q^{63} -512.000 q^{64} +(-339.516 - 196.020i) q^{65} +(-5339.23 - 818.496i) q^{66} +(-322.592 - 558.746i) q^{67} +(300.436 - 173.457i) q^{68} +(814.180 - 5311.07i) q^{69} +(137.449 - 238.069i) q^{70} +6397.63i q^{71} +(1788.90 - 398.849i) q^{72} -3196.15 q^{73} +(1720.05 + 993.069i) q^{74} +(2025.92 + 5200.37i) q^{75} +(2112.06 + 3658.20i) q^{76} +(8082.51 - 4666.44i) q^{77} +(3523.80 + 2824.67i) q^{78} +(4782.69 - 8283.86i) q^{79} -141.425i q^{80} +(-5939.59 + 2787.10i) q^{81} +1690.26 q^{82} +(-3074.70 - 1775.18i) q^{83} +(-1980.65 + 2470.89i) q^{84} +(47.9123 + 82.9866i) q^{85} +(225.904 - 130.426i) q^{86} +(3685.16 - 1435.64i) q^{87} +(2400.71 - 4158.15i) q^{88} -502.000i q^{89} +(110.170 + 494.130i) q^{90} -7803.06 q^{91} +(4136.22 + 2388.05i) q^{92} +(-13459.2 - 2063.28i) q^{93} +(-2433.72 - 4215.32i) q^{94} +(-1010.47 + 583.394i) q^{95} +(-246.866 + 1610.36i) q^{96} +(3714.42 - 6433.56i) q^{97} +1319.55i q^{98} +(-5148.73 + 16398.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22}+ \cdots - 22338 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9 - 720 * q^11 - 144 * q^12 + 10 * q^13 + 288 * q^14 + 1134 * q^15 - 256 * q^16 - 384 * q^18 + 100 * q^19 + 144 * q^20 + 438 * q^21 + 336 * q^22 + 1278 * q^23 + 384 * q^24 + 794 * q^25 - 1296 * q^27 - 416 * q^28 - 1854 * q^29 - 3456 * q^30 - 1478 * q^31 - 3384 * q^33 - 96 * q^34 + 1056 * q^36 - 32 * q^37 + 6768 * q^38 + 5274 * q^39 - 36 * q^41 + 2592 * q^42 - 68 * q^43 + 3402 * q^45 + 2112 * q^46 + 2214 * q^47 - 1536 * q^48 + 2442 * q^49 - 15552 * q^50 - 12006 * q^51 - 80 * q^52 + 7056 * q^54 - 3996 * q^55 + 2304 * q^56 + 10902 * q^57 - 2400 * q^58 + 9108 * q^59 + 6480 * q^60 - 4478 * q^61 - 6654 * q^63 - 4096 * q^64 - 22554 * q^65 - 19872 * q^66 + 7504 * q^67 - 11088 * q^68 - 5994 * q^69 + 6048 * q^70 + 5376 * q^72 + 20716 * q^73 + 15264 * q^74 + 16590 * q^75 + 400 * q^76 + 34434 * q^77 + 24096 * q^78 - 6050 * q^79 - 21150 * q^81 + 1152 * q^82 - 3834 * q^83 - 9600 * q^84 - 16092 * q^85 - 12528 * q^86 + 10170 * q^87 - 2688 * q^88 + 2592 * q^90 - 45868 * q^91 + 10224 * q^92 - 10926 * q^93 + 672 * q^94 + 20880 * q^95 + 31336 * q^97 - 22338 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more