LMFDB - Embedded newform 1045.6.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.96881 q^{2} +24.3951 q^{3} +3.62665 q^{4} +25.0000 q^{5} -145.610 q^{6} +53.9217 q^{7} +169.355 q^{8} +352.122 q^{9} +O(q^{10})$	\(q-5.96881 q^{2} +24.3951 q^{3} +3.62665 q^{4} +25.0000 q^{5} -145.610 q^{6} +53.9217 q^{7} +169.355 q^{8} +352.122 q^{9} -149.220 q^{10} -121.000 q^{11} +88.4725 q^{12} -589.418 q^{13} -321.848 q^{14} +609.878 q^{15} -1126.90 q^{16} -911.630 q^{17} -2101.75 q^{18} +361.000 q^{19} +90.6662 q^{20} +1315.43 q^{21} +722.226 q^{22} +344.381 q^{23} +4131.44 q^{24} +625.000 q^{25} +3518.12 q^{26} +2662.04 q^{27} +195.555 q^{28} +1214.06 q^{29} -3640.24 q^{30} +7033.17 q^{31} +1306.89 q^{32} -2951.81 q^{33} +5441.34 q^{34} +1348.04 q^{35} +1277.02 q^{36} -11068.3 q^{37} -2154.74 q^{38} -14378.9 q^{39} +4233.88 q^{40} +13159.7 q^{41} -7851.52 q^{42} -22943.6 q^{43} -438.824 q^{44} +8803.05 q^{45} -2055.55 q^{46} -18263.5 q^{47} -27490.9 q^{48} -13899.5 q^{49} -3730.50 q^{50} -22239.3 q^{51} -2137.61 q^{52} +10233.0 q^{53} -15889.2 q^{54} -3025.00 q^{55} +9131.91 q^{56} +8806.64 q^{57} -7246.47 q^{58} -11051.1 q^{59} +2211.81 q^{60} +38861.2 q^{61} -41979.6 q^{62} +18987.0 q^{63} +28260.2 q^{64} -14735.5 q^{65} +17618.8 q^{66} -51524.3 q^{67} -3306.16 q^{68} +8401.23 q^{69} -8046.20 q^{70} -39351.6 q^{71} +59633.6 q^{72} +70249.3 q^{73} +66064.3 q^{74} +15246.9 q^{75} +1309.22 q^{76} -6524.52 q^{77} +85825.1 q^{78} -61640.2 q^{79} -28172.5 q^{80} -20624.8 q^{81} -78548.0 q^{82} -85682.0 q^{83} +4770.58 q^{84} -22790.8 q^{85} +136946. q^{86} +29617.1 q^{87} -20492.0 q^{88} +74200.4 q^{89} -52543.7 q^{90} -31782.4 q^{91} +1248.95 q^{92} +171575. q^{93} +109011. q^{94} +9025.00 q^{95} +31881.7 q^{96} -60033.0 q^{97} +82963.1 q^{98} -42606.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * 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 $

$2$	−5.96881	−1.05515	−0.527573	−	0.849510i	$-0.676898\pi$
$2$	−5.96881	−1.05515	−0.527573	+	0.849510i	$0.676898\pi$
$3$	24.3951	1.56495	0.782474	−	0.622683i	$-0.213958\pi$
$3$	24.3951	1.56495	0.782474	+	0.622683i	$0.213958\pi$
$4$	3.62665	0.113333
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−145.610	−1.65125
$7$	53.9217	0.415928	0.207964	−	0.978136i	$-0.433316\pi$
$7$	53.9217	0.415928	0.207964	+	0.978136i	$0.433316\pi$
$8$	169.355	0.935563
$9$	352.122	1.44906
$10$	−149.220	−0.471876
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	88.4725	0.177360
$13$	−589.418	−0.967309	−0.483655	−	0.875259i	$-0.660691\pi$
$13$	−589.418	−0.967309	−0.483655	+	0.875259i	$0.660691\pi$
$14$	−321.848	−0.438865
$15$	609.878	0.699866
$16$	−1126.90	−1.10049
$17$	−911.630	−0.765062	−0.382531	−	0.923943i	$-0.624947\pi$
$17$	−911.630	−0.765062	−0.382531	+	0.923943i	$0.624947\pi$
$18$	−2101.75	−1.52897
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	90.6662	0.0506839
$21$	1315.43	0.650906
$22$	722.226	0.318138
$23$	344.381	0.135744	0.0678719	−	0.997694i	$-0.478379\pi$
$23$	344.381	0.135744	0.0678719	+	0.997694i	$0.478379\pi$
$24$	4131.44	1.46411
$25$	625.000	0.200000
$26$	3518.12	1.02065
$27$	2662.04	0.702757
$28$	195.555	0.0471383
$29$	1214.06	0.268067	0.134034	−	0.990977i	$-0.457207\pi$
$29$	1214.06	0.268067	0.134034	+	0.990977i	$0.457207\pi$
$30$	−3640.24	−0.738461
$31$	7033.17	1.31446	0.657229	−	0.753691i	$-0.271728\pi$
$31$	7033.17	1.31446	0.657229	+	0.753691i	$0.271728\pi$
$32$	1306.89	0.225612
$33$	−2951.81	−0.471849
$34$	5441.34	0.807251
$35$	1348.04	0.186009
$36$	1277.02	0.164226
$37$	−11068.3	−1.32915	−0.664577	−	0.747220i	$-0.731388\pi$
$37$	−11068.3	−1.32915	−0.664577	+	0.747220i	$0.731388\pi$
$38$	−2154.74	−0.242067
$39$	−14378.9	−1.51379
$40$	4233.88	0.418397
$41$	13159.7	1.22261	0.611305	−	0.791395i	$-0.290645\pi$
$41$	13159.7	1.22261	0.611305	+	0.791395i	$0.290645\pi$
$42$	−7851.52	−0.686800
$43$	−22943.6	−1.89230	−0.946149	−	0.323730i	$-0.895063\pi$
$43$	−22943.6	−1.89230	−0.946149	+	0.323730i	$0.895063\pi$
$44$	−438.824	−0.0341711
$45$	8803.05	0.648040
$46$	−2055.55	−0.143230
$47$	−18263.5	−1.20598	−0.602989	−	0.797749i	$-0.706024\pi$
$47$	−18263.5	−1.20598	−0.602989	+	0.797749i	$0.706024\pi$
$48$	−27490.9	−1.72221
$49$	−13899.5	−0.827004
$50$	−3730.50	−0.211029
$51$	−22239.3	−1.19728
$52$	−2137.61	−0.109628
$53$	10233.0	0.500395	0.250198	−	0.968195i	$-0.419504\pi$
$53$	10233.0	0.500395	0.250198	+	0.968195i	$0.419504\pi$
$54$	−15889.2	−0.741511
$55$	−3025.00	−0.134840
$56$	9131.91	0.389127
$57$	8806.64	0.359024
$58$	−7246.47	−0.282850
$59$	−11051.1	−0.413309	−0.206654	−	0.978414i	$-0.566258\pi$
$59$	−11051.1	−0.413309	−0.206654	+	0.978414i	$0.566258\pi$
$60$	2211.81	0.0793177
$61$	38861.2	1.33718	0.668592	−	0.743629i	$-0.266897\pi$
$61$	38861.2	1.33718	0.668592	+	0.743629i	$0.266897\pi$
$62$	−41979.6	−1.38694
$63$	18987.0	0.602705
$64$	28260.2	0.862434
$65$	−14735.5	−0.432594
$66$	17618.8	0.497870
$67$	−51524.3	−1.40225	−0.701125	−	0.713038i	$-0.747319\pi$
$67$	−51524.3	−1.40225	−0.701125	+	0.713038i	$0.747319\pi$
$68$	−3306.16	−0.0867065
$69$	8401.23	0.212432
$70$	−8046.20	−0.196266
$71$	−39351.6	−0.926438	−0.463219	−	0.886244i	$-0.653306\pi$
$71$	−39351.6	−0.926438	−0.463219	+	0.886244i	$0.653306\pi$
$72$	59633.6	1.35569
$73$	70249.3	1.54289	0.771445	−	0.636296i	$-0.219534\pi$
$73$	70249.3	1.54289	0.771445	+	0.636296i	$0.219534\pi$
$74$	66064.3	1.40245
$75$	15246.9	0.312990
$76$	1309.22	0.0260003
$77$	−6524.52	−0.125407
$78$	85825.1	1.59727
$79$	−61640.2	−1.11121	−0.555605	−	0.831446i	$-0.687513\pi$
$79$	−61640.2	−1.11121	−0.555605	+	0.831446i	$0.687513\pi$
$80$	−28172.5	−0.492153
$81$	−20624.8	−0.349283
$82$	−78548.0	−1.29003
$83$	−85682.0	−1.36519	−0.682597	−	0.730795i	$-0.739149\pi$
$83$	−85682.0	−1.36519	−0.682597	+	0.730795i	$0.739149\pi$
$84$	4770.58	0.0737689
$85$	−22790.8	−0.342146
$86$	136946.	1.99665
$87$	29617.1	0.419512
$88$	−20492.0	−0.282083
$89$	74200.4	0.992959	0.496479	−	0.868049i	$-0.334626\pi$
$89$	74200.4	0.992959	0.496479	+	0.868049i	$0.334626\pi$
$90$	−52543.7	−0.683777
$91$	−31782.4	−0.402331
$92$	1248.95	0.0153842
$93$	171575.	2.05706
$94$	109011.	1.27248
$95$	9025.00	0.102598
$96$	31881.7	0.353072
$97$	−60033.0	−0.647829	−0.323915	−	0.946086i	$-0.604999\pi$
$97$	−60033.0	−0.647829	−0.323915	+	0.946086i	$0.604999\pi$
$98$	82963.1	0.872610
$99$	−42606.7	−0.436908
$100$	2266.65	0.0226665
$101$	−82600.8	−0.805714	−0.402857	−	0.915263i	$-0.631983\pi$
$101$	−82600.8	−0.805714	−0.402857	+	0.915263i	$0.631983\pi$
$102$	132742.	1.26331
$103$	−148774.	−1.38177	−0.690883	−	0.722967i	$-0.742778\pi$
$103$	−148774.	−1.38177	−0.690883	+	0.722967i	$0.742778\pi$
$104$	−99821.0	−0.904979
$105$	32885.6	0.291094
$106$	−61078.8	−0.527990
$107$	−35832.4	−0.302564	−0.151282	−	0.988491i	$-0.548340\pi$
$107$	−35832.4	−0.302564	−0.151282	+	0.988491i	$0.548340\pi$
$108$	9654.28	0.0796454
$109$	86900.1	0.700574	0.350287	−	0.936642i	$-0.386084\pi$
$109$	86900.1	0.700574	0.350287	+	0.936642i	$0.386084\pi$
$110$	18055.6	0.142276
$111$	−270012.	−2.08006
$112$	−60764.3	−0.457724
$113$	10274.5	0.0756947	0.0378473	−	0.999284i	$-0.487950\pi$
$113$	10274.5	0.0756947	0.0378473	+	0.999284i	$0.487950\pi$
$114$	−52565.1	−0.378822
$115$	8609.53	0.0607065
$116$	4402.96	0.0303808
$117$	−207547.	−1.40169
$118$	65961.8	0.436101
$119$	−49156.6	−0.318211
$120$	103286.	0.654769
$121$	14641.0	0.0909091
$122$	−231955.	−1.41092
$123$	321034.	1.91332
$124$	25506.8	0.148971
$125$	15625.0	0.0894427
$126$	−113330.	−0.635942
$127$	−201004.	−1.10585	−0.552923	−	0.833232i	$-0.686488\pi$
$127$	−201004.	−1.10585	−0.552923	+	0.833232i	$0.686488\pi$
$128$	−210500.	−1.13561
$129$	−559711.	−2.96135
$130$	87953.1	0.456450
$131$	137944.	0.702303	0.351151	−	0.936319i	$-0.385790\pi$
$131$	137944.	0.702303	0.351151	+	0.936319i	$0.385790\pi$
$132$	−10705.2	−0.0534760
$133$	19465.7	0.0954204
$134$	307539.	1.47958
$135$	66551.0	0.314283
$136$	−154389.	−0.715763
$137$	304042.	1.38399	0.691993	−	0.721904i	$-0.256733\pi$
$137$	304042.	1.38399	0.691993	+	0.721904i	$0.256733\pi$
$138$	−50145.3	−0.224147
$139$	745.394	0.00327227	0.00163613	−	0.999999i	$-0.499479\pi$
$139$	745.394	0.00327227	0.00163613	+	0.999999i	$0.499479\pi$
$140$	4888.87	0.0210809
$141$	−445541.	−1.88729
$142$	234882.	0.977527
$143$	71319.6	0.291655
$144$	−396806.	−1.59467
$145$	30351.4	0.119883
$146$	−419304.	−1.62797
$147$	−339079.	−1.29422
$148$	−40140.7	−0.150637
$149$	153636.	0.566926	0.283463	−	0.958983i	$-0.408517\pi$
$149$	153636.	0.566926	0.283463	+	0.958983i	$0.408517\pi$
$150$	−91006.1	−0.330250
$151$	379112.	1.35309	0.676543	−	0.736403i	$-0.263477\pi$
$151$	379112.	1.35309	0.676543	+	0.736403i	$0.263477\pi$
$152$	61137.2	0.214633
$153$	−321005.	−1.10862
$154$	38943.6	0.132323
$155$	175829.	0.587843
$156$	−52147.3	−0.171562
$157$	−459707.	−1.48844	−0.744221	−	0.667934i	$-0.767179\pi$
$157$	−459707.	−1.48844	−0.744221	+	0.667934i	$0.767179\pi$
$158$	367919.	1.17249
$159$	249635.	0.783092
$160$	32672.2	0.100897
$161$	18569.6	0.0564597
$162$	123106.	0.368544
$163$	−61561.6	−0.181485	−0.0907425	−	0.995874i	$-0.528924\pi$
$163$	−61561.6	−0.181485	−0.0907425	+	0.995874i	$0.528924\pi$
$164$	47725.8	0.138562
$165$	−73795.2	−0.211017
$166$	511419.	1.44048
$167$	−149132.	−0.413789	−0.206894	−	0.978363i	$-0.566336\pi$
$167$	−149132.	−0.413789	−0.206894	+	0.978363i	$0.566336\pi$
$168$	222774.	0.608963
$169$	−23879.0	−0.0643131
$170$	136034.	0.361014
$171$	127116.	0.332437
$172$	−83208.2	−0.214459
$173$	60700.3	0.154197	0.0770984	−	0.997023i	$-0.475434\pi$
$173$	60700.3	0.154197	0.0770984	+	0.997023i	$0.475434\pi$
$174$	−176779.	−0.442646
$175$	33701.0	0.0831856
$176$	136355.	0.331810
$177$	−269592.	−0.646807
$178$	−442888.	−1.04772
$179$	−60631.2	−0.141437	−0.0707185	−	0.997496i	$-0.522529\pi$
$179$	−60631.2	−0.141437	−0.0707185	+	0.997496i	$0.522529\pi$
$180$	31925.5	0.0734441
$181$	83581.1	0.189632	0.0948160	−	0.995495i	$-0.469774\pi$
$181$	83581.1	0.189632	0.0948160	+	0.995495i	$0.469774\pi$
$182$	189703.	0.424518
$183$	948023.	2.09262
$184$	58322.7	0.126997
$185$	−276706.	−0.594415
$186$	−1.02410e6	−2.17050
$187$	110307.	0.230675
$188$	−66235.3	−0.136677
$189$	143542.	0.292296
$190$	−53868.5	−0.108256
$191$	−773377.	−1.53394	−0.766969	−	0.641685i	$-0.778236\pi$
$191$	−773377.	−1.53394	−0.766969	+	0.641685i	$0.778236\pi$
$192$	689412.	1.34966
$193$	359411.	0.694541	0.347270	−	0.937765i	$-0.387109\pi$
$193$	359411.	0.694541	0.347270	+	0.937765i	$0.387109\pi$
$194$	358325.	0.683555
$195$	−359473.	−0.676987
$196$	−50408.4	−0.0937266
$197$	−468010.	−0.859192	−0.429596	−	0.903021i	$-0.641344\pi$
$197$	−468010.	−0.859192	−0.429596	+	0.903021i	$0.641344\pi$
$198$	254311.	0.461002
$199$	−126423.	−0.226304	−0.113152	−	0.993578i	$-0.536095\pi$
$199$	−126423.	−0.226304	−0.113152	+	0.993578i	$0.536095\pi$
$200$	105847.	0.187113
$201$	−1.25694e6	−2.19445
$202$	493028.	0.850146
$203$	65464.0	0.111497
$204$	−80654.2	−0.135691
$205$	328994.	0.546768
$206$	888004.	1.45796
$207$	121264.	0.196701
$208$	664216.	1.06451
$209$	−43681.0	−0.0691714
$210$	−196288.	−0.307146
$211$	−1.01235e6	−1.56540	−0.782700	−	0.622399i	$-0.786158\pi$
$211$	−1.01235e6	−1.56540	−0.782700	+	0.622399i	$0.786158\pi$
$212$	37111.5	0.0567111
$213$	−959987.	−1.44983
$214$	213877.	0.319249
$215$	−573589.	−0.846262
$216$	450830.	0.657474
$217$	379240.	0.546720
$218$	−518690.	−0.739208
$219$	1.71374e6	2.41454
$220$	−10970.6	−0.0152818
$221$	537332.	0.740051
$222$	1.61165e6	2.19476
$223$	894687.	1.20478	0.602392	−	0.798200i	$-0.294214\pi$
$223$	894687.	1.20478	0.602392	+	0.798200i	$0.294214\pi$
$224$	70469.5	0.0938385
$225$	220076.	0.289812
$226$	−61326.6	−0.0798689
$227$	−161913.	−0.208554	−0.104277	−	0.994548i	$-0.533253\pi$
$227$	−161913.	−0.208554	−0.104277	+	0.994548i	$0.533253\pi$
$228$	31938.6	0.0406891
$229$	1.42881e6	1.80047	0.900236	−	0.435403i	$-0.143394\pi$
$229$	1.42881e6	1.80047	0.900236	+	0.435403i	$0.143394\pi$
$230$	−51388.6	−0.0640542
$231$	−159166.	−0.196255
$232$	205607.	0.250794
$233$	1.01694e6	1.22717	0.613583	−	0.789630i	$-0.289728\pi$
$233$	1.01694e6	1.22717	0.613583	+	0.789630i	$0.289728\pi$
$234$	1.23881e6	1.47899
$235$	−456588.	−0.539330
$236$	−40078.4	−0.0468414
$237$	−1.50372e6	−1.73899
$238$	293406.	0.335759
$239$	−597443.	−0.676552	−0.338276	−	0.941047i	$-0.609844\pi$
$239$	−597443.	−0.676552	−0.338276	+	0.941047i	$0.609844\pi$
$240$	−687272.	−0.770194
$241$	−445615.	−0.494217	−0.247108	−	0.968988i	$-0.579480\pi$
$241$	−445615.	−0.494217	−0.247108	+	0.968988i	$0.579480\pi$
$242$	−87389.3	−0.0959223
$243$	−1.15002e6	−1.24937
$244$	140936.	0.151547
$245$	−347486.	−0.369847
$246$	−1.91619e6	−2.01883
$247$	−212780.	−0.221916
$248$	1.19110e6	1.22976
$249$	−2.09022e6	−2.13646
$250$	−93262.6	−0.0943751
$251$	1.44417e6	1.44689	0.723444	−	0.690383i	$-0.242558\pi$
$251$	1.44417e6	1.44689	0.723444	+	0.690383i	$0.242558\pi$
$252$	68859.1	0.0683062
$253$	−41670.1	−0.0409283
$254$	1.19975e6	1.16683
$255$	−555983.	−0.535440
$256$	352108.	0.335796
$257$	−54979.5	−0.0519240	−0.0259620	−	0.999663i	$-0.508265\pi$
$257$	−54979.5	−0.0519240	−0.0259620	+	0.999663i	$0.508265\pi$
$258$	3.34081e6	3.12465
$259$	−596819.	−0.552832
$260$	−53440.3	−0.0490270
$261$	427496.	0.388446
$262$	−823361.	−0.741032
$263$	1.68414e6	1.50137	0.750686	−	0.660659i	$-0.229723\pi$
$263$	1.68414e6	1.50137	0.750686	+	0.660659i	$0.229723\pi$
$264$	−499904.	−0.441445
$265$	255825.	0.223783
$266$	−116187.	−0.100682
$267$	1.81013e6	1.55393
$268$	−186861.	−0.158921
$269$	882027.	0.743192	0.371596	−	0.928394i	$-0.378811\pi$
$269$	882027.	0.743192	0.371596	+	0.928394i	$0.378811\pi$
$270$	−397230.	−0.331614
$271$	−525047.	−0.434285	−0.217142	−	0.976140i	$-0.569674\pi$
$271$	−525047.	−0.434285	−0.217142	+	0.976140i	$0.569674\pi$
$272$	1.02732e6	0.841941
$273$	−775336.	−0.629627
$274$	−1.81477e6	−1.46031
$275$	−75625.0	−0.0603023
$276$	30468.3	0.0240755
$277$	103127.	0.0807555	0.0403778	−	0.999184i	$-0.487144\pi$
$277$	103127.	0.0807555	0.0403778	+	0.999184i	$0.487144\pi$
$278$	−4449.11	−0.00345272
$279$	2.47653e6	1.90473
$280$	228298.	0.174023
$281$	364888.	0.275673	0.137836	−	0.990455i	$-0.455985\pi$
$281$	364888.	0.275673	0.137836	+	0.990455i	$0.455985\pi$
$282$	2.65935e6	1.99137
$283$	591001.	0.438654	0.219327	−	0.975651i	$-0.429614\pi$
$283$	591001.	0.438654	0.219327	+	0.975651i	$0.429614\pi$
$284$	−142714.	−0.104996
$285$	220166.	0.160560
$286$	−425693.	−0.307738
$287$	709596.	0.508518
$288$	460183.	0.326926
$289$	−588788.	−0.414681
$290$	−181162.	−0.126494
$291$	−1.46451e6	−1.01382
$292$	254769.	0.174860
$293$	1.09503e6	0.745169	0.372585	−	0.927998i	$-0.378472\pi$
$293$	1.09503e6	0.745169	0.372585	+	0.927998i	$0.378472\pi$
$294$	2.02390e6	1.36559
$295$	−276277.	−0.184837
$296$	−1.87447e6	−1.24351
$297$	−322107.	−0.211889
$298$	−917022.	−0.598190
$299$	−202985.	−0.131306
$300$	55295.3	0.0354720
$301$	−1.23716e6	−0.787060
$302$	−2.26285e6	−1.42770
$303$	−2.01506e6	−1.26090
$304$	−406811.	−0.252469
$305$	971529.	0.598007
$306$	1.91602e6	1.16976
$307$	−1.20196e6	−0.727857	−0.363928	−	0.931427i	$-0.618565\pi$
$307$	−1.20196e6	−0.727857	−0.363928	+	0.931427i	$0.618565\pi$
$308$	−23662.1	−0.0142127
$309$	−3.62936e6	−2.16239
$310$	−1.04949e6	−0.620261
$311$	−2.47133e6	−1.44887	−0.724435	−	0.689343i	$-0.757899\pi$
$311$	−2.47133e6	−1.44887	−0.724435	+	0.689343i	$0.757899\pi$
$312$	−2.43514e6	−1.41624
$313$	−2.37723e6	−1.37155	−0.685774	−	0.727815i	$-0.740536\pi$
$313$	−2.37723e6	−1.37155	−0.685774	+	0.727815i	$0.740536\pi$
$314$	2.74390e6	1.57052
$315$	474675.	0.269538
$316$	−223547.	−0.125937
$317$	−1.74946e6	−0.977813	−0.488907	−	0.872336i	$-0.662604\pi$
$317$	−1.74946e6	−0.977813	−0.488907	+	0.872336i	$0.662604\pi$
$318$	−1.49002e6	−0.826276
$319$	−146901.	−0.0808254
$320$	706506.	0.385692
$321$	−874136.	−0.473496
$322$	−110838.	−0.0595732
$323$	−329098.	−0.175517
$324$	−74798.9	−0.0395852
$325$	−368386.	−0.193462
$326$	367449.	0.191493
$327$	2.11994e6	1.09636
$328$	2.22867e6	1.14383
$329$	−984799.	−0.501600
$330$	440469.	0.222654
$331$	−3.19635e6	−1.60356	−0.801778	−	0.597622i	$-0.796113\pi$
$331$	−3.19635e6	−1.60356	−0.801778	+	0.597622i	$0.796113\pi$
$332$	−310738.	−0.154721
$333$	−3.89738e6	−1.92602
$334$	890138.	0.436608
$335$	−1.28811e6	−0.627105
$336$	−1.48235e6	−0.716314
$337$	−2.89652e6	−1.38932	−0.694659	−	0.719339i	$-0.744445\pi$
$337$	−2.89652e6	−1.38932	−0.694659	+	0.719339i	$0.744445\pi$
$338$	142529.	0.0678597
$339$	250648.	0.118458
$340$	−82654.0	−0.0387763
$341$	−851013.	−0.396324
$342$	−758731.	−0.350770
$343$	−1.65574e6	−0.759902
$344$	−3.88561e6	−1.77037
$345$	210031.	0.0950025
$346$	−362308.	−0.162700
$347$	1.25824e6	0.560972	0.280486	−	0.959858i	$-0.409504\pi$
$347$	1.25824e6	0.560972	0.280486	+	0.959858i	$0.409504\pi$
$348$	107411.	0.0475444
$349$	−2.53262e6	−1.11303	−0.556515	−	0.830838i	$-0.687862\pi$
$349$	−2.53262e6	−1.11303	−0.556515	+	0.830838i	$0.687862\pi$
$350$	−201155.	−0.0877729
$351$	−1.56906e6	−0.679783
$352$	−158133.	−0.0680247
$353$	1.03002e6	0.439955	0.219977	−	0.975505i	$-0.429402\pi$
$353$	1.03002e6	0.439955	0.219977	+	0.975505i	$0.429402\pi$
$354$	1.60915e6	0.682475
$355$	−983790.	−0.414316
$356$	269099.	0.112535
$357$	−1.19918e6	−0.497983
$358$	361896.	0.149237
$359$	−3.49206e6	−1.43003	−0.715015	−	0.699109i	$-0.753580\pi$
$359$	−3.49206e6	−1.43003	−0.715015	+	0.699109i	$0.753580\pi$
$360$	1.49084e6	0.606282
$361$	130321.	0.0526316
$362$	−498879.	−0.200089
$363$	357169.	0.142268
$364$	−115264.	−0.0455973
$365$	1.75623e6	0.690001
$366$	−5.65857e6	−2.20802
$367$	−2.29313e6	−0.888719	−0.444359	−	0.895849i	$-0.646569\pi$
$367$	−2.29313e6	−0.888719	−0.444359	+	0.895849i	$0.646569\pi$
$368$	−388083.	−0.149385
$369$	4.63384e6	1.77164
$370$	1.65161e6	0.627195
$371$	551780.	0.208128
$372$	622242.	0.233132
$373$	−764548.	−0.284533	−0.142267	−	0.989828i	$-0.545439\pi$
$373$	−764548.	−0.284533	−0.142267	+	0.989828i	$0.545439\pi$
$374$	−658403.	−0.243395
$375$	381174.	0.139973
$376$	−3.09302e6	−1.12827
$377$	−715588.	−0.259304
$378$	−856772.	−0.308415
$379$	3.57695e6	1.27913	0.639565	−	0.768737i	$-0.279115\pi$
$379$	3.57695e6	1.27913	0.639565	+	0.768737i	$0.279115\pi$
$380$	32730.5	0.0116277
$381$	−4.90351e6	−1.73059
$382$	4.61613e6	1.61853
$383$	−3.42993e6	−1.19478	−0.597391	−	0.801950i	$-0.703796\pi$
$383$	−3.42993e6	−1.19478	−0.597391	+	0.801950i	$0.703796\pi$
$384$	−5.13518e6	−1.77716
$385$	−163113.	−0.0560837
$386$	−2.14525e6	−0.732842
$387$	−8.07893e6	−2.74206
$388$	−217718.	−0.0734203
$389$	−3.75559e6	−1.25836	−0.629178	−	0.777261i	$-0.716608\pi$
$389$	−3.75559e6	−1.25836	−0.629178	+	0.777261i	$0.716608\pi$
$390$	2.14563e6	0.714320
$391$	−313948.	−0.103852
$392$	−2.35394e6	−0.773714
$393$	3.36516e6	1.09907
$394$	2.79346e6	0.906572
$395$	−1.54101e6	−0.496949
$396$	−154520.	−0.0495160
$397$	−552403.	−0.175906	−0.0879528	−	0.996125i	$-0.528032\pi$
$397$	−552403.	−0.175906	−0.0879528	+	0.996125i	$0.528032\pi$
$398$	754593.	0.238784
$399$	474869.	0.149328
$400$	−704313.	−0.220098
$401$	146689.	0.0455551	0.0227775	−	0.999741i	$-0.492749\pi$
$401$	146689.	0.0455551	0.0227775	+	0.999741i	$0.492749\pi$
$402$	7.50245e6	2.31546
$403$	−4.14548e6	−1.27149
$404$	−299564.	−0.0913138
$405$	−515620.	−0.156204
$406$	−390742.	−0.117645
$407$	1.33926e6	0.400755
$408$	−3.76634e6	−1.12013
$409$	−787907.	−0.232898	−0.116449	−	0.993197i	$-0.537151\pi$
$409$	−787907.	−0.232898	−0.116449	+	0.993197i	$0.537151\pi$
$410$	−1.96370e6	−0.576920
$411$	7.41714e6	2.16587
$412$	−539551.	−0.156599
$413$	−595893.	−0.171907
$414$	−723803.	−0.207548
$415$	−2.14205e6	−0.610533
$416$	−770303.	−0.218237
$417$	18184.0	0.00512093
$418$	260723.	0.0729860
$419$	1.04657e6	0.291228	0.145614	−	0.989341i	$-0.453484\pi$
$419$	1.04657e6	0.291228	0.145614	+	0.989341i	$0.453484\pi$
$420$	119265.	0.0329905
$421$	−53587.5	−0.0147353	−0.00736763	−	0.999973i	$-0.502345\pi$
$421$	−53587.5	−0.0147353	−0.00736763	+	0.999973i	$0.502345\pi$
$422$	6.04253e6	1.65173
$423$	−6.43098e6	−1.74754
$424$	1.73301e6	0.468151
$425$	−569769.	−0.153012
$426$	5.72998e6	1.52978
$427$	2.09546e6	0.556172
$428$	−129952.	−0.0342904
$429$	1.73985e6	0.456424
$430$	3.42364e6	0.892930
$431$	−3.10362e6	−0.804776	−0.402388	−	0.915469i	$-0.631820\pi$
$431$	−3.10362e6	−0.804776	−0.402388	+	0.915469i	$0.631820\pi$
$432$	−2.99985e6	−0.773376
$433$	−1.94466e6	−0.498454	−0.249227	−	0.968445i	$-0.580177\pi$
$433$	−1.94466e6	−0.498454	−0.249227	+	0.968445i	$0.580177\pi$
$434$	−2.26361e6	−0.576869
$435$	740427.	0.187611
$436$	315156.	0.0793980
$437$	124322.	0.0311418
$438$	−1.02290e7	−2.54769
$439$	5.22508e6	1.29399	0.646996	−	0.762494i	$-0.276025\pi$
$439$	5.22508e6	1.29399	0.646996	+	0.762494i	$0.276025\pi$
$440$	−512299.	−0.126151
$441$	−4.89430e6	−1.19838
$442$	−3.20723e6	−0.780862
$443$	−2.19966e6	−0.532533	−0.266266	−	0.963899i	$-0.585790\pi$
$443$	−2.19966e6	−0.532533	−0.266266	+	0.963899i	$0.585790\pi$
$444$	−979236.	−0.235738
$445$	1.85501e6	0.444065
$446$	−5.34022e6	−1.27122
$447$	3.74796e6	0.887210
$448$	1.52384e6	0.358711
$449$	−660328.	−0.154577	−0.0772883	−	0.997009i	$-0.524626\pi$
$449$	−660328.	−0.154577	−0.0772883	+	0.997009i	$0.524626\pi$
$450$	−1.31359e6	−0.305794
$451$	−1.59233e6	−0.368631
$452$	37262.0	0.00857868
$453$	9.24849e6	2.11751
$454$	966430.	0.220055
$455$	−794560.	−0.179928
$456$	1.49145e6	0.335889
$457$	5.27148e6	1.18071	0.590354	−	0.807145i	$-0.298988\pi$
$457$	5.27148e6	1.18071	0.590354	+	0.807145i	$0.298988\pi$
$458$	−8.52830e6	−1.89976
$459$	−2.42680e6	−0.537652
$460$	31223.7	0.00688003
$461$	1.31657e6	0.288530	0.144265	−	0.989539i	$-0.453918\pi$
$461$	1.31657e6	0.288530	0.144265	+	0.989539i	$0.453918\pi$
$462$	950034.	0.207078
$463$	−3.49668e6	−0.758060	−0.379030	−	0.925384i	$-0.623742\pi$
$463$	−3.49668e6	−0.758060	−0.379030	+	0.925384i	$0.623742\pi$
$464$	−1.36812e6	−0.295005
$465$	4.28937e6	0.919944
$466$	−6.06989e6	−1.29484
$467$	−1.88891e6	−0.400793	−0.200396	−	0.979715i	$-0.564223\pi$
$467$	−1.88891e6	−0.400793	−0.200396	+	0.979715i	$0.564223\pi$
$468$	−752700.	−0.158857
$469$	−2.77828e6	−0.583235
$470$	2.72528e6	0.569072
$471$	−1.12146e7	−2.32933
$472$	−1.87156e6	−0.386677
$473$	2.77617e6	0.570550
$474$	8.97542e6	1.83488
$475$	225625.	0.0458831
$476$	−178274.	−0.0360637
$477$	3.60326e6	0.725103
$478$	3.56602e6	0.713861
$479$	−67358.5	−0.0134139	−0.00670693	−	0.999978i	$-0.502135\pi$
$479$	−67358.5	−0.0134139	−0.00670693	+	0.999978i	$0.502135\pi$
$480$	797042.	0.157898
$481$	6.52384e6	1.28570
$482$	2.65979e6	0.521471
$483$	453008.	0.0883564
$484$	53097.7	0.0103030
$485$	−1.50083e6	−0.289718
$486$	6.86425e6	1.31826
$487$	4.99594e6	0.954541	0.477271	−	0.878756i	$-0.341626\pi$
$487$	4.99594e6	0.954541	0.477271	+	0.878756i	$0.341626\pi$
$488$	6.58134e6	1.25102
$489$	−1.50180e6	−0.284015
$490$	2.07408e6	0.390243
$491$	4.48653e6	0.839860	0.419930	−	0.907556i	$-0.362055\pi$
$491$	4.48653e6	0.839860	0.419930	+	0.907556i	$0.362055\pi$
$492$	1.16428e6	0.216842
$493$	−1.10677e6	−0.205088
$494$	1.27004e6	0.234154
$495$	−1.06517e6	−0.195391
$496$	−7.92568e6	−1.44655
$497$	−2.12190e6	−0.385332
$498$	1.24761e7	2.25427
$499$	−1.10830e7	−1.99254	−0.996271	−	0.0862761i	$-0.972503\pi$
$499$	−1.10830e7	−1.99254	−0.996271	+	0.0862761i	$0.972503\pi$
$500$	56666.4	0.0101368
$501$	−3.63809e6	−0.647558
$502$	−8.61999e6	−1.52668
$503$	8.69423e6	1.53218	0.766092	−	0.642731i	$-0.222199\pi$
$503$	8.69423e6	1.53218	0.766092	+	0.642731i	$0.222199\pi$
$504$	3.21554e6	0.563869
$505$	−2.06502e6	−0.360326
$506$	248721.	0.0431853
$507$	−582531.	−0.100647
$508$	−728969.	−0.125329
$509$	−7.79826e6	−1.33415	−0.667073	−	0.744993i	$-0.732453\pi$
$509$	−7.79826e6	−1.33415	−0.667073	+	0.744993i	$0.732453\pi$
$510$	3.31856e6	0.564968
$511$	3.78796e6	0.641731
$512$	4.63435e6	0.781293
$513$	960997.	0.161224
$514$	328162.	0.0547874
$515$	−3.71935e6	−0.617944
$516$	−2.02987e6	−0.335618
$517$	2.20989e6	0.363616
$518$	3.56230e6	0.583318
$519$	1.48079e6	0.241310
$520$	−2.49552e6	−0.404719
$521$	3.11694e6	0.503076	0.251538	−	0.967847i	$-0.419064\pi$
$521$	3.11694e6	0.503076	0.251538	+	0.967847i	$0.419064\pi$
$522$	−2.55164e6	−0.409867
$523$	−1.08937e7	−1.74149	−0.870743	−	0.491739i	$-0.836361\pi$
$523$	−1.08937e7	−1.74149	−0.870743	+	0.491739i	$0.836361\pi$
$524$	500274.	0.0795939
$525$	822141.	0.130181
$526$	−1.00523e7	−1.58417
$527$	−6.41165e6	−1.00564
$528$	3.32639e6	0.519265
$529$	−6.31774e6	−0.981574
$530$	−1.52697e6	−0.236124
$531$	−3.89133e6	−0.598910
$532$	70595.3	0.0108143
$533$	−7.75660e6	−1.18264
$534$	−1.08043e7	−1.63962
$535$	−895811.	−0.135311
$536$	−8.72591e6	−1.31189
$537$	−1.47910e6	−0.221342
$538$	−5.26465e6	−0.784176
$539$	1.68183e6	0.249351
$540$	241357.	0.0356185
$541$	1.26561e7	1.85912	0.929559	−	0.368674i	$-0.120188\pi$
$541$	1.26561e7	1.85912	0.929559	+	0.368674i	$0.120188\pi$
$542$	3.13390e6	0.458234
$543$	2.03897e6	0.296764
$544$	−1.19140e6	−0.172607
$545$	2.17250e6	0.313306
$546$	4.62783e6	0.664348
$547$	1.26671e7	1.81013	0.905063	−	0.425278i	$-0.139824\pi$
$547$	1.26671e7	1.81013	0.905063	+	0.425278i	$0.139824\pi$
$548$	1.10265e6	0.156851
$549$	1.36839e7	1.93766
$550$	451391.	0.0636277
$551$	438275.	0.0614989
$552$	1.42279e6	0.198744
$553$	−3.32374e6	−0.462184
$554$	−615544.	−0.0852089
$555$	−6.75029e6	−0.930229
$556$	2703.28	0.000370855 0
$557$	−8.51260e6	−1.16258	−0.581292	−	0.813695i	$-0.697452\pi$
$557$	−8.51260e6	−1.16258	−0.581292	+	0.813695i	$0.697452\pi$
$558$	−1.47819e7	−2.00977
$559$	1.35234e7	1.83044
$560$	−1.51911e6	−0.204700
$561$	2.69096e6	0.360994
$562$	−2.17795e6	−0.290875
$563$	−1.02513e7	−1.36304	−0.681519	−	0.731801i	$-0.738680\pi$
$563$	−1.02513e7	−1.36304	−0.681519	+	0.731801i	$0.738680\pi$
$564$	−1.61582e6	−0.213892
$565$	256863.	0.0338517
$566$	−3.52757e6	−0.462844
$567$	−1.11212e6	−0.145277
$568$	−6.66439e6	−0.866742
$569$	1.05700e7	1.36866	0.684331	−	0.729172i	$-0.260095\pi$
$569$	1.05700e7	1.36866	0.684331	+	0.729172i	$0.260095\pi$
$570$	−1.31413e6	−0.169414
$571$	6.97676e6	0.895495	0.447748	−	0.894160i	$-0.352226\pi$
$571$	6.97676e6	0.895495	0.447748	+	0.894160i	$0.352226\pi$
$572$	258651.	0.0330540
$573$	−1.88666e7	−2.40053
$574$	−4.23544e6	−0.536560
$575$	215238.	0.0271488
$576$	9.95105e6	1.24972
$577$	1.40752e7	1.76001	0.880006	−	0.474963i	$-0.157539\pi$
$577$	1.40752e7	1.76001	0.880006	+	0.474963i	$0.157539\pi$
$578$	3.51436e6	0.437549
$579$	8.76787e6	1.08692
$580$	110074.	0.0135867
$581$	−4.62011e6	−0.567822
$582$	8.74139e6	1.06973
$583$	−1.23819e6	−0.150875
$584$	1.18971e7	1.44347
$585$	−5.18868e6	−0.626855
$586$	−6.53599e6	−0.786262
$587$	−3.40100e6	−0.407391	−0.203695	−	0.979034i	$-0.565295\pi$
$587$	−3.40100e6	−0.407391	−0.203695	+	0.979034i	$0.565295\pi$
$588$	−1.22972e6	−0.146677
$589$	2.53897e6	0.301557
$590$	1.64904e6	0.195030
$591$	−1.14172e7	−1.34459
$592$	1.24728e7	1.46272
$593$	1.51601e7	1.77037	0.885185	−	0.465239i	$-0.154032\pi$
$593$	1.51601e7	1.77037	0.885185	+	0.465239i	$0.154032\pi$
$594$	1.92259e6	0.223574
$595$	−1.22892e6	−0.142308
$596$	557182.	0.0642513
$597$	−3.08410e6	−0.354154
$598$	1.21158e6	0.138547
$599$	2.19236e6	0.249658	0.124829	−	0.992178i	$-0.460162\pi$
$599$	2.19236e6	0.249658	0.124829	+	0.992178i	$0.460162\pi$
$600$	2.58215e6	0.292822
$601$	−5.35494e6	−0.604740	−0.302370	−	0.953191i	$-0.597778\pi$
$601$	−5.35494e6	−0.604740	−0.302370	+	0.953191i	$0.597778\pi$
$602$	7.38434e6	0.830463
$603$	−1.81428e7	−2.03195
$604$	1.37491e6	0.153349
$605$	366025.	0.0406558
$606$	1.20275e7	1.33043
$607$	−8.16112e6	−0.899038	−0.449519	−	0.893271i	$-0.648405\pi$
$607$	−8.16112e6	−0.899038	−0.449519	+	0.893271i	$0.648405\pi$
$608$	471786.	0.0517590
$609$	1.59700e6	0.174487
$610$	−5.79887e6	−0.630985
$611$	1.07649e7	1.16655
$612$	−1.16417e6	−0.125643
$613$	−1.22923e7	−1.32124	−0.660620	−	0.750720i	$-0.729707\pi$
$613$	−1.22923e7	−1.32124	−0.660620	+	0.750720i	$0.729707\pi$
$614$	7.17430e6	0.767995
$615$	8.02584e6	0.855663
$616$	−1.10496e6	−0.117326
$617$	−9.66469e6	−1.02206	−0.511028	−	0.859564i	$-0.670735\pi$
$617$	−9.66469e6	−1.02206	−0.511028	+	0.859564i	$0.670735\pi$
$618$	2.16630e7	2.28164
$619$	1.34357e7	1.40940	0.704700	−	0.709506i	$-0.251082\pi$
$619$	1.34357e7	1.40940	0.704700	+	0.709506i	$0.251082\pi$
$620$	637670.	0.0666219
$621$	916757.	0.0953949
$622$	1.47509e7	1.52877
$623$	4.00101e6	0.412999
$624$	1.62036e7	1.66591
$625$	390625.	0.0400000
$626$	1.41892e7	1.44718
$627$	−1.06560e6	−0.108250
$628$	−1.66719e6	−0.168689
$629$	1.00902e7	1.01688
$630$	−2.83324e6	−0.284402
$631$	5.24842e6	0.524753	0.262377	−	0.964966i	$-0.415494\pi$
$631$	5.24842e6	0.524753	0.262377	+	0.964966i	$0.415494\pi$
$632$	−1.04391e7	−1.03961
$633$	−2.46964e7	−2.44977
$634$	1.04422e7	1.03174
$635$	−5.02509e6	−0.494549
$636$	905338.	0.0887499
$637$	8.19259e6	0.799968
$638$	876823.	0.0852826
$639$	−1.38566e7	−1.34247
$640$	−5.26251e6	−0.507859
$641$	−1.45330e7	−1.39704	−0.698522	−	0.715589i	$-0.746159\pi$
$641$	−1.45330e7	−1.39704	−0.698522	+	0.715589i	$0.746159\pi$
$642$	5.21755e6	0.499608
$643$	−9.13238e6	−0.871077	−0.435539	−	0.900170i	$-0.643442\pi$
$643$	−9.13238e6	−0.871077	−0.435539	+	0.900170i	$0.643442\pi$
$644$	67345.4	0.00639873
$645$	−1.39928e7	−1.32436
$646$	1.96432e6	0.185196
$647$	−1.92530e7	−1.80817	−0.904083	−	0.427356i	$-0.859445\pi$
$647$	−1.92530e7	−1.80817	−0.904083	+	0.427356i	$0.859445\pi$
$648$	−3.49292e6	−0.326776
$649$	1.33718e6	0.124617
$650$	2.19883e6	0.204130
$651$	9.25161e6	0.855588
$652$	−223262.	−0.0205682
$653$	−9.97979e6	−0.915879	−0.457940	−	0.888983i	$-0.651412\pi$
$653$	−9.97979e6	−0.915879	−0.457940	+	0.888983i	$0.651412\pi$
$654$	−1.26535e7	−1.15682
$655$	3.44860e6	0.314079
$656$	−1.48297e7	−1.34547
$657$	2.47363e7	2.23574
$658$	5.87808e6	0.529262
$659$	−1.10065e7	−0.987268	−0.493634	−	0.869670i	$-0.664332\pi$
$659$	−1.10065e7	−0.987268	−0.493634	+	0.869670i	$0.664332\pi$
$660$	−267629.	−0.0239152
$661$	4.73063e6	0.421129	0.210564	−	0.977580i	$-0.432470\pi$
$661$	4.73063e6	0.421129	0.210564	+	0.977580i	$0.432470\pi$
$662$	1.90784e7	1.69199
$663$	1.31083e7	1.15814
$664$	−1.45107e7	−1.27723
$665$	486643.	0.0426733
$666$	2.32627e7	2.03224
$667$	418099.	0.0363885
$668$	−540848.	−0.0468958
$669$	2.18260e7	1.88542
$670$	7.68847e6	0.661688
$671$	−4.70220e6	−0.403176
$672$	1.71911e6	0.146852
$673$	−1.03824e7	−0.883606	−0.441803	−	0.897112i	$-0.645661\pi$
$673$	−1.03824e7	−0.883606	−0.441803	+	0.897112i	$0.645661\pi$
$674$	1.72888e7	1.46593
$675$	1.66378e6	0.140551
$676$	−86600.8	−0.00728878
$677$	3.94950e6	0.331185	0.165593	−	0.986194i	$-0.447046\pi$
$677$	3.94950e6	0.331185	0.165593	+	0.986194i	$0.447046\pi$
$678$	−1.49607e6	−0.124991
$679$	−3.23708e6	−0.269450
$680$	−3.85973e6	−0.320099
$681$	−3.94990e6	−0.326376
$682$	5.07953e6	0.418180
$683$	−1.46260e7	−1.19971	−0.599853	−	0.800111i	$-0.704774\pi$
$683$	−1.46260e7	−1.19971	−0.599853	+	0.800111i	$0.704774\pi$
$684$	461005.	0.0376760
$685$	7.60105e6	0.618938
$686$	9.88281e6	0.801808
$687$	3.48560e7	2.81764
$688$	2.58551e7	2.08245
$689$	−6.03151e6	−0.484037
$690$	−1.25363e6	−0.100241
$691$	1.25433e7	0.999352	0.499676	−	0.866212i	$-0.333452\pi$
$691$	1.25433e7	0.999352	0.499676	+	0.866212i	$0.333452\pi$
$692$	220138.	0.0174755
$693$	−2.29743e6	−0.181722
$694$	−7.51022e6	−0.591908
$695$	18634.9	0.00146340
$696$	5.01580e6	0.392480
$697$	−1.19968e7	−0.935372
$698$	1.51167e7	1.17441
$699$	2.48083e7	1.92045
$700$	122222.	0.00942765
$701$	−2.43688e7	−1.87301	−0.936503	−	0.350660i	$-0.885957\pi$
$701$	−2.43688e7	−1.87301	−0.936503	+	0.350660i	$0.885957\pi$
$702$	9.36539e6	0.717271
$703$	−3.99564e6	−0.304929
$704$	−3.41949e6	−0.260034
$705$	−1.11385e7	−0.844023
$706$	−6.14798e6	−0.464216
$707$	−4.45397e6	−0.335119
$708$	−977717.	−0.0733044
$709$	1.29906e7	0.970542	0.485271	−	0.874364i	$-0.338721\pi$
$709$	1.29906e7	0.970542	0.485271	+	0.874364i	$0.338721\pi$
$710$	5.87205e6	0.437164
$711$	−2.17049e7	−1.61021
$712$	1.25662e7	0.928976
$713$	2.42209e6	0.178430
$714$	7.15768e6	0.525444
$715$	1.78299e6	0.130432
$716$	−219888.	−0.0160294
$717$	−1.45747e7	−1.05877
$718$	2.08434e7	1.50889
$719$	1.19515e7	0.862187	0.431093	−	0.902307i	$-0.358128\pi$
$719$	1.19515e7	0.862187	0.431093	+	0.902307i	$0.358128\pi$
$720$	−9.92015e6	−0.713160
$721$	−8.02215e6	−0.574715
$722$	−777861.	−0.0555340
$723$	−1.08708e7	−0.773423
$724$	303119.	0.0214915
$725$	758786.	0.0536135
$726$	−2.13187e6	−0.150113
$727$	−6.98865e6	−0.490408	−0.245204	−	0.969472i	$-0.578855\pi$
$727$	−6.98865e6	−0.490408	−0.245204	+	0.969472i	$0.578855\pi$
$728$	−5.38251e6	−0.376406
$729$	−2.30431e7	−1.60591
$730$	−1.04826e7	−0.728052
$731$	2.09160e7	1.44772
$732$	3.43814e6	0.237163
$733$	1.45103e7	0.997511	0.498756	−	0.866743i	$-0.333790\pi$
$733$	1.45103e7	0.997511	0.498756	+	0.866743i	$0.333790\pi$
$734$	1.36873e7	0.937728
$735$	−8.47697e6	−0.578792
$736$	450068.	0.0306255
$737$	6.23445e6	0.422794
$738$	−2.76585e7	−1.86934
$739$	2.42435e7	1.63300	0.816498	−	0.577348i	$-0.195913\pi$
$739$	2.42435e7	1.63300	0.816498	+	0.577348i	$0.195913\pi$
$740$	−1.00352e6	−0.0673667
$741$	−5.19079e6	−0.347287
$742$	−3.29347e6	−0.219606
$743$	−1.92297e6	−0.127791	−0.0638956	−	0.997957i	$-0.520352\pi$
$743$	−1.92297e6	−0.127791	−0.0638956	+	0.997957i	$0.520352\pi$
$744$	2.90571e7	1.92451
$745$	3.84089e6	0.253537
$746$	4.56344e6	0.300224
$747$	−3.01705e7	−1.97825
$748$	400045.	0.0261430
$749$	−1.93214e6	−0.125845
$750$	−2.27515e6	−0.147692
$751$	−1.72411e7	−1.11549	−0.557744	−	0.830013i	$-0.688333\pi$
$751$	−1.72411e7	−1.11549	−0.557744	+	0.830013i	$0.688333\pi$
$752$	2.05812e7	1.32717
$753$	3.52308e7	2.26430
$754$	4.27120e6	0.273604
$755$	9.47781e6	0.605119
$756$	520575.	0.0331267
$757$	1.97925e7	1.25534	0.627668	−	0.778481i	$-0.284010\pi$
$757$	1.97925e7	1.25534	0.627668	+	0.778481i	$0.284010\pi$
$758$	−2.13501e7	−1.34967
$759$	−1.01655e6	−0.0640507
$760$	1.52843e6	0.0959868
$761$	1.34408e7	0.841323	0.420662	−	0.907218i	$-0.361798\pi$
$761$	1.34408e7	0.841323	0.420662	+	0.907218i	$0.361798\pi$
$762$	2.92681e7	1.82603
$763$	4.68580e6	0.291388
$764$	−2.80476e6	−0.173845
$765$	−8.02512e6	−0.495790
$766$	2.04726e7	1.26067
$767$	6.51371e6	0.399797
$768$	8.58971e6	0.525503
$769$	2.00144e7	1.22047	0.610236	−	0.792220i	$-0.291075\pi$
$769$	2.00144e7	1.22047	0.610236	+	0.792220i	$0.291075\pi$
$770$	973590.	0.0591765
$771$	−1.34123e6	−0.0812583
$772$	1.30346e6	0.0787142
$773$	1.16852e7	0.703377	0.351688	−	0.936117i	$-0.385608\pi$
$773$	1.16852e7	0.703377	0.351688	+	0.936117i	$0.385608\pi$
$774$	4.82216e7	2.89327
$775$	4.39573e6	0.262892
$776$	−1.01669e7	−0.606085
$777$	−1.45595e7	−0.865153
$778$	2.24164e7	1.32775
$779$	4.75067e6	0.280486
$780$	−1.30368e6	−0.0767247
$781$	4.76154e6	0.279332
$782$	1.87390e6	0.109579
$783$	3.23187e6	0.188386
$784$	1.56633e7	0.910108
$785$	−1.14927e7	−0.665651
$786$	−2.00860e7	−1.15968
$787$	4.11365e6	0.236750	0.118375	−	0.992969i	$-0.462231\pi$
$787$	4.11365e6	0.236750	0.118375	+	0.992969i	$0.462231\pi$
$788$	−1.69731e6	−0.0973745
$789$	4.10848e7	2.34957
$790$	9.19796e6	0.524353
$791$	554019.	0.0314835
$792$	−7.21567e6	−0.408755
$793$	−2.29055e7	−1.29347
$794$	3.29719e6	0.185606
$795$	6.24088e6	0.350209
$796$	−458491.	−0.0256477
$797$	1.61010e7	0.897859	0.448929	−	0.893567i	$-0.351806\pi$
$797$	1.61010e7	0.897859	0.448929	+	0.893567i	$0.351806\pi$
$798$	−2.83440e6	−0.157563
$799$	1.66496e7	0.922648
$800$	816804.	0.0451225
$801$	2.61276e7	1.43886
$802$	−875559.	−0.0480673
$803$	−8.50017e6	−0.465199
$804$	−4.55849e6	−0.248703
$805$	464240.	0.0252495
$806$	2.47436e7	1.34160
$807$	2.15172e7	1.16306
$808$	−1.39889e7	−0.753796
$809$	−6.40179e6	−0.343899	−0.171949	−	0.985106i	$-0.555007\pi$
$809$	−6.40179e6	−0.343899	−0.171949	+	0.985106i	$0.555007\pi$
$810$	3.07764e6	0.164818
$811$	1.01807e7	0.543533	0.271766	−	0.962363i	$-0.412392\pi$
$811$	1.01807e7	0.543533	0.271766	+	0.962363i	$0.412392\pi$
$812$	237415.	0.0126362
$813$	−1.28086e7	−0.679633
$814$	−7.99378e6	−0.422855
$815$	−1.53904e6	−0.0811626
$816$	2.50615e7	1.31759
$817$	−8.28263e6	−0.434123
$818$	4.70286e6	0.245742
$819$	−1.11913e7	−0.583002
$820$	1.19314e6	0.0619667
$821$	−1.24836e7	−0.646373	−0.323186	−	0.946335i	$-0.604754\pi$
$821$	−1.24836e7	−0.646373	−0.323186	+	0.946335i	$0.604754\pi$
$822$	−4.42714e7	−2.28531
$823$	6.10289e6	0.314077	0.157039	−	0.987592i	$-0.449805\pi$
$823$	6.10289e6	0.314077	0.157039	+	0.987592i	$0.449805\pi$
$824$	−2.51956e7	−1.29273
$825$	−1.84488e6	−0.0943699
$826$	3.55677e6	0.181387
$827$	−3.16070e6	−0.160701	−0.0803507	−	0.996767i	$-0.525604\pi$
$827$	−3.16070e6	−0.160701	−0.0803507	+	0.996767i	$0.525604\pi$
$828$	439782.	0.0222927
$829$	3.64279e7	1.84097	0.920487	−	0.390773i	$-0.127792\pi$
$829$	3.64279e7	1.84097	0.920487	+	0.390773i	$0.127792\pi$
$830$	1.27855e7	0.644202
$831$	2.51579e6	0.126378
$832$	−1.66571e7	−0.834241
$833$	1.26712e7	0.632709
$834$	−108537.	−0.00540333
$835$	−3.72829e6	−0.185052
$836$	−158416.	−0.00783939
$837$	1.87226e7	0.923745
$838$	−6.24677e6	−0.307288
$839$	2.24016e7	1.09869	0.549344	−	0.835596i	$-0.314878\pi$
$839$	2.24016e7	1.09869	0.549344	+	0.835596i	$0.314878\pi$
$840$	5.56935e6	0.272337
$841$	−1.90372e7	−0.928140
$842$	319853.	0.0155479
$843$	8.90149e6	0.431414
$844$	−3.67144e6	−0.177411
$845$	−596975.	−0.0287617
$846$	3.83853e7	1.84391
$847$	789467.	0.0378116
$848$	−1.15316e7	−0.550679
$849$	1.44175e7	0.686471
$850$	3.40084e6	0.161450
$851$	−3.81170e6	−0.180424
$852$	−3.48153e6	−0.164313
$853$	2.34139e7	1.10179	0.550897	−	0.834573i	$-0.314286\pi$
$853$	2.34139e7	1.10179	0.550897	+	0.834573i	$0.314286\pi$
$854$	−1.25074e7	−0.586843
$855$	3.17790e6	0.148671
$856$	−6.06840e6	−0.283067
$857$	−2.35002e7	−1.09300	−0.546500	−	0.837459i	$-0.684040\pi$
$857$	−2.35002e7	−1.09300	−0.546500	+	0.837459i	$0.684040\pi$
$858$	−1.03848e7	−0.481594
$859$	−2.95640e7	−1.36704	−0.683519	−	0.729933i	$-0.739551\pi$
$859$	−2.95640e7	−1.36704	−0.683519	+	0.729933i	$0.739551\pi$
$860$	−2.08020e6	−0.0959091
$861$	1.73107e7	0.795804
$862$	1.85249e7	0.849156
$863$	−2.25015e7	−1.02845	−0.514226	−	0.857655i	$-0.671921\pi$
$863$	−2.25015e7	−1.02845	−0.514226	+	0.857655i	$0.671921\pi$
$864$	3.47899e6	0.158551
$865$	1.51751e6	0.0689589
$866$	1.16073e7	0.525942
$867$	−1.43635e7	−0.648954
$868$	1.37537e6	0.0619613
$869$	7.45847e6	0.335043
$870$	−4.41946e6	−0.197957
$871$	3.03694e7	1.35641
$872$	1.47170e7	0.655431
$873$	−2.11389e7	−0.938745
$874$	−742052.	−0.0328591
$875$	842526.	0.0372017
$876$	6.21513e6	0.273647
$877$	−3.05847e7	−1.34278	−0.671390	−	0.741104i	$-0.734302\pi$
$877$	−3.05847e7	−1.34278	−0.671390	+	0.741104i	$0.734302\pi$
$878$	−3.11875e7	−1.36535
$879$	2.67133e7	1.16615
$880$	3.40887e6	0.148390
$881$	−1.10721e7	−0.480608	−0.240304	−	0.970698i	$-0.577247\pi$
$881$	−1.10721e7	−0.480608	−0.240304	+	0.970698i	$0.577247\pi$
$882$	2.92131e7	1.26446
$883$	−1.45818e7	−0.629375	−0.314687	−	0.949195i	$-0.601900\pi$
$883$	−1.45818e7	−0.629375	−0.314687	+	0.949195i	$0.601900\pi$
$884$	1.94871e6	0.0838720
$885$	−6.73981e6	−0.289261
$886$	1.31293e7	0.561900
$887$	8.48881e6	0.362274	0.181137	−	0.983458i	$-0.442022\pi$
$887$	8.48881e6	0.362274	0.181137	+	0.983458i	$0.442022\pi$
$888$	−4.57278e7	−1.94602
$889$	−1.08385e7	−0.459952
$890$	−1.10722e7	−0.468553
$891$	2.49560e6	0.105313
$892$	3.24472e6	0.136541
$893$	−6.59313e6	−0.276671
$894$	−2.23709e7	−0.936136
$895$	−1.51578e6	−0.0632526
$896$	−1.13505e7	−0.472331
$897$	−4.95184e6	−0.205487
$898$	3.94137e6	0.163101
$899$	8.53867e6	0.352363
$900$	798139.	0.0328452
$901$	−9.32870e6	−0.382833
$902$	9.50431e6	0.388959
$903$	−3.01805e7	−1.23171
$904$	1.74004e6	0.0708172
$905$	2.08953e6	0.0848060
$906$	−5.52024e7	−2.23428
$907$	3.98950e7	1.61028	0.805138	−	0.593088i	$-0.202091\pi$
$907$	3.98950e7	1.61028	0.805138	+	0.593088i	$0.202091\pi$
$908$	−587203.	−0.0236360
$909$	−2.90856e7	−1.16753
$910$	4.74258e6	0.189850
$911$	−9.20811e6	−0.367599	−0.183800	−	0.982964i	$-0.558840\pi$
$911$	−9.20811e6	−0.367599	−0.183800	+	0.982964i	$0.558840\pi$
$912$	−9.92420e6	−0.395101
$913$	1.03675e7	0.411621
$914$	−3.14645e7	−1.24582
$915$	2.37006e7	0.935850
$916$	5.18180e6	0.204052
$917$	7.43817e6	0.292107
$918$	1.44851e7	0.567302
$919$	4.58165e7	1.78951	0.894753	−	0.446561i	$-0.147351\pi$
$919$	4.58165e7	1.78951	0.894753	+	0.446561i	$0.147351\pi$
$920$	1.45807e6	0.0567948
$921$	−2.93221e7	−1.13906
$922$	−7.85833e6	−0.304441
$923$	2.31946e7	0.896152
$924$	−577241.	−0.0222422
$925$	−6.91766e6	−0.265831
$926$	2.08710e7	0.799864
$927$	−5.23866e7	−2.00226
$928$	1.58664e6	0.0604794
$929$	1.55448e7	0.590943	0.295472	−	0.955351i	$-0.404523\pi$
$929$	1.55448e7	0.590943	0.295472	+	0.955351i	$0.404523\pi$
$930$	−2.56024e7	−0.970675
$931$	−5.01770e6	−0.189728
$932$	3.68806e6	0.139078
$933$	−6.02884e7	−2.26741
$934$	1.12746e7	0.422895
$935$	2.75768e6	0.103161
$936$	−3.51491e7	−1.31137
$937$	3.55918e7	1.32434	0.662171	−	0.749352i	$-0.269635\pi$
$937$	3.55918e7	1.32434	0.662171	+	0.749352i	$0.269635\pi$
$938$	1.65830e7	0.615398
$939$	−5.79929e7	−2.14640
$940$	−1.65588e6	−0.0611238
$941$	2.07708e7	0.764677	0.382339	−	0.924022i	$-0.375119\pi$
$941$	2.07708e7	0.764677	0.382339	+	0.924022i	$0.375119\pi$
$942$	6.69378e7	2.45779
$943$	4.53197e6	0.165962
$944$	1.24535e7	0.454842
$945$	3.58854e6	0.130719
$946$	−1.65704e7	−0.602013
$947$	−3.41143e7	−1.23612	−0.618062	−	0.786130i	$-0.712082\pi$
$947$	−3.41143e7	−1.23612	−0.618062	+	0.786130i	$0.712082\pi$
$948$	−5.45346e6	−0.197084
$949$	−4.14062e7	−1.49245
$950$	−1.34671e6	−0.0484134
$951$	−4.26783e7	−1.53023
$952$	−8.32492e6	−0.297706
$953$	−1.74137e7	−0.621095	−0.310547	−	0.950558i	$-0.600512\pi$
$953$	−1.74137e7	−0.621095	−0.310547	+	0.950558i	$0.600512\pi$
$954$	−2.15072e7	−0.765089
$955$	−1.93344e7	−0.685998
$956$	−2.16671e6	−0.0766755
$957$	−3.58367e6	−0.126487
$958$	402050.	0.0141536
$959$	1.63944e7	0.575639
$960$	1.72353e7	0.603588
$961$	2.08363e7	0.727800
$962$	−3.89395e7	−1.35660
$963$	−1.26174e7	−0.438433
$964$	−1.61609e6	−0.0560109
$965$	8.98527e6	0.310608
$966$	−2.70392e6	−0.0932289
$967$	8.35418e6	0.287302	0.143651	−	0.989628i	$-0.454116\pi$
$967$	8.35418e6	0.287302	0.143651	+	0.989628i	$0.454116\pi$
$968$	2.47953e6	0.0850512
$969$	−8.02840e6	−0.274675
$970$	8.95813e6	0.305695
$971$	−4.04073e7	−1.37535	−0.687673	−	0.726020i	$-0.741368\pi$
$971$	−4.04073e7	−1.37535	−0.687673	+	0.726020i	$0.741368\pi$
$972$	−4.17072e6	−0.141594
$973$	40192.9	0.00136103
$974$	−2.98198e7	−1.00718
$975$	−8.98683e6	−0.302758
$976$	−4.37927e7	−1.47156
$977$	4.70349e7	1.57646	0.788231	−	0.615380i	$-0.210997\pi$
$977$	4.70349e7	1.57646	0.788231	+	0.615380i	$0.210997\pi$
$978$	8.96397e6	0.299677
$979$	−8.97825e6	−0.299388
$980$	−1.26021e6	−0.0419158
$981$	3.05994e7	1.01517
$982$	−2.67792e7	−0.886175
$983$	−1.75400e7	−0.578956	−0.289478	−	0.957185i	$-0.593482\pi$
$983$	−1.75400e7	−0.578956	−0.289478	+	0.957185i	$0.593482\pi$
$984$	5.43687e7	1.79003
$985$	−1.17003e7	−0.384242
$986$	6.60610e6	0.216398
$987$	−2.40243e7	−0.784978
$988$	−771678.	−0.0251503
$989$	−7.90134e6	−0.256868
$990$	6.35778e6	0.206166
$991$	−1.22553e7	−0.396406	−0.198203	−	0.980161i	$-0.563510\pi$
$991$	−1.22553e7	−0.396406	−0.198203	+	0.980161i	$0.563510\pi$
$992$	9.19156e6	0.296558
$993$	−7.79753e7	−2.50948
$994$	1.26652e7	0.406581
$995$	−3.16057e6	−0.101206
$996$	−7.58050e6	−0.242130
$997$	4.32991e7	1.37956	0.689780	−	0.724019i	$-0.257707\pi$
$997$	4.32991e7	1.37956	0.689780	+	0.724019i	$0.257707\pi$
$998$	6.61525e7	2.10242
$999$	−2.94642e7	−0.934072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.11	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-5.96881 q^{2} +24.3951 q^{3} +3.62665 q^{4} +25.0000 q^{5} -145.610 q^{6} +53.9217 q^{7} +169.355 q^{8} +352.122 q^{9} +O(q^{10})\)	\(q-5.96881 q^{2} +24.3951 q^{3} +3.62665 q^{4} +25.0000 q^{5} -145.610 q^{6} +53.9217 q^{7} +169.355 q^{8} +352.122 q^{9} -149.220 q^{10} -121.000 q^{11} +88.4725 q^{12} -589.418 q^{13} -321.848 q^{14} +609.878 q^{15} -1126.90 q^{16} -911.630 q^{17} -2101.75 q^{18} +361.000 q^{19} +90.6662 q^{20} +1315.43 q^{21} +722.226 q^{22} +344.381 q^{23} +4131.44 q^{24} +625.000 q^{25} +3518.12 q^{26} +2662.04 q^{27} +195.555 q^{28} +1214.06 q^{29} -3640.24 q^{30} +7033.17 q^{31} +1306.89 q^{32} -2951.81 q^{33} +5441.34 q^{34} +1348.04 q^{35} +1277.02 q^{36} -11068.3 q^{37} -2154.74 q^{38} -14378.9 q^{39} +4233.88 q^{40} +13159.7 q^{41} -7851.52 q^{42} -22943.6 q^{43} -438.824 q^{44} +8803.05 q^{45} -2055.55 q^{46} -18263.5 q^{47} -27490.9 q^{48} -13899.5 q^{49} -3730.50 q^{50} -22239.3 q^{51} -2137.61 q^{52} +10233.0 q^{53} -15889.2 q^{54} -3025.00 q^{55} +9131.91 q^{56} +8806.64 q^{57} -7246.47 q^{58} -11051.1 q^{59} +2211.81 q^{60} +38861.2 q^{61} -41979.6 q^{62} +18987.0 q^{63} +28260.2 q^{64} -14735.5 q^{65} +17618.8 q^{66} -51524.3 q^{67} -3306.16 q^{68} +8401.23 q^{69} -8046.20 q^{70} -39351.6 q^{71} +59633.6 q^{72} +70249.3 q^{73} +66064.3 q^{74} +15246.9 q^{75} +1309.22 q^{76} -6524.52 q^{77} +85825.1 q^{78} -61640.2 q^{79} -28172.5 q^{80} -20624.8 q^{81} -78548.0 q^{82} -85682.0 q^{83} +4770.58 q^{84} -22790.8 q^{85} +136946. q^{86} +29617.1 q^{87} -20492.0 q^{88} +74200.4 q^{89} -52543.7 q^{90} -31782.4 q^{91} +1248.95 q^{92} +171575. q^{93} +109011. q^{94} +9025.00 q^{95} +31881.7 q^{96} -60033.0 q^{97} +82963.1 q^{98} -42606.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

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