LMFDB - Embedded newform 43.6.a.b.1.6

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			1.6
Root			$-1.48720$ 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)

$f(q)$	$=$	$q+2.48720 q^{2} -27.5943 q^{3} -25.8138 q^{4} +101.308 q^{5} -68.6327 q^{6} +15.7005 q^{7} -143.795 q^{8} +518.448 q^{9} +O(q^{10})$	\(q+2.48720 q^{2} -27.5943 q^{3} -25.8138 q^{4} +101.308 q^{5} -68.6327 q^{6} +15.7005 q^{7} -143.795 q^{8} +518.448 q^{9} +251.974 q^{10} +394.739 q^{11} +712.316 q^{12} +666.939 q^{13} +39.0503 q^{14} -2795.53 q^{15} +468.396 q^{16} +172.038 q^{17} +1289.48 q^{18} -1280.86 q^{19} -2615.15 q^{20} -433.245 q^{21} +981.796 q^{22} +569.882 q^{23} +3967.92 q^{24} +7138.34 q^{25} +1658.81 q^{26} -7600.80 q^{27} -405.290 q^{28} -6328.41 q^{29} -6953.05 q^{30} +7795.01 q^{31} +5766.42 q^{32} -10892.6 q^{33} +427.892 q^{34} +1590.59 q^{35} -13383.1 q^{36} +16252.3 q^{37} -3185.75 q^{38} -18403.7 q^{39} -14567.6 q^{40} +7454.95 q^{41} -1077.57 q^{42} +1849.00 q^{43} -10189.7 q^{44} +52523.0 q^{45} +1417.41 q^{46} -5628.68 q^{47} -12925.1 q^{48} -16560.5 q^{49} +17754.5 q^{50} -4747.27 q^{51} -17216.2 q^{52} +22460.1 q^{53} -18904.7 q^{54} +39990.3 q^{55} -2257.65 q^{56} +35344.4 q^{57} -15740.0 q^{58} -9061.48 q^{59} +72163.4 q^{60} -18280.8 q^{61} +19387.8 q^{62} +8139.89 q^{63} -646.417 q^{64} +67566.3 q^{65} -27092.0 q^{66} -27428.5 q^{67} -4440.95 q^{68} -15725.5 q^{69} +3956.11 q^{70} -12860.9 q^{71} -74550.0 q^{72} -63446.5 q^{73} +40422.7 q^{74} -196978. q^{75} +33063.8 q^{76} +6197.60 q^{77} -45773.8 q^{78} -1911.26 q^{79} +47452.4 q^{80} +83756.3 q^{81} +18542.0 q^{82} -52124.9 q^{83} +11183.7 q^{84} +17428.8 q^{85} +4598.84 q^{86} +174628. q^{87} -56761.4 q^{88} +66185.2 q^{89} +130635. q^{90} +10471.3 q^{91} -14710.8 q^{92} -215098. q^{93} -13999.7 q^{94} -129761. q^{95} -159121. q^{96} +37497.8 q^{97} -41189.3 q^{98} +204652. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.48720	0.439679	0.219840	−	0.975536i	$-0.429447\pi$
$2$	2.48720	0.439679	0.219840	+	0.975536i	$0.429447\pi$
$3$	−27.5943	−1.77018	−0.885089	−	0.465422i	$-0.845903\pi$
$3$	−27.5943	−1.77018	−0.885089	+	0.465422i	$0.845903\pi$
$4$	−25.8138	−0.806682
$5$	101.308	1.81226	0.906128	−	0.423004i	$-0.139024\pi$
$5$	101.308	1.81226	0.906128	+	0.423004i	$0.139024\pi$
$6$	−68.6327	−0.778311
$7$	15.7005	0.121107	0.0605534	−	0.998165i	$-0.480713\pi$
$7$	15.7005	0.121107	0.0605534	+	0.998165i	$0.480713\pi$
$8$	−143.795	−0.794361
$9$	518.448	2.13353
$10$	251.974	0.796811
$11$	394.739	0.983623	0.491811	−	0.870702i	$-0.336335\pi$
$11$	394.739	0.983623	0.491811	+	0.870702i	$0.336335\pi$
$12$	712.316	1.42797
$13$	666.939	1.09453	0.547265	−	0.836959i	$-0.315669\pi$
$13$	666.939	1.09453	0.547265	+	0.836959i	$0.315669\pi$
$14$	39.0503	0.0532481
$15$	−2795.53	−3.20801
$16$	468.396	0.457418
$17$	172.038	0.144378	0.0721890	−	0.997391i	$-0.477002\pi$
$17$	172.038	0.144378	0.0721890	+	0.997391i	$0.477002\pi$
$18$	1289.48	0.938069
$19$	−1280.86	−0.813985	−0.406992	−	0.913432i	$-0.633422\pi$
$19$	−1280.86	−0.813985	−0.406992	+	0.913432i	$0.633422\pi$
$20$	−2615.15	−1.46191
$21$	−433.245	−0.214380
$22$	981.796	0.432479
$23$	569.882	0.224629	0.112314	−	0.993673i	$-0.464174\pi$
$23$	569.882	0.224629	0.112314	+	0.993673i	$0.464174\pi$
$24$	3967.92	1.40616
$25$	7138.34	2.28427
$26$	1658.81	0.481242
$27$	−7600.80	−2.00655
$28$	−405.290	−0.0976946
$29$	−6328.41	−1.39733	−0.698666	−	0.715448i	$-0.746223\pi$
$29$	−6328.41	−1.39733	−0.698666	+	0.715448i	$0.746223\pi$
$30$	−6953.05	−1.41050
$31$	7795.01	1.45684	0.728421	−	0.685129i	$-0.240254\pi$
$31$	7795.01	1.45684	0.728421	+	0.685129i	$0.240254\pi$
$32$	5766.42	0.995478
$33$	−10892.6	−1.74119
$34$	427.892	0.0634800
$35$	1590.59	0.219476
$36$	−13383.1	−1.72108
$37$	16252.3	1.95169	0.975844	−	0.218469i	$-0.0701061\pi$
$37$	16252.3	1.95169	0.975844	+	0.218469i	$0.0701061\pi$
$38$	−3185.75	−0.357892
$39$	−18403.7	−1.93751
$40$	−14567.6	−1.43958
$41$	7454.95	0.692604	0.346302	−	0.938123i	$-0.387437\pi$
$41$	7454.95	0.692604	0.346302	+	0.938123i	$0.387437\pi$
$42$	−1077.57	−0.0942587
$43$	1849.00	0.152499
$43$	1849.00	0.152499
$44$	−10189.7	−0.793471
$45$	52523.0	3.86650
$46$	1417.41	0.0987646
$47$	−5628.68	−0.371673	−0.185837	−	0.982581i	$-0.559500\pi$
$47$	−5628.68	−0.371673	−0.185837	+	0.982581i	$0.559500\pi$
$48$	−12925.1	−0.809712
$49$	−16560.5	−0.985333
$50$	17754.5	1.00435
$51$	−4747.27	−0.255575
$52$	−17216.2	−0.882938
$53$	22460.1	1.09830	0.549151	−	0.835723i	$-0.314951\pi$
$53$	22460.1	1.09830	0.549151	+	0.835723i	$0.314951\pi$
$54$	−18904.7	−0.882238
$55$	39990.3	1.78258
$56$	−2257.65	−0.0962024
$57$	35344.4	1.44090
$58$	−15740.0	−0.614378
$59$	−9061.48	−0.338898	−0.169449	−	0.985539i	$-0.554199\pi$
$59$	−9061.48	−0.338898	−0.169449	+	0.985539i	$0.554199\pi$
$60$	72163.4	2.58785
$61$	−18280.8	−0.629029	−0.314514	−	0.949253i	$-0.601842\pi$
$61$	−18280.8	−0.629029	−0.314514	+	0.949253i	$0.601842\pi$
$62$	19387.8	0.640544
$63$	8139.89	0.258385
$64$	−646.417	−0.0197271
$65$	67566.3	1.98357
$66$	−27092.0	−0.765564
$67$	−27428.5	−0.746474	−0.373237	−	0.927736i	$-0.621752\pi$
$67$	−27428.5	−0.746474	−0.373237	+	0.927736i	$0.621752\pi$
$68$	−4440.95	−0.116467
$69$	−15725.5	−0.397633
$70$	3956.11	0.0964992
$71$	−12860.9	−0.302780	−0.151390	−	0.988474i	$-0.548375\pi$
$71$	−12860.9	−0.302780	−0.151390	+	0.988474i	$0.548375\pi$
$72$	−74550.0	−1.69479
$73$	−63446.5	−1.39348	−0.696740	−	0.717324i	$-0.745367\pi$
$73$	−63446.5	−1.39348	−0.696740	+	0.717324i	$0.745367\pi$
$74$	40422.7	0.858117
$75$	−196978.	−4.04356
$76$	33063.8	0.656627
$77$	6197.60	0.119123
$78$	−45773.8	−0.851884
$79$	−1911.26	−0.0344549	−0.0172275	−	0.999852i	$-0.505484\pi$
$79$	−1911.26	−0.0344549	−0.0172275	+	0.999852i	$0.505484\pi$
$80$	47452.4	0.828959
$81$	83756.3	1.41842
$82$	18542.0	0.304524
$83$	−52124.9	−0.830520	−0.415260	−	0.909703i	$-0.636309\pi$
$83$	−52124.9	−0.830520	−0.415260	+	0.909703i	$0.636309\pi$
$84$	11183.7	0.172937
$85$	17428.8	0.261650
$86$	4598.84	0.0670505
$87$	174628.	2.47353
$88$	−56761.4	−0.781351
$89$	66185.2	0.885698	0.442849	−	0.896596i	$-0.353968\pi$
$89$	66185.2	0.885698	0.442849	+	0.896596i	$0.353968\pi$
$90$	130635.	1.70002
$91$	10471.3	0.132555
$92$	−14710.8	−0.181204
$93$	−215098.	−2.57887
$94$	−13999.7	−0.163417
$95$	−129761.	−1.47515
$96$	−159121.	−1.76217
$97$	37497.8	0.404648	0.202324	−	0.979319i	$-0.435151\pi$
$97$	37497.8	0.404648	0.202324	+	0.979319i	$0.435151\pi$
$98$	−41189.3	−0.433231
$99$	204652.	2.09859
$100$	−184268.	−1.84268
$101$	−35537.7	−0.346646	−0.173323	−	0.984865i	$-0.555450\pi$
$101$	−35537.7	−0.346646	−0.173323	+	0.984865i	$0.555450\pi$
$102$	−11807.4	−0.112371
$103$	177955.	1.65279	0.826395	−	0.563091i	$-0.190388\pi$
$103$	177955.	1.65279	0.826395	+	0.563091i	$0.190388\pi$
$104$	−95902.2	−0.869451
$105$	−43891.2	−0.388512
$106$	55862.8	0.482901
$107$	43589.8	0.368065	0.184033	−	0.982920i	$-0.441085\pi$
$107$	43589.8	0.368065	0.184033	+	0.982920i	$0.441085\pi$
$108$	196206.	1.61865
$109$	−49084.5	−0.395711	−0.197856	−	0.980231i	$-0.563398\pi$
$109$	−49084.5	−0.395711	−0.197856	+	0.980231i	$0.563398\pi$
$110$	99464.0	0.783762
$111$	−448471.	−3.45484
$112$	7354.05	0.0553964
$113$	−34530.0	−0.254390	−0.127195	−	0.991878i	$-0.540597\pi$
$113$	−34530.0	−0.254390	−0.127195	+	0.991878i	$0.540597\pi$
$114$	87908.6	0.633533
$115$	57733.7	0.407085
$116$	163360.	1.12720
$117$	345773.	2.33521
$118$	−22537.7	−0.149006
$119$	2701.08	0.0174852
$120$	401983.	2.54832
$121$	−5231.89	−0.0324859
$122$	−45468.0	−0.276571
$123$	−205715.	−1.22603
$124$	−201219.	−1.17521
$125$	406584.	2.32742
$126$	20245.5	0.113606
$127$	−10008.6	−0.0550637	−0.0275318	−	0.999621i	$-0.508765\pi$
$127$	−10008.6	−0.0550637	−0.0275318	+	0.999621i	$0.508765\pi$
$128$	−186133.	−1.00415
$129$	−51021.9	−0.269950
$130$	168051.	0.872133
$131$	336036.	1.71083	0.855415	−	0.517943i	$-0.173302\pi$
$131$	336036.	1.71083	0.855415	+	0.517943i	$0.173302\pi$
$132$	281179.	1.40458
$133$	−20110.1	−0.0985791
$134$	−68220.2	−0.328209
$135$	−770023.	−3.63638
$136$	−24738.1	−0.114688
$137$	−1217.37	−0.00554141	−0.00277071	−	0.999996i	$-0.500882\pi$
$137$	−1217.37	−0.00554141	−0.00277071	+	0.999996i	$0.500882\pi$
$138$	−39112.5	−0.174831
$139$	−157629.	−0.691989	−0.345995	−	0.938237i	$-0.612458\pi$
$139$	−157629.	−0.691989	−0.345995	+	0.938237i	$0.612458\pi$
$140$	−41059.2	−0.177048
$141$	155320.	0.657928
$142$	−31987.8	−0.133126
$143$	263267.	1.07660
$144$	242839.	0.975915
$145$	−641119.	−2.53232
$146$	−157804.	−0.612684
$147$	456976.	1.74422
$148$	−419534.	−1.57439
$149$	−501641.	−1.85109	−0.925545	−	0.378639i	$-0.876392\pi$
$149$	−501641.	−1.85109	−0.925545	+	0.378639i	$0.876392\pi$
$150$	−489924.	−1.77787
$151$	−430865.	−1.53780	−0.768899	−	0.639370i	$-0.779195\pi$
$151$	−430865.	−1.53780	−0.768899	+	0.639370i	$0.779195\pi$
$152$	184180.	0.646598
$153$	89192.5	0.308035
$154$	15414.7	0.0523761
$155$	789698.	2.64017
$156$	475071.	1.56296
$157$	157952.	0.511418	0.255709	−	0.966754i	$-0.417691\pi$
$157$	157952.	0.511418	0.255709	+	0.966754i	$0.417691\pi$
$158$	−4753.68	−0.0151491
$159$	−619772.	−1.94419
$160$	584186.	1.80406
$161$	8947.43	0.0272041
$162$	208319.	0.623650
$163$	405846.	1.19645	0.598223	−	0.801330i	$-0.295874\pi$
$163$	405846.	1.19645	0.598223	+	0.801330i	$0.295874\pi$
$164$	−192441.	−0.558712
$165$	−1.10351e6	−3.15548
$166$	−129645.	−0.365162
$167$	166792.	0.462789	0.231394	−	0.972860i	$-0.425671\pi$
$167$	166792.	0.462789	0.231394	+	0.972860i	$0.425671\pi$
$168$	62298.3	0.170295
$169$	73514.3	0.197995
$170$	43349.0	0.115042
$171$	−664057.	−1.73666
$172$	−47729.8	−0.123018
$173$	−287751.	−0.730973	−0.365487	−	0.930817i	$-0.619097\pi$
$173$	−287751.	−0.730973	−0.365487	+	0.930817i	$0.619097\pi$
$174$	434336.	1.08756
$175$	112076.	0.276640
$176$	184894.	0.449927
$177$	250045.	0.599910
$178$	164616.	0.389423
$179$	522579.	1.21904	0.609522	−	0.792769i	$-0.291361\pi$
$179$	522579.	1.21904	0.609522	+	0.792769i	$0.291361\pi$
$180$	−1.35582e6	−3.11904
$181$	81268.9	0.184386	0.0921930	−	0.995741i	$-0.470612\pi$
$181$	81268.9	0.184386	0.0921930	+	0.995741i	$0.470612\pi$
$182$	26044.2	0.0582817
$183$	504447.	1.11349
$184$	−81946.0	−0.178436
$185$	1.64649e6	3.53696
$186$	−534993.	−1.13388
$187$	67910.0	0.142014
$188$	145298.	0.299822
$189$	−119336.	−0.243007
$190$	−322742.	−0.648592
$191$	−608799.	−1.20751	−0.603755	−	0.797170i	$-0.706329\pi$
$191$	−608799.	−1.20751	−0.603755	+	0.797170i	$0.706329\pi$
$192$	17837.5	0.0349205
$193$	184959.	0.357423	0.178712	−	0.983902i	$-0.442807\pi$
$193$	184959.	0.357423	0.178712	+	0.983902i	$0.442807\pi$
$194$	93264.7	0.177915
$195$	−1.86445e6	−3.51127
$196$	427490.	0.794851
$197$	200949.	0.368910	0.184455	−	0.982841i	$-0.440948\pi$
$197$	200949.	0.368910	0.184455	+	0.982841i	$0.440948\pi$
$198$	509010.	0.922706
$199$	−233653.	−0.418253	−0.209127	−	0.977889i	$-0.567062\pi$
$199$	−233653.	−0.418253	−0.209127	+	0.977889i	$0.567062\pi$
$200$	−1.02646e6	−1.81453
$201$	756871.	1.32139
$202$	−88389.5	−0.152413
$203$	−99359.2	−0.169226
$204$	122545.	0.206168
$205$	755248.	1.25518
$206$	442610.	0.726697
$207$	295454.	0.479252
$208$	312392.	0.500658
$209$	−505604.	−0.800654
$210$	−109166.	−0.170821
$211$	200513.	0.310054	0.155027	−	0.987910i	$-0.450454\pi$
$211$	200513.	0.310054	0.155027	+	0.987910i	$0.450454\pi$
$212$	−579781.	−0.885981
$213$	354889.	0.535974
$214$	108417.	0.161831
$215$	187319.	0.276366
$216$	1.09295e6	1.59392
$217$	122386.	0.176433
$218$	−122083.	−0.173986
$219$	1.75076e6	2.46671
$220$	−1.03230e6	−1.43797
$221$	114739.	0.158026
$222$	−1.11544e6	−1.51902
$223$	347051.	0.467338	0.233669	−	0.972316i	$-0.424927\pi$
$223$	347051.	0.467338	0.233669	+	0.972316i	$0.424927\pi$
$224$	90535.7	0.120559
$225$	3.70086e6	4.87356
$226$	−85883.2	−0.111850
$227$	−212111.	−0.273212	−0.136606	−	0.990625i	$-0.543619\pi$
$227$	−212111.	−0.273212	−0.136606	+	0.990625i	$0.543619\pi$
$228$	−912374.	−1.16235
$229$	−470629.	−0.593049	−0.296524	−	0.955025i	$-0.595828\pi$
$229$	−470629.	−0.593049	−0.296524	+	0.955025i	$0.595828\pi$
$230$	143595.	0.178987
$231$	−171019.	−0.210870
$232$	909991.	1.10999
$233$	−952248.	−1.14911	−0.574553	−	0.818467i	$-0.694824\pi$
$233$	−952248.	−1.14911	−0.574553	+	0.818467i	$0.694824\pi$
$234$	860007.	1.02674
$235$	−570231.	−0.673567
$236$	233911.	0.273383
$237$	52739.9	0.0609914
$238$	6718.12	0.00768786
$239$	−1.63690e6	−1.85365	−0.926824	−	0.375497i	$-0.877472\pi$
$239$	−1.63690e6	−1.85365	−0.926824	+	0.375497i	$0.877472\pi$
$240$	−1.30942e6	−1.46740
$241$	−695944.	−0.771848	−0.385924	−	0.922531i	$-0.626117\pi$
$241$	−695944.	−0.771848	−0.385924	+	0.922531i	$0.626117\pi$
$242$	−13012.8	−0.0142834
$243$	−464206.	−0.504307
$244$	471897.	0.507426
$245$	−1.67771e6	−1.78568
$246$	−511654.	−0.539061
$247$	−854253.	−0.890931
$248$	−1.12088e6	−1.15726
$249$	1.43835e6	1.47017
$250$	1.01126e6	1.02332
$251$	657886.	0.659123	0.329561	−	0.944134i	$-0.393099\pi$
$251$	657886.	0.659123	0.329561	+	0.944134i	$0.393099\pi$
$252$	−210122.	−0.208434
$253$	224955.	0.220950
$254$	−24893.5	−0.0242104
$255$	−480937.	−0.463167
$256$	−442266.	−0.421778
$257$	−599821.	−0.566486	−0.283243	−	0.959048i	$-0.591410\pi$
$257$	−599821.	−0.566486	−0.283243	+	0.959048i	$0.591410\pi$
$258$	−126902.	−0.118691
$259$	255169.	0.236363
$260$	−1.74415e6	−1.60011
$261$	−3.28095e6	−2.98125
$262$	835788.	0.752217
$263$	−1.62868e6	−1.45194	−0.725968	−	0.687728i	$-0.758608\pi$
$263$	−1.62868e6	−1.45194	−0.725968	+	0.687728i	$0.758608\pi$
$264$	1.56629e6	1.38313
$265$	2.27539e6	1.99040
$266$	−50017.8	−0.0433432
$267$	−1.82634e6	−1.56784
$268$	708034.	0.602167
$269$	1.99405e6	1.68017	0.840087	−	0.542451i	$-0.182504\pi$
$269$	1.99405e6	1.68017	0.840087	+	0.542451i	$0.182504\pi$
$270$	−1.91520e6	−1.59884
$271$	−1.89207e6	−1.56500	−0.782501	−	0.622650i	$-0.786056\pi$
$271$	−1.89207e6	−1.56500	−0.782501	+	0.622650i	$0.786056\pi$
$272$	80581.8	0.0660411
$273$	−288948.	−0.234646
$274$	−3027.84	−0.00243644
$275$	2.81778e6	2.24686
$276$	405936.	0.320763
$277$	−2.11477e6	−1.65601	−0.828007	−	0.560717i	$-0.810525\pi$
$277$	−2.11477e6	−1.65601	−0.828007	+	0.560717i	$0.810525\pi$
$278$	−392055.	−0.304253
$279$	4.04131e6	3.10822
$280$	−228718.	−0.174343
$281$	−80948.7	−0.0611567	−0.0305784	−	0.999532i	$-0.509735\pi$
$281$	−80948.7	−0.0611567	−0.0305784	+	0.999532i	$0.509735\pi$
$282$	386311.	0.289277
$283$	1.01158e6	0.750814	0.375407	−	0.926860i	$-0.377503\pi$
$283$	1.01158e6	0.750814	0.375407	+	0.926860i	$0.377503\pi$
$284$	331990.	0.244247
$285$	3.58067e6	2.61128
$286$	654798.	0.473361
$287$	117046.	0.0838791
$288$	2.98959e6	2.12388
$289$	−1.39026e6	−0.979155
$290$	−1.59459e6	−1.11341
$291$	−1.03473e6	−0.716298
$292$	1.63780e6	1.12409
$293$	786392.	0.535143	0.267572	−	0.963538i	$-0.413779\pi$
$293$	786392.	0.535143	0.267572	+	0.963538i	$0.413779\pi$
$294$	1.13659e6	0.766895
$295$	−918001.	−0.614170
$296$	−2.33699e6	−1.55034
$297$	−3.00034e6	−1.97369
$298$	−1.24768e6	−0.813886
$299$	380076.	0.245863
$300$	5.08475e6	3.26187
$301$	29030.2	0.0184686
$302$	−1.07165e6	−0.676138
$303$	980641.	0.613625
$304$	−599948.	−0.372332
$305$	−1.85199e6	−1.13996
$306$	221840.	0.135437
$307$	106306.	0.0643744	0.0321872	−	0.999482i	$-0.489753\pi$
$307$	106306.	0.0643744	0.0321872	+	0.999482i	$0.489753\pi$
$308$	−159984.	−0.0960947
$309$	−4.91056e6	−2.92573
$310$	1.96414e6	1.16083
$311$	−82617.8	−0.0484365	−0.0242183	−	0.999707i	$-0.507710\pi$
$311$	−82617.8	−0.0484365	−0.0242183	+	0.999707i	$0.507710\pi$
$312$	2.64636e6	1.53908
$313$	1.38431e6	0.798681	0.399341	−	0.916803i	$-0.369239\pi$
$313$	1.38431e6	0.798681	0.399341	+	0.916803i	$0.369239\pi$
$314$	392859.	0.224860
$315$	824637.	0.468259
$316$	49336.9	0.0277942
$317$	964944.	0.539329	0.269665	−	0.962954i	$-0.413087\pi$
$317$	964944.	0.539329	0.269665	+	0.962954i	$0.413087\pi$
$318$	−1.54150e6	−0.854820
$319$	−2.49807e6	−1.37445
$320$	−65487.3	−0.0357505
$321$	−1.20283e6	−0.651541
$322$	22254.1	0.0119611
$323$	−220356.	−0.117522
$324$	−2.16207e6	−1.14421
$325$	4.76084e6	2.50020
$326$	1.00942e6	0.526052
$327$	1.35446e6	0.700479
$328$	−1.07198e6	−0.550178
$329$	−88373.0	−0.0450122
$330$	−2.74464e6	−1.38740
$331$	−3.21355e6	−1.61218	−0.806092	−	0.591790i	$-0.798422\pi$
$331$	−3.21355e6	−1.61218	−0.806092	+	0.591790i	$0.798422\pi$
$332$	1.34554e6	0.669966
$333$	8.42597e6	4.16398
$334$	414844.	0.203479
$335$	−2.77873e6	−1.35280
$336$	−202930.	−0.0980615
$337$	835398.	0.400699	0.200350	−	0.979724i	$-0.435792\pi$
$337$	835398.	0.400699	0.200350	+	0.979724i	$0.435792\pi$
$338$	182845.	0.0870544
$339$	952834.	0.450316
$340$	−449904.	−0.211068
$341$	3.07700e6	1.43298
$342$	−1.65164e6	−0.763574
$343$	−523886.	−0.240437
$344$	−265876.	−0.121139
$345$	−1.59312e6	−0.720612
$346$	−715695.	−0.321394
$347$	2.19943e6	0.980589	0.490295	−	0.871557i	$-0.336889\pi$
$347$	2.19943e6	0.980589	0.490295	+	0.871557i	$0.336889\pi$
$348$	−4.50782e6	−1.99535
$349$	2.90995e6	1.27886	0.639428	−	0.768851i	$-0.279171\pi$
$349$	2.90995e6	1.27886	0.639428	+	0.768851i	$0.279171\pi$
$350$	278754.	0.121633
$351$	−5.06927e6	−2.19623
$352$	2.27623e6	0.979175
$353$	2.63861e6	1.12704	0.563518	−	0.826104i	$-0.309448\pi$
$353$	2.63861e6	1.12704	0.563518	+	0.826104i	$0.309448\pi$
$354$	621914.	0.263768
$355$	−1.30292e6	−0.548714
$356$	−1.70849e6	−0.714477
$357$	−74534.4	−0.0309518
$358$	1.29976e6	0.535988
$359$	−37197.0	−0.0152325	−0.00761626	−	0.999971i	$-0.502424\pi$
$359$	−37197.0	−0.0152325	−0.00761626	+	0.999971i	$0.502424\pi$
$360$	−7.55253e6	−3.07140
$361$	−835506.	−0.337428
$362$	202132.	0.0810707
$363$	144371.	0.0575059
$364$	−270304.	−0.106930
$365$	−6.42765e6	−2.52534
$366$	1.25466e6	0.489580
$367$	2.27179e6	0.880447	0.440224	−	0.897888i	$-0.354899\pi$
$367$	2.27179e6	0.880447	0.440224	+	0.897888i	$0.354899\pi$
$368$	266930.	0.102749
$369$	3.86500e6	1.47769
$370$	4.09515e6	1.55513
$371$	352635.	0.133012
$372$	5.55251e6	2.08033
$373$	2.42341e6	0.901892	0.450946	−	0.892551i	$-0.351087\pi$
$373$	2.42341e6	0.901892	0.450946	+	0.892551i	$0.351087\pi$
$374$	168906.	0.0624404
$375$	−1.12194e7	−4.11996
$376$	809373.	0.295243
$377$	−4.22066e6	−1.52942
$378$	−296814.	−0.106845
$379$	−2.23180e6	−0.798101	−0.399050	−	0.916929i	$-0.630660\pi$
$379$	−2.23180e6	−0.798101	−0.399050	+	0.916929i	$0.630660\pi$
$380$	3.34963e6	1.18998
$381$	276182.	0.0974725
$382$	−1.51421e6	−0.530917
$383$	−1.13758e6	−0.396263	−0.198131	−	0.980175i	$-0.563487\pi$
$383$	−1.13758e6	−0.396263	−0.198131	+	0.980175i	$0.563487\pi$
$384$	5.13623e6	1.77753
$385$	627868.	0.215882
$386$	460031.	0.157152
$387$	958610.	0.325360
$388$	−967963.	−0.326422
$389$	1.97034e6	0.660188	0.330094	−	0.943948i	$-0.392920\pi$
$389$	1.97034e6	0.660188	0.330094	+	0.943948i	$0.392920\pi$
$390$	−4.63726e6	−1.54383
$391$	98041.1	0.0324315
$392$	2.38131e6	0.782710
$393$	−9.27268e6	−3.02847
$394$	499800.	0.162202
$395$	−193626.	−0.0624412
$396$	−5.28284e6	−1.69289
$397$	−5.13128e6	−1.63399	−0.816996	−	0.576644i	$-0.804362\pi$
$397$	−5.13128e6	−1.63399	−0.816996	+	0.576644i	$0.804362\pi$
$398$	−581143.	−0.183897
$399$	554925.	0.174503
$400$	3.34357e6	1.04487
$401$	−2.92332e6	−0.907852	−0.453926	−	0.891039i	$-0.649977\pi$
$401$	−2.92332e6	−0.907852	−0.453926	+	0.891039i	$0.649977\pi$
$402$	1.88249e6	0.580989
$403$	5.19880e6	1.59456
$404$	917365.	0.279633
$405$	8.48520e6	2.57054
$406$	−247126.	−0.0744053
$407$	6.41542e6	1.91973
$408$	682631.	0.203019
$409$	−2.10623e6	−0.622582	−0.311291	−	0.950315i	$-0.600761\pi$
$409$	−2.10623e6	−0.622582	−0.311291	+	0.950315i	$0.600761\pi$
$410$	1.87845e6	0.551875
$411$	33592.5	0.00980929
$412$	−4.59370e6	−1.33328
$413$	−142270.	−0.0410428
$414$	734854.	0.210717
$415$	−5.28068e6	−1.50511
$416$	3.84585e6	1.08958
$417$	4.34967e6	1.22494
$418$	−1.25754e6	−0.352031
$419$	−787697.	−0.219192	−0.109596	−	0.993976i	$-0.534956\pi$
$419$	−787697.	−0.219192	−0.109596	+	0.993976i	$0.534956\pi$
$420$	1.13300e6	0.313406
$421$	−2.73861e6	−0.753051	−0.376526	−	0.926406i	$-0.622881\pi$
$421$	−2.73861e6	−0.753051	−0.376526	+	0.926406i	$0.622881\pi$
$422$	498717.	0.136324
$423$	−2.91817e6	−0.792977
$424$	−3.22964e6	−0.872448
$425$	1.22806e6	0.329798
$426$	882681.	0.235657
$427$	−287018.	−0.0761796
$428$	−1.12522e6	−0.296912
$429$	−7.26468e6	−1.90578
$430$	465900.	0.121513
$431$	2.23642e6	0.579911	0.289955	−	0.957040i	$-0.406360\pi$
$431$	2.23642e6	0.579911	0.289955	+	0.957040i	$0.406360\pi$
$432$	−3.56019e6	−0.917832
$433$	−7.32309e6	−1.87704	−0.938522	−	0.345219i	$-0.887804\pi$
$433$	−7.32309e6	−1.87704	−0.938522	+	0.345219i	$0.887804\pi$
$434$	304398.	0.0775741
$435$	1.76913e7	4.48266
$436$	1.26706e6	0.319213
$437$	−729937.	−0.182844
$438$	4.35450e6	1.08456
$439$	4.05522e6	1.00428	0.502138	−	0.864788i	$-0.332547\pi$
$439$	4.05522e6	1.00428	0.502138	+	0.864788i	$0.332547\pi$
$440$	−5.75039e6	−1.41601
$441$	−8.58575e6	−2.10224
$442$	285378.	0.0694808
$443$	2.23385e6	0.540810	0.270405	−	0.962747i	$-0.412842\pi$
$443$	2.23385e6	0.540810	0.270405	+	0.962747i	$0.412842\pi$
$444$	1.15768e7	2.78695
$445$	6.70510e6	1.60511
$446$	863185.	0.205479
$447$	1.38425e7	3.27676
$448$	−10149.1	−0.00238908
$449$	−3.90186e6	−0.913389	−0.456695	−	0.889623i	$-0.650967\pi$
$449$	−3.90186e6	−0.913389	−0.456695	+	0.889623i	$0.650967\pi$
$450$	9.20478e6	2.14280
$451$	2.94276e6	0.681262
$452$	891352.	0.205212
$453$	1.18894e7	2.72218
$454$	−527564.	−0.120126
$455$	1.06083e6	0.240223
$456$	−5.08233e6	−1.14459
$457$	−184098.	−0.0412343	−0.0206172	−	0.999787i	$-0.506563\pi$
$457$	−184098.	−0.0412343	−0.0206172	+	0.999787i	$0.506563\pi$
$458$	−1.17055e6	−0.260751
$459$	−1.30762e6	−0.289702
$460$	−1.49033e6	−0.328388
$461$	−4.89953e6	−1.07375	−0.536873	−	0.843663i	$-0.680395\pi$
$461$	−4.89953e6	−1.07375	−0.536873	+	0.843663i	$0.680395\pi$
$462$	−425358.	−0.0927150
$463$	−2.72830e6	−0.591479	−0.295740	−	0.955269i	$-0.595566\pi$
$463$	−2.72830e6	−0.591479	−0.295740	+	0.955269i	$0.595566\pi$
$464$	−2.96420e6	−0.639165
$465$	−2.17912e7	−4.67357
$466$	−2.36843e6	−0.505238
$467$	3.18682e6	0.676185	0.338093	−	0.941113i	$-0.390218\pi$
$467$	3.18682e6	0.676185	0.338093	+	0.941113i	$0.390218\pi$
$468$	−8.92572e6	−1.88377
$469$	−430641.	−0.0904031
$470$	−1.41828e6	−0.296154
$471$	−4.35859e6	−0.905302
$472$	1.30299e6	0.269207
$473$	729873.	0.150001
$474$	131175.	0.0268167
$475$	−9.14319e6	−1.85936
$476$	−69725.1	−0.0141050
$477$	1.16444e7	2.34326
$478$	−4.07130e6	−0.815010
$479$	4.93825e6	0.983410	0.491705	−	0.870762i	$-0.336374\pi$
$479$	4.93825e6	0.983410	0.491705	+	0.870762i	$0.336374\pi$
$480$	−1.61202e7	−3.19351
$481$	1.08393e7	2.13618
$482$	−1.73095e6	−0.339365
$483$	−246898.	−0.0481560
$484$	135055.	0.0262058
$485$	3.79884e6	0.733325
$486$	−1.15457e6	−0.221733
$487$	534531.	0.102129	0.0510646	−	0.998695i	$-0.483739\pi$
$487$	534531.	0.102129	0.0510646	+	0.998695i	$0.483739\pi$
$488$	2.62868e6	0.499676
$489$	−1.11991e7	−2.11792
$490$	−4.17281e6	−0.785124
$491$	4.65073e6	0.870597	0.435299	−	0.900286i	$-0.356643\pi$
$491$	4.65073e6	0.870597	0.435299	+	0.900286i	$0.356643\pi$
$492$	5.31028e6	0.989019
$493$	−1.08872e6	−0.201744
$494$	−2.12470e6	−0.391724
$495$	2.07329e7	3.80318
$496$	3.65115e6	0.666386
$497$	−201923.	−0.0366687
$498$	3.57747e6	0.646403
$499$	−215791.	−0.0387955	−0.0193977	−	0.999812i	$-0.506175\pi$
$499$	−215791.	−0.0387955	−0.0193977	+	0.999812i	$0.506175\pi$
$500$	−1.04955e7	−1.87749
$501$	−4.60250e6	−0.819219
$502$	1.63629e6	0.289803
$503$	−6.45815e6	−1.13812	−0.569060	−	0.822296i	$-0.692693\pi$
$503$	−6.45815e6	−1.13812	−0.569060	+	0.822296i	$0.692693\pi$
$504$	−1.17047e6	−0.205251
$505$	−3.60026e6	−0.628211
$506$	559508.	0.0971471
$507$	−2.02858e6	−0.350487
$508$	258361.	0.0444189
$509$	3.88028e6	0.663847	0.331924	−	0.943306i	$-0.392302\pi$
$509$	3.88028e6	0.663847	0.331924	+	0.943306i	$0.392302\pi$
$510$	−1.19619e6	−0.203645
$511$	−996142.	−0.168760
$512$	4.85626e6	0.818705
$513$	9.73553e6	1.63330
$514$	−1.49188e6	−0.249072
$515$	1.80283e7	2.99528
$516$	1.31707e6	0.217764
$517$	−2.22186e6	−0.365587
$518$	634657.	0.103924
$519$	7.94030e6	1.29395
$520$	−9.71568e6	−1.57567
$521$	2.45313e6	0.395937	0.197969	−	0.980208i	$-0.436566\pi$
$521$	2.45313e6	0.395937	0.197969	+	0.980208i	$0.436566\pi$
$522$	−8.16038e6	−1.31079
$523$	−1.91833e6	−0.306668	−0.153334	−	0.988174i	$-0.549001\pi$
$523$	−1.91833e6	−0.306668	−0.153334	+	0.988174i	$0.549001\pi$
$524$	−8.67436e6	−1.38010
$525$	−3.09265e6	−0.489703
$526$	−4.05087e6	−0.638386
$527$	1.34104e6	0.210336
$528$	−5.10204e6	−0.796451
$529$	−6.11158e6	−0.949542
$530$	5.65936e6	0.875139
$531$	−4.69790e6	−0.723049
$532$	519118.	0.0795220
$533$	4.97200e6	0.758076
$534$	−4.54247e6	−0.689348
$535$	4.41600e6	0.667029
$536$	3.94407e6	0.592970
$537$	−1.44202e7	−2.15792
$538$	4.95959e6	0.738738
$539$	−6.53708e6	−0.969196
$540$	1.98772e7	2.93340
$541$	−6.89363e6	−1.01264	−0.506320	−	0.862346i	$-0.668995\pi$
$541$	−6.89363e6	−1.01264	−0.506320	+	0.862346i	$0.668995\pi$
$542$	−4.70597e6	−0.688099
$543$	−2.24256e6	−0.326396
$544$	992042.	0.143725
$545$	−4.97266e6	−0.717130
$546$	−718672.	−0.103169
$547$	4.78180e6	0.683319	0.341659	−	0.939824i	$-0.389011\pi$
$547$	4.78180e6	0.683319	0.341659	+	0.939824i	$0.389011\pi$
$548$	31424.9	0.00447016
$549$	−9.47764e6	−1.34205
$550$	7.00840e6	0.987898
$551$	8.10578e6	1.13741
$552$	2.26125e6	0.315864
$553$	−30007.7	−0.00417273
$554$	−5.25986e6	−0.728115
$555$	−4.54338e7	−6.26104
$556$	4.06901e6	0.558215
$557$	−1.16813e7	−1.59534	−0.797672	−	0.603091i	$-0.793935\pi$
$557$	−1.16813e7	−1.59534	−0.797672	+	0.603091i	$0.793935\pi$
$558$	1.00515e7	1.36662
$559$	1.23317e6	0.166914
$560$	745026.	0.100392
$561$	−1.87393e6	−0.251389
$562$	−201336.	−0.0268893
$563$	9.15272e6	1.21697	0.608484	−	0.793566i	$-0.291778\pi$
$563$	9.15272e6	1.21697	0.608484	+	0.793566i	$0.291778\pi$
$564$	−4.00939e6	−0.530739
$565$	−3.49817e6	−0.461021
$566$	2.51599e6	0.330117
$567$	1.31502e6	0.171780
$568$	1.84933e6	0.240516
$569$	−4.46016e6	−0.577523	−0.288762	−	0.957401i	$-0.593243\pi$
$569$	−4.46016e6	−0.577523	−0.288762	+	0.957401i	$0.593243\pi$
$570$	8.90586e6	1.14812
$571$	3.82289e6	0.490684	0.245342	−	0.969437i	$-0.421100\pi$
$571$	3.82289e6	0.490684	0.245342	+	0.969437i	$0.421100\pi$
$572$	−6.79593e6	−0.868478
$573$	1.67994e7	2.13751
$574$	291118.	0.0368799
$575$	4.06801e6	0.513112
$576$	−335134.	−0.0420883
$577$	1.15777e7	1.44772	0.723858	−	0.689949i	$-0.242367\pi$
$577$	1.15777e7	1.44772	0.723858	+	0.689949i	$0.242367\pi$
$578$	−3.45786e6	−0.430514
$579$	−5.10383e6	−0.632702
$580$	1.65497e7	2.04278
$581$	−818387.	−0.100582
$582$	−2.57358e6	−0.314941
$583$	8.86588e6	1.08032
$584$	9.12327e6	1.10693
$585$	3.50296e7	4.23200
$586$	1.95592e6	0.235291
$587$	2.16236e6	0.259020	0.129510	−	0.991578i	$-0.458660\pi$
$587$	2.16236e6	0.259020	0.129510	+	0.991578i	$0.458660\pi$
$588$	−1.17963e7	−1.40703
$589$	−9.98429e6	−1.18585
$590$	−2.28325e6	−0.270038
$591$	−5.54505e6	−0.653036
$592$	7.61251e6	0.892738
$593$	1.42792e7	1.66751	0.833753	−	0.552137i	$-0.186188\pi$
$593$	1.42792e7	1.66751	0.833753	+	0.552137i	$0.186188\pi$
$594$	−7.46244e6	−0.867790
$595$	273641.	0.0316876
$596$	1.29493e7	1.49324
$597$	6.44751e6	0.740382
$598$	945326.	0.108101
$599$	1.13983e7	1.29799	0.648997	−	0.760791i	$-0.275189\pi$
$599$	1.13983e7	1.29799	0.648997	+	0.760791i	$0.275189\pi$
$600$	2.83244e7	3.21205
$601$	−665939.	−0.0752053	−0.0376026	−	0.999293i	$-0.511972\pi$
$601$	−665939.	−0.0752053	−0.0376026	+	0.999293i	$0.511972\pi$
$602$	72204.0	0.00812026
$603$	−1.42202e7	−1.59263
$604$	1.11223e7	1.24051
$605$	−530033.	−0.0588728
$606$	2.43905e6	0.269798
$607$	−1.35927e7	−1.49738	−0.748692	−	0.662918i	$-0.769318\pi$
$607$	−1.35927e7	−1.49738	−0.748692	+	0.662918i	$0.769318\pi$
$608$	−7.38596e6	−0.810304
$609$	2.74175e6	0.299561
$610$	−4.60628e6	−0.501217
$611$	−3.75398e6	−0.406808
$612$	−2.30240e6	−0.248486
$613$	−1.08635e7	−1.16767	−0.583833	−	0.811874i	$-0.698448\pi$
$613$	−1.08635e7	−1.16767	−0.583833	+	0.811874i	$0.698448\pi$
$614$	264405.	0.0283041
$615$	−2.08406e7	−2.22189
$616$	−891182.	−0.0946269
$617$	−1.62403e6	−0.171744	−0.0858720	−	0.996306i	$-0.527368\pi$
$617$	−1.62403e6	−0.171744	−0.0858720	+	0.996306i	$0.527368\pi$
$618$	−1.22135e7	−1.28638
$619$	3.82440e6	0.401177	0.200589	−	0.979676i	$-0.435715\pi$
$619$	3.82440e6	0.401177	0.200589	+	0.979676i	$0.435715\pi$
$620$	−2.03851e7	−2.12978
$621$	−4.33156e6	−0.450729
$622$	−205487.	−0.0212965
$623$	1.03914e6	0.107264
$624$	−8.62024e6	−0.886253
$625$	1.88830e7	1.93362
$626$	3.44307e6	0.351164
$627$	1.39518e7	1.41730
$628$	−4.07735e6	−0.412552
$629$	2.79601e6	0.281781
$630$	2.05104e6	0.205884
$631$	−4.03571e6	−0.403503	−0.201751	−	0.979437i	$-0.564663\pi$
$631$	−4.03571e6	−0.403503	−0.201751	+	0.979437i	$0.564663\pi$
$632$	274829.	0.0273697
$633$	−5.53303e6	−0.548850
$634$	2.40001e6	0.237132
$635$	−1.01396e6	−0.0997894
$636$	1.59987e7	1.56834
$637$	−1.10448e7	−1.07848
$638$	−6.21321e6	−0.604316
$639$	−6.66773e6	−0.645990
$640$	−1.88568e7	−1.81978
$641$	1.03975e7	0.999505	0.499753	−	0.866168i	$-0.333424\pi$
$641$	1.03975e7	0.999505	0.499753	+	0.866168i	$0.333424\pi$
$642$	−2.99168e6	−0.286469
$643$	−703463.	−0.0670986	−0.0335493	−	0.999437i	$-0.510681\pi$
$643$	−703463.	−0.0670986	−0.0335493	+	0.999437i	$0.510681\pi$
$644$	−230967.	−0.0219450
$645$	−5.16894e6	−0.489218
$646$	−548069.	−0.0516718
$647$	−1.39550e7	−1.31060	−0.655300	−	0.755369i	$-0.727458\pi$
$647$	−1.39550e7	−1.31060	−0.655300	+	0.755369i	$0.727458\pi$
$648$	−1.20437e7	−1.12674
$649$	−3.57692e6	−0.333348
$650$	1.18412e7	1.09929
$651$	−3.37715e6	−0.312319
$652$	−1.04765e7	−0.965151
$653$	4.10881e6	0.377079	0.188540	−	0.982066i	$-0.439625\pi$
$653$	4.10881e6	0.377079	0.188540	+	0.982066i	$0.439625\pi$
$654$	3.36880e6	0.307986
$655$	3.40431e7	3.10046
$656$	3.49187e6	0.316810
$657$	−3.28937e7	−2.97303
$658$	−219802.	−0.0197909
$659$	4.28147e6	0.384042	0.192021	−	0.981391i	$-0.438496\pi$
$659$	4.28147e6	0.384042	0.192021	+	0.981391i	$0.438496\pi$
$660$	2.84857e7	2.54547
$661$	−6.69686e6	−0.596166	−0.298083	−	0.954540i	$-0.596347\pi$
$661$	−6.69686e6	−0.596166	−0.298083	+	0.954540i	$0.596347\pi$
$662$	−7.99274e6	−0.708844
$663$	−3.16614e6	−0.279734
$664$	7.49528e6	0.659732
$665$	−2.03732e6	−0.178650
$666$	2.09571e7	1.83082
$667$	−3.60645e6	−0.313881
$668$	−4.30553e6	−0.373323
$669$	−9.57663e6	−0.827271
$670$	−6.91126e6	−0.594799
$671$	−7.21615e6	−0.618727
$672$	−2.49827e6	−0.213411
$673$	−1.29636e7	−1.10329	−0.551644	−	0.834080i	$-0.685999\pi$
$673$	−1.29636e7	−1.10329	−0.551644	+	0.834080i	$0.685999\pi$
$674$	2.07780e6	0.176179
$675$	−5.42571e7	−4.58350
$676$	−1.89768e6	−0.159719
$677$	1.00392e7	0.841833	0.420916	−	0.907099i	$-0.361709\pi$
$677$	1.00392e7	0.841833	0.420916	+	0.907099i	$0.361709\pi$
$678$	2.36989e6	0.197995
$679$	588735.	0.0490055
$680$	−2.50617e6	−0.207844
$681$	5.85308e6	0.483633
$682$	7.65312e6	0.630053
$683$	1.37778e7	1.13013	0.565063	−	0.825048i	$-0.308852\pi$
$683$	1.37778e7	1.13013	0.565063	+	0.825048i	$0.308852\pi$
$684$	1.71419e7	1.40093
$685$	−123329.	−0.0100425
$686$	−1.30301e6	−0.105715
$687$	1.29867e7	1.04980
$688$	866065.	0.0697556
$689$	1.49795e7	1.20212
$690$	−3.96242e6	−0.316838
$691$	−2.12787e7	−1.69532	−0.847658	−	0.530544i	$-0.821988\pi$
$691$	−2.12787e7	−1.69532	−0.847658	+	0.530544i	$0.821988\pi$
$692$	7.42795e6	0.589663
$693$	3.21313e6	0.254153
$694$	5.47044e6	0.431145
$695$	−1.59691e7	−1.25406
$696$	−2.51106e7	−1.96487
$697$	1.28253e6	0.0999969
$698$	7.23763e6	0.562287
$699$	2.62767e7	2.03412
$700$	−2.89310e6	−0.223161
$701$	2.07790e7	1.59709	0.798547	−	0.601933i	$-0.205602\pi$
$701$	2.07790e7	1.59709	0.798547	+	0.601933i	$0.205602\pi$
$702$	−1.26083e7	−0.965636
$703$	−2.08169e7	−1.58864
$704$	−255166.	−0.0194040
$705$	1.57351e7	1.19233
$706$	6.56274e6	0.495534
$707$	−557960.	−0.0419812
$708$	−6.45463e6	−0.483936
$709$	4.16247e6	0.310982	0.155491	−	0.987837i	$-0.450304\pi$
$709$	4.16247e6	0.310982	0.155491	+	0.987837i	$0.450304\pi$
$710$	−3.24062e6	−0.241258
$711$	−990888.	−0.0735107
$712$	−9.51708e6	−0.703564
$713$	4.44224e6	0.327249
$714$	−185382.	−0.0136089
$715$	2.66711e7	1.95108
$716$	−1.34898e7	−0.983381
$717$	4.51692e7	3.28129
$718$	−92516.4	−0.00669742
$719$	−1.69124e7	−1.22007	−0.610033	−	0.792376i	$-0.708844\pi$
$719$	−1.69124e7	−1.22007	−0.610033	+	0.792376i	$0.708844\pi$
$720$	2.46016e7	1.76861
$721$	2.79399e6	0.200164
$722$	−2.07807e6	−0.148360
$723$	1.92041e7	1.36631
$724$	−2.09786e6	−0.148741
$725$	−4.51743e7	−3.19188
$726$	359079.	0.0252841
$727$	1.27084e7	0.891776	0.445888	−	0.895089i	$-0.352888\pi$
$727$	1.27084e7	0.891776	0.445888	+	0.895089i	$0.352888\pi$
$728$	−1.50571e6	−0.105296
$729$	−7.54333e6	−0.525708
$730$	−1.59869e7	−1.11034
$731$	318098.	0.0220174
$732$	−1.30217e7	−0.898235
$733$	1.32015e6	0.0907535	0.0453767	−	0.998970i	$-0.485551\pi$
$733$	1.32015e6	0.0907535	0.0453767	+	0.998970i	$0.485551\pi$
$734$	5.65040e6	0.387114
$735$	4.62954e7	3.16096
$736$	3.28618e6	0.223613
$737$	−1.08271e7	−0.734249
$738$	9.61304e6	0.649711
$739$	2.42511e7	1.63351	0.816753	−	0.576988i	$-0.195772\pi$
$739$	2.42511e7	1.63351	0.816753	+	0.576988i	$0.195772\pi$
$740$	−4.25022e7	−2.85320
$741$	2.35725e7	1.57711
$742$	877073.	0.0584825
$743$	−1.31970e7	−0.877009	−0.438504	−	0.898729i	$-0.644492\pi$
$743$	−1.31970e7	−0.877009	−0.438504	+	0.898729i	$0.644492\pi$
$744$	3.09300e7	2.04855
$745$	−5.08203e7	−3.35465
$746$	6.02750e6	0.396543
$747$	−2.70240e7	−1.77194
$748$	−1.75302e6	−0.114560
$749$	684381.	0.0445752
$750$	−2.79050e7	−1.81146
$751$	−1.06321e7	−0.687891	−0.343945	−	0.938990i	$-0.611763\pi$
$751$	−1.06321e7	−0.687891	−0.343945	+	0.938990i	$0.611763\pi$
$752$	−2.63645e6	−0.170010
$753$	−1.81539e7	−1.16676
$754$	−1.04976e7	−0.672455
$755$	−4.36502e7	−2.78688
$756$	3.08053e6	0.196029
$757$	2.44667e7	1.55180	0.775900	−	0.630856i	$-0.217296\pi$
$757$	2.44667e7	1.55180	0.775900	+	0.630856i	$0.217296\pi$
$758$	−5.55094e6	−0.350908
$759$	−6.20748e6	−0.391121
$760$	1.86590e7	1.17180
$761$	2.20641e7	1.38110	0.690550	−	0.723285i	$-0.257369\pi$
$761$	2.20641e7	1.38110	0.690550	+	0.723285i	$0.257369\pi$
$762$	686919.	0.0428566
$763$	−770652.	−0.0479233
$764$	1.57154e7	0.974076
$765$	9.03593e6	0.558238
$766$	−2.82938e6	−0.174228
$767$	−6.04345e6	−0.370934
$768$	1.22040e7	0.746621
$769$	2.58590e7	1.57687	0.788434	−	0.615119i	$-0.210892\pi$
$769$	2.58590e7	1.57687	0.788434	+	0.615119i	$0.210892\pi$
$770$	1.56163e6	0.0949188
$771$	1.65517e7	1.00278
$772$	−4.77450e6	−0.288327
$773$	−1.57927e7	−0.950620	−0.475310	−	0.879818i	$-0.657664\pi$
$773$	−1.57927e7	−0.950620	−0.475310	+	0.879818i	$0.657664\pi$
$774$	2.38426e6	0.143054
$775$	5.56435e7	3.32782
$776$	−5.39199e6	−0.321436
$777$	−7.04122e6	−0.418404
$778$	4.90064e6	0.290271
$779$	−9.54872e6	−0.563770
$780$	4.81286e7	2.83248
$781$	−5.07672e6	−0.297821
$782$	243848.	0.0142594
$783$	4.81010e7	2.80382
$784$	−7.75687e6	−0.450709
$785$	1.60018e7	0.926821
$786$	−2.30630e7	−1.33156
$787$	−2.14880e7	−1.23669	−0.618344	−	0.785908i	$-0.712196\pi$
$787$	−2.14880e7	−1.23669	−0.618344	+	0.785908i	$0.712196\pi$
$788$	−5.18726e6	−0.297593
$789$	4.49425e7	2.57019
$790$	−481587.	−0.0274541
$791$	−542139.	−0.0308084
$792$	−2.94278e7	−1.66704
$793$	−1.21922e7	−0.688491
$794$	−1.27625e7	−0.718432
$795$	−6.27879e7	−3.52337
$796$	6.03148e6	0.337397
$797$	−1.54431e7	−0.861170	−0.430585	−	0.902550i	$-0.641693\pi$
$797$	−1.54431e7	−0.861170	−0.430585	+	0.902550i	$0.641693\pi$
$798$	1.38021e6	0.0767251
$799$	−968344.	−0.0536615
$800$	4.11627e7	2.27394
$801$	3.43136e7	1.88966
$802$	−7.27088e6	−0.399164
$803$	−2.50448e7	−1.37066
$804$	−1.95377e7	−1.06594
$805$	906448.	0.0493007
$806$	1.29305e7	0.701094
$807$	−5.50244e7	−2.97421
$808$	5.11014e6	0.275362
$809$	−5.05884e6	−0.271756	−0.135878	−	0.990726i	$-0.543386\pi$
$809$	−5.05884e6	−0.271756	−0.135878	+	0.990726i	$0.543386\pi$
$810$	2.11044e7	1.13021
$811$	2.95840e7	1.57944	0.789722	−	0.613465i	$-0.210225\pi$
$811$	2.95840e7	1.57944	0.789722	+	0.613465i	$0.210225\pi$
$812$	2.56484e6	0.136512
$813$	5.22105e7	2.77033
$814$	1.59564e7	0.844063
$815$	4.11156e7	2.16826
$816$	−2.22360e6	−0.116905
$817$	−2.36830e6	−0.124132
$818$	−5.23861e6	−0.273737
$819$	5.42881e6	0.282810
$820$	−1.94958e7	−1.01253
$821$	4.56831e6	0.236536	0.118268	−	0.992982i	$-0.462266\pi$
$821$	4.56831e6	0.236536	0.118268	+	0.992982i	$0.462266\pi$
$822$	83551.3	0.00431294
$823$	3.99029e6	0.205355	0.102677	−	0.994715i	$-0.467259\pi$
$823$	3.99029e6	0.205355	0.102677	+	0.994715i	$0.467259\pi$
$824$	−2.55890e7	−1.31291
$825$	−7.77549e7	−3.97734
$826$	−353853.	−0.0180457
$827$	7.46365e6	0.379479	0.189739	−	0.981835i	$-0.439236\pi$
$827$	7.46365e6	0.379479	0.189739	+	0.981835i	$0.439236\pi$
$828$	−7.62680e6	−0.386604
$829$	−1.22180e7	−0.617467	−0.308734	−	0.951149i	$-0.599905\pi$
$829$	−1.22180e7	−0.617467	−0.308734	+	0.951149i	$0.599905\pi$
$830$	−1.31341e7	−0.661768
$831$	5.83557e7	2.93144
$832$	−431121.	−0.0215919
$833$	−2.84903e6	−0.142260
$834$	1.08185e7	0.538582
$835$	1.68973e7	0.838692
$836$	1.30516e7	0.645874
$837$	−5.92484e7	−2.92323
$838$	−1.95916e6	−0.0963740
$839$	−1.83694e7	−0.900929	−0.450464	−	0.892794i	$-0.648742\pi$
$839$	−1.83694e7	−0.900929	−0.450464	+	0.892794i	$0.648742\pi$
$840$	6.31133e6	0.308619
$841$	1.95376e7	0.952536
$842$	−6.81147e6	−0.331101
$843$	2.23373e6	0.108258
$844$	−5.17601e6	−0.250115
$845$	7.44760e6	0.358818
$846$	−7.25809e6	−0.348655
$847$	−82143.3	−0.00393426
$848$	1.05202e7	0.502383
$849$	−2.79138e7	−1.32907
$850$	3.05444e6	0.145006
$851$	9.26189e6	0.438405
$852$	−9.16105e6	−0.432361
$853$	−3.51699e7	−1.65500	−0.827501	−	0.561465i	$-0.810238\pi$
$853$	−3.51699e7	−1.65500	−0.827501	+	0.561465i	$0.810238\pi$
$854$	−713871.	−0.0334946
$855$	−6.72744e7	−3.14727
$856$	−6.26798e6	−0.292377
$857$	−1.23215e7	−0.573076	−0.286538	−	0.958069i	$-0.592504\pi$
$857$	−1.23215e7	−0.573076	−0.286538	+	0.958069i	$0.592504\pi$
$858$	−1.80687e7	−0.837933
$859$	2.32476e6	0.107497	0.0537484	−	0.998555i	$-0.482883\pi$
$859$	2.32476e6	0.107497	0.0537484	+	0.998555i	$0.482883\pi$
$860$	−4.83541e6	−0.222940
$861$	−3.22982e6	−0.148481
$862$	5.56244e6	0.254975
$863$	1.53407e7	0.701163	0.350582	−	0.936532i	$-0.385984\pi$
$863$	1.53407e7	0.701163	0.350582	+	0.936532i	$0.385984\pi$
$864$	−4.38294e7	−1.99748
$865$	−2.91515e7	−1.32471
$866$	−1.82140e7	−0.825297
$867$	3.83633e7	1.73328
$868$	−3.15924e6	−0.142326
$869$	−754449.	−0.0338907
$870$	4.40018e7	1.97093
$871$	−1.82931e7	−0.817038
$872$	7.05809e6	0.314337
$873$	1.94407e7	0.863328
$874$	−1.81550e6	−0.0803929
$875$	6.38358e6	0.281867
$876$	−4.51939e7	−1.98985
$877$	1.21207e7	0.532142	0.266071	−	0.963953i	$-0.414274\pi$
$877$	1.21207e7	0.532142	0.266071	+	0.963953i	$0.414274\pi$
$878$	1.00861e7	0.441559
$879$	−2.17000e7	−0.947299
$880$	1.87313e7	0.815383
$881$	208397.	0.00904589	0.00452294	−	0.999990i	$-0.498560\pi$
$881$	208397.	0.00904589	0.00452294	+	0.999990i	$0.498560\pi$
$882$	−2.13545e7	−0.924310
$883$	−3.57371e7	−1.54247	−0.771237	−	0.636548i	$-0.780362\pi$
$883$	−3.57371e7	−1.54247	−0.771237	+	0.636548i	$0.780362\pi$
$884$	−2.96184e6	−0.127477
$885$	2.53316e7	1.08719
$886$	5.55604e6	0.237783
$887$	4.64203e7	1.98107	0.990533	−	0.137276i	$-0.0438346\pi$
$887$	4.64203e7	1.98107	0.990533	+	0.137276i	$0.0438346\pi$
$888$	6.44878e7	2.74439
$889$	−157140.	−0.00666858
$890$	1.66769e7	0.705734
$891$	3.30619e7	1.39519
$892$	−8.95871e6	−0.376993
$893$	7.20952e6	0.302537
$894$	3.44290e7	1.44072
$895$	5.29415e7	2.20922
$896$	−2.92239e6	−0.121610
$897$	−1.04880e7	−0.435221
$898$	−9.70472e6	−0.401598
$899$	−4.93300e7	−2.03569
$900$	−9.55333e7	−3.93141
$901$	3.86398e6	0.158571
$902$	7.31924e6	0.299537
$903$	−801070.	−0.0326927
$904$	4.96523e6	0.202078
$905$	8.23320e6	0.334155
$906$	2.95715e7	1.19688
$907$	−2.81640e7	−1.13678	−0.568390	−	0.822759i	$-0.692434\pi$
$907$	−2.81640e7	−1.13678	−0.568390	+	0.822759i	$0.692434\pi$
$908$	5.47541e6	0.220395
$909$	−1.84245e7	−0.739580
$910$	2.63849e6	0.105621
$911$	8.25253e6	0.329451	0.164726	−	0.986339i	$-0.447326\pi$
$911$	8.25253e6	0.329451	0.164726	+	0.986339i	$0.447326\pi$
$912$	1.65552e7	0.659093
$913$	−2.05758e7	−0.816919
$914$	−457889.	−0.0181299
$915$	5.11045e7	2.01793
$916$	1.21487e7	0.478402
$917$	5.27593e6	0.207193
$918$	−3.25232e6	−0.127376
$919$	−1.14244e6	−0.0446217	−0.0223108	−	0.999751i	$-0.507102\pi$
$919$	−1.14244e6	−0.0446217	−0.0223108	+	0.999751i	$0.507102\pi$
$920$	−8.30179e6	−0.323372
$921$	−2.93346e6	−0.113954
$922$	−1.21861e7	−0.472104
$923$	−8.57746e6	−0.331401
$924$	4.41465e6	0.170105
$925$	1.16014e8	4.45818
$926$	−6.78583e6	−0.260061
$927$	9.22605e7	3.52628
$928$	−3.64923e7	−1.39101
$929$	−3.37164e7	−1.28175	−0.640873	−	0.767647i	$-0.721428\pi$
$929$	−3.37164e7	−1.28175	−0.640873	+	0.767647i	$0.721428\pi$
$930$	−5.41991e7	−2.05487
$931$	2.12116e7	0.802046
$932$	2.45812e7	0.926963
$933$	2.27979e6	0.0857413
$934$	7.92627e6	0.297305
$935$	6.87984e6	0.257365
$936$	−4.97203e7	−1.85500
$937$	−4.06327e7	−1.51191	−0.755955	−	0.654623i	$-0.772827\pi$
$937$	−4.06327e7	−1.51191	−0.755955	+	0.654623i	$0.772827\pi$
$938$	−1.07109e6	−0.0397484
$939$	−3.81992e7	−1.41381
$940$	1.47198e7	0.543355
$941$	4.51496e7	1.66219	0.831093	−	0.556134i	$-0.187716\pi$
$941$	4.51496e7	1.66219	0.831093	+	0.556134i	$0.187716\pi$
$942$	−1.08407e7	−0.398042
$943$	4.24844e6	0.155579
$944$	−4.24436e6	−0.155018
$945$	−1.20897e7	−0.440390
$946$	1.81534e6	0.0659524
$947$	−1.85178e7	−0.670986	−0.335493	−	0.942043i	$-0.608903\pi$
$947$	−1.85178e7	−0.670986	−0.335493	+	0.942043i	$0.608903\pi$
$948$	−1.36142e6	−0.0492007
$949$	−4.23149e7	−1.52520
$950$	−2.27410e7	−0.817523
$951$	−2.66270e7	−0.954709
$952$	−388400.	−0.0138895
$953$	−3.17478e7	−1.13235	−0.566176	−	0.824284i	$-0.691578\pi$
$953$	−3.17478e7	−1.13235	−0.566176	+	0.824284i	$0.691578\pi$
$954$	2.89619e7	1.03028
$955$	−6.16763e7	−2.18832
$956$	4.22546e7	1.49530
$957$	6.89326e7	2.43302
$958$	1.22824e7	0.432385
$959$	−19113.3	−0.000671103 0
$960$	1.80708e6	0.0632848
$961$	3.21331e7	1.12239
$962$	2.69595e7	0.939234
$963$	2.25990e7	0.785279
$964$	1.79650e7	0.622636
$965$	1.87379e7	0.647742
$966$	−614086.	−0.0211732
$967$	4.45707e7	1.53279	0.766396	−	0.642368i	$-0.222048\pi$
$967$	4.45707e7	1.53279	0.766396	+	0.642368i	$0.222048\pi$
$968$	752318.	0.0258055
$969$	6.08057e6	0.208034
$970$	9.44847e6	0.322428
$971$	2.22017e7	0.755679	0.377840	−	0.925871i	$-0.376667\pi$
$971$	2.22017e7	0.755679	0.377840	+	0.925871i	$0.376667\pi$
$972$	1.19829e7	0.406815
$973$	−2.47485e6	−0.0838045
$974$	1.32949e6	0.0449041
$975$	−1.31372e8	−4.42580
$976$	−8.56265e6	−0.287729
$977$	−3.20865e6	−0.107544	−0.0537719	−	0.998553i	$-0.517124\pi$
$977$	−3.20865e6	−0.107544	−0.0537719	+	0.998553i	$0.517124\pi$
$978$	−2.78543e7	−0.931206
$979$	2.61259e7	0.871193
$980$	4.33082e7	1.44047
$981$	−2.54478e7	−0.844262
$982$	1.15673e7	0.382783
$983$	−4.20453e7	−1.38782	−0.693910	−	0.720061i	$-0.744114\pi$
$983$	−4.20453e7	−1.38782	−0.693910	+	0.720061i	$0.744114\pi$
$984$	2.95806e7	0.973913
$985$	2.03578e7	0.668558
$986$	−2.70788e6	−0.0887027
$987$	2.43860e6	0.0796795
$988$	2.20515e7	0.718698
$989$	1.05371e6	0.0342556
$990$	5.15669e7	1.67218
$991$	1.08440e7	0.350755	0.175377	−	0.984501i	$-0.443885\pi$
$991$	1.08440e7	0.350755	0.175377	+	0.984501i	$0.443885\pi$
$992$	4.49494e7	1.45025
$993$	8.86757e7	2.85385
$994$	−502224.	−0.0161225
$995$	−2.36710e7	−0.757981
$996$	−3.71294e7	−1.18596
$997$	3.29287e7	1.04915	0.524574	−	0.851365i	$-0.324225\pi$
$997$	3.29287e7	1.04915	0.524574	+	0.851365i	$0.324225\pi$
$998$	−536715.	−0.0170576
$999$	−1.23530e8	−3.91616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.b.1.6	✓	10
3.2	odd	2		387.6.a.e.1.5		10
4.3	odd	2		688.6.a.h.1.10		10
5.4	even	2		1075.6.a.b.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.6	✓	10	1.1	even	1	trivial
387.6.a.e.1.5		10	3.2	odd	2
688.6.a.h.1.10		10	4.3	odd	2
1075.6.a.b.1.5		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)

\(f(q)\)	\(=\)	\(q+2.48720 q^{2} -27.5943 q^{3} -25.8138 q^{4} +101.308 q^{5} -68.6327 q^{6} +15.7005 q^{7} -143.795 q^{8} +518.448 q^{9} +O(q^{10})\)	\(q+2.48720 q^{2} -27.5943 q^{3} -25.8138 q^{4} +101.308 q^{5} -68.6327 q^{6} +15.7005 q^{7} -143.795 q^{8} +518.448 q^{9} +251.974 q^{10} +394.739 q^{11} +712.316 q^{12} +666.939 q^{13} +39.0503 q^{14} -2795.53 q^{15} +468.396 q^{16} +172.038 q^{17} +1289.48 q^{18} -1280.86 q^{19} -2615.15 q^{20} -433.245 q^{21} +981.796 q^{22} +569.882 q^{23} +3967.92 q^{24} +7138.34 q^{25} +1658.81 q^{26} -7600.80 q^{27} -405.290 q^{28} -6328.41 q^{29} -6953.05 q^{30} +7795.01 q^{31} +5766.42 q^{32} -10892.6 q^{33} +427.892 q^{34} +1590.59 q^{35} -13383.1 q^{36} +16252.3 q^{37} -3185.75 q^{38} -18403.7 q^{39} -14567.6 q^{40} +7454.95 q^{41} -1077.57 q^{42} +1849.00 q^{43} -10189.7 q^{44} +52523.0 q^{45} +1417.41 q^{46} -5628.68 q^{47} -12925.1 q^{48} -16560.5 q^{49} +17754.5 q^{50} -4747.27 q^{51} -17216.2 q^{52} +22460.1 q^{53} -18904.7 q^{54} +39990.3 q^{55} -2257.65 q^{56} +35344.4 q^{57} -15740.0 q^{58} -9061.48 q^{59} +72163.4 q^{60} -18280.8 q^{61} +19387.8 q^{62} +8139.89 q^{63} -646.417 q^{64} +67566.3 q^{65} -27092.0 q^{66} -27428.5 q^{67} -4440.95 q^{68} -15725.5 q^{69} +3956.11 q^{70} -12860.9 q^{71} -74550.0 q^{72} -63446.5 q^{73} +40422.7 q^{74} -196978. q^{75} +33063.8 q^{76} +6197.60 q^{77} -45773.8 q^{78} -1911.26 q^{79} +47452.4 q^{80} +83756.3 q^{81} +18542.0 q^{82} -52124.9 q^{83} +11183.7 q^{84} +17428.8 q^{85} +4598.84 q^{86} +174628. q^{87} -56761.4 q^{88} +66185.2 q^{89} +130635. q^{90} +10471.3 q^{91} -14710.8 q^{92} -215098. q^{93} -13999.7 q^{94} -129761. q^{95} -159121. q^{96} +37497.8 q^{97} -41189.3 q^{98} +204652. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} + 28 q^{3} + 202 q^{4} + 138 q^{5} + 75 q^{6} + 60 q^{7} + 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 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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