LMFDB - Embedded newform 11.10.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,10,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	11.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:	$5.66539419780$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.2659452.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 306x - 836 $ x^3 - 306*x - 836
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.80408$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.60816 q^{2} +5.22371 q^{3} -480.549 q^{4} -529.708 q^{5} +29.2954 q^{6} -3708.24 q^{7} -5566.37 q^{8} -19655.7 q^{9} +O(q^{10})$	\(q+5.60816 q^{2} +5.22371 q^{3} -480.549 q^{4} -529.708 q^{5} +29.2954 q^{6} -3708.24 q^{7} -5566.37 q^{8} -19655.7 q^{9} -2970.69 q^{10} -14641.0 q^{11} -2510.24 q^{12} +30987.3 q^{13} -20796.4 q^{14} -2767.04 q^{15} +214824. q^{16} +250862. q^{17} -110232. q^{18} +438057. q^{19} +254551. q^{20} -19370.8 q^{21} -82109.0 q^{22} -1.78151e6 q^{23} -29077.1 q^{24} -1.67253e6 q^{25} +173782. q^{26} -205494. q^{27} +1.78199e6 q^{28} -2.59808e6 q^{29} -15518.0 q^{30} -2.09835e6 q^{31} +4.05475e6 q^{32} -76480.3 q^{33} +1.40687e6 q^{34} +1.96429e6 q^{35} +9.44552e6 q^{36} +2.62219e6 q^{37} +2.45669e6 q^{38} +161869. q^{39} +2.94855e6 q^{40} -2.91565e6 q^{41} -108634. q^{42} -3.01262e7 q^{43} +7.03571e6 q^{44} +1.04118e7 q^{45} -9.99100e6 q^{46} +1.45140e6 q^{47} +1.12218e6 q^{48} -2.66025e7 q^{49} -9.37983e6 q^{50} +1.31043e6 q^{51} -1.48909e7 q^{52} -3.32876e7 q^{53} -1.15244e6 q^{54} +7.75546e6 q^{55} +2.06415e7 q^{56} +2.28828e6 q^{57} -1.45704e7 q^{58} +1.40814e8 q^{59} +1.32970e6 q^{60} +1.32753e8 q^{61} -1.17678e7 q^{62} +7.28882e7 q^{63} -8.72501e7 q^{64} -1.64142e7 q^{65} -428913. q^{66} -4.13586e7 q^{67} -1.20551e8 q^{68} -9.30609e6 q^{69} +1.10160e7 q^{70} +1.81824e8 q^{71} +1.09411e8 q^{72} -4.13968e8 q^{73} +1.47056e7 q^{74} -8.73683e6 q^{75} -2.10508e8 q^{76} +5.42924e7 q^{77} +907785. q^{78} -5.90824e8 q^{79} -1.13794e8 q^{80} +3.85810e8 q^{81} -1.63514e7 q^{82} +6.29014e8 q^{83} +9.30860e6 q^{84} -1.32884e8 q^{85} -1.68953e8 q^{86} -1.35716e7 q^{87} +8.14972e7 q^{88} +7.73395e8 q^{89} +5.83910e7 q^{90} -1.14909e8 q^{91} +8.56103e8 q^{92} -1.09611e7 q^{93} +8.13966e6 q^{94} -2.32042e8 q^{95} +2.11808e7 q^{96} -1.00362e9 q^{97} -1.49191e8 q^{98} +2.87779e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9}+O(q^{10}) $ 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9	\( 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9} - 86724 q^{10} - 43923 q^{11} - 71040 q^{12} - 93258 q^{13} + 324264 q^{14} + 540330 q^{15} + 22656 q^{16} + 18678 q^{17} + 1997028 q^{18} - 1027356 q^{19} - 156576 q^{20} - 1287924 q^{21} + 1674690 q^{23} - 947232 q^{24} - 1560729 q^{25} - 2162088 q^{26} - 10285434 q^{27} - 2570304 q^{28} - 2693658 q^{29} + 14272500 q^{30} - 4525302 q^{31} + 160512 q^{32} + 2723226 q^{33} + 19899408 q^{34} - 7933860 q^{35} + 20908368 q^{36} - 8820204 q^{37} + 23297712 q^{38} + 24922920 q^{39} - 5145888 q^{40} - 9771102 q^{41} - 8130360 q^{42} + 18795744 q^{43} - 13352592 q^{44} - 91915398 q^{45} - 68671020 q^{46} - 31155816 q^{47} + 76391808 q^{48} - 54229677 q^{49} + 103405236 q^{50} - 62110884 q^{51} - 86345952 q^{52} + 47500122 q^{53} - 153828180 q^{54} + 26705184 q^{55} + 113407680 q^{56} + 62103096 q^{57} - 120644760 q^{58} + 332138370 q^{59} + 290804160 q^{60} - 49031730 q^{61} - 86992620 q^{62} + 319652784 q^{63} - 421220352 q^{64} + 161689572 q^{65} + 160406796 q^{66} + 330560082 q^{67} - 382273056 q^{68} - 104664822 q^{69} - 22907160 q^{70} - 57835050 q^{71} + 302075136 q^{72} - 458816886 q^{73} - 528939708 q^{74} - 562184580 q^{75} - 1324671744 q^{76} + 106293660 q^{77} + 903869520 q^{78} - 798908748 q^{79} + 442084224 q^{80} + 1544572395 q^{81} - 376730664 q^{82} + 1239784920 q^{83} - 809016384 q^{84} - 632001744 q^{85} + 627638088 q^{86} + 505901880 q^{87} + 293757024 q^{88} - 699523368 q^{89} - 2575080288 q^{90} - 268926960 q^{91} + 3537302976 q^{92} + 614745786 q^{93} + 3327514080 q^{94} + 107303856 q^{95} + 2520807168 q^{96} - 2207436012 q^{97} - 1261919472 q^{98} - 213070473 q^{99}+O(q^{100}) \) 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9 - 86724 * q^10 - 43923 * q^11 - 71040 * q^12 - 93258 * q^13 + 324264 * q^14 + 540330 * q^15 + 22656 * q^16 + 18678 * q^17 + 1997028 * q^18 - 1027356 * q^19 - 156576 * q^20 - 1287924 * q^21 + 1674690 * q^23 - 947232 * q^24 - 1560729 * q^25 - 2162088 * q^26 - 10285434 * q^27 - 2570304 * q^28 - 2693658 * q^29 + 14272500 * q^30 - 4525302 * q^31 + 160512 * q^32 + 2723226 * q^33 + 19899408 * q^34 - 7933860 * q^35 + 20908368 * q^36 - 8820204 * q^37 + 23297712 * q^38 + 24922920 * q^39 - 5145888 * q^40 - 9771102 * q^41 - 8130360 * q^42 + 18795744 * q^43 - 13352592 * q^44 - 91915398 * q^45 - 68671020 * q^46 - 31155816 * q^47 + 76391808 * q^48 - 54229677 * q^49 + 103405236 * q^50 - 62110884 * q^51 - 86345952 * q^52 + 47500122 * q^53 - 153828180 * q^54 + 26705184 * q^55 + 113407680 * q^56 + 62103096 * q^57 - 120644760 * q^58 + 332138370 * q^59 + 290804160 * q^60 - 49031730 * q^61 - 86992620 * q^62 + 319652784 * q^63 - 421220352 * q^64 + 161689572 * q^65 + 160406796 * q^66 + 330560082 * q^67 - 382273056 * q^68 - 104664822 * q^69 - 22907160 * q^70 - 57835050 * q^71 + 302075136 * q^72 - 458816886 * q^73 - 528939708 * q^74 - 562184580 * q^75 - 1324671744 * q^76 + 106293660 * q^77 + 903869520 * q^78 - 798908748 * q^79 + 442084224 * q^80 + 1544572395 * q^81 - 376730664 * q^82 + 1239784920 * q^83 - 809016384 * q^84 - 632001744 * q^85 + 627638088 * q^86 + 505901880 * q^87 + 293757024 * q^88 - 699523368 * q^89 - 2575080288 * q^90 - 268926960 * q^91 + 3537302976 * q^92 + 614745786 * q^93 + 3327514080 * q^94 + 107303856 * q^95 + 2520807168 * q^96 - 2207436012 * q^97 - 1261919472 * q^98 - 213070473 * 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 $

$2$	5.60816	0.247848	0.123924	−	0.992292i	$-0.460452\pi$
$2$	5.60816	0.247848	0.123924	+	0.992292i	$0.460452\pi$
$3$	5.22371	0.0372334	0.0186167	−	0.999827i	$-0.494074\pi$
$3$	5.22371	0.0372334	0.0186167	+	0.999827i	$0.494074\pi$
$4$	−480.549	−0.938571
$5$	−529.708	−0.379028	−0.189514	−	0.981878i	$-0.560691\pi$
$5$	−529.708	−0.379028	−0.189514	+	0.981878i	$0.560691\pi$
$6$	29.2954	0.00922823
$7$	−3708.24	−0.583750	−0.291875	−	0.956456i	$-0.594279\pi$
$7$	−3708.24	−0.583750	−0.291875	+	0.956456i	$0.594279\pi$
$8$	−5566.37	−0.480471
$9$	−19655.7	−0.998614
$10$	−2970.69	−0.0939414
$11$	−14641.0	−0.301511
$11$	−14641.0	−0.301511
$12$	−2510.24	−0.0349462
$13$	30987.3	0.300912	0.150456	−	0.988617i	$-0.451926\pi$
$13$	30987.3	0.300912	0.150456	+	0.988617i	$0.451926\pi$
$14$	−20796.4	−0.144681
$15$	−2767.04	−0.0141125
$16$	214824.	0.819488
$17$	250862.	0.728476	0.364238	−	0.931306i	$-0.381330\pi$
$17$	250862.	0.728476	0.364238	+	0.931306i	$0.381330\pi$
$18$	−110232.	−0.247504
$19$	438057.	0.771150	0.385575	−	0.922676i	$-0.374003\pi$
$19$	438057.	0.771150	0.385575	+	0.922676i	$0.374003\pi$
$20$	254551.	0.355745
$21$	−19370.8	−0.0217350
$22$	−82109.0	−0.0747289
$23$	−1.78151e6	−1.32744	−0.663718	−	0.747983i	$-0.731022\pi$
$23$	−1.78151e6	−1.32744	−0.663718	+	0.747983i	$0.731022\pi$
$24$	−29077.1	−0.0178896
$25$	−1.67253e6	−0.856337
$26$	173782.	0.0745803
$27$	−205494.	−0.0744153
$28$	1.78199e6	0.547891
$29$	−2.59808e6	−0.682120	−0.341060	−	0.940041i	$-0.610786\pi$
$29$	−2.59808e6	−0.682120	−0.341060	+	0.940041i	$0.610786\pi$
$30$	−15518.0	−0.00349776
$31$	−2.09835e6	−0.408084	−0.204042	−	0.978962i	$-0.565408\pi$
$31$	−2.09835e6	−0.408084	−0.204042	+	0.978962i	$0.565408\pi$
$32$	4.05475e6	0.683579
$33$	−76480.3	−0.0112263
$34$	1.40687e6	0.180551
$35$	1.96429e6	0.221258
$36$	9.44552e6	0.937270
$37$	2.62219e6	0.230015	0.115008	−	0.993365i	$-0.463311\pi$
$37$	2.62219e6	0.230015	0.115008	+	0.993365i	$0.463311\pi$
$38$	2.45669e6	0.191128
$39$	161869.	0.0112040
$40$	2.94855e6	0.182112
$41$	−2.91565e6	−0.161142	−0.0805708	−	0.996749i	$-0.525674\pi$
$41$	−2.91565e6	−0.161142	−0.0805708	+	0.996749i	$0.525674\pi$
$42$	−108634.	−0.00538698
$43$	−3.01262e7	−1.34381	−0.671903	−	0.740639i	$-0.734523\pi$
$43$	−3.01262e7	−1.34381	−0.671903	+	0.740639i	$0.734523\pi$
$44$	7.03571e6	0.282990
$45$	1.04118e7	0.378503
$46$	−9.99100e6	−0.329002
$47$	1.45140e6	0.0433856	0.0216928	−	0.999765i	$-0.493094\pi$
$47$	1.45140e6	0.0433856	0.0216928	+	0.999765i	$0.493094\pi$
$48$	1.12218e6	0.0305123
$49$	−2.66025e7	−0.659236
$50$	−9.37983e6	−0.212241
$51$	1.31043e6	0.0271236
$52$	−1.48909e7	−0.282427
$53$	−3.32876e7	−0.579483	−0.289742	−	0.957105i	$-0.593569\pi$
$53$	−3.32876e7	−0.579483	−0.289742	+	0.957105i	$0.593569\pi$
$54$	−1.15244e6	−0.0184437
$55$	7.75546e6	0.114281
$56$	2.06415e7	0.280475
$57$	2.28828e6	0.0287126
$58$	−1.45704e7	−0.169062
$59$	1.40814e8	1.51291	0.756455	−	0.654045i	$-0.226929\pi$
$59$	1.40814e8	1.51291	0.756455	+	0.654045i	$0.226929\pi$
$60$	1.32970e6	0.0132456
$61$	1.32753e8	1.22761	0.613806	−	0.789457i	$-0.289638\pi$
$61$	1.32753e8	1.22761	0.613806	+	0.789457i	$0.289638\pi$
$62$	−1.17678e7	−0.101143
$63$	7.28882e7	0.582941
$64$	−8.72501e7	−0.650064
$65$	−1.64142e7	−0.114054
$66$	−428913.	−0.00278242
$67$	−4.13586e7	−0.250743	−0.125372	−	0.992110i	$-0.540012\pi$
$67$	−4.13586e7	−0.250743	−0.125372	+	0.992110i	$0.540012\pi$
$68$	−1.20551e8	−0.683726
$69$	−9.30609e6	−0.0494250
$70$	1.10160e7	0.0548383
$71$	1.81824e8	0.849161	0.424580	−	0.905390i	$-0.360422\pi$
$71$	1.81824e8	0.849161	0.424580	+	0.905390i	$0.360422\pi$
$72$	1.09411e8	0.479805
$73$	−4.13968e8	−1.70614	−0.853068	−	0.521800i	$-0.825261\pi$
$73$	−4.13968e8	−1.70614	−0.853068	+	0.521800i	$0.825261\pi$
$74$	1.47056e7	0.0570087
$75$	−8.73683e6	−0.0318844
$76$	−2.10508e8	−0.723780
$77$	5.42924e7	0.176007
$78$	907785.	0.00277688
$79$	−5.90824e8	−1.70662	−0.853308	−	0.521407i	$-0.825407\pi$
$79$	−5.90824e8	−1.70662	−0.853308	+	0.521407i	$0.825407\pi$
$80$	−1.13794e8	−0.310609
$81$	3.85810e8	0.995843
$82$	−1.63514e7	−0.0399386
$83$	6.29014e8	1.45482	0.727409	−	0.686204i	$-0.240724\pi$
$83$	6.29014e8	1.45482	0.727409	+	0.686204i	$0.240724\pi$
$84$	9.30860e6	0.0203999
$85$	−1.32884e8	−0.276113
$86$	−1.68953e8	−0.333059
$87$	−1.35716e7	−0.0253977
$88$	8.14972e7	0.144867
$89$	7.73395e8	1.30661	0.653305	−	0.757095i	$-0.273382\pi$
$89$	7.73395e8	1.30661	0.653305	+	0.757095i	$0.273382\pi$
$90$	5.83910e7	0.0938112
$91$	−1.14909e8	−0.175657
$92$	8.56103e8	1.24589
$93$	−1.09611e7	−0.0151944
$94$	8.13966e6	0.0107530
$95$	−2.32042e8	−0.292288
$96$	2.11808e7	0.0254520
$97$	−1.00362e9	−1.15105	−0.575527	−	0.817783i	$-0.695203\pi$
$97$	−1.00362e9	−1.15105	−0.575527	+	0.817783i	$0.695203\pi$
$98$	−1.49191e8	−0.163390
$99$	2.87779e8	0.301093
$100$	8.03734e8	0.803734
$101$	−1.74307e9	−1.66674	−0.833371	−	0.552713i	$-0.813592\pi$
$101$	−1.74307e9	−1.66674	−0.833371	+	0.552713i	$0.813592\pi$
$102$	7.34910e6	0.00672254
$103$	1.51125e9	1.32302	0.661512	−	0.749935i	$-0.269915\pi$
$103$	1.51125e9	1.32302	0.661512	+	0.749935i	$0.269915\pi$
$104$	−1.72487e8	−0.144579
$105$	1.02609e7	0.00823819
$106$	−1.86682e8	−0.143624
$107$	−2.47353e8	−0.182428	−0.0912139	−	0.995831i	$-0.529075\pi$
$107$	−2.47353e8	−0.182428	−0.0912139	+	0.995831i	$0.529075\pi$
$108$	9.87498e7	0.0698440
$109$	−2.26894e9	−1.53958	−0.769792	−	0.638295i	$-0.779640\pi$
$109$	−2.26894e9	−1.53958	−0.769792	+	0.638295i	$0.779640\pi$
$110$	4.34938e7	0.0283244
$111$	1.36975e7	0.00856425
$112$	−7.96619e8	−0.478376
$113$	−8.92175e8	−0.514751	−0.257375	−	0.966311i	$-0.582858\pi$
$113$	−8.92175e8	−0.514751	−0.257375	+	0.966311i	$0.582858\pi$
$114$	1.28330e7	0.00711635
$115$	9.43682e8	0.503136
$116$	1.24850e9	0.640219
$117$	−6.09078e8	−0.300494
$118$	7.89710e8	0.374972
$119$	−9.30258e8	−0.425248
$120$	1.54024e7	0.00678066
$121$	2.14359e8	0.0909091
$122$	7.44502e8	0.304261
$123$	−1.52305e7	−0.00599985
$124$	1.00836e9	0.383016
$125$	1.92054e9	0.703605
$126$	4.08768e8	0.144481
$127$	4.19678e9	1.43153	0.715764	−	0.698343i	$-0.246079\pi$
$127$	4.19678e9	1.43153	0.715764	+	0.698343i	$0.246079\pi$
$128$	−2.56534e9	−0.844696
$129$	−1.57371e8	−0.0500345
$130$	−9.20536e7	−0.0282680
$131$	2.76730e9	0.820986	0.410493	−	0.911864i	$-0.365357\pi$
$131$	2.76730e9	0.820986	0.410493	+	0.911864i	$0.365357\pi$
$132$	3.67525e7	0.0105367
$133$	−1.62442e9	−0.450159
$134$	−2.31946e8	−0.0621462
$135$	1.08852e8	0.0282055
$136$	−1.39639e9	−0.350011
$137$	−7.75035e8	−0.187966	−0.0939829	−	0.995574i	$-0.529960\pi$
$137$	−7.75035e8	−0.187966	−0.0939829	+	0.995574i	$0.529960\pi$
$138$	−5.21900e7	−0.0122499
$139$	5.04823e7	0.0114702	0.00573512	−	0.999984i	$-0.498174\pi$
$139$	5.04823e7	0.0114702	0.00573512	+	0.999984i	$0.498174\pi$
$140$	−9.43936e8	−0.207666
$141$	7.58167e6	0.00161539
$142$	1.01970e9	0.210463
$143$	−4.53685e8	−0.0907282
$144$	−4.22251e9	−0.818352
$145$	1.37622e9	0.258543
$146$	−2.32160e9	−0.422862
$147$	−1.38964e8	−0.0245456
$148$	−1.26009e9	−0.215886
$149$	−6.50662e9	−1.08148	−0.540738	−	0.841191i	$-0.681855\pi$
$149$	−6.50662e9	−1.08148	−0.540738	+	0.841191i	$0.681855\pi$
$150$	−4.89975e7	−0.00790248
$151$	3.28654e9	0.514450	0.257225	−	0.966352i	$-0.417192\pi$
$151$	3.28654e9	0.514450	0.257225	+	0.966352i	$0.417192\pi$
$152$	−2.43838e9	−0.370515
$153$	−4.93087e9	−0.727466
$154$	3.04480e8	0.0436230
$155$	1.11151e9	0.154675
$156$	−7.77857e7	−0.0105157
$157$	6.69227e9	0.879073	0.439536	−	0.898225i	$-0.355143\pi$
$157$	6.69227e9	0.879073	0.439536	+	0.898225i	$0.355143\pi$
$158$	−3.31343e9	−0.422981
$159$	−1.73885e8	−0.0215762
$160$	−2.14783e9	−0.259096
$161$	6.60628e9	0.774891
$162$	2.16368e9	0.246818
$163$	1.08581e10	1.20478	0.602391	−	0.798201i	$-0.294215\pi$
$163$	1.08581e10	1.20478	0.602391	+	0.798201i	$0.294215\pi$
$164$	1.40111e9	0.151243
$165$	4.05122e7	0.00425509
$166$	3.52761e9	0.360574
$167$	1.59966e10	1.59149	0.795743	−	0.605634i	$-0.207080\pi$
$167$	1.59966e10	1.59149	0.795743	+	0.605634i	$0.207080\pi$
$168$	1.07825e8	0.0104430
$169$	−9.64429e9	−0.909452
$170$	−7.45233e8	−0.0684340
$171$	−8.61032e9	−0.770081
$172$	1.44771e10	1.26126
$173$	−1.72311e10	−1.46253	−0.731266	−	0.682093i	$-0.761070\pi$
$173$	−1.72311e10	−1.46253	−0.731266	+	0.682093i	$0.761070\pi$
$174$	−7.61116e7	−0.00629476
$175$	6.20216e9	0.499887
$176$	−3.14524e9	−0.247085
$177$	7.35574e8	0.0563309
$178$	4.33732e9	0.323841
$179$	−3.19245e9	−0.232426	−0.116213	−	0.993224i	$-0.537076\pi$
$179$	−3.19245e9	−0.232426	−0.116213	+	0.993224i	$0.537076\pi$
$180$	−5.00337e9	−0.355252
$181$	−5.63080e9	−0.389957	−0.194978	−	0.980808i	$-0.562464\pi$
$181$	−5.63080e9	−0.389957	−0.194978	+	0.980808i	$0.562464\pi$
$182$	−6.44425e8	−0.0435363
$183$	6.93465e8	0.0457082
$184$	9.91655e9	0.637794
$185$	−1.38900e9	−0.0871822
$186$	−6.14718e7	−0.00376589
$187$	−3.67287e9	−0.219644
$188$	−6.97466e8	−0.0407205
$189$	7.62021e8	0.0434399
$190$	−1.30133e9	−0.0724429
$191$	−2.18322e10	−1.18699	−0.593497	−	0.804837i	$-0.702253\pi$
$191$	−2.18322e10	−1.18699	−0.593497	+	0.804837i	$0.702253\pi$
$192$	−4.55769e8	−0.0242041
$193$	−2.78398e10	−1.44430	−0.722152	−	0.691735i	$-0.756847\pi$
$193$	−2.78398e10	−1.44430	−0.722152	+	0.691735i	$0.756847\pi$
$194$	−5.62845e9	−0.285286
$195$	−8.57432e7	−0.00424662
$196$	1.27838e10	0.618740
$197$	2.88647e10	1.36543	0.682714	−	0.730686i	$-0.260800\pi$
$197$	2.88647e10	1.36543	0.682714	+	0.730686i	$0.260800\pi$
$198$	1.61391e9	0.0746253
$199$	−3.43514e10	−1.55276	−0.776382	−	0.630263i	$-0.782947\pi$
$199$	−3.43514e10	−1.55276	−0.776382	+	0.630263i	$0.782947\pi$
$200$	9.30994e9	0.411445
$201$	−2.16045e8	−0.00933604
$202$	−9.77541e9	−0.413099
$203$	9.63431e9	0.398188
$204$	−6.29725e8	−0.0254575
$205$	1.54444e9	0.0610772
$206$	8.47530e9	0.327908
$207$	3.50169e10	1.32560
$208$	6.65681e9	0.246593
$209$	−6.41359e9	−0.232511
$210$	5.75445e7	0.00204182
$211$	2.85142e9	0.0990355	0.0495177	−	0.998773i	$-0.484232\pi$
$211$	2.85142e9	0.0990355	0.0495177	+	0.998773i	$0.484232\pi$
$212$	1.59963e10	0.543886
$213$	9.49798e8	0.0316172
$214$	−1.38720e9	−0.0452143
$215$	1.59581e10	0.509341
$216$	1.14385e9	0.0357544
$217$	7.78118e9	0.238219
$218$	−1.27246e10	−0.381583
$219$	−2.16245e9	−0.0635253
$220$	−3.72688e9	−0.107261
$221$	7.77354e9	0.219207
$222$	7.68180e7	0.00212263
$223$	−2.76836e10	−0.749638	−0.374819	−	0.927098i	$-0.622295\pi$
$223$	−2.76836e10	−0.749638	−0.374819	+	0.927098i	$0.622295\pi$
$224$	−1.50360e10	−0.399040
$225$	3.28748e10	0.855150
$226$	−5.00346e9	−0.127580
$227$	1.72906e10	0.432208	0.216104	−	0.976370i	$-0.430665\pi$
$227$	1.72906e10	0.432208	0.216104	+	0.976370i	$0.430665\pi$
$228$	−1.09963e9	−0.0269488
$229$	−1.78101e10	−0.427963	−0.213981	−	0.976838i	$-0.568643\pi$
$229$	−1.78101e10	−0.427963	−0.213981	+	0.976838i	$0.568643\pi$
$230$	5.29232e9	0.124701
$231$	2.83608e8	0.00655336
$232$	1.44619e10	0.327739
$233$	3.95162e10	0.878361	0.439181	−	0.898399i	$-0.355269\pi$
$233$	3.95162e10	0.878361	0.439181	+	0.898399i	$0.355269\pi$
$234$	−3.41580e9	−0.0744769
$235$	−7.68817e8	−0.0164444
$236$	−6.76682e10	−1.41997
$237$	−3.08629e9	−0.0635432
$238$	−5.21703e9	−0.105397
$239$	−5.30678e10	−1.05206	−0.526030	−	0.850466i	$-0.676320\pi$
$239$	−5.30678e10	−1.05206	−0.526030	+	0.850466i	$0.676320\pi$
$240$	−5.94426e8	−0.0115650
$241$	−4.31673e10	−0.824287	−0.412143	−	0.911119i	$-0.635220\pi$
$241$	−4.31673e10	−0.824287	−0.412143	+	0.911119i	$0.635220\pi$
$242$	1.20216e9	0.0225316
$243$	6.06009e9	0.111494
$244$	−6.37945e10	−1.15220
$245$	1.40916e10	0.249869
$246$	−8.54149e7	−0.00148705
$247$	1.35742e10	0.232048
$248$	1.16802e10	0.196072
$249$	3.28578e9	0.0541679
$250$	1.07707e10	0.174387
$251$	−4.92500e10	−0.783204	−0.391602	−	0.920135i	$-0.628079\pi$
$251$	−4.92500e10	−0.783204	−0.391602	+	0.920135i	$0.628079\pi$
$252$	−3.50263e10	−0.547132
$253$	2.60831e10	0.400237
$254$	2.35362e10	0.354801
$255$	−6.94146e8	−0.0102806
$256$	3.02852e10	0.440708
$257$	1.28287e11	1.83435	0.917177	−	0.398480i	$-0.130462\pi$
$257$	1.28287e11	1.83435	0.917177	+	0.398480i	$0.130462\pi$
$258$	−8.82559e8	−0.0124009
$259$	−9.72372e9	−0.134271
$260$	7.88784e9	0.107048
$261$	5.10671e10	0.681175
$262$	1.55195e10	0.203480
$263$	−9.72911e9	−0.125393	−0.0626963	−	0.998033i	$-0.519970\pi$
$263$	−9.72911e9	−0.125393	−0.0626963	+	0.998033i	$0.519970\pi$
$264$	4.25717e8	0.00539391
$265$	1.76327e10	0.219641
$266$	−9.11001e9	−0.111571
$267$	4.03999e9	0.0486496
$268$	1.98748e10	0.235341
$269$	2.92266e10	0.340324	0.170162	−	0.985416i	$-0.445571\pi$
$269$	2.92266e10	0.340324	0.170162	+	0.985416i	$0.445571\pi$
$270$	6.10458e8	0.00699067
$271$	−7.01891e10	−0.790511	−0.395255	−	0.918571i	$-0.629344\pi$
$271$	−7.01891e10	−0.790511	−0.395255	+	0.918571i	$0.629344\pi$
$272$	5.38912e10	0.596977
$273$	−6.00248e8	−0.00654032
$274$	−4.34652e9	−0.0465869
$275$	2.44876e10	0.258195
$276$	4.47203e9	0.0463889
$277$	−7.01760e10	−0.716192	−0.358096	−	0.933685i	$-0.616574\pi$
$277$	−7.01760e10	−0.716192	−0.358096	+	0.933685i	$0.616574\pi$
$278$	2.83113e8	0.00284287
$279$	4.12445e10	0.407518
$280$	−1.09340e10	−0.106308
$281$	1.32522e11	1.26798	0.633988	−	0.773343i	$-0.281417\pi$
$281$	1.32522e11	1.26798	0.633988	+	0.773343i	$0.281417\pi$
$282$	4.25192e7	0.000400372 0
$283$	−1.12265e11	−1.04041	−0.520206	−	0.854041i	$-0.674145\pi$
$283$	−1.12265e11	−1.04041	−0.520206	+	0.854041i	$0.674145\pi$
$284$	−8.73755e10	−0.796998
$285$	−1.21212e9	−0.0108829
$286$	−2.54434e9	−0.0224868
$287$	1.08119e10	0.0940664
$288$	−7.96989e10	−0.682631
$289$	−5.56561e10	−0.469323
$290$	7.71808e9	0.0640794
$291$	−5.24260e9	−0.0428577
$292$	1.98932e11	1.60133
$293$	−2.51673e11	−1.99495	−0.997474	−	0.0710283i	$-0.977372\pi$
$293$	−2.51673e11	−1.99495	−0.997474	+	0.0710283i	$0.977372\pi$
$294$	−7.79331e8	−0.00608358
$295$	−7.45906e10	−0.573436
$296$	−1.45961e10	−0.110516
$297$	3.00864e9	0.0224370
$298$	−3.64901e10	−0.268042
$299$	−5.52043e10	−0.399441
$300$	4.19847e9	0.0299258
$301$	1.11715e11	0.784447
$302$	1.84314e10	0.127505
$303$	−9.10528e9	−0.0620586
$304$	9.41050e10	0.631948
$305$	−7.03206e10	−0.465300
$306$	−2.76531e10	−0.180301
$307$	−9.35853e10	−0.601291	−0.300646	−	0.953736i	$-0.597202\pi$
$307$	−9.35853e10	−0.601291	−0.300646	+	0.953736i	$0.597202\pi$
$308$	−2.60901e10	−0.165195
$309$	7.89430e9	0.0492607
$310$	6.23353e9	0.0383360
$311$	−9.71358e10	−0.588786	−0.294393	−	0.955684i	$-0.595117\pi$
$311$	−9.71358e10	−0.588786	−0.294393	+	0.955684i	$0.595117\pi$
$312$	−9.01020e8	−0.00538318
$313$	2.31565e11	1.36372	0.681858	−	0.731485i	$-0.261172\pi$
$313$	2.31565e11	1.36372	0.681858	+	0.731485i	$0.261172\pi$
$314$	3.75313e10	0.217876
$315$	−3.86095e10	−0.220951
$316$	2.83919e11	1.60178
$317$	7.29141e10	0.405550	0.202775	−	0.979225i	$-0.435004\pi$
$317$	7.29141e10	0.405550	0.202775	+	0.979225i	$0.435004\pi$
$318$	−9.75172e8	−0.00534760
$319$	3.80385e10	0.205667
$320$	4.62171e10	0.246393
$321$	−1.29210e9	−0.00679241
$322$	3.70491e10	0.192055
$323$	1.09892e11	0.561764
$324$	−1.85400e11	−0.934670
$325$	−5.18273e10	−0.257682
$326$	6.08938e10	0.298603
$327$	−1.18523e10	−0.0573240
$328$	1.62296e10	0.0774238
$329$	−5.38213e9	−0.0253264
$330$	2.27199e8	0.00105461
$331$	1.50837e11	0.690689	0.345345	−	0.938476i	$-0.387762\pi$
$331$	1.50837e11	0.690689	0.345345	+	0.938476i	$0.387762\pi$
$332$	−3.02272e11	−1.36545
$333$	−5.15410e10	−0.229696
$334$	8.97113e10	0.394447
$335$	2.19080e10	0.0950389
$336$	−4.16130e9	−0.0178116
$337$	8.16746e10	0.344947	0.172474	−	0.985014i	$-0.444824\pi$
$337$	8.16746e10	0.344947	0.172474	+	0.985014i	$0.444824\pi$
$338$	−5.40867e10	−0.225406
$339$	−4.66046e9	−0.0191659
$340$	6.38571e10	0.259152
$341$	3.07219e10	0.123042
$342$	−4.82880e10	−0.190863
$343$	2.48290e11	0.968579
$344$	1.67694e11	0.645660
$345$	4.92952e9	0.0187335
$346$	−9.66347e10	−0.362485
$347$	−3.94411e11	−1.46038	−0.730190	−	0.683244i	$-0.760569\pi$
$347$	−3.94411e11	−1.46038	−0.730190	+	0.683244i	$0.760569\pi$
$348$	6.52181e9	0.0238375
$349$	−2.68708e11	−0.969543	−0.484771	−	0.874641i	$-0.661097\pi$
$349$	−2.68708e11	−0.969543	−0.484771	+	0.874641i	$0.661097\pi$
$350$	3.47827e10	0.123896
$351$	−6.36770e9	−0.0223924
$352$	−5.93655e10	−0.206107
$353$	5.21832e10	0.178873	0.0894365	−	0.995993i	$-0.471493\pi$
$353$	5.21832e10	0.178873	0.0894365	+	0.995993i	$0.471493\pi$
$354$	4.12521e9	0.0139615
$355$	−9.63140e10	−0.321856
$356$	−3.71654e11	−1.22635
$357$	−4.85939e9	−0.0158334
$358$	−1.79038e10	−0.0576064
$359$	1.98420e11	0.630464	0.315232	−	0.949015i	$-0.397918\pi$
$359$	1.98420e11	0.630464	0.315232	+	0.949015i	$0.397918\pi$
$360$	−5.79559e10	−0.181860
$361$	−1.30794e11	−0.405327
$362$	−3.15784e10	−0.0966500
$363$	1.11975e9	0.00338486
$364$	5.52191e10	0.164867
$365$	2.19282e11	0.646674
$366$	3.88906e9	0.0113287
$367$	−2.39772e11	−0.689923	−0.344962	−	0.938617i	$-0.612108\pi$
$367$	−2.39772e11	−0.689923	−0.344962	+	0.938617i	$0.612108\pi$
$368$	−3.82711e11	−1.08782
$369$	5.73091e10	0.160918
$370$	−7.78971e9	−0.0216079
$371$	1.23438e11	0.338274
$372$	5.26736e9	0.0142610
$373$	2.65767e11	0.710905	0.355452	−	0.934694i	$-0.384327\pi$
$373$	2.65767e11	0.710905	0.355452	+	0.934694i	$0.384327\pi$
$374$	−2.05980e10	−0.0544382
$375$	1.00323e10	0.0261976
$376$	−8.07901e9	−0.0208455
$377$	−8.05074e10	−0.205258
$378$	4.27354e9	0.0107665
$379$	4.82730e11	1.20179	0.600894	−	0.799328i	$-0.294811\pi$
$379$	4.82730e11	1.20179	0.600894	+	0.799328i	$0.294811\pi$
$380$	1.11508e11	0.274333
$381$	2.19228e10	0.0533007
$382$	−1.22439e11	−0.294194
$383$	7.38224e11	1.75305	0.876523	−	0.481360i	$-0.159857\pi$
$383$	7.38224e11	1.75305	0.876523	+	0.481360i	$0.159857\pi$
$384$	−1.34006e10	−0.0314509
$385$	−2.87591e10	−0.0667118
$386$	−1.56130e11	−0.357968
$387$	5.92152e11	1.34194
$388$	4.82287e11	1.08035
$389$	−4.09731e11	−0.907247	−0.453623	−	0.891194i	$-0.649869\pi$
$389$	−4.09731e11	−0.907247	−0.453623	+	0.891194i	$0.649869\pi$
$390$	−4.80861e8	−0.00105252
$391$	−4.46914e11	−0.967004
$392$	1.48079e11	0.316743
$393$	1.44556e10	0.0305681
$394$	1.61878e11	0.338418
$395$	3.12964e11	0.646856
$396$	−1.38292e11	−0.282598
$397$	−8.31366e11	−1.67971	−0.839856	−	0.542809i	$-0.817361\pi$
$397$	−8.31366e11	−1.67971	−0.839856	+	0.542809i	$0.817361\pi$
$398$	−1.92648e11	−0.384849
$399$	−8.48550e9	−0.0167610
$400$	−3.59300e11	−0.701758
$401$	4.18990e11	0.809196	0.404598	−	0.914495i	$-0.367411\pi$
$401$	4.18990e11	0.809196	0.404598	+	0.914495i	$0.367411\pi$
$402$	−1.21162e9	−0.00231392
$403$	−6.50221e10	−0.122797
$404$	8.37630e11	1.56436
$405$	−2.04367e11	−0.377453
$406$	5.40307e10	0.0986901
$407$	−3.83915e10	−0.0693521
$408$	−7.29434e9	−0.0130321
$409$	6.44702e11	1.13921	0.569606	−	0.821918i	$-0.307096\pi$
$409$	6.44702e11	1.13921	0.569606	+	0.821918i	$0.307096\pi$
$410$	8.66147e9	0.0151379
$411$	−4.04855e9	−0.00699861
$412$	−7.26227e11	−1.24175
$413$	−5.22175e11	−0.883162
$414$	1.96380e11	0.328546
$415$	−3.33194e11	−0.551418
$416$	1.25646e11	0.205697
$417$	2.63705e8	0.000427076 0
$418$	−3.59684e10	−0.0576273
$419$	−6.39601e11	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$419$	−6.39601e11	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$420$	−4.93084e9	−0.00773213
$421$	−8.52505e11	−1.32260	−0.661298	−	0.750123i	$-0.729994\pi$
$421$	−8.52505e11	−1.32260	−0.661298	+	0.750123i	$0.729994\pi$
$422$	1.59912e10	0.0245457
$423$	−2.85282e10	−0.0433255
$424$	1.85291e11	0.278425
$425$	−4.19575e11	−0.623821
$426$	5.32662e9	0.00783625
$427$	−4.92282e11	−0.716619
$428$	1.18865e11	0.171221
$429$	−2.36992e9	−0.00337812
$430$	8.94956e10	0.126239
$431$	5.99391e11	0.836686	0.418343	−	0.908289i	$-0.362611\pi$
$431$	5.99391e11	0.836686	0.418343	+	0.908289i	$0.362611\pi$
$432$	−4.41450e10	−0.0609824
$433$	−5.93237e11	−0.811022	−0.405511	−	0.914090i	$-0.632906\pi$
$433$	−5.93237e11	−0.811022	−0.405511	+	0.914090i	$0.632906\pi$
$434$	4.36381e10	0.0590421
$435$	7.18899e9	0.00962645
$436$	1.09034e12	1.44501
$437$	−7.80403e11	−1.02365
$438$	−1.21273e10	−0.0157446
$439$	3.41487e11	0.438818	0.219409	−	0.975633i	$-0.429587\pi$
$439$	3.41487e11	0.438818	0.219409	+	0.975633i	$0.429587\pi$
$440$	−4.31697e10	−0.0549089
$441$	5.22892e11	0.658322
$442$	4.35953e10	0.0543299
$443$	1.10692e12	1.36553	0.682763	−	0.730640i	$-0.260778\pi$
$443$	1.10692e12	1.36553	0.682763	+	0.730640i	$0.260778\pi$
$444$	−6.58234e9	−0.00803816
$445$	−4.09674e11	−0.495243
$446$	−1.55254e11	−0.185796
$447$	−3.39887e10	−0.0402671
$448$	3.23545e11	0.379475
$449$	1.13756e12	1.32089	0.660447	−	0.750873i	$-0.270367\pi$
$449$	1.13756e12	1.32089	0.660447	+	0.750873i	$0.270367\pi$
$450$	1.84367e11	0.211947
$451$	4.26880e10	0.0485860
$452$	4.28733e11	0.483130
$453$	1.71679e10	0.0191547
$454$	9.69683e10	0.107122
$455$	6.08680e10	0.0665791
$456$	−1.27374e10	−0.0137956
$457$	−3.31654e11	−0.355682	−0.177841	−	0.984059i	$-0.556911\pi$
$457$	−3.31654e11	−0.355682	−0.177841	+	0.984059i	$0.556911\pi$
$458$	−9.98816e10	−0.106070
$459$	−5.15506e10	−0.0542097
$460$	−4.53485e11	−0.472229
$461$	−8.99517e11	−0.927589	−0.463794	−	0.885943i	$-0.653512\pi$
$461$	−8.99517e11	−0.927589	−0.463794	+	0.885943i	$0.653512\pi$
$462$	1.59052e9	0.00162424
$463$	4.95814e11	0.501423	0.250712	−	0.968062i	$-0.419335\pi$
$463$	4.95814e11	0.501423	0.250712	+	0.968062i	$0.419335\pi$
$464$	−5.58129e11	−0.558989
$465$	5.80621e9	0.00575909
$466$	2.21613e11	0.217700
$467$	8.16039e11	0.793935	0.396968	−	0.917833i	$-0.370063\pi$
$467$	8.16039e11	0.793935	0.396968	+	0.917833i	$0.370063\pi$
$468$	2.92691e11	0.282035
$469$	1.53368e11	0.146372
$470$	−4.31165e9	−0.00407570
$471$	3.49584e10	0.0327309
$472$	−7.83825e11	−0.726909
$473$	4.41078e11	0.405173
$474$	−1.73084e10	−0.0157490
$475$	−7.32665e11	−0.660365
$476$	4.47034e11	0.399125
$477$	6.54291e11	0.578680
$478$	−2.97612e11	−0.260751
$479$	−1.51546e11	−0.131533	−0.0657664	−	0.997835i	$-0.520949\pi$
$479$	−1.51546e11	−0.131533	−0.0657664	+	0.997835i	$0.520949\pi$
$480$	−1.12196e10	−0.00964703
$481$	8.12546e10	0.0692142
$482$	−2.42089e11	−0.204298
$483$	3.45093e10	0.0288519
$484$	−1.03010e11	−0.0853247
$485$	5.31625e11	0.436282
$486$	3.39860e10	0.0276335
$487$	−1.14773e12	−0.924613	−0.462307	−	0.886720i	$-0.652978\pi$
$487$	−1.14773e12	−0.924613	−0.462307	+	0.886720i	$0.652978\pi$
$488$	−7.38954e11	−0.589832
$489$	5.67194e10	0.0448582
$490$	7.90278e10	0.0619295
$491$	−1.37836e12	−1.07027	−0.535137	−	0.844766i	$-0.679740\pi$
$491$	−1.37836e12	−1.07027	−0.535137	+	0.844766i	$0.679740\pi$
$492$	7.31898e9	0.00563129
$493$	−6.51759e11	−0.496908
$494$	7.61262e10	0.0575126
$495$	−1.52439e11	−0.114123
$496$	−4.50774e11	−0.334420
$497$	−6.74250e11	−0.495698
$498$	1.84272e10	0.0134254
$499$	2.00071e12	1.44454	0.722272	−	0.691609i	$-0.243098\pi$
$499$	2.00071e12	1.44454	0.722272	+	0.691609i	$0.243098\pi$
$500$	−9.22914e11	−0.660383
$501$	8.35614e10	0.0592565
$502$	−2.76202e11	−0.194115
$503$	−4.54476e11	−0.316559	−0.158280	−	0.987394i	$-0.550595\pi$
$503$	−4.54476e11	−0.316559	−0.158280	+	0.987394i	$0.550595\pi$
$504$	−4.05722e11	−0.280086
$505$	9.23319e11	0.631743
$506$	1.46278e11	0.0991979
$507$	−5.03789e10	−0.0338620
$508$	−2.01676e12	−1.34359
$509$	−1.38416e11	−0.0914020	−0.0457010	−	0.998955i	$-0.514552\pi$
$509$	−1.38416e11	−0.0914020	−0.0457010	+	0.998955i	$0.514552\pi$
$510$	−3.89288e9	−0.00254803
$511$	1.53509e12	0.995958
$512$	1.48330e12	0.953925
$513$	−9.00180e10	−0.0573854
$514$	7.19453e11	0.454641
$515$	−8.00519e11	−0.501463
$516$	7.56242e10	0.0469610
$517$	−2.12499e10	−0.0130813
$518$	−5.45321e10	−0.0332789
$519$	−9.00101e10	−0.0544551
$520$	9.13677e10	0.0547996
$521$	2.39269e12	1.42271	0.711357	−	0.702831i	$-0.248081\pi$
$521$	2.39269e12	1.42271	0.711357	+	0.702831i	$0.248081\pi$
$522$	2.86392e11	0.168828
$523$	2.87811e12	1.68209	0.841045	−	0.540965i	$-0.181941\pi$
$523$	2.87811e12	1.68209	0.841045	+	0.540965i	$0.181941\pi$
$524$	−1.32982e12	−0.770554
$525$	3.23983e10	0.0186125
$526$	−5.45624e10	−0.0310783
$527$	−5.26395e11	−0.297279
$528$	−1.64298e10	−0.00919982
$529$	1.37263e12	0.762085
$530$	9.88870e10	0.0544375
$531$	−2.76781e12	−1.51081
$532$	7.80613e11	0.422507
$533$	−9.03480e10	−0.0484893
$534$	2.26569e10	0.0120577
$535$	1.31025e11	0.0691453
$536$	2.30217e11	0.120475
$537$	−1.66764e10	−0.00865403
$538$	1.63907e11	0.0843486
$539$	3.89488e11	0.198767
$540$	−5.23086e10	−0.0264729
$541$	1.80734e11	0.0907093	0.0453546	−	0.998971i	$-0.485558\pi$
$541$	1.80734e11	0.0907093	0.0453546	+	0.998971i	$0.485558\pi$
$542$	−3.93632e11	−0.195926
$543$	−2.94137e10	−0.0145194
$544$	1.01718e12	0.497971
$545$	1.20188e12	0.583546
$546$	−3.36629e9	−0.00162100
$547$	1.26284e12	0.603122	0.301561	−	0.953447i	$-0.402492\pi$
$547$	1.26284e12	0.603122	0.301561	+	0.953447i	$0.402492\pi$
$548$	3.72442e11	0.176419
$549$	−2.60936e12	−1.22591
$550$	1.37330e11	0.0639932
$551$	−1.13811e12	−0.526018
$552$	5.18012e10	0.0237473
$553$	2.19092e12	0.996238
$554$	−3.93558e11	−0.177507
$555$	−7.25570e9	−0.00324609
$556$	−2.42592e10	−0.0107656
$557$	−7.61625e11	−0.335269	−0.167634	−	0.985849i	$-0.553613\pi$
$557$	−7.61625e11	−0.335269	−0.167634	+	0.985849i	$0.553613\pi$
$558$	2.31305e11	0.101002
$559$	−9.33531e11	−0.404367
$560$	4.21976e11	0.181318
$561$	−1.91860e10	−0.00817809
$562$	7.43207e11	0.314265
$563$	−3.96419e12	−1.66290	−0.831452	−	0.555597i	$-0.812490\pi$
$563$	−3.96419e12	−1.66290	−0.831452	+	0.555597i	$0.812490\pi$
$564$	−3.64336e9	−0.00151616
$565$	4.72593e11	0.195105
$566$	−6.29600e11	−0.257864
$567$	−1.43068e12	−0.581324
$568$	−1.01210e12	−0.407997
$569$	−2.63858e12	−1.05528	−0.527638	−	0.849470i	$-0.676922\pi$
$569$	−2.63858e12	−1.05528	−0.527638	+	0.849470i	$0.676922\pi$
$570$	−6.79776e9	−0.00269730
$571$	−3.58732e12	−1.41224	−0.706118	−	0.708094i	$-0.749555\pi$
$571$	−3.58732e12	−1.41224	−0.706118	+	0.708094i	$0.749555\pi$
$572$	2.18018e11	0.0851549
$573$	−1.14045e11	−0.0441958
$574$	6.06350e10	0.0233142
$575$	2.97964e12	1.13673
$576$	1.71496e12	0.649163
$577$	1.52047e11	0.0571066	0.0285533	−	0.999592i	$-0.490910\pi$
$577$	1.52047e11	0.0571066	0.0285533	+	0.999592i	$0.490910\pi$
$578$	−3.12128e11	−0.116321
$579$	−1.45427e11	−0.0537764
$580$	−6.61342e11	−0.242661
$581$	−2.33254e12	−0.849251
$582$	−2.94013e10	−0.0106222
$583$	4.87364e11	0.174721
$584$	2.30430e12	0.819749
$585$	3.22634e11	0.113896
$586$	−1.41142e12	−0.494444
$587$	−1.08736e12	−0.378007	−0.189004	−	0.981976i	$-0.560526\pi$
$587$	−1.08736e12	−0.378007	−0.189004	+	0.981976i	$0.560526\pi$
$588$	6.67789e10	0.0230378
$589$	−9.19194e11	−0.314694
$590$	−4.18316e11	−0.142125
$591$	1.50781e11	0.0508396
$592$	5.63309e11	0.188495
$593$	5.96110e12	1.97961	0.989806	−	0.142420i	$-0.0454885\pi$
$593$	5.96110e12	1.97961	0.989806	+	0.142420i	$0.0454885\pi$
$594$	1.68729e10	0.00556097
$595$	4.92765e11	0.161181
$596$	3.12675e12	1.01504
$597$	−1.79442e11	−0.0578147
$598$	−3.09594e11	−0.0990005
$599$	−3.89502e12	−1.23620	−0.618100	−	0.786099i	$-0.712097\pi$
$599$	−3.89502e12	−1.23620	−0.618100	+	0.786099i	$0.712097\pi$
$600$	4.86324e10	0.0153195
$601$	4.36888e12	1.36595	0.682975	−	0.730442i	$-0.260686\pi$
$601$	4.36888e12	1.36595	0.682975	+	0.730442i	$0.260686\pi$
$602$	6.26517e11	0.194424
$603$	8.12934e11	0.250396
$604$	−1.57934e12	−0.482848
$605$	−1.13548e11	−0.0344571
$606$	−5.10639e10	−0.0153811
$607$	2.33142e12	0.697062	0.348531	−	0.937297i	$-0.386681\pi$
$607$	2.33142e12	0.697062	0.348531	+	0.937297i	$0.386681\pi$
$608$	1.77621e12	0.527142
$609$	5.03268e10	0.0148259
$610$	−3.94369e11	−0.115324
$611$	4.49749e10	0.0130552
$612$	2.36952e12	0.682778
$613$	7.55641e11	0.216144	0.108072	−	0.994143i	$-0.465532\pi$
$613$	7.55641e11	0.216144	0.108072	+	0.994143i	$0.465532\pi$
$614$	−5.24841e11	−0.149029
$615$	8.06771e9	0.00227411
$616$	−3.02212e11	−0.0845664
$617$	1.61073e11	0.0447446	0.0223723	−	0.999750i	$-0.492878\pi$
$617$	1.61073e11	0.0447446	0.0223723	+	0.999750i	$0.492878\pi$
$618$	4.42725e10	0.0122092
$619$	−1.34219e12	−0.367457	−0.183728	−	0.982977i	$-0.558817\pi$
$619$	−1.34219e12	−0.367457	−0.183728	+	0.982977i	$0.558817\pi$
$620$	−5.34135e11	−0.145174
$621$	3.66090e11	0.0987815
$622$	−5.44753e11	−0.145929
$623$	−2.86794e12	−0.762734
$624$	3.47732e10	0.00918152
$625$	2.24934e12	0.589651
$626$	1.29865e12	0.337994
$627$	−3.35027e10	−0.00865717
$628$	−3.21596e12	−0.825072
$629$	6.57808e11	0.167560
$630$	−2.16528e11	−0.0547623
$631$	−2.02548e12	−0.508622	−0.254311	−	0.967123i	$-0.581849\pi$
$631$	−2.02548e12	−0.508622	−0.254311	+	0.967123i	$0.581849\pi$
$632$	3.28874e12	0.819979
$633$	1.48950e10	0.00368743
$634$	4.08914e11	0.100515
$635$	−2.22307e12	−0.542589
$636$	8.35600e10	0.0202508
$637$	−8.24341e11	−0.198372
$638$	2.13326e11	0.0509741
$639$	−3.57389e12	−0.847983
$640$	1.35888e12	0.320164
$641$	2.60291e12	0.608973	0.304487	−	0.952517i	$-0.401515\pi$
$641$	2.60291e12	0.608973	0.304487	+	0.952517i	$0.401515\pi$
$642$	−7.24631e9	−0.00168348
$643$	−1.83218e12	−0.422686	−0.211343	−	0.977412i	$-0.567784\pi$
$643$	−1.83218e12	−0.422686	−0.211343	+	0.977412i	$0.567784\pi$
$644$	−3.17464e12	−0.727291
$645$	8.33605e10	0.0189645
$646$	6.16291e11	0.139232
$647$	4.93674e12	1.10757	0.553785	−	0.832660i	$-0.313183\pi$
$647$	4.93674e12	1.10757	0.553785	+	0.832660i	$0.313183\pi$
$648$	−2.14756e12	−0.478473
$649$	−2.06166e12	−0.456160
$650$	−2.90656e11	−0.0638659
$651$	4.06466e10	0.00886971
$652$	−5.21783e12	−1.13077
$653$	−9.07722e12	−1.95364	−0.976818	−	0.214071i	$-0.931328\pi$
$653$	−9.07722e12	−1.95364	−0.976818	+	0.214071i	$0.931328\pi$
$654$	−6.64694e10	−0.0142076
$655$	−1.46586e12	−0.311177
$656$	−6.26350e11	−0.132054
$657$	8.13683e12	1.70377
$658$	−3.01838e10	−0.00627708
$659$	5.03990e12	1.04097	0.520484	−	0.853871i	$-0.325752\pi$
$659$	5.03990e12	1.04097	0.520484	+	0.853871i	$0.325752\pi$
$660$	−1.94681e10	−0.00399370
$661$	−4.92729e12	−1.00392	−0.501962	−	0.864889i	$-0.667388\pi$
$661$	−4.92729e12	−1.00392	−0.501962	+	0.864889i	$0.667388\pi$
$662$	8.45919e11	0.171186
$663$	4.06067e10	0.00816182
$664$	−3.50132e12	−0.698998
$665$	8.60469e11	0.170623
$666$	−2.89050e11	−0.0569297
$667$	4.62851e12	0.905471
$668$	−7.68713e12	−1.49372
$669$	−1.44611e11	−0.0279116
$670$	1.22864e11	0.0235552
$671$	−1.94364e12	−0.370139
$672$	−7.85436e10	−0.0148576
$673$	3.86297e12	0.725862	0.362931	−	0.931816i	$-0.381776\pi$
$673$	3.86297e12	0.725862	0.362931	+	0.931816i	$0.381776\pi$
$674$	4.58044e11	0.0854944
$675$	3.43696e11	0.0637246
$676$	4.63455e12	0.853586
$677$	1.38306e12	0.253041	0.126521	−	0.991964i	$-0.459619\pi$
$677$	1.38306e12	0.253041	0.126521	+	0.991964i	$0.459619\pi$
$678$	−2.61366e10	−0.00475024
$679$	3.72166e12	0.671928
$680$	7.39680e11	0.132664
$681$	9.03209e10	0.0160926
$682$	1.72293e11	0.0304957
$683$	5.13051e12	0.902126	0.451063	−	0.892492i	$-0.351045\pi$
$683$	5.13051e12	0.902126	0.451063	+	0.892492i	$0.351045\pi$
$684$	4.13768e12	0.722776
$685$	4.10542e11	0.0712444
$686$	1.39245e12	0.240060
$687$	−9.30345e10	−0.0159345
$688$	−6.47183e12	−1.10123
$689$	−1.03149e12	−0.174373
$690$	2.76455e10	0.00464305
$691$	9.00411e11	0.150241	0.0751207	−	0.997174i	$-0.476066\pi$
$691$	9.00411e11	0.150241	0.0751207	+	0.997174i	$0.476066\pi$
$692$	8.28038e12	1.37269
$693$	−1.06716e12	−0.175763
$694$	−2.21192e12	−0.361952
$695$	−2.67409e10	−0.00434754
$696$	7.55445e10	0.0122028
$697$	−7.31425e11	−0.117388
$698$	−1.50696e12	−0.240299
$699$	2.06421e11	0.0327044
$700$	−2.98044e12	−0.469180
$701$	−2.41626e12	−0.377931	−0.188965	−	0.981984i	$-0.560513\pi$
$701$	−2.41626e12	−0.377931	−0.188965	+	0.981984i	$0.560513\pi$
$702$	−3.57111e10	−0.00554991
$703$	1.14867e12	0.177376
$704$	1.27743e12	0.196002
$705$	−4.01607e9	−0.000612281 0
$706$	2.92652e11	0.0443333
$707$	6.46373e12	0.972962
$708$	−3.53479e11	−0.0528705
$709$	−6.12006e12	−0.909593	−0.454797	−	0.890595i	$-0.650288\pi$
$709$	−6.12006e12	−0.909593	−0.454797	+	0.890595i	$0.650288\pi$
$710$	−5.40144e11	−0.0797713
$711$	1.16131e13	1.70425
$712$	−4.30500e12	−0.627788
$713$	3.73823e12	0.541705
$714$	−2.72522e10	−0.00392428
$715$	2.40321e11	0.0343886
$716$	1.53413e12	0.218149
$717$	−2.77210e11	−0.0391718
$718$	1.11277e12	0.156259
$719$	−7.06953e12	−0.986531	−0.493265	−	0.869879i	$-0.664197\pi$
$719$	−7.06953e12	−0.986531	−0.493265	+	0.869879i	$0.664197\pi$
$720$	2.23670e12	0.310179
$721$	−5.60407e12	−0.772315
$722$	−7.33514e11	−0.100459
$723$	−2.25493e11	−0.0306910
$724$	2.70587e12	0.366002
$725$	4.34537e12	0.584125
$726$	6.27972e9	0.000838930 0
$727$	2.24698e12	0.298328	0.149164	−	0.988812i	$-0.452342\pi$
$727$	2.24698e12	0.298328	0.149164	+	0.988812i	$0.452342\pi$
$728$	6.39623e11	0.0843982
$729$	−7.56224e12	−0.991692
$730$	1.22977e12	0.160277
$731$	−7.55753e12	−0.978930
$732$	−3.33243e11	−0.0429004
$733$	−1.79642e12	−0.229848	−0.114924	−	0.993374i	$-0.536662\pi$
$733$	−1.79642e12	−0.229848	−0.114924	+	0.993374i	$0.536662\pi$
$734$	−1.34468e12	−0.170996
$735$	7.36103e10	0.00930348
$736$	−7.22358e12	−0.907407
$737$	6.05532e11	0.0756020
$738$	3.21398e11	0.0398832
$739$	−3.21690e12	−0.396768	−0.198384	−	0.980124i	$-0.563569\pi$
$739$	−3.21690e12	−0.396768	−0.198384	+	0.980124i	$0.563569\pi$
$740$	6.67480e11	0.0818268
$741$	7.09076e10	0.00863995
$742$	6.92262e11	0.0838404
$743$	−3.29564e12	−0.396726	−0.198363	−	0.980129i	$-0.563562\pi$
$743$	−3.29564e12	−0.396726	−0.198363	+	0.980129i	$0.563562\pi$
$744$	6.10137e10	0.00730045
$745$	3.44661e12	0.409910
$746$	1.49046e12	0.176196
$747$	−1.23637e13	−1.45280
$748$	1.76499e12	0.206151
$749$	9.17247e11	0.106492
$750$	5.62630e10	0.00649302
$751$	−3.77798e12	−0.433391	−0.216696	−	0.976239i	$-0.569528\pi$
$751$	−3.77798e12	−0.433391	−0.216696	+	0.976239i	$0.569528\pi$
$752$	3.11794e11	0.0355540
$753$	−2.57268e11	−0.0291614
$754$	−4.51498e11	−0.0508727
$755$	−1.74091e12	−0.194991
$756$	−3.66188e11	−0.0407715
$757$	−9.63988e12	−1.06694	−0.533470	−	0.845819i	$-0.679112\pi$
$757$	−9.63988e12	−1.06694	−0.533470	+	0.845819i	$0.679112\pi$
$758$	2.70723e12	0.297861
$759$	1.36251e11	0.0149022
$760$	1.29163e12	0.140436
$761$	−1.31733e13	−1.42385	−0.711924	−	0.702257i	$-0.752176\pi$
$761$	−1.31733e13	−1.42385	−0.711924	+	0.702257i	$0.752176\pi$
$762$	1.22946e11	0.0132105
$763$	8.41378e12	0.898733
$764$	1.04915e13	1.11408
$765$	2.61193e12	0.275730
$766$	4.14007e12	0.434489
$767$	4.36346e12	0.455252
$768$	1.58201e11	0.0164091
$769$	−2.42224e12	−0.249775	−0.124887	−	0.992171i	$-0.539857\pi$
$769$	−2.42224e12	−0.249775	−0.124887	+	0.992171i	$0.539857\pi$
$770$	−1.61286e11	−0.0165344
$771$	6.70133e11	0.0682993
$772$	1.33784e13	1.35558
$773$	1.52375e13	1.53499	0.767496	−	0.641053i	$-0.221502\pi$
$773$	1.52375e13	1.53499	0.767496	+	0.641053i	$0.221502\pi$
$774$	3.32088e12	0.332598
$775$	3.50955e12	0.349457
$776$	5.58651e12	0.553048
$777$	−5.07938e10	−0.00499938
$778$	−2.29783e12	−0.224859
$779$	−1.27722e12	−0.124264
$780$	4.12037e10	0.00398576
$781$	−2.66209e12	−0.256032
$782$	−2.50636e12	−0.239670
$783$	5.33889e11	0.0507602
$784$	−5.71486e12	−0.540235
$785$	−3.54495e12	−0.333193
$786$	8.10691e10	0.00757625
$787$	1.63008e13	1.51469	0.757344	−	0.653017i	$-0.226497\pi$
$787$	1.63008e13	1.51469	0.757344	+	0.653017i	$0.226497\pi$
$788$	−1.38709e13	−1.28155
$789$	−5.08220e10	−0.00466880
$790$	1.75515e12	0.160322
$791$	3.30840e12	0.300486
$792$	−1.60189e12	−0.144667
$793$	4.11367e12	0.369403
$794$	−4.66243e12	−0.416313
$795$	9.21081e10	0.00817797
$796$	1.65075e13	1.45738
$797$	−1.14787e13	−1.00770	−0.503849	−	0.863792i	$-0.668083\pi$
$797$	−1.14787e13	−1.00770	−0.503849	+	0.863792i	$0.668083\pi$
$798$	−4.75880e10	−0.00415417
$799$	3.64100e11	0.0316053
$800$	−6.78170e12	−0.585374
$801$	−1.52016e13	−1.30480
$802$	2.34976e12	0.200558
$803$	6.06090e12	0.514419
$804$	1.03820e11	0.00876254
$805$	−3.49940e12	−0.293706
$806$	−3.64654e11	−0.0304350
$807$	1.52671e11	0.0126714
$808$	9.70257e12	0.800821
$809$	1.77062e13	1.45330	0.726652	−	0.687006i	$-0.241075\pi$
$809$	1.77062e13	1.45330	0.726652	+	0.687006i	$0.241075\pi$
$810$	−1.14612e12	−0.0935509
$811$	1.77688e13	1.44233	0.721165	−	0.692764i	$-0.243607\pi$
$811$	1.77688e13	1.44233	0.721165	+	0.692764i	$0.243607\pi$
$812$	−4.62975e12	−0.373728
$813$	−3.66647e11	−0.0294334
$814$	−2.15305e11	−0.0171888
$815$	−5.75162e12	−0.456647
$816$	2.81512e11	0.0222275
$817$	−1.31970e13	−1.03628
$818$	3.61559e12	0.282351
$819$	2.25861e12	0.175414
$820$	−7.42179e11	−0.0573253
$821$	−1.77751e13	−1.36542	−0.682711	−	0.730689i	$-0.739199\pi$
$821$	−1.77751e13	−1.36542	−0.682711	+	0.730689i	$0.739199\pi$
$822$	−2.27049e10	−0.00173459
$823$	−8.47797e11	−0.0644158	−0.0322079	−	0.999481i	$-0.510254\pi$
$823$	−8.47797e11	−0.0644158	−0.0322079	+	0.999481i	$0.510254\pi$
$824$	−8.41215e12	−0.635674
$825$	1.27916e11	0.00961350
$826$	−2.92844e12	−0.218890
$827$	−2.10429e13	−1.56434	−0.782171	−	0.623064i	$-0.785888\pi$
$827$	−2.10429e13	−1.56434	−0.782171	+	0.623064i	$0.785888\pi$
$828$	−1.68273e13	−1.24417
$829$	1.35400e13	0.995690	0.497845	−	0.867266i	$-0.334125\pi$
$829$	1.35400e13	0.995690	0.497845	+	0.867266i	$0.334125\pi$
$830$	−1.86860e12	−0.136668
$831$	−3.66579e11	−0.0266663
$832$	−2.70365e12	−0.195612
$833$	−6.67357e12	−0.480237
$834$	1.47890e9	0.000105850 0
$835$	−8.47352e12	−0.603219
$836$	3.08204e12	0.218228
$837$	4.31197e11	0.0303677
$838$	−3.58699e12	−0.251265
$839$	2.38029e13	1.65844	0.829222	−	0.558919i	$-0.188784\pi$
$839$	2.38029e13	1.65844	0.829222	+	0.558919i	$0.188784\pi$
$840$	−5.71157e10	−0.00395821
$841$	−7.75714e12	−0.534712
$842$	−4.78098e12	−0.327803
$843$	6.92258e11	0.0472111
$844$	−1.37025e12	−0.0929519
$845$	5.10866e12	0.344708
$846$	−1.59991e11	−0.0107381
$847$	−7.94895e11	−0.0530682
$848$	−7.15097e12	−0.474879
$849$	−5.86440e11	−0.0387381
$850$	−2.35305e12	−0.154613
$851$	−4.67146e12	−0.305330
$852$	−4.56424e11	−0.0296750
$853$	1.51971e13	0.982856	0.491428	−	0.870918i	$-0.336475\pi$
$853$	1.51971e13	0.982856	0.491428	+	0.870918i	$0.336475\pi$
$854$	−2.76079e12	−0.177613
$855$	4.56096e12	0.291883
$856$	1.37686e12	0.0876512
$857$	3.05480e12	0.193450	0.0967250	−	0.995311i	$-0.469163\pi$
$857$	3.05480e12	0.193450	0.0967250	+	0.995311i	$0.469163\pi$
$858$	−1.32909e10	−0.000837261 0
$859$	1.36447e13	0.855059	0.427530	−	0.904001i	$-0.359384\pi$
$859$	1.36447e13	0.855059	0.427530	+	0.904001i	$0.359384\pi$
$860$	−7.66865e12	−0.478053
$861$	5.64783e10	0.00350242
$862$	3.36148e12	0.207371
$863$	1.17673e13	0.722153	0.361076	−	0.932536i	$-0.382409\pi$
$863$	1.17673e13	0.722153	0.361076	+	0.932536i	$0.382409\pi$
$864$	−8.33226e11	−0.0508687
$865$	9.12745e12	0.554341
$866$	−3.32697e12	−0.201010
$867$	−2.90731e11	−0.0174745
$868$	−3.73923e12	−0.223586
$869$	8.65025e12	0.514564
$870$	4.03170e10	0.00238589
$871$	−1.28159e12	−0.0754516
$872$	1.26297e13	0.739725
$873$	1.97268e13	1.14946
$874$	−4.37662e12	−0.253710
$875$	−7.12184e12	−0.410729
$876$	1.03916e12	0.0596230
$877$	−1.01045e13	−0.576786	−0.288393	−	0.957512i	$-0.593121\pi$
$877$	−1.01045e13	−0.576786	−0.288393	+	0.957512i	$0.593121\pi$
$878$	1.91511e12	0.108760
$879$	−1.31466e12	−0.0742788
$880$	1.66606e12	0.0936522
$881$	2.43859e13	1.36379	0.681896	−	0.731450i	$-0.261156\pi$
$881$	2.43859e13	1.36379	0.681896	+	0.731450i	$0.261156\pi$
$882$	2.93246e12	0.163164
$883$	−6.02239e12	−0.333385	−0.166692	−	0.986009i	$-0.553309\pi$
$883$	−6.02239e12	−0.333385	−0.166692	+	0.986009i	$0.553309\pi$
$884$	−3.73556e12	−0.205741
$885$	−3.89639e11	−0.0213510
$886$	6.20779e12	0.338443
$887$	−1.56282e13	−0.847722	−0.423861	−	0.905727i	$-0.639326\pi$
$887$	−1.56282e13	−0.847722	−0.423861	+	0.905727i	$0.639326\pi$
$888$	−7.62456e10	−0.00411487
$889$	−1.55627e13	−0.835654
$890$	−2.29751e12	−0.122745
$891$	−5.64864e12	−0.300258
$892$	1.33033e13	0.703588
$893$	6.35794e11	0.0334568
$894$	−1.90614e11	−0.00998011
$895$	1.69107e12	0.0880962
$896$	9.51292e12	0.493092
$897$	−2.88371e11	−0.0148725
$898$	6.37964e12	0.327381
$899$	5.45166e12	0.278362
$900$	−1.57980e13	−0.802620
$901$	−8.35059e12	−0.422139
$902$	2.39401e11	0.0120419
$903$	5.83568e11	0.0292077
$904$	4.96617e12	0.247323
$905$	2.98268e12	0.147805
$906$	9.62804e10	0.00474746
$907$	−1.09661e13	−0.538046	−0.269023	−	0.963134i	$-0.586701\pi$
$907$	−1.09661e13	−0.538046	−0.269023	+	0.963134i	$0.586701\pi$
$908$	−8.30896e12	−0.405658
$909$	3.42613e13	1.66443
$910$	3.41357e11	0.0165015
$911$	1.50567e13	0.724263	0.362132	−	0.932127i	$-0.382049\pi$
$911$	1.50567e13	0.724263	0.362132	+	0.932127i	$0.382049\pi$
$912$	4.91577e11	0.0235296
$913$	−9.20939e12	−0.438644
$914$	−1.85997e12	−0.0881550
$915$	−3.67334e11	−0.0173247
$916$	8.55860e12	0.401673
$917$	−1.02618e13	−0.479251
$918$	−2.89104e11	−0.0134358
$919$	−2.10066e13	−0.971483	−0.485741	−	0.874103i	$-0.661450\pi$
$919$	−2.10066e13	−0.971483	−0.485741	+	0.874103i	$0.661450\pi$
$920$	−5.25288e12	−0.241742
$921$	−4.88862e11	−0.0223881
$922$	−5.04464e12	−0.229901
$923$	5.63425e12	0.255522
$924$	−1.36287e11	−0.00615079
$925$	−4.38570e12	−0.196971
$926$	2.78060e12	0.124277
$927$	−2.97046e13	−1.32119
$928$	−1.05345e13	−0.466283
$929$	−2.64027e12	−0.116299	−0.0581497	−	0.998308i	$-0.518520\pi$
$929$	−2.64027e12	−0.116299	−0.0581497	+	0.998308i	$0.518520\pi$
$930$	3.25621e10	0.00142738
$931$	−1.16534e13	−0.508370
$932$	−1.89894e13	−0.824405
$933$	−5.07409e11	−0.0219225
$934$	4.57648e12	0.196775
$935$	1.94555e12	0.0832512
$936$	3.39035e12	0.144379
$937$	−2.09523e12	−0.0887982	−0.0443991	−	0.999014i	$-0.514137\pi$
$937$	−2.09523e12	−0.0887982	−0.0443991	+	0.999014i	$0.514137\pi$
$938$	8.60112e11	0.0362779
$939$	1.20963e12	0.0507758
$940$	3.69454e11	0.0154342
$941$	−5.03581e12	−0.209371	−0.104685	−	0.994505i	$-0.533384\pi$
$941$	−5.03581e12	−0.209371	−0.104685	+	0.994505i	$0.533384\pi$
$942$	1.96052e11	0.00811228
$943$	5.19426e12	0.213905
$944$	3.02503e13	1.23981
$945$	−4.03649e11	−0.0164650
$946$	2.47363e12	0.100421
$947$	−4.54381e13	−1.83588	−0.917942	−	0.396714i	$-0.870150\pi$
$947$	−4.54381e13	−1.83588	−0.917942	+	0.396714i	$0.870150\pi$
$948$	1.48311e12	0.0596398
$949$	−1.28277e13	−0.513396
$950$	−4.10890e12	−0.163670
$951$	3.80882e11	0.0151000
$952$	5.17816e12	0.204319
$953$	−4.37622e12	−0.171863	−0.0859313	−	0.996301i	$-0.527387\pi$
$953$	−4.37622e12	−0.171863	−0.0859313	+	0.996301i	$0.527387\pi$
$954$	3.66937e12	0.143425
$955$	1.15647e13	0.449904
$956$	2.55016e13	0.987433
$957$	1.98702e11	0.00765769
$958$	−8.49892e11	−0.0326001
$959$	2.87402e12	0.109725
$960$	2.41425e11	0.00917405
$961$	−2.20366e13	−0.833468
$962$	4.55689e11	0.0171546
$963$	4.86191e12	0.182175
$964$	2.07440e13	0.773652
$965$	1.47470e13	0.547432
$966$	1.93533e11	0.00715087
$967$	−4.63740e12	−0.170551	−0.0852757	−	0.996357i	$-0.527177\pi$
$967$	−4.63740e12	−0.170551	−0.0852757	+	0.996357i	$0.527177\pi$
$968$	−1.19320e12	−0.0436792
$969$	5.74043e11	0.0209164
$970$	2.98143e12	0.108132
$971$	2.39575e13	0.864878	0.432439	−	0.901663i	$-0.357653\pi$
$971$	2.39575e13	0.864878	0.432439	+	0.901663i	$0.357653\pi$
$972$	−2.91217e12	−0.104645
$973$	−1.87201e11	−0.00669575
$974$	−6.43666e12	−0.229163
$975$	−2.70731e11	−0.00959438
$976$	2.85186e13	1.00601
$977$	2.95408e13	1.03728	0.518641	−	0.854992i	$-0.326438\pi$
$977$	2.95408e13	1.03728	0.518641	+	0.854992i	$0.326438\pi$
$978$	3.18091e11	0.0111180
$979$	−1.13233e13	−0.393958
$980$	−6.77169e12	−0.234520
$981$	4.45976e13	1.53745
$982$	−7.73004e12	−0.265265
$983$	−3.21747e13	−1.09907	−0.549533	−	0.835472i	$-0.685194\pi$
$983$	−3.21747e13	−1.09907	−0.549533	+	0.835472i	$0.685194\pi$
$984$	8.47785e10	0.00288275
$985$	−1.52899e13	−0.517536
$986$	−3.65517e12	−0.123158
$987$	−2.81147e10	−0.000942987 0
$988$	−6.52306e12	−0.217794
$989$	5.36702e13	1.78382
$990$	−8.54902e11	−0.0282851
$991$	−3.24515e13	−1.06882	−0.534408	−	0.845226i	$-0.679466\pi$
$991$	−3.24515e13	−1.06882	−0.534408	+	0.845226i	$0.679466\pi$
$992$	−8.50826e12	−0.278958
$993$	7.87929e11	0.0257167
$994$	−3.78130e12	−0.122858
$995$	1.81962e13	0.588542
$996$	−1.57898e12	−0.0508404
$997$	5.54117e12	0.177613	0.0888063	−	0.996049i	$-0.471695\pi$
$997$	5.54117e12	0.177613	0.0888063	+	0.996049i	$0.471695\pi$
$998$	1.12203e13	0.358027
$999$	−5.38844e11	−0.0171166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.10.a.a.1.2	✓	3
3.2	odd	2		99.10.a.b.1.2		3
4.3	odd	2		176.10.a.g.1.2		3
5.4	even	2		275.10.a.a.1.2		3
11.10	odd	2		121.10.a.b.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.10.a.a.1.2	✓	3	1.1	even	1	trivial
99.10.a.b.1.2		3	3.2	odd	2
121.10.a.b.1.2		3	11.10	odd	2
176.10.a.g.1.2		3	4.3	odd	2
275.10.a.a.1.2		3	5.4	even	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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+5.60816 q^{2} +5.22371 q^{3} -480.549 q^{4} -529.708 q^{5} +29.2954 q^{6} -3708.24 q^{7} -5566.37 q^{8} -19655.7 q^{9} +O(q^{10})\)	\(q+5.60816 q^{2} +5.22371 q^{3} -480.549 q^{4} -529.708 q^{5} +29.2954 q^{6} -3708.24 q^{7} -5566.37 q^{8} -19655.7 q^{9} -2970.69 q^{10} -14641.0 q^{11} -2510.24 q^{12} +30987.3 q^{13} -20796.4 q^{14} -2767.04 q^{15} +214824. q^{16} +250862. q^{17} -110232. q^{18} +438057. q^{19} +254551. q^{20} -19370.8 q^{21} -82109.0 q^{22} -1.78151e6 q^{23} -29077.1 q^{24} -1.67253e6 q^{25} +173782. q^{26} -205494. q^{27} +1.78199e6 q^{28} -2.59808e6 q^{29} -15518.0 q^{30} -2.09835e6 q^{31} +4.05475e6 q^{32} -76480.3 q^{33} +1.40687e6 q^{34} +1.96429e6 q^{35} +9.44552e6 q^{36} +2.62219e6 q^{37} +2.45669e6 q^{38} +161869. q^{39} +2.94855e6 q^{40} -2.91565e6 q^{41} -108634. q^{42} -3.01262e7 q^{43} +7.03571e6 q^{44} +1.04118e7 q^{45} -9.99100e6 q^{46} +1.45140e6 q^{47} +1.12218e6 q^{48} -2.66025e7 q^{49} -9.37983e6 q^{50} +1.31043e6 q^{51} -1.48909e7 q^{52} -3.32876e7 q^{53} -1.15244e6 q^{54} +7.75546e6 q^{55} +2.06415e7 q^{56} +2.28828e6 q^{57} -1.45704e7 q^{58} +1.40814e8 q^{59} +1.32970e6 q^{60} +1.32753e8 q^{61} -1.17678e7 q^{62} +7.28882e7 q^{63} -8.72501e7 q^{64} -1.64142e7 q^{65} -428913. q^{66} -4.13586e7 q^{67} -1.20551e8 q^{68} -9.30609e6 q^{69} +1.10160e7 q^{70} +1.81824e8 q^{71} +1.09411e8 q^{72} -4.13968e8 q^{73} +1.47056e7 q^{74} -8.73683e6 q^{75} -2.10508e8 q^{76} +5.42924e7 q^{77} +907785. q^{78} -5.90824e8 q^{79} -1.13794e8 q^{80} +3.85810e8 q^{81} -1.63514e7 q^{82} +6.29014e8 q^{83} +9.30860e6 q^{84} -1.32884e8 q^{85} -1.68953e8 q^{86} -1.35716e7 q^{87} +8.14972e7 q^{88} +7.73395e8 q^{89} +5.83910e7 q^{90} -1.14909e8 q^{91} +8.56103e8 q^{92} -1.09611e7 q^{93} +8.13966e6 q^{94} -2.32042e8 q^{95} +2.11808e7 q^{96} -1.00362e9 q^{97} -1.49191e8 q^{98} +2.87779e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9}+O(q^{10}) \) 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9	\( 3 q - 186 q^{3} + 912 q^{4} - 1824 q^{5} - 10956 q^{6} - 7260 q^{7} - 20064 q^{8} + 14553 q^{9} - 86724 q^{10} - 43923 q^{11} - 71040 q^{12} - 93258 q^{13} + 324264 q^{14} + 540330 q^{15} + 22656 q^{16} + 18678 q^{17} + 1997028 q^{18} - 1027356 q^{19} - 156576 q^{20} - 1287924 q^{21} + 1674690 q^{23} - 947232 q^{24} - 1560729 q^{25} - 2162088 q^{26} - 10285434 q^{27} - 2570304 q^{28} - 2693658 q^{29} + 14272500 q^{30} - 4525302 q^{31} + 160512 q^{32} + 2723226 q^{33} + 19899408 q^{34} - 7933860 q^{35} + 20908368 q^{36} - 8820204 q^{37} + 23297712 q^{38} + 24922920 q^{39} - 5145888 q^{40} - 9771102 q^{41} - 8130360 q^{42} + 18795744 q^{43} - 13352592 q^{44} - 91915398 q^{45} - 68671020 q^{46} - 31155816 q^{47} + 76391808 q^{48} - 54229677 q^{49} + 103405236 q^{50} - 62110884 q^{51} - 86345952 q^{52} + 47500122 q^{53} - 153828180 q^{54} + 26705184 q^{55} + 113407680 q^{56} + 62103096 q^{57} - 120644760 q^{58} + 332138370 q^{59} + 290804160 q^{60} - 49031730 q^{61} - 86992620 q^{62} + 319652784 q^{63} - 421220352 q^{64} + 161689572 q^{65} + 160406796 q^{66} + 330560082 q^{67} - 382273056 q^{68} - 104664822 q^{69} - 22907160 q^{70} - 57835050 q^{71} + 302075136 q^{72} - 458816886 q^{73} - 528939708 q^{74} - 562184580 q^{75} - 1324671744 q^{76} + 106293660 q^{77} + 903869520 q^{78} - 798908748 q^{79} + 442084224 q^{80} + 1544572395 q^{81} - 376730664 q^{82} + 1239784920 q^{83} - 809016384 q^{84} - 632001744 q^{85} + 627638088 q^{86} + 505901880 q^{87} + 293757024 q^{88} - 699523368 q^{89} - 2575080288 q^{90} - 268926960 q^{91} + 3537302976 q^{92} + 614745786 q^{93} + 3327514080 q^{94} + 107303856 q^{95} + 2520807168 q^{96} - 2207436012 q^{97} - 1261919472 q^{98} - 213070473 q^{99}+O(q^{100}) \) 3 * q - 186 * q^3 + 912 * q^4 - 1824 * q^5 - 10956 * q^6 - 7260 * q^7 - 20064 * q^8 + 14553 * q^9 - 86724 * q^10 - 43923 * q^11 - 71040 * q^12 - 93258 * q^13 + 324264 * q^14 + 540330 * q^15 + 22656 * q^16 + 18678 * q^17 + 1997028 * q^18 - 1027356 * q^19 - 156576 * q^20 - 1287924 * q^21 + 1674690 * q^23 - 947232 * q^24 - 1560729 * q^25 - 2162088 * q^26 - 10285434 * q^27 - 2570304 * q^28 - 2693658 * q^29 + 14272500 * q^30 - 4525302 * q^31 + 160512 * q^32 + 2723226 * q^33 + 19899408 * q^34 - 7933860 * q^35 + 20908368 * q^36 - 8820204 * q^37 + 23297712 * q^38 + 24922920 * q^39 - 5145888 * q^40 - 9771102 * q^41 - 8130360 * q^42 + 18795744 * q^43 - 13352592 * q^44 - 91915398 * q^45 - 68671020 * q^46 - 31155816 * q^47 + 76391808 * q^48 - 54229677 * q^49 + 103405236 * q^50 - 62110884 * q^51 - 86345952 * q^52 + 47500122 * q^53 - 153828180 * q^54 + 26705184 * q^55 + 113407680 * q^56 + 62103096 * q^57 - 120644760 * q^58 + 332138370 * q^59 + 290804160 * q^60 - 49031730 * q^61 - 86992620 * q^62 + 319652784 * q^63 - 421220352 * q^64 + 161689572 * q^65 + 160406796 * q^66 + 330560082 * q^67 - 382273056 * q^68 - 104664822 * q^69 - 22907160 * q^70 - 57835050 * q^71 + 302075136 * q^72 - 458816886 * q^73 - 528939708 * q^74 - 562184580 * q^75 - 1324671744 * q^76 + 106293660 * q^77 + 903869520 * q^78 - 798908748 * q^79 + 442084224 * q^80 + 1544572395 * q^81 - 376730664 * q^82 + 1239784920 * q^83 - 809016384 * q^84 - 632001744 * q^85 + 627638088 * q^86 + 505901880 * q^87 + 293757024 * q^88 - 699523368 * q^89 - 2575080288 * q^90 - 268926960 * q^91 + 3537302976 * q^92 + 614745786 * q^93 + 3327514080 * q^94 + 107303856 * q^95 + 2520807168 * q^96 - 2207436012 * q^97 - 1261919472 * q^98 - 213070473 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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