LMFDB - Embedded newform 150.6.g.b.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, 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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	150.91
Dual form			150.6.g.b.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(10.3231 + 54.9403i) q^{5} +(11.1246 - 34.2380i) q^{6} +175.692 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(10.3231 + 54.9403i) q^{5} +(11.1246 - 34.2380i) q^{6} +175.692 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(95.7661 - 202.061i) q^{10} +(201.117 + 146.120i) q^{11} +(-116.498 + 84.6411i) q^{12} +(779.331 - 566.217i) q^{13} +(-568.552 - 413.077i) q^{14} +(-441.552 + 241.158i) q^{15} +(-207.108 + 150.473i) q^{16} +(61.6746 - 189.815i) q^{17} +324.000 q^{18} +(151.706 - 466.903i) q^{19} +(-784.981 + 428.725i) q^{20} +(488.627 + 1503.84i) q^{21} +(-307.279 - 945.708i) q^{22} +(990.820 + 719.873i) q^{23} +576.000 q^{24} +(-2911.87 + 1134.31i) q^{25} -3853.22 q^{26} +(-589.773 - 428.495i) q^{27} +(868.670 + 2673.49i) q^{28} +(632.817 + 1947.61i) q^{29} +(1995.89 + 257.747i) q^{30} +(-455.299 + 1401.27i) q^{31} +1024.00 q^{32} +(-691.378 + 2127.84i) q^{33} +(-645.864 + 469.248i) q^{34} +(1813.69 + 9652.58i) q^{35} +(-1048.49 - 761.770i) q^{36} +(5427.89 - 3943.60i) q^{37} +(-1588.69 + 1154.25i) q^{38} +(7013.98 + 5095.95i) q^{39} +(3548.24 + 458.217i) q^{40} +(6081.55 - 4418.50i) q^{41} +(1954.51 - 6015.36i) q^{42} -5367.13 q^{43} +(-1229.12 + 3782.83i) q^{44} +(-3292.22 - 3108.77i) q^{45} +(-1513.84 - 4659.12i) q^{46} +(691.203 + 2127.30i) q^{47} +(-1863.98 - 1354.26i) q^{48} +14060.8 q^{49} +(12089.9 + 3175.52i) q^{50} +1796.25 q^{51} +(12469.3 + 9059.47i) q^{52} +(11458.4 + 35265.2i) q^{53} +(901.094 + 2773.28i) q^{54} +(-5951.72 + 12557.8i) q^{55} +(3474.68 - 10694.0i) q^{56} +4418.38 q^{57} +(2531.27 - 7790.44i) q^{58} +(-8367.58 + 6079.40i) q^{59} +(-5852.83 - 5526.70i) q^{60} +(44592.3 + 32398.2i) q^{61} +(4767.96 - 3464.12i) q^{62} +(-11513.2 + 8364.81i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(39153.2 + 36971.6i) q^{65} +(7240.20 - 5260.32i) q^{66} +(-1089.68 + 3353.69i) q^{67} +3193.33 q^{68} +(-3406.14 + 10483.0i) q^{69} +(16825.4 - 35500.6i) q^{70} +(5762.75 + 17735.9i) q^{71} +(1601.94 + 4930.28i) q^{72} +(-46388.0 - 33702.8i) q^{73} -26837.0 q^{74} +(-17807.5 - 21769.5i) q^{75} +7854.89 q^{76} +(35334.7 + 25672.1i) q^{77} +(-10716.4 - 32981.7i) q^{78} +(-31994.4 - 98468.7i) q^{79} +(-10405.0 - 9825.24i) q^{80} +(2027.46 - 6239.88i) q^{81} -30068.8 q^{82} +(-33878.5 + 104267. i) q^{83} +(-20467.9 + 14870.8i) q^{84} +(11065.1 + 1428.94i) q^{85} +(17368.4 + 12618.9i) q^{86} +(-14910.6 + 10833.2i) q^{87} +(12871.5 - 9351.67i) q^{88} +(-81142.8 - 58953.7i) q^{89} +(3344.68 + 17800.6i) q^{90} +(136922. - 99479.9i) q^{91} +(-6055.36 + 18636.5i) q^{92} -13260.4 q^{93} +(2764.81 - 8509.21i) q^{94} +(27217.8 + 3514.89i) q^{95} +(2847.90 + 8764.94i) q^{96} +(-9783.40 - 30110.2i) q^{97} +(-45501.6 - 33058.8i) q^{98} -20136.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	10.3231	+	54.9403i	0.184665	+	0.982802i
$5$	10.3231	+	54.9403i	0.184665	+	0.982802i
$6$	11.1246	−	34.2380i	0.126156	−	0.388267i
$7$	175.692			1.35521			0.677606	−	0.735425i	$-0.263017\pi$
$7$	175.692			1.35521			0.677606	+	0.735425i	$0.263017\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	95.7661	−	202.061i	0.302839	−	0.638975i
$11$	201.117	+	146.120i	0.501149	+	0.364106i	0.809456	−	0.587181i	$-0.199762\pi$
$11$	201.117	+	146.120i	0.501149	+	0.364106i	−0.308307	+	0.951287i	$0.599762\pi$
$12$	−116.498	+	84.6411i	−0.233543	+	0.169679i
$13$	779.331	−	566.217i	1.27898	−	0.929233i	0.279458	−	0.960158i	$-0.409845\pi$
$13$	779.331	−	566.217i	1.27898	−	0.929233i	0.999522	+	0.0309252i	$0.00984537\pi$
$14$	−568.552	−	413.077i	−0.775265	−	0.563263i
$15$	−441.552	+	241.158i	−0.506703	+	0.276741i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	61.6746	−	189.815i	0.0517587	−	0.159297i	−0.921836	−	0.387580i	$-0.873311\pi$
$17$	61.6746	−	189.815i	0.0517587	−	0.159297i	0.973595	+	0.228283i	$0.0733111\pi$
$18$	324.000			0.235702
$19$	151.706	−	466.903i	0.0964092	−	0.296717i	−0.891209	−	0.453593i	$-0.850142\pi$
$19$	151.706	−	466.903i	0.0964092	−	0.296717i	0.987618	+	0.156875i	$0.0501421\pi$
$20$	−784.981	+	428.725i	−0.438818	+	0.239665i
$21$	488.627	+	1503.84i	0.241785	+	0.744137i
$22$	−307.279	−	945.708i	−0.135356	−	0.416582i
$23$	990.820	+	719.873i	0.390549	+	0.283750i	0.765680	−	0.643221i	$-0.222402\pi$
$23$	990.820	+	719.873i	0.390549	+	0.283750i	−0.375132	+	0.926972i	$0.622402\pi$
$24$	576.000			0.204124
$25$	−2911.87	+	1134.31i	−0.931798	+	0.362978i
$26$	−3853.22			−1.11787
$27$	−589.773	−	428.495i	−0.155695	−	0.113119i
$28$	868.670	+	2673.49i	0.209392	+	0.644442i
$29$	632.817	+	1947.61i	0.139728	+	0.430038i	0.996295	−	0.0859966i	$-0.0274074\pi$
$29$	632.817	+	1947.61i	0.139728	+	0.430038i	−0.856567	+	0.516035i	$0.827407\pi$
$30$	1995.89	+	257.747i	0.404886	+	0.0522867i
$31$	−455.299	+	1401.27i	−0.0850928	+	0.261889i	−0.984545	−	0.175130i	$-0.943966\pi$
$31$	−455.299	+	1401.27i	−0.0850928	+	0.261889i	0.899453	+	0.437018i	$0.143966\pi$
$32$	1024.00			0.176777
$33$	−691.378	+	2127.84i	−0.110517	+	0.340138i
$34$	−645.864	+	469.248i	−0.0958173	+	0.0696154i
$35$	1813.69	+	9652.58i	0.250260	+	1.33191i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	5427.89	−	3943.60i	0.651819	−	0.473574i	−0.212071	−	0.977254i	$-0.568021\pi$
$37$	5427.89	−	3943.60i	0.651819	−	0.473574i	0.863890	+	0.503680i	$0.168021\pi$
$38$	−1588.69	+	1154.25i	−0.178476	+	0.129670i
$39$	7013.98	+	5095.95i	0.738419	+	0.536493i
$40$	3548.24	+	458.217i	0.350642	+	0.0452816i
$41$	6081.55	−	4418.50i	0.565008	−	0.410502i	−0.268280	−	0.963341i	$-0.586455\pi$
$41$	6081.55	−	4418.50i	0.565008	−	0.410502i	0.833288	+	0.552839i	$0.186455\pi$
$42$	1954.51	−	6015.36i	0.170968	−	0.526185i
$43$	−5367.13			−0.442661			−0.221330	−	0.975199i	$-0.571040\pi$
$43$	−5367.13			−0.442661			−0.221330	+	0.975199i	$0.571040\pi$
$44$	−1229.12	+	3782.83i	−0.0957109	+	0.294568i
$45$	−3292.22	−	3108.77i	−0.242358	−	0.228853i
$46$	−1513.84	−	4659.12i	−0.105484	−	0.324645i
$47$	691.203	+	2127.30i	0.0456416	+	0.140470i	0.971280	−	0.237938i	$-0.0764715\pi$
$47$	691.203	+	2127.30i	0.0456416	+	0.140470i	−0.925639	+	0.378408i	$0.876472\pi$
$48$	−1863.98	−	1354.26i	−0.116772	−	0.0848395i
$49$	14060.8			0.836602
$50$	12089.9	+	3175.52i	0.683909	+	0.179635i
$51$	1796.25			0.0967032
$52$	12469.3	+	9059.47i	0.639490	+	0.464616i
$53$	11458.4	+	35265.2i	0.560316	+	1.72447i	0.681475	+	0.731841i	$0.261339\pi$
$53$	11458.4	+	35265.2i	0.560316	+	1.72447i	−0.121160	+	0.992633i	$0.538661\pi$
$54$	901.094	+	2773.28i	0.0420519	+	0.129422i
$55$	−5951.72	+	12557.8i	−0.265299	+	0.559767i
$56$	3474.68	−	10694.0i	0.148062	−	0.455689i
$57$	4418.38			0.180126
$58$	2531.27	−	7790.44i	0.0988026	−	0.304083i
$59$	−8367.58	+	6079.40i	−0.312946	+	0.227369i	−0.733160	−	0.680057i	$-0.761955\pi$
$59$	−8367.58	+	6079.40i	−0.312946	+	0.227369i	0.420213	+	0.907425i	$0.361955\pi$
$60$	−5852.83	−	5526.70i	−0.209888	−	0.198193i
$61$	44592.3	+	32398.2i	1.53439	+	1.11480i	0.953736	+	0.300646i	$0.0972022\pi$
$61$	44592.3	+	32398.2i	1.53439	+	1.11480i	0.580652	+	0.814152i	$0.302798\pi$
$62$	4767.96	−	3464.12i	0.157526	−	0.114450i
$63$	−11513.2	+	8364.81i	−0.365463	+	0.265525i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	39153.2	+	36971.6i	1.14943	+	1.08539i
$66$	7240.20	−	5260.32i	0.204593	−	0.148646i
$67$	−1089.68	+	3353.69i	−0.0296559	+	0.0912715i	−0.964789	−	0.263025i	$-0.915280\pi$
$67$	−1089.68	+	3353.69i	−0.0296559	+	0.0912715i	0.935133	+	0.354297i	$0.115280\pi$
$68$	3193.33			0.0837474
$69$	−3406.14	+	10483.0i	−0.0861270	+	0.265072i
$70$	16825.4	−	35500.6i	0.410411	−	0.865946i
$71$	5762.75	+	17735.9i	0.135670	+	0.417549i	0.995694	−	0.0927050i	$-0.0295513\pi$
$71$	5762.75	+	17735.9i	0.135670	+	0.417549i	−0.860024	+	0.510254i	$0.829551\pi$
$72$	1601.94	+	4930.28i	0.0364180	+	0.112083i
$73$	−46388.0	−	33702.8i	−1.01882	−	0.740218i	−0.0527810	−	0.998606i	$-0.516809\pi$
$73$	−46388.0	−	33702.8i	−1.01882	−	0.740218i	−0.966041	+	0.258389i	$0.916809\pi$
$74$	−26837.0			−0.569711
$75$	−17807.5	−	21769.5i	−0.365552	−	0.446884i
$76$	7854.89			0.155993
$77$	35334.7	+	25672.1i	0.679163	+	0.493441i
$78$	−10716.4	−	32981.7i	−0.199440	−	0.613814i
$79$	−31994.4	−	98468.7i	−0.576775	−	1.77513i	−0.630054	−	0.776551i	$-0.716967\pi$
$79$	−31994.4	−	98468.7i	−0.576775	−	1.77513i	0.0532788	−	0.998580i	$-0.483033\pi$
$80$	−10405.0	−	9825.24i	−0.181768	−	0.171640i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	−30068.8			−0.493835
$83$	−33878.5	+	104267.i	−0.539795	+	1.66132i	0.193260	+	0.981148i	$0.438094\pi$
$83$	−33878.5	+	104267.i	−0.539795	+	1.66132i	−0.733055	+	0.680169i	$0.761906\pi$
$84$	−20467.9	+	14870.8i	−0.316501	+	0.229951i
$85$	11065.1	+	1428.94i	0.166115	+	0.0214520i
$86$	17368.4	+	12618.9i	0.253229	+	0.183982i
$87$	−14910.6	+	10833.2i	−0.211202	+	0.153447i
$88$	12871.5	−	9351.67i	0.177183	−	0.128731i
$89$	−81142.8	−	58953.7i	−1.08586	−	0.788926i	−0.107167	−	0.994241i	$-0.534178\pi$
$89$	−81142.8	−	58953.7i	−1.08586	−	0.788926i	−0.978696	+	0.205315i	$0.934178\pi$
$90$	3344.68	+	17800.6i	0.0435259	+	0.231649i
$91$	136922.	−	99479.9i	1.73329	−	1.25931i
$92$	−6055.36	+	18636.5i	−0.0745882	+	0.229559i
$93$	−13260.4			−0.158983
$94$	2764.81	−	8509.21i	0.0322735	−	0.0993275i
$95$	27217.8	+	3514.89i	0.309417	+	0.0399579i
$96$	2847.90	+	8764.94i	0.0315389	+	0.0970668i
$97$	−9783.40	−	30110.2i	−0.105575	−	0.324926i	0.884290	−	0.466938i	$-0.154643\pi$
$97$	−9783.40	−	30110.2i	−0.105575	−	0.324926i	−0.989865	+	0.142012i	$0.954643\pi$
$98$	−45501.6	−	33058.8i	−0.478587	−	0.347714i
$99$	−20136.1			−0.206485
$100$	−31657.7	−	38701.3i	−0.316577	−	0.387013i
$101$	−102910.			−1.00382			−0.501910	−	0.864920i	$-0.667369\pi$
$101$	−102910.			−1.00382			−0.501910	+	0.864920i	$0.667369\pi$
$102$	−5812.78	−	4223.23i	−0.0553202	−	0.0401924i
$103$	14719.0	+	45300.4i	0.136705	+	0.420735i	0.995851	−	0.0909949i	$-0.0290047\pi$
$103$	14719.0	+	45300.4i	0.136705	+	0.420735i	−0.859146	+	0.511730i	$0.829005\pi$
$104$	−19051.4	−	58634.1i	−0.172720	−	0.531578i
$105$	−77577.2	+	42369.6i	−0.686690	+	0.375043i
$106$	45833.4	−	141061.i	0.396203	−	1.21939i
$107$	−108679.			−0.917671			−0.458835	−	0.888521i	$-0.651733\pi$
$107$	−108679.			−0.917671			−0.458835	+	0.888521i	$0.651733\pi$
$108$	3604.37	−	11093.1i	0.0297352	−	0.0915155i
$109$	−70483.4	+	51209.2i	−0.568225	+	0.412840i	−0.834460	−	0.551069i	$-0.814220\pi$
$109$	−70483.4	+	51209.2i	−0.568225	+	0.412840i	0.266235	+	0.963908i	$0.414220\pi$
$110$	48785.4	−	26644.6i	0.384422	−	0.209956i
$111$	48851.1	+	35492.4i	0.376328	+	0.273418i
$112$	−36387.3	+	26436.9i	−0.274098	+	0.199144i
$113$	−147977.	+	107512.i	−1.09018	+	0.792064i	−0.979430	−	0.201783i	$-0.935326\pi$
$113$	−147977.	+	107512.i	−1.09018	+	0.792064i	−0.110753	+	0.993848i	$0.535326\pi$
$114$	−14298.2	−	10388.2i	−0.103043	−	0.0748651i
$115$	−29321.7	+	61867.3i	−0.206750	+	0.436231i
$116$	−26507.8	+	19259.0i	−0.182906	+	0.132889i
$117$	−24111.9	+	74208.8i	−0.162842	+	0.501177i
$118$	41371.6			0.273525
$119$	10835.7	−	33349.0i	0.0701441	−	0.215881i
$120$	5946.09	+	31645.6i	0.0376946	+	0.200614i
$121$	−30670.6	−	94394.3i	−0.190440	−	0.586114i
$122$	−68130.9	−	209685.i	−0.414424	−	1.27547i
$123$	54733.9	+	39766.5i	0.326208	+	0.237004i
$124$	−23574.1			−0.137683
$125$	−92378.5	−	148269.i	−0.528806	−	0.848743i
$126$	56924.3			0.319427
$127$	−7644.20	−	5553.84i	−0.0420555	−	0.0305551i	0.566559	−	0.824021i	$-0.308274\pi$
$127$	−7644.20	−	5553.84i	−0.0420555	−	0.0305551i	−0.608614	+	0.793466i	$0.708274\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	−14926.8	−	45940.0i	−0.0789755	−	0.243062i
$130$	−39777.1	−	211697.i	−0.206431	−	1.09864i
$131$	27630.1	−	85036.8i	0.140671	−	0.432941i	−0.855758	−	0.517376i	$-0.826909\pi$
$131$	27630.1	−	85036.8i	0.140671	−	0.432941i	0.996429	+	0.0844355i	$0.0269087\pi$
$132$	−35797.5			−0.178821
$133$	26653.6	−	82031.2i	0.130655	−	0.402115i
$134$	11411.3	−	8290.77i	0.0548999	−	0.0398871i
$135$	17453.4	−	36825.7i	0.0824224	−	0.173907i
$136$	−10333.8	−	7507.97i	−0.0479087	−	0.0348077i
$137$	199897.	−	145233.i	0.909921	−	0.661096i	−0.0310737	−	0.999517i	$-0.509893\pi$
$137$	199897.	−	145233.i	0.909921	−	0.661096i	0.940995	+	0.338421i	$0.109893\pi$
$138$	35669.5	−	25915.4i	0.159441	−	0.115841i
$139$	137519.	+	99913.2i	0.603705	+	0.438618i	0.847192	−	0.531287i	$-0.178291\pi$
$139$	137519.	+	99913.2i	0.603705	+	0.438618i	−0.243487	+	0.969904i	$0.578291\pi$
$140$	−137915.	+	75323.7i	−0.594691	+	0.324796i
$141$	−16286.3	+	11832.7i	−0.0689883	+	0.0501229i
$142$	23051.0	−	70943.6i	0.0959331	−	0.295252i
$143$	239472.			0.979298
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	−100470.	+	54872.5i	−0.396840	+	0.216738i
$146$	70874.5	+	218129.i	0.275174	+	0.846900i
$147$	39105.1	+	120353.i	0.149259	+	0.459372i
$148$	86846.3	+	63097.5i	0.325910	+	0.236787i
$149$	215549.			0.795389			0.397694	−	0.917518i	$-0.369810\pi$
$149$	215549.			0.795389			0.397694	+	0.917518i	$0.369810\pi$
$150$	6443.00	+	112315.i	0.0233808	+	0.407578i
$151$	304329.			1.08618			0.543090	−	0.839675i	$-0.317254\pi$
$151$	304329.			1.08618			0.543090	+	0.839675i	$0.317254\pi$
$152$	−25419.0	−	18468.0i	−0.0892378	−	0.0648351i
$153$	4995.64	+	15375.0i	0.0172529	+	0.0530990i
$154$	−53986.6	−	166154.i	−0.183436	−	0.564557i
$155$	−81686.1	−	10548.9i	−0.273098	−	0.0352677i
$156$	−42865.6	+	131927.i	−0.141025	+	0.434032i
$157$	−94934.4			−0.307379			−0.153690	−	0.988119i	$-0.549116\pi$
$157$	−94934.4			−0.307379			−0.153690	+	0.988119i	$0.549116\pi$
$158$	−127978.	+	393875.i	−0.407842	+	1.25521i
$159$	−269985.	+	196156.i	−0.846930	+	0.615330i
$160$	10570.8	+	56258.8i	0.0326444	+	0.173736i
$161$	174079.	+	126476.i	0.529277	+	0.384542i
$162$	−21231.8	+	15425.8i	−0.0635624	+	0.0461808i
$163$	519876.	−	377712.i	1.53261	−	1.11350i	0.577838	−	0.816151i	$-0.303896\pi$
$163$	519876.	−	377712.i	1.53261	−	1.11350i	0.954768	−	0.297352i	$-0.0961035\pi$
$164$	97304.8	+	70696.1i	0.282504	+	0.205251i
$165$	−124041.	−	16018.6i	−0.354696	−	0.0458052i
$166$	354780.	−	257763.i	0.999284	−	0.726022i
$167$	−156947.	+	483032.i	−0.435473	+	1.34025i	0.457129	+	0.889401i	$0.348878\pi$
$167$	−156947.	+	483032.i	−0.435473	+	1.34025i	−0.892601	+	0.450847i	$0.851122\pi$
$168$	101199.			0.276632
$169$	172019.	−	529420.i	0.463297	−	1.42588i
$170$	−32447.9	−	30639.9i	−0.0861122	−	0.0813139i
$171$	12288.2	+	37819.1i	0.0321364	+	0.0989057i
$172$	−26536.5	−	81671.1i	−0.0683948	−	0.210498i
$173$	250125.	+	181726.i	0.635391	+	0.461639i	0.858264	−	0.513209i	$-0.171543\pi$
$173$	250125.	+	181726.i	0.635391	+	0.461639i	−0.222872	+	0.974848i	$0.571543\pi$
$174$	73722.2			0.184597
$175$	−511593.	+	199289.i	−1.26278	+	0.491912i
$176$	−63640.1			−0.154863
$177$	−75308.2	−	54714.6i	−0.180680	−	0.131271i
$178$	123975.	+	381556.i	0.293282	+	0.902628i
$179$	−217569.	−	669609.i	−0.507533	−	1.56203i	−0.796469	−	0.604679i	$-0.793301\pi$
$179$	−217569.	−	669609.i	−0.507533	−	1.56203i	0.288936	−	0.957348i	$-0.406699\pi$
$180$	31028.2	−	65467.9i	0.0713799	−	0.150608i
$181$	−60823.1	+	187194.i	−0.137998	+	0.424714i	−0.996044	−	0.0888585i	$-0.971678\pi$
$181$	−60823.1	+	187194.i	−0.137998	+	0.424714i	0.858046	+	0.513572i	$0.171678\pi$
$182$	−676982.			−1.51495
$183$	−153295.	+	471792.i	−0.338376	+	1.04141i
$184$	63412.5	−	46071.9i	0.138080	−	0.100321i
$185$	272695.	+	257500.i	0.585798	+	0.553156i
$186$	42911.6	+	31177.1i	0.0909479	+	0.0660775i
$187$	40139.5	−	29163.1i	0.0839398	−	0.0609858i
$188$	−28953.5	+	21035.9i	−0.0597456	+	0.0434077i
$189$	−103619.	−	75283.3i	−0.211000	−	0.153301i
$190$	−79814.8	−	75367.4i	−0.160398	−	0.151461i
$191$	569469.	−	413743.i	1.12950	−	0.820630i	0.143878	−	0.989595i	$-0.454043\pi$
$191$	569469.	−	413743.i	1.12950	−	0.820630i	0.985622	+	0.168965i	$0.0540426\pi$
$192$	11391.6	−	35059.7i	0.0223014	−	0.0686366i
$193$	−872418.			−1.68590			−0.842949	−	0.537993i	$-0.819183\pi$
$193$	−872418.			−1.68590			−0.842949	+	0.537993i	$0.819183\pi$
$194$	−39133.6	+	120441.i	−0.0746527	+	0.229757i
$195$	−207567.	+	437956.i	−0.390906	+	0.824791i
$196$	69520.2	+	213961.i	0.129262	+	0.397828i
$197$	35364.2	+	108840.i	0.0649230	+	0.199812i	0.978256	−	0.207401i	$-0.0665005\pi$
$197$	35364.2	+	108840.i	0.0649230	+	0.199812i	−0.913333	+	0.407213i	$0.866501\pi$
$198$	65161.8	+	47342.8i	0.118122	+	0.0858206i
$199$	329774.			0.590315			0.295158	−	0.955449i	$-0.404628\pi$
$199$	329774.			0.590315			0.295158	+	0.955449i	$0.404628\pi$
$200$	11454.2	+	199672.i	0.0202484	+	0.352973i
$201$	−31736.5			−0.0554075
$202$	333025.	+	241957.i	0.574247	+	0.417215i
$203$	111181.	+	342180.i	0.189361	+	0.582793i
$204$	8881.14	+	27333.3i	0.0149415	+	0.0459851i
$205$	305534.	+	288509.i	0.507780	+	0.479485i
$206$	58876.0	−	181202.i	0.0966652	−	0.297505i
$207$	−99202.4			−0.160915
$208$	−76205.5	+	234537.i	−0.122132	+	0.375883i
$209$	98734.4	−	71734.8i	0.156352	−	0.113596i
$210$	350662.	+	45284.2i	0.548707	+	0.0708595i
$211$	−136988.	−	99527.9i	−0.211825	−	0.153900i	0.476814	−	0.879004i	$-0.341792\pi$
$211$	−136988.	−	99527.9i	−0.211825	−	0.153900i	−0.688639	+	0.725104i	$0.741792\pi$
$212$	−479974.	+	348721.i	−0.733463	+	0.532892i
$213$	−135784.	+	98652.6i	−0.205068	+	0.148991i
$214$	351693.	+	255520.i	0.524964	+	0.381409i
$215$	−55405.3	−	294871.i	−0.0817439	−	0.435047i
$216$	−37745.5	+	27423.7i	−0.0550466	+	0.0399937i
$217$	−79992.6	+	246192.i	−0.115319	+	0.354915i
$218$	348489.			0.496647
$219$	159468.	−	490791.i	0.224679	−	0.691491i
$220$	−220518.	−	28477.5i	−0.307176	−	0.0396685i
$221$	−59411.5	−	182850.i	−0.0818257	−	0.251834i
$222$	−74637.8	−	229711.i	−0.101643	−	0.312824i
$223$	844689.	+	613702.i	1.13746	+	0.826410i	0.986763	−	0.162171i	$-0.0518495\pi$
$223$	844689.	+	613702.i	1.13746	+	0.826410i	0.150693	+	0.988581i	$0.451850\pi$
$224$	179909.			0.239570
$225$	136811.	−	212967.i	0.180162	−	0.280451i
$226$	731641.			0.952855
$227$	−773584.	−	562042.i	−0.996421	−	0.723942i	−0.0351034	−	0.999384i	$-0.511176\pi$
$227$	−773584.	−	562042.i	−0.996421	−	0.723942i	−0.961318	+	0.275441i	$0.911176\pi$
$228$	21845.7	+	67234.0i	0.0278309	+	0.0856548i
$229$	−468814.	−	1.44286e6i	−0.590761	−	1.81818i	−0.574785	−	0.818304i	$-0.694915\pi$
$229$	−468814.	−	1.44286e6i	−0.590761	−	1.81818i	−0.0159759	−	0.999872i	$-0.505085\pi$
$230$	240346.	−	131267.i	0.299583	−	0.163620i
$231$	−121470.	+	373845.i	−0.149775	+	0.460959i
$232$	131062.			0.159866
$233$	12390.7	−	38134.6i	0.0149522	−	0.0460182i	−0.943302	−	0.331936i	$-0.892298\pi$
$233$	12390.7	−	38134.6i	0.0149522	−	0.0460182i	0.958254	+	0.285917i	$0.0922983\pi$
$234$	252503.	−	183454.i	0.301458	−	0.219022i
$235$	−109739.	+	59935.2i	−0.129626	+	0.0707966i
$236$	−133881.	−	97270.4i	−0.156473	−	0.113684i
$237$	753862.	−	547713.i	0.871809	−	0.633406i
$238$	−113473.	+	82443.2i	−0.129853	+	0.0943436i
$239$	10916.2	+	7931.12i	0.0123617	+	0.00898131i	0.593949	−	0.804503i	$-0.297568\pi$
$239$	10916.2	+	7931.12i	0.0123617	+	0.00898131i	−0.581587	+	0.813484i	$0.697568\pi$
$240$	55161.3	−	116387.i	0.0618168	−	0.130430i
$241$	−106450.	+	77340.6i	−0.118060	+	0.0857758i	−0.645249	−	0.763973i	$-0.723246\pi$
$241$	−106450.	+	77340.6i	−0.118060	+	0.0857758i	0.527188	+	0.849748i	$0.323246\pi$
$242$	−122682.	+	377577.i	−0.134661	+	0.414445i
$243$	59049.0			0.0641500
$244$	−272524.	+	838742.i	−0.293042	+	0.901890i
$245$	145150.	+	772502.i	0.154491	+	0.822213i
$246$	−83626.0	−	257374.i	−0.0881056	−	0.271161i
$247$	−146139.	−	449770.i	−0.152414	−	0.469082i
$248$	76287.3	+	55426.0i	0.0787631	+	0.0572248i
$249$	−986697.			−1.00852
$250$	−49658.8	+	697004.i	−0.0502512	+	0.705319i
$251$	456406.			0.457264			0.228632	−	0.973513i	$-0.426575\pi$
$251$	456406.			0.457264			0.228632	+	0.973513i	$0.426575\pi$
$252$	−184211.	−	133837.i	−0.182732	−	0.132762i
$253$	94082.8	+	289557.i	0.0924079	+	0.284402i
$254$	11679.3	+	35945.2i	0.0113588	+	0.0349588i
$255$	18542.8	+	98686.3i	0.0178577	+	0.0950400i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−1.41173e6			−1.33327			−0.666634	−	0.745385i	$-0.732266\pi$
$257$	−1.41173e6			−1.33327			−0.666634	+	0.745385i	$0.732266\pi$
$258$	−59707.2	+	183760.i	−0.0558441	+	0.171871i
$259$	953639.	−	692859.i	0.883354	−	0.641794i
$260$	−369008.	+	778588.i	−0.338534	+	0.714290i
$261$	−134196.	−	97498.9i	−0.121937	−	0.0885928i
$262$	−289346.	+	210223.i	−0.260414	+	0.189202i
$263$	1.26167e6	−	916659.i	1.12475	−	0.817181i	0.139831	−	0.990175i	$-0.455344\pi$
$263$	1.26167e6	−	916659.i	1.12475	−	0.817181i	0.984923	+	0.172994i	$0.0553442\pi$
$264$	115843.	+	84165.1i	0.102297	+	0.0743228i
$265$	−1.81919e6	+	993571.i	−1.59135	+	0.869129i
$266$	−279120.	+	202792.i	−0.241872	+	0.175731i
$267$	278944.	−	858502.i	0.239463	−	0.736992i
$268$	−56420.4			−0.0479843
$269$	610501.	−	1.87893e6i	0.514405	−	1.58318i	−0.269956	−	0.962873i	$-0.587009\pi$
$269$	610501.	−	1.87893e6i	0.514405	−	1.58318i	0.784361	−	0.620304i	$-0.212991\pi$
$270$	−143063.	+	78135.1i	−0.119431	+	0.0652284i
$271$	96520.5	+	297060.i	0.0798355	+	0.245709i	0.983006	−	0.183574i	$-0.0587666\pi$
$271$	96520.5	+	297060.i	0.0798355	+	0.245709i	−0.903170	+	0.429282i	$0.858767\pi$
$272$	15788.7	+	48592.6i	0.0129397	+	0.0398243i
$273$	1.23230e6	+	895319.i	1.00071	+	0.727062i
$274$	−988343.			−0.795300
$275$	−751370.	−	197354.i	−0.599132	−	0.157367i
$276$	−176360.			−0.139356
$277$	−232133.	−	168654.i	−0.181776	−	0.132068i	0.493176	−	0.869929i	$-0.335836\pi$
$277$	−232133.	−	168654.i	−0.181776	−	0.132068i	−0.674952	+	0.737861i	$0.735836\pi$
$278$	−210110.	−	646652.i	−0.163055	−	0.501832i
$279$	−36879.2	−	113503.i	−0.0283643	−	0.0872962i
$280$	623399.	+	80505.2i	0.475194	+	0.0613662i
$281$	−49328.1	+	151816.i	−0.0372674	+	0.114697i	−0.967960	−	0.251106i	$-0.919206\pi$
$281$	−49328.1	+	151816.i	−0.0372674	+	0.114697i	0.930692	+	0.365803i	$0.119206\pi$
$282$	80524.0			0.0602980
$283$	454608.	−	1.39914e6i	0.337420	−	1.03847i	−0.628097	−	0.778135i	$-0.716166\pi$
$283$	454608.	−	1.39914e6i	0.337420	−	1.03847i	0.965517	−	0.260338i	$-0.0838341\pi$
$284$	−241393.	+	175382.i	−0.177594	+	0.129030i
$285$	45611.3	+	242747.i	0.0332629	+	0.177028i
$286$	−774948.	−	563033.i	−0.560219	−	0.407023i
$287$	1.06848e6	−	776297.i	0.765706	−	0.556318i
$288$	−67103.1	+	48753.3i	−0.0476718	+	0.0346356i
$289$	1.11646e6	+	811158.i	0.786320	+	0.571295i
$290$	454140.	+	58647.2i	0.317099	+	0.0409499i
$291$	230519.	−	167482.i	0.159579	−	0.115941i
$292$	283498.	−	872517.i	0.194578	−	0.598849i
$293$	606462.			0.412700			0.206350	−	0.978478i	$-0.433841\pi$
$293$	606462.			0.412700			0.206350	+	0.978478i	$0.433841\pi$
$294$	156421.	−	481413.i	0.105542	−	0.324825i
$295$	−420383.	−	396959.i	−0.281248	−	0.265577i
$296$	−132689.	−	408376.i	−0.0880252	−	0.270914i
$297$	−56001.6	−	172355.i	−0.0368391	−	0.113379i
$298$	−697530.	−	506785.i	−0.455011	−	0.330585i
$299$	1.17978e6			0.763174
$300$	243219.	−	378609.i	0.156025	−	0.242877i
$301$	−942963.			−0.599899
$302$	−984831.	−	715522.i	−0.621361	−	0.451446i
$303$	−286210.	−	880863.i	−0.179093	−	0.551191i
$304$	38836.7	+	119527.i	0.0241023	+	0.0741793i
$305$	−1.31964e6	+	2.78436e6i	−0.812278	+	1.71386i
$306$	19982.6	−	61500.0i	0.0121997	−	0.0375467i
$307$	−1.98819e6			−1.20396			−0.601980	−	0.798511i	$-0.705621\pi$
$307$	−1.98819e6			−1.20396			−0.601980	+	0.798511i	$0.705621\pi$
$308$	−215946.	+	664614.i	−0.129709	+	0.399202i
$309$	−346813.	+	251975.i	−0.206633	+	0.150128i
$310$	239540.	+	226192.i	0.141571	+	0.133682i
$311$	2.43784e6	+	1.77120e6i	1.42924	+	1.03840i	0.990158	+	0.139955i	$0.0446959\pi$
$311$	2.43784e6	+	1.77120e6i	1.42924	+	1.03840i	0.439081	+	0.898447i	$0.355304\pi$
$312$	448895.	−	326141.i	0.261071	−	0.189679i
$313$	−664302.	+	482644.i	−0.383270	+	0.278462i	−0.762692	−	0.646762i	$-0.776123\pi$
$313$	−664302.	+	482644.i	−0.383270	+	0.278462i	0.379422	+	0.925224i	$0.376123\pi$
$314$	307214.	+	223204.i	0.175840	+	0.127755i
$315$	−578417.	−	546187.i	−0.328446	−	0.310145i
$316$	1.34020e6	−	973712.i	0.755008	−	0.548546i
$317$	684978.	−	2.10815e6i	0.382850	−	1.17829i	−0.555178	−	0.831732i	$-0.687350\pi$
$317$	684978.	−	2.10815e6i	0.382850	−	1.17829i	0.938028	−	0.346560i	$-0.112650\pi$
$318$	1.33488e6			0.740244
$319$	−157315.	+	484164.i	−0.0865550	+	0.266389i
$320$	98064.5	−	206911.i	0.0535349	−	0.112956i
$321$	−302253.	−	930240.i	−0.163723	−	0.503886i
$322$	−265970.	−	818571.i	−0.142953	−	0.439963i
$323$	−79268.7	−	57592.1i	−0.0422761	−	0.0307154i
$324$	104976.			0.0555556
$325$	−1.62705e6	+	2.53275e6i	−0.854459	+	1.33010i
$326$	−2.57041e6			−1.33955
$327$	−634350.	−	460882.i	−0.328065	−	0.238353i
$328$	−148669.	−	457555.i	−0.0763017	−	0.234833i
$329$	121439.	+	373751.i	0.0618541	+	0.190367i
$330$	363744.	+	343476.i	0.183870	+	0.173625i
$331$	1.07455e6	−	3.30712e6i	0.539083	−	1.65913i	−0.195575	−	0.980689i	$-0.562657\pi$
$331$	1.07455e6	−	3.30712e6i	0.539083	−	1.65913i	0.734658	−	0.678438i	$-0.237343\pi$
$332$	−1.75413e6			−0.873406
$333$	−167935.	+	516851.i	−0.0829909	+	0.255420i
$334$	1.64357e6	−	1.19412e6i	0.806160	−	0.585710i
$335$	−195501.	−	25246.9i	−0.0951782	−	0.0122912i
$336$	−327486.	−	237932.i	−0.158250	−	0.114976i
$337$	−2.73428e6	+	1.98657e6i	−1.31150	+	0.952861i	−0.311504	+	0.950245i	$0.600833\pi$
$337$	−2.73428e6	+	1.98657e6i	−1.31150	+	0.952861i	−0.999997	+	0.00261607i	$0.999167\pi$
$338$	−1.80141e6	+	1.30880e6i	−0.857670	+	0.623134i
$339$	−1.33180e6	−	967607.i	−0.629418	−	0.457299i
$340$	32965.0	+	175442.i	0.0154652	+	0.0823071i
$341$	−296321.	+	215290.i	−0.137999	+	0.100262i
$342$	49152.7	−	151277.i	0.0227239	−	0.0699369i
$343$	−482492.			−0.221440
$344$	−106146.	+	326684.i	−0.0483624	+	0.148844i
$345$	−611101.	−	78917.1i	−0.276418	−	0.0356963i
$346$	−382157.	−	1.17616e6i	−0.171613	−	0.528172i
$347$	−537294.	−	1.65362e6i	−0.239546	−	0.737246i	−0.996486	−	0.0837619i	$-0.973306\pi$
$347$	−537294.	−	1.65362e6i	−0.239546	−	0.737246i	0.756940	−	0.653484i	$-0.226694\pi$
$348$	−238570.	−	173331.i	−0.105601	−	0.0767236i
$349$	−3.56625e6			−1.56728			−0.783642	−	0.621212i	$-0.786640\pi$
$349$	−3.56625e6			−1.56728			−0.783642	+	0.621212i	$0.786640\pi$
$350$	2.12410e6	+	557914.i	0.926842	+	0.243443i
$351$	−702250.			−0.304245
$352$	205944.	+	149627.i	0.0885914	+	0.0643654i
$353$	−406967.	−	1.25252e6i	−0.173829	−	0.534991i	0.825749	−	0.564038i	$-0.190753\pi$
$353$	−406967.	−	1.25252e6i	−0.173829	−	0.534991i	−0.999578	+	0.0290469i	$0.990753\pi$
$354$	115061.	+	354120.i	0.0487999	+	0.150191i
$355$	−914926.	+	499696.i	−0.385314	+	0.210443i
$356$	495901.	−	1.52623e6i	0.207381	−	0.638254i
$357$	315587.			0.131053
$358$	−870276.	+	2.67844e6i	−0.358880	+	1.10452i
$359$	304871.	−	221502.i	0.124848	−	0.0907071i	−0.523609	−	0.851959i	$-0.675415\pi$
$359$	304871.	−	221502.i	0.124848	−	0.0907071i	0.648457	+	0.761252i	$0.275415\pi$
$360$	−254334.	+	138907.i	−0.103430	+	0.0564895i
$361$	1.80822e6	+	1.31375e6i	0.730271	+	0.530573i
$362$	636948.	−	462770.i	0.255466	−	0.185607i
$363$	722669.	−	525050.i	0.287854	−	0.209138i
$364$	2.19076e6	+	1.59168e6i	0.866645	+	0.629654i
$365$	1.37278e6	−	2.89649e6i	0.539346	−	1.13799i
$366$	1.60532e6	−	1.16633e6i	0.626411	−	0.455114i
$367$	206913.	−	636814.i	0.0801906	−	0.246801i	−0.902922	−	0.429805i	$-0.858582\pi$
$367$	206913.	−	636814.i	0.0801906	−	0.246801i	0.983112	+	0.183004i	$0.0585822\pi$
$368$	−313529.			−0.120686
$369$	−188159.	+	579093.i	−0.0719380	+	0.221402i
$370$	−277040.	−	1.47443e6i	−0.105206	−	0.559913i
$371$	2.01314e6	+	6.19582e6i	0.759347	+	2.33703i
$372$	−65563.1	−	201782.i	−0.0245642	−	0.0756008i
$373$	1.27722e6	+	927958.i	0.475330	+	0.345347i	0.799515	−	0.600646i	$-0.205090\pi$
$373$	1.27722e6	+	927958.i	0.475330	+	0.345347i	−0.324185	+	0.945994i	$0.605090\pi$
$374$	−198461.			−0.0733661
$375$	1.01219e6	−	1.20307e6i	0.371694	−	0.441788i
$376$	143154.			0.0522196
$377$	1.59594e6	+	1.15952e6i	0.578315	+	0.420170i
$378$	158315.	+	487244.i	0.0569893	+	0.175395i
$379$	1.35931e6	+	4.18353e6i	0.486094	+	1.49604i	0.830390	+	0.557183i	$0.188118\pi$
$379$	1.35931e6	+	4.18353e6i	0.486094	+	1.49604i	−0.344296	+	0.938861i	$0.611882\pi$
$380$	81086.7	+	431550.i	0.0288065	+	0.153311i
$381$	26278.4	−	80876.7i	0.00927442	−	0.0285437i
$382$	−2.81561e6			−0.987219
$383$	820442.	−	2.52506e6i	0.285793	−	0.879579i	−0.700367	−	0.713783i	$-0.746980\pi$
$383$	820442.	−	2.52506e6i	0.285793	−	0.879579i	0.986160	−	0.165797i	$-0.0530196\pi$
$384$	−119294.	+	86672.5i	−0.0412850	+	0.0299953i
$385$	−1.04567e6	+	2.20631e6i	−0.359537	+	0.758604i
$386$	2.82320e6	+	2.05118e6i	0.964437	+	0.700705i
$387$	351710.	−	255532.i	0.119373	−	0.0867298i
$388$	409812.	−	297746.i	0.138199	−	0.100408i
$389$	−2.59621e6	−	1.88626e6i	−0.869892	−	0.632014i	0.0606657	−	0.998158i	$-0.480678\pi$
$389$	−2.59621e6	−	1.88626e6i	−0.869892	−	0.632014i	−0.930558	+	0.366144i	$0.880678\pi$
$390$	1.70140e6	−	929235.i	0.566427	−	0.309360i
$391$	197751.	−	143674.i	0.0654149	−	0.0475267i
$392$	278081.	−	855845.i	0.0914021	−	0.281307i
$393$	804717.			0.262822
$394$	141457.	−	435359.i	0.0459075	−	0.141289i
$395$	5.07962e6	−	2.77428e6i	1.63809	−	0.894660i
$396$	−99558.4	−	306409.i	−0.0319036	−	0.0981893i
$397$	1.60356e6	+	4.93526e6i	0.510634	+	1.57157i	0.791089	+	0.611701i	$0.209515\pi$
$397$	1.60356e6	+	4.93526e6i	0.510634	+	1.57157i	−0.280455	+	0.959867i	$0.590485\pi$
$398$	−1.06717e6	−	775346.i	−0.337697	−	0.245351i
$399$	776274.			0.244109
$400$	432390.	−	673082.i	0.135122	−	0.210338i
$401$	−3.50739e6			−1.08924			−0.544619	−	0.838683i	$-0.683326\pi$
$401$	−3.50739e6			−1.08924			−0.544619	+	0.838683i	$0.683326\pi$
$402$	102701.	+	74616.9i	0.0316965	+	0.0230288i
$403$	438593.	+	1.34985e6i	0.134524	+	0.414021i
$404$	−508817.	−	1.56598e6i	−0.155099	−	0.477345i
$405$	363750.	+	46974.4i	0.110196	+	0.0142306i
$406$	444724.	−	1.36872e6i	0.133899	−	0.412097i
$407$	1.66788e6			0.499090
$408$	35524.5	−	109333.i	0.0105652	−	0.0325164i
$409$	−3.63236e6	+	2.63906e6i	−1.07369	+	0.780085i	−0.976573	−	0.215188i	$-0.930964\pi$
$409$	−3.63236e6	+	2.63906e6i	−1.07369	+	0.780085i	−0.0971218	+	0.995272i	$0.530964\pi$
$410$	−310403.	−	1.65199e6i	−0.0911940	−	0.485342i
$411$	1.79907e6	+	1.30710e6i	0.525343	+	0.381684i
$412$	−616557.	+	447955.i	−0.178949	+	0.130014i
$413$	−1.47012e6	+	1.06810e6i	−0.424109	+	0.308133i
$414$	321026.	+	233239.i	0.0920532	+	0.0668806i
$415$	−6.07820e6	−	784934.i	−1.73243	−	0.223724i
$416$	798035.	−	579806.i	0.226094	−	0.164267i
$417$	−472747.	+	1.45497e6i	−0.133134	+	0.409744i
$418$	−488170.			−0.136656
$419$	1.97942e6	−	6.09202e6i	0.550811	−	1.69522i	−0.155946	−	0.987766i	$-0.549843\pi$
$419$	1.97942e6	−	6.09202e6i	0.550811	−	1.69522i	0.706757	−	0.707456i	$-0.250157\pi$
$420$	−1.02830e6	−	970998.i	−0.284443	−	0.268593i
$421$	1.77311e6	+	5.45709e6i	0.487564	+	1.50057i	0.828233	+	0.560384i	$0.189346\pi$
$421$	1.77311e6	+	5.45709e6i	0.487564	+	1.50057i	−0.340669	+	0.940183i	$0.610654\pi$
$422$	209300.	+	644158.i	0.0572120	+	0.176081i
$423$	−146577.	−	106494.i	−0.0398304	−	0.0289385i
$424$	2.37312e6			0.641070
$425$	35719.8	+	622673.i	0.00959262	+	0.167220i
$426$	671351.			0.179236
$427$	7.83452e6	+	5.69211e6i	2.07942	+	1.51079i
$428$	−537339.	−	1.65376e6i	−0.141788	−	0.436378i
$429$	666009.	+	2.04976e6i	0.174718	+	0.537725i
$430$	−513989.	+	1.08449e6i	−0.134055	+	0.282849i
$431$	−2.17400e6	+	6.69087e6i	−0.563723	+	1.73496i	0.107993	+	0.994152i	$0.465557\pi$
$431$	−2.17400e6	+	6.69087e6i	−0.563723	+	1.73496i	−0.671716	+	0.740809i	$0.734443\pi$
$432$	186624.			0.0481125
$433$	1.24984e6	−	3.84660e6i	0.320356	−	0.985955i	−0.653137	−	0.757240i	$-0.726547\pi$
$433$	1.24984e6	−	3.84660e6i	0.320356	−	0.985955i	0.973493	−	0.228716i	$-0.0734526\pi$
$434$	837693.	−	608620.i	0.213482	−	0.155103i
$435$	−749103.	−	707362.i	−0.189810	−	0.179233i
$436$	−1.12773e6	−	819346.i	−0.284112	−	0.206420i
$437$	486424.	−	353408.i	0.121846	−	0.0885264i
$438$	−1.66997e6	+	1.21330e6i	−0.415932	+	0.302193i
$439$	−459147.	−	333590.i	−0.113708	−	0.0826136i	0.529478	−	0.848324i	$-0.322388\pi$
$439$	−459147.	−	333590.i	−0.113708	−	0.0826136i	−0.643186	+	0.765710i	$0.722388\pi$
$440$	646657.	+	610624.i	0.159236	+	0.150363i
$441$	−921407.	+	669441.i	−0.225608	+	0.163914i
$442$	−237646.	+	731399.i	−0.0578595	+	0.178073i
$443$	2.60897e6			0.631625			0.315812	−	0.948822i	$-0.397723\pi$
$443$	2.60897e6			0.631625			0.315812	+	0.948822i	$0.397723\pi$
$444$	−298551.	+	918846.i	−0.0718722	+	0.221200i
$445$	2.40129e6	−	5.06659e6i	0.574837	−	1.21287i
$446$	−1.29057e6	−	3.97196e6i	−0.307216	−	0.945514i
$447$	599473.	+	1.84499e6i	0.141906	+	0.436742i
$448$	−582197.	−	422991.i	−0.137049	−	0.0995718i
$449$	−4.75138e6			−1.11225			−0.556127	−	0.831098i	$-0.687713\pi$
$449$	−4.75138e6			−1.11225			−0.556127	+	0.831098i	$0.687713\pi$
$450$	−943445.	+	367515.i	−0.219627	+	0.0855547i
$451$	1.86873e6			0.432619
$452$	−2.36764e6	−	1.72019e6i	−0.545092	−	0.396032i
$453$	846387.	+	2.60491e6i	0.193786	+	0.596413i
$454$	1.18193e6	+	3.63761e6i	0.269124	+	0.828279i
$455$	6.87892e6	+	6.49561e6i	1.55773	+	1.47093i
$456$	87382.6	−	268936.i	0.0196795	−	0.0605671i
$457$	8.10938e6			1.81634			0.908169	−	0.418603i	$-0.137480\pi$
$457$	8.10938e6			1.81634			0.908169	+	0.418603i	$0.137480\pi$
$458$	−1.87526e6	+	5.77145e6i	−0.417731	+	1.28564i
$459$	−117709.	+	85520.4i	−0.0260782	+	0.0189469i
$460$	−1.08640e6	−	140297.i	−0.239385	−	0.0309139i
$461$	−4.66381e6	−	3.38846e6i	−1.02209	−	0.742591i	−0.0553792	−	0.998465i	$-0.517637\pi$
$461$	−4.66381e6	−	3.38846e6i	−1.02209	−	0.742591i	−0.966710	+	0.255874i	$0.917637\pi$
$462$	1.27205e6	−	924197.i	0.277267	−	0.201446i
$463$	33593.8	−	24407.3i	0.00728294	−	0.00529137i	−0.584138	−	0.811654i	$-0.698567\pi$
$463$	33593.8	−	24407.3i	0.00728294	−	0.00529137i	0.591421	+	0.806363i	$0.298567\pi$
$464$	−424125.	−	308145.i	−0.0914531	−	0.0664446i
$465$	−136888.	−	728531.i	−0.0293585	−	0.156248i
$466$	−129757.	+	94273.9i	−0.0276800	+	0.0201107i
$467$	−2.27774e6	+	7.01016e6i	−0.483294	+	1.48743i	0.351142	+	0.936322i	$0.385793\pi$
$467$	−2.27774e6	+	7.01016e6i	−0.483294	+	1.48743i	−0.834436	+	0.551105i	$0.814207\pi$
$468$	−1.24844e6			−0.263484
$469$	−191448.	+	589217.i	−0.0401901	+	0.123692i
$470$	496040.	+	64058.2i	0.103579	+	0.0133761i
$471$	−264027.	−	812591.i	−0.0548398	−	0.168780i
$472$	204552.	+	629547.i	0.0422619	+	0.130069i
$473$	−1.07942e6	−	784244.i	−0.221839	−	0.161175i
$474$	−3.72730e6			−0.761989
$475$	87863.0	+	1.53164e6i	0.0178678	+	0.311475i
$476$	561043.			0.113496
$477$	−2.42987e6	−	1.76540e6i	−0.488975	−	0.355261i
$478$	−16678.5	−	51331.3i	−0.00333878	−	0.0102757i
$479$	−698641.	−	2.15019e6i	−0.139128	−	0.428192i	0.857081	−	0.515182i	$-0.172275\pi$
$479$	−698641.	−	2.15019e6i	−0.139128	−	0.428192i	−0.996209	+	0.0869890i	$0.972275\pi$
$480$	−452149.	+	246946.i	−0.0895733	+	0.0489213i
$481$	1.99719e6	−	6.14673e6i	0.393602	−	1.21138i
$482$	526319.			0.103188
$483$	−598432.	+	1.84178e6i	−0.116720	+	0.359229i
$484$	1.28474e6	−	933422.i	0.249289	−	0.181119i
$485$	1.55327e6	−	848332.i	0.299842	−	0.163761i
$486$	−191087.	−	138833.i	−0.0366978	−	0.0266625i
$487$	464663.	−	337597.i	0.0887800	−	0.0645025i	−0.542510	−	0.840049i	$-0.682526\pi$
$487$	464663.	−	337597.i	0.0887800	−	0.0645025i	0.631290	+	0.775547i	$0.282526\pi$
$488$	2.85391e6	−	2.07348e6i	0.542488	−	0.394141i
$489$	4.67888e6	+	3.39941e6i	0.884851	+	0.642882i
$490$	1.34655e6	−	2.84114e6i	0.253356	−	0.534567i
$491$	−2.70892e6	+	1.96815e6i	−0.507099	+	0.368429i	−0.811722	−	0.584044i	$-0.801470\pi$
$491$	−2.70892e6	+	1.96815e6i	−0.507099	+	0.368429i	0.304623	+	0.952473i	$0.401470\pi$
$492$	−334504.	+	1.02950e6i	−0.0623001	+	0.191740i
$493$	408714.			0.0757360
$494$	−584557.	+	1.79908e6i	−0.107773	+	0.331691i
$495$	−207867.	−	1.10628e6i	−0.0381305	−	0.202933i
$496$	−116557.	−	358724.i	−0.0212732	−	0.0654722i
$497$	1.01247e6	+	3.11606e6i	0.183862	+	0.565868i
$498$	3.19302e6	+	2.31986e6i	0.576937	+	0.419169i
$499$	−1.36953e6			−0.246219			−0.123109	−	0.992393i	$-0.539287\pi$
$499$	−1.36953e6			−0.246219			−0.123109	+	0.992393i	$0.539287\pi$
$500$	1.79946e6	−	2.13880e6i	0.321896	−	0.382600i
$501$	−4.57101e6			−0.813613
$502$	−1.47696e6	−	1.07308e6i	−0.261583	−	0.190051i
$503$	−2.53394e6	−	7.79866e6i	−0.446556	−	1.37436i	−0.880768	−	0.473548i	$-0.842973\pi$
$503$	−2.53394e6	−	7.79866e6i	−0.446556	−	1.37436i	0.434212	−	0.900811i	$-0.357027\pi$
$504$	281449.	+	866211.i	0.0493541	+	0.151896i
$505$	−1.06235e6	−	5.65393e6i	−0.185370	−	0.986556i
$506$	376331.	−	1.15823e6i	0.0653422	−	0.201103i
$507$	5.00999e6			0.865599
$508$	46717.2	−	143781.i	0.00803189	−	0.0247196i
$509$	2.07721e6	−	1.50918e6i	0.355375	−	0.258195i	−0.395746	−	0.918360i	$-0.629514\pi$
$509$	2.07721e6	−	1.50918e6i	0.355375	−	0.258195i	0.751120	+	0.660165i	$0.229514\pi$
$510$	172020.	−	362952.i	0.0292855	−	0.0617909i
$511$	−8.15001e6	−	5.92133e6i	−1.38072	−	1.00315i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−289538.	+	210362.i	−0.0485749	+	0.0352917i
$514$	4.56844e6	+	3.31917e6i	0.762712	+	0.554142i
$515$	−2.33687e6	+	1.27631e6i	−0.388255	+	0.212049i
$516$	625262.	−	454279.i	0.103380	−	0.0751102i
$517$	−171829.	+	528835.i	−0.0282729	+	0.0870149i
$518$	−4.71505e6			−0.772079
$519$	−859852.	+	2.64635e6i	−0.140122	+	0.431250i
$520$	3.02471e6	−	1.65197e6i	0.490541	−	0.267914i
$521$	250587.	+	771228.i	0.0404450	+	0.124477i	0.969240	−	0.246116i	$-0.0791545\pi$
$521$	250587.	+	771228.i	0.0404450	+	0.124477i	−0.928795	+	0.370593i	$0.879154\pi$
$522$	205033.	+	631026.i	0.0329342	+	0.101361i
$523$	2.27181e6	+	1.65056e6i	0.363176	+	0.263863i	0.754376	−	0.656443i	$-0.227940\pi$
$523$	2.27181e6	+	1.65056e6i	0.363176	+	0.263863i	−0.391200	+	0.920306i	$0.627940\pi$
$524$	1.43061e6			0.227611
$525$	−3.12863e6	−	3.82473e6i	−0.495400	−	0.605623i
$526$	−6.23805e6			−0.983071
$527$	237901.	+	172845.i	0.0373138	+	0.0271101i
$528$	−176993.	−	544728.i	−0.0276294	−	0.0850344i
$529$	−1.52543e6	−	4.69480e6i	−0.237003	−	0.729420i
$530$	8.22306e6	+	1.06192e6i	1.27158	+	0.164211i
$531$	258886.	−	796771.i	0.0398449	−	0.122630i
$532$	1.38004e6			0.211404
$533$	2.23771e6	−	6.88695e6i	0.341181	−	1.05005i
$534$	−2.92114e6	+	2.12233e6i	−0.443302	+	0.322078i
$535$	−1.12190e6	−	5.97086e6i	−0.169462	−	0.901888i
$536$	182580.	+	132652.i	0.0274500	+	0.0199436i
$537$	5.12643e6	−	3.72457e6i	0.767148	−	0.557366i
$538$	−6.39325e6	+	4.64497e6i	−0.952283	+	0.691874i
$539$	2.82786e6	+	2.05456e6i	0.419262	+	0.304612i
$540$	646668.	+	83510.1i	0.0954326	+	0.0123241i
$541$	−821256.	+	596677.i	−0.120638	+	0.0876489i	−0.646468	−	0.762941i	$-0.723755\pi$
$541$	−821256.	+	596677.i	−0.120638	+	0.0876489i	0.525830	+	0.850590i	$0.323755\pi$
$542$	386082.	−	1.18824e6i	0.0564523	−	0.173742i
$543$	−1.77145e6			−0.257827
$544$	63154.8	−	194370.i	0.00914974	−	0.0281600i
$545$	−3.54105e6	−	3.34374e6i	−0.510671	−	0.482215i
$546$	−1.88279e6	−	5.79463e6i	−0.270284	−	0.831848i
$547$	−3.55817e6	−	1.09509e7i	−0.508462	−	1.56488i	−0.794872	−	0.606777i	$-0.792462\pi$
$547$	−3.55817e6	−	1.09509e7i	−0.508462	−	1.56488i	0.286411	−	0.958107i	$-0.407538\pi$
$548$	3.19834e6	+	2.32373e6i	0.454961	+	0.330548i
$549$	−4.46465e6			−0.632202
$550$	1.96748e6	+	2.40523e6i	0.277334	+	0.339039i
$551$	1.00535e6			0.141071
$552$	570713.	+	414647.i	0.0797204	+	0.0579203i
$553$	−5.62117e6	−	1.73002e7i	−0.781653	−	2.40568i
$554$	354667.	+	1.09155e6i	0.0490961	+	0.151102i
$555$	−1.44567e6	+	3.05028e6i	−0.199221	+	0.420346i
$556$	−840440.	+	2.58661e6i	−0.115297	+	0.354849i
$557$	−6.45778e6			−0.881952			−0.440976	−	0.897519i	$-0.645368\pi$
$557$	−6.45778e6			−0.881952			−0.440976	+	0.897519i	$0.645368\pi$
$558$	−147517.	+	454011.i	−0.0200566	+	0.0617278i
$559$	−4.18277e6	+	3.03896e6i	−0.566154	+	0.411335i
$560$	−1.82808e6	−	1.72622e6i	−0.246335	−	0.232609i
$561$	361256.	+	262468.i	0.0484627	+	0.0352102i
$562$	516571.	−	375310.i	0.0689904	−	0.0501245i
$563$	−878851.	+	638522.i	−0.116854	+	0.0848995i	−0.644677	−	0.764455i	$-0.723008\pi$
$563$	−878851.	+	638522.i	−0.116854	+	0.0848995i	0.527823	+	0.849354i	$0.323008\pi$
$564$	−260581.	−	189323.i	−0.0344941	−	0.0250615i
$565$	−7.43432e6	−	7.02007e6i	−0.979761	−	0.925167i
$566$	−4.76072e6	+	3.45887e6i	−0.624643	+	0.453829i
$567$	356209.	−	1.09630e6i	0.0465315	−	0.143209i
$568$	1.19351e6			0.155223
$569$	−235484.	+	724747.i	−0.0304917	+	0.0938438i	−0.965144	−	0.261719i	$-0.915711\pi$
$569$	−235484.	+	724747.i	−0.0304917	+	0.0938438i	0.934652	+	0.355563i	$0.115711\pi$
$570$	423131.	−	892784.i	0.0545491	−	0.115096i
$571$	−389383.	−	1.19840e6i	−0.0499789	−	0.153819i	0.922952	−	0.384914i	$-0.125769\pi$
$571$	−389383.	−	1.19840e6i	−0.0499789	−	0.153819i	−0.972931	+	0.231095i	$0.925769\pi$
$572$	1.18402e6	+	3.64402e6i	0.151310	+	0.465684i
$573$	5.12522e6	+	3.72369e6i	0.652117	+	0.473791i
$574$	−5.28286e6			−0.669252
$575$	−3.70169e6	−	972282.i	−0.466908	−	0.122637i
$576$	331776.			0.0416667
$577$	9.41255e6	+	6.83862e6i	1.17698	+	0.855124i	0.991827	−	0.127587i	$-0.0407232\pi$
$577$	9.41255e6	+	6.83862e6i	1.17698	+	0.855124i	0.185149	+	0.982710i	$0.440723\pi$
$578$	−1.70580e6	−	5.24992e6i	−0.212378	−	0.653632i
$579$	−2.42633e6	−	7.46747e6i	−0.300783	−	0.925715i
$580$	−1.33174e6	−	1.25753e6i	−0.164380	−	0.155221i
$581$	−5.95218e6	+	1.83189e7i	−0.731537	+	2.25144i
$582$	−1.13975e6			−0.139477
$583$	−2.84848e6	+	8.76672e6i	−0.347090	+	1.06823i
$584$	−2.96883e6	+	2.15698e6i	−0.360208	+	0.261706i
$585$	−4.32596e6	−	558651.i	−0.522629	−	0.0674918i
$586$	−1.96255e6	−	1.42588e6i	−0.236090	−	0.171529i
$587$	5.67381e6	−	4.12226e6i	0.679641	−	0.493788i	−0.193598	−	0.981081i	$-0.562016\pi$
$587$	5.67381e6	−	4.12226e6i	0.679641	−	0.493788i	0.873239	+	0.487293i	$0.162016\pi$
$588$	−1.63806e6	+	1.19012e6i	−0.195383	+	0.141954i
$589$	585184.	+	425161.i	0.0695031	+	0.0504970i
$590$	427082.	+	2.27297e6i	0.0505105	+	0.268821i
$591$	−833262.	+	605401.i	−0.0981326	+	0.0712975i
$592$	−530757.	+	1.63350e6i	−0.0622432	+	0.191565i
$593$	−1.25445e7			−1.46493			−0.732467	−	0.680803i	$-0.761631\pi$
$593$	−1.25445e7			−1.46493			−0.732467	+	0.680803i	$0.761631\pi$
$594$	−224006.	+	689421.i	−0.0260492	+	0.0801712i
$595$	1.94406e6	+	251054.i	0.225122	+	0.0290720i
$596$	1.06573e6	+	3.27998e6i	0.122894	+	0.378230i
$597$	917153.	+	2.82271e6i	0.105319	+	0.324138i
$598$	−3.81785e6	−	2.77383e6i	−0.436582	−	0.317196i
$599$	−3.11359e6			−0.354564			−0.177282	−	0.984160i	$-0.556730\pi$
$599$	−3.11359e6			−0.354564			−0.177282	+	0.984160i	$0.556730\pi$
$600$	−1.67724e6	+	653360.i	−0.190202	+	0.0740925i
$601$	1.99896e6			0.225745			0.112872	−	0.993609i	$-0.463995\pi$
$601$	1.99896e6			0.225745			0.112872	+	0.993609i	$0.463995\pi$
$602$	3.05149e6	+	2.21704e6i	0.343179	+	0.249334i
$603$	−88264.0	−	271649.i	−0.00988531	−	0.0304238i
$604$	1.50469e6	+	4.63095e6i	0.167824	+	0.516509i
$605$	4.86943e6	−	2.65949e6i	0.540866	−	0.295399i
$606$	−1.14484e6	+	3.52345e6i	−0.126638	+	0.389751i
$607$	1.05545e7			1.16270			0.581349	−	0.813655i	$-0.302525\pi$
$607$	1.05545e7			1.16270			0.581349	+	0.813655i	$0.302525\pi$
$608$	155347.	−	478109.i	0.0170429	−	0.0524527i
$609$	−2.61968e6	+	1.90331e6i	−0.286224	+	0.207954i
$610$	1.08169e7	−	5.90773e6i	1.17700	−	0.642830i
$611$	1.74319e6	+	1.26650e6i	0.188904	+	0.137247i
$612$	−209260.	+	152036.i	−0.0225844	+	0.0164085i
$613$	−5.17637e6	+	3.76085e6i	−0.556384	+	0.404236i	−0.830134	−	0.557565i	$-0.811736\pi$
$613$	−5.17637e6	+	3.76085e6i	−0.556384	+	0.404236i	0.273750	+	0.961801i	$0.411736\pi$
$614$	6.43392e6	+	4.67452e6i	0.688739	+	0.500398i
$615$	−1.61976e6	+	3.41761e6i	−0.172688	+	0.364364i
$616$	2.26142e6	−	1.64302e6i	0.240120	−	0.174458i
$617$	−4.78177e6	+	1.47168e7i	−0.505680	+	1.55632i	0.293943	+	0.955823i	$0.405032\pi$
$617$	−4.78177e6	+	1.47168e7i	−0.505680	+	1.55632i	−0.799624	+	0.600502i	$0.794968\pi$
$618$	1.71474e6			0.180604
$619$	3.80948e6	−	1.17244e7i	0.399613	−	1.22988i	−0.525697	−	0.850672i	$-0.676196\pi$
$619$	3.80948e6	−	1.17244e7i	0.399613	−	1.22988i	0.925310	−	0.379211i	$-0.123804\pi$
$620$	−243357.	−	1.29517e6i	−0.0254252	−	0.135315i
$621$	−275897.	−	849124.i	−0.0287090	−	0.0883572i
$622$	−3.72469e6	−	1.14634e7i	−0.386024	−	1.18806i
$623$	−1.42562e7	−	1.03577e7i	−1.47158	−	1.06916i
$624$	−2.21946e6			−0.228184
$625$	7.19233e6	−	6.60590e6i	0.736494	−	0.676444i
$626$	3.28449e6			0.334990
$627$	888610.	+	645613.i	0.0902697	+	0.0655848i
$628$	−469381.	−	1.44461e6i	−0.0474927	−	0.146167i
$629$	−413790.	−	1.27351e6i	−0.0417017	−	0.128344i
$630$	587634.	+	3.12744e6i	0.0589869	+	0.313933i
$631$	3.58366e6	−	1.10294e7i	0.358305	−	1.10275i	−0.595763	−	0.803161i	$-0.703150\pi$
$631$	3.58366e6	−	1.10294e7i	0.358305	−	1.10275i	0.954068	−	0.299590i	$-0.0968499\pi$
$632$	−6.62631e6			−0.659901
$633$	470924.	−	1.44936e6i	0.0467134	−	0.143769i
$634$	−7.17319e6	+	5.21163e6i	−0.708743	+	0.514932i
$635$	226218.	−	477307.i	0.0222634	−	0.0469747i
$636$	−4.31977e6	−	3.13849e6i	−0.423465	−	0.307665i
$637$	1.09580e7	−	7.96144e6i	1.07000	−	0.777398i
$638$	1.64742e6	−	1.19692e6i	0.160233	−	0.116416i
$639$	−1.22205e6	−	887873.i	−0.118396	−	0.0860199i
$640$	−803820.	+	439014.i	−0.0775727	+	0.0423671i
$641$	−4.43863e6	+	3.22485e6i	−0.426682	+	0.310002i	−0.780321	−	0.625380i	$-0.784944\pi$
$641$	−4.43863e6	+	3.22485e6i	−0.426682	+	0.310002i	0.353639	+	0.935382i	$0.384944\pi$
$642$	−1.20901e6	+	3.72096e6i	−0.115769	+	0.356301i
$643$	1.91989e7			1.83126			0.915629	−	0.402024i	$-0.131693\pi$
$643$	1.91989e7			1.83126			0.915629	+	0.402024i	$0.131693\pi$
$644$	−1.06388e6	+	3.27428e6i	−0.101083	+	0.311101i
$645$	2.36986e6	−	1.29432e6i	0.224297	−	0.122502i
$646$	121112.	+	372744.i	0.0114184	+	0.0351422i
$647$	−528873.	−	1.62770e6i	−0.0496696	−	0.152867i	0.923145	−	0.384451i	$-0.125609\pi$
$647$	−528873.	−	1.62770e6i	−0.0496696	−	0.152867i	−0.972815	+	0.231584i	$0.925609\pi$
$648$	−339709.	−	246813.i	−0.0317812	−	0.0230904i
$649$	−2.57118e6			−0.239619
$650$	1.12201e7	−	4.37073e6i	1.04163	−	0.405762i
$651$	−2.32975e6			−0.215455
$652$	8.31801e6	+	6.04339e6i	0.766303	+	0.556752i
$653$	−5.57766e6	−	1.71663e7i	−0.511881	−	1.57541i	−0.788887	−	0.614539i	$-0.789342\pi$
$653$	−5.57766e6	−	1.71663e7i	−0.511881	−	1.57541i	0.277006	−	0.960868i	$-0.410658\pi$
$654$	969201.	+	2.98289e6i	0.0886073	+	0.272705i
$655$	4.95717e6	+	640165.i	0.451472	+	0.0583027i
$656$	−594674.	+	1.83022e6i	−0.0539535	+	0.166052i
$657$	4.64443e6			0.419778
$658$	485756.	−	1.49500e6i	0.0437374	−	0.134610i
$659$	9.29312e6	−	6.75185e6i	0.833582	−	0.605633i	−0.0869887	−	0.996209i	$-0.527724\pi$
$659$	9.29312e6	−	6.75185e6i	0.833582	−	0.605633i	0.920570	+	0.390577i	$0.127724\pi$
$660$	−369541.	−	1.96673e6i	−0.0330219	−	0.175745i
$661$	−4.83340e6	−	3.51167e6i	−0.430278	−	0.312615i	0.351482	−	0.936195i	$-0.385678\pi$
$661$	−4.83340e6	−	3.51167e6i	−0.430278	−	0.312615i	−0.781760	+	0.623579i	$0.785678\pi$
$662$	−1.12528e7	+	8.17564e6i	−0.997966	+	0.725065i
$663$	1.39987e6	−	1.01707e6i	0.123681	−	0.0898598i
$664$	5.67648e6	+	4.12420e6i	0.499642	+	0.363011i
$665$	4.78196e6	+	617539.i	0.419326	+	0.0541515i
$666$	1.75864e6	−	1.27773e6i	0.153635	−	0.111623i
$667$	−775025.	+	2.38528e6i	−0.0674529	+	0.207599i
$668$	−8.12624e6			−0.704610
$669$	−2.90378e6	+	8.93692e6i	−0.250841	+	0.772009i
$670$	573296.	+	541352.i	0.0493392	+	0.0465900i
$671$	4.23424e6	+	1.30316e7i	0.363052	+	1.11736i
$672$	500354.	+	1.53993e6i	0.0427419	+	0.131546i
$673$	1.14554e7	+	8.32286e6i	0.974931	+	0.708329i	0.956570	−	0.291502i	$-0.0941551\pi$
$673$	1.14554e7	+	8.32286e6i	0.974931	+	0.708329i	0.0183613	+	0.999831i	$0.494155\pi$
$674$	1.35190e7			1.14629
$675$	2.20339e6	+	578739.i	0.186136	+	0.0488903i
$676$	8.90665e6			0.749631
$677$	−1.28013e6	−	930071.i	−0.107345	−	0.0779910i	0.532818	−	0.846230i	$-0.321133\pi$
$677$	−1.28013e6	−	930071.i	−0.107345	−	0.0779910i	−0.640163	+	0.768239i	$0.721133\pi$
$678$	2.03481e6	+	6.26249e6i	0.170000	+	0.523206i
$679$	−1.71887e6	−	5.29013e6i	−0.143076	−	0.440344i
$680$	305813.	−	645249.i	0.0253620	−	0.0535125i
$681$	2.65935e6	−	8.18463e6i	0.219739	−	0.676287i
$682$	1.46509e6			0.120616
$683$	−1.34854e6	+	4.15039e6i	−0.110615	+	0.340437i	−0.991007	−	0.133809i	$-0.957279\pi$
$683$	−1.34854e6	+	4.15039e6i	−0.110615	+	0.340437i	0.880392	+	0.474246i	$0.157279\pi$
$684$	−514734.	+	373976.i	−0.0420671	+	0.0305635i
$685$	1.00427e7	+	9.48311e6i	0.817757	+	0.772191i
$686$	1.56138e6	+	1.13441e6i	0.126677	+	0.0920362i
$687$	1.10463e7	−	8.02564e6i	0.892949	−	0.648766i
$688$	1.11158e6	−	807608.i	0.0895300	−	0.0650473i
$689$	2.88976e7	+	2.09953e7i	2.31907	+	1.68490i
$690$	1.79202e6	+	1.69217e6i	0.143291	+	0.135307i
$691$	−1.35831e6	+	986871.i	−0.108219	+	0.0786258i	−0.640579	−	0.767893i	$-0.721305\pi$
$691$	−1.35831e6	+	986871.i	−0.108219	+	0.0786258i	0.532359	+	0.846518i	$0.321305\pi$
$692$	−1.52863e6	+	4.70463e6i	−0.121349	+	0.373474i
$693$	−3.53776e6			−0.279831
$694$	−2.14918e6	+	6.61449e6i	−0.169384	+	0.521312i
$695$	−4.06964e6	+	8.58673e6i	−0.319591	+	0.674320i
$696$	364503.	+	1.12182e6i	0.0285218	+	0.0877812i
$697$	−463621.	−	1.42688e6i	−0.0361477	−	0.111251i
$698$	1.15406e7	+	8.38475e6i	0.896583	+	0.651406i
$699$	360874.			0.0279359
$700$	−5.56201e6	−	6.79952e6i	−0.429029	−	0.524485i
$701$	6.10627e6			0.469333			0.234667	−	0.972076i	$-0.424600\pi$
$701$	6.10627e6			0.469333			0.234667	+	0.972076i	$0.424600\pi$
$702$	2.27253e6	+	1.65109e6i	0.174047	+	0.126453i
$703$	−1.01783e6	−	3.13257e6i	−0.0776762	−	0.239063i
$704$	−314654.	−	968405.i	−0.0239277	−	0.0736420i
$705$	−818217.	−	772625.i	−0.0620006	−	0.0585459i
$706$	−1.62787e6	+	5.01006e6i	−0.122916	+	0.378296i
$707$	−1.80806e7			−1.36039
$708$	460243.	−	1.41648e6i	0.0345067	−	0.106201i
$709$	−1.45531e7	+	1.05735e7i	−1.08728	+	0.789953i	−0.978937	−	0.204161i	$-0.934553\pi$
$709$	−1.45531e7	+	1.05735e7i	−1.08728	+	0.789953i	−0.108340	+	0.994114i	$0.534553\pi$
$710$	4.13562e6	+	534071.i	0.307889	+	0.0397606i
$711$	6.78476e6	+	4.92942e6i	0.503339	+	0.365697i
$712$	−5.19314e6	+	3.77304e6i	−0.383911	+	0.278927i
$713$	−1.45985e6	+	1.06065e6i	−0.107544	+	0.0781352i
$714$	−1.02126e6	−	741989.i	−0.0749706	−	0.0544693i
$715$	2.47209e6	+	1.31567e7i	0.180842	+	0.962456i
$716$	9.11365e6	−	6.62146e6i	0.664370	−	0.482693i
$717$	−37526.7	+	115495.i	−0.00272611	+	0.00839009i
$718$	−1.50737e6			−0.109121
$719$	137630.	−	423581.i	0.00992865	−	0.0305573i	−0.945969	−	0.324256i	$-0.894886\pi$
$719$	137630.	−	423581.i	0.00992865	−	0.0305573i	0.955898	+	0.293698i	$0.0948862\pi$
$720$	1.14963e6	+	148462.i	0.0826470	+	0.0106730i
$721$	2.58601e6	+	7.95893e6i	0.185265	+	0.570186i
$722$	−2.76272e6	−	8.50277e6i	−0.197239	−	0.607040i
$723$	−958052.	−	696065.i	−0.0681621	−	0.0495227i
$724$	−3.14924e6			−0.223285
$725$	−4.05187e6	−	4.95338e6i	−0.286293	−	0.349991i
$726$	−3.57307e6			−0.251594
$727$	−2.58996e6	−	1.88172e6i	−0.181743	−	0.132044i	0.493194	−	0.869919i	$-0.335829\pi$
$727$	−2.58996e6	−	1.88172e6i	−0.181743	−	0.132044i	−0.674937	+	0.737875i	$0.735829\pi$
$728$	−3.34718e6	−	1.03016e7i	−0.234073	−	0.720402i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	−1.12524e7	+	6.14563e6i	−0.781519	+	0.426834i
$731$	−331015.	+	1.01876e6i	−0.0229116	+	0.0705145i
$732$	−7.93715e6			−0.547503
$733$	5.68664e6	−	1.75017e7i	0.390927	−	1.20315i	−0.541162	−	0.840919i	$-0.682015\pi$
$733$	5.68664e6	−	1.75017e7i	0.390927	−	1.20315i	0.932089	−	0.362231i	$-0.117985\pi$
$734$	−2.16682e6	+	1.57429e6i	−0.148451	+	0.107856i
$735$	−6.20855e6	+	3.39086e6i	−0.423908	+	0.231522i
$736$	1.01460e6	+	737150.i	0.0690399	+	0.0501604i
$737$	−709193.	+	515259.i	−0.0480945	+	0.0349427i
$738$	1.97042e6	−	1.43160e6i	0.133174	−	0.0967563i
$739$	9.37421e6	+	6.81076e6i	0.631427	+	0.458759i	0.856894	−	0.515492i	$-0.172391\pi$
$739$	9.37421e6	+	6.81076e6i	0.631427	+	0.458759i	−0.225467	+	0.974251i	$0.572391\pi$
$740$	−2.57007e6	+	5.42272e6i	−0.172531	+	0.364031i
$741$	3.44338e6	−	2.50176e6i	0.230377	−	0.167379i
$742$	8.05258e6	−	2.47833e7i	0.536939	−	1.65253i
$743$	1.04544e7			0.694747			0.347373	−	0.937727i	$-0.387074\pi$
$743$	1.04544e7			0.694747			0.347373	+	0.937727i	$0.387074\pi$
$744$	−262252.	+	807130.i	−0.0173695	+	0.0534578i
$745$	2.22512e6	+	1.18423e7i	0.146880	+	0.781709i
$746$	−1.95142e6	−	6.00587e6i	−0.128382	−	0.395120i
$747$	−2.74416e6	−	8.44564e6i	−0.179932	−	0.553772i
$748$	642232.	+	466609.i	0.0419699	+	0.0304929i
$749$	−1.90941e7			−1.24364
$750$	−6.10412e6	+	1.51342e6i	−0.396251	+	0.0982441i
$751$	−2.89770e7			−1.87479			−0.937397	−	0.348263i	$-0.886772\pi$
$751$	−2.89770e7			−1.87479			−0.937397	+	0.348263i	$0.886772\pi$
$752$	−463256.	−	336575.i	−0.0298728	−	0.0217039i
$753$	1.26934e6	+	3.90661e6i	0.0815810	+	0.251081i
$754$	−2.43839e6	−	7.50458e6i	−0.156198	−	0.480727i
$755$	3.14162e6	+	1.67199e7i	0.200579	+	1.06750i
$756$	633261.	−	1.94898e6i	0.0402975	−	0.124023i
$757$	3.34034e6			0.211861			0.105930	−	0.994374i	$-0.466218\pi$
$757$	3.34034e6			0.211861			0.105930	+	0.994374i	$0.466218\pi$
$758$	5.43724e6	−	1.67341e7i	0.343721	−	1.05786i
$759$	−2.21681e6	+	1.61061e6i	−0.139677	+	0.101481i
$760$	752233.	−	1.58717e6i	0.0472409	−	0.0996758i
$761$	−1.13523e6	−	824793.i	−0.0710595	−	0.0516278i	0.551688	−	0.834050i	$-0.313984\pi$
$761$	−1.13523e6	−	824793.i	−0.0710595	−	0.0516278i	−0.622748	+	0.782423i	$0.713984\pi$
$762$	−275191.	+	199938.i	−0.0171691	+	0.0124741i
$763$	−1.23834e7	+	8.99705e6i	−0.770066	+	0.559485i
$764$	9.11150e6	+	6.61989e6i	0.564750	+	0.410315i
$765$	−793136.	+	433179.i	−0.0489998	+	0.0267617i
$766$	−8.59178e6	+	6.24230e6i	−0.529068	+	0.384390i
$767$	−3.07885e6	+	9.47573e6i	−0.188973	+	0.581600i
$768$	589824.			0.0360844
$769$	−8.72699e6	+	2.68589e7i	−0.532168	+	1.63784i	0.217522	+	0.976055i	$0.430202\pi$
$769$	−8.72699e6	+	2.68589e7i	−0.532168	+	1.63784i	−0.749690	+	0.661789i	$0.769798\pi$
$770$	8.57121e6	−	4.68125e6i	0.520973	−	0.284535i
$771$	−3.92623e6	−	1.20837e7i	−0.237870	−	0.732088i
$772$	−4.31347e6	−	1.32755e7i	−0.260486	−	0.801692i
$773$	−7.58972e6	−	5.51426e6i	−0.456854	−	0.331924i	0.335442	−	0.942061i	$-0.391114\pi$
$773$	−7.58972e6	−	5.51426e6i	−0.456854	−	0.331924i	−0.792296	+	0.610137i	$0.791114\pi$
$774$	−1.73895e6			−0.104336
$775$	−263694.	−	4.59675e6i	−0.0157705	−	0.274914i
$776$	−2.02622e6			−0.120791
$777$	8.58275e6	+	6.23573e6i	0.510004	+	0.370540i
$778$	3.96665e6	+	1.22081e7i	0.234950	+	0.723101i
$779$	−1.14041e6	−	3.50981e6i	−0.0673311	−	0.207224i
$780$	−7.69060e6	−	993158.i	−0.452610	−	0.0584496i
$781$	−1.43258e6	+	4.40904e6i	−0.0840413	+	0.258652i
$782$	−977735.			−0.0571747
$783$	461324.	−	1.41981e6i	0.0268907	−	0.0827609i
$784$	−2.91210e6	+	2.11577e6i	−0.169206	+	0.122936i
$785$	−980015.	−	5.21572e6i	−0.0567621	−	0.302093i
$786$	−2.60412e6	−	1.89200e6i	−0.150350	−	0.109236i
$787$	−9.36024e6	+	6.80061e6i	−0.538704	+	0.391391i	−0.823603	−	0.567166i	$-0.808040\pi$
$787$	−9.36024e6	+	6.80061e6i	−0.538704	+	0.391391i	0.284899	+	0.958557i	$0.408040\pi$
$788$	−1.48136e6	+	1.07627e6i	−0.0849853	+	0.0617454i
$789$	1.13551e7	+	8.24993e6i	0.649377	+	0.471800i
$790$	−2.29607e7	−	2.96513e6i	−1.30893	−	0.169035i
$791$	−2.59985e7	+	1.88890e7i	−1.47743	+	1.07342i
$792$	−398234.	+	1.22564e6i	−0.0225593	+	0.0694303i
$793$	5.30965e7			2.99836
$794$	6.41425e6	−	1.97410e7i	0.361072	−	1.11127i
$795$	−1.35639e7	−	1.28081e7i	−0.761146	−	0.718734i
$796$	1.63049e6	+	5.01814e6i	0.0912087	+	0.280712i
$797$	−1.30509e6	−	4.01666e6i	−0.0727772	−	0.223985i	0.908051	−	0.418860i	$-0.137570\pi$
$797$	−1.30509e6	−	4.01666e6i	−0.0727772	−	0.223985i	−0.980828	+	0.194874i	$0.937570\pi$
$798$	−2.51208e6	−	1.82513e6i	−0.139645	−	0.101458i
$799$	446423.			0.0247389
$800$	−2.98175e6	+	1.16153e6i	−0.164720	+	0.0641660i
$801$	8.12414e6			0.447400
$802$	1.13501e7	+	8.24636e6i	0.623111	+	0.452717i
$803$	−4.40475e6	−	1.35564e7i	−0.241064	−	0.741918i
$804$	−156914.	−	482931.i	−0.00856093	−	0.0263478i
$805$	−5.15160e6	+	1.08696e7i	−0.280190	+	0.591185i
$806$	1.75437e6	−	5.39940e6i	0.0951226	−	0.292757i
$807$	1.77806e7			0.961087
$808$	−2.03527e6	+	6.26391e6i	−0.109671	+	0.337534i
$809$	2.04331e7	−	1.48455e7i	1.09765	−	0.797489i	0.116975	−	0.993135i	$-0.462680\pi$
$809$	2.04331e7	−	1.48455e7i	1.09765	−	0.797489i	0.980675	+	0.195646i	$0.0626804\pi$
$810$	−1.06668e6	−	1.00724e6i	−0.0571243	−	0.0539412i
$811$	−3.67755e6	−	2.67190e6i	−0.196339	−	0.142649i	0.485272	−	0.874363i	$-0.338720\pi$
$811$	−3.67755e6	−	2.67190e6i	−0.196339	−	0.142649i	−0.681611	+	0.731714i	$0.738720\pi$
$812$	−4.65721e6	+	3.38366e6i	−0.247877	+	0.180093i
$813$	−2.27425e6	+	1.65234e6i	−0.120673	+	0.0876742i
$814$	−5.39737e6	−	3.92142e6i	−0.285510	−	0.207435i
$815$	2.61183e7	+	2.46630e7i	1.37737	+	1.30062i
$816$	−372018.	+	270287.i	−0.0195586	+	0.0142102i
$817$	−814225.	+	2.50593e6i	−0.0426766	+	0.131345i
$818$	1.79594e7			0.938443
$819$	−4.23628e6	+	1.30379e7i	−0.220686	+	0.679201i
$820$	−2.87958e6	+	6.07575e6i	−0.149553	+	0.315548i
$821$	−5.94262e6	−	1.82895e7i	−0.307695	−	0.946988i	−0.978658	−	0.205497i	$-0.934119\pi$
$821$	−5.94262e6	−	1.82895e7i	−0.307695	−	0.946988i	0.670963	−	0.741491i	$-0.265881\pi$
$822$	−2.74873e6	−	8.45973e6i	−0.141890	−	0.436694i
$823$	−6.51126e6	−	4.73071e6i	−0.335093	−	0.243459i	0.407496	−	0.913207i	$-0.366402\pi$
$823$	−6.51126e6	−	4.73071e6i	−0.335093	−	0.243459i	−0.742589	+	0.669748i	$0.766402\pi$
$824$	3.04843e6			0.156408
$825$	−400423.	−	6.98023e6i	−0.0204826	−	0.357055i
$826$	7.26866e6			0.370685
$827$	−8.13981e6	−	5.91392e6i	−0.413857	−	0.300685i	0.361304	−	0.932448i	$-0.382332\pi$
$827$	−8.13981e6	−	5.91392e6i	−0.413857	−	0.300685i	−0.775161	+	0.631763i	$0.782332\pi$
$828$	−490484.	−	1.50955e6i	−0.0248627	−	0.0765196i
$829$	−8.62220e6	−	2.65364e7i	−0.435744	−	1.34108i	−0.892322	−	0.451400i	$-0.850925\pi$
$829$	−8.62220e6	−	2.65364e7i	−0.435744	−	1.34108i	0.456578	−	0.889684i	$-0.349075\pi$
$830$	1.78240e7	+	1.68308e7i	0.898068	+	0.848027i
$831$	798001.	−	2.45600e6i	0.0400868	−	0.123374i
$832$	−3.94570e6			−0.197613
$833$	867191.	−	2.66894e6i	0.0433015	−	0.133268i
$834$	4.95068e6	−	3.59688e6i	0.246462	−	0.179065i
$835$	−2.81581e7	−	3.63631e6i	−1.39761	−	0.180487i
$836$	1.57975e6	+	1.14776e6i	0.0781759	+	0.0567981i
$837$	868960.	−	631336.i	0.0428732	−	0.0311492i
$838$	−2.07287e7	+	1.50603e7i	−1.01968	+	0.740839i
$839$	1.04919e7	+	7.62279e6i	0.514574	+	0.373860i	0.814556	−	0.580085i	$-0.196981\pi$
$839$	1.04919e7	+	7.62279e6i	0.514574	+	0.373860i	−0.299982	+	0.953945i	$0.596981\pi$
$840$	1.04468e6	+	5.55989e6i	0.0510842	+	0.271874i
$841$	1.32011e7	−	9.59119e6i	0.643608	−	0.467609i
$842$	7.09246e6	−	2.18283e7i	0.344760	−	1.06106i
$843$	−1.43666e6			−0.0696283
$844$	837199.	−	2.57663e6i	0.0404550	−	0.124508i
$845$	3.08623e7	+	3.98553e6i	1.48691	+	0.192019i
$846$	223950.	+	689246.i	0.0107578	+	0.0331092i
$847$	−5.38858e6	−	1.65843e7i	−0.258087	−	0.794309i
$848$	−7.67958e6	−	5.57954e6i	−0.366731	−	0.266446i
$849$	1.32403e7			0.630418
$850$	1.34840e6	−	2.09900e6i	0.0640135	−	0.0996470i
$851$	8.21696e6			0.388944
$852$	−2.17254e6	−	1.57844e6i	−0.102534	−	0.0744954i
$853$	4.33558e6	+	1.33435e7i	0.204021	+	0.627912i	0.999752	+	0.0222619i	$0.00708677\pi$
$853$	4.33558e6	+	1.33435e7i	0.204021	+	0.627912i	−0.795731	+	0.605650i	$0.792913\pi$
$854$	−1.19701e7	−	3.68401e7i	−0.561633	−	1.72853i
$855$	−1.95094e6	+	1.06553e6i	−0.0912702	+	0.0498481i
$856$	−2.14936e6	+	6.61504e6i	−0.100259	+	0.308566i
$857$	−2.30963e7			−1.07421			−0.537106	−	0.843515i	$-0.680483\pi$
$857$	−2.30963e7			−1.07421			−0.537106	+	0.843515i	$0.680483\pi$
$858$	2.66403e6	−	8.19905e6i	0.123544	−	0.380229i
$859$	5.99054e6	−	4.35238e6i	0.277002	−	0.201254i	−0.440607	−	0.897700i	$-0.645237\pi$
$859$	5.99054e6	−	4.35238e6i	0.277002	−	0.201254i	0.717609	+	0.696446i	$0.245237\pi$
$860$	4.21309e6	−	2.30102e6i	0.194247	−	0.106090i
$861$	9.61633e6	+	6.98667e6i	0.442081	+	0.321190i
$862$	2.27664e7	−	1.65407e7i	1.04358	−	0.758205i
$863$	−2.63850e7	+	1.91698e7i	−1.20595	+	0.876176i	−0.994857	−	0.101289i	$-0.967703\pi$
$863$	−2.63850e7	+	1.91698e7i	−1.20595	+	0.876176i	−0.211096	+	0.977465i	$0.567703\pi$
$864$	−603928.	−	438779.i	−0.0275233	−	0.0199969i
$865$	−7.40203e6	+	1.56179e7i	−0.336365	+	0.709712i
$866$	−1.30885e7	+	9.50932e6i	−0.593053	+	0.430878i
$867$	−3.83806e6	+	1.18123e7i	−0.173406	+	0.533688i
$868$	−4.14178e6			−0.186590
$869$	7.95362e6	−	2.44787e7i	0.357286	−	1.09961i
$870$	761040.	+	4.05032e6i	0.0340886	+	0.181422i
$871$	1.04969e6	+	3.23063e6i	0.0468832	+	0.144292i
$872$	1.72302e6	+	5.30292e6i	0.0767362	+	0.236170i
$873$	2.07467e6	+	1.50734e6i	0.0921328	+	0.0669384i
$874$	−2.40501e6			−0.106497
$875$	−1.62302e7	−	2.60498e7i	−0.716644	−	1.15023i
$876$	8.25677e6			0.363538
$877$	−1.52151e7	−	1.10544e7i	−0.667999	−	0.485330i	0.201356	−	0.979518i	$-0.435465\pi$
$877$	−1.52151e7	−	1.10544e7i	−0.667999	−	0.485330i	−0.869355	+	0.494189i	$0.835465\pi$
$878$	701515.	+	2.15904e6i	0.0307115	+	0.0945201i
$879$	1.68666e6	+	5.19102e6i	0.0736303	+	0.226611i
$880$	−656962.	−	3.49640e6i	−0.0285978	−	0.152200i
$881$	6.98222e6	−	2.14891e7i	0.303078	−	0.932777i	−0.677310	−	0.735698i	$-0.736854\pi$
$881$	6.98222e6	−	2.14891e7i	0.303078	−	0.932777i	0.980388	−	0.197079i	$-0.0631456\pi$
$882$	4.55569e6			0.197189
$883$	−9.27560e6	+	2.85474e7i	−0.400350	+	1.23215i	0.524366	+	0.851493i	$0.324303\pi$
$883$	−9.27560e6	+	2.85474e7i	−0.400350	+	1.23215i	−0.924716	+	0.380658i	$0.875697\pi$
$884$	2.48866e6	−	1.80812e6i	0.107111	−	0.0778208i
$885$	2.22862e6	−	4.70228e6i	0.0956485	−	0.201813i
$886$	−8.44279e6	−	6.13405e6i	−0.361328	−	0.262520i
$887$	−1.19575e7	+	8.68762e6i	−0.510306	+	0.370759i	−0.812940	−	0.582348i	$-0.802134\pi$
$887$	−1.19575e7	+	8.68762e6i	−0.510306	+	0.370759i	0.302633	+	0.953107i	$0.402134\pi$
$888$	3.12647e6	−	2.27151e6i	0.133052	−	0.0966680i
$889$	−1.34303e6	−	975766.i	−0.0569942	−	0.0414087i
$890$	−1.96830e7	+	1.07501e7i	−0.832945	+	0.454921i
$891$	1.31953e6	−	958693.i	0.0556832	−	0.0404562i
$892$	−5.16228e6	+	1.58879e7i	−0.217235	+	0.668580i
$893$	1.09810e6			0.0460802
$894$	2.39789e6	−	7.37996e6i	0.100343	−	0.308823i
$895$	3.45425e7	−	1.88657e7i	1.44144	−	0.787256i
$896$	889518.	+	2.73766e6i	0.0370156	+	0.113922i
$897$	3.28115e6	+	1.00983e7i	0.136159	+	0.419053i
$898$	1.53758e7	+	1.11712e7i	0.636277	+	0.462282i
$899$	−3.01724e6			−0.124512
$900$	3.91713e6	+	1.02887e6i	0.161199	+	0.0423403i
$901$	7.40055e6			0.303705
$902$	−6.04735e6	−	4.39366e6i	−0.247485	−	0.179808i
$903$	−2.62252e6	−	8.07130e6i	−0.107029	−	0.329400i
$904$	3.61743e6	+	1.11333e7i	0.147224	+	0.453110i
$905$	−1.09124e7	−	1.40922e6i	−0.442893	−	0.0571948i
$906$	3.38555e6	−	1.04196e7i	0.137028	−	0.421728i
$907$	−4.01304e7			−1.61978			−0.809888	−	0.586585i	$-0.800472\pi$
$907$	−4.01304e7			−1.61978			−0.809888	+	0.586585i	$0.800472\pi$
$908$	4.72773e6	−	1.45504e7i	0.190300	−	0.585682i
$909$	6.74376e6	−	4.89963e6i	0.270703	−	0.196677i
$910$	−6.98854e6	−	3.71936e7i	−0.279758	−	1.48890i
$911$	8.90273e6	+	6.46821e6i	0.355408	+	0.258219i	0.751134	−	0.660150i	$-0.229507\pi$
$911$	8.90273e6	+	6.46821e6i	0.355408	+	0.258219i	−0.395726	+	0.918369i	$0.629507\pi$
$912$	−915083.	+	664846.i	−0.0364312	+	0.0264688i
$913$	−2.20490e7	+	1.60196e7i	−0.875413	+	0.636024i
$914$	−2.62425e7	−	1.90663e7i	−1.03906	−	0.754919i
$915$	−2.75029e7	−	3.55170e6i	−1.08599	−	0.140244i
$916$	1.96379e7	−	1.42678e7i	0.773317	−	0.561847i
$917$	4.85440e6	−	1.49403e7i	0.190639	−	0.586727i
$918$	581984.			0.0227932
$919$	−3.94462e6	+	1.21403e7i	−0.154069	+	0.474176i	−0.998065	−	0.0621729i	$-0.980197\pi$
$919$	−3.94462e6	+	1.21403e7i	−0.154069	+	0.474176i	0.843996	+	0.536349i	$0.180197\pi$
$920$	3.18581e6	+	3.00830e6i	0.124094	+	0.117179i
$921$	−5.52946e6	−	1.70179e7i	−0.214800	−	0.661086i
$922$	7.12567e6	+	2.19306e7i	0.276057	+	0.849616i
$923$	1.45335e7	+	1.05592e7i	0.561519	+	0.407968i
$924$	−6.28935e6			−0.242340
$925$	−1.13321e7	+	1.76401e7i	−0.435467	+	0.677871i
$926$	−166097.			−0.00636552
$927$	−3.12132e6	−	2.26777e6i	−0.119300	−	0.0866763i
$928$	648005.	+	1.99435e6i	0.0247006	+	0.0760208i
$929$	−1.41030e7	−	4.34045e7i	−0.536132	−	1.65004i	−0.741191	−	0.671294i	$-0.765739\pi$
$929$	−1.41030e7	−	4.34045e7i	−0.536132	−	1.65004i	0.205060	−	0.978750i	$-0.434261\pi$
$930$	−1.26990e6	+	2.67942e6i	−0.0481462	+	0.101586i
$931$	2.13310e6	−	6.56501e6i	0.0806561	−	0.248234i
$932$	641553.			0.0241932
$933$	−8.38056e6	+	2.57927e7i	−0.315187	+	0.970047i
$934$	2.38528e7	−	1.73301e7i	0.894689	−	0.650029i
$935$	2.01659e6	+	1.90422e6i	0.0754377	+	0.0712342i
$936$	4.04005e6	+	2.93527e6i	0.150729	+	0.109511i
$937$	8.67579e6	−	6.30333e6i	0.322820	−	0.234542i	−0.414558	−	0.910023i	$-0.636064\pi$
$937$	8.67579e6	−	6.30333e6i	0.322820	−	0.234542i	0.737378	+	0.675481i	$0.236064\pi$
$938$	2.00487e6	−	1.45662e6i	0.0744011	−	0.0540555i
$939$	−5.97872e6	−	4.34379e6i	−0.221281	−	0.160770i
$940$	−1.45461e6	−	1.37356e6i	−0.0536941	−	0.0507022i
$941$	1.65671e6	−	1.20367e6i	0.0609919	−	0.0443132i	−0.556872	−	0.830599i	$-0.687998\pi$
$941$	1.65671e6	−	1.20367e6i	0.0609919	−	0.0443132i	0.617863	+	0.786285i	$0.287998\pi$
$942$	−1.05611e6	+	3.25037e6i	−0.0387776	+	0.119345i
$943$	9.20649e6			0.337143
$944$	818209.	−	2.51819e6i	0.0298837	−	0.0919726i
$945$	3.06642e6	−	6.46999e6i	0.111700	−	0.235681i
$946$	1.64921e6	+	5.07574e6i	0.0599166	+	0.184404i
$947$	−4.65973e6	−	1.43412e7i	−0.168844	−	0.519648i	0.830455	−	0.557086i	$-0.188081\pi$
$947$	−4.65973e6	−	1.43412e7i	−0.168844	−	0.519648i	−0.999299	+	0.0374374i	$0.988081\pi$
$948$	1.20618e7	+	8.76341e6i	0.435904	+	0.316703i
$949$	−5.52347e7			−1.99089
$950$	3.31677e6	−	5.16307e6i	0.119236	−	0.185609i
$951$	1.99497e7			0.715296
$952$	−1.81557e6	−	1.31909e6i	−0.0649264	−	0.0471718i
$953$	5.76844e6	+	1.77534e7i	0.205744	+	0.633214i	0.999682	+	0.0252157i	$0.00802724\pi$
$953$	5.76844e6	+	1.77534e7i	0.205744	+	0.633214i	−0.793938	+	0.607998i	$0.791973\pi$
$954$	3.71251e6	+	1.14259e7i	0.132068	+	0.406462i
$955$	2.86098e7	+	2.70157e7i	1.01510	+	0.958533i
$956$	−66714.2	+	205325.i	−0.00236088	+	0.00726603i
$957$	−4.58173e6			−0.161715
$958$	−2.79456e6	+	8.60078e6i	−0.0983785	+	0.302778i
$959$	3.51203e7	−	2.55164e7i	1.23314	−	0.895926i
$960$	2.04379e6	+	263933.i	0.0715744	+	0.00924306i
$961$	2.14052e7	+	1.55518e7i	0.747672	+	0.543216i
$962$	−2.09149e7	+	1.51956e7i	−0.728648	+	0.529394i
$963$	7.12179e6	−	5.17428e6i	0.247470	−	0.179798i
$964$	−1.70320e6	−	1.23745e6i	−0.0590302	−	0.0428879i
$965$	−9.00604e6	−	4.79309e7i	−0.311326	−	1.65690i
$966$	6.26686e6	−	4.55314e6i	0.216076	−	0.156989i
$967$	−1.22993e7	+	3.78535e7i	−0.422976	+	1.30179i	0.481943	+	0.876202i	$0.339931\pi$
$967$	−1.22993e7	+	3.78535e7i	−0.422976	+	1.30179i	−0.904919	+	0.425583i	$0.860069\pi$
$968$	−6.35213e6			−0.217887
$969$	272501.	−	838673.i	0.00932308	−	0.0286935i
$970$	−7.02103e6	−	906690.i	−0.239592	−	0.0309406i
$971$	1.43245e7	+	4.40863e7i	0.487563	+	1.50057i	0.828233	+	0.560383i	$0.189346\pi$
$971$	1.43245e7	+	4.40863e7i	0.487563	+	1.50057i	−0.340670	+	0.940183i	$0.610654\pi$
$972$	291954.	+	898543.i	0.00991172	+	0.0305052i
$973$	2.41610e7	+	1.75540e7i	0.818149	+	0.594420i
$974$	−2.29742e6			−0.0775966
$975$	−2.62041e7	−	6.88275e6i	−0.882792	−	0.231873i
$976$	−1.41105e7			−0.474152
$977$	−7.96862e6	−	5.78954e6i	−0.267083	−	0.194047i	0.446181	−	0.894943i	$-0.352784\pi$
$977$	−7.96862e6	−	5.78954e6i	−0.267083	−	0.194047i	−0.713264	+	0.700896i	$0.752784\pi$
$978$	−7.14869e6	−	2.20014e7i	−0.238990	−	0.735535i
$979$	−7.70487e6	−	2.37132e7i	−0.256926	−	0.790738i
$980$	−1.10374e7	+	6.02820e6i	−0.367116	+	0.200504i
$981$	2.18070e6	−	6.71151e6i	0.0723475	−	0.222663i
$982$	1.33936e7			0.443221
$983$	−3.54604e6	+	1.09136e7i	−0.117047	+	0.360233i	−0.992368	−	0.123308i	$-0.960650\pi$
$983$	−3.54604e6	+	1.09136e7i	−0.117047	+	0.360233i	0.875322	+	0.483541i	$0.160650\pi$
$984$	3.50297e6	−	2.54506e6i	0.115332	−	0.0837934i
$985$	−5.61462e6	+	3.06648e6i	−0.184387	+	0.100705i
$986$	−1.32263e6	−	960944.i	−0.0433256	−	0.0314779i
$987$	−2.86138e6	+	2.07892e6i	−0.0934938	+	0.0679272i
$988$	6.12156e6	−	4.44757e6i	0.199512	−	0.144954i
$989$	−5.31786e6	−	3.86365e6i	−0.172881	−	0.125605i
$990$	−1.92836e6	+	4.06873e6i	−0.0625316	+	0.131938i
$991$	−1.07660e7	+	7.82193e6i	−0.348232	+	0.253005i	−0.748127	−	0.663556i	$-0.769047\pi$
$991$	−1.07660e7	+	7.82193e6i	−0.348232	+	0.253005i	0.399895	+	0.916561i	$0.369047\pi$
$992$	−466227.	+	1.43490e6i	−0.0150424	+	0.0462958i
$993$	3.12958e7			1.00719
$994$	4.04988e6	−	1.24642e7i	0.130010	−	0.400129i
$995$	3.40429e6	+	1.81179e7i	0.109011	+	0.580163i
$996$	−4.87850e6	−	1.50145e7i	−0.155825	−	0.479581i
$997$	1.20607e7	+	3.71190e7i	0.384269	+	1.18266i	0.937009	+	0.349304i	$0.113582\pi$
$997$	1.20607e7	+	3.71190e7i	0.384269	+	1.18266i	−0.552741	+	0.833353i	$0.686418\pi$
$998$	4.43191e6	+	3.21997e6i	0.140852	+	0.102335i
$999$	−4.89104e6			−0.155056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.b.91.4	yes	24
25.11	even	5	inner	150.6.g.b.61.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.b.61.4	✓	24	25.11	even	5	inner
150.6.g.b.91.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(10.3231 + 54.9403i) q^{5} +(11.1246 - 34.2380i) q^{6} +175.692 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(10.3231 + 54.9403i) q^{5} +(11.1246 - 34.2380i) q^{6} +175.692 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(95.7661 - 202.061i) q^{10} +(201.117 + 146.120i) q^{11} +(-116.498 + 84.6411i) q^{12} +(779.331 - 566.217i) q^{13} +(-568.552 - 413.077i) q^{14} +(-441.552 + 241.158i) q^{15} +(-207.108 + 150.473i) q^{16} +(61.6746 - 189.815i) q^{17} +324.000 q^{18} +(151.706 - 466.903i) q^{19} +(-784.981 + 428.725i) q^{20} +(488.627 + 1503.84i) q^{21} +(-307.279 - 945.708i) q^{22} +(990.820 + 719.873i) q^{23} +576.000 q^{24} +(-2911.87 + 1134.31i) q^{25} -3853.22 q^{26} +(-589.773 - 428.495i) q^{27} +(868.670 + 2673.49i) q^{28} +(632.817 + 1947.61i) q^{29} +(1995.89 + 257.747i) q^{30} +(-455.299 + 1401.27i) q^{31} +1024.00 q^{32} +(-691.378 + 2127.84i) q^{33} +(-645.864 + 469.248i) q^{34} +(1813.69 + 9652.58i) q^{35} +(-1048.49 - 761.770i) q^{36} +(5427.89 - 3943.60i) q^{37} +(-1588.69 + 1154.25i) q^{38} +(7013.98 + 5095.95i) q^{39} +(3548.24 + 458.217i) q^{40} +(6081.55 - 4418.50i) q^{41} +(1954.51 - 6015.36i) q^{42} -5367.13 q^{43} +(-1229.12 + 3782.83i) q^{44} +(-3292.22 - 3108.77i) q^{45} +(-1513.84 - 4659.12i) q^{46} +(691.203 + 2127.30i) q^{47} +(-1863.98 - 1354.26i) q^{48} +14060.8 q^{49} +(12089.9 + 3175.52i) q^{50} +1796.25 q^{51} +(12469.3 + 9059.47i) q^{52} +(11458.4 + 35265.2i) q^{53} +(901.094 + 2773.28i) q^{54} +(-5951.72 + 12557.8i) q^{55} +(3474.68 - 10694.0i) q^{56} +4418.38 q^{57} +(2531.27 - 7790.44i) q^{58} +(-8367.58 + 6079.40i) q^{59} +(-5852.83 - 5526.70i) q^{60} +(44592.3 + 32398.2i) q^{61} +(4767.96 - 3464.12i) q^{62} +(-11513.2 + 8364.81i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(39153.2 + 36971.6i) q^{65} +(7240.20 - 5260.32i) q^{66} +(-1089.68 + 3353.69i) q^{67} +3193.33 q^{68} +(-3406.14 + 10483.0i) q^{69} +(16825.4 - 35500.6i) q^{70} +(5762.75 + 17735.9i) q^{71} +(1601.94 + 4930.28i) q^{72} +(-46388.0 - 33702.8i) q^{73} -26837.0 q^{74} +(-17807.5 - 21769.5i) q^{75} +7854.89 q^{76} +(35334.7 + 25672.1i) q^{77} +(-10716.4 - 32981.7i) q^{78} +(-31994.4 - 98468.7i) q^{79} +(-10405.0 - 9825.24i) q^{80} +(2027.46 - 6239.88i) q^{81} -30068.8 q^{82} +(-33878.5 + 104267. i) q^{83} +(-20467.9 + 14870.8i) q^{84} +(11065.1 + 1428.94i) q^{85} +(17368.4 + 12618.9i) q^{86} +(-14910.6 + 10833.2i) q^{87} +(12871.5 - 9351.67i) q^{88} +(-81142.8 - 58953.7i) q^{89} +(3344.68 + 17800.6i) q^{90} +(136922. - 99479.9i) q^{91} +(-6055.36 + 18636.5i) q^{92} -13260.4 q^{93} +(2764.81 - 8509.21i) q^{94} +(27217.8 + 3514.89i) q^{95} +(2847.90 + 8764.94i) q^{96} +(-9783.40 - 30110.2i) q^{97} +(-45501.6 - 33058.8i) q^{98} -20136.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Introduction

L-functions

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