LMFDB - Embedded newform 38.6.e.b.35.2

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			35.2
Character	$\chi$	$=$	38.35
Dual form			38.6.e.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.06418 + 2.57115i) q^{2} +(-10.3802 + 3.77808i) q^{3} +(2.77837 + 15.7569i) q^{4} +(-9.06643 + 51.4183i) q^{5} +(-41.5207 - 15.1123i) q^{6} +(-107.823 - 186.754i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-92.6745 + 77.7631i) q^{9} +O(q^{10})$	\(q+(3.06418 + 2.57115i) q^{2} +(-10.3802 + 3.77808i) q^{3} +(2.77837 + 15.7569i) q^{4} +(-9.06643 + 51.4183i) q^{5} +(-41.5207 - 15.1123i) q^{6} +(-107.823 - 186.754i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-92.6745 + 77.7631i) q^{9} +(-159.985 + 134.244i) q^{10} +(-273.445 + 473.620i) q^{11} +(-88.3709 - 153.063i) q^{12} +(-242.293 - 88.1874i) q^{13} +(149.786 - 849.477i) q^{14} +(-100.151 - 567.985i) q^{15} +(-240.561 + 87.5572i) q^{16} +(1451.68 + 1218.11i) q^{17} -483.912 q^{18} +(-61.8077 - 1572.35i) q^{19} -835.384 q^{20} +(1824.79 + 1531.18i) q^{21} +(-2055.63 + 748.189i) q^{22} +(387.696 + 2198.73i) q^{23} +(122.764 - 696.226i) q^{24} +(374.898 + 136.452i) q^{25} +(-515.685 - 893.193i) q^{26} +(2010.32 - 3481.97i) q^{27} +(2643.10 - 2217.83i) q^{28} +(-2744.42 + 2302.84i) q^{29} +(1153.49 - 1997.91i) q^{30} +(4221.89 + 7312.54i) q^{31} +(-962.245 - 350.229i) q^{32} +(1049.03 - 5949.36i) q^{33} +(1316.28 + 7465.00i) q^{34} +(10580.2 - 3850.86i) q^{35} +(-1482.79 - 1244.21i) q^{36} -3258.91 q^{37} +(3853.35 - 4976.87i) q^{38} +2848.22 q^{39} +(-2559.77 - 2147.90i) q^{40} +(-8419.78 + 3064.55i) q^{41} +(1654.59 + 9383.62i) q^{42} +(3131.84 - 17761.6i) q^{43} +(-8222.52 - 2992.75i) q^{44} +(-3158.22 - 5470.20i) q^{45} +(-4465.30 + 7734.13i) q^{46} +(-15539.1 + 13038.9i) q^{47} +(2166.27 - 1817.72i) q^{48} +(-14847.9 + 25717.4i) q^{49} +(797.917 + 1382.03i) q^{50} +(-19670.9 - 7159.60i) q^{51} +(716.383 - 4062.81i) q^{52} +(623.877 + 3538.18i) q^{53} +(15112.6 - 5500.55i) q^{54} +(-21873.6 - 18354.1i) q^{55} +13801.3 q^{56} +(6582.03 + 16087.7i) q^{57} -14330.3 q^{58} +(-2351.74 - 1973.34i) q^{59} +(8671.44 - 3156.15i) q^{60} +(-1002.59 - 5685.96i) q^{61} +(-5864.99 + 33262.0i) q^{62} +(24515.0 + 8922.74i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(6731.18 - 11658.7i) q^{65} +(18511.1 - 15532.7i) q^{66} +(29630.1 - 24862.6i) q^{67} +(-15160.3 + 26258.4i) q^{68} +(-12331.3 - 21358.5i) q^{69} +(42320.6 + 15403.4i) q^{70} +(7395.34 - 41941.1i) q^{71} +(-1344.49 - 7624.96i) q^{72} +(-41684.2 + 15171.8i) q^{73} +(-9985.89 - 8379.15i) q^{74} -4407.04 q^{75} +(24603.6 - 5342.47i) q^{76} +117934. q^{77} +(8727.46 + 7323.21i) q^{78} +(-10378.5 + 3777.46i) q^{79} +(-2321.01 - 13163.1i) q^{80} +(-2607.45 + 14787.6i) q^{81} +(-33679.1 - 12258.2i) q^{82} +(10760.8 + 18638.3i) q^{83} +(-19056.8 + 33007.3i) q^{84} +(-75794.6 + 63599.3i) q^{85} +(55264.2 - 46372.1i) q^{86} +(19787.2 - 34272.5i) q^{87} +(-17500.5 - 30311.7i) q^{88} +(57745.6 + 21017.7i) q^{89} +(4387.36 - 24881.9i) q^{90} +(9655.28 + 54757.8i) q^{91} +(-33568.1 + 12217.8i) q^{92} +(-71451.3 - 59954.8i) q^{93} -81139.5 q^{94} +(81407.8 + 11077.5i) q^{95} +11311.5 q^{96} +(120513. + 101122. i) q^{97} +(-111620. + 40626.4i) q^{98} +(-11488.8 - 65156.4i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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
$3$	−10.3802	+	3.77808i	−0.665889	+	0.242364i	−0.652777	−	0.757550i	$-0.726396\pi$
$3$	−10.3802	+	3.77808i	−0.665889	+	0.242364i	−0.0131121	+	0.999914i	$0.504174\pi$
$4$	2.77837	+	15.7569i	0.0868241	+	0.492404i
$5$	−9.06643	+	51.4183i	−0.162185	+	0.919798i	0.789734	+	0.613449i	$0.210219\pi$
$5$	−9.06643	+	51.4183i	−0.162185	+	0.919798i	−0.951919	+	0.306349i	$0.900893\pi$
$6$	−41.5207	−	15.1123i	−0.470855	−	0.171377i
$7$	−107.823	−	186.754i	−0.831697	−	1.44054i	−0.896692	−	0.442655i	$-0.854037\pi$
$7$	−107.823	−	186.754i	−0.831697	−	1.44054i	0.0649954	−	0.997886i	$-0.479297\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	−92.6745	+	77.7631i	−0.381377	+	0.320013i
$10$	−159.985	+	134.244i	−0.505918	+	0.424516i
$11$	−273.445	+	473.620i	−0.681377	+	1.18018i	0.293183	+	0.956056i	$0.405285\pi$
$11$	−273.445	+	473.620i	−0.681377	+	1.18018i	−0.974561	+	0.224124i	$0.928048\pi$
$12$	−88.3709	−	153.063i	−0.177156	−	0.306843i
$13$	−242.293	−	88.1874i	−0.397633	−	0.144727i	0.135461	−	0.990783i	$-0.456748\pi$
$13$	−242.293	−	88.1874i	−0.397633	−	0.144727i	−0.533094	+	0.846056i	$0.678971\pi$
$14$	149.786	−	849.477i	0.204244	−	1.15833i
$15$	−100.151	−	567.985i	−0.114928	−	0.651791i
$16$	−240.561	+	87.5572i	−0.234923	+	0.0855050i
$17$	1451.68	+	1218.11i	1.21829	+	1.02226i	0.998912	+	0.0466244i	$0.0148464\pi$
$17$	1451.68	+	1218.11i	1.21829	+	1.02226i	0.219375	+	0.975641i	$0.429598\pi$
$18$	−483.912			−0.352034
$19$	−61.8077	−	1572.35i	−0.0392788	−	0.999228i
$19$	−61.8077	−	1572.35i	−0.0392788	−	0.999228i
$20$	−835.384			−0.466994
$21$	1824.79	+	1531.18i	0.902952	+	0.757667i
$22$	−2055.63	+	748.189i	−0.905500	+	0.329575i
$23$	387.696	+	2198.73i	0.152817	+	0.866668i	0.960755	+	0.277400i	$0.0894727\pi$
$23$	387.696	+	2198.73i	0.152817	+	0.866668i	−0.807938	+	0.589268i	$0.799416\pi$
$24$	122.764	−	696.226i	0.0435052	−	0.246730i
$25$	374.898	+	136.452i	0.119967	+	0.0436646i
$26$	−515.685	−	893.193i	−0.149607	−	0.259127i
$27$	2010.32	−	3481.97i	0.530707	−	0.919211i
$28$	2643.10	−	2217.83i	0.637117	−	0.534604i
$29$	−2744.42	+	2302.84i	−0.605976	+	0.508474i	−0.893360	−	0.449341i	$-0.851659\pi$
$29$	−2744.42	+	2302.84i	−0.605976	+	0.508474i	0.287385	+	0.957815i	$0.407214\pi$
$30$	1153.49	−	1997.91i	0.233998	−	0.405296i
$31$	4221.89	+	7312.54i	0.789047	+	1.36667i	0.926551	+	0.376169i	$0.122759\pi$
$31$	4221.89	+	7312.54i	0.789047	+	1.36667i	−0.137504	+	0.990501i	$0.543908\pi$
$32$	−962.245	−	350.229i	−0.166116	−	0.0604612i
$33$	1049.03	−	5949.36i	0.167689	−	0.951010i
$34$	1316.28	+	7465.00i	0.195277	+	1.10747i
$35$	10580.2	−	3850.86i	1.45990	−	0.531359i
$36$	−1482.79	−	1244.21i	−0.190688	−	0.160006i
$37$	−3258.91			−0.391353			−0.195676	−	0.980669i	$-0.562690\pi$
$37$	−3258.91			−0.391353			−0.195676	+	0.980669i	$0.562690\pi$
$38$	3853.35	−	4976.87i	0.432892	−	0.559110i
$39$	2848.22			0.299856
$40$	−2559.77	−	2147.90i	−0.252959	−	0.212258i
$41$	−8419.78	+	3064.55i	−0.782242	+	0.284713i	−0.702107	−	0.712071i	$-0.747757\pi$
$41$	−8419.78	+	3064.55i	−0.782242	+	0.284713i	−0.0801350	+	0.996784i	$0.525535\pi$
$42$	1654.59	+	9383.62i	0.144733	+	0.820819i
$43$	3131.84	−	17761.6i	0.258303	−	1.46491i	−0.529148	−	0.848529i	$-0.677488\pi$
$43$	3131.84	−	17761.6i	0.258303	−	1.46491i	0.787451	−	0.616378i	$-0.211400\pi$
$44$	−8222.52	−	2992.75i	−0.640285	−	0.233045i
$45$	−3158.22	−	5470.20i	−0.232494	−	0.402691i
$46$	−4465.30	+	7734.13i	−0.311140	+	0.538911i
$47$	−15539.1	+	13038.9i	−1.02608	+	0.860985i	−0.990380	−	0.138378i	$-0.955811\pi$
$47$	−15539.1	+	13038.9i	−1.02608	+	0.860985i	−0.0357021	+	0.999362i	$0.511367\pi$
$48$	2166.27	−	1817.72i	0.135709	−	0.113874i
$49$	−14847.9	+	25717.4i	−0.883438	+	1.53016i
$50$	797.917	+	1382.03i	0.0451370	+	0.0781795i
$51$	−19670.9	−	7159.60i	−1.05900	−	0.385446i
$52$	716.383	−	4062.81i	0.0367398	−	0.208362i
$53$	623.877	+	3538.18i	0.0305077	+	0.173018i	0.996255	−	0.0864681i	$-0.0275581\pi$
$53$	623.877	+	3538.18i	0.0305077	+	0.173018i	−0.965747	+	0.259486i	$0.916447\pi$
$54$	15112.6	−	5500.55i	0.705270	−	0.256697i
$55$	−21873.6	−	18354.1i	−0.975019	−	0.818138i
$56$	13801.3			0.588098
$57$	6582.03	+	16087.7i	0.268332	+	0.655855i
$58$	−14330.3			−0.559353
$59$	−2351.74	−	1973.34i	−0.0879547	−	0.0738028i	0.597750	−	0.801682i	$-0.296061\pi$
$59$	−2351.74	−	1973.34i	−0.0879547	−	0.0738028i	−0.685705	+	0.727880i	$0.740506\pi$
$60$	8671.44	−	3156.15i	0.310966	−	0.113182i
$61$	−1002.59	−	5685.96i	−0.0344983	−	0.195650i	0.962688	−	0.270614i	$-0.0872268\pi$
$61$	−1002.59	−	5685.96i	−0.0344983	−	0.195650i	−0.997186	+	0.0749644i	$0.976116\pi$
$62$	−5864.99	+	33262.0i	−0.193771	+	1.09893i
$63$	24515.0	+	8922.74i	0.778181	+	0.283235i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	6731.18	−	11658.7i	0.197609	−	0.342270i
$66$	18511.1	−	15532.7i	0.523085	−	0.438921i
$67$	29630.1	−	24862.6i	0.806391	−	0.676642i	−0.143352	−	0.989672i	$-0.545788\pi$
$67$	29630.1	−	24862.6i	0.806391	−	0.676642i	0.949743	+	0.313029i	$0.101344\pi$
$68$	−15160.3	+	26258.4i	−0.397590	+	0.688647i
$69$	−12331.3	−	21358.5i	−0.311808	−	0.540067i
$70$	42320.6	+	15403.4i	1.03230	+	0.375727i
$71$	7395.34	−	41941.1i	0.174105	−	0.987401i	−0.765066	−	0.643952i	$-0.777294\pi$
$71$	7395.34	−	41941.1i	0.174105	−	0.987401i	0.939171	−	0.343449i	$-0.111595\pi$
$72$	−1344.49	−	7624.96i	−0.0305651	−	0.173343i
$73$	−41684.2	+	15171.8i	−0.915513	+	0.333219i	−0.756452	−	0.654049i	$-0.773069\pi$
$73$	−41684.2	+	15171.8i	−0.915513	+	0.333219i	−0.159061	+	0.987269i	$0.550847\pi$
$74$	−9985.89	−	8379.15i	−0.211986	−	0.177877i
$75$	−4407.04			−0.0904677
$76$	24603.6	−	5342.47i	0.488614	−	0.106098i
$77$	117934.			2.26680
$78$	8727.46	+	7323.21i	0.162424	+	0.136290i
$79$	−10378.5	+	3777.46i	−0.187097	+	0.0680976i	−0.433869	−	0.900976i	$-0.642852\pi$
$79$	−10378.5	+	3777.46i	−0.187097	+	0.0680976i	0.246773	+	0.969073i	$0.420630\pi$
$80$	−2321.01	−	13163.1i	−0.0405463	−	0.229950i
$81$	−2607.45	+	14787.6i	−0.0441573	+	0.250429i
$82$	−33679.1	−	12258.2i	−0.553129	−	0.201322i
$83$	10760.8	+	18638.3i	0.171455	+	0.296969i	0.938929	−	0.344112i	$-0.111820\pi$
$83$	10760.8	+	18638.3i	0.171455	+	0.296969i	−0.767474	+	0.641080i	$0.778487\pi$
$84$	−19056.8	+	33007.3i	−0.294680	+	0.510401i
$85$	−75794.6	+	63599.3i	−1.13787	+	0.954783i
$86$	55264.2	−	46372.1i	0.805745	−	0.676100i
$87$	19787.2	−	34272.5i	0.280277	−	0.485454i
$88$	−17500.5	−	30311.7i	−0.240903	−	0.417257i
$89$	57745.6	+	21017.7i	0.772759	+	0.281261i	0.698150	−	0.715952i	$-0.254007\pi$
$89$	57745.6	+	21017.7i	0.772759	+	0.281261i	0.0746089	+	0.997213i	$0.476229\pi$
$90$	4387.36	−	24881.9i	0.0570948	−	0.323801i
$91$	9655.28	+	54757.8i	0.122225	+	0.693175i
$92$	−33568.1	+	12217.8i	−0.413482	+	0.150495i
$93$	−71451.3	−	59954.8i	−0.856649	−	0.718814i
$94$	−81139.5			−0.947137
$95$	81407.8	+	11077.5i	0.925459	+	0.125932i
$96$	11311.5			0.125268
$97$	120513.	+	101122.i	1.30048	+	1.09123i	0.990062	+	0.140630i	$0.0449128\pi$
$97$	120513.	+	101122.i	1.30048	+	1.09123i	0.310416	+	0.950601i	$0.399532\pi$
$98$	−111620.	+	40626.4i	−1.17402	+	0.427310i
$99$	−11488.8	−	65156.4i	−0.117812	−	0.668143i
$100$	−1108.45	+	6286.36i	−0.0110845	+	0.0628636i
$101$	−72411.3	−	26355.5i	−0.706322	−	0.257080i	−0.0362143	−	0.999344i	$-0.511530\pi$
$101$	−72411.3	−	26355.5i	−0.706322	−	0.257080i	−0.670108	+	0.742264i	$0.733752\pi$
$102$	−41866.6	−	72515.0i	−0.398444	−	0.690125i
$103$	−66453.7	+	115101.i	−0.617200	+	1.06902i	0.372794	+	0.927914i	$0.378400\pi$
$103$	−66453.7	+	115101.i	−0.617200	+	1.06902i	−0.989994	+	0.141108i	$0.954933\pi$
$104$	12641.2	−	10607.2i	0.114605	−	0.0961654i
$105$	−95275.1	+	79945.3i	−0.843347	+	0.707652i
$106$	−7185.53	+	12445.7i	−0.0621146	+	0.107586i
$107$	−56112.7	−	97190.1i	−0.473808	−	0.820659i	0.525743	−	0.850644i	$-0.323787\pi$
$107$	−56112.7	−	97190.1i	−0.473808	−	0.820659i	−0.999550	+	0.0299849i	$0.990454\pi$
$108$	60450.5	+	22002.2i	0.498701	+	0.181512i
$109$	−10542.4	+	59789.1i	−0.0849914	+	0.482010i	0.912367	+	0.409373i	$0.134253\pi$
$109$	−10542.4	+	59789.1i	−0.0849914	+	0.482010i	−0.997358	+	0.0726369i	$0.976859\pi$
$110$	−19833.3	−	112480.i	−0.156284	−	0.886330i
$111$	33828.1	−	12312.4i	0.260597	−	0.0948497i
$112$	42289.6	+	35485.2i	0.318558	+	0.267302i
$113$	44583.9			0.328459			0.164230	−	0.986422i	$-0.447486\pi$
$113$	44583.9			0.328459			0.164230	+	0.986422i	$0.447486\pi$
$114$	−21195.5	+	66219.1i	−0.152750	+	0.477223i
$115$	−116570.			−0.821944
$116$	−43910.7	−	36845.4i	−0.302988	−	0.254237i
$117$	29312.1	−	10668.7i	0.197962	−	0.0720524i
$118$	−2132.38	−	12093.4i	−0.0140981	−	0.0799543i
$119$	70962.4	−	402448.i	0.459368	−	2.60521i
$120$	34685.8	+	12624.6i	0.219886	+	0.0800320i
$121$	−69018.4	−	119543.i	−0.428550	−	0.742270i
$122$	11547.4	−	20000.6i	0.0702397	−	0.121659i
$123$	75820.8	−	63621.2i	0.451882	−	0.379174i
$124$	−103493.	+	86841.0i	−0.604445	+	0.507190i
$125$	−91995.6	+	159341.i	−0.526613	+	0.912121i
$126$	52176.7	+	90372.6i	0.292786	+	0.507120i
$127$	288101.	+	104860.i	1.58502	+	0.576900i	0.976288	−	0.216475i	$-0.0694561\pi$
$127$	288101.	+	104860.i	1.58502	+	0.576900i	0.608732	+	0.793376i	$0.291678\pi$
$128$	2845.05	−	16135.1i	0.0153485	−	0.0870455i
$129$	34595.5	+	196201.i	0.183039	+	1.03807i
$130$	50601.9	−	18417.6i	0.262608	−	0.0955816i
$131$	15292.6	+	12832.0i	0.0778579	+	0.0653305i	0.680886	−	0.732389i	$-0.261595\pi$
$131$	15292.6	+	12832.0i	0.0778579	+	0.0653305i	−0.603028	+	0.797720i	$0.706039\pi$
$132$	96658.1			0.482840
$133$	−286979.	+	181078.i	−1.40676	+	0.887637i
$134$	154717.			0.744349
$135$	160811.	+	134936.i	0.759416	+	0.637226i
$136$	−113968.	+	41481.1i	−0.528368	+	0.192310i
$137$	25170.1	+	142747.i	0.114573	+	0.649777i	0.986961	+	0.160962i	$0.0514596\pi$
$137$	25170.1	+	142747.i	0.114573	+	0.649777i	−0.872387	+	0.488815i	$0.837429\pi$
$138$	17130.5	−	97151.9i	0.0765724	−	0.434264i
$139$	−86029.8	−	31312.3i	−0.377669	−	0.137460i	0.146208	−	0.989254i	$-0.453293\pi$
$139$	−86029.8	−	31312.3i	−0.377669	−	0.137460i	−0.523878	+	0.851793i	$0.675515\pi$
$140$	90073.3	+	156012.i	0.388397	+	0.672724i
$141$	112037.	−	194054.i	0.474585	−	0.822005i
$142$	130497.	−	109500.i	0.543102	−	0.455716i
$143$	108021.	−	90640.4i	0.441741	−	0.370665i
$144$	15485.2	−	26821.1i	0.0622315	−	0.107788i
$145$	−93526.0	−	161992.i	−0.369413	−	0.639842i
$146$	−166737.	−	60687.3i	−0.647365	−	0.235622i
$147$	56962.1	−	323048.i	0.217416	−	1.23303i
$148$	−9054.47	−	51350.4i	−0.0339788	−	0.192704i
$149$	244159.	−	88866.7i	0.900964	−	0.327924i	0.150325	−	0.988637i	$-0.451968\pi$
$149$	244159.	−	88866.7i	0.900964	−	0.327924i	0.750639	+	0.660712i	$0.229746\pi$
$150$	−13503.9	−	11331.2i	−0.0490041	−	0.0411193i
$151$	−172996.			−0.617438			−0.308719	−	0.951153i	$-0.599900\pi$
$151$	−172996.			−0.617438			−0.308719	+	0.951153i	$0.599900\pi$
$152$	89126.2	+	46889.4i	0.312894	+	0.164614i
$153$	−229258.			−0.791764
$154$	361371.	+	303226.i	1.22787	+	1.03030i
$155$	−414276.	+	150784.i	−1.38503	+	0.504111i
$156$	7913.42	+	44879.2i	0.0260347	+	0.147650i
$157$	5642.77	−	32001.8i	0.0182702	−	0.103616i	−0.974309	−	0.225215i	$-0.927691\pi$
$157$	5642.77	−	32001.8i	0.0182702	−	0.103616i	0.992579	+	0.121600i	$0.0388025\pi$
$158$	−41513.9	−	15109.8i	−0.132297	−	0.0481522i
$159$	−19843.5	−	34369.9i	−0.0622479	−	0.107817i
$160$	26732.3	−	46301.7i	0.0825536	−	0.142987i
$161$	368820.	−	309477.i	1.12137	−	0.940944i
$162$	−46010.7	+	38607.6i	−0.137744	+	0.115581i
$163$	−111277.	+	192737.i	−0.328047	+	0.568194i	−0.982124	−	0.188234i	$-0.939724\pi$
$163$	−111277.	+	192737.i	−0.328047	+	0.568194i	0.654077	+	0.756428i	$0.273057\pi$
$164$	−71681.2	−	124155.i	−0.208111	−	0.360459i
$165$	296395.	+	107879.i	0.847541	+	0.308480i
$166$	−14948.8	+	84778.7i	−0.0421051	+	0.238790i
$167$	69772.9	+	395702.i	0.193596	+	1.09794i	0.914405	+	0.404801i	$0.132659\pi$
$167$	69772.9	+	395702.i	0.193596	+	1.09794i	−0.720809	+	0.693134i	$0.756230\pi$
$168$	−143260.	+	52142.4i	−0.391608	+	0.142534i
$169$	−233498.	−	195928.i	−0.628878	−	0.527692i
$170$	−395771.			−1.05032
$171$	127999.	+	140910.i	0.334746	+	0.368513i
$172$	288569.			0.743753
$173$	−222142.	−	186400.i	−0.564308	−	0.473511i	0.315444	−	0.948944i	$-0.397847\pi$
$173$	−222142.	−	186400.i	−0.564308	−	0.473511i	−0.879752	+	0.475434i	$0.842291\pi$
$174$	148751.	−	54141.1i	0.372467	−	0.135567i
$175$	−14939.6	−	84726.4i	−0.0368759	−	0.209134i
$176$	24311.4	−	137877.i	0.0591600	−	0.335513i
$177$	31866.9	+	11598.6i	0.0764552	+	0.0278274i
$178$	122903.	+	212875.i	0.290746	+	0.503586i
$179$	154078.	−	266872.i	0.359426	−	0.622544i	−0.628439	−	0.777859i	$-0.716306\pi$
$179$	154078.	−	266872.i	0.359426	−	0.622544i	0.987865	+	0.155315i	$0.0496392\pi$
$180$	77418.8	−	64962.1i	0.178101	−	0.149444i
$181$	−100141.	+	84028.1i	−0.227203	+	0.190646i	−0.749282	−	0.662251i	$-0.769601\pi$
$181$	−100141.	+	84028.1i	−0.227203	+	0.190646i	0.522079	+	0.852897i	$0.325157\pi$
$182$	−111205.	+	192613.i	−0.248855	+	0.431029i
$183$	31889.1	+	55233.5i	0.0703905	+	0.121920i
$184$	−134272.	−	48871.1i	−0.292376	−	0.106416i
$185$	29546.7	−	167568.i	0.0634717	−	0.359966i
$186$	−64786.8	−	367424.i	−0.137311	−	0.778728i
$187$	−973876.	+	354462.i	−2.03657	+	0.741251i
$188$	−248626.	−	208622.i	−0.513041	−	0.430492i
$189$	−867030.			−1.76555
$190$	220966.	+	243255.i	0.444060	+	0.488853i
$191$	−828301.			−1.64288			−0.821438	−	0.570297i	$-0.806828\pi$
$191$	−828301.			−1.64288			−0.821438	+	0.570297i	$0.806828\pi$
$192$	34660.4	+	29083.5i	0.0678547	+	0.0569369i
$193$	702710.	−	255765.i	1.35795	−	0.494252i	0.442528	−	0.896755i	$-0.354082\pi$
$193$	702710.	−	255765.i	1.35795	−	0.494252i	0.915419	+	0.402503i	$0.131860\pi$
$194$	109272.	+	619712.i	0.208451	+	1.18219i
$195$	−25823.2	+	146451.i	−0.0486322	+	0.275807i
$196$	−446480.	−	162506.i	−0.830160	−	0.302154i
$197$	358327.	+	620640.i	0.657830	+	1.13939i	0.981176	+	0.193114i	$0.0618588\pi$
$197$	358327.	+	620640.i	0.657830	+	1.13939i	−0.323346	+	0.946281i	$0.604808\pi$
$198$	132323.	−	229190.i	0.239868	−	0.415464i
$199$	196686.	−	165040.i	0.352080	−	0.295430i	−0.449544	−	0.893258i	$-0.648414\pi$
$199$	196686.	−	165040.i	0.352080	−	0.295430i	0.801625	+	0.597827i	$0.203969\pi$
$200$	−19559.7	+	16412.5i	−0.0345769	+	0.0290135i
$201$	−213633.	+	370023.i	−0.372973	+	0.646009i
$202$	−154117.	−	266938.i	−0.265749	−	0.460291i
$203$	725976.	+	264233.i	1.23647	+	0.450037i
$204$	58160.4	−	329844.i	0.0978480	−	0.554924i
$205$	−81236.6	−	460716.i	−0.135010	−	0.765682i
$206$	−499568.	+	181828.i	−0.820214	+	0.298533i
$207$	−206910.	−	173618.i	−0.335626	−	0.281623i
$208$	66007.7			0.105788
$209$	761596.	+	400677.i	1.20603	+	0.634495i
$210$	−497491.			−0.778461
$211$	230240.	+	193194.i	0.356020	+	0.298736i	0.803202	−	0.595707i	$-0.203128\pi$
$211$	230240.	+	193194.i	0.356020	+	0.298736i	−0.447182	+	0.894443i	$0.647572\pi$
$212$	−54017.5	+	19660.8i	−0.0825458	+	0.0300442i
$213$	81691.6	+	463296.i	0.123375	+	0.699696i
$214$	77951.0	−	442082.i	0.116356	−	0.659885i
$215$	884875.	+	322068.i	1.30553	+	0.475173i
$216$	128660.	+	222846.i	0.187633	+	0.324990i
$217$	910432.	−	1.57691e6i	1.31250	−	2.27331i
$218$	−186031.	+	156098.i	−0.265121	+	0.222463i
$219$	375369.	−	314972.i	0.528870	−	0.443774i
$220$	228431.	−	395655.i	0.318199	−	0.551137i
$221$	−244311.	−	423159.i	−0.336482	−	0.582805i
$222$	135312.	+	49249.7i	0.184270	+	0.0670689i
$223$	−194457.	+	1.10282e6i	−0.261856	+	1.48506i	0.515986	+	0.856597i	$0.327426\pi$
$223$	−194457.	+	1.10282e6i	−0.261856	+	1.48506i	−0.777841	+	0.628461i	$0.783685\pi$
$224$	38345.1	+	217466.i	0.0510611	+	0.289582i
$225$	−45354.4	+	16507.7i	−0.0597260	+	0.0217385i
$226$	136613.	+	114632.i	0.177918	+	0.149291i
$227$	1.42711e6			1.83820			0.919099	−	0.394026i	$-0.128918\pi$
$227$	1.42711e6			1.83820			0.919099	+	0.394026i	$0.128918\pi$
$228$	−235206.	+	148410.i	−0.299648	+	0.189072i
$229$	843458.			1.06286			0.531428	−	0.847103i	$-0.321656\pi$
$229$	843458.			1.06286			0.531428	+	0.847103i	$0.321656\pi$
$230$	−357191.	−	299719.i	−0.445227	−	0.373590i
$231$	−1.22418e6	+	445564.i	−1.50943	+	0.549389i
$232$	−39815.0	−	225802.i	−0.0485653	−	0.275428i
$233$	83713.3	−	474762.i	0.101019	−	0.572910i	−0.891716	−	0.452595i	$-0.850498\pi$
$233$	83713.3	−	474762.i	0.101019	−	0.572910i	0.992736	−	0.120315i	$-0.0383904\pi$
$234$	117248.	+	42674.9i	0.139980	+	0.0509487i
$235$	−529552.	−	917211.i	−0.625517	−	1.08343i
$236$	24559.8	−	42538.9i	0.0287042	−	0.0497171i
$237$	93458.9	−	78421.3i	0.108081	−	0.0906908i
$238$	1.25220e6	−	1.05072e6i	1.43295	−	1.20238i
$239$	−357944.	+	619977.i	−0.405341	+	0.702071i	−0.994361	−	0.106047i	$-0.966180\pi$
$239$	−357944.	+	619977.i	−0.405341	+	0.702071i	0.589020	+	0.808118i	$0.299514\pi$
$240$	73823.6	+	127866.i	0.0827308	+	0.143294i
$241$	1.49099e6	+	542677.i	1.65361	+	0.601864i	0.989339	−	0.145629i	$-0.0465206\pi$
$241$	1.49099e6	+	542677.i	1.65361	+	0.601864i	0.664269	+	0.747493i	$0.268743\pi$
$242$	95879.4	−	543759.i	0.105241	−	0.596854i
$243$	140854.	+	798822.i	0.153022	+	0.867829i
$244$	86807.7	−	31595.4i	0.0933434	−	0.0339742i
$245$	−1.18773e6	−	996621.i	−1.26416	−	1.06075i
$246$	395908.			0.417116
$247$	−123686.	+	386419.i	−0.128996	+	0.403011i
$248$	−540402.			−0.557941
$249$	−182116.	−	152814.i	−0.186144	−	0.156194i
$250$	−691581.	+	251715.i	−0.699830	+	0.254717i
$251$	48780.5	+	276648.i	0.0488722	+	0.277168i	0.999444	−	0.0333363i	$-0.0106132\pi$
$251$	48780.5	+	276648.i	0.0488722	+	0.277168i	−0.950572	+	0.310504i	$0.899502\pi$
$252$	−72483.1	+	411072.i	−0.0719010	+	0.407771i
$253$	−1.14738e6	−	417611.i	−1.12695	−	0.410176i
$254$	613180.	+	1.06206e6i	0.596354	+	1.03292i
$255$	546479.	−	946530.i	0.526288	−	0.911557i
$256$	50203.5	−	42125.7i	0.0478778	−	0.0401742i
$257$	−1.45513e6	+	1.22100e6i	−1.37426	+	1.15314i	−0.402979	+	0.915209i	$0.632025\pi$
$257$	−1.45513e6	+	1.22100e6i	−1.37426	+	1.15314i	−0.971282	+	0.237933i	$0.923530\pi$
$258$	−398455.	+	690144.i	−0.372674	+	0.645491i
$259$	351385.	+	608616.i	0.325487	+	0.563760i
$260$	202408.	+	73670.4i	0.185692	+	0.0675864i
$261$	75261.5	−	426829.i	0.0683867	−	0.387840i
$262$	13866.2	+	78639.0i	0.0124797	+	0.0707758i
$263$	−1.62751e6	+	592364.i	−1.45089	+	0.528079i	−0.942838	−	0.333250i	$-0.891855\pi$
$263$	−1.62751e6	+	592364.i	−1.45089	+	0.528079i	−0.508047	+	0.861329i	$0.669632\pi$
$264$	296178.	+	248523.i	0.261543	+	0.219460i
$265$	−187584.			−0.164089
$266$	−1.34493e6	−	183011.i	−1.16546	−	0.158589i
$267$	−678816.			−0.582739
$268$	474081.	+	397801.i	0.403196	+	0.338321i
$269$	−540547.	+	196743.i	−0.455463	+	0.165775i	−0.559556	−	0.828793i	$-0.689028\pi$
$269$	−540547.	+	196743.i	−0.455463	+	0.165775i	0.104093	+	0.994568i	$0.466806\pi$
$270$	145811.	+	826936.i	0.121725	+	0.690339i
$271$	297272.	−	1.68591e6i	0.245884	−	1.39448i	−0.572546	−	0.819872i	$-0.694044\pi$
$271$	297272.	−	1.68591e6i	0.245884	−	1.39448i	0.818431	−	0.574605i	$-0.194844\pi$
$272$	−455873.	−	165924.i	−0.373613	−	0.135984i
$273$	−307103.	−	531918.i	−0.249389	−	0.431954i
$274$	−289897.	+	502117.i	−0.233275	+	0.404044i
$275$	−167140.	+	140247.i	−0.133275	+	0.111831i
$276$	302283.	−	253646.i	0.238859	−	0.200426i
$277$	1.19075e6	−	2.06244e6i	0.932442	−	1.61504i	0.153310	−	0.988178i	$-0.451007\pi$
$277$	1.19075e6	−	2.06244e6i	0.932442	−	1.61504i	0.779133	−	0.626859i	$-0.215660\pi$
$278$	−183102.	−	317142.i	−0.142096	−	0.246117i
$279$	−959908.	−	349378.i	−0.738276	−	0.268711i
$280$	−125129.	+	709639.i	−0.0953809	+	0.540932i
$281$	−161383.	−	915250.i	−0.121925	−	0.691471i	−0.983087	−	0.183140i	$-0.941374\pi$
$281$	−161383.	−	915250.i	−0.121925	−	0.691471i	0.861162	−	0.508331i	$-0.169737\pi$
$282$	842243.	−	306551.i	0.630688	−	0.229552i
$283$	246547.	+	206878.i	0.182993	+	0.153549i	0.729683	−	0.683786i	$-0.239668\pi$
$283$	246547.	+	206878.i	0.182993	+	0.153549i	−0.546690	+	0.837335i	$0.684112\pi$
$284$	681409.			0.501317
$285$	−886880.	+	192578.i	−0.646774	+	0.140441i
$286$	564046.			0.407755
$287$	1.48016e6	+	1.24200e6i	1.06073	+	0.890057i
$288$	116410.	−	42370.0i	0.0827010	−	0.0301007i
$289$	377045.	+	2.13833e6i	0.265552	+	1.50602i
$290$	129925.	−	736841.i	0.0907189	−	0.514492i
$291$	−1.63299e6	−	594360.i	−1.13045	−	0.411450i
$292$	−354875.	−	614662.i	−0.243567	−	0.421871i
$293$	143607.	−	248734.i	0.0977250	−	0.169265i	−0.813018	−	0.582239i	$-0.802177\pi$
$293$	143607.	−	248734.i	0.0977250	−	0.169265i	0.910743	+	0.412974i	$0.135510\pi$
$294$	1.00515e6	−	843418.i	0.678205	−	0.569082i
$295$	122788.	−	103031.i	0.0821487	−	0.0689309i
$296$	104285.	−	180627.i	0.0691820	−	0.119827i
$297$	1.09942e6	+	1.90425e6i	0.723223	+	1.25266i
$298$	976637.	+	355467.i	0.637078	+	0.231877i
$299$	99964.5	−	566927.i	0.0646648	−	0.366732i
$300$	−12244.4	−	69441.3i	−0.00785477	−	0.0445466i
$301$	−3.65473e6	+	1.33021e6i	−2.32509	+	0.846263i
$302$	−530090.	−	444798.i	−0.334451	−	0.280638i
$303$	851215.			0.532639
$304$	152539.	+	372834.i	0.0946666	+	0.231383i
$305$	301452.			0.185554
$306$	−702487.	−	589457.i	−0.428879	−	0.359872i
$307$	67079.1	−	24414.8i	0.0406201	−	0.0147845i	−0.321630	−	0.946865i	$-0.604231\pi$
$307$	67079.1	−	24414.8i	0.0406201	−	0.0147845i	0.362250	+	0.932081i	$0.382009\pi$
$308$	327665.	+	1.85828e6i	0.196813	+	1.11618i
$309$	254940.	−	1.44584e6i	0.151895	−	0.861437i
$310$	−1.65710e6	−	603136.i	−0.979366	−	0.356460i
$311$	−956342.	−	1.65643e6i	−0.560676	−	0.971120i	−0.997438	−	0.0715424i	$-0.977208\pi$
$311$	−956342.	−	1.65643e6i	−0.560676	−	0.971120i	0.436761	−	0.899577i	$-0.356125\pi$
$312$	−91143.1	+	157865.i	−0.0530075	+	0.0918117i
$313$	661808.	−	555323.i	0.381831	−	0.320394i	−0.431590	−	0.902070i	$-0.642047\pi$
$313$	661808.	−	555323.i	0.381831	−	0.320394i	0.813421	+	0.581676i	$0.197603\pi$
$314$	99571.8	−	83550.7i	0.0569918	−	0.0478218i
$315$	−681056.	+	1.17962e6i	−0.386729	+	0.669833i
$316$	−88356.3	−	153038.i	−0.0497760	−	0.0862145i
$317$	2.34554e6	+	853705.i	1.31097	+	0.477155i	0.900555	−	0.434742i	$-0.143160\pi$
$317$	2.34554e6	+	853705.i	1.31097	+	0.477155i	0.410419	+	0.911897i	$0.365383\pi$
$318$	27566.3	−	156336.i	0.0152866	−	0.0866945i
$319$	−340225.	−	1.92951e6i	−0.187193	−	1.06162i
$320$	200961.	−	73143.9i	0.109708	−	0.0399303i
$321$	949652.	+	796853.i	0.514401	+	0.431634i
$322$	1.92584e6			1.03510
$323$	1.82556e6	−	2.35784e6i	0.973623	−	1.25750i
$324$	−240251.			−0.127146
$325$	−78801.8	−	66122.6i	−0.0413836	−	0.0347249i
$326$	−836528.	+	304471.i	−0.435950	+	0.158673i
$327$	−116456.	−	660452.i	−0.0602269	−	0.341564i
$328$	99578.4	−	564737.i	0.0511070	−	0.289842i
$329$	4.11054e6	+	1.49611e6i	2.09367	+	0.762034i
$330$	630833.	+	1.09264e6i	0.318882	+	0.552320i
$331$	−614547.	+	1.06443e6i	−0.308308	+	0.534006i	−0.977992	−	0.208640i	$-0.933096\pi$
$331$	−614547.	+	1.06443e6i	−0.308308	+	0.534006i	0.669684	+	0.742646i	$0.266430\pi$
$332$	−263784.	+	221341.i	−0.131342	+	0.110209i
$333$	302018.	−	253423.i	0.149253	−	0.125238i
$334$	−803612.	+	1.39190e6i	−0.394167	+	0.682717i
$335$	1.00975e6	+	1.74894e6i	0.491590	+	0.851459i
$336$	−573040.	−	208569.i	−0.276909	−	0.100787i
$337$	157172.	−	891365.i	0.0753876	−	0.427544i	−0.923632	−	0.383280i	$-0.874794\pi$
$337$	157172.	−	891365.i	0.0753876	−	0.427544i	0.999020	−	0.0442644i	$-0.0140944\pi$
$338$	−211719.	−	1.20072e6i	−0.100802	−	0.571675i
$339$	−462789.	+	168441.i	−0.218717	+	0.0796066i
$340$	−1.21271e6	−	1.01759e6i	−0.568933	−	0.477392i
$341$	−4.61782e6			−2.15056
$342$	29909.5	+	760878.i	0.0138275	+	0.351763i
$343$	2.77943e6			1.27562
$344$	884227.	+	741954.i	0.402872	+	0.338050i
$345$	1.21002e6	−	440411.i	0.547324	−	0.199210i
$346$	−201422.	−	1.14232e6i	−0.0904519	−	0.512978i
$347$	−276396.	+	1.56752e6i	−0.123227	+	0.698858i	0.859117	+	0.511779i	$0.171013\pi$
$347$	−276396.	+	1.56752e6i	−0.123227	+	0.698858i	−0.982345	+	0.187079i	$0.940098\pi$
$348$	595006.	+	216564.i	0.263374	+	0.0958603i
$349$	50694.6	+	87805.6i	0.0222791	+	0.0385886i	0.876950	−	0.480582i	$-0.159574\pi$
$349$	50694.6	+	87805.6i	0.0222791	+	0.0385886i	−0.854671	+	0.519170i	$0.826241\pi$
$350$	172067.	−	298029.i	0.0750805	−	0.130043i
$351$	−794151.	+	666372.i	−0.344061	+	0.288701i
$352$	428996.	−	359970.i	0.184543	−	0.154850i
$353$	562313.	−	973954.i	0.240182	−	0.416008i	−0.720584	−	0.693368i	$-0.756126\pi$
$353$	562313.	−	973954.i	0.240182	−	0.416008i	0.960766	+	0.277360i	$0.0894594\pi$
$354$	67824.2	+	117475.i	0.0287658	+	0.0498238i
$355$	2.08949e6	+	760512.i	0.879973	+	0.320284i
$356$	−170735.	+	968288.i	−0.0714000	+	0.404930i
$357$	783876.	+	4.44558e6i	0.325520	+	1.84611i
$358$	1.15829e6	−	421583.i	0.477650	−	0.173851i
$359$	−2.45256e6	−	2.05794e6i	−1.00435	−	0.842747i	−0.0167656	−	0.999859i	$-0.505337\pi$
$359$	−2.45256e6	−	2.05794e6i	−1.00435	−	0.842747i	−0.987581	+	0.157113i	$0.949781\pi$
$360$	404252.			0.164398
$361$	−2.46846e6	+	194366.i	−0.996914	+	0.0784971i
$362$	−522898.			−0.209723
$363$	1.16807e6	+	980125.i	0.465266	+	0.390405i
$364$	−835989.	+	304275.i	−0.330710	+	0.120369i
$365$	−402182.	−	2.28089e6i	−0.158012	−	0.896131i
$366$	−44299.8	+	251237.i	−0.0172862	+	0.0980348i
$367$	1.56576e6	+	569890.i	0.606820	+	0.220864i	0.627111	−	0.778930i	$-0.284237\pi$
$367$	1.56576e6	+	569890.i	0.606820	+	0.220864i	−0.0202912	+	0.999794i	$0.506459\pi$
$368$	−285779.	−	494984.i	−0.110005	−	0.190534i
$369$	541990.	−	938755.i	0.207217	−	0.358911i
$370$	521378.	−	437488.i	0.197992	−	0.166135i
$371$	593503.	−	498008.i	0.223866	−	0.187846i
$372$	746185.	−	1.29243e6i	0.279569	−	0.484228i
$373$	−2.03094e6	−	3.51769e6i	−0.755832	−	1.30914i	−0.944960	−	0.327187i	$-0.893899\pi$
$373$	−2.03094e6	−	3.51769e6i	−0.755832	−	1.30914i	0.189127	−	0.981953i	$-0.439434\pi$
$374$	−3.89550e6	−	1.41785e6i	−1.44007	−	0.524144i
$375$	352928.	−	2.00156e6i	0.129601	−	0.735003i
$376$	−225436.	−	1.27851e6i	−0.0822343	−	0.466374i
$377$	868034.	−	315939.i	0.314545	−	0.114485i
$378$	−2.65673e6	−	2.22926e6i	−0.956354	−	0.802476i
$379$	122287.			0.0437302			0.0218651	−	0.999761i	$-0.493040\pi$
$379$	122287.			0.0437302			0.0218651	+	0.999761i	$0.493040\pi$
$380$	51633.2	+	1.31351e6i	0.0183430	+	0.466634i
$381$	−3.38671e6			−1.19527
$382$	−2.53806e6	−	2.12969e6i	−0.889906	−	0.746720i
$383$	1.33782e6	−	486928.i	0.466017	−	0.169616i	−0.0983301	−	0.995154i	$-0.531350\pi$
$383$	1.33782e6	−	486928.i	0.466017	−	0.169616i	0.564347	+	0.825537i	$0.309128\pi$
$384$	31427.5	+	178234.i	0.0108763	+	0.0616826i
$385$	−1.06924e6	+	6.06397e6i	−0.367641	+	2.08500i
$386$	2.81084e6	+	1.02306e6i	0.960213	+	0.349489i
$387$	1.09095e6	+	1.88959e6i	0.370279	+	0.641341i
$388$	−1.25854e6	+	2.17986e6i	−0.424413	+	0.735106i
$389$	−1.59588e6	+	1.33910e6i	−0.534719	+	0.448682i	−0.869727	−	0.493533i	$-0.835705\pi$
$389$	−1.59588e6	+	1.33910e6i	−0.534719	+	0.448682i	0.335008	+	0.942215i	$0.391261\pi$
$390$	−455674.	+	382356.i	−0.151702	+	0.127293i
$391$	−2.11548e6	+	3.66412e6i	−0.699789	+	1.21207i
$392$	−950269.	−	1.64591e6i	−0.312343	−	0.540993i
$393$	−207220.	−	75421.9i	−0.0676784	−	0.0246329i
$394$	−497782.	+	2.82306e6i	−0.161547	+	0.916178i
$395$	−100135.	−	567891.i	−0.0322917	−	0.183136i
$396$	994744.	−	362057.i	0.318767	−	0.116022i
$397$	1.41209e6	+	1.18489e6i	0.449663	+	0.377312i	0.839311	−	0.543652i	$-0.182959\pi$
$397$	1.41209e6	+	1.18489e6i	0.449663	+	0.377312i	−0.389648	+	0.920964i	$0.627403\pi$
$398$	1.02702e6			0.324992
$399$	2.29476e6	−	2.96385e6i	0.721615	−	0.932016i
$400$	−102133.			−0.0319167
$401$	−34080.2	−	28596.7i	−0.0105838	−	0.00888085i	0.637480	−	0.770467i	$-0.279977\pi$
$401$	−34080.2	−	28596.7i	−0.0105838	−	0.00888085i	−0.648064	+	0.761586i	$0.724421\pi$
$402$	−1.60599e6	+	584534.i	−0.495654	+	0.180403i
$403$	−378061.	−	2.14409e6i	−0.115958	−	0.657629i
$404$	214097.	−	1.21420e6i	0.0652615	−	0.370116i
$405$	−736711.	−	268141.i	−0.223182	−	0.0812317i
$406$	1.54513e6	+	2.67625e6i	0.465212	+	0.805771i
$407$	891132.	−	1.54349e6i	0.266659	−	0.461867i
$408$	1.02629e6	−	861162.i	0.305226	−	0.256115i
$409$	−537784.	+	451255.i	−0.158964	+	0.133387i	−0.718801	−	0.695216i	$-0.755309\pi$
$409$	−537784.	+	451255.i	−0.158964	+	0.133387i	0.559836	+	0.828603i	$0.310864\pi$
$410$	935646.	−	1.62059e6i	0.274885	−	0.476116i
$411$	−800577.	−	1.38664e6i	−0.233775	−	0.404911i
$412$	−1.99827e6	−	727312.i	−0.579979	−	0.211095i
$413$	−114960.	+	651969.i	−0.0331643	+	0.188084i
$414$	−187611.	−	1.06399e6i	−0.0537968	−	0.305097i
$415$	−1.05591e6	+	384320.i	−0.300959	+	0.109540i
$416$	202259.	+	169716.i	0.0573027	+	0.0480827i
$417$	1.01131e6			0.284801
$418$	1.30347e6	+	3.18592e6i	0.364888	+	0.891856i
$419$	−5.55566e6			−1.54597			−0.772984	−	0.634425i	$-0.781237\pi$
$419$	−5.55566e6			−1.54597			−0.772984	+	0.634425i	$0.781237\pi$
$420$	−1.52440e6	−	1.27912e6i	−0.421673	−	0.353826i
$421$	1.98468e6	−	722364.i	0.545739	−	0.198633i	−0.0544135	−	0.998518i	$-0.517329\pi$
$421$	1.98468e6	−	722364.i	0.545739	−	0.198633i	0.600152	+	0.799886i	$0.295107\pi$
$422$	208765.	+	1.18396e6i	0.0570658	+	0.323636i
$423$	426137.	−	2.41674e6i	0.115797	−	0.656719i
$424$	−216070.	−	78643.1i	−0.0583687	−	0.0212445i
$425$	378021.	+	654751.i	0.101518	+	0.175835i
$426$	−940886.	+	1.62966e6i	−0.251196	+	0.435085i
$427$	−953776.	+	800313.i	−0.253149	+	0.212418i
$428$	1.37551e6	−	1.15419e6i	0.362958	−	0.304558i
$429$	−778831.	+	1.34898e6i	−0.204315	+	0.353884i
$430$	1.88333e6	+	3.26202e6i	0.491196	+	0.850776i
$431$	−497724.	−	181157.i	−0.129061	−	0.0469744i	0.276682	−	0.960961i	$-0.410765\pi$
$431$	−497724.	−	181157.i	−0.129061	−	0.0469744i	−0.405743	+	0.913987i	$0.632987\pi$
$432$	−178733.	+	1.01364e6i	−0.0460782	+	0.261322i
$433$	591076.	+	3.35216e6i	0.151504	+	0.859220i	0.961913	+	0.273356i	$0.0881337\pi$
$433$	591076.	+	3.35216e6i	0.151504	+	0.859220i	−0.810409	+	0.585864i	$0.800755\pi$
$434$	6.84421e6	−	2.49109e6i	1.74421	−	0.634841i
$435$	1.58283e6	+	1.32816e6i	0.401063	+	0.336532i
$436$	−971384.			−0.244723
$437$	3.43321e6	−	745491.i	0.859997	−	0.186741i
$438$	1.96004e6			0.488180
$439$	435222.	+	365194.i	0.107783	+	0.0904404i	0.695086	−	0.718926i	$-0.255366\pi$
$439$	435222.	+	365194.i	0.107783	+	0.0904404i	−0.587304	+	0.809367i	$0.699811\pi$
$440$	1.71724e6	−	625025.i	0.422863	−	0.153910i
$441$	−623840.	−	3.53797e6i	−0.152748	−	0.866279i
$442$	339393.	−	1.92480e6i	0.0826319	−	0.468629i
$443$	−3.00104e6	−	1.09229e6i	−0.726546	−	0.264441i	−0.0478438	−	0.998855i	$-0.515235\pi$
$443$	−3.00104e6	−	1.09229e6i	−0.726546	−	0.264441i	−0.678702	+	0.734414i	$0.737457\pi$
$444$	287993.	+	498818.i	0.0693305	+	0.120084i
$445$	−1.60424e6	+	2.77863e6i	−0.384034	+	0.665166i
$446$	−3.43137e6	+	2.87926e6i	−0.816828	+	0.685400i
$447$	−2.19867e6	+	1.84491e6i	−0.520465	+	0.436722i
$448$	−441642.	+	764946.i	−0.103962	+	0.180068i
$449$	−639853.	−	1.10826e6i	−0.149784	−	0.259433i	0.781364	−	0.624076i	$-0.214524\pi$
$449$	−639853.	−	1.10826e6i	−0.149784	−	0.259433i	−0.931147	+	0.364643i	$0.881191\pi$
$450$	−181418.	−	66030.6i	−0.0422327	−	0.0153714i
$451$	850912.	−	4.82576e6i	0.196990	−	1.11718i
$452$	123870.	+	702504.i	0.0285182	+	0.161735i
$453$	1.79573e6	−	653592.i	0.411145	−	0.149645i
$454$	4.37291e6	+	3.66931e6i	0.995706	+	0.835497i
$455$	−2.90309e6			−0.657404
$456$	−1.10230e6	−	149995.i	−0.248249	−	0.0337804i
$457$	5.15509e6			1.15464			0.577319	−	0.816519i	$-0.304099\pi$
$457$	5.15509e6			1.15464			0.577319	+	0.816519i	$0.304099\pi$
$458$	2.58450e6	+	2.16866e6i	0.575723	+	0.483089i
$459$	7.15976e6	−	2.60594e6i	1.58623	−	0.577341i
$460$	−323875.	−	1.83679e6i	−0.0713646	−	0.404729i
$461$	−648738.	+	3.67918e6i	−0.142173	+	0.806303i	0.827421	+	0.561583i	$0.189807\pi$
$461$	−648738.	+	3.67918e6i	−0.142173	+	0.806303i	−0.969594	+	0.244720i	$0.921304\pi$
$462$	−4.89671e6	−	1.78226e6i	−1.06733	−	0.388477i
$463$	−3.78630e6	−	6.55806e6i	−0.820848	−	1.42175i	−0.905052	−	0.425301i	$-0.860168\pi$
$463$	−3.78630e6	−	6.55806e6i	−0.820848	−	1.42175i	0.0842044	−	0.996449i	$-0.473165\pi$
$464$	458571.	−	794267.i	0.0988806	−	0.171266i
$465$	3.73058e6	−	3.13033e6i	0.800100	−	0.671364i
$466$	1.47720e6	−	1.23952e6i	0.315118	−	0.264416i
$467$	4.02309e6	−	6.96820e6i	0.853626	−	1.47852i	−0.0242874	−	0.999705i	$-0.507732\pi$
$467$	4.02309e6	−	6.96820e6i	0.853626	−	1.47852i	0.877914	−	0.478819i	$-0.158935\pi$
$468$	249546.	+	432227.i	0.0526668	+	0.0912215i
$469$	−7.83799e6	−	2.85279e6i	−1.64540	−	0.598878i
$470$	735646.	−	4.17206e6i	0.153612	−	0.871175i
$471$	62332.1	+	353503.i	0.0129467	+	0.0734245i
$472$	184630.	−	67199.6i	0.0381457	−	0.0138839i
$473$	7.55585e6	+	6.34011e6i	1.55285	+	1.30300i
$474$	488008.			0.0997656
$475$	191378.	−	597904.i	0.0389187	−	0.121590i
$476$	6.53850e6			1.32270
$477$	−332958.	−	279385.i	−0.0670028	−	0.0562220i
$478$	−2.69086e6	+	979392.i	−0.538668	+	0.196059i
$479$	−53782.5	−	305016.i	−0.0107103	−	0.0607412i	0.978984	−	0.203936i	$-0.0653735\pi$
$479$	−53782.5	−	305016.i	−0.0107103	−	0.0607412i	−0.989694	+	0.143195i	$0.954262\pi$
$480$	−102555.	+	581617.i	−0.0203167	+	0.115222i
$481$	789611.	+	287395.i	0.155615	+	0.0566391i
$482$	3.17336e6	+	5.49642e6i	0.622160	+	1.07761i
$483$	−2.65919e6	+	4.60586e6i	−0.518659	+	0.898344i
$484$	1.69188e6	−	1.41965e6i	0.328288	−	0.275467i
$485$	−6.29214e6	+	5.27974e6i	−1.21463	+	1.01920i
$486$	−1.62229e6	+	2.80989e6i	−0.311557	+	0.539633i
$487$	1.61598e6	+	2.79895e6i	0.308754	+	0.534778i	0.978090	−	0.208182i	$-0.0667547\pi$
$487$	1.61598e6	+	2.79895e6i	0.308754	+	0.534778i	−0.669336	+	0.742960i	$0.733421\pi$
$488$	347231.	+	126382.i	0.0660038	+	0.0240234i
$489$	426898.	−	2.42106e6i	0.0807332	−	0.457861i
$490$	−1.07694e6	−	6.10765e6i	−0.202629	−	1.14917i
$491$	6.87972e6	−	2.50401e6i	1.28786	−	0.468741i	0.394833	−	0.918753i	$-0.370803\pi$
$491$	6.87972e6	−	2.50401e6i	1.28786	−	0.468741i	0.893022	+	0.450012i	$0.148580\pi$
$492$	1.21313e6	+	1.01794e6i	0.225941	+	0.189587i
$493$	−6.78914e6			−1.25805
$494$	−1.37254e6	+	866043.i	−0.253050	+	0.159670i
$495$	3.45439e6			0.633664
$496$	−1.65589e6	−	1.38946e6i	−0.302223	−	0.253595i
$497$	−8.63006e6	+	3.14108e6i	−1.56719	+	0.570412i
$498$	−165129.	−	936496.i	−0.0298367	−	0.169212i
$499$	−749484.	+	4.25054e6i	−0.134745	+	0.764174i	0.840293	+	0.542133i	$0.182383\pi$
$499$	−749484.	+	4.25054e6i	−0.134745	+	0.764174i	−0.975037	+	0.222041i	$0.928728\pi$
$500$	−2.76632e6	−	1.00686e6i	−0.494855	−	0.180112i
$501$	−2.21925e6	−	3.84385e6i	−0.395013	−	0.684182i
$502$	−561831.	+	973120.i	−0.0995054	+	0.172348i
$503$	−3.55744e6	+	2.98504e6i	−0.626928	+	0.526055i	−0.899973	−	0.435947i	$-0.856414\pi$
$503$	−3.55744e6	+	2.98504e6i	−0.626928	+	0.526055i	0.273045	+	0.962001i	$0.411969\pi$
$504$	−1.27903e6	+	1.07323e6i	−0.224287	+	0.188199i
$505$	2.01167e6	−	3.48431e6i	0.351017	−	0.607979i
$506$	−2.44203e6	−	4.22971e6i	−0.424008	−	0.734403i
$507$	3.16398e6	+	1.15160e6i	0.546656	+	0.198967i
$508$	−851821.	+	4.83092e6i	−0.146450	+	0.830559i
$509$	1.26671e6	+	7.18388e6i	0.216712	+	1.22904i	0.877911	+	0.478824i	$0.158937\pi$
$509$	1.26671e6	+	7.18388e6i	0.216712	+	1.22904i	−0.661199	+	0.750211i	$0.729952\pi$
$510$	4.10818e6	−	1.49526e6i	0.699397	−	0.254560i
$511$	7.32790e6	+	6.14884e6i	1.24145	+	1.04170i
$512$	262144.			0.0441942
$513$	−5.59912e6	−	2.94570e6i	−0.939348	−	0.494192i
$514$	−7.59815e6			−1.26853
$515$	−5.31581e6	−	4.46049e6i	−0.883184	−	0.741080i
$516$	−2.99540e6	+	1.09024e6i	−0.495257	+	0.180259i
$517$	−1.92638e6	−	1.09250e7i	−0.316968	−	1.79762i
$518$	−488138.	+	2.76837e6i	−0.0799316	+	0.453315i
$519$	3.01011e6	+	1.09559e6i	0.490528	+	0.178538i
$520$	430795.	+	746160.i	0.0698655	+	0.121011i
$521$	3.55949e6	−	6.16522e6i	0.574505	−	0.995071i	−0.421591	−	0.906786i	$-0.638528\pi$
$521$	3.55949e6	−	6.16522e6i	0.574505	−	0.995071i	0.996095	−	0.0882850i	$-0.0281386\pi$
$522$	1.32806e6	−	1.11437e6i	0.213324	−	0.179000i
$523$	−8.94397e6	+	7.50488e6i	−1.42980	+	1.19975i	−0.483973	+	0.875083i	$0.660807\pi$
$523$	−8.94397e6	+	7.50488e6i	−1.42980	+	1.19975i	−0.945830	+	0.324664i	$0.894749\pi$
$524$	−159704.	+	276616.i	−0.0254091	+	0.0440098i
$525$	475178.	+	823033.i	0.0752417	+	0.130322i
$526$	−6.51002e6	−	2.36945e6i	−1.02593	−	0.373408i
$527$	−2.77860e6	+	1.57582e7i	−0.435812	+	2.47161i
$528$	268552.	+	1.52304e6i	0.0419222	+	0.237753i
$529$	1.36407e6	−	496481.i	0.211933	−	0.0771371i
$530$	−574790.	−	482306.i	−0.0888831	−	0.0745818i
$531$	371400.			0.0571617
$532$	−3.65056e6	−	4.01880e6i	−0.559217	−	0.615626i
$533$	2.31031e6			0.352251
$534$	−2.08001e6	−	1.74534e6i	−0.315655	−	0.264866i
$535$	5.50609e6	−	2.00405e6i	0.831685	−	0.302709i
$536$	429862.	+	2.43787e6i	0.0646274	+	0.366520i
$537$	−591100.	+	3.35230e6i	−0.0884556	+	0.501657i
$538$	−2.16219e6	−	786972.i	−0.322061	−	0.117221i
$539$	−8.12018e6	−	1.40646e7i	−1.20391	−	2.08523i
$540$	−1.67939e6	+	2.90878e6i	−0.247837	+	0.429266i
$541$	−4.15762e6	+	3.48866e6i	−0.610733	+	0.512466i	−0.894875	−	0.446316i	$-0.852736\pi$
$541$	−4.15762e6	+	3.48866e6i	−0.610733	+	0.512466i	0.284142	+	0.958782i	$0.408291\pi$
$542$	5.24563e6	−	4.40160e6i	0.767007	−	0.643595i
$543$	722015.	−	1.25057e6i	0.105086	−	0.182015i
$544$	−970260.	−	1.68054e6i	−0.140569	−	0.243473i
$545$	−2.97867e6	−	1.08415e6i	−0.429568	−	0.156350i
$546$	426623.	−	2.41950e6i	0.0612439	−	0.347331i
$547$	321355.	+	1.82250e6i	0.0459216	+	0.260435i	0.999122	−	0.0419062i	$-0.0133431\pi$
$547$	321355.	+	1.82250e6i	0.0459216	+	0.260435i	−0.953200	+	0.302341i	$0.902232\pi$
$548$	−2.17931e6	+	793206.i	−0.310005	+	0.112833i
$549$	535073.	+	448979.i	0.0757673	+	0.0635763i
$550$	−872744.			−0.123021
$551$	3.79049e6	+	4.17285e6i	0.531884	+	0.585536i
$552$	1.57841e6			0.220482
$553$	1.82449e6	+	1.53093e6i	0.253705	+	0.212884i
$554$	8.95153e6	−	3.25809e6i	1.23915	−	0.451013i
$555$	326384.	+	1.85101e6i	0.0449776	+	0.255080i
$556$	254363.	−	1.44256e6i	0.0348952	−	0.197901i
$557$	2935.09	+	1068.29i	0.000400852	+	0.000145898i	0.342221	−	0.939620i	$-0.388821\pi$
$557$	2935.09	+	1068.29i	0.000400852	+	0.000145898i	−0.341820	+	0.939766i	$0.611043\pi$
$558$	−2.04303e6	−	3.53862e6i	−0.277772	−	0.481115i
$559$	−2.32517e6	+	4.02731e6i	−0.314721	+	0.545112i
$560$	−2.20801e6	+	1.85274e6i	−0.297530	+	0.249657i
$561$	8.76982e6	−	7.35875e6i	1.17648	−	0.987182i
$562$	1.85874e6	−	3.21943e6i	0.248243	−	0.429970i
$563$	−1.72631e6	−	2.99005e6i	−0.229534	−	0.397565i	0.728136	−	0.685433i	$-0.240387\pi$
$563$	−1.72631e6	−	2.99005e6i	−0.229534	−	0.397565i	−0.957670	+	0.287868i	$0.907054\pi$
$564$	3.36897e6	+	1.22621e6i	0.445964	+	0.162318i
$565$	−404217.	+	2.29243e6i	−0.0532713	+	0.302116i
$566$	223551.	+	1.26782e6i	0.0293316	+	0.166348i
$567$	3.04278e6	−	1.10748e6i	0.397478	−	0.144670i
$568$	2.08796e6	+	1.75201e6i	0.271551	+	0.227858i
$569$	9.38291e6			1.21495			0.607473	−	0.794341i	$-0.292183\pi$
$569$	9.38291e6			1.21495			0.607473	+	0.794341i	$0.292183\pi$
$570$	−3.21271e6	−	1.69021e6i	−0.414175	−	0.217898i
$571$	8.27080e6			1.06159			0.530796	−	0.847500i	$-0.321893\pi$
$571$	8.27080e6			1.06159			0.530796	+	0.847500i	$0.321893\pi$
$572$	1.72834e6	+	1.45025e6i	0.220871	+	0.185333i
$573$	8.59792e6	−	3.12939e6i	1.09397	−	0.398174i
$574$	1.34210e6	+	7.61144e6i	0.170022	+	0.964244i
$575$	−154674.	+	877202.i	−0.0195096	+	0.110645i
$576$	465642.	+	169480.i	0.0584785	+	0.0212844i
$577$	2.73790e6	+	4.74218e6i	0.342356	+	0.592978i	0.984870	−	0.173296i	$-0.0554417\pi$
$577$	2.73790e6	+	4.74218e6i	0.342356	+	0.592978i	−0.642514	+	0.766274i	$0.722108\pi$
$578$	−4.34264e6	+	7.52167e6i	−0.540672	+	0.936471i
$579$	−6.32795e6	+	5.30978e6i	−0.784453	+	0.658234i
$580$	2.29264e6	−	1.92376e6i	0.282987	−	0.237454i
$581$	2.32052e6	−	4.01926e6i	0.285197	−	0.493976i
$582$	−3.47558e6	−	6.01988e6i	−0.425324	−	0.736683i
$583$	−1.84635e6	−	672016.i	−0.224979	−	0.0818858i
$584$	492988.	−	2.79587e6i	0.0598141	−	0.339223i
$585$	282812.	+	1.60391e6i	0.0341671	+	0.193771i
$586$	1.07957e6	−	392931.i	0.129869	−	0.0472686i
$587$	−8.96349e6	−	7.52126e6i	−1.07370	−	0.900939i	−0.0783152	−	0.996929i	$-0.524954\pi$
$587$	−8.96349e6	−	7.52126e6i	−1.07370	−	0.900939i	−0.995382	+	0.0959895i	$0.969398\pi$
$588$	5.24850e6			0.626026
$589$	1.12369e7	−	7.09026e6i	1.33462	−	0.842120i
$590$	641153.			0.0758283
$591$	−6.06432e6	−	5.08857e6i	−0.714190	−	0.599276i
$592$	783968.	−	285341.i	0.0919378	−	0.0334626i
$593$	−1.22767e6	−	6.96246e6i	−0.143366	−	0.813066i	−0.968665	−	0.248371i	$-0.920105\pi$
$593$	−1.22767e6	−	6.96246e6i	−0.143366	−	0.813066i	0.825299	−	0.564695i	$-0.191006\pi$
$594$	−1.52730e6	+	8.66174e6i	−0.177606	+	1.00725i
$595$	2.00498e7	+	7.29754e6i	2.32176	+	0.845053i
$596$	2.07863e6	+	3.60030e6i	0.239697	+	0.415167i
$597$	−1.41811e6	+	2.45624e6i	−0.162845	+	0.282055i
$598$	1.76396e6	−	1.48014e6i	0.201714	−	0.169258i
$599$	−3.98768e6	+	3.34606e6i	−0.454102	+	0.381037i	−0.840955	−	0.541105i	$-0.818006\pi$
$599$	−3.98768e6	+	3.34606e6i	−0.454102	+	0.381037i	0.386854	+	0.922141i	$0.373562\pi$
$600$	141025.	−	244263.i	0.0159926	−	0.0277000i
$601$	4.05200e6	+	7.01826e6i	0.457597	+	0.792580i	0.998833	−	0.0482897i	$-0.0153771\pi$
$601$	4.05200e6	+	7.01826e6i	0.457597	+	0.792580i	−0.541237	+	0.840870i	$0.682044\pi$
$602$	−1.46189e7	−	5.32085e6i	−1.64409	−	0.598398i
$603$	−812560.	+	4.60826e6i	−0.0910043	+	0.516111i
$604$	−480647.	−	2.72588e6i	−0.0536085	−	0.304029i
$605$	6.77247e6	−	2.46498e6i	0.752244	−	0.273794i
$606$	2.60828e6	+	2.18860e6i	0.288517	+	0.242095i
$607$	−5.55114e6			−0.611520			−0.305760	−	0.952109i	$-0.598910\pi$
$607$	−5.55114e6			−0.611520			−0.305760	+	0.952109i	$0.598910\pi$
$608$	−491207.	+	1.53463e6i	−0.0538897	+	0.168362i
$609$	−8.53405e6			−0.932421
$610$	923704.	+	775080.i	0.100510	+	0.0843377i
$611$	4.91488e6	−	1.78887e6i	0.532611	−	0.193855i
$612$	−636964.	−	3.61240e6i	−0.0687442	−	0.389868i
$613$	1.74607e6	−	9.90245e6i	0.187677	−	1.06437i	−0.734791	−	0.678293i	$-0.762720\pi$
$613$	1.74607e6	−	9.90245e6i	0.187677	−	1.06437i	0.922468	−	0.386074i	$-0.126169\pi$
$614$	268316.	+	97659.2i	0.0287228	+	0.0104542i
$615$	2.58387e6	+	4.47539e6i	0.275475	+	0.477137i
$616$	−3.77389e6	+	6.53657e6i	−0.400717	+	0.694062i
$617$	−1.20780e6	+	1.01347e6i	−0.127727	+	0.107176i	−0.704414	−	0.709790i	$-0.748790\pi$
$617$	−1.20780e6	+	1.01347e6i	−0.127727	+	0.107176i	0.576686	+	0.816966i	$0.304345\pi$
$618$	4.49865e6	−	3.77482e6i	0.473817	−	0.397580i
$619$	−5.78438e6	+	1.00188e7i	−0.606779	+	1.05097i	0.384989	+	0.922921i	$0.374205\pi$
$619$	−5.78438e6	+	1.00188e7i	−0.606779	+	1.05097i	−0.991768	+	0.128051i	$0.959128\pi$
$620$	−3.52690e6	−	6.10878e6i	−0.368480	−	0.638227i
$621$	8.43531e6	+	3.07020e6i	0.877752	+	0.319476i
$622$	1.32854e6	−	7.53450e6i	0.137688	−	0.780870i
$623$	−2.30114e6	−	1.30504e7i	−0.237533	−	1.34711i
$624$	−685172.	+	249382.i	−0.0704431	+	0.0256392i
$625$	−6.40391e6	−	5.37352e6i	−0.655761	−	0.550248i
$626$	3.45572e6			0.352454
$627$	−9.41930e6	−	1.28173e6i	−0.956863	−	0.130205i
$628$	519927.			0.0526070
$629$	−4.73091e6	−	3.96971e6i	−0.476780	−	0.400066i
$630$	−5.11986e6	+	1.86348e6i	−0.513934	+	0.187057i
$631$	−838260.	−	4.75401e6i	−0.0838119	−	0.475321i	−0.997607	−	0.0691445i	$-0.977973\pi$
$631$	−838260.	−	4.75401e6i	−0.0838119	−	0.475321i	0.913795	−	0.406176i	$-0.133138\pi$
$632$	122743.	−	696112.i	0.0122238	−	0.0693244i
$633$	−3.11983e6	−	1.13553e6i	−0.309473	−	0.112639i
$634$	4.99213e6	+	8.64663e6i	0.493246	+	0.854326i
$635$	−8.00377e6	+	1.38629e7i	−0.787699	+	1.36433i
$636$	486432.	−	408165.i	0.0476847	−	0.0400122i
$637$	5.86550e6	−	4.92174e6i	0.572739	−	0.480585i
$638$	3.91855e6	−	6.78713e6i	0.381131	−	0.660138i
$639$	2.57611e6	+	4.46195e6i	0.249581	+	0.432288i
$640$	803844.	+	292575.i	0.0775751	+	0.0282350i
$641$	−3.47865e6	+	1.97284e7i	−0.334400	+	1.89647i	0.0986804	+	0.995119i	$0.468538\pi$
$641$	−3.47865e6	+	1.97284e7i	−0.334400	+	1.89647i	−0.433080	+	0.901355i	$0.642573\pi$
$642$	861074.	+	4.88340e6i	0.0824524	+	0.467611i
$643$	−5.62640e6	+	2.04784e6i	−0.536665	+	0.195330i	−0.596112	−	0.802901i	$-0.703288\pi$
$643$	−5.62640e6	+	2.04784e6i	−0.536665	+	0.195330i	0.0594470	+	0.998231i	$0.481066\pi$
$644$	5.90112e6	+	4.95163e6i	0.560686	+	0.470472i
$645$	−1.04020e7			−0.984500
$646$	1.16562e7	−	2.53105e6i	1.09895	−	0.238627i
$647$	1.64159e6			0.154172			0.0770859	−	0.997024i	$-0.475438\pi$
$647$	1.64159e6			0.154172			0.0770859	+	0.997024i	$0.475438\pi$
$648$	−736171.	−	617721.i	−0.0688718	−	0.0577903i
$649$	1.57769e6	−	574231.i	0.147031	−	0.0535149i
$650$	−71451.7	−	405223.i	−0.00663329	−	0.0376193i
$651$	−3.49274e6	+	1.98083e7i	−0.323009	+	1.83187i
$652$	−3.34611e6	−	1.21789e6i	−0.308263	−	0.112199i
$653$	3.28829e6	+	5.69549e6i	0.301778	+	0.522694i	0.976539	−	0.215342i	$-0.0690866\pi$
$653$	3.28829e6	+	5.69549e6i	0.301778	+	0.522694i	−0.674761	+	0.738036i	$0.735753\pi$
$654$	1.34128e6	−	2.32317e6i	0.122624	−	0.212391i
$655$	−798449.	+	669978.i	−0.0727183	+	0.0610179i
$656$	1.75715e6	−	1.47442e6i	0.159422	−	0.133771i
$657$	2.68326e6	−	4.64754e6i	0.242521	−	0.420058i
$658$	8.74868e6	+	1.51532e7i	0.787731	+	1.36439i
$659$	−1.27687e7	−	4.64742e6i	−1.14534	−	0.416868i	−0.301498	−	0.953467i	$-0.597487\pi$
$659$	−1.27687e7	−	4.64742e6i	−1.14534	−	0.416868i	−0.843838	+	0.536599i	$0.819709\pi$
$660$	−876345.	+	4.97000e6i	−0.0783096	+	0.444116i
$661$	−1.62833e6	−	9.23469e6i	−0.144956	−	0.822089i	−0.967402	−	0.253245i	$-0.918502\pi$
$661$	−1.62833e6	−	9.23469e6i	−0.144956	−	0.822089i	0.822446	−	0.568844i	$-0.192609\pi$
$662$	−4.61988e6	+	1.68150e6i	−0.409719	+	0.149125i
$663$	4.13472e6	+	3.46944e6i	0.365311	+	0.306532i
$664$	−1.37738e6			−0.121237
$665$	−6.70883e6	−	1.63977e7i	−0.588292	−	1.43790i
$666$	1.57703e6			0.137770
$667$	−6.12733e6	−	5.14144e6i	−0.533281	−	0.447476i
$668$	−6.04119e6	+	2.19881e6i	−0.523819	+	0.190654i
$669$	−2.14805e6	−	1.21822e7i	−0.185557	−	1.05235i
$670$	−1.40273e6	+	7.95530e6i	−0.120722	+	0.684651i
$671$	2.96714e6	+	1.07995e6i	0.254408	+	0.0925971i
$672$	−1.21963e6	−	2.11247e6i	−0.104185	−	0.180454i
$673$	1.07619e7	−	1.86402e7i	0.915908	−	1.58640i	0.110343	−	0.993894i	$-0.464805\pi$
$673$	1.07619e7	−	1.86402e7i	0.915908	−	1.58640i	0.805566	−	0.592506i	$-0.201861\pi$
$674$	2.77344e6	−	2.32719e6i	0.235163	−	0.197325i
$675$	1.22878e6	−	1.03107e6i	0.103805	−	0.0871023i
$676$	2.43848e6	−	4.22357e6i	0.205236	−	0.355478i
$677$	7.21906e6	+	1.25038e7i	0.605353	+	1.04850i	0.991996	+	0.126273i	$0.0403014\pi$
$677$	7.21906e6	+	1.25038e7i	0.605353	+	1.04850i	−0.386643	+	0.922230i	$0.626365\pi$
$678$	−1.85115e6	−	673765.i	−0.154657	−	0.0562904i
$679$	5.89100e6	−	3.34095e7i	0.490359	−	2.78096i
$680$	−1.09960e6	−	6.23614e6i	−0.0911932	−	0.517182i
$681$	−1.48136e7	+	5.39173e6i	−1.22404	+	0.445513i
$682$	−1.41498e7	−	1.18731e7i	−1.16490	−	0.977470i
$683$	1.39407e7			1.14349			0.571747	−	0.820430i	$-0.306266\pi$
$683$	1.39407e7			1.14349			0.571747	+	0.820430i	$0.306266\pi$
$684$	−1.86468e6	+	2.40837e6i	−0.152393	+	0.196826i
$685$	−7.56799e6			−0.616246
$686$	8.51667e6	+	7.14633e6i	0.690970	+	0.579793i
$687$	−8.75524e6	+	3.18665e6i	−0.707744	+	0.257598i
$688$	801752.	+	4.54696e6i	0.0645757	+	0.366227i
$689$	160862.	−	912294.i	0.0129094	−	0.0732128i
$690$	4.84007e6	+	1.76164e6i	0.387016	+	0.140862i
$691$	−3.42012e6	−	5.92382e6i	−0.272487	−	0.471961i	0.697011	−	0.717060i	$-0.254513\pi$
$691$	−3.42012e6	−	5.92382e6i	−0.272487	−	0.471961i	−0.969498	+	0.245099i	$0.921180\pi$
$692$	2.31989e6	−	4.01817e6i	0.184163	−	0.318980i
$693$	−1.09295e7	+	9.17093e6i	−0.864503	+	0.725404i
$694$	−4.87725e6	+	4.09250e6i	−0.384394	+	0.322545i
$695$	2.39001e6	−	4.13962e6i	0.187688	−	0.325086i
$696$	1.26638e6	+	2.19344e6i	0.0990928	+	0.171634i
$697$	−1.59558e7	−	5.80744e6i	−1.24405	−	0.452797i
$698$	−70424.2	+	399395.i	−0.00547121	+	0.0310288i
$699$	924728.	+	5.24439e6i	0.0715848	+	0.405978i
$700$	1.29352e6	−	470803.i	0.0997765	−	0.0363157i
$701$	−4.86696e6	−	4.08387e6i	−0.374079	−	0.313889i	0.436294	−	0.899804i	$-0.356291\pi$
$701$	−4.86696e6	−	4.08387e6i	−0.374079	−	0.313889i	−0.810373	+	0.585915i	$0.800735\pi$
$702$	−4.14676e6			−0.317590
$703$	201426.	+	5.12415e6i	0.0153719	+	0.391051i
$704$	2.24006e6			0.170344
$705$	8.96214e6	+	7.52013e6i	0.679108	+	0.569840i
$706$	4.22721e6	−	1.53858e6i	0.319185	−	0.116174i
$707$	2.88556e6	+	1.63648e7i	0.217111	+	1.23130i
$708$	−94220.3	+	534350.i	−0.00706418	+	0.0400629i
$709$	−1.21841e6	−	443464.i	−0.0910284	−	0.0331316i	0.296105	−	0.955156i	$-0.404312\pi$
$709$	−1.21841e6	−	443464.i	−0.0910284	−	0.0331316i	−0.387133	+	0.922024i	$0.626535\pi$
$710$	4.44718e6	+	7.70273e6i	0.331084	+	0.573455i
$711$	668073.	−	1.15714e6i	0.0495621	−	0.0858441i
$712$	−3.01278e6	+	2.52802e6i	−0.222724	+	0.186888i
$713$	−1.44415e7	+	1.21179e7i	−1.06387	+	0.892692i
$714$	−9.02833e6	+	1.56375e7i	−0.662768	+	1.14795i
$715$	3.68121e6	+	6.37604e6i	0.269293	+	0.466429i
$716$	4.63316e6	+	1.68633e6i	0.337750	+	0.122931i
$717$	1.37320e6	−	7.78781e6i	0.0997554	−	0.565741i
$718$	−2.22380e6	−	1.26118e7i	−0.160985	−	0.912990i
$719$	−3.35062e6	+	1.21953e6i	−0.241715	+	0.0879769i	−0.460037	−	0.887900i	$-0.652164\pi$
$719$	−3.35062e6	+	1.21953e6i	−0.241715	+	0.0879769i	0.218322	+	0.975877i	$0.429942\pi$
$720$	1.23870e6	+	1.03939e6i	0.0890503	+	0.0747221i
$721$	2.86609e7			2.05329
$722$	−8.06354e6	−	5.75120e6i	−0.575682	−	0.410597i
$723$	−1.75270e7			−1.24699
$724$	−1.60225e6	−	1.34445e6i	−0.113602	−	0.0953231i
$725$	−1.34310e6	+	488850.i	−0.0948996	+	0.0345406i
$726$	1.05912e6	+	6.00656e6i	0.0745766	+	0.422945i
$727$	−725067.	+	4.11206e6i	−0.0508794	+	0.288551i	−0.999622	−	0.0274989i	$-0.991246\pi$
$727$	−725067.	+	4.11206e6i	−0.0508794	+	0.288551i	0.948742	+	0.316050i	$0.102357\pi$
$728$	−3.34396e6	−	1.21710e6i	−0.233847	−	0.0851134i
$729$	−6.30450e6	−	1.09197e7i	−0.439372	−	0.761014i
$730$	4.63214e6	−	8.02311e6i	0.321718	−	0.557231i
$731$	2.61819e7	−	2.19693e7i	1.81221	−	1.52062i
$732$	−781710.	+	655932.i	−0.0539222	+	0.0452461i
$733$	−6.38207e6	+	1.10541e7i	−0.438734	+	0.759910i	−0.997592	−	0.0693533i	$-0.977906\pi$
$733$	−6.38207e6	+	1.10541e7i	−0.438734	+	0.759910i	0.558858	+	0.829263i	$0.311240\pi$
$734$	3.33249e6	+	5.77205e6i	0.228312	+	0.395448i
$735$	1.60941e7	+	5.85779e6i	1.09888	+	0.399959i
$736$	397000.	−	2.25150e6i	0.0270145	−	0.153207i
$737$	3.67323e6	+	2.08319e7i	0.249103	+	1.41274i
$738$	4.07443e6	−	1.48297e6i	0.275376	−	0.100229i
$739$	1.21917e7	+	1.02300e7i	0.821206	+	0.689074i	0.953254	−	0.302169i	$-0.0977109\pi$
$739$	1.21917e7	+	1.02300e7i	0.821206	+	0.689074i	−0.132048	+	0.991243i	$0.542155\pi$
$740$	2.72244e6			0.182759
$741$	−176042.	−	4.47840e6i	−0.0117780	−	0.299624i
$742$	3.09905e6			0.206642
$743$	−7.63798e6	−	6.40903e6i	−0.507582	−	0.425912i	0.352695	−	0.935738i	$-0.385265\pi$
$743$	−7.63798e6	−	6.40903e6i	−0.507582	−	0.425912i	−0.860277	+	0.509826i	$0.829710\pi$
$744$	5.60948e6	−	2.04168e6i	0.371527	−	0.135225i
$745$	2.35572e6	+	1.33600e7i	0.155501	+	0.881890i
$746$	2.82135e6	−	1.60007e7i	0.185614	−	1.05267i
$747$	−2.44662e6	−	890499.i	−0.160423	−	0.0583891i
$748$	−8.29101e6	−	1.43605e7i	−0.541818	−	0.938457i
$749$	−1.21004e7	+	2.09586e7i	−0.788128	+	1.36508i
$750$	6.22773e6	−	5.22569e6i	0.404275	−	0.339227i
$751$	421588.	−	353754.i	0.0272765	−	0.0228877i	−0.629048	−	0.777367i	$-0.716555\pi$
$751$	421588.	−	353754.i	0.0272765	−	0.0228877i	0.656324	+	0.754479i	$0.272110\pi$
$752$	2.59647e6	−	4.49721e6i	0.167432	−	0.290000i
$753$	−1.55155e6	−	2.68736e6i	−0.0997189	−	0.172718i
$754$	3.47214e6	+	1.26375e6i	0.222417	+	0.0809533i
$755$	1.56846e6	−	8.89515e6i	0.100139	−	0.567918i
$756$	−2.40893e6	−	1.36617e7i	−0.153292	−	0.869363i
$757$	2.36414e7	−	8.60477e6i	1.49946	−	0.545757i	0.543536	−	0.839386i	$-0.317085\pi$
$757$	2.36414e7	−	8.60477e6i	1.49946	−	0.545757i	0.955919	+	0.293629i	$0.0948630\pi$
$758$	374708.	+	314418.i	0.0236876	+	0.0198762i
$759$	1.34877e7			0.849835
$760$	−3.21903e6	+	4.15760e6i	−0.202158	+	0.261101i
$761$	9.64716e6			0.603862			0.301931	−	0.953330i	$-0.402369\pi$
$761$	9.64716e6			0.603862			0.301931	+	0.953330i	$0.402369\pi$
$762$	−1.03775e7	−	8.70773e6i	−0.647447	−	0.543272i
$763$	1.23026e7	−	4.47778e6i	0.765042	−	0.278453i
$764$	−2.30133e6	−	1.30515e7i	−0.142641	−	0.808959i
$765$	2.07855e6	−	1.17881e7i	0.128413	−	0.728264i
$766$	5.35129e6	+	1.94771e6i	0.329524	+	0.119937i
$767$	395786.	+	685521.i	0.0242925	+	0.0420758i
$768$	−361967.	+	626945.i	−0.0221445	+	0.0383554i
$769$	−1.59326e7	+	1.33690e7i	−0.971563	+	0.815238i	−0.982795	−	0.184698i	$-0.940869\pi$
$769$	−1.59326e7	+	1.33690e7i	−0.971563	+	0.815238i	0.0112319	+	0.999937i	$0.496425\pi$
$770$	−1.88677e7	+	1.58319e7i	−1.14681	+	0.962291i
$771$	1.04915e7	−	1.81718e7i	0.635625	−	1.10094i
$772$	5.98246e6	+	1.03619e7i	0.361274	+	0.625745i
$773$	1.93564e7	+	7.04515e6i	1.16513	+	0.424074i	0.850929	−	0.525281i	$-0.176040\pi$
$773$	1.93564e7	+	7.04515e6i	1.16513	+	0.424074i	0.314205	+	0.949355i	$0.398262\pi$
$774$	−1.51554e6	+	8.59503e6i	−0.0909314	+	0.515698i
$775$	584972.	+	3.31754e6i	0.0349849	+	0.198409i
$776$	−9.46116e6	+	3.44358e6i	−0.564014	+	0.205284i
$777$	−5.94683e6	−	4.98999e6i	−0.353373	−	0.296515i
$778$	−8.33308e6			−0.493579
$779$	5.33895e6	+	1.30494e7i	0.315219	+	0.770455i
$780$	−2.37936e6			−0.140031
$781$	1.78419e7	+	1.49711e7i	1.04668	+	0.878268i
$782$	−1.59032e7	+	5.78830e6i	−0.929968	+	0.338481i
$783$	2.50127e6	+	1.41854e7i	0.145800	+	0.826870i
$784$	1.32010e6	−	7.48666e6i	0.0767037	−	0.435008i
$785$	1.59432e6	+	580284.i	0.0923422	+	0.0336098i
$786$	−441038.	−	763900.i	−0.0254636	−	0.0441042i
$787$	1.57192e7	−	2.72264e7i	0.904677	−	1.56695i	0.0833264	−	0.996522i	$-0.473446\pi$
$787$	1.57192e7	−	2.72264e7i	0.904677	−	1.56695i	0.821350	−	0.570424i	$-0.193221\pi$
$788$	−8.78381e6	+	7.37050e6i	−0.503927	+	0.422845i
$789$	1.46558e7	−	1.22977e7i	0.838141	−	0.703284i
$790$	1.15330e6	−	1.99758e6i	0.0657470	−	0.113877i
$791$	−4.80715e6	−	8.32623e6i	−0.273178	−	0.473159i
$792$	3.97898e6	+	1.44823e6i	0.225402	+	0.0820398i
$793$	−258510.	+	1.46608e6i	−0.0145980	+	0.0827896i
$794$	1.28038e6	+	7.26141e6i	0.0720757	+	0.408761i
$795$	1.94715e6	−	708705.i	0.109265	−	0.0397693i
$796$	3.14698e6	+	2.64063e6i	0.176040	+	0.147715i
$797$	−1.25351e7			−0.699006			−0.349503	−	0.936935i	$-0.613650\pi$
$797$	−1.25351e7			−0.699006			−0.349503	+	0.936935i	$0.613650\pi$
$798$	1.46521e7	−	3.18157e6i	0.814500	−	0.176862i
$799$	−3.84407e7			−2.13022
$800$	−312955.	−	262600.i	−0.0172885	−	0.0145067i
$801$	−6.98595e6	+	2.54268e6i	−0.384719	+	0.140026i
$802$	−30901.4	−	175250.i	−0.00169645	−	0.00962107i
$803$	4.21265e6	−	2.38911e7i	0.230551	−	1.30752i
$804$	−6.42397e6	−	2.33813e6i	−0.350480	−	0.127564i
$805$	1.25689e7	+	2.17700e7i	0.683608	+	1.18404i
$806$	4.35434e6	−	7.54194e6i	0.236094	−	0.408926i
$807$	4.86767e6	−	4.08446e6i	0.263110	−	0.220775i
$808$	3.77793e6	−	3.17006e6i	0.203576	−	0.170820i
$809$	7.57117e6	−	1.31136e7i	0.406716	−	0.704453i	−0.587803	−	0.809004i	$-0.700007\pi$
$809$	7.57117e6	−	1.31136e7i	0.406716	−	0.704453i	0.994520	+	0.104551i	$0.0333405\pi$
$810$	−1.56798e6	−	2.71583e6i	−0.0839709	−	0.145442i
$811$	−2.98854e6	−	1.08774e6i	−0.159554	−	0.0580728i	0.261009	−	0.965336i	$-0.415945\pi$
$811$	−2.98854e6	−	1.08774e6i	−0.159554	−	0.0580728i	−0.420562	+	0.907264i	$0.638167\pi$
$812$	−2.14648e6	+	1.21733e7i	−0.114245	+	0.647914i
$813$	3.28377e6	+	1.86232e7i	0.174239	+	0.988161i
$814$	6.69912e6	−	2.43828e6i	0.354370	−	0.128980i
$815$	−8.90133e6	−	7.46911e6i	−0.469419	−	0.393890i
$816$	5.35892e6			0.281742
$817$	−2.81209e7	−	3.82655e6i	−1.47392	−	0.200563i
$818$	−2.80811e6			−0.146734
$819$	−5.15294e6	−	4.32383e6i	−0.268439	−	0.225247i
$820$	7.03375e6	−	2.56008e6i	0.365302	−	0.132959i
$821$	2.78992e6	+	1.58224e7i	0.144455	+	0.819246i	0.967803	+	0.251709i	$0.0809926\pi$
$821$	2.78992e6	+	1.58224e7i	0.144455	+	0.819246i	−0.823348	+	0.567537i	$0.807896\pi$
$822$	1.11215e6	−	6.30732e6i	0.0574095	−	0.325586i
$823$	−1.66869e7	−	6.07354e6i	−0.858769	−	0.312566i	−0.125159	−	0.992137i	$-0.539944\pi$
$823$	−1.66869e7	−	6.07354e6i	−0.858769	−	0.312566i	−0.733610	+	0.679570i	$0.762166\pi$
$824$	−4.25304e6	−	7.36648e6i	−0.218213	−	0.377956i
$825$	1.20508e6	−	2.08726e6i	0.0616426	−	0.106768i
$826$	−2.02857e6	+	1.70217e6i	−0.103452	+	0.0868066i
$827$	1.37433e6	−	1.15320e6i	0.0698760	−	0.0586329i	−0.607181	−	0.794564i	$-0.707700\pi$
$827$	1.37433e6	−	1.15320e6i	0.0698760	−	0.0586329i	0.677057	+	0.735931i	$0.263255\pi$
$828$	2.16081e6	−	3.74264e6i	0.109532	−	0.189715i
$829$	−1.18964e7	−	2.06051e7i	−0.601212	−	1.04133i	−0.992638	−	0.121120i	$-0.961351\pi$
$829$	−1.18964e7	−	2.06051e7i	−0.601212	−	1.04133i	0.391426	−	0.920210i	$-0.371982\pi$
$830$	−4.22364e6	−	1.53728e6i	−0.212810	−	0.0774565i
$831$	−4.56815e6	+	2.59073e7i	−0.229476	+	1.30143i
$832$	183394.	+	1.04008e6i	0.00918495	+	0.0520904i
$833$	−5.28811e7	+	1.92471e7i	−2.64051	+	0.961067i
$834$	3.09882e6	+	2.60022e6i	0.154270	+	0.129448i
$835$	−2.09789e7			−1.04128
$836$	−4.19744e6	+	1.31136e7i	−0.207715	+	0.648945i
$837$	3.39494e7			1.67501
$838$	−1.70235e7	−	1.42844e7i	−0.837413	−	0.702673i
$839$	4.53816e6	−	1.65175e6i	0.222574	−	0.0810104i	−0.228326	−	0.973585i	$-0.573325\pi$
$839$	4.53816e6	−	1.65175e6i	0.222574	−	0.0810104i	0.450900	+	0.892574i	$0.351103\pi$
$840$	−1.38221e6	−	7.83893e6i	−0.0675892	−	0.383317i
$841$	−1.33297e6	+	7.55963e6i	−0.0649875	+	0.368562i
$842$	7.93871e6	+	2.88945e6i	0.385896	+	0.140454i
$843$	5.13307e6	+	8.89075e6i	0.248776	+	0.430893i
$844$	−2.40445e6	+	4.16464e6i	−0.116188	+	0.201243i
$845$	1.21913e7	−	1.02297e7i	0.587365	−	0.492858i
$846$	7.51957e6	−	6.30967e6i	0.361216	−	0.303096i
$847$	−1.48835e7	+	2.57790e7i	−0.712847	+	1.23469i
$848$	−459874.	−	796525.i	−0.0219608	−	0.0380373i
$849$	−3.34080e6	−	1.21595e6i	−0.159068	−	0.0578959i
$850$	−525141.	+	2.97822e6i	−0.0249304	+	0.141387i
$851$	−1.26347e6	−	7.16547e6i	−0.0598053	−	0.339173i
$852$	−7.07315e6	+	2.57442e6i	−0.333821	+	0.121501i
$853$	2.23170e6	+	1.87262e6i	0.105018	+	0.0881205i	0.693785	−	0.720182i	$-0.255942\pi$
$853$	2.23170e6	+	1.87262e6i	0.105018	+	0.0881205i	−0.588767	+	0.808303i	$0.700386\pi$
$854$	−4.98027e6			−0.233673
$855$	−8.40586e6	+	5.30392e6i	−0.393248	+	0.248132i
$856$	7.18243e6			0.335033
$857$	4.45676e6	+	3.73966e6i	0.207285	+	0.173932i	0.740520	−	0.672035i	$-0.234579\pi$
$857$	4.45676e6	+	3.73966e6i	0.207285	+	0.173932i	−0.533235	+	0.845967i	$0.679024\pi$
$858$	−5.85490e6	+	2.13101e6i	−0.271519	+	0.0988250i
$859$	2.65729e6	+	1.50703e7i	0.122873	+	0.696847i	0.982548	+	0.186007i	$0.0595546\pi$
$859$	2.65729e6	+	1.50703e7i	0.122873	+	0.696847i	−0.859676	+	0.510841i	$0.829334\pi$
$860$	−2.61629e6	+	1.48377e7i	−0.120626	+	0.684103i
$861$	−2.00567e7	−	7.30005e6i	−0.922045	−	0.335597i
$862$	−1.05933e6	−	1.83482e6i	−0.0485585	−	0.0841057i
$863$	1.29032e7	−	2.23490e7i	0.589754	−	1.02148i	−0.404511	−	0.914533i	$-0.632558\pi$
$863$	1.29032e7	−	2.23490e7i	0.589754	−	1.02148i	0.994264	−	0.106950i	$-0.0341085\pi$
$864$	−3.15390e6	+	2.64644e6i	−0.143735	+	0.120608i
$865$	1.15984e7	−	9.73220e6i	0.527057	−	0.442253i
$866$	−6.80774e6	+	1.17913e7i	−0.308467	+	0.534280i
$867$	−1.19926e7	−	2.07718e7i	−0.541832	−	0.938481i
$868$	2.73768e7	+	9.96435e6i	1.23334	+	0.448900i
$869$	1.04886e6	−	5.94838e6i	0.0471159	−	0.267208i
$870$	1.43520e6	+	8.13941e6i	0.0642856	+	0.364582i
$871$	−9.37172e6	+	3.41103e6i	−0.418576	+	0.152349i
$872$	−2.97649e6	−	2.49757e6i	−0.132560	−	0.111231i
$873$	−1.90320e7			−0.845180
$874$	1.24367e7	+	6.54298e6i	0.550716	+	0.289732i
$875$	3.96768e7			1.75193
$876$	6.00591e6	+	5.03956e6i	0.264435	+	0.221887i
$877$	−3.77041e7	+	1.37232e7i	−1.65535	+	0.602497i	−0.989621	−	0.143699i	$-0.954100\pi$
$877$	−3.77041e7	+	1.37232e7i	−1.65535	+	0.602497i	−0.665726	+	0.746196i	$0.731878\pi$
$878$	394627.	+	2.23804e6i	0.0172763	+	0.0979787i
$879$	−550927.	+	3.12446e6i	−0.0240504	+	0.136396i
$880$	6.86897e6	+	2.50010e6i	0.299009	+	0.108830i
$881$	8.57520e6	+	1.48527e7i	0.372224	+	0.644711i	0.989907	−	0.141716i	$-0.0452619\pi$
$881$	8.57520e6	+	1.48527e7i	0.372224	+	0.644711i	−0.617683	+	0.786427i	$0.711929\pi$
$882$	7.18510e6	−	1.24450e7i	0.311001	−	0.538669i
$883$	8.40421e6	−	7.05197e6i	0.362740	−	0.304375i	−0.443142	−	0.896452i	$-0.646136\pi$
$883$	8.40421e6	−	7.05197e6i	0.362740	−	0.304375i	0.805882	+	0.592077i	$0.201692\pi$
$884$	5.98890e6	−	5.02528e6i	0.257761	−	0.216287i
$885$	−885300.	+	1.53339e6i	−0.0379955	+	0.0658102i
$886$	−6.38729e6	−	1.10631e7i	−0.273358	−	0.473470i
$887$	1.64746e7	+	5.99626e6i	0.703082	+	0.255901i	0.668726	−	0.743509i	$-0.266840\pi$
$887$	1.64746e7	+	5.99626e6i	0.703082	+	0.255901i	0.0343556	+	0.999410i	$0.489062\pi$
$888$	−400076.	+	2.26894e6i	−0.0170259	+	0.0965586i
$889$	−1.14807e7	−	6.51103e7i	−0.487208	−	2.76309i
$890$	−1.20599e7	+	4.38946e6i	−0.510352	+	0.185753i
$891$	−6.29069e6	−	5.27852e6i	−0.265463	−	0.222750i
$892$	−1.79174e7			−0.753984
$893$	2.14621e7	+	2.36270e7i	0.900624	+	0.991471i
$894$	−1.14807e7			−0.480422
$895$	1.23251e7	+	1.03420e7i	0.514321	+	0.431567i
$896$	−3.32006e6	+	1.20840e6i	−0.138158	+	0.0502854i
$897$	1.10424e6	+	6.26248e6i	0.0458230	+	0.259875i
$898$	888874.	−	5.04106e6i	0.0367832	−	0.208608i
$899$	−2.84262e7	−	1.03463e7i	−1.17306	−	0.426959i
$900$	−386121.	−	668782.i	−0.0158898	−	0.0275219i
$901$	−3.40421e6	+	5.89627e6i	−0.139703	+	0.241972i
$902$	1.50151e7	−	1.25992e7i	0.614486	−	0.515615i
$903$	3.29111e7	−	2.76157e7i	1.34315	−	1.12703i
$904$	−1.42668e6	+	2.47109e6i	−0.0580639	+	0.100570i
$905$	−3.41266e6	−	5.91091e6i	−0.138507	−	0.239901i
$906$	7.18291e6	+	2.61437e6i	0.290723	+	0.105815i
$907$	−7.55972e6	+	4.28733e7i	−0.305132	+	1.73049i	0.317752	+	0.948174i	$0.397072\pi$
$907$	−7.55972e6	+	4.28733e7i	−0.305132	+	1.73049i	−0.622884	+	0.782315i	$0.714039\pi$
$908$	3.96504e6	+	2.24868e7i	0.159600	+	0.905136i
$909$	8.76017e6	−	3.18844e6i	0.351644	−	0.127988i
$910$	−8.89560e6	−	7.46429e6i	−0.356100	−	0.298803i
$911$	−6.91498e6			−0.276055			−0.138027	−	0.990428i	$-0.544076\pi$
$911$	−6.91498e6			−0.276055			−0.138027	+	0.990428i	$0.544076\pi$
$912$	−2.99198e6	−	3.29379e6i	−0.119116	−	0.131132i
$913$	−1.17699e7			−0.467302
$914$	1.57961e7	+	1.32545e7i	0.625439	+	0.524806i
$915$	−3.12913e6	+	1.13891e6i	−0.123558	+	0.0449714i
$916$	2.34344e6	+	1.32903e7i	0.0922815	+	0.523355i
$917$	747544.	−	4.23953e6i	0.0293571	−	0.166493i
$918$	2.86390e7	+	1.04238e7i	1.12164	+	0.408242i
$919$	−7.10540e6	−	1.23069e7i	−0.277523	−	0.480685i	0.693245	−	0.720702i	$-0.256180\pi$
$919$	−7.10540e6	−	1.23069e7i	−0.277523	−	0.480685i	−0.970769	+	0.240017i	$0.922847\pi$
$920$	3.73024e6	−	6.46097e6i	0.145301	−	0.251668i
$921$	−604052.	+	506860.i	−0.0234653	+	0.0196897i
$922$	−1.14476e7	+	9.60565e6i	−0.443492	+	0.372134i
$923$	−5.49051e6	+	9.50985e6i	−0.212133	+	0.367425i
$924$	−1.04219e7	−	1.80513e7i	−0.401577	−	0.695551i
$925$	−1.22176e6	−	444684.i	−0.0469496	−	0.0170882i
$926$	5.25987e6	−	2.98302e7i	0.201580	−	1.14322i
$927$	−2.79207e6	−	1.58346e7i	−0.106715	−	0.605212i
$928$	3.44732e6	−	1.25472e6i	0.131405	−	0.0478275i
$929$	−3.44600e6	−	2.89154e6i	−0.131001	−	0.109923i	0.574933	−	0.818201i	$-0.305028\pi$
$929$	−3.44600e6	−	2.89154e6i	−0.131001	−	0.109923i	−0.705934	+	0.708277i	$0.749473\pi$
$930$	1.94797e7			0.738542
$931$	4.13544e7	+	2.17566e7i	1.56368	+	0.822654i
$932$	7.71338e6			0.290874
$933$	1.61851e7	+	1.35809e7i	0.608712	+	0.510770i
$934$	3.02438e7	−	1.10078e7i	1.13441	−	0.412890i
$935$	−9.39624e6	−	5.32887e7i	−0.351500	−	1.99345i
$936$	−346666.	+	1.96604e6i	−0.0129337	+	0.0733505i
$937$	1.85891e7	+	6.76588e6i	0.691687	+	0.251754i	0.663857	−	0.747859i	$-0.268918\pi$
$937$	1.85891e7	+	6.76588e6i	0.691687	+	0.251754i	0.0278297	+	0.999613i	$0.491140\pi$
$938$	−1.66820e7	−	2.88941e7i	−0.619073	−	1.07227i
$939$	−4.77163e6	+	8.26471e6i	−0.176605	+	0.305889i
$940$	1.29811e7	−	1.08925e7i	0.479174	−	0.402075i
$941$	−3.07757e6	+	2.58239e6i	−0.113301	+	0.0950708i	−0.697678	−	0.716411i	$-0.745783\pi$
$941$	−3.07757e6	+	2.58239e6i	−0.113301	+	0.0950708i	0.584377	+	0.811482i	$0.301339\pi$
$942$	−717913.	+	1.24346e6i	−0.0263599	+	0.0456567i
$943$	−1.00024e7	−	1.73247e7i	−0.366291	−	0.634435i
$944$	738518.	+	268799.i	0.0269731	+	0.00981741i
$945$	7.86087e6	−	4.45812e7i	0.286346	−	1.62395i
$946$	6.85108e6	+	3.88544e7i	0.248904	+	1.41160i
$947$	1.20042e7	−	4.36917e6i	0.434969	−	0.158316i	−0.115250	−	0.993337i	$-0.536767\pi$
$947$	1.20042e7	−	4.36917e6i	0.434969	−	0.158316i	0.550218	+	0.835021i	$0.314545\pi$
$948$	1.49534e6	+	1.25474e6i	0.0540406	+	0.0453454i
$949$	1.14378e7			0.412264
$950$	2.12372e6	−	1.34002e6i	0.0763463	−	0.0481730i
$951$	−2.75725e7			−0.988608
$952$	2.00351e7	+	1.68115e7i	0.716473	+	0.601192i
$953$	2.43850e7	−	8.87542e6i	0.869743	−	0.316561i	0.131680	−	0.991292i	$-0.457963\pi$
$953$	2.43850e7	−	8.87542e6i	0.869743	−	0.316561i	0.738063	+	0.674732i	$0.235741\pi$
$954$	−301901.	−	1.71217e6i	−0.0107398	−	0.0609082i
$955$	7.50974e6	−	4.25899e7i	0.266450	−	1.51112i
$956$	−1.07634e7	−	3.91757e6i	−0.380896	−	0.138635i
$957$	1.08214e7	+	1.87433e7i	0.381949	+	0.661554i
$958$	619442.	−	1.07290e6i	0.0218065	−	0.0377700i
$959$	2.39446e7	−	2.00919e7i	0.840740	−	0.705464i
$960$	−1.80967e6	+	1.51849e6i	−0.0633755	+	0.0531783i
$961$	−2.13342e7	+	3.69519e7i	−0.745192	+	1.29071i
$962$	1.68057e6	+	2.91084e6i	0.0585491	+	0.101410i
$963$	1.27580e7	+	4.64354e6i	0.443320	+	0.161355i
$964$	−4.40839e6	+	2.50012e7i	−0.152787	+	0.866500i
$965$	6.77995e6	+	3.84510e7i	0.234373	+	1.32920i
$966$	−1.99906e7	+	7.27598e6i	−0.689260	+	0.250870i
$967$	2.77809e7	+	2.33109e7i	0.955389	+	0.801666i	0.980197	−	0.198026i	$-0.0634531\pi$
$967$	2.77809e7	+	2.33109e7i	0.955389	+	0.801666i	−0.0248082	+	0.999692i	$0.507898\pi$
$968$	8.83436e6			0.303031
$969$	−1.00416e7	+	3.13719e7i	−0.343552	+	1.07333i
$970$	−3.28552e7			−1.12118
$971$	5.38198e6	+	4.51602e6i	0.183187	+	0.153712i	0.729770	−	0.683693i	$-0.239627\pi$
$971$	5.38198e6	+	4.51602e6i	0.183187	+	0.153712i	−0.546583	+	0.837405i	$0.684072\pi$
$972$	−1.21956e7	+	4.43885e6i	−0.414036	+	0.150697i
$973$	3.42826e6	+	1.94426e7i	0.116089	+	0.658374i
$974$	−2.24489e6	+	1.27314e7i	−0.0758224	+	0.430010i
$975$	1.06779e6	+	388645.i	0.0359729	+	0.0130931i
$976$	739031.	+	1.28004e6i	0.0248335	+	0.0430129i
$977$	1.72076e7	−	2.98044e7i	0.576744	−	0.998949i	−0.419106	−	0.907937i	$-0.637656\pi$
$977$	1.72076e7	−	2.98044e7i	0.576744	−	0.998949i	0.995850	−	0.0910122i	$-0.0290102\pi$
$978$	7.53300e6	−	6.32094e6i	0.251838	−	0.211317i
$979$	−2.57446e7	+	2.16023e7i	−0.858479	+	0.720349i
$980$	1.24037e7	−	2.14839e7i	0.412560	−	0.714575i
$981$	−3.67238e6	−	6.36074e6i	−0.121836	−	0.211026i
$982$	2.75189e7	+	1.00161e7i	0.910651	+	0.331450i
$983$	1.61036e6	−	9.13281e6i	0.0531544	−	0.301454i	−0.946628	−	0.322329i	$-0.895534\pi$
$983$	1.61036e6	−	9.13281e6i	0.0531544	−	0.301454i	0.999782	+	0.0208754i	$0.00664533\pi$
$984$	1.09998e6	+	6.23829e6i	0.0362157	+	0.205389i
$985$	−3.51610e7	+	1.27976e7i	−1.15470	+	0.420278i
$986$	−2.08031e7	−	1.74559e7i	−0.681453	−	0.571807i
$987$	−4.83205e7			−1.57884
$988$	−6.43243e6	−	875290.i	−0.209644	−	0.0285272i
$989$	4.02671e7			1.30906
$990$	1.05849e7	+	8.88177e6i	0.343240	+	0.288013i
$991$	−3.53238e7	+	1.28568e7i	−1.14257	+	0.415862i	−0.842842	−	0.538162i	$-0.819119\pi$
$991$	−3.53238e7	+	1.28568e7i	−1.14257	+	0.415862i	−0.299730	+	0.954024i	$0.596897\pi$
$992$	−1.50144e6	−	8.51508e6i	−0.0484427	−	0.274732i
$993$	2.35762e6	−	1.33708e7i	0.0758755	−	0.430311i
$994$	−3.45202e7	−	1.25643e7i	−1.10817	−	0.403342i
$995$	6.70281e6	+	1.16096e7i	0.214634	+	0.371757i
$996$	1.90189e6	−	3.29416e6i	0.0607486	−	0.105220i
$997$	−5.49638e6	+	4.61201e6i	−0.175121	+	0.146944i	−0.726135	−	0.687552i	$-0.758685\pi$
$997$	−5.49638e6	+	4.61201e6i	−0.175121	+	0.146944i	0.551014	+	0.834496i	$0.314241\pi$
$998$	−1.32253e7	+	1.10974e7i	−0.420320	+	0.352690i
$999$	−6.55144e6	+	1.13474e7i	−0.207694	+	0.359736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.35.2	yes	30
19.5	even	9		722.6.a.r.1.11		15
19.6	even	9	inner	38.6.e.b.25.2	✓	30
19.14	odd	18		722.6.a.q.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.25.2	✓	30	19.6	even	9	inner
38.6.e.b.35.2	yes	30	1.1	even	1	trivial
722.6.a.q.1.5		15	19.14	odd	18
722.6.a.r.1.11		15	19.5	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)

\(f(q)\)	\(=\)	\(q+(3.06418 + 2.57115i) q^{2} +(-10.3802 + 3.77808i) q^{3} +(2.77837 + 15.7569i) q^{4} +(-9.06643 + 51.4183i) q^{5} +(-41.5207 - 15.1123i) q^{6} +(-107.823 - 186.754i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-92.6745 + 77.7631i) q^{9} +O(q^{10})\)	\(q+(3.06418 + 2.57115i) q^{2} +(-10.3802 + 3.77808i) q^{3} +(2.77837 + 15.7569i) q^{4} +(-9.06643 + 51.4183i) q^{5} +(-41.5207 - 15.1123i) q^{6} +(-107.823 - 186.754i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-92.6745 + 77.7631i) q^{9} +(-159.985 + 134.244i) q^{10} +(-273.445 + 473.620i) q^{11} +(-88.3709 - 153.063i) q^{12} +(-242.293 - 88.1874i) q^{13} +(149.786 - 849.477i) q^{14} +(-100.151 - 567.985i) q^{15} +(-240.561 + 87.5572i) q^{16} +(1451.68 + 1218.11i) q^{17} -483.912 q^{18} +(-61.8077 - 1572.35i) q^{19} -835.384 q^{20} +(1824.79 + 1531.18i) q^{21} +(-2055.63 + 748.189i) q^{22} +(387.696 + 2198.73i) q^{23} +(122.764 - 696.226i) q^{24} +(374.898 + 136.452i) q^{25} +(-515.685 - 893.193i) q^{26} +(2010.32 - 3481.97i) q^{27} +(2643.10 - 2217.83i) q^{28} +(-2744.42 + 2302.84i) q^{29} +(1153.49 - 1997.91i) q^{30} +(4221.89 + 7312.54i) q^{31} +(-962.245 - 350.229i) q^{32} +(1049.03 - 5949.36i) q^{33} +(1316.28 + 7465.00i) q^{34} +(10580.2 - 3850.86i) q^{35} +(-1482.79 - 1244.21i) q^{36} -3258.91 q^{37} +(3853.35 - 4976.87i) q^{38} +2848.22 q^{39} +(-2559.77 - 2147.90i) q^{40} +(-8419.78 + 3064.55i) q^{41} +(1654.59 + 9383.62i) q^{42} +(3131.84 - 17761.6i) q^{43} +(-8222.52 - 2992.75i) q^{44} +(-3158.22 - 5470.20i) q^{45} +(-4465.30 + 7734.13i) q^{46} +(-15539.1 + 13038.9i) q^{47} +(2166.27 - 1817.72i) q^{48} +(-14847.9 + 25717.4i) q^{49} +(797.917 + 1382.03i) q^{50} +(-19670.9 - 7159.60i) q^{51} +(716.383 - 4062.81i) q^{52} +(623.877 + 3538.18i) q^{53} +(15112.6 - 5500.55i) q^{54} +(-21873.6 - 18354.1i) q^{55} +13801.3 q^{56} +(6582.03 + 16087.7i) q^{57} -14330.3 q^{58} +(-2351.74 - 1973.34i) q^{59} +(8671.44 - 3156.15i) q^{60} +(-1002.59 - 5685.96i) q^{61} +(-5864.99 + 33262.0i) q^{62} +(24515.0 + 8922.74i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(6731.18 - 11658.7i) q^{65} +(18511.1 - 15532.7i) q^{66} +(29630.1 - 24862.6i) q^{67} +(-15160.3 + 26258.4i) q^{68} +(-12331.3 - 21358.5i) q^{69} +(42320.6 + 15403.4i) q^{70} +(7395.34 - 41941.1i) q^{71} +(-1344.49 - 7624.96i) q^{72} +(-41684.2 + 15171.8i) q^{73} +(-9985.89 - 8379.15i) q^{74} -4407.04 q^{75} +(24603.6 - 5342.47i) q^{76} +117934. q^{77} +(8727.46 + 7323.21i) q^{78} +(-10378.5 + 3777.46i) q^{79} +(-2321.01 - 13163.1i) q^{80} +(-2607.45 + 14787.6i) q^{81} +(-33679.1 - 12258.2i) q^{82} +(10760.8 + 18638.3i) q^{83} +(-19056.8 + 33007.3i) q^{84} +(-75794.6 + 63599.3i) q^{85} +(55264.2 - 46372.1i) q^{86} +(19787.2 - 34272.5i) q^{87} +(-17500.5 - 30311.7i) q^{88} +(57745.6 + 21017.7i) q^{89} +(4387.36 - 24881.9i) q^{90} +(9655.28 + 54757.8i) q^{91} +(-33568.1 + 12217.8i) q^{92} +(-71451.3 - 59954.8i) q^{93} -81139.5 q^{94} +(81407.8 + 11077.5i) q^{95} +11311.5 q^{96} +(120513. + 101122. i) q^{97} +(-111620. + 40626.4i) q^{98} +(-11488.8 - 65156.4i) 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

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