LMFDB - Embedded newform 43.8.a.a.1.9

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			1.9
Root			$-14.3182$ 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)

$f(q)$	$=$	$q+12.3182 q^{2} -46.7197 q^{3} +23.7379 q^{4} +330.186 q^{5} -575.503 q^{6} -467.397 q^{7} -1284.32 q^{8} -4.26512 q^{9} +O(q^{10})$	\(q+12.3182 q^{2} -46.7197 q^{3} +23.7379 q^{4} +330.186 q^{5} -575.503 q^{6} -467.397 q^{7} -1284.32 q^{8} -4.26512 q^{9} +4067.29 q^{10} -359.251 q^{11} -1109.03 q^{12} -11439.7 q^{13} -5757.49 q^{14} -15426.2 q^{15} -18859.0 q^{16} -19000.7 q^{17} -52.5385 q^{18} -3671.03 q^{19} +7837.90 q^{20} +21836.7 q^{21} -4425.32 q^{22} -3785.73 q^{23} +60003.2 q^{24} +30897.5 q^{25} -140917. q^{26} +102375. q^{27} -11095.0 q^{28} +115539. q^{29} -190023. q^{30} +15139.6 q^{31} -67915.2 q^{32} +16784.1 q^{33} -234054. q^{34} -154328. q^{35} -101.245 q^{36} -357942. q^{37} -45220.5 q^{38} +534461. q^{39} -424064. q^{40} +540673. q^{41} +268988. q^{42} +79507.0 q^{43} -8527.85 q^{44} -1408.28 q^{45} -46633.3 q^{46} +289961. q^{47} +881086. q^{48} -605083. q^{49} +380601. q^{50} +887708. q^{51} -271555. q^{52} -329115. q^{53} +1.26108e6 q^{54} -118619. q^{55} +600288. q^{56} +171510. q^{57} +1.42323e6 q^{58} +2.44911e6 q^{59} -366185. q^{60} -1.25749e6 q^{61} +186492. q^{62} +1993.50 q^{63} +1.57735e6 q^{64} -3.77723e6 q^{65} +206750. q^{66} -1.70199e6 q^{67} -451036. q^{68} +176868. q^{69} -1.90104e6 q^{70} -3.75585e6 q^{71} +5477.78 q^{72} -5.83440e6 q^{73} -4.40920e6 q^{74} -1.44352e6 q^{75} -87142.4 q^{76} +167913. q^{77} +6.58360e6 q^{78} +3.48456e6 q^{79} -6.22696e6 q^{80} -4.77362e6 q^{81} +6.66012e6 q^{82} +5.17957e6 q^{83} +518356. q^{84} -6.27376e6 q^{85} +979383. q^{86} -5.39795e6 q^{87} +461394. q^{88} +5.98803e6 q^{89} -17347.5 q^{90} +5.34690e6 q^{91} -89865.1 q^{92} -707317. q^{93} +3.57180e6 q^{94} -1.21212e6 q^{95} +3.17298e6 q^{96} -5.18336e6 q^{97} -7.45353e6 q^{98} +1532.25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	12.3182	1.08878	0.544392	−	0.838831i	$-0.316760\pi$
$2$	12.3182	1.08878	0.544392	+	0.838831i	$0.316760\pi$
$3$	−46.7197	−0.999024	−0.499512	−	0.866307i	$-0.666487\pi$
$3$	−46.7197	−0.999024	−0.499512	+	0.866307i	$0.666487\pi$
$4$	23.7379	0.185452
$5$	330.186	1.18131	0.590654	−	0.806925i	$-0.298870\pi$
$5$	330.186	1.18131	0.590654	+	0.806925i	$0.298870\pi$
$6$	−575.503	−1.08772
$7$	−467.397	−0.515042	−0.257521	−	0.966273i	$-0.582906\pi$
$7$	−467.397	−0.515042	−0.257521	+	0.966273i	$0.582906\pi$
$8$	−1284.32	−0.886867
$9$	−4.26512	−0.00195021
$10$	4067.29	1.28619
$11$	−359.251	−0.0813811	−0.0406906	−	0.999172i	$-0.512956\pi$
$11$	−359.251	−0.0813811	−0.0406906	+	0.999172i	$0.512956\pi$
$12$	−1109.03	−0.185271
$13$	−11439.7	−1.44416	−0.722078	−	0.691812i	$-0.756813\pi$
$13$	−11439.7	−1.44416	−0.722078	+	0.691812i	$0.756813\pi$
$14$	−5757.49	−0.560770
$15$	−15426.2	−1.18016
$16$	−18859.0	−1.15106
$17$	−19000.7	−0.937990	−0.468995	−	0.883201i	$-0.655384\pi$
$17$	−19000.7	−0.937990	−0.468995	+	0.883201i	$0.655384\pi$
$18$	−52.5385	−0.00212336
$19$	−3671.03	−0.122786	−0.0613932	−	0.998114i	$-0.519554\pi$
$19$	−3671.03	−0.122786	−0.0613932	+	0.998114i	$0.519554\pi$
$20$	7837.90	0.219076
$21$	21836.7	0.514540
$22$	−4425.32	−0.0886065
$23$	−3785.73	−0.0648787	−0.0324393	−	0.999474i	$-0.510328\pi$
$23$	−3785.73	−0.0648787	−0.0324393	+	0.999474i	$0.510328\pi$
$24$	60003.2	0.886002
$25$	30897.5	0.395488
$26$	−140917.	−1.57237
$27$	102375.	1.00097
$28$	−11095.0	−0.0955157
$29$	115539.	0.879702	0.439851	−	0.898071i	$-0.355031\pi$
$29$	115539.	0.879702	0.439851	+	0.898071i	$0.355031\pi$
$30$	−190023.	−1.28493
$31$	15139.6	0.0912741	0.0456371	−	0.998958i	$-0.485468\pi$
$31$	15139.6	0.0912741	0.0456371	+	0.998958i	$0.485468\pi$
$32$	−67915.2	−0.366389
$33$	16784.1	0.0813017
$34$	−234054.	−1.02127
$35$	−154328.	−0.608424
$36$	−101.245	−0.000361671 0
$37$	−357942.	−1.16173	−0.580867	−	0.813998i	$-0.697286\pi$
$37$	−357942.	−1.16173	−0.580867	+	0.813998i	$0.697286\pi$
$38$	−45220.5	−0.133688
$39$	534461.	1.44275
$40$	−424064.	−1.04766
$41$	540673.	1.22516	0.612578	−	0.790410i	$-0.290133\pi$
$41$	540673.	1.22516	0.612578	+	0.790410i	$0.290133\pi$
$42$	268988.	0.560223
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	−8527.85	−0.0150923
$45$	−1408.28	−0.00230380
$46$	−46633.3	−0.0706389
$47$	289961.	0.407378	0.203689	−	0.979036i	$-0.434707\pi$
$47$	289961.	0.407378	0.203689	+	0.979036i	$0.434707\pi$
$48$	881086.	1.14994
$49$	−605083.	−0.734731
$50$	380601.	0.430601
$51$	887708.	0.937075
$52$	−271555.	−0.267822
$53$	−329115.	−0.303656	−0.151828	−	0.988407i	$-0.548516\pi$
$53$	−329115.	−0.303656	−0.151828	+	0.988407i	$0.548516\pi$
$54$	1.26108e6	1.08984
$55$	−118619.	−0.0961361
$56$	600288.	0.456774
$57$	171510.	0.122667
$58$	1.42323e6	0.957806
$59$	2.44911e6	1.55248	0.776240	−	0.630437i	$-0.217124\pi$
$59$	2.44911e6	1.55248	0.776240	+	0.630437i	$0.217124\pi$
$60$	−366185.	−0.218862
$61$	−1.25749e6	−0.709333	−0.354666	−	0.934993i	$-0.615406\pi$
$61$	−1.25749e6	−0.709333	−0.354666	+	0.934993i	$0.615406\pi$
$62$	186492.	0.0993779
$63$	1993.50	0.00100444
$64$	1.57735e6	0.752141
$65$	−3.77723e6	−1.70599
$66$	206750.	0.0885201
$67$	−1.70199e6	−0.691347	−0.345673	−	0.938355i	$-0.612350\pi$
$67$	−1.70199e6	−0.691347	−0.345673	+	0.938355i	$0.612350\pi$
$68$	−451036.	−0.173952
$69$	176868.	0.0648154
$70$	−1.90104e6	−0.662442
$71$	−3.75585e6	−1.24539	−0.622693	−	0.782466i	$-0.713961\pi$
$71$	−3.75585e6	−1.24539	−0.622693	+	0.782466i	$0.713961\pi$
$72$	5477.78	0.00172958
$73$	−5.83440e6	−1.75536	−0.877680	−	0.479247i	$-0.840910\pi$
$73$	−5.83440e6	−1.75536	−0.877680	+	0.479247i	$0.840910\pi$
$74$	−4.40920e6	−1.26488
$75$	−1.44352e6	−0.395102
$76$	−87142.4	−0.0227710
$77$	167913.	0.0419147
$78$	6.58360e6	1.57084
$79$	3.48456e6	0.795158	0.397579	−	0.917568i	$-0.369851\pi$
$79$	3.48456e6	0.795158	0.397579	+	0.917568i	$0.369851\pi$
$80$	−6.22696e6	−1.35976
$81$	−4.77362e6	−0.998046
$82$	6.66012e6	1.33393
$83$	5.17957e6	0.994307	0.497154	−	0.867663i	$-0.334379\pi$
$83$	5.17957e6	0.994307	0.497154	+	0.867663i	$0.334379\pi$
$84$	518356.	0.0954225
$85$	−6.27376e6	−1.10806
$86$	979383.	0.166038
$87$	−5.39795e6	−0.878844
$88$	461394.	0.0721743
$89$	5.98803e6	0.900365	0.450183	−	0.892936i	$-0.351359\pi$
$89$	5.98803e6	0.900365	0.450183	+	0.892936i	$0.351359\pi$
$90$	−17347.5	−0.00250834
$91$	5.34690e6	0.743801
$92$	−89865.1	−0.0120319
$93$	−707317.	−0.0911851
$94$	3.57180e6	0.443547
$95$	−1.21212e6	−0.145049
$96$	3.17298e6	0.366031
$97$	−5.18336e6	−0.576647	−0.288324	−	0.957533i	$-0.593098\pi$
$97$	−5.18336e6	−0.576647	−0.288324	+	0.957533i	$0.593098\pi$
$98$	−7.45353e6	−0.799964
$99$	1532.25	0.000158711 0
$100$	733440.	0.0733440
$101$	−930045.	−0.0898213	−0.0449106	−	0.998991i	$-0.514300\pi$
$101$	−930045.	−0.0898213	−0.0449106	+	0.998991i	$0.514300\pi$
$102$	1.09350e7	1.02027
$103$	−1.70172e7	−1.53447	−0.767233	−	0.641368i	$-0.778367\pi$
$103$	−1.70172e7	−1.53447	−0.767233	+	0.641368i	$0.778367\pi$
$104$	1.46923e7	1.28077
$105$	7.21016e6	0.607830
$106$	−4.05410e6	−0.330616
$107$	1.27256e7	1.00423	0.502116	−	0.864800i	$-0.332555\pi$
$107$	1.27256e7	1.00423	0.502116	+	0.864800i	$0.332555\pi$
$108$	2.43017e6	0.185632
$109$	−1.67891e7	−1.24175	−0.620874	−	0.783910i	$-0.713222\pi$
$109$	−1.67891e7	−1.24175	−0.620874	+	0.783910i	$0.713222\pi$
$110$	−1.46118e6	−0.104672
$111$	1.67230e7	1.16060
$112$	8.81463e6	0.592845
$113$	1.36793e7	0.891842	0.445921	−	0.895072i	$-0.352876\pi$
$113$	1.36793e7	0.891842	0.445921	+	0.895072i	$0.352876\pi$
$114$	2.11269e6	0.133558
$115$	−1.24999e6	−0.0766417
$116$	2.74265e6	0.163143
$117$	48791.8	0.00281641
$118$	3.01686e7	1.69032
$119$	8.88087e6	0.483105
$120$	1.98122e7	1.04664
$121$	−1.93581e7	−0.993377
$122$	−1.54900e7	−0.772311
$123$	−2.52601e7	−1.22396
$124$	359381.	0.0169270
$125$	−1.55938e7	−0.714115
$126$	24556.4	0.00109362
$127$	1.29034e6	0.0558972	0.0279486	−	0.999609i	$-0.491103\pi$
$127$	1.29034e6	0.0558972	0.0279486	+	0.999609i	$0.491103\pi$
$128$	2.81233e7	1.18531
$129$	−3.71455e6	−0.152350
$130$	−4.65287e7	−1.85746
$131$	−3.96207e7	−1.53983	−0.769915	−	0.638146i	$-0.779701\pi$
$131$	−3.96207e7	−1.53983	−0.769915	+	0.638146i	$0.779701\pi$
$132$	398419.	0.0150776
$133$	1.71583e6	0.0632402
$134$	−2.09655e7	−0.752728
$135$	3.38029e7	1.18246
$136$	2.44030e7	0.831873
$137$	−1.20603e7	−0.400715	−0.200358	−	0.979723i	$-0.564210\pi$
$137$	−1.20603e7	−0.400715	−0.200358	+	0.979723i	$0.564210\pi$
$138$	2.17870e6	0.0705700
$139$	3.45946e7	1.09259	0.546294	−	0.837594i	$-0.316038\pi$
$139$	3.45946e7	1.09259	0.546294	+	0.837594i	$0.316038\pi$
$140$	−3.66341e6	−0.112833
$141$	−1.35469e7	−0.406981
$142$	−4.62653e7	−1.35596
$143$	4.10973e6	0.117527
$144$	80435.7	0.00224481
$145$	3.81493e7	1.03920
$146$	−7.18693e7	−1.91121
$147$	2.82693e7	0.734014
$148$	−8.49678e6	−0.215446
$149$	3.46074e7	0.857072	0.428536	−	0.903525i	$-0.359030\pi$
$149$	3.46074e7	0.857072	0.428536	+	0.903525i	$0.359030\pi$
$150$	−1.77816e7	−0.430181
$151$	−2.74859e7	−0.649666	−0.324833	−	0.945771i	$-0.605308\pi$
$151$	−2.74859e7	−0.649666	−0.324833	+	0.945771i	$0.605308\pi$
$152$	4.71478e6	0.108895
$153$	81040.2	0.00182928
$154$	2.06838e6	0.0456361
$155$	4.99887e6	0.107823
$156$	1.26870e7	0.267560
$157$	−3.91834e7	−0.808078	−0.404039	−	0.914742i	$-0.632394\pi$
$157$	−3.91834e7	−0.808078	−0.404039	+	0.914742i	$0.632394\pi$
$158$	4.29235e7	0.865756
$159$	1.53762e7	0.303360
$160$	−2.24246e7	−0.432818
$161$	1.76944e6	0.0334153
$162$	−5.88024e7	−1.08666
$163$	4.81506e7	0.870854	0.435427	−	0.900224i	$-0.356597\pi$
$163$	4.81506e7	0.870854	0.435427	+	0.900224i	$0.356597\pi$
$164$	1.28344e7	0.227208
$165$	5.54187e6	0.0960423
$166$	6.38030e7	1.08259
$167$	−5.80547e7	−0.964561	−0.482280	−	0.876017i	$-0.660191\pi$
$167$	−5.80547e7	−0.964561	−0.482280	+	0.876017i	$0.660191\pi$
$168$	−2.80453e7	−0.456329
$169$	6.81189e7	1.08559
$170$	−7.72813e7	−1.20643
$171$	15657.4	0.000239460 0
$172$	1.88733e6	0.0282812
$173$	−3.04236e7	−0.446735	−0.223367	−	0.974734i	$-0.571705\pi$
$173$	−3.04236e7	−0.446735	−0.223367	+	0.974734i	$0.571705\pi$
$174$	−6.64930e7	−0.956872
$175$	−1.44414e7	−0.203693
$176$	6.77510e6	0.0936745
$177$	−1.14422e8	−1.55097
$178$	7.37617e7	0.980304
$179$	6.08790e6	0.0793382	0.0396691	−	0.999213i	$-0.487370\pi$
$179$	6.08790e6	0.0793382	0.0396691	+	0.999213i	$0.487370\pi$
$180$	−33429.6	−0.000427245 0
$181$	1.51213e8	1.89546	0.947728	−	0.319079i	$-0.103373\pi$
$181$	1.51213e8	1.89546	0.947728	+	0.319079i	$0.103373\pi$
$182$	6.58641e7	0.809840
$183$	5.87496e7	0.708641
$184$	4.86209e6	0.0575388
$185$	−1.18187e8	−1.37237
$186$	−8.71287e6	−0.0992809
$187$	6.82602e6	0.0763347
$188$	6.88307e6	0.0755491
$189$	−4.78500e7	−0.515543
$190$	−1.49311e7	−0.157927
$191$	1.15042e8	1.19465	0.597323	−	0.802000i	$-0.296231\pi$
$191$	1.15042e8	1.19465	0.597323	+	0.802000i	$0.296231\pi$
$192$	−7.36936e7	−0.751407
$193$	5.16665e7	0.517319	0.258659	−	0.965969i	$-0.416719\pi$
$193$	5.16665e7	0.517319	0.258659	+	0.965969i	$0.416719\pi$
$194$	−6.38496e7	−0.627845
$195$	1.76471e8	1.70433
$196$	−1.43634e7	−0.136257
$197$	−7.84505e7	−0.731078	−0.365539	−	0.930796i	$-0.619115\pi$
$197$	−7.84505e7	−0.731078	−0.365539	+	0.930796i	$0.619115\pi$
$198$	18874.5	0.000172802 0
$199$	−7.08100e7	−0.636955	−0.318478	−	0.947930i	$-0.603172\pi$
$199$	−7.08100e7	−0.636955	−0.318478	+	0.947930i	$0.603172\pi$
$200$	−3.96823e7	−0.350745
$201$	7.95167e7	0.690672
$202$	−1.14565e7	−0.0977960
$203$	−5.40026e7	−0.453084
$204$	2.10723e7	0.173783
$205$	1.78522e8	1.44729
$206$	−2.09621e8	−1.67070
$207$	16146.6	0.000126527 0
$208$	2.15741e8	1.66231
$209$	1.31882e6	0.00999250
$210$	8.88161e7	0.661796
$211$	−1.44130e8	−1.05625	−0.528124	−	0.849167i	$-0.677104\pi$
$211$	−1.44130e8	−1.05625	−0.528124	+	0.849167i	$0.677104\pi$
$212$	−7.81248e6	−0.0563136
$213$	1.75472e8	1.24417
$214$	1.56756e8	1.09339
$215$	2.62521e7	0.180148
$216$	−1.31483e8	−0.887730
$217$	−7.07619e6	−0.0470101
$218$	−2.06811e8	−1.35200
$219$	2.72582e8	1.75365
$220$	−2.81577e6	−0.0178286
$221$	2.17363e8	1.35460
$222$	2.05997e8	1.26364
$223$	1.64343e8	0.992396	0.496198	−	0.868209i	$-0.334729\pi$
$223$	1.64343e8	0.992396	0.496198	+	0.868209i	$0.334729\pi$
$224$	3.17434e7	0.188706
$225$	−131781.	−0.000771285 0
$226$	1.68504e8	0.971024
$227$	−3.36542e8	−1.90963	−0.954814	−	0.297204i	$-0.903946\pi$
$227$	−3.36542e8	−1.90963	−0.954814	+	0.297204i	$0.903946\pi$
$228$	4.07127e6	0.0227488
$229$	−5.78696e7	−0.318439	−0.159220	−	0.987243i	$-0.550898\pi$
$229$	−5.78696e7	−0.318439	−0.159220	+	0.987243i	$0.550898\pi$
$230$	−1.53976e7	−0.0834463
$231$	−7.84485e6	−0.0418738
$232$	−1.48389e8	−0.780179
$233$	−2.71239e8	−1.40477	−0.702386	−	0.711797i	$-0.747882\pi$
$233$	−2.71239e8	−1.40477	−0.702386	+	0.711797i	$0.747882\pi$
$234$	601027.	0.00306647
$235$	9.57411e7	0.481239
$236$	5.81366e7	0.287911
$237$	−1.62798e8	−0.794382
$238$	1.09396e8	0.525997
$239$	−1.16728e8	−0.553075	−0.276537	−	0.961003i	$-0.589187\pi$
$239$	−1.16728e8	−0.553075	−0.276537	+	0.961003i	$0.589187\pi$
$240$	2.90922e8	1.35843
$241$	−4.09158e8	−1.88292	−0.941460	−	0.337126i	$-0.890545\pi$
$241$	−4.09158e8	−1.88292	−0.941460	+	0.337126i	$0.890545\pi$
$242$	−2.38457e8	−1.08157
$243$	−872436.	−0.00390042
$244$	−2.98501e7	−0.131547
$245$	−1.99790e8	−0.867944
$246$	−3.11159e8	−1.33263
$247$	4.19956e7	0.177323
$248$	−1.94441e7	−0.0809480
$249$	−2.41988e8	−0.993337
$250$	−1.92088e8	−0.777517
$251$	−3.43101e8	−1.36950	−0.684752	−	0.728776i	$-0.740090\pi$
$251$	−3.43101e8	−1.36950	−0.684752	+	0.728776i	$0.740090\pi$
$252$	47321.5	0.000186276 0
$253$	1.36003e6	0.00527990
$254$	1.58946e7	0.0608601
$255$	2.93108e8	1.10697
$256$	1.44527e8	0.538405
$257$	7.47286e7	0.274613	0.137307	−	0.990529i	$-0.456155\pi$
$257$	7.47286e7	0.274613	0.137307	+	0.990529i	$0.456155\pi$
$258$	−4.57565e7	−0.165876
$259$	1.67301e8	0.598343
$260$	−8.96634e7	−0.316380
$261$	−492787.	−0.00171561
$262$	−4.88056e8	−1.67654
$263$	2.57577e8	0.873097	0.436549	−	0.899681i	$-0.356201\pi$
$263$	2.57577e8	0.873097	0.436549	+	0.899681i	$0.356201\pi$
$264$	−2.15562e7	−0.0721038
$265$	−1.08669e8	−0.358711
$266$	2.11359e7	0.0688550
$267$	−2.79759e8	−0.899487
$268$	−4.04017e7	−0.128212
$269$	−3.45824e8	−1.08323	−0.541617	−	0.840625i	$-0.682188\pi$
$269$	−3.45824e8	−1.08323	−0.541617	+	0.840625i	$0.682188\pi$
$270$	4.16390e8	1.28744
$271$	−2.24146e8	−0.684129	−0.342065	−	0.939676i	$-0.611126\pi$
$271$	−2.24146e8	−0.684129	−0.342065	+	0.939676i	$0.611126\pi$
$272$	3.58333e8	1.07968
$273$	−2.49806e8	−0.743076
$274$	−1.48561e8	−0.436293
$275$	−1.11000e7	−0.0321852
$276$	4.19847e6	0.0120201
$277$	2.45845e8	0.694995	0.347497	−	0.937681i	$-0.387032\pi$
$277$	2.45845e8	0.694995	0.347497	+	0.937681i	$0.387032\pi$
$278$	4.26143e8	1.18959
$279$	−64572.0	−0.000178004 0
$280$	1.98206e8	0.539591
$281$	4.79601e8	1.28946	0.644731	−	0.764410i	$-0.276970\pi$
$281$	4.79601e8	1.28946	0.644731	+	0.764410i	$0.276970\pi$
$282$	−1.66874e8	−0.443114
$283$	5.71921e8	1.49997	0.749987	−	0.661452i	$-0.230060\pi$
$283$	5.71921e8	1.49997	0.749987	+	0.661452i	$0.230060\pi$
$284$	−8.91559e7	−0.230959
$285$	5.66300e7	0.144907
$286$	5.06245e7	0.127962
$287$	−2.52709e8	−0.631007
$288$	289666.	0.000714536 0
$289$	−4.93122e7	−0.120174
$290$	4.69930e8	1.13146
$291$	2.42165e8	0.576085
$292$	−1.38496e8	−0.325535
$293$	4.33629e8	1.00712	0.503560	−	0.863960i	$-0.332023\pi$
$293$	4.33629e8	1.00712	0.503560	+	0.863960i	$0.332023\pi$
$294$	3.48227e8	0.799184
$295$	8.08661e8	1.83396
$296$	4.59713e8	1.03030
$297$	−3.67785e7	−0.0814603
$298$	4.26301e8	0.933167
$299$	4.33077e7	0.0936949
$300$	−3.42661e7	−0.0732725
$301$	−3.71614e7	−0.0785432
$302$	−3.38576e8	−0.707346
$303$	4.34515e7	0.0897336
$304$	6.92318e7	0.141335
$305$	−4.15205e8	−0.837940
$306$	998269.	0.00199169
$307$	−5.42296e8	−1.06968	−0.534838	−	0.844955i	$-0.679627\pi$
$307$	−5.42296e8	−1.06968	−0.534838	+	0.844955i	$0.679627\pi$
$308$	3.98589e6	0.00777317
$309$	7.95038e8	1.53297
$310$	6.15770e7	0.117396
$311$	−8.11532e8	−1.52983	−0.764917	−	0.644129i	$-0.777220\pi$
$311$	−8.11532e8	−1.52983	−0.764917	+	0.644129i	$0.777220\pi$
$312$	−6.86420e8	−1.27952
$313$	−8.40388e8	−1.54908	−0.774541	−	0.632524i	$-0.782019\pi$
$313$	−8.40388e8	−1.54908	−0.774541	+	0.632524i	$0.782019\pi$
$314$	−4.82669e8	−0.879823
$315$	658226.	0.00118656
$316$	8.27160e7	0.147464
$317$	3.45739e8	0.609595	0.304797	−	0.952417i	$-0.401411\pi$
$317$	3.45739e8	0.609595	0.304797	+	0.952417i	$0.401411\pi$
$318$	1.89406e8	0.330293
$319$	−4.15075e7	−0.0715911
$320$	5.20820e8	0.888510
$321$	−5.94535e8	−1.00325
$322$	2.17963e7	0.0363820
$323$	6.97521e7	0.115172
$324$	−1.13316e8	−0.185090
$325$	−3.53459e8	−0.571146
$326$	5.93129e8	0.948173
$327$	7.84380e8	1.24054
$328$	−6.94398e8	−1.08655
$329$	−1.35527e8	−0.209817
$330$	6.82659e7	0.104569
$331$	5.89707e8	0.893796	0.446898	−	0.894585i	$-0.352529\pi$
$331$	5.89707e8	0.893796	0.446898	+	0.894585i	$0.352529\pi$
$332$	1.22952e8	0.184396
$333$	1.52667e6	0.00226563
$334$	−7.15129e8	−1.05020
$335$	−5.61974e8	−0.816693
$336$	−4.11817e8	−0.592266
$337$	4.92765e8	0.701351	0.350676	−	0.936497i	$-0.385952\pi$
$337$	4.92765e8	0.701351	0.350676	+	0.936497i	$0.385952\pi$
$338$	8.39101e8	1.18197
$339$	−6.39091e8	−0.890972
$340$	−1.48926e8	−0.205491
$341$	−5.43891e6	−0.00742799
$342$	192871.	0.000260720 0
$343$	6.67736e8	0.893460
$344$	−1.02113e8	−0.135246
$345$	5.83993e7	0.0765669
$346$	−3.74764e8	−0.486398
$347$	9.83108e8	1.26313	0.631565	−	0.775323i	$-0.282413\pi$
$347$	9.83108e8	1.26313	0.631565	+	0.775323i	$0.282413\pi$
$348$	−1.28136e8	−0.162983
$349$	1.25957e9	1.58611	0.793053	−	0.609153i	$-0.208491\pi$
$349$	1.25957e9	1.58611	0.793053	+	0.609153i	$0.208491\pi$
$350$	−1.77892e8	−0.221778
$351$	−1.17115e9	−1.44556
$352$	2.43986e7	0.0298171
$353$	−8.97531e7	−0.108602	−0.0543010	−	0.998525i	$-0.517293\pi$
$353$	−8.97531e7	−0.108602	−0.0543010	+	0.998525i	$0.517293\pi$
$354$	−1.40947e9	−1.68867
$355$	−1.24013e9	−1.47118
$356$	1.42143e8	0.166975
$357$	−4.14912e8	−0.482634
$358$	7.49920e7	0.0863822
$359$	1.81494e8	0.207029	0.103515	−	0.994628i	$-0.466991\pi$
$359$	1.81494e8	0.207029	0.103515	+	0.994628i	$0.466991\pi$
$360$	1.80868e6	0.00204317
$361$	−8.80395e8	−0.984923
$362$	1.86267e9	2.06374
$363$	9.04406e8	0.992408
$364$	1.26924e8	0.137940
$365$	−1.92643e9	−2.07362
$366$	7.23689e8	0.771557
$367$	1.07414e9	1.13430	0.567150	−	0.823614i	$-0.308046\pi$
$367$	1.07414e9	1.13430	0.567150	+	0.823614i	$0.308046\pi$
$368$	7.13949e7	0.0746792
$369$	−2.30603e6	−0.00238932
$370$	−1.45585e9	−1.49421
$371$	1.53827e8	0.156396
$372$	−1.67902e7	−0.0169105
$373$	−1.39148e9	−1.38834	−0.694169	−	0.719812i	$-0.744228\pi$
$373$	−1.39148e9	−1.38834	−0.694169	+	0.719812i	$0.744228\pi$
$374$	8.40842e7	0.0831120
$375$	7.28540e8	0.713418
$376$	−3.72404e8	−0.361290
$377$	−1.32173e9	−1.27043
$378$	−5.89425e8	−0.561316
$379$	−1.85979e8	−0.175480	−0.0877400	−	0.996143i	$-0.527964\pi$
$379$	−1.85979e8	−0.175480	−0.0877400	+	0.996143i	$0.527964\pi$
$380$	−2.87732e7	−0.0268996
$381$	−6.02843e7	−0.0558427
$382$	1.41711e9	1.30071
$383$	8.12564e8	0.739029	0.369515	−	0.929225i	$-0.379524\pi$
$383$	8.12564e8	0.739029	0.369515	+	0.929225i	$0.379524\pi$
$384$	−1.31391e9	−1.18415
$385$	5.54424e7	0.0495142
$386$	6.36437e8	0.563249
$387$	−339107.	−0.000297405 0
$388$	−1.23042e8	−0.106940
$389$	−3.04526e8	−0.262301	−0.131151	−	0.991362i	$-0.541867\pi$
$389$	−3.04526e8	−0.262301	−0.131151	+	0.991362i	$0.541867\pi$
$390$	2.17381e9	1.85565
$391$	7.19315e7	0.0608556
$392$	7.77121e8	0.651609
$393$	1.85107e9	1.53833
$394$	−9.66368e8	−0.795986
$395$	1.15055e9	0.939326
$396$	36372.3	2.94332e−5 0
$397$	−2.15202e9	−1.72616	−0.863078	−	0.505071i	$-0.831466\pi$
$397$	−2.15202e9	−1.72616	−0.863078	+	0.505071i	$0.831466\pi$
$398$	−8.72251e8	−0.693507
$399$	−8.01631e7	−0.0631785
$400$	−5.82694e8	−0.455230
$401$	1.32277e9	1.02442	0.512211	−	0.858860i	$-0.328827\pi$
$401$	1.32277e9	1.02442	0.512211	+	0.858860i	$0.328827\pi$
$402$	9.79502e8	0.751994
$403$	−1.73193e8	−0.131814
$404$	−2.20773e7	−0.0166575
$405$	−1.57618e9	−1.17900
$406$	−6.65215e8	−0.493311
$407$	1.28591e8	0.0945433
$408$	−1.14010e9	−0.831061
$409$	5.69273e8	0.411423	0.205712	−	0.978613i	$-0.434049\pi$
$409$	5.69273e8	0.411423	0.205712	+	0.978613i	$0.434049\pi$
$410$	2.19907e9	1.57578
$411$	5.63454e8	0.400325
$412$	−4.03951e8	−0.284570
$413$	−1.14471e9	−0.799594
$414$	198897.	0.000137761 0
$415$	1.71022e9	1.17458
$416$	7.76931e8	0.529122
$417$	−1.61625e9	−1.09152
$418$	1.62455e7	0.0108797
$419$	−2.17734e9	−1.44603	−0.723016	−	0.690831i	$-0.757245\pi$
$419$	−2.17734e9	−1.44603	−0.723016	+	0.690831i	$0.757245\pi$
$420$	1.71154e8	0.112723
$421$	−2.30881e8	−0.150800	−0.0754001	−	0.997153i	$-0.524023\pi$
$421$	−2.30881e8	−0.150800	−0.0754001	+	0.997153i	$0.524023\pi$
$422$	−1.77542e9	−1.15003
$423$	−1.23672e6	−0.000794474 0
$424$	4.22689e8	0.269302
$425$	−5.87074e8	−0.370964
$426$	2.16150e9	1.35463
$427$	5.87747e8	0.365336
$428$	3.02078e8	0.186237
$429$	−1.92006e8	−0.117412
$430$	3.23378e8	0.196142
$431$	2.33302e9	1.40361	0.701807	−	0.712367i	$-0.252377\pi$
$431$	2.33302e9	1.40361	0.701807	+	0.712367i	$0.252377\pi$
$432$	−1.93069e9	−1.15218
$433$	−2.85667e8	−0.169104	−0.0845518	−	0.996419i	$-0.526946\pi$
$433$	−2.85667e8	−0.169104	−0.0845518	+	0.996419i	$0.526946\pi$
$434$	−8.71659e7	−0.0511838
$435$	−1.78233e9	−1.03818
$436$	−3.98536e8	−0.230285
$437$	1.38975e7	0.00796622
$438$	3.35771e9	1.90934
$439$	2.53362e9	1.42927	0.714636	−	0.699496i	$-0.246592\pi$
$439$	2.53362e9	1.42927	0.714636	+	0.699496i	$0.246592\pi$
$440$	1.52346e8	0.0852600
$441$	2.58075e6	0.00143288
$442$	2.67752e9	1.47487
$443$	−6.54414e8	−0.357635	−0.178817	−	0.983882i	$-0.557227\pi$
$443$	−6.54414e8	−0.357635	−0.178817	+	0.983882i	$0.557227\pi$
$444$	3.96968e8	0.215236
$445$	1.97716e9	1.06361
$446$	2.02441e9	1.08051
$447$	−1.61685e9	−0.856236
$448$	−7.37251e8	−0.387385
$449$	2.92747e9	1.52627	0.763133	−	0.646241i	$-0.223660\pi$
$449$	2.92747e9	1.52627	0.763133	+	0.646241i	$0.223660\pi$
$450$	−1.62331e6	−0.000839764 0
$451$	−1.94237e8	−0.0997046
$452$	3.24716e8	0.165394
$453$	1.28413e9	0.649032
$454$	−4.14559e9	−2.07917
$455$	1.76547e9	0.878658
$456$	−2.20273e8	−0.108789
$457$	−2.45680e9	−1.20410	−0.602050	−	0.798459i	$-0.705649\pi$
$457$	−2.45680e9	−1.20410	−0.602050	+	0.798459i	$0.705649\pi$
$458$	−7.12849e8	−0.346712
$459$	−1.94520e9	−0.938903
$460$	−2.96721e7	−0.0142134
$461$	1.25968e9	0.598832	0.299416	−	0.954123i	$-0.403208\pi$
$461$	1.25968e9	0.598832	0.299416	+	0.954123i	$0.403208\pi$
$462$	−9.66344e7	−0.0455916
$463$	1.60779e9	0.752829	0.376414	−	0.926451i	$-0.377157\pi$
$463$	1.60779e9	0.752829	0.376414	+	0.926451i	$0.377157\pi$
$464$	−2.17895e9	−1.01259
$465$	−2.33546e8	−0.107718
$466$	−3.34117e9	−1.52949
$467$	1.74456e9	0.792643	0.396321	−	0.918112i	$-0.370287\pi$
$467$	1.74456e9	0.792643	0.396321	+	0.918112i	$0.370287\pi$
$468$	1.15821e6	0.000522309 0
$469$	7.95507e8	0.356073
$470$	1.17936e9	0.523966
$471$	1.83064e9	0.807290
$472$	−3.14544e9	−1.37684
$473$	−2.85630e7	−0.0124105
$474$	−2.00537e9	−0.864911
$475$	−1.13426e8	−0.0485605
$476$	2.10813e8	0.0895928
$477$	1.40371e6	0.000592194 0
$478$	−1.43788e9	−0.602179
$479$	2.90237e9	1.20664	0.603322	−	0.797498i	$-0.293844\pi$
$479$	2.90237e9	1.20664	0.603322	+	0.797498i	$0.293844\pi$
$480$	1.04767e9	0.432396
$481$	4.09476e9	1.67773
$482$	−5.04009e9	−2.05009
$483$	−8.26677e7	−0.0333827
$484$	−4.59520e8	−0.184224
$485$	−1.71147e9	−0.681198
$486$	−1.07468e7	−0.00424672
$487$	9.92687e8	0.389458	0.194729	−	0.980857i	$-0.437617\pi$
$487$	9.92687e8	0.389458	0.194729	+	0.980857i	$0.437617\pi$
$488$	1.61502e9	0.629084
$489$	−2.24959e9	−0.870005
$490$	−2.46105e9	−0.945004
$491$	4.20047e9	1.60145	0.800723	−	0.599034i	$-0.204449\pi$
$491$	4.20047e9	1.60145	0.800723	+	0.599034i	$0.204449\pi$
$492$	−5.99621e8	−0.226986
$493$	−2.19532e9	−0.825152
$494$	5.17310e8	0.193066
$495$	505926.	0.000187486 0
$496$	−2.85517e8	−0.105062
$497$	1.75547e9	0.641427
$498$	−2.98086e9	−1.08153
$499$	3.12871e9	1.12723	0.563616	−	0.826037i	$-0.309410\pi$
$499$	3.12871e9	1.12723	0.563616	+	0.826037i	$0.309410\pi$
$500$	−3.70165e8	−0.132434
$501$	2.71230e9	0.963620
$502$	−4.22638e9	−1.49110
$503$	3.86209e8	0.135311	0.0676556	−	0.997709i	$-0.478448\pi$
$503$	3.86209e8	0.135311	0.0676556	+	0.997709i	$0.478448\pi$
$504$	−2.56030e6	−0.000890808 0
$505$	−3.07087e8	−0.106107
$506$	1.67531e7	0.00574867
$507$	−3.18250e9	−1.08453
$508$	3.06299e7	0.0103663
$509$	−1.34663e9	−0.452621	−0.226311	−	0.974055i	$-0.572666\pi$
$509$	−1.34663e9	−0.452621	−0.226311	+	0.974055i	$0.572666\pi$
$510$	3.61056e9	1.20526
$511$	2.72698e9	0.904085
$512$	−1.81947e9	−0.599102
$513$	−3.75823e8	−0.122906
$514$	9.20522e8	0.298994
$515$	−5.61883e9	−1.81268
$516$	−8.81754e7	−0.0282536
$517$	−1.04169e8	−0.0331529
$518$	2.06085e9	0.651466
$519$	1.42138e9	0.446299
$520$	4.85118e9	1.51299
$521$	−4.59610e9	−1.42383	−0.711914	−	0.702267i	$-0.752171\pi$
$521$	−4.59610e9	−1.42383	−0.711914	+	0.702267i	$0.752171\pi$
$522$	−6.07025e6	−0.00186793
$523$	−3.76968e9	−1.15226	−0.576128	−	0.817359i	$-0.695437\pi$
$523$	−3.76968e9	−1.15226	−0.576128	+	0.817359i	$0.695437\pi$
$524$	−9.40511e8	−0.285565
$525$	6.74698e8	0.203494
$526$	3.17289e9	0.950615
$527$	−2.87662e8	−0.0856142
$528$	−3.16531e8	−0.0935831
$529$	−3.39049e9	−0.995791
$530$	−1.33860e9	−0.390559
$531$	−1.04457e7	−0.00302767
$532$	4.07301e7	0.0117280
$533$	−6.18515e9	−1.76932
$534$	−3.44613e9	−0.979348
$535$	4.20180e9	1.18631
$536$	2.18591e9	0.613133
$537$	−2.84425e8	−0.0792608
$538$	−4.25993e9	−1.17941
$539$	2.17377e8	0.0597933
$540$	8.02408e8	0.219289
$541$	6.00863e9	1.63149	0.815746	−	0.578410i	$-0.196327\pi$
$541$	6.00863e9	1.63149	0.815746	+	0.578410i	$0.196327\pi$
$542$	−2.76107e9	−0.744869
$543$	−7.06463e9	−1.89361
$544$	1.29044e9	0.343669
$545$	−5.54350e9	−1.46689
$546$	−3.07715e9	−0.809050
$547$	2.57778e9	0.673427	0.336714	−	0.941607i	$-0.390685\pi$
$547$	2.57778e9	0.673427	0.336714	+	0.941607i	$0.390685\pi$
$548$	−2.86286e8	−0.0743135
$549$	5.36334e6	0.00138335
$550$	−1.36731e8	−0.0350428
$551$	−4.24147e8	−0.108015
$552$	−2.27156e8	−0.0574826
$553$	−1.62867e9	−0.409540
$554$	3.02836e9	0.756700
$555$	5.52168e9	1.37103
$556$	8.21202e8	0.202623
$557$	−1.73000e9	−0.424181	−0.212091	−	0.977250i	$-0.568027\pi$
$557$	−1.73000e9	−0.424181	−0.212091	+	0.977250i	$0.568027\pi$
$558$	−795411.	−0.000193808 0
$559$	−9.09538e8	−0.220232
$560$	2.91046e9	0.700332
$561$	−3.18910e8	−0.0762602
$562$	5.90782e9	1.40395
$563$	−4.68663e9	−1.10683	−0.553416	−	0.832905i	$-0.686676\pi$
$563$	−4.68663e9	−1.10683	−0.553416	+	0.832905i	$0.686676\pi$
$564$	−3.21575e8	−0.0754754
$565$	4.51669e9	1.05354
$566$	7.04504e9	1.63315
$567$	2.23118e9	0.514036
$568$	4.82372e9	1.10449
$569$	8.45042e9	1.92303	0.961513	−	0.274759i	$-0.0885981\pi$
$569$	8.45042e9	1.92303	0.961513	+	0.274759i	$0.0885981\pi$
$570$	6.97579e8	0.157773
$571$	3.74129e8	0.0840998	0.0420499	−	0.999116i	$-0.486611\pi$
$571$	3.74129e8	0.0840998	0.0420499	+	0.999116i	$0.486611\pi$
$572$	9.75563e7	0.0217956
$573$	−5.37473e9	−1.19348
$574$	−3.11292e9	−0.687031
$575$	−1.16969e8	−0.0256587
$576$	−6.72760e6	−0.00146684
$577$	5.59761e7	0.0121307	0.00606537	−	0.999982i	$-0.498069\pi$
$577$	5.59761e7	0.0121307	0.00606537	+	0.999982i	$0.498069\pi$
$578$	−6.07437e8	−0.130844
$579$	−2.41384e9	−0.516814
$580$	9.05583e8	0.192722
$581$	−2.42092e9	−0.512111
$582$	2.98304e9	0.627232
$583$	1.18235e8	0.0247119
$584$	7.49324e9	1.55677
$585$	1.61103e7	0.00332705
$586$	5.34153e9	1.09654
$587$	−4.41966e9	−0.901894	−0.450947	−	0.892551i	$-0.648914\pi$
$587$	−4.41966e9	−0.901894	−0.450947	+	0.892551i	$0.648914\pi$
$588$	6.71053e8	0.136124
$589$	−5.55778e7	−0.0112072
$590$	9.96124e9	1.99678
$591$	3.66519e9	0.730365
$592$	6.75042e9	1.33723
$593$	4.30470e9	0.847718	0.423859	−	0.905728i	$-0.360675\pi$
$593$	4.30470e9	0.847718	0.423859	+	0.905728i	$0.360675\pi$
$594$	−4.53044e8	−0.0886927
$595$	2.93234e9	0.570695
$596$	8.21506e8	0.158946
$597$	3.30823e9	0.636334
$598$	5.33472e8	0.102014
$599$	−2.79184e9	−0.530758	−0.265379	−	0.964144i	$-0.585497\pi$
$599$	−2.79184e9	−0.530758	−0.265379	+	0.964144i	$0.585497\pi$
$600$	1.85395e9	0.350403
$601$	9.53719e9	1.79209	0.896045	−	0.443963i	$-0.146428\pi$
$601$	9.53719e9	1.79209	0.896045	+	0.443963i	$0.146428\pi$
$602$	−4.57761e8	−0.0855167
$603$	7.25920e6	0.00134827
$604$	−6.52455e8	−0.120482
$605$	−6.39177e9	−1.17348
$606$	5.35244e8	0.0977006
$607$	−1.03426e10	−1.87703	−0.938515	−	0.345240i	$-0.887798\pi$
$607$	−1.03426e10	−1.87703	−0.938515	+	0.345240i	$0.887798\pi$
$608$	2.49319e8	0.0449876
$609$	2.52299e9	0.452642
$610$	−5.11457e9	−0.912336
$611$	−3.31708e9	−0.588317
$612$	1.92372e6	0.000339244 0
$613$	−2.76574e7	−0.00484954	−0.00242477	−	0.999997i	$-0.500772\pi$
$613$	−2.76574e7	−0.00484954	−0.00242477	+	0.999997i	$0.500772\pi$
$614$	−6.68011e9	−1.16465
$615$	−8.34052e9	−1.44587
$616$	−2.15654e8	−0.0371728
$617$	5.52656e9	0.947234	0.473617	−	0.880731i	$-0.342948\pi$
$617$	5.52656e9	0.947234	0.473617	+	0.880731i	$0.342948\pi$
$618$	9.79344e9	1.66907
$619$	−1.07166e10	−1.81609	−0.908046	−	0.418871i	$-0.862426\pi$
$619$	−1.07166e10	−1.81609	−0.908046	+	0.418871i	$0.862426\pi$
$620$	1.18662e8	0.0199960
$621$	−3.87565e8	−0.0649418
$622$	−9.99661e9	−1.66566
$623$	−2.79879e9	−0.463726
$624$	−1.00794e10	−1.66069
$625$	−7.56273e9	−1.23908
$626$	−1.03521e10	−1.68662
$627$	−6.16150e7	−0.00998275
$628$	−9.30130e8	−0.149860
$629$	6.80115e9	1.08970
$630$	8.10816e6	0.00129190
$631$	−6.12871e7	−0.00971105	−0.00485552	−	0.999988i	$-0.501546\pi$
$631$	−6.12871e7	−0.00971105	−0.00485552	+	0.999988i	$0.501546\pi$
$632$	−4.47530e9	−0.705199
$633$	6.73372e9	1.05522
$634$	4.25888e9	0.663717
$635$	4.26051e8	0.0660318
$636$	3.64997e8	0.0562587
$637$	6.92198e9	1.06107
$638$	−5.11297e8	−0.0779473
$639$	1.60191e7	0.00242877
$640$	9.28591e9	1.40021
$641$	9.04843e9	1.35697	0.678485	−	0.734614i	$-0.262637\pi$
$641$	9.04843e9	1.35697	0.678485	+	0.734614i	$0.262637\pi$
$642$	−7.32360e9	−1.09233
$643$	−6.45538e9	−0.957599	−0.478799	−	0.877924i	$-0.658928\pi$
$643$	−6.45538e9	−0.957599	−0.478799	+	0.877924i	$0.658928\pi$
$644$	4.20027e7	0.00619693
$645$	−1.22649e9	−0.179972
$646$	8.59220e8	0.125398
$647$	2.44098e8	0.0354322	0.0177161	−	0.999843i	$-0.494360\pi$
$647$	2.44098e8	0.0354322	0.0177161	+	0.999843i	$0.494360\pi$
$648$	6.13086e9	0.885134
$649$	−8.79845e8	−0.126343
$650$	−4.35397e9	−0.621855
$651$	3.30598e8	0.0469642
$652$	1.14299e9	0.161502
$653$	3.48013e9	0.489102	0.244551	−	0.969636i	$-0.421359\pi$
$653$	3.48013e9	0.489102	0.244551	+	0.969636i	$0.421359\pi$
$654$	9.66215e9	1.35068
$655$	−1.30822e10	−1.81901
$656$	−1.01965e10	−1.41023
$657$	2.48844e7	0.00342333
$658$	−1.66945e9	−0.228446
$659$	−9.27568e9	−1.26254	−0.631272	−	0.775561i	$-0.717467\pi$
$659$	−9.27568e9	−1.26254	−0.631272	+	0.775561i	$0.717467\pi$
$660$	1.31552e8	0.0178113
$661$	−3.16224e9	−0.425882	−0.212941	−	0.977065i	$-0.568304\pi$
$661$	−3.16224e9	−0.425882	−0.212941	+	0.977065i	$0.568304\pi$
$662$	7.26412e9	0.973151
$663$	−1.01551e10	−1.35328
$664$	−6.65223e9	−0.881819
$665$	5.66542e8	0.0747062
$666$	1.88058e7	0.00246678
$667$	−4.37399e8	−0.0570739
$668$	−1.37809e9	−0.178880
$669$	−7.67808e9	−0.991428
$670$	−6.92250e9	−0.889203
$671$	4.51754e8	0.0577263
$672$	−1.48304e9	−0.188522
$673$	−2.80981e9	−0.355323	−0.177662	−	0.984092i	$-0.556853\pi$
$673$	−2.80981e9	−0.355323	−0.177662	+	0.984092i	$0.556853\pi$
$674$	6.06998e9	0.763620
$675$	3.16314e9	0.395872
$676$	1.61700e9	0.201324
$677$	−1.54447e10	−1.91302	−0.956511	−	0.291696i	$-0.905780\pi$
$677$	−1.54447e10	−1.91302	−0.956511	+	0.291696i	$0.905780\pi$
$678$	−7.87245e9	−0.970076
$679$	2.42269e9	0.296998
$680$	8.05752e9	0.982698
$681$	1.57232e10	1.90776
$682$	−6.69975e7	−0.00808748
$683$	−8.31895e9	−0.999070	−0.499535	−	0.866294i	$-0.666496\pi$
$683$	−8.31895e9	−0.999070	−0.499535	+	0.866294i	$0.666496\pi$
$684$	371673.	4.44083e−5 0
$685$	−3.98214e9	−0.473368
$686$	8.22530e9	0.972786
$687$	2.70365e9	0.318128
$688$	−1.49942e9	−0.175535
$689$	3.76498e9	0.438526
$690$	7.19374e8	0.0833649
$691$	9.72394e9	1.12116	0.560582	−	0.828099i	$-0.310577\pi$
$691$	9.72394e9	1.12116	0.560582	+	0.828099i	$0.310577\pi$
$692$	−7.22192e8	−0.0828479
$693$	−716168.	−8.17427e−5 0
$694$	1.21101e10	1.37528
$695$	1.14226e10	1.29068
$696$	6.93270e9	0.779418
$697$	−1.02732e10	−1.14918
$698$	1.55156e10	1.72693
$699$	1.26722e10	1.40340
$700$	−3.42808e8	−0.0377753
$701$	−2.48982e8	−0.0272995	−0.0136498	−	0.999907i	$-0.504345\pi$
$701$	−2.48982e8	−0.0272995	−0.0136498	+	0.999907i	$0.504345\pi$
$702$	−1.44264e10	−1.57390
$703$	1.31402e9	0.142645
$704$	−5.66666e8	−0.0612101
$705$	−4.47300e9	−0.480769
$706$	−1.10560e9	−0.118244
$707$	4.34701e8	0.0462618
$708$	−2.71613e9	−0.287630
$709$	7.54233e9	0.794774	0.397387	−	0.917651i	$-0.369917\pi$
$709$	7.54233e9	0.794774	0.397387	+	0.917651i	$0.369917\pi$
$710$	−1.52761e10	−1.60180
$711$	−1.48621e7	−0.00155073
$712$	−7.69055e9	−0.798505
$713$	−5.73143e7	−0.00592174
$714$	−5.11097e9	−0.525484
$715$	1.35697e9	0.138836
$716$	1.44514e8	0.0147134
$717$	5.45352e9	0.552535
$718$	2.23568e9	0.225410
$719$	6.70726e9	0.672967	0.336484	−	0.941689i	$-0.390762\pi$
$719$	6.70726e9	0.672967	0.336484	+	0.941689i	$0.390762\pi$
$720$	2.65587e7	0.00265181
$721$	7.95378e9	0.790315
$722$	−1.08449e10	−1.07237
$723$	1.91158e10	1.88108
$724$	3.58947e9	0.351516
$725$	3.56986e9	0.347911
$726$	1.11406e10	1.08052
$727$	1.58709e10	1.53190	0.765951	−	0.642899i	$-0.222269\pi$
$727$	1.58709e10	1.53190	0.765951	+	0.642899i	$0.222269\pi$
$728$	−6.86713e9	−0.659653
$729$	1.04807e10	1.00194
$730$	−2.37302e10	−2.25773
$731$	−1.51069e9	−0.143042
$732$	1.39459e9	0.131419
$733$	−2.20320e9	−0.206629	−0.103314	−	0.994649i	$-0.532945\pi$
$733$	−2.20320e9	−0.206629	−0.103314	+	0.994649i	$0.532945\pi$
$734$	1.32314e10	1.23501
$735$	9.33412e9	0.867097
$736$	2.57108e8	0.0237708
$737$	6.11443e8	0.0562626
$738$	−2.84062e7	−0.00260145
$739$	−1.48017e10	−1.34913	−0.674567	−	0.738214i	$-0.735670\pi$
$739$	−1.48017e10	−1.34913	−0.674567	+	0.738214i	$0.735670\pi$
$740$	−2.80551e9	−0.254508
$741$	−1.96202e9	−0.177150
$742$	1.89487e9	0.170281
$743$	−2.07320e10	−1.85430	−0.927152	−	0.374686i	$-0.877750\pi$
$743$	−2.07320e10	−1.85430	−0.927152	+	0.374686i	$0.877750\pi$
$744$	9.08422e8	0.0808691
$745$	1.14269e10	1.01247
$746$	−1.71405e10	−1.51160
$747$	−2.20915e7	−0.00193911
$748$	1.62035e8	0.0141564
$749$	−5.94790e9	−0.517222
$750$	8.97430e9	0.776759
$751$	−2.94907e9	−0.254065	−0.127033	−	0.991899i	$-0.540545\pi$
$751$	−2.94907e9	−0.254065	−0.127033	+	0.991899i	$0.540545\pi$
$752$	−5.46837e9	−0.468917
$753$	1.60296e10	1.36817
$754$	−1.62814e10	−1.38322
$755$	−9.07543e9	−0.767455
$756$	−1.13586e9	−0.0956086
$757$	−9.04947e9	−0.758207	−0.379103	−	0.925354i	$-0.623768\pi$
$757$	−9.04947e9	−0.758207	−0.379103	+	0.925354i	$0.623768\pi$
$758$	−2.29093e9	−0.191060
$759$	−6.35401e7	−0.00527475
$760$	1.55675e9	0.128639
$761$	2.07707e10	1.70846	0.854230	−	0.519896i	$-0.174029\pi$
$761$	2.07707e10	1.70846	0.854230	+	0.519896i	$0.174029\pi$
$762$	−7.42593e8	−0.0608007
$763$	7.84716e9	0.639553
$764$	2.73085e9	0.221550
$765$	2.67583e7	0.00216094
$766$	1.00093e10	0.804644
$767$	−2.80172e10	−2.24202
$768$	−6.75226e9	−0.537879
$769$	−1.18493e9	−0.0939617	−0.0469808	−	0.998896i	$-0.514960\pi$
$769$	−1.18493e9	−0.0939617	−0.0469808	+	0.998896i	$0.514960\pi$
$770$	6.82951e8	0.0539103
$771$	−3.49130e9	−0.274345
$772$	1.22645e9	0.0959378
$773$	−1.66232e9	−0.129446	−0.0647228	−	0.997903i	$-0.520616\pi$
$773$	−1.66232e9	−0.129446	−0.0647228	+	0.997903i	$0.520616\pi$
$774$	−4.17718e6	−0.000323810 0
$775$	4.67775e8	0.0360978
$776$	6.65710e9	0.511410
$777$	−7.81627e9	−0.597759
$778$	−3.75121e9	−0.285590
$779$	−1.98483e9	−0.150433
$780$	4.18905e9	0.316071
$781$	1.34929e9	0.101351
$782$	8.86066e8	0.0662586
$783$	1.18283e10	0.880558
$784$	1.14112e10	0.845719
$785$	−1.29378e10	−0.954589
$786$	2.28018e10	1.67491
$787$	2.65010e10	1.93799	0.968993	−	0.247088i	$-0.0794736\pi$
$787$	2.65010e10	1.93799	0.968993	+	0.247088i	$0.0794736\pi$
$788$	−1.86225e9	−0.135580
$789$	−1.20340e10	−0.872246
$790$	1.41727e10	1.02272
$791$	−6.39365e9	−0.459336
$792$	−1.96790e6	−0.000140755 0
$793$	1.43853e10	1.02439
$794$	−2.65090e10	−1.87941
$795$	5.07698e9	0.358361
$796$	−1.68088e9	−0.118125
$797$	−2.48128e7	−0.00173609	−0.000868045	−	1.00000i	$-0.500276\pi$
$797$	−2.48128e7	−0.00173609	−0.000868045		1.00000i	$0.500276\pi$
$798$	−9.87465e8	−0.0687878
$799$	−5.50947e9	−0.382117
$800$	−2.09841e9	−0.144902
$801$	−2.55396e7	−0.00175590
$802$	1.62941e10	1.11537
$803$	2.09601e9	0.142853
$804$	1.88756e9	0.128087
$805$	5.84243e8	0.0394737
$806$	−2.13342e9	−0.143517
$807$	1.61568e10	1.08218
$808$	1.19448e9	0.0796596
$809$	−2.21936e8	−0.0147369	−0.00736847	−	0.999973i	$-0.502345\pi$
$809$	−2.21936e8	−0.0147369	−0.00736847	+	0.999973i	$0.502345\pi$
$810$	−1.94157e10	−1.28368
$811$	1.47954e10	0.973987	0.486994	−	0.873405i	$-0.338093\pi$
$811$	1.47954e10	0.973987	0.486994	+	0.873405i	$0.338093\pi$
$812$	−1.28191e9	−0.0840253
$813$	1.04720e10	0.683462
$814$	1.58401e9	0.102937
$815$	1.58986e10	1.02875
$816$	−1.67412e10	−1.07863
$817$	−2.91873e8	−0.0187248
$818$	7.01241e9	0.447951
$819$	−2.28051e7	−0.00145057
$820$	4.23774e9	0.268402
$821$	−2.55026e10	−1.60836	−0.804181	−	0.594384i	$-0.797396\pi$
$821$	−2.55026e10	−1.60836	−0.804181	+	0.594384i	$0.797396\pi$
$822$	6.94074e9	0.435867
$823$	1.87610e9	0.117316	0.0586578	−	0.998278i	$-0.481318\pi$
$823$	1.87610e9	0.117316	0.0586578	+	0.998278i	$0.481318\pi$
$824$	2.18555e10	1.36087
$825$	5.18587e8	0.0321538
$826$	−1.41007e10	−0.870585
$827$	−2.34241e10	−1.44010	−0.720052	−	0.693920i	$-0.755882\pi$
$827$	−2.34241e10	−1.44010	−0.720052	+	0.693920i	$0.755882\pi$
$828$	383285.	2.34647e−5 0
$829$	2.88836e10	1.76080	0.880402	−	0.474228i	$-0.157273\pi$
$829$	2.88836e10	1.76080	0.880402	+	0.474228i	$0.157273\pi$
$830$	2.10668e10	1.27887
$831$	−1.14858e10	−0.694317
$832$	−1.80445e10	−1.08621
$833$	1.14970e10	0.689171
$834$	−1.99093e10	−1.18843
$835$	−1.91688e10	−1.13944
$836$	3.13060e7	0.00185313
$837$	1.54992e9	0.0913629
$838$	−2.68209e10	−1.57442
$839$	8.35473e9	0.488388	0.244194	−	0.969726i	$-0.421477\pi$
$839$	8.35473e9	0.488388	0.244194	+	0.969726i	$0.421477\pi$
$840$	−9.26016e9	−0.539065
$841$	−3.90062e9	−0.226124
$842$	−2.84404e9	−0.164189
$843$	−2.24069e10	−1.28820
$844$	−3.42134e9	−0.195883
$845$	2.24919e10	1.28241
$846$	−1.52341e7	−0.000865012 0
$847$	9.04793e9	0.511631
$848$	6.20676e9	0.349526
$849$	−2.67200e10	−1.49851
$850$	−7.23169e9	−0.403899
$851$	1.35507e9	0.0753718
$852$	4.16534e9	0.230734
$853$	−2.54143e10	−1.40203	−0.701014	−	0.713147i	$-0.747269\pi$
$853$	−2.54143e10	−1.40203	−0.701014	+	0.713147i	$0.747269\pi$
$854$	7.23998e9	0.397773
$855$	5.16984e6	0.000282876 0
$856$	−1.63437e10	−0.890620
$857$	−2.93738e10	−1.59414	−0.797071	−	0.603885i	$-0.793619\pi$
$857$	−2.93738e10	−1.59414	−0.797071	+	0.603885i	$0.793619\pi$
$858$	−2.36516e9	−0.127837
$859$	−7.87923e9	−0.424138	−0.212069	−	0.977255i	$-0.568020\pi$
$859$	−7.87923e9	−0.424138	−0.212069	+	0.977255i	$0.568020\pi$
$860$	6.23168e8	0.0334088
$861$	1.18065e10	0.630392
$862$	2.87386e10	1.52823
$863$	−1.41785e10	−0.750916	−0.375458	−	0.926839i	$-0.622515\pi$
$863$	−1.41785e10	−0.750916	−0.375458	+	0.926839i	$0.622515\pi$
$864$	−6.95284e9	−0.366745
$865$	−1.00454e10	−0.527731
$866$	−3.51890e9	−0.184117
$867$	2.30385e9	0.120057
$868$	−1.67974e8	−0.00871811
$869$	−1.25183e9	−0.0647108
$870$	−2.19550e10	−1.13036
$871$	1.94703e10	0.998412
$872$	2.15625e10	1.10127
$873$	2.21076e7	0.00112459
$874$	1.71192e8	0.00867350
$875$	7.28852e9	0.367800
$876$	6.47051e9	0.325218
$877$	−9.31500e9	−0.466320	−0.233160	−	0.972438i	$-0.574907\pi$
$877$	−9.31500e9	−0.466320	−0.233160	+	0.972438i	$0.574907\pi$
$878$	3.12096e10	1.55617
$879$	−2.02590e10	−1.00614
$880$	2.23704e9	0.110658
$881$	1.57869e10	0.777826	0.388913	−	0.921275i	$-0.372851\pi$
$881$	1.57869e10	0.777826	0.388913	+	0.921275i	$0.372851\pi$
$882$	3.17902e7	0.00156010
$883$	−9.82559e9	−0.480282	−0.240141	−	0.970738i	$-0.577194\pi$
$883$	−9.82559e9	−0.480282	−0.240141	+	0.970738i	$0.577194\pi$
$884$	5.15973e9	0.251214
$885$	−3.77804e10	−1.83217
$886$	−8.06120e9	−0.389387
$887$	−5.02494e9	−0.241768	−0.120884	−	0.992667i	$-0.538573\pi$
$887$	−5.02494e9	−0.241768	−0.120884	+	0.992667i	$0.538573\pi$
$888$	−2.14777e10	−1.02930
$889$	−6.03100e8	−0.0287895
$890$	2.43550e10	1.15804
$891$	1.71493e9	0.0812221
$892$	3.90116e9	0.184042
$893$	−1.06446e9	−0.0500205
$894$	−1.99167e10	−0.932256
$895$	2.01014e9	0.0937228
$896$	−1.31448e10	−0.610484
$897$	−2.02332e9	−0.0936035
$898$	3.60611e10	1.66178
$899$	1.74921e9	0.0802940
$900$	−3.12821e6	−0.000143036 0
$901$	6.25341e9	0.284826
$902$	−2.39265e9	−0.108557
$903$	1.73617e9	0.0784666
$904$	−1.75686e10	−0.790945
$905$	4.99283e10	2.23912
$906$	1.58182e10	0.706656
$907$	−3.57868e9	−0.159257	−0.0796283	−	0.996825i	$-0.525373\pi$
$907$	−3.57868e9	−0.159257	−0.0796283	+	0.996825i	$0.525373\pi$
$908$	−7.98879e9	−0.354144
$909$	3.96675e6	0.000175171 0
$910$	2.17474e10	0.956670
$911$	−2.81588e10	−1.23396	−0.616978	−	0.786980i	$-0.711643\pi$
$911$	−2.81588e10	−1.23396	−0.616978	+	0.786980i	$0.711643\pi$
$912$	−3.23449e9	−0.141197
$913$	−1.86077e9	−0.0809178
$914$	−3.02633e10	−1.31100
$915$	1.93983e10	0.837123
$916$	−1.37370e9	−0.0590552
$917$	1.85186e10	0.793078
$918$	−2.39614e10	−1.02226
$919$	−4.74290e9	−0.201576	−0.100788	−	0.994908i	$-0.532136\pi$
$919$	−4.74290e9	−0.201576	−0.100788	+	0.994908i	$0.532136\pi$
$920$	1.60539e9	0.0679710
$921$	2.53359e10	1.06863
$922$	1.55169e10	0.652000
$923$	4.29659e10	1.79853
$924$	−1.86220e8	−0.00776559
$925$	−1.10595e10	−0.459452
$926$	1.98051e10	0.819668
$927$	7.25803e7	0.00299254
$928$	−7.84685e9	−0.322313
$929$	−2.37371e10	−0.971344	−0.485672	−	0.874141i	$-0.661425\pi$
$929$	−2.37371e10	−0.971344	−0.485672	+	0.874141i	$0.661425\pi$
$930$	−2.87686e9	−0.117281
$931$	2.22128e9	0.0902150
$932$	−6.43862e9	−0.260518
$933$	3.79146e10	1.52834
$934$	2.14899e10	0.863018
$935$	2.25385e9	0.0901748
$936$	−6.26643e7	−0.00249778
$937$	−1.59383e10	−0.632926	−0.316463	−	0.948605i	$-0.602495\pi$
$937$	−1.59383e10	−0.632926	−0.316463	+	0.948605i	$0.602495\pi$
$938$	9.79921e9	0.387687
$939$	3.92627e10	1.54757
$940$	2.27269e9	0.0892468
$941$	−4.38313e10	−1.71483	−0.857415	−	0.514626i	$-0.827931\pi$
$941$	−4.38313e10	−1.71483	−0.857415	+	0.514626i	$0.827931\pi$
$942$	2.25502e10	0.878965
$943$	−2.04684e9	−0.0794865
$944$	−4.61877e10	−1.78700
$945$	−1.57994e10	−0.609015
$946$	−3.51844e8	−0.0135124
$947$	−3.68371e10	−1.40948	−0.704742	−	0.709464i	$-0.748937\pi$
$947$	−3.68371e10	−1.40948	−0.704742	+	0.709464i	$0.748937\pi$
$948$	−3.86447e9	−0.147320
$949$	6.67440e10	2.53501
$950$	−1.39720e9	−0.0528720
$951$	−1.61528e10	−0.609000
$952$	−1.14059e10	−0.428450
$953$	3.58699e10	1.34247	0.671236	−	0.741244i	$-0.265764\pi$
$953$	3.58699e10	1.34247	0.671236	+	0.741244i	$0.265764\pi$
$954$	1.72912e7	0.000644772 0
$955$	3.79852e10	1.41125
$956$	−2.77088e9	−0.102569
$957$	1.93922e9	0.0715213
$958$	3.57520e10	1.31377
$959$	5.63695e9	0.206385
$960$	−2.43326e10	−0.887643
$961$	−2.72834e10	−0.991669
$962$	5.04401e10	1.82668
$963$	−5.42760e7	−0.00195847
$964$	−9.71254e9	−0.349191
$965$	1.70595e10	0.611112
$966$	−1.01832e9	−0.0363465
$967$	−6.33260e9	−0.225211	−0.112605	−	0.993640i	$-0.535920\pi$
$967$	−6.33260e9	−0.225211	−0.112605	+	0.993640i	$0.535920\pi$
$968$	2.48620e10	0.880994
$969$	−3.25880e9	−0.115060
$970$	−2.10822e10	−0.741678
$971$	−3.71924e10	−1.30373	−0.651864	−	0.758336i	$-0.726013\pi$
$971$	−3.71924e10	−1.30373	−0.651864	+	0.758336i	$0.726013\pi$
$972$	−2.07098e7	−0.000723341 0
$973$	−1.61694e10	−0.562729
$974$	1.22281e10	0.424036
$975$	1.65135e10	0.570589
$976$	2.37149e10	0.816484
$977$	3.55570e10	1.21982	0.609908	−	0.792472i	$-0.291206\pi$
$977$	3.55570e10	1.21982	0.609908	+	0.792472i	$0.291206\pi$
$978$	−2.77108e10	−0.947248
$979$	−2.15121e9	−0.0732727
$980$	−4.74258e9	−0.160962
$981$	7.16073e7	0.00242167
$982$	5.17422e10	1.74363
$983$	−2.71260e10	−0.910854	−0.455427	−	0.890273i	$-0.650513\pi$
$983$	−2.71260e10	−0.910854	−0.455427	+	0.890273i	$0.650513\pi$
$984$	3.24421e10	1.08549
$985$	−2.59032e10	−0.863628
$986$	−2.70424e10	−0.898413
$987$	6.33180e9	0.209612
$988$	9.96886e8	0.0328849
$989$	−3.00992e8	−0.00989390
$990$	6.23209e6	0.000204132 0
$991$	−1.89518e10	−0.618575	−0.309287	−	0.950969i	$-0.600091\pi$
$991$	−1.89518e10	−0.618575	−0.309287	+	0.950969i	$0.600091\pi$
$992$	−1.02821e9	−0.0334418
$993$	−2.75510e10	−0.892924
$994$	2.16243e10	0.698376
$995$	−2.33804e10	−0.752440
$996$	−5.74429e9	−0.184216
$997$	8.54283e9	0.273004	0.136502	−	0.990640i	$-0.456414\pi$
$997$	8.54283e9	0.273004	0.136502	+	0.990640i	$0.456414\pi$
$998$	3.85401e10	1.22731
$999$	−3.66445e10	−1.16286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.9	✓	11
3.2	odd	2		387.8.a.b.1.3		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.9	✓	11	1.1	even	1	trivial
387.8.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+12.3182 q^{2} -46.7197 q^{3} +23.7379 q^{4} +330.186 q^{5} -575.503 q^{6} -467.397 q^{7} -1284.32 q^{8} -4.26512 q^{9} +O(q^{10})\)	\(q+12.3182 q^{2} -46.7197 q^{3} +23.7379 q^{4} +330.186 q^{5} -575.503 q^{6} -467.397 q^{7} -1284.32 q^{8} -4.26512 q^{9} +4067.29 q^{10} -359.251 q^{11} -1109.03 q^{12} -11439.7 q^{13} -5757.49 q^{14} -15426.2 q^{15} -18859.0 q^{16} -19000.7 q^{17} -52.5385 q^{18} -3671.03 q^{19} +7837.90 q^{20} +21836.7 q^{21} -4425.32 q^{22} -3785.73 q^{23} +60003.2 q^{24} +30897.5 q^{25} -140917. q^{26} +102375. q^{27} -11095.0 q^{28} +115539. q^{29} -190023. q^{30} +15139.6 q^{31} -67915.2 q^{32} +16784.1 q^{33} -234054. q^{34} -154328. q^{35} -101.245 q^{36} -357942. q^{37} -45220.5 q^{38} +534461. q^{39} -424064. q^{40} +540673. q^{41} +268988. q^{42} +79507.0 q^{43} -8527.85 q^{44} -1408.28 q^{45} -46633.3 q^{46} +289961. q^{47} +881086. q^{48} -605083. q^{49} +380601. q^{50} +887708. q^{51} -271555. q^{52} -329115. q^{53} +1.26108e6 q^{54} -118619. q^{55} +600288. q^{56} +171510. q^{57} +1.42323e6 q^{58} +2.44911e6 q^{59} -366185. q^{60} -1.25749e6 q^{61} +186492. q^{62} +1993.50 q^{63} +1.57735e6 q^{64} -3.77723e6 q^{65} +206750. q^{66} -1.70199e6 q^{67} -451036. q^{68} +176868. q^{69} -1.90104e6 q^{70} -3.75585e6 q^{71} +5477.78 q^{72} -5.83440e6 q^{73} -4.40920e6 q^{74} -1.44352e6 q^{75} -87142.4 q^{76} +167913. q^{77} +6.58360e6 q^{78} +3.48456e6 q^{79} -6.22696e6 q^{80} -4.77362e6 q^{81} +6.66012e6 q^{82} +5.17957e6 q^{83} +518356. q^{84} -6.27376e6 q^{85} +979383. q^{86} -5.39795e6 q^{87} +461394. q^{88} +5.98803e6 q^{89} -17347.5 q^{90} +5.34690e6 q^{91} -89865.1 q^{92} -707317. q^{93} +3.57180e6 q^{94} -1.21212e6 q^{95} +3.17298e6 q^{96} -5.18336e6 q^{97} -7.45353e6 q^{98} +1532.25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 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

Properties

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