LMFDB - Embedded newform 43.8.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,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, 8, names="a")

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
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:	$13.4325560958$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 $ x^11 - 2x^10 - 977x^9 + 2592x^8 + 344686x^7 - 1160956x^6 - 53409536x^5 + 209758592x^4 + 3410917248x^3 - 14180732672x^2 - 60918607872x + 238240894976
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$6.31419$ 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)

$f(q)$	$=$	$q-8.31419 q^{2} +11.6940 q^{3} -58.8742 q^{4} +148.086 q^{5} -97.2261 q^{6} +122.189 q^{7} +1553.71 q^{8} -2050.25 q^{9} +O(q^{10})$	\(q-8.31419 q^{2} +11.6940 q^{3} -58.8742 q^{4} +148.086 q^{5} -97.2261 q^{6} +122.189 q^{7} +1553.71 q^{8} -2050.25 q^{9} -1231.21 q^{10} +5634.96 q^{11} -688.475 q^{12} -7738.55 q^{13} -1015.90 q^{14} +1731.71 q^{15} -5381.93 q^{16} +1712.43 q^{17} +17046.2 q^{18} -51155.1 q^{19} -8718.44 q^{20} +1428.88 q^{21} -46850.2 q^{22} -77057.3 q^{23} +18169.1 q^{24} -56195.6 q^{25} +64339.8 q^{26} -49550.4 q^{27} -7193.77 q^{28} -48088.8 q^{29} -14397.8 q^{30} -192432. q^{31} -154128. q^{32} +65895.2 q^{33} -14237.5 q^{34} +18094.4 q^{35} +120707. q^{36} +461302. q^{37} +425313. q^{38} -90494.6 q^{39} +230082. q^{40} +688771. q^{41} -11879.9 q^{42} +79507.0 q^{43} -331754. q^{44} -303613. q^{45} +640669. q^{46} -619513. q^{47} -62936.2 q^{48} -808613. q^{49} +467221. q^{50} +20025.1 q^{51} +455601. q^{52} +574333. q^{53} +411971. q^{54} +834458. q^{55} +189846. q^{56} -598208. q^{57} +399820. q^{58} -1.01363e6 q^{59} -101953. q^{60} -3.23249e6 q^{61} +1.59991e6 q^{62} -250518. q^{63} +1.97034e6 q^{64} -1.14597e6 q^{65} -547866. q^{66} +3.15895e6 q^{67} -100818. q^{68} -901108. q^{69} -150441. q^{70} +2.46302e6 q^{71} -3.18549e6 q^{72} -4.02731e6 q^{73} -3.83535e6 q^{74} -657151. q^{75} +3.01172e6 q^{76} +688530. q^{77} +752389. q^{78} -463495. q^{79} -796987. q^{80} +3.90446e6 q^{81} -5.72657e6 q^{82} -5.49654e6 q^{83} -84123.9 q^{84} +253587. q^{85} -661036. q^{86} -562351. q^{87} +8.75509e6 q^{88} -8.18997e6 q^{89} +2.52430e6 q^{90} -945564. q^{91} +4.53669e6 q^{92} -2.25030e6 q^{93} +5.15075e6 q^{94} -7.57535e6 q^{95} -1.80237e6 q^{96} +1.20009e7 q^{97} +6.72296e6 q^{98} -1.15531e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) $ 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9} - 1333 q^{10} + 1333 q^{11} + 5089 q^{12} - 17967 q^{13} - 22352 q^{14} - 49504 q^{15} - 34406 q^{16} - 63095 q^{17} - 165931 q^{18} - 54524 q^{19} - 280995 q^{20} - 139788 q^{21} - 289358 q^{22} - 138139 q^{23} - 429583 q^{24} + 3455 q^{25} - 132946 q^{26} - 240356 q^{27} - 12704 q^{28} - 308658 q^{29} + 421284 q^{30} - 209523 q^{31} - 644934 q^{32} + 96814 q^{33} + 762435 q^{34} - 578892 q^{35} + 426161 q^{36} - 298472 q^{37} - 369707 q^{38} + 292298 q^{39} + 2633173 q^{40} - 1346735 q^{41} + 1173266 q^{42} + 874577 q^{43} + 3134292 q^{44} + 1893784 q^{45} + 3588111 q^{46} + 499284 q^{47} + 5647533 q^{48} + 2544563 q^{49} + 3049745 q^{50} + 1258424 q^{51} + 983088 q^{52} - 2210495 q^{53} + 6789698 q^{54} - 1855072 q^{55} - 469976 q^{56} - 1238444 q^{57} + 4397067 q^{58} - 5824216 q^{59} - 2889372 q^{60} - 4453034 q^{61} + 1002789 q^{62} - 6240564 q^{63} + 4757538 q^{64} - 2162872 q^{65} - 258940 q^{66} - 6859513 q^{67} - 9397005 q^{68} - 10040030 q^{69} + 845078 q^{70} - 10726554 q^{71} + 1199517 q^{72} - 4456898 q^{73} + 1046637 q^{74} - 3349114 q^{75} + 5861267 q^{76} - 17019816 q^{77} + 1999122 q^{78} - 15541320 q^{79} - 15680911 q^{80} - 12976697 q^{81} + 20233655 q^{82} - 11146767 q^{83} + 12348278 q^{84} - 12471976 q^{85} - 1908168 q^{86} - 18648900 q^{87} - 24463544 q^{88} - 13531356 q^{89} + 20858990 q^{90} - 19746448 q^{91} - 26023161 q^{92} - 21903110 q^{93} + 20288857 q^{94} - 12291624 q^{95} - 13954503 q^{96} - 10999901 q^{97} + 29909168 q^{98} + 29396057 q^{99}+O(q^{100}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9 - 1333 * q^10 + 1333 * q^11 + 5089 * q^12 - 17967 * q^13 - 22352 * q^14 - 49504 * q^15 - 34406 * q^16 - 63095 * q^17 - 165931 * q^18 - 54524 * q^19 - 280995 * q^20 - 139788 * q^21 - 289358 * q^22 - 138139 * q^23 - 429583 * q^24 + 3455 * q^25 - 132946 * q^26 - 240356 * q^27 - 12704 * q^28 - 308658 * q^29 + 421284 * q^30 - 209523 * q^31 - 644934 * q^32 + 96814 * q^33 + 762435 * q^34 - 578892 * q^35 + 426161 * q^36 - 298472 * q^37 - 369707 * q^38 + 292298 * q^39 + 2633173 * q^40 - 1346735 * q^41 + 1173266 * q^42 + 874577 * q^43 + 3134292 * q^44 + 1893784 * q^45 + 3588111 * q^46 + 499284 * q^47 + 5647533 * q^48 + 2544563 * q^49 + 3049745 * q^50 + 1258424 * q^51 + 983088 * q^52 - 2210495 * q^53 + 6789698 * q^54 - 1855072 * q^55 - 469976 * q^56 - 1238444 * q^57 + 4397067 * q^58 - 5824216 * q^59 - 2889372 * q^60 - 4453034 * q^61 + 1002789 * q^62 - 6240564 * q^63 + 4757538 * q^64 - 2162872 * q^65 - 258940 * q^66 - 6859513 * q^67 - 9397005 * q^68 - 10040030 * q^69 + 845078 * q^70 - 10726554 * q^71 + 1199517 * q^72 - 4456898 * q^73 + 1046637 * q^74 - 3349114 * q^75 + 5861267 * q^76 - 17019816 * q^77 + 1999122 * q^78 - 15541320 * q^79 - 15680911 * q^80 - 12976697 * q^81 + 20233655 * q^82 - 11146767 * q^83 + 12348278 * q^84 - 12471976 * q^85 - 1908168 * q^86 - 18648900 * q^87 - 24463544 * q^88 - 13531356 * q^89 + 20858990 * q^90 - 19746448 * q^91 - 26023161 * q^92 - 21903110 * q^93 + 20288857 * q^94 - 12291624 * q^95 - 13954503 * q^96 - 10999901 * q^97 + 29909168 * q^98 + 29396057 * 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 $

$2$	−8.31419	−0.734878	−0.367439	−	0.930048i	$-0.619765\pi$
$2$	−8.31419	−0.734878	−0.367439	+	0.930048i	$0.619765\pi$
$3$	11.6940	0.250057	0.125028	−	0.992153i	$-0.460098\pi$
$3$	11.6940	0.250057	0.125028	+	0.992153i	$0.460098\pi$
$4$	−58.8742	−0.459955
$5$	148.086	0.529808	0.264904	−	0.964275i	$-0.414660\pi$
$5$	148.086	0.529808	0.264904	+	0.964275i	$0.414660\pi$
$6$	−97.2261	−0.183761
$7$	122.189	0.134644	0.0673222	−	0.997731i	$-0.478554\pi$
$7$	122.189	0.134644	0.0673222	+	0.997731i	$0.478554\pi$
$8$	1553.71	1.07289
$9$	−2050.25	−0.937472
$10$	−1231.21	−0.389344
$11$	5634.96	1.27649	0.638244	−	0.769834i	$-0.279661\pi$
$11$	5634.96	1.27649	0.638244	+	0.769834i	$0.279661\pi$
$12$	−688.475	−0.115015
$13$	−7738.55	−0.976917	−0.488459	−	0.872587i	$-0.662441\pi$
$13$	−7738.55	−0.976917	−0.488459	+	0.872587i	$0.662441\pi$
$14$	−1015.90	−0.0989472
$15$	1731.71	0.132482
$16$	−5381.93	−0.328487
$17$	1712.43	0.0845360	0.0422680	−	0.999106i	$-0.486542\pi$
$17$	1712.43	0.0845360	0.0422680	+	0.999106i	$0.486542\pi$
$18$	17046.2	0.688927
$19$	−51155.1	−1.71101	−0.855503	−	0.517798i	$-0.826752\pi$
$19$	−51155.1	−1.71101	−0.855503	+	0.517798i	$0.826752\pi$
$20$	−8718.44	−0.243688
$21$	1428.88	0.0336687
$22$	−46850.2	−0.938062
$23$	−77057.3	−1.32058	−0.660292	−	0.751009i	$-0.729568\pi$
$23$	−77057.3	−1.32058	−0.660292	+	0.751009i	$0.729568\pi$
$24$	18169.1	0.268283
$25$	−56195.6	−0.719304
$26$	64339.8	0.717915
$27$	−49550.4	−0.484478
$28$	−7193.77	−0.0619304
$29$	−48088.8	−0.366143	−0.183072	−	0.983100i	$-0.558604\pi$
$29$	−48088.8	−0.366143	−0.183072	+	0.983100i	$0.558604\pi$
$30$	−14397.8	−0.0973581
$31$	−192432.	−1.16014	−0.580070	−	0.814566i	$-0.696975\pi$
$31$	−192432.	−1.16014	−0.580070	+	0.814566i	$0.696975\pi$
$32$	−154128.	−0.831491
$33$	65895.2	0.319194
$34$	−14237.5	−0.0621236
$35$	18094.4	0.0713357
$36$	120707.	0.431195
$37$	461302.	1.49720	0.748599	−	0.663023i	$-0.230727\pi$
$37$	461302.	1.49720	0.748599	+	0.663023i	$0.230727\pi$
$38$	425313.	1.25738
$39$	−90494.6	−0.244285
$40$	230082.	0.568425
$41$	688771.	1.56074	0.780371	−	0.625316i	$-0.215030\pi$
$41$	688771.	1.56074	0.780371	+	0.625316i	$0.215030\pi$
$42$	−11879.9	−0.0247424
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	−331754.	−0.587127
$45$	−303613.	−0.496680
$46$	640669.	0.970468
$47$	−619513.	−0.870379	−0.435189	−	0.900339i	$-0.643319\pi$
$47$	−619513.	−0.870379	−0.435189	+	0.900339i	$0.643319\pi$
$48$	−62936.2	−0.0821403
$49$	−808613.	−0.981871
$50$	467221.	0.528600
$51$	20025.1	0.0211388
$52$	455601.	0.449338
$53$	574333.	0.529905	0.264952	−	0.964261i	$-0.414644\pi$
$53$	574333.	0.529905	0.264952	+	0.964261i	$0.414644\pi$
$54$	411971.	0.356032
$55$	834458.	0.676293
$56$	189846.	0.144458
$57$	−598208.	−0.427848
$58$	399820.	0.269071
$59$	−1.01363e6	−0.642539	−0.321269	−	0.946988i	$-0.604109\pi$
$59$	−1.01363e6	−0.642539	−0.321269	+	0.946988i	$0.604109\pi$
$60$	−101953.	−0.0609357
$61$	−3.23249e6	−1.82340	−0.911702	−	0.410852i	$-0.865231\pi$
$61$	−3.23249e6	−1.82340	−0.911702	+	0.410852i	$0.865231\pi$
$62$	1.59991e6	0.852561
$63$	−250518.	−0.126225
$64$	1.97034e6	0.939531
$65$	−1.14597e6	−0.517579
$66$	−547866.	−0.234569
$67$	3.15895e6	1.28316	0.641580	−	0.767056i	$-0.278279\pi$
$67$	3.15895e6	1.28316	0.641580	+	0.767056i	$0.278279\pi$
$68$	−100818.	−0.0388827
$69$	−901108.	−0.330221
$70$	−150441.	−0.0524230
$71$	2.46302e6	0.816701	0.408350	−	0.912825i	$-0.366104\pi$
$71$	2.46302e6	0.816701	0.408350	+	0.912825i	$0.366104\pi$
$72$	−3.18549e6	−1.00580
$73$	−4.02731e6	−1.21167	−0.605836	−	0.795590i	$-0.707161\pi$
$73$	−4.02731e6	−1.21167	−0.605836	+	0.795590i	$0.707161\pi$
$74$	−3.83535e6	−1.10026
$75$	−657151.	−0.179867
$76$	3.01172e6	0.786985
$77$	688530.	0.171872
$78$	752389.	0.179519
$79$	−463495.	−0.105767	−0.0528835	−	0.998601i	$-0.516841\pi$
$79$	−463495.	−0.105767	−0.0528835	+	0.998601i	$0.516841\pi$
$80$	−796987.	−0.174035
$81$	3.90446e6	0.816325
$82$	−5.72657e6	−1.14696
$83$	−5.49654e6	−1.05516	−0.527578	−	0.849507i	$-0.676900\pi$
$83$	−5.49654e6	−1.05516	−0.527578	+	0.849507i	$0.676900\pi$
$84$	−84123.9	−0.0154861
$85$	253587.	0.0447878
$86$	−661036.	−0.112068
$87$	−562351.	−0.0915566
$88$	8.75509e6	1.36953
$89$	−8.18997e6	−1.23145	−0.615726	−	0.787960i	$-0.711137\pi$
$89$	−8.18997e6	−1.23145	−0.615726	+	0.787960i	$0.711137\pi$
$90$	2.52430e6	0.364999
$91$	−945564.	−0.131536
$92$	4.53669e6	0.607409
$93$	−2.25030e6	−0.290101
$94$	5.15075e6	0.639622
$95$	−7.57535e6	−0.906505
$96$	−1.80237e6	−0.207920
$97$	1.20009e7	1.33510	0.667548	−	0.744567i	$-0.267344\pi$
$97$	1.20009e7	1.33510	0.667548	+	0.744567i	$0.267344\pi$
$98$	6.72296e6	0.721555
$99$	−1.15531e7	−1.19667
$100$	3.30847e6	0.330847
$101$	−1.45741e7	−1.40752	−0.703762	−	0.710436i	$-0.748498\pi$
$101$	−1.45741e7	−1.40752	−0.703762	+	0.710436i	$0.748498\pi$
$102$	−166493.	−0.0155344
$103$	3.29091e6	0.296747	0.148373	−	0.988931i	$-0.452596\pi$
$103$	3.29091e6	0.296747	0.148373	+	0.988931i	$0.452596\pi$
$104$	−1.20234e7	−1.04812
$105$	211596.	0.0178380
$106$	−4.77511e6	−0.389415
$107$	2.34488e7	1.85045	0.925226	−	0.379416i	$-0.123875\pi$
$107$	2.34488e7	1.85045	0.925226	+	0.379416i	$0.123875\pi$
$108$	2.91724e6	0.222838
$109$	2.05051e7	1.51659	0.758296	−	0.651910i	$-0.226032\pi$
$109$	2.05051e7	1.51659	0.758296	+	0.651910i	$0.226032\pi$
$110$	−6.93785e6	−0.496993
$111$	5.39446e6	0.374384
$112$	−657611.	−0.0442289
$113$	−4.02775e6	−0.262596	−0.131298	−	0.991343i	$-0.541914\pi$
$113$	−4.02775e6	−0.262596	−0.131298	+	0.991343i	$0.541914\pi$
$114$	4.97361e6	0.314416
$115$	−1.14111e7	−0.699656
$116$	2.83119e6	0.168409
$117$	1.58660e7	0.915832
$118$	8.42755e6	0.472187
$119$	209240.	0.0113823
$120$	2.69058e6	0.142138
$121$	1.22656e7	0.629421
$122$	2.68755e7	1.33998
$123$	8.05448e6	0.390274
$124$	1.13293e7	0.533612
$125$	−1.98910e7	−0.910901
$126$	2.08285e6	0.0927602
$127$	−1.44813e7	−0.627328	−0.313664	−	0.949534i	$-0.601557\pi$
$127$	−1.44813e7	−0.627328	−0.313664	+	0.949534i	$0.601557\pi$
$128$	3.34664e6	0.141050
$129$	929754.	0.0381333
$130$	9.52781e6	0.380357
$131$	−1.55714e7	−0.605170	−0.302585	−	0.953122i	$-0.597850\pi$
$131$	−1.55714e7	−0.605170	−0.302585	+	0.953122i	$0.597850\pi$
$132$	−3.87953e6	−0.146815
$133$	−6.25058e6	−0.230377
$134$	−2.62641e7	−0.942966
$135$	−7.33771e6	−0.256680
$136$	2.66062e6	0.0906976
$137$	−2.42862e7	−0.806932	−0.403466	−	0.914995i	$-0.632195\pi$
$137$	−2.42862e7	−0.806932	−0.403466	+	0.914995i	$0.632195\pi$
$138$	7.49198e6	0.242672
$139$	5.15045e7	1.62665	0.813323	−	0.581812i	$-0.197656\pi$
$139$	5.15045e7	1.62665	0.813323	+	0.581812i	$0.197656\pi$
$140$	−1.06530e6	−0.0328112
$141$	−7.24459e6	−0.217644
$142$	−2.04780e7	−0.600175
$143$	−4.36064e7	−1.24702
$144$	1.10343e7	0.307947
$145$	−7.12128e6	−0.193986
$146$	3.34838e7	0.890431
$147$	−9.45591e6	−0.245523
$148$	−2.71588e7	−0.688644
$149$	2.03855e7	0.504858	0.252429	−	0.967615i	$-0.418771\pi$
$149$	2.03855e7	0.504858	0.252429	+	0.967615i	$0.418771\pi$
$150$	5.46368e6	0.132180
$151$	−1.46726e7	−0.346806	−0.173403	−	0.984851i	$-0.555476\pi$
$151$	−1.46726e7	−0.346806	−0.173403	+	0.984851i	$0.555476\pi$
$152$	−7.94801e7	−1.83572
$153$	−3.51091e6	−0.0792501
$154$	−5.72457e6	−0.126305
$155$	−2.84964e7	−0.614652
$156$	5.32780e6	0.112360
$157$	−1.07322e7	−0.221329	−0.110665	−	0.993858i	$-0.535298\pi$
$157$	−1.07322e7	−0.221329	−0.110665	+	0.993858i	$0.535298\pi$
$158$	3.85358e6	0.0777257
$159$	6.71624e6	0.132506
$160$	−2.28242e7	−0.440530
$161$	−9.41554e6	−0.177809
$162$	−3.24624e7	−0.599899
$163$	−3.08777e7	−0.558454	−0.279227	−	0.960225i	$-0.590078\pi$
$163$	−3.08777e7	−0.558454	−0.279227	+	0.960225i	$0.590078\pi$
$164$	−4.05509e7	−0.717871
$165$	9.75815e6	0.169112
$166$	4.56993e7	0.775410
$167$	−9.20853e6	−0.152997	−0.0764985	−	0.997070i	$-0.524374\pi$
$167$	−9.20853e6	−0.152997	−0.0764985	+	0.997070i	$0.524374\pi$
$168$	2.22006e6	0.0361228
$169$	−2.86337e6	−0.0456325
$170$	−2.10837e6	−0.0329136
$171$	1.04881e8	1.60402
$172$	−4.68091e6	−0.0701425
$173$	1.49747e7	0.219885	0.109943	−	0.993938i	$-0.464933\pi$
$173$	1.49747e7	0.219885	0.109943	+	0.993938i	$0.464933\pi$
$174$	4.67549e6	0.0672829
$175$	−6.86647e6	−0.0968502
$176$	−3.03270e7	−0.419309
$177$	−1.18534e7	−0.160671
$178$	6.80930e7	0.904967
$179$	8.89995e7	1.15985	0.579925	−	0.814670i	$-0.303082\pi$
$179$	8.89995e7	1.15985	0.579925	+	0.814670i	$0.303082\pi$
$180$	1.78750e7	0.228450
$181$	5.85628e7	0.734086	0.367043	−	0.930204i	$-0.380370\pi$
$181$	5.85628e7	0.734086	0.367043	+	0.930204i	$0.380370\pi$
$182$	7.86160e6	0.0966632
$183$	−3.78007e7	−0.455954
$184$	−1.19725e8	−1.41684
$185$	6.83123e7	0.793228
$186$	1.87094e7	0.213189
$187$	9.64948e6	0.107909
$188$	3.64734e7	0.400335
$189$	−6.05450e6	−0.0652322
$190$	6.29829e7	0.666170
$191$	2.81969e7	0.292809	0.146404	−	0.989225i	$-0.453230\pi$
$191$	2.81969e7	0.292809	0.146404	+	0.989225i	$0.453230\pi$
$192$	2.30411e7	0.234936
$193$	−1.42485e8	−1.42665	−0.713325	−	0.700833i	$-0.752812\pi$
$193$	−1.42485e8	−1.42665	−0.713325	+	0.700833i	$0.752812\pi$
$194$	−9.97778e7	−0.981133
$195$	−1.34010e7	−0.129424
$196$	4.76064e7	0.451616
$197$	1.07088e8	0.997951	0.498976	−	0.866616i	$-0.333710\pi$
$197$	1.07088e8	0.997951	0.498976	+	0.866616i	$0.333710\pi$
$198$	9.60546e7	0.879407
$199$	1.37599e8	1.23774	0.618871	−	0.785493i	$-0.287590\pi$
$199$	1.37599e8	1.23774	0.618871	+	0.785493i	$0.287590\pi$
$200$	−8.73115e7	−0.771732
$201$	3.69407e7	0.320863
$202$	1.21171e8	1.03436
$203$	−5.87592e6	−0.0492992
$204$	−1.17896e6	−0.00972288
$205$	1.01997e8	0.826894
$206$	−2.73613e7	−0.218073
$207$	1.57987e8	1.23801
$208$	4.16483e7	0.320904
$209$	−2.88257e8	−2.18408
$210$	−1.75925e6	−0.0131087
$211$	1.52091e8	1.11459	0.557295	−	0.830314i	$-0.311839\pi$
$211$	1.52091e8	1.11459	0.557295	+	0.830314i	$0.311839\pi$
$212$	−3.38134e7	−0.243732
$213$	2.88025e7	0.204222
$214$	−1.94958e8	−1.35986
$215$	1.17739e7	0.0807950
$216$	−7.69868e7	−0.519790
$217$	−2.35130e7	−0.156206
$218$	−1.70483e8	−1.11451
$219$	−4.70953e7	−0.302987
$220$	−4.91281e7	−0.311064
$221$	−1.32517e7	−0.0825846
$222$	−4.48506e7	−0.275127
$223$	−1.58102e8	−0.954709	−0.477354	−	0.878711i	$-0.658404\pi$
$223$	−1.58102e8	−0.954709	−0.477354	+	0.878711i	$0.658404\pi$
$224$	−1.88328e7	−0.111956
$225$	1.15215e8	0.674327
$226$	3.34875e7	0.192976
$227$	1.42553e8	0.808886	0.404443	−	0.914563i	$-0.367465\pi$
$227$	1.42553e8	0.808886	0.404443	+	0.914563i	$0.367465\pi$
$228$	3.52190e7	0.196791
$229$	−1.08019e7	−0.0594395	−0.0297198	−	0.999558i	$-0.509461\pi$
$229$	−1.08019e7	−0.0594395	−0.0297198	+	0.999558i	$0.509461\pi$
$230$	9.48740e7	0.514162
$231$	8.05166e6	0.0429777
$232$	−7.47160e7	−0.392831
$233$	4.31324e7	0.223387	0.111694	−	0.993743i	$-0.464373\pi$
$233$	4.31324e7	0.223387	0.111694	+	0.993743i	$0.464373\pi$
$234$	−1.31913e8	−0.673025
$235$	−9.17412e7	−0.461134
$236$	5.96769e7	0.295539
$237$	−5.42010e6	−0.0264477
$238$	−1.73966e6	−0.00836459
$239$	−1.51247e8	−0.716631	−0.358315	−	0.933601i	$-0.616649\pi$
$239$	−1.51247e8	−0.716631	−0.358315	+	0.933601i	$0.616649\pi$
$240$	−9.31996e6	−0.0435186
$241$	−1.16354e7	−0.0535453	−0.0267726	−	0.999642i	$-0.508523\pi$
$241$	−1.16354e7	−0.0535453	−0.0267726	+	0.999642i	$0.508523\pi$
$242$	−1.01979e8	−0.462548
$243$	1.54025e8	0.688605
$244$	1.90310e8	0.838683
$245$	−1.19744e8	−0.520203
$246$	−6.69665e7	−0.286804
$247$	3.95866e8	1.67151
$248$	−2.98983e8	−1.24470
$249$	−6.42766e7	−0.263849
$250$	1.65377e8	0.669401
$251$	−1.76350e8	−0.703910	−0.351955	−	0.936017i	$-0.614483\pi$
$251$	−1.76350e8	−0.703910	−0.351955	+	0.936017i	$0.614483\pi$
$252$	1.47490e7	0.0580580
$253$	−4.34215e8	−1.68571
$254$	1.20400e8	0.461009
$255$	2.96544e6	0.0111995
$256$	−2.80028e8	−1.04319
$257$	−3.46637e8	−1.27382	−0.636912	−	0.770937i	$-0.719789\pi$
$257$	−3.46637e8	−1.27382	−0.636912	+	0.770937i	$0.719789\pi$
$258$	−7.73016e6	−0.0280233
$259$	5.63660e7	0.201589
$260$	6.74681e7	0.238063
$261$	9.85942e7	0.343249
$262$	1.29463e8	0.444726
$263$	3.71975e8	1.26087	0.630433	−	0.776244i	$-0.282878\pi$
$263$	3.71975e8	1.26087	0.630433	+	0.776244i	$0.282878\pi$
$264$	1.02382e8	0.342460
$265$	8.50505e7	0.280748
$266$	5.19686e7	0.169299
$267$	−9.57735e7	−0.307933
$268$	−1.85981e8	−0.590196
$269$	3.76594e8	1.17962	0.589808	−	0.807544i	$-0.299203\pi$
$269$	3.76594e8	1.17962	0.589808	+	0.807544i	$0.299203\pi$
$270$	6.10071e7	0.188629
$271$	1.87035e8	0.570862	0.285431	−	0.958399i	$-0.407863\pi$
$271$	1.87035e8	0.570862	0.285431	+	0.958399i	$0.407863\pi$
$272$	−9.21617e6	−0.0277689
$273$	−1.10574e7	−0.0328916
$274$	2.01920e8	0.592996
$275$	−3.16660e8	−0.918182
$276$	5.30520e7	0.151887
$277$	−2.58454e8	−0.730642	−0.365321	−	0.930882i	$-0.619041\pi$
$277$	−2.58454e8	−0.730642	−0.365321	+	0.930882i	$0.619041\pi$
$278$	−4.28218e8	−1.19539
$279$	3.94533e8	1.08760
$280$	2.81135e7	0.0765352
$281$	−3.07159e8	−0.825831	−0.412916	−	0.910769i	$-0.635490\pi$
$281$	−3.07159e8	−0.825831	−0.412916	+	0.910769i	$0.635490\pi$
$282$	6.02329e7	0.159942
$283$	−6.04080e8	−1.58432	−0.792159	−	0.610315i	$-0.791043\pi$
$283$	−6.04080e8	−1.58432	−0.792159	+	0.610315i	$0.791043\pi$
$284$	−1.45008e8	−0.375646
$285$	−8.85861e7	−0.226678
$286$	3.62552e8	0.916409
$287$	8.41601e7	0.210145
$288$	3.16002e8	0.779499
$289$	−4.07406e8	−0.992854
$290$	5.92077e7	0.142556
$291$	1.40338e8	0.333850
$292$	2.37105e8	0.557314
$293$	−1.79377e8	−0.416610	−0.208305	−	0.978064i	$-0.566795\pi$
$293$	−1.79377e8	−0.416610	−0.208305	+	0.978064i	$0.566795\pi$
$294$	7.86183e7	0.180430
$295$	−1.50105e8	−0.340422
$296$	7.16729e8	1.60633
$297$	−2.79215e8	−0.618430
$298$	−1.69489e8	−0.371009
$299$	5.96312e8	1.29010
$300$	3.86892e7	0.0827305
$301$	9.71487e6	0.0205331
$302$	1.21991e8	0.254860
$303$	−1.70429e8	−0.351961
$304$	2.75313e8	0.562043
$305$	−4.78686e8	−0.966054
$306$	2.91904e7	0.0582391
$307$	−1.45485e8	−0.286969	−0.143484	−	0.989653i	$-0.545831\pi$
$307$	−1.45485e8	−0.286969	−0.143484	+	0.989653i	$0.545831\pi$
$308$	−4.05366e7	−0.0790533
$309$	3.84839e7	0.0742036
$310$	2.36925e8	0.451694
$311$	3.56832e8	0.672670	0.336335	−	0.941742i	$-0.390813\pi$
$311$	3.56832e8	0.672670	0.336335	+	0.941742i	$0.390813\pi$
$312$	−1.40602e8	−0.262090
$313$	6.50132e8	1.19838	0.599192	−	0.800605i	$-0.295489\pi$
$313$	6.50132e8	1.19838	0.599192	+	0.800605i	$0.295489\pi$
$314$	8.92293e7	0.162650
$315$	−3.70981e7	−0.0668752
$316$	2.72879e7	0.0486480
$317$	−1.34462e8	−0.237078	−0.118539	−	0.992949i	$-0.537821\pi$
$317$	−1.34462e8	−0.237078	−0.118539	+	0.992949i	$0.537821\pi$
$318$	−5.58401e7	−0.0973759
$319$	−2.70979e8	−0.467378
$320$	2.91779e8	0.497771
$321$	2.74210e8	0.462718
$322$	7.82826e7	0.130668
$323$	−8.75995e7	−0.144642
$324$	−2.29872e8	−0.375472
$325$	4.34872e8	0.702700
$326$	2.56723e8	0.410396
$327$	2.39786e8	0.379234
$328$	1.07015e9	1.67450
$329$	−7.56976e7	−0.117192
$330$	−8.11311e7	−0.124276
$331$	6.61036e8	1.00191	0.500953	−	0.865474i	$-0.332983\pi$
$331$	6.61036e8	1.00191	0.500953	+	0.865474i	$0.332983\pi$
$332$	3.23605e8	0.485324
$333$	−9.45785e8	−1.40358
$334$	7.65615e7	0.112434
$335$	4.67796e8	0.679828
$336$	−7.69010e6	−0.0110597
$337$	−2.64722e8	−0.376778	−0.188389	−	0.982094i	$-0.560327\pi$
$337$	−2.64722e8	−0.376778	−0.188389	+	0.982094i	$0.560327\pi$
$338$	2.38066e7	0.0335343
$339$	−4.71005e7	−0.0656638
$340$	−1.49297e7	−0.0206004
$341$	−1.08435e9	−1.48091
$342$	−8.71999e8	−1.17876
$343$	−1.99431e8	−0.266848
$344$	1.23531e8	0.163614
$345$	−1.33441e8	−0.174954
$346$	−1.24502e8	−0.161589
$347$	−3.92072e8	−0.503748	−0.251874	−	0.967760i	$-0.581047\pi$
$347$	−3.92072e8	−0.503748	−0.251874	+	0.967760i	$0.581047\pi$
$348$	3.31080e7	0.0421119
$349$	−2.58464e8	−0.325470	−0.162735	−	0.986670i	$-0.552032\pi$
$349$	−2.58464e8	−0.325470	−0.162735	+	0.986670i	$0.552032\pi$
$350$	5.70892e7	0.0711731
$351$	3.83448e8	0.473295
$352$	−8.68507e8	−1.06139
$353$	−2.36908e8	−0.286661	−0.143331	−	0.989675i	$-0.545781\pi$
$353$	−2.36908e8	−0.286661	−0.143331	+	0.989675i	$0.545781\pi$
$354$	9.85517e7	0.118074
$355$	3.64738e8	0.432695
$356$	4.82178e8	0.566412
$357$	2.44685e6	0.00284622
$358$	−7.39959e8	−0.852348
$359$	−1.22528e9	−1.39767	−0.698836	−	0.715282i	$-0.746298\pi$
$359$	−1.22528e9	−1.39767	−0.698836	+	0.715282i	$0.746298\pi$
$360$	−4.71726e8	−0.532882
$361$	1.72297e9	1.92754
$362$	−4.86903e8	−0.539464
$363$	1.43434e8	0.157391
$364$	5.56694e7	0.0605008
$365$	−5.96388e8	−0.641953
$366$	3.14283e8	0.335071
$367$	−4.80402e8	−0.507311	−0.253655	−	0.967295i	$-0.581633\pi$
$367$	−4.80402e8	−0.507311	−0.253655	+	0.967295i	$0.581633\pi$
$368$	4.14717e8	0.433795
$369$	−1.41215e9	−1.46315
$370$	−5.67962e8	−0.582925
$371$	7.01770e7	0.0713488
$372$	1.32484e8	0.133433
$373$	−1.06518e9	−1.06278	−0.531389	−	0.847128i	$-0.678330\pi$
$373$	−1.06518e9	−1.06278	−0.531389	+	0.847128i	$0.678330\pi$
$374$	−8.02276e7	−0.0793000
$375$	−2.32605e8	−0.227777
$376$	−9.62543e8	−0.933819
$377$	3.72138e8	0.357692
$378$	5.03383e7	0.0479377
$379$	1.57397e9	1.48511	0.742554	−	0.669786i	$-0.233614\pi$
$379$	1.57397e9	1.48511	0.742554	+	0.669786i	$0.233614\pi$
$380$	4.45993e8	0.416951
$381$	−1.69344e8	−0.156867
$382$	−2.34434e8	−0.215179
$383$	−8.92980e8	−0.812168	−0.406084	−	0.913836i	$-0.633106\pi$
$383$	−8.92980e8	−0.812168	−0.406084	+	0.913836i	$0.633106\pi$
$384$	3.91356e7	0.0352706
$385$	1.01961e8	0.0910591
$386$	1.18464e9	1.04841
$387$	−1.63009e8	−0.142963
$388$	−7.06543e8	−0.614084
$389$	2.17007e9	1.86917	0.934586	−	0.355737i	$-0.115770\pi$
$389$	2.17007e9	1.86917	0.934586	+	0.355737i	$0.115770\pi$
$390$	1.11418e8	0.0951108
$391$	−1.31955e8	−0.111637
$392$	−1.25635e9	−1.05344
$393$	−1.82092e8	−0.151327
$394$	−8.90351e8	−0.733372
$395$	−6.86370e7	−0.0560362
$396$	6.80179e8	0.550415
$397$	−1.33189e9	−1.06832	−0.534162	−	0.845382i	$-0.679373\pi$
$397$	−1.33189e9	−1.06832	−0.534162	+	0.845382i	$0.679373\pi$
$398$	−1.14403e9	−0.909589
$399$	−7.30943e7	−0.0576074
$400$	3.02441e8	0.236282
$401$	3.57769e8	0.277075	0.138538	−	0.990357i	$-0.455760\pi$
$401$	3.57769e8	0.277075	0.138538	+	0.990357i	$0.455760\pi$
$402$	−3.07132e8	−0.235795
$403$	1.48914e9	1.13336
$404$	8.58036e8	0.647397
$405$	5.78195e8	0.432495
$406$	4.88535e7	0.0362289
$407$	2.59942e9	1.91116
$408$	3.11132e7	0.0226795
$409$	7.47840e8	0.540477	0.270238	−	0.962793i	$-0.412897\pi$
$409$	7.47840e8	0.540477	0.270238	+	0.962793i	$0.412897\pi$
$410$	−8.48024e8	−0.607666
$411$	−2.84002e8	−0.201779
$412$	−1.93750e8	−0.136490
$413$	−1.23855e8	−0.0865143
$414$	−1.31353e9	−0.909787
$415$	−8.13960e8	−0.559030
$416$	1.19273e9	0.812298
$417$	6.02293e8	0.406754
$418$	2.39663e9	1.60503
$419$	9.00703e8	0.598181	0.299091	−	0.954225i	$-0.403317\pi$
$419$	9.00703e8	0.598181	0.299091	+	0.954225i	$0.403317\pi$
$420$	−1.24576e7	−0.00820466
$421$	−1.70587e9	−1.11419	−0.557094	−	0.830449i	$-0.688084\pi$
$421$	−1.70587e9	−1.11419	−0.557094	+	0.830449i	$0.688084\pi$
$422$	−1.26451e9	−0.819088
$423$	1.27016e9	0.815955
$424$	8.92345e8	0.568529
$425$	−9.62310e7	−0.0608070
$426$	−2.39470e8	−0.150078
$427$	−3.94974e8	−0.245511
$428$	−1.38053e9	−0.851124
$429$	−5.09933e8	−0.311826
$430$	−9.78901e7	−0.0593744
$431$	1.88962e9	1.13685	0.568425	−	0.822735i	$-0.307553\pi$
$431$	1.88962e9	1.13685	0.568425	+	0.822735i	$0.307553\pi$
$432$	2.66677e8	0.159145
$433$	7.46212e7	0.0441728	0.0220864	−	0.999756i	$-0.492969\pi$
$433$	7.46212e7	0.0441728	0.0220864	+	0.999756i	$0.492969\pi$
$434$	1.95492e8	0.114793
$435$	−8.32762e7	−0.0485074
$436$	−1.20722e9	−0.697564
$437$	3.94188e9	2.25953
$438$	3.91560e8	0.222658
$439$	−1.72954e9	−0.975677	−0.487838	−	0.872934i	$-0.662214\pi$
$439$	−1.72954e9	−0.975677	−0.487838	+	0.872934i	$0.662214\pi$
$440$	1.29650e9	0.725587
$441$	1.65786e9	0.920476
$442$	1.10177e8	0.0606896
$443$	3.58748e9	1.96054	0.980270	−	0.197661i	$-0.0633346\pi$
$443$	3.58748e9	1.96054	0.980270	+	0.197661i	$0.0633346\pi$
$444$	−3.17595e8	−0.172200
$445$	−1.21282e9	−0.652433
$446$	1.31449e9	0.701594
$447$	2.38388e8	0.126243
$448$	2.40753e8	0.126503
$449$	−3.27797e9	−1.70900	−0.854502	−	0.519447i	$-0.826138\pi$
$449$	−3.27797e9	−1.70900	−0.854502	+	0.519447i	$0.826138\pi$
$450$	−9.57920e8	−0.495548
$451$	3.88120e9	1.99227
$452$	2.37130e8	0.120782
$453$	−1.71581e8	−0.0867213
$454$	−1.18522e9	−0.594432
$455$	−1.40025e8	−0.0696891
$456$	−9.29440e8	−0.459034
$457$	−1.77071e9	−0.867842	−0.433921	−	0.900951i	$-0.642870\pi$
$457$	−1.77071e9	−0.867842	−0.433921	+	0.900951i	$0.642870\pi$
$458$	8.98089e7	0.0436808
$459$	−8.48515e7	−0.0409558
$460$	6.71819e8	0.321810
$461$	2.35457e9	1.11933	0.559664	−	0.828719i	$-0.310930\pi$
$461$	2.35457e9	1.11933	0.559664	+	0.828719i	$0.310930\pi$
$462$	−6.69431e7	−0.0315834
$463$	−4.94391e8	−0.231493	−0.115746	−	0.993279i	$-0.536926\pi$
$463$	−4.94391e8	−0.231493	−0.115746	+	0.993279i	$0.536926\pi$
$464$	2.58811e8	0.120273
$465$	−3.33237e8	−0.153698
$466$	−3.58611e8	−0.164162
$467$	−3.45960e9	−1.57187	−0.785935	−	0.618309i	$-0.787818\pi$
$467$	−3.45960e9	−1.57187	−0.785935	+	0.618309i	$0.787818\pi$
$468$	−9.34096e8	−0.421241
$469$	3.85988e8	0.172770
$470$	7.62754e8	0.338877
$471$	−1.25502e8	−0.0553449
$472$	−1.57489e9	−0.689372
$473$	4.48019e8	0.194663
$474$	4.50638e7	0.0194358
$475$	2.87469e9	1.23073
$476$	−1.23188e7	−0.00523534
$477$	−1.17753e9	−0.496771
$478$	1.25750e9	0.526636
$479$	−2.26891e9	−0.943284	−0.471642	−	0.881790i	$-0.656338\pi$
$479$	−2.26891e9	−0.943284	−0.471642	+	0.881790i	$0.656338\pi$
$480$	−2.66906e8	−0.110158
$481$	−3.56981e9	−1.46264
$482$	9.67389e7	0.0393492
$483$	−1.10105e8	−0.0444624
$484$	−7.22130e8	−0.289505
$485$	1.77716e9	0.707345
$486$	−1.28060e9	−0.506041
$487$	−2.51843e9	−0.988051	−0.494025	−	0.869447i	$-0.664475\pi$
$487$	−2.51843e9	−0.988051	−0.494025	+	0.869447i	$0.664475\pi$
$488$	−5.02235e9	−1.95631
$489$	−3.61083e8	−0.139645
$490$	9.95576e8	0.382286
$491$	7.20363e8	0.274642	0.137321	−	0.990527i	$-0.456151\pi$
$491$	7.20363e8	0.274642	0.137321	+	0.990527i	$0.456151\pi$
$492$	−4.74201e8	−0.179508
$493$	−8.23487e7	−0.0309523
$494$	−3.29131e9	−1.22836
$495$	−1.71085e9	−0.634006
$496$	1.03565e9	0.381091
$497$	3.00953e8	0.109964
$498$	5.34408e8	0.193896
$499$	−2.15427e9	−0.776154	−0.388077	−	0.921627i	$-0.626861\pi$
$499$	−2.15427e9	−0.776154	−0.388077	+	0.921627i	$0.626861\pi$
$500$	1.17107e9	0.418973
$501$	−1.07684e8	−0.0382579
$502$	1.46621e9	0.517288
$503$	2.80736e9	0.983579	0.491790	−	0.870714i	$-0.336343\pi$
$503$	2.80736e9	0.983579	0.491790	+	0.870714i	$0.336343\pi$
$504$	−3.89231e8	−0.135426
$505$	−2.15821e9	−0.745717
$506$	3.61015e9	1.23879
$507$	−3.34842e7	−0.0114107
$508$	8.52575e8	0.288542
$509$	−2.99574e9	−1.00691	−0.503457	−	0.864020i	$-0.667939\pi$
$509$	−2.99574e9	−1.00691	−0.503457	+	0.864020i	$0.667939\pi$
$510$	−2.46552e7	−0.00823026
$511$	−4.92092e8	−0.163145
$512$	1.89984e9	0.625563
$513$	2.53476e9	0.828944
$514$	2.88201e9	0.936105
$515$	4.87338e8	0.157219
$516$	−5.47386e7	−0.0175396
$517$	−3.49094e9	−1.11103
$518$	−4.68637e8	−0.148144
$519$	1.75114e8	0.0549838
$520$	−1.78050e9	−0.555304
$521$	2.58005e9	0.799275	0.399637	−	0.916673i	$-0.369136\pi$
$521$	2.58005e9	0.799275	0.399637	+	0.916673i	$0.369136\pi$
$522$	−8.19731e8	−0.252246
$523$	1.70818e9	0.522129	0.261064	−	0.965321i	$-0.415926\pi$
$523$	1.70818e9	0.522129	0.261064	+	0.965321i	$0.415926\pi$
$524$	9.16753e8	0.278351
$525$	−8.02965e7	−0.0242180
$526$	−3.09267e9	−0.926582
$527$	−3.29526e8	−0.0980736
$528$	−3.54643e8	−0.104851
$529$	2.53300e9	0.743944
$530$	−7.07126e8	−0.206315
$531$	2.07820e9	0.602362
$532$	3.67998e8	0.105963
$533$	−5.33009e9	−1.52472
$534$	7.96279e8	0.226293
$535$	3.47244e9	0.980384
$536$	4.90809e9	1.37669
$537$	1.04076e9	0.290028
$538$	−3.13108e9	−0.866873
$539$	−4.55650e9	−1.25335
$540$	4.32002e8	0.118061
$541$	−4.88301e9	−1.32586	−0.662929	−	0.748682i	$-0.730687\pi$
$541$	−4.88301e9	−1.32586	−0.662929	+	0.748682i	$0.730687\pi$
$542$	−1.55505e9	−0.419514
$543$	6.84834e8	0.183563
$544$	−2.63934e8	−0.0702909
$545$	3.03651e9	0.803503
$546$	9.19335e7	0.0241713
$547$	−6.00910e9	−1.56984	−0.784918	−	0.619600i	$-0.787295\pi$
$547$	−6.00910e9	−1.56984	−0.784918	+	0.619600i	$0.787295\pi$
$548$	1.42983e9	0.371152
$549$	6.62742e9	1.70939
$550$	2.63277e9	0.674752
$551$	2.45999e9	0.626474
$552$	−1.40006e9	−0.354290
$553$	−5.66339e7	−0.0142409
$554$	2.14884e9	0.536932
$555$	7.98844e8	0.198352
$556$	−3.03229e9	−0.748184
$557$	−3.64266e9	−0.893152	−0.446576	−	0.894746i	$-0.647357\pi$
$557$	−3.64266e9	−0.893152	−0.446576	+	0.894746i	$0.647357\pi$
$558$	−3.28022e9	−0.799252
$559$	−6.15269e8	−0.148979
$560$	−9.73829e7	−0.0234328
$561$	1.12841e8	0.0269834
$562$	2.55378e9	0.606885
$563$	9.78473e8	0.231084	0.115542	−	0.993303i	$-0.463140\pi$
$563$	9.78473e8	0.231084	0.115542	+	0.993303i	$0.463140\pi$
$564$	4.26519e8	0.100106
$565$	−5.96452e8	−0.139125
$566$	5.02244e9	1.16428
$567$	4.77081e8	0.109914
$568$	3.82681e9	0.876229
$569$	−2.98433e9	−0.679131	−0.339566	−	0.940582i	$-0.610280\pi$
$569$	−2.98433e9	−0.679131	−0.339566	+	0.940582i	$0.610280\pi$
$570$	7.36522e8	0.166580
$571$	4.09176e9	0.919779	0.459890	−	0.887976i	$-0.347889\pi$
$571$	4.09176e9	0.919779	0.459890	+	0.887976i	$0.347889\pi$
$572$	2.56729e9	0.573574
$573$	3.29734e8	0.0732188
$574$	−6.99723e8	−0.154431
$575$	4.33028e9	0.949901
$576$	−4.03969e9	−0.880783
$577$	−3.21664e9	−0.697087	−0.348544	−	0.937293i	$-0.613324\pi$
$577$	−3.21664e9	−0.697087	−0.348544	+	0.937293i	$0.613324\pi$
$578$	3.38725e9	0.729626
$579$	−1.66621e9	−0.356743
$580$	4.19260e8	0.0892247
$581$	−6.71616e8	−0.142071
$582$	−1.16680e9	−0.245339
$583$	3.23634e9	0.676417
$584$	−6.25726e9	−1.29999
$585$	2.34952e9	0.485215
$586$	1.49137e9	0.306157
$587$	−3.18322e9	−0.649582	−0.324791	−	0.945786i	$-0.605294\pi$
$587$	−3.18322e9	−0.649582	−0.324791	+	0.945786i	$0.605294\pi$
$588$	5.56710e8	0.112930
$589$	9.84387e9	1.98501
$590$	1.24800e9	0.250169
$591$	1.25229e9	0.249544
$592$	−2.48269e9	−0.491810
$593$	−1.62368e9	−0.319749	−0.159875	−	0.987137i	$-0.551109\pi$
$593$	−1.62368e9	−0.319749	−0.159875	+	0.987137i	$0.551109\pi$
$594$	2.32144e9	0.454470
$595$	3.09854e7	0.00603043
$596$	−1.20018e9	−0.232212
$597$	1.60908e9	0.309506
$598$	−4.95785e9	−0.948067
$599$	−3.68608e9	−0.700763	−0.350382	−	0.936607i	$-0.613948\pi$
$599$	−3.68608e9	−0.700763	−0.350382	+	0.936607i	$0.613948\pi$
$600$	−1.02102e9	−0.192977
$601$	−2.91768e9	−0.548248	−0.274124	−	0.961694i	$-0.588388\pi$
$601$	−2.91768e9	−0.548248	−0.274124	+	0.961694i	$0.588388\pi$
$602$	−8.07713e7	−0.0150893
$603$	−6.47664e9	−1.20293
$604$	8.63837e8	0.159515
$605$	1.81637e9	0.333472
$606$	1.41698e9	0.258648
$607$	−3.35727e9	−0.609292	−0.304646	−	0.952466i	$-0.598538\pi$
$607$	−3.35727e9	−0.609292	−0.304646	+	0.952466i	$0.598538\pi$
$608$	7.88445e9	1.42269
$609$	−6.87130e7	−0.0123276
$610$	3.97989e9	0.709931
$611$	4.79414e9	0.850288
$612$	2.06702e8	0.0364514
$613$	1.51150e9	0.265030	0.132515	−	0.991181i	$-0.457695\pi$
$613$	1.51150e9	0.265030	0.132515	+	0.991181i	$0.457695\pi$
$614$	1.20959e9	0.210887
$615$	1.19275e9	0.206770
$616$	1.06977e9	0.184399
$617$	−5.64788e9	−0.968026	−0.484013	−	0.875061i	$-0.660821\pi$
$617$	−5.64788e9	−0.968026	−0.484013	+	0.875061i	$0.660821\pi$
$618$	−3.19963e8	−0.0545305
$619$	−2.42139e9	−0.410343	−0.205172	−	0.978726i	$-0.565775\pi$
$619$	−2.42139e9	−0.410343	−0.205172	+	0.978726i	$0.565775\pi$
$620$	1.67770e9	0.282712
$621$	3.81822e9	0.639794
$622$	−2.96677e9	−0.494330
$623$	−1.00072e9	−0.165808
$624$	4.87035e8	0.0802443
$625$	1.44471e9	0.236701
$626$	−5.40532e9	−0.880666
$627$	−3.37088e9	−0.546143
$628$	6.31848e8	0.101801
$629$	7.89947e8	0.126567
$630$	3.08441e8	0.0491451
$631$	7.99860e9	1.26739	0.633696	−	0.773582i	$-0.281537\pi$
$631$	7.99860e9	1.26739	0.633696	+	0.773582i	$0.281537\pi$
$632$	−7.20135e8	−0.113476
$633$	1.77855e9	0.278711
$634$	1.11794e9	0.174223
$635$	−2.14448e9	−0.332363
$636$	−3.95414e8	−0.0609469
$637$	6.25749e9	0.959207
$638$	2.25297e9	0.343465
$639$	−5.04980e9	−0.765634
$640$	4.95591e8	0.0747297
$641$	9.69674e8	0.145419	0.0727097	−	0.997353i	$-0.476835\pi$
$641$	9.69674e8	0.145419	0.0727097	+	0.997353i	$0.476835\pi$
$642$	−2.27984e9	−0.340041
$643$	3.12786e9	0.463990	0.231995	−	0.972717i	$-0.425475\pi$
$643$	3.12786e9	0.463990	0.231995	+	0.972717i	$0.425475\pi$
$644$	5.54333e8	0.0817843
$645$	1.37683e8	0.0202033
$646$	7.28319e8	0.106294
$647$	−1.05397e10	−1.52990	−0.764949	−	0.644091i	$-0.777236\pi$
$647$	−1.05397e10	−1.52990	−0.764949	+	0.644091i	$0.777236\pi$
$648$	6.06638e9	0.875825
$649$	−5.71179e9	−0.820193
$650$	−3.61561e9	−0.516399
$651$	−2.74961e8	−0.0390605
$652$	1.81790e9	0.256864
$653$	−1.16184e10	−1.63286	−0.816430	−	0.577444i	$-0.804050\pi$
$653$	−1.16184e10	−1.63286	−0.816430	+	0.577444i	$0.804050\pi$
$654$	−1.99363e9	−0.278691
$655$	−2.30590e9	−0.320624
$656$	−3.70692e9	−0.512683
$657$	8.25699e9	1.13591
$658$	6.29365e8	0.0861215
$659$	−5.81607e9	−0.791645	−0.395822	−	0.918327i	$-0.629540\pi$
$659$	−5.81607e9	−0.791645	−0.395822	+	0.918327i	$0.629540\pi$
$660$	−5.74503e8	−0.0777837
$661$	8.71459e9	1.17366	0.586830	−	0.809710i	$-0.300376\pi$
$661$	8.71459e9	1.17366	0.586830	+	0.809710i	$0.300376\pi$
$662$	−5.49598e9	−0.736278
$663$	−1.54966e8	−0.0206508
$664$	−8.54003e9	−1.13206
$665$	−9.25623e8	−0.122056
$666$	7.86344e9	1.03146
$667$	3.70560e9	0.483524
$668$	5.42145e8	0.0703717
$669$	−1.84885e9	−0.238731
$670$	−3.88934e9	−0.499591
$671$	−1.82150e10	−2.32755
$672$	−2.20230e8	−0.0279952
$673$	1.52007e10	1.92226	0.961129	−	0.276098i	$-0.0890415\pi$
$673$	1.52007e10	1.92226	0.961129	+	0.276098i	$0.0890415\pi$
$674$	2.20095e9	0.276886
$675$	2.78451e9	0.348487
$676$	1.68579e8	0.0209889
$677$	−7.66446e9	−0.949339	−0.474670	−	0.880164i	$-0.657432\pi$
$677$	−7.66446e9	−0.949339	−0.474670	+	0.880164i	$0.657432\pi$
$678$	3.91602e8	0.0482549
$679$	1.46638e9	0.179763
$680$	3.93999e8	0.0480523
$681$	1.66702e9	0.202267
$682$	9.01546e9	1.08828
$683$	−5.86341e9	−0.704170	−0.352085	−	0.935968i	$-0.614527\pi$
$683$	−5.86341e9	−0.704170	−0.352085	+	0.935968i	$0.614527\pi$
$684$	−6.17478e9	−0.737776
$685$	−3.59644e9	−0.427519
$686$	1.65811e9	0.196101
$687$	−1.26317e8	−0.0148632
$688$	−4.27901e8	−0.0500938
$689$	−4.44450e9	−0.517673
$690$	1.10946e9	0.128570
$691$	−2.93527e9	−0.338435	−0.169218	−	0.985579i	$-0.554124\pi$
$691$	−2.93527e9	−0.338435	−0.169218	+	0.985579i	$0.554124\pi$
$692$	−8.81623e8	−0.101137
$693$	−1.41166e9	−0.161125
$694$	3.25976e9	0.370193
$695$	7.62708e9	0.861810
$696$	−8.73729e8	−0.0982300
$697$	1.17947e9	0.131939
$698$	2.14892e9	0.239181
$699$	5.04390e8	0.0558594
$700$	4.04258e8	0.0445467
$701$	−1.59500e10	−1.74883	−0.874415	−	0.485178i	$-0.838755\pi$
$701$	−1.59500e10	−1.74883	−0.874415	+	0.485178i	$0.838755\pi$
$702$	−3.18806e9	−0.347814
$703$	−2.35980e10	−2.56172
$704$	1.11028e10	1.19930
$705$	−1.07282e9	−0.115310
$706$	1.96970e9	0.210661
$707$	−1.78079e9	−0.189515
$708$	6.97862e8	0.0739015
$709$	−5.26013e9	−0.554287	−0.277143	−	0.960829i	$-0.589388\pi$
$709$	−5.26013e9	−0.554287	−0.277143	+	0.960829i	$0.589388\pi$
$710$	−3.03250e9	−0.317978
$711$	9.50280e8	0.0991535
$712$	−1.27248e10	−1.32121
$713$	1.48283e10	1.53206
$714$	−2.03436e7	−0.00209162
$715$	−6.45750e9	−0.660683
$716$	−5.23978e9	−0.533479
$717$	−1.76869e9	−0.179198
$718$	1.01872e10	1.02712
$719$	1.60266e10	1.60802	0.804008	−	0.594618i	$-0.202697\pi$
$719$	1.60266e10	1.60802	0.804008	+	0.594618i	$0.202697\pi$
$720$	1.63402e9	0.163153
$721$	4.02113e8	0.0399553
$722$	−1.43251e10	−1.41651
$723$	−1.36064e8	−0.0133894
$724$	−3.44784e9	−0.337647
$725$	2.70238e9	0.263368
$726$	−1.19254e9	−0.115663
$727$	1.07033e10	1.03311	0.516556	−	0.856253i	$-0.327214\pi$
$727$	1.07033e10	1.03311	0.516556	+	0.856253i	$0.327214\pi$
$728$	−1.46913e9	−0.141124
$729$	−6.73787e9	−0.644134
$730$	4.95848e9	0.471757
$731$	1.36150e8	0.0128916
$732$	2.22549e9	0.209718
$733$	1.43369e10	1.34460	0.672298	−	0.740280i	$-0.265307\pi$
$733$	1.43369e10	1.34460	0.672298	+	0.740280i	$0.265307\pi$
$734$	3.99416e9	0.372811
$735$	−1.40029e9	−0.130080
$736$	1.18767e10	1.09805
$737$	1.78006e10	1.63794
$738$	1.17409e10	1.07524
$739$	2.07369e10	1.89012	0.945060	−	0.326898i	$-0.106003\pi$
$739$	2.07369e10	1.89012	0.945060	+	0.326898i	$0.106003\pi$
$740$	−4.02183e9	−0.364849
$741$	4.62926e9	0.417973
$742$	−5.83465e8	−0.0524326
$743$	−5.43590e9	−0.486196	−0.243098	−	0.970002i	$-0.578164\pi$
$743$	−5.43590e9	−0.486196	−0.243098	+	0.970002i	$0.578164\pi$
$744$	−3.49630e9	−0.311246
$745$	3.01880e9	0.267478
$746$	8.85612e9	0.781012
$747$	1.12693e10	0.989178
$748$	−5.68105e8	−0.0496333
$749$	2.86518e9	0.249153
$750$	1.93392e9	0.167388
$751$	−3.49854e9	−0.301403	−0.150701	−	0.988579i	$-0.548153\pi$
$751$	−3.49854e9	−0.301403	−0.150701	+	0.988579i	$0.548153\pi$
$752$	3.33418e9	0.285908
$753$	−2.06223e9	−0.176017
$754$	−3.09403e9	−0.262860
$755$	−2.17280e9	−0.183741
$756$	3.56454e8	0.0300039
$757$	−2.02699e10	−1.69831	−0.849153	−	0.528148i	$-0.822887\pi$
$757$	−2.02699e10	−1.69831	−0.849153	+	0.528148i	$0.822887\pi$
$758$	−1.30862e10	−1.09137
$759$	−5.07771e9	−0.421523
$760$	−1.17699e10	−0.972578
$761$	1.16941e10	0.961876	0.480938	−	0.876755i	$-0.340296\pi$
$761$	1.16941e10	0.961876	0.480938	+	0.876755i	$0.340296\pi$
$762$	1.40796e9	0.115278
$763$	2.50549e9	0.204201
$764$	−1.66007e9	−0.134679
$765$	−5.19916e8	−0.0419873
$766$	7.42441e9	0.596844
$767$	7.84406e9	0.627707
$768$	−3.27465e9	−0.260856
$769$	1.64924e10	1.30780	0.653899	−	0.756582i	$-0.273132\pi$
$769$	1.64924e10	1.30780	0.653899	+	0.756582i	$0.273132\pi$
$770$	−8.47727e8	−0.0669173
$771$	−4.05358e9	−0.318528
$772$	8.38867e9	0.656195
$773$	−4.04094e9	−0.314669	−0.157334	−	0.987545i	$-0.550290\pi$
$773$	−4.04094e9	−0.314669	−0.157334	+	0.987545i	$0.550290\pi$
$774$	1.35529e9	0.105060
$775$	1.08138e10	0.834493
$776$	1.86459e10	1.43241
$777$	6.59143e8	0.0504088
$778$	−1.80423e10	−1.37361
$779$	−3.52342e10	−2.67044
$780$	7.88971e8	0.0595292
$781$	1.38790e10	1.04251
$782$	1.09710e9	0.0820395
$783$	2.38282e9	0.177388
$784$	4.35190e9	0.322532
$785$	−1.58928e9	−0.117262
$786$	1.51394e9	0.111207
$787$	2.46052e10	1.79935	0.899675	−	0.436560i	$-0.143803\pi$
$787$	2.46052e10	1.79935	0.899675	+	0.436560i	$0.143803\pi$
$788$	−6.30473e9	−0.459012
$789$	4.34987e9	0.315288
$790$	5.70661e8	0.0411797
$791$	−4.92146e8	−0.0353571
$792$	−1.79501e10	−1.28389
$793$	2.50148e10	1.78131
$794$	1.10736e10	0.785087
$795$	9.94580e8	0.0702029
$796$	−8.10105e9	−0.569305
$797$	−1.84665e10	−1.29205	−0.646026	−	0.763316i	$-0.723570\pi$
$797$	−1.84665e10	−1.29205	−0.646026	+	0.763316i	$0.723570\pi$
$798$	6.07720e8	0.0423344
$799$	−1.06087e9	−0.0735783
$800$	8.66133e9	0.598094
$801$	1.67915e10	1.15445
$802$	−2.97456e9	−0.203616
$803$	−2.26937e10	−1.54668
$804$	−2.17486e9	−0.147582
$805$	−1.39431e9	−0.0942048
$806$	−1.23810e10	−0.832882
$807$	4.40389e9	0.294971
$808$	−2.26438e10	−1.51012
$809$	1.80517e10	1.19867	0.599333	−	0.800500i	$-0.295433\pi$
$809$	1.80517e10	1.19867	0.599333	+	0.800500i	$0.295433\pi$
$810$	−4.80722e9	−0.317831
$811$	1.23449e10	0.812673	0.406337	−	0.913723i	$-0.366806\pi$
$811$	1.23449e10	0.812673	0.406337	+	0.913723i	$0.366806\pi$
$812$	3.45940e8	0.0226754
$813$	2.18719e9	0.142748
$814$	−2.16121e10	−1.40447
$815$	−4.57254e9	−0.295874
$816$	−1.07774e8	−0.00694381
$817$	−4.06719e9	−0.260926
$818$	−6.21768e9	−0.397184
$819$	1.93864e9	0.123312
$820$	−6.00501e9	−0.380334
$821$	−1.36091e10	−0.858276	−0.429138	−	0.903239i	$-0.641183\pi$
$821$	−1.36091e10	−0.858276	−0.429138	+	0.903239i	$0.641183\pi$
$822$	2.36125e9	0.148283
$823$	−1.55999e10	−0.975490	−0.487745	−	0.872986i	$-0.662180\pi$
$823$	−1.55999e10	−0.975490	−0.487745	+	0.872986i	$0.662180\pi$
$824$	5.11312e9	0.318376
$825$	−3.70302e9	−0.229598
$826$	1.02975e9	0.0635774
$827$	−1.54413e10	−0.949325	−0.474662	−	0.880168i	$-0.657430\pi$
$827$	−1.54413e10	−0.949325	−0.474662	+	0.880168i	$0.657430\pi$
$828$	−9.30135e9	−0.569429
$829$	−5.48114e9	−0.334141	−0.167071	−	0.985945i	$-0.553431\pi$
$829$	−5.48114e9	−0.334141	−0.167071	+	0.985945i	$0.553431\pi$
$830$	6.76742e9	0.410818
$831$	−3.02236e9	−0.182702
$832$	−1.52476e10	−0.917844
$833$	−1.38469e9	−0.0830034
$834$	−5.00758e9	−0.298914
$835$	−1.36365e9	−0.0810590
$836$	1.69709e10	1.00458
$837$	9.53506e9	0.562062
$838$	−7.48862e9	−0.439590
$839$	−9.70181e9	−0.567134	−0.283567	−	0.958952i	$-0.591518\pi$
$839$	−9.70181e9	−0.567134	−0.283567	+	0.958952i	$0.591518\pi$
$840$	3.28759e8	0.0191381
$841$	−1.49373e10	−0.865939
$842$	1.41829e10	0.818792
$843$	−3.59192e9	−0.206505
$844$	−8.95425e9	−0.512661
$845$	−4.24025e8	−0.0241764
$846$	−1.05603e10	−0.599627
$847$	1.49872e9	0.0847481
$848$	−3.09102e9	−0.174067
$849$	−7.06411e9	−0.396169
$850$	8.00083e8	0.0446857
$851$	−3.55467e10	−1.97718
$852$	−1.69572e9	−0.0939327
$853$	7.25754e9	0.400376	0.200188	−	0.979758i	$-0.435845\pi$
$853$	7.25754e9	0.400376	0.200188	+	0.979758i	$0.435845\pi$
$854$	3.28389e9	0.180421
$855$	1.55314e10	0.849822
$856$	3.64326e10	1.98533
$857$	2.87404e10	1.55977	0.779884	−	0.625923i	$-0.215278\pi$
$857$	2.87404e10	1.55977	0.779884	+	0.625923i	$0.215278\pi$
$858$	4.23968e9	0.229154
$859$	−7.30578e9	−0.393270	−0.196635	−	0.980477i	$-0.563001\pi$
$859$	−7.30578e9	−0.393270	−0.196635	+	0.980477i	$0.563001\pi$
$860$	−6.93177e8	−0.0371620
$861$	9.84168e8	0.0525482
$862$	−1.57106e10	−0.835446
$863$	3.12604e10	1.65560	0.827802	−	0.561021i	$-0.189591\pi$
$863$	3.12604e10	1.65560	0.827802	+	0.561021i	$0.189591\pi$
$864$	7.63711e9	0.402839
$865$	2.21754e9	0.116497
$866$	−6.20415e8	−0.0324616
$867$	−4.76421e9	−0.248270
$868$	1.38431e9	0.0718479
$869$	−2.61177e9	−0.135010
$870$	6.92374e8	0.0356470
$871$	−2.44457e10	−1.25354
$872$	3.18589e10	1.62713
$873$	−2.46048e10	−1.25162
$874$	−3.27735e10	−1.66048
$875$	−2.43046e9	−0.122648
$876$	2.77270e9	0.139360
$877$	−1.16138e10	−0.581403	−0.290702	−	0.956814i	$-0.593889\pi$
$877$	−1.16138e10	−0.581403	−0.290702	+	0.956814i	$0.593889\pi$
$878$	1.43798e10	0.717003
$879$	−2.09763e9	−0.104176
$880$	−4.49099e9	−0.222153
$881$	−5.59437e9	−0.275636	−0.137818	−	0.990458i	$-0.544009\pi$
$881$	−5.59437e9	−0.275636	−0.137818	+	0.990458i	$0.544009\pi$
$882$	−1.37838e10	−0.676437
$883$	2.50609e10	1.22500	0.612498	−	0.790472i	$-0.290165\pi$
$883$	2.50609e10	1.22500	0.612498	+	0.790472i	$0.290165\pi$
$884$	7.80185e8	0.0379852
$885$	−1.75533e9	−0.0851248
$886$	−2.98270e10	−1.44076
$887$	−1.82957e10	−0.880271	−0.440135	−	0.897931i	$-0.645070\pi$
$887$	−1.82957e10	−0.880271	−0.440135	+	0.897931i	$0.645070\pi$
$888$	8.38142e9	0.401673
$889$	−1.76945e9	−0.0844662
$890$	1.00836e10	0.479459
$891$	2.20015e10	1.04203
$892$	9.30815e9	0.439123
$893$	3.16913e10	1.48922
$894$	−1.98200e9	−0.0927733
$895$	1.31796e10	0.614498
$896$	4.08923e8	0.0189917
$897$	6.97327e9	0.322599
$898$	2.72537e10	1.25591
$899$	9.25382e9	0.424778
$900$	−6.78319e9	−0.310160
$901$	9.83504e8	0.0447960
$902$	−3.22690e10	−1.46407
$903$	1.13606e8	0.00513444
$904$	−6.25794e9	−0.281736
$905$	8.67233e9	0.388925
$906$	1.42656e9	0.0637295
$907$	−7.13828e9	−0.317664	−0.158832	−	0.987306i	$-0.550773\pi$
$907$	−7.13828e9	−0.317664	−0.158832	+	0.987306i	$0.550773\pi$
$908$	−8.39272e9	−0.372051
$909$	2.98805e10	1.31951
$910$	1.16419e9	0.0512129
$911$	3.00662e10	1.31754	0.658770	−	0.752344i	$-0.271077\pi$
$911$	3.00662e10	1.31754	0.658770	+	0.752344i	$0.271077\pi$
$912$	3.21951e9	0.140543
$913$	−3.09728e10	−1.34689
$914$	1.47220e10	0.637758
$915$	−5.59775e9	−0.241568
$916$	6.35952e8	0.0273395
$917$	−1.90265e9	−0.0814828
$918$	7.05472e8	0.0300975
$919$	1.16122e10	0.493524	0.246762	−	0.969076i	$-0.420633\pi$
$919$	1.16122e10	0.493524	0.246762	+	0.969076i	$0.420633\pi$
$920$	−1.77295e10	−0.750653
$921$	−1.70130e9	−0.0717585
$922$	−1.95763e10	−0.822570
$923$	−1.90602e10	−0.797849
$924$	−4.74035e8	−0.0197678
$925$	−2.59231e10	−1.07694
$926$	4.11046e9	0.170119
$927$	−6.74720e9	−0.278192
$928$	7.41185e9	0.304445
$929$	9.40477e8	0.0384851	0.0192426	−	0.999815i	$-0.493875\pi$
$929$	9.40477e8	0.0384851	0.0192426	+	0.999815i	$0.493875\pi$
$930$	2.77059e9	0.112949
$931$	4.13647e10	1.67999
$932$	−2.53939e9	−0.102748
$933$	4.17279e9	0.168206
$934$	2.87638e10	1.15513
$935$	1.42895e9	0.0571711
$936$	2.46511e10	0.982586
$937$	4.42595e9	0.175759	0.0878796	−	0.996131i	$-0.471991\pi$
$937$	4.42595e9	0.175759	0.0878796	+	0.996131i	$0.471991\pi$
$938$	−3.20918e9	−0.126965
$939$	7.60264e9	0.299664
$940$	5.40119e9	0.212101
$941$	1.67372e10	0.654814	0.327407	−	0.944883i	$-0.393825\pi$
$941$	1.67372e10	0.654814	0.327407	+	0.944883i	$0.393825\pi$
$942$	1.04345e9	0.0406717
$943$	−5.30748e10	−2.06109
$944$	5.45531e9	0.211065
$945$	−8.96586e8	−0.0345606
$946$	−3.72492e9	−0.143053
$947$	2.33893e10	0.894935	0.447468	−	0.894300i	$-0.352326\pi$
$947$	2.33893e10	0.894935	0.447468	+	0.894300i	$0.352326\pi$
$948$	3.19104e8	0.0121648
$949$	3.11655e10	1.18370
$950$	−2.39007e10	−0.904438
$951$	−1.57239e9	−0.0592829
$952$	3.25098e8	0.0122119
$953$	1.32227e10	0.494875	0.247437	−	0.968904i	$-0.420412\pi$
$953$	1.32227e10	0.494875	0.247437	+	0.968904i	$0.420412\pi$
$954$	9.79018e9	0.365066
$955$	4.17556e9	0.155132
$956$	8.90457e9	0.329618
$957$	−3.16882e9	−0.116871
$958$	1.88641e10	0.693198
$959$	−2.96750e9	−0.108649
$960$	3.41206e9	0.124471
$961$	9.51734e9	0.345926
$962$	2.96801e10	1.07486
$963$	−4.80760e10	−1.73475
$964$	6.85024e8	0.0246284
$965$	−2.11000e10	−0.755851
$966$	9.15436e8	0.0326744
$967$	−1.96959e10	−0.700459	−0.350229	−	0.936664i	$-0.613896\pi$
$967$	−1.96959e10	−0.700459	−0.350229	+	0.936664i	$0.613896\pi$
$968$	1.90572e10	0.675299
$969$	−1.02439e9	−0.0361686
$970$	−1.47757e10	−0.519812
$971$	−4.75127e10	−1.66549	−0.832746	−	0.553655i	$-0.813232\pi$
$971$	−4.75127e10	−1.66549	−0.832746	+	0.553655i	$0.813232\pi$
$972$	−9.06812e9	−0.316727
$973$	6.29327e9	0.219019
$974$	2.09387e10	0.726097
$975$	5.08539e9	0.175715
$976$	1.73970e10	0.598964
$977$	4.37334e10	1.50031	0.750157	−	0.661260i	$-0.229978\pi$
$977$	4.37334e10	1.50031	0.750157	+	0.661260i	$0.229978\pi$
$978$	3.00211e9	0.102622
$979$	−4.61502e10	−1.57193
$980$	7.04984e9	0.239270
$981$	−4.20406e10	−1.42176
$982$	−5.98924e9	−0.201828
$983$	1.27037e10	0.426572	0.213286	−	0.976990i	$-0.431583\pi$
$983$	1.27037e10	0.426572	0.213286	+	0.976990i	$0.431583\pi$
$984$	1.25143e10	0.418721
$985$	1.58582e10	0.528722
$986$	6.84663e8	0.0227461
$987$	−8.85208e8	−0.0293046
$988$	−2.33063e10	−0.768820
$989$	−6.12659e9	−0.201387
$990$	1.42243e10	0.465917
$991$	−2.85362e10	−0.931404	−0.465702	−	0.884941i	$-0.654198\pi$
$991$	−2.85362e10	−0.931404	−0.465702	+	0.884941i	$0.654198\pi$
$992$	2.96592e10	0.964646
$993$	7.73015e9	0.250533
$994$	−2.50218e9	−0.0808103
$995$	2.03765e10	0.655766
$996$	3.78423e9	0.121358
$997$	3.65067e10	1.16665	0.583323	−	0.812240i	$-0.301752\pi$
$997$	3.65067e10	1.16665	0.583323	+	0.812240i	$0.301752\pi$
$998$	1.79110e10	0.570378
$999$	−2.28577e10	−0.725359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.5	✓	11
3.2	odd	2		387.8.a.b.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.5	✓	11	1.1	even	1	trivial
387.8.a.b.1.7		11	3.2	odd	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-8.31419 q^{2} +11.6940 q^{3} -58.8742 q^{4} +148.086 q^{5} -97.2261 q^{6} +122.189 q^{7} +1553.71 q^{8} -2050.25 q^{9} +O(q^{10})\)	\(q-8.31419 q^{2} +11.6940 q^{3} -58.8742 q^{4} +148.086 q^{5} -97.2261 q^{6} +122.189 q^{7} +1553.71 q^{8} -2050.25 q^{9} -1231.21 q^{10} +5634.96 q^{11} -688.475 q^{12} -7738.55 q^{13} -1015.90 q^{14} +1731.71 q^{15} -5381.93 q^{16} +1712.43 q^{17} +17046.2 q^{18} -51155.1 q^{19} -8718.44 q^{20} +1428.88 q^{21} -46850.2 q^{22} -77057.3 q^{23} +18169.1 q^{24} -56195.6 q^{25} +64339.8 q^{26} -49550.4 q^{27} -7193.77 q^{28} -48088.8 q^{29} -14397.8 q^{30} -192432. q^{31} -154128. q^{32} +65895.2 q^{33} -14237.5 q^{34} +18094.4 q^{35} +120707. q^{36} +461302. q^{37} +425313. q^{38} -90494.6 q^{39} +230082. q^{40} +688771. q^{41} -11879.9 q^{42} +79507.0 q^{43} -331754. q^{44} -303613. q^{45} +640669. q^{46} -619513. q^{47} -62936.2 q^{48} -808613. q^{49} +467221. q^{50} +20025.1 q^{51} +455601. q^{52} +574333. q^{53} +411971. q^{54} +834458. q^{55} +189846. q^{56} -598208. q^{57} +399820. q^{58} -1.01363e6 q^{59} -101953. q^{60} -3.23249e6 q^{61} +1.59991e6 q^{62} -250518. q^{63} +1.97034e6 q^{64} -1.14597e6 q^{65} -547866. q^{66} +3.15895e6 q^{67} -100818. q^{68} -901108. q^{69} -150441. q^{70} +2.46302e6 q^{71} -3.18549e6 q^{72} -4.02731e6 q^{73} -3.83535e6 q^{74} -657151. q^{75} +3.01172e6 q^{76} +688530. q^{77} +752389. q^{78} -463495. q^{79} -796987. q^{80} +3.90446e6 q^{81} -5.72657e6 q^{82} -5.49654e6 q^{83} -84123.9 q^{84} +253587. q^{85} -661036. q^{86} -562351. q^{87} +8.75509e6 q^{88} -8.18997e6 q^{89} +2.52430e6 q^{90} -945564. q^{91} +4.53669e6 q^{92} -2.25030e6 q^{93} +5.15075e6 q^{94} -7.57535e6 q^{95} -1.80237e6 q^{96} +1.20009e7 q^{97} +6.72296e6 q^{98} -1.15531e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9} - 1333 q^{10} + 1333 q^{11} + 5089 q^{12} - 17967 q^{13} - 22352 q^{14} - 49504 q^{15} - 34406 q^{16} - 63095 q^{17} - 165931 q^{18} - 54524 q^{19} - 280995 q^{20} - 139788 q^{21} - 289358 q^{22} - 138139 q^{23} - 429583 q^{24} + 3455 q^{25} - 132946 q^{26} - 240356 q^{27} - 12704 q^{28} - 308658 q^{29} + 421284 q^{30} - 209523 q^{31} - 644934 q^{32} + 96814 q^{33} + 762435 q^{34} - 578892 q^{35} + 426161 q^{36} - 298472 q^{37} - 369707 q^{38} + 292298 q^{39} + 2633173 q^{40} - 1346735 q^{41} + 1173266 q^{42} + 874577 q^{43} + 3134292 q^{44} + 1893784 q^{45} + 3588111 q^{46} + 499284 q^{47} + 5647533 q^{48} + 2544563 q^{49} + 3049745 q^{50} + 1258424 q^{51} + 983088 q^{52} - 2210495 q^{53} + 6789698 q^{54} - 1855072 q^{55} - 469976 q^{56} - 1238444 q^{57} + 4397067 q^{58} - 5824216 q^{59} - 2889372 q^{60} - 4453034 q^{61} + 1002789 q^{62} - 6240564 q^{63} + 4757538 q^{64} - 2162872 q^{65} - 258940 q^{66} - 6859513 q^{67} - 9397005 q^{68} - 10040030 q^{69} + 845078 q^{70} - 10726554 q^{71} + 1199517 q^{72} - 4456898 q^{73} + 1046637 q^{74} - 3349114 q^{75} + 5861267 q^{76} - 17019816 q^{77} + 1999122 q^{78} - 15541320 q^{79} - 15680911 q^{80} - 12976697 q^{81} + 20233655 q^{82} - 11146767 q^{83} + 12348278 q^{84} - 12471976 q^{85} - 1908168 q^{86} - 18648900 q^{87} - 24463544 q^{88} - 13531356 q^{89} + 20858990 q^{90} - 19746448 q^{91} - 26023161 q^{92} - 21903110 q^{93} + 20288857 q^{94} - 12291624 q^{95} - 13954503 q^{96} - 10999901 q^{97} + 29909168 q^{98} + 29396057 q^{99}+O(q^{100}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9 - 1333 * q^10 + 1333 * q^11 + 5089 * q^12 - 17967 * q^13 - 22352 * q^14 - 49504 * q^15 - 34406 * q^16 - 63095 * q^17 - 165931 * q^18 - 54524 * q^19 - 280995 * q^20 - 139788 * q^21 - 289358 * q^22 - 138139 * q^23 - 429583 * q^24 + 3455 * q^25 - 132946 * q^26 - 240356 * q^27 - 12704 * q^28 - 308658 * q^29 + 421284 * q^30 - 209523 * q^31 - 644934 * q^32 + 96814 * q^33 + 762435 * q^34 - 578892 * q^35 + 426161 * q^36 - 298472 * q^37 - 369707 * q^38 + 292298 * q^39 + 2633173 * q^40 - 1346735 * q^41 + 1173266 * q^42 + 874577 * q^43 + 3134292 * q^44 + 1893784 * q^45 + 3588111 * q^46 + 499284 * q^47 + 5647533 * q^48 + 2544563 * q^49 + 3049745 * q^50 + 1258424 * q^51 + 983088 * q^52 - 2210495 * q^53 + 6789698 * q^54 - 1855072 * q^55 - 469976 * q^56 - 1238444 * q^57 + 4397067 * q^58 - 5824216 * q^59 - 2889372 * q^60 - 4453034 * q^61 + 1002789 * q^62 - 6240564 * q^63 + 4757538 * q^64 - 2162872 * q^65 - 258940 * q^66 - 6859513 * q^67 - 9397005 * q^68 - 10040030 * q^69 + 845078 * q^70 - 10726554 * q^71 + 1199517 * q^72 - 4456898 * q^73 + 1046637 * q^74 - 3349114 * q^75 + 5861267 * q^76 - 17019816 * q^77 + 1999122 * q^78 - 15541320 * q^79 - 15680911 * q^80 - 12976697 * q^81 + 20233655 * q^82 - 11146767 * q^83 + 12348278 * q^84 - 12471976 * q^85 - 1908168 * q^86 - 18648900 * q^87 - 24463544 * q^88 - 13531356 * q^89 + 20858990 * q^90 - 19746448 * q^91 - 26023161 * q^92 - 21903110 * q^93 + 20288857 * q^94 - 12291624 * q^95 - 13954503 * q^96 - 10999901 * q^97 + 29909168 * q^98 + 29396057 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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