LMFDB - Embedded newform 50.6.e.a.9.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(9,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.e (of order $10$, 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:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.11
Character	$\chi$	$=$	50.9
Dual form			50.6.e.a.39.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.35114 - 3.23607i) q^{2} +(18.4329 - 5.98921i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(49.2396 - 26.4662i) q^{5} +(23.9569 - 73.7316i) q^{6} +28.3664i q^{7} +(-60.8676 - 19.7771i) q^{8} +(107.310 - 77.9654i) q^{9} +O(q^{10})$	\(q+(2.35114 - 3.23607i) q^{2} +(18.4329 - 5.98921i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(49.2396 - 26.4662i) q^{5} +(23.9569 - 73.7316i) q^{6} +28.3664i q^{7} +(-60.8676 - 19.7771i) q^{8} +(107.310 - 77.9654i) q^{9} +(30.1231 - 221.569i) q^{10} +(86.3788 + 62.7579i) q^{11} +(-182.275 - 250.879i) q^{12} +(71.8547 + 98.8995i) q^{13} +(91.7957 + 66.6935i) q^{14} +(749.118 - 782.755i) q^{15} +(-207.108 + 150.473i) q^{16} +(-1224.73 - 397.938i) q^{17} -530.571i q^{18} +(-189.166 + 582.192i) q^{19} +(-646.187 - 618.419i) q^{20} +(169.893 + 522.876i) q^{21} +(406.177 - 131.975i) q^{22} +(2164.12 - 2978.66i) q^{23} -1240.42 q^{24} +(1724.09 - 2606.37i) q^{25} +488.986 q^{26} +(-1257.21 + 1730.40i) q^{27} +(431.649 - 140.251i) q^{28} +(1107.91 + 3409.79i) q^{29} +(-771.765 - 4264.56i) q^{30} +(-3200.84 + 9851.16i) q^{31} +1024.00i q^{32} +(1968.08 + 639.469i) q^{33} +(-4167.26 + 3027.69i) q^{34} +(750.750 + 1396.75i) q^{35} +(-1716.96 - 1247.45i) q^{36} +(5498.34 + 7567.81i) q^{37} +(1439.26 + 1980.97i) q^{38} +(1916.82 + 1392.65i) q^{39} +(-3520.52 + 637.115i) q^{40} +(-3545.98 + 2576.30i) q^{41} +(2091.50 + 679.571i) q^{42} +5014.85i q^{43} +(527.900 - 1624.71i) q^{44} +(3220.47 - 6679.08i) q^{45} +(-4550.99 - 14006.5i) q^{46} +(-4835.83 + 1571.26i) q^{47} +(-2916.39 + 4014.07i) q^{48} +16002.3 q^{49} +(-4380.82 - 11707.2i) q^{50} -24958.6 q^{51} +(1149.68 - 1582.39i) q^{52} +(-5555.56 + 1805.11i) q^{53} +(2643.81 + 8136.82i) q^{54} +(5914.22 + 804.060i) q^{55} +(561.005 - 1726.60i) q^{56} +11864.4i q^{57} +(13639.2 + 4431.64i) q^{58} +(25192.6 - 18303.5i) q^{59} +(-15615.0 - 7529.11i) q^{60} +(-35807.1 - 26015.4i) q^{61} +(24353.4 + 33519.6i) q^{62} +(2211.60 + 3044.01i) q^{63} +(3313.73 + 2407.57i) q^{64} +(6155.59 + 2968.06i) q^{65} +(6696.60 - 4865.37i) q^{66} +(-15904.3 - 5167.62i) q^{67} +20604.1i q^{68} +(22051.3 - 67866.8i) q^{69} +(6285.11 + 854.484i) q^{70} +(-11285.0 - 34731.7i) q^{71} +(-8073.65 + 2623.29i) q^{72} +(11434.3 - 15737.9i) q^{73} +37417.3 q^{74} +(16169.8 - 58368.9i) q^{75} +9794.44 q^{76} +(-1780.22 + 2450.26i) q^{77} +(9013.43 - 2928.64i) q^{78} +(-25912.9 - 79751.6i) q^{79} +(-6215.50 + 12890.6i) q^{80} +(-22770.6 + 70080.6i) q^{81} +17532.3i q^{82} +(26924.1 + 8748.18i) q^{83} +(7116.56 - 5170.48i) q^{84} +(-70837.0 + 12819.5i) q^{85} +(16228.4 + 11790.6i) q^{86} +(40844.0 + 56216.9i) q^{87} +(-4016.50 - 5528.24i) q^{88} +(31693.8 + 23026.9i) q^{89} +(-14042.2 - 26125.1i) q^{90} +(-2805.43 + 2038.26i) q^{91} +(-56026.0 - 18204.0i) q^{92} +200756. i q^{93} +(-6285.03 + 19343.3i) q^{94} +(6093.93 + 33673.4i) q^{95} +(6132.96 + 18875.3i) q^{96} +(-168974. + 54902.9i) q^{97} +(37623.8 - 51784.7i) q^{98} +14162.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9}+O(q^{10}) $ 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + 80 q^{10} + 716 q^{11} - 160 q^{12} - 784 q^{14} - 940 q^{15} - 3072 q^{16} + 1910 q^{17} - 5990 q^{19} - 640 q^{20} - 4344 q^{21} + 4720 q^{22} + 12410 q^{23} + 4608 q^{24} + 23660 q^{25} - 15248 q^{26} + 27600 q^{27} - 3040 q^{28} - 17170 q^{29} - 14720 q^{30} - 18834 q^{31} - 56930 q^{33} + 11696 q^{34} + 28450 q^{35} - 10976 q^{36} + 3540 q^{37} + 13432 q^{39} - 1280 q^{40} + 37146 q^{41} - 43560 q^{42} + 1184 q^{44} + 75240 q^{45} + 28672 q^{46} - 17830 q^{47} - 2560 q^{48} - 54656 q^{49} + 8800 q^{50} - 85984 q^{51} + 22350 q^{53} + 16080 q^{54} - 64730 q^{55} + 12544 q^{56} + 18000 q^{59} + 78720 q^{60} + 67086 q^{61} - 159600 q^{62} + 132820 q^{63} + 49152 q^{64} - 195820 q^{65} - 52256 q^{66} - 90790 q^{67} - 212608 q^{69} + 180080 q^{70} - 122874 q^{71} + 121200 q^{73} + 281456 q^{74} + 672810 q^{75} - 102400 q^{76} + 434040 q^{77} + 170720 q^{78} + 113600 q^{79} - 28160 q^{80} + 115878 q^{81} - 582750 q^{83} - 174816 q^{84} + 107770 q^{85} - 26888 q^{86} - 911580 q^{87} - 56960 q^{88} - 357730 q^{89} - 282920 q^{90} - 216324 q^{91} + 451040 q^{92} + 79136 q^{94} + 135000 q^{95} + 18432 q^{96} - 123520 q^{97} - 206240 q^{98} + 235252 q^{99}+O(q^{100}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9 + 80 * q^10 + 716 * q^11 - 160 * q^12 - 784 * q^14 - 940 * q^15 - 3072 * q^16 + 1910 * q^17 - 5990 * q^19 - 640 * q^20 - 4344 * q^21 + 4720 * q^22 + 12410 * q^23 + 4608 * q^24 + 23660 * q^25 - 15248 * q^26 + 27600 * q^27 - 3040 * q^28 - 17170 * q^29 - 14720 * q^30 - 18834 * q^31 - 56930 * q^33 + 11696 * q^34 + 28450 * q^35 - 10976 * q^36 + 3540 * q^37 + 13432 * q^39 - 1280 * q^40 + 37146 * q^41 - 43560 * q^42 + 1184 * q^44 + 75240 * q^45 + 28672 * q^46 - 17830 * q^47 - 2560 * q^48 - 54656 * q^49 + 8800 * q^50 - 85984 * q^51 + 22350 * q^53 + 16080 * q^54 - 64730 * q^55 + 12544 * q^56 + 18000 * q^59 + 78720 * q^60 + 67086 * q^61 - 159600 * q^62 + 132820 * q^63 + 49152 * q^64 - 195820 * q^65 - 52256 * q^66 - 90790 * q^67 - 212608 * q^69 + 180080 * q^70 - 122874 * q^71 + 121200 * q^73 + 281456 * q^74 + 672810 * q^75 - 102400 * q^76 + 434040 * q^77 + 170720 * q^78 + 113600 * q^79 - 28160 * q^80 + 115878 * q^81 - 582750 * q^83 - 174816 * q^84 + 107770 * q^85 - 26888 * q^86 - 911580 * q^87 - 56960 * q^88 - 357730 * q^89 - 282920 * q^90 - 216324 * q^91 + 451040 * q^92 + 79136 * q^94 + 135000 * q^95 + 18432 * q^96 - 123520 * q^97 - 206240 * q^98 + 235252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	2.35114	−	3.23607i	0.415627	−	0.572061i
$2$	2.35114	−	3.23607i	0.415627	−	0.572061i
$3$	18.4329	−	5.98921i	1.18247	−	0.384208i	0.349187	−	0.937053i	$-0.386458\pi$
$3$	18.4329	−	5.98921i	1.18247	−	0.384208i	0.833284	+	0.552845i	$0.186458\pi$
$4$	−4.94427	−	15.2169i	−0.154508	−	0.475528i
$5$	49.2396	−	26.4662i	0.880826	−	0.473441i
$5$	49.2396	−	26.4662i	0.880826	−	0.473441i
$6$	23.9569	−	73.7316i	0.271676	−	0.836134i
$7$			28.3664i			0.218806i	0.993997	+	0.109403i	$0.0348939\pi$
$7$			28.3664i			0.218806i	−0.993997	+	0.109403i	$0.965106\pi$
$8$	−60.8676	−	19.7771i	−0.336249	−	0.109254i
$9$	107.310	−	77.9654i	0.441606	−	0.320845i
$10$	30.1231	−	221.569i	0.0952575	−	0.700661i
$11$	86.3788	+	62.7579i	0.215241	+	0.156382i	0.690182	−	0.723636i	$-0.257531\pi$
$11$	86.3788	+	62.7579i	0.215241	+	0.156382i	−0.474941	+	0.880018i	$0.657531\pi$
$12$	−182.275	−	250.879i	−0.365404	−	0.502935i
$13$	71.8547	+	98.8995i	0.117923	+	0.162306i	0.863898	−	0.503667i	$-0.168016\pi$
$13$	71.8547	+	98.8995i	0.117923	+	0.162306i	−0.745975	+	0.665974i	$0.768016\pi$
$14$	91.7957	+	66.6935i	0.125171	+	0.0909418i
$15$	749.118	−	782.755i	0.859651	−	0.898251i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−1224.73	−	397.938i	−1.02782	−	0.333959i	−0.253892	−	0.967233i	$-0.581711\pi$
$17$	−1224.73	−	397.938i	−1.02782	−	0.333959i	−0.773928	+	0.633274i	$0.781711\pi$
$18$		−	530.571i		−	0.385978i
$19$	−189.166	+	582.192i	−0.120215	+	0.369983i	−0.992999	−	0.118123i	$-0.962312\pi$
$19$	−189.166	+	582.192i	−0.120215	+	0.369983i	0.872784	+	0.488106i	$0.162312\pi$
$20$	−646.187	−	618.419i	−0.361230	−	0.345707i
$21$	169.893	+	522.876i	0.0840672	+	0.258732i
$22$	406.177	−	131.975i	0.178920	−	0.0581346i
$23$	2164.12	−	2978.66i	0.853026	−	1.17409i	−0.130161	−	0.991493i	$-0.541550\pi$
$23$	2164.12	−	2978.66i	0.853026	−	1.17409i	0.983188	−	0.182597i	$-0.0584505\pi$
$24$	−1240.42			−0.439581
$25$	1724.09	−	2606.37i	0.551707	−	0.834038i
$26$	488.986			0.141861
$27$	−1257.21	+	1730.40i	−0.331893	+	0.456811i
$28$	431.649	−	140.251i	0.104049	−	0.0338074i
$29$	1107.91	+	3409.79i	0.244630	+	0.752893i	0.995697	+	0.0926671i	$0.0295392\pi$
$29$	1107.91	+	3409.79i	0.244630	+	0.752893i	−0.751068	+	0.660225i	$0.770461\pi$
$30$	−771.765	−	4264.56i	−0.156560	−	0.865111i
$31$	−3200.84	+	9851.16i	−0.598218	+	1.84113i	−0.0602096	+	0.998186i	$0.519177\pi$
$31$	−3200.84	+	9851.16i	−0.598218	+	1.84113i	−0.538008	+	0.842940i	$0.680823\pi$
$32$			1024.00i			0.176777i
$33$	1968.08	+	639.469i	0.314600	+	0.102220i
$34$	−4167.26	+	3027.69i	−0.618234	+	0.449174i
$35$	750.750	+	1396.75i	0.103592	+	0.192730i
$36$	−1716.96	−	1247.45i	−0.220803	−	0.160423i
$37$	5498.34	+	7567.81i	0.660279	+	0.908796i	0.999491	−	0.0319144i	$-0.0101604\pi$
$37$	5498.34	+	7567.81i	0.660279	+	0.908796i	−0.339212	+	0.940710i	$0.610160\pi$
$38$	1439.26	+	1980.97i	0.161689	+	0.222545i
$39$	1916.82	+	1392.65i	0.201799	+	0.146616i
$40$	−3520.52	+	637.115i	−0.347902	+	0.0629605i
$41$	−3545.98	+	2576.30i	−0.329440	+	0.239352i	−0.740193	−	0.672394i	$-0.765266\pi$
$41$	−3545.98	+	2576.30i	−0.329440	+	0.239352i	0.410753	+	0.911747i	$0.365266\pi$
$42$	2091.50	+	679.571i	0.182951	+	0.0594445i
$43$			5014.85i			0.413606i	0.978383	+	0.206803i	$0.0663059\pi$
$43$			5014.85i			0.413606i	−0.978383	+	0.206803i	$0.933694\pi$
$44$	527.900	−	1624.71i	0.0411074	−	0.126516i
$45$	3220.47	−	6679.08i	0.237076	−	0.491683i
$46$	−4550.99	−	14006.5i	−0.317111	−	0.975967i
$47$	−4835.83	+	1571.26i	−0.319320	+	0.103753i	−0.464292	−	0.885682i	$-0.653691\pi$
$47$	−4835.83	+	1571.26i	−0.319320	+	0.103753i	0.144971	+	0.989436i	$0.453691\pi$
$48$	−2916.39	+	4014.07i	−0.182702	+	0.251468i
$49$	16002.3			0.952124
$50$	−4380.82	−	11707.2i	−0.247816	−	0.662259i
$51$	−24958.6			−1.34368
$52$	1149.68	−	1582.39i	0.0589613	−	0.0811532i
$53$	−5555.56	+	1805.11i	−0.271668	+	0.0882702i	−0.441683	−	0.897171i	$-0.645618\pi$
$53$	−5555.56	+	1805.11i	−0.271668	+	0.0882702i	0.170015	+	0.985441i	$0.445618\pi$
$54$	2643.81	+	8136.82i	0.123380	+	0.379726i
$55$	5914.22	+	804.060i	0.263627	+	0.0358412i
$56$	561.005	−	1726.60i	0.0239055	−	0.0735734i
$57$			11864.4i			0.483682i
$58$	13639.2	+	4431.64i	0.532375	+	0.172979i
$59$	25192.6	−	18303.5i	0.942199	−	0.684547i	−0.00675015	−	0.999977i	$-0.502149\pi$
$59$	25192.6	−	18303.5i	0.942199	−	0.684547i	0.948949	+	0.315430i	$0.102149\pi$
$60$	−15615.0	−	7529.11i	−0.559967	−	0.270001i
$61$	−35807.1	−	26015.4i	−1.23210	−	0.895170i	−0.235051	−	0.971983i	$-0.575526\pi$
$61$	−35807.1	−	26015.4i	−1.23210	−	0.895170i	−0.997046	+	0.0768129i	$0.975526\pi$
$62$	24353.4	+	33519.6i	0.804601	+	1.10744i
$63$	2211.60	+	3044.01i	0.0702030	+	0.0966261i
$64$	3313.73	+	2407.57i	0.101127	+	0.0734732i
$65$	6155.59	+	2968.06i	0.180712	+	0.0871343i
$66$	6696.60	−	4865.37i	0.189232	−	0.137485i
$67$	−15904.3	−	5167.62i	−0.432840	−	0.140638i	0.0844898	−	0.996424i	$-0.473074\pi$
$67$	−15904.3	−	5167.62i	−0.432840	−	0.140638i	−0.517330	+	0.855786i	$0.673074\pi$
$68$			20604.1i			0.540357i
$69$	22051.3	−	67866.8i	0.557584	−	1.71607i
$70$	6285.11	+	854.484i	0.153309	+	0.0208429i
$71$	−11285.0	−	34731.7i	−0.265678	−	0.817674i	−0.991536	−	0.129829i	$-0.958557\pi$
$71$	−11285.0	−	34731.7i	−0.265678	−	0.817674i	0.725858	−	0.687844i	$-0.241443\pi$
$72$	−8073.65	+	2623.29i	−0.183543	+	0.0596368i
$73$	11434.3	−	15737.9i	0.251131	−	0.345653i	−0.664776	−	0.747043i	$-0.731473\pi$
$73$	11434.3	−	15737.9i	0.251131	−	0.345653i	0.915907	+	0.401390i	$0.131473\pi$
$74$	37417.3			0.794316
$75$	16169.8	−	58368.9i	0.331934	−	1.19820i
$76$	9794.44			0.194512
$77$	−1780.22	+	2450.26i	−0.0342173	+	0.0470961i
$78$	9013.43	−	2928.64i	0.167747	−	0.0545042i
$79$	−25912.9	−	79751.6i	−0.467141	−	1.43771i	−0.856270	−	0.516528i	$-0.827224\pi$
$79$	−25912.9	−	79751.6i	−0.467141	−	1.43771i	0.389130	−	0.921183i	$-0.372776\pi$
$80$	−6215.50	+	12890.6i	−0.108580	+	0.225190i
$81$	−22770.6	+	70080.6i	−0.385621	+	1.18682i
$82$			17532.3i			0.287941i
$83$	26924.1	+	8748.18i	0.428989	+	0.139387i	0.515550	−	0.856860i	$-0.327588\pi$
$83$	26924.1	+	8748.18i	0.428989	+	0.139387i	−0.0865608	+	0.996247i	$0.527588\pi$
$84$	7116.56	−	5170.48i	0.110045	−	0.0799526i
$85$	−70837.0	+	12819.5i	−1.06344	+	0.192452i
$86$	16228.4	+	11790.6i	0.236608	+	0.171906i
$87$	40844.0	+	56216.9i	0.578535	+	0.796285i
$88$	−4016.50	−	5528.24i	−0.0552893	−	0.0760992i
$89$	31693.8	+	23026.9i	0.424130	+	0.308148i	0.779297	−	0.626654i	$-0.215576\pi$
$89$	31693.8	+	23026.9i	0.424130	+	0.308148i	−0.355167	+	0.934803i	$0.615576\pi$
$90$	−14042.2	−	26125.1i	−0.182738	−	0.339979i
$91$	−2805.43	+	2038.26i	−0.0355137	+	0.0258022i
$92$	−56026.0	−	18204.0i	−0.690113	−	0.224231i
$93$			200756.i			2.40692i
$94$	−6285.03	+	19343.3i	−0.0733648	+	0.225794i
$95$	6093.93	+	33673.4i	0.0692769	+	0.382805i
$96$	6132.96	+	18875.3i	0.0679191	+	0.209033i
$97$	−168974.	+	54902.9i	−1.82343	+	0.592469i	−0.823759	+	0.566941i	$0.808127\pi$
$97$	−168974.	+	54902.9i	−1.82343	+	0.592469i	−0.999674	+	0.0255284i	$0.991873\pi$
$98$	37623.8	−	51784.7i	0.395728	−	0.544673i
$99$	14162.3			0.145226
$100$	−48185.2	−	13348.6i	−0.481852	−	0.133486i
$101$	−120966.			−1.17994			−0.589969	−	0.807426i	$-0.700860\pi$
$101$	−120966.			−1.17994			−0.589969	+	0.807426i	$0.700860\pi$
$102$	−58681.2	+	80767.8i	−0.558468	+	0.768666i
$103$	122372.	−	39761.1i	1.13655	−	0.369288i	0.320489	−	0.947252i	$-0.396153\pi$
$103$	122372.	−	39761.1i	1.13655	−	0.369288i	0.816062	+	0.577964i	$0.196153\pi$
$104$	−2417.68	−	7440.85i	−0.0219187	−	0.0674589i
$105$	22204.0	+	21249.8i	0.196543	+	0.188097i
$106$	−7220.45	+	22222.2i	−0.0624165	+	0.192098i
$107$		−	105308.i		−	0.889208i	−0.895727	−	0.444604i	$-0.853344\pi$
$107$		−	105308.i		−	0.889208i	0.895727	−	0.444604i	$-0.146656\pi$
$108$	32547.3	+	10575.3i	0.268507	+	0.0872432i
$109$	−96272.6	+	69946.2i	−0.776134	+	0.563894i	−0.903816	−	0.427921i	$-0.859246\pi$
$109$	−96272.6	+	69946.2i	−0.776134	+	0.563894i	0.127682	+	0.991815i	$0.459246\pi$
$110$	16507.2	−	17248.4i	0.130074	−	0.135915i
$111$	146676.	+	106566.i	1.12993	+	0.820940i
$112$	−4268.38	−	5874.93i	−0.0321528	−	0.0442545i
$113$	115178.	+	158528.i	0.848539	+	1.16791i	0.984183	+	0.177156i	$0.0566898\pi$
$113$	115178.	+	158528.i	0.848539	+	1.16791i	−0.135644	+	0.990758i	$0.543310\pi$
$114$	38394.1	+	27895.0i	0.276696	+	0.201031i
$115$	27727.0	−	203944.i	0.195505	−	1.43803i
$116$	46408.7	−	33717.9i	0.320224	−	0.232657i
$117$	15421.5	+	5010.74i	0.104151	+	0.0338406i
$118$		−	124559.i		−	0.823512i
$119$	11288.1	−	34741.1i	0.0730723	−	0.224893i
$120$	−61077.7	+	32829.0i	−0.387195	+	0.208116i
$121$	−46244.8	−	142327.i	−0.287144	−	0.883737i
$122$	−168375.	+	54708.4i	−1.02418	+	0.332778i
$123$	−49932.7	+	68726.4i	−0.297592	+	0.409601i
$124$	165730.			0.967937
$125$	15912.8	−	173967.i	0.0910902	−	0.995843i
$126$	15050.4			0.0844543
$127$	191866.	−	264080.i	1.05557	−	1.45287i	0.171695	−	0.985150i	$-0.445076\pi$
$127$	191866.	−	264080.i	1.05557	−	1.45287i	0.883877	−	0.467719i	$-0.154924\pi$
$128$	15582.1	−	5062.93i	0.0840623	−	0.0273135i
$129$	30035.0	+	92438.2i	0.158911	+	0.489077i
$130$	24077.5	−	12941.6i	0.124955	−	0.0671628i
$131$	34264.6	−	105456.i	0.174449	−	0.536897i	−0.825159	−	0.564900i	$-0.808915\pi$
$131$	34264.6	−	105456.i	0.174449	−	0.536897i	0.999608	+	0.0280027i	$0.00891470\pi$
$132$		−	33109.8i		−	0.165395i
$133$	−16514.7	−	5365.95i	−0.0809546	−	0.0263038i
$134$	−54116.0	+	39317.6i	−0.260354	+	0.189158i
$135$	−16107.5	+	118478.i	−0.0760665	+	0.559503i
$136$	66676.1	+	48443.1i	0.309117	+	0.224587i
$137$	167018.	+	229881.i	0.760262	+	1.04641i	0.997192	+	0.0748839i	$0.0238586\pi$
$137$	167018.	+	229881.i	0.760262	+	1.04641i	−0.236931	+	0.971527i	$0.576141\pi$
$138$	−167776.	−	230924.i	−0.749949	−	1.03222i
$139$	−218956.	−	159081.i	−0.961216	−	0.698364i	−0.00778290	−	0.999970i	$-0.502477\pi$
$139$	−218956.	−	159081.i	−0.961216	−	0.698364i	−0.953433	+	0.301606i	$0.902477\pi$
$140$	17542.3	−	18330.0i	0.0756428	−	0.0790393i
$141$	−79727.8	+	57925.7i	−0.337724	+	0.245371i
$142$	−138927.	−	45140.0i	−0.578183	−	0.187863i
$143$			13052.3i			0.0533760i
$144$	−10493.1	+	32294.6i	−0.0421696	+	0.129785i
$145$	144797.	+	138575.i	0.571926	+	0.547349i
$146$	−24045.4	−	74004.1i	−0.0933576	−	0.287325i
$147$	294970.	−	95841.5i	1.12586	−	0.365814i
$148$	87973.4	−	121085.i	0.330139	−	0.454398i
$149$	−171508.			−0.632877			−0.316439	−	0.948613i	$-0.602487\pi$
$149$	−171508.			−0.632877			−0.316439	+	0.948613i	$0.602487\pi$
$150$	−150868.	−	189560.i	−0.547481	−	0.687889i
$151$	−240315.			−0.857705			−0.428853	−	0.903374i	$-0.641082\pi$
$151$	−240315.			−0.857705			−0.428853	+	0.903374i	$0.641082\pi$
$152$	23028.1	−	31695.5i	0.0808443	−	0.111273i
$153$	−162451.	+	52783.6i	−0.561040	+	0.182293i
$154$	3743.66	+	11521.8i	0.0127202	+	0.0391488i
$155$	103114.	+	569782.i	0.344739	+	1.90493i
$156$	11714.6	−	36053.7i	0.0385403	−	0.118615i
$157$		−	149100.i		−	0.482756i	−0.970431	−	0.241378i	$-0.922401\pi$
$157$		−	149100.i		−	0.482756i	0.970431	−	0.241378i	$-0.0775994\pi$
$158$	−319006.	−	103651.i	−1.01662	−	0.330318i
$159$	−91593.9	+	66546.9i	−0.287325	+	0.208754i
$160$	27101.3	+	50421.4i	0.0836933	+	0.155709i
$161$	84494.0	+	61388.5i	0.256898	+	0.186648i
$162$	173249.	+	238456.i	0.518660	+	0.713874i
$163$	−247697.	−	340925.i	−0.730216	−	1.00506i	−0.999122	−	0.0418897i	$-0.986662\pi$
$163$	−247697.	−	340925.i	−0.730216	−	1.00506i	0.268906	−	0.963166i	$-0.413338\pi$
$164$	56735.7	+	41220.9i	0.164720	+	0.119676i
$165$	113832.	−	20600.4i	0.325502	−	0.0589067i
$166$	91612.1	−	66560.1i	0.258037	−	0.187475i
$167$	258251.	+	83910.7i	0.716556	+	0.232823i	0.644529	−	0.764580i	$-0.277053\pi$
$167$	258251.	+	83910.7i	0.716556	+	0.232823i	0.0720266	+	0.997403i	$0.477053\pi$
$168$		−	35186.2i		−	0.0961832i
$169$	110118.	−	338908.i	0.296579	−	0.912777i
$170$	−125063.	+	259374.i	−0.331900	+	0.688341i
$171$	25091.4	+	77223.5i	0.0656198	+	0.201957i
$172$	76310.5	−	24794.8i	0.196681	−	0.0639056i
$173$	−66194.5	+	91108.9i	−0.168154	+	0.231444i	−0.884775	−	0.466019i	$-0.845688\pi$
$173$	−66194.5	+	91108.9i	−0.168154	+	0.231444i	0.716621	+	0.697463i	$0.245688\pi$
$174$	277952.			0.695979
$175$	73933.4	+	48906.2i	0.182493	+	0.120717i
$176$	−27333.1			−0.0665132
$177$	354749.	−	488270.i	0.851114	−	1.17146i
$178$	149033.	−	48423.8i	0.352560	−	0.114554i
$179$	125062.	+	384900.i	0.291737	+	0.897874i	0.984298	+	0.176515i	$0.0564823\pi$
$179$	125062.	+	384900.i	0.291737	+	0.897874i	−0.692561	+	0.721359i	$0.743518\pi$
$180$	−117558.	−	15982.4i	−0.270440	−	0.0367673i
$181$	40923.1	−	125948.i	0.0928478	−	0.285756i	−0.893839	−	0.448388i	$-0.851998\pi$
$181$	40923.1	−	125948.i	0.0928478	−	0.285756i	0.986687	+	0.162632i	$0.0519983\pi$
$182$			13870.8i			0.0310401i
$183$	−815841.	−	265083.i	−1.80085	−	0.585132i
$184$	−190634.	+	138504.i	−0.415104	+	0.301590i
$185$	471027.	+	227117.i	1.01185	+	0.487887i
$186$	649660.	+	472006.i	1.37691	+	1.00038i
$187$	−80816.7	−	111235.i	−0.169004	−	0.232614i
$188$	47819.3	+	65817.7i	0.0986754	+	0.135815i
$189$	−49085.2	−	35662.5i	−0.0999531	−	0.0726202i
$190$	123297.	+	59450.5i	0.247781	+	0.119474i
$191$	−149047.	+	108289.i	−0.295625	+	0.214784i	−0.725704	−	0.688007i	$-0.758486\pi$
$191$	−149047.	+	108289.i	−0.295625	+	0.214784i	0.430079	+	0.902791i	$0.358486\pi$
$192$	75501.2	+	24531.8i	0.147809	+	0.0480260i
$193$			550813.i			1.06441i	0.846614	+	0.532207i	$0.178637\pi$
$193$			550813.i			1.06441i	−0.846614	+	0.532207i	$0.821363\pi$
$194$	−219612.	+	675895.i	−0.418939	+	1.28936i
$195$	131242.	+	17842.8i	0.247164	+	0.0336029i
$196$	−79119.9	−	243506.i	−0.147111	−	0.452762i
$197$	−679159.	+	220672.i	−1.24683	+	0.405118i	−0.856782	−	0.515678i	$-0.827540\pi$
$197$	−679159.	+	220672.i	−1.24683	+	0.405118i	−0.390043	+	0.920796i	$0.627540\pi$
$198$	33297.5	−	45830.1i	0.0603599	−	0.0830783i
$199$	−838071.			−1.50020			−0.750099	−	0.661326i	$-0.769994\pi$
$199$	−838071.			−1.50020			−0.750099	+	0.661326i	$0.769994\pi$
$200$	−156487.	+	124546.i	−0.276633	+	0.220168i
$201$	−324112.			−0.565855
$202$	−284408.	+	391454.i	−0.490414	+	0.674997i
$203$	−96723.7	+	31427.4i	−0.164738	+	0.0535265i
$204$	123402.	+	379793.i	0.207610	+	0.638956i
$205$	−106418.	+	220705.i	−0.176860	+	0.366798i
$206$	159044.	−	489488.i	0.261126	−	0.803663i
$207$		−	488368.i		−	0.792175i
$208$	−29763.4	−	9670.72i	−0.0477007	−	0.0154989i
$209$	−52877.0	+	38417.4i	−0.0837338	+	0.0608362i
$210$	120971.	−	21892.2i	0.189292	−	0.0342564i
$211$	766500.	+	556895.i	1.18524	+	0.861127i	0.992753	−	0.120172i	$-0.0383447\pi$
$211$	766500.	+	556895.i	1.18524	+	0.861127i	0.192487	+	0.981300i	$0.438345\pi$
$212$	54936.4	+	75613.5i	0.0839500	+	0.115547i
$213$	−416031.	−	572618.i	−0.628314	−	0.864800i
$214$	−340785.	−	247595.i	−0.508682	−	0.369579i
$215$	132724.	+	246929.i	0.195818	+	0.364315i
$216$	110745.	−	80461.3i	0.161507	−	0.117342i
$217$	−279442.	−	90796.4i	−0.402850	−	0.130894i
$218$			475998.i			0.678366i
$219$	116509.	−	358578.i	0.164153	−	0.505211i
$220$	−17006.2	−	93971.6i	−0.0236892	−	0.130900i
$221$	−48646.5	−	149719.i	−0.0669994	−	0.206203i
$222$	689710.	−	224100.i	0.939256	−	0.305183i
$223$	761027.	−	1.04746e6i	1.02480	−	1.41051i	0.116012	−	0.993248i	$-0.462989\pi$
$223$	761027.	−	1.04746e6i	1.02480	−	1.41051i	0.908785	−	0.417265i	$-0.137011\pi$
$224$	−29047.2			−0.0386798
$225$	−18194.7	−	414109.i	−0.0239600	−	0.545329i
$226$	783807.			1.02079
$227$	512250.	−	705051.i	0.659807	−	0.908146i	−0.339668	−	0.940545i	$-0.610315\pi$
$227$	512250.	−	705051.i	0.659807	−	0.908146i	0.999475	+	0.0323990i	$0.0103147\pi$
$228$	180540.	−	58661.0i	0.230004	−	0.0747330i
$229$	116040.	+	357134.i	0.146224	+	0.450031i	0.997166	−	0.0752278i	$-0.0239684\pi$
$229$	116040.	+	357134.i	0.146224	+	0.450031i	−0.850942	+	0.525259i	$0.823968\pi$
$230$	−594787.	−	569228.i	−0.741382	−	0.709523i
$231$	−18139.4	+	55827.5i	−0.0223663	+	0.0688364i
$232$		−	229457.i		−	0.279886i
$233$	937524.	+	304620.i	1.13134	+	0.367594i	0.814085	−	0.580746i	$-0.197239\pi$
$233$	937524.	+	304620.i	1.13134	+	0.367594i	0.317254	+	0.948340i	$0.397239\pi$
$234$	52473.2	−	38124.0i	0.0626466	−	0.0455155i
$235$	−196529.	+	205354.i	−0.232144	+	0.242568i
$236$	−403081.	−	292856.i	−0.471099	−	0.342274i
$237$	−955299.	−	1.31486e6i	−1.10476	−	1.52057i
$238$	−85884.8	−	118210.i	−0.0982820	−	0.135274i
$239$	−633160.	−	460018.i	−0.716999	−	0.520931i	0.168425	−	0.985715i	$-0.446132\pi$
$239$	−633160.	−	460018.i	−0.716999	−	0.520931i	−0.885424	+	0.464784i	$0.846132\pi$
$240$	−37365.2	+	274837.i	−0.0418734	+	0.307998i
$241$	−371074.	+	269601.i	−0.411546	+	0.299005i	−0.774227	−	0.632908i	$-0.781861\pi$
$241$	−371074.	+	269601.i	−0.411546	+	0.299005i	0.362682	+	0.931913i	$0.381861\pi$
$242$	−569307.	−	184979.i	−0.624896	−	0.203041i
$243$			908416.i			0.986891i
$244$	−218834.	+	673500.i	−0.235309	+	0.724208i
$245$	787950.	−	423521.i	0.838655	−	0.450774i
$246$	105005.	+	323171.i	0.110629	+	0.340482i
$247$	−71170.9	+	23124.8i	−0.0742267	+	0.0241177i
$248$	389655.	−	536314.i	0.402301	−	0.553719i
$249$	548684.			0.560821
$250$	−525554.	−	460515.i	−0.531824	−	0.466008i
$251$	1.41832e6			1.42099			0.710495	−	0.703702i	$-0.248471\pi$
$251$	1.41832e6			1.42099			0.710495	+	0.703702i	$0.248471\pi$
$252$	35385.6	−	48704.1i	0.0351015	−	0.0483131i
$253$	373869.	−	121477.i	0.367213	−	0.119315i
$254$	−403479.	−	1.24178e6i	−0.392407	−	1.20770i
$255$	−1.22895e6	+	660558.i	−1.18355	+	0.636152i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$			1.26068e6i			1.19061i	0.803499	+	0.595306i	$0.202969\pi$
$257$			1.26068e6i			1.19061i	−0.803499	+	0.595306i	$0.797031\pi$
$258$	369753.	+	120140.i	0.345830	+	0.112367i
$259$	−214672.	+	155968.i	−0.198850	+	0.144473i
$260$	14729.8	−	108344.i	0.0135133	−	0.0993965i
$261$	384736.	+	279527.i	0.349592	+	0.253993i
$262$	−260701.	−	358823.i	−0.234633	−	0.322944i
$263$	−169271.	−	232981.i	−0.150901	−	0.207698i	0.726873	−	0.686771i	$-0.240973\pi$
$263$	−169271.	−	232981.i	−0.150901	−	0.207698i	−0.877775	+	0.479074i	$0.840973\pi$
$264$	−107146.	−	77845.9i	−0.0946160	−	0.0687426i
$265$	−225780.	+	235917.i	−0.197501	+	0.206369i
$266$	−56193.0	+	40826.6i	−0.0486943	+	0.0353785i
$267$	722121.	+	234631.i	0.619915	+	0.201423i
$268$			267564.i			0.227557i
$269$	429217.	−	1.32099e6i	0.361656	−	1.11306i	−0.590392	−	0.807117i	$-0.701027\pi$
$269$	429217.	−	1.32099e6i	0.361656	−	1.11306i	0.952048	−	0.305947i	$-0.0989731\pi$
$270$	345531.	+	330683.i	0.288455	+	0.276059i
$271$	143228.	+	440811.i	0.118469	+	0.364611i	0.992655	−	0.120981i	$-0.0386041\pi$
$271$	143228.	+	440811.i	0.118469	+	0.364611i	−0.874186	+	0.485592i	$0.838604\pi$
$272$	313530.	−	101872.i	0.256955	−	0.0834897i
$273$	−39504.6	+	54373.4i	−0.0320805	+	0.0441550i
$274$	1.13660e6			0.914596
$275$	312494.	−	116935.i	0.249178	−	0.0932423i
$276$	−1.14175e6			−0.902190
$277$	−1.17722e6	+	1.62030e6i	−0.921843	+	1.26881i	0.0411151	+	0.999154i	$0.486909\pi$
$277$	−1.17722e6	+	1.62030e6i	−0.921843	+	1.26881i	−0.962958	+	0.269653i	$0.913091\pi$
$278$	−1.02960e6	+	334536.i	−0.799014	+	0.259615i
$279$	424568.	+	1.30669e6i	0.326540	+	1.00499i
$280$	−18072.7	−	99864.7i	−0.0137761	−	0.0761232i
$281$	786449.	−	2.42044e6i	0.594162	−	1.82864i	0.0353083	−	0.999376i	$-0.488759\pi$
$281$	786449.	−	2.42044e6i	0.594162	−	1.82864i	0.558854	−	0.829266i	$-0.311241\pi$
$282$			394196.i			0.295182i
$283$	886727.	+	288115.i	0.658149	+	0.213845i	0.619004	−	0.785388i	$-0.287537\pi$
$283$	886727.	+	288115.i	0.658149	+	0.213845i	0.0391450	+	0.999234i	$0.487537\pi$
$284$	−472713.	+	343446.i	−0.347777	+	0.252675i
$285$	314006.	+	584201.i	0.228995	+	0.426040i
$286$	42238.0	+	30687.7i	0.0305343	+	0.0221845i
$287$	−73080.6	−	100587.i	−0.0523718	−	0.0720835i
$288$	79836.6	+	109886.i	0.0567180	+	0.0780656i
$289$	192913.	+	140159.i	0.135868	+	0.0987136i
$290$	788876.	−	142764.i	0.550825	−	0.0996838i
$291$	−2.78585e6	+	2.02404e6i	−1.92853	+	1.40116i
$292$	−296016.	−	96181.5i	−0.203169	−	0.0660138i
$293$			1.24997e6i			0.850613i	0.905049	+	0.425307i	$0.139834\pi$
$293$			1.24997e6i			0.850613i	−0.905049	+	0.425307i	$0.860166\pi$
$294$	383366.	−	1.17988e6i	0.258669	−	0.796103i
$295$	756051.	−	1.56801e6i	0.505820	−	1.04904i
$296$	−185001.	−	569376.i	−0.122729	−	0.377720i
$297$	−217192.	+	70570.0i	−0.142874	+	0.0464226i
$298$	−403240.	+	555012.i	−0.263041	+	0.362045i
$299$	450090.			0.291153
$300$	−968141.	+	42537.1i	−0.621063	+	0.0272876i
$301$	−142253.			−0.0904995
$302$	−565014.	+	777675.i	−0.356485	+	0.490660i
$303$	−2.22975e6	+	724490.i	−1.39524	+	0.453342i
$304$	−48426.4	−	149041.i	−0.0300537	−	0.0924958i
$305$	−2.45166e6	−	333312.i	−1.50907	−	0.205164i
$306$	−211134.	+	649804.i	−0.128901	+	0.396715i
$307$			2.01443e6i			1.21985i	0.792459	+	0.609926i	$0.208801\pi$
$307$			2.01443e6i			1.21985i	−0.792459	+	0.609926i	$0.791199\pi$
$308$	46087.2	+	14974.6i	0.0276824	+	0.00899456i
$309$	2.01753e6	−	1.46582e6i	1.20206	−	0.873345i
$310$	2.08629e6	+	1.00595e6i	1.23302	+	0.594529i
$311$	−1.21408e6	−	882082.i	−0.711782	−	0.517140i	0.171966	−	0.985103i	$-0.444988\pi$
$311$	−1.21408e6	−	882082.i	−0.711782	−	0.517140i	−0.883748	+	0.467963i	$0.844988\pi$
$312$	−89129.7	−	122677.i	−0.0518366	−	0.0713469i
$313$	306549.	+	421928.i	0.176864	+	0.243432i	0.888240	−	0.459379i	$-0.151928\pi$
$313$	306549.	+	421928.i	0.176864	+	0.243432i	−0.711377	+	0.702811i	$0.751928\pi$
$314$	−482497.	−	350555.i	−0.276166	−	0.200646i
$315$	189462.	+	91353.3i	0.107583	+	0.0518738i
$316$	−1.08545e6	+	788627.i	−0.611495	+	0.444277i
$317$	3.01131e6	+	978435.i	1.68309	+	0.546870i	0.985507	−	0.169633i	$-0.0542582\pi$
$317$	3.01131e6	+	978435.i	1.68309	+	0.546870i	0.697584	+	0.716503i	$0.254258\pi$
$318$			452865.i			0.251132i
$319$	−118291.	+	364064.i	−0.0650844	+	0.200309i
$320$	226886.	+	30846.0i	0.123861	+	0.0168393i
$321$	−630715.	−	1.94114e6i	−0.341641	−	1.05146i
$322$	397315.	−	129095.i	0.213548	−	0.0693858i
$323$	463352.	−	637750.i	0.247118	−	0.340129i
$324$	1.17899e6			0.623949
$325$	381652.	−	16768.6i	0.200428	−	0.00880620i
$326$	−1.68563e6			−0.878451
$327$	−1.35566e6	+	1.86591e6i	−0.701103	+	0.964986i
$328$	266787.	−	86684.4i	0.136924	−	0.0444894i
$329$	−44571.0	−	137175.i	−0.0227019	−	0.0698693i
$330$	200971.	−	416802.i	0.101589	−	0.210691i
$331$	297870.	−	916751.i	0.149437	−	0.459919i	−0.848118	−	0.529807i	$-0.822264\pi$
$331$	297870.	−	916751.i	0.149437	−	0.459919i	0.997555	+	0.0698883i	$0.0222643\pi$
$332$		−	452955.i		−	0.225533i
$333$	1.18006e6	+	383423.i	0.583166	+	0.189482i
$334$	878724.	−	638430.i	0.431009	−	0.313146i
$335$	−919889.	+	166474.i	−0.447840	+	0.0810464i
$336$	−113865.	−	82727.7i	−0.0550227	−	0.0399763i
$337$	50146.3	+	69020.4i	0.0240527	+	0.0331057i	0.820874	−	0.571109i	$-0.193487\pi$
$337$	50146.3	+	69020.4i	0.0240527	+	0.0331057i	−0.796821	+	0.604215i	$0.793487\pi$
$338$	−837826.	−	1.15317e6i	−0.398898	−	0.549036i
$339$	3.07252e6	+	2.23232e6i	1.45210	+	1.05501i
$340$	545310.	+	1.01454e6i	0.255827	+	0.475960i
$341$	−894722.	+	650054.i	−0.416680	+	0.302736i
$342$	308894.	+	100366.i	0.142805	+	0.0464002i
$343$			930684.i			0.427137i
$344$	99179.1	−	305242.i	0.0451881	−	0.139075i
$345$	−710377.	−	3.92535e6i	−0.321322	−	1.77554i
$346$	139202.	+	428420.i	0.0625108	+	0.192389i
$347$	1.69020e6	−	549180.i	0.753555	−	0.244845i	0.0930446	−	0.995662i	$-0.470340\pi$
$347$	1.69020e6	−	549180.i	0.753555	−	0.244845i	0.660510	+	0.750817i	$0.270340\pi$
$348$	653503.	−	899470.i	0.289268	−	0.398143i
$349$	−1.93343e6			−0.849698			−0.424849	−	0.905264i	$-0.639673\pi$
$349$	−1.93343e6			−0.849698			−0.424849	+	0.905264i	$0.639673\pi$
$350$	332091.	−	124268.i	0.144906	−	0.0542238i
$351$	−261472.			−0.113281
$352$	−64264.0	+	88451.9i	−0.0276447	+	0.0380496i
$353$	1.37227e6	−	445878.i	0.586143	−	0.190449i	−0.000907609	−	1.00000i	$-0.500289\pi$
$353$	1.37227e6	−	445878.i	0.586143	−	0.190449i	0.587051	+	0.809550i	$0.300289\pi$
$354$	−746010.	−	2.29598e6i	−0.316400	−	0.973779i
$355$	−1.47488e6	−	1.41150e6i	−0.621136	−	0.594445i
$356$	193695.	−	596132.i	0.0810016	−	0.249297i
$357$		−	707987.i		−	0.294005i
$358$	1.53960e6	+	500247.i	0.634893	+	0.206289i
$359$	−589103.	+	428008.i	−0.241243	+	0.175273i	−0.701837	−	0.712338i	$-0.747637\pi$
$359$	−589103.	+	428008.i	−0.241243	+	0.175273i	0.460594	+	0.887611i	$0.347637\pi$
$360$	−328115.	+	342848.i	−0.133435	+	0.139427i
$361$	1.70004e6	+	1.23515e6i	0.686581	+	0.498830i
$362$	−311361.	−	428552.i	−0.124880	−	0.171883i
$363$	−1.70485e6	−	2.34653e6i	−0.679078	−	0.934671i
$364$	44886.8	+	32612.2i	0.0177568	+	0.0129011i
$365$	146497.	−	1.07755e6i	0.0575568	−	0.423355i
$366$	−2.77598e6	+	2.01687e6i	−1.08321	+	0.787000i
$367$	−1.19325e6	−	387712.i	−0.462453	−	0.150260i	0.0685183	−	0.997650i	$-0.478173\pi$
$367$	−1.19325e6	−	387712.i	−0.462453	−	0.150260i	−0.530971	+	0.847390i	$0.678173\pi$
$368$			942548.i			0.362814i
$369$	−179657.	+	552928.i	−0.0686876	+	0.211399i
$370$	1.84242e6	−	990293.i	0.699654	−	0.376062i
$371$	−51204.6	−	157591.i	−0.0193141	−	0.0594426i
$372$	3.05489e6	−	992593.i	1.14456	−	0.371889i
$373$	2.39844e6	−	3.30118e6i	0.892601	−	1.22856i	−0.0801671	−	0.996781i	$-0.525545\pi$
$373$	2.39844e6	−	3.30118e6i	0.892601	−	1.22856i	0.972768	−	0.231779i	$-0.0744546\pi$
$374$	−549974.			−0.203312
$375$	−748604.	−	3.30201e6i	−0.274899	−	1.21255i
$376$	325420.			0.118707
$377$	−257618.	+	354581.i	−0.0933519	+	0.128488i
$378$	−230813.	+	74995.6i	−0.0830864	+	0.0269964i
$379$	−6375.78	−	19622.6i	−0.00228000	−	0.00701712i	0.949910	−	0.312523i	$-0.101174\pi$
$379$	−6375.78	−	19622.6i	−0.00228000	−	0.00701712i	−0.952190	+	0.305506i	$0.901174\pi$
$380$	482275.	−	259221.i	0.171331	−	0.0920898i
$381$	1.95501e6	−	6.01689e6i	0.689979	−	2.12354i
$382$			736931.i			0.258386i
$383$	1.54564e6	+	502209.i	0.538408	+	0.174939i	0.565583	−	0.824691i	$-0.308651\pi$
$383$	1.54564e6	+	502209.i	0.538408	+	0.174939i	−0.0271752	+	0.999631i	$0.508651\pi$
$384$	256901.	−	186649.i	0.0889072	−	0.0645949i
$385$	−22808.3	+	167765.i	−0.00784227	+	0.0576833i
$386$	1.78247e6	+	1.29504e6i	0.608910	+	0.442399i
$387$	390985.	+	538144.i	0.132704	+	0.182651i
$388$	1.67090e6	+	2.29980e6i	0.563472	+	0.775552i
$389$	−402395.	−	292357.i	−0.134828	−	0.0979580i	0.518327	−	0.855182i	$-0.326555\pi$
$389$	−402395.	−	292357.i	−0.134828	−	0.0979580i	−0.653155	+	0.757224i	$0.726555\pi$
$390$	366308.	−	382756.i	0.121951	−	0.127427i
$391$	−3.83578e6	+	2.78686e6i	−1.26886	+	0.921877i
$392$	−974025.	−	316480.i	−0.320151	−	0.104023i
$393$		−	2.14907e6i		−	0.701890i
$394$	−882688.	+	2.71664e6i	−0.286462	+	0.881639i
$395$	−3.38666e6	−	3.24113e6i	−1.09214	−	1.04521i
$396$	−70022.1	−	215506.i	−0.0224387	−	0.0690591i
$397$	−4.36975e6	+	1.41982e6i	−1.39149	+	0.452123i	−0.906430	−	0.422357i	$-0.861203\pi$
$397$	−4.36975e6	+	1.41982e6i	−1.39149	+	0.452123i	−0.485062	+	0.874480i	$0.661203\pi$
$398$	−1.97042e6	+	2.71206e6i	−0.623522	+	0.858205i
$399$	−336552.			−0.105833
$400$	35115.6	+	799229.i	0.0109736	+	0.249759i
$401$	−611510.			−0.189908			−0.0949539	−	0.995482i	$-0.530270\pi$
$401$	−611510.			−0.189908			−0.0949539	+	0.995482i	$0.530270\pi$
$402$	−762034.	+	1.04885e6i	−0.235185	+	0.323704i
$403$	−1.20427e6	+	391291.i	−0.369370	+	0.120016i
$404$	598088.	+	1.84073e6i	0.182310	+	0.561094i
$405$	733549.	+	4.05339e6i	0.222224	+	1.22795i
$406$	−125710.	+	386895.i	−0.0378489	+	0.116487i
$407$			998762.i			0.298866i
$408$	1.51917e6	+	493609.i	0.451810	+	0.146802i
$409$	−1.53683e6	+	1.11657e6i	−0.454273	+	0.330049i	−0.791281	−	0.611453i	$-0.790585\pi$
$409$	−1.53683e6	+	1.11657e6i	−0.454273	+	0.330049i	0.337007	+	0.941502i	$0.390585\pi$
$410$	464012.	+	863283.i	0.136323	+	0.253626i
$411$	4.45544e6	+	3.23707e6i	1.30103	+	0.945252i
$412$	−1.21008e6	−	1.66553e6i	−0.351214	−	0.483404i
$413$	519204.	+	714624.i	0.149783	+	0.206159i
$414$	−1.58039e6	−	1.14822e6i	−0.453173	−	0.329249i
$415$	1.55726e6	−	281821.i	0.443856	−	0.0803254i
$416$	−101273.	+	73579.2i	−0.0286920	+	0.0208460i
$417$	−4.98878e6	−	1.62095e6i	−1.40493	−	0.456489i
$418$			261438.i			0.0731861i
$419$	−521261.	+	1.60428e6i	−0.145051	+	0.446420i	−0.997018	−	0.0771756i	$-0.975410\pi$
$419$	−521261.	+	1.60428e6i	−0.145051	+	0.446420i	0.851967	+	0.523596i	$0.175410\pi$
$420$	213574.	−	442941.i	0.0590779	−	0.122524i
$421$	1.57358e6	+	4.84298e6i	0.432697	+	1.33170i	0.895428	+	0.445206i	$0.146870\pi$
$421$	1.57358e6	+	4.84298e6i	0.432697	+	1.33170i	−0.462731	+	0.886499i	$0.653130\pi$
$422$	3.60430e6	−	1.17111e6i	0.985235	−	0.320122i
$423$	−396430.	+	545640.i	−0.107725	+	0.148271i
$424$	373854.			0.100992
$425$	−3.14871e6	+	2.50601e6i	−0.845590	+	0.672993i
$426$	−2.83118e6			−0.755863
$427$	737964.	−	1.01572e6i	0.195869	−	0.269590i
$428$	−1.60247e6	+	520673.i	−0.422844	+	0.137390i
$429$	78172.8	+	240591.i	0.0205075	+	0.0631156i
$430$	1.11113e6	+	151063.i	0.289798	+	0.0393991i
$431$	1.06949e6	−	3.29155e6i	0.277322	−	0.853508i	−0.711274	−	0.702915i	$-0.751882\pi$
$431$	1.06949e6	−	3.29155e6i	0.277322	−	0.853508i	0.988596	−	0.150594i	$-0.0481185\pi$
$432$		−	547556.i		−	0.141162i
$433$	2.06788e6	+	671894.i	0.530036	+	0.172219i	0.561795	−	0.827276i	$-0.310111\pi$
$433$	2.06788e6	+	671894.i	0.530036	+	0.172219i	−0.0317592	+	0.999496i	$0.510111\pi$
$434$	−950832.	+	690820.i	−0.242314	+	0.176052i
$435$	3.49899e6	+	1.68712e6i	0.886583	+	0.427486i
$436$	1.54036e6	+	1.11914e6i	0.388067	+	0.281947i
$437$	1.32477e6	+	1.82339e6i	0.331847	+	0.456748i
$438$	−886452.	−	1.22010e6i	−0.220785	−	0.303885i
$439$	5.24729e6	+	3.81238e6i	1.29949	+	0.944136i	0.999951	−	0.00994769i	$-0.00316650\pi$
$439$	5.24729e6	+	3.81238e6i	1.29949	+	0.944136i	0.299541	+	0.954083i	$0.403167\pi$
$440$	−344082.	−	165907.i	−0.0847288	−	0.0408539i
$441$	1.71722e6	−	1.24763e6i	0.420463	−	0.305485i
$442$	−598874.	−	194586.i	−0.145808	−	0.0473757i
$443$		−	739849.i		−	0.179116i	−0.995982	−	0.0895579i	$-0.971455\pi$
$443$		−	739849.i		−	0.179116i	0.995982	−	0.0895579i	$-0.0285454\pi$
$444$	896402.	−	2.75884e6i	0.215797	−	0.664155i
$445$	2.17002e6	+	295023.i	0.519475	+	0.0706245i
$446$	−1.60038e6	−	4.92547e6i	−0.380966	−	1.17249i
$447$	−3.16140e6	+	1.02720e6i	−0.748359	+	0.243157i
$448$	−68294.1	+	93998.8i	−0.0160764	+	0.0221272i
$449$	−1.27396e6			−0.298223			−0.149112	−	0.988820i	$-0.547641\pi$
$449$	−1.27396e6			−0.298223			−0.149112	+	0.988820i	$0.547641\pi$
$450$	−1.38286e6	−	914749.i	−0.321920	−	0.212947i
$451$	−467981.			−0.108339
$452$	1.84284e6	−	2.53645e6i	0.424270	−	0.583957i
$453$	−4.42970e6	+	1.43930e6i	−1.01421	+	0.329537i
$454$	−1.07722e6	−	3.31535e6i	−0.245282	−	0.754900i
$455$	−84193.2	+	174612.i	−0.0190655	+	0.0395408i
$456$	234644.	−	722160.i	0.0528442	−	0.162638i
$457$		−	5.85849e6i		−	1.31219i	−0.754680	−	0.656093i	$-0.772208\pi$
$457$		−	5.85849e6i		−	1.31219i	0.754680	−	0.656093i	$-0.227792\pi$
$458$	1.42854e6	+	464160.i	0.318220	+	0.103396i
$459$	2.22833e6	−	1.61897e6i	0.493682	−	0.358681i
$460$	−3.24049e6	+	586437.i	−0.714029	+	0.129219i
$461$	7.12605e6	+	5.17738e6i	1.56170	+	1.13464i	0.934602	+	0.355694i	$0.115756\pi$
$461$	7.12605e6	+	5.17738e6i	1.56170	+	1.13464i	0.627093	+	0.778944i	$0.284244\pi$
$462$	138013.	+	189959.i	0.0300826	+	0.0414051i
$463$	−3.86711e6	−	5.32262e6i	−0.838366	−	1.15391i	−0.986308	−	0.164916i	$-0.947265\pi$
$463$	−3.86711e6	−	5.32262e6i	−0.838366	−	1.15391i	0.147941	−	0.988996i	$-0.452735\pi$
$464$	−742539.	−	539486.i	−0.160112	−	0.116328i
$465$	5.31324e6	+	9.88516e6i	1.13953	+	2.12008i
$466$	3.19002e6	−	2.31769e6i	0.680502	−	0.494413i
$467$	3.40125e6	+	1.10513e6i	0.721683	+	0.234489i	0.646753	−	0.762700i	$-0.276127\pi$
$467$	3.40125e6	+	1.10513e6i	0.721683	+	0.234489i	0.0749302	+	0.997189i	$0.476127\pi$
$468$		−	259442.i		−	0.0547552i
$469$	146587.	−	451148.i	0.0307725	−	0.0947081i
$470$	202471.	+	1.11880e6i	0.0422783	+	0.233619i
$471$	−892990.	−	2.74834e6i	−0.185479	−	0.570845i
$472$	−1.89540e6	+	615853.i	−0.391603	+	0.127240i
$473$	−314721.	+	433176.i	−0.0646804	+	0.0890250i
$474$	−6.50101e6			−1.32903
$475$	1.19127e6	+	1.49678e6i	0.242257	+	0.304386i
$476$	−584464.			−0.118233
$477$	−455432.	+	626849.i	−0.0916490	+	0.126144i
$478$	−2.97730e6	+	967383.i	−0.596009	+	0.193655i
$479$	−1.11050e6	−	3.41777e6i	−0.221147	−	0.680620i	−0.998660	−	0.0517530i	$-0.983519\pi$
$479$	−1.11050e6	−	3.41777e6i	−0.221147	−	0.680620i	0.777513	−	0.628867i	$-0.216481\pi$
$480$	801541.	+	767097.i	0.158790	+	0.151966i
$481$	−353372.	+	1.08757e6i	−0.0696416	+	0.214335i
$482$			1.83469e6i			0.359704i
$483$	1.92514e6	+	625515.i	0.375486	+	0.122003i
$484$	−1.93713e6	+	1.40740e6i	−0.375876	+	0.273090i
$485$	−6.86714e6	+	7.17548e6i	−1.32563	+	1.38515i
$486$	2.93970e6	+	2.13582e6i	0.564562	+	0.410179i
$487$	1.32866e6	+	1.82874e6i	0.253858	+	0.349406i	0.916858	−	0.399214i	$-0.130717\pi$
$487$	1.32866e6	+	1.82874e6i	0.253858	+	0.349406i	−0.662999	+	0.748620i	$0.730717\pi$
$488$	1.66498e6	+	2.29165e6i	0.316490	+	0.435612i
$489$	−6.60765e6	−	4.80074e6i	−1.24961	−	0.907895i
$490$	482040.	−	3.54562e6i	0.0906970	−	0.667116i
$491$	−1.13014e6	+	821092.i	−0.211557	+	0.153705i	−0.688518	−	0.725219i	$-0.741738\pi$
$491$	−1.13014e6	+	821092.i	−0.211557	+	0.153705i	0.476961	+	0.878924i	$0.341738\pi$
$492$	1.29268e6	+	420018.i	0.240757	+	0.0782268i
$493$		−	4.61694e6i		−	0.855534i
$494$	−92499.3	+	284684.i	−0.0170538	+	0.0524862i
$495$	697345.	−	374821.i	0.127919	−	0.0687560i
$496$	−819414.	−	2.52190e6i	−0.149554	−	0.460281i
$497$	985214.	−	320115.i	0.178912	−	0.0581321i
$498$	1.29003e6	−	1.77558e6i	0.233092	−	0.320824i
$499$	7.53414e6			1.35451			0.677255	−	0.735748i	$-0.263169\pi$
$499$	7.53414e6			1.35451			0.677255	+	0.735748i	$0.263169\pi$
$500$	−2.72591e6	+	617994.i	−0.487626	+	0.110550i
$501$	5.26287e6			0.936759
$502$	3.33468e6	−	4.58979e6i	0.590602	−	0.812894i
$503$	−9.27481e6	+	3.01357e6i	−1.63450	+	0.531081i	−0.975300	−	0.220886i	$-0.929105\pi$
$503$	−9.27481e6	+	3.01357e6i	−1.63450	+	0.531081i	−0.659200	+	0.751967i	$0.729105\pi$
$504$	−74413.3	−	229021.i	−0.0130489	−	0.0401604i
$505$	−5.95631e6	+	3.20150e6i	−1.03932	+	0.558631i
$506$	485909.	−	1.49547e6i	0.0843682	−	0.259659i
$507$		−	6.90658e6i		−	1.19328i
$508$	−4.96712e6	−	1.61392e6i	−0.853975	−	0.277473i
$509$	−2.12602e6	+	1.54464e6i	−0.363725	+	0.264261i	−0.754604	−	0.656180i	$-0.772171\pi$
$509$	−2.12602e6	+	1.54464e6i	−0.363725	+	0.264261i	0.390879	+	0.920442i	$0.372171\pi$
$510$	−751830.	+	5.53004e6i	−0.127995	+	0.941462i
$511$	446428.	+	324349.i	0.0756309	+	0.0549491i
$512$	−154084.	−	212079.i	−0.0259767	−	0.0357538i
$513$	−769603.	−	1.05927e6i	−0.129114	−	0.177710i
$514$	4.07963e6	+	2.96403e6i	0.681103	+	0.494851i
$515$	4.97323e6	−	5.19654e6i	0.826268	−	0.863368i
$516$	1.25812e6	−	914079.i	0.208017	−	0.151133i
$517$	−516322.	−	167763.i	−0.0849560	−	0.0276039i
$518$			1.06140e6i			0.173801i
$519$	−674486.	+	2.07585e6i	−0.109914	+	0.338282i
$520$	−315976.	−	302398.i	−0.0512444	−	0.0490423i
$521$	−1.24674e6	−	3.83709e6i	−0.201226	−	0.619309i	−0.999847	−	0.0174754i	$-0.994437\pi$
$521$	−1.24674e6	−	3.83709e6i	−0.201226	−	0.619309i	0.798622	−	0.601833i	$-0.205563\pi$
$522$	1.80914e6	−	587824.i	0.290600	−	0.0944216i
$523$	1.98974e6	−	2.73864e6i	0.318084	−	0.437806i	−0.619797	−	0.784762i	$-0.712785\pi$
$523$	1.98974e6	−	2.73864e6i	0.318084	−	0.437806i	0.937881	+	0.346957i	$0.112785\pi$
$524$	−1.77412e6			−0.282264
$525$	1.65572e6	+	458680.i	0.262173	+	0.0726292i
$526$	−1.15192e6			−0.181534
$527$	7.84030e6	−	1.07913e7i	1.22972	−	1.69256i
$528$	−503829.	+	163704.i	−0.0786499	+	0.0255549i
$529$	−2.20005e6	−	6.77106e6i	−0.341817	−	1.05200i
$530$	232605.	+	1.28531e6i	0.0359691	+	0.198756i
$531$	1.27638e6	−	3.92830e6i	0.196447	−	0.604600i
$532$			277833.i			0.0425604i
$533$	−509590.	−	165576.i	−0.0776968	−	0.0252452i
$534$	2.45709e6	−	1.78518e6i	0.372879	−	0.270913i
$535$	−2.78711e6	−	5.18535e6i	−0.420988	−	0.783238i
$536$	865856.	+	629081.i	0.130177	+	0.0945790i
$537$	4.61050e6	+	6.34581e6i	0.689941	+	0.949623i
$538$	−3.26568e6	−	4.49482e6i	−0.486427	−	0.669509i
$539$	1.38226e6	+	1.00427e6i	0.204936	+	0.148895i
$540$	1.88250e6	−	340680.i	0.277812	−	0.0502761i
$541$	436795.	−	317350.i	0.0641630	−	0.0466172i	−0.555241	−	0.831689i	$-0.687374\pi$
$541$	436795.	−	317350.i	0.0641630	−	0.0466172i	0.619404	+	0.785072i	$0.287374\pi$
$542$	1.76324e6	+	572913.i	0.257819	+	0.0837704i
$543$		−	2.56669e6i		−	0.373572i
$544$	407488.	−	1.25412e6i	0.0590361	−	0.181695i
$545$	−2.88922e6	+	5.99209e6i	−0.416668	+	0.864146i
$546$	83075.1	+	255679.i	0.0119259	+	0.0367040i
$547$	−2.70216e6	+	877986.i	−0.386139	+	0.125464i	−0.495652	−	0.868521i	$-0.665071\pi$
$547$	−2.70216e6	+	877986.i	−0.386139	+	0.125464i	0.109513	+	0.993985i	$0.465071\pi$
$548$	2.67230e6	−	3.67810e6i	0.380131	−	0.523205i
$549$	−5.87077e6			−0.831312
$550$	356309.	−	1.28618e6i	0.0502250	−	0.181299i
$551$	−2.19473e6			−0.307966
$552$	−2.68441e6	+	3.69478e6i	−0.374975	+	0.516108i
$553$	2.26227e6	−	735056.i	0.314580	−	0.102213i
$554$	2.47560e6	+	7.61910e6i	0.342693	+	1.05470i
$555$	1.00427e7	+	1.36534e6i	1.38394	+	0.188151i
$556$	−1.33814e6	+	4.11838e6i	−0.183576	+	0.564988i
$557$		−	4.66478e6i		−	0.637079i	−0.947910	−	0.318539i	$-0.896808\pi$
$557$		−	4.66478e6i		−	0.637079i	0.947910	−	0.318539i	$-0.103192\pi$
$558$	5.22674e6	+	1.69827e6i	0.710633	+	0.230899i
$559$	−495966.	+	360340.i	−0.0671309	+	0.0487734i
$560$	−365660.	−	176312.i	−0.0492729	−	0.0237580i
$561$	−2.15589e6	−	1.56635e6i	−0.289215	−	0.210127i
$562$	−5.98366e6	−	8.23580e6i	−0.799146	−	1.09993i
$563$	3.26165e6	+	4.48927e6i	0.433676	+	0.596904i	0.968792	−	0.247874i	$-0.0797320\pi$
$563$	3.26165e6	+	4.48927e6i	0.433676	+	0.596904i	−0.535116	+	0.844779i	$0.679732\pi$
$564$	1.27565e6	+	926811.i	0.168862	+	0.122685i
$565$	9.86694e6	+	4.75757e6i	1.30035	+	0.626995i
$566$	3.01718e6	−	2.19211e6i	0.395877	−	0.287622i
$567$	−1.98794e6	−	645920.i	−0.259684	−	0.0843764i
$568$			2.33722e6i			0.303969i
$569$	−4.62447e6	+	1.42327e7i	−0.598799	+	1.84291i	−0.0639737	+	0.997952i	$0.520377\pi$
$569$	−4.62447e6	+	1.42327e7i	−0.598799	+	1.84291i	−0.534825	+	0.844963i	$0.679623\pi$
$570$	2.62879e6	+	357393.i	0.338897	+	0.0460744i
$571$	−1.32073e6	−	4.06480e6i	−0.169521	−	0.521734i	0.829820	−	0.558032i	$-0.188443\pi$
$571$	−1.32073e6	−	4.06480e6i	−0.169521	−	0.521734i	−0.999341	+	0.0362984i	$0.988443\pi$
$572$	198615.	−	64533.9i	0.0253818	−	0.00824704i
$573$	−2.09881e6	+	2.88876e6i	−0.267046	+	0.367558i
$574$	−497328.			−0.0630033
$575$	−4.03235e6	−	1.07760e7i	−0.508615	−	1.35921i
$576$	543305.			0.0682319
$577$	2.33511e6	−	3.21400e6i	0.291989	−	0.401889i	−0.637670	−	0.770310i	$-0.720101\pi$
$577$	2.33511e6	−	3.21400e6i	0.291989	−	0.401889i	0.929659	+	0.368421i	$0.120101\pi$
$578$	907130.	−	294744.i	0.112941	−	0.0366966i
$579$	3.29894e6	+	1.01531e7i	0.408957	+	1.25864i
$580$	1.39276e6	−	2.88852e6i	0.171913	−	0.356537i
$581$	−248155.	+	763741.i	−0.0304987	+	0.0938655i
$582$			1.37740e7i			1.68559i
$583$	−593167.	−	192732.i	−0.0722780	−	0.0234845i
$584$	−1.00723e6	+	731792.i	−0.122207	+	0.0887883i
$585$	891964.	−	161420.i	0.107760	−	0.0195015i
$586$	4.04500e6	+	2.93887e6i	0.486603	+	0.353538i
$587$	6.90966e6	+	9.51033e6i	0.827678	+	1.13920i	0.988351	+	0.152193i	$0.0486335\pi$
$587$	6.90966e6	+	9.51033e6i	0.827678	+	1.13920i	−0.160673	+	0.987008i	$0.551367\pi$
$588$	−2.91682e6	−	4.01466e6i	−0.347910	−	0.478857i
$589$	−5.12978e6	−	3.72700e6i	−0.609271	−	0.442661i
$590$	−3.29660e6	−	6.13324e6i	−0.389884	−	0.725370i
$591$	−1.11972e7	+	8.13526e6i	−1.31869	+	0.958082i
$592$	−2.27750e6	−	740006.i	−0.267088	−	0.0867822i
$593$			9.64641e6i			1.12649i	0.826288	+	0.563247i	$0.190448\pi$
$593$			9.64641e6i			1.12649i	−0.826288	+	0.563247i	$0.809552\pi$
$594$	−282280.	+	868769.i	−0.0328257	+	0.101027i
$595$	−363643.	−	2.00939e6i	−0.0421098	−	0.232687i
$596$	847983.	+	2.60982e6i	0.0977849	+	0.300951i
$597$	−1.54481e7	+	5.01939e6i	−1.77394	+	0.576388i
$598$	1.05823e6	−	1.45652e6i	0.121011	−	0.166558i
$599$	−3.89987e6			−0.444103			−0.222051	−	0.975035i	$-0.571275\pi$
$599$	−3.89987e6			−0.444103			−0.222051	+	0.975035i	$0.571275\pi$
$600$	−2.13858e6	+	3.23298e6i	−0.242520	+	0.366628i
$601$	−113640.			−0.0128335			−0.00641677	−	0.999979i	$-0.502043\pi$
$601$	−113640.			−0.0128335			−0.00641677	+	0.999979i	$0.502043\pi$
$602$	−334458.	+	460342.i	−0.0376140	+	0.0517713i
$603$	−2.10959e6	+	685447.i	−0.236268	+	0.0767681i
$604$	1.18818e6	+	3.65685e6i	0.132523	+	0.407863i
$605$	−6.04392e6	−	5.78420e6i	−0.671321	−	0.642473i
$606$	−2.89796e6	+	8.91901e6i	−0.320561	+	0.986586i
$607$		−	1.02110e7i		−	1.12485i	−0.826847	−	0.562426i	$-0.809868\pi$
$607$		−	1.02110e7i		−	1.12485i	0.826847	−	0.562426i	$-0.190132\pi$
$608$	−596164.	−	193706.i	−0.0654044	−	0.0212512i
$609$	−1.59467e6	+	1.15860e6i	−0.174232	+	0.126587i
$610$	−6.84281e6	+	7.15006e6i	−0.744577	+	0.778010i
$611$	−502874.	−	365359.i	−0.0544949	−	0.0395929i
$612$	1.60640e6	+	2.21103e6i	0.173371	+	0.238625i
$613$	−3.71221e6	−	5.10942e6i	−0.399008	−	0.549187i	0.561487	−	0.827486i	$-0.310230\pi$
$613$	−3.71221e6	−	5.10942e6i	−0.399008	−	0.549187i	−0.960495	+	0.278299i	$0.910230\pi$
$614$	6.51884e6	+	4.73622e6i	0.697830	+	0.507003i
$615$	−639743.	+	4.70559e6i	−0.0682052	+	0.501679i
$616$	156817.	−	113934.i	0.0166510	−	0.0120977i
$617$	4.74891e6	+	1.54302e6i	0.502205	+	0.163176i	0.549154	−	0.835721i	$-0.314950\pi$
$617$	4.74891e6	+	1.54302e6i	0.502205	+	0.163176i	−0.0469491	+	0.998897i	$0.514950\pi$
$618$		−	9.97524e6i		−	1.05064i
$619$	−868228.	+	2.67213e6i	−0.0910767	+	0.280305i	−0.986211	−	0.165491i	$-0.947079\pi$
$619$	−868228.	+	2.67213e6i	−0.0910767	+	0.280305i	0.895135	+	0.445796i	$0.147079\pi$
$620$	8.16049e6	−	4.38624e6i	0.852584	−	0.458261i
$621$	2.43352e6	+	7.48959e6i	0.253224	+	0.779344i
$622$	−5.70895e6	+	1.85495e6i	−0.591671	+	0.192246i
$623$	−653190.	+	899040.i	−0.0674248	+	0.0928023i
$624$	−606546.			−0.0623595
$625$	−3.82068e6	−	8.98720e6i	−0.391238	−	0.920289i
$626$	2.08613e6			0.212767
$627$	−744587.	+	1.02484e6i	−0.0756391	+	0.104108i
$628$	−2.26884e6	+	737190.i	−0.229564	+	0.0745899i
$629$	−3.72244e6	−	1.14565e7i	−0.375147	−	1.15458i
$630$	741077.	−	398326.i	0.0743895	−	0.0399841i
$631$	−5.59687e6	+	1.72254e7i	−0.559593	+	1.72225i	0.123903	+	0.992294i	$0.460459\pi$
$631$	−5.59687e6	+	1.72254e7i	−0.559593	+	1.72225i	−0.683496	+	0.729955i	$0.739541\pi$
$632$			5.36677e6i			0.534466i
$633$	1.74642e7	+	5.67446e6i	1.73236	+	0.562879i
$634$	1.02463e7	−	7.44438e6i	1.01238	−	0.735538i
$635$	2.45820e6	−	1.80812e7i	0.241926	−	1.77948i
$636$	1.46550e6	+	1.06475e6i	0.143663	+	0.104377i
$637$	1.14984e6	+	1.58262e6i	0.112277	+	0.154536i
$638$	900015.	+	1.23876e6i	0.0875383	+	0.120486i
$639$	−3.91887e6	−	2.84722e6i	−0.379672	−	0.275848i
$640$	633261.	−	661696.i	0.0611129	−	0.0638570i
$641$	9.42840e6	−	6.85013e6i	0.906344	−	0.658497i	−0.0337439	−	0.999431i	$-0.510743\pi$
$641$	9.42840e6	−	6.85013e6i	0.906344	−	0.658497i	0.940087	+	0.340933i	$0.110743\pi$
$642$	−7.76456e6	−	2.52286e6i	−0.743497	−	0.241577i
$643$			6.40279e6i			0.610720i	0.952237	+	0.305360i	$0.0987767\pi$
$643$			6.40279e6i			0.610720i	−0.952237	+	0.305360i	$0.901223\pi$
$644$	516381.	−	1.58926e6i	0.0490632	−	0.151001i
$645$	3.92540e6	+	3.75671e6i	0.371522	+	0.355557i
$646$	−974395.	−	2.99888e6i	−0.0918657	−	0.282734i
$647$	4.75005e6	−	1.54338e6i	0.446105	−	0.144948i	−0.0773453	−	0.997004i	$-0.524644\pi$
$647$	4.75005e6	−	1.54338e6i	0.446105	−	0.144948i	0.523451	+	0.852056i	$0.324644\pi$
$648$	2.77198e6	−	3.81530e6i	0.259330	−	0.356937i
$649$	3.32479e6			0.309851
$650$	843054.	−	1.27448e6i	0.0782658	−	0.118317i
$651$	−5.69474e6			−0.526649
$652$	−3.96315e6	+	5.45481e6i	−0.365108	+	0.502528i
$653$	6.37079e6	−	2.07000e6i	0.584670	−	0.189971i	−0.00172171	−	0.999999i	$-0.500548\pi$
$653$	6.37079e6	−	2.07000e6i	0.584670	−	0.189971i	0.586391	+	0.810028i	$0.300548\pi$
$654$	2.85085e6	+	8.77403e6i	0.260634	+	0.802148i
$655$	−1.10383e6	−	6.09945e6i	−0.100530	−	0.555504i
$656$	346737.	−	1.06715e6i	0.0314587	−	0.0968200i
$657$		−	2.58031e6i		−	0.233216i
$658$	−548701.	−	178284.i	−0.0494050	−	0.0160527i
$659$	−1.65071e6	+	1.19931e6i	−0.148067	+	0.107577i	−0.659352	−	0.751834i	$-0.729169\pi$
$659$	−1.65071e6	+	1.19931e6i	−0.148067	+	0.107577i	0.511286	+	0.859411i	$0.329169\pi$
$660$	−876290.	−	1.63032e6i	−0.0783047	−	0.145684i
$661$	−1.34535e7	−	9.77453e6i	−1.19765	−	0.870146i	−0.203601	−	0.979054i	$-0.565265\pi$
$661$	−1.34535e7	−	9.77453e6i	−1.19765	−	0.870146i	−0.994052	+	0.108908i	$0.965265\pi$
$662$	−2.26633e6	−	3.11934e6i	−0.200992	−	0.276642i
$663$	−1.79339e6	−	2.46839e6i	−0.158450	−	0.218087i
$664$	−1.46579e6	−	1.06496e6i	−0.129019	−	0.0937376i
$665$	−955194.	+	172863.i	−0.0837602	+	0.0151582i
$666$	4.01526e6	−	2.91726e6i	0.350775	−	0.254853i
$667$	1.25543e7	+	4.07913e6i	1.09264	+	0.355020i
$668$		−	4.34465e6i		−	0.376716i
$669$	7.75446e6	−	2.38658e7i	0.669863	−	2.06163i
$670$	−1.62407e6	+	3.36823e6i	−0.139771	+	0.289877i
$671$	−1.46030e6	−	4.49435e6i	−0.125209	−	0.385355i
$672$	−535425.	+	173970.i	−0.0457378	+	0.0148611i
$673$	−762087.	+	1.04892e6i	−0.0648585	+	0.0892701i	−0.840214	−	0.542255i	$-0.817571\pi$
$673$	−762087.	+	1.04892e6i	−0.0648585	+	0.0892701i	0.775355	+	0.631525i	$0.217571\pi$
$674$	341256.			0.0289355
$675$	2.34252e6	+	6.26010e6i	0.197890	+	0.528837i
$676$	−5.70158e6			−0.479875
$677$	−1.31010e6	+	1.80320e6i	−0.109859	+	0.151207i	−0.860406	−	0.509609i	$-0.829790\pi$
$677$	−1.31010e6	+	1.80320e6i	−0.109859	+	0.151207i	0.750547	+	0.660817i	$0.229790\pi$
$678$	1.44478e7	−	4.69439e6i	1.20706	−	0.392198i
$679$	−1.55740e6	−	4.79318e6i	−0.129636	−	0.398978i
$680$	4.56521e6	+	620658.i	0.378607	+	0.0514730i
$681$	5.21955e6	−	1.60641e7i	0.431286	−	1.32736i
$682$			4.42375e6i			0.364191i
$683$	−2.86026e6	−	929356.i	−0.234614	−	0.0762308i	0.189350	−	0.981910i	$-0.439362\pi$
$683$	−2.86026e6	−	929356.i	−0.234614	−	0.0762308i	−0.423964	+	0.905679i	$0.639362\pi$
$684$	1.05104e6	−	763628.i	0.0858975	−	0.0624082i
$685$	1.43080e7	+	6.89893e6i	1.16507	+	0.561766i
$686$	3.01176e6	+	2.18817e6i	0.244349	+	0.177530i
$687$	4.27791e6	+	5.88803e6i	0.345812	+	0.475969i
$688$	−754599.	−	1.03862e6i	−0.0607778	−	0.0836535i
$689$	−577718.	−	419737.i	−0.0463626	−	0.0336844i
$690$	−1.43729e7	−	6.93022e6i	−1.14927	−	0.554146i
$691$	−1.33306e7	+	9.68521e6i	−1.06207	+	0.771639i	−0.974470	−	0.224517i	$-0.927920\pi$
$691$	−1.33306e7	+	9.68521e6i	−1.06207	+	0.771639i	−0.0875996	+	0.996156i	$0.527920\pi$
$692$	1.71368e6	+	556808.i	0.136039	+	0.0442018i
$693$			401733.i			0.0317764i
$694$	2.19672e6	−	6.76080e6i	0.173131	−	0.532844i
$695$	−1.49916e7	−	2.03817e6i	−1.17730	−	0.160058i
$696$	−1.37427e6	−	4.22956e6i	−0.107535	−	0.330958i
$697$	5.36806e6	−	1.74419e6i	0.418539	−	0.135992i
$698$	−4.54576e6	+	6.25670e6i	−0.353157	+	0.486079i
$699$	1.91057e7			1.47901
$700$	378654.	−	1.36684e6i	0.0292077	−	0.105432i
$701$	−8.92304e6			−0.685832			−0.342916	−	0.939366i	$-0.611415\pi$
$701$	−8.92304e6			−0.685832			−0.342916	+	0.939366i	$0.611415\pi$
$702$	−614757.	+	846141.i	−0.0470826	+	0.0648037i
$703$	−5.44601e6	+	1.76952e6i	−0.415614	+	0.135041i
$704$	135142.	+	415926.i	0.0102769	+	0.0316289i
$705$	−2.39270e6	+	4.96233e6i	−0.181307	+	0.376021i
$706$	1.78351e6	−	5.48909e6i	0.134668	−	0.414466i
$707$		−	3.43137e6i		−	0.258178i
$708$	−9.18393e6	−	2.98404e6i	−0.688566	−	0.223729i
$709$	1.89744e7	−	1.37857e7i	1.41760	−	1.02995i	0.425437	−	0.904988i	$-0.360120\pi$
$709$	1.89744e7	−	1.37857e7i	1.41760	−	1.02995i	0.992162	−	0.124958i	$-0.0398797\pi$
$710$	−8.03539e6	+	1.45418e6i	−0.598220	+	0.108261i
$711$	−8.99858e6	−	6.53785e6i	−0.667575	−	0.485022i
$712$	−1.47372e6	−	2.02840e6i	−0.108947	−	0.149953i
$713$	2.24163e7	+	3.08533e7i	1.65135	+	2.27289i
$714$	−2.29109e6	−	1.66458e6i	−0.168189	−	0.122196i
$715$	345443.	+	642689.i	0.0252704	+	0.0470149i
$716$	5.23865e6	−	3.80610e6i	0.381889	−	0.277458i
$717$	−1.44261e7	−	4.68733e6i	−1.04798	−	0.340508i
$718$			2.91269e6i			0.210854i
$719$	−1.61726e6	+	4.97742e6i	−0.116670	+	0.359073i	−0.992292	−	0.123925i	$-0.960452\pi$
$719$	−1.61726e6	+	4.97742e6i	−0.116670	+	0.359073i	0.875622	+	0.482997i	$0.160452\pi$
$720$	338035.	+	1.86789e6i	0.0243013	+	0.134282i
$721$	1.12788e6	+	3.47126e6i	0.0808025	+	0.248685i
$722$	7.99408e6	−	2.59743e6i	0.570723	−	0.185439i
$723$	−5.22528e6	+	7.19197e6i	−0.371761	+	0.511685i
$724$	−2.11888e6			−0.150231
$725$	1.07973e7	+	2.99116e6i	0.762905	+	0.211346i
$726$	−1.16019e7			−0.816932
$727$	−9.11011e6	+	1.25390e7i	−0.639275	+	0.879887i	−0.998577	−	0.0533348i	$-0.983015\pi$
$727$	−9.11011e6	+	1.25390e7i	−0.639275	+	0.879887i	0.359302	+	0.933222i	$0.383015\pi$
$728$	211070.	−	68581.0i	0.0147604	−	0.00479595i
$729$	−92546.4	−	284829.i	−0.00644972	−	0.0198502i
$730$	−3.14259e6	−	3.00755e6i	−0.218263	−	0.208884i
$731$	1.99560e6	−	6.14182e6i	0.138127	−	0.425112i
$732$			1.37252e7i			0.946763i
$733$	−1.55469e7	−	5.05150e6i	−1.06877	−	0.347265i	−0.278762	−	0.960360i	$-0.589924\pi$
$733$	−1.55469e7	−	5.05150e6i	−1.06877	−	0.347265i	−0.790009	+	0.613096i	$0.789924\pi$
$734$	−4.06017e6	+	2.94989e6i	−0.278166	+	0.202099i
$735$	1.19876e7	−	1.25259e7i	0.818494	−	0.855246i
$736$	3.05015e6	+	2.21606e6i	0.207552	+	0.150795i
$737$	−1.04948e6	−	1.44449e6i	−0.0711717	−	0.0979595i
$738$	1.36691e6	+	1.88139e6i	0.0923846	+	0.127157i
$739$	−644177.	−	468022.i	−0.0433905	−	0.0315250i	0.565879	−	0.824489i	$-0.308537\pi$
$739$	−644177.	−	468022.i	−0.0433905	−	0.0315250i	−0.609269	+	0.792964i	$0.708537\pi$
$740$	1.12713e6	−	8.29050e6i	0.0756646	−	0.556547i
$741$	−1.17339e6	+	852515.i	−0.0785047	+	0.0570370i
$742$	−630366.	−	204818.i	−0.0420323	−	0.0136571i
$743$			2.69405e7i			1.79033i	0.445732	+	0.895166i	$0.352943\pi$
$743$			2.69405e7i			1.79033i	−0.445732	+	0.895166i	$0.647057\pi$
$744$	3.97037e6	−	1.22195e7i	0.262965	−	0.809325i
$745$	−8.44501e6	+	4.53916e6i	−0.557454	+	0.299630i
$746$	−5.04375e6	−	1.55231e7i	−0.331823	−	1.02125i
$747$	3.57129e6	−	1.16038e6i	0.234166	−	0.0760851i
$748$	−1.29307e6	+	1.77975e6i	−0.0845020	+	0.116307i
$749$	2.98722e6			0.194564
$750$	−1.24456e7	−	5.34097e6i	−0.807910	−	0.346710i
$751$	1.23754e7			0.800680			0.400340	−	0.916367i	$-0.368892\pi$
$751$	1.23754e7			0.800680			0.400340	+	0.916367i	$0.368892\pi$
$752$	765109.	−	1.05308e6i	0.0493377	−	0.0679075i
$753$	2.61438e7	−	8.49465e6i	1.68028	−	0.545956i
$754$	541752.	+	1.66734e6i	0.0347034	+	0.106806i
$755$	−1.18330e7	+	6.36021e6i	−0.755489	+	0.406073i
$756$	−299982.	+	923251.i	−0.0190893	+	0.0587510i
$757$			1.95083e7i			1.23731i	0.785661	+	0.618657i	$0.212323\pi$
$757$			1.95083e7i			1.23731i	−0.785661	+	0.618657i	$0.787677\pi$
$758$	−78490.5	−	25503.1i	−0.00496185	−	0.00161220i
$759$	6.16393e6	−	4.47836e6i	0.388377	−	0.282172i
$760$	295039.	−	2.17014e6i	0.0185287	−	0.136287i
$761$	−1.60336e7	−	1.16491e7i	−1.00362	−	0.729172i	−0.0407578	−	0.999169i	$-0.512977\pi$
$761$	−1.60336e7	−	1.16491e7i	−1.00362	−	0.729172i	−0.962861	+	0.269997i	$0.912977\pi$
$762$	−1.48746e7	−	2.04731e7i	−0.928019	−	1.27731i
$763$	−1.98412e6	−	2.73091e6i	−0.123384	−	0.169823i
$764$	2.38476e6	+	1.73263e6i	0.147813	+	0.107392i
$765$	−6.60206e6	+	6.89850e6i	−0.407874	+	0.426188i
$766$	5.25920e6	−	3.82103e6i	0.323853	−	0.235293i
$767$	3.62041e6	+	1.17634e6i	0.222213	+	0.0722013i
$768$		−	1.27019e6i		−	0.0777078i
$769$	1.35093e6	−	4.15774e6i	0.0823791	−	0.253537i	−0.901380	−	0.433028i	$-0.857445\pi$
$769$	1.35093e6	−	4.15774e6i	0.0823791	−	0.253537i	0.983760	+	0.179491i	$0.0574451\pi$
$770$	489274.	+	468249.i	0.0297390	+	0.0284610i
$771$	7.55045e6	+	2.32379e7i	0.457443	+	1.40787i
$772$	8.38167e6	−	2.72337e6i	0.506159	−	0.164461i
$773$	−4.51394e6	+	6.21290e6i	−0.271711	+	0.373978i	−0.922966	−	0.384881i	$-0.874243\pi$
$773$	−4.51394e6	+	6.21290e6i	−0.271711	+	0.373978i	0.651256	+	0.758858i	$0.274243\pi$
$774$	2.66073e6			0.159643
$775$	2.01572e7	+	2.53268e7i	1.20553	+	1.51470i
$776$	1.13708e7			0.677858
$777$	−3.02290e6	+	4.16067e6i	−0.179627	+	0.247235i
$778$	−1.89218e6	+	614805.i	−0.112076	+	0.0364157i
$779$	−829126.	−	2.55179e6i	−0.0489527	−	0.150661i
$780$	−377382.	−	2.08531e6i	−0.0222098	−	0.122725i
$781$	1.20490e6	−	3.70830e6i	0.0706844	−	0.217544i
$782$			1.89652e7i			1.10902i
$783$	−7.29317e6	−	2.36970e6i	−0.425120	−	0.138130i
$784$	−3.31422e6	+	2.40792e6i	−0.192571	+	0.139911i
$785$	−3.94610e6	−	7.34162e6i	−0.228557	−	0.425224i
$786$	−6.95454e6	−	5.05277e6i	−0.401524	−	0.291725i
$787$	3.25531e6	+	4.48055e6i	0.187351	+	0.257866i	0.892352	−	0.451340i	$-0.149054\pi$
$787$	3.25531e6	+	4.48055e6i	0.187351	+	0.257866i	−0.705002	+	0.709206i	$0.749054\pi$
$788$	6.71589e6	+	9.24363e6i	0.385290	+	0.530307i
$789$	−4.51553e6	−	3.28072e6i	−0.258235	−	0.187619i
$790$	−1.84510e7	+	3.33911e6i	−1.05185	+	0.190355i
$791$	−4.49688e6	+	3.26718e6i	−0.255547	+	0.185666i
$792$	−862024.	−	280088.i	−0.0488322	−	0.0158665i
$793$		−	5.41063e6i		−	0.305538i
$794$	−5.67928e6	+	1.74790e7i	−0.319699	+	0.983933i
$795$	−2.74881e6	+	5.70089e6i	−0.154251	+	0.319908i
$796$	4.14365e6	+	1.27529e7i	0.231793	+	0.713386i
$797$	−2.39793e7	+	7.79135e6i	−1.33718	+	0.434477i	−0.888362	−	0.459144i	$-0.848156\pi$
$797$	−2.39793e7	+	7.79135e6i	−1.33718	+	0.434477i	−0.448822	+	0.893621i	$0.648156\pi$
$798$	−791281.	+	1.08910e6i	−0.0439869	+	0.0605428i
$799$	6.54783e6			0.362853
$800$	2.66892e6	+	1.76546e6i	0.147438	+	0.0975290i
$801$	5.19637e6			0.286166
$802$	−1.43775e6	+	1.97889e6i	−0.0789308	+	0.108639i
$803$	1.97535e6	−	641831.i	0.108108	−	0.0351263i
$804$	1.60250e6	+	4.93199e6i	0.0874295	+	0.269080i
$805$	5.78517e6	+	786516.i	0.314649	+	0.0427777i
$806$	−1.56516e6	+	4.81708e6i	−0.0848638	+	0.261184i
$807$		−	2.69204e7i		−	1.45512i
$808$	7.36290e6	+	2.39235e6i	0.396753	+	0.128913i
$809$	−2.40222e7	+	1.74532e7i	−1.29045	+	0.937569i	−0.999814	−	0.0192641i	$-0.993868\pi$
$809$	−2.40222e7	+	1.74532e7i	−1.29045	+	0.937569i	−0.290638	+	0.956833i	$0.593868\pi$
$810$	1.48417e7	+	7.15628e6i	0.794826	+	0.383244i
$811$	−6.67955e6	−	4.85298e6i	−0.356611	−	0.259093i	0.395026	−	0.918670i	$-0.370736\pi$
$811$	−6.67955e6	−	4.85298e6i	−0.356611	−	0.259093i	−0.751637	+	0.659577i	$0.770736\pi$
$812$	956456.	+	1.31645e6i	0.0509067	+	0.0700671i
$813$	5.28023e6	+	7.26761e6i	0.280173	+	0.385625i
$814$	3.23206e6	+	2.34823e6i	0.170970	+	0.124217i
$815$	−2.12195e7	−	1.02315e7i	−1.11903	−	0.539565i
$816$	5.16914e6	−	3.75560e6i	0.271764	−	0.197448i
$817$	−2.91960e6	−	948636.i	−0.153027	−	0.0497215i
$818$			7.59850e6i			0.397049i
$819$	−142137.	+	437453.i	−0.00740453	+	0.0227888i
$820$	3.88460e6	+	528126.i	0.201749	+	0.0274286i
$821$	7.16925e6	+	2.20647e7i	0.371207	+	1.14246i	0.946002	+	0.324160i	$0.105082\pi$
$821$	7.16925e6	+	2.20647e7i	0.371207	+	1.14246i	−0.574795	+	0.818297i	$0.694918\pi$
$822$	2.09508e7	−	6.80731e6i	1.08148	−	0.351395i
$823$	1.42092e7	−	1.95572e7i	0.731255	−	1.00649i	−0.267819	−	0.963469i	$-0.586303\pi$
$823$	1.42092e7	−	1.95572e7i	0.731255	−	1.00649i	0.999074	−	0.0430173i	$-0.0136971\pi$
$824$	−8.23485e6			−0.422511
$825$	5.05983e6	−	4.02705e6i	0.258822	−	0.205993i
$826$	3.53329e6			0.180190
$827$	3.09980e6	−	4.26651e6i	0.157605	−	0.216925i	−0.722911	−	0.690941i	$-0.757196\pi$
$827$	3.09980e6	−	4.26651e6i	0.157605	−	0.216925i	0.880516	+	0.474017i	$0.157196\pi$
$828$	−7.43144e6	+	2.41462e6i	−0.376701	+	0.122398i
$829$	−3.46883e6	−	1.06760e7i	−0.175306	−	0.539537i	0.824341	−	0.566093i	$-0.191546\pi$
$829$	−3.46883e6	−	1.06760e7i	−0.175306	−	0.539537i	−0.999647	+	0.0265565i	$0.991546\pi$
$830$	2.74936e6	−	5.70201e6i	0.138528	−	0.287298i
$831$	−1.19952e7	+	3.69174e7i	−0.602566	+	1.85451i
$832$			500722.i			0.0250777i
$833$	−1.95985e7	−	6.36794e6i	−0.978612	−	0.317970i
$834$	−1.69748e7	+	1.23329e7i	−0.845065	+	0.613976i
$835$	1.49370e7	−	2.70317e6i	0.741389	−	0.134170i
$836$	846032.	+	614678.i	0.0418669	+	0.0304181i
$837$	−1.30223e7	−	1.79237e7i	−0.642502	−	0.884329i
$838$	3.96599e6	+	5.45871e6i	0.195093	+	0.268522i
$839$	−4.43328e6	−	3.22097e6i	−0.217430	−	0.157972i	0.473739	−	0.880665i	$-0.342904\pi$
$839$	−4.43328e6	−	3.22097e6i	−0.217430	−	0.157972i	−0.691169	+	0.722693i	$0.742904\pi$
$840$	−931243.	−	1.73256e6i	−0.0455370	−	0.0847206i
$841$	6.19464e6	−	4.50067e6i	0.302013	−	0.219426i
$842$	1.93719e7	+	6.29432e6i	0.941657	+	0.305963i
$843$		−	4.93260e7i		−	2.39060i
$844$	4.68443e6	−	1.44172e7i	0.226361	−	0.696667i
$845$	−3.54742e6	−	1.96021e7i	−0.170912	−	0.944410i
$846$	833663.	+	2.56575e6i	0.0400465	+	0.123250i
$847$	4.03730e6	−	1.31180e6i	0.193367	−	0.0628288i
$848$	878983.	−	1.20982e6i	0.0419750	−	0.0577736i
$849$	1.80705e7			0.860403
$850$	706567.	+	1.60814e7i	0.0335433	+	0.763443i
$851$	3.44410e7			1.63024
$852$	−6.65650e6	+	9.16188e6i	−0.314157	+	0.432400i
$853$	2.96806e7	−	9.64382e6i	1.39669	−	0.453813i	0.488572	−	0.872523i	$-0.337518\pi$
$853$	2.96806e7	−	9.64382e6i	1.39669	−	0.453813i	0.908120	+	0.418711i	$0.137518\pi$
$854$	−1.55188e6	−	4.77620e6i	−0.0728138	−	0.224098i
$855$	3.27930e6	+	3.13838e6i	0.153414	+	0.146822i
$856$	−2.08269e6	+	6.40987e6i	−0.0971496	+	0.298996i
$857$		−	2.42903e7i		−	1.12975i	−0.825177	−	0.564874i	$-0.808925\pi$
$857$		−	2.42903e7i		−	1.12975i	0.825177	−	0.564874i	$-0.191075\pi$
$858$	962365.	+	312691.i	0.0446294	+	0.0145010i
$859$	−1.89297e7	+	1.37532e7i	−0.875307	+	0.635948i	−0.932006	−	0.362444i	$-0.881943\pi$
$859$	−1.89297e7	+	1.37532e7i	−0.875307	+	0.635948i	0.0566988	+	0.998391i	$0.481943\pi$
$860$	3.10128e6	−	3.24053e6i	0.142986	−	0.149407i
$861$	−1.94952e6	−	1.41641e6i	−0.0896232	−	0.0651151i
$862$	−8.13717e6	−	1.11998e7i	−0.372997	−	0.513386i
$863$	−1.89025e7	−	2.60171e7i	−0.863958	−	1.18914i	−0.980611	−	0.195964i	$-0.937216\pi$
$863$	−1.89025e7	−	2.60171e7i	−0.863958	−	1.18914i	0.116653	−	0.993173i	$-0.462784\pi$
$864$	−1.77193e6	−	1.28738e6i	−0.0807536	−	0.0586709i
$865$	−848091.	+	6.23808e6i	−0.0385392	+	0.283473i
$866$	7.03617e6	−	5.11208e6i	0.318817	−	0.231634i
$867$	4.39539e6	+	1.42815e6i	0.198586	+	0.0645246i
$868$			4.70117e6i			0.211791i
$869$	2.76672e6	−	8.51508e6i	0.124284	−	0.382507i
$870$	1.36862e7	−	7.35631e6i	0.613036	−	0.329505i
$871$	−631723.	−	1.94424e6i	−0.0282151	−	0.0868371i
$872$	7.24322e6	−	2.35346e6i	0.322582	−	0.104813i
$873$	−1.38521e7	+	1.90657e7i	−0.615147	+	0.846678i
$874$	9.01536e6			0.399213
$875$	4.93481e6	+	451390.i	0.217897	+	0.0199311i
$876$	−6.03249e6			−0.265605
$877$	−9.22922e6	+	1.27029e7i	−0.405197	+	0.557705i	−0.962039	−	0.272913i	$-0.912013\pi$
$877$	−9.22922e6	+	1.27029e7i	−0.405197	+	0.557705i	0.556842	+	0.830618i	$0.312013\pi$
$878$	2.46742e7	−	8.01714e6i	1.08021	−	0.350981i
$879$	7.48637e6	+	2.30407e7i	0.326813	+	1.00583i
$880$	−1.34587e6	+	723403.i	−0.0585865	+	0.0314901i
$881$	1.39809e7	−	4.30287e7i	0.606868	−	1.86775i	0.123469	−	0.992348i	$-0.460598\pi$
$881$	1.39809e7	−	4.30287e7i	0.606868	−	1.86775i	0.483399	−	0.875400i	$-0.339402\pi$
$882$		−	8.49038e6i		−	0.367499i
$883$	−3.71403e7	−	1.20676e7i	−1.60304	−	0.520858i	−0.635180	−	0.772364i	$-0.719074\pi$
$883$	−3.71403e7	−	1.20676e7i	−1.60304	−	0.520858i	−0.967856	+	0.251506i	$0.919074\pi$
$884$	−2.03773e6	+	1.48050e6i	−0.0877034	+	0.0637202i
$885$	4.54508e6	−	3.34311e7i	0.195067	−	1.43480i
$886$	−2.39420e6	−	1.73949e6i	−0.102465	−	0.0744453i
$887$	−1.92692e6	−	2.65218e6i	−0.0822346	−	0.113186i	0.765918	−	0.642938i	$-0.222285\pi$
$887$	−1.92692e6	−	2.65218e6i	−0.0822346	−	0.113186i	−0.848152	+	0.529752i	$0.822285\pi$
$888$	−6.82023e6	−	9.38724e6i	−0.290246	−	0.399490i
$889$	7.49102e6	+	5.44254e6i	0.317897	+	0.230966i
$890$	6.05674e6	−	6.32870e6i	0.256309	−	0.267818i
$891$	−6.36500e6	+	4.62444e6i	−0.268599	+	0.195148i
$892$	−1.97019e7	−	6.40153e6i	−0.829078	−	0.269384i
$893$		−	3.11261e6i		−	0.130616i
$894$	−4.10880e6	+	1.26456e7i	−0.171938	+	0.529170i
$895$	1.63448e7	+	1.56424e7i	0.682060	+	0.652750i
$896$	143617.	+	442009.i	0.00597636	+	0.0183934i
$897$	8.29648e6	−	2.69569e6i	0.344281	−	0.111864i
$898$	−2.99527e6	+	4.12264e6i	−0.123950	+	0.170602i
$899$	−3.71367e7			−1.53251
$900$	−6.21150e6	+	2.32433e6i	−0.255617	+	0.0956516i
$901$	7.52237e6			0.308704
$902$	−1.10029e6	+	1.51442e6i	−0.0450288	+	0.0619768i
$903$	−2.62214e6	+	851986.i	−0.107013	+	0.0347707i
$904$	−3.87536e6	−	1.19271e7i	−0.157721	−	0.485417i
$905$	−1.31833e6	−	7.28472e6i	−0.0535060	−	0.295659i
$906$	−5.75719e6	+	1.77188e7i	−0.233018	+	0.717156i
$907$			1.03768e7i			0.418837i	0.977826	+	0.209418i	$0.0671570\pi$
$907$			1.03768e7i			0.418837i	−0.977826	+	0.209418i	$0.932843\pi$
$908$	−1.32614e7	−	4.30889e6i	−0.533795	−	0.173441i
$909$	−1.29809e7	+	9.43115e6i	−0.521068	+	0.378578i
$910$	367106.	+	682993.i	0.0146956	+	0.0273409i
$911$	−1.22075e7	−	8.86924e6i	−0.487337	−	0.354071i	0.316822	−	0.948485i	$-0.397384\pi$
$911$	−1.22075e7	−	8.86924e6i	−0.487337	−	0.354071i	−0.804159	+	0.594414i	$0.797384\pi$
$912$	−1.78528e6	−	2.45722e6i	−0.0710753	−	0.0978268i
$913$	1.77666e6	+	2.44536e6i	0.0705385	+	0.0970879i
$914$	−1.89585e7	−	1.37741e7i	−0.750651	−	0.545380i
$915$	−4.71874e7	+	8.53959e6i	−1.86326	+	0.337197i
$916$	4.86074e6	−	3.53154e6i	0.191410	−	0.139067i
$917$	2.99140e6	+	971964.i	0.117476	+	0.0381704i
$918$		−	1.10175e7i		−	0.431494i
$919$	−1.03774e7	+	3.19383e7i	−0.405321	+	1.24745i	0.515305	+	0.857007i	$0.327679\pi$
$919$	−1.03774e7	+	3.19383e7i	−0.405321	+	1.24745i	−0.920627	+	0.390444i	$0.872321\pi$
$920$	−5.72110e6	+	1.18652e7i	−0.222849	+	0.462176i
$921$	1.20649e7	+	3.71319e7i	0.468677	+	1.44244i
$922$	3.35087e7	−	1.08876e7i	1.29817	−	0.421800i
$923$	2.62407e6	−	3.61172e6i	0.101384	−	0.139543i
$924$	939208.			0.0361894
$925$	2.92041e7	−	1.28314e6i	1.12225	−	0.0493082i
$926$	−2.63165e7			−1.00856
$927$	1.00318e7	−	1.38076e7i	0.383423	−	0.527737i
$928$	−3.49163e6	+	1.13450e6i	−0.133094	+	0.0432448i
$929$	8.44179e6	+	2.59812e7i	0.320919	+	0.987687i	0.973249	+	0.229752i	$0.0737915\pi$
$929$	8.44179e6	+	2.59812e7i	0.320919	+	0.987687i	−0.652330	+	0.757935i	$0.726208\pi$
$930$	4.44812e7	+	6.04739e6i	1.68643	+	0.229277i
$931$	−3.02709e6	+	9.31643e6i	−0.114459	+	0.352270i
$932$		−	1.57723e7i		−	0.594780i
$933$	−2.76620e7	−	8.98794e6i	−1.04035	−	0.338031i
$934$	1.15731e7	−	8.40835e6i	0.434093	−	0.315387i
$935$	−6.92334e6	−	3.33825e6i	−0.258992	−	0.124879i
$936$	−839571.	−	609984.i	−0.0313233	−	0.0227577i
$937$	1.35362e6	+	1.86310e6i	0.0503673	+	0.0693247i	0.833458	−	0.552583i	$-0.186358\pi$
$937$	1.35362e6	+	1.86310e6i	0.0503673	+	0.0693247i	−0.783090	+	0.621908i	$0.786358\pi$
$938$	−1.11530e6	−	1.53508e6i	−0.0413890	−	0.0569670i
$939$	8.17760e6	+	5.94137e6i	0.302665	+	0.219899i
$940$	4.09655e6	+	1.97524e6i	0.151216	+	0.0729124i
$941$	3.96767e7	−	2.88268e7i	1.46070	−	1.06126i	0.477520	−	0.878621i	$-0.341536\pi$
$941$	3.96767e7	−	2.88268e7i	1.46070	−	1.06126i	0.983180	−	0.182640i	$-0.0584644\pi$
$942$	−1.09934e7	−	3.57196e6i	−0.403649	−	0.131153i
$943$			1.61377e7i			0.590966i
$944$	−2.46341e6	+	7.58161e6i	−0.0899720	+	0.276905i
$945$	−3.36079e6	−	456912.i	−0.122423	−	0.0166438i
$946$	661835.	+	2.03692e6i	0.0240448	+	0.0740024i
$947$	8.13373e6	−	2.64281e6i	0.294724	−	0.0957615i	−0.157923	−	0.987451i	$-0.550480\pi$
$947$	8.13373e6	−	2.64281e6i	0.294724	−	0.0957615i	0.452647	+	0.891690i	$0.350480\pi$
$948$	−1.52848e7	+	2.10377e7i	−0.552381	+	0.760287i
$949$	2.37808e6			0.0857157
$950$	7.64453e6	−	335877.i	0.274816	−	0.0120746i
$951$	6.13673e7			2.20032
$952$	−1.37416e6	+	1.89136e6i	−0.0491410	+	0.0676368i
$953$	1.63300e7	−	5.30595e6i	0.582445	−	0.189248i	−0.00295078	−	0.999996i	$-0.500939\pi$
$953$	1.63300e7	−	5.30595e6i	0.582445	−	0.189248i	0.585395	+	0.810748i	$0.300939\pi$
$954$	957740.	+	2.94762e6i	0.0340703	+	0.104858i
$955$	−4.47304e6	+	9.27684e6i	−0.158706	+	0.329148i
$956$	−3.86953e6	+	1.19092e7i	−0.136935	+	0.421442i
$957$			7.41922e6i			0.261866i
$958$	−1.36711e7	−	4.44201e6i	−0.481271	−	0.156374i
$959$	−6.52091e6	+	4.73772e6i	−0.228961	+	0.166350i
$960$	4.36691e6	−	790288.i	0.152931	−	0.0276762i
$961$	−6.36386e7	−	4.62362e7i	−2.22286	−	1.61500i
$962$	2.68861e6	+	3.70056e6i	0.0936678	+	0.128923i
$963$	−8.21042e6	−	1.13007e7i	−0.285298	−	0.392680i
$964$	5.93719e6	+	4.31362e6i	0.205773	+	0.149503i
$965$	1.45779e7	+	2.71218e7i	0.503937	+	0.937563i
$966$	6.55048e6	−	4.75920e6i	0.225855	−	0.164094i
$967$	3.86395e7	+	1.25547e7i	1.32882	+	0.431759i	0.885514	−	0.464613i	$-0.153806\pi$
$967$	3.86395e7	+	1.25547e7i	1.32882	+	0.431759i	0.443303	+	0.896372i	$0.353806\pi$
$968$			9.57767e6i			0.328527i
$969$	4.72131e6	−	1.45307e7i	0.161530	−	0.497138i
$970$	7.07474e6	+	3.90931e7i	0.241424	+	1.33405i
$971$	−6.34750e6	−	1.95356e7i	−0.216050	−	0.664934i	−0.999077	−	0.0429467i	$-0.986325\pi$
$971$	−6.34750e6	−	1.95356e7i	−0.216050	−	0.664934i	0.783027	−	0.621988i	$-0.213675\pi$
$972$	1.38233e7	−	4.49146e6i	0.469295	−	0.152483i
$973$	4.51257e6	−	6.21102e6i	0.152806	−	0.210320i
$974$	9.04181e6			0.305392
$975$	6.93453e6	−	2.59489e6i	0.233617	−	0.0874193i
$976$	1.13306e7			0.380739
$977$	4.84305e6	−	6.66589e6i	0.162324	−	0.223420i	−0.720105	−	0.693865i	$-0.755907\pi$
$977$	4.84305e6	−	6.66589e6i	0.162324	−	0.223420i	0.882429	+	0.470445i	$0.155907\pi$
$978$	−3.10710e7	+	1.00956e7i	−1.03874	+	0.337508i
$979$	1.29255e6	+	3.97807e6i	0.0431014	+	0.132652i
$980$	−1.03405e7	−	9.89616e6i	−0.343935	−	0.329156i
$981$	−4.87765e6	+	1.50119e7i	−0.161822	+	0.498038i
$982$			5.58770e6i			0.184907i
$983$	2.07803e7	+	6.75193e6i	0.685911	+	0.222866i	0.631182	−	0.775635i	$-0.282570\pi$
$983$	2.07803e7	+	6.75193e6i	0.685911	+	0.222866i	0.0547297	+	0.998501i	$0.482570\pi$
$984$	4.39849e6	−	3.19569e6i	0.144816	−	0.105215i
$985$	−2.76012e7	+	2.88405e7i	−0.906436	+	0.947137i
$986$	−1.49407e7	−	1.08551e7i	−0.489418	−	0.355583i
$987$	−1.64314e6	−	2.26159e6i	−0.0536887	−	0.0738962i
$988$	703776.	+	968665.i	0.0229373	+	0.0315705i
$989$	1.49375e7	+	1.08528e7i	0.485611	+	0.352817i
$990$	426611.	−	3.13791e6i	0.0138339	−	0.101754i
$991$	2.51737e7	−	1.82898e7i	0.814261	−	0.591595i	−0.100802	−	0.994907i	$-0.532141\pi$
$991$	2.51737e7	−	1.82898e7i	0.814261	−	0.591595i	0.915063	+	0.403311i	$0.132141\pi$
$992$	−1.00876e7	−	3.27766e6i	−0.325468	−	0.105751i
$993$		−	1.86824e7i		−	0.601256i
$994$	1.28046e6	−	3.94086e6i	0.0411056	−	0.126510i
$995$	−4.12663e7	+	2.21805e7i	−1.32141	+	0.710255i
$996$	−2.71285e6	−	8.34928e6i	−0.0866516	−	0.266686i
$997$	−6.67428e6	+	2.16860e6i	−0.212651	+	0.0690943i	−0.413405	−	0.910547i	$-0.635661\pi$
$997$	−6.67428e6	+	2.16860e6i	−0.212651	+	0.0690943i	0.200755	+	0.979642i	$0.435661\pi$
$998$	1.77138e7	−	2.43810e7i	0.562971	−	0.774863i
$999$	−2.00079e7			−0.634290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.e.a.9.11	✓	48
25.14	even	10	inner	50.6.e.a.39.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.e.a.9.11	✓	48	1.1	even	1	trivial
50.6.e.a.39.11	yes	48	25.14	even	10	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.35114 - 3.23607i) q^{2} +(18.4329 - 5.98921i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(49.2396 - 26.4662i) q^{5} +(23.9569 - 73.7316i) q^{6} +28.3664i q^{7} +(-60.8676 - 19.7771i) q^{8} +(107.310 - 77.9654i) q^{9} +O(q^{10})\)	\(q+(2.35114 - 3.23607i) q^{2} +(18.4329 - 5.98921i) q^{3} +(-4.94427 - 15.2169i) q^{4} +(49.2396 - 26.4662i) q^{5} +(23.9569 - 73.7316i) q^{6} +28.3664i q^{7} +(-60.8676 - 19.7771i) q^{8} +(107.310 - 77.9654i) q^{9} +(30.1231 - 221.569i) q^{10} +(86.3788 + 62.7579i) q^{11} +(-182.275 - 250.879i) q^{12} +(71.8547 + 98.8995i) q^{13} +(91.7957 + 66.6935i) q^{14} +(749.118 - 782.755i) q^{15} +(-207.108 + 150.473i) q^{16} +(-1224.73 - 397.938i) q^{17} -530.571i q^{18} +(-189.166 + 582.192i) q^{19} +(-646.187 - 618.419i) q^{20} +(169.893 + 522.876i) q^{21} +(406.177 - 131.975i) q^{22} +(2164.12 - 2978.66i) q^{23} -1240.42 q^{24} +(1724.09 - 2606.37i) q^{25} +488.986 q^{26} +(-1257.21 + 1730.40i) q^{27} +(431.649 - 140.251i) q^{28} +(1107.91 + 3409.79i) q^{29} +(-771.765 - 4264.56i) q^{30} +(-3200.84 + 9851.16i) q^{31} +1024.00i q^{32} +(1968.08 + 639.469i) q^{33} +(-4167.26 + 3027.69i) q^{34} +(750.750 + 1396.75i) q^{35} +(-1716.96 - 1247.45i) q^{36} +(5498.34 + 7567.81i) q^{37} +(1439.26 + 1980.97i) q^{38} +(1916.82 + 1392.65i) q^{39} +(-3520.52 + 637.115i) q^{40} +(-3545.98 + 2576.30i) q^{41} +(2091.50 + 679.571i) q^{42} +5014.85i q^{43} +(527.900 - 1624.71i) q^{44} +(3220.47 - 6679.08i) q^{45} +(-4550.99 - 14006.5i) q^{46} +(-4835.83 + 1571.26i) q^{47} +(-2916.39 + 4014.07i) q^{48} +16002.3 q^{49} +(-4380.82 - 11707.2i) q^{50} -24958.6 q^{51} +(1149.68 - 1582.39i) q^{52} +(-5555.56 + 1805.11i) q^{53} +(2643.81 + 8136.82i) q^{54} +(5914.22 + 804.060i) q^{55} +(561.005 - 1726.60i) q^{56} +11864.4i q^{57} +(13639.2 + 4431.64i) q^{58} +(25192.6 - 18303.5i) q^{59} +(-15615.0 - 7529.11i) q^{60} +(-35807.1 - 26015.4i) q^{61} +(24353.4 + 33519.6i) q^{62} +(2211.60 + 3044.01i) q^{63} +(3313.73 + 2407.57i) q^{64} +(6155.59 + 2968.06i) q^{65} +(6696.60 - 4865.37i) q^{66} +(-15904.3 - 5167.62i) q^{67} +20604.1i q^{68} +(22051.3 - 67866.8i) q^{69} +(6285.11 + 854.484i) q^{70} +(-11285.0 - 34731.7i) q^{71} +(-8073.65 + 2623.29i) q^{72} +(11434.3 - 15737.9i) q^{73} +37417.3 q^{74} +(16169.8 - 58368.9i) q^{75} +9794.44 q^{76} +(-1780.22 + 2450.26i) q^{77} +(9013.43 - 2928.64i) q^{78} +(-25912.9 - 79751.6i) q^{79} +(-6215.50 + 12890.6i) q^{80} +(-22770.6 + 70080.6i) q^{81} +17532.3i q^{82} +(26924.1 + 8748.18i) q^{83} +(7116.56 - 5170.48i) q^{84} +(-70837.0 + 12819.5i) q^{85} +(16228.4 + 11790.6i) q^{86} +(40844.0 + 56216.9i) q^{87} +(-4016.50 - 5528.24i) q^{88} +(31693.8 + 23026.9i) q^{89} +(-14042.2 - 26125.1i) q^{90} +(-2805.43 + 2038.26i) q^{91} +(-56026.0 - 18204.0i) q^{92} +200756. i q^{93} +(-6285.03 + 19343.3i) q^{94} +(6093.93 + 33673.4i) q^{95} +(6132.96 + 18875.3i) q^{96} +(-168974. + 54902.9i) q^{97} +(37623.8 - 51784.7i) q^{98} +14162.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9}+O(q^{10}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + 80 q^{10} + 716 q^{11} - 160 q^{12} - 784 q^{14} - 940 q^{15} - 3072 q^{16} + 1910 q^{17} - 5990 q^{19} - 640 q^{20} - 4344 q^{21} + 4720 q^{22} + 12410 q^{23} + 4608 q^{24} + 23660 q^{25} - 15248 q^{26} + 27600 q^{27} - 3040 q^{28} - 17170 q^{29} - 14720 q^{30} - 18834 q^{31} - 56930 q^{33} + 11696 q^{34} + 28450 q^{35} - 10976 q^{36} + 3540 q^{37} + 13432 q^{39} - 1280 q^{40} + 37146 q^{41} - 43560 q^{42} + 1184 q^{44} + 75240 q^{45} + 28672 q^{46} - 17830 q^{47} - 2560 q^{48} - 54656 q^{49} + 8800 q^{50} - 85984 q^{51} + 22350 q^{53} + 16080 q^{54} - 64730 q^{55} + 12544 q^{56} + 18000 q^{59} + 78720 q^{60} + 67086 q^{61} - 159600 q^{62} + 132820 q^{63} + 49152 q^{64} - 195820 q^{65} - 52256 q^{66} - 90790 q^{67} - 212608 q^{69} + 180080 q^{70} - 122874 q^{71} + 121200 q^{73} + 281456 q^{74} + 672810 q^{75} - 102400 q^{76} + 434040 q^{77} + 170720 q^{78} + 113600 q^{79} - 28160 q^{80} + 115878 q^{81} - 582750 q^{83} - 174816 q^{84} + 107770 q^{85} - 26888 q^{86} - 911580 q^{87} - 56960 q^{88} - 357730 q^{89} - 282920 q^{90} - 216324 q^{91} + 451040 q^{92} + 79136 q^{94} + 135000 q^{95} + 18432 q^{96} - 123520 q^{97} - 206240 q^{98} + 235252 q^{99}+O(q^{100}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9 + 80 * q^10 + 716 * q^11 - 160 * q^12 - 784 * q^14 - 940 * q^15 - 3072 * q^16 + 1910 * q^17 - 5990 * q^19 - 640 * q^20 - 4344 * q^21 + 4720 * q^22 + 12410 * q^23 + 4608 * q^24 + 23660 * q^25 - 15248 * q^26 + 27600 * q^27 - 3040 * q^28 - 17170 * q^29 - 14720 * q^30 - 18834 * q^31 - 56930 * q^33 + 11696 * q^34 + 28450 * q^35 - 10976 * q^36 + 3540 * q^37 + 13432 * q^39 - 1280 * q^40 + 37146 * q^41 - 43560 * q^42 + 1184 * q^44 + 75240 * q^45 + 28672 * q^46 - 17830 * q^47 - 2560 * q^48 - 54656 * q^49 + 8800 * q^50 - 85984 * q^51 + 22350 * q^53 + 16080 * q^54 - 64730 * q^55 + 12544 * q^56 + 18000 * q^59 + 78720 * q^60 + 67086 * q^61 - 159600 * q^62 + 132820 * q^63 + 49152 * q^64 - 195820 * q^65 - 52256 * q^66 - 90790 * q^67 - 212608 * q^69 + 180080 * q^70 - 122874 * q^71 + 121200 * q^73 + 281456 * q^74 + 672810 * q^75 - 102400 * q^76 + 434040 * q^77 + 170720 * q^78 + 113600 * q^79 - 28160 * q^80 + 115878 * q^81 - 582750 * q^83 - 174816 * q^84 + 107770 * q^85 - 26888 * q^86 - 911580 * q^87 - 56960 * q^88 - 357730 * q^89 - 282920 * q^90 - 216324 * q^91 + 451040 * q^92 + 79136 * q^94 + 135000 * q^95 + 18432 * q^96 - 123520 * q^97 - 206240 * q^98 + 235252 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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