LMFDB - Embedded newform 177.10.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.7720 q^{2} -81.0000 q^{3} +1069.81 q^{4} +1152.50 q^{5} +3221.53 q^{6} -1754.07 q^{7} -22185.4 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-39.7720 q^{2} -81.0000 q^{3} +1069.81 q^{4} +1152.50 q^{5} +3221.53 q^{6} -1754.07 q^{7} -22185.4 q^{8} +6561.00 q^{9} -45837.2 q^{10} +74114.4 q^{11} -86654.9 q^{12} +124475. q^{13} +69762.8 q^{14} -93352.4 q^{15} +334612. q^{16} -282894. q^{17} -260944. q^{18} +498014. q^{19} +1.23296e6 q^{20} +142079. q^{21} -2.94768e6 q^{22} -1.32368e6 q^{23} +1.79701e6 q^{24} -624872. q^{25} -4.95061e6 q^{26} -531441. q^{27} -1.87652e6 q^{28} -2.58997e6 q^{29} +3.71281e6 q^{30} -8.69842e6 q^{31} -1.94930e6 q^{32} -6.00327e6 q^{33} +1.12512e7 q^{34} -2.02156e6 q^{35} +7.01905e6 q^{36} -1.67010e7 q^{37} -1.98070e7 q^{38} -1.00824e7 q^{39} -2.55686e7 q^{40} +3.96049e6 q^{41} -5.65078e6 q^{42} +3.80945e7 q^{43} +7.92886e7 q^{44} +7.56154e6 q^{45} +5.26455e7 q^{46} +8.57711e6 q^{47} -2.71036e7 q^{48} -3.72769e7 q^{49} +2.48524e7 q^{50} +2.29144e7 q^{51} +1.33165e8 q^{52} -2.60493e7 q^{53} +2.11365e7 q^{54} +8.54168e7 q^{55} +3.89146e7 q^{56} -4.03391e7 q^{57} +1.03008e8 q^{58} -1.21174e7 q^{59} -9.98696e7 q^{60} +1.24109e8 q^{61} +3.45954e8 q^{62} -1.15084e7 q^{63} -9.37939e7 q^{64} +1.43457e8 q^{65} +2.38762e8 q^{66} -2.73027e8 q^{67} -3.02643e8 q^{68} +1.07218e8 q^{69} +8.04015e7 q^{70} +9.64618e7 q^{71} -1.45558e8 q^{72} -4.37807e8 q^{73} +6.64231e8 q^{74} +5.06146e7 q^{75} +5.32782e8 q^{76} -1.30002e8 q^{77} +4.00999e8 q^{78} -3.71631e8 q^{79} +3.85640e8 q^{80} +4.30467e7 q^{81} -1.57517e8 q^{82} +7.07879e8 q^{83} +1.51998e8 q^{84} -3.26034e8 q^{85} -1.51509e9 q^{86} +2.09787e8 q^{87} -1.64426e9 q^{88} +8.00284e8 q^{89} -3.00738e8 q^{90} -2.18337e8 q^{91} -1.41609e9 q^{92} +7.04572e8 q^{93} -3.41129e8 q^{94} +5.73960e8 q^{95} +1.57893e8 q^{96} +8.70957e8 q^{97} +1.48258e9 q^{98} +4.86265e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	−39.7720	−1.75769	−0.878846	−	0.477106i	$-0.841686\pi$
$2$	−39.7720	−1.75769	−0.878846	+	0.477106i	$0.841686\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1069.81	2.08948
$5$	1152.50	0.824661	0.412330	−	0.911034i	$-0.364715\pi$
$5$	1152.50	0.824661	0.412330	+	0.911034i	$0.364715\pi$
$6$	3221.53	1.01480
$7$	−1754.07	−0.276124	−0.138062	−	0.990424i	$-0.544087\pi$
$7$	−1754.07	−0.276124	−0.138062	+	0.990424i	$0.544087\pi$
$8$	−22185.4	−1.91497
$9$	6561.00	0.333333
$10$	−45837.2	−1.44950
$11$	74114.4	1.52628	0.763142	−	0.646230i	$-0.223655\pi$
$11$	74114.4	1.52628	0.763142	+	0.646230i	$0.223655\pi$
$12$	−86654.9	−1.20636
$13$	124475.	1.20875	0.604374	−	0.796701i	$-0.293423\pi$
$13$	124475.	1.20875	0.604374	+	0.796701i	$0.293423\pi$
$14$	69762.8	0.485342
$15$	−93352.4	−0.476118
$16$	334612.	1.27644
$17$	−282894.	−0.821491	−0.410746	−	0.911750i	$-0.634732\pi$
$17$	−282894.	−0.821491	−0.410746	+	0.911750i	$0.634732\pi$
$18$	−260944.	−0.585897
$19$	498014.	0.876698	0.438349	−	0.898805i	$-0.355563\pi$
$19$	498014.	0.876698	0.438349	+	0.898805i	$0.355563\pi$
$20$	1.23296e6	1.72311
$21$	142079.	0.159421
$22$	−2.94768e6	−2.68274
$23$	−1.32368e6	−0.986299	−0.493150	−	0.869945i	$-0.664154\pi$
$23$	−1.32368e6	−0.986299	−0.493150	+	0.869945i	$0.664154\pi$
$24$	1.79701e6	1.10561
$25$	−624872.	−0.319934
$26$	−4.95061e6	−2.12461
$27$	−531441.	−0.192450
$28$	−1.87652e6	−0.576956
$29$	−2.58997e6	−0.679991	−0.339996	−	0.940427i	$-0.610426\pi$
$29$	−2.58997e6	−0.679991	−0.339996	+	0.940427i	$0.610426\pi$
$30$	3.71281e6	0.836869
$31$	−8.69842e6	−1.69166	−0.845830	−	0.533453i	$-0.820894\pi$
$31$	−8.69842e6	−1.69166	−0.845830	+	0.533453i	$0.820894\pi$
$32$	−1.94930e6	−0.328627
$33$	−6.00327e6	−0.881201
$34$	1.12512e7	1.44393
$35$	−2.02156e6	−0.227709
$36$	7.01905e6	0.696493
$37$	−1.67010e7	−1.46499	−0.732493	−	0.680775i	$-0.761643\pi$
$37$	−1.67010e7	−1.46499	−0.732493	+	0.680775i	$0.761643\pi$
$38$	−1.98070e7	−1.54097
$39$	−1.00824e7	−0.697871
$40$	−2.55686e7	−1.57920
$41$	3.96049e6	0.218888	0.109444	−	0.993993i	$-0.465093\pi$
$41$	3.96049e6	0.218888	0.109444	+	0.993993i	$0.465093\pi$
$42$	−5.65078e6	−0.280212
$43$	3.80945e7	1.69924	0.849618	−	0.527399i	$-0.176833\pi$
$43$	3.80945e7	1.69924	0.849618	+	0.527399i	$0.176833\pi$
$44$	7.92886e7	3.18914
$45$	7.56154e6	0.274887
$46$	5.26455e7	1.73361
$47$	8.57711e6	0.256390	0.128195	−	0.991749i	$-0.459082\pi$
$47$	8.57711e6	0.256390	0.128195	+	0.991749i	$0.459082\pi$
$48$	−2.71036e7	−0.736956
$49$	−3.72769e7	−0.923755
$50$	2.48524e7	0.562346
$51$	2.29144e7	0.474288
$52$	1.33165e8	2.52565
$53$	−2.60493e7	−0.453476	−0.226738	−	0.973956i	$-0.572806\pi$
$53$	−2.60493e7	−0.453476	−0.226738	+	0.973956i	$0.572806\pi$
$54$	2.11365e7	0.338268
$55$	8.54168e7	1.25867
$56$	3.89146e7	0.528770
$57$	−4.03391e7	−0.506162
$58$	1.03008e8	1.19521
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−9.98696e7	−0.994839
$61$	1.24109e8	1.14767	0.573835	−	0.818971i	$-0.305455\pi$
$61$	1.24109e8	1.14767	0.573835	+	0.818971i	$0.305455\pi$
$62$	3.45954e8	2.97342
$63$	−1.15084e7	−0.0920415
$64$	−9.37939e7	−0.698819
$65$	1.43457e8	0.996807
$66$	2.38762e8	1.54888
$67$	−2.73027e8	−1.65527	−0.827634	−	0.561269i	$-0.810313\pi$
$67$	−2.73027e8	−1.65527	−0.827634	+	0.561269i	$0.810313\pi$
$68$	−3.02643e8	−1.71649
$69$	1.07218e8	0.569440
$70$	8.04015e7	0.400242
$71$	9.64618e7	0.450498	0.225249	−	0.974301i	$-0.427680\pi$
$71$	9.64618e7	0.450498	0.225249	+	0.974301i	$0.427680\pi$
$72$	−1.45558e8	−0.638323
$73$	−4.37807e8	−1.80439	−0.902194	−	0.431330i	$-0.858045\pi$
$73$	−4.37807e8	−1.80439	−0.902194	+	0.431330i	$0.858045\pi$
$74$	6.64231e8	2.57499
$75$	5.06146e7	0.184714
$76$	5.32782e8	1.83184
$77$	−1.30002e8	−0.421445
$78$	4.00999e8	1.22664
$79$	−3.71631e8	−1.07347	−0.536736	−	0.843751i	$-0.680343\pi$
$79$	−3.71631e8	−1.07347	−0.536736	+	0.843751i	$0.680343\pi$
$80$	3.85640e8	1.05263
$81$	4.30467e7	0.111111
$82$	−1.57517e8	−0.384737
$83$	7.07879e8	1.63722	0.818611	−	0.574348i	$-0.194744\pi$
$83$	7.07879e8	1.63722	0.818611	+	0.574348i	$0.194744\pi$
$84$	1.51998e8	0.333106
$85$	−3.26034e8	−0.677452
$86$	−1.51509e9	−2.98673
$87$	2.09787e8	0.392593
$88$	−1.64426e9	−2.92279
$89$	8.00284e8	1.35204	0.676019	−	0.736884i	$-0.263704\pi$
$89$	8.00284e8	1.35204	0.676019	+	0.736884i	$0.263704\pi$
$90$	−3.00738e8	−0.483166
$91$	−2.18337e8	−0.333765
$92$	−1.41609e9	−2.06085
$93$	7.04572e8	0.976680
$94$	−3.41129e8	−0.450654
$95$	5.73960e8	0.722979
$96$	1.57893e8	0.189733
$97$	8.70957e8	0.998904	0.499452	−	0.866341i	$-0.333535\pi$
$97$	8.70957e8	0.998904	0.499452	+	0.866341i	$0.333535\pi$
$98$	1.48258e9	1.62368
$99$	4.86265e8	0.508762
$100$	−6.68496e8	−0.668496
$101$	1.96316e9	1.87719	0.938597	−	0.345014i	$-0.112126\pi$
$101$	1.96316e9	1.87719	0.938597	+	0.345014i	$0.112126\pi$
$102$	−9.11351e8	−0.833652
$103$	−3.06917e8	−0.268691	−0.134345	−	0.990935i	$-0.542893\pi$
$103$	−3.06917e8	−0.268691	−0.134345	+	0.990935i	$0.542893\pi$
$104$	−2.76152e9	−2.31471
$105$	1.63746e8	0.131468
$106$	1.03603e9	0.797071
$107$	−1.66746e9	−1.22978	−0.614890	−	0.788613i	$-0.710800\pi$
$107$	−1.66746e9	−1.22978	−0.614890	+	0.788613i	$0.710800\pi$
$108$	−5.68543e8	−0.402120
$109$	−1.86533e9	−1.26572	−0.632858	−	0.774268i	$-0.718118\pi$
$109$	−1.86533e9	−1.26572	−0.632858	+	0.774268i	$0.718118\pi$
$110$	−3.39720e9	−2.21235
$111$	1.35278e9	0.845810
$112$	−5.86932e8	−0.352457
$113$	−1.52291e9	−0.878662	−0.439331	−	0.898325i	$-0.644784\pi$
$113$	−1.52291e9	−0.878662	−0.439331	+	0.898325i	$0.644784\pi$
$114$	1.60437e9	0.889677
$115$	−1.52554e9	−0.813362
$116$	−2.77078e9	−1.42083
$117$	8.16678e8	0.402916
$118$	4.81932e8	0.228832
$119$	4.96214e8	0.226834
$120$	2.07106e9	0.911751
$121$	3.13500e9	1.32955
$122$	−4.93605e9	−2.01725
$123$	−3.20799e8	−0.126375
$124$	−9.30569e9	−3.53469
$125$	−2.97114e9	−1.08850
$126$	4.57713e8	0.161781
$127$	−4.56037e9	−1.55555	−0.777773	−	0.628545i	$-0.783651\pi$
$127$	−4.56037e9	−1.55555	−0.777773	+	0.628545i	$0.783651\pi$
$128$	4.72842e9	1.55694
$129$	−3.08565e9	−0.981054
$130$	−5.70557e9	−1.75208
$131$	1.59631e9	0.473584	0.236792	−	0.971560i	$-0.423904\pi$
$131$	1.59631e9	0.473584	0.236792	+	0.971560i	$0.423904\pi$
$132$	−6.42238e9	−1.84125
$133$	−8.73549e8	−0.242078
$134$	1.08588e10	2.90945
$135$	−6.12485e8	−0.158706
$136$	6.27610e9	1.57313
$137$	−3.08714e9	−0.748711	−0.374355	−	0.927285i	$-0.622136\pi$
$137$	−3.08714e9	−0.748711	−0.374355	+	0.927285i	$0.622136\pi$
$138$	−4.26429e9	−1.00090
$139$	1.68833e9	0.383610	0.191805	−	0.981433i	$-0.438566\pi$
$139$	1.68833e9	0.383610	0.191805	+	0.981433i	$0.438566\pi$
$140$	−2.16269e9	−0.475793
$141$	−6.94746e8	−0.148027
$142$	−3.83648e9	−0.791836
$143$	9.22537e9	1.84489
$144$	2.19539e9	0.425482
$145$	−2.98493e9	−0.560762
$146$	1.74125e10	3.17156
$147$	3.01943e9	0.533330
$148$	−1.78669e10	−3.06106
$149$	3.27902e9	0.545012	0.272506	−	0.962154i	$-0.412148\pi$
$149$	3.27902e9	0.545012	0.272506	+	0.962154i	$0.412148\pi$
$150$	−2.01305e9	−0.324671
$151$	−3.26329e9	−0.510809	−0.255405	−	0.966834i	$-0.582209\pi$
$151$	−3.26329e9	−0.510809	−0.255405	+	0.966834i	$0.582209\pi$
$152$	−1.10486e10	−1.67885
$153$	−1.85606e9	−0.273830
$154$	5.17043e9	0.740769
$155$	−1.00249e10	−1.39505
$156$	−1.07863e10	−1.45819
$157$	−1.01602e10	−1.33460	−0.667301	−	0.744788i	$-0.732551\pi$
$157$	−1.01602e10	−1.33460	−0.667301	+	0.744788i	$0.732551\pi$
$158$	1.47805e10	1.88683
$159$	2.10999e9	0.261815
$160$	−2.24656e9	−0.271006
$161$	2.32183e9	0.272341
$162$	−1.71205e9	−0.195299
$163$	4.63462e9	0.514245	0.257123	−	0.966379i	$-0.417226\pi$
$163$	4.63462e9	0.514245	0.257123	+	0.966379i	$0.417226\pi$
$164$	4.23698e9	0.457361
$165$	−6.91876e9	−0.726692
$166$	−2.81538e10	−2.87773
$167$	5.62382e8	0.0559509	0.0279754	−	0.999609i	$-0.491094\pi$
$167$	5.62382e8	0.0559509	0.0279754	+	0.999609i	$0.491094\pi$
$168$	−3.15208e9	−0.305285
$169$	4.88944e9	0.461072
$170$	1.29670e10	1.19075
$171$	3.26747e9	0.292233
$172$	4.07540e10	3.55052
$173$	−1.09709e10	−0.931186	−0.465593	−	0.884999i	$-0.654159\pi$
$173$	−1.09709e10	−0.931186	−0.465593	+	0.884999i	$0.654159\pi$
$174$	−8.34366e9	−0.690057
$175$	1.09607e9	0.0883417
$176$	2.47996e10	1.94822
$177$	9.81506e8	0.0751646
$178$	−3.18289e10	−2.37647
$179$	−1.54049e10	−1.12155	−0.560777	−	0.827967i	$-0.689498\pi$
$179$	−1.54049e10	−1.12155	−0.560777	+	0.827967i	$0.689498\pi$
$180$	8.08944e9	0.574371
$181$	7.95236e9	0.550735	0.275367	−	0.961339i	$-0.411201\pi$
$181$	7.95236e9	0.550735	0.275367	+	0.961339i	$0.411201\pi$
$182$	8.68369e9	0.586656
$183$	−1.00528e10	−0.662608
$184$	2.93664e10	1.88873
$185$	−1.92478e10	−1.20812
$186$	−2.80223e10	−1.71670
$187$	−2.09665e10	−1.25383
$188$	9.17590e9	0.535721
$189$	9.32183e8	0.0531402
$190$	−2.28276e10	−1.27077
$191$	−4.91634e9	−0.267296	−0.133648	−	0.991029i	$-0.542669\pi$
$191$	−4.91634e9	−0.267296	−0.133648	+	0.991029i	$0.542669\pi$
$192$	7.59731e9	0.403464
$193$	1.64699e10	0.854441	0.427221	−	0.904147i	$-0.359493\pi$
$193$	1.64699e10	0.854441	0.427221	+	0.904147i	$0.359493\pi$
$194$	−3.46397e10	−1.75577
$195$	−1.16200e10	−0.575507
$196$	−3.98793e10	−1.93017
$197$	1.15190e10	0.544898	0.272449	−	0.962170i	$-0.412166\pi$
$197$	1.15190e10	0.544898	0.272449	+	0.962170i	$0.412166\pi$
$198$	−1.93397e10	−0.894246
$199$	2.25046e9	0.101726	0.0508630	−	0.998706i	$-0.483803\pi$
$199$	2.25046e9	0.101726	0.0508630	+	0.998706i	$0.483803\pi$
$200$	1.38630e10	0.612664
$201$	2.21151e10	0.955669
$202$	−7.80788e10	−3.29953
$203$	4.54297e9	0.187762
$204$	2.45141e10	0.991015
$205$	4.56445e9	0.180508
$206$	1.22067e10	0.472276
$207$	−8.68468e9	−0.328766
$208$	4.16508e10	1.54290
$209$	3.69100e10	1.33809
$210$	−6.51252e9	−0.231080
$211$	1.52648e10	0.530175	0.265088	−	0.964224i	$-0.414599\pi$
$211$	1.52648e10	0.530175	0.265088	+	0.964224i	$0.414599\pi$
$212$	−2.78679e10	−0.947529
$213$	−7.81340e9	−0.260095
$214$	6.63181e10	2.16157
$215$	4.39038e10	1.40129
$216$	1.17902e10	0.368536
$217$	1.52576e10	0.467108
$218$	7.41879e10	2.22474
$219$	3.54624e10	1.04176
$220$	9.13800e10	2.62996
$221$	−3.52131e10	−0.992976
$222$	−5.38027e10	−1.48667
$223$	−5.65463e10	−1.53120	−0.765601	−	0.643316i	$-0.777558\pi$
$223$	−5.65463e10	−1.53120	−0.765601	+	0.643316i	$0.777558\pi$
$224$	3.41920e9	0.0907420
$225$	−4.09978e9	−0.106645
$226$	6.05693e10	1.54442
$227$	−2.12964e10	−0.532341	−0.266170	−	0.963926i	$-0.585758\pi$
$227$	−2.12964e10	−0.532341	−0.266170	+	0.963926i	$0.585758\pi$
$228$	−4.31553e10	−1.05762
$229$	−7.88715e9	−0.189522	−0.0947612	−	0.995500i	$-0.530209\pi$
$229$	−7.88715e9	−0.189522	−0.0947612	+	0.995500i	$0.530209\pi$
$230$	6.06739e10	1.42964
$231$	1.05301e10	0.243321
$232$	5.74594e10	1.30216
$233$	−1.78278e10	−0.396275	−0.198137	−	0.980174i	$-0.563489\pi$
$233$	−1.78278e10	−0.396275	−0.198137	+	0.980174i	$0.563489\pi$
$234$	−3.24809e10	−0.708202
$235$	9.88510e9	0.211435
$236$	−1.29633e10	−0.272027
$237$	3.01021e10	0.619769
$238$	−1.97354e10	−0.398704
$239$	−1.96048e10	−0.388662	−0.194331	−	0.980936i	$-0.562254\pi$
$239$	−1.96048e10	−0.388662	−0.194331	+	0.980936i	$0.562254\pi$
$240$	−3.12369e10	−0.607738
$241$	5.90159e10	1.12692	0.563459	−	0.826144i	$-0.309470\pi$
$241$	5.90159e10	1.12692	0.563459	+	0.826144i	$0.309470\pi$
$242$	−1.24685e11	−2.33693
$243$	−3.48678e9	−0.0641500
$244$	1.32773e11	2.39803
$245$	−4.29615e10	−0.761785
$246$	1.27588e10	0.222128
$247$	6.19901e10	1.05971
$248$	1.92978e11	3.23947
$249$	−5.73382e10	−0.945251
$250$	1.18168e11	1.91324
$251$	5.30307e10	0.843326	0.421663	−	0.906753i	$-0.361447\pi$
$251$	5.30307e10	0.843326	0.421663	+	0.906753i	$0.361447\pi$
$252$	−1.23119e10	−0.192319
$253$	−9.81040e10	−1.50537
$254$	1.81375e11	2.73417
$255$	2.64088e10	0.391127
$256$	−1.40036e11	−2.03779
$257$	9.08290e10	1.29875	0.649375	−	0.760468i	$-0.275031\pi$
$257$	9.08290e10	1.29875	0.649375	+	0.760468i	$0.275031\pi$
$258$	1.22723e11	1.72439
$259$	2.92946e10	0.404518
$260$	1.53472e11	2.08281
$261$	−1.69928e10	−0.226664
$262$	−6.34886e10	−0.832415
$263$	−1.48249e11	−1.91070	−0.955348	−	0.295484i	$-0.904519\pi$
$263$	−1.48249e11	−1.91070	−0.955348	+	0.295484i	$0.904519\pi$
$264$	1.33185e11	1.68747
$265$	−3.00218e10	−0.373964
$266$	3.47428e10	0.425498
$267$	−6.48230e10	−0.780600
$268$	−2.92087e11	−3.45865
$269$	3.71116e10	0.432140	0.216070	−	0.976378i	$-0.430676\pi$
$269$	3.71116e10	0.432140	0.216070	+	0.976378i	$0.430676\pi$
$270$	2.43598e10	0.278956
$271$	−2.65662e10	−0.299204	−0.149602	−	0.988746i	$-0.547799\pi$
$271$	−2.65662e10	−0.299204	−0.149602	+	0.988746i	$0.547799\pi$
$272$	−9.46597e10	−1.04859
$273$	1.76853e10	0.192699
$274$	1.22782e11	1.31600
$275$	−4.63120e10	−0.488311
$276$	1.14704e11	1.18983
$277$	−1.48091e11	−1.51137	−0.755686	−	0.654935i	$-0.772696\pi$
$277$	−1.48091e11	−1.51137	−0.755686	+	0.654935i	$0.772696\pi$
$278$	−6.71481e10	−0.674268
$279$	−5.70704e10	−0.563887
$280$	4.48490e10	0.436056
$281$	1.98809e10	0.190221	0.0951105	−	0.995467i	$-0.469680\pi$
$281$	1.98809e10	0.190221	0.0951105	+	0.995467i	$0.469680\pi$
$282$	2.76314e10	0.260185
$283$	−9.03809e10	−0.837602	−0.418801	−	0.908078i	$-0.637550\pi$
$283$	−9.03809e10	−0.837602	−0.418801	+	0.908078i	$0.637550\pi$
$284$	1.03196e11	0.941306
$285$	−4.64908e10	−0.417412
$286$	−3.66911e11	−3.24275
$287$	−6.94695e9	−0.0604402
$288$	−1.27893e10	−0.109542
$289$	−3.85591e10	−0.325152
$290$	1.18717e11	0.985647
$291$	−7.05475e10	−0.576718
$292$	−4.68372e11	−3.77023
$293$	9.32623e10	0.739268	0.369634	−	0.929178i	$-0.379483\pi$
$293$	9.32623e10	0.739268	0.369634	+	0.929178i	$0.379483\pi$
$294$	−1.20089e11	−0.937430
$295$	−1.39652e10	−0.107362
$296$	3.70517e11	2.80540
$297$	−3.93874e10	−0.293734
$298$	−1.30413e11	−0.957962
$299$	−1.64765e11	−1.19219
$300$	5.41482e10	0.385957
$301$	−6.68202e10	−0.469201
$302$	1.29787e11	0.897845
$303$	−1.59016e11	−1.08380
$304$	1.66642e11	1.11906
$305$	1.43035e11	0.946439
$306$	7.38194e10	0.481309
$307$	1.60471e11	1.03104	0.515519	−	0.856878i	$-0.327599\pi$
$307$	1.60471e11	1.03104	0.515519	+	0.856878i	$0.327599\pi$
$308$	−1.39077e11	−0.880600
$309$	2.48603e10	0.155129
$310$	3.98711e11	2.45206
$311$	−8.93285e10	−0.541462	−0.270731	−	0.962655i	$-0.587265\pi$
$311$	−8.93285e10	−0.541462	−0.270731	+	0.962655i	$0.587265\pi$
$312$	2.23683e11	1.33640
$313$	1.18187e11	0.696018	0.348009	−	0.937491i	$-0.386858\pi$
$313$	1.18187e11	0.696018	0.348009	+	0.937491i	$0.386858\pi$
$314$	4.04090e11	2.34582
$315$	−1.32634e10	−0.0759030
$316$	−3.97576e11	−2.24300
$317$	−1.60397e11	−0.892131	−0.446066	−	0.895000i	$-0.647175\pi$
$317$	−1.60397e11	−0.892131	−0.446066	+	0.895000i	$0.647175\pi$
$318$	−8.39186e10	−0.460189
$319$	−1.91954e11	−1.03786
$320$	−1.08097e11	−0.576289
$321$	1.35064e11	0.710014
$322$	−9.23438e10	−0.478692
$323$	−1.40885e11	−0.720200
$324$	4.60520e10	0.232164
$325$	−7.77807e10	−0.386720
$326$	−1.84328e11	−0.903884
$327$	1.51092e11	0.730761
$328$	−8.78648e10	−0.419163
$329$	−1.50448e10	−0.0707954
$330$	2.75173e11	1.27730
$331$	−1.93237e11	−0.884837	−0.442419	−	0.896809i	$-0.645879\pi$
$331$	−1.93237e11	−0.884837	−0.442419	+	0.896809i	$0.645879\pi$
$332$	7.57299e11	3.42094
$333$	−1.09575e11	−0.488329
$334$	−2.23670e10	−0.0983444
$335$	−3.14663e11	−1.36503
$336$	4.75415e10	0.203491
$337$	−1.27963e11	−0.540441	−0.270221	−	0.962798i	$-0.587097\pi$
$337$	−1.27963e11	−0.540441	−0.270221	+	0.962798i	$0.587097\pi$
$338$	−1.94463e11	−0.810423
$339$	1.23356e11	0.507296
$340$	−3.48796e11	−1.41552
$341$	−6.44679e11	−2.58195
$342$	−1.29954e11	−0.513655
$343$	1.36169e11	0.531196
$344$	−8.45139e11	−3.25398
$345$	1.23569e11	0.469595
$346$	4.36337e11	1.63674
$347$	1.92497e11	0.712755	0.356378	−	0.934342i	$-0.384012\pi$
$347$	1.92497e11	0.712755	0.356378	+	0.934342i	$0.384012\pi$
$348$	2.24433e11	0.820315
$349$	−4.61360e11	−1.66466	−0.832329	−	0.554282i	$-0.812993\pi$
$349$	−4.61360e11	−1.66466	−0.832329	+	0.554282i	$0.812993\pi$
$350$	−4.35928e10	−0.155277
$351$	−6.61509e10	−0.232624
$352$	−1.44471e11	−0.501579
$353$	2.93844e11	1.00724	0.503618	−	0.863926i	$-0.332002\pi$
$353$	2.93844e11	1.00724	0.503618	+	0.863926i	$0.332002\pi$
$354$	−3.90365e10	−0.132116
$355$	1.11172e11	0.371508
$356$	8.56154e11	2.82506
$357$	−4.01933e10	−0.130963
$358$	6.12684e11	1.97135
$359$	7.15931e10	0.227482	0.113741	−	0.993510i	$-0.463717\pi$
$359$	7.15931e10	0.227482	0.113741	+	0.993510i	$0.463717\pi$
$360$	−1.67756e11	−0.526400
$361$	−7.46700e10	−0.231400
$362$	−3.16281e11	−0.968021
$363$	−2.53935e11	−0.767613
$364$	−2.33580e11	−0.697395
$365$	−5.04572e11	−1.48801
$366$	3.99820e11	1.16466
$367$	2.29259e11	0.659672	0.329836	−	0.944038i	$-0.393007\pi$
$367$	2.29259e11	0.659672	0.329836	+	0.944038i	$0.393007\pi$
$368$	−4.42921e11	−1.25896
$369$	2.59847e10	0.0729625
$370$	7.65525e11	2.12350
$371$	4.56922e10	0.125216
$372$	7.53761e11	2.04075
$373$	6.54074e11	1.74959	0.874797	−	0.484489i	$-0.160994\pi$
$373$	6.54074e11	1.74959	0.874797	+	0.484489i	$0.160994\pi$
$374$	8.33880e11	2.20385
$375$	2.40662e11	0.628445
$376$	−1.90286e11	−0.490978
$377$	−3.22385e11	−0.821938
$378$	−3.70748e10	−0.0934040
$379$	−4.97719e11	−1.23910	−0.619552	−	0.784955i	$-0.712686\pi$
$379$	−4.97719e11	−1.23910	−0.619552	+	0.784955i	$0.712686\pi$
$380$	6.14030e11	1.51065
$381$	3.69390e11	0.898095
$382$	1.95533e11	0.469824
$383$	1.45916e11	0.346505	0.173253	−	0.984877i	$-0.444572\pi$
$383$	1.45916e11	0.346505	0.173253	+	0.984877i	$0.444572\pi$
$384$	−3.83002e11	−0.898897
$385$	−1.49827e11	−0.347549
$386$	−6.55040e11	−1.50184
$387$	2.49938e11	0.566412
$388$	9.31761e11	2.08719
$389$	−1.67014e11	−0.369812	−0.184906	−	0.982756i	$-0.559198\pi$
$389$	−1.67014e11	−0.369812	−0.184906	+	0.982756i	$0.559198\pi$
$390$	4.62151e11	1.01156
$391$	3.74461e11	0.810236
$392$	8.27001e11	1.76896
$393$	−1.29301e11	−0.273424
$394$	−4.58132e11	−0.957763
$395$	−4.28305e11	−0.885250
$396$	5.20212e11	1.06305
$397$	9.16620e11	1.85196	0.925981	−	0.377570i	$-0.123240\pi$
$397$	9.16620e11	1.85196	0.925981	+	0.377570i	$0.123240\pi$
$398$	−8.95053e10	−0.178803
$399$	7.07575e10	0.139764
$400$	−2.09090e11	−0.408378
$401$	7.07689e11	1.36676	0.683381	−	0.730062i	$-0.260509\pi$
$401$	7.07689e11	1.36676	0.683381	+	0.730062i	$0.260509\pi$
$402$	−8.79564e11	−1.67977
$403$	−1.08273e12	−2.04479
$404$	2.10021e12	3.92236
$405$	4.96113e10	0.0916290
$406$	−1.80683e11	−0.330028
$407$	−1.23778e12	−2.23599
$408$	−5.08364e11	−0.908247
$409$	7.48832e11	1.32321	0.661606	−	0.749852i	$-0.269875\pi$
$409$	7.48832e11	1.32321	0.661606	+	0.749852i	$0.269875\pi$
$410$	−1.81538e11	−0.317277
$411$	2.50059e11	0.432268
$412$	−3.28344e11	−0.561424
$413$	2.12547e10	0.0359483
$414$	3.45407e11	0.577870
$415$	8.15830e11	1.35015
$416$	−2.42638e11	−0.397228
$417$	−1.36754e11	−0.221477
$418$	−1.46799e12	−2.35195
$419$	−8.42398e11	−1.33522	−0.667612	−	0.744510i	$-0.732683\pi$
$419$	−8.42398e11	−1.33522	−0.667612	+	0.744510i	$0.732683\pi$
$420$	1.75178e11	0.274699
$421$	−1.16454e11	−0.180670	−0.0903351	−	0.995911i	$-0.528794\pi$
$421$	−1.16454e11	−0.180670	−0.0903351	+	0.995911i	$0.528794\pi$
$422$	−6.07111e11	−0.931885
$423$	5.62744e10	0.0854632
$424$	5.77913e11	0.868392
$425$	1.76772e11	0.262823
$426$	3.10755e11	0.457167
$427$	−2.17695e11	−0.316900
$428$	−1.78387e12	−2.56960
$429$	−7.47255e11	−1.06515
$430$	−1.74614e12	−2.46304
$431$	1.58044e11	0.220613	0.110306	−	0.993898i	$-0.464817\pi$
$431$	1.58044e11	0.220613	0.110306	+	0.993898i	$0.464817\pi$
$432$	−1.77827e11	−0.245652
$433$	−1.02201e12	−1.39721	−0.698604	−	0.715508i	$-0.746195\pi$
$433$	−1.02201e12	−1.39721	−0.698604	+	0.715508i	$0.746195\pi$
$434$	−6.06826e11	−0.821033
$435$	2.41780e11	0.323756
$436$	−1.99555e12	−2.64469
$437$	−6.59212e11	−0.864687
$438$	−1.41041e12	−1.83110
$439$	−1.14406e12	−1.47014	−0.735072	−	0.677989i	$-0.762852\pi$
$439$	−1.14406e12	−1.47014	−0.735072	+	0.677989i	$0.762852\pi$
$440$	−1.89500e12	−2.41031
$441$	−2.44573e11	−0.307918
$442$	1.40050e12	1.74535
$443$	−5.61863e11	−0.693129	−0.346564	−	0.938026i	$-0.612652\pi$
$443$	−5.61863e11	−0.693129	−0.346564	+	0.938026i	$0.612652\pi$
$444$	1.44722e12	1.76730
$445$	9.22326e11	1.11497
$446$	2.24896e12	2.69138
$447$	−2.65601e11	−0.314663
$448$	1.64521e11	0.192961
$449$	−3.36126e11	−0.390296	−0.195148	−	0.980774i	$-0.562519\pi$
$449$	−3.36126e11	−0.390296	−0.195148	+	0.980774i	$0.562519\pi$
$450$	1.63057e11	0.187449
$451$	2.93529e11	0.334085
$452$	−1.62923e12	−1.83595
$453$	2.64326e11	0.294916
$454$	8.47000e11	0.935691
$455$	−2.51633e11	−0.275243
$456$	8.94938e11	0.969284
$457$	−3.44761e11	−0.369739	−0.184869	−	0.982763i	$-0.559186\pi$
$457$	−3.44761e11	−0.369739	−0.184869	+	0.982763i	$0.559186\pi$
$458$	3.13688e11	0.333122
$459$	1.50341e11	0.158096
$460$	−1.63205e12	−1.69950
$461$	1.37614e12	1.41909	0.709543	−	0.704662i	$-0.248902\pi$
$461$	1.37614e12	1.41909	0.709543	+	0.704662i	$0.248902\pi$
$462$	−4.18804e11	−0.427683
$463$	−5.46956e11	−0.553144	−0.276572	−	0.960993i	$-0.589198\pi$
$463$	−5.46956e11	−0.553144	−0.276572	+	0.960993i	$0.589198\pi$
$464$	−8.66635e11	−0.867971
$465$	8.12019e11	0.805430
$466$	7.09048e11	0.696528
$467$	−1.43232e12	−1.39352	−0.696762	−	0.717302i	$-0.745377\pi$
$467$	−1.43232e12	−1.39352	−0.696762	+	0.717302i	$0.745377\pi$
$468$	8.73693e11	0.841885
$469$	4.78907e11	0.457060
$470$	−3.93151e11	−0.371637
$471$	8.22973e11	0.770533
$472$	2.68828e11	0.249308
$473$	2.82335e12	2.59352
$474$	−1.19722e12	−1.08936
$475$	−3.11195e11	−0.280486
$476$	5.30856e11	0.473964
$477$	−1.70909e11	−0.151159
$478$	7.79722e11	0.683147
$479$	1.06013e12	0.920126	0.460063	−	0.887886i	$-0.347827\pi$
$479$	1.06013e12	0.920126	0.460063	+	0.887886i	$0.347827\pi$
$480$	1.81972e11	0.156465
$481$	−2.07885e12	−1.77080
$482$	−2.34718e12	−1.98077
$483$	−1.88068e11	−0.157236
$484$	3.35386e12	2.77806
$485$	1.00378e12	0.823757
$486$	1.38676e11	0.112756
$487$	8.36469e11	0.673860	0.336930	−	0.941530i	$-0.390611\pi$
$487$	8.36469e11	0.673860	0.336930	+	0.941530i	$0.390611\pi$
$488$	−2.75339e12	−2.19775
$489$	−3.75404e11	−0.296899
$490$	1.70867e12	1.33898
$491$	−1.26919e12	−0.985504	−0.492752	−	0.870170i	$-0.664009\pi$
$491$	−1.26919e12	−0.985504	−0.492752	+	0.870170i	$0.664009\pi$
$492$	−3.43195e11	−0.264058
$493$	7.32685e11	0.558607
$494$	−2.46547e12	−1.86264
$495$	5.60419e11	0.419556
$496$	−2.91060e12	−2.15931
$497$	−1.69200e11	−0.124393
$498$	2.28046e12	1.66146
$499$	6.69271e11	0.483225	0.241613	−	0.970373i	$-0.422324\pi$
$499$	6.69271e11	0.483225	0.241613	+	0.970373i	$0.422324\pi$
$500$	−3.17856e12	−2.27439
$501$	−4.55529e10	−0.0323033
$502$	−2.10914e12	−1.48231
$503$	−1.58991e12	−1.10743	−0.553717	−	0.832705i	$-0.686791\pi$
$503$	−1.58991e12	−1.10743	−0.553717	+	0.832705i	$0.686791\pi$
$504$	2.55319e11	0.176257
$505$	2.26254e12	1.54805
$506$	3.90179e12	2.64598
$507$	−3.96045e11	−0.266200
$508$	−4.87874e12	−3.25028
$509$	−2.11937e12	−1.39951	−0.699755	−	0.714382i	$-0.746708\pi$
$509$	−2.11937e12	−1.39951	−0.699755	+	0.714382i	$0.746708\pi$
$510$	−1.05033e12	−0.687480
$511$	7.67943e11	0.498236
$512$	3.14857e12	2.02488
$513$	−2.64665e11	−0.168721
$514$	−3.61245e12	−2.28280
$515$	−3.53721e11	−0.221579
$516$	−3.30107e12	−2.04989
$517$	6.35687e11	0.391324
$518$	−1.16510e12	−0.711019
$519$	8.88646e11	0.537621
$520$	−3.18264e12	−1.90885
$521$	1.08323e12	0.644097	0.322049	−	0.946723i	$-0.395629\pi$
$521$	1.08323e12	0.644097	0.322049	+	0.946723i	$0.395629\pi$
$522$	6.75837e11	0.398405
$523$	2.01209e10	0.0117596	0.00587978	−	0.999983i	$-0.498128\pi$
$523$	2.01209e10	0.0117596	0.00587978	+	0.999983i	$0.498128\pi$
$524$	1.70776e12	0.989545
$525$	−8.87814e10	−0.0510041
$526$	5.89617e12	3.35841
$527$	2.46073e12	1.38968
$528$	−2.00877e12	−1.12480
$529$	−4.90165e10	−0.0272140
$530$	1.19403e12	0.657313
$531$	−7.95020e10	−0.0433963
$532$	−9.34535e11	−0.505817
$533$	4.92980e11	0.264580
$534$	2.57814e12	1.37205
$535$	−1.92174e12	−1.01415
$536$	6.05719e12	3.16979
$537$	1.24780e12	0.647530
$538$	−1.47600e12	−0.759568
$539$	−2.76275e12	−1.40991
$540$	−6.55245e11	−0.331613
$541$	8.36978e11	0.420075	0.210037	−	0.977693i	$-0.432641\pi$
$541$	8.36978e11	0.420075	0.210037	+	0.977693i	$0.432641\pi$
$542$	1.05659e12	0.525909
$543$	−6.44141e11	−0.317967
$544$	5.51444e11	0.269964
$545$	−2.14979e12	−1.04379
$546$	−7.03379e11	−0.338706
$547$	6.32552e10	0.0302102	0.0151051	−	0.999886i	$-0.495192\pi$
$547$	6.32552e10	0.0302102	0.0151051	+	0.999886i	$0.495192\pi$
$548$	−3.30267e12	−1.56442
$549$	8.14276e11	0.382557
$550$	1.84192e12	0.858300
$551$	−1.28984e12	−0.596147
$552$	−2.37868e12	−1.09046
$553$	6.51866e11	0.296412
$554$	5.88990e12	2.65652
$555$	1.55907e12	0.697507
$556$	1.80619e12	0.801545
$557$	−3.22149e12	−1.41810	−0.709052	−	0.705156i	$-0.750877\pi$
$557$	−3.22149e12	−1.41810	−0.709052	+	0.705156i	$0.750877\pi$
$558$	2.26980e12	0.991139
$559$	4.74179e12	2.05395
$560$	−6.76438e11	−0.290658
$561$	1.69829e12	0.723899
$562$	−7.90705e11	−0.334350
$563$	2.97740e11	0.124896	0.0624481	−	0.998048i	$-0.480109\pi$
$563$	2.97740e11	0.124896	0.0624481	+	0.998048i	$0.480109\pi$
$564$	−7.43248e11	−0.309299
$565$	−1.75515e12	−0.724598
$566$	3.59463e12	1.47225
$567$	−7.55068e10	−0.0306805
$568$	−2.14004e12	−0.862689
$569$	3.07736e12	1.23076	0.615380	−	0.788231i	$-0.289003\pi$
$569$	3.07736e12	1.23076	0.615380	+	0.788231i	$0.289003\pi$
$570$	1.84903e12	0.733682
$571$	−1.52734e12	−0.601277	−0.300638	−	0.953738i	$-0.597200\pi$
$571$	−1.52734e12	−0.601277	−0.300638	+	0.953738i	$0.597200\pi$
$572$	9.86942e12	3.85487
$573$	3.98224e11	0.154323
$574$	2.76294e11	0.106235
$575$	8.27132e11	0.315551
$576$	−6.15382e11	−0.232940
$577$	2.28483e12	0.858148	0.429074	−	0.903269i	$-0.358840\pi$
$577$	2.28483e12	0.858148	0.429074	+	0.903269i	$0.358840\pi$
$578$	1.53357e12	0.571517
$579$	−1.33406e12	−0.493312
$580$	−3.19332e12	−1.17170
$581$	−1.24167e12	−0.452077
$582$	2.80582e12	1.01369
$583$	−1.93063e12	−0.692134
$584$	9.71291e12	3.45535
$585$	9.41221e11	0.332269
$586$	−3.70923e12	−1.29940
$587$	−3.97506e10	−0.0138189	−0.00690943	−	0.999976i	$-0.502199\pi$
$587$	−3.97506e10	−0.0138189	−0.00690943	+	0.999976i	$0.502199\pi$
$588$	3.23022e12	1.11438
$589$	−4.33194e12	−1.48308
$590$	5.55426e11	0.188709
$591$	−9.33036e11	−0.314597
$592$	−5.58834e12	−1.86997
$593$	5.18902e12	1.72321	0.861607	−	0.507576i	$-0.169458\pi$
$593$	5.18902e12	1.72321	0.861607	+	0.507576i	$0.169458\pi$
$594$	1.56652e12	0.516293
$595$	5.71886e11	0.187061
$596$	3.50794e12	1.13879
$597$	−1.82287e11	−0.0587316
$598$	6.55304e12	2.09550
$599$	−1.37203e12	−0.435454	−0.217727	−	0.976010i	$-0.569864\pi$
$599$	−1.37203e12	−0.435454	−0.217727	+	0.976010i	$0.569864\pi$
$600$	−1.12290e12	−0.353722
$601$	1.19015e12	0.372105	0.186053	−	0.982540i	$-0.440431\pi$
$601$	1.19015e12	0.372105	0.186053	+	0.982540i	$0.440431\pi$
$602$	2.65757e12	0.824710
$603$	−1.79133e12	−0.551756
$604$	−3.49111e12	−1.06733
$605$	3.61308e12	1.09642
$606$	6.32438e12	1.90498
$607$	−2.77137e12	−0.828601	−0.414300	−	0.910140i	$-0.635974\pi$
$607$	−2.77137e12	−0.828601	−0.414300	+	0.910140i	$0.635974\pi$
$608$	−9.70778e11	−0.288107
$609$	−3.67981e11	−0.108405
$610$	−5.68879e12	−1.66355
$611$	1.06763e12	0.309911
$612$	−1.98564e12	−0.572163
$613$	−6.07233e12	−1.73693	−0.868467	−	0.495746i	$-0.834895\pi$
$613$	−6.07233e12	−1.73693	−0.868467	+	0.495746i	$0.834895\pi$
$614$	−6.38227e12	−1.81225
$615$	−3.69721e11	−0.104216
$616$	2.88413e12	0.807053
$617$	2.19148e12	0.608772	0.304386	−	0.952549i	$-0.401549\pi$
$617$	2.19148e12	0.608772	0.304386	+	0.952549i	$0.401549\pi$
$618$	−9.88743e11	−0.272669
$619$	4.79703e12	1.31330	0.656651	−	0.754195i	$-0.271972\pi$
$619$	4.79703e12	1.31330	0.656651	+	0.754195i	$0.271972\pi$
$620$	−1.07248e13	−2.91492
$621$	7.03459e11	0.189813
$622$	3.55277e12	0.951724
$623$	−1.40375e12	−0.373331
$624$	−3.37371e12	−0.890794
$625$	−2.20378e12	−0.577708
$626$	−4.70054e12	−1.22338
$627$	−2.98971e12	−0.772547
$628$	−1.08695e13	−2.78862
$629$	4.72459e12	1.20347
$630$	5.27514e11	0.133414
$631$	6.52235e12	1.63784	0.818921	−	0.573907i	$-0.194573\pi$
$631$	6.52235e12	1.63784	0.818921	+	0.573907i	$0.194573\pi$
$632$	8.24478e12	2.05566
$633$	−1.23645e12	−0.306097
$634$	6.37930e12	1.56809
$635$	−5.25582e12	−1.28280
$636$	2.25730e12	0.547056
$637$	−4.64002e12	−1.11659
$638$	7.63439e12	1.82424
$639$	6.32886e11	0.150166
$640$	5.44949e12	1.28394
$641$	6.39535e12	1.49625	0.748123	−	0.663560i	$-0.230955\pi$
$641$	6.39535e12	1.49625	0.748123	+	0.663560i	$0.230955\pi$
$642$	−5.37177e12	−1.24799
$643$	1.91656e12	0.442154	0.221077	−	0.975256i	$-0.429043\pi$
$643$	1.91656e12	0.442154	0.221077	+	0.975256i	$0.429043\pi$
$644$	2.48392e12	0.569051
$645$	−3.55621e12	−0.809037
$646$	5.60328e12	1.26589
$647$	−1.05257e12	−0.236147	−0.118073	−	0.993005i	$-0.537672\pi$
$647$	−1.05257e12	−0.236147	−0.118073	+	0.993005i	$0.537672\pi$
$648$	−9.55007e11	−0.212774
$649$	−8.98071e11	−0.198705
$650$	3.09350e12	0.679735
$651$	−1.23587e12	−0.269685
$652$	4.95818e12	1.07450
$653$	−2.09151e12	−0.450143	−0.225072	−	0.974342i	$-0.572262\pi$
$653$	−2.09151e12	−0.450143	−0.225072	+	0.974342i	$0.572262\pi$
$654$	−6.00922e12	−1.28445
$655$	1.83975e12	0.390547
$656$	1.32523e12	0.279398
$657$	−2.87245e12	−0.601463
$658$	5.98363e11	0.124437
$659$	−2.76756e12	−0.571626	−0.285813	−	0.958285i	$-0.592264\pi$
$659$	−2.76756e12	−0.571626	−0.285813	+	0.958285i	$0.592264\pi$
$660$	−7.40178e12	−1.51841
$661$	−4.96249e12	−1.01110	−0.505549	−	0.862798i	$-0.668710\pi$
$661$	−4.96249e12	−1.01110	−0.505549	+	0.862798i	$0.668710\pi$
$662$	7.68541e12	1.55527
$663$	2.85226e12	0.573295
$664$	−1.57046e13	−3.13523
$665$	−1.00676e12	−0.199632
$666$	4.35802e12	0.858331
$667$	3.42829e12	0.670675
$668$	6.01643e11	0.116908
$669$	4.58025e12	0.884040
$670$	1.25148e13	2.39931
$671$	9.19823e12	1.75167
$672$	−2.76955e11	−0.0523899
$673$	−7.88631e12	−1.48186	−0.740928	−	0.671584i	$-0.765614\pi$
$673$	−7.88631e12	−1.48186	−0.740928	+	0.671584i	$0.765614\pi$
$674$	5.08933e12	0.949929
$675$	3.32083e11	0.0615714
$676$	5.23079e12	0.963401
$677$	−8.80468e12	−1.61089	−0.805443	−	0.592673i	$-0.798073\pi$
$677$	−8.80468e12	−1.61089	−0.805443	+	0.592673i	$0.798073\pi$
$678$	−4.90611e12	−0.891669
$679$	−1.52772e12	−0.275822
$680$	7.23319e12	1.29730
$681$	1.72501e12	0.307347
$682$	2.56402e13	4.53828
$683$	−5.13195e11	−0.0902380	−0.0451190	−	0.998982i	$-0.514367\pi$
$683$	−5.13195e11	−0.0902380	−0.0451190	+	0.998982i	$0.514367\pi$
$684$	3.49558e12	0.610614
$685$	−3.55793e12	−0.617433
$686$	−5.41571e12	−0.933678
$687$	6.38859e11	0.109421
$688$	1.27469e13	2.16898
$689$	−3.24248e12	−0.548138
$690$	−4.91459e12	−0.825403
$691$	7.47766e12	1.24771	0.623856	−	0.781539i	$-0.285565\pi$
$691$	7.47766e12	1.24771	0.623856	+	0.781539i	$0.285565\pi$
$692$	−1.17369e13	−1.94569
$693$	−8.52940e11	−0.140482
$694$	−7.65598e12	−1.25280
$695$	1.94579e12	0.316348
$696$	−4.65421e12	−0.751803
$697$	−1.12040e12	−0.179814
$698$	1.83492e13	2.92596
$699$	1.44405e12	0.228789
$700$	1.17259e12	0.184588
$701$	−7.62118e11	−0.119204	−0.0596020	−	0.998222i	$-0.518983\pi$
$701$	−7.62118e11	−0.119204	−0.0596020	+	0.998222i	$0.518983\pi$
$702$	2.63096e12	0.408881
$703$	−8.31730e12	−1.28435
$704$	−6.95148e12	−1.06660
$705$	−8.00693e11	−0.122072
$706$	−1.16868e13	−1.77041
$707$	−3.44351e12	−0.518339
$708$	1.05003e12	0.157055
$709$	−5.96209e12	−0.886116	−0.443058	−	0.896493i	$-0.646106\pi$
$709$	−5.96209e12	−0.886116	−0.443058	+	0.896493i	$0.646106\pi$
$710$	−4.42154e12	−0.652996
$711$	−2.43827e12	−0.357824
$712$	−1.77546e13	−2.58911
$713$	1.15140e13	1.66848
$714$	1.59857e12	0.230192
$715$	1.06322e13	1.52141
$716$	−1.64804e13	−2.34347
$717$	1.58799e12	0.224394
$718$	−2.84740e12	−0.399843
$719$	−5.49982e12	−0.767483	−0.383741	−	0.923441i	$-0.625365\pi$
$719$	−5.49982e12	−0.767483	−0.383741	+	0.923441i	$0.625365\pi$
$720$	2.53019e12	0.350878
$721$	5.38352e11	0.0741921
$722$	2.96977e12	0.406730
$723$	−4.78029e12	−0.650627
$724$	8.50754e12	1.15075
$725$	1.61840e12	0.217552
$726$	1.00995e13	1.34923
$727$	−9.18960e12	−1.22009	−0.610045	−	0.792367i	$-0.708849\pi$
$727$	−9.18960e12	−1.22009	−0.610045	+	0.792367i	$0.708849\pi$
$728$	4.84388e12	0.639149
$729$	2.82430e11	0.0370370
$730$	2.00679e13	2.61546
$731$	−1.07767e13	−1.39591
$732$	−1.07546e13	−1.38451
$733$	4.38244e12	0.560722	0.280361	−	0.959895i	$-0.409546\pi$
$733$	4.38244e12	0.560722	0.280361	+	0.959895i	$0.409546\pi$
$734$	−9.11807e12	−1.15950
$735$	3.47988e12	0.439817
$736$	2.58025e12	0.324125
$737$	−2.02352e13	−2.52641
$738$	−1.03347e12	−0.128246
$739$	−9.16996e12	−1.13101	−0.565506	−	0.824744i	$-0.691319\pi$
$739$	−9.16996e12	−1.13101	−0.565506	+	0.824744i	$0.691319\pi$
$740$	−2.05916e13	−2.52433
$741$	−5.02120e12	−0.611822
$742$	−1.81727e12	−0.220091
$743$	−6.46289e12	−0.777996	−0.388998	−	0.921239i	$-0.627179\pi$
$743$	−6.46289e12	−0.777996	−0.388998	+	0.921239i	$0.627179\pi$
$744$	−1.56312e13	−1.87031
$745$	3.77906e12	0.449450
$746$	−2.60139e13	−3.07525
$747$	4.64440e12	0.545741
$748$	−2.24302e13	−2.61985
$749$	2.92483e12	0.339572
$750$	−9.57162e12	−1.10461
$751$	5.46521e12	0.626942	0.313471	−	0.949598i	$-0.398508\pi$
$751$	5.46521e12	0.626942	0.313471	+	0.949598i	$0.398508\pi$
$752$	2.87001e12	0.327267
$753$	−4.29549e12	−0.486895
$754$	1.28219e13	1.44471
$755$	−3.76093e12	−0.421244
$756$	9.97262e11	0.111035
$757$	−1.05794e13	−1.17092	−0.585462	−	0.810700i	$-0.699087\pi$
$757$	−1.05794e13	−1.17092	−0.585462	+	0.810700i	$0.699087\pi$
$758$	1.97953e13	2.17796
$759$	7.94642e12	0.869128
$760$	−1.27335e13	−1.38448
$761$	−1.77850e13	−1.92231	−0.961156	−	0.276006i	$-0.910989\pi$
$761$	−1.77850e13	−1.92231	−0.961156	+	0.276006i	$0.910989\pi$
$762$	−1.46914e13	−1.57857
$763$	3.27191e12	0.349495
$764$	−5.25957e12	−0.558509
$765$	−2.13911e12	−0.225817
$766$	−5.80339e12	−0.609049
$767$	−1.50830e12	−0.157366
$768$	1.13429e13	1.17652
$769$	1.89029e13	1.94922	0.974610	−	0.223910i	$-0.0718823\pi$
$769$	1.89029e13	1.94922	0.974610	+	0.223910i	$0.0718823\pi$
$770$	5.95891e12	0.610884
$771$	−7.35715e12	−0.749834
$772$	1.76197e13	1.78534
$773$	1.69443e13	1.70693	0.853465	−	0.521150i	$-0.174497\pi$
$773$	1.69443e13	1.70693	0.853465	+	0.521150i	$0.174497\pi$
$774$	−9.94053e12	−0.995577
$775$	5.43540e12	0.541220
$776$	−1.93225e13	−1.91287
$777$	−2.37286e12	−0.233549
$778$	6.64250e12	0.650015
$779$	1.97238e12	0.191898
$780$	−1.24312e13	−1.20251
$781$	7.14921e12	0.687588
$782$	−1.48931e13	−1.42415
$783$	1.37641e12	0.130864
$784$	−1.24733e13	−1.17912
$785$	−1.17096e13	−1.10059
$786$	5.14258e12	0.480595
$787$	−4.43370e12	−0.411983	−0.205992	−	0.978554i	$-0.566042\pi$
$787$	−4.43370e12	−0.411983	−0.205992	+	0.978554i	$0.566042\pi$
$788$	1.23231e13	1.13855
$789$	1.20082e13	1.10314
$790$	1.70345e13	1.55600
$791$	2.67129e12	0.242620
$792$	−1.07880e13	−0.974263
$793$	1.54484e13	1.38725
$794$	−3.64558e13	−3.25518
$795$	2.43176e12	0.215908
$796$	2.40757e12	0.212555
$797$	−1.36101e13	−1.19481	−0.597406	−	0.801939i	$-0.703802\pi$
$797$	−1.36101e13	−1.19481	−0.597406	+	0.801939i	$0.703802\pi$
$798$	−2.81417e12	−0.245661
$799$	−2.42641e12	−0.210622
$800$	1.21806e12	0.105139
$801$	5.25066e12	0.450679
$802$	−2.81462e13	−2.40235
$803$	−3.24478e13	−2.75401
$804$	2.36591e13	1.99685
$805$	2.67590e12	0.224589
$806$	4.30625e13	3.59411
$807$	−3.00604e12	−0.249496
$808$	−4.35534e13	−3.59477
$809$	−1.44698e13	−1.18766	−0.593832	−	0.804589i	$-0.702386\pi$
$809$	−1.44698e13	−1.18766	−0.593832	+	0.804589i	$0.702386\pi$
$810$	−1.97314e12	−0.161055
$811$	−2.01968e12	−0.163942	−0.0819708	−	0.996635i	$-0.526121\pi$
$811$	−2.01968e12	−0.163942	−0.0819708	+	0.996635i	$0.526121\pi$
$812$	4.86013e12	0.392325
$813$	2.15186e12	0.172746
$814$	4.92291e13	3.93017
$815$	5.34140e12	0.424078
$816$	7.66743e12	0.605403
$817$	1.89716e13	1.48972
$818$	−2.97825e13	−2.32580
$819$	−1.43251e12	−0.111255
$820$	4.88311e12	0.377168
$821$	−2.01085e12	−0.154467	−0.0772335	−	0.997013i	$-0.524609\pi$
$821$	−2.01085e12	−0.154467	−0.0772335	+	0.997013i	$0.524609\pi$
$822$	−9.94533e12	−0.759795
$823$	1.20717e13	0.917212	0.458606	−	0.888640i	$-0.348349\pi$
$823$	1.20717e13	0.917212	0.458606	+	0.888640i	$0.348349\pi$
$824$	6.80906e12	0.514535
$825$	3.75127e12	0.281926
$826$	−8.45340e11	−0.0631861
$827$	−9.24762e12	−0.687472	−0.343736	−	0.939066i	$-0.611693\pi$
$827$	−9.24762e12	−0.687472	−0.343736	+	0.939066i	$0.611693\pi$
$828$	−9.29099e12	−0.686951
$829$	8.27922e12	0.608827	0.304414	−	0.952540i	$-0.401540\pi$
$829$	8.27922e12	0.608827	0.304414	+	0.952540i	$0.401540\pi$
$830$	−3.24472e13	−2.37315
$831$	1.19954e13	0.872590
$832$	−1.16750e13	−0.844697
$833$	1.05454e13	0.758857
$834$	5.43900e12	0.389289
$835$	6.48144e11	0.0461405
$836$	3.94868e13	2.79591
$837$	4.62270e12	0.325560
$838$	3.35039e13	2.34691
$839$	−1.50143e13	−1.04611	−0.523053	−	0.852300i	$-0.675207\pi$
$839$	−1.50143e13	−1.04611	−0.523053	+	0.852300i	$0.675207\pi$
$840$	−3.63277e12	−0.251757
$841$	−7.79922e12	−0.537612
$842$	4.63163e12	0.317563
$843$	−1.61036e12	−0.109824
$844$	1.63305e13	1.10779
$845$	5.63508e12	0.380228
$846$	−2.23815e12	−0.150218
$847$	−5.49900e12	−0.367120
$848$	−8.71641e12	−0.578837
$849$	7.32086e12	0.483590
$850$	−7.03059e12	−0.461962
$851$	2.21068e13	1.44491
$852$	−8.35888e12	−0.543463
$853$	−2.93288e13	−1.89681	−0.948403	−	0.317066i	$-0.897302\pi$
$853$	−2.93288e13	−1.89681	−0.948403	+	0.317066i	$0.897302\pi$
$854$	8.65815e12	0.557012
$855$	3.76575e12	0.240993
$856$	3.69931e13	2.35499
$857$	1.11635e13	0.706946	0.353473	−	0.935445i	$-0.385001\pi$
$857$	1.11635e13	0.706946	0.353473	+	0.935445i	$0.385001\pi$
$858$	2.97198e13	1.87221
$859$	−6.02793e12	−0.377745	−0.188873	−	0.982002i	$-0.560483\pi$
$859$	−6.02793e12	−0.377745	−0.188873	+	0.982002i	$0.560483\pi$
$860$	4.69689e13	2.92797
$861$	5.62703e11	0.0348952
$862$	−6.28573e12	−0.387769
$863$	−6.78324e12	−0.416283	−0.208142	−	0.978099i	$-0.566741\pi$
$863$	−6.78324e12	−0.416283	−0.208142	+	0.978099i	$0.566741\pi$
$864$	1.03594e12	0.0632443
$865$	−1.26440e13	−0.767913
$866$	4.06475e13	2.45586
$867$	3.12329e12	0.187727
$868$	1.63228e13	0.976014
$869$	−2.75432e13	−1.63842
$870$	−9.61606e12	−0.569063
$871$	−3.39849e13	−2.00080
$872$	4.13830e13	2.42380
$873$	5.71435e12	0.332968
$874$	2.62182e13	1.51985
$875$	5.21157e12	0.300561
$876$	3.79381e13	2.17674
$877$	2.63908e13	1.50645	0.753225	−	0.657763i	$-0.228497\pi$
$877$	2.63908e13	1.50645	0.753225	+	0.657763i	$0.228497\pi$
$878$	4.55017e13	2.58406
$879$	−7.55424e12	−0.426816
$880$	2.85815e13	1.60662
$881$	−1.55550e12	−0.0869920	−0.0434960	−	0.999054i	$-0.513850\pi$
$881$	−1.55550e12	−0.0869920	−0.0434960	+	0.999054i	$0.513850\pi$
$882$	9.72718e12	0.541226
$883$	1.11147e13	0.615283	0.307642	−	0.951502i	$-0.400460\pi$
$883$	1.11147e13	0.615283	0.307642	+	0.951502i	$0.400460\pi$
$884$	−3.76714e13	−2.07480
$885$	1.13118e12	0.0619853
$886$	2.23464e13	1.21831
$887$	−1.87813e13	−1.01876	−0.509378	−	0.860543i	$-0.670125\pi$
$887$	−1.87813e13	−1.01876	−0.509378	+	0.860543i	$0.670125\pi$
$888$	−3.00119e13	−1.61970
$889$	7.99918e12	0.429524
$890$	−3.66828e13	−1.95978
$891$	3.19038e12	0.169587
$892$	−6.04940e13	−3.19941
$893$	4.27152e12	0.224776
$894$	1.05635e13	0.553080
$895$	−1.77541e13	−0.924902
$896$	−8.29395e12	−0.429908
$897$	1.33460e13	0.688310
$898$	1.33684e13	0.686020
$899$	2.25286e13	1.15031
$900$	−4.38600e12	−0.222832
$901$	7.36917e12	0.372527
$902$	−1.16742e13	−0.587218
$903$	5.41244e12	0.270893
$904$	3.37863e13	1.68261
$905$	9.16508e12	0.454169
$906$	−1.05128e13	−0.518371
$907$	−2.28696e13	−1.12208	−0.561041	−	0.827788i	$-0.689599\pi$
$907$	−2.28696e13	−1.12208	−0.561041	+	0.827788i	$0.689599\pi$
$908$	−2.27832e13	−1.11231
$909$	1.28803e13	0.625732
$910$	1.00079e13	0.483792
$911$	2.28776e13	1.10047	0.550234	−	0.835011i	$-0.314539\pi$
$911$	2.28776e13	1.10047	0.550234	+	0.835011i	$0.314539\pi$
$912$	−1.34980e13	−0.646088
$913$	5.24641e13	2.49887
$914$	1.37118e13	0.649887
$915$	−1.15858e13	−0.546427
$916$	−8.43778e12	−0.396003
$917$	−2.80004e12	−0.130768
$918$	−5.97937e12	−0.277884
$919$	−3.93536e13	−1.81997	−0.909985	−	0.414640i	$-0.863907\pi$
$919$	−3.93536e13	−1.81997	−0.909985	+	0.414640i	$0.863907\pi$
$920$	3.38447e13	1.55756
$921$	−1.29982e13	−0.595270
$922$	−5.47319e13	−2.49431
$923$	1.20070e13	0.544538
$924$	1.12653e13	0.508414
$925$	1.04360e13	0.468699
$926$	2.17536e13	0.972257
$927$	−2.01368e12	−0.0895637
$928$	5.04862e12	0.223464
$929$	−1.33437e13	−0.587770	−0.293885	−	0.955841i	$-0.594948\pi$
$929$	−1.33437e13	−0.587770	−0.293885	+	0.955841i	$0.594948\pi$
$930$	−3.22956e13	−1.41570
$931$	−1.85644e13	−0.809855
$932$	−1.90724e13	−0.828007
$933$	7.23561e12	0.312613
$934$	5.69663e13	2.44938
$935$	−2.41639e13	−1.03398
$936$	−1.81183e13	−0.771572
$937$	−2.48681e13	−1.05394	−0.526969	−	0.849885i	$-0.676672\pi$
$937$	−2.48681e13	−1.05394	−0.526969	+	0.849885i	$0.676672\pi$
$938$	−1.90471e13	−0.803370
$939$	−9.57315e12	−0.401846
$940$	1.05752e13	0.441788
$941$	−1.95665e13	−0.813503	−0.406751	−	0.913539i	$-0.633338\pi$
$941$	−1.95665e13	−0.813503	−0.406751	+	0.913539i	$0.633338\pi$
$942$	−3.27313e13	−1.35436
$943$	−5.24243e12	−0.215889
$944$	−4.05462e12	−0.166179
$945$	1.07434e12	0.0438226
$946$	−1.12290e14	−4.55860
$947$	−1.14035e13	−0.460748	−0.230374	−	0.973102i	$-0.573995\pi$
$947$	−1.14035e13	−0.460748	−0.230374	+	0.973102i	$0.573995\pi$
$948$	3.22037e13	1.29499
$949$	−5.44959e13	−2.18105
$950$	1.23768e13	0.493008
$951$	1.29921e13	0.515072
$952$	−1.10087e13	−0.434380
$953$	−1.44702e13	−0.568272	−0.284136	−	0.958784i	$-0.591707\pi$
$953$	−1.44702e13	−0.568272	−0.284136	+	0.958784i	$0.591707\pi$
$954$	6.79741e12	0.265690
$955$	−5.66608e12	−0.220428
$956$	−2.09735e13	−0.812100
$957$	1.55483e13	0.599209
$958$	−4.21633e13	−1.61730
$959$	5.41505e12	0.206737
$960$	8.75589e12	0.332721
$961$	4.92230e13	1.86171
$962$	8.26799e13	3.11252
$963$	−1.09402e13	−0.409927
$964$	6.31360e13	2.35467
$965$	1.89815e13	0.704624
$966$	7.47984e12	0.276373
$967$	−2.49135e13	−0.916252	−0.458126	−	0.888887i	$-0.651479\pi$
$967$	−2.49135e13	−0.916252	−0.458126	+	0.888887i	$0.651479\pi$
$968$	−6.95511e13	−2.54604
$969$	1.14117e13	0.415808
$970$	−3.99222e13	−1.44791
$971$	−2.58118e13	−0.931819	−0.465910	−	0.884832i	$-0.654273\pi$
$971$	−2.58118e13	−0.931819	−0.465910	+	0.884832i	$0.654273\pi$
$972$	−3.73021e12	−0.134040
$973$	−2.96144e12	−0.105924
$974$	−3.32681e13	−1.18444
$975$	6.30024e12	0.223273
$976$	4.15282e13	1.46494
$977$	1.21393e13	0.426255	0.213127	−	0.977024i	$-0.431635\pi$
$977$	1.21393e13	0.426255	0.213127	+	0.977024i	$0.431635\pi$
$978$	1.49306e13	0.521858
$979$	5.93126e13	2.06360
$980$	−4.59608e13	−1.59173
$981$	−1.22384e13	−0.421905
$982$	5.04781e13	1.73221
$983$	−1.04154e13	−0.355782	−0.177891	−	0.984050i	$-0.556927\pi$
$983$	−1.04154e13	−0.355782	−0.177891	+	0.984050i	$0.556927\pi$
$984$	7.11705e12	0.242004
$985$	1.32756e13	0.449356
$986$	−2.91404e13	−0.981858
$987$	1.21863e12	0.0408738
$988$	6.63178e13	2.21424
$989$	−5.04250e13	−1.67595
$990$	−2.22890e13	−0.737450
$991$	1.65937e13	0.546527	0.273264	−	0.961939i	$-0.411897\pi$
$991$	1.65937e13	0.546527	0.273264	+	0.961939i	$0.411897\pi$
$992$	1.69558e13	0.555925
$993$	1.56522e13	0.510861
$994$	6.72944e12	0.218645
$995$	2.59365e12	0.0838895
$996$	−6.13412e13	−1.97508
$997$	2.39331e13	0.767134	0.383567	−	0.923513i	$-0.374695\pi$
$997$	2.39331e13	0.767134	0.383567	+	0.923513i	$0.374695\pi$
$998$	−2.66183e13	−0.849361
$999$	8.87557e12	0.281937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.2	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.2	✓	21	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-39.7720 q^{2} -81.0000 q^{3} +1069.81 q^{4} +1152.50 q^{5} +3221.53 q^{6} -1754.07 q^{7} -22185.4 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-39.7720 q^{2} -81.0000 q^{3} +1069.81 q^{4} +1152.50 q^{5} +3221.53 q^{6} -1754.07 q^{7} -22185.4 q^{8} +6561.00 q^{9} -45837.2 q^{10} +74114.4 q^{11} -86654.9 q^{12} +124475. q^{13} +69762.8 q^{14} -93352.4 q^{15} +334612. q^{16} -282894. q^{17} -260944. q^{18} +498014. q^{19} +1.23296e6 q^{20} +142079. q^{21} -2.94768e6 q^{22} -1.32368e6 q^{23} +1.79701e6 q^{24} -624872. q^{25} -4.95061e6 q^{26} -531441. q^{27} -1.87652e6 q^{28} -2.58997e6 q^{29} +3.71281e6 q^{30} -8.69842e6 q^{31} -1.94930e6 q^{32} -6.00327e6 q^{33} +1.12512e7 q^{34} -2.02156e6 q^{35} +7.01905e6 q^{36} -1.67010e7 q^{37} -1.98070e7 q^{38} -1.00824e7 q^{39} -2.55686e7 q^{40} +3.96049e6 q^{41} -5.65078e6 q^{42} +3.80945e7 q^{43} +7.92886e7 q^{44} +7.56154e6 q^{45} +5.26455e7 q^{46} +8.57711e6 q^{47} -2.71036e7 q^{48} -3.72769e7 q^{49} +2.48524e7 q^{50} +2.29144e7 q^{51} +1.33165e8 q^{52} -2.60493e7 q^{53} +2.11365e7 q^{54} +8.54168e7 q^{55} +3.89146e7 q^{56} -4.03391e7 q^{57} +1.03008e8 q^{58} -1.21174e7 q^{59} -9.98696e7 q^{60} +1.24109e8 q^{61} +3.45954e8 q^{62} -1.15084e7 q^{63} -9.37939e7 q^{64} +1.43457e8 q^{65} +2.38762e8 q^{66} -2.73027e8 q^{67} -3.02643e8 q^{68} +1.07218e8 q^{69} +8.04015e7 q^{70} +9.64618e7 q^{71} -1.45558e8 q^{72} -4.37807e8 q^{73} +6.64231e8 q^{74} +5.06146e7 q^{75} +5.32782e8 q^{76} -1.30002e8 q^{77} +4.00999e8 q^{78} -3.71631e8 q^{79} +3.85640e8 q^{80} +4.30467e7 q^{81} -1.57517e8 q^{82} +7.07879e8 q^{83} +1.51998e8 q^{84} -3.26034e8 q^{85} -1.51509e9 q^{86} +2.09787e8 q^{87} -1.64426e9 q^{88} +8.00284e8 q^{89} -3.00738e8 q^{90} -2.18337e8 q^{91} -1.41609e9 q^{92} +7.04572e8 q^{93} -3.41129e8 q^{94} +5.73960e8 q^{95} +1.57893e8 q^{96} +8.70957e8 q^{97} +1.48258e9 q^{98} +4.86265e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

Introduction

L-functions

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