LMFDB - Embedded newform 177.8.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,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, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
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:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$24.0278$ of defining polynomial
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)

$f(q)$	$=$	$q+22.0278 q^{2} +27.0000 q^{3} +357.226 q^{4} -492.460 q^{5} +594.752 q^{6} -1209.81 q^{7} +5049.35 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+22.0278 q^{2} +27.0000 q^{3} +357.226 q^{4} -492.460 q^{5} +594.752 q^{6} -1209.81 q^{7} +5049.35 q^{8} +729.000 q^{9} -10847.8 q^{10} -7759.91 q^{11} +9645.10 q^{12} +1927.14 q^{13} -26649.5 q^{14} -13296.4 q^{15} +65501.4 q^{16} -21871.8 q^{17} +16058.3 q^{18} -31682.0 q^{19} -175919. q^{20} -32664.9 q^{21} -170934. q^{22} +76017.8 q^{23} +136332. q^{24} +164392. q^{25} +42450.8 q^{26} +19683.0 q^{27} -432176. q^{28} -107474. q^{29} -292891. q^{30} -56872.6 q^{31} +796537. q^{32} -209518. q^{33} -481789. q^{34} +595783. q^{35} +260418. q^{36} -72532.0 q^{37} -697885. q^{38} +52032.8 q^{39} -2.48660e6 q^{40} -598173. q^{41} -719537. q^{42} -127161. q^{43} -2.77204e6 q^{44} -359003. q^{45} +1.67451e6 q^{46} +20753.9 q^{47} +1.76854e6 q^{48} +640100. q^{49} +3.62120e6 q^{50} -590540. q^{51} +688425. q^{52} +1.52906e6 q^{53} +433574. q^{54} +3.82145e6 q^{55} -6.10876e6 q^{56} -855413. q^{57} -2.36741e6 q^{58} -205379. q^{59} -4.74982e6 q^{60} +2.40366e6 q^{61} -1.25278e6 q^{62} -881952. q^{63} +9.16182e6 q^{64} -949040. q^{65} -4.61522e6 q^{66} -606916. q^{67} -7.81319e6 q^{68} +2.05248e6 q^{69} +1.31238e7 q^{70} -3.52312e6 q^{71} +3.68098e6 q^{72} +1.27495e6 q^{73} -1.59772e6 q^{74} +4.43858e6 q^{75} -1.13176e7 q^{76} +9.38803e6 q^{77} +1.14617e6 q^{78} +3.89830e6 q^{79} -3.22568e7 q^{80} +531441. q^{81} -1.31765e7 q^{82} -4.03800e6 q^{83} -1.16687e7 q^{84} +1.07710e7 q^{85} -2.80108e6 q^{86} -2.90179e6 q^{87} -3.91825e7 q^{88} +5.97046e6 q^{89} -7.90807e6 q^{90} -2.33148e6 q^{91} +2.71555e7 q^{92} -1.53556e6 q^{93} +457163. q^{94} +1.56021e7 q^{95} +2.15065e7 q^{96} -1.98127e6 q^{97} +1.41000e7 q^{98} -5.65698e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * 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 $

$2$	22.0278	1.94700	0.973502	−	0.228677i	$-0.0734401\pi$
$2$	22.0278	1.94700	0.973502	+	0.228677i	$0.0734401\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	357.226	2.79083
$5$	−492.460	−1.76188	−0.880939	−	0.473230i	$-0.843088\pi$
$5$	−492.460	−1.76188	−0.880939	+	0.473230i	$0.843088\pi$
$6$	594.752	1.12410
$7$	−1209.81	−1.33314	−0.666568	−	0.745444i	$-0.732237\pi$
$7$	−1209.81	−1.33314	−0.666568	+	0.745444i	$0.732237\pi$
$8$	5049.35	3.48675
$9$	729.000	0.333333
$10$	−10847.8	−3.43038
$11$	−7759.91	−1.75785	−0.878926	−	0.476958i	$-0.841739\pi$
$11$	−7759.91	−1.75785	−0.878926	+	0.476958i	$0.841739\pi$
$12$	9645.10	1.61128
$13$	1927.14	0.243283	0.121642	−	0.992574i	$-0.461184\pi$
$13$	1927.14	0.243283	0.121642	+	0.992574i	$0.461184\pi$
$14$	−26649.5	−2.59562
$15$	−13296.4	−1.01722
$16$	65501.4	3.99789
$17$	−21871.8	−1.07973	−0.539864	−	0.841752i	$-0.681524\pi$
$17$	−21871.8	−1.07973	−0.539864	+	0.841752i	$0.681524\pi$
$18$	16058.3	0.649001
$19$	−31682.0	−1.05968	−0.529839	−	0.848098i	$-0.677748\pi$
$19$	−31682.0	−1.05968	−0.529839	+	0.848098i	$0.677748\pi$
$20$	−175919.	−4.91710
$21$	−32664.9	−0.769686
$22$	−170934.	−3.42255
$23$	76017.8	1.30277	0.651385	−	0.758747i	$-0.274188\pi$
$23$	76017.8	1.30277	0.651385	+	0.758747i	$0.274188\pi$
$24$	136332.	2.01307
$25$	164392.	2.10421
$26$	42450.8	0.473673
$27$	19683.0	0.192450
$28$	−432176.	−3.72055
$29$	−107474.	−0.818293	−0.409146	−	0.912469i	$-0.634173\pi$
$29$	−107474.	−0.818293	−0.409146	+	0.912469i	$0.634173\pi$
$30$	−292891.	−1.98053
$31$	−56872.6	−0.342876	−0.171438	−	0.985195i	$-0.554841\pi$
$31$	−56872.6	−0.342876	−0.171438	+	0.985195i	$0.554841\pi$
$32$	796537.	4.29715
$33$	−209518.	−1.01490
$34$	−481789.	−2.10223
$35$	595783.	2.34882
$36$	260418.	0.930276
$37$	−72532.0	−0.235409	−0.117705	−	0.993049i	$-0.537554\pi$
$37$	−72532.0	−0.235409	−0.117705	+	0.993049i	$0.537554\pi$
$38$	−697885.	−2.06320
$39$	52032.8	0.140460
$40$	−2.48660e6	−6.14322
$41$	−598173.	−1.35545	−0.677725	−	0.735316i	$-0.737034\pi$
$41$	−598173.	−1.35545	−0.677725	+	0.735316i	$0.737034\pi$
$42$	−719537.	−1.49858
$43$	−127161.	−0.243902	−0.121951	−	0.992536i	$-0.538915\pi$
$43$	−127161.	−0.243902	−0.121951	+	0.992536i	$0.538915\pi$
$44$	−2.77204e6	−4.90586
$45$	−359003.	−0.587293
$46$	1.67451e6	2.53650
$47$	20753.9	0.0291579	0.0145790	−	0.999894i	$-0.495359\pi$
$47$	20753.9	0.0291579	0.0145790	+	0.999894i	$0.495359\pi$
$48$	1.76854e6	2.30818
$49$	640100.	0.777252
$50$	3.62120e6	4.09691
$51$	−590540.	−0.623381
$52$	688425.	0.678961
$53$	1.52906e6	1.41078	0.705389	−	0.708821i	$-0.250772\pi$
$53$	1.52906e6	1.41078	0.705389	+	0.708821i	$0.250772\pi$
$54$	433574.	0.374701
$55$	3.82145e6	3.09712
$56$	−6.10876e6	−4.64831
$57$	−855413.	−0.611806
$58$	−2.36741e6	−1.59322
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−4.74982e6	−2.83889
$61$	2.40366e6	1.35587	0.677935	−	0.735122i	$-0.262875\pi$
$61$	2.40366e6	1.35587	0.677935	+	0.735122i	$0.262875\pi$
$62$	−1.25278e6	−0.667582
$63$	−881952.	−0.444379
$64$	9.16182e6	4.36869
$65$	−949040.	−0.428635
$66$	−4.61522e6	−1.97601
$67$	−606916.	−0.246528	−0.123264	−	0.992374i	$-0.539336\pi$
$67$	−606916.	−0.246528	−0.123264	+	0.992374i	$0.539336\pi$
$68$	−7.81319e6	−3.01333
$69$	2.05248e6	0.752155
$70$	1.31238e7	4.57317
$71$	−3.52312e6	−1.16822	−0.584108	−	0.811676i	$-0.698556\pi$
$71$	−3.52312e6	−1.16822	−0.584108	+	0.811676i	$0.698556\pi$
$72$	3.68098e6	1.16225
$73$	1.27495e6	0.383585	0.191793	−	0.981435i	$-0.438570\pi$
$73$	1.27495e6	0.383585	0.191793	+	0.981435i	$0.438570\pi$
$74$	−1.59772e6	−0.458343
$75$	4.43858e6	1.21487
$76$	−1.13176e7	−2.95738
$77$	9.38803e6	2.34346
$78$	1.14617e6	0.273475
$79$	3.89830e6	0.889571	0.444786	−	0.895637i	$-0.353280\pi$
$79$	3.89830e6	0.889571	0.444786	+	0.895637i	$0.353280\pi$
$80$	−3.22568e7	−7.04379
$81$	531441.	0.111111
$82$	−1.31765e7	−2.63907
$83$	−4.03800e6	−0.775164	−0.387582	−	0.921835i	$-0.626690\pi$
$83$	−4.03800e6	−0.775164	−0.387582	+	0.921835i	$0.626690\pi$
$84$	−1.16687e7	−2.14806
$85$	1.07710e7	1.90235
$86$	−2.80108e6	−0.474877
$87$	−2.90179e6	−0.472442
$88$	−3.91825e7	−6.12919
$89$	5.97046e6	0.897724	0.448862	−	0.893601i	$-0.351830\pi$
$89$	5.97046e6	0.897724	0.448862	+	0.893601i	$0.351830\pi$
$90$	−7.90807e6	−1.14346
$91$	−2.33148e6	−0.324330
$92$	2.71555e7	3.63581
$93$	−1.53556e6	−0.197960
$94$	457163.	0.0567706
$95$	1.56021e7	1.86703
$96$	2.15065e7	2.48096
$97$	−1.98127e6	−0.220415	−0.110208	−	0.993909i	$-0.535152\pi$
$97$	−1.98127e6	−0.220415	−0.110208	+	0.993909i	$0.535152\pi$
$98$	1.41000e7	1.51331
$99$	−5.65698e6	−0.585951
$100$	5.87250e7	5.87250
$101$	−1.54871e7	−1.49570	−0.747851	−	0.663867i	$-0.768914\pi$
$101$	−1.54871e7	−1.49570	−0.747851	+	0.663867i	$0.768914\pi$
$102$	−1.30083e7	−1.21373
$103$	−1.20275e7	−1.08454	−0.542269	−	0.840205i	$-0.682435\pi$
$103$	−1.20275e7	−1.08454	−0.542269	+	0.840205i	$0.682435\pi$
$104$	9.73081e6	0.848267
$105$	1.60862e7	1.35609
$106$	3.36819e7	2.74679
$107$	−7.69022e6	−0.606870	−0.303435	−	0.952852i	$-0.598134\pi$
$107$	−7.69022e6	−0.606870	−0.303435	+	0.952852i	$0.598134\pi$
$108$	7.03128e6	0.537095
$109$	−2.11383e6	−0.156342	−0.0781711	−	0.996940i	$-0.524908\pi$
$109$	−2.11383e6	−0.156342	−0.0781711	+	0.996940i	$0.524908\pi$
$110$	8.41782e7	6.03011
$111$	−1.95836e6	−0.135914
$112$	−7.92443e7	−5.32973
$113$	2.03050e6	0.132382	0.0661909	−	0.997807i	$-0.478915\pi$
$113$	2.03050e6	0.132382	0.0661909	+	0.997807i	$0.478915\pi$
$114$	−1.88429e7	−1.19119
$115$	−3.74357e7	−2.29532
$116$	−3.83923e7	−2.28371
$117$	1.40489e6	0.0810944
$118$	−4.52406e6	−0.253478
$119$	2.64608e7	1.43942
$120$	−6.71383e7	−3.54679
$121$	4.07291e7	2.09005
$122$	5.29474e7	2.63989
$123$	−1.61507e7	−0.782569
$124$	−2.03164e7	−0.956908
$125$	−4.24829e7	−1.94549
$126$	−1.94275e7	−0.865207
$127$	1.37874e7	0.597269	0.298635	−	0.954367i	$-0.403469\pi$
$127$	1.37874e7	0.597269	0.298635	+	0.954367i	$0.403469\pi$
$128$	9.98583e7	4.20871
$129$	−3.43335e6	−0.140817
$130$	−2.09053e7	−0.834555
$131$	−845013.	−0.0328408	−0.0164204	−	0.999865i	$-0.505227\pi$
$131$	−845013.	−0.0328408	−0.0164204	+	0.999865i	$0.505227\pi$
$132$	−7.48451e7	−2.83240
$133$	3.83292e7	1.41270
$134$	−1.33690e7	−0.479992
$135$	−9.69309e6	−0.339074
$136$	−1.10439e8	−3.76474
$137$	−4.84595e7	−1.61012	−0.805058	−	0.593196i	$-0.797866\pi$
$137$	−4.84595e7	−1.61012	−0.805058	+	0.593196i	$0.797866\pi$
$138$	4.52117e7	1.46445
$139$	−2.05210e6	−0.0648106	−0.0324053	−	0.999475i	$-0.510317\pi$
$139$	−2.05210e6	−0.0648106	−0.0324053	+	0.999475i	$0.510317\pi$
$140$	2.12829e8	6.55516
$141$	560354.	0.0168343
$142$	−7.76067e7	−2.27452
$143$	−1.49545e7	−0.427656
$144$	4.77505e7	1.33263
$145$	5.29264e7	1.44173
$146$	2.80843e7	0.746842
$147$	1.72827e7	0.448746
$148$	−2.59103e7	−0.656987
$149$	−2.53433e6	−0.0627641	−0.0313821	−	0.999507i	$-0.509991\pi$
$149$	−2.53433e6	−0.0627641	−0.0313821	+	0.999507i	$0.509991\pi$
$150$	9.77723e7	2.36535
$151$	−5.49477e7	−1.29876	−0.649382	−	0.760462i	$-0.724972\pi$
$151$	−5.49477e7	−1.29876	−0.649382	+	0.760462i	$0.724972\pi$
$152$	−1.59973e8	−3.69483
$153$	−1.59446e7	−0.359909
$154$	2.06798e8	4.56272
$155$	2.80075e7	0.604106
$156$	1.85875e7	0.391998
$157$	7.27529e7	1.50038	0.750191	−	0.661221i	$-0.229962\pi$
$157$	7.27529e7	1.50038	0.750191	+	0.661221i	$0.229962\pi$
$158$	8.58712e7	1.73200
$159$	4.12846e7	0.814513
$160$	−3.92263e8	−7.57106
$161$	−9.19672e7	−1.73677
$162$	1.17065e7	0.216334
$163$	1.99055e6	0.0360011	0.0180006	−	0.999838i	$-0.494270\pi$
$163$	1.99055e6	0.0360011	0.0180006	+	0.999838i	$0.494270\pi$
$164$	−2.13683e8	−3.78283
$165$	1.03179e8	1.78812
$166$	−8.89485e7	−1.50925
$167$	−3.49476e7	−0.580643	−0.290322	−	0.956929i	$-0.593762\pi$
$167$	−3.49476e7	−0.580643	−0.290322	+	0.956929i	$0.593762\pi$
$168$	−1.64937e8	−2.68370
$169$	−5.90346e7	−0.940813
$170$	2.37262e8	3.70388
$171$	−2.30961e7	−0.353226
$172$	−4.54252e7	−0.680687
$173$	−2.91994e7	−0.428759	−0.214380	−	0.976750i	$-0.568773\pi$
$173$	−2.91994e7	−0.428759	−0.214380	+	0.976750i	$0.568773\pi$
$174$	−6.39201e7	−0.919846
$175$	−1.98883e8	−2.80520
$176$	−5.08285e8	−7.02769
$177$	−5.54523e6	−0.0751646
$178$	1.31516e8	1.74787
$179$	1.31626e8	1.71536	0.857680	−	0.514184i	$-0.171905\pi$
$179$	1.31626e8	1.71536	0.857680	+	0.514184i	$0.171905\pi$
$180$	−1.28245e8	−1.63903
$181$	−1.51957e8	−1.90479	−0.952393	−	0.304872i	$-0.901386\pi$
$181$	−1.51957e8	−1.90479	−0.952393	+	0.304872i	$0.901386\pi$
$182$	−5.13574e7	−0.631471
$183$	6.48987e7	0.782812
$184$	3.83840e8	4.54243
$185$	3.57191e7	0.414763
$186$	−3.38251e7	−0.385428
$187$	1.69724e8	1.89800
$188$	7.41382e6	0.0813747
$189$	−2.38127e7	−0.256562
$190$	3.43680e8	3.63511
$191$	−1.21713e8	−1.26392	−0.631962	−	0.775000i	$-0.717750\pi$
$191$	−1.21713e8	−1.26392	−0.631962	+	0.775000i	$0.717750\pi$
$192$	2.47369e8	2.52227
$193$	1.32612e8	1.32780	0.663900	−	0.747821i	$-0.268900\pi$
$193$	1.32612e8	1.32780	0.663900	+	0.747821i	$0.268900\pi$
$194$	−4.36430e7	−0.429149
$195$	−2.56241e7	−0.247473
$196$	2.28660e8	2.16917
$197$	1.11991e8	1.04364	0.521819	−	0.853056i	$-0.325254\pi$
$197$	1.11991e8	1.04364	0.521819	+	0.853056i	$0.325254\pi$
$198$	−1.24611e8	−1.14085
$199$	−1.81688e8	−1.63433	−0.817165	−	0.576403i	$-0.804456\pi$
$199$	−1.81688e8	−1.63433	−0.817165	+	0.576403i	$0.804456\pi$
$200$	8.30071e8	7.33686
$201$	−1.63867e7	−0.142333
$202$	−3.41147e8	−2.91214
$203$	1.30023e8	1.09090
$204$	−2.10956e8	−1.73975
$205$	2.94576e8	2.38814
$206$	−2.64940e8	−2.11160
$207$	5.54170e7	0.434257
$208$	1.26230e8	0.972618
$209$	2.45849e8	1.86276
$210$	3.54343e8	2.64032
$211$	−3.34639e6	−0.0245238	−0.0122619	−	0.999925i	$-0.503903\pi$
$211$	−3.34639e6	−0.0245238	−0.0122619	+	0.999925i	$0.503903\pi$
$212$	5.46219e8	3.93724
$213$	−9.51243e7	−0.674470
$214$	−1.69399e8	−1.18158
$215$	6.26217e7	0.429725
$216$	9.93863e7	0.671025
$217$	6.88051e7	0.457101
$218$	−4.65630e7	−0.304399
$219$	3.44236e7	0.221463
$220$	1.36512e9	8.64353
$221$	−4.21501e7	−0.262679
$222$	−4.31385e7	−0.264624
$223$	3.23603e7	0.195410	0.0977048	−	0.995215i	$-0.468850\pi$
$223$	3.23603e7	0.195410	0.0977048	+	0.995215i	$0.468850\pi$
$224$	−9.63659e8	−5.72869
$225$	1.19842e8	0.701405
$226$	4.47275e7	0.257748
$227$	1.60575e8	0.911145	0.455573	−	0.890199i	$-0.349435\pi$
$227$	1.60575e8	0.911145	0.455573	+	0.890199i	$0.349435\pi$
$228$	−3.05575e8	−1.70744
$229$	4.34106e7	0.238876	0.119438	−	0.992842i	$-0.461891\pi$
$229$	4.34106e7	0.238876	0.119438	+	0.992842i	$0.461891\pi$
$230$	−8.24628e8	−4.46900
$231$	2.53477e8	1.35300
$232$	−5.42672e8	−2.85318
$233$	−2.86270e7	−0.148262	−0.0741310	−	0.997249i	$-0.523618\pi$
$233$	−2.86270e7	−0.148262	−0.0741310	+	0.997249i	$0.523618\pi$
$234$	3.09466e7	0.157891
$235$	−1.02204e7	−0.0513727
$236$	−7.33667e7	−0.363335
$237$	1.05254e8	0.513594
$238$	5.82874e8	2.80256
$239$	−6.06584e7	−0.287408	−0.143704	−	0.989621i	$-0.545901\pi$
$239$	−6.06584e7	−0.287408	−0.143704	+	0.989621i	$0.545901\pi$
$240$	−8.70933e8	−4.06673
$241$	5.03046e7	0.231498	0.115749	−	0.993278i	$-0.463073\pi$
$241$	5.03046e7	0.231498	0.115749	+	0.993278i	$0.463073\pi$
$242$	8.97173e8	4.06933
$243$	1.43489e7	0.0641500
$244$	8.58648e8	3.78400
$245$	−3.15224e8	−1.36942
$246$	−3.55765e8	−1.52367
$247$	−6.10556e7	−0.257802
$248$	−2.87170e8	−1.19552
$249$	−1.09026e8	−0.447541
$250$	−9.35807e8	−3.78788
$251$	1.79753e8	0.717494	0.358747	−	0.933435i	$-0.383204\pi$
$251$	1.79753e8	0.717494	0.358747	+	0.933435i	$0.383204\pi$
$252$	−3.15056e8	−1.24018
$253$	−5.89891e8	−2.29008
$254$	3.03707e8	1.16289
$255$	2.90817e8	1.09832
$256$	1.02695e9	3.82569
$257$	8.52960e7	0.313446	0.156723	−	0.987643i	$-0.449907\pi$
$257$	8.52960e7	0.313446	0.156723	+	0.987643i	$0.449907\pi$
$258$	−7.56293e7	−0.274171
$259$	8.77500e7	0.313833
$260$	−3.39022e8	−1.19625
$261$	−7.83483e7	−0.272764
$262$	−1.86138e7	−0.0639412
$263$	4.14430e8	1.40477	0.702386	−	0.711796i	$-0.252118\pi$
$263$	4.14430e8	1.40477	0.702386	+	0.711796i	$0.252118\pi$
$264$	−1.05793e9	−3.53869
$265$	−7.53000e8	−2.48562
$266$	8.44309e8	2.75053
$267$	1.61202e8	0.518301
$268$	−2.16806e8	−0.688018
$269$	−3.07821e8	−0.964196	−0.482098	−	0.876117i	$-0.660125\pi$
$269$	−3.07821e8	−0.964196	−0.482098	+	0.876117i	$0.660125\pi$
$270$	−2.13518e8	−0.660178
$271$	−2.35783e8	−0.719646	−0.359823	−	0.933021i	$-0.617163\pi$
$271$	−2.35783e8	−0.719646	−0.359823	+	0.933021i	$0.617163\pi$
$272$	−1.43264e9	−4.31663
$273$	−6.29499e7	−0.187252
$274$	−1.06746e9	−3.13490
$275$	−1.27567e9	−3.69890
$276$	7.33199e8	2.09913
$277$	−2.15483e8	−0.609165	−0.304582	−	0.952486i	$-0.598517\pi$
$277$	−2.15483e8	−0.609165	−0.304582	+	0.952486i	$0.598517\pi$
$278$	−4.52032e7	−0.126186
$279$	−4.14601e7	−0.114292
$280$	3.00832e9	8.18975
$281$	−2.06356e8	−0.554810	−0.277405	−	0.960753i	$-0.589474\pi$
$281$	−2.06356e8	−0.554810	−0.277405	+	0.960753i	$0.589474\pi$
$282$	1.23434e7	0.0327765
$283$	6.73678e8	1.76685	0.883426	−	0.468571i	$-0.155231\pi$
$283$	6.73678e8	1.76685	0.883426	+	0.468571i	$0.155231\pi$
$284$	−1.25855e9	−3.26029
$285$	4.21256e8	1.07793
$286$	−3.29414e8	−0.832648
$287$	7.23677e8	1.80700
$288$	5.80675e8	1.43238
$289$	6.80388e7	0.165811
$290$	1.16586e9	2.80706
$291$	−5.34942e7	−0.127257
$292$	4.55444e8	1.07052
$293$	−2.68265e8	−0.623056	−0.311528	−	0.950237i	$-0.600841\pi$
$293$	−2.68265e8	−0.623056	−0.311528	+	0.950237i	$0.600841\pi$
$294$	3.80701e8	0.873711
$295$	1.01141e8	0.229377
$296$	−3.66239e8	−0.820813
$297$	−1.52738e8	−0.338299
$298$	−5.58259e7	−0.122202
$299$	1.46497e8	0.316942
$300$	1.58557e9	3.39049
$301$	1.53841e8	0.325154
$302$	−1.21038e9	−2.52870
$303$	−4.18152e8	−0.863544
$304$	−2.07521e9	−4.23648
$305$	−1.18370e9	−2.38888
$306$	−3.51225e8	−0.700745
$307$	6.59253e8	1.30037	0.650186	−	0.759775i	$-0.274691\pi$
$307$	6.59253e8	1.30037	0.650186	+	0.759775i	$0.274691\pi$
$308$	3.35365e9	6.54018
$309$	−3.24742e8	−0.626158
$310$	6.16945e8	1.17620
$311$	−8.73613e8	−1.64686	−0.823432	−	0.567415i	$-0.807944\pi$
$311$	−8.73613e8	−1.64686	−0.823432	+	0.567415i	$0.807944\pi$
$312$	2.62732e8	0.489747
$313$	2.84022e8	0.523537	0.261768	−	0.965131i	$-0.415694\pi$
$313$	2.84022e8	0.523537	0.261768	+	0.965131i	$0.415694\pi$
$314$	1.60259e9	2.92125
$315$	4.34326e8	0.782941
$316$	1.39257e9	2.48264
$317$	−2.16935e8	−0.382491	−0.191246	−	0.981542i	$-0.561253\pi$
$317$	−2.16935e8	−0.382491	−0.191246	+	0.981542i	$0.561253\pi$
$318$	9.09410e8	1.58586
$319$	8.33986e8	1.43844
$320$	−4.51183e9	−7.69711
$321$	−2.07636e8	−0.350377
$322$	−2.02584e9	−3.38150
$323$	6.92943e8	1.14416
$324$	1.89844e8	0.310092
$325$	3.16806e8	0.511920
$326$	4.38475e7	0.0700943
$327$	−5.70733e7	−0.0902643
$328$	−3.02039e9	−4.72611
$329$	−2.51083e7	−0.0388715
$330$	2.27281e9	3.48149
$331$	−9.98498e8	−1.51338	−0.756692	−	0.653772i	$-0.773186\pi$
$331$	−9.98498e8	−1.51338	−0.756692	+	0.653772i	$0.773186\pi$
$332$	−1.44248e9	−2.16335
$333$	−5.28758e7	−0.0784698
$334$	−7.69820e8	−1.13052
$335$	2.98882e8	0.434353
$336$	−2.13960e9	−3.07712
$337$	−1.17882e9	−1.67780	−0.838902	−	0.544282i	$-0.816802\pi$
$337$	−1.17882e9	−1.67780	−0.838902	+	0.544282i	$0.816802\pi$
$338$	−1.30041e9	−1.83177
$339$	5.48234e7	0.0764306
$340$	3.84768e9	5.30912
$341$	4.41327e8	0.602726
$342$	−5.08758e8	−0.687733
$343$	2.21931e8	0.296954
$344$	−6.42081e8	−0.850423
$345$	−1.01076e9	−1.32521
$346$	−6.43201e8	−0.834796
$347$	−8.46545e8	−1.08767	−0.543835	−	0.839192i	$-0.683028\pi$
$347$	−8.46545e8	−1.08767	−0.543835	+	0.839192i	$0.683028\pi$
$348$	−1.03659e9	−1.31850
$349$	6.62378e8	0.834098	0.417049	−	0.908884i	$-0.363064\pi$
$349$	6.62378e8	0.834098	0.417049	+	0.908884i	$0.363064\pi$
$350$	−4.38096e9	−5.46174
$351$	3.79319e7	0.0468199
$352$	−6.18106e9	−7.55376
$353$	8.83004e8	1.06844	0.534221	−	0.845345i	$-0.320605\pi$
$353$	8.83004e8	1.06844	0.534221	+	0.845345i	$0.320605\pi$
$354$	−1.22150e8	−0.146346
$355$	1.73500e9	2.05825
$356$	2.13280e9	2.50539
$357$	7.14442e8	0.831052
$358$	2.89943e9	3.33981
$359$	7.02849e7	0.0801736	0.0400868	−	0.999196i	$-0.487237\pi$
$359$	7.02849e7	0.0801736	0.0400868	+	0.999196i	$0.487237\pi$
$360$	−1.81273e9	−2.04774
$361$	1.09874e8	0.122919
$362$	−3.34729e9	−3.70863
$363$	1.09968e9	1.20669
$364$	−8.32864e8	−0.905147
$365$	−6.27860e8	−0.675830
$366$	1.42958e9	1.52414
$367$	−1.46843e9	−1.55068	−0.775340	−	0.631544i	$-0.782421\pi$
$367$	−1.46843e9	−1.55068	−0.775340	+	0.631544i	$0.782421\pi$
$368$	4.97927e9	5.20833
$369$	−4.36068e8	−0.451817
$370$	7.86815e8	0.807544
$371$	−1.84987e9	−1.88076
$372$	−5.48542e8	−0.552471
$373$	1.19545e9	1.19275	0.596376	−	0.802705i	$-0.296607\pi$
$373$	1.19545e9	1.19275	0.596376	+	0.802705i	$0.296607\pi$
$374$	3.73864e9	3.69542
$375$	−1.14704e9	−1.12323
$376$	1.04794e8	0.101666
$377$	−2.07117e8	−0.199077
$378$	−5.24543e8	−0.499528
$379$	1.21004e9	1.14173	0.570863	−	0.821045i	$-0.306609\pi$
$379$	1.21004e9	1.14173	0.570863	+	0.821045i	$0.306609\pi$
$380$	5.57347e9	5.21054
$381$	3.72261e8	0.344834
$382$	−2.68108e9	−2.46086
$383$	−1.02900e9	−0.935876	−0.467938	−	0.883761i	$-0.655003\pi$
$383$	−1.02900e9	−0.935876	−0.467938	+	0.883761i	$0.655003\pi$
$384$	2.69617e9	2.42990
$385$	−4.62323e9	−4.12888
$386$	2.92116e9	2.58523
$387$	−9.27004e7	−0.0813005
$388$	−7.07759e8	−0.615141
$389$	−2.22572e9	−1.91711	−0.958556	−	0.284904i	$-0.908038\pi$
$389$	−2.22572e9	−1.91711	−0.958556	+	0.284904i	$0.908038\pi$
$390$	−5.64443e8	−0.481830
$391$	−1.66265e9	−1.40664
$392$	3.23209e9	2.71008
$393$	−2.28153e7	−0.0189606
$394$	2.46691e9	2.03197
$395$	−1.91976e9	−1.56732
$396$	−2.02082e9	−1.63529
$397$	9.68593e8	0.776917	0.388458	−	0.921466i	$-0.373008\pi$
$397$	9.68593e8	0.776917	0.388458	+	0.921466i	$0.373008\pi$
$398$	−4.00219e9	−3.18205
$399$	1.03489e9	0.815620
$400$	1.07679e10	8.41241
$401$	9.25332e6	0.00716626	0.00358313	−	0.999994i	$-0.498859\pi$
$401$	9.25332e6	0.00716626	0.00358313	+	0.999994i	$0.498859\pi$
$402$	−3.60964e8	−0.277123
$403$	−1.09602e8	−0.0834160
$404$	−5.53239e9	−4.17425
$405$	−2.61713e8	−0.195764
$406$	2.86412e9	2.12398
$407$	5.62842e8	0.413815
$408$	−2.98184e9	−2.17357
$409$	4.22397e8	0.305274	0.152637	−	0.988282i	$-0.451224\pi$
$409$	4.22397e8	0.305274	0.152637	+	0.988282i	$0.451224\pi$
$410$	6.48888e9	4.64971
$411$	−1.30841e9	−0.929601
$412$	−4.29653e9	−3.02676
$413$	2.48470e8	0.173560
$414$	1.22072e9	0.845500
$415$	1.98856e9	1.36574
$416$	1.53504e9	1.04543
$417$	−5.54066e7	−0.0374184
$418$	5.41553e9	3.62680
$419$	−1.30988e9	−0.869925	−0.434962	−	0.900449i	$-0.643238\pi$
$419$	−1.30988e9	−0.869925	−0.434962	+	0.900449i	$0.643238\pi$
$420$	5.74639e9	3.78462
$421$	2.15584e9	1.40809	0.704043	−	0.710158i	$-0.251376\pi$
$421$	2.15584e9	1.40809	0.704043	+	0.710158i	$0.251376\pi$
$422$	−7.37137e7	−0.0477479
$423$	1.51296e7	0.00971931
$424$	7.72075e9	4.91902
$425$	−3.59555e9	−2.27198
$426$	−2.09538e9	−1.31320
$427$	−2.90797e9	−1.80756
$428$	−2.74715e9	−1.69367
$429$	−4.03770e8	−0.246907
$430$	1.37942e9	0.836676
$431$	8.50792e8	0.511862	0.255931	−	0.966695i	$-0.417618\pi$
$431$	8.50792e8	0.511862	0.255931	+	0.966695i	$0.417618\pi$
$432$	1.28926e9	0.769394
$433$	−1.01714e9	−0.602109	−0.301054	−	0.953607i	$-0.597339\pi$
$433$	−1.01714e9	−0.602109	−0.301054	+	0.953607i	$0.597339\pi$
$434$	1.51563e9	0.889977
$435$	1.42901e9	0.832385
$436$	−7.55113e8	−0.436324
$437$	−2.40839e9	−1.38052
$438$	7.58277e8	0.431190
$439$	−1.42920e9	−0.806245	−0.403123	−	0.915146i	$-0.632075\pi$
$439$	−1.42920e9	−0.806245	−0.403123	+	0.915146i	$0.632075\pi$
$440$	1.92958e10	10.7989
$441$	4.66633e8	0.259084
$442$	−9.28477e8	−0.511438
$443$	2.71763e8	0.148517	0.0742586	−	0.997239i	$-0.476341\pi$
$443$	2.71763e8	0.148517	0.0742586	+	0.997239i	$0.476341\pi$
$444$	−6.99578e8	−0.379311
$445$	−2.94021e9	−1.58168
$446$	7.12828e8	0.380463
$447$	−6.84270e7	−0.0362369
$448$	−1.10841e10	−5.82406
$449$	−1.24125e9	−0.647138	−0.323569	−	0.946205i	$-0.604883\pi$
$449$	−1.24125e9	−0.647138	−0.323569	+	0.946205i	$0.604883\pi$
$450$	2.63985e9	1.36564
$451$	4.64177e9	2.38268
$452$	7.25346e8	0.369454
$453$	−1.48359e9	−0.749842
$454$	3.53712e9	1.77400
$455$	1.14816e9	0.571429
$456$	−4.31928e9	−2.13321
$457$	−3.37198e9	−1.65264	−0.826320	−	0.563201i	$-0.809570\pi$
$457$	−3.37198e9	−1.65264	−0.826320	+	0.563201i	$0.809570\pi$
$458$	9.56242e8	0.465092
$459$	−4.30503e8	−0.207794
$460$	−1.33730e10	−6.40585
$461$	−2.86356e9	−1.36130	−0.680650	−	0.732609i	$-0.738302\pi$
$461$	−2.86356e9	−1.36130	−0.680650	+	0.732609i	$0.738302\pi$
$462$	5.58355e9	2.63429
$463$	4.00910e8	0.187721	0.0938607	−	0.995585i	$-0.470079\pi$
$463$	4.00910e8	0.187721	0.0938607	+	0.995585i	$0.470079\pi$
$464$	−7.03967e9	−3.27144
$465$	7.56202e8	0.348781
$466$	−6.30591e8	−0.288667
$467$	−8.05487e8	−0.365973	−0.182987	−	0.983115i	$-0.558577\pi$
$467$	−8.05487e8	−0.365973	−0.182987	+	0.983115i	$0.558577\pi$
$468$	5.01862e8	0.226320
$469$	7.34254e8	0.328656
$470$	−2.25134e8	−0.100023
$471$	1.96433e9	0.866246
$472$	−1.03703e9	−0.453936
$473$	9.86759e8	0.428743
$474$	2.31852e9	0.999970
$475$	−5.20825e9	−2.22979
$476$	9.45248e9	4.01718
$477$	1.11468e9	0.470259
$478$	−1.33617e9	−0.559584
$479$	−1.45641e9	−0.605495	−0.302747	−	0.953071i	$-0.597904\pi$
$479$	−1.45641e9	−0.605495	−0.302747	+	0.953071i	$0.597904\pi$
$480$	−1.05911e10	−4.37116
$481$	−1.39779e8	−0.0572711
$482$	1.10810e9	0.450728
$483$	−2.48311e9	−1.00272
$484$	1.45495e10	5.83295
$485$	9.75694e8	0.388345
$486$	3.16075e8	0.124900
$487$	1.91160e9	0.749973	0.374986	−	0.927030i	$-0.377647\pi$
$487$	1.91160e9	0.749973	0.374986	+	0.927030i	$0.377647\pi$
$488$	1.21369e10	4.72758
$489$	5.37448e7	0.0207853
$490$	−6.94370e9	−2.66627
$491$	3.11951e8	0.118933	0.0594663	−	0.998230i	$-0.481060\pi$
$491$	3.11951e8	0.118933	0.0594663	+	0.998230i	$0.481060\pi$
$492$	−5.76944e9	−2.18402
$493$	2.35065e9	0.883533
$494$	−1.34492e9	−0.501942
$495$	2.78583e9	1.03237
$496$	−3.72524e9	−1.37078
$497$	4.26231e9	1.55739
$498$	−2.40161e9	−0.871364
$499$	−1.10424e9	−0.397844	−0.198922	−	0.980015i	$-0.563744\pi$
$499$	−1.10424e9	−0.397844	−0.198922	+	0.980015i	$0.563744\pi$
$500$	−1.51760e10	−5.42953
$501$	−9.43585e8	−0.335235
$502$	3.95957e9	1.39696
$503$	−3.17067e9	−1.11087	−0.555434	−	0.831560i	$-0.687448\pi$
$503$	−3.17067e9	−1.11087	−0.555434	+	0.831560i	$0.687448\pi$
$504$	−4.45329e9	−1.54944
$505$	7.62677e9	2.63524
$506$	−1.29940e10	−4.45879
$507$	−1.59394e9	−0.543179
$508$	4.92523e9	1.66688
$509$	1.80020e9	0.605074	0.302537	−	0.953138i	$-0.402166\pi$
$509$	1.80020e9	0.605074	0.302537	+	0.953138i	$0.402166\pi$
$510$	6.40607e9	2.13844
$511$	−1.54244e9	−0.511371
$512$	9.83963e9	3.23992
$513$	−6.23596e8	−0.203935
$514$	1.87889e9	0.610281
$515$	5.92306e9	1.91082
$516$	−1.22648e9	−0.392995
$517$	−1.61048e8	−0.0512553
$518$	1.93294e9	0.611034
$519$	−7.88385e8	−0.247544
$520$	−4.79204e9	−1.49454
$521$	−1.90764e9	−0.590968	−0.295484	−	0.955348i	$-0.595481\pi$
$521$	−1.90764e9	−0.590968	−0.295484	+	0.955348i	$0.595481\pi$
$522$	−1.72584e9	−0.531073
$523$	1.01205e9	0.309347	0.154673	−	0.987966i	$-0.450567\pi$
$523$	1.01205e9	0.309347	0.154673	+	0.987966i	$0.450567\pi$
$524$	−3.01860e8	−0.0916530
$525$	−5.36984e9	−1.61959
$526$	9.12900e9	2.73510
$527$	1.24391e9	0.370213
$528$	−1.37237e10	−4.05744
$529$	2.37388e9	0.697211
$530$	−1.65870e10	−4.83951
$531$	−1.49721e8	−0.0433963
$532$	1.36922e10	3.94259
$533$	−1.15276e9	−0.329758
$534$	3.55094e9	1.00913
$535$	3.78713e9	1.06923
$536$	−3.06453e9	−0.859582
$537$	3.55389e9	0.990363
$538$	−6.78063e9	−1.87729
$539$	−4.96712e9	−1.36629
$540$	−3.46262e9	−0.946296
$541$	−5.50100e9	−1.49366	−0.746829	−	0.665016i	$-0.768425\pi$
$541$	−5.50100e9	−1.49366	−0.746829	+	0.665016i	$0.768425\pi$
$542$	−5.19378e9	−1.40115
$543$	−4.10285e9	−1.09973
$544$	−1.74217e10	−4.63976
$545$	1.04097e9	0.275456
$546$	−1.38665e9	−0.364580
$547$	4.40039e9	1.14957	0.574786	−	0.818304i	$-0.305085\pi$
$547$	4.40039e9	1.14957	0.574786	+	0.818304i	$0.305085\pi$
$548$	−1.73110e10	−4.49355
$549$	1.75227e9	0.451957
$550$	−2.81002e10	−7.20177
$551$	3.40497e9	0.867128
$552$	1.03637e10	2.62257
$553$	−4.71621e9	−1.18592
$554$	−4.74664e9	−1.18605
$555$	9.64416e8	0.239463
$556$	−7.33062e8	−0.180875
$557$	5.20574e9	1.27641	0.638203	−	0.769868i	$-0.279678\pi$
$557$	5.20574e9	1.27641	0.638203	+	0.769868i	$0.279678\pi$
$558$	−9.13278e8	−0.222527
$559$	−2.45057e8	−0.0593371
$560$	3.90246e10	9.39033
$561$	4.58254e9	1.09581
$562$	−4.54557e9	−1.08022
$563$	6.20253e9	1.46484	0.732419	−	0.680854i	$-0.238391\pi$
$563$	6.20253e9	1.46484	0.732419	+	0.680854i	$0.238391\pi$
$564$	2.00173e8	0.0469817
$565$	−9.99939e8	−0.233240
$566$	1.48397e10	3.44007
$567$	−6.42943e8	−0.148126
$568$	−1.77895e10	−4.07328
$569$	6.72094e9	1.52946	0.764728	−	0.644353i	$-0.222873\pi$
$569$	6.72094e9	1.52946	0.764728	+	0.644353i	$0.222873\pi$
$570$	9.27937e9	2.09873
$571$	3.74441e8	0.0841700	0.0420850	−	0.999114i	$-0.486600\pi$
$571$	3.74441e8	0.0841700	0.0420850	+	0.999114i	$0.486600\pi$
$572$	−5.34212e9	−1.19351
$573$	−3.28626e9	−0.729727
$574$	1.59410e10	3.51824
$575$	1.24967e10	2.74131
$576$	6.67896e9	1.45623
$577$	1.91890e9	0.415851	0.207925	−	0.978145i	$-0.433329\pi$
$577$	1.91890e9	0.415851	0.207925	+	0.978145i	$0.433329\pi$
$578$	1.49875e9	0.322835
$579$	3.58053e9	0.766606
$580$	1.89067e10	4.02362
$581$	4.88522e9	1.03340
$582$	−1.17836e9	−0.247770
$583$	−1.18654e10	−2.47994
$584$	6.43765e9	1.33746
$585$	−6.91850e8	−0.142878
$586$	−5.90929e9	−1.21309
$587$	−9.08556e9	−1.85404	−0.927018	−	0.375016i	$-0.877637\pi$
$587$	−9.08556e9	−1.85404	−0.927018	+	0.375016i	$0.877637\pi$
$588$	6.17383e9	1.25237
$589$	1.80184e9	0.363339
$590$	2.22792e9	0.446598
$591$	3.02375e9	0.602545
$592$	−4.75095e9	−0.941140
$593$	−1.90930e9	−0.375997	−0.187998	−	0.982169i	$-0.560200\pi$
$593$	−1.90930e9	−0.375997	−0.187998	+	0.982169i	$0.560200\pi$
$594$	−3.36450e9	−0.658669
$595$	−1.30309e10	−2.53609
$596$	−9.05329e8	−0.175164
$597$	−4.90557e9	−0.943581
$598$	3.22701e9	0.617088
$599$	−5.47139e9	−1.04017	−0.520084	−	0.854115i	$-0.674099\pi$
$599$	−5.47139e9	−1.04017	−0.520084	+	0.854115i	$0.674099\pi$
$600$	2.24119e10	4.23594
$601$	3.55169e9	0.667381	0.333691	−	0.942683i	$-0.391706\pi$
$601$	3.55169e9	0.667381	0.333691	+	0.942683i	$0.391706\pi$
$602$	3.38878e9	0.633076
$603$	−4.42442e8	−0.0821761
$604$	−1.96287e10	−3.62463
$605$	−2.00574e10	−3.68240
$606$	−9.21098e9	−1.68132
$607$	5.38370e9	0.977057	0.488529	−	0.872548i	$-0.337534\pi$
$607$	5.38370e9	0.977057	0.488529	+	0.872548i	$0.337534\pi$
$608$	−2.52358e10	−4.55360
$609$	3.51061e9	0.629829
$610$	−2.60745e10	−4.65116
$611$	3.99956e7	0.00709363
$612$	−5.69581e9	−1.00444
$613$	5.24608e9	0.919863	0.459932	−	0.887954i	$-0.347874\pi$
$613$	5.24608e9	0.919863	0.459932	+	0.887954i	$0.347874\pi$
$614$	1.45219e10	2.53183
$615$	7.95356e9	1.37879
$616$	4.74034e10	8.17104
$617$	6.88172e9	1.17950	0.589751	−	0.807585i	$-0.299226\pi$
$617$	6.88172e9	1.17950	0.589751	+	0.807585i	$0.299226\pi$
$618$	−7.15337e9	−1.21913
$619$	5.67281e9	0.961350	0.480675	−	0.876899i	$-0.340392\pi$
$619$	5.67281e9	0.961350	0.480675	+	0.876899i	$0.340392\pi$
$620$	1.00050e10	1.68596
$621$	1.49626e9	0.250718
$622$	−1.92438e10	−3.20645
$623$	−7.22313e9	−1.19679
$624$	3.40822e9	0.561541
$625$	8.07802e9	1.32350
$626$	6.25640e9	1.01933
$627$	6.63793e9	1.07546
$628$	2.59892e10	4.18730
$629$	1.58641e9	0.254178
$630$	9.56727e9	1.52439
$631$	1.88338e9	0.298425	0.149212	−	0.988805i	$-0.452326\pi$
$631$	1.88338e9	0.298425	0.149212	+	0.988805i	$0.452326\pi$
$632$	1.96839e10	3.10171
$633$	−9.03524e7	−0.0141588
$634$	−4.77860e9	−0.744713
$635$	−6.78976e9	−1.05232
$636$	1.47479e10	2.27316
$637$	1.23356e9	0.189092
$638$	1.83709e10	2.80065
$639$	−2.56836e9	−0.389405
$640$	−4.91762e10	−7.41524
$641$	5.23503e9	0.785084	0.392542	−	0.919734i	$-0.371596\pi$
$641$	5.23503e9	0.785084	0.392542	+	0.919734i	$0.371596\pi$
$642$	−4.57377e9	−0.682185
$643$	−7.39762e8	−0.109737	−0.0548686	−	0.998494i	$-0.517474\pi$
$643$	−7.39762e8	−0.109737	−0.0548686	+	0.998494i	$0.517474\pi$
$644$	−3.28530e10	−4.84702
$645$	1.69079e9	0.248102
$646$	1.52640e10	2.22769
$647$	−7.49507e9	−1.08796	−0.543978	−	0.839100i	$-0.683082\pi$
$647$	−7.49507e9	−1.08796	−0.543978	+	0.839100i	$0.683082\pi$
$648$	2.68343e9	0.387416
$649$	1.59372e9	0.228853
$650$	6.97856e9	0.996710
$651$	1.85774e9	0.263907
$652$	7.11075e8	0.100473
$653$	9.12022e9	1.28177	0.640884	−	0.767638i	$-0.278568\pi$
$653$	9.12022e9	1.28177	0.640884	+	0.767638i	$0.278568\pi$
$654$	−1.25720e9	−0.175745
$655$	4.16135e8	0.0578615
$656$	−3.91812e10	−5.41893
$657$	9.29436e8	0.127862
$658$	−5.53081e8	−0.0756829
$659$	8.11531e9	1.10460	0.552301	−	0.833645i	$-0.313750\pi$
$659$	8.11531e9	1.10460	0.552301	+	0.833645i	$0.313750\pi$
$660$	3.68582e10	4.99034
$661$	6.72245e9	0.905362	0.452681	−	0.891672i	$-0.350468\pi$
$661$	6.72245e9	0.905362	0.452681	+	0.891672i	$0.350468\pi$
$662$	−2.19947e10	−2.94656
$663$	−1.13805e9	−0.151658
$664$	−2.03893e10	−2.70280
$665$	−1.88756e10	−2.48900
$666$	−1.16474e9	−0.152781
$667$	−8.16991e9	−1.06605
$668$	−1.24842e10	−1.62047
$669$	8.73729e8	0.112820
$670$	6.58372e9	0.845687
$671$	−1.86522e10	−2.38342
$672$	−2.60188e10	−3.30746
$673$	1.14461e10	1.44745	0.723725	−	0.690089i	$-0.242429\pi$
$673$	1.14461e10	1.44745	0.723725	+	0.690089i	$0.242429\pi$
$674$	−2.59668e10	−3.26669
$675$	3.23572e9	0.404956
$676$	−2.10887e10	−2.62565
$677$	−4.26750e9	−0.528583	−0.264292	−	0.964443i	$-0.585138\pi$
$677$	−4.26750e9	−0.528583	−0.264292	+	0.964443i	$0.585138\pi$
$678$	1.20764e9	0.148811
$679$	2.39696e9	0.293843
$680$	5.43866e10	6.63301
$681$	4.33553e9	0.526050
$682$	9.72147e9	1.17351
$683$	6.74829e9	0.810441	0.405220	−	0.914219i	$-0.367195\pi$
$683$	6.74829e9	0.810441	0.405220	+	0.914219i	$0.367195\pi$
$684$	−8.25054e9	−0.985793
$685$	2.38644e10	2.83683
$686$	4.88867e9	0.578171
$687$	1.17209e9	0.137915
$688$	−8.32922e9	−0.975091
$689$	2.94671e9	0.343218
$690$	−2.22650e10	−2.58018
$691$	−6.41648e9	−0.739816	−0.369908	−	0.929068i	$-0.620611\pi$
$691$	−6.41648e9	−0.739816	−0.369908	+	0.929068i	$0.620611\pi$
$692$	−1.04308e10	−1.19659
$693$	6.84387e9	0.781152
$694$	−1.86476e10	−2.11770
$695$	1.01057e9	0.114188
$696$	−1.46521e10	−1.64728
$697$	1.30832e10	1.46352
$698$	1.45908e10	1.62399
$699$	−7.72929e8	−0.0855991
$700$	−7.10461e10	−7.82884
$701$	−1.49165e10	−1.63552	−0.817758	−	0.575562i	$-0.804784\pi$
$701$	−1.49165e10	−1.63552	−0.817758	+	0.575562i	$0.804784\pi$
$702$	8.35559e8	0.0911585
$703$	2.29796e9	0.249458
$704$	−7.10949e10	−7.67952
$705$	−2.75952e8	−0.0296600
$706$	1.94507e10	2.08026
$707$	1.87365e10	1.99397
$708$	−1.98090e9	−0.209771
$709$	5.36963e9	0.565826	0.282913	−	0.959146i	$-0.408699\pi$
$709$	5.36963e9	0.565826	0.282913	+	0.959146i	$0.408699\pi$
$710$	3.82182e10	4.00743
$711$	2.84186e9	0.296524
$712$	3.01469e10	3.13014
$713$	−4.32333e9	−0.446689
$714$	1.57376e10	1.61806
$715$	7.36447e9	0.753477
$716$	4.70201e10	4.78727
$717$	−1.63778e9	−0.165935
$718$	1.54822e9	0.156098
$719$	−2.42754e9	−0.243565	−0.121783	−	0.992557i	$-0.538861\pi$
$719$	−2.42754e9	−0.243565	−0.121783	+	0.992557i	$0.538861\pi$
$720$	−2.35152e10	−2.34793
$721$	1.45510e10	1.44584
$722$	2.42029e9	0.239325
$723$	1.35822e9	0.133656
$724$	−5.42830e10	−5.31593
$725$	−1.76678e10	−1.72186
$726$	2.42237e10	2.34943
$727$	1.20971e10	1.16764	0.583822	−	0.811882i	$-0.301557\pi$
$727$	1.20971e10	1.16764	0.583822	+	0.811882i	$0.301557\pi$
$728$	−1.17724e10	−1.13086
$729$	3.87420e8	0.0370370
$730$	−1.38304e10	−1.31584
$731$	2.78125e9	0.263347
$732$	2.31835e10	2.18469
$733$	3.52480e7	0.00330575	0.00165288	−	0.999999i	$-0.499474\pi$
$733$	3.52480e7	0.00330575	0.00165288	+	0.999999i	$0.499474\pi$
$734$	−3.23463e10	−3.01918
$735$	−8.51104e9	−0.790636
$736$	6.05510e10	5.59821
$737$	4.70962e9	0.433360
$738$	−9.60564e9	−0.879689
$739$	9.27198e9	0.845118	0.422559	−	0.906336i	$-0.361132\pi$
$739$	9.27198e9	0.845118	0.422559	+	0.906336i	$0.361132\pi$
$740$	1.27598e10	1.15753
$741$	−1.64850e9	−0.148842
$742$	−4.07487e10	−3.66184
$743$	−1.63793e10	−1.46499	−0.732494	−	0.680773i	$-0.761644\pi$
$743$	−1.63793e10	−1.46499	−0.732494	+	0.680773i	$0.761644\pi$
$744$	−7.75358e9	−0.690235
$745$	1.24806e9	0.110583
$746$	2.63331e10	2.32229
$747$	−2.94371e9	−0.258388
$748$	6.06296e10	5.29699
$749$	9.30372e9	0.809040
$750$	−2.52668e10	−2.18693
$751$	2.46248e9	0.212145	0.106073	−	0.994358i	$-0.466172\pi$
$751$	2.46248e9	0.212145	0.106073	+	0.994358i	$0.466172\pi$
$752$	1.35941e9	0.116570
$753$	4.85334e9	0.414246
$754$	−4.56234e9	−0.387604
$755$	2.70596e10	2.28826
$756$	−8.50652e9	−0.716020
$757$	7.88850e9	0.660935	0.330468	−	0.943817i	$-0.392794\pi$
$757$	7.88850e9	0.660935	0.330468	+	0.943817i	$0.392794\pi$
$758$	2.66545e10	2.22295
$759$	−1.59271e10	−1.32218
$760$	7.87804e10	6.50984
$761$	−2.28543e10	−1.87984	−0.939922	−	0.341390i	$-0.889102\pi$
$761$	−2.28543e10	−1.87984	−0.939922	+	0.341390i	$0.889102\pi$
$762$	8.20010e9	0.671393
$763$	2.55733e9	0.208426
$764$	−4.34791e10	−3.52739
$765$	7.85206e9	0.634116
$766$	−2.26666e10	−1.82216
$767$	−3.95795e8	−0.0316728
$768$	2.77276e10	2.20876
$769$	3.75836e9	0.298028	0.149014	−	0.988835i	$-0.452390\pi$
$769$	3.75836e9	0.298028	0.149014	+	0.988835i	$0.452390\pi$
$770$	−1.01840e11	−8.03896
$771$	2.30299e9	0.180968
$772$	4.73725e10	3.70566
$773$	−2.31574e10	−1.80327	−0.901637	−	0.432494i	$-0.857634\pi$
$773$	−2.31574e10	−1.80327	−0.901637	+	0.432494i	$0.857634\pi$
$774$	−2.04199e9	−0.158292
$775$	−9.34939e9	−0.721485
$776$	−1.00041e10	−0.768532
$777$	2.36925e9	0.181191
$778$	−4.90279e10	−3.73263
$779$	1.89513e10	1.43634
$780$	−9.15358e9	−0.690653
$781$	2.73391e10	2.05355
$782$	−3.66246e10	−2.73873
$783$	−2.11540e9	−0.157481
$784$	4.19274e10	3.10736
$785$	−3.58279e10	−2.64349
$786$	−5.02573e8	−0.0369165
$787$	7.24985e8	0.0530173	0.0265087	−	0.999649i	$-0.491561\pi$
$787$	7.24985e8	0.0530173	0.0265087	+	0.999649i	$0.491561\pi$
$788$	4.00059e10	2.91261
$789$	1.11896e10	0.811046
$790$	−4.22881e10	−3.05157
$791$	−2.45652e9	−0.176483
$792$	−2.85640e10	−2.04306
$793$	4.63219e9	0.329860
$794$	2.13360e10	1.51266
$795$	−2.03310e10	−1.43507
$796$	−6.49036e10	−4.56113
$797$	1.66646e10	1.16598	0.582989	−	0.812480i	$-0.301883\pi$
$797$	1.66646e10	1.16598	0.582989	+	0.812480i	$0.301883\pi$
$798$	2.27963e10	1.58802
$799$	−4.53925e8	−0.0314826
$800$	1.30944e11	9.04213
$801$	4.35247e9	0.299241
$802$	2.03831e8	0.0139527
$803$	−9.89347e9	−0.674286
$804$	−5.85376e9	−0.397227
$805$	4.52901e10	3.05998
$806$	−2.41429e9	−0.162411
$807$	−8.31117e9	−0.556679
$808$	−7.81997e10	−5.21514
$809$	−1.50299e10	−0.998010	−0.499005	−	0.866599i	$-0.666301\pi$
$809$	−1.50299e10	−0.998010	−0.499005	+	0.866599i	$0.666301\pi$
$810$	−5.76498e9	−0.381154
$811$	−1.62482e10	−1.06963	−0.534813	−	0.844971i	$-0.679618\pi$
$811$	−1.62482e10	−1.06963	−0.534813	+	0.844971i	$0.679618\pi$
$812$	4.64475e10	3.04450
$813$	−6.36613e9	−0.415488
$814$	1.23982e10	0.805699
$815$	−9.80265e8	−0.0634296
$816$	−3.86812e10	−2.49221
$817$	4.02871e9	0.258457
$818$	9.30449e9	0.594369
$819$	−1.69965e9	−0.108110
$820$	1.05230e11	6.66488
$821$	−2.31309e10	−1.45879	−0.729393	−	0.684095i	$-0.760197\pi$
$821$	−2.31309e10	−1.45879	−0.729393	+	0.684095i	$0.760197\pi$
$822$	−2.88214e10	−1.80994
$823$	−2.00237e10	−1.25211	−0.626057	−	0.779777i	$-0.715332\pi$
$823$	−2.00237e10	−1.25211	−0.626057	+	0.779777i	$0.715332\pi$
$824$	−6.07310e10	−3.78151
$825$	−3.44430e10	−2.13556
$826$	5.47325e9	0.337921
$827$	−1.75153e10	−1.07683	−0.538417	−	0.842679i	$-0.680977\pi$
$827$	−1.75153e10	−1.07683	−0.538417	+	0.842679i	$0.680977\pi$
$828$	1.97964e10	1.21194
$829$	1.27473e10	0.777099	0.388550	−	0.921428i	$-0.372976\pi$
$829$	1.27473e10	0.777099	0.388550	+	0.921428i	$0.372976\pi$
$830$	4.38036e10	2.65911
$831$	−5.81805e9	−0.351701
$832$	1.76561e10	1.06283
$833$	−1.40002e10	−0.839220
$834$	−1.22049e9	−0.0728538
$835$	1.72103e10	1.02302
$836$	8.78237e10	5.19864
$837$	−1.11942e9	−0.0659866
$838$	−2.88538e10	−1.69375
$839$	1.43905e10	0.841217	0.420609	−	0.907242i	$-0.361817\pi$
$839$	1.43905e10	0.841217	0.420609	+	0.907242i	$0.361817\pi$
$840$	8.12246e10	4.72836
$841$	−5.69930e9	−0.330397
$842$	4.74885e10	2.74155
$843$	−5.57160e9	−0.320320
$844$	−1.19542e9	−0.0684416
$845$	2.90722e10	1.65760
$846$	3.33272e8	0.0189235
$847$	−4.92745e10	−2.78631
$848$	1.00155e11	5.64013
$849$	1.81893e10	1.02009
$850$	−7.92022e10	−4.42355
$851$	−5.51372e9	−0.306684
$852$	−3.39808e10	−1.88233
$853$	−2.47811e10	−1.36710	−0.683549	−	0.729905i	$-0.739564\pi$
$853$	−2.47811e10	−1.36710	−0.683549	+	0.729905i	$0.739564\pi$
$854$	−6.40563e10	−3.51933
$855$	1.13739e10	0.622342
$856$	−3.88306e10	−2.11600
$857$	1.34333e10	0.729036	0.364518	−	0.931196i	$-0.381234\pi$
$857$	1.34333e10	0.729036	0.364518	+	0.931196i	$0.381234\pi$
$858$	−8.89419e9	−0.480729
$859$	1.54319e10	0.830701	0.415350	−	0.909662i	$-0.363659\pi$
$859$	1.54319e10	0.830701	0.415350	+	0.909662i	$0.363659\pi$
$860$	2.23701e10	1.19929
$861$	1.95393e10	1.04327
$862$	1.87411e10	0.996598
$863$	−1.32034e10	−0.699273	−0.349636	−	0.936885i	$-0.613695\pi$
$863$	−1.32034e10	−0.699273	−0.349636	+	0.936885i	$0.613695\pi$
$864$	1.56782e10	0.826988
$865$	1.43796e10	0.755421
$866$	−2.24055e10	−1.17231
$867$	1.83705e9	0.0957312
$868$	2.45790e10	1.27569
$869$	−3.02505e10	−1.56373
$870$	3.14781e10	1.62066
$871$	−1.16961e9	−0.0599762
$872$	−1.06734e10	−0.545126
$873$	−1.44434e9	−0.0734717
$874$	−5.30517e10	−2.68788
$875$	5.13963e10	2.59360
$876$	1.22970e10	0.618065
$877$	−1.39419e10	−0.697949	−0.348975	−	0.937132i	$-0.613470\pi$
$877$	−1.39419e10	−0.697949	−0.348975	+	0.937132i	$0.613470\pi$
$878$	−3.14822e10	−1.56976
$879$	−7.24315e9	−0.359721
$880$	2.50310e11	12.3819
$881$	1.37479e10	0.677360	0.338680	−	0.940902i	$-0.390020\pi$
$881$	1.37479e10	0.677360	0.338680	+	0.940902i	$0.390020\pi$
$882$	1.02789e10	0.504437
$883$	8.50641e9	0.415799	0.207900	−	0.978150i	$-0.433337\pi$
$883$	8.50641e9	0.415799	0.207900	+	0.978150i	$0.433337\pi$
$884$	−1.50571e10	−0.733093
$885$	2.73080e9	0.132431
$886$	5.98635e9	0.289164
$887$	−1.27701e10	−0.614417	−0.307208	−	0.951642i	$-0.599395\pi$
$887$	−1.27701e10	−0.614417	−0.307208	+	0.951642i	$0.599395\pi$
$888$	−9.88846e9	−0.473896
$889$	−1.66802e10	−0.796241
$890$	−6.47665e10	−3.07954
$891$	−4.12394e9	−0.195317
$892$	1.15599e10	0.545354
$893$	−6.57523e8	−0.0308980
$894$	−1.50730e9	−0.0705534
$895$	−6.48204e10	−3.02225
$896$	−1.20810e11	−5.61079
$897$	3.95542e9	0.182987
$898$	−2.73420e10	−1.25998
$899$	6.11231e9	0.280573
$900$	4.28105e10	1.95750
$901$	−3.34433e10	−1.52326
$902$	1.02248e11	4.63909
$903$	4.15370e9	0.187728
$904$	1.02527e10	0.461582
$905$	7.48328e10	3.35600
$906$	−3.26803e10	−1.45995
$907$	3.70884e10	1.65049	0.825244	−	0.564776i	$-0.191037\pi$
$907$	3.70884e10	1.65049	0.825244	+	0.564776i	$0.191037\pi$
$908$	5.73616e10	2.54285
$909$	−1.12901e10	−0.498567
$910$	2.52915e10	1.11257
$911$	1.58470e10	0.694436	0.347218	−	0.937784i	$-0.387126\pi$
$911$	1.58470e10	0.694436	0.347218	+	0.937784i	$0.387126\pi$
$912$	−5.60307e10	−2.44593
$913$	3.13346e10	1.36262
$914$	−7.42774e10	−3.21770
$915$	−3.19600e10	−1.37922
$916$	1.55074e10	0.666660
$917$	1.02231e9	0.0437813
$918$	−9.48306e9	−0.404575
$919$	1.09730e10	0.466359	0.233180	−	0.972434i	$-0.425087\pi$
$919$	1.09730e10	0.466359	0.233180	+	0.972434i	$0.425087\pi$
$920$	−1.89026e11	−8.00321
$921$	1.77998e10	0.750770
$922$	−6.30781e10	−2.65046
$923$	−6.78955e9	−0.284207
$924$	9.05484e10	3.77597
$925$	−1.19237e10	−0.495352
$926$	8.83119e9	0.365494
$927$	−8.76804e9	−0.361513
$928$	−8.56067e10	−3.51633
$929$	3.30298e10	1.35161	0.675804	−	0.737081i	$-0.263797\pi$
$929$	3.30298e10	1.35161	0.675804	+	0.737081i	$0.263797\pi$
$930$	1.66575e10	0.679078
$931$	−2.02796e10	−0.823637
$932$	−1.02263e10	−0.413774
$933$	−2.35876e10	−0.950818
$934$	−1.77431e10	−0.712552
$935$	−8.35821e10	−3.34405
$936$	7.09376e9	0.282756
$937$	−1.81069e10	−0.719045	−0.359522	−	0.933136i	$-0.617060\pi$
$937$	−1.81069e10	−0.719045	−0.359522	+	0.933136i	$0.617060\pi$
$938$	1.61740e10	0.639894
$939$	7.66860e9	0.302264
$940$	−3.65101e9	−0.143372
$941$	2.38460e10	0.932938	0.466469	−	0.884538i	$-0.345526\pi$
$941$	2.38460e10	0.932938	0.466469	+	0.884538i	$0.345526\pi$
$942$	4.32699e10	1.68658
$943$	−4.54718e10	−1.76584
$944$	−1.34526e10	−0.520480
$945$	1.17268e10	0.452031
$946$	2.17362e10	0.834764
$947$	2.50480e10	0.958404	0.479202	−	0.877705i	$-0.340926\pi$
$947$	2.50480e10	0.958404	0.479202	+	0.877705i	$0.340926\pi$
$948$	3.75995e10	1.43335
$949$	2.45700e9	0.0933198
$950$	−1.14727e11	−4.34141
$951$	−5.85724e9	−0.220832
$952$	1.33610e11	5.01891
$953$	−2.27700e10	−0.852194	−0.426097	−	0.904677i	$-0.640112\pi$
$953$	−2.27700e10	−0.852194	−0.426097	+	0.904677i	$0.640112\pi$
$954$	2.45541e10	0.915597
$955$	5.99389e10	2.22688
$956$	−2.16688e10	−0.802105
$957$	2.25176e10	0.830483
$958$	−3.20816e10	−1.17890
$959$	5.86269e10	2.14650
$960$	−1.21819e11	−4.44393
$961$	−2.42781e10	−0.882436
$962$	−3.07904e9	−0.111507
$963$	−5.60617e9	−0.202290
$964$	1.79701e10	0.646072
$965$	−6.53062e10	−2.33942
$966$	−5.46976e10	−1.95231
$967$	1.53182e10	0.544772	0.272386	−	0.962188i	$-0.412187\pi$
$967$	1.53182e10	0.544772	0.272386	+	0.962188i	$0.412187\pi$
$968$	2.05655e11	7.28746
$969$	1.87095e10	0.660584
$970$	2.14924e10	0.756109
$971$	1.35596e10	0.475314	0.237657	−	0.971349i	$-0.423621\pi$
$971$	1.35596e10	0.475314	0.237657	+	0.971349i	$0.423621\pi$
$972$	5.12580e9	0.179032
$973$	2.48265e9	0.0864013
$974$	4.21084e10	1.46020
$975$	8.55377e9	0.295557
$976$	1.57443e11	5.42061
$977$	5.16415e10	1.77161	0.885804	−	0.464060i	$-0.153608\pi$
$977$	5.16415e10	1.77161	0.885804	+	0.464060i	$0.153608\pi$
$978$	1.18388e9	0.0404690
$979$	−4.63302e10	−1.57807
$980$	−1.12606e11	−3.82182
$981$	−1.54098e9	−0.0521141
$982$	6.87160e9	0.231562
$983$	2.68451e10	0.901421	0.450711	−	0.892670i	$-0.351171\pi$
$983$	2.68451e10	0.901421	0.450711	+	0.892670i	$0.351171\pi$
$984$	−8.15504e10	−2.72862
$985$	−5.51509e10	−1.83876
$986$	5.17796e10	1.72024
$987$	−6.77923e8	−0.0224425
$988$	−2.18106e10	−0.719481
$989$	−9.66650e9	−0.317748
$990$	6.13659e10	2.01004
$991$	3.98369e10	1.30025	0.650126	−	0.759826i	$-0.274716\pi$
$991$	3.98369e10	1.30025	0.650126	+	0.759826i	$0.274716\pi$
$992$	−4.53012e10	−1.47339
$993$	−2.69594e10	−0.873753
$994$	9.38895e10	3.03225
$995$	8.94740e10	2.87949
$996$	−3.89469e10	−1.24901
$997$	−5.65997e9	−0.180876	−0.0904380	−	0.995902i	$-0.528827\pi$
$997$	−5.65997e9	−0.180876	−0.0904380	+	0.995902i	$0.528827\pi$
$998$	−2.43241e10	−0.774605
$999$	−1.42765e9	−0.0453045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.17	✓	17
3.2	odd	2		531.8.a.d.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.17	✓	17	1.1	even	1	trivial
531.8.a.d.1.1		17	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+22.0278 q^{2} +27.0000 q^{3} +357.226 q^{4} -492.460 q^{5} +594.752 q^{6} -1209.81 q^{7} +5049.35 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+22.0278 q^{2} +27.0000 q^{3} +357.226 q^{4} -492.460 q^{5} +594.752 q^{6} -1209.81 q^{7} +5049.35 q^{8} +729.000 q^{9} -10847.8 q^{10} -7759.91 q^{11} +9645.10 q^{12} +1927.14 q^{13} -26649.5 q^{14} -13296.4 q^{15} +65501.4 q^{16} -21871.8 q^{17} +16058.3 q^{18} -31682.0 q^{19} -175919. q^{20} -32664.9 q^{21} -170934. q^{22} +76017.8 q^{23} +136332. q^{24} +164392. q^{25} +42450.8 q^{26} +19683.0 q^{27} -432176. q^{28} -107474. q^{29} -292891. q^{30} -56872.6 q^{31} +796537. q^{32} -209518. q^{33} -481789. q^{34} +595783. q^{35} +260418. q^{36} -72532.0 q^{37} -697885. q^{38} +52032.8 q^{39} -2.48660e6 q^{40} -598173. q^{41} -719537. q^{42} -127161. q^{43} -2.77204e6 q^{44} -359003. q^{45} +1.67451e6 q^{46} +20753.9 q^{47} +1.76854e6 q^{48} +640100. q^{49} +3.62120e6 q^{50} -590540. q^{51} +688425. q^{52} +1.52906e6 q^{53} +433574. q^{54} +3.82145e6 q^{55} -6.10876e6 q^{56} -855413. q^{57} -2.36741e6 q^{58} -205379. q^{59} -4.74982e6 q^{60} +2.40366e6 q^{61} -1.25278e6 q^{62} -881952. q^{63} +9.16182e6 q^{64} -949040. q^{65} -4.61522e6 q^{66} -606916. q^{67} -7.81319e6 q^{68} +2.05248e6 q^{69} +1.31238e7 q^{70} -3.52312e6 q^{71} +3.68098e6 q^{72} +1.27495e6 q^{73} -1.59772e6 q^{74} +4.43858e6 q^{75} -1.13176e7 q^{76} +9.38803e6 q^{77} +1.14617e6 q^{78} +3.89830e6 q^{79} -3.22568e7 q^{80} +531441. q^{81} -1.31765e7 q^{82} -4.03800e6 q^{83} -1.16687e7 q^{84} +1.07710e7 q^{85} -2.80108e6 q^{86} -2.90179e6 q^{87} -3.91825e7 q^{88} +5.97046e6 q^{89} -7.90807e6 q^{90} -2.33148e6 q^{91} +2.71555e7 q^{92} -1.53556e6 q^{93} +457163. q^{94} +1.56021e7 q^{95} +2.15065e7 q^{96} -1.98127e6 q^{97} +1.41000e7 q^{98} -5.65698e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

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