LMFDB - Embedded newform 38.6.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	38.25
Dual form			38.6.e.b.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.06418 - 2.57115i) q^{2} +(-24.7753 - 9.01748i) q^{3} +(2.77837 - 15.7569i) q^{4} +(14.6771 + 83.2381i) q^{5} +(-99.1013 + 36.0699i) q^{6} +(-7.63036 + 13.2162i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(346.353 + 290.625i) q^{9} +O(q^{10})$	\(q+(3.06418 - 2.57115i) q^{2} +(-24.7753 - 9.01748i) q^{3} +(2.77837 - 15.7569i) q^{4} +(14.6771 + 83.2381i) q^{5} +(-99.1013 + 36.0699i) q^{6} +(-7.63036 + 13.2162i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(346.353 + 290.625i) q^{9} +(258.991 + 217.319i) q^{10} +(225.199 + 390.055i) q^{11} +(-210.923 + 365.329i) q^{12} +(-754.055 + 274.454i) q^{13} +(10.6000 + 60.1155i) q^{14} +(386.967 - 2194.60i) q^{15} +(-240.561 - 87.5572i) q^{16} +(-1019.05 + 855.086i) q^{17} +1808.53 q^{18} +(-1505.05 - 459.273i) q^{19} +1352.35 q^{20} +(308.221 - 258.628i) q^{21} +(1692.94 + 616.180i) q^{22} +(65.9455 - 373.996i) q^{23} +(293.011 + 1661.75i) q^{24} +(-3776.62 + 1374.58i) q^{25} +(-1604.90 + 2779.76i) q^{26} +(-2756.91 - 4775.11i) q^{27} +(187.046 + 156.951i) q^{28} +(6383.20 + 5356.14i) q^{29} +(-4456.91 - 7719.60i) q^{30} +(3343.54 - 5791.19i) q^{31} +(-962.245 + 350.229i) q^{32} +(-2062.05 - 11694.5i) q^{33} +(-924.001 + 5240.27i) q^{34} +(-1212.08 - 441.161i) q^{35} +(5541.65 - 4649.99i) q^{36} -4855.55 q^{37} +(-5792.59 + 2462.41i) q^{38} +21156.8 q^{39} +(4143.85 - 3477.11i) q^{40} +(-11819.7 - 4302.01i) q^{41} +(279.472 - 1584.97i) q^{42} +(2557.11 + 14502.1i) q^{43} +(6771.76 - 2464.72i) q^{44} +(-19107.6 + 33095.3i) q^{45} +(-759.530 - 1315.54i) q^{46} +(-9450.14 - 7929.61i) q^{47} +(5170.44 + 4338.51i) q^{48} +(8287.06 + 14353.6i) q^{49} +(-8037.98 + 13922.2i) q^{50} +(32958.1 - 11995.8i) q^{51} +(2229.50 + 12644.1i) q^{52} +(286.317 - 1623.79i) q^{53} +(-20725.2 - 7543.36i) q^{54} +(-29162.2 + 24470.0i) q^{55} +976.687 q^{56} +(33146.6 + 24950.4i) q^{57} +33330.7 q^{58} +(4241.71 - 3559.22i) q^{59} +(-33505.0 - 12194.8i) q^{60} +(5837.77 - 33107.6i) q^{61} +(-4644.80 - 26342.0i) q^{62} +(-6483.75 + 2359.89i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-33912.3 - 58737.9i) q^{65} +(-36386.7 - 30532.1i) q^{66} +(824.112 + 691.512i) q^{67} +(10642.2 + 18432.9i) q^{68} +(-5006.32 + 8671.20i) q^{69} +(-4848.32 + 1764.65i) q^{70} +(4281.36 + 24280.8i) q^{71} +(5024.76 - 28496.8i) q^{72} +(46793.6 + 17031.5i) q^{73} +(-14878.3 + 12484.4i) q^{74} +105962. q^{75} +(-11418.3 + 22438.9i) q^{76} -6873.39 q^{77} +(64828.3 - 54397.4i) q^{78} +(-28912.3 - 10523.2i) q^{79} +(3757.34 - 21308.9i) q^{80} +(6165.55 + 34966.6i) q^{81} +(-47278.7 + 17208.0i) q^{82} +(-18807.0 + 32574.7i) q^{83} +(-3218.84 - 5575.19i) q^{84} +(-86132.4 - 72273.7i) q^{85} +(45122.4 + 37862.2i) q^{86} +(-109847. - 190260. i) q^{87} +(14412.7 - 24963.5i) q^{88} +(87151.9 - 31720.7i) q^{89} +(26543.9 + 150538. i) q^{90} +(2126.49 - 12059.9i) q^{91} +(-5709.80 - 2078.20i) q^{92} +(-135059. + 113328. i) q^{93} -49345.1 q^{94} +(16139.2 - 132018. i) q^{95} +26998.1 q^{96} +(-87838.7 + 73705.4i) q^{97} +(62298.3 + 22674.7i) q^{98} +(-35361.5 + 200545. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) $ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	3.06418	−	2.57115i	0.541675	−	0.454519i
$2$	3.06418	−	2.57115i	0.541675	−	0.454519i
$3$	−24.7753	−	9.01748i	−1.58934	−	0.578472i	−0.612130	−	0.790757i	$-0.709687\pi$
$3$	−24.7753	−	9.01748i	−1.58934	−	0.578472i	−0.977208	+	0.212286i	$0.931909\pi$
$4$	2.77837	−	15.7569i	0.0868241	−	0.492404i
$5$	14.6771	+	83.2381i	0.262552	+	1.48901i	0.775916	+	0.630836i	$0.217288\pi$
$5$	14.6771	+	83.2381i	0.262552	+	1.48901i	−0.513364	+	0.858171i	$0.671601\pi$
$6$	−99.1013	+	36.0699i	−1.12383	+	0.409041i
$7$	−7.63036	+	13.2162i	−0.0588573	+	0.101944i	−0.893953	−	0.448161i	$-0.852079\pi$
$7$	−7.63036	+	13.2162i	−0.0588573	+	0.101944i	0.835095	+	0.550105i	$0.185412\pi$
$8$	−32.0000	−	55.4256i	−0.176777	−	0.306186i
$9$	346.353	+	290.625i	1.42532	+	1.19599i
$10$	258.991	+	217.319i	0.819001	+	0.687223i
$11$	225.199	+	390.055i	0.561156	+	0.971952i	0.997396	+	0.0721209i	$0.0229767\pi$
$11$	225.199	+	390.055i	0.561156	+	0.971952i	−0.436239	+	0.899831i	$0.643690\pi$
$12$	−210.923	+	365.329i	−0.422834	+	0.732371i
$13$	−754.055	+	274.454i	−1.23750	+	0.450413i	−0.876159	−	0.482022i	$-0.839903\pi$
$13$	−754.055	+	274.454i	−1.23750	+	0.450413i	−0.361339	+	0.932434i	$0.617680\pi$
$14$	10.6000	+	60.1155i	0.0144539	+	0.0819722i
$15$	386.967	−	2194.60i	0.444065	−	2.51841i
$16$	−240.561	−	87.5572i	−0.234923	−	0.0855050i
$17$	−1019.05	+	855.086i	−0.855212	+	0.717608i	−0.960931	−	0.276788i	$-0.910730\pi$
$17$	−1019.05	+	855.086i	−0.855212	+	0.717608i	0.105719	+	0.994396i	$0.466286\pi$
$18$	1808.53			1.31566
$19$	−1505.05	−	459.273i	−0.956459	−	0.291868i
$19$	−1505.05	−	459.273i	−0.956459	−	0.291868i
$20$	1352.35			0.755989
$21$	308.221	−	258.628i	0.152516	−	0.127976i
$22$	1692.94	+	616.180i	0.745735	+	0.271426i
$23$	65.9455	−	373.996i	0.0259936	−	0.147417i	−0.969049	−	0.246870i	$-0.920598\pi$
$23$	65.9455	−	373.996i	0.0259936	−	0.147417i	0.995042	+	0.0994527i	$0.0317092\pi$
$24$	293.011	+	1661.75i	0.103838	+	0.588894i
$25$	−3776.62	+	1374.58i	−1.20852	+	0.439864i
$26$	−1604.90	+	2779.76i	−0.465601	+	0.806444i
$27$	−2756.91	−	4775.11i	−0.727803	−	1.26059i
$28$	187.046	+	156.951i	0.0450873	+	0.0378327i
$29$	6383.20	+	5356.14i	1.40943	+	1.18265i	0.956726	+	0.290990i	$0.0939846\pi$
$29$	6383.20	+	5356.14i	1.40943	+	1.18265i	0.452703	+	0.891661i	$0.350460\pi$
$30$	−4456.91	−	7719.60i	−0.904130	−	1.56600i
$31$	3343.54	−	5791.19i	0.624889	−	1.08234i	−0.363674	−	0.931526i	$-0.618478\pi$
$31$	3343.54	−	5791.19i	0.624889	−	1.08234i	0.988562	−	0.150813i	$-0.0481890\pi$
$32$	−962.245	+	350.229i	−0.166116	+	0.0604612i
$33$	−2062.05	−	11694.5i	−0.329621	−	1.86937i
$34$	−924.001	+	5240.27i	−0.137080	+	0.777421i
$35$	−1212.08	−	441.161i	−0.167248	−	0.0608734i
$36$	5541.65	−	4649.99i	0.712660	−	0.597993i
$37$	−4855.55			−0.583088			−0.291544	−	0.956557i	$-0.594169\pi$
$37$	−4855.55			−0.583088			−0.291544	+	0.956557i	$0.594169\pi$
$38$	−5792.59	+	2462.41i	−0.650750	+	0.276631i
$39$	21156.8			2.22735
$40$	4143.85	−	3477.11i	0.409501	−	0.343612i
$41$	−11819.7	−	4302.01i	−1.09811	−	0.399679i	−0.271491	−	0.962441i	$-0.587517\pi$
$41$	−11819.7	−	4302.01i	−1.09811	−	0.399679i	−0.826619	+	0.562762i	$0.809739\pi$
$42$	279.472	−	1584.97i	0.0244465	−	0.138643i
$43$	2557.11	+	14502.1i	0.210900	+	1.19608i	0.887880	+	0.460074i	$0.152177\pi$
$43$	2557.11	+	14502.1i	0.210900	+	1.19608i	−0.676980	+	0.736001i	$0.736712\pi$
$44$	6771.76	−	2464.72i	0.527315	−	0.191927i
$45$	−19107.6	+	33095.3i	−1.40661	+	2.43632i
$46$	−759.530	−	1315.54i	−0.0529237	−	0.0916666i
$47$	−9450.14	−	7929.61i	−0.624013	−	0.523609i	0.275049	−	0.961430i	$-0.411306\pi$
$47$	−9450.14	−	7929.61i	−0.624013	−	0.523609i	−0.899062	+	0.437821i	$0.855750\pi$
$48$	5170.44	+	4338.51i	0.323910	+	0.271793i
$49$	8287.06	+	14353.6i	0.493072	+	0.854025i
$50$	−8037.98	+	13922.2i	−0.454697	+	0.787558i
$51$	32958.1	−	11995.8i	1.77434	−	0.645806i
$52$	2229.50	+	12644.1i	0.114340	+	0.648456i
$53$	286.317	−	1623.79i	0.0140010	−	0.0794034i	−0.977007	−	0.213209i	$-0.931609\pi$
$53$	286.317	−	1623.79i	0.0140010	−	0.0794034i	0.991008	+	0.133805i	$0.0427197\pi$
$54$	−20725.2	−	7543.36i	−0.967196	−	0.352031i
$55$	−29162.2	+	24470.0i	−1.29991	+	1.09075i
$56$	976.687			0.0416184
$57$	33146.6	+	24950.4i	1.35130	+	1.01716i
$58$	33330.7			1.30099
$59$	4241.71	−	3559.22i	0.158639	−	0.133114i	−0.560013	−	0.828484i	$-0.689204\pi$
$59$	4241.71	−	3559.22i	0.158639	−	0.133114i	0.718652	+	0.695370i	$0.244759\pi$
$60$	−33505.0	−	12194.8i	−1.20152	−	0.437318i
$61$	5837.77	−	33107.6i	0.200873	−	1.13921i	−0.702929	−	0.711260i	$-0.748125\pi$
$61$	5837.77	−	33107.6i	0.200873	−	1.13921i	0.903803	−	0.427949i	$-0.140764\pi$
$62$	−4644.80	−	26342.0i	−0.153457	−	0.870300i
$63$	−6483.75	+	2359.89i	−0.205814	+	0.0749101i
$64$	−2048.00	+	3547.24i	−0.0625000	+	0.108253i
$65$	−33912.3	−	58737.9i	−0.995576	−	1.72439i
$66$	−36386.7	−	30532.1i	−1.02821	−	0.862774i
$67$	824.112	+	691.512i	0.0224285	+	0.0188197i	0.653933	−	0.756553i	$-0.273118\pi$
$67$	824.112	+	691.512i	0.0224285	+	0.0188197i	−0.631505	+	0.775372i	$0.717562\pi$
$68$	10642.2	+	18432.9i	0.279100	+	0.483416i
$69$	−5006.32	+	8671.20i	−0.126589	+	0.219259i
$70$	−4848.32	+	1764.65i	−0.118262	+	0.0430440i
$71$	4281.36	+	24280.8i	0.100794	+	0.571633i	0.992817	+	0.119643i	$0.0381749\pi$
$71$	4281.36	+	24280.8i	0.100794	+	0.571633i	−0.892023	+	0.451991i	$0.850714\pi$
$72$	5024.76	−	28496.8i	0.114231	−	0.647836i
$73$	46793.6	+	17031.5i	1.02773	+	0.374063i	0.800216	−	0.599712i	$-0.204718\pi$
$73$	46793.6	+	17031.5i	1.02773	+	0.374063i	0.227514	+	0.973775i	$0.426940\pi$
$74$	−14878.3	+	12484.4i	−0.315845	+	0.265025i
$75$	105962.			2.17519
$76$	−11418.3	+	22438.9i	−0.226761	+	0.445623i
$77$	−6873.39			−0.132113
$78$	64828.3	−	54397.4i	1.20650	−	1.01238i
$79$	−28912.3	−	10523.2i	−0.521213	−	0.189706i	0.0679979	−	0.997685i	$-0.478339\pi$
$79$	−28912.3	−	10523.2i	−0.521213	−	0.189706i	−0.589210	+	0.807980i	$0.700561\pi$
$80$	3757.34	−	21308.9i	0.0656381	−	0.372252i
$81$	6165.55	+	34966.6i	0.104414	+	0.592162i
$82$	−47278.7	+	17208.0i	−0.776481	+	0.282616i
$83$	−18807.0	+	32574.7i	−0.299657	+	0.519021i	−0.976057	−	0.217513i	$-0.930206\pi$
$83$	−18807.0	+	32574.7i	−0.299657	+	0.519021i	0.676400	+	0.736534i	$0.263539\pi$
$84$	−3218.84	−	5575.19i	−0.0497738	−	0.0862107i
$85$	−86132.4	−	72273.7i	−1.29306	−	1.08501i
$86$	45122.4	+	37862.2i	0.657879	+	0.552026i
$87$	−109847.	−	190260.i	−1.55593	−	2.69495i
$88$	14412.7	−	24963.5i	0.198399	−	0.343637i
$89$	87151.9	−	31720.7i	1.16628	−	0.424490i	0.314942	−	0.949111i	$-0.398015\pi$
$89$	87151.9	−	31720.7i	1.16628	−	0.424490i	0.851336	+	0.524621i	$0.175793\pi$
$90$	26543.9	+	150538.i	0.345429	+	1.95903i
$91$	2126.49	−	12059.9i	0.0269190	−	0.152665i
$92$	−5709.80	−	2078.20i	−0.0703317	−	0.0255987i
$93$	−135059.	+	113328.i	−1.61926	+	1.35872i
$94$	−49345.1			−0.576003
$95$	16139.2	−	132018.i	0.183473	−	1.50080i
$96$	26998.1			0.298989
$97$	−87838.7	+	73705.4i	−0.947887	+	0.795372i	−0.978940	−	0.204146i	$-0.934558\pi$
$97$	−87838.7	+	73705.4i	−0.947887	+	0.795372i	0.0310533	+	0.999518i	$0.490114\pi$
$98$	62298.3	+	22674.7i	0.655256	+	0.238494i
$99$	−35361.5	+	200545.i	−0.362612	+	2.05648i
$100$	11166.2	+	63326.9i	0.111662	+	0.633269i
$101$	42500.7	−	15469.0i	0.414565	−	0.150889i	−0.126313	−	0.991990i	$-0.540314\pi$
$101$	42500.7	−	15469.0i	0.414565	−	0.150889i	0.540878	+	0.841101i	$0.318092\pi$
$102$	70146.5	−	121497.i	0.667583	−	1.15629i
$103$	23710.4	+	41067.6i	0.220214	+	0.381422i	0.954873	−	0.297015i	$-0.0959910\pi$
$103$	23710.4	+	41067.6i	0.220214	+	0.381422i	−0.734659	+	0.678437i	$0.762658\pi$
$104$	39341.5	+	33011.5i	0.356671	+	0.299283i
$105$	26051.5	+	21859.8i	0.230600	+	0.193497i
$106$	−3297.67	−	5711.73i	−0.0285064	−	0.0493745i
$107$	107106.	−	185514.i	0.904390	−	1.56645i	0.0826555	−	0.996578i	$-0.473660\pi$
$107$	107106.	−	185514.i	0.904390	−	1.56645i	0.821734	−	0.569871i	$-0.193007\pi$
$108$	−82900.8	+	30173.4i	−0.683911	+	0.248923i
$109$	39394.6	+	223418.i	0.317593	+	1.80116i	0.557297	+	0.830313i	$0.311839\pi$
$109$	39394.6	+	223418.i	0.317593	+	1.80116i	−0.239704	+	0.970846i	$0.577050\pi$
$110$	−26442.1	+	149961.i	−0.208360	+	1.18167i
$111$	120298.	+	43784.9i	0.926724	+	0.337300i
$112$	2992.74	−	2511.21i	0.0225436	−	0.0189164i
$113$	16431.9			0.121058			0.0605288	−	0.998166i	$-0.480721\pi$
$113$	16431.9			0.121058			0.0605288	+	0.998166i	$0.480721\pi$
$114$	165718.	−	8772.44i	1.19428	−	0.0632205i
$115$	32098.6			0.226329
$116$	102131.	−	85698.2i	0.704714	−	0.591326i
$117$	−340932.	−	124089.i	−2.30252	−	0.838048i
$118$	3846.07	−	21812.1i	0.0254280	−	0.144209i
$119$	−3525.23	−	19992.6i	−0.0228202	−	0.129420i
$120$	−134020.	+	48779.3i	−0.849604	+	0.309231i
$121$	−20903.3	+	36205.6i	−0.129793	+	0.224808i
$122$	−67236.7	−	116457.i	−0.408985	−	0.708382i
$123$	254043.	+	213167.i	1.51406	+	1.27045i
$124$	−81961.7	−	68774.0i	−0.478693	−	0.401671i
$125$	−37781.1	−	65438.7i	−0.216271	−	0.374593i
$126$	−13799.7	+	23901.8i	−0.0774362	+	0.134123i
$127$	−43365.6	+	15783.8i	−0.238581	+	0.0868364i	−0.458544	−	0.888672i	$-0.651629\pi$
$127$	−43365.6	+	15783.8i	−0.238581	+	0.0868364i	0.219963	+	0.975508i	$0.429406\pi$
$128$	2845.05	+	16135.1i	0.0153485	+	0.0870455i
$129$	67419.0	−	382352.i	0.356704	−	2.02297i
$130$	−254937.	−	92789.6i	−1.32305	−	0.481550i
$131$	−229381.	+	192473.i	−1.16783	+	0.979923i	−0.999983	−	0.00589038i	$-0.998125\pi$
$131$	−229381.	+	192473.i	−1.16783	+	0.979923i	−0.167844	+	0.985814i	$0.553681\pi$
$132$	−189998.			−0.949105
$133$	17553.9	−	16386.6i	0.0860487	−	0.0803265i
$134$	4303.21			0.0207029
$135$	357008.	−	299565.i	1.68594	−	1.41467i
$136$	80003.3	+	29118.8i	0.370903	+	0.134998i
$137$	23780.9	−	134868.i	0.108250	−	0.613916i	−0.881622	−	0.471955i	$-0.843548\pi$
$137$	23780.9	−	134868.i	0.108250	−	0.613916i	0.989872	−	0.141960i	$-0.0453406\pi$
$138$	6954.71	+	39442.1i	0.0310872	+	0.176304i
$139$	277169.	−	100881.i	1.21677	−	0.442868i	0.347722	−	0.937598i	$-0.386955\pi$
$139$	277169.	−	100881.i	1.21677	−	0.442868i	0.869047	+	0.494730i	$0.164733\pi$
$140$	−10319.0	+	17873.0i	−0.0444955	+	0.0770684i
$141$	162625.	+	281675.i	0.688875	+	1.19317i
$142$	75548.5	+	63392.7i	0.314416	+	0.263827i
$143$	−276864.	−	232317.i	−1.13221	−	0.950036i
$144$	−57872.8	−	100239.i	−0.232578	−	0.402837i
$145$	−352148.	+	609937.i	−1.39093	+	2.40916i
$146$	187174.	−	68125.9i	0.726715	−	0.264503i
$147$	−75881.2	−	430343.i	−0.289628	−	1.64256i
$148$	−13490.5	+	76508.6i	−0.0506261	+	0.287115i
$149$	172765.	+	62881.3i	0.637514	+	0.232036i	0.640499	−	0.767959i	$-0.278728\pi$
$149$	172765.	+	62881.3i	0.637514	+	0.232036i	−0.00298448	+	0.999996i	$0.500950\pi$
$150$	324687.	−	272445.i	1.17825	−	0.988667i
$151$	−444021.			−1.58475			−0.792376	−	0.610033i	$-0.791156\pi$
$151$	−444021.			−1.58475			−0.792376	+	0.610033i	$0.791156\pi$
$152$	22706.0	+	98114.9i	0.0797136	+	0.344450i
$153$	−601460.			−2.07720
$154$	−21061.3	+	17672.5i	−0.0715621	+	0.0600477i
$155$	531121.	+	193312.i	1.77568	+	0.646294i
$156$	58781.5	−	333367.i	0.193388	−	1.09676i
$157$	80446.5	+	456235.i	0.260470	+	1.47720i	0.781631	+	0.623741i	$0.214388\pi$
$157$	80446.5	+	456235.i	0.260470	+	1.47720i	−0.521161	+	0.853459i	$0.674501\pi$
$158$	−115649.	+	42092.9i	−0.368553	+	0.134142i
$159$	−21736.1	+	37647.9i	−0.0681848	+	0.118100i
$160$	−43275.3	−	74955.1i	−0.133641	−	0.231473i
$161$	4439.60	+	3725.27i	0.0134983	+	0.0113264i
$162$	108797.	+	91291.2i	0.325708	+	0.273301i
$163$	54985.8	+	95238.2i	0.162099	+	0.280765i	0.935621	−	0.353005i	$-0.114840\pi$
$163$	54985.8	+	95238.2i	0.162099	+	0.280765i	−0.773522	+	0.633769i	$0.781507\pi$
$164$	−100626.	+	174289.i	−0.292146	+	0.506012i
$165$	943160.	−	343282.i	2.69697	−	0.981616i
$166$	26126.4	+	148170.i	0.0735884	+	0.417341i
$167$	9781.11	−	55471.4i	0.0271392	−	0.153914i	−0.968227	−	0.250074i	$-0.919545\pi$
$167$	9781.11	−	55471.4i	0.0271392	−	0.153914i	0.995366	+	0.0961601i	$0.0306561\pi$
$168$	−24197.7	−	8807.25i	−0.0661457	−	0.0240751i
$169$	208847.	−	175244.i	0.562486	−	0.471982i
$170$	−449752.			−1.19358
$171$	−387802.	−	596474.i	−1.01419	−	1.55992i
$172$	235613.			0.607264
$173$	−39485.6	+	33132.4i	−0.100305	+	0.0841662i	−0.691561	−	0.722318i	$-0.743077\pi$
$173$	−39485.6	+	33132.4i	−0.100305	+	0.0841662i	0.591256	+	0.806484i	$0.298632\pi$
$174$	−825778.	−	300559.i	−2.06771	−	0.752586i
$175$	10650.3	−	60401.0i	0.0262886	−	0.149090i
$176$	−20021.9	−	113550.i	−0.0487219	−	0.276316i
$177$	−137185.	+	49931.2i	−0.329134	+	0.119795i
$178$	185490.	−	321279.i	0.438805	−	0.760032i
$179$	324052.	+	561274.i	0.755930	+	1.30931i	0.944910	+	0.327329i	$0.106149\pi$
$179$	324052.	+	561274.i	0.755930	+	1.30931i	−0.188980	+	0.981981i	$0.560518\pi$
$180$	468392.	+	393027.i	1.07753	+	0.904152i
$181$	377172.	+	316485.i	0.855742	+	0.718053i	0.961046	−	0.276387i	$-0.0891373\pi$
$181$	377172.	+	316485.i	0.855742	+	0.718053i	−0.105305	+	0.994440i	$0.533582\pi$
$182$	−24491.9	−	42421.2i	−0.0548080	−	0.0949303i
$183$	−443180.	+	767610.i	−0.978256	+	1.69439i
$184$	−22839.2	+	8312.79i	−0.0497320	+	0.0181010i
$185$	−71265.5	−	404167.i	−0.153091	−	0.868223i
$186$	−122462.	+	694515.i	−0.259548	+	1.47197i
$187$	−563020.	−	204922.i	−1.17739	−	0.428534i
$188$	−151202.	+	126874.i	−0.312007	+	0.261805i
$189$	84145.0			0.171346
$190$	−289985.	−	446023.i	−0.582762	−	0.896341i
$191$	67382.2			0.133648			0.0668239	−	0.997765i	$-0.478713\pi$
$191$	67382.2			0.133648			0.0668239	+	0.997765i	$0.478713\pi$
$192$	82727.0	−	69416.2i	0.161955	−	0.135896i
$193$	189313.	+	68904.3i	0.365836	+	0.133154i	0.518396	−	0.855141i	$-0.326529\pi$
$193$	189313.	+	68904.3i	0.365836	+	0.133154i	−0.152560	+	0.988294i	$0.548752\pi$
$194$	−79645.7	+	451693.i	−0.151935	+	0.861666i
$195$	310521.	+	1.76105e6i	0.584797	+	3.31655i
$196$	249193.	−	90698.9i	0.463336	−	0.168640i
$197$	47585.2	−	82420.0i	0.0873587	−	0.151310i	−0.819035	−	0.573743i	$-0.805491\pi$
$197$	47585.2	−	82420.0i	0.0873587	−	0.151310i	0.906394	+	0.422434i	$0.138824\pi$
$198$	407278.	+	705425.i	0.738291	+	1.27876i
$199$	−92470.0	−	77591.5i	−0.165527	−	0.138893i	0.556262	−	0.831007i	$-0.312235\pi$
$199$	−92470.0	−	77591.5i	−0.165527	−	0.138893i	−0.721788	+	0.692114i	$0.756680\pi$
$200$	197038.	+	165335.i	0.348318	+	0.292274i
$201$	−14181.9	−	24563.9i	−0.0247597	−	0.0428851i
$202$	90456.7	−	156676.i	0.155978	−	0.270161i
$203$	−119494.	+	43492.2i	−0.203519	+	0.0740749i
$204$	−97446.4	−	552646.i	−0.163942	−	0.929762i
$205$	184612.	−	1.04699e6i	0.306814	−	1.74003i
$206$	178244.	+	64875.4i	0.292648	+	0.106515i
$207$	131533.	−	110369.i	0.213358	−	0.179028i
$208$	205427.			0.329230
$209$	−159793.	−	690479.i	−0.253041	−	1.09342i
$210$	136031.			0.212859
$211$	−296048.	+	248414.i	−0.457780	+	0.384123i	−0.842313	−	0.538988i	$-0.818807\pi$
$211$	−296048.	+	248414.i	−0.457780	+	0.384123i	0.384534	+	0.923111i	$0.374362\pi$
$212$	−24790.4	−	9022.95i	−0.0378829	−	0.0137882i
$213$	112880.	−	640172.i	0.170477	−	0.966825i
$214$	−148791.	−	843833.i	−0.222096	−	1.25957i
$215$	−1.16959e6	+	425697.i	−1.72559	+	0.628065i
$216$	−176442.	+	305607.i	−0.257317	+	0.445686i
$217$	51024.9	+	88377.7i	0.0735585	+	0.127407i
$218$	695154.	+	583303.i	0.990694	+	0.831291i
$219$	−1.00574e6	−	843920.i	−1.41702	−	1.18903i
$220$	304548.	+	527493.i	0.424228	+	0.734785i
$221$	533740.	−	924464.i	0.735104	−	1.27324i
$222$	481192.	−	175139.i	0.655293	−	0.238507i
$223$	−78603.2	−	445781.i	−0.105847	−	0.600287i	−0.990879	−	0.134757i	$-0.956975\pi$
$223$	−78603.2	−	445781.i	−0.105847	−	0.600287i	0.885032	−	0.465531i	$-0.154136\pi$
$224$	2713.60	−	15389.6i	0.00361348	−	0.0204931i
$225$	−1.70753e6	−	621489.i	−2.24860	−	0.818422i
$226$	50350.3	−	42248.9i	0.0655739	−	0.0550230i
$227$	23094.4			0.0297469			0.0148734	−	0.999889i	$-0.495265\pi$
$227$	23094.4			0.0297469			0.0148734	+	0.999889i	$0.495265\pi$
$228$	485234.	−	452966.i	0.618179	−	0.577070i
$229$	311552.			0.392593			0.196296	−	0.980545i	$-0.437109\pi$
$229$	311552.			0.392593			0.196296	+	0.980545i	$0.437109\pi$
$230$	98355.7	−	82530.2i	0.122597	−	0.102871i
$231$	170290.	+	61980.7i	0.209972	+	0.0764234i
$232$	92605.0	−	525189.i	0.112957	−	0.640613i
$233$	−145651.	−	826026.i	−0.175761	−	0.996791i	−0.937262	−	0.348627i	$-0.886648\pi$
$233$	−145651.	−	826026.i	−0.175761	−	0.996791i	0.761501	−	0.648164i	$-0.224463\pi$
$234$	−1.36373e6	+	496356.i	−1.62813	+	0.592590i
$235$	521345.	−	902995.i	0.615822	−	1.06664i
$236$	−44297.3	−	76725.1i	−0.0517722	−	0.0896721i
$237$	621419.	+	521432.i	0.718643	+	0.603013i
$238$	−62205.9	−	52196.9i	−0.0711851	−	0.0597314i
$239$	−139180.	−	241068.i	−0.157610	−	0.272988i	0.776396	−	0.630245i	$-0.217046\pi$
$239$	−139180.	−	241068.i	−0.157610	−	0.272988i	−0.934006	+	0.357257i	$0.883712\pi$
$240$	−285242.	+	494054.i	−0.319658	+	0.553664i
$241$	904603.	−	329248.i	1.00326	−	0.365158i	0.212422	−	0.977178i	$-0.431865\pi$
$241$	904603.	−	329248.i	1.00326	−	0.365158i	0.790842	+	0.612020i	$0.209643\pi$
$242$	29038.6	+	164686.i	0.0318740	+	0.180767i
$243$	−70107.4	+	397599.i	−0.0761637	+	0.431946i
$244$	−505455.	−	183971.i	−0.543510	−	0.197822i
$245$	−1.07314e6	+	900468.i	−1.14219	+	0.958414i
$246$	1.32652e6			1.39758
$247$	1.26094e6	−	66748.9i	1.31508	−	0.0696148i
$248$	−427974.			−0.441863
$249$	759691.	−	637457.i	0.776495	−	0.651557i
$250$	−284021.	−	103375.i	−0.287409	−	0.104608i
$251$	−61197.6	+	347069.i	−0.0613126	+	0.347721i	0.938683	+	0.344781i	$0.112047\pi$
$251$	−61197.6	+	347069.i	−0.0613126	+	0.347721i	−0.999996	+	0.00293984i	$0.999064\pi$
$252$	19170.4	+	108721.i	0.0190164	+	0.107848i
$253$	160730.	−	58500.9i	0.157868	−	0.0574594i
$254$	−92297.3	+	159864.i	−0.0897646	+	0.155477i
$255$	1.48223e6	+	2.56730e6i	1.42747	+	2.47244i
$256$	50203.5	+	42125.7i	0.0478778	+	0.0401742i
$257$	1.21932e6	+	1.02313e6i	1.15156	+	0.966270i	0.999755	−	0.0221408i	$-0.00704820\pi$
$257$	1.21932e6	+	1.02313e6i	1.15156	+	0.966270i	0.151801	+	0.988411i	$0.451493\pi$
$258$	−776501.	−	1.34494e6i	−0.726261	−	1.25792i
$259$	37049.6	−	64171.9i	0.0343190	−	0.0594423i
$260$	−1.01975e6	+	371158.i	−0.935535	+	0.340507i
$261$	654213.	+	3.71023e6i	0.594454	+	3.37131i
$262$	−207985.	+	1.17954e6i	−0.187189	+	1.06160i
$263$	−1.48102e6	−	539046.i	−1.32029	−	0.480548i	−0.416741	−	0.909025i	$-0.636828\pi$
$263$	−1.48102e6	−	539046.i	−1.32029	−	0.480548i	−0.903552	+	0.428478i	$0.859050\pi$
$264$	−582188.	+	488514.i	−0.514107	+	0.431387i
$265$	139363.			0.121908
$266$	11655.9	−	95345.0i	0.0101005	−	0.0826217i
$267$	−2.44526e6			−2.09916
$268$	13185.8	−	11064.2i	0.0112142	−	0.00940985i
$269$	−1.00933e6	−	367366.i	−0.850458	−	0.309541i	−0.120231	−	0.992746i	$-0.538363\pi$
$269$	−1.00933e6	−	367366.i	−0.850458	−	0.309541i	−0.730227	+	0.683205i	$0.760586\pi$
$270$	323708.	−	1.83584e6i	0.270237	−	1.53259i
$271$	144071.	+	817069.i	0.119167	+	0.675827i	0.984603	+	0.174808i	$0.0559303\pi$
$271$	144071.	+	817069.i	0.119167	+	0.675827i	−0.865436	+	0.501019i	$0.832959\pi$
$272$	320013.	−	116475.i	0.262268	−	0.0954579i
$273$	−161434.	+	279613.i	−0.131096	+	0.227065i
$274$	−273898.	−	474405.i	−0.220400	−	0.381745i
$275$	−1.38665e6	−	1.16354e6i	−1.10569	−	0.927788i
$276$	122722.	+	102976.i	0.0969728	+	0.0813698i
$277$	−273311.	−	473388.i	−0.214021	−	0.370696i	0.738948	−	0.673762i	$-0.235323\pi$
$277$	−273311.	−	473388.i	−0.214021	−	0.370696i	−0.952969	+	0.303067i	$0.901990\pi$
$278$	589915.	−	1.02176e6i	0.457802	−	0.792936i
$279$	2.84111e6	−	1.03408e6i	2.18513	−	0.795322i
$280$	14334.9	+	81297.5i	0.0109270	+	0.0619701i
$281$	134466.	−	762592.i	0.101589	−	0.576138i	−0.890939	−	0.454122i	$-0.849953\pi$
$281$	134466.	−	762592.i	0.101589	−	0.576138i	0.992528	−	0.122016i	$-0.0389359\pi$
$282$	1.22254e6	+	444969.i	0.915463	+	0.333201i
$283$	487926.	−	409419.i	0.362149	−	0.303880i	−0.443497	−	0.896276i	$-0.646262\pi$
$283$	487926.	−	409419.i	0.362149	−	0.303880i	0.805647	+	0.592396i	$0.201818\pi$
$284$	394486.			0.290226
$285$	−1.59032e6	+	3.12525e6i	−1.15977	+	2.27915i
$286$	−1.44568e6			−1.04510
$287$	147044.	−	123385.i	0.105377	−	0.0884214i
$288$	−435061.	−	158349.i	−0.309079	−	0.112496i
$289$	60738.9	−	344467.i	0.0427782	−	0.242607i
$290$	489198.	+	2.77438e6i	0.341578	+	1.93719i
$291$	2.84087e6	−	1.03399e6i	1.96661	−	0.715789i
$292$	398373.	−	690003.i	0.273422	−	0.473580i
$293$	575866.	+	997430.i	0.391880	+	0.678755i	0.992697	−	0.120631i	$-0.0384916\pi$
$293$	575866.	+	997430.i	0.391880	+	0.678755i	−0.600818	+	0.799386i	$0.705158\pi$
$294$	−1.33899e6	−	1.12355e6i	−0.903461	−	0.758094i
$295$	358518.	+	300833.i	0.239859	+	0.201266i
$296$	155378.	+	269122.i	0.103076	+	0.178534i
$297$	1.24171e6	−	2.15070e6i	0.816822	−	1.41478i
$298$	691059.	−	251525.i	0.450790	−	0.164074i
$299$	52917.9	+	300112.i	0.0342314	+	0.194136i
$300$	294402.	−	1.66964e6i	0.188859	−	1.07107i
$301$	−211174.	−	76860.9i	−0.134346	−	0.0488978i
$302$	−1.36056e6	+	1.14165e6i	−0.858421	+	0.720301i
$303$	−1.19246e6			−0.746170
$304$	321844.	+	242261.i	0.199738	+	0.150349i
$305$	2.84150e6			1.74903
$306$	−1.84298e6	+	1.54645e6i	−1.12517	+	0.944128i
$307$	−2.03047e6	−	739029.i	−1.22956	−	0.447523i	−0.356113	−	0.934443i	$-0.615898\pi$
$307$	−2.03047e6	−	739029.i	−1.22956	−	0.447523i	−0.873447	+	0.486920i	$0.838120\pi$
$308$	−19096.8	+	108303.i	−0.0114706	+	0.0650527i
$309$	−217106.	−	1.23127e6i	−0.129353	−	0.733596i
$310$	2.12448e6	−	773249.i	1.25559	−	0.456999i
$311$	−986009.	+	1.70782e6i	−0.578069	+	1.00124i	0.417632	+	0.908616i	$0.362860\pi$
$311$	−986009.	+	1.70782e6i	−0.578069	+	1.00124i	−0.995701	+	0.0926285i	$0.970473\pi$
$312$	−677019.	−	1.17263e6i	−0.393744	−	0.681985i
$313$	−403840.	−	338862.i	−0.232996	−	0.195507i	0.518813	−	0.854888i	$-0.326374\pi$
$313$	−403840.	−	338862.i	−0.232996	−	0.195507i	−0.751809	+	0.659381i	$0.770819\pi$
$314$	1.41955e6	+	1.19114e6i	0.812506	+	0.681774i
$315$	−291595.	−	505058.i	−0.165579	−	0.286791i
$316$	−246143.	+	426331.i	−0.138666	+	0.240176i
$317$	−1.62609e6	+	591847.i	−0.908856	+	0.330797i	−0.753796	−	0.657108i	$-0.771779\pi$
$317$	−1.62609e6	+	591847.i	−0.908856	+	0.330797i	−0.155060	+	0.987905i	$0.549557\pi$
$318$	30195.4	+	171247.i	0.0167445	+	0.0949630i
$319$	−651704.	+	3.69599e6i	−0.358570	+	2.03355i
$320$	−325324.	−	118408.i	−0.177599	−	0.0646409i
$321$	−4.32646e6	+	3.63033e6i	−2.34353	+	1.96645i
$322$	23182.0			0.0124598
$323$	1.92644e6	−	818922.i	1.02742	−	0.436754i
$324$	568096.			0.300648
$325$	2.47052e6	−	2.07301e6i	1.29742	−	1.08866i
$326$	413358.	+	150450.i	0.215418	+	0.0784058i
$327$	1.03865e6	−	5.89050e6i	0.537157	−	3.04637i
$328$	139788.	+	792777.i	0.0717439	+	0.406880i
$329$	176907.	−	64389.0i	0.0901064	−	0.0327961i
$330$	2.00738e6	−	3.47688e6i	1.01472	−	1.75754i
$331$	−542483.	−	939609.i	−0.272155	−	0.471386i	0.697258	−	0.716820i	$-0.254403\pi$
$331$	−542483.	−	939609.i	−0.272155	−	0.471386i	−0.969413	+	0.245434i	$0.921070\pi$
$332$	461024.	+	386845.i	0.229551	+	0.192616i
$333$	−1.68173e6	−	1.41114e6i	−0.831088	−	0.697366i
$334$	−112654.	−	195123.i	−0.0552563	−	0.0957067i
$335$	−45464.5	+	78746.9i	−0.0221340	+	0.0383373i
$336$	−96790.9	+	35229.0i	−0.0467720	+	0.0170236i
$337$	−333546.	−	1.89163e6i	−0.159986	−	0.907323i	−0.954085	−	0.299536i	$-0.903168\pi$
$337$	−333546.	−	1.89163e6i	−0.159986	−	0.907323i	0.794100	−	0.607788i	$-0.207943\pi$
$338$	189367.	−	1.07396e6i	0.0901599	−	0.511322i
$339$	−407106.	−	148174.i	−0.192401	−	0.0700283i
$340$	−1.37812e6	+	1.15638e6i	−0.646531	+	0.542504i
$341$	3.01185e6			1.40264
$342$	−2.72192e6	−	830606.i	−1.25837	−	0.383999i
$343$	−509420.			−0.233798
$344$	721959.	−	605795.i	0.328940	−	0.276013i
$345$	−795252.	−	289448.i	−0.359714	−	0.130925i
$346$	−35802.7	+	203047.i	−0.0160777	+	0.0911814i
$347$	−297885.	−	1.68939e6i	−0.132808	−	0.753193i	−0.976361	−	0.216147i	$-0.930651\pi$
$347$	−297885.	−	1.68939e6i	−0.132808	−	0.753193i	0.843553	−	0.537046i	$-0.180460\pi$
$348$	−3.30311e6	+	1.20224e6i	−1.46209	+	0.532159i
$349$	−1.67663e6	+	2.90401e6i	−0.736842	+	1.27625i	0.217069	+	0.976156i	$0.430350\pi$
$349$	−1.67663e6	+	2.90401e6i	−0.736842	+	1.27625i	−0.953911	+	0.300091i	$0.902983\pi$
$350$	−122665.	−	212463.i	−0.0535245	−	0.0927071i
$351$	3.38941e6	+	2.84405e6i	1.46844	+	1.23217i
$352$	−353305.	−	296458.i	−0.151982	−	0.127528i
$353$	−1.00588e6	−	1.74223e6i	−0.429644	−	0.744166i	0.567197	−	0.823582i	$-0.308028\pi$
$353$	−1.00588e6	−	1.74223e6i	−0.429644	−	0.744166i	−0.996842	+	0.0794160i	$0.974694\pi$
$354$	−291978.	+	505721.i	−0.123835	+	0.214488i
$355$	−1.95825e6	+	712745.i	−0.824703	+	0.300167i
$356$	−257680.	−	1.46138e6i	−0.107760	−	0.611136i
$357$	−92944.0	+	527112.i	−0.0385968	+	0.218893i
$358$	2.43607e6	+	886658.i	1.00458	+	0.365636i
$359$	1.55592e6	−	1.30557e6i	0.637162	−	0.534643i	−0.265983	−	0.963978i	$-0.585697\pi$
$359$	1.55592e6	−	1.30557e6i	0.637162	−	0.534643i	0.903145	+	0.429335i	$0.141252\pi$
$360$	2.44577e6			0.994624
$361$	2.05424e6	+	1.38245e6i	0.829626	+	0.558319i
$362$	1.96945e6			0.789903
$363$	844370.	−	708510.i	0.336330	−	0.282215i
$364$	−184119.	−	67013.8i	−0.0728358	−	0.0265101i
$365$	−730871.	+	4.14498e6i	−0.287150	+	1.62851i
$366$	615659.	+	3.49158e6i	0.240236	+	1.36244i
$367$	−332177.	+	120902.i	−0.128737	+	0.0468565i	−0.405585	−	0.914057i	$-0.632932\pi$
$367$	−332177.	+	120902.i	−0.128737	+	0.0468565i	0.276848	+	0.960914i	$0.410710\pi$
$368$	−48609.9	+	84194.9i	−0.0187114	+	0.0324090i
$369$	−2.84351e6	−	4.92510e6i	−1.08715	−	1.88299i
$370$	−1.25754e6	−	1.05520e6i	−0.477550	−	0.400712i
$371$	19275.5	+	16174.1i	0.00727062	+	0.00610078i
$372$	1.41046e6	+	2.44299e6i	0.528449	+	0.915301i
$373$	1.38080e6	−	2.39162e6i	0.513876	−	0.890060i	−0.485994	−	0.873962i	$-0.661542\pi$
$373$	1.38080e6	−	2.39162e6i	0.513876	−	0.890060i	0.999870	−	0.0160979i	$-0.00512433\pi$
$374$	−2.25208e6	+	819690.i	−0.832539	+	0.303020i
$375$	345946.	+	1.96195e6i	0.127037	+	0.720462i
$376$	−137099.	+	777528.i	−0.0500109	+	0.283626i
$377$	−6.28329e6	−	2.28693e6i	−2.27685	−	0.828705i
$378$	257835.	−	216349.i	0.0928139	−	0.0778801i
$379$	−2.01627e6			−0.721025			−0.360513	−	0.932754i	$-0.617398\pi$
$379$	−2.01627e6			−0.721025			−0.360513	+	0.932754i	$0.617398\pi$
$380$	−2.03536e6	−	621099.i	−0.723072	−	0.220649i
$381$	1.21673e6			0.429418
$382$	206471.	−	173250.i	0.0723937	−	0.0607456i
$383$	5.30794e6	+	1.93193e6i	1.84897	+	0.672969i	0.985769	+	0.168106i	$0.0537651\pi$
$383$	5.30794e6	+	1.93193e6i	1.84897	+	0.672969i	0.863199	+	0.504863i	$0.168457\pi$
$384$	75010.8	−	425407.i	0.0259595	−	0.147223i
$385$	−100882.	−	572128.i	−0.0346865	−	0.196717i
$386$	757252.	−	275617.i	0.258685	−	0.0941538i
$387$	−3.32900e6	+	5.76599e6i	−1.12989	+	1.95703i
$388$	917322.	+	1.58885e6i	0.309345	+	0.535801i
$389$	2.36851e6	+	1.98742e6i	0.793601	+	0.665910i	0.946634	−	0.322311i	$-0.104460\pi$
$389$	2.36851e6	+	1.98742e6i	0.793601	+	0.665910i	−0.153033	+	0.988221i	$0.548904\pi$
$390$	5.47943e6	+	4.59779e6i	1.82420	+	1.53069i
$391$	252596.	+	437510.i	0.0835575	+	0.144726i
$392$	530372.	−	918630.i	0.174327	−	0.301943i
$393$	7.41860e6	−	2.70015e6i	2.42293	−	0.881874i
$394$	−66104.6	−	374898.i	−0.0214532	−	0.121667i
$395$	451583.	−	2.56105e6i	0.145628	−	0.825897i
$396$	3.06173e6	+	1.11438e6i	0.981134	+	0.357104i
$397$	1.23209e6	−	1.03385e6i	0.392343	−	0.329215i	−0.425182	−	0.905108i	$-0.639790\pi$
$397$	1.23209e6	−	1.03385e6i	0.392343	−	0.329215i	0.817525	+	0.575893i	$0.195345\pi$
$398$	−482844.			−0.152791
$399$	−582669.	+	247690.i	−0.183227	+	0.0778892i
$400$	1.02886e6			0.321519
$401$	−1.99214e6	+	1.67160e6i	−0.618670	+	0.519126i	−0.897385	−	0.441248i	$-0.854536\pi$
$401$	−1.99214e6	+	1.67160e6i	−0.618670	+	0.519126i	0.278715	+	0.960374i	$0.410091\pi$
$402$	−106613.	−	38804.1i	−0.0329038	−	0.0119760i
$403$	−931804.	+	5.28452e6i	−0.285800	+	1.62085i
$404$	−125661.	−	712660.i	−0.0383043	−	0.217234i
$405$	−2.82006e6	+	1.02642e6i	−0.854319	+	0.310947i
$406$	−254325.	+	440504.i	−0.0765728	+	0.132628i
$407$	−1.09346e6	−	1.89393e6i	−0.327204	−	0.566734i
$408$	−1.71953e6	−	1.44286e6i	−0.511398	−	0.429114i
$409$	−950034.	−	797173.i	−0.280822	−	0.235637i	0.491487	−	0.870885i	$-0.336454\pi$
$409$	−950034.	−	797173.i	−0.280822	−	0.235637i	−0.772309	+	0.635248i	$0.780898\pi$
$410$	−2.12628e6	−	3.68282e6i	−0.624684	−	1.08198i
$411$	−1.80535e6	+	3.12696e6i	−0.527179	+	0.913100i
$412$	712975.	−	259502.i	0.206934	−	0.0753177i
$413$	14673.5	+	83217.3i	0.00423309	+	0.0240070i
$414$	119264.	−	676381.i	0.0341987	−	0.193950i
$415$	−2.98749e6	−	1.08736e6i	−0.851502	−	0.309921i
$416$	629464.	−	528183.i	0.178335	−	0.149641i
$417$	−7.77665e6			−2.19004
$418$	−2.26496e6	−	1.70490e6i	−0.634045	−	0.477264i
$419$	1.66141e6			0.462318			0.231159	−	0.972916i	$-0.425748\pi$
$419$	1.66141e6			0.462318			0.231159	+	0.972916i	$0.425748\pi$
$420$	416824.	−	349757.i	0.115300	−	0.0967483i
$421$	−4.82440e6	−	1.75594e6i	−1.32659	−	0.482841i	−0.421028	−	0.907047i	$-0.638331\pi$
$421$	−4.82440e6	−	1.75594e6i	−1.32659	−	0.482841i	−0.905565	+	0.424207i	$0.860553\pi$
$422$	−268435.	+	1.52237e6i	−0.0733766	+	0.416139i
$423$	−968544.	−	5.49289e6i	−0.263189	−	1.49262i
$424$	−99161.5	+	36091.8i	−0.0267873	+	0.00974976i
$425$	2.67319e6	−	4.63010e6i	0.717889	−	1.24342i
$426$	−1.30010e6	−	2.25183e6i	−0.347097	−	0.601190i
$427$	393012.	+	329776.i	0.104312	+	0.0875285i
$428$	−2.62554e6	−	2.20309e6i	−0.692803	−	0.581331i
$429$	4.76449e6	+	8.25234e6i	1.24989	+	2.16488i
$430$	−2.48931e6	+	4.31161e6i	−0.649244	+	1.12452i
$431$	1.10159e6	−	400946.i	0.285645	−	0.103966i	−0.195224	−	0.980759i	$-0.562543\pi$
$431$	1.10159e6	−	400946.i	0.285645	−	0.103966i	0.480869	+	0.876792i	$0.340321\pi$
$432$	245111.	+	1.39010e6i	0.0631908	+	0.358373i
$433$	−609469.	+	3.45647e6i	−0.156218	+	0.885959i	0.801445	+	0.598068i	$0.204065\pi$
$433$	−609469.	+	3.45647e6i	−0.156218	+	0.885959i	−0.957663	+	0.287890i	$0.907046\pi$
$434$	383582.	+	139612.i	0.0977538	+	0.0355795i
$435$	1.42247e7	−	1.19359e7i	3.60428	−	3.02435i
$436$	3.62984e6			0.914473
$437$	−271017.	+	532594.i	−0.0678880	+	0.133411i
$438$	−5.25163e6			−1.30800
$439$	−2.58621e6	+	2.17009e6i	−0.640476	+	0.537423i	−0.904164	−	0.427185i	$-0.859505\pi$
$439$	−2.58621e6	+	2.17009e6i	−0.640476	+	0.537423i	0.263688	+	0.964608i	$0.415061\pi$
$440$	2.28945e6	+	833293.i	0.563768	+	0.205195i
$441$	−1.30126e6	+	7.37983e6i	−0.318617	+	1.80697i
$442$	−741463.	−	4.20505e6i	−0.180524	−	1.02380i
$443$	−1.41694e6	+	515724.i	−0.343038	+	0.124856i	−0.507793	−	0.861479i	$-0.669539\pi$
$443$	−1.41694e6	+	515724.i	−0.343038	+	0.124856i	0.164756	+	0.986334i	$0.447316\pi$
$444$	1.02415e6	−	1.77387e6i	0.246550	−	0.427037i
$445$	3.91951e6	+	6.78879e6i	0.938278	+	1.62515i
$446$	−1.38702e6	−	1.16385e6i	−0.330177	−	0.277051i
$447$	−3.71327e6	−	3.11581e6i	−0.878999	−	0.737568i
$448$	−31254.0	−	54133.5i	−0.00735716	−	0.0127430i
$449$	91903.4	−	159181.i	0.0215137	−	0.0372629i	−0.855068	−	0.518516i	$-0.826485\pi$
$449$	91903.4	−	159181.i	0.0215137	−	0.0372629i	0.876582	+	0.481253i	$0.159818\pi$
$450$	−6.83011e6	+	2.48596e6i	−1.59000	+	0.578712i
$451$	−983751.	−	5.57913e6i	−0.227742	−	1.29159i
$452$	45653.9	−	258916.i	0.0105107	−	0.0596092i
$453$	1.10008e7	+	4.00395e6i	2.51871	+	0.916734i
$454$	70765.3	−	59379.1i	0.0161132	−	0.0135205i
$455$	1.03505e6			0.234388
$456$	322200.	−	2.63558e6i	0.0725626	−	0.593559i
$457$	5.18883e6			1.16219			0.581097	−	0.813834i	$-0.302624\pi$
$457$	5.18883e6			1.16219			0.581097	+	0.813834i	$0.302624\pi$
$458$	954651.	−	801048.i	0.212658	−	0.178441i
$459$	6.89257e6	+	2.50869e6i	1.52704	+	0.555796i
$460$	89181.7	−	505775.i	0.0196508	−	0.111445i
$461$	601201.	+	3.40958e6i	0.131755	+	0.747221i	0.977065	+	0.212943i	$0.0683050\pi$
$461$	601201.	+	3.40958e6i	0.131755	+	0.747221i	−0.845309	+	0.534277i	$0.820584\pi$
$462$	681162.	−	247923.i	0.148472	−	0.0540395i
$463$	1.39393e6	−	2.41436e6i	0.302196	−	0.523419i	−0.674437	−	0.738332i	$-0.735614\pi$
$463$	1.39393e6	−	2.41436e6i	0.302196	−	0.523419i	0.976633	+	0.214914i	$0.0689470\pi$
$464$	−1.06658e6	−	1.84737e6i	−0.229985	−	0.398345i
$465$	−1.14155e7	−	9.57874e6i	−2.44829	−	2.05436i
$466$	−2.57014e6	−	2.15660e6i	−0.548266	−	0.460050i
$467$	−89906.0	−	155722.i	−0.0190764	−	0.0330413i	0.856330	−	0.516430i	$-0.172739\pi$
$467$	−89906.0	−	155722.i	−0.0190764	−	0.0330413i	−0.875406	+	0.483388i	$0.839406\pi$
$468$	−2.90250e6	+	5.02728e6i	−0.612572	+	1.06101i
$469$	−15427.4	+	5615.12i	−0.00323863	+	0.00117876i
$470$	−724244.	−	4.10739e6i	−0.151231	−	0.857673i
$471$	2.12100e6	−	1.20288e7i	0.440543	−	2.49844i
$472$	−333006.	−	121204.i	−0.0688015	−	0.0250417i
$473$	−5.08075e6	+	4.26326e6i	−1.04418	+	0.876171i
$474$	3.24482e6			0.663353
$475$	6.31529e6	−	334306.i	1.28428	−	0.0679845i
$476$	−324816.			−0.0657083
$477$	571079.	−	479192.i	0.114921	−	0.0964303i
$478$	−1.04629e6	−	380820.i	−0.209452	−	0.0762343i
$479$	−563215.	+	3.19415e6i	−0.112159	+	0.636087i	0.875958	+	0.482387i	$0.160230\pi$
$479$	−563215.	+	3.19415e6i	−0.112159	+	0.636087i	−0.988118	+	0.153700i	$0.950881\pi$
$480$	396254.	+	2.24727e6i	0.0785003	+	0.445197i
$481$	3.66135e6	−	1.33262e6i	0.721571	−	0.262630i
$482$	1.92532e6	−	3.33474e6i	0.377472	−	0.653800i
$483$	−76400.1	−	132329.i	−0.0149014	−	0.0258099i
$484$	512412.	+	429965.i	0.0994273	+	0.0834294i
$485$	−7.42432e6	−	6.22974e6i	−1.43318	−	1.20258i
$486$	807465.	+	1.39857e6i	0.155072	+	0.268592i
$487$	−2.73983e6	+	4.74553e6i	−0.523482	+	0.906697i	0.476144	+	0.879367i	$0.342034\pi$
$487$	−2.73983e6	+	4.74553e6i	−0.523482	+	0.906697i	−0.999626	+	0.0273303i	$0.991299\pi$
$488$	−2.02182e6	+	735882.i	−0.384320	+	0.139881i
$489$	−503482.	−	2.85539e6i	−0.0952165	−	0.540000i
$490$	−973041.	+	5.51839e6i	−0.183080	+	1.03830i
$491$	6.07179e6	+	2.20995e6i	1.13661	+	0.413694i	0.840690	−	0.541517i	$-0.182150\pi$
$491$	6.07179e6	+	2.20995e6i	1.13661	+	0.413694i	0.295925	+	0.955211i	$0.404372\pi$
$492$	4.06469e6	−	3.41068e6i	0.757032	−	0.635225i
$493$	−1.10848e7			−2.05404
$494$	3.69212e6	−	3.44659e6i	0.680703	−	0.635437i
$495$	−1.72120e7			−3.15732
$496$	−1.31139e6	+	1.10038e6i	−0.239346	+	0.200835i
$497$	−353568.	−	128688.i	−0.0642070	−	0.0233694i
$498$	688832.	−	3.90656e6i	0.124463	−	0.705864i
$499$	37422.4	+	212233.i	0.00672791	+	0.0381559i	0.987987	−	0.154538i	$-0.0493888\pi$
$499$	37422.4	+	212233.i	0.00672791	+	0.0381559i	−0.981259	+	0.192694i	$0.938278\pi$
$500$	−1.13608e6	+	413500.i	−0.203229	+	0.0739692i
$501$	−742543.	+	1.28612e6i	−0.132168	+	0.228922i
$502$	704845.	+	1.22083e6i	0.124834	+	0.216220i
$503$	7.33859e6	+	6.15781e6i	1.29328	+	1.08519i	0.991265	+	0.131888i	$0.0421038\pi$
$503$	7.33859e6	+	6.15781e6i	1.29328	+	1.08519i	0.302015	+	0.953303i	$0.402341\pi$
$504$	338278.	+	283849.i	0.0593195	+	0.0497750i
$505$	1.91140e6	+	3.31064e6i	0.333521	+	0.577675i
$506$	342090.	−	592518.i	0.0593970	−	0.102879i
$507$	−6.75451e6	+	2.45844e6i	−1.16701	+	0.424757i
$508$	128218.	+	727161.i	0.0220440	+	0.125018i
$509$	266478.	−	1.51127e6i	0.0455897	−	0.258552i	−0.953491	−	0.301421i	$-0.902539\pi$
$509$	266478.	−	1.51127e6i	0.0455897	−	0.258552i	0.999081	+	0.0428696i	$0.0136500\pi$
$510$	1.11427e7	+	4.05563e6i	1.89700	+	0.690450i
$511$	−582143.	+	488476.i	−0.0986228	+	0.0827544i
$512$	262144.			0.0441942
$513$	1.95621e6	+	8.45295e6i	0.328187	+	1.41813i
$514$	6.36684e6			1.06296
$515$	−3.07039e6	+	2.57636e6i	−0.510123	+	0.428044i
$516$	−5.83738e6	−	2.12463e6i	−0.965147	−	0.351285i
$517$	964829.	−	5.47182e6i	0.158754	−	0.900337i
$518$	−51468.8	−	291894.i	−0.00842791	−	0.0477971i
$519$	1.27704e6	−	464805.i	0.208107	−	0.0757447i
$520$	−2.17039e6	+	3.75922e6i	−0.351989	+	0.609663i
$521$	3.12420e6	+	5.41127e6i	0.504248	+	0.873383i	0.999988	+	0.00491194i	$0.00156353\pi$
$521$	3.12420e6	+	5.41127e6i	0.504248	+	0.873383i	−0.495740	+	0.868471i	$0.665103\pi$
$522$	1.15442e7	+	9.68671e6i	1.85433	+	1.55597i
$523$	−1.11946e6	−	939337.i	−0.178959	−	0.150165i	0.548908	−	0.835883i	$-0.315044\pi$
$523$	−1.11946e6	−	939337.i	−0.178959	−	0.150165i	−0.727867	+	0.685718i	$0.759488\pi$
$524$	2.39548e6	+	4.14909e6i	0.381122	+	0.660123i
$525$	−808530.	+	1.40041e6i	−0.128026	+	0.221747i
$526$	−5.92407e6	+	2.15618e6i	−0.933589	+	0.339798i
$527$	1.54472e6	+	8.76054e6i	0.242283	+	1.37406i
$528$	−527885.	+	2.99378e6i	−0.0824052	+	0.467343i
$529$	5.91266e6	+	2.15203e6i	0.918637	+	0.334356i
$530$	427033.	−	358323.i	0.0660346	−	0.0554096i
$531$	2.50352e6			0.385315
$532$	−209431.	−	322123.i	−0.0320820	−	0.0493450i
$533$	1.00934e7			1.53893
$534$	−7.49270e6	+	6.28713e6i	−1.13707	+	0.954111i
$535$	1.70138e7	+	6.19252e6i	2.56990	+	0.935369i
$536$	11955.9	−	67805.3i	0.00179751	−	0.0101942i
$537$	−2.96721e6	−	1.68279e7i	−0.444030	−	2.51822i
$538$	−4.03732e6	+	1.46946e6i	−0.601364	+	0.218879i
$539$	−3.73247e6	+	6.46482e6i	−0.553381	+	0.958483i
$540$	−3.72832e6	−	6.45765e6i	−0.550211	−	0.952993i
$541$	−7.49442e6	−	6.28856e6i	−1.10089	−	0.923758i	−0.103407	−	0.994639i	$-0.532975\pi$
$541$	−7.49442e6	−	6.28856e6i	−1.10089	−	0.923758i	−0.997485	+	0.0708809i	$0.977419\pi$
$542$	2.54227e6	+	2.13322e6i	0.371726	+	0.311915i
$543$	−6.49066e6	−	1.12421e7i	−0.944690	−	1.63625i
$544$	681102.	−	1.17970e6i	0.0986768	−	0.170913i
$545$	−1.80187e7	+	6.55827e6i	−2.59856	+	0.945797i
$546$	224262.	+	1.27185e6i	0.0321940	+	0.182581i
$547$	−2.03532e6	+	1.15429e7i	−0.290847	+	1.64947i	0.392772	+	0.919636i	$0.371516\pi$
$547$	−2.03532e6	+	1.15429e7i	−0.290847	+	1.64947i	−0.683619	+	0.729839i	$0.739595\pi$
$548$	−2.05904e6	−	749429.i	−0.292896	−	0.106605i
$549$	1.16438e7	−	9.77032e6i	1.64879	−	1.38350i
$550$	−7.24057e6			−1.02062
$551$	−7.14709e6	−	1.09929e7i	−1.00288	−	1.54252i
$552$	640809.			0.0895119
$553$	359688.	−	301814.i	0.0500165	−	0.0419688i
$554$	−2.05462e6	−	747822.i	−0.284419	−	0.103520i
$555$	−1.87894e6	+	1.06560e7i	−0.258929	+	1.46846i
$556$	−819501.	−	4.64762e6i	−0.112425	−	0.637593i
$557$	1.01845e7	−	3.70687e6i	1.39092	−	0.506255i	0.465453	−	0.885073i	$-0.345891\pi$
$557$	1.01845e7	−	3.70687e6i	1.39092	−	0.506255i	0.925471	+	0.378818i	$0.123669\pi$
$558$	6.04689e6	−	1.04735e7i	0.822141	−	1.42399i
$559$	−5.90834e6	−	1.02335e7i	−0.799717	−	1.38515i
$560$	252953.	+	212253.i	0.0340855	+	0.0286011i
$561$	1.21011e7	+	1.01540e7i	1.62337	+	1.36217i
$562$	−1.54871e6	−	2.68245e6i	−0.206838	−	0.358254i
$563$	3.90000e6	−	6.75500e6i	0.518554	−	0.898161i	−0.481214	−	0.876603i	$-0.659804\pi$
$563$	3.90000e6	−	6.75500e6i	0.518554	−	0.898161i	0.999768	−	0.0215580i	$-0.00686265\pi$
$564$	4.89017e6	−	1.77988e6i	0.647330	−	0.235609i
$565$	241173.	+	1.36776e6i	0.0317839	+	0.180256i
$566$	442415.	−	2.50906e6i	0.0580483	−	0.329208i
$567$	−509170.	−	185323.i	−0.0665128	−	0.0242087i
$568$	1.20878e6	−	1.01428e6i	0.157208	−	0.131913i
$569$	−5.60370e6			−0.725594			−0.362797	−	0.931868i	$-0.618178\pi$
$569$	−5.60370e6			−0.725594			−0.362797	+	0.931868i	$0.618178\pi$
$570$	3.16246e6	+	1.36653e7i	0.407698	+	1.76170i
$571$	−8.49811e6			−1.09077			−0.545383	−	0.838187i	$-0.683616\pi$
$571$	−8.49811e6			−1.09077			−0.545383	+	0.838187i	$0.683616\pi$
$572$	−4.42983e6	+	3.71707e6i	−0.566105	+	0.475018i
$573$	−1.66942e6	−	607618.i	−0.212412	−	0.0773115i
$574$	133329.	−	756147.i	0.0168906	−	0.0957914i
$575$	265035.	+	1.50309e6i	0.0334297	+	0.189589i
$576$	−1.74025e6	+	633398.i	−0.218552	+	0.0795463i
$577$	4.82863e6	−	8.36343e6i	0.603788	−	1.04579i	−0.388454	−	0.921468i	$-0.626991\pi$
$577$	4.82863e6	−	8.36343e6i	0.603788	−	1.04579i	0.992242	−	0.124323i	$-0.0396760\pi$
$578$	−699563.	−	1.21168e6i	−0.0870978	−	0.150858i
$579$	−4.06895e6	−	3.41425e6i	−0.504412	−	0.423252i
$580$	8.63234e6	+	7.24339e6i	1.06551	+	0.894071i
$581$	−287009.	−	497113.i	−0.0352740	−	0.0610963i
$582$	6.04638e6	−	1.04726e7i	0.739926	−	1.28159i
$583$	697844.	−	253995.i	0.0850329	−	0.0309495i
$584$	−553414.	−	3.13857e6i	−0.0671457	−	0.380802i
$585$	5.32504e6	−	3.01998e7i	0.643329	−	3.64850i
$586$	4.32910e6	+	1.57566e6i	0.520779	+	0.189548i
$587$	−1.26082e6	+	1.05795e6i	−0.151028	+	0.126728i	−0.715171	−	0.698950i	$-0.753651\pi$
$587$	−1.26082e6	+	1.05795e6i	−0.151028	+	0.126728i	0.564143	+	0.825677i	$0.309207\pi$
$588$	−6.99171e6			−0.833951
$589$	−7.69192e6	+	7.18041e6i	−0.913580	+	0.852828i
$590$	1.87205e6			0.221405
$591$	−1.92216e6	+	1.61288e6i	−0.226371	+	0.189948i
$592$	1.16806e6	+	425138.i	0.136981	+	0.0498570i
$593$	−1.06945e6	+	6.06514e6i	−0.124889	+	0.708278i	0.856485	+	0.516171i	$0.172643\pi$
$593$	−1.06945e6	+	6.06514e6i	−0.124889	+	0.708278i	−0.981374	+	0.192107i	$0.938468\pi$
$594$	−1.72496e6	−	9.78273e6i	−0.200592	−	1.13761i
$595$	1.61240e6	−	586867.i	0.186716	−	0.0679591i
$596$	1.47082e6	−	2.54754e6i	0.169607	−	0.293768i
$597$	1.59129e6	+	2.75620e6i	0.182732	+	0.316501i
$598$	933784.	+	783537.i	0.106781	+	0.0895997i
$599$	−9.19012e6	−	7.71143e6i	−1.04654	−	0.878148i	−0.0538109	−	0.998551i	$-0.517137\pi$
$599$	−9.19012e6	−	7.71143e6i	−1.04654	−	0.878148i	−0.992725	+	0.120403i	$0.961581\pi$
$600$	−3.39079e6	−	5.87302e6i	−0.384523	−	0.666014i
$601$	4.26867e6	−	7.39355e6i	0.482066	−	0.834963i	−0.517722	−	0.855549i	$-0.673220\pi$
$601$	4.26867e6	−	7.39355e6i	0.482066	−	0.834963i	0.999788	+	0.0205861i	$0.00655321\pi$
$602$	−844694.	+	307444.i	−0.0949966	+	0.0345760i
$603$	84463.2	+	479014.i	0.00945963	+	0.0536482i
$604$	−1.23366e6	+	6.99641e6i	−0.137595	+	0.780338i
$605$	−3.32048e6	−	1.20856e6i	−0.368819	−	0.134239i
$606$	−3.65391e6	+	3.06600e6i	−0.404182	+	0.339149i
$607$	6.86609e6			0.756376			0.378188	−	0.925729i	$-0.376547\pi$
$607$	6.86609e6			0.756376			0.378188	+	0.925729i	$0.376547\pi$
$608$	1.60908e6	−	85177.9i	0.176530	−	0.00934475i
$609$	3.35269e6			0.366311
$610$	8.70685e6	−	7.30591e6i	0.947407	−	0.794968i
$611$	9.30224e6	+	3.38574e6i	1.00806	+	0.366902i
$612$	−1.67108e6	+	9.47717e6i	−0.180351	+	1.02282i
$613$	2.07423e6	+	1.17635e7i	0.222949	+	1.26441i	0.866568	+	0.499060i	$0.166321\pi$
$613$	2.07423e6	+	1.17635e7i	0.222949	+	1.26441i	−0.643619	+	0.765346i	$0.722568\pi$
$614$	−8.12186e6	+	2.95612e6i	−0.869430	+	0.316447i
$615$	−1.40150e7	+	2.42747e7i	−1.49419	+	2.58801i
$616$	219948.	+	380962.i	0.0233544	+	0.0404511i
$617$	986736.	+	827970.i	0.104349	+	0.0875591i	0.693469	−	0.720486i	$-0.256081\pi$
$617$	986736.	+	827970.i	0.104349	+	0.0875591i	−0.589121	+	0.808045i	$0.700526\pi$
$618$	−3.83103e6	−	3.21462e6i	−0.403501	−	0.338578i
$619$	−2.63657e6	−	4.56666e6i	−0.276574	−	0.479041i	0.693957	−	0.720017i	$-0.255866\pi$
$619$	−2.63657e6	−	4.56666e6i	−0.276574	−	0.479041i	−0.970531	+	0.240976i	$0.922533\pi$
$620$	4.52165e6	−	7.83174e6i	0.472409	−	0.818236i
$621$	−1.96768e6	+	716176.i	−0.204750	+	0.0745231i
$622$	1.36975e6	+	7.76823e6i	0.141960	+	0.805093i
$623$	−245774.	+	1.39386e6i	−0.0253698	+	0.143879i
$624$	−5.08952e6	−	1.85243e6i	−0.523257	−	0.190450i
$625$	−4.72855e6	+	3.96772e6i	−0.484203	+	0.406295i
$626$	−2.10870e6			−0.215070
$627$	−2.26747e6	+	1.85478e7i	−0.230341	+	1.88418i
$628$	7.41237e6			0.749994
$629$	4.94806e6	−	4.15192e6i	0.498664	−	0.418429i
$630$	−2.19208e6	−	797852.i	−0.220042	−	0.0800886i
$631$	2.02633e6	−	1.14919e7i	0.202599	−	1.14900i	−0.698575	−	0.715537i	$-0.746182\pi$
$631$	2.02633e6	−	1.14919e7i	0.202599	−	1.14900i	0.901174	−	0.433458i	$-0.142707\pi$
$632$	341938.	+	1.93922e6i	0.0340529	+	0.193124i
$633$	9.57476e6	−	3.48493e6i	0.949770	−	0.345688i
$634$	−3.46089e6	+	5.99443e6i	−0.341951	+	0.592277i
$635$	−1.95029e6	−	3.37801e6i	−0.191940	−	0.332450i
$636$	532825.	+	447093.i	0.0522326	+	0.0438284i
$637$	−1.01883e7	−	8.54899e6i	−0.994839	−	0.834769i
$638$	7.50602e6	+	1.30008e7i	0.730059	+	1.26450i
$639$	−5.57374e6	+	9.65400e6i	−0.540001	+	0.935309i
$640$	−1.30130e6	+	473633.i	−0.125582	+	0.0457080i
$641$	−2.12612e6	−	1.20578e7i	−0.204382	−	1.15911i	−0.898410	−	0.439158i	$-0.855277\pi$
$641$	−2.12612e6	−	1.20578e7i	−0.204382	−	1.15911i	0.694028	−	0.719948i	$-0.255834\pi$
$642$	−3.92291e6	+	2.22480e7i	−0.375639	+	2.13036i
$643$	−9.69727e6	−	3.52952e6i	−0.924958	−	0.336657i	−0.164749	−	0.986336i	$-0.552681\pi$
$643$	−9.69727e6	−	3.52952e6i	−0.924958	−	0.336657i	−0.760209	+	0.649678i	$0.774904\pi$
$644$	71033.7	−	59604.3i	0.00674916	−	0.00566322i
$645$	3.28158e7			3.10587
$646$	3.79738e6	−	7.46249e6i	0.358016	−	0.703562i
$647$	1.41105e7			1.32520			0.662601	−	0.748972i	$-0.269452\pi$
$647$	1.41105e7			1.32520			0.662601	+	0.748972i	$0.269452\pi$
$648$	1.74075e6	−	1.46066e6i	0.162854	−	0.136651i
$649$	2.34352e6	+	852971.i	0.218402	+	0.0794918i
$650$	2.24009e6	−	1.27042e7i	0.207961	−	1.17940i
$651$	−467214.	−	2.64970e6i	−0.0432079	−	0.245044i
$652$	1.65343e6	−	601800.i	0.152324	−	0.0554413i
$653$	−4.02555e6	+	6.97246e6i	−0.369439	+	0.639887i	−0.989478	−	0.144684i	$-0.953783\pi$
$653$	−4.02555e6	+	6.97246e6i	−0.369439	+	0.639887i	0.620039	+	0.784571i	$0.287117\pi$
$654$	−1.19627e7	−	2.07201e7i	−1.09367	−	1.89429i
$655$	−1.93877e7	−	1.62682e7i	−1.76573	−	1.48162i
$656$	2.46668e6	+	2.06979e6i	0.223797	+	0.187788i
$657$	1.12573e7	+	1.94983e7i	1.01747	+	1.76231i
$658$	376521.	−	652154.i	0.0339020	−	0.0587199i
$659$	−3.28997e6	+	1.19745e6i	−0.295106	+	0.107410i	−0.485331	−	0.874331i	$-0.661301\pi$
$659$	−3.28997e6	+	1.19745e6i	−0.295106	+	0.107410i	0.190224	+	0.981741i	$0.439079\pi$
$660$	−2.78862e6	−	1.58151e7i	−0.249190	−	1.41322i
$661$	1.40477e6	−	7.96682e6i	0.125055	−	0.709221i	−0.856221	−	0.516610i	$-0.827194\pi$
$661$	1.40477e6	−	7.96682e6i	0.125055	−	0.709221i	0.981275	−	0.192610i	$-0.0616953\pi$
$662$	−4.07814e6	−	1.48432e6i	−0.361674	−	0.131639i
$663$	−2.15599e7	+	1.80909e7i	−1.90486	+	1.59837i
$664$	2.40730e6			0.211889
$665$	1.62163e6	+	1.22064e6i	0.142199	+	0.107037i
$666$	−8.78140e6			−0.767146
$667$	2.42412e6	−	2.03407e6i	0.210979	−	0.177032i
$668$	−846884.	−	308240.i	−0.0734315	−	0.0267269i
$669$	−2.07240e6	+	1.17532e7i	−0.179023	+	1.01529i
$670$	63158.7	+	358191.i	0.00543558	+	0.0308267i
$671$	1.42285e7	−	5.17874e6i	1.21998	−	0.444035i
$672$	−206005.	+	356812.i	−0.0175977	+	0.0304801i
$673$	−2.83240e6	−	4.90586e6i	−0.241055	−	0.417520i	0.719960	−	0.694016i	$-0.244160\pi$
$673$	−2.83240e6	−	4.90586e6i	−0.241055	−	0.417520i	−0.961015	+	0.276496i	$0.910827\pi$
$674$	−5.88572e6	−	4.93870e6i	−0.499056	−	0.418758i
$675$	1.69756e7	+	1.42442e7i	1.43405	+	1.20331i
$676$	−2.18105e6	−	3.77768e6i	−0.183568	−	0.317950i
$677$	−2.12473e6	+	3.68014e6i	−0.178169	+	0.308598i	−0.941253	−	0.337701i	$-0.890351\pi$
$677$	−2.12473e6	+	3.68014e6i	−0.178169	+	0.308598i	0.763084	+	0.646299i	$0.223684\pi$
$678$	−1.62842e6	+	592697.i	−0.136048	+	0.0495175i
$679$	−303863.	−	1.72329e6i	−0.0252932	−	0.143445i
$680$	−1.24958e6	+	7.08670e6i	−0.103631	+	0.587722i
$681$	−572171.	−	208253.i	−0.0472779	−	0.0172077i
$682$	9.22883e6	−	7.74391e6i	0.759776	−	0.637528i
$683$	2.09008e7			1.71440			0.857200	−	0.514984i	$-0.172202\pi$
$683$	2.09008e7			1.71440			0.857200	+	0.514984i	$0.172202\pi$
$684$	−1.04761e7	+	4.45333e6i	−0.856165	+	0.363953i
$685$	1.15752e7			0.942547
$686$	−1.56095e6	+	1.30980e6i	−0.126643	+	0.106266i
$687$	−7.71881e6	−	2.80942e6i	−0.623962	−	0.227104i
$688$	654619.	−	3.71253e6i	0.0527251	−	0.299019i
$689$	229755.	+	1.30300e6i	0.0184381	+	0.104568i
$690$	−3.18101e6	+	1.15779e6i	−0.254356	+	0.0925780i
$691$	4.48689e6	−	7.77152e6i	0.357479	−	0.619171i	−0.630060	−	0.776546i	$-0.716970\pi$
$691$	4.48689e6	−	7.77152e6i	0.357479	−	0.619171i	0.987539	+	0.157375i	$0.0503032\pi$
$692$	412359.	+	714226.i	0.0327348	+	0.0566984i
$693$	−2.38062e6	−	1.99758e6i	−0.188303	−	0.158005i
$694$	−5.25645e6	−	4.41069e6i	−0.414280	−	0.347622i
$695$	1.24652e7	+	2.15904e7i	0.978899	+	1.69550i
$696$	−7.03020e6	+	1.21767e7i	−0.550104	+	0.952808i
$697$	1.57234e7	−	5.72286e6i	1.22593	−	0.446202i
$698$	2.32915e6	+	1.32093e7i	0.180950	+	1.02622i
$699$	−3.84013e6	+	2.17785e7i	−0.297271	+	1.68591i
$700$	−922143.	−	335633.i	−0.0711301	−	0.0258892i
$701$	−1.19347e7	+	1.00144e7i	−0.917308	+	0.769713i	−0.973495	−	0.228708i	$-0.926550\pi$
$701$	−1.19347e7	+	1.00144e7i	−0.917308	+	0.769713i	0.0561873	+	0.998420i	$0.482106\pi$
$702$	1.76982e7			1.35546
$703$	7.30784e6	+	2.23002e6i	0.557700	+	0.170185i
$704$	−1.84483e6			−0.140289
$705$	−2.10592e7	+	1.76708e7i	−1.59577	+	1.33901i
$706$	−7.56174e6	−	2.75225e6i	−0.570966	−	0.207815i
$707$	−119855.	+	679732.i	−0.00901795	+	0.0511433i
$708$	405612.	+	2.30034e6i	0.0304108	+	0.172468i
$709$	−4.27191e6	+	1.55485e6i	−0.319159	+	0.116164i	−0.496632	−	0.867961i	$-0.665430\pi$
$709$	−4.27191e6	+	1.55485e6i	−0.319159	+	0.116164i	0.177473	+	0.984126i	$0.443208\pi$
$710$	−4.16785e6	+	7.21893e6i	−0.310289	+	0.537436i
$711$	−6.95555e6	−	1.20474e7i	−0.516009	−	0.893754i
$712$	−4.54700e6	−	3.81539e6i	−0.336144	−	0.282058i
$713$	−1.94539e6	−	1.63237e6i	−0.143312	−	0.120253i
$714$	1.07049e6	+	1.85414e6i	0.0785843	+	0.136112i
$715$	1.52740e7	−	2.64554e7i	1.11735	−	1.93530i
$716$	9.74429e6	−	3.54663e6i	0.710342	−	0.258543i
$717$	1.27442e6	+	7.22759e6i	0.0925793	+	0.525044i
$718$	1.41079e6	−	8.00099e6i	0.102130	−	0.579205i
$719$	1.67340e7	+	6.09068e6i	1.20720	+	0.439383i	0.865730	−	0.500511i	$-0.166855\pi$
$719$	1.67340e7	+	6.09068e6i	1.20720	+	0.439383i	0.341465	+	0.939894i	$0.389077\pi$
$720$	7.49427e6	−	6.28844e6i	0.538763	−	0.452076i
$721$	−723675.			−0.0518448
$722$	9.84904e6	−	1.04567e6i	0.703155	−	0.0746535i
$723$	−2.53808e7			−1.80576
$724$	6.03475e6	−	5.06375e6i	0.427871	−	0.359026i
$725$	−3.14693e7	−	1.14539e7i	−2.22353	−	0.809297i
$726$	765612.	−	4.34200e6i	0.0539098	−	0.305737i
$727$	3.85304e6	+	2.18517e7i	0.270376	+	1.53338i	0.753278	+	0.657703i	$0.228472\pi$
$727$	3.85304e6	+	2.18517e7i	0.270376	+	1.53338i	−0.482902	+	0.875675i	$0.660417\pi$
$728$	−736475.	+	268055.i	−0.0515027	+	0.0187454i
$729$	9.63625e6	−	1.66905e7i	0.671567	−	1.16319i
$730$	8.41784e6	+	1.45801e7i	0.584647	+	1.01264i
$731$	−1.50063e7	−	1.25918e7i	−1.03868	−	0.871555i
$732$	1.08639e7	+	9.11586e6i	0.749387	+	0.628811i
$733$	698199.	+	1.20932e6i	0.0479976	+	0.0831342i	0.889026	−	0.457857i	$-0.151383\pi$
$733$	698199.	+	1.20932e6i	0.0479976	+	0.0831342i	−0.841028	+	0.540991i	$0.818049\pi$
$734$	−706990.	+	1.22454e6i	−0.0484366	+	0.0838946i
$735$	3.47072e7	−	1.26324e7i	2.36975	−	0.862517i
$736$	67528.2	+	382972.i	0.00459505	+	0.0260599i
$737$	−84139.2	+	477177.i	−0.00570597	+	0.0323602i
$738$	−2.13762e7	−	7.78029e6i	−1.44474	−	0.525842i
$739$	1.89056e7	−	1.58636e7i	1.27344	−	1.06854i	0.279327	−	0.960196i	$-0.409889\pi$
$739$	1.89056e7	−	1.58636e7i	1.27344	−	1.06854i	0.994113	−	0.108347i	$-0.0345557\pi$
$740$	−6.56643e6			−0.440808
$741$	−3.18420e7	−	9.71675e6i	−2.13037	−	0.650093i
$742$	100650.			0.00671124
$743$	2.76356e6	−	2.31890e6i	0.183652	−	0.154103i	−0.546327	−	0.837572i	$-0.683974\pi$
$743$	2.76356e6	−	2.31890e6i	0.183652	−	0.154103i	0.729979	+	0.683470i	$0.239530\pi$
$744$	1.06032e7	+	3.85924e6i	0.702270	+	0.255605i
$745$	−2.69842e6	+	1.53035e7i	−0.178123	+	1.01018i
$746$	−1.91819e6	−	1.08786e7i	−0.126196	−	0.715690i
$747$	−1.59809e7	+	5.81656e6i	−1.04785	+	0.381386i
$748$	−4.79323e6	+	8.30211e6i	−0.313238	+	0.542543i
$749$	1.63452e6	+	2.83107e6i	0.106460	+	0.184394i
$750$	6.10452e6	+	5.12230e6i	0.396277	+	0.332515i
$751$	−1.14869e7	−	9.63869e6i	−0.743198	−	0.623617i	0.190496	−	0.981688i	$-0.438990\pi$
$751$	−1.14869e7	−	9.63869e6i	−0.743198	−	0.623617i	−0.933695	+	0.358071i	$0.883435\pi$
$752$	1.57904e6	+	2.73499e6i	0.101824	+	0.176364i
$753$	4.64587e6	−	8.04689e6i	0.298593	−	0.517179i
$754$	−2.51332e7	+	9.14772e6i	−1.60997	+	0.585983i
$755$	−6.51695e6	−	3.69595e7i	−0.416080	−	2.35971i
$756$	233786.	−	1.32587e6i	0.0148770	−	0.0843714i
$757$	−1.09992e7	−	4.00338e6i	−0.697624	−	0.253914i	−0.0312277	−	0.999512i	$-0.509942\pi$
$757$	−1.09992e7	−	4.00338e6i	−0.697624	−	0.253914i	−0.666396	+	0.745598i	$0.732164\pi$
$758$	−6.17821e6	+	5.18413e6i	−0.390561	+	0.327720i
$759$	−4.50966e6			−0.284145
$760$	−7.83364e6	+	3.33005e6i	−0.491960	+	0.209130i
$761$	−1.09596e7			−0.686016			−0.343008	−	0.939333i	$-0.611446\pi$
$761$	−1.09596e7			−0.686016			−0.343008	+	0.939333i	$0.611446\pi$
$762$	3.72826e6	−	3.12839e6i	0.232605	−	0.195179i
$763$	−3.25333e6	−	1.18412e6i	−0.202310	−	0.0736347i
$764$	187213.	−	1.06174e6i	0.0116039	−	0.0658087i
$765$	−8.82770e6	−	5.00644e7i	−0.545374	−	3.09297i
$766$	2.12318e7	−	7.72774e6i	1.30742	−	0.475861i
$767$	−2.22164e6	+	3.84800e6i	−0.136360	+	0.236182i
$768$	−863940.	−	1.49639e6i	−0.0528543	−	0.0915463i
$769$	2.23810e7	+	1.87799e7i	1.36478	+	1.14519i	0.974473	+	0.224504i	$0.0720763\pi$
$769$	2.23810e7	+	1.87799e7i	1.36478	+	1.14519i	0.390309	+	0.920684i	$0.372368\pi$
$770$	−1.78015e6	−	1.49372e6i	−0.108200	−	0.0907909i
$771$	−2.09830e7	−	3.63436e7i	−1.27125	−	2.20187i
$772$	1.61170e6	−	2.79155e6i	0.0973288	−	0.168578i
$773$	8.49410e6	−	3.09160e6i	0.511291	−	0.186095i	−0.0734743	−	0.997297i	$-0.523409\pi$
$773$	8.49410e6	−	3.09160e6i	0.511291	−	0.186095i	0.584766	+	0.811202i	$0.301186\pi$
$774$	4.62459e6	+	2.62274e7i	0.277473	+	1.57363i
$775$	−4.66686e6	+	2.64671e7i	−0.279107	+	1.58289i
$776$	6.89601e6	+	2.50994e6i	0.411096	+	0.149627i
$777$	−1.49659e6	+	1.25578e6i	−0.0889301	+	0.0746212i
$778$	1.23675e7			0.732543
$779$	1.58134e7	+	1.19032e7i	0.933643	+	0.702780i
$780$	2.86115e7			1.68385
$781$	−8.50671e6	+	7.13798e6i	−0.499038	+	0.418743i
$782$	1.89890e6	+	691145.i	0.111042	+	0.0404159i
$783$	7.97825e6	−	4.52469e7i	0.465054	−	2.63745i
$784$	−736784.	−	4.17851e6i	−0.0428105	−	0.242790i
$785$	−3.67954e7	+	1.33924e7i	−2.13118	+	0.775684i
$786$	1.57894e7	−	2.73481e7i	0.911612	−	1.57896i
$787$	−5.27843e6	−	9.14251e6i	−0.303786	−	0.526173i	0.673204	−	0.739457i	$-0.264918\pi$
$787$	−5.27843e6	−	9.14251e6i	−0.303786	−	0.526173i	−0.976990	+	0.213284i	$0.931584\pi$
$788$	−1.16648e6	−	978789.i	−0.0669206	−	0.0561531i
$789$	3.18318e7	+	2.67101e7i	1.82041	+	1.52750i
$790$	−5.20112e6	−	9.00861e6i	−0.296503	−	0.513559i
$791$	−125381.	+	217167.i	−0.00712512	+	0.0123411i
$792$	1.22469e7	−	4.45751e6i	0.693767	−	0.252510i
$793$	4.68451e6	+	2.65672e7i	0.264534	+	1.50025i
$794$	1.11717e6	−	6.33578e6i	0.0628880	−	0.356655i
$795$	−3.45276e6	−	1.25670e6i	−0.193753	−	0.0705204i
$796$	−1.47952e6	+	1.24146e6i	−0.0827634	+	0.0694467i
$797$	−3.23295e7			−1.80282			−0.901411	−	0.432964i	$-0.857468\pi$
$797$	−3.23295e7			−1.80282			−0.901411	+	0.432964i	$0.857468\pi$
$798$	−1.14855e6	+	2.25710e6i	−0.0638474	+	0.125471i
$799$	1.64107e7			0.909410
$800$	3.15262e6	−	2.64536e6i	0.174159	−	0.146137i
$801$	3.94041e7	+	1.43419e7i	2.17000	+	0.789817i
$802$	−1.80633e6	+	1.02442e7i	−0.0991654	+	0.562395i
$803$	3.89463e6	+	2.20875e7i	0.213146	+	1.20881i
$804$	−426453.	+	155216.i	−0.0232665	+	0.00846832i
$805$	−244924.	+	424220.i	−0.0133211	+	0.0230729i
$806$	1.07321e7	+	1.85885e7i	0.581898	+	1.00788i
$807$	2.16938e7	+	1.82032e7i	1.17260	+	0.983931i
$808$	−2.21740e6	−	1.86062e6i	−0.119486	−	0.100260i
$809$	−210232.	−	364133.i	−0.0112935	−	0.0195609i	0.860323	−	0.509749i	$-0.170262\pi$
$809$	−210232.	−	364133.i	−0.0112935	−	0.0195609i	−0.871617	+	0.490188i	$0.836928\pi$
$810$	−6.00208e6	+	1.03959e7i	−0.321432	+	0.556737i
$811$	−2.42202e7	+	8.81543e6i	−1.29308	+	0.470643i	−0.894737	−	0.446594i	$-0.852637\pi$
$811$	−2.42202e7	+	8.81543e6i	−1.29308	+	0.470643i	−0.398343	+	0.917236i	$0.630415\pi$
$812$	353305.	+	2.00369e6i	0.0188044	+	0.106645i
$813$	3.79849e6	−	2.15423e7i	0.201551	−	1.14305i
$814$	−8.22016e6	−	2.99189e6i	−0.434830	−	0.158265i
$815$	−7.12041e6	+	5.97473e6i	−0.375501	+	0.315083i
$816$	−8.97875e6			−0.472053
$817$	2.81184e6	−	2.30007e7i	0.147379	−	1.20555i
$818$	−4.96072e6			−0.259216
$819$	4.24142e6	−	3.55897e6i	0.220954	−	0.185402i
$820$	−1.59844e7	−	5.81784e6i	−0.830159	−	0.302153i
$821$	2.94683e6	−	1.67123e7i	0.152580	−	0.865323i	−0.808386	−	0.588653i	$-0.799658\pi$
$821$	2.94683e6	−	1.67123e7i	0.152580	−	0.865323i	0.960965	−	0.276669i	$-0.0892306\pi$
$822$	2.50797e6	+	1.42234e7i	0.129462	+	0.734217i
$823$	1.55992e7	−	5.67765e6i	0.802792	−	0.292192i	0.0921489	−	0.995745i	$-0.470626\pi$
$823$	1.55992e7	−	5.67765e6i	0.802792	−	0.292192i	0.710643	+	0.703553i	$0.248404\pi$
$824$	1.51746e6	−	2.62832e6i	0.0778575	−	0.134853i
$825$	2.38625e7	+	4.13311e7i	1.22062	+	2.11418i
$826$	258926.	+	217265.i	0.0132046	+	0.0110800i
$827$	−1.62051e7	−	1.35977e7i	−0.823925	−	0.691355i	0.129963	−	0.991519i	$-0.458514\pi$
$827$	−1.62051e7	−	1.35977e7i	−0.823925	−	0.691355i	−0.953888	+	0.300164i	$0.902959\pi$
$828$	−1.37363e6	−	2.37920e6i	−0.0696296	−	0.120602i
$829$	3.06318e6	−	5.30559e6i	0.154806	−	0.268131i	−0.778183	−	0.628038i	$-0.783858\pi$
$829$	3.06318e6	−	5.30559e6i	0.154806	−	0.268131i	0.932988	+	0.359907i	$0.117192\pi$
$830$	−1.19499e7	+	4.34942e6i	−0.602103	+	0.219147i
$831$	2.50259e6	+	1.41929e7i	0.125715	+	0.712966i
$832$	570752.	−	3.23689e6i	0.0285851	−	0.162114i
$833$	−2.07185e7	−	7.54092e6i	−1.03454	−	0.376540i
$834$	−2.38290e7	+	1.99949e7i	−1.18629	+	0.995417i
$835$	4.76089e6			0.236305
$836$	−1.13238e7	+	599435.i	−0.560372	+	0.0296638i
$837$	−3.68714e7			−1.81918
$838$	5.09084e6	−	4.27172e6i	0.250426	−	0.210132i
$839$	5.77715e6	+	2.10271e6i	0.283341	+	0.103128i	0.479781	−	0.877388i	$-0.340716\pi$
$839$	5.77715e6	+	2.10271e6i	0.283341	+	0.103128i	−0.196441	+	0.980516i	$0.562938\pi$
$840$	377946.	−	2.14344e6i	0.0184812	−	0.104812i
$841$	8.49526e6	+	4.81790e7i	0.414178	+	2.34892i
$842$	−1.92976e7	+	7.02375e6i	−0.938043	+	0.341420i
$843$	−1.02081e7	+	1.76809e7i	−0.494738	+	0.856912i
$844$	3.09171e6	+	5.35500e6i	0.149397	+	0.258764i
$845$	1.76522e7	+	1.48120e7i	0.850467	+	0.713626i
$846$	−1.70908e7	−	1.43409e7i	−0.820989	−	0.688891i
$847$	−319000.	−	552524.i	−0.0152785	−	0.0264632i
$848$	−211051.	+	365551.i	−0.0100785	+	0.0174565i
$849$	−1.57804e7	+	5.74361e6i	−0.751364	+	0.273474i
$850$	−3.71355e6	−	2.10606e7i	−0.176296	−	0.999824i
$851$	−320202.	+	1.81596e6i	−0.0151565	+	0.0859570i
$852$	−9.77352e6	−	3.55727e6i	−0.461267	−	0.167887i
$853$	1.10277e7	−	9.25337e6i	0.518936	−	0.435439i	−0.345325	−	0.938483i	$-0.612231\pi$
$853$	1.10277e7	−	9.25337e6i	0.518936	−	0.435439i	0.864261	+	0.503044i	$0.167787\pi$
$854$	2.05216e6			0.0962869
$855$	4.39575e7	−	4.10344e7i	2.05645	−	1.91970i
$856$	−1.37096e7			−0.639500
$857$	2.49003e7	−	2.08938e7i	1.15812	−	0.971775i	0.158238	−	0.987401i	$-0.449419\pi$
$857$	2.49003e7	−	2.08938e7i	1.15812	−	0.971775i	0.999878	+	0.0156261i	$0.00497415\pi$
$858$	3.58172e7	+	1.30364e7i	1.66102	+	0.604561i
$859$	−2.73937e6	+	1.55357e7i	−0.126668	+	0.718371i	0.853635	+	0.520872i	$0.174393\pi$
$859$	−2.73937e6	+	1.55357e7i	−0.126668	+	0.718371i	−0.980303	+	0.197499i	$0.936718\pi$
$860$	3.45811e6	+	1.96119e7i	0.159438	+	0.904220i
$861$	−4.75570e6	+	1.73093e6i	−0.218628	+	0.0795742i
$862$	2.34458e6	−	4.06093e6i	0.107472	−	0.186147i
$863$	1.89580e7	+	3.28362e7i	0.866493	+	1.50081i	0.865557	+	0.500810i	$0.166965\pi$
$863$	1.89580e7	+	3.28362e7i	0.866493	+	1.50081i	0.000935924		1.00000i	$0.499702\pi$
$864$	4.32521e6	+	3.62928e6i	0.197116	+	0.165400i
$865$	−3.33741e6	−	2.80042e6i	−0.151659	−	0.127257i
$866$	7.01959e6	+	1.21583e7i	0.318066	+	0.550906i
$867$	−4.61105e6	+	7.98658e6i	−0.208330	+	0.360839i
$868$	1.53433e6	−	558450.i	0.0691224	−	0.0251585i
$869$	−2.40637e6	−	1.36472e7i	−0.108097	−	0.613048i
$870$	1.28979e7	−	7.31475e7i	0.577724	−	3.27643i
$871$	−811214.	−	295258.i	−0.0362318	−	0.0131873i
$872$	1.11225e7	−	9.33285e6i	0.495347	−	0.415646i
$873$	−5.18438e7			−2.30230
$874$	538935.	+	2.32879e6i	0.0238648	+	0.103122i
$875$	1.15313e6			0.0509166
$876$	−1.60919e7	+	1.35027e7i	−0.708512	+	0.594513i
$877$	5.33740e6	+	1.94266e6i	0.234332	+	0.0852898i	0.456517	−	0.889715i	$-0.349097\pi$
$877$	5.33740e6	+	1.94266e6i	0.234332	+	0.0852898i	−0.222185	+	0.975004i	$0.571319\pi$
$878$	−2.34499e6	+	1.32991e7i	−0.102661	+	0.582218i
$879$	−5.27297e6	−	2.99045e7i	−0.230188	−	1.30546i
$880$	9.15782e6	−	3.33317e6i	0.398644	−	0.145095i
$881$	1.66210e7	−	2.87883e7i	0.721467	−	1.24962i	−0.238945	−	0.971033i	$-0.576802\pi$
$881$	1.66210e7	−	2.87883e7i	0.721467	−	1.24962i	0.960412	−	0.278584i	$-0.0898650\pi$
$882$	1.49874e7	+	2.59589e7i	0.648714	+	1.12361i
$883$	1.53288e7	+	1.28624e7i	0.661616	+	0.555162i	0.910571	−	0.413354i	$-0.135643\pi$
$883$	1.53288e7	+	1.28624e7i	0.661616	+	0.555162i	−0.248955	+	0.968515i	$0.580087\pi$
$884$	−1.30838e7	−	1.09786e7i	−0.563122	−	0.472516i
$885$	−6.16966e6	−	1.06862e7i	−0.264791	−	0.458631i
$886$	−3.01575e6	+	5.22344e6i	−0.129066	+	0.223549i
$887$	−3.80020e7	+	1.38316e7i	−1.62180	+	0.590287i	−0.983724	−	0.179687i	$-0.942491\pi$
$887$	−3.80020e7	+	1.38316e7i	−1.62180	+	0.590287i	−0.638075	+	0.769974i	$0.720269\pi$
$888$	−1.42273e6	−	8.06870e6i	−0.0605466	−	0.343377i
$889$	122294.	−	693563.i	0.00518980	−	0.0294328i
$890$	2.94651e7	+	1.07244e7i	1.24690	+	0.453835i
$891$	−1.22504e7	+	1.02793e7i	−0.516960	+	0.433781i
$892$	−7.24252e6			−0.304774
$893$	1.05811e7	+	1.62746e7i	0.444018	+	0.682940i
$894$	−1.93893e7			−0.811371
$895$	−4.19632e7	+	3.52113e7i	−1.75110	+	1.46935i
$896$	−234953.	−	85515.9i	−0.00977712	−	0.00355858i
$897$	1.39520e6	−	7.91256e6i	0.0578968	−	0.328349i
$898$	−127671.	−	724058.i	−0.00528325	−	0.0299628i
$899$	5.23609e7	−	1.90578e7i	2.16077	−	0.786455i
$900$	−1.45369e7	+	2.51787e7i	−0.598227	+	1.03616i
$901$	1.09670e6	+	1.89955e6i	0.0450067	+	0.0779539i
$902$	−1.73592e7	−	1.45661e7i	−0.710416	−	0.596110i
$903$	4.53880e6	+	3.80851e6i	0.185234	+	0.155430i
$904$	−525821.	−	910749.i	−0.0214001	−	0.0370661i
$905$	−2.08078e7	+	3.60401e7i	−0.844509	+	1.46273i
$906$	4.40031e7	−	1.60158e7i	1.78099	−	0.648229i
$907$	503735.	+	2.85682e6i	0.0203322	+	0.115310i	0.993285	−	0.115696i	$-0.0369097\pi$
$907$	503735.	+	2.85682e6i	0.0203322	+	0.115310i	−0.972953	+	0.231005i	$0.925799\pi$
$908$	64164.7	−	363896.i	0.00258275	−	0.0146475i
$909$	1.92159e7	+	6.99403e6i	0.771350	+	0.280749i
$910$	3.17159e6	−	2.66128e6i	0.126962	−	0.106534i
$911$	2.43185e7			0.970824			0.485412	−	0.874286i	$-0.338670\pi$
$911$	2.43185e7			0.970824			0.485412	+	0.874286i	$0.338670\pi$
$912$	−5.78920e6	−	8.90431e6i	−0.230479	−	0.354497i
$913$	−1.69412e7			−0.672618
$914$	1.58995e7	−	1.33413e7i	0.629532	−	0.528240i
$915$	−7.03990e7	−	2.56231e7i	−2.77980	−	1.01176i
$916$	865607.	−	4.90910e6i	0.0340865	−	0.193314i
$917$	−793502.	−	4.50018e6i	−0.0311620	−	0.176728i
$918$	2.75703e7	−	1.00348e7i	1.07978	−	0.393007i
$919$	−4.11263e6	+	7.12328e6i	−0.160631	+	0.278222i	−0.935095	−	0.354396i	$-0.884686\pi$
$919$	−4.11263e6	+	7.12328e6i	−0.160631	+	0.278222i	0.774464	+	0.632618i	$0.218020\pi$
$920$	−1.02715e6	−	1.77908e6i	−0.0400098	−	0.0692989i
$921$	4.36413e7	+	3.66194e7i	1.69531	+	1.42253i
$922$	1.06087e7	+	8.90179e6i	0.410995	+	0.344866i
$923$	−9.89234e6	−	1.71340e7i	−0.382204	−	0.661996i
$924$	1.44975e6	−	2.51105e6i	0.0558618	−	0.0967554i
$925$	1.83376e7	−	6.67433e6i	0.704673	−	0.256480i
$926$	−1.93643e6	−	1.09820e7i	−0.0742119	−	0.420877i
$927$	−3.72309e6	+	2.11147e7i	−0.142300	+	0.807022i
$928$	−8.01807e6	−	2.91834e6i	−0.305633	−	0.111241i
$929$	3.21003e7	−	2.69354e7i	1.22031	−	1.02396i	0.221501	−	0.975160i	$-0.428904\pi$
$929$	3.21003e7	−	2.69354e7i	1.22031	−	1.02396i	0.998808	−	0.0488016i	$-0.0155402\pi$
$930$	−5.96075e7			−2.25992
$931$	−5.88020e6	−	2.54089e7i	−0.222340	−	0.960752i
$932$	−1.34203e7			−0.506084
$933$	3.98289e7	−	3.34204e7i	1.49794	−	1.25692i
$934$	−675872.	−	245997.i	−0.0253511	−	0.00922705i
$935$	8.79384e6	−	4.98724e7i	0.328965	−	1.86565i
$936$	4.03211e6	+	2.28672e7i	0.150433	+	0.853147i
$937$	−2.61409e7	+	9.51451e6i	−0.972684	+	0.354028i	−0.778992	−	0.627034i	$-0.784269\pi$
$937$	−2.61409e7	+	9.51451e6i	−0.972684	+	0.354028i	−0.193692	+	0.981062i	$0.562046\pi$
$938$	−32835.0	+	56872.0i	−0.00121851	+	0.00211053i
$939$	6.94959e6	+	1.20370e7i	0.257214	+	0.445508i
$940$	−1.27799e7	−	1.07236e7i	−0.471747	−	0.395843i
$941$	−1.47209e7	−	1.23523e7i	−0.541952	−	0.454752i	0.330253	−	0.943892i	$-0.392866\pi$
$941$	−1.47209e7	−	1.23523e7i	−0.541952	−	0.454752i	−0.872205	+	0.489141i	$0.837310\pi$
$942$	−2.44287e7	−	4.23118e7i	−0.896960	−	1.55358i
$943$	−2.38839e6	+	4.13681e6i	−0.0874632	+	0.151491i
$944$	−1.33203e6	+	484818.i	−0.0486500	+	0.0177071i
$945$	1.23501e6	+	7.00407e6i	0.0449873	+	0.255135i
$946$	−4.60685e6	+	2.61268e7i	−0.167370	+	0.949200i
$947$	1.74418e7	+	6.34829e6i	0.631999	+	0.230029i	0.638101	−	0.769953i	$-0.279720\pi$
$947$	1.74418e7	+	6.34829e6i	0.631999	+	0.230029i	−0.00610225	+	0.999981i	$0.501942\pi$
$948$	9.94270e6	−	8.34291e6i	0.359322	−	0.301507i
$949$	−3.99593e7			−1.44030
$950$	1.84916e7	−	1.72619e7i	0.664762	−	0.620555i
$951$	4.56238e7			1.63584
$952$	−995294.	+	835151.i	−0.0355926	+	0.0298657i
$953$	−4.55750e7	−	1.65879e7i	−1.62553	−	0.591644i	−0.641104	−	0.767454i	$-0.721523\pi$
$953$	−4.55750e7	−	1.65879e7i	−1.62553	−	0.591644i	−0.984424	+	0.175810i	$0.943746\pi$
$954$	517812.	−	2.93666e6i	0.0184205	−	0.104468i
$955$	988977.	+	5.60877e6i	0.0350895	+	0.199003i
$956$	−4.18518e6	+	1.52328e6i	−0.148105	+	0.0539058i
$957$	4.94747e7	−	8.56927e7i	1.74624	−	3.02457i
$958$	6.48685e6	+	1.12356e7i	0.228360	+	0.395531i
$959$	1.60099e6	+	1.34339e6i	0.0562136	+	0.0471688i
$960$	6.99227e6	+	5.86721e6i	0.244872	+	0.205472i
$961$	−8.04399e6	−	1.39326e7i	−0.280972	−	0.486658i
$962$	7.79266e6	−	1.34973e7i	0.271487	−	0.470228i
$963$	9.10114e7	−	3.31254e7i	3.16250	−	1.15105i
$964$	−2.67462e6	−	1.51685e7i	−0.0926978	−	0.525716i
$965$	−2.95689e6	+	1.67694e7i	−0.102216	+	0.579693i
$966$	−574341.	−	209043.i	−0.0198028	−	0.00720763i
$967$	−7.83372e6	+	6.57327e6i	−0.269403	+	0.226056i	−0.767473	−	0.641081i	$-0.778486\pi$
$967$	−7.83372e6	+	6.57327e6i	−0.269403	+	0.226056i	0.498071	+	0.867136i	$0.334042\pi$
$968$	2.67562e6			0.0917776
$969$	−5.51128e7	+	2.91744e6i	−1.88557	+	0.0998144i
$970$	−3.87670e7			−1.32292
$971$	3.44728e7	−	2.89261e7i	1.17335	−	0.984559i	0.173352	−	0.984860i	$-0.444540\pi$
$971$	3.44728e7	−	2.89261e7i	1.17335	−	0.984559i	1.00000		0.000301134i	$9.58540e-5\pi$
$972$	6.07015e6	+	2.20935e6i	0.206079	+	0.0750066i
$973$	−781636.	+	4.43288e6i	−0.0264681	+	0.150108i
$974$	3.80614e6	+	2.15857e7i	0.128554	+	0.729068i
$975$	−7.99013e7	+	2.90817e7i	−2.69180	+	0.979734i
$976$	−4.30315e6	+	7.45327e6i	−0.144598	+	0.250451i
$977$	−6.74789e6	−	1.16877e7i	−0.226168	−	0.391735i	0.730501	−	0.682911i	$-0.239287\pi$
$977$	−6.74789e6	−	1.16877e7i	−0.226168	−	0.391735i	−0.956669	+	0.291177i	$0.905953\pi$
$978$	−8.88440e6	−	7.45490e6i	−0.297017	−	0.249227i
$979$	3.19993e7	+	2.68506e7i	1.06705	+	0.895360i
$980$	1.12070e7	+	1.94112e7i	0.372757	+	0.645634i
$981$	−5.12863e7	+	8.88306e7i	−1.70149	+	2.94707i
$982$	2.42872e7	−	8.83981e6i	0.803708	−	0.292526i
$983$	2.77587e6	+	1.57428e7i	0.0916254	+	0.519634i	0.995729	+	0.0923208i	$0.0294285\pi$
$983$	2.77587e6	+	1.57428e7i	0.0916254	+	0.519634i	−0.904104	+	0.427313i	$0.859460\pi$
$984$	3.68556e6	−	2.09018e7i	0.121343	−	0.688171i
$985$	7.55889e6	+	2.75121e6i	0.248238	+	0.0903511i
$986$	−3.39657e7	+	2.85006e7i	−1.11262	+	0.933602i
$987$	−4.96356e6			−0.162181
$988$	2.45159e6	−	2.00539e7i	0.0799018	−	0.653593i
$989$	5.59234e6			0.181804
$990$	−5.27406e7	+	4.42546e7i	−1.71024	+	1.43506i
$991$	−5.58040e6	−	2.03110e6i	−0.180502	−	0.0656973i	0.250188	−	0.968197i	$-0.419508\pi$
$991$	−5.58040e6	−	2.03110e6i	−0.180502	−	0.0656973i	−0.430690	+	0.902500i	$0.641730\pi$
$992$	−1.18907e6	+	6.74355e6i	−0.0383644	+	0.217575i
$993$	4.96730e6	+	2.81709e7i	0.159863	+	0.906626i
$994$	−1.41427e6	+	514753.i	−0.0454012	+	0.0165247i
$995$	5.10138e6	−	8.83584e6i	0.163354	−	0.282937i
$996$	−7.93365e6	−	1.37415e7i	−0.253411	−	0.438920i
$997$	−1.30164e7	−	1.09221e7i	−0.414719	−	0.347991i	0.411431	−	0.911441i	$-0.365029\pi$
$997$	−1.30164e7	−	1.09221e7i	−0.414719	−	0.347991i	−0.826150	+	0.563450i	$0.809474\pi$
$998$	660352.	+	554101.i	0.0209869	+	0.0176101i
$999$	1.33863e7	+	2.31858e7i	0.424373	+	0.735036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.25.1	✓	30
19.4	even	9		722.6.a.r.1.15		15
19.15	odd	18		722.6.a.q.1.1		15
19.16	even	9	inner	38.6.e.b.35.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.25.1	✓	30	1.1	even	1	trivial
38.6.e.b.35.1	yes	30	19.16	even	9	inner
722.6.a.q.1.1		15	19.15	odd	18
722.6.a.r.1.15		15	19.4	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.06418 - 2.57115i) q^{2} +(-24.7753 - 9.01748i) q^{3} +(2.77837 - 15.7569i) q^{4} +(14.6771 + 83.2381i) q^{5} +(-99.1013 + 36.0699i) q^{6} +(-7.63036 + 13.2162i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(346.353 + 290.625i) q^{9} +O(q^{10})\)	\(q+(3.06418 - 2.57115i) q^{2} +(-24.7753 - 9.01748i) q^{3} +(2.77837 - 15.7569i) q^{4} +(14.6771 + 83.2381i) q^{5} +(-99.1013 + 36.0699i) q^{6} +(-7.63036 + 13.2162i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(346.353 + 290.625i) q^{9} +(258.991 + 217.319i) q^{10} +(225.199 + 390.055i) q^{11} +(-210.923 + 365.329i) q^{12} +(-754.055 + 274.454i) q^{13} +(10.6000 + 60.1155i) q^{14} +(386.967 - 2194.60i) q^{15} +(-240.561 - 87.5572i) q^{16} +(-1019.05 + 855.086i) q^{17} +1808.53 q^{18} +(-1505.05 - 459.273i) q^{19} +1352.35 q^{20} +(308.221 - 258.628i) q^{21} +(1692.94 + 616.180i) q^{22} +(65.9455 - 373.996i) q^{23} +(293.011 + 1661.75i) q^{24} +(-3776.62 + 1374.58i) q^{25} +(-1604.90 + 2779.76i) q^{26} +(-2756.91 - 4775.11i) q^{27} +(187.046 + 156.951i) q^{28} +(6383.20 + 5356.14i) q^{29} +(-4456.91 - 7719.60i) q^{30} +(3343.54 - 5791.19i) q^{31} +(-962.245 + 350.229i) q^{32} +(-2062.05 - 11694.5i) q^{33} +(-924.001 + 5240.27i) q^{34} +(-1212.08 - 441.161i) q^{35} +(5541.65 - 4649.99i) q^{36} -4855.55 q^{37} +(-5792.59 + 2462.41i) q^{38} +21156.8 q^{39} +(4143.85 - 3477.11i) q^{40} +(-11819.7 - 4302.01i) q^{41} +(279.472 - 1584.97i) q^{42} +(2557.11 + 14502.1i) q^{43} +(6771.76 - 2464.72i) q^{44} +(-19107.6 + 33095.3i) q^{45} +(-759.530 - 1315.54i) q^{46} +(-9450.14 - 7929.61i) q^{47} +(5170.44 + 4338.51i) q^{48} +(8287.06 + 14353.6i) q^{49} +(-8037.98 + 13922.2i) q^{50} +(32958.1 - 11995.8i) q^{51} +(2229.50 + 12644.1i) q^{52} +(286.317 - 1623.79i) q^{53} +(-20725.2 - 7543.36i) q^{54} +(-29162.2 + 24470.0i) q^{55} +976.687 q^{56} +(33146.6 + 24950.4i) q^{57} +33330.7 q^{58} +(4241.71 - 3559.22i) q^{59} +(-33505.0 - 12194.8i) q^{60} +(5837.77 - 33107.6i) q^{61} +(-4644.80 - 26342.0i) q^{62} +(-6483.75 + 2359.89i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-33912.3 - 58737.9i) q^{65} +(-36386.7 - 30532.1i) q^{66} +(824.112 + 691.512i) q^{67} +(10642.2 + 18432.9i) q^{68} +(-5006.32 + 8671.20i) q^{69} +(-4848.32 + 1764.65i) q^{70} +(4281.36 + 24280.8i) q^{71} +(5024.76 - 28496.8i) q^{72} +(46793.6 + 17031.5i) q^{73} +(-14878.3 + 12484.4i) q^{74} +105962. q^{75} +(-11418.3 + 22438.9i) q^{76} -6873.39 q^{77} +(64828.3 - 54397.4i) q^{78} +(-28912.3 - 10523.2i) q^{79} +(3757.34 - 21308.9i) q^{80} +(6165.55 + 34966.6i) q^{81} +(-47278.7 + 17208.0i) q^{82} +(-18807.0 + 32574.7i) q^{83} +(-3218.84 - 5575.19i) q^{84} +(-86132.4 - 72273.7i) q^{85} +(45122.4 + 37862.2i) q^{86} +(-109847. - 190260. i) q^{87} +(14412.7 - 24963.5i) q^{88} +(87151.9 - 31720.7i) q^{89} +(26543.9 + 150538. i) q^{90} +(2126.49 - 12059.9i) q^{91} +(-5709.80 - 2078.20i) q^{92} +(-135059. + 113328. i) q^{93} -49345.1 q^{94} +(16139.2 - 132018. i) q^{95} +26998.1 q^{96} +(-87838.7 + 73705.4i) q^{97} +(62298.3 + 22674.7i) q^{98} +(-35361.5 + 200545. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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