LMFDB - Embedded newform 43.6.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 $ x^10 - 2x^9 - 256x^8 + 266x^7 + 21986x^6 - 10450x^5 - 719484x^4 + 384582x^3 + 8437093x^2 - 5752252*x - 22734604
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.31531$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.31531 q^{2} -23.8469 q^{3} -13.3781 q^{4} -52.5837 q^{5} +102.907 q^{6} -174.859 q^{7} +195.821 q^{8} +325.673 q^{9} +O(q^{10})$	\(q-4.31531 q^{2} -23.8469 q^{3} -13.3781 q^{4} -52.5837 q^{5} +102.907 q^{6} -174.859 q^{7} +195.821 q^{8} +325.673 q^{9} +226.915 q^{10} -447.981 q^{11} +319.027 q^{12} +669.141 q^{13} +754.569 q^{14} +1253.96 q^{15} -416.925 q^{16} -849.648 q^{17} -1405.38 q^{18} -1288.87 q^{19} +703.471 q^{20} +4169.83 q^{21} +1933.18 q^{22} -378.254 q^{23} -4669.71 q^{24} -359.956 q^{25} -2887.55 q^{26} -1971.50 q^{27} +2339.28 q^{28} +765.100 q^{29} -5411.21 q^{30} -7094.59 q^{31} -4467.10 q^{32} +10683.0 q^{33} +3666.49 q^{34} +9194.71 q^{35} -4356.90 q^{36} -7908.22 q^{37} +5561.87 q^{38} -15956.9 q^{39} -10297.0 q^{40} +12855.9 q^{41} -17994.1 q^{42} +1849.00 q^{43} +5993.15 q^{44} -17125.1 q^{45} +1632.28 q^{46} +26785.7 q^{47} +9942.37 q^{48} +13768.5 q^{49} +1553.32 q^{50} +20261.5 q^{51} -8951.86 q^{52} +30000.7 q^{53} +8507.60 q^{54} +23556.5 q^{55} -34240.9 q^{56} +30735.5 q^{57} -3301.64 q^{58} +1247.64 q^{59} -16775.6 q^{60} -48441.4 q^{61} +30615.3 q^{62} -56946.8 q^{63} +32618.5 q^{64} -35185.9 q^{65} -46100.2 q^{66} +67004.8 q^{67} +11366.7 q^{68} +9020.17 q^{69} -39678.0 q^{70} -74553.1 q^{71} +63773.5 q^{72} -18066.8 q^{73} +34126.4 q^{74} +8583.82 q^{75} +17242.7 q^{76} +78333.4 q^{77} +68859.0 q^{78} -63230.5 q^{79} +21923.5 q^{80} -32124.6 q^{81} -55477.3 q^{82} -88066.7 q^{83} -55784.5 q^{84} +44677.6 q^{85} -7979.00 q^{86} -18245.2 q^{87} -87724.0 q^{88} +50373.5 q^{89} +73900.0 q^{90} -117005. q^{91} +5060.33 q^{92} +169184. q^{93} -115588. q^{94} +67773.5 q^{95} +106526. q^{96} +17502.1 q^{97} -59415.5 q^{98} -145895. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) $ 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * 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 $

$2$	−4.31531	−0.762846	−0.381423	−	0.924401i	$-0.624566\pi$
$2$	−4.31531	−0.762846	−0.381423	+	0.924401i	$0.624566\pi$
$3$	−23.8469	−1.52978	−0.764889	−	0.644163i	$-0.777206\pi$
$3$	−23.8469	−1.52978	−0.764889	+	0.644163i	$0.777206\pi$
$4$	−13.3781	−0.418067
$5$	−52.5837	−0.940646	−0.470323	−	0.882494i	$-0.655863\pi$
$5$	−52.5837	−0.940646	−0.470323	+	0.882494i	$0.655863\pi$
$6$	102.907	1.16698
$7$	−174.859	−1.34878	−0.674391	−	0.738374i	$-0.735594\pi$
$7$	−174.859	−1.34878	−0.674391	+	0.738374i	$0.735594\pi$
$8$	195.821	1.08177
$9$	325.673	1.34022
$10$	226.915	0.717567
$11$	−447.981	−1.11629	−0.558147	−	0.829742i	$-0.688487\pi$
$11$	−447.981	−1.11629	−0.558147	+	0.829742i	$0.688487\pi$
$12$	319.027	0.639549
$13$	669.141	1.09814	0.549072	−	0.835775i	$-0.314981\pi$
$13$	669.141	1.09814	0.549072	+	0.835775i	$0.314981\pi$
$14$	754.569	1.02891
$15$	1253.96	1.43898
$16$	−416.925	−0.407154
$17$	−849.648	−0.713045	−0.356522	−	0.934287i	$-0.616038\pi$
$17$	−849.648	−0.713045	−0.356522	+	0.934287i	$0.616038\pi$
$18$	−1405.38	−1.02238
$19$	−1288.87	−0.819078	−0.409539	−	0.912293i	$-0.634310\pi$
$19$	−1288.87	−0.819078	−0.409539	+	0.912293i	$0.634310\pi$
$20$	703.471	0.393253
$21$	4169.83	2.06334
$22$	1933.18	0.851559
$23$	−378.254	−0.149095	−0.0745476	−	0.997217i	$-0.523751\pi$
$23$	−378.254	−0.149095	−0.0745476	+	0.997217i	$0.523751\pi$
$24$	−4669.71	−1.65486
$25$	−359.956	−0.115186
$26$	−2887.55	−0.837715
$27$	−1971.50	−0.520459
$28$	2339.28	0.563881
$29$	765.100	0.168936	0.0844682	−	0.996426i	$-0.473081\pi$
$29$	765.100	0.168936	0.0844682	+	0.996426i	$0.473081\pi$
$30$	−5411.21	−1.09772
$31$	−7094.59	−1.32594	−0.662969	−	0.748647i	$-0.730704\pi$
$31$	−7094.59	−1.32594	−0.662969	+	0.748647i	$0.730704\pi$
$32$	−4467.10	−0.771170
$33$	10683.0	1.70768
$34$	3666.49	0.543943
$35$	9194.71	1.26873
$36$	−4356.90	−0.560301
$37$	−7908.22	−0.949674	−0.474837	−	0.880074i	$-0.657493\pi$
$37$	−7908.22	−0.949674	−0.474837	+	0.880074i	$0.657493\pi$
$38$	5561.87	0.624830
$39$	−15956.9	−1.67992
$40$	−10297.0	−1.01756
$41$	12855.9	1.19438	0.597192	−	0.802098i	$-0.296283\pi$
$41$	12855.9	1.19438	0.597192	+	0.802098i	$0.296283\pi$
$42$	−17994.1	−1.57401
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	5993.15	0.466685
$45$	−17125.1	−1.26067
$46$	1632.28	0.113737
$47$	26785.7	1.76871	0.884357	−	0.466811i	$-0.154597\pi$
$47$	26785.7	1.76871	0.884357	+	0.466811i	$0.154597\pi$
$48$	9942.37	0.622855
$49$	13768.5	0.819215
$50$	1553.32	0.0878690
$51$	20261.5	1.09080
$52$	−8951.86	−0.459098
$53$	30000.7	1.46704	0.733520	−	0.679668i	$-0.237876\pi$
$53$	30000.7	1.46704	0.733520	+	0.679668i	$0.237876\pi$
$54$	8507.60	0.397030
$55$	23556.5	1.05004
$56$	−34240.9	−1.45907
$57$	30735.5	1.25301
$58$	−3301.64	−0.128872
$59$	1247.64	0.0466614	0.0233307	−	0.999728i	$-0.492573\pi$
$59$	1247.64	0.0466614	0.0233307	+	0.999728i	$0.492573\pi$
$60$	−16775.6	−0.601589
$61$	−48441.4	−1.66683	−0.833417	−	0.552644i	$-0.813619\pi$
$61$	−48441.4	−1.66683	−0.833417	+	0.552644i	$0.813619\pi$
$62$	30615.3	1.01149
$63$	−56946.8	−1.80766
$64$	32618.5	0.995438
$65$	−35185.9	−1.03296
$66$	−46100.2	−1.30270
$67$	67004.8	1.82356	0.911778	−	0.410683i	$-0.134710\pi$
$67$	67004.8	1.82356	0.911778	+	0.410683i	$0.134710\pi$
$68$	11366.7	0.298100
$69$	9020.17	0.228082
$70$	−39678.0	−0.967842
$71$	−74553.1	−1.75517	−0.877587	−	0.479418i	$-0.840848\pi$
$71$	−74553.1	−1.75517	−0.877587	+	0.479418i	$0.840848\pi$
$72$	63773.5	1.44980
$73$	−18066.8	−0.396802	−0.198401	−	0.980121i	$-0.563575\pi$
$73$	−18066.8	−0.396802	−0.198401	+	0.980121i	$0.563575\pi$
$74$	34126.4	0.724454
$75$	8583.82	0.176209
$76$	17242.7	0.342429
$77$	78333.4	1.50564
$78$	68859.0	1.28152
$79$	−63230.5	−1.13988	−0.569939	−	0.821687i	$-0.693033\pi$
$79$	−63230.5	−1.13988	−0.569939	+	0.821687i	$0.693033\pi$
$80$	21923.5	0.382987
$81$	−32124.6	−0.544033
$82$	−55477.3	−0.911131
$83$	−88066.7	−1.40319	−0.701595	−	0.712576i	$-0.747528\pi$
$83$	−88066.7	−1.40319	−0.701595	+	0.712576i	$0.747528\pi$
$84$	−55784.5	−0.862612
$85$	44677.6	0.670723
$86$	−7979.00	−0.116333
$87$	−18245.2	−0.258435
$88$	−87724.0	−1.20757
$89$	50373.5	0.674104	0.337052	−	0.941486i	$-0.390570\pi$
$89$	50373.5	0.674104	0.337052	+	0.941486i	$0.390570\pi$
$90$	73900.0	0.961697
$91$	−117005.	−1.48116
$92$	5060.33	0.0623317
$93$	169184.	2.02839
$94$	−115588.	−1.34926
$95$	67773.5	0.770462
$96$	106526.	1.17972
$97$	17502.1	0.188869	0.0944345	−	0.995531i	$-0.469896\pi$
$97$	17502.1	0.188869	0.0944345	+	0.995531i	$0.469896\pi$
$98$	−59415.5	−0.624934
$99$	−145895.	−1.49608
$100$	4815.54	0.0481554
$101$	182669.	1.78181	0.890906	−	0.454188i	$-0.150071\pi$
$101$	182669.	1.78181	0.890906	+	0.454188i	$0.150071\pi$
$102$	−87434.4	−0.832112
$103$	−110578.	−1.02702	−0.513508	−	0.858085i	$-0.671654\pi$
$103$	−110578.	−1.02702	−0.513508	+	0.858085i	$0.671654\pi$
$104$	131032.	1.18794
$105$	−219265.	−1.94087
$106$	−129462.	−1.11913
$107$	−43935.4	−0.370984	−0.185492	−	0.982646i	$-0.559388\pi$
$107$	−43935.4	−0.370984	−0.185492	+	0.982646i	$0.559388\pi$
$108$	26374.9	0.217586
$109$	−78170.4	−0.630197	−0.315098	−	0.949059i	$-0.602038\pi$
$109$	−78170.4	−0.630197	−0.315098	+	0.949059i	$0.602038\pi$
$110$	−101654.	−0.801015
$111$	188586.	1.45279
$112$	72903.0	0.549162
$113$	23097.5	0.170165	0.0850823	−	0.996374i	$-0.472885\pi$
$113$	23097.5	0.170165	0.0850823	+	0.996374i	$0.472885\pi$
$114$	−132633.	−0.955850
$115$	19890.0	0.140246
$116$	−10235.6	−0.0706267
$117$	217921.	1.47175
$118$	−5383.93	−0.0355955
$119$	148568.	0.961743
$120$	245550.	1.55664
$121$	39636.3	0.246110
$122$	209040.	1.27154
$123$	−306574.	−1.82714
$124$	94912.4	0.554330
$125$	183252.	1.04899
$126$	245743.	1.37897
$127$	218127.	1.20005	0.600027	−	0.799980i	$-0.295156\pi$
$127$	218127.	1.20005	0.600027	+	0.799980i	$0.295156\pi$
$128$	2188.25	0.0118052
$129$	−44092.9	−0.233289
$130$	151838.	0.787993
$131$	107160.	0.545575	0.272787	−	0.962074i	$-0.412054\pi$
$131$	107160.	0.545575	0.272787	+	0.962074i	$0.412054\pi$
$132$	−142918.	−0.713924
$133$	225370.	1.10476
$134$	−289146.	−1.39109
$135$	103668.	0.489567
$136$	−166379.	−0.771348
$137$	−168770.	−0.768234	−0.384117	−	0.923284i	$-0.625494\pi$
$137$	−168770.	−0.768234	−0.384117	+	0.923284i	$0.625494\pi$
$138$	−38924.8	−0.173992
$139$	294636.	1.29345	0.646725	−	0.762723i	$-0.276138\pi$
$139$	294636.	1.29345	0.646725	+	0.762723i	$0.276138\pi$
$140$	−123008.	−0.530412
$141$	−638754.	−2.70574
$142$	321720.	1.33893
$143$	−299763.	−1.22585
$144$	−135781.	−0.545675
$145$	−40231.8	−0.158909
$146$	77963.8	0.302699
$147$	−328337.	−1.25322
$148$	105797.	0.397027
$149$	121995.	0.450169	0.225084	−	0.974339i	$-0.427734\pi$
$149$	121995.	0.450169	0.225084	+	0.974339i	$0.427734\pi$
$150$	−37041.8	−0.134420
$151$	−515468.	−1.83975	−0.919877	−	0.392208i	$-0.871711\pi$
$151$	−515468.	−1.83975	−0.919877	+	0.392208i	$0.871711\pi$
$152$	−252387.	−0.886050
$153$	−276708.	−0.955636
$154$	−338033.	−1.14857
$155$	373060.	1.24724
$156$	213474.	0.702317
$157$	178197.	0.576969	0.288484	−	0.957485i	$-0.406849\pi$
$157$	178197.	0.576969	0.288484	+	0.957485i	$0.406849\pi$
$158$	272859.	0.869552
$159$	−715423.	−2.24424
$160$	234896.	0.725398
$161$	66140.9	0.201097
$162$	138627.	0.415013
$163$	−111853.	−0.329747	−0.164873	−	0.986315i	$-0.552722\pi$
$163$	−111853.	−0.329747	−0.164873	+	0.986315i	$0.552722\pi$
$164$	−171988.	−0.499332
$165$	−561749.	−1.60632
$166$	380035.	1.07042
$167$	−128666.	−0.357003	−0.178501	−	0.983940i	$-0.557125\pi$
$167$	−128666.	−0.357003	−0.178501	+	0.983940i	$0.557125\pi$
$168$	816538.	2.23205
$169$	76457.2	0.205922
$170$	−192798.	−0.511658
$171$	−419750.	−1.09774
$172$	−24736.2	−0.0637546
$173$	553314.	1.40558	0.702792	−	0.711396i	$-0.251937\pi$
$173$	553314.	1.40558	0.702792	+	0.711396i	$0.251937\pi$
$174$	78733.8	0.197146
$175$	62941.4	0.155361
$176$	186775.	0.454503
$177$	−29752.2	−0.0713816
$178$	−217377.	−0.514238
$179$	−302733.	−0.706200	−0.353100	−	0.935586i	$-0.614872\pi$
$179$	−302733.	−0.706200	−0.353100	+	0.935586i	$0.614872\pi$
$180$	229102.	0.527044
$181$	−702706.	−1.59433	−0.797164	−	0.603763i	$-0.793667\pi$
$181$	−702706.	−1.59433	−0.797164	+	0.603763i	$0.793667\pi$
$182$	504913.	1.12990
$183$	1.15518e6	2.54989
$184$	−74069.9	−0.161286
$185$	415843.	0.893306
$186$	−730080.	−1.54735
$187$	380627.	0.795967
$188$	−358342.	−0.739440
$189$	344733.	0.701986
$190$	−292464.	−0.587743
$191$	105355.	0.208965	0.104482	−	0.994527i	$-0.466681\pi$
$191$	105355.	0.208965	0.104482	+	0.994527i	$0.466681\pi$
$192$	−777849.	−1.52280
$193$	11272.6	0.0217836	0.0108918	−	0.999941i	$-0.496533\pi$
$193$	11272.6	0.0217836	0.0108918	+	0.999941i	$0.496533\pi$
$194$	−75526.9	−0.144078
$195$	839074.	1.58021
$196$	−184197.	−0.342486
$197$	44453.7	0.0816098	0.0408049	−	0.999167i	$-0.487008\pi$
$197$	44453.7	0.0816098	0.0408049	+	0.999167i	$0.487008\pi$
$198$	629584.	1.14128
$199$	1.01040e6	1.80867	0.904333	−	0.426827i	$-0.140369\pi$
$199$	1.01040e6	1.80867	0.904333	+	0.426827i	$0.140369\pi$
$200$	−70486.7	−0.124604
$201$	−1.59786e6	−2.78963
$202$	−788273.	−1.35925
$203$	−133784.	−0.227858
$204$	−271060.	−0.456027
$205$	−676013.	−1.12349
$206$	477180.	0.783455
$207$	−123187.	−0.199820
$208$	−278982.	−0.447114
$209$	577390.	0.914331
$210$	946196.	1.48058
$211$	758827.	1.17337	0.586687	−	0.809814i	$-0.300432\pi$
$211$	758827.	1.17337	0.586687	+	0.809814i	$0.300432\pi$
$212$	−401354.	−0.613321
$213$	1.77786e6	2.68502
$214$	189595.	0.283003
$215$	−97227.2	−0.143447
$216$	−386059.	−0.563014
$217$	1.24055e6	1.78840
$218$	337329.	0.480743
$219$	430837.	0.607019
$220$	−315142.	−0.438985
$221$	−568535.	−0.783026
$222$	−813807.	−1.10825
$223$	−517178.	−0.696431	−0.348215	−	0.937415i	$-0.613212\pi$
$223$	−517178.	−0.696431	−0.348215	+	0.937415i	$0.613212\pi$
$224$	781110.	1.04014
$225$	−117228.	−0.154374
$226$	−99672.9	−0.129809
$227$	627619.	0.808409	0.404205	−	0.914669i	$-0.367548\pi$
$227$	627619.	0.808409	0.404205	+	0.914669i	$0.367548\pi$
$228$	−411184.	−0.523840
$229$	800425.	1.00863	0.504315	−	0.863520i	$-0.331745\pi$
$229$	800425.	1.00863	0.504315	+	0.863520i	$0.331745\pi$
$230$	−85831.3	−0.106986
$231$	−1.86801e6	−2.30329
$232$	149822.	0.182750
$233$	102393.	0.123560	0.0617802	−	0.998090i	$-0.480322\pi$
$233$	102393.	0.123560	0.0617802	+	0.998090i	$0.480322\pi$
$234$	−940397.	−1.12272
$235$	−1.40849e6	−1.66373
$236$	−16691.0	−0.0195076
$237$	1.50785e6	1.74376
$238$	−641118.	−0.733661
$239$	−879306.	−0.995739	−0.497869	−	0.867252i	$-0.665884\pi$
$239$	−879306.	−0.995739	−0.497869	+	0.867252i	$0.665884\pi$
$240$	−522806.	−0.585885
$241$	196740.	0.218198	0.109099	−	0.994031i	$-0.465203\pi$
$241$	196740.	0.218198	0.109099	+	0.994031i	$0.465203\pi$
$242$	−171043.	−0.187744
$243$	1.24514e6	1.35271
$244$	648056.	0.696848
$245$	−724001.	−0.770591
$246$	1.32296e6	1.39383
$247$	−862436.	−0.899466
$248$	−1.38927e6	−1.43435
$249$	2.10011e6	2.14657
$250$	−790788.	−0.800221
$251$	−798778.	−0.800280	−0.400140	−	0.916454i	$-0.631038\pi$
$251$	−798778.	−0.800280	−0.400140	+	0.916454i	$0.631038\pi$
$252$	761841.	0.755724
$253$	169451.	0.166434
$254$	−941287.	−0.915456
$255$	−1.06542e6	−1.02606
$256$	−1.05324e6	−1.00444
$257$	−93933.3	−0.0887129	−0.0443565	−	0.999016i	$-0.514124\pi$
$257$	−93933.3	−0.0887129	−0.0443565	+	0.999016i	$0.514124\pi$
$258$	190274.	0.177963
$259$	1.38282e6	1.28090
$260$	470722.	0.431848
$261$	249173.	0.226412
$262$	−462428.	−0.416189
$263$	−898502.	−0.800995	−0.400497	−	0.916298i	$-0.631163\pi$
$263$	−898502.	−0.800995	−0.400497	+	0.916298i	$0.631163\pi$
$264$	2.09194e6	1.84731
$265$	−1.57755e6	−1.37996
$266$	−972541.	−0.842760
$267$	−1.20125e6	−1.03123
$268$	−896400.	−0.762368
$269$	−921887.	−0.776778	−0.388389	−	0.921495i	$-0.626968\pi$
$269$	−921887.	−0.776778	−0.388389	+	0.921495i	$0.626968\pi$
$270$	−447361.	−0.373464
$271$	−227722.	−0.188357	−0.0941784	−	0.995555i	$-0.530022\pi$
$271$	−227722.	−0.188357	−0.0941784	+	0.995555i	$0.530022\pi$
$272$	354240.	0.290319
$273$	2.79021e6	2.26584
$274$	728294.	0.586044
$275$	161253.	0.128581
$276$	−120673.	−0.0953537
$277$	1.76180e6	1.37961	0.689806	−	0.723994i	$-0.257696\pi$
$277$	1.76180e6	1.37961	0.689806	+	0.723994i	$0.257696\pi$
$278$	−1.27145e6	−0.986702
$279$	−2.31052e6	−1.77705
$280$	1.80051e6	1.37246
$281$	−270410.	−0.204295	−0.102147	−	0.994769i	$-0.532571\pi$
$281$	−270410.	−0.204295	−0.102147	+	0.994769i	$0.532571\pi$
$282$	2.75642e6	2.06406
$283$	2.04589e6	1.51851	0.759254	−	0.650795i	$-0.225564\pi$
$283$	2.04589e6	1.51851	0.759254	+	0.650795i	$0.225564\pi$
$284$	997381.	0.733779
$285$	−1.61619e6	−1.17863
$286$	1.29357e6	0.935135
$287$	−2.24797e6	−1.61096
$288$	−1.45481e6	−1.03354
$289$	−697955.	−0.491567
$290$	173612.	0.121223
$291$	−417370.	−0.288927
$292$	241700.	0.165890
$293$	1.15172e6	0.783751	0.391875	−	0.920018i	$-0.371826\pi$
$293$	1.15172e6	0.783751	0.391875	+	0.920018i	$0.371826\pi$
$294$	1.41687e6	0.956010
$295$	−65605.3	−0.0438919
$296$	−1.54859e6	−1.02732
$297$	883193.	0.580984
$298$	−526445.	−0.343409
$299$	−253105.	−0.163728
$300$	−114835.	−0.0736670
$301$	−323314.	−0.205687
$302$	2.22440e6	1.40345
$303$	−4.35609e6	−2.72578
$304$	537363.	0.333490
$305$	2.54723e6	1.56790
$306$	1.19408e6	0.729003
$307$	−1.88053e6	−1.13877	−0.569384	−	0.822072i	$-0.692818\pi$
$307$	−1.88053e6	−1.13877	−0.569384	+	0.822072i	$0.692818\pi$
$308$	−1.04795e6	−0.629456
$309$	2.63695e6	1.57111
$310$	−1.60987e6	−0.951450
$311$	1.94805e6	1.14209	0.571043	−	0.820920i	$-0.306539\pi$
$311$	1.94805e6	1.14209	0.571043	+	0.820920i	$0.306539\pi$
$312$	−3.12469e6	−1.81728
$313$	−944428.	−0.544889	−0.272445	−	0.962171i	$-0.587832\pi$
$313$	−944428.	−0.544889	−0.272445	+	0.962171i	$0.587832\pi$
$314$	−768977.	−0.440138
$315$	2.99447e6	1.70037
$316$	845906.	0.476545
$317$	34149.2	0.0190868	0.00954339	−	0.999954i	$-0.496962\pi$
$317$	34149.2	0.0190868	0.00954339	+	0.999954i	$0.496962\pi$
$318$	3.08727e6	1.71201
$319$	−342751.	−0.188583
$320$	−1.71520e6	−0.936354
$321$	1.04772e6	0.567522
$322$	−285418.	−0.153406
$323$	1.09509e6	0.584039
$324$	429767.	0.227442
$325$	−240861.	−0.126491
$326$	482682.	0.251546
$327$	1.86412e6	0.964061
$328$	2.51746e6	1.29204
$329$	−4.68370e6	−2.38561
$330$	2.42412e6	1.22538
$331$	1.73996e6	0.872908	0.436454	−	0.899727i	$-0.356234\pi$
$331$	1.73996e6	0.872908	0.436454	+	0.899727i	$0.356234\pi$
$332$	1.17817e6	0.586627
$333$	−2.57549e6	−1.27277
$334$	555232.	0.272338
$335$	−3.52336e6	−1.71532
$336$	−1.73851e6	−0.840095
$337$	−1.09453e6	−0.524990	−0.262495	−	0.964933i	$-0.584545\pi$
$337$	−1.09453e6	−0.524990	−0.262495	+	0.964933i	$0.584545\pi$
$338$	−329936.	−0.157086
$339$	−550804.	−0.260314
$340$	−597703.	−0.280407
$341$	3.17825e6	1.48014
$342$	1.81135e6	0.837408
$343$	531301.	0.243840
$344$	362072.	0.164968
$345$	−474314.	−0.214545
$346$	−2.38772e6	−1.07224
$347$	−561799.	−0.250471	−0.125236	−	0.992127i	$-0.539969\pi$
$347$	−561799.	−0.250471	−0.125236	+	0.992127i	$0.539969\pi$
$348$	244087.	0.108043
$349$	2.06827e6	0.908957	0.454478	−	0.890758i	$-0.349826\pi$
$349$	2.06827e6	0.908957	0.454478	+	0.890758i	$0.349826\pi$
$350$	−271611.	−0.118516
$351$	−1.31921e6	−0.571539
$352$	2.00118e6	0.860852
$353$	568169.	0.242684	0.121342	−	0.992611i	$-0.461280\pi$
$353$	568169.	0.242684	0.121342	+	0.992611i	$0.461280\pi$
$354$	128390.	0.0544531
$355$	3.92028e6	1.65100
$356$	−673903.	−0.281821
$357$	−3.54289e6	−1.47125
$358$	1.30639e6	0.538722
$359$	2.57455e6	1.05430	0.527151	−	0.849771i	$-0.323260\pi$
$359$	2.57455e6	1.05430	0.527151	+	0.849771i	$0.323260\pi$
$360$	−3.35345e6	−1.36375
$361$	−814914.	−0.329112
$362$	3.03239e6	1.21623
$363$	−945202.	−0.376494
$364$	1.56531e6	0.619223
$365$	950019.	0.373250
$366$	−4.98494e6	−1.94517
$367$	272102.	0.105455	0.0527274	−	0.998609i	$-0.483209\pi$
$367$	272102.	0.105455	0.0527274	+	0.998609i	$0.483209\pi$
$368$	157704.	0.0607047
$369$	4.18683e6	1.60074
$370$	−1.79449e6	−0.681455
$371$	−5.24589e6	−1.97872
$372$	−2.26336e6	−0.848002
$373$	−268967.	−0.100098	−0.0500491	−	0.998747i	$-0.515938\pi$
$373$	−268967.	−0.100098	−0.0500491	+	0.998747i	$0.515938\pi$
$374$	−1.64252e6	−0.607200
$375$	−4.36998e6	−1.60473
$376$	5.24518e6	1.91333
$377$	511960.	0.185517
$378$	−1.48763e6	−0.535507
$379$	−522052.	−0.186688	−0.0933438	−	0.995634i	$-0.529756\pi$
$379$	−522052.	−0.186688	−0.0933438	+	0.995634i	$0.529756\pi$
$380$	−906683.	−0.322104
$381$	−5.20166e6	−1.83582
$382$	−454640.	−0.159408
$383$	2.00529e6	0.698523	0.349262	−	0.937025i	$-0.386432\pi$
$383$	2.00529e6	0.698523	0.349262	+	0.937025i	$0.386432\pi$
$384$	−52183.0	−0.0180593
$385$	−4.11906e6	−1.41627
$386$	−48644.5	−0.0166175
$387$	602170.	0.204381
$388$	−234145.	−0.0789598
$389$	−1.10827e6	−0.371340	−0.185670	−	0.982612i	$-0.559446\pi$
$389$	−1.10827e6	−0.371340	−0.185670	+	0.982612i	$0.559446\pi$
$390$	−3.62086e6	−1.20545
$391$	321383.	0.106312
$392$	2.69616e6	0.886198
$393$	−2.55543e6	−0.834608
$394$	−191831.	−0.0622557
$395$	3.32489e6	1.07222
$396$	1.95181e6	0.625460
$397$	−3.77816e6	−1.20311	−0.601554	−	0.798832i	$-0.705452\pi$
$397$	−3.77816e6	−1.20311	−0.601554	+	0.798832i	$0.705452\pi$
$398$	−4.36016e6	−1.37973
$399$	−5.37437e6	−1.69003
$400$	150075.	0.0468983
$401$	1.64922e6	0.512173	0.256086	−	0.966654i	$-0.417567\pi$
$401$	1.64922e6	0.512173	0.256086	+	0.966654i	$0.417567\pi$
$402$	6.89524e6	2.12806
$403$	−4.74729e6	−1.45607
$404$	−2.44377e6	−0.744916
$405$	1.68923e6	0.511742
$406$	577320.	0.173821
$407$	3.54273e6	1.06011
$408$	3.96761e6	1.17999
$409$	−2.14199e6	−0.633153	−0.316577	−	0.948567i	$-0.602533\pi$
$409$	−2.14199e6	−0.633153	−0.316577	+	0.948567i	$0.602533\pi$
$410$	2.91720e6	0.857051
$411$	4.02463e6	1.17523
$412$	1.47933e6	0.429361
$413$	−218160.	−0.0629361
$414$	531590.	0.152432
$415$	4.63087e6	1.31990
$416$	−2.98912e6	−0.846857
$417$	−7.02616e6	−1.97869
$418$	−2.49161e6	−0.697493
$419$	6.49479e6	1.80730	0.903650	−	0.428272i	$-0.140877\pi$
$419$	6.49479e6	1.80730	0.903650	+	0.428272i	$0.140877\pi$
$420$	2.93336e6	0.811413
$421$	3.30359e6	0.908408	0.454204	−	0.890898i	$-0.349924\pi$
$421$	3.30359e6	0.908408	0.454204	+	0.890898i	$0.349924\pi$
$422$	−3.27457e6	−0.895103
$423$	8.72337e6	2.37046
$424$	5.87476e6	1.58699
$425$	305836.	0.0821327
$426$	−7.67200e6	−2.04826
$427$	8.47040e6	2.24820
$428$	587773.	0.155096
$429$	7.14841e6	1.87528
$430$	419565.	0.109428
$431$	−2.23343e6	−0.579133	−0.289567	−	0.957158i	$-0.593511\pi$
$431$	−2.23343e6	−0.579133	−0.289567	+	0.957158i	$0.593511\pi$
$432$	821966.	0.211907
$433$	−3.81775e6	−0.978561	−0.489280	−	0.872127i	$-0.662741\pi$
$433$	−3.81775e6	−0.978561	−0.489280	+	0.872127i	$0.662741\pi$
$434$	−5.35336e6	−1.36427
$435$	959402.	0.243096
$436$	1.04577e6	0.263464
$437$	487520.	0.122121
$438$	−1.85919e6	−0.463062
$439$	4.94254e6	1.22402	0.612011	−	0.790850i	$-0.290361\pi$
$439$	4.94254e6	1.22402	0.612011	+	0.790850i	$0.290361\pi$
$440$	4.61285e6	1.13589
$441$	4.48404e6	1.09793
$442$	2.45340e6	0.597328
$443$	−740033.	−0.179160	−0.0895802	−	0.995980i	$-0.528553\pi$
$443$	−740033.	−0.179160	−0.0895802	+	0.995980i	$0.528553\pi$
$444$	−2.52293e6	−0.607363
$445$	−2.64882e6	−0.634093
$446$	2.23178e6	0.531269
$447$	−2.90919e6	−0.688658
$448$	−5.70363e6	−1.34263
$449$	−1.75356e6	−0.410492	−0.205246	−	0.978710i	$-0.565799\pi$
$449$	−1.75356e6	−0.410492	−0.205246	+	0.978710i	$0.565799\pi$
$450$	505874.	0.117764
$451$	−5.75922e6	−1.33328
$452$	−309002.	−0.0711402
$453$	1.22923e7	2.81441
$454$	−2.70837e6	−0.616692
$455$	6.15256e6	1.39325
$456$	6.01864e6	1.35546
$457$	1.43140e6	0.320605	0.160302	−	0.987068i	$-0.448753\pi$
$457$	1.43140e6	0.320605	0.160302	+	0.987068i	$0.448753\pi$
$458$	−3.45408e6	−0.769429
$459$	1.67508e6	0.371110
$460$	−266091.	−0.0586321
$461$	−8.02421e6	−1.75853	−0.879265	−	0.476332i	$-0.841966\pi$
$461$	−8.02421e6	−1.75853	−0.879265	+	0.476332i	$0.841966\pi$
$462$	8.06102e6	1.75705
$463$	−5.42639e6	−1.17641	−0.588205	−	0.808712i	$-0.700165\pi$
$463$	−5.42639e6	−1.17641	−0.588205	+	0.808712i	$0.700165\pi$
$464$	−318990.	−0.0687831
$465$	−8.89631e6	−1.90800
$466$	−441856.	−0.0942575
$467$	−4.68842e6	−0.994796	−0.497398	−	0.867522i	$-0.665711\pi$
$467$	−4.68842e6	−0.994796	−0.497398	+	0.867522i	$0.665711\pi$
$468$	−2.91538e6	−0.615291
$469$	−1.17164e7	−2.45958
$470$	6.07806e6	1.26917
$471$	−4.24945e6	−0.882634
$472$	244313.	0.0504768
$473$	−828318.	−0.170233
$474$	−6.50683e6	−1.33022
$475$	463936.	0.0943461
$476$	−1.98757e6	−0.402072
$477$	9.77043e6	1.96615
$478$	3.79448e6	0.759595
$479$	2.64873e6	0.527471	0.263735	−	0.964595i	$-0.415045\pi$
$479$	2.64873e6	0.527471	0.263735	+	0.964595i	$0.415045\pi$
$480$	−5.60154e6	−1.10970
$481$	−5.29172e6	−1.04288
$482$	−848994.	−0.166451
$483$	−1.57725e6	−0.307634
$484$	−530260.	−0.102890
$485$	−920324.	−0.177659
$486$	−5.37318e6	−1.03191
$487$	2.23774e6	0.427550	0.213775	−	0.976883i	$-0.431424\pi$
$487$	2.23774e6	0.427550	0.213775	+	0.976883i	$0.431424\pi$
$488$	−9.48583e6	−1.80312
$489$	2.66736e6	0.504439
$490$	3.12428e6	0.587842
$491$	3.10094e6	0.580484	0.290242	−	0.956953i	$-0.406264\pi$
$491$	3.10094e6	0.580484	0.290242	+	0.956953i	$0.406264\pi$
$492$	4.10138e6	0.763867
$493$	−650066.	−0.120459
$494$	3.72168e6	0.686153
$495$	7.67172e6	1.40728
$496$	2.95792e6	0.539861
$497$	1.30363e7	2.36735
$498$	−9.06264e6	−1.63750
$499$	5.58008e6	1.00320	0.501601	−	0.865099i	$-0.332744\pi$
$499$	5.58008e6	1.00320	0.501601	+	0.865099i	$0.332744\pi$
$500$	−2.45157e6	−0.438550
$501$	3.06827e6	0.546135
$502$	3.44697e6	0.610490
$503$	5.10876e6	0.900317	0.450158	−	0.892949i	$-0.351368\pi$
$503$	5.10876e6	0.900317	0.450158	+	0.892949i	$0.351368\pi$
$504$	−1.11513e7	−1.95547
$505$	−9.60542e6	−1.67605
$506$	−731231.	−0.126963
$507$	−1.82327e6	−0.315014
$508$	−2.91814e6	−0.501703
$509$	2.93415e6	0.501982	0.250991	−	0.967989i	$-0.419244\pi$
$509$	2.93415e6	0.501982	0.250991	+	0.967989i	$0.419244\pi$
$510$	4.59762e6	0.782722
$511$	3.15914e6	0.535200
$512$	4.47501e6	0.754430
$513$	2.54100e6	0.426296
$514$	405351.	0.0676743
$515$	5.81462e6	0.966058
$516$	589880.	0.0975303
$517$	−1.19995e7	−1.97440
$518$	−5.96729e6	−0.977131
$519$	−1.31948e7	−2.15023
$520$	−6.89013e6	−1.11743
$521$	−9.22452e6	−1.48885	−0.744423	−	0.667709i	$-0.767275\pi$
$521$	−9.22452e6	−1.48885	−0.744423	+	0.667709i	$0.767275\pi$
$522$	−1.07526e6	−0.172717
$523$	−4.64359e6	−0.742335	−0.371168	−	0.928566i	$-0.621042\pi$
$523$	−4.64359e6	−0.742335	−0.371168	+	0.928566i	$0.621042\pi$
$524$	−1.43360e6	−0.228087
$525$	−1.50095e6	−0.237667
$526$	3.87731e6	0.611035
$527$	6.02791e6	0.945453
$528$	−4.45399e6	−0.695288
$529$	−6.29327e6	−0.977771
$530$	6.80761e6	1.05270
$531$	406322.	0.0625365
$532$	−3.01503e6	−0.461862
$533$	8.60244e6	1.31161
$534$	5.18376e6	0.786669
$535$	2.31028e6	0.348964
$536$	1.31209e7	1.97266
$537$	7.21924e6	1.08033
$538$	3.97823e6	0.592562
$539$	−6.16805e6	−0.914484
$540$	−1.38689e6	−0.204672
$541$	3.62594e6	0.532632	0.266316	−	0.963886i	$-0.414193\pi$
$541$	3.62594e6	0.532632	0.266316	+	0.963886i	$0.414193\pi$
$542$	982690.	0.143687
$543$	1.67573e7	2.43897
$544$	3.79546e6	0.549879
$545$	4.11049e6	0.592792
$546$	−1.20406e7	−1.72849
$547$	−5.56425e6	−0.795131	−0.397565	−	0.917574i	$-0.630145\pi$
$547$	−5.56425e6	−0.795131	−0.397565	+	0.917574i	$0.630145\pi$
$548$	2.25782e6	0.321173
$549$	−1.57761e7	−2.23392
$550$	−695858.	−0.0980876
$551$	−986114.	−0.138372
$552$	1.76633e6	0.246732
$553$	1.10564e7	1.53745
$554$	−7.60271e6	−1.05243
$555$	−9.91656e6	−1.36656
$556$	−3.94169e6	−0.540748
$557$	6.83963e6	0.934103	0.467052	−	0.884230i	$-0.345316\pi$
$557$	6.83963e6	0.934103	0.467052	+	0.884230i	$0.345316\pi$
$558$	9.97059e6	1.35561
$559$	1.23724e6	0.167465
$560$	−3.83351e6	−0.516567
$561$	−9.07675e6	−1.21765
$562$	1.16690e6	0.155845
$563$	−5.62439e6	−0.747833	−0.373916	−	0.927462i	$-0.621985\pi$
$563$	−5.62439e6	−0.747833	−0.373916	+	0.927462i	$0.621985\pi$
$564$	8.54534e6	1.13118
$565$	−1.21455e6	−0.160065
$566$	−8.82866e6	−1.15839
$567$	5.61726e6	0.733782
$568$	−1.45990e7	−1.89869
$569$	−4.17021e6	−0.539979	−0.269990	−	0.962863i	$-0.587020\pi$
$569$	−4.17021e6	−0.539979	−0.269990	+	0.962863i	$0.587020\pi$
$570$	6.97434e6	0.899116
$571$	−8.60607e6	−1.10462	−0.552312	−	0.833637i	$-0.686254\pi$
$571$	−8.60607e6	−1.10462	−0.552312	+	0.833637i	$0.686254\pi$
$572$	4.01027e6	0.512487
$573$	−2.51239e6	−0.319669
$574$	9.70069e6	1.22892
$575$	136155.	0.0171737
$576$	1.06230e7	1.33410
$577$	−3.23538e6	−0.404563	−0.202282	−	0.979327i	$-0.564836\pi$
$577$	−3.23538e6	−0.404563	−0.202282	+	0.979327i	$0.564836\pi$
$578$	3.01189e6	0.374990
$579$	−268815.	−0.0333240
$580$	538226.	0.0664347
$581$	1.53992e7	1.89260
$582$	1.80108e6	0.220407
$583$	−1.34398e7	−1.63765
$584$	−3.53785e6	−0.429247
$585$	−1.14591e7	−1.38440
$586$	−4.97003e6	−0.597881
$587$	−1.12970e7	−1.35322	−0.676609	−	0.736342i	$-0.736551\pi$
$587$	−1.12970e7	−1.35322	−0.676609	+	0.736342i	$0.736551\pi$
$588$	4.39253e6	0.523928
$589$	9.14401e6	1.08605
$590$	283107.	0.0334827
$591$	−1.06008e6	−0.124845
$592$	3.29714e6	0.386663
$593$	1.61368e7	1.88444	0.942218	−	0.335000i	$-0.108736\pi$
$593$	1.61368e7	1.88444	0.942218	+	0.335000i	$0.108736\pi$
$594$	−3.81125e6	−0.443201
$595$	−7.81227e6	−0.904659
$596$	−1.63206e6	−0.188201
$597$	−2.40948e7	−2.76686
$598$	1.09223e6	0.124899
$599$	1.14121e7	1.29957	0.649785	−	0.760118i	$-0.274859\pi$
$599$	1.14121e7	1.29957	0.649785	+	0.760118i	$0.274859\pi$
$600$	1.68089e6	0.190617
$601$	1.15192e7	1.30088	0.650438	−	0.759559i	$-0.274585\pi$
$601$	1.15192e7	1.30088	0.650438	+	0.759559i	$0.274585\pi$
$602$	1.39520e6	0.156908
$603$	2.18217e7	2.44396
$604$	6.89600e6	0.769139
$605$	−2.08422e6	−0.231503
$606$	1.87979e7	2.07935
$607$	1.48986e7	1.64125	0.820625	−	0.571466i	$-0.193625\pi$
$607$	1.48986e7	1.64125	0.820625	+	0.571466i	$0.193625\pi$
$608$	5.75751e6	0.631648
$609$	3.19034e6	0.348573
$610$	−1.09921e7	−1.19607
$611$	1.79234e7	1.94230
$612$	3.70183e6	0.399520
$613$	−5.39999e6	−0.580419	−0.290210	−	0.956963i	$-0.593725\pi$
$613$	−5.39999e6	−0.580419	−0.290210	+	0.956963i	$0.593725\pi$
$614$	8.11508e6	0.868704
$615$	1.61208e7	1.71869
$616$	1.53393e7	1.62875
$617$	−1.26228e7	−1.33489	−0.667443	−	0.744660i	$-0.732611\pi$
$617$	−1.26228e7	−1.33489	−0.667443	+	0.744660i	$0.732611\pi$
$618$	−1.13792e7	−1.19851
$619$	1.43557e7	1.50591	0.752953	−	0.658074i	$-0.228629\pi$
$619$	1.43557e7	1.50591	0.752953	+	0.658074i	$0.228629\pi$
$620$	−4.99084e6	−0.521428
$621$	745725.	0.0775979
$622$	−8.40642e6	−0.871235
$623$	−8.80824e6	−0.909220
$624$	6.65285e6	0.683984
$625$	−8.51120e6	−0.871546
$626$	4.07550e6	0.415666
$627$	−1.37689e7	−1.39872
$628$	−2.38395e6	−0.241211
$629$	6.71920e6	0.677160
$630$	−1.29221e7	−1.29712
$631$	−6.76873e6	−0.676759	−0.338379	−	0.941010i	$-0.609879\pi$
$631$	−6.76873e6	−0.676759	−0.338379	+	0.941010i	$0.609879\pi$
$632$	−1.23818e7	−1.23308
$633$	−1.80956e7	−1.79500
$634$	−147364.	−0.0145603
$635$	−1.14699e7	−1.12883
$636$	9.57103e6	0.938244
$637$	9.21310e6	0.899616
$638$	1.47907e6	0.143859
$639$	−2.42799e7	−2.35232
$640$	−115066.	−0.0111045
$641$	−1.51643e6	−0.145773	−0.0728867	−	0.997340i	$-0.523221\pi$
$641$	−1.51643e6	−0.145773	−0.0728867	+	0.997340i	$0.523221\pi$
$642$	−4.52124e6	−0.432932
$643$	6.58876e6	0.628458	0.314229	−	0.949347i	$-0.398254\pi$
$643$	6.58876e6	0.628458	0.314229	+	0.949347i	$0.398254\pi$
$644$	−884842.	−0.0840719
$645$	2.31857e6	0.219442
$646$	−4.72563e6	−0.445532
$647$	9.99129e6	0.938341	0.469171	−	0.883108i	$-0.344553\pi$
$647$	9.99129e6	0.938341	0.469171	+	0.883108i	$0.344553\pi$
$648$	−6.29065e6	−0.588516
$649$	−558918.	−0.0520878
$650$	1.03939e6	0.0964929
$651$	−2.95833e7	−2.73586
$652$	1.49639e6	0.137856
$653$	−1.32714e7	−1.21796	−0.608980	−	0.793186i	$-0.708421\pi$
$653$	−1.32714e7	−1.21796	−0.608980	+	0.793186i	$0.708421\pi$
$654$	−8.04425e6	−0.735430
$655$	−5.63486e6	−0.513192
$656$	−5.35997e6	−0.486298
$657$	−5.88387e6	−0.531802
$658$	2.02116e7	1.81985
$659$	3.69381e6	0.331330	0.165665	−	0.986182i	$-0.447023\pi$
$659$	3.69381e6	0.331330	0.165665	+	0.986182i	$0.447023\pi$
$660$	7.51515e6	0.671549
$661$	8.97800e6	0.799238	0.399619	−	0.916681i	$-0.369142\pi$
$661$	8.97800e6	0.799238	0.399619	+	0.916681i	$0.369142\pi$
$662$	−7.50845e6	−0.665894
$663$	1.35578e7	1.19786
$664$	−1.72453e7	−1.51792
$665$	−1.18508e7	−1.03919
$666$	1.11140e7	0.970927
$667$	−289402.	−0.0251876
$668$	1.72131e6	0.149251
$669$	1.23331e7	1.06538
$670$	1.52044e7	1.30852
$671$	2.17009e7	1.86068
$672$	−1.86270e7	−1.59118
$673$	8.59992e6	0.731909	0.365954	−	0.930633i	$-0.380743\pi$
$673$	8.59992e6	0.731909	0.365954	+	0.930633i	$0.380743\pi$
$674$	4.72322e6	0.400487
$675$	709651.	0.0599495
$676$	−1.02285e6	−0.0860889
$677$	−8.01663e6	−0.672233	−0.336117	−	0.941820i	$-0.609114\pi$
$677$	−8.01663e6	−0.672233	−0.336117	+	0.941820i	$0.609114\pi$
$678$	2.37689e6	0.198579
$679$	−3.06039e6	−0.254743
$680$	8.74880e6	0.725565
$681$	−1.49667e7	−1.23669
$682$	−1.37151e7	−1.12911
$683$	2.81320e6	0.230754	0.115377	−	0.993322i	$-0.463192\pi$
$683$	2.81320e6	0.230754	0.115377	+	0.993322i	$0.463192\pi$
$684$	5.61547e6	0.458930
$685$	8.87454e6	0.722636
$686$	−2.29273e6	−0.186012
$687$	−1.90876e7	−1.54298
$688$	−770895.	−0.0620904
$689$	2.00747e7	1.61102
$690$	2.04681e6	0.163665
$691$	1.04922e7	0.835935	0.417967	−	0.908462i	$-0.362743\pi$
$691$	1.04922e7	0.835935	0.417967	+	0.908462i	$0.362743\pi$
$692$	−7.40231e6	−0.587628
$693$	2.55111e7	2.01788
$694$	2.42434e6	0.191071
$695$	−1.54931e7	−1.21668
$696$	−3.57279e6	−0.279566
$697$	−1.09230e7	−0.851650
$698$	−8.92521e6	−0.693394
$699$	−2.44175e6	−0.189020
$700$	−842038.	−0.0649511
$701$	−2.37537e7	−1.82573	−0.912865	−	0.408263i	$-0.866135\pi$
$701$	−2.37537e7	−1.82573	−0.912865	+	0.408263i	$0.866135\pi$
$702$	5.69279e6	0.435996
$703$	1.01927e7	0.777856
$704$	−1.46125e7	−1.11120
$705$	3.35880e7	2.54514
$706$	−2.45182e6	−0.185130
$707$	−3.19413e7	−2.40328
$708$	398029.	0.0298423
$709$	−1.72000e7	−1.28503	−0.642516	−	0.766273i	$-0.722109\pi$
$709$	−1.72000e7	−1.28503	−0.642516	+	0.766273i	$0.722109\pi$
$710$	−1.69172e7	−1.25945
$711$	−2.05925e7	−1.52769
$712$	9.86417e6	0.729223
$713$	2.68356e6	0.197691
$714$	1.52887e7	1.12234
$715$	1.57626e7	1.15309
$716$	4.05001e6	0.295239
$717$	2.09687e7	1.52326
$718$	−1.11100e7	−0.804270
$719$	2.22034e7	1.60176	0.800878	−	0.598827i	$-0.204366\pi$
$719$	2.22034e7	1.60176	0.800878	+	0.598827i	$0.204366\pi$
$720$	7.13989e6	0.513287
$721$	1.93356e7	1.38522
$722$	3.51660e6	0.251062
$723$	−4.69164e6	−0.333794
$724$	9.40090e6	0.666535
$725$	−275402.	−0.0194591
$726$	4.07884e6	0.287207
$727$	−1.95017e7	−1.36847	−0.684236	−	0.729261i	$-0.739864\pi$
$727$	−1.95017e7	−1.36847	−0.684236	+	0.729261i	$0.739864\pi$
$728$	−2.29120e7	−1.60227
$729$	−2.18865e7	−1.52531
$730$	−4.09962e6	−0.284732
$731$	−1.57100e6	−0.108738
$732$	−1.54541e7	−1.06602
$733$	1.07906e7	0.741798	0.370899	−	0.928673i	$-0.379050\pi$
$733$	1.07906e7	0.741798	0.370899	+	0.928673i	$0.379050\pi$
$734$	−1.17420e6	−0.0804457
$735$	1.72651e7	1.17883
$736$	1.68970e6	0.114978
$737$	−3.00169e7	−2.03562
$738$	−1.80675e7	−1.22111
$739$	−1.44802e7	−0.975358	−0.487679	−	0.873023i	$-0.662156\pi$
$739$	−1.44802e7	−0.975358	−0.487679	+	0.873023i	$0.662156\pi$
$740$	−5.56321e6	−0.373462
$741$	2.05664e7	1.37598
$742$	2.26376e7	1.50946
$743$	5.44908e6	0.362119	0.181059	−	0.983472i	$-0.442047\pi$
$743$	5.44908e6	0.362119	0.181059	+	0.983472i	$0.442047\pi$
$744$	3.31297e7	2.19424
$745$	−6.41493e6	−0.423449
$746$	1.16067e6	0.0763594
$747$	−2.86809e7	−1.88058
$748$	−5.09207e6	−0.332767
$749$	7.68248e6	0.500376
$750$	1.88578e7	1.22416
$751$	−2.78004e6	−0.179867	−0.0899335	−	0.995948i	$-0.528665\pi$
$751$	−2.78004e6	−0.179867	−0.0899335	+	0.995948i	$0.528665\pi$
$752$	−1.11676e7	−0.720139
$753$	1.90484e7	1.22425
$754$	−2.20926e6	−0.141521
$755$	2.71052e7	1.73056
$756$	−4.61188e6	−0.293477
$757$	2.46778e7	1.56519	0.782595	−	0.622531i	$-0.213895\pi$
$757$	2.46778e7	1.56519	0.782595	+	0.622531i	$0.213895\pi$
$758$	2.25281e6	0.142414
$759$	−4.04087e6	−0.254607
$760$	1.32714e7	0.833459
$761$	−8.63006e6	−0.540197	−0.270098	−	0.962833i	$-0.587056\pi$
$761$	−8.63006e6	−0.540197	−0.270098	+	0.962833i	$0.587056\pi$
$762$	2.24467e7	1.40044
$763$	1.36688e7	0.849999
$764$	−1.40946e6	−0.0873611
$765$	1.45503e7	0.898915
$766$	−8.65345e6	−0.532865
$767$	834845.	0.0512410
$768$	2.51164e7	1.53657
$769$	−1.79104e6	−0.109217	−0.0546083	−	0.998508i	$-0.517391\pi$
$769$	−1.79104e6	−0.109217	−0.0546083	+	0.998508i	$0.517391\pi$
$770$	1.77750e7	1.08040
$771$	2.24002e6	0.135711
$772$	−150806.	−0.00910698
$773$	−2.64220e7	−1.59044	−0.795219	−	0.606322i	$-0.792644\pi$
$773$	−2.64220e7	−1.59044	−0.795219	+	0.606322i	$0.792644\pi$
$774$	−2.59855e6	−0.155911
$775$	2.55374e6	0.152729
$776$	3.42727e6	0.204312
$777$	−3.29759e7	−1.95950
$778$	4.78253e6	0.283275
$779$	−1.65696e7	−0.978293
$780$	−1.12252e7	−0.660631
$781$	3.33984e7	1.95929
$782$	−1.38686e6	−0.0810993
$783$	−1.50839e6	−0.0879244
$784$	−5.74045e6	−0.333546
$785$	−9.37028e6	−0.542723
$786$	1.10275e7	0.636677
$787$	4.11413e6	0.236778	0.118389	−	0.992967i	$-0.462227\pi$
$787$	4.11413e6	0.236778	0.118389	+	0.992967i	$0.462227\pi$
$788$	−594708.	−0.0341184
$789$	2.14265e7	1.22534
$790$	−1.43479e7	−0.817940
$791$	−4.03880e6	−0.229515
$792$	−2.85693e7	−1.61840
$793$	−3.24142e7	−1.83043
$794$	1.63039e7	0.917786
$795$	3.76196e7	2.11104
$796$	−1.35172e7	−0.756143
$797$	3.23381e6	0.180330	0.0901651	−	0.995927i	$-0.471261\pi$
$797$	3.23381e6	0.180330	0.0901651	+	0.995927i	$0.471261\pi$
$798$	2.31920e7	1.28923
$799$	−2.27584e7	−1.26117
$800$	1.60796e6	0.0888279
$801$	1.64053e7	0.903447
$802$	−7.11687e6	−0.390709
$803$	8.09359e6	0.442948
$804$	2.13763e7	1.16625
$805$	−3.47793e6	−0.189161
$806$	2.04860e7	1.11076
$807$	2.19841e7	1.18830
$808$	3.57704e7	1.92750
$809$	−1.52689e7	−0.820231	−0.410115	−	0.912034i	$-0.634512\pi$
$809$	−1.52689e7	−0.820231	−0.410115	+	0.912034i	$0.634512\pi$
$810$	−7.28954e6	−0.390380
$811$	−3.04480e7	−1.62558	−0.812788	−	0.582560i	$-0.802051\pi$
$811$	−3.04480e7	−1.62558	−0.812788	+	0.582560i	$0.802051\pi$
$812$	1.78978e6	0.0952600
$813$	5.43045e6	0.288144
$814$	−1.52880e7	−0.808703
$815$	5.88167e6	0.310175
$816$	−8.44751e6	−0.444123
$817$	−2.38312e6	−0.124908
$818$	9.24334e6	0.482998
$819$	−3.81054e7	−1.98508
$820$	9.04378e6	0.469695
$821$	−2.25035e6	−0.116518	−0.0582590	−	0.998302i	$-0.518555\pi$
$821$	−2.25035e6	−0.116518	−0.0582590	+	0.998302i	$0.518555\pi$
$822$	−1.73675e7	−0.896516
$823$	−1.66620e7	−0.857485	−0.428743	−	0.903427i	$-0.641043\pi$
$823$	−1.66620e7	−0.857485	−0.428743	+	0.903427i	$0.641043\pi$
$824$	−2.16535e7	−1.11099
$825$	−3.84539e6	−0.196701
$826$	941428.	0.0480106
$827$	3.70905e7	1.88581	0.942907	−	0.333056i	$-0.108080\pi$
$827$	3.70905e7	1.88581	0.942907	+	0.333056i	$0.108080\pi$
$828$	1.64801e6	0.0835381
$829$	2.88276e7	1.45688	0.728438	−	0.685111i	$-0.240246\pi$
$829$	2.88276e7	1.45688	0.728438	+	0.685111i	$0.240246\pi$
$830$	−1.99836e7	−1.00688
$831$	−4.20134e7	−2.11050
$832$	2.18264e7	1.09313
$833$	−1.16984e7	−0.584137
$834$	3.03200e7	1.50943
$835$	6.76572e6	0.335813
$836$	−7.72439e6	−0.382251
$837$	1.39870e7	0.690096
$838$	−2.80270e7	−1.37869
$839$	−7.10869e6	−0.348646	−0.174323	−	0.984689i	$-0.555774\pi$
$839$	−7.10869e6	−0.348646	−0.174323	+	0.984689i	$0.555774\pi$
$840$	−4.29366e7	−2.09957
$841$	−1.99258e7	−0.971460
$842$	−1.42560e7	−0.692975
$843$	6.44843e6	0.312525
$844$	−1.01517e7	−0.490548
$845$	−4.02040e6	−0.193699
$846$	−3.76440e7	−1.80830
$847$	−6.93075e6	−0.331949
$848$	−1.25081e7	−0.597311
$849$	−4.87882e7	−2.32298
$850$	−1.31978e6	−0.0626546
$851$	2.99131e6	0.141592
$852$	−2.37844e7	−1.12252
$853$	6.01755e6	0.283170	0.141585	−	0.989926i	$-0.454780\pi$
$853$	6.01755e6	0.283170	0.141585	+	0.989926i	$0.454780\pi$
$854$	−3.65524e7	−1.71503
$855$	2.20720e7	1.03259
$856$	−8.60345e6	−0.401317
$857$	1.40484e7	0.653392	0.326696	−	0.945129i	$-0.394065\pi$
$857$	1.40484e7	0.653392	0.326696	+	0.945129i	$0.394065\pi$
$858$	−3.08476e7	−1.43055
$859$	2.38780e7	1.10412	0.552060	−	0.833805i	$-0.313842\pi$
$859$	2.38780e7	1.10412	0.552060	+	0.833805i	$0.313842\pi$
$860$	1.30072e6	0.0599704
$861$	5.36071e7	2.46442
$862$	9.63792e6	0.441789
$863$	3.12051e7	1.42626	0.713131	−	0.701031i	$-0.247277\pi$
$863$	3.12051e7	1.42626	0.713131	+	0.701031i	$0.247277\pi$
$864$	8.80686e6	0.401362
$865$	−2.90953e7	−1.32216
$866$	1.64748e7	0.746491
$867$	1.66440e7	0.751988
$868$	−1.65963e7	−0.747671
$869$	2.83261e7	1.27244
$870$	−4.14011e6	−0.185445
$871$	4.48357e7	2.00253
$872$	−1.53074e7	−0.681725
$873$	5.69996e6	0.253126
$874$	−2.10380e6	−0.0931591
$875$	−3.20432e7	−1.41487
$876$	−5.76379e6	−0.253775
$877$	−2.97111e6	−0.130443	−0.0652213	−	0.997871i	$-0.520775\pi$
$877$	−2.97111e6	−0.130443	−0.0652213	+	0.997871i	$0.520775\pi$
$878$	−2.13286e7	−0.933739
$879$	−2.74649e7	−1.19896
$880$	−9.82131e6	−0.427526
$881$	3.55211e7	1.54187	0.770934	−	0.636915i	$-0.219790\pi$
$881$	3.55211e7	1.54187	0.770934	+	0.636915i	$0.219790\pi$
$882$	−1.93500e7	−0.837549
$883$	1.87105e7	0.807576	0.403788	−	0.914853i	$-0.367693\pi$
$883$	1.87105e7	0.807576	0.403788	+	0.914853i	$0.367693\pi$
$884$	7.60593e6	0.327357
$885$	1.56448e6	0.0671448
$886$	3.19347e6	0.136672
$887$	9.33897e6	0.398557	0.199278	−	0.979943i	$-0.436140\pi$
$887$	9.33897e6	0.398557	0.199278	+	0.979943i	$0.436140\pi$
$888$	3.69291e7	1.57158
$889$	−3.81415e7	−1.61861
$890$	1.14305e7	0.483715
$891$	1.43912e7	0.607300
$892$	6.91887e6	0.291154
$893$	−3.45232e7	−1.44871
$894$	1.25541e7	0.525340
$895$	1.59188e7	0.664284
$896$	−382635.	−0.0159226
$897$	6.03577e6	0.250468
$898$	7.56715e6	0.313142
$899$	−5.42807e6	−0.223999
$900$	1.56829e6	0.0645387
$901$	−2.54901e7	−1.04607
$902$	2.48528e7	1.01709
$903$	7.71002e6	0.314656
$904$	4.52297e6	0.184078
$905$	3.69509e7	1.49970
$906$	−5.30451e7	−2.14696
$907$	3.89432e7	1.57186	0.785930	−	0.618315i	$-0.212184\pi$
$907$	3.89432e7	1.57186	0.785930	+	0.618315i	$0.212184\pi$
$908$	−8.39637e6	−0.337969
$909$	5.94904e7	2.38802
$910$	−2.65502e7	−1.06283
$911$	4.28351e7	1.71003	0.855015	−	0.518604i	$-0.173548\pi$
$911$	4.28351e7	1.71003	0.855015	+	0.518604i	$0.173548\pi$
$912$	−1.28144e7	−0.510166
$913$	3.94522e7	1.56637
$914$	−6.17692e6	−0.244572
$915$	−6.07435e7	−2.39854
$916$	−1.07082e7	−0.421675
$917$	−1.87378e7	−0.735862
$918$	−7.22847e6	−0.283100
$919$	881759.	0.0344398	0.0172199	−	0.999852i	$-0.494518\pi$
$919$	881759.	0.0344398	0.0172199	+	0.999852i	$0.494518\pi$
$920$	3.89487e6	0.151713
$921$	4.48448e7	1.74206
$922$	3.46269e7	1.34149
$923$	−4.98866e7	−1.92743
$924$	2.49904e7	0.962928
$925$	2.84661e6	0.109389
$926$	2.34165e7	0.897419
$927$	−3.60124e7	−1.37643
$928$	−3.41778e6	−0.130279
$929$	−1.81365e7	−0.689468	−0.344734	−	0.938700i	$-0.612031\pi$
$929$	−1.81365e7	−0.689468	−0.344734	+	0.938700i	$0.612031\pi$
$930$	3.83903e7	1.45551
$931$	−1.77459e7	−0.671000
$932$	−1.36982e6	−0.0516565
$933$	−4.64548e7	−1.74714
$934$	2.02320e7	0.758876
$935$	−2.00148e7	−0.748723
$936$	4.26735e7	1.59209
$937$	−1.75363e7	−0.652512	−0.326256	−	0.945281i	$-0.605787\pi$
$937$	−1.75363e7	−0.652512	−0.326256	+	0.945281i	$0.605787\pi$
$938$	5.05597e7	1.87628
$939$	2.25217e7	0.833559
$940$	1.88429e7	0.695551
$941$	7.69478e6	0.283284	0.141642	−	0.989918i	$-0.454762\pi$
$941$	7.69478e6	0.283284	0.141642	+	0.989918i	$0.454762\pi$
$942$	1.83377e7	0.673313
$943$	−4.86281e6	−0.178077
$944$	−520171.	−0.0189984
$945$	−1.81273e7	−0.660320
$946$	3.57444e6	0.129862
$947$	−3.00889e7	−1.09026	−0.545131	−	0.838351i	$-0.683520\pi$
$947$	−3.00889e7	−1.09026	−0.545131	+	0.838351i	$0.683520\pi$
$948$	−2.01722e7	−0.729008
$949$	−1.20892e7	−0.435746
$950$	−2.00203e6	−0.0719715
$951$	−814352.	−0.0291985
$952$	2.90927e7	1.04038
$953$	2.31755e7	0.826601	0.413301	−	0.910595i	$-0.364376\pi$
$953$	2.31755e7	0.826601	0.413301	+	0.910595i	$0.364376\pi$
$954$	−4.21624e7	−1.49987
$955$	−5.53997e6	−0.196562
$956$	1.17635e7	0.416285
$957$	8.17353e6	0.288489
$958$	−1.14301e7	−0.402379
$959$	2.95109e7	1.03618
$960$	4.09022e7	1.43241
$961$	2.17041e7	0.758112
$962$	2.28354e7	0.795556
$963$	−1.43086e7	−0.497199
$964$	−2.63202e6	−0.0912212
$965$	−592752.	−0.0204906
$966$	6.80633e6	0.234677
$967$	−3.96944e7	−1.36510	−0.682548	−	0.730841i	$-0.739128\pi$
$967$	−3.96944e7	−1.36510	−0.682548	+	0.730841i	$0.739128\pi$
$968$	7.76160e6	0.266234
$969$	−2.61144e7	−0.893450
$970$	3.97148e6	0.135526
$971$	−6.90625e6	−0.235068	−0.117534	−	0.993069i	$-0.537499\pi$
$971$	−6.90625e6	−0.235068	−0.117534	+	0.993069i	$0.537499\pi$
$972$	−1.66577e7	−0.565522
$973$	−5.15197e7	−1.74458
$974$	−9.65654e6	−0.326155
$975$	5.74379e6	0.193503
$976$	2.01965e7	0.678658
$977$	−1.38767e7	−0.465104	−0.232552	−	0.972584i	$-0.574708\pi$
$977$	−1.38767e7	−0.465104	−0.232552	+	0.972584i	$0.574708\pi$
$978$	−1.15105e7	−0.384809
$979$	−2.25664e7	−0.752498
$980$	9.68578e6	0.322158
$981$	−2.54580e7	−0.844602
$982$	−1.33815e7	−0.442819
$983$	1.20330e7	0.397183	0.198591	−	0.980082i	$-0.436363\pi$
$983$	1.20330e7	0.397183	0.198591	+	0.980082i	$0.436363\pi$
$984$	−6.00335e7	−1.97654
$985$	−2.33754e6	−0.0767659
$986$	2.80523e6	0.0918918
$987$	1.11692e8	3.64945
$988$	1.15378e7	0.376037
$989$	−699391.	−0.0227368
$990$	−3.31058e7	−1.07354
$991$	9.67955e6	0.313091	0.156546	−	0.987671i	$-0.449964\pi$
$991$	9.67955e6	0.313091	0.156546	+	0.987671i	$0.449964\pi$
$992$	3.16922e7	1.02252
$993$	−4.14925e7	−1.33535
$994$	−5.62554e7	−1.80592
$995$	−5.31303e7	−1.70131
$996$	−2.80956e7	−0.897408
$997$	−273483.	−0.00871351	−0.00435676	−	0.999991i	$-0.501387\pi$
$997$	−273483.	−0.00871351	−0.00435676	+	0.999991i	$0.501387\pi$
$998$	−2.40797e7	−0.765289
$999$	1.55910e7	0.494266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.b.1.3	✓	10
3.2	odd	2		387.6.a.e.1.8		10
4.3	odd	2		688.6.a.h.1.9		10
5.4	even	2		1075.6.a.b.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.3	✓	10	1.1	even	1	trivial
387.6.a.e.1.8		10	3.2	odd	2
688.6.a.h.1.9		10	4.3	odd	2
1075.6.a.b.1.8		10	5.4	even	2

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-4.31531 q^{2} -23.8469 q^{3} -13.3781 q^{4} -52.5837 q^{5} +102.907 q^{6} -174.859 q^{7} +195.821 q^{8} +325.673 q^{9} +O(q^{10})\)	\(q-4.31531 q^{2} -23.8469 q^{3} -13.3781 q^{4} -52.5837 q^{5} +102.907 q^{6} -174.859 q^{7} +195.821 q^{8} +325.673 q^{9} +226.915 q^{10} -447.981 q^{11} +319.027 q^{12} +669.141 q^{13} +754.569 q^{14} +1253.96 q^{15} -416.925 q^{16} -849.648 q^{17} -1405.38 q^{18} -1288.87 q^{19} +703.471 q^{20} +4169.83 q^{21} +1933.18 q^{22} -378.254 q^{23} -4669.71 q^{24} -359.956 q^{25} -2887.55 q^{26} -1971.50 q^{27} +2339.28 q^{28} +765.100 q^{29} -5411.21 q^{30} -7094.59 q^{31} -4467.10 q^{32} +10683.0 q^{33} +3666.49 q^{34} +9194.71 q^{35} -4356.90 q^{36} -7908.22 q^{37} +5561.87 q^{38} -15956.9 q^{39} -10297.0 q^{40} +12855.9 q^{41} -17994.1 q^{42} +1849.00 q^{43} +5993.15 q^{44} -17125.1 q^{45} +1632.28 q^{46} +26785.7 q^{47} +9942.37 q^{48} +13768.5 q^{49} +1553.32 q^{50} +20261.5 q^{51} -8951.86 q^{52} +30000.7 q^{53} +8507.60 q^{54} +23556.5 q^{55} -34240.9 q^{56} +30735.5 q^{57} -3301.64 q^{58} +1247.64 q^{59} -16775.6 q^{60} -48441.4 q^{61} +30615.3 q^{62} -56946.8 q^{63} +32618.5 q^{64} -35185.9 q^{65} -46100.2 q^{66} +67004.8 q^{67} +11366.7 q^{68} +9020.17 q^{69} -39678.0 q^{70} -74553.1 q^{71} +63773.5 q^{72} -18066.8 q^{73} +34126.4 q^{74} +8583.82 q^{75} +17242.7 q^{76} +78333.4 q^{77} +68859.0 q^{78} -63230.5 q^{79} +21923.5 q^{80} -32124.6 q^{81} -55477.3 q^{82} -88066.7 q^{83} -55784.5 q^{84} +44677.6 q^{85} -7979.00 q^{86} -18245.2 q^{87} -87724.0 q^{88} +50373.5 q^{89} +73900.0 q^{90} -117005. q^{91} +5060.33 q^{92} +169184. q^{93} -115588. q^{94} +67773.5 q^{95} +106526. q^{96} +17502.1 q^{97} -59415.5 q^{98} -145895. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9} - 17 q^{10} + 745 q^{11} + 4627 q^{12} + 1917 q^{13} + 1936 q^{14} + 1688 q^{15} + 5354 q^{16} + 4017 q^{17} - 2725 q^{18} - 2404 q^{19} + 1311 q^{20} - 228 q^{21} - 5836 q^{22} + 1733 q^{23} - 10711 q^{24} + 7120 q^{25} - 1484 q^{26} - 2324 q^{27} - 15028 q^{28} + 6996 q^{29} - 48420 q^{30} - 4899 q^{31} - 7554 q^{32} - 15734 q^{33} - 27033 q^{34} + 7084 q^{35} + 4433 q^{36} + 1466 q^{37} + 13905 q^{38} - 26542 q^{39} - 93211 q^{40} + 10297 q^{41} - 37642 q^{42} + 18490 q^{43} - 36140 q^{44} + 73822 q^{45} + 17991 q^{46} + 48592 q^{47} + 83607 q^{48} + 29458 q^{49} + 983 q^{50} + 92972 q^{51} + 14232 q^{52} + 127165 q^{53} - 92002 q^{54} + 106672 q^{55} - 7780 q^{56} + 34060 q^{57} - 10305 q^{58} + 99372 q^{59} + 111372 q^{60} + 17408 q^{61} + 28265 q^{62} + 2244 q^{63} + 47202 q^{64} + 54484 q^{65} - 150292 q^{66} - 2021 q^{67} + 192151 q^{68} + 1654 q^{69} - 33194 q^{70} + 11286 q^{71} - 298365 q^{72} + 49892 q^{73} - 125431 q^{74} - 44662 q^{75} - 249803 q^{76} + 98144 q^{77} - 28494 q^{78} - 91524 q^{79} + 12251 q^{80} - 26450 q^{81} - 158909 q^{82} - 105203 q^{83} - 357682 q^{84} - 87212 q^{85} + 14792 q^{86} + 181200 q^{87} - 461824 q^{88} - 62682 q^{89} - 522670 q^{90} - 295304 q^{91} + 183783 q^{92} - 238430 q^{93} + 7259 q^{94} - 305340 q^{95} - 162399 q^{96} + 108383 q^{97} + 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q + 8 * q^2 + 28 * q^3 + 202 * q^4 + 138 * q^5 + 75 * q^6 + 60 * q^7 + 294 * q^8 + 1356 * q^9 - 17 * q^10 + 745 * q^11 + 4627 * q^12 + 1917 * q^13 + 1936 * q^14 + 1688 * q^15 + 5354 * q^16 + 4017 * q^17 - 2725 * q^18 - 2404 * q^19 + 1311 * q^20 - 228 * q^21 - 5836 * q^22 + 1733 * q^23 - 10711 * q^24 + 7120 * q^25 - 1484 * q^26 - 2324 * q^27 - 15028 * q^28 + 6996 * q^29 - 48420 * q^30 - 4899 * q^31 - 7554 * q^32 - 15734 * q^33 - 27033 * q^34 + 7084 * q^35 + 4433 * q^36 + 1466 * q^37 + 13905 * q^38 - 26542 * q^39 - 93211 * q^40 + 10297 * q^41 - 37642 * q^42 + 18490 * q^43 - 36140 * q^44 + 73822 * q^45 + 17991 * q^46 + 48592 * q^47 + 83607 * q^48 + 29458 * q^49 + 983 * q^50 + 92972 * q^51 + 14232 * q^52 + 127165 * q^53 - 92002 * q^54 + 106672 * q^55 - 7780 * q^56 + 34060 * q^57 - 10305 * q^58 + 99372 * q^59 + 111372 * q^60 + 17408 * q^61 + 28265 * q^62 + 2244 * q^63 + 47202 * q^64 + 54484 * q^65 - 150292 * q^66 - 2021 * q^67 + 192151 * q^68 + 1654 * q^69 - 33194 * q^70 + 11286 * q^71 - 298365 * q^72 + 49892 * q^73 - 125431 * q^74 - 44662 * q^75 - 249803 * q^76 + 98144 * q^77 - 28494 * q^78 - 91524 * q^79 + 12251 * q^80 - 26450 * q^81 - 158909 * q^82 - 105203 * q^83 - 357682 * q^84 - 87212 * q^85 + 14792 * q^86 + 181200 * q^87 - 461824 * q^88 - 62682 * q^89 - 522670 * q^90 - 295304 * q^91 + 183783 * q^92 - 238430 * q^93 + 7259 * q^94 - 305340 * q^95 - 162399 * q^96 + 108383 * q^97 + 354656 * q^98 - 270499 * q^99

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