LMFDB - Embedded newform 1045.6.a.g.1.21

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			1.21
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)

$f(q)$	$=$	$q+0.832155 q^{2} -19.4861 q^{3} -31.3075 q^{4} -25.0000 q^{5} -16.2155 q^{6} +142.635 q^{7} -52.6817 q^{8} +136.709 q^{9} +O(q^{10})$	\(q+0.832155 q^{2} -19.4861 q^{3} -31.3075 q^{4} -25.0000 q^{5} -16.2155 q^{6} +142.635 q^{7} -52.6817 q^{8} +136.709 q^{9} -20.8039 q^{10} -121.000 q^{11} +610.062 q^{12} +1034.49 q^{13} +118.694 q^{14} +487.153 q^{15} +958.001 q^{16} +273.009 q^{17} +113.763 q^{18} +361.000 q^{19} +782.688 q^{20} -2779.40 q^{21} -100.691 q^{22} +1676.52 q^{23} +1026.56 q^{24} +625.000 q^{25} +860.859 q^{26} +2071.20 q^{27} -4465.54 q^{28} +7565.88 q^{29} +405.387 q^{30} +1996.18 q^{31} +2483.02 q^{32} +2357.82 q^{33} +227.186 q^{34} -3565.87 q^{35} -4280.03 q^{36} -338.864 q^{37} +300.408 q^{38} -20158.3 q^{39} +1317.04 q^{40} -4419.06 q^{41} -2312.89 q^{42} +19565.3 q^{43} +3788.21 q^{44} -3417.73 q^{45} +1395.12 q^{46} +9834.46 q^{47} -18667.7 q^{48} +3537.68 q^{49} +520.097 q^{50} -5319.88 q^{51} -32387.4 q^{52} +1342.31 q^{53} +1723.56 q^{54} +3025.00 q^{55} -7514.24 q^{56} -7034.49 q^{57} +6295.99 q^{58} -29146.1 q^{59} -15251.6 q^{60} -10181.4 q^{61} +1661.13 q^{62} +19499.5 q^{63} -28589.8 q^{64} -25862.3 q^{65} +1962.07 q^{66} -21858.5 q^{67} -8547.23 q^{68} -32668.8 q^{69} -2967.36 q^{70} -20348.7 q^{71} -7202.07 q^{72} +32733.9 q^{73} -281.988 q^{74} -12178.8 q^{75} -11302.0 q^{76} -17258.8 q^{77} -16774.8 q^{78} -46298.3 q^{79} -23950.0 q^{80} -73579.9 q^{81} -3677.35 q^{82} -38286.7 q^{83} +87016.1 q^{84} -6825.22 q^{85} +16281.4 q^{86} -147430. q^{87} +6374.48 q^{88} +108470. q^{89} -2844.08 q^{90} +147555. q^{91} -52487.6 q^{92} -38897.9 q^{93} +8183.80 q^{94} -9025.00 q^{95} -48384.4 q^{96} +54348.6 q^{97} +2943.90 q^{98} -16541.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.832155	0.147106	0.0735528	−	0.997291i	$-0.476566\pi$
$2$	0.832155	0.147106	0.0735528	+	0.997291i	$0.476566\pi$
$3$	−19.4861	−1.25004	−0.625018	−	0.780610i	$-0.714908\pi$
$3$	−19.4861	−1.25004	−0.625018	+	0.780610i	$0.714908\pi$
$4$	−31.3075	−0.978360
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−16.2155	−0.183887
$7$	142.635	1.10022	0.550111	−	0.835092i	$-0.314585\pi$
$7$	142.635	1.10022	0.550111	+	0.835092i	$0.314585\pi$
$8$	−52.6817	−0.291028
$9$	136.709	0.562590
$10$	−20.8039	−0.0657877
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	610.062	1.22298
$13$	1034.49	1.69773	0.848866	−	0.528607i	$-0.177286\pi$
$13$	1034.49	1.69773	0.848866	+	0.528607i	$0.177286\pi$
$14$	118.694	0.161849
$15$	487.153	0.559033
$16$	958.001	0.935548
$17$	273.009	0.229115	0.114558	−	0.993417i	$-0.463455\pi$
$17$	273.009	0.229115	0.114558	+	0.993417i	$0.463455\pi$
$18$	113.763	0.0827601
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	782.688	0.437536
$21$	−2779.40	−1.37532
$22$	−100.691	−0.0443540
$23$	1676.52	0.660828	0.330414	−	0.943836i	$-0.392812\pi$
$23$	1676.52	0.660828	0.330414	+	0.943836i	$0.392812\pi$
$24$	1026.56	0.363795
$25$	625.000	0.200000
$26$	860.859	0.249746
$27$	2071.20	0.546779
$28$	−4465.54	−1.07641
$29$	7565.88	1.67057	0.835285	−	0.549818i	$-0.185303\pi$
$29$	7565.88	1.67057	0.835285	+	0.549818i	$0.185303\pi$
$30$	405.387	0.0822369
$31$	1996.18	0.373075	0.186537	−	0.982448i	$-0.440273\pi$
$31$	1996.18	0.373075	0.186537	+	0.982448i	$0.440273\pi$
$32$	2483.02	0.428652
$33$	2357.82	0.376900
$34$	227.186	0.0337042
$35$	−3565.87	−0.492034
$36$	−4280.03	−0.550415
$37$	−338.864	−0.0406932	−0.0203466	−	0.999793i	$-0.506477\pi$
$37$	−338.864	−0.0406932	−0.0203466	+	0.999793i	$0.506477\pi$
$38$	300.408	0.0337484
$39$	−20158.3	−2.12223
$40$	1317.04	0.130152
$41$	−4419.06	−0.410554	−0.205277	−	0.978704i	$-0.565810\pi$
$41$	−4419.06	−0.410554	−0.205277	+	0.978704i	$0.565810\pi$
$42$	−2312.89	−0.202317
$43$	19565.3	1.61367	0.806837	−	0.590774i	$-0.201177\pi$
$43$	19565.3	1.61367	0.806837	+	0.590774i	$0.201177\pi$
$44$	3788.21	0.294987
$45$	−3417.73	−0.251598
$46$	1395.12	0.0972115
$47$	9834.46	0.649390	0.324695	−	0.945819i	$-0.394738\pi$
$47$	9834.46	0.649390	0.324695	+	0.945819i	$0.394738\pi$
$48$	−18667.7	−1.16947
$49$	3537.68	0.210489
$50$	520.097	0.0294211
$51$	−5319.88	−0.286402
$52$	−32387.4	−1.66099
$53$	1342.31	0.0656392	0.0328196	−	0.999461i	$-0.489551\pi$
$53$	1342.31	0.0656392	0.0328196	+	0.999461i	$0.489551\pi$
$54$	1723.56	0.0804342
$55$	3025.00	0.134840
$56$	−7514.24	−0.320195
$57$	−7034.49	−0.286778
$58$	6295.99	0.245750
$59$	−29146.1	−1.09006	−0.545030	−	0.838416i	$-0.683482\pi$
$59$	−29146.1	−1.09006	−0.545030	+	0.838416i	$0.683482\pi$
$60$	−15251.6	−0.546935
$61$	−10181.4	−0.350333	−0.175166	−	0.984539i	$-0.556046\pi$
$61$	−10181.4	−0.350333	−0.175166	+	0.984539i	$0.556046\pi$
$62$	1661.13	0.0548814
$63$	19499.5	0.618973
$64$	−28589.8	−0.872491
$65$	−25862.3	−0.759249
$66$	1962.07	0.0554441
$67$	−21858.5	−0.594886	−0.297443	−	0.954740i	$-0.596134\pi$
$67$	−21858.5	−0.594886	−0.297443	+	0.954740i	$0.596134\pi$
$68$	−8547.23	−0.224157
$69$	−32668.8	−0.826058
$70$	−2967.36	−0.0723810
$71$	−20348.7	−0.479062	−0.239531	−	0.970889i	$-0.576994\pi$
$71$	−20348.7	−0.479062	−0.239531	+	0.970889i	$0.576994\pi$
$72$	−7202.07	−0.163729
$73$	32733.9	0.718936	0.359468	−	0.933157i	$-0.382958\pi$
$73$	32733.9	0.718936	0.359468	+	0.933157i	$0.382958\pi$
$74$	−281.988	−0.00598620
$75$	−12178.8	−0.250007
$76$	−11302.0	−0.224451
$77$	−17258.8	−0.331729
$78$	−16774.8	−0.312192
$79$	−46298.3	−0.834637	−0.417319	−	0.908760i	$-0.637030\pi$
$79$	−46298.3	−0.834637	−0.417319	+	0.908760i	$0.637030\pi$
$80$	−23950.0	−0.418390
$81$	−73579.9	−1.24608
$82$	−3677.35	−0.0603949
$83$	−38286.7	−0.610032	−0.305016	−	0.952347i	$-0.598662\pi$
$83$	−38286.7	−0.610032	−0.305016	+	0.952347i	$0.598662\pi$
$84$	87016.1	1.34555
$85$	−6825.22	−0.102464
$86$	16281.4	0.237381
$87$	−147430.	−2.08827
$88$	6374.48	0.0877482
$89$	108470.	1.45156	0.725778	−	0.687929i	$-0.241480\pi$
$89$	108470.	1.45156	0.725778	+	0.687929i	$0.241480\pi$
$90$	−2844.08	−0.0370114
$91$	147555.	1.86788
$92$	−52487.6	−0.646527
$93$	−38897.9	−0.466357
$94$	8183.80	0.0955290
$95$	−9025.00	−0.102598
$96$	−48384.4	−0.535831
$97$	54348.6	0.586488	0.293244	−	0.956038i	$-0.405265\pi$
$97$	54348.6	0.586488	0.293244	+	0.956038i	$0.405265\pi$
$98$	2943.90	0.0309641
$99$	−16541.8	−0.169627
$100$	−19567.2	−0.195672
$101$	−71190.4	−0.694413	−0.347207	−	0.937789i	$-0.612870\pi$
$101$	−71190.4	−0.694413	−0.347207	+	0.937789i	$0.612870\pi$
$102$	−4426.97	−0.0421314
$103$	164221.	1.52523	0.762616	−	0.646852i	$-0.223915\pi$
$103$	164221.	1.52523	0.762616	+	0.646852i	$0.223915\pi$
$104$	−54498.9	−0.494088
$105$	69485.0	0.615060
$106$	1117.01	0.00965590
$107$	204898.	1.73012	0.865062	−	0.501664i	$-0.167279\pi$
$107$	204898.	1.73012	0.865062	+	0.501664i	$0.167279\pi$
$108$	−64844.0	−0.534946
$109$	−179096.	−1.44384	−0.721920	−	0.691976i	$-0.756740\pi$
$109$	−179096.	−1.44384	−0.721920	+	0.691976i	$0.756740\pi$
$110$	2517.27	0.0198357
$111$	6603.16	0.0508679
$112$	136644.	1.02931
$113$	100632.	0.741379	0.370689	−	0.928757i	$-0.379121\pi$
$113$	100632.	0.741379	0.370689	+	0.928757i	$0.379121\pi$
$114$	−5853.79	−0.0421866
$115$	−41912.9	−0.295531
$116$	−236869.	−1.63442
$117$	141425.	0.955127
$118$	−24254.1	−0.160354
$119$	38940.5	0.252078
$120$	−25664.1	−0.162694
$121$	14641.0	0.0909091
$122$	−8472.47	−0.0515359
$123$	86110.4	0.513208
$124$	−62495.5	−0.365002
$125$	−15625.0	−0.0894427
$126$	16226.6	0.0910545
$127$	−266825.	−1.46797	−0.733985	−	0.679166i	$-0.762342\pi$
$127$	−266825.	−1.46797	−0.733985	+	0.679166i	$0.762342\pi$
$128$	−103248.	−0.557001
$129$	−381252.	−2.01715
$130$	−21521.5	−0.111690
$131$	−3094.44	−0.0157545	−0.00787723	−	0.999969i	$-0.502507\pi$
$131$	−3094.44	−0.0157545	−0.00787723	+	0.999969i	$0.502507\pi$
$132$	−73817.5	−0.368744
$133$	51491.2	0.252408
$134$	−18189.7	−0.0875111
$135$	−51779.9	−0.244527
$136$	−14382.6	−0.0666790
$137$	308768.	1.40550	0.702749	−	0.711438i	$-0.251956\pi$
$137$	308768.	1.40550	0.702749	+	0.711438i	$0.251956\pi$
$138$	−27185.5	−0.121518
$139$	−7755.24	−0.0340454	−0.0170227	−	0.999855i	$-0.505419\pi$
$139$	−7755.24	−0.0340454	−0.0170227	+	0.999855i	$0.505419\pi$
$140$	111639.	0.481387
$141$	−191636.	−0.811761
$142$	−16933.3	−0.0704727
$143$	−125174.	−0.511886
$144$	130968.	0.526330
$145$	−189147.	−0.747101
$146$	27239.7	0.105760
$147$	−68935.7	−0.263118
$148$	10609.0	0.0398126
$149$	−181817.	−0.670916	−0.335458	−	0.942055i	$-0.608891\pi$
$149$	−181817.	−0.670916	−0.335458	+	0.942055i	$0.608891\pi$
$150$	−10134.7	−0.0367775
$151$	−294623.	−1.05154	−0.525769	−	0.850627i	$-0.676222\pi$
$151$	−294623.	−1.05154	−0.525769	+	0.850627i	$0.676222\pi$
$152$	−19018.1	−0.0667664
$153$	37322.8	0.128898
$154$	−14362.0	−0.0487993
$155$	−49904.6	−0.166844
$156$	631105.	2.07630
$157$	−19221.9	−0.0622369	−0.0311185	−	0.999516i	$-0.509907\pi$
$157$	−19221.9	−0.0622369	−0.0311185	+	0.999516i	$0.509907\pi$
$158$	−38527.4	−0.122780
$159$	−26156.4	−0.0820513
$160$	−62075.5	−0.191699
$161$	239130.	0.727057
$162$	−61229.9	−0.183306
$163$	599989.	1.76878	0.884391	−	0.466746i	$-0.154574\pi$
$163$	599989.	1.76878	0.884391	+	0.466746i	$0.154574\pi$
$164$	138350.	0.401670
$165$	−58945.5	−0.168555
$166$	−31860.5	−0.0897392
$167$	657911.	1.82548	0.912738	−	0.408546i	$-0.133964\pi$
$167$	657911.	1.82548	0.912738	+	0.408546i	$0.133964\pi$
$168$	146423.	0.400256
$169$	698884.	1.88230
$170$	−5679.64	−0.0150730
$171$	49352.0	0.129067
$172$	−612542.	−1.57875
$173$	−107554.	−0.273220	−0.136610	−	0.990625i	$-0.543621\pi$
$173$	−107554.	−0.273220	−0.136610	+	0.990625i	$0.543621\pi$
$174$	−122684.	−0.307197
$175$	89146.7	0.220044
$176$	−115918.	−0.282078
$177$	567945.	1.36262
$178$	90263.7	0.213532
$179$	−214058.	−0.499343	−0.249671	−	0.968331i	$-0.580323\pi$
$179$	−214058.	−0.499343	−0.249671	+	0.968331i	$0.580323\pi$
$180$	107001.	0.246153
$181$	341020.	0.773719	0.386860	−	0.922139i	$-0.373560\pi$
$181$	341020.	0.773719	0.386860	+	0.922139i	$0.373560\pi$
$182$	122788.	0.274776
$183$	198395.	0.437929
$184$	−88321.7	−0.192319
$185$	8471.61	0.0181985
$186$	−32369.1	−0.0686038
$187$	−33034.1	−0.0690809
$188$	−307892.	−0.635337
$189$	295424.	0.601578
$190$	−7510.20	−0.0150927
$191$	517260.	1.02595	0.512975	−	0.858404i	$-0.328544\pi$
$191$	517260.	1.02595	0.512975	+	0.858404i	$0.328544\pi$
$192$	557104.	1.09064
$193$	−195222.	−0.377256	−0.188628	−	0.982049i	$-0.560404\pi$
$193$	−195222.	−0.377256	−0.188628	+	0.982049i	$0.560404\pi$
$194$	45226.5	0.0862757
$195$	503957.	0.949089
$196$	−110756.	−0.205934
$197$	−47037.3	−0.0863528	−0.0431764	−	0.999067i	$-0.513748\pi$
$197$	−47037.3	−0.0863528	−0.0431764	+	0.999067i	$0.513748\pi$
$198$	−13765.4	−0.0249531
$199$	−1.07502e6	−1.92435	−0.962174	−	0.272436i	$-0.912171\pi$
$199$	−1.07502e6	−1.92435	−0.962174	+	0.272436i	$0.912171\pi$
$200$	−32926.1	−0.0582056
$201$	425938.	0.743629
$202$	−59241.5	−0.102152
$203$	1.07916e6	1.83800
$204$	166552.	0.280205
$205$	110477.	0.183605
$206$	136657.	0.224370
$207$	229195.	0.371775
$208$	991046.	1.58831
$209$	−43681.0	−0.0691714
$210$	57822.3	0.0904789
$211$	628027.	0.971119	0.485559	−	0.874204i	$-0.338616\pi$
$211$	628027.	0.971119	0.485559	+	0.874204i	$0.338616\pi$
$212$	−42024.4	−0.0642188
$213$	396518.	0.598844
$214$	170507.	0.254511
$215$	−489133.	−0.721657
$216$	−109114.	−0.159128
$217$	284725.	0.410465
$218$	−149036.	−0.212397
$219$	−637857.	−0.898696
$220$	−94705.2	−0.131922
$221$	282426.	0.388977
$222$	5494.85	0.00748296
$223$	−68370.5	−0.0920676	−0.0460338	−	0.998940i	$-0.514658\pi$
$223$	−68370.5	−0.0920676	−0.0460338	+	0.998940i	$0.514658\pi$
$224$	354165.	0.471613
$225$	85443.3	0.112518
$226$	83741.5	0.109061
$227$	801219.	1.03202	0.516008	−	0.856584i	$-0.327417\pi$
$227$	801219.	1.03202	0.516008	+	0.856584i	$0.327417\pi$
$228$	220233.	0.280572
$229$	−1.09459e6	−1.37931	−0.689654	−	0.724139i	$-0.742237\pi$
$229$	−1.09459e6	−1.37931	−0.689654	+	0.724139i	$0.742237\pi$
$230$	−34878.1	−0.0434743
$231$	336307.	0.414674
$232$	−398583.	−0.486182
$233$	1.13830e6	1.37363	0.686813	−	0.726834i	$-0.259009\pi$
$233$	1.13830e6	1.37363	0.686813	+	0.726834i	$0.259009\pi$
$234$	117687.	0.140505
$235$	−245861.	−0.290416
$236$	912493.	1.06647
$237$	902176.	1.04333
$238$	32404.6	0.0370821
$239$	187214.	0.212004	0.106002	−	0.994366i	$-0.466195\pi$
$239$	187214.	0.212004	0.106002	+	0.994366i	$0.466195\pi$
$240$	466693.	0.523002
$241$	−453894.	−0.503399	−0.251699	−	0.967805i	$-0.580989\pi$
$241$	−453894.	−0.503399	−0.251699	+	0.967805i	$0.580989\pi$
$242$	12183.6	0.0133732
$243$	930488.	1.01087
$244$	318753.	0.342752
$245$	−88442.0	−0.0941333
$246$	71657.3	0.0754957
$247$	373452.	0.389487
$248$	−105162.	−0.108575
$249$	746060.	0.762562
$250$	−13002.4	−0.0131575
$251$	1.71829e6	1.72152	0.860759	−	0.509012i	$-0.169989\pi$
$251$	1.71829e6	1.72152	0.860759	+	0.509012i	$0.169989\pi$
$252$	−610481.	−0.605579
$253$	−202859.	−0.199247
$254$	−222040.	−0.215947
$255$	132997.	0.128083
$256$	828955.	0.790553
$257$	−516937.	−0.488208	−0.244104	−	0.969749i	$-0.578494\pi$
$257$	−516937.	−0.488208	−0.244104	+	0.969749i	$0.578494\pi$
$258$	−317261.	−0.296734
$259$	−48333.9	−0.0447715
$260$	809685.	0.742819
$261$	1.03433e6	0.939845
$262$	−2575.05	−0.00231757
$263$	196057.	0.174781	0.0873903	−	0.996174i	$-0.472147\pi$
$263$	196057.	0.174781	0.0873903	+	0.996174i	$0.472147\pi$
$264$	−124214.	−0.109688
$265$	−33557.8	−0.0293547
$266$	42848.6	0.0371307
$267$	−2.11366e6	−1.81450
$268$	684336.	0.582013
$269$	932273.	0.785529	0.392765	−	0.919639i	$-0.371519\pi$
$269$	932273.	0.785529	0.392765	+	0.919639i	$0.371519\pi$
$270$	−43088.9	−0.0359713
$271$	−1.77631e6	−1.46925	−0.734623	−	0.678476i	$-0.762641\pi$
$271$	−1.77631e6	−1.46925	−0.734623	+	0.678476i	$0.762641\pi$
$272$	261543.	0.214348
$273$	−2.87527e6	−2.33492
$274$	256943.	0.206757
$275$	−75625.0	−0.0603023
$276$	1.02278e6	0.808182
$277$	−2.33079e6	−1.82517	−0.912584	−	0.408889i	$-0.865916\pi$
$277$	−2.33079e6	−1.82517	−0.912584	+	0.408889i	$0.865916\pi$
$278$	−6453.56	−0.00500827
$279$	272897.	0.209888
$280$	187856.	0.143196
$281$	1.43374e6	1.08319	0.541594	−	0.840640i	$-0.317821\pi$
$281$	1.43374e6	1.08319	0.541594	+	0.840640i	$0.317821\pi$
$282$	−159471.	−0.119415
$283$	−353776.	−0.262581	−0.131290	−	0.991344i	$-0.541912\pi$
$283$	−353776.	−0.262581	−0.131290	+	0.991344i	$0.541912\pi$
$284$	637068.	0.468695
$285$	175862.	0.128251
$286$	−104164.	−0.0753013
$287$	−630312.	−0.451701
$288$	339452.	0.241155
$289$	−1.34532e6	−0.947506
$290$	−157400.	−0.109903
$291$	−1.05904e6	−0.733131
$292$	−1.02482e6	−0.703379
$293$	279403.	0.190135	0.0950674	−	0.995471i	$-0.469693\pi$
$293$	279403.	0.190135	0.0950674	+	0.995471i	$0.469693\pi$
$294$	−57365.2	−0.0387062
$295$	728653.	0.487490
$296$	17852.0	0.0118429
$297$	−250615.	−0.164860
$298$	−151300.	−0.0986955
$299$	1.73435e6	1.12191
$300$	381289.	0.244597
$301$	2.79070e6	1.77540
$302$	−245172.	−0.154687
$303$	1.38723e6	0.868041
$304$	345838.	0.214629
$305$	254534.	0.156674
$306$	31058.4	0.0189616
$307$	−2.65261e6	−1.60630	−0.803152	−	0.595774i	$-0.796845\pi$
$307$	−2.65261e6	−1.60630	−0.803152	+	0.595774i	$0.796845\pi$
$308$	540330.	0.324551
$309$	−3.20003e6	−1.90659
$310$	−41528.4	−0.0245437
$311$	953550.	0.559039	0.279520	−	0.960140i	$-0.409825\pi$
$311$	953550.	0.559039	0.279520	+	0.960140i	$0.409825\pi$
$312$	1.06197e6	0.617627
$313$	−491507.	−0.283576	−0.141788	−	0.989897i	$-0.545285\pi$
$313$	−491507.	−0.283576	−0.141788	+	0.989897i	$0.545285\pi$
$314$	−15995.6	−0.00915540
$315$	−487487.	−0.276813
$316$	1.44949e6	0.816576
$317$	1.18334e6	0.661397	0.330699	−	0.943736i	$-0.392716\pi$
$317$	1.18334e6	0.661397	0.330699	+	0.943736i	$0.392716\pi$
$318$	−21766.2	−0.0120702
$319$	−915471.	−0.503696
$320$	714745.	0.390190
$321$	−3.99266e6	−2.16272
$322$	198993.	0.106954
$323$	98556.2	0.0525627
$324$	2.30360e6	1.21912
$325$	646558.	0.339547
$326$	499284.	0.260198
$327$	3.48988e6	1.80485
$328$	232804.	0.119483
$329$	1.40274e6	0.714474
$330$	−49051.8	−0.0247954
$331$	2.10320e6	1.05514	0.527570	−	0.849511i	$-0.323103\pi$
$331$	2.10320e6	1.05514	0.527570	+	0.849511i	$0.323103\pi$
$332$	1.19866e6	0.596831
$333$	−46325.9	−0.0228936
$334$	547484.	0.268538
$335$	546463.	0.266041
$336$	−2.66267e6	−1.28668
$337$	2.97319e6	1.42609	0.713046	−	0.701117i	$-0.247315\pi$
$337$	2.97319e6	1.42609	0.713046	+	0.701117i	$0.247315\pi$
$338$	581580.	0.276896
$339$	−1.96093e6	−0.926750
$340$	213681.	0.100246
$341$	−241538.	−0.112486
$342$	41068.6	0.0189865
$343$	−1.89267e6	−0.868638
$344$	−1.03073e6	−0.469624
$345$	816721.	0.369425
$346$	−89502.0	−0.0401923
$347$	−2.18326e6	−0.973380	−0.486690	−	0.873575i	$-0.661796\pi$
$347$	−2.18326e6	−0.973380	−0.486690	+	0.873575i	$0.661796\pi$
$348$	4.61566e6	2.04308
$349$	−1.70523e6	−0.749409	−0.374704	−	0.927144i	$-0.622256\pi$
$349$	−1.70523e6	−0.749409	−0.374704	+	0.927144i	$0.622256\pi$
$350$	74183.9	0.0323698
$351$	2.14264e6	0.928284
$352$	−300445.	−0.129244
$353$	−822132.	−0.351160	−0.175580	−	0.984465i	$-0.556180\pi$
$353$	−822132.	−0.351160	−0.175580	+	0.984465i	$0.556180\pi$
$354$	472619.	0.200448
$355$	508718.	0.214243
$356$	−3.39592e6	−1.42014
$357$	−758801.	−0.315106
$358$	−178129.	−0.0734561
$359$	−4.48725e6	−1.83757	−0.918786	−	0.394757i	$-0.870829\pi$
$359$	−4.48725e6	−1.83757	−0.918786	+	0.394757i	$0.870829\pi$
$360$	180052.	0.0732220
$361$	130321.	0.0526316
$362$	283782.	0.113818
$363$	−285296.	−0.113640
$364$	−4.61957e6	−1.82746
$365$	−818347.	−0.321518
$366$	165096.	0.0644218
$367$	1.58216e6	0.613177	0.306588	−	0.951842i	$-0.400812\pi$
$367$	1.58216e6	0.613177	0.306588	+	0.951842i	$0.400812\pi$
$368$	1.60611e6	0.618236
$369$	−604127.	−0.230974
$370$	7049.70	0.00267711
$371$	191460.	0.0722177
$372$	1.21780e6	0.456265
$373$	−4.56094e6	−1.69739	−0.848696	−	0.528881i	$-0.822612\pi$
$373$	−4.56094e6	−1.69739	−0.848696	+	0.528881i	$0.822612\pi$
$374$	−27489.5	−0.0101622
$375$	304471.	0.111807
$376$	−518096.	−0.188991
$377$	7.82685e6	2.83618
$378$	245839.	0.0884955
$379$	−887674.	−0.317435	−0.158718	−	0.987324i	$-0.550736\pi$
$379$	−887674.	−0.317435	−0.158718	+	0.987324i	$0.550736\pi$
$380$	282550.	0.100378
$381$	5.19938e6	1.83501
$382$	430441.	0.150923
$383$	−1.92986e6	−0.672247	−0.336124	−	0.941818i	$-0.609116\pi$
$383$	−1.92986e6	−0.672247	−0.336124	+	0.941818i	$0.609116\pi$
$384$	2.01190e6	0.696271
$385$	431470.	0.148354
$386$	−162455.	−0.0554965
$387$	2.67476e6	0.907836
$388$	−1.70152e6	−0.573796
$389$	−2.34713e6	−0.786436	−0.393218	−	0.919445i	$-0.628638\pi$
$389$	−2.34713e6	−0.786436	−0.393218	+	0.919445i	$0.628638\pi$
$390$	419370.	0.139616
$391$	457704.	0.151406
$392$	−186371.	−0.0612580
$393$	60298.6	0.0196936
$394$	−39142.3	−0.0127030
$395$	1.15746e6	0.373261
$396$	517883.	0.165956
$397$	2.17012e6	0.691048	0.345524	−	0.938410i	$-0.387701\pi$
$397$	2.17012e6	0.691048	0.345524	+	0.938410i	$0.387701\pi$
$398$	−894583.	−0.283082
$399$	−1.00336e6	−0.315519
$400$	598751.	0.187110
$401$	−2.14443e6	−0.665964	−0.332982	−	0.942933i	$-0.608055\pi$
$401$	−2.14443e6	−0.665964	−0.332982	+	0.942933i	$0.608055\pi$
$402$	354447.	0.109392
$403$	2.06504e6	0.633382
$404$	2.22879e6	0.679386
$405$	1.83950e6	0.557265
$406$	898027.	0.270380
$407$	41002.6	0.0122695
$408$	280260.	0.0833511
$409$	2.98549e6	0.882484	0.441242	−	0.897388i	$-0.354538\pi$
$409$	2.98549e6	0.882484	0.441242	+	0.897388i	$0.354538\pi$
$410$	91933.7	0.0270094
$411$	−6.01669e6	−1.75692
$412$	−5.14135e6	−1.49223
$413$	−4.15725e6	−1.19931
$414$	190726.	0.0546902
$415$	957168.	0.272815
$416$	2.56867e6	0.727737
$417$	151120.	0.0425579
$418$	−36349.4	−0.0101755
$419$	2.02886e6	0.564570	0.282285	−	0.959331i	$-0.408908\pi$
$419$	2.02886e6	0.564570	0.282285	+	0.959331i	$0.408908\pi$
$420$	−2.17540e6	−0.601750
$421$	6.43490e6	1.76944	0.884721	−	0.466121i	$-0.154349\pi$
$421$	6.43490e6	1.76944	0.884721	+	0.466121i	$0.154349\pi$
$422$	522616.	0.142857
$423$	1.34446e6	0.365340
$424$	−70715.2	−0.0191028
$425$	170630.	0.0458231
$426$	329964.	0.0880934
$427$	−1.45221e6	−0.385444
$428$	−6.41483e6	−1.69268
$429$	2.43915e6	0.639875
$430$	−407035.	−0.106160
$431$	404805.	0.104967	0.0524835	−	0.998622i	$-0.483286\pi$
$431$	404805.	0.104967	0.0524835	+	0.998622i	$0.483286\pi$
$432$	1.98421e6	0.511538
$433$	−1.25254e6	−0.321048	−0.160524	−	0.987032i	$-0.551318\pi$
$433$	−1.25254e6	−0.321048	−0.160524	+	0.987032i	$0.551318\pi$
$434$	236936.	0.0603818
$435$	3.68574e6	0.933903
$436$	5.60705e6	1.41260
$437$	605223.	0.151604
$438$	−530796.	−0.132203
$439$	3.83650e6	0.950109	0.475054	−	0.879956i	$-0.342428\pi$
$439$	3.83650e6	0.950109	0.475054	+	0.879956i	$0.342428\pi$
$440$	−159362.	−0.0392422
$441$	483634.	0.118419
$442$	235022.	0.0572207
$443$	3.09472e6	0.749225	0.374612	−	0.927182i	$-0.377776\pi$
$443$	3.09472e6	0.749225	0.374612	+	0.927182i	$0.377776\pi$
$444$	−206728.	−0.0497672
$445$	−2.71174e6	−0.649156
$446$	−56894.9	−0.0135437
$447$	3.54290e6	0.838669
$448$	−4.07790e6	−0.959934
$449$	−4.91184e6	−1.14982	−0.574908	−	0.818218i	$-0.694962\pi$
$449$	−4.91184e6	−1.14982	−0.574908	+	0.818218i	$0.694962\pi$
$450$	71102.1	0.0165520
$451$	534707.	0.123787
$452$	−3.15054e6	−0.725335
$453$	5.74107e6	1.31446
$454$	666739.	0.151815
$455$	−3.68887e6	−0.835343
$456$	370589.	0.0834604
$457$	620475.	0.138974	0.0694870	−	0.997583i	$-0.477864\pi$
$457$	620475.	0.138974	0.0694870	+	0.997583i	$0.477864\pi$
$458$	−910865.	−0.202904
$459$	565454.	0.125275
$460$	1.31219e6	0.289136
$461$	4.18369e6	0.916868	0.458434	−	0.888728i	$-0.348410\pi$
$461$	4.18369e6	0.916868	0.458434	+	0.888728i	$0.348410\pi$
$462$	279860.	0.0610008
$463$	−3.11890e6	−0.676160	−0.338080	−	0.941117i	$-0.609777\pi$
$463$	−3.11890e6	−0.676160	−0.338080	+	0.941117i	$0.609777\pi$
$464$	7.24812e6	1.56290
$465$	972447.	0.208561
$466$	947246.	0.202068
$467$	−5.55390e6	−1.17843	−0.589217	−	0.807975i	$-0.700564\pi$
$467$	−5.55390e6	−1.17843	−0.589217	+	0.807975i	$0.700564\pi$
$468$	−4.42766e6	−0.934458
$469$	−3.11779e6	−0.654507
$470$	−204595.	−0.0427219
$471$	374561.	0.0777984
$472$	1.53547e6	0.317238
$473$	−2.36740e6	−0.486541
$474$	750750.	0.153479
$475$	225625.	0.0458831
$476$	−1.21913e6	−0.246623
$477$	183506.	0.0369279
$478$	155791.	0.0311870
$479$	−4.08392e6	−0.813277	−0.406639	−	0.913589i	$-0.633299\pi$
$479$	−4.08392e6	−0.813277	−0.406639	+	0.913589i	$0.633299\pi$
$480$	1.20961e6	0.239631
$481$	−350553.	−0.0690862
$482$	−377710.	−0.0740528
$483$	−4.65971e6	−0.908848
$484$	−458373.	−0.0889418
$485$	−1.35871e6	−0.262285
$486$	774310.	0.148705
$487$	−1.96497e6	−0.375434	−0.187717	−	0.982223i	$-0.560109\pi$
$487$	−1.96497e6	−0.375434	−0.187717	+	0.982223i	$0.560109\pi$
$488$	536371.	0.101957
$489$	−1.16915e7	−2.21104
$490$	−73597.5	−0.0138475
$491$	2.64698e6	0.495504	0.247752	−	0.968823i	$-0.420308\pi$
$491$	2.64698e6	0.495504	0.247752	+	0.968823i	$0.420308\pi$
$492$	−2.69590e6	−0.502102
$493$	2.06555e6	0.382753
$494$	310770.	0.0572957
$495$	413546.	0.0758596
$496$	1.91235e6	0.349030
$497$	−2.90244e6	−0.527074
$498$	620838.	0.112177
$499$	451910.	0.0812457	0.0406229	−	0.999175i	$-0.487066\pi$
$499$	451910.	0.0812457	0.0406229	+	0.999175i	$0.487066\pi$
$500$	489180.	0.0875072
$501$	−1.28201e7	−2.28191
$502$	1.42988e6	0.253245
$503$	−1.96954e6	−0.347092	−0.173546	−	0.984826i	$-0.555523\pi$
$503$	−1.96954e6	−0.347092	−0.173546	+	0.984826i	$0.555523\pi$
$504$	−1.02727e6	−0.180139
$505$	1.77976e6	0.310551
$506$	−168810.	−0.0293104
$507$	−1.36185e7	−2.35294
$508$	8.35363e6	1.43620
$509$	−6.00949e6	−1.02812	−0.514059	−	0.857755i	$-0.671859\pi$
$509$	−6.00949e6	−1.02812	−0.514059	+	0.857755i	$0.671859\pi$
$510$	110674.	0.0188417
$511$	4.66899e6	0.790990
$512$	3.99375e6	0.673296
$513$	747701.	0.125440
$514$	−430172.	−0.0718182
$515$	−4.10553e6	−0.682104
$516$	1.19361e7	1.97350
$517$	−1.18997e6	−0.195799
$518$	−40221.3	−0.00658615
$519$	2.09582e6	0.341535
$520$	1.36247e6	0.220963
$521$	1.04031e7	1.67907	0.839537	−	0.543302i	$-0.182826\pi$
$521$	1.04031e7	1.67907	0.839537	+	0.543302i	$0.182826\pi$
$522$	860720.	0.138256
$523$	6.76976e6	1.08223	0.541114	−	0.840949i	$-0.318003\pi$
$523$	6.76976e6	1.08223	0.541114	+	0.840949i	$0.318003\pi$
$524$	96879.1	0.0154135
$525$	−1.73712e6	−0.275063
$526$	163150.	0.0257112
$527$	544975.	0.0854772
$528$	2.25880e6	0.352608
$529$	−3.62563e6	−0.563307
$530$	−27925.3	−0.00431825
$531$	−3.98454e6	−0.613257
$532$	−1.61206e6	−0.246946
$533$	−4.57149e6	−0.697011
$534$	−1.75889e6	−0.266923
$535$	−5.12244e6	−0.773735
$536$	1.15154e6	0.173128
$537$	4.17116e6	0.624196
$538$	775796.	0.115556
$539$	−428059.	−0.0634647
$540$	1.62110e6	0.239235
$541$	−7.65401e6	−1.12434	−0.562168	−	0.827023i	$-0.690032\pi$
$541$	−7.65401e6	−1.12434	−0.562168	+	0.827023i	$0.690032\pi$
$542$	−1.47816e6	−0.216134
$543$	−6.64516e6	−0.967177
$544$	677886.	0.0982109
$545$	4.47740e6	0.645705
$546$	−2.39267e6	−0.343480
$547$	6.40165e6	0.914794	0.457397	−	0.889263i	$-0.348782\pi$
$547$	6.40165e6	0.914794	0.457397	+	0.889263i	$0.348782\pi$
$548$	−9.66675e6	−1.37508
$549$	−1.39188e6	−0.197094
$550$	−62931.7	−0.00887081
$551$	2.73128e6	0.383255
$552$	1.72105e6	0.240406
$553$	−6.60375e6	−0.918286
$554$	−1.93958e6	−0.268493
$555$	−165079.	−0.0227488
$556$	242797.	0.0333086
$557$	9.96376e6	1.36077	0.680386	−	0.732854i	$-0.261812\pi$
$557$	9.96376e6	1.36077	0.680386	+	0.732854i	$0.261812\pi$
$558$	227092.	0.0308757
$559$	2.02402e7	2.73959
$560$	−3.41611e6	−0.460322
$561$	643706.	0.0863536
$562$	1.19309e6	0.159343
$563$	534451.	0.0710619	0.0355310	−	0.999369i	$-0.488688\pi$
$563$	534451.	0.0710619	0.0355310	+	0.999369i	$0.488688\pi$
$564$	5.99963e6	0.794195
$565$	−2.51580e6	−0.331555
$566$	−294397.	−0.0386271
$567$	−1.04951e7	−1.37097
$568$	1.07201e6	0.139420
$569$	−1.25208e7	−1.62126	−0.810628	−	0.585561i	$-0.800874\pi$
$569$	−1.25208e7	−1.62126	−0.810628	+	0.585561i	$0.800874\pi$
$570$	146345.	0.0188664
$571$	9.57992e6	1.22962	0.614811	−	0.788675i	$-0.289232\pi$
$571$	9.57992e6	1.22962	0.614811	+	0.788675i	$0.289232\pi$
$572$	3.91888e6	0.500808
$573$	−1.00794e7	−1.28247
$574$	−524518.	−0.0664477
$575$	1.04782e6	0.132166
$576$	−3.90849e6	−0.490854
$577$	3.76820e6	0.471188	0.235594	−	0.971852i	$-0.424296\pi$
$577$	3.76820e6	0.471188	0.235594	+	0.971852i	$0.424296\pi$
$578$	−1.11952e6	−0.139384
$579$	3.80413e6	0.471583
$580$	5.92172e6	0.730934
$581$	−5.46102e6	−0.671171
$582$	−881289.	−0.107848
$583$	−162420.	−0.0197910
$584$	−1.72448e6	−0.209231
$585$	−3.53562e6	−0.427146
$586$	232507.	0.0279699
$587$	−4.19715e6	−0.502759	−0.251379	−	0.967889i	$-0.580884\pi$
$587$	−4.19715e6	−0.502759	−0.251379	+	0.967889i	$0.580884\pi$
$588$	2.15821e6	0.257424
$589$	720622.	0.0855893
$590$	606352.	0.0717125
$591$	916575.	0.107944
$592$	−324633.	−0.0380704
$593$	6.14595e6	0.717716	0.358858	−	0.933392i	$-0.383166\pi$
$593$	6.14595e6	0.717716	0.358858	+	0.933392i	$0.383166\pi$
$594$	−208550.	−0.0242518
$595$	−973514.	−0.112733
$596$	5.69223e6	0.656397
$597$	2.09480e7	2.40550
$598$	1.44324e6	0.165039
$599$	1.65756e7	1.88757	0.943783	−	0.330565i	$-0.107239\pi$
$599$	1.65756e7	1.88757	0.943783	+	0.330565i	$0.107239\pi$
$600$	641601.	0.0727591
$601$	−1.59210e7	−1.79798	−0.898991	−	0.437967i	$-0.855699\pi$
$601$	−1.59210e7	−1.79798	−0.898991	+	0.437967i	$0.855699\pi$
$602$	2.32229e6	0.261171
$603$	−2.98826e6	−0.334677
$604$	9.22393e6	1.02878
$605$	−366025.	−0.0406558
$606$	1.15439e6	0.127694
$607$	−1.50965e7	−1.66305	−0.831525	−	0.555488i	$-0.812532\pi$
$607$	−1.50965e7	−1.66305	−0.831525	+	0.555488i	$0.812532\pi$
$608$	896370.	0.0983396
$609$	−2.10286e7	−2.29756
$610$	211812.	0.0230476
$611$	1.01737e7	1.10249
$612$	−1.16849e6	−0.126109
$613$	1.40376e6	0.150883	0.0754416	−	0.997150i	$-0.475963\pi$
$613$	1.40376e6	0.150883	0.0754416	+	0.997150i	$0.475963\pi$
$614$	−2.20739e6	−0.236296
$615$	−2.15276e6	−0.229513
$616$	909223.	0.0965425
$617$	−3.57668e6	−0.378240	−0.189120	−	0.981954i	$-0.560564\pi$
$617$	−3.57668e6	−0.378240	−0.189120	+	0.981954i	$0.560564\pi$
$618$	−2.66292e6	−0.280471
$619$	5.88995e6	0.617852	0.308926	−	0.951086i	$-0.400030\pi$
$619$	5.88995e6	0.617852	0.308926	+	0.951086i	$0.400030\pi$
$620$	1.56239e6	0.163234
$621$	3.47239e6	0.361327
$622$	793501.	0.0822378
$623$	1.54716e7	1.59703
$624$	−1.93116e7	−1.98545
$625$	390625.	0.0400000
$626$	−409010.	−0.0417156
$627$	851174.	0.0864668
$628$	601791.	0.0608901
$629$	−92513.0	−0.00932344
$630$	−405665.	−0.0407208
$631$	1.77157e6	0.177128	0.0885638	−	0.996071i	$-0.471772\pi$
$631$	1.77157e6	0.177128	0.0885638	+	0.996071i	$0.471772\pi$
$632$	2.43908e6	0.242903
$633$	−1.22378e7	−1.21393
$634$	984725.	0.0972953
$635$	6.67062e6	0.656496
$636$	818893.	0.0802757
$637$	3.65971e6	0.357353
$638$	−761814.	−0.0740965
$639$	−2.78186e6	−0.269515
$640$	2.58119e6	0.249098
$641$	1.29029e7	1.24035	0.620174	−	0.784464i	$-0.287062\pi$
$641$	1.29029e7	1.24035	0.620174	+	0.784464i	$0.287062\pi$
$642$	−3.32251e6	−0.318148
$643$	1.52922e7	1.45862	0.729310	−	0.684183i	$-0.239841\pi$
$643$	1.52922e7	1.45862	0.729310	+	0.684183i	$0.239841\pi$
$644$	−7.48655e6	−0.711324
$645$	9.53131e6	0.902097
$646$	82014.0	0.00773227
$647$	1.05491e7	0.990732	0.495366	−	0.868684i	$-0.335034\pi$
$647$	1.05491e7	0.990732	0.495366	+	0.868684i	$0.335034\pi$
$648$	3.87631e6	0.362645
$649$	3.52668e6	0.328666
$650$	538037.	0.0499492
$651$	−5.54819e6	−0.513096
$652$	−1.87842e7	−1.73051
$653$	1.47904e7	1.35737	0.678683	−	0.734431i	$-0.262551\pi$
$653$	1.47904e7	1.35737	0.678683	+	0.734431i	$0.262551\pi$
$654$	2.90413e6	0.265504
$655$	77360.9	0.00704561
$656$	−4.23347e6	−0.384093
$657$	4.47503e6	0.404466
$658$	1.16729e6	0.105103
$659$	−9.76539e6	−0.875943	−0.437972	−	0.898989i	$-0.644303\pi$
$659$	−9.76539e6	−0.875943	−0.437972	+	0.898989i	$0.644303\pi$
$660$	1.84544e6	0.164907
$661$	−1.44015e7	−1.28205	−0.641024	−	0.767521i	$-0.721490\pi$
$661$	−1.44015e7	−1.28205	−0.641024	+	0.767521i	$0.721490\pi$
$662$	1.75019e6	0.155217
$663$	−5.50339e6	−0.486235
$664$	2.01701e6	0.177536
$665$	−1.28728e6	−0.112880
$666$	−38550.3	−0.00336777
$667$	1.26843e7	1.10396
$668$	−2.05976e7	−1.78597
$669$	1.33228e6	0.115088
$670$	454742.	0.0391362
$671$	1.23194e6	0.105629
$672$	−6.90130e6	−0.589533
$673$	1.08864e7	0.926506	0.463253	−	0.886226i	$-0.346682\pi$
$673$	1.08864e7	0.926506	0.463253	+	0.886226i	$0.346682\pi$
$674$	2.47415e6	0.209786
$675$	1.29450e6	0.109356
$676$	−2.18803e7	−1.84156
$677$	−1.87437e7	−1.57175	−0.785873	−	0.618388i	$-0.787786\pi$
$677$	−1.87437e7	−1.57175	−0.785873	+	0.618388i	$0.787786\pi$
$678$	−1.63180e6	−0.136330
$679$	7.75200e6	0.645267
$680$	359564.	0.0298197
$681$	−1.56127e7	−1.29006
$682$	−200997.	−0.0165474
$683$	−1.70583e7	−1.39921	−0.699606	−	0.714529i	$-0.746641\pi$
$683$	−1.70583e7	−1.39921	−0.699606	+	0.714529i	$0.746641\pi$
$684$	−1.54509e6	−0.126274
$685$	−7.71919e6	−0.628558
$686$	−1.57499e6	−0.127782
$687$	2.13292e7	1.72418
$688$	1.87436e7	1.50967
$689$	1.38861e6	0.111438
$690$	679638.	0.0543444
$691$	−1.39498e7	−1.11141	−0.555703	−	0.831381i	$-0.687551\pi$
$691$	−1.39498e7	−1.11141	−0.555703	+	0.831381i	$0.687551\pi$
$692$	3.36726e6	0.267308
$693$	−2.35944e6	−0.186628
$694$	−1.81681e6	−0.143190
$695$	193881.	0.0152255
$696$	7.76685e6	0.607745
$697$	−1.20644e6	−0.0940643
$698$	−1.41901e6	−0.110242
$699$	−2.21811e7	−1.71708
$700$	−2.79096e6	−0.215283
$701$	1.34576e7	1.03436	0.517182	−	0.855875i	$-0.326981\pi$
$701$	1.34576e7	1.03436	0.517182	+	0.855875i	$0.326981\pi$
$702$	1.78301e6	0.136556
$703$	−122330.	−0.00933566
$704$	3.45936e6	0.263066
$705$	4.79089e6	0.363031
$706$	−684141.	−0.0516576
$707$	−1.01542e7	−0.764009
$708$	−1.77810e7	−1.33313
$709$	−1.39796e7	−1.04443	−0.522214	−	0.852815i	$-0.674894\pi$
$709$	−1.39796e7	−1.04443	−0.522214	+	0.852815i	$0.674894\pi$
$710$	423332.	0.0315163
$711$	−6.32941e6	−0.469558
$712$	−5.71437e6	−0.422443
$713$	3.34663e6	0.246538
$714$	−631440.	−0.0463539
$715$	3.12934e6	0.228922
$716$	6.70162e6	0.488537
$717$	−3.64808e6	−0.265013
$718$	−3.73409e6	−0.270317
$719$	5.25465e6	0.379072	0.189536	−	0.981874i	$-0.439302\pi$
$719$	5.25465e6	0.379072	0.189536	+	0.981874i	$0.439302\pi$
$720$	−3.27419e6	−0.235382
$721$	2.34236e7	1.67809
$722$	108447.	0.00774240
$723$	8.84464e6	0.629266
$724$	−1.06765e7	−0.756976
$725$	4.72868e6	0.334114
$726$	−237411.	−0.0167170
$727$	−2.77659e7	−1.94839	−0.974196	−	0.225705i	$-0.927532\pi$
$727$	−2.77659e7	−1.94839	−0.974196	+	0.225705i	$0.927532\pi$
$728$	−7.77343e6	−0.543606
$729$	−251680.	−0.0175400
$730$	−680992.	−0.0472971
$731$	5.34150e6	0.369718
$732$	−6.21126e6	−0.428452
$733$	9.41107e6	0.646962	0.323481	−	0.946235i	$-0.395147\pi$
$733$	9.41107e6	0.646962	0.323481	+	0.946235i	$0.395147\pi$
$734$	1.31660e6	0.0902018
$735$	1.72339e6	0.117670
$736$	4.16282e6	0.283265
$737$	2.64488e6	0.179365
$738$	−502727.	−0.0339775
$739$	4.69651e6	0.316347	0.158174	−	0.987411i	$-0.449439\pi$
$739$	4.69651e6	0.316347	0.158174	+	0.987411i	$0.449439\pi$
$740$	−265225.	−0.0178047
$741$	−7.27714e6	−0.486872
$742$	159325.	0.0106236
$743$	1.90440e7	1.26557	0.632784	−	0.774328i	$-0.281912\pi$
$743$	1.90440e7	1.26557	0.632784	+	0.774328i	$0.281912\pi$
$744$	2.04921e6	0.135723
$745$	4.54542e6	0.300043
$746$	−3.79541e6	−0.249696
$747$	−5.23415e6	−0.343198
$748$	1.03421e6	0.0675860
$749$	2.92255e7	1.90352
$750$	253367.	0.0164474
$751$	2.21789e7	1.43496	0.717480	−	0.696579i	$-0.245296\pi$
$751$	2.21789e7	1.43496	0.717480	+	0.696579i	$0.245296\pi$
$752$	9.42142e6	0.607536
$753$	−3.34828e7	−2.15196
$754$	6.51316e6	0.417218
$755$	7.36559e6	0.470262
$756$	−9.24901e6	−0.588560
$757$	−1.65957e7	−1.05258	−0.526292	−	0.850304i	$-0.676418\pi$
$757$	−1.65957e7	−1.05258	−0.526292	+	0.850304i	$0.676418\pi$
$758$	−738682.	−0.0466965
$759$	3.95293e6	0.249066
$760$	475452.	0.0298588
$761$	2.60988e7	1.63365	0.816823	−	0.576888i	$-0.195733\pi$
$761$	2.60988e7	1.63365	0.816823	+	0.576888i	$0.195733\pi$
$762$	4.32670e6	0.269941
$763$	−2.55453e7	−1.58855
$764$	−1.61941e7	−1.00375
$765$	−933071.	−0.0576449
$766$	−1.60594e6	−0.0988914
$767$	−3.01515e7	−1.85063
$768$	−1.61531e7	−0.988219
$769$	2.12032e7	1.29296	0.646480	−	0.762931i	$-0.276240\pi$
$769$	2.12032e7	1.29296	0.646480	+	0.762931i	$0.276240\pi$
$770$	359050.	0.0218237
$771$	1.00731e7	0.610278
$772$	6.11192e6	0.369092
$773$	−3.54969e6	−0.213669	−0.106834	−	0.994277i	$-0.534071\pi$
$773$	−3.54969e6	−0.213669	−0.106834	+	0.994277i	$0.534071\pi$
$774$	2.22582e6	0.133548
$775$	1.24761e6	0.0746150
$776$	−2.86318e6	−0.170684
$777$	941840.	0.0559660
$778$	−1.95318e6	−0.115689
$779$	−1.59528e6	−0.0941876
$780$	−1.57776e7	−0.928550
$781$	2.46220e6	0.144443
$782$	380881.	0.0222727
$783$	1.56704e7	0.913432
$784$	3.38910e6	0.196922
$785$	480548.	0.0278332
$786$	50177.8	0.00289704
$787$	−9.02621e6	−0.519480	−0.259740	−	0.965679i	$-0.583637\pi$
$787$	−9.02621e6	−0.519480	−0.259740	+	0.965679i	$0.583637\pi$
$788$	1.47262e6	0.0844842
$789$	−3.82040e6	−0.218482
$790$	963185.	0.0549088
$791$	1.43536e7	0.815681
$792$	871451.	0.0493662
$793$	−1.05325e7	−0.594772
$794$	1.80588e6	0.101657
$795$	653911.	0.0366945
$796$	3.36562e7	1.88270
$797$	−2.63028e7	−1.46675	−0.733374	−	0.679825i	$-0.762056\pi$
$797$	−2.63028e7	−1.46675	−0.733374	+	0.679825i	$0.762056\pi$
$798$	−834954.	−0.0464147
$799$	2.68489e6	0.148785
$800$	1.55189e6	0.0857305
$801$	1.48288e7	0.816630
$802$	−1.78450e6	−0.0979671
$803$	−3.96080e6	−0.216767
$804$	−1.33351e7	−0.727537
$805$	−5.97824e6	−0.325150
$806$	1.71843e6	0.0931740
$807$	−1.81664e7	−0.981940
$808$	3.75043e6	0.202094
$809$	3.41842e7	1.83634	0.918171	−	0.396184i	$-0.129666\pi$
$809$	3.41842e7	1.83634	0.918171	+	0.396184i	$0.129666\pi$
$810$	1.53075e6	0.0819768
$811$	1.01840e6	0.0543711	0.0271856	−	0.999630i	$-0.491346\pi$
$811$	1.01840e6	0.0543711	0.0271856	+	0.999630i	$0.491346\pi$
$812$	−3.37857e7	−1.79822
$813$	3.46133e7	1.83661
$814$	34120.5	0.00180491
$815$	−1.49997e7	−0.791024
$816$	−5.09646e6	−0.267943
$817$	7.06308e6	0.370202
$818$	2.48439e6	0.129818
$819$	2.01721e7	1.05085
$820$	−3.45875e6	−0.179632
$821$	−2.07409e7	−1.07392	−0.536958	−	0.843609i	$-0.680427\pi$
$821$	−2.07409e7	−1.07392	−0.536958	+	0.843609i	$0.680427\pi$
$822$	−5.00682e6	−0.258453
$823$	1.46114e7	0.751958	0.375979	−	0.926628i	$-0.377307\pi$
$823$	1.46114e7	0.751958	0.375979	+	0.926628i	$0.377307\pi$
$824$	−8.65144e6	−0.443885
$825$	1.47364e6	0.0753800
$826$	−3.45948e6	−0.176425
$827$	−3.62455e6	−0.184285	−0.0921426	−	0.995746i	$-0.529372\pi$
$827$	−3.62455e6	−0.184285	−0.0921426	+	0.995746i	$0.529372\pi$
$828$	−7.17554e6	−0.363730
$829$	−2.41476e7	−1.22036	−0.610180	−	0.792263i	$-0.708903\pi$
$829$	−2.41476e7	−1.22036	−0.610180	+	0.792263i	$0.708903\pi$
$830$	796512.	0.0401326
$831$	4.54180e7	2.28153
$832$	−2.95759e7	−1.48126
$833$	965818.	0.0482262
$834$	125755.	0.00626051
$835$	−1.64478e7	−0.816378
$836$	1.36754e6	0.0676746
$837$	4.13448e6	0.203989
$838$	1.68833e6	0.0830515
$839$	−3.41130e7	−1.67308	−0.836538	−	0.547909i	$-0.815424\pi$
$839$	−3.41130e7	−1.67308	−0.836538	+	0.547909i	$0.815424\pi$
$840$	−3.66059e6	−0.179000
$841$	3.67314e7	1.79080
$842$	5.35483e6	0.260295
$843$	−2.79380e7	−1.35402
$844$	−1.96620e7	−0.950104
$845$	−1.74721e7	−0.841789
$846$	1.11880e6	0.0537436
$847$	2.08832e6	0.100020
$848$	1.28593e6	0.0614086
$849$	6.89373e6	0.328235
$850$	141991.	0.00674083
$851$	−568112.	−0.0268912
$852$	−1.24140e7	−0.585885
$853$	−2.39101e6	−0.112514	−0.0562572	−	0.998416i	$-0.517917\pi$
$853$	−2.39101e6	−0.112514	−0.0562572	+	0.998416i	$0.517917\pi$
$854$	−1.20847e6	−0.0567010
$855$	−1.23380e6	−0.0577205
$856$	−1.07943e7	−0.503515
$857$	−8.04091e6	−0.373984	−0.186992	−	0.982361i	$-0.559874\pi$
$857$	−8.04091e6	−0.373984	−0.186992	+	0.982361i	$0.559874\pi$
$858$	2.02975e6	0.0941293
$859$	3.20810e7	1.48342	0.741712	−	0.670719i	$-0.234014\pi$
$859$	3.20810e7	1.48342	0.741712	+	0.670719i	$0.234014\pi$
$860$	1.53135e7	0.706040
$861$	1.22823e7	0.564642
$862$	336861.	0.0154412
$863$	−3.26954e7	−1.49437	−0.747187	−	0.664614i	$-0.768596\pi$
$863$	−3.26954e7	−1.49437	−0.747187	+	0.664614i	$0.768596\pi$
$864$	5.14282e6	0.234378
$865$	2.68886e6	0.122188
$866$	−1.04230e6	−0.0472280
$867$	2.62151e7	1.18442
$868$	−8.91404e6	−0.401583
$869$	5.60210e6	0.251653
$870$	3.06711e6	0.137382
$871$	−2.26125e7	−1.00996
$872$	9.43507e6	0.420198
$873$	7.42996e6	0.329952
$874$	503639.	0.0223018
$875$	−2.22867e6	−0.0984069
$876$	1.99697e7	0.879248
$877$	1.93494e7	0.849512	0.424756	−	0.905308i	$-0.360360\pi$
$877$	1.93494e7	0.849512	0.424756	+	0.905308i	$0.360360\pi$
$878$	3.19256e6	0.139766
$879$	−5.44448e6	−0.237675
$880$	2.89795e6	0.126149
$881$	−2.28553e7	−0.992081	−0.496040	−	0.868299i	$-0.665213\pi$
$881$	−2.28553e7	−0.992081	−0.496040	+	0.868299i	$0.665213\pi$
$882$	402458.	0.0174201
$883$	−2.52766e6	−0.109098	−0.0545490	−	0.998511i	$-0.517372\pi$
$883$	−2.52766e6	−0.109098	−0.0545490	+	0.998511i	$0.517372\pi$
$884$	−8.84205e6	−0.380559
$885$	−1.41986e7	−0.609380
$886$	2.57529e6	0.110215
$887$	−1.65430e7	−0.706000	−0.353000	−	0.935623i	$-0.614838\pi$
$887$	−1.65430e7	−0.706000	−0.353000	+	0.935623i	$0.614838\pi$
$888$	−347865.	−0.0148040
$889$	−3.80585e7	−1.61509
$890$	−2.25659e6	−0.0954945
$891$	8.90317e6	0.375708
$892$	2.14051e6	0.0900752
$893$	3.55024e6	0.148980
$894$	2.94824e6	0.123373
$895$	5.35145e6	0.223313
$896$	−1.47267e7	−0.612824
$897$	−3.37957e7	−1.40243
$898$	−4.08741e6	−0.169144
$899$	1.51029e7	0.623248
$900$	−2.67502e6	−0.110083
$901$	366462.	0.0150389
$902$	444959.	0.0182097
$903$	−5.43799e7	−2.21931
$904$	−5.30147e6	−0.215762
$905$	−8.52550e6	−0.346018
$906$	4.77746e6	0.193365
$907$	3.71939e7	1.50125	0.750626	−	0.660727i	$-0.229752\pi$
$907$	3.71939e7	1.50125	0.750626	+	0.660727i	$0.229752\pi$
$908$	−2.50842e7	−1.00968
$909$	−9.73238e6	−0.390670
$910$	−3.06971e6	−0.122884
$911$	−3.45810e7	−1.38052	−0.690259	−	0.723562i	$-0.742503\pi$
$911$	−3.45810e7	−1.38052	−0.690259	+	0.723562i	$0.742503\pi$
$912$	−6.73905e6	−0.268294
$913$	4.63269e6	0.183932
$914$	516332.	0.0204439
$915$	−4.95988e6	−0.195848
$916$	3.42688e7	1.34946
$917$	−441374.	−0.0173334
$918$	470546.	0.0184287
$919$	−3.96856e7	−1.55004	−0.775022	−	0.631934i	$-0.782261\pi$
$919$	−3.96856e7	−1.55004	−0.775022	+	0.631934i	$0.782261\pi$
$920$	2.20804e6	0.0860078
$921$	5.16891e7	2.00794
$922$	3.48148e6	0.134877
$923$	−2.10506e7	−0.813319
$924$	−1.05289e7	−0.405700
$925$	−211790.	−0.00813864
$926$	−2.59541e6	−0.0994670
$927$	2.24505e7	0.858079
$928$	1.87862e7	0.716093
$929$	−6.61794e6	−0.251584	−0.125792	−	0.992057i	$-0.540147\pi$
$929$	−6.61794e6	−0.251584	−0.125792	+	0.992057i	$0.540147\pi$
$930$	809227.	0.0306805
$931$	1.27710e6	0.0482894
$932$	−3.56375e7	−1.34390
$933$	−1.85810e7	−0.698819
$934$	−4.62170e6	−0.173354
$935$	825852.	0.0308939
$936$	−7.45050e6	−0.277969
$937$	6.96182e6	0.259044	0.129522	−	0.991577i	$-0.458656\pi$
$937$	6.96182e6	0.259044	0.129522	+	0.991577i	$0.458656\pi$
$938$	−2.59448e6	−0.0962817
$939$	9.57757e6	0.354480
$940$	7.69731e6	0.284132
$941$	3.33711e7	1.22856	0.614281	−	0.789088i	$-0.289446\pi$
$941$	3.33711e7	1.22856	0.614281	+	0.789088i	$0.289446\pi$
$942$	311693.	0.0114446
$943$	−7.40863e6	−0.271306
$944$	−2.79220e7	−1.01980
$945$	−7.38561e6	−0.269034
$946$	−1.97005e6	−0.0715730
$947$	9.43874e6	0.342010	0.171005	−	0.985270i	$-0.445299\pi$
$947$	9.43874e6	0.342010	0.171005	+	0.985270i	$0.445299\pi$
$948$	−2.82449e7	−1.02075
$949$	3.38630e7	1.22056
$950$	187755.	0.00674967
$951$	−2.30588e7	−0.826770
$952$	−2.05145e6	−0.0733617
$953$	3.68276e7	1.31353	0.656766	−	0.754094i	$-0.271924\pi$
$953$	3.68276e7	1.31353	0.656766	+	0.754094i	$0.271924\pi$
$954$	152706.	0.00543231
$955$	−1.29315e7	−0.458818
$956$	−5.86122e6	−0.207416
$957$	1.78390e7	0.629637
$958$	−3.39846e6	−0.119638
$959$	4.40410e7	1.54636
$960$	−1.39276e7	−0.487751
$961$	−2.46444e7	−0.860815
$962$	−291715.	−0.0101630
$963$	2.80114e7	0.973350
$964$	1.42103e7	0.492505
$965$	4.88056e6	0.168714
$966$	−3.87760e6	−0.133697
$967$	3.04930e6	0.104866	0.0524329	−	0.998624i	$-0.483302\pi$
$967$	3.04930e6	0.104866	0.0524329	+	0.998624i	$0.483302\pi$
$968$	−771313.	−0.0264571
$969$	−1.92048e6	−0.0657052
$970$	−1.13066e6	−0.0385837
$971$	1.12033e7	0.381326	0.190663	−	0.981656i	$-0.438936\pi$
$971$	1.12033e7	0.381326	0.190663	+	0.981656i	$0.438936\pi$
$972$	−2.91313e7	−0.988994
$973$	−1.10617e6	−0.0374575
$974$	−1.63516e6	−0.0552285
$975$	−1.25989e7	−0.424445
$976$	−9.75375e6	−0.327753
$977$	9.19112e6	0.308058	0.154029	−	0.988066i	$-0.450775\pi$
$977$	9.19112e6	0.308058	0.154029	+	0.988066i	$0.450775\pi$
$978$	−9.72912e6	−0.325257
$979$	−1.31248e7	−0.437661
$980$	2.76890e6	0.0920963
$981$	−2.44841e7	−0.812289
$982$	2.20270e6	0.0728915
$983$	2.66790e7	0.880615	0.440308	−	0.897847i	$-0.354869\pi$
$983$	2.66790e7	0.880615	0.440308	+	0.897847i	$0.354869\pi$
$984$	−4.53644e6	−0.149358
$985$	1.17593e6	0.0386182
$986$	1.71886e6	0.0563052
$987$	−2.73339e7	−0.893118
$988$	−1.16919e7	−0.381058
$989$	3.28016e7	1.06636
$990$	344134.	0.0111594
$991$	1.52372e6	0.0492856	0.0246428	−	0.999696i	$-0.492155\pi$
$991$	1.52372e6	0.0492856	0.0246428	+	0.999696i	$0.492155\pi$
$992$	4.95656e6	0.159919
$993$	−4.09832e7	−1.31896
$994$	−2.41528e6	−0.0775356
$995$	2.68755e7	0.860594
$996$	−2.33573e7	−0.746060
$997$	3.16114e7	1.00718	0.503589	−	0.863943i	$-0.332013\pi$
$997$	3.16114e7	1.00718	0.503589	+	0.863943i	$0.332013\pi$
$998$	376059.	0.0119517
$999$	−701854.	−0.0222502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.21	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.21	✓	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)

\(f(q)\)	\(=\)	\(q+0.832155 q^{2} -19.4861 q^{3} -31.3075 q^{4} -25.0000 q^{5} -16.2155 q^{6} +142.635 q^{7} -52.6817 q^{8} +136.709 q^{9} +O(q^{10})\)	\(q+0.832155 q^{2} -19.4861 q^{3} -31.3075 q^{4} -25.0000 q^{5} -16.2155 q^{6} +142.635 q^{7} -52.6817 q^{8} +136.709 q^{9} -20.8039 q^{10} -121.000 q^{11} +610.062 q^{12} +1034.49 q^{13} +118.694 q^{14} +487.153 q^{15} +958.001 q^{16} +273.009 q^{17} +113.763 q^{18} +361.000 q^{19} +782.688 q^{20} -2779.40 q^{21} -100.691 q^{22} +1676.52 q^{23} +1026.56 q^{24} +625.000 q^{25} +860.859 q^{26} +2071.20 q^{27} -4465.54 q^{28} +7565.88 q^{29} +405.387 q^{30} +1996.18 q^{31} +2483.02 q^{32} +2357.82 q^{33} +227.186 q^{34} -3565.87 q^{35} -4280.03 q^{36} -338.864 q^{37} +300.408 q^{38} -20158.3 q^{39} +1317.04 q^{40} -4419.06 q^{41} -2312.89 q^{42} +19565.3 q^{43} +3788.21 q^{44} -3417.73 q^{45} +1395.12 q^{46} +9834.46 q^{47} -18667.7 q^{48} +3537.68 q^{49} +520.097 q^{50} -5319.88 q^{51} -32387.4 q^{52} +1342.31 q^{53} +1723.56 q^{54} +3025.00 q^{55} -7514.24 q^{56} -7034.49 q^{57} +6295.99 q^{58} -29146.1 q^{59} -15251.6 q^{60} -10181.4 q^{61} +1661.13 q^{62} +19499.5 q^{63} -28589.8 q^{64} -25862.3 q^{65} +1962.07 q^{66} -21858.5 q^{67} -8547.23 q^{68} -32668.8 q^{69} -2967.36 q^{70} -20348.7 q^{71} -7202.07 q^{72} +32733.9 q^{73} -281.988 q^{74} -12178.8 q^{75} -11302.0 q^{76} -17258.8 q^{77} -16774.8 q^{78} -46298.3 q^{79} -23950.0 q^{80} -73579.9 q^{81} -3677.35 q^{82} -38286.7 q^{83} +87016.1 q^{84} -6825.22 q^{85} +16281.4 q^{86} -147430. q^{87} +6374.48 q^{88} +108470. q^{89} -2844.08 q^{90} +147555. q^{91} -52487.6 q^{92} -38897.9 q^{93} +8183.80 q^{94} -9025.00 q^{95} -48384.4 q^{96} +54348.6 q^{97} +2943.90 q^{98} -16541.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 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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