LMFDB - Embedded newform 22.14.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,14,Mod(1,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	22.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:	$23.5908043694$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{45769}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 11442 $ x^2 - x - 11442
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-106.468$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+64.0000 q^{2} -35.1262 q^{3} +4096.00 q^{4} +21994.9 q^{5} -2248.08 q^{6} -579474. q^{7} +262144. q^{8} -1.59309e6 q^{9} +O(q^{10})$	\(q+64.0000 q^{2} -35.1262 q^{3} +4096.00 q^{4} +21994.9 q^{5} -2248.08 q^{6} -579474. q^{7} +262144. q^{8} -1.59309e6 q^{9} +1.40768e6 q^{10} +1.77156e6 q^{11} -143877. q^{12} +8.20008e6 q^{13} -3.70864e7 q^{14} -772598. q^{15} +1.67772e7 q^{16} -1.51534e8 q^{17} -1.01958e8 q^{18} +1.95331e7 q^{19} +9.00913e7 q^{20} +2.03547e7 q^{21} +1.13380e8 q^{22} -9.90716e8 q^{23} -9.20812e6 q^{24} -7.36926e8 q^{25} +5.24805e8 q^{26} +1.11962e8 q^{27} -2.37353e9 q^{28} +2.43690e9 q^{29} -4.94463e7 q^{30} -2.45734e9 q^{31} +1.07374e9 q^{32} -6.22282e7 q^{33} -9.69815e9 q^{34} -1.27455e10 q^{35} -6.52529e9 q^{36} -2.02196e10 q^{37} +1.25012e9 q^{38} -2.88038e8 q^{39} +5.76584e9 q^{40} +4.17716e10 q^{41} +1.30270e9 q^{42} -7.65490e10 q^{43} +7.25631e9 q^{44} -3.50399e10 q^{45} -6.34058e10 q^{46} +3.54293e10 q^{47} -5.89320e8 q^{48} +2.38901e11 q^{49} -4.71632e10 q^{50} +5.32280e9 q^{51} +3.35875e10 q^{52} +2.95888e11 q^{53} +7.16554e9 q^{54} +3.89654e10 q^{55} -1.51906e11 q^{56} -6.86124e8 q^{57} +1.55961e11 q^{58} +3.47641e11 q^{59} -3.16456e9 q^{60} -4.64780e11 q^{61} -1.57270e11 q^{62} +9.23154e11 q^{63} +6.87195e10 q^{64} +1.80360e11 q^{65} -3.98260e9 q^{66} +6.09113e11 q^{67} -6.20682e11 q^{68} +3.48001e10 q^{69} -8.15712e11 q^{70} -1.22660e12 q^{71} -4.17619e11 q^{72} -5.52075e11 q^{73} -1.29405e12 q^{74} +2.58854e10 q^{75} +8.00077e10 q^{76} -1.02657e12 q^{77} -1.84344e10 q^{78} +1.21140e12 q^{79} +3.69014e11 q^{80} +2.53597e12 q^{81} +2.67338e12 q^{82} -1.64015e12 q^{83} +8.33729e10 q^{84} -3.33297e12 q^{85} -4.89914e12 q^{86} -8.55989e10 q^{87} +4.64404e11 q^{88} +5.98108e12 q^{89} -2.24255e12 q^{90} -4.75173e12 q^{91} -4.05797e12 q^{92} +8.63171e10 q^{93} +2.26748e12 q^{94} +4.29630e11 q^{95} -3.77165e10 q^{96} -5.75139e12 q^{97} +1.52897e13 q^{98} -2.82225e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9}+O(q^{10}) $ 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9	\( 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9} + 186496 q^{10} + 3543122 q^{11} - 3792896 q^{12} - 6948916 q^{13} - 10915840 q^{14} + 16226114 q^{15} + 33554432 q^{16} - 280144288 q^{17} - 153200384 q^{18} - 349231788 q^{19} + 11935744 q^{20} - 343936280 q^{21} + 226759808 q^{22} - 151278294 q^{23} - 242745344 q^{24} - 1593546344 q^{25} - 444730624 q^{26} + 2245595374 q^{27} - 698613760 q^{28} - 771621928 q^{29} + 1038471296 q^{30} - 8626482070 q^{31} + 2147483648 q^{32} - 1640465486 q^{33} - 17929234432 q^{34} - 20547972800 q^{35} - 9804824576 q^{36} - 26333898490 q^{37} - 22350834432 q^{38} + 13207805428 q^{39} + 763887616 q^{40} - 3560991836 q^{41} - 22011921920 q^{42} - 16329995932 q^{43} + 14512627712 q^{44} - 19762426588 q^{45} - 9681810816 q^{46} + 9513351704 q^{47} - 15535702016 q^{48} + 309223257786 q^{49} - 101986966016 q^{50} + 119898691720 q^{51} - 28462759936 q^{52} + 291363898652 q^{53} + 143718103936 q^{54} + 5162328754 q^{55} - 44711280640 q^{56} + 327836886300 q^{57} - 49383803392 q^{58} + 712019011182 q^{59} + 66462162944 q^{60} + 138918582944 q^{61} - 552094852480 q^{62} + 595750060240 q^{63} + 137438953472 q^{64} + 469417380748 q^{65} - 104989791104 q^{66} + 912599195574 q^{67} - 1147471003648 q^{68} - 713033152350 q^{69} - 1315070259200 q^{70} - 1560848343722 q^{71} - 627508772864 q^{72} + 407382417996 q^{73} - 1685369503360 q^{74} + 789026369816 q^{75} - 1430453403648 q^{76} - 302157444160 q^{77} + 845299547392 q^{78} - 48102676468 q^{79} + 48888807424 q^{80} + 1911689036650 q^{81} - 227903477504 q^{82} - 6313820551012 q^{83} - 1408763002880 q^{84} - 878959681568 q^{85} - 1045119739648 q^{86} + 2772785468872 q^{87} + 928808173568 q^{88} + 977692325462 q^{89} - 1264795301632 q^{90} - 10946374648120 q^{91} - 619635892224 q^{92} + 5582240738434 q^{93} + 608854509056 q^{94} + 7466012570772 q^{95} - 994284929024 q^{96} - 1024977303502 q^{97} + 19790288498304 q^{98} - 4240684773116 q^{99}+O(q^{100}) \) 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9 + 186496 * q^10 + 3543122 * q^11 - 3792896 * q^12 - 6948916 * q^13 - 10915840 * q^14 + 16226114 * q^15 + 33554432 * q^16 - 280144288 * q^17 - 153200384 * q^18 - 349231788 * q^19 + 11935744 * q^20 - 343936280 * q^21 + 226759808 * q^22 - 151278294 * q^23 - 242745344 * q^24 - 1593546344 * q^25 - 444730624 * q^26 + 2245595374 * q^27 - 698613760 * q^28 - 771621928 * q^29 + 1038471296 * q^30 - 8626482070 * q^31 + 2147483648 * q^32 - 1640465486 * q^33 - 17929234432 * q^34 - 20547972800 * q^35 - 9804824576 * q^36 - 26333898490 * q^37 - 22350834432 * q^38 + 13207805428 * q^39 + 763887616 * q^40 - 3560991836 * q^41 - 22011921920 * q^42 - 16329995932 * q^43 + 14512627712 * q^44 - 19762426588 * q^45 - 9681810816 * q^46 + 9513351704 * q^47 - 15535702016 * q^48 + 309223257786 * q^49 - 101986966016 * q^50 + 119898691720 * q^51 - 28462759936 * q^52 + 291363898652 * q^53 + 143718103936 * q^54 + 5162328754 * q^55 - 44711280640 * q^56 + 327836886300 * q^57 - 49383803392 * q^58 + 712019011182 * q^59 + 66462162944 * q^60 + 138918582944 * q^61 - 552094852480 * q^62 + 595750060240 * q^63 + 137438953472 * q^64 + 469417380748 * q^65 - 104989791104 * q^66 + 912599195574 * q^67 - 1147471003648 * q^68 - 713033152350 * q^69 - 1315070259200 * q^70 - 1560848343722 * q^71 - 627508772864 * q^72 + 407382417996 * q^73 - 1685369503360 * q^74 + 789026369816 * q^75 - 1430453403648 * q^76 - 302157444160 * q^77 + 845299547392 * q^78 - 48102676468 * q^79 + 48888807424 * q^80 + 1911689036650 * q^81 - 227903477504 * q^82 - 6313820551012 * q^83 - 1408763002880 * q^84 - 878959681568 * q^85 - 1045119739648 * q^86 + 2772785468872 * q^87 + 928808173568 * q^88 + 977692325462 * q^89 - 1264795301632 * q^90 - 10946374648120 * q^91 - 619635892224 * q^92 + 5582240738434 * q^93 + 608854509056 * q^94 + 7466012570772 * q^95 - 994284929024 * q^96 - 1024977303502 * q^97 + 19790288498304 * q^98 - 4240684773116 * 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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	−35.1262	−0.0278191	−0.0139095	−	0.999903i	$-0.504428\pi$
$3$	−35.1262	−0.0278191	−0.0139095	+	0.999903i	$0.504428\pi$
$4$	4096.00	0.500000
$5$	21994.9	0.629532	0.314766	−	0.949169i	$-0.398074\pi$
$5$	21994.9	0.629532	0.314766	+	0.949169i	$0.398074\pi$
$6$	−2248.08	−0.0196711
$7$	−579474.	−1.86165	−0.930823	−	0.365471i	$-0.880908\pi$
$7$	−579474.	−1.86165	−0.930823	+	0.365471i	$0.880908\pi$
$8$	262144.	0.353553
$9$	−1.59309e6	−0.999226
$10$	1.40768e6	0.445146
$11$	1.77156e6	0.301511
$11$	1.77156e6	0.301511
$12$	−143877.	−0.0139095
$13$	8.20008e6	0.471179	0.235590	−	0.971853i	$-0.424298\pi$
$13$	8.20008e6	0.471179	0.235590	+	0.971853i	$0.424298\pi$
$14$	−3.70864e7	−1.31638
$15$	−772598.	−0.0175130
$16$	1.67772e7	0.250000
$17$	−1.51534e8	−1.52262	−0.761309	−	0.648389i	$-0.775443\pi$
$17$	−1.51534e8	−1.52262	−0.761309	+	0.648389i	$0.775443\pi$
$18$	−1.01958e8	−0.706560
$19$	1.95331e7	0.0952519	0.0476259	−	0.998865i	$-0.484834\pi$
$19$	1.95331e7	0.0952519	0.0476259	+	0.998865i	$0.484834\pi$
$20$	9.00913e7	0.314766
$21$	2.03547e7	0.0517893
$22$	1.13380e8	0.213201
$23$	−9.90716e8	−1.39546	−0.697731	−	0.716359i	$-0.745807\pi$
$23$	−9.90716e8	−1.39546	−0.697731	+	0.716359i	$0.745807\pi$
$24$	−9.20812e6	−0.00983553
$25$	−7.36926e8	−0.603689
$26$	5.24805e8	0.333174
$27$	1.11962e8	0.0556166
$28$	−2.37353e9	−0.930823
$29$	2.43690e9	0.760764	0.380382	−	0.924829i	$-0.375793\pi$
$29$	2.43690e9	0.760764	0.380382	+	0.924829i	$0.375793\pi$
$30$	−4.94463e7	−0.0123836
$31$	−2.45734e9	−0.497296	−0.248648	−	0.968594i	$-0.579986\pi$
$31$	−2.45734e9	−0.497296	−0.248648	+	0.968594i	$0.579986\pi$
$32$	1.07374e9	0.176777
$33$	−6.22282e7	−0.00838777
$34$	−9.69815e9	−1.07665
$35$	−1.27455e10	−1.17197
$36$	−6.52529e9	−0.499613
$37$	−2.02196e10	−1.29557	−0.647786	−	0.761823i	$-0.724305\pi$
$37$	−2.02196e10	−1.29557	−0.647786	+	0.761823i	$0.724305\pi$
$38$	1.25012e9	0.0673532
$39$	−2.88038e8	−0.0131078
$40$	5.76584e9	0.222573
$41$	4.17716e10	1.37336	0.686682	−	0.726958i	$-0.259066\pi$
$41$	4.17716e10	1.37336	0.686682	+	0.726958i	$0.259066\pi$
$42$	1.30270e9	0.0366205
$43$	−7.65490e10	−1.84669	−0.923347	−	0.383967i	$-0.874558\pi$
$43$	−7.65490e10	−1.84669	−0.923347	+	0.383967i	$0.874558\pi$
$44$	7.25631e9	0.150756
$45$	−3.50399e10	−0.629045
$46$	−6.34058e10	−0.986741
$47$	3.54293e10	0.479431	0.239716	−	0.970843i	$-0.422946\pi$
$47$	3.54293e10	0.479431	0.239716	+	0.970843i	$0.422946\pi$
$48$	−5.89320e8	−0.00695477
$49$	2.38901e11	2.46572
$50$	−4.71632e10	−0.426873
$51$	5.32280e9	0.0423578
$52$	3.35875e10	0.235590
$53$	2.95888e11	1.83372	0.916862	−	0.399204i	$-0.130713\pi$
$53$	2.95888e11	1.83372	0.916862	+	0.399204i	$0.130713\pi$
$54$	7.16554e9	0.0393269
$55$	3.89654e10	0.189811
$56$	−1.51906e11	−0.658191
$57$	−6.86124e8	−0.00264982
$58$	1.55961e11	0.537941
$59$	3.47641e11	1.07298	0.536491	−	0.843906i	$-0.319749\pi$
$59$	3.47641e11	1.07298	0.536491	+	0.843906i	$0.319749\pi$
$60$	−3.16456e9	−0.00875650
$61$	−4.64780e11	−1.15506	−0.577529	−	0.816370i	$-0.695983\pi$
$61$	−4.64780e11	−1.15506	−0.577529	+	0.816370i	$0.695983\pi$
$62$	−1.57270e11	−0.351641
$63$	9.23154e11	1.86020
$64$	6.87195e10	0.125000
$65$	1.80360e11	0.296622
$66$	−3.98260e9	−0.00593105
$67$	6.09113e11	0.822644	0.411322	−	0.911490i	$-0.365067\pi$
$67$	6.09113e11	0.822644	0.411322	+	0.911490i	$0.365067\pi$
$68$	−6.20682e11	−0.761309
$69$	3.48001e10	0.0388205
$70$	−8.15712e11	−0.828705
$71$	−1.22660e12	−1.13638	−0.568190	−	0.822897i	$-0.692356\pi$
$71$	−1.22660e12	−1.13638	−0.568190	+	0.822897i	$0.692356\pi$
$72$	−4.17619e11	−0.353280
$73$	−5.52075e11	−0.426972	−0.213486	−	0.976946i	$-0.568482\pi$
$73$	−5.52075e11	−0.426972	−0.213486	+	0.976946i	$0.568482\pi$
$74$	−1.29405e12	−0.916107
$75$	2.58854e10	0.0167941
$76$	8.00077e10	0.0476259
$77$	−1.02657e12	−0.561307
$78$	−1.84344e10	−0.00926860
$79$	1.21140e12	0.560674	0.280337	−	0.959902i	$-0.409554\pi$
$79$	1.21140e12	0.560674	0.280337	+	0.959902i	$0.409554\pi$
$80$	3.69014e11	0.157383
$81$	2.53597e12	0.997679
$82$	2.67338e12	0.971115
$83$	−1.64015e12	−0.550651	−0.275326	−	0.961351i	$-0.588786\pi$
$83$	−1.64015e12	−0.550651	−0.275326	+	0.961351i	$0.588786\pi$
$84$	8.33729e10	0.0258946
$85$	−3.33297e12	−0.958537
$86$	−4.89914e12	−1.30581
$87$	−8.55989e10	−0.0211638
$88$	4.64404e11	0.106600
$89$	5.98108e12	1.27569	0.637844	−	0.770166i	$-0.279826\pi$
$89$	5.98108e12	1.27569	0.637844	+	0.770166i	$0.279826\pi$
$90$	−2.24255e12	−0.444802
$91$	−4.75173e12	−0.877169
$92$	−4.05797e12	−0.697731
$93$	8.63171e10	0.0138343
$94$	2.26748e12	0.339009
$95$	4.29630e11	0.0599641
$96$	−3.77165e10	−0.00491777
$97$	−5.75139e12	−0.701063	−0.350531	−	0.936551i	$-0.613999\pi$
$97$	−5.75139e12	−0.701063	−0.350531	+	0.936551i	$0.613999\pi$
$98$	1.52897e13	1.74353
$99$	−2.82225e12	−0.301278
$100$	−3.01845e12	−0.301845
$101$	4.60730e12	0.431874	0.215937	−	0.976407i	$-0.430719\pi$
$101$	4.60730e12	0.431874	0.215937	+	0.976407i	$0.430719\pi$
$102$	3.40659e11	0.0299515
$103$	1.39999e12	0.115526	0.0577632	−	0.998330i	$-0.481603\pi$
$103$	1.39999e12	0.115526	0.0577632	+	0.998330i	$0.481603\pi$
$104$	2.14960e12	0.166587
$105$	4.47701e11	0.0326030
$106$	1.89368e13	1.29664
$107$	−1.25349e12	−0.0807467	−0.0403733	−	0.999185i	$-0.512855\pi$
$107$	−1.25349e12	−0.0807467	−0.0403733	+	0.999185i	$0.512855\pi$
$108$	4.58595e11	0.0278083
$109$	3.91334e12	0.223499	0.111749	−	0.993736i	$-0.464355\pi$
$109$	3.91334e12	0.223499	0.111749	+	0.993736i	$0.464355\pi$
$110$	2.49378e12	0.134217
$111$	7.10237e11	0.0360416
$112$	−9.72196e12	−0.465411
$113$	3.11501e12	0.140751	0.0703753	−	0.997521i	$-0.477580\pi$
$113$	3.11501e12	0.140751	0.0703753	+	0.997521i	$0.477580\pi$
$114$	−4.39120e10	−0.00187371
$115$	−2.17907e13	−0.878489
$116$	9.98152e12	0.380382
$117$	−1.30635e13	−0.470815
$118$	2.22490e13	0.758713
$119$	8.78098e13	2.83457
$120$	−2.02532e11	−0.00619178
$121$	3.13843e12	0.0909091
$122$	−2.97459e13	−0.816749
$123$	−1.46728e12	−0.0382057
$124$	−1.00653e13	−0.248648
$125$	−4.30579e13	−1.00957
$126$	5.90819e13	1.31536
$127$	−5.36986e13	−1.13564	−0.567818	−	0.823154i	$-0.692212\pi$
$127$	−5.36986e13	−1.13564	−0.567818	+	0.823154i	$0.692212\pi$
$128$	4.39805e12	0.0883883
$129$	2.68888e12	0.0513733
$130$	1.15431e13	0.209744
$131$	−9.09984e13	−1.57315	−0.786576	−	0.617494i	$-0.788148\pi$
$131$	−9.09984e13	−1.57315	−0.786576	+	0.617494i	$0.788148\pi$
$132$	−2.54887e11	−0.00419388
$133$	−1.13189e13	−0.177325
$134$	3.89833e13	0.581697
$135$	2.46259e12	0.0350125
$136$	−3.97236e13	−0.538327
$137$	−6.25016e13	−0.807621	−0.403810	−	0.914843i	$-0.632314\pi$
$137$	−6.25016e13	−0.807621	−0.403810	+	0.914843i	$0.632314\pi$
$138$	2.22721e12	0.0274502
$139$	−3.56587e13	−0.419343	−0.209671	−	0.977772i	$-0.567239\pi$
$139$	−3.56587e13	−0.419343	−0.209671	+	0.977772i	$0.567239\pi$
$140$	−5.22056e13	−0.585983
$141$	−1.24450e12	−0.0133373
$142$	−7.85024e13	−0.803543
$143$	1.45269e13	0.142066
$144$	−2.67276e13	−0.249807
$145$	5.35994e13	0.478925
$146$	−3.53328e13	−0.301915
$147$	−8.39170e12	−0.0685941
$148$	−8.28195e13	−0.647786
$149$	−4.90124e13	−0.366940	−0.183470	−	0.983025i	$-0.558733\pi$
$149$	−4.90124e13	−0.366940	−0.183470	+	0.983025i	$0.558733\pi$
$150$	1.65666e12	0.0118752
$151$	−1.17787e13	−0.0808626	−0.0404313	−	0.999182i	$-0.512873\pi$
$151$	−1.17787e13	−0.0808626	−0.0404313	+	0.999182i	$0.512873\pi$
$152$	5.12049e12	0.0336766
$153$	2.41407e14	1.52144
$154$	−6.57007e13	−0.396904
$155$	−5.40491e13	−0.313064
$156$	−1.17980e12	−0.00655389
$157$	1.85609e14	0.989126	0.494563	−	0.869142i	$-0.335328\pi$
$157$	1.85609e14	0.989126	0.494563	+	0.869142i	$0.335328\pi$
$158$	7.75294e13	0.396456
$159$	−1.03934e13	−0.0510125
$160$	2.36169e13	0.111287
$161$	5.74095e14	2.59786
$162$	1.62302e14	0.705466
$163$	−2.13117e14	−0.890018	−0.445009	−	0.895526i	$-0.646800\pi$
$163$	−2.13117e14	−0.890018	−0.445009	+	0.895526i	$0.646800\pi$
$164$	1.71096e14	0.686682
$165$	−1.36871e12	−0.00528037
$166$	−1.04970e14	−0.389369
$167$	4.09543e14	1.46097	0.730487	−	0.682926i	$-0.239293\pi$
$167$	4.09543e14	1.46097	0.730487	+	0.682926i	$0.239293\pi$
$168$	5.33587e12	0.0183103
$169$	−2.35634e14	−0.777990
$170$	−2.13310e14	−0.677788
$171$	−3.11180e13	−0.0951781
$172$	−3.13545e14	−0.923347
$173$	−3.86307e14	−1.09555	−0.547776	−	0.836625i	$-0.684525\pi$
$173$	−3.86307e14	−1.09555	−0.547776	+	0.836625i	$0.684525\pi$
$174$	−5.47833e12	−0.0149650
$175$	4.27029e14	1.12386
$176$	2.97219e13	0.0753778
$177$	−1.22113e13	−0.0298494
$178$	3.82789e14	0.902048
$179$	2.98585e14	0.678459	0.339230	−	0.940704i	$-0.389834\pi$
$179$	2.98585e14	0.678459	0.339230	+	0.940704i	$0.389834\pi$
$180$	−1.43523e14	−0.314522
$181$	8.04505e14	1.70066	0.850331	−	0.526248i	$-0.176401\pi$
$181$	8.04505e14	1.70066	0.850331	+	0.526248i	$0.176401\pi$
$182$	−3.04111e14	−0.620252
$183$	1.63260e13	0.0321327
$184$	−2.59710e14	−0.493371
$185$	−4.44729e14	−0.815604
$186$	5.52430e12	0.00978234
$187$	−2.68451e14	−0.459087
$188$	1.45118e14	0.239716
$189$	−6.48789e13	−0.103538
$190$	2.74963e13	0.0424010
$191$	−4.13293e14	−0.615945	−0.307972	−	0.951395i	$-0.599650\pi$
$191$	−4.13293e14	−0.615945	−0.307972	+	0.951395i	$0.599650\pi$
$192$	−2.41385e12	−0.00347739
$193$	−3.67912e14	−0.512415	−0.256207	−	0.966622i	$-0.582473\pi$
$193$	−3.67912e14	−0.512415	−0.256207	+	0.966622i	$0.582473\pi$
$194$	−3.68089e14	−0.495726
$195$	−6.33537e12	−0.00825177
$196$	9.78540e14	1.23286
$197$	−8.14491e14	−0.992787	−0.496393	−	0.868098i	$-0.665343\pi$
$197$	−8.14491e14	−0.992787	−0.496393	+	0.868098i	$0.665343\pi$
$198$	−1.80624e14	−0.213036
$199$	−1.04312e15	−1.19067	−0.595334	−	0.803479i	$-0.702980\pi$
$199$	−1.04312e15	−1.19067	−0.595334	+	0.803479i	$0.702980\pi$
$200$	−1.93181e14	−0.213436
$201$	−2.13958e13	−0.0228852
$202$	2.94867e14	0.305381
$203$	−1.41212e15	−1.41627
$204$	2.18022e13	0.0211789
$205$	9.18764e14	0.864577
$206$	8.95991e13	0.0816896
$207$	1.57830e15	1.39438
$208$	1.37574e14	0.117795
$209$	3.46041e13	0.0287195
$210$	2.86529e13	0.0230538
$211$	−1.23313e15	−0.961995	−0.480998	−	0.876722i	$-0.659725\pi$
$211$	−1.23313e15	−0.961995	−0.480998	+	0.876722i	$0.659725\pi$
$212$	1.21196e15	0.916862
$213$	4.30858e13	0.0316131
$214$	−8.02230e13	−0.0570965
$215$	−1.68369e15	−1.16255
$216$	2.93501e13	0.0196635
$217$	1.42397e15	0.925789
$218$	2.50454e14	0.158037
$219$	1.93923e13	0.0118780
$220$	1.59602e14	0.0949055
$221$	−1.24259e15	−0.717426
$222$	4.54552e13	0.0254853
$223$	−2.92795e15	−1.59434	−0.797172	−	0.603753i	$-0.793672\pi$
$223$	−2.92795e15	−1.59434	−0.797172	+	0.603753i	$0.793672\pi$
$224$	−6.22206e14	−0.329095
$225$	1.17399e15	0.603222
$226$	1.99361e14	0.0995257
$227$	−1.04028e14	−0.0504640	−0.0252320	−	0.999682i	$-0.508032\pi$
$227$	−1.04028e14	−0.0504640	−0.0252320	+	0.999682i	$0.508032\pi$
$228$	−2.81037e12	−0.00132491
$229$	3.53444e15	1.61953	0.809766	−	0.586753i	$-0.199594\pi$
$229$	3.53444e15	1.61953	0.809766	+	0.586753i	$0.199594\pi$
$230$	−1.39461e15	−0.621185
$231$	3.60596e13	0.0156151
$232$	6.38818e14	0.268971
$233$	1.53018e15	0.626512	0.313256	−	0.949669i	$-0.398580\pi$
$233$	1.53018e15	0.626512	0.313256	+	0.949669i	$0.398580\pi$
$234$	−8.36061e14	−0.332916
$235$	7.79265e14	0.301817
$236$	1.42394e15	0.536491
$237$	−4.25518e13	−0.0155974
$238$	5.61983e15	2.00435
$239$	−5.19779e15	−1.80398	−0.901991	−	0.431755i	$-0.857894\pi$
$239$	−5.19779e15	−1.80398	−0.901991	+	0.431755i	$0.857894\pi$
$240$	−1.29621e13	−0.00437825
$241$	1.08399e15	0.356381	0.178190	−	0.983996i	$-0.442976\pi$
$241$	1.08399e15	0.356381	0.178190	+	0.983996i	$0.442976\pi$
$242$	2.00859e14	0.0642824
$243$	−2.67582e14	−0.0833712
$244$	−1.90374e15	−0.577529
$245$	5.25462e15	1.55225
$246$	−9.39057e13	−0.0270155
$247$	1.60173e14	0.0448807
$248$	−6.44178e14	−0.175821
$249$	5.76123e13	0.0153186
$250$	−2.75571e15	−0.713877
$251$	−1.61666e15	−0.408075	−0.204037	−	0.978963i	$-0.565406\pi$
$251$	−1.61666e15	−0.408075	−0.204037	+	0.978963i	$0.565406\pi$
$252$	3.78124e15	0.930102
$253$	−1.75511e15	−0.420748
$254$	−3.43671e15	−0.803016
$255$	1.17075e14	0.0266656
$256$	2.81475e14	0.0625000
$257$	3.43737e15	0.744151	0.372076	−	0.928202i	$-0.378646\pi$
$257$	3.43737e15	0.744151	0.372076	+	0.928202i	$0.378646\pi$
$258$	1.72088e14	0.0363264
$259$	1.17167e16	2.41189
$260$	7.38756e14	0.148311
$261$	−3.88219e15	−0.760175
$262$	−5.82390e15	−1.11239
$263$	1.41562e15	0.263776	0.131888	−	0.991265i	$-0.457896\pi$
$263$	1.41562e15	0.263776	0.131888	+	0.991265i	$0.457896\pi$
$264$	−1.63127e13	−0.00296552
$265$	6.50804e15	1.15439
$266$	−7.24413e14	−0.125388
$267$	−2.10092e14	−0.0354885
$268$	2.49493e15	0.411322
$269$	−5.73820e15	−0.923391	−0.461695	−	0.887039i	$-0.652759\pi$
$269$	−5.73820e15	−0.923391	−0.461695	+	0.887039i	$0.652759\pi$
$270$	1.57606e14	0.0247575
$271$	−4.86806e15	−0.746545	−0.373272	−	0.927722i	$-0.621764\pi$
$271$	−4.86806e15	−0.746545	−0.373272	+	0.927722i	$0.621764\pi$
$272$	−2.54231e15	−0.380654
$273$	1.66910e14	0.0244020
$274$	−4.00010e15	−0.571074
$275$	−1.30551e15	−0.182019
$276$	1.42541e14	0.0194103
$277$	−3.95910e15	−0.526597	−0.263298	−	0.964714i	$-0.584810\pi$
$277$	−3.95910e15	−0.526597	−0.263298	+	0.964714i	$0.584810\pi$
$278$	−2.28216e15	−0.296520
$279$	3.91477e15	0.496911
$280$	−3.34116e15	−0.414352
$281$	−4.18835e15	−0.507519	−0.253759	−	0.967267i	$-0.581667\pi$
$281$	−4.18835e15	−0.507519	−0.253759	+	0.967267i	$0.581667\pi$
$282$	−7.96478e13	−0.00943093
$283$	−5.26529e15	−0.609271	−0.304635	−	0.952469i	$-0.598535\pi$
$283$	−5.26529e15	−0.609271	−0.304635	+	0.952469i	$0.598535\pi$
$284$	−5.02416e15	−0.568190
$285$	−1.50913e13	−0.00166815
$286$	9.29724e14	0.100456
$287$	−2.42056e16	−2.55672
$288$	−1.71057e15	−0.176640
$289$	1.30579e16	1.31837
$290$	3.43036e15	0.338651
$291$	2.02025e14	0.0195029
$292$	−2.26130e15	−0.213486
$293$	−3.99956e15	−0.369294	−0.184647	−	0.982805i	$-0.559114\pi$
$293$	−3.99956e15	−0.369294	−0.184647	+	0.982805i	$0.559114\pi$
$294$	−5.37068e14	−0.0485034
$295$	7.64634e15	0.675477
$296$	−5.30045e15	−0.458054
$297$	1.98347e14	0.0167690
$298$	−3.13679e15	−0.259466
$299$	−8.12395e15	−0.657513
$300$	1.06027e14	0.00839704
$301$	4.43582e16	3.43789
$302$	−7.53837e14	−0.0571785
$303$	−1.61837e14	−0.0120143
$304$	3.27712e14	0.0238130
$305$	−1.02228e16	−0.727146
$306$	1.54500e16	1.07582
$307$	−1.64414e16	−1.12083	−0.560416	−	0.828211i	$-0.689359\pi$
$307$	−1.64414e16	−1.12083	−0.560416	+	0.828211i	$0.689359\pi$
$308$	−4.20485e15	−0.280654
$309$	−4.91761e13	−0.00321384
$310$	−3.45914e15	−0.221369
$311$	−4.36826e15	−0.273758	−0.136879	−	0.990588i	$-0.543707\pi$
$311$	−4.36826e15	−0.273758	−0.136879	+	0.990588i	$0.543707\pi$
$312$	−7.55073e13	−0.00463430
$313$	1.44738e16	0.870049	0.435024	−	0.900419i	$-0.356740\pi$
$313$	1.44738e16	0.870049	0.435024	+	0.900419i	$0.356740\pi$
$314$	1.18790e16	0.699418
$315$	2.03047e16	1.17106
$316$	4.96188e15	0.280337
$317$	−2.46090e15	−0.136210	−0.0681050	−	0.997678i	$-0.521695\pi$
$317$	−2.46090e15	−0.136210	−0.0681050	+	0.997678i	$0.521695\pi$
$318$	−6.65179e14	−0.0360713
$319$	4.31711e15	0.229379
$320$	1.51148e15	0.0786915
$321$	4.40301e13	0.00224630
$322$	3.67420e16	1.83696
$323$	−2.95993e15	−0.145032
$324$	1.03873e16	0.498839
$325$	−6.04285e15	−0.284446
$326$	−1.36395e16	−0.629338
$327$	−1.37461e14	−0.00621753
$328$	1.09502e16	0.485558
$329$	−2.05304e16	−0.892531
$330$	−8.75971e13	−0.00373379
$331$	−2.45578e16	−1.02638	−0.513189	−	0.858276i	$-0.671536\pi$
$331$	−2.45578e16	−1.02638	−0.513189	+	0.858276i	$0.671536\pi$
$332$	−6.71806e15	−0.275326
$333$	3.22116e16	1.29457
$334$	2.62108e16	1.03307
$335$	1.33974e16	0.517881
$336$	3.41496e14	0.0129473
$337$	4.12735e16	1.53489	0.767445	−	0.641115i	$-0.221528\pi$
$337$	4.12735e16	1.53489	0.767445	+	0.641115i	$0.221528\pi$
$338$	−1.50806e16	−0.550122
$339$	−1.09419e14	−0.00391555
$340$	−1.36519e16	−0.479268
$341$	−4.35333e15	−0.149940
$342$	−1.99155e15	−0.0673011
$343$	−8.22925e16	−2.72865
$344$	−2.00669e16	−0.652905
$345$	7.65426e14	0.0244387
$346$	−2.47237e16	−0.774672
$347$	4.83673e16	1.48734	0.743670	−	0.668547i	$-0.233083\pi$
$347$	4.83673e16	1.48734	0.743670	+	0.668547i	$0.233083\pi$
$348$	−3.50613e14	−0.0105819
$349$	−4.16047e16	−1.23247	−0.616236	−	0.787562i	$-0.711343\pi$
$349$	−4.16047e16	−1.23247	−0.616236	+	0.787562i	$0.711343\pi$
$350$	2.73299e16	0.794686
$351$	9.18094e14	0.0262054
$352$	1.90220e15	0.0533002
$353$	−2.60684e16	−0.717098	−0.358549	−	0.933511i	$-0.616728\pi$
$353$	−2.60684e16	−0.717098	−0.358549	+	0.933511i	$0.616728\pi$
$354$	−7.81523e14	−0.0211067
$355$	−2.69790e16	−0.715388
$356$	2.44985e16	0.637844
$357$	−3.08442e15	−0.0788553
$358$	1.91095e16	0.479743
$359$	2.70381e16	0.666595	0.333298	−	0.942822i	$-0.391839\pi$
$359$	2.70381e16	0.666595	0.333298	+	0.942822i	$0.391839\pi$
$360$	−9.18550e15	−0.222401
$361$	−4.16714e16	−0.990927
$362$	5.14883e16	1.20255
$363$	−1.10241e14	−0.00252901
$364$	−1.94631e16	−0.438584
$365$	−1.21429e16	−0.268793
$366$	1.04486e15	0.0227212
$367$	7.30778e16	1.56119	0.780596	−	0.625036i	$-0.214916\pi$
$367$	7.30778e16	1.56119	0.780596	+	0.625036i	$0.214916\pi$
$368$	−1.66215e16	−0.348866
$369$	−6.65459e16	−1.37230
$370$	−2.84626e16	−0.576719
$371$	−1.71459e17	−3.41374
$372$	3.53555e14	0.00691716
$373$	2.72907e16	0.524695	0.262347	−	0.964973i	$-0.415503\pi$
$373$	2.72907e16	0.524695	0.262347	+	0.964973i	$0.415503\pi$
$374$	−1.71809e16	−0.324623
$375$	1.51246e15	0.0280854
$376$	9.28758e15	0.169505
$377$	1.99827e16	0.358456
$378$	−4.15225e15	−0.0732127
$379$	−3.40685e16	−0.590471	−0.295236	−	0.955425i	$-0.595398\pi$
$379$	−3.40685e16	−0.590471	−0.295236	+	0.955425i	$0.595398\pi$
$380$	1.75977e15	0.0299820
$381$	1.88623e15	0.0315923
$382$	−2.64508e16	−0.435539
$383$	1.04633e17	1.69386	0.846928	−	0.531708i	$-0.178450\pi$
$383$	1.04633e17	1.69386	0.846928	+	0.531708i	$0.178450\pi$
$384$	−1.54487e14	−0.00245888
$385$	−2.25794e16	−0.353361
$386$	−2.35464e16	−0.362332
$387$	1.21949e17	1.84526
$388$	−2.35577e16	−0.350531
$389$	4.43138e16	0.648436	0.324218	−	0.945982i	$-0.394899\pi$
$389$	4.43138e16	0.648436	0.324218	+	0.945982i	$0.394899\pi$
$390$	−4.05464e14	−0.00583488
$391$	1.50127e17	2.12476
$392$	6.26266e16	0.871765
$393$	3.19643e15	0.0437636
$394$	−5.21274e16	−0.702006
$395$	2.66446e16	0.352962
$396$	−1.15600e16	−0.150639
$397$	2.87609e15	0.0368693	0.0184346	−	0.999830i	$-0.494132\pi$
$397$	2.87609e15	0.0368693	0.0184346	+	0.999830i	$0.494132\pi$
$398$	−6.67599e16	−0.841929
$399$	3.97591e14	0.00493302
$400$	−1.23636e16	−0.150922
$401$	3.56486e16	0.428158	0.214079	−	0.976816i	$-0.431325\pi$
$401$	3.56486e16	0.428158	0.214079	+	0.976816i	$0.431325\pi$
$402$	−1.36933e15	−0.0161823
$403$	−2.01504e16	−0.234316
$404$	1.88715e16	0.215937
$405$	5.57784e16	0.628071
$406$	−9.03756e16	−1.00146
$407$	−3.58202e16	−0.390629
$408$	1.39534e15	0.0149758
$409$	−1.02377e17	−1.08144	−0.540719	−	0.841203i	$-0.681848\pi$
$409$	−1.02377e17	−1.08144	−0.540719	+	0.841203i	$0.681848\pi$
$410$	5.88009e16	0.611348
$411$	2.19544e15	0.0224673
$412$	5.73434e15	0.0577632
$413$	−2.01449e17	−1.99751
$414$	1.01011e17	0.985978
$415$	−3.60751e16	−0.346653
$416$	8.80477e15	0.0832935
$417$	1.25255e15	0.0116657
$418$	2.21466e15	0.0203078
$419$	−3.95912e16	−0.357444	−0.178722	−	0.983900i	$-0.557196\pi$
$419$	−3.95912e16	−0.357444	−0.178722	+	0.983900i	$0.557196\pi$
$420$	1.83378e15	0.0163015
$421$	2.07721e17	1.81823	0.909113	−	0.416550i	$-0.136761\pi$
$421$	2.07721e17	1.81823	0.909113	+	0.416550i	$0.136761\pi$
$422$	−7.89203e16	−0.680234
$423$	−5.64420e16	−0.479060
$424$	7.75652e16	0.648320
$425$	1.11669e17	0.919188
$426$	2.75749e15	0.0223538
$427$	2.69328e17	2.15031
$428$	−5.13427e15	−0.0403733
$429$	−5.10276e14	−0.00395214
$430$	−1.07756e17	−0.822049
$431$	9.55013e16	0.717641	0.358820	−	0.933407i	$-0.383179\pi$
$431$	9.55013e16	0.717641	0.358820	+	0.933407i	$0.383179\pi$
$432$	1.87840e15	0.0139042
$433$	2.16470e17	1.57843	0.789216	−	0.614116i	$-0.210487\pi$
$433$	2.16470e17	1.57843	0.789216	+	0.614116i	$0.210487\pi$
$434$	9.11339e16	0.654631
$435$	−1.88274e15	−0.0133233
$436$	1.60290e16	0.111749
$437$	−1.93518e16	−0.132920
$438$	1.24111e15	0.00839900
$439$	−1.02302e17	−0.682125	−0.341063	−	0.940041i	$-0.610787\pi$
$439$	−1.02302e17	−0.682125	−0.341063	+	0.940041i	$0.610787\pi$
$440$	1.02145e16	0.0671083
$441$	−3.80591e17	−2.46381
$442$	−7.95256e16	−0.507297
$443$	2.20360e16	0.138519	0.0692594	−	0.997599i	$-0.477936\pi$
$443$	2.20360e16	0.138519	0.0692594	+	0.997599i	$0.477936\pi$
$444$	2.90913e15	0.0180208
$445$	1.31553e17	0.803086
$446$	−1.87389e17	−1.12737
$447$	1.72162e15	0.0102079
$448$	−3.98212e16	−0.232706
$449$	−3.67960e16	−0.211933	−0.105967	−	0.994370i	$-0.533794\pi$
$449$	−3.67960e16	−0.211933	−0.105967	+	0.994370i	$0.533794\pi$
$450$	7.51352e16	0.426543
$451$	7.40009e16	0.414085
$452$	1.27591e16	0.0703753
$453$	4.13741e14	0.00224952
$454$	−6.65779e15	−0.0356835
$455$	−1.04514e17	−0.552206
$456$	−1.79863e14	−0.000936853 0
$457$	−2.60934e17	−1.33991	−0.669956	−	0.742401i	$-0.733687\pi$
$457$	−2.60934e17	−1.33991	−0.669956	+	0.742401i	$0.733687\pi$
$458$	2.26204e17	1.14518
$459$	−1.69659e16	−0.0846829
$460$	−8.92549e16	−0.439244
$461$	3.51460e15	0.0170537	0.00852687	−	0.999964i	$-0.497286\pi$
$461$	3.51460e15	0.0170537	0.00852687	+	0.999964i	$0.497286\pi$
$462$	2.30782e15	0.0110415
$463$	5.66517e16	0.267261	0.133631	−	0.991031i	$-0.457336\pi$
$463$	5.66517e16	0.267261	0.133631	+	0.991031i	$0.457336\pi$
$464$	4.08843e16	0.190191
$465$	1.89854e15	0.00870915
$466$	9.79316e16	0.443011
$467$	−5.14673e16	−0.229600	−0.114800	−	0.993389i	$-0.536623\pi$
$467$	−5.14673e16	−0.229600	−0.114800	+	0.993389i	$0.536623\pi$
$468$	−5.35079e16	−0.235407
$469$	−3.52965e17	−1.53147
$470$	4.98730e16	0.213417
$471$	−6.51974e15	−0.0275166
$472$	9.11320e16	0.379357
$473$	−1.35611e17	−0.556799
$474$	−2.72331e15	−0.0110291
$475$	−1.43945e16	−0.0575025
$476$	3.59669e17	1.41729
$477$	−4.71376e17	−1.83231
$478$	−3.32658e17	−1.27561
$479$	1.31356e17	0.496899	0.248449	−	0.968645i	$-0.420079\pi$
$479$	1.31356e17	0.496899	0.248449	+	0.968645i	$0.420079\pi$
$480$	−8.29571e14	−0.00309589
$481$	−1.65802e17	−0.610446
$482$	6.93754e16	0.251999
$483$	−2.01658e16	−0.0722700
$484$	1.28550e16	0.0454545
$485$	−1.26502e17	−0.441341
$486$	−1.71252e16	−0.0589523
$487$	−2.66791e17	−0.906218	−0.453109	−	0.891455i	$-0.649685\pi$
$487$	−2.66791e17	−0.906218	−0.453109	+	0.891455i	$0.649685\pi$
$488$	−1.21839e17	−0.408375
$489$	7.48599e15	0.0247595
$490$	3.36296e17	1.09761
$491$	3.55202e17	1.14405	0.572027	−	0.820235i	$-0.306157\pi$
$491$	3.55202e17	1.14405	0.572027	+	0.820235i	$0.306157\pi$
$492$	−6.00996e15	−0.0191029
$493$	−3.69272e17	−1.15835
$494$	1.02511e16	0.0317355
$495$	−6.20753e16	−0.189664
$496$	−4.12274e16	−0.124324
$497$	7.10783e17	2.11554
$498$	3.68719e15	0.0108319
$499$	4.99794e17	1.44923	0.724615	−	0.689154i	$-0.242018\pi$
$499$	4.99794e17	1.44923	0.724615	+	0.689154i	$0.242018\pi$
$500$	−1.76365e17	−0.504787
$501$	−1.43857e16	−0.0406430
$502$	−1.03466e17	−0.288552
$503$	−2.69799e17	−0.742759	−0.371379	−	0.928481i	$-0.621115\pi$
$503$	−2.69799e17	−0.742759	−0.371379	+	0.928481i	$0.621115\pi$
$504$	2.41999e17	0.657682
$505$	1.01337e17	0.271879
$506$	−1.12327e17	−0.297514
$507$	8.27692e15	0.0216430
$508$	−2.19950e17	−0.567818
$509$	−7.07838e16	−0.180413	−0.0902066	−	0.995923i	$-0.528753\pi$
$509$	−7.07838e16	−0.180413	−0.0902066	+	0.995923i	$0.528753\pi$
$510$	7.49278e15	0.0188554
$511$	3.19913e17	0.794870
$512$	1.80144e16	0.0441942
$513$	2.18696e15	0.00529759
$514$	2.19992e17	0.526194
$515$	3.07926e16	0.0727276
$516$	1.10136e16	0.0256867
$517$	6.27652e16	0.144554
$518$	7.49871e17	1.70547
$519$	1.35695e16	0.0304773
$520$	4.72804e16	0.104872
$521$	−8.57670e16	−0.187878	−0.0939388	−	0.995578i	$-0.529946\pi$
$521$	−8.57670e16	−0.187878	−0.0939388	+	0.995578i	$0.529946\pi$
$522$	−2.48460e17	−0.537525
$523$	5.00831e17	1.07011	0.535057	−	0.844816i	$-0.320290\pi$
$523$	5.00831e17	1.07011	0.535057	+	0.844816i	$0.320290\pi$
$524$	−3.72730e17	−0.786576
$525$	−1.49999e16	−0.0312646
$526$	9.05998e16	0.186518
$527$	3.72370e17	0.757192
$528$	−1.04402e15	−0.00209694
$529$	4.77482e17	0.947317
$530$	4.16514e17	0.816276
$531$	−5.53823e17	−1.07215
$532$	−4.63624e16	−0.0886626
$533$	3.42530e17	0.647101
$534$	−1.34459e16	−0.0250941
$535$	−2.75703e16	−0.0508326
$536$	1.59675e17	0.290849
$537$	−1.04882e16	−0.0188741
$538$	−3.67244e17	−0.652936
$539$	4.23228e17	0.743443
$540$	1.00868e16	0.0175062
$541$	−1.88030e17	−0.322437	−0.161219	−	0.986919i	$-0.551542\pi$
$541$	−1.88030e17	−0.322437	−0.161219	+	0.986919i	$0.551542\pi$
$542$	−3.11556e17	−0.527887
$543$	−2.82592e16	−0.0473109
$544$	−1.62708e17	−0.269163
$545$	8.60736e16	0.140700
$546$	1.06823e16	0.0172548
$547$	3.56059e17	0.568335	0.284167	−	0.958775i	$-0.408283\pi$
$547$	3.56059e17	0.568335	0.284167	+	0.958775i	$0.408283\pi$
$548$	−2.56007e17	−0.403810
$549$	7.40436e17	1.15416
$550$	−8.35526e16	−0.128707
$551$	4.76002e16	0.0724642
$552$	9.12263e15	0.0137251
$553$	−7.01973e17	−1.04378
$554$	−2.53383e17	−0.372360
$555$	1.56216e16	0.0226893
$556$	−1.46058e17	−0.209671
$557$	−1.98758e17	−0.282011	−0.141006	−	0.990009i	$-0.545034\pi$
$557$	−1.98758e17	−0.282011	−0.141006	+	0.990009i	$0.545034\pi$
$558$	2.50545e17	0.351369
$559$	−6.27708e17	−0.870124
$560$	−2.13834e17	−0.292991
$561$	9.42966e15	0.0127714
$562$	−2.68054e17	−0.358870
$563$	−8.82175e17	−1.16748	−0.583741	−	0.811940i	$-0.698412\pi$
$563$	−8.82175e17	−1.16748	−0.583741	+	0.811940i	$0.698412\pi$
$564$	−5.09746e15	−0.00666867
$565$	6.85146e16	0.0886070
$566$	−3.36979e17	−0.430820
$567$	−1.46953e18	−1.85732
$568$	−3.21546e17	−0.401771
$569$	5.55142e17	0.685764	0.342882	−	0.939379i	$-0.388597\pi$
$569$	5.55142e17	0.685764	0.342882	+	0.939379i	$0.388597\pi$
$570$	−9.65841e14	−0.00117956
$571$	−9.08657e17	−1.09715	−0.548574	−	0.836102i	$-0.684829\pi$
$571$	−9.08657e17	−1.09715	−0.548574	+	0.836102i	$0.684829\pi$
$572$	5.95023e16	0.0710330
$573$	1.45174e16	0.0171350
$574$	−1.54916e18	−1.80787
$575$	7.30084e17	0.842426
$576$	−1.09476e17	−0.124903
$577$	7.99874e17	0.902358	0.451179	−	0.892434i	$-0.351004\pi$
$577$	7.99874e17	0.902358	0.451179	+	0.892434i	$0.351004\pi$
$578$	8.35703e17	0.932225
$579$	1.29234e16	0.0142549
$580$	2.19543e17	0.239463
$581$	9.50426e17	1.02512
$582$	1.29296e16	0.0137906
$583$	5.24184e17	0.552889
$584$	−1.44723e17	−0.150957
$585$	−2.87330e17	−0.296393
$586$	−2.55972e17	−0.261130
$587$	−1.39424e18	−1.40666	−0.703332	−	0.710861i	$-0.748305\pi$
$587$	−1.39424e18	−1.40666	−0.703332	+	0.710861i	$0.748305\pi$
$588$	−3.43724e16	−0.0342971
$589$	−4.79996e16	−0.0473684
$590$	4.89366e17	0.477634
$591$	2.86100e16	0.0276184
$592$	−3.39229e17	−0.323893
$593$	−1.47998e18	−1.39766	−0.698828	−	0.715290i	$-0.746295\pi$
$593$	−1.47998e18	−1.39766	−0.698828	+	0.715290i	$0.746295\pi$
$594$	1.26942e16	0.0118575
$595$	1.93137e18	1.78446
$596$	−2.00755e17	−0.183470
$597$	3.66409e16	0.0331233
$598$	−5.19933e17	−0.464932
$599$	1.63026e18	1.44205	0.721027	−	0.692907i	$-0.243670\pi$
$599$	1.63026e18	1.44205	0.721027	+	0.692907i	$0.243670\pi$
$600$	6.78570e15	0.00593761
$601$	−2.02912e18	−1.75640	−0.878199	−	0.478296i	$-0.841255\pi$
$601$	−2.02912e18	−1.75640	−0.878199	+	0.478296i	$0.841255\pi$
$602$	2.83892e18	2.43095
$603$	−9.70372e17	−0.822007
$604$	−4.82456e16	−0.0404313
$605$	6.90296e16	0.0572302
$606$	−1.03576e16	−0.00849542
$607$	1.56469e18	1.26970	0.634852	−	0.772634i	$-0.281061\pi$
$607$	1.56469e18	1.26970	0.634852	+	0.772634i	$0.281061\pi$
$608$	2.09735e16	0.0168383
$609$	4.96023e16	0.0393994
$610$	−6.54260e17	−0.514170
$611$	2.90523e17	0.225898
$612$	9.88801e17	0.760720
$613$	1.05221e18	0.800956	0.400478	−	0.916306i	$-0.368844\pi$
$613$	1.05221e18	0.800956	0.400478	+	0.916306i	$0.368844\pi$
$614$	−1.05225e18	−0.792547
$615$	−3.22727e16	−0.0240517
$616$	−2.69110e17	−0.198452
$617$	1.05797e18	0.772007	0.386004	−	0.922497i	$-0.373855\pi$
$617$	1.05797e18	0.772007	0.386004	+	0.922497i	$0.373855\pi$
$618$	−3.14727e15	−0.00227253
$619$	−1.53111e18	−1.09400	−0.546998	−	0.837134i	$-0.684230\pi$
$619$	−1.53111e18	−1.09400	−0.546998	+	0.837134i	$0.684230\pi$
$620$	−2.21385e17	−0.156532
$621$	−1.10922e17	−0.0776110
$622$	−2.79569e17	−0.193576
$623$	−3.46588e18	−2.37488
$624$	−4.83247e15	−0.00327694
$625$	−4.74894e16	−0.0318696
$626$	9.26322e17	0.615217
$627$	−1.21551e15	−0.000798951 0
$628$	7.60255e17	0.494563
$629$	3.06395e18	1.97266
$630$	1.29950e18	0.828063
$631$	2.70087e18	1.70339	0.851694	−	0.524040i	$-0.175576\pi$
$631$	2.70087e18	1.70339	0.851694	+	0.524040i	$0.175576\pi$
$632$	3.17560e17	0.198228
$633$	4.33152e16	0.0267618
$634$	−1.57498e17	−0.0963150
$635$	−1.18110e18	−0.714919
$636$	−4.25714e16	−0.0255063
$637$	1.95901e18	1.16180
$638$	2.76295e17	0.162195
$639$	1.95408e18	1.13550
$640$	9.67348e16	0.0556433
$641$	−2.30327e18	−1.31150	−0.655748	−	0.754980i	$-0.727647\pi$
$641$	−2.30327e18	−1.31150	−0.655748	+	0.754980i	$0.727647\pi$
$642$	2.81793e15	0.00158837
$643$	−1.81161e18	−1.01086	−0.505432	−	0.862866i	$-0.668667\pi$
$643$	−1.81161e18	−1.01086	−0.505432	+	0.862866i	$0.668667\pi$
$644$	2.35149e18	1.29893
$645$	5.91417e16	0.0323412
$646$	−1.89435e17	−0.102553
$647$	−3.42722e18	−1.83681	−0.918406	−	0.395640i	$-0.870523\pi$
$647$	−3.42722e18	−1.83681	−0.918406	+	0.395640i	$0.870523\pi$
$648$	6.64788e17	0.352733
$649$	6.15867e17	0.323516
$650$	−3.86742e17	−0.201134
$651$	−5.00185e16	−0.0257546
$652$	−8.72928e17	−0.445009
$653$	−6.74972e17	−0.340682	−0.170341	−	0.985385i	$-0.554487\pi$
$653$	−6.74972e17	−0.340682	−0.170341	+	0.985385i	$0.554487\pi$
$654$	−8.79748e15	−0.00439646
$655$	−2.00151e18	−0.990349
$656$	7.00811e17	0.343341
$657$	8.79505e17	0.426642
$658$	−1.31394e18	−0.631115
$659$	−3.52350e17	−0.167579	−0.0837893	−	0.996483i	$-0.526702\pi$
$659$	−3.52350e17	−0.167579	−0.0837893	+	0.996483i	$0.526702\pi$
$660$	−5.60622e15	−0.00264018
$661$	1.50874e17	0.0703565	0.0351783	−	0.999381i	$-0.488800\pi$
$661$	1.50874e17	0.0703565	0.0351783	+	0.999381i	$0.488800\pi$
$662$	−1.57170e18	−0.725758
$663$	4.36474e16	0.0199581
$664$	−4.29956e17	−0.194685
$665$	−2.48960e17	−0.111632
$666$	2.06154e18	0.915398
$667$	−2.41427e18	−1.06162
$668$	1.67749e18	0.730487
$669$	1.02848e17	0.0443532
$670$	8.57434e17	0.366197
$671$	−8.23387e17	−0.348263
$672$	2.18557e16	0.00915513
$673$	4.29559e18	1.78207	0.891036	−	0.453932i	$-0.149979\pi$
$673$	4.29559e18	1.78207	0.891036	+	0.453932i	$0.149979\pi$
$674$	2.64151e18	1.08533
$675$	−8.25074e16	−0.0335752
$676$	−9.65156e17	−0.388995
$677$	4.54144e17	0.181287	0.0906437	−	0.995883i	$-0.471108\pi$
$677$	4.54144e17	0.181287	0.0906437	+	0.995883i	$0.471108\pi$
$678$	−7.00279e15	−0.00276871
$679$	3.33278e18	1.30513
$680$	−8.73719e17	−0.338894
$681$	3.65411e15	0.00140386
$682$	−2.78613e17	−0.106024
$683$	−1.40763e18	−0.530582	−0.265291	−	0.964168i	$-0.585468\pi$
$683$	−1.40763e18	−0.530582	−0.265291	+	0.964168i	$0.585468\pi$
$684$	−1.27459e17	−0.0475891
$685$	−1.37472e18	−0.508423
$686$	−5.26672e18	−1.92945
$687$	−1.24151e17	−0.0450539
$688$	−1.28428e18	−0.461673
$689$	2.42630e18	0.864013
$690$	4.89873e16	0.0172808
$691$	7.13074e17	0.249188	0.124594	−	0.992208i	$-0.460237\pi$
$691$	7.13074e17	0.249188	0.124594	+	0.992208i	$0.460237\pi$
$692$	−1.58231e18	−0.547776
$693$	1.63542e18	0.560873
$694$	3.09551e18	1.05171
$695$	−7.84311e17	−0.263990
$696$	−2.24392e16	−0.00748252
$697$	−6.32980e18	−2.09111
$698$	−2.66270e18	−0.871489
$699$	−5.37494e16	−0.0174290
$700$	1.74911e18	0.561928
$701$	−5.11626e18	−1.62849	−0.814246	−	0.580519i	$-0.802850\pi$
$701$	−5.11626e18	−1.62849	−0.814246	+	0.580519i	$0.802850\pi$
$702$	5.87580e16	0.0185300
$703$	−3.94952e17	−0.123406
$704$	1.21741e17	0.0376889
$705$	−2.73726e16	−0.00839628
$706$	−1.66838e18	−0.507065
$707$	−2.66981e18	−0.803996
$708$	−5.00175e16	−0.0149247
$709$	4.12930e18	1.22089	0.610444	−	0.792059i	$-0.290991\pi$
$709$	4.12930e18	1.22089	0.610444	+	0.792059i	$0.290991\pi$
$710$	−1.72666e18	−0.505856
$711$	−1.92986e18	−0.560240
$712$	1.56790e18	0.451024
$713$	2.43453e18	0.693958
$714$	−1.97403e17	−0.0557591
$715$	3.19519e17	0.0894350
$716$	1.22301e18	0.339230
$717$	1.82578e17	0.0501851
$718$	1.73044e18	0.471354
$719$	8.43713e17	0.227749	0.113875	−	0.993495i	$-0.463674\pi$
$719$	8.43713e17	0.227749	0.113875	+	0.993495i	$0.463674\pi$
$720$	−5.87872e17	−0.157261
$721$	−8.11255e17	−0.215069
$722$	−2.66697e18	−0.700691
$723$	−3.80764e16	−0.00991419
$724$	3.29525e18	0.850331
$725$	−1.79581e18	−0.459265
$726$	−7.05543e15	−0.00178828
$727$	−3.54258e18	−0.889909	−0.444955	−	0.895553i	$-0.646780\pi$
$727$	−3.54258e18	−0.889909	−0.444955	+	0.895553i	$0.646780\pi$
$728$	−1.24564e18	−0.310126
$729$	−4.03375e18	−0.995360
$730$	−7.77143e17	−0.190065
$731$	1.15998e19	2.81181
$732$	6.68711e16	0.0160663
$733$	4.87970e18	1.16203	0.581014	−	0.813893i	$-0.302656\pi$
$733$	4.87970e18	1.16203	0.581014	+	0.813893i	$0.302656\pi$
$734$	4.67698e18	1.10393
$735$	−1.84575e17	−0.0431822
$736$	−1.06377e18	−0.246685
$737$	1.07908e18	0.248036
$738$	−4.25893e18	−0.970364
$739$	7.73357e18	1.74659	0.873295	−	0.487192i	$-0.161979\pi$
$739$	7.73357e18	1.74659	0.873295	+	0.487192i	$0.161979\pi$
$740$	−1.82161e18	−0.407802
$741$	−5.62627e15	−0.00124854
$742$	−1.09734e19	−2.41388
$743$	−8.47141e18	−1.84726	−0.923630	−	0.383284i	$-0.874793\pi$
$743$	−8.47141e18	−1.84726	−0.923630	+	0.383284i	$0.874793\pi$
$744$	2.26275e16	0.00489117
$745$	−1.07802e18	−0.231001
$746$	1.74660e18	0.371015
$747$	2.61291e18	0.550225
$748$	−1.09958e18	−0.229543
$749$	7.26362e17	0.150322
$750$	9.67975e16	0.0198594
$751$	5.60063e18	1.13914	0.569570	−	0.821943i	$-0.307110\pi$
$751$	5.60063e18	1.13914	0.569570	+	0.821943i	$0.307110\pi$
$752$	5.94405e17	0.119858
$753$	5.67871e16	0.0113523
$754$	1.27890e18	0.253467
$755$	−2.59072e17	−0.0509056
$756$	−2.65744e17	−0.0517692
$757$	7.82826e18	1.51197	0.755983	−	0.654591i	$-0.227159\pi$
$757$	7.82826e18	1.51197	0.755983	+	0.654591i	$0.227159\pi$
$758$	−2.18039e18	−0.417526
$759$	6.16505e16	0.0117048
$760$	1.12625e17	0.0212005
$761$	−6.32208e18	−1.17994	−0.589970	−	0.807425i	$-0.700860\pi$
$761$	−6.32208e18	−1.17994	−0.589970	+	0.807425i	$0.700860\pi$
$762$	1.20719e17	0.0223392
$763$	−2.26768e18	−0.416075
$764$	−1.69285e18	−0.307972
$765$	5.30972e18	0.957795
$766$	6.69651e18	1.19774
$767$	2.85068e18	0.505567
$768$	−9.88714e15	−0.00173869
$769$	9.09882e18	1.58659	0.793294	−	0.608839i	$-0.208364\pi$
$769$	9.09882e18	1.58659	0.793294	+	0.608839i	$0.208364\pi$
$770$	−1.44508e18	−0.249864
$771$	−1.20742e17	−0.0207016
$772$	−1.50697e18	−0.256207
$773$	−1.88424e18	−0.317665	−0.158833	−	0.987306i	$-0.550773\pi$
$773$	−1.88424e18	−0.317665	−0.158833	+	0.987306i	$0.550773\pi$
$774$	7.80476e18	1.30480
$775$	1.81088e18	0.300212
$776$	−1.50769e18	−0.247863
$777$	−4.11564e17	−0.0670967
$778$	2.83609e18	0.458513
$779$	8.15930e17	0.130816
$780$	−2.59497e16	−0.00412588
$781$	−2.17300e18	−0.342632
$782$	9.60811e18	1.50243
$783$	2.72839e17	0.0423111
$784$	4.00810e18	0.616431
$785$	4.08246e18	0.622687
$786$	2.04571e17	0.0309456
$787$	−2.28502e18	−0.342811	−0.171405	−	0.985201i	$-0.554831\pi$
$787$	−2.28502e18	−0.342811	−0.171405	+	0.985201i	$0.554831\pi$
$788$	−3.33616e18	−0.496393
$789$	−4.97254e16	−0.00733800
$790$	1.70525e18	0.249582
$791$	−1.80507e18	−0.262028
$792$	−7.39837e17	−0.106518
$793$	−3.81124e18	−0.544239
$794$	1.84070e17	0.0260705
$795$	−2.28603e17	−0.0321140
$796$	−4.27263e18	−0.595334
$797$	−4.87649e18	−0.673951	−0.336975	−	0.941513i	$-0.609404\pi$
$797$	−4.87649e18	−0.673951	−0.336975	+	0.941513i	$0.609404\pi$
$798$	2.54459e16	0.00348817
$799$	−5.36873e18	−0.729991
$800$	−7.91268e17	−0.106718
$801$	−9.52839e18	−1.27470
$802$	2.28151e18	0.302753
$803$	−9.78035e17	−0.128737
$804$	−8.76373e16	−0.0114426
$805$	1.26272e19	1.63543
$806$	−1.28963e18	−0.165686
$807$	2.01561e17	0.0256879
$808$	1.20778e18	0.152691
$809$	−6.12820e18	−0.768542	−0.384271	−	0.923220i	$-0.625547\pi$
$809$	−6.12820e18	−0.768542	−0.384271	+	0.923220i	$0.625547\pi$
$810$	3.56982e18	0.444113
$811$	−1.23192e19	−1.52036	−0.760181	−	0.649711i	$-0.774890\pi$
$811$	−1.23192e19	−1.52036	−0.760181	+	0.649711i	$0.774890\pi$
$812$	−5.78404e18	−0.708136
$813$	1.70997e17	0.0207682
$814$	−2.29250e18	−0.276217
$815$	−4.68750e18	−0.560295
$816$	8.93017e16	0.0105895
$817$	−1.49524e18	−0.175901
$818$	−6.55214e18	−0.764692
$819$	7.56994e18	0.876490
$820$	3.76326e18	0.432288
$821$	1.10397e18	0.125813	0.0629066	−	0.998019i	$-0.479963\pi$
$821$	1.10397e18	0.125813	0.0629066	+	0.998019i	$0.479963\pi$
$822$	1.40508e17	0.0158868
$823$	2.59484e18	0.291079	0.145539	−	0.989352i	$-0.453508\pi$
$823$	2.59484e18	0.291079	0.145539	+	0.989352i	$0.453508\pi$
$824$	3.66998e17	0.0408448
$825$	4.58575e16	0.00506361
$826$	−1.28927e19	−1.41245
$827$	−9.06313e18	−0.985127	−0.492564	−	0.870277i	$-0.663940\pi$
$827$	−9.06313e18	−0.985127	−0.492564	+	0.870277i	$0.663940\pi$
$828$	6.46471e18	0.697192
$829$	1.97949e18	0.211811	0.105905	−	0.994376i	$-0.466226\pi$
$829$	1.97949e18	0.211811	0.105905	+	0.994376i	$0.466226\pi$
$830$	−2.30880e18	−0.245120
$831$	1.39068e17	0.0146494
$832$	5.63505e17	0.0588974
$833$	−3.62016e19	−3.75435
$834$	8.01635e16	0.00824892
$835$	9.00788e18	0.919730
$836$	1.41739e17	0.0143598
$837$	−2.75128e17	−0.0276579
$838$	−2.53384e18	−0.252751
$839$	6.00147e18	0.594025	0.297013	−	0.954874i	$-0.404010\pi$
$839$	6.00147e18	0.594025	0.297013	+	0.954874i	$0.404010\pi$
$840$	1.17362e17	0.0115269
$841$	−4.32217e18	−0.421238
$842$	1.32942e19	1.28568
$843$	1.47121e17	0.0141187
$844$	−5.05090e18	−0.480998
$845$	−5.18275e18	−0.489770
$846$	−3.61229e18	−0.338747
$847$	−1.81864e18	−0.169240
$848$	4.96418e18	0.458431
$849$	1.84950e17	0.0169494
$850$	7.14682e18	0.649964
$851$	2.00319e19	1.80792
$852$	1.76479e17	0.0158065
$853$	−1.67908e19	−1.49246	−0.746229	−	0.665689i	$-0.768138\pi$
$853$	−1.67908e19	−1.49246	−0.746229	+	0.665689i	$0.768138\pi$
$854$	1.72370e19	1.52050
$855$	−6.84439e17	−0.0599177
$856$	−3.28594e17	−0.0285483
$857$	−1.40112e19	−1.20809	−0.604046	−	0.796949i	$-0.706446\pi$
$857$	−1.40112e19	−1.20809	−0.604046	+	0.796949i	$0.706446\pi$
$858$	−3.26577e16	−0.00279459
$859$	−6.43590e18	−0.546580	−0.273290	−	0.961932i	$-0.588112\pi$
$859$	−6.43590e18	−0.546580	−0.273290	+	0.961932i	$0.588112\pi$
$860$	−6.89640e18	−0.581276
$861$	8.50249e17	0.0711255
$862$	6.11209e18	0.507449
$863$	6.89563e18	0.568203	0.284102	−	0.958794i	$-0.408305\pi$
$863$	6.89563e18	0.568203	0.284102	+	0.958794i	$0.408305\pi$
$864$	1.20218e17	0.00983173
$865$	−8.49680e18	−0.689685
$866$	1.38541e19	1.11612
$867$	−4.58673e17	−0.0366757
$868$	5.83257e18	0.462894
$869$	2.14606e18	0.169050
$870$	−1.20495e17	−0.00942097
$871$	4.99478e18	0.387613
$872$	1.02586e18	0.0790187
$873$	9.16248e18	0.700520
$874$	−1.23851e18	−0.0939890
$875$	2.49510e19	1.87947
$876$	7.94308e16	0.00593899
$877$	1.32210e19	0.981220	0.490610	−	0.871379i	$-0.336774\pi$
$877$	1.32210e19	0.981220	0.490610	+	0.871379i	$0.336774\pi$
$878$	−6.54732e18	−0.482335
$879$	1.40489e17	0.0102734
$880$	6.53731e17	0.0474528
$881$	−1.00849e19	−0.726652	−0.363326	−	0.931662i	$-0.618359\pi$
$881$	−1.00849e19	−0.726652	−0.363326	+	0.931662i	$0.618359\pi$
$882$	−2.43578e19	−1.74218
$883$	−2.93971e18	−0.208718	−0.104359	−	0.994540i	$-0.533279\pi$
$883$	−2.93971e18	−0.208718	−0.104359	+	0.994540i	$0.533279\pi$
$884$	−5.08964e18	−0.358713
$885$	−2.68587e17	−0.0187912
$886$	1.41030e18	0.0979476
$887$	2.54284e19	1.75314	0.876568	−	0.481279i	$-0.159828\pi$
$887$	2.54284e19	1.75314	0.876568	+	0.481279i	$0.159828\pi$
$888$	1.86184e17	0.0127426
$889$	3.11170e19	2.11415
$890$	8.41942e18	0.567868
$891$	4.49262e18	0.300812
$892$	−1.19929e19	−0.797172
$893$	6.92045e17	0.0456667
$894$	1.10184e17	0.00721810
$895$	6.56737e18	0.427112
$896$	−2.54855e18	−0.164548
$897$	2.85363e17	0.0182914
$898$	−2.35494e18	−0.149859
$899$	−5.98829e18	−0.378325
$900$	4.80866e18	0.301611
$901$	−4.48370e19	−2.79206
$902$	4.73606e18	0.292802
$903$	−1.55813e18	−0.0956389
$904$	8.16582e17	0.0497628
$905$	1.76950e19	1.07062
$906$	2.64794e16	0.00159065
$907$	−1.64328e19	−0.980085	−0.490043	−	0.871698i	$-0.663019\pi$
$907$	−1.64328e19	−0.980085	−0.490043	+	0.871698i	$0.663019\pi$
$908$	−4.26098e17	−0.0252320
$909$	−7.33983e18	−0.431540
$910$	−6.68890e18	−0.390468
$911$	2.76250e19	1.60115	0.800576	−	0.599231i	$-0.204527\pi$
$911$	2.76250e19	1.60115	0.800576	+	0.599231i	$0.204527\pi$
$912$	−1.15113e16	−0.000662455 0
$913$	−2.90563e18	−0.166028
$914$	−1.66998e19	−0.947461
$915$	3.59089e17	0.0202285
$916$	1.44771e19	0.809766
$917$	5.27312e19	2.92865
$918$	−1.08582e18	−0.0598799
$919$	−1.01159e19	−0.553927	−0.276964	−	0.960880i	$-0.589328\pi$
$919$	−1.01159e19	−0.553927	−0.276964	+	0.960880i	$0.589328\pi$
$920$	−5.71231e18	−0.310593
$921$	5.77525e17	0.0311805
$922$	2.24934e17	0.0120588
$923$	−1.00582e19	−0.535439
$924$	1.47700e17	0.00780753
$925$	1.49003e19	0.782123
$926$	3.62571e18	0.188982
$927$	−2.23030e18	−0.115437
$928$	2.61660e18	0.134485
$929$	1.87359e19	0.956250	0.478125	−	0.878292i	$-0.341317\pi$
$929$	1.87359e19	0.956250	0.478125	+	0.878292i	$0.341317\pi$
$930$	1.21507e17	0.00615830
$931$	4.66649e18	0.234865
$932$	6.26762e18	0.313256
$933$	1.53440e17	0.00761569
$934$	−3.29391e18	−0.162352
$935$	−5.90456e18	−0.289010
$936$	−3.42451e18	−0.166458
$937$	−4.01242e19	−1.93686	−0.968431	−	0.249280i	$-0.919806\pi$
$937$	−4.01242e19	−1.93686	−0.968431	+	0.249280i	$0.919806\pi$
$938$	−2.25898e19	−1.08291
$939$	−5.08408e17	−0.0242040
$940$	3.19187e18	0.150909
$941$	3.26128e19	1.53128	0.765642	−	0.643267i	$-0.222421\pi$
$941$	3.26128e19	1.53128	0.765642	+	0.643267i	$0.222421\pi$
$942$	−4.17263e17	−0.0194572
$943$	−4.13838e19	−1.91648
$944$	5.83245e18	0.268246
$945$	−1.42701e18	−0.0651808
$946$	−8.67912e18	−0.393716
$947$	−2.60703e19	−1.17455	−0.587275	−	0.809388i	$-0.699799\pi$
$947$	−2.60703e19	−1.17455	−0.587275	+	0.809388i	$0.699799\pi$
$948$	−1.74292e17	−0.00779872
$949$	−4.52706e18	−0.201180
$950$	−9.21246e17	−0.0406604
$951$	8.64421e16	0.00378924
$952$	2.30188e19	1.00217
$953$	−1.27014e19	−0.549220	−0.274610	−	0.961556i	$-0.588549\pi$
$953$	−1.27014e19	−0.549220	−0.274610	+	0.961556i	$0.588549\pi$
$954$	−3.01681e19	−1.29564
$955$	−9.09037e18	−0.387757
$956$	−2.12901e19	−0.901991
$957$	−1.51644e17	−0.00638111
$958$	8.40676e18	0.351361
$959$	3.62181e19	1.50350
$960$	−5.30926e16	−0.00218913
$961$	−1.83790e19	−0.752697
$962$	−1.06113e19	−0.431651
$963$	1.99691e18	0.0806842
$964$	4.44002e18	0.178190
$965$	−8.09221e18	−0.322581
$966$	−1.29061e18	−0.0511026
$967$	1.92177e19	0.755838	0.377919	−	0.925839i	$-0.376640\pi$
$967$	1.92177e19	0.755838	0.377919	+	0.925839i	$0.376640\pi$
$968$	8.22720e17	0.0321412
$969$	1.03971e17	0.00403466
$970$	−8.09610e18	−0.312075
$971$	3.52880e18	0.135114	0.0675572	−	0.997715i	$-0.478479\pi$
$971$	3.52880e18	0.135114	0.0675572	+	0.997715i	$0.478479\pi$
$972$	−1.09602e18	−0.0416856
$973$	2.06633e19	0.780668
$974$	−1.70746e19	−0.640793
$975$	2.12262e17	0.00791303
$976$	−7.79772e18	−0.288764
$977$	−4.58324e19	−1.68600	−0.843001	−	0.537911i	$-0.819213\pi$
$977$	−4.58324e19	−1.68600	−0.843001	+	0.537911i	$0.819213\pi$
$978$	4.79103e17	0.0175076
$979$	1.05958e19	0.384634
$980$	2.15229e19	0.776126
$981$	−6.23430e18	−0.223326
$982$	2.27330e19	0.808968
$983$	2.77192e18	0.0979903	0.0489951	−	0.998799i	$-0.484398\pi$
$983$	2.77192e18	0.0979903	0.0489951	+	0.998799i	$0.484398\pi$
$984$	−3.84638e17	−0.0135078
$985$	−1.79147e19	−0.624991
$986$	−2.36334e19	−0.819079
$987$	7.21154e17	0.0248294
$988$	6.56070e17	0.0224404
$989$	7.58384e19	2.57699
$990$	−3.97282e18	−0.134113
$991$	2.09483e19	0.702537	0.351269	−	0.936275i	$-0.385750\pi$
$991$	2.09483e19	0.702537	0.351269	+	0.936275i	$0.385750\pi$
$992$	−2.63855e18	−0.0879103
$993$	8.62621e17	0.0285529
$994$	4.54901e19	1.49591
$995$	−2.29434e19	−0.749563
$996$	2.35980e17	0.00765931
$997$	1.35572e19	0.437172	0.218586	−	0.975818i	$-0.429856\pi$
$997$	1.35572e19	0.437172	0.218586	+	0.975818i	$0.429856\pi$
$998$	3.19868e19	1.02476
$999$	−2.26382e18	−0.0720553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.14.a.c.1.2	✓	2
3.2	odd	2		198.14.a.a.1.1		2
4.3	odd	2		176.14.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.14.a.c.1.2	✓	2	1.1	even	1	trivial
176.14.a.c.1.1		2	4.3	odd	2
198.14.a.a.1.1		2	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} -35.1262 q^{3} +4096.00 q^{4} +21994.9 q^{5} -2248.08 q^{6} -579474. q^{7} +262144. q^{8} -1.59309e6 q^{9} +O(q^{10})\)	\(q+64.0000 q^{2} -35.1262 q^{3} +4096.00 q^{4} +21994.9 q^{5} -2248.08 q^{6} -579474. q^{7} +262144. q^{8} -1.59309e6 q^{9} +1.40768e6 q^{10} +1.77156e6 q^{11} -143877. q^{12} +8.20008e6 q^{13} -3.70864e7 q^{14} -772598. q^{15} +1.67772e7 q^{16} -1.51534e8 q^{17} -1.01958e8 q^{18} +1.95331e7 q^{19} +9.00913e7 q^{20} +2.03547e7 q^{21} +1.13380e8 q^{22} -9.90716e8 q^{23} -9.20812e6 q^{24} -7.36926e8 q^{25} +5.24805e8 q^{26} +1.11962e8 q^{27} -2.37353e9 q^{28} +2.43690e9 q^{29} -4.94463e7 q^{30} -2.45734e9 q^{31} +1.07374e9 q^{32} -6.22282e7 q^{33} -9.69815e9 q^{34} -1.27455e10 q^{35} -6.52529e9 q^{36} -2.02196e10 q^{37} +1.25012e9 q^{38} -2.88038e8 q^{39} +5.76584e9 q^{40} +4.17716e10 q^{41} +1.30270e9 q^{42} -7.65490e10 q^{43} +7.25631e9 q^{44} -3.50399e10 q^{45} -6.34058e10 q^{46} +3.54293e10 q^{47} -5.89320e8 q^{48} +2.38901e11 q^{49} -4.71632e10 q^{50} +5.32280e9 q^{51} +3.35875e10 q^{52} +2.95888e11 q^{53} +7.16554e9 q^{54} +3.89654e10 q^{55} -1.51906e11 q^{56} -6.86124e8 q^{57} +1.55961e11 q^{58} +3.47641e11 q^{59} -3.16456e9 q^{60} -4.64780e11 q^{61} -1.57270e11 q^{62} +9.23154e11 q^{63} +6.87195e10 q^{64} +1.80360e11 q^{65} -3.98260e9 q^{66} +6.09113e11 q^{67} -6.20682e11 q^{68} +3.48001e10 q^{69} -8.15712e11 q^{70} -1.22660e12 q^{71} -4.17619e11 q^{72} -5.52075e11 q^{73} -1.29405e12 q^{74} +2.58854e10 q^{75} +8.00077e10 q^{76} -1.02657e12 q^{77} -1.84344e10 q^{78} +1.21140e12 q^{79} +3.69014e11 q^{80} +2.53597e12 q^{81} +2.67338e12 q^{82} -1.64015e12 q^{83} +8.33729e10 q^{84} -3.33297e12 q^{85} -4.89914e12 q^{86} -8.55989e10 q^{87} +4.64404e11 q^{88} +5.98108e12 q^{89} -2.24255e12 q^{90} -4.75173e12 q^{91} -4.05797e12 q^{92} +8.63171e10 q^{93} +2.26748e12 q^{94} +4.29630e11 q^{95} -3.77165e10 q^{96} -5.75139e12 q^{97} +1.52897e13 q^{98} -2.82225e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9}+O(q^{10}) \) 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9	\( 2 q + 128 q^{2} - 926 q^{3} + 8192 q^{4} + 2914 q^{5} - 59264 q^{6} - 170560 q^{7} + 524288 q^{8} - 2393756 q^{9} + 186496 q^{10} + 3543122 q^{11} - 3792896 q^{12} - 6948916 q^{13} - 10915840 q^{14} + 16226114 q^{15} + 33554432 q^{16} - 280144288 q^{17} - 153200384 q^{18} - 349231788 q^{19} + 11935744 q^{20} - 343936280 q^{21} + 226759808 q^{22} - 151278294 q^{23} - 242745344 q^{24} - 1593546344 q^{25} - 444730624 q^{26} + 2245595374 q^{27} - 698613760 q^{28} - 771621928 q^{29} + 1038471296 q^{30} - 8626482070 q^{31} + 2147483648 q^{32} - 1640465486 q^{33} - 17929234432 q^{34} - 20547972800 q^{35} - 9804824576 q^{36} - 26333898490 q^{37} - 22350834432 q^{38} + 13207805428 q^{39} + 763887616 q^{40} - 3560991836 q^{41} - 22011921920 q^{42} - 16329995932 q^{43} + 14512627712 q^{44} - 19762426588 q^{45} - 9681810816 q^{46} + 9513351704 q^{47} - 15535702016 q^{48} + 309223257786 q^{49} - 101986966016 q^{50} + 119898691720 q^{51} - 28462759936 q^{52} + 291363898652 q^{53} + 143718103936 q^{54} + 5162328754 q^{55} - 44711280640 q^{56} + 327836886300 q^{57} - 49383803392 q^{58} + 712019011182 q^{59} + 66462162944 q^{60} + 138918582944 q^{61} - 552094852480 q^{62} + 595750060240 q^{63} + 137438953472 q^{64} + 469417380748 q^{65} - 104989791104 q^{66} + 912599195574 q^{67} - 1147471003648 q^{68} - 713033152350 q^{69} - 1315070259200 q^{70} - 1560848343722 q^{71} - 627508772864 q^{72} + 407382417996 q^{73} - 1685369503360 q^{74} + 789026369816 q^{75} - 1430453403648 q^{76} - 302157444160 q^{77} + 845299547392 q^{78} - 48102676468 q^{79} + 48888807424 q^{80} + 1911689036650 q^{81} - 227903477504 q^{82} - 6313820551012 q^{83} - 1408763002880 q^{84} - 878959681568 q^{85} - 1045119739648 q^{86} + 2772785468872 q^{87} + 928808173568 q^{88} + 977692325462 q^{89} - 1264795301632 q^{90} - 10946374648120 q^{91} - 619635892224 q^{92} + 5582240738434 q^{93} + 608854509056 q^{94} + 7466012570772 q^{95} - 994284929024 q^{96} - 1024977303502 q^{97} + 19790288498304 q^{98} - 4240684773116 q^{99}+O(q^{100}) \) 2 * q + 128 * q^2 - 926 * q^3 + 8192 * q^4 + 2914 * q^5 - 59264 * q^6 - 170560 * q^7 + 524288 * q^8 - 2393756 * q^9 + 186496 * q^10 + 3543122 * q^11 - 3792896 * q^12 - 6948916 * q^13 - 10915840 * q^14 + 16226114 * q^15 + 33554432 * q^16 - 280144288 * q^17 - 153200384 * q^18 - 349231788 * q^19 + 11935744 * q^20 - 343936280 * q^21 + 226759808 * q^22 - 151278294 * q^23 - 242745344 * q^24 - 1593546344 * q^25 - 444730624 * q^26 + 2245595374 * q^27 - 698613760 * q^28 - 771621928 * q^29 + 1038471296 * q^30 - 8626482070 * q^31 + 2147483648 * q^32 - 1640465486 * q^33 - 17929234432 * q^34 - 20547972800 * q^35 - 9804824576 * q^36 - 26333898490 * q^37 - 22350834432 * q^38 + 13207805428 * q^39 + 763887616 * q^40 - 3560991836 * q^41 - 22011921920 * q^42 - 16329995932 * q^43 + 14512627712 * q^44 - 19762426588 * q^45 - 9681810816 * q^46 + 9513351704 * q^47 - 15535702016 * q^48 + 309223257786 * q^49 - 101986966016 * q^50 + 119898691720 * q^51 - 28462759936 * q^52 + 291363898652 * q^53 + 143718103936 * q^54 + 5162328754 * q^55 - 44711280640 * q^56 + 327836886300 * q^57 - 49383803392 * q^58 + 712019011182 * q^59 + 66462162944 * q^60 + 138918582944 * q^61 - 552094852480 * q^62 + 595750060240 * q^63 + 137438953472 * q^64 + 469417380748 * q^65 - 104989791104 * q^66 + 912599195574 * q^67 - 1147471003648 * q^68 - 713033152350 * q^69 - 1315070259200 * q^70 - 1560848343722 * q^71 - 627508772864 * q^72 + 407382417996 * q^73 - 1685369503360 * q^74 + 789026369816 * q^75 - 1430453403648 * q^76 - 302157444160 * q^77 + 845299547392 * q^78 - 48102676468 * q^79 + 48888807424 * q^80 + 1911689036650 * q^81 - 227903477504 * q^82 - 6313820551012 * q^83 - 1408763002880 * q^84 - 878959681568 * q^85 - 1045119739648 * q^86 + 2772785468872 * q^87 + 928808173568 * q^88 + 977692325462 * q^89 - 1264795301632 * q^90 - 10946374648120 * q^91 - 619635892224 * q^92 + 5582240738434 * q^93 + 608854509056 * q^94 + 7466012570772 * q^95 - 994284929024 * q^96 - 1024977303502 * q^97 + 19790288498304 * q^98 - 4240684773116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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