LMFDB - Embedded newform 1045.6.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-6.61608 q^{2} +9.41089 q^{3} +11.7725 q^{4} -25.0000 q^{5} -62.2632 q^{6} -82.7561 q^{7} +133.827 q^{8} -154.435 q^{9} +O(q^{10})$	\(q-6.61608 q^{2} +9.41089 q^{3} +11.7725 q^{4} -25.0000 q^{5} -62.2632 q^{6} -82.7561 q^{7} +133.827 q^{8} -154.435 q^{9} +165.402 q^{10} -121.000 q^{11} +110.789 q^{12} +261.080 q^{13} +547.521 q^{14} -235.272 q^{15} -1262.13 q^{16} +1321.12 q^{17} +1021.76 q^{18} +361.000 q^{19} -294.312 q^{20} -778.809 q^{21} +800.545 q^{22} +3173.38 q^{23} +1259.43 q^{24} +625.000 q^{25} -1727.32 q^{26} -3740.22 q^{27} -974.244 q^{28} -105.133 q^{29} +1556.58 q^{30} -3139.09 q^{31} +4067.88 q^{32} -1138.72 q^{33} -8740.61 q^{34} +2068.90 q^{35} -1818.08 q^{36} -5929.61 q^{37} -2388.40 q^{38} +2456.99 q^{39} -3345.67 q^{40} +300.327 q^{41} +5152.66 q^{42} +21826.2 q^{43} -1424.47 q^{44} +3860.88 q^{45} -20995.3 q^{46} -16302.7 q^{47} -11877.7 q^{48} -9958.42 q^{49} -4135.05 q^{50} +12432.9 q^{51} +3073.56 q^{52} -19337.2 q^{53} +24745.6 q^{54} +3025.00 q^{55} -11075.0 q^{56} +3397.33 q^{57} +695.566 q^{58} -40693.4 q^{59} -2769.74 q^{60} -25500.0 q^{61} +20768.5 q^{62} +12780.5 q^{63} +13474.7 q^{64} -6527.00 q^{65} +7533.84 q^{66} +9615.89 q^{67} +15552.8 q^{68} +29864.3 q^{69} -13688.0 q^{70} -48423.5 q^{71} -20667.6 q^{72} +87237.8 q^{73} +39230.7 q^{74} +5881.80 q^{75} +4249.86 q^{76} +10013.5 q^{77} -16255.7 q^{78} -36015.2 q^{79} +31553.2 q^{80} +2328.98 q^{81} -1986.99 q^{82} +41943.1 q^{83} -9168.50 q^{84} -33027.9 q^{85} -144404. q^{86} -989.392 q^{87} -16193.1 q^{88} -100651. q^{89} -25543.9 q^{90} -21606.0 q^{91} +37358.5 q^{92} -29541.6 q^{93} +107860. q^{94} -9025.00 q^{95} +38282.3 q^{96} +24120.6 q^{97} +65885.7 q^{98} +18686.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−6.61608	−1.16957	−0.584784	−	0.811189i	$-0.698821\pi$
$2$	−6.61608	−1.16957	−0.584784	+	0.811189i	$0.698821\pi$
$3$	9.41089	0.603709	0.301854	−	0.953354i	$-0.402394\pi$
$3$	9.41089	0.603709	0.301854	+	0.953354i	$0.402394\pi$
$4$	11.7725	0.367890
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−62.2632	−0.706079
$7$	−82.7561	−0.638344	−0.319172	−	0.947697i	$-0.603405\pi$
$7$	−82.7561	−0.638344	−0.319172	+	0.947697i	$0.603405\pi$
$8$	133.827	0.739296
$9$	−154.435	−0.635536
$10$	165.402	0.523047
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	110.789	0.222098
$13$	261.080	0.428465	0.214232	−	0.976783i	$-0.431275\pi$
$13$	261.080	0.428465	0.214232	+	0.976783i	$0.431275\pi$
$14$	547.521	0.746587
$15$	−235.272	−0.269987
$16$	−1262.13	−1.23255
$17$	1321.12	1.10871	0.554356	−	0.832280i	$-0.312965\pi$
$17$	1321.12	1.10871	0.554356	+	0.832280i	$0.312965\pi$
$18$	1021.76	0.743302
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−294.312	−0.164525
$21$	−778.809	−0.385374
$22$	800.545	0.352638
$23$	3173.38	1.25084	0.625421	−	0.780287i	$-0.284927\pi$
$23$	3173.38	1.25084	0.625421	+	0.780287i	$0.284927\pi$
$24$	1259.43	0.446319
$25$	625.000	0.200000
$26$	−1727.32	−0.501119
$27$	−3740.22	−0.987387
$28$	−974.244	−0.234840
$29$	−105.133	−0.0232136	−0.0116068	−	0.999933i	$-0.503695\pi$
$29$	−105.133	−0.0232136	−0.0116068	+	0.999933i	$0.503695\pi$
$30$	1556.58	0.315768
$31$	−3139.09	−0.586678	−0.293339	−	0.956009i	$-0.594766\pi$
$31$	−3139.09	−0.586678	−0.293339	+	0.956009i	$0.594766\pi$
$32$	4067.88	0.702252
$33$	−1138.72	−0.182025
$34$	−8740.61	−1.29671
$35$	2068.90	0.285476
$36$	−1818.08	−0.233807
$37$	−5929.61	−0.712068	−0.356034	−	0.934473i	$-0.615871\pi$
$37$	−5929.61	−0.712068	−0.356034	+	0.934473i	$0.615871\pi$
$38$	−2388.40	−0.268317
$39$	2456.99	0.258668
$40$	−3345.67	−0.330623
$41$	300.327	0.0279020	0.0139510	−	0.999903i	$-0.495559\pi$
$41$	300.327	0.0279020	0.0139510	+	0.999903i	$0.495559\pi$
$42$	5152.66	0.450721
$43$	21826.2	1.80014	0.900071	−	0.435743i	$-0.143514\pi$
$43$	21826.2	1.80014	0.900071	+	0.435743i	$0.143514\pi$
$44$	−1424.47	−0.110923
$45$	3860.88	0.284220
$46$	−20995.3	−1.46295
$47$	−16302.7	−1.07650	−0.538250	−	0.842785i	$-0.680914\pi$
$47$	−16302.7	−1.07650	−0.538250	+	0.842785i	$0.680914\pi$
$48$	−11877.7	−0.744099
$49$	−9958.42	−0.592516
$50$	−4135.05	−0.233914
$51$	12432.9	0.669339
$52$	3073.56	0.157628
$53$	−19337.2	−0.945592	−0.472796	−	0.881172i	$-0.656755\pi$
$53$	−19337.2	−0.945592	−0.472796	+	0.881172i	$0.656755\pi$
$54$	24745.6	1.15482
$55$	3025.00	0.134840
$56$	−11075.0	−0.471926
$57$	3397.33	0.138500
$58$	695.566	0.0271499
$59$	−40693.4	−1.52193	−0.760964	−	0.648795i	$-0.775273\pi$
$59$	−40693.4	−1.52193	−0.760964	+	0.648795i	$0.775273\pi$
$60$	−2769.74	−0.0993253
$61$	−25500.0	−0.877436	−0.438718	−	0.898625i	$-0.644567\pi$
$61$	−25500.0	−0.877436	−0.438718	+	0.898625i	$0.644567\pi$
$62$	20768.5	0.686159
$63$	12780.5	0.405691
$64$	13474.7	0.411216
$65$	−6527.00	−0.191615
$66$	7533.84	0.212891
$67$	9615.89	0.261699	0.130850	−	0.991402i	$-0.458230\pi$
$67$	9615.89	0.261699	0.130850	+	0.991402i	$0.458230\pi$
$68$	15552.8	0.407884
$69$	29864.3	0.755144
$70$	−13688.0	−0.333884
$71$	−48423.5	−1.14001	−0.570007	−	0.821640i	$-0.693060\pi$
$71$	−48423.5	−1.14001	−0.570007	+	0.821640i	$0.693060\pi$
$72$	−20667.6	−0.469849
$73$	87237.8	1.91601	0.958004	−	0.286754i	$-0.0925764\pi$
$73$	87237.8	1.91601	0.958004	+	0.286754i	$0.0925764\pi$
$74$	39230.7	0.832813
$75$	5881.80	0.120742
$76$	4249.86	0.0843997
$77$	10013.5	0.192468
$78$	−16255.7	−0.302530
$79$	−36015.2	−0.649258	−0.324629	−	0.945841i	$-0.605240\pi$
$79$	−36015.2	−0.649258	−0.324629	+	0.945841i	$0.605240\pi$
$80$	31553.2	0.551212
$81$	2328.98	0.0394415
$82$	−1986.99	−0.0326333
$83$	41943.1	0.668291	0.334146	−	0.942521i	$-0.391552\pi$
$83$	41943.1	0.668291	0.334146	+	0.942521i	$0.391552\pi$
$84$	−9168.50	−0.141775
$85$	−33027.9	−0.495831
$86$	−144404.	−2.10539
$87$	−989.392	−0.0140143
$88$	−16193.1	−0.222906
$89$	−100651.	−1.34693	−0.673463	−	0.739221i	$-0.735194\pi$
$89$	−100651.	−1.34693	−0.673463	+	0.739221i	$0.735194\pi$
$90$	−25543.9	−0.332415
$91$	−21606.0	−0.273508
$92$	37358.5	0.460172
$93$	−29541.6	−0.354182
$94$	107860.	1.25904
$95$	−9025.00	−0.102598
$96$	38282.3	0.423955
$97$	24120.6	0.260291	0.130146	−	0.991495i	$-0.458456\pi$
$97$	24120.6	0.260291	0.130146	+	0.991495i	$0.458456\pi$
$98$	65885.7	0.692988
$99$	18686.7	0.191621
$100$	7357.79	0.0735779
$101$	−89240.6	−0.870481	−0.435240	−	0.900314i	$-0.643337\pi$
$101$	−89240.6	−0.870481	−0.435240	+	0.900314i	$0.643337\pi$
$102$	−82256.9	−0.782838
$103$	111784.	1.03821	0.519105	−	0.854711i	$-0.326266\pi$
$103$	111784.	1.03821	0.519105	+	0.854711i	$0.326266\pi$
$104$	34939.5	0.316762
$105$	19470.2	0.172345
$106$	127936.	1.10593
$107$	−135177.	−1.14141	−0.570707	−	0.821154i	$-0.693331\pi$
$107$	−135177.	−1.14141	−0.570707	+	0.821154i	$0.693331\pi$
$108$	−44031.6	−0.363250
$109$	10583.2	0.0853202	0.0426601	−	0.999090i	$-0.486417\pi$
$109$	10583.2	0.0853202	0.0426601	+	0.999090i	$0.486417\pi$
$110$	−20013.6	−0.157705
$111$	−55802.9	−0.429882
$112$	104449.	0.786790
$113$	219120.	1.61430	0.807151	−	0.590344i	$-0.201008\pi$
$113$	219120.	1.61430	0.807151	+	0.590344i	$0.201008\pi$
$114$	−22477.0	−0.161986
$115$	−79334.5	−0.559394
$116$	−1237.67	−0.00854005
$117$	−40319.9	−0.272305
$118$	269231.	1.78000
$119$	−109330.	−0.707740
$120$	−31485.7	−0.199600
$121$	14641.0	0.0909091
$122$	168710.	1.02622
$123$	2826.35	0.0168447
$124$	−36954.8	−0.215833
$125$	−15625.0	−0.0894427
$126$	−84556.5	−0.474483
$127$	−171521.	−0.943645	−0.471822	−	0.881694i	$-0.656404\pi$
$127$	−171521.	−0.943645	−0.471822	+	0.881694i	$0.656404\pi$
$128$	−219322.	−1.18320
$129$	205404.	1.08676
$130$	43183.1	0.224107
$131$	195643.	0.996061	0.498031	−	0.867160i	$-0.334057\pi$
$131$	195643.	0.996061	0.498031	+	0.867160i	$0.334057\pi$
$132$	−13405.5	−0.0669651
$133$	−29875.0	−0.146446
$134$	−63619.4	−0.306075
$135$	93505.4	0.441573
$136$	176801.	0.819666
$137$	315333.	1.43538	0.717692	−	0.696360i	$-0.245198\pi$
$137$	315333.	1.43538	0.717692	+	0.696360i	$0.245198\pi$
$138$	−197585.	−0.883193
$139$	28210.4	0.123843	0.0619217	−	0.998081i	$-0.480277\pi$
$139$	28210.4	0.123843	0.0619217	+	0.998081i	$0.480277\pi$
$140$	24356.1	0.105024
$141$	−153423.	−0.649893
$142$	320374.	1.33332
$143$	−31590.7	−0.129187
$144$	194917.	0.783328
$145$	2628.32	0.0103814
$146$	−577172.	−2.24090
$147$	−93717.6	−0.357707
$148$	−69806.1	−0.261963
$149$	332763.	1.22792	0.613959	−	0.789338i	$-0.289576\pi$
$149$	332763.	1.22792	0.613959	+	0.789338i	$0.289576\pi$
$150$	−38914.5	−0.141216
$151$	180255.	0.643348	0.321674	−	0.946850i	$-0.395754\pi$
$151$	180255.	0.643348	0.321674	+	0.946850i	$0.395754\pi$
$152$	48311.5	0.169606
$153$	−204027.	−0.704626
$154$	−66250.0	−0.225105
$155$	78477.2	0.262370
$156$	28924.9	0.0951613
$157$	−237550.	−0.769142	−0.384571	−	0.923095i	$-0.625651\pi$
$157$	−237550.	−0.769142	−0.384571	+	0.923095i	$0.625651\pi$
$158$	238279.	0.759352
$159$	−181980.	−0.570862
$160$	−101697.	−0.314056
$161$	−262617.	−0.798468
$162$	−15408.7	−0.0461295
$163$	484928.	1.42958	0.714789	−	0.699340i	$-0.246523\pi$
$163$	484928.	1.42958	0.714789	+	0.699340i	$0.246523\pi$
$164$	3535.60	0.0102649
$165$	28467.9	0.0814041
$166$	−277499.	−0.781612
$167$	−430009.	−1.19313	−0.596563	−	0.802566i	$-0.703467\pi$
$167$	−430009.	−1.19313	−0.596563	+	0.802566i	$0.703467\pi$
$168$	−104226.	−0.284906
$169$	−303130.	−0.816418
$170$	218515.	0.579908
$171$	−55751.1	−0.145802
$172$	256948.	0.662254
$173$	−258948.	−0.657805	−0.328903	−	0.944364i	$-0.606679\pi$
$173$	−258948.	−0.657805	−0.328903	+	0.944364i	$0.606679\pi$
$174$	6545.90	0.0163906
$175$	−51722.6	−0.127669
$176$	152717.	0.371627
$177$	−382961.	−0.918801
$178$	665916.	1.57532
$179$	−691176.	−1.61234	−0.806169	−	0.591685i	$-0.798463\pi$
$179$	−691176.	−1.61234	−0.806169	+	0.591685i	$0.798463\pi$
$180$	45452.1	0.104562
$181$	−47570.9	−0.107931	−0.0539653	−	0.998543i	$-0.517186\pi$
$181$	−47570.9	−0.107931	−0.0539653	+	0.998543i	$0.517186\pi$
$182$	142947.	0.319886
$183$	−239978.	−0.529716
$184$	424684.	0.924743
$185$	148240.	0.318447
$186$	195450.	0.414240
$187$	−159855.	−0.334289
$188$	−191923.	−0.396033
$189$	309526.	0.630293
$190$	59710.1	0.119995
$191$	332537.	0.659563	0.329782	−	0.944057i	$-0.393025\pi$
$191$	332537.	0.659563	0.329782	+	0.944057i	$0.393025\pi$
$192$	126809.	0.248255
$193$	−756519.	−1.46193	−0.730965	−	0.682415i	$-0.760930\pi$
$193$	−756519.	−1.46193	−0.730965	+	0.682415i	$0.760930\pi$
$194$	−159584.	−0.304428
$195$	−61424.9	−0.115680
$196$	−117235.	−0.217981
$197$	648974.	1.19141	0.595705	−	0.803203i	$-0.296873\pi$
$197$	648974.	1.19141	0.595705	+	0.803203i	$0.296873\pi$
$198$	−123632.	−0.224114
$199$	−217459.	−0.389264	−0.194632	−	0.980876i	$-0.562351\pi$
$199$	−217459.	−0.389264	−0.194632	+	0.980876i	$0.562351\pi$
$200$	83641.8	0.147859
$201$	90494.0	0.157990
$202$	590423.	1.01809
$203$	8700.38	0.0148183
$204$	146366.	0.246243
$205$	−7508.19	−0.0124782
$206$	−739569.	−1.21426
$207$	−490082.	−0.794955
$208$	−329516.	−0.528103
$209$	−43681.0	−0.0691714
$210$	−128816.	−0.201569
$211$	−323595.	−0.500375	−0.250188	−	0.968197i	$-0.580492\pi$
$211$	−323595.	−0.500375	−0.250188	+	0.968197i	$0.580492\pi$
$212$	−227646.	−0.347873
$213$	−455708.	−0.688237
$214$	894341.	1.33496
$215$	−545655.	−0.805048
$216$	−500542.	−0.729971
$217$	259779.	0.374502
$218$	−70019.5	−0.0997878
$219$	820985.	1.15671
$220$	35611.7	0.0496062
$221$	344917.	0.475044
$222$	369196.	0.502776
$223$	−644930.	−0.868462	−0.434231	−	0.900802i	$-0.642980\pi$
$223$	−644930.	−0.868462	−0.434231	+	0.900802i	$0.642980\pi$
$224$	−336642.	−0.448278
$225$	−96522.0	−0.127107
$226$	−1.44971e6	−1.88804
$227$	661967.	0.852652	0.426326	−	0.904570i	$-0.359808\pi$
$227$	661967.	0.852652	0.426326	+	0.904570i	$0.359808\pi$
$228$	39995.0	0.0509528
$229$	−1.37690e6	−1.73505	−0.867526	−	0.497392i	$-0.834291\pi$
$229$	−1.37690e6	−1.73505	−0.867526	+	0.497392i	$0.834291\pi$
$230$	524883.	0.654249
$231$	94235.9	0.116195
$232$	−14069.6	−0.0171617
$233$	−373718.	−0.450977	−0.225488	−	0.974246i	$-0.572398\pi$
$233$	−373718.	−0.450977	−0.225488	+	0.974246i	$0.572398\pi$
$234$	266760.	0.318479
$235$	407567.	0.481426
$236$	−479062.	−0.559901
$237$	−338935.	−0.391963
$238$	723339.	0.827750
$239$	726301.	0.822474	0.411237	−	0.911529i	$-0.365097\pi$
$239$	726301.	0.822474	0.411237	+	0.911529i	$0.365097\pi$
$240$	296944.	0.332771
$241$	499404.	0.553872	0.276936	−	0.960888i	$-0.410681\pi$
$241$	499404.	0.553872	0.276936	+	0.960888i	$0.410681\pi$
$242$	−96866.0	−0.106324
$243$	930791.	1.01120
$244$	−300198.	−0.322800
$245$	248961.	0.264981
$246$	−18699.3	−0.0197010
$247$	94249.9	0.0982966
$248$	−420095.	−0.433728
$249$	394722.	0.403453
$250$	103376.	0.104609
$251$	360345.	0.361023	0.180511	−	0.983573i	$-0.442225\pi$
$251$	360345.	0.361023	0.180511	+	0.983573i	$0.442225\pi$
$252$	150458.	0.149249
$253$	−383979.	−0.377143
$254$	1.13480e6	1.10366
$255$	−310822.	−0.299338
$256$	1.01986e6	0.972613
$257$	436368.	0.412116	0.206058	−	0.978540i	$-0.433936\pi$
$257$	436368.	0.412116	0.206058	+	0.978540i	$0.433936\pi$
$258$	−1.35897e6	−1.27104
$259$	490712.	0.454545
$260$	−76838.9	−0.0704933
$261$	16236.2	0.0147531
$262$	−1.29439e6	−1.16496
$263$	965411.	0.860643	0.430321	−	0.902676i	$-0.358400\pi$
$263$	965411.	0.860643	0.430321	+	0.902676i	$0.358400\pi$
$264$	−152391.	−0.134570
$265$	483430.	0.422881
$266$	197655.	0.171279
$267$	−947217.	−0.813151
$268$	113203.	0.0962764
$269$	1.07719e6	0.907634	0.453817	−	0.891095i	$-0.350062\pi$
$269$	1.07719e6	0.907634	0.453817	+	0.891095i	$0.350062\pi$
$270$	−618639.	−0.516450
$271$	55539.5	0.0459387	0.0229694	−	0.999736i	$-0.492688\pi$
$271$	55539.5	0.0459387	0.0229694	+	0.999736i	$0.492688\pi$
$272$	−1.66742e6	−1.36654
$273$	−203331.	−0.165119
$274$	−2.08627e6	−1.67878
$275$	−75625.0	−0.0603023
$276$	351577.	0.277810
$277$	−84747.3	−0.0663631	−0.0331815	−	0.999449i	$-0.510564\pi$
$277$	−84747.3	−0.0663631	−0.0331815	+	0.999449i	$0.510564\pi$
$278$	−186642.	−0.144843
$279$	484786.	0.372855
$280$	276875.	0.211052
$281$	1.01385e6	0.765962	0.382981	−	0.923756i	$-0.374897\pi$
$281$	1.01385e6	0.765962	0.382981	+	0.923756i	$0.374897\pi$
$282$	1.01506e6	0.760094
$283$	1.71090e6	1.26987	0.634935	−	0.772565i	$-0.281027\pi$
$283$	1.71090e6	1.26987	0.634935	+	0.772565i	$0.281027\pi$
$284$	−570064.	−0.419400
$285$	−84933.3	−0.0619392
$286$	209006.	0.151093
$287$	−24853.9	−0.0178111
$288$	−628223.	−0.446306
$289$	325491.	0.229242
$290$	−17389.2	−0.0121418
$291$	226996.	0.157140
$292$	1.02700e6	0.704880
$293$	136358.	0.0927922	0.0463961	−	0.998923i	$-0.485226\pi$
$293$	136358.	0.0927922	0.0463961	+	0.998923i	$0.485226\pi$
$294$	620043.	0.418363
$295$	1.01733e6	0.680626
$296$	−793541.	−0.526429
$297$	452566.	0.297708
$298$	−2.20159e6	−1.43613
$299$	828506.	0.535942
$300$	69243.4	0.0444196
$301$	−1.80625e6	−1.14911
$302$	−1.19258e6	−0.752440
$303$	−839833.	−0.525517
$304$	−455628.	−0.282766
$305$	637500.	0.392401
$306$	1.34986e6	0.824108
$307$	2.66340e6	1.61284	0.806419	−	0.591344i	$-0.201402\pi$
$307$	2.66340e6	1.61284	0.806419	+	0.591344i	$0.201402\pi$
$308$	117884.	0.0708070
$309$	1.05198e6	0.626776
$310$	−519211.	−0.306860
$311$	−1.53260e6	−0.898518	−0.449259	−	0.893401i	$-0.648312\pi$
$311$	−1.53260e6	−0.898518	−0.449259	+	0.893401i	$0.648312\pi$
$312$	328812.	0.191232
$313$	163143.	0.0941257	0.0470628	−	0.998892i	$-0.485014\pi$
$313$	163143.	0.0941257	0.0470628	+	0.998892i	$0.485014\pi$
$314$	1.57165e6	0.899564
$315$	−319512.	−0.181430
$316$	−423987.	−0.238855
$317$	329636.	0.184241	0.0921205	−	0.995748i	$-0.470636\pi$
$317$	329636.	0.184241	0.0921205	+	0.995748i	$0.470636\pi$
$318$	1.20399e6	0.667662
$319$	12721.1	0.00699917
$320$	−336868.	−0.183901
$321$	−1.27213e6	−0.689082
$322$	1.73749e6	0.933863
$323$	476923.	0.254356
$324$	27417.9	0.0145101
$325$	163175.	0.0856930
$326$	−3.20832e6	−1.67199
$327$	99597.6	0.0515086
$328$	40191.9	0.0206278
$329$	1.34915e6	0.687178
$330$	−188346.	−0.0952076
$331$	313250.	0.157152	0.0785762	−	0.996908i	$-0.474963\pi$
$331$	313250.	0.157152	0.0785762	+	0.996908i	$0.474963\pi$
$332$	493774.	0.245857
$333$	915740.	0.452545
$334$	2.84497e6	1.39544
$335$	−240397.	−0.117035
$336$	982956.	0.474992
$337$	1.42107e6	0.681617	0.340808	−	0.940133i	$-0.389299\pi$
$337$	1.42107e6	0.681617	0.340808	+	0.940133i	$0.389299\pi$
$338$	2.00553e6	0.954856
$339$	2.06211e6	0.974569
$340$	−388820.	−0.182411
$341$	379830.	0.176890
$342$	368854.	0.170525
$343$	2.21500e6	1.01657
$344$	2.92093e6	1.33084
$345$	−746608.	−0.337711
$346$	1.71322e6	0.769348
$347$	2.97345e6	1.32568	0.662838	−	0.748763i	$-0.269352\pi$
$347$	2.97345e6	1.32568	0.662838	+	0.748763i	$0.269352\pi$
$348$	−11647.6	−0.00515570
$349$	1.98440e6	0.872098	0.436049	−	0.899923i	$-0.356377\pi$
$349$	1.98440e6	0.872098	0.436049	+	0.899923i	$0.356377\pi$
$350$	342201.	0.149317
$351$	−976496.	−0.423061
$352$	−492213.	−0.211737
$353$	1.39006e6	0.593739	0.296869	−	0.954918i	$-0.404057\pi$
$353$	1.39006e6	0.593739	0.296869	+	0.954918i	$0.404057\pi$
$354$	2.53370e6	1.07460
$355$	1.21059e6	0.509830
$356$	−1.18491e6	−0.495520
$357$	−1.02890e6	−0.427269
$358$	4.57288e6	1.88574
$359$	2.49635e6	1.02228	0.511139	−	0.859498i	$-0.329224\pi$
$359$	2.49635e6	1.02228	0.511139	+	0.859498i	$0.329224\pi$
$360$	516690.	0.210123
$361$	130321.	0.0526316
$362$	314732.	0.126232
$363$	137785.	0.0548826
$364$	−254356.	−0.100621
$365$	−2.18094e6	−0.856865
$366$	1.58771e6	0.619539
$367$	2.40082e6	0.930453	0.465226	−	0.885192i	$-0.345973\pi$
$367$	2.40082e6	0.930453	0.465226	+	0.885192i	$0.345973\pi$
$368$	−4.00521e6	−1.54172
$369$	−46381.1	−0.0177327
$370$	−980769.	−0.372445
$371$	1.60027e6	0.603613
$372$	−347778.	−0.130300
$373$	1.35378e6	0.503822	0.251911	−	0.967750i	$-0.418941\pi$
$373$	1.35378e6	0.503822	0.251911	+	0.967750i	$0.418941\pi$
$374$	1.05761e6	0.390974
$375$	−147045.	−0.0539973
$376$	−2.18174e6	−0.795853
$377$	−27448.0	−0.00994622
$378$	−2.04785e6	−0.737171
$379$	−371861.	−0.132979	−0.0664894	−	0.997787i	$-0.521180\pi$
$379$	−371861.	−0.132979	−0.0664894	+	0.997787i	$0.521180\pi$
$380$	−106247.	−0.0377447
$381$	−1.61417e6	−0.569686
$382$	−2.20009e6	−0.771404
$383$	2.00360e6	0.697934	0.348967	−	0.937135i	$-0.386533\pi$
$383$	2.00360e6	0.697934	0.348967	+	0.937135i	$0.386533\pi$
$384$	−2.06401e6	−0.714306
$385$	−250337.	−0.0860744
$386$	5.00519e6	1.70983
$387$	−3.37073e6	−1.14405
$388$	283959.	0.0957584
$389$	−2.14327e6	−0.718128	−0.359064	−	0.933313i	$-0.616904\pi$
$389$	−2.14327e6	−0.718128	−0.359064	+	0.933313i	$0.616904\pi$
$390$	406392.	0.135295
$391$	4.19240e6	1.38682
$392$	−1.33270e6	−0.438045
$393$	1.84117e6	0.601331
$394$	−4.29366e6	−1.39344
$395$	900379.	0.290357
$396$	219988.	0.0704955
$397$	2.26311e6	0.720657	0.360329	−	0.932825i	$-0.382665\pi$
$397$	2.26311e6	0.720657	0.360329	+	0.932825i	$0.382665\pi$
$398$	1.43873e6	0.455271
$399$	−281150.	−0.0884109
$400$	−788830.	−0.246509
$401$	−2.35869e6	−0.732503	−0.366251	−	0.930516i	$-0.619359\pi$
$401$	−2.35869e6	−0.732503	−0.366251	+	0.930516i	$0.619359\pi$
$402$	−598715.	−0.184780
$403$	−819553.	−0.251371
$404$	−1.05058e6	−0.320241
$405$	−58224.5	−0.0176388
$406$	−57562.4	−0.0173310
$407$	717483.	0.214697
$408$	1.66385e6	0.494840
$409$	2.87664e6	0.850311	0.425155	−	0.905120i	$-0.360219\pi$
$409$	2.87664e6	0.850311	0.425155	+	0.905120i	$0.360219\pi$
$410$	49674.7	0.0145941
$411$	2.96757e6	0.866554
$412$	1.31597e6	0.381946
$413$	3.36763e6	0.971514
$414$	3.24242e6	0.929754
$415$	−1.04858e6	−0.298869
$416$	1.06204e6	0.300890
$417$	265485.	0.0747653
$418$	288997.	0.0809007
$419$	3.91363e6	1.08904	0.544521	−	0.838747i	$-0.316711\pi$
$419$	3.91363e6	1.08904	0.544521	+	0.838747i	$0.316711\pi$
$420$	229213.	0.0634038
$421$	−3.22519e6	−0.886851	−0.443426	−	0.896311i	$-0.646237\pi$
$421$	−3.22519e6	−0.886851	−0.443426	+	0.896311i	$0.646237\pi$
$422$	2.14093e6	0.585223
$423$	2.51771e6	0.684155
$424$	−2.58784e6	−0.699072
$425$	825698.	0.221742
$426$	3.01500e6	0.804940
$427$	2.11028e6	0.560107
$428$	−1.59137e6	−0.419914
$429$	−297296.	−0.0779913
$430$	3.61009e6	0.941559
$431$	1.09470e6	0.283858	0.141929	−	0.989877i	$-0.454669\pi$
$431$	1.09470e6	0.283858	0.141929	+	0.989877i	$0.454669\pi$
$432$	4.72063e6	1.21700
$433$	5.52147e6	1.41526	0.707628	−	0.706586i	$-0.249765\pi$
$433$	5.52147e6	1.41526	0.707628	+	0.706586i	$0.249765\pi$
$434$	−1.71872e6	−0.438006
$435$	24734.8	0.00626737
$436$	124591.	0.0313884
$437$	1.14559e6	0.286963
$438$	−5.43170e6	−1.35285
$439$	4.16959e6	1.03260	0.516300	−	0.856408i	$-0.327309\pi$
$439$	4.16959e6	1.03260	0.516300	+	0.856408i	$0.327309\pi$
$440$	404826.	0.0996867
$441$	1.53793e6	0.376565
$442$	−2.28200e6	−0.555596
$443$	−3.67819e6	−0.890481	−0.445240	−	0.895411i	$-0.646882\pi$
$443$	−3.67819e6	−0.890481	−0.445240	+	0.895411i	$0.646882\pi$
$444$	−656938.	−0.158149
$445$	2.51628e6	0.602364
$446$	4.26691e6	1.01573
$447$	3.13160e6	0.741305
$448$	−1.11512e6	−0.262497
$449$	7.61540e6	1.78269	0.891347	−	0.453322i	$-0.149761\pi$
$449$	7.61540e6	1.78269	0.891347	+	0.453322i	$0.149761\pi$
$450$	638597.	0.148660
$451$	−36339.6	−0.00841277
$452$	2.57958e6	0.593885
$453$	1.69636e6	0.388395
$454$	−4.37962e6	−0.997234
$455$	540149.	0.122317
$456$	454654.	0.102393
$457$	−4.81875e6	−1.07930	−0.539652	−	0.841888i	$-0.681444\pi$
$457$	−4.81875e6	−1.07930	−0.539652	+	0.841888i	$0.681444\pi$
$458$	9.10965e6	2.02926
$459$	−4.94126e6	−1.09473
$460$	−933963.	−0.205795
$461$	3.53224e6	0.774102	0.387051	−	0.922058i	$-0.373494\pi$
$461$	3.53224e6	0.774102	0.387051	+	0.922058i	$0.373494\pi$
$462$	−623472.	−0.135898
$463$	4.51379e6	0.978564	0.489282	−	0.872126i	$-0.337259\pi$
$463$	4.51379e6	0.978564	0.489282	+	0.872126i	$0.337259\pi$
$464$	132691.	0.0286119
$465$	738541.	0.158395
$466$	2.47255e6	0.527448
$467$	−4.65431e6	−0.987560	−0.493780	−	0.869587i	$-0.664385\pi$
$467$	−4.65431e6	−0.987560	−0.493780	+	0.869587i	$0.664385\pi$
$468$	−474665.	−0.100178
$469$	−795774.	−0.167054
$470$	−2.69649e6	−0.563060
$471$	−2.23556e6	−0.464338
$472$	−5.44587e6	−1.12515
$473$	−2.64097e6	−0.542763
$474$	2.24242e6	0.458427
$475$	225625.	0.0458831
$476$	−1.28709e6	−0.260370
$477$	2.98634e6	0.600957
$478$	−4.80526e6	−0.961939
$479$	−3.63054e6	−0.722991	−0.361496	−	0.932374i	$-0.617734\pi$
$479$	−3.63054e6	−0.722991	−0.361496	+	0.932374i	$0.617734\pi$
$480$	−957058.	−0.189599
$481$	−1.54810e6	−0.305096
$482$	−3.30409e6	−0.647791
$483$	−2.47146e6	−0.482042
$484$	172361.	0.0334445
$485$	−603016.	−0.116406
$486$	−6.15818e6	−1.18267
$487$	−5.99712e6	−1.14583	−0.572915	−	0.819614i	$-0.694188\pi$
$487$	−5.99712e6	−1.14583	−0.572915	+	0.819614i	$0.694188\pi$
$488$	−3.41259e6	−0.648685
$489$	4.56360e6	0.863049
$490$	−1.64714e6	−0.309914
$491$	2.67772e6	0.501258	0.250629	−	0.968083i	$-0.419363\pi$
$491$	2.67772e6	0.501258	0.250629	+	0.968083i	$0.419363\pi$
$492$	33273.1	0.00619699
$493$	−138893.	−0.0257372
$494$	−623564.	−0.114965
$495$	−467166.	−0.0856956
$496$	3.96193e6	0.723108
$497$	4.00734e6	0.727722
$498$	−2.61151e6	−0.471866
$499$	1.98915e6	0.357615	0.178807	−	0.983884i	$-0.442776\pi$
$499$	1.98915e6	0.357615	0.178807	+	0.983884i	$0.442776\pi$
$500$	−183945.	−0.0329051
$501$	−4.04676e6	−0.720300
$502$	−2.38407e6	−0.422241
$503$	−1.79204e6	−0.315812	−0.157906	−	0.987454i	$-0.550474\pi$
$503$	−1.79204e6	−0.315812	−0.157906	+	0.987454i	$0.550474\pi$
$504$	1.71037e6	0.299926
$505$	2.23102e6	0.389291
$506$	2.54043e6	0.441095
$507$	−2.85272e6	−0.492879
$508$	−2.01923e6	−0.347157
$509$	6.51846e6	1.11519	0.557597	−	0.830112i	$-0.311723\pi$
$509$	6.51846e6	1.11519	0.557597	+	0.830112i	$0.311723\pi$
$510$	2.05642e6	0.350096
$511$	−7.21946e6	−1.22307
$512$	270834.	0.0456591
$513$	−1.35022e6	−0.226522
$514$	−2.88704e6	−0.481998
$515$	−2.79459e6	−0.464301
$516$	2.41811e6	0.399808
$517$	1.97262e6	0.324577
$518$	−3.24659e6	−0.531621
$519$	−2.43693e6	−0.397123
$520$	−873488.	−0.141660
$521$	−2.98563e6	−0.481882	−0.240941	−	0.970540i	$-0.577456\pi$
$521$	−2.98563e6	−0.481882	−0.240941	+	0.970540i	$0.577456\pi$
$522$	−107420.	−0.0172547
$523$	−4.80355e6	−0.767906	−0.383953	−	0.923353i	$-0.625438\pi$
$523$	−4.80355e6	−0.767906	−0.383953	+	0.923353i	$0.625438\pi$
$524$	2.30320e6	0.366441
$525$	−486755.	−0.0770748
$526$	−6.38723e6	−1.00658
$527$	−4.14710e6	−0.650457
$528$	1.43721e6	0.224354
$529$	3.63400e6	0.564606
$530$	−3.19841e6	−0.494589
$531$	6.28449e6	0.967239
$532$	−351702.	−0.0538761
$533$	78409.5	0.0119550
$534$	6.26686e6	0.951036
$535$	3.37942e6	0.510456
$536$	1.28686e6	0.193473
$537$	−6.50458e6	−0.973383
$538$	−7.12675e6	−1.06154
$539$	1.20497e6	0.178650
$540$	1.10079e6	0.162450
$541$	4.89070e6	0.718419	0.359210	−	0.933257i	$-0.383046\pi$
$541$	4.89070e6	0.718419	0.359210	+	0.933257i	$0.383046\pi$
$542$	−367454.	−0.0537285
$543$	−447684.	−0.0651586
$544$	5.37414e6	0.778595
$545$	−264581.	−0.0381564
$546$	1.34526e6	0.193118
$547$	−5.60900e6	−0.801525	−0.400762	−	0.916182i	$-0.631255\pi$
$547$	−5.60900e6	−0.801525	−0.400762	+	0.916182i	$0.631255\pi$
$548$	3.71225e6	0.528063
$549$	3.93810e6	0.557642
$550$	500341.	0.0705276
$551$	−37952.9	−0.00532557
$552$	3.99665e6	0.558275
$553$	2.98048e6	0.414451
$554$	560695.	0.0776161
$555$	1.39507e6	0.192249
$556$	332106.	0.0455607
$557$	−1.19205e6	−0.162801	−0.0814004	−	0.996681i	$-0.525939\pi$
$557$	−1.19205e6	−0.162801	−0.0814004	+	0.996681i	$0.525939\pi$
$558$	−3.20738e6	−0.436079
$559$	5.69838e6	0.771298
$560$	−2.61122e6	−0.351863
$561$	−1.50438e6	−0.201813
$562$	−6.70770e6	−0.895845
$563$	3.45482e6	0.459362	0.229681	−	0.973266i	$-0.426232\pi$
$563$	3.45482e6	0.459362	0.229681	+	0.973266i	$0.426232\pi$
$564$	−1.80616e6	−0.239089
$565$	−5.47799e6	−0.721938
$566$	−1.13195e7	−1.48520
$567$	−192737.	−0.0251773
$568$	−6.48037e6	−0.842808
$569$	7.84585e6	1.01592	0.507960	−	0.861381i	$-0.330400\pi$
$569$	7.84585e6	1.01592	0.507960	+	0.861381i	$0.330400\pi$
$570$	561925.	0.0724421
$571$	−3.05232e6	−0.391778	−0.195889	−	0.980626i	$-0.562759\pi$
$571$	−3.05232e6	−0.391778	−0.195889	+	0.980626i	$0.562759\pi$
$572$	−371900.	−0.0475266
$573$	3.12947e6	0.398184
$574$	164436.	0.0208313
$575$	1.98336e6	0.250168
$576$	−2.08097e6	−0.261342
$577$	8.83084e6	1.10424	0.552119	−	0.833765i	$-0.313819\pi$
$577$	8.83084e6	1.10424	0.552119	+	0.833765i	$0.313819\pi$
$578$	−2.15348e6	−0.268115
$579$	−7.11951e6	−0.882579
$580$	30941.8	0.00381923
$581$	−3.47105e6	−0.426600
$582$	−1.50183e6	−0.183786
$583$	2.33980e6	0.285107
$584$	1.16748e7	1.41650
$585$	1.00800e6	0.121778
$586$	−902155.	−0.108527
$587$	9.57602e6	1.14707	0.573535	−	0.819181i	$-0.305572\pi$
$587$	9.57602e6	1.14707	0.573535	+	0.819181i	$0.305572\pi$
$588$	−1.10329e6	−0.131597
$589$	−1.13321e6	−0.134593
$590$	−6.73076e6	−0.796039
$591$	6.10742e6	0.719265
$592$	7.48393e6	0.877658
$593$	−6.38507e6	−0.745639	−0.372820	−	0.927904i	$-0.621609\pi$
$593$	−6.38507e6	−0.745639	−0.372820	+	0.927904i	$0.621609\pi$
$594$	−2.99421e6	−0.348190
$595$	2.73326e6	0.316511
$596$	3.91745e6	0.451739
$597$	−2.04648e6	−0.235002
$598$	−5.48146e6	−0.626820
$599$	3.98259e6	0.453522	0.226761	−	0.973950i	$-0.427186\pi$
$599$	3.98259e6	0.453522	0.226761	+	0.973950i	$0.427186\pi$
$600$	787144.	0.0892639
$601$	−1.09352e7	−1.23493	−0.617464	−	0.786599i	$-0.711840\pi$
$601$	−1.09352e7	−1.23493	−0.617464	+	0.786599i	$0.711840\pi$
$602$	1.19503e7	1.34396
$603$	−1.48503e6	−0.166319
$604$	2.12205e6	0.236681
$605$	−366025.	−0.0406558
$606$	5.55640e6	0.614628
$607$	−6.22650e6	−0.685918	−0.342959	−	0.939350i	$-0.611429\pi$
$607$	−6.22650e6	−0.685918	−0.342959	+	0.939350i	$0.611429\pi$
$608$	1.46850e6	0.161108
$609$	81878.3	0.00894593
$610$	−4.21775e6	−0.458940
$611$	−4.25630e6	−0.461243
$612$	−2.40190e6	−0.259225
$613$	−3.81930e6	−0.410518	−0.205259	−	0.978708i	$-0.565804\pi$
$613$	−3.81930e6	−0.410518	−0.205259	+	0.978708i	$0.565804\pi$
$614$	−1.76213e7	−1.88632
$615$	−70658.7	−0.00753317
$616$	1.34007e6	0.142291
$617$	7.08348e6	0.749090	0.374545	−	0.927209i	$-0.377799\pi$
$617$	7.08348e6	0.749090	0.374545	+	0.927209i	$0.377799\pi$
$618$	−6.96000e6	−0.733057
$619$	8.54363e6	0.896223	0.448111	−	0.893978i	$-0.352097\pi$
$619$	8.54363e6	0.896223	0.448111	+	0.893978i	$0.352097\pi$
$620$	923871.	0.0965233
$621$	−1.18691e7	−1.23507
$622$	1.01398e7	1.05088
$623$	8.32950e6	0.859803
$624$	−3.10104e6	−0.318820
$625$	390625.	0.0400000
$626$	−1.07937e6	−0.110086
$627$	−411077.	−0.0417594
$628$	−2.79655e6	−0.282959
$629$	−7.83370e6	−0.789479
$630$	2.11391e6	0.212195
$631$	−800548.	−0.0800413	−0.0400206	−	0.999199i	$-0.512742\pi$
$631$	−800548.	−0.0800413	−0.0400206	+	0.999199i	$0.512742\pi$
$632$	−4.81980e6	−0.479994
$633$	−3.04532e6	−0.302081
$634$	−2.18090e6	−0.215482
$635$	4.28803e6	0.422011
$636$	−2.14236e6	−0.210014
$637$	−2.59994e6	−0.253872
$638$	−84163.5	−0.00818601
$639$	7.47829e6	0.724520
$640$	5.48304e6	0.529142
$641$	6.70291e6	0.644345	0.322172	−	0.946681i	$-0.395587\pi$
$641$	6.70291e6	0.644345	0.322172	+	0.946681i	$0.395587\pi$
$642$	8.41654e6	0.805928
$643$	−1.36584e6	−0.130278	−0.0651392	−	0.997876i	$-0.520749\pi$
$643$	−1.36584e6	−0.130278	−0.0651392	+	0.997876i	$0.520749\pi$
$644$	−3.09165e6	−0.293748
$645$	−5.13510e6	−0.486015
$646$	−3.15536e6	−0.297487
$647$	−732540.	−0.0687972	−0.0343986	−	0.999408i	$-0.510952\pi$
$647$	−732540.	−0.0687972	−0.0343986	+	0.999408i	$0.510952\pi$
$648$	311680.	0.0291589
$649$	4.92390e6	0.458878
$650$	−1.07958e6	−0.100224
$651$	2.44475e6	0.226090
$652$	5.70880e6	0.525927
$653$	−1.07279e6	−0.0984535	−0.0492268	−	0.998788i	$-0.515676\pi$
$653$	−1.07279e6	−0.0984535	−0.0492268	+	0.998788i	$0.515676\pi$
$654$	−658945.	−0.0602428
$655$	−4.89107e6	−0.445452
$656$	−379052.	−0.0343905
$657$	−1.34726e7	−1.21769
$658$	−8.92606e6	−0.803702
$659$	1.09932e7	0.986073	0.493036	−	0.870009i	$-0.335887\pi$
$659$	1.09932e7	0.986073	0.493036	+	0.870009i	$0.335887\pi$
$660$	335138.	0.0299477
$661$	8.12200e6	0.723035	0.361517	−	0.932365i	$-0.382259\pi$
$661$	8.12200e6	0.723035	0.361517	+	0.932365i	$0.382259\pi$
$662$	−2.07249e6	−0.183801
$663$	3.24598e6	0.286788
$664$	5.61312e6	0.494065
$665$	746874.	0.0654928
$666$	−6.05861e6	−0.529282
$667$	−333626.	−0.0290366
$668$	−5.06227e6	−0.438939
$669$	−6.06937e6	−0.524298
$670$	1.59049e6	0.136881
$671$	3.08550e6	0.264557
$672$	−3.16810e6	−0.270630
$673$	−1.81566e7	−1.54524	−0.772622	−	0.634867i	$-0.781055\pi$
$673$	−1.81566e7	−1.54524	−0.772622	+	0.634867i	$0.781055\pi$
$674$	−9.40190e6	−0.797197
$675$	−2.33764e6	−0.197477
$676$	−3.56859e6	−0.300352
$677$	5.81863e6	0.487921	0.243960	−	0.969785i	$-0.421553\pi$
$677$	5.81863e6	0.487921	0.243960	+	0.969785i	$0.421553\pi$
$678$	−1.36431e7	−1.13982
$679$	−1.99613e6	−0.166155
$680$	−4.42002e6	−0.366566
$681$	6.22970e6	0.514753
$682$	−2.51298e6	−0.206885
$683$	−7.75687e6	−0.636260	−0.318130	−	0.948047i	$-0.603055\pi$
$683$	−7.75687e6	−0.636260	−0.318130	+	0.948047i	$0.603055\pi$
$684$	−656328.	−0.0536390
$685$	−7.88333e6	−0.641923
$686$	−1.46546e7	−1.18895
$687$	−1.29578e7	−1.04747
$688$	−2.75474e7	−2.21876
$689$	−5.04855e6	−0.405153
$690$	4.93962e6	0.394976
$691$	4.56758e6	0.363908	0.181954	−	0.983307i	$-0.441758\pi$
$691$	4.56758e6	0.363908	0.181954	+	0.983307i	$0.441758\pi$
$692$	−3.04846e6	−0.242000
$693$	−1.54644e6	−0.122320
$694$	−1.96726e7	−1.55047
$695$	−705261.	−0.0553844
$696$	−132407.	−0.0103607
$697$	396768.	0.0309353
$698$	−1.31289e7	−1.01998
$699$	−3.51702e6	−0.272259
$700$	−608903.	−0.0469681
$701$	−1.47186e7	−1.13128	−0.565640	−	0.824652i	$-0.691371\pi$
$701$	−1.47186e7	−1.13128	−0.565640	+	0.824652i	$0.691371\pi$
$702$	6.46057e6	0.494798
$703$	−2.14059e6	−0.163360
$704$	−1.63044e6	−0.123986
$705$	3.83557e6	0.290641
$706$	−9.19672e6	−0.694418
$707$	7.38521e6	0.555667
$708$	−4.50840e6	−0.338017
$709$	1.64501e7	1.22900	0.614501	−	0.788916i	$-0.289358\pi$
$709$	1.64501e7	1.22900	0.614501	+	0.788916i	$0.289358\pi$
$710$	−8.00934e6	−0.596281
$711$	5.56201e6	0.412627
$712$	−1.34698e7	−0.995777
$713$	−9.96152e6	−0.733841
$714$	6.80726e6	0.499720
$715$	789767.	0.0577742
$716$	−8.13685e6	−0.593163
$717$	6.83514e6	0.496534
$718$	−1.65160e7	−1.19562
$719$	−2.10347e7	−1.51745	−0.758725	−	0.651411i	$-0.774178\pi$
$719$	−2.10347e7	−1.51745	−0.758725	+	0.651411i	$0.774178\pi$
$720$	−4.87292e6	−0.350315
$721$	−9.25078e6	−0.662735
$722$	−862214.	−0.0615562
$723$	4.69983e6	0.334377
$724$	−560027.	−0.0397066
$725$	−65708.0	−0.00464272
$726$	−911595.	−0.0641890
$727$	−4.65578e6	−0.326706	−0.163353	−	0.986568i	$-0.552231\pi$
$727$	−4.65578e6	−0.326706	−0.163353	+	0.986568i	$0.552231\pi$
$728$	−2.89146e6	−0.202203
$729$	8.19362e6	0.571028
$730$	1.44293e7	1.00216
$731$	2.88349e7	1.99584
$732$	−2.82513e6	−0.194877
$733$	−2.03719e7	−1.40046	−0.700230	−	0.713917i	$-0.746919\pi$
$733$	−2.03719e7	−1.40046	−0.700230	+	0.713917i	$0.746919\pi$
$734$	−1.58840e7	−1.08823
$735$	2.34294e6	0.159972
$736$	1.29089e7	0.878406
$737$	−1.16352e6	−0.0789053
$738$	306861.	0.0207396
$739$	1.05663e7	0.711723	0.355862	−	0.934539i	$-0.384187\pi$
$739$	1.05663e7	0.711723	0.355862	+	0.934539i	$0.384187\pi$
$740$	1.74515e6	0.117153
$741$	886975.	0.0593425
$742$	−1.05875e7	−0.705967
$743$	−1.61701e7	−1.07459	−0.537293	−	0.843396i	$-0.680553\pi$
$743$	−1.61701e7	−1.07459	−0.537293	+	0.843396i	$0.680553\pi$
$744$	−3.95346e6	−0.261846
$745$	−8.31908e6	−0.549142
$746$	−8.95673e6	−0.589254
$747$	−6.47750e6	−0.424723
$748$	−1.88189e6	−0.122982
$749$	1.11867e7	0.728615
$750$	972862.	0.0631536
$751$	−6.58933e6	−0.426326	−0.213163	−	0.977017i	$-0.568377\pi$
$751$	−6.58933e6	−0.426326	−0.213163	+	0.977017i	$0.568377\pi$
$752$	2.05761e7	1.32684
$753$	3.39117e6	0.217953
$754$	181598.	0.0116328
$755$	−4.50639e6	−0.287714
$756$	3.64389e6	0.231878
$757$	2.89867e7	1.83848	0.919241	−	0.393696i	$-0.128804\pi$
$757$	2.89867e7	1.83848	0.919241	+	0.393696i	$0.128804\pi$
$758$	2.46026e6	0.155528
$759$	−3.61358e6	−0.227685
$760$	−1.20779e6	−0.0758502
$761$	204137.	0.0127779	0.00638897	−	0.999980i	$-0.497966\pi$
$761$	204137.	0.0127779	0.00638897	+	0.999980i	$0.497966\pi$
$762$	1.06794e7	0.666287
$763$	−875827.	−0.0544637
$764$	3.91478e6	0.242647
$765$	5.10067e6	0.315118
$766$	−1.32560e7	−0.816281
$767$	−1.06242e7	−0.652092
$768$	9.59778e6	0.587175
$769$	−941496.	−0.0574120	−0.0287060	−	0.999588i	$-0.509139\pi$
$769$	−941496.	−0.0574120	−0.0287060	+	0.999588i	$0.509139\pi$
$770$	1.65625e6	0.100670
$771$	4.10661e6	0.248798
$772$	−8.90609e6	−0.537829
$773$	4.07459e6	0.245265	0.122632	−	0.992452i	$-0.460866\pi$
$773$	4.07459e6	0.245265	0.122632	+	0.992452i	$0.460866\pi$
$774$	2.23010e7	1.33805
$775$	−1.96193e6	−0.117336
$776$	3.22799e6	0.192432
$777$	4.61803e6	0.274413
$778$	1.41800e7	0.839900
$779$	108418.	0.00640116
$780$	−723122.	−0.0425574
$781$	5.85924e6	0.343727
$782$	−2.77373e7	−1.62198
$783$	393219.	0.0229208
$784$	1.25688e7	0.730304
$785$	5.93876e6	0.343971
$786$	−1.21813e7	−0.703297
$787$	−8.61631e6	−0.495889	−0.247944	−	0.968774i	$-0.579755\pi$
$787$	−8.61631e6	−0.495889	−0.247944	+	0.968774i	$0.579755\pi$
$788$	7.64002e6	0.438308
$789$	9.08537e6	0.519577
$790$	−5.95698e6	−0.339593
$791$	−1.81335e7	−1.03048
$792$	2.50078e6	0.141665
$793$	−6.65754e6	−0.375951
$794$	−1.49729e7	−0.842858
$795$	4.54950e6	0.255297
$796$	−2.56003e6	−0.143206
$797$	1.48277e7	0.826855	0.413427	−	0.910537i	$-0.364332\pi$
$797$	1.48277e7	0.826855	0.413427	+	0.910537i	$0.364332\pi$
$798$	1.86011e6	0.103403
$799$	−2.15377e7	−1.19353
$800$	2.54242e6	0.140450
$801$	1.55441e7	0.856020
$802$	1.56052e7	0.856712
$803$	−1.05558e7	−0.577698
$804$	1.06534e6	0.0581229
$805$	6.56542e6	0.357086
$806$	5.42223e6	0.293995
$807$	1.01373e7	0.547946
$808$	−1.19428e7	−0.643543
$809$	−2.96855e7	−1.59468	−0.797339	−	0.603532i	$-0.793759\pi$
$809$	−2.96855e7	−1.59468	−0.797339	+	0.603532i	$0.793759\pi$
$810$	385218.	0.0206297
$811$	2.40118e7	1.28195	0.640976	−	0.767561i	$-0.278530\pi$
$811$	2.40118e7	1.28195	0.640976	+	0.767561i	$0.278530\pi$
$812$	102425.	0.00545150
$813$	522676.	0.0277336
$814$	−4.74692e6	−0.251102
$815$	−1.21232e7	−0.639327
$816$	−1.56919e7	−0.824992
$817$	7.87925e6	0.412981
$818$	−1.90321e7	−0.994497
$819$	3.33672e6	0.173824
$820$	−88389.9	−0.00459059
$821$	1.38129e7	0.715199	0.357599	−	0.933875i	$-0.383595\pi$
$821$	1.38129e7	0.715199	0.357599	+	0.933875i	$0.383595\pi$
$822$	−1.96336e7	−1.01349
$823$	3.72736e7	1.91824	0.959119	−	0.283005i	$-0.0913312\pi$
$823$	3.72736e7	1.91824	0.959119	+	0.283005i	$0.0913312\pi$
$824$	1.49596e7	0.767544
$825$	−711698.	−0.0364050
$826$	−2.22805e7	−1.13625
$827$	1.53873e7	0.782348	0.391174	−	0.920317i	$-0.372069\pi$
$827$	1.53873e7	0.782348	0.391174	+	0.920317i	$0.372069\pi$
$828$	−5.76947e6	−0.292456
$829$	4.27430e6	0.216012	0.108006	−	0.994150i	$-0.465553\pi$
$829$	4.27430e6	0.216012	0.108006	+	0.994150i	$0.465553\pi$
$830$	6.93748e6	0.349548
$831$	−797547.	−0.0400640
$832$	3.51798e6	0.176192
$833$	−1.31562e7	−0.656930
$834$	−1.75647e6	−0.0874431
$835$	1.07502e7	0.533582
$836$	−514233.	−0.0254475
$837$	1.17409e7	0.579278
$838$	−2.58929e7	−1.27371
$839$	3.78339e6	0.185556	0.0927781	−	0.995687i	$-0.470425\pi$
$839$	3.78339e6	0.185556	0.0927781	+	0.995687i	$0.470425\pi$
$840$	2.60564e6	0.127414
$841$	−2.05001e7	−0.999461
$842$	2.13381e7	1.03723
$843$	9.54122e6	0.462418
$844$	−3.80952e6	−0.184083
$845$	7.57826e6	0.365113
$846$	−1.66573e7	−0.800165
$847$	−1.21163e6	−0.0580313
$848$	2.44060e7	1.16549
$849$	1.61011e7	0.766632
$850$	−5.46288e6	−0.259343
$851$	−1.88169e7	−0.890685
$852$	−5.36481e6	−0.253195
$853$	1.04338e7	0.490987	0.245494	−	0.969398i	$-0.421050\pi$
$853$	1.04338e7	0.490987	0.245494	+	0.969398i	$0.421050\pi$
$854$	−1.39618e7	−0.655083
$855$	1.39378e6	0.0652046
$856$	−1.80903e7	−0.843843
$857$	2.05211e7	0.954442	0.477221	−	0.878783i	$-0.341644\pi$
$857$	2.05211e7	0.954442	0.477221	+	0.878783i	$0.341644\pi$
$858$	1.96694e6	0.0912162
$859$	−2.06013e7	−0.952603	−0.476302	−	0.879282i	$-0.658023\pi$
$859$	−2.06013e7	−0.952603	−0.476302	+	0.879282i	$0.658023\pi$
$860$	−6.42370e6	−0.296169
$861$	−233898.	−0.0107527
$862$	−7.24262e6	−0.331992
$863$	−3.43025e7	−1.56783	−0.783916	−	0.620867i	$-0.786781\pi$
$863$	−3.43025e7	−1.56783	−0.783916	+	0.620867i	$0.786781\pi$
$864$	−1.52147e7	−0.693394
$865$	6.47370e6	0.294179
$866$	−3.65305e7	−1.65524
$867$	3.06316e6	0.138396
$868$	3.05824e6	0.137776
$869$	4.35783e6	0.195759
$870$	−163647.	−0.00733012
$871$	2.51052e6	0.112129
$872$	1.41632e6	0.0630769
$873$	−3.72507e6	−0.165424
$874$	−7.57931e6	−0.335623
$875$	1.29306e6	0.0570953
$876$	9.66502e6	0.425542
$877$	−1.97124e7	−0.865449	−0.432724	−	0.901526i	$-0.642448\pi$
$877$	−1.97124e7	−0.865449	−0.432724	+	0.901526i	$0.642448\pi$
$878$	−2.75864e7	−1.20770
$879$	1.28325e6	0.0560195
$880$	−3.81794e6	−0.166197
$881$	−5.67142e6	−0.246179	−0.123090	−	0.992396i	$-0.539280\pi$
$881$	−5.67142e6	−0.246179	−0.123090	+	0.992396i	$0.539280\pi$
$882$	−1.01751e7	−0.440419
$883$	−3.81666e7	−1.64734	−0.823668	−	0.567073i	$-0.808076\pi$
$883$	−3.81666e7	−1.64734	−0.823668	+	0.567073i	$0.808076\pi$
$884$	4.06053e6	0.174764
$885$	9.57402e6	0.410900
$886$	2.43352e7	1.04148
$887$	1.97922e7	0.844668	0.422334	−	0.906440i	$-0.361211\pi$
$887$	1.97922e7	0.844668	0.422334	+	0.906440i	$0.361211\pi$
$888$	−7.46793e6	−0.317810
$889$	1.41944e7	0.602370
$890$	−1.66479e7	−0.704505
$891$	−281807.	−0.0118921
$892$	−7.59242e6	−0.319498
$893$	−5.88527e6	−0.246966
$894$	−2.07189e7	−0.867007
$895$	1.72794e7	0.721060
$896$	1.81502e7	0.755287
$897$	7.79698e6	0.323553
$898$	−5.03841e7	−2.08498
$899$	330021.	0.0136189
$900$	−1.13630e6	−0.0467614
$901$	−2.55467e7	−1.04839
$902$	240426.	0.00983931
$903$	−1.69984e7	−0.693728
$904$	2.93241e7	1.19345
$905$	1.18927e6	0.0482680
$906$	−1.12233e7	−0.454254
$907$	−2.78574e7	−1.12440	−0.562202	−	0.827000i	$-0.690046\pi$
$907$	−2.78574e7	−1.12440	−0.562202	+	0.827000i	$0.690046\pi$
$908$	7.79299e6	0.313682
$909$	1.37819e7	0.553222
$910$	−3.57367e6	−0.143058
$911$	4.25249e7	1.69764	0.848822	−	0.528678i	$-0.177312\pi$
$911$	4.25249e7	1.69764	0.848822	+	0.528678i	$0.177312\pi$
$912$	−4.28787e6	−0.170708
$913$	−5.07512e6	−0.201497
$914$	3.18812e7	1.26232
$915$	5.99944e6	0.236896
$916$	−1.62095e7	−0.638308
$917$	−1.61907e7	−0.635830
$918$	3.26918e7	1.28036
$919$	−2.15176e7	−0.840437	−0.420218	−	0.907423i	$-0.638047\pi$
$919$	−2.15176e7	−0.840437	−0.420218	+	0.907423i	$0.638047\pi$
$920$	−1.06171e7	−0.413557
$921$	2.50650e7	0.973685
$922$	−2.33696e7	−0.905365
$923$	−1.26424e7	−0.488456
$924$	1.10939e6	0.0427468
$925$	−3.70601e6	−0.142414
$926$	−2.98636e7	−1.14450
$927$	−1.72633e7	−0.659819
$928$	−427667.	−0.0163018
$929$	3.18180e7	1.20958	0.604788	−	0.796387i	$-0.293258\pi$
$929$	3.18180e7	1.20958	0.604788	+	0.796387i	$0.293258\pi$
$930$	−4.88624e6	−0.185254
$931$	−3.59499e6	−0.135933
$932$	−4.39958e6	−0.165910
$933$	−1.44231e7	−0.542443
$934$	3.07933e7	1.15502
$935$	3.99638e6	0.149499
$936$	−5.39589e6	−0.201314
$937$	5.42678e6	0.201927	0.100963	−	0.994890i	$-0.467808\pi$
$937$	5.42678e6	0.201927	0.100963	+	0.994890i	$0.467808\pi$
$938$	5.26490e6	0.195381
$939$	1.53532e6	0.0568245
$940$	4.79807e6	0.177112
$941$	1.60381e7	0.590443	0.295222	−	0.955429i	$-0.404607\pi$
$941$	1.60381e7	0.590443	0.295222	+	0.955429i	$0.404607\pi$
$942$	1.47906e7	0.543074
$943$	953053.	0.0349010
$944$	5.13603e7	1.87585
$945$	−7.73815e6	−0.281876
$946$	1.74729e7	0.634799
$947$	2.23862e7	0.811157	0.405579	−	0.914060i	$-0.367070\pi$
$947$	2.23862e7	0.811157	0.405579	+	0.914060i	$0.367070\pi$
$948$	−3.99010e6	−0.144199
$949$	2.27760e7	0.820942
$950$	−1.49275e6	−0.0536635
$951$	3.10217e6	0.111228
$952$	−1.46314e7	−0.523230
$953$	5.94378e6	0.211997	0.105999	−	0.994366i	$-0.466196\pi$
$953$	5.94378e6	0.211997	0.105999	+	0.994366i	$0.466196\pi$
$954$	−1.97579e7	−0.702860
$955$	−8.31342e6	−0.294966
$956$	8.55036e6	0.302580
$957$	119716.	0.00422546
$958$	2.40200e7	0.845587
$959$	−2.60958e7	−0.916270
$960$	−3.17023e6	−0.111023
$961$	−1.87753e7	−0.655809
$962$	1.02424e7	0.356831
$963$	2.08761e7	0.725409
$964$	5.87922e6	0.203764
$965$	1.89130e7	0.653795
$966$	1.63513e7	0.563781
$967$	4.02383e7	1.38380	0.691900	−	0.721993i	$-0.256774\pi$
$967$	4.02383e7	1.38380	0.691900	+	0.721993i	$0.256774\pi$
$968$	1.95936e6	0.0672087
$969$	4.48827e6	0.153557
$970$	3.98960e6	0.136144
$971$	−3.45418e7	−1.17570	−0.587850	−	0.808970i	$-0.700026\pi$
$971$	−3.45418e7	−1.17570	−0.587850	+	0.808970i	$0.700026\pi$
$972$	1.09577e7	0.372009
$973$	−2.33459e6	−0.0790547
$974$	3.96774e7	1.34013
$975$	1.53562e6	0.0517336
$976$	3.21843e7	1.08148
$977$	2.18851e7	0.733521	0.366761	−	0.930315i	$-0.380467\pi$
$977$	2.18851e7	0.733521	0.366761	+	0.930315i	$0.380467\pi$
$978$	−3.01931e7	−1.00939
$979$	1.21788e7	0.406113
$980$	2.93088e6	0.0974839
$981$	−1.63442e6	−0.0542241
$982$	−1.77160e7	−0.586256
$983$	4.77836e7	1.57723	0.788616	−	0.614886i	$-0.210798\pi$
$983$	4.77836e7	1.57723	0.788616	+	0.614886i	$0.210798\pi$
$984$	378241.	0.0124532
$985$	−1.62243e7	−0.532815
$986$	918924.	0.0301014
$987$	1.26967e7	0.414855
$988$	1.10955e6	0.0361623
$989$	6.92628e7	2.25169
$990$	3.09081e6	0.100227
$991$	−5.33735e7	−1.72640	−0.863200	−	0.504862i	$-0.831543\pi$
$991$	−5.33735e7	−1.72640	−0.863200	+	0.504862i	$0.831543\pi$
$992$	−1.27694e7	−0.411995
$993$	2.94796e6	0.0948743
$994$	−2.65129e7	−0.851120
$995$	5.43647e6	0.174084
$996$	4.64686e6	0.148426
$997$	−5.03569e7	−1.60443	−0.802216	−	0.597034i	$-0.796346\pi$
$997$	−5.03569e7	−1.60443	−0.802216	+	0.597034i	$0.796346\pi$
$998$	−1.31604e7	−0.418255
$999$	2.21780e7	0.703087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.10	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.10	✓	39	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)

\(f(q)\)	\(=\)	\(q-6.61608 q^{2} +9.41089 q^{3} +11.7725 q^{4} -25.0000 q^{5} -62.2632 q^{6} -82.7561 q^{7} +133.827 q^{8} -154.435 q^{9} +O(q^{10})\)	\(q-6.61608 q^{2} +9.41089 q^{3} +11.7725 q^{4} -25.0000 q^{5} -62.2632 q^{6} -82.7561 q^{7} +133.827 q^{8} -154.435 q^{9} +165.402 q^{10} -121.000 q^{11} +110.789 q^{12} +261.080 q^{13} +547.521 q^{14} -235.272 q^{15} -1262.13 q^{16} +1321.12 q^{17} +1021.76 q^{18} +361.000 q^{19} -294.312 q^{20} -778.809 q^{21} +800.545 q^{22} +3173.38 q^{23} +1259.43 q^{24} +625.000 q^{25} -1727.32 q^{26} -3740.22 q^{27} -974.244 q^{28} -105.133 q^{29} +1556.58 q^{30} -3139.09 q^{31} +4067.88 q^{32} -1138.72 q^{33} -8740.61 q^{34} +2068.90 q^{35} -1818.08 q^{36} -5929.61 q^{37} -2388.40 q^{38} +2456.99 q^{39} -3345.67 q^{40} +300.327 q^{41} +5152.66 q^{42} +21826.2 q^{43} -1424.47 q^{44} +3860.88 q^{45} -20995.3 q^{46} -16302.7 q^{47} -11877.7 q^{48} -9958.42 q^{49} -4135.05 q^{50} +12432.9 q^{51} +3073.56 q^{52} -19337.2 q^{53} +24745.6 q^{54} +3025.00 q^{55} -11075.0 q^{56} +3397.33 q^{57} +695.566 q^{58} -40693.4 q^{59} -2769.74 q^{60} -25500.0 q^{61} +20768.5 q^{62} +12780.5 q^{63} +13474.7 q^{64} -6527.00 q^{65} +7533.84 q^{66} +9615.89 q^{67} +15552.8 q^{68} +29864.3 q^{69} -13688.0 q^{70} -48423.5 q^{71} -20667.6 q^{72} +87237.8 q^{73} +39230.7 q^{74} +5881.80 q^{75} +4249.86 q^{76} +10013.5 q^{77} -16255.7 q^{78} -36015.2 q^{79} +31553.2 q^{80} +2328.98 q^{81} -1986.99 q^{82} +41943.1 q^{83} -9168.50 q^{84} -33027.9 q^{85} -144404. q^{86} -989.392 q^{87} -16193.1 q^{88} -100651. q^{89} -25543.9 q^{90} -21606.0 q^{91} +37358.5 q^{92} -29541.6 q^{93} +107860. q^{94} -9025.00 q^{95} +38282.3 q^{96} +24120.6 q^{97} +65885.7 q^{98} +18686.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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