LMFDB - Embedded newform 150.6.g.b.61.5

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			61.5
Character	$\chi$	$=$	150.61
Dual form			150.6.g.b.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 + 2.35114i) q^{2} +(2.78115 - 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(49.1876 - 26.5627i) q^{5} +(11.1246 + 34.2380i) q^{6} -149.411 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})$	\(q+(-3.23607 + 2.35114i) q^{2} +(2.78115 - 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(49.1876 - 26.5627i) q^{5} +(11.1246 + 34.2380i) q^{6} -149.411 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-96.7217 + 201.606i) q^{10} +(502.003 - 364.726i) q^{11} +(-116.498 - 84.6411i) q^{12} +(-570.117 - 414.214i) q^{13} +(483.505 - 351.287i) q^{14} +(-90.5657 - 494.897i) q^{15} +(-207.108 - 150.473i) q^{16} +(-211.839 - 651.972i) q^{17} +324.000 q^{18} +(651.424 + 2004.88i) q^{19} +(-161.006 - 879.817i) q^{20} +(-415.535 + 1278.89i) q^{21} +(-766.992 + 2360.56i) q^{22} +(-1786.14 + 1297.71i) q^{23} +576.000 q^{24} +(1713.84 - 2613.12i) q^{25} +2818.81 q^{26} +(-589.773 + 428.495i) q^{27} +(-738.729 + 2273.58i) q^{28} +(-1685.98 + 5188.91i) q^{29} +(1456.65 + 1388.59i) q^{30} +(-1393.48 - 4288.68i) q^{31} +1024.00 q^{32} +(-1725.73 - 5311.26i) q^{33} +(2218.40 + 1611.76i) q^{34} +(-7349.18 + 3968.77i) q^{35} +(-1048.49 + 761.770i) q^{36} +(-4054.44 - 2945.72i) q^{37} +(-6821.80 - 4956.33i) q^{38} +(-5131.05 + 3727.93i) q^{39} +(2589.60 + 2468.60i) q^{40} +(-12000.7 - 8719.01i) q^{41} +(-1662.14 - 5115.54i) q^{42} -7818.54 q^{43} +(-3067.97 - 9442.23i) q^{44} +(-4487.95 - 601.186i) q^{45} +(2728.98 - 8398.93i) q^{46} +(7132.97 - 21953.0i) q^{47} +(-1863.98 + 1354.26i) q^{48} +5516.70 q^{49} +(597.692 + 12485.7i) q^{50} -6169.72 q^{51} +(-9121.86 + 6627.42i) q^{52} +(-11902.4 + 36631.8i) q^{53} +(901.094 - 2773.28i) q^{54} +(15004.2 - 31274.6i) q^{55} +(-2954.92 - 9094.30i) q^{56} +18972.5 q^{57} +(-6743.91 - 20755.6i) q^{58} +(-34937.9 - 25383.9i) q^{59} +(-7978.58 - 1068.77i) q^{60} +(14004.0 - 10174.5i) q^{61} +(14592.7 + 10602.2i) q^{62} +(9790.97 + 7113.56i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-39045.3 - 5230.34i) q^{65} +(18072.1 + 13130.1i) q^{66} +(-7868.76 - 24217.5i) q^{67} -10968.4 q^{68} +(6140.20 + 18897.6i) q^{69} +(14451.3 - 30122.2i) q^{70} +(-8483.99 + 26111.1i) q^{71} +(1601.94 - 4930.28i) q^{72} +(-35858.5 + 26052.7i) q^{73} +20046.2 q^{74} +(-17600.5 - 21937.1i) q^{75} +33728.8 q^{76} +(-75004.8 + 54494.2i) q^{77} +(7839.54 - 24127.6i) q^{78} +(-1484.16 + 4567.77i) q^{79} +(-14184.1 - 1900.04i) q^{80} +(2027.46 + 6239.88i) q^{81} +59334.6 q^{82} +(-33151.4 - 102030. i) q^{83} +(17406.2 + 12646.3i) q^{84} +(-27738.0 - 26441.9i) q^{85} +(25301.3 - 18382.5i) q^{86} +(39725.5 + 28862.3i) q^{87} +(32128.2 + 23342.5i) q^{88} +(-59634.3 + 43326.9i) q^{89} +(15936.8 - 8606.33i) q^{90} +(85181.8 + 61888.2i) q^{91} +(10915.9 + 33595.7i) q^{92} -40584.5 q^{93} +(28531.9 + 87812.0i) q^{94} +(85297.0 + 81311.5i) q^{95} +(2847.90 - 8764.94i) q^{96} +(6251.94 - 19241.5i) q^{97} +(-17852.4 + 12970.5i) q^{98} -50261.3 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$3$	2.78115	−	8.55951i	0.178411	−	0.549093i
$3$	2.78115	−	8.55951i	0.178411	−	0.549093i
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	49.1876	−	26.5627i	0.879895	−	0.475169i
$5$	49.1876	−	26.5627i	0.879895	−	0.475169i
$6$	11.1246	+	34.2380i	0.126156	+	0.388267i
$7$	−149.411			−1.15249			−0.576246	−	0.817276i	$-0.695483\pi$
$7$	−149.411			−1.15249			−0.576246	+	0.817276i	$0.695483\pi$
$8$	19.7771	+	60.8676i	0.109254	+	0.336249i
$9$	−65.5304	−	47.6106i	−0.269672	−	0.195928i
$10$	−96.7217	+	201.606i	−0.305861	+	0.637534i
$11$	502.003	−	364.726i	1.25090	−	0.908836i	0.252631	−	0.967563i	$-0.418704\pi$
$11$	502.003	−	364.726i	1.25090	−	0.908836i	0.998274	+	0.0587271i	$0.0187042\pi$
$12$	−116.498	−	84.6411i	−0.233543	−	0.169679i
$13$	−570.117	−	414.214i	−0.935632	−	0.679777i	0.0117330	−	0.999931i	$-0.496265\pi$
$13$	−570.117	−	414.214i	−0.935632	−	0.679777i	−0.947365	+	0.320154i	$0.896265\pi$
$14$	483.505	−	351.287i	0.659296	−	0.479007i
$15$	−90.5657	−	494.897i	−0.103929	−	0.567919i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	−211.839	−	651.972i	−0.177780	−	0.547151i	0.821970	−	0.569531i	$-0.192875\pi$
$17$	−211.839	−	651.972i	−0.177780	−	0.547151i	−0.999750	+	0.0223809i	$0.992875\pi$
$18$	324.000			0.235702
$19$	651.424	+	2004.88i	0.413980	+	1.27410i	0.913160	+	0.407602i	$0.133635\pi$
$19$	651.424	+	2004.88i	0.413980	+	1.27410i	−0.499180	+	0.866499i	$0.666365\pi$
$20$	−161.006	−	879.817i	−0.0900049	−	0.491832i
$21$	−415.535	+	1278.89i	−0.205617	+	0.632825i
$22$	−766.992	+	2360.56i	−0.337858	+	1.03982i
$23$	−1786.14	+	1297.71i	−0.704037	+	0.511513i	−0.881245	−	0.472661i	$-0.843294\pi$
$23$	−1786.14	+	1297.71i	−0.704037	+	0.511513i	0.177207	+	0.984174i	$0.443294\pi$
$24$	576.000			0.204124
$25$	1713.84	−	2613.12i	0.548429	−	0.836197i
$26$	2818.81			0.817773
$27$	−589.773	+	428.495i	−0.155695	+	0.113119i
$28$	−738.729	+	2273.58i	−0.178070	+	0.548043i
$29$	−1685.98	+	5188.91i	−0.372269	+	1.14573i	0.573034	+	0.819532i	$0.305766\pi$
$29$	−1685.98	+	5188.91i	−0.372269	+	1.14573i	−0.945303	+	0.326194i	$0.894234\pi$
$30$	1456.65	+	1388.59i	0.295496	+	0.281689i
$31$	−1393.48	−	4288.68i	−0.260433	−	0.801530i	−0.992710	−	0.120524i	$-0.961543\pi$
$31$	−1393.48	−	4288.68i	−0.260433	−	0.801530i	0.732277	−	0.681006i	$-0.238457\pi$
$32$	1024.00			0.176777
$33$	−1725.73	−	5311.26i	−0.275860	−	0.849009i
$34$	2218.40	+	1611.76i	0.329112	+	0.239114i
$35$	−7349.18	+	3968.77i	−1.01407	+	0.547628i
$36$	−1048.49	+	761.770i	−0.134836	+	0.0979642i
$37$	−4054.44	−	2945.72i	−0.486885	−	0.353743i	0.317100	−	0.948392i	$-0.397291\pi$
$37$	−4054.44	−	2945.72i	−0.486885	−	0.353743i	−0.803985	+	0.594650i	$0.797291\pi$
$38$	−6821.80	−	4956.33i	−0.766372	−	0.556802i
$39$	−5131.05	+	3727.93i	−0.540188	+	0.392469i
$40$	2589.60	+	2468.60i	0.255907	+	0.243950i
$41$	−12000.7	−	8719.01i	−1.11493	−	0.810042i	−0.131494	−	0.991317i	$-0.541978\pi$
$41$	−12000.7	−	8719.01i	−1.11493	−	0.810042i	−0.983432	+	0.181275i	$0.941978\pi$
$42$	−1662.14	−	5115.54i	−0.145393	−	0.447475i
$43$	−7818.54			−0.644843			−0.322422	−	0.946596i	$-0.604497\pi$
$43$	−7818.54			−0.644843			−0.322422	+	0.946596i	$0.604497\pi$
$44$	−3067.97	−	9442.23i	−0.238902	−	0.735264i
$45$	−4487.95	−	601.186i	−0.330382	−	0.0442565i
$46$	2728.98	−	8398.93i	0.190154	−	0.585234i
$47$	7132.97	−	21953.0i	0.471005	−	1.44960i	−0.380266	−	0.924877i	$-0.624167\pi$
$47$	7132.97	−	21953.0i	0.471005	−	1.44960i	0.851271	−	0.524727i	$-0.175833\pi$
$48$	−1863.98	+	1354.26i	−0.116772	+	0.0848395i
$49$	5516.70			0.328238
$50$	597.692	+	12485.7i	0.0338106	+	0.706298i
$51$	−6169.72			−0.332154
$52$	−9121.86	+	6627.42i	−0.467816	+	0.339888i
$53$	−11902.4	+	36631.8i	−0.582029	+	1.79130i	0.0288601	+	0.999583i	$0.490812\pi$
$53$	−11902.4	+	36631.8i	−0.582029	+	1.79130i	−0.610889	+	0.791716i	$0.709188\pi$
$54$	901.094	−	2773.28i	0.0420519	−	0.129422i
$55$	15004.2	−	31274.6i	0.668814	−	1.39407i
$56$	−2954.92	−	9094.30i	−0.125914	−	0.387525i
$57$	18972.5			0.773458
$58$	−6743.91	−	20755.6i	−0.263234	−	0.810151i
$59$	−34937.9	−	25383.9i	−1.30667	−	0.949354i	−0.306676	−	0.951814i	$-0.599217\pi$
$59$	−34937.9	−	25383.9i	−1.30667	−	0.949354i	−0.999997	+	0.00246041i	$0.999217\pi$
$60$	−7978.58	−	1068.77i	−0.286119	−	0.0383273i
$61$	14004.0	−	10174.5i	0.481866	−	0.350096i	−0.320182	−	0.947356i	$-0.603744\pi$
$61$	14004.0	−	10174.5i	0.481866	−	0.350096i	0.802048	+	0.597260i	$0.203744\pi$
$62$	14592.7	+	10602.2i	0.482121	+	0.350282i
$63$	9790.97	+	7113.56i	0.310795	+	0.225806i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−39045.3	−	5230.34i	−1.14627	−	0.153549i
$66$	18072.1	+	13130.1i	0.510680	+	0.371031i
$67$	−7868.76	−	24217.5i	−0.214150	−	0.659087i	−0.999213	−	0.0396707i	$-0.987369\pi$
$67$	−7868.76	−	24217.5i	−0.214150	−	0.659087i	0.785062	−	0.619417i	$-0.212631\pi$
$68$	−10968.4			−0.287654
$69$	6140.20	+	18897.6i	0.155260	+	0.477841i
$70$	14451.3	−	30122.2i	0.352502	−	0.734752i
$71$	−8483.99	+	26111.1i	−0.199735	+	0.614722i	0.800153	+	0.599795i	$0.204751\pi$
$71$	−8483.99	+	26111.1i	−0.199735	+	0.614722i	−0.999889	+	0.0149262i	$0.995249\pi$
$72$	1601.94	−	4930.28i	0.0364180	−	0.112083i
$73$	−35858.5	+	26052.7i	−0.787563	+	0.572198i	−0.907239	−	0.420615i	$-0.861814\pi$
$73$	−35858.5	+	26052.7i	−0.787563	+	0.572198i	0.119676	+	0.992813i	$0.461814\pi$
$74$	20046.2			0.425553
$75$	−17600.5	−	21937.1i	−0.361304	−	0.450325i
$76$	33728.8			0.669834
$77$	−75004.8	+	54494.2i	−1.44166	+	1.04743i
$78$	7839.54	−	24127.6i	0.145900	−	0.449033i
$79$	−1484.16	+	4567.77i	−0.0267555	+	0.0823448i	−0.963543	−	0.267555i	$-0.913784\pi$
$79$	−1484.16	+	4567.77i	−0.0267555	+	0.0823448i	0.936787	+	0.349900i	$0.113784\pi$
$80$	−14184.1	−	1900.04i	−0.247787	−	0.0331924i
$81$	2027.46	+	6239.88i	0.0343352	+	0.105673i
$82$	59334.6			0.974482
$83$	−33151.4	−	102030.i	−0.528211	−	1.62567i	−0.757878	−	0.652396i	$-0.773764\pi$
$83$	−33151.4	−	102030.i	−0.528211	−	1.62567i	0.229668	−	0.973269i	$-0.426236\pi$
$84$	17406.2	+	12646.3i	0.269157	+	0.195554i
$85$	−27738.0	−	26441.9i	−0.416416	−	0.396959i
$86$	25301.3	−	18382.5i	0.368890	−	0.268014i
$87$	39725.5	+	28862.3i	0.562693	+	0.408820i
$88$	32128.2	+	23342.5i	0.442262	+	0.321322i
$89$	−59634.3	+	43326.9i	−0.798033	+	0.579805i	−0.910337	−	0.413869i	$-0.864177\pi$
$89$	−59634.3	+	43326.9i	−0.798033	+	0.579805i	0.112303	+	0.993674i	$0.464177\pi$
$90$	15936.8	−	8606.33i	0.207393	−	0.111998i
$91$	85181.8	+	61888.2i	1.07831	+	0.783437i
$92$	10915.9	+	33595.7i	0.134459	+	0.413823i
$93$	−40584.5			−0.486579
$94$	28531.9	+	87812.0i	0.333051	+	1.02502i
$95$	85297.0	+	81311.5i	0.969671	+	0.924364i
$96$	2847.90	−	8764.94i	0.0315389	−	0.0970668i
$97$	6251.94	−	19241.5i	0.0674661	−	0.207639i	−0.911640	−	0.410990i	$-0.865183\pi$
$97$	6251.94	−	19241.5i	0.0674661	−	0.207639i	0.979106	+	0.203351i	$0.0651831\pi$
$98$	−17852.4	+	12970.5i	−0.187772	+	0.136425i
$99$	−50261.3			−0.515401
$100$	−31289.8	−	38999.3i	−0.312898	−	0.389993i
$101$	163803.			1.59778			0.798890	−	0.601477i	$-0.205421\pi$
$101$	163803.			1.59778			0.798890	+	0.601477i	$0.205421\pi$
$102$	19965.6	−	14505.9i	0.190013	−	0.138052i
$103$	9370.29	−	28838.8i	0.0870282	−	0.267845i	−0.898066	−	0.439861i	$-0.855028\pi$
$103$	9370.29	−	28838.8i	0.0870282	−	0.267845i	0.985094	+	0.172015i	$0.0550279\pi$
$104$	13937.0	−	42893.6i	0.126353	−	0.388874i
$105$	13531.5	+	73943.1i	0.119777	+	0.654522i
$106$	−47609.5	−	146527.i	−0.411556	−	1.26664i
$107$	−79115.6			−0.668041			−0.334020	−	0.942566i	$-0.608405\pi$
$107$	−79115.6			−0.668041			−0.334020	+	0.942566i	$0.608405\pi$
$108$	3604.37	+	11093.1i	0.0297352	+	0.0915155i
$109$	156315.	+	113569.i	1.26018	+	0.915578i	0.998767	−	0.0496481i	$-0.0158100\pi$
$109$	156315.	+	113569.i	1.26018	+	0.915578i	0.261418	+	0.965226i	$0.415810\pi$
$110$	24976.4	+	136484.i	0.196810	+	1.07547i
$111$	−36489.9	+	26511.5i	−0.281103	+	0.204233i
$112$	30944.3	+	22482.3i	0.233096	+	0.169354i
$113$	191985.	+	139485.i	1.41440	+	1.02762i	0.992665	+	0.120901i	$0.0385785\pi$
$113$	191985.	+	139485.i	1.41440	+	1.02762i	0.421734	+	0.906719i	$0.361421\pi$
$114$	−61396.2	+	44606.9i	−0.442465	+	0.321470i
$115$	−53385.3	+	111276.i	−0.376424	+	0.784614i
$116$	70623.2	+	51310.7i	0.487306	+	0.354049i
$117$	17639.0	+	54287.2i	0.119127	+	0.366634i
$118$	172743.			1.14207
$119$	31651.1	+	97411.9i	0.204890	+	0.630587i
$120$	28332.1	−	15300.1i	0.179608	−	0.0969934i
$121$	69213.9	−	213019.i	0.429764	−	1.32268i
$122$	−21396.1	+	65850.5i	−0.130148	+	0.400553i
$123$	−108006.	+	78471.1i	−0.643703	+	0.467678i
$124$	−72150.2			−0.421389
$125$	14888.3	−	174057.i	0.0852257	−	0.996362i
$126$	−48409.2			−0.271645
$127$	112559.	−	81778.6i	0.619255	−	0.449915i	−0.233406	−	0.972379i	$-0.574987\pi$
$127$	112559.	−	81778.6i	0.619255	−	0.449915i	0.852661	+	0.522464i	$0.174987\pi$
$128$	5062.93	−	15582.1i	0.0273135	−	0.0840623i
$129$	−21744.5	+	66922.8i	−0.115047	+	0.354079i
$130$	138651.	−	74875.3i	0.719554	−	0.388580i
$131$	−18810.1	−	57891.6i	−0.0957665	−	0.294739i	0.891686	−	0.452654i	$-0.149523\pi$
$131$	−18810.1	−	57891.6i	−0.0957665	−	0.294739i	−0.987453	+	0.157915i	$0.949523\pi$
$132$	−89353.4			−0.446351
$133$	−97330.0	−	299551.i	−0.477109	−	1.46839i
$134$	82402.7	+	59869.1i	0.396442	+	0.288032i
$135$	−17627.5	+	36742.7i	−0.0832448	+	0.173515i
$136$	35494.4	−	25788.2i	0.164556	−	0.119557i
$137$	−238027.	−	172937.i	−1.08349	−	0.787202i	−0.105203	−	0.994451i	$-0.533549\pi$
$137$	−238027.	−	172937.i	−1.08349	−	0.787202i	−0.978288	+	0.207249i	$0.933549\pi$
$138$	−64301.0	−	46717.4i	−0.287422	−	0.208824i
$139$	48304.2	−	35095.1i	0.212055	−	0.154067i	−0.476688	−	0.879073i	$-0.658163\pi$
$139$	48304.2	−	35095.1i	0.212055	−	0.154067i	0.688743	+	0.725006i	$0.258163\pi$
$140$	24056.0	+	131454.i	0.103730	+	0.566833i
$141$	−168069.	−	122109.i	−0.711935	−	0.517251i
$142$	−33936.0	−	104444.i	−0.141234	−	0.434674i
$143$	−437275.			−1.78819
$144$	6407.78	+	19721.1i	0.0257514	+	0.0792547i
$145$	54902.3	+	300014.i	0.216856	+	1.18501i
$146$	54786.9	−	168617.i	0.212713	−	0.654665i
$147$	15342.8	−	47220.2i	0.0585613	−	0.180233i
$148$	−64871.0	+	47131.5i	−0.243442	+	0.176871i
$149$	229940.			0.848496			0.424248	−	0.905546i	$-0.360539\pi$
$149$	229940.			0.848496			0.424248	+	0.905546i	$0.360539\pi$
$150$	108534.	+	29608.7i	0.393855	+	0.107446i
$151$	231184.			0.825118			0.412559	−	0.910931i	$-0.364635\pi$
$151$	231184.			0.825118			0.412559	+	0.910931i	$0.364635\pi$
$152$	−109149.	+	79301.2i	−0.383186	+	0.278401i
$153$	−17158.9	+	52809.8i	−0.0592600	+	0.182384i
$154$	114597.	−	352694.i	0.389379	−	1.19838i
$155$	−182461.	−	173936.i	−0.610016	−	0.581513i
$156$	31358.2	+	96510.6i	0.103167	+	0.317514i
$157$	151858.			0.491686			0.245843	−	0.969310i	$-0.420935\pi$
$157$	151858.			0.491686			0.245843	+	0.969310i	$0.420935\pi$
$158$	−5936.63	−	18271.1i	−0.0189190	−	0.0582266i
$159$	280448.	+	203757.i	0.879749	+	0.639175i
$160$	50368.1	−	27200.2i	0.155545	−	0.0839987i
$161$	266869.	−	193892.i	0.811397	−	0.589515i
$162$	−21231.8	−	15425.8i	−0.0635624	−	0.0461808i
$163$	−387450.	−	281499.i	−1.14221	−	0.829866i	−0.154787	−	0.987948i	$-0.549469\pi$
$163$	−387450.	−	281499.i	−1.14221	−	0.829866i	−0.987426	+	0.158082i	$0.949469\pi$
$164$	−192011.	+	139504.i	−0.557463	+	0.405021i
$165$	−225966.	−	215408.i	−0.646150	−	0.615959i
$166$	347166.	+	252231.i	0.977839	+	0.710442i
$167$	101899.	+	313612.i	0.282734	+	0.870165i	0.987069	+	0.160297i	$0.0512452\pi$
$167$	101899.	+	313612.i	0.282734	+	0.870165i	−0.704335	+	0.709868i	$0.748755\pi$
$168$	−86060.8			−0.235251
$169$	38723.9	+	119180.i	0.104295	+	0.320986i
$170$	151931.	+	20352.0i	0.403203	+	0.0540113i
$171$	52765.3	−	162395.i	0.137993	−	0.424700i
$172$	−38657.0	+	118974.i	−0.0996338	+	0.306641i
$173$	147653.	−	107276.i	0.375081	−	0.272513i	−0.384233	−	0.923236i	$-0.625534\pi$
$173$	147653.	−	107276.i	0.375081	−	0.272513i	0.759315	+	0.650723i	$0.225534\pi$
$174$	−196414.			−0.491812
$175$	−256067.	+	390429.i	−0.632061	+	0.963710i
$176$	−158850.			−0.386551
$177$	−314441.	+	228455.i	−0.754408	+	0.548110i
$178$	91113.1	−	280417.i	0.215541	−	0.663368i
$179$	5863.61	−	18046.3i	0.0136783	−	0.0420975i	−0.943984	−	0.329990i	$-0.892955\pi$
$179$	5863.61	−	18046.3i	0.0136783	−	0.0420975i	0.957663	+	0.287893i	$0.0929546\pi$
$180$	−31337.8	+	65320.3i	−0.0720921	+	0.150268i
$181$	−70374.2	−	216590.i	−0.159668	−	0.491407i	0.838936	−	0.544230i	$-0.183178\pi$
$181$	−70374.2	−	216590.i	−0.159668	−	0.491407i	−0.998604	+	0.0528230i	$0.983178\pi$
$182$	−421162.			−0.942477
$183$	−48141.3	−	148164.i	−0.106265	−	0.327050i
$184$	−114313.	−	83053.2i	−0.248915	−	0.180847i
$185$	−277674.	−	37196.0i	−0.596495	−	0.0799038i
$186$	131334.	−	95419.9i	0.278353	−	0.202235i
$187$	−344135.	−	250029.i	−0.719656	−	0.522861i
$188$	−298790.	−	217083.i	−0.616554	−	0.447952i
$189$	88118.7	−	64022.0i	0.179438	−	0.130369i
$190$	−467202.	−	62584.2i	−0.938902	−	0.125771i
$191$	−191269.	−	138965.i	−0.379369	−	0.275628i	0.381716	−	0.924280i	$-0.375333\pi$
$191$	−191269.	−	138965.i	−0.379369	−	0.275628i	−0.761085	+	0.648652i	$0.775333\pi$
$192$	11391.6	+	35059.7i	0.0223014	+	0.0686366i
$193$	606882.			1.17276			0.586382	−	0.810034i	$-0.300552\pi$
$193$	606882.			1.17276			0.586382	+	0.810034i	$0.300552\pi$
$194$	25007.8	+	76966.0i	0.0477057	+	0.146823i
$195$	−153360.	+	319662.i	−0.288819	+	0.602012i
$196$	27276.0	−	83947.0i	0.0507156	−	0.156086i
$197$	−211144.	+	649833.i	−0.387625	+	1.19299i	0.546932	+	0.837177i	$0.315796\pi$
$197$	−211144.	+	649833.i	−0.387625	+	1.19299i	−0.934558	+	0.355812i	$0.884204\pi$
$198$	162649.	−	118171.i	0.294841	−	0.214215i
$199$	62343.7			0.111599			0.0557995	−	0.998442i	$-0.482229\pi$
$199$	62343.7			0.111599			0.0557995	+	0.998442i	$0.482229\pi$
$200$	192949.	+	52637.7i	0.341089	+	0.0930512i
$201$	−229174.			−0.400107
$202$	−530076.	+	385123.i	−0.914029	+	0.664081i
$203$	251904.	−	775281.i	0.429037	−	1.32044i
$204$	−30504.8	+	93884.0i	−0.0513207	+	0.157949i
$205$	−821886.	−	110096.i	−1.36592	−	0.182973i
$206$	37481.2	+	115355.i	0.0615382	+	0.189395i
$207$	178831.			0.290079
$208$	55747.9	+	171574.i	0.0893449	+	0.274975i
$209$	1.05825e6	+	768862.i	1.67580	+	1.21754i
$210$	−217640.	−	207470.i	−0.340557	−	0.324644i
$211$	634183.	−	460761.i	0.980637	−	0.712475i	0.0227863	−	0.999740i	$-0.492746\pi$
$211$	634183.	−	460761.i	0.980637	−	0.712475i	0.957851	+	0.287266i	$0.0927463\pi$
$212$	498574.	+	362235.i	0.761885	+	0.553542i
$213$	199902.	+	145238.i	0.301904	+	0.219346i
$214$	256024.	−	186012.i	0.382160	−	0.277656i
$215$	−384575.	+	207682.i	−0.567394	+	0.306409i
$216$	−37745.5	−	27423.7i	−0.0550466	−	0.0399937i
$217$	208201.	+	640777.i	0.300147	+	0.923757i
$218$	−772863.			−1.10144
$219$	123271.	+	379388.i	0.173680	+	0.534531i
$220$	−401718.	−	382947.i	−0.559582	−	0.533436i
$221$	−149283.	+	459447.i	−0.205603	+	0.632782i
$222$	55751.7	−	171586.i	0.0759233	−	0.233668i
$223$	480395.	−	349028.i	0.646899	−	0.470000i	−0.215314	−	0.976545i	$-0.569078\pi$
$223$	480395.	−	349028.i	0.646899	−	0.470000i	0.862214	+	0.506545i	$0.169078\pi$
$224$	−152997.			−0.203734
$225$	−236721.	+	89641.4i	−0.311731	+	0.118046i
$226$	−949228.			−1.23623
$227$	695507.	−	505316.i	0.895853	−	0.650876i	−0.0415441	−	0.999137i	$-0.513228\pi$
$227$	695507.	−	505316.i	0.895853	−	0.650876i	0.937398	+	0.348261i	$0.113228\pi$
$228$	93805.0	−	288702.i	0.119506	−	0.367801i
$229$	−15932.9	+	49036.5i	−0.0200774	+	0.0617918i	−0.960593	−	0.277958i	$-0.910342\pi$
$229$	−15932.9	+	49036.5i	−0.0200774	+	0.0617918i	0.940516	+	0.339750i	$0.110342\pi$
$230$	−88866.6	−	485612.i	−0.110769	−	0.605299i
$231$	257844.	+	793561.i	0.317926	+	0.978476i
$232$	−349180.			−0.425921
$233$	−401269.	−	1.23498e6i	−0.484224	−	1.49029i	−0.833102	−	0.553120i	$-0.813437\pi$
$233$	−401269.	−	1.23498e6i	−0.484224	−	1.49029i	0.348878	−	0.937168i	$-0.386563\pi$
$234$	−184718.	−	134205.i	−0.220531	−	0.160225i
$235$	−232278.	−	1.26929e6i	−0.274372	−	1.49931i
$236$	−559007.	+	406142.i	−0.653337	+	0.474677i
$237$	34970.2	+	25407.3i	0.0404415	+	0.0293825i
$238$	−331454.	−	240816.i	−0.379298	−	0.275576i
$239$	1.14062e6	−	828709.i	1.29165	−	0.938442i	0.291817	−	0.956474i	$-0.405740\pi$
$239$	1.14062e6	−	828709.i	1.29165	−	0.938442i	0.999837	+	0.0180328i	$0.00574032\pi$
$240$	−55711.7	+	116125.i	−0.0624336	+	0.130136i
$241$	855634.	+	621654.i	0.948954	+	0.689456i	0.950559	−	0.310543i	$-0.100511\pi$
$241$	855634.	+	621654.i	0.948954	+	0.689456i	−0.00160489	+	0.999999i	$0.500511\pi$
$242$	276856.	+	852074.i	0.303889	+	0.935274i
$243$	59049.0			0.0641500
$244$	−85584.6	−	263402.i	−0.0920282	−	0.283234i
$245$	271353.	−	146539.i	0.288815	−	0.155968i
$246$	165019.	−	507875.i	0.173858	−	0.535081i
$247$	459060.	−	1.41284e6i	0.478770	−	1.47350i
$248$	233483.	−	169635.i	0.241061	−	0.175141i
$249$	−965523.			−0.986880
$250$	361053.	+	598266.i	0.365360	+	0.605402i
$251$	−1.26184e6			−1.26421			−0.632106	−	0.774882i	$-0.717809\pi$
$251$	−1.26184e6			−1.26421			−0.632106	+	0.774882i	$0.717809\pi$
$252$	156656.	−	113817.i	0.155398	−	0.112903i
$253$	−423339.	+	1.30290e6i	−0.415802	+	1.27971i
$254$	−171974.	+	529282.i	−0.167255	+	0.514758i
$255$	−303474.	+	163885.i	−0.292261	+	0.157829i
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−599127.			−0.565830			−0.282915	−	0.959145i	$-0.591302\pi$
$257$	−599127.			−0.565830			−0.282915	+	0.959145i	$0.591302\pi$
$258$	−86978.2	−	267691.i	−0.0813507	−	0.250372i
$259$	605778.	+	440124.i	0.561131	+	0.407685i
$260$	−272640.	+	568289.i	−0.250125	+	0.521358i
$261$	357530.	−	259761.i	0.324871	−	0.236033i
$262$	196982.	+	143116.i	0.177286	+	0.128806i
$263$	−29427.8	−	21380.6i	−0.0262343	−	0.0190603i	0.574591	−	0.818441i	$-0.305161\pi$
$263$	−29427.8	−	21380.6i	−0.0262343	−	0.0190603i	−0.600825	+	0.799380i	$0.705161\pi$
$264$	289154.	−	210082.i	0.255340	−	0.185515i
$265$	387590.	+	2.11799e6i	0.339046	+	1.85272i
$266$	1.01925e6	+	740531.i	0.883238	+	0.641710i
$267$	205004.	+	630939.i	0.175989	+	0.541638i
$268$	−407421.			−0.346503
$269$	−185306.	−	570313.i	−0.156138	−	0.480544i	0.842136	−	0.539265i	$-0.181298\pi$
$269$	−185306.	−	570313.i	−0.156138	−	0.480544i	−0.998274	+	0.0587211i	$0.981298\pi$
$270$	−29343.3	−	160347.i	−0.0244962	−	0.133860i
$271$	203286.	−	625651.i	0.168145	−	0.517498i	−0.831109	−	0.556110i	$-0.812294\pi$
$271$	203286.	−	625651.i	0.168145	−	0.517498i	0.999254	+	0.0386116i	$0.0122935\pi$
$272$	−54230.7	+	166905.i	−0.0444450	+	0.136788i
$273$	766636.	−	556994.i	0.622562	−	0.452318i
$274$	1.17687e6			0.947006
$275$	−92718.4	−	1.93687e6i	−0.0739323	−	1.54444i
$276$	317922.			0.251216
$277$	−1.82419e6	+	1.32535e6i	−1.42847	+	1.03784i	−0.438170	+	0.898892i	$0.644373\pi$
$277$	−1.82419e6	+	1.32535e6i	−1.42847	+	1.03784i	−0.990299	+	0.138951i	$0.955627\pi$
$278$	−73802.3	+	227140.i	−0.0572741	+	0.176271i
$279$	−112872.	+	347383.i	−0.0868110	+	0.267177i
$280$	−386915.	−	368836.i	−0.294931	−	0.281150i
$281$	−356355.	−	1.09675e6i	−0.269226	−	0.828593i	−0.990690	−	0.136140i	$-0.956530\pi$
$281$	−356355.	−	1.09675e6i	−0.269226	−	0.828593i	0.721463	−	0.692453i	$-0.243470\pi$
$282$	830979.			0.622254
$283$	140457.	+	432283.i	0.104250	+	0.320850i	0.989554	−	0.144164i	$-0.0460493\pi$
$283$	140457.	+	432283.i	0.104250	+	0.320850i	−0.885303	+	0.465014i	$0.846049\pi$
$284$	355382.	+	258200.i	0.261457	+	0.189959i
$285$	933210.	−	503961.i	0.680561	−	0.367523i
$286$	1.41505e6	−	1.02809e6i	1.02296	−	0.743221i
$287$	1.79304e6	+	1.30272e6i	1.28494	+	0.933567i
$288$	−67103.1	−	48753.3i	−0.0476718	−	0.0346356i
$289$	768496.	−	558345.i	0.541249	−	0.393240i
$290$	−883043.	−	841783.i	−0.616576	−	0.587767i
$291$	−147310.	−	107027.i	−0.101977	−	0.0740903i
$292$	219148.	+	674467.i	0.150411	+	0.462918i
$293$	592499.			0.403198			0.201599	−	0.979468i	$-0.435386\pi$
$293$	592499.			0.403198			0.201599	+	0.979468i	$0.435386\pi$
$294$	61371.1	+	188881.i	0.0414091	+	0.127444i
$295$	−2.39278e6	−	320526.i	−1.60084	−	0.214441i
$296$	99114.0	−	305042.i	0.0657515	−	0.202362i
$297$	−139784.	+	430212.i	−0.0919533	+	0.283003i
$298$	−744103.	+	540622.i	−0.485392	+	0.352658i
$299$	1.55583e6			1.00643
$300$	−420837.	+	159362.i	−0.269967	+	0.102231i
$301$	1.16818e6			0.743177
$302$	−748128.	+	543547.i	−0.472018	+	0.342941i
$303$	455560.	−	1.40207e6i	0.285062	−	0.877330i
$304$	166764.	−	513248.i	0.103495	−	0.318525i
$305$	418559.	−	872441.i	0.257637	−	0.537015i
$306$	−68635.7	−	211239.i	−0.0419031	−	0.128965i
$307$	−1.84778e6			−1.11893			−0.559467	−	0.828853i	$-0.688994\pi$
$307$	−1.84778e6			−1.11893			−0.559467	+	0.828853i	$0.688994\pi$
$308$	458389.	+	1.41077e6i	0.275332	+	0.847385i
$309$	−220786.	−	160410.i	−0.131545	−	0.0955731i
$310$	999403.	+	133876.i	0.590659	+	0.0791220i
$311$	728088.	−	528987.i	0.426858	−	0.310130i	−0.353533	−	0.935422i	$-0.615020\pi$
$311$	728088.	−	528987.i	0.426858	−	0.310130i	0.780391	+	0.625292i	$0.215020\pi$
$312$	−328387.	−	238587.i	−0.190985	−	0.138759i
$313$	546604.	+	397131.i	0.315364	+	0.229125i	0.734195	−	0.678939i	$-0.237560\pi$
$313$	546604.	+	397131.i	0.315364	+	0.229125i	−0.418831	+	0.908064i	$0.637560\pi$
$314$	−491422.	+	357039.i	−0.281275	+	0.204358i
$315$	670550.	+	89823.9i	0.380763	+	0.0510053i
$316$	62169.2	+	45168.6i	0.0350234	+	0.0254460i
$317$	−176680.	−	543764.i	−0.0987503	−	0.303922i	0.889463	−	0.457008i	$-0.151079\pi$
$317$	−176680.	−	543764.i	−0.0987503	−	0.303922i	−0.988213	+	0.153086i	$0.951079\pi$
$318$	−1.38661e6			−0.768929
$319$	1.04617e6	+	3.21977e6i	0.575604	+	1.77153i
$320$	−99043.0	+	206444.i	−0.0540691	+	0.112701i
$321$	−220033.	+	677191.i	−0.119186	+	0.366816i
$322$	−407740.	+	1.25489e6i	−0.219151	+	0.674477i
$323$	1.16913e6	−	849421.i	0.623527	−	0.453019i
$324$	104976.			0.0555556
$325$	−2.05948e6	+	779883.i	−1.08156	+	0.409563i
$326$	1.91566e6			0.998331
$327$	1.40683e6	−	1.02212e6i	0.727568	−	0.528609i
$328$	293367.	−	902890.i	0.150566	−	0.463394i
$329$	−1.06574e6	+	3.28002e6i	−0.542829	+	1.67066i
$330$	1.23770e6	+	165796.i	0.625647	+	0.0838088i
$331$	145230.	+	446971.i	0.0728593	+	0.224238i	0.980854	−	0.194743i	$-0.0623874\pi$
$331$	145230.	+	446971.i	0.0728593	+	0.224238i	−0.907995	+	0.418981i	$0.862387\pi$
$332$	−1.71648e6			−0.854663
$333$	125441.	+	386068.i	0.0619911	+	0.190789i
$334$	−1.06710e6	−	775291.i	−0.523405	−	0.380276i
$335$	−1.03033e6	−	982187.i	−0.501608	−	0.478170i
$336$	278499.	−	202341.i	0.134578	−	0.0977768i
$337$	2.64758e6	+	1.92358e6i	1.26991	+	0.922645i	0.999199	−	0.0400150i	$-0.0127406\pi$
$337$	2.64758e6	+	1.92358e6i	1.26991	+	0.922645i	0.270713	+	0.962660i	$0.412741\pi$
$338$	−405521.	−	294629.i	−0.193073	−	0.140276i
$339$	1.72787e6	−	1.25537e6i	0.816604	−	0.593297i
$340$	−539509.	+	291350.i	−0.253105	+	0.136684i
$341$	−2.26373e6	−	1.64469e6i	−1.05424	−	0.765947i
$342$	211061.	+	649580.i	0.0975761	+	0.300308i
$343$	1.68690e6			0.774200
$344$	−154628.	−	475896.i	−0.0704517	−	0.216828i
$345$	803993.	+	766427.i	0.363668	+	0.346675i
$346$	−225593.	+	694304.i	−0.101306	+	0.311788i
$347$	−1.14771e6	+	3.53230e6i	−0.511693	+	1.57483i	0.277526	+	0.960718i	$0.410486\pi$
$347$	−1.14771e6	+	3.53230e6i	−0.511693	+	1.57483i	−0.789219	+	0.614112i	$0.789514\pi$
$348$	635608.	−	461797.i	0.281347	−	0.204410i
$349$	−3.63391e6			−1.59702			−0.798511	−	0.601980i	$-0.794379\pi$
$349$	−3.63391e6			−1.59702			−0.798511	+	0.601980i	$0.794379\pi$
$350$	−89301.9	−	1.86550e6i	−0.0389664	−	0.814003i
$351$	513728.			0.222570
$352$	514051.	−	373480.i	0.221131	−	0.160661i
$353$	−742143.	+	2.28408e6i	−0.316994	+	0.975606i	0.657932	+	0.753077i	$0.271431\pi$
$353$	−742143.	+	2.28408e6i	−0.316994	+	0.975606i	−0.974926	+	0.222529i	$0.928569\pi$
$354$	480423.	−	1.47859e6i	0.203759	−	0.627105i
$355$	276274.	+	1.50970e6i	0.116351	+	0.635798i
$356$	364452.	+	1.12167e6i	0.152411	+	0.469072i
$357$	921825.			0.382805
$358$	23454.4	+	72185.3i	0.00967202	+	0.0297674i
$359$	−292878.	−	212789.i	−0.119936	−	0.0871390i	0.526200	−	0.850361i	$-0.323616\pi$
$359$	−292878.	−	212789.i	−0.119936	−	0.0871390i	−0.646136	+	0.763222i	$0.723616\pi$
$360$	−52165.8	−	285061.i	−0.0212144	−	0.115926i
$361$	−1.59197e6	+	1.15663e6i	−0.642935	+	0.467119i
$362$	736969.	+	535439.i	0.295582	+	0.214753i
$363$	−1.63084e6	−	1.18487e6i	−0.649598	−	0.471961i
$364$	1.36291e6	−	990211.i	0.539154	−	0.391719i
$365$	−1.07176e6	+	2.23397e6i	−0.421082	+	0.877699i
$366$	504142.	+	366281.i	0.196721	+	0.142926i
$367$	−860363.	−	2.64792e6i	−0.333439	−	1.02622i	−0.967486	−	0.252925i	$-0.918607\pi$
$367$	−860363.	−	2.64792e6i	−0.333439	−	1.02622i	0.634047	−	0.773295i	$-0.281393\pi$
$368$	565194.			0.217559
$369$	371292.	+	1.14272e6i	0.141955	+	0.436892i
$370$	986027.	−	532483.i	0.374442	−	0.202209i
$371$	1.77835e6	−	5.47320e6i	0.670783	−	2.06446i
$372$	−200661.	+	617571.i	−0.0751805	+	0.231382i
$373$	990627.	−	719733.i	0.368670	−	0.267855i	−0.387989	−	0.921664i	$-0.626830\pi$
$373$	990627.	−	719733.i	0.368670	−	0.267855i	0.756659	+	0.653809i	$0.226830\pi$
$374$	1.70150e6			0.629002
$375$	−1.44844e6	−	611516.i	−0.531890	−	0.224559i
$376$	1.47730e6			0.538888
$377$	3.11052e6	−	2.25993e6i	1.12714	−	0.818919i
$378$	−134633.	+	414359.i	−0.0484645	+	0.149158i
$379$	336636.	−	1.03606e6i	0.120382	−	0.370499i	−0.872649	−	0.488348i	$-0.837600\pi$
$379$	336636.	−	1.03606e6i	0.120382	−	0.370499i	0.993032	+	0.117849i	$0.0375998\pi$
$380$	1.65904e6	−	895930.i	0.589383	−	0.318284i
$381$	−386942.	−	1.19088e6i	−0.136563	−	0.420298i
$382$	945688.			0.331581
$383$	−851853.	−	2.62173e6i	−0.296734	−	0.913254i	−0.982633	−	0.185557i	$-0.940591\pi$
$383$	−851853.	−	2.62173e6i	−0.296734	−	0.913254i	0.685899	−	0.727696i	$-0.259409\pi$
$384$	−119294.	−	86672.5i	−0.0412850	−	0.0299953i
$385$	−2.24179e6	+	4.67277e6i	−0.770803	+	1.60666i
$386$	−1.96391e6	+	1.42686e6i	−0.670893	+	0.487433i
$387$	512352.	+	372245.i	0.173896	+	0.126343i
$388$	−261885.	−	190270.i	−0.0883142	−	0.0641641i
$389$	87604.3	−	63648.2i	0.0293529	−	0.0213261i	−0.573012	−	0.819547i	$-0.694225\pi$
$389$	87604.3	−	63648.2i	0.0293529	−	0.0213261i	0.602365	+	0.798221i	$0.294225\pi$
$390$	−255288.	−	1.39502e6i	−0.0849901	−	0.464429i
$391$	1.22444e6	+	889609.i	0.405038	+	0.294278i
$392$	109104.	+	335788.i	0.0358613	+	0.110370i
$393$	−547838.			−0.178925
$394$	−844574.	−	2.59933e6i	−0.274093	−	0.843570i
$395$	48330.3	+	264101.i	0.0155857	+	0.0851682i
$396$	−248505.	+	764821.i	−0.0796339	+	0.245088i
$397$	573771.	−	1.76589e6i	0.182710	−	0.562323i	−0.817191	−	0.576366i	$-0.804470\pi$
$397$	573771.	−	1.76589e6i	0.182710	−	0.562323i	0.999901	+	0.0140429i	$0.00447015\pi$
$398$	−201749.	+	146579.i	−0.0638414	+	0.0463835i
$399$	−2.83470e6			−0.891404
$400$	−748154.	+	283311.i	−0.233798	+	0.0885347i
$401$	−3.13928e6			−0.974921			−0.487461	−	0.873145i	$-0.662077\pi$
$401$	−3.13928e6			−0.974921			−0.487461	+	0.873145i	$0.662077\pi$
$402$	741624.	−	538821.i	0.228886	−	0.166295i
$403$	−981988.	+	3.02225e6i	−0.301192	+	0.926974i
$404$	809884.	−	2.49257e6i	0.246871	−	0.759790i
$405$	265474.	+	253070.i	0.0804239	+	0.0766660i
$406$	1.00762e6	+	3.10112e6i	0.303375	+	0.933692i
$407$	−3.10972e6			−0.930540
$408$	−122019.	−	375536.i	−0.0362892	−	0.111687i
$409$	−5.21628e6	−	3.78985e6i	−1.54189	−	1.12025i	−0.949139	−	0.314857i	$-0.898043\pi$
$409$	−5.21628e6	−	3.78985e6i	−1.54189	−	1.12025i	−0.592747	−	0.805389i	$-0.701957\pi$
$410$	2.91853e6	−	1.57609e6i	0.857441	−	0.463043i
$411$	−2.14225e6	+	1.55643e6i	−0.625554	+	0.454491i
$412$	−392508.	−	285174.i	−0.113921	−	0.0827687i
$413$	5.22011e6	+	3.79264e6i	1.50593	+	1.09412i
$414$	−578709.	+	420457.i	−0.165943	+	0.120565i
$415$	−4.34083e6	−	4.13800e6i	−1.23723	−	1.17943i
$416$	−583799.	−	424155.i	−0.165398	−	0.120169i
$417$	−166055.	−	511065.i	−0.0467641	−	0.143925i
$418$	−5.23226e6			−1.46470
$419$	−732316.	−	2.25384e6i	−0.203781	−	0.627173i	−0.999761	−	0.0218506i	$-0.993044\pi$
$419$	−732316.	−	2.25384e6i	−0.203781	−	0.627173i	0.795980	−	0.605322i	$-0.206956\pi$
$420$	1.19209e6	+	159687.i	0.329750	+	0.0441719i
$421$	−52078.9	+	160282.i	−0.0143204	+	0.0440738i	−0.957961	−	0.286897i	$-0.907376\pi$
$421$	−52078.9	+	160282.i	−0.0143204	+	0.0440738i	0.943641	+	0.330971i	$0.107376\pi$
$422$	−968945.	+	2.98211e6i	−0.264861	+	0.815159i
$423$	−1.51262e6	+	1.09898e6i	−0.411036	+	0.298635i
$424$	−2.46508e6			−0.665912
$425$	−2.06674e6	−	563819.i	−0.555025	−	0.151414i
$426$	−988372.			−0.263874
$427$	−2.09235e6	+	1.52018e6i	−0.555347	+	0.403483i
$428$	−391169.	+	1.20389e6i	−0.103218	+	0.317672i
$429$	−1.21613e6	+	3.74286e6i	−0.319033	+	0.981884i
$430$	756222.	−	1.57626e6i	0.197232	−	0.411109i
$431$	−1.19518e6	−	3.67840e6i	−0.309914	−	0.953818i	−0.977797	−	0.209552i	$-0.932799\pi$
$431$	−1.19518e6	−	3.67840e6i	−0.309914	−	0.953818i	0.667883	−	0.744266i	$-0.267201\pi$
$432$	186624.			0.0481125
$433$	−1.56732e6	−	4.82373e6i	−0.401735	−	1.23641i	−0.923591	−	0.383379i	$-0.874760\pi$
$433$	−1.56732e6	−	4.82373e6i	−0.401735	−	1.23641i	0.521857	−	0.853033i	$-0.325240\pi$
$434$	−2.18031e6	−	1.58409e6i	−0.555641	−	0.403697i
$435$	2.72066e6	+	364448.i	0.689369	+	0.0923448i
$436$	2.50104e6	−	1.81711e6i	0.630092	−	0.457789i
$437$	−3.76527e6	−	2.73563e6i	−0.943176	−	0.685257i
$438$	−1.29091e6	−	937898.i	−0.321521	−	0.233599i
$439$	262895.	−	191004.i	0.0651060	−	0.0473023i	−0.554756	−	0.832013i	$-0.687188\pi$
$439$	262895.	−	191004.i	0.0651060	−	0.0473023i	0.619862	+	0.784711i	$0.287188\pi$
$440$	2.20035e6	+	294749.i	0.541826	+	0.0725806i
$441$	−361511.	−	262653.i	−0.0885167	−	0.0643111i
$442$	−597133.	−	1.83779e6i	−0.145384	−	0.447445i
$443$	6.11251e6			1.47982			0.739912	−	0.672703i	$-0.234867\pi$
$443$	6.11251e6			1.47982			0.739912	+	0.672703i	$0.234867\pi$
$444$	223007.	+	686344.i	0.0536859	+	0.165228i
$445$	−1.78239e6	+	3.71519e6i	−0.426680	+	0.889368i
$446$	−733979.	+	2.25895e6i	−0.174721	+	0.537737i
$447$	639500.	−	1.96818e6i	0.151381	−	0.465903i
$448$	495109.	−	359718.i	0.116548	−	0.0846772i
$449$	6.11027e6			1.43036			0.715179	−	0.698941i	$-0.246345\pi$
$449$	6.11027e6			1.43036			0.715179	+	0.698941i	$0.246345\pi$
$450$	555285.	−	846649.i	0.129266	−	0.197093i
$451$	−9.20443e6			−2.13086
$452$	3.07177e6	−	2.23177e6i	0.707199	−	0.513810i
$453$	642959.	−	1.97882e6i	0.147210	−	0.453066i
$454$	−1.06264e6	+	3.27047e6i	−0.241962	+	0.744682i
$455$	5.83381e6	+	781471.i	1.32106	+	0.176964i
$456$	375220.	+	1.15481e6i	0.0845034	+	0.260075i
$457$	−4.21726e6			−0.944582			−0.472291	−	0.881443i	$-0.656573\pi$
$457$	−4.21726e6			−0.944582			−0.472291	+	0.881443i	$0.656573\pi$
$458$	−63731.7	−	196146.i	−0.0141969	−	0.0436934i
$459$	404304.	+	293744.i	0.0895728	+	0.0650785i
$460$	1.42932e6	+	1.36254e6i	0.314945	+	0.300230i
$461$	−119051.	+	86495.8i	−0.0260905	+	0.0189558i	−0.600754	−	0.799434i	$-0.705133\pi$
$461$	−119051.	+	86495.8i	−0.0260905	+	0.0189558i	0.574664	+	0.818390i	$0.305133\pi$
$462$	−2.70017e6	−	1.96179e6i	−0.588554	−	0.427610i
$463$	−3.10495e6	−	2.25587e6i	−0.673134	−	0.489060i	0.197939	−	0.980214i	$-0.436575\pi$
$463$	−3.10495e6	−	2.25587e6i	−0.673134	−	0.489060i	−0.871073	+	0.491154i	$0.836575\pi$
$464$	1.12997e6	−	820972.i	0.243653	−	0.177024i
$465$	−1.99626e6	+	1.07804e6i	−0.428138	+	0.231207i
$466$	4.20215e6	+	3.05304e6i	0.896410	+	0.651280i
$467$	−1.95447e6	−	6.01525e6i	−0.414703	−	1.27633i	−0.912516	−	0.409041i	$-0.865863\pi$
$467$	−1.95447e6	−	6.01525e6i	−0.414703	−	1.27633i	0.497813	−	0.867285i	$-0.334137\pi$
$468$	913295.			0.192751
$469$	1.17568e6	+	3.61837e6i	0.246807	+	0.759593i
$470$	3.73594e6	+	3.56138e6i	0.780109	+	0.743659i
$471$	422340.	−	1.29983e6i	0.0877222	−	0.269981i
$472$	854086.	−	2.62861e6i	0.176460	−	0.543089i
$473$	−3.92493e6	+	2.85163e6i	−0.806638	+	0.586057i
$474$	−172902.			−0.0353472
$475$	6.35541e6	+	1.73380e6i	1.29244	+	0.352585i
$476$	1.63880e6			0.331519
$477$	2.52403e6	−	1.83381e6i	0.507924	−	0.369028i
$478$	−1.74271e6	+	5.36352e6i	−0.348864	+	1.07369i
$479$	−1.57955e6	+	4.86134e6i	−0.314553	+	0.968093i	0.661386	+	0.750046i	$0.269969\pi$
$479$	−1.57955e6	+	4.86134e6i	−0.314553	+	0.968093i	−0.975938	+	0.218047i	$0.930031\pi$
$480$	−92739.3	−	506774.i	−0.0183722	−	0.100395i
$481$	1.09134e6	+	3.35881e6i	0.215079	+	0.661946i
$482$	−4.23049e6			−0.829417
$483$	−917414.	−	2.82351e6i	−0.178936	−	0.550708i
$484$	−2.89927e6	−	2.10644e6i	−0.562568	−	0.408730i
$485$	−203589.	−	1.11251e6i	−0.0393006	−	0.214758i
$486$	−191087.	+	138833.i	−0.0366978	+	0.0266625i
$487$	4.01838e6	+	2.91953e6i	0.767766	+	0.557815i	0.901282	−	0.433232i	$-0.142627\pi$
$487$	4.01838e6	+	2.91953e6i	0.767766	+	0.557815i	−0.133517	+	0.991047i	$0.542627\pi$
$488$	896253.	+	651166.i	0.170365	+	0.123778i
$489$	−3.48705e6	+	2.53349e6i	−0.659457	+	0.479123i
$490$	−533584.	+	1.11220e6i	−0.100395	+	0.209263i
$491$	−4.85579e6	−	3.52794e6i	−0.908984	−	0.660416i	0.0317734	−	0.999495i	$-0.489885\pi$
$491$	−4.85579e6	−	3.52794e6i	−0.908984	−	0.660416i	−0.940758	+	0.339079i	$0.889885\pi$
$492$	660075.	+	2.03150e6i	0.122936	+	0.378359i
$493$	3.74018e6			0.693067
$494$	1.83624e6	+	5.65137e6i	0.338542	+	1.04192i
$495$	−2.47223e6	+	1.33508e6i	−0.453499	+	0.244903i
$496$	−356730.	+	1.09790e6i	−0.0651082	+	0.200383i
$497$	1.26760e6	−	3.90128e6i	0.230193	−	0.708462i
$498$	3.12450e6	−	2.27008e6i	0.564556	−	0.410174i
$499$	4.43768e6			0.797820			0.398910	−	0.916990i	$-0.369389\pi$
$499$	4.43768e6			0.797820			0.398910	+	0.916990i	$0.369389\pi$
$500$	−2.57500e6	−	1.08714e6i	−0.460630	−	0.194474i
$501$	2.96776e6			0.528244
$502$	4.08340e6	−	2.96676e6i	0.723207	−	0.525441i
$503$	−2.28869e6	+	7.04387e6i	−0.403336	+	1.24134i	0.518940	+	0.854810i	$0.326327\pi$
$503$	−2.28869e6	+	7.04387e6i	−0.403336	+	1.24134i	−0.922277	+	0.386531i	$0.873673\pi$
$504$	−239348.	+	736638.i	−0.0419715	+	0.129175i
$505$	8.05705e6	−	4.35104e6i	1.40588	−	0.759215i
$506$	−1.69336e6	−	5.21161e6i	−0.294017	−	0.904890i
$507$	1.12782e6			0.194858
$508$	−687897.	−	2.11713e6i	−0.118267	−	0.363989i
$509$	−74501.2	−	54128.3i	−0.0127459	−	0.00926041i	0.581394	−	0.813622i	$-0.302507\pi$
$509$	−74501.2	−	54128.3i	−0.0127459	−	0.00926041i	−0.594140	+	0.804362i	$0.702507\pi$
$510$	596746.	−	1.24385e6i	0.101593	−	0.211760i
$511$	5.35766e6	−	3.89257e6i	0.907660	−	0.659453i
$512$	−212079.	−	154084.i	−0.0357538	−	0.0259767i
$513$	−1.24327e6	−	903291.i	−0.208580	−	0.151542i
$514$	1.93882e6	−	1.40863e6i	0.323690	−	0.235174i
$515$	−305135.	−	1.66741e6i	−0.0506960	−	0.277029i
$516$	910847.	+	661769.i	0.150599	+	0.109416i
$517$	−4.42607e6	−	1.36221e7i	−0.728270	−	2.24138i
$518$	−2.99513e6			−0.490446
$519$	−507584.	−	1.56218e6i	−0.0827160	−	0.254574i
$520$	−453845.	−	2.48004e6i	−0.0736036	−	0.402207i
$521$	−1.41168e6	+	4.34470e6i	−0.227846	+	0.701238i	0.770144	+	0.637870i	$0.220184\pi$
$521$	−1.41168e6	+	4.34470e6i	−0.227846	+	0.701238i	−0.997990	+	0.0633680i	$0.979816\pi$
$522$	−546257.	+	1.68121e6i	−0.0877446	+	0.270050i
$523$	5.07005e6	−	3.68361e6i	0.810510	−	0.588870i	−0.103469	−	0.994633i	$-0.532994\pi$
$523$	5.07005e6	−	3.68361e6i	0.810510	−	0.588870i	0.913978	+	0.405763i	$0.132994\pi$
$524$	−973933.			−0.154953
$525$	2.62971e6	+	3.27765e6i	0.416400	+	0.518996i
$526$	145499.			0.0229296
$527$	−2.50091e6	+	1.81702e6i	−0.392258	+	0.284992i
$528$	−441787.	+	1.35968e6i	−0.0689649	+	0.212252i
$529$	−482689.	+	1.48556e6i	−0.0749942	+	0.230808i
$530$	−6.23396e6	−	5.94268e6i	−0.963994	−	0.918951i
$531$	1.08095e6	+	3.32683e6i	0.166368	+	0.512029i
$532$	−5.03946e6			−0.771978
$533$	3.23025e6	+	9.94170e6i	0.492514	+	1.51580i
$534$	−2.14683e6	−	1.55977e6i	−0.325796	−	0.236704i
$535$	−3.89151e6	+	2.10153e6i	−0.587805	+	0.317432i
$536$	1.31844e6	−	957905.i	0.198221	−	0.144016i
$537$	−138160.	−	100379.i	−0.0206751	−	0.0150213i
$538$	1.94055e6	+	1.40989e6i	0.289047	+	0.210005i
$539$	2.76940e6	−	2.01208e6i	0.410595	−	0.298314i
$540$	471954.	+	449902.i	0.0696491	+	0.0663947i
$541$	7.87453e6	+	5.72118e6i	1.15673	+	0.840412i	0.989361	−	0.145482i	$-0.0464734\pi$
$541$	7.87453e6	+	5.72118e6i	1.15673	+	0.840412i	0.167367	+	0.985895i	$0.446473\pi$
$542$	813145.	+	2.50260e6i	0.118897	+	0.365926i
$543$	−2.04962e6			−0.298314
$544$	−216923.	−	667620.i	−0.0314274	−	0.0967235i
$545$	1.07055e7	+	1.43406e6i	1.54388	+	0.206812i
$546$	−1.17132e6	+	3.60494e6i	−0.168148	+	0.517507i
$547$	3.48965e6	−	1.07400e7i	0.498670	−	1.53475i	−0.312488	−	0.949922i	$-0.601162\pi$
$547$	3.48965e6	−	1.07400e7i	0.498670	−	1.53475i	0.811158	−	0.584827i	$-0.198838\pi$
$548$	−3.80844e6	+	2.76699e6i	−0.541745	+	0.393601i
$549$	−1.40210e6			−0.198540
$550$	4.85391e6	+	6.04986e6i	0.684203	+	0.852783i
$551$	−1.15014e7			−1.61388
$552$	−1.02882e6	+	747478.i	−0.143711	+	0.104412i
$553$	221750.	−	682476.i	0.0308355	−	0.0949018i
$554$	2.78712e6	−	8.57786e6i	0.385816	−	1.18742i
$555$	−1.09063e6	+	2.27331e6i	−0.150296	+	0.313275i
$556$	−295209.	−	908561.i	−0.0404989	−	0.124643i
$557$	8.05694e6			1.10035			0.550177	−	0.835048i	$-0.314560\pi$
$557$	8.05694e6			1.10035			0.550177	+	0.835048i	$0.314560\pi$
$558$	−451487.	−	1.38953e6i	−0.0613846	−	0.188922i
$559$	4.45748e6	+	3.23855e6i	0.603336	+	0.438350i
$560$	2.11927e6	+	283888.i	0.285572	+	0.0382540i
$561$	−3.09722e6	+	2.25026e6i	−0.415493	+	0.301874i
$562$	3.73180e6	+	2.71131e6i	0.498399	+	0.362108i
$563$	−1.53773e6	−	1.11723e6i	−0.204460	−	0.148549i	0.480843	−	0.876806i	$-0.340331\pi$
$563$	−1.53773e6	−	1.11723e6i	−0.204460	−	0.148549i	−0.685304	+	0.728257i	$0.740331\pi$
$564$	−2.68911e6	+	1.95375e6i	−0.355967	+	0.258625i
$565$	1.31484e7	+	1.76130e6i	1.73282	+	0.232120i
$566$	−1.47089e6	−	1.06866e6i	−0.192992	−	0.140217i
$567$	−302925.	−	932308.i	−0.0395711	−	0.121787i
$568$	−1.75711e6			−0.228522
$569$	4.10910e6	+	1.26465e7i	0.532067	+	1.63753i	0.749903	+	0.661548i	$0.230100\pi$
$569$	4.10910e6	+	1.26465e7i	0.532067	+	1.63753i	−0.217836	+	0.975985i	$0.569900\pi$
$570$	−1.83505e6	+	3.82496e6i	−0.236571	+	0.493105i
$571$	1.19643e6	−	3.68224e6i	0.153567	−	0.472631i	−0.844446	−	0.535641i	$-0.820070\pi$
$571$	1.19643e6	−	3.68224e6i	0.153567	−	0.472631i	0.998013	+	0.0630101i	$0.0200700\pi$
$572$	−2.16201e6	+	6.65397e6i	−0.276291	+	0.850336i
$573$	−1.72142e6	+	1.25069e6i	−0.219029	+	0.159134i
$574$	−8.86526e6			−1.12308
$575$	329895.	+	6.89145e6i	0.0416107	+	0.869242i
$576$	331776.			0.0416667
$577$	7.85401e6	−	5.70627e6i	0.982092	−	0.713532i	0.0239167	−	0.999714i	$-0.492386\pi$
$577$	7.85401e6	−	5.70627e6i	0.982092	−	0.713532i	0.958175	+	0.286182i	$0.0923863\pi$
$578$	−1.17416e6	+	3.61369e6i	−0.146186	+	0.449915i
$579$	1.68783e6	−	5.19461e6i	0.209234	−	0.643957i
$580$	4.83674e6	+	647908.i	0.597011	+	0.0799730i
$581$	4.95319e6	+	1.52444e7i	0.608759	+	1.87357i
$582$	728341.			0.0891307
$583$	7.38554e6	+	2.27304e7i	0.899935	+	2.76971i
$584$	−2.29494e6	−	1.66738e6i	−0.278445	−	0.202302i
$585$	2.30964e6	+	2.20172e6i	0.279032	+	0.265994i
$586$	−1.91737e6	+	1.39305e6i	−0.230654	+	0.167580i
$587$	−640.885	−	465.630i	−7.67689e−5	−	5.57758e-5i	0.587747	−	0.809045i	$-0.300015\pi$
$587$	−640.885	−	465.630i	−7.67689e−5	−	5.57758e-5i	−0.587824	+	0.808989i	$0.700015\pi$
$588$	−642687.	−	466939.i	−0.0766577	−	0.0556951i
$589$	7.69054e6	−	5.58750e6i	0.913416	−	0.663635i
$590$	8.49679e6	−	4.58851e6i	1.00491	−	0.542678i
$591$	4.97503e6	+	3.61457e6i	0.585905	+	0.425685i
$592$	396456.	+	1.22017e6i	0.0464934	+	0.143092i
$593$	4.68247e6			0.546812			0.273406	−	0.961899i	$-0.411850\pi$
$593$	4.68247e6			0.546812			0.273406	+	0.961899i	$0.411850\pi$
$594$	−559137.	−	1.72085e6i	−0.0650208	−	0.200113i
$595$	4.14437e6	+	3.95072e6i	0.479917	+	0.457493i
$596$	1.13689e6	−	3.49898e6i	0.131100	−	0.403484i
$597$	173387.	−	533632.i	0.0199105	−	0.0612782i
$598$	−5.03479e6	+	3.65799e6i	−0.575742	+	0.418301i
$599$	−1.54968e7			−1.76472			−0.882360	−	0.470576i	$-0.844046\pi$
$599$	−1.54968e7			−1.76472			−0.882360	+	0.470576i	$0.844046\pi$
$600$	987173.	−	1.50515e6i	0.111948	−	0.170688i
$601$	−6.79001e6			−0.766803			−0.383402	−	0.923582i	$-0.625248\pi$
$601$	−6.79001e6			−0.766803			−0.383402	+	0.923582i	$0.625248\pi$
$602$	−3.78030e6	+	2.74655e6i	−0.425143	+	0.308884i
$603$	−637369.	+	1.96162e6i	−0.0713835	+	0.219696i
$604$	1.14304e6	−	3.51791e6i	0.127488	−	0.392367i
$605$	−2.25389e6	−	1.23164e7i	−0.250348	−	1.36803i
$606$	1.82224e6	+	5.60828e6i	0.201569	+	0.620366i
$607$	1.64442e7			1.81152			0.905758	−	0.423795i	$-0.139302\pi$
$607$	1.64442e7			1.81152			0.905758	+	0.423795i	$0.139302\pi$
$608$	667058.	+	2.05299e6i	0.0731821	+	0.225231i
$609$	−5.93544e6	−	4.31235e6i	−0.648499	−	0.471162i
$610$	696746.	+	3.80737e6i	0.0758140	+	0.414286i
$611$	−1.31599e7	+	9.56120e6i	−1.42609	+	1.03612i
$612$	718763.	+	522212.i	0.0775723	+	0.0563596i
$613$	−4.58501e6	−	3.33120e6i	−0.492821	−	0.358055i	0.313447	−	0.949606i	$-0.398516\pi$
$613$	−4.58501e6	−	3.33120e6i	−0.492821	−	0.358055i	−0.806268	+	0.591550i	$0.798516\pi$
$614$	5.97954e6	−	4.34439e6i	0.640099	−	0.465059i
$615$	−3.22816e6	+	6.72874e6i	−0.344165	+	0.717375i
$616$	−4.80031e6	−	3.48763e6i	−0.509703	−	0.370321i
$617$	1.11691e6	+	3.43750e6i	0.118115	+	0.363521i	0.992584	−	0.121561i	$-0.0387899\pi$
$617$	1.11691e6	+	3.43750e6i	0.118115	+	0.363521i	−0.874469	+	0.485082i	$0.838790\pi$
$618$	1.09162e6			0.114975
$619$	−3.25021e6	−	1.00031e7i	−0.340946	−	1.04932i	−0.963719	−	0.266920i	$-0.913994\pi$
$619$	−3.25021e6	−	1.00031e7i	−0.340946	−	1.04932i	0.622773	−	0.782403i	$-0.286006\pi$
$620$	−3.54890e6	+	1.91651e6i	−0.370778	+	0.200231i
$621$	497356.	−	1.53070e6i	0.0517533	−	0.159280i
$622$	−1.11242e6	+	3.42368e6i	−0.115290	+	0.354827i
$623$	8.91003e6	−	6.47352e6i	0.919727	−	0.668221i
$624$	1.62364e6			0.166927
$625$	−3.89112e6	−	8.95693e6i	−0.398450	−	0.917190i
$626$	−2.70256e6			−0.275638
$627$	9.52423e6	−	6.91976e6i	0.967522	−	0.702946i
$628$	750826.	−	2.31081e6i	0.0759697	−	0.233811i
$629$	−1.06164e6	+	3.26740e6i	−0.106992	+	0.329288i
$630$	−2.38113e6	+	1.28588e6i	−0.239019	+	0.129077i
$631$	−4.20139e6	−	1.29305e7i	−0.420068	−	1.29284i	−0.907639	−	0.419753i	$-0.862117\pi$
$631$	−4.20139e6	−	1.29305e7i	−0.420068	−	1.29284i	0.487571	−	0.873084i	$-0.337883\pi$
$632$	−307382.			−0.0306115
$633$	−2.18013e6	−	6.70974e6i	−0.216258	−	0.665574i
$634$	1.85021e6	+	1.34426e6i	0.182809	+	0.132819i
$635$	3.36422e6	−	7.01236e6i	0.331093	−	0.690128i
$636$	4.48716e6	−	3.26011e6i	0.439875	−	0.319588i
$637$	−3.14516e6	−	2.28509e6i	−0.307110	−	0.223129i
$638$	−1.09556e7	−	7.95970e6i	−1.06557	−	0.774185i
$639$	1.79912e6	−	1.30714e6i	0.174304	−	0.126640i
$640$	−164870.	−	900932.i	−0.0159108	−	0.0869445i
$641$	−1.17047e7	−	8.50396e6i	−1.12516	−	0.817478i	−0.140179	−	0.990126i	$-0.544768\pi$
$641$	−1.17047e7	−	8.50396e6i	−1.12516	−	0.817478i	−0.984984	+	0.172648i	$0.944768\pi$
$642$	−880131.	−	2.70876e6i	−0.0842771	−	0.259378i
$643$	1.17106e7			1.11700			0.558499	−	0.829505i	$-0.311378\pi$
$643$	1.17106e7			1.11700			0.558499	+	0.829505i	$0.311378\pi$
$644$	−1.63096e6	−	5.01957e6i	−0.154963	−	0.476927i
$645$	708091.	+	3.86937e6i	0.0670178	+	0.366219i
$646$	−1.78627e6	+	5.49757e6i	−0.168409	+	0.518309i
$647$	−1.22227e6	+	3.76175e6i	−0.114790	+	0.353288i	−0.991903	−	0.126996i	$-0.959466\pi$
$647$	−1.22227e6	+	3.76175e6i	−0.114790	+	0.353288i	0.877113	+	0.480284i	$0.159466\pi$
$648$	−339709.	+	246813.i	−0.0317812	+	0.0230904i
$649$	−2.67971e7			−2.49733
$650$	4.83100e6	−	7.36588e6i	0.448491	−	0.683819i
$651$	6.06378e6			0.560778
$652$	−6.19920e6	+	4.50399e6i	−0.571106	+	0.414933i
$653$	−4.86986e6	+	1.49879e7i	−0.446924	+	1.37549i	0.433435	+	0.901185i	$0.357301\pi$
$653$	−4.86986e6	+	1.49879e7i	−0.446924	+	1.37549i	−0.880360	+	0.474307i	$0.842699\pi$
$654$	−2.14945e6	+	6.61533e6i	−0.196509	+	0.604794i
$655$	−2.46298e6	−	2.34790e6i	−0.224315	−	0.213834i
$656$	1.17347e6	+	3.61156e6i	0.106466	+	0.327669i
$657$	3.59021e6			0.324494
$658$	−4.26298e6	−	1.31201e7i	−0.383838	−	1.18133i
$659$	7.34165e6	+	5.33402e6i	0.658537	+	0.478455i	0.866168	−	0.499752i	$-0.166576\pi$
$659$	7.34165e6	+	5.33402e6i	0.658537	+	0.478455i	−0.207632	+	0.978207i	$0.566576\pi$
$660$	−4.39508e6	+	2.37347e6i	−0.392741	+	0.212092i
$661$	−5.22951e6	+	3.79946e6i	−0.465540	+	0.338235i	−0.795701	−	0.605690i	$-0.792897\pi$
$661$	−5.22951e6	+	3.79946e6i	−0.465540	+	0.338235i	0.330160	+	0.943925i	$0.392897\pi$
$662$	−1.52086e6	−	1.10497e6i	−0.134879	−	0.0979955i
$663$	3.51746e6	+	2.55558e6i	0.310774	+	0.225791i
$664$	5.55466e6	−	4.03570e6i	0.488920	−	0.355221i
$665$	−1.27443e7	−	1.21488e7i	−1.11754	−	1.06532i
$666$	−1.31364e6	−	954414.i	−0.114760	−	0.0833779i
$667$	−3.72228e6	−	1.14560e7i	−0.323962	−	0.997054i
$668$	5.27602e6			0.457473
$669$	−1.65145e6	−	5.08265e6i	−0.142659	−	0.439061i
$670$	5.64348e6	+	755975.i	0.485691	+	0.0650610i
$671$	3.31913e6	−	1.02152e7i	0.284589	−	0.875874i
$672$	−425508.	+	1.30958e6i	−0.0363483	+	0.111869i
$673$	1.27067e7	−	9.23195e6i	1.08142	−	0.785698i	0.103491	−	0.994630i	$-0.466999\pi$
$673$	1.27067e7	−	9.23195e6i	1.08142	−	0.785698i	0.977930	+	0.208932i	$0.0669987\pi$
$674$	−1.30903e7			−1.10994
$675$	108929.	+	2.27552e6i	0.00920208	+	0.192230i
$676$	2.00501e6			0.168752
$677$	−4.72289e6	+	3.43138e6i	−0.396037	+	0.287738i	−0.767925	−	0.640540i	$-0.778711\pi$
$677$	−4.72289e6	+	3.43138e6i	−0.396037	+	0.287738i	0.371888	+	0.928278i	$0.378711\pi$
$678$	−2.63995e6	+	8.12492e6i	−0.220557	+	0.678805i
$679$	−934110.	+	2.87489e6i	−0.0777541	+	0.239303i
$680$	1.06088e6	−	2.21129e6i	0.0879821	−	0.183389i
$681$	−2.39094e6	−	7.35856e6i	−0.197561	−	0.608030i
$682$	1.11925e7			0.921436
$683$	4.46029e6	+	1.37274e7i	0.365857	+	1.12599i	0.949443	+	0.313940i	$0.101649\pi$
$683$	4.46029e6	+	1.37274e7i	0.365857	+	1.12599i	−0.583586	+	0.812051i	$0.698351\pi$
$684$	−2.21026e6	−	1.60585e6i	−0.180636	−	0.131240i
$685$	−1.63017e7	−	2.18370e6i	−1.32741	−	0.177814i
$686$	−5.45891e6	+	3.96613e6i	−0.442890	+	0.321779i
$687$	375417.	+	272756.i	0.0303474	+	0.0220487i
$688$	1.61928e6	+	1.17648e6i	0.130422	+	0.0947574i
$689$	2.19591e7	−	1.59542e7i	1.76225	−	1.28035i
$690$	−4.40375e6	−	589907.i	−0.352128	−	0.0471695i
$691$	8.86353e6	+	6.43973e6i	0.706174	+	0.513065i	0.881937	−	0.471367i	$-0.156239\pi$
$691$	8.86353e6	+	6.43973e6i	0.706174	+	0.513065i	−0.175763	+	0.984432i	$0.556239\pi$
$692$	−902372.	−	2.77721e6i	−0.0716342	−	0.220467i
$693$	7.50959e6			0.593996
$694$	−4.59085e6	−	1.41292e7i	−0.361822	−	1.11357i
$695$	1.44375e6	−	3.00934e6i	0.113378	−	0.236324i
$696$	−971123.	+	2.98881e6i	−0.0759891	+	0.233870i
$697$	−3.14234e6	+	9.67114e6i	−0.245003	+	0.754042i
$698$	1.17596e7	−	8.54385e6i	0.913595	−	0.663766i
$699$	−1.16868e7			−0.904697
$700$	4.67505e6	+	5.82693e6i	0.360613	+	0.449464i
$701$	−2.21590e6			−0.170316			−0.0851580	−	0.996367i	$-0.527139\pi$
$701$	−2.21590e6			−0.170316			−0.0851580	+	0.996367i	$0.527139\pi$
$702$	−1.66246e6	+	1.20785e6i	−0.127323	+	0.0925059i
$703$	3.26465e6	−	1.00476e7i	0.249143	−	0.766782i
$704$	−785400.	+	2.41721e6i	−0.0597254	+	0.183816i
$705$	−1.15105e7	−	1.54189e6i	−0.872209	−	0.116837i
$706$	−2.96857e6	−	9.13632e6i	−0.224148	−	0.689858i
$707$	−2.44739e7			−1.84143
$708$	1.92169e6	+	5.91437e6i	0.144079	+	0.443430i
$709$	−415165.	−	301635.i	−0.0310174	−	0.0225354i	0.572169	−	0.820136i	$-0.306102\pi$
$709$	−415165.	−	301635.i	−0.0310174	−	0.0225354i	−0.603186	+	0.797601i	$0.706102\pi$
$710$	−4.44355e6	−	4.23593e6i	−0.330815	−	0.315357i
$711$	314732.	−	228666.i	0.0233489	−	0.0169640i
$712$	−3.81659e6	−	2.77292e6i	−0.282147	−	0.204992i
$713$	8.05439e6	+	5.85186e6i	0.593347	+	0.431092i
$714$	−2.98309e6	+	2.16734e6i	−0.218988	+	0.159104i
$715$	−2.15085e7	+	1.16152e7i	−1.57342	+	0.849693i
$716$	−245618.	−	178452.i	−0.0179051	−	0.0130088i
$717$	−3.92110e6	−	1.20679e7i	−0.284846	−	0.876666i
$718$	1.44807e6			0.104828
$719$	−787280.	−	2.42300e6i	−0.0567946	−	0.174796i	0.918635	−	0.395107i	$-0.129293\pi$
$719$	−787280.	−	2.42300e6i	−0.0567946	−	0.174796i	−0.975430	+	0.220312i	$0.929293\pi$
$720$	839030.	+	799826.i	0.0603179	+	0.0574995i
$721$	−1.40003e6	+	4.30884e6i	−0.100299	+	0.308690i
$722$	2.43231e6	−	7.48589e6i	0.173651	−	0.534442i
$723$	7.70071e6	−	5.59489e6i	0.547879	−	0.398057i
$724$	−3.64377e6			−0.258348
$725$	1.06697e7	+	1.32986e7i	0.753889	+	0.939640i
$726$	8.06331e6			0.567769
$727$	4.22473e6	−	3.06945e6i	0.296458	−	0.215389i	−0.429606	−	0.903016i	$-0.641348\pi$
$727$	4.22473e6	−	3.06945e6i	0.296458	−	0.215389i	0.726064	+	0.687627i	$0.241348\pi$
$728$	−2.08234e6	+	6.40878e6i	−0.145621	+	0.448174i
$729$	164224.	−	505430.i	0.0114451	−	0.0352243i
$730$	−1.78409e6	−	9.74915e6i	−0.123911	−	0.677111i
$731$	1.65627e6	+	5.09747e6i	0.114640	+	0.352826i
$732$	−2.49262e6			−0.171940
$733$	−937428.	−	2.88511e6i	−0.0644433	−	0.198336i	0.913651	−	0.406501i	$-0.133251\pi$
$733$	−937428.	−	2.88511e6i	−0.0644433	−	0.198336i	−0.978094	+	0.208164i	$0.933251\pi$
$734$	9.00983e6	+	6.54603e6i	0.617272	+	0.448474i
$735$	−499623.	−	2.73020e6i	−0.0341134	−	0.186413i
$736$	−1.82901e6	+	1.32885e6i	−0.124457	+	0.0904236i
$737$	−1.27829e7	−	9.28733e6i	−0.866884	−	0.629828i
$738$	−3.88822e6	−	2.82496e6i	−0.262791	−	0.190929i
$739$	−1.49973e7	+	1.08961e7i	−1.01018	+	0.733942i	−0.964248	−	0.265002i	$-0.914627\pi$
$739$	−1.49973e7	+	1.08961e7i	−1.01018	+	0.733942i	−0.0459370	+	0.998944i	$0.514627\pi$
$740$	−1.93891e6	+	4.04144e6i	−0.130160	+	0.271304i
$741$	−1.08165e7	−	7.85866e6i	−0.723672	−	0.525779i
$742$	7.11340e6	+	2.18928e7i	0.474315	+	1.45979i
$743$	−1.45641e7			−0.967859			−0.483929	−	0.875107i	$-0.660791\pi$
$743$	−1.45641e7			−0.967859			−0.483929	+	0.875107i	$0.660791\pi$
$744$	−802643.	−	2.47028e6i	−0.0531607	−	0.163612i
$745$	1.13102e7	−	6.10785e6i	0.746587	−	0.403179i
$746$	−1.51354e6	+	4.65821e6i	−0.0995745	+	0.306459i
$747$	−2.68527e6	+	8.26440e6i	−0.176070	+	0.541888i
$748$	−5.50616e6	+	4.00046e6i	−0.359828	+	0.261430i
$749$	1.18208e7			0.769911
$750$	6.12500e6	−	1.42657e6i	0.397606	−	0.0926063i
$751$	2.52686e7			1.63486			0.817431	−	0.576027i	$-0.195398\pi$
$751$	2.52686e7			1.63486			0.817431	+	0.576027i	$0.195398\pi$
$752$	−4.78063e6	+	3.47333e6i	−0.308277	+	0.223976i
$753$	−3.50937e6	+	1.08007e7i	−0.225549	+	0.694170i
$754$	−4.75245e6	+	1.46265e7i	−0.304431	+	0.936944i
$755$	1.13714e7	−	6.14089e6i	0.726017	−	0.392070i
$756$	−538534.	−	1.65744e6i	−0.0342696	−	0.105471i
$757$	1.13102e7			0.717350			0.358675	−	0.933463i	$-0.383229\pi$
$757$	1.13102e7			0.717350			0.358675	+	0.933463i	$0.383229\pi$
$758$	1.34654e6	+	4.14424e6i	0.0851231	+	0.261982i
$759$	9.97484e6	+	7.24715e6i	0.628495	+	0.456628i
$760$	−3.26231e6	+	6.79993e6i	−0.204876	+	0.427042i
$761$	−3.77534e6	+	2.74295e6i	−0.236317	+	0.171694i	−0.699641	−	0.714495i	$-0.746657\pi$
$761$	−3.77534e6	+	2.74295e6i	−0.236317	+	0.171694i	0.463324	+	0.886189i	$0.346657\pi$
$762$	4.05211e6	+	2.94403e6i	0.252810	+	0.183677i
$763$	−2.33552e7	−	1.69685e7i	−1.45235	−	1.05520i
$764$	−3.06031e6	+	2.22345e6i	−0.189685	+	0.137814i
$765$	558765.	+	3.05337e6i	0.0345204	+	0.188637i
$766$	8.92072e6	+	6.48128e6i	0.549323	+	0.399107i
$767$	9.40433e6	+	2.89435e7i	0.577217	+	1.77649i
$768$	589824.			0.0360844
$769$	1.33062e6	+	4.09524e6i	0.0811408	+	0.249726i	0.983395	−	0.181479i	$-0.0580886\pi$
$769$	1.33062e6	+	4.09524e6i	0.0811408	+	0.249726i	−0.902254	+	0.431205i	$0.858089\pi$
$770$	−3.73175e6	−	2.03922e7i	−0.226822	−	1.23947i
$771$	−1.66626e6	+	5.12824e6i	−0.100950	+	0.310693i
$772$	3.00059e6	−	9.23486e6i	0.181202	−	0.557683i
$773$	−1.92759e7	+	1.40048e7i	−1.16029	+	0.842999i	−0.989815	−	0.142363i	$-0.954530\pi$
$773$	−1.92759e7	+	1.40048e7i	−1.16029	+	0.842999i	−0.170474	+	0.985362i	$0.554530\pi$
$774$	−2.53321e6			−0.151991
$775$	−1.35950e7	−	3.70881e6i	−0.813066	−	0.221810i
$776$	1.29483e6			0.0771895
$777$	5.45200e6	−	3.96111e6i	0.323969	−	0.235377i
$778$	−133847.	+	411940.i	−0.00792795	+	0.0243997i
$779$	9.66300e6	−	2.97397e7i	0.570517	−	1.75587i
$780$	4.10602e6	+	3.91416e6i	0.241649	+	0.230358i
$781$	5.26440e6	+	1.62022e7i	0.308831	+	0.950485i
$782$	−6.05397e6			−0.354016
$783$	−1.22908e6	−	3.78271e6i	−0.0716432	−	0.220495i
$784$	−1.14255e6	−	830114.i	−0.0663875	−	0.0482334i
$785$	7.46952e6	−	4.03376e6i	0.432632	−	0.233634i
$786$	1.77284e6	−	1.28804e6i	0.102356	−	0.0743659i
$787$	1.84161e7	+	1.33801e7i	1.05989	+	0.770056i	0.974068	−	0.226254i	$-0.0726480\pi$
$787$	1.84161e7	+	1.33801e7i	1.05989	+	0.770056i	0.0858230	+	0.996310i	$0.472648\pi$
$788$	8.84450e6	+	6.42590e6i	0.507408	+	0.368654i
$789$	−264850.	+	192425.i	−0.0151464	+	0.0110045i
$790$	−777339.	−	741017.i	−0.0443142	−	0.0422436i
$791$	−2.86847e7	−	2.08407e7i	−1.63008	−	1.18432i
$792$	−994021.	−	3.05928e6i	−0.0563096	−	0.173303i
$793$	−1.21983e7			−0.688836
$794$	2.29508e6	+	7.06354e6i	0.129195	+	0.397623i
$795$	1.92069e7	+	2.57287e6i	1.07780	+	0.144378i
$796$	308244.	−	948678.i	0.0172430	−	0.0530684i
$797$	−3.14103e6	+	9.66709e6i	−0.175156	+	0.539076i	−0.999641	−	0.0268090i	$-0.991465\pi$
$797$	−3.14103e6	+	9.66709e6i	−0.175156	+	0.539076i	0.824484	+	0.565885i	$0.191465\pi$
$798$	9.17328e6	−	6.66477e6i	0.509938	−	0.370491i
$799$	−1.58238e7			−0.876887
$800$	1.75497e6	−	2.67583e6i	0.0969496	−	0.147820i
$801$	5.97068e6			0.328808
$802$	1.01589e7	−	7.38090e6i	0.557715	−	0.405204i
$803$	−8.49895e6	+	2.61571e7i	−0.465132	+	1.43153i
$804$	−1.13310e6	+	3.48733e6i	−0.0618199	+	0.190262i
$805$	7.97636e6	−	1.66258e7i	0.433825	−	0.904261i
$806$	−3.92795e6	−	1.20890e7i	−0.212975	−	0.655470i
$807$	−5.39697e6			−0.291720
$808$	3.23954e6	+	9.97027e6i	0.174564	+	0.537252i
$809$	1.18559e6	+	861381.i	0.0636888	+	0.0462726i	0.619174	−	0.785254i	$-0.287468\pi$
$809$	1.18559e6	+	861381.i	0.0636888	+	0.0462726i	−0.555485	+	0.831526i	$0.687468\pi$
$810$	−1.45410e6	−	194784.i	−0.0778719	−	0.0104314i
$811$	−1.65376e7	+	1.20153e7i	−0.882919	+	0.641478i	−0.934022	−	0.357215i	$-0.883726\pi$
$811$	−1.65376e7	+	1.20153e7i	−0.882919	+	0.641478i	0.0511032	+	0.998693i	$0.483726\pi$
$812$	−1.05519e7	−	7.66640e6i	−0.561617	−	0.408038i
$813$	−4.78989e6	−	3.48006e6i	−0.254155	−	0.184655i
$814$	1.00633e7	−	7.31139e6i	0.532326	−	0.386758i
$815$	−2.65351e7	−	3.55453e6i	−1.39935	−	0.187451i
$816$	1.27780e6	+	928376.i	0.0671796	+	0.0488089i
$817$	−5.09318e6	−	1.56752e7i	−0.266952	−	0.821595i
$818$	2.57907e7			1.34766
$819$	−2.63546e6	−	8.11111e6i	−0.137292	−	0.422543i
$820$	−5.73895e6	+	1.19622e7i	−0.298056	+	0.621265i
$821$	4.90338e6	−	1.50911e7i	0.253885	−	0.781379i	−0.740162	−	0.672429i	$-0.765251\pi$
$821$	4.90338e6	−	1.50911e7i	0.253885	−	0.781379i	0.994047	−	0.108950i	$-0.0347489\pi$
$822$	3.27306e6	−	1.00734e7i	0.168956	−	0.519994i
$823$	1.06559e7	−	7.74196e6i	0.548391	−	0.398429i	−0.278801	−	0.960349i	$-0.589937\pi$
$823$	1.06559e7	−	7.74196e6i	0.548391	−	0.398429i	0.827192	+	0.561920i	$0.189937\pi$
$824$	1.94067e6			0.0995710
$825$	−1.68366e7	−	4.59312e6i	−0.861228	−	0.234949i
$826$	−2.58097e7			−1.31623
$827$	−2.12321e7	+	1.54260e7i	−1.07952	+	0.784316i	−0.977599	−	0.210477i	$-0.932498\pi$
$827$	−2.12321e7	+	1.54260e7i	−1.07952	+	0.784316i	−0.101919	+	0.994793i	$0.532498\pi$
$828$	884188.	−	2.72125e6i	0.0448197	−	0.137941i
$829$	−7.38760e6	+	2.27367e7i	−0.373351	+	1.14905i	0.571234	+	0.820787i	$0.306465\pi$
$829$	−7.38760e6	+	2.27367e7i	−0.373351	+	1.14905i	−0.944585	+	0.328268i	$0.893535\pi$
$830$	2.37762e7	+	3.18496e6i	1.19798	+	0.160475i
$831$	6.27101e6	+	1.93002e7i	0.315018	+	0.969525i
$832$	2.88646e6			0.144563
$833$	−1.16865e6	−	3.59673e6i	−0.0583541	−	0.179596i
$834$	1.73895e6	+	1.26342e6i	0.0865710	+	0.0628975i
$835$	1.33425e7	+	1.27191e7i	0.662251	+	0.631307i
$836$	1.69320e7	−	1.23018e7i	0.837899	−	0.608769i
$837$	2.65952e6	+	1.93225e6i	0.131217	+	0.0953346i
$838$	7.66891e6	+	5.57179e6i	0.377245	+	0.274085i
$839$	2.58678e7	−	1.87940e7i	1.26869	−	0.921754i	0.269536	−	0.962990i	$-0.413130\pi$
$839$	2.58678e7	−	1.87940e7i	1.26869	−	0.921754i	0.999149	+	0.0412368i	$0.0131298\pi$
$840$	−4.23313e6	+	2.28601e6i	−0.206997	+	0.111784i
$841$	−7.48836e6	−	5.44061e6i	−0.365087	−	0.265251i
$842$	−208315.	−	641129.i	−0.0101261	−	0.0311649i
$843$	−1.03787e7			−0.503007
$844$	−3.87578e6	−	1.19284e7i	−0.187285	−	0.576404i
$845$	5.07047e6	+	4.83356e6i	0.244291	+	0.232876i
$846$	2.31108e6	−	7.11278e6i	0.111017	−	0.341675i
$847$	−1.03413e7	+	3.18274e7i	−0.495300	+	1.52438i
$848$	7.97718e6	−	5.79576e6i	0.380943	−	0.276771i
$849$	4.09076e6			0.194776
$850$	8.01372e6	−	3.03463e6i	0.380440	−	0.144065i
$851$	1.10645e7			0.523729
$852$	3.19844e6	−	2.32380e6i	0.150952	−	0.109673i
$853$	6.10507e6	−	1.87895e7i	0.287288	−	0.884183i	−0.698415	−	0.715693i	$-0.746111\pi$
$853$	6.10507e6	−	1.87895e7i	0.287288	−	0.884183i	0.985703	−	0.168490i	$-0.0538890\pi$
$854$	3.19682e6	−	9.83881e6i	0.149994	−	0.461634i
$855$	−1.71825e6	−	9.38941e6i	−0.0803845	−	0.439261i
$856$	−1.56468e6	−	4.81558e6i	−0.0729861	−	0.224628i
$857$	2.56697e7			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$857$	2.56697e7			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$858$	−4.86451e6	−	1.49714e7i	−0.225591	−	0.694297i
$859$	1.32959e7	+	9.66000e6i	0.614799	+	0.446678i	0.851101	−	0.525002i	$-0.175935\pi$
$859$	1.32959e7	+	9.66000e6i	0.614799	+	0.446678i	−0.236302	+	0.971680i	$0.575935\pi$
$860$	1.25883e6	+	6.87888e6i	0.0580391	+	0.317155i
$861$	1.61373e7	−	1.17245e7i	0.741863	−	0.538995i
$862$	1.25161e7	+	9.09350e6i	0.573723	+	0.416834i
$863$	−6.39698e6	−	4.64768e6i	−0.292380	−	0.212427i	0.431919	−	0.901912i	$-0.357837\pi$
$863$	−6.39698e6	−	4.64768e6i	−0.292380	−	0.212427i	−0.724299	+	0.689486i	$0.757837\pi$
$864$	−603928.	+	438779.i	−0.0275233	+	0.0199969i
$865$	4.41313e6	−	9.19870e6i	0.200543	−	0.418009i
$866$	1.64132e7	+	1.19249e7i	0.743703	+	0.540332i
$867$	−2.64185e6	−	8.13079e6i	−0.119361	−	0.367354i
$868$	1.07801e7			0.485648
$869$	920934.	+	2.83434e6i	0.0413694	+	0.127322i
$870$	−9.66113e6	+	5.21729e6i	−0.432743	+	0.233694i
$871$	−5.54513e6	+	1.70662e7i	−0.247666	+	0.762238i
$872$	−3.82125e6	+	1.17606e7i	−0.170182	+	0.523767i
$873$	−1.32579e6	+	963244.i	−0.0588762	+	0.0427760i
$874$	1.86165e7			0.824366
$875$	−2.22448e6	+	2.60061e7i	−0.0982219	+	1.14830i
$876$	6.38259e6			0.281020
$877$	−1.83277e7	+	1.33159e7i	−0.804654	+	0.584616i	−0.912276	−	0.409576i	$-0.865677\pi$
$877$	−1.83277e7	+	1.33159e7i	−0.804654	+	0.584616i	0.107621	+	0.994192i	$0.465677\pi$
$878$	−401668.	+	1.23621e6i	−0.0175845	+	0.0541196i
$879$	1.64783e6	−	5.07150e6i	0.0719351	−	0.221393i
$880$	−7.81347e6	+	4.21950e6i	−0.340124	+	0.183677i
$881$	−7.24979e6	−	2.23126e7i	−0.314692	−	0.968523i	−0.975881	−	0.218303i	$-0.929948\pi$
$881$	−7.24979e6	−	2.23126e7i	−0.314692	−	0.968523i	0.661189	−	0.750219i	$-0.270052\pi$
$882$	1.78741e6			0.0773664
$883$	−8.64690e6	−	2.66124e7i	−0.373215	−	1.14864i	−0.944675	−	0.328007i	$-0.893623\pi$
$883$	−8.64690e6	−	2.66124e7i	−0.373215	−	1.14864i	0.571460	−	0.820630i	$-0.306377\pi$
$884$	6.25326e6	+	4.54326e6i	0.269138	+	0.195541i
$885$	−9.39822e6	+	1.95896e7i	−0.403355	+	0.840750i
$886$	−1.97805e7	+	1.43714e7i	−0.846551	+	0.615055i
$887$	1.64936e7	+	1.19833e7i	0.703894	+	0.511409i	0.881198	−	0.472747i	$-0.156738\pi$
$887$	1.64936e7	+	1.19833e7i	0.703894	+	0.511409i	−0.177304	+	0.984156i	$0.556738\pi$
$888$	−2.33536e6	−	1.69674e6i	−0.0993849	−	0.0722074i
$889$	−1.68175e7	+	1.22186e7i	−0.713686	+	0.518523i
$890$	−2.96701e6	−	1.62133e7i	−0.125558	−	0.686113i
$891$	3.29364e6	+	2.39297e6i	0.138989	+	0.100982i
$892$	−2.93591e6	−	9.03582e6i	−0.123547	−	0.380238i
$893$	4.86597e7			2.04193
$894$	2.55800e6	+	7.87271e6i	0.107043	+	0.329443i
$895$	−190943.	−	1.04341e6i	−0.00796794	−	0.0435409i
$896$	−756459.	+	2.32814e6i	−0.0314786	+	0.0968812i
$897$	4.32701e6	−	1.33172e7i	0.179559	−	0.552626i
$898$	−1.97733e7	+	1.43661e7i	−0.818253	+	0.594495i
$899$	2.46030e7			1.01529
$900$	193652.	+	4.04537e6i	0.00796923	+	0.166476i
$901$	2.64043e7			1.08358
$902$	2.97862e7	−	2.16409e7i	1.21898	−	0.885644i
$903$	3.24888e6	−	9.99902e6i	0.132591	−	0.408073i
$904$	−4.69324e6	+	1.44443e7i	−0.191008	+	0.587862i
$905$	−9.21476e6	−	8.78420e6i	−0.373992	−	0.356517i
$906$	2.57183e6	+	7.91529e6i	0.104093	+	0.320366i
$907$	−2.21412e7			−0.893680			−0.446840	−	0.894614i	$-0.647451\pi$
$907$	−2.21412e7			−0.893680			−0.446840	+	0.894614i	$0.647451\pi$
$908$	−4.25056e6	−	1.30819e7i	−0.171093	−	0.526569i
$909$	−1.07340e7	−	7.79874e6i	−0.430877	−	0.313051i
$910$	−2.07159e7	+	1.11872e7i	−0.829280	+	0.447835i
$911$	2.28125e7	−	1.65743e7i	0.910705	−	0.661666i	−0.0304878	−	0.999535i	$-0.509706\pi$
$911$	2.28125e7	−	1.65743e7i	0.910705	−	0.661666i	0.941193	+	0.337869i	$0.109706\pi$
$912$	−3.92936e6	−	2.85484e6i	−0.156435	−	0.113657i
$913$	−5.38550e7	−	3.91279e7i	−2.13820	−	1.55350i
$914$	1.36473e7	−	9.91537e6i	0.540359	−	0.392594i
$915$	−6.30359e6	−	6.00905e6i	−0.248906	−	0.237276i
$916$	667407.	+	484900.i	0.0262816	+	0.0190947i
$917$	2.81044e6	+	8.64965e6i	0.110370	+	0.339684i
$918$	−1.99899e6			−0.0782895
$919$	1.35059e7	+	4.15668e7i	0.527514	+	1.62352i	0.759290	+	0.650752i	$0.225546\pi$
$919$	1.35059e7	+	4.15668e7i	0.527514	+	1.62352i	−0.231776	+	0.972769i	$0.574454\pi$
$920$	−7.82890e6	−	1.04872e6i	−0.304952	−	0.0408500i
$921$	−5.13896e6	+	1.58161e7i	−0.199630	+	0.614398i
$922$	181894.	−	559813.i	0.00704679	−	0.0216878i
$923$	1.56524e7	−	1.13722e7i	0.604752	−	0.439378i
$924$	1.33504e7			0.514415
$925$	−1.46462e7	+	5.54621e6i	−0.562820	+	0.213129i
$926$	1.53517e7			0.588341
$927$	−1.98707e6	+	1.44369e6i	−0.0759476	+	0.0551792i
$928$	−1.72644e6	+	5.31344e6i	−0.0658085	+	0.202538i
$929$	−1.00163e6	+	3.08271e6i	−0.0380776	+	0.117191i	−0.968289	−	0.249835i	$-0.919624\pi$
$929$	−1.00163e6	+	3.08271e6i	−0.0380776	+	0.117191i	0.930211	+	0.367025i	$0.119624\pi$
$930$	3.92540e6	−	8.18207e6i	0.148825	−	0.310210i
$931$	3.59371e6	+	1.10603e7i	0.135884	+	0.418208i
$932$	−2.07766e7			−0.783491
$933$	−2.50295e6	−	7.70327e6i	−0.0941342	−	0.289715i
$934$	2.04675e7	+	1.48705e7i	0.767711	+	0.557775i
$935$	−2.35686e7	−	3.15715e6i	−0.881668	−	0.118104i
$936$	−2.95548e6	+	2.14728e6i	−0.110265	+	0.0801125i
$937$	−1.12420e7	−	8.16776e6i	−0.418305	−	0.303916i	0.358651	−	0.933472i	$-0.383237\pi$
$937$	−1.12420e7	−	8.16776e6i	−0.418305	−	0.303916i	−0.776955	+	0.629556i	$0.783237\pi$
$938$	−1.23119e7	−	8.94511e6i	−0.456896	−	0.331954i
$939$	4.91944e6	−	3.57418e6i	0.182076	−	0.132286i
$940$	−2.04631e7	−	2.74114e6i	−0.755355	−	0.101184i
$941$	−65898.7	−	47878.2i	−0.00242607	−	0.00176264i	0.586572	−	0.809897i	$-0.300477\pi$
$941$	−65898.7	−	47878.2i	−0.00242607	−	0.00176264i	−0.588998	+	0.808135i	$0.700477\pi$
$942$	1.68936e6	+	5.19931e6i	0.0620290	+	0.190906i
$943$	3.27496e7			1.19930
$944$	3.41634e6	+	1.05144e7i	0.124776	+	0.384022i
$945$	2.63375e6	−	5.48976e6i	0.0959390	−	0.199974i
$946$	5.99675e6	−	1.84561e7i	0.217865	−	0.670521i
$947$	−816730.	+	2.51364e6i	−0.0295940	+	0.0910809i	−0.964763	−	0.263122i	$-0.915248\pi$
$947$	−816730.	+	2.51364e6i	−0.0295940	+	0.0910809i	0.935169	+	0.354203i	$0.115248\pi$
$948$	559523.	−	406517.i	0.0202207	−	0.0146912i
$949$	3.12349e7			1.12584
$950$	−2.46429e7	+	9.33178e6i	−0.885897	+	0.335471i
$951$	−5.14573e6			−0.184500
$952$	−5.30327e6	+	3.85305e6i	−0.189649	+	0.137788i
$953$	710439.	−	2.18651e6i	0.0253393	−	0.0779863i	−0.937587	−	0.347750i	$-0.886946\pi$
$953$	710439.	−	2.18651e6i	0.0253393	−	0.0779863i	0.962926	+	0.269764i	$0.0869457\pi$
$954$	−3.85637e6	+	1.18687e7i	−0.137185	+	0.422213i
$955$	−1.30994e7	−	1.75474e6i	−0.464775	−	0.0622592i
$956$	−6.97085e6	−	2.14541e7i	−0.246684	−	0.759215i
$957$	3.04692e7			1.07543
$958$	−6.31818e6	−	1.94454e7i	−0.222422	−	0.684545i
$959$	3.55639e7	+	2.58387e7i	1.24871	+	0.907244i
$960$	1.49161e6	+	1.42191e6i	0.0522368	+	0.0497961i
$961$	6.71043e6	−	4.87542e6i	0.234392	−	0.170295i
$962$	−1.14287e7	−	8.30343e6i	−0.398161	−	0.289281i
$963$	5.18448e6	+	3.76674e6i	0.180152	+	0.130888i
$964$	1.36901e7	−	9.94647e6i	0.474477	−	0.344728i
$965$	2.98511e7	−	1.61204e7i	1.03191	−	0.557261i
$966$	9.60728e6	+	6.98010e6i	0.331251	+	0.240668i
$967$	1.24230e7	+	3.82341e7i	0.427229	+	1.31488i	0.900844	+	0.434144i	$0.142949\pi$
$967$	1.24230e7	+	3.82341e7i	0.427229	+	1.31488i	−0.473615	+	0.880732i	$0.657051\pi$
$968$	1.43348e7			0.491703
$969$	−4.01910e6	−	1.23695e7i	−0.137505	−	0.423198i
$970$	3.27450e6	+	3.12150e6i	0.111742	+	0.106521i
$971$	−1.46517e7	+	4.50933e7i	−0.498701	+	1.53484i	0.312409	+	0.949948i	$0.398864\pi$
$971$	−1.46517e7	+	4.50933e7i	−0.498701	+	1.53484i	−0.811109	+	0.584895i	$0.801136\pi$
$972$	291954.	−	898543.i	0.00991172	−	0.0305052i
$973$	−7.21719e6	+	5.24360e6i	−0.244392	+	0.177561i
$974$	−1.98680e7			−0.671052
$975$	947690.	+	1.97971e7i	0.0319267	+	0.666945i
$976$	−4.43132e6			−0.148905
$977$	−1.15706e7	+	8.40651e6i	−0.387809	+	0.281760i	−0.764557	−	0.644556i	$-0.777042\pi$
$977$	−1.15706e7	+	8.40651e6i	−0.387809	+	0.281760i	0.376748	+	0.926316i	$0.377042\pi$
$978$	5.32774e6	−	1.63971e7i	0.178113	−	0.548176i
$979$	−1.41341e7	+	4.35004e7i	−0.471316	+	1.45056i
$980$	−888219.	−	4.85368e6i	−0.0295430	−	0.161438i
$981$	−4.83627e6	−	1.48845e7i	−0.160449	−	0.493812i
$982$	2.40084e7			0.794482
$983$	1.90126e6	+	5.85149e6i	0.0627565	+	0.193145i	0.977519	−	0.210847i	$-0.0676223\pi$
$983$	1.90126e6	+	5.85149e6i	0.0627565	+	0.193145i	−0.914762	+	0.403992i	$0.867622\pi$
$984$	−6.91239e6	−	5.02215e6i	−0.227584	−	0.165349i
$985$	6.87570e6	+	3.75723e7i	0.225801	+	1.23389i
$986$	−1.21035e7	+	8.79369e6i	−0.396477	+	0.288057i
$987$	2.51114e7	+	1.82445e7i	0.820499	+	0.596127i
$988$	−1.92294e7	−	1.39709e7i	−0.626718	−	0.455338i
$989$	1.39650e7	−	1.01462e7i	0.453994	−	0.329846i
$990$	4.86136e6	−	1.01330e7i	0.157641	−	0.328586i
$991$	−4.23362e6	−	3.07591e6i	−0.136939	−	0.0994922i	0.517207	−	0.855860i	$-0.326972\pi$
$991$	−4.23362e6	−	3.07591e6i	−0.136939	−	0.0994922i	−0.654146	+	0.756368i	$0.726972\pi$
$992$	−1.42692e6	−	4.39161e6i	−0.0460385	−	0.141692i
$993$	4.22975e6			0.136126
$994$	5.07041e6	+	1.56051e7i	0.162771	+	0.500958i
$995$	3.06654e6	−	1.65602e6i	0.0981953	−	0.0530283i
$996$	−4.77381e6	+	1.46923e7i	−0.152481	+	0.469289i
$997$	3.75110e6	−	1.15447e7i	0.119515	−	0.367828i	−0.873347	−	0.487098i	$-0.838055\pi$
$997$	3.75110e6	−	1.15447e7i	0.119515	−	0.367828i	0.992862	+	0.119270i	$0.0380554\pi$
$998$	−1.43606e7	+	1.04336e7i	−0.456402	+	0.331596i
$999$	3.65343e6			0.115821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.b.61.5	✓	24
25.16	even	5	inner	150.6.g.b.91.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.b.61.5	✓	24	1.1	even	1	trivial
150.6.g.b.91.5	yes	24	25.16	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)

\(f(q)\)	\(=\)	\(q+(-3.23607 + 2.35114i) q^{2} +(2.78115 - 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(49.1876 - 26.5627i) q^{5} +(11.1246 + 34.2380i) q^{6} -149.411 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})\)	\(q+(-3.23607 + 2.35114i) q^{2} +(2.78115 - 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(49.1876 - 26.5627i) q^{5} +(11.1246 + 34.2380i) q^{6} -149.411 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-96.7217 + 201.606i) q^{10} +(502.003 - 364.726i) q^{11} +(-116.498 - 84.6411i) q^{12} +(-570.117 - 414.214i) q^{13} +(483.505 - 351.287i) q^{14} +(-90.5657 - 494.897i) q^{15} +(-207.108 - 150.473i) q^{16} +(-211.839 - 651.972i) q^{17} +324.000 q^{18} +(651.424 + 2004.88i) q^{19} +(-161.006 - 879.817i) q^{20} +(-415.535 + 1278.89i) q^{21} +(-766.992 + 2360.56i) q^{22} +(-1786.14 + 1297.71i) q^{23} +576.000 q^{24} +(1713.84 - 2613.12i) q^{25} +2818.81 q^{26} +(-589.773 + 428.495i) q^{27} +(-738.729 + 2273.58i) q^{28} +(-1685.98 + 5188.91i) q^{29} +(1456.65 + 1388.59i) q^{30} +(-1393.48 - 4288.68i) q^{31} +1024.00 q^{32} +(-1725.73 - 5311.26i) q^{33} +(2218.40 + 1611.76i) q^{34} +(-7349.18 + 3968.77i) q^{35} +(-1048.49 + 761.770i) q^{36} +(-4054.44 - 2945.72i) q^{37} +(-6821.80 - 4956.33i) q^{38} +(-5131.05 + 3727.93i) q^{39} +(2589.60 + 2468.60i) q^{40} +(-12000.7 - 8719.01i) q^{41} +(-1662.14 - 5115.54i) q^{42} -7818.54 q^{43} +(-3067.97 - 9442.23i) q^{44} +(-4487.95 - 601.186i) q^{45} +(2728.98 - 8398.93i) q^{46} +(7132.97 - 21953.0i) q^{47} +(-1863.98 + 1354.26i) q^{48} +5516.70 q^{49} +(597.692 + 12485.7i) q^{50} -6169.72 q^{51} +(-9121.86 + 6627.42i) q^{52} +(-11902.4 + 36631.8i) q^{53} +(901.094 - 2773.28i) q^{54} +(15004.2 - 31274.6i) q^{55} +(-2954.92 - 9094.30i) q^{56} +18972.5 q^{57} +(-6743.91 - 20755.6i) q^{58} +(-34937.9 - 25383.9i) q^{59} +(-7978.58 - 1068.77i) q^{60} +(14004.0 - 10174.5i) q^{61} +(14592.7 + 10602.2i) q^{62} +(9790.97 + 7113.56i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(-39045.3 - 5230.34i) q^{65} +(18072.1 + 13130.1i) q^{66} +(-7868.76 - 24217.5i) q^{67} -10968.4 q^{68} +(6140.20 + 18897.6i) q^{69} +(14451.3 - 30122.2i) q^{70} +(-8483.99 + 26111.1i) q^{71} +(1601.94 - 4930.28i) q^{72} +(-35858.5 + 26052.7i) q^{73} +20046.2 q^{74} +(-17600.5 - 21937.1i) q^{75} +33728.8 q^{76} +(-75004.8 + 54494.2i) q^{77} +(7839.54 - 24127.6i) q^{78} +(-1484.16 + 4567.77i) q^{79} +(-14184.1 - 1900.04i) q^{80} +(2027.46 + 6239.88i) q^{81} +59334.6 q^{82} +(-33151.4 - 102030. i) q^{83} +(17406.2 + 12646.3i) q^{84} +(-27738.0 - 26441.9i) q^{85} +(25301.3 - 18382.5i) q^{86} +(39725.5 + 28862.3i) q^{87} +(32128.2 + 23342.5i) q^{88} +(-59634.3 + 43326.9i) q^{89} +(15936.8 - 8606.33i) q^{90} +(85181.8 + 61888.2i) q^{91} +(10915.9 + 33595.7i) q^{92} -40584.5 q^{93} +(28531.9 + 87812.0i) q^{94} +(85297.0 + 81311.5i) q^{95} +(2847.90 - 8764.94i) q^{96} +(6251.94 - 19241.5i) q^{97} +(-17852.4 + 12970.5i) q^{98} -50261.3 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

Modular forms

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