LMFDB - Embedded newform 1003.6.a.c.1.16

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:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-8.06402 q^{2} +25.0583 q^{3} +33.0284 q^{4} +13.6048 q^{5} -202.071 q^{6} +208.151 q^{7} -8.29333 q^{8} +384.918 q^{9} +O(q^{10})$	\(q-8.06402 q^{2} +25.0583 q^{3} +33.0284 q^{4} +13.6048 q^{5} -202.071 q^{6} +208.151 q^{7} -8.29333 q^{8} +384.918 q^{9} -109.709 q^{10} +744.226 q^{11} +827.636 q^{12} -222.474 q^{13} -1678.53 q^{14} +340.913 q^{15} -990.032 q^{16} +289.000 q^{17} -3103.99 q^{18} +1181.60 q^{19} +449.346 q^{20} +5215.91 q^{21} -6001.45 q^{22} -4065.70 q^{23} -207.817 q^{24} -2939.91 q^{25} +1794.04 q^{26} +3556.23 q^{27} +6874.90 q^{28} -2489.72 q^{29} -2749.13 q^{30} +9530.07 q^{31} +8249.03 q^{32} +18649.0 q^{33} -2330.50 q^{34} +2831.85 q^{35} +12713.3 q^{36} +2890.91 q^{37} -9528.42 q^{38} -5574.82 q^{39} -112.829 q^{40} +12453.1 q^{41} -42061.2 q^{42} -1238.62 q^{43} +24580.6 q^{44} +5236.74 q^{45} +32785.9 q^{46} -1473.58 q^{47} -24808.5 q^{48} +26519.8 q^{49} +23707.5 q^{50} +7241.85 q^{51} -7347.97 q^{52} +23802.6 q^{53} -28677.5 q^{54} +10125.1 q^{55} -1726.26 q^{56} +29608.8 q^{57} +20077.2 q^{58} -3481.00 q^{59} +11259.8 q^{60} -8626.84 q^{61} -76850.6 q^{62} +80121.1 q^{63} -34839.3 q^{64} -3026.72 q^{65} -150386. q^{66} -34830.5 q^{67} +9545.22 q^{68} -101880. q^{69} -22836.1 q^{70} -53647.1 q^{71} -3192.26 q^{72} -15244.8 q^{73} -23312.3 q^{74} -73669.1 q^{75} +39026.3 q^{76} +154911. q^{77} +44955.5 q^{78} +86800.3 q^{79} -13469.2 q^{80} -4421.99 q^{81} -100422. q^{82} +32456.7 q^{83} +172273. q^{84} +3931.79 q^{85} +9988.26 q^{86} -62388.2 q^{87} -6172.11 q^{88} +122571. q^{89} -42229.2 q^{90} -46308.2 q^{91} -134284. q^{92} +238807. q^{93} +11883.0 q^{94} +16075.4 q^{95} +206707. q^{96} +72378.4 q^{97} -213856. q^{98} +286466. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 25 q^{2} + 45 q^{3} + 1611 q^{4} + 541 q^{5} + 305 q^{6} + 247 q^{7} + 1425 q^{8} + 8873 q^{9}+O(q^{10}) $ 98 * q + 25 * q^2 + 45 * q^3 + 1611 * q^4 + 541 * q^5 + 305 * q^6 + 247 * q^7 + 1425 * q^8 + 8873 * q^9	\( 98 q + 25 q^{2} + 45 q^{3} + 1611 q^{4} + 541 q^{5} + 305 q^{6} + 247 q^{7} + 1425 q^{8} + 8873 q^{9} + 1000 q^{10} + 2842 q^{11} + 2304 q^{12} + 3246 q^{13} + 2245 q^{14} + 999 q^{15} + 29551 q^{16} + 28322 q^{17} + 1540 q^{18} + 932 q^{19} + 18297 q^{20} + 1112 q^{21} + 7918 q^{22} + 12457 q^{23} + 18405 q^{24} + 65623 q^{25} + 16159 q^{26} + 12633 q^{27} + 23731 q^{28} + 28451 q^{29} - 19285 q^{30} + 21493 q^{31} + 52885 q^{32} + 39707 q^{33} + 7225 q^{34} + 20313 q^{35} + 155100 q^{36} + 71740 q^{37} + 78949 q^{38} + 42612 q^{39} + 9854 q^{40} + 39545 q^{41} - 113891 q^{42} + 10477 q^{43} + 129131 q^{44} + 212203 q^{45} - 8801 q^{46} + 92561 q^{47} + 42263 q^{48} + 242447 q^{49} - 24646 q^{50} + 13005 q^{51} + 126145 q^{52} + 197573 q^{53} + 138637 q^{54} + 56894 q^{55} + 65301 q^{56} + 154798 q^{57} + 46454 q^{58} - 341138 q^{59} - 62712 q^{60} + 200139 q^{61} + 337089 q^{62} + 72251 q^{63} + 437269 q^{64} + 352383 q^{65} + 342440 q^{66} + 25262 q^{67} + 465579 q^{68} + 233418 q^{69} + 435463 q^{70} + 95619 q^{71} + 215863 q^{72} + 372862 q^{73} + 231761 q^{74} - 225892 q^{75} - 156705 q^{76} + 515725 q^{77} + 140085 q^{78} + 262158 q^{79} + 294401 q^{80} + 933702 q^{81} + 466955 q^{82} + 219868 q^{83} - 213492 q^{84} + 156349 q^{85} + 89392 q^{86} + 236040 q^{87} + 389548 q^{88} + 388400 q^{89} - 227892 q^{90} + 331873 q^{91} + 380277 q^{92} + 398803 q^{93} + 423436 q^{94} + 224444 q^{95} + 664910 q^{96} + 487367 q^{97} + 510307 q^{98} + 524962 q^{99}+O(q^{100}) \) 98 * q + 25 * q^2 + 45 * q^3 + 1611 * q^4 + 541 * q^5 + 305 * q^6 + 247 * q^7 + 1425 * q^8 + 8873 * q^9 + 1000 * q^10 + 2842 * q^11 + 2304 * q^12 + 3246 * q^13 + 2245 * q^14 + 999 * q^15 + 29551 * q^16 + 28322 * q^17 + 1540 * q^18 + 932 * q^19 + 18297 * q^20 + 1112 * q^21 + 7918 * q^22 + 12457 * q^23 + 18405 * q^24 + 65623 * q^25 + 16159 * q^26 + 12633 * q^27 + 23731 * q^28 + 28451 * q^29 - 19285 * q^30 + 21493 * q^31 + 52885 * q^32 + 39707 * q^33 + 7225 * q^34 + 20313 * q^35 + 155100 * q^36 + 71740 * q^37 + 78949 * q^38 + 42612 * q^39 + 9854 * q^40 + 39545 * q^41 - 113891 * q^42 + 10477 * q^43 + 129131 * q^44 + 212203 * q^45 - 8801 * q^46 + 92561 * q^47 + 42263 * q^48 + 242447 * q^49 - 24646 * q^50 + 13005 * q^51 + 126145 * q^52 + 197573 * q^53 + 138637 * q^54 + 56894 * q^55 + 65301 * q^56 + 154798 * q^57 + 46454 * q^58 - 341138 * q^59 - 62712 * q^60 + 200139 * q^61 + 337089 * q^62 + 72251 * q^63 + 437269 * q^64 + 352383 * q^65 + 342440 * q^66 + 25262 * q^67 + 465579 * q^68 + 233418 * q^69 + 435463 * q^70 + 95619 * q^71 + 215863 * q^72 + 372862 * q^73 + 231761 * q^74 - 225892 * q^75 - 156705 * q^76 + 515725 * q^77 + 140085 * q^78 + 262158 * q^79 + 294401 * q^80 + 933702 * q^81 + 466955 * q^82 + 219868 * q^83 - 213492 * q^84 + 156349 * q^85 + 89392 * q^86 + 236040 * q^87 + 389548 * q^88 + 388400 * q^89 - 227892 * q^90 + 331873 * q^91 + 380277 * q^92 + 398803 * q^93 + 423436 * q^94 + 224444 * q^95 + 664910 * q^96 + 487367 * q^97 + 510307 * q^98 + 524962 * 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 $

$2$	−8.06402	−1.42553	−0.712765	−	0.701402i	$-0.752558\pi$
$2$	−8.06402	−1.42553	−0.712765	+	0.701402i	$0.752558\pi$
$3$	25.0583	1.60749	0.803745	−	0.594973i	$-0.202837\pi$
$3$	25.0583	1.60749	0.803745	+	0.594973i	$0.202837\pi$
$4$	33.0284	1.03214
$5$	13.6048	0.243370	0.121685	−	0.992569i	$-0.461170\pi$
$5$	13.6048	0.243370	0.121685	+	0.992569i	$0.461170\pi$
$6$	−202.071	−2.29153
$7$	208.151	1.60558	0.802792	−	0.596259i	$-0.203347\pi$
$7$	208.151	1.60558	0.802792	+	0.596259i	$0.203347\pi$
$8$	−8.29333	−0.0458146
$9$	384.918	1.58403
$10$	−109.709	−0.346932
$11$	744.226	1.85448	0.927242	−	0.374463i	$-0.122173\pi$
$11$	744.226	1.85448	0.927242	+	0.374463i	$0.122173\pi$
$12$	827.636	1.65915
$13$	−222.474	−0.365108	−0.182554	−	0.983196i	$-0.558436\pi$
$13$	−222.474	−0.365108	−0.182554	+	0.983196i	$0.558436\pi$
$14$	−1678.53	−2.28881
$15$	340.913	0.391215
$16$	−990.032	−0.966828
$17$	289.000	0.242536
$17$	289.000	0.242536
$18$	−3103.99	−2.25808
$19$	1181.60	0.750905	0.375453	−	0.926842i	$-0.377487\pi$
$19$	1181.60	0.750905	0.375453	+	0.926842i	$0.377487\pi$
$20$	449.346	0.251192
$21$	5215.91	2.58096
$22$	−6001.45	−2.64362
$23$	−4065.70	−1.60257	−0.801283	−	0.598286i	$-0.795849\pi$
$23$	−4065.70	−1.60257	−0.801283	+	0.598286i	$0.795849\pi$
$24$	−207.817	−0.0736466
$25$	−2939.91	−0.940771
$26$	1794.04	0.520472
$27$	3556.23	0.938817
$28$	6874.90	1.65719
$29$	−2489.72	−0.549738	−0.274869	−	0.961482i	$-0.588635\pi$
$29$	−2489.72	−0.549738	−0.274869	+	0.961482i	$0.588635\pi$
$30$	−2749.13	−0.557690
$31$	9530.07	1.78111	0.890557	−	0.454872i	$-0.150315\pi$
$31$	9530.07	1.78111	0.890557	+	0.454872i	$0.150315\pi$
$32$	8249.03	1.42406
$33$	18649.0	2.98107
$34$	−2330.50	−0.345742
$35$	2831.85	0.390752
$36$	12713.3	1.63493
$37$	2890.91	0.347160	0.173580	−	0.984820i	$-0.444466\pi$
$37$	2890.91	0.347160	0.173580	+	0.984820i	$0.444466\pi$
$38$	−9528.42	−1.07044
$39$	−5574.82	−0.586907
$40$	−112.829	−0.0111499
$41$	12453.1	1.15696	0.578480	−	0.815697i	$-0.303646\pi$
$41$	12453.1	1.15696	0.578480	+	0.815697i	$0.303646\pi$
$42$	−42061.2	−3.67924
$43$	−1238.62	−0.102157	−0.0510784	−	0.998695i	$-0.516266\pi$
$43$	−1238.62	−0.102157	−0.0510784	+	0.998695i	$0.516266\pi$
$44$	24580.6	1.91408
$45$	5236.74	0.385505
$46$	32785.9	2.28451
$47$	−1473.58	−0.0973040	−0.0486520	−	0.998816i	$-0.515493\pi$
$47$	−1473.58	−0.0973040	−0.0486520	+	0.998816i	$0.515493\pi$
$48$	−24808.5	−1.55417
$49$	26519.8	1.57790
$50$	23707.5	1.34110
$51$	7241.85	0.389874
$52$	−7347.97	−0.376842
$53$	23802.6	1.16395	0.581975	−	0.813206i	$-0.302280\pi$
$53$	23802.6	1.16395	0.581975	+	0.813206i	$0.302280\pi$
$54$	−28677.5	−1.33831
$55$	10125.1	0.451326
$56$	−1726.26	−0.0735592
$57$	29608.8	1.20707
$58$	20077.2	0.783669
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	11259.8	0.403789
$61$	−8626.84	−0.296843	−0.148422	−	0.988924i	$-0.547419\pi$
$61$	−8626.84	−0.296843	−0.148422	+	0.988924i	$0.547419\pi$
$62$	−76850.6	−2.53903
$63$	80121.1	2.54329
$64$	−34839.3	−1.06321
$65$	−3026.72	−0.0888564
$66$	−150386.	−4.24960
$67$	−34830.5	−0.947923	−0.473962	−	0.880545i	$-0.657176\pi$
$67$	−34830.5	−0.947923	−0.473962	+	0.880545i	$0.657176\pi$
$68$	9545.22	0.250330
$69$	−101880.	−2.57611
$70$	−22836.1	−0.557028
$71$	−53647.1	−1.26299	−0.631496	−	0.775379i	$-0.717559\pi$
$71$	−53647.1	−1.26299	−0.631496	+	0.775379i	$0.717559\pi$
$72$	−3192.26	−0.0725715
$73$	−15244.8	−0.334823	−0.167412	−	0.985887i	$-0.553541\pi$
$73$	−15244.8	−0.334823	−0.167412	+	0.985887i	$0.553541\pi$
$74$	−23312.3	−0.494888
$75$	−73669.1	−1.51228
$76$	39026.3	0.775038
$77$	154911.	2.97753
$78$	44955.5	0.836655
$79$	86800.3	1.56478	0.782390	−	0.622789i	$-0.214000\pi$
$79$	86800.3	1.56478	0.782390	+	0.622789i	$0.214000\pi$
$80$	−13469.2	−0.235297
$81$	−4421.99	−0.0748869
$82$	−100422.	−1.64928
$83$	32456.7	0.517141	0.258570	−	0.965992i	$-0.416749\pi$
$83$	32456.7	0.517141	0.258570	+	0.965992i	$0.416749\pi$
$84$	172273.	2.66391
$85$	3931.79	0.0590260
$86$	9988.26	0.145628
$87$	−62388.2	−0.883699
$88$	−6172.11	−0.0849624
$89$	122571.	1.64026	0.820129	−	0.572179i	$-0.193902\pi$
$89$	122571.	1.64026	0.820129	+	0.572179i	$0.193902\pi$
$90$	−42229.2	−0.549549
$91$	−46308.2	−0.586211
$92$	−134284.	−1.65407
$93$	238807.	2.86312
$94$	11883.0	0.138710
$95$	16075.4	0.182748
$96$	206707.	2.28916
$97$	72378.4	0.781052	0.390526	−	0.920592i	$-0.372293\pi$
$97$	72378.4	0.781052	0.390526	+	0.920592i	$0.372293\pi$
$98$	−213856.	−2.24935
$99$	286466.	2.93755
$100$	−97100.6	−0.971006
$101$	56699.4	0.553064	0.276532	−	0.961005i	$-0.410815\pi$
$101$	56699.4	0.553064	0.276532	+	0.961005i	$0.410815\pi$
$102$	−58398.4	−0.555777
$103$	−62027.9	−0.576095	−0.288047	−	0.957616i	$-0.593006\pi$
$103$	−62027.9	−0.576095	−0.288047	+	0.957616i	$0.593006\pi$
$104$	1845.05	0.0167273
$105$	70961.4	0.628129
$106$	−191945.	−1.65925
$107$	−100494.	−0.848560	−0.424280	−	0.905531i	$-0.639473\pi$
$107$	−100494.	−0.848560	−0.424280	+	0.905531i	$0.639473\pi$
$108$	117457.	0.968989
$109$	−50285.4	−0.405393	−0.202696	−	0.979242i	$-0.564970\pi$
$109$	−50285.4	−0.405393	−0.202696	+	0.979242i	$0.564970\pi$
$110$	−81648.6	−0.643380
$111$	72441.2	0.558057
$112$	−206076.	−1.55232
$113$	167538.	1.23429	0.617146	−	0.786848i	$-0.288289\pi$
$113$	167538.	1.23429	0.617146	+	0.786848i	$0.288289\pi$
$114$	−238766.	−1.72072
$115$	−55313.1	−0.390017
$116$	−82231.6	−0.567406
$117$	−85634.4	−0.578340
$118$	28070.9	0.185588
$119$	60155.6	0.389411
$120$	−2827.31	−0.0179234
$121$	392821.	2.43911
$122$	69567.0	0.423159
$123$	312054.	1.85980
$124$	314763.	1.83836
$125$	−82511.9	−0.472326
$126$	−646098.	−3.62554
$127$	158701.	0.873110	0.436555	−	0.899677i	$-0.356198\pi$
$127$	158701.	0.873110	0.436555	+	0.899677i	$0.356198\pi$
$128$	16976.0	0.0915819
$129$	−31037.7	−0.164216
$130$	24407.5	0.126668
$131$	−146328.	−0.744990	−0.372495	−	0.928034i	$-0.621498\pi$
$131$	−146328.	−0.744990	−0.372495	+	0.928034i	$0.621498\pi$
$132$	615948.	3.07687
$133$	245950.	1.20564
$134$	280874.	1.35129
$135$	48381.9	0.228480
$136$	−2396.77	−0.0111117
$137$	−392401.	−1.78619	−0.893096	−	0.449866i	$-0.851472\pi$
$137$	−392401.	−1.78619	−0.893096	+	0.449866i	$0.851472\pi$
$138$	821559.	3.67232
$139$	−273185.	−1.19928	−0.599638	−	0.800271i	$-0.704689\pi$
$139$	−273185.	−1.19928	−0.599638	+	0.800271i	$0.704689\pi$
$140$	93531.7	0.403310
$141$	−36925.5	−0.156415
$142$	432611.	1.80043
$143$	−165571.	−0.677086
$144$	−381082.	−1.53148
$145$	−33872.2	−0.133790
$146$	122935.	0.477301
$147$	664541.	2.53646
$148$	95482.2	0.358317
$149$	−214.130	−0.000790154 0	−0.000395077	−	1.00000i	$-0.500126\pi$
$149$	−214.130	−0.000790154 0	−0.000395077		1.00000i	$0.500126\pi$
$150$	594069.	2.15580
$151$	153604.	0.548227	0.274114	−	0.961697i	$-0.411616\pi$
$151$	153604.	0.548227	0.274114	+	0.961697i	$0.411616\pi$
$152$	−9799.37	−0.0344024
$153$	111241.	0.384183
$154$	−1.24921e6	−4.24456
$155$	129655.	0.433470
$156$	−184128.	−0.605770
$157$	26383.7	0.0854254	0.0427127	−	0.999087i	$-0.486400\pi$
$157$	26383.7	0.0854254	0.0427127	+	0.999087i	$0.486400\pi$
$158$	−699959.	−2.23064
$159$	596453.	1.87104
$160$	112226.	0.346574
$161$	−846279.	−2.57305
$162$	35659.1	0.106754
$163$	24563.7	0.0724143	0.0362072	−	0.999344i	$-0.488472\pi$
$163$	24563.7	0.0724143	0.0362072	+	0.999344i	$0.488472\pi$
$164$	411307.	1.19414
$165$	253717.	0.725503
$166$	−261731.	−0.737200
$167$	14357.9	0.0398383	0.0199191	−	0.999802i	$-0.493659\pi$
$167$	14357.9	0.0398383	0.0199191	+	0.999802i	$0.493659\pi$
$168$	−43257.2	−0.118246
$169$	−321798.	−0.866696
$170$	−31706.0	−0.0841433
$171$	454818.	1.18945
$172$	−40909.7	−0.105440
$173$	570234.	1.44856	0.724282	−	0.689504i	$-0.242171\pi$
$173$	570234.	1.44856	0.724282	+	0.689504i	$0.242171\pi$
$174$	503100.	1.25974
$175$	−611945.	−1.51049
$176$	−736808.	−1.79297
$177$	−87227.9	−0.209277
$178$	−988413.	−2.33824
$179$	−456933.	−1.06591	−0.532954	−	0.846144i	$-0.678918\pi$
$179$	−456933.	−1.06591	−0.532954	+	0.846144i	$0.678918\pi$
$180$	172961.	0.397895
$181$	−259913.	−0.589701	−0.294850	−	0.955543i	$-0.595270\pi$
$181$	−259913.	−0.589701	−0.294850	+	0.955543i	$0.595270\pi$
$182$	373430.	0.835662
$183$	−216174.	−0.477173
$184$	33718.2	0.0734209
$185$	39330.3	0.0844885
$186$	−1.92575e6	−4.08147
$187$	215081.	0.449778
$188$	−48670.2	−0.100431
$189$	740233.	1.50735
$190$	−129632.	−0.260513
$191$	−320676.	−0.636037	−0.318019	−	0.948084i	$-0.603017\pi$
$191$	−320676.	−0.636037	−0.318019	+	0.948084i	$0.603017\pi$
$192$	−873014.	−1.70910
$193$	626329.	1.21035	0.605173	−	0.796094i	$-0.293104\pi$
$193$	626329.	1.21035	0.605173	+	0.796094i	$0.293104\pi$
$194$	−583661.	−1.11341
$195$	−75844.4	−0.142836
$196$	875907.	1.62861
$197$	−594136.	−1.09074	−0.545369	−	0.838196i	$-0.683610\pi$
$197$	−594136.	−1.09074	−0.545369	+	0.838196i	$0.683610\pi$
$198$	−2.31007e6	−4.18757
$199$	−534569.	−0.956910	−0.478455	−	0.878112i	$-0.658803\pi$
$199$	−534569.	−0.956910	−0.478455	+	0.878112i	$0.658803\pi$
$200$	24381.6	0.0431011
$201$	−872794.	−1.52378
$202$	−457225.	−0.788410
$203$	−518238.	−0.882651
$204$	239187.	0.402404
$205$	169422.	0.281569
$206$	500194.	0.821241
$207$	−1.56496e6	−2.53851
$208$	220257.	0.352997
$209$	879375.	1.39254
$210$	−572235.	−0.895418
$211$	−931232.	−1.43997	−0.719983	−	0.693992i	$-0.755850\pi$
$211$	−931232.	−1.43997	−0.719983	+	0.693992i	$0.755850\pi$
$212$	786162.	1.20136
$213$	−1.34431e6	−2.03025
$214$	810389.	1.20965
$215$	−16851.2	−0.0248619
$216$	−29493.0	−0.0430115
$217$	1.98369e6	2.85973
$218$	405503.	0.577900
$219$	−382010.	−0.538225
$220$	334415.	0.465831
$221$	−64295.0	−0.0885516
$222$	−584168.	−0.795527
$223$	−991861.	−1.33564	−0.667819	−	0.744324i	$-0.732772\pi$
$223$	−991861.	−1.33564	−0.667819	+	0.744324i	$0.732772\pi$
$224$	1.71704e6	2.28645
$225$	−1.13163e6	−1.49021
$226$	−1.35103e6	−1.75952
$227$	948998.	1.22236	0.611182	−	0.791490i	$-0.290694\pi$
$227$	948998.	1.22236	0.611182	+	0.791490i	$0.290694\pi$
$228$	977932.	1.24587
$229$	1.10372e6	1.39081	0.695407	−	0.718616i	$-0.255224\pi$
$229$	1.10372e6	1.39081	0.695407	+	0.718616i	$0.255224\pi$
$230$	446046.	0.555981
$231$	3.88181e6	4.78635
$232$	20648.1	0.0251860
$233$	1.29921e6	1.56780	0.783899	−	0.620888i	$-0.213228\pi$
$233$	1.29921e6	1.56780	0.783899	+	0.620888i	$0.213228\pi$
$234$	690557.	0.824442
$235$	−20047.8	−0.0236809
$236$	−114972.	−0.134373
$237$	2.17507e6	2.51537
$238$	−485096.	−0.555118
$239$	−1.38120e6	−1.56409	−0.782044	−	0.623223i	$-0.785823\pi$
$239$	−1.38120e6	−1.56409	−0.782044	+	0.623223i	$0.785823\pi$
$240$	−337515.	−0.378238
$241$	−397201.	−0.440523	−0.220261	−	0.975441i	$-0.570691\pi$
$241$	−397201.	−0.440523	−0.220261	+	0.975441i	$0.570691\pi$
$242$	−3.16772e6	−3.47703
$243$	−974973.	−1.05920
$244$	−284931.	−0.306383
$245$	360797.	0.384014
$246$	−2.51641e6	−2.65120
$247$	−262875.	−0.274161
$248$	−79036.0	−0.0816010
$249$	813309.	0.831299
$250$	665378.	0.673315
$251$	−529279.	−0.530274	−0.265137	−	0.964211i	$-0.585417\pi$
$251$	−529279.	−0.530274	−0.265137	+	0.964211i	$0.585417\pi$
$252$	2.64627e6	2.62503
$253$	−3.02580e6	−2.97193
$254$	−1.27976e6	−1.24465
$255$	98524.0	0.0948837
$256$	977963.	0.932658
$257$	−1.19028e6	−1.12413	−0.562063	−	0.827095i	$-0.689992\pi$
$257$	−1.19028e6	−1.12413	−0.562063	+	0.827095i	$0.689992\pi$
$258$	250289.	0.234095
$259$	601745.	0.557395
$260$	−99967.8	−0.0917121
$261$	−958340.	−0.870800
$262$	1.18000e6	1.06201
$263$	1.84279e6	1.64281	0.821405	−	0.570346i	$-0.193191\pi$
$263$	1.84279e6	1.64281	0.821405	+	0.570346i	$0.193191\pi$
$264$	−154663.	−0.136576
$265$	323830.	0.283271
$266$	−1.98335e6	−1.71868
$267$	3.07142e6	2.63670
$268$	−1.15040e6	−0.978388
$269$	1.33152e6	1.12194	0.560968	−	0.827837i	$-0.310429\pi$
$269$	1.33152e6	1.12194	0.560968	+	0.827837i	$0.310429\pi$
$270$	−390153.	−0.325706
$271$	−729929.	−0.603750	−0.301875	−	0.953347i	$-0.597613\pi$
$271$	−729929.	−0.603750	−0.301875	+	0.953347i	$0.597613\pi$
$272$	−286119.	−0.234490
$273$	−1.16040e6	−0.942329
$274$	3.16433e6	2.54627
$275$	−2.18796e6	−1.74464
$276$	−3.36492e6	−2.65890
$277$	−1.02524e6	−0.802836	−0.401418	−	0.915895i	$-0.631483\pi$
$277$	−1.02524e6	−0.802836	−0.401418	+	0.915895i	$0.631483\pi$
$278$	2.20297e6	1.70961
$279$	3.66830e6	2.82133
$280$	−23485.5	−0.0179021
$281$	−856834.	−0.647338	−0.323669	−	0.946170i	$-0.604916\pi$
$281$	−856834.	−0.647338	−0.323669	+	0.946170i	$0.604916\pi$
$282$	297768.	0.222975
$283$	1.29773e6	0.963205	0.481603	−	0.876390i	$-0.340055\pi$
$283$	1.29773e6	0.963205	0.481603	+	0.876390i	$0.340055\pi$
$284$	−1.77188e6	−1.30358
$285$	402822.	0.293766
$286$	1.33517e6	0.965208
$287$	2.59212e6	1.85760
$288$	3.17520e6	2.25575
$289$	83521.0	0.0588235
$290$	273146.	0.190722
$291$	1.81368e6	1.25553
$292$	−503513.	−0.345584
$293$	2.51081e6	1.70862	0.854310	−	0.519763i	$-0.173980\pi$
$293$	2.51081e6	1.70862	0.854310	+	0.519763i	$0.173980\pi$
$294$	−5.35887e6	−3.61580
$295$	−47358.4	−0.0316841
$296$	−23975.3	−0.0159050
$297$	2.64664e6	1.74102
$298$	1726.75	0.00112639
$299$	904513.	0.585109
$300$	−2.43318e6	−1.56088
$301$	−257820.	−0.164021
$302$	−1.23867e6	−0.781515
$303$	1.42079e6	0.889045
$304$	−1.16982e6	−0.725997
$305$	−117367.	−0.0722428
$306$	−897053.	−0.547665
$307$	3.01530e6	1.82593	0.912966	−	0.408035i	$-0.133786\pi$
$307$	3.01530e6	1.82593	0.912966	+	0.408035i	$0.133786\pi$
$308$	5.11648e6	3.07322
$309$	−1.55431e6	−0.926067
$310$	−1.04554e6	−0.617925
$311$	−271964.	−0.159445	−0.0797224	−	0.996817i	$-0.525403\pi$
$311$	−271964.	−0.159445	−0.0797224	+	0.996817i	$0.525403\pi$
$312$	46233.8	0.0268889
$313$	−3.05595e6	−1.76313	−0.881566	−	0.472061i	$-0.843510\pi$
$313$	−3.05595e6	−1.76313	−0.881566	+	0.472061i	$0.843510\pi$
$314$	−212759.	−0.121777
$315$	1.09003e6	0.618961
$316$	2.86688e6	1.61507
$317$	2.73312e6	1.52761	0.763803	−	0.645450i	$-0.223330\pi$
$317$	2.73312e6	1.52761	0.763803	+	0.645450i	$0.223330\pi$
$318$	−4.80981e6	−2.66723
$319$	−1.85292e6	−1.01948
$320$	−473982.	−0.258754
$321$	−2.51822e6	−1.36405
$322$	6.82441e6	3.66797
$323$	341481.	0.182121
$324$	−146052.	−0.0772936
$325$	654054.	0.343483
$326$	−198082.	−0.103229
$327$	−1.26007e6	−0.651665
$328$	−103278.	−0.0530056
$329$	−306728.	−0.156230
$330$	−2.04598e6	−1.03423
$331$	438603.	0.220040	0.110020	−	0.993929i	$-0.464909\pi$
$331$	438603.	0.220040	0.110020	+	0.993929i	$0.464909\pi$
$332$	1.07199e6	0.533761
$333$	1.11276e6	0.549911
$334$	−115783.	−0.0567907
$335$	−473863.	−0.230696
$336$	−5.16392e6	−2.49535
$337$	647957.	0.310793	0.155396	−	0.987852i	$-0.450334\pi$
$337$	647957.	0.310793	0.155396	+	0.987852i	$0.450334\pi$
$338$	2.59499e6	1.23550
$339$	4.19823e6	1.98411
$340$	129861.	0.0609230
$341$	7.09252e6	3.30305
$342$	−3.66766e6	−1.69560
$343$	2.02172e6	0.927869
$344$	10272.3	0.00468027
$345$	−1.38605e6	−0.626949
$346$	−4.59838e6	−2.06497
$347$	705544.	0.314558	0.157279	−	0.987554i	$-0.449728\pi$
$347$	705544.	0.314558	0.157279	+	0.987554i	$0.449728\pi$
$348$	−2.06059e6	−0.912100
$349$	−1.36886e6	−0.601584	−0.300792	−	0.953690i	$-0.597251\pi$
$349$	−1.36886e6	−0.601584	−0.300792	+	0.953690i	$0.597251\pi$
$350$	4.93473e6	2.15325
$351$	−791170.	−0.342769
$352$	6.13914e6	2.64089
$353$	−1.86575e6	−0.796922	−0.398461	−	0.917185i	$-0.630456\pi$
$353$	−1.86575e6	−0.796922	−0.398461	+	0.917185i	$0.630456\pi$
$354$	703408.	0.298332
$355$	−729859.	−0.307375
$356$	4.04832e6	1.69297
$357$	1.50740e6	0.625975
$358$	3.68472e6	1.51949
$359$	−2.36139e6	−0.967011	−0.483506	−	0.875341i	$-0.660637\pi$
$359$	−2.36139e6	−0.967011	−0.483506	+	0.875341i	$0.660637\pi$
$360$	−43430.0	−0.0176618
$361$	−1.07993e6	−0.436141
$362$	2.09594e6	0.840637
$363$	9.84343e6	3.92085
$364$	−1.52949e6	−0.605051
$365$	−207403.	−0.0814860
$366$	1.74323e6	0.680224
$367$	−1.70048e6	−0.659031	−0.329515	−	0.944150i	$-0.606885\pi$
$367$	−1.70048e6	−0.659031	−0.329515	+	0.944150i	$0.606885\pi$
$368$	4.02518e6	1.54941
$369$	4.79343e6	1.83265
$370$	−317160.	−0.120441
$371$	4.95453e6	1.86882
$372$	7.88743e6	2.95514
$373$	1.71653e6	0.638823	0.319411	−	0.947616i	$-0.396515\pi$
$373$	1.71653e6	0.638823	0.319411	+	0.947616i	$0.396515\pi$
$374$	−1.73442e6	−0.641173
$375$	−2.06761e6	−0.759260
$376$	12220.9	0.00445794
$377$	553899.	0.200714
$378$	−5.96926e6	−2.14877
$379$	−3.15646e6	−1.12876	−0.564380	−	0.825515i	$-0.690885\pi$
$379$	−3.15646e6	−1.12876	−0.564380	+	0.825515i	$0.690885\pi$
$380$	530945.	0.188621
$381$	3.97677e6	1.40352
$382$	2.58593e6	0.906691
$383$	−1.17520e6	−0.409371	−0.204685	−	0.978828i	$-0.565617\pi$
$383$	−1.17520e6	−0.409371	−0.204685	+	0.978828i	$0.565617\pi$
$384$	425389.	0.147217
$385$	2.10754e6	0.724642
$386$	−5.05073e6	−1.72539
$387$	−476768.	−0.161819
$388$	2.39055e6	0.806154
$389$	−697644.	−0.233755	−0.116877	−	0.993146i	$-0.537288\pi$
$389$	−697644.	−0.233755	−0.116877	+	0.993146i	$0.537288\pi$
$390$	611611.	0.203617
$391$	−1.17499e6	−0.388679
$392$	−219937.	−0.0722909
$393$	−3.66674e6	−1.19756
$394$	4.79112e6	1.55488
$395$	1.18090e6	0.380821
$396$	9.46153e6	3.03196
$397$	734217.	0.233802	0.116901	−	0.993144i	$-0.462704\pi$
$397$	734217.	0.233802	0.116901	+	0.993144i	$0.462704\pi$
$398$	4.31078e6	1.36410
$399$	6.16310e6	1.93806
$400$	2.91061e6	0.909564
$401$	406205.	0.126149	0.0630746	−	0.998009i	$-0.479909\pi$
$401$	406205.	0.126149	0.0630746	+	0.998009i	$0.479909\pi$
$402$	7.03823e6	2.17219
$403$	−2.12019e6	−0.650298
$404$	1.87269e6	0.570839
$405$	−60160.4	−0.0182252
$406$	4.17908e6	1.25825
$407$	2.15149e6	0.643803
$408$	−60059.0	−0.0178619
$409$	−98249.3	−0.0290417	−0.0145208	−	0.999895i	$-0.504622\pi$
$409$	−98249.3	−0.0290417	−0.0145208	+	0.999895i	$0.504622\pi$
$410$	−1.36622e6	−0.401386
$411$	−9.83289e6	−2.87129
$412$	−2.04868e6	−0.594610
$413$	−724573.	−0.209029
$414$	1.26199e7	3.61872
$415$	441567.	0.125857
$416$	−1.83520e6	−0.519935
$417$	−6.84554e6	−1.92783
$418$	−7.09129e6	−1.98511
$419$	1.22877e6	0.341928	0.170964	−	0.985277i	$-0.445312\pi$
$419$	1.22877e6	0.341928	0.170964	+	0.985277i	$0.445312\pi$
$420$	2.34375e6	0.648317
$421$	−3.96412e6	−1.09004	−0.545019	−	0.838423i	$-0.683478\pi$
$421$	−3.96412e6	−1.09004	−0.545019	+	0.838423i	$0.683478\pi$
$422$	7.50948e6	2.05271
$423$	−567210.	−0.154132
$424$	−197403.	−0.0533260
$425$	−849634.	−0.228170
$426$	1.08405e7	2.89418
$427$	−1.79568e6	−0.476607
$428$	−3.31917e6	−0.875832
$429$	−4.14893e6	−1.08841
$430$	135888.	0.0354414
$431$	−2.02950e6	−0.526255	−0.263127	−	0.964761i	$-0.584754\pi$
$431$	−2.02950e6	−0.526255	−0.263127	+	0.964761i	$0.584754\pi$
$432$	−3.52079e6	−0.907675
$433$	−5.07156e6	−1.29994	−0.649968	−	0.759962i	$-0.725218\pi$
$433$	−5.07156e6	−1.29994	−0.649968	+	0.759962i	$0.725218\pi$
$434$	−1.59965e7	−4.07663
$435$	−848780.	−0.215066
$436$	−1.66085e6	−0.418421
$437$	−4.80402e6	−1.20338
$438$	3.08053e6	0.767257
$439$	4.45732e6	1.10386	0.551928	−	0.833892i	$-0.313892\pi$
$439$	4.45732e6	1.10386	0.551928	+	0.833892i	$0.313892\pi$
$440$	−83970.4	−0.0206773
$441$	1.02080e7	2.49944
$442$	518476.	0.126233
$443$	−238245.	−0.0576785	−0.0288392	−	0.999584i	$-0.509181\pi$
$443$	−238245.	−0.0576785	−0.0288392	+	0.999584i	$0.509181\pi$
$444$	2.39262e6	0.575992
$445$	1.66755e6	0.399190
$446$	7.99839e6	1.90399
$447$	−5365.73	−0.00127016
$448$	−7.25183e6	−1.70708
$449$	4.62606e6	1.08292	0.541459	−	0.840727i	$-0.317872\pi$
$449$	4.62606e6	1.08292	0.541459	+	0.840727i	$0.317872\pi$
$450$	9.12545e6	2.12433
$451$	9.26792e6	2.14556
$452$	5.53353e6	1.27396
$453$	3.84906e6	0.881270
$454$	−7.65274e6	−1.74252
$455$	−630014.	−0.142666
$456$	−245556.	−0.0553016
$457$	−2.30085e6	−0.515344	−0.257672	−	0.966232i	$-0.582955\pi$
$457$	−2.30085e6	−0.515344	−0.257672	+	0.966232i	$0.582955\pi$
$458$	−8.90040e6	−1.98265
$459$	1.02775e6	0.227697
$460$	−1.82691e6	−0.402552
$461$	7.05654e6	1.54646	0.773232	−	0.634124i	$-0.218639\pi$
$461$	7.05654e6	1.54646	0.773232	+	0.634124i	$0.218639\pi$
$462$	−3.13030e7	−6.82309
$463$	−1.22594e6	−0.265777	−0.132888	−	0.991131i	$-0.542425\pi$
$463$	−1.22594e6	−0.265777	−0.132888	+	0.991131i	$0.542425\pi$
$464$	2.46491e6	0.531503
$465$	3.24893e6	0.696799
$466$	−1.04769e7	−2.23495
$467$	8.44907e6	1.79274	0.896369	−	0.443310i	$-0.146196\pi$
$467$	8.44907e6	1.79274	0.896369	+	0.443310i	$0.146196\pi$
$468$	−2.82837e6	−0.596927
$469$	−7.25001e6	−1.52197
$470$	161666.	0.0337578
$471$	661132.	0.137321
$472$	28869.1	0.00596455
$473$	−921813.	−0.189448
$474$	−1.75398e7	−3.58574
$475$	−3.47379e6	−0.706430
$476$	1.98685e6	0.401927
$477$	9.16206e6	1.84373
$478$	1.11380e7	2.22966
$479$	5.08497e6	1.01263	0.506314	−	0.862349i	$-0.331008\pi$
$479$	5.08497e6	1.01263	0.506314	+	0.862349i	$0.331008\pi$
$480$	2.81220e6	0.557114
$481$	−643152.	−0.126751
$482$	3.20304e6	0.627979
$483$	−2.12063e7	−4.13616
$484$	1.29743e7	2.51750
$485$	984695.	0.190085
$486$	7.86220e6	1.50992
$487$	−1.37498e6	−0.262709	−0.131354	−	0.991335i	$-0.541933\pi$
$487$	−1.37498e6	−0.262709	−0.131354	+	0.991335i	$0.541933\pi$
$488$	71545.2	0.0135998
$489$	615524.	0.116405
$490$	−2.90947e6	−0.547424
$491$	3.56304e6	0.666987	0.333494	−	0.942752i	$-0.391772\pi$
$491$	3.56304e6	0.666987	0.333494	+	0.942752i	$0.391772\pi$
$492$	1.03066e7	1.91957
$493$	−719530.	−0.133331
$494$	2.11983e6	0.390825
$495$	3.89732e6	0.714913
$496$	−9.43507e6	−1.72203
$497$	−1.11667e7	−2.02784
$498$	−6.55854e6	−1.18504
$499$	−6.18539e6	−1.11203	−0.556014	−	0.831173i	$-0.687670\pi$
$499$	−6.18539e6	−1.11203	−0.556014	+	0.831173i	$0.687670\pi$
$500$	−2.72524e6	−0.487506
$501$	359785.	0.0640397
$502$	4.26812e6	0.755922
$503$	6.70731e6	1.18203	0.591015	−	0.806661i	$-0.298727\pi$
$503$	6.70731e6	1.18203	0.591015	+	0.806661i	$0.298727\pi$
$504$	−664471.	−0.116520
$505$	771385.	0.134599
$506$	2.44001e7	4.23658
$507$	−8.06372e6	−1.39321
$508$	5.24163e6	0.901171
$509$	−2.53640e6	−0.433934	−0.216967	−	0.976179i	$-0.569616\pi$
$509$	−2.53640e6	−0.433934	−0.216967	+	0.976179i	$0.569616\pi$
$510$	−794500.	−0.135260
$511$	−3.17323e6	−0.537587
$512$	−8.42955e6	−1.42112
$513$	4.20203e6	0.704963
$514$	9.59841e6	1.60248
$515$	−843878.	−0.140204
$516$	−1.02513e6	−0.169494
$517$	−1.09668e6	−0.180449
$518$	−4.85248e6	−0.794584
$519$	1.42891e7	2.32855
$520$	25101.6	0.00407092
$521$	−2.25380e6	−0.363766	−0.181883	−	0.983320i	$-0.558219\pi$
$521$	−2.25380e6	−0.363766	−0.181883	+	0.983320i	$0.558219\pi$
$522$	7.72807e6	1.24135
$523$	−6.82049e6	−1.09034	−0.545169	−	0.838326i	$-0.683535\pi$
$523$	−6.82049e6	−1.09034	−0.545169	+	0.838326i	$0.683535\pi$
$524$	−4.83300e6	−0.768933
$525$	−1.53343e7	−2.42809
$526$	−1.48603e7	−2.34188
$527$	2.75419e6	0.431984
$528$	−1.84631e7	−2.88218
$529$	1.00936e7	1.56822
$530$	−2.61137e6	−0.403812
$531$	−1.33990e6	−0.206223
$532$	8.12335e6	1.24439
$533$	−2.77049e6	−0.422415
$534$	−2.47680e7	−3.75870
$535$	−1.36721e6	−0.206514
$536$	288861.	0.0434287
$537$	−1.14500e7	−1.71344
$538$	−1.07374e7	−1.59936
$539$	1.97367e7	2.92619
$540$	1.59798e6	0.235823
$541$	1.23696e7	1.81704	0.908518	−	0.417846i	$-0.137215\pi$
$541$	1.23696e7	1.81704	0.908518	+	0.417846i	$0.137215\pi$
$542$	5.88616e6	0.860665
$543$	−6.51298e6	−0.947938
$544$	2.38397e6	0.345385
$545$	−684124.	−0.0986605
$546$	9.35752e6	1.34332
$547$	−4.22295e6	−0.603459	−0.301730	−	0.953394i	$-0.597564\pi$
$547$	−4.22295e6	−0.603459	−0.301730	+	0.953394i	$0.597564\pi$
$548$	−1.29604e7	−1.84360
$549$	−3.32063e6	−0.470207
$550$	1.76437e7	2.48704
$551$	−2.94185e6	−0.412801
$552$	844921.	0.118023
$553$	1.80675e7	2.51239
$554$	8.26758e6	1.14447
$555$	985549.	0.135814
$556$	−9.02286e6	−1.23782
$557$	−708616.	−0.0967772	−0.0483886	−	0.998829i	$-0.515409\pi$
$557$	−708616.	−0.0967772	−0.0483886	+	0.998829i	$0.515409\pi$
$558$	−2.95812e7	−4.02189
$559$	275561.	0.0372982
$560$	−2.80363e6	−0.377790
$561$	5.38957e6	0.723015
$562$	6.90953e6	0.922800
$563$	−8.99722e6	−1.19629	−0.598146	−	0.801387i	$-0.704096\pi$
$563$	−8.99722e6	−1.19629	−0.598146	+	0.801387i	$0.704096\pi$
$564$	−1.21959e6	−0.161442
$565$	2.27933e6	0.300390
$566$	−1.04649e7	−1.37308
$567$	−920442.	−0.120237
$568$	444913.	0.0578635
$569$	−5.53729e6	−0.716996	−0.358498	−	0.933530i	$-0.616711\pi$
$569$	−5.53729e6	−0.716996	−0.358498	+	0.933530i	$0.616711\pi$
$570$	−3.24837e6	−0.418772
$571$	5.68899e6	0.730205	0.365102	−	0.930967i	$-0.381034\pi$
$571$	5.68899e6	0.730205	0.365102	+	0.930967i	$0.381034\pi$
$572$	−5.46855e6	−0.698847
$573$	−8.03558e6	−1.02242
$574$	−2.09030e7	−2.64806
$575$	1.19528e7	1.50765
$576$	−1.34103e7	−1.68415
$577$	1.55537e6	0.194489	0.0972445	−	0.995261i	$-0.468997\pi$
$577$	1.55537e6	0.194489	0.0972445	+	0.995261i	$0.468997\pi$
$578$	−673515.	−0.0838548
$579$	1.56947e7	1.94562
$580$	−1.11875e6	−0.138090
$581$	6.75588e6	0.830313
$582$	−1.46256e7	−1.78980
$583$	1.77145e7	2.15853
$584$	126430.	0.0153398
$585$	−1.16504e6	−0.140751
$586$	−2.02473e7	−2.43569
$587$	−1.07063e7	−1.28247	−0.641233	−	0.767346i	$-0.721577\pi$
$587$	−1.07063e7	−1.28247	−0.641233	+	0.767346i	$0.721577\pi$
$588$	2.19487e7	2.61798
$589$	1.12607e7	1.33745
$590$	381899.	0.0451667
$591$	−1.48880e7	−1.75335
$592$	−2.86209e6	−0.335644
$593$	807100.	0.0942520	0.0471260	−	0.998889i	$-0.484994\pi$
$593$	807100.	0.0942520	0.0471260	+	0.998889i	$0.484994\pi$
$594$	−2.13426e7	−2.48188
$595$	818406.	0.0947712
$596$	−7072.38	−0.000815548 0
$597$	−1.33954e7	−1.53822
$598$	−7.29401e6	−0.834091
$599$	1.52584e7	1.73757	0.868787	−	0.495186i	$-0.164900\pi$
$599$	1.52584e7	1.73757	0.868787	+	0.495186i	$0.164900\pi$
$600$	610962.	0.0692845
$601$	9.94019e6	1.12256	0.561279	−	0.827627i	$-0.310310\pi$
$601$	9.94019e6	1.12256	0.561279	+	0.827627i	$0.310310\pi$
$602$	2.07907e6	0.233817
$603$	−1.34069e7	−1.50154
$604$	5.07330e6	0.565846
$605$	5.34426e6	0.593607
$606$	−1.14573e7	−1.26736
$607$	−1.74643e7	−1.92389	−0.961945	−	0.273242i	$-0.911904\pi$
$607$	−1.74643e7	−1.92389	−0.961945	+	0.273242i	$0.911904\pi$
$608$	9.74702e6	1.06933
$609$	−1.29862e7	−1.41885
$610$	946446.	0.102984
$611$	327834.	0.0355264
$612$	3.67413e6	0.396530
$613$	1.28826e7	1.38468	0.692342	−	0.721569i	$-0.256579\pi$
$613$	1.28826e7	1.38468	0.692342	+	0.721569i	$0.256579\pi$
$614$	−2.43155e7	−2.60292
$615$	4.24543e6	0.452620
$616$	−1.28473e6	−0.136414
$617$	1.37610e6	0.145525	0.0727624	−	0.997349i	$-0.476819\pi$
$617$	1.37610e6	0.145525	0.0727624	+	0.997349i	$0.476819\pi$
$618$	1.25340e7	1.32014
$619$	−7.63175e6	−0.800567	−0.400284	−	0.916391i	$-0.631088\pi$
$619$	−7.63175e6	−0.800567	−0.400284	+	0.916391i	$0.631088\pi$
$620$	4.28229e6	0.447401
$621$	−1.44586e7	−1.50452
$622$	2.19312e6	0.227294
$623$	2.55132e7	2.63357
$624$	5.51925e6	0.567439
$625$	8.06466e6	0.825821
$626$	2.46432e7	2.51340
$627$	2.20356e7	2.23850
$628$	871414.	0.0881709
$629$	835472.	0.0841987
$630$	−8.79005e6	−0.882348
$631$	2.38763e6	0.238723	0.119361	−	0.992851i	$-0.461915\pi$
$631$	2.38763e6	0.238723	0.119361	+	0.992851i	$0.461915\pi$
$632$	−719863.	−0.0716898
$633$	−2.33351e7	−2.31473
$634$	−2.20400e7	−2.17765
$635$	2.15909e6	0.212489
$636$	1.96999e7	1.93117
$637$	−5.89997e6	−0.576104
$638$	1.49420e7	1.45330
$639$	−2.06498e7	−2.00061
$640$	230955.	0.0222883
$641$	1.29400e7	1.24391	0.621956	−	0.783053i	$-0.286338\pi$
$641$	1.29400e7	1.24391	0.621956	+	0.783053i	$0.286338\pi$
$642$	2.03070e7	1.94450
$643$	4.99169e6	0.476124	0.238062	−	0.971250i	$-0.423488\pi$
$643$	4.99169e6	0.476124	0.238062	+	0.971250i	$0.423488\pi$
$644$	−2.79513e7	−2.65575
$645$	−422262.	−0.0399653
$646$	−2.75371e6	−0.259620
$647$	9.33709e6	0.876902	0.438451	−	0.898755i	$-0.355527\pi$
$647$	9.33709e6	0.876902	0.438451	+	0.898755i	$0.355527\pi$
$648$	36673.1	0.00343091
$649$	−2.59065e6	−0.241433
$650$	−5.27430e6	−0.489645
$651$	4.97079e7	4.59699
$652$	811300.	0.0747416
$653$	−3.20892e6	−0.294494	−0.147247	−	0.989100i	$-0.547041\pi$
$653$	−3.20892e6	−0.294494	−0.147247	+	0.989100i	$0.547041\pi$
$654$	1.01612e7	0.928968
$655$	−1.99077e6	−0.181308
$656$	−1.23290e7	−1.11858
$657$	−5.86802e6	−0.530369
$658$	2.47346e6	0.222710
$659$	−5.29936e6	−0.475346	−0.237673	−	0.971345i	$-0.576385\pi$
$659$	−5.29936e6	−0.475346	−0.237673	+	0.971345i	$0.576385\pi$
$660$	8.37986e6	0.748819
$661$	−6.90216e6	−0.614442	−0.307221	−	0.951638i	$-0.599399\pi$
$661$	−6.90216e6	−0.614442	−0.307221	+	0.951638i	$0.599399\pi$
$662$	−3.53690e6	−0.313674
$663$	−1.61112e6	−0.142346
$664$	−269174.	−0.0236926
$665$	3.34611e6	0.293417
$666$	−8.97335e6	−0.783915
$667$	1.01225e7	0.880992
$668$	474220.	0.0411186
$669$	−2.48543e7	−2.14702
$670$	3.82124e6	0.328865
$671$	−6.42032e6	−0.550491
$672$	4.30262e7	3.67544
$673$	−1.75943e7	−1.49739	−0.748695	−	0.662915i	$-0.769319\pi$
$673$	−1.75943e7	−1.49739	−0.748695	+	0.662915i	$0.769319\pi$
$674$	−5.22514e6	−0.443045
$675$	−1.04550e7	−0.883212
$676$	−1.06285e7	−0.894551
$677$	1.72911e7	1.44995	0.724973	−	0.688777i	$-0.241852\pi$
$677$	1.72911e7	1.44995	0.724973	+	0.688777i	$0.241852\pi$
$678$	−3.38546e7	−2.82842
$679$	1.50656e7	1.25404
$680$	−32607.6	−0.00270425
$681$	2.37803e7	1.96494
$682$	−5.71942e7	−4.70859
$683$	−1.43371e7	−1.17601	−0.588003	−	0.808859i	$-0.700086\pi$
$683$	−1.43371e7	−1.17601	−0.588003	+	0.808859i	$0.700086\pi$
$684$	1.50219e7	1.22768
$685$	−5.33854e6	−0.434706
$686$	−1.63032e7	−1.32271
$687$	2.76573e7	2.23572
$688$	1.22627e6	0.0987681
$689$	−5.29546e6	−0.424967
$690$	1.11772e7	0.893735
$691$	−1.99801e7	−1.59185	−0.795927	−	0.605393i	$-0.793016\pi$
$691$	−1.99801e7	−1.59185	−0.795927	+	0.605393i	$0.793016\pi$
$692$	1.88339e7	1.49512
$693$	5.96282e7	4.71649
$694$	−5.68952e6	−0.448412
$695$	−3.71663e6	−0.291868
$696$	517406.	0.0404863
$697$	3.59895e6	0.280604
$698$	1.10385e7	0.857577
$699$	3.25560e7	2.52022
$700$	−2.02116e7	−1.55903
$701$	5.71790e6	0.439482	0.219741	−	0.975558i	$-0.429479\pi$
$701$	5.71790e6	0.439482	0.219741	+	0.975558i	$0.429479\pi$
$702$	6.38001e6	0.488628
$703$	3.41589e6	0.260684
$704$	−2.59283e7	−1.97171
$705$	−502365.	−0.0380668
$706$	1.50454e7	1.13604
$707$	1.18020e7	0.887991
$708$	−2.88100e6	−0.216003
$709$	1.29651e7	0.968637	0.484318	−	0.874892i	$-0.339068\pi$
$709$	1.29651e7	0.968637	0.484318	+	0.874892i	$0.339068\pi$
$710$	5.88560e6	0.438172
$711$	3.34110e7	2.47865
$712$	−1.01652e6	−0.0751477
$713$	−3.87464e7	−2.85435
$714$	−1.21557e7	−0.892347
$715$	−2.25256e6	−0.164783
$716$	−1.50918e7	−1.10017
$717$	−3.46105e7	−2.51426
$718$	1.90423e7	1.37850
$719$	5.38425e6	0.388421	0.194210	−	0.980960i	$-0.437786\pi$
$719$	5.38425e6	0.388421	0.194210	+	0.980960i	$0.437786\pi$
$720$	−5.18454e6	−0.372717
$721$	−1.29112e7	−0.924969
$722$	8.70857e6	0.621733
$723$	−9.95319e6	−0.708136
$724$	−8.58452e6	−0.608653
$725$	7.31956e6	0.517178
$726$	−7.93776e7	−5.58929
$727$	−1.01202e7	−0.710154	−0.355077	−	0.934837i	$-0.615545\pi$
$727$	−1.01202e7	−0.710154	−0.355077	+	0.934837i	$0.615545\pi$
$728$	384049.	0.0268570
$729$	−2.33566e7	−1.62776
$730$	1.67250e6	0.116161
$731$	−357961.	−0.0247767
$732$	−7.13989e6	−0.492508
$733$	−1.74944e7	−1.20265	−0.601324	−	0.799005i	$-0.705360\pi$
$733$	−1.74944e7	−1.20265	−0.601324	+	0.799005i	$0.705360\pi$
$734$	1.37127e7	0.939469
$735$	9.04095e6	0.617299
$736$	−3.35381e7	−2.28215
$737$	−2.59218e7	−1.75791
$738$	−3.86543e7	−2.61250
$739$	−2.40368e7	−1.61907	−0.809534	−	0.587073i	$-0.800280\pi$
$739$	−2.40368e7	−1.61907	−0.809534	+	0.587073i	$0.800280\pi$
$740$	1.29902e6	0.0872038
$741$	−6.58719e6	−0.440712
$742$	−3.99534e7	−2.66406
$743$	2.91441e7	1.93677	0.968385	−	0.249462i	$-0.0802537\pi$
$743$	2.91441e7	1.93677	0.968385	+	0.249462i	$0.0802537\pi$
$744$	−1.98051e6	−0.131173
$745$	−2913.20	−0.000192300 0
$746$	−1.38422e7	−0.910662
$747$	1.24932e7	0.819164
$748$	7.10380e6	0.464234
$749$	−2.09180e7	−1.36244
$750$	1.66732e7	1.08235
$751$	−1.00006e7	−0.647030	−0.323515	−	0.946223i	$-0.604865\pi$
$751$	−1.00006e7	−0.647030	−0.323515	+	0.946223i	$0.604865\pi$
$752$	1.45890e6	0.0940762
$753$	−1.32628e7	−0.852411
$754$	−4.46665e6	−0.286124
$755$	2.08976e6	0.133422
$756$	2.44487e7	1.55579
$757$	2.09909e7	1.33135	0.665674	−	0.746243i	$-0.268144\pi$
$757$	2.09909e7	1.33135	0.665674	+	0.746243i	$0.268144\pi$
$758$	2.54537e7	1.60908
$759$	−7.58214e7	−4.77735
$760$	−133319.	−0.00837253
$761$	−1.55293e7	−0.972052	−0.486026	−	0.873944i	$-0.661554\pi$
$761$	−1.55293e7	−0.972052	−0.486026	+	0.873944i	$0.661554\pi$
$762$	−3.20687e7	−2.00076
$763$	−1.04670e7	−0.650892
$764$	−1.05914e7	−0.656478
$765$	1.51342e6	0.0934987
$766$	9.47688e6	0.583570
$767$	774432.	0.0475330
$768$	2.45061e7	1.49924
$769$	−1.55647e7	−0.949128	−0.474564	−	0.880221i	$-0.657394\pi$
$769$	−1.55647e7	−0.949128	−0.474564	+	0.880221i	$0.657394\pi$
$770$	−1.69952e7	−1.03300
$771$	−2.98263e7	−1.80702
$772$	2.06867e7	1.24924
$773$	−2.14693e6	−0.129232	−0.0646159	−	0.997910i	$-0.520582\pi$
$773$	−2.14693e6	−0.129232	−0.0646159	+	0.997910i	$0.520582\pi$
$774$	3.84467e6	0.230678
$775$	−2.80175e7	−1.67562
$776$	−600258.	−0.0357836
$777$	1.50787e7	0.896007
$778$	5.62582e6	0.333224
$779$	1.47145e7	0.868767
$780$	−2.50502e6	−0.147426
$781$	−3.99256e7	−2.34220
$782$	9.47513e6	0.554074
$783$	−8.85404e6	−0.516104
$784$	−2.62554e7	−1.52556
$785$	358946.	0.0207900
$786$	2.95687e7	1.70716
$787$	−9.12110e6	−0.524941	−0.262471	−	0.964940i	$-0.584537\pi$
$787$	−9.12110e6	−0.524941	−0.262471	+	0.964940i	$0.584537\pi$
$788$	−1.96234e7	−1.12579
$789$	4.61772e7	2.64080
$790$	−9.52281e6	−0.542872
$791$	3.48733e7	1.98176
$792$	−2.37576e6	−0.134583
$793$	1.91925e6	0.108380
$794$	−5.92074e6	−0.333292
$795$	8.11462e6	0.455356
$796$	−1.76560e7	−0.987664
$797$	−1.13746e7	−0.634294	−0.317147	−	0.948376i	$-0.602725\pi$
$797$	−1.13746e7	−0.634294	−0.317147	+	0.948376i	$0.602725\pi$
$798$	−4.96993e7	−2.76276
$799$	−425866.	−0.0235997
$800$	−2.42514e7	−1.33971
$801$	4.71798e7	2.59821
$802$	−3.27565e6	−0.179830
$803$	−1.13456e7	−0.620924
$804$	−2.88270e7	−1.57275
$805$	−1.15135e7	−0.626205
$806$	1.70973e7	0.927021
$807$	3.33657e7	1.80350
$808$	−470227.	−0.0253384
$809$	−1.37610e7	−0.739226	−0.369613	−	0.929186i	$-0.620510\pi$
$809$	−1.37610e7	−0.739226	−0.369613	+	0.929186i	$0.620510\pi$
$810$	485135.	0.0259806
$811$	2.09663e7	1.11936	0.559680	−	0.828709i	$-0.310924\pi$
$811$	2.09663e7	1.11936	0.559680	+	0.828709i	$0.310924\pi$
$812$	−1.71166e7	−0.911018
$813$	−1.82908e7	−0.970523
$814$	−1.73496e7	−0.917761
$815$	334184.	0.0176235
$816$	−7.16966e6	−0.376941
$817$	−1.46355e6	−0.0767101
$818$	792285.	0.0413998
$819$	−1.78249e7	−0.928574
$820$	5.59575e6	0.290619
$821$	−3.16775e6	−0.164019	−0.0820094	−	0.996632i	$-0.526134\pi$
$821$	−3.16775e6	−0.164019	−0.0820094	+	0.996632i	$0.526134\pi$
$822$	7.92926e7	4.09311
$823$	1.83227e7	0.942953	0.471476	−	0.881879i	$-0.343721\pi$
$823$	1.83227e7	0.942953	0.471476	+	0.881879i	$0.343721\pi$
$824$	514418.	0.0263936
$825$	−5.48265e7	−2.80450
$826$	5.84297e6	0.297978
$827$	1.63541e7	0.831501	0.415750	−	0.909479i	$-0.363519\pi$
$827$	1.63541e7	0.831501	0.415750	+	0.909479i	$0.363519\pi$
$828$	−5.16883e7	−2.62009
$829$	−3.00648e7	−1.51940	−0.759700	−	0.650274i	$-0.774654\pi$
$829$	−3.00648e7	−1.51940	−0.759700	+	0.650274i	$0.774654\pi$
$830$	−3.56080e6	−0.179413
$831$	−2.56908e7	−1.29055
$832$	7.75084e6	0.388187
$833$	7.66422e6	0.382697
$834$	5.52026e7	2.74817
$835$	195337.	0.00969545
$836$	2.90444e7	1.43730
$837$	3.38911e7	1.67214
$838$	−9.90881e6	−0.487429
$839$	−1.48434e7	−0.727995	−0.363997	−	0.931400i	$-0.618588\pi$
$839$	−1.48434e7	−0.727995	−0.363997	+	0.931400i	$0.618588\pi$
$840$	−588507.	−0.0287775
$841$	−1.43124e7	−0.697788
$842$	3.19668e7	1.55388
$843$	−2.14708e7	−1.04059
$844$	−3.07572e7	−1.48624
$845$	−4.37801e6	−0.210928
$846$	4.57399e6	0.219720
$847$	8.17661e7	3.91620
$848$	−2.35653e7	−1.12534
$849$	3.25189e7	1.54834
$850$	6.85146e6	0.325264
$851$	−1.17536e7	−0.556347
$852$	−4.44003e7	−2.09550
$853$	1.74167e7	0.819585	0.409792	−	0.912179i	$-0.365601\pi$
$853$	1.74167e7	0.819585	0.409792	+	0.912179i	$0.365601\pi$
$854$	1.44804e7	0.679418
$855$	6.18772e6	0.289478
$856$	833434.	0.0388765
$857$	−1.80268e7	−0.838431	−0.419216	−	0.907887i	$-0.637695\pi$
$857$	−1.80268e7	−0.838431	−0.419216	+	0.907887i	$0.637695\pi$
$858$	3.34570e7	1.55156
$859$	−2.73776e7	−1.26594	−0.632970	−	0.774177i	$-0.718164\pi$
$859$	−2.73776e7	−1.26594	−0.632970	+	0.774177i	$0.718164\pi$
$860$	−556569.	−0.0256609
$861$	6.49542e7	2.98607
$862$	1.63659e7	0.750193
$863$	3.79051e7	1.73249	0.866246	−	0.499618i	$-0.166526\pi$
$863$	3.79051e7	1.73249	0.866246	+	0.499618i	$0.166526\pi$
$864$	2.93355e7	1.33693
$865$	7.75793e6	0.352538
$866$	4.08972e7	1.85310
$867$	2.09289e6	0.0945583
$868$	6.55182e7	2.95164
$869$	6.45990e7	2.90186
$870$	6.84458e6	0.306583
$871$	7.74889e6	0.346094
$872$	417034.	0.0185729
$873$	2.78598e7	1.23721
$874$	3.87397e7	1.71545
$875$	−1.71749e7	−0.758359
$876$	−1.26172e7	−0.555523
$877$	−5.90416e6	−0.259215	−0.129607	−	0.991565i	$-0.541372\pi$
$877$	−5.90416e6	−0.259215	−0.129607	+	0.991565i	$0.541372\pi$
$878$	−3.59439e7	−1.57358
$879$	6.29167e7	2.74659
$880$	−1.00241e7	−0.436355
$881$	3.76637e7	1.63487	0.817435	−	0.576021i	$-0.195395\pi$
$881$	3.76637e7	1.63487	0.817435	+	0.576021i	$0.195395\pi$
$882$	−8.23172e7	−3.56303
$883$	2.20420e6	0.0951369	0.0475684	−	0.998868i	$-0.484853\pi$
$883$	2.20420e6	0.0951369	0.0475684	+	0.998868i	$0.484853\pi$
$884$	−2.12356e6	−0.0913976
$885$	−1.18672e6	−0.0509319
$886$	1.92121e6	0.0822225
$887$	3.30966e7	1.41245	0.706226	−	0.707986i	$-0.250396\pi$
$887$	3.30966e7	1.41245	0.706226	+	0.707986i	$0.250396\pi$
$888$	−600779.	−0.0255672
$889$	3.30337e7	1.40185
$890$	−1.34472e7	−0.569058
$891$	−3.29096e6	−0.138876
$892$	−3.27596e7	−1.37856
$893$	−1.74118e6	−0.0730660
$894$	43269.4	0.00181066
$895$	−6.21649e6	−0.259410
$896$	3.53356e6	0.147042
$897$	2.26656e7	0.940558
$898$	−3.73046e7	−1.54373
$899$	−2.37272e7	−0.979146
$900$	−3.73758e7	−1.53810
$901$	6.87895e6	0.282300
$902$	−7.47367e7	−3.05857
$903$	−6.46053e6	−0.263663
$904$	−1.38945e6	−0.0565486
$905$	−3.53607e6	−0.143516
$906$	−3.10389e7	−1.25628
$907$	−3.69982e7	−1.49335	−0.746677	−	0.665187i	$-0.768352\pi$
$907$	−3.69982e7	−1.49335	−0.746677	+	0.665187i	$0.768352\pi$
$908$	3.13439e7	1.26165
$909$	2.18247e7	0.876068
$910$	5.08045e6	0.203375
$911$	−1.26958e7	−0.506834	−0.253417	−	0.967357i	$-0.581554\pi$
$911$	−1.26958e7	−0.506834	−0.253417	+	0.967357i	$0.581554\pi$
$912$	−2.93137e7	−1.16703
$913$	2.41551e7	0.959029
$914$	1.85541e7	0.734639
$915$	−2.94101e6	−0.116130
$916$	3.64541e7	1.43551
$917$	−3.04584e7	−1.19614
$918$	−8.28781e6	−0.324588
$919$	3.47251e6	0.135630	0.0678149	−	0.997698i	$-0.478397\pi$
$919$	3.47251e6	0.135630	0.0678149	+	0.997698i	$0.478397\pi$
$920$	458730.	0.0178685
$921$	7.55583e7	2.93517
$922$	−5.69041e7	−2.20453
$923$	1.19351e7	0.461128
$924$	1.28210e8	4.94018
$925$	−8.49901e6	−0.326598
$926$	9.88600e6	0.378873
$927$	−2.38757e7	−0.912549
$928$	−2.05378e7	−0.782860
$929$	2.24322e7	0.852772	0.426386	−	0.904541i	$-0.359787\pi$
$929$	2.24322e7	0.852772	0.426386	+	0.904541i	$0.359787\pi$
$930$	−2.61994e7	−0.993309
$931$	3.13357e7	1.18485
$932$	4.29109e7	1.61819
$933$	−6.81495e6	−0.256306
$934$	−6.81335e7	−2.55560
$935$	2.92614e6	0.109463
$936$	710194.	0.0264964
$937$	2.76857e6	0.103016	0.0515082	−	0.998673i	$-0.483597\pi$
$937$	2.76857e6	0.103016	0.0515082	+	0.998673i	$0.483597\pi$
$938$	5.84642e7	2.16962
$939$	−7.65768e7	−2.83422
$940$	−662149.	−0.0244420
$941$	−4.05553e7	−1.49305	−0.746524	−	0.665359i	$-0.768278\pi$
$941$	−4.05553e7	−1.49305	−0.746524	+	0.665359i	$0.768278\pi$
$942$	−5.33138e6	−0.195755
$943$	−5.06306e7	−1.85410
$944$	3.44630e6	0.125870
$945$	1.00707e7	0.366844
$946$	7.43352e6	0.270064
$947$	3.79348e6	0.137456	0.0687278	−	0.997635i	$-0.478106\pi$
$947$	3.79348e6	0.137456	0.0687278	+	0.997635i	$0.478106\pi$
$948$	7.18391e7	2.59621
$949$	3.39158e6	0.122247
$950$	2.80127e7	1.00704
$951$	6.84874e7	2.45561
$952$	−498890.	−0.0178407
$953$	−5.97499e6	−0.213111	−0.106555	−	0.994307i	$-0.533982\pi$
$953$	−5.97499e6	−0.213111	−0.106555	+	0.994307i	$0.533982\pi$
$954$	−7.38830e7	−2.62829
$955$	−4.36273e6	−0.154793
$956$	−4.56188e7	−1.61436
$957$	−4.64309e7	−1.63881
$958$	−4.10053e7	−1.44353
$959$	−8.16785e7	−2.86788
$960$	−1.18772e7	−0.415945
$961$	6.21930e7	2.17237
$962$	5.18639e6	0.180687
$963$	−3.86822e7	−1.34414
$964$	−1.31189e7	−0.454680
$965$	8.52109e6	0.294562
$966$	1.71008e8	5.89623
$967$	−5.09665e7	−1.75275	−0.876373	−	0.481634i	$-0.840044\pi$
$967$	−5.09665e7	−1.75275	−0.876373	+	0.481634i	$0.840044\pi$
$968$	−3.25779e6	−0.111747
$969$	8.55694e6	0.292758
$970$	−7.94060e6	−0.270972
$971$	9.63709e6	0.328018	0.164009	−	0.986459i	$-0.447557\pi$
$971$	9.63709e6	0.328018	0.164009	+	0.986459i	$0.447557\pi$
$972$	−3.22018e7	−1.09324
$973$	−5.68636e7	−1.92554
$974$	1.10879e7	0.374499
$975$	1.63895e7	0.552145
$976$	8.54085e6	0.286996
$977$	−3.50330e7	−1.17420	−0.587098	−	0.809516i	$-0.699730\pi$
$977$	−3.50330e7	−1.17420	−0.587098	+	0.809516i	$0.699730\pi$
$978$	−4.96360e6	−0.165939
$979$	9.12203e7	3.04183
$980$	1.19166e7	0.396356
$981$	−1.93558e7	−0.642152
$982$	−2.87325e7	−0.950811
$983$	7.93665e6	0.261971	0.130986	−	0.991384i	$-0.458186\pi$
$983$	7.93665e6	0.261971	0.130986	+	0.991384i	$0.458186\pi$
$984$	−2.58796e6	−0.0852061
$985$	−8.08311e6	−0.265453
$986$	5.80230e6	0.190068
$987$	−7.68608e6	−0.251138
$988$	−8.68234e6	−0.282973
$989$	5.03586e6	0.163713
$990$	−3.14281e7	−1.01913
$991$	3.67868e7	1.18989	0.594947	−	0.803765i	$-0.297173\pi$
$991$	3.67868e7	1.18989	0.594947	+	0.803765i	$0.297173\pi$
$992$	7.86138e7	2.53641
$993$	1.09906e7	0.353712
$994$	9.00484e7	2.89075
$995$	−7.27271e6	−0.232883
$996$	2.68623e7	0.858016
$997$	−1.91338e7	−0.609627	−0.304814	−	0.952412i	$-0.598594\pi$
$997$	−1.91338e7	−0.609627	−0.304814	+	0.952412i	$0.598594\pi$
$998$	4.98791e7	1.58523
$999$	1.02807e7	0.325920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.6.a.c.1.16	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.6.a.c.1.16	✓	98	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)

\(f(q)\)	\(=\)	\(q-8.06402 q^{2} +25.0583 q^{3} +33.0284 q^{4} +13.6048 q^{5} -202.071 q^{6} +208.151 q^{7} -8.29333 q^{8} +384.918 q^{9} +O(q^{10})\)	\(q-8.06402 q^{2} +25.0583 q^{3} +33.0284 q^{4} +13.6048 q^{5} -202.071 q^{6} +208.151 q^{7} -8.29333 q^{8} +384.918 q^{9} -109.709 q^{10} +744.226 q^{11} +827.636 q^{12} -222.474 q^{13} -1678.53 q^{14} +340.913 q^{15} -990.032 q^{16} +289.000 q^{17} -3103.99 q^{18} +1181.60 q^{19} +449.346 q^{20} +5215.91 q^{21} -6001.45 q^{22} -4065.70 q^{23} -207.817 q^{24} -2939.91 q^{25} +1794.04 q^{26} +3556.23 q^{27} +6874.90 q^{28} -2489.72 q^{29} -2749.13 q^{30} +9530.07 q^{31} +8249.03 q^{32} +18649.0 q^{33} -2330.50 q^{34} +2831.85 q^{35} +12713.3 q^{36} +2890.91 q^{37} -9528.42 q^{38} -5574.82 q^{39} -112.829 q^{40} +12453.1 q^{41} -42061.2 q^{42} -1238.62 q^{43} +24580.6 q^{44} +5236.74 q^{45} +32785.9 q^{46} -1473.58 q^{47} -24808.5 q^{48} +26519.8 q^{49} +23707.5 q^{50} +7241.85 q^{51} -7347.97 q^{52} +23802.6 q^{53} -28677.5 q^{54} +10125.1 q^{55} -1726.26 q^{56} +29608.8 q^{57} +20077.2 q^{58} -3481.00 q^{59} +11259.8 q^{60} -8626.84 q^{61} -76850.6 q^{62} +80121.1 q^{63} -34839.3 q^{64} -3026.72 q^{65} -150386. q^{66} -34830.5 q^{67} +9545.22 q^{68} -101880. q^{69} -22836.1 q^{70} -53647.1 q^{71} -3192.26 q^{72} -15244.8 q^{73} -23312.3 q^{74} -73669.1 q^{75} +39026.3 q^{76} +154911. q^{77} +44955.5 q^{78} +86800.3 q^{79} -13469.2 q^{80} -4421.99 q^{81} -100422. q^{82} +32456.7 q^{83} +172273. q^{84} +3931.79 q^{85} +9988.26 q^{86} -62388.2 q^{87} -6172.11 q^{88} +122571. q^{89} -42229.2 q^{90} -46308.2 q^{91} -134284. q^{92} +238807. q^{93} +11883.0 q^{94} +16075.4 q^{95} +206707. q^{96} +72378.4 q^{97} -213856. q^{98} +286466. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 25 q^{2} + 45 q^{3} + 1611 q^{4} + 541 q^{5} + 305 q^{6} + 247 q^{7} + 1425 q^{8} + 8873 q^{9}+O(q^{10}) \) 98 * q + 25 * q^2 + 45 * q^3 + 1611 * q^4 + 541 * q^5 + 305 * q^6 + 247 * q^7 + 1425 * q^8 + 8873 * q^9	\( 98 q + 25 q^{2} + 45 q^{3} + 1611 q^{4} + 541 q^{5} + 305 q^{6} + 247 q^{7} + 1425 q^{8} + 8873 q^{9} + 1000 q^{10} + 2842 q^{11} + 2304 q^{12} + 3246 q^{13} + 2245 q^{14} + 999 q^{15} + 29551 q^{16} + 28322 q^{17} + 1540 q^{18} + 932 q^{19} + 18297 q^{20} + 1112 q^{21} + 7918 q^{22} + 12457 q^{23} + 18405 q^{24} + 65623 q^{25} + 16159 q^{26} + 12633 q^{27} + 23731 q^{28} + 28451 q^{29} - 19285 q^{30} + 21493 q^{31} + 52885 q^{32} + 39707 q^{33} + 7225 q^{34} + 20313 q^{35} + 155100 q^{36} + 71740 q^{37} + 78949 q^{38} + 42612 q^{39} + 9854 q^{40} + 39545 q^{41} - 113891 q^{42} + 10477 q^{43} + 129131 q^{44} + 212203 q^{45} - 8801 q^{46} + 92561 q^{47} + 42263 q^{48} + 242447 q^{49} - 24646 q^{50} + 13005 q^{51} + 126145 q^{52} + 197573 q^{53} + 138637 q^{54} + 56894 q^{55} + 65301 q^{56} + 154798 q^{57} + 46454 q^{58} - 341138 q^{59} - 62712 q^{60} + 200139 q^{61} + 337089 q^{62} + 72251 q^{63} + 437269 q^{64} + 352383 q^{65} + 342440 q^{66} + 25262 q^{67} + 465579 q^{68} + 233418 q^{69} + 435463 q^{70} + 95619 q^{71} + 215863 q^{72} + 372862 q^{73} + 231761 q^{74} - 225892 q^{75} - 156705 q^{76} + 515725 q^{77} + 140085 q^{78} + 262158 q^{79} + 294401 q^{80} + 933702 q^{81} + 466955 q^{82} + 219868 q^{83} - 213492 q^{84} + 156349 q^{85} + 89392 q^{86} + 236040 q^{87} + 389548 q^{88} + 388400 q^{89} - 227892 q^{90} + 331873 q^{91} + 380277 q^{92} + 398803 q^{93} + 423436 q^{94} + 224444 q^{95} + 664910 q^{96} + 487367 q^{97} + 510307 q^{98} + 524962 q^{99}+O(q^{100}) \) 98 * q + 25 * q^2 + 45 * q^3 + 1611 * q^4 + 541 * q^5 + 305 * q^6 + 247 * q^7 + 1425 * q^8 + 8873 * q^9 + 1000 * q^10 + 2842 * q^11 + 2304 * q^12 + 3246 * q^13 + 2245 * q^14 + 999 * q^15 + 29551 * q^16 + 28322 * q^17 + 1540 * q^18 + 932 * q^19 + 18297 * q^20 + 1112 * q^21 + 7918 * q^22 + 12457 * q^23 + 18405 * q^24 + 65623 * q^25 + 16159 * q^26 + 12633 * q^27 + 23731 * q^28 + 28451 * q^29 - 19285 * q^30 + 21493 * q^31 + 52885 * q^32 + 39707 * q^33 + 7225 * q^34 + 20313 * q^35 + 155100 * q^36 + 71740 * q^37 + 78949 * q^38 + 42612 * q^39 + 9854 * q^40 + 39545 * q^41 - 113891 * q^42 + 10477 * q^43 + 129131 * q^44 + 212203 * q^45 - 8801 * q^46 + 92561 * q^47 + 42263 * q^48 + 242447 * q^49 - 24646 * q^50 + 13005 * q^51 + 126145 * q^52 + 197573 * q^53 + 138637 * q^54 + 56894 * q^55 + 65301 * q^56 + 154798 * q^57 + 46454 * q^58 - 341138 * q^59 - 62712 * q^60 + 200139 * q^61 + 337089 * q^62 + 72251 * q^63 + 437269 * q^64 + 352383 * q^65 + 342440 * q^66 + 25262 * q^67 + 465579 * q^68 + 233418 * q^69 + 435463 * q^70 + 95619 * q^71 + 215863 * q^72 + 372862 * q^73 + 231761 * q^74 - 225892 * q^75 - 156705 * q^76 + 515725 * q^77 + 140085 * q^78 + 262158 * q^79 + 294401 * q^80 + 933702 * q^81 + 466955 * q^82 + 219868 * q^83 - 213492 * q^84 + 156349 * q^85 + 89392 * q^86 + 236040 * q^87 + 389548 * q^88 + 388400 * q^89 - 227892 * q^90 + 331873 * q^91 + 380277 * q^92 + 398803 * q^93 + 423436 * q^94 + 224444 * q^95 + 664910 * q^96 + 487367 * q^97 + 510307 * q^98 + 524962 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more