LMFDB - Embedded newform 1003.6.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,6,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1003.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1003.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:	$160.864971272$
Analytic rank:	$0$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.36177 q^{2} +7.91970 q^{3} +55.6428 q^{4} +15.2707 q^{5} -74.1424 q^{6} -60.9674 q^{7} -221.338 q^{8} -180.278 q^{9} +O(q^{10})$	\(q-9.36177 q^{2} +7.91970 q^{3} +55.6428 q^{4} +15.2707 q^{5} -74.1424 q^{6} -60.9674 q^{7} -221.338 q^{8} -180.278 q^{9} -142.961 q^{10} -631.954 q^{11} +440.674 q^{12} +312.583 q^{13} +570.763 q^{14} +120.940 q^{15} +291.549 q^{16} -289.000 q^{17} +1687.72 q^{18} +2162.94 q^{19} +849.705 q^{20} -482.844 q^{21} +5916.21 q^{22} +498.885 q^{23} -1752.93 q^{24} -2891.80 q^{25} -2926.33 q^{26} -3352.24 q^{27} -3392.40 q^{28} +2105.77 q^{29} -1132.21 q^{30} -6807.23 q^{31} +4353.40 q^{32} -5004.89 q^{33} +2705.55 q^{34} -931.017 q^{35} -10031.2 q^{36} -3918.64 q^{37} -20249.0 q^{38} +2475.56 q^{39} -3380.00 q^{40} -8331.66 q^{41} +4520.27 q^{42} +8601.91 q^{43} -35163.7 q^{44} -2752.98 q^{45} -4670.45 q^{46} -15419.4 q^{47} +2308.99 q^{48} -13090.0 q^{49} +27072.4 q^{50} -2288.79 q^{51} +17393.0 q^{52} +11330.3 q^{53} +31382.9 q^{54} -9650.39 q^{55} +13494.4 q^{56} +17129.8 q^{57} -19713.7 q^{58} +3481.00 q^{59} +6729.41 q^{60} -31978.9 q^{61} +63727.7 q^{62} +10991.1 q^{63} -50085.2 q^{64} +4773.37 q^{65} +46854.6 q^{66} +11598.6 q^{67} -16080.8 q^{68} +3951.02 q^{69} +8715.97 q^{70} +17274.4 q^{71} +39902.5 q^{72} -85384.2 q^{73} +36685.4 q^{74} -22902.2 q^{75} +120352. q^{76} +38528.6 q^{77} -23175.7 q^{78} +71268.6 q^{79} +4452.17 q^{80} +17258.9 q^{81} +77999.1 q^{82} +95058.5 q^{83} -26866.8 q^{84} -4413.24 q^{85} -80529.2 q^{86} +16677.1 q^{87} +139876. q^{88} -27731.4 q^{89} +25772.8 q^{90} -19057.4 q^{91} +27759.3 q^{92} -53911.2 q^{93} +144352. q^{94} +33029.7 q^{95} +34477.7 q^{96} -133723. q^{97} +122545. q^{98} +113928. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9}+O(q^{10}) $ 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9	\( 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9} + 424 q^{11} + 2880 q^{12} + 2426 q^{13} + 1069 q^{14} + 3699 q^{15} + 25895 q^{16} - 28900 q^{17} + 6644 q^{18} + 2224 q^{19} + 11919 q^{20} + 12248 q^{21} + 1160 q^{22} + 4675 q^{23} + 6477 q^{24} + 76925 q^{25} + 26507 q^{26} + 18465 q^{27} + 7371 q^{28} + 13905 q^{29} + 42029 q^{30} + 11503 q^{31} + 31765 q^{32} + 34053 q^{33} - 7225 q^{34} + 26861 q^{35} + 210764 q^{36} - 4418 q^{37} + 55637 q^{38} - 5718 q^{39} + 24116 q^{40} + 50715 q^{41} + 145355 q^{42} + 36979 q^{43} - 6793 q^{44} + 88939 q^{45} + 23917 q^{46} + 162533 q^{47} + 219761 q^{48} + 276061 q^{49} + 204874 q^{50} - 18207 q^{51} + 73665 q^{52} + 144329 q^{53} + 112241 q^{54} + 63002 q^{55} + 234871 q^{56} + 94768 q^{57} + 22318 q^{58} + 348100 q^{59} + 390780 q^{60} - 45447 q^{61} + 146617 q^{62} + 88467 q^{63} + 580433 q^{64} - 49981 q^{65} - 14744 q^{66} + 113930 q^{67} - 493323 q^{68} + 49070 q^{69} + 86899 q^{70} + 138703 q^{71} + 319055 q^{72} + 174214 q^{73} - 139931 q^{74} + 295788 q^{75} + 272539 q^{76} + 642017 q^{77} + 93149 q^{78} - 240788 q^{79} + 582895 q^{80} + 690560 q^{81} + 164633 q^{82} + 324136 q^{83} + 775436 q^{84} - 147101 q^{85} + 113296 q^{86} + 612596 q^{87} - 227510 q^{88} + 348396 q^{89} + 750464 q^{90} - 100399 q^{91} + 453265 q^{92} + 660393 q^{93} + 183864 q^{94} + 341370 q^{95} + 209486 q^{96} + 288603 q^{97} + 1100905 q^{98} + 301794 q^{99}+O(q^{100}) \) 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9 + 424 * q^11 + 2880 * q^12 + 2426 * q^13 + 1069 * q^14 + 3699 * q^15 + 25895 * q^16 - 28900 * q^17 + 6644 * q^18 + 2224 * q^19 + 11919 * q^20 + 12248 * q^21 + 1160 * q^22 + 4675 * q^23 + 6477 * q^24 + 76925 * q^25 + 26507 * q^26 + 18465 * q^27 + 7371 * q^28 + 13905 * q^29 + 42029 * q^30 + 11503 * q^31 + 31765 * q^32 + 34053 * q^33 - 7225 * q^34 + 26861 * q^35 + 210764 * q^36 - 4418 * q^37 + 55637 * q^38 - 5718 * q^39 + 24116 * q^40 + 50715 * q^41 + 145355 * q^42 + 36979 * q^43 - 6793 * q^44 + 88939 * q^45 + 23917 * q^46 + 162533 * q^47 + 219761 * q^48 + 276061 * q^49 + 204874 * q^50 - 18207 * q^51 + 73665 * q^52 + 144329 * q^53 + 112241 * q^54 + 63002 * q^55 + 234871 * q^56 + 94768 * q^57 + 22318 * q^58 + 348100 * q^59 + 390780 * q^60 - 45447 * q^61 + 146617 * q^62 + 88467 * q^63 + 580433 * q^64 - 49981 * q^65 - 14744 * q^66 + 113930 * q^67 - 493323 * q^68 + 49070 * q^69 + 86899 * q^70 + 138703 * q^71 + 319055 * q^72 + 174214 * q^73 - 139931 * q^74 + 295788 * q^75 + 272539 * q^76 + 642017 * q^77 + 93149 * q^78 - 240788 * q^79 + 582895 * q^80 + 690560 * q^81 + 164633 * q^82 + 324136 * q^83 + 775436 * q^84 - 147101 * q^85 + 113296 * q^86 + 612596 * q^87 - 227510 * q^88 + 348396 * q^89 + 750464 * q^90 - 100399 * q^91 + 453265 * q^92 + 660393 * q^93 + 183864 * q^94 + 341370 * q^95 + 209486 * q^96 + 288603 * q^97 + 1100905 * q^98 + 301794 * 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 $

$2$	−9.36177	−1.65494	−0.827472	−	0.561508i	$-0.810222\pi$
$2$	−9.36177	−1.65494	−0.827472	+	0.561508i	$0.810222\pi$
$3$	7.91970	0.508049	0.254025	−	0.967198i	$-0.418246\pi$
$3$	7.91970	0.508049	0.254025	+	0.967198i	$0.418246\pi$
$4$	55.6428	1.73884
$5$	15.2707	0.273171	0.136586	−	0.990628i	$-0.456387\pi$
$5$	15.2707	0.273171	0.136586	+	0.990628i	$0.456387\pi$
$6$	−74.1424	−0.840792
$7$	−60.9674	−0.470276	−0.235138	−	0.971962i	$-0.575554\pi$
$7$	−60.9674	−0.470276	−0.235138	+	0.971962i	$0.575554\pi$
$8$	−221.338	−1.22273
$9$	−180.278	−0.741886
$10$	−142.961	−0.452082
$11$	−631.954	−1.57472	−0.787361	−	0.616493i	$-0.788553\pi$
$11$	−631.954	−1.57472	−0.787361	+	0.616493i	$0.788553\pi$
$12$	440.674	0.883414
$13$	312.583	0.512987	0.256494	−	0.966546i	$-0.417433\pi$
$13$	312.583	0.512987	0.256494	+	0.966546i	$0.417433\pi$
$14$	570.763	0.778280
$15$	120.940	0.138784
$16$	291.549	0.284716
$17$	−289.000	−0.242536
$17$	−289.000	−0.242536
$18$	1687.72	1.22778
$19$	2162.94	1.37455	0.687275	−	0.726397i	$-0.258807\pi$
$19$	2162.94	1.37455	0.687275	+	0.726397i	$0.258807\pi$
$20$	849.705	0.475000
$21$	−482.844	−0.238923
$22$	5916.21	2.60607
$23$	498.885	0.196644	0.0983220	−	0.995155i	$-0.468652\pi$
$23$	498.885	0.196644	0.0983220	+	0.995155i	$0.468652\pi$
$24$	−1752.93	−0.621208
$25$	−2891.80	−0.925378
$26$	−2926.33	−0.848965
$27$	−3352.24	−0.884964
$28$	−3392.40	−0.817733
$29$	2105.77	0.464960	0.232480	−	0.972601i	$-0.425316\pi$
$29$	2105.77	0.464960	0.232480	+	0.972601i	$0.425316\pi$
$30$	−1132.21	−0.229680
$31$	−6807.23	−1.27223	−0.636116	−	0.771594i	$-0.719460\pi$
$31$	−6807.23	−1.27223	−0.636116	+	0.771594i	$0.719460\pi$
$32$	4353.40	0.751543
$33$	−5004.89	−0.800036
$34$	2705.55	0.401383
$35$	−931.017	−0.128466
$36$	−10031.2	−1.29002
$37$	−3918.64	−0.470578	−0.235289	−	0.971925i	$-0.575604\pi$
$37$	−3918.64	−0.470578	−0.235289	+	0.971925i	$0.575604\pi$
$38$	−20249.0	−2.27480
$39$	2475.56	0.260623
$40$	−3380.00	−0.334015
$41$	−8331.66	−0.774055	−0.387027	−	0.922068i	$-0.626498\pi$
$41$	−8331.66	−0.774055	−0.387027	+	0.922068i	$0.626498\pi$
$42$	4520.27	0.395404
$43$	8601.91	0.709454	0.354727	−	0.934970i	$-0.384574\pi$
$43$	8601.91	0.709454	0.354727	+	0.934970i	$0.384574\pi$
$44$	−35163.7	−2.73818
$45$	−2752.98	−0.202662
$46$	−4670.45	−0.325435
$47$	−15419.4	−1.01817	−0.509086	−	0.860715i	$-0.670017\pi$
$47$	−15419.4	−1.01817	−0.509086	+	0.860715i	$0.670017\pi$
$48$	2308.99	0.144650
$49$	−13090.0	−0.778841
$50$	27072.4	1.53145
$51$	−2288.79	−0.123220
$52$	17393.0	0.892001
$53$	11330.3	0.554053	0.277027	−	0.960862i	$-0.410651\pi$
$53$	11330.3	0.554053	0.277027	+	0.960862i	$0.410651\pi$
$54$	31382.9	1.46456
$55$	−9650.39	−0.430168
$56$	13494.4	0.575022
$57$	17129.8	0.698339
$58$	−19713.7	−0.769482
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	6729.41	0.241323
$61$	−31978.9	−1.10037	−0.550185	−	0.835043i	$-0.685443\pi$
$61$	−31978.9	−1.10037	−0.550185	+	0.835043i	$0.685443\pi$
$62$	63727.7	2.10547
$63$	10991.1	0.348891
$64$	−50085.2	−1.52848
$65$	4773.37	0.140133
$66$	46854.6	1.32401
$67$	11598.6	0.315660	0.157830	−	0.987466i	$-0.449550\pi$
$67$	11598.6	0.315660	0.157830	+	0.987466i	$0.449550\pi$
$68$	−16080.8	−0.421730
$69$	3951.02	0.0999048
$70$	8715.97	0.212603
$71$	17274.4	0.406684	0.203342	−	0.979108i	$-0.434820\pi$
$71$	17274.4	0.406684	0.203342	+	0.979108i	$0.434820\pi$
$72$	39902.5	0.907128
$73$	−85384.2	−1.87530	−0.937650	−	0.347582i	$-0.887003\pi$
$73$	−85384.2	−1.87530	−0.937650	+	0.347582i	$0.887003\pi$
$74$	36685.4	0.778779
$75$	−22902.2	−0.470137
$76$	120352.	2.39012
$77$	38528.6	0.740553
$78$	−23175.7	−0.431316
$79$	71268.6	1.28479	0.642393	−	0.766376i	$-0.277942\pi$
$79$	71268.6	1.28479	0.642393	+	0.766376i	$0.277942\pi$
$80$	4452.17	0.0777762
$81$	17258.9	0.292281
$82$	77999.1	1.28102
$83$	95058.5	1.51459	0.757296	−	0.653071i	$-0.226520\pi$
$83$	95058.5	1.51459	0.757296	+	0.653071i	$0.226520\pi$
$84$	−26866.8	−0.415449
$85$	−4413.24	−0.0662537
$86$	−80529.2	−1.17411
$87$	16677.1	0.236223
$88$	139876.	1.92546
$89$	−27731.4	−0.371104	−0.185552	−	0.982634i	$-0.559407\pi$
$89$	−27731.4	−0.371104	−0.185552	+	0.982634i	$0.559407\pi$
$90$	25772.8	0.335394
$91$	−19057.4	−0.241246
$92$	27759.3	0.341932
$93$	−53911.2	−0.646356
$94$	144352.	1.68502
$95$	33029.7	0.375487
$96$	34477.7	0.381821
$97$	−133723.	−1.44303	−0.721517	−	0.692397i	$-0.756555\pi$
$97$	−133723.	−1.44303	−0.721517	+	0.692397i	$0.756555\pi$
$98$	122545.	1.28894
$99$	113928.	1.16826
$100$	−160908.	−1.60908
$101$	72848.1	0.710583	0.355292	−	0.934756i	$-0.384382\pi$
$101$	72848.1	0.710583	0.355292	+	0.934756i	$0.384382\pi$
$102$	21427.2	0.203922
$103$	−104836.	−0.973687	−0.486843	−	0.873489i	$-0.661852\pi$
$103$	−104836.	−0.973687	−0.486843	+	0.873489i	$0.661852\pi$
$104$	−69186.5	−0.627246
$105$	−7373.37	−0.0652669
$106$	−106072.	−0.916926
$107$	−151607.	−1.28015	−0.640073	−	0.768314i	$-0.721096\pi$
$107$	−151607.	−1.28015	−0.640073	+	0.768314i	$0.721096\pi$
$108$	−186528.	−1.53881
$109$	169568.	1.36703	0.683516	−	0.729936i	$-0.260450\pi$
$109$	169568.	1.36703	0.683516	+	0.729936i	$0.260450\pi$
$110$	90344.8	0.711904
$111$	−31034.5	−0.239077
$112$	−17775.0	−0.133895
$113$	−82373.3	−0.606863	−0.303431	−	0.952853i	$-0.598132\pi$
$113$	−82373.3	−0.606863	−0.303431	+	0.952853i	$0.598132\pi$
$114$	−160366.	−1.15571
$115$	7618.33	0.0537174
$116$	117171.	0.808489
$117$	−56351.9	−0.380578
$118$	−32588.3	−0.215455
$119$	17619.6	0.114059
$120$	−26768.6	−0.169696
$121$	238315.	1.47975
$122$	299379.	1.82105
$123$	−65984.2	−0.393258
$124$	−378773.	−2.21220
$125$	−91881.0	−0.525957
$126$	−102896.	−0.577395
$127$	−79411.2	−0.436890	−0.218445	−	0.975849i	$-0.570098\pi$
$127$	−79411.2	−0.436890	−0.218445	+	0.975849i	$0.570098\pi$
$128$	329577.	1.77800
$129$	68124.6	0.360437
$130$	−44687.2	−0.231913
$131$	259849.	1.32295	0.661473	−	0.749969i	$-0.269932\pi$
$131$	259849.	1.32295	0.661473	+	0.749969i	$0.269932\pi$
$132$	−278486.	−1.39113
$133$	−131869.	−0.646418
$134$	−108584.	−0.522399
$135$	−51191.1	−0.241746
$136$	63966.8	0.296556
$137$	294196.	1.33917	0.669585	−	0.742736i	$-0.266472\pi$
$137$	294196.	1.33917	0.669585	+	0.742736i	$0.266472\pi$
$138$	−36988.5	−0.165337
$139$	19226.3	0.0844034	0.0422017	−	0.999109i	$-0.486563\pi$
$139$	19226.3	0.0844034	0.0422017	+	0.999109i	$0.486563\pi$
$140$	−51804.3	−0.223381
$141$	−122117.	−0.517282
$142$	−161719.	−0.673038
$143$	−197538.	−0.807812
$144$	−52560.0	−0.211227
$145$	32156.6	0.127014
$146$	799348.	3.10351
$147$	−103669.	−0.395689
$148$	−218044.	−0.818258
$149$	−42938.7	−0.158447	−0.0792234	−	0.996857i	$-0.525244\pi$
$149$	−42938.7	−0.158447	−0.0792234	+	0.996857i	$0.525244\pi$
$150$	214405.	0.778050
$151$	348998.	1.24560	0.622802	−	0.782379i	$-0.285994\pi$
$151$	348998.	1.24560	0.622802	+	0.782379i	$0.285994\pi$
$152$	−478741.	−1.68071
$153$	52100.4	0.179934
$154$	−360696.	−1.22557
$155$	−103951.	−0.347537
$156$	137747.	0.453181
$157$	36455.2	0.118035	0.0590174	−	0.998257i	$-0.481203\pi$
$157$	36455.2	0.118035	0.0590174	+	0.998257i	$0.481203\pi$
$158$	−667200.	−2.12625
$159$	89732.5	0.281486
$160$	66479.6	0.205300
$161$	−30415.7	−0.0924769
$162$	−161574.	−0.483708
$163$	−450876.	−1.32919	−0.664596	−	0.747203i	$-0.731396\pi$
$163$	−450876.	−1.32919	−0.664596	+	0.747203i	$0.731396\pi$
$164$	−463597.	−1.34595
$165$	−76428.2	−0.218547
$166$	−889916.	−2.50656
$167$	−96489.1	−0.267724	−0.133862	−	0.991000i	$-0.542738\pi$
$167$	−96489.1	−0.267724	−0.133862	+	0.991000i	$0.542738\pi$
$168$	106872.	0.292139
$169$	−273585.	−0.736844
$170$	41315.7	0.109646
$171$	−389931.	−1.01976
$172$	478634.	1.23362
$173$	−536984.	−1.36410	−0.682050	−	0.731306i	$-0.738911\pi$
$173$	−536984.	−1.36410	−0.682050	+	0.731306i	$0.738911\pi$
$174$	−156127.	−0.390935
$175$	176306.	0.435183
$176$	−184246.	−0.448349
$177$	27568.5	0.0661424
$178$	259615.	0.614157
$179$	−213270.	−0.497504	−0.248752	−	0.968567i	$-0.580020\pi$
$179$	−213270.	−0.497504	−0.248752	+	0.968567i	$0.580020\pi$
$180$	−153183.	−0.352396
$181$	275694.	0.625504	0.312752	−	0.949835i	$-0.398749\pi$
$181$	275694.	0.625504	0.312752	+	0.949835i	$0.398749\pi$
$182$	178411.	0.399248
$183$	−253263.	−0.559042
$184$	−110422.	−0.240443
$185$	−59840.5	−0.128548
$186$	504704.	1.06968
$187$	182635.	0.381926
$188$	−857975.	−1.77044
$189$	204377.	0.416177
$190$	−309216.	−0.621410
$191$	−384912.	−0.763446	−0.381723	−	0.924277i	$-0.624669\pi$
$191$	−384912.	−0.763446	−0.381723	+	0.924277i	$0.624669\pi$
$192$	−396660.	−0.776542
$193$	57269.9	0.110671	0.0553354	−	0.998468i	$-0.482377\pi$
$193$	57269.9	0.110671	0.0553354	+	0.998468i	$0.482377\pi$
$194$	1.25188e6	2.38814
$195$	37803.6	0.0711946
$196$	−728362.	−1.35428
$197$	−126442.	−0.232126	−0.116063	−	0.993242i	$-0.537028\pi$
$197$	−126442.	−0.232126	−0.116063	+	0.993242i	$0.537028\pi$
$198$	−1.06656e6	−1.93341
$199$	−255836.	−0.457962	−0.228981	−	0.973431i	$-0.573539\pi$
$199$	−255836.	−0.457962	−0.228981	+	0.973431i	$0.573539\pi$
$200$	640067.	1.13149
$201$	91857.7	0.160371
$202$	−681987.	−1.17597
$203$	−128383.	−0.218659
$204$	−127355.	−0.214259
$205$	−127230.	−0.211449
$206$	981455.	1.61140
$207$	−89938.1	−0.145887
$208$	91133.4	0.146056
$209$	−1.36688e6	−2.16453
$210$	69027.9	0.108013
$211$	364991.	0.564386	0.282193	−	0.959358i	$-0.408938\pi$
$211$	364991.	0.564386	0.282193	+	0.959358i	$0.408938\pi$
$212$	630449.	0.963408
$213$	136808.	0.206615
$214$	1.41931e6	2.11857
$215$	131357.	0.193802
$216$	741979.	1.08207
$217$	415019.	0.598300
$218$	−1.58746e6	−2.26236
$219$	−676218.	−0.952744
$220$	−536975.	−0.747992
$221$	−90336.4	−0.124418
$222$	290538.	0.395658
$223$	632900.	0.852262	0.426131	−	0.904661i	$-0.359876\pi$
$223$	632900.	0.852262	0.426131	+	0.904661i	$0.359876\pi$
$224$	−265416.	−0.353433
$225$	521330.	0.686525
$226$	771160.	1.00432
$227$	993665.	1.27990	0.639949	−	0.768418i	$-0.278956\pi$
$227$	993665.	1.27990	0.639949	+	0.768418i	$0.278956\pi$
$228$	953152.	1.21430
$229$	−656885.	−0.827752	−0.413876	−	0.910333i	$-0.635825\pi$
$229$	−656885.	−0.827752	−0.413876	+	0.910333i	$0.635825\pi$
$230$	−71321.1	−0.0888993
$231$	305135.	0.376238
$232$	−466087.	−0.568522
$233$	693295.	0.836619	0.418310	−	0.908304i	$-0.362623\pi$
$233$	693295.	0.836619	0.418310	+	0.908304i	$0.362623\pi$
$234$	527554.	0.629835
$235$	−235465.	−0.278135
$236$	193692.	0.226377
$237$	564426.	0.652734
$238$	−164951.	−0.188761
$239$	189464.	0.214552	0.107276	−	0.994229i	$-0.465787\pi$
$239$	189464.	0.214552	0.107276	+	0.994229i	$0.465787\pi$
$240$	35259.9	0.0395142
$241$	−135603.	−0.150392	−0.0751962	−	0.997169i	$-0.523958\pi$
$241$	−135603.	−0.150392	−0.0751962	+	0.997169i	$0.523958\pi$
$242$	−2.23105e6	−2.44890
$243$	951279.	1.03346
$244$	−1.77939e6	−1.91336
$245$	−199893.	−0.212757
$246$	617729.	0.650819
$247$	676098.	0.705127
$248$	1.50670e6	1.55560
$249$	752835.	0.769487
$250$	860169.	0.870429
$251$	−322667.	−0.323273	−0.161637	−	0.986850i	$-0.551677\pi$
$251$	−322667.	−0.323273	−0.161637	+	0.986850i	$0.551677\pi$
$252$	611576.	0.606665
$253$	−315272.	−0.309659
$254$	743430.	0.723029
$255$	−34951.5	−0.0336601
$256$	−1.48270e6	−1.41401
$257$	615164.	0.580976	0.290488	−	0.956879i	$-0.406182\pi$
$257$	615164.	0.580976	0.290488	+	0.956879i	$0.406182\pi$
$258$	−637767.	−0.596503
$259$	238910.	0.221301
$260$	265603.	0.243669
$261$	−379624.	−0.344947
$262$	−2.43264e6	−2.18940
$263$	1.15640e6	1.03091	0.515455	−	0.856917i	$-0.327623\pi$
$263$	1.15640e6	1.03091	0.515455	+	0.856917i	$0.327623\pi$
$264$	1.10777e6	0.978230
$265$	173022.	0.151351
$266$	1.23453e6	1.06978
$267$	−219624.	−0.188539
$268$	645380.	0.548881
$269$	−88099.8	−0.0742325	−0.0371163	−	0.999311i	$-0.511817\pi$
$269$	−88099.8	−0.0742325	−0.0371163	+	0.999311i	$0.511817\pi$
$270$	479239.	0.400077
$271$	−985958.	−0.815521	−0.407761	−	0.913089i	$-0.633690\pi$
$271$	−985958.	−0.815521	−0.407761	+	0.913089i	$0.633690\pi$
$272$	−84257.8	−0.0690538
$273$	−150929.	−0.122565
$274$	−2.75420e6	−2.21625
$275$	1.82749e6	1.45721
$276$	219846.	0.173718
$277$	−1.74369e6	−1.36543	−0.682715	−	0.730685i	$-0.739201\pi$
$277$	−1.74369e6	−1.36543	−0.682715	+	0.730685i	$0.739201\pi$
$278$	−179993.	−0.139683
$279$	1.22720e6	0.943850
$280$	206070.	0.157079
$281$	870063.	0.657332	0.328666	−	0.944446i	$-0.393401\pi$
$281$	870063.	0.657332	0.328666	+	0.944446i	$0.393401\pi$
$282$	1.14323e6	0.856072
$283$	−1.19260e6	−0.885175	−0.442587	−	0.896725i	$-0.645939\pi$
$283$	−1.19260e6	−0.885175	−0.442587	+	0.896725i	$0.645939\pi$
$284$	961195.	0.707156
$285$	261585.	0.190766
$286$	1.84930e6	1.33688
$287$	507960.	0.364019
$288$	−784824.	−0.557560
$289$	83521.0	0.0588235
$290$	−301043.	−0.210200
$291$	−1.05905e6	−0.733132
$292$	−4.75102e6	−3.26084
$293$	2.08418e6	1.41829	0.709147	−	0.705060i	$-0.249080\pi$
$293$	2.08418e6	1.41829	0.709147	+	0.705060i	$0.249080\pi$
$294$	970523.	0.654843
$295$	53157.4	0.0355638
$296$	867346.	0.575391
$297$	2.11846e6	1.39357
$298$	401982.	0.262220
$299$	155943.	0.100876
$300$	−1.27434e6	−0.817492
$301$	−524437.	−0.333639
$302$	−3.26724e6	−2.06140
$303$	576935.	0.361011
$304$	630604.	0.391357
$305$	−488340.	−0.300589
$306$	−487752.	−0.297780
$307$	2.04150e6	1.23624	0.618121	−	0.786083i	$-0.287894\pi$
$307$	2.04150e6	1.23624	0.618121	+	0.786083i	$0.287894\pi$
$308$	2.14384e6	1.28770
$309$	−830274.	−0.494681
$310$	973168.	0.575153
$311$	2.13244e6	1.25019	0.625094	−	0.780550i	$-0.285061\pi$
$311$	2.13244e6	1.25019	0.625094	+	0.780550i	$0.285061\pi$
$312$	−547937.	−0.318672
$313$	1.27140e6	0.733535	0.366767	−	0.930313i	$-0.380465\pi$
$313$	1.27140e6	0.733535	0.366767	+	0.930313i	$0.380465\pi$
$314$	−341285.	−0.195341
$315$	167842.	0.0953069
$316$	3.96558e6	2.23403
$317$	−20278.8	−0.0113343	−0.00566714	−	0.999984i	$-0.501804\pi$
$317$	−20278.8	−0.0113343	−0.00566714	+	0.999984i	$0.501804\pi$
$318$	−840055.	−0.465844
$319$	−1.33075e6	−0.732182
$320$	−764837.	−0.417536
$321$	−1.20068e6	−0.650377
$322$	284745.	0.153044
$323$	−625090.	−0.333377
$324$	960333.	0.508229
$325$	−903929.	−0.474707
$326$	4.22099e6	2.19974
$327$	1.34293e6	0.694519
$328$	1.84411e6	0.946462
$329$	940078.	0.478822
$330$	715504.	0.361682
$331$	1.60391e6	0.804655	0.402327	−	0.915496i	$-0.368201\pi$
$331$	1.60391e6	0.804655	0.402327	+	0.915496i	$0.368201\pi$
$332$	5.28932e6	2.63363
$333$	706446.	0.349115
$334$	903309.	0.443068
$335$	177119.	0.0862291
$336$	−140773.	−0.0680253
$337$	2.09521e6	1.00497	0.502485	−	0.864586i	$-0.332419\pi$
$337$	2.09521e6	1.00497	0.502485	+	0.864586i	$0.332419\pi$
$338$	2.56124e6	1.21943
$339$	−652372.	−0.308316
$340$	−245565.	−0.115204
$341$	4.30185e6	2.00341
$342$	3.65045e6	1.68764
$343$	1.82274e6	0.836546
$344$	−1.90393e6	−0.867472
$345$	60334.9	0.0272911
$346$	5.02712e6	2.25751
$347$	2.34225e6	1.04426	0.522132	−	0.852865i	$-0.325137\pi$
$347$	2.34225e6	1.04426	0.522132	+	0.852865i	$0.325137\pi$
$348$	927958.	0.410752
$349$	1.39172e6	0.611630	0.305815	−	0.952091i	$-0.401071\pi$
$349$	1.39172e6	0.611630	0.305815	+	0.952091i	$0.401071\pi$
$350$	−1.65054e6	−0.720203
$351$	−1.04785e6	−0.453975
$352$	−2.75115e6	−1.18347
$353$	−292895.	−0.125105	−0.0625525	−	0.998042i	$-0.519924\pi$
$353$	−292895.	−0.125105	−0.0625525	+	0.998042i	$0.519924\pi$
$354$	−258090.	−0.109462
$355$	263792.	0.111094
$356$	−1.54305e6	−0.645290
$357$	139542.	0.0579474
$358$	1.99658e6	0.823340
$359$	−674297.	−0.276131	−0.138065	−	0.990423i	$-0.544088\pi$
$359$	−674297.	−0.276131	−0.138065	+	0.990423i	$0.544088\pi$
$360$	609340.	0.247801
$361$	2.20221e6	0.889387
$362$	−2.58098e6	−1.03517
$363$	1.88738e6	0.751784
$364$	−1.06040e6	−0.419487
$365$	−1.30388e6	−0.512277
$366$	2.37099e6	0.925182
$367$	3.68150e6	1.42679	0.713393	−	0.700764i	$-0.247157\pi$
$367$	3.68150e6	1.42679	0.713393	+	0.700764i	$0.247157\pi$
$368$	145450.	0.0559877
$369$	1.50202e6	0.574261
$370$	560213.	0.212740
$371$	−690779.	−0.260558
$372$	−2.99977e6	−1.12391
$373$	3.06934e6	1.14228	0.571140	−	0.820853i	$-0.306502\pi$
$373$	3.06934e6	1.14228	0.571140	+	0.820853i	$0.306502\pi$
$374$	−1.70978e6	−0.632066
$375$	−727670.	−0.267212
$376$	3.41289e6	1.24495
$377$	658227.	0.238519
$378$	−1.91333e6	−0.688749
$379$	−5.28803e6	−1.89102	−0.945509	−	0.325595i	$-0.894435\pi$
$379$	−5.28803e6	−1.89102	−0.945509	+	0.325595i	$0.894435\pi$
$380$	1.83786e6	0.652911
$381$	−628913.	−0.221962
$382$	3.60346e6	1.26346
$383$	−3.46155e6	−1.20580	−0.602898	−	0.797818i	$-0.705987\pi$
$383$	−3.46155e6	−1.20580	−0.602898	+	0.797818i	$0.705987\pi$
$384$	2.61015e6	0.903312
$385$	588360.	0.202298
$386$	−536148.	−0.183154
$387$	−1.55074e6	−0.526334
$388$	−7.44071e6	−2.50920
$389$	457058.	0.153143	0.0765715	−	0.997064i	$-0.475603\pi$
$389$	457058.	0.153143	0.0765715	+	0.997064i	$0.475603\pi$
$390$	−353909.	−0.117823
$391$	−144178.	−0.0476932
$392$	2.89731e6	0.952314
$393$	2.05792e6	0.672121
$394$	1.18372e6	0.384156
$395$	1.08832e6	0.350966
$396$	6.33925e6	2.03142
$397$	−3.04048e6	−0.968201	−0.484100	−	0.875012i	$-0.660853\pi$
$397$	−3.04048e6	−0.968201	−0.484100	+	0.875012i	$0.660853\pi$
$398$	2.39508e6	0.757901
$399$	−1.04436e6	−0.328412
$400$	−843104.	−0.263470
$401$	−1.64793e6	−0.511772	−0.255886	−	0.966707i	$-0.582367\pi$
$401$	−1.64793e6	−0.511772	−0.255886	+	0.966707i	$0.582367\pi$
$402$	−859950.	−0.265404
$403$	−2.12782e6	−0.652639
$404$	4.05347e6	1.23559
$405$	263556.	0.0798427
$406$	1.20189e6	0.361869
$407$	2.47640e6	0.741029
$408$	506598.	0.150665
$409$	4.61691e6	1.36472	0.682359	−	0.731017i	$-0.260954\pi$
$409$	4.61691e6	1.36472	0.682359	+	0.731017i	$0.260954\pi$
$410$	1.19110e6	0.349937
$411$	2.32995e6	0.680364
$412$	−5.83339e6	−1.69308
$413$	−212228.	−0.0612247
$414$	841980.	0.241435
$415$	1.45161e6	0.413743
$416$	1.36080e6	0.385532
$417$	152267.	0.0428811
$418$	1.27964e7	3.58218
$419$	−3.40430e6	−0.947310	−0.473655	−	0.880710i	$-0.657066\pi$
$419$	−3.40430e6	−0.947310	−0.473655	+	0.880710i	$0.657066\pi$
$420$	−410275.	−0.113488
$421$	−882959.	−0.242792	−0.121396	−	0.992604i	$-0.538737\pi$
$421$	−882959.	−0.242792	−0.121396	+	0.992604i	$0.538737\pi$
$422$	−3.41697e6	−0.934027
$423$	2.77977e6	0.755368
$424$	−2.50783e6	−0.677459
$425$	835732.	0.224437
$426$	−1.28076e6	−0.341936
$427$	1.94967e6	0.517477
$428$	−8.43583e6	−2.22596
$429$	−1.56444e6	−0.410408
$430$	−1.22974e6	−0.320732
$431$	−1.43326e6	−0.371649	−0.185825	−	0.982583i	$-0.559496\pi$
$431$	−1.43326e6	−0.371649	−0.185825	+	0.982583i	$0.559496\pi$
$432$	−977343.	−0.251964
$433$	1.05106e6	0.269407	0.134703	−	0.990886i	$-0.456992\pi$
$433$	1.05106e6	0.269407	0.134703	+	0.990886i	$0.456992\pi$
$434$	−3.88531e6	−0.990152
$435$	254671.	0.0645291
$436$	9.43526e6	2.37705
$437$	1.07906e6	0.270297
$438$	6.33060e6	1.57674
$439$	1.01637e6	0.251704	0.125852	−	0.992049i	$-0.459834\pi$
$439$	1.01637e6	0.251704	0.125852	+	0.992049i	$0.459834\pi$
$440$	2.13600e6	0.525981
$441$	2.35984e6	0.577811
$442$	845709.	0.205904
$443$	−5.94334e6	−1.43887	−0.719435	−	0.694560i	$-0.755599\pi$
$443$	−5.94334e6	−1.43887	−0.719435	+	0.694560i	$0.755599\pi$
$444$	−1.72684e6	−0.415715
$445$	−423478.	−0.101375
$446$	−5.92507e6	−1.41045
$447$	−340062.	−0.0804987
$448$	3.05356e6	0.718806
$449$	3.79919e6	0.889355	0.444677	−	0.895691i	$-0.353318\pi$
$449$	3.79919e6	0.889355	0.444677	+	0.895691i	$0.353318\pi$
$450$	−4.88057e6	−1.13616
$451$	5.26522e6	1.21892
$452$	−4.58348e6	−1.05523
$453$	2.76396e6	0.632828
$454$	−9.30246e6	−2.11816
$455$	−291020.	−0.0659013
$456$	−3.79149e6	−0.853882
$457$	8.79823e6	1.97063	0.985315	−	0.170747i	$-0.0546182\pi$
$457$	8.79823e6	1.97063	0.985315	+	0.170747i	$0.0546182\pi$
$458$	6.14961e6	1.36988
$459$	968797.	0.214635
$460$	423905.	0.0934059
$461$	1.26157e6	0.276476	0.138238	−	0.990399i	$-0.455856\pi$
$461$	1.26157e6	0.276476	0.138238	+	0.990399i	$0.455856\pi$
$462$	−2.85660e6	−0.622652
$463$	−8.70110e6	−1.88635	−0.943174	−	0.332299i	$-0.892176\pi$
$463$	−8.70110e6	−1.88635	−0.943174	+	0.332299i	$0.892176\pi$
$464$	613936.	0.132382
$465$	−823263.	−0.176566
$466$	−6.49046e6	−1.38456
$467$	4.53493e6	0.962228	0.481114	−	0.876658i	$-0.340232\pi$
$467$	4.53493e6	0.962228	0.481114	+	0.876658i	$0.340232\pi$
$468$	−3.13558e6	−0.661763
$469$	−707138.	−0.148447
$470$	2.20437e6	0.460298
$471$	288714.	0.0599675
$472$	−770478.	−0.159186
$473$	−5.43601e6	−1.11719
$474$	−5.28403e6	−1.08024
$475$	−6.25480e6	−1.27198
$476$	980403.	0.198329
$477$	−2.04261e6	−0.411044
$478$	−1.77372e6	−0.355072
$479$	5.97540e6	1.18995	0.594975	−	0.803744i	$-0.297162\pi$
$479$	5.97540e6	1.18995	0.594975	+	0.803744i	$0.297162\pi$
$480$	526499.	0.104302
$481$	−1.22490e6	−0.241400
$482$	1.26948e6	0.248891
$483$	−240883.	−0.0469828
$484$	1.32605e7	2.57304
$485$	−2.04204e6	−0.394195
$486$	−8.90566e6	−1.71031
$487$	−1.44936e6	−0.276921	−0.138460	−	0.990368i	$-0.544215\pi$
$487$	−1.44936e6	−0.276921	−0.138460	+	0.990368i	$0.544215\pi$
$488$	7.07815e6	1.34546
$489$	−3.57080e6	−0.675295
$490$	1.87136e6	0.352100
$491$	4.15590e6	0.777967	0.388984	−	0.921245i	$-0.372826\pi$
$491$	4.15590e6	0.777967	0.388984	+	0.921245i	$0.372826\pi$
$492$	−3.67155e6	−0.683811
$493$	−608567.	−0.112769
$494$	−6.32947e6	−1.16694
$495$	1.73976e6	0.319136
$496$	−1.98464e6	−0.362225
$497$	−1.05317e6	−0.191253
$498$	−7.04787e6	−1.27346
$499$	8.10648e6	1.45741	0.728704	−	0.684829i	$-0.240123\pi$
$499$	8.10648e6	1.45741	0.728704	+	0.684829i	$0.240123\pi$
$500$	−5.11251e6	−0.914554
$501$	−764165.	−0.136017
$502$	3.02073e6	0.534999
$503$	−360234.	−0.0634841	−0.0317421	−	0.999496i	$-0.510106\pi$
$503$	−360234.	−0.0634841	−0.0317421	+	0.999496i	$0.510106\pi$
$504$	−2.43275e6	−0.426601
$505$	1.11244e6	0.194111
$506$	2.95151e6	0.512469
$507$	−2.16671e6	−0.374353
$508$	−4.41866e6	−0.759681
$509$	6.34891e6	1.08619	0.543094	−	0.839672i	$-0.317253\pi$
$509$	6.34891e6	1.08619	0.543094	+	0.839672i	$0.317253\pi$
$510$	327208.	0.0557056
$511$	5.20566e6	0.881908
$512$	3.33423e6	0.562109
$513$	−7.25069e6	−1.21643
$514$	−5.75903e6	−0.961482
$515$	−1.60093e6	−0.265983
$516$	3.79064e6	0.626742
$517$	9.74432e6	1.60334
$518$	−2.23662e6	−0.366241
$519$	−4.25275e6	−0.693030
$520$	−1.05653e6	−0.171346
$521$	2.33726e6	0.377236	0.188618	−	0.982051i	$-0.439599\pi$
$521$	2.33726e6	0.377236	0.188618	+	0.982051i	$0.439599\pi$
$522$	3.55396e6	0.570868
$523$	−4.05069e6	−0.647552	−0.323776	−	0.946134i	$-0.604953\pi$
$523$	−4.05069e6	−0.647552	−0.323776	+	0.946134i	$0.604953\pi$
$524$	1.44587e7	2.30039
$525$	1.39629e6	0.221094
$526$	−1.08260e7	−1.70610
$527$	1.96729e6	0.308561
$528$	−1.45917e6	−0.227783
$529$	−6.18746e6	−0.961331
$530$	−1.61979e6	−0.250478
$531$	−627549.	−0.0965853
$532$	−7.33755e6	−1.12401
$533$	−2.60433e6	−0.397080
$534$	2.05607e6	0.312022
$535$	−2.31515e6	−0.349699
$536$	−2.56722e6	−0.385968
$537$	−1.68903e6	−0.252756
$538$	824770.	0.122851
$539$	8.27226e6	1.22646
$540$	−2.84842e6	−0.420358
$541$	−7.58145e6	−1.11368	−0.556838	−	0.830621i	$-0.687986\pi$
$541$	−7.58145e6	−1.11368	−0.556838	+	0.830621i	$0.687986\pi$
$542$	9.23031e6	1.34964
$543$	2.18341e6	0.317787
$544$	−1.25813e6	−0.182276
$545$	2.58943e6	0.373434
$546$	1.41296e6	0.202837
$547$	−7.91924e6	−1.13166	−0.565829	−	0.824523i	$-0.691444\pi$
$547$	−7.91924e6	−1.13166	−0.565829	+	0.824523i	$0.691444\pi$
$548$	1.63699e7	2.32860
$549$	5.76510e6	0.816349
$550$	−1.71085e7	−2.41160
$551$	4.55465e6	0.639111
$552$	−874512.	−0.122157
$553$	−4.34506e6	−0.604203
$554$	1.63240e7	2.25971
$555$	−473919.	−0.0653088
$556$	1.06981e6	0.146764
$557$	−541843.	−0.0740007	−0.0370003	−	0.999315i	$-0.511780\pi$
$557$	−541843.	−0.0740007	−0.0370003	+	0.999315i	$0.511780\pi$
$558$	−1.14887e7	−1.56202
$559$	2.68881e6	0.363941
$560$	−271437.	−0.0365763
$561$	1.44641e6	0.194037
$562$	−8.14533e6	−1.08785
$563$	−4.09909e6	−0.545025	−0.272513	−	0.962152i	$-0.587855\pi$
$563$	−4.09909e6	−0.545025	−0.272513	+	0.962152i	$0.587855\pi$
$564$	−6.79491e6	−0.899468
$565$	−1.25790e6	−0.165777
$566$	1.11649e7	1.46491
$567$	−1.05223e6	−0.137453
$568$	−3.82348e6	−0.497265
$569$	−322481.	−0.0417564	−0.0208782	−	0.999782i	$-0.506646\pi$
$569$	−322481.	−0.0417564	−0.0208782	+	0.999782i	$0.506646\pi$
$570$	−2.44890e6	−0.315707
$571$	−5.67259e6	−0.728100	−0.364050	−	0.931379i	$-0.618606\pi$
$571$	−5.67259e6	−0.728100	−0.364050	+	0.931379i	$0.618606\pi$
$572$	−1.09916e7	−1.40465
$573$	−3.04839e6	−0.387868
$574$	−4.75540e6	−0.602431
$575$	−1.44268e6	−0.181970
$576$	9.02927e6	1.13396
$577$	7.35849e6	0.920129	0.460065	−	0.887885i	$-0.347826\pi$
$577$	7.35849e6	0.920129	0.460065	+	0.887885i	$0.347826\pi$
$578$	−781905.	−0.0973496
$579$	453561.	0.0562262
$580$	1.78928e6	0.220856
$581$	−5.79547e6	−0.712276
$582$	9.91454e6	1.21329
$583$	−7.16022e6	−0.872479
$584$	1.88988e7	2.29299
$585$	−860534.	−0.103963
$586$	−1.95116e7	−2.34720
$587$	9.38098e6	1.12371	0.561853	−	0.827237i	$-0.310089\pi$
$587$	9.38098e6	1.12371	0.561853	+	0.827237i	$0.310089\pi$
$588$	−5.76841e6	−0.688039
$589$	−1.47236e7	−1.74875
$590$	−497647.	−0.0588561
$591$	−1.00138e6	−0.117932
$592$	−1.14248e6	−0.133981
$593$	−1.14637e6	−0.133872	−0.0669359	−	0.997757i	$-0.521322\pi$
$593$	−1.14637e6	−0.133872	−0.0669359	+	0.997757i	$0.521322\pi$
$594$	−1.98325e7	−2.30628
$595$	269064.	0.0311575
$596$	−2.38923e6	−0.275513
$597$	−2.02615e6	−0.232667
$598$	−1.45990e6	−0.166944
$599$	−2.36624e6	−0.269459	−0.134729	−	0.990882i	$-0.543017\pi$
$599$	−2.36624e6	−0.269459	−0.134729	+	0.990882i	$0.543017\pi$
$600$	5.06914e6	0.574852
$601$	1.22575e7	1.38425	0.692127	−	0.721776i	$-0.256674\pi$
$601$	1.22575e7	1.38425	0.692127	+	0.721776i	$0.256674\pi$
$602$	4.90966e6	0.552153
$603$	−2.09098e6	−0.234184
$604$	1.94192e7	2.16590
$605$	3.63924e6	0.404224
$606$	−5.40114e6	−0.597453
$607$	−5.51298e6	−0.607316	−0.303658	−	0.952781i	$-0.598208\pi$
$607$	−5.51298e6	−0.607316	−0.303658	+	0.952781i	$0.598208\pi$
$608$	9.41615e6	1.03303
$609$	−1.01676e6	−0.111090
$610$	4.57173e6	0.497458
$611$	−4.81982e6	−0.522310
$612$	2.89901e6	0.312875
$613$	1.32302e7	1.42205	0.711024	−	0.703168i	$-0.248232\pi$
$613$	1.32302e7	1.42205	0.711024	+	0.703168i	$0.248232\pi$
$614$	−1.91120e7	−2.04591
$615$	−1.00763e6	−0.107427
$616$	−8.52785e6	−0.905499
$617$	−4.19258e6	−0.443372	−0.221686	−	0.975118i	$-0.571156\pi$
$617$	−4.19258e6	−0.443372	−0.221686	+	0.975118i	$0.571156\pi$
$618$	7.77283e6	0.818668
$619$	−1.15741e7	−1.21411	−0.607056	−	0.794659i	$-0.707650\pi$
$619$	−1.15741e7	−1.21411	−0.607056	+	0.794659i	$0.707650\pi$
$620$	−5.78414e6	−0.604309
$621$	−1.67238e6	−0.174023
$622$	−1.99634e7	−2.06899
$623$	1.69071e6	0.174521
$624$	721749.	0.0742036
$625$	7.63380e6	0.781701
$626$	−1.19025e7	−1.21396
$627$	−1.08253e7	−1.09969
$628$	2.02847e6	0.205243
$629$	1.13249e6	0.114132
$630$	−1.57130e6	−0.157728
$631$	2.88650e6	0.288601	0.144300	−	0.989534i	$-0.453907\pi$
$631$	2.88650e6	0.288601	0.144300	+	0.989534i	$0.453907\pi$
$632$	−1.57745e7	−1.57095
$633$	2.89062e6	0.286736
$634$	189846.	0.0187576
$635$	−1.21267e6	−0.119346
$636$	4.99297e6	0.489459
$637$	−4.09170e6	−0.399535
$638$	1.24582e7	1.21172
$639$	−3.11420e6	−0.301713
$640$	5.03288e6	0.485698
$641$	6.49448e6	0.624309	0.312155	−	0.950031i	$-0.398949\pi$
$641$	6.49448e6	0.624309	0.312155	+	0.950031i	$0.398949\pi$
$642$	1.12405e7	1.07634
$643$	6.13112e6	0.584807	0.292403	−	0.956295i	$-0.405545\pi$
$643$	6.13112e6	0.584807	0.292403	+	0.956295i	$0.405545\pi$
$644$	−1.69241e6	−0.160802
$645$	1.04031e6	0.0984610
$646$	5.85195e6	0.551720
$647$	9.85717e6	0.925746	0.462873	−	0.886425i	$-0.346819\pi$
$647$	9.85717e6	0.925746	0.462873	+	0.886425i	$0.346819\pi$
$648$	−3.82006e6	−0.357382
$649$	−2.19983e6	−0.205011
$650$	8.46237e6	0.785613
$651$	3.28683e6	0.303966
$652$	−2.50880e7	−2.31125
$653$	−2.84309e6	−0.260920	−0.130460	−	0.991454i	$-0.541645\pi$
$653$	−2.84309e6	−0.260920	−0.130460	+	0.991454i	$0.541645\pi$
$654$	−1.25722e7	−1.14939
$655$	3.96807e6	0.361390
$656$	−2.42909e6	−0.220386
$657$	1.53929e7	1.39126
$658$	−8.80080e6	−0.792423
$659$	−6.03723e6	−0.541532	−0.270766	−	0.962645i	$-0.587277\pi$
$659$	−6.03723e6	−0.541532	−0.270766	+	0.962645i	$0.587277\pi$
$660$	−4.25268e6	−0.380017
$661$	2.20269e7	1.96087	0.980437	−	0.196834i	$-0.0630660\pi$
$661$	2.20269e7	1.96087	0.980437	+	0.196834i	$0.0630660\pi$
$662$	−1.50154e7	−1.33166
$663$	−715438.	−0.0632103
$664$	−2.10401e7	−1.85194
$665$	−2.01373e6	−0.176583
$666$	−6.61359e6	−0.577766
$667$	1.05054e6	0.0914316
$668$	−5.36892e6	−0.465528
$669$	5.01238e6	0.432991
$670$	−1.65815e6	−0.142704
$671$	2.02092e7	1.73277
$672$	−2.10201e6	−0.179561
$673$	−1.56977e7	−1.33597	−0.667987	−	0.744173i	$-0.732844\pi$
$673$	−1.56977e7	−1.33597	−0.667987	+	0.744173i	$0.732844\pi$
$674$	−1.96149e7	−1.66317
$675$	9.69402e6	0.818926
$676$	−1.52230e7	−1.28125
$677$	2.35505e7	1.97482	0.987410	−	0.158180i	$-0.0505627\pi$
$677$	2.35505e7	1.97482	0.987410	+	0.158180i	$0.0505627\pi$
$678$	6.10736e6	0.510245
$679$	8.15274e6	0.678624
$680$	976819.	0.0810106
$681$	7.86953e6	0.650251
$682$	−4.02730e7	−3.31553
$683$	8.07710e6	0.662527	0.331264	−	0.943538i	$-0.392525\pi$
$683$	8.07710e6	0.662527	0.331264	+	0.943538i	$0.392525\pi$
$684$	−2.16969e7	−1.77320
$685$	4.49259e6	0.365822
$686$	−1.70641e7	−1.38444
$687$	−5.20233e6	−0.420539
$688$	2.50788e6	0.201993
$689$	3.54165e6	0.284222
$690$	−564842.	−0.0451652
$691$	845382.	0.0673532	0.0336766	−	0.999433i	$-0.489278\pi$
$691$	845382.	0.0673532	0.0336766	+	0.999433i	$0.489278\pi$
$692$	−2.98793e7	−2.37195
$693$	−6.94587e6	−0.549406
$694$	−2.19276e7	−1.72820
$695$	293600.	0.0230566
$696$	−3.69127e6	−0.288837
$697$	2.40785e6	0.187736
$698$	−1.30290e7	−1.01221
$699$	5.49069e6	0.425044
$700$	9.81015e6	0.756712
$701$	1.56892e7	1.20588	0.602942	−	0.797785i	$-0.293995\pi$
$701$	1.56892e7	1.20588	0.602942	+	0.797785i	$0.293995\pi$
$702$	9.80975e6	0.751303
$703$	−8.47579e6	−0.646833
$704$	3.16515e7	2.40693
$705$	−1.86481e6	−0.141306
$706$	2.74201e6	0.207042
$707$	−4.44136e6	−0.334170
$708$	1.53399e6	0.115011
$709$	8.58683e6	0.641530	0.320765	−	0.947159i	$-0.396060\pi$
$709$	8.58683e6	0.641530	0.320765	+	0.947159i	$0.396060\pi$
$710$	−2.46956e6	−0.183855
$711$	−1.28482e7	−0.953164
$712$	6.13801e6	0.453762
$713$	−3.39602e6	−0.250177
$714$	−1.30636e6	−0.0958997
$715$	−3.01655e6	−0.220671
$716$	−1.18669e7	−0.865078
$717$	1.50050e6	0.109003
$718$	6.31261e6	0.456981
$719$	−2.58476e6	−0.186466	−0.0932328	−	0.995644i	$-0.529720\pi$
$719$	−2.58476e6	−0.186466	−0.0932328	+	0.995644i	$0.529720\pi$
$720$	−802630.	−0.0577011
$721$	6.39161e6	0.457901
$722$	−2.06166e7	−1.47189
$723$	−1.07393e6	−0.0764067
$724$	1.53404e7	1.08765
$725$	−6.08947e6	−0.430264
$726$	−1.76692e7	−1.24416
$727$	−1.57238e7	−1.10337	−0.551685	−	0.834052i	$-0.686015\pi$
$727$	−1.57238e7	−1.10337	−0.551685	+	0.834052i	$0.686015\pi$
$728$	4.21812e6	0.294979
$729$	3.33994e6	0.232766
$730$	1.22066e7	0.847790
$731$	−2.48595e6	−0.172068
$732$	−1.40923e7	−0.972082
$733$	−990013.	−0.0680583	−0.0340291	−	0.999421i	$-0.510834\pi$
$733$	−990013.	−0.0680583	−0.0340291	+	0.999421i	$0.510834\pi$
$734$	−3.44653e7	−2.36125
$735$	−1.58310e6	−0.108091
$736$	2.17185e6	0.147786
$737$	−7.32980e6	−0.497076
$738$	−1.40615e7	−0.950369
$739$	−1.96620e6	−0.132439	−0.0662195	−	0.997805i	$-0.521094\pi$
$739$	−1.96620e6	−0.132439	−0.0662195	+	0.997805i	$0.521094\pi$
$740$	−3.32969e6	−0.223524
$741$	5.35449e6	0.358239
$742$	6.46691e6	0.431208
$743$	1.96721e7	1.30731	0.653654	−	0.756794i	$-0.273235\pi$
$743$	1.96721e7	1.30731	0.653654	+	0.756794i	$0.273235\pi$
$744$	1.19326e7	0.790320
$745$	−655705.	−0.0432831
$746$	−2.87344e7	−1.89041
$747$	−1.71370e7	−1.12366
$748$	1.01623e7	0.664107
$749$	9.24308e6	0.602022
$750$	6.81228e6	0.442221
$751$	1.51225e7	0.978414	0.489207	−	0.872168i	$-0.337286\pi$
$751$	1.51225e7	0.978414	0.489207	+	0.872168i	$0.337286\pi$
$752$	−4.49550e6	−0.289890
$753$	−2.55542e6	−0.164239
$754$	−6.16217e6	−0.394735
$755$	5.32945e6	0.340263
$756$	1.13721e7	0.723664
$757$	−9.73228e6	−0.617270	−0.308635	−	0.951181i	$-0.599872\pi$
$757$	−9.73228e6	−0.617270	−0.308635	+	0.951181i	$0.599872\pi$
$758$	4.95053e7	3.12953
$759$	−2.49686e6	−0.157322
$760$	−7.31073e6	−0.459120
$761$	1.01433e7	0.634919	0.317460	−	0.948272i	$-0.397170\pi$
$761$	1.01433e7	0.634919	0.317460	+	0.948272i	$0.397170\pi$
$762$	5.88774e6	0.367334
$763$	−1.03381e7	−0.642882
$764$	−2.14176e7	−1.32751
$765$	795611.	0.0491527
$766$	3.24063e7	1.99552
$767$	1.08810e6	0.0667853
$768$	−1.17425e7	−0.718387
$769$	3.19597e7	1.94889	0.974443	−	0.224634i	$-0.0721188\pi$
$769$	3.19597e7	1.94889	0.974443	+	0.224634i	$0.0721188\pi$
$770$	−5.50809e6	−0.334791
$771$	4.87192e6	0.295164
$772$	3.18666e6	0.192439
$773$	−7.68247e6	−0.462436	−0.231218	−	0.972902i	$-0.574271\pi$
$773$	−7.68247e6	−0.462436	−0.231218	+	0.972902i	$0.574271\pi$
$774$	1.45177e7	0.871052
$775$	1.96852e7	1.17729
$776$	2.95980e7	1.76444
$777$	1.89209e6	0.112432
$778$	−4.27887e6	−0.253443
$779$	−1.80209e7	−1.06398
$780$	2.10350e6	0.123796
$781$	−1.09166e7	−0.640413
$782$	1.34976e6	0.0789295
$783$	−7.05904e6	−0.411473
$784$	−3.81637e6	−0.221749
$785$	556697.	0.0322437
$786$	−1.92658e7	−1.11232
$787$	−1.42856e7	−0.822172	−0.411086	−	0.911597i	$-0.634850\pi$
$787$	−1.42856e7	−0.822172	−0.411086	+	0.911597i	$0.634850\pi$
$788$	−7.03556e6	−0.403630
$789$	9.15838e6	0.523753
$790$	−1.01886e7	−0.580829
$791$	5.02209e6	0.285393
$792$	−2.52165e7	−1.42847
$793$	−9.99604e6	−0.564476
$794$	2.84643e7	1.60232
$795$	1.37028e6	0.0768939
$796$	−1.42354e7	−0.796321
$797$	2.23930e7	1.24872	0.624362	−	0.781135i	$-0.285359\pi$
$797$	2.23930e7	1.24872	0.624362	+	0.781135i	$0.285359\pi$
$798$	9.77708e6	0.543503
$799$	4.45619e6	0.246943
$800$	−1.25892e7	−0.695461
$801$	4.99936e6	0.275317
$802$	1.54275e7	0.846954
$803$	5.39589e7	2.95307
$804$	5.11121e6	0.278859
$805$	−464470.	−0.0252620
$806$	1.99202e7	1.08008
$807$	−697724.	−0.0377138
$808$	−1.61241e7	−0.868853
$809$	1.38671e7	0.744927	0.372464	−	0.928047i	$-0.378513\pi$
$809$	1.38671e7	0.744927	0.372464	+	0.928047i	$0.378513\pi$
$810$	−2.46735e6	−0.132135
$811$	−1.61210e7	−0.860677	−0.430339	−	0.902668i	$-0.641606\pi$
$811$	−1.61210e7	−0.860677	−0.430339	+	0.902668i	$0.641606\pi$
$812$	−7.14360e6	−0.380213
$813$	−7.80849e6	−0.414325
$814$	−2.31835e7	−1.22636
$815$	−6.88520e6	−0.363097
$816$	−667297.	−0.0350827
$817$	1.86054e7	0.975179
$818$	−4.32224e7	−2.25853
$819$	3.43563e6	0.178977
$820$	−7.07945e6	−0.367676
$821$	−4.03962e6	−0.209162	−0.104581	−	0.994516i	$-0.533350\pi$
$821$	−4.03962e6	−0.209162	−0.104581	+	0.994516i	$0.533350\pi$
$822$	−2.18124e7	−1.12596
$823$	6.08356e6	0.313082	0.156541	−	0.987671i	$-0.449966\pi$
$823$	6.08356e6	0.313082	0.156541	+	0.987671i	$0.449966\pi$
$824$	2.32043e7	1.19056
$825$	1.44732e7	0.740335
$826$	1.98683e6	0.101323
$827$	3.60225e7	1.83151	0.915756	−	0.401735i	$-0.131593\pi$
$827$	3.60225e7	1.83151	0.915756	+	0.401735i	$0.131593\pi$
$828$	−5.00441e6	−0.253674
$829$	−2.15888e7	−1.09104	−0.545521	−	0.838097i	$-0.683668\pi$
$829$	−2.15888e7	−1.09104	−0.545521	+	0.838097i	$0.683668\pi$
$830$	−1.35897e7	−0.684721
$831$	−1.38095e7	−0.693706
$832$	−1.56558e7	−0.784090
$833$	3.78300e6	0.188897
$834$	−1.42549e6	−0.0709657
$835$	−1.47346e6	−0.0731344
$836$	−7.60569e7	−3.76377
$837$	2.28194e7	1.12588
$838$	3.18702e7	1.56774
$839$	−1.39906e7	−0.686167	−0.343084	−	0.939305i	$-0.611471\pi$
$839$	−1.39906e7	−0.686167	−0.343084	+	0.939305i	$0.611471\pi$
$840$	1.63201e6	0.0798040
$841$	−1.60769e7	−0.783812
$842$	8.26606e6	0.401808
$843$	6.89064e6	0.333957
$844$	2.03091e7	0.981376
$845$	−4.17784e6	−0.201284
$846$	−2.60236e7	−1.25009
$847$	−1.45294e7	−0.695889
$848$	3.30334e6	0.157748
$849$	−9.44504e6	−0.449712
$850$	−7.82393e6	−0.371431
$851$	−1.95495e6	−0.0925363
$852$	7.61237e6	0.359270
$853$	−2.06751e7	−0.972914	−0.486457	−	0.873705i	$-0.661711\pi$
$853$	−2.06751e7	−0.972914	−0.486457	+	0.873705i	$0.661711\pi$
$854$	−1.82524e7	−0.856395
$855$	−5.95453e6	−0.278569
$856$	3.35564e7	1.56528
$857$	2.74956e7	1.27883	0.639413	−	0.768863i	$-0.279177\pi$
$857$	2.74956e7	1.27883	0.639413	+	0.768863i	$0.279177\pi$
$858$	1.46459e7	0.679202
$859$	−2.26065e7	−1.04532	−0.522662	−	0.852540i	$-0.675061\pi$
$859$	−2.26065e7	−1.04532	−0.522662	+	0.852540i	$0.675061\pi$
$860$	7.30909e6	0.336990
$861$	4.02289e6	0.184940
$862$	1.34179e7	0.615058
$863$	1.64521e7	0.751960	0.375980	−	0.926628i	$-0.377306\pi$
$863$	1.64521e7	0.751960	0.375980	+	0.926628i	$0.377306\pi$
$864$	−1.45936e7	−0.665089
$865$	−8.20013e6	−0.372632
$866$	−9.83980e6	−0.445853
$867$	661461.	0.0298852
$868$	2.30928e7	1.04035
$869$	−4.50385e7	−2.02318
$870$	−2.38417e6	−0.106792
$871$	3.62553e6	0.161930
$872$	−3.75320e7	−1.67151
$873$	2.41073e7	1.07057
$874$	−1.01019e7	−0.447326
$875$	5.60175e6	0.247345
$876$	−3.76266e7	−1.65667
$877$	−2.23165e7	−0.979776	−0.489888	−	0.871785i	$-0.662962\pi$
$877$	−2.23165e7	−0.979776	−0.489888	+	0.871785i	$0.662962\pi$
$878$	−9.51501e6	−0.416556
$879$	1.65061e7	0.720564
$880$	−2.81357e6	−0.122476
$881$	−2.30357e6	−0.0999914	−0.0499957	−	0.998749i	$-0.515921\pi$
$881$	−2.30357e6	−0.0999914	−0.0499957	+	0.998749i	$0.515921\pi$
$882$	−2.20923e7	−0.956244
$883$	−1.99926e7	−0.862914	−0.431457	−	0.902134i	$-0.642000\pi$
$883$	−1.99926e7	−0.862914	−0.431457	+	0.902134i	$0.642000\pi$
$884$	−5.02657e6	−0.216342
$885$	420991.	0.0180682
$886$	5.56402e7	2.38125
$887$	2.60054e7	1.10983	0.554913	−	0.831908i	$-0.312752\pi$
$887$	2.60054e7	1.10983	0.554913	+	0.831908i	$0.312752\pi$
$888$	6.86912e6	0.292327
$889$	4.84150e6	0.205459
$890$	3.96450e6	0.167770
$891$	−1.09068e7	−0.460261
$892$	3.52163e7	1.48194
$893$	−3.33511e7	−1.39953
$894$	3.18358e6	0.133221
$895$	−3.25678e6	−0.135904
$896$	−2.00935e7	−0.836151
$897$	1.23502e6	0.0512499
$898$	−3.55671e7	−1.47183
$899$	−1.43344e7	−0.591537
$900$	2.90082e7	1.19375
$901$	−3.27445e6	−0.134378
$902$	−4.92918e7	−2.01724
$903$	−4.15338e6	−0.169505
$904$	1.82324e7	0.742031
$905$	4.21004e6	0.170870
$906$	−2.58755e7	−1.04729
$907$	−3.84937e6	−0.155372	−0.0776858	−	0.996978i	$-0.524753\pi$
$907$	−3.84937e6	−0.155372	−0.0776858	+	0.996978i	$0.524753\pi$
$908$	5.52903e7	2.22553
$909$	−1.31329e7	−0.527172
$910$	2.72446e6	0.109063
$911$	2.41198e7	0.962891	0.481446	−	0.876476i	$-0.340112\pi$
$911$	2.41198e7	0.962891	0.481446	+	0.876476i	$0.340112\pi$
$912$	4.99420e6	0.198828
$913$	−6.00726e7	−2.38506
$914$	−8.23671e7	−3.26128
$915$	−3.86751e6	−0.152714
$916$	−3.65509e7	−1.43933
$917$	−1.58423e7	−0.622149
$918$	−9.06966e6	−0.355209
$919$	−6.50718e6	−0.254158	−0.127079	−	0.991893i	$-0.540560\pi$
$919$	−6.50718e6	−0.254158	−0.127079	+	0.991893i	$0.540560\pi$
$920$	−1.68623e6	−0.0656821
$921$	1.61681e7	0.628071
$922$	−1.18105e7	−0.457552
$923$	5.39968e6	0.208624
$924$	1.69786e7	0.654216
$925$	1.13320e7	0.435462
$926$	8.14578e7	3.12180
$927$	1.88997e7	0.722365
$928$	9.16726e6	0.349438
$929$	3.52061e7	1.33838	0.669189	−	0.743092i	$-0.266641\pi$
$929$	3.52061e7	1.33838	0.669189	+	0.743092i	$0.266641\pi$
$930$	7.70720e6	0.292206
$931$	−2.83128e7	−1.07056
$932$	3.85768e7	1.45474
$933$	1.68883e7	0.635157
$934$	−4.24550e7	−1.59243
$935$	2.78896e6	0.104331
$936$	1.24728e7	0.465345
$937$	3.78858e7	1.40970	0.704851	−	0.709355i	$-0.251014\pi$
$937$	3.78858e7	1.40970	0.704851	+	0.709355i	$0.251014\pi$
$938$	6.62007e6	0.245672
$939$	1.00691e7	0.372672
$940$	−1.31019e7	−0.483632
$941$	−4.59252e7	−1.69074	−0.845371	−	0.534180i	$-0.820620\pi$
$941$	−4.59252e7	−1.69074	−0.845371	+	0.534180i	$0.820620\pi$
$942$	−2.70288e6	−0.0992428
$943$	−4.15654e6	−0.152213
$944$	1.01488e6	0.0370669
$945$	3.12099e6	0.113688
$946$	5.08907e7	1.84889
$947$	4.21077e7	1.52576	0.762880	−	0.646540i	$-0.223785\pi$
$947$	4.21077e7	1.52576	0.762880	+	0.646540i	$0.223785\pi$
$948$	3.14062e7	1.13500
$949$	−2.66896e7	−0.962005
$950$	5.85560e7	2.10505
$951$	−160602.	−0.00575838
$952$	−3.89989e6	−0.139463
$953$	2.60672e7	0.929742	0.464871	−	0.885378i	$-0.346101\pi$
$953$	2.60672e7	0.929742	0.464871	+	0.885378i	$0.346101\pi$
$954$	1.91224e7	0.680255
$955$	−5.87789e6	−0.208551
$956$	1.05423e7	0.373071
$957$	−1.05391e7	−0.371985
$958$	−5.59404e7	−1.96930
$959$	−1.79364e7	−0.629779
$960$	−6.05728e6	−0.212129
$961$	1.77092e7	0.618572
$962$	1.14672e7	0.399504
$963$	2.73314e7	0.949722
$964$	−7.54531e6	−0.261508
$965$	874553.	0.0302321
$966$	2.25510e6	0.0777539
$967$	−1.46979e7	−0.505461	−0.252731	−	0.967537i	$-0.581329\pi$
$967$	−1.46979e7	−0.505461	−0.252731	+	0.967537i	$0.581329\pi$
$968$	−5.27481e7	−1.80933
$969$	−4.95052e6	−0.169372
$970$	1.91172e7	0.652370
$971$	3.92072e7	1.33450	0.667249	−	0.744835i	$-0.267472\pi$
$971$	3.92072e7	1.33450	0.667249	+	0.744835i	$0.267472\pi$
$972$	5.29318e7	1.79701
$973$	−1.17218e6	−0.0396929
$974$	1.35686e7	0.458288
$975$	−7.15885e6	−0.241175
$976$	−9.32342e6	−0.313293
$977$	3.72912e7	1.24989	0.624943	−	0.780670i	$-0.285122\pi$
$977$	3.72912e7	1.24989	0.624943	+	0.780670i	$0.285122\pi$
$978$	3.34290e7	1.11757
$979$	1.75249e7	0.584386
$980$	−1.11226e7	−0.369949
$981$	−3.05695e7	−1.01418
$982$	−3.89066e7	−1.28749
$983$	−2.78034e7	−0.917730	−0.458865	−	0.888506i	$-0.651744\pi$
$983$	−2.78034e7	−0.917730	−0.458865	+	0.888506i	$0.651744\pi$
$984$	1.46048e7	0.480849
$985$	−1.93086e6	−0.0634102
$986$	5.69727e6	0.186627
$987$	7.44514e6	0.243265
$988$	3.76200e7	1.22610
$989$	4.29136e6	0.139510
$990$	−1.62872e7	−0.528152
$991$	8.83174e6	0.285668	0.142834	−	0.989747i	$-0.454378\pi$
$991$	8.83174e6	0.285668	0.142834	+	0.989747i	$0.454378\pi$
$992$	−2.96346e7	−0.956137
$993$	1.27025e7	0.408804
$994$	9.85958e6	0.316514
$995$	−3.90680e6	−0.125102
$996$	4.18898e7	1.33801
$997$	4.42919e7	1.41119	0.705596	−	0.708614i	$-0.250679\pi$
$997$	4.42919e7	1.41119	0.705596	+	0.708614i	$0.250679\pi$
$998$	−7.58910e7	−2.41193
$999$	1.31362e7	0.416444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.6.a.d.1.10	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.6.a.d.1.10	✓	100	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-9.36177 q^{2} +7.91970 q^{3} +55.6428 q^{4} +15.2707 q^{5} -74.1424 q^{6} -60.9674 q^{7} -221.338 q^{8} -180.278 q^{9} +O(q^{10})\)	\(q-9.36177 q^{2} +7.91970 q^{3} +55.6428 q^{4} +15.2707 q^{5} -74.1424 q^{6} -60.9674 q^{7} -221.338 q^{8} -180.278 q^{9} -142.961 q^{10} -631.954 q^{11} +440.674 q^{12} +312.583 q^{13} +570.763 q^{14} +120.940 q^{15} +291.549 q^{16} -289.000 q^{17} +1687.72 q^{18} +2162.94 q^{19} +849.705 q^{20} -482.844 q^{21} +5916.21 q^{22} +498.885 q^{23} -1752.93 q^{24} -2891.80 q^{25} -2926.33 q^{26} -3352.24 q^{27} -3392.40 q^{28} +2105.77 q^{29} -1132.21 q^{30} -6807.23 q^{31} +4353.40 q^{32} -5004.89 q^{33} +2705.55 q^{34} -931.017 q^{35} -10031.2 q^{36} -3918.64 q^{37} -20249.0 q^{38} +2475.56 q^{39} -3380.00 q^{40} -8331.66 q^{41} +4520.27 q^{42} +8601.91 q^{43} -35163.7 q^{44} -2752.98 q^{45} -4670.45 q^{46} -15419.4 q^{47} +2308.99 q^{48} -13090.0 q^{49} +27072.4 q^{50} -2288.79 q^{51} +17393.0 q^{52} +11330.3 q^{53} +31382.9 q^{54} -9650.39 q^{55} +13494.4 q^{56} +17129.8 q^{57} -19713.7 q^{58} +3481.00 q^{59} +6729.41 q^{60} -31978.9 q^{61} +63727.7 q^{62} +10991.1 q^{63} -50085.2 q^{64} +4773.37 q^{65} +46854.6 q^{66} +11598.6 q^{67} -16080.8 q^{68} +3951.02 q^{69} +8715.97 q^{70} +17274.4 q^{71} +39902.5 q^{72} -85384.2 q^{73} +36685.4 q^{74} -22902.2 q^{75} +120352. q^{76} +38528.6 q^{77} -23175.7 q^{78} +71268.6 q^{79} +4452.17 q^{80} +17258.9 q^{81} +77999.1 q^{82} +95058.5 q^{83} -26866.8 q^{84} -4413.24 q^{85} -80529.2 q^{86} +16677.1 q^{87} +139876. q^{88} -27731.4 q^{89} +25772.8 q^{90} -19057.4 q^{91} +27759.3 q^{92} -53911.2 q^{93} +144352. q^{94} +33029.7 q^{95} +34477.7 q^{96} -133723. q^{97} +122545. q^{98} +113928. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9}+O(q^{10}) \) 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9	\( 100 q + 25 q^{2} + 63 q^{3} + 1707 q^{4} + 509 q^{5} + 207 q^{6} + 247 q^{7} + 765 q^{8} + 9003 q^{9} + 424 q^{11} + 2880 q^{12} + 2426 q^{13} + 1069 q^{14} + 3699 q^{15} + 25895 q^{16} - 28900 q^{17} + 6644 q^{18} + 2224 q^{19} + 11919 q^{20} + 12248 q^{21} + 1160 q^{22} + 4675 q^{23} + 6477 q^{24} + 76925 q^{25} + 26507 q^{26} + 18465 q^{27} + 7371 q^{28} + 13905 q^{29} + 42029 q^{30} + 11503 q^{31} + 31765 q^{32} + 34053 q^{33} - 7225 q^{34} + 26861 q^{35} + 210764 q^{36} - 4418 q^{37} + 55637 q^{38} - 5718 q^{39} + 24116 q^{40} + 50715 q^{41} + 145355 q^{42} + 36979 q^{43} - 6793 q^{44} + 88939 q^{45} + 23917 q^{46} + 162533 q^{47} + 219761 q^{48} + 276061 q^{49} + 204874 q^{50} - 18207 q^{51} + 73665 q^{52} + 144329 q^{53} + 112241 q^{54} + 63002 q^{55} + 234871 q^{56} + 94768 q^{57} + 22318 q^{58} + 348100 q^{59} + 390780 q^{60} - 45447 q^{61} + 146617 q^{62} + 88467 q^{63} + 580433 q^{64} - 49981 q^{65} - 14744 q^{66} + 113930 q^{67} - 493323 q^{68} + 49070 q^{69} + 86899 q^{70} + 138703 q^{71} + 319055 q^{72} + 174214 q^{73} - 139931 q^{74} + 295788 q^{75} + 272539 q^{76} + 642017 q^{77} + 93149 q^{78} - 240788 q^{79} + 582895 q^{80} + 690560 q^{81} + 164633 q^{82} + 324136 q^{83} + 775436 q^{84} - 147101 q^{85} + 113296 q^{86} + 612596 q^{87} - 227510 q^{88} + 348396 q^{89} + 750464 q^{90} - 100399 q^{91} + 453265 q^{92} + 660393 q^{93} + 183864 q^{94} + 341370 q^{95} + 209486 q^{96} + 288603 q^{97} + 1100905 q^{98} + 301794 q^{99}+O(q^{100}) \) 100 * q + 25 * q^2 + 63 * q^3 + 1707 * q^4 + 509 * q^5 + 207 * q^6 + 247 * q^7 + 765 * q^8 + 9003 * q^9 + 424 * q^11 + 2880 * q^12 + 2426 * q^13 + 1069 * q^14 + 3699 * q^15 + 25895 * q^16 - 28900 * q^17 + 6644 * q^18 + 2224 * q^19 + 11919 * q^20 + 12248 * q^21 + 1160 * q^22 + 4675 * q^23 + 6477 * q^24 + 76925 * q^25 + 26507 * q^26 + 18465 * q^27 + 7371 * q^28 + 13905 * q^29 + 42029 * q^30 + 11503 * q^31 + 31765 * q^32 + 34053 * q^33 - 7225 * q^34 + 26861 * q^35 + 210764 * q^36 - 4418 * q^37 + 55637 * q^38 - 5718 * q^39 + 24116 * q^40 + 50715 * q^41 + 145355 * q^42 + 36979 * q^43 - 6793 * q^44 + 88939 * q^45 + 23917 * q^46 + 162533 * q^47 + 219761 * q^48 + 276061 * q^49 + 204874 * q^50 - 18207 * q^51 + 73665 * q^52 + 144329 * q^53 + 112241 * q^54 + 63002 * q^55 + 234871 * q^56 + 94768 * q^57 + 22318 * q^58 + 348100 * q^59 + 390780 * q^60 - 45447 * q^61 + 146617 * q^62 + 88467 * q^63 + 580433 * q^64 - 49981 * q^65 - 14744 * q^66 + 113930 * q^67 - 493323 * q^68 + 49070 * q^69 + 86899 * q^70 + 138703 * q^71 + 319055 * q^72 + 174214 * q^73 - 139931 * q^74 + 295788 * q^75 + 272539 * q^76 + 642017 * q^77 + 93149 * q^78 - 240788 * q^79 + 582895 * q^80 + 690560 * q^81 + 164633 * q^82 + 324136 * q^83 + 775436 * q^84 - 147101 * q^85 + 113296 * q^86 + 612596 * q^87 - 227510 * q^88 + 348396 * q^89 + 750464 * q^90 - 100399 * q^91 + 453265 * q^92 + 660393 * q^93 + 183864 * q^94 + 341370 * q^95 + 209486 * q^96 + 288603 * q^97 + 1100905 * q^98 + 301794 * q^99

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