LMFDB - Embedded newform 43.8.a.a.1.4

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			1.4
Root			$11.4671$ 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)

$f(q)$	$=$	$q-13.4671 q^{2} -87.0645 q^{3} +53.3630 q^{4} +131.138 q^{5} +1172.51 q^{6} -712.280 q^{7} +1005.14 q^{8} +5393.23 q^{9} +O(q^{10})$	\(q-13.4671 q^{2} -87.0645 q^{3} +53.3630 q^{4} +131.138 q^{5} +1172.51 q^{6} -712.280 q^{7} +1005.14 q^{8} +5393.23 q^{9} -1766.05 q^{10} +6103.13 q^{11} -4646.02 q^{12} -7927.36 q^{13} +9592.35 q^{14} -11417.5 q^{15} -20366.9 q^{16} -16334.5 q^{17} -72631.2 q^{18} +39583.9 q^{19} +6997.93 q^{20} +62014.3 q^{21} -82191.5 q^{22} +29296.2 q^{23} -87512.4 q^{24} -60927.8 q^{25} +106759. q^{26} -279148. q^{27} -38009.4 q^{28} +71148.2 q^{29} +153760. q^{30} +107693. q^{31} +145624. q^{32} -531366. q^{33} +219979. q^{34} -93407.1 q^{35} +287799. q^{36} +386329. q^{37} -533080. q^{38} +690192. q^{39} +131813. q^{40} -768609. q^{41} -835153. q^{42} +79507.0 q^{43} +325681. q^{44} +707258. q^{45} -394535. q^{46} +929733. q^{47} +1.77323e6 q^{48} -316201. q^{49} +820521. q^{50} +1.42216e6 q^{51} -423028. q^{52} -1.50722e6 q^{53} +3.75932e6 q^{54} +800354. q^{55} -715944. q^{56} -3.44635e6 q^{57} -958161. q^{58} -1.77396e6 q^{59} -609271. q^{60} -1.22781e6 q^{61} -1.45031e6 q^{62} -3.84148e6 q^{63} +645821. q^{64} -1.03958e6 q^{65} +7.15596e6 q^{66} -831926. q^{67} -871658. q^{68} -2.55066e6 q^{69} +1.25792e6 q^{70} -21047.1 q^{71} +5.42097e6 q^{72} -631213. q^{73} -5.20274e6 q^{74} +5.30464e6 q^{75} +2.11231e6 q^{76} -4.34713e6 q^{77} -9.29489e6 q^{78} -3.76509e6 q^{79} -2.67087e6 q^{80} +1.25089e7 q^{81} +1.03509e7 q^{82} +1.71861e6 q^{83} +3.30927e6 q^{84} -2.14208e6 q^{85} -1.07073e6 q^{86} -6.19448e6 q^{87} +6.13453e6 q^{88} -6.08728e6 q^{89} -9.52472e6 q^{90} +5.64650e6 q^{91} +1.56333e6 q^{92} -9.37623e6 q^{93} -1.25208e7 q^{94} +5.19096e6 q^{95} -1.26787e7 q^{96} -7.22067e6 q^{97} +4.25831e6 q^{98} +3.29156e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.4671	−1.19034	−0.595168	−	0.803602i	$-0.702914\pi$
$2$	−13.4671	−1.19034	−0.595168	+	0.803602i	$0.702914\pi$
$3$	−87.0645	−1.86173	−0.930865	−	0.365363i	$-0.880945\pi$
$3$	−87.0645	−1.86173	−0.930865	+	0.365363i	$0.880945\pi$
$4$	53.3630	0.416898
$5$	131.138	0.469174	0.234587	−	0.972095i	$-0.424626\pi$
$5$	131.138	0.469174	0.234587	+	0.972095i	$0.424626\pi$
$6$	1172.51	2.21608
$7$	−712.280	−0.784887	−0.392444	−	0.919776i	$-0.628370\pi$
$7$	−712.280	−0.784887	−0.392444	+	0.919776i	$0.628370\pi$
$8$	1005.14	0.694086
$9$	5393.23	2.46604
$10$	−1766.05	−0.558475
$11$	6103.13	1.38254	0.691271	−	0.722596i	$-0.257051\pi$
$11$	6103.13	1.38254	0.691271	+	0.722596i	$0.257051\pi$
$12$	−4646.02	−0.776152
$13$	−7927.36	−1.00075	−0.500377	−	0.865808i	$-0.666805\pi$
$13$	−7927.36	−1.00075	−0.500377	+	0.865808i	$0.666805\pi$
$14$	9592.35	0.934279
$15$	−11417.5	−0.873476
$16$	−20366.9	−1.24309
$17$	−16334.5	−0.806371	−0.403185	−	0.915118i	$-0.632097\pi$
$17$	−16334.5	−0.806371	−0.403185	+	0.915118i	$0.632097\pi$
$18$	−72631.2	−2.93541
$19$	39583.9	1.32398	0.661989	−	0.749514i	$-0.269713\pi$
$19$	39583.9	1.32398	0.661989	+	0.749514i	$0.269713\pi$
$20$	6997.93	0.195598
$21$	62014.3	1.46125
$22$	−82191.5	−1.64569
$23$	29296.2	0.502069	0.251035	−	0.967978i	$-0.419229\pi$
$23$	29296.2	0.502069	0.251035	+	0.967978i	$0.419229\pi$
$24$	−87512.4	−1.29220
$25$	−60927.8	−0.779875
$26$	106759.	1.19123
$27$	−279148.	−2.72937
$28$	−38009.4	−0.327218
$29$	71148.2	0.541715	0.270858	−	0.962619i	$-0.412693\pi$
$29$	71148.2	0.541715	0.270858	+	0.962619i	$0.412693\pi$
$30$	153760.	1.03973
$31$	107693.	0.649264	0.324632	−	0.945840i	$-0.394760\pi$
$31$	107693.	0.649264	0.324632	+	0.945840i	$0.394760\pi$
$32$	145624.	0.785613
$33$	−531366.	−2.57392
$34$	219979.	0.959852
$35$	−93407.1	−0.368249
$36$	287799.	1.02809
$37$	386329.	1.25387	0.626933	−	0.779073i	$-0.284310\pi$
$37$	386329.	1.25387	0.626933	+	0.779073i	$0.284310\pi$
$38$	−533080.	−1.57598
$39$	690192.	1.86313
$40$	131813.	0.325648
$41$	−768609.	−1.74165	−0.870827	−	0.491590i	$-0.836416\pi$
$41$	−768609.	−1.74165	−0.870827	+	0.491590i	$0.836416\pi$
$42$	−835153.	−1.73938
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	325681.	0.576380
$45$	707258.	1.15700
$46$	−394535.	−0.597631
$47$	929733.	1.30622	0.653109	−	0.757264i	$-0.273464\pi$
$47$	929733.	1.30622	0.653109	+	0.757264i	$0.273464\pi$
$48$	1.77323e6	2.31431
$49$	−316201.	−0.383952
$50$	820521.	0.928313
$51$	1.42216e6	1.50124
$52$	−423028.	−0.417213
$53$	−1.50722e6	−1.39063	−0.695314	−	0.718707i	$-0.744734\pi$
$53$	−1.50722e6	−1.39063	−0.695314	+	0.718707i	$0.744734\pi$
$54$	3.75932e6	3.24886
$55$	800354.	0.648653
$56$	−715944.	−0.544780
$57$	−3.44635e6	−2.46489
$58$	−958161.	−0.644823
$59$	−1.77396e6	−1.12450	−0.562252	−	0.826966i	$-0.690065\pi$
$59$	−1.77396e6	−1.12450	−0.562252	+	0.826966i	$0.690065\pi$
$60$	−609271.	−0.364151
$61$	−1.22781e6	−0.692591	−0.346295	−	0.938125i	$-0.612561\pi$
$61$	−1.22781e6	−0.692591	−0.346295	+	0.938125i	$0.612561\pi$
$62$	−1.45031e6	−0.772842
$63$	−3.84148e6	−1.93556
$64$	645821.	0.307952
$65$	−1.03958e6	−0.469528
$66$	7.15596e6	3.06383
$67$	−831926.	−0.337927	−0.168963	−	0.985622i	$-0.554042\pi$
$67$	−831926.	−0.337927	−0.168963	+	0.985622i	$0.554042\pi$
$68$	−871658.	−0.336175
$69$	−2.55066e6	−0.934717
$70$	1.25792e6	0.438340
$71$	−21047.1	−0.00697891	−0.00348945	−	0.999994i	$-0.501111\pi$
$71$	−21047.1	−0.00697891	−0.00348945	+	0.999994i	$0.501111\pi$
$72$	5.42097e6	1.71164
$73$	−631213.	−0.189909	−0.0949545	−	0.995482i	$-0.530271\pi$
$73$	−631213.	−0.189909	−0.0949545	+	0.995482i	$0.530271\pi$
$74$	−5.20274e6	−1.49252
$75$	5.30464e6	1.45192
$76$	2.11231e6	0.551964
$77$	−4.34713e6	−1.08514
$78$	−9.29489e6	−2.21775
$79$	−3.76509e6	−0.859173	−0.429587	−	0.903026i	$-0.641341\pi$
$79$	−3.76509e6	−0.859173	−0.429587	+	0.903026i	$0.641341\pi$
$80$	−2.67087e6	−0.583228
$81$	1.25089e7	2.61531
$82$	1.03509e7	2.07315
$83$	1.71861e6	0.329916	0.164958	−	0.986301i	$-0.447251\pi$
$83$	1.71861e6	0.329916	0.164958	+	0.986301i	$0.447251\pi$
$84$	3.30927e6	0.609192
$85$	−2.14208e6	−0.378329
$86$	−1.07073e6	−0.181524
$87$	−6.19448e6	−1.00853
$88$	6.13453e6	0.959604
$89$	−6.08728e6	−0.915288	−0.457644	−	0.889135i	$-0.651307\pi$
$89$	−6.08728e6	−0.915288	−0.457644	+	0.889135i	$0.651307\pi$
$90$	−9.52472e6	−1.37722
$91$	5.64650e6	0.785479
$92$	1.56333e6	0.209312
$93$	−9.37623e6	−1.20875
$94$	−1.25208e7	−1.55484
$95$	5.19096e6	0.621176
$96$	−1.26787e7	−1.46260
$97$	−7.22067e6	−0.803298	−0.401649	−	0.915794i	$-0.631563\pi$
$97$	−7.22067e6	−0.803298	−0.401649	+	0.915794i	$0.631563\pi$
$98$	4.25831e6	0.457032
$99$	3.29156e7	3.40940
$100$	−3.25129e6	−0.325129
$101$	9.01277e6	0.870429	0.435214	−	0.900327i	$-0.356673\pi$
$101$	9.01277e6	0.870429	0.435214	+	0.900327i	$0.356673\pi$
$102$	−1.91523e7	−1.78699
$103$	−3.97490e6	−0.358423	−0.179211	−	0.983811i	$-0.557355\pi$
$103$	−3.97490e6	−0.358423	−0.179211	+	0.983811i	$0.557355\pi$
$104$	−7.96815e6	−0.694609
$105$	8.13244e6	0.685580
$106$	2.02979e7	1.65531
$107$	−2.21874e7	−1.75091	−0.875454	−	0.483301i	$-0.839438\pi$
$107$	−2.21874e7	−1.75091	−0.875454	+	0.483301i	$0.839438\pi$
$108$	−1.48962e7	−1.13787
$109$	1.24187e7	0.918506	0.459253	−	0.888305i	$-0.348117\pi$
$109$	1.24187e7	0.918506	0.459253	+	0.888305i	$0.348117\pi$
$110$	−1.07785e7	−0.772115
$111$	−3.36355e7	−2.33436
$112$	1.45069e7	0.975689
$113$	2.56219e7	1.67046	0.835231	−	0.549899i	$-0.185334\pi$
$113$	2.56219e7	1.67046	0.835231	+	0.549899i	$0.185334\pi$
$114$	4.64123e7	2.93404
$115$	3.84185e6	0.235558
$116$	3.79668e6	0.225840
$117$	−4.27541e7	−2.46790
$118$	2.38901e7	1.33854
$119$	1.16347e7	0.632910
$120$	−1.14762e7	−0.606268
$121$	1.77610e7	0.911422
$122$	1.65351e7	0.824416
$123$	6.69185e7	3.24249
$124$	5.74682e6	0.270677
$125$	−1.82351e7	−0.835072
$126$	5.17337e7	2.30397
$127$	3.48811e7	1.51104	0.755522	−	0.655124i	$-0.227383\pi$
$127$	3.48811e7	1.51104	0.755522	+	0.655124i	$0.227383\pi$
$128$	−2.73372e7	−1.15218
$129$	−6.92224e6	−0.283911
$130$	1.40001e7	0.558896
$131$	7.90037e6	0.307042	0.153521	−	0.988145i	$-0.450939\pi$
$131$	7.90037e6	0.307042	0.153521	+	0.988145i	$0.450939\pi$
$132$	−2.83553e7	−1.07306
$133$	−2.81948e7	−1.03917
$134$	1.12036e7	0.402246
$135$	−3.66070e7	−1.28055
$136$	−1.64185e7	−0.559691
$137$	−2.61766e7	−0.869744	−0.434872	−	0.900492i	$-0.643206\pi$
$137$	−2.61766e7	−0.869744	−0.434872	+	0.900492i	$0.643206\pi$
$138$	3.43500e7	1.11263
$139$	−3.82597e7	−1.20834	−0.604171	−	0.796855i	$-0.706496\pi$
$139$	−3.82597e7	−1.20834	−0.604171	+	0.796855i	$0.706496\pi$
$140$	−4.98448e6	−0.153522
$141$	−8.09467e7	−2.43183
$142$	283443.	0.00830724
$143$	−4.83817e7	−1.38358
$144$	−1.09843e8	−3.06552
$145$	9.33025e6	0.254159
$146$	8.50061e6	0.226055
$147$	2.75299e7	0.714815
$148$	2.06157e7	0.522735
$149$	−7.50017e6	−0.185746	−0.0928729	−	0.995678i	$-0.529605\pi$
$149$	−7.50017e6	−0.185746	−0.0928729	+	0.995678i	$0.529605\pi$
$150$	−7.14382e7	−1.72827
$151$	7.15245e7	1.69058	0.845290	−	0.534308i	$-0.179428\pi$
$151$	7.15245e7	1.69058	0.845290	+	0.534308i	$0.179428\pi$
$152$	3.97875e7	0.918955
$153$	−8.80957e7	−1.98854
$154$	5.85433e7	1.29168
$155$	1.41227e7	0.304618
$156$	3.68307e7	0.776737
$157$	−1.03218e7	−0.212865	−0.106433	−	0.994320i	$-0.533943\pi$
$157$	−1.03218e7	−0.212865	−0.106433	+	0.994320i	$0.533943\pi$
$158$	5.07049e7	1.02270
$159$	1.31225e8	2.58897
$160$	1.90969e7	0.368589
$161$	−2.08671e7	−0.394068
$162$	−1.68459e8	−3.11309
$163$	−9.73117e7	−1.75998	−0.879992	−	0.474989i	$-0.842452\pi$
$163$	−9.73117e7	−1.75998	−0.879992	+	0.474989i	$0.842452\pi$
$164$	−4.10153e7	−0.726093
$165$	−6.96824e7	−1.20762
$166$	−2.31447e7	−0.392711
$167$	−1.15556e8	−1.91992	−0.959961	−	0.280133i	$-0.909621\pi$
$167$	−1.15556e8	−1.91992	−0.959961	+	0.280133i	$0.909621\pi$
$168$	6.23333e7	1.01423
$169$	94596.7	0.00150755
$170$	2.88476e7	0.450338
$171$	2.13485e8	3.26498
$172$	4.24273e6	0.0635764
$173$	4.06579e6	0.0597012	0.0298506	−	0.999554i	$-0.490497\pi$
$173$	4.06579e6	0.0597012	0.0298506	+	0.999554i	$0.490497\pi$
$174$	8.34218e7	1.20049
$175$	4.33976e7	0.612114
$176$	−1.24302e8	−1.71863
$177$	1.54449e8	2.09352
$178$	8.19780e7	1.08950
$179$	−8.18724e7	−1.06697	−0.533485	−	0.845810i	$-0.679118\pi$
$179$	−8.18724e7	−1.06697	−0.533485	+	0.845810i	$0.679118\pi$
$180$	3.77414e7	0.482352
$181$	−1.09002e8	−1.36634	−0.683168	−	0.730261i	$-0.739398\pi$
$181$	−1.09002e8	−1.36634	−0.683168	+	0.730261i	$0.739398\pi$
$182$	−7.60420e7	−0.934983
$183$	1.06899e8	1.28942
$184$	2.94469e7	0.348479
$185$	5.06625e7	0.588282
$186$	1.26271e8	1.43882
$187$	−9.96917e7	−1.11484
$188$	4.96133e7	0.544560
$189$	1.98832e8	2.14225
$190$	−6.99072e7	−0.739408
$191$	−2.66371e7	−0.276612	−0.138306	−	0.990390i	$-0.544166\pi$
$191$	−2.66371e7	−0.276612	−0.138306	+	0.990390i	$0.544166\pi$
$192$	−5.62281e7	−0.573323
$193$	1.74825e8	1.75047	0.875233	−	0.483701i	$-0.160708\pi$
$193$	1.74825e8	1.75047	0.875233	+	0.483701i	$0.160708\pi$
$194$	9.72416e7	0.956194
$195$	9.05106e7	0.874134
$196$	−1.68734e7	−0.160069
$197$	−5.70061e7	−0.531238	−0.265619	−	0.964078i	$-0.585576\pi$
$197$	−5.70061e7	−0.531238	−0.265619	+	0.964078i	$0.585576\pi$
$198$	−4.43277e8	−4.05833
$199$	−3.66798e7	−0.329945	−0.164972	−	0.986298i	$-0.552753\pi$
$199$	−3.66798e7	−0.329945	−0.164972	+	0.986298i	$0.552753\pi$
$200$	−6.12412e7	−0.541301
$201$	7.24312e7	0.629129
$202$	−1.21376e8	−1.03610
$203$	−5.06774e7	−0.425185
$204$	7.58905e7	0.625867
$205$	−1.00794e8	−0.817139
$206$	5.35304e7	0.426643
$207$	1.58001e8	1.23812
$208$	1.61455e8	1.24403
$209$	2.41585e8	1.83045
$210$	−1.09520e8	−0.816070
$211$	−1.29934e8	−0.952213	−0.476106	−	0.879388i	$-0.657952\pi$
$211$	−1.29934e8	−0.952213	−0.476106	+	0.879388i	$0.657952\pi$
$212$	−8.04297e7	−0.579750
$213$	1.83245e6	0.0129928
$214$	2.98800e8	2.08417
$215$	1.04264e7	0.0715484
$216$	−2.80584e8	−1.89442
$217$	−7.67075e7	−0.509599
$218$	−1.67243e8	−1.09333
$219$	5.49562e7	0.353559
$220$	4.27093e7	0.270423
$221$	1.29490e8	0.806979
$222$	4.52974e8	2.77867
$223$	−2.02158e8	−1.22074	−0.610370	−	0.792116i	$-0.708979\pi$
$223$	−2.02158e8	−1.22074	−0.610370	+	0.792116i	$0.708979\pi$
$224$	−1.03725e8	−0.616617
$225$	−3.28597e8	−1.92320
$226$	−3.45053e8	−1.98841
$227$	−3.00569e6	−0.0170551	−0.00852753	−	0.999964i	$-0.502714\pi$
$227$	−3.00569e6	−0.0170551	−0.00852753	+	0.999964i	$0.502714\pi$
$228$	−1.83907e8	−1.02761
$229$	2.04655e8	1.12616	0.563078	−	0.826404i	$-0.309617\pi$
$229$	2.04655e8	1.12616	0.563078	+	0.826404i	$0.309617\pi$
$230$	−5.17386e7	−0.280393
$231$	3.78481e8	2.02024
$232$	7.15142e7	0.375997
$233$	5.47940e7	0.283784	0.141892	−	0.989882i	$-0.454682\pi$
$233$	5.47940e7	0.283784	0.141892	+	0.989882i	$0.454682\pi$
$234$	5.75774e8	2.93762
$235$	1.21924e8	0.612844
$236$	−9.46637e7	−0.468804
$237$	3.27806e8	1.59955
$238$	−1.56686e8	−0.753376
$239$	−2.12739e8	−1.00799	−0.503994	−	0.863707i	$-0.668137\pi$
$239$	−2.12739e8	−1.00799	−0.503994	+	0.863707i	$0.668137\pi$
$240$	2.32538e8	1.08581
$241$	1.29896e8	0.597774	0.298887	−	0.954289i	$-0.403385\pi$
$241$	1.29896e8	0.597774	0.298887	+	0.954289i	$0.403385\pi$
$242$	−2.39190e8	−1.08490
$243$	−4.78586e8	−2.13963
$244$	−6.55196e7	−0.288740
$245$	−4.14660e7	−0.180140
$246$	−9.01199e8	−3.85965
$247$	−3.13796e8	−1.32497
$248$	1.08247e8	0.450645
$249$	−1.49630e8	−0.614214
$250$	2.45575e8	0.994016
$251$	4.05186e8	1.61732	0.808661	−	0.588274i	$-0.200193\pi$
$251$	4.05186e8	1.61732	0.808661	+	0.588274i	$0.200193\pi$
$252$	−2.04993e8	−0.806933
$253$	1.78798e8	0.694132
$254$	−4.69747e8	−1.79865
$255$	1.86499e8	0.704346
$256$	2.85488e8	1.06353
$257$	−4.32001e8	−1.58752	−0.793758	−	0.608233i	$-0.791879\pi$
$257$	−4.32001e8	−1.58752	−0.793758	+	0.608233i	$0.791879\pi$
$258$	9.32225e7	0.337949
$259$	−2.75174e8	−0.984144
$260$	−5.54751e7	−0.195745
$261$	3.83718e8	1.33589
$262$	−1.06395e8	−0.365483
$263$	9.96029e7	0.337619	0.168809	−	0.985649i	$-0.446008\pi$
$263$	9.96029e7	0.337619	0.168809	+	0.985649i	$0.446008\pi$
$264$	−5.34100e8	−1.78652
$265$	−1.97654e8	−0.652447
$266$	3.79702e8	1.23696
$267$	5.29986e8	1.70402
$268$	−4.43941e7	−0.140881
$269$	−4.54907e8	−1.42492	−0.712459	−	0.701713i	$-0.752419\pi$
$269$	−4.54907e8	−1.42492	−0.712459	+	0.701713i	$0.752419\pi$
$270$	4.92991e8	1.52428
$271$	−2.69553e8	−0.822718	−0.411359	−	0.911473i	$-0.634946\pi$
$271$	−2.69553e8	−0.822718	−0.411359	+	0.911473i	$0.634946\pi$
$272$	3.32683e8	1.00240
$273$	−4.91610e8	−1.46235
$274$	3.52523e8	1.03529
$275$	−3.71850e8	−1.07821
$276$	−1.36111e8	−0.389682
$277$	−9.07532e7	−0.256556	−0.128278	−	0.991738i	$-0.540945\pi$
$277$	−9.07532e7	−0.256556	−0.128278	+	0.991738i	$0.540945\pi$
$278$	5.15248e8	1.43833
$279$	5.80812e8	1.60111
$280$	−9.38876e7	−0.255597
$281$	−2.39385e7	−0.0643614	−0.0321807	−	0.999482i	$-0.510245\pi$
$281$	−2.39385e7	−0.0643614	−0.0321807	+	0.999482i	$0.510245\pi$
$282$	1.09012e9	2.89469
$283$	−3.89906e8	−1.02261	−0.511303	−	0.859401i	$-0.670837\pi$
$283$	−3.89906e8	−1.02261	−0.511303	+	0.859401i	$0.670837\pi$
$284$	−1.12313e6	−0.00290950
$285$	−4.51948e8	−1.15646
$286$	6.51562e8	1.64693
$287$	5.47464e8	1.36700
$288$	7.85384e8	1.93735
$289$	−1.43522e8	−0.349766
$290$	−1.25651e8	−0.302534
$291$	6.28664e8	1.49552
$292$	−3.36834e7	−0.0791728
$293$	−3.58463e8	−0.832544	−0.416272	−	0.909240i	$-0.636664\pi$
$293$	−3.58463e8	−0.832544	−0.416272	+	0.909240i	$0.636664\pi$
$294$	−3.70748e8	−0.850869
$295$	−2.32634e8	−0.527589
$296$	3.88317e8	0.870292
$297$	−1.70368e9	−3.77346
$298$	1.01006e8	0.221100
$299$	−2.32242e8	−0.502448
$300$	2.83072e8	0.605302
$301$	−5.66312e7	−0.119694
$302$	−9.63228e8	−2.01236
$303$	−7.84692e8	−1.62050
$304$	−8.06199e8	−1.64583
$305$	−1.61013e8	−0.324946
$306$	1.18639e9	2.36703
$307$	3.60914e8	0.711901	0.355951	−	0.934505i	$-0.384157\pi$
$307$	3.60914e8	0.711901	0.355951	+	0.934505i	$0.384157\pi$
$308$	−2.31976e8	−0.452393
$309$	3.46072e8	0.667287
$310$	−1.90191e8	−0.362598
$311$	5.61989e8	1.05942	0.529708	−	0.848180i	$-0.322302\pi$
$311$	5.61989e8	1.05942	0.529708	+	0.848180i	$0.322302\pi$
$312$	6.93743e8	1.29318
$313$	5.21602e8	0.961466	0.480733	−	0.876867i	$-0.340371\pi$
$313$	5.21602e8	0.961466	0.480733	+	0.876867i	$0.340371\pi$
$314$	1.39004e8	0.253381
$315$	−5.03765e8	−0.908116
$316$	−2.00917e8	−0.358188
$317$	−1.50341e8	−0.265076	−0.132538	−	0.991178i	$-0.542313\pi$
$317$	−1.50341e8	−0.265076	−0.132538	+	0.991178i	$0.542313\pi$
$318$	−1.76722e9	−3.08174
$319$	4.34227e8	0.748944
$320$	8.46919e7	0.144483
$321$	1.93174e9	3.25972
$322$	2.81019e8	0.469073
$323$	−6.46583e8	−1.06762
$324$	6.67514e8	1.09032
$325$	4.82997e8	0.780463
$326$	1.31051e9	2.09497
$327$	−1.08122e9	−1.71001
$328$	−7.72563e8	−1.20886
$329$	−6.62230e8	−1.02523
$330$	9.38420e8	1.43747
$331$	7.31126e8	1.10814	0.554070	−	0.832470i	$-0.313074\pi$
$331$	7.31126e8	1.10814	0.554070	+	0.832470i	$0.313074\pi$
$332$	9.17100e7	0.137541
$333$	2.08356e9	3.09208
$334$	1.55620e9	2.28535
$335$	−1.09097e8	−0.158547
$336$	−1.26304e9	−1.81647
$337$	−3.27389e8	−0.465972	−0.232986	−	0.972480i	$-0.574850\pi$
$337$	−3.27389e8	−0.465972	−0.232986	+	0.972480i	$0.574850\pi$
$338$	−1.27394e6	−0.00179449
$339$	−2.23076e9	−3.10995
$340$	−1.14308e8	−0.157725
$341$	6.57264e8	0.897635
$342$	−2.87502e9	−3.88642
$343$	8.11816e8	1.08625
$344$	7.99160e7	0.105847
$345$	−3.34489e8	−0.438545
$346$	−5.47544e7	−0.0710645
$347$	7.03971e8	0.904485	0.452243	−	0.891895i	$-0.350624\pi$
$347$	7.03971e8	0.904485	0.452243	+	0.891895i	$0.350624\pi$
$348$	−3.30556e8	−0.420453
$349$	−3.71304e8	−0.467563	−0.233782	−	0.972289i	$-0.575110\pi$
$349$	−3.71304e8	−0.467563	−0.233782	+	0.972289i	$0.575110\pi$
$350$	−5.84440e8	−0.728621
$351$	2.21291e9	2.73142
$352$	8.88763e8	1.08614
$353$	1.27959e9	1.54832	0.774160	−	0.632990i	$-0.218172\pi$
$353$	1.27959e9	1.54832	0.774160	+	0.632990i	$0.218172\pi$
$354$	−2.07998e9	−2.49200
$355$	−2.76008e6	−0.00327432
$356$	−3.24835e8	−0.381582
$357$	−1.01297e9	−1.17831
$358$	1.10258e9	1.27005
$359$	−3.54999e8	−0.404946	−0.202473	−	0.979288i	$-0.564898\pi$
$359$	−3.54999e8	−0.404946	−0.202473	+	0.979288i	$0.564898\pi$
$360$	7.10897e8	0.803059
$361$	6.73010e8	0.752915
$362$	1.46794e9	1.62640
$363$	−1.54636e9	−1.69682
$364$	3.01314e8	0.327465
$365$	−8.27761e7	−0.0891005
$366$	−1.43962e9	−1.53484
$367$	1.73415e9	1.83128	0.915639	−	0.402001i	$-0.131685\pi$
$367$	1.73415e9	1.83128	0.915639	+	0.402001i	$0.131685\pi$
$368$	−5.96671e8	−0.624119
$369$	−4.14528e9	−4.29498
$370$	−6.82278e8	−0.700253
$371$	1.07356e9	1.09149
$372$	−5.00344e8	−0.503928
$373$	−3.01486e8	−0.300805	−0.150403	−	0.988625i	$-0.548057\pi$
$373$	−3.01486e8	−0.300805	−0.150403	+	0.988625i	$0.548057\pi$
$374$	1.34256e9	1.32704
$375$	1.58763e9	1.55468
$376$	9.34516e8	0.906628
$377$	−5.64018e8	−0.542123
$378$	−2.67769e9	−2.54999
$379$	−9.79815e8	−0.924499	−0.462250	−	0.886750i	$-0.652958\pi$
$379$	−9.79815e8	−0.924499	−0.462250	+	0.886750i	$0.652958\pi$
$380$	2.77005e8	0.258967
$381$	−3.03690e9	−2.81315
$382$	3.58725e8	0.329261
$383$	−4.89981e8	−0.445639	−0.222820	−	0.974860i	$-0.571526\pi$
$383$	−4.89981e8	−0.445639	−0.222820	+	0.974860i	$0.571526\pi$
$384$	2.38010e9	2.14504
$385$	−5.70076e8	−0.509120
$386$	−2.35439e9	−2.08364
$387$	4.28799e8	0.376067
$388$	−3.85317e8	−0.334894
$389$	−1.81229e9	−1.56101	−0.780504	−	0.625151i	$-0.785037\pi$
$389$	−1.81229e9	−1.56101	−0.780504	+	0.625151i	$0.785037\pi$
$390$	−1.21892e9	−1.04051
$391$	−4.78539e8	−0.404854
$392$	−3.17828e8	−0.266496
$393$	−6.87841e8	−0.571629
$394$	7.67707e8	0.632352
$395$	−4.93748e8	−0.403102
$396$	1.75647e9	1.42137
$397$	−1.72818e9	−1.38619	−0.693096	−	0.720845i	$-0.743754\pi$
$397$	−1.72818e9	−1.38619	−0.693096	+	0.720845i	$0.743754\pi$
$398$	4.93971e8	0.392745
$399$	2.45476e9	1.93466
$400$	1.24091e9	0.969458
$401$	−8.93294e8	−0.691814	−0.345907	−	0.938269i	$-0.612429\pi$
$401$	−8.93294e8	−0.691814	−0.345907	+	0.938269i	$0.612429\pi$
$402$	−9.75439e8	−0.748874
$403$	−8.53721e8	−0.649753
$404$	4.80948e8	0.362880
$405$	1.64040e9	1.22703
$406$	6.82478e8	0.506113
$407$	2.35782e9	1.73352
$408$	1.42947e9	1.04199
$409$	−7.17563e8	−0.518595	−0.259298	−	0.965797i	$-0.583491\pi$
$409$	−7.17563e8	−0.518595	−0.259298	+	0.965797i	$0.583491\pi$
$410$	1.35740e9	0.972670
$411$	2.27905e9	1.61923
$412$	−2.12113e8	−0.149426
$413$	1.26355e9	0.882610
$414$	−2.12782e9	−1.47378
$415$	2.25375e8	0.154788
$416$	−1.15442e9	−0.786205
$417$	3.33106e9	2.24961
$418$	−3.25346e9	−2.17885
$419$	−8.34959e8	−0.554519	−0.277259	−	0.960795i	$-0.589426\pi$
$419$	−8.34959e8	−0.554519	−0.277259	+	0.960795i	$0.589426\pi$
$420$	4.33971e8	0.285817
$421$	2.75014e6	0.00179626	0.000898128	−	1.00000i	$-0.499714\pi$
$421$	2.75014e6	0.00179626	0.000898128		1.00000i	$0.499714\pi$
$422$	1.74983e9	1.13345
$423$	5.01426e9	3.22118
$424$	−1.51497e9	−0.965215
$425$	9.95225e8	0.628869
$426$	−2.46778e7	−0.0154658
$427$	8.74544e8	0.543606
$428$	−1.18399e9	−0.729951
$429$	4.21233e9	2.57586
$430$	−1.40414e8	−0.0851666
$431$	−1.21897e9	−0.733370	−0.366685	−	0.930345i	$-0.619507\pi$
$431$	−1.21897e9	−0.733370	−0.366685	+	0.930345i	$0.619507\pi$
$432$	5.68537e9	3.39286
$433$	−1.12096e9	−0.663561	−0.331781	−	0.943357i	$-0.607649\pi$
$433$	−1.12096e9	−0.663561	−0.331781	+	0.943357i	$0.607649\pi$
$434$	1.03303e9	0.606594
$435$	−8.12333e8	−0.473175
$436$	6.62697e8	0.382924
$437$	1.15966e9	0.664728
$438$	−7.40101e8	−0.420854
$439$	−5.95770e8	−0.336088	−0.168044	−	0.985779i	$-0.553745\pi$
$439$	−5.95770e8	−0.336088	−0.168044	+	0.985779i	$0.553745\pi$
$440$	8.04471e8	0.450221
$441$	−1.70534e9	−0.946840
$442$	−1.74385e9	−0.960575
$443$	2.21773e9	1.21198	0.605991	−	0.795472i	$-0.292777\pi$
$443$	2.21773e9	1.21198	0.605991	+	0.795472i	$0.292777\pi$
$444$	−1.79489e9	−0.973192
$445$	−7.98275e8	−0.429430
$446$	2.72248e9	1.45309
$447$	6.52998e8	0.345808
$448$	−4.60005e8	−0.241707
$449$	−7.44092e8	−0.387940	−0.193970	−	0.981007i	$-0.562136\pi$
$449$	−7.44092e8	−0.387940	−0.193970	+	0.981007i	$0.562136\pi$
$450$	4.42525e9	2.28926
$451$	−4.69092e9	−2.40791
$452$	1.36726e9	0.696413
$453$	−6.22725e9	−3.14740
$454$	4.04779e7	0.0203012
$455$	7.40472e8	0.368527
$456$	−3.46408e9	−1.71085
$457$	7.56617e8	0.370825	0.185413	−	0.982661i	$-0.440638\pi$
$457$	7.56617e8	0.370825	0.185413	+	0.982661i	$0.440638\pi$
$458$	−2.75612e9	−1.34050
$459$	4.55975e9	2.20088
$460$	2.05013e8	0.0982038
$461$	−8.02106e7	−0.0381310	−0.0190655	−	0.999818i	$-0.506069\pi$
$461$	−8.02106e7	−0.0381310	−0.0190655	+	0.999818i	$0.506069\pi$
$462$	−5.09705e9	−2.40476
$463$	1.38557e9	0.648778	0.324389	−	0.945924i	$-0.394841\pi$
$463$	1.38557e9	0.648778	0.324389	+	0.945924i	$0.394841\pi$
$464$	−1.44907e9	−0.673403
$465$	−1.22958e9	−0.567116
$466$	−7.37917e8	−0.337798
$467$	4.12145e9	1.87258	0.936292	−	0.351224i	$-0.114234\pi$
$467$	4.12145e9	1.87258	0.936292	+	0.351224i	$0.114234\pi$
$468$	−2.28149e9	−1.02886
$469$	5.92564e8	0.265235
$470$	−1.64196e9	−0.729490
$471$	8.98659e8	0.396298
$472$	−1.78308e9	−0.780504
$473$	4.85242e8	0.210836
$474$	−4.41460e9	−1.90400
$475$	−2.41176e9	−1.03254
$476$	6.20864e8	0.263859
$477$	−8.12877e9	−3.42934
$478$	2.86498e9	1.19984
$479$	−3.39610e8	−0.141191	−0.0705955	−	0.997505i	$-0.522490\pi$
$479$	−3.39610e8	−0.141191	−0.0705955	+	0.997505i	$0.522490\pi$
$480$	−1.66266e9	−0.686214
$481$	−3.06257e9	−1.25481
$482$	−1.74933e9	−0.711551
$483$	1.81678e9	0.733648
$484$	9.47782e8	0.379970
$485$	−9.46906e8	−0.376887
$486$	6.44517e9	2.54687
$487$	−2.35025e9	−0.922066	−0.461033	−	0.887383i	$-0.652521\pi$
$487$	−2.35025e9	−0.922066	−0.461033	+	0.887383i	$0.652521\pi$
$488$	−1.23413e9	−0.480718
$489$	8.47240e9	3.27661
$490$	5.58428e8	0.214428
$491$	−5.12182e8	−0.195272	−0.0976359	−	0.995222i	$-0.531128\pi$
$491$	−5.12182e8	−0.195272	−0.0976359	+	0.995222i	$0.531128\pi$
$492$	3.57097e9	1.35179
$493$	−1.16217e9	−0.436823
$494$	4.22592e9	1.57716
$495$	4.31649e9	1.59960
$496$	−2.19337e9	−0.807096
$497$	1.49914e7	0.00547766
$498$	2.01508e9	0.731121
$499$	−2.62730e9	−0.946582	−0.473291	−	0.880906i	$-0.656934\pi$
$499$	−2.62730e9	−0.946582	−0.473291	+	0.880906i	$0.656934\pi$
$500$	−9.73081e8	−0.348140
$501$	1.00608e10	3.57438
$502$	−5.45669e9	−1.92516
$503$	−1.27864e9	−0.447982	−0.223991	−	0.974591i	$-0.571909\pi$
$503$	−1.27864e9	−0.447982	−0.223991	+	0.974591i	$0.571909\pi$
$504$	−3.86125e9	−1.34345
$505$	1.18192e9	0.408383
$506$	−2.40790e9	−0.826250
$507$	−8.23601e6	−0.00280665
$508$	1.86136e9	0.629952
$509$	−3.34993e9	−1.12596	−0.562980	−	0.826470i	$-0.690345\pi$
$509$	−3.34993e9	−1.12596	−0.562980	+	0.826470i	$0.690345\pi$
$510$	−2.51160e9	−0.838408
$511$	4.49600e8	0.149057
$512$	−3.45536e8	−0.113776
$513$	−1.10498e10	−3.61362
$514$	5.81780e9	1.88968
$515$	−5.21261e8	−0.168163
$516$	−3.69391e8	−0.118362
$517$	5.67428e9	1.80590
$518$	3.70580e9	1.17146
$519$	−3.53986e8	−0.111148
$520$	−1.04493e9	−0.325893
$521$	3.15645e9	0.977837	0.488918	−	0.872330i	$-0.337392\pi$
$521$	3.15645e9	0.977837	0.488918	+	0.872330i	$0.337392\pi$
$522$	−5.16758e9	−1.59016
$523$	5.04134e8	0.154095	0.0770477	−	0.997027i	$-0.475451\pi$
$523$	5.04134e8	0.154095	0.0770477	+	0.997027i	$0.475451\pi$
$524$	4.21587e8	0.128005
$525$	−3.77839e9	−1.13959
$526$	−1.34136e9	−0.401880
$527$	−1.75911e9	−0.523548
$528$	1.08223e10	3.19962
$529$	−2.54656e9	−0.747926
$530$	2.66183e9	0.776630
$531$	−9.56736e9	−2.77307
$532$	−1.50456e9	−0.433230
$533$	6.09304e9	1.74297
$534$	−7.13737e9	−2.02836
$535$	−2.90962e9	−0.821481
$536$	−8.36206e8	−0.234550
$537$	7.12818e9	1.98641
$538$	6.12629e9	1.69613
$539$	−1.92982e9	−0.530830
$540$	−1.95346e9	−0.533859
$541$	−5.65936e9	−1.53666	−0.768329	−	0.640056i	$-0.778911\pi$
$541$	−5.65936e9	−1.53666	−0.768329	+	0.640056i	$0.778911\pi$
$542$	3.63010e9	0.979311
$543$	9.49016e9	2.54375
$544$	−2.37870e9	−0.633495
$545$	1.62856e9	0.430940
$546$	6.62056e9	1.74069
$547$	1.34725e9	0.351958	0.175979	−	0.984394i	$-0.443691\pi$
$547$	1.34725e9	0.351958	0.175979	+	0.984394i	$0.443691\pi$
$548$	−1.39686e9	−0.362595
$549$	−6.62186e9	−1.70796
$550$	5.00775e9	1.28343
$551$	2.81632e9	0.717218
$552$	−2.56378e9	−0.648775
$553$	2.68180e9	0.674354
$554$	1.22218e9	0.305388
$555$	−4.41091e9	−1.09522
$556$	−2.04165e9	−0.503756
$557$	−6.05230e9	−1.48398	−0.741989	−	0.670413i	$-0.766117\pi$
$557$	−6.05230e9	−1.48398	−0.741989	+	0.670413i	$0.766117\pi$
$558$	−7.82186e9	−1.90586
$559$	−6.30281e8	−0.152613
$560$	1.90241e9	0.457768
$561$	8.67960e9	2.07553
$562$	3.22383e8	0.0766116
$563$	−2.52625e9	−0.596619	−0.298310	−	0.954469i	$-0.596423\pi$
$563$	−2.52625e9	−0.596619	−0.298310	+	0.954469i	$0.596423\pi$
$564$	−4.31956e9	−1.01382
$565$	3.36001e9	0.783738
$566$	5.25091e9	1.21724
$567$	−8.90985e9	−2.05272
$568$	−2.11553e7	−0.00484396
$569$	1.07885e9	0.245509	0.122755	−	0.992437i	$-0.460827\pi$
$569$	1.07885e9	0.245509	0.122755	+	0.992437i	$0.460827\pi$
$570$	6.08643e9	1.37658
$571$	8.05110e9	1.80979	0.904897	−	0.425632i	$-0.139948\pi$
$571$	8.05110e9	1.80979	0.904897	+	0.425632i	$0.139948\pi$
$572$	−2.58180e9	−0.576814
$573$	2.31915e9	0.514976
$574$	−7.37276e9	−1.62719
$575$	−1.78495e9	−0.391551
$576$	3.48306e9	0.759421
$577$	4.42426e9	0.958795	0.479397	−	0.877598i	$-0.340855\pi$
$577$	4.42426e9	0.958795	0.479397	+	0.877598i	$0.340855\pi$
$578$	1.93283e9	0.416339
$579$	−1.52211e10	−3.25890
$580$	4.97890e8	0.105958
$581$	−1.22413e9	−0.258947
$582$	−8.46629e9	−1.78017
$583$	−9.19875e9	−1.92260
$584$	−6.34460e8	−0.131813
$585$	−5.60669e9	−1.15787
$586$	4.82745e9	0.991006
$587$	−3.26125e9	−0.665503	−0.332752	−	0.943015i	$-0.607977\pi$
$587$	−3.26125e9	−0.665503	−0.332752	+	0.943015i	$0.607977\pi$
$588$	1.46908e9	0.298005
$589$	4.26290e9	0.859611
$590$	3.13290e9	0.628008
$591$	4.96320e9	0.989022
$592$	−7.86831e9	−1.55867
$593$	−1.10562e9	−0.217727	−0.108864	−	0.994057i	$-0.534721\pi$
$593$	−1.10562e9	−0.217727	−0.108864	+	0.994057i	$0.534721\pi$
$594$	2.29436e10	4.49169
$595$	1.52576e9	0.296945
$596$	−4.00231e8	−0.0774371
$597$	3.19351e9	0.614268
$598$	3.12762e9	0.598081
$599$	4.87422e9	0.926640	0.463320	−	0.886191i	$-0.346658\pi$
$599$	4.87422e9	0.926640	0.463320	+	0.886191i	$0.346658\pi$
$600$	5.33193e9	1.00776
$601$	4.41328e9	0.829280	0.414640	−	0.909986i	$-0.363908\pi$
$601$	4.41328e9	0.829280	0.414640	+	0.909986i	$0.363908\pi$
$602$	7.62659e8	0.142476
$603$	−4.48676e9	−0.833341
$604$	3.81676e9	0.704800
$605$	2.32915e9	0.427616
$606$	1.05675e10	1.92894
$607$	9.64653e9	1.75070	0.875348	−	0.483494i	$-0.160632\pi$
$607$	9.64653e9	1.75070	0.875348	+	0.483494i	$0.160632\pi$
$608$	5.76436e9	1.04013
$609$	4.41220e9	0.791580
$610$	2.16838e9	0.386795
$611$	−7.37033e9	−1.30720
$612$	−4.70105e9	−0.829020
$613$	−1.75264e9	−0.307313	−0.153656	−	0.988124i	$-0.549105\pi$
$613$	−1.75264e9	−0.307313	−0.153656	+	0.988124i	$0.549105\pi$
$614$	−4.86047e9	−0.847401
$615$	8.77558e9	1.52129
$616$	−4.36950e9	−0.753181
$617$	3.17834e9	0.544757	0.272378	−	0.962190i	$-0.412190\pi$
$617$	3.17834e9	0.544757	0.272378	+	0.962190i	$0.412190\pi$
$618$	−4.66060e9	−0.794295
$619$	4.18253e9	0.708797	0.354398	−	0.935095i	$-0.384686\pi$
$619$	4.18253e9	0.708797	0.354398	+	0.935095i	$0.384686\pi$
$620$	7.53628e8	0.126995
$621$	−8.17798e9	−1.37033
$622$	−7.56836e9	−1.26106
$623$	4.33584e9	0.718398
$624$	−1.40570e10	−2.31605
$625$	2.36866e9	0.388081
$626$	−7.02447e9	−1.14447
$627$	−2.10335e10	−3.40781
$628$	−5.50800e8	−0.0887433
$629$	−6.31050e9	−1.01108
$630$	6.78426e9	1.08096
$631$	3.38318e9	0.536071	0.268035	−	0.963409i	$-0.413626\pi$
$631$	3.38318e9	0.536071	0.268035	+	0.963409i	$0.413626\pi$
$632$	−3.78446e9	−0.596341
$633$	1.13126e10	1.77276
$634$	2.02466e9	0.315529
$635$	4.57424e9	0.708943
$636$	7.00257e9	1.07934
$637$	2.50664e9	0.384241
$638$	−5.84778e9	−0.891494
$639$	−1.13512e8	−0.0172103
$640$	−3.58496e9	−0.540573
$641$	2.99478e9	0.449120	0.224560	−	0.974460i	$-0.427906\pi$
$641$	2.99478e9	0.449120	0.224560	+	0.974460i	$0.427906\pi$
$642$	−2.60149e10	−3.88016
$643$	1.17542e9	0.174363	0.0871817	−	0.996192i	$-0.472214\pi$
$643$	1.17542e9	0.174363	0.0871817	+	0.996192i	$0.472214\pi$
$644$	−1.11353e9	−0.164286
$645$	−9.07770e8	−0.133204
$646$	8.70760e9	1.27082
$647$	−5.64077e9	−0.818792	−0.409396	−	0.912357i	$-0.634261\pi$
$647$	−5.64077e9	−0.818792	−0.409396	+	0.912357i	$0.634261\pi$
$648$	1.25733e10	1.81525
$649$	−1.08267e10	−1.55467
$650$	−6.50457e9	−0.929013
$651$	6.67850e9	0.948736
$652$	−5.19285e9	−0.733734
$653$	−7.03306e9	−0.988435	−0.494217	−	0.869338i	$-0.664545\pi$
$653$	−7.03306e9	−0.988435	−0.494217	+	0.869338i	$0.664545\pi$
$654$	1.45610e10	2.03549
$655$	1.03604e9	0.144056
$656$	1.56541e10	2.16504
$657$	−3.40427e9	−0.468323
$658$	8.91832e9	1.22037
$659$	−5.30583e9	−0.722194	−0.361097	−	0.932528i	$-0.617598\pi$
$659$	−5.30583e9	−0.722194	−0.361097	+	0.932528i	$0.617598\pi$
$660$	−3.71846e9	−0.503454
$661$	−4.29135e9	−0.577949	−0.288974	−	0.957337i	$-0.593314\pi$
$661$	−4.29135e9	−0.577949	−0.288974	+	0.957337i	$0.593314\pi$
$662$	−9.84615e9	−1.31906
$663$	−1.12739e10	−1.50238
$664$	1.72745e9	0.228990
$665$	−3.69741e9	−0.487553
$666$	−2.80595e10	−3.68062
$667$	2.08437e9	0.271978
$668$	−6.16640e9	−0.800413
$669$	1.76008e10	2.27269
$670$	1.46922e9	0.188724
$671$	−7.49349e9	−0.957536
$672$	9.03077e9	1.14797
$673$	3.84315e9	0.485998	0.242999	−	0.970027i	$-0.421869\pi$
$673$	3.84315e9	0.485998	0.242999	+	0.970027i	$0.421869\pi$
$674$	4.40898e9	0.554662
$675$	1.70079e10	2.12857
$676$	5.04796e6	0.000628496 0
$677$	−1.03024e10	−1.27608	−0.638041	−	0.770002i	$-0.720255\pi$
$677$	−1.03024e10	−1.27608	−0.638041	+	0.770002i	$0.720255\pi$
$678$	3.00419e10	3.70188
$679$	5.14314e9	0.630498
$680$	−2.15310e9	−0.262593
$681$	2.61689e8	0.0317519
$682$	−8.85145e9	−1.06849
$683$	2.78807e8	0.0334835	0.0167417	−	0.999860i	$-0.494671\pi$
$683$	2.78807e8	0.0334835	0.0167417	+	0.999860i	$0.494671\pi$
$684$	1.13922e10	1.36116
$685$	−3.43276e9	−0.408062
$686$	−1.09328e10	−1.29300
$687$	−1.78182e10	−2.09660
$688$	−1.61931e9	−0.189570
$689$	1.19483e10	1.39167
$690$	4.50460e9	0.522016
$691$	1.57009e9	0.181030	0.0905151	−	0.995895i	$-0.471149\pi$
$691$	1.57009e9	0.181030	0.0905151	+	0.995895i	$0.471149\pi$
$692$	2.16963e8	0.0248893
$693$	−2.34451e10	−2.67600
$694$	−9.48045e9	−1.07664
$695$	−5.01731e9	−0.566923
$696$	−6.22635e9	−0.700005
$697$	1.25548e10	1.40442
$698$	5.00039e9	0.556557
$699$	−4.77061e9	−0.528328
$700$	2.31583e9	0.255189
$701$	1.55305e10	1.70284	0.851418	−	0.524488i	$-0.175743\pi$
$701$	1.55305e10	1.70284	0.851418	+	0.524488i	$0.175743\pi$
$702$	−2.98015e10	−3.25131
$703$	1.52924e10	1.66009
$704$	3.94153e9	0.425756
$705$	−1.06152e10	−1.14095
$706$	−1.72324e10	−1.84302
$707$	−6.41961e9	−0.683189
$708$	8.24185e9	0.872787
$709$	1.58882e10	1.67422	0.837112	−	0.547032i	$-0.184242\pi$
$709$	1.58882e10	1.67422	0.837112	+	0.547032i	$0.184242\pi$
$710$	3.71702e7	0.00389754
$711$	−2.03060e10	−2.11875
$712$	−6.11859e9	−0.635289
$713$	3.15499e9	0.325975
$714$	1.36418e10	1.40258
$715$	−6.34470e9	−0.649142
$716$	−4.36896e9	−0.444818
$717$	1.85220e10	1.87660
$718$	4.78082e9	0.482021
$719$	6.03906e9	0.605924	0.302962	−	0.953003i	$-0.402024\pi$
$719$	6.03906e9	0.605924	0.302962	+	0.953003i	$0.402024\pi$
$720$	−1.44046e10	−1.43826
$721$	2.83124e9	0.281322
$722$	−9.06349e9	−0.896222
$723$	−1.13093e10	−1.11289
$724$	−5.81665e9	−0.569624
$725$	−4.33490e9	−0.422470
$726$	2.08249e10	2.01979
$727$	1.96027e10	1.89211	0.946054	−	0.324008i	$-0.105030\pi$
$727$	1.96027e10	1.89211	0.946054	+	0.324008i	$0.105030\pi$
$728$	5.67555e9	0.545190
$729$	1.43108e10	1.36810
$730$	1.11475e9	0.106059
$731$	−1.29871e9	−0.122970
$732$	5.70443e9	0.537556
$733$	−4.74673e9	−0.445174	−0.222587	−	0.974913i	$-0.571450\pi$
$733$	−4.74673e9	−0.445174	−0.222587	+	0.974913i	$0.571450\pi$
$734$	−2.33539e10	−2.17984
$735$	3.61022e9	0.335373
$736$	4.26623e9	0.394432
$737$	−5.07735e9	−0.467198
$738$	5.58249e10	5.11247
$739$	−9.87972e9	−0.900512	−0.450256	−	0.892900i	$-0.648667\pi$
$739$	−9.87972e9	−0.900512	−0.450256	+	0.892900i	$0.648667\pi$
$740$	2.70350e9	0.245254
$741$	2.73205e10	2.46674
$742$	−1.44578e10	−1.29923
$743$	−1.28591e10	−1.15014	−0.575069	−	0.818105i	$-0.695025\pi$
$743$	−1.28591e10	−1.15014	−0.575069	+	0.818105i	$0.695025\pi$
$744$	−9.42447e9	−0.838980
$745$	−9.83559e8	−0.0871472
$746$	4.06014e9	0.358059
$747$	9.26884e9	0.813585
$748$	−5.31985e9	−0.464776
$749$	1.58036e10	1.37427
$750$	−2.13808e10	−1.85059
$751$	7.42726e9	0.639866	0.319933	−	0.947440i	$-0.396340\pi$
$751$	7.42726e9	0.639866	0.319933	+	0.947440i	$0.396340\pi$
$752$	−1.89357e10	−1.62375
$753$	−3.52773e10	−3.01102
$754$	7.59569e9	0.645309
$755$	9.37960e9	0.793177
$756$	1.06103e10	0.893099
$757$	7.19774e9	0.603060	0.301530	−	0.953457i	$-0.402503\pi$
$757$	7.19774e9	0.603060	0.301530	+	0.953457i	$0.402503\pi$
$758$	1.31953e10	1.10046
$759$	−1.55670e10	−1.29229
$760$	5.21766e9	0.431150
$761$	−1.01426e10	−0.834265	−0.417132	−	0.908846i	$-0.636965\pi$
$761$	−1.01426e10	−0.834265	−0.417132	+	0.908846i	$0.636965\pi$
$762$	4.08983e10	3.34860
$763$	−8.84556e9	−0.720924
$764$	−1.42144e9	−0.115319
$765$	−1.15527e10	−0.932973
$766$	6.59862e9	0.530460
$767$	1.40628e10	1.12535
$768$	−2.48559e10	−1.98000
$769$	−3.34842e9	−0.265521	−0.132760	−	0.991148i	$-0.542384\pi$
$769$	−3.34842e9	−0.265521	−0.132760	+	0.991148i	$0.542384\pi$
$770$	7.67727e9	0.606023
$771$	3.76119e10	2.95553
$772$	9.32920e9	0.729767
$773$	−1.64501e10	−1.28097	−0.640485	−	0.767970i	$-0.721267\pi$
$773$	−1.64501e10	−1.28097	−0.640485	+	0.767970i	$0.721267\pi$
$774$	−5.77468e9	−0.447646
$775$	−6.56149e9	−0.506345
$776$	−7.25782e9	−0.557558
$777$	2.39579e10	1.83221
$778$	2.44064e10	1.85812
$779$	−3.04245e10	−2.30591
$780$	4.82992e9	0.364425
$781$	−1.28453e8	−0.00964863
$782$	6.44453e9	0.481912
$783$	−1.98609e10	−1.47854
$784$	6.44002e9	0.477288
$785$	−1.35358e9	−0.0998710
$786$	9.26324e9	0.680431
$787$	−1.67903e9	−0.122786	−0.0613929	−	0.998114i	$-0.519554\pi$
$787$	−1.67903e9	−0.122786	−0.0613929	+	0.998114i	$0.519554\pi$
$788$	−3.04202e9	−0.221472
$789$	−8.67187e9	−0.628555
$790$	6.64935e9	0.479827
$791$	−1.82500e10	−1.31112
$792$	3.30849e10	2.36642
$793$	9.73330e9	0.693113
$794$	2.32736e10	1.65003
$795$	1.72086e10	1.21468
$796$	−1.95734e9	−0.137553
$797$	−1.88216e10	−1.31690	−0.658449	−	0.752625i	$-0.728787\pi$
$797$	−1.88216e10	−1.31690	−0.658449	+	0.752625i	$0.728787\pi$
$798$	−3.30586e10	−2.30289
$799$	−1.51867e10	−1.05330
$800$	−8.87255e9	−0.612680
$801$	−3.28301e10	−2.25714
$802$	1.20301e10	0.823491
$803$	−3.85237e9	−0.262557
$804$	3.86515e9	0.262283
$805$	−2.73647e9	−0.184887
$806$	1.14972e10	0.773424
$807$	3.96063e10	2.65281
$808$	9.05913e9	0.604153
$809$	1.07428e10	0.713342	0.356671	−	0.934230i	$-0.383912\pi$
$809$	1.07428e10	0.713342	0.356671	+	0.934230i	$0.383912\pi$
$810$	−2.20914e10	−1.46058
$811$	2.81229e10	1.85135	0.925673	−	0.378326i	$-0.123500\pi$
$811$	2.81229e10	1.85135	0.925673	+	0.378326i	$0.123500\pi$
$812$	−2.70430e9	−0.177259
$813$	2.34685e10	1.53168
$814$	−3.17530e10	−2.06347
$815$	−1.27613e10	−0.825739
$816$	−2.89648e10	−1.86619
$817$	3.14719e9	0.201905
$818$	9.66350e9	0.617302
$819$	3.04528e10	1.93702
$820$	−5.37867e9	−0.340664
$821$	1.62322e10	1.02371	0.511853	−	0.859073i	$-0.328959\pi$
$821$	1.62322e10	1.02371	0.511853	+	0.859073i	$0.328959\pi$
$822$	−3.06923e10	−1.92743
$823$	−6.36841e9	−0.398228	−0.199114	−	0.979976i	$-0.563806\pi$
$823$	−6.36841e9	−0.398228	−0.199114	+	0.979976i	$0.563806\pi$
$824$	−3.99535e9	−0.248776
$825$	3.23749e10	2.00734
$826$	−1.70164e10	−1.05060
$827$	−1.77050e10	−1.08850	−0.544248	−	0.838924i	$-0.683185\pi$
$827$	−1.77050e10	−1.08850	−0.544248	+	0.838924i	$0.683185\pi$
$828$	8.43140e9	0.516171
$829$	−3.43518e9	−0.209415	−0.104708	−	0.994503i	$-0.533391\pi$
$829$	−3.43518e9	−0.209415	−0.104708	+	0.994503i	$0.533391\pi$
$830$	−3.03515e9	−0.184250
$831$	7.90138e9	0.477639
$832$	−5.11966e9	−0.308184
$833$	5.16499e9	0.309608
$834$	−4.48598e10	−2.67779
$835$	−1.51538e10	−0.900778
$836$	1.28917e10	0.763113
$837$	−3.00623e10	−1.77208
$838$	1.12445e10	0.660063
$839$	−2.12784e10	−1.24386	−0.621930	−	0.783073i	$-0.713651\pi$
$839$	−2.12784e10	−1.24386	−0.621930	+	0.783073i	$0.713651\pi$
$840$	8.17428e9	0.475852
$841$	−1.21878e10	−0.706545
$842$	−3.70365e7	−0.00213815
$843$	2.08420e9	0.119823
$844$	−6.93367e9	−0.396976
$845$	1.24052e7	0.000707305 0
$846$	−6.75276e10	−3.83429
$847$	−1.26508e10	−0.715363
$848$	3.06973e10	1.72868
$849$	3.39470e10	1.90381
$850$	−1.34028e10	−0.748565
$851$	1.13180e10	0.629528
$852$	9.77852e7	0.00541669
$853$	−8.50432e9	−0.469157	−0.234578	−	0.972097i	$-0.575371\pi$
$853$	−8.50432e9	−0.469157	−0.234578	+	0.972097i	$0.575371\pi$
$854$	−1.17776e10	−0.647073
$855$	2.79960e10	1.53184
$856$	−2.23016e10	−1.21528
$857$	−8.11675e8	−0.0440503	−0.0220252	−	0.999757i	$-0.507011\pi$
$857$	−8.11675e8	−0.0440503	−0.0220252	+	0.999757i	$0.507011\pi$
$858$	−5.67279e10	−3.06614
$859$	−1.84624e10	−0.993832	−0.496916	−	0.867799i	$-0.665534\pi$
$859$	−1.84624e10	−0.993832	−0.496916	+	0.867799i	$0.665534\pi$
$860$	5.56384e8	0.0298284
$861$	−4.76647e10	−2.54499
$862$	1.64160e10	0.872957
$863$	1.83495e10	0.971823	0.485911	−	0.874008i	$-0.338488\pi$
$863$	1.83495e10	0.971823	0.485911	+	0.874008i	$0.338488\pi$
$864$	−4.06507e10	−2.14423
$865$	5.33180e8	0.0280103
$866$	1.50960e10	0.789860
$867$	1.24957e10	0.651170
$868$	−4.09334e9	−0.212451
$869$	−2.29789e10	−1.18784
$870$	1.09398e10	0.563237
$871$	6.59498e9	0.338182
$872$	1.24825e10	0.637523
$873$	−3.89427e10	−1.98096
$874$	−1.56172e10	−0.791250
$875$	1.29885e10	0.655437
$876$	2.93263e9	0.147398
$877$	3.41189e10	1.70803	0.854016	−	0.520247i	$-0.174160\pi$
$877$	3.41189e10	1.70803	0.854016	+	0.520247i	$0.174160\pi$
$878$	8.02330e9	0.400057
$879$	3.12094e10	1.54997
$880$	−1.63007e10	−0.806337
$881$	1.72277e10	0.848811	0.424406	−	0.905472i	$-0.360483\pi$
$881$	1.72277e10	0.848811	0.424406	+	0.905472i	$0.360483\pi$
$882$	2.29660e10	1.12706
$883$	2.58479e10	1.26347	0.631733	−	0.775186i	$-0.282344\pi$
$883$	2.58479e10	1.26347	0.631733	+	0.775186i	$0.282344\pi$
$884$	6.90995e9	0.336428
$885$	2.02541e10	0.982228
$886$	−2.98664e10	−1.44266
$887$	−3.51605e10	−1.69170	−0.845848	−	0.533424i	$-0.820905\pi$
$887$	−3.51605e10	−1.69170	−0.845848	+	0.533424i	$0.820905\pi$
$888$	−3.38086e10	−1.62025
$889$	−2.48451e10	−1.18600
$890$	1.07505e10	0.511166
$891$	7.63436e10	3.61577
$892$	−1.07877e10	−0.508925
$893$	3.68024e10	1.72940
$894$	−8.79400e9	−0.411628
$895$	−1.07366e10	−0.500595
$896$	1.94718e10	0.904330
$897$	2.02200e10	0.935422
$898$	1.00208e10	0.461778
$899$	7.66216e9	0.351716
$900$	−1.75349e10	−0.801780
$901$	2.46197e10	1.12136
$902$	6.31731e10	2.86622
$903$	4.93057e9	0.222838
$904$	2.57537e10	1.15945
$905$	−1.42943e10	−0.641050
$906$	8.38630e10	3.74647
$907$	1.84400e8	0.00820607	0.00410303	−	0.999992i	$-0.498694\pi$
$907$	1.84400e8	0.00820607	0.00410303	+	0.999992i	$0.498694\pi$
$908$	−1.60392e8	−0.00711023
$909$	4.86079e10	2.14651
$910$	−9.97202e9	−0.438670
$911$	−1.19294e10	−0.522761	−0.261380	−	0.965236i	$-0.584178\pi$
$911$	−1.19294e10	−0.522761	−0.261380	+	0.965236i	$0.584178\pi$
$912$	7.01913e10	3.06409
$913$	1.04889e10	0.456123
$914$	−1.01894e10	−0.441407
$915$	1.40185e10	0.604962
$916$	1.09210e10	0.469493
$917$	−5.62727e9	−0.240993
$918$	−6.14067e10	−2.61979
$919$	3.79246e10	1.61182	0.805910	−	0.592038i	$-0.201677\pi$
$919$	3.79246e10	1.61182	0.805910	+	0.592038i	$0.201677\pi$
$920$	3.86161e9	0.163498
$921$	−3.14228e10	−1.32537
$922$	1.08020e9	0.0453887
$923$	1.66848e8	0.00698417
$924$	2.01969e10	0.842234
$925$	−2.35382e10	−0.977860
$926$	−1.86597e10	−0.772263
$927$	−2.14375e10	−0.883885
$928$	1.03609e10	0.425578
$929$	−3.05711e10	−1.25099	−0.625497	−	0.780226i	$-0.715104\pi$
$929$	−3.05711e10	−1.25099	−0.625497	+	0.780226i	$0.715104\pi$
$930$	1.65589e10	0.675059
$931$	−1.25165e10	−0.508344
$932$	2.92397e9	0.118309
$933$	−4.89293e10	−1.97234
$934$	−5.55040e10	−2.22900
$935$	−1.30734e10	−0.523055
$936$	−4.29740e10	−1.71293
$937$	−1.29971e10	−0.516129	−0.258065	−	0.966128i	$-0.583085\pi$
$937$	−1.29971e10	−0.516129	−0.258065	+	0.966128i	$0.583085\pi$
$938$	−7.98012e9	−0.315718
$939$	−4.54130e10	−1.78999
$940$	6.50621e9	0.255494
$941$	−3.94818e10	−1.54466	−0.772330	−	0.635221i	$-0.780909\pi$
$941$	−3.94818e10	−1.54466	−0.772330	+	0.635221i	$0.780909\pi$
$942$	−1.21023e10	−0.471728
$943$	−2.25173e10	−0.874431
$944$	3.61299e10	1.39787
$945$	2.60744e10	1.00509
$946$	−6.53480e9	−0.250965
$947$	1.20683e10	0.461766	0.230883	−	0.972982i	$-0.425839\pi$
$947$	1.20683e10	0.461766	0.230883	+	0.972982i	$0.425839\pi$
$948$	1.74927e10	0.666849
$949$	5.00385e9	0.190052
$950$	3.24794e10	1.22907
$951$	1.30894e10	0.493499
$952$	1.16946e10	0.439294
$953$	8.06727e9	0.301927	0.150963	−	0.988539i	$-0.451762\pi$
$953$	8.06727e9	0.301927	0.150963	+	0.988539i	$0.451762\pi$
$954$	1.09471e11	4.08206
$955$	−3.49314e9	−0.129779
$956$	−1.13524e10	−0.420228
$957$	−3.78057e10	−1.39433
$958$	4.57357e9	0.168065
$959$	1.86451e10	0.682651
$960$	−7.37366e9	−0.268988
$961$	−1.59148e10	−0.578456
$962$	4.12440e10	1.49365
$963$	−1.19662e11	−4.31781
$964$	6.93165e9	0.249211
$965$	2.29263e10	0.821274
$966$	−2.44668e10	−0.873287
$967$	−2.31765e10	−0.824244	−0.412122	−	0.911129i	$-0.635212\pi$
$967$	−2.31765e10	−0.824244	−0.412122	+	0.911129i	$0.635212\pi$
$968$	1.78524e10	0.632606
$969$	5.62944e10	1.98761
$970$	1.27521e10	0.448622
$971$	6.13552e9	0.215072	0.107536	−	0.994201i	$-0.465704\pi$
$971$	6.13552e9	0.215072	0.107536	+	0.994201i	$0.465704\pi$
$972$	−2.55388e10	−0.892007
$973$	2.72516e10	0.948412
$974$	3.16510e10	1.09757
$975$	−4.20519e10	−1.45301
$976$	2.50066e10	0.860956
$977$	−2.15287e10	−0.738563	−0.369282	−	0.929317i	$-0.620396\pi$
$977$	−2.15287e10	−0.738563	−0.369282	+	0.929317i	$0.620396\pi$
$978$	−1.14099e11	−3.90027
$979$	−3.71514e10	−1.26542
$980$	−2.21275e9	−0.0751003
$981$	6.69766e10	2.26507
$982$	6.89761e9	0.232439
$983$	5.33254e8	0.0179059	0.00895296	−	0.999960i	$-0.497150\pi$
$983$	5.33254e8	0.0179059	0.00895296	+	0.999960i	$0.497150\pi$
$984$	6.72628e10	2.25057
$985$	−7.47568e9	−0.249243
$986$	1.56511e10	0.519966
$987$	5.76567e10	1.90871
$988$	−1.67451e10	−0.552380
$989$	2.32925e9	0.0765648
$990$	−5.81306e10	−1.90406
$991$	−2.96780e10	−0.968671	−0.484336	−	0.874882i	$-0.660939\pi$
$991$	−2.96780e10	−0.968671	−0.484336	+	0.874882i	$0.660939\pi$
$992$	1.56827e10	0.510070
$993$	−6.36551e10	−2.06306
$994$	−2.01891e8	−0.00652025
$995$	−4.81012e9	−0.154802
$996$	−7.98469e9	−0.256065
$997$	3.33968e10	1.06726	0.533632	−	0.845717i	$-0.320827\pi$
$997$	3.33968e10	1.06726	0.533632	+	0.845717i	$0.320827\pi$
$998$	3.53822e10	1.12675
$999$	−1.07843e11	−3.42226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.4	✓	11
3.2	odd	2		387.8.a.b.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.4	✓	11	1.1	even	1	trivial
387.8.a.b.1.8		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)

\(f(q)\)	\(=\)	\(q-13.4671 q^{2} -87.0645 q^{3} +53.3630 q^{4} +131.138 q^{5} +1172.51 q^{6} -712.280 q^{7} +1005.14 q^{8} +5393.23 q^{9} +O(q^{10})\)	\(q-13.4671 q^{2} -87.0645 q^{3} +53.3630 q^{4} +131.138 q^{5} +1172.51 q^{6} -712.280 q^{7} +1005.14 q^{8} +5393.23 q^{9} -1766.05 q^{10} +6103.13 q^{11} -4646.02 q^{12} -7927.36 q^{13} +9592.35 q^{14} -11417.5 q^{15} -20366.9 q^{16} -16334.5 q^{17} -72631.2 q^{18} +39583.9 q^{19} +6997.93 q^{20} +62014.3 q^{21} -82191.5 q^{22} +29296.2 q^{23} -87512.4 q^{24} -60927.8 q^{25} +106759. q^{26} -279148. q^{27} -38009.4 q^{28} +71148.2 q^{29} +153760. q^{30} +107693. q^{31} +145624. q^{32} -531366. q^{33} +219979. q^{34} -93407.1 q^{35} +287799. q^{36} +386329. q^{37} -533080. q^{38} +690192. q^{39} +131813. q^{40} -768609. q^{41} -835153. q^{42} +79507.0 q^{43} +325681. q^{44} +707258. q^{45} -394535. q^{46} +929733. q^{47} +1.77323e6 q^{48} -316201. q^{49} +820521. q^{50} +1.42216e6 q^{51} -423028. q^{52} -1.50722e6 q^{53} +3.75932e6 q^{54} +800354. q^{55} -715944. q^{56} -3.44635e6 q^{57} -958161. q^{58} -1.77396e6 q^{59} -609271. q^{60} -1.22781e6 q^{61} -1.45031e6 q^{62} -3.84148e6 q^{63} +645821. q^{64} -1.03958e6 q^{65} +7.15596e6 q^{66} -831926. q^{67} -871658. q^{68} -2.55066e6 q^{69} +1.25792e6 q^{70} -21047.1 q^{71} +5.42097e6 q^{72} -631213. q^{73} -5.20274e6 q^{74} +5.30464e6 q^{75} +2.11231e6 q^{76} -4.34713e6 q^{77} -9.29489e6 q^{78} -3.76509e6 q^{79} -2.67087e6 q^{80} +1.25089e7 q^{81} +1.03509e7 q^{82} +1.71861e6 q^{83} +3.30927e6 q^{84} -2.14208e6 q^{85} -1.07073e6 q^{86} -6.19448e6 q^{87} +6.13453e6 q^{88} -6.08728e6 q^{89} -9.52472e6 q^{90} +5.64650e6 q^{91} +1.56333e6 q^{92} -9.37623e6 q^{93} -1.25208e7 q^{94} +5.19096e6 q^{95} -1.26787e7 q^{96} -7.22067e6 q^{97} +4.25831e6 q^{98} +3.29156e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 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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