LMFDB - Embedded newform 547.8.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,8,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	547.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:	$170.874608940$
Analytic rank:	$0$
Dimension:	$162$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-20.7005 q^{2} -6.00300 q^{3} +300.512 q^{4} -17.8219 q^{5} +124.265 q^{6} -716.757 q^{7} -3571.08 q^{8} -2150.96 q^{9} +O(q^{10})$	\(q-20.7005 q^{2} -6.00300 q^{3} +300.512 q^{4} -17.8219 q^{5} +124.265 q^{6} -716.757 q^{7} -3571.08 q^{8} -2150.96 q^{9} +368.922 q^{10} +1777.09 q^{11} -1803.97 q^{12} -1298.78 q^{13} +14837.2 q^{14} +106.985 q^{15} +35457.7 q^{16} +6325.65 q^{17} +44526.1 q^{18} +36052.6 q^{19} -5355.68 q^{20} +4302.69 q^{21} -36786.6 q^{22} -34449.3 q^{23} +21437.2 q^{24} -77807.4 q^{25} +26885.3 q^{26} +26040.8 q^{27} -215394. q^{28} +68682.0 q^{29} -2214.64 q^{30} -251838. q^{31} -276895. q^{32} -10667.8 q^{33} -130944. q^{34} +12774.0 q^{35} -646390. q^{36} +84364.6 q^{37} -746309. q^{38} +7796.55 q^{39} +63643.3 q^{40} -98358.4 q^{41} -89068.0 q^{42} +335552. q^{43} +534035. q^{44} +38334.2 q^{45} +713119. q^{46} -1.28202e6 q^{47} -212853. q^{48} -309802. q^{49} +1.61065e6 q^{50} -37972.9 q^{51} -390297. q^{52} +1.04793e6 q^{53} -539058. q^{54} -31671.0 q^{55} +2.55960e6 q^{56} -216424. q^{57} -1.42175e6 q^{58} -1.20771e6 q^{59} +32150.2 q^{60} +2.87252e6 q^{61} +5.21318e6 q^{62} +1.54172e6 q^{63} +1.19329e6 q^{64} +23146.6 q^{65} +220830. q^{66} +1.24337e6 q^{67} +1.90093e6 q^{68} +206799. q^{69} -264428. q^{70} -4.90253e6 q^{71} +7.68126e6 q^{72} +4.25527e6 q^{73} -1.74639e6 q^{74} +467078. q^{75} +1.08342e7 q^{76} -1.27374e6 q^{77} -161393. q^{78} -4.82312e6 q^{79} -631923. q^{80} +4.54784e6 q^{81} +2.03607e6 q^{82} -8.43522e6 q^{83} +1.29301e6 q^{84} -112735. q^{85} -6.94609e6 q^{86} -412298. q^{87} -6.34612e6 q^{88} +366189. q^{89} -793538. q^{90} +930907. q^{91} -1.03524e7 q^{92} +1.51178e6 q^{93} +2.65385e7 q^{94} -642526. q^{95} +1.66220e6 q^{96} -1.20679e7 q^{97} +6.41307e6 q^{98} -3.82245e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) $ 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * 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 $

$2$	−20.7005	−1.82968	−0.914842	−	0.403811i	$-0.867685\pi$
$2$	−20.7005	−1.82968	−0.914842	+	0.403811i	$0.867685\pi$
$3$	−6.00300	−0.128364	−0.0641821	−	0.997938i	$-0.520444\pi$
$3$	−6.00300	−0.128364	−0.0641821	+	0.997938i	$0.520444\pi$
$4$	300.512	2.34775
$5$	−17.8219	−0.0637615	−0.0318807	−	0.999492i	$-0.510150\pi$
$5$	−17.8219	−0.0637615	−0.0318807	+	0.999492i	$0.510150\pi$
$6$	124.265	0.234866
$7$	−716.757	−0.789821	−0.394911	−	0.918719i	$-0.629224\pi$
$7$	−716.757	−0.789821	−0.394911	+	0.918719i	$0.629224\pi$
$8$	−3571.08	−2.46595
$9$	−2150.96	−0.983523
$10$	368.922	0.116663
$11$	1777.09	0.402563	0.201282	−	0.979533i	$-0.435489\pi$
$11$	1777.09	0.402563	0.201282	+	0.979533i	$0.435489\pi$
$12$	−1803.97	−0.301367
$13$	−1298.78	−0.163958	−0.0819790	−	0.996634i	$-0.526124\pi$
$13$	−1298.78	−0.163958	−0.0819790	+	0.996634i	$0.526124\pi$
$14$	14837.2	1.44512
$15$	106.985	0.00818469
$16$	35457.7	2.16417
$17$	6325.65	0.312273	0.156136	−	0.987736i	$-0.450096\pi$
$17$	6325.65	0.312273	0.156136	+	0.987736i	$0.450096\pi$
$18$	44526.1	1.79954
$19$	36052.6	1.20587	0.602934	−	0.797791i	$-0.293998\pi$
$19$	36052.6	1.20587	0.602934	+	0.797791i	$0.293998\pi$
$20$	−5355.68	−0.149696
$21$	4302.69	0.101385
$22$	−36786.6	−0.736564
$23$	−34449.3	−0.590382	−0.295191	−	0.955438i	$-0.595383\pi$
$23$	−34449.3	−0.590382	−0.295191	+	0.955438i	$0.595383\pi$
$24$	21437.2	0.316540
$25$	−77807.4	−0.995934
$26$	26885.3	0.299991
$27$	26040.8	0.254613
$28$	−215394.	−1.85430
$29$	68682.0	0.522938	0.261469	−	0.965212i	$-0.415793\pi$
$29$	68682.0	0.522938	0.261469	+	0.965212i	$0.415793\pi$
$30$	−2214.64	−0.0149754
$31$	−251838.	−1.51829	−0.759146	−	0.650920i	$-0.774383\pi$
$31$	−251838.	−1.51829	−0.759146	+	0.650920i	$0.774383\pi$
$32$	−276895.	−1.49379
$33$	−10667.8	−0.0516747
$34$	−130944.	−0.571360
$35$	12774.0	0.0503602
$36$	−646390.	−2.30906
$37$	84364.6	0.273813	0.136907	−	0.990584i	$-0.456284\pi$
$37$	84364.6	0.273813	0.136907	+	0.990584i	$0.456284\pi$
$38$	−746309.	−2.20636
$39$	7796.55	0.0210463
$40$	63643.3	0.157233
$41$	−98358.4	−0.222878	−0.111439	−	0.993771i	$-0.535546\pi$
$41$	−98358.4	−0.222878	−0.111439	+	0.993771i	$0.535546\pi$
$42$	−89068.0	−0.185502
$43$	335552.	0.643605	0.321803	−	0.946807i	$-0.395711\pi$
$43$	335552.	0.643605	0.321803	+	0.946807i	$0.395711\pi$
$44$	534035.	0.945116
$45$	38334.2	0.0627109
$46$	713119.	1.08021
$47$	−1.28202e6	−1.80116	−0.900579	−	0.434691i	$-0.856857\pi$
$47$	−1.28202e6	−1.80116	−0.900579	+	0.434691i	$0.856857\pi$
$48$	−212853.	−0.277802
$49$	−309802.	−0.376182
$50$	1.61065e6	1.82225
$51$	−37972.9	−0.0400846
$52$	−390297.	−0.384932
$53$	1.04793e6	0.966865	0.483432	−	0.875382i	$-0.339390\pi$
$53$	1.04793e6	0.966865	0.483432	+	0.875382i	$0.339390\pi$
$54$	−539058.	−0.465862
$55$	−31671.0	−0.0256680
$56$	2.55960e6	1.94766
$57$	−216424.	−0.154790
$58$	−1.42175e6	−0.956812
$59$	−1.20771e6	−0.765560	−0.382780	−	0.923839i	$-0.625033\pi$
$59$	−1.20771e6	−0.765560	−0.382780	+	0.923839i	$0.625033\pi$
$60$	32150.2	0.0192156
$61$	2.87252e6	1.62035	0.810176	−	0.586187i	$-0.199372\pi$
$61$	2.87252e6	1.62035	0.810176	+	0.586187i	$0.199372\pi$
$62$	5.21318e6	2.77800
$63$	1.54172e6	0.776807
$64$	1.19329e6	0.569004
$65$	23146.6	0.0104542
$66$	220830.	0.0945484
$67$	1.24337e6	0.505053	0.252526	−	0.967590i	$-0.418739\pi$
$67$	1.24337e6	0.505053	0.252526	+	0.967590i	$0.418739\pi$
$68$	1.90093e6	0.733137
$69$	206799.	0.0757840
$70$	−264428.	−0.0921433
$71$	−4.90253e6	−1.62561	−0.812805	−	0.582536i	$-0.802061\pi$
$71$	−4.90253e6	−1.62561	−0.812805	+	0.582536i	$0.802061\pi$
$72$	7.68126e6	2.42532
$73$	4.25527e6	1.28026	0.640129	−	0.768268i	$-0.278881\pi$
$73$	4.25527e6	1.28026	0.640129	+	0.768268i	$0.278881\pi$
$74$	−1.74639e6	−0.500992
$75$	467078.	0.127842
$76$	1.08342e7	2.83107
$77$	−1.27374e6	−0.317953
$78$	−161393.	−0.0385082
$79$	−4.82312e6	−1.10061	−0.550305	−	0.834964i	$-0.685489\pi$
$79$	−4.82312e6	−1.10061	−0.550305	+	0.834964i	$0.685489\pi$
$80$	−631923.	−0.137991
$81$	4.54784e6	0.950839
$82$	2.03607e6	0.407797
$83$	−8.43522e6	−1.61928	−0.809642	−	0.586924i	$-0.800339\pi$
$83$	−8.43522e6	−1.61928	−0.809642	+	0.586924i	$0.800339\pi$
$84$	1.29301e6	0.238026
$85$	−112735.	−0.0199110
$86$	−6.94609e6	−1.17759
$87$	−412298.	−0.0671265
$88$	−6.34612e6	−0.992701
$89$	366189.	0.0550604	0.0275302	−	0.999621i	$-0.491236\pi$
$89$	366189.	0.0550604	0.0275302	+	0.999621i	$0.491236\pi$
$90$	−793538.	−0.114741
$91$	930907.	0.129497
$92$	−1.03524e7	−1.38607
$93$	1.51178e6	0.194894
$94$	2.65385e7	3.29555
$95$	−642526.	−0.0768879
$96$	1.66220e6	0.191750
$97$	−1.20679e7	−1.34256	−0.671278	−	0.741206i	$-0.734254\pi$
$97$	−1.20679e7	−1.34256	−0.671278	+	0.741206i	$0.734254\pi$
$98$	6.41307e6	0.688295
$99$	−3.82245e6	−0.395930
$100$	−2.33820e7	−2.33820
$101$	3.93278e6	0.379818	0.189909	−	0.981802i	$-0.439181\pi$
$101$	3.93278e6	0.379818	0.189909	+	0.981802i	$0.439181\pi$
$102$	786058.	0.0733422
$103$	−400641.	−0.0361264	−0.0180632	−	0.999837i	$-0.505750\pi$
$103$	−400641.	−0.0361264	−0.0180632	+	0.999837i	$0.505750\pi$
$104$	4.63803e6	0.404312
$105$	−76682.1	−0.00646445
$106$	−2.16927e7	−1.76906
$107$	2.11634e7	1.67010	0.835051	−	0.550172i	$-0.185438\pi$
$107$	2.11634e7	1.67010	0.835051	+	0.550172i	$0.185438\pi$
$108$	7.82556e6	0.597768
$109$	−1.63565e7	−1.20975	−0.604877	−	0.796319i	$-0.706778\pi$
$109$	−1.63565e7	−1.20975	−0.604877	+	0.796319i	$0.706778\pi$
$110$	655606.	0.0469644
$111$	−506441.	−0.0351478
$112$	−2.54146e7	−1.70931
$113$	1.30607e7	0.851512	0.425756	−	0.904838i	$-0.360008\pi$
$113$	1.30607e7	0.851512	0.425756	+	0.904838i	$0.360008\pi$
$114$	4.48009e6	0.283217
$115$	613952.	0.0376436
$116$	2.06397e7	1.22773
$117$	2.79362e6	0.161256
$118$	2.50002e7	1.40073
$119$	−4.53395e6	−0.246640
$120$	−382051.	−0.0201831
$121$	−1.63291e7	−0.837943
$122$	−5.94627e7	−2.96473
$123$	590446.	0.0286096
$124$	−7.56803e7	−3.56457
$125$	2.77901e6	0.127264
$126$	−3.19144e7	−1.42131
$127$	−2.34683e6	−0.101664	−0.0508322	−	0.998707i	$-0.516187\pi$
$127$	−2.34683e6	−0.101664	−0.0508322	+	0.998707i	$0.516187\pi$
$128$	1.07409e7	0.452696
$129$	−2.01432e6	−0.0826159
$130$	−479147.	−0.0191279
$131$	−4.45694e7	−1.73216	−0.866079	−	0.499907i	$-0.833367\pi$
$131$	−4.45694e7	−1.73216	−0.866079	+	0.499907i	$0.833367\pi$
$132$	−3.20581e6	−0.121319
$133$	−2.58410e7	−0.952420
$134$	−2.57383e7	−0.924088
$135$	−464096.	−0.0162345
$136$	−2.25894e7	−0.770049
$137$	−2.43360e7	−0.808588	−0.404294	−	0.914629i	$-0.632483\pi$
$137$	−2.43360e7	−0.808588	−0.404294	+	0.914629i	$0.632483\pi$
$138$	−4.28085e6	−0.138661
$139$	1.72514e7	0.544844	0.272422	−	0.962178i	$-0.412175\pi$
$139$	1.72514e7	0.544844	0.272422	+	0.962178i	$0.412175\pi$
$140$	3.83872e6	0.118233
$141$	7.69596e6	0.231204
$142$	1.01485e8	2.97435
$143$	−2.30804e6	−0.0660034
$144$	−7.62683e7	−2.12851
$145$	−1.22404e6	−0.0333433
$146$	−8.80863e7	−2.34247
$147$	1.85974e6	0.0482883
$148$	2.53525e7	0.642844
$149$	−2.04261e7	−0.505864	−0.252932	−	0.967484i	$-0.581395\pi$
$149$	−2.04261e7	−0.505864	−0.252932	+	0.967484i	$0.581395\pi$
$150$	−9.66875e6	−0.233911
$151$	−5.71480e7	−1.35077	−0.675386	−	0.737465i	$-0.736023\pi$
$151$	−5.71480e7	−1.35077	−0.675386	+	0.737465i	$0.736023\pi$
$152$	−1.28747e8	−2.97361
$153$	−1.36062e7	−0.307127
$154$	2.63671e7	0.581754
$155$	4.48823e6	0.0968086
$156$	2.34295e6	0.0494115
$157$	−5.31641e7	−1.09640	−0.548201	−	0.836347i	$-0.684687\pi$
$157$	−5.31641e7	−1.09640	−0.548201	+	0.836347i	$0.684687\pi$
$158$	9.98412e7	2.01377
$159$	−6.29071e6	−0.124111
$160$	4.93479e6	0.0952465
$161$	2.46918e7	0.466297
$162$	−9.41426e7	−1.73974
$163$	−6.83854e7	−1.23682	−0.618410	−	0.785855i	$-0.712223\pi$
$163$	−6.83854e7	−1.23682	−0.618410	+	0.785855i	$0.712223\pi$
$164$	−2.95578e7	−0.523262
$165$	190121.	0.00329486
$166$	1.74613e8	2.96278
$167$	9.64575e7	1.60261	0.801306	−	0.598255i	$-0.204139\pi$
$167$	9.64575e7	1.60261	0.801306	+	0.598255i	$0.204139\pi$
$168$	−1.53653e7	−0.250010
$169$	−6.10617e7	−0.973118
$170$	2.33367e6	0.0364308
$171$	−7.75479e7	−1.18600
$172$	1.00837e8	1.51102
$173$	−4.16330e7	−0.611331	−0.305666	−	0.952139i	$-0.598879\pi$
$173$	−4.16330e7	−0.611331	−0.305666	+	0.952139i	$0.598879\pi$
$174$	8.53479e6	0.122820
$175$	5.57690e7	0.786610
$176$	6.30114e7	0.871214
$177$	7.24987e6	0.0982706
$178$	−7.58029e6	−0.100743
$179$	9.04886e7	1.17926	0.589628	−	0.807675i	$-0.299274\pi$
$179$	9.04886e7	1.17926	0.589628	+	0.807675i	$0.299274\pi$
$180$	1.15199e7	0.147229
$181$	−1.38527e7	−0.173644	−0.0868221	−	0.996224i	$-0.527671\pi$
$181$	−1.38527e7	−0.173644	−0.0868221	+	0.996224i	$0.527671\pi$
$182$	−1.92703e7	−0.236940
$183$	−1.72438e7	−0.207995
$184$	1.23021e8	1.45585
$185$	−1.50353e6	−0.0174587
$186$	−3.12947e7	−0.356595
$187$	1.12412e7	0.125709
$188$	−3.85262e8	−4.22866
$189$	−1.86649e7	−0.201099
$190$	1.33006e7	0.140681
$191$	1.75520e8	1.82268	0.911340	−	0.411654i	$-0.135049\pi$
$191$	1.75520e8	1.82268	0.911340	+	0.411654i	$0.135049\pi$
$192$	−7.16330e6	−0.0730397
$193$	−5.10034e7	−0.510680	−0.255340	−	0.966851i	$-0.582187\pi$
$193$	−5.10034e7	−0.510680	−0.255340	+	0.966851i	$0.582187\pi$
$194$	2.49813e8	2.45645
$195$	−138949.	−0.00134195
$196$	−9.30991e7	−0.883180
$197$	1.98761e8	1.85225	0.926125	−	0.377218i	$-0.123119\pi$
$197$	1.98761e8	1.85225	0.926125	+	0.377218i	$0.123119\pi$
$198$	7.91267e7	0.724427
$199$	−9.99383e7	−0.898972	−0.449486	−	0.893287i	$-0.648393\pi$
$199$	−9.99383e7	−0.898972	−0.449486	+	0.893287i	$0.648393\pi$
$200$	2.77856e8	2.45593
$201$	−7.46392e6	−0.0648307
$202$	−8.14106e7	−0.694947
$203$	−4.92283e7	−0.413028
$204$	−1.14113e7	−0.0941086
$205$	1.75293e6	0.0142111
$206$	8.29347e6	0.0660999
$207$	7.40993e7	0.580654
$208$	−4.60516e7	−0.354832
$209$	6.40687e7	0.485438
$210$	1.58736e6	0.0118279
$211$	−1.64867e8	−1.20822	−0.604110	−	0.796901i	$-0.706471\pi$
$211$	−1.64867e8	−1.20822	−0.604110	+	0.796901i	$0.706471\pi$
$212$	3.14914e8	2.26995
$213$	2.94299e7	0.208670
$214$	−4.38094e8	−3.05576
$215$	−5.98016e6	−0.0410372
$216$	−9.29938e7	−0.627864
$217$	1.80507e8	1.19918
$218$	3.38588e8	2.21347
$219$	−2.55444e7	−0.164339
$220$	−9.51750e6	−0.0602620
$221$	−8.21560e6	−0.0511996
$222$	1.04836e7	0.0643094
$223$	2.01630e7	0.121756	0.0608778	−	0.998145i	$-0.480610\pi$
$223$	2.01630e7	0.121756	0.0608778	+	0.998145i	$0.480610\pi$
$224$	1.98467e8	1.17983
$225$	1.67361e8	0.979524
$226$	−2.70363e8	−1.55800
$227$	1.78238e7	0.101137	0.0505683	−	0.998721i	$-0.483897\pi$
$227$	1.78238e7	0.101137	0.0505683	+	0.998721i	$0.483897\pi$
$228$	−6.50379e7	−0.363408
$229$	−4.30709e7	−0.237006	−0.118503	−	0.992954i	$-0.537810\pi$
$229$	−4.30709e7	−0.237006	−0.118503	+	0.992954i	$0.537810\pi$
$230$	−1.27091e7	−0.0688760
$231$	7.64626e6	0.0408138
$232$	−2.45269e8	−1.28954
$233$	−2.72630e8	−1.41198	−0.705989	−	0.708223i	$-0.749497\pi$
$233$	−2.72630e8	−1.41198	−0.705989	+	0.708223i	$0.749497\pi$
$234$	−5.78294e7	−0.295048
$235$	2.28480e7	0.114845
$236$	−3.62930e8	−1.79734
$237$	2.89532e7	0.141279
$238$	9.38552e7	0.451273
$239$	1.11230e8	0.527022	0.263511	−	0.964656i	$-0.415120\pi$
$239$	1.11230e8	0.527022	0.263511	+	0.964656i	$0.415120\pi$
$240$	3.79344e6	0.0177131
$241$	9.95976e7	0.458342	0.229171	−	0.973386i	$-0.426399\pi$
$241$	9.95976e7	0.458342	0.229171	+	0.973386i	$0.426399\pi$
$242$	3.38022e8	1.53317
$243$	−8.42519e7	−0.376667
$244$	8.63227e8	3.80417
$245$	5.52125e6	0.0239859
$246$	−1.22225e7	−0.0523466
$247$	−4.68243e7	−0.197711
$248$	8.99334e8	3.74404
$249$	5.06366e7	0.207858
$250$	−5.75269e7	−0.232853
$251$	−1.48045e8	−0.590930	−0.295465	−	0.955354i	$-0.595475\pi$
$251$	−1.48045e8	−0.590930	−0.295465	+	0.955354i	$0.595475\pi$
$252$	4.63304e8	1.82375
$253$	−6.12194e7	−0.237666
$254$	4.85806e7	0.186014
$255$	676748.	0.00255586
$256$	−3.75084e8	−1.39730
$257$	−2.14655e8	−0.788816	−0.394408	−	0.918935i	$-0.629050\pi$
$257$	−2.14655e8	−0.788816	−0.394408	+	0.918935i	$0.629050\pi$
$258$	4.16974e7	0.151161
$259$	−6.04689e7	−0.216263
$260$	6.95583e6	0.0245438
$261$	−1.47733e8	−0.514321
$262$	9.22610e8	3.16930
$263$	2.09869e8	0.711383	0.355691	−	0.934603i	$-0.384245\pi$
$263$	2.09869e8	0.711383	0.355691	+	0.934603i	$0.384245\pi$
$264$	3.80957e7	0.127427
$265$	−1.86760e7	−0.0616487
$266$	5.34922e8	1.74263
$267$	−2.19823e6	−0.00706779
$268$	3.73646e8	1.18574
$269$	−1.58744e8	−0.497237	−0.248619	−	0.968601i	$-0.579977\pi$
$269$	−1.58744e8	−0.497237	−0.248619	+	0.968601i	$0.579977\pi$
$270$	9.60703e6	0.0297041
$271$	−1.85359e8	−0.565744	−0.282872	−	0.959158i	$-0.591287\pi$
$271$	−1.85359e8	−0.565744	−0.282872	+	0.959158i	$0.591287\pi$
$272$	2.24293e8	0.675810
$273$	−5.58823e6	−0.0166228
$274$	5.03768e8	1.47946
$275$	−1.38270e8	−0.400927
$276$	6.21456e7	0.177922
$277$	−5.08774e8	−1.43829	−0.719144	−	0.694861i	$-0.755466\pi$
$277$	−5.08774e8	−1.43829	−0.719144	+	0.694861i	$0.755466\pi$
$278$	−3.57113e8	−0.996893
$279$	5.41695e8	1.49328
$280$	−4.56168e7	−0.124186
$281$	1.78809e8	0.480749	0.240374	−	0.970680i	$-0.422730\pi$
$281$	1.78809e8	0.480749	0.240374	+	0.970680i	$0.422730\pi$
$282$	−1.59310e8	−0.423031
$283$	7.29154e8	1.91235	0.956173	−	0.292802i	$-0.0945877\pi$
$283$	7.29154e8	1.91235	0.956173	+	0.292802i	$0.0945877\pi$
$284$	−1.47327e9	−3.81652
$285$	3.85708e6	0.00986965
$286$	4.77775e7	0.120765
$287$	7.04991e7	0.176034
$288$	5.95592e8	1.46918
$289$	−3.70325e8	−0.902486
$290$	2.53383e7	0.0610077
$291$	7.24439e7	0.172336
$292$	1.27876e9	3.00572
$293$	2.48193e8	0.576438	0.288219	−	0.957564i	$-0.406937\pi$
$293$	2.48193e8	0.576438	0.288219	+	0.957564i	$0.406937\pi$
$294$	−3.84976e7	−0.0883524
$295$	2.15236e7	0.0488133
$296$	−3.01273e8	−0.675210
$297$	4.62767e7	0.102498
$298$	4.22831e8	0.925571
$299$	4.47419e7	0.0967978
$300$	1.40362e8	0.300141
$301$	−2.40509e8	−0.508333
$302$	1.18299e9	2.47149
$303$	−2.36085e7	−0.0487550
$304$	1.27834e9	2.60970
$305$	−5.11938e7	−0.103316
$306$	2.81656e8	0.561946
$307$	4.79497e8	0.945805	0.472902	−	0.881115i	$-0.343206\pi$
$307$	4.79497e8	0.945805	0.472902	+	0.881115i	$0.343206\pi$
$308$	−3.82773e8	−0.746473
$309$	2.40505e6	0.00463734
$310$	−9.29086e7	−0.177129
$311$	6.88864e8	1.29859	0.649296	−	0.760536i	$-0.275064\pi$
$311$	6.88864e8	1.29859	0.649296	+	0.760536i	$0.275064\pi$
$312$	−2.78421e7	−0.0518992
$313$	7.82333e8	1.44207	0.721035	−	0.692899i	$-0.243667\pi$
$313$	7.82333e8	1.44207	0.721035	+	0.692899i	$0.243667\pi$
$314$	1.10052e9	2.00607
$315$	−2.74763e7	−0.0495304
$316$	−1.44940e9	−2.58395
$317$	−8.47658e7	−0.149456	−0.0747280	−	0.997204i	$-0.523809\pi$
$317$	−8.47658e7	−0.149456	−0.0747280	+	0.997204i	$0.523809\pi$
$318$	1.30221e8	0.227084
$319$	1.22054e8	0.210516
$320$	−2.12666e7	−0.0362805
$321$	−1.27044e8	−0.214381
$322$	−5.11133e8	−0.853176
$323$	2.28056e8	0.376559
$324$	1.36668e9	2.23233
$325$	1.01054e8	0.163291
$326$	1.41561e9	2.26299
$327$	9.81880e7	0.155289
$328$	3.51246e8	0.549607
$329$	9.18896e8	1.42259
$330$	−3.93561e6	−0.00602855
$331$	−4.08868e8	−0.619705	−0.309853	−	0.950785i	$-0.600280\pi$
$331$	−4.08868e8	−0.619705	−0.309853	+	0.950785i	$0.600280\pi$
$332$	−2.53488e9	−3.80167
$333$	−1.81465e8	−0.269301
$334$	−1.99672e9	−2.93227
$335$	−2.21591e7	−0.0322029
$336$	1.52564e8	0.219414
$337$	6.91183e8	0.983759	0.491879	−	0.870663i	$-0.336310\pi$
$337$	6.91183e8	0.983759	0.491879	+	0.870663i	$0.336310\pi$
$338$	1.26401e9	1.78050
$339$	−7.84032e7	−0.109304
$340$	−3.38781e7	−0.0467459
$341$	−4.47538e8	−0.611209
$342$	1.60528e9	2.17000
$343$	8.12333e8	1.08694
$344$	−1.19828e9	−1.58710
$345$	−3.68555e6	−0.00483210
$346$	8.61826e8	1.11854
$347$	−3.45081e8	−0.443371	−0.221686	−	0.975118i	$-0.571156\pi$
$347$	−3.45081e8	−0.443371	−0.221686	+	0.975118i	$0.571156\pi$
$348$	−1.23900e8	−0.157596
$349$	−9.86760e7	−0.124257	−0.0621287	−	0.998068i	$-0.519789\pi$
$349$	−9.86760e7	−0.124257	−0.0621287	+	0.998068i	$0.519789\pi$
$350$	−1.15445e9	−1.43925
$351$	−3.38212e7	−0.0417459
$352$	−4.92067e8	−0.601346
$353$	−6.23237e8	−0.754123	−0.377061	−	0.926188i	$-0.623065\pi$
$353$	−6.23237e8	−0.754123	−0.377061	+	0.926188i	$0.623065\pi$
$354$	−1.50076e8	−0.179804
$355$	8.73723e7	0.103651
$356$	1.10044e8	0.129268
$357$	2.72173e7	0.0316597
$358$	−1.87316e9	−2.15767
$359$	1.32003e9	1.50576	0.752878	−	0.658160i	$-0.228665\pi$
$359$	1.32003e9	1.50576	0.752878	+	0.658160i	$0.228665\pi$
$360$	−1.36895e8	−0.154642
$361$	4.05921e8	0.454116
$362$	2.86759e8	0.317714
$363$	9.80238e7	0.107562
$364$	2.79748e8	0.304027
$365$	−7.58369e7	−0.0816311
$366$	3.56955e8	0.380566
$367$	−6.02380e8	−0.636120	−0.318060	−	0.948071i	$-0.603031\pi$
$367$	−6.02380e8	−0.636120	−0.318060	+	0.948071i	$0.603031\pi$
$368$	−1.22149e9	−1.27769
$369$	2.11565e8	0.219206
$370$	3.11240e7	0.0319440
$371$	−7.51110e8	−0.763651
$372$	4.54309e8	0.457563
$373$	8.94592e8	0.892573	0.446287	−	0.894890i	$-0.352746\pi$
$373$	8.94592e8	0.892573	0.446287	+	0.894890i	$0.352746\pi$
$374$	−2.32699e8	−0.230009
$375$	−1.66824e7	−0.0163361
$376$	4.57819e9	4.44157
$377$	−8.92026e7	−0.0857398
$378$	3.86374e8	0.367948
$379$	6.48576e8	0.611961	0.305981	−	0.952038i	$-0.401016\pi$
$379$	6.48576e8	0.611961	0.305981	+	0.952038i	$0.401016\pi$
$380$	−1.93086e8	−0.180513
$381$	1.40880e7	0.0130501
$382$	−3.63336e9	−3.33493
$383$	−1.71921e9	−1.56363	−0.781813	−	0.623512i	$-0.785705\pi$
$383$	−1.71921e9	−1.56363	−0.781813	+	0.623512i	$0.785705\pi$
$384$	−6.44778e7	−0.0581100
$385$	2.27004e7	0.0202732
$386$	1.05580e9	0.934383
$387$	−7.21759e8	−0.633000
$388$	−3.62656e9	−3.15198
$389$	2.67897e8	0.230751	0.115375	−	0.993322i	$-0.463193\pi$
$389$	2.67897e8	0.230751	0.115375	+	0.993322i	$0.463193\pi$
$390$	2.87632e6	0.00245534
$391$	−2.17914e8	−0.184360
$392$	1.10633e9	0.927647
$393$	2.67550e8	0.222347
$394$	−4.11446e9	−3.38903
$395$	8.59571e7	0.0701765
$396$	−1.14869e9	−0.929543
$397$	−1.54354e9	−1.23809	−0.619043	−	0.785357i	$-0.712479\pi$
$397$	−1.54354e9	−1.23809	−0.619043	+	0.785357i	$0.712479\pi$
$398$	2.06878e9	1.64484
$399$	1.55123e8	0.122257
$400$	−2.75887e9	−2.15537
$401$	−1.78716e9	−1.38407	−0.692033	−	0.721866i	$-0.743285\pi$
$401$	−1.78716e9	−1.38407	−0.692033	+	0.721866i	$0.743285\pi$
$402$	1.54507e8	0.118620
$403$	3.27081e8	0.248936
$404$	1.18185e9	0.891716
$405$	−8.10510e7	−0.0606269
$406$	1.01905e9	0.755710
$407$	1.49923e8	0.110227
$408$	1.35604e8	0.0988468
$409$	1.53259e9	1.10763	0.553816	−	0.832639i	$-0.313171\pi$
$409$	1.53259e9	1.10763	0.553816	+	0.832639i	$0.313171\pi$
$410$	−3.62866e7	−0.0260018
$411$	1.46089e8	0.103794
$412$	−1.20397e8	−0.0848156
$413$	8.65633e8	0.604656
$414$	−1.53389e9	−1.06241
$415$	1.50331e8	0.103248
$416$	3.59625e8	0.244919
$417$	−1.03560e8	−0.0699385
$418$	−1.32625e9	−0.888198
$419$	8.47946e8	0.563143	0.281572	−	0.959540i	$-0.409144\pi$
$419$	8.47946e8	0.563143	0.281572	+	0.959540i	$0.409144\pi$
$420$	−2.30439e7	−0.0151769
$421$	−7.60143e8	−0.496487	−0.248244	−	0.968698i	$-0.579853\pi$
$421$	−7.60143e8	−0.496487	−0.248244	+	0.968698i	$0.579853\pi$
$422$	3.41284e9	2.21066
$423$	2.75758e9	1.77148
$424$	−3.74223e9	−2.38424
$425$	−4.92182e8	−0.311003
$426$	−6.09215e8	−0.381801
$427$	−2.05890e9	−1.27979
$428$	6.35986e9	3.92098
$429$	1.38551e7	0.00847248
$430$	1.23792e8	0.0750852
$431$	2.79095e9	1.67912	0.839561	−	0.543266i	$-0.182812\pi$
$431$	2.79095e9	1.67912	0.839561	+	0.543266i	$0.182812\pi$
$432$	9.23348e8	0.551026
$433$	3.08366e9	1.82540	0.912700	−	0.408630i	$-0.133993\pi$
$433$	3.08366e9	1.82540	0.912700	+	0.408630i	$0.133993\pi$
$434$	−3.73658e9	−2.19412
$435$	7.34793e6	0.00428009
$436$	−4.91531e9	−2.84020
$437$	−1.24199e9	−0.711923
$438$	5.28782e8	0.300689
$439$	−2.53061e9	−1.42758	−0.713790	−	0.700360i	$-0.753023\pi$
$439$	−2.53061e9	−1.42758	−0.713790	+	0.700360i	$0.753023\pi$
$440$	1.13100e8	0.0632961
$441$	6.66373e8	0.369984
$442$	1.70067e8	0.0936791
$443$	−4.18815e8	−0.228881	−0.114440	−	0.993430i	$-0.536507\pi$
$443$	−4.18815e8	−0.228881	−0.114440	+	0.993430i	$0.536507\pi$
$444$	−1.52191e8	−0.0825181
$445$	−6.52617e6	−0.00351074
$446$	−4.17385e8	−0.222774
$447$	1.22618e8	0.0649348
$448$	−8.55297e8	−0.449411
$449$	−3.33240e9	−1.73738	−0.868690	−	0.495357i	$-0.835037\pi$
$449$	−3.33240e9	−1.73738	−0.868690	+	0.495357i	$0.835037\pi$
$450$	−3.46446e9	−1.79222
$451$	−1.74791e8	−0.0897226
$452$	3.92488e9	1.99913
$453$	3.43060e8	0.173391
$454$	−3.68961e8	−0.185048
$455$	−1.65905e7	−0.00825695
$456$	7.72868e8	0.381705
$457$	4.03536e9	1.97777	0.988883	−	0.148693i	$-0.0475065\pi$
$457$	4.03536e9	1.97777	0.988883	+	0.148693i	$0.0475065\pi$
$458$	8.91590e8	0.433647
$459$	1.64725e8	0.0795088
$460$	1.84500e8	0.0883778
$461$	2.25415e9	1.07159	0.535796	−	0.844348i	$-0.320012\pi$
$461$	2.25415e9	1.07159	0.535796	+	0.844348i	$0.320012\pi$
$462$	−1.58282e8	−0.0746764
$463$	4.88794e8	0.228872	0.114436	−	0.993431i	$-0.463494\pi$
$463$	4.88794e8	0.228872	0.114436	+	0.993431i	$0.463494\pi$
$464$	2.43531e9	1.13173
$465$	−2.69428e7	−0.0124268
$466$	5.64358e9	2.58347
$467$	2.68922e9	1.22185	0.610925	−	0.791688i	$-0.290798\pi$
$467$	2.68922e9	1.22185	0.610925	+	0.791688i	$0.290798\pi$
$468$	8.39515e8	0.378589
$469$	−8.91191e8	−0.398902
$470$	−4.72965e8	−0.210129
$471$	3.19144e8	0.140739
$472$	4.31282e9	1.88784
$473$	5.96304e8	0.259092
$474$	−5.99347e8	−0.258496
$475$	−2.80516e9	−1.20096
$476$	−1.36251e9	−0.579047
$477$	−2.25405e9	−0.950934
$478$	−2.30251e9	−0.964283
$479$	4.47311e9	1.85967	0.929834	−	0.367980i	$-0.119951\pi$
$479$	4.47311e9	1.85967	0.929834	+	0.367980i	$0.119951\pi$
$480$	−2.96236e7	−0.0122262
$481$	−1.09571e8	−0.0448938
$482$	−2.06172e9	−0.838621
$483$	−1.48225e8	−0.0598558
$484$	−4.90709e9	−1.96728
$485$	2.15073e8	0.0856033
$486$	1.74406e9	0.689182
$487$	3.52043e9	1.38116	0.690580	−	0.723256i	$-0.257355\pi$
$487$	3.52043e9	1.38116	0.690580	+	0.723256i	$0.257355\pi$
$488$	−1.02580e10	−3.99571
$489$	4.10517e8	0.158763
$490$	−1.14293e8	−0.0438867
$491$	1.32531e9	0.505279	0.252639	−	0.967561i	$-0.418701\pi$
$491$	1.32531e9	0.505279	0.252639	+	0.967561i	$0.418701\pi$
$492$	1.77436e8	0.0671681
$493$	4.34458e8	0.163299
$494$	9.69287e8	0.361750
$495$	6.81232e7	0.0252451
$496$	−8.92961e9	−3.28584
$497$	3.51393e9	1.28394
$498$	−1.04820e9	−0.380315
$499$	−4.30702e9	−1.55176	−0.775880	−	0.630880i	$-0.782694\pi$
$499$	−4.30702e9	−1.55176	−0.775880	+	0.630880i	$0.782694\pi$
$500$	8.35124e8	0.298783
$501$	−5.79034e8	−0.205718
$502$	3.06461e9	1.08122
$503$	4.85642e9	1.70149	0.850743	−	0.525583i	$-0.176153\pi$
$503$	4.85642e9	1.70149	0.850743	+	0.525583i	$0.176153\pi$
$504$	−5.50560e9	−1.91557
$505$	−7.00896e7	−0.0242177
$506$	1.26727e9	0.434854
$507$	3.66553e8	0.124914
$508$	−7.05250e8	−0.238682
$509$	4.60799e9	1.54881	0.774407	−	0.632687i	$-0.218048\pi$
$509$	4.60799e9	1.54881	0.774407	+	0.632687i	$0.218048\pi$
$510$	−1.40090e7	−0.00467641
$511$	−3.05000e9	−1.01117
$512$	6.38959e9	2.10391
$513$	9.38840e8	0.307030
$514$	4.44348e9	1.44329
$515$	7.14017e6	0.00230347
$516$	−6.05325e8	−0.193961
$517$	−2.27826e9	−0.725080
$518$	1.25174e9	0.395694
$519$	2.49923e8	0.0784731
$520$	−8.26584e7	−0.0257796
$521$	−2.76123e8	−0.0855403	−0.0427701	−	0.999085i	$-0.513618\pi$
$521$	−2.76123e8	−0.0855403	−0.0427701	+	0.999085i	$0.513618\pi$
$522$	3.05814e9	0.941046
$523$	−1.89590e9	−0.579508	−0.289754	−	0.957101i	$-0.593574\pi$
$523$	−1.89590e9	−0.579508	−0.289754	+	0.957101i	$0.593574\pi$
$524$	−1.33936e10	−4.06667
$525$	−3.34781e8	−0.100973
$526$	−4.34440e9	−1.30161
$527$	−1.59304e9	−0.474121
$528$	−3.78258e8	−0.111833
$529$	−2.21807e9	−0.651449
$530$	3.86604e8	0.112798
$531$	2.59773e9	0.752946
$532$	−7.76552e9	−2.23604
$533$	1.27745e8	0.0365427
$534$	4.55045e7	0.0129318
$535$	−3.77172e8	−0.106488
$536$	−4.44016e9	−1.24544
$537$	−5.43203e8	−0.151374
$538$	3.28608e9	0.909788
$539$	−5.50545e8	−0.151437
$540$	−1.39466e8	−0.0381146
$541$	8.89156e8	0.241428	0.120714	−	0.992687i	$-0.461482\pi$
$541$	8.89156e8	0.241428	0.120714	+	0.992687i	$0.461482\pi$
$542$	3.83702e9	1.03513
$543$	8.31580e7	0.0222897
$544$	−1.75154e9	−0.466471
$545$	2.91503e8	0.0771358
$546$	1.15679e8	0.0304146
$547$	−1.63667e8	−0.0427569
$547$	−1.63667e8	−0.0427569
$548$	−7.31325e9	−1.89836
$549$	−6.17869e9	−1.59365
$550$	2.86227e9	0.733569
$551$	2.47617e9	0.630594
$552$	−7.38497e8	−0.186880
$553$	3.45701e9	0.869285
$554$	1.05319e10	2.63161
$555$	9.02572e6	0.00224108
$556$	5.18424e9	1.27916
$557$	−1.29372e8	−0.0317210	−0.0158605	−	0.999874i	$-0.505049\pi$
$557$	−1.29372e8	−0.0317210	−0.0158605	+	0.999874i	$0.505049\pi$
$558$	−1.12134e10	−2.73222
$559$	−4.35806e8	−0.105524
$560$	4.52936e8	0.108988
$561$	−6.74811e7	−0.0161366
$562$	−3.70145e9	−0.879619
$563$	−2.51030e9	−0.592851	−0.296426	−	0.955056i	$-0.595795\pi$
$563$	−2.51030e9	−0.592851	−0.296426	+	0.955056i	$0.595795\pi$
$564$	2.31273e9	0.542809
$565$	−2.32766e8	−0.0542937
$566$	−1.50939e10	−3.49899
$567$	−3.25969e9	−0.750993
$568$	1.75073e10	4.00868
$569$	4.24441e9	0.965883	0.482942	−	0.875653i	$-0.339568\pi$
$569$	4.24441e9	0.965883	0.482942	+	0.875653i	$0.339568\pi$
$570$	−7.98436e7	−0.0180584
$571$	−6.63642e9	−1.49179	−0.745895	−	0.666064i	$-0.767978\pi$
$571$	−6.63642e9	−1.49179	−0.745895	+	0.666064i	$0.767978\pi$
$572$	−6.93592e8	−0.154959
$573$	−1.05365e9	−0.233967
$574$	−1.45937e9	−0.322087
$575$	2.68041e9	0.587982
$576$	−2.56672e9	−0.559628
$577$	−8.38649e9	−1.81746	−0.908730	−	0.417384i	$-0.862947\pi$
$577$	−8.38649e9	−1.81746	−0.908730	+	0.417384i	$0.862947\pi$
$578$	7.66592e9	1.65126
$579$	3.06173e8	0.0655530
$580$	−3.67839e8	−0.0782816
$581$	6.04600e9	1.27895
$582$	−1.49963e9	−0.315321
$583$	1.86226e9	0.389224
$584$	−1.51959e10	−3.15705
$585$	−4.97875e7	−0.0102819
$586$	−5.13772e9	−1.05470
$587$	−4.05988e9	−0.828476	−0.414238	−	0.910169i	$-0.635952\pi$
$587$	−4.05988e9	−0.828476	−0.414238	+	0.910169i	$0.635952\pi$
$588$	5.58874e8	0.113369
$589$	−9.07943e9	−1.83086
$590$	−4.45550e8	−0.0893129
$591$	−1.19316e9	−0.237763
$592$	2.99138e9	0.592577
$593$	2.12750e9	0.418966	0.209483	−	0.977812i	$-0.432822\pi$
$593$	2.12750e9	0.418966	0.209483	+	0.977812i	$0.432822\pi$
$594$	−9.57953e8	−0.187539
$595$	8.08036e7	0.0157261
$596$	−6.13828e9	−1.18764
$597$	5.99930e8	0.115396
$598$	−9.26182e8	−0.177110
$599$	9.18661e9	1.74647	0.873235	−	0.487299i	$-0.162018\pi$
$599$	9.18661e9	1.74647	0.873235	+	0.487299i	$0.162018\pi$
$600$	−1.66797e9	−0.315253
$601$	9.23443e9	1.73520	0.867599	−	0.497264i	$-0.165662\pi$
$601$	9.23443e9	1.73520	0.867599	+	0.497264i	$0.165662\pi$
$602$	4.97866e9	0.930090
$603$	−2.67443e9	−0.496731
$604$	−1.71736e10	−3.17127
$605$	2.91016e8	0.0534285
$606$	4.88708e8	0.0892063
$607$	−1.71830e9	−0.311846	−0.155923	−	0.987769i	$-0.549835\pi$
$607$	−1.71830e9	−0.311846	−0.155923	+	0.987769i	$0.549835\pi$
$608$	−9.98281e9	−1.80132
$609$	2.95518e8	0.0530180
$610$	1.05974e9	0.189036
$611$	1.66506e9	0.295314
$612$	−4.08883e9	−0.721057
$613$	8.54866e9	1.49895	0.749474	−	0.662034i	$-0.230307\pi$
$613$	8.54866e9	1.49895	0.749474	+	0.662034i	$0.230307\pi$
$614$	−9.92584e9	−1.73052
$615$	−1.05228e7	−0.00182419
$616$	4.54862e9	0.784057
$617$	1.92863e9	0.330561	0.165280	−	0.986247i	$-0.447147\pi$
$617$	1.92863e9	0.330561	0.165280	+	0.986247i	$0.447147\pi$
$618$	−4.97857e7	−0.00848487
$619$	1.05792e10	1.79281	0.896407	−	0.443231i	$-0.146168\pi$
$619$	1.05792e10	1.79281	0.896407	+	0.443231i	$0.146168\pi$
$620$	1.34876e9	0.227282
$621$	−8.97088e8	−0.150319
$622$	−1.42599e10	−2.37601
$623$	−2.62468e8	−0.0434879
$624$	2.76448e8	0.0455478
$625$	6.02917e9	0.987820
$626$	−1.61947e10	−2.63853
$627$	−3.84604e8	−0.0623128
$628$	−1.59764e10	−2.57407
$629$	5.33661e8	0.0855043
$630$	5.68774e8	0.0906250
$631$	−7.94331e9	−1.25863	−0.629316	−	0.777150i	$-0.716665\pi$
$631$	−7.94331e9	−1.25863	−0.629316	+	0.777150i	$0.716665\pi$
$632$	1.72238e10	2.71405
$633$	9.89698e8	0.155092
$634$	1.75470e9	0.273457
$635$	4.18249e7	0.00648227
$636$	−1.89043e9	−0.291381
$637$	4.02363e8	0.0616780
$638$	−2.52658e9	−0.385177
$639$	1.05452e10	1.59882
$640$	−1.91424e8	−0.0288646
$641$	8.99375e9	1.34877	0.674385	−	0.738380i	$-0.264409\pi$
$641$	8.99375e9	1.34877	0.674385	+	0.738380i	$0.264409\pi$
$642$	2.62988e9	0.392251
$643$	9.90331e9	1.46907	0.734534	−	0.678572i	$-0.237401\pi$
$643$	9.90331e9	1.46907	0.734534	+	0.678572i	$0.237401\pi$
$644$	7.42017e9	1.09475
$645$	3.58989e7	0.00526771
$646$	−4.72089e9	−0.688985
$647$	−4.90427e9	−0.711885	−0.355942	−	0.934508i	$-0.615840\pi$
$647$	−4.90427e9	−0.711885	−0.355942	+	0.934508i	$0.615840\pi$
$648$	−1.62407e10	−2.34472
$649$	−2.14620e9	−0.308186
$650$	−2.09188e9	−0.298772
$651$	−1.08358e9	−0.153932
$652$	−2.05506e10	−2.90374
$653$	5.42813e9	0.762876	0.381438	−	0.924394i	$-0.375429\pi$
$653$	5.42813e9	0.762876	0.381438	+	0.924394i	$0.375429\pi$
$654$	−2.03254e9	−0.284130
$655$	7.94311e8	0.110445
$656$	−3.48757e9	−0.482346
$657$	−9.15294e9	−1.25916
$658$	−1.90216e10	−2.60290
$659$	−1.12297e10	−1.52851	−0.764256	−	0.644913i	$-0.776894\pi$
$659$	−1.12297e10	−1.52851	−0.764256	+	0.644913i	$0.776894\pi$
$660$	5.71336e7	0.00773549
$661$	6.19841e9	0.834786	0.417393	−	0.908726i	$-0.362944\pi$
$661$	6.19841e9	0.834786	0.417393	+	0.908726i	$0.362944\pi$
$662$	8.46378e9	1.13387
$663$	4.93182e7	0.00657219
$664$	3.01228e10	3.99308
$665$	4.60535e8	0.0607277
$666$	3.75642e9	0.492736
$667$	−2.36605e9	−0.308733
$668$	2.89866e10	3.76253
$669$	−1.21039e8	−0.0156291
$670$	4.58705e8	0.0589212
$671$	5.10472e9	0.652294
$672$	−1.19140e9	−0.151448
$673$	3.81553e9	0.482505	0.241252	−	0.970462i	$-0.422442\pi$
$673$	3.81553e9	0.482505	0.241252	+	0.970462i	$0.422442\pi$
$674$	−1.43079e10	−1.79997
$675$	−2.02617e9	−0.253578
$676$	−1.83497e10	−2.28463
$677$	1.28428e10	1.59074	0.795371	−	0.606123i	$-0.207276\pi$
$677$	1.28428e10	1.59074	0.795371	+	0.606123i	$0.207276\pi$
$678$	1.62299e9	0.199991
$679$	8.64979e9	1.06038
$680$	4.02585e8	0.0490995
$681$	−1.06996e8	−0.0129823
$682$	9.26427e9	1.11832
$683$	4.62590e9	0.555550	0.277775	−	0.960646i	$-0.410403\pi$
$683$	4.62590e9	0.555550	0.277775	+	0.960646i	$0.410403\pi$
$684$	−2.33041e10	−2.78442
$685$	4.33713e8	0.0515568
$686$	−1.68157e10	−1.98875
$687$	2.58555e8	0.0304231
$688$	1.18979e10	1.39287
$689$	−1.36102e9	−0.158525
$690$	7.62928e7	0.00884122
$691$	−5.52383e9	−0.636895	−0.318447	−	0.947941i	$-0.603161\pi$
$691$	−5.52383e9	−0.636895	−0.318447	+	0.947941i	$0.603161\pi$
$692$	−1.25112e10	−1.43525
$693$	2.73977e9	0.312714
$694$	7.14335e9	0.811230
$695$	−3.07452e8	−0.0347401
$696$	1.47235e9	0.165531
$697$	−6.22181e8	−0.0695988
$698$	2.04264e9	0.227352
$699$	1.63660e9	0.181247
$700$	1.67592e10	1.84676
$701$	−3.72999e9	−0.408973	−0.204487	−	0.978869i	$-0.565552\pi$
$701$	−3.72999e9	−0.408973	−0.204487	+	0.978869i	$0.565552\pi$
$702$	7.00116e8	0.0763818
$703$	3.04157e9	0.330182
$704$	2.12057e9	0.229060
$705$	−1.37156e8	−0.0147419
$706$	1.29013e10	1.37981
$707$	−2.81885e9	−0.299988
$708$	2.17867e9	0.230714
$709$	1.50640e9	0.158737	0.0793687	−	0.996845i	$-0.474710\pi$
$709$	1.50640e9	0.158737	0.0793687	+	0.996845i	$0.474710\pi$
$710$	−1.80865e9	−0.189649
$711$	1.03744e10	1.08247
$712$	−1.30769e9	−0.135776
$713$	8.67565e9	0.896373
$714$	−5.63413e8	−0.0579273
$715$	4.11335e7	0.00420848
$716$	2.71929e10	2.76860
$717$	−6.67712e8	−0.0676507
$718$	−2.73254e10	−2.75506
$719$	1.29936e10	1.30370	0.651852	−	0.758346i	$-0.273992\pi$
$719$	1.29936e10	1.30370	0.651852	+	0.758346i	$0.273992\pi$
$720$	1.35924e9	0.135717
$721$	2.87162e8	0.0285334
$722$	−8.40278e9	−0.830889
$723$	−5.97885e8	−0.0588347
$724$	−4.16291e9	−0.407673
$725$	−5.34397e9	−0.520812
$726$	−2.02914e9	−0.196804
$727$	4.43571e7	0.00428147	0.00214074	−	0.999998i	$-0.499319\pi$
$727$	4.43571e7	0.00428147	0.00214074	+	0.999998i	$0.499319\pi$
$728$	−3.32434e9	−0.319335
$729$	−9.44035e9	−0.902489
$730$	1.56986e9	0.149359
$731$	2.12258e9	0.200980
$732$	−5.18195e9	−0.488320
$733$	−3.11848e9	−0.292469	−0.146234	−	0.989250i	$-0.546715\pi$
$733$	−3.11848e9	−0.292469	−0.146234	+	0.989250i	$0.546715\pi$
$734$	1.24696e10	1.16390
$735$	−3.31441e7	−0.00307893
$736$	9.53886e9	0.881909
$737$	2.20957e9	0.203316
$738$	−4.37951e9	−0.401078
$739$	1.08994e10	0.993455	0.496728	−	0.867907i	$-0.334535\pi$
$739$	1.08994e10	0.993455	0.496728	+	0.867907i	$0.334535\pi$
$740$	−4.51830e8	−0.0409887
$741$	2.81086e8	0.0253791
$742$	1.55484e10	1.39724
$743$	1.51167e10	1.35206	0.676032	−	0.736872i	$-0.263698\pi$
$743$	1.51167e10	1.35206	0.676032	+	0.736872i	$0.263698\pi$
$744$	−5.39870e9	−0.480600
$745$	3.64032e8	0.0322546
$746$	−1.85185e10	−1.63313
$747$	1.81438e10	1.59260
$748$	3.37812e9	0.295134
$749$	−1.51691e10	−1.31908
$750$	3.45334e8	0.0298899
$751$	−1.83280e9	−0.157898	−0.0789490	−	0.996879i	$-0.525156\pi$
$751$	−1.83280e9	−0.157898	−0.0789490	+	0.996879i	$0.525156\pi$
$752$	−4.54575e10	−3.89801
$753$	8.88715e8	0.0758543
$754$	1.84654e9	0.156877
$755$	1.01849e9	0.0861272
$756$	−5.60903e9	−0.472130
$757$	8.23149e9	0.689672	0.344836	−	0.938663i	$-0.387935\pi$
$757$	8.23149e9	0.689672	0.344836	+	0.938663i	$0.387935\pi$
$758$	−1.34259e10	−1.11970
$759$	3.67500e8	0.0305078
$760$	2.29451e9	0.189602
$761$	−1.35466e9	−0.111425	−0.0557127	−	0.998447i	$-0.517743\pi$
$761$	−1.35466e9	−0.111425	−0.0557127	+	0.998447i	$0.517743\pi$
$762$	−2.91629e8	−0.0238775
$763$	1.17236e10	0.955490
$764$	5.27459e10	4.27919
$765$	2.42489e8	0.0195829
$766$	3.55885e10	2.86094
$767$	1.56854e9	0.125520
$768$	2.25163e9	0.179363
$769$	−5.31426e8	−0.0421406	−0.0210703	−	0.999778i	$-0.506707\pi$
$769$	−5.31426e8	−0.0421406	−0.0210703	+	0.999778i	$0.506707\pi$
$770$	−4.69911e8	−0.0370935
$771$	1.28858e9	0.101256
$772$	−1.53271e10	−1.19895
$773$	1.31891e10	1.02704	0.513521	−	0.858077i	$-0.328341\pi$
$773$	1.31891e10	1.02704	0.513521	+	0.858077i	$0.328341\pi$
$774$	1.49408e10	1.15819
$775$	1.95949e10	1.51212
$776$	4.30956e10	3.31068
$777$	3.62995e8	0.0277605
$778$	−5.54560e9	−0.422202
$779$	−3.54608e9	−0.268762
$780$	−4.17558e7	−0.00315055
$781$	−8.71222e9	−0.654411
$782$	4.51094e9	0.337321
$783$	1.78854e9	0.133147
$784$	−1.09849e10	−0.814121
$785$	9.47484e8	0.0699082
$786$	−5.53843e9	−0.406825
$787$	−1.98472e10	−1.45140	−0.725701	−	0.688011i	$-0.758484\pi$
$787$	−1.98472e10	−1.45140	−0.725701	+	0.688011i	$0.758484\pi$
$788$	5.97300e10	4.34861
$789$	−1.25984e9	−0.0913161
$790$	−1.77936e9	−0.128401
$791$	−9.36133e9	−0.672542
$792$	1.36503e10	0.976344
$793$	−3.73076e9	−0.265669
$794$	3.19521e10	2.26531
$795$	1.12112e8	0.00791349
$796$	−3.00326e10	−2.11056
$797$	−7.85628e9	−0.549684	−0.274842	−	0.961489i	$-0.588626\pi$
$797$	−7.85628e9	−0.549684	−0.274842	+	0.961489i	$0.588626\pi$
$798$	−3.21114e9	−0.223691
$799$	−8.10960e9	−0.562453
$800$	2.15445e10	1.48772
$801$	−7.87658e8	−0.0541532
$802$	3.69950e10	2.53241
$803$	7.56198e9	0.515384
$804$	−2.24299e9	−0.152206
$805$	−4.40054e8	−0.0297318
$806$	−6.77075e9	−0.455475
$807$	9.52939e8	0.0638275
$808$	−1.40443e10	−0.936612
$809$	−6.30709e9	−0.418802	−0.209401	−	0.977830i	$-0.567151\pi$
$809$	−6.30709e9	−0.418802	−0.209401	+	0.977830i	$0.567151\pi$
$810$	1.67780e9	0.110928
$811$	−7.80011e9	−0.513485	−0.256742	−	0.966480i	$-0.582649\pi$
$811$	−7.80011e9	−0.513485	−0.256742	+	0.966480i	$0.582649\pi$
$812$	−1.47937e10	−0.969684
$813$	1.11271e9	0.0726213
$814$	−3.10349e9	−0.201681
$815$	1.21876e9	0.0788615
$816$	−1.34643e9	−0.0867499
$817$	1.20975e10	0.776103
$818$	−3.17255e10	−2.02662
$819$	−2.00235e9	−0.127364
$820$	5.26776e8	0.0333640
$821$	1.97064e10	1.24282	0.621408	−	0.783487i	$-0.286561\pi$
$821$	1.97064e10	1.24282	0.621408	+	0.783487i	$0.286561\pi$
$822$	−3.02412e9	−0.189910
$823$	−2.41399e10	−1.50951	−0.754754	−	0.656007i	$-0.772244\pi$
$823$	−2.41399e10	−1.50951	−0.754754	+	0.656007i	$0.772244\pi$
$824$	1.43072e9	0.0890860
$825$	8.30037e8	0.0514646
$826$	−1.79190e10	−1.10633
$827$	−2.36877e10	−1.45631	−0.728154	−	0.685414i	$-0.759621\pi$
$827$	−2.36877e10	−1.45631	−0.728154	+	0.685414i	$0.759621\pi$
$828$	2.22677e10	1.36323
$829$	2.63002e10	1.60331	0.801657	−	0.597785i	$-0.203952\pi$
$829$	2.63002e10	1.60331	0.801657	+	0.597785i	$0.203952\pi$
$830$	−3.11194e9	−0.188911
$831$	3.05417e9	0.184625
$832$	−1.54981e9	−0.0932926
$833$	−1.95970e9	−0.117471
$834$	2.14375e9	0.127965
$835$	−1.71905e9	−0.102185
$836$	1.92534e10	1.13968
$837$	−6.55807e9	−0.386578
$838$	−1.75529e10	−1.03037
$839$	9.73659e9	0.569168	0.284584	−	0.958651i	$-0.408145\pi$
$839$	9.73659e9	0.569168	0.284584	+	0.958651i	$0.408145\pi$
$840$	2.73838e8	0.0159410
$841$	−1.25327e10	−0.726536
$842$	1.57354e10	0.908415
$843$	−1.07339e9	−0.0617109
$844$	−4.95445e10	−2.83659
$845$	1.08823e9	0.0620474
$846$	−5.70833e10	−3.24125
$847$	1.17040e10	0.661825
$848$	3.71571e10	2.09246
$849$	−4.37711e9	−0.245477
$850$	1.01884e10	0.569038
$851$	−2.90630e9	−0.161654
$852$	8.84403e9	0.489905
$853$	1.84287e10	1.01665	0.508327	−	0.861164i	$-0.330264\pi$
$853$	1.84287e10	1.01665	0.508327	+	0.861164i	$0.330264\pi$
$854$	4.26203e10	2.34161
$855$	1.38205e9	0.0756210
$856$	−7.55764e10	−4.11839
$857$	3.50398e10	1.90164	0.950821	−	0.309741i	$-0.100242\pi$
$857$	3.50398e10	1.90164	0.950821	+	0.309741i	$0.100242\pi$
$858$	−2.86809e8	−0.0155020
$859$	1.81748e10	0.978346	0.489173	−	0.872187i	$-0.337299\pi$
$859$	1.81748e10	0.978346	0.489173	+	0.872187i	$0.337299\pi$
$860$	−1.79711e9	−0.0963450
$861$	−4.23206e8	−0.0225965
$862$	−5.77742e10	−3.07226
$863$	7.19286e9	0.380946	0.190473	−	0.981692i	$-0.438998\pi$
$863$	7.19286e9	0.380946	0.190473	+	0.981692i	$0.438998\pi$
$864$	−7.21057e9	−0.380340
$865$	7.41979e8	0.0389794
$866$	−6.38333e10	−3.33991
$867$	2.22306e9	0.115847
$868$	5.42444e10	2.81537
$869$	−8.57110e9	−0.443065
$870$	−1.52106e8	−0.00783121
$871$	−1.61485e9	−0.0828074
$872$	5.84103e10	2.98320
$873$	2.59577e10	1.32043
$874$	2.57098e10	1.30259
$875$	−1.99187e9	−0.100516
$876$	−7.67639e9	−0.385827
$877$	3.02122e10	1.51246	0.756231	−	0.654305i	$-0.227039\pi$
$877$	3.02122e10	1.51246	0.756231	+	0.654305i	$0.227039\pi$
$878$	5.23850e10	2.61202
$879$	−1.48990e9	−0.0739941
$880$	−1.12298e9	−0.0555499
$881$	−2.30871e10	−1.13750	−0.568752	−	0.822509i	$-0.692574\pi$
$881$	−2.30871e10	−1.13750	−0.568752	+	0.822509i	$0.692574\pi$
$882$	−1.37943e10	−0.676953
$883$	1.51959e10	0.742788	0.371394	−	0.928475i	$-0.378880\pi$
$883$	1.51959e10	0.742788	0.371394	+	0.928475i	$0.378880\pi$
$884$	−2.46888e9	−0.120204
$885$	−1.29206e8	−0.00626588
$886$	8.66969e9	0.418780
$887$	−2.92369e8	−0.0140669	−0.00703346	−	0.999975i	$-0.502239\pi$
$887$	−2.92369e8	−0.0140669	−0.00703346	+	0.999975i	$0.502239\pi$
$888$	1.80854e9	0.0866728
$889$	1.68211e9	0.0802967
$890$	1.35095e8	0.00642354
$891$	8.08189e9	0.382773
$892$	6.05922e9	0.285851
$893$	−4.62202e10	−2.17196
$894$	−2.53825e9	−0.118810
$895$	−1.61268e9	−0.0751912
$896$	−7.69864e9	−0.357549
$897$	−2.68586e8	−0.0124254
$898$	6.89824e10	3.17886
$899$	−1.72968e10	−0.793973
$900$	5.02939e10	2.29967
$901$	6.62882e9	0.301925
$902$	3.61827e9	0.164164
$903$	1.44378e9	0.0652518
$904$	−4.66407e10	−2.09979
$905$	2.46882e8	0.0110718
$906$	−7.10151e9	−0.317250
$907$	−2.50545e10	−1.11496	−0.557481	−	0.830190i	$-0.688232\pi$
$907$	−2.50545e10	−1.11496	−0.557481	+	0.830190i	$0.688232\pi$
$908$	5.35625e9	0.237443
$909$	−8.45927e9	−0.373559
$910$	3.43432e8	0.0151076
$911$	−2.90234e9	−0.127185	−0.0635923	−	0.997976i	$-0.520256\pi$
$911$	−2.90234e9	−0.127185	−0.0635923	+	0.997976i	$0.520256\pi$
$912$	−7.67390e9	−0.334992
$913$	−1.49901e10	−0.651864
$914$	−8.35340e10	−3.61869
$915$	3.07316e8	0.0132621
$916$	−1.29433e10	−0.556431
$917$	3.19455e10	1.36810
$918$	−3.40989e9	−0.145476
$919$	−3.02796e10	−1.28690	−0.643451	−	0.765487i	$-0.722498\pi$
$919$	−3.02796e10	−1.28690	−0.643451	+	0.765487i	$0.722498\pi$
$920$	−2.19247e9	−0.0928274
$921$	−2.87842e9	−0.121407
$922$	−4.66621e10	−1.96068
$923$	6.36729e9	0.266532
$924$	2.29779e9	0.0958205
$925$	−6.56419e9	−0.272700
$926$	−1.01183e10	−0.418763
$927$	8.61764e8	0.0355311
$928$	−1.90177e10	−0.781161
$929$	4.50809e9	0.184475	0.0922374	−	0.995737i	$-0.470598\pi$
$929$	4.50809e9	0.184475	0.0922374	+	0.995737i	$0.470598\pi$
$930$	5.57731e8	0.0227371
$931$	−1.11692e10	−0.453626
$932$	−8.19284e10	−3.31497
$933$	−4.13525e9	−0.166693
$934$	−5.56683e10	−2.23560
$935$	−2.00340e8	−0.00801542
$936$	−9.97624e9	−0.397650
$937$	−2.19871e10	−0.873130	−0.436565	−	0.899673i	$-0.643805\pi$
$937$	−2.19871e10	−0.873130	−0.436565	+	0.899673i	$0.643805\pi$
$938$	1.84481e10	0.729864
$939$	−4.69634e9	−0.185110
$940$	6.86608e9	0.269626
$941$	4.27568e10	1.67279	0.836395	−	0.548127i	$-0.184659\pi$
$941$	4.27568e10	1.67279	0.836395	+	0.548127i	$0.184659\pi$
$942$	−6.60645e9	−0.257508
$943$	3.38838e9	0.131583
$944$	−4.28225e10	−1.65680
$945$	3.32644e8	0.0128224
$946$	−1.23438e10	−0.474056
$947$	4.04778e9	0.154879	0.0774395	−	0.996997i	$-0.475326\pi$
$947$	4.04778e9	0.154879	0.0774395	+	0.996997i	$0.475326\pi$
$948$	8.70077e9	0.331687
$949$	−5.52664e9	−0.209908
$950$	5.80683e10	2.19739
$951$	5.08849e8	0.0191848
$952$	1.61911e10	0.608201
$953$	−1.74951e10	−0.654775	−0.327387	−	0.944890i	$-0.606168\pi$
$953$	−1.74951e10	−0.654775	−0.327387	+	0.944890i	$0.606168\pi$
$954$	4.66601e10	1.73991
$955$	−3.12810e9	−0.116217
$956$	3.34258e10	1.23731
$957$	−7.32690e8	−0.0270227
$958$	−9.25957e10	−3.40261
$959$	1.74430e10	0.638640
$960$	1.27663e8	0.00465712
$961$	3.59098e10	1.30521
$962$	2.26817e9	0.0821415
$963$	−4.55218e10	−1.64258
$964$	2.99302e10	1.07607
$965$	9.08976e8	0.0325617
$966$	3.06833e9	0.109517
$967$	−2.01240e10	−0.715686	−0.357843	−	0.933782i	$-0.616488\pi$
$967$	−2.01240e10	−0.715686	−0.357843	+	0.933782i	$0.616488\pi$
$968$	5.83126e10	2.06633
$969$	−1.36902e9	−0.0483367
$970$	−4.45213e9	−0.156627
$971$	1.03420e9	0.0362523	0.0181262	−	0.999836i	$-0.494230\pi$
$971$	1.03420e9	0.0362523	0.0181262	+	0.999836i	$0.494230\pi$
$972$	−2.53187e10	−0.884319
$973$	−1.23651e10	−0.430330
$974$	−7.28747e10	−2.52709
$975$	−6.06629e8	−0.0209608
$976$	1.01853e11	3.50671
$977$	2.18717e10	0.750329	0.375165	−	0.926958i	$-0.377586\pi$
$977$	2.18717e10	0.750329	0.375165	+	0.926958i	$0.377586\pi$
$978$	−8.49793e9	−0.290487
$979$	6.50749e8	0.0221653
$980$	1.65920e9	0.0563129
$981$	3.51822e10	1.18982
$982$	−2.74345e10	−0.924501
$983$	−4.31858e10	−1.45012	−0.725059	−	0.688686i	$-0.758188\pi$
$983$	−4.31858e10	−1.45012	−0.725059	+	0.688686i	$0.758188\pi$
$984$	−2.10853e9	−0.0705499
$985$	−3.54229e9	−0.118102
$986$	−8.99352e9	−0.298786
$987$	−5.51614e9	−0.182610
$988$	−1.40712e10	−0.464176
$989$	−1.15595e10	−0.379973
$990$	−1.41019e9	−0.0461905
$991$	2.14705e10	0.700783	0.350392	−	0.936603i	$-0.386048\pi$
$991$	2.14705e10	0.700783	0.350392	+	0.936603i	$0.386048\pi$
$992$	6.97328e10	2.26802
$993$	2.45444e9	0.0795480
$994$	−7.27401e10	−2.34921
$995$	1.78109e9	0.0573198
$996$	1.52169e10	0.487998
$997$	7.04322e9	0.225081	0.112540	−	0.993647i	$-0.464101\pi$
$997$	7.04322e9	0.225081	0.112540	+	0.993647i	$0.464101\pi$
$998$	8.91575e10	2.83923
$999$	2.19692e9	0.0697164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.b.1.9	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.b.1.9	✓	162	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-20.7005 q^{2} -6.00300 q^{3} +300.512 q^{4} -17.8219 q^{5} +124.265 q^{6} -716.757 q^{7} -3571.08 q^{8} -2150.96 q^{9} +O(q^{10})\)	\(q-20.7005 q^{2} -6.00300 q^{3} +300.512 q^{4} -17.8219 q^{5} +124.265 q^{6} -716.757 q^{7} -3571.08 q^{8} -2150.96 q^{9} +368.922 q^{10} +1777.09 q^{11} -1803.97 q^{12} -1298.78 q^{13} +14837.2 q^{14} +106.985 q^{15} +35457.7 q^{16} +6325.65 q^{17} +44526.1 q^{18} +36052.6 q^{19} -5355.68 q^{20} +4302.69 q^{21} -36786.6 q^{22} -34449.3 q^{23} +21437.2 q^{24} -77807.4 q^{25} +26885.3 q^{26} +26040.8 q^{27} -215394. q^{28} +68682.0 q^{29} -2214.64 q^{30} -251838. q^{31} -276895. q^{32} -10667.8 q^{33} -130944. q^{34} +12774.0 q^{35} -646390. q^{36} +84364.6 q^{37} -746309. q^{38} +7796.55 q^{39} +63643.3 q^{40} -98358.4 q^{41} -89068.0 q^{42} +335552. q^{43} +534035. q^{44} +38334.2 q^{45} +713119. q^{46} -1.28202e6 q^{47} -212853. q^{48} -309802. q^{49} +1.61065e6 q^{50} -37972.9 q^{51} -390297. q^{52} +1.04793e6 q^{53} -539058. q^{54} -31671.0 q^{55} +2.55960e6 q^{56} -216424. q^{57} -1.42175e6 q^{58} -1.20771e6 q^{59} +32150.2 q^{60} +2.87252e6 q^{61} +5.21318e6 q^{62} +1.54172e6 q^{63} +1.19329e6 q^{64} +23146.6 q^{65} +220830. q^{66} +1.24337e6 q^{67} +1.90093e6 q^{68} +206799. q^{69} -264428. q^{70} -4.90253e6 q^{71} +7.68126e6 q^{72} +4.25527e6 q^{73} -1.74639e6 q^{74} +467078. q^{75} +1.08342e7 q^{76} -1.27374e6 q^{77} -161393. q^{78} -4.82312e6 q^{79} -631923. q^{80} +4.54784e6 q^{81} +2.03607e6 q^{82} -8.43522e6 q^{83} +1.29301e6 q^{84} -112735. q^{85} -6.94609e6 q^{86} -412298. q^{87} -6.34612e6 q^{88} +366189. q^{89} -793538. q^{90} +930907. q^{91} -1.03524e7 q^{92} +1.51178e6 q^{93} +2.65385e7 q^{94} -642526. q^{95} +1.66220e6 q^{96} -1.20679e7 q^{97} +6.41307e6 q^{98} -3.82245e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9}+O(q^{10}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9	\( 162 q + 48 q^{2} + 310 q^{3} + 10650 q^{4} + 3999 q^{5} + 1998 q^{6} + 4301 q^{7} + 9216 q^{8} + 124464 q^{9} + 7430 q^{10} + 19840 q^{11} + 55737 q^{12} + 51223 q^{13} + 75679 q^{14} + 44609 q^{15} + 709506 q^{16} + 258906 q^{17} + 135171 q^{18} + 80362 q^{19} + 506432 q^{20} + 138572 q^{21} + 158320 q^{22} + 571410 q^{23} + 325871 q^{24} + 2732541 q^{25} + 488640 q^{26} + 772231 q^{27} + 699304 q^{28} + 968170 q^{29} + 301526 q^{30} + 348203 q^{31} + 1078196 q^{32} + 1536618 q^{33} + 870073 q^{34} + 1089291 q^{35} + 8775356 q^{36} + 2226256 q^{37} + 3884597 q^{38} + 923555 q^{39} + 2518352 q^{40} + 1825935 q^{41} + 3419892 q^{42} + 1582376 q^{43} + 4352040 q^{44} + 9457186 q^{45} + 1012278 q^{46} + 4801410 q^{47} + 9073674 q^{48} + 21448221 q^{49} + 2366848 q^{50} + 3749747 q^{51} + 7035334 q^{52} + 17191348 q^{53} + 5748697 q^{54} + 5271331 q^{55} + 14854657 q^{56} + 5393884 q^{57} + 4036260 q^{58} + 8263804 q^{59} + 10193498 q^{60} + 12366404 q^{61} + 18470554 q^{62} + 15526895 q^{63} + 49399626 q^{64} + 17325330 q^{65} + 11279868 q^{66} + 5477434 q^{67} + 44562265 q^{68} + 26851278 q^{69} + 9428823 q^{70} + 12108395 q^{71} + 22153063 q^{72} + 13995388 q^{73} + 13478769 q^{74} + 24654171 q^{75} + 8225460 q^{76} + 61240119 q^{77} + 17624449 q^{78} + 8215066 q^{79} + 65708461 q^{80} + 112675190 q^{81} + 29179962 q^{82} + 33597369 q^{83} + 13895447 q^{84} + 24308391 q^{85} + 22043075 q^{86} + 25661967 q^{87} + 32743591 q^{88} + 47538968 q^{89} + 46132321 q^{90} + 24574095 q^{91} + 108017386 q^{92} + 63765304 q^{93} + 41203657 q^{94} + 38032578 q^{95} + 41465754 q^{96} + 45954628 q^{97} + 37164970 q^{98} + 43882333 q^{99}+O(q^{100}) \) 162 * q + 48 * q^2 + 310 * q^3 + 10650 * q^4 + 3999 * q^5 + 1998 * q^6 + 4301 * q^7 + 9216 * q^8 + 124464 * q^9 + 7430 * q^10 + 19840 * q^11 + 55737 * q^12 + 51223 * q^13 + 75679 * q^14 + 44609 * q^15 + 709506 * q^16 + 258906 * q^17 + 135171 * q^18 + 80362 * q^19 + 506432 * q^20 + 138572 * q^21 + 158320 * q^22 + 571410 * q^23 + 325871 * q^24 + 2732541 * q^25 + 488640 * q^26 + 772231 * q^27 + 699304 * q^28 + 968170 * q^29 + 301526 * q^30 + 348203 * q^31 + 1078196 * q^32 + 1536618 * q^33 + 870073 * q^34 + 1089291 * q^35 + 8775356 * q^36 + 2226256 * q^37 + 3884597 * q^38 + 923555 * q^39 + 2518352 * q^40 + 1825935 * q^41 + 3419892 * q^42 + 1582376 * q^43 + 4352040 * q^44 + 9457186 * q^45 + 1012278 * q^46 + 4801410 * q^47 + 9073674 * q^48 + 21448221 * q^49 + 2366848 * q^50 + 3749747 * q^51 + 7035334 * q^52 + 17191348 * q^53 + 5748697 * q^54 + 5271331 * q^55 + 14854657 * q^56 + 5393884 * q^57 + 4036260 * q^58 + 8263804 * q^59 + 10193498 * q^60 + 12366404 * q^61 + 18470554 * q^62 + 15526895 * q^63 + 49399626 * q^64 + 17325330 * q^65 + 11279868 * q^66 + 5477434 * q^67 + 44562265 * q^68 + 26851278 * q^69 + 9428823 * q^70 + 12108395 * q^71 + 22153063 * q^72 + 13995388 * q^73 + 13478769 * q^74 + 24654171 * q^75 + 8225460 * q^76 + 61240119 * q^77 + 17624449 * q^78 + 8215066 * q^79 + 65708461 * q^80 + 112675190 * q^81 + 29179962 * q^82 + 33597369 * q^83 + 13895447 * q^84 + 24308391 * q^85 + 22043075 * q^86 + 25661967 * q^87 + 32743591 * q^88 + 47538968 * q^89 + 46132321 * q^90 + 24574095 * q^91 + 108017386 * q^92 + 63765304 * q^93 + 41203657 * q^94 + 38032578 * q^95 + 41465754 * q^96 + 45954628 * q^97 + 37164970 * q^98 + 43882333 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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