LMFDB - Embedded newform 1045.6.a.d.1.2

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-9.72609 q^{2} -28.7123 q^{3} +62.5968 q^{4} -25.0000 q^{5} +279.258 q^{6} -28.8219 q^{7} -297.587 q^{8} +581.397 q^{9} +O(q^{10})$	\(q-9.72609 q^{2} -28.7123 q^{3} +62.5968 q^{4} -25.0000 q^{5} +279.258 q^{6} -28.8219 q^{7} -297.587 q^{8} +581.397 q^{9} +243.152 q^{10} +121.000 q^{11} -1797.30 q^{12} -385.150 q^{13} +280.324 q^{14} +717.808 q^{15} +891.261 q^{16} +296.619 q^{17} -5654.72 q^{18} -361.000 q^{19} -1564.92 q^{20} +827.543 q^{21} -1176.86 q^{22} -3768.31 q^{23} +8544.41 q^{24} +625.000 q^{25} +3746.01 q^{26} -9716.16 q^{27} -1804.16 q^{28} +3926.61 q^{29} -6981.46 q^{30} +8458.83 q^{31} +854.302 q^{32} -3474.19 q^{33} -2884.94 q^{34} +720.547 q^{35} +36393.6 q^{36} +6116.98 q^{37} +3511.12 q^{38} +11058.6 q^{39} +7439.68 q^{40} -2317.48 q^{41} -8048.75 q^{42} -2342.25 q^{43} +7574.21 q^{44} -14534.9 q^{45} +36650.9 q^{46} +21630.9 q^{47} -25590.2 q^{48} -15976.3 q^{49} -6078.81 q^{50} -8516.60 q^{51} -24109.2 q^{52} +15364.9 q^{53} +94500.2 q^{54} -3025.00 q^{55} +8577.02 q^{56} +10365.1 q^{57} -38190.5 q^{58} -30451.7 q^{59} +44932.5 q^{60} +43300.3 q^{61} -82271.3 q^{62} -16757.0 q^{63} -36829.4 q^{64} +9628.76 q^{65} +33790.3 q^{66} +61316.0 q^{67} +18567.4 q^{68} +108197. q^{69} -7008.10 q^{70} +48670.9 q^{71} -173016. q^{72} -64749.8 q^{73} -59494.3 q^{74} -17945.2 q^{75} -22597.4 q^{76} -3487.45 q^{77} -107557. q^{78} +102898. q^{79} -22281.5 q^{80} +137694. q^{81} +22540.0 q^{82} +117713. q^{83} +51801.5 q^{84} -7415.46 q^{85} +22781.0 q^{86} -112742. q^{87} -36008.0 q^{88} +109327. q^{89} +141368. q^{90} +11100.8 q^{91} -235884. q^{92} -242873. q^{93} -210384. q^{94} +9025.00 q^{95} -24529.0 q^{96} -97880.9 q^{97} +155387. q^{98} +70349.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * 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 $

$2$	−9.72609	−1.71935	−0.859673	−	0.510845i	$-0.829333\pi$
$2$	−9.72609	−1.71935	−0.859673	+	0.510845i	$0.829333\pi$
$3$	−28.7123	−1.84190	−0.920948	−	0.389686i	$-0.872584\pi$
$3$	−28.7123	−1.84190	−0.920948	+	0.389686i	$0.872584\pi$
$4$	62.5968	1.95615
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	279.258	3.16686
$7$	−28.8219	−0.222319	−0.111160	−	0.993803i	$-0.535456\pi$
$7$	−28.8219	−0.222319	−0.111160	+	0.993803i	$0.535456\pi$
$8$	−297.587	−1.64395
$9$	581.397	2.39258
$10$	243.152	0.768915
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−1797.30	−3.60302
$13$	−385.150	−0.632080	−0.316040	−	0.948746i	$-0.602353\pi$
$13$	−385.150	−0.632080	−0.316040	+	0.948746i	$0.602353\pi$
$14$	280.324	0.382244
$15$	717.808	0.823721
$16$	891.261	0.870372
$17$	296.619	0.248929	0.124465	−	0.992224i	$-0.460279\pi$
$17$	296.619	0.248929	0.124465	+	0.992224i	$0.460279\pi$
$18$	−5654.72	−4.11367
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−1564.92	−0.874817
$21$	827.543	0.409489
$22$	−1176.86	−0.518402
$23$	−3768.31	−1.48534	−0.742671	−	0.669656i	$-0.766442\pi$
$23$	−3768.31	−1.48534	−0.742671	+	0.669656i	$0.766442\pi$
$24$	8544.41	3.02799
$25$	625.000	0.200000
$26$	3746.01	1.08676
$27$	−9716.16	−2.56499
$28$	−1804.16	−0.434890
$29$	3926.61	0.867007	0.433503	−	0.901152i	$-0.357277\pi$
$29$	3926.61	0.867007	0.433503	+	0.901152i	$0.357277\pi$
$30$	−6981.46	−1.41626
$31$	8458.83	1.58091	0.790453	−	0.612522i	$-0.209845\pi$
$31$	8458.83	1.58091	0.790453	+	0.612522i	$0.209845\pi$
$32$	854.302	0.147481
$33$	−3474.19	−0.555352
$34$	−2884.94	−0.427996
$35$	720.547	0.0994242
$36$	36393.6	4.68024
$37$	6116.98	0.734569	0.367285	−	0.930109i	$-0.380288\pi$
$37$	6116.98	0.734569	0.367285	+	0.930109i	$0.380288\pi$
$38$	3511.12	0.394445
$39$	11058.6	1.16423
$40$	7439.68	0.735198
$41$	−2317.48	−0.215306	−0.107653	−	0.994189i	$-0.534334\pi$
$41$	−2317.48	−0.215306	−0.107653	+	0.994189i	$0.534334\pi$
$42$	−8048.75	−0.704053
$43$	−2342.25	−0.193180	−0.0965902	−	0.995324i	$-0.530794\pi$
$43$	−2342.25	−0.193180	−0.0965902	+	0.995324i	$0.530794\pi$
$44$	7574.21	0.589801
$45$	−14534.9	−1.06999
$46$	36650.9	2.55382
$47$	21630.9	1.42834	0.714168	−	0.699975i	$-0.246805\pi$
$47$	21630.9	1.42834	0.714168	+	0.699975i	$0.246805\pi$
$48$	−25590.2	−1.60314
$49$	−15976.3	−0.950574
$50$	−6078.81	−0.343869
$51$	−8516.60	−0.458502
$52$	−24109.2	−1.23644
$53$	15364.9	0.751347	0.375673	−	0.926752i	$-0.377411\pi$
$53$	15364.9	0.751347	0.375673	+	0.926752i	$0.377411\pi$
$54$	94500.2	4.41010
$55$	−3025.00	−0.134840
$56$	8577.02	0.365482
$57$	10365.1	0.422560
$58$	−38190.5	−1.49068
$59$	−30451.7	−1.13889	−0.569444	−	0.822030i	$-0.692841\pi$
$59$	−30451.7	−1.13889	−0.569444	+	0.822030i	$0.692841\pi$
$60$	44932.5	1.61132
$61$	43300.3	1.48993	0.744966	−	0.667102i	$-0.232465\pi$
$61$	43300.3	1.48993	0.744966	+	0.667102i	$0.232465\pi$
$62$	−82271.3	−2.71812
$63$	−16757.0	−0.531917
$64$	−36829.4	−1.12394
$65$	9628.76	0.282675
$66$	33790.3	0.954843
$67$	61316.0	1.66873	0.834367	−	0.551210i	$-0.185834\pi$
$67$	61316.0	1.66873	0.834367	+	0.551210i	$0.185834\pi$
$68$	18567.4	0.486943
$69$	108197.	2.73585
$70$	−7008.10	−0.170945
$71$	48670.9	1.14584	0.572920	−	0.819612i	$-0.305811\pi$
$71$	48670.9	1.14584	0.572920	+	0.819612i	$0.305811\pi$
$72$	−173016.	−3.93329
$73$	−64749.8	−1.42210	−0.711052	−	0.703139i	$-0.751781\pi$
$73$	−64749.8	−1.42210	−0.711052	+	0.703139i	$0.751781\pi$
$74$	−59494.3	−1.26298
$75$	−17945.2	−0.368379
$76$	−22597.4	−0.448772
$77$	−3487.45	−0.0670318
$78$	−107557.	−2.00171
$79$	102898.	1.85499	0.927494	−	0.373838i	$-0.121958\pi$
$79$	102898.	1.85499	0.927494	+	0.373838i	$0.121958\pi$
$80$	−22281.5	−0.389242
$81$	137694.	2.33186
$82$	22540.0	0.370186
$83$	117713.	1.87555	0.937774	−	0.347246i	$-0.112883\pi$
$83$	117713.	1.87555	0.937774	+	0.347246i	$0.112883\pi$
$84$	51801.5	0.801022
$85$	−7415.46	−0.111325
$86$	22781.0	0.332144
$87$	−112742.	−1.59694
$88$	−36008.0	−0.495670
$89$	109327.	1.46302	0.731511	−	0.681830i	$-0.238816\pi$
$89$	109327.	1.46302	0.731511	+	0.681830i	$0.238816\pi$
$90$	141368.	1.83969
$91$	11100.8	0.140524
$92$	−235884.	−2.90555
$93$	−242873.	−2.91186
$94$	−210384.	−2.45580
$95$	9025.00	0.102598
$96$	−24529.0	−0.271645
$97$	−97880.9	−1.05625	−0.528127	−	0.849165i	$-0.677106\pi$
$97$	−97880.9	−1.05625	−0.528127	+	0.849165i	$0.677106\pi$
$98$	155387.	1.63437
$99$	70349.0	0.721390
$100$	39123.0	0.391230
$101$	30068.0	0.293292	0.146646	−	0.989189i	$-0.453152\pi$
$101$	30068.0	0.293292	0.146646	+	0.989189i	$0.453152\pi$
$102$	82833.2	0.788323
$103$	−129981.	−1.20722	−0.603612	−	0.797278i	$-0.706272\pi$
$103$	−129981.	−1.20722	−0.603612	+	0.797278i	$0.706272\pi$
$104$	114616.	1.03911
$105$	−20688.6	−0.183129
$106$	−149440.	−1.29182
$107$	−176849.	−1.49329	−0.746645	−	0.665223i	$-0.768336\pi$
$107$	−176849.	−1.49329	−0.746645	+	0.665223i	$0.768336\pi$
$108$	−608200.	−5.01750
$109$	−88091.0	−0.710174	−0.355087	−	0.934833i	$-0.615549\pi$
$109$	−88091.0	−0.710174	−0.355087	+	0.934833i	$0.615549\pi$
$110$	29421.4	0.231837
$111$	−175633.	−1.35300
$112$	−25687.8	−0.193501
$113$	43819.8	0.322830	0.161415	−	0.986887i	$-0.448394\pi$
$113$	43819.8	0.322830	0.161415	+	0.986887i	$0.448394\pi$
$114$	−100812.	−0.726526
$115$	94207.7	0.664266
$116$	245793.	1.69599
$117$	−223925.	−1.51230
$118$	296175.	1.95814
$119$	−8549.10	−0.0553418
$120$	−213610.	−1.35416
$121$	14641.0	0.0909091
$122$	−421143.	−2.56171
$123$	66540.3	0.396572
$124$	529496.	3.09249
$125$	−15625.0	−0.0894427
$126$	162980.	0.914549
$127$	212077.	1.16677	0.583385	−	0.812196i	$-0.301728\pi$
$127$	212077.	1.16677	0.583385	+	0.812196i	$0.301728\pi$
$128$	330868.	1.78497
$129$	67251.5	0.355818
$130$	−93650.2	−0.486016
$131$	18032.1	0.0918054	0.0459027	−	0.998946i	$-0.485384\pi$
$131$	18032.1	0.0918054	0.0459027	+	0.998946i	$0.485384\pi$
$132$	−217473.	−1.08635
$133$	10404.7	0.0510035
$134$	−596365.	−2.86913
$135$	242904.	1.14710
$136$	−88269.9	−0.409228
$137$	−294314.	−1.33971	−0.669853	−	0.742493i	$-0.733643\pi$
$137$	−294314.	−1.33971	−0.669853	+	0.742493i	$0.733643\pi$
$138$	−1.05233e6	−4.70387
$139$	−184110.	−0.808241	−0.404120	−	0.914706i	$-0.632422\pi$
$139$	−184110.	−0.808241	−0.404120	+	0.914706i	$0.632422\pi$
$140$	45103.9	0.194489
$141$	−621074.	−2.63084
$142$	−473378.	−1.97009
$143$	−46603.2	−0.190579
$144$	518177.	2.08244
$145$	−98165.2	−0.387737
$146$	629762.	2.44509
$147$	458716.	1.75086
$148$	382903.	1.43693
$149$	−369221.	−1.36245	−0.681225	−	0.732074i	$-0.738553\pi$
$149$	−369221.	−1.36245	−0.681225	+	0.732074i	$0.738553\pi$
$150$	174537.	0.633371
$151$	−130617.	−0.466185	−0.233092	−	0.972455i	$-0.574884\pi$
$151$	−130617.	−0.466185	−0.233092	+	0.972455i	$0.574884\pi$
$152$	107429.	0.377148
$153$	172453.	0.595583
$154$	33919.2	0.115251
$155$	−211471.	−0.707003
$156$	692230.	2.27740
$157$	48190.9	0.156033	0.0780163	−	0.996952i	$-0.475141\pi$
$157$	48190.9	0.156033	0.0780163	+	0.996952i	$0.475141\pi$
$158$	−1.00080e6	−3.18937
$159$	−441162.	−1.38390
$160$	−21357.6	−0.0659556
$161$	108610.	0.330220
$162$	−1.33922e6	−4.00927
$163$	−99385.6	−0.292991	−0.146496	−	0.989211i	$-0.546799\pi$
$163$	−99385.6	−0.292991	−0.146496	+	0.989211i	$0.546799\pi$
$164$	−145067.	−0.421171
$165$	86854.7	0.248361
$166$	−1.14488e6	−3.22472
$167$	−22409.2	−0.0621778	−0.0310889	−	0.999517i	$-0.509898\pi$
$167$	−22409.2	−0.0621778	−0.0310889	+	0.999517i	$0.509898\pi$
$168$	−246266.	−0.673180
$169$	−222952.	−0.600475
$170$	72123.5	0.191405
$171$	−209884.	−0.548895
$172$	−146618.	−0.377890
$173$	167626.	0.425821	0.212911	−	0.977072i	$-0.431706\pi$
$173$	167626.	0.425821	0.212911	+	0.977072i	$0.431706\pi$
$174$	1.09654e6	2.74568
$175$	−18013.7	−0.0444639
$176$	107843.	0.262427
$177$	874337.	2.09771
$178$	−1.06332e6	−2.51544
$179$	−328479.	−0.766258	−0.383129	−	0.923695i	$-0.625154\pi$
$179$	−328479.	−0.766258	−0.383129	+	0.923695i	$0.625154\pi$
$180$	−909840.	−2.09307
$181$	1174.68	0.00266516	0.00133258	−	0.999999i	$-0.499576\pi$
$181$	1174.68	0.00266516	0.00133258	+	0.999999i	$0.499576\pi$
$182$	−107967.	−0.241609
$183$	−1.24325e6	−2.74430
$184$	1.12140e6	2.44183
$185$	−152924.	−0.328509
$186$	2.36220e6	5.00650
$187$	35890.8	0.0750550
$188$	1.35403e6	2.79404
$189$	280038.	0.570246
$190$	−87777.9	−0.176401
$191$	198085.	0.392887	0.196444	−	0.980515i	$-0.437061\pi$
$191$	198085.	0.392887	0.196444	+	0.980515i	$0.437061\pi$
$192$	1.05746e6	2.07019
$193$	15921.4	0.0307672	0.0153836	−	0.999882i	$-0.495103\pi$
$193$	15921.4	0.0307672	0.0153836	+	0.999882i	$0.495103\pi$
$194$	951998.	1.81607
$195$	−276464.	−0.520657
$196$	−1.00007e6	−1.85947
$197$	866251.	1.59030	0.795148	−	0.606415i	$-0.207393\pi$
$197$	866251.	1.59030	0.795148	+	0.606415i	$0.207393\pi$
$198$	−684221.	−1.24032
$199$	−264980.	−0.474329	−0.237165	−	0.971469i	$-0.576218\pi$
$199$	−264980.	−0.474329	−0.237165	+	0.971469i	$0.576218\pi$
$200$	−185992.	−0.328790
$201$	−1.76053e6	−3.07363
$202$	−292444.	−0.504271
$203$	−113172.	−0.192752
$204$	−533112.	−0.896898
$205$	57937.0	0.0962879
$206$	1.26421e6	2.07564
$207$	−2.19088e6	−3.55380
$208$	−343270.	−0.550145
$209$	−43681.0	−0.0691714
$210$	201219.	0.314862
$211$	792023.	1.22471	0.612353	−	0.790585i	$-0.290223\pi$
$211$	792023.	1.22471	0.612353	+	0.790585i	$0.290223\pi$
$212$	961794.	1.46975
$213$	−1.39745e6	−2.11052
$214$	1.72005e6	2.56748
$215$	58556.4	0.0863929
$216$	2.89140e6	4.21672
$217$	−243799.	−0.351466
$218$	856780.	1.22104
$219$	1.85912e6	2.61937
$220$	−189355.	−0.263767
$221$	−114243.	−0.157343
$222$	1.70822e6	2.32627
$223$	821530.	1.10627	0.553135	−	0.833091i	$-0.313431\pi$
$223$	821530.	1.10627	0.553135	+	0.833091i	$0.313431\pi$
$224$	−24622.6	−0.0327879
$225$	363373.	0.478516
$226$	−426195.	−0.555057
$227$	269712.	0.347405	0.173702	−	0.984798i	$-0.444427\pi$
$227$	269712.	0.347405	0.173702	+	0.984798i	$0.444427\pi$
$228$	648825.	0.826590
$229$	−1.01437e6	−1.27823	−0.639113	−	0.769113i	$-0.720698\pi$
$229$	−1.01437e6	−1.27823	−0.639113	+	0.769113i	$0.720698\pi$
$230$	−916272.	−1.14210
$231$	100133.	0.123466
$232$	−1.16851e6	−1.42532
$233$	−1.30558e6	−1.57548	−0.787741	−	0.616007i	$-0.788749\pi$
$233$	−1.30558e6	−1.57548	−0.787741	+	0.616007i	$0.788749\pi$
$234$	2.17792e6	2.60017
$235$	−540773.	−0.638771
$236$	−1.90618e6	−2.22783
$237$	−2.95445e6	−3.41669
$238$	83149.3	0.0951517
$239$	−745463.	−0.844172	−0.422086	−	0.906556i	$-0.638702\pi$
$239$	−745463.	−0.844172	−0.422086	+	0.906556i	$0.638702\pi$
$240$	639754.	0.716944
$241$	664512.	0.736987	0.368494	−	0.929630i	$-0.379874\pi$
$241$	664512.	0.736987	0.368494	+	0.929630i	$0.379874\pi$
$242$	−142400.	−0.156304
$243$	−1.59248e6	−1.73005
$244$	2.71046e6	2.91453
$245$	399407.	0.425110
$246$	−647176.	−0.681844
$247$	139039.	0.145009
$248$	−2.51724e6	−2.59893
$249$	−3.37981e6	−3.45456
$250$	151970.	0.153783
$251$	1.69874e6	1.70194	0.850968	−	0.525217i	$-0.176016\pi$
$251$	1.69874e6	1.70194	0.850968	+	0.525217i	$0.176016\pi$
$252$	−1.04893e6	−1.04051
$253$	−455965.	−0.447848
$254$	−2.06268e6	−2.00608
$255$	212915.	0.205048
$256$	−2.03951e6	−1.94503
$257$	636840.	0.601447	0.300724	−	0.953711i	$-0.402772\pi$
$257$	636840.	0.601447	0.300724	+	0.953711i	$0.402772\pi$
$258$	−654095.	−0.611774
$259$	−176303.	−0.163309
$260$	602730.	0.552954
$261$	2.28292e6	2.07438
$262$	−175382.	−0.157845
$263$	1.54686e6	1.37899	0.689497	−	0.724289i	$-0.257832\pi$
$263$	1.54686e6	1.37899	0.689497	+	0.724289i	$0.257832\pi$
$264$	1.03387e6	0.912973
$265$	−384123.	−0.336012
$266$	−101197.	−0.0876927
$267$	−3.13902e6	−2.69473
$268$	3.83819e6	3.26429
$269$	627827.	0.529004	0.264502	−	0.964385i	$-0.414792\pi$
$269$	627827.	0.529004	0.264502	+	0.964385i	$0.414792\pi$
$270$	−2.36251e6	−1.97226
$271$	151870.	0.125617	0.0628085	−	0.998026i	$-0.479994\pi$
$271$	151870.	0.125617	0.0628085	+	0.998026i	$0.479994\pi$
$272$	264365.	0.216661
$273$	−318728.	−0.258830
$274$	2.86253e6	2.30342
$275$	75625.0	0.0603023
$276$	6.77277e6	5.35173
$277$	−543003.	−0.425209	−0.212605	−	0.977138i	$-0.568195\pi$
$277$	−543003.	−0.425209	−0.212605	+	0.977138i	$0.568195\pi$
$278$	1.79067e6	1.38965
$279$	4.91794e6	3.78244
$280$	−214426.	−0.163449
$281$	−1.19326e6	−0.901504	−0.450752	−	0.892649i	$-0.648844\pi$
$281$	−1.19326e6	−0.901504	−0.450752	+	0.892649i	$0.648844\pi$
$282$	6.04062e6	4.52333
$283$	−1.91727e6	−1.42304	−0.711520	−	0.702666i	$-0.751993\pi$
$283$	−1.91727e6	−1.42304	−0.711520	+	0.702666i	$0.751993\pi$
$284$	3.04664e6	2.24143
$285$	−259129.	−0.188975
$286$	453267.	0.327672
$287$	66794.2	0.0478667
$288$	496689.	0.352860
$289$	−1.33187e6	−0.938034
$290$	954763.	0.666654
$291$	2.81039e6	1.94551
$292$	−4.05313e6	−2.78185
$293$	2.36344e6	1.60833	0.804167	−	0.594403i	$-0.202612\pi$
$293$	2.36344e6	1.60833	0.804167	+	0.594403i	$0.202612\pi$
$294$	−4.46152e6	−3.01033
$295$	761291.	0.509326
$296$	−1.82033e6	−1.20760
$297$	−1.17566e6	−0.773373
$298$	3.59108e6	2.34252
$299$	1.45137e6	0.938855
$300$	−1.12331e6	−0.720605
$301$	67508.2	0.0429477
$302$	1.27040e6	0.801533
$303$	−863320.	−0.540214
$304$	−321745.	−0.199677
$305$	−1.08251e6	−0.666318
$306$	−1.67729e6	−1.02401
$307$	−691941.	−0.419009	−0.209504	−	0.977808i	$-0.567185\pi$
$307$	−691941.	−0.419009	−0.209504	+	0.977808i	$0.567185\pi$
$308$	−218303.	−0.131124
$309$	3.73207e6	2.22358
$310$	2.05678e6	1.21558
$311$	2.58359e6	1.51469	0.757343	−	0.653017i	$-0.226497\pi$
$311$	2.58359e6	1.51469	0.757343	+	0.653017i	$0.226497\pi$
$312$	−3.29088e6	−1.91393
$313$	−2.42712e6	−1.40033	−0.700165	−	0.713981i	$-0.746890\pi$
$313$	−2.42712e6	−1.40033	−0.700165	+	0.713981i	$0.746890\pi$
$314$	−468709.	−0.268274
$315$	418924.	0.237880
$316$	6.44111e6	3.62863
$317$	−1.12755e6	−0.630216	−0.315108	−	0.949056i	$-0.602041\pi$
$317$	−1.12755e6	−0.630216	−0.315108	+	0.949056i	$0.602041\pi$
$318$	4.29078e6	2.37941
$319$	475119.	0.261412
$320$	920734.	0.502643
$321$	5.07775e6	2.75048
$322$	−1.05635e6	−0.567763
$323$	−107079.	−0.0571083
$324$	8.61920e6	4.56146
$325$	−240719.	−0.126416
$326$	966633.	0.503753
$327$	2.52929e6	1.30807
$328$	689653.	0.353953
$329$	−623444.	−0.317547
$330$	−844757.	−0.427019
$331$	1.23289e6	0.618521	0.309261	−	0.950977i	$-0.399918\pi$
$331$	1.23289e6	0.618521	0.309261	+	0.950977i	$0.399918\pi$
$332$	7.36844e6	3.66885
$333$	3.55639e6	1.75752
$334$	217954.	0.106905
$335$	−1.53290e6	−0.746280
$336$	737557.	0.356408
$337$	866716.	0.415721	0.207860	−	0.978158i	$-0.433350\pi$
$337$	866716.	0.415721	0.207860	+	0.978158i	$0.433350\pi$
$338$	2.16845e6	1.03242
$339$	−1.25817e6	−0.594619
$340$	−464184.	−0.217768
$341$	1.02352e6	0.476661
$342$	2.04135e6	0.943741
$343$	944876.	0.433650
$344$	697025.	0.317579
$345$	−2.70492e6	−1.22351
$346$	−1.63035e6	−0.732134
$347$	−560166.	−0.249743	−0.124871	−	0.992173i	$-0.539852\pi$
$347$	−560166.	−0.249743	−0.124871	+	0.992173i	$0.539852\pi$
$348$	−7.05728e6	−3.12385
$349$	−981669.	−0.431421	−0.215711	−	0.976457i	$-0.569207\pi$
$349$	−981669.	−0.431421	−0.215711	+	0.976457i	$0.569207\pi$
$350$	175203.	0.0764488
$351$	3.74218e6	1.62128
$352$	103371.	0.0444672
$353$	4.46593e6	1.90755	0.953773	−	0.300527i	$-0.0971626\pi$
$353$	4.46593e6	1.90755	0.953773	+	0.300527i	$0.0971626\pi$
$354$	−8.50388e6	−3.60669
$355$	−1.21677e6	−0.512435
$356$	6.84349e6	2.86189
$357$	245465.	0.101934
$358$	3.19482e6	1.31746
$359$	−3.61341e6	−1.47973	−0.739864	−	0.672757i	$-0.765110\pi$
$359$	−3.61341e6	−1.47973	−0.739864	+	0.672757i	$0.765110\pi$
$360$	4.32541e6	1.75902
$361$	130321.	0.0526316
$362$	−11425.0	−0.00458233
$363$	−420377.	−0.167445
$364$	694872.	0.274885
$365$	1.61875e6	0.635984
$366$	1.20920e7	4.71840
$367$	668890.	0.259232	0.129616	−	0.991564i	$-0.458625\pi$
$367$	668890.	0.259232	0.129616	+	0.991564i	$0.458625\pi$
$368$	−3.35855e6	−1.29280
$369$	−1.34738e6	−0.515137
$370$	1.48736e6	0.564821
$371$	−442846.	−0.167039
$372$	−1.52030e7	−5.69604
$373$	−3.54736e6	−1.32018	−0.660089	−	0.751187i	$-0.729482\pi$
$373$	−3.54736e6	−1.32018	−0.660089	+	0.751187i	$0.729482\pi$
$374$	−349078.	−0.129046
$375$	448630.	0.164744
$376$	−6.43708e6	−2.34812
$377$	−1.51233e6	−0.548017
$378$	−2.72367e6	−0.980450
$379$	−3.69777e6	−1.32234	−0.661168	−	0.750238i	$-0.729939\pi$
$379$	−3.69777e6	−1.32234	−0.661168	+	0.750238i	$0.729939\pi$
$380$	564936.	0.200697
$381$	−6.08923e6	−2.14907
$382$	−1.92659e6	−0.675509
$383$	−3.06902e6	−1.06906	−0.534530	−	0.845149i	$-0.679511\pi$
$383$	−3.06902e6	−1.06906	−0.534530	+	0.845149i	$0.679511\pi$
$384$	−9.49999e6	−3.28772
$385$	87186.2	0.0299775
$386$	−154853.	−0.0528994
$387$	−1.36178e6	−0.462199
$388$	−6.12703e6	−2.06619
$389$	2.21513e6	0.742209	0.371104	−	0.928591i	$-0.378979\pi$
$389$	2.21513e6	0.742209	0.371104	+	0.928591i	$0.378979\pi$
$390$	2.68891e6	0.895190
$391$	−1.11775e6	−0.369745
$392$	4.75434e6	1.56270
$393$	−517743.	−0.169096
$394$	−8.42523e6	−2.73427
$395$	−2.57246e6	−0.829576
$396$	4.40362e6	1.41115
$397$	547540.	0.174357	0.0871786	−	0.996193i	$-0.472215\pi$
$397$	547540.	0.174357	0.0871786	+	0.996193i	$0.472215\pi$
$398$	2.57722e6	0.815536
$399$	−298743.	−0.0939432
$400$	557038.	0.174074
$401$	−4.96243e6	−1.54111	−0.770555	−	0.637373i	$-0.780021\pi$
$401$	−4.96243e6	−1.54111	−0.770555	+	0.637373i	$0.780021\pi$
$402$	1.71230e7	5.28464
$403$	−3.25792e6	−0.999259
$404$	1.88216e6	0.573723
$405$	−3.44235e6	−1.04284
$406$	1.10072e6	0.331408
$407$	740154.	0.221481
$408$	2.53443e6	0.753755
$409$	−2.79672e6	−0.826687	−0.413343	−	0.910575i	$-0.635639\pi$
$409$	−2.79672e6	−0.826687	−0.413343	+	0.910575i	$0.635639\pi$
$410$	−563501.	−0.165552
$411$	8.45044e6	2.46760
$412$	−8.13642e6	−2.36151
$413$	877674.	0.253197
$414$	2.13087e7	6.11021
$415$	−2.94282e6	−0.838771
$416$	−329035.	−0.0932199
$417$	5.28623e6	1.48869
$418$	424845.	0.118930
$419$	−1.56408e6	−0.435236	−0.217618	−	0.976034i	$-0.569829\pi$
$419$	−1.56408e6	−0.435236	−0.217618	+	0.976034i	$0.569829\pi$
$420$	−1.29504e6	−0.358228
$421$	2.75927e6	0.758732	0.379366	−	0.925247i	$-0.376142\pi$
$421$	2.75927e6	0.758732	0.379366	+	0.925247i	$0.376142\pi$
$422$	−7.70329e6	−2.10569
$423$	1.25761e7	3.41741
$424$	−4.57240e6	−1.23518
$425$	185387.	0.0497859
$426$	1.35918e7	3.62871
$427$	−1.24800e6	−0.331241
$428$	−1.10702e7	−2.92110
$429$	1.33809e6	0.351027
$430$	−569524.	−0.148539
$431$	−4.44178e6	−1.15176	−0.575882	−	0.817533i	$-0.695341\pi$
$431$	−4.44178e6	−1.15176	−0.575882	+	0.817533i	$0.695341\pi$
$432$	−8.65963e6	−2.23249
$433$	−1.94449e6	−0.498410	−0.249205	−	0.968451i	$-0.580169\pi$
$433$	−1.94449e6	−0.498410	−0.249205	+	0.968451i	$0.580169\pi$
$434$	2.37121e6	0.604292
$435$	2.81855e6	0.714171
$436$	−5.51421e6	−1.38921
$437$	1.36036e6	0.340761
$438$	−1.80819e7	−4.50360
$439$	4.24843e6	1.05212	0.526062	−	0.850446i	$-0.323668\pi$
$439$	4.24843e6	1.05212	0.526062	+	0.850446i	$0.323668\pi$
$440$	900201.	0.221670
$441$	−9.28857e6	−2.27432
$442$	1.11114e6	0.270527
$443$	−6.67547e6	−1.61612	−0.808058	−	0.589102i	$-0.799481\pi$
$443$	−6.67547e6	−1.61612	−0.808058	+	0.589102i	$0.799481\pi$
$444$	−1.09940e7	−2.64667
$445$	−2.73316e6	−0.654283
$446$	−7.99028e6	−1.90206
$447$	1.06012e7	2.50949
$448$	1.06149e6	0.249874
$449$	−1.36034e6	−0.318442	−0.159221	−	0.987243i	$-0.550898\pi$
$449$	−1.36034e6	−0.318442	−0.159221	+	0.987243i	$0.550898\pi$
$450$	−3.53420e6	−0.822734
$451$	−280415.	−0.0649173
$452$	2.74298e6	0.631504
$453$	3.75032e6	0.858664
$454$	−2.62324e6	−0.597309
$455$	−277519.	−0.0628440
$456$	−3.08453e6	−0.694668
$457$	−7.30760e6	−1.63676	−0.818379	−	0.574679i	$-0.805127\pi$
$457$	−7.30760e6	−1.63676	−0.818379	+	0.574679i	$0.805127\pi$
$458$	9.86585e6	2.19771
$459$	−2.88199e6	−0.638500
$460$	5.89710e6	1.29940
$461$	−1.44384e6	−0.316421	−0.158211	−	0.987405i	$-0.550572\pi$
$461$	−1.44384e6	−0.316421	−0.158211	+	0.987405i	$0.550572\pi$
$462$	−973899.	−0.212280
$463$	3.55638e6	0.771003	0.385502	−	0.922707i	$-0.374028\pi$
$463$	3.55638e6	0.771003	0.385502	+	0.922707i	$0.374028\pi$
$464$	3.49963e6	0.754619
$465$	6.07182e6	1.30223
$466$	1.26982e7	2.70880
$467$	2.22503e6	0.472110	0.236055	−	0.971740i	$-0.424145\pi$
$467$	2.22503e6	0.472110	0.236055	+	0.971740i	$0.424145\pi$
$468$	−1.40170e7	−2.95829
$469$	−1.76724e6	−0.370992
$470$	5.25960e6	1.09827
$471$	−1.38367e6	−0.287396
$472$	9.06202e6	1.87228
$473$	−283413.	−0.0582461
$474$	2.87353e7	5.87448
$475$	−225625.	−0.0458831
$476$	−535147.	−0.108257
$477$	8.93311e6	1.79766
$478$	7.25043e6	1.45142
$479$	4.02274e6	0.801094	0.400547	−	0.916276i	$-0.368820\pi$
$479$	4.02274e6	0.801094	0.400547	+	0.916276i	$0.368820\pi$
$480$	613225.	0.121483
$481$	−2.35596e6	−0.464306
$482$	−6.46310e6	−1.26714
$483$	−3.11844e6	−0.608232
$484$	916480.	0.177832
$485$	2.44702e6	0.472371
$486$	1.54886e7	2.97456
$487$	−9.14637e6	−1.74754	−0.873768	−	0.486343i	$-0.838331\pi$
$487$	−9.14637e6	−1.74754	−0.873768	+	0.486343i	$0.838331\pi$
$488$	−1.28856e7	−2.44938
$489$	2.85359e6	0.539659
$490$	−3.88467e6	−0.730911
$491$	2.43254e6	0.455361	0.227680	−	0.973736i	$-0.426886\pi$
$491$	2.43254e6	0.455361	0.227680	+	0.973736i	$0.426886\pi$
$492$	4.16521e6	0.775754
$493$	1.16470e6	0.215823
$494$	−1.35231e6	−0.249321
$495$	−1.75873e6	−0.322615
$496$	7.53903e6	1.37598
$497$	−1.40279e6	−0.254742
$498$	3.28723e7	5.93959
$499$	−2.77766e6	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$499$	−2.77766e6	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$500$	−978075.	−0.174963
$501$	643421.	0.114525
$502$	−1.65221e7	−2.92622
$503$	6.40176e6	1.12818	0.564091	−	0.825712i	$-0.309227\pi$
$503$	6.40176e6	1.12818	0.564091	+	0.825712i	$0.309227\pi$
$504$	4.98665e6	0.874446
$505$	−751699.	−0.131164
$506$	4.43476e6	0.770005
$507$	6.40147e6	1.10601
$508$	1.32754e7	2.28238
$509$	6.88548e6	1.17798	0.588992	−	0.808139i	$-0.299525\pi$
$509$	6.88548e6	1.17798	0.588992	+	0.808139i	$0.299525\pi$
$510$	−2.07083e6	−0.352549
$511$	1.86621e6	0.316161
$512$	9.24870e6	1.55921
$513$	3.50753e6	0.588448
$514$	−6.19396e6	−1.03410
$515$	3.24953e6	0.539887
$516$	4.20973e6	0.696033
$517$	2.61734e6	0.430659
$518$	1.71474e6	0.280784
$519$	−4.81294e6	−0.784318
$520$	−2.86540e6	−0.464704
$521$	9.58165e6	1.54649	0.773243	−	0.634110i	$-0.218633\pi$
$521$	9.58165e6	1.54649	0.773243	+	0.634110i	$0.218633\pi$
$522$	−2.22039e7	−3.56658
$523$	874653.	0.139824	0.0699120	−	0.997553i	$-0.477728\pi$
$523$	874653.	0.139824	0.0699120	+	0.997553i	$0.477728\pi$
$524$	1.12875e6	0.179585
$525$	517214.	0.0818978
$526$	−1.50449e7	−2.37097
$527$	2.50905e6	0.393534
$528$	−3.09641e6	−0.483363
$529$	7.76380e6	1.20624
$530$	3.73601e6	0.577721
$531$	−1.77045e7	−2.72488
$532$	651301.	0.0997706
$533$	892579.	0.136091
$534$	3.05304e7	4.63318
$535$	4.42123e6	0.667819
$536$	−1.82469e7	−2.74332
$537$	9.43139e6	1.41137
$538$	−6.10630e6	−0.909541
$539$	−1.93313e6	−0.286609
$540$	1.52050e7	2.24389
$541$	−1.94544e6	−0.285775	−0.142888	−	0.989739i	$-0.545639\pi$
$541$	−1.94544e6	−0.285775	−0.142888	+	0.989739i	$0.545639\pi$
$542$	−1.47710e6	−0.215979
$543$	−33727.7	−0.00490894
$544$	253402.	0.0367124
$545$	2.20227e6	0.317600
$546$	3.09998e6	0.445018
$547$	−6.13444e6	−0.876610	−0.438305	−	0.898826i	$-0.644421\pi$
$547$	−6.13444e6	−0.876610	−0.438305	+	0.898826i	$0.644421\pi$
$548$	−1.84231e7	−2.62067
$549$	2.51747e7	3.56478
$550$	−735535.	−0.103680
$551$	−1.41750e6	−0.198905
$552$	−3.21980e7	−4.49760
$553$	−2.96573e6	−0.412400
$554$	5.28129e6	0.731082
$555$	4.39081e6	0.605080
$556$	−1.15247e7	−1.58104
$557$	1.08827e7	1.48627	0.743136	−	0.669140i	$-0.233337\pi$
$557$	1.08827e7	1.48627	0.743136	+	0.669140i	$0.233337\pi$
$558$	−4.78323e7	−6.50333
$559$	902120.	0.122105
$560$	642196.	0.0865361
$561$	−1.03051e6	−0.138243
$562$	1.16057e7	1.55000
$563$	575237.	0.0764849	0.0382424	−	0.999268i	$-0.487824\pi$
$563$	575237.	0.0764849	0.0382424	+	0.999268i	$0.487824\pi$
$564$	−3.88772e7	−5.14633
$565$	−1.09549e6	−0.144374
$566$	1.86475e7	2.44670
$567$	−3.96860e6	−0.518417
$568$	−1.44838e7	−1.88370
$569$	1.02946e7	1.33300	0.666498	−	0.745507i	$-0.267792\pi$
$569$	1.02946e7	1.33300	0.666498	+	0.745507i	$0.267792\pi$
$570$	2.52031e6	0.324913
$571$	−1.32886e7	−1.70564	−0.852820	−	0.522204i	$-0.825110\pi$
$571$	−1.32886e7	−1.70564	−0.852820	+	0.522204i	$0.825110\pi$
$572$	−2.91721e6	−0.372802
$573$	−5.68747e6	−0.723657
$574$	−649646.	−0.0822995
$575$	−2.35519e6	−0.297069
$576$	−2.14125e7	−2.68912
$577$	−6.79698e6	−0.849916	−0.424958	−	0.905213i	$-0.639711\pi$
$577$	−6.79698e6	−0.849916	−0.424958	+	0.905213i	$0.639711\pi$
$578$	1.29539e7	1.61281
$579$	−457140.	−0.0566699
$580$	−6.14482e6	−0.758472
$581$	−3.39270e6	−0.416971
$582$	−2.73341e7	−3.34501
$583$	1.85915e6	0.226540
$584$	1.92687e7	2.33787
$585$	5.59813e6	0.676322
$586$	−2.29871e7	−2.76528
$587$	−1.77782e6	−0.212957	−0.106478	−	0.994315i	$-0.533958\pi$
$587$	−1.77782e6	−0.212957	−0.106478	+	0.994315i	$0.533958\pi$
$588$	2.87142e7	3.42494
$589$	−3.05364e6	−0.362685
$590$	−7.40439e6	−0.875707
$591$	−2.48721e7	−2.92916
$592$	5.45183e6	0.639349
$593$	−6.77791e6	−0.791515	−0.395757	−	0.918355i	$-0.629518\pi$
$593$	−6.77791e6	−0.791515	−0.395757	+	0.918355i	$0.629518\pi$
$594$	1.14345e7	1.32969
$595$	213728.	0.0247496
$596$	−2.31121e7	−2.66516
$597$	7.60818e6	0.873665
$598$	−1.41161e7	−1.61422
$599$	−6.31737e6	−0.719399	−0.359699	−	0.933068i	$-0.617121\pi$
$599$	−6.31737e6	−0.719399	−0.359699	+	0.933068i	$0.617121\pi$
$600$	5.34026e6	0.605598
$601$	−8.79003e6	−0.992669	−0.496334	−	0.868131i	$-0.665321\pi$
$601$	−8.79003e6	−0.992669	−0.496334	+	0.868131i	$0.665321\pi$
$602$	−656591.	−0.0738420
$603$	3.56489e7	3.99258
$604$	−8.17622e6	−0.911928
$605$	−366025.	−0.0406558
$606$	8.39673e6	0.928814
$607$	1.02796e7	1.13241	0.566206	−	0.824264i	$-0.308411\pi$
$607$	1.02796e7	1.13241	0.566206	+	0.824264i	$0.308411\pi$
$608$	−308403.	−0.0338345
$609$	3.24943e6	0.355030
$610$	1.05286e7	1.14563
$611$	−8.33115e6	−0.902822
$612$	1.07950e7	1.16505
$613$	−2.93281e6	−0.315233	−0.157617	−	0.987500i	$-0.550381\pi$
$613$	−2.93281e6	−0.315233	−0.157617	+	0.987500i	$0.550381\pi$
$614$	6.72988e6	0.720421
$615$	−1.66351e6	−0.177352
$616$	1.03782e6	0.110197
$617$	−1.03157e6	−0.109090	−0.0545452	−	0.998511i	$-0.517371\pi$
$617$	−1.03157e6	−0.109090	−0.0545452	+	0.998511i	$0.517371\pi$
$618$	−3.62984e7	−3.82311
$619$	1.04692e7	1.09821	0.549105	−	0.835754i	$-0.314969\pi$
$619$	1.04692e7	1.09821	0.549105	+	0.835754i	$0.314969\pi$
$620$	−1.32374e7	−1.38300
$621$	3.66135e7	3.80988
$622$	−2.51282e7	−2.60427
$623$	−3.15100e6	−0.325258
$624$	9.85607e6	1.01331
$625$	390625.	0.0400000
$626$	2.36064e7	2.40765
$627$	1.25418e6	0.127407
$628$	3.01659e6	0.305223
$629$	1.81441e6	0.182856
$630$	−4.07449e6	−0.408999
$631$	−5.57318e6	−0.557224	−0.278612	−	0.960404i	$-0.589874\pi$
$631$	−5.57318e6	−0.557224	−0.278612	+	0.960404i	$0.589874\pi$
$632$	−3.06213e7	−3.04951
$633$	−2.27408e7	−2.25578
$634$	1.09667e7	1.08356
$635$	−5.30194e6	−0.521795
$636$	−2.76153e7	−2.70712
$637$	6.15328e6	0.600839
$638$	−4.62105e6	−0.449458
$639$	2.82971e7	2.74151
$640$	−8.27170e6	−0.798261
$641$	−3.45207e6	−0.331845	−0.165922	−	0.986139i	$-0.553060\pi$
$641$	−3.45207e6	−0.331845	−0.165922	+	0.986139i	$0.553060\pi$
$642$	−4.93867e7	−4.72903
$643$	−3.54710e6	−0.338334	−0.169167	−	0.985587i	$-0.554108\pi$
$643$	−3.54710e6	−0.338334	−0.169167	+	0.985587i	$0.554108\pi$
$644$	6.79862e6	0.645961
$645$	−1.68129e6	−0.159127
$646$	1.04146e6	0.0981889
$647$	1.05707e7	0.992759	0.496380	−	0.868106i	$-0.334662\pi$
$647$	1.05707e7	0.992759	0.496380	+	0.868106i	$0.334662\pi$
$648$	−4.09759e7	−3.83346
$649$	−3.68465e6	−0.343388
$650$	2.34125e6	0.217353
$651$	7.00005e6	0.647364
$652$	−6.22122e6	−0.573135
$653$	2.11276e7	1.93896	0.969479	−	0.245176i	$-0.0788458\pi$
$653$	2.11276e7	1.93896	0.969479	+	0.245176i	$0.0788458\pi$
$654$	−2.46001e7	−2.24902
$655$	−450803.	−0.0410566
$656$	−2.06548e6	−0.187397
$657$	−3.76453e7	−3.40250
$658$	6.06367e6	0.545972
$659$	−46854.9	−0.00420283	−0.00210141	−	0.999998i	$-0.500669\pi$
$659$	−46854.9	−0.00420283	−0.00210141	+	0.999998i	$0.500669\pi$
$660$	5.43683e6	0.485832
$661$	−932132.	−0.0829801	−0.0414900	−	0.999139i	$-0.513210\pi$
$661$	−932132.	−0.0829801	−0.0414900	+	0.999139i	$0.513210\pi$
$662$	−1.19912e7	−1.06345
$663$	3.28017e6	0.289810
$664$	−3.50298e7	−3.08331
$665$	−260117.	−0.0228095
$666$	−3.45898e7	−3.02178
$667$	−1.47967e7	−1.28780
$668$	−1.40275e6	−0.121629
$669$	−2.35880e7	−2.03764
$670$	1.49091e7	1.28311
$671$	5.23934e6	0.449232
$672$	706972.	0.0603919
$673$	−2.95870e6	−0.251805	−0.125902	−	0.992043i	$-0.540183\pi$
$673$	−2.95870e6	−0.251805	−0.125902	+	0.992043i	$0.540183\pi$
$674$	−8.42975e6	−0.714768
$675$	−6.07260e6	−0.512997
$676$	−1.39561e7	−1.17462
$677$	1.24769e7	1.04625	0.523126	−	0.852255i	$-0.324766\pi$
$677$	1.24769e7	1.04625	0.523126	+	0.852255i	$0.324766\pi$
$678$	1.22370e7	1.02236
$679$	2.82111e6	0.234826
$680$	2.20675e6	0.183012
$681$	−7.74406e6	−0.639883
$682$	−9.95483e6	−0.819545
$683$	1.97195e7	1.61750	0.808750	−	0.588152i	$-0.200144\pi$
$683$	1.97195e7	1.61750	0.808750	+	0.588152i	$0.200144\pi$
$684$	−1.31381e7	−1.07372
$685$	7.35785e6	0.599135
$686$	−9.18995e6	−0.745595
$687$	2.91249e7	2.35436
$688$	−2.08756e6	−0.168139
$689$	−5.91780e6	−0.474911
$690$	2.63083e7	2.10363
$691$	2.23547e7	1.78104	0.890518	−	0.454947i	$-0.150342\pi$
$691$	2.23547e7	1.78104	0.890518	+	0.454947i	$0.150342\pi$
$692$	1.04929e7	0.832970
$693$	−2.02759e6	−0.160379
$694$	5.44822e6	0.429394
$695$	4.60275e6	0.361456
$696$	3.35506e7	2.62529
$697$	−687408.	−0.0535960
$698$	9.54780e6	0.741763
$699$	3.74862e7	2.90187
$700$	−1.12760e6	−0.0869780
$701$	1.09452e7	0.841254	0.420627	−	0.907234i	$-0.361810\pi$
$701$	1.09452e7	0.841254	0.420627	+	0.907234i	$0.361810\pi$
$702$	−3.63968e7	−2.78753
$703$	−2.20823e6	−0.168522
$704$	−4.45635e6	−0.338882
$705$	1.55268e7	1.17655
$706$	−4.34360e7	−3.27973
$707$	−866615.	−0.0652045
$708$	5.47307e7	4.10344
$709$	−8.52354e6	−0.636802	−0.318401	−	0.947956i	$-0.603146\pi$
$709$	−8.52354e6	−0.636802	−0.318401	+	0.947956i	$0.603146\pi$
$710$	1.18344e7	0.881053
$711$	5.98248e7	4.43821
$712$	−3.25342e7	−2.40514
$713$	−3.18755e7	−2.34819
$714$	−2.38741e6	−0.175259
$715$	1.16508e6	0.0852296
$716$	−2.05617e7	−1.49892
$717$	2.14040e7	1.55488
$718$	3.51444e7	2.54416
$719$	3.60392e6	0.259988	0.129994	−	0.991515i	$-0.458504\pi$
$719$	3.60392e6	0.259988	0.129994	+	0.991515i	$0.458504\pi$
$720$	−1.29544e7	−0.931293
$721$	3.74631e6	0.268389
$722$	−1.26751e6	−0.0904919
$723$	−1.90797e7	−1.35745
$724$	73531.1	0.00521345
$725$	2.45413e6	0.173401
$726$	4.08862e6	0.287896
$727$	−8.08516e6	−0.567352	−0.283676	−	0.958920i	$-0.591554\pi$
$727$	−8.08516e6	−0.567352	−0.283676	+	0.958920i	$0.591554\pi$
$728$	−3.30344e6	−0.231014
$729$	1.22643e7	0.854719
$730$	−1.57441e7	−1.09348
$731$	−694756.	−0.0480883
$732$	−7.78236e7	−5.36826
$733$	−3.16925e6	−0.217870	−0.108935	−	0.994049i	$-0.534744\pi$
$733$	−3.16925e6	−0.217870	−0.108935	+	0.994049i	$0.534744\pi$
$734$	−6.50568e6	−0.445710
$735$	−1.14679e7	−0.783008
$736$	−3.21927e6	−0.219060
$737$	7.41924e6	0.503142
$738$	1.31047e7	0.885699
$739$	−1.64625e6	−0.110888	−0.0554439	−	0.998462i	$-0.517657\pi$
$739$	−1.64625e6	−0.110888	−0.0554439	+	0.998462i	$0.517657\pi$
$740$	−9.57258e6	−0.642613
$741$	−3.99214e6	−0.267092
$742$	4.30715e6	0.287198
$743$	−1.67172e7	−1.11094	−0.555472	−	0.831535i	$-0.687462\pi$
$743$	−1.67172e7	−1.11094	−0.555472	+	0.831535i	$0.687462\pi$
$744$	7.22758e7	4.78697
$745$	9.23053e6	0.609307
$746$	3.45019e7	2.26984
$747$	6.84378e7	4.48740
$748$	2.24665e6	0.146819
$749$	5.09713e6	0.331987
$750$	−4.36341e6	−0.283252
$751$	−1.62460e6	−0.105110	−0.0525552	−	0.998618i	$-0.516737\pi$
$751$	−1.62460e6	−0.105110	−0.0525552	+	0.998618i	$0.516737\pi$
$752$	1.92788e7	1.24318
$753$	−4.87748e7	−3.13479
$754$	1.47091e7	0.942231
$755$	3.26543e6	0.208484
$756$	1.75295e7	1.11549
$757$	1.46503e7	0.929198	0.464599	−	0.885521i	$-0.346199\pi$
$757$	1.46503e7	0.929198	0.464599	+	0.885521i	$0.346199\pi$
$758$	3.59648e7	2.27355
$759$	1.30918e7	0.824889
$760$	−2.68572e6	−0.168666
$761$	2.98310e6	0.186726	0.0933632	−	0.995632i	$-0.470238\pi$
$761$	2.98310e6	0.186726	0.0933632	+	0.995632i	$0.470238\pi$
$762$	5.92244e7	3.69499
$763$	2.53895e6	0.157886
$764$	1.23995e7	0.768546
$765$	−4.31133e6	−0.266353
$766$	2.98495e7	1.83808
$767$	1.17285e7	0.719868
$768$	5.85591e7	3.58254
$769$	−2.33525e7	−1.42403	−0.712013	−	0.702166i	$-0.752216\pi$
$769$	−2.33525e7	−1.42403	−0.712013	+	0.702166i	$0.752216\pi$
$770$	−847981.	−0.0515417
$771$	−1.82852e7	−1.10780
$772$	996628.	0.0601852
$773$	−1.12488e7	−0.677109	−0.338554	−	0.940947i	$-0.609938\pi$
$773$	−1.12488e7	−0.677109	−0.338554	+	0.940947i	$0.609938\pi$
$774$	1.32448e7	0.794681
$775$	5.28677e6	0.316181
$776$	2.91281e7	1.73643
$777$	5.06206e6	0.300798
$778$	−2.15446e7	−1.27611
$779$	836611.	0.0493946
$780$	−1.73058e7	−1.01848
$781$	5.88918e6	0.345484
$782$	1.08713e7	0.635720
$783$	−3.81515e7	−2.22386
$784$	−1.42391e7	−0.827353
$785$	−1.20477e6	−0.0697799
$786$	5.03562e6	0.290734
$787$	1.50277e7	0.864878	0.432439	−	0.901663i	$-0.357653\pi$
$787$	1.50277e7	0.864878	0.432439	+	0.901663i	$0.357653\pi$
$788$	5.42245e7	3.11086
$789$	−4.44140e7	−2.53996
$790$	2.50200e7	1.42633
$791$	−1.26297e6	−0.0717714
$792$	−2.09350e7	−1.18593
$793$	−1.66771e7	−0.941757
$794$	−5.32542e6	−0.299780
$795$	1.10291e7	0.618900
$796$	−1.65869e7	−0.927859
$797$	−1.60353e7	−0.894191	−0.447096	−	0.894486i	$-0.647542\pi$
$797$	−1.60353e7	−0.894191	−0.447096	+	0.894486i	$0.647542\pi$
$798$	2.90560e6	0.161521
$799$	6.41613e6	0.355555
$800$	533939.	0.0294962
$801$	6.35621e7	3.50040
$802$	4.82651e7	2.64970
$803$	−7.83473e6	−0.428781
$804$	−1.10203e8	−6.01249
$805$	−2.71524e6	−0.147679
$806$	3.16868e7	1.71807
$807$	−1.80264e7	−0.974371
$808$	−8.94784e6	−0.482158
$809$	−1.21981e7	−0.655270	−0.327635	−	0.944804i	$-0.606252\pi$
$809$	−1.21981e7	−0.655270	−0.327635	+	0.944804i	$0.606252\pi$
$810$	3.34806e7	1.79300
$811$	−4.53663e6	−0.242204	−0.121102	−	0.992640i	$-0.538643\pi$
$811$	−4.53663e6	−0.242204	−0.121102	+	0.992640i	$0.538643\pi$
$812$	−7.08422e6	−0.377052
$813$	−4.36054e6	−0.231373
$814$	−7.19881e6	−0.380802
$815$	2.48464e6	0.131030
$816$	−7.59052e6	−0.399067
$817$	845554.	0.0443186
$818$	2.72012e7	1.42136
$819$	6.45395e6	0.336214
$820$	3.62667e6	0.188354
$821$	1.47896e7	0.765770	0.382885	−	0.923796i	$-0.374931\pi$
$821$	1.47896e7	0.765770	0.382885	+	0.923796i	$0.374931\pi$
$822$	−8.21897e7	−4.24266
$823$	1.54392e7	0.794555	0.397278	−	0.917698i	$-0.369955\pi$
$823$	1.54392e7	0.794555	0.397278	+	0.917698i	$0.369955\pi$
$824$	3.86808e7	1.98462
$825$	−2.17137e6	−0.111070
$826$	−8.53633e6	−0.435333
$827$	2.60673e7	1.32536	0.662678	−	0.748904i	$-0.269420\pi$
$827$	2.60673e7	1.32536	0.662678	+	0.748904i	$0.269420\pi$
$828$	−1.37142e8	−6.95177
$829$	−2.56505e7	−1.29631	−0.648155	−	0.761509i	$-0.724459\pi$
$829$	−2.56505e7	−1.29631	−0.648155	+	0.761509i	$0.724459\pi$
$830$	2.86221e7	1.44214
$831$	1.55909e7	0.783191
$832$	1.41848e7	0.710422
$833$	−4.73887e6	−0.236626
$834$	−5.14143e7	−2.55958
$835$	560231.	0.0278068
$836$	−2.73429e6	−0.135310
$837$	−8.21873e7	−4.05500
$838$	1.52124e7	0.748321
$839$	−3.30668e7	−1.62176	−0.810882	−	0.585210i	$-0.801012\pi$
$839$	−3.30668e7	−1.62176	−0.810882	+	0.585210i	$0.801012\pi$
$840$	6.15665e6	0.301055
$841$	−5.09291e6	−0.248300
$842$	−2.68369e7	−1.30452
$843$	3.42611e7	1.66048
$844$	4.95781e7	2.39571
$845$	5.57380e6	0.268541
$846$	−1.22317e8	−5.87570
$847$	−421981.	−0.0202108
$848$	1.36941e7	0.653951
$849$	5.50492e7	2.62109
$850$	−1.80309e6	−0.0855991
$851$	−2.30507e7	−1.09109
$852$	−8.74762e7	−4.12849
$853$	1.02645e7	0.483022	0.241511	−	0.970398i	$-0.422357\pi$
$853$	1.02645e7	0.483022	0.241511	+	0.970398i	$0.422357\pi$
$854$	1.21381e7	0.569518
$855$	5.24711e6	0.245474
$856$	5.26281e7	2.45490
$857$	7.03992e6	0.327428	0.163714	−	0.986508i	$-0.447653\pi$
$857$	7.03992e6	0.327428	0.163714	+	0.986508i	$0.447653\pi$
$858$	−1.30143e7	−0.603537
$859$	−8.21216e6	−0.379730	−0.189865	−	0.981810i	$-0.560805\pi$
$859$	−8.21216e6	−0.379730	−0.189865	+	0.981810i	$0.560805\pi$
$860$	3.66544e6	0.168997
$861$	−1.91782e6	−0.0881656
$862$	4.32011e7	1.98028
$863$	1.62175e7	0.741237	0.370619	−	0.928785i	$-0.379146\pi$
$863$	1.62175e7	0.741237	0.370619	+	0.928785i	$0.379146\pi$
$864$	−8.30053e6	−0.378287
$865$	−4.19066e6	−0.190433
$866$	1.89123e7	0.856940
$867$	3.82412e7	1.72776
$868$	−1.52611e7	−0.687520
$869$	1.24507e7	0.559300
$870$	−2.74135e7	−1.22791
$871$	−2.36159e7	−1.05477
$872$	2.62147e7	1.16749
$873$	−5.69077e7	−2.52717
$874$	−1.32310e7	−0.585886
$875$	450342.	0.0198848
$876$	1.16375e8	5.12387
$877$	−1.32287e7	−0.580788	−0.290394	−	0.956907i	$-0.593786\pi$
$877$	−1.32287e7	−0.580788	−0.290394	+	0.956907i	$0.593786\pi$
$878$	−4.13206e7	−1.80896
$879$	−6.78599e7	−2.96238
$880$	−2.69607e6	−0.117361
$881$	−4.47995e7	−1.94461	−0.972306	−	0.233712i	$-0.924913\pi$
$881$	−4.47995e7	−1.94461	−0.972306	+	0.233712i	$0.924913\pi$
$882$	9.03415e7	3.91035
$883$	1.30583e7	0.563619	0.281810	−	0.959470i	$-0.409065\pi$
$883$	1.30583e7	0.563619	0.281810	+	0.959470i	$0.409065\pi$
$884$	−7.15123e6	−0.307787
$885$	−2.18584e7	−0.938125
$886$	6.49262e7	2.77866
$887$	1.30382e7	0.556428	0.278214	−	0.960519i	$-0.410258\pi$
$887$	1.30382e7	0.556428	0.278214	+	0.960519i	$0.410258\pi$
$888$	5.22660e7	2.22427
$889$	−6.11247e6	−0.259395
$890$	2.65830e7	1.12494
$891$	1.66610e7	0.703082
$892$	5.14252e7	2.16403
$893$	−7.80876e6	−0.327683
$894$	−1.03108e8	−4.31468
$895$	8.21198e6	0.342681
$896$	−9.53624e6	−0.396832
$897$	−4.16720e7	−1.72927
$898$	1.32308e7	0.547512
$899$	3.32145e7	1.37066
$900$	2.27460e7	0.936049
$901$	4.55752e6	0.187032
$902$	2.72734e6	0.111615
$903$	−1.93832e6	−0.0791052
$904$	−1.30402e7	−0.530717
$905$	−29367.0	−0.00119189
$906$	−3.64760e7	−1.47634
$907$	2.39502e7	0.966698	0.483349	−	0.875428i	$-0.339420\pi$
$907$	2.39502e7	0.966698	0.483349	+	0.875428i	$0.339420\pi$
$908$	1.68831e7	0.679576
$909$	1.74814e7	0.701725
$910$	2.69917e6	0.108051
$911$	−2.21589e7	−0.884612	−0.442306	−	0.896864i	$-0.645839\pi$
$911$	−2.21589e7	−0.884612	−0.442306	+	0.896864i	$0.645839\pi$
$912$	9.23805e6	0.367784
$913$	1.42432e7	0.565499
$914$	7.10744e7	2.81415
$915$	3.10813e7	1.22729
$916$	−6.34963e7	−2.50040
$917$	−519719.	−0.0204101
$918$	2.80305e7	1.09780
$919$	1.05696e7	0.412828	0.206414	−	0.978465i	$-0.433821\pi$
$919$	1.05696e7	0.412828	0.206414	+	0.978465i	$0.433821\pi$
$920$	−2.80350e7	−1.09202
$921$	1.98672e7	0.771771
$922$	1.40429e7	0.544037
$923$	−1.87456e7	−0.724262
$924$	6.26798e6	0.241517
$925$	3.82311e6	0.146914
$926$	−3.45897e7	−1.32562
$927$	−7.55708e7	−2.88838
$928$	3.35451e6	0.127867
$929$	1.34323e7	0.510635	0.255318	−	0.966857i	$-0.417820\pi$
$929$	1.34323e7	0.510635	0.255318	+	0.966857i	$0.417820\pi$
$930$	−5.90550e7	−2.23898
$931$	5.76744e6	0.218077
$932$	−8.17251e7	−3.08188
$933$	−7.41809e7	−2.78989
$934$	−2.16408e7	−0.811720
$935$	−897271.	−0.0335656
$936$	6.66373e7	2.48615
$937$	2.68151e7	0.997769	0.498885	−	0.866668i	$-0.333743\pi$
$937$	2.68151e7	0.997769	0.498885	+	0.866668i	$0.333743\pi$
$938$	1.71884e7	0.637863
$939$	6.96882e7	2.57926
$940$	−3.38506e7	−1.24953
$941$	−3.73828e7	−1.37625	−0.688127	−	0.725591i	$-0.741567\pi$
$941$	−3.73828e7	−1.37625	−0.688127	+	0.725591i	$0.741567\pi$
$942$	1.34577e7	0.494133
$943$	8.73298e6	0.319804
$944$	−2.71404e7	−0.991256
$945$	−7.00095e6	−0.255022
$946$	2.75650e6	0.100145
$947$	556994.	0.0201825	0.0100913	−	0.999949i	$-0.496788\pi$
$947$	556994.	0.0201825	0.0100913	+	0.999949i	$0.496788\pi$
$948$	−1.84939e8	−6.68357
$949$	2.49384e7	0.898883
$950$	2.19445e6	0.0788890
$951$	3.23747e7	1.16079
$952$	2.54410e6	0.0909793
$953$	4.39522e7	1.56765	0.783824	−	0.620983i	$-0.213266\pi$
$953$	4.39522e7	1.56765	0.783824	+	0.620983i	$0.213266\pi$
$954$	−8.68842e7	−3.09079
$955$	−4.95212e6	−0.175704
$956$	−4.66636e7	−1.65133
$957$	−1.36418e7	−0.481494
$958$	−3.91255e7	−1.37736
$959$	8.48269e6	0.297843
$960$	−2.64364e7	−0.925816
$961$	4.29227e7	1.49927
$962$	2.29142e7	0.798303
$963$	−1.02820e8	−3.57281
$964$	4.15963e7	1.44166
$965$	−398035.	−0.0137595
$966$	3.03302e7	1.04576
$967$	3.90822e7	1.34404	0.672020	−	0.740533i	$-0.265427\pi$
$967$	3.90822e7	1.34404	0.672020	+	0.740533i	$0.265427\pi$
$968$	−4.35697e6	−0.149450
$969$	3.07449e6	0.105188
$970$	−2.38000e7	−0.812170
$971$	1.69017e7	0.575282	0.287641	−	0.957738i	$-0.407129\pi$
$971$	1.69017e7	0.575282	0.287641	+	0.957738i	$0.407129\pi$
$972$	−9.96844e7	−3.38424
$973$	5.30640e6	0.179688
$974$	8.89584e7	3.00462
$975$	6.91160e6	0.232845
$976$	3.85919e7	1.29680
$977$	−1.90461e6	−0.0638367	−0.0319184	−	0.999490i	$-0.510162\pi$
$977$	−1.90461e6	−0.0638367	−0.0319184	+	0.999490i	$0.510162\pi$
$978$	−2.77543e7	−0.927861
$979$	1.32285e7	0.441118
$980$	2.50016e7	0.831578
$981$	−5.12158e7	−1.69915
$982$	−2.36591e7	−0.782923
$983$	1.56379e7	0.516172	0.258086	−	0.966122i	$-0.416908\pi$
$983$	1.56379e7	0.516172	0.258086	+	0.966122i	$0.416908\pi$
$984$	−1.98015e7	−0.651945
$985$	−2.16563e7	−0.711202
$986$	−1.13280e7	−0.371075
$987$	1.79005e7	0.584888
$988$	8.70341e6	0.283659
$989$	8.82634e6	0.286939
$990$	1.71055e7	0.554687
$991$	3.32467e7	1.07539	0.537694	−	0.843140i	$-0.319296\pi$
$991$	3.32467e7	1.07539	0.537694	+	0.843140i	$0.319296\pi$
$992$	7.22640e6	0.233154
$993$	−3.53991e7	−1.13925
$994$	1.36436e7	0.437990
$995$	6.62449e6	0.212126
$996$	−2.11565e8	−6.75765
$997$	3.55857e7	1.13380	0.566901	−	0.823786i	$-0.308142\pi$
$997$	3.55857e7	1.13380	0.566901	+	0.823786i	$0.308142\pi$
$998$	2.70157e7	0.858599
$999$	−5.94335e7	−1.88416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.2	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.2	✓	37	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)

\(f(q)\)	\(=\)	\(q-9.72609 q^{2} -28.7123 q^{3} +62.5968 q^{4} -25.0000 q^{5} +279.258 q^{6} -28.8219 q^{7} -297.587 q^{8} +581.397 q^{9} +O(q^{10})\)	\(q-9.72609 q^{2} -28.7123 q^{3} +62.5968 q^{4} -25.0000 q^{5} +279.258 q^{6} -28.8219 q^{7} -297.587 q^{8} +581.397 q^{9} +243.152 q^{10} +121.000 q^{11} -1797.30 q^{12} -385.150 q^{13} +280.324 q^{14} +717.808 q^{15} +891.261 q^{16} +296.619 q^{17} -5654.72 q^{18} -361.000 q^{19} -1564.92 q^{20} +827.543 q^{21} -1176.86 q^{22} -3768.31 q^{23} +8544.41 q^{24} +625.000 q^{25} +3746.01 q^{26} -9716.16 q^{27} -1804.16 q^{28} +3926.61 q^{29} -6981.46 q^{30} +8458.83 q^{31} +854.302 q^{32} -3474.19 q^{33} -2884.94 q^{34} +720.547 q^{35} +36393.6 q^{36} +6116.98 q^{37} +3511.12 q^{38} +11058.6 q^{39} +7439.68 q^{40} -2317.48 q^{41} -8048.75 q^{42} -2342.25 q^{43} +7574.21 q^{44} -14534.9 q^{45} +36650.9 q^{46} +21630.9 q^{47} -25590.2 q^{48} -15976.3 q^{49} -6078.81 q^{50} -8516.60 q^{51} -24109.2 q^{52} +15364.9 q^{53} +94500.2 q^{54} -3025.00 q^{55} +8577.02 q^{56} +10365.1 q^{57} -38190.5 q^{58} -30451.7 q^{59} +44932.5 q^{60} +43300.3 q^{61} -82271.3 q^{62} -16757.0 q^{63} -36829.4 q^{64} +9628.76 q^{65} +33790.3 q^{66} +61316.0 q^{67} +18567.4 q^{68} +108197. q^{69} -7008.10 q^{70} +48670.9 q^{71} -173016. q^{72} -64749.8 q^{73} -59494.3 q^{74} -17945.2 q^{75} -22597.4 q^{76} -3487.45 q^{77} -107557. q^{78} +102898. q^{79} -22281.5 q^{80} +137694. q^{81} +22540.0 q^{82} +117713. q^{83} +51801.5 q^{84} -7415.46 q^{85} +22781.0 q^{86} -112742. q^{87} -36008.0 q^{88} +109327. q^{89} +141368. q^{90} +11100.8 q^{91} -235884. q^{92} -242873. q^{93} -210384. q^{94} +9025.00 q^{95} -24529.0 q^{96} -97880.9 q^{97} +155387. q^{98} +70349.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

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