LMFDB - Embedded newform 41.6.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,6,Mod(1,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, 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("41.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	41.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:	$6.57573661233$
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} - 3 x^{9} - 259 x^{8} + 639 x^{7} + 22422 x^{6} - 38356 x^{5} - 735592 x^{4} + 422608 x^{3} + \cdots - 24923264 $ x^10 - 3x^9 - 259x^8 + 639x^7 + 22422x^6 - 38356x^5 - 735592x^4 + 422608x^3 + 8253728x^2 - 28352*x - 24923264
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.00833$ of defining polynomial
Character	$\chi$	$=$	41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00833 q^{2} -26.2398 q^{3} -27.9666 q^{4} +74.6642 q^{5} -52.6982 q^{6} +126.297 q^{7} -120.433 q^{8} +445.529 q^{9} +O(q^{10})$	\(q+2.00833 q^{2} -26.2398 q^{3} -27.9666 q^{4} +74.6642 q^{5} -52.6982 q^{6} +126.297 q^{7} -120.433 q^{8} +445.529 q^{9} +149.950 q^{10} +732.971 q^{11} +733.839 q^{12} -948.864 q^{13} +253.647 q^{14} -1959.18 q^{15} +653.063 q^{16} +447.346 q^{17} +894.769 q^{18} +506.762 q^{19} -2088.11 q^{20} -3314.02 q^{21} +1472.05 q^{22} +3649.99 q^{23} +3160.13 q^{24} +2449.75 q^{25} -1905.63 q^{26} -5314.32 q^{27} -3532.11 q^{28} +6037.46 q^{29} -3934.67 q^{30} -528.129 q^{31} +5165.41 q^{32} -19233.0 q^{33} +898.419 q^{34} +9429.91 q^{35} -12459.9 q^{36} -10277.5 q^{37} +1017.75 q^{38} +24898.0 q^{39} -8992.02 q^{40} +1681.00 q^{41} -6655.65 q^{42} -3661.14 q^{43} -20498.7 q^{44} +33265.1 q^{45} +7330.38 q^{46} +16793.7 q^{47} -17136.3 q^{48} -855.947 q^{49} +4919.90 q^{50} -11738.3 q^{51} +26536.5 q^{52} -6959.90 q^{53} -10672.9 q^{54} +54726.7 q^{55} -15210.3 q^{56} -13297.4 q^{57} +12125.2 q^{58} +5214.02 q^{59} +54791.6 q^{60} +18393.2 q^{61} -1060.66 q^{62} +56269.2 q^{63} -10524.2 q^{64} -70846.2 q^{65} -38626.3 q^{66} +21799.0 q^{67} -12510.8 q^{68} -95775.1 q^{69} +18938.4 q^{70} -45250.6 q^{71} -53656.2 q^{72} -31348.1 q^{73} -20640.5 q^{74} -64281.0 q^{75} -14172.4 q^{76} +92572.3 q^{77} +50003.5 q^{78} +71611.3 q^{79} +48760.5 q^{80} +31183.4 q^{81} +3376.00 q^{82} -8237.92 q^{83} +92682.0 q^{84} +33400.8 q^{85} -7352.77 q^{86} -158422. q^{87} -88273.6 q^{88} +444.314 q^{89} +66807.2 q^{90} -119839. q^{91} -102078. q^{92} +13858.0 q^{93} +33727.3 q^{94} +37837.0 q^{95} -135540. q^{96} +45300.6 q^{97} -1719.02 q^{98} +326560. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 28 q^{3} + 207 q^{4} + 32 q^{5} + 54 q^{6} + 342 q^{7} + 249 q^{8} + 1194 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 + 28 * q^3 + 207 * q^4 + 32 * q^5 + 54 * q^6 + 342 * q^7 + 249 * q^8 + 1194 * q^9	\( 10 q + 3 q^{2} + 28 q^{3} + 207 q^{4} + 32 q^{5} + 54 q^{6} + 342 q^{7} + 249 q^{8} + 1194 q^{9} + 102 q^{10} + 846 q^{11} + 4204 q^{12} + 1504 q^{13} + 3468 q^{14} + 1966 q^{15} + 5859 q^{16} + 560 q^{17} - 3713 q^{18} + 4240 q^{19} - 6182 q^{20} - 3096 q^{21} - 2628 q^{22} - 1508 q^{23} - 10166 q^{24} + 11734 q^{25} - 22014 q^{26} + 1882 q^{27} - 8662 q^{28} - 124 q^{29} - 45234 q^{30} + 10384 q^{31} - 6619 q^{32} - 22772 q^{33} + 802 q^{34} - 17890 q^{35} - 9657 q^{36} + 5524 q^{37} - 46098 q^{38} + 16844 q^{39} - 61738 q^{40} + 16810 q^{41} + 15476 q^{42} + 24160 q^{43} - 21594 q^{44} + 94688 q^{45} + 42404 q^{46} + 58984 q^{47} + 49296 q^{48} + 70326 q^{49} + 6817 q^{50} + 7336 q^{51} + 64374 q^{52} + 23456 q^{53} - 120694 q^{54} + 96426 q^{55} + 80184 q^{56} + 78004 q^{57} - 13378 q^{58} + 52428 q^{59} + 29422 q^{60} + 113540 q^{61} - 113008 q^{62} - 11036 q^{63} + 37363 q^{64} - 22340 q^{65} - 46224 q^{66} + 85506 q^{67} - 71406 q^{68} - 80004 q^{69} - 71946 q^{70} + 75236 q^{71} - 248911 q^{72} - 85148 q^{73} - 23462 q^{74} + 79652 q^{75} + 113376 q^{76} - 172896 q^{77} - 292760 q^{78} + 178200 q^{79} - 401850 q^{80} - 54126 q^{81} + 5043 q^{82} - 125412 q^{83} - 123276 q^{84} - 245912 q^{85} - 18848 q^{86} - 292760 q^{87} - 135952 q^{88} - 62696 q^{89} - 531830 q^{90} + 30056 q^{91} - 236372 q^{92} - 41700 q^{93} + 419014 q^{94} + 28002 q^{95} + 172086 q^{96} + 154548 q^{97} + 288367 q^{98} + 21952 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 + 28 * q^3 + 207 * q^4 + 32 * q^5 + 54 * q^6 + 342 * q^7 + 249 * q^8 + 1194 * q^9 + 102 * q^10 + 846 * q^11 + 4204 * q^12 + 1504 * q^13 + 3468 * q^14 + 1966 * q^15 + 5859 * q^16 + 560 * q^17 - 3713 * q^18 + 4240 * q^19 - 6182 * q^20 - 3096 * q^21 - 2628 * q^22 - 1508 * q^23 - 10166 * q^24 + 11734 * q^25 - 22014 * q^26 + 1882 * q^27 - 8662 * q^28 - 124 * q^29 - 45234 * q^30 + 10384 * q^31 - 6619 * q^32 - 22772 * q^33 + 802 * q^34 - 17890 * q^35 - 9657 * q^36 + 5524 * q^37 - 46098 * q^38 + 16844 * q^39 - 61738 * q^40 + 16810 * q^41 + 15476 * q^42 + 24160 * q^43 - 21594 * q^44 + 94688 * q^45 + 42404 * q^46 + 58984 * q^47 + 49296 * q^48 + 70326 * q^49 + 6817 * q^50 + 7336 * q^51 + 64374 * q^52 + 23456 * q^53 - 120694 * q^54 + 96426 * q^55 + 80184 * q^56 + 78004 * q^57 - 13378 * q^58 + 52428 * q^59 + 29422 * q^60 + 113540 * q^61 - 113008 * q^62 - 11036 * q^63 + 37363 * q^64 - 22340 * q^65 - 46224 * q^66 + 85506 * q^67 - 71406 * q^68 - 80004 * q^69 - 71946 * q^70 + 75236 * q^71 - 248911 * q^72 - 85148 * q^73 - 23462 * q^74 + 79652 * q^75 + 113376 * q^76 - 172896 * q^77 - 292760 * q^78 + 178200 * q^79 - 401850 * q^80 - 54126 * q^81 + 5043 * q^82 - 125412 * q^83 - 123276 * q^84 - 245912 * q^85 - 18848 * q^86 - 292760 * q^87 - 135952 * q^88 - 62696 * q^89 - 531830 * q^90 + 30056 * q^91 - 236372 * q^92 - 41700 * q^93 + 419014 * q^94 + 28002 * q^95 + 172086 * q^96 + 154548 * q^97 + 288367 * q^98 + 21952 * 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 $

$2$	2.00833	0.355026	0.177513	−	0.984118i	$-0.443195\pi$
$2$	2.00833	0.355026	0.177513	+	0.984118i	$0.443195\pi$
$3$	−26.2398	−1.68329	−0.841643	−	0.540034i	$-0.818411\pi$
$3$	−26.2398	−1.68329	−0.841643	+	0.540034i	$0.818411\pi$
$4$	−27.9666	−0.873957
$5$	74.6642	1.33563	0.667817	−	0.744325i	$-0.267229\pi$
$5$	74.6642	1.33563	0.667817	+	0.744325i	$0.267229\pi$
$6$	−52.6982	−0.597610
$7$	126.297	0.974203	0.487102	−	0.873345i	$-0.338054\pi$
$7$	126.297	0.974203	0.487102	+	0.873345i	$0.338054\pi$
$8$	−120.433	−0.665303
$9$	445.529	1.83345
$10$	149.950	0.474185
$11$	732.971	1.82644	0.913219	−	0.407469i	$-0.133589\pi$
$11$	732.971	1.82644	0.913219	+	0.407469i	$0.133589\pi$
$12$	733.839	1.47112
$13$	−948.864	−1.55720	−0.778602	−	0.627518i	$-0.784071\pi$
$13$	−948.864	−1.55720	−0.778602	+	0.627518i	$0.784071\pi$
$14$	253.647	0.345867
$15$	−1959.18	−2.24826
$16$	653.063	0.637757
$17$	447.346	0.375424	0.187712	−	0.982224i	$-0.439893\pi$
$17$	447.346	0.375424	0.187712	+	0.982224i	$0.439893\pi$
$18$	894.769	0.650923
$19$	506.762	0.322048	0.161024	−	0.986951i	$-0.448520\pi$
$19$	506.762	0.322048	0.161024	+	0.986951i	$0.448520\pi$
$20$	−2088.11	−1.16729
$21$	−3314.02	−1.63986
$22$	1472.05	0.648433
$23$	3649.99	1.43871	0.719353	−	0.694645i	$-0.244439\pi$
$23$	3649.99	1.43871	0.719353	+	0.694645i	$0.244439\pi$
$24$	3160.13	1.11990
$25$	2449.75	0.783920
$26$	−1905.63	−0.552848
$27$	−5314.32	−1.40294
$28$	−3532.11	−0.851411
$29$	6037.46	1.33309	0.666545	−	0.745465i	$-0.267773\pi$
$29$	6037.46	1.33309	0.666545	+	0.745465i	$0.267773\pi$
$30$	−3934.67	−0.798189
$31$	−528.129	−0.0987042	−0.0493521	−	0.998781i	$-0.515716\pi$
$31$	−528.129	−0.0987042	−0.0493521	+	0.998781i	$0.515716\pi$
$32$	5165.41	0.891723
$33$	−19233.0	−3.07442
$34$	898.419	0.133285
$35$	9429.91	1.30118
$36$	−12459.9	−1.60236
$37$	−10277.5	−1.23419	−0.617095	−	0.786889i	$-0.711691\pi$
$37$	−10277.5	−1.23419	−0.617095	+	0.786889i	$0.711691\pi$
$38$	1017.75	0.114335
$39$	24898.0	2.62122
$40$	−8992.02	−0.888602
$41$	1681.00	0.156174
$41$	1681.00	0.156174
$42$	−6655.65	−0.582194
$43$	−3661.14	−0.301957	−0.150978	−	0.988537i	$-0.548242\pi$
$43$	−3661.14	−0.301957	−0.150978	+	0.988537i	$0.548242\pi$
$44$	−20498.7	−1.59623
$45$	33265.1	2.44882
$46$	7330.38	0.510777
$47$	16793.7	1.10892	0.554462	−	0.832209i	$-0.312924\pi$
$47$	16793.7	1.10892	0.554462	+	0.832209i	$0.312924\pi$
$48$	−17136.3	−1.07353
$49$	−855.947	−0.0509280
$50$	4919.90	0.278312
$51$	−11738.3	−0.631945
$52$	26536.5	1.36093
$53$	−6959.90	−0.340340	−0.170170	−	0.985415i	$-0.554432\pi$
$53$	−6959.90	−0.340340	−0.170170	+	0.985415i	$0.554432\pi$
$54$	−10672.9	−0.498079
$55$	54726.7	2.43945
$56$	−15210.3	−0.648140
$57$	−13297.4	−0.542099
$58$	12125.2	0.473281
$59$	5214.02	0.195004	0.0975018	−	0.995235i	$-0.468915\pi$
$59$	5214.02	0.195004	0.0975018	+	0.995235i	$0.468915\pi$
$60$	54791.6	1.96488
$61$	18393.2	0.632898	0.316449	−	0.948610i	$-0.397509\pi$
$61$	18393.2	0.632898	0.316449	+	0.948610i	$0.397509\pi$
$62$	−1060.66	−0.0350425
$63$	56269.2	1.78615
$64$	−10524.2	−0.321172
$65$	−70846.2	−2.07986
$66$	−38626.3	−1.09150
$67$	21799.0	0.593266	0.296633	−	0.954992i	$-0.404136\pi$
$67$	21799.0	0.593266	0.296633	+	0.954992i	$0.404136\pi$
$68$	−12510.8	−0.328104
$69$	−95775.1	−2.42175
$70$	18938.4	0.461952
$71$	−45250.6	−1.06532	−0.532658	−	0.846330i	$-0.678807\pi$
$71$	−45250.6	−1.06532	−0.532658	+	0.846330i	$0.678807\pi$
$72$	−53656.2	−1.21980
$73$	−31348.1	−0.688501	−0.344250	−	0.938878i	$-0.611867\pi$
$73$	−31348.1	−0.688501	−0.344250	+	0.938878i	$0.611867\pi$
$74$	−20640.5	−0.438169
$75$	−64281.0	−1.31956
$76$	−14172.4	−0.281456
$77$	92572.3	1.77932
$78$	50003.5	0.930601
$79$	71611.3	1.29096	0.645482	−	0.763776i	$-0.276657\pi$
$79$	71611.3	1.29096	0.645482	+	0.763776i	$0.276657\pi$
$80$	48760.5	0.851810
$81$	31183.4	0.528094
$82$	3376.00	0.0554457
$83$	−8237.92	−0.131257	−0.0656285	−	0.997844i	$-0.520905\pi$
$83$	−8237.92	−0.131257	−0.0656285	+	0.997844i	$0.520905\pi$
$84$	92682.0	1.43317
$85$	33400.8	0.501429
$86$	−7352.77	−0.107202
$87$	−158422.	−2.24397
$88$	−88273.6	−1.21513
$89$	444.314	0.00594586	0.00297293	−	0.999996i	$-0.499054\pi$
$89$	444.314	0.00594586	0.00297293	+	0.999996i	$0.499054\pi$
$90$	66807.2	0.869395
$91$	−119839.	−1.51703
$92$	−102078.	−1.25737
$93$	13858.0	0.166147
$94$	33727.3	0.393696
$95$	37837.0	0.430138
$96$	−135540.	−1.50103
$97$	45300.6	0.488849	0.244424	−	0.969668i	$-0.421401\pi$
$97$	45300.6	0.488849	0.244424	+	0.969668i	$0.421401\pi$
$98$	−1719.02	−0.0180808
$99$	326560.	3.34869
$100$	−68511.2	−0.685112
$101$	−145004.	−1.41441	−0.707207	−	0.707007i	$-0.750045\pi$
$101$	−145004.	−1.41441	−0.707207	+	0.707007i	$0.750045\pi$
$102$	−23574.4	−0.224357
$103$	−42152.0	−0.391494	−0.195747	−	0.980654i	$-0.562713\pi$
$103$	−42152.0	−0.391494	−0.195747	+	0.980654i	$0.562713\pi$
$104$	114274.	1.03601
$105$	−247439.	−2.19026
$106$	−13977.8	−0.120830
$107$	2295.91	0.0193863	0.00969316	−	0.999953i	$-0.496915\pi$
$107$	2295.91	0.0193863	0.00969316	+	0.999953i	$0.496915\pi$
$108$	148624.	1.22611
$109$	18226.1	0.146936	0.0734678	−	0.997298i	$-0.476593\pi$
$109$	18226.1	0.146936	0.0734678	+	0.997298i	$0.476593\pi$
$110$	109909.	0.866069
$111$	269679.	2.07749
$112$	82480.2	0.621305
$113$	42216.8	0.311021	0.155510	−	0.987834i	$-0.450298\pi$
$113$	42216.8	0.311021	0.155510	+	0.987834i	$0.450298\pi$
$114$	−26705.5	−0.192459
$115$	272524.	1.92158
$116$	−168847.	−1.16506
$117$	−422746.	−2.85506
$118$	10471.5	0.0692313
$119$	56498.7	0.365739
$120$	235949.	1.49577
$121$	376195.	2.33587
$122$	36939.7	0.224695
$123$	−44109.2	−0.262885
$124$	14770.0	0.0862632
$125$	−50417.1	−0.288604
$126$	113007.	0.634131
$127$	−247425.	−1.36124	−0.680618	−	0.732638i	$-0.738289\pi$
$127$	−247425.	−1.36124	−0.680618	+	0.732638i	$0.738289\pi$
$128$	−186429.	−1.00575
$129$	96067.6	0.508280
$130$	−142283.	−0.738403
$131$	−109910.	−0.559574	−0.279787	−	0.960062i	$-0.590264\pi$
$131$	−109910.	−0.559574	−0.279787	+	0.960062i	$0.590264\pi$
$132$	537883.	2.68691
$133$	64002.8	0.313740
$134$	43779.5	0.210625
$135$	−396790.	−1.87381
$136$	−53875.1	−0.249770
$137$	105426.	0.479895	0.239948	−	0.970786i	$-0.422870\pi$
$137$	105426.	0.479895	0.239948	+	0.970786i	$0.422870\pi$
$138$	−192348.	−0.859785
$139$	−244289.	−1.07243	−0.536213	−	0.844082i	$-0.680146\pi$
$139$	−244289.	−1.07243	−0.536213	+	0.844082i	$0.680146\pi$
$140$	−263723.	−1.13717
$141$	−440664.	−1.86663
$142$	−90878.1	−0.378215
$143$	−695490.	−2.84414
$144$	290958.	1.16930
$145$	450782.	1.78052
$146$	−62957.4	−0.244436
$147$	22459.9	0.0857264
$148$	287426.	1.07863
$149$	226376.	0.835344	0.417672	−	0.908598i	$-0.362846\pi$
$149$	226376.	0.835344	0.417672	+	0.908598i	$0.362846\pi$
$150$	−129097.	−0.468478
$151$	388030.	1.38492	0.692458	−	0.721458i	$-0.256528\pi$
$151$	388030.	1.38492	0.692458	+	0.721458i	$0.256528\pi$
$152$	−61030.8	−0.214259
$153$	199306.	0.688321
$154$	185916.	0.631705
$155$	−39432.3	−0.131833
$156$	−696314.	−2.29083
$157$	−305827.	−0.990209	−0.495104	−	0.868833i	$-0.664870\pi$
$157$	−305827.	−0.990209	−0.495104	+	0.868833i	$0.664870\pi$
$158$	143819.	0.458325
$159$	182627.	0.572890
$160$	385672.	1.19102
$161$	460984.	1.40159
$162$	62626.6	0.187487
$163$	−436627.	−1.28719	−0.643593	−	0.765368i	$-0.722557\pi$
$163$	−436627.	−1.28719	−0.643593	+	0.765368i	$0.722557\pi$
$164$	−47011.9	−0.136489
$165$	−1.43602e6	−4.10630
$166$	−16544.5	−0.0465996
$167$	−29287.0	−0.0812613	−0.0406307	−	0.999174i	$-0.512937\pi$
$167$	−29287.0	−0.0812613	−0.0406307	+	0.999174i	$0.512937\pi$
$168$	399117.	1.09101
$169$	529051.	1.42489
$170$	67079.7	0.178020
$171$	225777.	0.590459
$172$	102390.	0.263897
$173$	171998.	0.436925	0.218463	−	0.975845i	$-0.429896\pi$
$173$	171998.	0.436925	0.218463	+	0.975845i	$0.429896\pi$
$174$	−318163.	−0.796667
$175$	309397.	0.763697
$176$	478676.	1.16482
$177$	−136815.	−0.328247
$178$	892.329	0.00211094
$179$	581307.	1.35604	0.678021	−	0.735043i	$-0.262838\pi$
$179$	581307.	1.35604	0.678021	+	0.735043i	$0.262838\pi$
$180$	−930311.	−2.14016
$181$	645486.	1.46450	0.732252	−	0.681034i	$-0.238469\pi$
$181$	645486.	1.46450	0.732252	+	0.681034i	$0.238469\pi$
$182$	−240677.	−0.538586
$183$	−482636.	−1.06535
$184$	−439578.	−0.957175
$185$	−767360.	−1.64843
$186$	27831.4	0.0589866
$187$	327892.	0.685688
$188$	−469663.	−0.969151
$189$	−671186.	−1.36675
$190$	75989.2	0.152710
$191$	525364.	1.04202	0.521011	−	0.853550i	$-0.325555\pi$
$191$	525364.	1.04202	0.521011	+	0.853550i	$0.325555\pi$
$192$	276152.	0.540625
$193$	−165595.	−0.320004	−0.160002	−	0.987117i	$-0.551150\pi$
$193$	−165595.	−0.320004	−0.160002	+	0.987117i	$0.551150\pi$
$194$	90978.5	0.173554
$195$	1.85899e6	3.50099
$196$	23937.9	0.0445089
$197$	−129599.	−0.237923	−0.118961	−	0.992899i	$-0.537956\pi$
$197$	−129599.	−0.237923	−0.118961	+	0.992899i	$0.537956\pi$
$198$	655839.	1.18887
$199$	−208362.	−0.372981	−0.186490	−	0.982457i	$-0.559711\pi$
$199$	−208362.	−0.372981	−0.186490	+	0.982457i	$0.559711\pi$
$200$	−295030.	−0.521544
$201$	−572002.	−0.998636
$202$	−291216.	−0.502153
$203$	762516.	1.29870
$204$	328280.	0.552293
$205$	125511.	0.208591
$206$	−84655.1	−0.138990
$207$	1.62617e6	2.63780
$208$	−619668.	−0.993118
$209$	371442.	0.588200
$210$	−496939.	−0.777598
$211$	−982645.	−1.51946	−0.759732	−	0.650237i	$-0.774670\pi$
$211$	−982645.	−1.51946	−0.759732	+	0.650237i	$0.774670\pi$
$212$	194645.	0.297443
$213$	1.18737e6	1.79323
$214$	4610.94	0.00688264
$215$	−273356.	−0.403304
$216$	640018.	0.933379
$217$	−66701.3	−0.0961579
$218$	36604.0	0.0521659
$219$	822570.	1.15894
$220$	−1.53052e6	−2.13198
$221$	−424471.	−0.584611
$222$	541604.	0.737564
$223$	178185.	0.239943	0.119971	−	0.992777i	$-0.461720\pi$
$223$	178185.	0.239943	0.119971	+	0.992777i	$0.461720\pi$
$224$	652379.	0.868720
$225$	1.09143e6	1.43728
$226$	84785.3	0.110420
$227$	−97981.4	−0.126206	−0.0631029	−	0.998007i	$-0.520100\pi$
$227$	−97981.4	−0.126206	−0.0631029	+	0.998007i	$0.520100\pi$
$228$	371882.	0.473771
$229$	−1.12371e6	−1.41601	−0.708004	−	0.706208i	$-0.750404\pi$
$229$	−1.12371e6	−1.41601	−0.708004	+	0.706208i	$0.750404\pi$
$230$	547317.	0.682212
$231$	−2.42908e6	−2.99511
$232$	−727107.	−0.886908
$233$	−948911.	−1.14508	−0.572540	−	0.819877i	$-0.694042\pi$
$233$	−948911.	−1.14508	−0.572540	+	0.819877i	$0.694042\pi$
$234$	−849014.	−1.01362
$235$	1.25389e6	1.48112
$236$	−145818.	−0.170425
$237$	−1.87907e6	−2.17306
$238$	113468.	0.129847
$239$	143412.	0.162402	0.0812010	−	0.996698i	$-0.474124\pi$
$239$	143412.	0.162402	0.0812010	+	0.996698i	$0.474124\pi$
$240$	−1.27947e6	−1.43384
$241$	−758845.	−0.841609	−0.420805	−	0.907151i	$-0.638252\pi$
$241$	−758845.	−0.841609	−0.420805	+	0.907151i	$0.638252\pi$
$242$	755523.	0.829296
$243$	473132.	0.514004
$244$	−514397.	−0.553125
$245$	−63908.7	−0.0680212
$246$	−88585.7	−0.0933310
$247$	−480849.	−0.501495
$248$	63604.0	0.0656682
$249$	216162.	0.220943
$250$	−101254.	−0.102462
$251$	−384559.	−0.385282	−0.192641	−	0.981269i	$-0.561705\pi$
$251$	−384559.	−0.385282	−0.192641	+	0.981269i	$0.561705\pi$
$252$	−1.57366e6	−1.56102
$253$	2.67533e6	2.62771
$254$	−496910.	−0.483274
$255$	−876431.	−0.844048
$256$	−37637.8	−0.0358942
$257$	−1.13441e6	−1.07136	−0.535682	−	0.844420i	$-0.679945\pi$
$257$	−1.13441e6	−1.07136	−0.535682	+	0.844420i	$0.679945\pi$
$258$	192935.	0.180452
$259$	−1.29802e6	−1.20235
$260$	1.98133e6	1.81770
$261$	2.68986e6	2.44415
$262$	−220735.	−0.198663
$263$	−951705.	−0.848424	−0.424212	−	0.905563i	$-0.639449\pi$
$263$	−951705.	−0.848424	−0.424212	+	0.905563i	$0.639449\pi$
$264$	2.31629e6	2.04542
$265$	−519656.	−0.454570
$266$	128539.	0.111386
$267$	−11658.7	−0.0100086
$268$	−609644.	−0.518488
$269$	−2.13808e6	−1.80154	−0.900768	−	0.434300i	$-0.856996\pi$
$269$	−2.13808e6	−1.80154	−0.900768	+	0.434300i	$0.856996\pi$
$270$	−796885.	−0.665252
$271$	1.43926e6	1.19046	0.595230	−	0.803555i	$-0.297061\pi$
$271$	1.43926e6	1.19046	0.595230	+	0.803555i	$0.297061\pi$
$272$	292145.	0.239429
$273$	3.14456e6	2.55360
$274$	211730.	0.170375
$275$	1.79559e6	1.43178
$276$	2.67850e6	2.11651
$277$	−1.14694e6	−0.898131	−0.449066	−	0.893499i	$-0.648243\pi$
$277$	−1.14694e6	−0.898131	−0.449066	+	0.893499i	$0.648243\pi$
$278$	−490614.	−0.380739
$279$	−235297.	−0.180969
$280$	−1.13567e6	−0.865679
$281$	1.94822e6	1.47188	0.735940	−	0.677046i	$-0.236740\pi$
$281$	1.94822e6	1.47188	0.735940	+	0.677046i	$0.236740\pi$
$282$	−884998.	−0.662704
$283$	−1.41049e6	−1.04690	−0.523450	−	0.852056i	$-0.675355\pi$
$283$	−1.41049e6	−1.04690	−0.523450	+	0.852056i	$0.675355\pi$
$284$	1.26551e6	0.931040
$285$	−992838.	−0.724046
$286$	−1.39677e6	−1.00974
$287$	212306.	0.152145
$288$	2.30134e6	1.63493
$289$	−1.21974e6	−0.859057
$290$	905319.	0.632131
$291$	−1.18868e6	−0.822872
$292$	876701.	0.601720
$293$	−976872.	−0.664766	−0.332383	−	0.943144i	$-0.607853\pi$
$293$	−976872.	−0.664766	−0.332383	+	0.943144i	$0.607853\pi$
$294$	45106.9	0.0304351
$295$	389301.	0.260453
$296$	1.23774e6	0.821110
$297$	−3.89524e6	−2.56238
$298$	454638.	0.296569
$299$	−3.46334e6	−2.24036
$300$	1.79772e6	1.15324
$301$	−462392.	−0.294167
$302$	779293.	0.491681
$303$	3.80488e6	2.38086
$304$	330948.	0.205388
$305$	1.37332e6	0.845321
$306$	400271.	0.244372
$307$	−1.96092e6	−1.18745	−0.593723	−	0.804670i	$-0.702342\pi$
$307$	−1.96092e6	−1.18745	−0.593723	+	0.804670i	$0.702342\pi$
$308$	−2.58893e6	−1.55505
$309$	1.10606e6	0.658996
$310$	−79193.1	−0.0468040
$311$	2.66867e6	1.56457	0.782284	−	0.622922i	$-0.214055\pi$
$311$	2.66867e6	1.56457	0.782284	+	0.622922i	$0.214055\pi$
$312$	−2.99854e6	−1.74391
$313$	2.29241e6	1.32261	0.661303	−	0.750118i	$-0.270004\pi$
$313$	2.29241e6	1.32261	0.661303	+	0.750118i	$0.270004\pi$
$314$	−614201.	−0.351550
$315$	4.20130e6	2.38565
$316$	−2.00273e6	−1.12825
$317$	−1.71583e6	−0.959015	−0.479508	−	0.877538i	$-0.659185\pi$
$317$	−1.71583e6	−0.959015	−0.479508	+	0.877538i	$0.659185\pi$
$318$	366775.	0.203391
$319$	4.42528e6	2.43480
$320$	−785779.	−0.428969
$321$	−60244.3	−0.0326327
$322$	925808.	0.497601
$323$	226698.	0.120904
$324$	−872095.	−0.461532
$325$	−2.32448e6	−1.22072
$326$	−876891.	−0.456984
$327$	−478249.	−0.247335
$328$	−202447.	−0.103903
$329$	2.12100e6	1.08032
$330$	−2.88400e6	−1.45784
$331$	2.03801e6	1.02244	0.511218	−	0.859451i	$-0.329194\pi$
$331$	2.03801e6	1.02244	0.511218	+	0.859451i	$0.329194\pi$
$332$	230387.	0.114713
$333$	−4.57891e6	−2.26283
$334$	−58817.9	−0.0288499
$335$	1.62760e6	0.792386
$336$	−2.16427e6	−1.04583
$337$	1.56295e6	0.749670	0.374835	−	0.927092i	$-0.377699\pi$
$337$	1.56295e6	0.749670	0.374835	+	0.927092i	$0.377699\pi$
$338$	1.06251e6	0.505872
$339$	−1.10776e6	−0.523537
$340$	−934106.	−0.438227
$341$	−387103.	−0.180277
$342$	453435.	0.209628
$343$	−2.23079e6	−1.02382
$344$	440921.	0.200893
$345$	−7.15097e6	−3.23458
$346$	345428.	0.155120
$347$	1.46841e6	0.654671	0.327336	−	0.944908i	$-0.393849\pi$
$347$	1.46841e6	0.654671	0.327336	+	0.944908i	$0.393849\pi$
$348$	4.43052e6	1.96113
$349$	−182768.	−0.0803224	−0.0401612	−	0.999193i	$-0.512787\pi$
$349$	−182768.	−0.0803224	−0.0401612	+	0.999193i	$0.512787\pi$
$350$	621371.	0.271132
$351$	5.04257e6	2.18466
$352$	3.78610e6	1.62868
$353$	1.89626e6	0.809956	0.404978	−	0.914326i	$-0.367279\pi$
$353$	1.89626e6	0.809956	0.404978	+	0.914326i	$0.367279\pi$
$354$	−274770.	−0.116536
$355$	−3.37860e6	−1.42287
$356$	−12426.0	−0.00519643
$357$	−1.48252e6	−0.615643
$358$	1.16746e6	0.481430
$359$	2.06782e6	0.846793	0.423397	−	0.905944i	$-0.360838\pi$
$359$	2.06782e6	0.846793	0.423397	+	0.905944i	$0.360838\pi$
$360$	−4.00620e6	−1.62921
$361$	−2.21929e6	−0.896285
$362$	1.29635e6	0.519937
$363$	−9.87129e6	−3.93195
$364$	3.35150e6	1.32582
$365$	−2.34058e6	−0.919586
$366$	−969291.	−0.378226
$367$	−1.37545e6	−0.533063	−0.266531	−	0.963826i	$-0.585878\pi$
$367$	−1.37545e6	−0.533063	−0.266531	+	0.963826i	$0.585878\pi$
$368$	2.38367e6	0.917544
$369$	748934.	0.286337
$370$	−1.54111e6	−0.585234
$371$	−879018.	−0.331561
$372$	−387562.	−0.145206
$373$	1.67587e6	0.623688	0.311844	−	0.950133i	$-0.399053\pi$
$373$	1.67587e6	0.623688	0.311844	+	0.950133i	$0.399053\pi$
$374$	658514.	0.243437
$375$	1.32294e6	0.485803
$376$	−2.02251e6	−0.737770
$377$	−5.72873e6	−2.07589
$378$	−1.34796e6	−0.485230
$379$	−1.66000e6	−0.593624	−0.296812	−	0.954936i	$-0.595923\pi$
$379$	−1.66000e6	−0.593624	−0.296812	+	0.954936i	$0.595923\pi$
$380$	−1.05817e6	−0.375922
$381$	6.49238e6	2.29135
$382$	1.05510e6	0.369944
$383$	−3.79497e6	−1.32194	−0.660969	−	0.750413i	$-0.729855\pi$
$383$	−3.79497e6	−1.32194	−0.660969	+	0.750413i	$0.729855\pi$
$384$	4.89187e6	1.69296
$385$	6.91184e6	2.37652
$386$	−332570.	−0.113610
$387$	−1.63114e6	−0.553623
$388$	−1.26690e6	−0.427232
$389$	−271386.	−0.0909315	−0.0454657	−	0.998966i	$-0.514477\pi$
$389$	−271386.	−0.0909315	−0.0454657	+	0.998966i	$0.514477\pi$
$390$	3.73347e6	1.24294
$391$	1.63281e6	0.540124
$392$	103084.	0.0338826
$393$	2.88401e6	0.941923
$394$	−260277.	−0.0844687
$395$	5.34681e6	1.72426
$396$	−9.13276e6	−2.92661
$397$	−1.08718e6	−0.346200	−0.173100	−	0.984904i	$-0.555378\pi$
$397$	−1.08718e6	−0.346200	−0.173100	+	0.984904i	$0.555378\pi$
$398$	−418460.	−0.132418
$399$	−1.67942e6	−0.528114
$400$	1.59984e6	0.499950
$401$	−4.08800e6	−1.26955	−0.634775	−	0.772697i	$-0.718907\pi$
$401$	−4.08800e6	−1.26955	−0.634775	+	0.772697i	$0.718907\pi$
$402$	−1.14877e6	−0.354541
$403$	501122.	0.153703
$404$	4.05527e6	1.23614
$405$	2.32829e6	0.705341
$406$	1.53138e6	0.461072
$407$	−7.53308e6	−2.25417
$408$	1.41367e6	0.420435
$409$	114795.	0.0339324	0.0169662	−	0.999856i	$-0.494599\pi$
$409$	114795.	0.0339324	0.0169662	+	0.999856i	$0.494599\pi$
$410$	252067.	0.0740552
$411$	−2.76636e6	−0.807801
$412$	1.17885e6	0.342149
$413$	658517.	0.189973
$414$	3.26589e6	0.936486
$415$	−615078.	−0.175311
$416$	−4.90128e6	−1.38860
$417$	6.41011e6	1.80520
$418$	745978.	0.208826
$419$	2.33238e6	0.649030	0.324515	−	0.945880i	$-0.394799\pi$
$419$	2.33238e6	0.649030	0.324515	+	0.945880i	$0.394799\pi$
$420$	6.92004e6	1.91419
$421$	−6.50089e6	−1.78759	−0.893794	−	0.448477i	$-0.851967\pi$
$421$	−6.50089e6	−1.78759	−0.893794	+	0.448477i	$0.851967\pi$
$422$	−1.97347e6	−0.539449
$423$	7.48207e6	2.03316
$424$	838200.	0.226429
$425$	1.09589e6	0.294302
$426$	2.38463e6	0.636644
$427$	2.32302e6	0.616571
$428$	−64208.8	−0.0169428
$429$	1.82495e7	4.78750
$430$	−548989.	−0.143183
$431$	2.19292e6	0.568629	0.284314	−	0.958731i	$-0.408234\pi$
$431$	2.19292e6	0.568629	0.284314	+	0.958731i	$0.408234\pi$
$432$	−3.47059e6	−0.894734
$433$	6.89217e6	1.76659	0.883296	−	0.468816i	$-0.155319\pi$
$433$	6.89217e6	1.76659	0.883296	+	0.468816i	$0.155319\pi$
$434$	−133958.	−0.0341385
$435$	−1.18285e7	−2.99712
$436$	−509721.	−0.128415
$437$	1.84968e6	0.463332
$438$	1.65199e6	0.411455
$439$	−5.27181e6	−1.30557	−0.652783	−	0.757545i	$-0.726398\pi$
$439$	−5.27181e6	−1.30557	−0.652783	+	0.757545i	$0.726398\pi$
$440$	−6.59088e6	−1.62298
$441$	−381349.	−0.0933741
$442$	−852477.	−0.207552
$443$	165140.	0.0399801	0.0199901	−	0.999800i	$-0.493637\pi$
$443$	165140.	0.0399801	0.0199901	+	0.999800i	$0.493637\pi$
$444$	−7.54201e6	−1.81564
$445$	33174.4	0.00794150
$446$	357853.	0.0851859
$447$	−5.94008e6	−1.40612
$448$	−1.32918e6	−0.312887
$449$	6.57754e6	1.53974	0.769870	−	0.638201i	$-0.220321\pi$
$449$	6.57754e6	1.53974	0.769870	+	0.638201i	$0.220321\pi$
$450$	2.19196e6	0.510271
$451$	1.23212e6	0.285242
$452$	−1.18066e6	−0.271819
$453$	−1.01819e7	−2.33121
$454$	−196779.	−0.0448063
$455$	−8.94770e6	−2.02620
$456$	1.60144e6	0.360660
$457$	6.54286e6	1.46547	0.732736	−	0.680513i	$-0.238243\pi$
$457$	6.54286e6	1.46547	0.732736	+	0.680513i	$0.238243\pi$
$458$	−2.25678e6	−0.502720
$459$	−2.37734e6	−0.526696
$460$	−7.62156e6	−1.67938
$461$	2.70103e6	0.591940	0.295970	−	0.955197i	$-0.404357\pi$
$461$	2.70103e6	0.591940	0.295970	+	0.955197i	$0.404357\pi$
$462$	−4.87840e6	−1.06334
$463$	−3.42507e6	−0.742534	−0.371267	−	0.928526i	$-0.621077\pi$
$463$	−3.42507e6	−0.742534	−0.371267	+	0.928526i	$0.621077\pi$
$464$	3.94284e6	0.850187
$465$	1.03470e6	0.221912
$466$	−1.90573e6	−0.406533
$467$	2.25373e6	0.478201	0.239100	−	0.970995i	$-0.423147\pi$
$467$	2.25373e6	0.478201	0.239100	+	0.970995i	$0.423147\pi$
$468$	1.18228e7	2.49520
$469$	2.75316e6	0.577961
$470$	2.51822e6	0.525834
$471$	8.02485e6	1.66680
$472$	−627938.	−0.129736
$473$	−2.68351e6	−0.551505
$474$	−3.77379e6	−0.771493
$475$	1.24144e6	0.252460
$476$	−1.58008e6	−0.319640
$477$	−3.10084e6	−0.623998
$478$	288019.	0.0576569
$479$	637109.	0.126875	0.0634373	−	0.997986i	$-0.479794\pi$
$479$	637109.	0.126875	0.0634373	+	0.997986i	$0.479794\pi$
$480$	−1.01200e7	−2.00482
$481$	9.75193e6	1.92189
$482$	−1.52401e6	−0.298793
$483$	−1.20961e7	−2.35928
$484$	−1.05209e7	−2.04145
$485$	3.38233e6	0.652923
$486$	950205.	0.182485
$487$	9.24018e6	1.76546	0.882730	−	0.469880i	$-0.155703\pi$
$487$	9.24018e6	1.76546	0.882730	+	0.469880i	$0.155703\pi$
$488$	−2.21515e6	−0.421069
$489$	1.14570e7	2.16670
$490$	−128350.	−0.0241493
$491$	−2.97142e6	−0.556238	−0.278119	−	0.960547i	$-0.589711\pi$
$491$	−2.97142e6	−0.556238	−0.278119	+	0.960547i	$0.589711\pi$
$492$	1.23358e6	0.229750
$493$	2.70083e6	0.500473
$494$	−965703.	−0.178044
$495$	2.43823e7	4.47262
$496$	−344901.	−0.0629493
$497$	−5.71504e6	−1.03783
$498$	434124.	0.0784405
$499$	−2.16754e6	−0.389688	−0.194844	−	0.980834i	$-0.562420\pi$
$499$	−2.16754e6	−0.389688	−0.194844	+	0.980834i	$0.562420\pi$
$500$	1.40999e6	0.252227
$501$	768486.	0.136786
$502$	−772322.	−0.136785
$503$	−444093.	−0.0782626	−0.0391313	−	0.999234i	$-0.512459\pi$
$503$	−444093.	−0.0782626	−0.0391313	+	0.999234i	$0.512459\pi$
$504$	−6.77665e6	−1.18833
$505$	−1.08266e7	−1.88914
$506$	5.37295e6	0.932903
$507$	−1.38822e7	−2.39849
$508$	6.91963e6	1.18966
$509$	−1.16617e7	−1.99511	−0.997555	−	0.0698795i	$-0.977739\pi$
$509$	−1.16617e7	−1.99511	−0.997555	+	0.0698795i	$0.977739\pi$
$510$	−1.76016e6	−0.299659
$511$	−3.95919e6	−0.670740
$512$	5.89015e6	0.993004
$513$	−2.69310e6	−0.451813
$514$	−2.27827e6	−0.380362
$515$	−3.14725e6	−0.522893
$516$	−2.68669e6	−0.444214
$517$	1.23093e7	2.02538
$518$	−2.60685e6	−0.426866
$519$	−4.51319e6	−0.735470
$520$	8.53220e6	1.38373
$521$	3.33390e6	0.538094	0.269047	−	0.963127i	$-0.413291\pi$
$521$	3.33390e6	0.538094	0.269047	+	0.963127i	$0.413291\pi$
$522$	5.40213e6	0.867738
$523$	−1.13005e7	−1.80652	−0.903259	−	0.429095i	$-0.858833\pi$
$523$	−1.13005e7	−1.80652	−0.903259	+	0.429095i	$0.858833\pi$
$524$	3.07380e6	0.489043
$525$	−8.11853e6	−1.28552
$526$	−1.91134e6	−0.301212
$527$	−236256.	−0.0370559
$528$	−1.25604e7	−1.96073
$529$	6.88607e6	1.06987
$530$	−1.04364e6	−0.161384
$531$	2.32300e6	0.357530
$532$	−1.78994e6	−0.274195
$533$	−1.59504e6	−0.243195
$534$	−23414.6	−0.00355331
$535$	171422.	0.0258930
$536$	−2.62531e6	−0.394701
$537$	−1.52534e7	−2.28261
$538$	−4.29397e6	−0.639592
$539$	−627384.	−0.0930169
$540$	1.10969e7	1.63763
$541$	9.27640e6	1.36266	0.681328	−	0.731978i	$-0.261403\pi$
$541$	9.27640e6	1.36266	0.681328	+	0.731978i	$0.261403\pi$
$542$	2.89050e6	0.422644
$543$	−1.69375e7	−2.46518
$544$	2.31073e6	0.334774
$545$	1.36084e6	0.196252
$546$	6.31531e6	0.906595
$547$	−4.38460e6	−0.626558	−0.313279	−	0.949661i	$-0.601428\pi$
$547$	−4.38460e6	−0.626558	−0.313279	+	0.949661i	$0.601428\pi$
$548$	−2.94841e6	−0.419408
$549$	8.19472e6	1.16039
$550$	3.60614e6	0.508319
$551$	3.05956e6	0.429319
$552$	1.15345e7	1.61120
$553$	9.04433e6	1.25766
$554$	−2.30342e6	−0.318860
$555$	2.01354e7	2.77477
$556$	6.83195e6	0.937255
$557$	−414479.	−0.0566063	−0.0283031	−	0.999599i	$-0.509010\pi$
$557$	−414479.	−0.0566063	−0.0283031	+	0.999599i	$0.509010\pi$
$558$	−472553.	−0.0642488
$559$	3.47392e6	0.470209
$560$	6.15832e6	0.829836
$561$	−8.60382e6	−1.15421
$562$	3.91267e6	0.522556
$563$	1.15148e7	1.53103	0.765516	−	0.643417i	$-0.222484\pi$
$563$	1.15148e7	1.53103	0.765516	+	0.643417i	$0.222484\pi$
$564$	1.23239e7	1.63136
$565$	3.15209e6	0.415410
$566$	−2.83274e6	−0.371677
$567$	3.93839e6	0.514471
$568$	5.44965e6	0.708758
$569$	−8.36373e6	−1.08298	−0.541489	−	0.840708i	$-0.682139\pi$
$569$	−8.36373e6	−1.08298	−0.541489	+	0.840708i	$0.682139\pi$
$570$	−1.99394e6	−0.257055
$571$	1.17323e7	1.50588	0.752942	−	0.658087i	$-0.228634\pi$
$571$	1.17323e7	1.50588	0.752942	+	0.658087i	$0.228634\pi$
$572$	1.94505e7	2.48565
$573$	−1.37855e7	−1.75402
$574$	426380.	0.0540154
$575$	8.94156e6	1.12783
$576$	−4.68882e6	−0.588854
$577$	934469.	0.116849	0.0584245	−	0.998292i	$-0.481392\pi$
$577$	934469.	0.116849	0.0584245	+	0.998292i	$0.481392\pi$
$578$	−2.44964e6	−0.304987
$579$	4.34519e6	0.538658
$580$	−1.26069e7	−1.55610
$581$	−1.04043e6	−0.127871
$582$	−2.38726e6	−0.292141
$583$	−5.10140e6	−0.621610
$584$	3.77534e6	0.458062
$585$	−3.15640e7	−3.81332
$586$	−1.96188e6	−0.236009
$587$	−3.06040e6	−0.366592	−0.183296	−	0.983058i	$-0.558677\pi$
$587$	−3.06040e6	−0.366592	−0.183296	+	0.983058i	$0.558677\pi$
$588$	−628128.	−0.0749212
$589$	−267636.	−0.0317875
$590$	781844.	0.0924677
$591$	3.40065e6	0.400492
$592$	−6.71184e6	−0.787113
$593$	1.82527e6	0.213152	0.106576	−	0.994305i	$-0.466011\pi$
$593$	1.82527e6	0.213152	0.106576	+	0.994305i	$0.466011\pi$
$594$	−7.82293e6	−0.909711
$595$	4.21843e6	0.488493
$596$	−6.33098e6	−0.730055
$597$	5.46739e6	0.627833
$598$	−6.95553e6	−0.795385
$599$	−9.09331e6	−1.03551	−0.517756	−	0.855528i	$-0.673232\pi$
$599$	−9.09331e6	−1.03551	−0.517756	+	0.855528i	$0.673232\pi$
$600$	7.74154e6	0.877908
$601$	2.93415e6	0.331357	0.165678	−	0.986180i	$-0.447019\pi$
$601$	2.93415e6	0.331357	0.165678	+	0.986180i	$0.447019\pi$
$602$	−928636.	−0.104437
$603$	9.71207e6	1.08772
$604$	−1.08519e7	−1.21036
$605$	2.80883e7	3.11987
$606$	7.64145e6	0.845268
$607$	5.23197e6	0.576360	0.288180	−	0.957576i	$-0.406950\pi$
$607$	5.23197e6	0.576360	0.288180	+	0.957576i	$0.406950\pi$
$608$	2.61764e6	0.287178
$609$	−2.00083e7	−2.18608
$610$	2.75807e6	0.300111
$611$	−1.59349e7	−1.72682
$612$	−5.57390e6	−0.601563
$613$	−1.32549e7	−1.42470	−0.712352	−	0.701823i	$-0.752370\pi$
$613$	−1.32549e7	−1.42470	−0.712352	+	0.701823i	$0.752370\pi$
$614$	−3.93817e6	−0.421574
$615$	−3.29338e6	−0.351118
$616$	−1.11487e7	−1.18379
$617$	8.83110e6	0.933903	0.466951	−	0.884283i	$-0.345352\pi$
$617$	8.83110e6	0.933903	0.466951	+	0.884283i	$0.345352\pi$
$618$	2.22133e6	0.233961
$619$	3.76389e6	0.394830	0.197415	−	0.980320i	$-0.436745\pi$
$619$	3.76389e6	0.394830	0.197415	+	0.980320i	$0.436745\pi$
$620$	1.10279e6	0.115216
$621$	−1.93972e7	−2.01841
$622$	5.35957e6	0.555462
$623$	56115.7	0.00579248
$624$	1.62600e7	1.67170
$625$	−1.14198e7	−1.16939
$626$	4.60391e6	0.469560
$627$	−9.74658e6	−0.990109
$628$	8.55295e6	0.865400
$629$	−4.59759e6	−0.463344
$630$	8.43758e6	0.846967
$631$	6.67735e6	0.667622	0.333811	−	0.942640i	$-0.391665\pi$
$631$	6.67735e6	0.667622	0.333811	+	0.942640i	$0.391665\pi$
$632$	−8.62435e6	−0.858882
$633$	2.57844e7	2.55769
$634$	−3.44595e6	−0.340475
$635$	−1.84738e7	−1.81811
$636$	−5.10745e6	−0.500681
$637$	812178.	0.0793054
$638$	8.88742e6	0.864418
$639$	−2.01605e7	−1.95321
$640$	−1.39196e7	−1.34331
$641$	−1.27863e7	−1.22913	−0.614566	−	0.788865i	$-0.710669\pi$
$641$	−1.27863e7	−1.22913	−0.614566	+	0.788865i	$0.710669\pi$
$642$	−120990.	−0.0115855
$643$	1.12041e7	1.06869	0.534344	−	0.845267i	$-0.320559\pi$
$643$	1.12041e7	1.06869	0.534344	+	0.845267i	$0.320559\pi$
$644$	−1.28922e7	−1.22493
$645$	7.17282e6	0.678876
$646$	455285.	0.0429242
$647$	−1.78490e7	−1.67631	−0.838154	−	0.545434i	$-0.816365\pi$
$647$	−1.78490e7	−1.67631	−0.838154	+	0.545434i	$0.816365\pi$
$648$	−3.75551e6	−0.351343
$649$	3.82172e6	0.356162
$650$	−4.66832e6	−0.433388
$651$	1.75023e6	0.161861
$652$	1.22110e7	1.12495
$653$	1.72317e7	1.58141	0.790706	−	0.612195i	$-0.209713\pi$
$653$	1.72317e7	1.58141	0.790706	+	0.612195i	$0.209713\pi$
$654$	−960482.	−0.0878101
$655$	−8.20632e6	−0.747386
$656$	1.09780e6	0.0996009
$657$	−1.39665e7	−1.26233
$658$	4.25967e6	0.383540
$659$	8.55241e6	0.767140	0.383570	−	0.923512i	$-0.374694\pi$
$659$	8.55241e6	0.767140	0.383570	+	0.923512i	$0.374694\pi$
$660$	4.01606e7	3.58873
$661$	−1.53106e7	−1.36297	−0.681487	−	0.731831i	$-0.738666\pi$
$661$	−1.53106e7	−1.36297	−0.681487	+	0.731831i	$0.738666\pi$
$662$	4.09300e6	0.362991
$663$	1.11380e7	0.984068
$664$	992115.	0.0873257
$665$	4.77872e6	0.419042
$666$	−9.19596e6	−0.803362
$667$	2.20366e7	1.91792
$668$	819058.	0.0710189
$669$	−4.67553e6	−0.403893
$670$	3.26877e6	0.281317
$671$	1.34817e7	1.15595
$672$	−1.71183e7	−1.46230
$673$	−6.91094e6	−0.588166	−0.294083	−	0.955780i	$-0.595014\pi$
$673$	−6.91094e6	−0.588166	−0.294083	+	0.955780i	$0.595014\pi$
$674$	3.13892e6	0.266152
$675$	−1.30188e7	−1.09979
$676$	−1.47958e7	−1.24529
$677$	1.32490e7	1.11099	0.555497	−	0.831519i	$-0.312528\pi$
$677$	1.32490e7	1.11099	0.555497	+	0.831519i	$0.312528\pi$
$678$	−2.22475e6	−0.185869
$679$	5.72135e6	0.476238
$680$	−4.02255e6	−0.333602
$681$	2.57102e6	0.212440
$682$	−777430.	−0.0640030
$683$	−9.66117e6	−0.792461	−0.396230	−	0.918151i	$-0.629682\pi$
$683$	−9.66117e6	−0.792461	−0.396230	+	0.918151i	$0.629682\pi$
$684$	−6.31423e6	−0.516036
$685$	7.87156e6	0.640965
$686$	−4.48015e6	−0.363482
$687$	2.94860e7	2.38355
$688$	−2.39095e6	−0.192575
$689$	6.60400e6	0.529980
$690$	−1.43615e7	−1.14836
$691$	−1.96634e7	−1.56662	−0.783311	−	0.621631i	$-0.786471\pi$
$691$	−1.96634e7	−1.56662	−0.783311	+	0.621631i	$0.786471\pi$
$692$	−4.81019e6	−0.381854
$693$	4.12436e7	3.26230
$694$	2.94905e6	0.232425
$695$	−1.82397e7	−1.43237
$696$	1.90792e7	1.49292
$697$	751989.	0.0586313
$698$	−367058.	−0.0285165
$699$	2.48993e7	1.92750
$700$	−8.65279e6	−0.667438
$701$	9.82975e6	0.755523	0.377761	−	0.925903i	$-0.376694\pi$
$701$	9.82975e6	0.755523	0.377761	+	0.925903i	$0.376694\pi$
$702$	1.01271e7	0.775611
$703$	−5.20824e6	−0.397468
$704$	−7.71391e6	−0.586601
$705$	−3.29018e7	−2.49314
$706$	3.80832e6	0.287555
$707$	−1.83136e7	−1.37793
$708$	3.82625e6	0.286873
$709$	−1.94356e7	−1.45205	−0.726026	−	0.687667i	$-0.758635\pi$
$709$	−1.94356e7	−1.45205	−0.726026	+	0.687667i	$0.758635\pi$
$710$	−6.78535e6	−0.505157
$711$	3.19049e7	2.36692
$712$	−53509.9	−0.00395580
$713$	−1.92766e6	−0.142006
$714$	−2.97738e6	−0.218569
$715$	−5.19282e7	−3.79873
$716$	−1.62572e7	−1.18512
$717$	−3.76311e6	−0.273369
$718$	4.15287e6	0.300633
$719$	8.16016e6	0.588676	0.294338	−	0.955701i	$-0.404901\pi$
$719$	8.16016e6	0.588676	0.294338	+	0.955701i	$0.404901\pi$
$720$	2.17242e7	1.56175
$721$	−5.32369e6	−0.381395
$722$	−4.45707e6	−0.318204
$723$	1.99120e7	1.41667
$724$	−1.80521e7	−1.27991
$725$	1.47903e7	1.04503
$726$	−1.98248e7	−1.39594
$727$	2.08807e7	1.46524	0.732620	−	0.680638i	$-0.238298\pi$
$727$	2.08807e7	1.46524	0.732620	+	0.680638i	$0.238298\pi$
$728$	1.44326e7	1.00929
$729$	−1.99925e7	−1.39331
$730$	−4.70066e6	−0.326477
$731$	−1.63780e6	−0.113362
$732$	1.34977e7	0.931068
$733$	−1.86849e7	−1.28449	−0.642247	−	0.766498i	$-0.721998\pi$
$733$	−1.86849e7	−1.28449	−0.642247	+	0.766498i	$0.721998\pi$
$734$	−2.76235e6	−0.189251
$735$	1.67695e6	0.114499
$736$	1.88537e7	1.28293
$737$	1.59780e7	1.08356
$738$	1.50411e6	0.101657
$739$	1.89041e7	1.27334	0.636669	−	0.771137i	$-0.280312\pi$
$739$	1.89041e7	1.27334	0.636669	+	0.771137i	$0.280312\pi$
$740$	2.14605e7	1.44065
$741$	1.26174e7	0.844159
$742$	−1.76536e6	−0.117713
$743$	1.64341e7	1.09213	0.546063	−	0.837744i	$-0.316126\pi$
$743$	1.64341e7	1.09213	0.546063	+	0.837744i	$0.316126\pi$
$744$	−1.66896e6	−0.110538
$745$	1.69022e7	1.11571
$746$	3.36569e6	0.221425
$747$	−3.67023e6	−0.240653
$748$	−9.17002e6	−0.599261
$749$	289968.	0.0188862
$750$	2.65689e6	0.172473
$751$	2.30723e7	1.49276	0.746382	−	0.665518i	$-0.231789\pi$
$751$	2.30723e7	1.49276	0.746382	+	0.665518i	$0.231789\pi$
$752$	1.09673e7	0.707223
$753$	1.00908e7	0.648540
$754$	−1.15052e7	−0.736996
$755$	2.89720e7	1.84974
$756$	1.87708e7	1.19448
$757$	−1.60940e7	−1.02076	−0.510381	−	0.859949i	$-0.670495\pi$
$757$	−1.60940e7	−1.02076	−0.510381	+	0.859949i	$0.670495\pi$
$758$	−3.33384e6	−0.210752
$759$	−7.02003e7	−4.42318
$760$	−4.55682e6	−0.286172
$761$	−2.87571e7	−1.80005	−0.900023	−	0.435842i	$-0.856451\pi$
$761$	−2.87571e7	−1.80005	−0.900023	+	0.435842i	$0.856451\pi$
$762$	1.30388e7	0.813488
$763$	2.30191e6	0.143145
$764$	−1.46926e7	−0.910681
$765$	1.48810e7	0.919345
$766$	−7.62154e6	−0.469322
$767$	−4.94740e6	−0.303660
$768$	987609.	0.0604202
$769$	−9.25896e6	−0.564607	−0.282304	−	0.959325i	$-0.591099\pi$
$769$	−9.25896e6	−0.564607	−0.282304	+	0.959325i	$0.591099\pi$
$770$	1.38813e7	0.843727
$771$	2.97667e7	1.80341
$772$	4.63114e6	0.279669
$773$	2.04713e7	1.23224	0.616122	−	0.787651i	$-0.288703\pi$
$773$	2.04713e7	1.23224	0.616122	+	0.787651i	$0.288703\pi$
$774$	−3.27587e6	−0.196551
$775$	−1.29378e6	−0.0773762
$776$	−5.45567e6	−0.325232
$777$	3.40598e7	2.02390
$778$	−545033.	−0.0322830
$779$	851868.	0.0502954
$780$	−5.19898e7	−3.05972
$781$	−3.31674e7	−1.94573
$782$	3.27922e6	0.191758
$783$	−3.20850e7	−1.87024
$784$	−558988.	−0.0324797
$785$	−2.28343e7	−1.32256
$786$	5.79204e6	0.334407
$787$	7.74235e6	0.445591	0.222795	−	0.974865i	$-0.428482\pi$
$787$	7.74235e6	0.445591	0.222795	+	0.974865i	$0.428482\pi$
$788$	3.62444e6	0.207934
$789$	2.49726e7	1.42814
$790$	1.07381e7	0.612155
$791$	5.33188e6	0.302998
$792$	−3.93285e7	−2.22789
$793$	−1.74527e7	−0.985552
$794$	−2.18343e6	−0.122910
$795$	1.36357e7	0.765172
$796$	5.82718e6	0.325969
$797$	2.40220e7	1.33956	0.669782	−	0.742558i	$-0.266387\pi$
$797$	2.40220e7	1.33956	0.669782	+	0.742558i	$0.266387\pi$
$798$	−3.37284e6	−0.187494
$799$	7.51259e6	0.416316
$800$	1.26540e7	0.699040
$801$	197955.	0.0109015
$802$	−8.21005e6	−0.450723
$803$	−2.29773e7	−1.25750
$804$	1.59969e7	0.872764
$805$	3.44190e7	1.87201
$806$	1.00642e6	0.0545684
$807$	5.61028e7	3.03250
$808$	1.74632e7	0.941013
$809$	−1.71095e7	−0.919105	−0.459552	−	0.888151i	$-0.651990\pi$
$809$	−1.71095e7	−0.919105	−0.459552	+	0.888151i	$0.651990\pi$
$810$	4.67597e6	0.250414
$811$	−3.10663e7	−1.65859	−0.829293	−	0.558814i	$-0.811256\pi$
$811$	−3.10663e7	−1.65859	−0.829293	+	0.558814i	$0.811256\pi$
$812$	−2.13250e7	−1.13501
$813$	−3.77659e7	−2.00389
$814$	−1.51289e7	−0.800289
$815$	−3.26004e7	−1.71921
$816$	−7.66584e6	−0.403027
$817$	−1.85533e6	−0.0972446
$818$	230546.	0.0120469
$819$	−5.33918e7	−2.78141
$820$	−3.51011e6	−0.182300
$821$	2.44442e6	0.126566	0.0632831	−	0.997996i	$-0.479843\pi$
$821$	2.44442e6	0.126566	0.0632831	+	0.997996i	$0.479843\pi$
$822$	−5.55577e6	−0.286790
$823$	−2.53877e7	−1.30654	−0.653271	−	0.757124i	$-0.726604\pi$
$823$	−2.53877e7	−1.30654	−0.653271	+	0.757124i	$0.726604\pi$
$824$	5.07648e6	0.260462
$825$	−4.71161e7	−2.41010
$826$	1.32252e6	0.0674454
$827$	2.63726e7	1.34088	0.670440	−	0.741964i	$-0.266106\pi$
$827$	2.63726e7	1.34088	0.670440	+	0.741964i	$0.266106\pi$
$828$	−4.54786e7	−2.30532
$829$	9.19562e6	0.464724	0.232362	−	0.972629i	$-0.425355\pi$
$829$	9.19562e6	0.464724	0.232362	+	0.972629i	$0.425355\pi$
$830$	−1.23528e6	−0.0622401
$831$	3.00954e7	1.51181
$832$	9.98601e6	0.500131
$833$	−382905.	−0.0191196
$834$	1.28736e7	0.640893
$835$	−2.18669e6	−0.108535
$836$	−1.03880e7	−0.514062
$837$	2.80665e6	0.138476
$838$	4.68420e6	0.230423
$839$	−2.29518e7	−1.12567	−0.562836	−	0.826568i	$-0.690290\pi$
$839$	−2.29518e7	−1.12567	−0.562836	+	0.826568i	$0.690290\pi$
$840$	2.97998e7	1.45718
$841$	1.59398e7	0.777126
$842$	−1.30559e7	−0.634640
$843$	−5.11210e7	−2.47760
$844$	2.74812e7	1.32795
$845$	3.95012e7	1.90313
$846$	1.50265e7	0.721823
$847$	4.75125e7	2.27562
$848$	−4.54526e6	−0.217054
$849$	3.70111e7	1.76223
$850$	2.20090e6	0.104485
$851$	−3.75126e7	−1.77564
$852$	−3.32067e7	−1.56721
$853$	−2.83018e7	−1.33181	−0.665904	−	0.746038i	$-0.731954\pi$
$853$	−2.83018e7	−1.33181	−0.665904	+	0.746038i	$0.731954\pi$
$854$	4.66539e6	0.218899
$855$	1.68575e7	0.788638
$856$	−276503.	−0.0128978
$857$	−1.91532e7	−0.890819	−0.445409	−	0.895327i	$-0.646942\pi$
$857$	−1.91532e7	−0.890819	−0.445409	+	0.895327i	$0.646942\pi$
$858$	3.66511e7	1.69969
$859$	1.24842e7	0.577267	0.288633	−	0.957440i	$-0.406799\pi$
$859$	1.24842e7	0.577267	0.288633	+	0.957440i	$0.406799\pi$
$860$	7.64484e6	0.352470
$861$	−5.57088e6	−0.256104
$862$	4.40410e6	0.201878
$863$	3.33719e7	1.52530	0.762648	−	0.646813i	$-0.223899\pi$
$863$	3.33719e7	1.52530	0.762648	+	0.646813i	$0.223899\pi$
$864$	−2.74507e7	−1.25103
$865$	1.28421e7	0.583572
$866$	1.38417e7	0.627185
$867$	3.20057e7	1.44604
$868$	1.86541e6	0.0840379
$869$	5.24890e7	2.35786
$870$	−2.37554e7	−1.06406
$871$	−2.06843e7	−0.923836
$872$	−2.19501e6	−0.0977566
$873$	2.01827e7	0.896280
$874$	3.71476e6	0.164495
$875$	−6.36755e6	−0.281159
$876$	−2.30045e7	−1.01287
$877$	−2.00140e6	−0.0878688	−0.0439344	−	0.999034i	$-0.513989\pi$
$877$	−2.00140e6	−0.0878688	−0.0439344	+	0.999034i	$0.513989\pi$
$878$	−1.05875e7	−0.463509
$879$	2.56330e7	1.11899
$880$	3.57400e7	1.55578
$881$	−7.28531e6	−0.316234	−0.158117	−	0.987420i	$-0.550542\pi$
$881$	−7.28531e6	−0.316234	−0.158117	+	0.987420i	$0.550542\pi$
$882$	−765875.	−0.0331502
$883$	−4.26084e7	−1.83905	−0.919525	−	0.393032i	$-0.871426\pi$
$883$	−4.26084e7	−1.83905	−0.919525	+	0.393032i	$0.871426\pi$
$884$	1.18710e7	0.510925
$885$	−1.02152e7	−0.438418
$886$	331656.	0.0141940
$887$	−3.71824e7	−1.58682	−0.793412	−	0.608685i	$-0.791697\pi$
$887$	−3.71824e7	−1.58682	−0.793412	+	0.608685i	$0.791697\pi$
$888$	−3.24782e7	−1.38216
$889$	−3.12491e7	−1.32612
$890$	66625.1	0.00281944
$891$	2.28565e7	0.964531
$892$	−4.98322e6	−0.209700
$893$	8.51041e6	0.357126
$894$	−1.19296e7	−0.499210
$895$	4.34029e7	1.81118
$896$	−2.35455e7	−0.979803
$897$	9.08775e7	3.77116
$898$	1.32099e7	0.546647
$899$	−3.18855e6	−0.131581
$900$	−3.05237e7	−1.25612
$901$	−3.11349e6	−0.127772
$902$	2.47451e6	0.101268
$903$	1.21331e7	0.495168
$904$	−5.08429e6	−0.206923
$905$	4.81947e7	1.95604
$906$	−2.04485e7	−0.827639
$907$	−1.55191e7	−0.626396	−0.313198	−	0.949688i	$-0.601400\pi$
$907$	−1.55191e7	−0.626396	−0.313198	+	0.949688i	$0.601400\pi$
$908$	2.74021e6	0.110298
$909$	−6.46034e7	−2.59326
$910$	−1.79699e7	−0.719354
$911$	2.03355e7	0.811818	0.405909	−	0.913913i	$-0.366955\pi$
$911$	2.03355e7	0.811818	0.405909	+	0.913913i	$0.366955\pi$
$912$	−8.68402e6	−0.345727
$913$	−6.03816e6	−0.239733
$914$	1.31402e7	0.520280
$915$	−3.60356e7	−1.42292
$916$	3.14264e7	1.23753
$917$	−1.38813e7	−0.545139
$918$	−4.77449e6	−0.186991
$919$	3.27109e7	1.27762	0.638812	−	0.769363i	$-0.279426\pi$
$919$	3.27109e7	1.27762	0.638812	+	0.769363i	$0.279426\pi$
$920$	−3.28208e7	−1.27844
$921$	5.14542e7	1.99881
$922$	5.42456e6	0.210154
$923$	4.29367e7	1.65892
$924$	6.79332e7	2.61759
$925$	−2.51772e7	−0.967506
$926$	−6.87866e6	−0.263619
$927$	−1.87799e7	−0.717785
$928$	3.11860e7	1.18875
$929$	9.88499e6	0.375783	0.187891	−	0.982190i	$-0.439835\pi$
$929$	9.88499e6	0.375783	0.187891	+	0.982190i	$0.439835\pi$
$930$	2.07801e6	0.0787845
$931$	−433762.	−0.0164013
$932$	2.65378e7	1.00075
$933$	−7.00255e7	−2.63361
$934$	4.52624e6	0.169774
$935$	2.44818e7	0.915828
$936$	5.09125e7	1.89948
$937$	−1.51794e7	−0.564816	−0.282408	−	0.959294i	$-0.591133\pi$
$937$	−1.51794e7	−0.564816	−0.282408	+	0.959294i	$0.591133\pi$
$938$	5.52924e6	0.205191
$939$	−6.01524e7	−2.22633
$940$	−3.50670e7	−1.29443
$941$	−1.74843e7	−0.643686	−0.321843	−	0.946793i	$-0.604302\pi$
$941$	−1.74843e7	−0.643686	−0.321843	+	0.946793i	$0.604302\pi$
$942$	1.61165e7	0.591759
$943$	6.13563e6	0.224688
$944$	3.40508e6	0.124365
$945$	−5.01136e7	−1.82547
$946$	−5.38936e6	−0.195799
$947$	1.22387e7	0.443468	0.221734	−	0.975107i	$-0.428828\pi$
$947$	1.22387e7	0.443468	0.221734	+	0.975107i	$0.428828\pi$
$948$	5.25512e7	1.89916
$949$	2.97451e7	1.07214
$950$	2.49322e6	0.0896297
$951$	4.50230e7	1.61430
$952$	−6.80429e6	−0.243327
$953$	−1.83349e7	−0.653953	−0.326977	−	0.945032i	$-0.606030\pi$
$953$	−1.83349e7	−0.653953	−0.326977	+	0.945032i	$0.606030\pi$
$954$	−6.22750e6	−0.221535
$955$	3.92259e7	1.39176
$956$	−4.01076e6	−0.141932
$957$	−1.16119e8	−4.09847
$958$	1.27952e6	0.0450438
$959$	1.33150e7	0.467516
$960$	2.06187e7	0.722077
$961$	−2.83502e7	−0.990257
$962$	1.95851e7	0.682319
$963$	1.02289e6	0.0355439
$964$	2.12223e7	0.735530
$965$	−1.23641e7	−0.427408
$966$	−2.42931e7	−0.837605
$967$	−1.52514e7	−0.524498	−0.262249	−	0.965000i	$-0.584464\pi$
$967$	−1.52514e7	−0.524498	−0.262249	+	0.965000i	$0.584464\pi$
$968$	−4.53062e7	−1.55406
$969$	−5.94853e6	−0.203517
$970$	6.79284e6	0.231805
$971$	1.47157e7	0.500878	0.250439	−	0.968132i	$-0.419425\pi$
$971$	1.47157e7	0.500878	0.250439	+	0.968132i	$0.419425\pi$
$972$	−1.32319e7	−0.449218
$973$	−3.08531e7	−1.04476
$974$	1.85573e7	0.626784
$975$	6.09940e7	2.05483
$976$	1.20119e7	0.403635
$977$	2.39180e6	0.0801655	0.0400828	−	0.999196i	$-0.487238\pi$
$977$	2.39180e6	0.0801655	0.0400828	+	0.999196i	$0.487238\pi$
$978$	2.30095e7	0.769235
$979$	325669.	0.0108597
$980$	1.78731e6	0.0594476
$981$	8.12024e6	0.269399
$982$	−5.96760e6	−0.197479
$983$	−3.20155e7	−1.05676	−0.528380	−	0.849008i	$-0.677200\pi$
$983$	−3.20155e7	−1.05676	−0.528380	+	0.849008i	$0.677200\pi$
$984$	5.31219e6	0.174898
$985$	−9.67641e6	−0.317778
$986$	5.42416e6	0.177681
$987$	−5.56547e7	−1.81848
$988$	1.34477e7	0.438284
$989$	−1.33631e7	−0.434427
$990$	4.89677e7	1.58790
$991$	2.54263e7	0.822432	0.411216	−	0.911538i	$-0.365104\pi$
$991$	2.54263e7	0.822432	0.411216	+	0.911538i	$0.365104\pi$
$992$	−2.72800e6	−0.0880168
$993$	−5.34770e7	−1.72105
$994$	−1.14777e7	−0.368458
$995$	−1.55572e7	−0.498166
$996$	−6.04531e6	−0.193095
$997$	4.79018e7	1.52621	0.763104	−	0.646276i	$-0.223674\pi$
$997$	4.79018e7	1.52621	0.763104	+	0.646276i	$0.223674\pi$
$998$	−4.35314e6	−0.138349
$999$	5.46178e7	1.73149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.6.a.b.1.6	✓	10
3.2	odd	2		369.6.a.e.1.5		10
4.3	odd	2		656.6.a.g.1.10		10
5.4	even	2		1025.6.a.b.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.6.a.b.1.6	✓	10	1.1	even	1	trivial
369.6.a.e.1.5		10	3.2	odd	2
656.6.a.g.1.10		10	4.3	odd	2
1025.6.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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	41.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00833 q^{2} -26.2398 q^{3} -27.9666 q^{4} +74.6642 q^{5} -52.6982 q^{6} +126.297 q^{7} -120.433 q^{8} +445.529 q^{9} +O(q^{10})\)	\(q+2.00833 q^{2} -26.2398 q^{3} -27.9666 q^{4} +74.6642 q^{5} -52.6982 q^{6} +126.297 q^{7} -120.433 q^{8} +445.529 q^{9} +149.950 q^{10} +732.971 q^{11} +733.839 q^{12} -948.864 q^{13} +253.647 q^{14} -1959.18 q^{15} +653.063 q^{16} +447.346 q^{17} +894.769 q^{18} +506.762 q^{19} -2088.11 q^{20} -3314.02 q^{21} +1472.05 q^{22} +3649.99 q^{23} +3160.13 q^{24} +2449.75 q^{25} -1905.63 q^{26} -5314.32 q^{27} -3532.11 q^{28} +6037.46 q^{29} -3934.67 q^{30} -528.129 q^{31} +5165.41 q^{32} -19233.0 q^{33} +898.419 q^{34} +9429.91 q^{35} -12459.9 q^{36} -10277.5 q^{37} +1017.75 q^{38} +24898.0 q^{39} -8992.02 q^{40} +1681.00 q^{41} -6655.65 q^{42} -3661.14 q^{43} -20498.7 q^{44} +33265.1 q^{45} +7330.38 q^{46} +16793.7 q^{47} -17136.3 q^{48} -855.947 q^{49} +4919.90 q^{50} -11738.3 q^{51} +26536.5 q^{52} -6959.90 q^{53} -10672.9 q^{54} +54726.7 q^{55} -15210.3 q^{56} -13297.4 q^{57} +12125.2 q^{58} +5214.02 q^{59} +54791.6 q^{60} +18393.2 q^{61} -1060.66 q^{62} +56269.2 q^{63} -10524.2 q^{64} -70846.2 q^{65} -38626.3 q^{66} +21799.0 q^{67} -12510.8 q^{68} -95775.1 q^{69} +18938.4 q^{70} -45250.6 q^{71} -53656.2 q^{72} -31348.1 q^{73} -20640.5 q^{74} -64281.0 q^{75} -14172.4 q^{76} +92572.3 q^{77} +50003.5 q^{78} +71611.3 q^{79} +48760.5 q^{80} +31183.4 q^{81} +3376.00 q^{82} -8237.92 q^{83} +92682.0 q^{84} +33400.8 q^{85} -7352.77 q^{86} -158422. q^{87} -88273.6 q^{88} +444.314 q^{89} +66807.2 q^{90} -119839. q^{91} -102078. q^{92} +13858.0 q^{93} +33727.3 q^{94} +37837.0 q^{95} -135540. q^{96} +45300.6 q^{97} -1719.02 q^{98} +326560. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 28 q^{3} + 207 q^{4} + 32 q^{5} + 54 q^{6} + 342 q^{7} + 249 q^{8} + 1194 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 + 28 * q^3 + 207 * q^4 + 32 * q^5 + 54 * q^6 + 342 * q^7 + 249 * q^8 + 1194 * q^9	\( 10 q + 3 q^{2} + 28 q^{3} + 207 q^{4} + 32 q^{5} + 54 q^{6} + 342 q^{7} + 249 q^{8} + 1194 q^{9} + 102 q^{10} + 846 q^{11} + 4204 q^{12} + 1504 q^{13} + 3468 q^{14} + 1966 q^{15} + 5859 q^{16} + 560 q^{17} - 3713 q^{18} + 4240 q^{19} - 6182 q^{20} - 3096 q^{21} - 2628 q^{22} - 1508 q^{23} - 10166 q^{24} + 11734 q^{25} - 22014 q^{26} + 1882 q^{27} - 8662 q^{28} - 124 q^{29} - 45234 q^{30} + 10384 q^{31} - 6619 q^{32} - 22772 q^{33} + 802 q^{34} - 17890 q^{35} - 9657 q^{36} + 5524 q^{37} - 46098 q^{38} + 16844 q^{39} - 61738 q^{40} + 16810 q^{41} + 15476 q^{42} + 24160 q^{43} - 21594 q^{44} + 94688 q^{45} + 42404 q^{46} + 58984 q^{47} + 49296 q^{48} + 70326 q^{49} + 6817 q^{50} + 7336 q^{51} + 64374 q^{52} + 23456 q^{53} - 120694 q^{54} + 96426 q^{55} + 80184 q^{56} + 78004 q^{57} - 13378 q^{58} + 52428 q^{59} + 29422 q^{60} + 113540 q^{61} - 113008 q^{62} - 11036 q^{63} + 37363 q^{64} - 22340 q^{65} - 46224 q^{66} + 85506 q^{67} - 71406 q^{68} - 80004 q^{69} - 71946 q^{70} + 75236 q^{71} - 248911 q^{72} - 85148 q^{73} - 23462 q^{74} + 79652 q^{75} + 113376 q^{76} - 172896 q^{77} - 292760 q^{78} + 178200 q^{79} - 401850 q^{80} - 54126 q^{81} + 5043 q^{82} - 125412 q^{83} - 123276 q^{84} - 245912 q^{85} - 18848 q^{86} - 292760 q^{87} - 135952 q^{88} - 62696 q^{89} - 531830 q^{90} + 30056 q^{91} - 236372 q^{92} - 41700 q^{93} + 419014 q^{94} + 28002 q^{95} + 172086 q^{96} + 154548 q^{97} + 288367 q^{98} + 21952 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 + 28 * q^3 + 207 * q^4 + 32 * q^5 + 54 * q^6 + 342 * q^7 + 249 * q^8 + 1194 * q^9 + 102 * q^10 + 846 * q^11 + 4204 * q^12 + 1504 * q^13 + 3468 * q^14 + 1966 * q^15 + 5859 * q^16 + 560 * q^17 - 3713 * q^18 + 4240 * q^19 - 6182 * q^20 - 3096 * q^21 - 2628 * q^22 - 1508 * q^23 - 10166 * q^24 + 11734 * q^25 - 22014 * q^26 + 1882 * q^27 - 8662 * q^28 - 124 * q^29 - 45234 * q^30 + 10384 * q^31 - 6619 * q^32 - 22772 * q^33 + 802 * q^34 - 17890 * q^35 - 9657 * q^36 + 5524 * q^37 - 46098 * q^38 + 16844 * q^39 - 61738 * q^40 + 16810 * q^41 + 15476 * q^42 + 24160 * q^43 - 21594 * q^44 + 94688 * q^45 + 42404 * q^46 + 58984 * q^47 + 49296 * q^48 + 70326 * q^49 + 6817 * q^50 + 7336 * q^51 + 64374 * q^52 + 23456 * q^53 - 120694 * q^54 + 96426 * q^55 + 80184 * q^56 + 78004 * q^57 - 13378 * q^58 + 52428 * q^59 + 29422 * q^60 + 113540 * q^61 - 113008 * q^62 - 11036 * q^63 + 37363 * q^64 - 22340 * q^65 - 46224 * q^66 + 85506 * q^67 - 71406 * q^68 - 80004 * q^69 - 71946 * q^70 + 75236 * q^71 - 248911 * q^72 - 85148 * q^73 - 23462 * q^74 + 79652 * q^75 + 113376 * q^76 - 172896 * q^77 - 292760 * q^78 + 178200 * q^79 - 401850 * q^80 - 54126 * q^81 + 5043 * q^82 - 125412 * q^83 - 123276 * q^84 - 245912 * q^85 - 18848 * q^86 - 292760 * q^87 - 135952 * q^88 - 62696 * q^89 - 531830 * q^90 + 30056 * q^91 - 236372 * q^92 - 41700 * q^93 + 419014 * q^94 + 28002 * q^95 + 172086 * q^96 + 154548 * q^97 + 288367 * q^98 + 21952 * q^99

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