LMFDB - Embedded newform 1045.6.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

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:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63769 q^{2} +28.9603 q^{3} -25.0426 q^{4} -25.0000 q^{5} -76.3883 q^{6} -13.2455 q^{7} +150.461 q^{8} +595.699 q^{9} +O(q^{10})$	\(q-2.63769 q^{2} +28.9603 q^{3} -25.0426 q^{4} -25.0000 q^{5} -76.3883 q^{6} -13.2455 q^{7} +150.461 q^{8} +595.699 q^{9} +65.9423 q^{10} -121.000 q^{11} -725.241 q^{12} +1116.07 q^{13} +34.9375 q^{14} -724.008 q^{15} +404.494 q^{16} -421.031 q^{17} -1571.27 q^{18} +361.000 q^{19} +626.065 q^{20} -383.593 q^{21} +319.161 q^{22} +60.1763 q^{23} +4357.39 q^{24} +625.000 q^{25} -2943.84 q^{26} +10214.3 q^{27} +331.701 q^{28} -7784.73 q^{29} +1909.71 q^{30} +1234.85 q^{31} -5881.67 q^{32} -3504.20 q^{33} +1110.55 q^{34} +331.137 q^{35} -14917.8 q^{36} +4730.22 q^{37} -952.207 q^{38} +32321.7 q^{39} -3761.52 q^{40} +14549.5 q^{41} +1011.80 q^{42} +23542.1 q^{43} +3030.15 q^{44} -14892.5 q^{45} -158.726 q^{46} -20362.8 q^{47} +11714.3 q^{48} -16631.6 q^{49} -1648.56 q^{50} -12193.2 q^{51} -27949.2 q^{52} +35343.1 q^{53} -26942.1 q^{54} +3025.00 q^{55} -1992.92 q^{56} +10454.7 q^{57} +20533.7 q^{58} +38823.0 q^{59} +18131.0 q^{60} +1987.77 q^{61} -3257.14 q^{62} -7890.32 q^{63} +2570.24 q^{64} -27901.7 q^{65} +9242.99 q^{66} -35232.1 q^{67} +10543.7 q^{68} +1742.72 q^{69} -873.437 q^{70} -23422.6 q^{71} +89629.3 q^{72} -84081.7 q^{73} -12476.9 q^{74} +18100.2 q^{75} -9040.37 q^{76} +1602.70 q^{77} -85254.6 q^{78} -82745.6 q^{79} -10112.3 q^{80} +151054. q^{81} -38377.1 q^{82} +111003. q^{83} +9606.16 q^{84} +10525.8 q^{85} -62096.8 q^{86} -225448. q^{87} -18205.7 q^{88} +4252.08 q^{89} +39281.8 q^{90} -14782.9 q^{91} -1506.97 q^{92} +35761.5 q^{93} +53710.7 q^{94} -9025.00 q^{95} -170335. q^{96} -100924. q^{97} +43868.9 q^{98} -72079.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.63769	−0.466282	−0.233141	−	0.972443i	$-0.574900\pi$
$2$	−2.63769	−0.466282	−0.233141	+	0.972443i	$0.574900\pi$
$3$	28.9603	1.85780	0.928902	−	0.370325i	$-0.120754\pi$
$3$	28.9603	1.85780	0.928902	+	0.370325i	$0.120754\pi$
$4$	−25.0426	−0.782581
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−76.3883	−0.866261
$7$	−13.2455	−0.102170	−0.0510849	−	0.998694i	$-0.516268\pi$
$7$	−13.2455	−0.102170	−0.0510849	+	0.998694i	$0.516268\pi$
$8$	150.461	0.831186
$9$	595.699	2.45144
$10$	65.9423	0.208528
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−725.241	−1.45388
$13$	1116.07	1.83161	0.915803	−	0.401627i	$-0.131555\pi$
$13$	1116.07	1.83161	0.915803	+	0.401627i	$0.131555\pi$
$14$	34.9375	0.0476400
$15$	−724.008	−0.830835
$16$	404.494	0.395013
$17$	−421.031	−0.353339	−0.176670	−	0.984270i	$-0.556532\pi$
$17$	−421.031	−0.353339	−0.176670	+	0.984270i	$0.556532\pi$
$18$	−1571.27	−1.14306
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	626.065	0.349981
$21$	−383.593	−0.189812
$22$	319.161	0.140589
$23$	60.1763	0.0237195	0.0118598	−	0.999930i	$-0.496225\pi$
$23$	60.1763	0.0237195	0.0118598	+	0.999930i	$0.496225\pi$
$24$	4357.39	1.54418
$25$	625.000	0.200000
$26$	−2943.84	−0.854046
$27$	10214.3	2.69649
$28$	331.701	0.0799561
$29$	−7784.73	−1.71889	−0.859446	−	0.511226i	$-0.829192\pi$
$29$	−7784.73	−1.71889	−0.859446	+	0.511226i	$0.829192\pi$
$30$	1909.71	0.387404
$31$	1234.85	0.230785	0.115393	−	0.993320i	$-0.463187\pi$
$31$	1234.85	0.230785	0.115393	+	0.993320i	$0.463187\pi$
$32$	−5881.67	−1.01537
$33$	−3504.20	−0.560149
$34$	1110.55	0.164756
$35$	331.137	0.0456917
$36$	−14917.8	−1.91845
$37$	4730.22	0.568038	0.284019	−	0.958819i	$-0.408332\pi$
$37$	4730.22	0.568038	0.284019	+	0.958819i	$0.408332\pi$
$38$	−952.207	−0.106973
$39$	32321.7	3.40277
$40$	−3761.52	−0.371718
$41$	14549.5	1.35173	0.675863	−	0.737027i	$-0.263771\pi$
$41$	14549.5	1.35173	0.675863	+	0.737027i	$0.263771\pi$
$42$	1011.80	0.0885058
$43$	23542.1	1.94166	0.970832	−	0.239761i	$-0.0770690\pi$
$43$	23542.1	1.94166	0.970832	+	0.239761i	$0.0770690\pi$
$44$	3030.15	0.235957
$45$	−14892.5	−1.09632
$46$	−158.726	−0.0110600
$47$	−20362.8	−1.34460	−0.672298	−	0.740280i	$-0.734693\pi$
$47$	−20362.8	−1.34460	−0.672298	+	0.740280i	$0.734693\pi$
$48$	11714.3	0.733858
$49$	−16631.6	−0.989561
$50$	−1648.56	−0.0932565
$51$	−12193.2	−0.656435
$52$	−27949.2	−1.43338
$53$	35343.1	1.72828	0.864142	−	0.503247i	$-0.167862\pi$
$53$	35343.1	1.72828	0.864142	+	0.503247i	$0.167862\pi$
$54$	−26942.1	−1.25732
$55$	3025.00	0.134840
$56$	−1992.92	−0.0849221
$57$	10454.7	0.426210
$58$	20533.7	0.801489
$59$	38823.0	1.45198	0.725988	−	0.687708i	$-0.241383\pi$
$59$	38823.0	1.45198	0.725988	+	0.687708i	$0.241383\pi$
$60$	18131.0	0.650196
$61$	1987.77	0.0683977	0.0341989	−	0.999415i	$-0.489112\pi$
$61$	1987.77	0.0683977	0.0341989	+	0.999415i	$0.489112\pi$
$62$	−3257.14	−0.107611
$63$	−7890.32	−0.250463
$64$	2570.24	0.0784375
$65$	−27901.7	−0.819120
$66$	9242.99	0.261188
$67$	−35232.1	−0.958851	−0.479426	−	0.877582i	$-0.659155\pi$
$67$	−35232.1	−0.958851	−0.479426	+	0.877582i	$0.659155\pi$
$68$	10543.7	0.276516
$69$	1742.72	0.0440662
$70$	−873.437	−0.0213052
$71$	−23422.6	−0.551427	−0.275714	−	0.961240i	$-0.588914\pi$
$71$	−23422.6	−0.551427	−0.275714	+	0.961240i	$0.588914\pi$
$72$	89629.3	2.03760
$73$	−84081.7	−1.84669	−0.923345	−	0.383971i	$-0.874556\pi$
$73$	−84081.7	−1.84669	−0.923345	+	0.383971i	$0.874556\pi$
$74$	−12476.9	−0.264866
$75$	18100.2	0.371561
$76$	−9040.37	−0.179536
$77$	1602.70	0.0308054
$78$	−85254.6	−1.58665
$79$	−82745.6	−1.49169	−0.745843	−	0.666122i	$-0.767953\pi$
$79$	−82745.6	−1.49169	−0.745843	+	0.666122i	$0.767953\pi$
$80$	−10112.3	−0.176655
$81$	151054.	2.55811
$82$	−38377.1	−0.630286
$83$	111003.	1.76864	0.884318	−	0.466885i	$-0.154624\pi$
$83$	111003.	1.76864	0.884318	+	0.466885i	$0.154624\pi$
$84$	9606.16	0.148543
$85$	10525.8	0.158018
$86$	−62096.8	−0.905364
$87$	−225448.	−3.19337
$88$	−18205.7	−0.250612
$89$	4252.08	0.0569019	0.0284509	−	0.999595i	$-0.490943\pi$
$89$	4252.08	0.0569019	0.0284509	+	0.999595i	$0.490943\pi$
$90$	39281.8	0.511193
$91$	−14782.9	−0.187135
$92$	−1506.97	−0.0185624
$93$	35761.5	0.428754
$94$	53710.7	0.626962
$95$	−9025.00	−0.102598
$96$	−170335.	−1.88637
$97$	−100924.	−1.08910	−0.544549	−	0.838729i	$-0.683299\pi$
$97$	−100924.	−1.08910	−0.544549	+	0.838729i	$0.683299\pi$
$98$	43868.9	0.461415
$99$	−72079.6	−0.739136
$100$	−15651.6	−0.156516
$101$	−53441.1	−0.521281	−0.260641	−	0.965436i	$-0.583934\pi$
$101$	−53441.1	−0.521281	−0.260641	+	0.965436i	$0.583934\pi$
$102$	32161.9	0.306084
$103$	−49304.4	−0.457923	−0.228962	−	0.973435i	$-0.573533\pi$
$103$	−49304.4	−0.457923	−0.228962	+	0.973435i	$0.573533\pi$
$104$	167924.	1.52241
$105$	9589.83	0.0848863
$106$	−93224.3	−0.805869
$107$	37515.2	0.316773	0.158386	−	0.987377i	$-0.449371\pi$
$107$	37515.2	0.316773	0.158386	+	0.987377i	$0.449371\pi$
$108$	−255792.	−2.11022
$109$	161848.	1.30479	0.652396	−	0.757879i	$-0.273764\pi$
$109$	161848.	1.30479	0.652396	+	0.757879i	$0.273764\pi$
$110$	−7979.02	−0.0628735
$111$	136989.	1.05530
$112$	−5357.71	−0.0403584
$113$	137322.	1.01168	0.505841	−	0.862627i	$-0.331182\pi$
$113$	137322.	1.01168	0.505841	+	0.862627i	$0.331182\pi$
$114$	−27576.2	−0.198734
$115$	−1504.41	−0.0106077
$116$	194950.	1.34517
$117$	664841.	4.49007
$118$	−102403.	−0.677031
$119$	5576.76	0.0361006
$120$	−108935.	−0.690579
$121$	14641.0	0.0909091
$122$	−5243.13	−0.0318927
$123$	421358.	2.51124
$124$	−30923.7	−0.180608
$125$	−15625.0	−0.0894427
$126$	20812.2	0.116786
$127$	−3280.06	−0.0180457	−0.00902284	−	0.999959i	$-0.502872\pi$
$127$	−3280.06	−0.0180457	−0.00902284	+	0.999959i	$0.502872\pi$
$128$	181434.	0.978800
$129$	681786.	3.60723
$130$	73596.1	0.381941
$131$	−32889.6	−0.167448	−0.0837240	−	0.996489i	$-0.526681\pi$
$131$	−32889.6	−0.167448	−0.0837240	+	0.996489i	$0.526681\pi$
$132$	87754.1	0.438362
$133$	−4781.62	−0.0234394
$134$	92931.4	0.447095
$135$	−255357.	−1.20591
$136$	−63348.6	−0.293691
$137$	186937.	0.850928	0.425464	−	0.904975i	$-0.360111\pi$
$137$	186937.	0.850928	0.425464	+	0.904975i	$0.360111\pi$
$138$	−4596.77	−0.0205473
$139$	300680.	1.31998	0.659991	−	0.751273i	$-0.270560\pi$
$139$	300680.	1.31998	0.659991	+	0.751273i	$0.270560\pi$
$140$	−8292.53	−0.0357575
$141$	−589712.	−2.49800
$142$	61781.5	0.257121
$143$	−135044.	−0.552250
$144$	240957.	0.968351
$145$	194618.	0.768712
$146$	221781.	0.861079
$147$	−481655.	−1.83841
$148$	−118457.	−0.444536
$149$	299952.	1.10684	0.553421	−	0.832902i	$-0.313322\pi$
$149$	299952.	1.10684	0.553421	+	0.832902i	$0.313322\pi$
$150$	−47742.7	−0.173252
$151$	−319761.	−1.14125	−0.570627	−	0.821209i	$-0.693300\pi$
$151$	−319761.	−1.14125	−0.570627	+	0.821209i	$0.693300\pi$
$152$	54316.3	0.190687
$153$	−250808.	−0.866189
$154$	−4227.44	−0.0143640
$155$	−30871.1	−0.103210
$156$	−809418.	−2.66294
$157$	47814.2	0.154813	0.0774065	−	0.997000i	$-0.475336\pi$
$157$	47814.2	0.154813	0.0774065	+	0.997000i	$0.475336\pi$
$158$	218257.	0.695547
$159$	1.02355e6	3.21082
$160$	147042.	0.454089
$161$	−797.064	−0.00242342
$162$	−398433.	−1.19280
$163$	−47343.2	−0.139569	−0.0697845	−	0.997562i	$-0.522231\pi$
$163$	−47343.2	−0.139569	−0.0697845	+	0.997562i	$0.522231\pi$
$164$	−364357.	−1.05783
$165$	87604.9	0.250506
$166$	−292791.	−0.824684
$167$	324471.	0.900295	0.450147	−	0.892954i	$-0.351371\pi$
$167$	324471.	0.900295	0.450147	+	0.892954i	$0.351371\pi$
$168$	−57715.7	−0.157769
$169$	874315.	2.35478
$170$	−27763.7	−0.0736810
$171$	215047.	0.562398
$172$	−589555.	−1.51951
$173$	−8405.62	−0.0213528	−0.0106764	−	0.999943i	$-0.503398\pi$
$173$	−8405.62	−0.0213528	−0.0106764	+	0.999943i	$0.503398\pi$
$174$	594663.	1.48901
$175$	−8278.42	−0.0204340
$176$	−48943.7	−0.119101
$177$	1.12433e6	2.69749
$178$	−11215.7	−0.0265323
$179$	−48257.9	−0.112573	−0.0562867	−	0.998415i	$-0.517926\pi$
$179$	−48257.9	−0.112573	−0.0562867	+	0.998415i	$0.517926\pi$
$180$	372946.	0.857956
$181$	393659.	0.893150	0.446575	−	0.894746i	$-0.352644\pi$
$181$	393659.	0.893150	0.446575	+	0.894746i	$0.352644\pi$
$182$	38992.6	0.0872577
$183$	57566.5	0.127070
$184$	9054.17	0.0197153
$185$	−118256.	−0.254034
$186$	−94327.8	−0.199920
$187$	50944.7	0.106536
$188$	509936.	1.05226
$189$	−135293.	−0.275500
$190$	23805.2	0.0478396
$191$	843151.	1.67233	0.836165	−	0.548478i	$-0.184793\pi$
$191$	843151.	1.67233	0.836165	+	0.548478i	$0.184793\pi$
$192$	74434.9	0.145721
$193$	928858.	1.79497	0.897483	−	0.441050i	$-0.145394\pi$
$193$	928858.	1.79497	0.897483	+	0.441050i	$0.145394\pi$
$194$	266207.	0.507827
$195$	−808042.	−1.52176
$196$	416497.	0.774412
$197$	−149364.	−0.274208	−0.137104	−	0.990557i	$-0.543780\pi$
$197$	−149364.	−0.274208	−0.137104	+	0.990557i	$0.543780\pi$
$198$	190124.	0.344646
$199$	−410297.	−0.734455	−0.367228	−	0.930131i	$-0.619693\pi$
$199$	−410297.	−0.734455	−0.367228	+	0.930131i	$0.619693\pi$
$200$	94038.0	0.166237
$201$	−1.02033e6	−1.78136
$202$	140961.	0.243064
$203$	103113.	0.175619
$204$	305349.	0.513713
$205$	−363738.	−0.604510
$206$	130050.	0.213522
$207$	35847.0	0.0581469
$208$	451442.	0.723509
$209$	−43681.0	−0.0691714
$210$	−25295.0	−0.0395810
$211$	−945928.	−1.46269	−0.731345	−	0.682008i	$-0.761107\pi$
$211$	−945928.	−1.46269	−0.731345	+	0.682008i	$0.761107\pi$
$212$	−885083.	−1.35252
$213$	−678324.	−1.02444
$214$	−98953.5	−0.147706
$215$	−588553.	−0.868339
$216$	1.53685e6	2.24128
$217$	−16356.1	−0.0235793
$218$	−426905.	−0.608401
$219$	−2.43503e6	−3.43079
$220$	−75753.8	−0.105523
$221$	−469899.	−0.647178
$222$	−361334.	−0.492069
$223$	970991.	1.30753	0.653767	−	0.756696i	$-0.273188\pi$
$223$	970991.	1.30753	0.653767	+	0.756696i	$0.273188\pi$
$224$	77905.6	0.103741
$225$	372312.	0.490287
$226$	−362213.	−0.471729
$227$	1.25562e6	1.61732	0.808659	−	0.588278i	$-0.200194\pi$
$227$	1.25562e6	1.61732	0.808659	+	0.588278i	$0.200194\pi$
$228$	−261812.	−0.333543
$229$	15245.5	0.0192112	0.00960558	−	0.999954i	$-0.496942\pi$
$229$	15245.5	0.0192112	0.00960558	+	0.999954i	$0.496942\pi$
$230$	3968.16	0.00494618
$231$	46414.8	0.0572303
$232$	−1.17130e6	−1.42872
$233$	−270190.	−0.326046	−0.163023	−	0.986622i	$-0.552125\pi$
$233$	−270190.	−0.326046	−0.163023	+	0.986622i	$0.552125\pi$
$234$	−1.75365e6	−2.09364
$235$	509069.	0.601322
$236$	−972229.	−1.13629
$237$	−2.39634e6	−2.77126
$238$	−14709.8	−0.0168331
$239$	−1.40917e6	−1.59577	−0.797883	−	0.602813i	$-0.794047\pi$
$239$	−1.40917e6	−1.59577	−0.797883	+	0.602813i	$0.794047\pi$
$240$	−292857.	−0.328191
$241$	539374.	0.598201	0.299100	−	0.954222i	$-0.403313\pi$
$241$	539374.	0.598201	0.299100	+	0.954222i	$0.403313\pi$
$242$	−38618.4	−0.0423893
$243$	1.89249e6	2.05598
$244$	−49778.9	−0.0535268
$245$	415789.	0.442545
$246$	−1.11141e6	−1.17095
$247$	402901.	0.420199
$248$	185796.	0.191826
$249$	3.21467e6	3.28578
$250$	41213.9	0.0417056
$251$	341061.	0.341703	0.170851	−	0.985297i	$-0.445348\pi$
$251$	341061.	0.341703	0.170851	+	0.985297i	$0.445348\pi$
$252$	197594.	0.196007
$253$	−7281.33	−0.00715170
$254$	8651.80	0.00841438
$255$	304830.	0.293567
$256$	−560815.	−0.534835
$257$	419458.	0.396146	0.198073	−	0.980187i	$-0.436532\pi$
$257$	419458.	0.396146	0.198073	+	0.980187i	$0.436532\pi$
$258$	−1.79834e6	−1.68199
$259$	−62654.1	−0.0580363
$260$	698731.	0.641027
$261$	−4.63736e6	−4.21376
$262$	86752.5	0.0780780
$263$	1.61846e6	1.44282	0.721410	−	0.692509i	$-0.243495\pi$
$263$	1.61846e6	1.44282	0.721410	+	0.692509i	$0.243495\pi$
$264$	−527244.	−0.465588
$265$	−883578.	−0.772912
$266$	12612.4	0.0109294
$267$	123142.	0.105713
$268$	882302.	0.750379
$269$	−971703.	−0.818753	−0.409377	−	0.912365i	$-0.634254\pi$
$269$	−971703.	−0.818753	−0.409377	+	0.912365i	$0.634254\pi$
$270$	673553.	0.562292
$271$	−174702.	−0.144503	−0.0722513	−	0.997386i	$-0.523018\pi$
$271$	−174702.	−0.144503	−0.0722513	+	0.997386i	$0.523018\pi$
$272$	−170304.	−0.139574
$273$	−428116.	−0.347660
$274$	−493081.	−0.396773
$275$	−75625.0	−0.0603023
$276$	−43642.3	−0.0344854
$277$	1.77895e6	1.39304	0.696522	−	0.717535i	$-0.254730\pi$
$277$	1.77895e6	1.39304	0.696522	+	0.717535i	$0.254730\pi$
$278$	−793102.	−0.615485
$279$	735596.	0.565756
$280$	49823.1	0.0379783
$281$	−955556.	−0.721922	−0.360961	−	0.932581i	$-0.617551\pi$
$281$	−955556.	−0.721922	−0.360961	+	0.932581i	$0.617551\pi$
$282$	1.55548e6	1.16477
$283$	1.95929e6	1.45423	0.727115	−	0.686515i	$-0.240861\pi$
$283$	1.95929e6	1.45423	0.727115	+	0.686515i	$0.240861\pi$
$284$	586561.	0.431536
$285$	−261367.	−0.190607
$286$	356205.	0.257505
$287$	−192715.	−0.138106
$288$	−3.50371e6	−2.48913
$289$	−1.24259e6	−0.875151
$290$	−513343.	−0.358437
$291$	−2.92280e6	−2.02333
$292$	2.10562e6	1.44518
$293$	1.76488e6	1.20101	0.600505	−	0.799621i	$-0.294966\pi$
$293$	1.76488e6	1.20101	0.600505	+	0.799621i	$0.294966\pi$
$294$	1.27046e6	0.857219
$295$	−970576.	−0.649343
$296$	711713.	0.472145
$297$	−1.23593e6	−0.813021
$298$	−791180.	−0.516101
$299$	67160.8	0.0434448
$300$	−453276.	−0.290776
$301$	−311826.	−0.198379
$302$	843430.	0.532147
$303$	−1.54767e6	−0.968438
$304$	146022.	0.0906223
$305$	−49694.3	−0.0305884
$306$	661554.	0.403889
$307$	−2.01834e6	−1.22222	−0.611109	−	0.791547i	$-0.709276\pi$
$307$	−2.01834e6	−1.22222	−0.611109	+	0.791547i	$0.709276\pi$
$308$	−40135.8	−0.0241077
$309$	−1.42787e6	−0.850732
$310$	81428.5	0.0481252
$311$	2.77984e6	1.62974	0.814870	−	0.579644i	$-0.196809\pi$
$311$	2.77984e6	1.62974	0.814870	+	0.579644i	$0.196809\pi$
$312$	4.86314e6	2.82833
$313$	1.70798e6	0.985424	0.492712	−	0.870193i	$-0.336006\pi$
$313$	1.70798e6	0.985424	0.492712	+	0.870193i	$0.336006\pi$
$314$	−126119.	−0.0721866
$315$	197258.	0.112010
$316$	2.07216e6	1.16736
$317$	1.89179e6	1.05736	0.528682	−	0.848820i	$-0.322686\pi$
$317$	1.89179e6	1.05736	0.528682	+	0.848820i	$0.322686\pi$
$318$	−2.69980e6	−1.49715
$319$	941953.	0.518266
$320$	−64256.0	−0.0350783
$321$	1.08645e6	0.588502
$322$	2102.41	0.00113000
$323$	−151992.	−0.0810616
$324$	−3.78277e6	−2.00193
$325$	697542.	0.366321
$326$	124877.	0.0650785
$327$	4.68717e6	2.42405
$328$	2.18913e6	1.12354
$329$	269715.	0.137377
$330$	−231075.	−0.116807
$331$	−249208.	−0.125023	−0.0625117	−	0.998044i	$-0.519911\pi$
$331$	−249208.	−0.125023	−0.0625117	+	0.998044i	$0.519911\pi$
$332$	−2.77980e6	−1.38410
$333$	2.81779e6	1.39251
$334$	−855854.	−0.419792
$335$	880802.	0.428811
$336$	−155161.	−0.0749781
$337$	−2.06614e6	−0.991025	−0.495513	−	0.868601i	$-0.665020\pi$
$337$	−2.06614e6	−0.991025	−0.495513	+	0.868601i	$0.665020\pi$
$338$	−2.30617e6	−1.09799
$339$	3.97688e6	1.87951
$340$	−263593.	−0.123662
$341$	−149416.	−0.0695844
$342$	−567229.	−0.262236
$343$	442910.	0.203273
$344$	3.54216e6	1.61388
$345$	−43568.1	−0.0197070
$346$	22171.4	0.00995643
$347$	415622.	0.185300	0.0926499	−	0.995699i	$-0.470466\pi$
$347$	415622.	0.185300	0.0926499	+	0.995699i	$0.470466\pi$
$348$	5.64581e6	2.49907
$349$	−3.55154e6	−1.56082	−0.780410	−	0.625268i	$-0.784990\pi$
$349$	−3.55154e6	−1.56082	−0.780410	+	0.625268i	$0.784990\pi$
$350$	21835.9	0.00952800
$351$	1.13998e7	4.93890
$352$	711682.	0.306147
$353$	2.86708e6	1.22462	0.612312	−	0.790616i	$-0.290240\pi$
$353$	2.86708e6	1.22462	0.612312	+	0.790616i	$0.290240\pi$
$354$	−2.96563e6	−1.25779
$355$	585564.	0.246606
$356$	−106483.	−0.0445303
$357$	161505.	0.0670678
$358$	127289.	0.0524910
$359$	−63997.7	−0.0262077	−0.0131038	−	0.999914i	$-0.504171\pi$
$359$	−63997.7	−0.0262077	−0.0131038	+	0.999914i	$0.504171\pi$
$360$	−2.24073e6	−0.911243
$361$	130321.	0.0526316
$362$	−1.03835e6	−0.416460
$363$	424008.	0.168891
$364$	370201.	0.146448
$365$	2.10204e6	0.825865
$366$	−151843.	−0.0592503
$367$	3.33223e6	1.29143	0.645714	−	0.763579i	$-0.276560\pi$
$367$	3.33223e6	1.29143	0.645714	+	0.763579i	$0.276560\pi$
$368$	24340.9	0.00936953
$369$	8.66713e6	3.31367
$370$	311922.	0.118452
$371$	−468137.	−0.176579
$372$	−895560.	−0.335535
$373$	−1.85978e6	−0.692133	−0.346067	−	0.938210i	$-0.612483\pi$
$373$	−1.85978e6	−0.692133	−0.346067	+	0.938210i	$0.612483\pi$
$374$	−134377.	−0.0496757
$375$	−452505.	−0.166167
$376$	−3.06380e6	−1.11761
$377$	−8.68829e6	−3.14834
$378$	356861.	0.128461
$379$	−2.64272e6	−0.945047	−0.472523	−	0.881318i	$-0.656657\pi$
$379$	−2.64272e6	−0.945047	−0.472523	+	0.881318i	$0.656657\pi$
$380$	226009.	0.0802911
$381$	−94991.7	−0.0335253
$382$	−2.22397e6	−0.779778
$383$	926171.	0.322622	0.161311	−	0.986904i	$-0.448428\pi$
$383$	926171.	0.322622	0.161311	+	0.986904i	$0.448428\pi$
$384$	5.25439e6	1.81842
$385$	−40067.6	−0.0137766
$386$	−2.45004e6	−0.836961
$387$	1.40240e7	4.75987
$388$	2.52741e6	0.852307
$389$	−1.22829e6	−0.411555	−0.205777	−	0.978599i	$-0.565972\pi$
$389$	−1.22829e6	−0.411555	−0.205777	+	0.978599i	$0.565972\pi$
$390$	2.13136e6	0.709572
$391$	−25336.1	−0.00838103
$392$	−2.50240e6	−0.822509
$393$	−952492.	−0.311085
$394$	393976.	0.127859
$395$	2.06864e6	0.667102
$396$	1.80506e6	0.578434
$397$	−3.98015e6	−1.26743	−0.633714	−	0.773567i	$-0.718470\pi$
$397$	−3.98015e6	−1.26743	−0.633714	+	0.773567i	$0.718470\pi$
$398$	1.08224e6	0.342464
$399$	−138477.	−0.0435457
$400$	252809.	0.0790027
$401$	−874110.	−0.271460	−0.135730	−	0.990746i	$-0.543338\pi$
$401$	−874110.	−0.271460	−0.135730	+	0.990746i	$0.543338\pi$
$402$	2.69132e6	0.830616
$403$	1.37817e6	0.422708
$404$	1.33830e6	0.407945
$405$	−3.77634e6	−1.14402
$406$	−271979.	−0.0818880
$407$	−572357.	−0.171270
$408$	−1.83460e6	−0.545620
$409$	947244.	0.279997	0.139999	−	0.990152i	$-0.455290\pi$
$409$	947244.	0.279997	0.139999	+	0.990152i	$0.455290\pi$
$410$	959428.	0.281872
$411$	5.41374e6	1.58086
$412$	1.23471e6	0.358362
$413$	−514229.	−0.148348
$414$	−94553.3	−0.0271129
$415$	−2.77507e6	−0.790958
$416$	−6.56435e6	−1.85977
$417$	8.70780e6	2.45227
$418$	115217.	0.0322534
$419$	624712.	0.173838	0.0869191	−	0.996215i	$-0.472298\pi$
$419$	624712.	0.173838	0.0869191	+	0.996215i	$0.472298\pi$
$420$	−240154.	−0.0664304
$421$	−3.60469e6	−0.991202	−0.495601	−	0.868550i	$-0.665052\pi$
$421$	−3.60469e6	−0.991202	−0.495601	+	0.868550i	$0.665052\pi$
$422$	2.49507e6	0.682026
$423$	−1.21301e7	−3.29620
$424$	5.31775e6	1.43653
$425$	−263144.	−0.0706678
$426$	1.78921e6	0.477680
$427$	−26329.0	−0.00698818
$428$	−939478.	−0.247900
$429$	−3.91092e6	−1.02597
$430$	1.55242e6	0.404891
$431$	1.90545e6	0.494089	0.247044	−	0.969004i	$-0.420541\pi$
$431$	1.90545e6	0.494089	0.247044	+	0.969004i	$0.420541\pi$
$432$	4.13161e6	1.06515
$433$	−3.74309e6	−0.959423	−0.479712	−	0.877426i	$-0.659259\pi$
$433$	−3.74309e6	−0.959423	−0.479712	+	0.877426i	$0.659259\pi$
$434$	43142.4	0.0109946
$435$	5.63621e6	1.42812
$436$	−4.05309e6	−1.02110
$437$	21723.6	0.00544163
$438$	6.42286e6	1.59972
$439$	−998766.	−0.247345	−0.123672	−	0.992323i	$-0.539467\pi$
$439$	−998766.	−0.247345	−0.123672	+	0.992323i	$0.539467\pi$
$440$	455144.	0.112077
$441$	−9.90741e6	−2.42585
$442$	1.23945e6	0.301768
$443$	6.62836e6	1.60471	0.802356	−	0.596846i	$-0.203580\pi$
$443$	6.62836e6	1.60471	0.802356	+	0.596846i	$0.203580\pi$
$444$	−3.43055e6	−0.825860
$445$	−106302.	−0.0254473
$446$	−2.56117e6	−0.609680
$447$	8.68669e6	2.05630
$448$	−34044.0	−0.00801394
$449$	2.31828e6	0.542687	0.271344	−	0.962483i	$-0.412532\pi$
$449$	2.31828e6	0.542687	0.271344	+	0.962483i	$0.412532\pi$
$450$	−982044.	−0.228612
$451$	−1.76049e6	−0.407561
$452$	−3.43890e6	−0.791722
$453$	−9.26036e6	−2.12023
$454$	−3.31195e6	−0.754126
$455$	369571.	0.0836893
$456$	1.57302e6	0.354259
$457$	3.69928e6	0.828566	0.414283	−	0.910148i	$-0.364032\pi$
$457$	3.69928e6	0.828566	0.414283	+	0.910148i	$0.364032\pi$
$458$	−40213.0	−0.00895783
$459$	−4.30053e6	−0.952774
$460$	37674.2	0.00830137
$461$	2727.39	0.000597717 0	0.000298859	−	1.00000i	$-0.499905\pi$
$461$	2727.39	0.000597717 0	0.000298859		1.00000i	$0.499905\pi$
$462$	−122428.	−0.0266855
$463$	2.64563e6	0.573557	0.286778	−	0.957997i	$-0.407416\pi$
$463$	2.64563e6	0.573557	0.286778	+	0.957997i	$0.407416\pi$
$464$	−3.14888e6	−0.678986
$465$	−894037.	−0.191745
$466$	712678.	0.152030
$467$	6.02838e6	1.27911	0.639555	−	0.768745i	$-0.279119\pi$
$467$	6.02838e6	1.27911	0.639555	+	0.768745i	$0.279119\pi$
$468$	−1.66493e7	−3.51384
$469$	466666.	0.0979657
$470$	−1.34277e6	−0.280386
$471$	1.38471e6	0.287612
$472$	5.84134e6	1.20686
$473$	−2.84859e6	−0.585434
$474$	6.32080e6	1.29219
$475$	225625.	0.0458831
$476$	−139656.	−0.0282516
$477$	2.10539e7	4.23678
$478$	3.71696e6	0.744077
$479$	103202.	0.0205517	0.0102759	−	0.999947i	$-0.496729\pi$
$479$	103202.	0.0205517	0.0102759	+	0.999947i	$0.496729\pi$
$480$	4.25838e6	0.843608
$481$	5.27925e6	1.04042
$482$	−1.42270e6	−0.278931
$483$	−23083.2	−0.00450224
$484$	−366648.	−0.0711437
$485$	2.52311e6	0.487059
$486$	−4.99181e6	−0.958666
$487$	9.54630e6	1.82395	0.911975	−	0.410246i	$-0.134557\pi$
$487$	9.54630e6	1.82395	0.911975	+	0.410246i	$0.134557\pi$
$488$	299082.	0.0568512
$489$	−1.37107e6	−0.259292
$490$	−1.09672e6	−0.206351
$491$	1.35010e6	0.252734	0.126367	−	0.991984i	$-0.459668\pi$
$491$	1.35010e6	0.252734	0.126367	+	0.991984i	$0.459668\pi$
$492$	−1.05519e7	−1.96525
$493$	3.27761e6	0.607352
$494$	−1.06273e6	−0.195932
$495$	1.80199e6	0.330552
$496$	499487.	0.0911633
$497$	310243.	0.0563392
$498$	−8.47932e6	−1.53210
$499$	−9.15984e6	−1.64678	−0.823391	−	0.567474i	$-0.807921\pi$
$499$	−9.15984e6	−1.64678	−0.823391	+	0.567474i	$0.807921\pi$
$500$	391290.	0.0699962
$501$	9.39678e6	1.67257
$502$	−899615.	−0.159330
$503$	−6.90510e6	−1.21689	−0.608443	−	0.793598i	$-0.708206\pi$
$503$	−6.90510e6	−1.21689	−0.608443	+	0.793598i	$0.708206\pi$
$504$	−1.18718e6	−0.208181
$505$	1.33603e6	0.233124
$506$	19205.9	0.00333471
$507$	2.53204e7	4.37473
$508$	82141.3	0.0141222
$509$	−4.96020e6	−0.848603	−0.424301	−	0.905521i	$-0.639480\pi$
$509$	−4.96020e6	−0.848603	−0.424301	+	0.905521i	$0.639480\pi$
$510$	−804046.	−0.136885
$511$	1.11370e6	0.188676
$512$	−4.32663e6	−0.729416
$513$	3.68735e6	0.618616
$514$	−1.10640e6	−0.184716
$515$	1.23261e6	0.204790
$516$	−1.70737e7	−2.82295
$517$	2.46389e6	0.405411
$518$	165262.	0.0270613
$519$	−243429.	−0.0396693
$520$	−4.19811e6	−0.680841
$521$	−1.08377e7	−1.74922	−0.874608	−	0.484830i	$-0.838881\pi$
$521$	−1.08377e7	−1.74922	−0.874608	+	0.484830i	$0.838881\pi$
$522$	1.22319e7	1.96480
$523$	−4.54245e6	−0.726166	−0.363083	−	0.931757i	$-0.618276\pi$
$523$	−4.54245e6	−0.726166	−0.363083	+	0.931757i	$0.618276\pi$
$524$	823639.	0.131042
$525$	−239746.	−0.0379623
$526$	−4.26899e6	−0.672761
$527$	−519908.	−0.0815455
$528$	−1.41743e6	−0.221266
$529$	−6.43272e6	−0.999437
$530$	2.33061e6	0.360395
$531$	2.31268e7	3.55943
$532$	119744.	0.0183432
$533$	1.62382e7	2.47583
$534$	−324810.	−0.0492919
$535$	−937880.	−0.141665
$536$	−5.30104e6	−0.796984
$537$	−1.39756e6	−0.209139
$538$	2.56305e6	0.381770
$539$	2.01242e6	0.298364
$540$	6.39480e6	0.943718
$541$	−3.36100e6	−0.493713	−0.246857	−	0.969052i	$-0.579398\pi$
$541$	−3.36100e6	−0.493713	−0.246857	+	0.969052i	$0.579398\pi$
$542$	460811.	0.0673790
$543$	1.14005e7	1.65930
$544$	2.47637e6	0.358771
$545$	−4.04620e6	−0.583520
$546$	1.12924e6	0.162108
$547$	1.22023e6	0.174371	0.0871853	−	0.996192i	$-0.472213\pi$
$547$	1.22023e6	0.174371	0.0871853	+	0.996192i	$0.472213\pi$
$548$	−4.68138e6	−0.665920
$549$	1.18411e6	0.167673
$550$	199475.	0.0281179
$551$	−2.81029e6	−0.394341
$552$	262212.	0.0366272
$553$	1.09601e6	0.152405
$554$	−4.69233e6	−0.649552
$555$	−3.42472e6	−0.471946
$556$	−7.52982e6	−1.03299
$557$	888822.	0.121388	0.0606942	−	0.998156i	$-0.480669\pi$
$557$	888822.	0.121388	0.0606942	+	0.998156i	$0.480669\pi$
$558$	−1.94028e6	−0.263802
$559$	2.62746e7	3.55637
$560$	133943.	0.0180488
$561$	1.47538e6	0.197923
$562$	2.52046e6	0.336620
$563$	−1.07192e7	−1.42525	−0.712626	−	0.701544i	$-0.752494\pi$
$563$	−1.07192e7	−1.42525	−0.712626	+	0.701544i	$0.752494\pi$
$564$	1.47679e7	1.95489
$565$	−3.43305e6	−0.452438
$566$	−5.16801e6	−0.678082
$567$	−2.00078e6	−0.261361
$568$	−3.52417e6	−0.458339
$569$	3.54510e6	0.459037	0.229518	−	0.973304i	$-0.426285\pi$
$569$	3.54510e6	0.459037	0.229518	+	0.973304i	$0.426285\pi$
$570$	689405.	0.0888765
$571$	1.35589e6	0.174035	0.0870173	−	0.996207i	$-0.472266\pi$
$571$	1.35589e6	0.174035	0.0870173	+	0.996207i	$0.472266\pi$
$572$	3.38186e6	0.432180
$573$	2.44179e7	3.10686
$574$	508323.	0.0643962
$575$	37610.2	0.00474390
$576$	1.53109e6	0.192285
$577$	1.27290e7	1.59167	0.795835	−	0.605513i	$-0.207032\pi$
$577$	1.27290e7	1.59167	0.795835	+	0.605513i	$0.207032\pi$
$578$	3.27757e6	0.408068
$579$	2.69000e7	3.33469
$580$	−4.87375e6	−0.601579
$581$	−1.47028e6	−0.180701
$582$	7.70945e6	0.943443
$583$	−4.27652e6	−0.521097
$584$	−1.26510e7	−1.53494
$585$	−1.66210e7	−2.00802
$586$	−4.65521e6	−0.560010
$587$	2.15545e6	0.258192	0.129096	−	0.991632i	$-0.458793\pi$
$587$	2.15545e6	0.258192	0.129096	+	0.991632i	$0.458793\pi$
$588$	1.20619e7	1.43871
$589$	445779.	0.0529458
$590$	2.56008e6	0.302777
$591$	−4.32563e6	−0.509426
$592$	1.91335e6	0.224383
$593$	−6.20938e6	−0.725123	−0.362562	−	0.931960i	$-0.618098\pi$
$593$	−6.20938e6	−0.725123	−0.362562	+	0.931960i	$0.618098\pi$
$594$	3.26000e6	0.379098
$595$	−139419.	−0.0161447
$596$	−7.51157e6	−0.866193
$597$	−1.18823e7	−1.36447
$598$	−177150.	−0.0202576
$599$	−2.41455e6	−0.274960	−0.137480	−	0.990505i	$-0.543900\pi$
$599$	−2.41455e6	−0.274960	−0.137480	+	0.990505i	$0.543900\pi$
$600$	2.72337e6	0.308836
$601$	−1.10390e7	−1.24665	−0.623326	−	0.781962i	$-0.714219\pi$
$601$	−1.10390e7	−1.24665	−0.623326	+	0.781962i	$0.714219\pi$
$602$	822502.	0.0925008
$603$	−2.09877e7	−2.35056
$604$	8.00763e6	0.893124
$605$	−366025.	−0.0406558
$606$	4.08228e6	0.451566
$607$	3.97127e6	0.437479	0.218740	−	0.975783i	$-0.429805\pi$
$607$	3.97127e6	0.437479	0.218740	+	0.975783i	$0.429805\pi$
$608$	−2.12328e6	−0.232943
$609$	2.98617e6	0.326266
$610$	131078.	0.0142628
$611$	−2.27262e7	−2.46277
$612$	6.28088e6	0.677863
$613$	−3.46188e6	−0.372101	−0.186050	−	0.982540i	$-0.559569\pi$
$613$	−3.46188e6	−0.372101	−0.186050	+	0.982540i	$0.559569\pi$
$614$	5.32376e6	0.569898
$615$	−1.05340e7	−1.12306
$616$	241144.	0.0256050
$617$	3.22889e6	0.341461	0.170730	−	0.985318i	$-0.445387\pi$
$617$	3.22889e6	0.341461	0.170730	+	0.985318i	$0.445387\pi$
$618$	3.76628e6	0.396681
$619$	−9.31754e6	−0.977406	−0.488703	−	0.872450i	$-0.662530\pi$
$619$	−9.31754e6	−0.977406	−0.488703	+	0.872450i	$0.662530\pi$
$620$	773093.	0.0807704
$621$	614657.	0.0639594
$622$	−7.33235e6	−0.759919
$623$	−56320.9	−0.00581365
$624$	1.30739e7	1.34414
$625$	390625.	0.0400000
$626$	−4.50514e6	−0.459486
$627$	−1.26502e6	−0.128507
$628$	−1.19739e6	−0.121154
$629$	−1.99157e6	−0.200710
$630$	−520306.	−0.0522285
$631$	1.86054e7	1.86023	0.930115	−	0.367268i	$-0.119707\pi$
$631$	1.86054e7	1.86023	0.930115	+	0.367268i	$0.119707\pi$
$632$	−1.24500e7	−1.23987
$633$	−2.73944e7	−2.71739
$634$	−4.98996e6	−0.493030
$635$	82001.6	0.00807027
$636$	−2.56323e7	−2.51272
$637$	−1.85619e7	−1.81249
$638$	−2.48458e6	−0.241658
$639$	−1.39528e7	−1.35179
$640$	−4.53585e6	−0.437733
$641$	1.85426e7	1.78249	0.891243	−	0.453526i	$-0.149834\pi$
$641$	1.85426e7	1.78249	0.891243	+	0.453526i	$0.149834\pi$
$642$	−2.86572e6	−0.274408
$643$	−1.02980e7	−0.982257	−0.491129	−	0.871087i	$-0.663415\pi$
$643$	−1.02980e7	−0.982257	−0.491129	+	0.871087i	$0.663415\pi$
$644$	19960.5	0.00189652
$645$	−1.70447e7	−1.61320
$646$	400908.	0.0377976
$647$	−347427.	−0.0326289	−0.0163145	−	0.999867i	$-0.505193\pi$
$647$	−347427.	−0.0326289	−0.0163145	+	0.999867i	$0.505193\pi$
$648$	2.27276e7	2.12626
$649$	−4.69759e6	−0.437787
$650$	−1.83990e6	−0.170809
$651$	−473678.	−0.0438057
$652$	1.18560e6	0.109224
$653$	−1.14826e7	−1.05379	−0.526897	−	0.849929i	$-0.676645\pi$
$653$	−1.14826e7	−1.05379	−0.526897	+	0.849929i	$0.676645\pi$
$654$	−1.23633e7	−1.13029
$655$	822239.	0.0748850
$656$	5.88518e6	0.533950
$657$	−5.00874e7	−4.52705
$658$	−711424.	−0.0640566
$659$	−1.75658e7	−1.57563	−0.787814	−	0.615913i	$-0.788787\pi$
$659$	−1.75658e7	−1.57563	−0.787814	+	0.615913i	$0.788787\pi$
$660$	−2.19385e6	−0.196041
$661$	1.10252e7	0.981487	0.490743	−	0.871304i	$-0.336725\pi$
$661$	1.10252e7	0.981487	0.490743	+	0.871304i	$0.336725\pi$
$662$	657333.	0.0582962
$663$	−1.36084e7	−1.20233
$664$	1.67016e7	1.47007
$665$	119540.	0.0104824
$666$	−7.43246e6	−0.649303
$667$	−468456.	−0.0407713
$668$	−8.12559e6	−0.704553
$669$	2.81202e7	2.42914
$670$	−2.32328e6	−0.199947
$671$	−240520.	−0.0206227
$672$	2.25617e6	0.192730
$673$	1.75142e7	1.49057	0.745284	−	0.666747i	$-0.232314\pi$
$673$	1.75142e7	1.49057	0.745284	+	0.666747i	$0.232314\pi$
$674$	5.44984e6	0.462098
$675$	6.38392e6	0.539297
$676$	−2.18951e7	−1.84281
$677$	−1.25430e7	−1.05179	−0.525895	−	0.850550i	$-0.676269\pi$
$677$	−1.25430e7	−1.05179	−0.525895	+	0.850550i	$0.676269\pi$
$678$	−1.04898e7	−0.876381
$679$	1.33679e6	0.111273
$680$	1.58372e6	0.131342
$681$	3.63633e7	3.00466
$682$	394114.	0.0324460
$683$	−2.26109e6	−0.185466	−0.0927332	−	0.995691i	$-0.529560\pi$
$683$	−2.26109e6	−0.185466	−0.0927332	+	0.995691i	$0.529560\pi$
$684$	−5.38534e6	−0.440122
$685$	−4.67341e6	−0.380547
$686$	−1.16826e6	−0.0947827
$687$	441515.	0.0356906
$688$	9.52263e6	0.766983
$689$	3.94453e7	3.16554
$690$	114919.	0.00918903
$691$	2.12302e6	0.169145	0.0845726	−	0.996417i	$-0.473048\pi$
$691$	2.12302e6	0.169145	0.0845726	+	0.996417i	$0.473048\pi$
$692$	210499.	0.0167103
$693$	954729.	0.0755174
$694$	−1.09628e6	−0.0864021
$695$	−7.51701e6	−0.590314
$696$	−3.39211e7	−2.65428
$697$	−6.12579e6	−0.477618
$698$	9.36786e6	0.727783
$699$	−7.82478e6	−0.605731
$700$	207313.	0.0159912
$701$	−3.60192e6	−0.276847	−0.138423	−	0.990373i	$-0.544203\pi$
$701$	−3.60192e6	−0.276847	−0.138423	+	0.990373i	$0.544203\pi$
$702$	−3.00692e7	−2.30292
$703$	1.70761e6	0.130317
$704$	−310999.	−0.0236498
$705$	1.47428e7	1.11714
$706$	−7.56247e6	−0.571020
$707$	707853.	0.0532592
$708$	−2.81560e7	−2.11100
$709$	−8.68706e6	−0.649019	−0.324509	−	0.945882i	$-0.605199\pi$
$709$	−8.68706e6	−0.649019	−0.324509	+	0.945882i	$0.605199\pi$
$710$	−1.54454e6	−0.114988
$711$	−4.92915e7	−3.65677
$712$	639771.	0.0472960
$713$	74308.4	0.00547412
$714$	−425999.	−0.0312725
$715$	3.37611e6	0.246974
$716$	1.20850e6	0.0880977
$717$	−4.08100e7	−2.96462
$718$	168806.	0.0122202
$719$	−2.25693e7	−1.62815	−0.814076	−	0.580758i	$-0.802756\pi$
$719$	−2.25693e7	−1.62815	−0.814076	+	0.580758i	$0.802756\pi$
$720$	−6.02392e6	−0.433060
$721$	653061.	0.0467859
$722$	−343747.	−0.0245412
$723$	1.56204e7	1.11134
$724$	−9.85825e6	−0.698962
$725$	−4.86546e6	−0.343779
$726$	−1.11840e6	−0.0787510
$727$	−2.09237e7	−1.46826	−0.734130	−	0.679009i	$-0.762410\pi$
$727$	−2.09237e7	−1.46826	−0.734130	+	0.679009i	$0.762410\pi$
$728$	−2.22424e6	−0.155544
$729$	1.81011e7	1.26150
$730$	−5.54454e6	−0.385086
$731$	−9.91195e6	−0.686066
$732$	−1.44161e6	−0.0994423
$733$	−2.61465e7	−1.79744	−0.898718	−	0.438527i	$-0.855500\pi$
$733$	−2.61465e7	−1.79744	−0.898718	+	0.438527i	$0.855500\pi$
$734$	−8.78940e6	−0.602170
$735$	1.20414e7	0.822163
$736$	−353937.	−0.0240842
$737$	4.26308e6	0.289105
$738$	−2.28612e7	−1.54511
$739$	−1.12258e7	−0.756148	−0.378074	−	0.925775i	$-0.623414\pi$
$739$	−1.12258e7	−0.756148	−0.378074	+	0.925775i	$0.623414\pi$
$740$	2.96143e6	0.198802
$741$	1.16681e7	0.780648
$742$	1.23480e6	0.0823354
$743$	−2.35392e6	−0.156430	−0.0782150	−	0.996937i	$-0.524922\pi$
$743$	−2.35392e6	−0.156430	−0.0782150	+	0.996937i	$0.524922\pi$
$744$	5.38070e6	0.356374
$745$	−7.49879e6	−0.494995
$746$	4.90553e6	0.322729
$747$	6.61243e7	4.33570
$748$	−1.27579e6	−0.0833728
$749$	−496907.	−0.0323646
$750$	1.19357e6	0.0774808
$751$	−6.91444e6	−0.447360	−0.223680	−	0.974663i	$-0.571807\pi$
$751$	−6.91444e6	−0.447360	−0.223680	+	0.974663i	$0.571807\pi$
$752$	−8.23661e6	−0.531134
$753$	9.87724e6	0.634817
$754$	2.29170e7	1.46801
$755$	7.99401e6	0.510385
$756$	3.38809e6	0.215601
$757$	−2.07163e6	−0.131393	−0.0656965	−	0.997840i	$-0.520927\pi$
$757$	−2.07163e6	−0.131393	−0.0656965	+	0.997840i	$0.520927\pi$
$758$	6.97068e6	0.440659
$759$	−210870.	−0.0132865
$760$	−1.35791e6	−0.0852779
$761$	4.27342e6	0.267494	0.133747	−	0.991016i	$-0.457299\pi$
$761$	4.27342e6	0.267494	0.133747	+	0.991016i	$0.457299\pi$
$762$	250559.	0.0156323
$763$	−2.14375e6	−0.133310
$764$	−2.11147e7	−1.30873
$765$	6.27020e6	0.387371
$766$	−2.44295e6	−0.150433
$767$	4.33291e7	2.65945
$768$	−1.62414e7	−0.993618
$769$	−2.13488e7	−1.30184	−0.650920	−	0.759146i	$-0.725617\pi$
$769$	−2.13488e7	−1.30184	−0.650920	+	0.759146i	$0.725617\pi$
$770$	105686.	0.00642377
$771$	1.21476e7	0.735962
$772$	−2.32610e7	−1.40471
$773$	1.37961e7	0.830439	0.415220	−	0.909721i	$-0.363705\pi$
$773$	1.37961e7	0.830439	0.415220	+	0.909721i	$0.363705\pi$
$774$	−3.69910e7	−2.21944
$775$	771778.	0.0461571
$776$	−1.51852e7	−0.905242
$777$	−1.81448e6	−0.107820
$778$	3.23986e6	0.191901
$779$	5.25237e6	0.310107
$780$	2.02355e7	1.19090
$781$	2.83413e6	0.166262
$782$	66828.8	0.00390793
$783$	−7.95154e7	−4.63497
$784$	−6.72736e6	−0.390890
$785$	−1.19535e6	−0.0692345
$786$	2.51238e6	0.145054
$787$	−1.04182e6	−0.0599595	−0.0299797	−	0.999551i	$-0.509544\pi$
$787$	−1.04182e6	−0.0599595	−0.0299797	+	0.999551i	$0.509544\pi$
$788$	3.74046e6	0.214590
$789$	4.68710e7	2.68048
$790$	−5.45644e6	−0.311058
$791$	−1.81889e6	−0.103363
$792$	−1.08452e7	−0.614360
$793$	2.21849e6	0.125278
$794$	1.04984e7	0.590979
$795$	−2.55887e7	−1.43592
$796$	1.02749e7	0.574771
$797$	−1.02568e6	−0.0571963	−0.0285982	−	0.999591i	$-0.509104\pi$
$797$	−1.02568e6	−0.0571963	−0.0285982	+	0.999591i	$0.509104\pi$
$798$	365260.	0.0203046
$799$	8.57335e6	0.475099
$800$	−3.67605e6	−0.203075
$801$	2.53296e6	0.139491
$802$	2.30563e6	0.126577
$803$	1.01739e7	0.556798
$804$	2.55517e7	1.39406
$805$	19926.6	0.00108379
$806$	−3.63519e6	−0.197101
$807$	−2.81408e7	−1.52108
$808$	−8.04079e6	−0.433282
$809$	−2.57521e7	−1.38338	−0.691691	−	0.722194i	$-0.743134\pi$
$809$	−2.57521e7	−1.38338	−0.691691	+	0.722194i	$0.743134\pi$
$810$	9.96083e6	0.533437
$811$	3.80441e6	0.203112	0.101556	−	0.994830i	$-0.467618\pi$
$811$	3.80441e6	0.203112	0.101556	+	0.994830i	$0.467618\pi$
$812$	−2.58220e6	−0.137436
$813$	−5.05944e6	−0.268458
$814$	1.50970e6	0.0798601
$815$	1.18358e6	0.0624171
$816$	−4.93207e6	−0.259301
$817$	8.49870e6	0.445448
$818$	−2.49854e6	−0.130558
$819$	−8.80614e6	−0.458749
$820$	9.10893e6	0.473078
$821$	−3.19605e7	−1.65484	−0.827420	−	0.561584i	$-0.810192\pi$
$821$	−3.19605e7	−1.65484	−0.827420	+	0.561584i	$0.810192\pi$
$822$	−1.42798e7	−0.737126
$823$	−1.69954e7	−0.874644	−0.437322	−	0.899305i	$-0.644073\pi$
$823$	−1.69954e7	−0.874644	−0.437322	+	0.899305i	$0.644073\pi$
$824$	−7.41838e6	−0.380619
$825$	−2.19012e6	−0.112030
$826$	1.35638e6	0.0691721
$827$	−2.31437e7	−1.17671	−0.588354	−	0.808604i	$-0.700224\pi$
$827$	−2.31437e7	−1.17671	−0.588354	+	0.808604i	$0.700224\pi$
$828$	−897701.	−0.0455047
$829$	3.41061e7	1.72364	0.861819	−	0.507216i	$-0.169326\pi$
$829$	3.41061e7	1.72364	0.861819	+	0.507216i	$0.169326\pi$
$830$	7.31978e6	0.368810
$831$	5.15190e7	2.58800
$832$	2.86856e6	0.143667
$833$	7.00240e6	0.349651
$834$	−2.29685e7	−1.14345
$835$	−8.11177e6	−0.402624
$836$	1.09389e6	0.0541322
$837$	1.26131e7	0.622310
$838$	−1.64780e6	−0.0810576
$839$	−300692.	−0.0147474	−0.00737371	−	0.999973i	$-0.502347\pi$
$839$	−300692.	−0.0147474	−0.00737371	+	0.999973i	$0.502347\pi$
$840$	1.44289e6	0.0705563
$841$	4.00909e7	1.95459
$842$	9.50805e6	0.462180
$843$	−2.76732e7	−1.34119
$844$	2.36885e7	1.14467
$845$	−2.18579e7	−1.05309
$846$	3.19954e7	1.53696
$847$	−193927.	−0.00928816
$848$	1.42961e7	0.682696
$849$	5.67417e7	2.70168
$850$	694094.	0.0329512
$851$	284647.	0.0134736
$852$	1.69870e7	0.801710
$853$	−1.92166e7	−0.904281	−0.452140	−	0.891947i	$-0.649339\pi$
$853$	−1.92166e7	−0.904281	−0.452140	+	0.891947i	$0.649339\pi$
$854$	69447.7	0.00325847
$855$	−5.37619e6	−0.251512
$856$	5.64456e6	0.263297
$857$	3.80144e7	1.76806	0.884029	−	0.467432i	$-0.154821\pi$
$857$	3.80144e7	1.76806	0.884029	+	0.467432i	$0.154821\pi$
$858$	1.03158e7	0.478393
$859$	7.56355e6	0.349738	0.174869	−	0.984592i	$-0.444050\pi$
$859$	7.56355e6	0.349738	0.174869	+	0.984592i	$0.444050\pi$
$860$	1.47389e7	0.679545
$861$	−5.58109e6	−0.256573
$862$	−5.02600e6	−0.230385
$863$	3.02445e7	1.38236	0.691178	−	0.722684i	$-0.257092\pi$
$863$	3.02445e7	1.38236	0.691178	+	0.722684i	$0.257092\pi$
$864$	−6.00770e7	−2.73794
$865$	210141.	0.00954926
$866$	9.87311e6	0.447362
$867$	−3.59858e7	−1.62586
$868$	409599.	0.0184527
$869$	1.00122e7	0.449760
$870$	−1.48666e7	−0.665906
$871$	−3.93214e7	−1.75624
$872$	2.43518e7	1.08452
$873$	−6.01206e7	−2.66985
$874$	−57300.3	−0.00253734
$875$	206961.	0.00913834
$876$	6.09795e7	2.68487
$877$	3.44726e7	1.51348	0.756738	−	0.653719i	$-0.226792\pi$
$877$	3.44726e7	1.51348	0.756738	+	0.653719i	$0.226792\pi$
$878$	2.63444e6	0.115332
$879$	5.11115e7	2.23124
$880$	1.22359e6	0.0532636
$881$	4.10240e7	1.78073	0.890366	−	0.455246i	$-0.150449\pi$
$881$	4.10240e7	1.78073	0.890366	+	0.455246i	$0.150449\pi$
$882$	2.61327e7	1.13113
$883$	2.05924e7	0.888803	0.444402	−	0.895828i	$-0.353416\pi$
$883$	2.05924e7	0.888803	0.444402	+	0.895828i	$0.353416\pi$
$884$	1.17675e7	0.506469
$885$	−2.81082e7	−1.20635
$886$	−1.74836e7	−0.748249
$887$	−1.21698e7	−0.519367	−0.259683	−	0.965694i	$-0.583618\pi$
$887$	−1.21698e7	−0.519367	−0.259683	+	0.965694i	$0.583618\pi$
$888$	2.06114e7	0.877153
$889$	43446.0	0.00184372
$890$	280392.	0.0118656
$891$	−1.82775e7	−0.771298
$892$	−2.43161e7	−1.02325
$893$	−7.35096e6	−0.308472
$894$	−2.29128e7	−0.958815
$895$	1.20645e6	0.0503443
$896$	−2.40318e6	−0.100004
$897$	1.94500e6	0.0807120
$898$	−6.11490e6	−0.253045
$899$	−9.61294e6	−0.396695
$900$	−9.32366e6	−0.383690
$901$	−1.48806e7	−0.610671
$902$	4.64363e6	0.190038
$903$	−9.03059e6	−0.368550
$904$	2.06616e7	0.840895
$905$	−9.84149e6	−0.399429
$906$	2.44260e7	0.988625
$907$	−1.29512e7	−0.522748	−0.261374	−	0.965238i	$-0.584176\pi$
$907$	−1.29512e7	−0.522748	−0.261374	+	0.965238i	$0.584176\pi$
$908$	−3.14441e7	−1.26568
$909$	−3.18348e7	−1.27789
$910$	−974815.	−0.0390228
$911$	−7.01115e6	−0.279894	−0.139947	−	0.990159i	$-0.544693\pi$
$911$	−7.01115e6	−0.279894	−0.139947	+	0.990159i	$0.544693\pi$
$912$	4.22885e6	0.168358
$913$	−1.34313e7	−0.533264
$914$	−9.75756e6	−0.386345
$915$	−1.43916e6	−0.0568273
$916$	−381787.	−0.0150343
$917$	435638.	0.0171081
$918$	1.13435e7	0.444262
$919$	−1.35572e7	−0.529519	−0.264760	−	0.964314i	$-0.585293\pi$
$919$	−1.35572e7	−0.529519	−0.264760	+	0.964314i	$0.585293\pi$
$920$	−226354.	−0.00881696
$921$	−5.84517e7	−2.27064
$922$	−7194.03	−0.000278705 0
$923$	−2.61412e7	−1.01000
$924$	−1.16235e6	−0.0447873
$925$	2.95639e6	0.113608
$926$	−6.97835e6	−0.267439
$927$	−2.93706e7	−1.12257
$928$	4.57873e7	1.74532
$929$	4.26581e7	1.62167	0.810835	−	0.585275i	$-0.199014\pi$
$929$	4.26581e7	1.62167	0.810835	+	0.585275i	$0.199014\pi$
$930$	2.35819e6	0.0894071
$931$	−6.00399e6	−0.227021
$932$	6.76626e6	0.255158
$933$	8.05049e7	3.02774
$934$	−1.59010e7	−0.596427
$935$	−1.27362e6	−0.0476442
$936$	1.00032e8	3.73208
$937$	−4.63032e7	−1.72291	−0.861454	−	0.507836i	$-0.830446\pi$
$937$	−4.63032e7	−1.72291	−0.861454	+	0.507836i	$0.830446\pi$
$938$	−1.23092e6	−0.0456797
$939$	4.94637e7	1.83072
$940$	−1.27484e7	−0.470583
$941$	−3.72951e7	−1.37302	−0.686511	−	0.727120i	$-0.740859\pi$
$941$	−3.72951e7	−1.37302	−0.686511	+	0.727120i	$0.740859\pi$
$942$	−3.65245e6	−0.134109
$943$	875536.	0.0320623
$944$	1.57037e7	0.573550
$945$	3.38233e6	0.123207
$946$	7.51371e6	0.272977
$947$	3.38961e7	1.22822	0.614108	−	0.789222i	$-0.289516\pi$
$947$	3.38961e7	1.22822	0.614108	+	0.789222i	$0.289516\pi$
$948$	6.00105e7	2.16873
$949$	−9.38409e7	−3.38241
$950$	−595129.	−0.0213945
$951$	5.47868e7	1.96438
$952$	839083.	0.0300063
$953$	−352174.	−0.0125610	−0.00628052	−	0.999980i	$-0.501999\pi$
$953$	−352174.	−0.0125610	−0.00628052	+	0.999980i	$0.501999\pi$
$954$	−5.55336e7	−1.97554
$955$	−2.10788e7	−0.747889
$956$	3.52893e7	1.24882
$957$	2.72792e7	0.962836
$958$	−272214.	−0.00958290
$959$	−2.47606e6	−0.0869392
$960$	−1.86087e6	−0.0651686
$961$	−2.71043e7	−0.946738
$962$	−1.39250e7	−0.485130
$963$	2.23478e7	0.776549
$964$	−1.35073e7	−0.468141
$965$	−2.32215e7	−0.802733
$966$	60886.4	0.00209931
$967$	−1.47782e7	−0.508223	−0.254111	−	0.967175i	$-0.581783\pi$
$967$	−1.47782e7	−0.508223	−0.254111	+	0.967175i	$0.581783\pi$
$968$	2.20290e6	0.0755624
$969$	−4.40174e6	−0.150597
$970$	−6.65518e6	−0.227107
$971$	1.88383e7	0.641202	0.320601	−	0.947214i	$-0.396115\pi$
$971$	1.88383e7	0.641202	0.320601	+	0.947214i	$0.396115\pi$
$972$	−4.73929e7	−1.60897
$973$	−3.98266e6	−0.134862
$974$	−2.51802e7	−0.850476
$975$	2.02010e7	0.680553
$976$	804041.	0.0270180
$977$	3.05947e7	1.02544	0.512719	−	0.858556i	$-0.328638\pi$
$977$	3.05947e7	1.02544	0.512719	+	0.858556i	$0.328638\pi$
$978$	3.61647e6	0.120903
$979$	−514502.	−0.0171566
$980$	−1.04124e7	−0.346327
$981$	9.64127e7	3.19861
$982$	−3.56115e6	−0.117845
$983$	8.34099e6	0.275317	0.137659	−	0.990480i	$-0.456042\pi$
$983$	8.34099e6	0.275317	0.137659	+	0.990480i	$0.456042\pi$
$984$	6.33979e7	2.08731
$985$	3.73410e6	0.122630
$986$	−8.64533e6	−0.283198
$987$	7.81102e6	0.255220
$988$	−1.00897e7	−0.328840
$989$	1.41668e6	0.0460553
$990$	−4.75309e6	−0.154130
$991$	−3.50085e7	−1.13237	−0.566187	−	0.824277i	$-0.691582\pi$
$991$	−3.50085e7	−1.13237	−0.566187	+	0.824277i	$0.691582\pi$
$992$	−7.26296e6	−0.234333
$993$	−7.21713e6	−0.232269
$994$	−818325.	−0.0262700
$995$	1.02574e7	0.328458
$996$	−8.05037e7	−2.57139
$997$	2.79250e7	0.889725	0.444863	−	0.895599i	$-0.353253\pi$
$997$	2.79250e7	0.889725	0.444863	+	0.895599i	$0.353253\pi$
$998$	2.41608e7	0.767866
$999$	4.83158e7	1.53171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.16	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.16	✓	39	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63769 q^{2} +28.9603 q^{3} -25.0426 q^{4} -25.0000 q^{5} -76.3883 q^{6} -13.2455 q^{7} +150.461 q^{8} +595.699 q^{9} +O(q^{10})\)	\(q-2.63769 q^{2} +28.9603 q^{3} -25.0426 q^{4} -25.0000 q^{5} -76.3883 q^{6} -13.2455 q^{7} +150.461 q^{8} +595.699 q^{9} +65.9423 q^{10} -121.000 q^{11} -725.241 q^{12} +1116.07 q^{13} +34.9375 q^{14} -724.008 q^{15} +404.494 q^{16} -421.031 q^{17} -1571.27 q^{18} +361.000 q^{19} +626.065 q^{20} -383.593 q^{21} +319.161 q^{22} +60.1763 q^{23} +4357.39 q^{24} +625.000 q^{25} -2943.84 q^{26} +10214.3 q^{27} +331.701 q^{28} -7784.73 q^{29} +1909.71 q^{30} +1234.85 q^{31} -5881.67 q^{32} -3504.20 q^{33} +1110.55 q^{34} +331.137 q^{35} -14917.8 q^{36} +4730.22 q^{37} -952.207 q^{38} +32321.7 q^{39} -3761.52 q^{40} +14549.5 q^{41} +1011.80 q^{42} +23542.1 q^{43} +3030.15 q^{44} -14892.5 q^{45} -158.726 q^{46} -20362.8 q^{47} +11714.3 q^{48} -16631.6 q^{49} -1648.56 q^{50} -12193.2 q^{51} -27949.2 q^{52} +35343.1 q^{53} -26942.1 q^{54} +3025.00 q^{55} -1992.92 q^{56} +10454.7 q^{57} +20533.7 q^{58} +38823.0 q^{59} +18131.0 q^{60} +1987.77 q^{61} -3257.14 q^{62} -7890.32 q^{63} +2570.24 q^{64} -27901.7 q^{65} +9242.99 q^{66} -35232.1 q^{67} +10543.7 q^{68} +1742.72 q^{69} -873.437 q^{70} -23422.6 q^{71} +89629.3 q^{72} -84081.7 q^{73} -12476.9 q^{74} +18100.2 q^{75} -9040.37 q^{76} +1602.70 q^{77} -85254.6 q^{78} -82745.6 q^{79} -10112.3 q^{80} +151054. q^{81} -38377.1 q^{82} +111003. q^{83} +9606.16 q^{84} +10525.8 q^{85} -62096.8 q^{86} -225448. q^{87} -18205.7 q^{88} +4252.08 q^{89} +39281.8 q^{90} -14782.9 q^{91} -1506.97 q^{92} +35761.5 q^{93} +53710.7 q^{94} -9025.00 q^{95} -170335. q^{96} -100924. q^{97} +43868.9 q^{98} -72079.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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