LMFDB - Embedded newform 18.5.d.a.5.4

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44949 - 1.41421i) q^{2} +(5.62909 + 7.02235i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-1.91371 - 1.10488i) q^{5} +(23.7195 + 9.24044i) q^{6} +(-21.9913 - 38.0900i) q^{7} -22.6274i q^{8} +(-17.6268 + 79.0588i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	0.461237	−	0.887277i	$-0.347406\pi$
$5$	−1.91371	−	1.10488i	−0.0765485	−	0.0441953i	−0.537786	+	0.843082i	$0.680739\pi$
$6$	23.7195	+	9.24044i	0.658875	+	0.256679i
$7$	−21.9913	−	38.0900i	−0.448802	−	0.777348i	0.549507	−	0.835489i	$-0.314816\pi$
$7$	−21.9913	−	38.0900i	−0.448802	−	0.777348i	−0.998308	+	0.0581419i	$0.981482\pi$
$8$		−	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	−0.518971	+	0.854792i	$0.673685\pi$
$11$	−183.766	+	106.097i	−1.51873	+	0.876838i	−0.999757	+	0.0220466i	$0.992982\pi$
$12$	71.1686	−	10.9101i	0.494226	−	0.0757643i
$13$	88.7063	−	153.644i	0.524889	−	0.909135i	−0.474691	−	0.880153i	$-0.657440\pi$
$13$	88.7063	−	153.644i	0.524889	−	0.909135i	0.999580	−	0.0289822i	$-0.00922662\pi$
$14$	−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	$0.0239035\pi$
$17$			43.3642i			0.150049i	−0.997182	+	0.0750246i	$0.976096\pi$
$18$	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	0.901475	−	0.432832i	$-0.142486\pi$
$23$	517.028	+	298.506i	0.977369	+	0.564284i	0.0758941	+	0.997116i	$0.475819\pi$
$24$	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	−0.256378	−	0.966577i	$-0.582529\pi$
$29$	380.563	−	219.718i	0.452513	−	0.261258i	0.708891	+	0.705318i	$0.249196\pi$
$30$	−35.1827	−	43.8908i	−0.0390918	−	0.0487675i
$31$	−756.471	+	1310.25i	−0.787170	+	1.36342i	0.140523	+	0.990077i	$0.455121\pi$
$31$	−756.471	+	1310.25i	−0.787170	+	1.36342i	−0.927694	+	0.373342i	$0.878212\pi$
$32$	−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	0.645974	−	0.763359i	$-0.276451\pi$
$41$	517.534	+	298.798i	0.307873	+	0.177750i	−0.338101	+	0.941110i	$0.609785\pi$
$42$	−169.653	−	1106.69i	−0.0961754	−	0.627373i
$43$	46.1125	+	79.8692i	0.0249392	+	0.0431959i	0.878226	−	0.478247i	$-0.158727\pi$
$43$	46.1125	+	79.8692i	0.0249392	+	0.0431959i	−0.853286	+	0.521442i	$0.825394\pi$
$44$			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	−0.797843	−	0.602865i	$-0.794026\pi$
$47$	−1490.34	+	860.449i	−0.674668	+	0.389520i	0.123175	+	0.992385i	$0.460692\pi$
$48$	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	$-0.924989\pi$
$53$		−	1311.69i		−	0.466958i	0.972362	−	0.233479i	$-0.0750111\pi$
$54$	−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	−0.0791193	−	0.996865i	$-0.525211\pi$
$59$	−3418.31	−	1973.56i	−0.981990	−	0.566952i	−0.902870	+	0.429913i	$0.858544\pi$
$60$	−148.250	−	57.7542i	−0.0411807	−	0.0160428i
$61$	−2112.34	−	3658.68i	−0.567681	−	0.983253i	−0.996795	−	0.0800020i	$-0.974507\pi$
$61$	−2112.34	−	3658.68i	−0.567681	−	0.983253i	0.429114	−	0.903251i	$-0.358826\pi$
$62$			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	−0.899718	−	0.436472i	$-0.856228\pi$
$67$	−322.592	+	558.746i	−0.0718628	+	0.124470i	0.827855	+	0.560942i	$0.189561\pi$
$68$	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	$-0.781181\pi$
$71$		−	6397.63i		−	1.26912i	0.772874	−	0.634560i	$-0.218819\pi$
$72$	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	0.939538	+	0.342444i	$0.111255\pi$
$79$	4782.69	+	8283.86i	0.766334	+	1.32733i	−0.173204	+	0.984886i	$0.555412\pi$
$80$			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	−0.706275	−	0.707938i	$-0.749626\pi$
$83$	−3074.70	+	1775.18i	−0.446321	+	0.257683i	0.259954	+	0.965621i	$0.416292\pi$
$84$	−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	$0.0100883\pi$
$89$			502.000i			0.0633759i	−0.999498	+	0.0316879i	$0.989912\pi$
$90$	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	0.993072	−	0.117506i	$-0.0374899\pi$
$97$	3714.42	+	6433.56i	0.394773	+	0.683767i	−0.598299	+	0.801273i	$0.704157\pi$
$98$		−	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	−0.538406	−	0.842685i	$-0.680973\pi$
$101$	−793.864	+	458.338i	−0.0778222	+	0.0449307i	0.460584	+	0.887616i	$0.347640\pi$
$102$	−400.705	+	1028.58i	−0.0385145	+	0.0988636i
$103$	1777.12	−	3078.07i	0.167511	−	0.290137i	−0.770033	−	0.638004i	$-0.779760\pi$
$103$	1777.12	−	3078.07i	0.167511	−	0.290137i	0.937544	+	0.347866i	$0.113094\pi$
$104$	−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	$-0.992347\pi$
$107$		−	550.477i		−	0.0480808i	0.999711	−	0.0240404i	$-0.00765304\pi$
$108$	−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	0.991948	−	0.126642i	$-0.0404200\pi$
$113$	17598.8	+	10160.7i	1.37825	+	0.795731i	0.386299	+	0.922374i	$0.373753\pi$
$114$	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	−0.997612	−	0.0690626i	$-0.977999\pi$
$131$	−26706.4	−	15419.0i	−1.55623	−	0.898489i	−0.558616	−	0.829426i	$-0.688667\pi$
$132$	−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	−0.731777	−	0.681545i	$-0.761309\pi$
$137$	−9523.95	+	5498.66i	−0.507430	+	0.292965i	0.224347	+	0.974509i	$0.427975\pi$
$138$	9505.31	+	11858.0i	0.499124	+	0.622663i
$139$	−8472.63	+	14675.0i	−0.438519	+	0.759537i	−0.997576	−	0.0695923i	$-0.977830\pi$
$139$	−8472.63	+	14675.0i	−0.438519	+	0.759537i	0.559056	+	0.829130i	$0.311163\pi$
$140$	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	0.139761	−	0.990185i	$-0.455367\pi$
$149$	−14383.7	−	8304.42i	−0.647885	−	0.374056i	−0.787645	+	0.616129i	$0.788700\pi$
$150$	−2391.97	−	15603.3i	−0.106310	−	0.693481i
$151$	5515.31	+	9552.80i	0.241889	+	0.418964i	0.961252	−	0.275670i	$-0.0888996\pi$
$151$	5515.31	+	9552.80i	0.241889	+	0.418964i	−0.719363	+	0.694634i	$0.755566\pi$
$152$		−	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	−0.994248	−	0.107104i	$-0.965842\pi$
$157$	−9967.29	+	17263.9i	−0.404369	+	0.700388i	0.589879	+	0.807492i	$0.299176\pi$
$158$	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	0.767390	−	0.641180i	$-0.221555\pi$
$167$	16616.5	+	9593.52i	0.595807	+	0.343989i	−0.171583	+	0.985170i	$0.554888\pi$
$168$	−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	0.510184	−	0.860065i	$-0.329577\pi$
$173$	45196.2	−	26094.1i	1.51011	−	0.871865i	0.999930	−	0.0118002i	$-0.00375621\pi$
$174$	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	$-0.939042\pi$
$179$		−	12197.1i		−	0.380672i	0.981719	−	0.190336i	$-0.0609578\pi$
$180$	−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	0.0815609	−	0.996668i	$-0.474009\pi$
$191$	35951.4	−	20756.5i	0.985482	−	0.568968i	0.903921	+	0.427700i	$0.140676\pi$
$192$	−2882.09	−	3595.44i	−0.0781818	−	0.0975326i
$193$	−29868.0	+	51732.9i	−0.801847	+	1.38884i	0.116553	+	0.993184i	$0.462816\pi$
$193$	−29868.0	+	51732.9i	−0.801847	+	1.38884i	−0.918399	+	0.395654i	$0.870518\pi$
$194$	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	$-0.949047\pi$
$197$		−	12371.6i		−	0.318783i	0.987215	−	0.159391i	$-0.0509532\pi$
$198$	−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	−0.492184	−	0.870491i	$-0.663801\pi$
$211$	22606.7	−	39155.9i	0.507776	−	0.879493i	0.999959	−	0.00900203i	$-0.00286547\pi$
$212$	−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	−0.999940	−	0.0109118i	$-0.996527\pi$
$223$	−25333.0	−	43878.0i	−0.509420	−	0.882341i	0.490520	−	0.871430i	$-0.336807\pi$
$224$			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	−0.124299	−	0.992245i	$-0.539668\pi$
$227$	34671.8	−	20017.8i	0.672860	−	0.388476i	0.797159	+	0.603769i	$0.206335\pi$
$228$	37578.1	−	5760.68i	0.722878	−	0.110816i
$229$	13383.7	−	23181.3i	0.255215	−	0.442045i	−0.709739	−	0.704465i	$-0.751187\pi$
$229$	13383.7	−	23181.3i	0.255215	−	0.442045i	0.964954	+	0.262419i	$0.0845204\pi$
$230$	−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	$0.119774\pi$
$233$			39898.5i			0.734927i	−0.930038	+	0.367464i	$0.880226\pi$
$234$	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	0.0682035	−	0.997671i	$-0.478273\pi$
$239$	−43509.3	−	25120.1i	−0.761704	−	0.439770i	−0.829907	+	0.557902i	$0.811607\pi$
$240$	−993.135	+	796.093i	−0.0172419	+	0.0138211i
$241$	34630.4	+	59981.6i	0.596243	+	1.03272i	0.993370	+	0.114960i	$0.0366740\pi$
$241$	34630.4	+	59981.6i	0.596243	+	1.03272i	−0.397127	+	0.917764i	$0.629993\pi$
$242$		−	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	$0.382468\pi$
$251$			117510.i			1.86521i	−0.360904	+	0.932603i	$0.617532\pi$
$252$	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	0.0385699	−	0.999256i	$-0.487720\pi$
$257$	−53336.3	−	30793.7i	−0.807526	−	0.466225i	−0.846096	+	0.533030i	$0.821053\pi$
$258$	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	−0.330853	−	0.943682i	$-0.607336\pi$
$263$	22201.4	−	12818.0i	0.320974	−	0.185314i	0.651827	+	0.758368i	$0.274003\pi$
$264$	−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	$-0.838155\pi$
$269$		−	70454.4i		−	0.973652i	0.873499	−	0.486826i	$-0.161845\pi$
$270$	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	0.971747	+	0.236023i	$0.0758441\pi$
$277$	52964.2	+	91736.6i	0.690276	+	1.19559i	−0.281472	+	0.959570i	$0.590823\pi$
$278$			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	−0.503964	−	0.863725i	$-0.668125\pi$
$281$	−626.791	+	361.878i	−0.00793798	+	0.00458300i	0.496026	+	0.868308i	$0.334792\pi$
$282$	−43301.1	+	6638.00i	−0.544503	+	0.0834716i
$283$	10787.6	−	18684.6i	0.134695	−	0.233299i	−0.790786	−	0.612093i	$-0.790328\pi$
$283$	10787.6	−	18684.6i	0.134695	−	0.233299i	0.925481	+	0.378794i	$0.123661\pi$
$284$	−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	0.923132	−	0.384484i	$-0.125621\pi$
$293$	90289.5	+	52128.7i	1.05172	+	0.607213i	0.128593	+	0.991697i	$0.458954\pi$
$294$	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	0.0749146	−	0.997190i	$-0.476132\pi$
$311$	−72658.7	−	41949.5i	−0.751220	−	0.433717i	−0.826135	+	0.563473i	$0.809465\pi$
$312$	−5474.65	−	35712.3i	−0.0562402	−	0.366867i
$313$	17717.5	+	30687.5i	0.180848	+	0.313237i	0.942169	−	0.335137i	$-0.108783\pi$
$313$	17717.5	+	30687.5i	0.180848	+	0.313237i	−0.761322	+	0.648374i	$0.775449\pi$
$314$			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	−0.982799	−	0.184677i	$-0.940876\pi$
$317$	−132069.	+	76250.1i	−1.31426	+	0.758791i	−0.331465	+	0.943468i	$0.607543\pi$
$318$	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	0.938253	−	0.345949i	$-0.112443\pi$
$331$	18573.5	+	32170.2i	0.169526	+	0.293628i	−0.768727	+	0.639577i	$0.779110\pi$
$332$			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	−0.758446	−	0.651736i	$-0.774041\pi$
$337$	21032.6	−	36429.5i	0.185197	−	0.320770i	0.943643	+	0.330966i	$0.107374\pi$
$338$	−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	0.0636189	−	0.997974i	$-0.479736\pi$
$347$	−92575.6	−	53448.5i	−0.768843	−	0.443892i	−0.832462	+	0.554083i	$0.813069\pi$
$348$	24687.0	−	19789.0i	0.203850	−	0.163405i
$349$	−94844.8	−	164276.i	−0.778686	−	1.34872i	−0.932699	−	0.360655i	$-0.882553\pi$
$349$	−94844.8	−	164276.i	−0.778686	−	1.34872i	0.154013	−	0.988069i	$-0.450780\pi$
$350$			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	−0.999994	−	0.00352519i	$-0.998878\pi$
$353$	−186532.	+	107694.i	−1.49694	+	0.864257i	−0.496944	+	0.867783i	$0.665545\pi$
$354$	−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	$0.149661\pi$
$359$			116777.i			0.906085i	−0.891489	+	0.453043i	$0.850339\pi$
$360$	−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	0.530852	−	0.847464i	$-0.321872\pi$
$367$	−63101.8	−	109295.i	−0.468500	−	0.811465i	−0.999352	+	0.0359992i	$0.988539\pi$
$368$		−	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	−0.993796	−	0.111218i	$-0.964525\pi$
$373$	−55732.4	+	96531.3i	−0.400581	+	0.693826i	0.593215	+	0.805044i	$0.297858\pi$
$374$	−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	0.706347	−	0.707865i	$-0.250342\pi$
$383$	65495.5	+	37813.8i	0.446492	+	0.257782i	−0.259856	+	0.965648i	$0.583675\pi$
$384$	−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	0.574874	−	0.818242i	$-0.305051\pi$
$389$	237715.	−	137245.i	1.57093	−	0.906977i	0.996055	−	0.0887346i	$-0.0282823\pi$
$390$	−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	0.455432	−	0.890271i	$-0.349485\pi$
$401$	−14126.3	−	8155.82i	−0.0878496	−	0.0507200i	−0.543281	+	0.839551i	$0.682818\pi$
$402$	−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	−0.854621	−	0.519252i	$-0.826210\pi$
$409$	3742.95	−	6482.97i	0.0223752	−	0.0387550i	0.876996	+	0.480497i	$0.159544\pi$
$410$	−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	0.206446	−	0.978458i	$-0.433810\pi$
$419$	−94399.3	−	54501.5i	−0.537701	−	0.310442i	−0.744147	+	0.668016i	$0.767144\pi$
$420$	1060.36	+	6916.96i	0.00601111	+	0.0392118i
$421$	−165636.	−	286890.i	−0.934525	−	1.61865i	−0.775478	−	0.631374i	$-0.782491\pi$
$421$	−165636.	−	286890.i	−0.934525	−	1.61865i	−0.159047	−	0.987271i	$-0.550842\pi$
$422$		−	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	$-0.740601\pi$
$431$		−	270347.i		−	1.45535i	0.685922	−	0.727675i	$-0.259399\pi$
$432$	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	0.965781	−	0.259360i	$-0.0835117\pi$
$439$	49775.5	+	86213.8i	0.258278	+	0.447350i	−0.707503	+	0.706710i	$0.750178\pi$
$440$		−	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	0.0776111	−	0.996984i	$-0.475271\pi$
$443$	192291.	−	111019.i	0.979830	−	0.565705i	0.902219	+	0.431279i	$0.141937\pi$
$444$	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	$0.340955\pi$
$449$			353910.i			1.75550i	−0.479122	+	0.877749i	$0.659045\pi$
$450$	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	0.989917	+	0.141647i	$0.0452399\pi$
$457$	128991.	+	223419.i	0.617629	+	1.06976i	−0.372288	+	0.928117i	$0.621427\pi$
$458$		−	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	−0.000858089	−	1.00000i	$-0.500273\pi$
$461$	183775.	−	106103.i	0.864738	−	0.499257i	0.865596	+	0.500743i	$0.166940\pi$
$462$	148593.	+	185371.i	0.696169	+	0.868478i
$463$	34545.2	−	59834.0i	0.161148	−	0.279117i	−0.774133	−	0.633024i	$-0.781814\pi$
$463$	34545.2	−	59834.0i	0.161148	−	0.279117i	0.935281	+	0.353907i	$0.115147\pi$
$464$	−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	$0.0933667\pi$
$467$			126113.i			0.578264i	−0.957289	+	0.289132i	$0.906633\pi$
$468$	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	−0.931945	−	0.362599i	$-0.881889\pi$
$479$	−248690.	+	143582.i	−1.08390	+	0.625788i	−0.151952	+	0.988388i	$0.548556\pi$
$480$	−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	−0.194024	−	0.980997i	$-0.562154\pi$
$491$	−274978.	−	158759.i	−1.14060	−	0.658528i	−0.946580	+	0.322469i	$0.895487\pi$
$492$	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	−0.600877	−	0.799341i	$-0.705182\pi$
$499$	97561.4	−	168981.i	0.391811	−	0.678637i	0.992688	+	0.120704i	$0.0385153\pi$
$500$	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	$0.0134490\pi$
$503$			21373.6i			0.0844777i	−0.999108	+	0.0422388i	$0.986551\pi$
$504$	−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	0.360543	−	0.932743i	$-0.382592\pi$
$509$	−69165.6	−	39932.8i	−0.266965	−	0.154132i	−0.627508	+	0.778610i	$0.715925\pi$
$510$	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	$0.0846839\pi$
$521$			142732.i			0.525830i	−0.964819	+	0.262915i	$0.915316\pi$
$522$	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	0.998940	−	0.0460355i	$-0.0146587\pi$
$547$	137517.	+	238187.i	0.459602	+	0.796054i	−0.539338	+	0.842090i	$0.681325\pi$
$548$			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	$-0.828363\pi$
$557$		−	318602.i		−	1.02692i	0.858112	−	0.513462i	$-0.171637\pi$
$558$	−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	0.433612	−	0.901100i	$-0.357239\pi$
$563$	−41192.5	−	23782.5i	−0.129958	−	0.0750311i	−0.563569	+	0.826069i	$0.690572\pi$
$564$	−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	−0.0177144	−	0.999843i	$-0.505639\pi$
$569$	271738.	−	156888.i	0.839318	−	0.484580i	0.857032	+	0.515263i	$0.172306\pi$
$570$	−18577.0	−	23175.0i	−0.0571775	−	0.0713296i
$571$	−162047.	+	280674.i	−0.497015	+	0.860856i	−0.999994	−	0.00344295i	$-0.998904\pi$
$571$	−162047.	+	280674.i	−0.497015	+	0.860856i	0.502979	+	0.864299i	$0.332237\pi$
$572$	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	−0.545734	−	0.837959i	$-0.683749\pi$
$587$	−32013.0	+	18482.7i	−0.0929073	+	0.0536400i	0.452827	+	0.891599i	$0.350416\pi$
$588$	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	$-0.997312\pi$
$593$		−	5939.58i		−	0.0168906i	0.999964	−	0.00844532i	$-0.00268826\pi$
$594$	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	0.676651	−	0.736304i	$-0.263431\pi$
$599$	135382.	+	78162.8i	0.377318	+	0.217845i	−0.299333	+	0.954149i	$0.596764\pi$
$600$	−117671.	−	45841.2i	−0.326864	−	0.127337i
$601$	−70819.1	−	122662.i	−0.196066	−	0.339596i	0.751184	−	0.660093i	$-0.229483\pi$
$601$	−70819.1	−	122662.i	−0.196066	−	0.339596i	−0.947249	+	0.320498i	$0.896150\pi$
$602$		−	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	−0.988485	−	0.151320i	$-0.951648\pi$
$607$	−133819.	+	231782.i	−0.363196	+	0.629074i	0.625289	+	0.780393i	$0.284981\pi$
$608$	−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	−0.00477496	−	0.999989i	$-0.501520\pi$
$617$	−332409.	−	191917.i	−0.873178	−	0.504130i	−0.868403	+	0.495859i	$0.834853\pi$
$618$	70595.2	−	56588.8i	0.184841	−	0.148168i
$619$	−60619.2	−	104996.i	−0.158208	−	0.274025i	0.776014	−	0.630715i	$-0.217238\pi$
$619$	−60619.2	−	104996.i	−0.158208	−	0.274025i	−0.934223	+	0.356691i	$0.883905\pi$
$620$		−	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	0.245312	−	0.969444i	$-0.421110\pi$
$641$	496152.	−	286453.i	1.20753	−	0.697168i	0.962219	+	0.272276i	$0.0877763\pi$
$642$	5086.66	−	13057.0i	0.0123413	−	0.0316792i
$643$	224632.	−	389074.i	0.543313	−	0.941046i	−0.455398	−	0.890288i	$-0.650503\pi$
$643$	224632.	−	389074.i	0.543313	−	0.941046i	0.998711	−	0.0507578i	$-0.0161637\pi$
$644$	−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	$0.204979\pi$
$647$			502638.i			1.20073i	−0.799725	+	0.600366i	$0.795021\pi$
$648$	−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	−0.402859	−	0.915262i	$-0.631983\pi$
$653$	−595663.	−	343906.i	−1.39693	−	0.806517i	−0.994070	+	0.108745i	$0.965317\pi$
$654$	−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	−0.743698	−	0.668516i	$-0.766930\pi$
$659$	−233033.	+	134542.i	−0.536595	+	0.309803i	0.207103	+	0.978319i	$0.433597\pi$
$660$	33371.0	−	5115.73i	0.0766093	−	0.0117441i
$661$	200626.	−	347494.i	0.459181	−	0.795324i	−0.539737	−	0.841834i	$-0.681476\pi$
$661$	200626.	−	347494.i	0.459181	−	0.795324i	0.998918	+	0.0465092i	$0.0148097\pi$
$662$	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	0.919782	−	0.392429i	$-0.128365\pi$
$673$	54368.5	+	94169.0i	0.120038	+	0.207911i	−0.799745	+	0.600340i	$0.795032\pi$
$674$		−	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	−0.587108	−	0.809509i	$-0.699734\pi$
$677$	−82318.9	+	47526.9i	−0.179607	+	0.103696i	0.407501	+	0.913205i	$0.366400\pi$
$678$	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	$-0.727644\pi$
$683$		−	704385.i		−	1.50997i	0.655741	−	0.754986i	$-0.272356\pi$
$684$	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	−0.791997	−	0.610525i	$-0.790959\pi$
$691$	−441540.	−	764770.i	−0.924729	−	1.60168i	−0.132731	−	0.991152i	$-0.542375\pi$
$692$		−	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	$0.258542\pi$
$701$			713342.i			1.45165i	−0.687879	+	0.725825i	$0.741458\pi$
$702$	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	0.824346	−	0.566086i	$-0.191543\pi$
$709$	−39245.0	−	67974.3i	−0.0780713	−	0.135223i	−0.902418	+	0.430862i	$0.858210\pi$
$710$			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	$-0.954836\pi$
$719$		−	146207.i		−	0.282820i	0.989951	−	0.141410i	$-0.0451636\pi$
$720$	−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	−0.978693	−	0.205328i	$-0.934174\pi$
$727$	−352617.	−	610750.i	−0.667166	−	1.15557i	0.311527	−	0.950237i	$-0.399159\pi$
$728$			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	−0.920555	−	0.390612i	$-0.872263\pi$
$733$	−65548.2	+	113533.i	−0.121998	+	0.211307i	0.798558	+	0.601919i	$0.205597\pi$
$734$	−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	0.982952	−	0.183865i	$-0.0588608\pi$
$743$	726053.	+	419187.i	1.31520	+	0.759329i	0.332244	+	0.943193i	$0.392194\pi$
$744$	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	−0.969696	−	0.244314i	$-0.921437\pi$
$751$	−154122.	+	266948.i	−0.273266	+	0.473311i	0.696430	+	0.717625i	$0.254771\pi$
$752$	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	0.666981	−	0.745075i	$-0.267586\pi$
$761$	205714.	+	118769.i	0.355218	+	0.205085i	−0.311763	+	0.950160i	$0.600920\pi$
$762$	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	0.407896	+	0.913029i	$0.366263\pi$
$769$	−346986.	+	600997.i	−0.586758	+	1.01629i	−0.994654	+	0.103266i	$0.967071\pi$
$770$	−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	$0.0283816\pi$
$773$			106414.i			0.178091i	−0.996028	+	0.0890454i	$0.971618\pi$
$774$	−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	−0.902422	−	0.430853i	$-0.858213\pi$
$787$	−48361.5	+	83764.7i	−0.0780820	+	0.135242i	0.824340	+	0.566094i	$0.191546\pi$
$788$	−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	0.823877	−	0.566768i	$-0.191806\pi$
$797$	473218.	+	273213.i	0.744980	+	0.430115i	−0.0788969	+	0.996883i	$0.525140\pi$
$798$	−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	$-0.883633\pi$
$809$		−	467941.i		−	0.714981i	0.933917	−	0.357490i	$-0.116367\pi$
$810$	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	−0.162995	−	0.986627i	$-0.552115\pi$
$821$	411132.	−	237367.i	0.609952	−	0.352156i	0.772947	+	0.634471i	$0.218782\pi$
$822$	−276713.	+	42419.8i	−0.409531	+	0.0627805i
$823$	599334.	−	1.03808e6i	0.884849	−	1.53260i	0.0389627	−	0.999241i	$-0.487595\pi$
$823$	599334.	−	1.03808e6i	0.884849	−	1.53260i	0.845886	−	0.533363i	$-0.179072\pi$
$824$	−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	$0.0532454\pi$
$827$			227743.i			0.332993i	−0.986042	+	0.166496i	$0.946755\pi$
$828$	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	−0.887102	−	0.461573i	$-0.847285\pi$
$839$	−655294.	+	378334.i	−0.930920	+	0.537467i	−0.0438177	+	0.999040i	$0.513952\pi$
$840$	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	0.992017	−	0.126105i	$-0.0402477\pi$
$853$	281438.	+	487465.i	0.386798	+	0.669954i	−0.605219	+	0.796059i	$0.706914\pi$
$854$			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	0.109874	−	0.993945i	$-0.464955\pi$
$857$	753246.	−	434887.i	1.02559	−	0.592127i	0.915719	+	0.401819i	$0.131622\pi$
$858$	−347866.	+	892945.i	−0.472539	+	1.21297i
$859$	−211385.	+	366130.i	−0.286476	+	0.496191i	−0.972966	−	0.230948i	$-0.925817\pi$
$859$	−211385.	+	366130.i	−0.286476	+	0.496191i	0.686490	+	0.727139i	$0.259151\pi$
$860$	−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	$-0.648255\pi$
$863$		−	1.33087e6i		−	1.78696i	0.449100	−	0.893482i	$-0.351745\pi$
$864$	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	−0.0679561	−	0.997688i	$-0.521648\pi$
$877$	638412.	−	1.10576e6i	0.830045	−	1.43768i	0.898001	−	0.439992i	$-0.145019\pi$
$878$	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	$0.0838194\pi$
$881$			404060.i			0.520588i	−0.965529	+	0.260294i	$0.916181\pi$
$882$	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	0.559064	−	0.829125i	$-0.311161\pi$
$887$	94847.0	+	54759.9i	0.120552	+	0.0696010i	−0.438511	+	0.898726i	$0.644494\pi$
$888$	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	0.863294	+	0.504702i	$0.168397\pi$
$907$	714661.	+	1.23783e6i	0.868731	+	1.50469i	0.00543754	+	0.999985i	$0.498269\pi$
$908$		−	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	−0.764048	−	0.645160i	$-0.776791\pi$
$911$	−487451.	+	281430.i	−0.587347	+	0.339105i	0.176701	+	0.984265i	$0.443457\pi$
$912$	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	−0.328522	−	0.944496i	$-0.606550\pi$
$929$	280640.	−	162027.i	0.325176	−	0.187740i	0.653697	+	0.756756i	$0.273217\pi$
$930$	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	0.526361	−	0.850261i	$-0.323556\pi$
$941$	47102.5	+	27194.6i	0.0531942	+	0.0307117i	−0.473167	+	0.880973i	$0.656889\pi$
$942$	−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	−0.329289	−	0.944229i	$-0.606809\pi$
$947$	290380.	−	167651.i	0.323793	−	0.186942i	0.653082	+	0.757287i	$0.273476\pi$
$948$	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	$-0.747599\pi$
$953$		−	1.29405e6i		−	1.42484i	0.701753	−	0.712421i	$-0.252401\pi$
$954$	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	0.469779	+	0.882784i	$0.344334\pi$
$967$	−495246.	+	857790.i	−0.529624	+	0.917336i	−0.999403	+	0.0345516i	$0.989000\pi$
$968$	−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	$0.213175\pi$
$971$			1.17055e6i			1.24152i	−0.784002	+	0.620758i	$0.786825\pi$
$972$	−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	0.718940	−	0.695072i	$-0.244628\pi$
$977$	454795.	+	262576.i	0.476460	+	0.275084i	−0.242480	+	0.970156i	$0.577961\pi$
$978$	−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	−0.989929	−	0.141563i	$-0.954787\pi$
$983$	−1.31637e6	+	760008.i	−1.36230	+	0.786522i	−0.372367	+	0.928086i	$0.621454\pi$
$984$	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	0.993616	−	0.112817i	$-0.0359872\pi$
$997$	396715.	+	687130.i	0.399106	+	0.691272i	−0.594510	+	0.804088i	$0.702654\pi$
$998$		−	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.5.4	✓	8
3.2	odd	2		54.5.d.a.17.2		8
4.3	odd	2		144.5.q.b.113.2		8
9.2	odd	6	inner	18.5.d.a.11.4	yes	8
9.4	even	3		162.5.b.c.161.7		8
9.5	odd	6		162.5.b.c.161.2		8
9.7	even	3		54.5.d.a.35.2		8
12.11	even	2		432.5.q.b.17.3		8
36.7	odd	6		432.5.q.b.305.3		8
36.11	even	6		144.5.q.b.65.2		8
36.23	even	6		1296.5.e.e.161.4		8
36.31	odd	6		1296.5.e.e.161.5		8

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

\(f(q)\)	\(=\)	\(q+(2.44949 - 1.41421i) q^{2} +(5.62909 + 7.02235i) q^{3} +(4.00000 - 6.92820i) q^{4} +(-1.91371 - 1.10488i) q^{5} +(23.7195 + 9.24044i) q^{6} +(-21.9913 - 38.0900i) q^{7} -22.6274i q^{8} +(-17.6268 + 79.0588i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 32 * q^4 + 18 * q^5 + 48 * q^6 - 26 * q^7 - 78 * q^9	\( 8 q + 6 q^{3} + 32 q^{4} + 18 q^{5} + 48 q^{6} - 26 q^{7} - 78 q^{9} - 720 q^{11} - 144 q^{12} + 10 q^{13} + 288 q^{14} + 1134 q^{15} - 256 q^{16} - 384 q^{18} + 100 q^{19} + 144 q^{20} + 438 q^{21} + 336 q^{22} + 1278 q^{23} + 384 q^{24} + 794 q^{25} - 1296 q^{27} - 416 q^{28} - 1854 q^{29} - 3456 q^{30} - 1478 q^{31} - 3384 q^{33} - 96 q^{34} + 1056 q^{36} - 32 q^{37} + 6768 q^{38} + 5274 q^{39} - 36 q^{41} + 2592 q^{42} - 68 q^{43} + 3402 q^{45} + 2112 q^{46} + 2214 q^{47} - 1536 q^{48} + 2442 q^{49} - 15552 q^{50} - 12006 q^{51} - 80 q^{52} + 7056 q^{54} - 3996 q^{55} + 2304 q^{56} + 10902 q^{57} - 2400 q^{58} + 9108 q^{59} + 6480 q^{60} - 4478 q^{61} - 6654 q^{63} - 4096 q^{64} - 22554 q^{65} - 19872 q^{66} + 7504 q^{67} - 11088 q^{68} - 5994 q^{69} + 6048 q^{70} + 5376 q^{72} + 20716 q^{73} + 15264 q^{74} + 16590 q^{75} + 400 q^{76} + 34434 q^{77} + 24096 q^{78} - 6050 q^{79} - 21150 q^{81} + 1152 q^{82} - 3834 q^{83} - 9600 q^{84} - 16092 q^{85} - 12528 q^{86} + 10170 q^{87} - 2688 q^{88} + 2592 q^{90} - 45868 q^{91} + 10224 q^{92} - 10926 q^{93} + 672 q^{94} + 20880 q^{95} + 31336 q^{97} - 22338 q^{99}+O(q^{100}) \) 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

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