LMFDB - Embedded newform 177.8.a.b.1.4

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			1.4
Root			$-15.8998$ 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)

$f(q)$	$=$	$q-17.8998 q^{2} +27.0000 q^{3} +192.403 q^{4} +255.355 q^{5} -483.295 q^{6} -1072.82 q^{7} -1152.80 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-17.8998 q^{2} +27.0000 q^{3} +192.403 q^{4} +255.355 q^{5} -483.295 q^{6} -1072.82 q^{7} -1152.80 q^{8} +729.000 q^{9} -4570.81 q^{10} +4742.70 q^{11} +5194.88 q^{12} +5721.05 q^{13} +19203.3 q^{14} +6894.59 q^{15} -3992.71 q^{16} -12850.6 q^{17} -13049.0 q^{18} -52123.1 q^{19} +49131.1 q^{20} -28966.2 q^{21} -84893.4 q^{22} -9824.17 q^{23} -31125.6 q^{24} -12918.7 q^{25} -102406. q^{26} +19683.0 q^{27} -206414. q^{28} -196436. q^{29} -123412. q^{30} +272544. q^{31} +219027. q^{32} +128053. q^{33} +230023. q^{34} -273951. q^{35} +140262. q^{36} +309341. q^{37} +932994. q^{38} +154468. q^{39} -294373. q^{40} -421229. q^{41} +518490. q^{42} -406292. q^{43} +912509. q^{44} +186154. q^{45} +175851. q^{46} -261121. q^{47} -107803. q^{48} +327408. q^{49} +231242. q^{50} -346967. q^{51} +1.10075e6 q^{52} +738907. q^{53} -352322. q^{54} +1.21107e6 q^{55} +1.23675e6 q^{56} -1.40732e6 q^{57} +3.51616e6 q^{58} -205379. q^{59} +1.32654e6 q^{60} +233563. q^{61} -4.87848e6 q^{62} -782089. q^{63} -3.40947e6 q^{64} +1.46090e6 q^{65} -2.29212e6 q^{66} +3.54145e6 q^{67} -2.47250e6 q^{68} -265253. q^{69} +4.90367e6 q^{70} +1.03036e6 q^{71} -840390. q^{72} -5.88757e6 q^{73} -5.53715e6 q^{74} -348804. q^{75} -1.00286e7 q^{76} -5.08808e6 q^{77} -2.76495e6 q^{78} +4.34224e6 q^{79} -1.01956e6 q^{80} +531441. q^{81} +7.53991e6 q^{82} -4.12014e6 q^{83} -5.57319e6 q^{84} -3.28147e6 q^{85} +7.27255e6 q^{86} -5.30376e6 q^{87} -5.46737e6 q^{88} -7.32690e6 q^{89} -3.33212e6 q^{90} -6.13768e6 q^{91} -1.89020e6 q^{92} +7.35868e6 q^{93} +4.67402e6 q^{94} -1.33099e7 q^{95} +5.91372e6 q^{96} +1.46546e7 q^{97} -5.86054e6 q^{98} +3.45743e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−17.8998	−1.58213	−0.791067	−	0.611730i	$-0.790474\pi$
$2$	−17.8998	−1.58213	−0.791067	+	0.611730i	$0.790474\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	192.403	1.50315
$5$	255.355	0.913587	0.456793	−	0.889573i	$-0.348998\pi$
$5$	255.355	0.913587	0.456793	+	0.889573i	$0.348998\pi$
$6$	−483.295	−0.913445
$7$	−1072.82	−1.18218	−0.591092	−	0.806604i	$-0.701303\pi$
$7$	−1072.82	−1.18218	−0.591092	+	0.806604i	$0.701303\pi$
$8$	−1152.80	−0.796046
$9$	729.000	0.333333
$10$	−4570.81	−1.44542
$11$	4742.70	1.07436	0.537182	−	0.843467i	$-0.319489\pi$
$11$	4742.70	1.07436	0.537182	+	0.843467i	$0.319489\pi$
$12$	5194.88	0.867843
$13$	5721.05	0.722227	0.361114	−	0.932522i	$-0.382397\pi$
$13$	5721.05	0.722227	0.361114	+	0.932522i	$0.382397\pi$
$14$	19203.3	1.87037
$15$	6894.59	0.527460
$16$	−3992.71	−0.243695
$17$	−12850.6	−0.634385	−0.317192	−	0.948361i	$-0.602740\pi$
$17$	−12850.6	−0.634385	−0.317192	+	0.948361i	$0.602740\pi$
$18$	−13049.0	−0.527378
$19$	−52123.1	−1.74338	−0.871692	−	0.490055i	$-0.836977\pi$
$19$	−52123.1	−1.74338	−0.871692	+	0.490055i	$0.836977\pi$
$20$	49131.1	1.37326
$21$	−28966.2	−0.682535
$22$	−84893.4	−1.69979
$23$	−9824.17	−0.168364	−0.0841818	−	0.996450i	$-0.526828\pi$
$23$	−9824.17	−0.168364	−0.0841818	+	0.996450i	$0.526828\pi$
$24$	−31125.6	−0.459598
$25$	−12918.7	−0.165359
$26$	−102406.	−1.14266
$27$	19683.0	0.192450
$28$	−206414.	−1.77700
$29$	−196436.	−1.49564	−0.747821	−	0.663901i	$-0.768900\pi$
$29$	−196436.	−1.49564	−0.747821	+	0.663901i	$0.768900\pi$
$30$	−123412.	−0.834512
$31$	272544.	1.64312	0.821562	−	0.570119i	$-0.193103\pi$
$31$	272544.	1.64312	0.821562	+	0.570119i	$0.193103\pi$
$32$	219027.	1.18161
$33$	128053.	0.620284
$34$	230023.	1.00368
$35$	−273951.	−1.08003
$36$	140262.	0.501049
$37$	309341.	1.00400	0.501998	−	0.864869i	$-0.332599\pi$
$37$	309341.	1.00400	0.501998	+	0.864869i	$0.332599\pi$
$38$	932994.	2.75827
$39$	154468.	0.416978
$40$	−294373.	−0.727258
$41$	−421229.	−0.954497	−0.477249	−	0.878768i	$-0.658366\pi$
$41$	−421229.	−0.954497	−0.477249	+	0.878768i	$0.658366\pi$
$42$	518490.	1.07986
$43$	−406292.	−0.779289	−0.389645	−	0.920965i	$-0.627402\pi$
$43$	−406292.	−0.779289	−0.389645	+	0.920965i	$0.627402\pi$
$44$	912509.	1.61493
$45$	186154.	0.304529
$46$	175851.	0.266374
$47$	−261121.	−0.366859	−0.183430	−	0.983033i	$-0.558720\pi$
$47$	−261121.	−0.366859	−0.183430	+	0.983033i	$0.558720\pi$
$48$	−107803.	−0.140698
$49$	327408.	0.397560
$50$	231242.	0.261620
$51$	−346967.	−0.366262
$52$	1.10075e6	1.08561
$53$	738907.	0.681748	0.340874	−	0.940109i	$-0.389277\pi$
$53$	738907.	0.681748	0.340874	+	0.940109i	$0.389277\pi$
$54$	−352322.	−0.304482
$55$	1.21107e6	0.981524
$56$	1.23675e6	0.941074
$57$	−1.40732e6	−1.00654
$58$	3.51616e6	2.36630
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	1.32654e6	0.792850
$61$	233563.	0.131750	0.0658748	−	0.997828i	$-0.479016\pi$
$61$	233563.	0.131750	0.0658748	+	0.997828i	$0.479016\pi$
$62$	−4.87848e6	−2.59964
$63$	−782089.	−0.394062
$64$	−3.40947e6	−1.62576
$65$	1.46090e6	0.659817
$66$	−2.29212e6	−0.981372
$67$	3.54145e6	1.43853	0.719265	−	0.694736i	$-0.244479\pi$
$67$	3.54145e6	1.43853	0.719265	+	0.694736i	$0.244479\pi$
$68$	−2.47250e6	−0.953574
$69$	−265253.	−0.0972048
$70$	4.90367e6	1.70875
$71$	1.03036e6	0.341652	0.170826	−	0.985301i	$-0.445356\pi$
$71$	1.03036e6	0.341652	0.170826	+	0.985301i	$0.445356\pi$
$72$	−840390.	−0.265349
$73$	−5.88757e6	−1.77136	−0.885679	−	0.464298i	$-0.846307\pi$
$73$	−5.88757e6	−1.77136	−0.885679	+	0.464298i	$0.846307\pi$
$74$	−5.53715e6	−1.58845
$75$	−348804.	−0.0954700
$76$	−1.00286e7	−2.62056
$77$	−5.08808e6	−1.27010
$78$	−2.76495e6	−0.659715
$79$	4.34224e6	0.990875	0.495437	−	0.868644i	$-0.335008\pi$
$79$	4.34224e6	0.990875	0.495437	+	0.868644i	$0.335008\pi$
$80$	−1.01956e6	−0.222637
$81$	531441.	0.111111
$82$	7.53991e6	1.51014
$83$	−4.12014e6	−0.790931	−0.395465	−	0.918481i	$-0.629417\pi$
$83$	−4.12014e6	−0.790931	−0.395465	+	0.918481i	$0.629417\pi$
$84$	−5.57319e6	−1.02595
$85$	−3.28147e6	−0.579566
$86$	7.27255e6	1.23294
$87$	−5.30376e6	−0.863509
$88$	−5.46737e6	−0.855243
$89$	−7.32690e6	−1.10168	−0.550840	−	0.834611i	$-0.685692\pi$
$89$	−7.32690e6	−1.10168	−0.550840	+	0.834611i	$0.685692\pi$
$90$	−3.33212e6	−0.481806
$91$	−6.13768e6	−0.853806
$92$	−1.89020e6	−0.253075
$93$	7.35868e6	0.948658
$94$	4.67402e6	0.580421
$95$	−1.33099e7	−1.59273
$96$	5.91372e6	0.682200
$97$	1.46546e7	1.63032	0.815158	−	0.579239i	$-0.196650\pi$
$97$	1.46546e7	1.63032	0.815158	+	0.579239i	$0.196650\pi$
$98$	−5.86054e6	−0.628994
$99$	3.45743e6	0.358121
$100$	−2.48559e6	−0.248559
$101$	3.05329e6	0.294878	0.147439	−	0.989071i	$-0.452897\pi$
$101$	3.05329e6	0.294878	0.147439	+	0.989071i	$0.452897\pi$
$102$	6.21063e6	0.579476
$103$	−1.49285e7	−1.34613	−0.673063	−	0.739585i	$-0.735022\pi$
$103$	−1.49285e7	−1.34613	−0.673063	+	0.739585i	$0.735022\pi$
$104$	−6.59521e6	−0.574926
$105$	−7.39668e6	−0.623555
$106$	−1.32263e7	−1.07862
$107$	−2.22015e7	−1.75202	−0.876011	−	0.482291i	$-0.839805\pi$
$107$	−2.22015e7	−1.75202	−0.876011	+	0.482291i	$0.839805\pi$
$108$	3.78707e6	0.289281
$109$	−2.47303e6	−0.182910	−0.0914549	−	0.995809i	$-0.529152\pi$
$109$	−2.47303e6	−0.182910	−0.0914549	+	0.995809i	$0.529152\pi$
$110$	−2.16780e7	−1.55290
$111$	8.35221e6	0.579657
$112$	4.28347e6	0.288093
$113$	−1.16610e7	−0.760260	−0.380130	−	0.924933i	$-0.624121\pi$
$113$	−1.16610e7	−0.760260	−0.380130	+	0.924933i	$0.624121\pi$
$114$	2.51908e7	1.59249
$115$	−2.50865e6	−0.153815
$116$	−3.77948e7	−2.24817
$117$	4.17064e6	0.240742
$118$	3.67624e6	0.205976
$119$	1.37864e7	0.749960
$120$	−7.94808e6	−0.419882
$121$	3.00601e6	0.154256
$122$	−4.18073e6	−0.208446
$123$	−1.13732e7	−0.551079
$124$	5.24382e7	2.46986
$125$	−2.32485e7	−1.06466
$126$	1.39992e7	0.623458
$127$	−3.47578e7	−1.50570	−0.752852	−	0.658190i	$-0.771322\pi$
$127$	−3.47578e7	−1.50570	−0.752852	+	0.658190i	$0.771322\pi$
$128$	3.29934e7	1.39057
$129$	−1.09699e7	−0.449923
$130$	−2.61498e7	−1.04392
$131$	−1.06271e7	−0.413016	−0.206508	−	0.978445i	$-0.566210\pi$
$131$	−1.06271e7	−0.413016	−0.206508	+	0.978445i	$0.566210\pi$
$132$	2.46377e7	0.932378
$133$	5.59189e7	2.06100
$134$	−6.33912e7	−2.27595
$135$	5.02616e6	0.175820
$136$	1.48142e7	0.505000
$137$	−4.64453e7	−1.54319	−0.771596	−	0.636112i	$-0.780541\pi$
$137$	−4.64453e7	−1.54319	−0.771596	+	0.636112i	$0.780541\pi$
$138$	4.74797e6	0.153791
$139$	−1.75461e7	−0.554151	−0.277076	−	0.960848i	$-0.589365\pi$
$139$	−1.75461e7	−0.554151	−0.277076	+	0.960848i	$0.589365\pi$
$140$	−5.27090e7	−1.62344
$141$	−7.05027e6	−0.211806
$142$	−1.84432e7	−0.540539
$143$	2.71332e7	0.775934
$144$	−2.91068e6	−0.0812318
$145$	−5.01609e7	−1.36640
$146$	1.05386e8	2.80253
$147$	8.84002e6	0.229532
$148$	5.95181e7	1.50915
$149$	6.90672e7	1.71049	0.855244	−	0.518225i	$-0.173407\pi$
$149$	6.90672e7	1.71049	0.855244	+	0.518225i	$0.173407\pi$
$150$	6.24352e6	0.151046
$151$	9.93956e6	0.234935	0.117468	−	0.993077i	$-0.462522\pi$
$151$	9.93956e6	0.234935	0.117468	+	0.993077i	$0.462522\pi$
$152$	6.00875e7	1.38781
$153$	−9.36810e6	−0.211462
$154$	9.10756e7	2.00946
$155$	6.95955e7	1.50114
$156$	2.97201e7	0.626780
$157$	−1.73655e7	−0.358128	−0.179064	−	0.983837i	$-0.557307\pi$
$157$	−1.73655e7	−0.358128	−0.179064	+	0.983837i	$0.557307\pi$
$158$	−7.77252e7	−1.56770
$159$	1.99505e7	0.393608
$160$	5.59297e7	1.07950
$161$	1.05396e7	0.199037
$162$	−9.51269e6	−0.175793
$163$	−8.66389e7	−1.56695	−0.783477	−	0.621421i	$-0.786556\pi$
$163$	−8.66389e7	−1.56695	−0.783477	+	0.621421i	$0.786556\pi$
$164$	−8.10456e7	−1.43475
$165$	3.26990e7	0.566683
$166$	7.37497e7	1.25136
$167$	−2.60451e7	−0.432732	−0.216366	−	0.976312i	$-0.569420\pi$
$167$	−2.60451e7	−0.432732	−0.216366	+	0.976312i	$0.569420\pi$
$168$	3.33922e7	0.543329
$169$	−3.00181e7	−0.478388
$170$	5.87377e7	0.916950
$171$	−3.79978e7	−0.581128
$172$	−7.81717e7	−1.17139
$173$	−2.86328e7	−0.420438	−0.210219	−	0.977654i	$-0.567418\pi$
$173$	−2.86328e7	−0.420438	−0.210219	+	0.977654i	$0.567418\pi$
$174$	9.49363e7	1.36619
$175$	1.38595e7	0.195485
$176$	−1.89362e7	−0.261817
$177$	−5.54523e6	−0.0751646
$178$	1.31150e8	1.74300
$179$	9.04329e6	0.117853	0.0589266	−	0.998262i	$-0.481232\pi$
$179$	9.04329e6	0.117853	0.0589266	+	0.998262i	$0.481232\pi$
$180$	3.58166e7	0.457752
$181$	9.04918e7	1.13432	0.567158	−	0.823609i	$-0.308043\pi$
$181$	9.04918e7	1.13432	0.567158	+	0.823609i	$0.308043\pi$
$182$	1.09863e8	1.35084
$183$	6.30620e6	0.0760657
$184$	1.13253e7	0.134025
$185$	7.89919e7	0.917237
$186$	−1.31719e8	−1.50090
$187$	−6.09466e7	−0.681559
$188$	−5.02405e7	−0.551444
$189$	−2.11164e7	−0.227512
$190$	2.38245e8	2.51992
$191$	−7.52927e7	−0.781873	−0.390936	−	0.920418i	$-0.627849\pi$
$191$	−7.52927e7	−0.781873	−0.390936	+	0.920418i	$0.627849\pi$
$192$	−9.20557e7	−0.938634
$193$	3.03390e7	0.303774	0.151887	−	0.988398i	$-0.451465\pi$
$193$	3.03390e7	0.303774	0.151887	+	0.988398i	$0.451465\pi$
$194$	−2.62314e8	−2.57938
$195$	3.94443e7	0.380946
$196$	6.29942e7	0.597592
$197$	5.75348e7	0.536165	0.268083	−	0.963396i	$-0.413610\pi$
$197$	5.75348e7	0.536165	0.268083	+	0.963396i	$0.413610\pi$
$198$	−6.18873e7	−0.566595
$199$	3.30510e6	0.0297303	0.0148651	−	0.999890i	$-0.495268\pi$
$199$	3.30510e6	0.0297303	0.0148651	+	0.999890i	$0.495268\pi$
$200$	1.48926e7	0.131633
$201$	9.56191e7	0.830536
$202$	−5.46532e7	−0.466537
$203$	2.10741e8	1.76812
$204$	−6.67574e7	−0.550546
$205$	−1.07563e8	−0.872016
$206$	2.67217e8	2.12975
$207$	−7.16182e6	−0.0561212
$208$	−2.28425e7	−0.176003
$209$	−2.47204e8	−1.87303
$210$	1.32399e8	0.986547
$211$	7.47470e7	0.547779	0.273890	−	0.961761i	$-0.411690\pi$
$211$	7.47470e7	0.547779	0.273890	+	0.961761i	$0.411690\pi$
$212$	1.42168e8	1.02477
$213$	2.78197e7	0.197253
$214$	3.97403e8	2.77193
$215$	−1.03749e8	−0.711948
$216$	−2.26905e7	−0.153199
$217$	−2.92391e8	−1.94248
$218$	4.42668e7	0.289388
$219$	−1.58964e8	−1.02269
$220$	2.33014e8	1.47538
$221$	−7.35190e7	−0.458170
$222$	−1.49503e8	−0.917095
$223$	−2.95302e8	−1.78320	−0.891599	−	0.452826i	$-0.850416\pi$
$223$	−2.95302e8	−1.78320	−0.891599	+	0.452826i	$0.850416\pi$
$224$	−2.34977e8	−1.39688
$225$	−9.41771e6	−0.0551196
$226$	2.08730e8	1.20283
$227$	−4.08714e6	−0.0231915	−0.0115957	−	0.999933i	$-0.503691\pi$
$227$	−4.08714e6	−0.0231915	−0.0115957	+	0.999933i	$0.503691\pi$
$228$	−2.70773e8	−1.51298
$229$	2.00230e8	1.10181	0.550903	−	0.834570i	$-0.314284\pi$
$229$	2.00230e8	1.10181	0.550903	+	0.834570i	$0.314284\pi$
$230$	4.49044e7	0.243356
$231$	−1.37378e8	−0.733290
$232$	2.26451e8	1.19060
$233$	−9.85532e7	−0.510417	−0.255208	−	0.966886i	$-0.582144\pi$
$233$	−9.85532e7	−0.510417	−0.255208	+	0.966886i	$0.582144\pi$
$234$	−7.46537e7	−0.380887
$235$	−6.66787e7	−0.335158
$236$	−3.95155e7	−0.195693
$237$	1.17240e8	0.572082
$238$	−2.46775e8	−1.18654
$239$	−3.06770e8	−1.45352	−0.726758	−	0.686894i	$-0.758974\pi$
$239$	−3.06770e8	−1.45352	−0.726758	+	0.686894i	$0.758974\pi$
$240$	−2.75281e7	−0.128540
$241$	3.30373e8	1.52035	0.760176	−	0.649717i	$-0.225112\pi$
$241$	3.30373e8	1.52035	0.760176	+	0.649717i	$0.225112\pi$
$242$	−5.38071e7	−0.244054
$243$	1.43489e7	0.0641500
$244$	4.49382e7	0.198039
$245$	8.36054e7	0.363206
$246$	2.03578e8	0.871881
$247$	−2.98199e8	−1.25912
$248$	−3.14188e8	−1.30800
$249$	−1.11244e8	−0.456644
$250$	4.16143e8	1.68443
$251$	−4.29400e8	−1.71397	−0.856987	−	0.515339i	$-0.827666\pi$
$251$	−4.29400e8	−1.71397	−0.856987	+	0.515339i	$0.827666\pi$
$252$	−1.50476e8	−0.592333
$253$	−4.65931e7	−0.180884
$254$	6.22158e8	2.38222
$255$	−8.85998e7	−0.334612
$256$	−1.54163e8	−0.574302
$257$	−3.01963e8	−1.10966	−0.554828	−	0.831965i	$-0.687216\pi$
$257$	−3.01963e8	−1.10966	−0.554828	+	0.831965i	$0.687216\pi$
$258$	1.96359e8	0.711838
$259$	−3.31869e8	−1.18691
$260$	2.81081e8	0.991803
$261$	−1.43202e8	−0.498547
$262$	1.90224e8	0.653447
$263$	−7.22951e7	−0.245055	−0.122528	−	0.992465i	$-0.539100\pi$
$263$	−7.22951e7	−0.245055	−0.122528	+	0.992465i	$0.539100\pi$
$264$	−1.47619e8	−0.493775
$265$	1.88684e8	0.622836
$266$	−1.00094e9	−3.26078
$267$	−1.97826e8	−0.636055
$268$	6.81384e8	2.16232
$269$	1.46096e8	0.457622	0.228811	−	0.973471i	$-0.426516\pi$
$269$	1.46096e8	0.457622	0.228811	+	0.973471i	$0.426516\pi$
$270$	−8.99672e7	−0.278171
$271$	−2.87297e8	−0.876876	−0.438438	−	0.898761i	$-0.644468\pi$
$271$	−2.87297e8	−0.876876	−0.438438	+	0.898761i	$0.644468\pi$
$272$	5.13087e7	0.154597
$273$	−1.65717e8	−0.492945
$274$	8.31362e8	2.44154
$275$	−6.12693e7	−0.177656
$276$	−5.10353e7	−0.146113
$277$	3.14837e8	0.890033	0.445016	−	0.895522i	$-0.353198\pi$
$277$	3.14837e8	0.890033	0.445016	+	0.895522i	$0.353198\pi$
$278$	3.14071e8	0.876741
$279$	1.98684e8	0.547708
$280$	3.15811e8	0.859753
$281$	7.28235e8	1.95794	0.978971	−	0.204002i	$-0.0653948\pi$
$281$	7.28235e8	1.95794	0.978971	+	0.204002i	$0.0653948\pi$
$282$	1.26198e8	0.335106
$283$	−2.37367e8	−0.622541	−0.311271	−	0.950321i	$-0.600755\pi$
$283$	−2.37367e8	−0.622541	−0.311271	+	0.950321i	$0.600755\pi$
$284$	1.98244e8	0.513553
$285$	−3.59368e8	−0.919564
$286$	−4.85679e8	−1.22763
$287$	4.51904e8	1.12839
$288$	1.59671e8	0.393868
$289$	−2.45200e8	−0.597556
$290$	8.97870e8	2.16182
$291$	3.95673e8	0.941263
$292$	−1.13279e9	−2.66261
$293$	−1.12840e7	−0.0262076	−0.0131038	−	0.999914i	$-0.504171\pi$
$293$	−1.12840e7	−0.0262076	−0.0131038	+	0.999914i	$0.504171\pi$
$294$	−1.58235e8	−0.363150
$295$	−5.24446e7	−0.118939
$296$	−3.56608e8	−0.799227
$297$	9.33505e7	0.206761
$298$	−1.23629e9	−2.70622
$299$	−5.62045e7	−0.121597
$300$	−6.71109e7	−0.143505
$301$	4.35880e8	0.921264
$302$	−1.77916e8	−0.371699
$303$	8.24388e7	0.170248
$304$	2.08112e8	0.424855
$305$	5.96416e7	0.120365
$306$	1.67687e8	0.334560
$307$	3.01581e8	0.594867	0.297433	−	0.954743i	$-0.403869\pi$
$307$	3.01581e8	0.594867	0.297433	+	0.954743i	$0.403869\pi$
$308$	−9.78961e8	−1.90914
$309$	−4.03069e8	−0.777186
$310$	−1.24575e9	−2.37500
$311$	7.94458e8	1.49765	0.748824	−	0.662769i	$-0.230619\pi$
$311$	7.94458e8	1.49765	0.748824	+	0.662769i	$0.230619\pi$
$312$	−1.78071e8	−0.331934
$313$	9.42174e8	1.73670	0.868352	−	0.495948i	$-0.165179\pi$
$313$	9.42174e8	1.73670	0.868352	+	0.495948i	$0.165179\pi$
$314$	3.10839e8	0.566607
$315$	−1.99710e8	−0.360009
$316$	8.35459e8	1.48943
$317$	−9.46323e7	−0.166852	−0.0834261	−	0.996514i	$-0.526586\pi$
$317$	−9.46323e7	−0.166852	−0.0834261	+	0.996514i	$0.526586\pi$
$318$	−3.57110e8	−0.622740
$319$	−9.31635e8	−1.60686
$320$	−8.70626e8	−1.48527
$321$	−5.99441e8	−1.01153
$322$	−1.88657e8	−0.314903
$323$	6.69814e8	1.10598
$324$	1.02251e8	0.167016
$325$	−7.39083e7	−0.119427
$326$	1.55082e9	2.47913
$327$	−6.67719e7	−0.105603
$328$	4.85592e8	0.759824
$329$	2.80137e8	0.433696
$330$	−5.85305e8	−0.896569
$331$	2.56756e8	0.389156	0.194578	−	0.980887i	$-0.437666\pi$
$331$	2.56756e8	0.389156	0.194578	+	0.980887i	$0.437666\pi$
$332$	−7.92726e8	−1.18889
$333$	2.25510e8	0.334665
$334$	4.66202e8	0.684639
$335$	9.04327e8	1.31422
$336$	1.15654e8	0.166331
$337$	9.60763e7	0.136745	0.0683725	−	0.997660i	$-0.478219\pi$
$337$	9.60763e7	0.136745	0.0683725	+	0.997660i	$0.478219\pi$
$338$	5.37318e8	0.756873
$339$	−3.14848e8	−0.438936
$340$	−6.31365e8	−0.871172
$341$	1.29259e9	1.76531
$342$	6.80152e8	0.919422
$343$	5.32265e8	0.712195
$344$	4.68373e8	0.620350
$345$	−6.77336e7	−0.0888050
$346$	5.12521e8	0.665189
$347$	4.17126e8	0.535937	0.267969	−	0.963428i	$-0.413648\pi$
$347$	4.17126e8	0.535937	0.267969	+	0.963428i	$0.413648\pi$
$348$	−1.02046e9	−1.29798
$349$	−5.98395e8	−0.753527	−0.376764	−	0.926309i	$-0.622963\pi$
$349$	−5.98395e8	−0.753527	−0.376764	+	0.926309i	$0.622963\pi$
$350$	−2.48081e8	−0.309283
$351$	1.12607e8	0.138993
$352$	1.03878e9	1.26947
$353$	−1.21639e9	−1.47184	−0.735921	−	0.677067i	$-0.763251\pi$
$353$	−1.21639e9	−1.47184	−0.735921	+	0.677067i	$0.763251\pi$
$354$	9.92586e7	0.118920
$355$	2.63107e8	0.312129
$356$	−1.40972e9	−1.65599
$357$	3.72234e8	0.432989
$358$	−1.61873e8	−0.186459
$359$	−1.46927e8	−0.167599	−0.0837993	−	0.996483i	$-0.526705\pi$
$359$	−1.46927e8	−0.167599	−0.0837993	+	0.996483i	$0.526705\pi$
$360$	−2.14598e8	−0.242419
$361$	1.82295e9	2.03939
$362$	−1.61979e9	−1.79464
$363$	8.11624e7	0.0890598
$364$	−1.18091e9	−1.28340
$365$	−1.50342e9	−1.61829
$366$	−1.12880e8	−0.120346
$367$	−1.54258e9	−1.62899	−0.814494	−	0.580172i	$-0.802985\pi$
$367$	−1.54258e9	−1.62899	−0.814494	+	0.580172i	$0.802985\pi$
$368$	3.92250e7	0.0410295
$369$	−3.07076e8	−0.318166
$370$	−1.41394e9	−1.45119
$371$	−7.92717e8	−0.805952
$372$	1.41583e9	1.42597
$373$	3.08393e8	0.307697	0.153849	−	0.988094i	$-0.450833\pi$
$373$	3.08393e8	0.307697	0.153849	+	0.988094i	$0.450833\pi$
$374$	1.09093e9	1.07832
$375$	−6.27709e8	−0.614680
$376$	3.01020e8	0.292037
$377$	−1.12382e9	−1.08019
$378$	3.77979e8	0.359954
$379$	−8.49811e8	−0.801835	−0.400918	−	0.916114i	$-0.631309\pi$
$379$	−8.49811e8	−0.801835	−0.400918	+	0.916114i	$0.631309\pi$
$380$	−2.56087e9	−2.39411
$381$	−9.38461e8	−0.869318
$382$	1.34772e9	1.23703
$383$	8.83511e8	0.803556	0.401778	−	0.915737i	$-0.368392\pi$
$383$	8.83511e8	0.803556	0.401778	+	0.915737i	$0.368392\pi$
$384$	8.90822e8	0.802845
$385$	−1.29927e9	−1.16034
$386$	−5.43062e8	−0.480612
$387$	−2.96187e8	−0.259763
$388$	2.81958e9	2.45061
$389$	−1.07810e9	−0.928616	−0.464308	−	0.885674i	$-0.653697\pi$
$389$	−1.07810e9	−0.928616	−0.464308	+	0.885674i	$0.653697\pi$
$390$	−7.06045e8	−0.602707
$391$	1.26247e8	0.106807
$392$	−3.77435e8	−0.316476
$393$	−2.86933e8	−0.238455
$394$	−1.02986e9	−0.848285
$395$	1.10881e9	0.905250
$396$	6.65219e8	0.538309
$397$	−2.25182e9	−1.80620	−0.903101	−	0.429427i	$-0.858715\pi$
$397$	−2.25182e9	−1.80620	−0.903101	+	0.429427i	$0.858715\pi$
$398$	−5.91607e7	−0.0470373
$399$	1.50981e9	1.18992
$400$	5.15804e7	0.0402972
$401$	2.61153e8	0.202250	0.101125	−	0.994874i	$-0.467756\pi$
$401$	2.61153e8	0.202250	0.101125	+	0.994874i	$0.467756\pi$
$402$	−1.71156e9	−1.31402
$403$	1.55924e9	1.18671
$404$	5.87461e8	0.443246
$405$	1.35706e8	0.101510
$406$	−3.77222e9	−2.79741
$407$	1.46711e9	1.07866
$408$	3.99983e8	0.291562
$409$	3.01019e8	0.217552	0.108776	−	0.994066i	$-0.465307\pi$
$409$	3.01019e8	0.217552	0.108776	+	0.994066i	$0.465307\pi$
$410$	1.92536e9	1.37965
$411$	−1.25402e9	−0.890963
$412$	−2.87228e9	−2.02343
$413$	2.20335e8	0.153907
$414$	1.28195e8	0.0887913
$415$	−1.05210e9	−0.722584
$416$	1.25306e9	0.853387
$417$	−4.73744e8	−0.319939
$418$	4.42491e9	2.96338
$419$	−2.40890e9	−1.59982	−0.799908	−	0.600123i	$-0.795118\pi$
$419$	−2.40890e9	−1.59982	−0.799908	+	0.600123i	$0.795118\pi$
$420$	−1.42314e9	−0.937295
$421$	1.27032e9	0.829711	0.414855	−	0.909887i	$-0.363832\pi$
$421$	1.27032e9	0.829711	0.414855	+	0.909887i	$0.363832\pi$
$422$	−1.33796e9	−0.866660
$423$	−1.90357e8	−0.122286
$424$	−8.51810e8	−0.542703
$425$	1.66013e8	0.104901
$426$	−4.97966e8	−0.312080
$427$	−2.50572e8	−0.155752
$428$	−4.27164e9	−2.63355
$429$	7.32597e8	0.447986
$430$	1.85708e9	1.12640
$431$	2.24959e9	1.35342	0.676710	−	0.736250i	$-0.263405\pi$
$431$	2.24959e9	1.35342	0.676710	+	0.736250i	$0.263405\pi$
$432$	−7.85884e7	−0.0468992
$433$	1.18429e9	0.701053	0.350527	−	0.936553i	$-0.386003\pi$
$433$	1.18429e9	0.701053	0.350527	+	0.936553i	$0.386003\pi$
$434$	5.23375e9	3.07326
$435$	−1.35434e9	−0.788890
$436$	−4.75819e8	−0.274940
$437$	5.12066e8	0.293522
$438$	2.84543e9	1.61804
$439$	1.33626e9	0.753818	0.376909	−	0.926250i	$-0.376987\pi$
$439$	1.33626e9	0.753818	0.376909	+	0.926250i	$0.376987\pi$
$440$	−1.39612e9	−0.781339
$441$	2.38680e8	0.132520
$442$	1.31598e9	0.724886
$443$	1.47906e8	0.0808299	0.0404149	−	0.999183i	$-0.487132\pi$
$443$	1.47906e8	0.0808299	0.0404149	+	0.999183i	$0.487132\pi$
$444$	1.60699e9	0.871310
$445$	−1.87096e9	−1.00648
$446$	5.28585e9	2.82126
$447$	1.86482e9	0.987551
$448$	3.65776e9	1.92195
$449$	2.18342e9	1.13835	0.569174	−	0.822217i	$-0.307263\pi$
$449$	2.18342e9	1.13835	0.569174	+	0.822217i	$0.307263\pi$
$450$	1.68575e8	0.0872066
$451$	−1.99776e9	−1.02548
$452$	−2.24362e9	−1.14278
$453$	2.68368e8	0.135640
$454$	7.31589e7	0.0366920
$455$	−1.56729e9	−0.780026
$456$	1.62236e9	0.801255
$457$	−9.95575e8	−0.487941	−0.243971	−	0.969783i	$-0.578450\pi$
$457$	−9.95575e8	−0.487941	−0.243971	+	0.969783i	$0.578450\pi$
$458$	−3.58408e9	−1.74320
$459$	−2.52939e8	−0.122087
$460$	−4.82672e8	−0.231206
$461$	−3.16168e9	−1.50302	−0.751509	−	0.659722i	$-0.770674\pi$
$461$	−3.16168e9	−1.50302	−0.751509	+	0.659722i	$0.770674\pi$
$462$	2.45904e9	1.16016
$463$	3.01390e9	1.41122	0.705612	−	0.708599i	$-0.250672\pi$
$463$	3.01390e9	1.41122	0.705612	+	0.708599i	$0.250672\pi$
$464$	7.84310e8	0.364481
$465$	1.87908e9	0.866681
$466$	1.76408e9	0.807547
$467$	8.11607e8	0.368754	0.184377	−	0.982856i	$-0.440973\pi$
$467$	8.11607e8	0.368754	0.184377	+	0.982856i	$0.440973\pi$
$468$	8.02444e8	0.361871
$469$	−3.79935e9	−1.70061
$470$	1.19354e9	0.530265
$471$	−4.68869e8	−0.206765
$472$	2.36761e8	0.103636
$473$	−1.92692e9	−0.837240
$474$	−2.09858e9	−0.905110
$475$	6.73361e8	0.288284
$476$	2.65255e9	1.12730
$477$	5.38663e8	0.227249
$478$	5.49112e9	2.29966
$479$	−2.44233e9	−1.01538	−0.507692	−	0.861538i	$-0.669501\pi$
$479$	−2.44233e9	−1.01538	−0.507692	+	0.861538i	$0.669501\pi$
$480$	1.51010e9	0.623249
$481$	1.76976e9	0.725113
$482$	−5.91360e9	−2.40540
$483$	2.84569e8	0.114914
$484$	5.78366e8	0.231870
$485$	3.74212e9	1.48944
$486$	−2.56843e8	−0.101494
$487$	−1.11140e8	−0.0436032	−0.0218016	−	0.999762i	$-0.506940\pi$
$487$	−1.11140e8	−0.0436032	−0.0218016	+	0.999762i	$0.506940\pi$
$488$	−2.69251e8	−0.104879
$489$	−2.33925e9	−0.904682
$490$	−1.49652e9	−0.574640
$491$	−1.10060e9	−0.419607	−0.209804	−	0.977744i	$-0.567282\pi$
$491$	−1.10060e9	−0.419607	−0.209804	+	0.977744i	$0.567282\pi$
$492$	−2.18823e9	−0.828353
$493$	2.52432e9	0.948812
$494$	5.33770e9	1.99209
$495$	8.82872e8	0.327175
$496$	−1.08819e9	−0.400422
$497$	−1.10539e9	−0.403896
$498$	1.99124e9	0.722472
$499$	1.19831e9	0.431735	0.215867	−	0.976423i	$-0.430742\pi$
$499$	1.19831e9	0.431735	0.215867	+	0.976423i	$0.430742\pi$
$500$	−4.47307e9	−1.60034
$501$	−7.03218e8	−0.249838
$502$	7.68617e9	2.71173
$503$	−4.77486e8	−0.167291	−0.0836456	−	0.996496i	$-0.526656\pi$
$503$	−4.77486e8	−0.167291	−0.0836456	+	0.996496i	$0.526656\pi$
$504$	9.01590e8	0.313691
$505$	7.79673e8	0.269397
$506$	8.34006e8	0.286182
$507$	−8.10489e8	−0.276197
$508$	−6.68750e9	−2.26329
$509$	−1.61594e9	−0.543140	−0.271570	−	0.962419i	$-0.587543\pi$
$509$	−1.61594e9	−0.543140	−0.271570	+	0.962419i	$0.587543\pi$
$510$	1.58592e9	0.529401
$511$	6.31633e9	2.09407
$512$	−1.46367e9	−0.481945
$513$	−1.02594e9	−0.335514
$514$	5.40509e9	1.75562
$515$	−3.81207e9	−1.22980
$516$	−2.11064e9	−0.676300
$517$	−1.23842e9	−0.394140
$518$	5.94038e9	1.87785
$519$	−7.73085e8	−0.242740
$520$	−1.68412e9	−0.525245
$521$	2.28015e9	0.706368	0.353184	−	0.935554i	$-0.385099\pi$
$521$	2.28015e9	0.706368	0.353184	+	0.935554i	$0.385099\pi$
$522$	2.56328e9	0.788768
$523$	−4.17653e8	−0.127661	−0.0638307	−	0.997961i	$-0.520332\pi$
$523$	−4.17653e8	−0.127661	−0.0638307	+	0.997961i	$0.520332\pi$
$524$	−2.04469e9	−0.620824
$525$	3.74205e8	0.112863
$526$	1.29407e9	0.387710
$527$	−3.50235e9	−1.04237
$528$	−5.11277e8	−0.151160
$529$	−3.30831e9	−0.971654
$530$	−3.37740e9	−0.985410
$531$	−1.49721e8	−0.0433963
$532$	1.07590e10	3.09799
$533$	−2.40987e9	−0.689364
$534$	3.54105e9	1.00632
$535$	−5.66928e9	−1.60062
$536$	−4.08257e9	−1.14514
$537$	2.44169e8	0.0680425
$538$	−2.61510e9	−0.724019
$539$	1.55280e9	0.427124
$540$	9.67047e8	0.264283
$541$	7.14439e9	1.93988	0.969940	−	0.243346i	$-0.0782450\pi$
$541$	7.14439e9	1.93988	0.969940	+	0.243346i	$0.0782450\pi$
$542$	5.14255e9	1.38734
$543$	2.44328e9	0.654898
$544$	−2.81463e9	−0.749592
$545$	−6.31502e8	−0.167104
$546$	2.96631e9	0.779905
$547$	−1.90559e9	−0.497822	−0.248911	−	0.968526i	$-0.580073\pi$
$547$	−1.90559e9	−0.497822	−0.248911	+	0.968526i	$0.580073\pi$
$548$	−8.93622e9	−2.31965
$549$	1.70267e8	0.0439166
$550$	1.09671e9	0.281075
$551$	1.02388e10	2.60748
$552$	3.05783e8	0.0773795
$553$	−4.65846e9	−1.17140
$554$	−5.63551e9	−1.40815
$555$	2.13278e9	0.529567
$556$	−3.37592e9	−0.832971
$557$	−8.13950e9	−1.99574	−0.997872	−	0.0652056i	$-0.979230\pi$
$557$	−8.13950e9	−1.99574	−0.997872	+	0.0652056i	$0.979230\pi$
$558$	−3.55641e9	−0.866547
$559$	−2.32442e9	−0.562824
$560$	1.09381e9	0.263198
$561$	−1.64556e9	−0.393499
$562$	−1.30353e10	−3.09772
$563$	3.38360e9	0.799098	0.399549	−	0.916712i	$-0.369167\pi$
$563$	3.38360e9	0.799098	0.399549	+	0.916712i	$0.369167\pi$
$564$	−1.35649e9	−0.318376
$565$	−2.97771e9	−0.694564
$566$	4.24883e9	0.984944
$567$	−5.70143e8	−0.131354
$568$	−1.18779e9	−0.271971
$569$	1.41168e9	0.321250	0.160625	−	0.987016i	$-0.448649\pi$
$569$	1.41168e9	0.321250	0.160625	+	0.987016i	$0.448649\pi$
$570$	6.43261e9	1.45487
$571$	3.06389e9	0.688726	0.344363	−	0.938837i	$-0.388095\pi$
$571$	3.06389e9	0.688726	0.344363	+	0.938837i	$0.388095\pi$
$572$	5.22051e9	1.16634
$573$	−2.03290e9	−0.451414
$574$	−8.08900e9	−1.78527
$575$	1.26915e8	0.0278404
$576$	−2.48550e9	−0.541921
$577$	5.11879e9	1.10931	0.554653	−	0.832082i	$-0.312851\pi$
$577$	5.11879e9	1.10931	0.554653	+	0.832082i	$0.312851\pi$
$578$	4.38904e9	0.945414
$579$	8.19154e8	0.175384
$580$	−9.65110e9	−2.05390
$581$	4.42018e9	0.935026
$582$	−7.08247e9	−1.48920
$583$	3.50441e9	0.732445
$584$	6.78718e9	1.41008
$585$	1.06500e9	0.219939
$586$	2.01982e8	0.0414639
$587$	5.18384e9	1.05784	0.528918	−	0.848673i	$-0.322598\pi$
$587$	5.18384e9	1.05784	0.528918	+	0.848673i	$0.322598\pi$
$588$	1.70084e9	0.345020
$589$	−1.42058e10	−2.86459
$590$	9.38748e8	0.188177
$591$	1.55344e9	0.309555
$592$	−1.23511e9	−0.244669
$593$	5.88946e9	1.15980	0.579902	−	0.814686i	$-0.303091\pi$
$593$	5.88946e9	1.15980	0.579902	+	0.814686i	$0.303091\pi$
$594$	−1.67096e9	−0.327124
$595$	3.52044e9	0.685153
$596$	1.32887e10	2.57112
$597$	8.92377e7	0.0171648
$598$	1.00605e9	0.192382
$599$	1.29167e9	0.245561	0.122780	−	0.992434i	$-0.460819\pi$
$599$	1.29167e9	0.245561	0.122780	+	0.992434i	$0.460819\pi$
$600$	4.02101e8	0.0759986
$601$	−4.79647e9	−0.901282	−0.450641	−	0.892705i	$-0.648805\pi$
$601$	−4.79647e9	−0.901282	−0.450641	+	0.892705i	$0.648805\pi$
$602$	−7.80216e9	−1.45756
$603$	2.58171e9	0.479510
$604$	1.91240e9	0.353142
$605$	7.67602e8	0.140926
$606$	−1.47564e9	−0.269355
$607$	−3.30008e9	−0.598914	−0.299457	−	0.954110i	$-0.596805\pi$
$607$	−3.30008e9	−0.598914	−0.299457	+	0.954110i	$0.596805\pi$
$608$	−1.14164e10	−2.05999
$609$	5.69000e9	1.02083
$610$	−1.06757e9	−0.190433
$611$	−1.49389e9	−0.264956
$612$	−1.80245e9	−0.317858
$613$	2.21730e9	0.388788	0.194394	−	0.980924i	$-0.437726\pi$
$613$	2.21730e9	0.388788	0.194394	+	0.980924i	$0.437726\pi$
$614$	−5.39824e9	−0.941159
$615$	−2.90420e9	−0.503459
$616$	5.86553e9	1.01105
$617$	−3.08716e9	−0.529128	−0.264564	−	0.964368i	$-0.585228\pi$
$617$	−3.08716e9	−0.529128	−0.264564	+	0.964368i	$0.585228\pi$
$618$	7.21486e9	1.22961
$619$	4.78027e9	0.810094	0.405047	−	0.914296i	$-0.367255\pi$
$619$	4.78027e9	0.810094	0.405047	+	0.914296i	$0.367255\pi$
$620$	1.33904e10	2.25643
$621$	−1.93369e8	−0.0324016
$622$	−1.42206e10	−2.36948
$623$	7.86047e9	1.30239
$624$	−6.16747e8	−0.101616
$625$	−4.92735e9	−0.807298
$626$	−1.68647e10	−2.74770
$627$	−6.67452e9	−1.08139
$628$	−3.34117e9	−0.538319
$629$	−3.97522e9	−0.636919
$630$	3.57478e9	0.569583
$631$	−4.87262e9	−0.772075	−0.386037	−	0.922483i	$-0.626156\pi$
$631$	−4.87262e9	−0.772075	−0.386037	+	0.922483i	$0.626156\pi$
$632$	−5.00573e9	−0.788782
$633$	2.01817e9	0.316260
$634$	1.69390e9	0.263982
$635$	−8.87559e9	−1.37559
$636$	3.83853e9	0.591650
$637$	1.87312e9	0.287129
$638$	1.66761e10	2.54227
$639$	7.51131e8	0.113884
$640$	8.42504e9	1.27040
$641$	2.85862e9	0.428700	0.214350	−	0.976757i	$-0.431237\pi$
$641$	2.85862e9	0.428700	0.214350	+	0.976757i	$0.431237\pi$
$642$	1.07299e10	1.60038
$643$	−7.22075e9	−1.07113	−0.535567	−	0.844493i	$-0.679902\pi$
$643$	−7.22075e9	−1.07113	−0.535567	+	0.844493i	$0.679902\pi$
$644$	2.02785e9	0.299182
$645$	−2.80122e9	−0.411044
$646$	−1.19895e10	−1.74980
$647$	−4.74606e8	−0.0688919	−0.0344460	−	0.999407i	$-0.510967\pi$
$647$	−4.74606e8	−0.0688919	−0.0344460	+	0.999407i	$0.510967\pi$
$648$	−6.12644e8	−0.0884496
$649$	−9.74051e8	−0.139870
$650$	1.32294e9	0.188949
$651$	−7.89457e9	−1.12149
$652$	−1.66696e10	−2.35536
$653$	−2.58487e9	−0.363281	−0.181640	−	0.983365i	$-0.558141\pi$
$653$	−2.58487e9	−0.363281	−0.181640	+	0.983365i	$0.558141\pi$
$654$	1.19520e9	0.167078
$655$	−2.71370e9	−0.377326
$656$	1.68184e9	0.232607
$657$	−4.29204e9	−0.590453
$658$	−5.01440e9	−0.686164
$659$	2.68455e9	0.365404	0.182702	−	0.983168i	$-0.441516\pi$
$659$	2.68455e9	0.365404	0.182702	+	0.983168i	$0.441516\pi$
$660$	6.29138e9	0.851808
$661$	−9.19497e9	−1.23835	−0.619177	−	0.785251i	$-0.712534\pi$
$661$	−9.19497e9	−1.23835	−0.619177	+	0.785251i	$0.712534\pi$
$662$	−4.59589e9	−0.615696
$663$	−1.98501e9	−0.264525
$664$	4.74969e9	0.629618
$665$	1.42792e10	1.88290
$666$	−4.03658e9	−0.529485
$667$	1.92982e9	0.251812
$668$	−5.01115e9	−0.650459
$669$	−7.97316e9	−1.02953
$670$	−1.61873e10	−2.07928
$671$	1.10772e9	0.141547
$672$	−6.34438e9	−0.806486
$673$	1.23253e10	1.55863	0.779317	−	0.626630i	$-0.215566\pi$
$673$	1.23253e10	1.55863	0.779317	+	0.626630i	$0.215566\pi$
$674$	−1.71975e9	−0.216349
$675$	−2.54278e8	−0.0318233
$676$	−5.77557e9	−0.719087
$677$	1.51222e10	1.87307	0.936537	−	0.350569i	$-0.114012\pi$
$677$	1.51222e10	1.87307	0.936537	+	0.350569i	$0.114012\pi$
$678$	5.63571e9	0.694456
$679$	−1.57218e10	−1.92733
$680$	3.78288e9	0.461361
$681$	−1.10353e8	−0.0133896
$682$	−2.31371e10	−2.79296
$683$	−2.68739e9	−0.322745	−0.161372	−	0.986894i	$-0.551592\pi$
$683$	−2.68739e9	−0.322745	−0.161372	+	0.986894i	$0.551592\pi$
$684$	−7.31088e9	−0.873521
$685$	−1.18601e10	−1.40984
$686$	−9.52744e9	−1.12679
$687$	5.40621e9	0.636127
$688$	1.62220e9	0.189909
$689$	4.22732e9	0.492377
$690$	1.21242e9	0.140501
$691$	−9.07091e9	−1.04587	−0.522935	−	0.852373i	$-0.675163\pi$
$691$	−9.07091e9	−1.04587	−0.522935	+	0.852373i	$0.675163\pi$
$692$	−5.50903e9	−0.631980
$693$	−3.70921e9	−0.423365
$694$	−7.46647e9	−0.847924
$695$	−4.48048e9	−0.506265
$696$	6.11417e9	0.687393
$697$	5.41305e9	0.605518
$698$	1.07111e10	1.19218
$699$	−2.66094e9	−0.294689
$700$	2.66660e9	0.293842
$701$	2.72996e9	0.299326	0.149663	−	0.988737i	$-0.452181\pi$
$701$	2.72996e9	0.299326	0.149663	+	0.988737i	$0.452181\pi$
$702$	−2.01565e9	−0.219905
$703$	−1.61238e10	−1.75035
$704$	−1.61701e10	−1.74666
$705$	−1.80032e9	−0.193504
$706$	2.17731e10	2.32865
$707$	−3.27564e9	−0.348601
$708$	−1.06692e9	−0.112983
$709$	−9.03726e8	−0.0952302	−0.0476151	−	0.998866i	$-0.515162\pi$
$709$	−9.03726e8	−0.0952302	−0.0476151	+	0.998866i	$0.515162\pi$
$710$	−4.70957e9	−0.493829
$711$	3.16549e9	0.330292
$712$	8.44644e9	0.876988
$713$	−2.67752e9	−0.276642
$714$	−6.66292e9	−0.685047
$715$	6.92861e9	0.708883
$716$	1.73996e9	0.177151
$717$	−8.28278e9	−0.839188
$718$	2.62996e9	0.265164
$719$	−6.51161e9	−0.653337	−0.326668	−	0.945139i	$-0.605926\pi$
$719$	−6.51161e9	−0.653337	−0.326668	+	0.945139i	$0.605926\pi$
$720$	−7.43258e8	−0.0742123
$721$	1.60156e10	1.59137
$722$	−3.26304e10	−3.22658
$723$	8.92006e9	0.877776
$724$	1.74109e10	1.70505
$725$	2.53769e9	0.247318
$726$	−1.45279e9	−0.140905
$727$	−6.14813e9	−0.593435	−0.296717	−	0.954965i	$-0.595892\pi$
$727$	−6.14813e9	−0.593435	−0.296717	+	0.954965i	$0.595892\pi$
$728$	7.07550e9	0.679669
$729$	3.87420e8	0.0370370
$730$	2.69110e10	2.56035
$731$	5.22110e9	0.494369
$732$	1.21333e9	0.114338
$733$	2.71313e9	0.254452	0.127226	−	0.991874i	$-0.459393\pi$
$733$	2.71313e9	0.254452	0.127226	+	0.991874i	$0.459393\pi$
$734$	2.76120e10	2.57728
$735$	2.25735e9	0.209697
$736$	−2.15176e9	−0.198939
$737$	1.67960e10	1.54550
$738$	5.49660e9	0.503381
$739$	1.10553e10	1.00766	0.503831	−	0.863802i	$-0.331924\pi$
$739$	1.10553e10	1.00766	0.503831	+	0.863802i	$0.331924\pi$
$740$	1.51983e10	1.37874
$741$	−8.05137e9	−0.726953
$742$	1.41895e10	1.27512
$743$	1.67697e10	1.49991	0.749954	−	0.661490i	$-0.230075\pi$
$743$	1.67697e10	1.49991	0.749954	+	0.661490i	$0.230075\pi$
$744$	−8.48307e9	−0.755176
$745$	1.76367e10	1.56268
$746$	−5.52017e9	−0.486818
$747$	−3.00358e9	−0.263644
$748$	−1.17263e10	−1.02448
$749$	2.38183e10	2.07121
$750$	1.12359e10	0.972506
$751$	7.82494e9	0.674126	0.337063	−	0.941482i	$-0.390566\pi$
$751$	7.82494e9	0.674126	0.337063	+	0.941482i	$0.390566\pi$
$752$	1.04258e9	0.0894020
$753$	−1.15938e10	−0.989563
$754$	2.01161e10	1.70901
$755$	2.53812e9	0.214634
$756$	−4.06285e9	−0.341983
$757$	1.40665e10	1.17856	0.589279	−	0.807930i	$-0.299412\pi$
$757$	1.40665e10	1.17856	0.589279	+	0.807930i	$0.299412\pi$
$758$	1.52115e10	1.26861
$759$	−1.25801e9	−0.104433
$760$	1.53437e10	1.26789
$761$	−4.85071e9	−0.398987	−0.199493	−	0.979899i	$-0.563930\pi$
$761$	−4.85071e9	−0.398987	−0.199493	+	0.979899i	$0.563930\pi$
$762$	1.67983e10	1.37538
$763$	2.65313e9	0.216233
$764$	−1.44865e10	−1.17527
$765$	−2.39219e9	−0.193189
$766$	−1.58147e10	−1.27133
$767$	−1.17498e9	−0.0940260
$768$	−4.16240e9	−0.331574
$769$	9.60096e9	0.761329	0.380665	−	0.924713i	$-0.375695\pi$
$769$	9.60096e9	0.761329	0.380665	+	0.924713i	$0.375695\pi$
$770$	2.32566e10	1.83582
$771$	−8.15301e9	−0.640660
$772$	5.83731e9	0.456617
$773$	−2.04008e10	−1.58862	−0.794309	−	0.607514i	$-0.792167\pi$
$773$	−2.04008e10	−1.58862	−0.794309	+	0.607514i	$0.792167\pi$
$774$	5.30169e9	0.410980
$775$	−3.52090e9	−0.271705
$776$	−1.68938e10	−1.29781
$777$	−8.96045e9	−0.685262
$778$	1.92978e10	1.46919
$779$	2.19558e10	1.66405
$780$	7.58920e9	0.572618
$781$	4.88668e9	0.367058
$782$	−2.25979e9	−0.168983
$783$	−3.86644e9	−0.287836
$784$	−1.30724e9	−0.0968836
$785$	−4.43437e9	−0.327181
$786$	5.13604e9	0.377268
$787$	1.60432e10	1.17322	0.586608	−	0.809871i	$-0.300463\pi$
$787$	1.60432e10	1.17322	0.586608	+	0.809871i	$0.300463\pi$
$788$	1.10699e10	0.805935
$789$	−1.95197e9	−0.141483
$790$	−1.98475e10	−1.43223
$791$	1.25102e10	0.898768
$792$	−3.98572e9	−0.285081
$793$	1.33623e9	0.0951532
$794$	4.03071e10	2.85765
$795$	5.09446e9	0.359595
$796$	6.35911e8	0.0446890
$797$	−1.85146e10	−1.29542	−0.647711	−	0.761886i	$-0.724273\pi$
$797$	−1.85146e10	−1.29542	−0.647711	+	0.761886i	$0.724273\pi$
$798$	−2.70253e10	−1.88261
$799$	3.35557e9	0.232730
$800$	−2.82953e9	−0.195389
$801$	−5.34131e9	−0.367226
$802$	−4.67458e9	−0.319987
$803$	−2.79230e10	−1.90308
$804$	1.83974e10	1.24842
$805$	2.69134e9	0.181838
$806$	−2.79100e10	−1.87753
$807$	3.94460e9	0.264208
$808$	−3.51983e9	−0.234737
$809$	1.01950e9	0.0676968	0.0338484	−	0.999427i	$-0.489224\pi$
$809$	1.01950e9	0.0676968	0.0338484	+	0.999427i	$0.489224\pi$
$810$	−2.42912e9	−0.160602
$811$	2.10382e10	1.38496	0.692478	−	0.721439i	$-0.256519\pi$
$811$	2.10382e10	1.38496	0.692478	+	0.721439i	$0.256519\pi$
$812$	4.05472e10	2.65775
$813$	−7.75701e9	−0.506265
$814$	−2.62610e10	−1.70658
$815$	−2.21237e10	−1.43155
$816$	1.38534e9	0.0892564
$817$	2.11772e10	1.35860
$818$	−5.38818e9	−0.344196
$819$	−4.47437e9	−0.284602
$820$	−2.06954e10	−1.31077
$821$	4.64433e9	0.292902	0.146451	−	0.989218i	$-0.453215\pi$
$821$	4.64433e9	0.292902	0.146451	+	0.989218i	$0.453215\pi$
$822$	2.24468e10	1.40962
$823$	−5.01145e9	−0.313375	−0.156687	−	0.987648i	$-0.550081\pi$
$823$	−5.01145e9	−0.313375	−0.156687	+	0.987648i	$0.550081\pi$
$824$	1.72095e10	1.07158
$825$	−1.65427e9	−0.102569
$826$	−3.94396e9	−0.243502
$827$	−2.72122e10	−1.67300	−0.836498	−	0.547970i	$-0.815401\pi$
$827$	−2.72122e10	−1.67300	−0.836498	+	0.547970i	$0.815401\pi$
$828$	−1.37795e9	−0.0843585
$829$	3.17275e10	1.93417	0.967086	−	0.254450i	$-0.0818943\pi$
$829$	3.17275e10	1.93417	0.967086	+	0.254450i	$0.0818943\pi$
$830$	1.88324e10	1.14322
$831$	8.50059e9	0.513861
$832$	−1.95057e10	−1.17417
$833$	−4.20739e9	−0.252206
$834$	8.47993e9	0.506187
$835$	−6.65076e9	−0.395338
$836$	−4.75628e10	−2.81544
$837$	5.36448e9	0.316219
$838$	4.31189e10	2.53112
$839$	−3.12839e9	−0.182875	−0.0914374	−	0.995811i	$-0.529146\pi$
$839$	−3.12839e9	−0.182875	−0.0914374	+	0.995811i	$0.529146\pi$
$840$	8.52689e9	0.496378
$841$	2.13371e10	1.23694
$842$	−2.27385e10	−1.31271
$843$	1.96624e10	1.13042
$844$	1.43815e10	0.823393
$845$	−7.66529e9	−0.437049
$846$	3.40736e9	0.193474
$847$	−3.22492e9	−0.182359
$848$	−2.95024e9	−0.166139
$849$	−6.40892e9	−0.359424
$850$	−2.97160e9	−0.165968
$851$	−3.03902e9	−0.169036
$852$	5.35258e9	0.296500
$853$	−3.10920e10	−1.71525	−0.857623	−	0.514278i	$-0.828060\pi$
$853$	−3.10920e10	−1.71525	−0.857623	+	0.514278i	$0.828060\pi$
$854$	4.48519e9	0.246421
$855$	−9.70293e9	−0.530911
$856$	2.55939e10	1.39469
$857$	−6.63199e9	−0.359924	−0.179962	−	0.983674i	$-0.557597\pi$
$857$	−6.63199e9	−0.359924	−0.179962	+	0.983674i	$0.557597\pi$
$858$	−1.31133e10	−0.708774
$859$	2.04251e9	0.109948	0.0549741	−	0.998488i	$-0.482492\pi$
$859$	2.04251e9	0.109948	0.0549741	+	0.998488i	$0.482492\pi$
$860$	−1.99616e10	−1.07016
$861$	1.22014e10	0.651477
$862$	−4.02672e10	−2.14129
$863$	6.09687e8	0.0322901	0.0161450	−	0.999870i	$-0.494861\pi$
$863$	6.09687e8	0.0322901	0.0161450	+	0.999870i	$0.494861\pi$
$864$	4.31110e9	0.227400
$865$	−7.31153e9	−0.384107
$866$	−2.11986e10	−1.10916
$867$	−6.62041e9	−0.344999
$868$	−5.62569e10	−2.91983
$869$	2.05939e10	1.06456
$870$	2.42425e10	1.24813
$871$	2.02608e10	1.03895
$872$	2.85091e9	0.145605
$873$	1.06832e10	0.543439
$874$	−9.16589e9	−0.464392
$875$	2.49415e10	1.25862
$876$	−3.05852e10	−1.53726
$877$	−1.17372e10	−0.587580	−0.293790	−	0.955870i	$-0.594917\pi$
$877$	−1.17372e10	−0.587580	−0.293790	+	0.955870i	$0.594917\pi$
$878$	−2.39189e10	−1.19264
$879$	−3.04668e8	−0.0151310
$880$	−4.83546e9	−0.239193
$881$	3.53359e10	1.74101	0.870504	−	0.492162i	$-0.163793\pi$
$881$	3.53359e10	1.74101	0.870504	+	0.492162i	$0.163793\pi$
$882$	−4.27233e9	−0.209665
$883$	2.20915e10	1.07985	0.539924	−	0.841714i	$-0.318453\pi$
$883$	2.20915e10	1.07985	0.539924	+	0.841714i	$0.318453\pi$
$884$	−1.41453e10	−0.688697
$885$	−1.41600e9	−0.0686694
$886$	−2.64748e9	−0.127884
$887$	−2.64826e10	−1.27417	−0.637085	−	0.770793i	$-0.719860\pi$
$887$	−2.64826e10	−1.27417	−0.637085	+	0.770793i	$0.719860\pi$
$888$	−9.62842e9	−0.461434
$889$	3.72890e10	1.78002
$890$	3.34899e10	1.59239
$891$	2.52046e9	0.119374
$892$	−5.68170e10	−2.68041
$893$	1.36105e10	0.639577
$894$	−3.33798e10	−1.56244
$895$	2.30925e9	0.107669
$896$	−3.53961e10	−1.64391
$897$	−1.51752e9	−0.0702040
$898$	−3.90828e10	−1.80102
$899$	−5.35373e10	−2.45752
$900$	−1.81199e9	−0.0828529
$901$	−9.49541e9	−0.432491
$902$	3.57595e10	1.62244
$903$	1.17688e10	0.531892
$904$	1.34428e10	0.605202
$905$	2.31076e10	1.03630
$906$	−4.80374e9	−0.214600
$907$	−1.70454e10	−0.758547	−0.379274	−	0.925285i	$-0.623826\pi$
$907$	−1.70454e10	−0.758547	−0.379274	+	0.925285i	$0.623826\pi$
$908$	−7.86377e8	−0.0348602
$909$	2.22585e9	0.0982928
$910$	2.80542e10	1.23411
$911$	−3.21064e10	−1.40695	−0.703473	−	0.710722i	$-0.748368\pi$
$911$	−3.21064e10	−1.40695	−0.703473	+	0.710722i	$0.748368\pi$
$912$	5.61903e9	0.245290
$913$	−1.95406e10	−0.849747
$914$	1.78206e10	0.771988
$915$	1.61032e9	0.0694927
$916$	3.85248e10	1.65618
$917$	1.14011e10	0.488261
$918$	4.52755e9	0.193159
$919$	9.83116e8	0.0417831	0.0208915	−	0.999782i	$-0.493350\pi$
$919$	9.83116e8	0.0417831	0.0208915	+	0.999782i	$0.493350\pi$
$920$	2.89197e9	0.122444
$921$	8.14269e9	0.343447
$922$	5.65934e10	2.37798
$923$	5.89473e9	0.246750
$924$	−2.64319e10	−1.10224
$925$	−3.99628e9	−0.166020
$926$	−5.39483e10	−2.23274
$927$	−1.08829e10	−0.448709
$928$	−4.30247e10	−1.76726
$929$	1.58139e10	0.647119	0.323559	−	0.946208i	$-0.395120\pi$
$929$	1.58139e10	0.647119	0.323559	+	0.946208i	$0.395120\pi$
$930$	−3.36351e10	−1.37121
$931$	−1.70655e10	−0.693100
$932$	−1.89619e10	−0.767231
$933$	2.14504e10	0.864668
$934$	−1.45276e10	−0.583418
$935$	−1.55630e10	−0.622664
$936$	−4.80791e9	−0.191642
$937$	1.93290e10	0.767576	0.383788	−	0.923421i	$-0.374619\pi$
$937$	1.93290e10	0.767576	0.383788	+	0.923421i	$0.374619\pi$
$938$	6.80076e10	2.69059
$939$	2.54387e10	1.00269
$940$	−1.28292e10	−0.503792
$941$	−1.84380e9	−0.0721356	−0.0360678	−	0.999349i	$-0.511483\pi$
$941$	−1.84380e9	−0.0721356	−0.0360678	+	0.999349i	$0.511483\pi$
$942$	8.39265e9	0.327131
$943$	4.13822e9	0.160703
$944$	8.20018e8	0.0317264
$945$	−5.39218e9	−0.207852
$946$	3.44915e10	1.32463
$947$	−3.45923e10	−1.32359	−0.661797	−	0.749683i	$-0.730206\pi$
$947$	−3.45923e10	−1.32359	−0.661797	+	0.749683i	$0.730206\pi$
$948$	2.25574e10	0.859923
$949$	−3.36831e10	−1.27932
$950$	−1.20530e10	−0.456104
$951$	−2.55507e9	−0.0963321
$952$	−1.58930e10	−0.597003
$953$	−2.99406e10	−1.12056	−0.560281	−	0.828303i	$-0.689307\pi$
$953$	−2.99406e10	−1.12056	−0.560281	+	0.828303i	$0.689307\pi$
$954$	−9.64196e9	−0.359539
$955$	−1.92264e10	−0.714309
$956$	−5.90234e10	−2.18485
$957$	−2.51542e10	−0.927722
$958$	4.37173e10	1.60647
$959$	4.98277e10	1.82434
$960$	−2.35069e10	−0.857524
$961$	4.67675e10	1.69986
$962$	−3.16783e10	−1.14723
$963$	−1.61849e10	−0.584007
$964$	6.35646e10	2.28531
$965$	7.74723e9	0.277524
$966$	−5.09373e9	−0.181809
$967$	3.35194e9	0.119207	0.0596037	−	0.998222i	$-0.481016\pi$
$967$	3.35194e9	0.119207	0.0596037	+	0.998222i	$0.481016\pi$
$968$	−3.46533e9	−0.122795
$969$	1.80850e10	0.638535
$970$	−6.69832e10	−2.35649
$971$	3.76669e10	1.32036	0.660180	−	0.751107i	$-0.270480\pi$
$971$	3.76669e10	1.32036	0.660180	+	0.751107i	$0.270480\pi$
$972$	2.76077e9	0.0964269
$973$	1.88239e10	0.655109
$974$	1.98938e9	0.0689861
$975$	−1.99552e9	−0.0689510
$976$	−9.32548e8	−0.0321068
$977$	2.34371e10	0.804030	0.402015	−	0.915633i	$-0.368310\pi$
$977$	2.34371e10	0.804030	0.402015	+	0.915633i	$0.368310\pi$
$978$	4.18721e10	1.43133
$979$	−3.47493e10	−1.18360
$980$	1.60859e10	0.545952
$981$	−1.80284e9	−0.0609699
$982$	1.97005e10	0.663875
$983$	3.82382e10	1.28399	0.641993	−	0.766710i	$-0.278108\pi$
$983$	3.82382e10	1.28399	0.641993	+	0.766710i	$0.278108\pi$
$984$	1.31110e10	0.438685
$985$	1.46918e10	0.489833
$986$	−4.51848e10	−1.50115
$987$	7.56370e9	0.250394
$988$	−5.73743e10	−1.89264
$989$	3.99148e9	0.131204
$990$	−1.58032e10	−0.517634
$991$	5.46278e10	1.78302	0.891510	−	0.453001i	$-0.149647\pi$
$991$	5.46278e10	1.78302	0.891510	+	0.453001i	$0.149647\pi$
$992$	5.96944e10	1.94152
$993$	6.93243e9	0.224679
$994$	1.97863e10	0.639017
$995$	8.43975e8	0.0271612
$996$	−2.14036e10	−0.686403
$997$	−2.14509e10	−0.685507	−0.342753	−	0.939425i	$-0.611360\pi$
$997$	−2.14509e10	−0.685507	−0.342753	+	0.939425i	$0.611360\pi$
$998$	−2.14495e10	−0.683062
$999$	6.08876e9	0.193219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.4	✓	17
3.2	odd	2		531.8.a.d.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.4	✓	17	1.1	even	1	trivial
531.8.a.d.1.14		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)

\(f(q)\)	\(=\)	\(q-17.8998 q^{2} +27.0000 q^{3} +192.403 q^{4} +255.355 q^{5} -483.295 q^{6} -1072.82 q^{7} -1152.80 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-17.8998 q^{2} +27.0000 q^{3} +192.403 q^{4} +255.355 q^{5} -483.295 q^{6} -1072.82 q^{7} -1152.80 q^{8} +729.000 q^{9} -4570.81 q^{10} +4742.70 q^{11} +5194.88 q^{12} +5721.05 q^{13} +19203.3 q^{14} +6894.59 q^{15} -3992.71 q^{16} -12850.6 q^{17} -13049.0 q^{18} -52123.1 q^{19} +49131.1 q^{20} -28966.2 q^{21} -84893.4 q^{22} -9824.17 q^{23} -31125.6 q^{24} -12918.7 q^{25} -102406. q^{26} +19683.0 q^{27} -206414. q^{28} -196436. q^{29} -123412. q^{30} +272544. q^{31} +219027. q^{32} +128053. q^{33} +230023. q^{34} -273951. q^{35} +140262. q^{36} +309341. q^{37} +932994. q^{38} +154468. q^{39} -294373. q^{40} -421229. q^{41} +518490. q^{42} -406292. q^{43} +912509. q^{44} +186154. q^{45} +175851. q^{46} -261121. q^{47} -107803. q^{48} +327408. q^{49} +231242. q^{50} -346967. q^{51} +1.10075e6 q^{52} +738907. q^{53} -352322. q^{54} +1.21107e6 q^{55} +1.23675e6 q^{56} -1.40732e6 q^{57} +3.51616e6 q^{58} -205379. q^{59} +1.32654e6 q^{60} +233563. q^{61} -4.87848e6 q^{62} -782089. q^{63} -3.40947e6 q^{64} +1.46090e6 q^{65} -2.29212e6 q^{66} +3.54145e6 q^{67} -2.47250e6 q^{68} -265253. q^{69} +4.90367e6 q^{70} +1.03036e6 q^{71} -840390. q^{72} -5.88757e6 q^{73} -5.53715e6 q^{74} -348804. q^{75} -1.00286e7 q^{76} -5.08808e6 q^{77} -2.76495e6 q^{78} +4.34224e6 q^{79} -1.01956e6 q^{80} +531441. q^{81} +7.53991e6 q^{82} -4.12014e6 q^{83} -5.57319e6 q^{84} -3.28147e6 q^{85} +7.27255e6 q^{86} -5.30376e6 q^{87} -5.46737e6 q^{88} -7.32690e6 q^{89} -3.33212e6 q^{90} -6.13768e6 q^{91} -1.89020e6 q^{92} +7.35868e6 q^{93} +4.67402e6 q^{94} -1.33099e7 q^{95} +5.91372e6 q^{96} +1.46546e7 q^{97} -5.86054e6 q^{98} +3.45743e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 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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