LMFDB - Embedded newform 177.8.a.b.1.11

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			1.11
Root			$4.11298$ 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)

$f(q)$	$=$	$q+2.11298 q^{2} +27.0000 q^{3} -123.535 q^{4} -537.118 q^{5} +57.0506 q^{6} +1259.15 q^{7} -531.490 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+2.11298 q^{2} +27.0000 q^{3} -123.535 q^{4} -537.118 q^{5} +57.0506 q^{6} +1259.15 q^{7} -531.490 q^{8} +729.000 q^{9} -1134.92 q^{10} +7730.24 q^{11} -3335.45 q^{12} -8860.73 q^{13} +2660.56 q^{14} -14502.2 q^{15} +14689.5 q^{16} +22368.4 q^{17} +1540.37 q^{18} -24886.1 q^{19} +66353.0 q^{20} +33997.0 q^{21} +16333.9 q^{22} -26686.2 q^{23} -14350.2 q^{24} +210371. q^{25} -18722.6 q^{26} +19683.0 q^{27} -155549. q^{28} +10101.0 q^{29} -30642.9 q^{30} -265180. q^{31} +99069.4 q^{32} +208717. q^{33} +47264.0 q^{34} -676311. q^{35} -90057.2 q^{36} +122638. q^{37} -52583.9 q^{38} -239240. q^{39} +285473. q^{40} -741866. q^{41} +71835.1 q^{42} -166554. q^{43} -954958. q^{44} -391559. q^{45} -56387.4 q^{46} -545699. q^{47} +396616. q^{48} +761910. q^{49} +444510. q^{50} +603946. q^{51} +1.09461e6 q^{52} -1.54083e6 q^{53} +41589.9 q^{54} -4.15205e6 q^{55} -669225. q^{56} -671924. q^{57} +21343.2 q^{58} -205379. q^{59} +1.79153e6 q^{60} +2.74259e6 q^{61} -560320. q^{62} +917919. q^{63} -1.67092e6 q^{64} +4.75926e6 q^{65} +441015. q^{66} -41604.4 q^{67} -2.76328e6 q^{68} -720526. q^{69} -1.42903e6 q^{70} -1.57840e6 q^{71} -387456. q^{72} +5.59479e6 q^{73} +259132. q^{74} +5.68001e6 q^{75} +3.07431e6 q^{76} +9.73352e6 q^{77} -505510. q^{78} -3.74825e6 q^{79} -7.88999e6 q^{80} +531441. q^{81} -1.56755e6 q^{82} -3.37715e6 q^{83} -4.19983e6 q^{84} -1.20144e7 q^{85} -351926. q^{86} +272726. q^{87} -4.10855e6 q^{88} -5.43486e6 q^{89} -827358. q^{90} -1.11570e7 q^{91} +3.29668e6 q^{92} -7.15985e6 q^{93} -1.15305e6 q^{94} +1.33668e7 q^{95} +2.67487e6 q^{96} -1.14400e7 q^{97} +1.60990e6 q^{98} +5.63535e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.11298	0.186763	0.0933816	−	0.995630i	$-0.470232\pi$
$2$	2.11298	0.186763	0.0933816	+	0.995630i	$0.470232\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−123.535	−0.965120
$5$	−537.118	−1.92165	−0.960826	−	0.277153i	$-0.910609\pi$
$5$	−537.118	−1.92165	−0.960826	+	0.277153i	$0.910609\pi$
$6$	57.0506	0.107828
$7$	1259.15	1.38750	0.693751	−	0.720215i	$-0.255957\pi$
$7$	1259.15	1.38750	0.693751	+	0.720215i	$0.255957\pi$
$8$	−531.490	−0.367012
$9$	729.000	0.333333
$10$	−1134.92	−0.358894
$11$	7730.24	1.75113	0.875566	−	0.483099i	$-0.160489\pi$
$11$	7730.24	1.75113	0.875566	+	0.483099i	$0.160489\pi$
$12$	−3335.45	−0.557212
$13$	−8860.73	−1.11858	−0.559291	−	0.828971i	$-0.688927\pi$
$13$	−8860.73	−1.11858	−0.559291	+	0.828971i	$0.688927\pi$
$14$	2660.56	0.259134
$15$	−14502.2	−1.10947
$16$	14689.5	0.896575
$17$	22368.4	1.10424	0.552119	−	0.833765i	$-0.313819\pi$
$17$	22368.4	1.10424	0.552119	+	0.833765i	$0.313819\pi$
$18$	1540.37	0.0622544
$19$	−24886.1	−0.832375	−0.416187	−	0.909279i	$-0.636634\pi$
$19$	−24886.1	−0.832375	−0.416187	+	0.909279i	$0.636634\pi$
$20$	66353.0	1.85462
$21$	33997.0	0.801075
$22$	16333.9	0.327047
$23$	−26686.2	−0.457339	−0.228670	−	0.973504i	$-0.573438\pi$
$23$	−26686.2	−0.457339	−0.228670	+	0.973504i	$0.573438\pi$
$24$	−14350.2	−0.211894
$25$	210371.	2.69275
$26$	−18722.6	−0.208910
$27$	19683.0	0.192450
$28$	−155549.	−1.33911
$29$	10101.0	0.0769077	0.0384539	−	0.999260i	$-0.487757\pi$
$29$	10101.0	0.0769077	0.0384539	+	0.999260i	$0.487757\pi$
$30$	−30642.9	−0.207207
$31$	−265180.	−1.59873	−0.799363	−	0.600848i	$-0.794830\pi$
$31$	−265180.	−1.59873	−0.799363	+	0.600848i	$0.794830\pi$
$32$	99069.4	0.534459
$33$	208717.	1.01102
$34$	47264.0	0.206231
$35$	−676311.	−2.66630
$36$	−90057.2	−0.321707
$37$	122638.	0.398032	0.199016	−	0.979996i	$-0.436225\pi$
$37$	122638.	0.398032	0.199016	+	0.979996i	$0.436225\pi$
$38$	−52583.9	−0.155457
$39$	−239240.	−0.645813
$40$	285473.	0.705269
$41$	−741866.	−1.68105	−0.840527	−	0.541769i	$-0.817755\pi$
$41$	−741866.	−1.68105	−0.840527	+	0.541769i	$0.817755\pi$
$42$	71835.1	0.149611
$43$	−166554.	−0.319459	−0.159730	−	0.987161i	$-0.551062\pi$
$43$	−166554.	−0.319459	−0.159730	+	0.987161i	$0.551062\pi$
$44$	−954958.	−1.69005
$45$	−391559.	−0.640551
$46$	−56387.4	−0.0854142
$47$	−545699.	−0.766674	−0.383337	−	0.923608i	$-0.625225\pi$
$47$	−545699.	−0.766674	−0.383337	+	0.923608i	$0.625225\pi$
$48$	396616.	0.517638
$49$	761910.	0.925161
$50$	444510.	0.502906
$51$	603946.	0.637532
$52$	1.09461e6	1.07957
$53$	−1.54083e6	−1.42164	−0.710819	−	0.703375i	$-0.751676\pi$
$53$	−1.54083e6	−1.42164	−0.710819	+	0.703375i	$0.751676\pi$
$54$	41589.9	0.0359426
$55$	−4.15205e6	−3.36506
$56$	−669225.	−0.509230
$57$	−671924.	−0.480572
$58$	21343.2	0.0143635
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	1.79153e6	1.07077
$61$	2.74259e6	1.54706	0.773529	−	0.633761i	$-0.218490\pi$
$61$	2.74259e6	1.54706	0.773529	+	0.633761i	$0.218490\pi$
$62$	−560320.	−0.298583
$63$	917919.	0.462501
$64$	−1.67092e6	−0.796758
$65$	4.75926e6	2.14952
$66$	441015.	0.188821
$67$	−41604.4	−0.0168996	−0.00844981	−	0.999964i	$-0.502690\pi$
$67$	−41604.4	−0.0168996	−0.00844981	+	0.999964i	$0.502690\pi$
$68$	−2.76328e6	−1.06572
$69$	−720526.	−0.264045
$70$	−1.42903e6	−0.497966
$71$	−1.57840e6	−0.523376	−0.261688	−	0.965152i	$-0.584279\pi$
$71$	−1.57840e6	−0.523376	−0.261688	+	0.965152i	$0.584279\pi$
$72$	−387456.	−0.122337
$73$	5.59479e6	1.68327	0.841635	−	0.540047i	$-0.181594\pi$
$73$	5.59479e6	1.68327	0.841635	+	0.540047i	$0.181594\pi$
$74$	259132.	0.0743378
$75$	5.68001e6	1.55466
$76$	3.07431e6	0.803341
$77$	9.73352e6	2.42970
$78$	−505510.	−0.120614
$79$	−3.74825e6	−0.855330	−0.427665	−	0.903937i	$-0.640664\pi$
$79$	−3.74825e6	−0.855330	−0.427665	+	0.903937i	$0.640664\pi$
$80$	−7.88999e6	−1.72291
$81$	531441.	0.111111
$82$	−1.56755e6	−0.313959
$83$	−3.37715e6	−0.648302	−0.324151	−	0.946005i	$-0.605079\pi$
$83$	−3.37715e6	−0.648302	−0.324151	+	0.946005i	$0.605079\pi$
$84$	−4.19983e6	−0.773133
$85$	−1.20144e7	−2.12196
$86$	−351926.	−0.0596632
$87$	272726.	0.0444027
$88$	−4.10855e6	−0.642686
$89$	−5.43486e6	−0.817191	−0.408595	−	0.912716i	$-0.633981\pi$
$89$	−5.43486e6	−0.817191	−0.408595	+	0.912716i	$0.633981\pi$
$90$	−827358.	−0.119631
$91$	−1.11570e7	−1.55203
$92$	3.29668e6	0.441387
$93$	−7.15985e6	−0.923025
$94$	−1.15305e6	−0.143187
$95$	1.33668e7	1.59953
$96$	2.67487e6	0.308570
$97$	−1.14400e7	−1.27270	−0.636349	−	0.771401i	$-0.719556\pi$
$97$	−1.14400e7	−1.27270	−0.636349	+	0.771401i	$0.719556\pi$
$98$	1.60990e6	0.172786
$99$	5.63535e6	0.583710
$100$	−2.59882e7	−2.59882
$101$	−1.39505e7	−1.34730	−0.673652	−	0.739049i	$-0.735275\pi$
$101$	−1.39505e7	−1.34730	−0.673652	+	0.739049i	$0.735275\pi$
$102$	1.27613e6	0.119068
$103$	−9.43458e6	−0.850731	−0.425366	−	0.905022i	$-0.639855\pi$
$103$	−9.43458e6	−0.850731	−0.425366	+	0.905022i	$0.639855\pi$
$104$	4.70939e6	0.410533
$105$	−1.82604e7	−1.53939
$106$	−3.25575e6	−0.265510
$107$	1.19603e7	0.943844	0.471922	−	0.881640i	$-0.343560\pi$
$107$	1.19603e7	0.943844	0.471922	+	0.881640i	$0.343560\pi$
$108$	−2.43155e6	−0.185737
$109$	2.39265e6	0.176964	0.0884822	−	0.996078i	$-0.471798\pi$
$109$	2.39265e6	0.176964	0.0884822	+	0.996078i	$0.471798\pi$
$110$	−8.77322e6	−0.628470
$111$	3.31122e6	0.229804
$112$	1.84962e7	1.24400
$113$	−4.09793e6	−0.267171	−0.133586	−	0.991037i	$-0.542649\pi$
$113$	−4.09793e6	−0.267171	−0.133586	+	0.991037i	$0.542649\pi$
$114$	−1.41976e6	−0.0897531
$115$	1.43336e7	0.878847
$116$	−1.24783e6	−0.0742251
$117$	−6.45947e6	−0.372861
$118$	−433963.	−0.0243145
$119$	2.81651e7	1.53213
$120$	7.70777e6	0.407187
$121$	4.02695e7	2.06646
$122$	5.79505e6	0.288933
$123$	−2.00304e7	−0.970557
$124$	3.27590e7	1.54296
$125$	−7.10316e7	−3.25287
$126$	1.93955e6	0.0863781
$127$	1.95190e7	0.845560	0.422780	−	0.906232i	$-0.361054\pi$
$127$	1.95190e7	0.845560	0.422780	+	0.906232i	$0.361054\pi$
$128$	−1.62115e7	−0.683264
$129$	−4.49696e6	−0.184440
$130$	1.00562e7	0.401452
$131$	−3.90620e6	−0.151811	−0.0759057	−	0.997115i	$-0.524185\pi$
$131$	−3.90620e6	−0.151811	−0.0759057	+	0.997115i	$0.524185\pi$
$132$	−2.57839e7	−0.975751
$133$	−3.13352e7	−1.15492
$134$	−87909.4	−0.00315623
$135$	−1.05721e7	−0.369822
$136$	−1.18886e7	−0.405269
$137$	−2.53665e7	−0.842828	−0.421414	−	0.906868i	$-0.638466\pi$
$137$	−2.53665e7	−0.842828	−0.421414	+	0.906868i	$0.638466\pi$
$138$	−1.52246e6	−0.0493139
$139$	4.42236e7	1.39670	0.698348	−	0.715758i	$-0.253919\pi$
$139$	4.42236e7	1.39670	0.698348	+	0.715758i	$0.253919\pi$
$140$	8.35483e7	2.57329
$141$	−1.47339e7	−0.442640
$142$	−3.33514e6	−0.0977474
$143$	−6.84956e7	−1.95878
$144$	1.07086e7	0.298858
$145$	−5.42541e6	−0.147790
$146$	1.18217e7	0.314373
$147$	2.05716e7	0.534142
$148$	−1.51501e7	−0.384149
$149$	2.22130e6	0.0550117	0.0275059	−	0.999622i	$-0.491244\pi$
$149$	2.22130e6	0.0550117	0.0275059	+	0.999622i	$0.491244\pi$
$150$	1.20018e7	0.290353
$151$	−4.02533e7	−0.951443	−0.475721	−	0.879596i	$-0.657813\pi$
$151$	−4.02533e7	−0.951443	−0.475721	+	0.879596i	$0.657813\pi$
$152$	1.32267e7	0.305491
$153$	1.63065e7	0.368079
$154$	2.05668e7	0.453778
$155$	1.42433e8	3.07220
$156$	2.95545e7	0.623287
$157$	3.47322e7	0.716281	0.358140	−	0.933668i	$-0.383411\pi$
$157$	3.47322e7	0.716281	0.358140	+	0.933668i	$0.383411\pi$
$158$	−7.91999e6	−0.159744
$159$	−4.16024e7	−0.820783
$160$	−5.32120e7	−1.02704
$161$	−3.36018e7	−0.634559
$162$	1.12293e6	0.0207515
$163$	−1.15628e7	−0.209126	−0.104563	−	0.994518i	$-0.533344\pi$
$163$	−1.15628e7	−0.209126	−0.104563	+	0.994518i	$0.533344\pi$
$164$	9.16466e7	1.62242
$165$	−1.12105e8	−1.94282
$166$	−7.13587e6	−0.121079
$167$	−1.06887e8	−1.77590	−0.887949	−	0.459941i	$-0.847870\pi$
$167$	−1.06887e8	−1.77590	−0.887949	+	0.459941i	$0.847870\pi$
$168$	−1.80691e7	−0.294004
$169$	1.57640e7	0.251225
$170$	−2.53863e7	−0.396304
$171$	−1.81419e7	−0.277458
$172$	2.05753e7	0.308316
$173$	−7.33625e7	−1.07724	−0.538621	−	0.842548i	$-0.681054\pi$
$173$	−7.33625e7	−1.07724	−0.538621	+	0.842548i	$0.681054\pi$
$174$	576266.	0.00829279
$175$	2.64888e8	3.73619
$176$	1.13553e8	1.57002
$177$	−5.54523e6	−0.0751646
$178$	−1.14838e7	−0.152621
$179$	−7.93198e7	−1.03370	−0.516852	−	0.856075i	$-0.672896\pi$
$179$	−7.93198e7	−1.03370	−0.516852	+	0.856075i	$0.672896\pi$
$180$	4.83714e7	0.618208
$181$	4.76795e7	0.597663	0.298831	−	0.954306i	$-0.403403\pi$
$181$	4.76795e7	0.597663	0.298831	+	0.954306i	$0.403403\pi$
$182$	−2.35745e7	−0.289863
$183$	7.40500e7	0.893194
$184$	1.41834e7	0.167849
$185$	−6.58710e7	−0.764880
$186$	−1.51286e7	−0.172387
$187$	1.72913e8	1.93367
$188$	6.74131e7	0.739932
$189$	2.47838e7	0.267025
$190$	2.82437e7	0.298734
$191$	−5.66760e7	−0.588549	−0.294274	−	0.955721i	$-0.595078\pi$
$191$	−5.66760e7	−0.588549	−0.294274	+	0.955721i	$0.595078\pi$
$192$	−4.51149e7	−0.460008
$193$	−1.76636e8	−1.76859	−0.884297	−	0.466924i	$-0.845362\pi$
$193$	−1.76636e8	−1.76859	−0.884297	+	0.466924i	$0.845362\pi$
$194$	−2.41726e7	−0.237693
$195$	1.28500e8	1.24103
$196$	−9.41228e7	−0.892891
$197$	1.27300e8	1.18630	0.593151	−	0.805091i	$-0.297884\pi$
$197$	1.27300e8	1.18630	0.593151	+	0.805091i	$0.297884\pi$
$198$	1.19074e7	0.109016
$199$	1.45827e8	1.31175	0.655877	−	0.754868i	$-0.272299\pi$
$199$	1.45827e8	1.31175	0.655877	+	0.754868i	$0.272299\pi$
$200$	−1.11810e8	−0.988270
$201$	−1.12332e6	−0.00975700
$202$	−2.94772e7	−0.251627
$203$	1.27186e7	0.106710
$204$	−7.46086e7	−0.615295
$205$	3.98469e8	3.23040
$206$	−1.99351e7	−0.158885
$207$	−1.94542e7	−0.152446
$208$	−1.30160e8	−1.00289
$209$	−1.92375e8	−1.45760
$210$	−3.85839e7	−0.287501
$211$	−1.57257e8	−1.15245	−0.576223	−	0.817292i	$-0.695474\pi$
$211$	−1.57257e8	−1.15245	−0.576223	+	0.817292i	$0.695474\pi$
$212$	1.90347e8	1.37205
$213$	−4.26169e7	−0.302171
$214$	2.52720e7	0.176275
$215$	8.94591e7	0.613889
$216$	−1.04613e7	−0.0706315
$217$	−3.33900e8	−2.21824
$218$	5.05563e6	0.0330504
$219$	1.51059e8	0.971836
$220$	5.12925e8	3.24769
$221$	−1.98200e8	−1.23518
$222$	6.99656e6	0.0429190
$223$	−1.56191e8	−0.943169	−0.471584	−	0.881821i	$-0.656318\pi$
$223$	−1.56191e8	−0.943169	−0.471584	+	0.881821i	$0.656318\pi$
$224$	1.24743e8	0.741563
$225$	1.53360e8	0.897582
$226$	−8.65886e6	−0.0498978
$227$	−1.43058e8	−0.811748	−0.405874	−	0.913929i	$-0.633033\pi$
$227$	−1.43058e8	−0.811748	−0.405874	+	0.913929i	$0.633033\pi$
$228$	8.30063e7	0.463809
$229$	−9.00963e7	−0.495773	−0.247886	−	0.968789i	$-0.579736\pi$
$229$	−9.00963e7	−0.495773	−0.247886	+	0.968789i	$0.579736\pi$
$230$	3.02867e7	0.164136
$231$	2.62805e8	1.40279
$232$	−5.36856e6	−0.0282261
$233$	1.58220e8	0.819437	0.409718	−	0.912212i	$-0.365627\pi$
$233$	1.58220e8	0.819437	0.409718	+	0.912212i	$0.365627\pi$
$234$	−1.36488e7	−0.0696366
$235$	2.93105e8	1.47328
$236$	2.53716e7	0.125648
$237$	−1.01203e8	−0.493825
$238$	5.95123e7	0.286146
$239$	−7.78834e7	−0.369022	−0.184511	−	0.982830i	$-0.559070\pi$
$239$	−7.78834e7	−0.369022	−0.184511	+	0.982830i	$0.559070\pi$
$240$	−2.13030e8	−0.994720
$241$	7.51343e7	0.345763	0.172882	−	0.984943i	$-0.444692\pi$
$241$	7.51343e7	0.345763	0.172882	+	0.984943i	$0.444692\pi$
$242$	8.50887e7	0.385939
$243$	1.43489e7	0.0641500
$244$	−3.38807e8	−1.49310
$245$	−4.09236e8	−1.77784
$246$	−4.23239e7	−0.181264
$247$	2.20509e8	0.931079
$248$	1.40940e8	0.586752
$249$	−9.11832e7	−0.374297
$250$	−1.50089e8	−0.607516
$251$	1.66455e8	0.664416	0.332208	−	0.943206i	$-0.392206\pi$
$251$	1.66455e8	0.664416	0.332208	+	0.943206i	$0.392206\pi$
$252$	−1.13395e8	−0.446368
$253$	−2.06290e8	−0.800861
$254$	4.12433e7	0.157919
$255$	−3.24390e8	−1.22512
$256$	1.79623e8	0.669149
$257$	−5.67936e7	−0.208705	−0.104353	−	0.994540i	$-0.533277\pi$
$257$	−5.67936e7	−0.208705	−0.104353	+	0.994540i	$0.533277\pi$
$258$	−9.50200e6	−0.0344466
$259$	1.54419e8	0.552271
$260$	−5.87936e8	−2.07455
$261$	7.36360e6	0.0256359
$262$	−8.25373e6	−0.0283528
$263$	−1.48859e8	−0.504581	−0.252291	−	0.967651i	$-0.581184\pi$
$263$	−1.48859e8	−0.504581	−0.252291	+	0.967651i	$0.581184\pi$
$264$	−1.10931e8	−0.371055
$265$	8.27608e8	2.73189
$266$	−6.62109e7	−0.215697
$267$	−1.46741e8	−0.471805
$268$	5.13961e6	0.0163102
$269$	−3.17458e7	−0.0994382	−0.0497191	−	0.998763i	$-0.515833\pi$
$269$	−3.17458e7	−0.0994382	−0.0497191	+	0.998763i	$0.515833\pi$
$270$	−2.23387e7	−0.0690691
$271$	470544.	0.00143618	0.000718089	−	1.00000i	$-0.499771\pi$
$271$	470544.	0.00143618	0.000718089		1.00000i	$0.499771\pi$
$272$	3.28580e8	0.990033
$273$	−3.01238e8	−0.896067
$274$	−5.35991e7	−0.157409
$275$	1.62622e9	4.71535
$276$	8.90104e7	0.254835
$277$	4.15036e8	1.17329	0.586646	−	0.809843i	$-0.300448\pi$
$277$	4.15036e8	1.17329	0.586646	+	0.809843i	$0.300448\pi$
$278$	9.34437e7	0.260851
$279$	−1.93316e8	−0.532909
$280$	3.59453e8	0.978562
$281$	4.91128e8	1.32045	0.660226	−	0.751067i	$-0.270461\pi$
$281$	4.91128e8	1.32045	0.660226	+	0.751067i	$0.270461\pi$
$282$	−3.11325e7	−0.0826688
$283$	−3.10302e8	−0.813827	−0.406914	−	0.913467i	$-0.633395\pi$
$283$	−3.10302e8	−0.813827	−0.406914	+	0.913467i	$0.633395\pi$
$284$	1.94989e8	0.505121
$285$	3.60902e8	0.923491
$286$	−1.44730e8	−0.365829
$287$	−9.34119e8	−2.33247
$288$	7.22216e7	0.178153
$289$	9.00046e7	0.219342
$290$	−1.14638e7	−0.0276017
$291$	−3.08880e8	−0.734793
$292$	−6.91154e8	−1.62456
$293$	−2.94684e8	−0.684415	−0.342208	−	0.939624i	$-0.611175\pi$
$293$	−2.94684e8	−0.684415	−0.342208	+	0.939624i	$0.611175\pi$
$294$	4.34674e7	0.0997581
$295$	1.10313e8	0.250178
$296$	−6.51808e7	−0.146083
$297$	1.52154e8	0.337005
$298$	4.69357e6	0.0102742
$299$	2.36459e8	0.511572
$300$	−7.01682e8	−1.50043
$301$	−2.09716e8	−0.443250
$302$	−8.50547e7	−0.177694
$303$	−3.76664e8	−0.777867
$304$	−3.65564e8	−0.746286
$305$	−1.47309e9	−2.97291
$306$	3.44554e7	0.0687437
$307$	2.26044e8	0.445871	0.222936	−	0.974833i	$-0.428436\pi$
$307$	2.26044e8	0.445871	0.222936	+	0.974833i	$0.428436\pi$
$308$	−1.20243e9	−2.34495
$309$	−2.54734e8	−0.491170
$310$	3.00958e8	0.573773
$311$	−4.63267e8	−0.873313	−0.436656	−	0.899628i	$-0.643837\pi$
$311$	−4.63267e8	−0.873313	−0.436656	+	0.899628i	$0.643837\pi$
$312$	1.27154e8	0.237021
$313$	6.22167e8	1.14684	0.573418	−	0.819263i	$-0.305617\pi$
$313$	6.22167e8	1.14684	0.573418	+	0.819263i	$0.305617\pi$
$314$	7.33885e7	0.133775
$315$	−4.93031e8	−0.888765
$316$	4.63041e8	0.825496
$317$	8.20133e8	1.44603	0.723014	−	0.690833i	$-0.242756\pi$
$317$	8.20133e8	1.44603	0.723014	+	0.690833i	$0.242756\pi$
$318$	−8.79052e7	−0.153292
$319$	7.80829e7	0.134675
$320$	8.97483e8	1.53109
$321$	3.22929e8	0.544929
$322$	−7.10001e7	−0.118512
$323$	−5.56661e8	−0.919140
$324$	−6.56517e7	−0.107236
$325$	−1.86404e9	−3.01206
$326$	−2.44321e7	−0.0390570
$327$	6.46015e7	0.102170
$328$	3.94294e8	0.616967
$329$	−6.87116e8	−1.06376
$330$	−2.36877e8	−0.362847
$331$	−4.99025e8	−0.756352	−0.378176	−	0.925734i	$-0.623449\pi$
$331$	−4.99025e8	−0.756352	−0.378176	+	0.925734i	$0.623449\pi$
$332$	4.17198e8	0.625689
$333$	8.94030e7	0.132677
$334$	−2.25851e8	−0.331672
$335$	2.23465e7	0.0324752
$336$	4.99398e8	0.718224
$337$	−2.16438e8	−0.308056	−0.154028	−	0.988066i	$-0.549225\pi$
$337$	−2.16438e8	−0.308056	−0.154028	+	0.988066i	$0.549225\pi$
$338$	3.33091e7	0.0469196
$339$	−1.10644e8	−0.154252
$340$	1.48421e9	2.04795
$341$	−2.04990e9	−2.79958
$342$	−3.83336e7	−0.0518190
$343$	−7.76048e7	−0.103839
$344$	8.85218e7	0.117245
$345$	3.87008e8	0.507403
$346$	−1.55014e8	−0.201189
$347$	2.49019e8	0.319948	0.159974	−	0.987121i	$-0.448859\pi$
$347$	2.49019e8	0.319948	0.159974	+	0.987121i	$0.448859\pi$
$348$	−3.36913e7	−0.0428539
$349$	−1.28064e9	−1.61264	−0.806319	−	0.591481i	$-0.798543\pi$
$349$	−1.28064e9	−1.61264	−0.806319	+	0.591481i	$0.798543\pi$
$350$	5.59704e8	0.697783
$351$	−1.74406e8	−0.215271
$352$	7.65830e8	0.935908
$353$	1.01386e8	0.122678	0.0613390	−	0.998117i	$-0.480463\pi$
$353$	1.01386e8	0.122678	0.0613390	+	0.998117i	$0.480463\pi$
$354$	−1.17170e7	−0.0140380
$355$	8.47790e8	1.00575
$356$	6.71397e8	0.788687
$357$	7.60457e8	0.884577
$358$	−1.67601e8	−0.193058
$359$	−9.38042e8	−1.07002	−0.535010	−	0.844846i	$-0.679692\pi$
$359$	−9.38042e8	−1.07002	−0.535010	+	0.844846i	$0.679692\pi$
$360$	2.08110e8	0.235090
$361$	−2.74555e8	−0.307153
$362$	1.00746e8	0.111621
$363$	1.08728e9	1.19307
$364$	1.37828e9	1.49790
$365$	−3.00506e9	−3.23466
$366$	1.56466e8	0.166816
$367$	7.40350e8	0.781818	0.390909	−	0.920429i	$-0.372161\pi$
$367$	7.40350e8	0.781818	0.390909	+	0.920429i	$0.372161\pi$
$368$	−3.92006e8	−0.410039
$369$	−5.40820e8	−0.560352
$370$	−1.39184e8	−0.142851
$371$	−1.94013e9	−1.97253
$372$	8.84494e8	0.890829
$373$	1.05390e9	1.05152	0.525761	−	0.850632i	$-0.323781\pi$
$373$	1.05390e9	1.05152	0.525761	+	0.850632i	$0.323781\pi$
$374$	3.65362e8	0.361138
$375$	−1.91785e9	−1.87804
$376$	2.90034e8	0.281379
$377$	−8.95019e7	−0.0860276
$378$	5.23678e7	0.0498704
$379$	1.16570e9	1.09989	0.549947	−	0.835199i	$-0.314648\pi$
$379$	1.16570e9	1.09989	0.549947	+	0.835199i	$0.314648\pi$
$380$	−1.65127e9	−1.54374
$381$	5.27013e8	0.488184
$382$	−1.19755e8	−0.109919
$383$	−1.70280e7	−0.0154870	−0.00774349	−	0.999970i	$-0.502465\pi$
$383$	−1.70280e7	−0.0154870	−0.00774349	+	0.999970i	$0.502465\pi$
$384$	−4.37711e8	−0.394483
$385$	−5.22805e9	−4.66903
$386$	−3.73229e8	−0.330308
$387$	−1.21418e8	−0.106486
$388$	1.41325e9	1.22831
$389$	3.59169e8	0.309368	0.154684	−	0.987964i	$-0.450564\pi$
$389$	3.59169e8	0.309368	0.154684	+	0.987964i	$0.450564\pi$
$390$	2.71518e8	0.231778
$391$	−5.96925e8	−0.505012
$392$	−4.04948e8	−0.339545
$393$	−1.05467e8	−0.0876484
$394$	2.68982e8	0.221558
$395$	2.01325e9	1.64365
$396$	−6.96164e8	−0.563350
$397$	−1.33556e9	−1.07127	−0.535634	−	0.844450i	$-0.679927\pi$
$397$	−1.33556e9	−1.07127	−0.535634	+	0.844450i	$0.679927\pi$
$398$	3.08130e8	0.244987
$399$	−8.46052e8	−0.666794
$400$	3.09024e9	2.41425
$401$	2.22573e9	1.72372	0.861862	−	0.507143i	$-0.169298\pi$
$401$	2.22573e9	1.72372	0.861862	+	0.507143i	$0.169298\pi$
$402$	−2.37355e6	−0.00182225
$403$	2.34968e9	1.78831
$404$	1.72338e9	1.30031
$405$	−2.85447e8	−0.213517
$406$	2.68742e7	0.0199294
$407$	9.48020e8	0.697007
$408$	−3.20991e8	−0.233982
$409$	1.44669e9	1.04555	0.522774	−	0.852471i	$-0.324897\pi$
$409$	1.44669e9	1.04555	0.522774	+	0.852471i	$0.324897\pi$
$410$	8.41960e8	0.603320
$411$	−6.84896e8	−0.486607
$412$	1.16550e9	0.821057
$413$	−2.58603e8	−0.180637
$414$	−4.11064e7	−0.0284714
$415$	1.81393e9	1.24581
$416$	−8.77827e8	−0.597836
$417$	1.19404e9	0.806383
$418$	−4.06486e8	−0.272225
$419$	−1.91705e9	−1.27316	−0.636581	−	0.771210i	$-0.719652\pi$
$419$	−1.91705e9	−1.27316	−0.636581	+	0.771210i	$0.719652\pi$
$420$	2.25580e9	1.48569
$421$	−1.78027e9	−1.16278	−0.581392	−	0.813623i	$-0.697492\pi$
$421$	−1.78027e9	−1.16278	−0.581392	+	0.813623i	$0.697492\pi$
$422$	−3.32281e8	−0.215235
$423$	−3.97815e8	−0.255558
$424$	8.18936e8	0.521758
$425$	4.70565e9	2.97343
$426$	−9.00489e7	−0.0564345
$427$	3.45333e9	2.14655
$428$	−1.47752e9	−0.910923
$429$	−1.84938e9	−1.13090
$430$	1.89026e8	0.114652
$431$	3.29923e8	0.198492	0.0992458	−	0.995063i	$-0.468357\pi$
$431$	3.29923e8	0.198492	0.0992458	+	0.995063i	$0.468357\pi$
$432$	2.89133e8	0.172546
$433$	−4.75888e7	−0.0281707	−0.0140853	−	0.999901i	$-0.504484\pi$
$433$	−4.75888e7	−0.0281707	−0.0140853	+	0.999901i	$0.504484\pi$
$434$	−7.05526e8	−0.414285
$435$	−1.46486e8	−0.0853265
$436$	−2.95576e8	−0.170792
$437$	6.64114e8	0.380678
$438$	3.19186e8	0.181503
$439$	−3.04664e8	−0.171868	−0.0859342	−	0.996301i	$-0.527387\pi$
$439$	−3.04664e8	−0.171868	−0.0859342	+	0.996301i	$0.527387\pi$
$440$	2.20677e9	1.23502
$441$	5.55433e8	0.308387
$442$	−4.18793e8	−0.230686
$443$	2.92263e9	1.59721	0.798603	−	0.601858i	$-0.205573\pi$
$443$	2.92263e9	1.59721	0.798603	+	0.601858i	$0.205573\pi$
$444$	−4.09053e8	−0.221788
$445$	2.91916e9	1.57036
$446$	−3.30029e8	−0.176149
$447$	5.99751e7	0.0317610
$448$	−2.10394e9	−1.10550
$449$	−3.10711e9	−1.61993	−0.809963	−	0.586481i	$-0.800513\pi$
$449$	−3.10711e9	−1.61993	−0.809963	+	0.586481i	$0.800513\pi$
$450$	3.24048e8	0.167635
$451$	−5.73480e9	−2.94375
$452$	5.06239e8	0.257852
$453$	−1.08684e9	−0.549316
$454$	−3.02279e8	−0.151605
$455$	5.99261e9	2.98247
$456$	3.57121e8	0.176376
$457$	−1.02063e8	−0.0500221	−0.0250110	−	0.999687i	$-0.507962\pi$
$457$	−1.02063e8	−0.0500221	−0.0250110	+	0.999687i	$0.507962\pi$
$458$	−1.90372e8	−0.0925921
$459$	4.40276e8	0.212511
$460$	−1.77071e9	−0.848192
$461$	−1.96777e9	−0.935452	−0.467726	−	0.883873i	$-0.654927\pi$
$461$	−1.96777e9	−0.935452	−0.467726	+	0.883873i	$0.654927\pi$
$462$	5.55303e8	0.261989
$463$	1.67779e9	0.785604	0.392802	−	0.919623i	$-0.371506\pi$
$463$	1.67779e9	0.785604	0.392802	+	0.919623i	$0.371506\pi$
$464$	1.48378e8	0.0689536
$465$	3.84568e9	1.77373
$466$	3.34316e8	0.153041
$467$	−1.19888e9	−0.544709	−0.272355	−	0.962197i	$-0.587802\pi$
$467$	−1.19888e9	−0.544709	−0.272355	+	0.962197i	$0.587802\pi$
$468$	7.97973e8	0.359855
$469$	−5.23860e7	−0.0234483
$470$	6.19326e8	0.275155
$471$	9.37769e8	0.413545
$472$	1.09157e8	0.0477809
$473$	−1.28750e9	−0.559415
$474$	−2.13840e8	−0.0922284
$475$	−5.23530e9	−2.24137
$476$	−3.47938e9	−1.47869
$477$	−1.12327e9	−0.473880
$478$	−1.64566e8	−0.0689197
$479$	−3.41930e9	−1.42155	−0.710777	−	0.703418i	$-0.751656\pi$
$479$	−3.41930e9	−1.42155	−0.710777	+	0.703418i	$0.751656\pi$
$480$	−1.43672e9	−0.592964
$481$	−1.08666e9	−0.445232
$482$	1.58758e8	0.0645758
$483$	−9.07249e8	−0.366363
$484$	−4.97470e9	−1.99438
$485$	6.14464e9	2.44568
$486$	3.03190e7	0.0119809
$487$	−1.02116e9	−0.400628	−0.200314	−	0.979732i	$-0.564196\pi$
$487$	−1.02116e9	−0.400628	−0.200314	+	0.979732i	$0.564196\pi$
$488$	−1.45766e9	−0.567789
$489$	−3.12196e8	−0.120739
$490$	−8.64709e8	−0.332035
$491$	3.59695e9	1.37135	0.685677	−	0.727906i	$-0.259506\pi$
$491$	3.59695e9	1.37135	0.685677	+	0.727906i	$0.259506\pi$
$492$	2.47446e9	0.936704
$493$	2.25942e8	0.0849245
$494$	4.65932e8	0.173891
$495$	−3.02685e9	−1.12169
$496$	−3.89535e9	−1.43338
$497$	−1.98744e9	−0.726186
$498$	−1.92669e8	−0.0699050
$499$	−1.17064e9	−0.421765	−0.210883	−	0.977511i	$-0.567634\pi$
$499$	−1.17064e9	−0.421765	−0.210883	+	0.977511i	$0.567634\pi$
$500$	8.77491e9	3.13941
$501$	−2.88596e9	−1.02532
$502$	3.51718e8	0.124088
$503$	−1.37007e9	−0.480014	−0.240007	−	0.970771i	$-0.577150\pi$
$503$	−1.37007e9	−0.480014	−0.240007	+	0.970771i	$0.577150\pi$
$504$	−4.87865e8	−0.169743
$505$	7.49308e9	2.58905
$506$	−4.35888e8	−0.149571
$507$	4.25628e8	0.145045
$508$	−2.41129e9	−0.816067
$509$	−6.94286e8	−0.233360	−0.116680	−	0.993170i	$-0.537225\pi$
$509$	−6.94286e8	−0.233360	−0.116680	+	0.993170i	$0.537225\pi$
$510$	−6.85431e8	−0.228806
$511$	7.04466e9	2.33554
$512$	2.45462e9	0.808237
$513$	−4.89833e8	−0.160191
$514$	−1.20004e8	−0.0389785
$515$	5.06748e9	1.63481
$516$	5.55533e8	0.178006
$517$	−4.21839e9	−1.34255
$518$	3.26285e8	0.103144
$519$	−1.98079e9	−0.621946
$520$	−2.52950e9	−0.788901
$521$	−3.26480e9	−1.01140	−0.505702	−	0.862708i	$-0.668767\pi$
$521$	−3.26480e9	−1.01140	−0.505702	+	0.862708i	$0.668767\pi$
$522$	1.55592e7	0.00478784
$523$	1.44867e9	0.442806	0.221403	−	0.975182i	$-0.428936\pi$
$523$	1.44867e9	0.442806	0.221403	+	0.975182i	$0.428936\pi$
$524$	4.82553e8	0.146516
$525$	7.15197e9	2.15709
$526$	−3.14538e8	−0.0942372
$527$	−5.93163e9	−1.76537
$528$	3.06594e9	0.906452
$529$	−2.69267e9	−0.790841
$530$	1.74872e9	0.510217
$531$	−1.49721e8	−0.0433963
$532$	3.87101e9	1.11464
$533$	6.57347e9	1.88040
$534$	−3.10062e8	−0.0881159
$535$	−6.42412e9	−1.81374
$536$	2.21123e7	0.00620237
$537$	−2.14163e9	−0.596809
$538$	−6.70784e7	−0.0185714
$539$	5.88975e9	1.62008
$540$	1.30603e9	0.356922
$541$	5.30499e9	1.44044	0.720218	−	0.693748i	$-0.244042\pi$
$541$	5.30499e9	1.44044	0.720218	+	0.693748i	$0.244042\pi$
$542$	994253.	0.000268225 0
$543$	1.28735e9	0.345061
$544$	2.21602e9	0.590170
$545$	−1.28513e9	−0.340064
$546$	−6.36511e8	−0.167352
$547$	2.77315e9	0.724465	0.362232	−	0.932088i	$-0.382015\pi$
$547$	2.77315e9	0.724465	0.362232	+	0.932088i	$0.382015\pi$
$548$	3.13366e9	0.813430
$549$	1.99935e9	0.515686
$550$	3.43617e9	0.880654
$551$	−2.51373e8	−0.0640160
$552$	3.82953e8	0.0969077
$553$	−4.71960e9	−1.18677
$554$	8.76964e8	0.219128
$555$	−1.77852e9	−0.441604
$556$	−5.46317e9	−1.34798
$557$	−2.33572e9	−0.572701	−0.286350	−	0.958125i	$-0.592442\pi$
$557$	−2.33572e9	−0.572701	−0.286350	+	0.958125i	$0.592442\pi$
$558$	−4.08473e8	−0.0995277
$559$	1.47579e9	0.357341
$560$	−9.93466e9	−2.39053
$561$	4.66864e9	1.11640
$562$	1.03775e9	0.246612
$563$	5.53231e9	1.30655	0.653276	−	0.757120i	$-0.273394\pi$
$563$	5.53231e9	1.30655	0.653276	+	0.757120i	$0.273394\pi$
$564$	1.82015e9	0.427200
$565$	2.20107e9	0.513411
$566$	−6.55663e8	−0.151993
$567$	6.69163e8	0.154167
$568$	8.38906e8	0.192085
$569$	5.01743e8	0.114180	0.0570898	−	0.998369i	$-0.481818\pi$
$569$	5.01743e8	0.114180	0.0570898	+	0.998369i	$0.481818\pi$
$570$	7.62581e8	0.172474
$571$	−1.45684e9	−0.327481	−0.163741	−	0.986503i	$-0.552356\pi$
$571$	−1.45684e9	−0.327481	−0.163741	+	0.986503i	$0.552356\pi$
$572$	8.46162e9	1.89046
$573$	−1.53025e9	−0.339799
$574$	−1.97378e9	−0.435619
$575$	−5.61399e9	−1.23150
$576$	−1.21810e9	−0.265586
$577$	−5.26247e9	−1.14044	−0.570222	−	0.821490i	$-0.693143\pi$
$577$	−5.26247e9	−1.14044	−0.570222	+	0.821490i	$0.693143\pi$
$578$	1.90178e8	0.0409650
$579$	−4.76917e9	−1.02110
$580$	6.70230e8	0.142635
$581$	−4.25234e9	−0.899521
$582$	−6.52659e8	−0.137232
$583$	−1.19110e10	−2.48948
$584$	−2.97357e9	−0.617780
$585$	3.46950e9	0.716508
$586$	−6.22662e8	−0.127824
$587$	−3.91337e9	−0.798579	−0.399290	−	0.916825i	$-0.630743\pi$
$587$	−3.91337e9	−0.798579	−0.399290	+	0.916825i	$0.630743\pi$
$588$	−2.54132e9	−0.515511
$589$	6.59928e9	1.33074
$590$	2.33089e8	0.0467240
$591$	3.43709e9	0.684912
$592$	1.80149e9	0.356866
$593$	6.52849e9	1.28564	0.642822	−	0.766015i	$-0.277763\pi$
$593$	6.52849e9	1.28564	0.642822	+	0.766015i	$0.277763\pi$
$594$	3.21500e8	0.0629402
$595$	−1.51280e10	−2.94423
$596$	−2.74409e8	−0.0530929
$597$	3.93733e9	0.757342
$598$	4.99634e8	0.0955427
$599$	8.24579e9	1.56761	0.783805	−	0.621007i	$-0.213276\pi$
$599$	8.24579e9	1.56761	0.783805	+	0.621007i	$0.213276\pi$
$600$	−3.01887e9	−0.570578
$601$	−6.15461e9	−1.15648	−0.578242	−	0.815865i	$-0.696261\pi$
$601$	−6.15461e9	−1.15648	−0.578242	+	0.815865i	$0.696261\pi$
$602$	−4.43127e8	−0.0827828
$603$	−3.03296e7	−0.00563321
$604$	4.97271e9	0.918256
$605$	−2.16295e10	−3.97102
$606$	−7.95885e8	−0.145277
$607$	7.75348e6	0.00140714	0.000703569	−	1.00000i	$-0.499776\pi$
$607$	7.75348e6	0.00140714	0.000703569		1.00000i	$0.499776\pi$
$608$	−2.46545e9	−0.444870
$609$	3.43402e8	0.0616088
$610$	−3.11263e9	−0.555230
$611$	4.83529e9	0.857588
$612$	−2.01443e9	−0.355241
$613$	5.41748e9	0.949917	0.474958	−	0.880008i	$-0.342463\pi$
$613$	5.41748e9	0.949917	0.474958	+	0.880008i	$0.342463\pi$
$614$	4.77628e8	0.0832723
$615$	1.07587e10	1.86507
$616$	−5.17327e9	−0.891728
$617$	−1.53588e9	−0.263245	−0.131622	−	0.991300i	$-0.542019\pi$
$617$	−1.53588e9	−0.263245	−0.131622	+	0.991300i	$0.542019\pi$
$618$	−5.38248e8	−0.0917325
$619$	−1.24887e9	−0.211641	−0.105821	−	0.994385i	$-0.533747\pi$
$619$	−1.24887e9	−0.211641	−0.105821	+	0.994385i	$0.533747\pi$
$620$	−1.75955e10	−2.96504
$621$	−5.25264e8	−0.0880150
$622$	−9.78875e8	−0.163103
$623$	−6.84329e9	−1.13385
$624$	−3.51431e9	−0.579020
$625$	2.17171e10	3.55813
$626$	1.31463e9	0.214187
$627$	−5.19413e9	−0.841544
$628$	−4.29065e9	−0.691296
$629$	2.74321e9	0.439523
$630$	−1.04177e9	−0.165989
$631$	−8.97235e9	−1.42169	−0.710843	−	0.703351i	$-0.751686\pi$
$631$	−8.97235e9	−1.42169	−0.710843	+	0.703351i	$0.751686\pi$
$632$	1.99216e9	0.313916
$633$	−4.24593e9	−0.665365
$634$	1.73293e9	0.270065
$635$	−1.04840e10	−1.62487
$636$	5.13937e9	0.792154
$637$	−6.75108e9	−1.03487
$638$	1.64988e8	0.0251524
$639$	−1.15066e9	−0.174459
$640$	8.70750e9	1.31300
$641$	−5.94956e9	−0.892240	−0.446120	−	0.894973i	$-0.647195\pi$
$641$	−5.94956e9	−0.892240	−0.446120	+	0.894973i	$0.647195\pi$
$642$	6.82344e8	0.101773
$643$	8.03210e9	1.19149	0.595745	−	0.803173i	$-0.296857\pi$
$643$	8.03210e9	1.19149	0.595745	+	0.803173i	$0.296857\pi$
$644$	4.15101e9	0.612426
$645$	2.41540e9	0.354429
$646$	−1.17621e9	−0.171661
$647$	−8.88936e9	−1.29034	−0.645172	−	0.764038i	$-0.723214\pi$
$647$	−8.88936e9	−1.29034	−0.645172	+	0.764038i	$0.723214\pi$
$648$	−2.82456e8	−0.0407791
$649$	−1.58763e9	−0.227978
$650$	−3.93868e9	−0.562541
$651$	−9.01531e9	−1.28070
$652$	1.42842e9	0.201831
$653$	−1.14448e10	−1.60846	−0.804231	−	0.594316i	$-0.797423\pi$
$653$	−1.14448e10	−1.60846	−0.804231	+	0.594316i	$0.797423\pi$
$654$	1.36502e8	0.0190817
$655$	2.09809e9	0.291729
$656$	−1.08976e10	−1.50719
$657$	4.07860e9	0.561090
$658$	−1.45187e9	−0.198672
$659$	9.40014e9	1.27949	0.639743	−	0.768589i	$-0.279041\pi$
$659$	9.40014e9	1.27949	0.639743	+	0.768589i	$0.279041\pi$
$660$	1.38490e10	1.87505
$661$	1.37618e9	0.185341	0.0926704	−	0.995697i	$-0.470460\pi$
$661$	1.37618e9	0.185341	0.0926704	+	0.995697i	$0.470460\pi$
$662$	−1.05443e9	−0.141259
$663$	−5.35140e9	−0.713132
$664$	1.79492e9	0.237935
$665$	1.68307e10	2.21936
$666$	1.88907e8	0.0247793
$667$	−2.69556e8	−0.0351729
$668$	1.32043e10	1.71395
$669$	−4.21716e9	−0.544539
$670$	4.72177e7	0.00606517
$671$	2.12009e10	2.70910
$672$	3.36806e9	0.428142
$673$	9.13119e9	1.15471	0.577357	−	0.816492i	$-0.304084\pi$
$673$	9.13119e9	1.15471	0.577357	+	0.816492i	$0.304084\pi$
$674$	−4.57331e8	−0.0575335
$675$	4.14073e9	0.518219
$676$	−1.94741e9	−0.242462
$677$	6.14968e9	0.761715	0.380857	−	0.924634i	$-0.375629\pi$
$677$	6.14968e9	0.761715	0.380857	+	0.924634i	$0.375629\pi$
$678$	−2.33789e8	−0.0288085
$679$	−1.44047e10	−1.76587
$680$	6.38556e9	0.778785
$681$	−3.86256e9	−0.468663
$682$	−4.33141e9	−0.522858
$683$	−1.15096e10	−1.38225	−0.691127	−	0.722734i	$-0.742885\pi$
$683$	−1.15096e10	−1.38225	−0.691127	+	0.722734i	$0.742885\pi$
$684$	2.24117e9	0.267780
$685$	1.36248e10	1.61962
$686$	−1.63978e8	−0.0193932
$687$	−2.43260e9	−0.286235
$688$	−2.44659e9	−0.286419
$689$	1.36529e10	1.59022
$690$	8.17741e8	0.0947641
$691$	−6.76616e9	−0.780134	−0.390067	−	0.920786i	$-0.627548\pi$
$691$	−6.76616e9	−0.780134	−0.390067	+	0.920786i	$0.627548\pi$
$692$	9.06286e9	1.03967
$693$	7.09573e9	0.809899
$694$	5.26173e8	0.0597545
$695$	−2.37533e10	−2.68396
$696$	−1.44951e8	−0.0162963
$697$	−1.65943e10	−1.85628
$698$	−2.70596e9	−0.301181
$699$	4.27194e9	0.473102
$700$	−3.27230e10	−3.60587
$701$	2.85225e9	0.312734	0.156367	−	0.987699i	$-0.450022\pi$
$701$	2.85225e9	0.312734	0.156367	+	0.987699i	$0.450022\pi$
$702$	−3.68517e8	−0.0402047
$703$	−3.05197e9	−0.331312
$704$	−1.29166e10	−1.39523
$705$	7.91383e9	0.850599
$706$	2.14227e8	0.0229117
$707$	−1.75658e10	−1.86939
$708$	6.85032e8	0.0725428
$709$	1.72710e10	1.81994	0.909969	−	0.414676i	$-0.136105\pi$
$709$	1.72710e10	1.81994	0.909969	+	0.414676i	$0.136105\pi$
$710$	1.79137e9	0.187837
$711$	−2.73247e9	−0.285110
$712$	2.88858e9	0.299919
$713$	7.07662e9	0.731161
$714$	1.60683e9	0.165206
$715$	3.67902e10	3.76410
$716$	9.79879e9	0.997647
$717$	−2.10285e9	−0.213055
$718$	−1.98207e9	−0.199840
$719$	6.37828e9	0.639959	0.319980	−	0.947424i	$-0.396324\pi$
$719$	6.37828e9	0.639959	0.319980	+	0.947424i	$0.396324\pi$
$720$	−5.75180e9	−0.574302
$721$	−1.18795e10	−1.18039
$722$	−5.80130e8	−0.0573648
$723$	2.02863e9	0.199626
$724$	−5.89010e9	−0.576816
$725$	2.12495e9	0.207093
$726$	2.29740e9	0.222822
$727$	1.75274e10	1.69179	0.845895	−	0.533350i	$-0.179067\pi$
$727$	1.75274e10	1.69179	0.845895	+	0.533350i	$0.179067\pi$
$728$	5.92982e9	0.569615
$729$	3.87420e8	0.0370370
$730$	−6.34965e9	−0.604115
$731$	−3.72554e9	−0.352759
$732$	−9.14778e9	−0.862039
$733$	6.90854e9	0.647922	0.323961	−	0.946070i	$-0.394985\pi$
$733$	6.90854e9	0.647922	0.323961	+	0.946070i	$0.394985\pi$
$734$	1.56435e9	0.146015
$735$	−1.10494e10	−1.02644
$736$	−2.64378e9	−0.244429
$737$	−3.21612e8	−0.0295935
$738$	−1.14274e9	−0.104653
$739$	1.05720e10	0.963610	0.481805	−	0.876278i	$-0.339981\pi$
$739$	1.05720e10	0.963610	0.481805	+	0.876278i	$0.339981\pi$
$740$	8.13739e9	0.738200
$741$	5.95374e9	0.537559
$742$	−4.09947e9	−0.368395
$743$	1.14806e10	1.02685	0.513423	−	0.858136i	$-0.328377\pi$
$743$	1.14806e10	1.02685	0.513423	+	0.858136i	$0.328377\pi$
$744$	3.80539e9	0.338761
$745$	−1.19310e9	−0.105713
$746$	2.22687e9	0.196386
$747$	−2.46195e9	−0.216101
$748$	−2.13608e10	−1.86622
$749$	1.50598e10	1.30959
$750$	−4.05239e9	−0.350749
$751$	−6.77468e9	−0.583645	−0.291823	−	0.956472i	$-0.594262\pi$
$751$	−6.77468e9	−0.583645	−0.291823	+	0.956472i	$0.594262\pi$
$752$	−8.01604e9	−0.687381
$753$	4.49430e9	0.383601
$754$	−1.89116e8	−0.0160668
$755$	2.16208e10	1.82834
$756$	−3.06167e9	−0.257711
$757$	−1.20655e10	−1.01090	−0.505451	−	0.862855i	$-0.668674\pi$
$757$	−1.20655e10	−1.01090	−0.505451	+	0.862855i	$0.668674\pi$
$758$	2.46311e9	0.205420
$759$	−5.56984e9	−0.462377
$760$	−7.10430e9	−0.587048
$761$	−6.97304e9	−0.573556	−0.286778	−	0.957997i	$-0.592584\pi$
$761$	−6.97304e9	−0.573556	−0.286778	+	0.957997i	$0.592584\pi$
$762$	1.11357e9	0.0911749
$763$	3.01270e9	0.245539
$764$	7.00149e9	0.568020
$765$	−8.75853e9	−0.707320
$766$	−3.59798e7	−0.00289240
$767$	1.81981e9	0.145627
$768$	4.84983e9	0.386334
$769$	−6.18686e9	−0.490600	−0.245300	−	0.969447i	$-0.578887\pi$
$769$	−6.18686e9	−0.490600	−0.245300	+	0.969447i	$0.578887\pi$
$770$	−1.10468e10	−0.872003
$771$	−1.53343e9	−0.120496
$772$	2.18208e10	1.70691
$773$	9.77041e9	0.760825	0.380412	−	0.924817i	$-0.375782\pi$
$773$	9.77041e9	0.760825	0.380412	+	0.924817i	$0.375782\pi$
$774$	−2.56554e8	−0.0198877
$775$	−5.57860e10	−4.30496
$776$	6.08025e9	0.467096
$777$	4.16932e9	0.318854
$778$	7.58918e8	0.0577785
$779$	1.84621e10	1.39927
$780$	−1.58743e10	−1.19774
$781$	−1.22014e10	−0.916501
$782$	−1.26129e9	−0.0943176
$783$	1.98817e8	0.0148009
$784$	1.11921e10	0.829477
$785$	−1.86553e10	−1.37644
$786$	−2.22851e8	−0.0163695
$787$	−3.17612e9	−0.232266	−0.116133	−	0.993234i	$-0.537050\pi$
$787$	−3.17612e9	−0.232266	−0.116133	+	0.993234i	$0.537050\pi$
$788$	−1.57260e10	−1.14492
$789$	−4.01921e9	−0.291320
$790$	4.25397e9	0.306973
$791$	−5.15990e9	−0.370701
$792$	−2.99513e9	−0.214229
$793$	−2.43014e10	−1.73051
$794$	−2.82203e9	−0.200073
$795$	2.23454e10	1.57726
$796$	−1.80148e10	−1.26600
$797$	−1.64367e10	−1.15003	−0.575016	−	0.818142i	$-0.695004\pi$
$797$	−1.64367e10	−1.15003	−0.575016	+	0.818142i	$0.695004\pi$
$798$	−1.78769e9	−0.124533
$799$	−1.22064e10	−0.846591
$800$	2.08413e10	1.43916
$801$	−3.96201e9	−0.272397
$802$	4.70294e9	0.321928
$803$	4.32491e10	2.94762
$804$	1.38769e8	0.00941668
$805$	1.80481e10	1.21940
$806$	4.96485e9	0.333990
$807$	−8.57137e8	−0.0574107
$808$	7.41457e9	0.494477
$809$	6.28475e9	0.417319	0.208659	−	0.977988i	$-0.433090\pi$
$809$	6.28475e9	0.417319	0.208659	+	0.977988i	$0.433090\pi$
$810$	−6.03144e8	−0.0398771
$811$	2.31027e10	1.52086	0.760432	−	0.649418i	$-0.224987\pi$
$811$	2.31027e10	1.52086	0.760432	+	0.649418i	$0.224987\pi$
$812$	−1.57120e9	−0.102988
$813$	1.27047e7	0.000829177 0
$814$	2.00315e9	0.130175
$815$	6.21060e9	0.401866
$816$	8.87165e9	0.571596
$817$	4.14487e9	0.265910
$818$	3.05683e9	0.195270
$819$	−8.13343e9	−0.517345
$820$	−4.92250e10	−3.11772
$821$	−2.91799e10	−1.84027	−0.920137	−	0.391597i	$-0.871923\pi$
$821$	−2.91799e10	−1.84027	−0.920137	+	0.391597i	$0.871923\pi$
$822$	−1.44717e9	−0.0908803
$823$	2.76539e10	1.72925	0.864624	−	0.502419i	$-0.167557\pi$
$823$	2.76539e10	1.72925	0.864624	+	0.502419i	$0.167557\pi$
$824$	5.01439e9	0.312229
$825$	4.39078e10	2.72241
$826$	−5.46423e8	−0.0337364
$827$	−5.03285e9	−0.309417	−0.154709	−	0.987960i	$-0.549444\pi$
$827$	−5.03285e9	−0.309417	−0.154709	+	0.987960i	$0.549444\pi$
$828$	2.40328e9	0.147129
$829$	1.94317e10	1.18459	0.592296	−	0.805720i	$-0.298222\pi$
$829$	1.94317e10	1.18459	0.592296	+	0.805720i	$0.298222\pi$
$830$	3.83281e9	0.232672
$831$	1.12060e10	0.677401
$832$	1.48056e10	0.891239
$833$	1.70427e10	1.02160
$834$	2.52298e9	0.150603
$835$	5.74111e10	3.41266
$836$	2.37651e10	1.40676
$837$	−5.21953e9	−0.307675
$838$	−4.05069e9	−0.237780
$839$	1.03412e10	0.604509	0.302255	−	0.953227i	$-0.402261\pi$
$839$	1.03412e10	0.604509	0.302255	+	0.953227i	$0.402261\pi$
$840$	9.70522e9	0.564973
$841$	−1.71478e10	−0.994085
$842$	−3.76169e9	−0.217165
$843$	1.32604e10	0.762363
$844$	1.94268e10	1.11225
$845$	−8.46713e9	−0.482767
$846$	−8.40576e8	−0.0477288
$847$	5.07052e10	2.86722
$848$	−2.26340e10	−1.27461
$849$	−8.37816e9	−0.469863
$850$	9.94296e9	0.555328
$851$	−3.27273e9	−0.182036
$852$	5.26469e9	0.291632
$853$	2.35292e10	1.29803	0.649016	−	0.760775i	$-0.275181\pi$
$853$	2.35292e10	1.29803	0.649016	+	0.760775i	$0.275181\pi$
$854$	7.29683e9	0.400896
$855$	9.74437e9	0.533178
$856$	−6.35680e9	−0.346402
$857$	−2.62808e10	−1.42628	−0.713142	−	0.701020i	$-0.752728\pi$
$857$	−2.62808e10	−1.42628	−0.713142	+	0.701020i	$0.752728\pi$
$858$	−3.90771e9	−0.211211
$859$	1.11154e9	0.0598339	0.0299170	−	0.999552i	$-0.490476\pi$
$859$	1.11154e9	0.0598339	0.0299170	+	0.999552i	$0.490476\pi$
$860$	−1.10514e10	−0.592476
$861$	−2.52212e10	−1.34665
$862$	6.97122e8	0.0370709
$863$	−1.39838e10	−0.740604	−0.370302	−	0.928911i	$-0.620746\pi$
$863$	−1.39838e10	−0.740604	−0.370302	+	0.928911i	$0.620746\pi$
$864$	1.94998e9	0.102857
$865$	3.94043e10	2.07008
$866$	−1.00554e8	−0.00526125
$867$	2.43012e9	0.126637
$868$	4.12485e10	2.14086
$869$	−2.89749e10	−1.49780
$870$	−3.09523e8	−0.0159359
$871$	3.68645e8	0.0189036
$872$	−1.27167e9	−0.0649481
$873$	−8.33977e9	−0.424233
$874$	1.40326e9	0.0710966
$875$	−8.94392e10	−4.51336
$876$	−1.86611e10	−0.937938
$877$	3.43482e10	1.71951	0.859756	−	0.510705i	$-0.170615\pi$
$877$	3.43482e10	1.71951	0.859756	+	0.510705i	$0.170615\pi$
$878$	−6.43751e8	−0.0320987
$879$	−7.95646e9	−0.395147
$880$	−6.09915e10	−3.01703
$881$	3.32281e10	1.63715	0.818576	−	0.574398i	$-0.194764\pi$
$881$	3.32281e10	1.63715	0.818576	+	0.574398i	$0.194764\pi$
$882$	1.17362e9	0.0575954
$883$	−2.10543e10	−1.02915	−0.514576	−	0.857445i	$-0.672051\pi$
$883$	−2.10543e10	−1.02915	−0.514576	+	0.857445i	$0.672051\pi$
$884$	2.44847e10	1.19210
$885$	2.97844e9	0.144440
$886$	6.17547e9	0.298299
$887$	1.23601e10	0.594688	0.297344	−	0.954770i	$-0.403899\pi$
$887$	1.23601e10	0.594688	0.297344	+	0.954770i	$0.403899\pi$
$888$	−1.75988e9	−0.0843409
$889$	2.45773e10	1.17322
$890$	6.16814e9	0.293285
$891$	4.10817e9	0.194570
$892$	1.92951e10	0.910271
$893$	1.35803e10	0.638160
$894$	1.26726e8	0.00593179
$895$	4.26041e10	1.98642
$896$	−2.04127e10	−0.948030
$897$	6.38439e9	0.295356
$898$	−6.56528e9	−0.302542
$899$	−2.67857e9	−0.122954
$900$	−1.89454e10	−0.866274
$901$	−3.44658e10	−1.56983
$902$	−1.21175e10	−0.549784
$903$	−5.66233e9	−0.255911
$904$	2.17801e9	0.0980551
$905$	−2.56095e10	−1.14850
$906$	−2.29648e9	−0.102592
$907$	1.40907e10	0.627058	0.313529	−	0.949579i	$-0.398489\pi$
$907$	1.40907e10	0.627058	0.313529	+	0.949579i	$0.398489\pi$
$908$	1.76727e10	0.783433
$909$	−1.01699e10	−0.449101
$910$	1.26623e10	0.557015
$911$	2.85261e10	1.25005	0.625027	−	0.780603i	$-0.285088\pi$
$911$	2.85261e10	1.25005	0.625027	+	0.780603i	$0.285088\pi$
$912$	−9.87022e9	−0.430869
$913$	−2.61062e10	−1.13526
$914$	−2.15657e8	−0.00934228
$915$	−3.97736e10	−1.71641
$916$	1.11301e10	0.478480
$917$	−4.91848e9	−0.210639
$918$	9.30297e8	0.0396892
$919$	−1.21759e10	−0.517485	−0.258742	−	0.965946i	$-0.583308\pi$
$919$	−1.21759e10	−0.517485	−0.258742	+	0.965946i	$0.583308\pi$
$920$	−7.61817e9	−0.322547
$921$	6.10320e9	0.257424
$922$	−4.15787e9	−0.174708
$923$	1.39858e10	0.585439
$924$	−3.24657e10	−1.35386
$925$	2.57994e10	1.07180
$926$	3.54514e9	0.146722
$927$	−6.87781e9	−0.283577
$928$	1.00070e9	0.0411040
$929$	−4.26915e9	−0.174697	−0.0873487	−	0.996178i	$-0.527839\pi$
$929$	−4.26915e9	−0.174697	−0.0873487	+	0.996178i	$0.527839\pi$
$930$	8.12587e9	0.331268
$931$	−1.89610e10	−0.770081
$932$	−1.95457e10	−0.790854
$933$	−1.25082e10	−0.504207
$934$	−2.53320e9	−0.101732
$935$	−9.28746e10	−3.71583
$936$	3.43315e9	0.136844
$937$	1.52673e10	0.606282	0.303141	−	0.952946i	$-0.401965\pi$
$937$	1.52673e10	0.606282	0.303141	+	0.952946i	$0.401965\pi$
$938$	−1.10691e8	−0.00437927
$939$	1.67985e10	0.662126
$940$	−3.62088e10	−1.42189
$941$	3.60621e10	1.41087	0.705435	−	0.708775i	$-0.250752\pi$
$941$	3.60621e10	1.41087	0.705435	+	0.708775i	$0.250752\pi$
$942$	1.98149e9	0.0772349
$943$	1.97975e10	0.768813
$944$	−3.01691e9	−0.116724
$945$	−1.33118e10	−0.513129
$946$	−2.72047e9	−0.104478
$947$	1.21747e10	0.465836	0.232918	−	0.972496i	$-0.425173\pi$
$947$	1.21747e10	0.465836	0.232918	+	0.972496i	$0.425173\pi$
$948$	1.25021e10	0.476600
$949$	−4.95739e10	−1.88287
$950$	−1.10621e10	−0.418606
$951$	2.21436e10	0.834865
$952$	−1.49695e10	−0.562311
$953$	−2.94721e10	−1.10303	−0.551514	−	0.834166i	$-0.685950\pi$
$953$	−2.94721e10	−1.10303	−0.551514	+	0.834166i	$0.685950\pi$
$954$	−2.37344e9	−0.0885032
$955$	3.04417e10	1.13099
$956$	9.62135e9	0.356150
$957$	2.10824e9	0.0777549
$958$	−7.22493e9	−0.265494
$959$	−3.19402e10	−1.16943
$960$	2.42320e10	0.883976
$961$	4.28076e10	1.55593
$962$	−2.29610e9	−0.0831529
$963$	8.71909e9	0.314615
$964$	−9.28174e9	−0.333703
$965$	9.48743e10	3.39862
$966$	−1.91700e9	−0.0684231
$967$	−3.39812e10	−1.20850	−0.604250	−	0.796795i	$-0.706527\pi$
$967$	−3.39812e10	−1.20850	−0.604250	+	0.796795i	$0.706527\pi$
$968$	−2.14028e10	−0.758415
$969$	−1.50298e10	−0.530666
$970$	1.29835e10	0.456764
$971$	−1.42757e9	−0.0500415	−0.0250208	−	0.999687i	$-0.507965\pi$
$971$	−1.42757e9	−0.0500415	−0.0250208	+	0.999687i	$0.507965\pi$
$972$	−1.77260e9	−0.0619124
$973$	5.56840e10	1.93792
$974$	−2.15769e9	−0.0748226
$975$	−5.03290e10	−1.73901
$976$	4.02873e10	1.38705
$977$	2.69567e10	0.924775	0.462388	−	0.886678i	$-0.346993\pi$
$977$	2.69567e10	0.924775	0.462388	+	0.886678i	$0.346993\pi$
$978$	−6.59665e8	−0.0225495
$979$	−4.20128e10	−1.43101
$980$	5.05551e10	1.71583
$981$	1.74424e9	0.0589882
$982$	7.60030e9	0.256118
$983$	−1.23730e10	−0.415469	−0.207735	−	0.978185i	$-0.566609\pi$
$983$	−1.23730e10	−0.415469	−0.207735	+	0.978185i	$0.566609\pi$
$984$	1.06459e10	0.356206
$985$	−6.83749e10	−2.27966
$986$	4.77412e8	0.0158608
$987$	−1.85521e10	−0.614163
$988$	−2.72406e10	−0.898602
$989$	4.44468e9	0.146101
$990$	−6.39568e9	−0.209490
$991$	−6.08067e10	−1.98470	−0.992348	−	0.123474i	$-0.960597\pi$
$991$	−6.08067e10	−1.98470	−0.992348	+	0.123474i	$0.960597\pi$
$992$	−2.62712e10	−0.854454
$993$	−1.34737e10	−0.436680
$994$	−4.19944e9	−0.135625
$995$	−7.83264e10	−2.52074
$996$	1.12643e10	0.361242
$997$	4.42391e10	1.41375	0.706876	−	0.707338i	$-0.250104\pi$
$997$	4.42391e10	1.41375	0.706876	+	0.707338i	$0.250104\pi$
$998$	−2.47354e9	−0.0787702
$999$	2.41388e9	0.0766014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.11	✓	17
3.2	odd	2		531.8.a.d.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.11	✓	17	1.1	even	1	trivial
531.8.a.d.1.7		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)

\(f(q)\)	\(=\)	\(q+2.11298 q^{2} +27.0000 q^{3} -123.535 q^{4} -537.118 q^{5} +57.0506 q^{6} +1259.15 q^{7} -531.490 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+2.11298 q^{2} +27.0000 q^{3} -123.535 q^{4} -537.118 q^{5} +57.0506 q^{6} +1259.15 q^{7} -531.490 q^{8} +729.000 q^{9} -1134.92 q^{10} +7730.24 q^{11} -3335.45 q^{12} -8860.73 q^{13} +2660.56 q^{14} -14502.2 q^{15} +14689.5 q^{16} +22368.4 q^{17} +1540.37 q^{18} -24886.1 q^{19} +66353.0 q^{20} +33997.0 q^{21} +16333.9 q^{22} -26686.2 q^{23} -14350.2 q^{24} +210371. q^{25} -18722.6 q^{26} +19683.0 q^{27} -155549. q^{28} +10101.0 q^{29} -30642.9 q^{30} -265180. q^{31} +99069.4 q^{32} +208717. q^{33} +47264.0 q^{34} -676311. q^{35} -90057.2 q^{36} +122638. q^{37} -52583.9 q^{38} -239240. q^{39} +285473. q^{40} -741866. q^{41} +71835.1 q^{42} -166554. q^{43} -954958. q^{44} -391559. q^{45} -56387.4 q^{46} -545699. q^{47} +396616. q^{48} +761910. q^{49} +444510. q^{50} +603946. q^{51} +1.09461e6 q^{52} -1.54083e6 q^{53} +41589.9 q^{54} -4.15205e6 q^{55} -669225. q^{56} -671924. q^{57} +21343.2 q^{58} -205379. q^{59} +1.79153e6 q^{60} +2.74259e6 q^{61} -560320. q^{62} +917919. q^{63} -1.67092e6 q^{64} +4.75926e6 q^{65} +441015. q^{66} -41604.4 q^{67} -2.76328e6 q^{68} -720526. q^{69} -1.42903e6 q^{70} -1.57840e6 q^{71} -387456. q^{72} +5.59479e6 q^{73} +259132. q^{74} +5.68001e6 q^{75} +3.07431e6 q^{76} +9.73352e6 q^{77} -505510. q^{78} -3.74825e6 q^{79} -7.88999e6 q^{80} +531441. q^{81} -1.56755e6 q^{82} -3.37715e6 q^{83} -4.19983e6 q^{84} -1.20144e7 q^{85} -351926. q^{86} +272726. q^{87} -4.10855e6 q^{88} -5.43486e6 q^{89} -827358. q^{90} -1.11570e7 q^{91} +3.29668e6 q^{92} -7.15985e6 q^{93} -1.15305e6 q^{94} +1.33668e7 q^{95} +2.67487e6 q^{96} -1.14400e7 q^{97} +1.60990e6 q^{98} +5.63535e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 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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