LMFDB - Embedded newform 150.6.g.c.31.4

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			31.4
Character	$\chi$	$=$	150.31
Dual form			150.6.g.c.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(22.4321 + 51.2035i) q^{5} +(29.1246 + 21.1603i) q^{6} +146.638 q^{7} +(51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(22.4321 + 51.2035i) q^{5} +(29.1246 + 21.1603i) q^{6} +146.638 q^{7} +(51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(167.062 - 148.628i) q^{10} +(-63.0959 - 194.189i) q^{11} +(44.4984 - 136.952i) q^{12} +(-108.926 + 335.241i) q^{13} +(-181.255 - 557.844i) q^{14} +(-434.202 - 254.154i) q^{15} +(79.1084 - 243.470i) q^{16} +(-164.407 - 119.449i) q^{17} -324.000 q^{18} +(-158.598 - 115.228i) q^{19} +(-771.914 - 451.829i) q^{20} +(-1067.69 + 775.725i) q^{21} +(-660.748 + 480.062i) q^{22} +(765.728 + 2356.67i) q^{23} -576.000 q^{24} +(-2118.60 + 2297.20i) q^{25} +1409.97 q^{26} +(225.273 + 693.320i) q^{27} +(-1898.12 + 1379.07i) q^{28} +(809.000 - 587.773i) q^{29} +(-430.155 + 1965.95i) q^{30} +(4921.62 + 3575.77i) q^{31} -1024.00 q^{32} +(1486.68 + 1080.14i) q^{33} +(-251.192 + 773.090i) q^{34} +(3289.40 + 7508.39i) q^{35} +(400.486 + 1232.57i) q^{36} +(856.814 - 2637.00i) q^{37} +(-242.317 + 745.774i) q^{38} +(-980.336 - 3017.16i) q^{39} +(-764.720 + 3495.03i) q^{40} +(-3617.22 + 11132.6i) q^{41} +(4270.78 + 3102.90i) q^{42} +1923.29 q^{43} +(2642.99 + 1920.25i) q^{44} +(4505.98 - 446.424i) q^{45} +(8018.80 - 5826.00i) q^{46} +(-6646.40 + 4828.89i) q^{47} +(711.975 + 2191.23i) q^{48} +4695.72 q^{49} +(11357.8 + 5220.15i) q^{50} +1828.97 q^{51} +(-1742.82 - 5363.85i) q^{52} +(-8981.59 + 6525.50i) q^{53} +(2359.09 - 1713.98i) q^{54} +(8527.80 - 7586.80i) q^{55} +(7592.49 + 5516.27i) q^{56} +1764.34 q^{57} +(-3236.00 - 2351.09i) q^{58} +(-4475.18 + 13773.2i) q^{59} +(8010.63 - 793.644i) q^{60} +(16271.0 + 50077.0i) q^{61} +(7519.57 - 23142.8i) q^{62} +(3670.41 - 11296.3i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-19608.9 + 1942.73i) q^{65} +(2271.45 - 6990.81i) q^{66} +(38468.6 + 27949.1i) q^{67} +3251.50 q^{68} +(-18042.3 - 13108.5i) q^{69} +(24497.7 - 21794.5i) q^{70} +(-63225.8 + 45936.2i) q^{71} +(4193.94 - 3047.08i) q^{72} +(3504.08 + 10784.5i) q^{73} -11090.8 q^{74} +(3273.52 - 27933.8i) q^{75} +3136.61 q^{76} +(-9252.25 - 28475.5i) q^{77} +(-10266.2 + 7458.84i) q^{78} +(4927.25 - 3579.86i) q^{79} +(14241.1 - 1410.92i) q^{80} +(-5307.96 - 3856.46i) q^{81} +46822.2 q^{82} +(-10892.3 - 7913.71i) q^{83} +(6525.17 - 20082.4i) q^{84} +(2428.21 - 11097.7i) q^{85} +(-2377.31 - 7316.61i) q^{86} +(-2781.09 + 8559.33i) q^{87} +(4038.13 - 12428.1i) q^{88} +(231.005 + 710.959i) q^{89} +(-7267.99 - 16589.9i) q^{90} +(-15972.7 + 49159.0i) q^{91} +(-32075.2 - 23304.0i) q^{92} -54751.1 q^{93} +(26585.6 + 19315.6i) q^{94} +(2342.41 - 10705.6i) q^{95} +(7455.90 - 5417.03i) q^{96} +(68826.2 - 50005.2i) q^{97} +(-5804.22 - 17863.6i) q^{98} -16538.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	22.4321	+	51.2035i	0.401277	+	0.915957i
$5$	22.4321	+	51.2035i	0.401277	+	0.915957i
$6$	29.1246	+	21.1603i	0.330280	+	0.239962i
$7$	146.638			1.13110			0.565551	−	0.824714i	$-0.308664\pi$
$7$	146.638			1.13110			0.565551	+	0.824714i	$0.308664\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	167.062	−	148.628i	0.528297	−	0.470002i
$11$	−63.0959	−	194.189i	−0.157224	−	0.483886i	0.841155	−	0.540794i	$-0.181876\pi$
$11$	−63.0959	−	194.189i	−0.157224	−	0.483886i	−0.998379	+	0.0569075i	$0.981876\pi$
$12$	44.4984	−	136.952i	0.0892055	−	0.274546i
$13$	−108.926	+	335.241i	−0.178762	+	0.550172i	−0.999785	−	0.0207226i	$-0.993403\pi$
$13$	−108.926	+	335.241i	−0.178762	+	0.550172i	0.821024	+	0.570894i	$0.193403\pi$
$14$	−181.255	−	557.844i	−0.247155	−	0.760664i
$15$	−434.202	−	254.154i	−0.498268	−	0.291654i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−164.407	−	119.449i	−0.137974	−	0.100244i	0.516657	−	0.856192i	$-0.327176\pi$
$17$	−164.407	−	119.449i	−0.137974	−	0.100244i	−0.654632	+	0.755948i	$0.727176\pi$
$18$	−324.000			−0.235702
$19$	−158.598	−	115.228i	−0.100789	−	0.0732277i	0.536249	−	0.844060i	$-0.319841\pi$
$19$	−158.598	−	115.228i	−0.100789	−	0.0732277i	−0.637038	+	0.770832i	$0.719841\pi$
$20$	−771.914	−	451.829i	−0.431513	−	0.252580i
$21$	−1067.69	+	775.725i	−0.528322	+	0.383848i
$22$	−660.748	+	480.062i	−0.291058	+	0.211466i
$23$	765.728	+	2356.67i	0.301825	+	0.928921i	0.980843	+	0.194799i	$0.0624056\pi$
$23$	765.728	+	2356.67i	0.301825	+	0.928921i	−0.679018	+	0.734121i	$0.737594\pi$
$24$	−576.000			−0.204124
$25$	−2118.60	+	2297.20i	−0.677953	+	0.735105i
$26$	1409.97			0.409050
$27$	225.273	+	693.320i	0.0594703	+	0.183031i
$28$	−1898.12	+	1379.07i	−0.457540	+	0.332422i
$29$	809.000	−	587.773i	0.178630	−	0.129782i	−0.494878	−	0.868963i	$-0.664787\pi$
$29$	809.000	−	587.773i	0.178630	−	0.129782i	0.673507	+	0.739181i	$0.264787\pi$
$30$	−430.155	+	1965.95i	−0.0872613	+	0.398813i
$31$	4921.62	+	3575.77i	0.919822	+	0.668290i	0.943480	−	0.331430i	$-0.107531\pi$
$31$	4921.62	+	3575.77i	0.919822	+	0.668290i	−0.0236575	+	0.999720i	$0.507531\pi$
$32$	−1024.00			−0.176777
$33$	1486.68	+	1080.14i	0.237648	+	0.172661i
$34$	−251.192	+	773.090i	−0.0372656	+	0.114692i
$35$	3289.40	+	7508.39i	0.453885	+	1.03604i
$36$	400.486	+	1232.57i	0.0515028	+	0.158509i
$37$	856.814	−	2637.00i	0.102892	−	0.316670i	−0.886338	−	0.463039i	$-0.846759\pi$
$37$	856.814	−	2637.00i	0.102892	−	0.316670i	0.989230	+	0.146370i	$0.0467589\pi$
$38$	−242.317	+	745.774i	−0.0272222	+	0.0837815i
$39$	−980.336	−	3017.16i	−0.103208	−	0.317642i
$40$	−764.720	+	3495.03i	−0.0755705	+	0.345383i
$41$	−3617.22	+	11132.6i	−0.336058	+	1.03428i	0.630140	+	0.776482i	$0.282998\pi$
$41$	−3617.22	+	11132.6i	−0.336058	+	1.03428i	−0.966198	+	0.257800i	$0.917002\pi$
$42$	4270.78	+	3102.90i	0.373580	+	0.271422i
$43$	1923.29			0.158625			0.0793127	−	0.996850i	$-0.474727\pi$
$43$	1923.29			0.158625			0.0793127	+	0.996850i	$0.474727\pi$
$44$	2642.99	+	1920.25i	0.205809	+	0.149529i
$45$	4505.98	−	446.424i	0.331709	−	0.0328637i
$46$	8018.80	−	5826.00i	0.558747	−	0.405953i
$47$	−6646.40	+	4828.89i	−0.438876	+	0.318862i	−0.785188	−	0.619257i	$-0.787434\pi$
$47$	−6646.40	+	4828.89i	−0.438876	+	0.318862i	0.346312	+	0.938119i	$0.387434\pi$
$48$	711.975	+	2191.23i	0.0446028	+	0.137273i
$49$	4695.72			0.279390
$50$	11357.8	+	5220.15i	0.642495	+	0.295296i
$51$	1828.97			0.0984647
$52$	−1742.82	−	5363.85i	−0.0893808	−	0.275086i
$53$	−8981.59	+	6525.50i	−0.439201	+	0.319098i	−0.785317	−	0.619093i	$-0.787500\pi$
$53$	−8981.59	+	6525.50i	−0.439201	+	0.319098i	0.346116	+	0.938192i	$0.387500\pi$
$54$	2359.09	−	1713.98i	0.110093	−	0.0799874i
$55$	8527.80	−	7586.80i	0.380128	−	0.338183i
$56$	7592.49	+	5516.27i	0.323530	+	0.235058i
$57$	1764.34			0.0719277
$58$	−3236.00	−	2351.09i	−0.126310	−	0.0917697i
$59$	−4475.18	+	13773.2i	−0.167371	+	0.515115i	−0.999203	−	0.0399123i	$-0.987292\pi$
$59$	−4475.18	+	13773.2i	−0.167371	+	0.515115i	0.831832	+	0.555027i	$0.187292\pi$
$60$	8010.63	−	793.644i	0.287269	−	0.0284608i
$61$	16271.0	+	50077.0i	0.559873	+	1.72311i	0.682715	+	0.730685i	$0.260799\pi$
$61$	16271.0	+	50077.0i	0.559873	+	1.72311i	−0.122842	+	0.992426i	$0.539201\pi$
$62$	7519.57	−	23142.8i	0.248435	−	0.764606i
$63$	3670.41	−	11296.3i	0.116510	−	0.358580i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−19608.9	+	1942.73i	−0.575666	+	0.0570335i
$66$	2271.45	−	6990.81i	0.0641865	−	0.197546i
$67$	38468.6	+	27949.1i	1.04694	+	0.760643i	0.971627	−	0.236517i	$-0.0760060\pi$
$67$	38468.6	+	27949.1i	1.04694	+	0.760643i	0.0753079	+	0.997160i	$0.476006\pi$
$68$	3251.50			0.0852729
$69$	−18042.3	−	13108.5i	−0.456215	−	0.331459i
$70$	24497.7	−	21794.5i	0.597558	−	0.531620i
$71$	−63225.8	+	45936.2i	−1.48850	+	1.08146i	−0.513806	+	0.857907i	$0.671765\pi$
$71$	−63225.8	+	45936.2i	−1.48850	+	1.08146i	−0.974692	+	0.223551i	$0.928235\pi$
$72$	4193.94	−	3047.08i	0.0953436	−	0.0692712i
$73$	3504.08	+	10784.5i	0.0769604	+	0.236860i	0.982134	−	0.188182i	$-0.0602594\pi$
$73$	3504.08	+	10784.5i	0.0769604	+	0.236860i	−0.905174	+	0.425042i	$0.860259\pi$
$74$	−11090.8			−0.235443
$75$	3273.52	−	27933.8i	0.0671988	−	0.573426i
$76$	3136.61			0.0622912
$77$	−9252.25	−	28475.5i	−0.177836	−	0.547324i
$78$	−10266.2	+	7458.84i	−0.191062	+	0.138815i
$79$	4927.25	−	3579.86i	0.0888254	−	0.0645354i	−0.542486	−	0.840065i	$-0.682517\pi$
$79$	4927.25	−	3579.86i	0.0888254	−	0.0645354i	0.631312	+	0.775529i	$0.282517\pi$
$80$	14241.1	−	1410.92i	0.248782	−	0.0246478i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	46822.2			0.768984
$83$	−10892.3	−	7913.71i	−0.173550	−	0.126091i	0.497619	−	0.867395i	$-0.334208\pi$
$83$	−10892.3	−	7913.71i	−0.173550	−	0.126091i	−0.671169	+	0.741304i	$0.734208\pi$
$84$	6525.17	−	20082.4i	0.100900	−	0.310540i
$85$	2428.21	−	11097.7i	0.0364534	−	0.166604i
$86$	−2377.31	−	7316.61i	−0.0346609	−	0.106675i
$87$	−2781.09	+	8559.33i	−0.0393929	+	0.121239i
$88$	4038.13	−	12428.1i	0.0555871	−	0.171080i
$89$	231.005	+	710.959i	0.00309133	+	0.00951414i	0.952590	−	0.304256i	$-0.0984078\pi$
$89$	231.005	+	710.959i	0.00309133	+	0.00951414i	−0.949499	+	0.313770i	$0.898408\pi$
$90$	−7267.99	−	16589.9i	−0.0945820	−	0.215893i
$91$	−15972.7	+	49159.0i	−0.202197	+	0.622300i
$92$	−32075.2	−	23304.0i	−0.395094	−	0.287052i
$93$	−54751.1			−0.656426
$94$	26585.6	+	19315.6i	0.310332	+	0.225470i
$95$	2342.41	−	10705.6i	0.0266290	−	0.121703i
$96$	7455.90	−	5417.03i	0.0825700	−	0.0599906i
$97$	68826.2	−	50005.2i	0.742719	−	0.539617i	−0.150842	−	0.988558i	$-0.548199\pi$
$97$	68826.2	−	50005.2i	0.742719	−	0.539617i	0.893562	+	0.448941i	$0.148199\pi$
$98$	−5804.22	−	17863.6i	−0.0610491	−	0.187890i
$99$	−16538.8			−0.169596
$100$	5819.58	−	49660.2i	0.0581958	−	0.496602i
$101$	−184525.			−1.79992			−0.899958	−	0.435978i	$-0.856403\pi$
$101$	−184525.			−1.79992			−0.899958	+	0.435978i	$0.856403\pi$
$102$	−2260.73	−	6957.81i	−0.0215153	−	0.0662174i
$103$	−99826.7	+	72528.4i	−0.927158	+	0.673620i	−0.945295	−	0.326216i	$-0.894226\pi$
$103$	−99826.7	+	72528.4i	−0.927158	+	0.673620i	0.0181372	+	0.999836i	$0.494226\pi$
$104$	−18251.0	+	13260.2i	−0.165464	+	0.120217i
$105$	−63670.5	−	37268.6i	−0.563592	−	0.329890i
$106$	35926.3	+	26102.0i	0.310562	+	0.225637i
$107$	−70274.6			−0.593388			−0.296694	−	0.954973i	$-0.595884\pi$
$107$	−70274.6			−0.593388			−0.296694	+	0.954973i	$0.595884\pi$
$108$	−9436.37	−	6855.93i	−0.0778477	−	0.0565597i
$109$	6882.75	−	21182.9i	0.0554876	−	0.170773i	−0.919472	−	0.393156i	$-0.871383\pi$
$109$	6882.75	−	21182.9i	0.0554876	−	0.170773i	0.974960	+	0.222382i	$0.0713834\pi$
$110$	−39402.8	−	23063.9i	−0.310489	−	0.181740i
$111$	7711.33	+	23733.0i	0.0594048	+	0.182829i
$112$	11600.3	−	35702.0i	0.0873824	−	0.268935i
$113$	59170.0	−	182107.i	0.435919	−	1.34162i	−0.456223	−	0.889865i	$-0.650798\pi$
$113$	59170.0	−	182107.i	0.435919	−	1.34162i	0.892142	−	0.451755i	$-0.149202\pi$
$114$	−2180.85	−	6711.96i	−0.0157168	−	0.0483713i
$115$	−103493.	+	92072.9i	−0.729736	+	0.649213i
$116$	−4944.17	+	15216.6i	−0.0341152	+	0.104996i
$117$	23099.0	+	16782.4i	0.156001	+	0.113342i
$118$	57927.9			0.382986
$119$	−24108.4	−	17515.8i	−0.156063	−	0.113387i
$120$	−12920.9	−	29493.2i	−0.0819104	−	0.186969i
$121$	96564.7	−	70158.3i	0.599591	−	0.435628i
$122$	170392.	−	123797.i	1.03645	−	0.753027i
$123$	−32554.9	−	100194.i	−0.194023	−	0.597143i
$124$	−97335.3			−0.568481
$125$	−165150.	−	56948.9i	−0.945372	−	0.325995i
$126$	−47510.7			−0.266603
$127$	−44205.3	−	136050.i	−0.243201	−	0.748495i	−0.995927	−	0.0901614i	$-0.971262\pi$
$127$	−44205.3	−	136050.i	−0.243201	−	0.748495i	0.752726	−	0.658333i	$-0.228738\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$	−14003.7	+	10174.3i	−0.0740917	+	0.0538308i
$130$	31628.6	+	72195.5i	0.164143	+	0.374672i
$131$	235811.	+	171327.i	1.20057	+	0.872262i	0.994340	−	0.106242i	$-0.0338820\pi$
$131$	235811.	+	171327.i	1.20057	+	0.872262i	0.206225	+	0.978504i	$0.433882\pi$
$132$	−29402.3			−0.146874
$133$	−23256.5	−	16896.9i	−0.114003	−	0.0828279i
$134$	58774.8	−	180890.i	0.282768	−	0.870269i
$135$	−30447.1	+	27087.4i	−0.143784	+	0.127918i
$136$	−4019.07	−	12369.4i	−0.0186328	−	0.0573459i
$137$	85212.3	−	262256.i	0.387883	−	1.19378i	−0.546484	−	0.837469i	$-0.684034\pi$
$137$	85212.3	−	262256.i	0.387883	−	1.19378i	0.934367	−	0.356312i	$-0.115966\pi$
$138$	−27566.2	+	84840.0i	−0.123219	+	0.379230i
$139$	−2098.28	−	6457.84i	−0.00921141	−	0.0283498i	0.946345	−	0.323158i	$-0.104744\pi$
$139$	−2098.28	−	6457.84i	−0.00921141	−	0.0283498i	−0.955557	+	0.294808i	$0.904744\pi$
$140$	−113192.	−	66255.3i	−0.488085	−	0.285693i
$141$	22848.3	−	70319.8i	0.0967845	−	0.297872i
$142$	252903.	+	183745.i	1.05253	+	0.764706i
$143$	71972.8			0.294326
$144$	−16775.8	−	12188.3i	−0.0674181	−	0.0489821i
$145$	48243.6	+	28238.7i	0.190555	+	0.111538i
$146$	36695.2	−	26660.7i	0.142471	−	0.103512i
$147$	−34190.2	+	24840.7i	−0.130499	+	0.0948134i
$148$	13709.0	+	42192.1i	0.0514461	+	0.158335i
$149$	85618.4			0.315938			0.157969	−	0.987444i	$-0.449505\pi$
$149$	85618.4			0.315938			0.157969	+	0.987444i	$0.449505\pi$
$150$	−110313.	+	22074.9i	−0.400312	+	0.0801072i
$151$	138427.			0.494059			0.247030	−	0.969008i	$-0.420545\pi$
$151$	138427.			0.494059			0.247030	+	0.969008i	$0.420545\pi$
$152$	−3877.06	−	11932.4i	−0.0136111	−	0.0418907i
$153$	−13317.0	+	9675.36i	−0.0459915	+	0.0334148i
$154$	−96890.9	+	70395.3i	−0.329216	+	0.239189i
$155$	−72689.7	+	332216.i	−0.243021	+	1.11069i
$156$	41064.9	+	29835.4i	0.135101	+	0.0981567i
$157$	512398.			1.65905			0.829523	−	0.558472i	$-0.188612\pi$
$157$	512398.			1.65905			0.829523	+	0.558472i	$0.188612\pi$
$158$	−19709.0	−	14319.4i	−0.0628090	−	0.0456334i
$159$	30875.9	−	95026.4i	0.0968562	−	0.298093i
$160$	−22970.4	−	52432.4i	−0.0709365	−	0.161920i
$161$	112285.	+	345577.i	0.341394	+	1.05070i
$162$	−8109.84	+	24959.5i	−0.0242787	+	0.0747221i
$163$	60863.9	−	187320.i	0.179428	−	0.552223i	−0.820380	−	0.571819i	$-0.806238\pi$
$163$	60863.9	−	187320.i	0.179428	−	0.552223i	0.999808	+	0.0195958i	$0.00623793\pi$
$164$	−57875.5	−	178122.i	−0.168029	−	0.517141i
$165$	−21957.5	+	100353.i	−0.0627876	+	0.286960i
$166$	−16641.9	+	51218.6i	−0.0468742	+	0.144264i
$167$	−11011.6	−	8000.37i	−0.0305533	−	0.0221983i	0.572404	−	0.819972i	$-0.306011\pi$
$167$	−11011.6	−	8000.37i	−0.0305533	−	0.0221983i	−0.602957	+	0.797774i	$0.706011\pi$
$168$	−84463.5			−0.230885
$169$	199861.	+	145208.i	0.538284	+	0.391086i
$170$	−45219.7	+	4480.09i	−0.120007	+	0.0118895i
$171$	−12846.5	+	9333.50i	−0.0335964	+	0.0244092i
$172$	−24895.5	+	18087.7i	−0.0641653	+	0.0466188i
$173$	−82521.9	−	253976.i	−0.209630	−	0.645176i	−0.999491	−	0.0318900i	$-0.989847\pi$
$173$	−82521.9	−	253976.i	−0.209630	−	0.645176i	0.789861	−	0.613286i	$-0.210153\pi$
$174$	35999.2			0.0901405
$175$	−310668.	+	336857.i	−0.766834	+	0.831478i
$176$	−52270.7			−0.127197
$177$	−40276.6	−	123959.i	−0.0966317	−	0.297402i
$178$	2419.11	−	1757.59i	0.00572277	−	0.00415783i
$179$	−496688.	+	360865.i	−1.15865	+	0.841807i	−0.989606	−	0.143802i	$-0.954067\pi$
$179$	−496688.	+	360865.i	−1.15865	+	0.841807i	−0.169041	+	0.985609i	$0.554067\pi$
$180$	−54128.2	+	48155.4i	−0.124521	+	0.110781i
$181$	304947.	+	221557.i	0.691876	+	0.502678i	0.877276	−	0.479985i	$-0.159358\pi$
$181$	304947.	+	221557.i	0.691876	+	0.502678i	−0.185400	+	0.982663i	$0.559358\pi$
$182$	206755.			0.462677
$183$	−383382.	−	278543.i	−0.846260	−	0.614844i
$184$	−49006.6	+	150827.i	−0.106711	+	0.328423i
$185$	154244.	−	15281.5i	0.331344	−	0.0328275i
$186$	67676.1	+	208286.i	0.143434	+	0.441445i
$187$	−12822.3	+	39462.8i	−0.0268139	+	0.0825248i
$188$	40619.2	−	125013.i	0.0838179	−	0.257965i
$189$	33033.6	+	101667.i	0.0672670	+	0.207027i
$190$	−43621.9	+	4321.79i	−0.0876639	+	0.00868520i
$191$	−36377.4	+	111958.i	−0.0721521	+	0.222061i	−0.980629	−	0.195873i	$-0.937246\pi$
$191$	−36377.4	+	111958.i	−0.0721521	+	0.222061i	0.908477	+	0.417935i	$0.137246\pi$
$192$	−29823.6	−	21668.1i	−0.0583858	−	0.0424197i
$193$	587622.			1.13555			0.567773	−	0.823185i	$-0.307805\pi$
$193$	587622.			1.13555			0.567773	+	0.823185i	$0.307805\pi$
$194$	−275305.	−	200021.i	−0.525182	−	0.381567i
$195$	132499.	−	117878.i	0.249531	−	0.221996i
$196$	−60782.6	+	44161.2i	−0.113016	+	0.0821108i
$197$	−263315.	+	191309.i	−0.483403	+	0.351213i	−0.802642	−	0.596462i	$-0.796573\pi$
$197$	−263315.	+	191309.i	−0.483403	+	0.351213i	0.319239	+	0.947674i	$0.396573\pi$
$198$	20443.1	+	62917.3i	0.0370581	+	0.114053i
$199$	145601.			0.260634			0.130317	−	0.991472i	$-0.458401\pi$
$199$	145601.			0.260634			0.130317	+	0.991472i	$0.458401\pi$
$200$	−196112.	+	39244.3i	−0.346680	+	0.0693748i
$201$	−427949.			−0.747139
$202$	228086.	+	701975.i	0.393296	+	1.21044i
$203$	118630.	−	86189.8i	0.202048	−	0.146797i
$204$	−23674.7	+	17200.6i	−0.0398298	+	0.0289380i
$205$	−651173.	+	64514.2i	−1.08221	+	0.107219i
$206$	399307.	+	290113.i	0.655600	+	0.476321i
$207$	200714.			0.325575
$208$	73004.2	+	53040.6i	0.117001	+	0.0850062i
$209$	−12369.2	+	38068.5i	−0.0195874	+	0.0602837i
$210$	−63077.1	+	288283.i	−0.0987014	+	0.451098i
$211$	360615.	+	1.10986e6i	0.557619	+	1.71617i	0.688925	+	0.724832i	$0.258083\pi$
$211$	360615.	+	1.10986e6i	0.557619	+	1.71617i	−0.131306	+	0.991342i	$0.541917\pi$
$212$	54890.6	−	168936.i	0.0838799	−	0.258156i
$213$	217351.	−	668937.i	0.328256	−	1.01027i
$214$	86864.1	+	267340.i	0.129660	+	0.399052i
$215$	43143.3	+	98479.0i	0.0636527	+	0.145294i
$216$	−14417.5	+	44372.5i	−0.0210259	+	0.0647112i
$217$	721697.	+	524343.i	1.04041	+	0.755904i
$218$	−89092.2			−0.126969
$219$	−82564.3	−	59986.5i	−0.116327	−	0.0845168i
$220$	−39035.6	+	178406.i	−0.0543756	+	0.248515i
$221$	57952.4	−	42104.9i	0.0798161	−	0.0579898i
$222$	80754.1	−	58671.3i	0.109972	−	0.0798993i
$223$	−384900.	−	1.18460e6i	−0.518305	−	1.59518i	−0.777187	−	0.629270i	$-0.783354\pi$
$223$	−384900.	−	1.18460e6i	−0.518305	−	1.59518i	0.258882	−	0.965909i	$-0.416646\pi$
$224$	−150157.			−0.199952
$225$	123937.	+	220708.i	0.163209	+	0.290644i
$226$	−765913.			−0.997489
$227$	286497.	+	881748.i	0.369025	+	1.13574i	0.947422	+	0.319987i	$0.103679\pi$
$227$	286497.	+	881748.i	0.369025	+	1.13574i	−0.578397	+	0.815756i	$0.696321\pi$
$228$	−22838.1	+	16592.9i	−0.0290954	+	0.0211390i
$229$	−467648.	+	339766.i	−0.589291	+	0.428145i	−0.842062	−	0.539381i	$-0.818658\pi$
$229$	−467648.	+	339766.i	−0.589291	+	0.428145i	0.252770	+	0.967526i	$0.418658\pi$
$230$	478190.	+	279902.i	0.596048	+	0.348888i
$231$	218004.	+	158389.i	0.268804	+	0.195297i
$232$	63998.6			0.0780640
$233$	−231280.	−	168034.i	−0.279092	−	0.202772i	0.439429	−	0.898277i	$-0.355181\pi$
$233$	−231280.	−	168034.i	−0.279092	−	0.202772i	−0.718521	+	0.695505i	$0.755181\pi$
$234$	35292.1	−	108618.i	0.0421345	−	0.129677i
$235$	−396349.	−	231997.i	−0.468175	−	0.274039i
$236$	−71602.8	−	220371.i	−0.0836855	−	0.257557i
$237$	−16938.4	+	52131.0i	−0.0195885	+	0.0602872i
$238$	−36834.3	+	113364.i	−0.0421512	+	0.129728i
$239$	−377254.	−	1.16107e6i	−0.427208	−	1.31481i	−0.900865	−	0.434100i	$-0.857066\pi$
$239$	−377254.	−	1.16107e6i	−0.427208	−	1.31481i	0.473657	−	0.880709i	$-0.342934\pi$
$240$	−96227.9	+	85609.6i	−0.107838	+	0.0959388i
$241$	474442.	−	1.46018e6i	0.526188	−	1.61944i	−0.235766	−	0.971810i	$-0.575760\pi$
$241$	474442.	−	1.46018e6i	0.526188	−	1.61944i	0.761955	−	0.647631i	$-0.224240\pi$
$242$	−386259.	−	280633.i	−0.423975	−	0.308036i
$243$	59049.0			0.0641500
$244$	−681568.	−	495188.i	−0.732883	−	0.532471i
$245$	105335.	+	240437.i	0.112113	+	0.255910i
$246$	−340920.	+	247693.i	−0.359182	+	0.260961i
$247$	55904.7	−	40617.2i	0.0583050	−	0.0423611i
$248$	120313.	+	370286.i	0.124218	+	0.382303i
$249$	121172.			0.123853
$250$	−12510.5	+	698659.i	−0.0126597	+	0.706993i
$251$	1.28840e6			1.29083			0.645413	−	0.763834i	$-0.276685\pi$
$251$	1.28840e6			1.29083			0.645413	+	0.763834i	$0.276685\pi$
$252$	58726.5	+	180742.i	0.0582549	+	0.179290i
$253$	409325.	−	297392.i	0.402038	−	0.292097i
$254$	−462924.	+	336334.i	−0.450220	+	0.327104i
$255$	41027.5	+	93649.6i	0.0395116	+	0.0901894i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	845589.			0.798595			0.399298	−	0.916821i	$-0.369254\pi$
$257$	845589.			0.798595			0.399298	+	0.916821i	$0.369254\pi$
$258$	56014.9	+	40697.2i	0.0523907	+	0.0380641i
$259$	125642.	−	386685.i	0.116382	−	0.358185i
$260$	235553.	−	209561.i	0.216100	−	0.192255i
$261$	−25029.8	−	77033.9i	−0.0227435	−	0.0699972i
$262$	360287.	−	1.10885e6i	0.324262	−	0.997975i
$263$	292345.	−	899747.i	0.260620	−	0.802104i	−0.732051	−	0.681250i	$-0.761437\pi$
$263$	292345.	−	899747.i	0.260620	−	0.802104i	0.992670	−	0.120854i	$-0.0385634\pi$
$264$	36343.2	+	111853.i	0.0320932	+	0.0987728i
$265$	−535604.	−	313508.i	−0.468521	−	0.274242i
$266$	−35532.8	+	109359.i	−0.0307911	+	0.0947653i
$267$	−5443.00	−	3954.57i	−0.00467262	−	0.00339486i
$268$	−760798.			−0.647041
$269$	−976090.	−	709171.i	−0.822449	−	0.597544i	0.0949640	−	0.995481i	$-0.469726\pi$
$269$	−976090.	−	709171.i	−0.822449	−	0.597544i	−0.917413	+	0.397937i	$0.869726\pi$
$270$	140681.	+	82345.7i	0.117443	+	0.0687435i
$271$	−9389.53	+	6821.89i	−0.00776642	+	0.00564263i	−0.591662	−	0.806186i	$-0.701528\pi$
$271$	−9389.53	+	6821.89i	−0.00776642	+	0.00564263i	0.583895	+	0.811829i	$0.301528\pi$
$272$	−42088.3	+	30578.9i	−0.0344936	+	0.0250611i
$273$	−143755.	−	442431.i	−0.116739	−	0.359285i
$274$	−1.10301e6			−0.887572
$275$	579767.	+	266466.i	0.462298	+	0.212476i
$276$	356824.			0.281956
$277$	−443436.	−	1.36476e6i	−0.347241	−	1.06870i	−0.960373	−	0.278718i	$-0.910090\pi$
$277$	−443436.	−	1.36476e6i	−0.347241	−	1.06870i	0.613131	−	0.789981i	$-0.289910\pi$
$278$	−21973.5	+	15964.6i	−0.0170524	+	0.0123893i
$279$	398651.	−	289637.i	0.306607	−	0.222763i
$280$	−112137.	+	512504.i	−0.0854779	+	0.390663i
$281$	436995.	+	317495.i	0.330149	+	0.239867i	0.740494	−	0.672063i	$-0.234592\pi$
$281$	436995.	+	317495.i	0.330149	+	0.239867i	−0.410345	+	0.911930i	$0.634592\pi$
$282$	−295754.			−0.221467
$283$	1.42979e6	+	1.03880e6i	1.06122	+	0.771023i	0.974314	−	0.225193i	$-0.0723012\pi$
$283$	1.42979e6	+	1.03880e6i	1.06122	+	0.771023i	0.0869086	+	0.996216i	$0.472301\pi$
$284$	386402.	−	1.18922e6i	0.284278	−	0.874917i
$285$	39577.9	+	90340.6i	0.0288629	+	0.0658826i
$286$	−88963.3	−	273801.i	−0.0643126	−	0.197934i
$287$	−530422.	+	1.63247e6i	−0.380116	+	1.16988i
$288$	−25631.1	+	78884.4i	−0.0182090	+	0.0560415i
$289$	−425998.	−	1.31109e6i	−0.300029	−	0.923394i
$290$	47794.0	−	218434.i	0.0333717	−	0.152520i
$291$	−236604.	+	728191.i	−0.163790	+	0.504095i
$292$	−146781.	−	106643.i	−0.100742	−	0.0731937i
$293$	737327.			0.501754			0.250877	−	0.968019i	$-0.419281\pi$
$293$	737327.			0.501754			0.250877	+	0.968019i	$0.419281\pi$
$294$	136761.	+	99362.6i	0.0922770	+	0.0670432i
$295$	−805623.	+	79816.1i	−0.538985	+	0.0533993i
$296$	143563.	−	104304.i	0.0952385	−	0.0691948i
$297$	120421.	−	87491.3i	0.0792159	−	0.0575537i
$298$	−105830.	−	325712.i	−0.0690349	−	0.212468i
$299$	−873458.			−0.565020
$300$	220332.	+	392369.i	0.141343	+	0.251705i
$301$	282027.			0.179421
$302$	−171105.	−	526608.i	−0.107956	−	0.332254i
$303$	1.34356e6	−	976150.i	0.840715	−	0.610816i
$304$	−40601.1	+	29498.5i	−0.0251973	+	0.0183069i
$305$	−2.19913e6	+	1.95646e6i	−1.35363	+	1.20426i
$306$	53268.0	+	38701.4i	0.0325209	+	0.0236278i
$307$	279009.			0.168956			0.0844779	−	0.996425i	$-0.473078\pi$
$307$	279009.			0.168956			0.0844779	+	0.996425i	$0.473078\pi$
$308$	387563.	+	281581.i	0.232791	+	0.169132i
$309$	343174.	−	1.05618e6i	0.204465	−	0.629277i
$310$	1.35368e6	−	134114.i	0.800037	−	0.0792628i
$311$	536687.	+	1.65175e6i	0.314645	+	0.968377i	0.975900	+	0.218216i	$0.0700238\pi$
$311$	536687.	+	1.65175e6i	0.314645	+	0.968377i	−0.661256	+	0.750160i	$0.729976\pi$
$312$	62741.5	−	193099.i	0.0364896	−	0.112303i
$313$	406633.	−	1.25149e6i	0.234607	−	0.722047i	−0.762566	−	0.646910i	$-0.776061\pi$
$313$	406633.	−	1.25149e6i	0.234607	−	0.722047i	0.997173	−	0.0751364i	$-0.0239392\pi$
$314$	−633359.	−	1.94928e6i	−0.362515	−	1.11571i
$315$	660748.	−	65462.8i	0.375197	−	0.0371722i
$316$	−30112.7	+	92677.3i	−0.0169641	+	0.0522102i
$317$	−1.00058e6	−	726965.i	−0.559248	−	0.406317i	0.271936	−	0.962315i	$-0.412336\pi$
$317$	−1.00058e6	−	726965.i	−0.559248	−	0.406317i	−0.831183	+	0.555998i	$0.812336\pi$
$318$	−399667.			−0.221631
$319$	−165184.	−	120013.i	−0.0908846	−	0.0660315i
$320$	−171072.	+	152195.i	−0.0933906	+	0.0830854i
$321$	511680.	−	371757.i	0.277163	−	0.201371i
$322$	1.17586e6	−	854313.i	0.631999	−	0.459174i
$323$	12310.8	+	37888.8i	0.00656569	+	0.0202071i
$324$	104976.			0.0555556
$325$	−539344.	−	960468.i	−0.283242	−	0.504399i
$326$	−787839.			−0.410576
$327$	61944.8	+	190646.i	0.0320358	+	0.0985960i
$328$	−606080.	+	440343.i	−0.311061	+	0.225999i
$329$	−974615.	+	708099.i	−0.496413	+	0.360665i
$330$	408907.	−	40512.0i	0.206700	−	0.0204785i
$331$	−535281.	−	388904.i	−0.268542	−	0.195107i	0.445363	−	0.895350i	$-0.353075\pi$
$331$	−535281.	−	388904.i	−0.268542	−	0.195107i	−0.713904	+	0.700243i	$0.753075\pi$
$332$	215418.			0.107260
$333$	−181697.	−	132010.i	−0.0897918	−	0.0652375i
$334$	−16824.2	+	51779.5i	−0.00825216	+	0.0253975i
$335$	−568161.	+	2.59669e6i	−0.276605	+	1.26418i
$336$	104403.	+	321318.i	0.0504502	+	0.155270i
$337$	596796.	−	1.83675e6i	0.286254	−	0.880999i	−0.699766	−	0.714372i	$-0.746713\pi$
$337$	596796.	−	1.83675e6i	0.286254	−	0.880999i	0.986020	−	0.166627i	$-0.0532875\pi$
$338$	305361.	−	939803.i	0.145386	−	0.447451i
$339$	532530.	+	1.63896e6i	0.251678	+	0.774585i
$340$	72937.9	+	166488.i	0.0342181	+	0.0781063i
$341$	383841.	−	1.18134e6i	0.178758	−	0.550160i
$342$	51385.8	+	37334.0i	0.0237563	+	0.0172599i
$343$	−1.77598e6			−0.815082
$344$	99582.1	+	72350.6i	0.0453717	+	0.0329645i
$345$	266475.	−	1.21788e6i	0.120534	−	0.550880i
$346$	−864181.	+	627864.i	−0.388074	+	0.281952i
$347$	−2.62173e6	+	1.90480e6i	−1.16886	+	0.849229i	−0.990872	−	0.134803i	$-0.956960\pi$
$347$	−2.62173e6	+	1.90480e6i	−1.16886	+	0.849229i	−0.177991	+	0.984032i	$0.556960\pi$
$348$	−44497.5	−	136949.i	−0.0196964	−	0.0606194i
$349$	−3.94065e6			−1.73183			−0.865913	−	0.500195i	$-0.833262\pi$
$349$	−3.94065e6			−1.73183			−0.865913	+	0.500195i	$0.833262\pi$
$350$	1.66549e6	+	765472.i	0.726727	+	0.334010i
$351$	−256967.			−0.111329
$352$	64610.2	+	198850.i	0.0277936	+	0.0855398i
$353$	1.55214e6	−	1.12770e6i	0.662972	−	0.481678i	−0.204693	−	0.978826i	$-0.565620\pi$
$353$	1.55214e6	−	1.12770e6i	0.662972	−	0.481678i	0.867665	+	0.497149i	$0.165620\pi$
$354$	−421782.	+	306442.i	−0.178887	+	0.129969i
$355$	−3.77038e6	−	2.20694e6i	−1.58787	−	0.929436i
$356$	−9676.45	−	7030.35i	−0.00404661	−	0.00294003i
$357$	268196.			0.111374
$358$	1.98675e6	+	1.44346e6i	0.819288	+	0.595247i
$359$	329896.	−	1.01532e6i	0.135096	−	0.415781i	−0.860509	−	0.509435i	$-0.829855\pi$
$359$	329896.	−	1.01532e6i	0.135096	−	0.415781i	0.995605	+	0.0936534i	$0.0298546\pi$
$360$	250100.	+	146392.i	0.101709	+	0.0595336i
$361$	−753281.	−	2.31836e6i	−0.304221	−	0.936295i
$362$	465918.	−	1.43395e6i	0.186869	−	0.575125i
$363$	−331960.	+	1.02167e6i	−0.132227	+	0.406952i
$364$	−255564.	−	786544.i	−0.101099	−	0.311150i
$365$	−473599.	+	421339.i	−0.186071	+	0.165539i
$366$	−585756.	+	1.80277e6i	−0.228567	+	0.703457i
$367$	1.25908e6	+	914773.i	0.487963	+	0.354526i	0.804400	−	0.594088i	$-0.202487\pi$
$367$	1.25908e6	+	914773.i	0.487963	+	0.354526i	−0.316437	+	0.948613i	$0.602487\pi$
$368$	634354.			0.244181
$369$	767070.	+	557309.i	0.293271	+	0.213074i
$370$	−248791.	−	567890.i	−0.0944778	−	0.215655i
$371$	−1.31704e6	+	956887.i	−0.496781	+	0.360932i
$372$	708713.	−	514910.i	0.265530	−	0.192919i
$373$	−665619.	−	2.04856e6i	−0.247716	−	0.762390i	−0.995178	−	0.0980860i	$-0.968728\pi$
$373$	−665619.	−	2.04856e6i	−0.247716	−	0.762390i	0.747462	−	0.664304i	$-0.231272\pi$
$374$	165975.			0.0613568
$375$	1.50374e6	−	458999.i	0.552199	−	0.168552i
$376$	−525786.			−0.191796
$377$	108924.	+	335233.i	0.0394703	+	0.121477i
$378$	345933.	−	251335.i	0.124527	−	0.0904739i
$379$	−3.03953e6	+	2.20835e6i	−1.08695	+	0.789714i	−0.978881	−	0.204430i	$-0.934466\pi$
$379$	−3.03953e6	+	2.20835e6i	−1.08695	+	0.789714i	−0.108066	+	0.994144i	$0.534466\pi$
$380$	70360.7	+	160606.i	0.0249960	+	0.0570560i
$381$	1.04158e6	+	756751.i	0.367603	+	0.267079i
$382$	470880.			0.165102
$383$	2.02525e6	+	1.47143e6i	0.705475	+	0.512557i	0.881711	−	0.471791i	$-0.156392\pi$
$383$	2.02525e6	+	1.47143e6i	0.705475	+	0.512557i	−0.176236	+	0.984348i	$0.556392\pi$
$384$	−45566.4	+	140239.i	−0.0157695	+	0.0485334i
$385$	1.25050e6	−	1.11251e6i	0.429964	−	0.382519i
$386$	−726340.	−	2.23545e6i	−0.248126	−	0.763653i
$387$	48140.6	−	148161.i	0.0163393	−	0.0502872i
$388$	−420628.	+	1.29456e6i	−0.141847	+	0.436559i
$389$	1.24300e6	+	3.82557e6i	0.416484	+	1.28181i	0.910916	+	0.412591i	$0.135376\pi$
$389$	1.24300e6	+	3.82557e6i	0.416484	+	1.28181i	−0.494432	+	0.869216i	$0.664624\pi$
$390$	−612212.	−	358349.i	−0.203817	−	0.119301i
$391$	155610.	−	478919.i	0.0514749	−	0.158424i
$392$	243130.	+	176645.i	0.0799143	+	0.0580611i
$393$	−2.62331e6			−0.856777
$394$	1.05326e6	+	765237.i	0.341817	+	0.248345i
$395$	293830.	+	171989.i	0.0947552	+	0.0554636i
$396$	214082.	−	155540.i	0.0686030	−	0.0498430i
$397$	664845.	−	483038.i	0.211711	−	0.153817i	−0.476876	−	0.878970i	$-0.658231\pi$
$397$	664845.	−	483038.i	0.211711	−	0.153817i	0.688588	+	0.725153i	$0.258231\pi$
$398$	−179972.	−	553898.i	−0.0569506	−	0.175276i
$399$	258720.			0.0813575
$400$	391702.	+	697545.i	0.122407	+	0.217983i
$401$	4.47747e6			1.39050			0.695251	−	0.718767i	$-0.255293\pi$
$401$	4.47747e6			1.39050			0.695251	+	0.718767i	$0.255293\pi$
$402$	528974.	+	1.62801e6i	0.163256	+	0.502450i
$403$	−1.73484e6	+	1.26043e6i	−0.532103	+	0.386595i
$404$	2.38854e6	−	1.73538e6i	0.728081	−	0.528982i
$405$	78395.7	−	358295.i	0.0237495	−	0.108543i
$406$	−474521.	−	344759.i	−0.142870	−	0.103801i
$407$	−566139.			−0.169409
$408$	94698.6	+	68802.6i	0.0281639	+	0.0204623i
$409$	−1.60703e6	+	4.94594e6i	−0.475025	+	1.46198i	0.370898	+	0.928674i	$0.379050\pi$
$409$	−1.60703e6	+	4.94594e6i	−0.475025	+	1.46198i	−0.845924	+	0.533304i	$0.820950\pi$
$410$	1.05032e6	+	2.39746e6i	0.308576	+	0.704356i
$411$	766911.	+	2.36031e6i	0.223944	+	0.689230i
$412$	610087.	−	1.87765e6i	0.177071	−	0.544970i
$413$	−656231.	+	2.01967e6i	−0.189314	+	0.582647i
$414$	−248096.	−	763560.i	−0.0711407	−	0.218949i
$415$	160873.	−	735245.i	0.0458526	−	0.209562i
$416$	111540.	−	343286.i	0.0316009	−	0.0972575i
$417$	49440.3	+	35920.5i	0.0139233	+	0.0101158i
$418$	160110.			0.0448207
$419$	1.95638e6	+	1.42140e6i	0.544401	+	0.395530i	0.825717	−	0.564085i	$-0.190771\pi$
$419$	1.95638e6	+	1.42140e6i	0.544401	+	0.395530i	−0.281316	+	0.959615i	$0.590771\pi$
$420$	1.17466e6	−	116378.i	0.324930	−	0.0321921i
$421$	−983370.	+	714460.i	−0.270403	+	0.196459i	−0.714721	−	0.699410i	$-0.753446\pi$
$421$	−983370.	+	714460.i	−0.270403	+	0.196459i	0.444318	+	0.895869i	$0.353446\pi$
$422$	3.77641e6	−	2.74372e6i	1.03228	−	0.749996i
$423$	205635.	+	632878.i	0.0558786	+	0.171977i
$424$	−710518.			−0.191938
$425$	622712.	−	124612.i	0.167230	−	0.0334648i
$426$	−2.81345e6			−0.751130
$427$	2.38595e6	+	7.34319e6i	0.633273	+	1.94901i
$428$	909653.	−	660902.i	0.240030	−	0.174392i
$429$	−524045.	+	380741.i	−0.137476	+	0.0998819i
$430$	321308.	−	285854.i	0.0838013	−	0.0745543i
$431$	−57916.5	−	42078.8i	−0.0150179	−	0.0109111i	0.580251	−	0.814438i	$-0.302954\pi$
$431$	−57916.5	−	42078.8i	−0.0150179	−	0.0109111i	−0.595269	+	0.803527i	$0.702954\pi$
$432$	186624.			0.0481125
$433$	586835.	+	426361.i	0.150417	+	0.109284i	0.660448	−	0.750872i	$-0.270366\pi$
$433$	586835.	+	426361.i	0.150417	+	0.109284i	−0.510032	+	0.860156i	$0.670366\pi$
$434$	1.10265e6	−	3.39362e6i	0.281006	−	0.864847i
$435$	−500653.	+	49601.7i	−0.126857	+	0.0125682i
$436$	110124.	+	338927.i	0.0277438	+	0.0853866i
$437$	150112.	−	461997.i	0.0376020	−	0.115727i
$438$	−126147.	+	388241.i	−0.0314190	+	0.0966976i
$439$	1.23647e6	+	3.80547e6i	0.306212	+	0.942424i	0.979222	+	0.202791i	$0.0650011\pi$
$439$	1.23647e6	+	3.80547e6i	0.306212	+	0.942424i	−0.673010	+	0.739633i	$0.734999\pi$
$440$	726946.	−	72021.4i	0.179007	−	0.0177349i
$441$	117536.	−	361737.i	0.0287788	−	0.0885720i
$442$	−231810.	−	168419.i	−0.0564385	−	0.0410050i
$443$	−2.27875e6			−0.551681			−0.275840	−	0.961203i	$-0.588956\pi$
$443$	−2.27875e6			−0.551681			−0.275840	+	0.961203i	$0.588956\pi$
$444$	−323016.	−	234685.i	−0.0777619	−	0.0564974i
$445$	−31221.7	+	27776.6i	−0.00747406	+	0.00664934i
$446$	−4.03072e6	+	2.92849e6i	−0.959502	+	0.697119i
$447$	−623401.	+	452927.i	−0.147570	+	0.107216i
$448$	185605.	+	571233.i	0.0436912	+	0.134468i
$449$	7.81036e6			1.82833			0.914166	−	0.405340i	$-0.132847\pi$
$449$	7.81036e6			1.82833			0.914166	+	0.405340i	$0.132847\pi$
$450$	686428.	−	744294.i	0.159795	−	0.173266i
$451$	2.39007e6			0.553311
$452$	946720.	+	2.91371e6i	0.217959	+	0.670810i
$453$	−1.00791e6	+	732289.i	−0.230768	+	0.167663i
$454$	3.00024e6	−	2.17980e6i	0.683150	−	0.496338i
$455$	−2.87542e6	+	284879.i	−0.651137	+	0.0645106i
$456$	91352.6	+	66371.5i	0.0205735	+	0.0149475i
$457$	−2.19127e6			−0.490800			−0.245400	−	0.969422i	$-0.578919\pi$
$457$	−2.19127e6			−0.490800			−0.245400	+	0.969422i	$0.578919\pi$
$458$	1.87059e6	+	1.35906e6i	0.416692	+	0.302744i
$459$	45779.7	−	140896.i	0.0101424	−	0.0312152i
$460$	473734.	−	2.16512e6i	0.104385	−	0.477076i
$461$	−764488.	−	2.35285e6i	−0.167540	−	0.515635i	0.831675	−	0.555263i	$-0.187383\pi$
$461$	−764488.	−	2.35285e6i	−0.167540	−	0.515635i	−0.999214	+	0.0396286i	$0.987383\pi$
$462$	333081.	−	1.02512e6i	0.0726014	−	0.223444i
$463$	−1.14143e6	+	3.51297e6i	−0.247456	+	0.761591i	0.747767	+	0.663962i	$0.231126\pi$
$463$	−1.14143e6	+	3.51297e6i	−0.247456	+	0.761591i	−0.995223	+	0.0976299i	$0.968874\pi$
$464$	−79106.7	−	243465.i	−0.0170576	−	0.0524979i
$465$	−1.22818e6	−	2.80345e6i	−0.263409	−	0.601258i
$466$	−353364.	+	1.08754e6i	−0.0753802	+	0.231996i
$467$	−4.98913e6	−	3.62482e6i	−1.05860	−	0.769119i	−0.0847726	−	0.996400i	$-0.527016\pi$
$467$	−4.98913e6	−	3.62482e6i	−1.05860	−	0.769119i	−0.973829	+	0.227281i	$0.927016\pi$
$468$	−456831.			−0.0964141
$469$	5.64097e6	+	4.09840e6i	1.18419	+	0.860364i
$470$	−392655.	+	1.79456e6i	−0.0819911	+	0.374727i
$471$	−3.73085e6	+	2.71062e6i	−0.774918	+	0.563011i
$472$	−749834.	+	544787.i	−0.154921	+	0.112557i
$473$	−121351.	−	373481.i	−0.0249397	−	0.0767566i
$474$	219255.			0.0448233
$475$	600710.	−	120209.i	0.122160	−	0.0244458i
$476$	476793.			0.0964523
$477$	277883.	+	855237.i	0.0559200	+	0.172104i
$478$	−3.95065e6	+	2.87032e6i	−0.790859	+	0.574593i
$479$	1.27704e6	−	927826.i	0.254312	−	0.184768i	−0.453324	−	0.891346i	$-0.649762\pi$
$479$	1.27704e6	−	927826.i	0.254312	−	0.184768i	0.707636	+	0.706577i	$0.249762\pi$
$480$	444622.	+	260253.i	0.0880822	+	0.0515576i
$481$	790701.	+	574478.i	0.155829	+	0.113217i
$482$	−6.14131e6			−1.20405
$483$	−2.64569e6	−	1.92221e6i	−0.516025	−	0.374914i
$484$	−590151.	+	1.81630e6i	−0.114512	+	0.352431i
$485$	4.10436e6	+	2.40243e6i	0.792302	+	0.463762i
$486$	−72988.6	−	224636.i	−0.0140173	−	0.0431408i
$487$	12357.4	−	38032.3i	0.00236105	−	0.00726657i	−0.949869	−	0.312648i	$-0.898784\pi$
$487$	12357.4	−	38032.3i	0.00236105	−	0.00726657i	0.952230	+	0.305381i	$0.0987840\pi$
$488$	−1.04134e6	+	3.20493e6i	−0.197945	+	0.609212i
$489$	547775.	+	1.68588e6i	0.103593	+	0.318826i
$490$	784477.	−	697914.i	0.147601	−	0.131314i
$491$	3.01455e6	−	9.27783e6i	0.564312	−	1.73677i	−0.105677	−	0.994401i	$-0.533701\pi$
$491$	3.01455e6	−	9.27783e6i	0.564312	−	1.73677i	0.669988	−	0.742372i	$-0.266299\pi$
$492$	1.36368e6	+	990771.i	0.253980	+	0.184527i
$493$	−203214.			−0.0376562
$494$	−223619.	−	162469.i	−0.0412279	−	0.0299538i
$495$	−370999.	−	846844.i	−0.0680550	−	0.155343i
$496$	1.25993e6	−	915396.i	0.229956	−	0.167072i
$497$	−9.27130e6	+	6.73600e6i	−1.68364	+	1.22324i
$498$	−149777.	−	460968.i	−0.0270628	−	0.0832908i
$499$	9.50838e6			1.70944			0.854722	−	0.519085i	$-0.173727\pi$
$499$	9.50838e6			1.70944			0.854722	+	0.519085i	$0.173727\pi$
$500$	2.67332e6	−	815998.i	0.478218	−	0.145970i
$501$	122499.			0.0218042
$502$	−1.59255e6	−	4.90138e6i	−0.282056	−	0.868079i
$503$	4.49469e6	−	3.26559e6i	0.792100	−	0.575494i	−0.116486	−	0.993192i	$-0.537163\pi$
$503$	4.49469e6	−	3.26559e6i	0.792100	−	0.575494i	0.908586	+	0.417698i	$0.137163\pi$
$504$	614992.	−	446818.i	0.107843	−	0.0783527i
$505$	−4.13928e6	−	9.44834e6i	−0.722265	−	1.64864i
$506$	−1.63730e6	−	1.18957e6i	−0.284284	−	0.206544i
$507$	−2.22338e6			−0.384143
$508$	1.85169e6	+	1.34533e6i	0.318354	+	0.231298i
$509$	2.63645e6	−	8.11415e6i	0.451050	−	1.38819i	−0.424661	−	0.905353i	$-0.639607\pi$
$509$	2.63645e6	−	8.11415e6i	0.451050	−	1.38819i	0.875711	−	0.482836i	$-0.160393\pi$
$510$	305551.	−	271835.i	0.0520186	−	0.0462786i
$511$	513832.	+	1.58141e6i	0.0870500	+	0.267912i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$	44162.2	−	135917.i	0.00740896	−	0.0228024i
$514$	−1.04521e6	−	3.21681e6i	−0.174499	−	0.537054i
$515$	−5.95303e6	−	3.48452e6i	−0.989054	−	0.578928i
$516$	85583.2	−	263398.i	0.0141503	−	0.0435500i
$517$	1.35708e6	+	985975.i	0.223295	+	0.162233i
$518$	−1.62634e6			−0.266309
$519$	1.94441e6	+	1.41269e6i	0.316861	+	0.230213i
$520$	−1.08838e6	−	637065.i	−0.176511	−	0.103318i
$521$	7.27793e6	−	5.28773e6i	1.17466	−	0.853443i	0.183104	−	0.983094i	$-0.441385\pi$
$521$	7.27793e6	−	5.28773e6i	1.17466	−	0.853443i	0.991560	+	0.129650i	$0.0413855\pi$
$522$	−262116.	+	190438.i	−0.0421034	+	0.0305899i
$523$	−2.17943e6	−	6.70759e6i	−0.348408	−	1.07229i	−0.959734	−	0.280911i	$-0.909363\pi$
$523$	−2.17943e6	−	6.70759e6i	−0.348408	−	1.07229i	0.611325	−	0.791379i	$-0.290637\pi$
$524$	−4.66366e6			−0.741990
$525$	480022.	−	4.09616e6i	0.0760086	−	0.648603i
$526$	−3.78420e6			−0.596362
$527$	−382029.	−	1.17576e6i	−0.0599197	−	0.184414i
$528$	380591.	−	276516.i	0.0594120	−	0.0431653i
$529$	239570.	−	174058.i	0.0372215	−	0.0270430i
$530$	−530613.	+	2.42508e6i	−0.0820518	+	0.375004i
$531$	949009.	+	689495.i	0.146061	+	0.106119i
$532$	459946.			0.0704577
$533$	−3.33810e6	−	2.42528e6i	−0.508958	−	0.369780i
$534$	−8316.17	+	25594.5i	−0.00126203	+	0.00388413i
$535$	−1.57640e6	−	3.59831e6i	−0.238113	−	0.543518i
$536$	940398.	+	2.89425e6i	0.141384	+	0.435134i
$537$	1.70746e6	−	5.25503e6i	0.255514	−	0.786393i
$538$	−1.49133e6	+	4.58985e6i	−0.222136	+	0.683664i
$539$	−296280.	−	911857.i	−0.0439269	−	0.135193i
$540$	139370.	−	636968.i	0.0205677	−	0.0940012i
$541$	1.77007e6	−	5.44771e6i	0.260014	−	0.800241i	−0.732786	−	0.680459i	$-0.761780\pi$
$541$	1.77007e6	−	5.44771e6i	0.260014	−	0.800241i	0.992800	−	0.119782i	$-0.0382195\pi$
$542$	37558.1	+	27287.6i	0.00549168	+	0.00398994i
$543$	−3.39242e6			−0.493754
$544$	168353.	+	122316.i	0.0243907	+	0.0177209i
$545$	1.23904e6	−	122756.i	0.178687	−	0.0177032i
$546$	−1.50542e6	+	1.09375e6i	−0.216110	+	0.157013i
$547$	1.47084e6	−	1.06862e6i	0.210182	−	0.152706i	−0.477714	−	0.878515i	$-0.658534\pi$
$547$	1.47084e6	−	1.06862e6i	0.210182	−	0.152706i	0.687896	+	0.725809i	$0.258534\pi$
$548$	1.36340e6	+	4.19610e6i	0.193942	+	0.596891i
$549$	4.26498e6			0.603929
$550$	297064.	−	2.53493e6i	0.0418739	−	0.357322i
$551$	−196034.			−0.0275076
$552$	−441059.	−	1.35744e6i	−0.0616097	−	0.189615i
$553$	722522.	−	524943.i	0.100470	−	0.0729961i
$554$	−4.64372e6	+	3.37386e6i	−0.642824	+	0.467039i
$555$	−1.04223e6	+	927229.i	−0.143626	+	0.127777i
$556$	87893.8	+	63858.6i	0.0120579	+	0.00876057i
$557$	−1.40428e7			−1.91785			−0.958927	−	0.283652i	$-0.908454\pi$
$557$	−1.40428e7			−1.91785			−0.958927	+	0.283652i	$0.908454\pi$
$558$	−1.59461e6	−	1.15855e6i	−0.216804	−	0.157517i
$559$	−209496.	+	644763.i	−0.0283561	+	0.0872711i
$560$	2.08829e6	−	206895.i	0.281398	−	0.0278792i
$561$	−115400.	−	355166.i	−0.0154810	−	0.0476457i
$562$	667668.	−	2.05487e6i	0.0891703	−	0.274438i
$563$	−3.50653e6	+	1.07920e7i	−0.466237	+	1.43493i	0.391184	+	0.920312i	$0.372066\pi$
$563$	−3.50653e6	+	1.07920e7i	−0.466237	+	1.43493i	−0.857421	+	0.514616i	$0.827934\pi$
$564$	365573.	+	1.12512e6i	0.0483923	+	0.148936i
$565$	1.06518e7	−	1.05532e6i	1.40379	−	0.139079i
$566$	2.18453e6	−	6.72328e6i	0.286626	−	0.882146i
$567$	−778349.	−	565504.i	−0.101676	−	0.0738716i
$568$	−5.00169e6			−0.650498
$569$	−979030.	−	711307.i	−0.126770	−	0.0921036i	0.522594	−	0.852582i	$-0.324965\pi$
$569$	−979030.	−	711307.i	−0.126770	−	0.0921036i	−0.649363	+	0.760478i	$0.724965\pi$
$570$	294755.	−	262230.i	0.0379992	−	0.0338062i
$571$	−8.66506e6	+	6.29553e6i	−1.11220	+	0.808058i	−0.983008	−	0.183562i	$-0.941237\pi$
$571$	−8.66506e6	+	6.29553e6i	−1.11220	+	0.808058i	−0.129188	+	0.991620i	$0.541237\pi$
$572$	−931636.	+	676873.i	−0.119057	+	0.0865002i
$573$	−327397.	−	1.00762e6i	−0.0416570	−	0.128207i
$574$	6.86592e6			0.869799
$575$	−7.03602e6	−	3.23381e6i	−0.887477	−	0.407892i
$576$	331776.			0.0416667
$577$	881637.	+	2.71340e6i	0.110243	+	0.339292i	0.990925	−	0.134415i	$-0.0429155\pi$
$577$	881637.	+	2.71340e6i	0.110243	+	0.339292i	−0.880682	+	0.473707i	$0.842915\pi$
$578$	−4.46111e6	+	3.24119e6i	−0.555422	+	0.403538i
$579$	−4.27856e6	+	3.10856e6i	−0.530398	+	0.385356i
$580$	−890051.	+	88180.7i	−0.109861	+	0.0108844i
$581$	−1.59722e6	−	1.16045e6i	−0.196302	−	0.142622i
$582$	3.06266e6			0.374793
$583$	1.83388e6	+	1.33239e6i	0.223460	+	0.162353i
$584$	−224261.	+	690206.i	−0.0272096	+	0.0837426i
$585$	−341160.	+	1.55921e6i	−0.0412162	+	0.188372i
$586$	−911387.	−	2.80496e6i	−0.109637	−	0.337429i
$587$	−748619.	+	2.30401e6i	−0.0896738	+	0.275987i	−0.985829	−	0.167753i	$-0.946349\pi$
$587$	−748619.	+	2.30401e6i	−0.0896738	+	0.275987i	0.896155	+	0.443741i	$0.146349\pi$
$588$	208952.	−	643088.i	0.0249232	−	0.0767056i
$589$	−368531.	−	1.13422e6i	−0.0437709	−	0.134713i
$590$	1.29944e6	+	2.96611e6i	0.153683	+	0.350798i
$591$	905195.	−	2.78590e6i	0.106604	−	0.328093i
$592$	−574251.	−	417218.i	−0.0673438	−	0.0489281i
$593$	4.58051e6			0.534906			0.267453	−	0.963571i	$-0.413818\pi$
$593$	4.58051e6			0.534906			0.267453	+	0.963571i	$0.413818\pi$
$594$	−481686.	−	349965.i	−0.0560141	−	0.0406966i
$595$	356068.	−	1.62735e6i	0.0412325	−	0.188447i
$596$	−1.10827e6	+	805204.i	−0.127800	+	0.0928518i
$597$	−1.06014e6	+	770238.i	−0.121738	+	0.0884482i
$598$	1.07965e6	+	3.32283e6i	0.123461	+	0.379975i
$599$	−4.93665e6			−0.562166			−0.281083	−	0.959683i	$-0.590694\pi$
$599$	−4.93665e6			−0.562166			−0.281083	+	0.959683i	$0.590694\pi$
$600$	1.22032e6	−	1.32319e6i	0.138387	−	0.150053i
$601$	−8.07758e6			−0.912210			−0.456105	−	0.889926i	$-0.650756\pi$
$601$	−8.07758e6			−0.912210			−0.456105	+	0.889926i	$0.650756\pi$
$602$	−348604.	−	1.07289e6i	−0.0392050	−	0.120661i
$603$	3.11596e6	−	2.26388e6i	0.348978	−	0.253548i
$604$	−1.79184e6	+	1.30185e6i	−0.199851	+	0.145200i
$605$	5.75850e6	+	3.37066e6i	0.639619	+	0.374391i
$606$	−5.37422e6	−	3.90460e6i	−0.594476	−	0.431912i
$607$	370094.			0.0407699			0.0203850	−	0.999792i	$-0.493511\pi$
$607$	370094.			0.0407699			0.0203850	+	0.999792i	$0.493511\pi$
$608$	162405.	+	117994.i	0.0178172	+	0.0129449i
$609$	−407814.	+	1.25512e6i	−0.0445573	+	0.137133i
$610$	1.01611e7	+	5.94765e6i	1.10565	+	0.647173i
$611$	−894873.	−	2.75414e6i	−0.0969747	−	0.298457i
$612$	81386.2	−	250481.i	0.00878359	−	0.0270331i
$613$	388368.	−	1.19527e6i	0.0417438	−	0.128474i	−0.928013	−	0.372548i	$-0.878484\pi$
$613$	388368.	−	1.19527e6i	0.0417438	−	0.128474i	0.969757	+	0.244074i	$0.0784841\pi$
$614$	−344875.	−	1.06141e6i	−0.0369182	−	0.113622i
$615$	4.40000e6	−	3.91448e6i	0.469100	−	0.417337i
$616$	592144.	−	1.82243e6i	0.0628747	−	0.193508i
$617$	−5.16103e6	−	3.74971e6i	−0.545787	−	0.396538i	0.280443	−	0.959871i	$-0.409519\pi$
$617$	−5.16103e6	−	3.74971e6i	−0.545787	−	0.396538i	−0.826230	+	0.563333i	$0.809519\pi$
$618$	−4.44213e6			−0.467865
$619$	1.43745e7	+	1.04437e7i	1.50788	+	1.09554i	0.967108	+	0.254368i	$0.0818674\pi$
$619$	1.43745e7	+	1.04437e7i	1.50788	+	1.09554i	0.540771	+	0.841170i	$0.318133\pi$
$620$	−2.18343e6	−	4.98391e6i	−0.228119	−	0.520704i
$621$	−1.46143e6	+	1.06179e6i	−0.152072	+	0.110486i
$622$	5.62026e6	−	4.08336e6i	0.582480	−	0.423196i
$623$	33874.1	+	104254.i	0.00349661	+	0.0107615i
$624$	−812143.			−0.0834971
$625$	−788662.	−	9.73373e6i	−0.0807590	−	0.996734i
$626$	−5.26356e6			−0.536839
$627$	−111323.	−	342616.i	−0.0113088	−	0.0348048i
$628$	−6.63262e6	+	4.81888e6i	−0.671098	+	0.487581i
$629$	−455854.	+	331197.i	−0.0459408	+	0.0333780i
$630$	−1.06576e6	−	2.43272e6i	−0.106982	−	0.244197i
$631$	4.66765e6	+	3.39125e6i	0.466687	+	0.339068i	0.796149	−	0.605101i	$-0.206867\pi$
$631$	4.66765e6	+	3.39125e6i	0.466687	+	0.339068i	−0.329462	+	0.944169i	$0.606867\pi$
$632$	389787.			0.0388181
$633$	−8.49692e6	−	6.17337e6i	−0.842853	−	0.612369i
$634$	−1.52875e6	+	4.70501e6i	−0.151048	+	0.464877i
$635$	5.97462e6	−	5.31535e6i	0.587998	−	0.523115i
$636$	494015.	+	1.52042e6i	0.0484281	+	0.149046i
$637$	−511487.	+	1.57419e6i	−0.0499443	+	0.153713i
$638$	−252378.	+	776740.i	−0.0245471	+	0.0755482i
$639$	1.95616e6	+	6.02043e6i	0.189519	+	0.583278i
$640$	790440.	+	462672.i	0.0762814	+	0.0446502i
$641$	4.34551e6	−	1.33741e7i	0.417730	−	1.28564i	−0.492057	−	0.870563i	$-0.663755\pi$
$641$	4.34551e6	−	1.33741e7i	0.417730	−	1.28564i	0.909786	−	0.415077i	$-0.136245\pi$
$642$	−2.04672e6	−	1.48703e6i	−0.195984	−	0.142391i
$643$	1.16712e7			1.11323			0.556617	−	0.830769i	$-0.312099\pi$
$643$	1.16712e7			1.11323			0.556617	+	0.830769i	$0.312099\pi$
$644$	−4.70345e6	−	3.41725e6i	−0.446891	−	0.324685i
$645$	−835093.	−	488810.i	−0.0790380	−	0.0462637i
$646$	128920.	−	93666.2i	0.0121546	−	0.00883083i
$647$	3.17223e6	−	2.30476e6i	0.297923	−	0.216453i	−0.428774	−	0.903412i	$-0.641054\pi$
$647$	3.17223e6	−	2.30476e6i	0.297923	−	0.216453i	0.726697	+	0.686958i	$0.241054\pi$
$648$	−129757.	−	399352.i	−0.0121393	−	0.0373610i
$649$	2.95697e6			0.275572
$650$	−2.98717e6	+	3.23899e6i	−0.277317	+	0.300695i
$651$	−8.02860e6			−0.742484
$652$	973822.	+	2.99712e6i	0.0897141	+	0.276112i
$653$	8.94856e6	−	6.50151e6i	0.821240	−	0.596666i	−0.0958272	−	0.995398i	$-0.530550\pi$
$653$	8.94856e6	−	6.50151e6i	0.821240	−	0.596666i	0.917067	+	0.398732i	$0.130550\pi$
$654$	648694.	−	471304.i	0.0593056	−	0.0430880i
$655$	−3.48280e6	+	1.59176e7i	−0.317195	+	1.44969i
$656$	2.42432e6	+	1.76137e6i	0.219953	+	0.159805i
$657$	918496.			0.0830164
$658$	3.89846e6	+	2.83240e6i	0.351017	+	0.255029i
$659$	1.94259e6	−	5.97867e6i	0.174248	−	0.536279i	−0.825351	−	0.564621i	$-0.809023\pi$
$659$	1.94259e6	−	5.97867e6i	0.174248	−	0.536279i	0.999598	+	0.0283412i	$0.00902250\pi$
$660$	−659554.	−	1.50550e6i	−0.0589374	−	0.134531i
$661$	4.48860e6	+	1.38145e7i	0.399583	+	1.22979i	0.925334	+	0.379152i	$0.123784\pi$
$661$	4.48860e6	+	1.38145e7i	0.399583	+	1.22979i	−0.525751	+	0.850639i	$0.676216\pi$
$662$	−817836.	+	2.51704e6i	−0.0725306	+	0.223226i
$663$	−199223.	+	613144.i	−0.0176017	+	0.0541725i
$664$	−266271.	−	819498.i	−0.0234371	−	0.0721319i
$665$	343487.	−	1.56985e6i	0.0301200	−	0.137659i
$666$	−277608.	+	854389.i	−0.0242519	+	0.0746397i
$667$	2.00466e6	+	1.45647e6i	0.174472	+	0.126761i
$668$	217777.			0.0188830
$669$	9.06912e6	+	6.58910e6i	0.783430	+	0.569195i
$670$	1.05807e7	−	1.04827e6i	0.910597	−	0.0902163i
$671$	8.69777e6	−	6.31930e6i	0.745764	−	0.541829i
$672$	1.09332e6	−	794343.i	0.0933950	−	0.0678554i
$673$	−691442.	−	2.12804e6i	−0.0588462	−	0.181110i	0.917313	−	0.398168i	$-0.130354\pi$
$673$	−691442.	−	2.12804e6i	−0.0588462	−	0.181110i	−0.976159	+	0.217058i	$0.930354\pi$
$674$	−7.72509e6			−0.655019
$675$	−2.06996e6	−	951372.i	−0.174865	−	0.0803694i
$676$	−3.95267e6			−0.332678
$677$	3.95419e6	+	1.21697e7i	0.331578	+	1.02049i	0.968383	+	0.249467i	$0.0802555\pi$
$677$	3.95419e6	+	1.21697e7i	0.331578	+	1.02049i	−0.636805	+	0.771025i	$0.719745\pi$
$678$	5.57673e6	−	4.05173e6i	0.465913	−	0.338506i
$679$	1.00925e7	−	7.33266e6i	0.840091	−	0.610362i
$680$	543203.	−	483263.i	0.0450494	−	0.0400785i
$681$	−6.75054e6	−	4.90455e6i	−0.557790	−	0.405258i
$682$	−4.96854e6			−0.409042
$683$	1.84765e7	+	1.34240e7i	1.51554	+	1.10111i	0.963643	+	0.267194i	$0.0860966\pi$
$683$	1.84765e7	+	1.34240e7i	1.51554	+	1.10111i	0.551899	+	0.833911i	$0.313903\pi$
$684$	78510.5	−	241631.i	0.00641635	−	0.0197475i
$685$	1.53399e7	−	1.51979e6i	1.24910	−	0.123753i
$686$	2.19523e6	+	6.75621e6i	0.178102	+	0.548142i
$687$	1.60763e6	−	4.94778e6i	0.129955	−	0.399961i
$688$	152148.	−	468263.i	0.0122545	−	0.0377154i
$689$	−1.20928e6	−	3.72179e6i	−0.0970465	−	0.298678i
$690$	−4.96248e6	+	491652.i	−0.396804	+	0.0393129i
$691$	4.93663e6	−	1.51934e7i	0.393310	−	1.21048i	−0.536959	−	0.843608i	$-0.680427\pi$
$691$	4.93663e6	−	1.51934e7i	0.393310	−	1.21048i	0.930270	−	0.366877i	$-0.119573\pi$
$692$	3.45672e6	+	2.51146e6i	0.274410	+	0.199370i
$693$	−2.42521e6			−0.191830
$694$	1.04869e7	+	7.61919e6i	0.826512	+	0.600496i
$695$	283595.	−	252302.i	0.0222709	−	0.0198134i
$696$	−465984.	+	338557.i	−0.0364626	+	0.0264916i
$697$	1.92448e6	−	1.39822e6i	0.150048	−	0.109017i
$698$	4.87091e6	+	1.49911e7i	0.378418	+	1.16465i
$699$	2.57289e6			0.199172
$700$	853373.	−	7.28207e6i	0.0658254	−	0.561707i
$701$	203427.			0.0156356			0.00781779	−	0.999969i	$-0.497511\pi$
$701$	203427.			0.0156356			0.00781779	+	0.999969i	$0.497511\pi$
$702$	317629.	+	977561.i	0.0243264	+	0.0748689i
$703$	−439747.	+	319495.i	−0.0335594	+	0.0243823i
$704$	676606.	−	491583.i	0.0514523	−	0.0373823i
$705$	4.11316e6	−	407506.i	0.311675	−	0.0308789i
$706$	−6.20858e6	−	4.51080e6i	−0.468792	−	0.340597i
$707$	−2.70584e7			−2.03589
$708$	1.68713e6	+	1.22577e6i	0.126492	+	0.0919022i
$709$	−6.97164e6	+	2.14565e7i	−0.520858	+	1.60304i	0.251507	+	0.967856i	$0.419074\pi$
$709$	−6.97164e6	+	2.14565e7i	−0.520858	+	1.60304i	−0.772364	+	0.635180i	$0.780926\pi$
$710$	−3.73524e6	+	1.70713e7i	−0.278082	+	1.27093i
$711$	−152445.	−	469179.i	−0.0113094	−	0.0348068i
$712$	−14784.3	+	45501.4i	−0.00109295	+	0.00336376i
$713$	−4.65827e6	+	1.43367e7i	−0.343163	+	1.05615i
$714$	−331509.	−	1.02028e6i	−0.0243360	−	0.0748986i
$715$	1.61450e6	+	3.68526e6i	0.118106	+	0.269590i
$716$	3.03549e6	−	9.34227e6i	0.221282	−	0.681036i
$717$	8.88897e6	+	6.45821e6i	0.645734	+	0.469153i
$718$	−4.27026e6			−0.309132
$719$	−1.81274e7	−	1.31703e7i	−1.30771	−	0.950110i	−0.307715	−	0.951479i	$-0.599564\pi$
$719$	−1.81274e7	−	1.31703e7i	−1.30771	−	0.950110i	−0.999999	+	0.00136898i	$0.999564\pi$
$720$	247769.	−	1.13239e6i	0.0178121	−	0.0814074i
$721$	−1.46384e7	+	1.06354e7i	−1.04871	+	0.761932i
$722$	−7.88846e6	+	5.73130e6i	−0.563183	+	0.409176i
$723$	4.26998e6	+	1.31417e7i	0.303795	+	0.934984i
$724$	−6.03097e6			−0.427603
$725$	−363716.	+	3.10369e6i	−0.0256991	+	0.219298i
$726$	4.29698e6			0.302567
$727$	2.72100e6	+	8.37439e6i	0.190938	+	0.587648i	1.00000		7.58761e-5i	$-2.41521e-5\pi$
$727$	2.72100e6	+	8.37439e6i	0.190938	+	0.587648i	−0.809062	+	0.587724i	$0.800024\pi$
$728$	−2.67630e6	+	1.94444e6i	−0.187157	+	0.135977i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	2.18827e6	+	1.28087e6i	0.151983	+	0.0889608i
$731$	−316202.	−	229734.i	−0.0218862	−	0.0159013i
$732$	7.58218e6			0.523018
$733$	−7.85695e6	−	5.70841e6i	−0.540125	−	0.392423i	0.284007	−	0.958822i	$-0.408336\pi$
$733$	−7.85695e6	−	5.70841e6i	−0.540125	−	0.392423i	−0.824131	+	0.566399i	$0.808336\pi$
$734$	1.92370e6	−	5.92053e6i	0.131794	−	0.405621i
$735$	−2.03889e6	−	1.19343e6i	−0.139211	−	0.0814854i
$736$	−784105.	−	2.41323e6i	−0.0533556	−	0.164212i
$737$	3.00020e6	−	9.23366e6i	0.203461	−	0.626189i
$738$	1.17198e6	−	3.60698e6i	0.0792097	−	0.243783i
$739$	−2.32111e6	−	7.14363e6i	−0.156345	−	0.481180i	0.841950	−	0.539556i	$-0.181408\pi$
$739$	−2.32111e6	−	7.14363e6i	−0.156345	−	0.481180i	−0.998295	+	0.0583757i	$0.981408\pi$
$740$	−1.85286e6	+	1.64841e6i	−0.124384	+	0.110659i
$741$	−192183.	+	591479.i	−0.0128579	+	0.0395726i
$742$	5.26817e6	+	3.82755e6i	0.351277	+	0.255218i
$743$	1.83814e7			1.22154			0.610768	−	0.791810i	$-0.290861\pi$
$743$	1.83814e7			1.22154			0.610768	+	0.791810i	$0.290861\pi$
$744$	−2.83485e6	−	2.05964e6i	−0.187758	−	0.136414i
$745$	1.92060e6	+	4.38397e6i	0.126779	+	0.289385i
$746$	−6.97045e6	+	5.06433e6i	−0.458578	+	0.333177i
$747$	−882275.	+	641011.i	−0.0578499	+	0.0420304i
$748$	−205156.	−	631405.i	−0.0134070	−	0.0412624i
$749$	−1.03049e7			−0.671182
$750$	−3.60486e6	−	5.15323e6i	−0.234011	−	0.334523i
$751$	−6.82366e6			−0.441487			−0.220743	−	0.975332i	$-0.570848\pi$
$751$	−6.82366e6			−0.441487			−0.220743	+	0.975332i	$0.570848\pi$
$752$	649907.	+	2.00021e6i	0.0419089	+	0.128982i
$753$	−9.38106e6	+	6.81574e6i	−0.602927	+	0.438052i
$754$	1.14067e6	−	828742.i	0.0730685	−	0.0530874i
$755$	3.10521e6	+	7.08796e6i	0.198255	+	0.452537i
$756$	−1.38373e6	−	1.00534e6i	−0.0880536	−	0.0639747i
$757$	−2.40172e7			−1.52329			−0.761647	−	0.647993i	$-0.775609\pi$
$757$	−2.40172e7			−1.52329			−0.761647	+	0.647993i	$0.775609\pi$
$758$	1.21581e7	+	8.83339e6i	0.768588	+	0.558412i
$759$	−1.40713e6	+	4.33071e6i	−0.0886606	+	0.272869i
$760$	524009.	−	466187.i	0.0329083	−	0.0292770i
$761$	1.57168e6	+	4.83712e6i	0.0983788	+	0.302779i	0.988120	−	0.153688i	$-0.0491149\pi$
$761$	1.57168e6	+	4.83712e6i	0.0983788	+	0.302779i	−0.889741	+	0.456466i	$0.849115\pi$
$762$	1.59139e6	−	4.89779e6i	0.0992863	−	0.305572i
$763$	1.00927e6	−	3.10622e6i	0.0627621	−	0.193162i
$764$	−582039.	−	1.79133e6i	−0.0360760	−	0.111031i
$765$	−794141.	−	464839.i	−0.0490618	−	0.0287176i
$766$	3.09430e6	−	9.52329e6i	0.190542	−	0.586429i
$767$	−4.12986e6	−	3.00052e6i	−0.253482	−	0.184165i
$768$	589824.			0.0360844
$769$	−1.41276e7	−	1.02643e7i	−0.861493	−	0.625912i	0.0667975	−	0.997767i	$-0.478722\pi$
$769$	−1.41276e7	−	1.02643e7i	−0.861493	−	0.625912i	−0.928291	+	0.371855i	$0.878722\pi$
$770$	−5.77795e6	−	3.38204e6i	−0.351194	−	0.205566i
$771$	−6.15686e6	+	4.47322e6i	−0.373013	+	0.271010i
$772$	−7.60633e6	+	5.52633e6i	−0.459338	+	0.333728i
$773$	3.00957e6	+	9.26252e6i	0.181157	+	0.557545i	0.999861	−	0.0166710i	$-0.00530679\pi$
$773$	3.00957e6	+	9.26252e6i	0.181157	+	0.557545i	−0.818704	+	0.574216i	$0.805307\pi$
$774$	−623144.			−0.0373883
$775$	−1.86412e7	+	3.73033e6i	−1.11486	+	0.223097i
$776$	5.44473e6			0.324580
$777$	1.13077e6	+	3.48017e6i	0.0671929	+	0.206798i
$778$	1.30169e7	−	9.45734e6i	0.771008	−	0.560170i
$779$	1.85648e6	−	1.34881e6i	0.109609	−	0.0796357i
$780$	−606506.	+	2.77193e6i	−0.0356943	+	0.163135i
$781$	1.29096e7	+	9.37937e6i	0.757330	+	0.550232i
$782$	−2.01426e6			−0.117787
$783$	589761.	+	428486.i	0.0343773	+	0.0249766i
$784$	371470.	−	1.14327e6i	0.0215841	−	0.0664290i
$785$	1.14942e7	+	2.62366e7i	0.665737	+	1.51961i
$786$	3.24259e6	+	9.97965e6i	0.187213	+	0.576181i
$787$	−148582.	+	457288.i	−0.00855124	+	0.0263180i	−0.955241	−	0.295828i	$-0.904404\pi$
$787$	−148582.	+	457288.i	−0.00855124	+	0.0263180i	0.946690	+	0.322146i	$0.104404\pi$
$788$	1.60924e6	−	4.95272e6i	0.0923217	−	0.284137i
$789$	2.63111e6	+	8.09772e6i	0.150469	+	0.463095i
$790$	291091.	−	1.33039e6i	0.0165944	−	0.0758420i
$791$	8.67658e6	−	2.67038e7i	0.493068	−	1.51751i
$792$	−856330.	−	622160.i	−0.0485097	−	0.0352443i
$793$	−1.85602e7			−1.04809
$794$	−2.65938e6	−	1.93215e6i	−0.149702	−	0.108765i
$795$	5.55830e6	−	550682.i	0.311906	−	0.0309017i
$796$	−1.88470e6	+	1.36931e6i	−0.105429	+	0.0765984i
$797$	−3.65649e6	+	2.65660e6i	−0.203901	+	0.148143i	−0.685050	−	0.728496i	$-0.740220\pi$
$797$	−3.65649e6	+	2.65660e6i	−0.203901	+	0.148143i	0.481149	+	0.876639i	$0.340220\pi$
$798$	−319795.	−	984229.i	−0.0177773	−	0.0547128i
$799$	1.66952e6			0.0925178
$800$	2.16945e6	−	2.35234e6i	0.119846	−	0.129949i
$801$	60551.3			0.00333459
$802$	−5.53445e6	−	1.70333e7i	−0.303836	−	0.935110i
$803$	1.87313e6	−	1.36091e6i	0.102513	−	0.0744801i
$804$	5.53948e6	−	4.02467e6i	0.302224	−	0.219579i
$805$	−1.51760e7	+	1.35014e7i	−0.825405	+	0.734326i
$806$	6.93934e6	+	5.04173e6i	0.376254	+	0.273364i
$807$	1.08586e7			0.586936
$808$	−9.55417e6	−	6.94151e6i	−0.514831	−	0.374047i
$809$	−4.75444e6	+	1.46327e7i	−0.255404	+	0.786054i	0.738345	+	0.674423i	$0.235607\pi$
$809$	−4.75444e6	+	1.46327e7i	−0.255404	+	0.786054i	−0.993750	+	0.111631i	$0.964393\pi$
$810$	−1.45994e6	+	144642.i	−0.0781846	+	0.00774605i
$811$	2.55676e6	+	7.86889e6i	0.136502	+	0.420108i	0.995821	−	0.0913315i	$-0.0291123\pi$
$811$	2.55676e6	+	7.86889e6i	0.136502	+	0.420108i	−0.859319	+	0.511440i	$0.829112\pi$
$812$	−725003.	+	2.23133e6i	−0.0385878	+	0.118761i
$813$	32278.3	−	99342.5i	0.00171271	−	0.00527119i
$814$	699786.	+	2.15372e6i	0.0370173	+	0.113927i
$815$	1.09567e7	−	1.08553e6i	0.577813	−	0.0572462i
$816$	144687.	−	445300.i	0.00760682	−	0.0234114i
$817$	−305030.	−	221617.i	−0.0159877	−	0.0116158i
$818$	2.08019e7			1.08697
$819$	3.38719e6	+	2.46094e6i	0.176453	+	0.128201i
$820$	7.82223e6	−	6.95908e6i	0.406252	−	0.361424i
$821$	1.03952e7	−	7.55252e6i	0.538236	−	0.391052i	−0.285193	−	0.958470i	$-0.592058\pi$
$821$	1.03952e7	−	7.55252e6i	0.538236	−	0.391052i	0.823430	+	0.567418i	$0.192058\pi$
$822$	8.03119e6	−	5.83500e6i	0.414572	−	0.301205i
$823$	−4.32731e6	−	1.33181e7i	−0.222699	−	0.685398i	−0.998517	−	0.0544408i	$-0.982662\pi$
$823$	−4.32731e6	−	1.33181e7i	−0.222699	−	0.685398i	0.775818	−	0.630957i	$-0.217338\pi$
$824$	−7.89713e6			−0.405183
$825$	−5.63099e6	+	1.12683e6i	−0.288038	+	0.0576399i
$826$	8.49443e6			0.433196
$827$	−4.40613e6	−	1.35607e7i	−0.224024	−	0.689474i	−0.998389	−	0.0567356i	$-0.981931\pi$
$827$	−4.40613e6	−	1.35607e7i	−0.224024	−	0.689474i	0.774366	−	0.632739i	$-0.218069\pi$
$828$	−2.59809e6	+	1.88762e6i	−0.131698	+	0.0956841i
$829$	3.54660e6	−	2.57676e6i	0.179236	−	0.130223i	−0.494550	−	0.869149i	$-0.664667\pi$
$829$	3.54660e6	−	2.57676e6i	0.179236	−	0.130223i	0.673786	+	0.738927i	$0.264667\pi$
$830$	−2.99589e6	+	296814.i	−0.150949	+	0.0149551i
$831$	1.04484e7	+	7.59119e6i	0.524863	+	0.381336i
$832$	−1.44381e6			−0.0723106
$833$	−772010.	−	560898.i	−0.0385488	−	0.0280073i
$834$	75538.0	−	232482.i	0.00376054	−	0.0115738i
$835$	162635.	−	743296.i	0.00807231	−	0.0368931i
$836$	−197907.	−	609096.i	−0.00979368	−	0.0301418i
$837$	−1.37044e6	+	4.21778e6i	−0.0676156	+	0.208099i
$838$	2.98909e6	−	9.19947e6i	0.147038	−	0.452535i
$839$	−3.59574e6	−	1.10666e7i	−0.176353	−	0.542760i	0.823339	−	0.567549i	$-0.192108\pi$
$839$	−3.59574e6	−	1.10666e7i	−0.176353	−	0.542760i	−0.999693	+	0.0247897i	$0.992108\pi$
$840$	−1.89469e6	−	4.32483e6i	−0.0926489	−	0.211481i
$841$	−6.02929e6	+	1.85562e7i	−0.293952	+	0.904691i
$842$	3.93348e6	+	2.85784e6i	0.191204	+	0.138918i
$843$	−4.86140e6			−0.235609
$844$	−1.51056e7	−	1.09749e7i	−0.729932	−	0.530327i
$845$	−2.95184e6	+	1.34909e7i	−0.142217	+	0.649979i
$846$	2.15343e6	−	1.56456e6i	0.103444	−	0.0751565i
$847$	1.41601e7	−	1.02879e7i	0.678198	−	0.492740i
$848$	878249.	+	2.70297e6i	0.0419400	+	0.129078i
$849$	−1.59059e7			−0.757335
$850$	−1.24377e6	−	2.21491e6i	−0.0590462	−	0.105150i
$851$	6.87063e6			0.325216
$852$	3.47761e6	+	1.07030e7i	0.164128	+	0.505134i
$853$	1.40170e7	−	1.01840e7i	0.659605	−	0.479231i	−0.206925	−	0.978357i	$-0.566345\pi$
$853$	1.40170e7	−	1.01840e7i	0.659605	−	0.479231i	0.866530	+	0.499126i	$0.166345\pi$
$854$	2.49860e7	−	1.81534e7i	1.17233	−	0.851750i
$855$	−766081.	−	448414.i	−0.0358393	−	0.0209780i
$856$	−3.63861e6	−	2.64361e6i	−0.169727	−	0.123314i
$857$	−1.57412e7			−0.732125			−0.366063	−	0.930590i	$-0.619294\pi$
$857$	−1.57412e7			−0.732125			−0.366063	+	0.930590i	$0.619294\pi$
$858$	2.09618e6	+	1.52296e6i	0.0972099	+	0.0706271i
$859$	6.32200e6	−	1.94571e7i	0.292329	−	0.899695i	−0.691777	−	0.722111i	$-0.743172\pi$
$859$	6.32200e6	−	1.94571e7i	0.292329	−	0.899695i	0.984106	−	0.177584i	$-0.0568281\pi$
$860$	−1.48461e6	−	868995.i	−0.0684489	−	0.0400656i
$861$	−4.77379e6	−	1.46922e7i	−0.219460	−	0.675429i
$862$	−88488.6	+	272340.i	−0.00405620	+	0.0124837i
$863$	6.35348e6	−	1.95540e7i	0.290392	−	0.893734i	−0.694339	−	0.719648i	$-0.744303\pi$
$863$	6.35348e6	−	1.95540e7i	0.290392	−	0.893734i	0.984730	−	0.174086i	$-0.0556970\pi$
$864$	−230680.	−	709960.i	−0.0105130	−	0.0323556i
$865$	1.11533e7	−	9.92263e6i	0.506833	−	0.450907i
$866$	896604.	−	2.75946e6i	0.0406262	−	0.125035i
$867$	1.00375e7	+	7.29267e6i	0.453501	+	0.329487i
$868$	−1.42731e7			−0.643010
$869$	−1.00606e6	−	730944.i	−0.0451933	−	0.0328348i
$870$	807538.	+	1.84329e6i	0.0361713	+	0.0825648i
$871$	−1.35599e7	+	9.85185e6i	−0.605636	+	0.440020i
$872$	1.15323e6	−	837873.i	0.0513601	−	0.0373153i
$873$	−2.12943e6	−	6.55372e6i	−0.0945645	−	0.291040i
$874$	−1.94309e6			−0.0860427
$875$	−2.42172e7	−	8.35088e6i	−1.06931	−	0.368733i
$876$	1.63288e6			0.0718943
$877$	8.35473e6	+	2.57132e7i	0.366803	+	1.12891i	0.948844	+	0.315745i	$0.102254\pi$
$877$	8.35473e6	+	2.57132e7i	0.366803	+	1.12891i	−0.582041	+	0.813160i	$0.697746\pi$
$878$	1.29485e7	−	9.40763e6i	0.566869	−	0.411855i
$879$	−5.36859e6	+	3.90051e6i	−0.234363	+	0.170274i
$880$	−1.17254e6	−	2.67645e6i	−0.0510413	−	0.116507i
$881$	−1.18666e7	−	8.62158e6i	−0.515093	−	0.374237i	0.299659	−	0.954046i	$-0.403127\pi$
$881$	−1.18666e7	−	8.62158e6i	−0.515093	−	0.374237i	−0.814752	+	0.579809i	$0.803127\pi$
$882$	−1.52141e6			−0.0658530
$883$	−2.45432e7	−	1.78317e7i	−1.05932	−	0.769645i	−0.0853615	−	0.996350i	$-0.527205\pi$
$883$	−2.45432e7	−	1.78317e7i	−1.05932	−	0.769645i	−0.973963	+	0.226706i	$0.927205\pi$
$884$	−354173.	+	1.09003e6i	−0.0152435	+	0.0469147i
$885$	5.44363e6	−	4.84295e6i	0.233631	−	0.207851i
$886$	2.81669e6	+	8.66889e6i	0.120547	+	0.371005i
$887$	1.37448e7	−	4.23022e7i	0.586584	−	1.80532i	−0.00623124	−	0.999981i	$-0.501983\pi$
$887$	1.37448e7	−	4.23022e7i	0.586584	−	1.80532i	0.592815	−	0.805339i	$-0.298017\pi$
$888$	−493525.	+	1.51891e6i	−0.0210028	+	0.0646399i
$889$	−6.48217e6	−	1.99501e7i	−0.275085	−	0.846623i
$890$	144260.	+	84440.8i	0.00610481	+	0.00357336i
$891$	−413972.	+	1.27407e6i	−0.0174693	+	0.0537651i
$892$	1.61229e7	+	1.17140e7i	0.678470	+	0.492937i
$893$	1.61053e6			0.0675835
$894$	2.49360e6	+	1.81171e6i	0.104348	+	0.0758132i
$895$	−2.96193e7	−	1.73372e7i	−1.23600	−	0.723473i
$896$	1.94368e6	−	1.41216e6i	0.0808824	−	0.0587645i
$897$	6.35978e6	−	4.62065e6i	0.263913	−	0.191744i
$898$	−9.65413e6	−	2.97124e7i	−0.399505	−	1.22955i
$899$	6.08333e6			0.251039
$900$	−3.67993e6	−	1.69133e6i	−0.151438	−	0.0696020i
$901$	2.25610e6			0.0925863
$902$	−2.95429e6	−	9.09237e6i	−0.120903	−	0.372101i
$903$	−2.05348e6	+	1.49194e6i	−0.0838052	+	0.0608881i
$904$	9.91418e6	−	7.20308e6i	0.403493	−	0.293155i
$905$	−4.50391e6	+	2.05844e7i	−0.182797	+	0.835442i
$906$	4.03164e6	+	2.92916e6i	0.163178	+	0.118556i
$907$	−2.02999e7			−0.819363			−0.409682	−	0.912229i	$-0.634360\pi$
$907$	−2.02999e7			−0.819363			−0.409682	+	0.912229i	$0.634360\pi$
$908$	−1.20010e7	−	8.71921e6i	−0.483060	−	0.350964i
$909$	−4.61873e6	+	1.42150e7i	−0.185401	+	0.570607i
$910$	4.63795e6	+	1.05866e7i	0.185662	+	0.423792i
$911$	4.12204e6	+	1.26863e7i	0.164557	+	0.506454i	0.999003	−	0.0446347i	$-0.0142124\pi$
$911$	4.12204e6	+	1.26863e7i	0.164557	+	0.506454i	−0.834446	+	0.551089i	$0.814212\pi$
$912$	139574.	−	429566.i	0.00555672	−	0.0171018i
$913$	−849498.	+	2.61449e6i	−0.0337276	+	0.103803i
$914$	2.70855e6	+	8.33607e6i	0.107244	+	0.330062i
$915$	5.66235e6	−	2.58788e7i	0.223586	−	1.02186i
$916$	2.85801e6	−	8.79604e6i	0.112545	−	0.346377i
$917$	3.45789e7	+	2.51230e7i	1.35796	+	0.986617i
$918$	−592585.			−0.0232084
$919$	−3.14137e7	−	2.28234e7i	−1.22696	−	0.891439i	−0.230302	−	0.973119i	$-0.573971\pi$
$919$	−3.14137e7	−	2.28234e7i	−1.22696	−	0.891439i	−0.996659	+	0.0816801i	$0.973971\pi$
$920$	−8.82218e6	+	874047.i	−0.343642	+	0.0340459i
$921$	−2.03151e6	+	1.47598e6i	−0.0789169	+	0.0573365i
$922$	−8.00582e6	+	5.81657e6i	−0.310155	+	0.225341i
$923$	−8.51273e6	−	2.61995e7i	−0.328901	−	1.01225i
$924$	−4.31149e6			−0.166130
$925$	4.24248e6	+	7.55504e6i	0.163029	+	0.290324i
$926$	1.47750e7			0.566240
$927$	3.08856e6	+	9.50562e6i	0.118048	+	0.363313i
$928$	−828416.	+	601879.i	−0.0315775	+	0.0229424i
$929$	−2.36067e7	+	1.71513e7i	−0.897422	+	0.652015i	−0.937803	−	0.347169i	$-0.887143\pi$
$929$	−2.36067e7	+	1.71513e7i	−0.897422	+	0.652015i	0.0403806	+	0.999184i	$0.487143\pi$
$930$	−9.14684e6	+	8.13754e6i	−0.346788	+	0.308522i
$931$	−744732.	−	541080.i	−0.0281596	−	0.0204591i
$932$	4.57404e6			0.172488
$933$	−1.26456e7	−	9.18756e6i	−0.475593	−	0.345538i
$934$	−7.62271e6	+	2.34603e7i	−0.285919	+	0.879967i
$935$	−2.30827e6	+	228689.i	−0.0863489	+	0.00855492i
$936$	564674.	+	1.73789e6i	0.0210673	+	0.0648383i
$937$	1.57246e7	−	4.83953e7i	0.585100	−	1.80075i	−0.0137703	−	0.999905i	$-0.504383\pi$
$937$	1.57246e7	−	4.83953e7i	0.585100	−	1.80075i	0.598870	−	0.800846i	$-0.295617\pi$
$938$	8.61863e6	−	2.65254e7i	0.319839	−	0.984362i
$939$	3.65969e6	+	1.12634e7i	0.135451	+	0.416874i
$940$	7.31228e6	−	724456.i	0.269919	−	0.0267419i
$941$	−2.95057e6	+	9.08091e6i	−0.108625	+	0.334315i	−0.990564	−	0.137049i	$-0.956238\pi$
$941$	−2.95057e6	+	9.08091e6i	−0.108625	+	0.334315i	0.881939	+	0.471364i	$0.156238\pi$
$942$	1.49234e7	+	1.08425e7i	0.547949	+	0.398109i
$943$	−2.90057e7			−1.06220
$944$	2.99934e6	+	2.17915e6i	0.109546	+	0.0795896i
$945$	−4.46470e6	+	3.97204e6i	−0.162635	+	0.144689i
$946$	−1.27081e6	+	923296.i	−0.0461692	+	0.0335439i
$947$	−3.34955e6	+	2.43359e6i	−0.121370	+	0.0881804i	−0.646814	−	0.762648i	$-0.723899\pi$
$947$	−3.34955e6	+	2.43359e6i	−0.121370	+	0.0881804i	0.525444	+	0.850828i	$0.323899\pi$
$948$	−271014.	−	834096.i	−0.00979425	−	0.0301436i
$949$	−3.99708e6			−0.144071
$950$	−1.19982e6	−	2.13665e6i	−0.0431328	−	0.0768111i
$951$	1.11311e7			0.399104
$952$	−589349.	−	1.81383e6i	−0.0210756	−	0.0648641i
$953$	1.69679e7	−	1.23279e7i	0.605195	−	0.439700i	−0.242524	−	0.970145i	$-0.577975\pi$
$953$	1.69679e7	−	1.23279e7i	0.605195	−	0.439700i	0.847719	+	0.530445i	$0.177975\pi$
$954$	2.91003e6	−	2.11426e6i	0.103521	−	0.0752122i
$955$	−6.54868e6	+	648803.i	−0.232351	+	0.0230200i
$956$	1.58026e7	+	1.14813e7i	0.559222	+	0.406299i
$957$	1.83760e6			0.0648592
$958$	−5.10817e6	−	3.71131e6i	−0.179826	−	0.130651i
$959$	1.24954e7	−	3.84568e7i	0.438735	−	1.35029i
$960$	440479.	−	2.01313e6i	0.0154258	−	0.0705009i
$961$	2.58935e6	+	7.96920e6i	0.0904445	+	0.278359i
$962$	1.20808e6	−	3.71810e6i	0.0420881	−	0.129534i
$963$	−1.75900e6	+	5.41364e6i	−0.0611223	+	0.188115i
$964$	7.59108e6	+	2.33629e7i	0.263094	+	0.809720i
$965$	1.31816e7	+	3.00883e7i	0.455669	+	1.04011i
$966$	−4.04225e6	+	1.24408e7i	−0.139374	+	0.428948i
$967$	4.14162e7	+	3.00907e7i	1.42431	+	1.03482i	0.991041	+	0.133557i	$0.0426400\pi$
$967$	4.14162e7	+	3.00907e7i	1.42431	+	1.03482i	0.433269	+	0.901265i	$0.357360\pi$
$968$	7.63907e6			0.262031
$969$	−290071.	−	210749.i	−0.00992418	−	0.00721034i
$970$	4.06611e6	−	1.85835e7i	0.138755	−	0.634158i
$971$	8.63241e6	−	6.27181e6i	0.293822	−	0.213474i	−0.431102	−	0.902303i	$-0.641875\pi$
$971$	8.63241e6	−	6.27181e6i	0.293822	−	0.213474i	0.724924	+	0.688829i	$0.241875\pi$
$972$	−764346.	+	555330.i	−0.0259492	+	0.0188532i
$973$	−307687.	−	946964.i	−0.0104190	−	0.0320665i
$974$	−159958.			−0.00540267
$975$	9.00798e6	+	4.14014e6i	0.303470	+	0.139477i
$976$	1.34794e7			0.452947
$977$	1.68919e7	+	5.19879e7i	0.566163	+	1.74247i	0.664470	+	0.747315i	$0.268657\pi$
$977$	1.68919e7	+	5.19879e7i	0.566163	+	1.74247i	−0.0983066	+	0.995156i	$0.531343\pi$
$978$	5.73638e6	−	4.16772e6i	0.191774	−	0.139332i
$979$	123485.	−	89717.2i	0.00411773	−	0.00299171i
$980$	−3.62469e6	−	2.12166e6i	−0.120561	−	0.0705684i
$981$	−1.45956e6	−	1.06043e6i	−0.0484228	−	0.0351812i
$982$	−3.90212e7			−1.29128
$983$	1.76374e7	+	1.28144e7i	0.582173	+	0.422973i	0.839507	−	0.543349i	$-0.182844\pi$
$983$	1.76374e7	+	1.28144e7i	0.582173	+	0.422973i	−0.257334	+	0.966323i	$0.582844\pi$
$984$	2.08352e6	−	6.41241e6i	0.0685977	−	0.211122i
$985$	−1.57024e7	−	9.19117e6i	−0.515674	−	0.301842i
$986$	251187.	+	773073.i	0.00822819	+	0.0253238i
$987$	3.35043e6	−	1.03116e7i	0.109473	−	0.336924i
$988$	−341659.	+	1.05152e6i	−0.0111353	+	0.0342708i
$989$	1.47271e6	+	4.53254e6i	0.0478770	+	0.147350i
$990$	−2.76301e6	+	2.45812e6i	−0.0895971	+	0.0797105i
$991$	−1.73928e7	+	5.35296e7i	−0.562582	+	1.73145i	0.112446	+	0.993658i	$0.464132\pi$
$991$	−1.73928e7	+	5.35296e7i	−0.562582	+	1.73145i	−0.675028	+	0.737792i	$0.735868\pi$
$992$	−5.03974e6	−	3.66159e6i	−0.162603	−	0.118138i
$993$	5.95479e6			0.191643
$994$	3.70852e7	+	2.69440e7i	1.19051	+	0.864960i
$995$	3.26613e6	+	7.45527e6i	0.104586	+	0.238729i
$996$	−1.56849e6	+	1.13957e6i	−0.0500995	+	0.0363994i
$997$	4.06730e7	−	2.95507e7i	1.29589	−	0.941521i	0.295986	−	0.955192i	$-0.404352\pi$
$997$	4.06730e7	−	2.95507e7i	1.29589	−	0.941521i	0.999907	+	0.0136717i	$0.00435197\pi$
$998$	−1.17530e7	−	3.61720e7i	−0.373527	−	1.14960i
$999$	2.02131e6			0.0640794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.c.31.4	✓	24
25.21	even	5	inner	150.6.g.c.121.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.c.31.4	✓	24	1.1	even	1	trivial
150.6.g.c.121.4	yes	24	25.21	even	5	inner

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)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(22.4321 + 51.2035i) q^{5} +(29.1246 + 21.1603i) q^{6} +146.638 q^{7} +(51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(22.4321 + 51.2035i) q^{5} +(29.1246 + 21.1603i) q^{6} +146.638 q^{7} +(51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(167.062 - 148.628i) q^{10} +(-63.0959 - 194.189i) q^{11} +(44.4984 - 136.952i) q^{12} +(-108.926 + 335.241i) q^{13} +(-181.255 - 557.844i) q^{14} +(-434.202 - 254.154i) q^{15} +(79.1084 - 243.470i) q^{16} +(-164.407 - 119.449i) q^{17} -324.000 q^{18} +(-158.598 - 115.228i) q^{19} +(-771.914 - 451.829i) q^{20} +(-1067.69 + 775.725i) q^{21} +(-660.748 + 480.062i) q^{22} +(765.728 + 2356.67i) q^{23} -576.000 q^{24} +(-2118.60 + 2297.20i) q^{25} +1409.97 q^{26} +(225.273 + 693.320i) q^{27} +(-1898.12 + 1379.07i) q^{28} +(809.000 - 587.773i) q^{29} +(-430.155 + 1965.95i) q^{30} +(4921.62 + 3575.77i) q^{31} -1024.00 q^{32} +(1486.68 + 1080.14i) q^{33} +(-251.192 + 773.090i) q^{34} +(3289.40 + 7508.39i) q^{35} +(400.486 + 1232.57i) q^{36} +(856.814 - 2637.00i) q^{37} +(-242.317 + 745.774i) q^{38} +(-980.336 - 3017.16i) q^{39} +(-764.720 + 3495.03i) q^{40} +(-3617.22 + 11132.6i) q^{41} +(4270.78 + 3102.90i) q^{42} +1923.29 q^{43} +(2642.99 + 1920.25i) q^{44} +(4505.98 - 446.424i) q^{45} +(8018.80 - 5826.00i) q^{46} +(-6646.40 + 4828.89i) q^{47} +(711.975 + 2191.23i) q^{48} +4695.72 q^{49} +(11357.8 + 5220.15i) q^{50} +1828.97 q^{51} +(-1742.82 - 5363.85i) q^{52} +(-8981.59 + 6525.50i) q^{53} +(2359.09 - 1713.98i) q^{54} +(8527.80 - 7586.80i) q^{55} +(7592.49 + 5516.27i) q^{56} +1764.34 q^{57} +(-3236.00 - 2351.09i) q^{58} +(-4475.18 + 13773.2i) q^{59} +(8010.63 - 793.644i) q^{60} +(16271.0 + 50077.0i) q^{61} +(7519.57 - 23142.8i) q^{62} +(3670.41 - 11296.3i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-19608.9 + 1942.73i) q^{65} +(2271.45 - 6990.81i) q^{66} +(38468.6 + 27949.1i) q^{67} +3251.50 q^{68} +(-18042.3 - 13108.5i) q^{69} +(24497.7 - 21794.5i) q^{70} +(-63225.8 + 45936.2i) q^{71} +(4193.94 - 3047.08i) q^{72} +(3504.08 + 10784.5i) q^{73} -11090.8 q^{74} +(3273.52 - 27933.8i) q^{75} +3136.61 q^{76} +(-9252.25 - 28475.5i) q^{77} +(-10266.2 + 7458.84i) q^{78} +(4927.25 - 3579.86i) q^{79} +(14241.1 - 1410.92i) q^{80} +(-5307.96 - 3856.46i) q^{81} +46822.2 q^{82} +(-10892.3 - 7913.71i) q^{83} +(6525.17 - 20082.4i) q^{84} +(2428.21 - 11097.7i) q^{85} +(-2377.31 - 7316.61i) q^{86} +(-2781.09 + 8559.33i) q^{87} +(4038.13 - 12428.1i) q^{88} +(231.005 + 710.959i) q^{89} +(-7267.99 - 16589.9i) q^{90} +(-15972.7 + 49159.0i) q^{91} +(-32075.2 - 23304.0i) q^{92} -54751.1 q^{93} +(26585.6 + 19315.6i) q^{94} +(2342.41 - 10705.6i) q^{95} +(7455.90 - 5417.03i) q^{96} +(68826.2 - 50005.2i) q^{97} +(-5804.22 - 17863.6i) q^{98} -16538.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Introduction

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