LMFDB - Embedded newform 43.8.a.a.1.11

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			1.11
Root			$-19.3827$ 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)

$f(q)$	$=$	$q+17.3827 q^{2} -29.0652 q^{3} +174.160 q^{4} -230.747 q^{5} -505.234 q^{6} -1110.68 q^{7} +802.384 q^{8} -1342.21 q^{9} +O(q^{10})$	\(q+17.3827 q^{2} -29.0652 q^{3} +174.160 q^{4} -230.747 q^{5} -505.234 q^{6} -1110.68 q^{7} +802.384 q^{8} -1342.21 q^{9} -4011.02 q^{10} -607.968 q^{11} -5062.00 q^{12} +13041.8 q^{13} -19306.6 q^{14} +6706.73 q^{15} -8344.81 q^{16} -20609.8 q^{17} -23331.3 q^{18} -24170.2 q^{19} -40186.9 q^{20} +32282.1 q^{21} -10568.2 q^{22} +60316.5 q^{23} -23321.5 q^{24} -24880.7 q^{25} +226703. q^{26} +102577. q^{27} -193435. q^{28} -77712.2 q^{29} +116581. q^{30} +34644.3 q^{31} -247761. q^{32} +17670.7 q^{33} -358255. q^{34} +256286. q^{35} -233759. q^{36} +489896. q^{37} -420144. q^{38} -379064. q^{39} -185148. q^{40} -809882. q^{41} +561152. q^{42} +79507.0 q^{43} -105884. q^{44} +309712. q^{45} +1.04847e6 q^{46} +289158. q^{47} +242544. q^{48} +410063. q^{49} -432494. q^{50} +599029. q^{51} +2.27136e6 q^{52} +892274. q^{53} +1.78308e6 q^{54} +140287. q^{55} -891191. q^{56} +702512. q^{57} -1.35085e6 q^{58} -1.51749e6 q^{59} +1.16804e6 q^{60} -160538. q^{61} +602213. q^{62} +1.49077e6 q^{63} -3.23863e6 q^{64} -3.00937e6 q^{65} +307166. q^{66} -2.42938e6 q^{67} -3.58940e6 q^{68} -1.75311e6 q^{69} +4.45495e6 q^{70} +993231. q^{71} -1.07697e6 q^{72} -2.67982e6 q^{73} +8.51574e6 q^{74} +723162. q^{75} -4.20947e6 q^{76} +675257. q^{77} -6.58917e6 q^{78} -4.46840e6 q^{79} +1.92554e6 q^{80} -46018.4 q^{81} -1.40780e7 q^{82} -4.10044e6 q^{83} +5.62225e6 q^{84} +4.75566e6 q^{85} +1.38205e6 q^{86} +2.25872e6 q^{87} -487824. q^{88} -2.96316e6 q^{89} +5.38364e6 q^{90} -1.44853e7 q^{91} +1.05047e7 q^{92} -1.00695e6 q^{93} +5.02636e6 q^{94} +5.57721e6 q^{95} +7.20123e6 q^{96} -9.83610e6 q^{97} +7.12801e6 q^{98} +816022. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	17.3827	1.53643	0.768216	−	0.640191i	$-0.221145\pi$
$2$	17.3827	1.53643	0.768216	+	0.640191i	$0.221145\pi$
$3$	−29.0652	−0.621512	−0.310756	−	0.950490i	$-0.600582\pi$
$3$	−29.0652	−0.621512	−0.310756	+	0.950490i	$0.600582\pi$
$4$	174.160	1.36062
$5$	−230.747	−0.825547	−0.412773	−	0.910834i	$-0.635440\pi$
$5$	−230.747	−0.825547	−0.412773	+	0.910834i	$0.635440\pi$
$6$	−505.234	−0.954911
$7$	−1110.68	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$7$	−1110.68	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$8$	802.384	0.554074
$9$	−1342.21	−0.613723
$10$	−4011.02	−1.26840
$11$	−607.968	−0.137723	−0.0688615	−	0.997626i	$-0.521937\pi$
$11$	−607.968	−0.137723	−0.0688615	+	0.997626i	$0.521937\pi$
$12$	−5062.00	−0.845644
$13$	13041.8	1.64640	0.823202	−	0.567748i	$-0.192185\pi$
$13$	13041.8	1.64640	0.823202	+	0.567748i	$0.192185\pi$
$14$	−19306.6	−1.88044
$15$	6706.73	0.513087
$16$	−8344.81	−0.509327
$17$	−20609.8	−1.01743	−0.508713	−	0.860936i	$-0.669878\pi$
$17$	−20609.8	−1.01743	−0.508713	+	0.860936i	$0.669878\pi$
$18$	−23331.3	−0.942944
$19$	−24170.2	−0.808430	−0.404215	−	0.914664i	$-0.632455\pi$
$19$	−24170.2	−0.808430	−0.404215	+	0.914664i	$0.632455\pi$
$20$	−40186.9	−1.12326
$21$	32282.1	0.760667
$22$	−10568.2	−0.211602
$23$	60316.5	1.03369	0.516843	−	0.856080i	$-0.327107\pi$
$23$	60316.5	1.03369	0.516843	+	0.856080i	$0.327107\pi$
$24$	−23321.5	−0.344363
$25$	−24880.7	−0.318472
$26$	226703.	2.52959
$27$	102577.	1.00295
$28$	−193435.	−1.66526
$29$	−77712.2	−0.591693	−0.295846	−	0.955236i	$-0.595602\pi$
$29$	−77712.2	−0.591693	−0.295846	+	0.955236i	$0.595602\pi$
$30$	116581.	0.788324
$31$	34644.3	0.208865	0.104433	−	0.994532i	$-0.466697\pi$
$31$	34644.3	0.208865	0.104433	+	0.994532i	$0.466697\pi$
$32$	−247761.	−1.33662
$33$	17670.7	0.0855965
$34$	−358255.	−1.56320
$35$	256286.	1.01038
$36$	−233759.	−0.835046
$37$	489896.	1.59000	0.795002	−	0.606607i	$-0.207470\pi$
$37$	489896.	1.59000	0.795002	+	0.606607i	$0.207470\pi$
$38$	−420144.	−1.24210
$39$	−379064.	−1.02326
$40$	−185148.	−0.457414
$41$	−809882.	−1.83518	−0.917589	−	0.397529i	$-0.869868\pi$
$41$	−809882.	−1.83518	−0.917589	+	0.397529i	$0.869868\pi$
$42$	561152.	1.16871
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	−105884.	−0.187389
$45$	309712.	0.506657
$46$	1.04847e6	1.58819
$47$	289158.	0.406249	0.203125	−	0.979153i	$-0.434890\pi$
$47$	289158.	0.406249	0.203125	+	0.979153i	$0.434890\pi$
$48$	242544.	0.316553
$49$	410063.	0.497925
$50$	−432494.	−0.489311
$51$	599029.	0.632342
$52$	2.27136e6	2.24014
$53$	892274.	0.823252	0.411626	−	0.911353i	$-0.364961\pi$
$53$	892274.	0.823252	0.411626	+	0.911353i	$0.364961\pi$
$54$	1.78308e6	1.54096
$55$	140287.	0.113697
$56$	−891191.	−0.678129
$57$	702512.	0.502449
$58$	−1.35085e6	−0.909096
$59$	−1.51749e6	−0.961930	−0.480965	−	0.876740i	$-0.659714\pi$
$59$	−1.51749e6	−0.961930	−0.480965	+	0.876740i	$0.659714\pi$
$60$	1.16804e6	0.698119
$61$	−160538.	−0.0905570	−0.0452785	−	0.998974i	$-0.514418\pi$
$61$	−160538.	−0.0905570	−0.0452785	+	0.998974i	$0.514418\pi$
$62$	602213.	0.320907
$63$	1.49077e6	0.751134
$64$	−3.23863e6	−1.54430
$65$	−3.00937e6	−1.35918
$66$	307166.	0.131513
$67$	−2.42938e6	−0.986811	−0.493406	−	0.869799i	$-0.664248\pi$
$67$	−2.42938e6	−0.986811	−0.493406	+	0.869799i	$0.664248\pi$
$68$	−3.58940e6	−1.38433
$69$	−1.75311e6	−0.642449
$70$	4.45495e6	1.55239
$71$	993231.	0.329341	0.164671	−	0.986349i	$-0.447344\pi$
$71$	993231.	0.329341	0.164671	+	0.986349i	$0.447344\pi$
$72$	−1.07697e6	−0.340048
$73$	−2.67982e6	−0.806262	−0.403131	−	0.915142i	$-0.632078\pi$
$73$	−2.67982e6	−0.806262	−0.403131	+	0.915142i	$0.632078\pi$
$74$	8.51574e6	2.44293
$75$	723162.	0.197934
$76$	−4.20947e6	−1.09997
$77$	675257.	0.168559
$78$	−6.58917e6	−1.57217
$79$	−4.46840e6	−1.01966	−0.509832	−	0.860274i	$-0.670292\pi$
$79$	−4.46840e6	−1.01966	−0.509832	+	0.860274i	$0.670292\pi$
$80$	1.92554e6	0.420473
$81$	−46018.4	−0.00962130
$82$	−1.40780e7	−2.81963
$83$	−4.10044e6	−0.787150	−0.393575	−	0.919292i	$-0.628762\pi$
$83$	−4.10044e6	−0.787150	−0.393575	+	0.919292i	$0.628762\pi$
$84$	5.62225e6	1.03498
$85$	4.75566e6	0.839932
$86$	1.38205e6	0.234304
$87$	2.25872e6	0.367744
$88$	−487824.	−0.0763087
$89$	−2.96316e6	−0.445543	−0.222772	−	0.974871i	$-0.571510\pi$
$89$	−2.96316e6	−0.445543	−0.222772	+	0.974871i	$0.571510\pi$
$90$	5.38364e6	0.778444
$91$	−1.44853e7	−2.01503
$92$	1.05047e7	1.40646
$93$	−1.00695e6	−0.129812
$94$	5.02636e6	0.624175
$95$	5.57721e6	0.667397
$96$	7.20123e6	0.830725
$97$	−9.83610e6	−1.09426	−0.547132	−	0.837046i	$-0.684280\pi$
$97$	−9.83610e6	−1.09426	−0.547132	+	0.837046i	$0.684280\pi$
$98$	7.12801e6	0.765028
$99$	816022.	0.0845238
$100$	−4.33321e6	−0.433321
$101$	−1.11991e7	−1.08158	−0.540788	−	0.841159i	$-0.681874\pi$
$101$	−1.11991e7	−1.08158	−0.540788	+	0.841159i	$0.681874\pi$
$102$	1.04128e7	0.971550
$103$	2.09902e6	0.189272	0.0946359	−	0.995512i	$-0.469831\pi$
$103$	2.09902e6	0.189272	0.0946359	+	0.995512i	$0.469831\pi$
$104$	1.04646e7	0.912229
$105$	−7.44901e6	−0.627966
$106$	1.55102e7	1.26487
$107$	1.39300e7	1.09928	0.549639	−	0.835402i	$-0.314765\pi$
$107$	1.39300e7	1.09928	0.549639	+	0.835402i	$0.314765\pi$
$108$	1.78649e7	1.36463
$109$	2.48819e7	1.84031	0.920154	−	0.391557i	$-0.128063\pi$
$109$	2.48819e7	1.84031	0.920154	+	0.391557i	$0.128063\pi$
$110$	2.43857e6	0.174687
$111$	−1.42390e7	−0.988206
$112$	9.26840e6	0.623364
$113$	−1.72023e7	−1.12153	−0.560766	−	0.827974i	$-0.689493\pi$
$113$	−1.72023e7	−1.12153	−0.560766	+	0.827974i	$0.689493\pi$
$114$	1.22116e7	0.771978
$115$	−1.39179e7	−0.853357
$116$	−1.35343e7	−0.805071
$117$	−1.75049e7	−1.01044
$118$	−2.63781e7	−1.47794
$119$	2.28908e7	1.24522
$120$	5.38137e6	0.284288
$121$	−1.91175e7	−0.981032
$122$	−2.79058e6	−0.139135
$123$	2.35394e7	1.14059
$124$	6.03365e6	0.284187
$125$	2.37683e7	1.08846
$126$	2.59136e7	1.15407
$127$	−3.68734e7	−1.59735	−0.798675	−	0.601763i	$-0.794465\pi$
$127$	−3.68734e7	−1.59735	−0.798675	+	0.601763i	$0.794465\pi$
$128$	−2.45829e7	−1.03609
$129$	−2.31089e6	−0.0947797
$130$	−5.23110e7	−2.08829
$131$	2.41863e7	0.939981	0.469991	−	0.882671i	$-0.344257\pi$
$131$	2.41863e7	0.939981	0.469991	+	0.882671i	$0.344257\pi$
$132$	3.07753e6	0.116465
$133$	2.68453e7	0.989435
$134$	−4.22293e7	−1.51617
$135$	−2.36695e7	−0.827981
$136$	−1.65370e7	−0.563729
$137$	−4.37084e6	−0.145226	−0.0726128	−	0.997360i	$-0.523134\pi$
$137$	−4.37084e6	−0.145226	−0.0726128	+	0.997360i	$0.523134\pi$
$138$	−3.04739e7	−0.987079
$139$	2.60325e7	0.822174	0.411087	−	0.911596i	$-0.365149\pi$
$139$	2.60325e7	0.822174	0.411087	+	0.911596i	$0.365149\pi$
$140$	4.46347e7	1.37475
$141$	−8.40445e6	−0.252489
$142$	1.72651e7	0.506010
$143$	−7.92901e6	−0.226748
$144$	1.12005e7	0.312586
$145$	1.79319e7	0.488470
$146$	−4.65827e7	−1.23877
$147$	−1.19186e7	−0.309466
$148$	8.53202e7	2.16340
$149$	2.65502e7	0.657530	0.328765	−	0.944412i	$-0.393368\pi$
$149$	2.65502e7	0.657530	0.328765	+	0.944412i	$0.393368\pi$
$150$	1.25705e7	0.304113
$151$	5.28071e7	1.24817	0.624084	−	0.781357i	$-0.285472\pi$
$151$	5.28071e7	1.24817	0.624084	+	0.781357i	$0.285472\pi$
$152$	−1.93938e7	−0.447930
$153$	2.76627e7	0.624417
$154$	1.17378e7	0.258979
$155$	−7.99408e6	−0.172428
$156$	−6.60177e7	−1.39227
$157$	−6.72632e7	−1.38717	−0.693584	−	0.720376i	$-0.743969\pi$
$157$	−6.72632e7	−1.38717	−0.693584	+	0.720376i	$0.743969\pi$
$158$	−7.76730e7	−1.56664
$159$	−2.59342e7	−0.511661
$160$	5.71702e7	1.10344
$161$	−6.69922e7	−1.26513
$162$	−799926.	−0.0147825
$163$	5.59234e7	1.01143	0.505717	−	0.862700i	$-0.331228\pi$
$163$	5.59234e7	1.01143	0.505717	+	0.862700i	$0.331228\pi$
$164$	−1.41049e8	−2.49699
$165$	−4.07748e6	−0.0706639
$166$	−7.12770e7	−1.20940
$167$	1.13304e7	0.188252	0.0941258	−	0.995560i	$-0.469994\pi$
$167$	1.13304e7	0.188252	0.0941258	+	0.995560i	$0.469994\pi$
$168$	2.59027e7	0.421466
$169$	1.07341e8	1.71065
$170$	8.26664e7	1.29050
$171$	3.24415e7	0.496152
$172$	1.38469e7	0.207493
$173$	−3.43489e7	−0.504373	−0.252186	−	0.967679i	$-0.581150\pi$
$173$	−3.43489e7	−0.504373	−0.252186	+	0.967679i	$0.581150\pi$
$174$	3.92628e7	0.565014
$175$	2.76344e7	0.389778
$176$	5.07338e6	0.0701460
$177$	4.41062e7	0.597851
$178$	−5.15078e7	−0.684547
$179$	1.06394e8	1.38654	0.693268	−	0.720680i	$-0.256170\pi$
$179$	1.06394e8	1.38654	0.693268	+	0.720680i	$0.256170\pi$
$180$	5.39394e7	0.689369
$181$	−1.03201e8	−1.29363	−0.646815	−	0.762647i	$-0.723899\pi$
$181$	−1.03201e8	−1.29363	−0.646815	+	0.762647i	$0.723899\pi$
$182$	−2.51794e8	−3.09596
$183$	4.66606e6	0.0562823
$184$	4.83970e7	0.572739
$185$	−1.13042e8	−1.31262
$186$	−1.75035e7	−0.199448
$187$	1.25301e7	0.140123
$188$	5.03597e7	0.552752
$189$	−1.13930e8	−1.22751
$190$	9.69471e7	1.02541
$191$	6.61411e7	0.686839	0.343419	−	0.939182i	$-0.388415\pi$
$191$	6.61411e7	0.686839	0.343419	+	0.939182i	$0.388415\pi$
$192$	9.41315e7	0.959800
$193$	5.13623e7	0.514273	0.257136	−	0.966375i	$-0.417221\pi$
$193$	5.13623e7	0.514273	0.257136	+	0.966375i	$0.417221\pi$
$194$	−1.70978e8	−1.68126
$195$	8.74679e7	0.844749
$196$	7.14164e7	0.677488
$197$	−9.19611e7	−0.856983	−0.428492	−	0.903546i	$-0.640955\pi$
$197$	−9.19611e7	−0.856983	−0.428492	+	0.903546i	$0.640955\pi$
$198$	1.41847e7	0.129865
$199$	6.18358e7	0.556230	0.278115	−	0.960548i	$-0.410290\pi$
$199$	6.18358e7	0.556230	0.278115	+	0.960548i	$0.410290\pi$
$200$	−1.99639e7	−0.176457
$201$	7.06106e7	0.613315
$202$	−1.94670e8	−1.66177
$203$	8.63132e7	0.724171
$204$	1.04327e8	0.860379
$205$	1.86878e8	1.51503
$206$	3.64867e7	0.290803
$207$	−8.09576e7	−0.634397
$208$	−1.08832e8	−0.838558
$209$	1.46947e7	0.111339
$210$	−1.29484e8	−0.964827
$211$	1.45231e8	1.06431	0.532157	−	0.846646i	$-0.321382\pi$
$211$	1.45231e8	1.06431	0.532157	+	0.846646i	$0.321382\pi$
$212$	1.55398e8	1.12014
$213$	−2.88685e7	−0.204689
$214$	2.42142e8	1.68897
$215$	−1.83460e7	−0.125895
$216$	8.23065e7	0.555707
$217$	−3.84787e7	−0.255630
$218$	4.32515e8	2.82751
$219$	7.78897e7	0.501101
$220$	2.44324e7	0.154699
$221$	−2.68789e8	−1.67509
$222$	−2.47512e8	−1.51831
$223$	1.18865e8	0.717775	0.358888	−	0.933381i	$-0.383156\pi$
$223$	1.18865e8	0.717775	0.358888	+	0.933381i	$0.383156\pi$
$224$	2.75183e8	1.63589
$225$	3.33951e7	0.195454
$226$	−2.99023e8	−1.72316
$227$	−2.33026e8	−1.32225	−0.661125	−	0.750276i	$-0.729921\pi$
$227$	−2.33026e8	−1.32225	−0.661125	+	0.750276i	$0.729921\pi$
$228$	1.22349e8	0.683644
$229$	2.52042e8	1.38691	0.693457	−	0.720498i	$-0.256087\pi$
$229$	2.52042e8	1.38691	0.693457	+	0.720498i	$0.256087\pi$
$230$	−2.41931e8	−1.31112
$231$	−1.96265e7	−0.104761
$232$	−6.23551e7	−0.327841
$233$	1.61379e8	0.835799	0.417899	−	0.908493i	$-0.362766\pi$
$233$	1.61379e8	0.835799	0.417899	+	0.908493i	$0.362766\pi$
$234$	−3.04283e8	−1.55247
$235$	−6.67224e7	−0.335378
$236$	−2.64286e8	−1.30882
$237$	1.29875e8	0.633733
$238$	3.97906e8	1.91320
$239$	−3.28589e8	−1.55690	−0.778449	−	0.627707i	$-0.783993\pi$
$239$	−3.28589e8	−1.55690	−0.778449	+	0.627707i	$0.783993\pi$
$240$	−5.59664e7	−0.261329
$241$	−5.95088e7	−0.273855	−0.136928	−	0.990581i	$-0.543723\pi$
$241$	−5.95088e7	−0.273855	−0.136928	+	0.990581i	$0.543723\pi$
$242$	−3.32315e8	−1.50729
$243$	−2.22999e8	−0.996968
$244$	−2.79592e7	−0.123214
$245$	−9.46209e7	−0.411060
$246$	4.09180e8	1.75243
$247$	−3.15223e8	−1.33100
$248$	2.77981e7	0.115727
$249$	1.19180e8	0.489223
$250$	4.13158e8	1.67235
$251$	−1.34270e8	−0.535944	−0.267972	−	0.963427i	$-0.586354\pi$
$251$	−1.34270e8	−0.535944	−0.267972	+	0.963427i	$0.586354\pi$
$252$	2.59631e8	1.02201
$253$	−3.66705e7	−0.142362
$254$	−6.40960e8	−2.45422
$255$	−1.38224e8	−0.522028
$256$	−1.27732e7	−0.0475837
$257$	−2.54950e8	−0.936892	−0.468446	−	0.883492i	$-0.655186\pi$
$257$	−2.54950e8	−0.936892	−0.468446	+	0.883492i	$0.655186\pi$
$258$	−4.01696e7	−0.145623
$259$	−5.44117e8	−1.94600
$260$	−5.24111e8	−1.84934
$261$	1.04306e8	0.363135
$262$	4.20424e8	1.44422
$263$	1.82117e8	0.617314	0.308657	−	0.951173i	$-0.400121\pi$
$263$	1.82117e8	0.617314	0.308657	+	0.951173i	$0.400121\pi$
$264$	1.41787e7	0.0474268
$265$	−2.05890e8	−0.679633
$266$	4.66645e8	1.52020
$267$	8.61249e7	0.276911
$268$	−4.23101e8	−1.34268
$269$	−4.86909e8	−1.52516	−0.762579	−	0.646895i	$-0.776067\pi$
$269$	−4.86909e8	−1.52516	−0.762579	+	0.646895i	$0.776067\pi$
$270$	−4.11440e8	−1.27214
$271$	−5.57858e7	−0.170267	−0.0851336	−	0.996370i	$-0.527132\pi$
$271$	−5.57858e7	−0.170267	−0.0851336	+	0.996370i	$0.527132\pi$
$272$	1.71985e8	0.518202
$273$	4.21018e8	1.25237
$274$	−7.59772e7	−0.223129
$275$	1.51266e7	0.0438610
$276$	−3.05322e8	−0.874131
$277$	6.88409e8	1.94611	0.973055	−	0.230572i	$-0.0740596\pi$
$277$	6.88409e8	1.94611	0.973055	+	0.230572i	$0.0740596\pi$
$278$	4.52516e8	1.26322
$279$	−4.65000e7	−0.128185
$280$	2.05640e8	0.559828
$281$	2.36816e8	0.636707	0.318353	−	0.947972i	$-0.396870\pi$
$281$	2.36816e8	0.636707	0.318353	+	0.947972i	$0.396870\pi$
$282$	−1.46092e8	−0.387932
$283$	3.02454e8	0.793245	0.396623	−	0.917982i	$-0.370182\pi$
$283$	3.02454e8	0.793245	0.396623	+	0.917982i	$0.370182\pi$
$284$	1.72981e8	0.448109
$285$	−1.62103e8	−0.414795
$286$	−1.37828e8	−0.348383
$287$	8.99518e8	2.24607
$288$	3.32548e8	0.820314
$289$	1.44250e7	0.0351539
$290$	3.11705e8	0.750501
$291$	2.85889e8	0.680098
$292$	−4.66718e8	−1.09702
$293$	−6.95562e8	−1.61547	−0.807735	−	0.589546i	$-0.799307\pi$
$293$	−6.95562e8	−1.61547	−0.807735	+	0.589546i	$0.799307\pi$
$294$	−2.07177e8	−0.475474
$295$	3.50157e8	0.794118
$296$	3.93085e8	0.880979
$297$	−6.23638e7	−0.138129
$298$	4.61515e8	1.01025
$299$	7.86637e8	1.70187
$300$	1.25946e8	0.269314
$301$	−8.83067e7	−0.186643
$302$	9.17932e8	1.91773
$303$	3.25503e8	0.672212
$304$	2.01696e8	0.411755
$305$	3.70436e7	0.0747591
$306$	4.80854e8	0.959374
$307$	6.66587e8	1.31484	0.657420	−	0.753525i	$-0.271648\pi$
$307$	6.66587e8	1.31484	0.657420	+	0.753525i	$0.271648\pi$
$308$	1.17603e8	0.229345
$309$	−6.10085e7	−0.117635
$310$	−1.38959e8	−0.264924
$311$	−8.68038e8	−1.63635	−0.818177	−	0.574967i	$-0.805015\pi$
$311$	−8.68038e8	−1.63635	−0.818177	+	0.574967i	$0.805015\pi$
$312$	−3.04155e8	−0.566962
$313$	6.01957e8	1.10958	0.554792	−	0.831989i	$-0.312798\pi$
$313$	6.01957e8	1.10958	0.554792	+	0.831989i	$0.312798\pi$
$314$	−1.16922e9	−2.13129
$315$	−3.43990e8	−0.620096
$316$	−7.78215e8	−1.38738
$317$	−8.81210e8	−1.55372	−0.776859	−	0.629675i	$-0.783188\pi$
$317$	−8.81210e8	−1.55372	−0.776859	+	0.629675i	$0.783188\pi$
$318$	−4.50807e8	−0.786132
$319$	4.72466e7	0.0814897
$320$	7.47305e8	1.27489
$321$	−4.04879e8	−0.683215
$322$	−1.16451e9	−1.94378
$323$	4.98143e8	0.822517
$324$	−8.01455e6	−0.0130910
$325$	−3.24489e8	−0.524334
$326$	9.72103e8	1.55400
$327$	−7.23198e8	−1.14377
$328$	−6.49837e8	−1.01682
$329$	−3.21161e8	−0.497208
$330$	−7.08777e7	−0.108570
$331$	−8.76684e8	−1.32876	−0.664378	−	0.747397i	$-0.731303\pi$
$331$	−8.76684e8	−1.32876	−0.664378	+	0.747397i	$0.731303\pi$
$332$	−7.14133e8	−1.07102
$333$	−6.57545e8	−0.975822
$334$	1.96954e8	0.289236
$335$	5.60574e8	0.814659
$336$	−2.69388e8	−0.387428
$337$	−3.84104e8	−0.546694	−0.273347	−	0.961916i	$-0.588131\pi$
$337$	−3.84104e8	−0.546694	−0.273347	+	0.961916i	$0.588131\pi$
$338$	1.86587e9	2.62829
$339$	4.99989e8	0.697046
$340$	8.28244e8	1.14283
$341$	−2.10626e7	−0.0287655
$342$	5.63922e8	0.762304
$343$	4.59244e8	0.614488
$344$	6.37952e7	0.0844954
$345$	4.04526e8	0.530371
$346$	−5.97078e8	−0.774934
$347$	−9.79801e8	−1.25888	−0.629441	−	0.777049i	$-0.716716\pi$
$347$	−9.79801e8	−1.25888	−0.629441	+	0.777049i	$0.716716\pi$
$348$	3.93379e8	0.500361
$349$	−1.02828e9	−1.29485	−0.647427	−	0.762128i	$-0.724155\pi$
$349$	−1.02828e9	−1.29485	−0.647427	+	0.762128i	$0.724155\pi$
$350$	4.80362e8	0.598867
$351$	1.33780e9	1.65126
$352$	1.50631e8	0.184083
$353$	−1.21223e9	−1.46680	−0.733402	−	0.679795i	$-0.762069\pi$
$353$	−1.21223e9	−1.46680	−0.733402	+	0.679795i	$0.762069\pi$
$354$	7.66686e8	0.918557
$355$	−2.29185e8	−0.271887
$356$	−5.16063e8	−0.606217
$357$	−6.65328e8	−0.773922
$358$	1.84942e9	2.13032
$359$	1.13679e9	1.29673	0.648365	−	0.761330i	$-0.275453\pi$
$359$	1.13679e9	1.29673	0.648365	+	0.761330i	$0.275453\pi$
$360$	2.48508e8	0.280725
$361$	−3.09674e8	−0.346441
$362$	−1.79392e9	−1.98757
$363$	5.55656e8	0.609723
$364$	−2.52275e9	−2.74170
$365$	6.18362e8	0.665607
$366$	8.11090e7	0.0864739
$367$	1.53409e9	1.62002	0.810009	−	0.586418i	$-0.199462\pi$
$367$	1.53409e9	1.62002	0.810009	+	0.586418i	$0.199462\pi$
$368$	−5.03330e8	−0.526484
$369$	1.08703e9	1.12629
$370$	−1.96498e9	−2.01676
$371$	−9.91029e8	−1.00758
$372$	−1.75369e8	−0.176626
$373$	−8.11683e8	−0.809852	−0.404926	−	0.914350i	$-0.632703\pi$
$373$	−8.11683e8	−0.809852	−0.404926	+	0.914350i	$0.632703\pi$
$374$	2.17808e8	0.215289
$375$	−6.90831e8	−0.676491
$376$	2.32016e8	0.225092
$377$	−1.01351e9	−0.974166
$378$	−1.98042e9	−1.88598
$379$	2.21198e8	0.208710	0.104355	−	0.994540i	$-0.466722\pi$
$379$	2.21198e8	0.208710	0.104355	+	0.994540i	$0.466722\pi$
$380$	9.71325e8	0.908076
$381$	1.07173e9	0.992772
$382$	1.14971e9	1.05528
$383$	1.31039e9	1.19180	0.595901	−	0.803058i	$-0.296795\pi$
$383$	1.31039e9	1.19180	0.595901	+	0.803058i	$0.296795\pi$
$384$	7.14507e8	0.643943
$385$	−1.55814e8	−0.139153
$386$	8.92817e8	0.790145
$387$	−1.06715e8	−0.0935919
$388$	−1.71305e9	−1.48888
$389$	2.22960e8	0.192045	0.0960226	−	0.995379i	$-0.469388\pi$
$389$	2.22960e8	0.192045	0.0960226	+	0.995379i	$0.469388\pi$
$390$	1.52043e9	1.29790
$391$	−1.24311e9	−1.05170
$392$	3.29028e8	0.275887
$393$	−7.02980e8	−0.584210
$394$	−1.59854e9	−1.31670
$395$	1.03107e9	0.841780
$396$	1.42118e8	0.115005
$397$	−6.55657e8	−0.525909	−0.262954	−	0.964808i	$-0.584697\pi$
$397$	−6.55657e8	−0.525909	−0.262954	+	0.964808i	$0.584697\pi$
$398$	1.07488e9	0.854610
$399$	−7.80265e8	−0.614946
$400$	2.07624e8	0.162207
$401$	−7.45083e8	−0.577031	−0.288516	−	0.957475i	$-0.593162\pi$
$401$	−7.45083e8	−0.577031	−0.288516	+	0.957475i	$0.593162\pi$
$402$	1.22741e9	0.942317
$403$	4.51825e8	0.343877
$404$	−1.95043e9	−1.47162
$405$	1.06186e7	0.00794283
$406$	1.50036e9	1.11264
$407$	−2.97841e8	−0.218980
$408$	4.80651e8	0.350364
$409$	−4.87681e8	−0.352456	−0.176228	−	0.984349i	$-0.556390\pi$
$409$	−4.87681e8	−0.352456	−0.176228	+	0.984349i	$0.556390\pi$
$410$	3.24846e9	2.32773
$411$	1.27040e8	0.0902594
$412$	3.65565e8	0.257528
$413$	1.68544e9	1.17730
$414$	−1.40726e9	−0.974708
$415$	9.46167e8	0.649829
$416$	−3.23125e9	−2.20062
$417$	−7.56641e8	−0.510991
$418$	2.55434e8	0.171065
$419$	1.39810e9	0.928518	0.464259	−	0.885700i	$-0.346321\pi$
$419$	1.39810e9	0.928518	0.464259	+	0.885700i	$0.346321\pi$
$420$	−1.29732e9	−0.854426
$421$	−2.54250e9	−1.66063	−0.830316	−	0.557293i	$-0.811840\pi$
$421$	−2.54250e9	−1.66063	−0.830316	+	0.557293i	$0.811840\pi$
$422$	2.52451e9	1.63525
$423$	−3.88111e8	−0.249325
$424$	7.15947e8	0.456142
$425$	5.12785e8	0.324022
$426$	−5.01814e8	−0.314491
$427$	1.78306e8	0.110833
$428$	2.42605e9	1.49570
$429$	2.30459e8	0.140926
$430$	−3.18904e8	−0.193429
$431$	6.45199e8	0.388171	0.194086	−	0.980985i	$-0.437826\pi$
$431$	6.45199e8	0.388171	0.194086	+	0.980985i	$0.437826\pi$
$432$	−8.55989e8	−0.510829
$433$	−1.41525e9	−0.837770	−0.418885	−	0.908039i	$-0.637579\pi$
$433$	−1.41525e9	−0.837770	−0.418885	+	0.908039i	$0.637579\pi$
$434$	−6.68865e8	−0.392757
$435$	−5.21195e8	−0.303590
$436$	4.33342e9	2.50397
$437$	−1.45786e9	−0.835663
$438$	1.35394e9	0.769908
$439$	3.20780e9	1.80959	0.904797	−	0.425844i	$-0.140023\pi$
$439$	3.20780e9	1.80959	0.904797	+	0.425844i	$0.140023\pi$
$440$	1.12564e8	0.0629964
$441$	−5.50391e8	−0.305588
$442$	−4.67230e9	−2.57367
$443$	−3.24734e9	−1.77466	−0.887328	−	0.461138i	$-0.847441\pi$
$443$	−3.24734e9	−1.77466	−0.887328	+	0.461138i	$0.847441\pi$
$444$	−2.47985e9	−1.34458
$445$	6.83741e8	0.367817
$446$	2.06621e9	1.10281
$447$	−7.71687e8	−0.408663
$448$	3.59707e9	1.89006
$449$	−9.00041e8	−0.469246	−0.234623	−	0.972086i	$-0.575385\pi$
$449$	−9.00041e8	−0.469246	−0.234623	+	0.972086i	$0.575385\pi$
$450$	5.80499e8	0.300302
$451$	4.92383e8	0.252746
$452$	−2.99595e9	−1.52598
$453$	−1.53485e9	−0.775751
$454$	−4.05063e9	−2.03155
$455$	3.34244e9	1.66350
$456$	5.63685e8	0.278394
$457$	3.56466e9	1.74708	0.873538	−	0.486756i	$-0.161820\pi$
$457$	3.56466e9	1.74708	0.873538	+	0.486756i	$0.161820\pi$
$458$	4.38119e9	2.13090
$459$	−2.11410e9	−1.02042
$460$	−2.42394e9	−1.16110
$461$	2.12032e9	1.00797	0.503986	−	0.863712i	$-0.331866\pi$
$461$	2.12032e9	1.00797	0.503986	+	0.863712i	$0.331866\pi$
$462$	−3.41163e8	−0.160959
$463$	−1.32103e9	−0.618555	−0.309278	−	0.950972i	$-0.600087\pi$
$463$	−1.32103e9	−0.618555	−0.309278	+	0.950972i	$0.600087\pi$
$464$	6.48494e8	0.301365
$465$	2.32350e8	0.107166
$466$	2.80521e9	1.28415
$467$	2.75292e7	0.0125079	0.00625395	−	0.999980i	$-0.498009\pi$
$467$	2.75292e7	0.0125079	0.00625395	+	0.999980i	$0.498009\pi$
$468$	−3.04865e9	−1.37482
$469$	2.69826e9	1.20776
$470$	−1.15982e9	−0.515285
$471$	1.95502e9	0.862141
$472$	−1.21761e9	−0.532980
$473$	−4.83377e7	−0.0210026
$474$	2.25758e9	0.973688
$475$	6.01370e8	0.257463
$476$	3.98667e9	1.69428
$477$	−1.19762e9	−0.505249
$478$	−5.71178e9	−2.39207
$479$	3.09426e9	1.28642	0.643209	−	0.765691i	$-0.277603\pi$
$479$	3.09426e9	1.28642	0.643209	+	0.765691i	$0.277603\pi$
$480$	−1.66167e9	−0.685803
$481$	6.38914e9	2.61779
$482$	−1.03443e9	−0.420760
$483$	1.94715e9	0.786291
$484$	−3.32951e9	−1.33482
$485$	2.26965e9	0.903366
$486$	−3.87634e9	−1.53177
$487$	2.45364e9	0.962629	0.481315	−	0.876548i	$-0.340159\pi$
$487$	2.45364e9	0.962629	0.481315	+	0.876548i	$0.340159\pi$
$488$	−1.28813e8	−0.0501753
$489$	−1.62543e9	−0.628618
$490$	−1.64477e9	−0.631566
$491$	−3.55312e9	−1.35464	−0.677321	−	0.735688i	$-0.736859\pi$
$491$	−3.55312e9	−1.35464	−0.677321	+	0.735688i	$0.736859\pi$
$492$	4.09962e9	1.55191
$493$	1.60163e9	0.602003
$494$	−5.47945e9	−2.04500
$495$	−1.88295e8	−0.0697783
$496$	−2.89100e8	−0.106381
$497$	−1.10316e9	−0.403080
$498$	2.07168e9	0.751658
$499$	1.61280e9	0.581069	0.290534	−	0.956865i	$-0.406167\pi$
$499$	1.61280e9	0.581069	0.290534	+	0.956865i	$0.406167\pi$
$500$	4.13948e9	1.48099
$501$	−3.29322e8	−0.117001
$502$	−2.33397e9	−0.823442
$503$	−3.82508e9	−1.34015	−0.670074	−	0.742294i	$-0.733738\pi$
$503$	−3.82508e9	−1.34015	−0.670074	+	0.742294i	$0.733738\pi$
$504$	1.19617e9	0.416184
$505$	2.58415e9	0.892891
$506$	−6.37435e8	−0.218730
$507$	−3.11988e9	−1.06319
$508$	−6.42186e9	−2.17339
$509$	9.34320e8	0.314039	0.157019	−	0.987596i	$-0.449811\pi$
$509$	9.34320e8	0.314039	0.157019	+	0.987596i	$0.449811\pi$
$510$	−2.40272e9	−0.802060
$511$	2.97642e9	0.986782
$512$	2.92457e9	0.962981
$513$	−2.47931e9	−0.810813
$514$	−4.43174e9	−1.43947
$515$	−4.84343e8	−0.156253
$516$	−4.02464e8	−0.128959
$517$	−1.75799e8	−0.0559499
$518$	−9.45825e9	−2.98990
$519$	9.98359e8	0.313474
$520$	−2.41467e9	−0.753088
$521$	1.99243e9	0.617237	0.308619	−	0.951186i	$-0.400133\pi$
$521$	1.99243e9	0.617237	0.308619	+	0.951186i	$0.400133\pi$
$522$	1.81313e9	0.557933
$523$	−2.41120e9	−0.737017	−0.368509	−	0.929624i	$-0.620132\pi$
$523$	−2.41120e9	−0.737017	−0.368509	+	0.929624i	$0.620132\pi$
$524$	4.21228e9	1.27896
$525$	−8.03200e8	−0.242251
$526$	3.16570e9	0.948460
$527$	−7.14012e8	−0.212505
$528$	−1.47459e8	−0.0435966
$529$	2.33258e8	0.0685081
$530$	−3.57893e9	−1.04421
$531$	2.03679e9	0.590358
$532$	4.67537e9	1.34625
$533$	−1.05623e10	−3.02145
$534$	1.49709e9	0.425454
$535$	−3.21431e9	−0.907506
$536$	−1.94930e9	−0.546766
$537$	−3.09236e9	−0.861749
$538$	−8.46382e9	−2.34330
$539$	−2.49305e8	−0.0685757
$540$	−4.12227e9	−1.12657
$541$	4.57719e9	1.24282	0.621410	−	0.783486i	$-0.286560\pi$
$541$	4.57719e9	1.24282	0.621410	+	0.783486i	$0.286560\pi$
$542$	−9.69710e8	−0.261604
$543$	2.99957e9	0.804006
$544$	5.10630e9	1.35991
$545$	−5.74143e9	−1.51926
$546$	7.31844e9	1.92417
$547$	1.95785e9	0.511475	0.255737	−	0.966746i	$-0.417682\pi$
$547$	1.95785e9	0.511475	0.255737	+	0.966746i	$0.417682\pi$
$548$	−7.61225e8	−0.197597
$549$	2.15475e8	0.0555769
$550$	2.62943e8	0.0673894
$551$	1.87832e9	0.478342
$552$	−1.40667e9	−0.355964
$553$	4.96295e9	1.24796
$554$	1.19664e10	2.99007
$555$	3.28560e9	0.815810
$556$	4.53381e9	1.11867
$557$	−5.46100e9	−1.33899	−0.669497	−	0.742814i	$-0.733490\pi$
$557$	−5.46100e9	−1.33899	−0.669497	+	0.742814i	$0.733490\pi$
$558$	−8.08298e8	−0.196948
$559$	1.03692e9	0.251074
$560$	−2.13866e9	−0.514616
$561$	−3.64190e8	−0.0870880
$562$	4.11652e9	0.978256
$563$	1.67608e9	0.395836	0.197918	−	0.980219i	$-0.436582\pi$
$563$	1.67608e9	0.395836	0.197918	+	0.980219i	$0.436582\pi$
$564$	−1.46372e9	−0.343542
$565$	3.96938e9	0.925877
$566$	5.25749e9	1.21877
$567$	5.11116e7	0.0117755
$568$	7.96953e8	0.182479
$569$	−6.70164e8	−0.152506	−0.0762532	−	0.997088i	$-0.524296\pi$
$569$	−6.70164e8	−0.152506	−0.0762532	+	0.997088i	$0.524296\pi$
$570$	−2.81779e9	−0.637304
$571$	−4.11196e9	−0.924320	−0.462160	−	0.886797i	$-0.652925\pi$
$571$	−4.11196e9	−0.924320	−0.462160	+	0.886797i	$0.652925\pi$
$572$	−1.38092e9	−0.308518
$573$	−1.92241e9	−0.426878
$574$	1.56361e10	3.45094
$575$	−1.50071e9	−0.329201
$576$	4.34693e9	0.947772
$577$	3.72343e9	0.806915	0.403458	−	0.914998i	$-0.367808\pi$
$577$	3.72343e9	0.806915	0.403458	+	0.914998i	$0.367808\pi$
$578$	2.50746e8	0.0540116
$579$	−1.49286e9	−0.319627
$580$	3.12301e9	0.664624
$581$	4.55427e9	0.963391
$582$	4.96953e9	1.04492
$583$	−5.42474e8	−0.113381
$584$	−2.15025e9	−0.446729
$585$	4.03921e9	0.834162
$586$	−1.20908e10	−2.48206
$587$	−5.57358e9	−1.13737	−0.568684	−	0.822556i	$-0.692547\pi$
$587$	−5.57358e9	−1.13737	−0.568684	+	0.822556i	$0.692547\pi$
$588$	−2.07574e9	−0.421067
$589$	−8.37359e8	−0.168853
$590$	6.08668e9	1.22011
$591$	2.67287e9	0.532625
$592$	−4.08809e9	−0.809832
$593$	−7.08618e9	−1.39547	−0.697735	−	0.716356i	$-0.745809\pi$
$593$	−7.08618e9	−1.39547	−0.697735	+	0.716356i	$0.745809\pi$
$594$	−1.08405e9	−0.212226
$595$	−5.28200e9	−1.02799
$596$	4.62397e9	0.894650
$597$	−1.79727e9	−0.345704
$598$	1.36739e10	2.61480
$599$	−9.43000e9	−1.79274	−0.896371	−	0.443304i	$-0.853806\pi$
$599$	−9.43000e9	−1.79274	−0.896371	+	0.443304i	$0.853806\pi$
$600$	5.80254e8	0.109670
$601$	−8.09030e9	−1.52021	−0.760106	−	0.649799i	$-0.774853\pi$
$601$	−8.09030e9	−1.52021	−0.760106	+	0.649799i	$0.774853\pi$
$602$	−1.53501e9	−0.286764
$603$	3.26075e9	0.605629
$604$	9.19688e9	1.69829
$605$	4.41132e9	0.809888
$606$	5.65814e9	1.03281
$607$	−5.71746e9	−1.03763	−0.518815	−	0.854886i	$-0.673627\pi$
$607$	−5.71746e9	−1.03763	−0.518815	+	0.854886i	$0.673627\pi$
$608$	5.98843e9	1.08056
$609$	−2.50871e9	−0.450081
$610$	6.43920e8	0.114862
$611$	3.77115e9	0.668851
$612$	4.81773e9	0.849597
$613$	−2.69282e9	−0.472166	−0.236083	−	0.971733i	$-0.575864\pi$
$613$	−2.69282e9	−0.472166	−0.236083	+	0.971733i	$0.575864\pi$
$614$	1.15871e10	2.02016
$615$	−5.43166e9	−0.941607
$616$	5.41816e8	0.0933940
$617$	3.24038e9	0.555390	0.277695	−	0.960669i	$-0.410429\pi$
$617$	3.24038e9	0.555390	0.277695	+	0.960669i	$0.410429\pi$
$618$	−1.06049e9	−0.180738
$619$	−2.96275e9	−0.502086	−0.251043	−	0.967976i	$-0.580773\pi$
$619$	−2.96275e9	−0.502086	−0.251043	+	0.967976i	$0.580773\pi$
$620$	−1.39225e9	−0.234610
$621$	6.18711e9	1.03673
$622$	−1.50889e10	−2.51415
$623$	3.29112e9	0.545299
$624$	3.16322e9	0.521174
$625$	−3.54067e9	−0.580103
$626$	1.04637e10	1.70480
$627$	−4.27105e8	−0.0691988
$628$	−1.17146e10	−1.88741
$629$	−1.00967e10	−1.61771
$630$	−5.97949e9	−0.952736
$631$	−2.21319e9	−0.350685	−0.175342	−	0.984508i	$-0.556103\pi$
$631$	−2.21319e9	−0.350685	−0.175342	+	0.984508i	$0.556103\pi$
$632$	−3.58537e9	−0.564969
$633$	−4.22116e9	−0.661483
$634$	−1.53179e10	−2.38718
$635$	8.50843e9	1.31869
$636$	−4.51669e9	−0.696178
$637$	5.34796e9	0.819786
$638$	8.21275e8	0.125203
$639$	−1.33313e9	−0.202124
$640$	5.67243e9	0.855341
$641$	−3.46476e9	−0.519600	−0.259800	−	0.965662i	$-0.583657\pi$
$641$	−3.46476e9	−0.519600	−0.259800	+	0.965662i	$0.583657\pi$
$642$	−7.03790e9	−1.04971
$643$	6.65219e9	0.986794	0.493397	−	0.869804i	$-0.335755\pi$
$643$	6.65219e9	0.986794	0.493397	+	0.869804i	$0.335755\pi$
$644$	−1.16674e10	−1.72136
$645$	5.33232e8	0.0782451
$646$	8.65908e9	1.26374
$647$	−5.79744e9	−0.841533	−0.420766	−	0.907169i	$-0.638239\pi$
$647$	−5.79744e9	−0.841533	−0.420766	+	0.907169i	$0.638239\pi$
$648$	−3.69244e7	−0.00533091
$649$	9.22585e8	0.132480
$650$	−5.64051e9	−0.805604
$651$	1.11839e9	0.158877
$652$	9.73962e9	1.37618
$653$	5.81937e9	0.817861	0.408931	−	0.912566i	$-0.365902\pi$
$653$	5.81937e9	0.817861	0.408931	+	0.912566i	$0.365902\pi$
$654$	−1.25712e10	−1.75733
$655$	−5.58092e9	−0.775999
$656$	6.75832e9	0.934706
$657$	3.59689e9	0.494821
$658$	−5.58267e9	−0.763926
$659$	−6.30400e9	−0.858059	−0.429029	−	0.903290i	$-0.641144\pi$
$659$	−6.30400e9	−0.858059	−0.429029	+	0.903290i	$0.641144\pi$
$660$	−7.10133e8	−0.0961470
$661$	−5.51668e9	−0.742973	−0.371486	−	0.928438i	$-0.621152\pi$
$661$	−5.51668e9	−0.742973	−0.371486	+	0.928438i	$0.621152\pi$
$662$	−1.52392e10	−2.04154
$663$	7.81242e9	1.04109
$664$	−3.29013e9	−0.436139
$665$	−6.19448e9	−0.816825
$666$	−1.14299e10	−1.49928
$667$	−4.68733e9	−0.611625
$668$	1.97331e9	0.256140
$669$	−3.45485e9	−0.446106
$670$	9.74431e9	1.25167
$671$	9.76017e7	0.0124718
$672$	−7.99825e9	−1.01672
$673$	5.21617e9	0.659628	0.329814	−	0.944046i	$-0.393014\pi$
$673$	5.21617e9	0.659628	0.329814	+	0.944046i	$0.393014\pi$
$674$	−6.67678e9	−0.839958
$675$	−2.55219e9	−0.319411
$676$	1.86944e10	2.32755
$677$	3.56727e9	0.441851	0.220925	−	0.975291i	$-0.429092\pi$
$677$	3.56727e9	0.441851	0.220925	+	0.975291i	$0.429092\pi$
$678$	8.69118e9	1.07096
$679$	1.09247e10	1.33927
$680$	3.81586e9	0.465384
$681$	6.77295e9	0.821794
$682$	−3.66127e8	−0.0441963
$683$	−6.40635e9	−0.769375	−0.384688	−	0.923047i	$-0.625691\pi$
$683$	−6.40635e9	−0.769375	−0.384688	+	0.923047i	$0.625691\pi$
$684$	5.65001e9	0.675076
$685$	1.00856e9	0.119890
$686$	7.98291e9	0.944120
$687$	−7.32567e9	−0.861983
$688$	−6.63471e8	−0.0776716
$689$	1.16369e10	1.35541
$690$	7.03178e9	0.814880
$691$	−1.21339e10	−1.39903	−0.699513	−	0.714620i	$-0.746600\pi$
$691$	−1.21339e10	−1.39903	−0.699513	+	0.714620i	$0.746600\pi$
$692$	−5.98220e9	−0.686261
$693$	−9.06338e8	−0.103448
$694$	−1.70316e10	−1.93419
$695$	−6.00693e9	−0.678744
$696$	1.81236e9	0.203757
$697$	1.66915e10	1.86716
$698$	−1.78743e10	−1.98946
$699$	−4.69052e9	−0.519459
$700$	4.81280e9	0.530341
$701$	1.62846e10	1.78552	0.892759	−	0.450535i	$-0.148767\pi$
$701$	1.62846e10	1.78552	0.892759	+	0.450535i	$0.148767\pi$
$702$	2.32546e10	2.53705
$703$	−1.18409e10	−1.28541
$704$	1.96898e9	0.212686
$705$	1.93930e9	0.208441
$706$	−2.10718e10	−2.25364
$707$	1.24386e10	1.32374
$708$	7.68152e9	0.813450
$709$	−3.23891e9	−0.341301	−0.170650	−	0.985332i	$-0.554587\pi$
$709$	−3.23891e9	−0.341301	−0.170650	+	0.985332i	$0.554587\pi$
$710$	−3.98387e9	−0.417735
$711$	5.99753e9	0.625791
$712$	−2.37759e9	−0.246864
$713$	2.08962e9	0.215901
$714$	−1.15652e10	−1.18908
$715$	1.82960e9	0.187191
$716$	1.85295e10	1.88655
$717$	9.55052e9	0.967631
$718$	1.97605e10	1.99234
$719$	8.54046e9	0.856900	0.428450	−	0.903565i	$-0.359060\pi$
$719$	8.54046e9	0.856900	0.428450	+	0.903565i	$0.359060\pi$
$720$	−2.58449e9	−0.258054
$721$	−2.33133e9	−0.231649
$722$	−5.38298e9	−0.532283
$723$	1.72964e9	0.170204
$724$	−1.79735e10	−1.76014
$725$	1.93353e9	0.188438
$726$	9.65883e9	0.936799
$727$	−9.39101e9	−0.906445	−0.453223	−	0.891397i	$-0.649726\pi$
$727$	−9.39101e9	−0.906445	−0.453223	+	0.891397i	$0.649726\pi$
$728$	−1.16228e10	−1.11648
$729$	6.58217e9	0.629249
$730$	1.07488e10	1.02266
$731$	−1.63862e9	−0.155156
$732$	8.12640e8	0.0765790
$733$	6.63206e9	0.621991	0.310996	−	0.950411i	$-0.399338\pi$
$733$	6.63206e9	0.621991	0.310996	+	0.950411i	$0.399338\pi$
$734$	2.66667e10	2.48905
$735$	2.75018e9	0.255479
$736$	−1.49441e10	−1.38165
$737$	1.47699e9	0.135907
$738$	1.88956e10	1.73047
$739$	9.73593e9	0.887405	0.443703	−	0.896174i	$-0.353665\pi$
$739$	9.73593e9	0.887405	0.443703	+	0.896174i	$0.353665\pi$
$740$	−1.96874e10	−1.78598
$741$	9.16204e9	0.827234
$742$	−1.72268e10	−1.54807
$743$	−1.04679e9	−0.0936265	−0.0468132	−	0.998904i	$-0.514907\pi$
$743$	−1.04679e9	−0.0936265	−0.0468132	+	0.998904i	$0.514907\pi$
$744$	−8.07957e8	−0.0719255
$745$	−6.12638e9	−0.542822
$746$	−1.41093e10	−1.24428
$747$	5.50367e9	0.483092
$748$	2.18224e9	0.190654
$749$	−1.54717e10	−1.34540
$750$	−1.20085e10	−1.03938
$751$	1.53753e10	1.32460	0.662300	−	0.749239i	$-0.269580\pi$
$751$	1.53753e10	1.32460	0.662300	+	0.749239i	$0.269580\pi$
$752$	−2.41297e9	−0.206914
$753$	3.90258e9	0.333096
$754$	−1.76176e10	−1.49674
$755$	−1.21851e10	−1.03042
$756$	−1.98421e10	−1.67017
$757$	−1.40954e9	−0.118098	−0.0590489	−	0.998255i	$-0.518807\pi$
$757$	−1.40954e9	−0.118098	−0.0590489	+	0.998255i	$0.518807\pi$
$758$	3.84502e9	0.320669
$759$	1.06584e9	0.0884800
$760$	4.47506e9	0.369787
$761$	−1.37074e10	−1.12748	−0.563740	−	0.825952i	$-0.690638\pi$
$761$	−1.37074e10	−1.12748	−0.563740	+	0.825952i	$0.690638\pi$
$762$	1.86297e10	1.52533
$763$	−2.76358e10	−2.25235
$764$	1.15191e10	0.934529
$765$	−6.38310e9	−0.515486
$766$	2.27781e10	1.83112
$767$	−1.97908e10	−1.58373
$768$	3.71255e8	0.0295738
$769$	−3.22094e9	−0.255412	−0.127706	−	0.991812i	$-0.540761\pi$
$769$	−3.22094e9	−0.255412	−0.127706	+	0.991812i	$0.540761\pi$
$770$	−2.70847e9	−0.213799
$771$	7.41019e9	0.582290
$772$	8.94524e9	0.699732
$773$	1.47558e10	1.14904	0.574518	−	0.818492i	$-0.305190\pi$
$773$	1.47558e10	1.14904	0.574518	+	0.818492i	$0.305190\pi$
$774$	−1.85500e9	−0.143798
$775$	−8.61973e8	−0.0665178
$776$	−7.89234e9	−0.606303
$777$	1.58149e10	1.20946
$778$	3.87566e9	0.295064
$779$	1.95750e10	1.48361
$780$	1.52334e10	1.14939
$781$	−6.03853e8	−0.0453579
$782$	−2.16087e10	−1.61586
$783$	−7.97152e9	−0.593437
$784$	−3.42190e9	−0.253607
$785$	1.55208e10	1.14517
$786$	−1.22197e10	−0.897599
$787$	−5.55719e9	−0.406390	−0.203195	−	0.979138i	$-0.565133\pi$
$787$	−5.55719e9	−0.406390	−0.203195	+	0.979138i	$0.565133\pi$
$788$	−1.60159e10	−1.16603
$789$	−5.29328e9	−0.383668
$790$	1.79228e10	1.29334
$791$	1.91062e10	1.37264
$792$	6.54764e8	0.0468324
$793$	−2.09370e9	−0.149094
$794$	−1.13971e10	−0.808023
$795$	5.98424e9	0.422400
$796$	1.07693e10	0.756820
$797$	−1.17611e10	−0.822891	−0.411446	−	0.911434i	$-0.634976\pi$
$797$	−1.17611e10	−0.822891	−0.411446	+	0.911434i	$0.634976\pi$
$798$	−1.35631e10	−0.944822
$799$	−5.95949e9	−0.413328
$800$	6.16446e9	0.425677
$801$	3.97719e9	0.273440
$802$	−1.29516e10	−0.886569
$803$	1.62925e9	0.111041
$804$	1.22975e10	0.834491
$805$	1.54583e10	1.04442
$806$	7.85396e9	0.528343
$807$	1.41521e10	0.947904
$808$	−8.98595e9	−0.599273
$809$	1.25815e10	0.835433	0.417717	−	0.908577i	$-0.362830\pi$
$809$	1.25815e10	0.835433	0.417717	+	0.908577i	$0.362830\pi$
$810$	1.84581e8	0.0122036
$811$	2.43090e10	1.60027	0.800136	−	0.599818i	$-0.204760\pi$
$811$	2.43090e10	1.60027	0.800136	+	0.599818i	$0.204760\pi$
$812$	1.50323e10	0.985325
$813$	1.62143e9	0.105823
$814$	−5.17730e9	−0.336448
$815$	−1.29042e10	−0.834986
$816$	−4.99878e9	−0.322069
$817$	−1.92170e9	−0.123284
$818$	−8.47724e9	−0.541524
$819$	1.94423e10	1.23667
$820$	3.25467e10	2.06138
$821$	−9.75294e9	−0.615084	−0.307542	−	0.951534i	$-0.599506\pi$
$821$	−9.75294e9	−0.615084	−0.307542	+	0.951534i	$0.599506\pi$
$822$	2.20830e9	0.138677
$823$	−1.00621e10	−0.629202	−0.314601	−	0.949224i	$-0.601871\pi$
$823$	−1.00621e10	−0.629202	−0.314601	+	0.949224i	$0.601871\pi$
$824$	1.68422e9	0.104871
$825$	−4.39660e8	−0.0272601
$826$	2.92976e10	1.80885
$827$	−1.80699e10	−1.11093	−0.555464	−	0.831541i	$-0.687459\pi$
$827$	−1.80699e10	−1.11093	−0.555464	+	0.831541i	$0.687459\pi$
$828$	−1.40996e10	−0.863176
$829$	−5.71510e9	−0.348404	−0.174202	−	0.984710i	$-0.555735\pi$
$829$	−5.71510e9	−0.348404	−0.174202	+	0.984710i	$0.555735\pi$
$830$	1.64470e10	0.998419
$831$	−2.00088e10	−1.20953
$832$	−4.22376e10	−2.54254
$833$	−8.45131e9	−0.506601
$834$	−1.31525e10	−0.785103
$835$	−2.61447e9	−0.155410
$836$	2.55923e9	0.151491
$837$	3.55372e9	0.209481
$838$	2.43029e10	1.42660
$839$	−1.09882e10	−0.642332	−0.321166	−	0.947023i	$-0.604075\pi$
$839$	−1.09882e10	−0.642332	−0.321166	+	0.947023i	$0.604075\pi$
$840$	−5.97697e9	−0.347940
$841$	−1.12107e10	−0.649900
$842$	−4.41956e10	−2.55145
$843$	−6.88312e9	−0.395721
$844$	2.52933e10	1.44813
$845$	−2.47686e10	−1.41222
$846$	−6.74644e9	−0.383070
$847$	2.12334e10	1.20068
$848$	−7.44586e9	−0.419305
$849$	−8.79091e9	−0.493011
$850$	8.91362e9	0.497838
$851$	2.95488e10	1.64357
$852$	−5.02773e9	−0.278505
$853$	2.69850e10	1.48868	0.744338	−	0.667803i	$-0.232765\pi$
$853$	2.69850e10	1.48868	0.744338	+	0.667803i	$0.232765\pi$
$854$	3.09944e9	0.170287
$855$	−7.48579e9	−0.409597
$856$	1.11772e10	0.609082
$857$	4.73891e9	0.257185	0.128593	−	0.991698i	$-0.458954\pi$
$857$	4.73891e9	0.257185	0.128593	+	0.991698i	$0.458954\pi$
$858$	4.00600e9	0.216524
$859$	−1.73970e10	−0.936479	−0.468239	−	0.883602i	$-0.655111\pi$
$859$	−1.73970e10	−0.936479	−0.468239	+	0.883602i	$0.655111\pi$
$860$	−3.19514e9	−0.171295
$861$	−2.61447e10	−1.39596
$862$	1.12153e10	0.596399
$863$	9.17138e9	0.485732	0.242866	−	0.970060i	$-0.421912\pi$
$863$	9.17138e9	0.485732	0.242866	+	0.970060i	$0.421912\pi$
$864$	−2.54147e10	−1.34056
$865$	7.92592e9	0.416383
$866$	−2.46009e10	−1.28718
$867$	−4.19266e8	−0.0218486
$868$	−6.70144e9	−0.347816
$869$	2.71664e9	0.140431
$870$	−9.05979e9	−0.466445
$871$	−3.16836e10	−1.62469
$872$	1.99648e10	1.01967
$873$	1.32021e10	0.671575
$874$	−2.53416e10	−1.28394
$875$	−2.63989e10	−1.33216
$876$	1.35653e10	0.681811
$877$	−4.84972e9	−0.242783	−0.121392	−	0.992605i	$-0.538736\pi$
$877$	−4.84972e9	−0.242783	−0.121392	+	0.992605i	$0.538736\pi$
$878$	5.57603e10	2.78032
$879$	2.02167e10	1.00403
$880$	−1.17067e9	−0.0579088
$881$	−5.10633e9	−0.251590	−0.125795	−	0.992056i	$-0.540148\pi$
$881$	−5.10633e9	−0.251590	−0.125795	+	0.992056i	$0.540148\pi$
$882$	−9.56730e9	−0.469515
$883$	2.88460e10	1.41001	0.705006	−	0.709201i	$-0.250944\pi$
$883$	2.88460e10	1.41001	0.705006	+	0.709201i	$0.250944\pi$
$884$	−4.68123e10	−2.27917
$885$	−1.01774e10	−0.493554
$886$	−5.64476e10	−2.72664
$887$	−7.47479e9	−0.359638	−0.179819	−	0.983700i	$-0.557551\pi$
$887$	−7.47479e9	−0.359638	−0.179819	+	0.983700i	$0.557551\pi$
$888$	−1.14251e10	−0.547539
$889$	4.09544e10	1.95499
$890$	1.18853e10	0.565126
$891$	2.79777e7	0.00132507
$892$	2.07016e10	0.976622
$893$	−6.98900e9	−0.328424
$894$	−1.34140e10	−0.627882
$895$	−2.45501e10	−1.14465
$896$	2.73037e10	1.26807
$897$	−2.28638e10	−1.05773
$898$	−1.56452e10	−0.720964
$899$	−2.69229e9	−0.123584
$900$	5.81609e9	0.265939
$901$	−1.83896e10	−0.837597
$902$	8.55896e9	0.388328
$903$	2.56665e9	0.116001
$904$	−1.38029e10	−0.621412
$905$	2.38134e10	1.06795
$906$	−2.66799e10	−1.19189
$907$	3.37329e9	0.150116	0.0750581	−	0.997179i	$-0.476086\pi$
$907$	3.37329e9	0.150116	0.0750581	+	0.997179i	$0.476086\pi$
$908$	−4.05837e10	−1.79908
$909$	1.50315e10	0.663788
$910$	5.81007e10	2.55586
$911$	−1.87342e10	−0.820958	−0.410479	−	0.911870i	$-0.634638\pi$
$911$	−1.87342e10	−0.820958	−0.410479	+	0.911870i	$0.634638\pi$
$912$	−5.86233e9	−0.255911
$913$	2.49294e9	0.108409
$914$	6.19636e10	2.68426
$915$	−1.07668e9	−0.0464637
$916$	4.38956e10	1.88707
$917$	−2.68632e10	−1.15044
$918$	−3.67488e10	−1.56781
$919$	2.69873e10	1.14698	0.573489	−	0.819214i	$-0.305590\pi$
$919$	2.69873e10	1.14698	0.573489	+	0.819214i	$0.305590\pi$
$920$	−1.11675e10	−0.472823
$921$	−1.93745e10	−0.817188
$922$	3.68570e10	1.54868
$923$	1.29535e10	0.542229
$924$	−3.41815e9	−0.142541
$925$	−1.21889e10	−0.506372
$926$	−2.29631e10	−0.950368
$927$	−2.81733e9	−0.116160
$928$	1.92541e10	0.790868
$929$	1.85412e10	0.758721	0.379360	−	0.925249i	$-0.376144\pi$
$929$	1.85412e10	0.758721	0.379360	+	0.925249i	$0.376144\pi$
$930$	4.03888e9	0.164653
$931$	−9.91129e9	−0.402537
$932$	2.81058e10	1.13721
$933$	2.52297e10	1.01701
$934$	4.78533e8	0.0192176
$935$	−2.89129e9	−0.115678
$936$	−1.40457e10	−0.559856
$937$	4.42644e10	1.75779	0.878893	−	0.477020i	$-0.158283\pi$
$937$	4.42644e10	1.75779	0.878893	+	0.477020i	$0.158283\pi$
$938$	4.69032e10	1.85563
$939$	−1.74960e10	−0.689620
$940$	−1.16204e10	−0.456323
$941$	3.74450e10	1.46498	0.732488	−	0.680780i	$-0.238359\pi$
$941$	3.74450e10	1.46498	0.732488	+	0.680780i	$0.238359\pi$
$942$	3.39837e10	1.32462
$943$	−4.88493e10	−1.89700
$944$	1.26632e10	0.489937
$945$	2.62891e10	1.01336
$946$	−8.40242e8	−0.0322690
$947$	−3.20475e10	−1.22622	−0.613111	−	0.789996i	$-0.710082\pi$
$947$	−3.20475e10	−1.22622	−0.613111	+	0.789996i	$0.710082\pi$
$948$	2.26190e10	0.862272
$949$	−3.49498e10	−1.32743
$950$	1.04535e10	0.395574
$951$	2.56126e10	0.965654
$952$	1.83673e10	0.689946
$953$	3.72778e10	1.39517	0.697583	−	0.716504i	$-0.254259\pi$
$953$	3.72778e10	1.39517	0.697583	+	0.716504i	$0.254259\pi$
$954$	−2.08179e10	−0.776280
$955$	−1.52619e10	−0.567018
$956$	−5.72270e10	−2.11835
$957$	−1.37323e9	−0.0506468
$958$	5.37867e10	1.97649
$959$	4.85460e9	0.177741
$960$	−2.17206e10	−0.792360
$961$	−2.63124e10	−0.956375
$962$	1.11061e11	4.02205
$963$	−1.86970e10	−0.674653
$964$	−1.03640e10	−0.372614
$965$	−1.18517e10	−0.424556
$966$	3.38467e10	1.20808
$967$	9.26852e8	0.0329623	0.0164812	−	0.999864i	$-0.494754\pi$
$967$	9.26852e8	0.0329623	0.0164812	+	0.999864i	$0.494754\pi$
$968$	−1.53396e10	−0.543564
$969$	−1.44786e10	−0.511204
$970$	3.94528e10	1.38796
$971$	−1.22212e10	−0.428398	−0.214199	−	0.976790i	$-0.568714\pi$
$971$	−1.22212e10	−0.428398	−0.214199	+	0.976790i	$0.568714\pi$
$972$	−3.88375e10	−1.35650
$973$	−2.89137e10	−1.00626
$974$	4.26510e10	1.47901
$975$	9.43135e9	0.325880
$976$	1.33966e9	0.0461231
$977$	−1.62117e10	−0.556157	−0.278078	−	0.960558i	$-0.589697\pi$
$977$	−1.62117e10	−0.556157	−0.278078	+	0.960558i	$0.589697\pi$
$978$	−2.82544e10	−0.965829
$979$	1.80151e9	0.0613616
$980$	−1.64792e10	−0.559298
$981$	−3.33968e10	−1.12944
$982$	−6.17630e10	−2.08132
$983$	−7.23772e9	−0.243033	−0.121516	−	0.992589i	$-0.538776\pi$
$983$	−7.23772e9	−0.243033	−0.121516	+	0.992589i	$0.538776\pi$
$984$	1.88877e10	0.631969
$985$	2.12198e10	0.707480
$986$	2.78408e10	0.924937
$987$	9.33463e9	0.309020
$988$	−5.48992e10	−1.81099
$989$	4.79559e9	0.157636
$990$	−3.27308e9	−0.107210
$991$	4.83836e10	1.57921	0.789606	−	0.613614i	$-0.210285\pi$
$991$	4.83836e10	1.57921	0.789606	+	0.613614i	$0.210285\pi$
$992$	−8.58351e9	−0.279173
$993$	2.54810e10	0.825838
$994$	−1.91759e10	−0.619305
$995$	−1.42685e10	−0.459194
$996$	2.07564e10	0.665649
$997$	−4.51500e10	−1.44286	−0.721431	−	0.692486i	$-0.756515\pi$
$997$	−4.51500e10	−1.44286	−0.721431	+	0.692486i	$0.756515\pi$
$998$	2.80348e10	0.892772
$999$	5.02523e10	1.59469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.11	✓	11
3.2	odd	2		387.8.a.b.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.11	✓	11	1.1	even	1	trivial
387.8.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q+17.3827 q^{2} -29.0652 q^{3} +174.160 q^{4} -230.747 q^{5} -505.234 q^{6} -1110.68 q^{7} +802.384 q^{8} -1342.21 q^{9} +O(q^{10})\)	\(q+17.3827 q^{2} -29.0652 q^{3} +174.160 q^{4} -230.747 q^{5} -505.234 q^{6} -1110.68 q^{7} +802.384 q^{8} -1342.21 q^{9} -4011.02 q^{10} -607.968 q^{11} -5062.00 q^{12} +13041.8 q^{13} -19306.6 q^{14} +6706.73 q^{15} -8344.81 q^{16} -20609.8 q^{17} -23331.3 q^{18} -24170.2 q^{19} -40186.9 q^{20} +32282.1 q^{21} -10568.2 q^{22} +60316.5 q^{23} -23321.5 q^{24} -24880.7 q^{25} +226703. q^{26} +102577. q^{27} -193435. q^{28} -77712.2 q^{29} +116581. q^{30} +34644.3 q^{31} -247761. q^{32} +17670.7 q^{33} -358255. q^{34} +256286. q^{35} -233759. q^{36} +489896. q^{37} -420144. q^{38} -379064. q^{39} -185148. q^{40} -809882. q^{41} +561152. q^{42} +79507.0 q^{43} -105884. q^{44} +309712. q^{45} +1.04847e6 q^{46} +289158. q^{47} +242544. q^{48} +410063. q^{49} -432494. q^{50} +599029. q^{51} +2.27136e6 q^{52} +892274. q^{53} +1.78308e6 q^{54} +140287. q^{55} -891191. q^{56} +702512. q^{57} -1.35085e6 q^{58} -1.51749e6 q^{59} +1.16804e6 q^{60} -160538. q^{61} +602213. q^{62} +1.49077e6 q^{63} -3.23863e6 q^{64} -3.00937e6 q^{65} +307166. q^{66} -2.42938e6 q^{67} -3.58940e6 q^{68} -1.75311e6 q^{69} +4.45495e6 q^{70} +993231. q^{71} -1.07697e6 q^{72} -2.67982e6 q^{73} +8.51574e6 q^{74} +723162. q^{75} -4.20947e6 q^{76} +675257. q^{77} -6.58917e6 q^{78} -4.46840e6 q^{79} +1.92554e6 q^{80} -46018.4 q^{81} -1.40780e7 q^{82} -4.10044e6 q^{83} +5.62225e6 q^{84} +4.75566e6 q^{85} +1.38205e6 q^{86} +2.25872e6 q^{87} -487824. q^{88} -2.96316e6 q^{89} +5.38364e6 q^{90} -1.44853e7 q^{91} +1.05047e7 q^{92} -1.00695e6 q^{93} +5.02636e6 q^{94} +5.57721e6 q^{95} +7.20123e6 q^{96} -9.83610e6 q^{97} +7.12801e6 q^{98} +816022. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 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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