LMFDB - Embedded newform 43.8.a.a.1.2

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			1.2
Root			$14.1572$ 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)

$f(q)$	$=$	$q-16.1572 q^{2} -48.3227 q^{3} +133.057 q^{4} -272.935 q^{5} +780.762 q^{6} +1101.65 q^{7} -81.7025 q^{8} +148.083 q^{9} +O(q^{10})$	\(q-16.1572 q^{2} -48.3227 q^{3} +133.057 q^{4} -272.935 q^{5} +780.762 q^{6} +1101.65 q^{7} -81.7025 q^{8} +148.083 q^{9} +4409.88 q^{10} +685.243 q^{11} -6429.66 q^{12} +13204.0 q^{13} -17799.7 q^{14} +13189.0 q^{15} -15711.2 q^{16} -1155.38 q^{17} -2392.62 q^{18} -12969.6 q^{19} -36315.9 q^{20} -53234.8 q^{21} -11071.6 q^{22} -106988. q^{23} +3948.09 q^{24} -3631.41 q^{25} -213341. q^{26} +98526.0 q^{27} +146582. q^{28} +71411.7 q^{29} -213097. q^{30} +229489. q^{31} +264307. q^{32} -33112.8 q^{33} +18667.8 q^{34} -300680. q^{35} +19703.5 q^{36} -279218. q^{37} +209553. q^{38} -638054. q^{39} +22299.5 q^{40} +345820. q^{41} +860128. q^{42} +79507.0 q^{43} +91176.2 q^{44} -40417.2 q^{45} +1.72863e6 q^{46} -735243. q^{47} +759206. q^{48} +390095. q^{49} +58673.6 q^{50} +55831.2 q^{51} +1.75688e6 q^{52} -714374. q^{53} -1.59191e6 q^{54} -187027. q^{55} -90007.8 q^{56} +626726. q^{57} -1.15382e6 q^{58} -915243. q^{59} +1.75488e6 q^{60} -575.793 q^{61} -3.70792e6 q^{62} +163136. q^{63} -2.25945e6 q^{64} -3.60384e6 q^{65} +535012. q^{66} -3.55836e6 q^{67} -153731. q^{68} +5.16993e6 q^{69} +4.85816e6 q^{70} -1.66804e6 q^{71} -12098.8 q^{72} -1.03269e6 q^{73} +4.51140e6 q^{74} +175480. q^{75} -1.72569e6 q^{76} +754900. q^{77} +1.03092e7 q^{78} +1.58783e6 q^{79} +4.28813e6 q^{80} -5.08490e6 q^{81} -5.58750e6 q^{82} -8.26293e6 q^{83} -7.08325e6 q^{84} +315344. q^{85} -1.28461e6 q^{86} -3.45080e6 q^{87} -55986.1 q^{88} +7.66713e6 q^{89} +653030. q^{90} +1.45462e7 q^{91} -1.42354e7 q^{92} -1.10895e7 q^{93} +1.18795e7 q^{94} +3.53986e6 q^{95} -1.27720e7 q^{96} -1.26607e7 q^{97} -6.30287e6 q^{98} +101473. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−16.1572	−1.42811	−0.714056	−	0.700088i	$-0.753144\pi$
$2$	−16.1572	−1.42811	−0.714056	+	0.700088i	$0.753144\pi$
$3$	−48.3227	−1.03330	−0.516650	−	0.856196i	$-0.672821\pi$
$3$	−48.3227	−1.03330	−0.516650	+	0.856196i	$0.672821\pi$
$4$	133.057	1.03951
$5$	−272.935	−0.976482	−0.488241	−	0.872709i	$-0.662361\pi$
$5$	−272.935	−0.976482	−0.488241	+	0.872709i	$0.662361\pi$
$6$	780.762	1.47567
$7$	1101.65	1.21395	0.606976	−	0.794720i	$-0.292382\pi$
$7$	1101.65	1.21395	0.606976	+	0.794720i	$0.292382\pi$
$8$	−81.7025	−0.0564184
$9$	148.083	0.0677108
$10$	4409.88	1.39453
$11$	685.243	0.155228	0.0776140	−	0.996983i	$-0.475270\pi$
$11$	685.243	0.155228	0.0776140	+	0.996983i	$0.475270\pi$
$12$	−6429.66	−1.07412
$13$	13204.0	1.66688	0.833440	−	0.552609i	$-0.186368\pi$
$13$	13204.0	1.66688	0.833440	+	0.552609i	$0.186368\pi$
$14$	−17799.7	−1.73366
$15$	13189.0	1.00900
$16$	−15711.2	−0.958934
$17$	−1155.38	−0.0570367	−0.0285184	−	0.999593i	$-0.509079\pi$
$17$	−1155.38	−0.0570367	−0.0285184	+	0.999593i	$0.509079\pi$
$18$	−2392.62	−0.0966986
$19$	−12969.6	−0.433800	−0.216900	−	0.976194i	$-0.569594\pi$
$19$	−12969.6	−0.433800	−0.216900	+	0.976194i	$0.569594\pi$
$20$	−36315.9	−1.01506
$21$	−53234.8	−1.25438
$22$	−11071.6	−0.221683
$23$	−106988.	−1.83352	−0.916761	−	0.399436i	$-0.869206\pi$
$23$	−106988.	−1.83352	−0.916761	+	0.399436i	$0.869206\pi$
$24$	3948.09	0.0582971
$25$	−3631.41	−0.0464820
$26$	−213341.	−2.38049
$27$	98526.0	0.963335
$28$	146582.	1.26191
$29$	71411.7	0.543721	0.271861	−	0.962337i	$-0.412361\pi$
$29$	71411.7	0.543721	0.271861	+	0.962337i	$0.412361\pi$
$30$	−213097.	−1.44097
$31$	229489.	1.38356	0.691778	−	0.722111i	$-0.256828\pi$
$31$	229489.	1.38356	0.691778	+	0.722111i	$0.256828\pi$
$32$	264307.	1.42588
$33$	−33112.8	−0.160397
$34$	18667.8	0.0814549
$35$	−300680.	−1.18540
$36$	19703.5	0.0703857
$37$	−279218.	−0.906229	−0.453115	−	0.891452i	$-0.649687\pi$
$37$	−279218.	−0.906229	−0.453115	+	0.891452i	$0.649687\pi$
$38$	209553.	0.619515
$39$	−638054.	−1.72239
$40$	22299.5	0.0550915
$41$	345820.	0.783622	0.391811	−	0.920046i	$-0.371849\pi$
$41$	345820.	0.783622	0.391811	+	0.920046i	$0.371849\pi$
$42$	860128.	1.79139
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	91176.2	0.161360
$45$	−40417.2	−0.0661184
$46$	1.72863e6	2.61848
$47$	−735243.	−1.03297	−0.516486	−	0.856296i	$-0.672760\pi$
$47$	−735243.	−1.03297	−0.516486	+	0.856296i	$0.672760\pi$
$48$	759206.	0.990867
$49$	390095.	0.473680
$50$	58673.6	0.0663816
$51$	55831.2	0.0589361
$52$	1.75688e6	1.73273
$53$	−714374.	−0.659113	−0.329557	−	0.944136i	$-0.606899\pi$
$53$	−714374.	−0.659113	−0.329557	+	0.944136i	$0.606899\pi$
$54$	−1.59191e6	−1.37575
$55$	−187027.	−0.151577
$56$	−90007.8	−0.0684892
$57$	626726.	0.448245
$58$	−1.15382e6	−0.776495
$59$	−915243.	−0.580169	−0.290084	−	0.957001i	$-0.593683\pi$
$59$	−915243.	−0.580169	−0.290084	+	0.957001i	$0.593683\pi$
$60$	1.75488e6	1.04886
$61$	−575.793	−0.000324797 0	−0.000162399	−	1.00000i	$-0.500052\pi$
$61$	−575.793	−0.000324797 0	−0.000162399		1.00000i	$0.500052\pi$
$62$	−3.70792e6	−1.97587
$63$	163136.	0.0821976
$64$	−2.25945e6	−1.07739
$65$	−3.60384e6	−1.62768
$66$	535012.	0.229065
$67$	−3.55836e6	−1.44540	−0.722700	−	0.691162i	$-0.757099\pi$
$67$	−3.55836e6	−1.44540	−0.722700	+	0.691162i	$0.757099\pi$
$68$	−153731.	−0.0592900
$69$	5.16993e6	1.89458
$70$	4.85816e6	1.69289
$71$	−1.66804e6	−0.553099	−0.276549	−	0.961000i	$-0.589191\pi$
$71$	−1.66804e6	−0.553099	−0.276549	+	0.961000i	$0.589191\pi$
$72$	−12098.8	−0.00382013
$73$	−1.03269e6	−0.310700	−0.155350	−	0.987860i	$-0.549650\pi$
$73$	−1.03269e6	−0.310700	−0.155350	+	0.987860i	$0.549650\pi$
$74$	4.51140e6	1.29420
$75$	175480.	0.0480299
$76$	−1.72569e6	−0.450937
$77$	754900.	0.188439
$78$	1.03092e7	2.45977
$79$	1.58783e6	0.362334	0.181167	−	0.983452i	$-0.442013\pi$
$79$	1.58783e6	0.362334	0.181167	+	0.983452i	$0.442013\pi$
$80$	4.28813e6	0.936382
$81$	−5.08490e6	−1.06313
$82$	−5.58750e6	−1.11910
$83$	−8.26293e6	−1.58621	−0.793105	−	0.609085i	$-0.791537\pi$
$83$	−8.26293e6	−1.58621	−0.793105	+	0.609085i	$0.791537\pi$
$84$	−7.08325e6	−1.30393
$85$	315344.	0.0556954
$86$	−1.28461e6	−0.217785
$87$	−3.45080e6	−0.561827
$88$	−55986.1	−0.00875771
$89$	7.66713e6	1.15284	0.576418	−	0.817155i	$-0.304450\pi$
$89$	7.66713e6	1.15284	0.576418	+	0.817155i	$0.304450\pi$
$90$	653030.	0.0944245
$91$	1.45462e7	2.02351
$92$	−1.42354e7	−1.90596
$93$	−1.10895e7	−1.42963
$94$	1.18795e7	1.47520
$95$	3.53986e6	0.423598
$96$	−1.27720e7	−1.47337
$97$	−1.26607e7	−1.40850	−0.704251	−	0.709951i	$-0.748717\pi$
$97$	−1.26607e7	−1.40850	−0.704251	+	0.709951i	$0.748717\pi$
$98$	−6.30287e6	−0.676468
$99$	101473.	0.0105106
$100$	−483183.	−0.0483183
$101$	−7.42880e6	−0.717454	−0.358727	−	0.933443i	$-0.616789\pi$
$101$	−7.42880e6	−0.717454	−0.358727	+	0.933443i	$0.616789\pi$
$102$	−902079.	−0.0841674
$103$	1.57866e7	1.42350	0.711752	−	0.702431i	$-0.247902\pi$
$103$	1.57866e7	1.42350	0.711752	+	0.702431i	$0.247902\pi$
$104$	−1.07880e6	−0.0940427
$105$	1.45297e7	1.22488
$106$	1.15423e7	0.941288
$107$	−1.40430e6	−0.110819	−0.0554097	−	0.998464i	$-0.517646\pi$
$107$	−1.40430e6	−0.110819	−0.0554097	+	0.998464i	$0.517646\pi$
$108$	1.31095e7	1.00139
$109$	−6.10839e6	−0.451787	−0.225894	−	0.974152i	$-0.572530\pi$
$109$	−6.10839e6	−0.451787	−0.225894	+	0.974152i	$0.572530\pi$
$110$	3.02184e6	0.216470
$111$	1.34926e7	0.936407
$112$	−1.73083e7	−1.16410
$113$	−8.10527e6	−0.528437	−0.264218	−	0.964463i	$-0.585114\pi$
$113$	−8.10527e6	−0.528437	−0.264218	+	0.964463i	$0.585114\pi$
$114$	−1.01262e7	−0.640145
$115$	2.92007e7	1.79040
$116$	9.50180e6	0.565201
$117$	1.95530e6	0.112866
$118$	1.47878e7	0.828546
$119$	−1.27283e6	−0.0692398
$120$	−1.07757e6	−0.0569261
$121$	−1.90176e7	−0.975904
$122$	9303.23	0.000463847 0
$123$	−1.67109e7	−0.809717
$124$	3.05351e7	1.43821
$125$	2.23142e7	1.02187
$126$	−2.63584e6	−0.117387
$127$	3.81416e7	1.65229	0.826145	−	0.563457i	$-0.190529\pi$
$127$	3.81416e7	1.65229	0.826145	+	0.563457i	$0.190529\pi$
$128$	2.67514e6	0.112749
$129$	−3.84199e6	−0.157577
$130$	5.82282e7	2.32451
$131$	476451.	0.0185169	0.00925845	−	0.999957i	$-0.497053\pi$
$131$	476451.	0.0185169	0.00925845	+	0.999957i	$0.497053\pi$
$132$	−4.40588e6	−0.166734
$133$	−1.42880e7	−0.526612
$134$	5.74933e7	2.06419
$135$	−2.68912e7	−0.940680
$136$	94397.6	0.00321792
$137$	−5.02778e7	−1.67053	−0.835265	−	0.549848i	$-0.814686\pi$
$137$	−5.02778e7	−1.67053	−0.835265	+	0.549848i	$0.814686\pi$
$138$	−8.35319e7	−2.70567
$139$	−5.83450e7	−1.84269	−0.921344	−	0.388748i	$-0.872908\pi$
$139$	−5.83450e7	−1.84269	−0.921344	+	0.388748i	$0.872908\pi$
$140$	−4.00075e7	−1.23223
$141$	3.55289e7	1.06737
$142$	2.69510e7	0.789887
$143$	9.04796e6	0.258747
$144$	−2.32656e6	−0.0649301
$145$	−1.94908e7	−0.530934
$146$	1.66855e7	0.443714
$147$	−1.88505e7	−0.489453
$148$	−3.71519e7	−0.942030
$149$	−6.73082e7	−1.66693	−0.833463	−	0.552575i	$-0.813645\pi$
$149$	−6.73082e7	−1.66693	−0.833463	+	0.552575i	$0.813645\pi$
$150$	−2.83527e6	−0.0685922
$151$	5.87220e7	1.38797	0.693987	−	0.719988i	$-0.255853\pi$
$151$	5.87220e7	1.38797	0.693987	+	0.719988i	$0.255853\pi$
$152$	1.05965e6	0.0244743
$153$	−171093.	−0.00386200
$154$	−1.21971e7	−0.269113
$155$	−6.26357e7	−1.35102
$156$	−8.48974e7	−1.79043
$157$	−5.66713e6	−0.116873	−0.0584365	−	0.998291i	$-0.518612\pi$
$157$	−5.66713e6	−0.116873	−0.0584365	+	0.998291i	$0.518612\pi$
$158$	−2.56550e7	−0.517454
$159$	3.45205e7	0.681062
$160$	−7.21387e7	−1.39235
$161$	−1.17863e8	−2.22581
$162$	8.21580e7	1.51826
$163$	2.44165e7	0.441598	0.220799	−	0.975319i	$-0.429134\pi$
$163$	2.44165e7	0.441598	0.220799	+	0.975319i	$0.429134\pi$
$164$	4.60136e7	0.814579
$165$	9.03765e6	0.156625
$166$	1.33506e8	2.26529
$167$	1.01135e7	0.168033	0.0840164	−	0.996464i	$-0.473225\pi$
$167$	1.01135e7	0.168033	0.0840164	+	0.996464i	$0.473225\pi$
$168$	4.34942e6	0.0707699
$169$	1.11598e8	1.77849
$170$	−5.09510e6	−0.0795392
$171$	−1.92058e6	−0.0293729
$172$	1.05789e7	0.158523
$173$	−4.24908e7	−0.623927	−0.311963	−	0.950094i	$-0.600987\pi$
$173$	−4.24908e7	−0.623927	−0.311963	+	0.950094i	$0.600987\pi$
$174$	5.57555e7	0.802353
$175$	−4.00055e6	−0.0564270
$176$	−1.07660e7	−0.148853
$177$	4.42270e7	0.599489
$178$	−1.23880e8	−1.64638
$179$	8.27387e7	1.07826	0.539129	−	0.842223i	$-0.318753\pi$
$179$	8.27387e7	1.07826	0.539129	+	0.842223i	$0.318753\pi$
$180$	−5.37778e6	−0.0687304
$181$	1.19734e7	0.150087	0.0750435	−	0.997180i	$-0.476090\pi$
$181$	1.19734e7	0.150087	0.0750435	+	0.997180i	$0.476090\pi$
$182$	−2.35027e8	−2.88980
$183$	27823.9	0.000335613 0
$184$	8.74116e6	0.103444
$185$	7.62085e7	0.884917
$186$	1.79176e8	2.04167
$187$	−791718.	−0.00885370
$188$	−9.78290e7	−1.07378
$189$	1.08541e8	1.16944
$190$	−5.71944e7	−0.604945
$191$	1.61956e8	1.68183	0.840914	−	0.541169i	$-0.182018\pi$
$191$	1.61956e8	1.68183	0.840914	+	0.541169i	$0.182018\pi$
$192$	1.09183e8	1.11327
$193$	−8.69257e7	−0.870357	−0.435178	−	0.900344i	$-0.643315\pi$
$193$	−8.69257e7	−0.870357	−0.435178	+	0.900344i	$0.643315\pi$
$194$	2.04562e8	2.01150
$195$	1.74147e8	1.68188
$196$	5.19048e7	0.492393
$197$	−1.25816e8	−1.17247	−0.586237	−	0.810139i	$-0.699391\pi$
$197$	−1.25816e8	−1.17247	−0.586237	+	0.810139i	$0.699391\pi$
$198$	−1.63953e6	−0.0150103
$199$	−1.43871e8	−1.29416	−0.647079	−	0.762423i	$-0.724009\pi$
$199$	−1.43871e8	−1.29416	−0.647079	+	0.762423i	$0.724009\pi$
$200$	296695.	0.00262244
$201$	1.71950e8	1.49353
$202$	1.20029e8	1.02460
$203$	7.86708e7	0.660051
$204$	7.42872e6	0.0612644
$205$	−9.43864e7	−0.765193
$206$	−2.55068e8	−2.03292
$207$	−1.58431e7	−0.124149
$208$	−2.07451e8	−1.59843
$209$	−8.88733e6	−0.0673379
$210$	−2.34759e8	−1.74926
$211$	−1.83659e8	−1.34593	−0.672966	−	0.739673i	$-0.734980\pi$
$211$	−1.83659e8	−1.34593	−0.672966	+	0.739673i	$0.734980\pi$
$212$	−9.50523e7	−0.685152
$213$	8.06042e7	0.571517
$214$	2.26896e7	0.158262
$215$	−2.17003e7	−0.148912
$216$	−8.04982e6	−0.0543498
$217$	2.52817e8	1.67957
$218$	9.86948e7	0.645203
$219$	4.99025e7	0.321046
$220$	−2.48852e7	−0.157566
$221$	−1.52557e7	−0.0950734
$222$	−2.18003e8	−1.33730
$223$	6.03715e7	0.364557	0.182278	−	0.983247i	$-0.441653\pi$
$223$	6.03715e7	0.364557	0.182278	+	0.983247i	$0.441653\pi$
$224$	2.91175e8	1.73095
$225$	−537752.	−0.00314733
$226$	1.30959e8	0.754667
$227$	5.49050e7	0.311545	0.155773	−	0.987793i	$-0.450213\pi$
$227$	5.49050e7	0.311545	0.155773	+	0.987793i	$0.450213\pi$
$228$	8.33901e7	0.465954
$229$	−1.05868e8	−0.582560	−0.291280	−	0.956638i	$-0.594081\pi$
$229$	−1.05868e8	−0.582560	−0.291280	+	0.956638i	$0.594081\pi$
$230$	−4.71803e8	−2.55690
$231$	−3.64788e7	−0.194715
$232$	−5.83451e6	−0.0306758
$233$	4.21892e7	0.218502	0.109251	−	0.994014i	$-0.465155\pi$
$233$	4.21892e7	0.218502	0.109251	+	0.994014i	$0.465155\pi$
$234$	−3.15922e7	−0.161185
$235$	2.00674e8	1.00868
$236$	−1.21779e8	−0.603089
$237$	−7.67282e7	−0.374400
$238$	2.05654e7	0.0988823
$239$	1.65597e8	0.784621	0.392310	−	0.919833i	$-0.371676\pi$
$239$	1.65597e8	0.784621	0.392310	+	0.919833i	$0.371676\pi$
$240$	−2.07214e8	−0.967564
$241$	−1.17817e8	−0.542185	−0.271093	−	0.962553i	$-0.587385\pi$
$241$	−1.17817e8	−0.542185	−0.271093	+	0.962553i	$0.587385\pi$
$242$	3.07272e8	1.39370
$243$	3.02398e7	0.135194
$244$	−76613.1	−0.000337628 0
$245$	−1.06471e8	−0.462540
$246$	2.70003e8	1.15637
$247$	−1.71251e8	−0.723092
$248$	−1.87498e7	−0.0780579
$249$	3.99287e8	1.63903
$250$	−3.60536e8	−1.45935
$251$	−1.68271e8	−0.671662	−0.335831	−	0.941922i	$-0.609017\pi$
$251$	−1.68271e8	−0.671662	−0.335831	+	0.941922i	$0.609017\pi$
$252$	2.17064e7	0.0854449
$253$	−7.33125e7	−0.284614
$254$	−6.16264e8	−2.35966
$255$	−1.52383e7	−0.0575501
$256$	2.45986e8	0.916371
$257$	4.08556e8	1.50136	0.750681	−	0.660665i	$-0.229726\pi$
$257$	4.08556e8	1.50136	0.750681	+	0.660665i	$0.229726\pi$
$258$	6.20760e7	0.225038
$259$	−3.07602e8	−1.10012
$260$	−4.79515e8	−1.69198
$261$	1.05749e7	0.0368158
$262$	−7.69813e6	−0.0264442
$263$	2.68865e8	0.911357	0.455679	−	0.890144i	$-0.349397\pi$
$263$	2.68865e8	0.911357	0.455679	+	0.890144i	$0.349397\pi$
$264$	2.70540e6	0.00904935
$265$	1.94978e8	0.643613
$266$	2.30855e8	0.752061
$267$	−3.70496e8	−1.19123
$268$	−4.73464e8	−1.50250
$269$	−4.68785e8	−1.46839	−0.734194	−	0.678939i	$-0.762440\pi$
$269$	−4.68785e8	−1.46839	−0.734194	+	0.678939i	$0.762440\pi$
$270$	4.34488e8	1.34340
$271$	7.19335e7	0.219553	0.109776	−	0.993956i	$-0.464987\pi$
$271$	7.19335e7	0.219553	0.109776	+	0.993956i	$0.464987\pi$
$272$	1.81524e7	0.0546944
$273$	−7.02914e8	−2.09090
$274$	8.12351e8	2.38570
$275$	−2.48840e6	−0.00721532
$276$	6.87894e8	1.96943
$277$	−1.86677e8	−0.527729	−0.263864	−	0.964560i	$-0.584997\pi$
$277$	−1.86677e8	−0.527729	−0.263864	+	0.964560i	$0.584997\pi$
$278$	9.42695e8	2.63157
$279$	3.39836e7	0.0936816
$280$	2.45663e7	0.0668785
$281$	4.97318e8	1.33709	0.668547	−	0.743670i	$-0.266917\pi$
$281$	4.97318e8	1.33709	0.668547	+	0.743670i	$0.266917\pi$
$282$	−5.74050e8	−1.52433
$283$	−5.31540e8	−1.39407	−0.697033	−	0.717039i	$-0.745497\pi$
$283$	−5.31540e8	−1.39407	−0.697033	+	0.717039i	$0.745497\pi$
$284$	−2.21944e8	−0.574949
$285$	−1.71056e8	−0.437704
$286$	−1.46190e8	−0.369519
$287$	3.80973e8	0.951279
$288$	3.91395e7	0.0965477
$289$	−4.09004e8	−0.996747
$290$	3.14917e8	0.758234
$291$	6.11800e8	1.45541
$292$	−1.37407e8	−0.322974
$293$	−6.12847e8	−1.42336	−0.711680	−	0.702503i	$-0.752066\pi$
$293$	−6.12847e8	−1.42336	−0.711680	+	0.702503i	$0.752066\pi$
$294$	3.04572e8	0.698995
$295$	2.49802e8	0.566525
$296$	2.28128e7	0.0511280
$297$	6.75142e7	0.149537
$298$	1.08752e9	2.38056
$299$	−1.41267e9	−3.05626
$300$	2.33487e7	0.0499274
$301$	8.75891e7	0.185126
$302$	−9.48785e8	−1.98218
$303$	3.58980e8	0.741346
$304$	2.03768e8	0.415985
$305$	157154.	0.000317159 0
$306$	2.76439e6	0.00551537
$307$	−5.15243e8	−1.01631	−0.508157	−	0.861264i	$-0.669673\pi$
$307$	−5.15243e8	−1.01631	−0.508157	+	0.861264i	$0.669673\pi$
$308$	1.00444e8	0.195884
$309$	−7.62852e8	−1.47091
$310$	1.01202e9	1.92940
$311$	6.25714e8	1.17954	0.589772	−	0.807570i	$-0.299218\pi$
$311$	6.25714e8	1.17954	0.589772	+	0.807570i	$0.299218\pi$
$312$	5.21306e7	0.0971744
$313$	−6.49995e8	−1.19813	−0.599066	−	0.800699i	$-0.704461\pi$
$313$	−6.49995e8	−1.19813	−0.599066	+	0.800699i	$0.704461\pi$
$314$	9.15652e7	0.166908
$315$	−4.45257e7	−0.0802645
$316$	2.11271e8	0.376648
$317$	7.98060e8	1.40711	0.703555	−	0.710641i	$-0.251595\pi$
$317$	7.98060e8	1.40711	0.703555	+	0.710641i	$0.251595\pi$
$318$	−5.57756e8	−0.972634
$319$	4.89343e7	0.0844008
$320$	6.16683e8	1.05205
$321$	6.78594e7	0.114510
$322$	1.90435e9	3.17870
$323$	1.49849e7	0.0247425
$324$	−6.76580e8	−1.10513
$325$	−4.79492e7	−0.0774800
$326$	−3.94504e8	−0.630652
$327$	2.95174e8	0.466832
$328$	−2.82543e7	−0.0442106
$329$	−8.09983e8	−1.25398
$330$	−1.46023e8	−0.223678
$331$	8.36375e8	1.26766	0.633831	−	0.773472i	$-0.281482\pi$
$331$	8.36375e8	1.26766	0.633831	+	0.773472i	$0.281482\pi$
$332$	−1.09944e9	−1.64887
$333$	−4.13476e7	−0.0613615
$334$	−1.63406e8	−0.239970
$335$	9.71202e8	1.41141
$336$	8.36382e8	1.20287
$337$	1.03465e9	1.47262	0.736310	−	0.676644i	$-0.236566\pi$
$337$	1.03465e9	1.47262	0.736310	+	0.676644i	$0.236566\pi$
$338$	−1.80311e9	−2.53989
$339$	3.91669e8	0.546034
$340$	4.19587e7	0.0578956
$341$	1.57256e8	0.214767
$342$	3.10313e7	0.0419478
$343$	−4.77509e8	−0.638928
$344$	−6.49592e6	−0.00860372
$345$	−1.41106e9	−1.85002
$346$	6.86534e8	0.891037
$347$	1.89330e8	0.243258	0.121629	−	0.992576i	$-0.461188\pi$
$347$	1.89330e8	0.243258	0.121629	+	0.992576i	$0.461188\pi$
$348$	−4.59153e8	−0.584023
$349$	3.29547e8	0.414981	0.207490	−	0.978237i	$-0.433470\pi$
$349$	3.29547e8	0.414981	0.207490	+	0.978237i	$0.433470\pi$
$350$	6.46379e7	0.0805841
$351$	1.30094e9	1.60577
$352$	1.81115e8	0.221337
$353$	−1.18738e9	−1.43674	−0.718371	−	0.695661i	$-0.755112\pi$
$353$	−1.18738e9	−1.43674	−0.718371	+	0.695661i	$0.755112\pi$
$354$	−7.14587e8	−0.856138
$355$	4.55267e8	0.540091
$356$	1.02016e9	1.19838
$357$	6.15066e7	0.0715456
$358$	−1.33683e9	−1.53987
$359$	−7.45557e7	−0.0850453	−0.0425226	−	0.999096i	$-0.513539\pi$
$359$	−7.45557e7	−0.0850453	−0.0425226	+	0.999096i	$0.513539\pi$
$360$	3.30218e6	0.00373029
$361$	−7.25661e8	−0.811818
$362$	−1.93458e8	−0.214341
$363$	9.18982e8	1.00840
$364$	1.93548e9	2.10345
$365$	2.81858e8	0.303393
$366$	−449557.	−0.000479293 0
$367$	−1.32724e9	−1.40158	−0.700789	−	0.713368i	$-0.747169\pi$
$367$	−1.32724e9	−1.40158	−0.700789	+	0.713368i	$0.747169\pi$
$368$	1.68090e9	1.75823
$369$	5.12102e7	0.0530596
$370$	−1.23132e9	−1.26376
$371$	−7.86992e8	−0.800132
$372$	−1.47554e9	−1.48611
$373$	1.54991e8	0.154641	0.0773207	−	0.997006i	$-0.475363\pi$
$373$	1.54991e8	0.154641	0.0773207	+	0.997006i	$0.475363\pi$
$374$	1.27920e7	0.0126441
$375$	−1.07828e9	−1.05590
$376$	6.00712e7	0.0582786
$377$	9.42921e8	0.906318
$378$	−1.75373e9	−1.67010
$379$	−1.15983e9	−1.09435	−0.547174	−	0.837019i	$-0.684296\pi$
$379$	−1.15983e9	−1.09435	−0.547174	+	0.837019i	$0.684296\pi$
$380$	4.71002e8	0.440332
$381$	−1.84311e9	−1.70731
$382$	−2.61677e9	−2.40184
$383$	−8.33044e8	−0.757656	−0.378828	−	0.925467i	$-0.623673\pi$
$383$	−8.33044e8	−0.757656	−0.378828	+	0.925467i	$0.623673\pi$
$384$	−1.29270e8	−0.116503
$385$	−2.06039e8	−0.184008
$386$	1.40448e9	1.24297
$387$	1.17737e7	0.0103258
$388$	−1.68459e9	−1.46415
$389$	−3.11695e8	−0.268477	−0.134238	−	0.990949i	$-0.542859\pi$
$389$	−3.11695e8	−0.268477	−0.134238	+	0.990949i	$0.542859\pi$
$390$	−2.81374e9	−2.40192
$391$	1.23612e8	0.104578
$392$	−3.18718e7	−0.0267242
$393$	−2.30234e7	−0.0191335
$394$	2.03284e9	1.67443
$395$	−4.33375e8	−0.353813
$396$	1.35017e7	0.0109258
$397$	−2.87056e8	−0.230250	−0.115125	−	0.993351i	$-0.536727\pi$
$397$	−2.87056e8	−0.230250	−0.115125	+	0.993351i	$0.536727\pi$
$398$	2.32456e9	1.84820
$399$	6.90435e8	0.544148
$400$	5.70537e7	0.0445732
$401$	8.00363e8	0.619843	0.309921	−	0.950762i	$-0.399697\pi$
$401$	8.00363e8	0.619843	0.309921	+	0.950762i	$0.399697\pi$
$402$	−2.77823e9	−2.13293
$403$	3.03018e9	2.30622
$404$	−9.88452e8	−0.745797
$405$	1.38785e9	1.03812
$406$	−1.27110e9	−0.942627
$407$	−1.91332e8	−0.140672
$408$	−4.56155e6	−0.00332508
$409$	−1.90519e9	−1.37691	−0.688456	−	0.725278i	$-0.741711\pi$
$409$	−1.90519e9	−1.37691	−0.688456	+	0.725278i	$0.741711\pi$
$410$	1.52502e9	1.09278
$411$	2.42956e9	1.72616
$412$	2.10052e9	1.47974
$413$	−1.00828e9	−0.704297
$414$	2.55981e8	0.177299
$415$	2.25524e9	1.54891
$416$	3.48992e9	2.37678
$417$	2.81939e9	1.90405
$418$	1.43595e8	0.0961660
$419$	1.79896e9	1.19474	0.597369	−	0.801967i	$-0.296213\pi$
$419$	1.79896e9	1.19474	0.597369	+	0.801967i	$0.296213\pi$
$420$	1.93327e9	1.27327
$421$	3.47444e7	0.0226933	0.0113467	−	0.999936i	$-0.496388\pi$
$421$	3.47444e7	0.0226933	0.0113467	+	0.999936i	$0.496388\pi$
$422$	2.96742e9	1.92214
$423$	−1.08877e8	−0.0699433
$424$	5.83661e7	0.0371861
$425$	4.19567e6	0.00265118
$426$	−1.30234e9	−0.816191
$427$	−634324.	−0.000394288 0
$428$	−1.86851e8	−0.115197
$429$	−4.37222e8	−0.267363
$430$	3.50616e8	0.212663
$431$	1.91702e9	1.15334	0.576669	−	0.816978i	$-0.304352\pi$
$431$	1.91702e9	1.15334	0.576669	+	0.816978i	$0.304352\pi$
$432$	−1.54796e9	−0.923775
$433$	−7.40677e8	−0.438451	−0.219226	−	0.975674i	$-0.570353\pi$
$433$	−7.40677e8	−0.438451	−0.219226	+	0.975674i	$0.570353\pi$
$434$	−4.08483e9	−2.39861
$435$	9.41846e8	0.548615
$436$	−8.12763e8	−0.469636
$437$	1.38759e9	0.795381
$438$	−8.06287e8	−0.458490
$439$	2.96692e9	1.67371	0.836856	−	0.547423i	$-0.184391\pi$
$439$	2.96692e9	1.67371	0.836856	+	0.547423i	$0.184391\pi$
$440$	1.52806e7	0.00855175
$441$	5.77667e7	0.0320732
$442$	2.46490e8	0.135776
$443$	1.34329e9	0.734102	0.367051	−	0.930201i	$-0.380367\pi$
$443$	1.34329e9	0.734102	0.367051	+	0.930201i	$0.380367\pi$
$444$	1.79528e9	0.973401
$445$	−2.09263e9	−1.12572
$446$	−9.75438e8	−0.520628
$447$	3.25252e9	1.72244
$448$	−2.48913e9	−1.30790
$449$	−3.37789e9	−1.76110	−0.880549	−	0.473954i	$-0.842826\pi$
$449$	−3.37789e9	−1.76110	−0.880549	+	0.473954i	$0.842826\pi$
$450$	8.68859e6	0.00449475
$451$	2.36971e8	0.121640
$452$	−1.07846e9	−0.549313
$453$	−2.83760e9	−1.43419
$454$	−8.87114e8	−0.444922
$455$	−3.97018e9	−1.97593
$456$	−5.12051e7	−0.0252893
$457$	2.50731e7	0.0122886	0.00614429	−	0.999981i	$-0.498044\pi$
$457$	2.50731e7	0.0122886	0.00614429	+	0.999981i	$0.498044\pi$
$458$	1.71054e9	0.831961
$459$	−1.13835e8	−0.0549455
$460$	3.88535e9	1.86113
$461$	−7.94770e8	−0.377823	−0.188911	−	0.981994i	$-0.560496\pi$
$461$	−7.94770e8	−0.377823	−0.188911	+	0.981994i	$0.560496\pi$
$462$	5.89397e8	0.278074
$463$	−3.63682e9	−1.70290	−0.851449	−	0.524438i	$-0.824276\pi$
$463$	−3.63682e9	−1.70290	−0.851449	+	0.524438i	$0.824276\pi$
$464$	−1.12196e9	−0.521392
$465$	3.02673e9	1.39601
$466$	−6.81662e8	−0.312046
$467$	−2.11944e8	−0.0962967	−0.0481483	−	0.998840i	$-0.515332\pi$
$467$	−2.11944e8	−0.0962967	−0.0481483	+	0.998840i	$0.515332\pi$
$468$	2.60165e8	0.117325
$469$	−3.92008e9	−1.75465
$470$	−3.24233e9	−1.44051
$471$	2.73851e8	0.120765
$472$	7.47777e7	0.0327322
$473$	5.44816e7	0.0236721
$474$	1.23972e9	0.534686
$475$	4.70979e7	0.0201639
$476$	−1.69359e8	−0.0719752
$477$	−1.05787e8	−0.0446291
$478$	−2.67559e9	−1.12053
$479$	2.49114e9	1.03568	0.517838	−	0.855479i	$-0.326737\pi$
$479$	2.49114e9	1.03568	0.517838	+	0.855479i	$0.326737\pi$
$480$	3.48594e9	1.43872
$481$	−3.68681e9	−1.51058
$482$	1.90360e9	0.774302
$483$	5.69547e9	2.29993
$484$	−2.53042e9	−1.01446
$485$	3.45556e9	1.37538
$486$	−4.88592e8	−0.193072
$487$	−6.93003e8	−0.271884	−0.135942	−	0.990717i	$-0.543406\pi$
$487$	−6.93003e8	−0.271884	−0.135942	+	0.990717i	$0.543406\pi$
$488$	47043.7	1.83245e−5 0
$489$	−1.17987e9	−0.456304
$490$	1.72027e9	0.660559
$491$	−2.43700e9	−0.929118	−0.464559	−	0.885542i	$-0.653787\pi$
$491$	−2.43700e9	−0.929118	−0.464559	+	0.885542i	$0.653787\pi$
$492$	−2.22350e9	−0.841705
$493$	−8.25078e7	−0.0310121
$494$	2.76694e9	1.03266
$495$	−2.76956e7	−0.0102634
$496$	−3.60555e9	−1.32674
$497$	−1.83760e9	−0.671435
$498$	−6.45138e9	−2.34072
$499$	−3.89667e9	−1.40392	−0.701959	−	0.712217i	$-0.747691\pi$
$499$	−3.89667e9	−1.40392	−0.701959	+	0.712217i	$0.747691\pi$
$500$	2.96905e9	1.06224
$501$	−4.88712e8	−0.173628
$502$	2.71879e9	0.959209
$503$	4.29376e9	1.50435	0.752176	−	0.658962i	$-0.229004\pi$
$503$	4.29376e9	1.50435	0.752176	+	0.658962i	$0.229004\pi$
$504$	−1.33287e7	−0.00463745
$505$	2.02758e9	0.700581
$506$	1.18453e9	0.406461
$507$	−5.39270e9	−1.83772
$508$	5.07500e9	1.71756
$509$	3.04510e9	1.02350	0.511751	−	0.859134i	$-0.328997\pi$
$509$	3.04510e9	1.02350	0.511751	+	0.859134i	$0.328997\pi$
$510$	2.46209e8	0.0821880
$511$	−1.13767e9	−0.377175
$512$	−4.31688e9	−1.42143
$513$	−1.27784e9	−0.417894
$514$	−6.60114e9	−2.14411
$515$	−4.30872e9	−1.39003
$516$	−5.11203e8	−0.163802
$517$	−5.03820e8	−0.160346
$518$	4.97000e9	1.57109
$519$	2.05327e9	0.644704
$520$	2.94443e8	0.0918310
$521$	6.13864e9	1.90169	0.950846	−	0.309665i	$-0.100217\pi$
$521$	6.13864e9	1.90169	0.950846	+	0.309665i	$0.100217\pi$
$522$	−1.70861e8	−0.0525770
$523$	−5.32103e9	−1.62645	−0.813223	−	0.581953i	$-0.802289\pi$
$523$	−5.32103e9	−1.62645	−0.813223	+	0.581953i	$0.802289\pi$
$524$	6.33949e7	0.0192484
$525$	1.93317e8	0.0583060
$526$	−4.34411e9	−1.30152
$527$	−2.65148e8	−0.0789134
$528$	5.20241e8	0.153810
$529$	8.04153e9	2.36180
$530$	−3.15030e9	−0.919151
$531$	−1.35532e8	−0.0392837
$532$	−1.90111e9	−0.547416
$533$	4.56621e9	1.30620
$534$	5.98620e9	1.70121
$535$	3.83282e8	0.108213
$536$	2.90727e8	0.0815471
$537$	−3.99816e9	−1.11417
$538$	7.57428e9	2.09702
$539$	2.67310e8	0.0735284
$540$	−3.57805e9	−0.977842
$541$	2.71071e9	0.736026	0.368013	−	0.929821i	$-0.380038\pi$
$541$	2.71071e9	0.736026	0.368013	+	0.929821i	$0.380038\pi$
$542$	−1.16225e9	−0.313546
$543$	−5.78588e8	−0.155085
$544$	−3.05376e8	−0.0813277
$545$	1.66720e9	0.441163
$546$	1.13572e10	2.98604
$547$	−2.01310e9	−0.525908	−0.262954	−	0.964808i	$-0.584697\pi$
$547$	−2.01310e9	−0.525908	−0.262954	+	0.964808i	$0.584697\pi$
$548$	−6.68980e9	−1.73652
$549$	−85265.4	−2.19923e−5 0
$550$	4.02057e7	0.0103043
$551$	−9.26181e8	−0.235866
$552$	−4.22396e8	−0.106889
$553$	1.74924e9	0.439856
$554$	3.01618e9	0.753656
$555$	−3.68260e9	−0.914385
$556$	−7.76319e9	−1.91548
$557$	1.55537e9	0.381364	0.190682	−	0.981652i	$-0.438930\pi$
$557$	1.55537e9	0.381364	0.190682	+	0.981652i	$0.438930\pi$
$558$	−5.49081e8	−0.133788
$559$	1.04981e9	0.254197
$560$	4.72403e9	1.13672
$561$	3.82579e7	0.00914854
$562$	−8.03529e9	−1.90952
$563$	−5.00376e9	−1.18173	−0.590863	−	0.806772i	$-0.701213\pi$
$563$	−5.00376e9	−1.18173	−0.590863	+	0.806772i	$0.701213\pi$
$564$	4.72736e9	1.10954
$565$	2.21221e9	0.516009
$566$	8.58822e9	1.99088
$567$	−5.60179e9	−1.29058
$568$	1.36283e8	0.0312049
$569$	−4.14184e9	−0.942542	−0.471271	−	0.881988i	$-0.656205\pi$
$569$	−4.14184e9	−0.942542	−0.471271	+	0.881988i	$0.656205\pi$
$570$	2.76379e9	0.625090
$571$	7.78342e9	1.74962	0.874810	−	0.484465i	$-0.160986\pi$
$571$	7.78342e9	1.74962	0.874810	+	0.484465i	$0.160986\pi$
$572$	1.20389e9	0.268969
$573$	−7.82617e9	−1.73783
$574$	−6.15548e9	−1.35853
$575$	3.88516e8	0.0852259
$576$	−3.34587e8	−0.0729508
$577$	−2.29128e9	−0.496551	−0.248275	−	0.968690i	$-0.579864\pi$
$577$	−2.29128e9	−0.496551	−0.248275	+	0.968690i	$0.579864\pi$
$578$	6.60838e9	1.42347
$579$	4.20048e9	0.899341
$580$	−2.59338e9	−0.551909
$581$	−9.10288e9	−1.92558
$582$	−9.88501e9	−2.07848
$583$	−4.89520e8	−0.102313
$584$	8.43735e7	0.0175292
$585$	−5.33669e8	−0.110211
$586$	9.90191e9	2.03272
$587$	4.43578e9	0.905184	0.452592	−	0.891718i	$-0.350499\pi$
$587$	4.43578e9	0.905184	0.452592	+	0.891718i	$0.350499\pi$
$588$	−2.50818e9	−0.508790
$589$	−2.97638e9	−0.600186
$590$	−4.03611e9	−0.809061
$591$	6.07976e9	1.21152
$592$	4.38685e9	0.869014
$593$	6.57596e9	1.29499	0.647496	−	0.762068i	$-0.275816\pi$
$593$	6.57596e9	1.29499	0.647496	+	0.762068i	$0.275816\pi$
$594$	−1.09084e9	−0.213555
$595$	3.47400e8	0.0676115
$596$	−8.95581e9	−1.73278
$597$	6.95223e9	1.33725
$598$	2.28248e10	4.36469
$599$	−9.99449e9	−1.90006	−0.950029	−	0.312162i	$-0.898947\pi$
$599$	−9.99449e9	−1.90006	−0.950029	+	0.312162i	$0.898947\pi$
$600$	−1.43371e7	−0.00270977
$601$	−8.94449e8	−0.168072	−0.0840359	−	0.996463i	$-0.526781\pi$
$601$	−8.94449e8	−0.168072	−0.0840359	+	0.996463i	$0.526781\pi$
$602$	−1.41520e9	−0.264381
$603$	−5.26934e8	−0.0978691
$604$	7.81335e9	1.44281
$605$	5.19057e9	0.952953
$606$	−5.80012e9	−1.05872
$607$	−6.24872e9	−1.13405	−0.567023	−	0.823702i	$-0.691905\pi$
$607$	−6.24872e9	−1.13405	−0.567023	+	0.823702i	$0.691905\pi$
$608$	−3.42796e9	−0.618548
$609$	−3.80159e9	−0.682032
$610$	−2.53918e6	−0.000452938 0
$611$	−9.70817e9	−1.72184
$612$	−2.27651e7	−0.00401457
$613$	4.93146e9	0.864696	0.432348	−	0.901707i	$-0.357685\pi$
$613$	4.93146e9	0.864696	0.432348	+	0.901707i	$0.357685\pi$
$614$	8.32491e9	1.45141
$615$	4.56100e9	0.790674
$616$	−6.16772e7	−0.0106314
$617$	−7.71513e9	−1.32235	−0.661173	−	0.750234i	$-0.729941\pi$
$617$	−7.71513e9	−1.32235	−0.661173	+	0.750234i	$0.729941\pi$
$618$	1.23256e10	2.10062
$619$	1.04934e10	1.77827	0.889137	−	0.457641i	$-0.151305\pi$
$619$	1.04934e10	1.77827	0.889137	+	0.457641i	$0.151305\pi$
$620$	−8.33410e9	−1.40439
$621$	−1.05411e10	−1.76630
$622$	−1.01098e10	−1.68452
$623$	8.44651e9	1.39949
$624$	1.00246e10	1.65166
$625$	−5.80662e9	−0.951357
$626$	1.05021e10	1.71107
$627$	4.29460e8	0.0695803
$628$	−7.54049e8	−0.121490
$629$	3.22604e8	0.0516883
$630$	7.19412e8	0.114627
$631$	5.59798e9	0.887010	0.443505	−	0.896272i	$-0.353735\pi$
$631$	5.59798e9	0.887010	0.443505	+	0.896272i	$0.353735\pi$
$632$	−1.29730e8	−0.0204423
$633$	8.87489e9	1.39075
$634$	−1.28945e10	−2.00951
$635$	−1.04102e10	−1.61343
$636$	4.59318e9	0.707968
$637$	5.15083e9	0.789567
$638$	−7.90644e8	−0.120534
$639$	−2.47009e8	−0.0374507
$640$	−7.30139e8	−0.110097
$641$	1.08513e10	1.62734	0.813670	−	0.581327i	$-0.197466\pi$
$641$	1.08513e10	1.62734	0.813670	+	0.581327i	$0.197466\pi$
$642$	−1.09642e9	−0.163533
$643$	−4.25867e9	−0.631736	−0.315868	−	0.948803i	$-0.602296\pi$
$643$	−4.25867e9	−0.631736	−0.315868	+	0.948803i	$0.602296\pi$
$644$	−1.56825e10	−2.31374
$645$	1.04861e9	0.153871
$646$	−2.42114e8	−0.0353351
$647$	3.03007e9	0.439833	0.219917	−	0.975519i	$-0.429421\pi$
$647$	3.03007e9	0.439833	0.219917	+	0.975519i	$0.429421\pi$
$648$	4.15449e8	0.0599798
$649$	−6.27164e8	−0.0900585
$650$	7.74727e8	0.110650
$651$	−1.22168e10	−1.73550
$652$	3.24878e9	0.459044
$653$	−3.93756e9	−0.553389	−0.276695	−	0.960958i	$-0.589239\pi$
$653$	−3.93756e9	−0.553389	−0.276695	+	0.960958i	$0.589239\pi$
$654$	−4.76920e9	−0.666689
$655$	−1.30040e8	−0.0180814
$656$	−5.43323e9	−0.751441
$657$	−1.52925e8	−0.0210377
$658$	1.30871e10	1.79082
$659$	9.30694e7	0.0126680	0.00633400	−	0.999980i	$-0.497984\pi$
$659$	9.30694e7	0.0126680	0.00633400	+	0.999980i	$0.497984\pi$
$660$	1.20252e9	0.162813
$661$	1.17439e10	1.58164	0.790818	−	0.612051i	$-0.209655\pi$
$661$	1.17439e10	1.58164	0.790818	+	0.612051i	$0.209655\pi$
$662$	−1.35135e10	−1.81036
$663$	7.37196e8	0.0982394
$664$	6.75102e8	0.0894914
$665$	3.89970e9	0.514227
$666$	6.68064e8	0.0876311
$667$	−7.64016e9	−0.996925
$668$	1.34567e9	0.174671
$669$	−2.91731e9	−0.376697
$670$	−1.56919e10	−2.01565
$671$	−394558.	−5.04176e−5 0
$672$	−1.40704e10	−1.78860
$673$	1.30594e9	0.165146	0.0825732	−	0.996585i	$-0.473686\pi$
$673$	1.30594e9	0.165146	0.0825732	+	0.996585i	$0.473686\pi$
$674$	−1.67172e10	−2.10307
$675$	−3.57788e8	−0.0447778
$676$	1.48488e10	1.84875
$677$	1.71912e9	0.212935	0.106467	−	0.994316i	$-0.466046\pi$
$677$	1.71912e9	0.212935	0.106467	+	0.994316i	$0.466046\pi$
$678$	−6.32829e9	−0.779798
$679$	−1.39477e10	−1.70985
$680$	−2.57644e7	−0.00314224
$681$	−2.65316e9	−0.321920
$682$	−2.54082e9	−0.306711
$683$	−4.52474e9	−0.543402	−0.271701	−	0.962382i	$-0.587586\pi$
$683$	−4.52474e9	−0.543402	−0.271701	+	0.962382i	$0.587586\pi$
$684$	−2.55546e8	−0.0305333
$685$	1.37226e10	1.63124
$686$	7.71523e9	0.912461
$687$	5.11583e9	0.601960
$688$	−1.24915e9	−0.146236
$689$	−9.43261e9	−1.09866
$690$	2.27988e10	2.64204
$691$	1.43457e10	1.65405	0.827025	−	0.562165i	$-0.190031\pi$
$691$	1.43457e10	1.65405	0.827025	+	0.562165i	$0.190031\pi$
$692$	−5.65368e9	−0.648575
$693$	1.11788e8	0.0127594
$694$	−3.05905e9	−0.347399
$695$	1.59244e10	1.79935
$696$	2.81939e8	0.0316974
$697$	−3.99554e8	−0.0446952
$698$	−5.32457e9	−0.592639
$699$	−2.03870e9	−0.225779
$700$	−5.32300e8	−0.0586561
$701$	1.24050e7	0.00136014	0.000680069	−	1.00000i	$-0.499784\pi$
$701$	1.24050e7	0.00136014	0.000680069		1.00000i	$0.499784\pi$
$702$	−2.10196e10	−2.29321
$703$	3.62135e9	0.393122
$704$	−1.54827e9	−0.167241
$705$	−9.69709e9	−1.04227
$706$	1.91848e10	2.05183
$707$	−8.18396e9	−0.870954
$708$	5.88470e9	0.623172
$709$	−1.13921e8	−0.0120044	−0.00600220	−	0.999982i	$-0.501911\pi$
$709$	−1.13921e8	−0.0120044	−0.00600220	+	0.999982i	$0.501911\pi$
$710$	−7.35586e9	−0.771311
$711$	2.35131e8	0.0245339
$712$	−6.26424e8	−0.0650412
$713$	−2.45525e10	−2.53678
$714$	−9.93777e8	−0.102175
$715$	−2.46951e9	−0.252662
$716$	1.10089e10	1.12086
$717$	−8.00210e9	−0.810750
$718$	1.20461e9	0.121454
$719$	−6.47748e8	−0.0649912	−0.0324956	−	0.999472i	$-0.510345\pi$
$719$	−6.47748e8	−0.0649912	−0.0324956	+	0.999472i	$0.510345\pi$
$720$	6.35001e8	0.0634031
$721$	1.73914e10	1.72807
$722$	1.17247e10	1.15937
$723$	5.69323e9	0.560241
$724$	1.59314e9	0.156016
$725$	−2.59325e8	−0.0252733
$726$	−1.48482e10	−1.44011
$727$	−5.68079e9	−0.548325	−0.274163	−	0.961683i	$-0.588401\pi$
$727$	−5.68079e9	−0.548325	−0.274163	+	0.961683i	$0.588401\pi$
$728$	−1.18846e9	−0.114163
$729$	9.65941e9	0.923430
$730$	−4.55405e9	−0.433279
$731$	−9.18610e7	−0.00869802
$732$	3.70215e6	0.000348872 0
$733$	−1.04141e10	−0.976697	−0.488348	−	0.872649i	$-0.662400\pi$
$733$	−1.04141e10	−0.976697	−0.488348	+	0.872649i	$0.662400\pi$
$734$	2.14445e10	2.00161
$735$	5.14495e9	0.477943
$736$	−2.82776e10	−2.61439
$737$	−2.43834e9	−0.224367
$738$	−8.27416e8	−0.0757751
$739$	7.74337e9	0.705788	0.352894	−	0.935663i	$-0.385198\pi$
$739$	7.74337e9	0.705788	0.352894	+	0.935663i	$0.385198\pi$
$740$	1.01401e10	0.919876
$741$	8.27531e9	0.747172
$742$	1.27156e10	1.14268
$743$	−5.39810e9	−0.482815	−0.241407	−	0.970424i	$-0.577609\pi$
$743$	−5.39810e9	−0.482815	−0.241407	+	0.970424i	$0.577609\pi$
$744$	9.06043e8	0.0806573
$745$	1.83708e10	1.62772
$746$	−2.50423e9	−0.220845
$747$	−1.22360e9	−0.107403
$748$	−1.05343e8	−0.00920347
$749$	−1.54705e9	−0.134529
$750$	1.74221e10	1.50794
$751$	−1.23730e10	−1.06595	−0.532973	−	0.846132i	$-0.678925\pi$
$751$	−1.23730e10	−1.06595	−0.532973	+	0.846132i	$0.678925\pi$
$752$	1.15515e10	0.990552
$753$	8.13130e9	0.694029
$754$	−1.52350e10	−1.29432
$755$	−1.60273e10	−1.35533
$756$	1.44422e10	1.21564
$757$	2.74811e9	0.230249	0.115125	−	0.993351i	$-0.463273\pi$
$757$	2.74811e9	0.230249	0.115125	+	0.993351i	$0.463273\pi$
$758$	1.87396e10	1.56285
$759$	3.54266e9	0.294092
$760$	−2.89215e8	−0.0238987
$761$	−6.98646e9	−0.574660	−0.287330	−	0.957832i	$-0.592768\pi$
$761$	−6.98646e9	−0.574660	−0.287330	+	0.957832i	$0.592768\pi$
$762$	2.97795e10	2.43824
$763$	−6.72933e9	−0.548448
$764$	2.15494e10	1.74827
$765$	4.66973e7	0.00377117
$766$	1.34597e10	1.08202
$767$	−1.20849e10	−0.967072
$768$	−1.18867e10	−0.946887
$769$	1.64020e10	1.30064	0.650318	−	0.759662i	$-0.274636\pi$
$769$	1.64020e10	1.30064	0.650318	+	0.759662i	$0.274636\pi$
$770$	3.32902e9	0.262784
$771$	−1.97425e10	−1.55136
$772$	−1.15660e10	−0.904741
$773$	−6.42318e9	−0.500175	−0.250087	−	0.968223i	$-0.580459\pi$
$773$	−6.42318e9	−0.500175	−0.250087	+	0.968223i	$0.580459\pi$
$774$	−1.90230e8	−0.0147464
$775$	−8.33370e8	−0.0643105
$776$	1.03441e9	0.0794654
$777$	1.48641e10	1.13675
$778$	5.03613e9	0.383415
$779$	−4.48515e9	−0.339935
$780$	2.31715e10	1.74833
$781$	−1.14301e9	−0.0858564
$782$	−1.99722e9	−0.149349
$783$	7.03590e9	0.523786
$784$	−6.12886e9	−0.454227
$785$	1.54676e9	0.114124
$786$	3.71994e8	0.0273248
$787$	8.36518e9	0.611735	0.305868	−	0.952074i	$-0.401053\pi$
$787$	8.36518e9	0.611735	0.305868	+	0.952074i	$0.401053\pi$
$788$	−1.67406e10	−1.21879
$789$	−1.29923e10	−0.941706
$790$	7.00214e9	0.505285
$791$	−8.92919e9	−0.641497
$792$	−8.29061e6	−0.000592991 0
$793$	−7.60279e6	−0.000541398 0
$794$	4.63804e9	0.328823
$795$	−9.42185e9	−0.665046
$796$	−1.91430e10	−1.34528
$797$	1.20395e10	0.842376	0.421188	−	0.906973i	$-0.361613\pi$
$797$	1.20395e10	0.842376	0.421188	+	0.906973i	$0.361613\pi$
$798$	−1.11555e10	−0.777105
$799$	8.49487e8	0.0589173
$800$	−9.59808e8	−0.0662780
$801$	1.13537e9	0.0780595
$802$	−1.29317e10	−0.885206
$803$	−7.07645e8	−0.0482293
$804$	2.28790e10	1.55254
$805$	3.21690e10	2.17346
$806$	−4.89594e10	−3.29354
$807$	2.26530e10	1.51729
$808$	6.06952e8	0.0404776
$809$	−2.68334e10	−1.78178	−0.890892	−	0.454215i	$-0.849920\pi$
$809$	−2.68334e10	−1.78178	−0.890892	+	0.454215i	$0.849920\pi$
$810$	−2.24238e10	−1.48256
$811$	7.68247e9	0.505741	0.252870	−	0.967500i	$-0.418625\pi$
$811$	7.68247e9	0.505741	0.252870	+	0.967500i	$0.418625\pi$
$812$	1.04677e10	0.686127
$813$	−3.47602e9	−0.226864
$814$	3.09141e9	0.200896
$815$	−6.66412e9	−0.431213
$816$	−8.77173e8	−0.0565158
$817$	−1.03117e9	−0.0661538
$818$	3.07826e10	1.96639
$819$	2.15406e9	0.137014
$820$	−1.25587e10	−0.795422
$821$	1.61885e10	1.02096	0.510478	−	0.859891i	$-0.329469\pi$
$821$	1.61885e10	1.02096	0.510478	+	0.859891i	$0.329469\pi$
$822$	−3.92550e10	−2.46515
$823$	2.11454e10	1.32226	0.661131	−	0.750271i	$-0.270077\pi$
$823$	2.11454e10	1.32226	0.661131	+	0.750271i	$0.270077\pi$
$824$	−1.28981e9	−0.0803118
$825$	1.20246e8	0.00745559
$826$	1.62910e10	1.00582
$827$	2.52181e10	1.55040	0.775198	−	0.631718i	$-0.217650\pi$
$827$	2.52181e10	1.55040	0.775198	+	0.631718i	$0.217650\pi$
$828$	−2.10803e9	−0.129054
$829$	1.48168e10	0.903260	0.451630	−	0.892205i	$-0.350843\pi$
$829$	1.48168e10	0.903260	0.451630	+	0.892205i	$0.350843\pi$
$830$	−3.64385e10	−2.21201
$831$	9.02072e9	0.545303
$832$	−2.98338e10	−1.79588
$833$	−4.50709e8	−0.0270171
$834$	−4.55536e10	−2.71920
$835$	−2.76033e9	−0.164081
$836$	−1.18252e9	−0.0699981
$837$	2.26106e10	1.33283
$838$	−2.90662e10	−1.70622
$839$	−1.45298e10	−0.849361	−0.424680	−	0.905343i	$-0.639614\pi$
$839$	−1.45298e10	−0.849361	−0.424680	+	0.905343i	$0.639614\pi$
$840$	−1.18711e9	−0.0691056
$841$	−1.21503e10	−0.704367
$842$	−5.61375e8	−0.0324086
$843$	−2.40317e10	−1.38162
$844$	−2.44370e10	−1.39910
$845$	−3.04589e10	−1.73667
$846$	1.75916e9	0.0998869
$847$	−2.09508e10	−1.18470
$848$	1.12237e10	0.632046
$849$	2.56854e10	1.44049
$850$	−6.77904e7	−0.00378619
$851$	2.98729e10	1.66159
$852$	1.07249e10	0.594095
$853$	−1.93358e10	−1.06669	−0.533347	−	0.845896i	$-0.679066\pi$
$853$	−1.93358e10	−1.06669	−0.533347	+	0.845896i	$0.679066\pi$
$854$	1.02489e7	0.000563088 0
$855$	5.24195e8	0.0286821
$856$	1.14735e8	0.00625224
$857$	3.62840e9	0.196916	0.0984582	−	0.995141i	$-0.468609\pi$
$857$	3.62840e9	0.196916	0.0984582	+	0.995141i	$0.468609\pi$
$858$	7.06431e9	0.381825
$859$	5.66924e9	0.305175	0.152588	−	0.988290i	$-0.451239\pi$
$859$	5.66924e9	0.305175	0.152588	+	0.988290i	$0.451239\pi$
$860$	−2.88736e9	−0.154795
$861$	−1.84097e10	−0.982957
$862$	−3.09738e10	−1.64710
$863$	−7.37525e9	−0.390606	−0.195303	−	0.980743i	$-0.562569\pi$
$863$	−7.37525e9	−0.390606	−0.195303	+	0.980743i	$0.562569\pi$
$864$	2.60411e10	1.37360
$865$	1.15972e10	0.609253
$866$	1.19673e10	0.626158
$867$	1.97642e10	1.02994
$868$	3.36391e10	1.74592
$869$	1.08805e9	0.0562444
$870$	−1.52176e10	−0.783483
$871$	−4.69847e10	−2.40931
$872$	4.99071e8	0.0254891
$873$	−1.87484e9	−0.0953707
$874$	−2.24196e10	−1.13589
$875$	2.45825e10	1.24050
$876$	6.63986e9	0.333729
$877$	−1.97900e10	−0.990711	−0.495355	−	0.868690i	$-0.664962\pi$
$877$	−1.97900e10	−0.990711	−0.495355	+	0.868690i	$0.664962\pi$
$878$	−4.79373e10	−2.39025
$879$	2.96144e10	1.47076
$880$	2.93841e9	0.145353
$881$	5.73994e9	0.282808	0.141404	−	0.989952i	$-0.454838\pi$
$881$	5.73994e9	0.282808	0.141404	+	0.989952i	$0.454838\pi$
$882$	−9.33350e8	−0.0458041
$883$	−3.59778e9	−0.175862	−0.0879311	−	0.996127i	$-0.528026\pi$
$883$	−3.59778e9	−0.175862	−0.0879311	+	0.996127i	$0.528026\pi$
$884$	−2.02987e9	−0.0988293
$885$	−1.20711e10	−0.585391
$886$	−2.17039e10	−1.04838
$887$	−2.01902e9	−0.0971422	−0.0485711	−	0.998820i	$-0.515467\pi$
$887$	−2.01902e9	−0.0971422	−0.0485711	+	0.998820i	$0.515467\pi$
$888$	−1.10238e9	−0.0528306
$889$	4.20188e10	2.00580
$890$	3.38111e10	1.60766
$891$	−3.48439e9	−0.165027
$892$	8.03284e9	0.378959
$893$	9.53581e9	0.448103
$894$	−5.25517e10	−2.45983
$895$	−2.25823e10	−1.05290
$896$	2.94707e9	0.136871
$897$	6.82639e10	3.15804
$898$	5.45775e10	2.51505
$899$	1.63882e10	0.752268
$900$	−7.15514e7	−0.00327167
$901$	8.25375e8	0.0375937
$902$	−3.82879e9	−0.173716
$903$	−4.23254e9	−0.191291
$904$	6.62221e8	0.0298135
$905$	−3.26797e9	−0.146557
$906$	4.58479e10	2.04819
$907$	9.54457e9	0.424748	0.212374	−	0.977188i	$-0.431881\pi$
$907$	9.54457e9	0.424748	0.212374	+	0.977188i	$0.431881\pi$
$908$	7.30548e9	0.323853
$909$	−1.10008e9	−0.0485793
$910$	6.41472e10	2.82184
$911$	1.73423e10	0.759964	0.379982	−	0.924994i	$-0.375930\pi$
$911$	1.73423e10	0.759964	0.379982	+	0.924994i	$0.375930\pi$
$912$	−9.84660e9	−0.429838
$913$	−5.66212e9	−0.246224
$914$	−4.05113e8	−0.0175495
$915$	−7.59411e6	−0.000327720 0
$916$	−1.40864e10	−0.605574
$917$	5.24883e8	0.0224786
$918$	1.83926e9	0.0784683
$919$	1.56927e8	0.00666949	0.00333475	−	0.999994i	$-0.498939\pi$
$919$	1.56927e8	0.00666949	0.00333475	+	0.999994i	$0.498939\pi$
$920$	−2.38577e9	−0.101012
$921$	2.48979e10	1.05016
$922$	1.28413e10	0.539574
$923$	−2.20249e10	−0.921949
$924$	−4.85375e9	−0.202407
$925$	1.01396e9	0.0421234
$926$	5.87610e10	2.43193
$927$	2.33774e9	0.0963866
$928$	1.88746e10	0.775283
$929$	−9.87406e9	−0.404055	−0.202028	−	0.979380i	$-0.564753\pi$
$929$	−9.87406e9	−0.404055	−0.202028	+	0.979380i	$0.564753\pi$
$930$	−4.89036e10	−1.99366
$931$	−5.05938e9	−0.205482
$932$	5.61356e9	0.227134
$933$	−3.02362e10	−1.21882
$934$	3.42443e9	0.137522
$935$	2.16088e8	0.00864548
$936$	−1.59753e8	−0.00636770
$937$	−1.57119e10	−0.623935	−0.311968	−	0.950093i	$-0.600988\pi$
$937$	−1.57119e10	−0.623935	−0.311968	+	0.950093i	$0.600988\pi$
$938$	6.33377e10	2.50583
$939$	3.14095e10	1.23803
$940$	2.67010e10	1.04853
$941$	9.28175e9	0.363133	0.181567	−	0.983379i	$-0.441883\pi$
$941$	9.28175e9	0.363133	0.181567	+	0.983379i	$0.441883\pi$
$942$	−4.42468e9	−0.172466
$943$	−3.69984e10	−1.43679
$944$	1.43795e10	0.556344
$945$	−2.96248e10	−1.14194
$946$	−8.80273e8	−0.0338064
$947$	−3.17945e10	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$947$	−3.17945e10	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$948$	−1.02092e10	−0.389191
$949$	−1.36357e10	−0.517899
$950$	−7.60973e8	−0.0287963
$951$	−3.85644e10	−1.45397
$952$	1.03993e8	0.00390640
$953$	−1.99879e10	−0.748070	−0.374035	−	0.927415i	$-0.622026\pi$
$953$	−1.99879e10	−0.748070	−0.374035	+	0.927415i	$0.622026\pi$
$954$	1.70923e9	0.0637353
$955$	−4.42036e10	−1.64228
$956$	2.20338e10	0.815618
$957$	−2.36464e9	−0.0872114
$958$	−4.02500e10	−1.47906
$959$	−5.53887e10	−2.02794
$960$	−2.97998e10	−1.08709
$961$	2.51527e10	0.914225
$962$	5.95687e10	2.15727
$963$	−2.07953e8	−0.00750366
$964$	−1.56763e10	−0.563605
$965$	2.37251e10	0.849888
$966$	−9.20231e10	−3.28456
$967$	5.44278e10	1.93566	0.967828	−	0.251611i	$-0.0809604\pi$
$967$	5.44278e10	1.93566	0.967828	+	0.251611i	$0.0809604\pi$
$968$	1.55379e9	0.0550589
$969$	−7.24108e8	−0.0255664
$970$	−5.58323e10	−1.96419
$971$	2.25661e10	0.791024	0.395512	−	0.918461i	$-0.370567\pi$
$971$	2.25661e10	0.791024	0.395512	+	0.918461i	$0.370567\pi$
$972$	4.02360e9	0.140535
$973$	−6.42759e10	−2.23693
$974$	1.11970e10	0.388281
$975$	2.31704e9	0.0800602
$976$	9.04638e6	0.000311459 0
$977$	−4.26254e9	−0.146230	−0.0731152	−	0.997324i	$-0.523294\pi$
$977$	−4.26254e9	−0.146230	−0.0731152	+	0.997324i	$0.523294\pi$
$978$	1.90635e10	0.651653
$979$	5.25385e9	0.178953
$980$	−1.41666e10	−0.480813
$981$	−9.04552e8	−0.0305909
$982$	3.93753e10	1.32688
$983$	−1.23804e10	−0.415717	−0.207858	−	0.978159i	$-0.566649\pi$
$983$	−1.23804e10	−0.415717	−0.207858	+	0.978159i	$0.566649\pi$
$984$	1.36533e9	0.0456829
$985$	3.43396e10	1.14490
$986$	1.33310e9	0.0442887
$987$	3.91405e10	1.29574
$988$	−2.27861e10	−0.751658
$989$	−8.50627e9	−0.279610
$990$	4.47484e8	0.0146573
$991$	3.54785e10	1.15800	0.578998	−	0.815329i	$-0.303444\pi$
$991$	3.54785e10	1.15800	0.578998	+	0.815329i	$0.303444\pi$
$992$	6.06557e10	1.97279
$993$	−4.04159e10	−1.30988
$994$	2.96906e10	0.958885
$995$	3.92674e10	1.26372
$996$	5.31278e10	1.70378
$997$	−1.77312e10	−0.566636	−0.283318	−	0.959026i	$-0.591435\pi$
$997$	−1.77312e10	−0.566636	−0.283318	+	0.959026i	$0.591435\pi$
$998$	6.29595e10	2.00495
$999$	−2.75103e10	−0.873003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.2	✓	11
3.2	odd	2		387.8.a.b.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.2	✓	11	1.1	even	1	trivial
387.8.a.b.1.10		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)

\(f(q)\)	\(=\)	\(q-16.1572 q^{2} -48.3227 q^{3} +133.057 q^{4} -272.935 q^{5} +780.762 q^{6} +1101.65 q^{7} -81.7025 q^{8} +148.083 q^{9} +O(q^{10})\)	\(q-16.1572 q^{2} -48.3227 q^{3} +133.057 q^{4} -272.935 q^{5} +780.762 q^{6} +1101.65 q^{7} -81.7025 q^{8} +148.083 q^{9} +4409.88 q^{10} +685.243 q^{11} -6429.66 q^{12} +13204.0 q^{13} -17799.7 q^{14} +13189.0 q^{15} -15711.2 q^{16} -1155.38 q^{17} -2392.62 q^{18} -12969.6 q^{19} -36315.9 q^{20} -53234.8 q^{21} -11071.6 q^{22} -106988. q^{23} +3948.09 q^{24} -3631.41 q^{25} -213341. q^{26} +98526.0 q^{27} +146582. q^{28} +71411.7 q^{29} -213097. q^{30} +229489. q^{31} +264307. q^{32} -33112.8 q^{33} +18667.8 q^{34} -300680. q^{35} +19703.5 q^{36} -279218. q^{37} +209553. q^{38} -638054. q^{39} +22299.5 q^{40} +345820. q^{41} +860128. q^{42} +79507.0 q^{43} +91176.2 q^{44} -40417.2 q^{45} +1.72863e6 q^{46} -735243. q^{47} +759206. q^{48} +390095. q^{49} +58673.6 q^{50} +55831.2 q^{51} +1.75688e6 q^{52} -714374. q^{53} -1.59191e6 q^{54} -187027. q^{55} -90007.8 q^{56} +626726. q^{57} -1.15382e6 q^{58} -915243. q^{59} +1.75488e6 q^{60} -575.793 q^{61} -3.70792e6 q^{62} +163136. q^{63} -2.25945e6 q^{64} -3.60384e6 q^{65} +535012. q^{66} -3.55836e6 q^{67} -153731. q^{68} +5.16993e6 q^{69} +4.85816e6 q^{70} -1.66804e6 q^{71} -12098.8 q^{72} -1.03269e6 q^{73} +4.51140e6 q^{74} +175480. q^{75} -1.72569e6 q^{76} +754900. q^{77} +1.03092e7 q^{78} +1.58783e6 q^{79} +4.28813e6 q^{80} -5.08490e6 q^{81} -5.58750e6 q^{82} -8.26293e6 q^{83} -7.08325e6 q^{84} +315344. q^{85} -1.28461e6 q^{86} -3.45080e6 q^{87} -55986.1 q^{88} +7.66713e6 q^{89} +653030. q^{90} +1.45462e7 q^{91} -1.42354e7 q^{92} -1.10895e7 q^{93} +1.18795e7 q^{94} +3.53986e6 q^{95} -1.27720e7 q^{96} -1.26607e7 q^{97} -6.30287e6 q^{98} +101473. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 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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