LMFDB - Embedded newform 150.6.g.b.121.1

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			121.1
Character	$\chi$	$=$	150.121
Dual form			150.6.g.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 - 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.5966 + 5.83204i) q^{5} +(-29.1246 + 21.1603i) q^{6} -184.364 q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(1.23607 - 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.5966 + 5.83204i) q^{5} +(-29.1246 + 21.1603i) q^{6} -184.364 q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-46.5348 + 218.711i) q^{10} +(-0.761061 + 2.34231i) q^{11} +(44.4984 + 136.952i) q^{12} +(-50.6926 - 156.016i) q^{13} +(-227.886 + 701.361i) q^{14} +(435.660 + 251.646i) q^{15} +(79.1084 + 243.470i) q^{16} +(983.698 - 714.698i) q^{17} +324.000 q^{18} +(-57.1750 + 41.5401i) q^{19} +(774.506 + 447.371i) q^{20} +(1342.38 + 975.296i) q^{21} +(7.96994 + 5.79050i) q^{22} +(-197.717 + 608.509i) q^{23} +576.000 q^{24} +(3056.97 - 648.484i) q^{25} -656.179 q^{26} +(225.273 - 693.320i) q^{27} +(2386.45 + 1733.86i) q^{28} +(-580.413 - 421.695i) q^{29} +(1495.82 - 1346.30i) q^{30} +(-3425.10 + 2488.48i) q^{31} +1024.00 q^{32} +(17.9324 - 13.0286i) q^{33} +(-1502.96 - 4625.62i) q^{34} +(10250.0 - 1075.22i) q^{35} +(400.486 - 1232.57i) q^{36} +(328.461 + 1010.90i) q^{37} +(87.3556 + 268.853i) q^{38} +(-456.234 + 1404.14i) q^{39} +(2659.24 - 2393.42i) q^{40} +(806.764 + 2482.97i) q^{41} +(5369.52 - 3901.18i) q^{42} +21189.4 q^{43} +(31.8797 - 23.1620i) q^{44} +(-1840.88 - 4136.94i) q^{45} +(2070.51 + 1504.32i) q^{46} +(-8436.44 - 6129.43i) q^{47} +(711.975 - 2191.23i) q^{48} +17182.9 q^{49} +(1311.65 - 12431.0i) q^{50} -10943.3 q^{51} +(-811.082 + 2496.25i) q^{52} +(-5257.14 - 3819.54i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(28.6520 - 134.663i) q^{55} +(9545.81 - 6935.44i) q^{56} +636.050 q^{57} +(-2321.65 + 1686.78i) q^{58} +(15886.9 + 48894.8i) q^{59} +(-3272.68 - 7354.56i) q^{60} +(5966.69 - 18363.6i) q^{61} +(5233.09 + 16105.8i) q^{62} +(-4614.69 - 14202.6i) q^{63} +(1265.73 - 3895.53i) q^{64} +(3728.23 + 8378.32i) q^{65} +(-27.3982 - 84.3230i) q^{66} +(-9250.57 + 6720.93i) q^{67} -19454.7 q^{68} +(4658.66 - 3384.71i) q^{69} +(8579.33 - 40322.4i) q^{70} +(10884.0 + 7907.69i) q^{71} +(-4193.94 - 3047.08i) q^{72} +(14054.4 - 43255.1i) q^{73} +4251.69 q^{74} +(-25688.8 - 11449.9i) q^{75} +1130.75 q^{76} +(140.312 - 431.836i) q^{77} +(4777.74 + 3471.23i) q^{78} +(52893.5 + 38429.4i) q^{79} +(-5818.09 - 13074.8i) q^{80} +(-5307.96 + 3856.46i) q^{81} +10443.0 q^{82} +(-37686.1 + 27380.5i) q^{83} +(-8203.89 - 25249.0i) q^{84} +(-50522.2 + 45471.8i) q^{85} +(26191.5 - 80609.3i) q^{86} +(1995.28 + 6140.85i) q^{87} +(-48.7079 - 149.908i) q^{88} +(-44846.4 + 138023. i) q^{89} +(-18013.3 + 1889.58i) q^{90} +(9345.87 + 28763.6i) q^{91} +(8282.06 - 6017.27i) q^{92} +38102.9 q^{93} +(-33745.8 + 24517.7i) q^{94} +(2936.47 - 2642.94i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(78420.9 + 56976.1i) q^{97} +(21239.3 - 65367.8i) q^{98} -199.490 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$5$	−55.5966	+	5.83204i	−0.994543	+	0.104327i
$5$	−55.5966	+	5.83204i	−0.994543	+	0.104327i
$6$	−29.1246	+	21.1603i	−0.330280	+	0.239962i
$7$	−184.364			−1.42210			−0.711050	−	0.703142i	$-0.751780\pi$
$7$	−184.364			−1.42210			−0.711050	+	0.703142i	$0.751780\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	−46.5348	+	218.711i	−0.147156	+	0.691625i
$11$	−0.761061	+	2.34231i	−0.00189643	+	0.00583663i	−0.952000	−	0.306097i	$-0.900977\pi$
$11$	−0.761061	+	2.34231i	−0.00189643	+	0.00583663i	0.950104	+	0.311934i	$0.100977\pi$
$12$	44.4984	+	136.952i	0.0892055	+	0.274546i
$13$	−50.6926	−	156.016i	−0.0831929	−	0.256041i	0.900804	−	0.434225i	$-0.142978\pi$
$13$	−50.6926	−	156.016i	−0.0831929	−	0.256041i	−0.983997	+	0.178184i	$0.942978\pi$
$14$	−227.886	+	701.361i	−0.310740	+	0.956360i
$15$	435.660	+	251.646i	0.499941	+	0.288777i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	983.698	−	714.698i	0.825542	−	0.599792i	−0.0927522	−	0.995689i	$-0.529566\pi$
$17$	983.698	−	714.698i	0.825542	−	0.599792i	0.918295	+	0.395897i	$0.129566\pi$
$18$	324.000			0.235702
$19$	−57.1750	+	41.5401i	−0.0363347	+	0.0263987i	−0.605804	−	0.795614i	$-0.707149\pi$
$19$	−57.1750	+	41.5401i	−0.0363347	+	0.0263987i	0.569470	+	0.822012i	$0.307149\pi$
$20$	774.506	+	447.371i	0.432962	+	0.250088i
$21$	1342.38	+	975.296i	0.664243	+	0.482601i
$22$	7.96994	+	5.79050i	0.00351074	+	0.00255070i
$23$	−197.717	+	608.509i	−0.0779334	+	0.239854i	−0.982432	−	0.186623i	$-0.940246\pi$
$23$	−197.717	+	608.509i	−0.0779334	+	0.239854i	0.904498	+	0.426477i	$0.140246\pi$
$24$	576.000			0.204124
$25$	3056.97	−	648.484i	0.978232	−	0.207515i
$26$	−656.179			−0.190366
$27$	225.273	−	693.320i	0.0594703	−	0.183031i
$28$	2386.45	+	1733.86i	0.575251	+	0.417945i
$29$	−580.413	−	421.695i	−0.128157	−	0.0931114i	0.521860	−	0.853031i	$-0.325238\pi$
$29$	−580.413	−	421.695i	−0.128157	−	0.0931114i	−0.650017	+	0.759920i	$0.725238\pi$
$30$	1495.82	−	1346.30i	0.303443	−	0.273110i
$31$	−3425.10	+	2488.48i	−0.640131	+	0.465083i	−0.859895	−	0.510470i	$-0.829471\pi$
$31$	−3425.10	+	2488.48i	−0.640131	+	0.465083i	0.219764	+	0.975553i	$0.429471\pi$
$32$	1024.00			0.176777
$33$	17.9324	−	13.0286i	0.00286650	−	0.00208264i
$34$	−1502.96	−	4625.62i	−0.222971	−	0.686235i
$35$	10250.0	−	1075.22i	1.41434	−	0.148363i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	328.461	+	1010.90i	0.0394439	+	0.121396i	0.968840	−	0.247689i	$-0.0796712\pi$
$37$	328.461	+	1010.90i	0.0394439	+	0.121396i	−0.929396	+	0.369085i	$0.879671\pi$
$38$	87.3556	+	268.853i	0.00981368	+	0.0302034i
$39$	−456.234	+	1404.14i	−0.0480314	+	0.147826i
$40$	2659.24	−	2393.42i	0.262789	−	0.236520i
$41$	806.764	+	2482.97i	0.0749527	+	0.230681i	0.981513	−	0.191396i	$-0.0613014\pi$
$41$	806.764	+	2482.97i	0.0749527	+	0.230681i	−0.906560	+	0.422076i	$0.861301\pi$
$42$	5369.52	−	3901.18i	0.469691	−	0.341250i
$43$	21189.4			1.74762			0.873811	−	0.486265i	$-0.161641\pi$
$43$	21189.4			1.74762			0.873811	+	0.486265i	$0.161641\pi$
$44$	31.8797	−	23.1620i	0.00248246	−	0.00180362i
$45$	−1840.88	−	4136.94i	−0.135517	−	0.304543i
$46$	2070.51	+	1504.32i	0.144273	+	0.104820i
$47$	−8436.44	−	6129.43i	−0.557076	−	0.404739i	0.273312	−	0.961926i	$-0.411881\pi$
$47$	−8436.44	−	6129.43i	−0.557076	−	0.404739i	−0.830388	+	0.557186i	$0.811881\pi$
$48$	711.975	−	2191.23i	0.0446028	−	0.137273i
$49$	17182.9			1.02237
$50$	1311.65	−	12431.0i	0.0741980	−	0.703203i
$51$	−10943.3			−0.589144
$52$	−811.082	+	2496.25i	−0.0415965	+	0.128021i
$53$	−5257.14	−	3819.54i	−0.257075	−	0.186776i	0.451781	−	0.892129i	$-0.350789\pi$
$53$	−5257.14	−	3819.54i	−0.257075	−	0.186776i	−0.708857	+	0.705353i	$0.750789\pi$
$54$	−2359.09	−	1713.98i	−0.110093	−	0.0799874i
$55$	28.6520	−	134.663i	0.00127717	−	0.00600262i
$56$	9545.81	−	6935.44i	0.406764	−	0.295532i
$57$	636.050			0.0259301
$58$	−2321.65	+	1686.78i	−0.0906206	+	0.0658397i
$59$	15886.9	+	48894.8i	0.594168	+	1.82866i	0.558826	+	0.829285i	$0.311252\pi$
$59$	15886.9	+	48894.8i	0.594168	+	1.82866i	0.0353413	+	0.999375i	$0.488748\pi$
$60$	−3272.68	−	7354.56i	−0.117361	−	0.263742i
$61$	5966.69	−	18363.6i	0.205309	−	0.631877i	−0.794391	−	0.607407i	$-0.792210\pi$
$61$	5966.69	−	18363.6i	0.205309	−	0.631877i	0.999701	−	0.0244709i	$-0.00779010\pi$
$62$	5233.09	+	16105.8i	0.172894	+	0.532112i
$63$	−4614.69	−	14202.6i	−0.146484	−	0.450832i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	3728.23	+	8378.32i	0.109451	+	0.245965i
$66$	−27.3982	−	84.3230i	−0.000774216	−	0.00238279i
$67$	−9250.57	+	6720.93i	−0.251757	+	0.182912i	−0.706505	−	0.707708i	$-0.749729\pi$
$67$	−9250.57	+	6720.93i	−0.251757	+	0.182912i	0.454748	+	0.890620i	$0.349729\pi$
$68$	−19454.7			−0.510213
$69$	4658.66	−	3384.71i	0.117798	−	0.0855853i
$70$	8579.33	−	40322.4i	0.209271	−	0.983560i
$71$	10884.0	+	7907.69i	0.256237	+	0.186167i	0.708487	−	0.705724i	$-0.249378\pi$
$71$	10884.0	+	7907.69i	0.256237	+	0.186167i	−0.452249	+	0.891892i	$0.649378\pi$
$72$	−4193.94	−	3047.08i	−0.0953436	−	0.0692712i
$73$	14054.4	−	43255.1i	0.308678	−	0.950013i	−0.669601	−	0.742721i	$-0.733535\pi$
$73$	14054.4	−	43255.1i	0.308678	−	0.950013i	0.978279	−	0.207292i	$-0.0664652\pi$
$74$	4251.69			0.0902572
$75$	−25688.8	−	11449.9i	−0.527340	−	0.235043i
$76$	1130.75			0.0224561
$77$	140.312	−	431.836i	0.00269692	−	0.00830026i
$78$	4777.74	+	3471.23i	0.0889172	+	0.0646022i
$79$	52893.5	+	38429.4i	0.953531	+	0.692781i	0.951639	−	0.307217i	$-0.0993979\pi$
$79$	52893.5	+	38429.4i	0.953531	+	0.692781i	0.00189171	+	0.999998i	$0.499398\pi$
$80$	−5818.09	−	13074.8i	−0.101638	−	0.228407i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	10443.0			0.171510
$83$	−37686.1	+	27380.5i	−0.600462	+	0.436261i	−0.846043	−	0.533115i	$-0.821021\pi$
$83$	−37686.1	+	27380.5i	−0.600462	+	0.436261i	0.245581	+	0.969376i	$0.421021\pi$
$84$	−8203.89	−	25249.0i	−0.126859	−	0.390432i
$85$	−50522.2	+	45471.8i	−0.758463	+	0.682645i
$86$	26191.5	−	80609.3i	0.381870	−	1.17527i
$87$	1995.28	+	6140.85i	0.0282622	+	0.0869821i
$88$	−48.7079	−	149.908i	−0.000670491	−	0.00206356i
$89$	−44846.4	+	138023.i	−0.600140	+	1.84704i	−0.0728714	+	0.997341i	$0.523216\pi$
$89$	−44846.4	+	138023.i	−0.600140	+	1.84704i	−0.527268	+	0.849699i	$0.676784\pi$
$90$	−18013.3	+	1889.58i	−0.234416	+	0.0245901i
$91$	9345.87	+	28763.6i	0.118309	+	0.364117i
$92$	8282.06	−	6017.27i	0.102016	−	0.0741190i
$93$	38102.9			0.456826
$94$	−33745.8	+	24517.7i	−0.393912	+	0.286194i
$95$	2936.47	−	2642.94i	0.0333824	−	0.0300454i
$96$	−7455.90	−	5417.03i	−0.0825700	−	0.0599906i
$97$	78420.9	+	56976.1i	0.846257	+	0.614842i	0.924112	−	0.382123i	$-0.124807\pi$
$97$	78420.9	+	56976.1i	0.846257	+	0.614842i	−0.0778542	+	0.996965i	$0.524807\pi$
$98$	21239.3	−	65367.8i	0.223396	−	0.687541i
$99$	−199.490			−0.00204566
$100$	−45669.0	−	20355.4i	−0.456690	−	0.203554i
$101$	−132723.			−1.29462			−0.647311	−	0.762226i	$-0.724106\pi$
$101$	−132723.			−1.29462			−0.647311	+	0.762226i	$0.724106\pi$
$102$	−13526.6	+	41630.6i	−0.128733	+	0.396198i
$103$	16830.1	+	12227.8i	0.156312	+	0.113568i	0.663192	−	0.748449i	$-0.269201\pi$
$103$	16830.1	+	12227.8i	0.156312	+	0.113568i	−0.506880	+	0.862017i	$0.669201\pi$
$104$	8493.76	+	6171.08i	0.0770046	+	0.0559471i
$105$	−80319.8	−	46394.4i	−0.710967	−	0.410669i
$106$	−21028.6	+	15278.2i	−0.181780	+	0.132071i
$107$	−101665.			−0.858447			−0.429224	−	0.903198i	$-0.641213\pi$
$107$	−101665.			−0.858447			−0.429224	+	0.903198i	$0.641213\pi$
$108$	−9436.37	+	6855.93i	−0.0778477	+	0.0565597i
$109$	26591.1	+	81838.9i	0.214373	+	0.659771i	0.999198	+	0.0400537i	$0.0127529\pi$
$109$	26591.1	+	81838.9i	0.214373	+	0.659771i	−0.784825	+	0.619718i	$0.787247\pi$
$110$	−476.872	−	275.451i	−0.00375768	−	0.00217052i
$111$	2956.15	−	9098.09i	0.0227729	−	0.0700879i
$112$	−14584.7	−	44887.1i	−0.109863	−	0.338124i
$113$	−7929.05	−	24403.1i	−0.0584151	−	0.179783i	0.917591	−	0.397525i	$-0.130131\pi$
$113$	−7929.05	−	24403.1i	−0.0584151	−	0.179783i	−0.976006	+	0.217742i	$0.930131\pi$
$114$	786.201	−	2419.68i	0.00566593	−	0.0174379i
$115$	7443.53	−	34984.2i	0.0524849	−	0.246676i
$116$	3547.17	+	10917.1i	0.0244758	+	0.0753287i
$117$	10749.9	−	7810.27i	0.0726006	−	0.0527474i
$118$	205644.			1.35960
$119$	−181358.	+	131764.i	−1.17400	+	0.852964i
$120$	−32023.7	+	3359.26i	−0.203010	+	0.0212956i
$121$	130288.	+	94659.8i	0.808987	+	0.587763i
$122$	−62484.0	−	45397.3i	−0.380075	−	0.276141i
$123$	7260.88	−	22346.7i	0.0432739	−	0.133183i
$124$	67738.5			0.395623
$125$	−166176.	+	53882.0i	−0.951244	+	0.308438i
$126$	−59733.8			−0.335192
$127$	−1129.39	+	3475.92i	−0.00621350	+	0.0191232i	−0.954115	−	0.299440i	$-0.903200\pi$
$127$	−1129.39	+	3475.92i	−0.00621350	+	0.0191232i	0.947902	+	0.318563i	$0.103200\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	−154283.	−	112093.i	−0.816290	−	0.593070i
$130$	36481.4	−	3826.86i	0.189327	−	0.0198603i
$131$	164770.	−	119712.i	0.838880	−	0.609482i	−0.0831774	−	0.996535i	$-0.526507\pi$
$131$	164770.	−	119712.i	0.838880	−	0.609482i	0.922058	+	0.387053i	$0.126507\pi$
$132$	−354.650			−0.00177160
$133$	10541.0	−	7658.48i	0.0516716	−	0.0375416i
$134$	14133.6	+	43498.8i	0.0679972	+	0.209274i
$135$	−8480.97	+	39860.1i	−0.0400508	+	0.188236i
$136$	−24047.3	+	74010.0i	−0.111486	+	0.343118i
$137$	−91747.9	−	282371.i	−0.417633	−	1.28534i	−0.909875	−	0.414883i	$-0.863822\pi$
$137$	−91747.9	−	282371.i	−0.417633	−	1.28534i	0.492242	−	0.870459i	$-0.336178\pi$
$138$	−7117.80	−	21906.3i	−0.0318162	−	0.0979201i
$139$	−71366.6	+	219644.i	−0.313298	+	0.964232i	0.663151	+	0.748485i	$0.269219\pi$
$139$	−71366.6	+	219644.i	−0.313298	+	0.964232i	−0.976449	+	0.215747i	$0.930781\pi$
$140$	−142791.	−	82478.9i	−0.615715	−	0.355650i
$141$	29001.9	+	89258.7i	0.122851	+	0.378096i
$142$	43536.0	−	31630.7i	0.181187	−	0.131640i
$143$	404.017			0.00165219
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	34728.4	+	20059.8i	0.137172	+	0.0792331i
$146$	−147180.	−	106932.i	−0.571434	−	0.415171i
$147$	−125112.	−	90898.9i	−0.477534	−	0.346949i
$148$	5255.37	−	16174.4i	0.0197219	−	0.0606979i
$149$	−425331.			−1.56950			−0.784750	−	0.619813i	$-0.787209\pi$
$149$	−425331.			−1.56950			−0.784750	+	0.619813i	$0.787209\pi$
$150$	−75311.1	+	83573.3i	−0.273294	+	0.303277i
$151$	−394371.			−1.40755			−0.703773	−	0.710425i	$-0.748503\pi$
$151$	−394371.			−1.40755			−0.703773	+	0.710425i	$0.748503\pi$
$152$	1397.69	−	4301.65i	0.00490684	−	0.0151017i
$153$	79679.5	+	57890.6i	0.275181	+	0.199931i
$154$	−1469.37	−	1067.56i	−0.00499262	−	0.00362735i
$155$	175911.	−	158327.i	0.588118	−	0.529328i
$156$	19111.0	−	13884.9i	0.0628740	−	0.0456806i
$157$	262842.			0.851030			0.425515	−	0.904951i	$-0.360093\pi$
$157$	262842.			0.851030			0.425515	+	0.904951i	$0.360093\pi$
$158$	211574.	−	153718.i	0.674248	−	0.489870i
$159$	18072.5	+	55621.3i	0.0566923	+	0.174481i
$160$	−56931.0	+	5972.01i	−0.175812	+	0.0184425i
$161$	36451.7	−	112187.i	0.110829	−	0.341097i
$162$	8109.84	+	24959.5i	0.0242787	+	0.0747221i
$163$	130351.	+	401179.i	0.384278	+	1.18269i	0.937003	+	0.349321i	$0.113588\pi$
$163$	130351.	+	401179.i	0.384278	+	1.18269i	−0.552725	+	0.833364i	$0.686412\pi$
$164$	12908.2	−	39727.4i	0.0374763	−	0.115340i
$165$	−920.995	+	828.930i	−0.00263359	+	0.00237033i
$166$	57579.2	+	177211.i	0.162179	+	0.499136i
$167$	253927.	−	184489.i	0.704559	−	0.511892i	−0.176855	−	0.984237i	$-0.556592\pi$
$167$	253927.	−	184489.i	0.704559	−	0.511892i	0.881414	+	0.472345i	$0.156592\pi$
$168$	−106193.			−0.290285
$169$	278611.	−	202423.i	0.750381	−	0.545184i
$170$	110536.	+	248404.i	0.293347	+	0.659229i
$171$	−4631.17	−	3364.75i	−0.0121116	−	0.00879958i
$172$	−274281.	−	199277.i	−0.706928	−	0.513613i
$173$	143603.	−	441965.i	0.364795	−	1.12272i	−0.585315	−	0.810806i	$-0.699029\pi$
$173$	143603.	−	441965.i	0.364795	−	1.12272i	0.950109	−	0.311917i	$-0.100971\pi$
$174$	25827.5			0.0646709
$175$	−563595.	+	119557.i	−1.39114	+	0.295107i
$176$	−630.488			−0.00153425
$177$	142982.	−	440054.i	0.343043	−	1.05578i
$178$	469637.	+	341212.i	1.11100	+	0.807186i
$179$	586047.	+	425788.i	1.36710	+	0.993255i	0.997957	+	0.0638820i	$0.0203481\pi$
$179$	586047.	+	425788.i	1.36710	+	0.993255i	0.369141	+	0.929373i	$0.379652\pi$
$180$	−15077.3	+	70862.4i	−0.0346850	+	0.163018i
$181$	661850.	−	480862.i	1.50163	−	1.09100i	0.531903	−	0.846805i	$-0.321477\pi$
$181$	661850.	−	480862.i	1.50163	−	1.09100i	0.969727	−	0.244192i	$-0.0785229\pi$
$182$	120976.			0.270719
$183$	−140589.	+	102144.i	−0.310330	+	0.225468i
$184$	−12653.9	−	38944.6i	−0.0275536	−	0.0848013i
$185$	−24156.9	−	54287.0i	−0.0518934	−	0.116618i
$186$	47097.8	−	144952.i	0.0998202	−	0.307215i
$187$	925.388	+	2848.05i	0.00193517	+	0.00595585i
$188$	51558.9	+	158682.i	0.106392	+	0.327441i
$189$	−41532.2	+	127823.i	−0.0845728	+	0.260288i
$190$	−6424.64	−	14437.9i	−0.0129112	−	0.0290148i
$191$	−6405.53	−	19714.2i	−0.0127049	−	0.0391017i	0.944503	−	0.328503i	$-0.106544\pi$
$191$	−6405.53	−	19714.2i	−0.0127049	−	0.0391017i	−0.957208	+	0.289401i	$0.906544\pi$
$192$	−29823.6	+	21668.1i	−0.0583858	+	0.0424197i
$193$	669281.			1.29335			0.646673	−	0.762767i	$-0.276160\pi$
$193$	669281.			1.29335			0.646673	+	0.762767i	$0.276160\pi$
$194$	313684.	−	227904.i	0.598394	−	0.434759i
$195$	17176.0	−	80726.4i	0.0323472	−	0.152030i
$196$	−222421.	−	161598.i	−0.413557	−	0.300466i
$197$	409612.	+	297601.i	0.751982	+	0.546347i	0.896441	−	0.443164i	$-0.146144\pi$
$197$	409612.	+	297601.i	0.751982	+	0.546347i	−0.144459	+	0.989511i	$0.546144\pi$
$198$	−246.584	+	758.907i	−0.000446994	+	0.00137571i
$199$	432368.			0.773964			0.386982	−	0.922087i	$-0.373518\pi$
$199$	432368.			0.773964			0.386982	+	0.922087i	$0.373518\pi$
$200$	−133886.	+	148575.i	−0.236680	+	0.262645i
$201$	102909.			0.179665
$202$	−164055.	+	504908.i	−0.282885	+	0.870631i
$203$	107007.	+	77745.1i	0.182252	+	0.132414i
$204$	141652.	+	102917.i	0.238314	+	0.173145i
$205$	−59334.2	−	133339.i	−0.0986098	−	0.221602i
$206$	67320.4	−	48911.1i	0.110530	−	0.0803044i
$207$	−51825.8			−0.0840659
$208$	33975.0	−	24684.3i	0.0544505	−	0.0395606i
$209$	−53.7859	−	165.536i	−8.51731e−5	−	0.000262136i
$210$	−275775.	+	248208.i	−0.431526	+	0.388390i
$211$	218769.	−	673302.i	0.338283	−	1.04113i	−0.626799	−	0.779181i	$-0.715635\pi$
$211$	218769.	−	673302.i	0.338283	−	1.04113i	0.965082	−	0.261947i	$-0.0843646\pi$
$212$	32128.8	+	98882.3i	0.0490970	+	0.151105i
$213$	−37415.8	−	115154.i	−0.0565076	−	0.173912i
$214$	−125665.	+	386758.i	−0.187578	+	0.577304i
$215$	−1.17806e6	+	123578.i	−1.73809	+	0.182324i
$216$	14417.5	+	44372.5i	0.0210259	+	0.0647112i
$217$	631464.	−	458785.i	0.910331	−	0.661394i
$218$	344202.			0.490537
$219$	−331155.	+	240598.i	−0.466574	+	0.338986i
$220$	−1637.33	+	1473.65i	−0.00228075	+	0.00205276i
$221$	−161370.	−	117243.i	−0.222251	−	0.161475i
$222$	−30957.2	−	22491.7i	−0.0421579	−	0.0306295i
$223$	−160571.	+	494185.i	−0.216224	+	0.665469i	0.782841	+	0.622222i	$0.213770\pi$
$223$	−160571.	+	494185.i	−0.216224	+	0.665469i	−0.999064	+	0.0432463i	$0.986230\pi$
$224$	−188788.			−0.251394
$225$	126474.	+	219264.i	0.166550	+	0.288743i
$226$	−102636.			−0.133668
$227$	−23569.6	+	72539.7i	−0.0303590	+	0.0934353i	−0.965088	−	0.261926i	$-0.915642\pi$
$227$	−23569.6	+	72539.7i	−0.0303590	+	0.0934353i	0.934729	+	0.355362i	$0.115642\pi$
$228$	−8233.20	−	5981.77i	−0.0104889	−	0.00762066i
$229$	806862.	+	586219.i	1.01674	+	0.738706i	0.965612	−	0.259987i	$-0.0837181\pi$
$229$	806862.	+	586219.i	1.01674	+	0.738706i	0.0511287	+	0.998692i	$0.483718\pi$
$230$	−123887.	−	71559.7i	−0.154421	−	0.0891967i
$231$	−3306.07	+	2402.00i	−0.00407645	+	0.00296172i
$232$	45915.5			0.0560066
$233$	374321.	−	271960.i	0.451705	−	0.328183i	−0.338564	−	0.940943i	$-0.609941\pi$
$233$	374321.	−	271960.i	0.451705	−	0.328183i	0.790269	+	0.612761i	$0.209941\pi$
$234$	−16424.4	−	50549.1i	−0.0196088	−	0.0603495i
$235$	504785.	+	291574.i	0.596261	+	0.344413i
$236$	254190.	−	782317.i	0.297084	−	0.914330i
$237$	−181832.	−	559621.i	−0.210280	−	0.647177i
$238$	277090.	+	852797.i	0.317088	+	0.975895i
$239$	−147467.	+	453856.i	−0.166993	+	0.513953i	−0.999178	−	0.0405464i	$-0.987090\pi$
$239$	−147467.	+	453856.i	−0.166993	+	0.513953i	0.832184	+	0.554499i	$0.187090\pi$
$240$	−26804.1	+	125978.i	−0.0300381	+	0.141177i
$241$	−280279.	−	862610.i	−0.310848	−	0.956691i	−0.977430	−	0.211260i	$-0.932243\pi$
$241$	−280279.	−	862610.i	−0.310848	−	0.956691i	0.666582	−	0.745432i	$-0.267757\pi$
$242$	521152.	−	378639.i	0.572040	−	0.415611i
$243$	59049.0			0.0641500
$244$	−249936.	+	181589.i	−0.268754	+	0.195261i
$245$	−955314.	+	100212.i	−1.01679	+	0.106660i
$246$	−76036.9	−	55244.1i	−0.0801100	−	0.0582033i
$247$	9379.26	+	6814.43i	0.00978197	+	0.00710701i
$248$	83729.4	−	257693.i	0.0864468	−	0.266056i
$249$	419243.			0.428516
$250$	−425.125	+	698771.i	−0.000430196	+	0.707107i
$251$	−1.52372e6			−1.52658			−0.763292	−	0.646054i	$-0.776418\pi$
$251$	−1.52372e6			−1.52658			−0.763292	+	0.646054i	$0.776418\pi$
$252$	−73835.0	+	227241.i	−0.0732422	+	0.225416i
$253$	−1274.84	−	926.225i	−0.00125214	−	0.000909736i
$254$	11827.2	+	8592.94i	0.0115026	+	0.00835714i
$255$	608408.	−	63821.6i	0.585929	−	0.0614635i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	410604.			0.387784			0.193892	−	0.981023i	$-0.437889\pi$
$257$	410604.			0.387784			0.193892	+	0.981023i	$0.437889\pi$
$258$	−617133.	+	448373.i	−0.577204	+	0.419364i
$259$	−60556.2	−	186373.i	−0.0560931	−	0.172637i
$260$	30535.2	−	143514.i	0.0280135	−	0.131662i
$261$	17957.5	−	55267.6i	0.0163172	−	0.0502192i
$262$	−251746.	−	774795.i	−0.226574	−	0.697322i
$263$	146807.	+	451825.i	0.130875	+	0.402792i	0.994926	−	0.100613i	$-0.0320804\pi$
$263$	146807.	+	451825.i	0.130875	+	0.402792i	−0.864051	+	0.503405i	$0.832080\pi$
$264$	−438.371	+	1349.17i	−0.000387108	+	0.00119140i
$265$	314555.	+	181694.i	0.275158	+	0.158937i
$266$	−16105.2	−	49566.7i	−0.0139560	−	0.0429523i
$267$	1.05668e6	−	767726.i	0.907125	−	0.659065i
$268$	182949.			0.155594
$269$	−1.17713e6	+	855234.i	−0.991844	+	0.720617i	−0.960324	−	0.278887i	$-0.910035\pi$
$269$	−1.17713e6	+	855234.i	−0.991844	+	0.720617i	−0.0315196	+	0.999503i	$0.510035\pi$
$270$	141154.	+	81533.3i	0.117837	+	0.0680653i
$271$	−1.51494e6	−	1.10067e6i	−1.25306	−	0.910402i	−0.254666	−	0.967029i	$-0.581965\pi$
$271$	−1.51494e6	−	1.10067e6i	−1.25306	−	0.910402i	−0.998395	+	0.0566272i	$0.981965\pi$
$272$	251827.	+	182963.i	0.206386	+	0.149948i
$273$	84112.9	−	258873.i	0.0683055	−	0.210223i
$274$	−1.18761e6			−0.955647
$275$	−807.597	+	7653.90i	−0.000643966	+	0.00610311i
$276$	−92134.7			−0.0728032
$277$	683704.	−	2.10423e6i	0.535388	−	1.64776i	−0.207420	−	0.978252i	$-0.566507\pi$
$277$	683704.	−	2.10423e6i	0.535388	−	1.64776i	0.742809	−	0.669504i	$-0.233493\pi$
$278$	747360.	+	542989.i	0.579987	+	0.421385i
$279$	−277433.	−	201567.i	−0.213377	−	0.155028i
$280$	−490267.	+	441259.i	−0.373713	+	0.336355i
$281$	−594731.	+	432098.i	−0.449319	+	0.326450i	−0.789327	−	0.613973i	$-0.789570\pi$
$281$	−594731.	+	432098.i	−0.449319	+	0.326450i	0.340008	+	0.940423i	$0.389570\pi$
$282$	375408.			0.281113
$283$	−1.04399e6	+	758503.i	−0.774872	+	0.562978i	−0.903436	−	0.428724i	$-0.858963\pi$
$283$	−1.04399e6	+	758503.i	−0.774872	+	0.562978i	0.128564	+	0.991701i	$0.458963\pi$
$284$	−66517.1	−	204718.i	−0.0489370	−	0.150613i
$285$	−35362.2	+	3709.47i	−0.0257886	+	0.00270520i
$286$	499.392	−	1536.97i	0.000361016	−	0.00111109i
$287$	−148738.	−	457768.i	−0.106590	−	0.328051i
$288$	25631.1	+	78884.4i	0.0182090	+	0.0560415i
$289$	18107.9	−	55730.3i	0.0127533	−	0.0392506i
$290$	119239.	−	107319.i	0.0832573	−	0.0749346i
$291$	−269587.	−	829704.i	−0.186624	−	0.574368i
$292$	−588719.	+	427730.i	−0.404065	+	0.293570i
$293$	−52534.3			−0.0357498			−0.0178749	−	0.999840i	$-0.505690\pi$
$293$	−52534.3			−0.0357498			−0.0178749	+	0.999840i	$0.505690\pi$
$294$	−500446.	+	363596.i	−0.337667	+	0.245330i
$295$	−1.16841e6	−	2.62574e6i	−0.781704	−	1.75669i
$296$	−55035.0	−	39985.3i	−0.0365098	−	0.0265259i
$297$	1452.52	+	1055.32i	0.000955501	+	0.000694212i
$298$	−525738.	+	1.61805e6i	−0.342948	+	1.05549i
$299$	104960.			0.0678961
$300$	224842.	+	389803.i	0.144236	+	0.250059i
$301$	−3.90655e6			−2.48529
$302$	−487469.	+	1.50028e6i	−0.307560	+	0.946572i
$303$	966376.	+	702113.i	0.604700	+	0.439340i
$304$	−14636.8	−	10634.3i	−0.00908369	−	0.00659968i
$305$	−224631.	+	1.05575e6i	−0.138267	+	0.649849i
$306$	318718.	−	231562.i	0.194582	−	0.141372i
$307$	−153243.			−0.0927972			−0.0463986	−	0.998923i	$-0.514774\pi$
$307$	−153243.			−0.0927972			−0.0463986	+	0.998923i	$0.514774\pi$
$308$	−5877.46	+	4270.23i	−0.00353031	+	0.00256492i
$309$	−57856.7	−	178065.i	−0.0344713	−	0.106092i
$310$	−384872.	−	864908.i	−0.227464	−	0.511171i
$311$	−484097.	+	1.48990e6i	−0.283812	+	0.873484i	0.702940	+	0.711249i	$0.251870\pi$
$311$	−484097.	+	1.48990e6i	−0.283812	+	0.873484i	−0.986752	+	0.162235i	$0.948130\pi$
$312$	−29198.9	−	89865.1i	−0.0169817	−	0.0522642i
$313$	−497348.	−	1.53068e6i	−0.286946	−	0.883127i	−0.985809	−	0.167872i	$-0.946310\pi$
$313$	−497348.	−	1.53068e6i	−0.286946	−	0.883127i	0.698863	−	0.715255i	$-0.253690\pi$
$314$	324890.	−	999909.i	0.185957	−	0.572317i
$315$	339391.	+	762701.i	0.192719	+	0.433090i
$316$	−323257.	−	994881.i	−0.182108	−	0.560472i
$317$	967847.	−	703182.i	0.540952	−	0.393024i	−0.283487	−	0.958976i	$-0.591491\pi$
$317$	967847.	−	703182.i	0.540952	−	0.393024i	0.824438	+	0.565952i	$0.191491\pi$
$318$	233935.			0.129726
$319$	1429.47	−	1038.57i	0.000786498	−	0.000571424i
$320$	−47651.7	+	223960.i	−0.0260138	+	0.122263i
$321$	740241.	+	537817.i	0.400969	+	0.291321i
$322$	−381728.	−	277341.i	−0.205170	−	0.149065i
$323$	−26554.3	+	81725.8i	−0.0141621	+	0.0435866i
$324$	104976.			0.0555556
$325$	−256140.	−	444063.i	−0.134514	−	0.233204i
$326$	1.68730e6			0.879322
$327$	239320.	−	736550.i	0.123768	−	0.380919i
$328$	−135177.	−	98211.7i	−0.0693773	−	0.0504056i
$329$	1.55537e6	+	1.13004e6i	0.792218	+	0.575580i
$330$	2015.02	+	4528.29i	0.00101858	+	0.00228902i
$331$	−1.74246e6	+	1.26597e6i	−0.874166	+	0.635118i	−0.931701	−	0.363225i	$-0.881676\pi$
$331$	−1.74246e6	+	1.26597e6i	−0.874166	+	0.635118i	0.0575359	+	0.998343i	$0.481676\pi$
$332$	745321.			0.371106
$333$	−69653.7	+	50606.4i	−0.0344218	+	0.0250089i
$334$	−387966.	−	1.19404e6i	−0.190295	−	0.585667i
$335$	475104.	−	427611.i	0.231300	−	0.208179i
$336$	−131262.	+	403984.i	−0.0634296	+	0.195216i
$337$	361951.	+	1.11397e6i	0.173610	+	0.534317i	0.999567	−	0.0294157i	$-0.00936467\pi$
$337$	361951.	+	1.11397e6i	0.173610	+	0.534317i	−0.825957	+	0.563733i	$0.809365\pi$
$338$	−425680.	−	1.31011e6i	−0.202671	−	0.623757i
$339$	−71361.5	+	219628.i	−0.0337260	+	0.103798i
$340$	1.08161e6	−	113461.i	0.507429	−	0.0532289i
$341$	−3222.07	−	9916.52i	−0.00150055	−	0.00461821i
$342$	−18524.7	+	13459.0i	−0.00856418	+	0.00622224i
$343$	−69309.3			−0.0318095
$344$	−1.09713e6	+	797108.i	−0.499874	+	0.363179i
$345$	−239266.	+	215348.i	−0.108226	+	0.0974078i
$346$	−1.50383e6	−	1.09260e6i	−0.675319	−	0.490648i
$347$	1.49384e6	+	1.08534e6i	0.666011	+	0.483886i	0.868688	−	0.495360i	$-0.164964\pi$
$347$	1.49384e6	+	1.08534e6i	0.666011	+	0.483886i	−0.202676	+	0.979246i	$0.564964\pi$
$348$	31924.5	−	98253.5i	0.0141311	−	0.0434911i
$349$	39714.7			0.0174537			0.00872686	−	0.999962i	$-0.497222\pi$
$349$	39714.7			0.0174537			0.00872686	+	0.999962i	$0.497222\pi$
$350$	−241820.	+	2.29182e6i	−0.105517	+	1.00003i
$351$	−119589.			−0.0518110
$352$	−779.327	+	2398.52i	−0.000335245	+	0.00103178i
$353$	1.05482e6	+	766375.i	0.450550	+	0.327344i	0.789813	−	0.613348i	$-0.210178\pi$
$353$	1.05482e6	+	766375.i	0.450550	+	0.327344i	−0.339263	+	0.940692i	$0.610178\pi$
$354$	−1.49733e6	−	1.08787e6i	−0.635051	−	0.461392i
$355$	−651232.	−	376165.i	−0.274261	−	0.158419i
$356$	1.87855e6	−	1.36485e6i	0.785593	−	0.570767i
$357$	2.01754e6			0.837821
$358$	2.34419e6	−	1.70315e6i	0.966685	−	0.702338i
$359$	1.19110e6	+	3.66582e6i	0.487765	+	1.50119i	0.827936	+	0.560823i	$0.189515\pi$
$359$	1.19110e6	+	3.66582e6i	0.487765	+	1.50119i	−0.340170	+	0.940364i	$0.610485\pi$
$360$	250940.	+	144948.i	0.102050	+	0.0589463i
$361$	−763613.	+	2.35016e6i	−0.308394	+	0.949138i
$362$	−1.01122e6	−	3.11220e6i	−0.405576	−	1.24824i
$363$	−447891.	−	1.37847e6i	−0.178404	−	0.549072i
$364$	149534.	−	460218.i	0.0591543	−	0.182058i
$365$	−529113.	+	2.48680e6i	−0.207882	+	0.977033i
$366$	214801.	+	661089.i	0.0838172	+	0.257963i
$367$	−940456.	+	683281.i	−0.364480	+	0.264810i	−0.754918	−	0.655819i	$-0.772323\pi$
$367$	−940456.	+	683281.i	−0.364480	+	0.264810i	0.390438	+	0.920629i	$0.372323\pi$
$368$	−163795.			−0.0630494
$369$	−171083.	+	124299.i	−0.0654095	+	0.0475228i
$370$	−236380.	+	24796.0i	−0.0897647	+	0.00941625i
$371$	969226.	+	704184.i	0.365587	+	0.265614i
$372$	−493215.	−	358341.i	−0.184790	−	0.134258i
$373$	−1.07217e6	+	3.29980e6i	−0.399018	+	1.22805i	0.526770	+	0.850008i	$0.323403\pi$
$373$	−1.07217e6	+	3.29980e6i	−0.399018	+	1.22805i	−0.925788	+	0.378043i	$0.876597\pi$
$374$	11978.5			0.00442815
$375$	1.49499e6	+	486757.i	0.548984	+	0.178745i
$376$	667393.			0.243451
$377$	−36368.4	+	111930.i	−0.0131786	+	0.0405597i
$378$	434931.	+	315996.i	0.156564	+	0.113750i
$379$	1.79209e6	+	1.30203e6i	0.640856	+	0.465609i	0.860144	−	0.510051i	$-0.170373\pi$
$379$	1.79209e6	+	1.30203e6i	0.640856	+	0.465609i	−0.219288	+	0.975660i	$0.570373\pi$
$380$	−62866.2	+	6594.61i	−0.0223336	+	0.00234277i
$381$	26611.1	−	19334.1i	0.00939184	−	0.00682357i
$382$	−82914.9			−0.0290720
$383$	−2.27594e6	+	1.65357e6i	−0.792799	+	0.576003i	−0.908793	−	0.417247i	$-0.862995\pi$
$383$	−2.27594e6	+	1.65357e6i	−0.792799	+	0.576003i	0.115993	+	0.993250i	$0.462995\pi$
$384$	45566.4	+	140239.i	0.0157695	+	0.0485334i
$385$	−5282.39	+	24826.9i	−0.00181626	+	0.00853633i
$386$	827276.	−	2.54610e6i	0.282607	−	0.869774i
$387$	530379.	+	1.63234e6i	0.180015	+	0.554029i
$388$	−479266.	−	1.47503e6i	−0.161621	−	0.497418i
$389$	−157559.	+	484916.i	−0.0527921	+	0.162477i	−0.973977	−	0.226649i	$-0.927223\pi$
$389$	−157559.	+	484916.i	−0.0527921	+	0.162477i	0.921184	+	0.389126i	$0.127223\pi$
$390$	−285871.	−	165125.i	−0.0951718	−	0.0549732i
$391$	240407.	+	739897.i	0.0795253	+	0.244754i
$392$	−889682.	+	646392.i	−0.292429	+	0.212462i
$393$	−1.83300e6			−0.598662
$394$	1.63845e6	−	1.19040e6i	0.531732	−	0.386326i
$395$	−3.16483e6	−	1.82807e6i	−1.02060	−	0.589522i
$396$	2582.26	+	1876.12i	0.000827488	+	0.000601205i
$397$	3.04272e6	+	2.21066e6i	0.968914	+	0.703957i	0.955204	−	0.295949i	$-0.0956359\pi$
$397$	3.04272e6	+	2.21066e6i	0.968914	+	0.703957i	0.0137099	+	0.999906i	$0.495636\pi$
$398$	534436.	−	1.64483e6i	0.169117	−	0.520490i
$399$	−117264.			−0.0368752
$400$	399719.	+	692983.i	0.124912	+	0.216557i
$401$	5.20050e6			1.61504			0.807522	−	0.589838i	$-0.200808\pi$
$401$	5.20050e6			1.61504			0.807522	+	0.589838i	$0.200808\pi$
$402$	127202.	−	391489.i	0.0392582	−	0.120824i
$403$	561870.	+	408222.i	0.172335	+	0.125209i
$404$	1.71800e6	+	1.24820e6i	0.523685	+	0.380480i
$405$	272614.	−	245362.i	0.0825867	−	0.0743311i
$406$	428028.	−	310981.i	0.128872	−	0.0936307i
$407$	−2617.81			−0.000783344
$408$	566610.	−	411666.i	0.168513	−	0.122432i
$409$	−1.23349e6	−	3.79628e6i	−0.364608	−	1.12215i	−0.950226	−	0.311560i	$-0.899148\pi$
$409$	−1.23349e6	−	3.79628e6i	−0.364608	−	1.12215i	0.585619	−	0.810587i	$-0.300852\pi$
$410$	−580595.	+	60903.9i	−0.170574	+	0.0178931i
$411$	−825731.	+	2.54134e6i	−0.241121	+	0.742093i
$412$	−102856.	−	316559.i	−0.0298530	−	0.0918781i
$413$	−2.92897e6	−	9.01443e6i	−0.844966	−	2.60054i
$414$	−64060.2	+	197157.i	−0.0183691	+	0.0565342i
$415$	1.93553e6	−	1.74205e6i	0.551672	−	0.496525i
$416$	−51909.2	−	159760.i	−0.0147066	−	0.0452622i
$417$	1.68156e6	−	1.22173e6i	0.473557	−	0.344059i
$418$	−696.219			−0.000194897
$419$	−2.50459e6	+	1.81969e6i	−0.696950	+	0.506364i	−0.878937	−	0.476937i	$-0.841747\pi$
$419$	−2.50459e6	+	1.81969e6i	−0.696950	+	0.506364i	0.181987	+	0.983301i	$0.441747\pi$
$420$	603362.	+	1.35591e6i	0.166899	+	0.375067i
$421$	242664.	+	176306.i	0.0667268	+	0.0484799i	0.620649	−	0.784089i	$-0.286869\pi$
$421$	242664.	+	176306.i	0.0667268	+	0.0484799i	−0.553922	+	0.832569i	$0.686869\pi$
$422$	−2.29098e6	−	1.66450e6i	−0.626239	−	0.454990i
$423$	261017.	−	803328.i	0.0709280	−	0.218294i
$424$	415884.			0.112346
$425$	2.54367e6	−	2.82273e6i	0.683106	−	0.758048i
$426$	−484321.			−0.129303
$427$	−1.10004e6	+	3.38558e6i	−0.291971	+	0.898593i
$428$	1.31598e6	+	956118.i	0.347249	+	0.252291i
$429$	−2941.71	−	2137.28i	−0.000771714	−	0.000560683i
$430$	−986045.	+	4.63436e6i	−0.257173	+	1.20870i
$431$	5.68111e6	−	4.12757e6i	1.47313	−	1.07029i	0.493433	−	0.869784i	$-0.335742\pi$
$431$	5.68111e6	−	4.12757e6i	1.47313	−	1.07029i	0.979693	−	0.200504i	$-0.0642581\pi$
$432$	186624.			0.0481125
$433$	4.78291e6	−	3.47499e6i	1.22595	−	0.890704i	0.229369	−	0.973340i	$-0.426334\pi$
$433$	4.78291e6	−	3.47499e6i	1.22595	−	0.890704i	0.996580	+	0.0826358i	$0.0263338\pi$
$434$	−964791.	−	2.96932e6i	−0.245872	−	0.756716i
$435$	−146745.	−	329774.i	−0.0371826	−	0.0835590i
$436$	425457.	−	1.30942e6i	0.107186	−	0.329886i
$437$	−13973.1	−	43004.7i	−0.00350016	−	0.0107724i
$438$	505959.	+	1.55718e6i	0.126017	+	0.387841i
$439$	202912.	−	624498.i	0.0502512	−	0.154657i	−0.922782	−	0.385322i	$-0.874090\pi$
$439$	202912.	−	624498.i	0.0502512	−	0.154657i	0.973033	+	0.230665i	$0.0740902\pi$
$440$	3582.26	+	8050.29i	0.000882116	+	0.00198235i
$441$	430095.	+	1.32370e6i	0.105310	+	0.324110i
$442$	−645482.	+	468970.i	−0.157155	+	0.114180i
$443$	−5.22716e6			−1.26548			−0.632742	−	0.774363i	$-0.718071\pi$
$443$	−5.22716e6			−1.26548			−0.632742	+	0.774363i	$0.718071\pi$
$444$	−123829.	+	89966.9i	−0.0298101	+	0.0216583i
$445$	1.68835e6	−	7.93516e6i	0.404169	−	1.89957i
$446$	1.68152e6	+	1.22169e6i	0.400280	+	0.290820i
$447$	3.09690e6	+	2.25003e6i	0.733092	+	0.532622i
$448$	−233355.	+	718193.i	−0.0549316	+	0.169062i
$449$	7.71409e6			1.80580			0.902898	−	0.429855i	$-0.141435\pi$
$449$	7.71409e6			1.80580			0.902898	+	0.429855i	$0.141435\pi$
$450$	990460.	−	210109.i	0.230571	−	0.0489117i
$451$	−6429.86			−0.00148854
$452$	−126865.	+	390450.i	−0.0292076	+	0.0898916i
$453$	2.87148e6	+	2.08625e6i	0.657445	+	0.477662i
$454$	246824.	+	179328.i	0.0562014	+	0.0408327i
$455$	−687350.	−	1.54466e6i	−0.155650	−	0.349787i
$456$	−32932.8	+	23927.1i	−0.00741680	+	0.00538862i
$457$	−1.51903e6			−0.340232			−0.170116	−	0.985424i	$-0.554414\pi$
$457$	−1.51903e6			−0.340232			−0.170116	+	0.985424i	$0.554414\pi$
$458$	3.22745e6	−	2.34488e6i	0.718944	−	0.522344i
$459$	−273914.	−	843020.i	−0.0606851	−	0.186770i
$460$	−425362.	+	382841.i	−0.0937268	+	0.0843576i
$461$	−146368.	+	450474.i	−0.0320770	+	0.0987227i	−0.965813	−	0.259239i	$-0.916528\pi$
$461$	−146368.	+	450474.i	−0.0320770	+	0.0987227i	0.933736	+	0.357962i	$0.116528\pi$
$462$	5051.23	+	15546.1i	0.00110101	+	0.00338857i
$463$	1.24356e6	+	3.82729e6i	0.269597	+	0.829734i	0.990599	+	0.136801i	$0.0436819\pi$
$463$	1.24356e6	+	3.82729e6i	0.269597	+	0.829734i	−0.721002	+	0.692933i	$0.756318\pi$
$464$	56754.7	−	174673.i	0.0122379	−	0.0376644i
$465$	−2.11839e6	+	222218.i	−0.454333	+	0.0476592i
$466$	−571912.	−	1.76016e6i	−0.122001	−	0.375481i
$467$	−5.71321e6	+	4.15089e6i	−1.21224	+	0.880743i	−0.995432	−	0.0954722i	$-0.969564\pi$
$467$	−5.71321e6	+	4.15089e6i	−1.21224	+	0.880743i	−0.216806	+	0.976215i	$0.569564\pi$
$468$	−212602.			−0.0448697
$469$	1.70547e6	−	1.23909e6i	0.358023	−	0.260119i
$470$	1.73316e6	−	1.55991e6i	0.361905	−	0.325728i
$471$	−1.91379e6	−	1.39045e6i	−0.397504	−	0.288804i
$472$	−2.66192e6	−	1.93399e6i	−0.549970	−	0.399577i
$473$	−16126.4	+	49632.1i	−0.00331425	+	0.0102002i
$474$	−2.35368e6			−0.481173
$475$	−147844.	+	164064.i	−0.0300657	+	0.0333641i
$476$	3.58673e6			0.725574
$477$	162652.	−	500592.i	0.0327313	−	0.100737i
$478$	1.54429e6	+	1.12199e6i	0.309143	+	0.224606i
$479$	−142753.	−	103716.i	−0.0284280	−	0.0206541i	0.573481	−	0.819219i	$-0.305593\pi$
$479$	−142753.	−	103716.i	−0.0284280	−	0.0206541i	−0.601909	+	0.798565i	$0.705593\pi$
$480$	446115.	+	257686.i	0.0883780	+	0.0510490i
$481$	141066.	−	102490.i	0.0278009	−	0.0201985i
$482$	−3.62801e6			−0.711296
$483$	−858887.	+	624018.i	−0.167521	+	0.121711i
$484$	−796250.	−	2.45061e6i	−0.154503	−	0.475510i
$485$	−4.69223e6	−	2.71033e6i	−0.905784	−	0.523199i
$486$	72988.6	−	224636.i	0.0140173	−	0.0431408i
$487$	−1.32106e6	−	4.06580e6i	−0.252406	−	0.776826i	−0.994330	−	0.106342i	$-0.966086\pi$
$487$	−1.32106e6	−	4.06580e6i	−0.252406	−	0.776826i	0.741924	−	0.670484i	$-0.233914\pi$
$488$	381868.	+	1.17527e6i	0.0725878	+	0.223402i
$489$	1.17316e6	−	3.61061e6i	0.221863	−	0.682824i
$490$	−799605.	+	3.75810e6i	−0.150448	+	0.707095i
$491$	2.28932e6	+	7.04581e6i	0.428552	+	1.31895i	0.899552	+	0.436814i	$0.143893\pi$
$491$	2.28932e6	+	7.04581e6i	0.428552	+	1.31895i	−0.471000	+	0.882133i	$0.656107\pi$
$492$	−304148.	+	220976.i	−0.0566463	+	0.0411560i
$493$	−872335.			−0.161646
$494$	37517.0	−	27257.7i	0.00691689	−	0.00502542i
$495$	11091.0	−	1163.44i	0.00203450	−	0.000213417i
$496$	−876826.	−	637051.i	−0.160033	−	0.116271i
$497$	−2.00661e6	−	1.45789e6i	−0.364395	−	0.264749i
$498$	518213.	−	1.59489e6i	0.0936342	−	0.288177i
$499$	−9.32143e6			−1.67584			−0.837918	−	0.545797i	$-0.816227\pi$
$499$	−9.32143e6			−1.67584			−0.837918	+	0.545797i	$0.816227\pi$
$500$	2.65776e6	+	865346.i	0.475434	+	0.154798i
$501$	−2.82484e6			−0.502804
$502$	−1.88342e6	+	5.79657e6i	−0.333571	+	1.02663i
$503$	−288610.	−	209687.i	−0.0508618	−	0.0369532i	0.562064	−	0.827094i	$-0.310007\pi$
$503$	−288610.	−	209687.i	−0.0508618	−	0.0369532i	−0.612926	+	0.790141i	$0.710007\pi$
$504$	773211.	+	561770.i	0.135588	+	0.0985105i
$505$	7.37895e6	−	774046.i	1.28756	−	0.135064i
$506$	−5099.36	+	3704.90i	−0.000885399	+	0.000643280i
$507$	−3.09944e6			−0.535505
$508$	47308.7	−	34371.8i	0.00813357	−	0.00590939i
$509$	1.06910e6	+	3.29036e6i	0.182905	+	0.562924i	0.999906	−	0.0137126i	$-0.00436501\pi$
$509$	1.06910e6	+	3.29036e6i	0.182905	+	0.562924i	−0.817001	+	0.576636i	$0.804365\pi$
$510$	509243.	−	2.39341e6i	0.0866960	−	0.407466i
$511$	−2.59112e6	+	7.97466e6i	−0.438971	+	1.35101i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	15920.6	+	48998.5i	0.00267095	+	0.00822032i
$514$	507534.	−	1.56203e6i	0.0847339	−	0.260784i
$515$	−1.00701e6	−	581670.i	−0.167308	−	0.0966403i
$516$	942896.	+	2.90193e6i	0.155898	+	0.479803i
$517$	20777.6	−	15095.8i	0.00341877	−	0.00248388i
$518$	−783856.			−0.128355
$519$	−3.38362e6	+	2.45834e6i	−0.551396	+	0.400612i
$520$	−508215.	−	293555.i	−0.0824212	−	0.0476082i
$521$	149259.	+	108443.i	0.0240904	+	0.0175027i	0.599765	−	0.800176i	$-0.295261\pi$
$521$	149259.	+	108443.i	0.0240904	+	0.0175027i	−0.575675	+	0.817679i	$0.695261\pi$
$522$	−188054.	−	136629.i	−0.0302069	−	0.0219466i
$523$	−2.93052e6	+	9.01922e6i	−0.468480	+	1.44183i	0.386074	+	0.922468i	$0.373831\pi$
$523$	−2.93052e6	+	9.01922e6i	−0.468480	+	1.44183i	−0.854553	+	0.519364i	$0.826169\pi$
$524$	−3.25867e6			−0.518457
$525$	4.73608e6	+	2.11094e6i	0.749931	+	0.334255i
$526$	1.90031e6			0.299474
$527$	−1.59075e6	+	4.89583e6i	−0.249503	+	0.767891i
$528$	4590.68	+	3335.33i	0.000716626	+	0.000520659i
$529$	4.87592e6	+	3.54256e6i	0.757561	+	0.550400i
$530$	1.08002e6	−	972054.i	0.167009	−	0.150314i
$531$	−3.36899e6	+	2.44771e6i	−0.518517	+	0.376725i
$532$	−208470.			−0.0319348
$533$	346485.	−	251736.i	0.0528283	−	0.0383820i
$534$	−1.61447e6	−	4.96883e6i	−0.245006	−	0.754051i
$535$	5.65225e6	−	592917.i	0.853763	−	0.0895590i
$536$	226138.	−	695980.i	0.0339986	−	0.104637i
$537$	−2.01465e6	−	6.20046e6i	−0.301484	−	0.927872i
$538$	1.79849e6	+	5.53519e6i	0.267888	+	0.824474i
$539$	−13077.3	+	40247.7i	−0.00193885	+	0.00596718i
$540$	484647.	−	436200.i	0.0715222	−	0.0643726i
$541$	1.82079e6	+	5.60381e6i	0.267464	+	0.823171i	0.991115	+	0.133005i	$0.0424625\pi$
$541$	1.82079e6	+	5.60381e6i	0.267464	+	0.823171i	−0.723651	+	0.690166i	$0.757537\pi$
$542$	−6.05976e6	+	4.40267e6i	−0.886048	+	0.643751i
$543$	−7.36282e6			−1.07163
$544$	1.00731e6	−	731851.i	0.145937	−	0.106029i
$545$	−1.95566e6	−	4.39489e6i	−0.282035	−	0.633806i
$546$	−880841.	−	639969.i	−0.126449	−	0.0918707i
$547$	−3.72365e6	−	2.70539e6i	−0.532109	−	0.386599i	0.289037	−	0.957318i	$-0.406665\pi$
$547$	−3.72365e6	−	2.70539e6i	−0.532109	−	0.386599i	−0.821146	+	0.570718i	$0.806665\pi$
$548$	−1.46797e6	+	4.51794e6i	−0.208816	+	0.642671i
$549$	1.56400e6			0.221465
$550$	28118.9	+	12533.0i	0.00396362	+	0.00176664i
$551$	50702.3			0.00711457
$552$	−113885.	+	350501.i	−0.0159081	+	0.0489600i
$553$	−9.75164e6	−	7.08498e6i	−1.35602	−	0.985204i
$554$	−7.15984e6	−	5.20193e6i	−0.991127	−	0.720096i
$555$	−111291.	+	523064.i	−0.0153366	+	0.0720812i
$556$	2.98944e6	−	2.17196e6i	0.410112	−	0.297964i
$557$	−4.52839e6			−0.618452			−0.309226	−	0.950989i	$-0.600070\pi$
$557$	−4.52839e6			−0.618452			−0.309226	+	0.950989i	$0.600070\pi$
$558$	−1.10973e6	+	806268.i	−0.150880	+	0.109621i
$559$	−1.07415e6	−	3.30588e6i	−0.145390	−	0.447464i
$560$	1.07264e6	+	2.41051e6i	0.144539	+	0.324818i
$561$	8328.49	−	25632.4i	0.00111727	−	0.00343861i
$562$	908669.	+	2.79659e6i	0.121357	+	0.373498i
$563$	−3.78708e6	−	1.16554e7i	−0.503539	−	1.54973i	−0.803213	−	0.595693i	$-0.796878\pi$
$563$	−3.78708e6	−	1.16554e7i	−0.503539	−	1.54973i	0.299673	−	0.954042i	$-0.403122\pi$
$564$	464030.	−	1.42814e6i	0.0614255	−	0.189048i
$565$	583149.	+	1.31049e6i	0.0768525	+	0.172708i
$566$	1.59507e6	+	4.90913e6i	0.209286	+	0.644115i
$567$	978595.	−	710991.i	0.127834	−	0.0928766i
$568$	−861015.			−0.111980
$569$	2.32029e6	−	1.68579e6i	0.300442	−	0.218284i	−0.427342	−	0.904090i	$-0.640550\pi$
$569$	2.32029e6	−	1.68579e6i	0.300442	−	0.218284i	0.727785	+	0.685806i	$0.240550\pi$
$570$	−29598.5	+	139111.i	−0.00381577	+	0.0179339i
$571$	1.18975e7	+	8.64406e6i	1.52710	+	1.10950i	0.957825	+	0.287351i	$0.0927746\pi$
$571$	1.18975e7	+	8.64406e6i	1.52710	+	1.10950i	0.569271	+	0.822150i	$0.307225\pi$
$572$	−5229.70	−	3799.60i	−0.000668324	−	0.000485566i
$573$	−57649.8	+	177428.i	−0.00733518	+	0.0225754i
$574$	−1.92531e6			−0.243905
$575$	−209806.	+	1.98841e6i	−0.0264636	+	0.250805i
$576$	331776.			0.0416667
$577$	−1.50702e6	+	4.63812e6i	−0.188442	+	0.579966i	−0.999991	−	0.00431916i	$-0.998625\pi$
$577$	−1.50702e6	+	4.63812e6i	−0.188442	+	0.579966i	0.811548	+	0.584285i	$0.198625\pi$
$578$	−189628.	−	137773.i	−0.0236093	−	0.0171531i
$579$	−4.87314e6	−	3.54054e6i	−0.604104	−	0.438908i
$580$	−260879.	−	586265.i	−0.0322010	−	0.0723642i
$581$	6.94794e6	−	5.04797e6i	0.853917	−	0.620407i
$582$	−3.48961e6			−0.427041
$583$	12947.5	−	9406.93i	0.00157767	−	0.00114624i
$584$	899483.	+	2.76832e6i	0.109134	+	0.335880i
$585$	−552109.	+	496919.i	−0.0667015	+	0.0600338i
$586$	−64935.9	+	199852.i	−0.00781162	+	0.0240417i
$587$	−477266.	−	1.46887e6i	−0.0571696	−	0.175950i	0.918394	−	0.395667i	$-0.129487\pi$
$587$	−477266.	−	1.46887e6i	−0.0571696	−	0.175950i	−0.975564	+	0.219717i	$0.929487\pi$
$588$	764614.	+	2.35324e6i	0.0912009	+	0.280687i
$589$	92458.5	−	284558.i	0.0109814	−	0.0337973i
$590$	−1.14331e7	+	1.19933e6i	−1.35218	+	0.141843i
$591$	−1.40812e6	−	4.33375e6i	−0.165833	−	0.510382i
$592$	−220140.	+	159941.i	−0.0258163	+	0.0187567i
$593$	−1.80867e6			−0.211214			−0.105607	−	0.994408i	$-0.533679\pi$
$593$	−1.80867e6			−0.211214			−0.105607	+	0.994408i	$0.533679\pi$
$594$	5810.08	−	4221.27i	0.000675641	−	0.000490882i
$595$	9.31445e6	−	8.38335e6i	1.07861	−	0.970789i
$596$	5.50560e6	+	4.00005e6i	0.634876	+	0.461264i
$597$	−3.14814e6	−	2.28726e6i	−0.361508	−	0.262651i
$598$	129737.	−	399291.i	0.0148358	−	0.0456601i
$599$	1.38396e7			1.57600			0.788000	−	0.615676i	$-0.211117\pi$
$599$	1.38396e7			1.57600			0.788000	+	0.615676i	$0.211117\pi$
$600$	1.76082e6	−	373527.i	0.199681	−	0.0423588i
$601$	−1.49966e7			−1.69358			−0.846791	−	0.531925i	$-0.821469\pi$
$601$	−1.49966e7			−1.69358			−0.846791	+	0.531925i	$0.821469\pi$
$602$	−4.82877e6	+	1.48614e7i	−0.543057	+	1.67136i
$603$	−749296.	−	544395.i	−0.0839189	−	0.0609707i
$604$	5.10484e6	+	3.70889e6i	0.569364	+	0.413667i
$605$	−7.79564e6	−	4.50292e6i	−0.865891	−	0.500157i
$606$	3.86551e6	−	2.80845e6i	0.427587	−	0.310660i
$607$	1.36124e7			1.49955			0.749777	−	0.661691i	$-0.230161\pi$
$607$	1.36124e7			1.49955			0.749777	+	0.661691i	$0.230161\pi$
$608$	−58547.2	+	42537.0i	−0.00642314	+	0.00466668i
$609$	−367857.	−	1.13215e6i	−0.0401917	−	0.123697i
$610$	3.73866e6	+	2.15953e6i	0.406810	+	0.234982i
$611$	−528623.	+	1.62693e6i	−0.0572853	+	0.176306i
$612$	−486958.	−	1.49870e6i	−0.0525549	−	0.161747i
$613$	−208170.	−	640681.i	−0.0223752	−	0.0688638i	0.939245	−	0.343246i	$-0.111527\pi$
$613$	−208170.	−	640681.i	−0.0223752	−	0.0688638i	−0.961621	+	0.274383i	$0.911527\pi$
$614$	−189419.	+	582971.i	−0.0202769	+	0.0624060i
$615$	−273354.	+	1.28475e6i	−0.0291432	+	0.136971i
$616$	8979.97	+	27637.5i	0.000953505	+	0.00293459i
$617$	−9.87646e6	+	7.17567e6i	−1.04445	+	0.758839i	−0.971150	−	0.238471i	$-0.923354\pi$
$617$	−9.87646e6	+	7.17567e6i	−1.04445	+	0.758839i	−0.0733025	+	0.997310i	$0.523354\pi$
$618$	−748913.			−0.0788788
$619$	7.61853e6	−	5.53519e6i	0.799180	−	0.580638i	−0.111493	−	0.993765i	$-0.535563\pi$
$619$	7.61853e6	−	5.53519e6i	0.799180	−	0.580638i	0.910674	+	0.413127i	$0.135563\pi$
$620$	−3.76604e6	+	395054.i	−0.393464	+	0.0412741i
$621$	377351.	+	274162.i	0.0392660	+	0.0285284i
$622$	5.06952e6	+	3.68323e6i	0.525401	+	0.381727i
$623$	8.26804e6	−	2.54464e7i	0.853459	−	2.62668i
$624$	−377959.			−0.0388583
$625$	8.92456e6	−	3.96480e6i	0.913875	−	0.405995i
$626$	−6.43781e6			−0.656602
$627$	−484.073	+	1489.82i	−4.91747e−5	+	0.000151344i
$628$	−3.40229e6	−	2.47191e6i	−0.344249	−	0.250112i
$629$	1.04559e6	+	759669.i	0.105375	+	0.0765592i
$630$	3.32100e6	−	348370.i	0.333363	−	0.0349695i
$631$	5.08701e6	−	3.69593e6i	0.508615	−	0.369530i	−0.303683	−	0.952773i	$-0.598216\pi$
$631$	5.08701e6	−	3.69593e6i	0.508615	−	0.369530i	0.812298	+	0.583243i	$0.198216\pi$
$632$	−4.18432e6			−0.416708
$633$	−5.15471e6	+	3.74511e6i	−0.511322	+	0.371497i
$634$	−1.47874e6	−	4.55109e6i	−0.146106	−	0.449668i
$635$	42518.8	−	199836.i	0.00418453	−	0.0196671i
$636$	289159.	−	889941.i	0.0283462	−	0.0872405i
$637$	−871048.	−	2.68081e6i	−0.0850538	−	0.261769i
$638$	−2184.03	−	6721.76i	−0.000212426	−	0.000653779i
$639$	−336743.	+	1.03639e6i	−0.0326247	+	0.100408i
$640$	793094.	+	458108.i	0.0765376	+	0.0442097i
$641$	2.33577e6	+	7.18877e6i	0.224536	+	0.691050i	0.998338	+	0.0576233i	$0.0183522\pi$
$641$	2.33577e6	+	7.18877e6i	0.224536	+	0.691050i	−0.773803	+	0.633427i	$0.781648\pi$
$642$	2.96096e6	−	2.15127e6i	0.283528	−	0.205995i
$643$	−1.28427e7			−1.22498			−0.612490	−	0.790478i	$-0.709832\pi$
$643$	−1.28427e7			−1.22498			−0.612490	+	0.790478i	$0.709832\pi$
$644$	−1.52691e6	+	1.10937e6i	−0.145077	+	0.105405i
$645$	9.23137e6	+	5.33223e6i	0.873709	+	0.504672i
$646$	278080.	+	202037.i	0.0262174	+	0.0190480i
$647$	9.13551e6	+	6.63734e6i	0.857970	+	0.623352i	0.927332	−	0.374240i	$-0.122096\pi$
$647$	9.13551e6	+	6.63734e6i	0.857970	+	0.623352i	−0.0693618	+	0.997592i	$0.522096\pi$
$648$	129757.	−	399352.i	0.0121393	−	0.0373610i
$649$	−126618.			−0.0118000
$650$	−2.00592e6	+	425522.i	−0.186222	+	0.0395038i
$651$	−7.02479e6			−0.649652
$652$	2.08561e6	−	6.41886e6i	0.192139	−	0.591343i
$653$	−1.28621e7	−	9.34485e6i	−1.18040	−	0.857609i	−0.188181	−	0.982134i	$-0.560259\pi$
$653$	−1.28621e7	−	9.34485e6i	−1.18040	−	0.857609i	−0.992216	+	0.124525i	$0.960259\pi$
$654$	−2.50619e6	−	1.82085e6i	−0.229123	−	0.166468i
$655$	−8.46249e6	+	7.61656e6i	−0.770717	+	0.693674i
$656$	−540707.	+	392847.i	−0.0490572	+	0.0356421i
$657$	3.68397e6			0.332968
$658$	6.22149e6	−	4.52018e6i	0.560183	−	0.406996i
$659$	−1.31742e6	−	4.05460e6i	−0.118171	−	0.363693i	0.874424	−	0.485162i	$-0.161239\pi$
$659$	−1.31742e6	−	4.05460e6i	−0.118171	−	0.363693i	−0.992595	+	0.121469i	$0.961239\pi$
$660$	19717.3	−	2068.33i	0.00176193	−	0.000184825i
$661$	2.63648e6	−	8.11425e6i	0.234704	−	0.722345i	−0.762456	−	0.647040i	$-0.776007\pi$
$661$	2.63648e6	−	8.11425e6i	0.234704	−	0.722345i	0.997161	−	0.0753053i	$-0.0239931\pi$
$662$	2.66225e6	+	8.19356e6i	0.236104	+	0.726654i
$663$	554742.	+	1.70732e6i	0.0490126	+	0.150845i
$664$	921267.	−	2.83537e6i	0.0810896	−	0.249568i
$665$	−541379.	+	487261.i	−0.0474731	+	0.0427275i
$666$	106421.	+	327531.i	0.00929701	+	0.0286132i
$667$	371362.	−	269810.i	0.0323209	−	0.0234825i
$668$	−5.02193e6			−0.435441
$669$	3.78341e6	−	2.74881e6i	0.326827	−	0.237454i
$670$	−1.03947e6	−	2.33596e6i	−0.0894590	−	0.201038i
$671$	38472.1	+	27951.6i	0.00329868	+	0.00239663i
$672$	1.37460e6	+	998703.i	0.117423	+	0.0853126i
$673$	−1.89471e6	+	5.83132e6i	−0.161252	+	0.496283i	−0.998741	−	0.0501722i	$-0.984023\pi$
$673$	−1.89471e6	+	5.83132e6i	−0.161252	+	0.496283i	0.837489	+	0.546455i	$0.184023\pi$
$674$	4.68519e6			0.397263
$675$	239048.	−	2.26555e6i	0.0201941	−	0.191388i
$676$	−5.51012e6			−0.463761
$677$	−3.34265e6	+	1.02876e7i	−0.280297	+	0.862667i	0.707472	+	0.706742i	$0.249836\pi$
$677$	−3.34265e6	+	1.02876e7i	−0.280297	+	0.862667i	−0.987769	+	0.155925i	$0.950164\pi$
$678$	747307.	+	542950.i	0.0624345	+	0.0453613i
$679$	−1.44580e7	−	1.05043e7i	−1.20346	−	0.874367i
$680$	905320.	−	4.25495e6i	0.0750810	−	0.352876i
$681$	555354.	−	403488.i	0.0458883	−	0.0333398i
$682$	−41707.4			−0.00343362
$683$	1.35895e6	−	987334.i	0.111468	−	0.0809865i	−0.530655	−	0.847588i	$-0.678054\pi$
$683$	1.35895e6	−	987334.i	0.111468	−	0.0809865i	0.642123	+	0.766602i	$0.278054\pi$
$684$	28303.2	+	87108.4i	0.00231311	+	0.00711901i
$685$	6.74768e6	+	1.51638e7i	0.549450	+	1.23476i
$686$	−85671.0	+	263668.i	−0.00695062	+	0.0213918i
$687$	−2.77374e6	−	8.53670e6i	−0.224220	−	0.690078i
$688$	1.67626e6	+	5.15899e6i	0.135011	+	0.415522i
$689$	−329410.	+	1.01382e6i	−0.0264356	+	0.0813604i
$690$	523484.	+	1.17641e6i	0.0418582	+	0.0940665i
$691$	6.14189e6	+	1.89028e7i	0.489336	+	1.50602i	0.825601	+	0.564254i	$0.190836\pi$
$691$	6.14189e6	+	1.89028e7i	0.489336	+	1.50602i	−0.336265	+	0.941767i	$0.609164\pi$
$692$	−6.01533e6	+	4.37039e6i	−0.477523	+	0.346940i
$693$	36778.8			0.00290914
$694$	5.97538e6	−	4.34137e6i	0.470941	−	0.342159i
$695$	2.68677e6	−	1.26277e7i	0.210993	−	0.991656i
$696$	−334318.	−	242896.i	−0.0261599	−	0.0190063i
$697$	2.56818e6	+	1.86589e6i	0.200237	+	0.145481i
$698$	49090.1	−	151084.i	0.00381378	−	0.0117376i
$699$	−4.16418e6			−0.322357
$700$	8.41971e6	+	3.75279e6i	0.649459	+	0.289473i
$701$	−1.68044e7			−1.29160			−0.645798	−	0.763508i	$-0.723475\pi$
$701$	−1.68044e7			−1.29160			−0.645798	+	0.763508i	$0.723475\pi$
$702$	−147820.	+	454942.i	−0.0113211	+	0.0348428i
$703$	−60772.6	−	44153.8i	−0.00463788	−	0.00336961i
$704$	8161.21	+	5929.47i	0.000620616	+	0.000450904i
$705$	−2.13297e6	−	4.79334e6i	−0.161626	−	0.363217i
$706$	4.21930e6	−	3.06550e6i	0.318587	−	0.231467i
$707$	2.44693e7			1.84108
$708$	−5.98931e6	+	4.35149e6i	−0.449049	+	0.326253i
$709$	3.68934e6	+	1.13546e7i	0.275634	+	0.848314i	0.989051	+	0.147574i	$0.0471466\pi$
$709$	3.68934e6	+	1.13546e7i	0.275634	+	0.848314i	−0.713417	+	0.700740i	$0.752853\pi$
$710$	−2.23598e6	+	2.01247e6i	−0.166465	+	0.149825i
$711$	−1.63649e6	+	5.03659e6i	−0.121405	+	0.373648i
$712$	−2.87017e6	−	8.83347e6i	−0.212181	−	0.653027i
$713$	−837064.	−	2.57622e6i	−0.0616645	−	0.189784i
$714$	2.49381e6	−	7.67517e6i	0.183071	−	0.563433i
$715$	−22462.0	+	2356.24i	−0.00164317	+	0.000172367i
$716$	−3.58160e6	−	1.10230e7i	−0.261093	−	0.803560i
$717$	3.47466e6	−	2.52449e6i	0.252414	−	0.183390i
$718$	1.54179e7			1.11613
$719$	−1.18098e7	+	8.58035e6i	−0.851965	+	0.618989i	−0.925687	−	0.378290i	$-0.876512\pi$
$719$	−1.18098e7	+	8.58035e6i	−0.851965	+	0.618989i	0.0737222	+	0.997279i	$0.476512\pi$
$720$	861594.	−	775467.i	0.0619400	−	0.0557483i
$721$	−3.10286e6	−	2.25436e6i	−0.222292	−	0.161504i
$722$	7.99666e6	+	5.80991e6i	0.570907	+	0.414789i
$723$	−2.52251e6	+	7.76349e6i	−0.179468	+	0.552346i
$724$	−1.30895e7			−0.928058
$725$	−2.04777e6	−	912721.i	−0.144689	−	0.0644901i
$726$	−5.79762e6			−0.408233
$727$	3.28452e6	−	1.01087e7i	0.230481	−	0.709349i	−0.767207	−	0.641399i	$-0.778354\pi$
$727$	3.28452e6	−	1.01087e7i	0.230481	−	0.709349i	0.997689	−	0.0679497i	$-0.0216457\pi$
$728$	−1.56594e6	−	1.13772e6i	−0.109508	−	0.0795624i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	8.80634e6	+	5.08672e6i	0.611629	+	0.353290i
$731$	2.08440e7	−	1.51440e7i	1.44274	−	1.04821i
$732$	2.78044e6			0.191794
$733$	−1.19832e7	+	8.70630e6i	−0.823782	+	0.598513i	−0.917793	−	0.397058i	$-0.870031\pi$
$733$	−1.19832e7	+	8.70630e6i	−0.823782	+	0.598513i	0.0940110	+	0.995571i	$0.470031\pi$
$734$	1.43689e6	+	4.42229e6i	0.0984426	+	0.302975i
$735$	7.48591e6	+	4.32402e6i	0.511124	+	0.295236i
$736$	−202462.	+	623113.i	−0.0137768	+	0.0424006i
$737$	−8702.22	−	26782.7i	−0.000590149	−	0.00181629i
$738$	261392.	+	804481.i	0.0176665	+	0.0543719i
$739$	4.04683e6	−	1.24549e7i	0.272586	−	0.838934i	−0.717262	−	0.696804i	$-0.754605\pi$
$739$	4.04683e6	−	1.24549e7i	0.272586	−	0.838934i	0.989848	−	0.142130i	$-0.0453952\pi$
$740$	−197852.	+	929891.i	−0.0132819	+	0.0624242i
$741$	−32243.0	−	99233.8i	−0.00215720	−	0.00663918i
$742$	3.87690e6	−	2.81674e6i	0.258509	−	0.187818i
$743$	2.49672e7			1.65920			0.829598	−	0.558361i	$-0.188569\pi$
$743$	2.49672e7			1.65920			0.829598	+	0.558361i	$0.188569\pi$
$744$	−1.97286e6	+	1.43337e6i	−0.130666	+	0.0949346i
$745$	2.36470e7	−	2.48055e6i	1.56093	−	0.163741i
$746$	1.12279e7	+	8.15757e6i	0.738673	+	0.536678i
$747$	−3.05257e6	−	2.21782e6i	−0.200154	−	0.145420i
$748$	14806.2	−	45568.8i	0.000967586	−	0.00297792i
$749$	1.87434e7			1.22080
$750$	3.69964e6	−	5.08561e6i	0.240163	−	0.330134i
$751$	4.43292e6			0.286807			0.143403	−	0.989664i	$-0.454195\pi$
$751$	4.43292e6			0.286807			0.143403	+	0.989664i	$0.454195\pi$
$752$	824943.	−	2.53891e6i	0.0531960	−	0.163721i
$753$	1.10944e7	+	8.06058e6i	0.713046	+	0.518058i
$754$	380855.	+	276707.i	0.0243967	+	0.0177252i
$755$	2.19257e7	−	2.29999e6i	1.39986	−	0.146845i
$756$	1.73972e6	−	1.26398e6i	0.110707	−	0.0804335i
$757$	2.98340e7			1.89222			0.946110	−	0.323844i	$-0.104975\pi$
$757$	2.98340e7			1.89222			0.946110	+	0.323844i	$0.104975\pi$
$758$	7.16834e6	−	5.20811e6i	0.453154	−	0.329236i
$759$	4382.51	+	13488.0i	0.000276133	+	0.000849850i
$760$	−52619.5	+	247309.i	−0.00330455	+	0.0155312i
$761$	−1.41743e6	+	4.36241e6i	−0.0887239	+	0.273064i	−0.985567	−	0.169284i	$-0.945854\pi$
$761$	−1.41743e6	+	4.36241e6i	−0.0887239	+	0.273064i	0.896843	+	0.442348i	$0.145854\pi$
$762$	−40658.2	−	125133.i	−0.00253665	−	0.00780700i
$763$	−4.90243e6	−	1.50881e7i	−0.304859	−	0.938261i
$764$	−102488.	+	315427.i	−0.00635245	+	0.0195508i
$765$	−4.76754e6	−	2.75383e6i	−0.294537	−	0.170131i
$766$	3.47732e6	+	1.07021e7i	0.214128	+	0.659018i
$767$	6.82302e6	−	4.95721e6i	0.418782	−	0.304263i
$768$	589824.			0.0360844
$769$	−8.17542e6	+	5.93979e6i	−0.498533	+	0.362206i	−0.808456	−	0.588556i	$-0.799697\pi$
$769$	−8.17542e6	+	5.93979e6i	−0.498533	+	0.362206i	0.309923	+	0.950762i	$0.399697\pi$
$770$	87917.9	+	50783.2i	0.00534380	+	0.00308669i
$771$	−2.98967e6	−	2.17212e6i	−0.181129	−	0.131598i
$772$	−8.66335e6	−	6.29429e6i	−0.523170	−	0.380105i
$773$	−6.59311e6	+	2.02915e7i	−0.396864	+	1.22142i	0.530636	+	0.847600i	$0.321953\pi$
$773$	−6.59311e6	+	2.02915e7i	−0.396864	+	1.22142i	−0.927500	+	0.373822i	$0.878047\pi$
$774$	6.86537e6			0.411919
$775$	−8.85671e6	+	9.82835e6i	−0.529685	+	0.587796i
$776$	−6.20375e6			−0.369828
$777$	−545006.	+	1.67736e6i	−0.0323854	+	0.0996719i
$778$	1.64998e6	+	1.19878e6i	0.0977303	+	0.0710052i
$779$	−149269.	−	108451.i	−0.00881306	−	0.00640307i
$780$	−981528.	+	883411.i	−0.0577652	+	0.0519908i
$781$	−26805.6	+	19475.4i	−0.00157253	+	0.00114251i
$782$	3.11189e6			0.181973
$783$	−423121.	+	307415.i	−0.0246638	+	0.0179193i
$784$	1.35931e6	+	4.18354e6i	0.0789823	+	0.243082i
$785$	−1.46131e7	+	1.53290e6i	−0.846386	+	0.0887852i
$786$	−2.26572e6	+	6.97316e6i	−0.130812	+	0.402599i
$787$	31005.0	+	95423.7i	0.00178441	+	0.00549186i	0.951945	−	0.306270i	$-0.0990810\pi$
$787$	31005.0	+	95423.7i	0.00178441	+	0.00549186i	−0.950160	+	0.311762i	$0.899081\pi$
$788$	−2.50333e6	−	7.70445e6i	−0.143616	−	0.442004i
$789$	1.32126e6	−	4.06642e6i	0.0755607	−	0.232552i
$790$	−1.08663e7	+	9.78009e6i	−0.619462	+	0.557539i
$791$	1.46183e6	+	4.49905e6i	0.0830721	+	0.255670i
$792$	10329.0	−	7504.48i	0.000585123	−	0.000425116i
$793$	−3.16748e6			−0.178867
$794$	1.21709e7	−	8.84265e6i	0.685125	−	0.497773i
$795$	−1.32915e6	−	2.98696e6i	−0.0745860	−	0.167614i
$796$	−5.59669e6	−	4.06623e6i	−0.313075	−	0.227462i
$797$	−2.33151e7	−	1.69394e7i	−1.30014	−	0.944610i	−0.300187	−	0.953881i	$-0.597049\pi$
$797$	−2.33151e7	−	1.69394e7i	−1.30014	−	0.944610i	−0.999957	+	0.00927090i	$0.997049\pi$
$798$	−144947.	+	446100.i	−0.00805752	+	0.0247985i
$799$	−1.26796e7			−0.702649
$800$	3.13034e6	−	664048.i	0.172929	−	0.0366838i
$801$	−1.17552e7			−0.647364
$802$	6.42817e6	−	1.97839e7i	0.352900	−	1.08611i
$803$	90620.3	+	65839.5i	0.00495948	+	0.00360328i
$804$	−1.33208e6	−	967814.i	−0.0726759	−	0.0528022i
$805$	−1.37232e6	+	6.44980e6i	−0.0746387	+	0.350798i
$806$	2.24748e6	−	1.63289e6i	0.121859	−	0.0885359i
$807$	1.30951e7			0.707823
$808$	6.87201e6	−	4.99281e6i	0.370301	−	0.269040i
$809$	6.93378e6	+	2.13400e7i	0.372477	+	1.14636i	0.945165	+	0.326592i	$0.105900\pi$
$809$	6.93378e6	+	2.13400e7i	0.372477	+	1.14636i	−0.572689	+	0.819773i	$0.694100\pi$
$810$	−596445.	−	1.34037e6i	−0.0319417	−	0.0717814i
$811$	−175461.	+	540013.i	−0.00936759	+	0.0288305i	−0.955631	−	0.294566i	$-0.904825\pi$
$811$	−175461.	+	540013.i	−0.00936759	+	0.0288305i	0.946263	+	0.323397i	$0.104825\pi$
$812$	−653969.	−	2.01271e6i	−0.0348070	−	0.107125i
$813$	5.20790e6	+	1.60283e7i	0.276335	+	0.850472i
$814$	−3235.79	+	9958.75i	−0.000171167	+	0.000526798i
$815$	−9.58677e6	−	2.15440e7i	−0.505566	−	1.13614i
$816$	−865703.	−	2.66436e6i	−0.0455138	−	0.140077i
$817$	−1.21150e6	+	880209.i	−0.0634994	+	0.0461350i
$818$	−1.59666e7			−0.834312
$819$	−1.98189e6	+	1.43993e6i	−0.103245	+	0.0750121i
$820$	−485962.	+	2.28399e6i	−0.0252387	+	0.118621i
$821$	−8.29096e6	−	6.02374e6i	−0.429286	−	0.311895i	0.352077	−	0.935971i	$-0.385475\pi$
$821$	−8.29096e6	−	6.02374e6i	−0.429286	−	0.311895i	−0.781364	+	0.624076i	$0.785475\pi$
$822$	8.64717e6	+	6.28254e6i	0.446369	+	0.324306i
$823$	−8.91386e6	+	2.74340e7i	−0.458740	+	1.41186i	0.407949	+	0.913005i	$0.366244\pi$
$823$	−8.91386e6	+	2.74340e7i	−0.458740	+	1.41186i	−0.866688	+	0.498850i	$0.833756\pi$
$824$	−1.33140e6			−0.0683110
$825$	46369.9	−	51457.0i	0.00237193	−	0.00263214i
$826$	−3.79133e7			−1.93349
$827$	−1.05967e7	+	3.26133e7i	−0.538775	+	1.65818i	0.196573	+	0.980489i	$0.437019\pi$
$827$	−1.05967e7	+	3.26133e7i	−0.538775	+	1.65818i	−0.735348	+	0.677690i	$0.762981\pi$
$828$	670847.	+	487399.i	0.0340054	+	0.0247063i
$829$	−2.39070e7	−	1.73695e7i	−1.20820	−	0.877810i	−0.213135	−	0.977023i	$-0.568367\pi$
$829$	−2.39070e7	−	1.73695e7i	−1.20820	−	0.877810i	−0.995066	+	0.0992130i	$0.968367\pi$
$830$	−4.23471e6	−	9.51651e6i	−0.213368	−	0.479493i
$831$	−1.61096e7	+	1.17043e7i	−0.809251	+	0.587956i
$832$	−671927.			−0.0336522
$833$	1.69028e7	−	1.22806e7i	0.844008	−	0.613208i
$834$	−2.56920e6	−	7.90717e6i	−0.127903	−	0.393646i
$835$	−1.30415e7	+	1.17379e7i	−0.647310	+	0.582603i
$836$	−860.574	+	2648.57i	−4.25865e−5	+	0.000131068i
$837$	953730.	+	2.93528e6i	0.0470557	+	0.144822i
$838$	3.82667e6	+	1.17773e7i	0.188240	+	0.579342i
$839$	−6.50586e6	+	2.00230e7i	−0.319080	+	0.982028i	0.654962	+	0.755662i	$0.272685\pi$
$839$	−6.50586e6	+	2.00230e7i	−0.319080	+	0.982028i	−0.974042	+	0.226366i	$0.927315\pi$
$840$	5.90400e6	−	619325.i	0.288701	−	0.0302845i
$841$	−6.17924e6	−	1.90177e7i	−0.301263	−	0.927191i
$842$	970657.	−	705223.i	0.0471830	−	0.0342804i
$843$	6.61616e6			0.320654
$844$	−9.16392e6	+	6.65798e6i	−0.442818	+	0.321726i
$845$	−1.43093e7	+	1.28789e7i	−0.689409	+	0.620493i
$846$	−2.73341e6	−	1.98594e6i	−0.131304	−	0.0953980i
$847$	−2.40204e7	−	1.74518e7i	−1.15046	−	0.835858i
$848$	514061.	−	1.58212e6i	0.0245485	−	0.0755525i
$849$	1.16140e7			0.552983
$850$	−7.59414e6	−	1.31658e7i	−0.360522	−	0.625027i
$851$	−680083.			−0.0321913
$852$	−598654.	+	1.84247e6i	−0.0282538	+	0.0869562i
$853$	−4.37473e6	−	3.17843e6i	−0.205863	−	0.149568i	0.480077	−	0.877226i	$-0.340609\pi$
$853$	−4.37473e6	−	3.17843e6i	−0.205863	−	0.149568i	−0.685940	+	0.727658i	$0.740609\pi$
$854$	1.15198e7	+	8.36961e6i	0.540504	+	0.392699i
$855$	277101.	+	160059.i	0.0129635	+	0.00748800i
$856$	5.26394e6	−	3.82447e6i	0.245542	−	0.178397i
$857$	1.43114e7			0.665624			0.332812	−	0.942993i	$-0.392003\pi$
$857$	1.43114e7			0.665624			0.332812	+	0.942993i	$0.392003\pi$
$858$	−11766.8	+	8549.11i	−0.000545684	+	0.000396463i
$859$	−6.26315e6	−	1.92760e7i	−0.289608	−	0.891321i	−0.984980	−	0.172671i	$-0.944760\pi$
$859$	−6.26315e6	−	1.92760e7i	−0.289608	−	0.891321i	0.695372	−	0.718650i	$-0.255240\pi$
$860$	1.64113e7	+	9.47952e6i	0.756654	+	0.437059i
$861$	−1.33864e6	+	4.11992e6i	−0.0615399	+	0.189400i
$862$	−8.67996e6	−	2.67142e7i	−0.397878	−	1.22454i
$863$	2.82849e6	+	8.70519e6i	0.129279	+	0.397879i	0.994656	−	0.103241i	$-0.0329214\pi$
$863$	2.82849e6	+	8.70519e6i	0.129279	+	0.397879i	−0.865378	+	0.501120i	$0.832921\pi$
$864$	230680.	−	709960.i	0.0105130	−	0.0323556i
$865$	−5.40629e6	+	2.54093e7i	−0.245674	+	1.15465i
$866$	−7.30763e6	−	2.24906e7i	−0.331117	−	1.01907i
$867$	−426663.	+	309989.i	−0.0192769	+	0.0140055i
$868$	−1.24885e7			−0.562615
$869$	−130269.	+	94645.7i	−0.00585181	+	0.00425159i
$870$	−1.43592e6	+	150627.i	−0.0643180	+	0.00674690i
$871$	1.51751e6	+	1.10253e6i	0.0677774	+	0.0492432i
$872$	−4.45544e6	−	3.23707e6i	−0.198427	−	0.144165i
$873$	−2.42628e6	+	7.46733e6i	−0.107747	+	0.331612i
$874$	−180871.			−0.00800923
$875$	3.06367e7	−	9.93387e6i	1.35276	−	0.438630i
$876$	6.54927e6			0.288359
$877$	−1.04178e7	+	3.20626e7i	−0.457378	+	1.40767i	0.410942	+	0.911662i	$0.365200\pi$
$877$	−1.04178e7	+	3.20626e7i	−0.457378	+	1.40767i	−0.868320	+	0.496004i	$0.834800\pi$
$878$	−2.12492e6	−	1.54384e6i	−0.0930264	−	0.0675877i
$879$	382510.	+	277910.i	0.0166982	+	0.0121320i
$880$	35053.0	−	3677.04i	0.00152588	−	0.000160063i
$881$	2.85352e7	−	2.07321e7i	1.23863	−	0.899917i	0.241124	−	0.970494i	$-0.422484\pi$
$881$	2.85352e7	−	2.07321e7i	1.23863	−	0.899917i	0.997506	+	0.0705769i	$0.0224840\pi$
$882$	5.56727e6			0.240974
$883$	−1.46136e7	+	1.06174e7i	−0.630746	+	0.458264i	−0.856658	−	0.515884i	$-0.827464\pi$
$883$	−1.46136e7	+	1.06174e7i	−0.630746	+	0.458264i	0.225913	+	0.974148i	$0.427464\pi$
$884$	986209.	+	3.03524e6i	0.0424461	+	0.130636i
$885$	−5.38291e6	+	2.52994e7i	−0.231025	+	1.08580i
$886$	−6.46113e6	+	1.98853e7i	−0.276518	+	0.851036i
$887$	−8.01400e6	−	2.46646e7i	−0.342011	−	1.05260i	−0.963164	−	0.268913i	$-0.913336\pi$
$887$	−8.01400e6	−	2.46646e7i	−0.342011	−	1.05260i	0.621153	−	0.783689i	$-0.286664\pi$
$888$	189193.	+	582278.i	0.00805144	+	0.0247798i
$889$	208219.	−	640833.i	0.00883621	−	0.0271951i
$890$	−2.81002e7	−	1.62313e7i	−1.18914	−	0.686875i
$891$	−4993.32	−	15367.9i	−0.000210715	−	0.000648514i
$892$	6.72607e6	−	4.88677e6i	0.283041	−	0.205641i
$893$	736970.			0.0309258
$894$	1.23876e7	−	9.00012e6i	0.518374	−	0.376621i
$895$	−3.50655e7	−	2.02545e7i	−1.46326	−	0.845210i
$896$	2.44373e6	+	1.77547e6i	0.101691	+	0.0738829i
$897$	−764228.	−	555244.i	−0.0317133	−	0.0230411i
$898$	9.53513e6	−	2.93461e7i	0.394581	−	1.21439i
$899$	3.03735e6			0.125342
$900$	424974.	−	4.02764e6i	0.0174886	−	0.165747i
$901$	−7.90126e6			−0.324253
$902$	−7947.74	+	24460.6i	−0.000325258	+	0.00100104i
$903$	2.84442e7	+	2.06659e7i	1.16085	+	0.843404i
$904$	1.32855e6	+	965245.i	0.0540699	+	0.0392841i
$905$	−3.39922e7	+	3.05942e7i	−1.37962	+	1.24170i
$906$	1.14859e7	−	8.34500e6i	0.464884	−	0.337758i
$907$	1.92718e7			0.777865			0.388932	−	0.921266i	$-0.372844\pi$
$907$	1.92718e7			0.777865			0.388932	+	0.921266i	$0.372844\pi$
$908$	987295.	−	717312.i	0.0397404	−	0.0288731i
$909$	−3.32211e6	−	1.02244e7i	−0.133353	−	0.410419i
$910$	−6.72583e6	+	705535.i	−0.269242	+	0.0282433i
$911$	1.02214e7	−	3.14581e7i	0.408050	−	1.25585i	−0.510272	−	0.860013i	$-0.670455\pi$
$911$	1.02214e7	−	3.14581e7i	0.408050	−	1.25585i	0.918322	−	0.395835i	$-0.129545\pi$
$912$	50316.8	+	154859.i	0.00200321	+	0.00616524i
$913$	−35452.2	−	109111.i	−0.00140756	−	0.00433201i
$914$	−1.87762e6	+	5.77873e6i	−0.0743435	+	0.228806i
$915$	7.22057e6	−	6.49878e6i	0.285114	−	0.256613i
$916$	−4.93110e6	−	1.51764e7i	−0.194180	−	0.597625i
$917$	−3.03776e7	+	2.20706e7i	−1.19297	+	0.866745i
$918$	−3.54562e6			−0.138862
$919$	5.44804e6	−	3.95823e6i	0.212790	−	0.154601i	−0.476285	−	0.879291i	$-0.658017\pi$
$919$	5.44804e6	−	3.95823e6i	0.212790	−	0.154601i	0.689075	+	0.724690i	$0.258017\pi$
$920$	930639.	+	2.09139e6i	0.0362503	+	0.0814640i
$921$	1.11579e6	+	810666.i	0.0433443	+	0.0314915i
$922$	1.53278e6	+	1.11363e6i	0.0593818	+	0.0431434i
$923$	681986.	−	2.09894e6i	0.0263494	−	0.0810952i
$924$	65384.5			0.00251939
$925$	1.65965e6	+	2.87729e6i	0.0637767	+	0.110568i
$926$	1.60970e7			0.616904
$927$	−520710.	+	1.60258e6i	−0.0199020	+	0.0612521i
$928$	−594343.	−	431815.i	−0.0226552	−	0.0164599i
$929$	1.08294e7	+	7.86799e6i	0.411684	+	0.299106i	0.774283	−	0.632839i	$-0.218111\pi$
$929$	1.08294e7	+	7.86799e6i	0.411684	+	0.299106i	−0.362599	+	0.931945i	$0.618111\pi$
$930$	−1.77311e6	+	8.33353e6i	−0.0672247	+	0.315952i
$931$	−982434.	+	713780.i	−0.0371475	+	0.0269892i
$932$	−7.40299e6			−0.279169
$933$	1.14064e7	−	8.28726e6i	0.428989	−	0.311678i
$934$	8.72901e6	+	2.68651e7i	0.327414	+	1.00768i
$935$	−68058.4	−	152945.i	−0.00254597	−	0.00572146i
$936$	−262791.	+	808786.i	−0.00980438	+	0.0301748i
$937$	−603012.	−	1.85588e6i	−0.0224376	−	0.0690559i	0.939211	−	0.343341i	$-0.111559\pi$
$937$	−603012.	−	1.85588e6i	−0.0224376	−	0.0690559i	−0.961648	+	0.274285i	$0.911559\pi$
$938$	−2.60572e6	−	8.01959e6i	−0.0966988	−	0.297608i
$939$	−4.47613e6	+	1.37761e7i	−0.165668	+	0.509874i
$940$	−3.79194e6	−	8.52150e6i	−0.139972	−	0.314555i
$941$	−8.46174e6	−	2.60426e7i	−0.311520	−	0.958760i	−0.977163	−	0.212490i	$-0.931843\pi$
$941$	−8.46174e6	−	2.60426e7i	−0.311520	−	0.958760i	0.665643	−	0.746270i	$-0.268157\pi$
$942$	−7.65516e6	+	5.56180e6i	−0.281078	+	0.204215i
$943$	−1.67042e6			−0.0611710
$944$	−1.06477e7	+	7.73598e6i	−0.388888	+	0.282544i
$945$	1.56358e6	−	7.34875e6i	0.0569562	−	0.267691i
$946$	168878.	+	122697.i	0.00613544	+	0.00445766i
$947$	−2.89119e7	−	2.10057e7i	−1.04761	−	0.761136i	−0.0758563	−	0.997119i	$-0.524169\pi$
$947$	−2.89119e7	−	2.10057e7i	−1.04761	−	0.761136i	−0.971757	+	0.235983i	$0.924169\pi$
$948$	−2.90931e6	+	8.95393e6i	−0.105140	+	0.323588i
$949$	−7.46093e6			−0.268923
$950$	441391.	+	765228.i	0.0158677	+	0.0275094i
$951$	−1.07669e7			−0.386047
$952$	4.43345e6	−	1.36447e7i	0.158544	−	0.487948i
$953$	−7.30772e6	−	5.30937e6i	−0.260645	−	0.189370i	0.449786	−	0.893136i	$-0.351500\pi$
$953$	−7.30772e6	−	5.30937e6i	−0.260645	−	0.189370i	−0.710431	+	0.703766i	$0.751500\pi$
$954$	−1.70331e6	−	1.23753e6i	−0.0605932	−	0.0440235i
$955$	471100.	+	1.05869e6i	0.0167149	+	0.0375629i
$956$	6.17717e6	−	4.48797e6i	0.218597	−	0.158820i
$957$	−15902.3			−0.000561280
$958$	−571011.	+	414864.i	−0.0201016	+	0.0146047i
$959$	1.69150e7	+	5.20589e7i	0.593916	+	1.82788i
$960$	1.53172e6	−	1.37861e6i	0.0536417	−	0.0482795i
$961$	−3.30812e6	+	1.01813e7i	−0.115551	+	0.355628i
$962$	−215529.	−	663331.i	−0.00750876	−	0.0231096i
$963$	−2.54472e6	−	7.83185e6i	−0.0884249	−	0.272144i
$964$	−4.48446e6	+	1.38018e7i	−0.155424	+	0.478346i
$965$	−3.72098e7	+	3.90327e6i	−1.28629	+	0.134931i
$966$	1.31226e6	+	4.03873e6i	0.0452458	+	0.139252i
$967$	−1.04456e7	+	7.58918e6i	−0.359226	+	0.260993i	−0.752729	−	0.658330i	$-0.771263\pi$
$967$	−1.04456e7	+	7.58918e6i	−0.359226	+	0.260993i	0.393503	+	0.919323i	$0.371263\pi$
$968$	−1.03069e7			−0.353540
$969$	625681.	−	454584.i	0.0214064	−	0.0155526i
$970$	−1.61106e7	+	1.45001e7i	−0.549772	+	0.494815i
$971$	2.56541e6	+	1.86388e6i	0.0873191	+	0.0634411i	0.630588	−	0.776118i	$-0.282814\pi$
$971$	2.56541e6	+	1.86388e6i	0.0873191	+	0.0634411i	−0.543269	+	0.839559i	$0.682814\pi$
$972$	−764346.	−	555330.i	−0.0259492	−	0.0188532i
$973$	1.31574e7	−	4.04943e7i	0.445541	−	1.37123i
$974$	−1.71001e7			−0.577567
$975$	−484130.	+	4.58829e6i	−0.0163099	+	0.154575i
$976$	4.94301e6			0.166099
$977$	−1.33084e6	+	4.09589e6i	−0.0446055	+	0.137282i	−0.970879	−	0.239570i	$-0.922993\pi$
$977$	−1.33084e6	+	4.09589e6i	−0.0446055	+	0.137282i	0.926274	+	0.376852i	$0.122993\pi$
$978$	−1.22855e7	−	8.92592e6i	−0.410719	−	0.298405i
$979$	−289161.	−	210088.i	−0.00964236	−	0.00700558i
$980$	1.33083e7	+	7.68714e6i	0.442646	+	0.255682i
$981$	−5.63892e6	+	4.09692e6i	−0.187078	+	0.135920i
$982$	2.96336e7			0.980632
$983$	2.44639e7	−	1.77740e7i	0.807497	−	0.586681i	−0.105607	−	0.994408i	$-0.533678\pi$
$983$	2.44639e7	−	1.77740e7i	0.807497	−	0.586681i	0.913104	+	0.407727i	$0.133678\pi$
$984$	464696.	+	1.43019e6i	0.0152996	+	0.0470875i
$985$	−2.45087e7	−	1.41567e7i	−0.804877	−	0.464914i
$986$	−1.07827e6	+	3.31856e6i	−0.0353210	+	0.108707i
$987$	−5.34689e6	−	1.64560e7i	−0.174706	−	0.537691i
$988$	−57320.9	−	176416.i	−0.00186819	−	0.00574969i
$989$	−4.18950e6	+	1.28939e7i	−0.136198	+	0.419175i
$990$	9283.25	−	43630.8i	0.000301032	−	0.00141483i
$991$	−1.59871e7	−	4.92031e7i	−0.517112	−	1.59151i	−0.779407	−	0.626518i	$-0.784479\pi$
$991$	−1.59871e7	−	4.92031e7i	−0.517112	−	1.59151i	0.262295	−	0.964988i	$-0.415521\pi$
$992$	−3.50730e6	+	2.54821e6i	−0.113160	+	0.0822158i
$993$	1.93842e7			0.623843
$994$	−8.02645e6	+	5.83156e6i	−0.257666	+	0.187206i
$995$	−2.40382e7	+	2.52159e6i	−0.769741	+	0.0807452i
$996$	−5.42679e6	−	3.94280e6i	−0.173338	−	0.125938i
$997$	−9.30626e6	−	6.76140e6i	−0.296509	−	0.215426i	0.429577	−	0.903030i	$-0.358663\pi$
$997$	−9.30626e6	−	6.76140e6i	−0.296509	−	0.215426i	−0.726086	+	0.687604i	$0.758663\pi$
$998$	−1.15219e7	+	3.54608e7i	−0.366183	+	1.12700i
$999$	774870.			0.0245649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.b.121.1	yes	24
25.6	even	5	inner	150.6.g.b.31.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.b.31.1	✓	24	25.6	even	5	inner
150.6.g.b.121.1	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)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.5966 + 5.83204i) q^{5} +(-29.1246 + 21.1603i) q^{6} -184.364 q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(1.23607 - 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-55.5966 + 5.83204i) q^{5} +(-29.1246 + 21.1603i) q^{6} -184.364 q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-46.5348 + 218.711i) q^{10} +(-0.761061 + 2.34231i) q^{11} +(44.4984 + 136.952i) q^{12} +(-50.6926 - 156.016i) q^{13} +(-227.886 + 701.361i) q^{14} +(435.660 + 251.646i) q^{15} +(79.1084 + 243.470i) q^{16} +(983.698 - 714.698i) q^{17} +324.000 q^{18} +(-57.1750 + 41.5401i) q^{19} +(774.506 + 447.371i) q^{20} +(1342.38 + 975.296i) q^{21} +(7.96994 + 5.79050i) q^{22} +(-197.717 + 608.509i) q^{23} +576.000 q^{24} +(3056.97 - 648.484i) q^{25} -656.179 q^{26} +(225.273 - 693.320i) q^{27} +(2386.45 + 1733.86i) q^{28} +(-580.413 - 421.695i) q^{29} +(1495.82 - 1346.30i) q^{30} +(-3425.10 + 2488.48i) q^{31} +1024.00 q^{32} +(17.9324 - 13.0286i) q^{33} +(-1502.96 - 4625.62i) q^{34} +(10250.0 - 1075.22i) q^{35} +(400.486 - 1232.57i) q^{36} +(328.461 + 1010.90i) q^{37} +(87.3556 + 268.853i) q^{38} +(-456.234 + 1404.14i) q^{39} +(2659.24 - 2393.42i) q^{40} +(806.764 + 2482.97i) q^{41} +(5369.52 - 3901.18i) q^{42} +21189.4 q^{43} +(31.8797 - 23.1620i) q^{44} +(-1840.88 - 4136.94i) q^{45} +(2070.51 + 1504.32i) q^{46} +(-8436.44 - 6129.43i) q^{47} +(711.975 - 2191.23i) q^{48} +17182.9 q^{49} +(1311.65 - 12431.0i) q^{50} -10943.3 q^{51} +(-811.082 + 2496.25i) q^{52} +(-5257.14 - 3819.54i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(28.6520 - 134.663i) q^{55} +(9545.81 - 6935.44i) q^{56} +636.050 q^{57} +(-2321.65 + 1686.78i) q^{58} +(15886.9 + 48894.8i) q^{59} +(-3272.68 - 7354.56i) q^{60} +(5966.69 - 18363.6i) q^{61} +(5233.09 + 16105.8i) q^{62} +(-4614.69 - 14202.6i) q^{63} +(1265.73 - 3895.53i) q^{64} +(3728.23 + 8378.32i) q^{65} +(-27.3982 - 84.3230i) q^{66} +(-9250.57 + 6720.93i) q^{67} -19454.7 q^{68} +(4658.66 - 3384.71i) q^{69} +(8579.33 - 40322.4i) q^{70} +(10884.0 + 7907.69i) q^{71} +(-4193.94 - 3047.08i) q^{72} +(14054.4 - 43255.1i) q^{73} +4251.69 q^{74} +(-25688.8 - 11449.9i) q^{75} +1130.75 q^{76} +(140.312 - 431.836i) q^{77} +(4777.74 + 3471.23i) q^{78} +(52893.5 + 38429.4i) q^{79} +(-5818.09 - 13074.8i) q^{80} +(-5307.96 + 3856.46i) q^{81} +10443.0 q^{82} +(-37686.1 + 27380.5i) q^{83} +(-8203.89 - 25249.0i) q^{84} +(-50522.2 + 45471.8i) q^{85} +(26191.5 - 80609.3i) q^{86} +(1995.28 + 6140.85i) q^{87} +(-48.7079 - 149.908i) q^{88} +(-44846.4 + 138023. i) q^{89} +(-18013.3 + 1889.58i) q^{90} +(9345.87 + 28763.6i) q^{91} +(8282.06 - 6017.27i) q^{92} +38102.9 q^{93} +(-33745.8 + 24517.7i) q^{94} +(2936.47 - 2642.94i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(78420.9 + 56976.1i) q^{97} +(21239.3 - 65367.8i) q^{98} -199.490 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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