LMFDB - Embedded newform 177.8.a.b.1.8

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			1.8
Root			$-4.01497$ 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)

$f(q)$	$=$	$q-6.01497 q^{2} +27.0000 q^{3} -91.8201 q^{4} -385.807 q^{5} -162.404 q^{6} +847.649 q^{7} +1322.21 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-6.01497 q^{2} +27.0000 q^{3} -91.8201 q^{4} -385.807 q^{5} -162.404 q^{6} +847.649 q^{7} +1322.21 q^{8} +729.000 q^{9} +2320.62 q^{10} -5526.47 q^{11} -2479.14 q^{12} +2987.05 q^{13} -5098.58 q^{14} -10416.8 q^{15} +3799.90 q^{16} -6651.02 q^{17} -4384.92 q^{18} +47421.5 q^{19} +35424.9 q^{20} +22886.5 q^{21} +33241.6 q^{22} +16902.5 q^{23} +35699.7 q^{24} +70722.2 q^{25} -17967.0 q^{26} +19683.0 q^{27} -77831.2 q^{28} +2638.69 q^{29} +62656.7 q^{30} +138735. q^{31} -192099. q^{32} -149215. q^{33} +40005.7 q^{34} -327029. q^{35} -66936.9 q^{36} -91219.9 q^{37} -285239. q^{38} +80650.4 q^{39} -510119. q^{40} +549406. q^{41} -137662. q^{42} -240843. q^{43} +507441. q^{44} -281253. q^{45} -101668. q^{46} -1.17880e6 q^{47} +102597. q^{48} -105035. q^{49} -425392. q^{50} -179578. q^{51} -274271. q^{52} -100058. q^{53} -118393. q^{54} +2.13215e6 q^{55} +1.12077e6 q^{56} +1.28038e6 q^{57} -15871.6 q^{58} -205379. q^{59} +956471. q^{60} +71464.3 q^{61} -834486. q^{62} +617936. q^{63} +669085. q^{64} -1.15243e6 q^{65} +897523. q^{66} -912586. q^{67} +610697. q^{68} +456367. q^{69} +1.96707e6 q^{70} -274897. q^{71} +963893. q^{72} -5.34005e6 q^{73} +548685. q^{74} +1.90950e6 q^{75} -4.35425e6 q^{76} -4.68451e6 q^{77} -485110. q^{78} +1.12488e6 q^{79} -1.46603e6 q^{80} +531441. q^{81} -3.30466e6 q^{82} -4.95003e6 q^{83} -2.10144e6 q^{84} +2.56601e6 q^{85} +1.44866e6 q^{86} +71244.6 q^{87} -7.30717e6 q^{88} -8.64528e6 q^{89} +1.69173e6 q^{90} +2.53197e6 q^{91} -1.55199e6 q^{92} +3.74584e6 q^{93} +7.09048e6 q^{94} -1.82956e7 q^{95} -5.18669e6 q^{96} -2.69412e6 q^{97} +631782. q^{98} -4.02880e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.01497	−0.531654	−0.265827	−	0.964021i	$-0.585645\pi$
$2$	−6.01497	−0.531654	−0.265827	+	0.964021i	$0.585645\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−91.8201	−0.717345
$5$	−385.807	−1.38031	−0.690153	−	0.723664i	$-0.742457\pi$
$5$	−385.807	−1.38031	−0.690153	+	0.723664i	$0.742457\pi$
$6$	−162.404	−0.306950
$7$	847.649	0.934055	0.467028	−	0.884243i	$-0.345325\pi$
$7$	847.649	0.934055	0.467028	+	0.884243i	$0.345325\pi$
$8$	1322.21	0.913032
$9$	729.000	0.333333
$10$	2320.62	0.733844
$11$	−5526.47	−1.25191	−0.625956	−	0.779859i	$-0.715291\pi$
$11$	−5526.47	−1.25191	−0.625956	+	0.779859i	$0.715291\pi$
$12$	−2479.14	−0.414159
$13$	2987.05	0.377087	0.188543	−	0.982065i	$-0.439623\pi$
$13$	2987.05	0.377087	0.188543	+	0.982065i	$0.439623\pi$
$14$	−5098.58	−0.496594
$15$	−10416.8	−0.796920
$16$	3799.90	0.231928
$17$	−6651.02	−0.328335	−0.164167	−	0.986432i	$-0.552494\pi$
$17$	−6651.02	−0.328335	−0.164167	+	0.986432i	$0.552494\pi$
$18$	−4384.92	−0.177218
$19$	47421.5	1.58613	0.793064	−	0.609139i	$-0.208485\pi$
$19$	47421.5	1.58613	0.793064	+	0.609139i	$0.208485\pi$
$20$	35424.9	0.990155
$21$	22886.5	0.539277
$22$	33241.6	0.665583
$23$	16902.5	0.289670	0.144835	−	0.989456i	$-0.453735\pi$
$23$	16902.5	0.289670	0.144835	+	0.989456i	$0.453735\pi$
$24$	35699.7	0.527139
$25$	70722.2	0.905244
$26$	−17967.0	−0.200479
$27$	19683.0	0.192450
$28$	−77831.2	−0.670040
$29$	2638.69	0.0200907	0.0100454	−	0.999950i	$-0.496802\pi$
$29$	2638.69	0.0200907	0.0100454	+	0.999950i	$0.496802\pi$
$30$	62656.7	0.423685
$31$	138735.	0.836410	0.418205	−	0.908353i	$-0.362659\pi$
$31$	138735.	0.836410	0.418205	+	0.908353i	$0.362659\pi$
$32$	−192099.	−1.03634
$33$	−149215.	−0.722791
$34$	40005.7	0.174560
$35$	−327029.	−1.28928
$36$	−66936.9	−0.239115
$37$	−91219.9	−0.296063	−0.148031	−	0.988983i	$-0.547294\pi$
$37$	−91219.9	−0.296063	−0.148031	+	0.988983i	$0.547294\pi$
$38$	−285239.	−0.843270
$39$	80650.4	0.217711
$40$	−510119.	−1.26026
$41$	549406.	1.24494	0.622472	−	0.782642i	$-0.286129\pi$
$41$	549406.	1.24494	0.622472	+	0.782642i	$0.286129\pi$
$42$	−137662.	−0.286709
$43$	−240843.	−0.461949	−0.230974	−	0.972960i	$-0.574191\pi$
$43$	−240843.	−0.461949	−0.230974	+	0.972960i	$0.574191\pi$
$44$	507441.	0.898052
$45$	−281253.	−0.460102
$46$	−101668.	−0.154004
$47$	−1.17880e6	−1.65615	−0.828074	−	0.560618i	$-0.810563\pi$
$47$	−1.17880e6	−1.65615	−0.828074	+	0.560618i	$0.810563\pi$
$48$	102597.	0.133904
$49$	−105035.	−0.127540
$50$	−425392.	−0.481276
$51$	−179578.	−0.189564
$52$	−274271.	−0.270501
$53$	−100058.	−0.0923184	−0.0461592	−	0.998934i	$-0.514698\pi$
$53$	−100058.	−0.0923184	−0.0461592	+	0.998934i	$0.514698\pi$
$54$	−118393.	−0.102317
$55$	2.13215e6	1.72802
$56$	1.12077e6	0.852823
$57$	1.28038e6	0.915751
$58$	−15871.6	−0.0106813
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	956471.	0.571666
$61$	71464.3	0.0403120	0.0201560	−	0.999797i	$-0.493584\pi$
$61$	71464.3	0.0403120	0.0201560	+	0.999797i	$0.493584\pi$
$62$	−834486.	−0.444680
$63$	617936.	0.311352
$64$	669085.	0.319045
$65$	−1.15243e6	−0.520495
$66$	897523.	0.384275
$67$	−912586.	−0.370691	−0.185345	−	0.982673i	$-0.559340\pi$
$67$	−912586.	−0.370691	−0.185345	+	0.982673i	$0.559340\pi$
$68$	610697.	0.235529
$69$	456367.	0.167241
$70$	1.96707e6	0.685451
$71$	−274897.	−0.0911520	−0.0455760	−	0.998961i	$-0.514512\pi$
$71$	−274897.	−0.0911520	−0.0455760	+	0.998961i	$0.514512\pi$
$72$	963893.	0.304344
$73$	−5.34005e6	−1.60663	−0.803315	−	0.595555i	$-0.796932\pi$
$73$	−5.34005e6	−1.60663	−0.803315	+	0.595555i	$0.796932\pi$
$74$	548685.	0.157403
$75$	1.90950e6	0.522643
$76$	−4.35425e6	−1.13780
$77$	−4.68451e6	−1.16935
$78$	−485110.	−0.115747
$79$	1.12488e6	0.256692	0.128346	−	0.991729i	$-0.459033\pi$
$79$	1.12488e6	0.256692	0.128346	+	0.991729i	$0.459033\pi$
$80$	−1.46603e6	−0.320131
$81$	531441.	0.111111
$82$	−3.30466e6	−0.661878
$83$	−4.95003e6	−0.950243	−0.475122	−	0.879920i	$-0.657596\pi$
$83$	−4.95003e6	−0.950243	−0.475122	+	0.879920i	$0.657596\pi$
$84$	−2.10144e6	−0.386848
$85$	2.56601e6	0.453202
$86$	1.44866e6	0.245597
$87$	71244.6	0.0115994
$88$	−7.30717e6	−1.14304
$89$	−8.64528e6	−1.29991	−0.649956	−	0.759972i	$-0.725213\pi$
$89$	−8.64528e6	−1.29991	−0.649956	+	0.759972i	$0.725213\pi$
$90$	1.69173e6	0.244615
$91$	2.53197e6	0.352220
$92$	−1.55199e6	−0.207793
$93$	3.74584e6	0.482902
$94$	7.09048e6	0.880497
$95$	−1.82956e7	−2.18934
$96$	−5.18669e6	−0.598330
$97$	−2.69412e6	−0.299720	−0.149860	−	0.988707i	$-0.547882\pi$
$97$	−2.69412e6	−0.299720	−0.149860	+	0.988707i	$0.547882\pi$
$98$	631782.	0.0678073
$99$	−4.02880e6	−0.417304
$100$	−6.49372e6	−0.649372
$101$	1.51552e7	1.46365	0.731826	−	0.681492i	$-0.238668\pi$
$101$	1.51552e7	1.46365	0.731826	+	0.681492i	$0.238668\pi$
$102$	1.08015e6	0.100782
$103$	−1.40028e7	−1.26266	−0.631328	−	0.775516i	$-0.717490\pi$
$103$	−1.40028e7	−1.26266	−0.631328	+	0.775516i	$0.717490\pi$
$104$	3.94952e6	0.344292
$105$	−8.82978e6	−0.744367
$106$	601849.	0.0490814
$107$	−8.87562e6	−0.700415	−0.350208	−	0.936672i	$-0.613889\pi$
$107$	−8.87562e6	−0.700415	−0.350208	+	0.936672i	$0.613889\pi$
$108$	−1.80730e6	−0.138053
$109$	−2.49654e7	−1.84648	−0.923242	−	0.384219i	$-0.874471\pi$
$109$	−2.49654e7	−1.84648	−0.923242	+	0.384219i	$0.874471\pi$
$110$	−1.28248e7	−0.918708
$111$	−2.46294e6	−0.170932
$112$	3.22098e6	0.216633
$113$	1.44492e7	0.942038	0.471019	−	0.882123i	$-0.343886\pi$
$113$	1.44492e7	0.942038	0.471019	+	0.882123i	$0.343886\pi$
$114$	−7.70146e6	−0.486862
$115$	−6.52110e6	−0.399833
$116$	−242285.	−0.0144120
$117$	2.17756e6	0.125696
$118$	1.23535e6	0.0692154
$119$	−5.63773e6	−0.306683
$120$	−1.37732e7	−0.727614
$121$	1.10547e7	0.567283
$122$	−429856.	−0.0214320
$123$	1.48339e7	0.718768
$124$	−1.27386e7	−0.599994
$125$	2.85605e6	0.130792
$126$	−3.71687e6	−0.165531
$127$	1.71357e7	0.742315	0.371157	−	0.928570i	$-0.378961\pi$
$127$	1.71357e7	0.742315	0.371157	+	0.928570i	$0.378961\pi$
$128$	2.05642e7	0.866716
$129$	−6.50275e6	−0.266706
$130$	6.93181e6	0.276723
$131$	−1.82887e7	−0.710777	−0.355388	−	0.934719i	$-0.615651\pi$
$131$	−1.82887e7	−0.710777	−0.355388	+	0.934719i	$0.615651\pi$
$132$	1.37009e7	0.518491
$133$	4.01968e7	1.48153
$134$	5.48918e6	0.197079
$135$	−7.59384e6	−0.265640
$136$	−8.79406e6	−0.299780
$137$	−4.79157e7	−1.59205	−0.796023	−	0.605266i	$-0.793067\pi$
$137$	−4.79157e7	−1.59205	−0.796023	+	0.605266i	$0.793067\pi$
$138$	−2.74504e6	−0.0889143
$139$	2.76336e7	0.872740	0.436370	−	0.899767i	$-0.356264\pi$
$139$	2.76336e7	0.872740	0.436370	+	0.899767i	$0.356264\pi$
$140$	3.00278e7	0.924860
$141$	−3.18277e7	−0.956178
$142$	1.65350e6	0.0484613
$143$	−1.65079e7	−0.472079
$144$	2.77013e6	0.0773092
$145$	−1.01803e6	−0.0277313
$146$	3.21203e7	0.854170
$147$	−2.83594e6	−0.0736355
$148$	8.37582e6	0.212379
$149$	6.17248e6	0.152865	0.0764325	−	0.997075i	$-0.475647\pi$
$149$	6.17248e6	0.152865	0.0764325	+	0.997075i	$0.475647\pi$
$150$	−1.14856e7	−0.277865
$151$	−2.68093e7	−0.633673	−0.316837	−	0.948480i	$-0.602621\pi$
$151$	−2.68093e7	−0.633673	−0.316837	+	0.948480i	$0.602621\pi$
$152$	6.27013e7	1.44819
$153$	−4.84859e6	−0.109445
$154$	2.81772e7	0.621692
$155$	−5.35249e7	−1.15450
$156$	−7.40533e6	−0.156174
$157$	1.87147e7	0.385952	0.192976	−	0.981203i	$-0.438186\pi$
$157$	1.87147e7	0.385952	0.192976	+	0.981203i	$0.438186\pi$
$158$	−6.76614e6	−0.136471
$159$	−2.70158e6	−0.0533000
$160$	7.41134e7	1.43046
$161$	1.43274e7	0.270568
$162$	−3.19660e6	−0.0590726
$163$	9.00787e7	1.62917	0.814583	−	0.580047i	$-0.196966\pi$
$163$	9.00787e7	1.62917	0.814583	+	0.580047i	$0.196966\pi$
$164$	−5.04465e7	−0.893053
$165$	5.75681e7	0.997673
$166$	2.97743e7	0.505200
$167$	−6.92715e7	−1.15093	−0.575463	−	0.817828i	$-0.695178\pi$
$167$	−6.92715e7	−1.15093	−0.575463	+	0.817828i	$0.695178\pi$
$168$	3.02608e7	0.492377
$169$	−5.38260e7	−0.857806
$170$	−1.54345e7	−0.240947
$171$	3.45703e7	0.528709
$172$	2.21142e7	0.331376
$173$	−1.01646e8	−1.49255	−0.746277	−	0.665635i	$-0.768161\pi$
$173$	−1.01646e8	−1.49255	−0.746277	+	0.665635i	$0.768161\pi$
$174$	−428534.	−0.00616685
$175$	5.99476e7	0.845548
$176$	−2.10001e7	−0.290353
$177$	−5.54523e6	−0.0751646
$178$	5.20011e7	0.691103
$179$	1.59338e7	0.207650	0.103825	−	0.994596i	$-0.466892\pi$
$179$	1.59338e7	0.207650	0.103825	+	0.994596i	$0.466892\pi$
$180$	2.58247e7	0.330052
$181$	8.29983e7	1.04038	0.520192	−	0.854049i	$-0.325860\pi$
$181$	8.29983e7	1.04038	0.520192	+	0.854049i	$0.325860\pi$
$182$	−1.52297e7	−0.187259
$183$	1.92953e6	0.0232742
$184$	2.23487e7	0.264478
$185$	3.51933e7	0.408657
$186$	−2.25311e7	−0.256736
$187$	3.67567e7	0.411046
$188$	1.08238e8	1.18803
$189$	1.66843e7	0.179759
$190$	1.10047e8	1.16397
$191$	−2.94448e7	−0.305768	−0.152884	−	0.988244i	$-0.548856\pi$
$191$	−2.94448e7	−0.305768	−0.152884	+	0.988244i	$0.548856\pi$
$192$	1.80653e7	0.184201
$193$	8.61854e7	0.862945	0.431473	−	0.902126i	$-0.357994\pi$
$193$	8.61854e7	0.862945	0.431473	+	0.902126i	$0.357994\pi$
$194$	1.62051e7	0.159347
$195$	−3.11155e7	−0.300508
$196$	9.64432e6	0.0914904
$197$	−1.74170e8	−1.62308	−0.811541	−	0.584296i	$-0.801371\pi$
$197$	−1.74170e8	−1.62308	−0.811541	+	0.584296i	$0.801371\pi$
$198$	2.42331e7	0.221861
$199$	9.07182e7	0.816035	0.408017	−	0.912974i	$-0.366220\pi$
$199$	9.07182e7	0.816035	0.408017	+	0.912974i	$0.366220\pi$
$200$	9.35098e7	0.826517
$201$	−2.46398e7	−0.214018
$202$	−9.11583e7	−0.778155
$203$	2.23668e6	0.0187658
$204$	1.64888e7	0.135983
$205$	−2.11965e8	−1.71840
$206$	8.42266e7	0.671296
$207$	1.23219e7	0.0965566
$208$	1.13505e7	0.0874568
$209$	−2.62074e8	−1.98569
$210$	5.31109e7	0.395746
$211$	−1.22589e8	−0.898387	−0.449194	−	0.893434i	$-0.648289\pi$
$211$	−1.22589e8	−0.898387	−0.449194	+	0.893434i	$0.648289\pi$
$212$	9.18737e6	0.0662241
$213$	−7.42223e6	−0.0526266
$214$	5.33866e7	0.372378
$215$	9.29188e7	0.637631
$216$	2.60251e7	0.175713
$217$	1.17598e8	0.781254
$218$	1.50166e8	0.981690
$219$	−1.44181e8	−0.927588
$220$	−1.95775e8	−1.23959
$221$	−1.98669e7	−0.123811
$222$	1.48145e7	0.0908765
$223$	−5.48773e7	−0.331380	−0.165690	−	0.986178i	$-0.552985\pi$
$223$	−5.48773e7	−0.331380	−0.165690	+	0.986178i	$0.552985\pi$
$224$	−1.62833e8	−0.967997
$225$	5.15565e7	0.301748
$226$	−8.69114e7	−0.500838
$227$	1.64956e8	0.936003	0.468001	−	0.883728i	$-0.344974\pi$
$227$	1.64956e8	0.936003	0.468001	+	0.883728i	$0.344974\pi$
$228$	−1.17565e8	−0.656909
$229$	1.18120e8	0.649980	0.324990	−	0.945717i	$-0.394639\pi$
$229$	1.18120e8	0.649980	0.324990	+	0.945717i	$0.394639\pi$
$230$	3.92243e7	0.212573
$231$	−1.26482e8	−0.675127
$232$	3.48891e6	0.0183435
$233$	−1.12335e8	−0.581795	−0.290898	−	0.956754i	$-0.593954\pi$
$233$	−1.12335e8	−0.581795	−0.290898	+	0.956754i	$0.593954\pi$
$234$	−1.30980e7	−0.0668265
$235$	4.54791e8	2.28599
$236$	1.88579e7	0.0933903
$237$	3.03718e7	0.148201
$238$	3.39108e7	0.163049
$239$	2.96755e8	1.40607	0.703033	−	0.711158i	$-0.251829\pi$
$239$	2.96755e8	1.40607	0.703033	+	0.711158i	$0.251829\pi$
$240$	−3.95828e7	−0.184828
$241$	1.37243e7	0.0631583	0.0315791	−	0.999501i	$-0.489946\pi$
$241$	1.37243e7	0.0631583	0.0315791	+	0.999501i	$0.489946\pi$
$242$	−6.64939e7	−0.301598
$243$	1.43489e7	0.0641500
$244$	−6.56186e6	−0.0289176
$245$	4.05232e7	0.176045
$246$	−8.92258e7	−0.382136
$247$	1.41651e8	0.598107
$248$	1.83437e8	0.763670
$249$	−1.33651e8	−0.548623
$250$	−1.71791e7	−0.0695359
$251$	−2.78781e7	−0.111277	−0.0556385	−	0.998451i	$-0.517719\pi$
$251$	−2.78781e7	−0.111277	−0.0556385	+	0.998451i	$0.517719\pi$
$252$	−5.67389e7	−0.223347
$253$	−9.34112e7	−0.362641
$254$	−1.03071e8	−0.394654
$255$	6.92823e7	0.261657
$256$	−2.09336e8	−0.779837
$257$	1.86791e8	0.686419	0.343209	−	0.939259i	$-0.388486\pi$
$257$	1.86791e8	0.686419	0.343209	+	0.939259i	$0.388486\pi$
$258$	3.91139e7	0.141795
$259$	−7.73224e7	−0.276539
$260$	1.05816e8	0.373374
$261$	1.92360e6	0.00669690
$262$	1.10006e8	0.377887
$263$	2.51415e8	0.852210	0.426105	−	0.904674i	$-0.359885\pi$
$263$	2.51415e8	0.852210	0.426105	+	0.904674i	$0.359885\pi$
$264$	−1.97294e8	−0.659932
$265$	3.86033e7	0.127428
$266$	−2.41783e8	−0.787661
$267$	−2.33422e8	−0.750504
$268$	8.37937e7	0.265913
$269$	−4.66642e8	−1.46168	−0.730838	−	0.682551i	$-0.760870\pi$
$269$	−4.66642e8	−1.46168	−0.730838	+	0.682551i	$0.760870\pi$
$270$	4.56768e7	0.141228
$271$	4.71085e8	1.43783	0.718914	−	0.695099i	$-0.244640\pi$
$271$	4.71085e8	1.43783	0.718914	+	0.695099i	$0.244640\pi$
$272$	−2.52732e7	−0.0761500
$273$	6.83632e7	0.203354
$274$	2.88212e8	0.846417
$275$	−3.90844e8	−1.13329
$276$	−4.19037e7	−0.119969
$277$	−4.94424e8	−1.39772	−0.698860	−	0.715259i	$-0.746309\pi$
$277$	−4.94424e8	−1.39772	−0.698860	+	0.715259i	$0.746309\pi$
$278$	−1.66215e8	−0.463995
$279$	1.01138e8	0.278803
$280$	−4.32402e8	−1.17716
$281$	−1.88387e8	−0.506499	−0.253249	−	0.967401i	$-0.581499\pi$
$281$	−1.88387e8	−0.506499	−0.253249	+	0.967401i	$0.581499\pi$
$282$	1.91443e8	0.508355
$283$	3.45526e8	0.906208	0.453104	−	0.891458i	$-0.350317\pi$
$283$	3.45526e8	0.906208	0.453104	+	0.891458i	$0.350317\pi$
$284$	2.52411e7	0.0653874
$285$	−4.93981e8	−1.26402
$286$	9.92943e7	0.250982
$287$	4.65703e8	1.16285
$288$	−1.40040e8	−0.345446
$289$	−3.66103e8	−0.892196
$290$	6.12340e6	0.0147435
$291$	−7.27413e7	−0.173044
$292$	4.90324e8	1.15251
$293$	4.35989e8	1.01260	0.506301	−	0.862357i	$-0.331012\pi$
$293$	4.35989e8	1.01260	0.506301	+	0.862357i	$0.331012\pi$
$294$	1.70581e7	0.0391485
$295$	7.92367e7	0.179701
$296$	−1.20612e8	−0.270315
$297$	−1.08778e8	−0.240930
$298$	−3.71273e7	−0.0812712
$299$	5.04886e7	0.109231
$300$	−1.75330e8	−0.374915
$301$	−2.04150e8	−0.431486
$302$	1.61257e8	0.336895
$303$	4.09191e8	0.845040
$304$	1.80197e8	0.367867
$305$	−2.75714e7	−0.0556429
$306$	2.91642e7	0.0581868
$307$	9.90146e8	1.95306	0.976529	−	0.215387i	$-0.0691013\pi$
$307$	9.90146e8	1.95306	0.976529	+	0.215387i	$0.0691013\pi$
$308$	4.30132e8	0.838830
$309$	−3.78076e8	−0.728995
$310$	3.21951e8	0.613795
$311$	−2.78364e8	−0.524750	−0.262375	−	0.964966i	$-0.584506\pi$
$311$	−2.78364e8	−0.524750	−0.262375	+	0.964966i	$0.584506\pi$
$312$	1.06637e8	0.198777
$313$	−7.58142e8	−1.39748	−0.698740	−	0.715376i	$-0.746256\pi$
$313$	−7.58142e8	−1.39748	−0.698740	+	0.715376i	$0.746256\pi$
$314$	−1.12568e8	−0.205193
$315$	−2.38404e8	−0.429761
$316$	−1.03287e8	−0.184137
$317$	−3.93211e8	−0.693296	−0.346648	−	0.937995i	$-0.612680\pi$
$317$	−3.93211e8	−0.693296	−0.346648	+	0.937995i	$0.612680\pi$
$318$	1.62499e7	0.0283371
$319$	−1.45826e7	−0.0251518
$320$	−2.58138e8	−0.440379
$321$	−2.39642e8	−0.404385
$322$	−8.61788e7	−0.143848
$323$	−3.15402e8	−0.520781
$324$	−4.87970e7	−0.0797049
$325$	2.11251e8	0.341355
$326$	−5.41821e8	−0.866152
$327$	−6.74066e8	−1.06607
$328$	7.26431e8	1.13667
$329$	−9.99212e8	−1.54693
$330$	−3.46271e8	−0.530417
$331$	−9.50914e7	−0.144126	−0.0720632	−	0.997400i	$-0.522958\pi$
$331$	−9.50914e7	−0.144126	−0.0720632	+	0.997400i	$0.522958\pi$
$332$	4.54512e8	0.681652
$333$	−6.64993e7	−0.0986876
$334$	4.16666e8	0.611894
$335$	3.52082e8	0.511667
$336$	8.69665e7	0.125073
$337$	−6.91531e8	−0.984254	−0.492127	−	0.870524i	$-0.663780\pi$
$337$	−6.91531e8	−0.984254	−0.492127	+	0.870524i	$0.663780\pi$
$338$	3.23762e8	0.456055
$339$	3.90128e8	0.543886
$340$	−2.35611e8	−0.325102
$341$	−7.66714e8	−1.04711
$342$	−2.07939e8	−0.281090
$343$	−7.87108e8	−1.05319
$344$	−3.18445e8	−0.421774
$345$	−1.76070e8	−0.230844
$346$	6.11400e8	0.793522
$347$	−5.15844e8	−0.662774	−0.331387	−	0.943495i	$-0.607516\pi$
$347$	−5.15844e8	−0.662774	−0.331387	+	0.943495i	$0.607516\pi$
$348$	−6.54169e6	−0.00832075
$349$	−8.89896e8	−1.12060	−0.560300	−	0.828290i	$-0.689314\pi$
$349$	−8.89896e8	−1.12060	−0.560300	+	0.828290i	$0.689314\pi$
$350$	−3.60583e8	−0.449539
$351$	5.87941e7	0.0725703
$352$	1.06163e9	1.29740
$353$	−3.85325e8	−0.466246	−0.233123	−	0.972447i	$-0.574895\pi$
$353$	−3.85325e8	−0.466246	−0.233123	+	0.972447i	$0.574895\pi$
$354$	3.33544e7	0.0399615
$355$	1.06057e8	0.125818
$356$	7.93810e8	0.932485
$357$	−1.52219e8	−0.177063
$358$	−9.58411e7	−0.110398
$359$	−1.51447e9	−1.72755	−0.863777	−	0.503875i	$-0.831907\pi$
$359$	−1.51447e9	−1.72755	−0.863777	+	0.503875i	$0.831907\pi$
$360$	−3.71877e8	−0.420088
$361$	1.35493e9	1.51580
$362$	−4.99232e8	−0.553124
$363$	2.98478e8	0.327521
$364$	−2.32486e8	−0.252663
$365$	2.06023e9	2.21764
$366$	−1.16061e7	−0.0123738
$367$	−8.13769e8	−0.859350	−0.429675	−	0.902984i	$-0.641372\pi$
$367$	−8.13769e8	−0.859350	−0.429675	+	0.902984i	$0.641372\pi$
$368$	6.42279e7	0.0671825
$369$	4.00517e8	0.414981
$370$	−2.11687e8	−0.217264
$371$	−8.48144e7	−0.0862305
$372$	−3.43943e8	−0.346407
$373$	−1.20212e9	−1.19940	−0.599702	−	0.800223i	$-0.704714\pi$
$373$	−1.20212e9	−1.19940	−0.599702	+	0.800223i	$0.704714\pi$
$374$	−2.21090e8	−0.218534
$375$	7.71133e7	0.0755127
$376$	−1.55863e9	−1.51212
$377$	7.88190e6	0.00757594
$378$	−1.00355e8	−0.0955695
$379$	−4.34931e8	−0.410377	−0.205189	−	0.978722i	$-0.565781\pi$
$379$	−4.34931e8	−0.410377	−0.205189	+	0.978722i	$0.565781\pi$
$380$	1.67990e9	1.57051
$381$	4.62663e8	0.428576
$382$	1.77110e8	0.162563
$383$	3.58726e7	0.0326263	0.0163131	−	0.999867i	$-0.494807\pi$
$383$	3.58726e7	0.0326263	0.0163131	+	0.999867i	$0.494807\pi$
$384$	5.55233e8	0.500399
$385$	1.80732e9	1.61407
$386$	−5.18403e8	−0.458788
$387$	−1.75574e8	−0.153983
$388$	2.47374e8	0.215003
$389$	−1.13638e9	−0.978815	−0.489407	−	0.872055i	$-0.662787\pi$
$389$	−1.13638e9	−0.978815	−0.489407	+	0.872055i	$0.662787\pi$
$390$	1.87159e8	0.159766
$391$	−1.12419e8	−0.0951087
$392$	−1.38878e8	−0.116448
$393$	−4.93795e8	−0.410367
$394$	1.04762e9	0.862917
$395$	−4.33988e8	−0.354314
$396$	3.69925e8	0.299351
$397$	−5.01657e8	−0.402383	−0.201192	−	0.979552i	$-0.564481\pi$
$397$	−5.01657e8	−0.402383	−0.201192	+	0.979552i	$0.564481\pi$
$398$	−5.45667e8	−0.433848
$399$	1.08531e9	0.855362
$400$	2.68738e8	0.209951
$401$	6.17044e8	0.477871	0.238936	−	0.971035i	$-0.423202\pi$
$401$	6.17044e8	0.477871	0.238936	+	0.971035i	$0.423202\pi$
$402$	1.48208e8	0.113784
$403$	4.14408e8	0.315399
$404$	−1.39155e9	−1.04994
$405$	−2.05034e8	−0.153367
$406$	−1.34536e7	−0.00997692
$407$	5.04124e8	0.370644
$408$	−2.37440e8	−0.173078
$409$	1.67124e9	1.20783	0.603915	−	0.797048i	$-0.293606\pi$
$409$	1.67124e9	1.20783	0.603915	+	0.797048i	$0.293606\pi$
$410$	1.27496e9	0.913595
$411$	−1.29372e9	−0.919168
$412$	1.28574e9	0.905760
$413$	−1.74089e8	−0.121604
$414$	−7.41160e7	−0.0513347
$415$	1.90976e9	1.31163
$416$	−5.73811e8	−0.390789
$417$	7.46106e8	0.503877
$418$	1.57637e9	1.05570
$419$	−6.96670e7	−0.0462677	−0.0231339	−	0.999732i	$-0.507364\pi$
$419$	−6.96670e7	−0.0462677	−0.0231339	+	0.999732i	$0.507364\pi$
$420$	8.10751e8	0.533968
$421$	−2.02237e9	−1.32091	−0.660457	−	0.750864i	$-0.729637\pi$
$421$	−2.02237e9	−1.32091	−0.660457	+	0.750864i	$0.729637\pi$
$422$	7.37371e8	0.477631
$423$	−8.59349e8	−0.552050
$424$	−1.32298e8	−0.0842896
$425$	−4.70375e8	−0.297223
$426$	4.46445e7	0.0279791
$427$	6.05766e7	0.0376537
$428$	8.14960e8	0.502439
$429$	−4.45712e8	−0.272555
$430$	−5.58904e8	−0.338999
$431$	−2.20133e9	−1.32439	−0.662193	−	0.749333i	$-0.730374\pi$
$431$	−2.20133e9	−1.32439	−0.662193	+	0.749333i	$0.730374\pi$
$432$	7.47935e7	0.0446345
$433$	−1.11885e9	−0.662316	−0.331158	−	0.943575i	$-0.607439\pi$
$433$	−1.11885e9	−0.662316	−0.331158	+	0.943575i	$0.607439\pi$
$434$	−7.07351e8	−0.415356
$435$	−2.74867e7	−0.0160107
$436$	2.29232e9	1.32457
$437$	8.01542e8	0.459453
$438$	8.67248e8	0.493155
$439$	3.23226e8	0.182340	0.0911698	−	0.995835i	$-0.470939\pi$
$439$	3.23226e8	0.182340	0.0911698	+	0.995835i	$0.470939\pi$
$440$	2.81916e9	1.57774
$441$	−7.65705e7	−0.0425134
$442$	1.19499e8	0.0658244
$443$	−2.28214e9	−1.24718	−0.623591	−	0.781751i	$-0.714327\pi$
$443$	−2.28214e9	−1.24718	−0.623591	+	0.781751i	$0.714327\pi$
$444$	2.26147e8	0.122617
$445$	3.33541e9	1.79428
$446$	3.30086e8	0.176179
$447$	1.66657e8	0.0882566
$448$	5.67149e8	0.298005
$449$	2.89839e9	1.51111	0.755553	−	0.655087i	$-0.227368\pi$
$449$	2.89839e9	1.51111	0.755553	+	0.655087i	$0.227368\pi$
$450$	−3.10111e8	−0.160425
$451$	−3.03627e9	−1.55856
$452$	−1.32672e9	−0.675766
$453$	−7.23850e8	−0.365852
$454$	−9.92205e8	−0.497629
$455$	−9.76852e8	−0.486171
$456$	1.69294e9	0.836110
$457$	−1.61157e9	−0.789844	−0.394922	−	0.918715i	$-0.629228\pi$
$457$	−1.61157e9	−0.789844	−0.394922	+	0.918715i	$0.629228\pi$
$458$	−7.10490e8	−0.345564
$459$	−1.30912e8	−0.0631881
$460$	5.98768e8	0.286818
$461$	4.98049e8	0.236766	0.118383	−	0.992968i	$-0.462229\pi$
$461$	4.98049e8	0.236766	0.118383	+	0.992968i	$0.462229\pi$
$462$	7.60784e8	0.358934
$463$	−1.13218e9	−0.530131	−0.265065	−	0.964230i	$-0.585394\pi$
$463$	−1.13218e9	−0.530131	−0.265065	+	0.964230i	$0.585394\pi$
$464$	1.00268e7	0.00465959
$465$	−1.44517e9	−0.666552
$466$	6.75693e8	0.309313
$467$	3.04377e9	1.38294	0.691470	−	0.722405i	$-0.256963\pi$
$467$	3.04377e9	1.38294	0.691470	+	0.722405i	$0.256963\pi$
$468$	−1.99944e8	−0.0901670
$469$	−7.73552e8	−0.346246
$470$	−2.73556e9	−1.21536
$471$	5.05296e8	0.222829
$472$	−2.71555e8	−0.118867
$473$	1.33101e9	0.578319
$474$	−1.82686e8	−0.0787917
$475$	3.35376e9	1.43583
$476$	5.17657e8	0.219997
$477$	−7.29426e7	−0.0307728
$478$	−1.78497e9	−0.747539
$479$	1.85843e9	0.772630	0.386315	−	0.922367i	$-0.373748\pi$
$479$	1.85843e9	0.772630	0.386315	+	0.922367i	$0.373748\pi$
$480$	2.00106e9	0.825878
$481$	−2.72479e8	−0.111641
$482$	−8.25512e7	−0.0335783
$483$	3.86839e8	0.156212
$484$	−1.01505e9	−0.406937
$485$	1.03941e9	0.413705
$486$	−8.63083e7	−0.0341056
$487$	−3.95871e8	−0.155311	−0.0776555	−	0.996980i	$-0.524743\pi$
$487$	−3.95871e8	−0.155311	−0.0776555	+	0.996980i	$0.524743\pi$
$488$	9.44909e7	0.0368062
$489$	2.43212e9	0.940600
$490$	−2.43746e8	−0.0935948
$491$	8.60610e8	0.328111	0.164056	−	0.986451i	$-0.447542\pi$
$491$	8.60610e8	0.328111	0.164056	+	0.986451i	$0.447542\pi$
$492$	−1.36205e9	−0.515605
$493$	−1.75500e7	−0.00659648
$494$	−8.52025e8	−0.317986
$495$	1.55434e9	0.576007
$496$	5.27179e8	0.193987
$497$	−2.33016e8	−0.0851410
$498$	8.03906e8	0.291677
$499$	2.92320e9	1.05319	0.526595	−	0.850116i	$-0.323469\pi$
$499$	2.92320e9	1.05319	0.526595	+	0.850116i	$0.323469\pi$
$500$	−2.62243e8	−0.0938228
$501$	−1.87033e9	−0.664487
$502$	1.67686e8	0.0591609
$503$	2.74156e9	0.960529	0.480264	−	0.877124i	$-0.340541\pi$
$503$	2.74156e9	0.960529	0.480264	+	0.877124i	$0.340541\pi$
$504$	8.17042e8	0.284274
$505$	−5.84700e9	−2.02029
$506$	5.61866e8	0.192799
$507$	−1.45330e9	−0.495254
$508$	−1.57340e9	−0.532495
$509$	3.66404e9	1.23154	0.615769	−	0.787927i	$-0.288846\pi$
$509$	3.66404e9	1.23154	0.615769	+	0.787927i	$0.288846\pi$
$510$	−4.16731e8	−0.139111
$511$	−4.52649e9	−1.50068
$512$	−1.37307e9	−0.452113
$513$	9.33398e8	0.305250
$514$	−1.12354e9	−0.364937
$515$	5.40239e9	1.74285
$516$	5.97083e8	0.191320
$517$	6.51463e9	2.07335
$518$	4.65092e8	0.147023
$519$	−2.74445e9	−0.861727
$520$	−1.52375e9	−0.475229
$521$	−4.43075e9	−1.37260	−0.686302	−	0.727317i	$-0.740767\pi$
$521$	−4.43075e9	−1.37260	−0.686302	+	0.727317i	$0.740767\pi$
$522$	−1.15704e7	−0.00356043
$523$	−5.16773e9	−1.57959	−0.789794	−	0.613372i	$-0.789813\pi$
$523$	−5.16773e9	−1.57959	−0.789794	+	0.613372i	$0.789813\pi$
$524$	1.67927e9	0.509872
$525$	1.61858e9	0.488178
$526$	−1.51226e9	−0.453080
$527$	−9.22728e8	−0.274623
$528$	−5.67002e8	−0.167635
$529$	−3.11913e9	−0.916091
$530$	−2.32198e8	−0.0677473
$531$	−1.49721e8	−0.0433963
$532$	−3.69087e9	−1.06277
$533$	1.64110e9	0.469451
$534$	1.40403e9	0.399008
$535$	3.42428e9	0.966787
$536$	−1.20663e9	−0.338453
$537$	4.30211e8	0.119887
$538$	2.80684e9	0.777105
$539$	5.80473e8	0.159669
$540$	6.97267e8	0.190555
$541$	5.16094e9	1.40132	0.700662	−	0.713493i	$-0.252888\pi$
$541$	5.16094e9	1.40132	0.700662	+	0.713493i	$0.252888\pi$
$542$	−2.83356e9	−0.764426
$543$	2.24095e9	0.600666
$544$	1.27766e9	0.340266
$545$	9.63183e9	2.54871
$546$	−4.11203e8	−0.108114
$547$	−1.77725e9	−0.464295	−0.232147	−	0.972681i	$-0.574575\pi$
$547$	−1.77725e9	−0.464295	−0.232147	+	0.972681i	$0.574575\pi$
$548$	4.39962e9	1.14205
$549$	5.20974e7	0.0134373
$550$	2.35092e9	0.602515
$551$	1.25131e8	0.0318664
$552$	6.03414e8	0.152696
$553$	9.53505e8	0.239765
$554$	2.97394e9	0.743102
$555$	9.50219e8	0.235938
$556$	−2.53732e9	−0.626055
$557$	−2.65766e9	−0.651637	−0.325819	−	0.945432i	$-0.605640\pi$
$557$	−2.65766e9	−0.651637	−0.325819	+	0.945432i	$0.605640\pi$
$558$	−6.08340e8	−0.148227
$559$	−7.19409e8	−0.174195
$560$	−1.24268e9	−0.299020
$561$	9.92430e8	0.237318
$562$	1.13314e9	0.269282
$563$	−2.85664e9	−0.674646	−0.337323	−	0.941389i	$-0.609522\pi$
$563$	−2.85664e9	−0.674646	−0.337323	+	0.941389i	$0.609522\pi$
$564$	2.92242e9	0.685909
$565$	−5.57459e9	−1.30030
$566$	−2.07833e9	−0.481789
$567$	4.50475e8	0.103784
$568$	−3.63472e8	−0.0832247
$569$	−1.18310e9	−0.269233	−0.134617	−	0.990898i	$-0.542980\pi$
$569$	−1.18310e9	−0.269233	−0.134617	+	0.990898i	$0.542980\pi$
$570$	2.97128e9	0.672019
$571$	7.04152e8	0.158285	0.0791426	−	0.996863i	$-0.474782\pi$
$571$	7.04152e8	0.158285	0.0791426	+	0.996863i	$0.474782\pi$
$572$	1.51575e9	0.338643
$573$	−7.95010e8	−0.176535
$574$	−2.80119e9	−0.618231
$575$	1.19538e9	0.262222
$576$	4.87763e8	0.106348
$577$	−5.26118e9	−1.14017	−0.570083	−	0.821587i	$-0.693089\pi$
$577$	−5.26118e9	−1.14017	−0.570083	+	0.821587i	$0.693089\pi$
$578$	2.20210e9	0.474339
$579$	2.32701e9	0.498222
$580$	9.34752e7	0.0198929
$581$	−4.19589e9	−0.887580
$582$	4.37537e8	0.0919992
$583$	5.52970e8	0.115574
$584$	−7.06068e9	−1.46690
$585$	−8.40119e8	−0.173498
$586$	−2.62246e9	−0.538354
$587$	7.97467e9	1.62734	0.813672	−	0.581324i	$-0.197465\pi$
$587$	7.97467e9	1.62734	0.813672	+	0.581324i	$0.197465\pi$
$588$	2.60397e8	0.0528220
$589$	6.57902e9	1.32665
$590$	−4.76607e8	−0.0955384
$591$	−4.70258e9	−0.937087
$592$	−3.46627e8	−0.0686651
$593$	−5.84550e9	−1.15115	−0.575573	−	0.817750i	$-0.695221\pi$
$593$	−5.84550e9	−1.15115	−0.575573	+	0.817750i	$0.695221\pi$
$594$	6.54294e8	0.128092
$595$	2.17508e9	0.423316
$596$	−5.66758e8	−0.109657
$597$	2.44939e9	0.471138
$598$	−3.03688e8	−0.0580729
$599$	−2.93990e9	−0.558906	−0.279453	−	0.960159i	$-0.590153\pi$
$599$	−2.93990e9	−0.558906	−0.279453	+	0.960159i	$0.590153\pi$
$600$	2.52476e9	0.477190
$601$	−6.68201e9	−1.25559	−0.627793	−	0.778380i	$-0.716042\pi$
$601$	−6.68201e9	−1.25559	−0.627793	+	0.778380i	$0.716042\pi$
$602$	1.22796e9	0.229401
$603$	−6.65275e8	−0.123564
$604$	2.46163e9	0.454562
$605$	−4.26500e9	−0.783024
$606$	−2.46127e9	−0.449268
$607$	4.48841e8	0.0814577	0.0407289	−	0.999170i	$-0.487032\pi$
$607$	4.48841e8	0.0814577	0.0407289	+	0.999170i	$0.487032\pi$
$608$	−9.10965e9	−1.64376
$609$	6.03904e7	0.0108345
$610$	1.65841e8	0.0295827
$611$	−3.52115e9	−0.624511
$612$	4.45198e8	0.0785097
$613$	7.78075e9	1.36430	0.682150	−	0.731212i	$-0.261045\pi$
$613$	7.78075e9	1.36430	0.682150	+	0.731212i	$0.261045\pi$
$614$	−5.95570e9	−1.03835
$615$	−5.72305e9	−0.992120
$616$	−6.19391e9	−1.06766
$617$	−6.97925e9	−1.19622	−0.598109	−	0.801414i	$-0.704081\pi$
$617$	−6.97925e9	−1.19622	−0.598109	+	0.801414i	$0.704081\pi$
$618$	2.27412e9	0.387573
$619$	−3.49030e9	−0.591488	−0.295744	−	0.955267i	$-0.595568\pi$
$619$	−3.49030e9	−0.591488	−0.295744	+	0.955267i	$0.595568\pi$
$620$	4.91466e9	0.828176
$621$	3.32692e8	0.0557470
$622$	1.67435e9	0.278985
$623$	−7.32816e9	−1.21419
$624$	3.06464e8	0.0504932
$625$	−6.62706e9	−1.08578
$626$	4.56021e9	0.742975
$627$	−7.07600e9	−1.14644
$628$	−1.71838e9	−0.276861
$629$	6.06705e8	0.0972077
$630$	1.43399e9	0.228484
$631$	−7.42461e9	−1.17644	−0.588222	−	0.808700i	$-0.700172\pi$
$631$	−7.42461e9	−1.17644	−0.588222	+	0.808700i	$0.700172\pi$
$632$	1.48733e9	0.234368
$633$	−3.30991e9	−0.518684
$634$	2.36516e9	0.368593
$635$	−6.61107e9	−1.02462
$636$	2.48059e8	0.0382345
$637$	−3.13745e8	−0.0480938
$638$	8.77142e7	0.0133720
$639$	−2.00400e8	−0.0303840
$640$	−7.93382e9	−1.19633
$641$	−2.52065e9	−0.378015	−0.189007	−	0.981976i	$-0.560527\pi$
$641$	−2.52065e9	−0.378015	−0.189007	+	0.981976i	$0.560527\pi$
$642$	1.44144e9	0.214993
$643$	−7.35494e9	−1.09104	−0.545520	−	0.838098i	$-0.683668\pi$
$643$	−7.35494e9	−1.09104	−0.545520	+	0.838098i	$0.683668\pi$
$644$	−1.31554e9	−0.194090
$645$	2.50881e9	0.368136
$646$	1.89713e9	0.276875
$647$	−9.35379e8	−0.135776	−0.0678879	−	0.997693i	$-0.521626\pi$
$647$	−9.35379e8	−0.135776	−0.0678879	+	0.997693i	$0.521626\pi$
$648$	7.02678e8	0.101448
$649$	1.13502e9	0.162985
$650$	−1.27067e9	−0.181483
$651$	3.17515e9	0.451057
$652$	−8.27103e9	−1.16867
$653$	1.22407e10	1.72032	0.860161	−	0.510022i	$-0.170363\pi$
$653$	1.22407e10	1.72032	0.860161	+	0.510022i	$0.170363\pi$
$654$	4.05449e9	0.566779
$655$	7.05591e9	0.981089
$656$	2.08769e9	0.288737
$657$	−3.89290e9	−0.535543
$658$	6.01023e9	0.822433
$659$	5.21215e9	0.709444	0.354722	−	0.934972i	$-0.384575\pi$
$659$	5.21215e9	0.709444	0.354722	+	0.934972i	$0.384575\pi$
$660$	−5.28591e9	−0.715676
$661$	−1.11350e10	−1.49964	−0.749820	−	0.661642i	$-0.769860\pi$
$661$	−1.11350e10	−1.49964	−0.749820	+	0.661642i	$0.769860\pi$
$662$	5.71972e8	0.0766253
$663$	−5.36407e8	−0.0714821
$664$	−6.54499e9	−0.867603
$665$	−1.55082e10	−2.04497
$666$	3.99992e8	0.0524676
$667$	4.46004e7	0.00581967
$668$	6.36052e9	0.825610
$669$	−1.48169e9	−0.191322
$670$	−2.11776e9	−0.272029
$671$	−3.94945e8	−0.0504671
$672$	−4.39649e9	−0.558873
$673$	9.15611e9	1.15787	0.578933	−	0.815375i	$-0.303469\pi$
$673$	9.15611e9	1.15787	0.578933	+	0.815375i	$0.303469\pi$
$674$	4.15954e9	0.523282
$675$	1.39203e9	0.174214
$676$	4.94231e9	0.615342
$677$	1.14733e10	1.42111	0.710557	−	0.703639i	$-0.248443\pi$
$677$	1.14733e10	1.42111	0.710557	+	0.703639i	$0.248443\pi$
$678$	−2.34661e9	−0.289159
$679$	−2.28367e9	−0.279955
$680$	3.39281e9	0.413788
$681$	4.45381e9	0.540401
$682$	4.61176e9	0.556701
$683$	−5.63555e9	−0.676806	−0.338403	−	0.941001i	$-0.609887\pi$
$683$	−5.63555e9	−0.676806	−0.338403	+	0.941001i	$0.609887\pi$
$684$	−3.17425e9	−0.379267
$685$	1.84862e10	2.19751
$686$	4.73443e9	0.559930
$687$	3.18924e9	0.375266
$688$	−9.15179e8	−0.107139
$689$	−2.98880e8	−0.0348120
$690$	1.05906e9	0.122729
$691$	−6.22407e9	−0.717632	−0.358816	−	0.933408i	$-0.616819\pi$
$691$	−6.22407e9	−0.717632	−0.358816	+	0.933408i	$0.616819\pi$
$692$	9.33317e9	1.07068
$693$	−3.41501e9	−0.389785
$694$	3.10279e9	0.352366
$695$	−1.06612e10	−1.20465
$696$	9.42005e7	0.0105906
$697$	−3.65411e9	−0.408758
$698$	5.35270e9	0.595771
$699$	−3.03305e9	−0.335900
$700$	−5.50439e9	−0.606550
$701$	8.57820e9	0.940553	0.470276	−	0.882519i	$-0.344154\pi$
$701$	8.57820e9	0.940553	0.470276	+	0.882519i	$0.344154\pi$
$702$	−3.53645e8	−0.0385823
$703$	−4.32579e9	−0.469593
$704$	−3.69768e9	−0.399416
$705$	1.22794e10	1.31982
$706$	2.31772e9	0.247881
$707$	1.28463e10	1.36713
$708$	5.09164e8	0.0539189
$709$	2.72444e9	0.287088	0.143544	−	0.989644i	$-0.454150\pi$
$709$	2.72444e9	0.287088	0.143544	+	0.989644i	$0.454150\pi$
$710$	−6.37932e8	−0.0668914
$711$	8.20039e8	0.0855640
$712$	−1.14309e10	−1.18686
$713$	2.34496e9	0.242283
$714$	9.15591e8	0.0941364
$715$	6.36885e9	0.651613
$716$	−1.46304e9	−0.148957
$717$	8.01239e9	0.811792
$718$	9.10952e9	0.918460
$719$	−2.39574e9	−0.240375	−0.120188	−	0.992751i	$-0.538350\pi$
$719$	−2.39574e9	−0.240375	−0.120188	+	0.992751i	$0.538350\pi$
$720$	−1.06874e9	−0.106710
$721$	−1.18695e10	−1.17939
$722$	−8.14988e9	−0.805881
$723$	3.70556e8	0.0364644
$724$	−7.62091e9	−0.746314
$725$	1.86614e8	0.0181870
$726$	−1.79534e9	−0.174128
$727$	1.12427e9	0.108517	0.0542586	−	0.998527i	$-0.482720\pi$
$727$	1.12427e9	0.108517	0.0542586	+	0.998527i	$0.482720\pi$
$728$	3.34780e9	0.321588
$729$	3.87420e8	0.0370370
$730$	−1.23922e10	−1.17902
$731$	1.60185e9	0.151674
$732$	−1.77170e8	−0.0166956
$733$	1.04255e10	0.977759	0.488880	−	0.872351i	$-0.337406\pi$
$733$	1.04255e10	0.977759	0.488880	+	0.872351i	$0.337406\pi$
$734$	4.89480e9	0.456876
$735$	1.09413e9	0.101639
$736$	−3.24696e9	−0.300196
$737$	5.04338e9	0.464072
$738$	−2.40910e9	−0.220626
$739$	−1.61439e8	−0.0147147	−0.00735737	−	0.999973i	$-0.502342\pi$
$739$	−1.61439e8	−0.0147147	−0.00735737	+	0.999973i	$0.502342\pi$
$740$	−3.23145e9	−0.293148
$741$	3.82457e9	0.345317
$742$	5.10156e8	0.0458447
$743$	1.59100e10	1.42302	0.711508	−	0.702678i	$-0.248013\pi$
$743$	1.59100e10	1.42302	0.711508	+	0.702678i	$0.248013\pi$
$744$	4.95279e9	0.440905
$745$	−2.38139e9	−0.211000
$746$	7.23070e9	0.637668
$747$	−3.60857e9	−0.316748
$748$	−3.37500e9	−0.294862
$749$	−7.52341e9	−0.654226
$750$	−4.63834e8	−0.0401466
$751$	9.63052e9	0.829679	0.414839	−	0.909895i	$-0.363838\pi$
$751$	9.63052e9	0.829679	0.414839	+	0.909895i	$0.363838\pi$
$752$	−4.47934e9	−0.384107
$753$	−7.52710e8	−0.0642459
$754$	−4.74094e7	−0.00402777
$755$	1.03432e10	0.874663
$756$	−1.53195e9	−0.128949
$757$	−1.23984e10	−1.03880	−0.519398	−	0.854532i	$-0.673844\pi$
$757$	−1.23984e10	−1.03880	−0.519398	+	0.854532i	$0.673844\pi$
$758$	2.61610e9	0.218178
$759$	−2.52210e9	−0.209371
$760$	−2.41906e10	−1.99894
$761$	−3.84482e9	−0.316249	−0.158125	−	0.987419i	$-0.550545\pi$
$761$	−3.84482e9	−0.316249	−0.158125	+	0.987419i	$0.550545\pi$
$762$	−2.78291e9	−0.227854
$763$	−2.11619e10	−1.72472
$764$	2.70363e9	0.219341
$765$	1.87062e9	0.151067
$766$	−2.15773e8	−0.0173459
$767$	−6.13478e8	−0.0490925
$768$	−5.65207e9	−0.450239
$769$	1.85468e10	1.47071	0.735354	−	0.677683i	$-0.237016\pi$
$769$	1.85468e10	1.47071	0.735354	+	0.677683i	$0.237016\pi$
$770$	−1.08710e10	−0.858125
$771$	5.04335e9	0.396304
$772$	−7.91355e9	−0.619029
$773$	9.18489e9	0.715230	0.357615	−	0.933869i	$-0.383590\pi$
$773$	9.18489e9	0.715230	0.357615	+	0.933869i	$0.383590\pi$
$774$	1.05607e9	0.0818656
$775$	9.81163e9	0.757156
$776$	−3.56220e9	−0.273654
$777$	−2.08771e9	−0.159660
$778$	6.83530e9	0.520390
$779$	2.60537e10	1.97464
$780$	2.85703e9	0.215568
$781$	1.51921e9	0.114114
$782$	6.76196e8	0.0505649
$783$	5.19373e7	0.00386646
$784$	−3.99123e8	−0.0295801
$785$	−7.22025e9	−0.532732
$786$	2.97016e9	0.218173
$787$	−1.00821e10	−0.737291	−0.368646	−	0.929570i	$-0.620178\pi$
$787$	−1.00821e10	−0.737291	−0.368646	+	0.929570i	$0.620178\pi$
$788$	1.59923e10	1.16431
$789$	6.78821e9	0.492024
$790$	2.61043e9	0.188372
$791$	1.22478e10	0.879916
$792$	−5.32693e9	−0.381012
$793$	2.13467e8	0.0152011
$794$	3.01745e9	0.213928
$795$	1.04229e9	0.0735703
$796$	−8.32975e9	−0.585378
$797$	−1.03385e10	−0.723361	−0.361681	−	0.932302i	$-0.617797\pi$
$797$	−1.03385e10	−0.723361	−0.361681	+	0.932302i	$0.617797\pi$
$798$	−6.52813e9	−0.454756
$799$	7.84025e9	0.543771
$800$	−1.35857e10	−0.938139
$801$	−6.30241e9	−0.433304
$802$	−3.71150e9	−0.254062
$803$	2.95117e10	2.01136
$804$	2.26243e9	0.153525
$805$	−5.52760e9	−0.373466
$806$	−2.49265e9	−0.167683
$807$	−1.25993e10	−0.843899
$808$	2.00384e10	1.33636
$809$	2.64371e10	1.75547	0.877735	−	0.479146i	$-0.159053\pi$
$809$	2.64371e10	1.75547	0.877735	+	0.479146i	$0.159053\pi$
$810$	1.23327e9	0.0815383
$811$	2.22378e10	1.46392	0.731961	−	0.681346i	$-0.238605\pi$
$811$	2.22378e10	1.46392	0.731961	+	0.681346i	$0.238605\pi$
$812$	−2.05372e8	−0.0134616
$813$	1.27193e10	0.830130
$814$	−3.03229e9	−0.197054
$815$	−3.47530e10	−2.24875
$816$	−6.82377e8	−0.0439652
$817$	−1.14211e10	−0.732710
$818$	−1.00524e10	−0.642147
$819$	1.84581e9	0.117407
$820$	1.94626e10	1.23269
$821$	1.19117e10	0.751229	0.375615	−	0.926776i	$-0.377432\pi$
$821$	1.19117e10	0.751229	0.375615	+	0.926776i	$0.377432\pi$
$822$	7.78171e9	0.488679
$823$	1.73151e9	0.108274	0.0541372	−	0.998534i	$-0.482759\pi$
$823$	1.73151e9	0.108274	0.0541372	+	0.998534i	$0.482759\pi$
$824$	−1.85147e10	−1.15285
$825$	−1.05528e10	−0.654303
$826$	1.04714e9	0.0646510
$827$	2.70946e10	1.66576	0.832882	−	0.553451i	$-0.186689\pi$
$827$	2.70946e10	1.66576	0.832882	+	0.553451i	$0.186689\pi$
$828$	−1.13140e9	−0.0692644
$829$	1.95311e10	1.19065	0.595326	−	0.803484i	$-0.297023\pi$
$829$	1.95311e10	1.19065	0.595326	+	0.803484i	$0.297023\pi$
$830$	−1.14871e10	−0.697331
$831$	−1.33494e10	−0.806974
$832$	1.99859e9	0.120307
$833$	6.98589e8	0.0418759
$834$	−4.48781e9	−0.267888
$835$	2.67255e10	1.58863
$836$	2.40637e10	1.42442
$837$	2.73072e9	0.160967
$838$	4.19045e8	0.0245984
$839$	−2.20343e10	−1.28805	−0.644024	−	0.765005i	$-0.722737\pi$
$839$	−2.20343e10	−1.28805	−0.644024	+	0.765005i	$0.722737\pi$
$840$	−1.16748e10	−0.679632
$841$	−1.72429e10	−0.999596
$842$	1.21645e10	0.702268
$843$	−5.08644e9	−0.292427
$844$	1.12562e10	0.644453
$845$	2.07665e10	1.18403
$846$	5.16896e9	0.293499
$847$	9.37053e9	0.529873
$848$	−3.80212e8	−0.0214112
$849$	9.32919e9	0.523199
$850$	2.82929e9	0.158020
$851$	−1.54184e9	−0.0857604
$852$	6.81510e8	0.0377514
$853$	2.56385e10	1.41440	0.707199	−	0.707014i	$-0.249958\pi$
$853$	2.56385e10	1.41440	0.707199	+	0.707014i	$0.249958\pi$
$854$	−3.64366e8	−0.0200187
$855$	−1.33375e10	−0.729780
$856$	−1.17354e10	−0.639502
$857$	−1.90552e10	−1.03414	−0.517072	−	0.855942i	$-0.672978\pi$
$857$	−1.90552e10	−1.03414	−0.517072	+	0.855942i	$0.672978\pi$
$858$	2.68095e9	0.144905
$859$	1.94648e10	1.04779	0.523896	−	0.851782i	$-0.324478\pi$
$859$	1.94648e10	1.04779	0.523896	+	0.851782i	$0.324478\pi$
$860$	−8.53182e9	−0.457401
$861$	1.25740e10	0.671369
$862$	1.32409e10	0.704115
$863$	−6.07650e9	−0.321822	−0.160911	−	0.986969i	$-0.551443\pi$
$863$	−6.07650e9	−0.321822	−0.160911	+	0.986969i	$0.551443\pi$
$864$	−3.78109e9	−0.199443
$865$	3.92159e10	2.06018
$866$	6.72987e9	0.352123
$867$	−9.88477e9	−0.515110
$868$	−1.07979e10	−0.560428
$869$	−6.21663e9	−0.321356
$870$	1.65332e8	0.00851214
$871$	−2.72594e9	−0.139783
$872$	−3.30095e10	−1.68590
$873$	−1.96401e9	−0.0999067
$874$	−4.82126e9	−0.244270
$875$	2.42092e9	0.122167
$876$	1.32388e10	0.665400
$877$	−1.82857e10	−0.915404	−0.457702	−	0.889106i	$-0.651327\pi$
$877$	−1.82857e10	−0.915404	−0.457702	+	0.889106i	$0.651327\pi$
$878$	−1.94420e9	−0.0969415
$879$	1.17717e10	0.584626
$880$	8.10198e9	0.400776
$881$	1.41923e10	0.699259	0.349629	−	0.936888i	$-0.386308\pi$
$881$	1.41923e10	0.699259	0.349629	+	0.936888i	$0.386308\pi$
$882$	4.60569e8	0.0226024
$883$	1.61031e10	0.787131	0.393566	−	0.919297i	$-0.371241\pi$
$883$	1.61031e10	0.787131	0.393566	+	0.919297i	$0.371241\pi$
$884$	1.82418e9	0.0888149
$885$	2.13939e9	0.103750
$886$	1.37270e10	0.663068
$887$	−1.49039e9	−0.0717077	−0.0358539	−	0.999357i	$-0.511415\pi$
$887$	−1.49039e9	−0.0717077	−0.0358539	+	0.999357i	$0.511415\pi$
$888$	−3.25653e9	−0.156066
$889$	1.45250e10	0.693363
$890$	−2.00624e10	−0.953933
$891$	−2.93699e9	−0.139101
$892$	5.03884e9	0.237713
$893$	−5.59007e10	−2.62686
$894$	−1.00244e9	−0.0469220
$895$	−6.14736e9	−0.286621
$896$	1.74312e10	0.809561
$897$	1.36319e9	0.0630643
$898$	−1.74338e10	−0.803385
$899$	3.66078e8	0.0168041
$900$	−4.73392e9	−0.216457
$901$	6.65490e8	0.0303113
$902$	1.82631e10	0.828613
$903$	−5.51205e9	−0.249118
$904$	1.91049e10	0.860111
$905$	−3.20213e10	−1.43605
$906$	4.35394e9	0.194506
$907$	−1.44651e10	−0.643717	−0.321858	−	0.946788i	$-0.604307\pi$
$907$	−1.44651e10	−0.643717	−0.321858	+	0.946788i	$0.604307\pi$
$908$	−1.51463e10	−0.671436
$909$	1.10482e10	0.487884
$910$	5.87574e9	0.258475
$911$	−2.79187e10	−1.22343	−0.611717	−	0.791077i	$-0.709521\pi$
$911$	−2.79187e10	−1.22343	−0.611717	+	0.791077i	$0.709521\pi$
$912$	4.86533e9	0.212388
$913$	2.73562e10	1.18962
$914$	9.69353e9	0.419923
$915$	−7.44429e8	−0.0321254
$916$	−1.08458e10	−0.466259
$917$	−1.55024e10	−0.663905
$918$	7.87432e8	0.0335942
$919$	1.89312e10	0.804590	0.402295	−	0.915510i	$-0.368213\pi$
$919$	1.89312e10	0.804590	0.402295	+	0.915510i	$0.368213\pi$
$920$	−8.62228e9	−0.365061
$921$	2.67339e10	1.12760
$922$	−2.99575e9	−0.125877
$923$	−8.21133e8	−0.0343722
$924$	1.16136e10	0.484299
$925$	−6.45127e9	−0.268009
$926$	6.81005e9	0.281846
$927$	−1.02081e10	−0.420886
$928$	−5.06891e8	−0.0208208
$929$	−3.58709e10	−1.46787	−0.733934	−	0.679221i	$-0.762318\pi$
$929$	−3.58709e10	−1.46787	−0.733934	+	0.679221i	$0.762318\pi$
$930$	8.69267e9	0.354375
$931$	−4.98092e9	−0.202295
$932$	1.03146e10	0.417348
$933$	−7.51584e9	−0.302964
$934$	−1.83082e10	−0.735245
$935$	−1.41810e10	−0.567369
$936$	2.87920e9	0.114764
$937$	1.18752e10	0.471577	0.235789	−	0.971804i	$-0.424233\pi$
$937$	1.18752e10	0.471577	0.235789	+	0.971804i	$0.424233\pi$
$938$	4.65289e9	0.184083
$939$	−2.04698e10	−0.806835
$940$	−4.17590e10	−1.63984
$941$	−2.99086e10	−1.17013	−0.585063	−	0.810988i	$-0.698930\pi$
$941$	−2.99086e10	−1.17013	−0.585063	+	0.810988i	$0.698930\pi$
$942$	−3.03934e9	−0.118468
$943$	9.28632e9	0.360623
$944$	−7.80420e8	−0.0301944
$945$	−6.43691e9	−0.248122
$946$	−8.00599e9	−0.307465
$947$	−1.97326e10	−0.755021	−0.377510	−	0.926005i	$-0.623220\pi$
$947$	−1.97326e10	−0.755021	−0.377510	+	0.926005i	$0.623220\pi$
$948$	−2.78874e9	−0.106311
$949$	−1.59510e10	−0.605838
$950$	−2.01728e10	−0.763366
$951$	−1.06167e10	−0.400275
$952$	−7.45427e9	−0.280011
$953$	3.05905e10	1.14488	0.572442	−	0.819945i	$-0.305996\pi$
$953$	3.05905e10	1.14488	0.572442	+	0.819945i	$0.305996\pi$
$954$	4.38748e8	0.0163605
$955$	1.13600e10	0.422053
$956$	−2.72481e10	−1.00863
$957$	−3.93731e8	−0.0145214
$958$	−1.11784e10	−0.410772
$959$	−4.06157e10	−1.48706
$960$	−6.96972e9	−0.254253
$961$	−8.26528e9	−0.300418
$962$	1.63895e9	0.0593545
$963$	−6.47033e9	−0.233472
$964$	−1.26017e9	−0.0453062
$965$	−3.32510e10	−1.19113
$966$	−2.32683e9	−0.0830509
$967$	1.80021e10	0.640221	0.320111	−	0.947380i	$-0.396280\pi$
$967$	1.80021e10	0.640221	0.320111	+	0.947380i	$0.396280\pi$
$968$	1.46167e10	0.517947
$969$	−8.51584e9	−0.300673
$970$	−6.25203e9	−0.219948
$971$	−6.56410e9	−0.230095	−0.115048	−	0.993360i	$-0.536702\pi$
$971$	−6.56410e9	−0.230095	−0.115048	+	0.993360i	$0.536702\pi$
$972$	−1.31752e9	−0.0460177
$973$	2.34235e10	0.815188
$974$	2.38115e9	0.0825716
$975$	5.70378e9	0.197082
$976$	2.71557e8	0.00934947
$977$	1.67236e10	0.573718	0.286859	−	0.957973i	$-0.407389\pi$
$977$	1.67236e10	0.573718	0.286859	+	0.957973i	$0.407389\pi$
$978$	−1.46292e10	−0.500073
$979$	4.77779e10	1.62737
$980$	−3.72085e9	−0.126285
$981$	−1.81998e10	−0.615495
$982$	−5.17655e9	−0.174442
$983$	−6.60882e9	−0.221915	−0.110957	−	0.993825i	$-0.535392\pi$
$983$	−6.60882e9	−0.221915	−0.110957	+	0.993825i	$0.535392\pi$
$984$	1.96136e10	0.656259
$985$	6.71959e10	2.24035
$986$	1.05563e8	0.00350704
$987$	−2.69787e10	−0.893123
$988$	−1.30064e10	−0.429049
$989$	−4.07084e9	−0.133813
$990$	−9.34931e9	−0.306236
$991$	−2.45768e10	−0.802173	−0.401086	−	0.916040i	$-0.631367\pi$
$991$	−2.45768e10	−0.802173	−0.401086	+	0.916040i	$0.631367\pi$
$992$	−2.66509e10	−0.866803
$993$	−2.56747e9	−0.0832114
$994$	1.40159e9	0.0452655
$995$	−3.49997e10	−1.12638
$996$	1.22718e10	0.393552
$997$	6.18690e10	1.97715	0.988575	−	0.150727i	$-0.0481614\pi$
$997$	6.18690e10	1.97715	0.988575	+	0.150727i	$0.0481614\pi$
$998$	−1.75830e10	−0.559932
$999$	−1.79548e9	−0.0569773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.8	✓	17
3.2	odd	2		531.8.a.d.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.8	✓	17	1.1	even	1	trivial
531.8.a.d.1.10		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)

\(f(q)\)	\(=\)	\(q-6.01497 q^{2} +27.0000 q^{3} -91.8201 q^{4} -385.807 q^{5} -162.404 q^{6} +847.649 q^{7} +1322.21 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-6.01497 q^{2} +27.0000 q^{3} -91.8201 q^{4} -385.807 q^{5} -162.404 q^{6} +847.649 q^{7} +1322.21 q^{8} +729.000 q^{9} +2320.62 q^{10} -5526.47 q^{11} -2479.14 q^{12} +2987.05 q^{13} -5098.58 q^{14} -10416.8 q^{15} +3799.90 q^{16} -6651.02 q^{17} -4384.92 q^{18} +47421.5 q^{19} +35424.9 q^{20} +22886.5 q^{21} +33241.6 q^{22} +16902.5 q^{23} +35699.7 q^{24} +70722.2 q^{25} -17967.0 q^{26} +19683.0 q^{27} -77831.2 q^{28} +2638.69 q^{29} +62656.7 q^{30} +138735. q^{31} -192099. q^{32} -149215. q^{33} +40005.7 q^{34} -327029. q^{35} -66936.9 q^{36} -91219.9 q^{37} -285239. q^{38} +80650.4 q^{39} -510119. q^{40} +549406. q^{41} -137662. q^{42} -240843. q^{43} +507441. q^{44} -281253. q^{45} -101668. q^{46} -1.17880e6 q^{47} +102597. q^{48} -105035. q^{49} -425392. q^{50} -179578. q^{51} -274271. q^{52} -100058. q^{53} -118393. q^{54} +2.13215e6 q^{55} +1.12077e6 q^{56} +1.28038e6 q^{57} -15871.6 q^{58} -205379. q^{59} +956471. q^{60} +71464.3 q^{61} -834486. q^{62} +617936. q^{63} +669085. q^{64} -1.15243e6 q^{65} +897523. q^{66} -912586. q^{67} +610697. q^{68} +456367. q^{69} +1.96707e6 q^{70} -274897. q^{71} +963893. q^{72} -5.34005e6 q^{73} +548685. q^{74} +1.90950e6 q^{75} -4.35425e6 q^{76} -4.68451e6 q^{77} -485110. q^{78} +1.12488e6 q^{79} -1.46603e6 q^{80} +531441. q^{81} -3.30466e6 q^{82} -4.95003e6 q^{83} -2.10144e6 q^{84} +2.56601e6 q^{85} +1.44866e6 q^{86} +71244.6 q^{87} -7.30717e6 q^{88} -8.64528e6 q^{89} +1.69173e6 q^{90} +2.53197e6 q^{91} -1.55199e6 q^{92} +3.74584e6 q^{93} +7.09048e6 q^{94} -1.82956e7 q^{95} -5.18669e6 q^{96} -2.69412e6 q^{97} +631782. q^{98} -4.02880e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more