LMFDB - Embedded newform 1045.6.a.a.1.14

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:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-3.41781 q^{2} -5.73624 q^{3} -20.3185 q^{4} -25.0000 q^{5} +19.6054 q^{6} +236.087 q^{7} +178.815 q^{8} -210.096 q^{9} +O(q^{10})$	\(q-3.41781 q^{2} -5.73624 q^{3} -20.3185 q^{4} -25.0000 q^{5} +19.6054 q^{6} +236.087 q^{7} +178.815 q^{8} -210.096 q^{9} +85.4453 q^{10} +121.000 q^{11} +116.552 q^{12} +1098.51 q^{13} -806.901 q^{14} +143.406 q^{15} +39.0369 q^{16} -1684.45 q^{17} +718.067 q^{18} +361.000 q^{19} +507.964 q^{20} -1354.25 q^{21} -413.555 q^{22} +572.885 q^{23} -1025.73 q^{24} +625.000 q^{25} -3754.50 q^{26} +2599.07 q^{27} -4796.94 q^{28} -7152.63 q^{29} -490.135 q^{30} -5931.81 q^{31} -5855.50 q^{32} -694.085 q^{33} +5757.12 q^{34} -5902.17 q^{35} +4268.84 q^{36} -517.766 q^{37} -1233.83 q^{38} -6301.31 q^{39} -4470.38 q^{40} +13316.4 q^{41} +4628.58 q^{42} +236.872 q^{43} -2458.54 q^{44} +5252.39 q^{45} -1958.02 q^{46} -6226.10 q^{47} -223.925 q^{48} +38930.0 q^{49} -2136.13 q^{50} +9662.39 q^{51} -22320.1 q^{52} -10320.6 q^{53} -8883.12 q^{54} -3025.00 q^{55} +42215.9 q^{56} -2070.78 q^{57} +24446.4 q^{58} -26292.5 q^{59} -2913.80 q^{60} -47638.3 q^{61} +20273.8 q^{62} -49600.8 q^{63} +18763.8 q^{64} -27462.7 q^{65} +2372.25 q^{66} +2169.96 q^{67} +34225.5 q^{68} -3286.21 q^{69} +20172.5 q^{70} +39721.2 q^{71} -37568.2 q^{72} +43366.3 q^{73} +1769.63 q^{74} -3585.15 q^{75} -7335.00 q^{76} +28566.5 q^{77} +21536.7 q^{78} -1411.98 q^{79} -975.923 q^{80} +36144.4 q^{81} -45513.0 q^{82} -40306.6 q^{83} +27516.4 q^{84} +42111.2 q^{85} -809.585 q^{86} +41029.2 q^{87} +21636.6 q^{88} +50147.5 q^{89} -17951.7 q^{90} +259344. q^{91} -11640.2 q^{92} +34026.3 q^{93} +21279.7 q^{94} -9025.00 q^{95} +33588.6 q^{96} -105029. q^{97} -133056. q^{98} -25421.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−3.41781	−0.604190	−0.302095	−	0.953278i	$-0.597686\pi$
$2$	−3.41781	−0.604190	−0.302095	+	0.953278i	$0.597686\pi$
$3$	−5.73624	−0.367980	−0.183990	−	0.982928i	$-0.558901\pi$
$3$	−5.73624	−0.367980	−0.183990	+	0.982928i	$0.558901\pi$
$4$	−20.3185	−0.634955
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	19.6054	0.222330
$7$	236.087	1.82107	0.910535	−	0.413431i	$-0.135670\pi$
$7$	236.087	1.82107	0.910535	+	0.413431i	$0.135670\pi$
$8$	178.815	0.987823
$9$	−210.096	−0.864591
$10$	85.4453	0.270202
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	116.552	0.233651
$13$	1098.51	1.80279	0.901395	−	0.432997i	$-0.142544\pi$
$13$	1098.51	1.80279	0.901395	+	0.432997i	$0.142544\pi$
$14$	−806.901	−1.10027
$15$	143.406	0.164566
$16$	39.0369	0.0381220
$17$	−1684.45	−1.41363	−0.706813	−	0.707400i	$-0.749868\pi$
$17$	−1684.45	−1.41363	−0.706813	+	0.707400i	$0.749868\pi$
$18$	718.067	0.522377
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	507.964	0.283960
$21$	−1354.25	−0.670118
$22$	−413.555	−0.182170
$23$	572.885	0.225813	0.112906	−	0.993606i	$-0.463984\pi$
$23$	572.885	0.225813	0.112906	+	0.993606i	$0.463984\pi$
$24$	−1025.73	−0.363499
$25$	625.000	0.200000
$26$	−3754.50	−1.08923
$27$	2599.07	0.686132
$28$	−4796.94	−1.15630
$29$	−7152.63	−1.57932	−0.789661	−	0.613543i	$-0.789744\pi$
$29$	−7152.63	−1.57932	−0.789661	+	0.613543i	$0.789744\pi$
$30$	−490.135	−0.0994289
$31$	−5931.81	−1.10862	−0.554310	−	0.832310i	$-0.687018\pi$
$31$	−5931.81	−1.10862	−0.554310	+	0.832310i	$0.687018\pi$
$32$	−5855.50	−1.01086
$33$	−694.085	−0.110950
$34$	5757.12	0.854099
$35$	−5902.17	−0.814408
$36$	4268.84	0.548976
$37$	−517.766	−0.0621769	−0.0310884	−	0.999517i	$-0.509897\pi$
$37$	−517.766	−0.0621769	−0.0310884	+	0.999517i	$0.509897\pi$
$38$	−1233.83	−0.138611
$39$	−6301.31	−0.663391
$40$	−4470.38	−0.441768
$41$	13316.4	1.23717	0.618583	−	0.785720i	$-0.287707\pi$
$41$	13316.4	1.23717	0.618583	+	0.785720i	$0.287707\pi$
$42$	4628.58	0.404878
$43$	236.872	0.0195363	0.00976816	−	0.999952i	$-0.496891\pi$
$43$	236.872	0.0195363	0.00976816	+	0.999952i	$0.496891\pi$
$44$	−2458.54	−0.191446
$45$	5252.39	0.386657
$46$	−1958.02	−0.136434
$47$	−6226.10	−0.411123	−0.205561	−	0.978644i	$-0.565902\pi$
$47$	−6226.10	−0.411123	−0.205561	+	0.978644i	$0.565902\pi$
$48$	−223.925	−0.0140281
$49$	38930.0	2.31630
$50$	−2136.13	−0.120838
$51$	9662.39	0.520186
$52$	−22320.1	−1.14469
$53$	−10320.6	−0.504681	−0.252341	−	0.967638i	$-0.581200\pi$
$53$	−10320.6	−0.504681	−0.252341	+	0.967638i	$0.581200\pi$
$54$	−8883.12	−0.414554
$55$	−3025.00	−0.134840
$56$	42215.9	1.79890
$57$	−2070.78	−0.0844204
$58$	24446.4	0.954211
$59$	−26292.5	−0.983337	−0.491668	−	0.870782i	$-0.663613\pi$
$59$	−26292.5	−0.983337	−0.491668	+	0.870782i	$0.663613\pi$
$60$	−2913.80	−0.104492
$61$	−47638.3	−1.63920	−0.819599	−	0.572937i	$-0.805804\pi$
$61$	−47638.3	−1.63920	−0.819599	+	0.572937i	$0.805804\pi$
$62$	20273.8	0.669817
$63$	−49600.8	−1.57448
$64$	18763.8	0.572627
$65$	−27462.7	−0.806232
$66$	2372.25	0.0670350
$67$	2169.96	0.0590560	0.0295280	−	0.999564i	$-0.490600\pi$
$67$	2169.96	0.0590560	0.0295280	+	0.999564i	$0.490600\pi$
$68$	34225.5	0.897589
$69$	−3286.21	−0.0830945
$70$	20172.5	0.492057
$71$	39721.2	0.935140	0.467570	−	0.883956i	$-0.345130\pi$
$71$	39721.2	0.935140	0.467570	+	0.883956i	$0.345130\pi$
$72$	−37568.2	−0.854063
$73$	43366.3	0.952457	0.476229	−	0.879322i	$-0.342003\pi$
$73$	43366.3	0.952457	0.476229	+	0.879322i	$0.342003\pi$
$74$	1769.63	0.0375666
$75$	−3585.15	−0.0735960
$76$	−7335.00	−0.145669
$77$	28566.5	0.549073
$78$	21536.7	0.400814
$79$	−1411.98	−0.0254543	−0.0127272	−	0.999919i	$-0.504051\pi$
$79$	−1411.98	−0.0254543	−0.0127272	+	0.999919i	$0.504051\pi$
$80$	−975.923	−0.0170487
$81$	36144.4	0.612108
$82$	−45513.0	−0.747483
$83$	−40306.6	−0.642215	−0.321108	−	0.947043i	$-0.604055\pi$
$83$	−40306.6	−0.642215	−0.321108	+	0.947043i	$0.604055\pi$
$84$	27516.4	0.425494
$85$	42111.2	0.632193
$86$	−809.585	−0.0118037
$87$	41029.2	0.581159
$88$	21636.6	0.297840
$89$	50147.5	0.671079	0.335540	−	0.942026i	$-0.391081\pi$
$89$	50147.5	0.671079	0.335540	+	0.942026i	$0.391081\pi$
$90$	−17951.7	−0.233614
$91$	259344.	3.28301
$92$	−11640.2	−0.143381
$93$	34026.3	0.407950
$94$	21279.7	0.248396
$95$	−9025.00	−0.102598
$96$	33588.6	0.371975
$97$	−105029.	−1.13339	−0.566695	−	0.823927i	$-0.691778\pi$
$97$	−105029.	−1.13339	−0.566695	+	0.823927i	$0.691778\pi$
$98$	−133056.	−1.39948
$99$	−25421.6	−0.260684
$100$	−12699.1	−0.126991
$101$	85767.0	0.836598	0.418299	−	0.908309i	$-0.362626\pi$
$101$	85767.0	0.836598	0.418299	+	0.908309i	$0.362626\pi$
$102$	−33024.2	−0.314291
$103$	178087.	1.65401	0.827006	−	0.562193i	$-0.190042\pi$
$103$	178087.	1.65401	0.827006	+	0.562193i	$0.190042\pi$
$104$	196430.	1.78084
$105$	33856.3	0.299686
$106$	35274.0	0.304923
$107$	−191715.	−1.61881	−0.809407	−	0.587248i	$-0.800211\pi$
$107$	−191715.	−1.61881	−0.809407	+	0.587248i	$0.800211\pi$
$108$	−52809.2	−0.435663
$109$	223406.	1.80106	0.900529	−	0.434796i	$-0.143179\pi$
$109$	223406.	1.80106	0.900529	+	0.434796i	$0.143179\pi$
$110$	10338.9	0.0814689
$111$	2970.03	0.0228799
$112$	9216.11	0.0694229
$113$	−102197.	−0.752905	−0.376453	−	0.926436i	$-0.622856\pi$
$113$	−102197.	−0.752905	−0.376453	+	0.926436i	$0.622856\pi$
$114$	7077.55	0.0510060
$115$	−14322.1	−0.100986
$116$	145331.	1.00280
$117$	−230792.	−1.55868
$118$	89863.0	0.594122
$119$	−397676.	−2.57431
$120$	25643.2	0.162562
$121$	14641.0	0.0909091
$122$	162819.	0.990387
$123$	−76386.2	−0.455252
$124$	120526.	0.703924
$125$	−15625.0	−0.0894427
$126$	169526.	0.951285
$127$	241906.	1.33087	0.665437	−	0.746454i	$-0.268245\pi$
$127$	241906.	1.33087	0.665437	+	0.746454i	$0.268245\pi$
$128$	123245.	0.664881
$129$	−1358.76	−0.00718898
$130$	93862.5	0.487117
$131$	−149310.	−0.760168	−0.380084	−	0.924952i	$-0.624105\pi$
$131$	−149310.	−0.760168	−0.380084	+	0.924952i	$0.624105\pi$
$132$	14102.8	0.0704483
$133$	85227.4	0.417782
$134$	−7416.50	−0.0356810
$135$	−64976.6	−0.306848
$136$	−301204.	−1.39641
$137$	−273223.	−1.24370	−0.621850	−	0.783136i	$-0.713619\pi$
$137$	−273223.	−1.24370	−0.621850	+	0.783136i	$0.713619\pi$
$138$	11231.6	0.0502049
$139$	−61086.6	−0.268169	−0.134085	−	0.990970i	$-0.542809\pi$
$139$	−61086.6	−0.268169	−0.134085	+	0.990970i	$0.542809\pi$
$140$	119924.	0.517112
$141$	35714.4	0.151285
$142$	−135760.	−0.565002
$143$	132920.	0.543562
$144$	−8201.49	−0.0329599
$145$	178816.	0.706294
$146$	−148218.	−0.575465
$147$	−223312.	−0.852351
$148$	10520.2	0.0394795
$149$	−220175.	−0.812462	−0.406231	−	0.913770i	$-0.633157\pi$
$149$	−220175.	−0.812462	−0.406231	+	0.913770i	$0.633157\pi$
$150$	12253.4	0.0444660
$151$	−61499.7	−0.219498	−0.109749	−	0.993959i	$-0.535005\pi$
$151$	−61499.7	−0.219498	−0.109749	+	0.993959i	$0.535005\pi$
$152$	64552.2	0.226622
$153$	353895.	1.22221
$154$	−97635.0	−0.331745
$155$	148295.	0.495790
$156$	128034.	0.421223
$157$	−355204.	−1.15008	−0.575041	−	0.818125i	$-0.695014\pi$
$157$	−355204.	−1.15008	−0.575041	+	0.818125i	$0.695014\pi$
$158$	4825.89	0.0153792
$159$	59201.7	0.185713
$160$	146388.	0.452069
$161$	135251.	0.411221
$162$	−123535.	−0.369829
$163$	127270.	0.375195	0.187597	−	0.982246i	$-0.439930\pi$
$163$	127270.	0.375195	0.187597	+	0.982246i	$0.439930\pi$
$164$	−270570.	−0.785544
$165$	17352.1	0.0496184
$166$	137760.	0.388020
$167$	−21696.3	−0.0601996	−0.0300998	−	0.999547i	$-0.509583\pi$
$167$	−21696.3	−0.0601996	−0.0300998	+	0.999547i	$0.509583\pi$
$168$	−242161.	−0.661958
$169$	835429.	2.25005
$170$	−143928.	−0.381965
$171$	−75844.5	−0.198351
$172$	−4812.90	−0.0124047
$173$	29097.1	0.0739152	0.0369576	−	0.999317i	$-0.488233\pi$
$173$	29097.1	0.0739152	0.0369576	+	0.999317i	$0.488233\pi$
$174$	−140230.	−0.351130
$175$	147554.	0.364214
$176$	4723.47	0.0114942
$177$	150820.	0.361848
$178$	−171395.	−0.405459
$179$	89218.6	0.208124	0.104062	−	0.994571i	$-0.466816\pi$
$179$	89218.6	0.208124	0.104062	+	0.994571i	$0.466816\pi$
$180$	−106721.	−0.245509
$181$	−418730.	−0.950032	−0.475016	−	0.879977i	$-0.657558\pi$
$181$	−418730.	−0.950032	−0.475016	+	0.879977i	$0.657558\pi$
$182$	−886388.	−1.98356
$183$	273265.	0.603192
$184$	102441.	0.223063
$185$	12944.1	0.0278064
$186$	−116296.	−0.246479
$187$	−203818.	−0.426225
$188$	126505.	0.261044
$189$	613605.	1.24950
$190$	30845.8	0.0619886
$191$	466344.	0.924960	0.462480	−	0.886630i	$-0.346960\pi$
$191$	466344.	0.924960	0.462480	+	0.886630i	$0.346960\pi$
$192$	−107634.	−0.210715
$193$	−884896.	−1.71001	−0.855006	−	0.518619i	$-0.826446\pi$
$193$	−884896.	−1.71001	−0.855006	+	0.518619i	$0.826446\pi$
$194$	358969.	0.684783
$195$	157533.	0.296677
$196$	−791001.	−1.47074
$197$	−509516.	−0.935388	−0.467694	−	0.883890i	$-0.654915\pi$
$197$	−509516.	−0.935388	−0.467694	+	0.883890i	$0.654915\pi$
$198$	86886.2	0.157503
$199$	281107.	0.503198	0.251599	−	0.967832i	$-0.419044\pi$
$199$	281107.	0.503198	0.251599	+	0.967832i	$0.419044\pi$
$200$	111759.	0.197565
$201$	−12447.4	−0.0217314
$202$	−293136.	−0.505464
$203$	−1.68864e6	−2.87606
$204$	−196326.	−0.330295
$205$	−332911.	−0.553277
$206$	−608668.	−0.999337
$207$	−120361.	−0.195235
$208$	42882.4	0.0687260
$209$	43681.0	0.0691714
$210$	−115714.	−0.181067
$211$	576837.	0.891963	0.445982	−	0.895042i	$-0.352855\pi$
$211$	576837.	0.891963	0.445982	+	0.895042i	$0.352855\pi$
$212$	209700.	0.320450
$213$	−227850.	−0.344113
$214$	655247.	0.978071
$215$	−5921.80	−0.00873691
$216$	464752.	0.677777
$217$	−1.40042e6	−2.01888
$218$	−763559.	−1.08818
$219$	−248760.	−0.350485
$220$	61463.6	0.0856173
$221$	−1.85038e6	−2.54847
$222$	−10151.0	−0.0138238
$223$	−469310.	−0.631972	−0.315986	−	0.948764i	$-0.602335\pi$
$223$	−469310.	−0.631972	−0.315986	+	0.948764i	$0.602335\pi$
$224$	−1.38241e6	−1.84084
$225$	−131310.	−0.172918
$226$	349289.	0.454898
$227$	1.28417e6	1.65409	0.827046	−	0.562135i	$-0.190020\pi$
$227$	1.28417e6	1.65409	0.827046	+	0.562135i	$0.190020\pi$
$228$	42075.3	0.0536031
$229$	560295.	0.706038	0.353019	−	0.935616i	$-0.385155\pi$
$229$	560295.	0.706038	0.353019	+	0.935616i	$0.385155\pi$
$230$	48950.4	0.0610150
$231$	−163864.	−0.202048
$232$	−1.27900e6	−1.56009
$233$	292566.	0.353049	0.176524	−	0.984296i	$-0.443515\pi$
$233$	292566.	0.353049	0.176524	+	0.984296i	$0.443515\pi$
$234$	788804.	0.941736
$235$	155652.	0.183860
$236$	534226.	0.624374
$237$	8099.47	0.00936669
$238$	1.35918e6	1.55537
$239$	788838.	0.893291	0.446645	−	0.894711i	$-0.352619\pi$
$239$	788838.	0.893291	0.446645	+	0.894711i	$0.352619\pi$
$240$	5598.13	0.00627357
$241$	−1.75229e6	−1.94341	−0.971705	−	0.236198i	$-0.924099\pi$
$241$	−1.75229e6	−1.94341	−0.971705	+	0.236198i	$0.924099\pi$
$242$	−50040.2	−0.0549263
$243$	−838906.	−0.911376
$244$	967941.	1.04082
$245$	−973251.	−1.03588
$246$	261074.	0.275059
$247$	396562.	0.413589
$248$	−1.06070e6	−1.09512
$249$	231208.	0.236322
$250$	53403.3	0.0540404
$251$	482174.	0.483080	0.241540	−	0.970391i	$-0.422347\pi$
$251$	482174.	0.483080	0.241540	+	0.970391i	$0.422347\pi$
$252$	1.00782e6	0.999724
$253$	69319.1	0.0680850
$254$	−826789.	−0.804101
$255$	−241560.	−0.232634
$256$	−1.02167e6	−0.974341
$257$	−2.05996e6	−1.94548	−0.972739	−	0.231904i	$-0.925504\pi$
$257$	−2.05996e6	−1.94548	−0.972739	+	0.231904i	$0.925504\pi$
$258$	4643.97	0.00434351
$259$	−122238.	−0.113229
$260$	558003.	0.511921
$261$	1.50274e6	1.36547
$262$	510313.	0.459286
$263$	−1.65746e6	−1.47758	−0.738792	−	0.673933i	$-0.764604\pi$
$263$	−1.65746e6	−1.47758	−0.738792	+	0.673933i	$0.764604\pi$
$264$	−124113.	−0.109599
$265$	258016.	0.225700
$266$	−291291.	−0.252420
$267$	−287658.	−0.246944
$268$	−44090.3	−0.0374979
$269$	−36691.7	−0.0309163	−0.0154581	−	0.999881i	$-0.504921\pi$
$269$	−36691.7	−0.0309163	−0.0154581	+	0.999881i	$0.504921\pi$
$270$	222078.	0.185394
$271$	−1.49900e6	−1.23988	−0.619940	−	0.784649i	$-0.712843\pi$
$271$	−1.49900e6	−1.23988	−0.619940	+	0.784649i	$0.712843\pi$
$272$	−65755.6	−0.0538903
$273$	−1.48766e6	−1.20808
$274$	933825.	0.751431
$275$	75625.0	0.0603023
$276$	66771.0	0.0527612
$277$	1.93169e6	1.51265	0.756324	−	0.654197i	$-0.226993\pi$
$277$	1.93169e6	1.51265	0.756324	+	0.654197i	$0.226993\pi$
$278$	208783.	0.162025
$279$	1.24625e6	0.958503
$280$	−1.05540e6	−0.804490
$281$	−817779.	−0.617832	−0.308916	−	0.951089i	$-0.599966\pi$
$281$	−817779.	−0.617832	−0.308916	+	0.951089i	$0.599966\pi$
$282$	−122065.	−0.0914048
$283$	2.33140e6	1.73041	0.865207	−	0.501415i	$-0.167187\pi$
$283$	2.33140e6	1.73041	0.865207	+	0.501415i	$0.167187\pi$
$284$	−807077.	−0.593771
$285$	51769.6	0.0377540
$286$	−454294.	−0.328415
$287$	3.14383e6	2.25297
$288$	1.23022e6	0.873977
$289$	1.41750e6	0.998341
$290$	−611159.	−0.426736
$291$	602471.	0.417065
$292$	−881141.	−0.604767
$293$	−367782.	−0.250277	−0.125139	−	0.992139i	$-0.539938\pi$
$293$	−367782.	−0.250277	−0.125139	+	0.992139i	$0.539938\pi$
$294$	763239.	0.514982
$295$	657313.	0.439762
$296$	−92584.3	−0.0614198
$297$	314487.	0.206877
$298$	752518.	0.490881
$299$	629320.	0.407093
$300$	72845.1	0.0467301
$301$	55922.4	0.0355770
$302$	210195.	0.132618
$303$	−491980.	−0.307851
$304$	14092.3	0.00874579
$305$	1.19096e6	0.733072
$306$	−1.20955e6	−0.738446
$307$	−96325.6	−0.0583305	−0.0291652	−	0.999575i	$-0.509285\pi$
$307$	−96325.6	−0.0583305	−0.0291652	+	0.999575i	$0.509285\pi$
$308$	−580430.	−0.348637
$309$	−1.02155e6	−0.608643
$310$	−506846.	−0.299551
$311$	862828.	0.505852	0.252926	−	0.967486i	$-0.418607\pi$
$311$	862828.	0.505852	0.252926	+	0.967486i	$0.418607\pi$
$312$	−1.12677e6	−0.655313
$313$	−3.31936e6	−1.91511	−0.957554	−	0.288253i	$-0.906925\pi$
$313$	−3.31936e6	−1.91511	−0.957554	+	0.288253i	$0.906925\pi$
$314$	1.21402e6	0.694867
$315$	1.24002e6	0.704129
$316$	28689.4	0.0161623
$317$	−1.42305e6	−0.795373	−0.397686	−	0.917521i	$-0.630187\pi$
$317$	−1.42305e6	−0.795373	−0.397686	+	0.917521i	$0.630187\pi$
$318$	−202340.	−0.112206
$319$	−865468.	−0.476184
$320$	−469096.	−0.256087
$321$	1.09972e6	0.595691
$322$	−462262.	−0.248455
$323$	−608085.	−0.324308
$324$	−734401.	−0.388661
$325$	686568.	0.360558
$326$	−434985.	−0.226689
$327$	−1.28151e6	−0.662753
$328$	2.38118e6	1.22210
$329$	−1.46990e6	−0.748683
$330$	−59306.3	−0.0299789
$331$	−2.21675e6	−1.11211	−0.556055	−	0.831146i	$-0.687686\pi$
$331$	−2.21675e6	−1.11211	−0.556055	+	0.831146i	$0.687686\pi$
$332$	818971.	0.407777
$333$	108780.	0.0537576
$334$	74153.8	0.0363720
$335$	−54248.9	−0.0264106
$336$	−52865.8	−0.0255462
$337$	613837.	0.294428	0.147214	−	0.989105i	$-0.452969\pi$
$337$	613837.	0.294428	0.147214	+	0.989105i	$0.452969\pi$
$338$	−2.85534e6	−1.35946
$339$	586224.	0.277054
$340$	−855637.	−0.401414
$341$	−717749.	−0.334262
$342$	259222.	0.119841
$343$	5.22296e6	2.39707
$344$	42356.3	0.0192984
$345$	82155.2	0.0371610
$346$	−99448.3	−0.0446588
$347$	4.21660e6	1.87992	0.939958	−	0.341290i	$-0.110864\pi$
$347$	4.21660e6	1.87992	0.939958	+	0.341290i	$0.110864\pi$
$348$	−833654.	−0.369010
$349$	1.85416e6	0.814861	0.407431	−	0.913236i	$-0.366425\pi$
$349$	1.85416e6	0.814861	0.407431	+	0.913236i	$0.366425\pi$
$350$	−504313.	−0.220054
$351$	2.85510e6	1.23695
$352$	−708516.	−0.304785
$353$	1.78541e6	0.762607	0.381303	−	0.924450i	$-0.375475\pi$
$353$	1.78541e6	0.762607	0.381303	+	0.924450i	$0.375475\pi$
$354$	−515476.	−0.218625
$355$	−993030.	−0.418207
$356$	−1.01892e6	−0.426105
$357$	2.28116e6	0.947296
$358$	−304933.	−0.125747
$359$	319891.	0.130999	0.0654993	−	0.997853i	$-0.479136\pi$
$359$	319891.	0.130999	0.0654993	+	0.997853i	$0.479136\pi$
$360$	939206.	0.381948
$361$	130321.	0.0526316
$362$	1.43114e6	0.574000
$363$	−83984.3	−0.0334527
$364$	−5.26949e6	−2.08456
$365$	−1.08416e6	−0.425952
$366$	−933968.	−0.364443
$367$	−1.54436e6	−0.598526	−0.299263	−	0.954171i	$-0.596741\pi$
$367$	−1.54436e6	−0.598526	−0.299263	+	0.954171i	$0.596741\pi$
$368$	22363.7	0.00860843
$369$	−2.79772e6	−1.06964
$370$	−44240.7	−0.0168003
$371$	−2.43657e6	−0.919060
$372$	−691365.	−0.259030
$373$	3.20754e6	1.19371	0.596857	−	0.802348i	$-0.296416\pi$
$373$	3.20754e6	1.19371	0.596857	+	0.802348i	$0.296416\pi$
$374$	696612.	0.257521
$375$	89628.8	0.0329131
$376$	−1.11332e6	−0.406116
$377$	−7.85723e6	−2.84719
$378$	−2.09719e6	−0.754932
$379$	−5.28024e6	−1.88823	−0.944117	−	0.329610i	$-0.893083\pi$
$379$	−5.28024e6	−1.88823	−0.944117	+	0.329610i	$0.893083\pi$
$380$	183375.	0.0651450
$381$	−1.38763e6	−0.489735
$382$	−1.59388e6	−0.558851
$383$	−4.27989e6	−1.49086	−0.745428	−	0.666587i	$-0.767755\pi$
$383$	−4.27989e6	−1.49086	−0.745428	+	0.666587i	$0.767755\pi$
$384$	−706962.	−0.244663
$385$	−714163.	−0.245553
$386$	3.02441e6	1.03317
$387$	−49765.8	−0.0168909
$388$	2.13404e6	0.719652
$389$	−3.32630e6	−1.11452	−0.557260	−	0.830338i	$-0.688147\pi$
$389$	−3.32630e6	−1.11452	−0.557260	+	0.830338i	$0.688147\pi$
$390$	−538418.	−0.179249
$391$	−964994.	−0.319215
$392$	6.96127e6	2.28809
$393$	856476.	0.279727
$394$	1.74143e6	0.565152
$395$	35299.6	0.0113835
$396$	516529.	0.165522
$397$	−3.84701e6	−1.22503	−0.612516	−	0.790458i	$-0.709842\pi$
$397$	−3.84701e6	−1.22503	−0.612516	+	0.790458i	$0.709842\pi$
$398$	−960771.	−0.304027
$399$	−488885.	−0.153736
$400$	24398.1	0.00762440
$401$	−5.57625e6	−1.73173	−0.865867	−	0.500275i	$-0.833232\pi$
$401$	−5.57625e6	−1.73173	−0.865867	+	0.500275i	$0.833232\pi$
$402$	42542.9	0.0131299
$403$	−6.51615e6	−1.99861
$404$	−1.74266e6	−0.531202
$405$	−903609.	−0.273743
$406$	5.77147e6	1.73768
$407$	−62649.7	−0.0187470
$408$	1.72778e6	0.513852
$409$	593095.	0.175314	0.0876568	−	0.996151i	$-0.472062\pi$
$409$	593095.	0.175314	0.0876568	+	0.996151i	$0.472062\pi$
$410$	1.13783e6	0.334285
$411$	1.56727e6	0.457657
$412$	−3.61847e6	−1.05022
$413$	−6.20732e6	−1.79073
$414$	411370.	0.117959
$415$	1.00766e6	0.287207
$416$	−6.43232e6	−1.82236
$417$	350408.	0.0986810
$418$	−149294.	−0.0417927
$419$	−96349.4	−0.0268111	−0.0134055	−	0.999910i	$-0.504267\pi$
$419$	−96349.4	−0.0268111	−0.0134055	+	0.999910i	$0.504267\pi$
$420$	−687910.	−0.190287
$421$	−5.01700e6	−1.37956	−0.689778	−	0.724021i	$-0.742292\pi$
$421$	−5.01700e6	−1.37956	−0.689778	+	0.724021i	$0.742292\pi$
$422$	−1.97152e6	−0.538915
$423$	1.30808e6	0.355453
$424$	−1.84549e6	−0.498536
$425$	−1.05278e6	−0.282725
$426$	778750.	0.207909
$427$	−1.12468e7	−2.98510
$428$	3.89537e6	1.02787
$429$	−762459.	−0.200020
$430$	20239.6	0.00527875
$431$	−3.85736e6	−1.00022	−0.500112	−	0.865961i	$-0.666708\pi$
$431$	−3.85736e6	−1.00022	−0.500112	+	0.865961i	$0.666708\pi$
$432$	101460.	0.0261567
$433$	6.13111e6	1.57152	0.785759	−	0.618532i	$-0.212272\pi$
$433$	6.13111e6	1.57152	0.785759	+	0.618532i	$0.212272\pi$
$434$	4.78638e6	1.21978
$435$	−1.02573e6	−0.259902
$436$	−4.53928e6	−1.14359
$437$	206812.	0.0518049
$438$	850214.	0.211760
$439$	−2.36700e6	−0.586189	−0.293094	−	0.956084i	$-0.594685\pi$
$439$	−2.36700e6	−0.586189	−0.293094	+	0.956084i	$0.594685\pi$
$440$	−540916.	−0.133198
$441$	−8.17902e6	−2.00265
$442$	6.32425e6	1.53976
$443$	1.39530e6	0.337799	0.168900	−	0.985633i	$-0.445979\pi$
$443$	1.39530e6	0.337799	0.168900	+	0.985633i	$0.445979\pi$
$444$	−60346.7	−0.0145277
$445$	−1.25369e6	−0.300116
$446$	1.60402e6	0.381831
$447$	1.26298e6	0.298970
$448$	4.42990e6	1.04279
$449$	1.30123e6	0.304606	0.152303	−	0.988334i	$-0.451331\pi$
$449$	1.30123e6	0.304606	0.152303	+	0.988334i	$0.451331\pi$
$450$	448792.	0.104475
$451$	1.61129e6	0.373019
$452$	2.07649e6	0.478061
$453$	352777.	0.0807709
$454$	−4.38907e6	−0.999385
$455$	−6.48359e6	−1.46821
$456$	−370287.	−0.0833924
$457$	−1.24236e6	−0.278263	−0.139132	−	0.990274i	$-0.544431\pi$
$457$	−1.24236e6	−0.278263	−0.139132	+	0.990274i	$0.544431\pi$
$458$	−1.91498e6	−0.426581
$459$	−4.37798e6	−0.969935
$460$	291005.	0.0641218
$461$	7.17762e6	1.57300	0.786499	−	0.617592i	$-0.211892\pi$
$461$	7.17762e6	1.57300	0.786499	+	0.617592i	$0.211892\pi$
$462$	560058.	0.122075
$463$	6.87295e6	1.49002	0.745008	−	0.667056i	$-0.232446\pi$
$463$	6.87295e6	1.49002	0.745008	+	0.667056i	$0.232446\pi$
$464$	−279217.	−0.0602069
$465$	−850657.	−0.182441
$466$	−999937.	−0.213308
$467$	−3.98903e6	−0.846399	−0.423199	−	0.906037i	$-0.639093\pi$
$467$	−3.98903e6	−0.846399	−0.423199	+	0.906037i	$0.639093\pi$
$468$	4.68936e6	0.989689
$469$	512298.	0.107545
$470$	−531991.	−0.111086
$471$	2.03753e6	0.423207
$472$	−4.70150e6	−0.971363
$473$	28661.5	0.00589042
$474$	−27682.5	−0.00565926
$475$	225625.	0.0458831
$476$	8.08019e6	1.63457
$477$	2.16832e6	0.436343
$478$	−2.69610e6	−0.539717
$479$	−95369.4	−0.0189920	−0.00949599	−	0.999955i	$-0.503023\pi$
$479$	−95369.4	−0.0189920	−0.00949599	+	0.999955i	$0.503023\pi$
$480$	−839714.	−0.166352
$481$	−568770.	−0.112092
$482$	5.98902e6	1.17419
$483$	−775831.	−0.151321
$484$	−297484.	−0.0577231
$485$	2.62572e6	0.506868
$486$	2.86722e6	0.550644
$487$	3.50447e6	0.669577	0.334789	−	0.942293i	$-0.391335\pi$
$487$	3.50447e6	0.669577	0.334789	+	0.942293i	$0.391335\pi$
$488$	−8.51844e6	−1.61924
$489$	−730050.	−0.138064
$490$	3.32639e6	0.625868
$491$	−208761.	−0.0390792	−0.0195396	−	0.999809i	$-0.506220\pi$
$491$	−208761.	−0.0390792	−0.0195396	+	0.999809i	$0.506220\pi$
$492$	1.55206e6	0.289065
$493$	1.20482e7	2.23257
$494$	−1.35537e6	−0.249886
$495$	635539.	0.116581
$496$	−231560.	−0.0422628
$497$	9.37766e6	1.70296
$498$	−790226.	−0.142784
$499$	−4.25258e6	−0.764541	−0.382271	−	0.924050i	$-0.624858\pi$
$499$	−4.25258e6	−0.764541	−0.382271	+	0.924050i	$0.624858\pi$
$500$	317477.	0.0567921
$501$	124455.	0.0221522
$502$	−1.64798e6	−0.291872
$503$	5.82156e6	1.02593	0.512967	−	0.858408i	$-0.328546\pi$
$503$	5.82156e6	1.02593	0.512967	+	0.858408i	$0.328546\pi$
$504$	−8.86937e6	−1.55531
$505$	−2.14418e6	−0.374138
$506$	−236920.	−0.0411363
$507$	−4.79222e6	−0.827975
$508$	−4.91518e6	−0.845045
$509$	−7.02234e6	−1.20140	−0.600700	−	0.799475i	$-0.705111\pi$
$509$	−7.02234e6	−1.20140	−0.600700	+	0.799475i	$0.705111\pi$
$510$	825606.	0.140555
$511$	1.02382e7	1.73449
$512$	−451953.	−0.0761936
$513$	938263.	0.157410
$514$	7.04056e6	1.17544
$515$	−4.45217e6	−0.739697
$516$	27607.9	0.00456467
$517$	−753358.	−0.123958
$518$	417786.	0.0684115
$519$	−166908.	−0.0271993
$520$	−4.91075e6	−0.796415
$521$	−2.34124e6	−0.377879	−0.188939	−	0.981989i	$-0.560505\pi$
$521$	−2.34124e6	−0.377879	−0.188939	+	0.981989i	$0.560505\pi$
$522$	−5.13607e6	−0.825002
$523$	−7.74916e6	−1.23880	−0.619399	−	0.785077i	$-0.712624\pi$
$523$	−7.74916e6	−1.23880	−0.619399	+	0.785077i	$0.712624\pi$
$524$	3.03376e6	0.482672
$525$	−846407.	−0.134024
$526$	5.66487e6	0.892742
$527$	9.99181e6	1.56718
$528$	−27095.0	−0.00422964
$529$	−6.10815e6	−0.949009
$530$	−881851.	−0.136366
$531$	5.52394e6	0.850184
$532$	−1.73170e6	−0.265273
$533$	1.46282e7	2.23035
$534$	983161.	0.149201
$535$	4.79288e6	0.723955
$536$	388021.	0.0583369
$537$	−511779.	−0.0765856
$538$	125405.	0.0186793
$539$	4.71053e6	0.698390
$540$	1.32023e6	0.194834
$541$	−9.60846e6	−1.41143	−0.705717	−	0.708494i	$-0.749375\pi$
$541$	−9.60846e6	−1.41143	−0.705717	+	0.708494i	$0.749375\pi$
$542$	5.12332e6	0.749123
$543$	2.40194e6	0.349593
$544$	9.86328e6	1.42897
$545$	−5.58514e6	−0.805458
$546$	5.08454e6	0.729911
$547$	300818.	0.0429869	0.0214934	−	0.999769i	$-0.493158\pi$
$547$	300818.	0.0429869	0.0214934	+	0.999769i	$0.493158\pi$
$548$	5.55149e6	0.789693
$549$	1.00086e7	1.41724
$550$	−258472.	−0.0364340
$551$	−2.58210e6	−0.362321
$552$	−587623.	−0.0820827
$553$	−333351.	−0.0463541
$554$	−6.60216e6	−0.913927
$555$	−74250.7	−0.0102322
$556$	1.24119e6	0.170275
$557$	−1.25311e7	−1.71140	−0.855701	−	0.517471i	$-0.826873\pi$
$557$	−1.25311e7	−1.71140	−0.855701	+	0.517471i	$0.826873\pi$
$558$	−4.25944e6	−0.579118
$559$	260206.	0.0352199
$560$	−230403.	−0.0310468
$561$	1.16915e6	0.156842
$562$	2.79502e6	0.373288
$563$	−1.28885e6	−0.171368	−0.0856840	−	0.996322i	$-0.527308\pi$
$563$	−1.28885e6	−0.171368	−0.0856840	+	0.996322i	$0.527308\pi$
$564$	−725665.	−0.0960591
$565$	2.55492e6	0.336710
$566$	−7.96828e6	−1.04550
$567$	8.53321e6	1.11469
$568$	7.10275e6	0.923753
$569$	1.03918e7	1.34558	0.672791	−	0.739832i	$-0.265095\pi$
$569$	1.03918e7	1.34558	0.672791	+	0.739832i	$0.265095\pi$
$570$	−176939.	−0.0228106
$571$	−7.95437e6	−1.02098	−0.510488	−	0.859885i	$-0.670535\pi$
$571$	−7.95437e6	−1.02098	−0.510488	+	0.859885i	$0.670535\pi$
$572$	−2.70073e6	−0.345137
$573$	−2.67506e6	−0.340367
$574$	−1.07450e7	−1.36122
$575$	358053.	0.0451625
$576$	−3.94220e6	−0.495088
$577$	6.48056e6	0.810351	0.405175	−	0.914239i	$-0.367210\pi$
$577$	6.48056e6	0.810351	0.405175	+	0.914239i	$0.367210\pi$
$578$	−4.84476e6	−0.603187
$579$	5.07598e6	0.629250
$580$	−3.63328e6	−0.448465
$581$	−9.51585e6	−1.16952
$582$	−2.05913e6	−0.251987
$583$	−1.24880e6	−0.152167
$584$	7.75455e6	0.940859
$585$	5.76980e6	0.697061
$586$	1.25701e6	0.151215
$587$	−1.00721e7	−1.20649	−0.603243	−	0.797557i	$-0.706125\pi$
$587$	−1.00721e7	−1.20649	−0.603243	+	0.797557i	$0.706125\pi$
$588$	4.53738e6	0.541204
$589$	−2.14138e6	−0.254335
$590$	−2.24657e6	−0.265700
$591$	2.92270e6	0.344204
$592$	−20212.0	−0.00237031
$593$	9.84085e6	1.14920	0.574600	−	0.818434i	$-0.305158\pi$
$593$	9.84085e6	1.14920	0.574600	+	0.818434i	$0.305158\pi$
$594$	−1.07486e6	−0.124993
$595$	9.94189e6	1.15127
$596$	4.47364e6	0.515876
$597$	−1.61250e6	−0.185167
$598$	−2.15090e6	−0.245961
$599$	1.00662e7	1.14630	0.573152	−	0.819449i	$-0.305720\pi$
$599$	1.00662e7	1.14630	0.573152	+	0.819449i	$0.305720\pi$
$600$	−641079.	−0.0726998
$601$	1.60284e6	0.181010	0.0905052	−	0.995896i	$-0.471152\pi$
$601$	1.60284e6	0.181010	0.0905052	+	0.995896i	$0.471152\pi$
$602$	−191132.	−0.0214953
$603$	−455898.	−0.0510593
$604$	1.24958e6	0.139371
$605$	−366025.	−0.0406558
$606$	1.68150e6	0.186001
$607$	−7.66961e6	−0.844893	−0.422446	−	0.906388i	$-0.638829\pi$
$607$	−7.66961e6	−0.844893	−0.422446	+	0.906388i	$0.638829\pi$
$608$	−2.11384e6	−0.231906
$609$	9.68646e6	1.05833
$610$	−4.07047e6	−0.442914
$611$	−6.83943e6	−0.741168
$612$	−7.19062e6	−0.776047
$613$	−1.61455e7	−1.73541	−0.867704	−	0.497082i	$-0.834405\pi$
$613$	−1.61455e7	−1.73541	−0.867704	+	0.497082i	$0.834405\pi$
$614$	329223.	0.0352427
$615$	1.90965e6	0.203595
$616$	5.10812e6	0.542387
$617$	−1.25538e7	−1.32759	−0.663794	−	0.747916i	$-0.731055\pi$
$617$	−1.25538e7	−1.32759	−0.663794	+	0.747916i	$0.731055\pi$
$618$	3.49146e6	0.367736
$619$	452704.	0.0474884	0.0237442	−	0.999718i	$-0.492441\pi$
$619$	452704.	0.0474884	0.0237442	+	0.999718i	$0.492441\pi$
$620$	−3.01314e6	−0.314804
$621$	1.48897e6	0.154937
$622$	−2.94898e6	−0.305630
$623$	1.18392e7	1.22208
$624$	−245984.	−0.0252898
$625$	390625.	0.0400000
$626$	1.13450e7	1.15709
$627$	−250565.	−0.0254537
$628$	7.21722e6	0.730249
$629$	872149.	0.0878949
$630$	−4.23816e6	−0.425428
$631$	−8.31235e6	−0.831094	−0.415547	−	0.909572i	$-0.636410\pi$
$631$	−8.31235e6	−0.831094	−0.415547	+	0.909572i	$0.636410\pi$
$632$	−252484.	−0.0251444
$633$	−3.30888e6	−0.328225
$634$	4.86370e6	0.480556
$635$	−6.04765e6	−0.595185
$636$	−1.20289e6	−0.117919
$637$	4.27650e7	4.17580
$638$	2.95801e6	0.287705
$639$	−8.34525e6	−0.808513
$640$	−3.08112e6	−0.297344
$641$	1.33667e7	1.28493	0.642463	−	0.766317i	$-0.277913\pi$
$641$	1.33667e7	1.28493	0.642463	+	0.766317i	$0.277913\pi$
$642$	−3.75865e6	−0.359911
$643$	1.61069e7	1.53633	0.768165	−	0.640252i	$-0.221170\pi$
$643$	1.61069e7	1.53633	0.768165	+	0.640252i	$0.221170\pi$
$644$	−2.74810e6	−0.261106
$645$	33968.9	0.00321501
$646$	2.07832e6	0.195944
$647$	2.93956e6	0.276072	0.138036	−	0.990427i	$-0.455921\pi$
$647$	2.93956e6	0.276072	0.138036	+	0.990427i	$0.455921\pi$
$648$	6.46315e6	0.604654
$649$	−3.18140e6	−0.296487
$650$	−2.34656e6	−0.217846
$651$	8.03316e6	0.742906
$652$	−2.58594e6	−0.238231
$653$	1.11105e7	1.01965	0.509824	−	0.860279i	$-0.329710\pi$
$653$	1.11105e7	1.01965	0.509824	+	0.860279i	$0.329710\pi$
$654$	4.37996e6	0.400429
$655$	3.73274e6	0.339958
$656$	519832.	0.0471632
$657$	−9.11107e6	−0.823486
$658$	5.02385e6	0.452347
$659$	9.44286e6	0.847012	0.423506	−	0.905893i	$-0.360799\pi$
$659$	9.44286e6	0.847012	0.423506	+	0.905893i	$0.360799\pi$
$660$	−352570.	−0.0315054
$661$	−2.12448e6	−0.189125	−0.0945624	−	0.995519i	$-0.530145\pi$
$661$	−2.12448e6	−0.189125	−0.0945624	+	0.995519i	$0.530145\pi$
$662$	7.57645e6	0.671925
$663$	1.06142e7	0.937787
$664$	−7.20742e6	−0.634395
$665$	−2.13068e6	−0.186838
$666$	−371791.	−0.0324798
$667$	−4.09764e6	−0.356631
$668$	440836.	0.0382240
$669$	2.69208e6	0.232553
$670$	185413.	0.0159570
$671$	−5.76423e6	−0.494237
$672$	7.92982e6	0.677392
$673$	−1.61237e7	−1.37223	−0.686114	−	0.727494i	$-0.740685\pi$
$673$	−1.61237e7	−1.37223	−0.686114	+	0.727494i	$0.740685\pi$
$674$	−2.09798e6	−0.177890
$675$	1.62442e6	0.137226
$676$	−1.69747e7	−1.42868
$677$	7.66094e6	0.642407	0.321204	−	0.947010i	$-0.395913\pi$
$677$	7.66094e6	0.642407	0.321204	+	0.947010i	$0.395913\pi$
$678$	−2.00361e6	−0.167393
$679$	−2.47960e7	−2.06398
$680$	7.53011e6	0.624495
$681$	−7.36633e6	−0.608672
$682$	2.45313e6	0.201958
$683$	−6.14461e6	−0.504014	−0.252007	−	0.967725i	$-0.581091\pi$
$683$	−6.14461e6	−0.504014	−0.252007	+	0.967725i	$0.581091\pi$
$684$	1.54105e6	0.125944
$685$	6.83057e6	0.556200
$686$	−1.78511e7	−1.44829
$687$	−3.21399e6	−0.259808
$688$	9246.76	0.000744764 0
$689$	−1.13373e7	−0.909834
$690$	−280791.	−0.0224523
$691$	5.87927e6	0.468412	0.234206	−	0.972187i	$-0.424751\pi$
$691$	5.87927e6	0.468412	0.234206	+	0.972187i	$0.424751\pi$
$692$	−591210.	−0.0469328
$693$	−6.00170e6	−0.474724
$694$	−1.44115e7	−1.13583
$695$	1.52717e6	0.119929
$696$	7.33664e6	0.574082
$697$	−2.24308e7	−1.74889
$698$	−6.33718e6	−0.492331
$699$	−1.67823e6	−0.129915
$700$	−2.99809e6	−0.231259
$701$	1.27093e7	0.976848	0.488424	−	0.872607i	$-0.337572\pi$
$701$	1.27093e7	0.976848	0.488424	+	0.872607i	$0.337572\pi$
$702$	−9.75819e6	−0.747354
$703$	−186913.	−0.0142644
$704$	2.27042e6	0.172654
$705$	−892860.	−0.0676567
$706$	−6.10219e6	−0.460759
$707$	2.02485e7	1.52350
$708$	−3.06445e6	−0.229757
$709$	−1.21990e7	−0.911401	−0.455701	−	0.890133i	$-0.650611\pi$
$709$	−1.21990e7	−0.911401	−0.455701	+	0.890133i	$0.650611\pi$
$710$	3.39399e6	0.252677
$711$	296651.	0.0220076
$712$	8.96712e6	0.662908
$713$	−3.39825e6	−0.250340
$714$	−7.79659e6	−0.572347
$715$	−3.32299e6	−0.243088
$716$	−1.81279e6	−0.132149
$717$	−4.52496e6	−0.328713
$718$	−1.09333e6	−0.0791480
$719$	−9.14959e6	−0.660054	−0.330027	−	0.943971i	$-0.607058\pi$
$719$	−9.14959e6	−0.660054	−0.330027	+	0.943971i	$0.607058\pi$
$720$	205037.	0.0147401
$721$	4.20440e7	3.01207
$722$	−445413.	−0.0317995
$723$	1.00516e7	0.715136
$724$	8.50800e6	0.603227
$725$	−4.47039e6	−0.315864
$726$	287043.	0.0202118
$727$	2.17127e7	1.52363	0.761813	−	0.647797i	$-0.224310\pi$
$727$	2.17127e7	1.52363	0.761813	+	0.647797i	$0.224310\pi$
$728$	4.63745e7	3.24303
$729$	−3.97091e6	−0.276740
$730$	3.70545e6	0.257356
$731$	−398998.	−0.0276171
$732$	−5.55234e6	−0.383000
$733$	−5.88745e6	−0.404732	−0.202366	−	0.979310i	$-0.564863\pi$
$733$	−5.88745e6	−0.404732	−0.202366	+	0.979310i	$0.564863\pi$
$734$	5.27833e6	0.361624
$735$	5.58280e6	0.381183
$736$	−3.35453e6	−0.228264
$737$	262565.	0.0178060
$738$	9.56209e6	0.646267
$739$	−1.21978e6	−0.0821618	−0.0410809	−	0.999156i	$-0.513080\pi$
$739$	−1.21978e6	−0.0821618	−0.0410809	+	0.999156i	$0.513080\pi$
$740$	−263006.	−0.0176558
$741$	−2.27477e6	−0.152192
$742$	8.32774e6	0.555287
$743$	597922.	0.0397349	0.0198675	−	0.999803i	$-0.493676\pi$
$743$	597922.	0.0397349	0.0198675	+	0.999803i	$0.493676\pi$
$744$	6.08441e6	0.402983
$745$	5.50438e6	0.363344
$746$	−1.09628e7	−0.721230
$747$	8.46823e6	0.555253
$748$	4.14129e6	0.270633
$749$	−4.52614e7	−2.94797
$750$	−306334.	−0.0198858
$751$	1.43076e7	0.925691	0.462846	−	0.886439i	$-0.346828\pi$
$751$	1.43076e7	0.925691	0.462846	+	0.886439i	$0.346828\pi$
$752$	−243048.	−0.0156728
$753$	−2.76587e6	−0.177764
$754$	2.68545e7	1.72024
$755$	1.53749e6	0.0981625
$756$	−1.24676e7	−0.793373
$757$	1.10342e7	0.699843	0.349921	−	0.936779i	$-0.386208\pi$
$757$	1.10342e7	0.699843	0.349921	+	0.936779i	$0.386208\pi$
$758$	1.80469e7	1.14085
$759$	−397631.	−0.0250539
$760$	−1.61381e6	−0.101349
$761$	−8.91498e6	−0.558031	−0.279016	−	0.960287i	$-0.590008\pi$
$761$	−8.91498e6	−0.558031	−0.279016	+	0.960287i	$0.590008\pi$
$762$	4.74266e6	0.295893
$763$	5.27431e7	3.27985
$764$	−9.47543e6	−0.587308
$765$	−8.84736e6	−0.546588
$766$	1.46279e7	0.900760
$767$	−2.88826e7	−1.77275
$768$	5.86055e6	0.358538
$769$	−9.32936e6	−0.568900	−0.284450	−	0.958691i	$-0.591811\pi$
$769$	−9.32936e6	−0.568900	−0.284450	+	0.958691i	$0.591811\pi$
$770$	2.44088e6	0.148361
$771$	1.18164e7	0.715897
$772$	1.79798e7	1.08578
$773$	−3.55894e6	−0.214226	−0.107113	−	0.994247i	$-0.534161\pi$
$773$	−3.55894e6	−0.214226	−0.107113	+	0.994247i	$0.534161\pi$
$774$	170090.	0.0102053
$775$	−3.70738e6	−0.221724
$776$	−1.87808e7	−1.11959
$777$	701185.	0.0416658
$778$	1.13687e7	0.673382
$779$	4.80723e6	0.283825
$780$	−3.20084e6	−0.188377
$781$	4.80627e6	0.281955
$782$	3.29817e6	0.192866
$783$	−1.85902e7	−1.08362
$784$	1.51971e6	0.0883019
$785$	8.88009e6	0.514332
$786$	−2.92728e6	−0.169008
$787$	−2.01041e7	−1.15704	−0.578520	−	0.815668i	$-0.696369\pi$
$787$	−2.01041e7	−1.15704	−0.578520	+	0.815668i	$0.696369\pi$
$788$	1.03526e7	0.593929
$789$	9.50756e6	0.543722
$790$	−120647.	−0.00687781
$791$	−2.41273e7	−1.37109
$792$	−4.54576e6	−0.257510
$793$	−5.23311e7	−2.95513
$794$	1.31484e7	0.740152
$795$	−1.48004e6	−0.0830532
$796$	−5.71169e6	−0.319508
$797$	345701.	0.0192777	0.00963883	−	0.999954i	$-0.496932\pi$
$797$	345701.	0.0192777	0.00963883	+	0.999954i	$0.496932\pi$
$798$	1.67092e6	0.0928854
$799$	1.04875e7	0.581174
$800$	−3.65969e6	−0.202171
$801$	−1.05358e7	−0.580209
$802$	1.90586e7	1.04630
$803$	5.24733e6	0.287177
$804$	252913.	0.0137985
$805$	−3.38127e6	−0.183903
$806$	2.22710e7	1.20754
$807$	210472.	0.0113766
$808$	1.53364e7	0.826411
$809$	−1.09720e7	−0.589405	−0.294702	−	0.955589i	$-0.595221\pi$
$809$	−1.09720e7	−0.589405	−0.294702	+	0.955589i	$0.595221\pi$
$810$	3.08837e6	0.165393
$811$	1.71520e7	0.915721	0.457860	−	0.889024i	$-0.348616\pi$
$811$	1.71520e7	0.915721	0.457860	+	0.889024i	$0.348616\pi$
$812$	3.43108e7	1.82617
$813$	8.59865e6	0.456251
$814$	214125.	0.0113268
$815$	−3.18175e6	−0.167792
$816$	377190.	0.0198305
$817$	85510.9	0.00448194
$818$	−2.02709e6	−0.105923
$819$	−5.44869e7	−2.83846
$820$	6.76426e6	0.351306
$821$	8.12449e6	0.420667	0.210333	−	0.977630i	$-0.432545\pi$
$821$	8.12449e6	0.420667	0.210333	+	0.977630i	$0.432545\pi$
$822$	−5.35664e6	−0.276512
$823$	2.81325e7	1.44780	0.723900	−	0.689905i	$-0.242347\pi$
$823$	2.81325e7	1.44780	0.723900	+	0.689905i	$0.242347\pi$
$824$	3.18446e7	1.63387
$825$	−433803.	−0.0221900
$826$	2.12155e7	1.08194
$827$	3.49923e7	1.77913	0.889567	−	0.456805i	$-0.151006\pi$
$827$	3.49923e7	1.77913	0.889567	+	0.456805i	$0.151006\pi$
$828$	2.44555e6	0.123966
$829$	−1.80539e7	−0.912401	−0.456201	−	0.889877i	$-0.650790\pi$
$829$	−1.80539e7	−0.912401	−0.456201	+	0.889877i	$0.650790\pi$
$830$	−3.44401e6	−0.173528
$831$	−1.10806e7	−0.556624
$832$	2.06122e7	1.03233
$833$	−6.55755e7	−3.27438
$834$	−1.19763e6	−0.0596220
$835$	542406.	0.0269221
$836$	−887534.	−0.0439207
$837$	−1.54172e7	−0.760660
$838$	329304.	0.0161990
$839$	−4.01660e6	−0.196994	−0.0984971	−	0.995137i	$-0.531404\pi$
$839$	−4.01660e6	−0.196994	−0.0984971	+	0.995137i	$0.531404\pi$
$840$	6.05401e6	0.296036
$841$	3.06490e7	1.49426
$842$	1.71472e7	0.833513
$843$	4.69098e6	0.227350
$844$	−1.17205e7	−0.566356
$845$	−2.08857e7	−1.00625
$846$	−4.47076e6	−0.214761
$847$	3.45655e6	0.165552
$848$	−402886.	−0.0192395
$849$	−1.33735e7	−0.636758
$850$	3.59820e6	0.170820
$851$	−296620.	−0.0140403
$852$	4.62959e6	0.218496
$853$	−1.96007e7	−0.922359	−0.461179	−	0.887307i	$-0.652574\pi$
$853$	−1.96007e7	−0.922359	−0.461179	+	0.887307i	$0.652574\pi$
$854$	3.84394e7	1.80356
$855$	1.89611e6	0.0887051
$856$	−3.42815e7	−1.59910
$857$	−2.06178e7	−0.958938	−0.479469	−	0.877559i	$-0.659171\pi$
$857$	−2.06178e7	−0.958938	−0.479469	+	0.877559i	$0.659171\pi$
$858$	2.60594e6	0.120850
$859$	3.76680e7	1.74177	0.870883	−	0.491490i	$-0.163547\pi$
$859$	3.76680e7	1.74177	0.870883	+	0.491490i	$0.163547\pi$
$860$	120322.	0.00554754
$861$	−1.80338e7	−0.829046
$862$	1.31838e7	0.604325
$863$	2.81066e6	0.128464	0.0642320	−	0.997935i	$-0.479540\pi$
$863$	2.81066e6	0.128464	0.0642320	+	0.997935i	$0.479540\pi$
$864$	−1.52188e7	−0.693581
$865$	−727427.	−0.0330559
$866$	−2.09550e7	−0.949496
$867$	−8.13113e6	−0.367370
$868$	2.84546e7	1.28189
$869$	−170850.	−0.00767477
$870$	3.50576e6	0.157030
$871$	2.38372e6	0.106466
$872$	3.99483e7	1.77913
$873$	2.20661e7	0.979919
$874$	−706843.	−0.0313000
$875$	−3.68886e6	−0.162882
$876$	5.05444e6	0.222542
$877$	−1.11984e7	−0.491652	−0.245826	−	0.969314i	$-0.579059\pi$
$877$	−1.11984e7	−0.491652	−0.245826	+	0.969314i	$0.579059\pi$
$878$	8.08997e6	0.354169
$879$	2.10969e6	0.0920971
$880$	−118087.	−0.00514037
$881$	1.97204e7	0.856004	0.428002	−	0.903778i	$-0.359218\pi$
$881$	1.97204e7	0.856004	0.428002	+	0.903778i	$0.359218\pi$
$882$	2.79544e7	1.20998
$883$	−2.24034e7	−0.966968	−0.483484	−	0.875353i	$-0.660629\pi$
$883$	−2.24034e7	−0.966968	−0.483484	+	0.875353i	$0.660629\pi$
$884$	3.75970e7	1.61816
$885$	−3.77051e6	−0.161824
$886$	−4.76888e6	−0.204095
$887$	−2.94286e7	−1.25591	−0.627957	−	0.778248i	$-0.716109\pi$
$887$	−2.94286e7	−1.25591	−0.627957	+	0.778248i	$0.716109\pi$
$888$	531086.	0.0226012
$889$	5.71108e7	2.42362
$890$	4.28487e6	0.181327
$891$	4.37347e6	0.184557
$892$	9.53571e6	0.401274
$893$	−2.24762e6	−0.0943180
$894$	−4.31663e6	−0.180634
$895$	−2.23046e6	−0.0930760
$896$	2.90965e7	1.21079
$897$	−3.60993e6	−0.149802
$898$	−4.44736e6	−0.184040
$899$	4.24280e7	1.75087
$900$	2.66802e6	0.109795
$901$	1.73846e7	0.713431
$902$	−5.50708e6	−0.225375
$903$	−320784.	−0.0130916
$904$	−1.82743e7	−0.743737
$905$	1.04683e7	0.424867
$906$	−1.20573e6	−0.0488009
$907$	3.23814e7	1.30700	0.653502	−	0.756924i	$-0.273299\pi$
$907$	3.23814e7	1.30700	0.653502	+	0.756924i	$0.273299\pi$
$908$	−2.60926e7	−1.05027
$909$	−1.80193e7	−0.723315
$910$	2.21597e7	0.887075
$911$	3.29982e7	1.31733	0.658665	−	0.752436i	$-0.271121\pi$
$911$	3.29982e7	1.31733	0.658665	+	0.752436i	$0.271121\pi$
$912$	−80837.0	−0.00321827
$913$	−4.87709e6	−0.193635
$914$	4.24615e6	0.168124
$915$	−6.83162e6	−0.269756
$916$	−1.13844e7	−0.448302
$917$	−3.52501e7	−1.38432
$918$	1.49631e7	0.586025
$919$	9.47429e6	0.370048	0.185024	−	0.982734i	$-0.440764\pi$
$919$	9.47429e6	0.370048	0.185024	+	0.982734i	$0.440764\pi$
$920$	−2.56101e6	−0.0997567
$921$	552547.	0.0214645
$922$	−2.45318e7	−0.950389
$923$	4.36341e7	1.68586
$924$	3.32949e6	0.128291
$925$	−323604.	−0.0124354
$926$	−2.34905e7	−0.900252
$927$	−3.74152e7	−1.43004
$928$	4.18823e7	1.59647
$929$	−1.22632e7	−0.466193	−0.233097	−	0.972454i	$-0.574886\pi$
$929$	−1.22632e7	−0.466193	−0.233097	+	0.972454i	$0.574886\pi$
$930$	2.90739e6	0.110229
$931$	1.40537e7	0.531395
$932$	−5.94452e6	−0.224170
$933$	−4.94939e6	−0.186143
$934$	1.36338e7	0.511386
$935$	5.09545e6	0.190613
$936$	−4.12691e7	−1.53970
$937$	−3.33632e7	−1.24142	−0.620709	−	0.784041i	$-0.713155\pi$
$937$	−3.33632e7	−1.24142	−0.620709	+	0.784041i	$0.713155\pi$
$938$	−1.75094e6	−0.0649777
$939$	1.90406e7	0.704722
$940$	−3.16263e6	−0.116743
$941$	−8.17030e6	−0.300790	−0.150395	−	0.988626i	$-0.548055\pi$
$941$	−8.17030e6	−0.300790	−0.150395	+	0.988626i	$0.548055\pi$
$942$	−6.96391e6	−0.255697
$943$	7.62878e6	0.279368
$944$	−1.02638e6	−0.0374868
$945$	−1.53401e7	−0.558791
$946$	−97959.8	−0.00355893
$947$	−5.24667e7	−1.90112	−0.950558	−	0.310548i	$-0.899487\pi$
$947$	−5.24667e7	−1.90112	−0.950558	+	0.310548i	$0.899487\pi$
$948$	−164570.	−0.00594742
$949$	4.76383e7	1.71708
$950$	−771144.	−0.0277221
$951$	8.16293e6	0.292681
$952$	−7.11104e7	−2.54297
$953$	−2.29902e7	−0.819993	−0.409997	−	0.912087i	$-0.634470\pi$
$953$	−2.29902e7	−0.819993	−0.409997	+	0.912087i	$0.634470\pi$
$954$	−7.41092e6	−0.263634
$955$	−1.16586e7	−0.413655
$956$	−1.60280e7	−0.567199
$957$	4.96453e6	0.175226
$958$	325955.	0.0114748
$959$	−6.45043e7	−2.26487
$960$	2.69085e6	0.0942347
$961$	6.55721e6	0.229040
$962$	1.94395e6	0.0677248
$963$	4.02785e7	1.39961
$964$	3.56041e7	1.23398
$965$	2.21224e7	0.764740
$966$	2.65164e6	0.0914266
$967$	−1.27287e7	−0.437743	−0.218871	−	0.975754i	$-0.570238\pi$
$967$	−1.27287e7	−0.437743	−0.218871	+	0.975754i	$0.570238\pi$
$968$	2.61803e6	0.0898021
$969$	3.48812e6	0.119339
$970$	−8.97423e6	−0.306244
$971$	−4.08742e6	−0.139124	−0.0695618	−	0.997578i	$-0.522160\pi$
$971$	−4.08742e6	−0.139124	−0.0695618	+	0.997578i	$0.522160\pi$
$972$	1.70453e7	0.578682
$973$	−1.44218e7	−0.488355
$974$	−1.19776e7	−0.404552
$975$	−3.93832e6	−0.132678
$976$	−1.85965e6	−0.0624895
$977$	−4.26434e7	−1.42927	−0.714636	−	0.699496i	$-0.753408\pi$
$977$	−4.26434e7	−1.42927	−0.714636	+	0.699496i	$0.753408\pi$
$978$	2.49518e6	0.0834169
$979$	6.06784e6	0.202338
$980$	1.97750e7	0.657737
$981$	−4.69365e7	−1.55718
$982$	713507.	0.0236113
$983$	−2.50275e7	−0.826103	−0.413051	−	0.910708i	$-0.635537\pi$
$983$	−2.50275e7	−0.826103	−0.413051	+	0.910708i	$0.635537\pi$
$984$	−1.36590e7	−0.449709
$985$	1.27379e7	0.418318
$986$	−4.11786e7	−1.34890
$987$	8.43170e6	0.275501
$988$	−8.05756e6	−0.262610
$989$	135701.	0.00441155
$990$	−2.17215e6	−0.0704373
$991$	−2.87908e7	−0.931258	−0.465629	−	0.884980i	$-0.654172\pi$
$991$	−2.87908e7	−0.931258	−0.465629	+	0.884980i	$0.654172\pi$
$992$	3.47337e7	1.12066
$993$	1.27158e7	0.409234
$994$	−3.20511e7	−1.02891
$995$	−7.02767e6	−0.225037
$996$	−4.69781e6	−0.150054
$997$	−2.55602e7	−0.814378	−0.407189	−	0.913344i	$-0.633491\pi$
$997$	−2.55602e7	−0.814378	−0.407189	+	0.913344i	$0.633491\pi$
$998$	1.45345e7	0.461928
$999$	−1.34571e6	−0.0426616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.14	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.14	✓	35	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)

\(f(q)\)	\(=\)	\(q-3.41781 q^{2} -5.73624 q^{3} -20.3185 q^{4} -25.0000 q^{5} +19.6054 q^{6} +236.087 q^{7} +178.815 q^{8} -210.096 q^{9} +O(q^{10})\)	\(q-3.41781 q^{2} -5.73624 q^{3} -20.3185 q^{4} -25.0000 q^{5} +19.6054 q^{6} +236.087 q^{7} +178.815 q^{8} -210.096 q^{9} +85.4453 q^{10} +121.000 q^{11} +116.552 q^{12} +1098.51 q^{13} -806.901 q^{14} +143.406 q^{15} +39.0369 q^{16} -1684.45 q^{17} +718.067 q^{18} +361.000 q^{19} +507.964 q^{20} -1354.25 q^{21} -413.555 q^{22} +572.885 q^{23} -1025.73 q^{24} +625.000 q^{25} -3754.50 q^{26} +2599.07 q^{27} -4796.94 q^{28} -7152.63 q^{29} -490.135 q^{30} -5931.81 q^{31} -5855.50 q^{32} -694.085 q^{33} +5757.12 q^{34} -5902.17 q^{35} +4268.84 q^{36} -517.766 q^{37} -1233.83 q^{38} -6301.31 q^{39} -4470.38 q^{40} +13316.4 q^{41} +4628.58 q^{42} +236.872 q^{43} -2458.54 q^{44} +5252.39 q^{45} -1958.02 q^{46} -6226.10 q^{47} -223.925 q^{48} +38930.0 q^{49} -2136.13 q^{50} +9662.39 q^{51} -22320.1 q^{52} -10320.6 q^{53} -8883.12 q^{54} -3025.00 q^{55} +42215.9 q^{56} -2070.78 q^{57} +24446.4 q^{58} -26292.5 q^{59} -2913.80 q^{60} -47638.3 q^{61} +20273.8 q^{62} -49600.8 q^{63} +18763.8 q^{64} -27462.7 q^{65} +2372.25 q^{66} +2169.96 q^{67} +34225.5 q^{68} -3286.21 q^{69} +20172.5 q^{70} +39721.2 q^{71} -37568.2 q^{72} +43366.3 q^{73} +1769.63 q^{74} -3585.15 q^{75} -7335.00 q^{76} +28566.5 q^{77} +21536.7 q^{78} -1411.98 q^{79} -975.923 q^{80} +36144.4 q^{81} -45513.0 q^{82} -40306.6 q^{83} +27516.4 q^{84} +42111.2 q^{85} -809.585 q^{86} +41029.2 q^{87} +21636.6 q^{88} +50147.5 q^{89} -17951.7 q^{90} +259344. q^{91} -11640.2 q^{92} +34026.3 q^{93} +21279.7 q^{94} -9025.00 q^{95} +33588.6 q^{96} -105029. q^{97} -133056. q^{98} -25421.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

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