LMFDB - Embedded newform 150.6.g.c.121.2

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			121.2
Character	$\chi$	$=$	150.121
Dual form			150.6.g.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-44.8368 + 33.3866i) q^{5} +(29.1246 - 21.1603i) q^{6} +131.563 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-44.8368 + 33.3866i) q^{5} +(29.1246 - 21.1603i) q^{6} +131.563 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-71.5889 - 211.837i) q^{10} +(-70.8836 + 218.157i) q^{11} +(44.4984 + 136.952i) q^{12} +(156.346 + 481.185i) q^{13} +(-162.621 + 500.497i) q^{14} +(503.081 - 5.90354i) q^{15} +(79.1084 + 243.470i) q^{16} +(-548.712 + 398.662i) q^{17} -324.000 q^{18} +(739.512 - 537.287i) q^{19} +(894.366 - 10.4952i) q^{20} +(-957.934 - 695.980i) q^{21} +(-742.303 - 539.315i) q^{22} +(-269.022 + 827.965i) q^{23} -576.000 q^{24} +(895.669 - 2993.89i) q^{25} -2023.79 q^{26} +(225.273 - 693.320i) q^{27} +(-1702.99 - 1237.30i) q^{28} +(-7144.78 - 5190.99i) q^{29} +(-599.383 + 1921.13i) q^{30} +(-3365.55 + 2445.22i) q^{31} -1024.00 q^{32} +(1670.18 - 1213.46i) q^{33} +(-838.357 - 2580.20i) q^{34} +(-5898.88 + 4392.46i) q^{35} +(400.486 - 1232.57i) q^{36} +(-1575.61 - 4849.24i) q^{37} +(1129.87 + 3477.39i) q^{38} +(1407.12 - 4330.66i) q^{39} +(-1065.57 + 3415.34i) q^{40} +(1315.55 + 4048.85i) q^{41} +(3831.73 - 2783.92i) q^{42} +3967.26 q^{43} +(2969.21 - 2157.26i) q^{44} +(-3694.24 - 2618.35i) q^{45} +(-2817.24 - 2046.84i) q^{46} +(-14899.0 - 10824.8i) q^{47} +(711.975 - 2191.23i) q^{48} +501.944 q^{49} +(10282.3 + 7107.98i) q^{50} +6104.20 q^{51} +(2501.54 - 7698.96i) q^{52} +(-28341.6 - 20591.4i) q^{53} +(2359.09 + 1713.98i) q^{54} +(-4105.34 - 12148.0i) q^{55} +(6811.97 - 4949.19i) q^{56} -8226.78 q^{57} +(28579.1 - 20764.0i) q^{58} +(-7994.64 - 24605.0i) q^{59} +(-6567.53 - 4654.84i) q^{60} +(-1709.52 + 5261.38i) q^{61} +(-5142.11 - 15825.8i) q^{62} +(3293.08 + 10135.1i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-23075.2 - 16354.9i) q^{65} +(2551.81 + 7853.67i) q^{66} +(-3529.13 + 2564.06i) q^{67} +10851.9 q^{68} +(6338.78 - 4605.39i) q^{69} +(-9418.49 - 27870.0i) q^{70} +(60936.8 + 44273.2i) q^{71} +(4193.94 + 3047.08i) q^{72} +(9452.77 - 29092.6i) q^{73} +20395.2 q^{74} +(-22359.4 + 17060.9i) q^{75} -14625.4 q^{76} +(-9325.70 + 28701.5i) q^{77} +(14735.5 + 10706.0i) q^{78} +(-19645.7 - 14273.4i) q^{79} +(-11675.6 - 8275.27i) q^{80} +(-5307.96 + 3856.46i) q^{81} -17028.8 q^{82} +(-46582.7 + 33844.3i) q^{83} +(5854.37 + 18017.9i) q^{84} +(11292.5 - 36194.3i) q^{85} +(-4903.81 + 15092.4i) q^{86} +(24561.6 + 75592.8i) q^{87} +(4536.55 + 13962.1i) q^{88} +(-43261.9 + 133146. i) q^{89} +(14527.1 - 10817.3i) q^{90} +(20569.5 + 63306.4i) q^{91} +(11268.9 - 8187.37i) q^{92} +37440.5 q^{93} +(59596.0 - 43299.0i) q^{94} +(-15219.1 + 48780.0i) q^{95} +(7455.90 + 5417.03i) q^{96} +(-121858. - 88534.7i) q^{97} +(-620.437 + 1909.51i) q^{98} -18580.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−44.8368	+	33.3866i	−0.802064	+	0.597238i
$5$	−44.8368	+	33.3866i	−0.802064	+	0.597238i
$6$	29.1246	−	21.1603i	0.330280	−	0.239962i
$7$	131.563			1.01482			0.507411	−	0.861704i	$-0.330602\pi$
$7$	131.563			1.01482			0.507411	+	0.861704i	$0.330602\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	−71.5889	−	211.837i	−0.226384	−	0.669888i
$11$	−70.8836	+	218.157i	−0.176630	+	0.543611i	−0.999704	−	0.0243228i	$-0.992257\pi$
$11$	−70.8836	+	218.157i	−0.176630	+	0.543611i	0.823074	+	0.567934i	$0.192257\pi$
$12$	44.4984	+	136.952i	0.0892055	+	0.274546i
$13$	156.346	+	481.185i	0.256584	+	0.789685i	0.993513	+	0.113715i	$0.0362750\pi$
$13$	156.346	+	481.185i	0.256584	+	0.789685i	−0.736929	+	0.675970i	$0.763725\pi$
$14$	−162.621	+	500.497i	−0.221747	+	0.682467i
$15$	503.081	−	5.90354i	0.577311	−	0.00677462i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−548.712	+	398.662i	−0.460492	+	0.334567i	−0.793724	−	0.608278i	$-0.791861\pi$
$17$	−548.712	+	398.662i	−0.460492	+	0.334567i	0.333232	+	0.942845i	$0.391861\pi$
$18$	−324.000			−0.235702
$19$	739.512	−	537.287i	0.469960	−	0.341446i	−0.327466	−	0.944863i	$-0.606195\pi$
$19$	739.512	−	537.287i	0.469960	−	0.341446i	0.797426	+	0.603417i	$0.206195\pi$
$20$	894.366	−	10.4952i	0.499966	−	0.00586699i
$21$	−957.934	−	695.980i	−0.474010	−	0.344388i
$22$	−742.303	−	539.315i	−0.326983	−	0.237567i
$23$	−269.022	+	827.965i	−0.106040	+	0.326356i	−0.989973	−	0.141256i	$-0.954886\pi$
$23$	−269.022	+	827.965i	−0.106040	+	0.326356i	0.883933	+	0.467613i	$0.154886\pi$
$24$	−576.000			−0.204124
$25$	895.669	−	2993.89i	0.286614	−	0.958046i
$26$	−2023.79			−0.587127
$27$	225.273	−	693.320i	0.0594703	−	0.183031i
$28$	−1702.99	−	1237.30i	−0.410504	−	0.298249i
$29$	−7144.78	−	5190.99i	−1.57759	−	1.14619i	−0.919393	−	0.393340i	$-0.871319\pi$
$29$	−7144.78	−	5190.99i	−1.57759	−	1.14619i	−0.658197	−	0.752846i	$-0.728681\pi$
$30$	−599.383	+	1921.13i	−0.121591	+	0.389721i
$31$	−3365.55	+	2445.22i	−0.629002	+	0.456997i	−0.856054	−	0.516886i	$-0.827091\pi$
$31$	−3365.55	+	2445.22i	−0.629002	+	0.456997i	0.227052	+	0.973883i	$0.427091\pi$
$32$	−1024.00			−0.176777
$33$	1670.18	−	1213.46i	0.266980	−	0.193972i
$34$	−838.357	−	2580.20i	−0.124375	−	0.382786i
$35$	−5898.88	+	4392.46i	−0.813953	+	0.606090i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	−1575.61	−	4849.24i	−0.189210	−	0.582330i	0.810785	−	0.585344i	$-0.199041\pi$
$37$	−1575.61	−	4849.24i	−0.189210	−	0.582330i	−0.999995	+	0.00301420i	$0.999041\pi$
$38$	1129.87	+	3477.39i	0.126932	+	0.390656i
$39$	1407.12	−	4330.66i	0.148139	−	0.455925i
$40$	−1065.57	+	3415.34i	−0.105301	+	0.337508i
$41$	1315.55	+	4048.85i	0.122222	+	0.376159i	0.993385	−	0.114834i	$-0.0366338\pi$
$41$	1315.55	+	4048.85i	0.122222	+	0.376159i	−0.871163	+	0.490994i	$0.836634\pi$
$42$	3831.73	−	2783.92i	0.335175	−	0.243519i
$43$	3967.26			0.327205			0.163603	−	0.986526i	$-0.447689\pi$
$43$	3967.26			0.327205			0.163603	+	0.986526i	$0.447689\pi$
$44$	2969.21	−	2157.26i	0.231212	−	0.167985i
$45$	−3694.24	−	2618.35i	−0.271953	−	0.192751i
$46$	−2817.24	−	2046.84i	−0.196304	−	0.142623i
$47$	−14899.0	−	10824.8i	−0.983813	−	0.714782i	−0.0252551	−	0.999681i	$-0.508040\pi$
$47$	−14899.0	−	10824.8i	−0.983813	−	0.714782i	−0.958557	+	0.284899i	$0.908040\pi$
$48$	711.975	−	2191.23i	0.0446028	−	0.137273i
$49$	501.944			0.0298652
$50$	10282.3	+	7107.98i	0.581657	+	0.402088i
$51$	6104.20			0.328627
$52$	2501.54	−	7698.96i	0.128292	−	0.394842i
$53$	−28341.6	−	20591.4i	−1.38591	−	1.00692i	−0.996300	−	0.0859415i	$-0.972610\pi$
$53$	−28341.6	−	20591.4i	−1.38591	−	1.00692i	−0.389609	−	0.920980i	$-0.627390\pi$
$54$	2359.09	+	1713.98i	0.110093	+	0.0799874i
$55$	−4105.34	−	12148.0i	−0.182996	−	0.541501i
$56$	6811.97	−	4949.19i	0.290270	−	0.210894i
$57$	−8226.78			−0.335384
$58$	28579.1	−	20764.0i	1.11552	−	0.810476i
$59$	−7994.64	−	24605.0i	−0.298998	−	0.920222i	−0.981849	−	0.189664i	$-0.939260\pi$
$59$	−7994.64	−	24605.0i	−0.298998	−	0.920222i	0.682851	−	0.730558i	$-0.260740\pi$
$60$	−6567.53	−	4654.84i	−0.235518	−	0.166927i
$61$	−1709.52	+	5261.38i	−0.0588235	+	0.181040i	−0.976151	−	0.217094i	$-0.930342\pi$
$61$	−1709.52	+	5261.38i	−0.0588235	+	0.181040i	0.917327	+	0.398134i	$0.130342\pi$
$62$	−5142.11	−	15825.8i	−0.169888	−	0.522860i
$63$	3293.08	+	10135.1i	0.104532	+	0.321718i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−23075.2	−	16354.9i	−0.677426	−	0.480136i
$66$	2551.81	+	7853.67i	0.0721089	+	0.221928i
$67$	−3529.13	+	2564.06i	−0.0960462	+	0.0697816i	−0.634772	−	0.772700i	$-0.718906\pi$
$67$	−3529.13	+	2564.06i	−0.0960462	+	0.0697816i	0.538726	+	0.842481i	$0.318906\pi$
$68$	10851.9			0.284600
$69$	6338.78	−	4605.39i	0.160281	−	0.116451i
$70$	−9418.49	−	27870.0i	−0.229740	−	0.679818i
$71$	60936.8	+	44273.2i	1.43461	+	1.04230i	0.989135	+	0.147010i	$0.0469650\pi$
$71$	60936.8	+	44273.2i	1.43461	+	1.04230i	0.445475	+	0.895295i	$0.353035\pi$
$72$	4193.94	+	3047.08i	0.0953436	+	0.0692712i
$73$	9452.77	−	29092.6i	0.207612	−	0.638963i	−0.791984	−	0.610542i	$-0.790952\pi$
$73$	9452.77	−	29092.6i	0.207612	−	0.638963i	0.999596	−	0.0284219i	$-0.00904818\pi$
$74$	20395.2			0.432960
$75$	−22359.4	+	17060.9i	−0.458994	+	0.350225i
$76$	−14625.4			−0.290451
$77$	−9325.70	+	28701.5i	−0.179248	+	0.551669i
$78$	14735.5	+	10706.0i	0.274239	+	0.199246i
$79$	−19645.7	−	14273.4i	−0.354160	−	0.257312i	0.396452	−	0.918055i	$-0.370241\pi$
$79$	−19645.7	−	14273.4i	−0.354160	−	0.257312i	−0.750612	+	0.660743i	$0.770241\pi$
$80$	−11675.6	−	8275.27i	−0.203965	−	0.144563i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	−17028.8			−0.279673
$83$	−46582.7	+	33844.3i	−0.742215	+	0.539250i	−0.893404	−	0.449254i	$-0.851690\pi$
$83$	−46582.7	+	33844.3i	−0.742215	+	0.539250i	0.151189	+	0.988505i	$0.451690\pi$
$84$	5854.37	+	18017.9i	0.0905278	+	0.278616i
$85$	11292.5	−	36194.3i	0.169528	−	0.543367i
$86$	−4903.81	+	15092.4i	−0.0714969	+	0.220045i
$87$	24561.6	+	75592.8i	0.347903	+	1.07074i
$88$	4536.55	+	13962.1i	0.0624481	+	0.192196i
$89$	−43261.9	+	133146.i	−0.578936	+	1.78178i	0.0434317	+	0.999056i	$0.486171\pi$
$89$	−43261.9	+	133146.i	−0.578936	+	1.78178i	−0.622368	+	0.782725i	$0.713829\pi$
$90$	14527.1	−	10817.3i	0.189048	−	0.140770i
$91$	20569.5	+	63306.4i	0.260387	+	0.801390i
$92$	11268.9	−	8187.37i	0.138808	−	0.100850i
$93$	37440.5			0.448884
$94$	59596.0	−	43299.0i	0.695661	−	0.505427i
$95$	−15219.1	+	48780.0i	−0.173014	+	0.554539i
$96$	7455.90	+	5417.03i	0.0825700	+	0.0599906i
$97$	−121858.	−	88534.7i	−1.31499	−	0.955397i	−0.999980	−	0.00630970i	$-0.997992\pi$
$97$	−121858.	−	88534.7i	−1.31499	−	0.955397i	−0.315012	−	0.949088i	$-0.602008\pi$
$98$	−620.437	+	1909.51i	−0.00652578	+	0.0200843i
$99$	−18580.1			−0.190529
$100$	−39750.1	+	30330.4i	−0.397501	+	0.303304i
$101$	58961.8			0.575132			0.287566	−	0.957761i	$-0.407154\pi$
$101$	58961.8			0.575132			0.287566	+	0.957761i	$0.407154\pi$
$102$	−7545.21	+	23221.8i	−0.0718077	+	0.221001i
$103$	−24485.4	−	17789.7i	−0.227413	−	0.165225i	0.468244	−	0.883599i	$-0.344887\pi$
$103$	−24485.4	−	17789.7i	−0.227413	−	0.165225i	−0.695657	+	0.718374i	$0.744887\pi$
$104$	26196.5	+	19032.9i	0.237498	+	0.172552i
$105$	66187.0	−	776.691i	0.585868	−	0.00687503i
$106$	113366.	−	82365.5i	0.979986	−	0.712001i
$107$	−97592.4			−0.824056			−0.412028	−	0.911171i	$-0.635179\pi$
$107$	−97592.4			−0.824056			−0.412028	+	0.911171i	$0.635179\pi$
$108$	−9436.37	+	6855.93i	−0.0778477	+	0.0565597i
$109$	−3608.29	−	11105.2i	−0.0290894	−	0.0895280i	0.935458	−	0.353439i	$-0.114988\pi$
$109$	−3608.29	−	11105.2i	−0.0290894	−	0.0895280i	−0.964547	+	0.263910i	$0.914988\pi$
$110$	51288.3	−	601.858i	0.404145	−	0.00474255i
$111$	−14180.5	+	43643.1i	−0.109241	+	0.336208i
$112$	10407.8	+	32031.8i	0.0783994	+	0.241288i
$113$	22676.9	+	69792.2i	0.167065	+	0.514175i	0.999183	−	0.0404253i	$-0.0128713\pi$
$113$	22676.9	+	69792.2i	0.167065	+	0.514175i	−0.832117	+	0.554600i	$0.812871\pi$
$114$	10168.9	−	31296.5i	0.0732841	−	0.225545i
$115$	−15580.9	−	46105.0i	−0.109862	−	0.325090i
$116$	43665.0	+	134387.i	0.301293	+	0.927284i
$117$	−33154.9	+	24088.5i	−0.223915	+	0.162684i
$118$	103485.			0.684182
$119$	−72190.4	+	52449.4i	−0.467318	+	0.339526i
$120$	25826.0	−	19230.7i	0.163721	−	0.121911i
$121$	87724.8	+	63735.8i	0.544702	+	0.395749i
$122$	−17902.4	−	13006.8i	−0.108896	−	0.0791174i
$123$	11840.0	−	36439.6i	0.0705647	−	0.217176i
$124$	66560.8			0.388745
$125$	59797.1	+	164140.i	0.342298	+	0.939591i
$126$	−42626.6			−0.239196
$127$	−2008.84	+	6182.56i	−0.0110519	+	0.0340141i	−0.956430	−	0.291961i	$-0.905692\pi$
$127$	−2008.84	+	6182.56i	−0.0110519	+	0.0340141i	0.945379	+	0.325975i	$0.105692\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	−28886.3	−	20987.1i	−0.152833	−	0.111040i
$130$	90740.2	−	67567.5i	0.470914	−	0.350655i
$131$	−61291.1	+	44530.6i	−0.312046	+	0.226715i	−0.732774	−	0.680472i	$-0.761775\pi$
$131$	−61291.1	+	44530.6i	−0.312046	+	0.226715i	0.420728	+	0.907187i	$0.361775\pi$
$132$	−33031.3			−0.165003
$133$	97292.7	−	70687.3i	0.476926	−	0.346507i
$134$	−5392.02	−	16594.9i	−0.0259412	−	0.0798388i
$135$	13047.1	+	38607.3i	0.0616139	+	0.182320i
$136$	−13413.7	+	41283.2i	−0.0621873	+	0.191393i
$137$	−32406.6	−	99737.4i	−0.147514	−	0.454001i	0.849812	−	0.527086i	$-0.176715\pi$
$137$	−32406.6	−	99737.4i	−0.147514	−	0.454001i	−0.997326	+	0.0730853i	$0.976715\pi$
$138$	9684.79	+	29806.7i	0.0432905	+	0.133234i
$139$	48943.2	−	150632.i	0.214860	−	0.661270i	−0.784304	−	0.620377i	$-0.786980\pi$
$139$	48943.2	−	150632.i	0.214860	−	0.661270i	0.999164	−	0.0408932i	$-0.0130204\pi$
$140$	117666.	−	1380.78i	0.507376	−	0.00595395i
$141$	51218.2	+	157633.i	0.216958	+	0.667729i
$142$	−243747.	+	177093.i	−1.01442	+	0.737021i
$143$	−116056.			−0.474602
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	493658.	−	5792.98i	1.94987	−	0.0228814i
$146$	98990.7	+	71921.0i	0.384337	+	0.279237i
$147$	−3654.73	−	2655.32i	−0.0139496	−	0.0101350i
$148$	−25209.8	+	77587.8i	−0.0946052	+	0.291165i
$149$	421016.			1.55358			0.776790	−	0.629760i	$-0.216847\pi$
$149$	421016.			1.55358			0.776790	+	0.629760i	$0.216847\pi$
$150$	−37265.6	−	106149.i	−0.135232	−	0.385200i
$151$	−470783.			−1.68027			−0.840134	−	0.542379i	$-0.817524\pi$
$151$	−470783.			−1.68027			−0.840134	+	0.542379i	$0.817524\pi$
$152$	18078.0	−	55638.3i	0.0634659	−	0.195328i
$153$	−44445.6	−	32291.7i	−0.153497	−	0.111522i
$154$	−97660.0	−	70954.1i	−0.331829	−	0.241088i
$155$	69262.9	−	222000.i	0.231564	−	0.742205i
$156$	−58942.1	+	42824.0i	−0.193916	+	0.140888i
$157$	−154844.			−0.501355			−0.250677	−	0.968071i	$-0.580653\pi$
$157$	−154844.			−0.501355			−0.250677	+	0.968071i	$0.580653\pi$
$158$	78582.8	−	57093.7i	0.250429	−	0.181947i
$159$	97429.8	+	299858.i	0.305632	+	0.940639i
$160$	45912.8	−	34187.9i	0.141786	−	0.105578i
$161$	−35393.5	+	108930.i	−0.107611	+	0.331194i
$162$	−8109.84	−	24959.5i	−0.0242787	−	0.0747221i
$163$	−154933.	−	476835.i	−0.456746	−	1.40572i	−0.869073	−	0.494684i	$-0.835284\pi$
$163$	−154933.	−	476835.i	−0.456746	−	1.40572i	0.412327	−	0.911036i	$-0.364716\pi$
$164$	21048.8	−	64781.6i	0.0611108	−	0.188080i
$165$	−34372.3	+	110169.i	−0.0982876	+	0.315029i
$166$	−71172.0	−	219045.i	−0.200465	−	0.616969i
$167$	129339.	−	93970.6i	0.358872	−	0.260736i	−0.393709	−	0.919235i	$-0.628808\pi$
$167$	129339.	−	93970.6i	0.358872	−	0.260736i	0.752582	+	0.658499i	$0.228808\pi$
$168$	−75780.6			−0.207150
$169$	93287.6	−	67777.4i	0.251251	−	0.182544i
$170$	123733.	+	87697.8i	0.328370	+	0.232737i
$171$	59900.4	+	43520.2i	0.156653	+	0.113815i
$172$	−51353.3	−	37310.4i	−0.132357	−	0.0961631i
$173$	134091.	−	412689.i	0.340630	−	1.04835i	−0.623251	−	0.782022i	$-0.714189\pi$
$173$	134091.	−	412689.i	0.340630	−	1.04835i	0.963882	−	0.266331i	$-0.0858114\pi$
$174$	−317932.			−0.796088
$175$	117837.	−	393887.i	0.290862	−	0.972247i
$176$	−58722.4			−0.142897
$177$	−71951.8	+	221445.i	−0.172627	+	0.531291i
$178$	−453044.	−	329156.i	−1.07174	−	0.778667i
$179$	−519015.	−	377087.i	−1.21073	−	0.879647i	−0.215434	−	0.976518i	$-0.569117\pi$
$179$	−519015.	−	377087.i	−1.21073	−	0.879647i	−0.995297	+	0.0968709i	$0.969117\pi$
$180$	23194.8	+	68635.3i	0.0533592	+	0.157894i
$181$	74485.5	−	54116.8i	0.168995	−	0.122782i	−0.500073	−	0.865983i	$-0.666693\pi$
$181$	74485.5	−	54116.8i	0.168995	−	0.122782i	0.669068	+	0.743201i	$0.266693\pi$
$182$	−266257.			−0.595830
$183$	40280.4	−	29265.4i	0.0889131	−	0.0645991i
$184$	17217.4	+	52989.7i	0.0374907	+	0.115384i
$185$	232545.	+	164820.i	0.499548	+	0.354062i
$186$	−46279.0	+	142432.i	−0.0980847	+	0.301874i
$187$	−48076.5	−	147964.i	−0.100538	−	0.309423i
$188$	91054.6	+	280237.i	0.187891	+	0.578271i
$189$	29637.7	−	91215.6i	0.0603519	−	0.185744i
$190$	−166758.	−	118192.i	−0.335122	−	0.237523i
$191$	280191.	+	862340.i	0.555739	+	1.71039i	0.693983	+	0.719991i	$0.255854\pi$
$191$	280191.	+	862340.i	0.555739	+	1.71039i	−0.138244	+	0.990398i	$0.544146\pi$
$192$	−29823.6	+	21668.1i	−0.0583858	+	0.0424197i
$193$	−178537.			−0.345012			−0.172506	−	0.985008i	$-0.555186\pi$
$193$	−178537.			−0.345012			−0.172506	+	0.985008i	$0.555186\pi$
$194$	487430.	−	354139.i	0.929840	−	0.675568i
$195$	81495.6	+	241152.i	0.153478	+	0.454155i
$196$	−6497.30	−	4720.57i	−0.0120807	−	0.00877716i
$197$	−382679.	−	278033.i	−0.702537	−	0.510423i	0.178220	−	0.983991i	$-0.442966\pi$
$197$	−382679.	−	278033.i	−0.702537	−	0.510423i	−0.880758	+	0.473567i	$0.842966\pi$
$198$	22966.3	−	70683.0i	0.0416321	−	0.128130i
$199$	20722.1			0.0370938			0.0185469	−	0.999828i	$-0.494096\pi$
$199$	20722.1			0.0370938			0.0185469	+	0.999828i	$0.494096\pi$
$200$	−66249.9	−	188709.i	−0.117114	−	0.333593i
$201$	39260.1			0.0685428
$202$	−72880.8	+	224304.i	−0.125671	+	0.386775i
$203$	−939993.	−	682945.i	−1.60097	−	1.16318i
$204$	−79014.5	−	57407.4i	−0.132933	−	0.0965811i
$205$	−194162.	−	137615.i	−0.322686	−	0.228709i
$206$	97941.7	−	71158.8i	0.160805	−	0.116832i
$207$	−70516.5			−0.114384
$208$	−104786.	+	76131.5i	−0.167936	+	0.122013i
$209$	64793.8	+	199415.i	0.102605	+	0.315785i
$210$	−78857.0	+	252750.i	−0.123393	+	0.395498i
$211$	25889.5	−	79679.8i	0.0400330	−	0.123209i	−0.929043	−	0.369972i	$-0.879367\pi$
$211$	25889.5	−	79679.8i	0.0400330	−	0.123209i	0.969076	+	0.246764i	$0.0793671\pi$
$212$	173208.	+	533081.i	0.264685	+	0.814617i
$213$	−209482.	−	644719.i	−0.316372	−	0.973692i
$214$	120631.	−	371264.i	0.180063	−	0.554176i
$215$	−177879.	+	132453.i	−0.262439	+	0.195419i
$216$	−14417.5	−	44372.5i	−0.0210259	−	0.0647112i
$217$	−442784.	+	321701.i	−0.638326	+	0.463771i
$218$	46706.7			0.0665637
$219$	−222729.	+	161822.i	−0.313810	+	0.227996i
$220$	−61106.3	+	195856.i	−0.0851195	+	0.272823i
$221$	−277619.	−	201702.i	−0.382357	−	0.277799i
$222$	−148500.	−	107892.i	−0.202230	−	0.146928i
$223$	46418.5	−	142862.i	0.0625071	−	0.192377i	−0.914926	−	0.403621i	$-0.867751\pi$
$223$	46418.5	−	142862.i	0.0625071	−	0.192377i	0.977433	+	0.211244i	$0.0677514\pi$
$224$	−134721.			−0.179397
$225$	253055.	−	5939.92i	0.333242	−	0.00782211i
$226$	−293535.			−0.382287
$227$	−284533.	+	875702.i	−0.366495	+	1.12795i	0.582545	+	0.812798i	$0.302057\pi$
$227$	−284533.	+	875702.i	−0.366495	+	1.12795i	−0.949040	+	0.315156i	$0.897943\pi$
$228$	106490.	+	77369.3i	0.135666	+	0.0985670i
$229$	477040.	+	346590.i	0.601126	+	0.436744i	0.846278	−	0.532741i	$-0.178838\pi$
$229$	477040.	+	346590.i	0.601126	+	0.436744i	−0.245152	+	0.969485i	$0.578838\pi$
$230$	194653.	−	2284.21i	0.242628	−	0.00284719i
$231$	219735.	−	159647.i	0.270937	−	0.196848i
$232$	−565212.			−0.689432
$233$	−181316.	+	131734.i	−0.218800	+	0.158967i	−0.691786	−	0.722102i	$-0.743176\pi$
$233$	−181316.	+	131734.i	−0.218800	+	0.158967i	0.472986	+	0.881070i	$0.343176\pi$
$234$	−50656.3	−	155904.i	−0.0604774	−	0.186130i
$235$	1.02942e6	−	12080.1i	1.21598	−	0.0142692i
$236$	−127914.	+	393680.i	−0.149499	+	0.460111i
$237$	67535.9	+	207854.i	0.0781023	+	0.240374i
$238$	−110297.	−	339460.i	−0.126218	−	0.388460i
$239$	468607.	−	1.44222e6i	0.530657	−	1.63319i	−0.222193	−	0.975003i	$-0.571322\pi$
$239$	468607.	−	1.44222e6i	0.530657	−	1.63319i	0.752850	−	0.658192i	$-0.228678\pi$
$240$	41235.2	+	122018.i	0.0462105	+	0.136740i
$241$	219226.	+	674710.i	0.243137	+	0.748298i	0.995937	+	0.0900491i	$0.0287024\pi$
$241$	219226.	+	674710.i	0.243137	+	0.748298i	−0.752801	+	0.658249i	$0.771298\pi$
$242$	−350899.	+	254943.i	−0.385163	+	0.279837i
$243$	59049.0			0.0641500
$244$	71609.5	−	52027.4i	0.0770010	−	0.0559445i
$245$	−22505.6	+	16758.2i	−0.0239538	+	0.0178366i
$246$	123990.	+	90083.7i	0.130631	+	0.0949092i
$247$	374154.	+	271839.i	0.390219	+	0.283511i
$248$	−82273.7	+	253212.i	−0.0849438	+	0.261430i
$249$	518215.			0.529677
$250$	−698338.	+	24593.6i	−0.706669	+	0.0248870i
$251$	−952078.			−0.953868			−0.476934	−	0.878939i	$-0.658252\pi$
$251$	−952078.			−0.953868			−0.476934	+	0.878939i	$0.658252\pi$
$252$	52689.3	−	162161.i	0.0522662	−	0.160859i
$253$	−161557.	−	117378.i	−0.158681	−	0.115289i
$254$	−21036.8	−	15284.1i	−0.0204595	−	0.0148647i
$255$	−273693.	+	203799.i	−0.263580	+	0.196269i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	1.69885e6			1.60443			0.802216	−	0.597034i	$-0.203654\pi$
$257$	1.69885e6			1.60443			0.802216	+	0.597034i	$0.203654\pi$
$258$	115545.	−	83948.4i	0.108069	−	0.0785169i
$259$	−207293.	−	637982.i	−0.192015	−	0.590962i
$260$	144881.	+	428714.i	0.132916	+	0.393310i
$261$	221054.	−	680335.i	0.200862	−	0.618189i
$262$	−93644.4	−	288208.i	−0.0842808	−	0.259390i
$263$	−209553.	−	644937.i	−0.186812	−	0.574947i	0.813163	−	0.582036i	$-0.197744\pi$
$263$	−209553.	−	644937.i	−0.186812	−	0.574947i	−0.999975	+	0.00708859i	$0.997744\pi$
$264$	40829.0	−	125659.i	0.0360544	−	0.110964i
$265$	1.95822e6	−	22979.3i	1.71296	−	0.0201012i
$266$	148650.	+	457498.i	0.128813	+	0.396447i
$267$	1.01935e6	−	740601.i	0.875075	−	0.635779i
$268$	69795.8			0.0593598
$269$	1.56535e6	−	1.13730e6i	1.31896	−	0.958281i	0.319017	−	0.947749i	$-0.396647\pi$
$269$	1.56535e6	−	1.13730e6i	1.31896	−	0.958281i	0.999945	−	0.0105324i	$-0.00335262\pi$
$270$	−162998.	+	1912.75i	−0.136073	+	0.00159679i
$271$	344725.	+	250457.i	0.285134	+	0.207162i	0.721154	−	0.692775i	$-0.243612\pi$
$271$	344725.	+	250457.i	0.285134	+	0.207162i	−0.436019	+	0.899937i	$0.643612\pi$
$272$	−140470.	−	102058.i	−0.115123	−	0.0836417i
$273$	185125.	−	569757.i	0.150335	−	0.462683i
$274$	419480.			0.337548
$275$	589652.	+	407615.i	0.470180	+	0.325026i
$276$	−125363.			−0.0990593
$277$	−215133.	+	662112.i	−0.168464	+	0.518480i	−0.999275	−	0.0380755i	$-0.987877\pi$
$277$	−215133.	+	662112.i	−0.168464	+	0.518480i	0.830811	+	0.556555i	$0.187877\pi$
$278$	512539.	+	372382.i	0.397755	+	0.288986i
$279$	−272610.	−	198063.i	−0.209667	−	0.152332i
$280$	−140190.	+	449334.i	−0.106862	+	0.342511i
$281$	−1.14376e6	+	830992.i	−0.864112	+	0.627814i	−0.929000	−	0.370079i	$-0.879331\pi$
$281$	−1.14376e6	+	830992.i	−0.864112	+	0.627814i	0.0648888	+	0.997892i	$0.479331\pi$
$282$	−662982.			−0.496454
$283$	83782.6	−	60871.6i	0.0621853	−	0.0451803i	−0.556258	−	0.831009i	$-0.687764\pi$
$283$	83782.6	−	60871.6i	0.0621853	−	0.0451803i	0.618444	+	0.785829i	$0.287764\pi$
$284$	−372413.	−	1.14617e6i	−0.273986	−	0.843242i
$285$	368862.	−	274664.i	0.269000	−	0.200304i
$286$	143454.	−	441505.i	0.103704	−	0.319169i
$287$	173078.	+	532680.i	0.124033	+	0.381735i
$288$	−25631.1	−	78884.4i	−0.0182090	−	0.0560415i
$289$	−296607.	+	912863.i	−0.208899	+	0.642926i
$290$	−588158.	+	1.88515e6i	−0.410675	+	1.31629i
$291$	418909.	+	1.28927e6i	0.289993	+	0.892506i
$292$	−395963.	+	287684.i	−0.271767	+	0.197451i
$293$	−2.03045e6			−1.38173			−0.690866	−	0.722983i	$-0.742771\pi$
$293$	−2.03045e6			−1.38173			−0.690866	+	0.722983i	$0.742771\pi$
$294$	14618.9	−	10621.3i	0.00986387	−	0.00716652i
$295$	1.17993e6	+	836293.i	0.789408	+	0.559504i
$296$	−264000.	−	191808.i	−0.175136	−	0.127244i
$297$	135285.	+	98290.1i	0.0889934	+	0.0646575i
$298$	−520405.	+	1.60164e6i	−0.339469	+	1.04478i
$299$	−440465.			−0.284927
$300$	449876.	−	10559.9i	0.288596	−	0.00677415i
$301$	521947.			0.332055
$302$	581920.	−	1.79096e6i	0.367152	−	1.12998i
$303$	−429310.	−	311912.i	−0.268636	−	0.195175i
$304$	189315.	+	137545.i	0.117490	+	0.0853615i
$305$	−99010.0	−	292978.i	−0.0609438	−	0.180337i
$306$	177783.	−	129167.i	0.108539	−	0.0788582i
$307$	−674319.			−0.408337			−0.204169	−	0.978936i	$-0.565449\pi$
$307$	−674319.			−0.408337			−0.204169	+	0.978936i	$0.565449\pi$
$308$	390640.	−	283816.i	0.234639	−	0.170475i
$309$	84173.4	+	259059.i	0.0501509	+	0.154349i
$310$	758924.	+	537899.i	0.448533	+	0.317904i
$311$	−351125.	+	1.08065e6i	−0.205855	+	0.633556i	0.793822	+	0.608150i	$0.208088\pi$
$311$	−351125.	+	1.08065e6i	−0.205855	+	0.633556i	−0.999677	+	0.0254063i	$0.991912\pi$
$312$	−90055.6	−	277163.i	−0.0523750	−	0.161194i
$313$	716156.	+	2.20410e6i	0.413187	+	1.27166i	0.913863	+	0.406024i	$0.133085\pi$
$313$	716156.	+	2.20410e6i	0.413187	+	1.27166i	−0.500676	+	0.865635i	$0.666915\pi$
$314$	191398.	−	589061.i	0.109550	−	0.337160i
$315$	−486027.	−	344479.i	−0.275984	−	0.195608i
$316$	120064.	+	369518.i	0.0676386	+	0.208170i
$317$	−930972.	+	676391.i	−0.520342	+	0.378050i	−0.816733	−	0.577016i	$-0.804217\pi$
$317$	−930972.	+	676391.i	−0.520342	+	0.378050i	0.296391	+	0.955067i	$0.404217\pi$
$318$	−1.26116e6			−0.699361
$319$	1.63890e6	−	1.19073e6i	0.901729	−	0.655144i
$320$	73307.1	+	216921.i	0.0400194	+	0.118421i
$321$	710585.	+	516270.i	0.384905	+	0.279650i
$322$	−370645.	−	269290.i	−0.199213	−	0.144737i
$323$	−191583.	+	589631.i	−0.102176	+	0.314466i
$324$	104976.			0.0555556
$325$	1.58065e6	−	37102.3i	0.830095	−	0.0194847i
$326$	2.00549e6			1.04515
$327$	−32474.6	+	99946.6i	−0.0167948	+	0.0516890i
$328$	220426.	+	160149.i	0.113130	+	0.0821938i
$329$	−1.96016e6	−	1.42414e6i	−0.998395	−	0.725377i
$330$	−376622.	−	266937.i	−0.190380	−	0.134935i
$331$	−1.51763e6	+	1.10263e6i	−0.761373	+	0.553170i	−0.899331	−	0.437268i	$-0.855946\pi$
$331$	−1.51763e6	+	1.10263e6i	−0.761373	+	0.553170i	0.137958	+	0.990438i	$0.455946\pi$
$332$	921270.			0.458714
$333$	334126.	−	242756.i	0.165120	−	0.119967i
$334$	197613.	+	608191.i	0.0969281	+	0.298314i
$335$	72629.3	−	232790.i	0.0353590	−	0.113332i
$336$	93669.9	−	288286.i	0.0452639	−	0.139308i
$337$	526799.	+	1.62132e6i	0.252680	+	0.777668i	0.994278	+	0.106824i	$0.0340680\pi$
$337$	526799.	+	1.62132e6i	0.252680	+	0.777668i	−0.741598	+	0.670844i	$0.765932\pi$
$338$	142531.	+	438665.i	0.0678605	+	0.208853i
$339$	204092.	−	628130.i	0.0964553	−	0.296859i
$340$	−486565.	+	362309.i	−0.228267	+	0.169974i
$341$	−294880.	−	907546.i	−0.137328	−	0.422652i
$342$	−239602.	+	174081.i	−0.110771	+	0.0804796i
$343$	−2.14515e6			−0.984515
$344$	205413.	−	149242.i	0.0935907	−	0.0679976i
$345$	−130452.	+	418121.i	−0.0590069	+	0.189127i
$346$	1.40422e6	+	1.02022e6i	0.630585	+	0.458147i
$347$	−707435.	−	513981.i	−0.315401	−	0.229152i	0.418810	−	0.908074i	$-0.362447\pi$
$347$	−707435.	−	513981.i	−0.315401	−	0.229152i	−0.734210	+	0.678922i	$0.762447\pi$
$348$	392985.	−	1.20948e6i	0.173952	−	0.535368i
$349$	3.41546e6			1.50102			0.750509	−	0.660860i	$-0.229808\pi$
$349$	3.41546e6			1.50102			0.750509	+	0.660860i	$0.229808\pi$
$350$	1.35278e6	+	935151.i	0.590279	+	0.408048i
$351$	368836.			0.159796
$352$	72584.8	−	223393.i	0.0312241	−	0.0960978i
$353$	−867931.	−	630589.i	−0.370722	−	0.269345i	0.386788	−	0.922169i	$-0.373584\pi$
$353$	−867931.	−	630589.i	−0.370722	−	0.269345i	−0.757510	+	0.652823i	$0.773584\pi$
$354$	−753489.	−	547442.i	−0.319572	−	0.232183i
$355$	−4.21034e6	+	49407.4i	−1.77315	+	0.0208076i
$356$	1.81218e6	−	1.31662e6i	0.757837	−	0.550601i
$357$	803090.			0.333498
$358$	2.07606e6	−	1.50835e6i	0.856116	−	0.622005i
$359$	314508.	+	967955.i	0.128794	+	0.396387i	0.994573	−	0.104039i	$-0.0331767\pi$
$359$	314508.	+	967955.i	0.128794	+	0.396387i	−0.865779	+	0.500426i	$0.833177\pi$
$360$	−289774.	+	3400.44i	−0.117843	+	0.00138286i
$361$	−506956.	+	1.56025e6i	−0.204740	+	0.630125i
$362$	113804.	+	350252.i	0.0456441	+	0.140478i
$363$	−301571.	−	928141.i	−0.120122	−	0.369698i
$364$	329112.	−	1.01290e6i	0.130194	−	0.400695i
$365$	547473.	+	1.62002e6i	0.215095	+	0.636483i
$366$	61542.9	+	189410.i	0.0240146	+	0.0739093i
$367$	−3.16931e6	+	2.30264e6i	−1.22829	+	0.892403i	−0.996761	−	0.0804251i	$-0.974372\pi$
$367$	−3.16931e6	+	2.30264e6i	−1.22829	+	0.892403i	−0.231527	+	0.972828i	$0.574372\pi$
$368$	−222867.			−0.0857879
$369$	−278977.	+	202688.i	−0.106660	+	0.0774931i
$370$	−914453.	+	680925.i	−0.347262	+	0.258580i
$371$	−3.72872e6	−	2.70907e6i	−1.40645	−	1.02185i
$372$	−484640.	−	352111.i	−0.181577	−	0.131924i
$373$	−1.10145e6	+	3.38991e6i	−0.409914	+	1.26159i	0.506808	+	0.862059i	$0.330825\pi$
$373$	−1.10145e6	+	3.38991e6i	−0.409914	+	1.26159i	−0.916722	+	0.399526i	$0.869175\pi$
$374$	622315.			0.230055
$375$	432919.	−	1.51146e6i	0.158975	−	0.555032i
$376$	−1.17864e6			−0.429942
$377$	1.38076e6	−	4.24956e6i	0.500341	−	1.53989i
$378$	310371.	+	225497.i	0.111725	+	0.0811731i
$379$	1.82552e6	+	1.32632e6i	0.652814	+	0.474297i	0.864229	−	0.503099i	$-0.167807\pi$
$379$	1.82552e6	+	1.32632e6i	0.652814	+	0.474297i	−0.211415	+	0.977396i	$0.567807\pi$
$380$	655755.	−	488292.i	0.232961	−	0.173468i
$381$	47332.8	−	34389.3i	0.0167051	−	0.0121370i
$382$	−3.62687e6			−1.27167
$383$	27923.8	−	20287.8i	0.00972696	−	0.00706705i	−0.582911	−	0.812536i	$-0.698086\pi$
$383$	27923.8	−	20287.8i	0.00972696	−	0.00706705i	0.592638	+	0.805469i	$0.298086\pi$
$384$	−45566.4	−	140239.i	−0.0157695	−	0.0485334i
$385$	−540113.	−	1.59824e6i	−0.185709	−	0.549528i
$386$	220683.	−	679193.i	0.0753878	−	0.232020i
$387$	99302.1	+	305620.i	0.0337040	+	0.103730i
$388$	744727.	+	2.29203e6i	0.251141	+	0.772933i
$389$	−324013.	+	997210.i	−0.108565	+	0.334128i	−0.990551	−	0.137148i	$-0.956206\pi$
$389$	−324013.	+	997210.i	−0.108565	+	0.334128i	0.881986	+	0.471276i	$0.156206\pi$
$390$	−1.01813e6	+	11947.5i	−0.338955	+	0.00397756i
$391$	−182463.	−	561563.i	−0.0603577	−	0.185762i
$392$	25989.2	−	18882.3i	0.00854236	−	0.00620639i
$393$	681839.			0.222690
$394$	1.53072e6	−	1.11213e6i	0.496769	−	0.360924i
$395$	1.35739e6	−	15928.7i	0.437736	−	0.00513674i
$396$	240506.	+	174738.i	0.0770705	+	0.0559950i
$397$	−1.20352e6	−	874409.i	−0.383246	−	0.278444i	0.379436	−	0.925218i	$-0.376118\pi$
$397$	−1.20352e6	−	874409.i	−0.383246	−	0.278444i	−0.762682	+	0.646773i	$0.776118\pi$
$398$	−25614.0	+	78831.7i	−0.00810530	+	0.0249456i
$399$	−1.08234e6			−0.340356
$400$	799780.	−	18773.1i	0.249931	−	0.00586659i
$401$	−224385.			−0.0696841			−0.0348420	−	0.999393i	$-0.511093\pi$
$401$	−224385.			−0.0696841			−0.0348420	+	0.999393i	$0.511093\pi$
$402$	−48528.2	+	149354.i	−0.0149771	+	0.0460949i
$403$	−1.70279e6	−	1.23715e6i	−0.522275	−	0.379455i
$404$	−763217.	−	554510.i	−0.232646	−	0.169027i
$405$	109238.	−	350126.i	0.0330929	−	0.106069i
$406$	3.75997e6	−	2.73178e6i	1.13206	−	0.822489i
$407$	1.16958e6			0.349981
$408$	316058.	−	229630.i	0.0939975	−	0.0682932i
$409$	1.57126e6	+	4.83584e6i	0.464450	+	1.42943i	0.859672	+	0.510846i	$0.170668\pi$
$409$	1.57126e6	+	4.83584e6i	0.464450	+	1.42943i	−0.395222	+	0.918586i	$0.629332\pi$
$410$	763518.	−	568535.i	0.224316	−	0.167031i
$411$	−291660.	+	897636.i	−0.0851671	+	0.262117i
$412$	149642.	+	460550.i	0.0434320	+	0.133670i
$413$	−1.05180e6	−	3.23712e6i	−0.303430	−	0.933863i
$414$	87163.1	−	268261.i	0.0249938	−	0.0769230i
$415$	958670.	−	3.07271e6i	0.273243	−	0.875792i
$416$	−160099.	−	492733.i	−0.0453581	−	0.139598i
$417$	−1.15321e6	+	837859.i	−0.324765	+	0.235956i
$418$	−838708.			−0.234785
$419$	−3.13056e6	+	2.27448e6i	−0.871137	+	0.632918i	−0.930892	−	0.365295i	$-0.880968\pi$
$419$	−3.13056e6	+	2.27448e6i	−0.871137	+	0.632918i	0.0597547	+	0.998213i	$0.480968\pi$
$420$	−864047.	−	612406.i	−0.239009	−	0.169401i
$421$	−4.61722e6	−	3.35461e6i	−1.26962	−	0.922437i	−0.270437	−	0.962738i	$-0.587168\pi$
$421$	−4.61722e6	−	3.35461e6i	−1.26962	−	0.922437i	−0.999188	+	0.0403011i	$0.987168\pi$
$422$	271119.	+	196979.i	0.0741103	+	0.0538443i
$423$	460964.	−	1.41870e6i	0.125261	−	0.385514i
$424$	−2.24206e6			−0.605664
$425$	702089.	+	1.99985e6i	0.188547	+	0.537064i
$426$	2.71159e6			0.723936
$427$	−224911.	+	692205.i	−0.0596954	+	0.183724i
$428$	1.26326e6	+	917814.i	0.333338	+	0.242184i
$429$	845025.	+	613946.i	0.221680	+	0.161060i
$430$	−284012.	−	840414.i	−0.0740740	−	0.219191i
$431$	−1.20703e6	+	876959.i	−0.312986	+	0.227398i	−0.733177	−	0.680038i	$-0.761963\pi$
$431$	−1.20703e6	+	876959.i	−0.312986	+	0.227398i	0.420191	+	0.907436i	$0.361963\pi$
$432$	186624.			0.0481125
$433$	4.49566e6	−	3.26629e6i	1.15232	−	0.837211i	0.163534	−	0.986538i	$-0.447711\pi$
$433$	4.49566e6	−	3.26629e6i	1.15232	−	0.837211i	0.988788	+	0.149326i	$0.0477105\pi$
$434$	−676513.	−	2.08209e6i	−0.172406	−	0.530611i
$435$	−3.62505e6	−	2.56931e6i	−0.918524	−	0.651018i
$436$	−57732.6	+	177683.i	−0.0145447	+	0.0447640i
$437$	245909.	+	756831.i	0.0615987	+	0.189581i
$438$	−340300.	−	1.04734e6i	−0.0847572	−	0.260856i
$439$	−1.86690e6	+	5.74572e6i	−0.462338	+	1.42293i	0.399963	+	0.916531i	$0.369023\pi$
$439$	−1.86690e6	+	5.74572e6i	−0.462338	+	1.42293i	−0.862300	+	0.506397i	$0.830977\pi$
$440$	−669551.	−	474554.i	−0.164874	−	0.116857i
$441$	12563.9	+	38667.6i	0.00307628	+	0.00946783i
$442$	1.11048e6	−	806809.i	0.270367	−	0.196433i
$443$	−1.96669e6			−0.476132			−0.238066	−	0.971249i	$-0.576513\pi$
$443$	−1.96669e6			−0.476132			−0.238066	+	0.971249i	$0.576513\pi$
$444$	594001.	−	431567.i	0.142998	−	0.103894i
$445$	−2.50558e6	−	7.41422e6i	−0.599803	−	1.77487i
$446$	486101.	+	353173.i	0.115715	+	0.0840719i
$447$	−3.06548e6	−	2.22721e6i	−0.725655	−	0.527219i
$448$	166524.	−	512509.i	0.0391997	−	0.120644i
$449$	−2.26547e6			−0.530326			−0.265163	−	0.964204i	$-0.585426\pi$
$449$	−2.26547e6			−0.530326			−0.265163	+	0.964204i	$0.585426\pi$
$450$	−290197.	+	970022.i	−0.0675556	+	0.225814i
$451$	−976537.			−0.226072
$452$	362830.	−	1.11668e6i	0.0835327	−	0.257087i
$453$	3.42784e6	+	2.49047e6i	0.784830	+	0.570212i
$454$	−2.97967e6	−	2.16485e6i	−0.678466	−	0.492934i
$455$	−3.03585e6	−	2.15171e6i	−0.687468	−	0.487253i
$456$	−425959.	+	309477.i	−0.0959302	+	0.0696974i
$457$	1.03596e6			0.232034			0.116017	−	0.993247i	$-0.462987\pi$
$457$	1.03596e6			0.232034			0.116017	+	0.993247i	$0.462987\pi$
$458$	−1.90816e6	+	1.38636e6i	−0.425061	+	0.308825i
$459$	152791.	+	470241.i	0.0338505	+	0.104181i
$460$	−231914.	+	743327.i	−0.0511014	+	0.163789i
$461$	829254.	−	2.55218e6i	0.181734	−	0.559318i	−0.818143	−	0.575014i	$-0.804996\pi$
$461$	829254.	−	2.55218e6i	0.181734	−	0.559318i	0.999877	+	0.0156961i	$0.00499642\pi$
$462$	335725.	+	1.03326e6i	0.0731777	+	0.225218i
$463$	−2.34393e6	−	7.21387e6i	−0.508150	−	1.56392i	−0.795410	−	0.606072i	$-0.792744\pi$
$463$	−2.34393e6	−	7.21387e6i	−0.508150	−	1.56392i	0.287260	−	0.957853i	$-0.407256\pi$
$464$	698641.	−	2.15019e6i	0.150646	−	0.463642i
$465$	−1.67871e6	+	1.25001e6i	−0.360034	+	0.268090i
$466$	−277027.	−	852600.i	−0.0590958	−	0.181878i
$467$	7.24768e6	−	5.26575e6i	1.53782	−	1.11729i	0.586143	−	0.810207i	$-0.300646\pi$
$467$	7.24768e6	−	5.26575e6i	1.53782	−	1.11729i	0.951681	−	0.307088i	$-0.0993544\pi$
$468$	655708.			0.138387
$469$	−464304.	+	337337.i	−0.0974698	+	0.0708160i
$470$	−1.22648e6	+	3.93110e6i	−0.256104	+	0.820860i
$471$	1.12744e6	+	819135.i	0.234176	+	0.170139i
$472$	−1.33954e6	−	973229.i	−0.276757	−	0.201076i
$473$	−281214.	+	865488.i	−0.0577942	+	0.177872i
$474$	−874203.			−0.178717
$475$	−946222.	−	2.69525e6i	−0.192424	−	0.548107i
$476$	1.42772e6			0.288818
$477$	876868.	−	2.69872e6i	0.176457	−	0.543078i
$478$	4.90731e6	+	3.56537e6i	0.982368	+	0.713732i
$479$	−5.07735e6	−	3.68891e6i	−1.01111	−	0.734614i	−0.0466680	−	0.998910i	$-0.514860\pi$
$479$	−5.07735e6	−	3.68891e6i	−1.01111	−	0.734614i	−0.964442	+	0.264296i	$0.914860\pi$
$480$	−515155.	+	6045.23i	−0.102055	+	0.00119759i
$481$	2.08704e6	−	1.51632e6i	0.411309	−	0.298833i
$482$	−2.83773e6			−0.556356
$483$	833952.	−	605901.i	0.162657	−	0.118177i
$484$	−536127.	−	1.65003e6i	−0.104029	−	0.320168i
$485$	8.41957e6	−	98801.9i	1.62531	−	0.0190726i
$486$	−72988.6	+	224636.i	−0.0140173	+	0.0431408i
$487$	1.59737e6	+	4.91619e6i	0.305198	+	0.939303i	0.979603	+	0.200942i	$0.0644002\pi$
$487$	1.59737e6	+	4.91619e6i	0.305198	+	0.939303i	−0.674405	+	0.738362i	$0.735600\pi$
$488$	109410.	+	336728.i	0.0207972	+	0.0640073i
$489$	−1.39440e6	+	4.29151e6i	−0.263702	+	0.811593i
$490$	−35933.7	−	106331.i	−0.00676100	−	0.0200063i
$491$	861272.	+	2.65072e6i	0.161227	+	0.496204i	0.998738	−	0.0502148i	$-0.0159906\pi$
$491$	861272.	+	2.65072e6i	0.161227	+	0.496204i	−0.837512	+	0.546419i	$0.815991\pi$
$492$	−495958.	+	360335.i	−0.0923703	+	0.0671110i
$493$	5.98988e6			1.10994
$494$	−1.49662e6	+	1.08736e6i	−0.275926	+	0.200472i
$495$	833072.	−	620327.i	0.152816	−	0.113791i
$496$	−861581.	−	625975.i	−0.157251	−	0.114249i
$497$	8.01706e6	+	5.82473e6i	1.45587	+	1.05775i
$498$	−640548.	+	1.97141e6i	−0.115739	+	0.356207i
$499$	−6.60917e6			−1.18822			−0.594108	−	0.804385i	$-0.702495\pi$
$499$	−6.60917e6			−1.18822			−0.594108	+	0.804385i	$0.702495\pi$
$500$	769634.	−	2.68704e6i	0.137676	−	0.480672i
$501$	−1.43885e6			−0.256107
$502$	1.17683e6	−	3.62192e6i	0.208428	−	0.641475i
$503$	8.19537e6	+	5.95429e6i	1.44427	+	1.04932i	0.987128	+	0.159931i	$0.0511273\pi$
$503$	8.19537e6	+	5.95429e6i	1.44427	+	1.04932i	0.457143	+	0.889393i	$0.348873\pi$
$504$	551770.	+	400884.i	0.0967568	+	0.0702979i
$505$	−2.64366e6	+	1.96853e6i	−0.461292	+	0.343490i
$506$	646229.	−	469513.i	0.112205	−	0.0815214i
$507$	−1.03779e6			−0.179304
$508$	84147.2	−	61136.5i	0.0144671	−	0.0105109i
$509$	1.71674e6	+	5.28359e6i	0.293705	+	0.903930i	0.983653	+	0.180072i	$0.0576331\pi$
$509$	1.71674e6	+	5.28359e6i	0.293705	+	0.903930i	−0.689949	+	0.723858i	$0.742367\pi$
$510$	−436993.	−	1.29310e6i	−0.0743960	−	0.220144i
$511$	1.24364e6	−	3.82753e6i	0.210689	−	0.648435i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−205919.	−	633755.i	−0.0345465	−	0.106323i
$514$	−2.09989e6	+	6.46279e6i	−0.350581	+	1.07898i
$515$	1.69179e6	−	19852.7i	0.281078	−	0.00329839i
$516$	176537.	+	543325.i	0.0291885	+	0.0898329i
$517$	3.41760e6	−	2.48303e6i	0.562334	−	0.408559i
$518$	2.68326e6			0.439378
$519$	−3.15949e6	+	2.29550e6i	−0.514870	+	0.374075i
$520$	−1.81001e6	+	21240.1i	−0.293543	+	0.00344467i
$521$	−5.55931e6	−	4.03908e6i	−0.897277	−	0.651910i	0.0404880	−	0.999180i	$-0.487109\pi$
$521$	−5.55931e6	−	4.03908e6i	−0.897277	−	0.651910i	−0.937765	+	0.347270i	$0.887109\pi$
$522$	2.31491e6	+	1.68188e6i	0.371841	+	0.270159i
$523$	−2.58120e6	+	7.94411e6i	−0.412636	+	1.26996i	0.501712	+	0.865035i	$0.332704\pi$
$523$	−2.58120e6	+	7.94411e6i	−0.412636	+	1.26996i	−0.914348	+	0.404929i	$0.867296\pi$
$524$	1.21216e6			0.192855
$525$	−2.94168e6	+	2.24458e6i	−0.465798	+	0.355417i
$526$	2.71251e6			0.427471
$527$	871902.	−	2.68344e6i	0.136754	−	0.420887i
$528$	427567.	+	310645.i	0.0667450	+	0.0484931i
$529$	4.59396e6	+	3.33771e6i	0.713753	+	0.518572i
$530$	−2.33308e6	+	7.47792e6i	−0.360777	+	1.15636i
$531$	1.69535e6	−	1.23174e6i	0.260929	−	0.189576i
$532$	−1.92417e6			−0.294757
$533$	−1.74256e6	+	1.26605e6i	−0.265687	+	0.193033i
$534$	1.55743e6	+	4.79327e6i	0.236350	+	0.727409i
$535$	4.37573e6	−	3.25828e6i	0.660946	−	0.492157i
$536$	−86272.4	+	265519.i	−0.0129706	+	0.0399194i
$537$	1.78422e6	+	5.49125e6i	0.267000	+	0.821742i
$538$	2.39165e6	+	7.36074e6i	0.356239	+	1.09639i
$539$	−35579.6	+	109503.i	−0.00527509	+	0.0162350i
$540$	194200.	−	622446.i	0.0286593	−	0.0918581i
$541$	3.89862e6	+	1.19987e7i	0.572687	+	1.76255i	0.643922	+	0.765091i	$0.277306\pi$
$541$	3.89862e6	+	1.19987e7i	0.572687	+	1.76255i	−0.0712349	+	0.997460i	$0.522694\pi$
$542$	−1.37890e6	+	1.00183e6i	−0.201620	+	0.146486i
$543$	−828622.			−0.120603
$544$	561881.	−	408230.i	0.0814042	−	0.0591436i
$545$	532548.	+	377451.i	0.0768011	+	0.0544339i
$546$	1.93866e6	+	1.40852e6i	0.278304	+	0.202200i
$547$	4.40722e6	+	3.20204e6i	0.629792	+	0.457570i	0.856328	−	0.516432i	$-0.172740\pi$
$547$	4.40722e6	+	3.20204e6i	0.629792	+	0.457570i	−0.226536	+	0.974003i	$0.572740\pi$
$548$	−518506.	+	1.59580e6i	−0.0737569	+	0.227000i
$549$	−448103.			−0.0634523
$550$	−2.27951e6	+	1.73933e6i	−0.321318	+	0.245174i
$551$	−8.07270e6			−1.13276
$552$	154957.	−	476908.i	0.0216453	−	0.0666172i
$553$	−2.58466e6	−	1.87786e6i	−0.359410	−	0.261126i
$554$	−2.25290e6	−	1.63683e6i	−0.311866	−	0.226584i
$555$	−821288.	−	2.43026e6i	−0.113178	−	0.334903i
$556$	−2.05016e6	+	1.48953e6i	−0.281255	+	0.204344i
$557$	8.65388e6			1.18188			0.590939	−	0.806716i	$-0.298757\pi$
$557$	8.65388e6			1.18188			0.590939	+	0.806716i	$0.298757\pi$
$558$	1.09044e6	−	792250.i	0.148257	−	0.107715i
$559$	620268.	+	1.90899e6i	0.0839556	+	0.258389i
$560$	−1.53608e6	−	1.08872e6i	−0.206988	−	0.146706i
$561$	−432688.	+	1.33168e6i	−0.0580454	+	0.178645i
$562$	−1.74751e6	−	5.37829e6i	−0.233389	−	0.718296i
$563$	1.26551e6	+	3.89483e6i	0.168265	+	0.517867i	0.999262	−	0.0384102i	$-0.0122294\pi$
$563$	1.26551e6	+	3.89483e6i	0.168265	+	0.517867i	−0.830997	+	0.556277i	$0.812229\pi$
$564$	819491.	−	2.52213e6i	0.108479	−	0.333865i
$565$	−3.34688e6	−	2.37215e6i	−0.441082	−	0.312623i
$566$	128008.	+	393969.i	0.0167957	+	0.0516918i
$567$	−698334.	+	507369.i	−0.0912232	+	0.0662775i
$568$	4.82061e6			0.626947
$569$	−2.46296e6	+	1.78944e6i	−0.318916	+	0.231706i	−0.735713	−	0.677294i	$-0.763153\pi$
$569$	−2.46296e6	+	1.78944e6i	−0.318916	+	0.231706i	0.416797	+	0.909000i	$0.363153\pi$
$570$	588946.	+	1.74274e6i	0.0759256	+	0.224670i
$571$	−2.59916e6	−	1.88840e6i	−0.333613	−	0.242384i	0.408349	−	0.912826i	$-0.366105\pi$
$571$	−2.59916e6	−	1.88840e6i	−0.333613	−	0.242384i	−0.741962	+	0.670442i	$0.766105\pi$
$572$	1.50227e6	+	1.09146e6i	0.191980	+	0.139482i
$573$	2.52172e6	−	7.76106e6i	0.320856	−	0.987494i
$574$	−2.24037e6			−0.283818
$575$	2.23788e6	+	1.54701e6i	0.282272	+	0.195129i
$576$	331776.			0.0416667
$577$	1.96967e6	−	6.06203e6i	0.246295	−	0.758017i	−0.749126	−	0.662427i	$-0.769526\pi$
$577$	1.96967e6	−	6.06203e6i	0.246295	−	0.758017i	0.995421	−	0.0955895i	$-0.0304736\pi$
$578$	−3.10611e6	−	2.25672e6i	−0.386721	−	0.280969i
$579$	1.29995e6	+	944470.i	0.161150	+	0.117082i
$580$	−6.44453e6	−	4.56766e6i	−0.795465	−	0.563798i
$581$	−6.12858e6	+	4.45268e6i	−0.753216	+	0.547244i
$582$	−5.42247e6			−0.663575
$583$	6.50112e6	−	4.72334e6i	0.792167	−	0.575543i
$584$	−604977.	−	1.86193e6i	−0.0734019	−	0.225908i
$585$	682328.	−	2.18698e6i	0.0824334	−	0.264214i
$586$	2.50978e6	−	7.72430e6i	0.301920	−	0.929213i
$587$	1.68409e6	+	5.18309e6i	0.201730	+	0.620860i	0.999832	+	0.0183380i	$0.00583748\pi$
$587$	1.68409e6	+	5.18309e6i	0.201730	+	0.620860i	−0.798102	+	0.602522i	$0.794163\pi$
$588$	22335.7	+	68742.3i	0.00266414	+	0.00819938i
$589$	−1.17508e6	+	3.61653e6i	−0.139566	+	0.429540i
$590$	−4.63992e6	+	3.45501e6i	−0.548758	+	0.408619i
$591$	1.31553e6	+	4.04880e6i	0.154929	+	0.476823i
$592$	1.05600e6	−	767230.i	0.123840	−	0.0899749i
$593$	2.71918e6			0.317542			0.158771	−	0.987315i	$-0.449247\pi$
$593$	2.71918e6			0.317542			0.158771	+	0.987315i	$0.449247\pi$
$594$	−541139.	+	393160.i	−0.0629278	+	0.0457197i
$595$	1.48568e6	−	4.76185e6i	0.172041	−	0.551421i
$596$	−5.44975e6	−	3.95948e6i	−0.628436	−	0.456585i
$597$	−150881.	−	109621.i	−0.0173260	−	0.0125881i
$598$	544444.	−	1.67563e6i	0.0622588	−	0.191613i
$599$	3.00311e6			0.341983			0.170991	−	0.985273i	$-0.445303\pi$
$599$	3.00311e6			0.341983			0.170991	+	0.985273i	$0.445303\pi$
$600$	−515905.	+	1.72448e6i	−0.0585049	+	0.195560i
$601$	6.84700e6			0.773239			0.386620	−	0.922239i	$-0.373643\pi$
$601$	6.84700e6			0.773239			0.386620	+	0.922239i	$0.373643\pi$
$602$	−645162.	+	1.98560e6i	−0.0725567	+	0.223307i
$603$	−285859.	−	207689.i	−0.0320154	−	0.0232605i
$604$	6.09394e6	+	4.42751e6i	0.679682	+	0.493818i
$605$	−6.06122e6	+	71127.1i	−0.673243	+	0.00790036i
$606$	1.71724e6	−	1.24765e6i	0.189954	−	0.138010i
$607$	−1.02716e7			−1.13153			−0.565763	−	0.824568i	$-0.691418\pi$
$607$	−1.02716e7			−1.13153			−0.565763	+	0.824568i	$0.691418\pi$
$608$	−757260.	+	550181.i	−0.0830780	+	0.0603597i
$609$	3.23141e6	+	9.94525e6i	0.353060	+	1.08661i
$610$	1.23694e6	−	14515.2i	0.134593	−	0.00157942i
$611$	2.87930e6	−	8.86158e6i	0.312021	−	0.960303i
$612$	271628.	+	835984.i	0.0293154	+	0.0902234i
$613$	−3.31093e6	−	1.01900e7i	−0.355876	−	1.09527i	−0.955500	−	0.294992i	$-0.904683\pi$
$613$	−3.31093e6	−	1.01900e7i	−0.355876	−	1.09527i	0.599624	−	0.800282i	$-0.295317\pi$
$614$	833504.	−	2.56526e6i	0.0892250	−	0.274606i
$615$	685730.	+	2.02913e6i	0.0731081	+	0.216333i
$616$	596845.	+	1.83690e6i	0.0633738	+	0.195044i
$617$	1.04012e7	−	7.55693e6i	1.09995	−	0.799158i	0.118895	−	0.992907i	$-0.462065\pi$
$617$	1.04012e7	−	7.55693e6i	1.09995	−	0.799158i	0.981051	+	0.193749i	$0.0620648\pi$
$618$	−1.08956e6			−0.114758
$619$	−3.92334e6	+	2.85047e6i	−0.411556	+	0.299013i	−0.774232	−	0.632902i	$-0.781863\pi$
$619$	−3.92334e6	+	2.85047e6i	−0.411556	+	0.299013i	0.362675	+	0.931916i	$0.381863\pi$
$620$	−2.98437e6	+	2.22224e6i	−0.311798	+	0.232173i
$621$	513441.	+	373037.i	0.0534271	+	0.0388171i
$622$	−3.67703e6	−	2.67152e6i	−0.381085	−	0.276874i
$623$	−5.69168e6	+	1.75172e7i	−0.587517	+	1.80819i
$624$	1.16570e6			0.119847
$625$	−8.16118e6	−	5.36308e6i	−0.835705	−	0.549179i
$626$	−9.27011e6			−0.945473
$627$	583144.	−	1.79473e6i	0.0592389	−	0.182319i
$628$	2.00434e6	+	1.45624e6i	0.202802	+	0.147344i
$629$	2.79777e6	+	2.03270e6i	0.281958	+	0.204855i
$630$	1.91124e6	−	1.42316e6i	0.191851	−	0.142857i
$631$	1.33246e7	−	9.68090e6i	1.33224	−	0.967926i	0.332545	−	0.943087i	$-0.392093\pi$
$631$	1.33246e7	−	9.68090e6i	1.33224	−	0.967926i	0.999691	−	0.0248388i	$-0.00790724\pi$
$632$	−1.55414e6			−0.154774
$633$	−610017.	+	443203.i	−0.0605108	+	0.0439637i
$634$	−1.42240e6	−	4.37769e6i	−0.140539	−	0.432536i
$635$	−116345.	−	344274.i	−0.0114502	−	0.0338821i
$636$	1.55888e6	−	4.79773e6i	0.152816	−	0.470319i
$637$	78477.2	+	241528.i	0.00766293	+	0.0235841i
$638$	2.50402e6	+	7.70657e6i	0.243549	+	0.749566i
$639$	−1.88534e6	+	5.80248e6i	−0.182657	+	0.562162i
$640$	−915830.	+	10747.1i	−0.0883823	+	0.00103715i
$641$	−220433.	−	678423.i	−0.0211900	−	0.0652162i	0.939902	−	0.341443i	$-0.110916\pi$
$641$	−220433.	−	678423.i	−0.0211900	−	0.0652162i	−0.961092	+	0.276227i	$0.910916\pi$
$642$	−2.84234e6	+	2.06508e6i	−0.272169	+	0.197742i
$643$	−1.62608e6			−0.155101			−0.0775505	−	0.996988i	$-0.524710\pi$
$643$	−1.62608e6			−0.155101			−0.0775505	+	0.996988i	$0.524710\pi$
$644$	1.48258e6	−	1.07716e6i	0.140865	−	0.102345i
$645$	1.99585e6	−	23420.9i	0.188899	−	0.00221669i
$646$	−2.00628e6	−	1.45765e6i	−0.189152	−	0.137427i
$647$	7.31608e6	+	5.31544e6i	0.687096	+	0.499205i	0.875704	−	0.482848i	$-0.160398\pi$
$647$	7.31608e6	+	5.31544e6i	0.687096	+	0.499205i	−0.188608	+	0.982052i	$0.560398\pi$
$648$	−129757.	+	399352.i	−0.0121393	+	0.0373610i
$649$	5.93445e6			0.553055
$650$	−1.81265e6	+	6.05902e6i	−0.168279	+	0.562495i
$651$	4.92580e6			0.455537
$652$	−2.47893e6	+	7.62935e6i	−0.228373	+	0.702860i
$653$	8.99213e6	+	6.53317e6i	0.825239	+	0.599571i	0.918208	−	0.396098i	$-0.129636\pi$
$653$	8.99213e6	+	6.53317e6i	0.825239	+	0.599571i	−0.0929693	+	0.995669i	$0.529636\pi$
$654$	−340078.	−	247081.i	−0.0310910	−	0.0225889i
$655$	1.26137e6	−	4.04291e6i	0.114878	−	0.368206i
$656$	−881704.	+	640595.i	−0.0799951	+	0.0581198i
$657$	2.47777e6			0.223949
$658$	7.84065e6	−	5.69657e6i	0.705972	−	0.512919i
$659$	1.87068e6	+	5.75735e6i	0.167797	+	0.516428i	0.999232	−	0.0391959i	$-0.0124796\pi$
$659$	1.87068e6	+	5.75735e6i	0.167797	+	0.516428i	−0.831434	+	0.555623i	$0.812480\pi$
$660$	1.48102e6	−	1.10280e6i	0.132343	−	0.0985459i
$661$	5.21545e6	−	1.60515e7i	0.464289	−	1.42893i	−0.395586	−	0.918429i	$-0.629458\pi$
$661$	5.21545e6	−	1.60515e7i	0.464289	−	1.42893i	0.859875	−	0.510505i	$-0.170542\pi$
$662$	−2.31874e6	−	7.13635e6i	−0.205640	−	0.632894i
$663$	954371.	+	2.93725e6i	0.0843205	+	0.259512i
$664$	−1.13875e6	+	3.50472e6i	−0.100233	+	0.308484i
$665$	−2.00228e6	+	6.41766e6i	−0.175578	+	0.562759i
$666$	510498.	+	1.57115e6i	0.0445973	+	0.137256i
$667$	6.22006e6	−	4.51914e6i	0.541352	−	0.393315i
$668$	−2.55796e6			−0.221795
$669$	−1.09373e6	+	794640.i	−0.0944809	+	0.0686444i
$670$	795810.	+	564042.i	0.0684892	+	0.0485428i
$671$	−1.02663e6	−	745891.i	−0.0880254	−	0.0639542i
$672$	980924.	+	712683.i	0.0837939	+	0.0608798i
$673$	4.47322e6	−	1.37672e7i	0.380700	−	1.17167i	−0.558852	−	0.829268i	$-0.688758\pi$
$673$	4.47322e6	−	1.37672e7i	0.380700	−	1.17167i	0.939552	−	0.342407i	$-0.111242\pi$
$674$	−6.81903e6			−0.578193
$675$	−1.87396e6	−	1.29543e6i	−0.158307	−	0.109435i
$676$	−1.84496e6			−0.155281
$677$	3.90114e6	−	1.20065e7i	0.327130	−	1.00680i	−0.643341	−	0.765580i	$-0.722452\pi$
$677$	3.90114e6	−	1.20065e7i	0.327130	−	1.00680i	0.970470	−	0.241221i	$-0.0775479\pi$
$678$	2.13728e6	+	1.55282e6i	0.178561	+	0.129732i
$679$	−1.60320e7	−	1.16479e7i	−1.33448	−	0.969559i
$680$	−776877.	−	2.29884e6i	−0.0644288	−	0.190650i
$681$	6.70425e6	−	4.87092e6i	0.553965	−	0.402479i
$682$	3.81700e6			0.314240
$683$	−1.49971e7	+	1.08960e7i	−1.23014	+	0.893749i	−0.996901	−	0.0786697i	$-0.974933\pi$
$683$	−1.49971e7	+	1.08960e7i	−1.23014	+	0.893749i	−0.233240	+	0.972419i	$0.574933\pi$
$684$	−366079.	−	1.12667e6i	−0.0299181	−	0.0920785i
$685$	4.78290e6	+	3.38995e6i	0.389462	+	0.276037i
$686$	2.65155e6	−	8.16063e6i	0.215124	−	0.662085i
$687$	−1.63992e6	−	5.04714e6i	−0.132565	−	0.407994i
$688$	313844.	+	965912.i	0.0252780	+	0.0777976i
$689$	5.47715e6	−	1.68569e7i	0.439548	−	1.35279i
$690$	−1.42938e6	−	1.01309e6i	−0.114294	−	0.0810079i
$691$	−414164.	−	1.27467e6i	−0.0329972	−	0.101555i	0.933201	−	0.359354i	$-0.117003\pi$
$691$	−414164.	−	1.27467e6i	−0.0329972	−	0.101555i	−0.966199	+	0.257799i	$0.917003\pi$
$692$	−5.61686e6	+	4.08089e6i	−0.445891	+	0.323959i
$693$	−2.44447e6			−0.193353
$694$	2.82974e6	−	2.05593e6i	0.223022	−	0.162035i
$695$	2.83462e6	+	8.38788e6i	0.222604	+	0.658703i
$696$	4.11540e6	+	2.99001e6i	0.322024	+	0.233964i
$697$	−2.33598e6	−	1.69719e6i	−0.182132	−	0.132327i
$698$	−4.22174e6	+	1.29932e7i	−0.327985	+	1.00943i
$699$	2.01707e6			0.156145
$700$	−5.22965e6	+	3.99037e6i	−0.403393	+	0.307800i
$701$	−1.84275e7			−1.41635			−0.708177	−	0.706035i	$-0.750482\pi$
$701$	−1.84275e7			−1.41635			−0.708177	+	0.706035i	$0.750482\pi$
$702$	−455906.	+	1.40314e6i	−0.0349167	+	0.107462i
$703$	−3.77061e6	−	2.73951e6i	−0.287756	−	0.209067i
$704$	760118.	+	552258.i	0.0578029	+	0.0419963i
$705$	−7.55930e6	−	5.35777e6i	−0.572808	−	0.405986i
$706$	3.47172e6	−	2.52235e6i	0.262140	−	0.190456i
$707$	7.75722e6			0.583657
$708$	3.01395e6	−	2.18977e6i	0.225971	−	0.164178i
$709$	−5.69775e6	−	1.75359e7i	−0.425684	−	1.31012i	−0.902337	−	0.431030i	$-0.858150\pi$
$709$	−5.69775e6	−	1.75359e7i	−0.425684	−	1.31012i	0.476653	−	0.879092i	$-0.341850\pi$
$710$	5.01631e6	−	1.60782e7i	0.373455	−	1.19699i
$711$	607823.	−	1.87069e6i	0.0450924	−	0.138780i
$712$	2.76876e6	+	8.52137e6i	0.204685	+	0.629955i
$713$	−1.11915e6	−	3.44438e6i	−0.0824447	−	0.253739i
$714$	−992674.	+	3.05514e6i	−0.0728721	+	0.224277i
$715$	5.20359e6	−	3.87473e6i	0.380661	−	0.283450i
$716$	3.17194e6	+	9.76223e6i	0.231229	+	0.711650i
$717$	−1.10415e7	+	8.02209e6i	−0.802100	+	0.582760i
$718$	−4.07107e6			−0.294712
$719$	1.87236e7	−	1.36035e7i	1.35073	−	0.981360i	0.351752	−	0.936093i	$-0.385586\pi$
$719$	1.87236e7	−	1.36035e7i	1.35073	−	0.981360i	0.998975	−	0.0452668i	$-0.0144138\pi$
$720$	345245.	−	1.10657e6i	0.0248197	−	0.0795514i
$721$	−3.22139e6	−	2.34048e6i	−0.230784	−	0.167674i
$722$	−5.30891e6	−	3.85715e6i	−0.379021	−	0.275375i
$723$	1.97304e6	−	6.07239e6i	0.140375	−	0.432030i
$724$	−1.47311e6			−0.104445
$725$	−2.19406e7	+	1.67413e7i	−1.55026	+	1.18289i
$726$	3.90362e6			0.274869
$727$	3.26713e6	−	1.00552e7i	0.229261	−	0.705593i	−0.768570	−	0.639766i	$-0.779031\pi$
$727$	3.26713e6	−	1.00552e7i	0.229261	−	0.705593i	0.997831	−	0.0658274i	$-0.0209687\pi$
$728$	3.44650e6	+	2.50403e6i	0.241018	+	0.175110i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	−6.83962e6	+	80261.5i	−0.475034	+	0.00557442i
$731$	−2.17688e6	+	1.58160e6i	−0.150675	+	0.109472i
$732$	−796628.			−0.0549513
$733$	−2.00027e7	+	1.45328e7i	−1.37508	+	0.999054i	−0.377759	+	0.925904i	$0.623305\pi$
$733$	−2.00027e7	+	1.45328e7i	−1.37508	+	0.999054i	−0.997321	+	0.0731502i	$0.976695\pi$
$734$	−4.84228e6	−	1.49030e7i	−0.331749	−	1.02102i
$735$	252518.	−	2963.25i	0.0172415	−	0.000202325i
$736$	275479.	−	847836.i	0.0187453	−	0.0576922i
$737$	−309211.	−	951655.i	−0.0209694	−	0.0645373i
$738$	−426238.	−	1.31183e6i	−0.0288079	−	0.0886616i
$739$	−6.49772e6	+	1.99979e7i	−0.437673	+	1.34702i	0.452649	+	0.891689i	$0.350479\pi$
$739$	−6.49772e6	+	1.99979e7i	−0.437673	+	1.34702i	−0.890322	+	0.455331i	$0.849521\pi$
$740$	−1.46007e6	−	4.32045e6i	−0.0980152	−	0.290035i
$741$	−1.28623e6	−	3.95860e6i	−0.0860543	−	0.264848i
$742$	1.49149e7	−	1.08363e7i	0.994512	−	0.722555i
$743$	−7.78045e6			−0.517050			−0.258525	−	0.966005i	$-0.583236\pi$
$743$	−7.78045e6			−0.517050			−0.258525	+	0.966005i	$0.583236\pi$
$744$	1.93856e6	−	1.40844e6i	0.128395	−	0.0932841i
$745$	−1.88770e7	+	1.40563e7i	−1.24607	+	0.927856i
$746$	−1.15345e7	−	8.38033e6i	−0.758845	−	0.551333i
$747$	−3.77320e6	−	2.74139e6i	−0.247405	−	0.179750i
$748$	−769223.	+	2.36743e6i	−0.0502688	+	0.154711i
$749$	−1.28396e7			−0.836270
$750$	5.21481e6	+	3.51519e6i	0.338521	+	0.228189i
$751$	−534821.			−0.0346026			−0.0173013	−	0.999850i	$-0.505507\pi$
$751$	−534821.			−0.0346026			−0.0173013	+	0.999850i	$0.505507\pi$
$752$	1.45687e6	−	4.48379e6i	0.0939457	−	0.289135i
$753$	6.93223e6	+	5.03656e6i	0.445539	+	0.323703i
$754$	1.44596e7	+	1.05055e7i	0.926246	+	0.672957i
$755$	2.11084e7	−	1.57178e7i	1.34768	−	1.00352i
$756$	−1.24148e6	+	901990.i	−0.0790016	+	0.0573980i
$757$	−1.89729e7			−1.20336			−0.601679	−	0.798738i	$-0.705501\pi$
$757$	−1.89729e7			−1.20336			−0.601679	+	0.798738i	$0.705501\pi$
$758$	−7.30209e6	+	5.30528e6i	−0.461609	+	0.335379i
$759$	555385.	+	1.70930e6i	0.0349937	+	0.107699i
$760$	1.04702e6	+	3.09820e6i	0.0657535	+	0.194570i
$761$	5.50184e6	−	1.69329e7i	0.344386	−	1.05991i	−0.617525	−	0.786551i	$-0.711865\pi$
$761$	5.50184e6	−	1.69329e7i	0.344386	−	1.05991i	0.961911	−	0.273361i	$-0.0881355\pi$
$762$	72318.1	+	222572.i	0.00451190	+	0.0138862i
$763$	−474719.	−	1.46104e6i	−0.0295206	−	0.0908551i
$764$	4.48306e6	−	1.37974e7i	0.277870	−	0.855195i
$765$	3.07091e6	−	36036.4i	0.189720	−	0.00222632i
$766$	42663.7	+	131305.i	0.00262716	+	0.00808557i
$767$	1.05896e7	−	7.69380e6i	0.649967	−	0.472229i
$768$	589824.			0.0360844
$769$	−9.54450e6	+	6.93448e6i	−0.582019	+	0.422862i	−0.839451	−	0.543435i	$-0.817124\pi$
$769$	−9.54450e6	+	6.93448e6i	−0.582019	+	0.422862i	0.257432	+	0.966296i	$0.417124\pi$
$770$	6.74767e6	−	79182.5i	0.410135	−	0.00481285i
$771$	−1.23696e7	−	8.98701e6i	−0.749408	−	0.544477i
$772$	2.31103e6	+	1.67906e6i	0.139560	+	0.101396i
$773$	−832070.	+	2.56085e6i	−0.0500854	+	0.154147i	−0.972971	−	0.230927i	$-0.925824\pi$
$773$	−832070.	+	2.56085e6i	−0.0500854	+	0.154147i	0.922886	+	0.385074i	$0.125824\pi$
$774$	−1.28539e6			−0.0771230
$775$	4.30630e6	+	1.22662e7i	0.257543	+	0.733595i
$776$	−9.63995e6			−0.574672
$777$	−1.86564e6	+	5.74184e6i	−0.110860	+	0.341192i
$778$	−3.39311e6	−	2.46524e6i	−0.200978	−	0.146019i
$779$	3.14826e6	+	2.28734e6i	0.185877	+	0.135048i
$780$	1.21303e6	−	3.88797e6i	0.0713894	−	0.228816i
$781$	−1.39779e7	+	1.01556e7i	−0.820003	+	0.595767i
$782$	2.36185e6			0.138113
$783$	−5.20855e6	+	3.78423e6i	−0.303607	+	0.220584i
$784$	39708.0	+	122209.i	0.00230721	+	0.00710087i
$785$	6.94270e6	−	5.16971e6i	0.402119	−	0.299428i
$786$	−842800.	+	2.59387e6i	−0.0486595	+	0.149759i
$787$	6.73421e6	+	2.07258e7i	0.387570	+	1.19282i	0.934599	+	0.355703i	$0.115759\pi$
$787$	6.73421e6	+	2.07258e7i	0.387570	+	1.19282i	−0.547029	+	0.837113i	$0.684241\pi$
$788$	2.33873e6	+	7.19786e6i	0.134173	+	0.412941i
$789$	−1.88597e6	+	5.80443e6i	−0.107856	+	0.331946i
$790$	−1.61723e6	+	5.18351e6i	−0.0921943	+	0.295499i
$791$	2.98345e6	+	9.18210e6i	0.169542	+	0.521796i
$792$	−962025.	+	698952.i	−0.0544971	+	0.0395945i
$793$	−2.79897e6			−0.158058
$794$	4.81409e6	−	3.49764e6i	0.270996	−	0.196890i
$795$	−1.43797e7	−	1.01918e7i	−0.806921	−	0.571918i
$796$	−268233.	−	194883.i	−0.0150048	−	0.0109016i
$797$	5.72730e6	+	4.16112e6i	0.319377	+	0.232041i	0.735910	−	0.677080i	$-0.236755\pi$
$797$	5.72730e6	+	4.16112e6i	0.319377	+	0.232041i	−0.416533	+	0.909121i	$0.636755\pi$
$798$	1.33785e6	−	4.11748e6i	0.0743704	−	0.228889i
$799$	1.24907e7			0.692180
$800$	−917165.	+	3.06575e6i	−0.0506667	+	0.169360i
$801$	−1.13399e7			−0.624492
$802$	277356.	−	853613.i	0.0152265	−	0.0468624i
$803$	5.67673e6	+	4.12438e6i	0.310677	+	0.225720i
$804$	−508194.	−	369225.i	−0.0277261	−	0.0201442i
$805$	−2.04987e6	−	6.06573e6i	−0.111490	−	0.329908i
$806$	6.81117e6	−	4.94861e6i	0.369304	−	0.268315i
$807$	−1.74140e7			−0.941269
$808$	3.05287e6	−	2.21804e6i	0.164505	−	0.119520i
$809$	−2.92937e6	−	9.01567e6i	−0.157363	−	0.484313i	0.841030	−	0.540989i	$-0.181950\pi$
$809$	−2.92937e6	−	9.01567e6i	−0.157363	−	0.484313i	−0.998393	+	0.0566756i	$0.981950\pi$
$810$	1.19693e6	+	848344.i	0.0640999	+	0.0454318i
$811$	−9.34414e6	+	2.87583e7i	−0.498870	+	1.53536i	0.311969	+	0.950092i	$0.399012\pi$
$811$	−9.34414e6	+	2.87583e7i	−0.498870	+	1.53536i	−0.810838	+	0.585270i	$0.800988\pi$
$812$	5.74472e6	+	1.76804e7i	0.305759	+	0.941029i
$813$	−1.18506e6	−	3.64724e6i	−0.0628802	−	0.193525i
$814$	−1.44568e6	+	4.44935e6i	−0.0764737	+	0.235362i
$815$	2.28666e7	+	1.62070e7i	1.20589	+	0.854692i
$816$	482894.	+	1.48619e6i	0.0253879	+	0.0781358i
$817$	2.93384e6	−	2.13156e6i	0.153773	−	0.111723i
$818$	−2.03388e7			−1.06278
$819$	−4.36198e6	+	3.16916e6i	−0.227234	+	0.165095i
$820$	1.21908e6	+	3.60734e6i	0.0633135	+	0.187350i
$821$	−1.55786e7	−	1.13185e7i	−0.806623	−	0.586046i	0.106227	−	0.994342i	$-0.466123\pi$
$821$	−1.55786e7	−	1.13185e7i	−0.806623	−	0.586046i	−0.912849	+	0.408296i	$0.866123\pi$
$822$	−3.05430e6	−	2.21908e6i	−0.157664	−	0.114550i
$823$	3.14679e6	−	9.68481e6i	0.161945	−	0.498416i	−0.836853	−	0.547427i	$-0.815607\pi$
$823$	3.14679e6	−	9.68481e6i	0.161945	−	0.498416i	0.998798	+	0.0490118i	$0.0156072\pi$
$824$	−1.93700e6			−0.0993830
$825$	−2.13704e6	−	6.08720e6i	−0.109314	−	0.311374i
$826$	1.36148e7			0.694323
$827$	9.52210e6	−	2.93060e7i	0.484138	−	1.49002i	−0.349088	−	0.937090i	$-0.613508\pi$
$827$	9.52210e6	−	2.93060e7i	0.484138	−	1.49002i	0.833226	−	0.552933i	$-0.186492\pi$
$828$	912784.	+	663177.i	0.0462692	+	0.0336166i
$829$	1.08096e7	+	7.85364e6i	0.546290	+	0.396903i	0.826416	−	0.563060i	$-0.190376\pi$
$829$	1.08096e7	+	7.85364e6i	0.546290	+	0.396903i	−0.280125	+	0.959963i	$0.590376\pi$
$830$	1.05043e7	+	7.44507e6i	0.529263	+	0.375123i
$831$	5.06903e6	−	3.68287e6i	0.254638	−	0.185005i
$832$	2.07236e6			0.103790
$833$	−275423.	+	200106.i	−0.0137527	+	0.00999190i
$834$	−1.76195e6	−	5.42274e6i	−0.0877161	−	0.269962i
$835$	−2.66180e6	+	8.53154e6i	−0.132117	+	0.423459i
$836$	1.03670e6	−	3.19064e6i	0.0513024	−	0.157893i
$837$	937149.	+	2.88425e6i	0.0462376	+	0.142305i
$838$	−4.78307e6	−	1.47208e7i	−0.235286	−	0.724136i
$839$	6.72874e6	−	2.07089e7i	0.330011	−	1.01567i	−0.639116	−	0.769110i	$-0.720700\pi$
$839$	6.72874e6	−	2.07089e7i	0.330011	−	1.01567i	0.969128	−	0.246560i	$-0.0793002\pi$
$840$	3.39775e6	−	2.53006e6i	0.166147	−	0.123718i
$841$	1.77633e7	+	5.46697e7i	0.866030	+	2.66537i
$842$	1.84689e7	−	1.34184e7i	0.897760	−	0.652261i
$843$	1.27239e7			0.616668
$844$	−1.08447e6	+	787917.i	−0.0524039	+	0.0380736i
$845$	−1.91986e6	+	6.15348e6i	−0.0924968	+	0.296469i
$846$	4.82727e6	+	3.50722e6i	0.231887	+	0.168476i
$847$	1.15414e7	+	8.38531e6i	0.552776	+	0.401615i
$848$	2.77134e6	−	8.52929e6i	0.132343	−	0.407308i
$849$	−932049.			−0.0443782
$850$	−8.47573e6	+	198949.i	−0.402374	+	0.00944484i
$851$	4.43887e6			0.210111
$852$	−3.35171e6	+	1.03155e7i	−0.158186	+	0.486846i
$853$	1.84192e6	+	1.33823e6i	0.0866757	+	0.0629736i	0.630279	−	0.776369i	$-0.282940\pi$
$853$	1.84192e6	+	1.33823e6i	0.0866757	+	0.0629736i	−0.543603	+	0.839342i	$0.682940\pi$
$854$	−2.35530e6	−	1.71122e6i	−0.110510	−	0.0802902i
$855$	−4.13873e6	+	48567.2i	−0.193621	+	0.00227210i
$856$	−5.05305e6	+	3.67126e6i	−0.235705	+	0.171250i
$857$	−3.49822e7			−1.62703			−0.813515	−	0.581544i	$-0.802449\pi$
$857$	−3.49822e7			−1.62703			−0.813515	+	0.581544i	$0.802449\pi$
$858$	−3.38010e6	+	2.45579e6i	−0.156751	+	0.113887i
$859$	−9.61165e6	−	2.95816e7i	−0.444442	−	1.36785i	−0.883094	−	0.469195i	$-0.844544\pi$
$859$	−9.61165e6	−	2.95816e7i	−0.444442	−	1.36785i	0.438652	−	0.898657i	$-0.355456\pi$
$860$	3.54818e6	−	41637.2i	0.163591	−	0.00191971i
$861$	1.55771e6	−	4.79412e6i	0.0716106	−	0.220395i
$862$	−1.84418e6	−	5.67580e6i	−0.0845346	−	0.260171i
$863$	−388031.	−	1.19424e6i	−0.0177353	−	0.0545837i	0.941797	−	0.336182i	$-0.109136\pi$
$863$	−388031.	−	1.19424e6i	−0.0177353	−	0.0545837i	−0.959533	+	0.281598i	$0.909136\pi$
$864$	−230680.	+	709960.i	−0.0105130	+	0.0323556i
$865$	7.76608e6	+	2.29805e7i	0.352908	+	1.04428i
$866$	6.86876e6	+	2.11399e7i	0.311232	+	0.957872i
$867$	6.98875e6	−	5.07762e6i	0.315756	−	0.229410i
$868$	8.75697e6			0.394507
$869$	4.50641e6	−	3.27410e6i	0.202433	−	0.147076i
$870$	1.42550e7	−	1.06147e7i	0.638513	−	0.475454i
$871$	−1.78555e6	−	1.29728e6i	−0.0797494	−	0.0579413i
$872$	−604584.	−	439256.i	−0.0269256	−	0.0195626i
$873$	3.77018e6	−	1.16034e7i	0.167427	−	0.515289i
$874$	−3.18312e6			−0.140953
$875$	7.86711e6	+	2.15948e7i	0.347372	+	0.953519i
$876$	4.40493e6			0.193945
$877$	−6.24487e6	+	1.92197e7i	−0.274173	+	0.843817i	0.715264	+	0.698854i	$0.246306\pi$
$877$	−6.24487e6	+	1.92197e7i	−0.274173	+	0.843817i	−0.989437	+	0.144963i	$0.953694\pi$
$878$	−1.95504e7	−	1.42042e7i	−0.855893	−	0.621843i
$879$	1.47840e7	+	1.07412e7i	0.645388	+	0.468902i
$880$	2.63292e6	−	1.96054e6i	0.114612	−	0.0853432i
$881$	2.09209e6	−	1.51999e6i	0.0908113	−	0.0659783i	−0.541453	−	0.840731i	$-0.682126\pi$
$881$	2.09209e6	−	1.51999e6i	0.0908113	−	0.0659783i	0.632264	+	0.774753i	$0.282126\pi$
$882$	−162630.			−0.00703929
$883$	2.24352e7	−	1.63001e7i	0.968340	−	0.703540i	0.0132675	−	0.999912i	$-0.495777\pi$
$883$	2.24352e7	−	1.63001e7i	0.968340	−	0.703540i	0.955073	+	0.296372i	$0.0957767\pi$
$884$	1.69666e6	+	5.22178e6i	0.0730237	+	0.224744i
$885$	−4.16721e6	−	1.23311e7i	−0.178849	−	0.529229i
$886$	2.43097e6	−	7.48174e6i	0.104039	−	0.320198i
$887$	1.10138e7	+	3.38969e7i	0.470031	+	1.44661i	0.852543	+	0.522657i	$0.175059\pi$
$887$	1.10138e7	+	3.38969e7i	0.470031	+	1.44661i	−0.382511	+	0.923951i	$0.624941\pi$
$888$	907553.	+	2.79316e6i	0.0386224	+	0.118868i
$889$	−264289.	+	813399.i	−0.0112157	+	0.0345183i
$890$	3.13024e7	−	367328.i	1.32466	−	0.0155446i
$891$	−465068.	−	1.43133e6i	−0.0196255	−	0.0604012i
$892$	−1.94441e6	+	1.41269e6i	−0.0818229	+	0.0594478i
$893$	−1.68340e7			−0.706412
$894$	1.22619e7	−	8.90882e6i	0.513116	−	0.372800i
$895$	3.58606e7	−	420817.i	1.49644	−	0.0175604i
$896$	1.74387e6	+	1.26699e6i	0.0725676	+	0.0527235i
$897$	3.20709e6	+	2.33009e6i	0.133085	+	0.0966922i
$898$	2.80028e6	−	8.61836e6i	0.115880	−	0.356643i
$899$	3.67392e7			1.51611
$900$	−3.33148e6	−	2.30299e6i	−0.137098	−	0.0947731i
$901$	2.37604e7			0.975082
$902$	1.20707e6	−	3.71497e6i	0.0493986	−	0.152033i
$903$	−3.80038e6	−	2.76113e6i	−0.155098	−	0.112686i
$904$	3.79960e6	+	2.76057e6i	0.154638	+	0.112351i
$905$	−1.53291e6	+	4.91324e6i	−0.0622149	+	0.199410i
$906$	−1.37114e7	+	9.96189e6i	−0.554958	+	0.403201i
$907$	−3.79163e7			−1.53041			−0.765205	−	0.643786i	$-0.777363\pi$
$907$	−3.79163e7			−1.53041			−0.765205	+	0.643786i	$0.777363\pi$
$908$	1.19187e7	−	8.65942e6i	0.479748	−	0.348557i
$909$	1.47584e6	+	4.54216e6i	0.0592418	+	0.182328i
$910$	1.19381e7	−	8.88942e6i	0.477894	−	0.355852i
$911$	−8.06003e6	+	2.48062e7i	−0.321767	+	0.990296i	0.651113	+	0.758981i	$0.274303\pi$
$911$	−8.06003e6	+	2.48062e7i	−0.321767	+	0.990296i	−0.972879	+	0.231314i	$0.925697\pi$
$912$	−650807.	−	2.00298e6i	−0.0259099	−	0.0797423i
$913$	−4.08144e6	−	1.25614e7i	−0.162045	−	0.498724i
$914$	−1.28052e6	+	3.94102e6i	−0.0507014	+	0.156043i
$915$	−828968.	+	2.65699e6i	−0.0327329	+	0.104915i
$916$	−2.91541e6	−	8.97270e6i	−0.114805	−	0.353333i
$917$	−8.06367e6	+	5.85860e6i	−0.316672	+	0.230075i
$918$	−1.97776e6			−0.0774582
$919$	−1.54318e7	+	1.12119e7i	−0.602737	+	0.437914i	−0.846849	−	0.531833i	$-0.821504\pi$
$919$	−1.54318e7	+	1.12119e7i	−0.602737	+	0.437914i	0.244112	+	0.969747i	$0.421504\pi$
$920$	−2.54112e6	−	1.80106e6i	−0.0989819	−	0.0701549i
$921$	4.90982e6	+	3.56719e6i	0.190729	+	0.138573i
$922$	8.68406e6	+	6.30934e6i	0.336431	+	0.244431i
$923$	−1.17763e7	+	3.62438e7i	−0.454994	+	1.40033i
$924$	−4.34572e6			−0.167449
$925$	−1.59293e7	+	373906.i	−0.612129	+	0.0143684i
$926$	3.03404e7			1.16277
$927$	757561.	−	2.33153e6i	0.0289546	−	0.0891132i
$928$	7.31626e6	+	5.31557e6i	0.278881	+	0.202619i
$929$	−8.29622e6	−	6.02755e6i	−0.315385	−	0.229140i	0.418819	−	0.908070i	$-0.362444\pi$
$929$	−8.29622e6	−	6.02755e6i	−0.315385	−	0.229140i	−0.734204	+	0.678929i	$0.762444\pi$
$930$	−2.68032e6	−	7.93128e6i	−0.101620	−	0.300702i
$931$	371194.	−	269688.i	0.0140354	−	0.0101974i
$932$	3.58591e6			0.135226
$933$	8.27332e6	−	6.01092e6i	0.311154	−	0.226067i
$934$	1.10735e7	+	3.40806e7i	0.415352	+	1.27832i
$935$	7.09561e6	+	5.02912e6i	0.265437	+	0.188132i
$936$	−810500.	+	2.49446e6i	−0.0302387	+	0.0930652i
$937$	1.14754e7	+	3.53175e7i	0.426990	+	1.31414i	0.901076	+	0.433661i	$0.142779\pi$
$937$	1.14754e7	+	3.53175e7i	0.426990	+	1.31414i	−0.474086	+	0.880478i	$0.657221\pi$
$938$	−709393.	−	2.18329e6i	−0.0263257	−	0.0810222i
$939$	6.44540e6	−	1.98369e7i	0.238554	−	0.734193i
$940$	−1.34388e7	−	9.52492e6i	−0.496066	−	0.351594i
$941$	−1.64646e7	−	5.06728e7i	−0.606145	−	1.86552i	−0.488719	−	0.872441i	$-0.662536\pi$
$941$	−1.64646e7	−	5.06728e7i	−0.606145	−	1.86552i	−0.117426	−	0.993082i	$-0.537464\pi$
$942$	−4.50977e6	+	3.27654e6i	−0.165587	+	0.120306i
$943$	−3.70621e6			−0.135722
$944$	5.35814e6	−	3.89292e6i	0.195697	−	0.142182i
$945$	1.71652e6	+	5.07932e6i	0.0625272	+	0.185023i
$946$	−2.94491e6	−	2.13960e6i	−0.106990	−	0.0777330i
$947$	−2.20128e7	−	1.59933e7i	−0.797629	−	0.579512i	0.112588	−	0.993642i	$-0.464086\pi$
$947$	−2.20128e7	−	1.59933e7i	−0.797629	−	0.579512i	−0.910218	+	0.414130i	$0.864086\pi$
$948$	1.08057e6	−	3.32567e6i	0.0390511	−	0.120187i
$949$	1.54768e7			0.557849
$950$	1.14229e7	−	268128.i	0.410647	−	0.00963904i
$951$	1.03567e7			0.371339
$952$	−1.76475e6	+	5.43135e6i	−0.0631091	+	0.194230i
$953$	−2.20709e7	−	1.60355e7i	−0.787206	−	0.571939i	0.119927	−	0.992783i	$-0.461734\pi$
$953$	−2.20709e7	−	1.60355e7i	−0.787206	−	0.571939i	−0.907133	+	0.420844i	$0.861734\pi$
$954$	9.18268e6	+	6.67161e6i	0.326662	+	0.237334i
$955$	−4.13535e7	−	2.93099e7i	−1.46725	−	1.03993i
$956$	−1.96293e7	+	1.42615e7i	−0.694639	+	0.504685i
$957$	−1.82321e7			−0.643514
$958$	2.03094e7	−	1.47556e7i	0.714962	−	0.519451i
$959$	−4.26353e6	−	1.31218e7i	−0.149700	−	0.460730i
$960$	613769.	−	1.96724e6i	0.0214945	−	0.0688936i
$961$	−3.49904e6	+	1.07689e7i	−0.122219	+	0.376153i
$962$	3.18871e6	+	9.81384e6i	0.111091	+	0.341902i
$963$	−2.44277e6	−	7.51809e6i	−0.0848824	−	0.261241i
$964$	3.50762e6	−	1.07954e7i	0.121568	−	0.374149i
$965$	8.00500e6	−	5.96073e6i	0.276722	−	0.206054i
$966$	1.27416e6	+	3.92148e6i	0.0439322	+	0.135209i
$967$	−2.78905e7	+	2.02636e7i	−0.959158	+	0.696869i	−0.952955	−	0.303112i	$-0.901974\pi$
$967$	−2.78905e7	+	2.02636e7i	−0.959158	+	0.696869i	−0.00620268	+	0.999981i	$0.501974\pi$
$968$	6.93977e6			0.238044
$969$	4.51413e6	−	3.27971e6i	0.154442	−	0.112208i
$970$	−1.00313e7	+	3.21521e7i	−0.342316	+	1.09718i
$971$	2.32013e7	+	1.68567e7i	0.789703	+	0.573753i	0.907875	−	0.419240i	$-0.137703\pi$
$971$	2.32013e7	+	1.68567e7i	0.789703	+	0.573753i	−0.118172	+	0.992993i	$0.537703\pi$
$972$	−764346.	−	555330.i	−0.0259492	−	0.0188532i
$973$	6.43913e6	−	1.98176e7i	0.218045	−	0.671072i
$974$	−2.06767e7			−0.698368
$975$	−1.17052e7	−	8.09160e6i	−0.394338	−	0.272598i
$976$	−1.41623e6			−0.0475892
$977$	2.24456e6	−	6.90804e6i	0.0752306	−	0.231536i	−0.906369	−	0.422487i	$-0.861157\pi$
$977$	2.24456e6	−	6.90804e6i	0.0752306	−	0.231536i	0.981600	+	0.190951i	$0.0611572\pi$
$978$	−1.46023e7	−	1.06092e7i	−0.488174	−	0.354679i
$979$	−2.59803e7	−	1.88758e7i	−0.866339	−	0.629432i
$980$	448922.	−	5268.00i	0.0149316	−	0.000175219i
$981$	765177.	−	555933.i	0.0253857	−	0.0184438i
$982$	−1.11485e7			−0.368926
$983$	1.49172e7	−	1.08380e7i	0.492383	−	0.357737i	−0.313717	−	0.949516i	$-0.601574\pi$
$983$	1.49172e7	−	1.08380e7i	0.492383	−	0.357737i	0.806100	+	0.591780i	$0.201574\pi$
$984$	−757757.	−	2.33214e6i	−0.0249484	−	0.0767832i
$985$	2.64407e7	−	310276.i	0.868324	−	0.0101896i
$986$	−7.40390e6	+	2.27869e7i	−0.242531	+	0.746435i
$987$	6.73844e6	+	2.07388e7i	0.220174	+	0.677627i
$988$	−2.28663e6	−	7.03751e6i	−0.0745252	−	0.229365i
$989$	−1.06728e6	+	3.28475e6i	−0.0346967	+	0.106785i
$990$	1.33013e6	+	3.93596e6i	0.0431327	+	0.127633i
$991$	1.77293e7	+	5.45651e7i	0.573465	+	1.76494i	0.641348	+	0.767250i	$0.278375\pi$
$991$	1.77293e7	+	5.45651e7i	0.573465	+	1.76494i	−0.0678834	+	0.997693i	$0.521625\pi$
$992$	3.44633e6	−	2.50390e6i	0.111193	−	0.0807864i
$993$	1.68831e7			0.543349
$994$	−3.20682e7	+	2.32989e7i	−1.02946	+	0.747945i
$995$	−929113.	+	691842.i	−0.0297516	+	0.0221538i
$996$	−6.70791e6	−	4.87358e6i	−0.214259	−	0.155668i
$997$	−1.05582e6	−	767096.i	−0.0336396	−	0.0244406i	0.570838	−	0.821062i	$-0.306618\pi$
$997$	−1.05582e6	−	767096.i	−0.0336396	−	0.0244406i	−0.604478	+	0.796622i	$0.706618\pi$
$998$	8.16939e6	−	2.51428e7i	0.259635	−	0.799074i
$999$	−3.71702e6			−0.117837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.c.121.2	yes	24
25.6	even	5	inner	150.6.g.c.31.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.c.31.2	✓	24	25.6	even	5	inner
150.6.g.c.121.2	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)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-44.8368 + 33.3866i) q^{5} +(29.1246 - 21.1603i) q^{6} +131.563 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-44.8368 + 33.3866i) q^{5} +(29.1246 - 21.1603i) q^{6} +131.563 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-71.5889 - 211.837i) q^{10} +(-70.8836 + 218.157i) q^{11} +(44.4984 + 136.952i) q^{12} +(156.346 + 481.185i) q^{13} +(-162.621 + 500.497i) q^{14} +(503.081 - 5.90354i) q^{15} +(79.1084 + 243.470i) q^{16} +(-548.712 + 398.662i) q^{17} -324.000 q^{18} +(739.512 - 537.287i) q^{19} +(894.366 - 10.4952i) q^{20} +(-957.934 - 695.980i) q^{21} +(-742.303 - 539.315i) q^{22} +(-269.022 + 827.965i) q^{23} -576.000 q^{24} +(895.669 - 2993.89i) q^{25} -2023.79 q^{26} +(225.273 - 693.320i) q^{27} +(-1702.99 - 1237.30i) q^{28} +(-7144.78 - 5190.99i) q^{29} +(-599.383 + 1921.13i) q^{30} +(-3365.55 + 2445.22i) q^{31} -1024.00 q^{32} +(1670.18 - 1213.46i) q^{33} +(-838.357 - 2580.20i) q^{34} +(-5898.88 + 4392.46i) q^{35} +(400.486 - 1232.57i) q^{36} +(-1575.61 - 4849.24i) q^{37} +(1129.87 + 3477.39i) q^{38} +(1407.12 - 4330.66i) q^{39} +(-1065.57 + 3415.34i) q^{40} +(1315.55 + 4048.85i) q^{41} +(3831.73 - 2783.92i) q^{42} +3967.26 q^{43} +(2969.21 - 2157.26i) q^{44} +(-3694.24 - 2618.35i) q^{45} +(-2817.24 - 2046.84i) q^{46} +(-14899.0 - 10824.8i) q^{47} +(711.975 - 2191.23i) q^{48} +501.944 q^{49} +(10282.3 + 7107.98i) q^{50} +6104.20 q^{51} +(2501.54 - 7698.96i) q^{52} +(-28341.6 - 20591.4i) q^{53} +(2359.09 + 1713.98i) q^{54} +(-4105.34 - 12148.0i) q^{55} +(6811.97 - 4949.19i) q^{56} -8226.78 q^{57} +(28579.1 - 20764.0i) q^{58} +(-7994.64 - 24605.0i) q^{59} +(-6567.53 - 4654.84i) q^{60} +(-1709.52 + 5261.38i) q^{61} +(-5142.11 - 15825.8i) q^{62} +(3293.08 + 10135.1i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-23075.2 - 16354.9i) q^{65} +(2551.81 + 7853.67i) q^{66} +(-3529.13 + 2564.06i) q^{67} +10851.9 q^{68} +(6338.78 - 4605.39i) q^{69} +(-9418.49 - 27870.0i) q^{70} +(60936.8 + 44273.2i) q^{71} +(4193.94 + 3047.08i) q^{72} +(9452.77 - 29092.6i) q^{73} +20395.2 q^{74} +(-22359.4 + 17060.9i) q^{75} -14625.4 q^{76} +(-9325.70 + 28701.5i) q^{77} +(14735.5 + 10706.0i) q^{78} +(-19645.7 - 14273.4i) q^{79} +(-11675.6 - 8275.27i) q^{80} +(-5307.96 + 3856.46i) q^{81} -17028.8 q^{82} +(-46582.7 + 33844.3i) q^{83} +(5854.37 + 18017.9i) q^{84} +(11292.5 - 36194.3i) q^{85} +(-4903.81 + 15092.4i) q^{86} +(24561.6 + 75592.8i) q^{87} +(4536.55 + 13962.1i) q^{88} +(-43261.9 + 133146. i) q^{89} +(14527.1 - 10817.3i) q^{90} +(20569.5 + 63306.4i) q^{91} +(11268.9 - 8187.37i) q^{92} +37440.5 q^{93} +(59596.0 - 43299.0i) q^{94} +(-15219.1 + 48780.0i) q^{95} +(7455.90 + 5417.03i) q^{96} +(-121858. - 88534.7i) q^{97} +(-620.437 + 1909.51i) q^{98} -18580.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Introduction

L-functions

Modular forms

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